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+\index{#1}% +\index{defun!#1}% +\index{#1!defun}} +\newcommand{\defmacro}[1]{% e.g. \defmacro{functionname} +\subsection{defmacro {#1}}% +\label{#1}% +\index{#1}% +\index{defmacro!#1}% +\index{#1!defmacro}} +\newcommand{\defvar}[1]{% e.g. \defvar{varname} +\subsection{defvar \${#1}}% +\label{#1}% +\index{#1}% +\index{defvar!#1}% +\index{#1!defvar}} +\newcommand{\defstruct}[1]{% e.g. \defstruct{varname} +\subsection{defstruct \${#1}}% +\label{#1}% +\index{#1}% +\index{defstruct!#1}% +\index{#1!defstruct}} +\newcommand{\defdollar}[1]{% e.g. \defdollar{functionname} +\subsection{defvar \${#1}}% +\label{#1}% +\index{\${#1}}% +\index{defvar!\${#1}}% +\index{\${#1}!defvar}} +\newcommand{\defconstant}[1]{% e.g. \defconst{varname} +\subsection{defconstant \${#1}}% +\label{#1}% +\index{#1}% +\index{defconstant!#1}% +\index{#1!defconstant}} +\newcommand{\defdollarconstant}[1]{% e.g. \defdollarconstant{functionname} +\subsection{defconstant \${#1}}% +\label{#1}% +\index{\${#1}}% +\index{defconstant!\${#1}}% +\index{\${#1}!defconstant}} +\newcommand{\pagehead}[2]{% e.g. \pagehead{name}{abb} +\dest{#1}% +\dest{#2}% +\subsection{#1 (#2)}% +\label{#1}% +\label{#2}% +\index{{#1}}% +\index{{#2}}} +\newcommand{\pagetitle}[3]{% e.g. \pagetitle{page}{file.ht}{title} +\subsection{#3}% +\label{#1}% +\index{pages!#1!#2}% +\index{#1!#2!pages}% +\index{#2!pages!#1}} +\newcommand{\calls}[2]{% e.g. \calls{thisfunc}{thatfunc} +[#2 p\pageref{#2}]\\% +\index{#2!{calledby #1}}% +\index{#1!{calls #2}}}% +\newcommand{\seebook}[3]{% e.g. \seebook{thisfunc}{thatfunc}{5} +[#1 #2 (vol#3)]\\% +\index{#2[#3]!{called by #1}}% +\index{#1!{calls #2[#3]}}}% +\newcommand{\throws}[2]{% e.g. \throws{thisfunc}{tagvar} +[#2 p\pageref{#2}]\\% +\index{throws!#1}% +\index{#1!throws}} +\newcommand{\catches}[2]{% e.g. \catches{thisfunc}{tagvar} +[#2 p\pageref{#2}]\\% +\index{catches!#1}% +\index{#1!catches}} +\newcommand{\uses}[2]{% e.g. \uses{thisfunc}{specialvar} +[#2 p\pageref{#2}]\\% +\index{#2!{usedby #1}}% +\index{#1!{uses #2}}}% +\newcommand{\callsdollar}[2]{% e.g. \callsdollar{thisfunc}{thatfunc} +[\$#2 p\pageref{#2}]\\% +\index{\$#2!{calledby \$#1}}% +\index{#1!{calls \$#2}}} +\newcommand{\usesdollar}[2]{% e.g. \usesdollar{thisfunc}{specialvar} +[\$#2 p\pageref{#2}]\\% +\index{\${#2}!{usedby #1}}% +\index{#1!{uses \${#2}}}} +\newcommand{\defsdollar}[2]{% e.g. \defsdollar{thisfunc}{specialvar} +[\$#2 p\pageref{#2}]\\% +\index{\${#2}!{local def #1}}% +\index{#1!{local def \${#2}}}} +\newcommand{\refsdollar}[2]{% e.g. \refsdollar{thisfunc}{specialvar} +[\$#2 p\pageref{#2}]\\% +\index{\${#2}!{local ref #1}}% +\index{#1!{local ref \${#2}}}} +\newcommand{\usesstruct}[2]{% e.g. \usesstruct{thisfunc}{structname} +[\$#2 p\pageref{#2}]\\% +\index{\${#2}!{usedby #1}}% +\index{#1!{uses \${#2}}}} +\newcommand{\tpdhere}[1]{% e.g. \tpdhere{Some note} +{\bf TPDHERE: #1}% +\index{TPDHERE!{#1}}} +\newcommand{\pagepic}[3]{% e.g. \pagepic{pathandfile}{abb}{scale} +\includegraphics[scale=#3]{#1}\\% +\index{images!#2}} +\newcommand{\refto}[1]{% e.g. \refto{name} +(p\pageref{#1}) #1} +\newcommand{\pageto}[2]{% e.g. \pageto{linkstring}{pagename} +\ \\${\bf\Rightarrow{}}${``#1''} (#2) \ref{#2} on page~\pageref{#2}} +\newcommand{\pagefrom}[2]{% e.g. \pagefrom{linkstring}{pagename} +\ \\${\bf\Leftarrow{}}${``#1''} (#2) \ref{#2} on page~\pageref{#2}} +\newcommand{\fnref}[1]{% e.g. \fnref{functionname} +``#1'' (\ref{#1} p~\pageref{#1})} +\newcommand{\varref}[1]{% e.g. \varref{variablename} +``#1'' (\ref{#1} p~\pageref{#1})} +\newcommand{\cross}[2]{% e.g. \pagefrom{cat}{funcname} +\index{#1!#2}% +\index{#2!#1}% +#2} +\newcommand{\lanb}{{\tt [}} +\newcommand{\ranb}{{\tt ]}} +\newcommand{\vertline}{$|$} +% axiom.sty -- LaTeX support for Axiom +% DON'T edit this file! Use src/doc/axiom.sty.pamphlet instead. +\usepackage{verbatim} + +\chardef\atcode=\catcode`\@ +\catcode`\@=11 +\renewcommand{\verbatim@font}{\ttfamily\small} +\catcode`\@=\atcode + +\newenvironment{chunk}[1]{% we need the chunkname as an argument +{\ }\newline\noindent% make sure we are in column 1 +%{\small $\backslash{}$begin\{chunk\}\{{\bf #1}\}}% alternate begin mark +\hbox{\hskip 2.0cm}{\bf --- #1 ---}% mark the beginning +\verbatim}% say exactly what we see +{\endverbatim% process \end{chunk} +\par{}% we add a newline +\noindent{}% start in column 1 +\hbox{\hskip 2.0cm}{\bf ----------}% mark the end +%$\backslash{}$end\{chunk\}% alternate end mark (commented) +\par% and a newline +\normalsize\noindent}% and return to the document + +\providecommand{\getchunk}[1]{% +\noindent% +{\small $\backslash{}$begin\{chunk\}\{{\bf #1}\}}}% mark the reference + +{\obeyspaces\AtBeginDocument{\global\let =\ }} % from texbook, p 381 +\def\nwopt@nomargintag{\let\nwmargintag=\@gobble} +\def\nwopt@margintag{% + \def\nwmargintag##1{\leavevmode\llap{##1\kern\nwmarginglue\kern\codemargin}}} +\def\nwopt@margintag{% + \def\nwmargintag##1{\leavevmode\kern-\codemargin\nwthemargintag{##1}\kern\codemargin}} +\def\nwthemargintag#1{\llap{#1\kern\nwmarginglue}} +\nwopt@margintag +\newdimen\nwmarginglue +\nwmarginglue=0.3in +\def\nwtagstyle{\footnotesize\Rm} +% make \hsize in code sufficient for 88 columns +\setbox0=\hbox{\tt m} +\newdimen\codehsize +\codehsize=91\wd0 % 88 columns wasn't enough; I don't know why +\newdimen\codemargin +\codemargin=0pt +\newdimen\nwdefspace +\nwdefspace=\codehsize +% need to use \textwidth in {\LaTeX} to handle styles with +% non-standard margins (David Bruce). Don't know why we sometimes +% wanted \hsize. 27 August 1997. +%% \advance\nwdefspace by -\hsize\relax +\ifx\textwidth\undefined + \advance\nwdefspace by -\hsize\relax +\else + \advance\nwdefspace by -\textwidth\relax +\fi +\chardef\other=12 +\def\setupcode{% + \chardef\\=`\\ + \chardef\{=`\{ + \chardef\}=`\} + \catcode`\$=\other + \catcode`\&=\other + \catcode`\#=\other + \catcode`\%=\other + \catcode`\~=\other + \catcode`\_=\other + \catcode`\^=\other + \catcode`\"=\other % fixes problem with german.sty + \obeyspaces\Tt +} +\let\nwlbrace=\{ +\let\nwrbrace=\} +\def\nwendquote{\relax\ifhmode\spacefactor=1000 \fi} +{\catcode`\^^M=\active % make CR an active character + \gdef\newlines{\catcode`\^^M=\active % make CR an active character + \def^^M{\par\startline}}% + \gdef\eatline#1^^M{\relax}% +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% DON'T \gdef^^M{\par\startline}}% in case ^^M appears in a \write +\def\startline{\noindent\hskip\parindent\ignorespaces} +\def\nwnewline{\ifvmode\else\hfil\break\leavevmode\hbox{}\fi} +\def\setupmodname{% + \catcode`\$=3 + \catcode`\&=4 + \catcode`\#=6 + \catcode`\%=14 + \catcode`\~=13 + \catcode`\_=8 + \catcode`\^=7 + \catcode`\ =10 + \catcode`\^^M=5 + \let\{\nwlbrace + \let\}\nwrbrace + % bad news --- don't know what catcode to give " + \Rm} +\def\LA{\begingroup\maybehbox\bgroup\setupmodname\It$\langle$} +\def\RA{\/$\rangle$\egroup\endgroup} +\def\code{\leavevmode\begingroup\setupcode\newlines} +\def\edoc{\endgroup} +\let\maybehbox\relax +\newbox\equivbox +\setbox\equivbox=\hbox{$\equiv$} +\newbox\plusequivbox +\setbox\plusequivbox=\hbox{$\mathord{+}\mathord{\equiv}$} +% \moddef can't have an argument because there might be \code...\edoc +\def\moddef{\leavevmode\kern-\codemargin\LA} +\def\endmoddef{\RA\ifmmode\equiv\else\unhcopy\equivbox\fi + \nobreak\hfill\nobreak} +\def\plusendmoddef{\RA\ifmmode\mathord{+}\mathord{\equiv}\else\unhcopy\plusequivbox\fi + \nobreak\hfill\nobreak} +\def\chunklist{% +\errhelp{I changed \chunklist to \nowebchunks. +I'll try to avoid such incompatible changes in the future.}% +\errmessage{Use \string\nowebchunks\space instead of \string\chunklist}} +\def\nowebchunks{\message{}} +\def\nowebindex{\message{}} +% here is support for the new-style (capitalized) font-changing commands +% thanks to Dave Love +\ifx\documentstyle\undefined + \let\Rm=\rm \let\It=\it \let\Tt=\tt % plain +\else\ifx\selectfont\undefined + \let\Rm=\rm \let\It=\it \let\Tt=\tt % LaTeX OFSS +\else % LaTeX NFSS + \def\Rm{\reset@font\rm} + \def\It{\reset@font\it} + \def\Tt{\reset@font\tt} + \def\Bf{\reset@font\bf} +\fi\fi +\ifx\reset@font\undefined \let\reset@font=\relax \fi +\def\noweboptions#1{% + \def\@nwoptionlist{#1}% + \@for\@nwoption:=\@nwoptionlist\do{% + \@ifundefined{nwopt@\@nwoption}{% + \@latexerr{There is no such noweb option as '\@nwoption'}\@eha}{% + \csname nwopt@\@nwoption\endcsname}}} +\codemargin=10pt +\advance\codehsize by \codemargin % make room for indentation of code +\advance\nwdefspace by \codemargin % and fix adjustment for def/use +\def\setcodemargin#1{% + \advance\codehsize by -\codemargin % make room for indentation of code + \advance\nwdefspace by -\codemargin % and fix adjustment for def/use + \codemargin=#1 + \advance\codehsize by \codemargin % make room for indentation of code + \advance\nwdefspace by \codemargin % and fix adjustment for + % def/use +} +\def\nwopt@shift{% + \dimen@=-0.8in + \if@twoside % Values for two-sided printing: + \advance\evensidemargin by \dimen@ + \else % Values for one-sided printing: + \advance\evensidemargin by \dimen@ + \advance\oddsidemargin by \dimen@ + \fi +% \advance \marginparwidth -\dimen@ +} +\let\nwopt@noshift\@empty +\def\nwbegincode#1{% + \begingroup + \topsep \nwcodetopsep + \@beginparpenalty \@highpenalty + \@endparpenalty -\@highpenalty + \@begincode } +\def\nwendcode{\endtrivlist \endgroup \filbreak} % keeps code on 1 page + +\newenvironment{webcode}{% + \@begincode +}{% + \endtrivlist} +\def\@begincode{% + \trivlist \item[]% + \leftskip\@totalleftmargin \advance\leftskip\codemargin + \rightskip\hsize \advance\rightskip -\codehsize + \parskip\z@ \parindent\z@ \parfillskip\@flushglue + \linewidth\codehsize + \@@par + \def\par{\leavevmode\null \@@par \penalty\nwcodepenalty}% + \obeylines + \@noligs \ifx\verbatim@nolig@list\undefined\else + \let\do=\nw@makeother \verbatim@nolig@list \do@noligs\` + \fi + \setupcode \frenchspacing \@vobeyspaces + \nowebsize \setupcode + \let\maybehbox\mbox } + \newskip\nwcodetopsep \nwcodetopsep = 3pt plus 1.2pt minus 1pt + \let\nowebsize=\normalsize + \def\nwopt@tinycode{\let\nowebsize=\tiny} + \def\nwopt@footnotesizecode{\let\nowebsize=\footnotesize} + \def\nwopt@scriptsizecode{\let\nowebsize=\scriptsize} + \def\nwopt@smallcode{\let\nowebsize=\small} + \def\nwopt@normalsizecode{\let\nowebsize=\normalsize} + \def\nwopt@largecode{\let\nowebsize=\large} + \def\nwopt@Largecode{\let\nowebsize=\Large} + \def\nwopt@LARGEcode{\let\nowebsize=\LARGE} + \def\nwopt@hugecode{\let\nowebsize=\huge} + \def\nwopt@Hugecode{\let\nowebsize=\Huge} +\newcount\nwcodepenalty \nwcodepenalty=\@highpenalty +\def\nw@makeother#1{\catcode`#1=12 } +\def\nwbegindocs#1{\ifvmode\noindent\fi} +\let\nwenddocs=\relax +\let\nwdocspar=\filbreak +\raggedbottom +\def\code{\leavevmode\begingroup\setupcode\@vobeyspaces\obeylines} +\let\edoc=\endgroup +\newdimen\@original@textwidth +\def\ps@noweb{% + \@original@textwidth=\textwidth + \let\@mkboth\@gobbletwo + \def\@oddfoot{}\def\@evenfoot{}% No feet. + \if@twoside % If two-sided printing. + \def\@evenhead{\hbox to \@original@textwidth{% + \Rm \thepage\qquad{\Tt\leftmark}\hfil\today}}% Left heading. + \def\@oddhead{\hbox to \@original@textwidth{% + \Rm \today\hfil{\Tt\leftmark}\qquad\thepage}}% Right heading. + \else % If one-sided printing. + \def\@oddhead{\hbox to \@original@textwidth{% + \Rm \today\hfil{\Tt\leftmark}\qquad\thepage}}% Right heading. + \let\@evenhead\@oddhead + \fi + \let\chaptermark\@gobble + \let\sectionmark\@gobble + \let\subsectionmark\@gobble + \let\subsubsectionmark\@gobble + \let\paragraphmark\@gobble + \let\subparagraphmark\@gobble + \def\nwfilename{\begingroup\let\do\@makeother\dospecials + \catcode`\{=1 \catcode`\}=2 \nw@filename} + \def\nw@filename##1{\endgroup\markboth{##1}{##1}\let\nw@filename=\nw@laterfilename}% +} +\def\nw@laterfilename#1{\endgroup\clearpage \markboth{#1}{#1}} +\let\nwfilename=\@gobble +\def\nwcodecomment#1{\@@par\penalty\nwcodepenalty + \if@firstnwcodecomment + \vskip\nwcodecommentsep\penalty\nwcodepenalty\@firstnwcodecommentfalse + \fi% + \hspace{-\codemargin}{% + \rightskip=0pt plus1in + \interlinepenalty\nwcodepenalty + \let\\\relax\footnotesize\Rm #1\@@par\penalty\nwcodepenalty}} +\def\@nwalsodefined#1{\nwcodecomment{\@nwlangdepdef\ \nwpageprep\ \@pagesl{#1}.}} +\def\@nwused#1{\nwcodecomment{\@nwlangdepcud\ \nwpageprep\ \@pagesl{#1}.}} +\def\@nwnotused#1{\nwcodecomment{\@nwlangdeprtc.}} +\def\nwoutput#1{\nwcodecomment{\@nwlangdepcwf\ {\Tt \@stripstar#1*\stripped}.}} +\def\@stripstar#1*#2\stripped{#1} +\providecommand{\nwprevdefptr}[1]{% + \mbox{$\mathord{\triangleleft}\,\mathord{\mbox{\subpageref{#1}}}$}} +\providecommand{\nwnextdefptr}[1]{% + \mbox{$\mathord{\mbox{\subpageref{#1}}}\,\mathord{\triangleright}$}} + +\providecommand{\@nwprevnextdefs}[2]{% + {\nwtagstyle + \ifx\relax#1\else ~~\nwprevdefptr{#1}\fi + \ifx\relax#2\else ~~\nwnextdefptr{#2}\fi}} +\providecommand{\@nwusesondefline}[1]{{\nwtagstyle~~(\@pagenumsl{#1})}} +\providecommand{\@nwstartdeflinemarkup}{\nobreak\hskip 1.5em plus 1fill\nobreak} +\providecommand{\@nwenddeflinemarkup}{\nobreak\hskip \nwdefspace minus\nwdefspace\nobreak} +\def\nwopt@longxref{% + \let\nwalsodefined\@nwalsodefined + \let\nwused\@nwused + \let\nwnotused\@nwnotused + \let\nwprevnextdefs\@gobbletwo + \let\nwusesondefline\@gobble + \let\nwstartdeflinemarkup\relax + \let\nwenddeflinemarkup\relax +} +\def\nwopt@shortxref{% + \let\nwalsodefined\@gobble + \let\nwused\@gobble + \let\nwnotused\@gobble + \let\nwprevnextdefs\@nwprevnextdefs + \let\nwusesondefline\@nwusesondefline + \let\nwstartdeflinemarkup\@nwstartdeflinemarkup + \let\nwenddeflinemarkup\@nwenddeflinemarkup +} +\def\nwopt@noxref{% + \let\nwalsodefined\@gobble + \let\nwused\@gobble + \let\nwnotused\@gobble + \let\nwprevnextdefs\@gobbletwo + \let\nwusesondefline\@gobble + \let\nwstartdeflinemarkup\relax + \let\nwenddeflinemarkup\relax +} +\nwopt@shortxref % to hell with backward compatibility! +\newskip\nwcodecommentsep \nwcodecommentsep=3pt plus 1pt minus 1pt +\newif\if@firstnwcodecomment\@firstnwcodecommenttrue +\newcount\@nwlopage\newcount\@nwhipage % range lo..hi-1 +\newcount\@nwlosub % subpage of lo +\newcount\@nwhisub % subpage of hi +\def\@nwfirstpage#1#2#3{% subpage page xref-tag + \@nwlopage=#2 \@nwlosub=#1 + \def\@nwloxreftag{#3}% + \advance\@nwpagecount by \@ne + \@nwhipage=\@nwlopage\advance\@nwhipage by \@ne } +\def\@nwnextpage#1#2#3{% subpage page xref-tag + \ifnum\@nwhipage=#2 + \advance\@nwhipage by \@ne + \advance\@nwpagecount by \@ne + \@nwhisub=#1 + \def\@nwhixreftag{#3}\else + \ifnum#2<\@nwlopage \advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa\@nwfirstpage{#1}{#2}{#3}\else + \ifnum#2>\@nwhipage \advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa\@nwfirstpage{#1}{#2}{#3}\else + \@nwlosub=0 \@nwhisub=0 + \fi\fi\fi + } +\newcount\@nwpagetemp +\newcount\@nwpagecount +\def\@nwfirstpagel#1{% label + \@ifundefined{r@#1}{\@warning{Reference `#1' on page \thepage \space undefined}% + \nwix@cons\nw@pages{\\{\bf ??}}}{% + \edef\@tempa{\noexpand\@nwfirstpage\subpagepair{#1}{#1}}\@tempa}} +\def\@nwnextpagel#1{% label + \@ifundefined{r@#1}{\@warning{Reference `#1' on page \thepage \space undefined}% + \nwix@cons\nw@pages{\\{\bf ??}}}{% + \edef\@tempa{\noexpand\@nwnextpage\subpagepair{#1}{#1}}\@tempa}} +\def\@pagesl#1{% list of labels + \gdef\nw@pages{}\@nwpagecount=0 + \def\\##1{\@nwfirstpagel{##1}\let\\=\@nwnextpagel}#1% + \advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa\def\\##1{\@nwhyperpagenum##1}% + \ifnum\@nwpagecount=1 \nwpageword \else \nwpagesword\fi~\commafy{\nw@pages}} +\def\@nwhyperpagenum#1#2{\nwhyperreference{#2}{#1}} + +\def\@pagenumsl#1{% list of labels -- doesn't include word `pages', commas, or `and' + \gdef\nw@pages{}\@nwpagecount=0 + \def\\##1{\@nwfirstpagel{##1}\let\\=\@nwnextpagel}#1% + \advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa% + \def\\##1{\@nwhyperpagenum##1\let\\=\@nwpagenumslrest}\nw@pages} +\def\@nwpagenumslrest#1{~\@nwhyperpagenum#1} +\def\subpages#1{% list of {{subpage}{page}} + \gdef\nw@pages{}\@nwpagecount=0 + \def\\##1{\edef\@tempa{\noexpand\@nwfirstpage##1{}}\@tempa + \def\\####1{\edef\@tempa{\noexpand\@nwnextpage####1}\@tempa}}#1% + \advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa\def\\##1{\@firstoftwo##1}% + \ifnum\@nwpagecount=1 \nwpageword \else \nwpagesword\fi~\commafy{\nw@pages}} +\def\@nwaddrange{\advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa} +\def\nwpageword{\@nwlangdepchk} % chunk, was page +\def\nwpagesword{\@nwlangdepchks} % chunk, was page +\def\nwpageprep{\@nwlangdepin} % in, was on +\providecommand\nw@genericref[2]{% what to do, name of ref + \expandafter\nw@g@nericref\csname r@#2\endcsname#1{#2}} +\providecommand\nw@g@nericref[3]{% control sequence, what to do, name + \ifx#1\relax + \ref{#3}% trigger the standard `undefined ref' mechanisms + \else + \expandafter#2#1.\\% + \fi} +\def\nw@selectone#1#2#3\\{#1} +\def\nw@selecttwo#1#2#3\\{#2} +\def\nw@selectonetwo#1#2#3\\{{#1}{#2}} +\providecommand{\subpageref}[1]{% + \nwhyperreference{#1}{\nw@genericref\@subpageref{#1}}} +\def\@subpageref#1#2#3\\{% + \@ifundefined{2on#2}{#2}{\nwthepagenum{#1}{#2}}} +\providecommand{\subpagepair}[1]{% % produces {subpage}{page} + \@ifundefined{r@#1}% + {{0}{0}}% + {\nw@genericref\@subpagepair{#1}}} +\def\@subpagepair#1#2#3\\{% + \@ifundefined{2on#2}{{0}{#2}}{{#1}{#2}}} +\providecommand{\sublabel}[1]{% + \@bsphack + \nwblindhyperanchor{#1}% + \if@filesw {\let\thepage\relax + \def\protect{\noexpand\noexpand\noexpand}% + \edef\@tempa{\write\@auxout{\string + \newsublabel{#1}{{}{\thepage}}}}% + \expandafter}\@tempa + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +\providecommand{\nosublabel}[1]{% + \@bsphack\if@filesw {\let\thepage\relax + \def\protect{\noexpand\noexpand\noexpand}% + \edef\@tempa{\write\@auxout{\string + \newlabel{#1}{{0}{\thepage}}}}% + \expandafter}\@tempa + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +\providecommand\newsublabel{% + \nw@settrailers + \global\let\newsublabel\@newsublabel + \@newsublabel} +\providecommand{\@newsublabel}[2]{% + \edef\this@page{\@cdr#2\@nil}% + \ifx\this@page\last@page\else + \sub@page=\z@ + \fi + \edef\last@page{\this@page} + \advance\sub@page by \@ne + \ifnum\sub@page=\tw@ + \global\@namedef{2on\this@page}{}% + \fi + \pendingsublabel{#1}% + \edef\@tempa##1{\noexpand\newlabel{##1}% + {{\number\sub@page}{\this@page}\nw@labeltrailers}}% + \pending@sublabels + \def\pending@sublabels{}} +\providecommand\nw@settrailers{% -- won't work on first run + \@ifpackageloaded{nameref}% + {\gdef\nw@labeltrailers{{}{}{}}}% + {\gdef\nw@labeltrailers{}}} +\renewcommand\nw@settrailers{% + \@ifundefined{@secondoffive}% + {\gdef\nw@labeltrailers{}}% + {\gdef\nw@labeltrailers{{}{}{}}}} +\providecommand{\nextchunklabel}[1]{% + \nwblindhyperanchor{#1}% % looks slightly bogus --- nr + \@bsphack\if@filesw {\let\thepage\relax + \edef\@tempa{\write\@auxout{\string\pendingsublabel{#1}}}% + \expandafter}\@tempa + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +\providecommand\pendingsublabel[1]{% + \def\@tempa{\noexpand\@tempa}% + \edef\pending@sublabels{\noexpand\@tempa{#1}\pending@sublabels}} +\def\pending@sublabels{} +\def\last@page{\relax} +\newcount\sub@page +\def\@alphasubpagenum#1#2{#2\ifnum#1=0 \else\@alph{#1}\fi} +\def\@nosubpagenum#1#2{#2} +\def\@numsubpagenum#1#2{#2\ifnum#1=0 \else.\@arabic{#1}\fi} +\def\nwopt@nosubpage{\let\nwthepagenum=\@nosubpagenum\nwopt@nomargintag} +\def\nwopt@numsubpage{\let\nwthepagenum=\@numsubpagenum} +\def\nwopt@alphasubpage{\let\nwthepagenum=\@alphasubpagenum} +\nwopt@alphasubpage +\newcount\@nwalph@n +\let\@nwalph@d\@tempcnta +\let\@nwalph@bound\@tempcntb +\def\@nwlongalph#1{{% + \@nwalph@n=#1\advance\@nwalph@n by-1 + \@nwalph@bound=26 + \loop\ifnum\@nwalph@n<\@nwalph@bound\else + \advance\@nwalph@n by -\@nwalph@bound + \multiply\@nwalph@bound by 26 + \repeat + \loop\ifnum\@nwalph@bound>1 + \divide\@nwalph@bound by 26 + \@nwalph@d=\@nwalph@n\divide\@nwalph@d by \@nwalph@bound + % d := d * bound ; n -:= d; d := d / bound --- saves a temporary + \multiply\@nwalph@d by \@nwalph@bound + \advance\@nwalph@n by -\@nwalph@d + \divide\@nwalph@d by \@nwalph@bound + \advance\@nwalph@d by 1 \@alph{\@nwalph@d}% + \repeat +}} +\newcount\nw@chunkcount +\nw@chunkcount=\@ne +\providecommand{\weblabel}[1]{% + \@bsphack + \nwblindhyperanchor{#1}% + \if@filesw {\let\thepage\relax + \def\protect{\noexpand\noexpand\noexpand}% + \edef\@tempa{\write\@auxout{\string + \newsublabel{#1}{{}{\number\nw@chunkcount}}}}% + \expandafter}\@tempa + \global\advance\nw@chunkcount by \@ne + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +\def\nwopt@webnumbering{% + \let\sublabel=\weblabel + \def\nwpageword{chunk}\def\nwpagesword{chunks}% + \def\nwpageprep{in}} +% \nwindexdefn{printable name}{identifying label}{label of chunk} +% \nwindexuse{printable name}{identifying label}{label of chunk} + +\def\nwindexdefn#1#2#3{\@auxix{\protect\nwixd}{#2}{#3}} +\def\nwindexuse#1#2#3{\@auxix{\protect\nwixu}{#2}{#3}} + +\def\@auxix#1#2#3{% {marker}{id label}{subpage label} + \@bsphack\if@filesw {\let\nwixd\relax\let\nwixu\relax + \def\protect{\noexpand\noexpand\noexpand}% + \edef\@tempa{\write\@auxout{\string\nwixadd{#1}{#2}{#3}}}% + \expandafter}\@tempa + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +% \nwixadd{marker}{idlabel}{subpage label} +\def\nwixadd#1#2#3{% + \@ifundefined{nwixl@#2}% + {\global\@namedef{nwixl@#2}{#1{#3}}}% + {\expandafter\nwix@cons\csname nwixl@#2\endcsname{#1{#3}}}} +\def\@nwsubscriptident#1#2{\mbox{$\mbox{#1}_{\mathrm{\subpageref{#2}}}$}} +\def\@nwnosubscriptident#1#2{#1} +\def\@nwhyperident#1#2{\leavevmode\nwhyperreference{#2}{#1}} +\def\nwopt@subscriptidents{% + \let\nwlinkedidentq\@nwsubscriptident + \let\nwlinkedidentc\@nwsubscriptident +} +\def\nwopt@nosubscriptidents{% + \let\nwlinkedidentq\@nwnosubscriptident + \let\nwlinkedidentc\@nwnosubscriptident +} +\def\nwopt@hyperidents{% + \let\nwlinkedidentq\@nwhyperident + \let\nwlinkedidentc\@nwhyperident +} +\def\nwopt@nohyperidents{% + \let\nwlinkedidentq\@nwnosubscriptident + \let\nwlinkedidentc\@nwnosubscriptident +} +\def\nwopt@subscriptquotedidents{% + \let\nwlinkedidentq\@nwsubscriptident +} +\def\nwopt@nosubscriptquotedidents{% + \let\nwlinkedidentq\@nwnosubscriptident +} +\def\nwopt@hyperquotedidents{% + \let\nwlinkedidentq\@nwhyperident +} +\def\nwopt@nohyperquotedidents{% + \let\nwlinkedidentq\@nwnosubscriptident +} +\nwopt@hyperidents +\newcount\@commacount +\def\commafy#1{% + {\nwix@listcount{#1}\@commacount=\nwix@counter + \let\@comma@each=\\% + \ifcase\@commacount\let\\=\@comma@each\or\let\\=\@comma@each\or + \def\\{\def\\{ \@nwlangdepand\ \@comma@each}\@comma@each}\else + \def\\{\def\\{, % + \advance\@commacount by \m@ne + \ifnum\@commacount=1 \@nwlangdepand~\fi\@comma@each}\@comma@each}\fi + #1}} +\def\nwix@cons#1#2{% {list}{\marker{element}} + {\toks0=\expandafter{#1}\def\@tempa{#2}\toks2=\expandafter{\@tempa}% + \xdef#1{\the\toks0 \the\toks2 }}} +\def\nwix@uses#1{% {label} + \def\nwixu{\\}\let\nwixd\@gobble\@nameuse{nwixl@#1}} +\def\nwix@defs#1{% {label} + \def\nwixd{\\}\let\nwixu\@gobble\@nameuse{nwixl@#1}} +\newcount\nwix@counter +\def\nwix@listcount#1{% {list with \\} + {\count@=0 + \def\\##1{\advance\count@ by \@ne }% + #1\global\nwix@counter=\count@ }} +\def\nwix@usecount#1{\nwix@listcount{\nwix@uses{#1}}} +\def\nwix@defcount#1{\nwix@listcount{\nwix@defs{#1}}} +\def\nwix@id@defs#1{% index pair + {{\Tt \@car#1\@nil}% + \def\\##1{~\subpageref{##1}}\nwix@defs{\@cdr#1\@nil}}} +\def\nwidentuses#1{% list of index pairs + \nwcodecomment{\@nwlangdepuss\ \let\\=\nwix@id@defs\commafy{#1}.}} +\def\nwix@totaluses#1{% list of index pairs + {\count@=0 + \def\\##1{\nwix@usecount{\@cdr##1\@nil}\advance\count@ by\nwix@counter}% + #1\global\nwix@counter\count@ }} +\def\nwix@id@uses#1#2{% {ident}{label} + \nwix@usecount{#2}\ifnum\nwix@counter>0 + {\advance\leftskip by \codemargin + \nwcodecomment{{\Tt #1}, \@nwlangdepusd\ \nwpageprep\ \@pagesl{\nwix@uses{#2}}.}}% + \else + \ifnw@hideunuseddefs\else + {\advance\leftskip by \codemargin \nwcodecomment{{\Tt #1}, \@nwlangdepnvu.}}% + \fi + \fi} +\def\nwidentdefs#1{% list of index pairs + \ifnw@hideunuseddefs\nwix@totaluses{#1}\else\nwix@listcount{#1}\fi + \ifnum\nwix@counter>0 + \nwcodecomment{\@nwlangdepdfs:}% + {\def\\##1{\nwix@id@uses ##1}#1}% + \fi} +\newif\ifnw@hideunuseddefs\nw@hideunuseddefsfalse +\def\nwopt@hideunuseddefs{\nw@hideunuseddefstrue} +\def\nwopt@noidentxref{% + \let\nwidentdefs\@gobble + \let\nwidentuses\@gobble} +\def\nw@underlinedefs{% {list with \nwixd, \nwixu} + \let\\=\relax\def\nw@comma{, } + \def\nwixd##1{\\\underline{\subpageref{##1}}\let\\\nw@comma}% + \def\nwixu##1{\\\subpageref{##1}\let\\\nw@comma}} + +\def\nw@indexline#1#2{% + {\indent {\Tt #1}: \nw@underlinedefs\@nameuse{nwixl@#2}\par}} + +\newenvironment{thenowebindex}{\parindent=-10pt \parskip=\z@ + \advance\leftskip by 10pt + \advance\rightskip by 0pt plus1in\par\@afterindenttrue + \def\\##1{\nw@indexline##1}}{} +\def\nowebindex{% + \@ifundefined{nwixs@i}% + {\@warning{The \string\nowebindex\space is empty}}% + {\begin{thenowebindex}\@nameuse{nwixs@i}\end{thenowebindex}}} +\def\nowebindex@external{% + {\let\nwixadds@c=\@gobble + \def\nwixadds@i##1{\nw@indexline##1}% + \def\nwixaddsx##1##2{\@nameuse{nwixadds@##1}{##2}}% + \begin{thenowebindex}\@input{\jobname.nwi}\end{thenowebindex}}} +\def\nwixlogsorted#1#2{% list data + \@bsphack\if@filesw + \toks0={#2}\immediate\write\@auxout{\string\nwixadds{#1}{\the\toks0}} + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +\def\nwixadds#1#2{% + \@ifundefined{nwixs@#1}% + {\global\@namedef{nwixs@#1}{\\{#2}}}% + {\expandafter\nwix@cons\csname nwixs@#1\endcsname{\\{#2}}}} +\let\nwixaddsx=\@gobbletwo +\def\nwopt@externalindex{% + \ifx\nwixadds\@gobbletwo % already called + \else + \let\nwixaddsx=\nwixadds \let\nwixadds=\@gobbletwo + \let\nowebindex=\nowebindex@external + \let\nowebchunks=\nowebchunks@external + \fi} +\def\nowebchunks{% + \@ifundefined{nwixs@c}% + {\@warning{The are no \string\nowebchunks}}% + {\begin{thenowebchunks}\@nameuse{nwixs@c}\end{thenowebchunks}}} +\def\nowebchunks@external{% + {\let\nwixadds@i=\@gobble + \def\nwixadds@c##1{\nw@onechunk##1}% + \def\nwixaddsx##1##2{\@nameuse{nwixadds@##1}{##2}}% + \begin{thenowebchunks}\@input{\jobname.nwi}\end{thenowebchunks}}} + \@namedef{r@nw@notdef}{{0}{(\@nwlangdepnvd)}} +\def\nw@chunkunderlinedefs{% {list of labels with \nwixd, \nwixu} + \let\\=\relax\def\nw@comma{, } + \def\nwixd##1{\\\underline{\subpageref{##1}}\let\\\nw@comma}% + \def\nwixu##1{\\\subpageref{##1}\let\\\nw@comma}} +\def\nw@onechunk#1#2#3{% {name}{label of first definition}{list with \nwixd, \nwixu} + \@ifundefined{r@#2}{}{% + \indent\LA #1~{\nwtagstyle\subpageref{#2}}\RA + \if@nwlongchunks{~\nw@chunkunderlinedefs#3}\fi\par}} +\newenvironment{thenowebchunks}{\vskip3pt + \parskip=\z@\parindent=-10pt \advance\leftskip by 10pt + \advance\rightskip by 0pt plus10pt \@afterindenttrue + \def\\##1{\nw@onechunk##1}}{} +\newif\if@nwlongchunks +\@nwlongchunksfalse +\let\nwopt@longchunks\@nwlongchunkstrue +\providecommand\@nw@hyper@ref{\hyperreference} % naras +\providecommand\@nw@hyper@anc{\blindhyperanchor} % naras +\providecommand\@nw@hyperref@ref[2]{\hyperlink{noweb.#1}{#2}} % nr +\providecommand\@nw@hyperref@anc[1]{\hypertarget{noweb.#1}{\relax}} % nr +%%\renewcommand\@nw@hyperref@ref[2]{{#2}} % nr +%%\renewcommand\@nw@hyperref@anc[1]{} % nr +\providecommand\nwhyperreference{% + \@ifundefined{hyperlink} + {\@ifundefined{hyperreference} + {\global\let\nwhyperreference\@gobble} + {\global\let\nwhyperreference\@nw@hyper@ref}} + {\global\let\nwhyperreference\@nw@hyperref@ref}% + \nwhyperreference +} + +\providecommand\nwblindhyperanchor{% + \@ifundefined{hyperlink} + {\@ifundefined{hyperreference} + {\global\let\nwblindhyperanchor\@gobble} + {\global\let\nwblindhyperanchor\@nw@hyper@anc}} + {\global\let\nwblindhyperanchor\@nw@hyperref@anc}% + \nwblindhyperanchor +} +\providecommand\nwanchorto{% + \begingroup\let\do\@makeother\dospecials + \catcode`\{=1 \catcode`\}=2 \nw@anchorto} +\providecommand\nw@anchorto[1]{\endgroup\def\nw@next{#1}\nw@anchortofin} +\providecommand\nw@anchortofin[1]{#1\footnote{See URL \texttt{\nw@next}.}} +\let\nwanchorname\@gobble +\newif\ifhtml +\htmlfalse +\let\nwixident=\relax +\def\nwbackslash{\char92} +\def\nwlbrace{\char123} +\def\nwrbrace{\char125} +\def\nwopt@english{% + \def\@nwlangdepdef{This definition is continued}% + \def\@nwlangdepcud{This code is used}% + \def\@nwlangdeprtc{Root chunk (not used in this document)}% + \def\@nwlangdepcwf{This code is written to file}% + \def\@nwlangdepchk{chunk}% + \def\@nwlangdepchks{chunks}% + \def\@nwlangdepin{in}% + \def\@nwlangdepand{and}% + \def\@nwlangdepuss{Uses}% + \def\@nwlangdepusd{used}% + \def\@nwlangdepnvu{never used}% + \def\@nwlangdepdfs{Defines}% + \def\@nwlangdepnvd{never defined}% +} +\let\nwopt@american\nwopt@english +\def\nwopt@portuges{% + \def\@nwlangdepdef{Defini\c{c}\~ao continuada em}% + % This definition is continued + \def\@nwlangdepcud{C\'odigo usado em}% + % This code is used + \def\@nwlangdeprtc{Fragmento de topo (sem uso no documento)}% + % Root chunk (not used in this document) + \def\@nwlangdepcwf{Este c\'odigo foi escrito no ficheiro}% + % This code is written to file + \def\@nwlangdepchk{fragmento}% + % chunk + \def\@nwlangdepchks{fragmentos}% + % chunks + \def\@nwlangdepin{no(s)}% + % in + \def\@nwlangdepand{e}% + % and + \def\@nwlangdepuss{Usa}% + % Uses + \def\@nwlangdepusd{usado}% + % used + \def\@nwlangdepnvu{nunca usado}% + % never used + \def\@nwlangdepdfs{Define}% + % Defines + \def\@nwlangdepnvd{nunca definido}% + % never defined +} +\def\nwopt@frenchb{% + \def\@nwlangdepdef{Cette d\'efinition suit}% + % This definition is continued + \def\@nwlangdepcud{Ce code est employ\'e}% + % This code is used + \def\@nwlangdeprtc{Morceau racine (pas employ\'e dans ce document)}% + % Root chunk (not used in this document) + \def\@nwlangdepcwf{Ce code est \'ecrit aux fichier}% + % This code is written to file + \def\@nwlangdepchk{le morceau}% + % chunk + \def\@nwlangdepchks{les morceaux}% + % chunks + \def\@nwlangdepin{dans}% + % in + \def\@nwlangdepand{et}% + % and + \def\@nwlangdepuss{Il emploie}% + % Uses + \def\@nwlangdepusd{employ\'{e}}% + % used + \def\@nwlangdepnvu{jamais employ\'{e}}% + % never used + \def\@nwlangdepdfs{Il d\'{e}fine}% + % Defines + % Cannot use the accent here: \def\@nwlangdepnvd{jamais d\'{e}fini}% + \def\@nwlangdepnvd{jamais defini}% + % never defined +} +\let\nwopt@french\nwopt@frenchb +\def\nwopt@german{% + \def\@nwlangdepdef{Diese Definition wird fortgesetzt}% + % This definition is continued + \def\@nwlangdepcud{Dieser Code wird benutzt}% + % This code is used + \def\@nwlangdeprtc{Hauptteil (nicht in diesem Dokument benutzt)}% + % Root chunk (not used in this document) + \def\@nwlangdepcwf{Dieser Code schreibt man zum File}% + % This code is written to file + \def\@nwlangdepchk{Teil}% + % chunk + \def\@nwlangdepchks{Teils}% + % chunks + \def\@nwlangdepin{im}% + % in + \def\@nwlangdepand{und}% + % and + \def\@nwlangdepuss{Benutztt}% + % Uses + \def\@nwlangdepusd{benutzt}% + % used + \def\@nwlangdepnvu{nicht benutzt}% + % never used + \def\@nwlangdepdfs{Definiert}% + % Defines + \def\@nwlangdepnvd{nicht definiert}% + % never defined +} +\let\nwopt@ngerman\nwopt@german +\ifx\languagename\undefined % default is English + \noweboptions{english} +\else + \@ifundefined{nwopt@\languagename} + {\noweboptions{english}} + {\expandafter\noweboptions\expandafter{\languagename}} +\fi +% Final names for the system and its components were in doubt so +% Language is used throughout the book to specify what the system is named. +\providecommand{\Language}{AXIOM} + +% HyperName was used to specify the name of the browser +\providecommand{\HyperName}{HyperDoc} + +% This is nothing more than inline math mode in Tex but has additional +% meaning within the browser. +\providecommand{\spad}[1]{${#1}$} + +% This is a way to say 8th, 100th, etc. +% We use providecommand so it doesn't clash with amsmath package +\providecommand{\eth}[1]{{#1}-th} + +% add the binom function for combfunc +\providecommand{\binom}[2]{\left(\begin{array}{c}#1\\#2\end{array}\right)} + +% spadcommands are the actual text that you type at the axiom prompt +\providecommand{\spadcommand}[1]% +{\begin{flushleft}{\tt #1}\end{flushleft}\vskip .1cm } + +% spadgraph are the actual text that you type at the axiom prompt for draw +\providecommand{\spadgraph}[1]% +{\begin{flushleft}{\tt #1}\end{flushleft}\vskip .1cm } + +%% spadsig gives the standard -> notation for signatures +\providecommand{\spadsig}[2]{{\sf #1 $\rightarrow$ #2}} + +% returnType is the type signature returned by the axiom interpreter +\providecommand{\returnType}[1]% +{\begin{flushright}{\tt #1}\end{flushright}\vskip .1cm} + +%%% Axiom commands are set off in a special boxed area. +%%% This is used to draw a line around that boxed area. +\providecommand\boxed[2]{% +\begin{center} +\begin{tabular}{|c|} +\hline +\begin{minipage}{#1} +\normalsize +{#2} +\end{minipage}\\ +\hline +\end{tabular} +\end{center}} + +% The book begins with some introductory material that is not really +% listed as a chapter. This creates a header similar to \chapter. +\providecommand{\pseudoChapter}[1]% +{\vskip .5in \noindent {\Huge{\bf #1}}\vskip .5in} + +% The book begins with some introductory material that is not really +% listed as a section. This creates a header similar to \section. +\providecommand{\pseudoSection}[1]% +{\vskip .25in \noindent {\large{\bf #1}}\vskip .25in} + +% spadofFrom records the operation in the index and the domain in the index +\providecommand{\spadopFrom}[2]{\index{library!operations!#1 @\begingroup \string\tt{} #1 \endgroup}\index{#2}``{\tt #1}''} + +% spadfunFrom records the function name and domain in the index +\providecommand{\spadfunFrom}[2]{{\bf #1}\index{#1 @\begingroup \string\bf{} #1 \endgroup}\index{#2}} + +% These are special markers within the text for Hypertex keywords +% They have no particular meaning in the book form. +\providecommand{\spadfun}[1]{{\it #1}} +\providecommand{\spadgloss}[1]{{\it #1}} +\providecommand{\spadkey}[1]{\index{#1 @\begingroup \string\tt{} #1 \endgroup}} + +% spadtype records the domain in the index +\providecommand{\spadtype}[1]{{\bf #1}\index{#1 @\begingroup \string\bf{} #1 \endgroup}} + +% This is used to create a caption on an included image +\providecommand{\simpleCaption}[1]{\def\thefigure{\@arabic\c@figure}\caption{#1}} + +% This is the name of the ``glossy'' pages in the physical book. +\providecommand{\Gallery}{\Language{} Images} + +% spadofFrom records the operation in the index and the domain in the index +\providecommand{\spadopFrom}[2]{\index{library!operations!#1 @\begingroup \string\tt{} #1 \endgroup}\index{#2}``{\tt #1}''} + +%% typeset e.g. and i.e. +\providecommand{\eg}{\emph{e.g.}} +\providecommand{\ie}{\emph{i.e.}} + +%% Typeset in-line code. +\providecommand{\Code}[1]{\texttt{#1}} + +%% Typeset a file name +\providecommand{\File}[1]{{\itshape{#1}}} + +%% Typeset a tool name, e.g. Axiom +\providecommand{\Tool}[1]{{\bfseries\sffamily{#1}}} +\providecommand\AXIOM{\vskip\parindent\indent{\bf AXIOM}\vskip\parindent\noindent\ignorespaces} +\providecommand\maxima{\vskip\parindent\noindent{\bf MAXIMA}\vskip\parindent\noindent\ignorespaces} +\providecommand\yacas{\vskip\parindent\noindent{\bf YACAS}\vskip\parindent\noindent\ignorespaces} diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index 60667b0..d2ad926 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -266,5 +266,140 @@ satisfies the original ordinary differential equation.

source pdf
+
+This portion of the CATS suite involves Albert Rich's Integration Suite. +They have been rewritten using Axiom syntax. +

+ algebraic000-099 + source + pdf
+ algebraic100-199 + source + pdf
+ algebraic200-299 + source + pdf
+ algebraic300-399 + source + pdf
+ algebraic400-461 + source + pdf
+
+ error000-078 + source + pdf
+
+ exponential + source + pdf
+
+ hyper000-099 + source + pdf
+ hyper100-199 + source + pdf
+ hyper100-199 + source + pdf
+ hyper200-299 + source + pdf
+ hyper300-399 + source + pdf
+ hyper400-499 + source + pdf
+ hyper500-599 + source + pdf
+ hyper600-699 + source + pdf
+ hyper700-799 + source + pdf
+ hyper800-899 + source + pdf
+ hyper900-999 + source + pdf
+ hyper1000-1098 + source + pdf
+
+ intfunc000-032 + source + pdf
+
+ invhyper000-099 + source + pdf
+ invhyper100-199 + source + pdf
+ invhyper200-296 + source + pdf
+
+ invtrig000-092 + source + pdf
+
+ log000-099 + source + pdf
+ log100-199 + source + pdf
+ log200-299 + source + pdf
+ log300-391 + source + pdf
+
+ rational + source + pdf
+
+ specfunc000-022 + source + pdf
+
+ trig000-099 + source + pdf
+ trig100-199 + source + pdf
+ trig200-299 + source + pdf
+ trig300-399 + source + pdf
+ trig400-499 + source + pdf
+ trig500-599 + source + pdf
+ trig600-699 + source + pdf
+ trig700-799 + source + pdf
+ trig800-899 + source + pdf
+ trig900-920 + source + pdf
+ - \ No newline at end of file + diff --git a/src/axiom-website/CATS/richalgebraic000-099.input.pamphlet b/src/axiom-website/CATS/richalgebraic000-099.input.pamphlet new file mode 100644 index 0000000..a93236a --- /dev/null +++ b/src/axiom-website/CATS/richalgebraic000-099.input.pamphlet @@ -0,0 +1,4982 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richalgebraic000-099.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic000-099.output +)spool richalgebraic000-099.output +)set message test on +)set message auto off +)clear all + +--S 1 of 518 +t0000:= (c*(a+b*x)^2)^(5/2) +--R +--R +--R (1) +--R +-----------------------+ +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 | 2 2 2 +--R (b c x + 4a b c x + 6a b c x + 4a b c x + a c )\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 1 + +--S 2 of 518 +r0000:= 1/6*(a+b*x)*(c*(a+b*x)^2)^(5/2)/b +--R +--R +--R (2) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R / +--R 6b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 518 +a0000:= integrate(t0000,x) +--R +--R +--R (3) +--R 5 2 6 4 2 5 2 3 2 4 3 2 2 3 4 2 2 5 2 +-+ +--R (b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a c x)\|c +--R ------------------------------------------------------------------------ +--R 6 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 518 +m0000:= a0000-r0000 +--R +--R +--R (4) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (- b c x - 5a b c x - 10a b c x - 10a b c x - 5a b c x - a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R + +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 5 2 +-+ +--R (b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x)\|c +--R / +--R 6b +--R Type: Expression(Integer) +--E 4 + +--S 5 of 518 +d0000:= D(m0000,x) +--R +--R +--R (5) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +-+ +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c )\|c +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R + +--R 6 3 6 5 3 5 2 4 3 4 3 3 3 3 4 2 3 2 5 3 +--R - b c x - 6a b c x - 15a b c x - 20a b c x - 15a b c x - 6a b c x +--R + +--R 6 3 +--R - a c +--R / +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 5 + +--S 6 of 518 +t0001:= (c*(a+b*x)^2)^(3/2) +--R +--R +--R +-----------------------+ +--R 2 2 2 | 2 2 2 +--R (6) (b c x + 2a b c x + a c)\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 6 + +--S 7 of 518 +r0001:= 1/4*(a+b*x)*(c*(a+b*x)^2)^(3/2)/b +--R +--R +--R +-----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c)\|b c x + 2a b c x + a c +--R (7) --------------------------------------------------------------- +--R 4b +--R Type: Expression(Integer) +--E 7 + +--S 8 of 518 +a0001:= integrate(t0001,x) +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (b c x + 4a b c x + 6a b c x + 4a c x)\|c +--R (8) --------------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 518 +m0001:= a0001-r0001 +--R +--R +--R (9) +--R +-----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (- b c x - 3a b c x - 3a b c x - a c)\|b c x + 2a b c x + a c +--R + +--R 4 4 3 3 2 2 2 3 +-+ +--R (b c x + 4a b c x + 6a b c x + 4a b c x)\|c +--R / +--R 4b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 518 +d0001:= D(m0001,x) +--R +--R +--R (10) +--R +-----------------------+ +--R 3 3 2 2 2 3 +-+ | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c)\|c \|b c x + 2a b c x + a c +--R + +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 +--R - b c x - 4a b c x - 6a b c x - 4a b c x - a c +--R / +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 10 + +--S 11 of 518 +t0002:= 1/(c/(a+b*x)^2)^(3/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (11) ---------------------- +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 518 +r0002:= 1/4*(a+b*x)/b/(c/(a+b*x)^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (12) ---------------------------- +--R +------------------+ +--R | c +--R 4b c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 12 + +--S 13 of 518 +a0002:= integrate(t0002,x) +--R +--R +--R 3 4 2 3 2 2 3 +--R b x + 4a b x + 6a b x + 4a x +--R (13) ------------------------------- +--R +-+ +--R 4c\|c +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 518 +m0002:= a0002-r0002 +--R +--R +--R (14) +--R 3 3 2 2 2 3 +-+ +--R (- b x - 3a b x - 3a b x - a )\|c +--R + +--R +------------------+ +--R 4 4 3 3 2 2 2 3 | c +--R (b x + 4a b x + 6a b x + 4a b x) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +------------------+ +--R | c +-+ +--R 4b c |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 14 + +--S 15 of 518 +d0002:= D(m0002,x) +--R +--R +--R (15) +--R +------------------+ +--R 3 3 2 2 2 3 | c +-+ 2 2 +--R (b x + 3a b x + 3a b x + a ) |------------------ \|c - b c x +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 +--R - 2a b c x - a c +--R / +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 15 + +--S 16 of 518 +t0003:= 1/(c/(a+b*x)^2)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (16) -------------------------------------- +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 518 +r0003:= 1/6*(a+b*x)/b/(c/(a+b*x)^2)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (17) -------------------------------------------------- +--R +------------------+ +--R 2 | c +--R 6b c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 17 + +--S 18 of 518 +a0003:= integrate(t0003,x) +--R +--R +--R 5 6 4 5 2 3 4 3 2 3 4 2 5 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a x +--R (18) ------------------------------------------------------ +--R 2 +-+ +--R 6c \|c +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 518 +m0003:= a0003-r0003 +--R +--R +--R (19) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-+ +--R (- b x - 5a b x - 10a b x - 10a b x - 5a b x - a )\|c +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x) +--R * +--R +------------------+ +--R | c +--R |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +------------------+ +--R 2 | c +-+ +--R 6b c |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 518 +d0003:= D(m0003,x) +--R +--R +--R (20) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a ) +--R * +--R +------------------+ +--R | c +-+ +--R |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - b c x - 4a b c x - 6a b c x - 4a b c x - a c +--R / +--R +------------------+ +--R 3 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 20 + +--S 21 of 518 +t0004:= 1/(2-3*x)^(1/2)/(2+3*x)^(1/2) +--R +--R +--R 1 +--R (21) -------------------- +--R +--------+ +------+ +--R \|- 3x + 2 \|3x + 2 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 518 +r0004:= 1/3*asin(3/2*x) +--R +--R +--R 3x +--R asin(--) +--R 2 +--R (22) -------- +--R 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 518 +--a0004:= integrate(t0004,x) +-- bug 7207: causes infinite loop in integrator. +--E 23 + +--S 24 of 518 +t0005:= 1/(3-x)^(1/2)/(5+x)^(1/2) +--R +--R +--R 1 +--R (23) ------------------ +--R +-------+ +-----+ +--R \|- x + 3 \|x + 5 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 518 +r0005:= asin(1/4+1/4*x) +--R +--R +--R x + 1 +--R (24) asin(-----) +--R 4 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 518 +--a0005:= integrate(t0005,x) +--E 26 + +--S 27 of 518 +--m0005:= a0005-r0005 +--E 28 + +--S 28 of 518 +--d0005:= D(m0005,x) +--E 28 + +--S 29 of 518 +t0006:= 1/(-3-x)^(1/2)/(5+x)^(1/2) +--R +--R +--R 1 +--R (25) ------------------ +--R +-------+ +-----+ +--R \|- x - 3 \|x + 5 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 518 +r0006:= asin(4+x) +--R +--R +--R (26) asin(x + 4) +--R Type: Expression(Integer) +--E 30 + +--S 31 of 518 +--a0006:= integrate(t0006,x) +--E 31 + +--S 32 of 518 +--m0006:= a0006-r0006 +--E 32 + +--S 33 of 518 +--d0006:= D(m0006,x) +--E 33 + +--S 34 of 518 +t0007:= (1-x)^(1/2)*(1+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (27) \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 518 +r0007:= 1/2*x*(1-x^2)^(1/2)+1/2*asin(x) +--R +--R +--R +--------+ +--R | 2 +--R x\|- x + 1 + asin(x) +--R (28) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 518 +--a0007:= integrate(t0007,x) +--E 36 + +--S 37 of 518 +--m0007:= a0007-r0007 +--E 37 + +--S 38 of 518 +--d0007:= D(m0007,x) +--E 38 + +--S 39 of 518 +t0008:= 1/(1-x)^(1/2)/(1+x)^(1/2) +--R +--R +--R 1 +--R (29) ------------------ +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 518 +r0008:= asin(x) +--R +--R +--R (30) asin(x) +--R Type: Expression(Integer) +--E 40 + +--S 41 of 518 +--a0008:= integrate(t0008,x) +--E 41 + +--S 42 of 518 +--m0008:= a0008-r0008 +--E 42 + +--S 43 of 518 +--d0008:= D(m0008,x) +--E 43 + +--S 44 of 518 +t0009:= 1/(1-x)^(3/2)/(1+x)^(3/2) +--R +--R +--R 1 +--R (31) - -------------------------- +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 518 +r0009:= x/(1-x^2)^(1/2) +--R +--R +--R x +--R (32) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 45 + +\end{chunk} +Occasionally we get a different answer to this same integration: +\begin{verbatim} + + + +-------+ +-----+ + x\|- x + 1 \|x + 1 + (33) - ------------------- + 2 + x - 1 +--R Type: Union(Expression(Integer),...) +\end{verbatim} +Both answers are correct as can be seen by taking the difference between +the original integrand and the derivative of the expression. +\begin{chunk}{*} +--S 46 of 518 ok to fail. there appear to be 2 answers (see above) +a0009:= integrate(t0009,x) +--R +--R +--R +-------+ +-----+ +--R x\|- x + 1 \|x + 1 +--R (33) - ------------------- +--R 2 +--R x - 1 +--R Type: Union(Expression(Integer),...) +--E 46 + +\end{chunk} +Occasionally we get a different answer to this same integration: +\begin{verbatim} + + + +--------+ + | 2 +-------+ +-----+ 3 + - x\|- x + 1 \|- x + 1 \|x + 1 - x + x + (34) ----------------------------------------- + +--------+ + 2 | 2 + (x - 1)\|- x + 1 +\end{verbatim} +Both answers are correct as can be seen by taking the difference between +the original integrand and the derivative of the expression. +\begin{chunk}{*} +--S 47 of 518 ok to fail. there appear to be 2 answers (see above) +m0009:= a0009-r0009 +--R +--R +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ 2 | 2 3 +--R - 3x\|- x + 1 \|- x + 1 \|x + 1 + (- 2x + 2)\|- x + 1 - 3x + 3x +--R (34) --------------------------------------------------------------------- +--R +--------+ +--R 2 | 2 +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 518 +d0009:= D(m0009,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- x + 1 \|x + 1 - \|- x + 1 +--R (35) ------------------------------------- +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 48 + +--S 49 of 518 +t0010:= (3-x)^(1/2)*(-2+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (36) \|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 518 +r0010:= -1/4*(5-2*x)*(-6+5*x-x^2)^(1/2)+1/8*asin(-5+2*x) +--R +--R +--R +-------------+ +--R | 2 +--R (4x - 10)\|- x + 5x - 6 + asin(2x - 5) +--R (37) ---------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 518 +--a0010:= integrate(t0010,x) +--E 51 + +--S 52 of 518 +--m0010:= a0010-r0010 +--E 52 + +--S 53 of 518 +--d0010:= D(m0010,x) +--E 53 + +--S 54 of 518 +t0011:= 1/(3-x)^(1/2)/(-2+x)^(1/2) +--R +--R +--R 1 +--R (38) ------------------ +--R +-------+ +-----+ +--R \|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 518 +r0011:= asin(-5+2*x) +--R +--R +--R (39) asin(2x - 5) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 518 +--a0011:= integrate(t0011,x) +--E 56 + +--S 57 of 518 +--m0011:= a0011-r0011 +--E 57 + +--S 58 of 518 +--d0011:= D(m0011,x) +--E 58 + +--S 59 of 518 +t0012:= x^(1/2)/(-a+b*x)^2 +--R +--R +--R +-+ +--R \|x +--R (40) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 59 + +--S 60 of 518 +r0012:= x^(1/2)/b/(a-b*x)-atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(1/2)/b^(3/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (- b x + a)atanh(--------) - \|a \|b \|x +--R +-+ +--R \|a +--R (41) ----------------------------------------- +--R 2 +-+ +-+ +--R (b x - a b)\|a \|b +--R Type: Expression(Integer) +--E 60 + +--S 61 of 518 +a0012:= integrate(t0012,x) +--R +--R +--R (42) +--R +-+ +---+ +--R - 2a b\|x + (b x + a)\|a b +---+ +-+ +--R (b x - a)log(----------------------------) - 2\|a b \|x +--R b x - a +--R [--------------------------------------------------------, +--R 2 +---+ +--R (2b x - 2a b)\|a b +--R +-----+ +-+ +--R \|- a b \|x +-----+ +-+ +--R (- b x + a)atan(------------) - \|- a b \|x +--R a +--R --------------------------------------------] +--R 2 +-----+ +--R (b x - a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 61 + +--S 62 of 518 +m0012a:= a0012.1-r0012 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(----------------------------) + 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (43) ------------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression(Integer) +--E 62 + +--S 63 of 518 +d0012a:= D(m0012a,x) +--R +--R +--R (44) 0 +--R Type: Expression(Integer) +--E 63 + +--S 64 of 518 +m0012b:= a0012.1-r0012 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(----------------------------) + 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (45) ------------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression(Integer) +--E 64 + +--S 65 of 518 +d0012b:= D(m0012b,x) +--R +--R +--R (46) 0 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 518 +t0013:= x^(1/2)/(-a+b*x)^3 +--R +--R +--R +-+ +--R \|x +--R (47) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 518 +r0013:= -1/2*x^(1/2)/b/(a-b*x)^2+1/4*x^(1/2)/a/b/(a-b*x)+_ + 1/4*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(3/2)/b^(3/2) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (b x - 2a b x + a )atanh(--------) + (- b x - a)\|a \|b \|x +--R +-+ +--R \|a +--R (48) ------------------------------------------------------------- +--R 3 2 2 2 3 +-+ +-+ +--R (4a b x - 8a b x + 4a b)\|a \|b +--R Type: Expression(Integer) +--E 67 + +--S 68 of 518 +a0013:= integrate(t0013,x) +--R +--R +--R (49) +--R [ +--R +-+ +---+ +--R 2 2 2 2a b\|x + (b x + a)\|a b +--R (b x - 2a b x + a )log(--------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (- 2b x - 2a)\|a b \|x +--R / +--R 3 2 2 2 3 +---+ +--R (8a b x - 16a b x + 8a b)\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (b x - 2a b x + a )atan(------------) + (- b x - a)\|- a b \|x +--R a +--R ----------------------------------------------------------------] +--R 3 2 2 2 3 +-----+ +--R (4a b x - 8a b x + 4a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 68 + +--S 69 of 518 +m0013a:= a0013.1-r0013 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(--------------------------) - 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (50) ---------------------------------------------------------------- +--R +-+ +-+ +---+ +--R 8a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 69 + +--S 70 of 518 +d0013a:= D(m0013a,x) +--R +--R +--R (51) 0 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 518 +m0013b:= a0013.2-r0013 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R - \|- a b atanh(--------) + \|a \|b atan(------------) +--R +-+ a +--R \|a +--R (52) ------------------------------------------------------ +--R +-----+ +-+ +-+ +--R 4a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 71 + +--S 72 of 518 +d0013b:= D(m0013b,x) +--R +--R +--R (53) 0 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 518 +t0014:= x^(3/2)/(-a+b*x)^2 +--R +--R +--R +-+ +--R x\|x +--R (54) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 73 + +--S 74 of 518 +r0014:= 3*x^(1/2)/b^2+x^(3/2)/b/(a-b*x)-_ + 3*a^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R (- 3b x + 3a)\|a atanh(--------) + (2b x - 3a)\|b \|x +--R +-+ +--R \|a +--R (55) ------------------------------------------------------ +--R 3 2 +-+ +--R (b x - a b )\|b +--R Type: Expression(Integer) +--E 74 + +--S 75 of 518 +a0014:= integrate(t0014,x) +--R +--R +--R (56) +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R |a \|b +-+ +--R (3b x - 3a) |- log(----------------------) + (4b x - 6a)\|x +--R \|b b x - a +--R [------------------------------------------------------------, +--R 3 2 +--R 2b x - 2a b +--R +---+ +-+ +--R | a \|x +-+ +--R (- 3b x + 3a) |- - atan(------) + (2b x - 3a)\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------] +--R 3 2 +--R b x - a b +--R Type: Union(List(Expression(Integer)),...) +--E 75 + +--S 76 of 518 +m0014a:= a0014.1-r0014 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 3 |- \|b log(---------------------- + 6\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (57) ----------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 76 + +--S 77 of 518 +d0014a:= D(m0014a,x) +--R +--R +--R (58) 0 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 518 +m0014b:= a0014.2-r0014 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 3\|a atanh(--------) - 3 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (59) ---------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 78 + +--S 79 of 518 +d0014b:= D(m0014b,x) +--R +--R +--R (60) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 518 +t0015:= x^(3/2)/(-a+b*x)^3 +--R +--R +--R +-+ +--R x\|x +--R (61) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 80 + +--S 81 of 518 +r0015:= -1/2*x^(3/2)/b/(a-b*x)^2+_ + 3/4*x^(1/2)/b^2/(a-b*x)-_ + 3/4*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(1/2)/b^(5/2) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (- 3b x + 6a b x - 3a )atanh(--------) + (- 5b x + 3a)\|a \|b \|x +--R +-+ +--R \|a +--R (62) ------------------------------------------------------------------- +--R 4 2 3 2 2 +-+ +-+ +--R (4b x - 8a b x + 4a b )\|a \|b +--R Type: Expression(Integer) +--E 81 + +--S 82 of 518 +a0015:= integrate(t0015,x) +--R +--R +--R (63) +--R [ +--R +-+ +---+ +--R 2 2 2 - 2a b\|x + (b x + a)\|a b +--R (3b x - 6a b x + 3a )log(----------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (- 10b x + 6a)\|a b \|x +--R / +--R 4 2 3 2 2 +---+ +--R (8b x - 16a b x + 8a b )\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (- 3b x + 6a b x - 3a )atan(------------) + (- 5b x + 3a)\|- a b \|x +--R a +--R ----------------------------------------------------------------------] +--R 4 2 3 2 2 +-----+ +--R (4b x - 8a b x + 4a b )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 82 + +--S 83 of 518 +m0015a:= a0015.1-r0015 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R 3\|a \|b log(----------------------------) + 6\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (64) ------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8b \|a \|b \|a b +--R Type: Expression(Integer) +--E 83 + +--S 84 of 518 +d0015a:= D(m0015a,x) +--R +--R +--R (65) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 518 +m0015b:= a0015.2-r0015 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R 3\|- a b atanh(--------) - 3\|a \|b atan(------------) +--R +-+ a +--R \|a +--R (66) ------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 4b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 85 + +--S 86 of 518 +d0015b:= D(m0015b,x) +--R +--R +--R (67) 0 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 518 +t0016:= x^(5/2)/(-a+b*x)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (68) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 518 +r0016:= 5*a*x^(1/2)/b^3+5/3*x^(3/2)/b^2+x^(5/2)/b/(a-b*x)-_ + 5*a^(3/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/b^(7/2) +--R +--R +--R (69) +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R (- 15a b x + 15a )\|a atanh(--------) + (2b x + 10a b x - 15a )\|b \|x +--R +-+ +--R \|a +--R ------------------------------------------------------------------------ +--R 4 3 +-+ +--R (3b x - 3a b )\|b +--R Type: Expression(Integer) +--E 88 + +--S 89 of 518 +a0016:= integrate(t0016,x) +--R +--R +--R (70) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 |a \|b +--R (15a b x - 15a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 2 2 2 +-+ +--R (4b x + 20a b x - 30a )\|x +--R / +--R 4 3 +--R 6b x - 6a b +--R , +--R +---+ +-+ +--R 2 | a \|x 2 2 2 +-+ +--R (- 15a b x + 15a ) |- - atan(------) + (2b x + 10a b x - 15a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------------------------] +--R 4 3 +--R 3b x - 3a b +--R Type: Union(List(Expression(Integer)),...) +--E 89 + +--S 90 of 518 +m0016a:= a0016.1-r0016 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 5a |- \|b log(----------------------) + 10a\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (71) -------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 90 + +--S 91 of 518 +d0016a:= D(m0016a,x) +--R +--R +--R (72) 0 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 518 +m0016b:= a0016.2-r0016 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 5a\|a atanh(--------) - 5a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (73) ------------------------------------------------ +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 92 + +--S 93 of 518 +d0016b:= D(m0016b,x) +--R +--R +--R (74) 0 +--R Type: Expression(Integer) +--E 93 + +--S 94 of 518 +t0017:= x^(5/2)/(-a+b*x)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (75) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 518 +r0017:= 15/4*x^(1/2)/b^3-1/2*x^(5/2)/b/(a-b*x)^2+_ + 5/4*x^(3/2)/b^2/(a-b*x)-_ + 15/4*a^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/b^(7/2) +--R +--R +--R (76) +--R +-+ +-+ +--R 2 2 2 +-+ \|b \|x +--R (- 15b x + 30a b x - 15a )\|a atanh(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +-+ +--R (8b x - 25a b x + 15a )\|b \|x +--R / +--R 5 2 4 2 3 +-+ +--R (4b x - 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 95 + +--S 96 of 518 +a0017:= integrate(t0017,x) +--R +--R +--R (77) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 2 2 |a \|b +--R (15b x - 30a b x + 15a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 2 2 2 +-+ +--R (16b x - 50a b x + 30a )\|x +--R / +--R 5 2 4 2 3 +--R 8b x - 16a b x + 8a b +--R , +--R +---+ +-+ +--R 2 2 2 | a \|x 2 2 2 +-+ +--R (- 15b x + 30a b x - 15a ) |- - atan(------) + (8b x - 25a b x + 15a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R ---------------------------------------------------------------------------- +--R 5 2 4 2 3 +--R 4b x - 8a b x + 4a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 96 + +--S 97 of 518 +m0017a:= a0017.1-r0017 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 15 |- \|b log(---------------------- + 30\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (78) ------------------------------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 97 + +--S 98 of 518 +d0017a:= D(m0017a,x) +--R +--R +--R (79) 0 +--R Type: Expression(Integer) +--E 98 + +--S 99 of 518 +m0017b:= a0017.2-r0017 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 15\|a atanh(--------) - 15 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (80) ------------------------------------------------ +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 99 + +--S 100 of 518 +d0017b:= D(m0017b,x) +--R +--R +--R (81) 0 +--R Type: Expression(Integer) +--E 100 + +--S 101 of 518 +t0018:= 1/x^(3/2)/(-a+b*x)^2 +--R +--R +--R 1 +--R (82) -------------------------- +--R 2 3 2 2 +-+ +--R (b x - 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 518 +r0018:= -2/a/x^(1/2)/(a-b*x)+3*b*x^(1/2)/a^2/(a-b*x)+_ + 3*b^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R (3b x - 3a)\|b \|x atanh(--------) + (- 3b x + 2a)\|a +--R +-+ +--R \|a +--R (83) ------------------------------------------------------ +--R 2 3 +-+ +-+ +--R (a b x - a )\|a \|x +--R Type: Expression(Integer) +--E 102 + +--S 103 of 518 +a0018:= integrate(t0018,x) +--R +--R +--R (84) +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +--R |b +-+ \|a +--R (3b x - 3a) |- \|x log(--------------------) - 6b x + 4a +--R \|a b x - a +--R [--------------------------------------------------------, +--R 2 3 +-+ +--R (2a b x - 2a )\|x +--R +---+ +-+ +--R | b +-+ b\|x +--R (3b x - 3a) |- - \|x atan(-------) - 3b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ----------------------------------------------] +--R 2 3 +-+ +--R (a b x - a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 103 + +--S 104 of 518 +m0018a:= a0018.1-r0018 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 3\|a |- log(--------------------) - 6\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (85) --------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 104 + +--S 105 of 518 +d0018a:= D(m0018a,x) +--R +--R +--R (86) 0 +--R Type: Expression(Integer) +--E 105 + +--S 106 of 518 +m0018b:= a0018.2-r0018 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R - 3\|b atanh(--------) + 3 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (87) ------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 106 + +--S 107 of 518 +d0018b:= D(m0018b,x) +--R +--R +--R (88) 0 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 518 +t0019:= 1/x^(3/2)/(-a+b*x)^3 +--R +--R +--R 1 +--R (89) ------------------------------------ +--R 3 4 2 3 2 2 3 +-+ +--R (b x - 3a b x + 3a b x - a x)\|x +--R Type: Expression(Integer) +--E 108 + +--S 109 of 518 +r0019:= 2/a/x^(1/2)/(a-b*x)^2-5/2*b*x^(1/2)/a^2/(a-b*x)^2-_ + 15/4*b*x^(1/2)/a^3/(a-b*x)-_ + 15/4*b^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (90) +--R +-+ +-+ +--R 2 2 2 +-+ +-+ \|b \|x +--R (- 15b x + 30a b x - 15a )\|b \|x atanh(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R (15b x - 25a b x + 8a )\|a +--R / +--R 3 2 2 4 5 +-+ +-+ +--R (4a b x - 8a b x + 4a )\|a \|x +--R Type: Expression(Integer) +--E 109 + +--S 110 of 518 +a0019:= integrate(t0019,x) +--R +--R +--R (91) +--R [ +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 2 2 2 |b +-+ \|a 2 2 +--R (15b x - 30a b x + 15a ) |- \|x log(----------------------) + 30b x +--R \|a b x - a +--R + +--R 2 +--R - 50a b x + 16a +--R / +--R 3 2 2 4 5 +-+ +--R (8a b x - 16a b x + 8a )\|x +--R , +--R +---+ +-+ +--R 2 2 2 | b +-+ b\|x 2 2 2 +--R (- 15b x + 30a b x - 15a ) |- - \|x atan(-------) + 15b x - 25a b x + 8a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ---------------------------------------------------------------------------] +--R 3 2 2 4 5 +-+ +--R (4a b x - 8a b x + 4a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 110 + +--S 111 of 518 +m0019a:= a0019.1-r0019 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 15\|a |- log(----------------------) + 30\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (92) ------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 111 + +--S 112 of 518 +d0019a:= D(m0019a,x) +--R +--R +--R (93) 0 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 518 +m0019b:= a0019.2-r0019 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 15\|b atanh(--------) - 15 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (94) ------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 113 + +--S 114 of 518 +d0019b:= D(m0019b,x) +--R +--R +--R (95) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 518 +t0020:= 1/x^(5/2)/(-a+b*x)^2 +--R +--R +--R 1 +--R (96) --------------------------- +--R 2 4 3 2 2 +-+ +--R (b x - 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 115 + +--S 116 of 518 +r0020:= -5/3/a^2/x^(3/2)-5*b/a^3/x^(1/2)+1/a/x^(3/2)/(a-b*x)+_ + 5*b^(3/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (97) +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R (15b x - 15a b x)\|b \|x atanh(--------) + (- 15b x + 10a b x + 2a )\|a +--R +-+ +--R \|a +--R -------------------------------------------------------------------------- +--R 3 2 4 +-+ +-+ +--R (3a b x - 3a x)\|a \|x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 518 +a0020:= integrate(t0020,x) +--R +--R +--R (98) +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +--R 2 2 |b +-+ \|a 2 2 2 +--R (15b x - 15a b x) |- \|x log(--------------------) - 30b x + 20a b x + 4a +--R \|a b x - a +--R [---------------------------------------------------------------------------- +--R 3 2 4 +-+ +--R (6a b x - 6a x)\|x +--R , +--R +---+ +-+ +--R 2 2 | b +-+ b\|x 2 2 2 +--R (15b x - 15a b x) |- - \|x atan(-------) - 15b x + 10a b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ------------------------------------------------------------------] +--R 3 2 4 +-+ +--R (3a b x - 3a x)\|x +--R Type: Union(List(Expression(Integer)),...) +--E 117 + +--S 118 of 518 +m0020a:= a0020.1-r0020 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 5b\|a |- log(--------------------) - 10b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (99) ------------------------------------------------------------ +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 118 + +--S 119 of 518 +d0020a:= D(m0020a,x) +--R +--R +--R (100) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 518 +m0020b:= a0020.2-r0020 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R - 5b\|b atanh(--------) + 5b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (101) --------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 120 + +--S 121 of 518 +d0020b:= D(m0020b,x) +--R +--R +--R (102) 0 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 518 +t0021:= 1/x^(5/2)/(-a+b*x)^3 +--R +--R +--R 1 +--R (103) ------------------------------------- +--R 3 5 2 4 2 3 3 2 +-+ +--R (b x - 3a b x + 3a b x - a x )\|x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 518 +r0021:= 2/3/a/x^(3/2)/(a-b*x)^2+14/3*b/a^2/x^(1/2)/(a-b*x)^2-_ + 35/6*b^2*x^(1/2)/a^3/(a-b*x)^2-35/4*b^2*x^(1/2)/a^4/(a-b*x)-_ + 35/4*b^(3/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(9/2) +--R +--R +--R (104) +--R +-+ +-+ +--R 3 3 2 2 2 +-+ +-+ \|b \|x +--R (- 105b x + 210a b x - 105a b x)\|b \|x atanh(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x - 175a b x + 56a b x + 8a )\|a +--R / +--R 4 2 3 5 2 6 +-+ +-+ +--R (12a b x - 24a b x + 12a x)\|a \|x +--R Type: Expression(Integer) +--E 123 + +--S 124 of 518 +a0021:= integrate(t0021,x) +--R +--R +--R (105) +--R [ +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 3 3 2 2 2 |b +-+ \|a +--R (105b x - 210a b x + 105a b x) |- \|x log(----------------------) +--R \|a b x - a +--R + +--R 3 3 2 2 2 3 +--R 210b x - 350a b x + 112a b x + 16a +--R / +--R 4 2 3 5 2 6 +-+ +--R (24a b x - 48a b x + 24a x)\|x +--R , +--R +--R +---+ +-+ +--R 3 3 2 2 2 | b +-+ b\|x 3 3 +--R (- 105b x + 210a b x - 105a b x) |- - \|x atan(-------) + 105b x +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R + +--R 2 2 2 3 +--R - 175a b x + 56a b x + 8a +--R / +--R 4 2 3 5 2 6 +-+ +--R (12a b x - 24a b x + 12a x)\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 124 + +--S 125 of 518 +m0021a:= a0021.1-r0021 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 35b\|a |- log(----------------------) + 70b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (106) --------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 125 + +--S 126 of 518 +d0021a:= D(m0021a,x) +--R +--R +--R (107) 0 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 518 +m0021b:= a0021.2-r0021 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 35b\|b atanh(--------) - 35b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (108) --------------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 127 + +--S 128 of 518 +d0021b:= D(m0021b,x) +--R +--R +--R (109) 0 +--R Type: Expression(Integer) +--E 128 + +--S 129 of 518 +t0022:= x^(1/2)*(2+b*x)^(1/2) +--R +--R +--R +-+ +-------+ +--R (110) \|x \|b x + 2 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 518 +r0022:= 1/2*x^(1/2)*(2+b*x)^(1/2)/b+1/2*x^(3/2)*(2+b*x)^(1/2)-_ + asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R - 2asinh(------------) + (b x + 1)\|b \|x \|b x + 2 +--R 2 +--R (111) ---------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 130 + +--S 131 of 518 +--a0022:= integrate(t0022,x) +--E 131 + +--S 132 of 518 +--m0022:= a0022-r0022 +--E 132 + +--S 133 of 518 +--d0022:= D(m0022,x) +--E 133 + +--S 134 of 518 +t0023:= x^(1/2)/(2+b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (112) ---------- +--R +-------+ +--R \|b x + 2 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 518 +r0023:= x^(1/2)*(2+b*x)^(1/2)/b-2*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R - 2asinh(------------) + \|b \|x \|b x + 2 +--R 2 +--R (113) ------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 135 + +--S 136 of 518 +--a0023:= integrate(t0023,x) +--E 136 + +--S 137 of 518 +--m0023:= a0023-r0023 +--E 137 + +--S 138 of 518 +--d0023:= D(m0023,x) +--E 138 + +--S 139 of 518 +t0024:= x^(3/2)/(2+b*x)^(1/2) +--R +--R +--R +-+ +--R x\|x +--R (114) ---------- +--R +-------+ +--R \|b x + 2 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 518 +r0024:= -3/2*x^(1/2)*(2+b*x)^(1/2)/b^2+1/2*x^(3/2)*(2+b*x)^(1/2)/b+_ + 3*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R 6asinh(------------) + (b x - 3)\|b \|x \|b x + 2 +--R 2 +--R (115) -------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 140 + +--S 141 of 518 +--a0024:= integrate(t0024,x) +--E 141 + +--S 142 of 518 +--m0024:= a0024-r0024 +--E 142 + +--S 143 of 518 +--d0024:= D(m0024,x) +--E 143 + +--S 144 of 518 +t0025:= x^(3/2)/(2+b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (116) ------------------- +--R +-------+ +--R (b x + 2)\|b x + 2 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 518 +r0025:= -2*x^(3/2)/b/(2+b*x)^(1/2)+3*x^(1/2)*(2+b*x)^(1/2)/b^2-_ + 6*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +-+ +--R +-------+ \|2 \|b \|x +-+ +-+ +--R - 6\|b x + 2 asinh(------------) + (b x + 6)\|b \|x +--R 2 +--R (117) ---------------------------------------------------- +--R 2 +-+ +-------+ +--R b \|b \|b x + 2 +--R Type: Expression(Integer) +--E 145 + +--S 146 of 518 +--a0025:= integrate(t0025,x) +--E 146 + +--S 147 of 518 +--m0025:= a0025-r0025 +--E 147 + +--S 148 of 518 +--d0025:= D(m0025,x) +--E 148 + +--S 149 of 518 +t0026:= x^(5/2)/(2+b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (118) ------------------- +--R +-------+ +--R (b x + 2)\|b x + 2 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 518 +r0026:= 1/2/b^(7/2)*(x^(5/2)*b^(5/2)-30*x^(1/2)*b^(1/2)-5*x^(3/2)*b^(3/2)+_ + 30*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))*(2+b*x)^(1/2))/(2+b*x)^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R +-------+ \|2 \|b \|x 2 2 +-+ +-+ +--R 30\|b x + 2 asinh(------------) + (b x - 5b x - 30)\|b \|x +--R 2 +--R (119) ------------------------------------------------------------ +--R 3 +-+ +-------+ +--R 2b \|b \|b x + 2 +--R Type: Expression(Integer) +--E 150 + +--S 151 of 518 +--a0026:= integrate(t0026,x) +--E 151 + +--S 152 of 518 +--m0026:= a0026-r0026 +--E 152 + +--S 153 of 518 +--d0026:= D(m0026,x) +--E 153 + +--S 154 of 518 +t0027:= x^(5/2)/(2+b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (120) --------------------------- +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 518 +r0027:= -2/3*x^(5/2)/b/(2+b*x)^(3/2)-10/3*x^(3/2)/b^2/(2+b*x)^(1/2)+_ + 5*x^(1/2)*(2+b*x)^(1/2)/b^3-_ + 10*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(7/2) +--R +--R +--R (121) +--R +-+ +-+ +-+ +--R +-------+ \|2 \|b \|x 2 2 +-+ +-+ +--R (- 30b x - 60)\|b x + 2 asinh(------------) + (3b x + 40b x + 60)\|b \|x +--R 2 +--R -------------------------------------------------------------------------- +--R 4 3 +-+ +-------+ +--R (3b x + 6b )\|b \|b x + 2 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 518 +--a0027:= integrate(t0027,x) +--E 156 + +--S 157 of 518 +--m0027:= a0027-r0027 +--E 157 + +--S 158 of 518 +--d0027:= D(m0027,x) +--E 158 + +--S 159 of 518 +t0028:= (2+b*x)^(1/2)/x^(1/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (122) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 159 + +--S 160 of 518 +r0028:= x^(1/2)*(2+b*x)^(1/2)+2*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R 2asinh(------------) + \|b \|x \|b x + 2 +--R 2 +--R (123) ----------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 160 + +--S 161 of 518 +--a0028:= integrate(t0028,x) +--E 161 + +--S 162 of 518 +--m0028:= a0028-r0028 +--E 162 + +--S 163 of 518 +--d0028:= D(m0028,x) +--E 163 + +--S 164 of 518 +t0029:= (2+b*x)^(3/2)/x^(1/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (124) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 164 + +--S 165 of 518 +r0029:= 3/2*x^(1/2)*(2+b*x)^(1/2)+1/2*x^(1/2)*(2+b*x)^(3/2)+_ + 3*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R 6asinh(------------) + (b x + 5)\|b \|x \|b x + 2 +--R 2 +--R (125) -------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 165 + +--S 166 of 518 +--a0029:= integrate(t0029,x) +--E 166 + +--S 167 of 518 +--m0029:= a0029-r0029 +--E 167 + +--S 168 of 518 +--d0029:= D(m0029,x) +--E 168 + +--S 169 of 518 +t0030:= 1/x^(1/2)/(2+b*x)^(1/2) +--R +--R +--R 1 +--R (126) -------------- +--R +-+ +-------+ +--R \|x \|b x + 2 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 518 +r0030:= 2*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +--R 2asinh(------------) +--R 2 +--R (127) -------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 170 + +--S 171 of 518 +--a0030:= integrate(t0030,x) +--E 171 + +--S 172 of 518 +--m0030:= a0030-r0030 +--E 172 + +--S 173 of 518 +--d0030:= D(m0030,x) +--E 173 + +--S 174 of 518 +t0031:= (2+b*x)^(1/2)/x^(3/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (128) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 174 + +--S 175 of 518 +r0031:= -2*(2+b*x)^(1/2)/x^(1/2)+2*b^(1/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +-------+ +--R 2\|b \|x asinh(------------) - 2\|b x + 2 +--R 2 +--R (129) ------------------------------------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 175 + +--S 176 of 518 +--a0031:= integrate(t0031,x) +--E 176 + +--S 177 of 518 +--m0031:= a0031-r0031 +--E 177 + +--S 178 of 518 +--d0031:= D(m0031,x) +--E 178 + +--S 179 of 518 +t0032:= (2+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (130) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 179 + +--S 180 of 518 +r0032:= 3*b*x^(1/2)*(2+b*x)^(1/2)-2*(2+b*x)^(3/2)/x^(1/2)+_ + 6*b^(1/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +-------+ +--R 6\|b \|x asinh(------------) + (b x - 4)\|b x + 2 +--R 2 +--R (131) -------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 180 + +--S 181 of 518 +--a0032:= integrate(t0032,x) +--E 181 + +--S 182 of 518 +--m0032:= a0032-r0032 +--E 182 + +--S 183 of 518 +--d0032:= D(m0032,x) +--E 183 + +--S 184 of 518 +t0033:= (2+b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R (132) --------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 184 + +--S 185 of 518 +r0033:= 15/2*b*x^(1/2)*(2+b*x)^(1/2)+5/2*b*x^(1/2)*(2+b*x)^(3/2)-_ + 2*(2+b*x)^(5/2)/x^(1/2)+15*b^(1/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +-------+ +--R 30\|b \|x asinh(------------) + (b x + 9b x - 16)\|b x + 2 +--R 2 +--R (133) ------------------------------------------------------------ +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 185 + +--S 186 of 518 +--a0033:= integrate(t0033,x) +--E 186 + +--S 187 of 518 +--m0033:= a0033-r0033 +--E 187 + +--S 188 of 518 +--d0033:= D(m0033,x) +--E 188 + +--S 189 of 518 +t0034:= (2+b*x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (134) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 189 + +--S 190 of 518 +r0034:= -2*b*(2+b*x)^(1/2)/x^(1/2)-2/3*(2+b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +-------+ +--R 6b x\|b \|x asinh(------------) + (- 8b x - 4)\|b x + 2 +--R 2 +--R (135) -------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 190 + +--S 191 of 518 +--a0034:= integrate(t0034,x) +--E 191 + +--S 192 of 518 +--m0034:= a0034-r0034 +--E 192 + +--S 193 of 518 +--d0034:= D(m0034,x) +--E 193 + +--S 194 of 518 +t0035:= (2+b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R (136) --------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 194 + +--S 195 of 518 +r0035:= 1/3*(3*b^2*x^2*(2+b*x)^(1/2)-28*b*x*(2+b*x)^(1/2)-8*(2+b*x)^(1/2)+_ + 30*b^(3/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))*x^(3/2))/x^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +-------+ +--R 30b x\|b \|x asinh(------------) + (3b x - 28b x - 8)\|b x + 2 +--R 2 +--R (137) ---------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 195 + +--S 196 of 518 +--a0035:= integrate(t0035,x) +--E 196 + +--S 197 of 518 +--m0035:= a0035-r0035 +--E 197 + +--S 198 of 518 +--d0035:= D(m0035,x) +--E 198 + +--S 199 of 518 +t0036:= x^(1/2)*(a+b*x)^(1/2) +--R +--R +--R +-+ +-------+ +--R (138) \|x \|b x + a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 518 +r0036:= 1/4*a*x^(1/2)*(a+b*x)^(1/2)/b+1/2*x^(3/2)*(a+b*x)^(1/2)-_ + 1/4*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R - a atanh(----------) + (2b x + a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (139) ---------------------------------------------------- +--R +-+ +--R 4b\|b +--R Type: Expression(Integer) +--E 200 + +--S 201 of 518 +--a0036:= integrate(t0036,x) +--E 201 + +--S 202 of 518 +--m0036:= a0036-r0036 +--E 202 + +--S 203 of 518 +--d0036:= D(m0036,x) +--E 203 + +--S 204 of 518 +t0037:= x^(1/2)*(a+b*x)^(3/2) +--R +--R +--R +-+ +-------+ +--R (140) (b x + a)\|x \|b x + a +--R Type: Expression(Integer) +--E 204 + +--S 205 of 518 +r0037:= -1/8*a^2*x^(1/2)*(a+b*x)^(1/2)/b-1/12*a*x^(1/2)*(a+b*x)^(3/2)/b+_ + 1/3*x^(1/2)*(a+b*x)^(5/2)/b-_ + 1/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R - 3a atanh(----------) + (8b x + 14a b x + 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (141) ------------------------------------------------------------------ +--R +-+ +--R 24b\|b +--R Type: Expression(Integer) +--E 205 + +--S 206 of 518 +--a0037:= integrate(t0037,x) +--E 206 + +--S 207 of 518 +--m0037:= a0037-r0037 +--E 207 + +--S 208 of 518 +--d0037:= D(m0037,x) +--E 208 + +--S 209 of 518 +t0038:= x^(1/2)/(a+b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (142) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 209 + +--S 210 of 518 +r0038:= x^(1/2)*(a+b*x)^(1/2)/b-a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R - a atanh(----------) + \|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (143) ------------------------------------------ +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 210 + +--S 211 of 518 +--a0038:= integrate(t0038,x) +--E 211 + +--S 212 of 518 +--m0038:= a0038-r0038 +--E 212 + +--S 213 of 518 +--d0038:= D(m0038,x) +--E 213 + +--S 214 of 518 +t0039:= x^(1/2)/(a+b*x)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (144) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 518 +r0039:= -2*x^(1/2)/b/(a+b*x)^(1/2)+_ + 2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R 2\|b x + a atanh(----------) - 2\|b \|x +--R +-------+ +--R \|b x + a +--R (145) ---------------------------------------- +--R +-+ +-------+ +--R b\|b \|b x + a +--R Type: Expression(Integer) +--E 215 + +--S 216 of 518 +--a0039:= integrate(t0039,x) +--E 216 + +--S 217 of 518 +--m0039:= a0039-r0039 +--E 217 + +--S 218 of 518 +--d0039:= D(m0039,x) +--E 218 + +--S 219 of 518 +t0040:= x^(3/2)*(a+b*x)^(1/2) +--R +--R +--R +-+ +-------+ +--R (146) x\|x \|b x + a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 518 +r0040:= -1/8*a^2*x^(1/2)*(a+b*x)^(1/2)/b^2+1/12*a*x^(3/2)*(a+b*x)^(1/2)/b+_ + 1/3*x^(5/2)*(a+b*x)^(1/2)+_ + 1/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R 3a atanh(----------) + (8b x + 2a b x - 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (147) --------------------------------------------------------------- +--R 2 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 220 + +--S 221 of 518 +--a0040:= integrate(t0040,x) +--E 221 + +--S 222 of 518 +--m0040:= a0040-r0040 +--E 222 + +--S 223 of 518 +--d0040:= D(m0040,x) +--E 223 + +--S 224 of 518 +t0041:= x^(3/2)/(a+b*x)^(1/2) +--R +--R +--R +-+ +--R x\|x +--R (148) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 518 +r0041:= -3/4*a*x^(1/2)*(a+b*x)^(1/2)/b^2+1/2*x^(3/2)*(a+b*x)^(1/2)/b+_ + 3/4*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R 3a atanh(----------) + (2b x - 3a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (149) ---------------------------------------------------- +--R 2 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 225 + +--S 226 of 518 +--a0041:= integrate(t0041,x) +--E 226 + +--S 227 of 518 +--m0041:= a0041-r0041 +--E 227 + +--S 228 of 518 +--d0041:= D(m0041,x) +--E 228 + +--S 229 of 518 +t0042:= x^(3/2)/(a+b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (150) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 518 +r0042:= -2*x^(3/2)/b/(a+b*x)^(1/2)+3*x^(1/2)*(a+b*x)^(1/2)/b^2-_ + 3*a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R - 3a\|b x + a atanh(----------) + (b x + 3a)\|b \|x +--R +-------+ +--R \|b x + a +--R (151) ---------------------------------------------------- +--R 2 +-+ +-------+ +--R b \|b \|b x + a +--R Type: Expression(Integer) +--E 230 + +--S 231 of 518 +--a0042:= integrate(t0042,x) +--E 231 + +--S 232 of 518 +--m0042:= a0042-r0042 +--E 232 + +--S 233 of 518 +--d0042:= D(m0042,x) +--E 233 + +--S 234 of 518 +t0043:= x^(3/2)/(a+b*x)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (152) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 234 + +--S 235 of 518 +r0043:= -2/3*x^(3/2)/b/(a+b*x)^(3/2)-2*x^(1/2)/b^2/(a+b*x)^(1/2)+_ + 2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R (6b x + 6a)\|b x + a atanh(----------) + (- 8b x - 6a)\|b \|x +--R +-------+ +--R \|b x + a +--R (153) -------------------------------------------------------------- +--R 3 2 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 518 +--a0043:= integrate(t0043,x) +--E 236 + +--S 237 of 518 +--m0043:= a0043-r0043 +--E 237 + +--S 238 of 518 +--d0043:= D(m0043,x) +--E 238 + +--S 239 of 518 +t0044:= x^(5/2)/(a+b*x)^(1/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (154) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 239 + +--S 240 of 518 +r0044:= 5/8*a^2*x^(1/2)*(a+b*x)^(1/2)/b^3-5/12*a*x^(3/2)*(a+b*x)^(1/2)/b^2+_ + 1/3*x^(5/2)*(a+b*x)^(1/2)/b-_ + 5/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(7/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R - 15a atanh(----------) + (8b x - 10a b x + 15a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (155) -------------------------------------------------------------------- +--R 3 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 240 + +--S 241 of 518 +--a0044:= integrate(t0044,x) +--E 241 + +--S 242 of 518 +--m0044:= a0044-r0044 +--E 242 + +--S 243 of 518 +--d0044:= D(m0044,x) +--E 243 + +--S 244 of 518 +t0045:= x^(5/2)/(a+b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (156) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 518 +r0045:= 1/4/b^(7/2)*(2*x^(5/2)*b^(5/2)-15*a^2*x^(1/2)*b^(1/2)-_ + 5*a*x^(3/2)*b^(3/2)+_ + 15*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))*(a+b*x)^(1/2))/_ + (a+b*x)^(1/2) +--R +--R +--R +-+ +-+ +--R 2 +-------+ \|b \|x 2 2 2 +-+ +-+ +--R 15a \|b x + a atanh(----------) + (2b x - 5a b x - 15a )\|b \|x +--R +-------+ +--R \|b x + a +--R (157) ----------------------------------------------------------------- +--R 3 +-+ +-------+ +--R 4b \|b \|b x + a +--R Type: Expression(Integer) +--E 245 + +--S 246 of 518 +--a0045:= integrate(t0045,x) +--E 246 + +--S 247 of 518 +--m0045:= a0045-r0045 +--E 247 + +--S 248 of 518 +--d0045:= D(m0045,x) +--E 248 + +--S 249 of 518 +t0046:= x^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (158) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 249 + +--S 250 of 518 +r0046:= -2/3*x^(5/2)/b/(a+b*x)^(3/2)-10/3*x^(3/2)/b^2/(a+b*x)^(1/2)+_ + 5*x^(1/2)*(a+b*x)^(1/2)/b^3-_ + 5*a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(7/2) +--R +--R +--R (159) +--R +-+ +-+ +--R 2 +-------+ \|b \|x +--R (- 15a b x - 15a )\|b x + a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 2 2 2 +-+ +-+ +--R (3b x + 20a b x + 15a )\|b \|x +--R / +--R 4 3 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 518 +--a0046:= integrate(t0046,x) +--E 251 + +--S 252 of 518 +--m0046:= a0046-r0046 +--E 252 + +--S 253 of 518 +--d0046:= D(m0046,x) +--E 253 + +--S 254 of 518 +t0047:= (a+b*x)^(1/2)/x^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (160) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 254 + +--S 255 of 518 +r0047:= x^(1/2)*(a+b*x)^(1/2)+a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R a atanh(----------) + \|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (161) ---------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 255 + +--S 256 of 518 +--a0047:= integrate(t0047,x) +--E 256 + +--S 257 of 518 +--m0047:= a0047-r0047 +--E 257 + +--S 258 of 518 +--d0047:= D(m0047,x) +--E 258 + +--S 259 of 518 +t0048:= (a+b*x)^(3/2)/x^(1/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (162) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 259 + +--S 260 of 518 +r0048:= 3/4*a*x^(1/2)*(a+b*x)^(1/2)+1/2*x^(1/2)*(a+b*x)^(3/2)+_ + 3/4*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R 3a atanh(----------) + (2b x + 5a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (163) ---------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 260 + +--S 261 of 518 +--a0048:= integrate(t0048,x) +--E 261 + +--S 262 of 518 +--m0048:= a0048-r0048 +--E 262 + +--S 263 of 518 +--d0048:= D(m0048,x) +--E 263 + +--S 264 of 518 +t0049:= (a+b*x)^(5/2)/x^(1/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (164) ------------------------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 518 +r0049:= 5/8*a^2*x^(1/2)*(a+b*x)^(1/2)+5/12*a*x^(1/2)*(a+b*x)^(3/2)+_ + 1/3*x^(1/2)*(a+b*x)^(5/2)+_ + 5/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R 15a atanh(----------) + (8b x + 26a b x + 33a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (165) ------------------------------------------------------------------ +--R +-+ +--R 24\|b +--R Type: Expression(Integer) +--E 265 + +--S 266 of 518 +--a0049:= integrate(t0049,x) +--E 266 + +--S 267 of 518 +--m0049:= a0049-r0049 +--E 267 + +--S 268 of 518 +--d0049:= D(m0049,x) +--E 268 + +--S 269 of 518 +t0050:= 1/x^(1/2)/(a+b*x)^(1/2) +--R +--R +--R 1 +--R (166) -------------- +--R +-+ +-------+ +--R \|x \|b x + a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 518 +r0050:= 2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atanh(----------) +--R +-------+ +--R \|b x + a +--R (167) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 270 + +--S 271 of 518 +--a0050:= integrate(t0050,x) +--E 271 + +--S 272 of 518 +--m0050:= a0050-r0050 +--E 272 + +--S 273 of 518 +--d0050:= D(m0050,x) +--E 273 + +--S 274 of 518 +t0051:= (a+b*x)^(1/2)/x^(3/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (168) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 274 + +--S 275 of 518 +r0051:= -2*(a+b*x)^(1/2)/x^(1/2)+2*b^(1/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 2\|b \|x atanh(----------) - 2\|b x + a +--R +-------+ +--R \|b x + a +--R (169) ---------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 275 + +--S 276 of 518 +--a0051:= integrate(t0051,x) +--E 276 + +--S 277 of 518 +--m0051:= a0051-r0051 +--E 277 + +--S 278 of 518 +--d0051:= D(m0051,x) +--E 278 + +--S 279 of 518 +t0052:= (a+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (170) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 279 + +--S 280 of 518 +r0052:= 3*b*x^(1/2)*(a+b*x)^(1/2)-2*(a+b*x)^(3/2)/x^(1/2)+_ + 3*a*b^(1/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 3a\|b \|x atanh(----------) + (b x - 2a)\|b x + a +--R +-------+ +--R \|b x + a +--R (171) -------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 280 + +--S 281 of 518 +--a0052:= integrate(t0052,x) +--E 281 + +--S 282 of 518 +--m0052:= a0052-r0052 +--E 282 + +--S 283 of 518 +--d0052:= D(m0052,x) +--E 283 + +--S 284 of 518 +t0053:= (a+b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (172) ------------------------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 284 + +--S 285 of 518 +r0053:= 15/4*a*b*x^(1/2)*(a+b*x)^(1/2)+5/2*b*x^(1/2)*(a+b*x)^(3/2)-_ + 2*(a+b*x)^(5/2)/x^(1/2)+_ + 15/4*a^2*b^(1/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R 2 +-+ +-+ \|b \|x 2 2 2 +-------+ +--R 15a \|b \|x atanh(----------) + (2b x + 9a b x - 8a )\|b x + a +--R +-------+ +--R \|b x + a +--R (173) ---------------------------------------------------------------- +--R +-+ +--R 4\|x +--R Type: Expression(Integer) +--E 285 + +--S 286 of 518 +--a0053:= integrate(t0053,x) +--E 286 + +--S 287 of 518 +--m0053:= a0053-r0053 +--E 287 + +--S 288 of 518 +--d0053:= D(m0053,x) +--E 288 + +--S 289 of 518 +t0054:= (a+b*x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (174) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 289 + +--S 290 of 518 +r0054:= -2*b*(a+b*x)^(1/2)/x^(1/2)-2/3*(a+b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 6b x\|b \|x atanh(----------) + (- 8b x - 2a)\|b x + a +--R +-------+ +--R \|b x + a +--R (175) ------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 290 + +--S 291 of 518 +--a0054:= integrate(t0054,x) +--E 291 + +--S 292 of 518 +--m0054:= a0054-r0054 +--E 292 + +--S 293 of 518 +--d0054:= D(m0054,x) +--E 293 + +--S 294 of 518 +t0055:= (a+b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (176) ------------------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 294 + +--S 295 of 518 +r0055:= 5*b^2*x^(1/2)*(a+b*x)^(1/2)-10/3*b*(a+b*x)^(3/2)/x^(1/2)-_ + 2/3*(a+b*x)^(5/2)/x^(3/2)+_ + 5*a*b^(3/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 2 +-------+ +--R 15a b x\|b \|x atanh(----------) + (3b x - 14a b x - 2a )\|b x + a +--R +-------+ +--R \|b x + a +--R (177) -------------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 295 + +--S 296 of 518 +--a0055:= integrate(t0055,x) +--E 296 + +--S 297 of 518 +--m0055:= a0055-r0055 +--E 297 + +--S 298 of 518 +--d0055:= D(m0055,x) +--E 298 + +--S 299 of 518 +t0056:= x^(1/2)*(2-b*x)^(1/2) +--R +--R +--R +---------+ +-+ +--R (178) \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 299 + +--S 300 of 518 +r0056:= -1/2*x^(1/2)*(2-b*x)^(1/2)/b+1/2*x^(3/2)*(2-b*x)^(1/2)+_ + asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 2asin(------------) + (b x - 1)\|- b x + 2 \|b \|x +--R 2 +--R (179) --------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 300 + +--S 301 of 518 +--a0056:= integrate(t0056,x) +--E 301 + +--S 302 of 518 +--m0056:= a0056-r0056 +--E 302 + +--S 303 of 518 +--d0056:= D(m0056,x) +--E 303 + +--S 304 of 518 +t0057:= x^(1/2)/(1-x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (180) ---------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 518 +r0057:= -(1-x)^(1/2)*x^(1/2)-asin((1-x)^(1/2)) +--R +--R +--R +-------+ +-------+ +-+ +--R (181) - asin(\|- x + 1 ) - \|- x + 1 \|x +--R Type: Expression(Integer) +--E 305 + +--S 306 of 518 +--a0057:= integrate(t0057,x) +--E 306 + +--S 307 of 518 +--m0057:= a0057-r0057 +--E 307 + +--S 308 of 518 +--d0057:= D(m0057,x) +--E 308 + +--S 309 of 518 +t0058:= x^(1/2)/(2-b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (182) ------------ +--R +---------+ +--R \|- b x + 2 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 518 +r0058:= -x^(1/2)*(2-b*x)^(1/2)/b+2*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 2asin(------------) - \|- b x + 2 \|b \|x +--R 2 +--R (183) ------------------------------------------ +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 310 + +--S 311 of 518 +--a0058:= integrate(t0058,x) +--E 311 + +--S 312 of 518 +--m0058:= a0058-r0058 +--E 312 + +--S 313 of 518 +--d0058:= D(m0058,x) +--E 313 + +--S 314 of 518 +t0059:= x^(3/2)/(2-b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (184) - --------------------- +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 518 +r0059:= 2*x^(3/2)/b/(2-b*x)^(1/2)+3*x^(1/2)*(2-b*x)^(1/2)/b^2-_ + 6*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +-+ +--R +---------+ \|2 \|b \|x +-+ +-+ +--R - 6\|- b x + 2 asin(------------) + (- b x + 6)\|b \|x +--R 2 +--R (185) ------------------------------------------------------- +--R 2 +---------+ +-+ +--R b \|- b x + 2 \|b +--R Type: Expression(Integer) +--E 315 + +--S 316 of 518 +--a0059:= integrate(t0059,x) +--E 316 + +--S 317 of 518 +--m0059:= a0059-r0059 +--E 317 + +--S 318 of 518 +--d0059:= D(m0059,x) +--E 318 + +--S 319 of 518 +t0060:= x^(5/2)/(2-b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (186) - --------------------- +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 518 +r0060:= -1/2/b^(7/2)*(x^(5/2)*b^(5/2)-30*x^(1/2)*b^(1/2)+5*x^(3/2)*b^(3/2)+_ + 30*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))*(2-b*x)^(1/2))/(2-b*x)^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R +---------+ \|2 \|b \|x 2 2 +-+ +-+ +--R - 30\|- b x + 2 asin(------------) + (- b x - 5b x + 30)\|b \|x +--R 2 +--R (187) ----------------------------------------------------------------- +--R 3 +---------+ +-+ +--R 2b \|- b x + 2 \|b +--R Type: Expression(Integer) +--E 320 + +--S 321 of 518 +--a0060:= integrate(t0060,x) +--E 321 + +--S 322 of 518 +--m0060:= a0060-r0060 +--E 322 + +--S 323 of 518 +--d0060:= D(m0060,x) +--E 323 + +--S 324 of 518 +t0061:= x^(5/2)/(2-b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (188) ----------------------------- +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 518 +r0061:= 2/3*x^(5/2)/b/(2-b*x)^(3/2)-10/3*x^(3/2)/b^2/(2-b*x)^(1/2)-_ + 5*x^(1/2)*(2-b*x)^(1/2)/b^3+_ + 10*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(7/2) +--R +--R +--R (189) +--R +-+ +-+ +-+ +--R +---------+ \|2 \|b \|x 2 2 +-+ +-+ +--R (30b x - 60)\|- b x + 2 asin(------------) + (3b x - 40b x + 60)\|b \|x +--R 2 +--R ------------------------------------------------------------------------- +--R 4 3 +---------+ +-+ +--R (3b x - 6b )\|- b x + 2 \|b +--R Type: Expression(Integer) +--E 325 + +--S 326 of 518 +--a0061:= integrate(t0061,x) +--E 326 + +--S 327 of 518 +--m0061:= a0061-r0061 +--E 327 + +--S 328 of 518 +--d0061:= D(m0061,x) +--E 328 + +--S 329 of 518 +t0062:= (2-b*x)^(1/2)/x^(1/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (190) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 329 + +--S 330 of 518 +r0062:= x^(1/2)*(2-b*x)^(1/2)+2*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 2asin(------------) + \|- b x + 2 \|b \|x +--R 2 +--R (191) ------------------------------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 330 + +--S 331 of 518 +--a0062:= integrate(t0062,x) +--E 331 + +--S 332 of 518 +--m0062:= a0062-r0062 +--E 332 + +--S 333 of 518 +--d0062:= D(m0062,x) +--E 333 + +--S 334 of 518 +t0063:= (2-b*x)^(3/2)/x^(1/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (192) ----------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 334 + +--S 335 of 518 +r0063:= 3/2*x^(1/2)*(2-b*x)^(1/2)+1/2*x^(1/2)*(2-b*x)^(3/2)+_ + 3*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 6asin(------------) + (- b x + 5)\|- b x + 2 \|b \|x +--R 2 +--R (193) ----------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 335 + +--S 336 of 518 +--a0063:= integrate(t0063,x) +--E 336 + +--S 337 of 518 +--m0063:= a0063-r0063 +--E 337 + +--S 338 of 518 +--d0063:= D(m0063,x) +--E 338 + +--S 339 of 518 +t0064:= 1/x^(1/2)/(2-b*x)^(1/2) +--R +--R +--R 1 +--R (194) ---------------- +--R +---------+ +-+ +--R \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 339 + +--S 340 of 518 +r0064:= 2*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +--R 2asin(------------) +--R 2 +--R (195) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 340 + +--S 341 of 518 +--a0064:= integrate(t0064,x) +--E 341 + +--S 342 of 518 +--m0064:= a0064-r0064 +--E 342 + +--S 343 of 518 +--d0064:= D(m0064,x) +--E 343 + +--S 344 of 518 +t0065:= (2-b*x)^(1/2)/x^(3/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (196) ------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 344 + +--S 345 of 518 +r0065:= -2*(2-b*x)^(1/2)/x^(1/2)-2*b^(1/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +---------+ +--R - 2\|b \|x asin(------------) - 2\|- b x + 2 +--R 2 +--R (197) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 345 + +--S 346 of 518 +--a0065:= integrate(t0065,x) +--E 346 + +--S 347 of 518 +--m0065:= a0065-r0065 +--E 347 + +--S 348 of 518 +--d0065:= D(m0065,x) +--E 348 + +--S 349 of 518 +t0066:= (2-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (198) ----------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 349 + +--S 350 of 518 +r0066:= -3*b*x^(1/2)*(2-b*x)^(1/2)-2*(2-b*x)^(3/2)/x^(1/2)-_ + 6*b^(1/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +---------+ +--R - 6\|b \|x asin(------------) + (- b x - 4)\|- b x + 2 +--R 2 +--R (199) ------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 350 + +--S 351 of 518 +--a0066:= integrate(t0066,x) +--E 351 + +--S 352 of 518 +--m0066:= a0066-r0066 +--E 352 + +--S 353 of 518 +--d0066:= D(m0066,x) +--E 353 + +--S 354 of 518 +t0067:= (2-b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R (200) ----------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 354 + +--S 355 of 518 +r0067:= -15/2*b*x^(1/2)*(2-b*x)^(1/2)-5/2*b*x^(1/2)*(2-b*x)^(3/2)-_ + 2*(2-b*x)^(5/2)/x^(1/2)-15*b^(1/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +---------+ +--R - 30\|b \|x asin(------------) + (b x - 9b x - 16)\|- b x + 2 +--R 2 +--R (201) --------------------------------------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 355 + +--S 356 of 518 +--a0067:= integrate(t0067,x) +--E 356 + +--S 357 of 518 +--m0067:= a0067-r0067 +--E 357 + +--S 358 of 518 +--d0067:= D(m0067,x) +--E 358 + +--S 359 of 518 +t0068:= (2-b*x)^(3/2)/x^(5/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (202) ----------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 359 + +--S 360 of 518 +r0068:= 2*b*(2-b*x)^(1/2)/x^(1/2)-2/3*(2-b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +---------+ +--R 6b x\|b \|x asin(------------) + (8b x - 4)\|- b x + 2 +--R 2 +--R (203) ------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 360 + +--S 361 of 518 +--a0068:= integrate(t0068,x) +--E 361 + +--S 362 of 518 +--m0068:= a0068-r0068 +--E 362 + +--S 363 of 518 +--d0068:= D(m0068,x) +--E 363 + +--S 364 of 518 +t0069:= (2-b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R (204) ----------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 364 + +--S 365 of 518 +r0069:= 1/3*(3*b^2*x^2*(2-b*x)^(1/2)+28*b*x*(2-b*x)^(1/2)-8*(2-b*x)^(1/2)+_ + 30*b^(3/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))*x^(3/2))/x^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +---------+ +--R 30b x\|b \|x asin(------------) + (3b x + 28b x - 8)\|- b x + 2 +--R 2 +--R (205) ----------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 365 + +--S 366 of 518 +--a0069:= integrate(t0069,x) +--E 366 + +--S 367 of 518 +--m0069:= a0069-r0069 +--E 367 + +--S 368 of 518 +--d0069:= D(m0069,x) +--E 368 + +--S 369 of 518 +t0070:= x^(1/2)*(a-b*x)^(1/2) +--R +--R +--R +---------+ +-+ +--R (206) \|- b x + a \|x +--R Type: Expression(Integer) +--E 369 + +--S 370 of 518 +r0070:= -1/4*a*x^(1/2)*(a-b*x)^(1/2)/b+1/2*x^(3/2)*(a-b*x)^(1/2)+_ + 1/4*a^2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R a atan(------------) + (2b x - a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (207) ----------------------------------------------------- +--R +-+ +--R 4b\|b +--R Type: Expression(Integer) +--E 370 + +--S 371 of 518 +--a0070:= integrate(t0070,x) +--E 371 + +--S 372 of 518 +--m0070:= a0070-r0070 +--E 372 + +--S 373 of 518 +--d0070:= D(m0070,x) +--E 373 + +--S 374 of 518 +t0071:= x^(1/2)/(a-b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (208) ------------ +--R +---------+ +--R \|- b x + a +--R Type: Expression(Integer) +--E 374 + +--S 375 of 518 +r0071:= -x^(1/2)*(a-b*x)^(1/2)/b+a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R a atan(------------) - \|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (209) ------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 375 + +--S 376 of 518 +--a0071:= integrate(t0071,x) +--E 376 + +--S 377 of 518 +--m0071:= a0071-r0071 +--E 377 + +--S 378 of 518 +--d0071:= D(m0071,x) +--E 378 + +--S 379 of 518 +t0072:= x^(1/2)/(a-b*x)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (210) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression(Integer) +--E 379 + +--S 380 of 518 +r0072:= 2*x^(1/2)/b/(a-b*x)^(1/2)-2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R - 2\|- b x + a atan(------------) + 2\|b \|x +--R +---------+ +--R \|- b x + a +--R (211) --------------------------------------------- +--R +---------+ +-+ +--R b\|- b x + a \|b +--R Type: Expression(Integer) +--E 380 + +--S 381 of 518 +--a0072:= integrate(t0072,x) +--E 381 + +--S 382 of 518 +--m0072:= a0072-r0072 +--E 382 + +--S 383 of 518 +--d0072:= D(m0072,x) +--E 383 + +--S 384 of 518 +t0073:= x^(3/2)/(a-b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (212) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression(Integer) +--E 384 + +--S 385 of 518 +r0073:= 2*x^(3/2)/b/(a-b*x)^(1/2)+3*x^(1/2)*(a-b*x)^(1/2)/b^2-_ + 3*a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R - 3a\|- b x + a atan(------------) + (- b x + 3a)\|b \|x +--R +---------+ +--R \|- b x + a +--R (213) --------------------------------------------------------- +--R 2 +---------+ +-+ +--R b \|- b x + a \|b +--R Type: Expression(Integer) +--E 385 + +--S 386 of 518 +--a0073:= integrate(t0073,x) +--E 386 + +--S 387 of 518 +--m0073:= a0073-r0073 +--E 387 + +--S 388 of 518 +--d0073:= D(m0073,x) +--E 388 + +--S 389 of 518 +t0074:= x^(3/2)/(a-b*x)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (214) -------------------------------- +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R Type: Expression(Integer) +--E 389 + +--S 390 of 518 +r0074:= 2/3*x^(3/2)/b/(a-b*x)^(3/2)-2*x^(1/2)/b^2/(a-b*x)^(1/2)+_ + 2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R (6b x - 6a)\|- b x + a atan(------------) + (- 8b x + 6a)\|b \|x +--R +---------+ +--R \|- b x + a +--R (215) ----------------------------------------------------------------- +--R 3 2 +---------+ +-+ +--R (3b x - 3a b )\|- b x + a \|b +--R Type: Expression(Integer) +--E 390 + +--S 391 of 518 +--a0074:= integrate(t0074,x) +--E 391 + +--S 392 of 518 +--m0074:= a0074-r0074 +--E 392 + +--S 393 of 518 +--d0074:= D(m0074,x) +--E 393 + +--S 394 of 518 +t0075:= x^(5/2)/(a-b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (216) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 518 +r0075:= -1/4/b^(7/2)*(2*x^(5/2)*b^(5/2)-15*a^2*x^(1/2)*b^(1/2)+_ + 5*a*x^(3/2)*b^(3/2)+_ + 15*a^2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))*(a-b*x)^(1/2))/(a-b*x)^(1/2) +--R +--R +--R (217) +--R +-+ +-+ +--R 2 +---------+ \|b \|x 2 2 2 +-+ +-+ +--R - 15a \|- b x + a atan(------------) + (- 2b x - 5a b x + 15a )\|b \|x +--R +---------+ +--R \|- b x + a +--R ------------------------------------------------------------------------ +--R 3 +---------+ +-+ +--R 4b \|- b x + a \|b +--R Type: Expression(Integer) +--E 395 + +--S 396 of 518 +--a0075:= integrate(t0075,x) +--E 396 + +--S 397 of 518 +--m0075:= a0075-r0075 +--E 397 + +--S 398 of 518 +--d0075:= D(m0075,x) +--E 398 + +--S 399 of 518 +t0076:= x^(5/2)/(a-b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (218) -------------------------------- +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R Type: Expression(Integer) +--E 399 + +--S 400 of 518 +r0076:= 2/3*x^(5/2)/b/(a-b*x)^(3/2)-10/3*x^(3/2)/b^2/(a-b*x)^(1/2)-_ + 5*x^(1/2)*(a-b*x)^(1/2)/b^3+_ + 5*a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(7/2) +--R +--R +--R (219) +--R +-+ +-+ +--R 2 +---------+ \|b \|x +--R (15a b x - 15a )\|- b x + a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 2 2 2 +-+ +-+ +--R (3b x - 20a b x + 15a )\|b \|x +--R / +--R 4 3 +---------+ +-+ +--R (3b x - 3a b )\|- b x + a \|b +--R Type: Expression(Integer) +--E 400 + +--S 401 of 518 +--a0076:= integrate(t0076,x) +--E 401 + +--S 402 of 518 +--m0076:= a0076-r0076 +--E 402 + +--S 403 of 518 +--d0076:= D(m0076,x) +--E 403 + +--S 404 of 518 +t0077:= (a-b*x)^(1/2)/x^(1/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (220) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 404 + +--S 405 of 518 +r0077:= x^(1/2)*(a-b*x)^(1/2)+a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R a atan(------------) + \|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (221) ------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 405 + +--S 406 of 518 +--a0077:= integrate(t0077,x) +--E 406 + +--S 407 of 518 +--m0077:= a0077-r0077 +--E 407 + +--S 408 of 518 +--d0077:= D(m0077,x) +--E 408 + +--S 409 of 518 +t0078:= (a-b*x)^(3/2)/x^(1/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (222) ----------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 409 + +--S 410 of 518 +r0078:= 3/4*a*x^(1/2)*(a-b*x)^(1/2)+1/2*x^(1/2)*(a-b*x)^(3/2)+_ + 3/4*a^2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R 3a atan(------------) + (- 2b x + 5a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (223) --------------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 410 + +--S 411 of 518 +--a0078:= integrate(t0078,x) +--E 411 + +--S 412 of 518 +--m0078:= a0078-r0078 +--E 412 + +--S 413 of 518 +--d0078:= D(m0078,x) +--E 413 + +--S 414 of 518 +t0079:= 1/x^(1/2)/(a-b*x)^(1/2) +--R +--R +--R 1 +--R (224) ---------------- +--R +---------+ +-+ +--R \|- b x + a \|x +--R Type: Expression(Integer) +--E 414 + +--S 415 of 518 +r0079:= 2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atan(------------) +--R +---------+ +--R \|- b x + a +--R (225) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 415 + +--S 416 of 518 +--a0079:= integrate(t0079,x) +--E 416 + +--S 417 of 518 +--m0079:= a0079-r0079 +--E 417 + +--S 418 of 518 +--d0079:= D(m0079,x) +--E 418 + +--S 419 of 518 +t0080:= (a-b*x)^(1/2)/x^(3/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (226) ------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 518 +r0080:= -2*(a-b*x)^(1/2)/x^(1/2)-2*b^(1/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 2\|b \|x atan(------------) - 2\|- b x + a +--R +---------+ +--R \|- b x + a +--R (227) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 420 + +--S 421 of 518 +--a0080:= integrate(t0080,x) +--E 421 + +--S 422 of 518 +--m0080:= a0080-r0080 +--E 422 + +--S 423 of 518 +--d0080:= D(m0080,x) +--E 423 + +--S 424 of 518 +t0081:= (a-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (228) ----------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 424 + +--S 425 of 518 +r0081:= -3*b*x^(1/2)*(a-b*x)^(1/2)-2*(a-b*x)^(3/2)/x^(1/2)-_ + 3*a*b^(1/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 3a\|b \|x atan(------------) + (- b x - 2a)\|- b x + a +--R +---------+ +--R \|- b x + a +--R (229) --------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 425 + +--S 426 of 518 +--a0081:= integrate(t0081,x) +--E 426 + +--S 427 of 518 +--m0081:= a0081-r0081 +--E 427 + +--S 428 of 518 +--d0081:= D(m0081,x) +--E 428 + +--S 429 of 518 +t0082:= (a-b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R (230) -------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 429 + +--S 430 of 518 +r0082:= -15/4*a*b*x^(1/2)*(a-b*x)^(1/2)-5/2*b*x^(1/2)*(a-b*x)^(3/2)-_ + 2*(a-b*x)^(5/2)/x^(1/2)-_ + 15/4*a^2*b^(1/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R (231) +--R +-+ +-+ +--R 2 +-+ +-+ \|b \|x 2 2 2 +---------+ +--R - 15a \|b \|x atan(------------) + (2b x - 9a b x - 8a )\|- b x + a +--R +---------+ +--R \|- b x + a +--R --------------------------------------------------------------------- +--R +-+ +--R 4\|x +--R Type: Expression(Integer) +--E 430 + +--S 431 of 518 +--a0082:= integrate(t0082,x) +--E 431 + +--S 432 of 518 +--m0082:= a0082-r0082 +--E 432 + +--S 433 of 518 +--d0082:= D(m0082,x) +--E 433 + +--S 434 of 518 +t0083:= (a-b*x)^(3/2)/x^(5/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (232) ----------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 434 + +--S 435 of 518 +r0083:= 2*b*(a-b*x)^(1/2)/x^(1/2)-2/3*(a-b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R 6b x\|b \|x atan(------------) + (8b x - 2a)\|- b x + a +--R +---------+ +--R \|- b x + a +--R (233) -------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 435 + +--S 436 of 518 +--a0083:= integrate(t0083,x) +--E 436 + +--S 437 of 518 +--m0083:= a0083-r0083 +--E 437 + +--S 438 of 518 +--d0083:= D(m0083,x) +--E 438 + +--S 439 of 518 +t0084:= (a-b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R (234) -------------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 518 +r0084:= 5*b^2*x^(1/2)*(a-b*x)^(1/2)+10/3*b*(a-b*x)^(3/2)/x^(1/2)-_ + 2/3*(a-b*x)^(5/2)/x^(3/2)+_ + 5*a*b^(3/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R (235) +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 2 +---------+ +--R 15a b x\|b \|x atan(------------) + (3b x + 14a b x - 2a )\|- b x + a +--R +---------+ +--R \|- b x + a +--R ----------------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 440 + +--S 441 of 518 +--a0084:= integrate(t0084,x) +--E 441 + +--S 442 of 518 +--m0084:= a0084-r0084 +--E 442 + +--S 443 of 518 +--d0084:= D(m0084,x) +--E 443 + +--S 444 of 518 +t0085:= x^3/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 3 +--R x +--R (236) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 444 + +--S 445 of 518 +r0085:= -2/3*a*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 5/8*(b*c+a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3-_ + 5/12*(b*c+a*d)*x*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 1/3*x^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d+_ + 3/2*a*c*(b*c+a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(5/2)/d^(5/2)-5/8*(b*c+a*d)^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(7/2) +--R +--R +--R (237) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (- 15a d - 9a b c d - 9a b c d - 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (8b d x + (- 10a b d - 10b c d)x + 15a d + 14a b c d + 15b c )\|b +--R * +--R +-+ +-------+ +-------+ +--R \|d \|b x + a \|d x + c +--R / +--R 3 3 +-+ +-+ +--R 24b d \|b \|d +--R Type: Expression(Integer) +--E 445 + +--S 446 of 518 +--a0085:= integrate(t0085,x) +--E 446 + +--S 447 of 518 +--m0085:= a0085-r0085 +--E 447 + +--S 448 of 518 +--d0085:= D(m0085,x) +--E 448 + +--S 449 of 518 +t0086:= x^2/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 2 +--R x +--R (238) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 449 + +--S 450 of 518 +r0086:= -3/4*(b*c+a*d)*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 1/2*x*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d-_ + a*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/_ + d^(3/2)+3/4*(b*c+a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(5/2) +--R +--R +--R (239) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (3a d + 2a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x - 3a d - 3b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 2 +-+ +-+ +--R 4b d \|b \|d +--R Type: Expression(Integer) +--E 450 + +--S 451 of 518 +--a0086:= integrate(t0086,x) +--E 451 + +--S 452 of 518 +--m0086:= a0086-r0086 +--E 452 + +--S 453 of 518 +--d0086:= D(m0086,x) +--E 453 + +--S 454 of 518 +t0087:= x/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R x +--R (240) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 454 + +--S 455 of 518 +r0087:= (a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d-_ + (b*c+a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(3/2)/d^(3/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +-+ +-+ +-------+ +-------+ +--R (- a d - b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c +--R +-+ +-------+ +--R \|b \|d x + c +--R (241) ----------------------------------------------------------------- +--R +-+ +-+ +--R b d\|b \|d +--R Type: Expression(Integer) +--E 455 + +--S 456 of 518 +--a0087:= integrate(t0087,x) +--E 456 + +--S 457 of 518 +--m0087:= a0087-r0087 +--E 457 + +--S 458 of 518 +--d0087:= D(m0087,x) +--E 458 + +--S 459 of 518 +t0088:= 1/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (242) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 459 + +--S 460 of 518 +r0088:= 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (243) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 460 + +--S 461 of 518 +--a0088:= integrate(t0088,x) +--E 461 + +--S 462 of 518 +--m0088:= a0088-r0088 +--E 462 + +--S 463 of 518 +--d0088:= D(m0088,x) +--E 463 + +--S 464 of 518 +t0089:= 1/x/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (244) --------------------- +--R +-------+ +-------+ +--R x\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 464 + +--S 465 of 518 +r0089:= -2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(1/2) +--R +--R +--R +-+ +-------+ +--R \|c \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R (245) - ---------------------- +--R +-+ +-+ +--R \|a \|c +--R Type: Expression(Integer) +--E 465 + +--S 466 of 518 +--a0089:= integrate(t0089,x) +--E 466 + +--S 467 of 518 +--m0089:= a0089-r0089 +--E 467 + +--S 468 of 518 +--d0089:= D(m0089,x) +--E 468 + +--S 469 of 518 +t0090:= 1/x^2/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (246) ---------------------- +--R 2 +-------+ +-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 469 + +--S 470 of 518 +r0090:= -(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c/x+_ + (b*c+a*d)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + a^(3/2)/c^(3/2) +--R +--R +--R +-+ +-------+ +--R \|c \|b x + a +-+ +-+ +-------+ +-------+ +--R (a d + b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c +--R +-+ +-------+ +--R \|a \|d x + c +--R (247) ----------------------------------------------------------------- +--R +-+ +-+ +--R a c x\|a \|c +--R Type: Expression(Integer) +--E 470 + +--S 471 of 518 +--a0090:= integrate(t0090,x) +--E 471 + +--S 472 of 518 +--m0090:= a0090-r0090 +--E 472 + +--S 473 of 518 +--d0090:= D(m0090,x) +--E 473 + +--S 474 of 518 +t0091:= 1/x^3/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (248) ---------------------- +--R 3 +-------+ +-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 474 + +--S 475 of 518 +r0091:= -1/2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c/x^2+_ + 3/4*(b*c+a*d)*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a^2/c^2/x+_ + b*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/_ + c^(3/2)-3/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(5/2)/c^(5/2) +--R +--R +--R (249) +--R +-+ +-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 3a d - 2a b c d - 3b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R ((3a d + 3b c)x - 2a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 2 2 +-+ +-+ +--R 4a c x \|a \|c +--R Type: Expression(Integer) +--E 475 + +--S 476 of 518 +--a0091:= integrate(t0091,x) +--E 476 + +--S 477 of 518 +--m0091:= a0091-r0091 +--E 477 + +--S 478 of 518 +--d0091:= D(m0091,x) +--E 478 + +--S 479 of 518 +t0092:= x^3/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 3 +--R x +--R (250) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 479 + +--S 480 of 518 +r0092:= -2*c^3*(a+b*x)^(1/2)/d^3/(b*c-a*d)/(c+d*x)^(1/2)-_ + 7/4*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^3-_ + 3/4*a*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 1/2*x*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^2+_ + 3*c^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/_ + d^(7/2)+3/4*(b*c+a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(7/2) +--R +--R +--R (251) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 +-------+ \|d \|b x + a +--R (3a d + 3a b c d + 9a b c d - 15b c )\|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 2 2 2 2 3 2 2 2 2 2 +--R (2a b d - 2b c d )x + (- 3a d - 2a b c d + 5b c d)x - 3a c d +--R + +--R 2 2 3 +--R - 4a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 4 3 3 +-+ +-+ +-------+ +--R (4a b d - 4b c d )\|b \|d \|d x + c +--R Type: Expression(Integer) +--E 480 + +--S 481 of 518 +--a0092:= integrate(t0092,x) +--E 481 + +--S 482 of 518 +--m0092:= a0092-r0092 +--E 482 + +--S 483 of 518 +--d0092:= D(m0092,x) +--E 483 + +--S 484 of 518 +t0093:= x^2/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 2 +--R x +--R (252) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 484 + +--S 485 of 518 +r0093:= 2*c^2*(a+b*x)^(1/2)/d^2/(b*c-a*d)/(c+d*x)^(1/2)+_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^2-_ + 3*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/_ + d^(5/2)-a*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(3/2)/d^(3/2) +--R +--R +--R (253) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ \|d \|b x + a +--R (- a d - 2a b c d + 3b c )\|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 +-+ +-+ +-------+ +--R ((a d - b c d)x + a c d - 3b c )\|b \|d \|b x + a +--R / +--R 3 2 2 +-+ +-+ +-------+ +--R (a b d - b c d )\|b \|d \|d x + c +--R Type: Expression(Integer) +--E 485 + +--S 486 of 518 +--a0093:= integrate(t0093,x) +--E 486 + +--S 487 of 518 +--m0093:= a0093-r0093 +--E 487 + +--S 488 of 518 +--d0093:= D(m0093,x) +--E 488 + +--S 489 of 518 +t0094:= x/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R x +--R (254) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 489 + +--S 490 of 518 +r0094:= -2*c*(a+b*x)^(1/2)/d/(b*c-a*d)/(c+d*x)^(1/2)+_ + 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +-+ +-+ +-------+ +--R (2a d - 2b c)\|d x + c atanh(--------------) + 2c\|b \|d \|b x + a +--R +-+ +-------+ +--R \|b \|d x + c +--R (255) ------------------------------------------------------------------- +--R 2 +-+ +-+ +-------+ +--R (a d - b c d)\|b \|d \|d x + c +--R Type: Expression(Integer) +--E 490 + +--S 491 of 518 +--a0094:= integrate(t0094,x) +--E 491 + +--S 492 of 518 +--m0094:= a0094-r0094 +--E 492 + +--S 493 of 518 +--d0094:= D(m0094,x) +--E 493 + +--S 494 of 518 +t0095:= 1/x/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (256) -------------------------------- +--R 2 +-------+ +-------+ +--R (d x + c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 494 + +--S 495 of 518 +r0095:= -2*d*(a+b*x)^(1/2)/c/(b*c-a*d)/(c+d*x)^(1/2)-_ + 2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(3/2) +--R +--R +--R (257) +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +-+ +-+ +-------+ +--R (- 2a d + 2b c)\|d x + c atanh(--------------) + 2d\|a \|c \|b x + a +--R +-+ +-------+ +--R \|a \|d x + c +--R --------------------------------------------------------------------- +--R 2 +-+ +-+ +-------+ +--R (a c d - b c )\|a \|c \|d x + c +--R Type: Expression(Integer) +--E 495 + +--S 496 of 518 +--a0095:= integrate(t0095,x) +--E 496 + +--S 497 of 518 +--m0095:= a0095-r0095 +--E 497 + +--S 498 of 518 +--d0095:= D(m0095,x) +--E 498 + +--S 499 of 518 +t0096:= 1/x^2/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (258) --------------------------------- +--R 3 2 +-------+ +-------+ +--R (d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 499 + +--S 500 of 518 +r0096:= 2*d^2*(a+b*x)^(1/2)/c^2/(b*c-a*d)/(c+d*x)^(1/2)-_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^2/x+_ + b*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/c^(3/2)+_ + 3*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(5/2) +--R +--R +--R (259) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ \|c \|b x + a +--R (3a d - 2a b c d - b c )x\|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 +-+ +-+ +-------+ +--R ((- 3a d + b c d)x - a c d + b c )\|a \|c \|b x + a +--R / +--R 2 2 3 +-+ +-+ +-------+ +--R (a c d - a b c )x\|a \|c \|d x + c +--R Type: Expression(Integer) +--E 500 + +--S 501 of 518 +--a0096:= integrate(t0096,x) +--E 501 + +--S 502 of 518 +--m0096:= a0096-r0096 +--E 502 + +--S 503 of 518 +--d0096:= D(m0096,x) +--E 503 + +--S 504 of 518 +t0097:= 1/x^3/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (260) --------------------------------- +--R 4 3 +-------+ +-------+ +--R (d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 504 + +--S 505 of 518 +r0097:= -2*d^3*(a+b*x)^(1/2)/c^3/(b*c-a*d)/(c+d*x)^(1/2)-_ + 1/2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^2/x^2+_ + 3/4*b*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a^2/c^2/x+_ + 7/4*d*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^3/x-_ + 3*d^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/_ + c^(7/2)-3/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(5/2)/c^(7/2) +--R +--R +--R (261) +--R 3 3 2 2 2 2 3 3 2 +-------+ +--R (- 15a d + 9a b c d + 3a b c d + 3b c )x \|d x + c +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 3 2 2 2 2 2 2 2 2 3 +--R (15a d - 4a b c d - 3b c d)x + (5a c d - 2a b c d - 3b c )x +--R + +--R 2 2 3 +--R - 2a c d + 2a b c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|b x + a +--R / +--R 3 3 2 4 2 +-+ +-+ +-------+ +--R (4a c d - 4a b c )x \|a \|c \|d x + c +--R Type: Expression(Integer) +--E 505 + +--S 506 of 518 +--a0097:= integrate(t0097,x) +--E 506 + +--S 507 of 518 +--m0097:= a0097-r0097 +--E 507 + +--S 508 of 518 +--d0097:= D(m0097,x) +--E 508 + +--S 509 of 518 +t0098:= x^5/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 5 +--R x +--R (262) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 509 + +--S 510 of 518 +r0098:= -2/3*a^5*(a+b*x)^(1/2)/b^5/(b*c-a*d)/(c+d*x)^(3/2)+_ + 20/3*a^3*(a+b*x)^(3/2)/b^5/d/(c+d*x)^(3/2)+_ + 10/3*a^4*(a+b*x)^(3/2)/b^5/(b*c-a*d)/(c+d*x)^(3/2)-_ + 20/3*a^2*(a+b*x)^(5/2)/b^5/d/(c+d*x)^(3/2)+_ + 10/3*a*(a+b*x)^(7/2)/b^5/d/(c+d*x)^(3/2)-_ + 2/3*(a+b*x)^(9/2)/b^5/d/(c+d*x)^(3/2)+_ + 20*a^3*(a+b*x)^(1/2)/b^4/d^2/(c+d*x)^(1/2)-_ + 4/3*a^5*(a+b*x)^(1/2)/b^4/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 100/3*a^2*(a+b*x)^(3/2)/b^4/d^2/(c+d*x)^(1/2)+_ + 70/3*a*(a+b*x)^(5/2)/b^4/d^2/(c+d*x)^(1/2)-_ + 6*(a+b*x)^(7/2)/b^4/d^2/(c+d*x)^(1/2)+_ + 50*a^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3+_ + 175/4*a*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^4+_ + 105/8*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^5-_ + 175/6*a*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b^3/d^3-_ + 35/4*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b^3/d^4+_ + 7*(a+b*x)^(5/2)*(c+d*x)^(1/2)/b^3/d^3-_ + 20*a^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/_ + d^(5/2)-50*a^2*(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(7/2)-_ + 175/4*a*(b*c-a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(9/2)-_ + 105/8*(b*c-a*d)^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(11/2) +--R +--R +--R (263) +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R - 15a d - 15a b c d - 30a b c d - 150a b c d + 525a b c d +--R + +--R 5 5 +--R - 315b c d +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R - 15a c d - 15a b c d - 30a b c d - 150a b c d + 525a b c d +--R + +--R 5 6 +--R - 315b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (8a b d - 16a b c d + 8b c d )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (- 10a b d + 2a b c d + 26a b c d - 18b c d )x +--R + +--R 4 6 2 2 2 4 3 3 3 4 4 2 2 +--R (15a d + 18a b c d - 96a b c d + 63b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (30a c d + 30a b c d + 62a b c d - 574a b c d + 420b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 15a c d + 20a b c d + 38a b c d - 420a b c d + 315b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 3 8 4 7 5 2 6 2 3 7 4 2 6 +--R (24a b d - 48a b c d + 24b c d )x + 24a b c d - 48a b c d +--R + +--R 5 3 5 +--R 24b c d +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R Type: Expression(Integer) +--E 510 + +--S 511 of 518 +--a0098:= integrate(t0098,x) +--E 511 + +--S 512 of 518 +--m0098:= a0098-r0098 +--E 512 + +--S 513 of 518 +--d0098:= D(m0098,x) +--E 513 + +--S 514 of 518 +t0099:= x^4/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 4 +--R x +--R (264) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 514 + +--S 515 of 518 +r0099:= 2/3*a^4*(a+b*x)^(1/2)/b^4/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4*a^2*(a+b*x)^(3/2)/b^4/d/(c+d*x)^(3/2)-8/3*a^3*(a+b*x)^(3/2)/_ + b^4/(b*c-a*d)/(c+d*x)^(3/2)+8/3*a*(a+b*x)^(5/2)/b^4/d/(c+d*x)^(3/2)-_ + 2/3*(a+b*x)^(7/2)/b^4/d/(c+d*x)^(3/2)-_ + 12*a^2*(a+b*x)^(1/2)/b^3/d^2/(c+d*x)^(1/2)+4/3*a^4*(a+b*x)^(1/2)/_ + b^3/(b*c-a*d)^2/(c+d*x)^(1/2)+40/3*a*(a+b*x)^(3/2)/b^3/d^2/_ + (c+d*x)^(1/2)-14/3*(a+b*x)^(5/2)/b^3/d^2/(c+d*x)^(1/2)-_ + 20*a*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^3-35/4*(b*c-a*d)*_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^4+_ + 35/6*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b^2/d^3+_ + 12*a^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/_ + d^(5/2)+20*a*(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(7/2)+35/4*(b*c-a*d)^2*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/d^(9/2) +--R +--R +--R (265) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 4 +--R (9a d + 12a b c d + 54a b c d - 180a b c d + 105b c d)x + 9a c d +--R + +--R 3 2 3 2 2 3 2 3 4 4 5 +--R 12a b c d + 54a b c d - 180a b c d + 105b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 5 2 4 3 2 3 3 +--R (6a b d - 12a b c d + 6b c d )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 9a d - 3a b c d + 33a b c d - 21b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (- 18a c d - 24a b c d + 198a b c d - 140b c d)x - 9a c d +--R + +--R 2 3 2 2 4 3 5 +--R - 15a b c d + 145a b c d - 105b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 2 7 3 6 4 2 5 2 2 6 3 2 5 +--R (12a b d - 24a b c d + 12b c d )x + 12a b c d - 24a b c d +--R + +--R 4 3 4 +--R 12b c d +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R Type: Expression(Integer) +--E 515 + +--S 516 of 518 +--a0099:= integrate(t0099,x) +--E 516 + +--S 517 of 518 +--m0099:= a0099-r0099 +--E 517 + +--S 518 of 518 +--d0099:= D(m0099,x) +--E 518 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richalgebraic000-099.input.pdf b/src/axiom-website/CATS/richalgebraic000-099.input.pdf new file mode 100644 index 0000000..0ea2edb Binary files /dev/null and b/src/axiom-website/CATS/richalgebraic000-099.input.pdf differ diff --git a/src/axiom-website/CATS/richalgebraic100-199.input.pamphlet b/src/axiom-website/CATS/richalgebraic100-199.input.pamphlet new file mode 100644 index 0000000..e4f1350 --- /dev/null +++ b/src/axiom-website/CATS/richalgebraic100-199.input.pamphlet @@ -0,0 +1,13567 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richalgebraic100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic100-199.output +)spool richalgebraic100-199.output +)set message test on +)set message auto off +)clear all + +--S 1 of 512 +t0100:= x^3/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 3 +--R x +--R (1) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1 + +--S 2 of 512 +r0100:= -2/3*c^3*(a+b*x)^(1/2)/d^3/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4/3*b*c^3*(a+b*x)^(1/2)/d^3/(b*c-a*d)^2/(c+d*x)^(1/2)+_ + 6*c^2*(a+b*x)^(1/2)/d^3/(b*c-a*d)/(c+d*x)^(1/2)+(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b/d^3-5*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(1/2)/d^(7/2)-a*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/d^(5/2) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (- 3a d - 9a b c d + 27a b c d - 15b c d)x - 3a c d - 9a b c d +--R + +--R 2 3 3 4 +--R 27a b c d - 15b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +--R (3a d - 6a b c d + 3b c d )x + (6a c d - 30a b c d + 20b c d)x +--R + +--R 2 2 2 3 2 4 +--R 3a c d - 22a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 6 2 5 3 2 4 2 5 2 2 4 3 3 3 +-+ +--R ((3a b d - 6a b c d + 3b c d )x + 3a b c d - 6a b c d + 3b c d )\|b +--R * +--R +-+ +-------+ +--R \|d \|d x + c +--R Type: Expression(Integer) +--E 2 + +--S 3 of 512 +--a0100:= integrate(t0100,x) +--E 3 + +--S 4 of 512 +--m0100:= a0100-r0100 +--E 4 + +--S 5 of 512 +--d0100:= D(m0100,x) +--E 5 + +--S 6 of 512 +t0101:= x^2/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 2 +--R x +--R (3) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 6 + +--S 7 of 512 +r0101:= 2/3*c^2*(a+b*x)^(1/2)/d^2/(b*c-a*d)/(c+d*x)^(3/2)+_ + 4/3*b*c^2*(a+b*x)^(1/2)/d^2/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 4*c*(a+b*x)^(1/2)/d^2/(b*c-a*d)/(c+d*x)^(1/2)+_ + 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(5/2) +--R +--R +--R (4) +--R 2 3 2 2 2 2 2 2 2 3 +--R ((6a d - 12a b c d + 6b c d)x + 6a c d - 12a b c d + 6b c ) +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 3 +-+ +-+ +-------+ +--R ((12a c d - 8b c d)x + 10a c d - 6b c )\|b \|d \|b x + a +--R / +--R 2 5 4 2 2 3 2 4 2 3 2 3 2 +-+ +-+ +--R ((3a d - 6a b c d + 3b c d )x + 3a c d - 6a b c d + 3b c d )\|b \|d +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 7 + +--S 8 of 512 +--a0101:= integrate(t0101,x) +--E 8 + +--S 9 of 512 +--m0101:= a0101-r0101 +--E 9 + +--S 10 of 512 +--d0101:= D(m0101,x) +--E 10 + +--S 11 of 512 +t0102:= 1/x/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 1 +--R (5) ------------------------------------------ +--R 2 3 2 2 +-------+ +-------+ +--R (d x + 2c d x + c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 11 + +--S 12 of 512 +r0102:= -2/3*d*(a+b*x)^(1/2)/c/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4/3*b*d*(a+b*x)^(1/2)/c/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 2*d*(a+b*x)^(1/2)/c^2/(b*c-a*d)/(c+d*x)^(1/2)-_ + 2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(5/2) +--R +--R +--R (6) +--R 2 3 2 2 2 2 2 2 2 3 +--R ((- 6a d + 12a b c d - 6b c d)x - 6a c d + 12a b c d - 6b c ) +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 2 2 2 +-+ +-+ +-------+ +--R ((6a d - 10b c d )x + 8a c d - 12b c d)\|a \|c \|b x + a +--R / +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +-+ +-+ +--R ((3a c d - 6a b c d + 3b c d)x + 3a c d - 6a b c d + 3b c )\|a \|c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 12 + +--S 13 of 512 +--a0102:= integrate(t0102,x) +--E 13 + +--S 14 of 512 +--m0102:= a0102-r0102 +--E 14 + +--S 15 of 512 +--d0102:= D(m0102,x) +--E 15 + +--S 16 of 512 +t0103:= 1/x^2/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 1 +--R (7) ------------------------------------------- +--R 2 4 3 2 2 +-------+ +-------+ +--R (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 16 + +--S 17 of 512 +r0103:= 2/3*d^2*(a+b*x)^(1/2)/c^2/(b*c-a*d)/(c+d*x)^(3/2)+_ + 4/3*b*d^2*(a+b*x)^(1/2)/c^2/(b*c-a*d)^2/(c+d*x)^(1/2)+_ + 4*d^2*(a+b*x)^(1/2)/c^3/(b*c-a*d)/(c+d*x)^(1/2)-_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^3/x+_ + b*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/c^(5/2)+_ + 5*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(7/2) +--R +--R +--R (8) +--R 3 4 2 3 2 2 2 3 3 2 +--R (15a d - 27a b c d + 9a b c d + 3b c d)x +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (15a c d - 27a b c d + 9a b c d + 3b c )x +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 4 3 2 2 2 2 +--R (- 15a d + 22a b c d - 3b c d )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 20a c d + 30a b c d - 6b c d)x - 3a c d + 6a b c d - 3b c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|b x + a +--R / +--R 3 3 3 2 4 2 2 5 2 3 4 2 2 5 2 6 +--R ((3a c d - 6a b c d + 3a b c d)x + (3a c d - 6a b c d + 3a b c )x) +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|d x + c +--R Type: Expression(Integer) +--E 17 + +--S 18 of 512 +--a0103:= integrate(t0103,x) +--E 18 + +--S 19 of 512 +--m0103:= a0103-r0103 +--E 19 + +--S 20 of 512 +--d0103:= D(m0103,x) +--E 20 + +--S 21 of 512 +t0104:= 1/x^3/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 1 +--R (9) ------------------------------------------- +--R 2 5 4 2 3 +-------+ +-------+ +--R (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 21 + +--S 22 of 512 +r0104:= -2/3*d^3*(a+b*x)^(1/2)/c^3/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4/3*b*d^3*(a+b*x)^(1/2)/c^3/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 6*d^3*(a+b*x)^(1/2)/c^4/(b*c-a*d)/(c+d*x)^(1/2)-_ + 1/2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^3/x^2+3/4*b*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/a^2/c^3/x+11/4*d*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^4/x-_ + b*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/_ + c^(7/2)-8*d^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + a^(1/2)/c^(9/2)-3/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/_ + a^(1/2)/(c+d*x)^(1/2))/a^(5/2)/c^(9/2) +--R +--R +--R (10) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 +--R (- 105a d + 180a b c d - 54a b c d - 12a b c d - 9b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 2 +--R (- 105a c d + 180a b c d - 54a b c d - 12a b c d - 9b c )x +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 5 2 4 2 2 3 3 3 2 3 +--R (105a d - 145a b c d + 15a b c d + 9b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 2 +--R (140a c d - 198a b c d + 24a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 3 2 2 4 +--R (21a c d - 33a b c d + 3a b c d + 9b c )x - 6a c d + 12a b c d +--R + +--R 2 5 +--R - 6a b c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|b x + a +--R / +--R 4 4 3 3 5 2 2 2 6 3 +--R (12a c d - 24a b c d + 12a b c d)x +--R + +--R 4 5 2 3 6 2 2 7 2 +--R (12a c d - 24a b c d + 12a b c )x +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|d x + c +--R Type: Expression(Integer) +--E 22 + +--S 23 of 512 +--a0104:= integrate(t0104,x) +--E 23 + +--S 24 of 512 +--m0104:= a0104-r0104 +--E 24 + +--S 25 of 512 +--d0104:= D(m0104,x) +--E 25 + +--S 26 of 512 +t0105:= x^3/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 3 +--R x +--R (11) ------------------------------------------------- +--R 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 26 + +--S 27 of 512 +r0105:= 2*a*c/b^2/d^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+_ + 2*a*c*(b*c+a*d)/b^2/d^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 3/4*(b*c+a*d)^2/b^3/d^3/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 3/4*(b*c+a*d)^3/b^3/d^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+_ + 3/2*(b*c+a*d)*x/b^2/d^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+x^2/b/d/_ + (a+b*x)^(1/2)/(c+d*x)^(1/2)-4*a*c*(b*c+a*d)*(c+d*x)^(1/2)/b/d^2/_ + (b*c-a*d)^2/(a+b*x)^(1/2)+3/2*(b*c+a*d)^3*(c+d*x)^(1/2)/b^2/d^3/_ + (b*c-a*d)^2/(a+b*x)^(1/2)-3*(b*c+a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/d^(5/2) +--R +--R +--R (12) +--R 3 3 2 2 2 2 3 3 +-------+ +-------+ +--R (- 3a d + 3a b c d + 3a b c d - 3b c )\|b x + a \|d x + c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 3 2 2 3 2 2 +--R (a b d - 2a b c d + b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (3a d - a b c d - a b c d + 3b c )x + 3a c d - 2a b c d + 3a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 2 2 4 3 3 4 2 2 +-+ +-+ +-------+ +-------+ +--R (a b d - 2a b c d + b c d )\|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 27 + +--S 28 of 512 +--a0105:= integrate(t0105,x) +--E 28 + +--S 29 of 512 +--m0105:= a0105-r0105 +--E 29 + +--S 30 of 512 +--d0105:= D(m0105,x) +--E 30 + +--S 31 of 512 +t0106:= x^2/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 2 +--R x +--R (13) ------------------------------------------------- +--R 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 31 + +--S 32 of 512 +r0106:= 1/2*(b*c+a*d)/b^2/d^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+_ + 1/2*(b*c+a*d)^2/b^2/d^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + x/b/d/(a+b*x)^(1/2)/(c+d*x)^(1/2)-(b*c+a*d)^2*(c+d*x)^(1/2)/b/d^2/_ + (b*c-a*d)^2/(a+b*x)^(1/2)+2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(3/2)/d^(3/2) +--R +--R +--R (14) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ +-------+ \|d \|b x + a +--R (2a d - 4a b c d + 2b c )\|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 +-+ +-+ +--R ((- 2a d - 2b c )x - 2a c d - 2a b c )\|b \|d +--R / +--R 2 3 2 2 3 2 +-+ +-+ +-------+ +-------+ +--R (a b d - 2a b c d + b c d)\|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 32 + +--S 33 of 512 +--a0106:= integrate(t0106,x) +--E 33 + +--S 34 of 512 +--m0106:= a0106-r0106 +--E 34 + +--S 35 of 512 +--d0106:= D(m0106,x) +--E 35 + +--S 36 of 512 +t0107:= 1/x/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (15) ---------------------------------------------------- +--R 3 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 36 + +--S 37 of 512 +r0107:= 1/a/c/(a+b*x)^(1/2)/(c+d*x)^(1/2)-(b*c+a*d)/a/c/(b*c-a*d)/_ + (a+b*x)^(1/2)/(c+d*x)^(1/2)+2*b*(b*c+a*d)*(c+d*x)^(1/2)/a/c/_ + (b*c-a*d)^2/(a+b*x)^(1/2)-2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(3/2)/c^(3/2) +--R +--R +--R (16) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ +-------+ \|c \|b x + a +--R (- 2a d + 4a b c d - 2b c )\|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 +-+ +-+ +--R ((2a b d + 2b c d)x + 2a d + 2b c )\|a \|c +--R / +--R 3 2 2 2 2 3 +-+ +-+ +-------+ +-------+ +--R (a c d - 2a b c d + a b c )\|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 37 + +--S 38 of 512 +--a0107:= integrate(t0107,x) +--E 38 + +--S 39 of 512 +--m0107:= a0107-r0107 +--E 39 + +--S 40 of 512 +--d0107:= D(m0107,x) +--E 40 + +--S 41 of 512 +t0108:= 1/x^2/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (17) ----------------------------------------------------- +--R 4 3 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 41 + +--S 42 of 512 +r0108:= -4*b*d/a/c/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-3/2*(b*c+a*d)/_ + a^2/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+3/2*(b*c+a*d)^2/a^2/c^2/_ + (b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-1/a/c/x/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+8*b^2*d*(c+d*x)^(1/2)/a/c/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 3*b*(b*c+a*d)^2*(c+d*x)^(1/2)/a^2/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 3*(b*c+a*d)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + a^(5/2)/c^(5/2) +--R +--R +--R (18) +--R 3 3 2 2 2 2 3 3 +-------+ +-------+ +--R (3a d - 3a b c d - 3a b c d + 3b c )x\|b x + a \|d x + c +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 3 2 2 3 2 2 +--R (- 3a b d + 2a b c d - 3b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 3a d + a b c d + a b c d - 3b c )x - a c d + 2a b c d - a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 3 2 2 4 +-+ +-+ +-------+ +-------+ +--R (a c d - 2a b c d + a b c )x\|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 42 + +--S 43 of 512 +--a0108:= integrate(t0108,x) +--E 43 + +--S 44 of 512 +--m0108:= a0108-r0108 +--E 44 + +--S 45 of 512 +--d0108:= D(m0108,x) +--E 45 + +--S 46 of 512 +t0109:= 1/x^3/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (19) ----------------------------------------------------- +--R 5 4 3 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 46 + +--S 47 of 512 +r0109:= -3/2*b*d/a^2/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+13/2*b*d*(b*c+a*d)/_ + a^2/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+15/8*(b*c+a*d)^2/_ + a^3/c^3/(a+b*x)^(1/2)/(c+d*x)^(1/2)-15/8*(b*c+a*d)^3/a^3/c^3/_ + (b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-1/2/a/c/x^2/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+5/4*(b*c+a*d)/a^2/c^2/x/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 13*b^2*d*(b*c+a*d)*(c+d*x)^(1/2)/a^2/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 15/4*b*(b*c+a*d)^3*(c+d*x)^(1/2)/a^3/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 3*b*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(5/2)/_ + c^(5/2)-15/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(7/2)/c^(7/2) +--R +--R +--R (20) +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +-------+ +--R (- 15a d + 12a b c d + 6a b c d + 12a b c d - 15b c )x \|b x + a +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (15a b d - 7a b c d - 7a b c d + 15b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (15a d - 2a b c d - 10a b c d - 2a b c d + 15b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (5a c d - 5a b c d - 5a b c d + 5a b c )x - 2a c d + 4a b c d +--R + +--R 2 2 4 +--R - 2a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 3 2 4 4 3 2 5 2 +-+ +-+ +-------+ +-------+ +--R (4a c d - 8a b c d + 4a b c )x \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 47 + +--S 48 of 512 +--a0109:= integrate(t0109,x) +--E 48 + +--S 49 of 512 +--m0109:= a0109-r0109 +--E 49 + +--S 50 of 512 +--d0109:= D(m0109,x) +--E 50 + +--S 51 of 512 +t0110:= x^5/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (21) +--R 5 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 51 + +--S 52 of 512 +r0110:= 2*a^5/b^5/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)+8/3*a^5*d*_ + (a+b*x)^(1/2)/b^5/(b*c-a*d)^2/(c+d*x)^(3/2)+10/3*a^4*(a+b*x)^(1/2)/_ + b^5/(b*c-a*d)/(c+d*x)^(3/2)-20/3*a^2*(a+b*x)^(3/2)/b^5/d/_ + (c+d*x)^(3/2)-20/3*a^3*(a+b*x)^(3/2)/b^5/(b*c-a*d)/(c+d*x)^(3/2)+_ + 10/3*a*(a+b*x)^(5/2)/b^5/d/(c+d*x)^(3/2)-2/3*(a+b*x)^(7/2)/b^5/d/_ + (c+d*x)^(3/2)-20*a^2*(a+b*x)^(1/2)/b^4/d^2/(c+d*x)^(1/2)+16/3*a^5*_ + d*(a+b*x)^(1/2)/b^4/(b*c-a*d)^3/(c+d*x)^(1/2)+20/3*a^4*_ + (a+b*x)^(1/2)/b^4/(b*c-a*d)^2/(c+d*x)^(1/2)+50/3*a*(a+b*x)^(3/2)/_ + b^4/d^2/(c+d*x)^(1/2)-14/3*(a+b*x)^(5/2)/b^4/d^2/(c+d*x)^(1/2)-_ + 25*a*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3-35/4*(b*c-a*d)*_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^4+35/6*(a+b*x)^(3/2)*_ + (c+d*x)^(1/2)/b^3/d^3+20*a^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(5/2)+25*a*(b*c-a*d)*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/d^(7/2)+35/4*_ + (b*c-a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(7/2)/d^(9/2) +--R +--R +--R (22) +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 45a d - 45a b c d - 30a b c d - 90a b c d + 225a b c d +--R + +--R 5 5 +--R - 105b c d +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R 45a c d - 45a b c d - 30a b c d - 90a b c d + 225a b c d - 105b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 4 +--R (6a b d - 18a b c d + 18a b c d - 6b c d )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (- 15a b d + 24a b c d + 18a b c d - 48a b c d + 21b c d )x +--R + +--R 5 6 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (- 45a d + 66a b c d + 12a b c d - 237a b c d + 140b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R - 90a c d + 45a b c d + 84a b c d - 222a b c d - 50a b c d +--R + +--R 5 6 +--R 105b c +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R - 45a c d + 30a b c d + 36a b c d - 190a b c d + 105a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 3 8 2 4 7 5 2 6 6 3 5 3 3 7 +--R (12a b d - 36a b c d + 36a b c d - 12b c d )x + 12a b c d +--R + +--R 2 4 2 6 5 3 5 6 4 4 +--R - 36a b c d + 36a b c d - 12b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 52 + +--S 53 of 512 +--a0110:= integrate(t0110,x) +--E 53 + +--S 54 of 512 +--m0110:= a0110-r0110 +--E 54 + +--S 55 of 512 +--d0110:= D(m0110,x) +--E 55 + +--S 56 of 512 +t0111:= x^4/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (23) +--R 4 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 56 + +--S 57 of 512 +r0111:= -2*a^4/b^4/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)-8/3*a^4*d*_ + (a+b*x)^(1/2)/b^4/(b*c-a*d)^2/(c+d*x)^(3/2)-8/3*a^3*(a+b*x)^(1/2)/_ + b^4/(b*c-a*d)/(c+d*x)^(3/2)+8/3*a*(a+b*x)^(3/2)/b^4/d/(c+d*x)^(3/2)+_ + 4*a^2*(a+b*x)^(3/2)/b^4/(b*c-a*d)/(c+d*x)^(3/2)-2/3*(a+b*x)^(5/2)/_ + b^4/d/(c+d*x)^(3/2)+8*a*(a+b*x)^(1/2)/b^3/d^2/(c+d*x)^(1/2)-_ + 16/3*a^4*d*(a+b*x)^(1/2)/b^3/(b*c-a*d)^3/(c+d*x)^(1/2)-_ + 16/3*a^3*(a+b*x)^(1/2)/b^3/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 10/3*(a+b*x)^(3/2)/b^3/d^2/(c+d*x)^(1/2)+5*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b^2/d^3-5*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(3/2)/d^(7/2)-3*a*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/d^(5/2) +--R +--R +--R (24) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 4 +--R (- 9a d + 12a b c d + 18a b c d - 36a b c d + 15b c d)x - 9a c d +--R + +--R 3 2 3 2 2 3 2 3 4 4 5 +--R 12a b c d + 18a b c d - 36a b c d + 15b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (9a d - 3a b c d - 9a b c d + 39a b c d - 20b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (18a c d - 15a b c d + 33a b c d + 11a b c d - 15b c )x + 9a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 9a b c d + 31a b c d - 15a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 2 7 2 3 6 4 2 5 5 3 4 3 2 6 2 3 2 5 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 4 3 4 5 4 3 +--R 9a b c d - 3b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 57 + +--S 58 of 512 +--a0111:= integrate(t0111,x) +--E 58 + +--S 59 of 512 +--m0111:= a0111-r0111 +--E 59 + +--S 60 of 512 +--d0111:= D(m0111,x) +--E 60 + +--S 61 of 512 +t0112:= x^3/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (25) +--R 3 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 61 + +--S 62 of 512 +r0112:= 2*a^3/b^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)+8/3*a^3*d*_ + (a+b*x)^(1/2)/b^3/(b*c-a*d)^2/(c+d*x)^(3/2)+2*a^2*(a+b*x)^(1/2)/_ + b^3/(b*c-a*d)/(c+d*x)^(3/2)-2/3*(a+b*x)^(3/2)/b^3/d/(c+d*x)^(3/2)-_ + 2*a*(a+b*x)^(3/2)/b^3/(b*c-a*d)/(c+d*x)^(3/2)-2*(a+b*x)^(1/2)/_ + b^2/d^2/(c+d*x)^(1/2)+16/3*a^3*d*(a+b*x)^(1/2)/b^2/(b*c-a*d)^3/_ + (c+d*x)^(1/2)+4*a^2*(a+b*x)^(1/2)/b^2/(b*c-a*d)^2/(c+d*x)^(1/2)+_ + 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/d^(5/2) +--R +--R +--R (26) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (6a d - 18a b c d + 18a b c d - 6b c d)x + 6a c d - 18a b c d +--R + +--R 2 3 3 4 +--R 18a b c d - 6b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 4 2 2 2 3 3 2 +--R (- 6a d - 18a b c d + 8b c d)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 2 3 +--R (- 12a c d - 18a b c d - 8a b c d + 6b c )x - 6a c d - 16a b c d +--R + +--R 2 4 +--R 6a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 6 2 2 5 3 2 4 4 3 3 3 5 2 2 2 4 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 3 3 3 4 4 2 +--R 9a b c d - 3b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 62 + +--S 63 of 512 +--a0112:= integrate(t0112,x) +--E 63 + +--S 64 of 512 +--m0112:= a0112-r0112 +--E 64 + +--S 65 of 512 +--d0112:= D(m0112,x) +--E 65 + +--S 66 of 512 +t0113:= 1/x/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (27) +--R 1 +--R ---------------------------------------------------------------------------- +--R 2 4 2 3 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 66 + +--S 67 of 512 +r0113:= 2*d/c/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)+8/3*d^2*(a+b*x)^(1/2)/_ + c/(b*c-a*d)^2/(c+d*x)^(3/2)+1/a/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + (b*c+a*d)/a/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+16/3*b*d^2*_ + (a+b*x)^(1/2)/c/(b*c-a*d)^3/(c+d*x)^(1/2)+2*b*(b*c+a*d)*_ + (c+d*x)^(1/2)/a/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)-2*atanh(c^(1/2)*_ + (a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/c^(5/2) +--R +--R +--R (28) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c d)x - 6a c d + 18a b c d +--R + +--R 2 3 3 4 +--R - 18a b c d + 6b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 4 2 3 3 2 2 2 +--R (6a b d - 16a b c d - 6b c d )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (6a d - 8a b c d - 18a b c d - 12b c d)x + 8a c d - 18a b c d +--R + +--R 3 4 +--R - 6b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 3 3 3 4 2 +--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x + 3a c d - 9a b c d +--R + +--R 2 2 5 3 6 +--R 9a b c d - 3a b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 67 + +--S 68 of 512 +--a0113:= integrate(t0113,x) +--E 68 + +--S 69 of 512 +--m0113:= a0113-r0113 +--E 69 + +--S 70 of 512 +--d0113:= D(m0113,x) +--E 70 + +--S 71 of 512 +t0114:= 1/x^2/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (29) +--R 1 +--R ----------------------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 71 + +--S 72 of 512 +r0114:= -2*d^2/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)-8/3*d^3*_ + (a+b*x)^(1/2)/c^2/(b*c-a*d)^2/(c+d*x)^(3/2)-d/a/c^3/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)-4*b*d/a/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 3/2*(b*c+a*d)/a^2/c^3/(a+b*x)^(1/2)/(c+d*x)^(1/2)+d*(b*c+a*d)/a/_ + c^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+3/2*(b*c+a*d)^2/a^2/_ + c^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-1/a/c^2/x/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)-16/3*b*d^3*(a+b*x)^(1/2)/c^2/(b*c-a*d)^3/_ + (c+d*x)^(1/2)+8*b^2*d*(c+d*x)^(1/2)/a/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 2*b*d*(b*c+a*d)*(c+d*x)^(1/2)/a/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 3*b*(b*c+a*d)^2*(c+d*x)^(1/2)/a^2/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 2*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/_ + c^(7/2)+3*(b*c+a*d)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(5/2)/c^(7/2) +--R +--R +--R (30) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (15a d - 36a b c d + 18a b c d + 12a b c d - 9b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R (15a c d - 36a b c d + 18a b c d + 12a b c d - 9b c )x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (- 15a b d + 31a b c d - 9a b c d + 9b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 15a d + 11a b c d + 33a b c d - 15a b c d + 18b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (- 20a c d + 39a b c d - 9a b c d - 3a b c d + 9b c )x - 3a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R 9a b c d - 9a b c d + 3a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 2 +--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 +--R (3a c d - 9a b c d + 9a b c d - 3a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 72 + +--S 73 of 512 +--a0114:= integrate(t0114,x) +--E 73 + +--S 74 of 512 +--m0114:= a0114-r0114 +--E 74 + +--S 75 of 512 +--d0114:= D(m0114,x) +--E 75 + +--S 76 of 512 +t0115:= 1/x/(a+b*x)^(5/2)/(c+d*x)^(5/2) +--R +--R +--R (31) +--R 1 +--R / +--R 2 2 5 2 2 4 2 2 2 2 3 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 76 + +--S 77 of 512 +r0115:= 1/3/a/c/(a+b*x)^(3/2)/(c+d*x)^(3/2)-1/3*(b*c+a*d)/a/c/(b*c-a*d)/_ + (a+b*x)^(3/2)/(c+d*x)^(3/2)-2*b*(b*c+a*d)/a/c/(b*c-a*d)^2/_ + (a+b*x)^(3/2)/(c+d*x)^(1/2)+1/a^2/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + (b*c+a*d)/a^2/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+8/3*b^2*_ + (b*c+a*d)*(c+d*x)^(1/2)/a/c/(b*c-a*d)^3/(a+b*x)^(3/2)-16/3*b^2*d*_ + (b*c+a*d)*(c+d*x)^(1/2)/a/c/(b*c-a*d)^4/(a+b*x)^(1/2)+2*b*_ + (b*c+a*d)*(c+d*x)^(1/2)/a^2/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(5/2)/c^(5/2) +--R +--R +--R (32) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (- 6a b d + 24a b c d - 36a b c d + 24a b c d - 6b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (- 6a d + 18a b c d - 12a b c d - 12a b c d + 18a b c d - 6b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R - 6a c d + 24a b c d - 36a b c d + 24a b c d - 6a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (6a b d - 22a b c d - 22a b c d + 6b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (12a b d - 36a b c d - 48a b c d - 36a b c d + 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (6a d - 6a b c d - 48a b c d - 48a b c d - 6a b c d + 6b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R 8a c d - 24a b c d - 24a b c d + 8a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 2 5 6 2 +--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 77 + +--S 78 of 512 +--a0115:= integrate(t0115,x) +--E 78 + +--S 79 of 512 +--m0115:= a0115-r0115 +--E 79 + +--S 80 of 512 +--d0115:= D(m0115,x) +--E 80 + +--S 81 of 512 +t0116:= 1/x^2/(a+b*x)^(5/2)/(c+d*x)^(5/2) +--R +--R +--R (33) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 3 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 81 + +--S 82 of 512 +r0116:= -8/3*b*d/a/c/(b*c-a*d)/(a+b*x)^(3/2)/(c+d*x)^(3/2)-_ + 5/6*(b*c+a*d)/a^2/c^2/(a+b*x)^(3/2)/(c+d*x)^(3/2)+_ + 5/6*(b*c+a*d)^2/a^2/c^2/(b*c-a*d)/(a+b*x)^(3/2)/(c+d*x)^(3/2)-_ + 1/a/c/x/(a+b*x)^(3/2)/(c+d*x)^(3/2)-16*b^2*d/a/c/(b*c-a*d)^2/_ + (a+b*x)^(3/2)/(c+d*x)^(1/2)+5*b*(b*c+a*d)^2/a^2/c^2/(b*c-a*d)^2/_ + (a+b*x)^(3/2)/(c+d*x)^(1/2)-5/2*(b*c+a*d)/a^3/c^3/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+5/2*(b*c+a*d)^2/a^3/c^3/(b*c-a*d)/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+64/3*b^3*d*(c+d*x)^(1/2)/a/c/(b*c-a*d)^3/_ + (a+b*x)^(3/2)-20/3*b^2*(b*c+a*d)^2*(c+d*x)^(1/2)/a^2/c^2/_ + (b*c-a*d)^3/(a+b*x)^(3/2)-128/3*b^3*d^2*(c+d*x)^(1/2)/a/c/_ + (b*c-a*d)^4/(a+b*x)^(1/2)+40/3*b^2*d*(b*c+a*d)^2*(c+d*x)^(1/2)/_ + a^2/c^2/(b*c-a*d)^4/(a+b*x)^(1/2)-5*b*(b*c+a*d)^2*(c+d*x)^(1/2)/_ + a^3/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)+5*(b*c+a*d)*_ + atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(7/2)/c^(7/2) +--R +--R +--R (34) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 15a b d - 45a b c d + 30a b c d + 30a b c d - 45a b c d +--R + +--R 6 5 +--R 15b c d +--R * +--R 3 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 15a d - 30a b c d - 15a b c d + 60a b c d - 15a b c d +--R + +--R 5 5 6 6 +--R - 30a b c d + 15b c +--R * +--R 2 +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R 15a c d - 45a b c d + 30a b c d + 30a b c d - 45a b c d +--R + +--R 5 6 +--R 15a b c +--R * +--R x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (- 15a b d + 40a b c d - 18a b c d + 40a b c d - 15b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 30a b d + 60a b c d + 18a b c d + 18a b c d + 60a b c d +--R + +--R 6 5 +--R - 30b c d +--R * +--R 3 +--R x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (- 15a d + 87a b c d - 48a b c d + 87a b c d - 15b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R - 20a c d + 48a b c d - 12a b c d - 12a b c d + 48a b c d +--R + +--R 5 6 +--R - 20a b c +--R * +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R - 3a c d + 12a b c d - 18a b c d + 12a b c d - 3a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 3 5 7 3 +--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 2 +--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x +--R + +--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8 +--R (3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 82 + +--S 83 of 512 +--a0116:= integrate(t0116,x) +--E 83 + +--S 84 of 512 +--m0116:= a0116-r0116 +--E 84 + +--S 85 of 512 +--d0116:= D(m0116,x) +--E 858 + +--S 86 of 512 +t0117:= x^3*(a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 5 4 2 3 +-------+ +-------+ +--R (35) (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 86 + +--S 87 of 512 +r0117:= -33/1024*(b*c-a*d)^6*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^6/d^4-_ + 11/512*(b*c-a*d)^5*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^5/d^4-_ + 11/640*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^4/d^4-_ + 33/2240*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b^3/d^4-_ + 11/840*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(9/2)/b^2/d^4-_ + 1/84*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(11/2)/b/d^4+5/64*c^3*_ + (b*c-a*d)^4*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(7/2)/d^(9/2)-21/128*c^2*(b*c-a*d)^5*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(9/2)/d^(9/2)+_ + 63/512*c*(b*c-a*d)^6*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(11/2)/d^(9/2)+1/7*(a+b*x)^(1/2)*_ + (c+d*x)^(13/2)/d^4-1/4*c^3*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d^4+_ + 3/5*c^2*(a+b*x)^(1/2)*(c+d*x)^(9/2)/d^4-1/2*c*(a+b*x)^(1/2)*_ + (c+d*x)^(11/2)/d^4-33/1024*(b*c-a*d)^7*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(13/2)/d^(9/2)+_ + 5/64*c^3*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^4-_ + 21/128*c^2*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^4/d^4+_ + 63/512*c*(b*c-a*d)^5*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^5/d^4+_ + 5/96*c^3*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d^4-_ + 7/64*c^2*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^3/d^4+_ + 21/256*c*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^4/d^4+_ + 1/24*c^3*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d^4-_ + 7/80*c^2*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^2/d^4+_ + 21/320*c*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^3/d^4-_ + 3/40*c^2*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b/d^4+_ + 9/160*c*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b^2/d^4+_ + 1/20*c*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(9/2)/b/d^4 +--R +--R +--R (36) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 3465a d - 11025a b c d + 11025a b c d - 2625a b c d - 525a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 315a b c d - 525a b c d + 525b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 6 6 6 5 6 6 5 5 +--R 15360b d x + (1280a b d + 37120b c d )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1408a b d + 3840a b c d + 23680b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1584a b d - 4336a b c d + 3280a b c d + 240b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1848a b d + 5088a b c d - 3888a b c d + 160a b c d +--R + +--R 6 4 2 +--R - 280b c d +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 2310a b d - 6426a b c d + 5004a b c d - 260a b c d +--R + +--R 5 4 2 6 5 +--R - 210a b c d + 350b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 3465a d + 9870a b c d - 8043a b c d + 660a b c d + 385a b c d +--R + +--R 5 5 6 6 +--R 350a b c d - 525b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 6 4 +-+ +-+ +--R 107520b d \|b \|d +--R Type: Expression(Integer) +--E 87 + +--S 88 of 512 +--a0117:= integrate(t0117,x) +--E 88 + +--S 89 of 512 +--m0117:= a0117-r0117 +--E 89 + +--S 90 of 512 +--d0117:= D(m0117,x) +--E 90 + +--S 91 of 512 +t0118:= x^2*(a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 4 3 2 2 +-------+ +-------+ +--R (37) (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 91 + +--S 92 of 512 +r0118:= -5/64*c^2*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3+_ + 7/64*c*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^4/d^3-_ + 21/512*(b*c-a*d)^5*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^5/d^3-_ + 5/96*c^2*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d^3+_ + 7/96*c*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^3/d^3-_ + 7/256*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^4/d^3-_ + 1/24*c^2*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d^3+_ + 7/120*c*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^2/d^3-_ + 7/320*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^3/d^3+_ + 1/4*c^2*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d^3+1/20*c*_ + (b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b/d^3-3/160*(b*c-a*d)^2*_ + (a+b*x)^(1/2)*(c+d*x)^(7/2)/b^2/d^3-2/5*c*(a+b*x)^(1/2)*_ + (c+d*x)^(9/2)/d^3-1/60*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(9/2)/_ + b/d^3+1/6*(a+b*x)^(1/2)*(c+d*x)^(11/2)/d^3-5/64*c^2*(b*c-a*d)^4*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/d^(7/2)+_ + 7/64*c*(b*c-a*d)^5*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(9/2)/d^(7/2)-21/512*(b*c-a*d)^6*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(11/2)/d^(7/2) +--R +--R +--R (38) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 315a d + 1050a b c d - 1125a b c d + 300a b c d + 75a b c d +--R + +--R 5 5 6 6 +--R 90a b c d - 75b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 5 5 5 4 5 5 4 4 +--R 1280b d x + (128a b d + 3200b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 144a b d + 416a b c d + 2160b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (168a b d - 488a b c d + 408a b c d + 40b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b d + 616a b c d - 524a b c d + 40a b c d - 50b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 315a d - 945a b c d + 838a b c d - 90a b c d - 65a b c d + 75b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 5 3 +-+ +-+ +--R 7680b d \|b \|d +--R Type: Expression(Integer) +--E 92 + +--S 93 of 512 +--a0118:= integrate(t0118,x) +--E 93 + +--S 94 of 512 +--m0118:= a0118-r0118 +--E 94 + +--S 95 of 512 +--d0118:= D(m0118,x) +--E 95 + +--S 96 of 512 +t0119:= x*(a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 3 2 2 +-------+ +-------+ +--R (39) (d x + 2c d x + c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 96 + +--S 97 of 512 +r0119:= 5/64*c*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^2-_ + 7/128*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^4/d^2+_ + 5/96*c*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d^2-_ + 7/192*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^3/d^2+_ + 1/24*c*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d^2-_ + 7/240*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^2/d^2-_ + 11/40*c*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d^2+1/40*a*(a+b*x)^(1/2)*_ + (c+d*x)^(7/2)/b/d+1/5*(a+b*x)^(1/2)*(c+d*x)^(9/2)/d^2+_ + 5/64*c*(b*c-a*d)^4*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(5/2)-7/128*(b*c-a*d)^5*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(9/2)/d^(5/2) +--R +--R +--R (40) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 105a d - 375a b c d + 450a b c d - 150a b c d - 75a b c d +--R + +--R 5 5 +--R 45b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 384b d x + (48a b d + 1008b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 56a b d + 176a b c d + 744b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (70a b d - 222a b c d + 218a b c d + 30b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 340a b c d - 346a b c d + 60a b c d - 45b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 2 +-+ +-+ +--R 1920b d \|b \|d +--R Type: Expression(Integer) +--E 97 + +--S 98 of 512 +--a0119:= integrate(t0119,x) +--E 98 + +--S 99 of 512 +--m0119:= a0119-r0119 +--E 99 + +--S 100 of 512 +--d0119:= D(m0119,x) +--E 100 + +--S 101 of 512 +t0120:= (a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (41) (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 101 + +--S 102 of 512 +r0120:= -5/64*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d-_ + 5/96*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d-_ + 1/24*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d+_ + 1/4*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d-5/64*(b*c-a*d)^4*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/d^(3/2) +--R +--R +--R (42) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 60a b c d - 90a b c d + 60a b c d - 15b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (8a b d + 136b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 10a b d + 36a b c d + 118b c d)x + 15a d - 55a b c d +--R + +--R 2 2 3 3 +--R 73a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 +-+ +-+ +--R 192b d\|b \|d +--R Type: Expression(Integer) +--E 102 + +--S 103 of 512 +--a0120:= integrate(t0120,x) +--E 103 + +--S 104 of 512 +--m0120:= a0120-r0120 +--E 104 + +--S 105 of 512 +--d0120:= D(m0120,x) +--E 105 + +--S 106 of 512 +t0121:= (a+b*x)^(1/2)*(c+d*x)^(5/2)/x +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R (43) ---------------------------------------- +--R x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 512 +r0121:= 1/24/b^(5/2)*(-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*a^2*d^(5/2)*b^(1/2)+_ + 45*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*a*b^2*d*c^2-_ + 15*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*a^2*b*d^2*c+_ + 15*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*b^3*c^3+_ + 3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*a^3*d^3+_ + 14*(a+b*x)^(1/2)*(c+d*x)^(1/2)*a*d^(3/2)*b^(3/2)*c+33*c^2*_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)*b^(5/2)*d^(1/2)-48*a^(1/2)*c^(5/2)*_ + atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))*b^(5/2)*d^(1/2)+_ + 2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*d^(5/2)*b^(3/2)*a*x+_ + 26*(a+b*x)^(1/2)*(c+d*x)^(1/2)*b^(5/2)*d^(3/2)*c*x+_ + 8*(a+b*x)^(1/2)*(c+d*x)^(1/2)*d^(5/2)*b^(5/2)*x^2)/d^(1/2) +--R +--R +--R (44) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d - 15a b c d + 45a b c d + 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a +--R - 48b c \|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d + 26b c d)x - 3a d + 14a b c d + 33b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 24b \|b \|d +--R Type: Expression(Integer) +--E 107 + +--S 108 of 512 +--a0121:= integrate(t0121,x) +--E 108 + +--S 109 of 512 +--m0121:= a0121-r0121 +--E 109 + +--S 110 of 512 +--d0121:= D(m0121,x) +--E 110 + +--S 111 of 512 +t0122:= x^3*(1+x)^(1/2)/(1-x)^(5/2) +--R +--R +--R 3 +-----+ +--R x \|x + 1 +--R (45) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 512 +r0122:= -6*(1+x)^(1/2)/(1-x)^(1/2)-3*(1-x)^(1/2)*(1+x)^(1/2)+_ + 1/3*(1+x)^(3/2)/(1-x)^(3/2)-1/2*x*(1-x^2)^(1/2)+11/2*asin(x) +--R +--R +--R (46) +--R 2 +-----+ +--R (18x - 74x + 52)\|x + 1 +--R + +--R +--------+ +--R 2 | 2 +-------+ +--R ((- 3x + 3x)\|- x + 1 + (33x - 33)asin(x))\|- x + 1 +--R / +--R +-------+ +--R (6x - 6)\|- x + 1 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 512 +--a0122:= integrate(t0122,x) +--E 113 + +--S 114 of 512 +--m0122:= a0122-r0122 +--E 114 + +--S 115 of 512 +--d0122:= D(m0122,x) +--E 115 + +--S 116 of 512 +t0123:= x^2*(1+x)^(1/2)/(1-x)^(5/2) +--R +--R +--R 2 +-----+ +--R x \|x + 1 +--R (47) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 512 +r0123:= -4*(1+x)^(1/2)/(1-x)^(1/2)-(1-x)^(1/2)*(1+x)^(1/2)+_ + 1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*asin(x) +--R +--R +--R 2 +-----+ +-------+ +--R (3x - 19x + 14)\|x + 1 + (9x - 9)asin(x)\|- x + 1 +--R (48) ---------------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 512 +--a0123:= integrate(t0123,x) +--E 118 + +--S 119 of 512 +--m0123:= a0123-r0123 +--E 119 + +--S 120 of 512 +--d0123:= D(m0123,x) +--E 120 + +--S 121 of 512 +t0124:= x*(1+x)^(1/2)/(1-x)^(5/2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (49) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 512 +r0124:= -2*(1+x)^(1/2)/(1-x)^(1/2)+1/3*(1+x)^(3/2)/(1-x)^(3/2)+asin(x) +--R +--R +--R +-----+ +-------+ +--R (- 7x + 5)\|x + 1 + (3x - 3)asin(x)\|- x + 1 +--R (50) ---------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 512 +--a0124:= integrate(t0124,x) +--E 123 + +--S 124 of 512 +--m0124:= a0124-r0124 +--E 124 + +--S 125 of 512 +--d0124:= D(m0124,x) +--E 125 + +--S 126 of 512 +t0125:= x^2*(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 2 +-------+ +--R x \|b x + a +--R (51) ------------ +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 126 + +--S 127 of 512 +r0125:= 3/2*a*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^2-1/2*a^2*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b^2/d+5/8*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/_ + b^2/d^3-5/12*c*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b/d^2-7/12*a*_ + (a+b*x)^(3/2)*(c+d*x)^(1/2)/b^2/d+1/3*(a+b*x)^(5/2)*(c+d*x)^(1/2)/_ + b^2/d-a^2*(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(3/2)-3/2*a*(b*c-a*d)^2*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/_ + d^(5/2)-5/8*(b*c-a*d)^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(7/2) +--R +--R +--R (52) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d + 3a b c d + 9a b c d - 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d - 10b c d)x - 3a d - 4a b c d + 15b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 3 +-+ +-+ +--R 24b d \|b \|d +--R Type: Expression(Integer) +--E 127 + +--S 128 of 512 +--a0125:= integrate(t0125,x) +--E 128 + +--S 129 of 512 +--m0125:= a0125-r0125 +--E 129 + +--S 130 of 512 +--d0125:= D(m0125,x) +--E 130 + +--S 131 of 512 +t0126:= x*(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R x\|b x + a +--R (53) ----------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 131 + +--S 132 of 512 +r0126:= -3/4*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/d^2-1/4*a*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b/d+1/2*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b/d+a*_ + (b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(3/2)/d^(3/2)+3/4*(b*c-a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/d^(5/2) +--R +--R +--R (54) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- a d - 2a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x + a d - 3b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4b d \|b \|d +--R Type: Expression(Integer) +--E 132 + +--S 133 of 512 +--a0126:= integrate(t0126,x) +--E 133 + +--S 134 of 512 +--m0126:= a0126-r0126 +--E 134 + +--S 135 of 512 +--d0126:= D(m0126,x) +--E 135 + +--S 136 of 512 +t0127:= (a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (55) ---------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 136 + +--S 137 of 512 +r0127:= (a+b*x)^(1/2)*(c+d*x)^(1/2)/d-(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +-+ +-+ +-------+ +-------+ +--R (a d - b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c +--R +-+ +-------+ +--R \|b \|d x + c +--R (56) --------------------------------------------------------------- +--R +-+ +-+ +--R d\|b \|d +--R Type: Expression(Integer) +--E 137 + +--S 138 of 512 +--a0127:= integrate(t0127,x) +--E 138 + +--S 139 of 512 +--m0127:= a0127-r0127 +--E 139 + +--S 140 of 512 +--d0127:= D(m0127,x) +--E 140 + +--S 141 of 512 +t0128:= (a+b*x)^(1/2)/x/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (57) ----------- +--R +-------+ +--R x\|d x + c +--R Type: Expression(Integer) +--E 141 + +--S 142 of 512 +r0128:= -2*a^(1/2)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + c^(1/2)+2*b^(1/2)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/d^(1/2) +--R +--R +--R +-+ +-------+ +-+ +-------+ +--R +-+ +-+ \|d \|b x + a +-+ +-+ \|c \|b x + a +--R 2\|b \|c atanh(--------------) - 2\|a \|d atanh(--------------) +--R +-+ +-------+ +-+ +-------+ +--R \|b \|d x + c \|a \|d x + c +--R (58) --------------------------------------------------------------- +--R +-+ +-+ +--R \|c \|d +--R Type: Expression(Integer) +--E 142 + +--S 143 of 512 +--a0128:= integrate(t0128,x) +--E 143 + +--S 144 of 512 +--m0128:= a0128-r0128 +--E 144 + +--S 145 of 512 +--d0128:= D(m0128,x) +-- >> Error detected within library code: +-- integrate: implementation incomplete (non-algebraic residues) +--E 145 + +--S 146 of 512 +t0129:= (a+b*x)^(1/2)/x^2/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (59) ------------ +--R 2 +-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 146 + +--S 147 of 512 +r0129:= -(a+b*x)^(1/2)*(c+d*x)^(1/2)/c/x-(b*c-a*d)*_ + atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(3/2) +--R +--R +--R +-+ +-------+ +--R \|c \|b x + a +-+ +-+ +-------+ +-------+ +--R (a d - b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c +--R +-+ +-------+ +--R \|a \|d x + c +--R (60) ----------------------------------------------------------------- +--R +-+ +-+ +--R c x\|a \|c +--R Type: Expression(Integer) +--E 147 + +--S 148 of 512 +--a0129:= integrate(t0129,x) +--E 148 + +--S 149 of 512 +--m0129:= a0129-r0129 +--E 149 + +--S 150 of 512 +--d0129:= D(m0129,x) +--E 150 + +--S 151 of 512 +t0130:= x^2/(-1+x)^(1/2)/(1+x)^(1/2) +--R +--R +--R 2 +--R x +--R (61) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 512 +r0130:= 1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/2*acosh(x) +--R +--R +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 + acosh(x) +--R (62) ---------------------------- +--R 2 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 512 +--a0130:= integrate(t0130,x) +--E 153 + +--S 154 of 512 +--m0130:= a0130-r0130 +--E 154 + +--S 155 of 512 +--d0130:= D(m0130,x) +--E 155 + +--S 156 of 512 +t0131:= 1/(-1+x)^(1/2)/(1+x)^(1/2) +--R +--R +--R 1 +--R (63) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 512 +r0131:= acosh(x) +--R +--R +--R (64) acosh(x) +--R Type: Expression(Integer) +--E 157 + + +-- +-----+ +-----+ +-- (65) - log(- \|x - 1 \|x + 1 + x) +-- Type: Union(Expression(Integer),...) + +--S 158 of 512 ok to fail. seems there are 2 answers (see above) +a0131:= integrate(t0131,x) +--R +--R +--R +-----+ +-----+ +--R (65) - 2log(\|x + 1 - \|x - 1 ) +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 512 ok to fail. due to 2 answers (see above) +m0131:= a0131-r0131 +--R +--R +--R +-----+ +-----+ +--R (66) - 2log(\|x + 1 - \|x - 1 ) - acosh(x) +--R Type: Expression(Integer) +--E 159 + +--S 160 of 512 +d0131:= D(m0131,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (67) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 512 +t0132:= 1/(-1+x)^(1/2)/x/(1+x)^(1/2) +--R +--R +--R 1 +--R (68) ----------------- +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 512 +r0132:= 2*atan((-1+x)^(1/2)/(1+x)^(1/2)) +--R +--R +--R +-----+ +--R \|x - 1 +--R (69) 2atan(--------) +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 162 + + + +-- +-----+ +-----+ +-- 220\|x - 1 \|x + 1 - 21 +-- (70) atan(------------------------) +-- +-----+ +-----+ +-- 21\|x - 1 \|x + 1 + 220 +-- Type: Union(Expression(Integer),...) + +--S 163 of 512 ok to fail. seems there are 2 answers (see above) +a0132:= integrate(t0132,x) +--R +--R +--R +-----+ +-----+ +--R 416\|x - 1 \|x + 1 + 87 +--R (70) - atan(------------------------) +--R +-----+ +-----+ +--R 87\|x - 1 \|x + 1 - 416 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 512ok to fail. due to 2 answers (see above) +m0132:= a0132-r0132 +--R +--R +--R +-----+ +-----+ +-----+ +--R 416\|x - 1 \|x + 1 + 87 \|x - 1 +--R (71) - atan(------------------------) - 2atan(--------) +--R +-----+ +-----+ +-----+ +--R 87\|x - 1 \|x + 1 - 416 \|x + 1 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 512 +d0132:= D(m0132,x) +--R +--R +--R (72) 0 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 512 +t0133:= x^2*(-1+x)^(1/2)*(1+x)^(1/2) +--R +--R +--R 2 +-----+ +-----+ +--R (73) x \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 512 +r0133:= -1/8*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/4*(-1+x)^(1/2)*x^3*(1+x)^(1/2)-_ + 1/8*acosh(x) +--R +--R +--R 3 +-----+ +-----+ +--R (2x - x)\|x - 1 \|x + 1 - acosh(x) +--R (74) ------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 167 + + + +-- +-----+ +-----+ 3 +-----+ +-----+ +-- - log(- \|x - 1 \|x + 1 - x) + (2x - x)\|x - 1 \|x + 1 +-- (75) --------------------------------------------------------- +-- 8 +-- Type: Union(Expression(Integer),...) + +--S 168 of 512 ok to fail. seems there are 2 answers (see above) +a0133:= integrate(t0133,x) +--R +--R +--R +-----+ +-----+ 3 +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 + x) + (2x - x)\|x - 1 \|x + 1 +--R (75) ------------------------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 512 ok to fail. due to 2 answers (see above) +m0133:= a0133-r0133 +--R +--R +--R +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 + x) + acosh(x) +--R (76) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 512 +d0133:= D(m0133,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R - \|x - 1 + \|x - 1 \|x + 1 +--R (77) ------------------------------ +--R +------+ +--R +-----+ +-----+ | 2 +--R 8\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 512 +t0134:= (-1+x)^(1/2)*(1+x)^(1/2) +--R +--R +--R +-----+ +-----+ +--R (78) \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 512 +r0134:= 1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)-1/2*acosh(x) +--R +--R +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 - acosh(x) +--R (79) ---------------------------- +--R 2 +--R Type: Expression(Integer) +--E 172 + + + +-- +-----+ +-----+ +-----+ +-----+ +-- - log(\|x - 1 \|x + 1 + x) + x\|x - 1 \|x + 1 +-- (80) ----------------------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 173 of 512 ok to fail. seems there are 2 answers (see above) +a0134:= integrate(t0134,x) +--R +--R +--R (80) +--R +-----+ +-----+ 2 +-----+ +-----+ +--R (4x\|x - 1 \|x + 1 - 4x + 2)log(\|x + 1 - \|x - 1 ) +--R + +--R 3 +-----+ +-----+ 4 2 +--R (- 2x + x)\|x - 1 \|x + 1 + 2x - 2x +--R / +--R +-----+ +-----+ 2 +--R 4x\|x - 1 \|x + 1 - 4x + 2 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 512 ok to fail. due to 2 answers, see above +m0134:= a0134-r0134 +--R +--R +--R +-----+ +-----+ +--R 2log(\|x + 1 - \|x - 1 ) + acosh(x) +--R (81) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 512 +d0134:= D(m0134,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R - \|x - 1 + \|x - 1 \|x + 1 +--R (82) ------------------------------ +--R +------+ +--R +-----+ +-----+ | 2 +--R 2\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 175 + +--S 176 of 512 +t0135:= (-1+x)^(1/2)*(1+x)^(1/2)/x^2 +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (83) ---------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 512 +r0135:= -(-1+x)^(1/2)*(1+x)^(1/2)/x+acosh(x) +--R +--R +--R +-----+ +-----+ +--R - \|x - 1 \|x + 1 + x acosh(x) +--R (84) ------------------------------- +--R x +--R Type: Expression(Integer) +--E 177 + + + +-- +-----+ +-----+ +-----+ +-----+ +-- - 16x log(- \|x - 1 \|x + 1 + x) - 16\|x - 1 \|x + 1 + 19x +-- (85) ------------------------------------------------------------ +-- 16x +-- Type: Union(Expression(Integer),...) + +--S 178 of 512 ok to fail. seems there are 2 answers (see above) +a0135:= integrate(t0135,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R - x log(\|x - 1 \|x + 1 - x) - \|x - 1 \|x + 1 + x +--R (85) ---------------------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 512 ok to fail. due to 2 answers (see above) +m0135:= a0135-r0135 +--R +--R +--R +-----+ +-----+ +--R (86) - log(\|x - 1 \|x + 1 - x) - acosh(x) + 1 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 512 +d0135:= D(m0135,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (87) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 180 + +--S 181 of 512 +t0136:= 1/(1+2*x)^(1/2)/(3+2*x)^(1/2) +--R +--R +--R 1 +--R (88) ------------------ +--R +------+ +------+ +--R \|2x + 1 \|2x + 3 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 512 +r0136:= asinh(1/2*(1+2*x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +------+ +--R \|2 \|2x + 1 +--R (89) asinh(-------------) +--R 2 +--R Type: Expression(Integer) +--E 182 + + + +-- +------+ +------+ +-- log(- \|2x + 1 \|2x + 3 + 2x + 2) +-- (90) - ---------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 183 of 512 ok to fail. seems there are 2 answers (see above) +a0136:= integrate(t0136,x) +--R +--R +--R +------+ +------+ +--R (90) - log(\|2x + 3 - \|2x + 1 ) +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 512 ok to fail. due to 2 answers (see above) +m0136:= a0136-r0136 +--R +--R +--R +-+ +------+ +--R +------+ +------+ \|2 \|2x + 1 +--R (91) - log(\|2x + 3 - \|2x + 1 ) - asinh(-------------) +--R 2 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 512 +d0136:= D(m0136,x) +--R +--R +--R (92) 0 +--R Type: Expression(Integer) +--E 185 + +--S 186 of 512 +t0137:= 1/x/(-2+3*x)^(1/2)/(3+5*x)^(1/2) +--R +--R +--R 1 +--R (93) ------------------- +--R +------+ +------+ +--R x\|3x - 2 \|5x + 3 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 512 +r0137:= 1/3*6^(1/2)*atan(1/2*6^(1/2)*(-2+3*x)^(1/2)/(3+5*x)^(1/2)) +--R +--R +--R +-+ +------+ +--R +-+ \|6 \|3x - 2 +--R \|6 atan(-------------) +--R +------+ +--R 2\|5x + 3 +--R (94) ----------------------- +--R 3 +--R Type: Expression(Integer) +--E 187 + + + +-- +-+ +-+ +------+ +------+ +-+ +-+ +-- +-+ +-+ 3192\|2 \|3 \|3x - 2 \|5x + 3 + (67x + 804)\|2 \|3 +-- \|2 \|3 atan(----------------------------------------------------) +-- +------+ +------+ +-- 804\|3x - 2 \|5x + 3 - 1596x - 19152 +-- (95) - ------------------------------------------------------------------ +-- 6 +-- Type: Union(Expression(Integer),...) + +--S 188 of 512 ok to fail. seems there are 2 answers (see above) +a0137:= integrate(t0137,x) +--R +--R +--R +-+ +-+ +------+ +------+ +-+ +-+ +--R +-+ +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (337x + 4044)\|2 \|3 +--R \|2 \|3 atan(-----------------------------------------------------) +--R +------+ +------+ +--R 4044\|3x - 2 \|5x + 3 - 456x - 5472 +--R (95) - ------------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 512 ok to fail. due to 2 answers (see above) +m0137:= a0137-r0137 +--R +--R +--R (96) +--R +-+ +-+ +------+ +------+ +-+ +-+ +--R +-+ +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (337x + 4044)\|2 \|3 +--R - \|2 \|3 atan(-----------------------------------------------------) +--R +------+ +------+ +--R 4044\|3x - 2 \|5x + 3 - 456x - 5472 +--R + +--R +-+ +------+ +--R +-+ \|6 \|3x - 2 +--R - 2\|6 atan(-------------) +--R +------+ +--R 2\|5x + 3 +--R / +--R 6 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 512 +d0137:= D(m0137,x) +--R +--R +--R (97) 0 +--R Type: Expression(Integer) +--E 190 + +--S 191 of 512 +t0138:= 1/(-1+x)^(3/2)/x/(1+x)^(3/2) +--R +--R +--R 1 +--R (98) ------------------------ +--R 3 +-----+ +-----+ +--R (x - x)\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 512 +r0138:= -1/(-1+x)^(1/2)/(1+x)^(1/2)-2*atan((-1+x)^(1/2)/(1+x)^(1/2)) +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x - 1 +--R - 2\|x - 1 \|x + 1 atan(--------) - 1 +--R +-----+ +--R \|x + 1 +--R (99) ------------------------------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 192 + + + +-- (100) +-- +-----+ +-----+ +-- 2 416\|x - 1 \|x + 1 + 87 +-----+ +-----+ 2 +-- (24x - 24)atan(------------------------) - 24\|x - 1 \|x + 1 + 19x - 19 +-- +-----+ +-----+ +-- 87\|x - 1 \|x + 1 - 416 +-- -------------------------------------------------------------------------- +-- 2 +-- 24x - 24 +-- Type: Union(Expression(Integer),...) + +--S 193 of 512 ok to fail. seems there are 2 answers (see above) +a0138:= integrate(t0138,x) +--R +--R +--R (100) +--R +-----+ +-----+ 2 +-----+ +-----+ +--R (- 2x\|x - 1 \|x + 1 + 2x - 2)atan(\|x - 1 \|x + 1 - x) +--R + +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 - x +--R / +--R +-----+ +-----+ 2 +--R x\|x - 1 \|x + 1 - x + 1 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 512 ok to fail. due to 2 answers (see above) +m0138:= a0138-r0138 +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x - 1 +--R (101) - 2atan(\|x - 1 \|x + 1 - x) + 2atan(--------) +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 512 +d0138:= D(m0138,x) +--R +--R +--R (102) 0 +--R Type: Expression(Integer) +--E 195 + +--S 196 of 512 +t0139:= x*(1-x)^(1/2)*(1+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (103) x\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 512 +r0139:= -1/3*(1-x^2)^(3/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (x - 1)\|- x + 1 +--R (104) ------------------- +--R 3 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 512 +a0139:= integrate(t0139,x) +--R +--R +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R (105) -------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 512 +m0139:= a0139-r0139 +--R +--R +--R +--------+ +--R 2 +-------+ +-----+ 2 | 2 +--R (x - 1)\|- x + 1 \|x + 1 + (- x + 1)\|- x + 1 +--R (106) -------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 512 +d0139:= D(m0139,x) +--R +--R +--R +--------+ +--R 3 +-------+ +-----+ 3 | 2 +--R (x - x)\|- x + 1 \|x + 1 + (- x + x)\|- x + 1 +--R (107) -------------------------------------------------- +--R +--------+ +--R | 2 +-------+ +-----+ +--R \|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 512 +t0140:= x*(1+(1-x)^(1/2)*(1+x)^(1/2)) +--R +--R +--R +-------+ +-----+ +--R (108) x\|- x + 1 \|x + 1 + x +--R Type: Expression(Integer) +--E 201 + +--S 202 of 512 +r0140:= 1/2*x^2-1/3*(1-x^2)^(3/2) +--R +--R +--R +--------+ +--R 2 | 2 2 +--R (2x - 2)\|- x + 1 + 3x +--R (109) -------------------------- +--R 6 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 512 +a0140:= integrate(t0140,x) +--R +--R +--R 2 +-------+ +-----+ 2 +--R (2x - 2)\|- x + 1 \|x + 1 + 3x +--R (110) --------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 512 +m0140:= a0140-r0140 +--R +--R +--R +--------+ +--R 2 +-------+ +-----+ 2 | 2 +--R (x - 1)\|- x + 1 \|x + 1 + (- x + 1)\|- x + 1 +--R (111) -------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 512 +d0140:= D(m0140,x) +--R +--R +--R +--------+ +--R 3 +-------+ +-----+ 3 | 2 +--R (x - x)\|- x + 1 \|x + 1 + (- x + x)\|- x + 1 +--R (112) -------------------------------------------------- +--R +--------+ +--R | 2 +-------+ +-----+ +--R \|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 205 + +--S 206 of 512 +t0141:= x*(1+1/(2+x)^(1/2)/(3+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R x\|x + 2 \|x + 3 + x +--R (113) --------------------- +--R +-----+ +-----+ +--R \|x + 2 \|x + 3 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 512 +r0141:= 1/2*x^2+(2+x)^(1/2)*(3+x)^(1/2)-5*asinh((2+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +-----+ 2 +--R - 10asinh(\|x + 2 ) + 2\|x + 2 \|x + 3 + x +--R (114) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 207 + + + +-- (115) +-- +-----+ +-----+ 2 +-- ((- 640x - 1600)\|x + 2 \|x + 3 - 640x - 3200x - 3920) +-- * +-- +-----+ +-----+ +-- log(\|x + 3 + \|x + 2 ) +-- + +-- 3 2 +-----+ +-----+ 4 3 2 +-- (64x + 288x + 232x - 236)\|x + 2 \|x + 3 + 64x + 448x + 944x + 328x +-- + +-- - 579 +-- / +-- +-----+ +-----+ 2 +-- (128x + 320)\|x + 2 \|x + 3 + 128x + 640x + 784 +-- Type: Union(Expression(Integer),...) + +--S 208 of 512 ok to fail. seems there are 2 answers (see above) +a0141:= integrate(t0141,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ 2 +--R - 5log(- 2\|x + 2 \|x + 3 - 2x - 5) + 2\|x + 2 \|x + 3 + x +--R (115) ------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 512 ok to fail. due to 2 answers (see above) +m0141:= a0141-r0141 +--R +--R +--R +-----+ +-----+ +-----+ +--R - 5log(- 2\|x + 2 \|x + 3 - 2x - 5) + 10asinh(\|x + 2 ) +--R (116) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 512 +d0141:= D(m0141,x) +--R +--R +--R (117) 0 +--R Type: Expression(Integer) +--E 210 + +--S 211 of 512 +t0142:= x^(-3+n)/((a+b*x)^n) +--R +--R +--R n - 3 +--R x +--R (118) ---------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 512 +r0142:= 1/a^2/(-1+n)/(-2+n)*(a+b*x)^(-n)*(-x^(-2+n)*a^2+x^(-2+n)*a^2*n+_ + x^(-1+n)*a*n*b+x^n*b^2) +--R +--R +--R 2 n n - 1 2 2 n - 2 - n +--R (b x + a b n x + (a n - a )x )(b x + a) +--R (119) ---------------------------------------------------- +--R 2 2 2 2 +--R a n - 3a n + 2a +--R Type: Expression(Integer) +--E 212 + +--S 213 of 512 +a0142:= integrate(t0142,x) +--R +--R +--R 2 3 2 2 2 (n - 3)log(x) +--R (b x + a b n x + (a n - a )x)%e +--R (120) ---------------------------------------------- +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 512 +m0142:= a0142-r0142 +--R +--R +--R (121) +--R 2 n n - 1 2 2 n - 2 - n n log(b x + a) +--R (- b x - a b n x + (- a n + a )x )(b x + a) %e +--R + +--R 2 3 2 2 2 (n - 3)log(x) +--R (b x + a b n x + (a n - a )x)%e +--R / +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Expression(Integer) +--E 214 + +--S 215 of 512 +d0142:= D(m0142,x) +--R +--R +--R (122) +--R 2 n - 1 2 n - 2 +--R - b n x + (- a b n + a b n)x +--R + +--R 2 2 2 2 n - 3 +--R (- a n + 3a n - 2a )x +--R * +--R - n +--R (b x + a) +--R + +--R 3 n 2 2 n - 1 2 2 2 n - 2 - n - 1 +--R (b n x + a b n x + (a b n - a b n)x )(b x + a) +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 2 2 2 (n - 3)log(x) +--R (a n - 3a n + 2a )%e +--R / +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Expression(Integer) +--E 215 + +--S 216 of 512 +t0143:= (a+b*x^(1/2))^3 +--R +--R +--R 3 2 +-+ 2 3 +--R (123) (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 216 + +--S 217 of 512 +r0143:= 1/10*(a+b*x^(1/2))^4*(-a+4*b*x^(1/2))/b^2 +--R +--R +--R 5 2 2 3 +-+ 4 2 3 2 5 +--R (4b x + 20a b x)\|x + 15a b x + 10a b x - a +--R (124) ----------------------------------------------- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 217 + +--S 218 of 512 +a0143:= integrate(t0143,x) +--R +--R +--R 3 2 2 +-+ 2 2 3 +--R (4b x + 20a b x)\|x + 15a b x + 10a x +--R (125) ---------------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 512 +m0143:= a0143-r0143 +--R +--R +--R 5 +--R a +--R (126) ---- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 219 + +--S 220 of 512 +d0143:= D(m0143,x) +--R +--R +--R (127) 0 +--R Type: Expression(Integer) +--E 220 + +--S 221 of 512 +t0144:= (a+b*x^(1/2))^4 +--R +--R +--R 3 3 +-+ 4 2 2 2 4 +--R (128) (4a b x + 4a b)\|x + b x + 6a b x + a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 512 +r0144:= 1/15*(a+b*x^(1/2))^5*(-a+5*b*x^(1/2))/b^2 +--R +--R +--R 5 2 3 3 +-+ 6 3 2 4 2 4 2 6 +--R (24a b x + 40a b x)\|x + 5b x + 45a b x + 15a b x - a +--R (129) ---------------------------------------------------------- +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 222 + +--S 223 of 512 +a0144:= integrate(t0144,x) +--R +--R +--R 3 2 3 +-+ 4 3 2 2 2 4 +--R (24a b x + 40a b x)\|x + 5b x + 45a b x + 15a x +--R (130) --------------------------------------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 512 +m0144:= a0144-r0144 +--R +--R +--R 6 +--R a +--R (131) ---- +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 224 + +--S 225 of 512 +d0144:= D(m0144,x) +--R +--R +--R (132) 0 +--R Type: Expression(Integer) +--E 225 + +--S 226 of 512 +t0145:= (a+b*x^(1/2))^5 +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (133) (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 512 +r0145:= 1/21*(a+b*x^(1/2))^6*(-a+6*b*x^(1/2))/b^2 +--R +--R +--R (134) +--R 7 3 2 5 2 4 3 +-+ 6 3 3 4 2 5 2 7 +--R (6b x + 84a b x + 70a b x)\|x + 35a b x + 105a b x + 21a b x - a +--R ---------------------------------------------------------------------- +--R 2 +--R 21b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 512 +a0145:= integrate(t0145,x) +--R +--R +--R 5 3 2 3 2 4 +-+ 4 3 3 2 2 5 +--R (6b x + 84a b x + 70a b x)\|x + 35a b x + 105a b x + 21a x +--R (135) --------------------------------------------------------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 512 +m0145:= a0145-r0145 +--R +--R +--R 7 +--R a +--R (136) ---- +--R 2 +--R 21b +--R Type: Expression(Integer) +--E 229 + +--S 230 of 512 +d0145:= D(m0145,x) +--R +--R +--R (137) 0 +--R Type: Expression(Integer) +--E 230 + +--S 231 of 512 +t0146:= (a+b*x^(1/2))^6 +--R +--R +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 6 +--R (138) (6a b x + 20a b x + 6a b)\|x + b x + 15a b x + 15a b x + a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 512 +r0146:= 1/28*(a+b*x^(1/2))^7*(-a+7*b*x^(1/2))/b^2 +--R +--R +--R (139) +--R 7 3 3 5 2 5 3 +-+ 8 4 2 6 3 4 4 2 +--R (48a b x + 224a b x + 112a b x)\|x + 7b x + 140a b x + 210a b x +--R + +--R 6 2 8 +--R 28a b x - a +--R / +--R 2 +--R 28b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 512 +a0146:= integrate(t0146,x) +--R +--R +--R (140) +--R 5 3 3 3 2 5 +-+ 6 4 2 4 3 4 2 2 6 +--R (48a b x + 224a b x + 112a b x)\|x + 7b x + 140a b x + 210a b x + 28a x +--R ----------------------------------------------------------------------------- +--R 28 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 512 +m0146:= a0146-r0146 +--R +--R +--R 8 +--R a +--R (141) ---- +--R 2 +--R 28b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 512 +d0146:= D(m0146,x) +--R +--R +--R (142) 0 +--R Type: Expression(Integer) +--E 235 + +--S 236 of 512 +t0147:= (a+b*x^(1/2))^7 +--R +--R +--R (143) +--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2 5 2 7 +--R (b x + 21a b x + 35a b x + 7a b)\|x + 7a b x + 35a b x + 21a b x + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 512 +r0147:= 1/36*(a+b*x^(1/2))^8*(-a+8*b*x^(1/2))/b^2 +--R +--R +--R (144) +--R 9 4 2 7 3 4 5 2 6 3 +-+ 8 4 3 6 3 +--R (8b x + 216a b x + 504a b x + 168a b x)\|x + 63a b x + 420a b x +--R + +--R 5 4 2 7 2 9 +--R 378a b x + 36a b x - a +--R / +--R 2 +--R 36b +--R Type: Expression(Integer) +--E 237 + +--S 238 of 512 +a0147:= integrate(t0147,x) +--R +--R +--R (145) +--R 7 4 2 5 3 4 3 2 6 +-+ 6 4 3 4 3 +--R (8b x + 216a b x + 504a b x + 168a b x)\|x + 63a b x + 420a b x +--R + +--R 5 2 2 7 +--R 378a b x + 36a x +--R / +--R 36 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 512 +m0147:= a0147-r0147 +--R +--R +--R 9 +--R a +--R (146) ---- +--R 2 +--R 36b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 512 +d0147:= D(m0147,x) +--R +--R +--R (147) 0 +--R Type: Expression(Integer) +--E 240 + +--S 241 of 512 +t0148:= (a+b*x^(1/2))^8 +--R +--R +--R (148) +--R 7 3 3 5 2 5 3 7 +-+ 8 4 2 6 3 4 4 2 +--R (8a b x + 56a b x + 56a b x + 8a b)\|x + b x + 28a b x + 70a b x +--R + +--R 6 2 8 +--R 28a b x + a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 512 +r0148:= 1/45*(a+b*x^(1/2))^9*(-a+9*b*x^(1/2))/b^2 +--R +--R +--R (149) +--R 9 4 3 7 3 5 5 2 7 3 +-+ 10 5 2 8 4 +--R (80a b x + 720a b x + 1008a b x + 240a b x)\|x + 9b x + 315a b x +--R + +--R 4 6 3 6 4 2 8 2 10 +--R 1050a b x + 630a b x + 45a b x - a +--R / +--R 2 +--R 45b +--R Type: Expression(Integer) +--E 242 + +--S 243 of 512 +a0148:= integrate(t0148,x) +--R +--R +--R (150) +--R 7 4 3 5 3 5 3 2 7 +-+ 8 5 2 6 4 +--R (80a b x + 720a b x + 1008a b x + 240a b x)\|x + 9b x + 315a b x +--R + +--R 4 4 3 6 2 2 8 +--R 1050a b x + 630a b x + 45a x +--R / +--R 45 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 512 +m0148:= a0148-r0148 +--R +--R +--R 10 +--R a +--R (151) ---- +--R 2 +--R 45b +--R Type: Expression(Integer) +--E 244 + +--S 245 of 512 +d0148:= D(m0148,x) +--R +--R +--R (152) 0 +--R Type: Expression(Integer) +--E 245 + +--S 246 of 512 +t0149:= 1/(4+b*x)^(1/2)/(-4+b*x)^(1/2) +--R +--R +--R 1 +--R (153) -------------------- +--R +-------+ +-------+ +--R \|b x - 4 \|b x + 4 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 512 +r0149:= acosh(1/4*b*x)/b +--R +--R +--R b x +--R acosh(---) +--R 4 +--R (154) ---------- +--R b +--R Type: Expression(Integer) +--E 247 + +--S 248 of 512 +--a0149:= integrate(t0149,x) +--E 248 + +--S 249 of 512 +--m0149:= a0149-r0149 +--E 249 + +--S 250 of 512 +--d0149:= D(m0149,x) +-- >> Error detected within library code: +-- integrate: implementation incomplete (non-algebraic residues) +--E 250 + +--S 251 of 512 +t0150:= 1/((-b+b*c)/d+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (155) ---------------------------- +--R +---------------+ +--R |b d x + b c - b +-------+ +--R |--------------- \|d x + c +--R \| d +--R Type: Expression(Integer) +--E 251 + +--S 252 of 512 +r0150:= 2*asinh(d^(1/2)*(b*(-1+c+d*x)/d)^(1/2)/b^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +---------------+ +--R +-+ |b d x + b c - b +--R \|d |--------------- +--R \| d +--R 2asinh(----------------------) +--R +-+ +--R \|b +--R (156) ------------------------------ +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 252 + +--S 253 of 512 +--a0150:= integrate(t0150,x) +--E 253 + +--S 254 of 512 +--m0150:= a0150-r0150 +--E 254 + +--S 255 of 512 +--d0150:= D(m0150,x) +--E 255 + +--S 256 of 512 +t0151:= 1/x^(1/2)/(-3+2*x)^(1/2) +--R +--R +--R 1 +--R (157) ------------- +--R +-+ +------+ +--R \|x \|2x - 3 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 512 +r0151:= 2^(1/2)*asinh(1/3*(-3+2*x)^(1/2)*3^(1/2)) +--R +--R +--R +-+ +------+ +--R +-+ \|3 \|2x - 3 +--R (158) \|2 asinh(-------------) +--R 3 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 512 +--a0151:= integrate(t0151,x) +--E 258 + +--S 259 of 512 +--m0151:= a0151-r0151 +--E 259 + +--S 260 of 512 +--d0151:= D(m0151,x) +--E 260 + +--S 261 of 512 +t0152:= 1/(2+3*x)^(1/2)/(-3+2*x)^(1/2) +--R +--R +--R 1 +--R (159) ------------------ +--R +------+ +------+ +--R \|2x - 3 \|3x + 2 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 512 +r0152:= 1/3*6^(1/2)*asinh(1/13*39^(1/2)*(-3+2*x)^(1/2)) +--R +--R +--R +--+ +------+ +--R +-+ \|39 \|2x - 3 +--R \|6 asinh(--------------) +--R 13 +--R (160) ------------------------- +--R 3 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 512 +--a0152:= integrate(t0152,x) +--E 263 + +--S 264 of 512 +--m0152:= a0152-r0152 +--E 264 + +--S 265 of 512 +--d0152:= D(m0152,x) +--E 265 + +--S 266 of 512 +t0153:= 1/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (161) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 266 + +--S 267 of 512 +r0153:= 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (162) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 267 + +--S 268 of 512 +--a0153:= integrate(t0153,x) +--E 268 + +--S 269 of 512 +--m0153:= a0153-r0153 +--E 269 + +--S 270 of 512 +--d0153:= D(m0153,x) +--E 270 + +--S 271 of 512 +t0154:= 1/((b-b*c)/d+b*x)^(1/2)/(c-d*x)^(1/2) +--R +--R +--R 1 +--R (163) ------------------------------ +--R +---------------+ +--R +---------+ |b d x - b c + b +--R \|- d x + c |--------------- +--R \| d +--R Type: Expression(Integer) +--E 271 + +--S 272 of 512 +r0154:= 2*asin(d^(1/2)*(-b*(-1+c-d*x)/d)^(1/2)/b^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +---------------+ +--R +-+ |b d x - b c + b +--R \|d |--------------- +--R \| d +--R 2asin(----------------------) +--R +-+ +--R \|b +--R (164) ----------------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 272 + +--S 273 of 512 +--a0154:= integrate(t0154,x) +--E 273 + +--S 274 of 512 +--m0154:= a0154-r0154 +--E 274 + +--S 275 of 512 +--d0154:= D(m0154,x) +--E 275 + +--S 276 of 512 +t0155:= 1/(4-x)^(1/2)/x^(1/2) +--R +--R +--R 1 +--R (165) -------------- +--R +-------+ +-+ +--R \|- x + 4 \|x +--R Type: Expression(Integer) +--E 276 + +--S 277 of 512 +r0155:= 2*asin(1/2*x^(1/2)) +--R +--R +--R +-+ +--R \|x +--R (166) 2asin(----) +--R 2 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 512 +--a0155:= integrate(t0155,x) +--E 278 + +--S 279 of 512 +--m0155:= a0155-r0155 +--E 279 + +--S 280 of 512 +--d0155:= D(m0155,x) +--E 280 + +--S 281 of 512 +t0156:= 1/x^(1/2)/(3-2*x)^(1/2) +--R +--R +--R 1 +--R (167) --------------- +--R +--------+ +-+ +--R \|- 2x + 3 \|x +--R Type: Expression(Integer) +--E 281 + +--S 282 of 512 +r0156:= 2^(1/2)*asin(1/3*6^(1/2)*x^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ \|6 \|x +--R (168) \|2 asin(--------) +--R 3 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 512 +--a0156:= integrate(t0156,x) +--E 283 + +--S 284 of 512 +--m0156:= a0156-r0156 +--E 284 + +--S 285 of 512 +--d0156:= D(m0156,x) +--E 285 + +--S 286 of 512 +t0157:= 1/(3+5*x)^(1/2)/(3-2*x)^(1/2) +--R +--R +--R 1 +--R (169) -------------------- +--R +--------+ +------+ +--R \|- 2x + 3 \|5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 512 +r0157:= 1/5*10^(1/2)*asin(1/21*42^(1/2)*(3+5*x)^(1/2)) +--R +--R +--R +--+ +------+ +--R +--+ \|42 \|5x + 3 +--R \|10 asin(--------------) +--R 21 +--R (170) ------------------------- +--R 5 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 512 +--a0157:= integrate(t0157,x) +--E 288 + +--S 289 of 512 +--m0157:= a0157-r0157 +--E 289 + +--S 290 of 512 +--d0157:= D(m0157,x) +--E 290 + +--S 291 of 512 +t0158:= 1/(a-b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (171) ---------------------- +--R +---------+ +-------+ +--R \|- b x + a \|d x + c +--R Type: Expression(Integer) +--E 291 + +--S 292 of 512 +r0158:= -2*atan(d^(1/2)*(a-b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +---------+ +-+ +--R \|- b x + a \|d +--R 2atan(----------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (172) - ----------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 292 + +--S 293 of 512 +--a0158:= integrate(t0158,x) +--E 293 + +--S 294 of 512 +--m0158:= a0158-r0158 +--E 294 + +--S 295 of 512 +--d0158:= D(m0158,x) +--E 295 + +--S 296 of 512 +t0159:= 1/(a+b*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (173) --------------- +--R +-------+ +--R b\|d x + c + a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 512 +r0159:= -2*(-b*(c+d*x)^(1/2)+a*log(a+b*(c+d*x)^(1/2)))/b^2/d +--R +--R +--R +-------+ +-------+ +--R - 2a log(b\|d x + c + a) + 2b\|d x + c +--R (174) ---------------------------------------- +--R 2 +--R b d +--R Type: Expression(Integer) +--E 297 + +--S 298 of 512 +a0159:= integrate(t0159,x) +--R +--R +--R +-------+ +-------+ +--R - 2a log(b\|d x + c + a) + 2b\|d x + c +--R (175) ---------------------------------------- +--R 2 +--R b d +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 512 +m0159:= a0159-r0159 +--R +--R +--R (176) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 512 +d0159:= D(m0159,x) +--R +--R +--R (177) 0 +--R Type: Expression(Integer) +--E 300 + +--S 301 of 512 +t0160:= x^(1/2)/(1-x^2) +--R +--R +--R +-+ +--R \|x +--R (178) - ------ +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 512 +r0160:= -atan(x^(1/2))+atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (179) atanh(\|x ) - atan(\|x ) +--R Type: Expression(Integer) +--E 302 + +--S 303 of 512 +a0160:= integrate(t0160,x) +--R +--R +--R +-+ +-+ +-+ +--R log(\|x + 1) - log(\|x - 1) - 2atan(\|x ) +--R (180) ------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 512 +m0160:= a0160-r0160 +--R +--R +--R +-+ +-+ +-+ +--R log(\|x + 1) - log(\|x - 1) - 2atanh(\|x ) +--R (181) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 512 +d0160:= D(m0160,x) +--R +--R +--R (182) 0 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 512 +t0161:= x^(1/2)/(a-b*x^2) +--R +--R +--R +-+ +--R \|x +--R (183) - -------- +--R 2 +--R b x - a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 512 +r0161:= -(atan(b^(1/4)*x^(1/2)/a^(1/4))-_ + atanh(b^(1/4)*x^(1/2)/a^(1/4)))/a^(1/4)/b^(3/4) +--R +--R +--R 4+-+ +-+ 4+-+ +-+ +--R \|b \|x \|b \|x +--R atanh(--------) - atan(--------) +--R 4+-+ 4+-+ +--R \|a \|a +--R (184) -------------------------------- +--R 4+-+4+-+3 +--R \|a \|b +--R Type: Expression(Integer) +--E 307 + +--S 308 of 512 +a0161:= integrate(t0161,x) +--R +--R +--R (185) +--R +------+ +------+3 +------+ +------+3 +--R | 1 +-+ 2 | 1 | 1 +-+ 2 | 1 +--R |------ log(\|x + 8a b |------ ) - |------ log(\|x - 8a b |------ ) +--R 4| 3 4| 3 4| 3 4| 3 +--R \|16a b \|16a b \|16a b \|16a b +--R + +--R +------+3 +--R 2 | 1 +--R 8a b |------ +--R +------+ 4| 3 +--R | 1 \|16a b +--R 2 |------ atan(---------------) +--R 4| 3 +-+ +--R \|16a b \|x +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 512 +m0161:= a0161-r0161 +--R +--R +--R (186) +--R +------+ +------+3 +--R | 1 4+-+4+-+3 +-+ 2 | 1 +--R |------ \|a \|b log(\|x + 8a b |------ ) +--R 4| 3 4| 3 +--R \|16a b \|16a b +--R + +--R +------+ +------+3 4+-+ +-+ +--R | 1 4+-+4+-+3 +-+ 2 | 1 \|b \|x +--R - |------ \|a \|b log(\|x - 8a b |------ ) - atanh(--------) +--R 4| 3 4| 3 4+-+ +--R \|16a b \|16a b \|a +--R + +--R +------+3 +--R 2 | 1 +--R 8a b |------ +--R 4+-+ +-+ +------+ 4| 3 +--R \|b \|x | 1 4+-+4+-+3 \|16a b +--R atan(--------) + 2 |------ \|a \|b atan(---------------) +--R 4+-+ 4| 3 +-+ +--R \|a \|16a b \|x +--R / +--R 4+-+4+-+3 +--R \|a \|b +--R Type: Expression(Integer) +--E 309 + +--S 310 of 512 +d0161:= D(m0161,x) +--R +--R +--R (187) 0 +--R Type: Expression(Integer) +--E 310 + +--S 311 of 512 +t0162:= (2+3*x)^(1/2)/(a+b*x^2) +--R +--R +--R +------+ +--R \|3x + 2 +--R (188) --------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 512 +r0162:= -(-(-3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2)*_ + atanh((-b)^(1/2)*(2+3*x)^(1/2)/(-3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2))+_ + (3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2)*_ + atanh((-b)^(1/2)*(2+3*x)^(1/2)/_ + (3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2)))/a^(1/2)/b +--R +--R +--R (189) +--R +------------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R \|- 3\|- b \|a - 2b atanh(---------------------) +--R +------------------+ +--R | +---+ +-+ +--R \|- 3\|- b \|a - 2b +--R + +--R +----------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R - \|3\|- b \|a - 2b atanh(-------------------) +--R +----------------+ +--R | +---+ +-+ +--R \|3\|- b \|a - 2b +--R / +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 312 + +--S 313 of 512 +a0162:= integrate(t0162,x) +--R +--R +--R (190) +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 512 +m0162:= a0162-r0162 +--R +--R +--R (191) +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +------------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R - 2\|- 3\|- b \|a - 2b atanh(---------------------) +--R +------------------+ +--R | +---+ +-+ +--R \|- 3\|- b \|a - 2b +--R + +--R +----------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R 2\|3\|- b \|a - 2b atanh(-------------------) +--R +----------------+ +--R | +---+ +-+ +--R \|3\|- b \|a - 2b +--R / +--R +-+ +--R 2b\|a +--R Type: Expression(Integer) +--E 314 + +--S 315 of 512 +d0162:= D(m0162,x) +--R +--R +--R (192) 0 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 512 +t0163:= (2+3*x)^(1/2)/(a-b*x^2) +--R +--R +--R +------+ +--R \|3x + 2 +--R (193) - --------- +--R 2 +--R b x - a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 512 +r0163:= -(-3*a^(1/2)*b^(1/2)+2*b)^(1/2)*atanh(b^(1/2)*(2+3*x)^(1/2)/_ + (-3*a^(1/2)*b^(1/2)+2*b)^(1/2))/a^(1/2)/b+_ + (3*a^(1/2)*b^(1/2)+2*b)^(1/2)*_ + atanh(b^(1/2)*(2+3*x)^(1/2)/(3*a^(1/2)*b^(1/2)+2*b)^(1/2))/a^(1/2)/b +--R +--R +--R (194) +--R +----------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R - \|- 3\|a \|b + 2b atanh(-------------------) +--R +----------------+ +--R | +-+ +-+ +--R \|- 3\|a \|b + 2b +--R + +--R +--------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R \|3\|a \|b + 2b atanh(-----------------) +--R +--------------+ +--R | +-+ +-+ +--R \|3\|a \|b + 2b +--R / +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 317 + +--S 318 of 512 +a0163:= integrate(t0163,x) +--R +--R +--R (195) +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 1 | | 1 +--R |6a b |----- + 2 |6a b |----- + 2 +--R | | 3 +-----+ | | 3 +--R | \|4a b 2 | 1 | \|4a b +------+ +--R |---------------- log(2a b |----- |---------------- + \|3x + 2 ) +--R \| a b | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(- 2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 1 | | 1 +--R |6a b |----- + 2 |6a b |----- + 2 +--R | | 3 +-----+ | | 3 +--R | \|4a b 2 | 1 | \|4a b +------+ +--R - |---------------- log(- 2a b |----- |---------------- + \|3x + 2 ) +--R \| a b | 3 \| a b +--R \|4a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 512 +m0163:= a0163-r0163 +--R +--R +--R (196) +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 1 | | 1 +--R |6a b |----- + 2 |6a b |----- + 2 +--R | | 3 +-----+ | | 3 +--R +-+ | \|4a b 2 | 1 | \|4a b +------+ +--R b\|a |---------------- log(2a b |----- |---------------- + \|3x + 2 ) +--R \| a b | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(- 2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R - +--R +----------------+ +--R | +-----+ +--R | | 1 +--R |6a b |----- + 2 +--R | | 3 +--R +-+ | \|4a b +--R b\|a |---------------- +--R \| a b +--R * +--R +----------------+ +--R | +-----+ +--R | | 1 +--R |6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(- 2a b |----- |---------------- + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +----------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R 2\|- 3\|a \|b + 2b atanh(-------------------) +--R +----------------+ +--R | +-+ +-+ +--R \|- 3\|a \|b + 2b +--R + +--R +--------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R - 2\|3\|a \|b + 2b atanh(-----------------) +--R +--------------+ +--R | +-+ +-+ +--R \|3\|a \|b + 2b +--R / +--R +-+ +--R 2b\|a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 512 +d0163:= D(m0163,x) +--R +--R +--R (197) 0 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 512 +t0164:= (c+d*x)^(1/2)/(1+x^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (198) ---------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 512 +r0164:= d*((c-(-d^2)^(1/2))^(1/2)*atanh((c+d*x)^(1/2)/_ + (c-(-d^2)^(1/2))^(1/2))-(c+(-d^2)^(1/2))^(1/2)*_ + atanh((c+d*x)^(1/2)/(c+(-d^2)^(1/2))^(1/2)))/(-d^2)^(1/2) +--R +--R +--R (199) +--R +-------------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R d\|- \|- d + c atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- d + c +--R + +--R +-----------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R - d\|\|- d + c atanh(--------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- d + c +--R / +--R +----+ +--R | 2 +--R \|- d +--R Type: Expression(Integer) +--E 322 + +--S 323 of 512 +a0164:= integrate(t0164,x) +--R +--R +--R (200) +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R - 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R 2\|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) - d\|d x + c +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R 2\|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) + d\|d x + c +--R 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 512 +m0164:= a0164-r0164 +--R +--R +--R (201) +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|- d \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|- d \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R - 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R 2\|- d \|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) - d\|d x + c +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R 2\|- d \|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) + d\|d x + c +--R 2 +--R + +--R +-------------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R - 2d\|- \|- d + c atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- d + c +--R + +--R +-----------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R 2d\|\|- d + c atanh(--------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- d + c +--R / +--R +----+ +--R | 2 +--R 2\|- d +--R Type: Expression(Integer) +--E 324 + +--S 325 of 512 +d0164:= D(m0164,x) +--R +--R +--R (202) +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- d - 3c d - 3c d - c d)x - c d - 3c d - 3c d - c ) +--R * +--R +--+ 12 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- 4d - 12c d - 12c d - 4c d)x - 4c d - 12c d - 12c d - 4c ) +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (6d + 12c d + 6c d )x + (12c d + 24c d + 12c d)x + 6c d +--R + +--R 4 2 6 +--R 12c d + 6c +--R * +--R +-------+2 +--R 4| 2 2 +--R \|d + c +--R * +--R +--+ 10 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 4c d - 2c d)x + (- 2c d - 4c d - 2c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 2d - 4c d - 2c d)x - 2c d - 4c d - 2c +--R * +--R +--+ +--+ 9 +--R | 2 | 2 +--R \|d \|d +--R +--+ +-------+2 atan(-----) atan(-----) +--R | 2 4| 2 2 c c +--R \|d \|d + c cos(-----------)sin(-----------) +--R 2 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- 6d - 18c d - 18c d - 6c d)x - 6c d - 18c d - 18c d - 6c ) +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (12d + 24c d + 12c d )x + (24c d + 48c d + 24c d)x + 12c d +--R + +--R 4 2 6 +--R 24c d + 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- 15d - 30c d - 15c d )x + (- 45c d - 90c d - 45c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 45c d - 90c d - 45c d)x - 15c d - 30c d - 15c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 4d - 8c d - 4c d)x + (- 4c d - 8c d - 4c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 4d - 8c d - 4c d)x - 4c d - 8c d - 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (8d + 16c d + 8c d )x + (16c d + 32c d + 16c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (8d + 24c d + 24c d + 8c )x + (16c d + 32c d + 16c d)x +--R + +--R 2 4 4 2 6 +--R 8c d + 16c d + 8c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R * +--R +--+ 7 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- 4d - 12c d - 12c d - 4c d)x - 4c d - 12c d - 12c d - 4c ) +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (8d + 16c d + 8c d )x + (16c d + 32c d + 16c d)x + 8c d +--R + +--R 4 2 6 +--R 16c d + 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- 8d - 16c d - 8c d )x + (- 24c d - 48c d - 24c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 24c d - 48c d - 24c d)x - 8c d - 16c d - 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (20d + 20c d )x + (80c d + 80c d )x + (120c d + 120c d )x +--R + +--R 3 3 5 4 2 6 +--R (80c d + 80c d)x + 20c d + 20c +--R * +--R +-------+2 +--R 4| 2 2 +--R \|d + c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 4c d - 2c d)x + (- 2c d - 4c d - 2c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 2d - 4c d - 2c d)x - 2c d - 4c d - 2c +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (4d + 12c d + 12c d + 4c )x + (8c d + 16c d + 8c d)x +--R + +--R 2 4 4 2 6 +--R 4c d + 8c d + 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 12d - 12c d )x + (- 36c d - 36c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 12d - 48c d - 36c d)x + (- 36c d - 48c d - 12c )x +--R + +--R 2 3 4 3 2 5 +--R (- 36c d - 36c d)x - 12c d - 12c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- d - 3c d - 3c d - c d)x - c d - 3c d - 3c d - c ) +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x + 4c d +--R + +--R 4 2 6 +--R 8c d + 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- 4d - 8c d - 4c d )x + (- 12c d - 24c d - 12c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 12c d - 24c d - 12c d)x - 4c d - 8c d - 4c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (- 8d - 8c d )x + (- 32c d - 32c d )x + (- 48c d - 48c d )x +--R + +--R 3 3 5 4 2 6 +--R (- 32c d - 32c d)x - 8c d - 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 5 6 3 4 4 2 5 4 3 3 +--R (- 15d - 15c d )x + (- 75c d - 75c d )x + (- 150c d - 150c d )x +--R + +--R 3 4 5 2 2 4 3 6 5 2 7 +--R (- 150c d - 150c d )x + (- 75c d - 75c d)x - 15c d - 15c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (4d + 12c d + 12c d + 4c )x + (8c d + 16c d + 8c d)x +--R + +--R 2 4 4 2 6 +--R 4c d + 8c d + 4c +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 5 2 3 4 3 +--R (4d + 4c d )x + (12c d + 12c d )x + (4d + 16c d + 12c d)x +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R (12c d + 16c d + 4c )x + (12c d + 12c d)x + 4c d + 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 6 2 4 4 2 4 +--R (8d + 8c d )x + (32c d + 32c d )x + (8d + 56c d + 48c d )x +--R + +--R 5 3 3 5 3 2 4 4 2 6 2 +--R (32c d + 64c d + 32c d)x + (48c d + 56c d + 8c )x +--R + +--R 3 3 5 4 2 6 +--R (32c d + 32c d)x + 8c d + 8c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 4 2 +--R (2d + 4c d + 2c d )x + (4c d + 8c d + 4c d)x + 2c d + 4c d +--R + +--R 6 +--R 2c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (4d + 8c d + 4c d )x + (12c d + 24c d + 12c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (12c d + 24c d + 12c d)x + 4c d + 8c d + 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (8d + 8c d )x + (32c d + 32c d )x + (48c d + 48c d )x +--R + +--R 3 3 5 4 2 6 +--R (32c d + 32c d)x + 8c d + 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 5 6 3 4 4 2 5 4 3 3 +--R (12d + 12c d )x + (60c d + 60c d )x + (120c d + 120c d )x +--R + +--R 3 4 5 2 2 4 3 6 5 2 7 +--R (120c d + 120c d )x + (60c d + 60c d)x + 12c d + 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 6d x + 36c d x + 90c d x + 120c d x + 90c d x + 36c d x +--R + +--R 6 +--R 6c +--R * +--R +-------+2 +--R 4| 2 2 +--R \|d + c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 2d - 2c d )x + (- 6c d - 6c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 8c d - 6c d)x + (- 6c d - 8c d - 2c )x +--R + +--R 2 3 4 3 2 5 +--R (- 6c d - 6c d)x - 2c d - 2c +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 +--R (- 4d - 4c d )x + (- 16c d - 16c d )x +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (- 4d - 28c d - 24c d )x + (- 16c d - 32c d - 16c d)x +--R + +--R 2 4 4 2 6 2 3 3 5 4 2 6 +--R (- 24c d - 28c d - 4c )x + (- 16c d - 16c d)x - 4c d - 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R + +--R 5 7 4 6 5 2 3 5 4 3 2 4 +--R - 2d x - 10c d x + (- 2d - 20c d )x + (- 10c d - 20c d )x +--R + +--R 2 3 4 3 3 2 5 2 4 5 +--R (- 20c d - 10c d)x + (- 20c d - 2c )x - 10c d x - 2c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- d - 2c d - c d )x + (- 3c d - 6c d - 3c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 3c d - 6c d - 3c d)x - c d - 2c d - c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (- 4d - 4c d )x + (- 16c d - 16c d )x + (- 24c d - 24c d )x +--R + +--R 3 3 5 4 2 6 +--R (- 16c d - 16c d)x - 4c d - 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 5 6 3 4 4 2 5 4 3 3 +--R (- 6d - 6c d )x + (- 30c d - 30c d )x + (- 60c d - 60c d )x +--R + +--R 3 4 5 2 2 4 3 6 5 2 7 +--R (- 60c d - 60c d )x + (- 30c d - 30c d)x - 6c d - 6c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- 4d x - 24c d x - 60c d x - 80c d x - 60c d x - 24c d x - 4c ) +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - d x - 7c d x - 21c d x - 35c d x - 35c d x - 21c d x - 7c d x - c +--R / +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +-------+ +--R ((d + 3c d + 3c d + c )x + d + 3c d + 3c d + c )\|d x + c +--R * +--R +--+ 12 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R ((4d + 12c d + 12c d + 4c )x + 4d + 12c d + 12c d + 4c ) +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 6d - 12c d - 6c d)x + (- 6c d - 12c d - 6c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 6d - 12c d - 6c d)x - 6c d - 12c d - 6c +--R * +--R +-------+2 +--R 4| 2 2 +-------+ +--R \|d + c \|d x + c +--R * +--R +--+ 10 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R ((6d + 18c d + 18c d + 6c )x + 6d + 18c d + 18c d + 6c ) +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 12d - 24c d - 12c d)x + (- 12c d - 24c d - 12c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 12d - 24c d - 12c d)x - 12c d - 24c d - 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (15d + 30c d + 15c d )x + (30c d + 60c d + 30c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (15d + 45c d + 45c d + 15c )x + (30c d + 60c d + 30c d)x +--R + +--R 2 4 4 2 6 +--R 15c d + 30c d + 15c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R ((4d + 12c d + 12c d + 4c )x + 4d + 12c d + 12c d + 4c ) +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 8d - 16c d - 8c d)x + (- 8c d - 16c d - 8c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 8d - 16c d - 8c d)x - 8c d - 16c d - 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (8d + 16c d + 8c d )x + (16c d + 32c d + 16c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (8d + 24c d + 24c d + 8c )x + (16c d + 32c d + 16c d)x +--R + +--R 2 4 4 2 6 +--R 8c d + 16c d + 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 20d - 20c d )x + (- 60c d - 60c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 20d - 80c d - 60c d)x + (- 60c d - 80c d - 20c )x +--R + +--R 2 3 4 3 2 5 +--R (- 60c d - 60c d)x - 20c d - 20c +--R * +--R +-------+2 +--R 4| 2 2 +-------+ +--R \|d + c \|d x + c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +-------+ +--R ((d + 3c d + 3c d + c )x + d + 3c d + 3c d + c )\|d x + c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 4d - 8c d - 4c d)x + (- 4c d - 8c d - 4c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 4d - 8c d - 4c d)x - 4c d - 8c d - 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (4d + 12c d + 12c d + 4c )x + (8c d + 16c d + 8c d)x +--R + +--R 2 4 4 2 6 +--R 4c d + 8c d + 4c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 5 2 3 4 3 +--R (8d + 8c d )x + (24c d + 24c d )x + (8d + 32c d + 24c d)x +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R (24c d + 32c d + 8c )x + (24c d + 24c d)x + 8c d + 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 +--R (15d + 15c d )x + (60c d + 60c d )x +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (15d + 105c d + 90c d )x + (60c d + 120c d + 60c d)x +--R + +--R 2 4 4 2 6 2 3 3 5 4 2 6 +--R (90c d + 105c d + 15c )x + (60c d + 60c d)x + 15c d + 15c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 4c d - 2c d)x + (- 2c d - 4c d - 2c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 2d - 4c d - 2c d)x - 2c d - 4c d - 2c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (- 4d - 8c d - 4c d )x + (- 8c d - 16c d - 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (- 4d - 12c d - 12c d - 4c )x + (- 8c d - 16c d - 8c d)x +--R + +--R 2 4 4 2 6 +--R - 4c d - 8c d - 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 8d - 8c d )x + (- 24c d - 24c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 8d - 32c d - 24c d)x + (- 24c d - 32c d - 8c )x +--R + +--R 2 3 4 3 2 5 +--R (- 24c d - 24c d)x - 8c d - 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 +--R (- 12d - 12c d )x + (- 48c d - 48c d )x +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (- 12d - 84c d - 72c d )x + (- 48c d - 96c d - 48c d)x +--R + +--R 2 4 4 2 6 2 3 3 5 4 2 6 +--R (- 72c d - 84c d - 12c )x + (- 48c d - 48c d)x - 12c d - 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 7 4 6 5 2 3 5 4 3 2 4 +--R - 6d x - 30c d x + (- 6d - 60c d )x + (- 30c d - 60c d )x +--R + +--R 2 3 4 3 3 2 5 2 4 5 +--R (- 60c d - 30c d)x + (- 60c d - 6c )x - 30c d x - 6c +--R * +--R +-------+2 +--R 4| 2 2 +-------+ +--R \|d + c \|d x + c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (d + 2c d + c d )x + (2c d + 4c d + 2c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 2 4 4 2 +--R (d + 3c d + 3c d + c )x + (2c d + 4c d + 2c d)x + c d + 2c d +--R + +--R 6 +--R c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 5 2 3 4 3 +--R (4d + 4c d )x + (12c d + 12c d )x + (4d + 16c d + 12c d)x +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R (12c d + 16c d + 4c )x + (12c d + 12c d)x + 4c d + 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 6 2 4 4 2 4 +--R (6d + 6c d )x + (24c d + 24c d )x + (6d + 42c d + 36c d )x +--R + +--R 5 3 3 5 3 2 4 4 2 6 2 +--R (24c d + 48c d + 24c d)x + (36c d + 42c d + 6c )x +--R + +--R 3 3 5 4 2 6 +--R (24c d + 24c d)x + 6c d + 6c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 7 4 6 5 2 3 5 4 3 2 4 +--R 4d x + 20c d x + (4d + 40c d )x + (20c d + 40c d )x +--R + +--R 2 3 4 3 3 2 5 2 4 5 +--R (40c d + 20c d)x + (40c d + 4c )x + 20c d x + 4c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 8 5 7 6 2 4 6 5 3 3 5 +--R d x + 6c d x + (d + 15c d )x + (6c d + 20c d )x +--R + +--R 2 4 4 2 4 3 3 5 3 4 2 6 2 5 6 +--R (15c d + 15c d )x + (20c d + 6c d)x + (15c d + c )x + 6c d x + c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 325 + +--S 326 of 512 +t0165:= (c+d*x)^(1/2)/(a+b*x^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (203) ---------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 512 +r0165:= -(-(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2)*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2))+_ + (b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2)))/_ + a^(1/2)/(-b)^(1/2)/b^(1/2) +--R +--R +--R (204) +--R +-------------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R \|- d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-----------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R - \|d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +---+ +-+ +-+ +--R \|- b \|a \|b +--R Type: Expression(Integer) +--E 327 + +--S 328 of 512 +a0165:= integrate(t0165,x) +--R +--R +--R (205) +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 512 +m0165:= a0165-r0165 +--R +--R +--R (206) +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +-------------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R - 2\|- d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-----------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R 2\|d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +---+ +-+ +-+ +--R 2\|- b \|a \|b +--R Type: Expression(Integer) +--E 329 + +--S 330 of 512 +d0165:= D(m0165,x) +--R +--R +--R (207) 0 +--R Type: Expression(Integer) +--E 330 + +--S 331 of 512 +t0166:= (c+d*x)^(1/2)/(a-b*x^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (208) - ---------- +--R 2 +--R b x - a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 512 +r0166:= -(b*c-a^(1/2)*b^(1/2)*d)^(1/2)*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c-a^(1/2)*b^(1/2)*d)^(1/2))/a^(1/2)/b+_ + (b*c+a^(1/2)*b^(1/2)*d)^(1/2)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+a^(1/2)*b^(1/2)*d)^(1/2))/a^(1/2)/b +--R +--R +--R (209) +--R +-----------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R - \|- d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +---------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R \|d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 512 +a0166:= integrate(t0166,x) +--R +--R +--R (210) +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 2 | | 2 +--R | | d | | d +--R |2a b |----- + c +-----+ |2a b |----- + c +--R | | 3 | 2 | | 3 +--R | \|4a b 2 | d | \|4a b +-------+ +--R |---------------- log(2a b |----- |---------------- + d\|d x + c ) +--R \| a b | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(- 2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 2 | | 2 +--R | | d | | d +--R |2a b |----- + c +-----+ |2a b |----- + c +--R | | 3 | 2 | | 3 +--R | \|4a b 2 | d | \|4a b +-------+ +--R - |---------------- log(- 2a b |----- |---------------- + d\|d x + c ) +--R \| a b | 3 \| a b +--R \|4a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 512 +m0166:= a0166-r0166 +--R +--R +--R (211) +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |---------------- +--R \| a b +--R * +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(2a b |----- |---------------- + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(- 2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R - +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |---------------- +--R \| a b +--R * +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(- 2a b |----- |---------------- + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +-----------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R 2\|- d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +---------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R - 2\|d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-+ +--R 2b\|a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 512 +d0166:= D(m0166,x) +--R +--R +--R (212) 0 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 512 +t0167:= 1/(c+d*x)^(1/2)/(a+b*x^2) +--R +--R +--R 1 +--R (213) -------------------- +--R 2 +-------+ +--R (b x + a)\|d x + c +--R Type: Expression(Integer) +--E 336 + +--S 337 of 512 +r0167:= b^(1/2)*atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2))/_ + a^(1/2)/(-b)^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2)-b^(1/2)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2))/_ + a^(1/2)/(-b)^(1/2)/(b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2) +--R +--R +--R (214) +--R +-----------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R \|b \|d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R - \|b \|- d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R +---+ +-+ | +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression(Integer) +--E 337 + +--S 338 of 512 +a0167:= integrate(t0167,x) +--R +--R +--R (215) +--R - +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (2a b c d + 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d 2 +--R ((2a b c d + 2a b c ) |- ----------------------------- + a d ) +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R - +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 512 +m0167:= a0167-r0167 +--R +--R +--R (216) +--R - +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (2a b c d + 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d 2 +--R ((2a b c d + 2a b c ) |- ----------------------------- + a d ) +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R - +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R - 2\|b \|d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R 2\|b \|- d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R +---+ +-+ | +---+ +-+ | +---+ +-+ +--R 2\|- b \|a \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression(Integer) +--E 339 + +--S 340 of 512 +d0167:= D(m0167,x) +--R +--R +--R (217) 0 +--R Type: Expression(Integer) +--E 340 + +--S 341 of 512 +t0168:= (c+d*x)^(3/2)/(a-b*x^2) +--R +--R +--R +-------+ +--R (- d x - c)\|d x + c +--R (218) --------------------- +--R 2 +--R b x - a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 512 +r0168:= -2*d*(c+d*x)^(1/2)/b+(2*b^(1/2)*c*d-(b*c^2+a*d^2)/a^(1/2))*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*b^(1/2)*d)^(1/2))/_ + b/(b*c-a^(1/2)*b^(1/2)*d)^(1/2)+(2*b^(1/2)*c*d+(b*c^2+a*d^2)/_ + a^(1/2))*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c+a^(1/2)*b^(1/2)*d)^(1/2))/b/(b*c+a^(1/2)*b^(1/2)*d)^(1/2) +--R +--R +--R (219) +--R +---------------+ +-+ +-------+ +--R +-+ +-+ 2 2 | +-+ +-+ \|b \|d x + c +--R (2c d\|a \|b - a d - b c )\|d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ +-+ 2 2 | +-+ +-+ \|b \|d x + c +--R (2c d\|a \|b + a d + b c )\|- d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R + +--R +-----------------+ +---------------+ +--R +-+ +-------+ | +-+ +-+ | +-+ +-+ +--R - 2d\|a \|d x + c \|- d\|a \|b + b c \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression(Integer) +--E 342 + +--S 343 of 512 +a0168:= integrate(t0168,x) +--R +--R +--R (220) +--R - +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R - +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-------+ +--R - 4d\|d x + c +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 512 +m0168:= a0168-r0168 +--R +--R +--R (221) +--R - +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R +-+ | \| 4a b +--R b\|a |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R +-----------------+ +---------------+ +--R | +-+ +-+ | +-+ +-+ +--R \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R - +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R +-+ | \| 4a b +--R b\|a |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R +-----------------+ +---------------+ +--R | +-+ +-+ | +-+ +-+ +--R \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +---------------+ +--R +-+ +-+ 2 2 | +-+ +-+ +--R (- 4c d\|a \|b + 2a d + 2b c )\|d\|a \|b + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +--R +-+ +-+ 2 2 | +-+ +-+ +--R (- 4c d\|a \|b - 2a d - 2b c )\|- d\|a \|b + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R 2b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression(Integer) +--E 344 + +--S 345 of 512 +d0168:= D(m0168,x) +--R +--R +--R (222) 0 +--R Type: Expression(Integer) +--E 345 + +--S 346 of 512 +t0169:= 1/(c+d*x)^(3/2)/(a+b*x^2) +--R +--R +--R 1 +--R (223) ----------------------------------------- +--R 3 2 +-------+ +--R (b d x + b c x + a d x + a c)\|d x + c +--R Type: Expression(Integer) +--E 346 + +--S 347 of 512 +r0169:= -2*d/(b*c^2+a*d^2)/(c+d*x)^(1/2)+((-b)^(3/2)*c/a^(1/2)+b*d)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2))/_ + b^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2)/(b*c^2+a*d^2)-_ + ((-b)^(3/2)*c/a^(1/2)-b*d)*atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+_ + a^(1/2)*(-b)^(1/2)*d)^(1/2))/b^(1/2)/(b*c+a^(1/2)*_ + (-b)^(1/2)*d)^(1/2)/(b*c^2+a*d^2) +--R +--R +--R (224) +--R +-----------------+ +--R +-+ +---+ +-------+ | +---+ +-+ +--R (b d\|a - b c\|- b )\|d x + c \|d\|- b \|a + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +--R +-+ +---+ +-------+ | +---+ +-+ +--R (b d\|a + b c\|- b )\|d x + c \|- d\|- b \|a + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R + +--R +-------------------+ +-----------------+ +--R +-+ +-+ | +---+ +-+ | +---+ +-+ +--R - 2d\|a \|b \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R 2 2 +-+ +-+ +-------+ | +---+ +-+ | +---+ +-+ +--R (a d + b c )\|a \|b \|d x + c \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression(Integer) +--E 347 + +--S 348 of 512 +a0169:= integrate(t0169,x) +--R +--R +--R (225) +--R 2 2 +-------+ +--R (- a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (- a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R - 4d +--R / +--R 2 2 +-------+ +--R (2a d + 2b c )\|d x + c +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 512 +m0169:= a0169-r0169 +--R +--R +--R (226) +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (- a d - b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (a d + b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (- a d - b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (a d + b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-----------------+ +--R +-+ +---+ | +---+ +-+ +--R (- 2b d\|a + 2b c\|- b )\|d\|- b \|a + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +-+ +-------+ +--R +-+ +---+ | +---+ +-+ \|b \|d x + c +--R (- 2b d\|a - 2b c\|- b )\|- d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R 2 2 +-+ +-+ | +---+ +-+ | +---+ +-+ +--R (2a d + 2b c )\|a \|b \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression(Integer) +--E 349 + +--S 350 of 512 +d0169:= D(m0169,x) +--R +--R +--R (227) 0 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 512 +t0170:= 1/(c+d*x)^(3/2)/(a-b*x^2) +--R +--R +--R 1 +--R (228) - ----------------------------------------- +--R 3 2 +-------+ +--R (b d x + b c x - a d x - a c)\|d x + c +--R Type: Expression(Integer) +--E 351 + +--S 352 of 512 +r0170:= 2*d/(b*c^2-a*d^2)/(c+d*x)^(1/2)-b^(1/2)*(b^(1/2)*c/a^(1/2)+d)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*b^(1/2)*d)^(1/2))/_ + (b*c-a^(1/2)*b^(1/2)*d)^(1/2)/(b*c^2-a*d^2)+b^(1/2)*(b^(1/2)*c/_ + a^(1/2)-d)*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c+a^(1/2)*b^(1/2)*d)^(1/2))/(b*c+a^(1/2)*b^(1/2)*d)^(1/2)/_ + (b*c^2-a*d^2) +--R +--R +--R (229) +--R +---------------+ +-+ +-------+ +--R +-+ +-+ +-------+ | +-+ +-+ \|b \|d x + c +--R (d\|a \|b + b c)\|d x + c \|d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ +-+ +-------+ | +-+ +-+ \|b \|d x + c +--R (d\|a \|b - b c)\|d x + c \|- d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R + +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R - 2d\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R 2 2 +-+ +-------+ | +-+ +-+ | +-+ +-+ +--R (a d - b c )\|a \|d x + c \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression(Integer) +--E 352 + +--S 353 of 512 +a0170:= integrate(t0170,x) +--R +--R +--R (230) +--R 2 2 +-------+ +--R (a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (- a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (- a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R - 4d +--R / +--R 2 2 +-------+ +--R (2a d - 2b c )\|d x + c +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 512 +m0170:= a0170-r0170 +--R +--R +--R (231) +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (a d - b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (- a d + b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (a d - b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (- a d + b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +---------------+ +-+ +-------+ +--R +-+ +-+ | +-+ +-+ \|b \|d x + c +--R (- 2d\|a \|b - 2b c)\|d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ +-+ | +-+ +-+ \|b \|d x + c +--R (- 2d\|a \|b + 2b c)\|- d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R 2 2 +-+ | +-+ +-+ | +-+ +-+ +--R (2a d - 2b c )\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression(Integer) +--E 354 + +--S 355 of 512 +d0170:= D(m0170,x) +--R +--R +--R (232) 0 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 512 +t0171:= (d+e*x)^(1/2)/(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R \|e x + d +--R (233) -------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 512 +r0171:= 2^(1/2)*(e-(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atan(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)/(-2*c*d+_ + (b+(b^2-4*a*c)^(1/2))*e)^(1/2))/c^(1/2)/_ + (-2*c*d+(b+(b^2-4*a*c)^(1/2))*e)^(1/2)-2^(1/2)*_ + (e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*atanh(2^(1/2)*c^(1/2)*_ + (d+e*x)^(1/2)/(2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2))/_ + c^(1/2)/(2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2) +--R +--R +--R (234) +--R +-----------+ +--R +-+ | 2 +-+ +--R (- e\|2 \|- 4a c + b + (b e - 2c d)\|2 ) +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R (e\|2 \|- 4a c + b + (b e - 2c d)\|2 )\|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-+ | | 2 +--R \|- 4a c + b \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R Type: Expression(Integer) +--E 357 + +--S 358 of 512 +a0171:= integrate(t0171,x) +--R +--R +--R (235) +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 512 +m0171:= a0171-r0171 +--R +--R +--R (236) +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 ) +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (- 2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 ) +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-+ | | 2 +--R 2\|- 4a c + b \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R Type: Expression(Integer) +--E 359 + +--S 360 of 512 +d0171:= D(m0171,x) +--R +--R +--R (237) 0 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 512 +t0172:= 1/(d+e*x)^(3/2)/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (238) ------------------------------------------------------- +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 361 + +--S 362 of 512 +r0172:= -2*e/(c*d^2-b*d*e+a*e^2)/(d+e*x)^(1/2)-2^(1/2)*c^(1/2)*_ + (e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*atan(2^(1/2)*c^(1/2)*_ + (d+e*x)^(1/2)/(-2*c*d+(b+(b^2-4*a*c)^(1/2))*e)^(1/2))/_ + (-2*c*d+(b+(b^2-4*a*c)^(1/2))*e)^(1/2)/(c*d^2-b*d*e+a*e^2)+_ + 2^(1/2)*c^(1/2)*(e-(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)/_ + (2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2))/_ + (2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2)/(c*d^2-b*d*e+a*e^2) +--R +--R +--R (239) +--R +-----------+ +--R +-+ | 2 +-+ +-+ +-------+ +--R (e\|2 \|- 4a c + b + (b e - 2c d)\|2 )\|c \|e x + d +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-+ +-------+ +--R (- e\|2 \|- 4a c + b + (b e - 2c d)\|2 )\|c \|e x + d +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R + +--R - +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R 2e\|- 4a c + b \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +-----------+ +--R 2 2 | 2 +-------+ +--R (a e - b d e + c d )\|- 4a c + b \|e x + d +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R Type: Expression(Integer) +--E 362 + +--S 363 of 512 +a0172:= integrate(t0172,x) +--R +--R +--R (240) +--R 2 2 +-------+ +--R (- a e + b d e - c d )\|e x + d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (8a c - 6a b c + a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (- 16a b c + 16a b c - 3a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (16a c - 16a b c - 9a b c + 3a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (40a b c - 6a b c - b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (- 60a b c - 5a b c + 5b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (48a b c + 32a b c - 11b c )d e +--R + +--R 2 5 2 4 4 3 6 2 5 3 4 7 +--R (- 16a c - 48a b c + 13b c )d e + (32a b c - 8b c )d e +--R + +--R 6 2 5 8 +--R (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (4a b c - 5a b c + b )e + (- 8a c + 22a b c - 5b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (- 36a b c + 9b c )d e + (24a c - 6b c )d e +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (24a c + 18a b c - 6b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (- 24a b c + 6b c )d e + (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 5 3 2 2 2 4 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 3 4 4 2 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (80a c + 340a b c + 30a b c - 26a b c - b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R 2 2 +-------+ +--R (a e - b d e + c d )\|e x + d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (- 8a c + 2a b )e + (24a b c - 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (- 24a c - 18a b c + 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (48a b c - 4a b c - 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (- 24a c - 18a b c + 6b c)d e + (24a b c - 6b c )d e +--R + +--R 4 2 3 6 +--R (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 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15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R - 4e +--R / +--R 2 2 +-------+ +--R (2a e - 2b d e + 2c d )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 512 +m0172:= a0172-r0172 +--R +--R +--R (241) +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (- a e + b d e - 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9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (- 8a c + 6a b c - a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (16a b c - 16a b c + 3a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (- 16a c + 16a b c + 9a b c - 3a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (- 40a b c + 6a b c + b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (60a b c + 5a b c - 5b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (- 48a b c - 32a b c + 11b c )d e +--R + +--R 2 5 2 4 4 3 6 2 5 3 4 7 +--R (16a c + 48a b c - 13b c )d e + (- 32a b c + 8b c )d e +--R + +--R 6 2 5 8 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 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6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (- 24a c - 18a b c + 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (48a b c - 4a b c - 2b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (- 24a c - 18a b c + 6b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (24a b c - 6b c )d e + (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 5 3 2 2 2 4 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 3 4 4 2 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (80a c + 340a b c + 30a b c - 26a b c - b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (a e - b d e + c d )\|- 4a c + b \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (- 8a c + 6a b c - a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (16a b c - 16a b c + 3a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (- 16a c + 16a b c + 9a b c - 3a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (- 40a b c + 6a b c + b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (60a b c + 5a b c - 5b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (- 48a b c - 32a b c + 11b c )d e +--R + +--R 2 5 2 4 4 3 6 2 5 3 4 7 +--R (16a c + 48a b c - 13b c )d e + (- 32a b c + 8b c )d e +--R + +--R 6 2 5 8 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (- 4a b c + 5a b c - b )e + (8a c - 22a b c + 5b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (36a b c - 9b c )d e + (- 24a c + 6b c )d e +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (24a c + 18a b c - 6b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (- 24a b c + 6b c )d e + (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 5 3 2 2 2 4 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 3 4 4 2 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (80a c + 340a b c + 30a b c - 26a b c - b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-+ +--R (- 2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 )\|c +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-+ +--R (2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 )\|c +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R Type: Expression(Integer) +--E 364 + +--S 365 of 512 +d0172:= D(m0172,x) +--R +--R +--R (242) 0 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 512 +t0173:= 1/(-2+x)/(2+x)^(1/2) +--R +--R +--R 1 +--R (243) --------------- +--R +-----+ +--R (x - 2)\|x + 2 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 512 +r0173:= -atanh(1/2*(2+x)^(1/2)) +--R +--R +--R +-----+ +--R \|x + 2 +--R (244) - atanh(--------) +--R 2 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 512 +a0173:= integrate(t0173,x) +--R +--R +--R +-----+ +-----+ +--R - log(\|x + 2 + 2) + log(\|x + 2 - 2) +--R (245) --------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 512 +m0173:= a0173-r0173 +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x + 2 +--R - log(\|x + 2 + 2) + log(\|x + 2 - 2) + 2atanh(--------) +--R 2 +--R (246) ---------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 512 +d0173:= D(m0173,x) +--R +--R +--R (247) 0 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 512 +t0174:= 1/(1+x-(2+x)^(1/2)) +--R +--R +--R 1 +--R (248) - ---------------- +--R +-----+ +--R \|x + 2 - x - 1 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 512 +r0174:= 2/5*atanh(1/5*(1-2*(2+x)^(1/2))*5^(1/2))*5^(1/2)+log(-1-x+(2+x)^(1/2)) +--R +--R +--R +-+ +-----+ +-+ +--R +-----+ +-+ 2\|5 \|x + 2 - \|5 +--R 5log(\|x + 2 - x - 1) - 2\|5 atanh(--------------------) +--R 5 +--R (249) --------------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 512 +a0174:= integrate(t0174,x) +--R +--R +--R (250) +--R +-+ +-----+ +-+ +--R (2\|5 + 10)\|x + 2 + (- 2x - 7)\|5 - 5 +-+ +-----+ +--R log(-----------------------------------------) + \|5 log(- \|x + 2 + x + 1) +--R +-----+ +--R \|x + 2 - x - 1 +--R ---------------------------------------------------------------------------- +--R +-+ +--R \|5 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 512 +m0174:= a0174-r0174 +--R +--R +--R (251) +--R +-+ +-----+ +--R - \|5 log(\|x + 2 - x - 1) +--R + +--R +-+ +-----+ +-+ +--R (2\|5 + 10)\|x + 2 + (- 2x - 7)\|5 - 5 +--R log(-----------------------------------------) +--R +-----+ +--R \|x + 2 - x - 1 +--R + +--R +-+ +-----+ +-+ +--R +-+ +-----+ 2\|5 \|x + 2 - \|5 +--R \|5 log(- \|x + 2 + x + 1) + 2atanh(--------------------) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 512 +d0174:= D(m0174,x) +--R +--R +--R (252) 0 +--R Type: Expression(Integer) +--E 375 + +--S 376 of 512 +t0175:= 1/(x-(1+x)^(1/2)) +--R +--R +--R 1 +--R (253) - ------------ +--R +-----+ +--R \|x + 1 - x +--R Type: Expression(Integer) +--E 376 + +--S 377 of 512 +r0175:= 2/5*atanh(1/5*(1-2*(1+x)^(1/2))*5^(1/2))*5^(1/2)+log(-x+(1+x)^(1/2)) +--R +--R +--R +-+ +-----+ +-+ +--R +-----+ +-+ 2\|5 \|x + 1 - \|5 +--R 5log(\|x + 1 - x) - 2\|5 atanh(--------------------) +--R 5 +--R (254) ----------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 512 +a0175:= integrate(t0175,x) +--R +--R +--R (255) +--R +-+ +-----+ +-+ +--R (2\|5 + 10)\|x + 1 + (- 2x - 5)\|5 - 5 +-+ +-----+ +--R log(-----------------------------------------) + \|5 log(- \|x + 1 + x) +--R +-----+ +--R \|x + 1 - x +--R ------------------------------------------------------------------------ +--R +-+ +--R \|5 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 512 +m0175:= a0175-r0175 +--R +--R +--R (256) +--R +-+ +-----+ +-+ +--R +-+ +-----+ (2\|5 + 10)\|x + 1 + (- 2x - 5)\|5 - 5 +--R - \|5 log(\|x + 1 - x) + log(-----------------------------------------) +--R +-----+ +--R \|x + 1 - x +--R + +--R +-+ +-----+ +-+ +--R +-+ +-----+ 2\|5 \|x + 1 - \|5 +--R \|5 log(- \|x + 1 + x) + 2atanh(--------------------) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 512 +d0175:= D(m0175,x) +--R +--R +--R (257) 0 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 512 +t0176:= 1/(x-(2+x)^(1/2)) +--R +--R +--R 1 +--R (258) - ------------ +--R +-----+ +--R \|x + 2 - x +--R Type: Expression(Integer) +--E 381 + +--S 382 of 512 +r0176:= 4/3*log(2-(2+x)^(1/2))+2/3*log(1+(2+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R 2log(\|x + 2 + 1) + 4log(- \|x + 2 + 2) +--R (259) ----------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 512 +a0176:= integrate(t0176,x) +--R +--R +--R +-----+ +-----+ +--R 2log(\|x + 2 + 1) + 4log(\|x + 2 - 2) +--R (260) --------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 512 +m0176:= a0176-r0176 +--R +--R +--R +-----+ +-----+ +--R 4log(\|x + 2 - 2) - 4log(- \|x + 2 + 2) +--R (261) ----------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 512 +d0176:= D(m0176,x) +--R +--R +--R (262) 0 +--R Type: Expression(Integer) +--E 385 + +--S 386 of 512 +t0177:= 1/(x-(1-x)^(1/2)) +--R +--R +--R 1 +--R (263) - -------------- +--R +-------+ +--R \|- x + 1 - x +--R Type: Expression(Integer) +--E 386 + +--S 387 of 512 +r0177:= 2/5*atanh(1/5*(1+2*(1-x)^(1/2))*5^(1/2))*5^(1/2)+log(x-(1-x)^(1/2)) +--R +--R +--R +-+ +-------+ +-+ +--R +-------+ +-+ 2\|5 \|- x + 1 + \|5 +--R 5log(- \|- x + 1 + x) + 2\|5 atanh(----------------------) +--R 5 +--R (264) ----------------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 512 +a0177:= integrate(t0177,x) +--R +--R +--R (265) +--R +-+ +-------+ +-+ +--R +-+ +-------+ (2\|5 + 10)\|- x + 1 + (- 2x + 5)\|5 + 5 +--R \|5 log(\|- x + 1 - x) + log(-------------------------------------------) +--R +-------+ +--R \|- x + 1 - x +--R -------------------------------------------------------------------------- +--R +-+ +--R \|5 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 512 +m0177:= a0177-r0177 +--R +--R +--R (266) +--R +-+ +-------+ +--R \|5 log(\|- x + 1 - x) +--R + +--R +-+ +-------+ +-+ +--R (2\|5 + 10)\|- x + 1 + (- 2x + 5)\|5 + 5 +--R log(-------------------------------------------) +--R +-------+ +--R \|- x + 1 - x +--R + +--R +-+ +-------+ +-+ +--R +-+ +-------+ 2\|5 \|- x + 1 + \|5 +--R - \|5 log(- \|- x + 1 + x) - 2atanh(----------------------) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 512 +d0177:= D(m0177,x) +--R +--R +--R (267) 0 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 512 +t0178:= 1/(4+(4-x)^(1/2)-x) +--R +--R +--R 1 +--R (268) ------------------ +--R +-------+ +--R \|- x + 4 - x + 4 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 512 +r0178:= -2*log(1+(4-x)^(1/2)) +--R +--R +--R +-------+ +--R (269) - 2log(\|- x + 4 + 1) +--R Type: Expression(Integer) +--E 392 + +--S 393 of 512 +a0178:= integrate(t0178,x) +--R +--R +--R +-------+ +--R (270) - 2log(\|- x + 4 + 1) +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 512 +m0178:= a0178-r0178 +--R +--R +--R (271) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 512 +d0178:= D(m0178,x) +--R +--R +--R (272) 0 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 512 +t0179:= ((1-x)^(1/2)+(1+x)^(1/2))*(1-x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (273) \|- x + 1 \|x + 1 - x + 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 512 +r0179:= x-1/2*x^2+1/2*x*(1-x^2)^(1/2)+1/2*asin(x) +--R +--R +--R +--------+ +--R | 2 2 +--R x\|- x + 1 + asin(x) - x + 2x +--R (274) -------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 512 +--a0179:= integrate(t0179,x) +--E 398 + +--S 399 of 512 +--m0179:= a0179-r0179 +--E 399 + +--S 400 of 512 +--d0179:= D(m0179,x) +--E 400 + +--S 401 of 512 +t0180:= ((1-x)^(1/2)+(1+x)^(1/2))^2 +--R +--R +--R +-------+ +-----+ +--R (275) 2\|- x + 1 \|x + 1 + 2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 512 +r0180:= 2*x+x*(1-x^2)^(1/2)+asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (276) x\|- x + 1 + asin(x) + 2x +--R Type: Expression(Integer) +--E 402 + +--S 403 of 512 +--a0180:= integrate(t0180,x) +--E 403 + +--S 404 of 512 +--m0180:= a0180-r0180 +--E 404 + +--S 405 of 512 +--d0180:= D(m0180,x) +--E 405 + +--S 406 of 512 +t0181:= (-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-------+ +-----+ +--R (277) - 2\|- x + 1 \|x + 1 - 2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 512 +r0181:= -2*x-x*(1-x^2)^(1/2)-asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (278) - x\|- x + 1 - asin(x) - 2x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 512 +--a0181:= integrate(t0181,x) +--E 408 + +--S 409 of 512 +--m0181:= a0181-r0181 +--E 409 + +--S 410 of 512 +--d0181:= D(m0181,x) +--E 410 + +--S 411 of 512 +t0182:= ((1-x)^(1/2)+(1+x)^(1/2))^2/x +--R +--R +--R +-------+ +-----+ +--R 2\|- x + 1 \|x + 1 + 2 +--R (279) ----------------------- +--R x +--R Type: Expression(Integer) +--E 411 + +--S 412 of 512 +r0182:= 2*(1-x^2)^(1/2)-2*atanh((1-x^2)^(1/2))+2*log(x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R (280) - 2atanh(\|- x + 1 ) + 2\|- x + 1 + 2log(x) +--R Type: Expression(Integer) +--E 412 + + +-- +-------+ +-----+ +-- - \|- x + 1 \|x + 1 - 1 +-------+ +-----+ +-- (281) - 2log(------------------------) + 2\|- x + 1 \|x + 1 +-- 2 +-- x +-- Type: Union(Expression(Integer),...) + +--S 413 of 512 ok to fail due to sign changes (see above) +a0182:= integrate(t0182,x) +--R +--R +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 + 1 +-------+ +-----+ +--R (281) - 2log(----------------------) + 2\|- x + 1 \|x + 1 +--R 2 +--R x +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 512 ok to fail due to sign changes (see above) +m0182:= a0182-r0182 +--R +--R +--R (282) +--R +-------+ +-----+ +--------+ +--R \|- x + 1 \|x + 1 + 1 | 2 +-------+ +-----+ +--R - 2log(----------------------) + 2atanh(\|- x + 1 ) + 2\|- x + 1 \|x + 1 +--R 2 +--R x +--R + +--R +--------+ +--R | 2 +--R - 2\|- x + 1 - 2log(x) +--R Type: Expression(Integer) +--E 414 + +--S 415 of 512 +d0182:= D(m0182,x) +--R +--R +--R (283) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-----+ 2 | 2 2 +--R (2\|- x + 1 + 2x - 2)\|- x + 1 \|x + 1 + (- 2x + 2)\|- x + 1 + 2x - 2 +--R ----------------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R x\|- x + 1 \|- x + 1 \|x + 1 + x\|- x + 1 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 512 +t0183:= (-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2))/x +--R +--R +--R +-------+ +-----+ +--R - 2\|- x + 1 \|x + 1 - 2 +--R (284) ------------------------- +--R x +--R Type: Expression(Integer) +--E 416 + +--S 417 of 512 +r0183:= -2*(1-x^2)^(1/2)+2*atanh((1-x^2)^(1/2))-2*log(x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R (285) 2atanh(\|- x + 1 ) - 2\|- x + 1 - 2log(x) +--R Type: Expression(Integer) +--E 417 + +--S 418 of 512 +a0183:= integrate(t0183,x) +--R +--R +--R +-------+ +-----+ +-------+ +-----+ +--R (286) - 2log(\|- x + 1 \|x + 1 - 1) - 2\|- x + 1 \|x + 1 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 512 +m0183:= a0183-r0183 +--R +--R +--R (287) +--R +--------+ +--R +-------+ +-----+ | 2 +-------+ +-----+ +--R - 2log(\|- x + 1 \|x + 1 - 1) - 2atanh(\|- x + 1 ) - 2\|- x + 1 \|x + 1 +--R + +--R +--------+ +--R | 2 +--R 2\|- x + 1 + 2log(x) +--R Type: Expression(Integer) +--E 419 + +--S 420 of 512 +d0183:= D(m0183,x) +--R +--R +--R (288) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-----+ 2 | 2 2 +--R (2\|- x + 1 - 2x + 2)\|- x + 1 \|x + 1 + (2x - 2)\|- x + 1 + 2x - 2 +--R --------------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R x\|- x + 1 \|- x + 1 \|x + 1 - x\|- x + 1 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 512 +t0184:= ((1-x)^(1/2)+(1+x)^(1/2))/(-(1-x)^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-----+ +-------+ +--R \|x + 1 + \|- x + 1 +--R (289) --------------------- +--R +-----+ +-------+ +--R \|x + 1 - \|- x + 1 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 512 +r0184:= (1-x^2)^(1/2)-atanh((1-x^2)^(1/2))+log(x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R (290) - atanh(\|- x + 1 ) + \|- x + 1 + log(x) +--R Type: Expression(Integer) +--E 422 + + + +-- +-------+ +-----+ +-- - \|- x + 1 \|x + 1 - 1 +-------+ +-----+ +-- (291) - log(------------------------) + \|- x + 1 \|x + 1 +-- 2 +-- x +-- Type: Union(Expression(Integer),...) + +--S 423 of 512 ok to fail. seems there are 2 answers (see above) +a0184:= integrate(t0184,x) +--R +--R +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 + 1 +-------+ +-----+ +--R (291) - log(----------------------) + \|- x + 1 \|x + 1 +--R 2 +--R x +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 512 ok to fail. due to 2 answers (see above) +m0184:= a0184-r0184 +--R +--R +--R (292) +--R +-------+ +-----+ +--------+ +--R \|- x + 1 \|x + 1 + 1 | 2 +-------+ +-----+ +--R - log(----------------------) + atanh(\|- x + 1 ) + \|- x + 1 \|x + 1 +--R 2 +--R x +--R + +--R +--------+ +--R | 2 +--R - \|- x + 1 - log(x) +--R Type: Expression(Integer) +--E 424 + +--S 425 of 512 +d0184:= D(m0184,x) +--R +--R +--R (293) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-----+ 2 | 2 2 +--R (\|- x + 1 + x - 1)\|- x + 1 \|x + 1 + (- x + 1)\|- x + 1 + x - 1 +--R ------------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R x\|- x + 1 \|- x + 1 \|x + 1 + x\|- x + 1 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 512 +t0185:= (-(-1+x)^(1/2)+(1+x)^(1/2))/((-1+x)^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R \|x + 1 - \|x - 1 +--R (294) ------------------- +--R +-----+ +-----+ +--R \|x + 1 + \|x - 1 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 512 +r0185:= 1/2*x^2-1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/2*acosh(x) +--R +--R +--R +-----+ +-----+ 2 +--R - x\|x - 1 \|x + 1 + acosh(x) + x +--R (295) ----------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 427 + + + +-- +-----+ +-----+ +-----+ +-----+ 2 +-- - log(- \|x - 1 \|x + 1 + x) - x\|x - 1 \|x + 1 + x +-- (296) ------------------------------------------------------ +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 428 of 512 ok to fail. seems there are 2 answers (see above) +a0185:= integrate(t0185,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ 2 +--R - log(\|x - 1 \|x + 1 - x) - x\|x - 1 \|x + 1 + x +--R (296) ---------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 512 ok to fail. due to 2 answers (see above) +m0185:= a0185-r0185 +--R +--R +--R +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 - x) - acosh(x) +--R (297) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 512 +d0185:= D(m0185,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (298) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R 2\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 512 +t0186:= (2*(3-x)^(1/2)+3/(1+x)^(1/2))^2/x +--R +--R +--R +-------+ +-----+ 2 +--R 12\|- x + 3 \|x + 1 - 4x + 8x + 21 +--R (299) ------------------------------------ +--R 2 +--R x + x +--R Type: Expression(Integer) +--E 431 + +--S 432 of 512 +r0186:= -4*x-12*asin(-1/2+1/2*x)-24*3^(1/2)*_ + atanh(1/3*(3-x)^(1/2)*3^(1/2)/(1+x)^(1/2))+21*log(x)-9*log(1+x) +--R +--R +--R (300) +--R +-+ +-------+ +--R +-+ \|3 \|- x + 3 x - 1 +--R - 24\|3 atanh(--------------) - 9log(x + 1) + 21log(x) - 12asin(-----) - 4x +--R +-----+ 2 +--R 3\|x + 1 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 512 +--a0186:= integrate(t0186,x) +--E 433 + +--S 434 of 512 +--m0186:= a0186-r0186 +--E 434 + +--S 435 of 512 +--d0186:= D(m0186,x) +-- >> Error detected within library code: +-- integrate: +-- implementation incomplete (residue poly has multiple non-linear factors) +--E 435 + +--S 436 of 512 +t0187:= (1-x)^(1/2)/(1+x^(1/2)) +--R +--R +--R +-------+ +--R \|- x + 1 +--R (301) ---------- +--R +-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 512 +r0187:= -2*(1-x)^(1/2)+(1-x)^(1/2)*x^(1/2)-asin(x^(1/2)) +--R +--R +--R +-+ +-------+ +-+ +-------+ +--R (302) - asin(\|x ) + \|- x + 1 \|x - 2\|- x + 1 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 512 +--a0187:= integrate(t0187,x) +--E 438 + +--S 439 of 512 +--m0187:= a0187-r0187 +--E 439 + +--S 440 of 512 +--d0187:= D(m0187,x) +--E 440 + +--S 441 of 512 +t0188:= (1-x)^(1/2)/(1-x^(1/2)) +--R +--R +--R +-------+ +--R \|- x + 1 +--R (303) - ---------- +--R +-+ +--R \|x - 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 512 +r0188:= -2*(1-x)^(1/2)-(1-x)^(1/2)*x^(1/2)+asin(x^(1/2)) +--R +--R +--R +-+ +-------+ +-+ +-------+ +--R (304) asin(\|x ) - \|- x + 1 \|x - 2\|- x + 1 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 512 +--a0188:= integrate(t0188,x) +--E 443 + +--S 444 of 512 +--m0188:= a0188-r0188 +--E 444 + +--S 445 of 512 +--d0188:= D(m0188,x) +--E 445 + +--S 446 of 512 +t0189:= x/(1+x)/(2+x)^(1/2) +--R +--R +--R x +--R (305) --------------- +--R +-----+ +--R (x + 1)\|x + 2 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 512 +r0189:= 2*(2+x)^(1/2)+2*atanh((2+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R (306) 2atanh(\|x + 2 ) + 2\|x + 2 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 512 +a0189:= integrate(t0189,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R (307) log(\|x + 2 + 1) - log(\|x + 2 - 1) + 2\|x + 2 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 512 +m0189:= a0189-r0189 +--R +--R +--R +-----+ +-----+ +-----+ +--R (308) log(\|x + 2 + 1) - log(\|x + 2 - 1) - 2atanh(\|x + 2 ) +--R Type: Expression(Integer) +--E 449 + +--S 450 of 512 +d0189:= D(m0189,x) +--R +--R +--R (309) 0 +--R Type: Expression(Integer) +--E 450 + +--S 451 of 512 +t0190:= (1+x^2)^(1/2)/(-1+x^2) +--R +--R +--R +------+ +--R | 2 +--R \|x + 1 +--R (310) --------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 512 +r0190:= asinh(x)-2^(1/2)*atanh(2^(1/2)*x/(1+x^2)^(1/2)) +--R +--R +--R +-+ +--R +-+ x\|2 +--R (311) - \|2 atanh(---------) + asinh(x) +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 512 +a0190:= integrate(t0190,x) +--R +--R +--R (312) +--R +------+ +--R | 2 +--R - 2log(\|x + 1 - x) +--R + +--R +------+ +--R +-+ 3 | 2 2 +-+ 4 2 +--R +-+ (2x\|2 + 2x - 2x)\|x + 1 + (- 2x + 2)\|2 - 2x + x - 3 +--R \|2 log(-------------------------------------------------------------) +--R +------+ +--R 3 | 2 4 2 +--R (2x - 2x)\|x + 1 - 2x + x + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 512 +m0190:= a0190-r0190 +--R +--R +--R (313) +--R +------+ +--R | 2 +--R - 2log(\|x + 1 - x) +--R + +--R +------+ +--R +-+ 3 | 2 2 +-+ 4 2 +--R +-+ (2x\|2 + 2x - 2x)\|x + 1 + (- 2x + 2)\|2 - 2x + x - 3 +--R \|2 log(-------------------------------------------------------------) +--R +------+ +--R 3 | 2 4 2 +--R (2x - 2x)\|x + 1 - 2x + x + 1 +--R + +--R +-+ +--R +-+ x\|2 +--R 2\|2 atanh(---------) - 2asinh(x) +--R +------+ +--R | 2 +--R \|x + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 512 +d0190:= D(m0190,x) +--R +--R +--R (314) 0 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 512 +t0191:= (1+x)^(1/2)*(1+x^3)/(1+x^2) +--R +--R +--R 3 +-----+ +--R (x + 1)\|x + 1 +--R (315) ---------------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 512 +r0191:= -2*(1+x)^(1/2)-2/3*(1+x)^(3/2)+2/5*(1+x)^(5/2)-_ + atan(((2+2*2^(1/2))^(1/2)-2*(1+x)^(1/2))/_ + (-2+2*2^(1/2))^(1/2))/(2^(1/2)-1)^(1/2)+_ + atan(((2+2*2^(1/2))^(1/2)+2*(1+x)^(1/2))/_ + (-2+2*2^(1/2))^(1/2))/(2^(1/2)-1)^(1/2)-_ + 1/2*log(1+2^(1/2)+x-(2+2*2^(1/2))^(1/2)*(1+x)^(1/2))/_ + (1+2^(1/2))^(1/2)+1/2*log(1+2^(1/2)+x+_ + (2+2*2^(1/2))^(1/2)*(1+x)^(1/2))/(1+2^(1/2))^(1/2) +--R +--R +--R (316) +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R 15\|\|2 - 1 log(\|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R - 15\|\|2 - 1 log(- \|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 + 2\|x + 1 +--R 30\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 - 2\|x + 1 +--R - 30\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +--------+ +--------+ +--R 2 +-----+ | +-+ | +-+ +--R (12x + 4x - 68)\|x + 1 \|\|2 - 1 \|\|2 + 1 +--R / +--R +--------+ +--------+ +--R | +-+ | +-+ +--R 30\|\|2 - 1 \|\|2 + 1 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 512 +a0191:= integrate(t0191,x) +--R +--R +--R (317) +--R - +--R 4+-+ %pi +--R 15\|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (2\|8 sin(---) - 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi +--R 15\|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (- 2\|8 sin(---) + 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 30\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 - \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 30\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 + \|8 sin(---) - \|8 cos(---) +--R 8 8 +--R + +--R 2 +-----+ +--R (12x + 4x - 68)\|x + 1 +--R / +--R 30 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 512 +m0191:= a0191-r0191 +--R +--R +--R (318) +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R - \|\|2 - 1 log(\|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R \|8 cos(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (2\|8 sin(---) - 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R \|8 cos(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (- 2\|8 sin(---) + 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R \|\|2 - 1 log(- \|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 + 2\|x + 1 +--R - 2\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 - 2\|x + 1 +--R 2\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|8 sin(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R atan(---------------------------------------) +--R +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 - \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|8 sin(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R atan(---------------------------------------) +--R +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 + \|8 sin(---) - \|8 cos(---) +--R 8 8 +--R / +--R +--------+ +--------+ +--R | +-+ | +-+ +--R 2\|\|2 - 1 \|\|2 + 1 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 512 +d0191:= D(m0191,x) +--R +--R +--R (319) +--R +-+ %pi 12 +--R ((4x + 8)\|2 - 4x - 12)sin(---) +--R 8 +--R + +--R +-+ %pi %pi 11 +--R ((- 16x - 32)\|2 + 16x + 48)cos(---)sin(---) +--R 8 8 +--R + +--R +-+ %pi 2 +--R ((40x + 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 +--R ((- 4x - 12x - 8)\|2 + 4x + 16x + 12)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 3 +--R ((- 80x - 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi +--R ((16x + 48x + 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 4 +--R ((124x + 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 2 +--R ((- 52x - 156x - 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (12x + 48x + 60x + 24)\|2 - 12x - 60x - 84x - 36 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 5 +--R ((- 160x - 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 3 +--R ((96x + 288x + 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((- 80x - 320x - 400x - 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 6 +--R ((176x + 352)\|2 - 176x - 528)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 4 +--R ((- 136x - 408x - 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (224x + 896x + 1120x + 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 4x - 20x - 36x - 28x - 8)\|2 + 4x + 24x + 48x + 40x +--R + +--R 12 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 7 +--R ((- 160x - 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 5 +--R ((160x + 480x + 320)\|2 - 160x - 640x - 480)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 368x - 1472x - 1840x - 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (28x + 140x + 252x + 196x + 56)\|2 - 28x - 168x - 336x +--R + +--R - 280x - 84 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 8 +--R ((124x + 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 6 +--R ((- 136x - 408x - 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (552x + 2208x + 2760x + 1104)\|2 - 552x - 2760x - 3864x +--R + +--R - 1656 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 60x - 300x - 540x - 420x - 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 3 +--R (9x + 54x + 126x + 144x + 81x + 18)\|2 - 9x - 63x - 162x +--R + +--R 2 +--R - 198x - 117x - 27 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 9 +--R ((- 80x - 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 7 +--R ((96x + 288x + 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 368x - 1472x - 1840x - 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (136x + 680x + 1224x + 952x + 272)\|2 - 136x - 816x +--R + +--R 2 +--R - 1632x - 1360x - 408 +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 36x - 216x - 504x - 576x - 324x - 72)\|2 + 36x +--R + +--R 4 3 2 +--R 252x + 648x + 792x + 468x + 108 +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 10 +--R ((40x + 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 8 +--R ((- 52x - 156x - 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (224x + 896x + 1120x + 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 60x - 300x - 540x - 420x - 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (150x + 900x + 2100x + 2400x + 1350x + 300)\|2 - 150x +--R + +--R 4 3 2 +--R - 1050x - 2700x - 3300x - 1950x - 450 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 +--R (- x - 7x - 20x - 30x - 25x - 11x - 2)\|2 + x + 8x +--R + +--R 4 3 2 +--R 25x + 40x + 35x + 16x + 3 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 11 +--R ((- 16x - 32)\|2 + 16x + 48)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 9 +--R ((16x + 48x + 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((- 80x - 320x - 400x - 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (28x + 140x + 252x + 196x + 56)\|2 - 28x - 168x - 336x +--R + +--R - 280x - 84 +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 36x - 216x - 504x - 576x - 324x - 72)\|2 + 36x +--R + +--R 4 3 2 +--R 252x + 648x + 792x + 468x + 108 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (10x + 70x + 200x + 300x + 250x + 110x + 20)\|2 - 10x +--R + +--R 5 4 3 2 +--R - 80x - 250x - 400x - 350x - 160x - 30 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R +-+ %pi 12 +--R ((4x + 8)\|2 - 4x - 12)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 10 +--R ((- 4x - 12x - 8)\|2 + 4x + 16x + 12)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 8 +--R ((12x + 48x + 60x + 24)\|2 - 12x - 60x - 84x - 36)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 4x - 20x - 36x - 28x - 8)\|2 + 4x + 24x + 48x + 40x +--R + +--R 12 +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 3 +--R (9x + 54x + 126x + 144x + 81x + 18)\|2 - 9x - 63x - 162x +--R + +--R 2 +--R - 198x - 117x - 27 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 4 +--R (- x - 7x - 20x - 30x - 25x - 11x - 2)\|2 + x + 8x + 25x +--R + +--R 3 2 +--R 40x + 35x + 16x + 3 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 6 +--R (2x + 16x + 54x + 100x + 110x + 72x + 26x + 4)\|2 - 2x - 18x +--R + +--R 5 4 3 2 +--R - 66x - 130x - 150x - 102x - 38x - 6 +--R * +--R +--------+ +---------+ +--R +-----+ | +-+ | +-+ +--R \|x + 1 \|\|2 + 1 \|2\|2 + 2 +--R + +--R +-+ %pi 12 +--R ((- 4x - 8)\|2 - 4x - 12)sin(---) +--R 8 +--R + +--R +-+ %pi %pi 11 +--R ((16x + 32)\|2 + 16x + 48)cos(---)sin(---) +--R 8 8 +--R + +--R +-+ %pi 2 +--R ((- 40x - 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 +--R ((4x + 12x + 8)\|2 + 4x + 16x + 12)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 3 +--R ((80x + 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi +--R ((- 16x - 48x - 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 4 +--R ((- 124x - 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 2 +--R ((52x + 156x + 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 12x - 48x - 60x - 24)\|2 - 12x - 60x - 84x - 36 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 5 +--R ((160x + 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 3 +--R ((- 96x - 288x - 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((80x + 320x + 400x + 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 6 +--R ((- 176x - 352)\|2 - 176x - 528)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 4 +--R ((136x + 408x + 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 224x - 896x - 1120x - 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (4x + 20x + 36x + 28x + 8)\|2 + 4x + 24x + 48x + 40x +--R + +--R 12 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 7 +--R ((160x + 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 5 +--R ((- 160x - 480x - 320)\|2 - 160x - 640x - 480)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (368x + 1472x + 1840x + 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 28x - 140x - 252x - 196x - 56)\|2 - 28x - 168x +--R + +--R 2 +--R - 336x - 280x - 84 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 8 +--R ((- 124x - 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 6 +--R ((136x + 408x + 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 552x - 2208x - 2760x - 1104)\|2 - 552x - 2760x +--R + +--R - 3864x - 1656 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (60x + 300x + 540x + 420x + 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (- 9x - 54x - 126x - 144x - 81x - 18)\|2 - 9x - 63x +--R + +--R 3 2 +--R - 162x - 198x - 117x - 27 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 9 +--R ((80x + 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 7 +--R ((- 96x - 288x - 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (368x + 1472x + 1840x + 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 136x - 680x - 1224x - 952x - 272)\|2 - 136x - 816x +--R + +--R 2 +--R - 1632x - 1360x - 408 +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (36x + 216x + 504x + 576x + 324x + 72)\|2 + 36x + 252x +--R + +--R 3 2 +--R 648x + 792x + 468x + 108 +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 10 +--R ((- 40x - 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 8 +--R ((52x + 156x + 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 224x - 896x - 1120x - 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (60x + 300x + 540x + 420x + 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 150x - 900x - 2100x - 2400x - 1350x - 300)\|2 - 150x +--R + +--R 4 3 2 +--R - 1050x - 2700x - 3300x - 1950x - 450 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 +--R (x + 7x + 20x + 30x + 25x + 11x + 2)\|2 + x + 8x +--R + +--R 4 3 2 +--R 25x + 40x + 35x + 16x + 3 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 11 +--R ((16x + 32)\|2 + 16x + 48)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 9 +--R ((- 16x - 48x - 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((80x + 320x + 400x + 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 28x - 140x - 252x - 196x - 56)\|2 - 28x - 168x +--R + +--R 2 +--R - 336x - 280x - 84 +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (36x + 216x + 504x + 576x + 324x + 72)\|2 + 36x + 252x +--R + +--R 3 2 +--R 648x + 792x + 468x + 108 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ +--R (- 10x - 70x - 200x - 300x - 250x - 110x - 20)\|2 +--R + +--R 6 5 4 3 2 +--R - 10x - 80x - 250x - 400x - 350x - 160x - 30 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R +-+ %pi 12 +--R ((- 4x - 8)\|2 - 4x - 12)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 10 +--R ((4x + 12x + 8)\|2 + 4x + 16x + 12)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 8 +--R ((- 12x - 48x - 60x - 24)\|2 - 12x - 60x - 84x - 36)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R ((4x + 20x + 36x + 28x + 8)\|2 + 4x + 24x + 48x + 40x + 12) +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (- 9x - 54x - 126x - 144x - 81x - 18)\|2 - 9x - 63x +--R + +--R 3 2 +--R - 162x - 198x - 117x - 27 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 4 +--R (x + 7x + 20x + 30x + 25x + 11x + 2)\|2 + x + 8x + 25x +--R + +--R 3 2 +--R 40x + 35x + 16x + 3 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 +--R (- 2x - 16x - 54x - 100x - 110x - 72x - 26x - 4)\|2 - 2x +--R + +--R 6 5 4 3 2 +--R - 18x - 66x - 130x - 150x - 102x - 38x - 6 +--R * +--R +--------+ +---------+ +--R +-----+ | +-+ | +-+ +--R \|x + 1 \|\|2 - 1 \|2\|2 - 2 +--R + +--R 2 %pi 12 2 %pi %pi 11 +--R (8x + 8)sin(---) + (- 32x - 32)cos(---)sin(---) +--R 8 8 8 +--R + +--R 2 %pi 2 3 2 4+-+2 %pi 10 +--R ((80x + 80)cos(---) + (- 6x - 6x - 6x - 6)\|8 )sin(---) +--R 8 8 +--R + +--R 2 %pi 3 3 2 4+-+2 %pi +--R ((- 160x - 160)cos(---) + (20x + 20x + 20x + 20)\|8 cos(---)) +--R 8 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 2 %pi 4 3 2 4+-+2 %pi 2 +--R (248x + 248)cos(---) + (- 74x - 74x - 74x - 74)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 +--R 4x + 8x + 8x + 8x + 4 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 5 +--R (- 320x - 320)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 3 +--R (144x + 144x + 144x + 144)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi +--R (- 64x - 128x - 128x - 128x - 64)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 +--R (352x + 352)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 4 +--R (- 212x - 212x - 212x - 212)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 2 +--R (224x + 448x + 448x + 448x + 224)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (x + 3x + 4x + 4x + 3x + 1)\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 7 +--R (- 320x - 320)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 5 +--R (264x + 264x + 264x + 264)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (- 352x - 704x - 704x - 704x - 352)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (14x + 42x + 56x + 56x + 42x + 14)\|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 +--R (248x + 248)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 6 +--R (- 236x - 236x - 236x - 236)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (728x + 1456x + 1456x + 1456x + 728)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 +--R (- 11x - 33x - 44x - 44x - 33x - 11)\|8 cos(---) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 9 +--R (- 160x - 160)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 7 +--R (176x + 176x + 176x + 176)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (- 576x - 1152x - 1152x - 1152x - 576)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (140x + 420x + 560x + 560x + 420x + 140)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi +--R (32x + 128x + 224x + 256x + 224x + 128x + 32)cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 +--R (80x + 80)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 8 +--R (- 102x - 102x - 102x - 102)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (416x + 832x + 832x + 832x + 416)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (- 93x - 279x - 372x - 372x - 279x - 93)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (112x + 448x + 784x + 896x + 784x + 448x + 112)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (2x + 10x + 22x + 30x + 30x + 22x + 10x + 2)\|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 11 3 2 4+-+2 %pi 9 +--R (- 32x - 32)cos(---) + (36x + 36x + 36x + 36)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 7 +--R (- 160x - 320x - 320x - 320x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (54x + 162x + 216x + 216x + 162x + 54)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 3 +--R (- 64x - 256x - 448x - 512x - 448x - 256x - 64)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi +--R (4x + 20x + 44x + 60x + 60x + 44x + 20x + 4)\|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (8x + 8)cos(---) + (- 10x - 10x - 10x - 10)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (36x + 72x + 72x + 72x + 36)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (- 9x - 27x - 36x - 36x - 27x - 9)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (16x + 64x + 112x + 128x + 112x + 64x + 16)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 +--R (- 2x - 10x - 22x - 30x - 30x - 22x - 10x - 2)\|8 cos(---) +--R 8 +--R * +--R +-----+ +--R \|x + 1 +--R / +--R 3 2 %pi 12 +--R (8x + 8x + 8x + 8)sin(---) +--R 8 +--R + +--R 3 2 %pi %pi 11 +--R (- 32x - 32x - 32x - 32)cos(---)sin(---) +--R 8 8 +--R + +--R 3 2 %pi 2 +--R (80x + 80x + 80x + 80)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 +--R (- 8x - 16x - 16x - 16x - 8)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 3 +--R (- 160x - 160x - 160x - 160)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi +--R (32x + 64x + 64x + 64x + 32)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 4 +--R (248x + 248x + 248x + 248)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 2 5 4 +--R (- 104x - 208x - 208x - 208x - 104)\|8 cos(---) + 24x + 72x +--R 8 +--R + +--R 3 2 +--R 96x + 96x + 72x + 24 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 5 +--R (- 320x - 320x - 320x - 320)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 3 +--R (192x + 384x + 384x + 384x + 192)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi +--R (- 160x - 480x - 640x - 640x - 480x - 160)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 6 +--R (352x + 352x + 352x + 352)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 4 +--R (- 272x - 544x - 544x - 544x - 272)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 2 +--R (448x + 1344x + 1792x + 1792x + 1344x + 448)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 +--R (- 8x - 32x - 56x - 64x - 56x - 32x - 8)\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 7 +--R (- 320x - 320x - 320x - 320)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 5 +--R (320x + 640x + 640x + 640x + 320)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 3 +--R (- 736x - 2208x - 2944x - 2944x - 2208x - 736)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi +--R (56x + 224x + 392x + 448x + 392x + 224x + 56)\|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 8 +--R (248x + 248x + 248x + 248)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 6 +--R (- 272x - 544x - 544x - 544x - 272)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 4 +--R (1104x + 3312x + 4416x + 4416x + 3312x + 1104)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 2 +--R (- 120x - 480x - 840x - 960x - 840x - 480x - 120)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R 18x + 90x + 198x + 270x + 270x + 198x + 90x + 18 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 9 +--R (- 160x - 160x - 160x - 160)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 7 +--R (192x + 384x + 384x + 384x + 192)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 5 +--R (- 736x - 2208x - 2944x - 2944x - 2208x - 736)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 +--R (272x + 1088x + 1904x + 2176x + 1904x + 1088x + 272)\|8 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi +--R (- 72x - 360x - 792x - 1080x - 1080x - 792x - 360x - 72)cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 10 +--R (80x + 80x + 80x + 80)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 8 +--R (- 104x - 208x - 208x - 208x - 104)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 6 +--R (448x + 1344x + 1792x + 1792x + 1344x + 448)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 4 +--R (- 120x - 480x - 840x - 960x - 840x - 480x - 120)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (300x + 1500x + 3300x + 4500x + 4500x + 3300x + 1500x + 300) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 4+-+2 +--R (- 2x - 12x - 32x - 52x - 60x - 52x - 32x - 12x - 2)\|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 11 +--R (- 32x - 32x - 32x - 32)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 9 +--R (32x + 64x + 64x + 64x + 32)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 7 +--R (- 160x - 480x - 640x - 640x - 480x - 160)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 5 +--R (56x + 224x + 392x + 448x + 392x + 224x + 56)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 72x - 360x - 792x - 1080x - 1080x - 792x - 360x - 72) +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (20x + 120x + 320x + 520x + 600x + 520x + 320x + 120x + 20) +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 12 +--R (8x + 8x + 8x + 8)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 10 +--R (- 8x - 16x - 16x - 16x - 8)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 8 +--R (24x + 72x + 96x + 96x + 72x + 24)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 6 +--R (- 8x - 32x - 56x - 64x - 56x - 32x - 8)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi 4 +--R (18x + 90x + 198x + 270x + 270x + 198x + 90x + 18)cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 4+-+2 %pi 2 +--R (- 2x - 12x - 32x - 52x - 60x - 52x - 32x - 12x - 2)\|8 cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 2 +--R 4x + 28x + 88x + 168x + 224x + 224x + 168x + 88x + 28x + 4 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 512 +t0192:= (-1+x)^(1/3)/(1+x)^(1/3) +--R +--R +--R 3+-----+ +--R \|x - 1 +--R (320) -------- +--R 3+-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 512 +r0192:= (-1+x)^(1/3)*(1+x)^(2/3)-2/3*_ + atan(1/3*(1+2*(-1+x)^(1/3)/(1+x)^(1/3))*3^(1/2))*3^(1/2)+_ + 2/3*log(1-(-1+x)^(1/3)/(1+x)^(1/3))-_ + 1/3*log(1+(-1+x)^(2/3)/(1+x)^(2/3)+(-1+x)^(1/3)/(1+x)^(1/3)) +--R +--R +--R (321) +--R 3+-----+2 3+-----+3+-----+ 3+-----+2 +--R \|x + 1 + \|x - 1 \|x + 1 + \|x - 1 +--R - log(----------------------------------------) +--R 3+-----+2 +--R \|x + 1 +--R + +--R 3+-----+ 3+-----+ +-+3+-----+ +-+3+-----+ +--R \|x + 1 - \|x - 1 +-+ \|3 \|x + 1 + 2\|3 \|x - 1 +--R 2log(-------------------) - 2\|3 atan(----------------------------) +--R 3+-----+ 3+-----+ +--R \|x + 1 3\|x + 1 +--R + +--R 3+-----+3+-----+2 +--R 3\|x - 1 \|x + 1 +--R / +--R 3 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 512 +--a0192:= integrate(t0192,x) +--E 463 + +--S 464 of 512 +--m0192:= a0192-r0192 +--E 464 + +--S 465 of 512 +--d0192:= D(m0192,x) +--E 465 + +--S 466 of 512 +t0193:= x^(1/2)/((2-x)^(1/2)-x^(1/2)) +--R +--R +--R +-+ +--R \|x +--R (322) - ----------------- +--R +-+ +-------+ +--R \|x - \|- x + 2 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 512 +r0193:= -1/2*x-1/2*(-(-2+x)*x)^(1/2)+atanh((2-x)^(1/2)/x^(1/2))-1/2*log(1-x) +--R +--R +--R +-------+ +---------+ +--R \|- x + 2 | 2 +--R 2atanh(----------) - \|- x + 2x - log(- x + 1) - x +--R +-+ +--R \|x +--R (323) ---------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 467 + + +-- +-------+ +-+ +-- - \|- x + 2 \|x - 1 +-------+ +-+ +-- log(--------------------) - \|- x + 2 \|x - x +-- 2 +-- x - 2x + 1 +-- (324) ---------------------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 468 of 512 ok to fail. seems there are 2 answers (see above) +a0193:= integrate(t0193,x) +--R +--R +--R +-------+ +-+ +--R \|- x + 2 \|x + 1 +-------+ +-+ +--R log(------------------) - \|- x + 2 \|x - x +--R 2 +--R x - 2x + 1 +--R (324) -------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 512 ok to fail. due to 2 answers (see above) +m0193:= a0193-r0193 +--R +--R +--R (325) +--R +-------+ +-+ +-------+ +--R \|- x + 2 \|x + 1 \|- x + 2 +-------+ +-+ +--R log(------------------) - 2atanh(----------) - \|- x + 2 \|x +--R 2 +-+ +--R x - 2x + 1 \|x +--R + +--R +---------+ +--R | 2 +--R \|- x + 2x + log(- x + 1) +--R / +--R 2 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 512 +d0193:= D(m0193,x) +--R +--R +--R +---------+ +--R +-------+ +-+ | 2 +--R (- x + 1)\|- x + 2 \|x + (x - 1)\|- x + 2x +--R (326) --------------------------------------------- +--R +---------+ +--R | 2 +-------+ +-+ +--R 2\|- x + 2x \|- x + 2 \|x +--R Type: Expression(Integer) +--E 470 + +--S 471 of 512 +t0194:= 1/(9+b*x^2)^(1/2) +--R +--R +--R 1 +--R (327) ----------- +--R +--------+ +--R | 2 +--R \|b x + 9 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 512 +r0194:= asinh(1/3*b^(1/2)*x)/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asinh(-----) +--R 3 +--R (328) ------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 472 + +--S 473 of 512 +a0194:= integrate(t0194,x) +--R +--R +--R (329) +--R +--------+ +--R +-+ | 2 2 +-+ +--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x +--R log(--------------------------------------------------) +--R +--------+ +--R | 2 +--R \|b x + 9 - 3 +--R [-------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +--R \|- b \|b x + 9 - 3\|- b +--R 2atan(---------------------------) +--R b x +--R ----------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 473 + +--S 474 of 512 +m0194a:= a0194.1-r0194 +--R +--R +--R (330) +--R +--------+ +--R +-+ | 2 2 +-+ +-+ +--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x x\|b +--R log(--------------------------------------------------) - asinh(-----) +--R +--------+ 3 +--R | 2 +--R \|b x + 9 - 3 +--R ---------------------------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 474 + +--S 475 of 512 +d0194a:= D(m0194a,x) +--R +--R +--R (331) 0 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 512 +m0194b:= a0194.2-r0194 +--R +--R +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R +-+ \|- b \|b x + 9 - 3\|- b +---+ x\|b +--R 2\|b atan(---------------------------) - \|- b asinh(-----) +--R b x 3 +--R (332) ----------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 476 + +--S 477 of 512 +d0194b:= D(m0194a,x) +--R +--R +--R (333) 0 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 512 +t0195:= 1/(9-b*x^2)^(1/2) +--R +--R +--R 1 +--R (334) ------------- +--R +----------+ +--R | 2 +--R \|- b x + 9 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 512 +r0195:= asin(1/3*b^(1/2)*x)/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asin(-----) +--R 3 +--R (335) ----------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 479 + +--S 480 of 512 +a0195:= integrate(t0195,x) +--R +--R +--R (336) +--R +----------+ +----------+ +--R | 2 2 +---+ | 2 +--R (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x +--R log(-----------------------------------------------------------) +--R +----------+ +--R | 2 +--R \|- b x + 9 - 3 +--R [----------------------------------------------------------------, +--R +---+ +--R \|- b +--R +----------+ +--R | 2 +-+ +--R (\|- b x + 9 - 3)\|b +--R 2atan(-----------------------) +--R b x +--R - ------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 480 + +--S 481 of 512 +m0195a:= a0195.1-r0195 +--R +--R +--R (337) +--R +----------+ +----------+ +--R | 2 2 +---+ | 2 +--R +-+ (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x +--R \|b log(-----------------------------------------------------------) +--R +----------+ +--R | 2 +--R \|- b x + 9 - 3 +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b asin(-----) +--R 3 +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 481 + +--S 482 of 512 +d0195a:= D(m0195a,x) +--R +--R +--R (338) 0 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 512 +m0195b:= a0195.2-r0195 +--R +--R +--R +----------+ +--R | 2 +-+ +-+ +--R (\|- b x + 9 - 3)\|b x\|b +--R - 2atan(-----------------------) - asin(-----) +--R b x 3 +--R (339) ---------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 483 + +--S 484 of 512 +d0195b:= D(m0195b,x) +--R +--R +--R (340) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 512 +t0196:= 1/(%pi+b*x^2)^(1/2) +--R +--R +--R 1 +--R (341) ------------- +--R +----------+ +--R | 2 +--R \|b x + %pi +--R Type: Expression(Integer) +--E 485 + +--S 486 of 512 +r0196:= asinh(b^(1/2)*x/%pi^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asinh(------) +--R +---+ +--R \|%pi +--R (342) ------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 486 + +--S 487 of 512 +a0196:= integrate(t0196,x) +--R +--R +--R (343) +--R +----------+ +--R +-+ +---+ | 2 +---+ 2 +-+ +--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b +--R log(----------------------------------------------------------------) +--R +----------+ +--R +---+ | 2 +--R \|%pi \|b x + %pi - %pi +--R [---------------------------------------------------------------------, +--R +-+ +--R \|b +--R +----------+ +--R +---+ | 2 +---+ +---+ +--R \|- b \|b x + %pi - \|- b \|%pi +--R 2atan(----------------------------------) +--R b x +--R -----------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 487 + +--S 488 of 512 +m0196a:= a0196.1-r0196 +--R +--R +--R (344) +--R +----------+ +--R +-+ +---+ | 2 +---+ 2 +-+ +--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b +--R log(----------------------------------------------------------------) +--R +----------+ +--R +---+ | 2 +--R \|%pi \|b x + %pi - %pi +--R + +--R +-+ +--R x\|b +--R - asinh(------) +--R +---+ +--R \|%pi +--R / +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 488 + +--S 489 of 512 +d0196a:= D(m0196a,x) +--R +--R +--R (345) +--R +----------+ +--R | 2 +--R 2 2 +-+ +---+ 2 3 2 |b x + %pi +--R ((3b %pi x + 4%pi )\|b \|%pi - b %pi x - 4b %pi x) |---------- +--R \| %pi +--R + +--R 2 4 2 2 +-+ +---+ 2 3 2 +--R (b x + 5b %pi x + 4%pi )\|b \|%pi - 3b %pi x - 4b %pi x +--R * +--R +----------+ +--R | 2 +--R \|b x + %pi +--R + +--R 2 3 2 +---+ 2 4 2 2 3 +-+ +--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b ) +--R * +--R +----------+ +--R | 2 +--R |b x + %pi +--R |---------- +--R \| %pi +--R + +--R 3 5 2 3 2 +---+ 2 4 2 2 3 +-+ +--R (b x + 5b %pi x + 4b %pi x)\|%pi + (- 3b %pi x - 7b %pi x - 4%pi )\|b +--R / +--R 2 3 2 +---+ 2 4 2 2 3 +-+ +--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b ) +--R * +--R +----------+ +--R | 2 +----------+ +--R |b x + %pi | 2 +--R |---------- \|b x + %pi +--R \| %pi +--R + +--R 2 4 2 2 3 +-+ +---+ 3 5 2 2 3 +--R (3b %pi x + 7b %pi x + 4%pi )\|b \|%pi - b %pi x - 5b %pi x +--R + +--R 3 +--R - 4b %pi x +--R * +--R +----------+ +--R | 2 +--R |b x + %pi +--R |---------- +--R \| %pi +--R Type: Expression(Integer) +--E 489 + +--S 490 of 512 +m0196b:= a0196.2-r0196 +--R +--R +--R +----------+ +--R +---+ | 2 +---+ +---+ +-+ +--R +-+ \|- b \|b x + %pi - \|- b \|%pi +---+ x\|b +--R 2\|b atan(----------------------------------) - \|- b asinh(------) +--R b x +---+ +--R \|%pi +--R (346) ------------------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 490 + +--S 491 of 512 +d0196b:= D(m0196b,x) +--R +--R +--R +----------+ +--R +----------+ | 2 +--R +---+ | 2 |b x + %pi +--R - \|%pi \|b x + %pi + %pi |---------- +--R \| %pi +--R (347) ---------------------------------------- +--R +----------+ +--R | 2 +----------+ +--R |b x + %pi | 2 +--R %pi |---------- \|b x + %pi +--R \| %pi +--R Type: Expression(Integer) +--E 491 + +--S 492 of 512 +t0197:= 1/(%pi-b*x^2)^(1/2) +--R +--R +--R 1 +--R (348) --------------- +--R +------------+ +--R | 2 +--R \|- b x + %pi +--R Type: Expression(Integer) +--E 492 + +--S 493 of 512 +r0197:= asin(b^(1/2)*x/%pi^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asin(------) +--R +---+ +--R \|%pi +--R (349) ------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 493 + +--S 494 of 512 +a0197:= integrate(t0197,x) +--R +--R +--R (350) +--R [ +--R log +--R +------------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b +--R + +--R +------------+ +--R | 2 +--R b x\|- b x + %pi +--R / +--R +------------+ +--R | 2 +---+ +--R \|- b x + %pi \|%pi - %pi +--R / +--R +---+ +--R \|- b +--R , +--R +------------+ +--R +-+ +---+ | 2 +-+ +--R \|b \|%pi - \|- b x + %pi \|b +--R 2atan(--------------------------------) +--R b x +--R ---------------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 494 + +--S 495 of 512 +m0197a:= a0197.1-r0197 +--R +--R +--R (351) +--R +-+ +--R \|b +--R * +--R log +--R +------------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b +--R + +--R +------------+ +--R | 2 +--R b x\|- b x + %pi +--R / +--R +------------+ +--R | 2 +---+ +--R \|- b x + %pi \|%pi - %pi +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b asin(------) +--R +---+ +--R \|%pi +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 495 + +--S 496 of 512 +d0197a:= D(m0197a,x) +--R +--R +--R (352) +--R +------------+ +--R +------------+ | 2 +--R 2 2 | 2 |- b x + %pi +--R (- 3b %pi x + 4%pi )\|- b x + %pi |------------ +--R \| %pi +--R + +--R +------------+ +--R 2 4 2 2 | 2 +--R (b x - 5b %pi x + 4%pi )\|- b x + %pi +--R * +--R +---+ +--R \|- b +--R + +--R +------------+ +--R | 2 +--R 2 3 2 |- b x + %pi 3 5 2 3 2 +--R (3b %pi x - 4b %pi x) |------------ - b x + 5b %pi x - 4b %pi x +--R \| %pi +--R * +--R +---+ +--R \|%pi +--R + +--R +------------+ +--R | 2 +--R 2 4 2 2 3 |- b x + %pi 2 4 +--R (- b %pi x + 5b %pi x - 4%pi ) |------------ - 3b %pi x +--R \| %pi +--R + +--R 2 2 3 +--R 7b %pi x - 4%pi +--R * +--R +---+ +--R \|- b +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 3 2 | 2 |- b x + %pi +--R (- b %pi x + 4b %pi x)\|- b x + %pi |------------ +--R \| %pi +--R + +--R +------------+ +--R 2 3 2 | 2 +--R (- 3b %pi x + 4b %pi x)\|- b x + %pi +--R / +--R +------------+ +--R | 2 +--R 2 4 2 2 3 |- b x + %pi +---+ +--R (3b %pi x - 7b %pi x + 4%pi ) |------------ \|- b +--R \| %pi +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 3 2 | 2 |- b x + %pi +--R (3b %pi x - 4b %pi x)\|- b x + %pi |------------ +--R \| %pi +--R * +--R +---+ +--R \|%pi +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 4 2 2 3 | 2 |- b x + %pi +---+ +--R (- b %pi x + 5b %pi x - 4%pi )\|- b x + %pi |------------ \|- b +--R \| %pi +--R + +--R +------------+ +--R | 2 +--R 3 5 2 2 3 3 |- b x + %pi +--R (b %pi x - 5b %pi x + 4b %pi x) |------------ +--R \| %pi +--R Type: Expression(Integer) +--E 496 + +--S 497 of 512 +m0197b:= a0197.2-r0197 +--R +--R +--R +------------+ +--R +-+ +---+ | 2 +-+ +-+ +--R \|b \|%pi - \|- b x + %pi \|b x\|b +--R 2atan(--------------------------------) - asin(------) +--R b x +---+ +--R \|%pi +--R (353) ------------------------------------------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 497 + +--S 498 of 512 +d0197b:= D(m0197b,x) +--R +--R +--R +------------+ +--R +------------+ | 2 +--R | 2 +---+ |- b x + %pi +--R - \|- b x + %pi \|%pi + %pi |------------ +--R \| %pi +--R (354) -------------------------------------------- +--R +------------+ +--R +------------+ | 2 +--R | 2 |- b x + %pi +--R %pi\|- b x + %pi |------------ +--R \| %pi +--R Type: Expression(Integer) +--E 498 + +--S 499 of 512 +t0198:= 1/(a+b*x)/(c+d*x^2)^(1/2) +--R +--R +--R 1 +--R (355) -------------------- +--R +--------+ +--R | 2 +--R (b x + a)\|d x + c +--R Type: Expression(Integer) +--E 499 + +--S 500 of 512 +r0198:= atanh((b^2*c+a^2*d)^(1/2)*(c+d*x^2)^(1/2)/_ + (-b*c+a*d*x))/(b^2*c+a^2*d)^(1/2) +--R +--R +--R +---------+ +--------+ +--R | 2 2 | 2 +--R \|a d + b c \|d x + c +--R atanh(-----------------------) +--R a d x - b c +--R (356) ------------------------------ +--R +---------+ +--R | 2 2 +--R \|a d + b c +--R Type: Expression(Integer) +--E 500 + +--S 501 of 512 +a0198:= integrate(t0198,x) +--R +--R +--R (357) +--R [ +--R log +--R +---------+ +--------+ +--R 2 +-+ | 2 2 3 2 | 2 +--R ((a b x + a )\|c \|a d + b c + (- a d - a b c)x)\|d x + c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d - b c)x - a b c x - a c)\|a d + b c +--R + +--R 2 3 2 3 2 +-+ +--R ((a b d + b c)x + (a d + a b c)x)\|c +--R / +--R +--------+ +--R +-+ | 2 +--R (b x + a)\|c \|d x + c - b c x - a c +--R / +--R +---------+ +--R | 2 2 +--R \|a d + b c +--R , +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +-+ +--R a\|- a d - b c \|d x + c + (- b x - a)\|- a d - b c \|c +--R 2atan(----------------------------------------------------------) +--R 2 2 +--R (a d + b c)x +--R -----------------------------------------------------------------] +--R +-----------+ +--R | 2 2 +--R \|- a d - b c +--R Type: Union(List(Expression(Integer)),...) +--E 501 + +--S 502 of 512 +m0198a:= a0198.1-r0198 +--R +--R +--R (358) +--R log +--R +---------+ +--------+ +--R 2 +-+ | 2 2 3 2 | 2 +--R ((a b x + a )\|c \|a d + b c + (- a d - a b c)x)\|d x + c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d - b c)x - a b c x - a c)\|a d + b c +--R + +--R 2 3 2 3 2 +-+ +--R ((a b d + b c)x + (a d + a b c)x)\|c +--R / +--R +--------+ +--R +-+ | 2 +--R (b x + a)\|c \|d x + c - b c x - a c +--R + +--R +---------+ +--------+ +--R | 2 2 | 2 +--R \|a d + b c \|d x + c +--R - atanh(-----------------------) +--R a d x - b c +--R / +--R +---------+ +--R | 2 2 +--R \|a d + b c +--R Type: Expression(Integer) +--E 502 + +--S 503 of 512 +d0198a:= D(m0198a,x) +--R +--R +--R (359) 0 +--R Type: Expression(Integer) +--E 503 + +--S 504 of 512 +m0198b:= a0198.2-r0198 +--R +--R +--R (360) +--R +---------+ +--------+ +--R +-----------+ | 2 2 | 2 +--R | 2 2 \|a d + b c \|d x + c +--R - \|- a d - b c atanh(-----------------------) +--R a d x - b c +--R + +--R +---------+ +--R | 2 2 +--R 2\|a d + b c +--R * +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +-+ +--R a\|- a d - b c \|d x + c + (- b x - a)\|- a d - b c \|c +--R atan(----------------------------------------------------------) +--R 2 2 +--R (a d + b c)x +--R / +--R +-----------+ +---------+ +--R | 2 2 | 2 2 +--R \|- a d - b c \|a d + b c +--R Type: Expression(Integer) +--E 504 + +--S 505 of 512 +d0198b:= D(m0198b,x) +--R +--R +--R (361) 0 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 512 +t0199:= 1/(a+b*x)/(-c+d*x^2)^(1/2) +--R +--R +--R 1 +--R (362) -------------------- +--R +--------+ +--R | 2 +--R (b x + a)\|d x - c +--R Type: Expression(Integer) +--E 506 + +--S 507 of 512 +r0199:= atan((b^2*c-a^2*d)^(1/2)*(-c+d*x^2)^(1/2)/(b*c+a*d*x))/(b^2*c-a^2*d)^(1/2) +--R +--R +--R +-----------+ +--------+ +--R | 2 2 | 2 +--R \|- a d + b c \|d x - c +--R atan(-------------------------) +--R a d x + b c +--R (363) ------------------------------- +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R Type: Expression(Integer) +--E 507 + +--S 508 of 512 +a0199:= integrate(t0199,x) +--R +--R +--R (364) +--R [ +--R log +--R +---------+ +--------+ +--R 2 +---+ | 2 2 3 2 | 2 +--R ((a b x + a )\|- c \|a d - b c + (- a d + a b c)x)\|d x - c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d + b c)x + a b c x + a c)\|a d - b c +--R + +--R 2 3 2 3 2 +---+ +--R ((a b d - b c)x + (a d - a b c)x)\|- c +--R / +--R +--------+ +--R +---+ | 2 +--R (b x + a)\|- c \|d x - c + b c x + a c +--R / +--R +---------+ +--R | 2 2 +--R \|a d - b c +--R , +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +---+ +--R a\|- a d + b c \|d x - c + (- b x - a)\|- a d + b c \|- c +--R 2atan(------------------------------------------------------------) +--R 2 2 +--R (a d - b c)x +--R -------------------------------------------------------------------] +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R Type: Union(List(Expression(Integer)),...) +--E 508 + +--S 509 of 512 +m0199a:= a0199.1-r0199 +--R +--R +--R (365) +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R * +--R log +--R +---------+ +--------+ +--R 2 +---+ | 2 2 3 2 | 2 +--R ((a b x + a )\|- c \|a d - b c + (- a d + a b c)x)\|d x - c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d + b c)x + a b c x + a c)\|a d - b c +--R + +--R 2 3 2 3 2 +---+ +--R ((a b d - b c)x + (a d - a b c)x)\|- c +--R / +--R +--------+ +--R +---+ | 2 +--R (b x + a)\|- c \|d x - c + b c x + a c +--R + +--R +-----------+ +--------+ +--R +---------+ | 2 2 | 2 +--R | 2 2 \|- a d + b c \|d x - c +--R - \|a d - b c atan(-------------------------) +--R a d x + b c +--R / +--R +-----------+ +---------+ +--R | 2 2 | 2 2 +--R \|- a d + b c \|a d - b c +--R Type: Expression(Integer) +--E 509 + +--S 510 of 512 +d0199a:= D(m0199a,x) +--R +--R +--R (366) 0 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 512 +m0199b:= a0199.2-r0199 +--R +--R +--R (367) +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +---+ +--R a\|- a d + b c \|d x - c + (- b x - a)\|- a d + b c \|- c +--R 2atan(------------------------------------------------------------) +--R 2 2 +--R (a d - b c)x +--R + +--R +-----------+ +--------+ +--R | 2 2 | 2 +--R \|- a d + b c \|d x - c +--R - atan(-------------------------) +--R a d x + b c +--R / +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R Type: Expression(Integer) +--E 511 + +--S 512 of 512 +d0199b:= D(m0199b,x) +--R +--R +--R (368) 0 +--R Type: Expression(Integer) +--E 512 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richalgebraic100-199.input.pdf b/src/axiom-website/CATS/richalgebraic100-199.input.pdf new file mode 100644 index 0000000..4070994 Binary files /dev/null and b/src/axiom-website/CATS/richalgebraic100-199.input.pdf differ diff --git a/src/axiom-website/CATS/richalgebraic200-299.input.pamphlet b/src/axiom-website/CATS/richalgebraic200-299.input.pamphlet new file mode 100644 index 0000000..fc6e6ee --- /dev/null +++ b/src/axiom-website/CATS/richalgebraic200-299.input.pamphlet @@ -0,0 +1,10314 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richalgebraic200-299.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic200-299.output +)spool richalgebraic200-299.output +)set message test on +)set message auto off +)clear all + +--S 1 of 554 +t0200:= x^2/(1-a^2-2*a*b*x-b^2*x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (1) --------------------------- +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 554 +r0200:= 1/2*(3*a*(1-a^2-2*a*b*x-b^2*x^2)^(1/2)-_ + x*(1-a^2-2*a*b*x-b^2*x^2)^(1/2)*b+asin(a+b*x)+2*a^2*asin(a+b*x))/b^3 +--R +--R +--R +------------------------+ +--R | 2 2 2 2 +--R (- b x + 3a)\|- b x - 2a b x - a + 1 + (2a + 1)asin(b x + a) +--R (2) ---------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 554 +a0200:= integrate(t0200,x) +--R +--R +--R (3) +--R +------------------------+ +--------+ +--R 3 4 2 | 2 2 2 | 2 +--R ((8a + 4a)b x + 8a - 4a - 4)\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 4 2 2 5 3 6 4 +--R (8a - 2)b x + (16a - 8a - 8a)b x + 8a - 12a + 4 +--R * +--R +--------+ +------------------------+ +--R | 2 | 2 2 2 +--R \|- a + 1 - \|- b x - 2a b x - a + 1 +--R atan(-----------------------------------------) +--R b x +--R + +--R +--------+ +--R 4 4 3 3 3 2 2 4 2 | 2 +--R (2a b x - 2b x + (- 6a - 3a)b x + (- 4a + 2a + 2)b x)\|- a + 1 +--R + +--R 2 3 3 3 2 2 4 2 +--R ((- 2a + 1)b x + (2a + a)b x + (4a - 2a - 2)b x) +--R * +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R +------------------------+ +--------+ +--R 4 2 3 | 2 2 2 | 2 +--R (4a b x + (4a - 4)b )\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 2 5 2 3 4 4 2 3 +--R (4a - 2)b x + (8a - 8a)b x + (4a - 8a + 4)b +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 554 +m0200:= a0200-r0200 +--R +--R +--R (4) +--R +------------------------+ +--------+ +--R 3 4 2 | 2 2 2 | 2 +--R ((8a + 4a)b x + 8a - 4a - 4)\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 4 2 2 5 3 6 4 +--R (8a - 2)b x + (16a - 8a - 8a)b x + 8a - 12a + 4 +--R * +--R +--------+ +------------------------+ +--R | 2 | 2 2 2 +--R \|- a + 1 - \|- b x - 2a b x - a + 1 +--R atan(-----------------------------------------) +--R b x +--R + +--R 3 4 2 +--R ((- 4a - 2a)b x - 4a + 2a + 2)asin(b x + a) +--R * +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R 3 2 2 4 2 5 3 +--R (6a - 3a)b x + (12a - 12a )b x + 6a - 12a + 6a +--R * +--R +--------+ +--R | 2 +--R \|- a + 1 +--R + +--R +------------------------+ +--R 4 2 5 3 | 2 2 2 +--R ((- 6a + 6a )b x - 6a + 12a - 6a)\|- b x - 2a b x - a + 1 +--R + +--R 4 2 2 5 3 6 4 +--R ((- 4a + 1)b x + (- 8a + 4a + 4a)b x - 4a + 6a - 2)asin(b x + a) +--R / +--R +------------------------+ +--------+ +--R 4 2 3 | 2 2 2 | 2 +--R (4a b x + (4a - 4)b )\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 2 5 2 3 4 4 2 3 +--R (4a - 2)b x + (8a - 8a)b x + (4a - 8a + 4)b +--R Type: Expression(Integer) +--E 4 + +--S 5 of 554 +d0200:= D(m0200,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 554 +t0201:= x^2/(1+a^2+2*a*b*x+b^2*x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (6) ------------------------- +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 554 +r0201:= -1/2*(3*a*(1+a^2+2*a*b*x+b^2*x^2)^(1/2)-_ + x*(1+a^2+2*a*b*x+b^2*x^2)^(1/2)*b+asinh(a+b*x)-2*a^2*asinh(a+b*x))/b^3 +--R +--R +--R +----------------------+ +--R | 2 2 2 2 +--R (b x - 3a)\|b x + 2a b x + a + 1 + (2a - 1)asinh(b x + a) +--R (7) ------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 7 + +--S 8 of 554 +a0201:= integrate(t0201,x) +--R +--R +--R (8) +--R +----------------------+ +--R 2 3 | 2 2 2 +--R ((- 16a + 8)b x - 16a + 8a)\|b x + 2a b x + a + 1 +--R + +--R 2 2 2 3 4 +--R (16a - 8)b x + (32a - 16a)b x + 16a - 4 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a + 1 - b x - a) +--R + +--R +----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (- 8b x + 8a b x + (26a - 4)b x + 10a + 12a)\|b x + 2a b x + a + 1 +--R + +--R 4 4 2 2 2 3 4 2 +--R 8b x + (- 34a + 8)b x + (- 36a - 16a)b x - 10a - 17a +--R / +--R +----------------------+ +--R 4 3 | 2 2 2 5 2 4 +--R (16b x + 16a b )\|b x + 2a b x + a + 1 - 16b x - 32a b x +--R + +--R 2 3 +--R (- 16a - 8)b +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 554 +m0201:= a0201-r0201 +--R +--R +--R (9) +--R +----------------------+ +--R 2 | 2 2 2 +--R (- 8a + 4)log(\|b x + 2a b x + a + 1 - b x - a) +--R + +--R 2 2 +--R (- 8a + 4)asinh(b x + a) - 7a +--R / +--R 3 +--R 8b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 554 +d0201:= D(m0201,x) +--R +--R +--R (10) 0 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 554 +t0202:= 1/(x-(1-x^2)^(1/2)) +--R +--R +--R 1 +--R (11) - --------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 554 +r0202:= -1/2*asin(x)-1/2*atanh(x/(1-x^2)^(1/2))+1/4*log(1-2*x^2) +--R +--R +--R x 2 +--R - 2atanh(-----------) + log(- 2x + 1) - 2asin(x) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R (12) ------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 554 +a0202:= integrate(t0202,x) +--R +--R +--R (13) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R - log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--------+ +--R | 2 2 | 2 +--R (- x - 1)\|- x + 1 - x + x + 1 \|- x + 1 - 1 +--R log(---------------------------------) + 4atan(---------------) +--R 2 x +--R x +--R + +--R 2 +--R log(2x - 1) +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 554 +m0202:= a0202-r0202 +--R +--R +--R (14) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R - log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R | 2 2 +--R (- x - 1)\|- x + 1 - x + x + 1 x +--R log(---------------------------------) + 2atanh(-----------) +--R 2 +--------+ +--R x | 2 +--R \|- x + 1 +--R + +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 2 2 +--R 4atan(---------------) + log(2x - 1) - log(- 2x + 1) + 2asin(x) +--R x +--R / +--R 4 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 554 +d0202:= D(m0202,x) +--R +--R +--R (15) 0 +--R Type: Expression(Integer) +--E 15 + +--S 16 of 554 +t0203:= x/(x-(1-x^2)^(1/2)) +--R +--R +--R x +--R (16) - --------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 554 +r0203:= 1/2*x+1/2*(1-x^2)^(1/2)-1/4*atanh(x*2^(1/2))*2^(1/2)-_ + 1/4*atanh(2^(1/2)*(1-x^2)^(1/2))*2^(1/2) +--R +--R +--R +--------+ +--------+ +--R +-+ +-+ | 2 | 2 +-+ +-+ +--R - \|2 atanh(\|2 \|- x + 1 ) + 2\|- x + 1 - \|2 atanh(x\|2 ) + 2x +--R (17) ------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 554 +a0203:= integrate(t0203,x) +--R +--R +--R (18) +--R +--------+ +--R | 2 +--R (\|- x + 1 - 1) +--R * +--R +--------+ +--R 2 +-+ 2 | 2 4 2 +-+ 4 2 +--R ((4x - 2)\|2 - 4x )\|- x + 1 + (6x - 5x + 2)\|2 - 8x + 4x +--R log(------------------------------------------------------------------) +--R +--------+ +--R 2 | 2 4 2 +--R (4x - 2)\|- x + 1 + 2x - 5x + 2 +--R + +--R 2 +-+ +--------+ 2 +-+ +--R (2x + 1)\|2 - 4x +-+ | 2 (2x + 1)\|2 - 4x +--R (log(------------------) + 2x\|2 )\|- x + 1 - log(------------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R 2 +-+ +--R (- 2x - 2x)\|2 +--R / +--R +--------+ +--R +-+ | 2 +-+ +--R 4\|2 \|- x + 1 - 4\|2 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 554 +m0203:= a0203-r0203 +--R +--R +--R (19) +--R +--------+ +--R 2 +-+ 2 | 2 4 2 +-+ 4 2 +--R ((4x - 2)\|2 - 4x )\|- x + 1 + (6x - 5x + 2)\|2 - 8x + 4x +--R log(------------------------------------------------------------------) +--R +--------+ +--R 2 | 2 4 2 +--R (4x - 2)\|- x + 1 + 2x - 5x + 2 +--R + +--R +--------+ 2 +-+ +--R +-+ | 2 (2x + 1)\|2 - 4x +-+ +-+ +--R 2atanh(\|2 \|- x + 1 ) + log(------------------) + 2atanh(x\|2 ) + 2\|2 +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 554 +d0203:= D(m0203,x) +--R +--R +--R (20) 0 +--R Type: Expression(Integer) +--E 20 + +--S 21 of 554 +t0204:= 1/(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R 1 +--R (21) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 554 +r0204:= 1/2*EllipticF(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)*_ + 2^(1/2)/(-d)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 554 +a0204:= integrate(t0204,x) +--R +--R +--R x +--R ++ 1 +--R (22) | ---------------------- d%T +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 554 +m0204:= a0204-r0204 +--R +--R +--R x +--R ++ 1 +--R (23) | ---------------------- d%T - r0204 +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 554 +d0204:= D(m0204,x) +--R +--R +--R 1 +--R (24) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 554 +t0205:= x/(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R x +--R (25) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 554 +r0205:= atanh(d^(1/2)*(2+b*x^2)^(1/2)/b^(1/2)/(3+d*x^2)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R \|d \|b x + 2 +--R atanh(---------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + 3 +--R (26) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 27 + +--S 28 of 554 +--a0205:= integrate(t0205,x) +--E 28 + +--S 29 of 554 +--m0205:= a0205-r0205 +--E 29 + +--S 30 of 554 +--d0205:= D(m0205,x) +--E 30 + +--S 31 of 554 +t0206:= x^2/(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (27) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 554 +r0206:= 2^(1/2)*(EllipticE(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)-_ + EllipticF(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d))/b/(-d)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 554 +a0206:= integrate(t0206,x) +--R +--R +--R x 2 +--R ++ %T +--R (28) | ---------------------- d%T +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 554 +m0206:= a0206-r0206 +--R +--R +--R x 2 +--R ++ %T +--R (29) | ---------------------- d%T - r0206 +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 554 +d0206:= D(m0206,x) +--R +--R +--R 2 +--R x +--R (30) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 554 +t0207:= x/(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R x +--R (31) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 36 + +--S 37 of 554 +r0207:= atanh(d^(1/2)*(a+b*x^2)^(1/2)/b^(1/2)/(c+d*x^2)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R \|d \|b x + a +--R atanh(---------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + c +--R (32) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 37 + +--S 38 of 554 +--a0207:= integrate(t0207,x) +--E 38 + +--S 39 of 554 +--m0207:= a0207-r0207 +--E 39 + +--S 40 of 554 +--d0207:= D(m0207,x) +--E 40 + +--S 41 of 554 +t0208:= 1/(1-x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (33) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 554 +r0208:= 1/2*EllipticF(asin(x),3/2)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 of 554 +a0208:= integrate(t0208,x) +--R +--R +--R x +--R ++ 1 +--R (34) | ----------------------- d%T +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|3%T + 2 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 554 +m0208:= a0208-r0208 +--R +--R +--R x +--R ++ 1 +--R (35) | ----------------------- d%T - r0208 +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|3%T + 2 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 554 +d0208:= D(m0208,x) +--R +--R +--R 1 +--R (36) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 45 + +--S 46 of 554 +t0209:= 1/(1-x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (37) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 554 +r0209:= 1/2*EllipticF(asin(x),3/2)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 47 + +--S 48 of 554 +a0209:= integrate(t0209,x) +--R +--R +--R x +--R ++ 1 +--R (38) | ------------------------- d%T +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 1 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 554 +m0209:= a0209-r0209 +--R +--R +--R x +--R ++ 1 +--R (39) | ------------------------- d%T - r0209 +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 1 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 554 +d0209:= D(m0209,x) +--R +--R +--R 1 +--R (40) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 1 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 554 +t0210:= 1/(4-x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (41) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 4 \|3x + 2 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 554 +r0210:= 1/2*EllipticF(asin(1/2*x),6)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 554 +a0210:= integrate(t0210,x) +--R +--R +--R x +--R ++ 1 +--R (42) | ----------------------- d%T +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 4 \|3%T + 2 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 554 +m0210:= a0210-r0210 +--R +--R +--R x +--R ++ 1 +--R (43) | ----------------------- d%T - r0210 +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 4 \|3%T + 2 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 554 +d0210:= D(m0210,x) +--R +--R +--R 1 +--R (44) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 4 \|3x + 2 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 554 +t0211:= 1/(4-x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (45) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 4 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 554 +r0211:= 1/2*EllipticF(asin(1/2*x),6)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 554 +a0211:= integrate(t0211,x) +--R +--R +--R x +--R ++ 1 +--R (46) | ------------------------- d%T +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 4 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 554 +m0211:= a0211-r0211 +--R +--R +--R x +--R ++ 1 +--R (47) | ------------------------- d%T - r0211 +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 4 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 554 +d0211:= D(m0211,x) +--R +--R +--R 1 +--R (48) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 4 +--R Type: Expression(Integer) +--E 60 + +--S 61 of 554 +t0212:= 1/(1-4*x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (49) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 4x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 554 +r0212:= 1/4*EllipticF(asin(2*x),3/8)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 554 +a0212:= integrate(t0212,x) +--R +--R +--R x +--R ++ 1 +--R (50) | ------------------------ d%T +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|3%T + 2 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 554 +m0212:= a0212-r0212 +--R +--R +--R x +--R ++ 1 +--R (51) | ------------------------ d%T - r0212 +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|3%T + 2 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 554 +d0212:= D(m0212,x) +--R +--R +--R 1 +--R (52) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 4x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 554 +t0213:= 1/(1-4*x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (53) ------------------------ +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 1 \|- 3x + 2 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 554 +r0213:= 1/4*EllipticF(asin(2*x),3/8)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 of 554 +a0213:= integrate(t0213,x) +--R +--R +--R x +--R ++ 1 +--R (54) | -------------------------- d%T +--R ++ +----------+ +----------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|- 3%T + 2 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 554 +m0213:= a0213-r0213 +--R +--R +--R x +--R ++ 1 +--R (55) | -------------------------- d%T - r0213 +--R ++ +----------+ +----------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|- 3%T + 2 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 554 +d0213:= D(m0213,x) +--R +--R +--R 1 +--R (56) ------------------------ +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 1 \|- 3x + 2 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 554 +t0214:= 1/(1+x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (57) ------------------- +--R +------+ +-------+ +--R | 2 | 2 +--R \|x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 554 +r0214:= -1/2*%i*EllipticF(%i*asinh(x),3/2)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 72 + +--S 73 of 554 +a0214:= integrate(t0214,x) +--R +--R +--R x +--R ++ 1 +--R (58) | --------------------- d%T +--R ++ +-------+ +--------+ +--R | 2 | 2 +--R \|%T + 1 \|3%T + 2 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 554 +m0214:= a0214-r0214 +--R +--R +--R x +--R ++ 1 +--R (59) | --------------------- d%T - r0214 +--R ++ +-------+ +--------+ +--R | 2 | 2 +--R \|%T + 1 \|3%T + 2 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 554 +d0214:= D(m0214,x) +--R +--R +--R 1 +--R (60) ------------------- +--R +------+ +-------+ +--R | 2 | 2 +--R \|x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 75 + +--S 76 of 554 +t0215:= 1/(1+x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (61) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 554 +r0215:= 1/3*EllipticF(asin(1/2*6^(1/2)*x),2/3)*3^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 554 +a0215:= integrate(t0215,x) +--R +--R +--R x +--R ++ 1 +--R (62) | ----------------------- d%T +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 1 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 554 +m0215:= a0215-r0215 +--R +--R +--R x +--R ++ 1 +--R (63) | ----------------------- d%T - r0215 +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 1 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 554 +d0215:= D(m0215,x) +--R +--R +--R 1 +--R (64) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 1 +--R Type: Expression(Integer) +--E 80 + +--S 81 of 554 +t0216:= 1/(4+x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (65) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 4 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 554 +r0216:= 1/6*EllipticF(asin(1/2*6^(1/2)*x),1/6)*3^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 554 +a0216:= integrate(t0216,x) +--R +--R +--R x +--R ++ 1 +--R (66) | ----------------------- d%T +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 4 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 554 +m0216:= a0216-r0216 +--R +--R +--R x +--R ++ 1 +--R (67) | ----------------------- d%T - r0216 +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 4 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 554 +d0216:= D(m0216,x) +--R +--R +--R 1 +--R (68) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 4 +--R Type: Expression(Integer) +--E 85 + +--S 86 of 554 +t0217:= 1/(1+4*x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (69) -------------------- +--R +-------+ +-------+ +--R | 2 | 2 +--R \|3x + 2 \|4x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 554 +r0217:= -1/4*%i*EllipticF(%i*asinh(2*x),3/8)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 554 +a0217:= integrate(t0217,x) +--R +--R +--R x +--R ++ 1 +--R (70) | ---------------------- d%T +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|3%T + 2 \|4%T + 1 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 554 +m0217:= a0217-r0217 +--R +--R +--R x +--R ++ 1 +--R (71) | ---------------------- d%T - r0217 +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|3%T + 2 \|4%T + 1 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 554 +d0217:= D(m0217,x) +--R +--R +--R 1 +--R (72) -------------------- +--R +-------+ +-------+ +--R | 2 | 2 +--R \|3x + 2 \|4x + 1 +--R Type: Expression(Integer) +--E 90 + +--S 91 of 554 +t0218:= 1/(1+4*x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (73) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 3x + 2 \|4x + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 554 +r0218:= 1/3*EllipticF(asin(1/2*6^(1/2)*x),8/3)*3^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 554 +a0218:= integrate(t0218,x) +--R +--R +--R x +--R ++ 1 +--R (74) | ------------------------ d%T +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|4%T + 1 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 554 +m0218:= a0218-r0218 +--R +--R +--R x +--R ++ 1 +--R (75) | ------------------------ d%T - r0218 +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|4%T + 1 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 554 +d0218:= D(m0218,x) +--R +--R +--R 1 +--R (76) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 3x + 2 \|4x + 1 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 554 +t0219:= 1/(1-x^2)^(1/2)/(-1+2*x^2)^(1/2) +--R +--R +--R 1 +--R (77) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|2x - 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 554 +r0219:= -EllipticF(acos(x),2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 554 +a0219:= integrate(t0219,x) +--R +--R +--R x +--R ++ 1 +--R (78) | ----------------------- d%T +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|2%T - 1 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 554 +m0219:= a0219-r0219 +--R +--R +--R x +--R ++ 1 +--R (79) | ----------------------- d%T - r0219 +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|2%T - 1 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 554 +d0219:= D(m0219,x) +--R +--R +--R 1 +--R (80) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|2x - 1 +--R Type: Expression(Integer) +--E 100 + +--S 101 of 554 +t0220:= 1/(-1+x)^(1/2)/(1+x)^(1/2)/(-1+2*x^2)^(1/2) +--R +--R +--R 1 +--R (81) -------------------------- +--R +-------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|2x - 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 554 +r0220:= -%i*EllipticF(%i*acosh(x),2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 554 +a0220:= integrate(t0220,x) +--R +--R +--R x +--R ++ 1 +--R (82) | ----------------------------- d%T +--R ++ +--------+ +--R +------+ +------+ | 2 +--R \|%T - 1 \|%T + 1 \|2%T - 1 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 554 +m0220:= a0220-r0220 +--R +--R +--R x +--R ++ 1 +--R (83) | ----------------------------- d%T - r0220 +--R ++ +--------+ +--R +------+ +------+ | 2 +--R \|%T - 1 \|%T + 1 \|2%T - 1 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 554 +d0220:= D(m0220,x) +--R +--R +--R 1 +--R (84) -------------------------- +--R +-------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|2x - 1 +--R Type: Expression(Integer) +--E 105 + +--S 106 of 554 +t0221:= (2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + 2 +--R (85) ----------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 554 +r0221:= 2^(1/2)*EllipticE(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)/(-d)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 554 +a0221:= integrate(t0221,x) +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + 2 +--R (86) | ----------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 554 +m0221:= a0221-r0221 +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + 2 +--R (87) | ----------- d%T - r0221 +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 554 +d0221:= D(m0221,x) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + 2 +--R (88) ----------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 554 +t0222:= x*(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R x\|b x + 2 +--R (89) ------------ +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 554 +r0222:= 1/2*(2+b*x^2)^(1/2)*(3+d*x^2)^(1/2)/d-1/2*(3*b-2*d)*_ + atanh(d^(1/2)*(2+b*x^2)^(1/2)/b^(1/2)/(3+d*x^2)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--------+ +--------+ +--R \|d \|b x + 2 +-+ +-+ | 2 | 2 +--R (2d - 3b)atanh(---------------) + \|b \|d \|b x + 2 \|d x + 3 +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + 3 +--R (90) ---------------------------------------------------------------- +--R +-+ +-+ +--R 2d\|b \|d +--R Type: Expression(Integer) +--E 112 + +--S 113 of 554 +--a0222:= integrate(t0222,x) +--E 113 + +--S 114 of 554 +--m0222:= a0222-r0222 +--E 114 + +--S 115 of 554 +--d0222:= D(m0222,x) +--E 115 + +--S 116 of 554 +t0223:= x^2*(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + 2 +--R (91) ------------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 554 +r0223:= 1/3*x*(2+b*x^2)^(1/2)*(3+d*x^2)^(1/2)/d-_ + 2/3*(3*b-d)*EllipticE(asin(1/2*(-b)^(1/2)*x*2^(1/2)),2/3*d/b)*_ + 3^(1/2)/(-b)^(1/2)/d^2+2^(1/2)*(3*b-2*d)*_ + EllipticF(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)/(-d)^(5/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 554 +a0223:= integrate(t0223,x) +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + 2 +--R (92) | -------------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 554 +m0223:= a0223-r0223 +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + 2 +--R (93) | -------------- d%T - r0223 +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 554 +d0223:= D(m0223,x) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + 2 +--R (94) ------------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression(Integer) +--E 120 + +--S 121 of 554 +t0224:= (a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (95) ----------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression(Integer) +--E 121 + +--S 122 of 554 +r0224:= c^(1/2)*(a+b*x^2)^(1/2)*((c+d*x^2)/c)^(1/2)*_ + EllipticE(asin((-d)^(1/2)*x/c^(1/2)),b*c/a/d)/(-d)^(1/2)/_ + ((a+b*x^2)/a)^(1/2)/(c+d*x^2)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 554 +a0224:= integrate(t0224,x) +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + a +--R (96) | ----------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 554 +m0224:= a0224-r0224 +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + a +--R (97) | ----------- d%T - r0224 +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Expression(Integer) +--E 124 + +--S 125 of 554 +d0224:= D(m0224,x) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (98) ----------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression(Integer) +--E 125 + +--S 126 of 554 +t0225:= x*(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R x\|b x + a +--R (99) ------------ +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression(Integer) +--E 126 + +--S 127 of 554 +r0225:= 1/2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)/d-1/2*(b*c-a*d)*_ + atanh(d^(1/2)*(a+b*x^2)^(1/2)/b^(1/2)/(c+d*x^2)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--------+ +--------+ +--R \|d \|b x + a +-+ +-+ | 2 | 2 +--R (a d - b c)atanh(---------------) + \|b \|d \|b x + a \|d x + c +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + c +--R (100) ------------------------------------------------------------------ +--R +-+ +-+ +--R 2d\|b \|d +--R Type: Expression(Integer) +--E 127 + +--S 128 of 554 +--a0225:= integrate(t0225,x) +--E 128 + +--S 129 of 554 +--m0225:= a0225-r0225 +--E 129 + +--S 130 of 554 +--d0225:= D(m0225,x) +--E 130 + +--S 131 of 554 +t0226:= x^2*(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + a +--R (101) ------------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression(Integer) +--E 131 + +--S 132 of 554 +r0226:= 1/3*x*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)/d+1/3*%i*c*(2*b*c-a*d)*_ + (1+b*x^2/a)^(1/2)*(1+d*x^2/c)^(1/2)*_ + EllipticE(%i*asinh((b/a)^(1/2)*x),a*d/b/c)/(b/a)^(1/2)/d^2/_ + (a+b*x^2)^(1/2)/(c+d*x^2)^(1/2)-2/3*%i*c*(b*c-a*d)*_ + (1+b*x^2/a)^(1/2)*(1+d*x^2/c)^(1/2)*_ + EllipticF(%i*asinh((b/a)^(1/2)*x),a*d/b/c)/(b/a)^(1/2)/_ + d^2/(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 554 +a0226:= integrate(t0226,x) +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + a +--R (102) | -------------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 554 +m0226:= a0226-r0226 +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + a +--R (103) | -------------- d%T - r0226 +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Expression(Integer) +--E 134 + +--S 135 of 554 +d0226:= D(m0226,x) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + a +--R (104) ------------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression(Integer) +--E 135 + +--S 136 of 554 +t0227:= (x-(-4+x^2)^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +------+ +--R | | 2 +--R (105) \|- \|x - 4 + x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 554 +r0227:= 2/3*(x-(-4+x^2)^(1/2))^(1/2)*(2*x+(-4+x^2)^(1/2)) +--R +--R +--R +---------------+ +--R +------+ | +------+ +--R | 2 | | 2 +--R (2\|x - 4 + 4x)\|- \|x - 4 + x +--R (106) ----------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 554 +a0227:= integrate(t0227,x) +--R +--R +--R +------+ +--R | 2 2 +--R - 2x\|x - 4 + 2x + 8 +--R (107) ----------------------- +--R +---------------+ +--R | +------+ +--R | | 2 +--R 3\|- \|x - 4 + x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 554 +m0227:= a0227-r0227 +--R +--R +--R (108) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 554 +d0227:= D(m0227,x) +--R +--R +--R (109) 0 +--R Type: Expression(Integer) +--E 140 + +--S 141 of 554 +t0228:= (1+(1-x^2)^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +--------+ +--R | | 2 +--R (110) \|\|- x + 1 + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 554 +r0228:= 2/3*(1+x^2-(1-x^2)^(1/2))*(1+(1-x^2)^(1/2))^(1/2)/x +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R | 2 2 | | 2 +--R (- 2\|- x + 1 + 2x + 2)\|\|- x + 1 + 1 +--R (111) -------------------------------------------- +--R 3x +--R Type: Expression(Integer) +--E 142 + +--S 143 of 554 +a0228:= integrate(t0228,x) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R | 2 2 | | 2 +--R (- 2\|- x + 1 + 2x + 2)\|\|- x + 1 + 1 +--R (112) -------------------------------------------- +--R 3x +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 554 +m0228:= a0228-r0228 +--R +--R +--R (113) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 554 +d0228:= D(m0228,x) +--R +--R +--R (114) 0 +--R Type: Expression(Integer) +--E 145 + +--S 146 of 554 +t0229:= (-1+4*x^2)^(1/2)/(x+(-1+4*x^2)^(1/2)) +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 1 +--R (115) -------------- +--R +-------+ +--R | 2 +--R \|4x - 1 + x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 554 +r0229:= 4/3*x-1/3*(-1+4*x^2)^(1/2)-1/9*atanh(3^(1/2)*x)*3^(1/2)+_ + 1/9*atanh(3^(1/2)*(-1+4*x^2)^(1/2))*3^(1/2) +--R +--R +--R +-------+ +-------+ +--R +-+ +-+ | 2 | 2 +-+ +-+ +--R \|3 atanh(\|3 \|4x - 1 ) - 3\|4x - 1 - \|3 atanh(x\|3 ) + 12x +--R (116) ---------------------------------------------------------------- +--R 9 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 554 +a0229:= integrate(t0229,x) +--R +--R +--R (117) +--R +-------+ +--R | 2 +--R (\|4x - 1 - 2x) +--R * +--R log +--R +-------+ +--R 3 +-+ 2 | 2 4 2 +-+ +--R ((24x - 4x)\|3 - 24x + 3)\|4x - 1 + (- 48x + 14x - 1)\|3 +--R + +--R 3 +--R 48x - 12x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (12x - 4x)\|4x - 1 - 24x + 11x - 1 +--R + +--R 2 +-+ +-------+ +--R (3x + 1)\|3 - 6x +-+ | 2 +--R (log(------------------) + 12x\|3 )\|4x - 1 +--R 2 +--R 3x - 1 +--R + +--R 2 +-+ +--R (3x + 1)\|3 - 6x 2 +-+ +--R - 2x log(------------------) + (- 24x + 2)\|3 +--R 2 +--R 3x - 1 +--R / +--R +-------+ +--R +-+ | 2 +-+ +--R 6\|3 \|4x - 1 - 12x\|3 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 554 +m0229:= a0229-r0229 +--R +--R +--R (118) +--R log +--R +-------+ +--R 3 +-+ 2 | 2 4 2 +-+ +--R ((24x - 4x)\|3 - 24x + 3)\|4x - 1 + (- 48x + 14x - 1)\|3 +--R + +--R 3 +--R 48x - 12x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (12x - 4x)\|4x - 1 - 24x + 11x - 1 +--R + +--R +-------+ 2 +-+ +--R +-+ | 2 (3x + 1)\|3 - 6x +-+ +--R - 2atanh(\|3 \|4x - 1 ) + log(------------------) + 2atanh(x\|3 ) +--R 2 +--R 3x - 1 +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 554 +d0229:= D(m0229,x) +--R +--R +--R (119) 0 +--R Type: Expression(Integer) +--E 150 + +--S 151 of 554 +t0230:= (-1+x+x^2)/(1+(1+x^2)^(1/2)) +--R +--R +--R 2 +--R x + x - 1 +--R (120) ------------- +--R +------+ +--R | 2 +--R \|x + 1 + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 554 +r0230:= -1/x-x+(1+1/x+1/2*x)*(1+x^2)^(1/2)-1/2*asinh(x)-log(1+(1+x^2)^(1/2)) +--R +--R +--R (121) +--R +------+ +------+ +--R | 2 2 | 2 2 +--R - 2x log(\|x + 1 + 1) + (x + 2x + 2)\|x + 1 - x asinh(x) - 2x - 2 +--R ----------------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 554 +a0230:= integrate(t0230,x) +--R +--R +--R (122) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((- 8x - 2x)\|x + 1 + 8x + 6x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((4x + x)\|x + 1 - 4x - 3x )log(\|x + 1 - x) +--R + +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((8x + 2x)\|x + 1 - 8x - 6x )log(\|x + 1 - x - 1) +--R + +--R +------+ +--R 3 5 4 3 2 | 2 +--R ((- 8x - 2x)log(x) - 4x - 16x - 3x - 16x - 4x - 2)\|x + 1 +--R + +--R 4 2 6 5 4 3 2 +--R (8x + 6x )log(x) + 4x + 16x + 5x + 24x + 5x + 8x + 2 +--R / +--R +------+ +--R 3 | 2 4 2 +--R (8x + 2x)\|x + 1 - 8x - 6x +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 554 +m0230:= a0230-r0230 +--R +--R +--R (123) +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R 2log(\|x + 1 + 1) - 2log(\|x + 1 - x + 1) + log(\|x + 1 - x) +--R + +--R +------+ +--R | 2 +--R 2log(\|x + 1 - x - 1) - 2log(x) + asinh(x) + 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 554 +d0230:= D(m0230,x) +--R +--R +--R (124) 0 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 554 +t0231:= (-1+x+x^2)/(1+x+(1+x^2)^(1/2)) +--R +--R +--R 2 +--R x + x - 1 +--R (125) ----------------- +--R +------+ +--R | 2 +--R \|x + 1 + x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 554 +r0231:= 1/2*x^2+1/6*x^3+1/12*(4-3*x-2*x^2)*(1+x^2)^(1/2)-_ + 1/4*asinh(x)-1/2*log(1+(1+x^2)^(1/2)) +--R +--R +--R (126) +--R +------+ +------+ +--R | 2 2 | 2 3 2 +--R - 6log(\|x + 1 + 1) + (- 2x - 3x + 4)\|x + 1 - 3asinh(x) + 2x + 6x +--R ------------------------------------------------------------------------- +--R 12 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 554 +a0231:= integrate(t0231,x) +--R +--R +--R (127) +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((- 24x - 6)\|x + 1 + 24x + 18x)log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((12x + 3)\|x + 1 - 12x - 9x)log(\|x + 1 - x) +--R + +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((24x + 6)\|x + 1 - 24x - 18x)log(\|x + 1 - x - 1) +--R + +--R +------+ +--R 2 5 4 3 2 | 2 +--R ((- 24x - 6)log(x) + 16x + 36x - 8x + 15x - 12x)\|x + 1 +--R + +--R 3 6 5 3 2 +--R (24x + 18x)log(x) - 16x - 36x - 33x + 18x - 3x + 4 +--R / +--R +------+ +--R 2 | 2 3 +--R (48x + 12)\|x + 1 - 48x - 36x +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 554 +m0231:= a0231-r0231 +--R +--R +--R (128) +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R 2log(\|x + 1 + 1) - 2log(\|x + 1 - x + 1) + log(\|x + 1 - x) +--R + +--R +------+ +--R | 2 +--R 2log(\|x + 1 - x - 1) - 2log(x) + asinh(x) +--R / +--R 4 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 554 +d0231:= D(m0231,x) +--R +--R +--R (129) 0 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 554 +t0232:= x/(1-x^3)^(2/3) +--R +--R +--R x +--R (130) ------------ +--R +--------+2 +--R 3| 3 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 554 +r0232:= -1/3*atan(1/3*(1-2*x/(1-x^3)^(1/3))*3^(1/2))*3^(1/2)+_ + 1/6*log(1+x^2/(1-x^3)^(2/3)-x/(1-x^3)^(1/3))-1/3*log(1+x/(1-x^3)^(1/3)) +--R +--R +--R (131) +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R \|- x + 1 + x \|- x + 1 - x\|- x + 1 + x +--R - 2log(---------------) + log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--R +-+3| 3 +-+ +--R +-+ \|3 \|- x + 1 - 2x\|3 +--R - 2\|3 atan(------------------------) +--R +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R 6 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 554 +a0232:= integrate(t0232,x) +--R +--R +--R (132) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--R +-+3| 3 +-+ +--R 2\|3 \|- x + 1 - x\|3 +--R - 6atan(------------------------) +--R 3x +--R / +--R +-+ +--R 6\|3 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 554 +m0232:= a0232-r0232 +--R +--R +--R (133) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R +-+ \|- x + 1 + x +-+ \|- x + 1 - x\|- x + 1 + x +--R 2\|3 log(---------------) - \|3 log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--------+ +--R +-+3| 3 +-+ +-+3| 3 +-+ +--R 2\|3 \|- x + 1 - x\|3 \|3 \|- x + 1 - 2x\|3 +--R - 6atan(------------------------) + 6atan(------------------------) +--R 3x +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 554 +d0232:= D(m0232,x) +--R +--R +--R (134) 0 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 554 +t0233:= x*(1-x^3)^(1/3) +--R +--R +--R +--------+ +--R 3| 3 +--R (135) x\|- x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 554 +r0233:= 1/3*x^2*(1-x^3)^(1/3)-1/9*atan(1/3*(1-2*x/(1-x^3)^(1/3))*3^(1/2))*_ + 3^(1/2)+1/18*log(1+x^2/(1-x^3)^(2/3)-x/(1-x^3)^(1/3))-_ + 1/9*log(1+x/(1-x^3)^(1/3)) +--R +--R +--R (136) +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R \|- x + 1 + x \|- x + 1 - x\|- x + 1 + x +--R - 2log(---------------) + log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--R +-+3| 3 +-+ +--------+ +--R +-+ \|3 \|- x + 1 - 2x\|3 2 3| 3 +--R - 2\|3 atan(------------------------) + 6x \|- x + 1 +--R +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R 18 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 554 +a0233:= integrate(t0233,x) +--R +--R +--R (137) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--R +-+3| 3 +-+ +--------+ +--R 2\|3 \|- x + 1 - x\|3 2 +-+3| 3 +--R - 6atan(------------------------) + 6x \|3 \|- x + 1 +--R 3x +--R / +--R +-+ +--R 18\|3 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 554 +m0233:= a0233-r0233 +--R +--R +--R (138) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R +-+ \|- x + 1 + x +-+ \|- x + 1 - x\|- x + 1 + x +--R 2\|3 log(---------------) - \|3 log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--------+ +--R +-+3| 3 +-+ +-+3| 3 +-+ +--R 2\|3 \|- x + 1 - x\|3 \|3 \|- x + 1 - 2x\|3 +--R - 6atan(------------------------) + 6atan(------------------------) +--R 3x +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 554 +d0233:= D(m0233,x) +--R +--R +--R (139) 0 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 554 +t0234:= (a+b*x^4)^(3/2) +--R +--R +--R +--------+ +--R 4 | 4 +--R (140) (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 554 +r0234:= 2/7*a*x*(a+b*x^4)^(1/2)+1/7*x*(a+b*x^4)^(3/2)+4/7*a^(9/4)*_ + ((a+b*x^4)/a)^(1/2)*atanh(asin((-b)^(1/4)*x/a^(1/4)))/_ + (-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R (141) +--R +--------+ +--R | 4 4+---+ +--R 2 4+-+ |b x + a x\|- b 2 9 5 2 4+---+ +--R 4a \|a |-------- atanh(asin(-------) + (b x + 4a b x + 3a x)\|- b +--R \| a 4+-+ +--R \|a +--R ---------------------------------------------------------------------- +--R +--------+ +--R 4+---+ | 4 +--R 7\|- b \|b x + a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 554 +a0234:= integrate(t0234,x) +--R +--R +--R x +--------+ +--R ++ 4 | 4 +--R (142) | (%T b + a)\|%T b + a d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 554 +m0234:= a0234-r0234 +--R +--R +--R (143) +--R +--------+ +--R | 4 4+---+ +--R 2 4+-+ |b x + a x\|- b +--R - 4a \|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--------+ +--R 4+---+ | 4 ++ 4 | 4 +--R 7\|- b \|b x + a | (%T b + a)\|%T b + a d%T +--R ++ +--R + +--R 2 9 5 2 4+---+ +--R (- b x - 4a b x - 3a x)\|- b +--R / +--R +--------+ +--R 4+---+ | 4 +--R 7\|- b \|b x + a +--R Type: Expression(Integer) +--E 174 + +--S 175 of 554 +d0234:= D(m0234,x) +--R +--R +--R (144) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R 2 |b x + a x\|- b 2 |b x + a |\|a - x \|- b +--R (4a |-------- asin(-------) - 4a |-------- ) |----------------- +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R + +--R 4 2 +--R 4a b x + 4a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R |b x + a | 4 x\|- b |b x + a | 4 +--R (7 |-------- \|b x + a asin(-------) - 7 |-------- \|b x + a) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression(Integer) +--E 175 + +--S 176 of 554 +t0235:= (a+b*x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (145) \|b x + a +--R Type: Expression(Integer) +--E 176 + +--S 177 of 554 +r0235:= 1/3*x*(a+b*x^4)^(1/2)+2/3*a^(5/4)*((a+b*x^4)/a)^(1/2)*_ + atanh(asin((-b)^(1/4)*x/a^(1/4)))/(-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b 5 4+---+ +--R 2a\|a |-------- atanh(asin(-------)) + (b x + a x)\|- b +--R \| a 4+-+ +--R \|a +--R (146) ---------------------------------------------------------- +--R +--------+ +--R 4+---+ | 4 +--R 3\|- b \|b x + a +--R Type: Expression(Integer) +--E 177 + +--S 178 of 554 +a0235:= integrate(t0235,x) +--R +--R +--R x +--------+ +--R ++ | 4 +--R (147) | \|%T b + a d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 554 +m0235:= a0235-r0235 +--R +--R +--R (148) +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b +--R - 2a\|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--------+ +--R 4+---+ | 4 ++ | 4 5 4+---+ +--R 3\|- b \|b x + a | \|%T b + a d%T + (- b x - a x)\|- b +--R ++ +--R / +--R +--------+ +--R 4+---+ | 4 +--R 3\|- b \|b x + a +--R Type: Expression(Integer) +--E 179 + +--S 180 of 554 +d0235:= D(m0235,x) +--R +--R +--R (149) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (2a |-------- asin(-------) - 2a |-------- ) |----------------- + 2b x +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R + +--R 2a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R |b x + a | 4 x\|- b |b x + a | 4 +--R (3 |-------- \|b x + a asin(-------) - 3 |-------- \|b x + a) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression(Integer) +--E 180 + +--S 181 of 554 +t0236:= 1/(a+b*x^4)^(1/2) +--R +--R +--R 1 +--R (150) ----------- +--R +--------+ +--R | 4 +--R \|b x + a +--R Type: Expression(Integer) +--E 181 + +--S 182 of 554 +r0236:= a^(1/4)*((a+b*x^4)/a)^(1/2)*atanh(asin((-b)^(1/4)*x/a^(1/4)))/_ + (-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b +--R \|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R (151) ----------------------------------- +--R +--------+ +--R 4+---+ | 4 +--R \|- b \|b x + a +--R Type: Expression(Integer) +--E 182 + +--S 183 of 554 +a0236:= integrate(t0236,x) +--R +--R +--R x +--R ++ 1 +--R (152) | ----------- d%T +--R ++ +--------+ +--R | 4 +--R \|%T b + a +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 554 +m0236:= a0236-r0236 +--R +--R +--R (153) +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b +--R - \|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--R 4+---+ | 4 ++ 1 +--R \|- b \|b x + a | ----------- d%T +--R ++ +--------+ +--R | 4 +--R \|%T b + a +--R / +--R +--------+ +--R 4+---+ | 4 +--R \|- b \|b x + a +--R Type: Expression(Integer) +--E 184 + +--S 185 of 554 +d0236:= D(m0236,x) +--R +--R +--R (154) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (a |-------- asin(-------) - a |-------- ) |----------------- + b x + a +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R |b x + a | 4 x\|- b |b x + a | 4 +--R (a |-------- \|b x + a asin(-------) - a |-------- \|b x + a ) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression(Integer) +--E 185 + +--S 186 of 554 +t0237:= 1/(a+b*x^4)^(3/2) +--R +--R +--R 1 +--R (155) --------------------- +--R +--------+ +--R 4 | 4 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 186 + +--S 187 of 554 +r0237:= 1/2*(x*a^(3/4)*(-b)^(1/4)+((a+b*x^4)/a)^(1/2)*_ + atanh(asin((-b)^(1/4)*x/a^(1/4)))*a)/a^(7/4)/(a+b*x^4)^(1/2)/(-b)^(1/4) +--R +--R +--R +--------+ +--R | 4 4+---+ +--R |b x + a x\|- b 4+---+4+-+3 +--R a |-------- atanh(asin(-------)) + x\|- b \|a +--R \| a 4+-+ +--R \|a +--R (156) ----------------------------------------------- +--R +--------+ +--R 4+---+4+-+3 | 4 +--R 2a\|- b \|a \|b x + a +--R Type: Expression(Integer) +--E 187 + +--S 188 of 554 +a0237:= integrate(t0237,x) +--R +--R +--R x +--R ++ 1 +--R (157) | --------------------- d%T +--R ++ +--------+ +--R 4 | 4 +--R (%T b + a)\|%T b + a +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 554 +m0237:= a0237-r0237 +--R +--R +--R (158) +--R +--------+ +--R | 4 4+---+ +--R |b x + a x\|- b +--R - a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--R 4+---+4+-+3 | 4 ++ 1 4+---+4+-+3 +--R 2a\|- b \|a \|b x + a | --------------------- d%T - x\|- b \|a +--R ++ +--------+ +--R 4 | 4 +--R (%T b + a)\|%T b + a +--R / +--R +--------+ +--R 4+---+4+-+3 | 4 +--R 2a\|- b \|a \|b x + a +--R Type: Expression(Integer) +--E 189 + +--S 190 of 554 +d0237:= D(m0237,x) +--R +--R +--R (159) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (a |-------- asin(-------) - a |-------- ) |----------------- + b x + a +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R 2 |b x + a | 4 x\|- b 2 |b x + a | 4 +--R (2a |-------- \|b x + a asin(-------) - 2a |-------- \|b x + a ) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 554 +t0238:= 1/(a+b*x^4)^(5/2) +--R +--R +--R 1 +--R (160) -------------------------------- +--R +--------+ +--R 2 8 4 2 | 4 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 191 + +--S 192 of 554 +r0238:= 1/6*x/a/(a+b*x^4)^(3/2)+5/12*x/a^2/(a+b*x^4)^(1/2)+_ + 5/12*((a+b*x^4)/a)^(1/2)*atanh(asin((-b)^(1/4)*x/a^(1/4)))/_ + a^(7/4)/(-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R (161) +--R +--------+ +--R | 4 4+---+ +--R 4 2 |b x + a x\|- b 5 4+---+4+-+3 +--R (5a b x + 5a ) |-------- atanh(asin(-------)) + (5b x + 7a x)\|- b \|a +--R \| a 4+-+ +--R \|a +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 4 3 4+---+4+-+3 | 4 +--R (12a b x + 12a )\|- b \|a \|b x + a +--R Type: Expression(Integer) +--E 192 + +--S 193 of 554 +a0238:= integrate(t0238,x) +--R +--R +--R x +--R ++ 1 +--R (162) | --------------------------------- d%T +--R ++ +--------+ +--R 8 2 4 2 | 4 +--R (%T b + 2%T a b + a )\|%T b + a +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 554 +m0238:= a0238-r0238 +--R +--R +--R (163) +--R +--------+ +--R | 4 4+---+ +--R 4 2 |b x + a x\|- b +--R (- 5a b x - 5a ) |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ +--R 2 4 3 4+---+4+-+3 | 4 +--R (12a b x + 12a )\|- b \|a \|b x + a +--R * +--R x +--R ++ 1 +--R | --------------------------------- d%T +--R ++ +--------+ +--R 8 2 4 2 | 4 +--R (%T b + 2%T a b + a )\|%T b + a +--R + +--R 5 4+---+4+-+3 +--R (- 5b x - 7a x)\|- b \|a +--R / +--R +--------+ +--R 2 4 3 4+---+4+-+3 | 4 +--R (12a b x + 12a )\|- b \|a \|b x + a +--R Type: Expression(Integer) +--E 194 + +--S 195 of 554 +d0238:= D(m0238,x) +--R +--R +--R (164) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (5a |-------- asin(-------) - 5a |-------- ) |----------------- + 5b x +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R + +--R 5a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R 3 |b x + a | 4 x\|- b 3 |b x + a | 4 +--R (12a |-------- \|b x + a asin(-------) - 12a |-------- \|b x + a ) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression(Integer) +--E 195 + +--S 196 of 554 +t0239:= (1+x^4)^(3/2) +--R +--R +--R +------+ +--R 4 | 4 +--R (165) (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 554 +r0239:= 2/7*x*(1+x^4)^(1/2)+1/7*x*(1+x^4)^(3/2)-4/7*(-1)^(3/4)*_ + atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +---+ +------+ +--R +---+ x\|- 1 + x 5 +-+ | 4 +--R (- 4\|- 1 + 4)atanh(asin(-----------)) + (x + 3x)\|2 \|x + 1 +--R +-+ +--R \|2 +--R (166) ---------------------------------------------------------------- +--R +-+ +--R 7\|2 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 554 +a0239:= integrate(t0239,x) +--R +--R +--R x +-------+ +--R ++ 4 | 4 +--R (167) | (%T + 1)\|%T + 1 d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 554 +m0239:= a0239-r0239 +--R +--R +--R (168) +--R x +-------+ +---+ +--R +-+ ++ 4 | 4 +---+ x\|- 1 + x +--R 7\|2 | (%T + 1)\|%T + 1 d%T + (4\|- 1 - 4)atanh(asin(-----------)) +--R ++ +-+ +--R \|2 +--R + +--R +------+ +--R 5 +-+ | 4 +--R (- x - 3x)\|2 \|x + 1 +--R / +--R +-+ +--R 7\|2 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 554 +d0239:= D(m0239,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R 4\|x + 1 + (4asin(-----------) - 4)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (169) ------------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (7asin(-----------) - 7)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 554 +t0240:= (1+x^4)^(1/2) +--R +--R +--R +------+ +--R | 4 +--R (170) \|x + 1 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 554 +r0240:= 1/3*x*(1+x^4)^(1/2)-2/3*(-1)^(3/4)*atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +---+ +------+ +--R +---+ x\|- 1 + x +-+ | 4 +--R (- 2\|- 1 + 2)atanh(asin(-----------)) + x\|2 \|x + 1 +--R +-+ +--R \|2 +--R (171) -------------------------------------------------------- +--R +-+ +--R 3\|2 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 554 +a0240:= integrate(t0240,x) +--R +--R +--R x +-------+ +--R ++ | 4 +--R (172) | \|%T + 1 d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 554 +m0240:= a0240-r0240 +--R +--R +--R (173) +--R x +-------+ +---+ +--R +-+ ++ | 4 +---+ x\|- 1 + x +--R 3\|2 | \|%T + 1 d%T + (2\|- 1 - 2)atanh(asin(-----------)) +--R ++ +-+ +--R \|2 +--R + +--R +------+ +--R +-+ | 4 +--R - x\|2 \|x + 1 +--R / +--R +-+ +--R 3\|2 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 554 +d0240:= D(m0240,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R 2\|x + 1 + (2asin(-----------) - 2)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (174) ------------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (3asin(-----------) - 3)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 205 + +--S 206 of 554 +t0241:= 1/(1+x^4)^(1/2) +--R +--R +--R 1 +--R (175) --------- +--R +------+ +--R | 4 +--R \|x + 1 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 554 +r0241:= -(-1)^(3/4)*atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +---+ +--R +---+ x\|- 1 + x +--R (- \|- 1 + 1)atanh(asin(-----------)) +--R +-+ +--R \|2 +--R (176) -------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 554 +a0241:= integrate(t0241,x) +--R +--R +--R x +--R ++ 1 +--R (177) | ---------- d%T +--R ++ +-------+ +--R | 4 +--R \|%T + 1 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 554 +m0241:= a0241-r0241 +--R +--R +--R x +---+ +--R +-+ ++ 1 +---+ x\|- 1 + x +--R \|2 | ---------- d%T + (\|- 1 - 1)atanh(asin(-----------)) +--R ++ +-------+ +-+ +--R | 4 \|2 +--R \|%T + 1 +--R (178) --------------------------------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 554 +d0241:= D(m0241,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R \|x + 1 + (asin(-----------) - 1)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (179) ----------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (asin(-----------) - 1)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 210 + +--S 211 of 554 +t0242:= 1/(1+x^4)^(3/2) +--R +--R +--R 1 +--R (180) ----------------- +--R +------+ +--R 4 | 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 554 +r0242:= 1/2*x/(1+x^4)^(1/2)-1/2*(-1)^(3/4)*atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +------+ +---+ +--R +---+ | 4 x\|- 1 + x +-+ +--R (- \|- 1 + 1)\|x + 1 atanh(asin(-----------)) + x\|2 +--R +-+ +--R \|2 +--R (181) ------------------------------------------------------- +--R +------+ +--R +-+ | 4 +--R 2\|2 \|x + 1 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 554 +a0242:= integrate(t0242,x) +--R +--R +--R x +--R ++ 1 +--R (182) | ------------------- d%T +--R ++ +-------+ +--R 4 | 4 +--R (%T + 1)\|%T + 1 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 554 +m0242:= a0242-r0242 +--R +--R +--R (183) +--R +------+ x +--R +-+ | 4 ++ 1 +--R 2\|2 \|x + 1 | ------------------- d%T +--R ++ +-------+ +--R 4 | 4 +--R (%T + 1)\|%T + 1 +--R + +--R +------+ +---+ +--R +---+ | 4 x\|- 1 + x +-+ +--R (\|- 1 - 1)\|x + 1 atanh(asin(-----------)) - x\|2 +--R +-+ +--R \|2 +--R / +--R +------+ +--R +-+ | 4 +--R 2\|2 \|x + 1 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 554 +d0242:= D(m0242,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R \|x + 1 + (asin(-----------) - 1)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (184) ----------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (2asin(-----------) - 2)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 215 + +--S 216 of 554 +t0243:= 1/(1+x^4)^(5/2) +--R +--R +--R 1 +--R (185) ----------------------- +--R +------+ +--R 8 4 | 4 +--R (x + 2x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 554 +r0243:= 1/6*x/(1+x^4)^(3/2)+5/12*x/(1+x^4)^(1/2)-5/12*(-1)^(3/4)*_ + atanh(asin((-1)^(1/4)*x)) +--R +--R +--R (186) +--R +------+ +---+ +--R 4 +---+ 4 | 4 x\|- 1 + x +--R ((- 5x - 5)\|- 1 + 5x + 5)\|x + 1 atanh(asin(-----------)) +--R +-+ +--R \|2 +--R + +--R 5 +-+ +--R (5x + 7x)\|2 +--R / +--R +------+ +--R 4 +-+ | 4 +--R (12x + 12)\|2 \|x + 1 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 554 +a0243:= integrate(t0243,x) +--R +--R +--R x +--R ++ 1 +--R (187) | -------------------------- d%T +--R ++ +-------+ +--R 8 4 | 4 +--R (%T + 2%T + 1)\|%T + 1 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 554 +m0243:= a0243-r0243 +--R +--R +--R (188) +--R +------+ x +--R 4 +-+ | 4 ++ 1 +--R (12x + 12)\|2 \|x + 1 | -------------------------- d%T +--R ++ +-------+ +--R 8 4 | 4 +--R (%T + 2%T + 1)\|%T + 1 +--R + +--R +------+ +---+ +--R 4 +---+ 4 | 4 x\|- 1 + x +--R ((5x + 5)\|- 1 - 5x - 5)\|x + 1 atanh(asin(-----------)) +--R +-+ +--R \|2 +--R + +--R 5 +-+ +--R (- 5x - 7x)\|2 +--R / +--R +------+ +--R 4 +-+ | 4 +--R (12x + 12)\|2 \|x + 1 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 554 +d0243:= D(m0243,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R 5\|x + 1 + (5asin(-----------) - 5)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (189) ------------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (12asin(-----------) - 12)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 220 + +--S 221 of 554 +t0244:= (1-x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (190) \|- x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 554 +r0244:= 1/3*x*(1-x^4)^(1/2)+2/3*atanh(asin(x)) +--R +--R +--R +--------+ +--R | 4 +--R 2atanh(asin(x)) + x\|- x + 1 +--R (191) ------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 554 +a0244:= integrate(t0244,x) +--R +--R +--R x +---------+ +--R ++ | 4 +--R (192) | \|- %T + 1 d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 554 +m0244:= a0244-r0244 +--R +--R +--R x +---------+ +--------+ +--R ++ | 4 | 4 +--R 3 | \|- %T + 1 d%T - 2atanh(asin(x)) - x\|- x + 1 +--R ++ +--R (193) ------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 554 +d0244:= D(m0244,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (2asin(x) - 2)\|- x + 1 + 2\|- x + 1 +--R (194) ----------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (3asin(x) - 3)\|- x + 1 \|- x + 1 +--R Type: Expression(Integer) +--E 225 + +--S 226 of 554 +t0245:= 1/(1-x^4)^(1/2) +--R +--R +--R 1 +--R (195) ----------- +--R +--------+ +--R | 4 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 554 +r0245:= atanh(asin(x)) +--R +--R +--R (196) atanh(asin(x)) +--R Type: Expression(Integer) +--E 227 + +--S 228 of 554 +a0245:= integrate(t0245,x) +--R +--R +--R x +--R ++ 1 +--R (197) | ------------ d%T +--R ++ +---------+ +--R | 4 +--R \|- %T + 1 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 554 +m0245:= a0245-r0245 +--R +--R +--R x +--R ++ 1 +--R (198) | ------------ d%T - atanh(asin(x)) +--R ++ +---------+ +--R | 4 +--R \|- %T + 1 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 554 +d0245:= D(m0245,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (asin(x) - 1)\|- x + 1 + \|- x + 1 +--R (199) --------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (asin(x) - 1)\|- x + 1 \|- x + 1 +--R Type: Expression(Integer) +--E 230 + +--S 231 of 554 +t0246:= 1/(1-x^4)^(3/2) +--R +--R +--R 1 +--R (200) - ------------------- +--R +--------+ +--R 4 | 4 +--R (x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 554 +r0246:= 1/2*x/(1-x^4)^(1/2)+1/2*atanh(asin(x)) +--R +--R +--R +--------+ +--R | 4 +--R \|- x + 1 atanh(asin(x)) + x +--R (201) ----------------------------- +--R +--------+ +--R | 4 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 554 +a0246:= integrate(t0246,x) +--R +--R +--R x +--R ++ 1 +--R (202) | - --------------------- d%T +--R ++ +---------+ +--R 4 | 4 +--R (%T - 1)\|- %T + 1 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 554 +m0246:= a0246-r0246 +--R +--R +--R (203) +--R +--------+ x +--------+ +--R | 4 ++ 1 | 4 +--R 2\|- x + 1 | - --------------------- d%T - \|- x + 1 atanh(asin(x)) - x +--R ++ +---------+ +--R 4 | 4 +--R (%T - 1)\|- %T + 1 +--R ----------------------------------------------------------------------------- +--R +--------+ +--R | 4 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 554 +d0246:= D(m0246,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (asin(x) - 1)\|- x + 1 + \|- x + 1 +--R (204) --------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (2asin(x) - 2)\|- x + 1 \|- x + 1 +--R Type: Expression(Integer) +--E 235 + +--S 236 of 554 +t0247:= 1/(1-x^4)^(5/2) +--R +--R +--R 1 +--R (205) ------------------------- +--R +--------+ +--R 8 4 | 4 +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 554 +r0247:= 1/6*x/(1-x^4)^(3/2)+5/12*x/(1-x^4)^(1/2)+5/12*atanh(asin(x)) +--R +--R +--R +--------+ +--R 4 | 4 5 +--R (5x - 5)\|- x + 1 atanh(asin(x)) + 5x - 7x +--R (206) --------------------------------------------- +--R +--------+ +--R 4 | 4 +--R (12x - 12)\|- x + 1 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 554 +a0247:= integrate(t0247,x) +--R +--R +--R x +--R ++ 1 +--R (207) | ---------------------------- d%T +--R ++ +---------+ +--R 8 4 | 4 +--R (%T - 2%T + 1)\|- %T + 1 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 554 +m0247:= a0247-r0247 +--R +--R +--R (208) +--R +--------+ x +--R 4 | 4 ++ 1 +--R (12x - 12)\|- x + 1 | ---------------------------- d%T +--R ++ +---------+ +--R 8 4 | 4 +--R (%T - 2%T + 1)\|- %T + 1 +--R + +--R +--------+ +--R 4 | 4 5 +--R (- 5x + 5)\|- x + 1 atanh(asin(x)) - 5x + 7x +--R / +--R +--------+ +--R 4 | 4 +--R (12x - 12)\|- x + 1 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 554 +d0247:= D(m0247,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (5asin(x) - 5)\|- x + 1 + 5\|- x + 1 +--R (209) ----------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (12asin(x) - 12)\|- x + 1 \|- x + 1 +--R Type: Expression(Integer) +--E 240 + +--S 241 of 554 +t0248:= 1/x/(1+x^6)^(1/2) +--R +--R +--R 1 +--R (210) ---------- +--R +------+ +--R | 6 +--R x\|x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 554 +r0248:= -1/3*atanh((1+x^6)^(1/2)) +--R +--R +--R +------+ +--R | 6 +--R atanh(\|x + 1 ) +--R (211) - ---------------- +--R 3 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 554 +a0248:= integrate(t0248,x) +--R +--R +--R +------+ +------+ +--R | 6 | 6 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) +--R (212) ----------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 554 +m0248:= a0248-r0248 +--R +--R +--R +------+ +------+ +------+ +--R | 6 | 6 | 6 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (213) ------------------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 554 +d0248:= D(m0248,x) +--R +--R +--R (214) 0 +--R Type: Expression(Integer) +--E 245 + +--S 246 of 554 +t0249:= 1/x/(-25+x^6)^(1/2) +--R +--R +--R 1 +--R (215) ----------- +--R +-------+ +--R | 6 +--R x\|x - 25 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 554 +r0249:= 1/15*atan(1/5*(-25+x^6)^(1/2)) +--R +--R +--R +-------+ +--R | 6 +--R \|x - 25 +--R atan(----------) +--R 5 +--R (216) ---------------- +--R 15 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 554 +a0249:= integrate(t0249,x) +--R +--R +--R +-------+ +--R | 6 +--R \|x - 25 +--R atan(----------) +--R 5 +--R (217) ---------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 554 +m0249:= a0249-r0249 +--R +--R +--R (218) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 554 +d0249:= D(m0249,x) +--R +--R +--R (219) 0 +--R Type: Expression(Integer) +--E 250 + +--S 251 of 554 +t0250:= x^8*(-1+4*x^6)^(1/2) +--R +--R +--R +-------+ +--R 8 | 6 +--R (220) x \|4x - 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 554 +r0250:= -1/96*x^3*(-1+4*x^6)^(1/2)+1/12*x^9*(-1+4*x^6)^(1/2)-_ + 1/192*atanh(1/2*(-1+4*x^6)^(1/2)/x^3) +--R +--R +--R +-------+ +--R | 6 +-------+ +--R \|4x - 1 9 3 | 6 +--R - atanh(----------) + (16x - 2x )\|4x - 1 +--R 3 +--R 2x +--R (221) -------------------------------------------- +--R 192 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 554 +a0250:= integrate(t0250,x) +--R +--R +--R (222) +--R +-------+ +-------+ +--R 9 3 | 6 12 6 | 6 3 +--R ((64x - 8x )\|4x - 1 - 128x + 32x - 1)log(\|4x - 1 - 2x ) +--R + +--R +-------+ +--R 21 15 9 3 | 6 24 18 12 +--R (- 2048x + 768x - 80x + 2x )\|4x - 1 + 4096x - 2048x + 320x +--R + +--R 6 +--R - 16x +--R / +--R +-------+ +--R 9 3 | 6 12 6 +--R (12288x - 1536x )\|4x - 1 - 24576x + 6144x - 192 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 554 +m0250:= a0250-r0250 +--R +--R +--R +-------+ +--R +-------+ | 6 +--R | 6 3 \|4x - 1 +--R log(\|4x - 1 - 2x ) + atanh(----------) +--R 3 +--R 2x +--R (223) ----------------------------------------- +--R 192 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 554 +d0250:= D(m0250,x) +--R +--R +--R (224) 0 +--R Type: Expression(Integer) +--E 255 + +--S 256 of 554 +t0251:= x^2*(-2+x^6)^(1/2) +--R +--R +--R +------+ +--R 2 | 6 +--R (225) x \|x - 2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 554 +r0251:= 1/6*x^3*(-2+x^6)^(1/2)-1/3*atanh((-2+x^6)^(1/2)/x^3) +--R +--R +--R +------+ +--R | 6 +------+ +--R \|x - 2 3 | 6 +--R - 2atanh(---------) + x \|x - 2 +--R 3 +--R x +--R (226) --------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 554 +a0251:= integrate(t0251,x) +--R +--R +--R (227) +--R +------+ +------+ +------+ +--R 3 | 6 6 | 6 3 9 3 | 6 12 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x +--R + +--R 6 +--R - 2x +--R / +--R +------+ +--R 3 | 6 6 +--R 6x \|x - 2 - 6x + 6 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 554 +m0251:= a0251-r0251 +--R +--R +--R +------+ +--R +------+ | 6 +--R | 6 3 \|x - 2 +--R log(\|x - 2 - x ) + atanh(---------) +--R 3 +--R x +--R (228) -------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 554 +d0251:= D(m0251,x) +--R +--R +--R (229) 0 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 554 +t0252:= 1/x/(1+x^8)^(1/2) +--R +--R +--R 1 +--R (230) ---------- +--R +------+ +--R | 8 +--R x\|x + 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 554 +r0252:= -1/4*atanh((1+x^8)^(1/2)) +--R +--R +--R +------+ +--R | 8 +--R atanh(\|x + 1 ) +--R (231) - ---------------- +--R 4 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 554 +a0252:= integrate(t0252,x) +--R +--R +--R +------+ +------+ +--R | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) +--R (232) ----------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 554 +m0252:= a0252-r0252 +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (233) ------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 554 +d0252:= D(m0252,x) +--R +--R +--R (234) 0 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 554 +t0253:= x^3*(-2+x^8)^(1/2) +--R +--R +--R +------+ +--R 3 | 8 +--R (235) x \|x - 2 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 554 +r0253:= 1/8*x^4*(-2+x^8)^(1/2)-1/4*atanh((-2+x^8)^(1/2)/x^4) +--R +--R +--R +------+ +--R | 8 +------+ +--R \|x - 2 4 | 8 +--R - 2atanh(---------) + x \|x - 2 +--R 4 +--R x +--R (236) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 554 +a0253:= integrate(t0253,x) +--R +--R +--R (237) +--R +------+ +------+ +------+ +--R 4 | 8 8 | 8 4 12 4 | 8 16 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x +--R + +--R 8 +--R - 2x +--R / +--R +------+ +--R 4 | 8 8 +--R 8x \|x - 2 - 8x + 8 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 554 +m0253:= a0253-r0253 +--R +--R +--R +------+ +--R +------+ | 8 +--R | 8 4 \|x - 2 +--R log(\|x - 2 - x ) + atanh(---------) +--R 4 +--R x +--R (238) -------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 554 +d0253:= D(m0253,x) +--R +--R +--R (239) 0 +--R Type: Expression(Integer) +--E 270 + +--S 271 of 554 +t0254:= (1+x^8)^(1/2)*(1+2*x^8)/(x+2*x^9+x^17) +--R +--R +--R +------+ +--R 8 | 8 +--R (2x + 1)\|x + 1 +--R (240) ------------------ +--R 17 9 +--R x + 2x + x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 554 +r0254:= -1/4/(1+x^8)^(1/2)-1/4*atanh((1+x^8)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 8 | 8 +--R - \|x + 1 atanh(\|x + 1 ) - 1 +--R (241) ------------------------------- +--R +------+ +--R | 8 +--R 4\|x + 1 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 554 +a0254:= integrate(t0254,x) +--R +--R +--R +------+ +------+ +------+ +------+ +--R | 8 | 8 | 8 | 8 +--R - \|x + 1 log(\|x + 1 + 1) + \|x + 1 log(\|x + 1 - 1) - 2 +--R (242) --------------------------------------------------------------- +--R +------+ +--R | 8 +--R 8\|x + 1 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 554 +m0254:= a0254-r0254 +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (243) ------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 554 +d0254:= D(m0254,x) +--R +--R +--R (244) 0 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 554 +t0255:= x^4/(-2+x^10)^(1/2) +--R +--R +--R 4 +--R x +--R (245) ---------- +--R +-------+ +--R | 10 +--R \|x - 2 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 554 +r0255:= 1/5*atanh((-2+x^10)^(1/2)/x^5) +--R +--R +--R +-------+ +--R | 10 +--R \|x - 2 +--R atanh(----------) +--R 5 +--R x +--R (246) ----------------- +--R 5 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 554 +a0255:= integrate(t0255,x) +--R +--R +--R +-------+ +--R | 10 5 +--R log(\|x - 2 - x ) +--R (247) - -------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 554 +m0255:= a0255-r0255 +--R +--R +--R +-------+ +--R +-------+ | 10 +--R | 10 5 \|x - 2 +--R - log(\|x - 2 - x ) - atanh(----------) +--R 5 +--R x +--R (248) ------------------------------------------ +--R 5 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 554 +d0255:= D(m0255,x) +--R +--R +--R (249) 0 +--R Type: Expression(Integer) +--E 280 + +--S 281 of 554 +t0256:= x^31*(1+x^16)^(1/2)/(1-x^16) +--R +--R +--R +-------+ +--R 31 | 16 +--R x \|x + 1 +--R (250) - ------------- +--R 16 +--R x - 1 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 554 +r0256:= -1/8*(1+x^16)^(1/2)-1/24*(1+x^16)^(3/2)+1/8*_ + atanh(1/2*(1+x^16)^(1/2)*2^(1/2))*2^(1/2) +--R +--R +--R +-------+ +--R +-+ | 16 +-------+ +--R +-+ \|2 \|x + 1 16 | 16 +--R 3\|2 atanh(--------------) + (- x - 4)\|x + 1 +--R 2 +--R (251) -------------------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 554 +a0256:= integrate(t0256,x) +--R +--R +--R +-------+ +--R | 16 16 +-+ +-------+ +--R 4\|x + 1 + (x + 3)\|2 16 +-+ | 16 +--R 3log(---------------------------) + (- x - 4)\|2 \|x + 1 +--R 16 +--R x - 1 +--R (252) ------------------------------------------------------------- +--R +-+ +--R 24\|2 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 554 +m0256:= a0256-r0256 +--R +--R +--R +-------+ +-------+ +--R | 16 16 +-+ +-+ | 16 +--R 4\|x + 1 + (x + 3)\|2 \|2 \|x + 1 +--R log(---------------------------) - 2atanh(--------------) +--R 16 2 +--R x - 1 +--R (253) --------------------------------------------------------- +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 554 +d0256:= D(m0256,x) +--R +--R +--R (254) 0 +--R Type: Expression(Integer) +--E 285 + +--S 286 of 554 +t0257:= x^3*(a+b/x)^(1/2) +--R +--R +--R +-------+ +--R 3 |a x + b +--R (255) x |------- +--R \| x +--R Type: Expression(Integer) +--E 286 + +--S 287 of 554 +r0257:= 5/64*b^3*(a+b/x)^(1/2)*x/a^3-5/96*b^2*(a+b/x)^(1/2)*x^2/a^2+_ + 1/24*b*(a+b/x)^(1/2)*x^3/a+1/4*(a+b/x)^(1/2)*x^4-_ + 5/64*b^4*atanh((a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (256) +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 4 \| x 3 4 2 3 2 2 3 +-+ |a x + b +--R - 15b atanh(----------) + (48a x + 8a b x - 10a b x + 15b x)\|a |------- +--R +-+ \| x +--R \|a +--R ----------------------------------------------------------------------------- +--R 3 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 554 +a0257:= integrate(t0257,x) +--R +--R +--R (257) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x + 16a b x - 20a b x + 30b x)\|a |------- +--R \| x +--R / +--R 3 +-+ +--R 384a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R - 15b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x + 8a b x - 10a b x + 15b x)\|- a |------- +--R \| x +--R / +--R 3 +---+ +--R 192a \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 288 + +--S 289 of 554 +m0257a:= a0257.1-r0257 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (258) ----------------------------------------------------------------- +--R 3 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 554 +d0257a:= D(m0257a,x) +--R +--R +--R (259) 0 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 554 +m0257b:= a0257.2-r0257 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (260) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 554 +d0257b:= D(m0257b,x) +--R +--R +--R (261) 0 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 554 +t0258:= x^2*(a+b/x)^(1/2) +--R +--R +--R +-------+ +--R 2 |a x + b +--R (262) x |------- +--R \| x +--R Type: Expression(Integer) +--E 293 + +--S 294 of 554 +r0258:= -1/8*b^2*(a+b/x)^(1/2)*x/a^2+1/12*b*(a+b/x)^(1/2)*x^2/a+_ + 1/3*x^3*(a+b/x)^(1/2)+1/8*b^3*atanh((a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R 3b atanh(----------) + (8a x + 2a b x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (263) ------------------------------------------------------------- +--R 2 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 554 +a0258:= integrate(t0258,x) +--R +--R +--R (264) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 3b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x + 4a b x - 6b x)\|a |------- +--R \| x +--R / +--R 2 +-+ +--R 48a \|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R 3b atan(----------------) + (8a x + 2a b x - 3b x)\|- a |------- +--R a \| x +--R --------------------------------------------------------------------] +--R 2 +---+ +--R 24a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 295 + +--S 296 of 554 +m0258a:= a0258.1-r0258 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (265) ------------------------------------------------------------- +--R 2 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 554 +d0258a:= D(m0258a,x) +--R +--R +--R (266) 0 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 554 +m0258b:= a0258.2-r0258 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R - b \|- a atanh(----------) + b \|a atan(----------------) +--R +-+ a +--R \|a +--R (267) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 554 +d0258b:= D(m0258b,x) +--R +--R +--R (268) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 554 +t0259:= x*(a+b/x)^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R (269) x |------- +--R \| x +--R Type: Expression(Integer) +--E 300 + +--S 301 of 554 +r0259:= 1/4*b*(a+b/x)^(1/2)*x/a+1/2*x^2*(a+b/x)^(1/2)-_ + 1/4*b^2*atanh((a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R - b atanh(----------) + (2a x + b x)\|a |------- +--R +-+ \| x +--R \|a +--R (270) --------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 554 +a0259:= integrate(t0259,x) +--R +--R +--R (271) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R b log(- 2a x |------- + (2a x + b)\|a ) + (4a x + 2b x)\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------------------, +--R +-+ +--R 8a\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R - b atan(----------------) + (2a x + b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R +---+ +--R 4a\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 302 + +--S 303 of 554 +m0259a:= a0259.1-r0259 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (272) --------------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 303 + +--S 304 of 554 +d0259a:= D(m0259a,x) +--R +--R +--R (273) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 554 +m0259b:= a0259.2-r0259 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R b \|- a atanh(----------) - b \|a atan(----------------) +--R +-+ a +--R \|a +--R (274) -------------------------------------------------------- +--R +---+ +-+ +--R 4a\|- a \|a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 554 +d0259b:= D(m0259b,x) +--R +--R +--R (275) 0 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 554 +t0260:= (a+b/x)^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R (276) |------- +--R \| x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 554 +r0260:= x*(a+b/x)^(1/2)+b*atanh((a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R \| x +-+ |a x + b +--R b atanh(----------) + x\|a |------- +--R +-+ \| x +--R \|a +--R (277) ------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 554 +a0260:= integrate(t0260,x) +--R +--R +--R (278) +--R +-------+ +-------+ +--R |a x + b +-+ +-+ |a x + b +--R b log(2a x |------- + (2a x + b)\|a ) + 2x\|a |------- +--R \| x \| x +--R [---------------------------------------------------------, +--R +-+ +--R 2\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R \| x +---+ |a x + b +--R b atan(----------------) + x\|- a |------- +--R a \| x +--R --------------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 309 + +--S 310 of 554 +m0260a:= a0260.1-r0260 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (279) ------------------------------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 554 +d0260a:= D(m0260a,x) +--R +--R +--R (280) 0 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 554 +m0260b:= a0260.2-r0260 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - b\|- a atanh(----------) + b\|a atan(----------------) +--R +-+ a +--R \|a +--R (281) -------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 312 + +--S 313 of 554 +d0260b:= D(m0260b,x) +--R +--R +--R (282) 0 +--R Type: Expression(Integer) +--E 313 + +--S 314 of 554 +t0261:= (a+b/x)^(1/2)/x +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (283) ---------- +--R x +--R Type: Expression(Integer) +--E 314 + +--S 315 of 554 +r0261:= -2*(a+b/x)^(1/2)+2*a^(1/2)*atanh((a+b/x)^(1/2)/a^(1/2)) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x |a x + b +--R (284) 2\|a atanh(----------) - 2 |------- +--R +-+ \| x +--R \|a +--R Type: Expression(Integer) +--E 315 + +--S 316 of 554 +a0261:= integrate(t0261,x) +--R +--R +--R (285) +--R +-------+ +-------+ +--R +-+ +-+ |a x + b |a x + b +--R [\|a log(2x\|a |------- + 2a x + b) - 2 |-------, +--R \| x \| x +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x |a x + b +--R 2\|- a atan(----------) - 2 |-------] +--R +---+ \| x +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 316 + +--S 317 of 554 +m0261a:= a0261.1-r0261 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R (286) \|a log(2x\|a |------- + 2a x + b) - 2\|a atanh(----------) +--R \| x +-+ +--R \|a +--R Type: Expression(Integer) +--E 317 + +--S 318 of 554 +d0261a:= D(m0261a,x) +--R +--R +--R (287) 0 +--R Type: Expression(Integer) +--E 318 + +--S 319 of 554 +m0261b:= a0261.2-r0261 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (288) - 2\|a atanh(----------) + 2\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 554 +d0261b:= D(m0261b,x) +--R +--R +--R (289) 0 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 554 +t0262:= x^3*(-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R 3 |- a x + b +--R (290) x |--------- +--R \| x +--R Type: Expression(Integer) +--E 321 + +--S 322 of 554 +r0262:= -5/64*b^3*(-a+b/x)^(1/2)*x/a^3-5/96*b^2*(-a+b/x)^(1/2)*x^2/a^2-_ + 1/24*b*(-a+b/x)^(1/2)*x^3/a+1/4*(-a+b/x)^(1/2)*x^4-_ + 5/64*b^4*atan((-a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (291) +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 \| x +--R - 15b atan(------------) +--R +-+ +--R \|a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (48a x - 8a b x - 10a b x - 15b x) |--------- \|a +--R \| x +--R / +--R 3 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 554 +a0262:= integrate(t0262,x) +--R +--R +--R (292) +--R [ +--R +---------+ +--R 4 |- a x + b +---+ +--R 15b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 +---+ |- a x + b +--R (96a x - 16a b x - 20a b x - 30b x)\|- a |--------- +--R \| x +--R / +--R 3 +---+ +--R 384a \|- a +--R , +--R +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +--R 4 \| x +--R - 15b atan(----------------) +--R a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (48a x - 8a b x - 10a b x - 15b x) |--------- \|a +--R \| x +--R / +--R 3 +-+ +--R 192a \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 323 + +--S 324 of 554 +m0262a:= a0262.1-r0262 +--R +--R +--R (293) +--R +---------+ +--R 4 +-+ |- a x + b +---+ +--R 5b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 +---+ \| x +--R 10b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 3 +---+ +-+ +--R 128a \|- a \|a +--R Type: Expression(Integer) +--E 324 + +--S 325 of 554 +d0262a:= D(m0262a,x) +--R +--R +--R (294) 0 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 554 +m0262b:= a0262.2-r0262 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 4 \| x 4 \| x +--R - 5b atan(----------------) + 5b atan(------------) +--R a +-+ +--R \|a +--R (295) --------------------------------------------------- +--R 3 +-+ +--R 64a \|a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 554 +d0262b:= D(m0262b,x) +--R +--R +--R (296) 0 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 554 +t0263:= x^2*(-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R 2 |- a x + b +--R (297) x |--------- +--R \| x +--R Type: Expression(Integer) +--E 328 + +--S 329 of 554 +r0263:= -1/8*b^2*(-a+b/x)^(1/2)*x/a^2-1/12*b*(-a+b/x)^(1/2)*x^2/a+_ + 1/3*x^3*(-a+b/x)^(1/2)-1/8*b^3*atan((-a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 3b atan(------------) + (8a x - 2a b x - 3b x) |--------- \|a +--R +-+ \| x +--R \|a +--R (298) ------------------------------------------------------------------ +--R 2 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 329 + +--S 330 of 554 +a0263:= integrate(t0263,x) +--R +--R +--R (299) +--R [ +--R +---------+ +--R 3 |- a x + b +---+ +--R 3b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 3 2 2 +---+ |- a x + b +--R (16a x - 4a b x - 6b x)\|- a |--------- +--R \| x +--R / +--R 2 +---+ +--R 48a \|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 3b atan(----------------) + (8a x - 2a b x - 3b x) |--------- \|a +--R a \| x +--R ----------------------------------------------------------------------] +--R 2 +-+ +--R 24a \|a +--R Type: Union(List(Expression(Integer)),...) +--E 330 + +--S 331 of 554 +m0263a:= a0263.1-r0263 +--R +--R +--R (300) +--R +---------+ +--R 3 +-+ |- a x + b +---+ +--R b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 3 +---+ \| x +--R 2b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 2 +---+ +-+ +--R 16a \|- a \|a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 554 +d0263a:= D(m0263a,x) +--R +--R +--R (301) 0 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 554 +m0263b:= a0263.2-r0263 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 3 \| x 3 \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (302) ------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 554 +d0263b:= D(m0263b,x) +--R +--R +--R (303) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 554 +t0264:= x*(-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R (304) x |--------- +--R \| x +--R Type: Expression(Integer) +--E 335 + +--S 336 of 554 +r0264:= -1/4*b*(-a+b/x)^(1/2)*x/a+1/2*x^2*(-a+b/x)^(1/2)-_ + 1/4*b^2*atan((-a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - b atan(------------) + (2a x - b x) |--------- \|a +--R +-+ \| x +--R \|a +--R (305) ------------------------------------------------------ +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 336 + +--S 337 of 554 +a0264:= integrate(t0264,x) +--R +--R +--R (306) +--R [ +--R +---------+ +--R 2 |- a x + b +---+ +--R b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 +---+ |- a x + b +--R (4a x - 2b x)\|- a |--------- +--R \| x +--R / +--R +---+ +--R 8a\|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - b atan(----------------) + (2a x - b x) |--------- \|a +--R a \| x +--R ----------------------------------------------------------] +--R +-+ +--R 4a\|a +--R Type: Union(List(Expression(Integer)),...) +--E 337 + +--S 338 of 554 +m0264a:= a0264.1-r0264 +--R +--R +--R (307) +--R +---------+ +--R 2 +-+ |- a x + b +---+ +--R b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 2 +---+ \| x +--R 2b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R 8a\|- a \|a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 554 +d0264a:= D(m0264a,x) +--R +--R +--R (308) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 554 +m0264b:= a0264.2-r0264 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 2 \| x 2 \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (309) ------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 554 +d0264b:= D(m0264b,x) +--R +--R +--R (310) 0 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 554 +t0265:= (-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R (311) |--------- +--R \| x +--R Type: Expression(Integer) +--E 342 + +--S 343 of 554 +r0265:= x*(-a+b/x)^(1/2)-b*atan((-a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R \| x |- a x + b +-+ +--R - b atan(------------) + x |--------- \|a +--R +-+ \| x +--R \|a +--R (312) ------------------------------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 554 +a0265:= integrate(t0265,x) +--R +--R +--R (313) +--R +---------+ +---------+ +--R |- a x + b +---+ +---+ |- a x + b +--R b log(- 2a x |--------- + (- 2a x + b)\|- a ) + 2x\|- a |--------- +--R \| x \| x +--R [---------------------------------------------------------------------, +--R +---+ +--R 2\|- a +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R \| x |- a x + b +-+ +--R - b atan(----------------) + x |--------- \|a +--R a \| x +--R ----------------------------------------------] +--R +-+ +--R \|a +--R Type: Union(List(Expression(Integer)),...) +--E 344 + +--S 345 of 554 +m0265a:= a0265.1-r0265 +--R +--R +--R (314) +--R +---------+ +--R +-+ |- a x + b +---+ +--R b\|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R +---+ \| x +--R 2b\|- a atan(------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R 2\|- a \|a +--R Type: Expression(Integer) +--E 345 + +--S 346 of 554 +d0265a:= D(m0265a,x) +--R +--R +--R (315) 0 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 554 +m0265b:= a0265.2-r0265 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R \| x \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (316) ------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 554 +d0265b:= D(m0265b,x) +--R +--R +--R (317) 0 +--R Type: Expression(Integer) +--E 348 + +--S 349 of 554 +t0266:= (-a+b/x)^(1/2)/x +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R (318) ------------ +--R x +--R Type: Expression(Integer) +--E 349 + +--S 350 of 554 +r0266:= -2*(-a+b/x)^(1/2)+2*a^(1/2)*atan((-a+b/x)^(1/2)/a^(1/2)) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R +-+ \| x |- a x + b +--R (319) 2\|a atan(------------) - 2 |--------- +--R +-+ \| x +--R \|a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 554 +a0266:= integrate(t0266,x) +--R +--R +--R (320) +--R +---------+ +---------+ +--R +---+ +---+ |- a x + b |- a x + b +--R [\|- a log(2x\|- a |--------- - 2a x + b) - 2 |---------, +--R \| x \| x +--R +-+ +---------+ +--R +-+ \|a |- a x + b +--R - 2\|a atan(------------) - 2 |---------] +--R +---------+ \| x +--R |- a x + b +--R |--------- +--R \| x +--R Type: Union(List(Expression(Integer)),...) +--E 351 + +--S 352 of 554 +m0266a:= a0266.1-r0266 +--R +--R +--R +---------+ +--R |- a x + b +--R +---------+ |--------- +--R +---+ +---+ |- a x + b +-+ \| x +--R (321) \|- a log(2x\|- a |--------- - 2a x + b) - 2\|a atan(------------) +--R \| x +-+ +--R \|a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 554 +d0266a:= D(m0266a,x) +--R +--R +--R (322) 0 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 554 +m0266b:= a0266.2-r0266 +--R +--R +--R +---------+ +--R |- a x + b +--R +-+ |--------- +--R +-+ \|a +-+ \| x +--R (323) - 2\|a atan(------------) - 2\|a atan(------------) +--R +---------+ +-+ +--R |- a x + b \|a +--R |--------- +--R \| x +--R Type: Expression(Integer) +--E 354 + +--S 355 of 554 +d0266b:= D(m0266b,x) +--R +--R +--R (324) 0 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 554 +t0267:= x^3/(a+b/x)^(1/2) +--R +--R +--R 3 +--R x +--R (325) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 356 + +--S 357 of 554 +r0267:= -35/64*b^3*(a+b/x)^(1/2)*x/a^4+35/96*b^2*(a+b/x)^(1/2)*x^2/a^3-_ + 7/24*b*(a+b/x)^(1/2)*x^3/a^2+1/4*(a+b/x)^(1/2)*x^4/a+_ + 35/64*b^4*atanh((a+b/x)^(1/2)/a^(1/2))/a^(9/2) +--R +--R +--R (326) +--R +-------+ +--R |a x + b +--R |------- +--R 4 \| x +--R 105b atanh(----------) +--R +-+ +--R \|a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (48a x - 56a b x + 70a b x - 105b x)\|a |------- +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 357 + +--S 358 of 554 +a0267:= integrate(t0267,x) +--R +--R +--R (327) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 105b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x - 112a b x + 140a b x - 210b x)\|a |------- +--R \| x +--R / +--R 4 +-+ +--R 384a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R 105b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x - 56a b x + 70a b x - 105b x)\|- a |------- +--R \| x +--R / +--R 4 +---+ +--R 192a \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 358 + +--S 359 of 554 +m0267a:= a0267.1-r0267 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 35b log(2a x |------- + (2a x + b)\|a ) - 70b atanh(----------) +--R \| x +-+ +--R \|a +--R (328) ---------------------------------------------------------------- +--R 4 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 359 + +--S 360 of 554 +d0267a:= D(m0267a,x) +--R +--R +--R (329) 0 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 554 +m0267b:= a0267.2-r0267 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R - 35b \|- a atanh(----------) + 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (330) -------------------------------------------------------------- +--R 4 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 554 +d0267b:= D(m0267b,x) +--R +--R +--R (331) 0 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 554 +t0268:= x^2/(a+b/x)^(1/2) +--R +--R +--R 2 +--R x +--R (332) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 363 + +--S 364 of 554 +r0268:= 5/8*b^2*(a+b/x)^(1/2)*x/a^3-5/12*b*(a+b/x)^(1/2)*x^2/a^2+_ + 1/3*(a+b/x)^(1/2)*x^3/a-5/8*b^3*atanh((a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R - 15b atanh(----------) + (8a x - 10a b x + 15b x)\|a |------- +--R +-+ \| x +--R \|a +--R (333) ------------------------------------------------------------------ +--R 3 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 364 + +--S 365 of 554 +a0268:= integrate(t0268,x) +--R +--R +--R (334) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x - 20a b x + 30b x)\|a |------- +--R \| x +--R / +--R 3 +-+ +--R 48a \|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R - 15b atan(----------------) + (8a x - 10a b x + 15b x)\|- a |------- +--R a \| x +--R -------------------------------------------------------------------------] +--R 3 +---+ +--R 24a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 365 + +--S 366 of 554 +m0268a:= a0268.1-r0268 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (335) ----------------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 366 + +--S 367 of 554 +d0268a:= D(m0268a,x) +--R +--R +--R (336) 0 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 554 +m0268b:= a0268.2-r0268 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (337) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 368 + +--S 369 of 554 +d0268b:= D(m0268b,x) +--R +--R +--R (338) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 554 +t0269:= x/(a+b/x)^(1/2) +--R +--R +--R x +--R (339) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 370 + +--S 371 of 554 +r0269:= -3/4*b*(a+b/x)^(1/2)*x/a^2+1/2*(a+b/x)^(1/2)*x^2/a+_ + 3/4*b^2*atanh((a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R 3b atanh(----------) + (2a x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (340) --------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 371 + +--S 372 of 554 +a0269:= integrate(t0269,x) +--R +--R +--R (341) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R 3b log(2a x |------- + (2a x + b)\|a ) + (4a x - 6b x)\|a |------- +--R \| x \| x +--R [----------------------------------------------------------------------, +--R 2 +-+ +--R 8a \|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R 3b atan(----------------) + (2a x - 3b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R 2 +---+ +--R 4a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 372 + +--S 373 of 554 +m0269a:= a0269.1-r0269 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (342) -------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 373 + +--S 374 of 554 +d0269a:= D(m0269a,x) +--R +--R +--R (343) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 554 +m0269b:= a0269.2-r0269 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (344) ------------------------------------------------------------ +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 375 + +--S 376 of 554 +d0269b:= D(m0269b,x) +--R +--R +--R (345) 0 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 554 +t0270:= 1/(a+b/x)^(1/2) +--R +--R +--R 1 +--R (346) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 377 + +--S 378 of 554 +r0270:= (a+b/x)^(1/2)*x/a-b*atanh((a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R \| x +-+ |a x + b +--R - b atanh(----------) + x\|a |------- +--R +-+ \| x +--R \|a +--R (347) --------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 378 + +--S 379 of 554 +a0270:= integrate(t0270,x) +--R +--R +--R (348) +--R +-------+ +-------+ +--R |a x + b +-+ +-+ |a x + b +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2x\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------, +--R +-+ +--R 2a\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R \| x +---+ |a x + b +--R - b atan(----------------) + x\|- a |------- +--R a \| x +--R ----------------------------------------------] +--R +---+ +--R a\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 379 + +--S 380 of 554 +m0270a:= a0270.1-r0270 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (349) --------------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 380 + +--S 381 of 554 +d0270a:= D(m0270a,x) +--R +--R +--R (350) 0 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 554 +m0270b:= a0270.2-r0270 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R b\|- a atanh(----------) - b\|a atan(----------------) +--R +-+ a +--R \|a +--R (351) ------------------------------------------------------ +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 382 + +--S 383 of 554 +d0270b:= D(m0270b,x) +--R +--R +--R (352) 0 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 554 +t0271:= 1/x/(a+b/x)^(1/2) +--R +--R +--R 1 +--R (353) ----------- +--R +-------+ +--R |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 384 + +--S 385 of 554 +r0271:= 2*atanh((a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R 2atanh(----------) +--R +-+ +--R \|a +--R (354) ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 385 + +--S 386 of 554 +a0271:= integrate(t0271,x) +--R +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) 2atan(----------------) +--R \| x a +--R (355) [------------------------------------,-----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 386 + +--S 387 of 554 +m0271a:= a0271.1-r0271 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------) +--R \| x +-+ +--R \|a +--R (356) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 387 + +--S 388 of 554 +d0271a:= D(m0271a,x) +--R +--R +--R (357) 0 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 554 +m0271b:= a0271.2-r0271 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - 2\|- a atanh(----------) + 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (358) -------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 389 + +--S 390 of 554 +d0271b:= D(m0271b,x) +--R +--R +--R (359) 0 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 554 +t0272:= x^3/(-a+b/x)^(1/2) +--R +--R +--R 3 +--R x +--R (360) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression(Integer) +--E 391 + +--S 392 of 554 +r0272:= -35/64*b^3*(-a+b/x)^(1/2)*x/a^4-35/96*b^2*(-a+b/x)^(1/2)*x^2/a^3-_ + 7/24*b*(-a+b/x)^(1/2)*x^3/a^2-1/4*(-a+b/x)^(1/2)*x^4/a-_ + 35/64*b^4*atan((-a+b/x)^(1/2)/a^(1/2))/a^(9/2) +--R +--R +--R (361) +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 \| x +--R - 105b atan(------------) +--R +-+ +--R \|a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (- 48a x - 56a b x - 70a b x - 105b x) |--------- \|a +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 392 + +--S 393 of 554 +a0272:= integrate(t0272,x) +--R +--R +--R (362) +--R [ +--R +---------+ +--R 4 |- a x + b +---+ +--R 105b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 +---+ |- a x + b +--R (- 96a x - 112a b x - 140a b x - 210b x)\|- a |--------- +--R \| x +--R / +--R 4 +---+ +--R 384a \|- a +--R , +--R +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +--R 4 \| x +--R - 105b atan(----------------) +--R a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (- 48a x - 56a b x - 70a b x - 105b x) |--------- \|a +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 393 + +--S 394 of 554 +m0272a:= a0272.1-r0272 +--R +--R +--R (363) +--R +---------+ +--R 4 +-+ |- a x + b +---+ +--R 35b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 +---+ \| x +--R 70b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 4 +---+ +-+ +--R 128a \|- a \|a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 554 +d0272a:= D(m0272a,x) +--R +--R +--R (364) 0 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 554 +m0272b:= a0272.2-r0272 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 4 \| x 4 \| x +--R - 35b atan(----------------) + 35b atan(------------) +--R a +-+ +--R \|a +--R (365) ----------------------------------------------------- +--R 4 +-+ +--R 64a \|a +--R Type: Expression(Integer) +--E 396 + +--S 397 of 554 +d0272b:= D(m0272b,x) +--R +--R +--R (366) 0 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 554 +t0273:= x^2/(-a+b/x)^(1/2) +--R +--R +--R 2 +--R x +--R (367) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression(Integer) +--E 398 + +--S 399 of 554 +r0273:= -5/8*b^2*(-a+b/x)^(1/2)*x/a^3-5/12*b*(-a+b/x)^(1/2)*x^2/a^2-_ + 1/3*(-a+b/x)^(1/2)*x^3/a-5/8*b^3*atan((-a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (368) +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 15b atan(------------) + (- 8a x - 10a b x - 15b x) |--------- \|a +--R +-+ \| x +--R \|a +--R ----------------------------------------------------------------------- +--R 3 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 399 + +--S 400 of 554 +a0273:= integrate(t0273,x) +--R +--R +--R (369) +--R [ +--R +---------+ +--R 3 |- a x + b +---+ +--R 15b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 3 2 2 +---+ |- a x + b +--R (- 16a x - 20a b x - 30b x)\|- a |--------- +--R \| x +--R / +--R 3 +---+ +--R 48a \|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 15b atan(----------------) + (- 8a x - 10a b x - 15b x) |--------- \|a +--R a \| x +--R ---------------------------------------------------------------------------] +--R 3 +-+ +--R 24a \|a +--R Type: Union(List(Expression(Integer)),...) +--E 400 + +--S 401 of 554 +m0273a:= a0273.1-r0273 +--R +--R +--R (370) +--R +---------+ +--R 3 +-+ |- a x + b +---+ +--R 5b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 3 +---+ \| x +--R 10b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 3 +---+ +-+ +--R 16a \|- a \|a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 554 +d0273a:= D(m0273a,x) +--R +--R +--R (371) 0 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 554 +m0273b:= a0273.2-r0273 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 3 \| x 3 \| x +--R - 5b atan(----------------) + 5b atan(------------) +--R a +-+ +--R \|a +--R (372) --------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 554 +d0273b:= D(m0273b,x) +--R +--R +--R (373) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 554 +t0274:= x/(-a+b/x)^(1/2) +--R +--R +--R x +--R (374) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression(Integer) +--E 405 + +--S 406 of 554 +r0274:= -3/4*b*(-a+b/x)^(1/2)*x/a^2-1/2*(-a+b/x)^(1/2)*x^2/a-_ + 3/4*b^2*atan((-a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - 3b atan(------------) + (- 2a x - 3b x) |--------- \|a +--R +-+ \| x +--R \|a +--R (375) ---------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 554 +a0274:= integrate(t0274,x) +--R +--R +--R (376) +--R [ +--R +---------+ +--R 2 |- a x + b +---+ +--R 3b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 +---+ |- a x + b +--R (- 4a x - 6b x)\|- a |--------- +--R \| x +--R / +--R 2 +---+ +--R 8a \|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - 3b atan(----------------) + (- 2a x - 3b x) |--------- \|a +--R a \| x +--R --------------------------------------------------------------] +--R 2 +-+ +--R 4a \|a +--R Type: Union(List(Expression(Integer)),...) +--E 407 + +--S 408 of 554 +m0274a:= a0274.1-r0274 +--R +--R +--R (377) +--R +---------+ +--R 2 +-+ |- a x + b +---+ +--R 3b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 2 +---+ \| x +--R 6b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 408 + +--S 409 of 554 +d0274a:= D(m0274a,x) +--R +--R +--R (378) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 554 +m0274b:= a0274.2-r0274 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 2 \| x 2 \| x +--R - 3b atan(----------------) + 3b atan(------------) +--R a +-+ +--R \|a +--R (379) --------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 554 +d0274b:= D(m0274b,x) +--R +--R +--R (380) 0 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 554 +t0275:= 1/(-a+b/x)^(1/2) +--R +--R +--R 1 +--R (381) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression(Integer) +--E 412 + +--S 413 of 554 +r0275:= -(-a+b/x)^(1/2)*x/a-b*atan((-a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R \| x |- a x + b +-+ +--R - b atan(------------) - x |--------- \|a +--R +-+ \| x +--R \|a +--R (382) ------------------------------------------ +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 554 +a0275:= integrate(t0275,x) +--R +--R +--R (383) +--R +---------+ +---------+ +--R |- a x + b +---+ +---+ |- a x + b +--R b log(- 2a x |--------- + (- 2a x + b)\|- a ) - 2x\|- a |--------- +--R \| x \| x +--R [---------------------------------------------------------------------, +--R +---+ +--R 2a\|- a +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R \| x |- a x + b +-+ +--R - b atan(----------------) - x |--------- \|a +--R a \| x +--R ----------------------------------------------] +--R +-+ +--R a\|a +--R Type: Union(List(Expression(Integer)),...) +--E 414 + +--S 415 of 554 +m0275a:= a0275.1-r0275 +--R +--R +--R (384) +--R +---------+ +--R +-+ |- a x + b +---+ +--R b\|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R +---+ \| x +--R 2b\|- a atan(------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression(Integer) +--E 415 + +--S 416 of 554 +d0275a:= D(m0275a,x) +--R +--R +--R (385) 0 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 554 +m0275b:= a0275.2-r0275 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R \| x \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (386) ------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 417 + +--S 418 of 554 +d0275b:= D(m0275b,x) +--R +--R +--R (387) 0 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 554 +t0276:= 1/x/(-a+b/x)^(1/2) +--R +--R +--R 1 +--R (388) ------------- +--R +---------+ +--R |- a x + b +--R x |--------- +--R \| x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 554 +r0276:= -2*atan((-a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R 2atan(------------) +--R +-+ +--R \|a +--R (389) - ------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 420 + +--S 421 of 554 +a0276:= integrate(t0276,x) +--R +--R +--R (390) +--R +---------+ +--R |- a x + b +-+ +--R +---------+ |--------- \|a +--R |- a x + b +---+ \| x +--R log(- 2a x |--------- + (- 2a x + b)\|- a ) 2atan(----------------) +--R \| x a +--R [--------------------------------------------,- -----------------------] +--R +---+ +-+ +--R \|- a \|a +--R Type: Union(List(Expression(Integer)),...) +--E 421 + +--S 422 of 554 +m0276a:= a0276.1-r0276 +--R +--R +--R (391) +--R +---------+ +--R |- a x + b +--R +---------+ |--------- +--R +-+ |- a x + b +---+ +---+ \| x +--R \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) + 2\|- a atan(------------) +--R \| x +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 554 +d0276a:= D(m0276a,x) +--R +--R +--R (392) 0 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 554 +m0276b:= a0276.2-r0276 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R \| x \| x +--R - 2atan(----------------) + 2atan(------------) +--R a +-+ +--R \|a +--R (393) ----------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 554 +d0276b:= D(m0276b,x) +--R +--R +--R (394) 0 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 554 +t0277:= x^3/(a+b/x^2)^(1/2) +--R +--R +--R 3 +--R x +--R (395) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 426 + +--S 427 of 554 +r0277:= -3/8*b*(a+b/x^2)^(1/2)*x^2/a^2+1/4*(a+b/x^2)^(1/2)*x^4/a+_ + 3/8*b^2*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R 3b atanh(-----------) + (2a x - 3b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (396) ------------------------------------------------------ +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 554 +a0277:= integrate(t0277,x) +--R +--R +--R (397) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 13a b x + 8a b x + 24b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48b )\|b \|a x + b - 6a b x - 48a b x - 48b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|b +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 +--R (32a x + 64a b)\|- a \|b \|a x + b +--R + +--R 4 4 3 2 2 2 +---+ +--R (- 8a x - 64a b x - 64a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 428 + +--S 429 of 554 +m0277a:= a0277.1-r0277 +--R +--R +--R (398) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 12a b x - 24b )\|b \|a x + b + 3a b x + 24a b x + 24b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 4a b x + 24b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 13a b x + 8a b x + 24b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 13a b x - 8a b x - 24b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R Type: Expression(Integer) +--E 429 + +--S 430 of 554 +d0277a:= D(m0277a,x) +--R +--R +--R (399) +--R 5 14 4 12 3 2 10 2 3 8 4 6 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 4 +--R 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x +--R + +--R 5 4 +--R - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x +--R + +--R 5 5 +--R - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x +--R + +--R 5 5 6 3 +--R 3328a b x + 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 5 5 6 3 +--R - 3840a b x - 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 16 5 14 4 2 12 3 3 10 2 4 8 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 6 6 4 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 16 6 14 5 2 12 4 3 10 3 4 8 2 5 6 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x +--R + +--R 6 4 +--R 1024a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 2 6 +--R - 3328a b x - 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 5 2 6 +--R 3840a b x + 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 3 6 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 430 + +--S 431 of 554 +m0277b:= a0277.2-r0277 +--R +--R +--R (400) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (- 12a b x - 24b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (3a b x + 24a b x + 24b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (24a b x + 48b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (- 6a b x - 48a b x - 48b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 4a b x + 24b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 13a b x - 8a b x - 24b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ +-+ | 2 +--R (32a x + 64a b)\|- a \|a \|b \|a x + b +--R + +--R 4 4 3 2 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64a b )\|- a \|a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 554 +d0277b:= D(m0277b,x) +--R +--R +--R (401) +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +-+ 4 11 +--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 9 2 2 7 3 5 4 3 +--R - 32a b x - 160a b x - 256a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 11 3 9 2 2 7 3 5 4 3 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 432 + +--S 433 of 554 +t0278:= x/(a+b/x^2)^(1/2) +--R +--R +--R x +--R (402) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 433 + +--S 434 of 554 +r0278:= 1/2*(a+b/x^2)^(1/2)*x^2/a-1/2*b*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R \| x 2 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (403) ------------------------------------------ +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 554 +a0278:= integrate(t0278,x) +--R +--R +--R (404) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a +--R , +--R +--R +--------+ +--R +-+ | 2 2 2 +--R (- 4b\|b \|a x + b + 2a b x + 4b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R 4a\|- a \|b \|a x + b + (- 2a x - 4a b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 435 + +--S 436 of 554 +m0278a:= a0278.1-r0278 +--R +--R +--R (405) +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 2 2 \| x +--R (2b\|b \|a x + b - a b x - 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b +-+ 3 +-+ | 2 +--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +-+ +-+ 4 2 +-+ |a x + b +--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 554 +d0278a:= D(m0278a,x) +--R +--R +--R (406) +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (- 7a x - 56a b x - 112a b x - 64b x )\|a |-------- - 7a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 +--R - 56a b x - 112a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +--R (- a x - 24a b x - 80a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b x )\|a |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R a x + 25a b x + 104a b x + 144a b x + 64a b x +--R / +--R +--------+ +--R | 2 +--R 4 7 3 5 2 2 3 3 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +-+ +--R (- 7a x - 63a b x - 168a b x - 176a b x - 64b )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 9 4 7 3 2 5 2 3 3 4 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 437 + +--S 438 of 554 +m0278b:= a0278.2-r0278 +--R +--R +--R (407) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 2 2 +---+ \| x +--R (2b\|- a \|b \|a x + b + (- a b x - 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R (- 4b\|a \|b \|a x + b + (2a b x + 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b +--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 2 2 2 +---+ +-+ +--R 4a\|- a \|a \|b \|a x + b + (- 2a x - 4a b)\|- a \|a +--R Type: Expression(Integer) +--E 438 + +--S 439 of 554 +d0278b:= D(m0278b,x) +--R +--R +--R (408) +--R +--------+ +--R | 2 +--------+ +--R 4 2 |a x + b +-+ 2 5 3 2 | 2 +--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x)\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ 2 6 4 2 2 |a x + b +--R (4a x + 12a b x + 8b x)\|b + (a x + 8a b x + 8b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b | 2 +--R (a x + 8a b x + 8b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 554 +t0279:= 1/x/(a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (409) ------------ +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 440 + +--S 441 of 554 +r0279:= atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R (410) ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 441 + +--S 442 of 554 +a0279:= integrate(t0279,x) +--R +--R +--R (411) +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R [-------------------------------------------------------------, +--R +-+ +--R \|a +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R 2atan(------------------------------) +--R a x +--R -------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 442 + +--S 443 of 554 +m0279a:= a0279.1-r0279 +--R +--R +--R (412) +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R - atanh(-----------) +--R +-+ +--R \|a +--R / +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 443 + +--S 444 of 554 +d0279a:= D(m0279a,x) +--R +--R +--R (413) +--R +--------+ +--R | 2 +--R 3 +-+ |a x + b 2 3 +-+ +--R ((3a x + 4b x)\|a |-------- - 3a x - 4a b x)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b 2 4 2 2 +-+ +--R (- a x - 4a b x ) |-------- + (a x + 5a b x + 4b )\|a +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b 2 4 2 2 +-+ +-+ +--R ((3a x + 4a b x ) |-------- + (- 3a x - 7a b x - 4b )\|a )\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b 3 5 2 3 2 +--R (- a x - 5a b x - 4b x)\|a |-------- + a x + 5a b x + 4a b x +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b +-+ +--R (3a x + 4a b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +--R (- a x - 5a b x - 4b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +-+ +--R (3a x + 7a b x + 4b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 |a x + b +--R (- a x - 5a b x - 4a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 444 + +--S 445 of 554 +m0279b:= a0279.2-r0279 +--R +--R +--R (414) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 +---+ | 2 +---+ +-+ +--R +---+ \| x +-+ \|- a \|a x + b - \|- a \|b +--R - \|- a atanh(-----------) + 2\|a atan(------------------------------) +--R +-+ a x +--R \|a +--R ---------------------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 554 +d0279b:= D(m0279b,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 |a x + b +--R - \|a x + b + x |-------- +--R | 2 +--R \| x +--R (415) ---------------------------- +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R x |-------- \|a x + b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 446 + +--S 447 of 554 +t0280:= 1/x/(-a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (416) -------------- +--R +----------+ +--R | 2 +--R |- a x + b +--R x |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 447 + +--S 448 of 554 +r0280:= -atan((-a+b/x^2)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R atan(-------------) +--R +-+ +--R \|a +--R (417) - ------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 448 + +--S 449 of 554 +a0280:= integrate(t0280,x) +--R +--R +--R (418) +--R +----------+ +----------+ +--R | 2 +---+ +-+ 2 +---+ | 2 +--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a + a x\|- a x + b +--R log(---------------------------------------------------------------------) +--R +----------+ +--R | 2 +-+ +--R \|- a x + b \|b - b +--R [--------------------------------------------------------------------------, +--R +---+ +--R \|- a +--R +----------+ +--R +-+ +-+ | 2 +-+ +--R \|a \|b - \|- a x + b \|a +--R 2atan(----------------------------) +--R a x +--R -----------------------------------] +--R +-+ +--R \|a +--R Type: Union(List(Expression(Integer)),...) +--E 449 + +--S 450 of 554 +m0280a:= a0280.1-r0280 +--R +--R +--R (419) +--R +-+ +--R \|a +--R * +--R log +--R +----------+ +--R | 2 +---+ +-+ 2 +---+ +--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a +--R + +--R +----------+ +--R | 2 +--R a x\|- a x + b +--R / +--R +----------+ +--R | 2 +-+ +--R \|- a x + b \|b - b +--R + +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R +---+ \| x +--R \|- a atan(-------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 450 + +--S 451 of 554 +d0280a:= D(m0280a,x) +--R +--R +--R (420) +--R +----------+ +--R +----------+ | 2 +--R 3 | 2 +---+ 2 4 2 |- a x + b +--R ((- 3a x + 4b x)\|- a x + b \|- a + 3a x - 4a b x ) |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 4 2 2 +---+ 2 3 | 2 +--R (- 3a x + 7a b x - 4b )\|- a + (- 3a x + 4a b x)\|- a x + b +--R * +--R +-+ +--R \|b +--R + +--R +----------+ +--R 2 5 3 2 +---+ 2 4 2 | 2 +--R ((- a x + 5a b x - 4b x)\|- a + (- a x + 4a b x )\|- a x + b ) +--R * +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 4 2 2 | 2 +---+ 3 5 2 3 2 +--R (a x - 5a b x + 4b )\|- a x + b \|- a - a x + 5a b x - 4a b x +--R / +--R +----------+ +--R 2 5 3 2 +---+ 2 4 2 | 2 +--R ((3a x - 7a b x + 4b x)\|- a + (3a x - 4a b x )\|- a x + b ) +--R * +--R +----------+ +--R | 2 +--R |- a x + b +-+ +--R |---------- \|b +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 5 3 2 | 2 +---+ 3 6 2 4 +--R (- a x + 5a b x - 4b x)\|- a x + b \|- a + a x - 5a b x +--R + +--R 2 2 +--R 4a b x +--R * +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 451 + +--S 452 of 554 +m0280b:= a0280.2-r0280 +--R +--R +--R +----------+ +--R | 2 +--R |- a x + b +--R +----------+ |---------- +--R +-+ +-+ | 2 +-+ | 2 +--R \|a \|b - \|- a x + b \|a \| x +--R 2atan(----------------------------) + atan(-------------) +--R a x +-+ +--R \|a +--R (421) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 554 +d0280b:= D(m0280b,x) +--R +--R +--R +----------+ +--R | 2 +----------+ +--R |- a x + b | 2 +--R x |---------- - \|- a x + b +--R | 2 +--R \| x +--R (422) ------------------------------ +--R +----------+ +--R +----------+ | 2 +--R | 2 |- a x + b +--R x\|- a x + b |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 453 + +--S 454 of 554 +t0281:= 1/x^2/(2+b/x^2)^(1/2) +--R +--R +--R 1 +--R (423) ------------ +--R +-------+ +--R | 2 +--R 2 |2x + b +--R x |------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 454 + +--S 455 of 554 +r0281:= -asinh(1/2*b^(1/2)*2^(1/2)/x)/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 \|b +--R asinh(--------) +--R 2x +--R (424) - --------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 455 + +--S 456 of 554 +a0281:= integrate(t0281,x) +--R +--R +--R +-------+ +--R | 2 +-+ +--R +-+ \|2x + b - \|b +--R \|b log(-----------------) +--R x +--R (425) -------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 554 +m0281:= a0281-r0281 +--R +--R +--R +-------+ +--R | 2 +-+ +-+ +-+ +--R \|2x + b - \|b \|2 \|b +--R log(-----------------) + asinh(--------) +--R x 2x +--R (426) ---------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 457 + +--S 458 of 554 +d0281:= D(m0281,x) +--R +--R +--R (427) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R +-+ +-+ |2x + b | 2 |2x + b +-+ 2 +-+ +--R (- \|2 \|b - 2x |------- )\|2x + b + 2x |------- \|b + (2x + b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ------------------------------------------------------------------------ +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 |2x + b +-+ | 2 4 2 |2x + b +--R 2x |------- \|b \|2x + b + (- 4x - 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression(Integer) +--E 458 + +--S 459 of 554 +t0282:= 1/x^2/(2-b/x^2)^(1/2) +--R +--R +--R 1 +--R (428) ------------ +--R +-------+ +--R | 2 +--R 2 |2x - b +--R x |------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 554 +r0282:= -asin(1/2*b^(1/2)*2^(1/2)/x)/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 \|b +--R asin(--------) +--R 2x +--R (429) - -------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 460 + +--S 461 of 554 +a0282:= integrate(t0282,x) +--R +--R +--R +-------+ +--R | 2 +---+ +--R +---+ \|2x - b - \|- b +--R \|- b log(-------------------) +--R x +--R (430) - ------------------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 554 +m0282:= a0282-r0282 +--R +--R +--R +-------+ +--R | 2 +---+ +-+ +-+ +--R +---+ +-+ \|2x - b - \|- b \|2 \|b +--R - \|- b \|b log(-------------------) + b asin(--------) +--R x 2x +--R (431) ------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 462 + +--S 463 of 554 +d0282:= D(m0282,x) +--R +--R +--R (432) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R |2x - b +-+ +---+ | 2 +---+ |2x - b 2 +-+ +--R (- 2x |------- - \|2 \|- b )\|2x - b + 2x\|- b |------- + (2x - b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ---------------------------------------------------------------------------- +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 +---+ |2x - b | 2 4 2 |2x - b +--R 2x \|- b |------- \|2x - b + (- 4x + 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression(Integer) +--E 463 + +--S 464 of 554 +t0283:= 1/x^2/(a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (433) ------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 554 +r0283:= -atanh((a+b/x^2)^(1/2)*x/b^(1/2))/b^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R atanh(------------) +--R +-+ +--R \|b +--R (434) - ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 465 + +--S 466 of 554 +a0283:= integrate(t0283,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R +-+ \|a x + b - \|b +--R \|b log(------------------) +--R x +--R (435) --------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 554 +m0283:= a0283-r0283 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ x |-------- +--R | 2 +-+ | 2 +--R \|a x + b - \|b \| x +--R log(------------------) + atanh(------------) +--R x +-+ +--R \|b +--R (436) --------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 467 + +--S 468 of 554 +d0283:= D(m0283,x) +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (- \|b - x |-------- )\|a x + b + x |-------- \|b + a x + b +--R | 2 | 2 +--R \| x \| x +--R (437) ---------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 |a x + b +-+ | 2 4 2 |a x + b +--R x |-------- \|b \|a x + b + (- a x - b x ) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 468 + +--S 469 of 554 +t0284:= x^3*(a+b/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (438) x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 554 +r0284:= 1/8*b*(a+b/x^2)^(1/2)*x^2/a+1/4*(a+b/x^2)^(1/2)*x^4-_ + 1/8*b^2*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R - b atanh(-----------) + (2a x + b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (439) ------------------------------------------------------ +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 470 + +--S 471 of 554 +a0284:= integrate(t0284,x) +--R +--R +--R (440) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 17a b x - 24a b x - 8b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 8a b x - 16b )\|b \|a x + b + 2a b x + 16a b x + 16b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|b +--R / +--R +--------+ +--R 2 2 +---+ +-+ | 2 +--R (32a x + 64a b)\|- a \|b \|a x + b +--R + +--R 3 4 2 2 2 +---+ +--R (- 8a x - 64a b x - 64a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 471 + +--S 472 of 554 +m0284a:= a0284.1-r0284 +--R +--R +--R (441) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 20a b x - 8b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 17a b x - 24a b x - 8b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 17a b x + 24a b x + 8b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 554 +d0284a:= D(m0284a,x) +--R +--R +--R (442) +--R 6 14 5 12 4 2 10 3 3 8 +--R - 11a x - 231a b x - 1452a b x - 4048a b x +--R + +--R 2 4 6 5 4 6 2 +--R - 5632a b x - 3840a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 2 5 4 6 2 +--R - 3840a b x - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 5 6 3 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x +--R + +--R 2 5 5 6 3 7 +--R - 7424a b x - 4352a b x - 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 2 5 5 6 3 +--R 3840a b x + 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 2 5 5 6 3 7 +--R 9472a b x + 4864a b x + 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 16 6 14 5 2 12 4 3 10 3 4 8 +--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x +--R + +--R 2 5 6 6 4 7 2 +--R 7424a b x + 4352a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x + 7424a b x +--R + +--R 2 6 4 7 2 +--R 4352a b x + 1024a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x +--R + +--R 5 2 6 +--R 3328a b x + 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 5 2 6 +--R - 3840a b x - 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 3 6 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 473 + +--S 474 of 554 +m0284b:= a0284.2-r0284 +--R +--R +--R (443) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (4a b x + 8b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (- a b x - 8a b x - 8b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (- 8a b x - 16b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (2a b x + 16a b x + 16b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 20a b x - 8b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 17a b x + 24a b x + 8b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +---+ +-+ +-+ | 2 +--R (32a x + 64a b)\|- a \|a \|b \|a x + b +--R + +--R 3 4 2 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64a b )\|- a \|a +--R Type: Expression(Integer) +--E 474 + +--S 475 of 554 +d0284b:= D(m0284b,x) +--R +--R +--R (444) +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 |a x + b +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R - a x - 33a b x - 192a b x - 416a b x - 384a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+ +--R (8a x + 96a b x + 360a b x + 592a b x + 448a b x + 128b x)\|b +--R + +--R 5 12 4 10 3 2 8 2 3 6 4 4 5 2 +--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 475 + +--S 476 of 554 +t0285:= x*(a+b/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R (445) x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 476 + +--S 477 of 554 +r0285:= 1/2*x^2*(a+b/x^2)^(1/2)+1/2*b*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R \| x 2 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (446) ---------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 554 +a0285:= integrate(t0285,x) +--R +--R +--R (447) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 2 \|- a \|a x + b - \|- a \|b +--R (4b\|b \|a x + b - 2a b x - 4b )atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 +---+ +--R 4\|- a \|b \|a x + b + (- 2a x - 4b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 478 + +--S 479 of 554 +m0285a:= a0285.1-r0285 +--R +--R +--R (448) +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 2 2 \| x +--R (- 2b\|b \|a x + b + a b x + 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b +-+ 3 +-+ | 2 +--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +-+ +-+ 4 2 +-+ |a x + b +--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a +--R Type: Expression(Integer) +--E 479 + +--S 480 of 554 +d0285a:= D(m0285a,x) +--R +--R +--R (449) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- +--R | 2 +--R \| x +--R + +--R 5 9 4 7 3 2 5 2 3 3 4 +--R - 7a x - 63a b x - 168a b x - 176a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (a x + 26a b x + 129a b x + 248a b x + 208a b x + 64b )\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (7a x + 63a b x + 168a b x + 176a b x + 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|a +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+ +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x)\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 5 +--R a x + 26a b x + 129a b x + 248a b x + 208a b x + 64a b x +--R / +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 480 + +--S 481 of 554 +m0285b:= a0285.2-r0285 +--R +--R +--R (450) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 2 2 +---+ \| x +--R (- 2b\|- a \|b \|a x + b + (a b x + 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R (4b\|a \|b \|a x + b + (- 2a b x - 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b +--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 2 2 +---+ +-+ +--R 4\|- a \|a \|b \|a x + b + (- 2a x - 4b)\|- a \|a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 554 +d0285b:= D(m0285b,x) +--R +--R +--R (451) +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 +--R (- 4a x - 12a b x - 8b x) |-------- \|b - a x - 9a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R - 16a b x - 8b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (4a x + 16a b x + 20a b x + 8b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (a x + 9a b x + 16a b x + 8b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b | 2 +--R (a x + 8a b x + 8b x) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 482 + +--S 483 of 554 +t0286:= (a+b/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R (452) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 483 + +--S 484 of 554 +r0286:= x*(a+b/x^2)^(1/2)-b^(1/2)*atanh((a+b/x^2)^(1/2)*x/b^(1/2)) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x |a x + b +--R (453) - \|b atanh(------------) + x |-------- +--R +-+ | 2 +--R \|b \| x +--R Type: Expression(Integer) +--E 484 + +--S 485 of 554 +a0286:= integrate(t0286,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|a x + b - \|b 2 +-+ +--R (b\|a x + b - b\|b )log(------------------) + a x \|b +--R x +--R (454) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 554 +m0286:= a0286-r0286 +--R +--R +--R (455) +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|a x + b - \|b +--R (b\|a x + b - b\|b )log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--------+ +--R +--------+ | 2 | 2 +--------+ +--R | 2 +-+ \| x |a x + b +-+ | 2 +--R (b\|a x + b - b\|b )atanh(------------) - x |-------- \|b \|a x + b +--R +-+ | 2 +--R \|b \| x +--R + +--R +--------+ +--R | 2 +--R 2 +-+ |a x + b +--R a x \|b + b x |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R Type: Expression(Integer) +--E 486 + +--S 487 of 554 +d0286:= D(m0286,x) +--R +--R +--R (456) +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((- 3a x - 7a b x - 4b )\|b + (- a x - 5a b x - 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (3a x + 7a b x + 4b x) |-------- \|b + a x + 6a b x + 9a b x + 4b +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 2 |a x + b +-+ | 2 +--R (3a x + 4b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |a x + b +--R (- a x - 5a b x - 4b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 487 + +--S 488 of 554 +t0287:= (a+b/x^2)^(1/2)/x +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (457) ----------- +--R x +--R Type: Expression(Integer) +--E 488 + +--S 489 of 554 +r0287:= -(a+b/x^2)^(1/2)+a^(1/2)*atanh((a+b/x^2)^(1/2)/a^(1/2)) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x |a x + b +--R (458) \|a atanh(-----------) - |-------- +--R +-+ | 2 +--R \|a \| x +--R Type: Expression(Integer) +--E 489 + +--S 490 of 554 +a0287:= integrate(t0287,x) +--R +--R +--R (459) +--R [ +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R (x\|a \|a x + b - x\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R , +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R +---+ | 2 +---+ +-+ \|a x + b - \|b +--R (2x\|- a \|a x + b - 2x\|- a \|b )atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 490 + +--S 491 of 554 +m0287a:= a0287.1-r0287 +--R +--R +--R (460) +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R (x\|a \|a x + b - x\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 +-+ +-+ \| x +--R (- x\|a \|a x + b + x\|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 2 | 2 +--R \| x \| x +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R Type: Expression(Integer) +--E 491 + +--S 492 of 554 +d0287a:= D(m0287a,x) +--R +--R +--R (461) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (5a x + 25a b x + 36a b x + 16b x) |-------- +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R 14a b x + 41a b x + 44a b x + 16b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (5a x + 25a b x + 36a b x + 16b x )\|a |-------- - 5a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 30a b x - 61a b x - 52a b x - 16b +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16b x) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (a x + 14a b x + 41a b x + 44a b x + 16b x)\|a +--R / +--R +--------+ +--R | 2 +--R 2 8 6 2 4 +-+ |a x + b +-+ +--R (5a x + 20a b x + 16b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +-+ +--R (5a x + 25a b x + 36a b x + 16b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 +-+ |a x + b +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 492 + +--S 493 of 554 +m0287b:= a0287.2-r0287 +--R +--R +--R (462) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 +-+ +-+ \| x +--R (- x\|a \|a x + b + x\|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +--------+ | 2 +-+ +--R +---+ | 2 +---+ +-+ \|a x + b - \|b +--R (2x\|- a \|a x + b - 2x\|- a \|b )atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 2 | 2 +--R \| x \| x +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R Type: Expression(Integer) +--E 493 + +--S 494 of 554 +d0287b:= D(m0287b,x) +--R +--R +--R (463) +--R +--------+ +--R | 2 +--------+ +--R 3 |a x + b +-+ 2 4 2 2 | 2 +--R ((- 2a x - 2b x) |-------- \|b - a x - 3a b x - 2b )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R (2a x + 4a b x + 2b )\|b + (a x + 3a b x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 5 3 |a x + b | 2 5 3 |a x + b +-+ +--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 494 + +--S 495 of 554 +t0288:= (a+b/x^2)^(1/2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (464) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 495 + +--S 496 of 554 +r0288:= -1/2*(a+b/x^2)^(1/2)/x-1/2*a*atanh((a+b/x^2)^(1/2)*x/b^(1/2))/b^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--------+ +--R | 2 | 2 +--R \| x |a x + b +-+ +--R - a x atanh(------------) - |-------- \|b +--R +-+ | 2 +--R \|b \| x +--R (465) ------------------------------------------- +--R +-+ +--R 2x\|b +--R Type: Expression(Integer) +--E 496 + +--S 497 of 554 +a0288:= integrate(t0288,x) +--R +--R +--R (466) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 4 2 +-+ \|a x + b - \|b +--R (2a b x \|a x + b + (- a x - 2a b x )\|b )log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + 2b )\|a x + b + (- 2a b x - 2b )\|b +--R / +--R +--------+ +--R 2 +-+ | 2 4 2 2 +--R 4b x \|b \|a x + b - 2a b x - 4b x +--R Type: Union(Expression(Integer),...) +--E 497 + +--S 498 of 554 +m0288:= a0288-r0288 +--R +--R +--R (467) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 +-+ | 2 2 4 2 \|a x + b - \|b +--R (2a x \|b \|a x + b - a x - 2a b x )log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R +--------+ | 2 +--R 2 +-+ | 2 2 4 2 \| x +--R (2a x \|b \|a x + b - a x - 2a b x )atanh(------------) +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b | 2 +--R ((a x + 2b)\|b + 2b x |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +-+ 2 2 +--R (- a x - 2b x) |-------- \|b - 2a b x - 2b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 | 2 4 2 +-+ +--R 4b x \|a x + b + (- 2a x - 4b x )\|b +--R Type: Expression(Integer) +--E 498 + +--S 499 of 554 +d0288:= D(m0288,x) +--R +--R +--R (468) +--R 3 6 2 4 2 2 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6 +--R (5a x + 25a b x + 36a b x + 16b x) |-------- \|b + a x + 14a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R 41a b x + 44a b x + 16b +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 8 6 2 4 |a x + b +-+ | 2 +--R (5a x + 20a b x + 16b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 499 + +--S 500 of 554 +t0289:= (2+b/x^2)^(1/2)/(b+2*x^2) +--R +--R +--R +-------+ +--R | 2 +--R |2x + b +--R |------- +--R | 2 +--R \| x +--R (469) ---------- +--R 2 +--R 2x + b +--R Type: Expression(Integer) +--E 500 + +--S 501 of 554 +r0289:= -asinh(1/2*b^(1/2)*2^(1/2)/x)/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 \|b +--R asinh(--------) +--R 2x +--R (470) - --------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 501 + +--S 502 of 554 +a0289:= integrate(t0289,x) +--R +--R +--R +-------+ +--R | 2 +-+ +--R +-+ \|2x + b - \|b +--R \|b log(-----------------) +--R x +--R (471) -------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 502 + +--S 503 of 554 +m0289:= a0289-r0289 +--R +--R +--R +-------+ +--R | 2 +-+ +-+ +-+ +--R \|2x + b - \|b \|2 \|b +--R log(-----------------) + asinh(--------) +--R x 2x +--R (472) ---------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 503 + +--S 504 of 554 +d0289:= D(m0289,x) +--R +--R +--R (473) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R +-+ +-+ |2x + b | 2 |2x + b +-+ 2 +-+ +--R (- \|2 \|b - 2x |------- )\|2x + b + 2x |------- \|b + (2x + b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ------------------------------------------------------------------------ +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 |2x + b +-+ | 2 4 2 |2x + b +--R 2x |------- \|b \|2x + b + (- 4x - 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression(Integer) +--E 504 + +--S 505 of 554 +t0290:= (2-b/x^2)^(1/2)/(-b+2*x^2) +--R +--R +--R +-------+ +--R | 2 +--R |2x - b +--R |------- +--R | 2 +--R \| x +--R (474) ---------- +--R 2 +--R 2x - b +--R Type: Expression(Integer) +--E 505 + +--S 506 of 554 +r0290:= -asin(1/2*b^(1/2)*2^(1/2)/x)/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 \|b +--R asin(--------) +--R 2x +--R (475) - -------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 506 + +--S 507 of 554 +a0290:= integrate(t0290,x) +--R +--R +--R +-------+ +--R | 2 +---+ +--R +---+ \|2x - b - \|- b +--R \|- b log(-------------------) +--R x +--R (476) - ------------------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 507 + +--S 508 of 554 +m0290:= a0290-r0290 +--R +--R +--R +-------+ +--R | 2 +---+ +-+ +-+ +--R +---+ +-+ \|2x - b - \|- b \|2 \|b +--R - \|- b \|b log(-------------------) + b asin(--------) +--R x 2x +--R (477) ------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 508 + +--S 509 of 554 +d0290:= D(m0290,x) +--R +--R +--R (478) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R |2x - b +-+ +---+ | 2 +---+ |2x - b 2 +-+ +--R (- 2x |------- - \|2 \|- b )\|2x - b + 2x\|- b |------- + (2x - b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ---------------------------------------------------------------------------- +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 +---+ |2x - b | 2 4 2 |2x - b +--R 2x \|- b |------- \|2x - b + (- 4x + 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression(Integer) +--E 509 + +--S 510 of 554 +t0291:= (-1+1/x^2)^(1/2)*(-1+x^2)/x +--R +--R +--R +--------+ +--R | 2 +--R 2 |- x + 1 +--R (x - 1) |-------- +--R | 2 +--R \| x +--R (479) ------------------- +--R x +--R Type: Expression(Integer) +--E 510 + +--S 511 of 554 +r0291:= (-1+1/x^2)^(1/2)+1/2*(-1+1/x^2)^(1/2)*x^2-3/2*atan((-1+1/x^2)^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R |- x + 1 2 |- x + 1 +--R - 3atan( |-------- ) + (x + 2) |-------- +--R | 2 | 2 +--R \| x \| x +--R (480) ------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 511 + +--S 512 of 554 +a0291:= integrate(t0291,x) +--R +--R +--R (481) +--R +--------+ +--R +--------+ | 2 +--R 3 | 2 3 \|- x + 1 - 1 +--R ((- 6x + 24x)\|- x + 1 + 18x - 24x)atan(---------------) +--R x +--R + +--R +--------+ +--R 4 2 | 2 6 4 2 +--R (- 3x - 2x + 8)\|- x + 1 - x + 3x + 6x - 8 +--R / +--R +--------+ +--R 3 | 2 3 +--R (2x - 8x)\|- x + 1 - 6x + 8x +--R Type: Union(Expression(Integer),...) +--E 512 + +--S 513 of 554 +m0291:= a0291-r0291 +--R +--R +--R (482) +--R +--------+ +--R +--------+ | 2 +--R 3 | 2 3 |- x + 1 +--R ((3x - 12x)\|- x + 1 - 9x + 12x)atan( |-------- ) +--R | 2 +--R \| x +--R + +--R +--------+ +--R +--------+ | 2 +--R 3 | 2 3 \|- x + 1 - 1 +--R ((- 6x + 24x)\|- x + 1 + 18x - 24x)atan(---------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--R 5 3 | 2 5 3 |- x + 1 +--R ((- x + 2x + 8x)\|- x + 1 + 3x + 2x - 8x) |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R 4 2 | 2 6 4 2 +--R (- 3x - 2x + 8)\|- x + 1 - x + 3x + 6x - 8 +--R / +--R +--------+ +--R 3 | 2 3 +--R (2x - 8x)\|- x + 1 - 6x + 8x +--R Type: Expression(Integer) +--E 513 + +--S 514 of 554 +d0291:= D(m0291,x) +--R +--R +--R (483) +--R +--------+ +--R 9 7 5 3 | 2 11 9 7 +--R (- 6x + 44x - 102x + 96x - 32x)\|- x + 1 - x + 20x - 85x +--R + +--R 5 3 +--R 146x - 112x + 32x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R 10 8 6 4 2 | 2 10 8 6 +--R (x - 20x + 85x - 146x + 112x - 32)\|- x + 1 - 6x + 50x - 146x +--R + +--R 4 2 +--R 198x - 128x + 32 +--R / +--R +--------+ +--R 9 7 5 3 | 2 9 7 5 3 +--R ((x - 18x + 48x - 32x )\|- x + 1 - 6x + 38x - 64x + 32x ) +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 514 + +--S 515 of 554 +t0292:= (-1+1/x^2)^(1/2)*(-1+x^2)^2/x +--R +--R +--R +--------+ +--R | 2 +--R 4 2 |- x + 1 +--R (x - 2x + 1) |-------- +--R | 2 +--R \| x +--R (484) ------------------------- +--R x +--R Type: Expression(Integer) +--E 515 + +--S 516 of 554 +r0292:= -(-1+1/x^2)^(1/2)-9/8*(-1+1/x^2)^(1/2)*x^2+1/4*(-1+1/x^2)^(1/2)*x^4+_ + 15/8*atan((-1+1/x^2)^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R |- x + 1 4 2 |- x + 1 +--R 15atan( |-------- ) + (2x - 9x - 8) |-------- +--R | 2 | 2 +--R \| x \| x +--R (485) ------------------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 516 + +--S 517 of 554 +a0292:= integrate(t0292,x) +--R +--R +--R (486) +--R +--------+ +--R 5 3 | 2 5 3 +--R ((30x - 360x + 480x)\|- x + 1 - 150x + 600x - 480x) +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R atan(---------------) +--R x +--R + +--R +--------+ +--R 8 6 4 2 | 2 10 8 6 +--R (- 10x + 85x - 172x - 16x + 128)\|- x + 1 - 2x + 35x - 165x +--R + +--R 4 2 +--R 180x + 80x - 128 +--R / +--R +--------+ +--R 5 3 | 2 5 3 +--R (8x - 96x + 128x)\|- x + 1 - 40x + 160x - 128x +--R Type: Union(Expression(Integer),...) +--E 517 + +--S 518 of 554 +m0292:= a0292-r0292 +--R +--R +--R (487) +--R +--------+ +--R 5 3 | 2 5 3 +--R ((- 15x + 180x - 240x)\|- x + 1 + 75x - 300x + 240x) +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R atan( |-------- ) +--R | 2 +--R \| x +--R + +--R +--------+ +--R 5 3 | 2 5 3 +--R ((30x - 360x + 480x)\|- x + 1 - 150x + 600x - 480x) +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R atan(---------------) +--R x +--R + +--R +--------+ +--R 9 7 5 3 | 2 9 7 5 +--R (- 2x + 33x - 132x + 48x + 128x)\|- x + 1 + 10x - 85x + 172x +--R + +--R 3 +--R 16x - 128x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R 8 6 4 2 | 2 10 8 6 +--R (- 10x + 85x - 172x - 16x + 128)\|- x + 1 - 2x + 35x - 165x +--R + +--R 4 2 +--R 180x + 80x - 128 +--R / +--R +--------+ +--R 5 3 | 2 5 3 +--R (8x - 96x + 128x)\|- x + 1 - 40x + 160x - 128x +--R Type: Expression(Integer) +--E 518 + +--S 519 of 554 +d0292:= D(m0292,x) +--R +--R +--R (488) +--R 15 13 11 9 7 5 3 +--R - 10x + 190x - 1182x + 3530x - 5760x + 5280x - 2560x +--R + +--R 512x +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 17 15 13 11 9 7 5 3 +--R - x + 53x - 553x + 2471x - 5890x + 8112x - 6496x + 2816x +--R + +--R - 512x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R + +--R 16 14 12 10 8 6 4 2 +--R x - 53x + 553x - 2471x + 5890x - 8112x + 6496x - 2816x +--R + +--R 512 +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 16 14 12 10 8 6 4 2 +--R - 10x + 200x - 1372x + 4712x - 9290x + 11040x - 7840x + 3072x +--R + +--R - 512 +--R / +--R +--------+ +--R 13 11 9 7 5 3 | 2 13 +--R (x - 50x + 400x - 1120x + 1280x - 512x )\|- x + 1 - 10x +--R + +--R 11 9 7 5 3 +--R 170x - 832x + 1696x - 1536x + 512x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 519 + +--S 520 of 554 +t0293:= (-1+1/x^2)^(1/2)*(-1+x^2)^3/x +--R +--R +--R +--------+ +--R | 2 +--R 6 4 2 |- x + 1 +--R (x - 3x + 3x - 1) |-------- +--R | 2 +--R \| x +--R (489) ------------------------------- +--R x +--R Type: Expression(Integer) +--E 520 + +--S 521 of 554 +r0293:= (-1+1/x^2)^(1/2)+29/16*(-1+1/x^2)^(1/2)*x^2-19/24*_ + (-1+1/x^2)^(1/2)*x^4+1/6*(-1+1/x^2)^(1/2)*x^6-_ + 35/16*atan((-1+1/x^2)^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R |- x + 1 6 4 2 |- x + 1 +--R - 105atan( |-------- ) + (8x - 38x + 87x + 48) |-------- +--R | 2 | 2 +--R \| x \| x +--R (490) ------------------------------------------------------------ +--R 48 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 554 +a0293:= integrate(t0293,x) +--R +--R +--R (491) +--R +--------+ +--R 7 5 3 | 2 7 5 +--R (- 210x + 5040x - 16800x + 13440x)\|- x + 1 + 1470x - 11760x +--R + +--R 3 +--R 23520x - 13440x +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R atan(---------------) +--R x +--R + +--R +--------+ +--R 12 10 8 6 4 2 | 2 +--R (- 56x + 714x - 3633x + 9304x - 9488x + 192x + 3072)\|- x + 1 +--R + +--R 14 12 10 8 6 4 2 +--R - 8x + 238x - 1869x + 7231x - 13832x + 9968x + 1344x - 3072 +--R / +--R +--------+ +--R 7 5 3 | 2 7 5 3 +--R (48x - 1152x + 3840x - 3072x)\|- x + 1 - 336x + 2688x - 5376x +--R + +--R 3072x +--R Type: Union(Expression(Integer),...) +--E 522 + +--S 523 of 554 +m0293:= a0293-r0293 +--R +--R +--R (492) +--R +--------+ +--R 7 5 3 | 2 7 5 +--R (105x - 2520x + 8400x - 6720x)\|- x + 1 - 735x + 5880x +--R + +--R 3 +--R - 11760x + 6720x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R atan( |-------- ) +--R | 2 +--R \| x +--R + +--R +--------+ +--R 7 5 3 | 2 7 5 +--R (- 210x + 5040x - 16800x + 13440x)\|- x + 1 + 1470x - 11760x +--R + +--R 3 +--R 23520x - 13440x +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R atan(---------------) +--R x +--R + +--R 13 11 9 7 5 3 +--R (- 8x + 230x - 1639x + 5592x - 8240x + 1728x + 3072x) +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 13 11 9 7 5 3 +--R 56x - 714x + 3633x - 9304x + 9488x - 192x - 3072x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R 12 10 8 6 4 2 | 2 +--R (- 56x + 714x - 3633x + 9304x - 9488x + 192x + 3072)\|- x + 1 +--R + +--R 14 12 10 8 6 4 2 +--R - 8x + 238x - 1869x + 7231x - 13832x + 9968x + 1344x - 3072 +--R / +--R +--------+ +--R 7 5 3 | 2 7 5 3 +--R (48x - 1152x + 3840x - 3072x)\|- x + 1 - 336x + 2688x - 5376x +--R + +--R 3072x +--R Type: Expression(Integer) +--E 523 + +--S 524 of 554 +d0293:= D(m0293,x) +--R +--R +--R (493) +--R 21 19 17 15 13 11 +--R - 14x + 504x - 5908x + 34232x - 115598x + 245952x +--R + +--R 9 7 5 3 +--R - 340928x + 308224x - 175616x + 57344x - 8192x +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 23 21 19 17 15 13 +--R - x + 102x - 1966x + 16272x - 74313x + 209762x +--R + +--R 11 9 7 5 3 +--R - 386848x + 476352x - 389376x + 203264x - 61440x + 8192x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R + +--R 22 20 18 16 14 12 10 +--R x - 102x + 1966x - 16272x + 74313x - 209762x + 386848x +--R + +--R 8 6 4 2 +--R - 476352x + 389376x - 203264x + 61440x - 8192 +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 22 20 18 16 14 12 10 +--R - 14x + 518x - 6412x + 40140x - 149830x + 361550x - 586880x +--R + +--R 8 6 4 2 +--R 649152x - 483840x + 232960x - 65536x + 8192 +--R / +--R 17 15 13 11 9 7 5 +--R x - 98x + 1568x - 9408x + 26880x - 39424x + 28672x +--R + +--R 3 +--R - 8192x +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 17 15 13 11 9 7 5 +--R - 14x + 462x - 4480x + 19392x - 43520x + 52736x - 32768x +--R + +--R 3 +--R 8192x +--R * +--R +--------+ +--R | 2 +--R |- x + 1 +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 524 + +--S 525 of 554 +t0294:= 1/x/(a+b/x^3)^(1/2) +--R +--R +--R 1 +--R (494) ------------ +--R +--------+ +--R | 3 +--R |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 525 + +--S 526 of 554 +r0294:= 2/3*atanh((a+b/x^3)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (495) ------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 526 + +--S 527 of 554 +a0294:= integrate(t0294,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 3 +--R |1 2 |1 |a x + b 3 +--R |- log(2a x |- |-------- - 2a x - b) +--R \|a \|a \| x +--R (496) - ----------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 527 + +--S 528 of 554 +m0294:= a0294-r0294 +--R +--R +--R (497) +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R +-+ +-+ | 3 | 3 +--R |1 +-+ 2 |1 |a x + b 3 \| x +--R - |- \|a log(2a x |- |-------- - 2a x - b) - 2atanh(-----------) +--R \|a \|a \| x +-+ +--R \|a +--R --------------------------------------------------------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 528 + +--S 529 of 554 +d0294:= D(m0294,x) +--R +--R +--R (498) +--R +--------+ +--------+ +--R +-+ | 3 | 3 +--R 3 |1 |a x + b 3 |a x + b +--R (- 2a x |- |-------- - 2a x - b) |-------- +--R \|a | 3 \| x +--R \| x +--R + +--R +--------+ +--R | 3 +-+ +--R 4 |a x + b 2 4 |1 +--R (2a x + b x) |-------- + (2a x + 2a b x) |- +--R | 3 \|a +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 3 | 3 +-+ | 3 +--R 4 |a x + b |a x + b 2 5 2 |1 |a x + b +--R (2a x + b x) |-------- |-------- + (- 2a x - 2a b x ) |- |-------- +--R | 3 \| x \|a | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 529 + +--S 530 of 554 +t0295:= 1/x/(-a+b/x^3)^(1/2) +--R +--R +--R 1 +--R (499) -------------- +--R +----------+ +--R | 3 +--R |- a x + b +--R x |---------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 530 + +--S 531 of 554 +r0295:= -2/3*atan((-a+b/x^3)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +----------+ +--R | 3 +--R |- a x + b +--R |---------- +--R | 3 +--R \| x +--R 2atan(-------------) +--R +-+ +--R \|a +--R (500) - -------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 531 + +--S 532 of 554 +a0295:= integrate(t0295,x) +--R +--R +--R +----------+ +--R +---+ | 3 +---+ +--R | 1 2 |- a x + b | 1 3 +--R |- - log(2a x |---------- |- - - 2a x + b) +--R \| a \| x \| a +--R (501) - ----------------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 532 + +--S 533 of 554 +m0295:= a0295-r0295 +--R +--R +--R (502) +--R +----------+ +--R | 3 +--R |- a x + b +--R +----------+ |---------- +--R +---+ | 3 +---+ | 3 +--R | 1 +-+ 2 |- a x + b | 1 3 \| x +--R - |- - \|a log(2a x |---------- |- - - 2a x + b) + 2atan(-------------) +--R \| a \| x \| a +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 533 + +--S 534 of 554 +d0295:= D(m0295,x) +--R +--R +--R (503) +--R +----------+ +----------+ +--R | 3 | 3 +---+ +--R 3 |- a x + b |- a x + b 2 4 | 1 +--R (- 2a x |---------- |---------- - 2a x + 2a b x) |- - +--R \| x | 3 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 3 | 3 +--R 4 |- a x + b 3 |- a x + b +--R (2a x - b x) |---------- + (- 2a x + b) |---------- +--R | 3 \| x +--R \| x +--R / +--R +----------+ +--R | 3 +---+ +--R 2 5 2 |- a x + b | 1 +--R (2a x - 2a b x ) |---------- |- - +--R | 3 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 3 | 3 +--R 4 |- a x + b |- a x + b +--R (2a x - b x) |---------- |---------- +--R \| x | 3 +--R \| x +--R Type: Expression(Integer) +--E 534 + +--S 535 of 554 +t0296:= x^2/(a+b/x^3)^(1/2) +--R +--R +--R 2 +--R x +--R (504) ----------- +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 535 + +--S 536 of 554 +r0296:= 1/3*(a+b/x^3)^(1/2)*x^3/a-1/3*b*atanh((a+b/x^3)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R \| x 3 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (505) ------------------------------------------ +--R +-+ +--R 3a\|a +--R Type: Expression(Integer) +--E 536 + +--S 537 of 554 +a0296:= integrate(t0296,x) +--R +--R +--R +--+ +--+ +--------+ +--------+ +--R | 2 | 2 | 3 | 3 +--R |b 2 2 |b |a x + b 3 2 2 |a x + b +--R - a |-- log(2a x |-- |-------- + 2a b x + b ) + 2x |-------- +--R | 3 | 3 \| x \| x +--R \|a \|a +--R (506) ------------------------------------------------------------------ +--R 6a +--R Type: Union(Expression(Integer),...) +--E 537 + +--S 538 of 554 +m0296:= a0296-r0296 +--R +--R +--R (507) +--R +--+ +--+ +--------+ +--R | 2 | 2 | 3 +--R +-+ |b 2 2 |b |a x + b 3 2 +--R - a\|a |-- log(2a x |-- |-------- + 2a b x + b ) +--R | 3 | 3 \| x +--R \|a \|a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--------+ +--R | 3 | 3 | 3 +--R \| x 2 +-+ |a x + b 3 +-+ |a x + b +--R 2b atanh(-----------) + 2x \|a |-------- - 2x \|a |-------- +--R +-+ \| x | 3 +--R \|a \| x +--R / +--R +-+ +--R 6a\|a +--R Type: Expression(Integer) +--E 538 + +--S 539 of 554 +d0296:= D(m0296,x) +--R +--R +--R (508) +--R +--+ +--------+ +--------+ +--R | 2 | 3 | 3 +--R 3 7 2 4 |b 7 2 4 |a x + b |a x + b +--R ((- 2a x - 2a b x ) |-- + (2a b x + b x ) |-------- ) |-------- +--R | 3 | 3 \| x +--R \|a \| x +--R + +--R +--------+ +--+ +--R | 3 | 2 +--R 3 8 2 5 |a x + b |b 2 8 2 5 3 2 +--R (2a x + 2a b x ) |-------- |-- - 2a b x - 3a b x - b x +--R | 3 | 3 +--R \| x \|a +--R / +--R +--------+ +--+ +--------+ +--R | 3 | 2 | 3 +--R 3 5 2 2 |a x + b |b |a x + b +--R (2a x + 2a b x ) |-------- |-- |-------- +--R | 3 | 3 \| x +--R \| x \|a +--R + +--R +--------+ +--R | 3 +--R 2 6 2 3 3 |a x + b +--R (2a b x + 3a b x + b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 539 + +--S 540 of 554 +t0297:= (a+b/x^3)^(1/2)/x +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R (509) ----------- +--R x +--R Type: Expression(Integer) +--E 540 + +--S 541 of 554 +r0297:= -2/3*(a+b/x^3)^(1/2)+2/3*a^(1/2)*atanh((a+b/x^3)^(1/2)/a^(1/2)) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R +-+ \| x |a x + b +--R 2\|a atanh(-----------) - 2 |-------- +--R +-+ | 3 +--R \|a \| x +--R (510) -------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 554 +a0297:= integrate(t0297,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R +--+ 2 +--+ |a x + b 3 |a x + b +--R - x\|4a log(x \|4a |-------- - 2a x - b) - 4 |-------- +--R \| x \| x +--R (511) ---------------------------------------------------------- +--R 6x +--R Type: Union(Expression(Integer),...) +--E 542 + +--S 543 of 554 +m0297:= a0297-r0297 +--R +--R +--R (512) +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R +--+ 2 +--+ |a x + b 3 +-+ \| x +--R - x\|4a log(x \|4a |-------- - 2a x - b) - 4x\|a atanh(-----------) +--R \| x +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b |a x + b +--R - 4 |-------- + 4x |-------- +--R \| x | 3 +--R \| x +--R / +--R 6x +--R Type: Expression(Integer) +--E 543 + +--S 544 of 554 +d0297:= D(m0297,x) +--R +--R +--R (513) +--R +--------+ +--------+ +--R | 3 | 3 +--R 5 2 +--+ 5 2 |a x + b |a x + b +--R ((- a x - b x )\|4a + (- 2a x - b x ) |-------- ) |-------- +--R | 3 \| x +--R \| x +--R + +--R +--------+ +--R | 3 +--R 6 3 |a x + b +--+ 2 6 3 2 +--R (a x + b x ) |-------- \|4a + 2a x + 3a b x + b +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 3 | 3 | 3 +--R 6 |a x + b +--+ |a x + b 7 4 |a x + b +--R x |-------- \|4a |-------- + (- 2a x - b x ) |-------- +--R | 3 \| x | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 544 + +--S 545 of 554 +t0298:= (-a+b/x^3)^(1/2)/x +--R +--R +--R +----------+ +--R | 3 +--R |- a x + b +--R |---------- +--R | 3 +--R \| x +--R (514) ------------- +--R x +--R Type: Expression(Integer) +--E 545 + +--S 546 of 554 +r0298:= -2/3*(-a+b/x^3)^(1/2)+2/3*a^(1/2)*atan((-a+b/x^3)^(1/2)/a^(1/2)) +--R +--R +--R +----------+ +--R | 3 +--R |- a x + b +--R |---------- +----------+ +--R | 3 | 3 +--R +-+ \| x |- a x + b +--R 2\|a atan(-------------) - 2 |---------- +--R +-+ | 3 +--R \|a \| x +--R (515) ----------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 546 + +--S 547 of 554 +a0298:= integrate(t0298,x) +--R +--R +--R +----------+ +----------+ +--R | 3 | 3 +--R +----+ 2 |- a x + b +----+ 3 |- a x + b +--R - x\|- 4a log(x |---------- \|- 4a + 2a x - b) - 4 |---------- +--R \| x \| x +--R (516) ------------------------------------------------------------------ +--R 6x +--R Type: Union(Expression(Integer),...) +--E 547 + +--S 548 of 554 +m0298:= a0298-r0298 +--R +--R +--R (517) +--R +----------+ +--R | 3 +--R +----+ 2 |- a x + b +----+ 3 +--R - x\|- 4a log(x |---------- \|- 4a + 2a x - b) +--R \| x +--R + +--R +----------+ +--R | 3 +--R |- a x + b +--R |---------- +----------+ +----------+ +--R | 3 | 3 | 3 +--R +-+ \| x |- a x + b |- a x + b +--R - 4x\|a atan(-------------) + 4x |---------- - 4 |---------- +--R +-+ | 3 \| x +--R \|a \| x +--R / +--R 6x +--R Type: Expression(Integer) +--E 548 + +--S 549 of 554 +d0298:= D(m0298,x) +--R +--R +--R (518) +--R +----------+ +----------+ +--R | 3 | 3 +--R 6 3 +----+ 5 2 |- a x + b |- a x + b +--R ((- a x + b x )\|- 4a + (2a x - b x ) |---------- ) |---------- +--R \| x | 3 +--R \| x +--R + +--R +----------+ +--R | 3 +--R 5 2 |- a x + b +----+ 2 6 3 2 +--R (a x - b x ) |---------- \|- 4a + 2a x - 3a b x + b +--R \| x +--R / +--R +----------+ +----------+ +--R | 3 | 3 +--R 6 |- a x + b +----+ 7 4 |- a x + b +--R (x |---------- \|- 4a + 2a x - b x ) |---------- +--R \| x | 3 +--R \| x +--R Type: Expression(Integer) +--E 549 + +--S 550 of 554 +t0299:= x^2*(a+b/x^3)^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R 2 |a x + b +--R (519) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 550 + +--S 551 of 554 +r0299:= 1/3*(a+b/x^3)^(1/2)*x^3+1/3*b*atanh((a+b/x^3)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R \| x 3 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (520) ---------------------------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 551 + +--S 552 of 554 +a0299:= integrate(t0299,x) +--R +--R +--R +--+ +--+ +--------+ +--------+ +--R | 2 | 2 | 3 | 3 +--R |b 2 |b |a x + b 3 2 2 |a x + b +--R - |-- log(2a x |-- |-------- - 2a b x - b ) + 2x |-------- +--R \| a \| a \| x \| x +--R (521) ----------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 552 + +--S 553 of 554 +m0299:= a0299-r0299 +--R +--R +--R (522) +--R +--+ +--+ +--------+ +--R | 2 | 2 | 3 +--R +-+ |b 2 |b |a x + b 3 2 +--R - \|a |-- log(2a x |-- |-------- - 2a b x - b ) +--R \| a \| a \| x +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--------+ +--R | 3 | 3 | 3 +--R \| x 2 +-+ |a x + b 3 +-+ |a x + b +--R - 2b atanh(-----------) + 2x \|a |-------- - 2x \|a |-------- +--R +-+ \| x | 3 +--R \|a \| x +--R / +--R +-+ +--R 6\|a +--R Type: Expression(Integer) +--E 553 + +--S 554 of 554 +d0299:= D(m0299,x) +--R +--R +--R (523) +--R +--------+ +--+ +--------+ +--R | 3 | 2 | 3 +--R 4 |a x + b |b 4 2 |a x + b +--R (- 2a x |-------- |-- - 2a b x - b x) |-------- +--R | 3 \| a \| x +--R \| x +--R + +--R +--+ +--------+ +--R | 2 | 3 +--R 2 5 2 |b 5 2 2 |a x + b +--R (2a x + 2a b x ) |-- + (2a b x + b x ) |-------- +--R \| a | 3 +--R \| x +--R / +--R +--+ +--------+ +--R | 2 | 3 +--R 2 |b |a x + b 3 2 +--R 2a x |-- |-------- - 2a b x - b +--R \| a \| x +--R Type: Expression(Integer) +--E 554 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richalgebraic200-299.input.pdf b/src/axiom-website/CATS/richalgebraic200-299.input.pdf new file mode 100644 index 0000000..6086252 Binary files /dev/null and b/src/axiom-website/CATS/richalgebraic200-299.input.pdf differ diff --git a/src/axiom-website/CATS/richalgebraic300-399.input.pamphlet b/src/axiom-website/CATS/richalgebraic300-399.input.pamphlet new file mode 100644 index 0000000..c34e483 --- /dev/null +++ b/src/axiom-website/CATS/richalgebraic300-399.input.pamphlet @@ -0,0 +1,15031 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richalgebraic300-399.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic300-399.output +)spool richalgebraic300-399.output +)set message test on +)set message auto off +)clear all + +--S 1 of 486 +t0300:= 1/(a+b/x^4)^(1/2)/x^3 +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 4 +--R 3 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 486 +r0300:= -1/2*atanh((a+b/x^4)^(1/2)*x^2/b^(1/2))/b^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R atanh(-------------) +--R +-+ +--R \|b +--R (2) - -------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 486 +a0300:= integrate(t0300,x) +--R +--R +--R +--------+ +--R | 4 4 +-+ +--------+ +--R - 2b\|a x + b + (a x + 2b)\|b +---+ | 4 +--R log(---------------------------------) \|- b \|a x + b +--R 4 atan(-----------------) +--R x b +--R (3) [--------------------------------------,- -----------------------] +--R +-+ +---+ +--R 4\|b 2\|- b +--R Type: Union(List(Expression(Integer)),...) +--E 3 + +--S 4 of 486 +m0300a:= a0300.1-r0300 +--R +--R +--R +--------+ +--R | 4 +--R 2 |a x + b +--R +--------+ x |-------- +--R | 4 4 +-+ | 4 +--R - 2b\|a x + b + (a x + 2b)\|b \| x +--R log(---------------------------------) + 2atanh(-------------) +--R 4 +-+ +--R x \|b +--R (4) -------------------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 4 + +--S 5 of 486 +d0300a:= D(m0300a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--------+ +--R 4 +-+ 2 |a x + b | 4 +--R ((- a x - 2b)\|b - 2b x |-------- )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 |a x + b +-+ 4 2 +--R (a x + 2b x ) |-------- \|b + 2a b x + 2b +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 7 3 |a x + b +-+ | 4 7 2 3 |a x + b +--R (a x + 2b x ) |-------- \|b \|a x + b + (- 2a b x - 2b x ) |-------- +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 5 + +--S 6 of 486 +m0300b:= a0300.2-r0300 +--R +--R +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--------+ +--R | 4 +---+ | 4 +--R +---+ \| x +-+ \|- b \|a x + b +--R \|- b atanh(-------------) - \|b atan(-----------------) +--R +-+ b +--R \|b +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 6 + +--S 7 of 486 +d0300b:= D(m0300b,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R - \|a x + b + x |-------- +--R | 4 +--R \| x +--R (7) ----------------------------- +--R +--------+ +--R | 4 +--------+ +--R 3 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 7 + +--S 8 of 486 +t0301:= x^m/(a+b*x^(2+2*m))^(1/2) +--R +--R +--R m +--R x +--R (8) ---------------- +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 8 + +--S 9 of 486 +r0301:= atanh(x^(-1-m)*(a+b*x^(2+2*m))^(1/2)/b^(1/2))/b^(1/2)/(1+m) +--R +--R +--R +-------------+ +--R - m - 1 | 2m + 2 +--R x \|b x + a +--R atanh(------------------------) +--R +-+ +--R \|b +--R (9) ------------------------------- +--R +-+ +--R (m + 1)\|b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 486 +--a0301:= integrate(t0301,x) +--E 10 + +--S 11 of 486 +--m0301:= a0301-r0301 +--E 11 + +--S 12 of 486 +--d0301:= D(m0301,x) +-- >> Error detected within library code: +-- integrate: implementation incomplete (constant residues) +--E 12 + +--S 13 of 486 +t0302:= 1/(a+b/x^5)^(1/2)/x +--R +--R +--R 1 +--R (10) ------------ +--R +--------+ +--R | 5 +--R |a x + b +--R x |-------- +--R | 5 +--R \| x +--R Type: Expression(Integer) +--E 13 + +--S 14 of 486 +r0302:= 2/5*atanh((a+b/x^5)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 5 +--R |a x + b +--R |-------- +--R | 5 +--R \| x +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (11) ------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 14 + +--S 15 of 486 +a0302:= integrate(t0302,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 5 +--R |1 3 |1 |a x + b 5 +--R |- log(2a x |- |-------- - 2a x - b) +--R \|a \|a \| x +--R (12) - ----------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 15 + +--S 16 of 486 +m0302:= a0302-r0302 +--R +--R +--R +--------+ +--R | 5 +--R |a x + b +--R +--------+ |-------- +--R +-+ +-+ | 5 | 5 +--R |1 +-+ 3 |1 |a x + b 5 \| x +--R - |- \|a log(2a x |- |-------- - 2a x - b) - 2atanh(-----------) +--R \|a \|a \| x +-+ +--R \|a +--R (13) --------------------------------------------------------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 486 +d0302:= D(m0302,x) +--R +--R +--R (14) +--R +--------+ +--------+ +--R +-+ | 5 | 5 +--R 5 |1 |a x + b 5 |a x + b +--R (- 2a x |- |-------- - 2a x - b) |-------- +--R \|a | 5 \| x +--R \| x +--R + +--R +--------+ +--R | 5 +-+ +--R 7 2 |a x + b 2 7 2 |1 +--R (2a x + b x ) |-------- + (2a x + 2a b x ) |- +--R | 5 \|a +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 5 | 5 +-+ | 5 +--R 6 |a x + b |a x + b 2 8 3 |1 |a x + b +--R (2a x + b x) |-------- |-------- + (- 2a x - 2a b x ) |- |-------- +--R | 5 \| x \|a | 5 +--R \| x \| x +--R Type: Expression(Integer) +--E 17 + +--S 18 of 486 +t0303:= 1/(-a+b/x^5)^(1/2)/x +--R +--R +--R 1 +--R (15) -------------- +--R +----------+ +--R | 5 +--R |- a x + b +--R x |---------- +--R | 5 +--R \| x +--R Type: Expression(Integer) +--E 18 + +--S 19 of 486 +r0303:= -2/5*atan((-a+b/x^5)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +----------+ +--R | 5 +--R |- a x + b +--R |---------- +--R | 5 +--R \| x +--R 2atan(-------------) +--R +-+ +--R \|a +--R (16) - -------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 486 +a0303:= integrate(t0303,x) +--R +--R +--R +----------+ +--R +---+ | 5 +---+ +--R | 1 3 |- a x + b | 1 5 +--R |- - log(2a x |---------- |- - - 2a x + b) +--R \| a \| x \| a +--R (17) - ----------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 20 + +--S 21 of 486 +m0303:= a0303-r0303 +--R +--R +--R (18) +--R +----------+ +--R | 5 +--R |- a x + b +--R +----------+ |---------- +--R +---+ | 5 +---+ | 5 +--R | 1 +-+ 3 |- a x + b | 1 5 \| x +--R - |- - \|a log(2a x |---------- |- - - 2a x + b) + 2atan(-------------) +--R \| a \| x \| a +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 21 + +--S 22 of 486 +d0303:= D(m0303,x) +--R +--R +--R (19) +--R +----------+ +----------+ +--R | 5 | 5 +---+ +--R 5 |- a x + b |- a x + b 2 7 2 | 1 +--R (- 2a x |---------- |---------- - 2a x + 2a b x ) |- - +--R \| x | 5 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 7 2 |- a x + b 5 |- a x + b +--R (2a x - b x ) |---------- + (- 2a x + b) |---------- +--R | 5 \| x +--R \| x +--R / +--R +----------+ +--R | 5 +---+ +--R 2 8 3 |- a x + b | 1 +--R (2a x - 2a b x ) |---------- |- - +--R | 5 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 6 |- a x + b |- a x + b +--R (2a x - b x) |---------- |---------- +--R \| x | 5 +--R \| x +--R Type: Expression(Integer) +--E 22 + +--S 23 of 486 +t0304:= x^(1/3)/(1-x^6) +--R +--R +--R 3+-+ +--R \|x +--R (20) - ------ +--R 6 +--R x - 1 +--R Type: Expression(Integer) +--E 23 + +--S 24 of 486 +r0304:= -1/6*atan(1/3*(1+2*x^(2/3))*3^(1/2))*3^(1/2)-1/3*atan((x^(2/3)+_ + cos(1/9*%pi))*csc(1/9*%pi))*(1-cos(2/9*%pi))*cot(1/9*%pi)-_ + 1/6*log(1-x^(2/3))+1/12*log(1+x^(2/3)+x^(4/3))-_ + 1/6*cos(2/9*%pi)*log(1+x^(4/3)+2*x^(2/3)*cos(1/9*%pi))+_ + 1/6*cos(1/9*%pi)*log(1+x^(4/3)-2*x^(2/3)*sin(1/18*%pi))+_ + 1/3*atan((x^(2/3)-cos(2/9*%pi))*csc(2/9*%pi))*cot(2/9*%pi)*_ + (1-sin(1/18*%pi))-1/6*log(1+x^(4/3)-2*x^(2/3)*cos(2/9*%pi))*_ + sin(1/18*%pi)+1/3*atan(sec(1/18*%pi)*(x^(2/3)-sin(1/18*%pi)))*_ + (1+cos(1/9*%pi))*tan(1/18*%pi) +--R +--R +--R (21) +--R 2%pi %pi 3+-+2 3+-+ 3+-+2 3+-+ +--R - 2cos(----)log(2cos(---)\|x + x\|x + 1) + log(\|x + x\|x + 1) +--R 9 9 +--R + +--R 3+-+2 %pi 2%pi 3+-+2 3+-+ +--R - 2log(- \|x + 1) - 2sin(---)log(- 2cos(----)\|x + x\|x + 1) +--R 18 9 +--R + +--R %pi %pi 3+-+2 3+-+ +--R 2cos(---)log(- 2sin(---)\|x + x\|x + 1) +--R 9 18 +--R + +--R %pi %pi %pi 3+-+2 %pi %pi +--R (4cos(---) + 4)tan(---)atan(sec(---)\|x - sec(---)sin(---)) +--R 9 18 18 18 18 +--R + +--R 2%pi %pi 2%pi +--R (- 4cot(----)sin(---) + 4cot(----)) +--R 9 18 9 +--R * +--R 2%pi 3+-+2 2%pi 2%pi +--R atan(csc(----)\|x - cos(----)csc(----)) +--R 9 9 9 +--R + +--R 2%pi %pi %pi 3+-+2 %pi %pi +--R (4cos(----) - 4)cot(---)atan(csc(---)\|x + cos(---)csc(---)) +--R 9 9 9 9 9 +--R + +--R +-+3+-+2 +-+ +--R +-+ 2\|3 \|x + \|3 +--R - 2\|3 atan(-----------------) +--R 3 +--R / +--R 12 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 486 +a0304:= integrate(t0304,x) +--R +--R +--R (22) +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) + 2\|x )sin(----------) +--R 3 3 3 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 3+-+2 \|3 3+-+ +--R cos(----------) - 2\|x cos(----------) + x\|x +--R 3 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (- 3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R - 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) + 6cos(----------)) +--R 3 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) + 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) - 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 4\|3 sin(----------) +--R 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) - 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) + 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) - 6cos(----------)) +--R 3 3 +--R * +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 +--R 2cos(----------)sin(----------) +--R 3 3 +--R atan(-------------------------------------------) +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 3+-+2 +--R sin(----------) - cos(----------) + \|x +--R 3 3 +--R + +--R +-+ 3+-+2 3+-+ +-+ 3+-+2 +--R \|3 log(\|x + x\|x + 1) - 2\|3 log(\|x - 1) +--R + +--R +-+3+-+2 +-+ +--R 2\|3 \|x + \|3 +--R 3atan(-------------------) +--R 3+-+2 3+-+ +--R 2\|x + 2x\|x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 25 + +--S 26 of 486 +m0304:= a0304-r0304 +--R +--R +--R (23) +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) + 2\|x )sin(----------) +--R 3 3 3 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 3+-+2 \|3 3+-+ +--R cos(----------) - 2\|x cos(----------) + x\|x +--R 3 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (- 3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R - 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) + 6cos(----------)) +--R 3 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) + 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) - 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 4\|3 sin(----------) +--R 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) - 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) + 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) - 6cos(----------)) +--R 3 3 +--R * +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 +--R 2cos(----------)sin(----------) +--R 3 3 +--R atan(-------------------------------------------) +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 3+-+2 +--R sin(----------) - cos(----------) + \|x +--R 3 3 +--R + +--R +-+ 2%pi %pi 3+-+2 3+-+ +-+ 3+-+2 +--R 2\|3 cos(----)log(2cos(---)\|x + x\|x + 1) - 2\|3 log(\|x - 1) +--R 9 9 +--R + +--R +-+ 3+-+2 +-+ %pi 2%pi 3+-+2 3+-+ +--R 2\|3 log(- \|x + 1) + 2\|3 sin(---)log(- 2cos(----)\|x + x\|x + 1) +--R 18 9 +--R + +--R +-+ %pi %pi 3+-+2 3+-+ +--R - 2\|3 cos(---)log(- 2sin(---)\|x + x\|x + 1) +--R 9 18 +--R + +--R +-+ %pi +-+ %pi %pi 3+-+2 %pi %pi +--R (- 4\|3 cos(---) - 4\|3 )tan(---)atan(sec(---)\|x - sec(---)sin(---)) +--R 9 18 18 18 18 +--R + +--R +-+ 2%pi %pi +-+ 2%pi +--R (4\|3 cot(----)sin(---) - 4\|3 cot(----)) +--R 9 18 9 +--R * +--R 2%pi 3+-+2 2%pi 2%pi +--R atan(csc(----)\|x - cos(----)csc(----)) +--R 9 9 9 +--R + +--R +-+ 2%pi +-+ %pi %pi 3+-+2 %pi %pi +--R (- 4\|3 cos(----) + 4\|3 )cot(---)atan(csc(---)\|x + cos(---)csc(---)) +--R 9 9 9 9 9 +--R + +--R +-+3+-+2 +-+ +-+3+-+2 +-+ +--R 2\|3 \|x + \|3 2\|3 \|x + \|3 +--R 6atan(-----------------) + 3atan(-------------------) +--R 3 3+-+2 3+-+ +--R 2\|x + 2x\|x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 486 +--d0304:= D(m0304,x) +--E 27 + +--S 28 of 486 +t0305:= 1/(1+(1/x)^(1/2))^(1/2) +--R +--R +--R 1 +--R (24) ----------- +--R +--------+ +--R | +-+ +--R | |1 +--R | |- + 1 +--R \|\|x +--R Type: Expression(Integer) +--E 28 + +--S 29 of 486 +r0305:= -3/2*(1+(1/x)^(1/2))^(1/2)/(1/x)^(1/2)+(1+(1/x)^(1/2))^(1/2)*x+_ + 3/2*atanh((1+(1/x)^(1/2))^(1/2)) +--R +--R +--R +--------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R |1 | |1 |1 | |1 +--R 3 |- atanh( | |- + 1 + (2x |- - 3) | |- + 1 +--R \|x \|\|x \|x \|\|x +--R (25) ------------------------------------------------- +--R +-+ +--R |1 +--R 2 |- +--R \|x +--R Type: Expression(Integer) +--E 29 + +--S 30 of 486 +a0305:= integrate(t0305,x) +--R +--R +--R (26) +--R +--------+ +--------+ +--------+ +--R | +-+ | +-+ +-+ | +-+ +--R | |1 | |1 |1 | |1 +--R 3log( | |- + 1 + 1) - 3log( | |- + 1 - 1) + (- 6x |- + 4x) | |- + 1 +--R \|\|x \|\|x \|x \|\|x +--R -------------------------------------------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 30 + +--S 31 of 486 +m0305:= a0305-r0305 +--R +--R +--R +--------+ +--------+ +--------+ +--R | +-+ | +-+ | +-+ +--R | |1 | |1 | |1 +--R 3log( | |- + 1 + 1) - 3log( | |- + 1 - 1) - 6atanh( | |- + 1 ) +--R \|\|x \|\|x \|\|x +--R (27) ------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 486 +d0305:= D(m0305,x) +--R +--R +--R (28) 0 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 486 +t0306:= 1/(1+1/x^(1/2))^(1/2) +--R +--R +--R 1 +--R (29) ----------- +--R +--------+ +--R | +-+ +--R |\|x + 1 +--R |-------- +--R | +-+ +--R \| \|x +--R Type: Expression(Integer) +--E 33 + +--S 34 of 486 +r0306:= -3/2*(1+1/x^(1/2))^(1/2)*x^(1/2)+(1+1/x^(1/2))^(1/2)*x+_ + 3/2*atanh((1+1/x^(1/2))^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | +-+ | +-+ +--R |\|x + 1 +-+ |\|x + 1 +--R 3atanh( |-------- ) + (- 3\|x + 2x) |-------- +--R | +-+ | +-+ +--R \| \|x \| \|x +--R (30) ----------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 486 +a0306:= integrate(t0306,x) +--R +--R +--R (31) +--R +--------+ +--------+ +--R | +-+ | +-+ +--R +-+ |\|x + 1 +-+ |\|x + 1 +--R 3\|x log( |-------- + 1) - 3\|x log( |-------- - 1) +--R | +-+ | +-+ +--R \| \|x \| \|x +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|x + 1 +--R (4x\|x - 6x) |-------- +--R | +-+ +--R \| \|x +--R / +--R +-+ +--R 4\|x +--R Type: Union(Expression(Integer),...) +--E 35 + +--S 36 of 486 +m0306:= a0306-r0306 +--R +--R +--R +--------+ +--------+ +--------+ +--R | +-+ | +-+ | +-+ +--R |\|x + 1 |\|x + 1 |\|x + 1 +--R 3log( |-------- + 1) - 3log( |-------- - 1) - 6atanh( |-------- ) +--R | +-+ | +-+ | +-+ +--R \| \|x \| \|x \| \|x +--R (32) ------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 486 +d0306:= D(m0306,x) +--R +--R +--R (33) 0 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 486 +t0307:= (3-1/x^(1/2))^(1/2) +--R +--R +--R +---------+ +--R | +-+ +--R |3\|x - 1 +--R (34) |--------- +--R | +-+ +--R \| \|x +--R Type: Expression(Integer) +--E 38 + +--S 39 of 486 +r0307:= -1/6*(3-1/x^(1/2))^(1/2)*x^(1/2)+(3-1/x^(1/2))^(1/2)*x-_ + 1/18*atanh(1/3*(3-1/x^(1/2))^(1/2)*3^(1/2))*3^(1/2) +--R +--R +--R +---------+ +--R | +-+ +--R +-+ |3\|x - 1 +--R \|3 |--------- +---------+ +--R | +-+ | +-+ +--R +-+ \| \|x +-+ |3\|x - 1 +--R - \|3 atanh(----------------) + (- 3\|x + 18x) |--------- +--R 3 | +-+ +--R \| \|x +--R (35) ----------------------------------------------------------- +--R 18 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 486 +a0307:= integrate(t0307,x) +--R +--R +--R (36) +--R +---------+ +--R | +-+ +--R +-+ +-+ |3\|x - 1 +-+ +-+ +-+ +--R \|x log(6\|x |--------- - 6\|3 \|x + \|3 ) +--R | +-+ +--R \| \|x +--R + +--R +---------+ +--R | +-+ +--R +-+ +-+ +-+ |3\|x - 1 +--R (12x\|3 \|x - 2x\|3 ) |--------- +--R | +-+ +--R \| \|x +--R / +--R +-+ +-+ +--R 12\|3 \|x +--R Type: Union(Expression(Integer),...) +--E 40 + +--S 41 of 486 +m0307:= a0307-r0307 +--R +--R +--R +---------+ +--R | +-+ +--R +-+ |3\|x - 1 +--R +---------+ \|3 |--------- +--R | +-+ | +-+ +--R +-+ |3\|x - 1 +-+ +-+ +-+ \| \|x +--R log(6\|x |--------- - 6\|3 \|x + \|3 ) + 2atanh(----------------) +--R | +-+ 3 +--R \| \|x +--R (37) -------------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 486 +d0307:= D(m0307,x) +--R +--R +--R (38) 0 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 486 +t0308:= x^3*(a+b*x+c*x^2)^(1/2) +--R +--R +--R +--------------+ +--R 3 | 2 +--R (39) x \|c x + b x + a +--R Type: Expression(Integer) +--E 43 + +--S 44 of 486 +r0308:= -7/128*b^3*(b+2*c*x)*(a+b*x+c*x^2)^(1/2)/c^4+3/32*a*b*(b+2*c*x)*_ + (a+b*x+c*x^2)^(1/2)/c^3+7/48*b^2*(a+b*x+c*x^2)^(3/2)/c^3-2/15*a*_ + (a+b*x+c*x^2)^(3/2)/c^2-7/40*b*x*(a+b*x+c*x^2)^(3/2)/c^2+1/5*x^2*_ + (a+b*x+c*x^2)^(3/2)/c+7/256*b^5*atanh(2*c^(1/2)*_ + (a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(9/2)-3/64*a*b*(10/3*b^2-4*a*c)*_ + atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(7/2) +--R +--R +--R (40) +--R +--------------+ +--R +-+ | 2 +--R 2 2 3 5 2\|c \|c x + b x + a +--R (720a b c - 600a b c + 105b )atanh(----------------------) +--R 2c x + b +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R 768c x + 96b c x + (256a c - 112b c )x + (- 464a b c + 140b c)x +--R + +--R 2 2 2 4 +--R - 512a c + 920a b c - 210b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R / +--R 4 +-+ +--R 3840c \|c +--R Type: Expression(Integer) +--E 44 + +--S 45 of 486 +a0308:= integrate(t0308,x) +--R +--R +--R (41) +--R [ +--R 4 4 3 3 3 2 5 2 7 +--R 23040a b c + 38400a b c - 37440a b c + 2400a b c +--R + +--R 9 +--R 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (276480a b c - 115200a b c - 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (276480a b c + 253440a b c - 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c - 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R - 307200a b c + 53760a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c + 19200a b c + 14880a b c - 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c - 192000a b c + 187200a b c - 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (- 691200a b c + 288000a b c + 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (- 460800a b c - 422400a b c + 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c + 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R 307200a b c - 53760a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 6 3 5 5 4 9 +--R (- 61440a b c - 30720a b c - 768b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (- 122880a c - 314880a b c - 42240a b c - 96b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (- 773120a b c - 346880a b c - 576a b c + 112b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (- 532480a c - 999680a b c + 960a b c + 464a b c - 140b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (- 1175040a b c + 7680a b c - 7488a b c + 480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 491520a c + 153600a b c - 70400a b c - 25600a b c +--R + +--R 8 +--R 8400a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (215040a b c + 166400a b c - 256640a b c + 50400a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (645120a b c - 537600a b c + 94080a b )x +--R + +--R 6 2 5 3 4 5 +--R (368640a b c - 307200a b c + 53760a b )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 7 2 6 4 5 10 +--R (24576a c + 61440a b c + 7680b c )x +--R + +--R 2 6 3 5 5 4 9 +--R (322560a b c + 192000a b c + 8640b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (327680a c + 929280a b c + 147200a b c - 160b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (1507840a b c + 730240a b c - 1440a b c + 280b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (778240a c + 1514240a b c + 4800a b c + 2320a b c - 700b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (1359360a b c - 87040a b c + 95808a b c - 9920a b c - 1890b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 491520a c - 491520a b c + 236800a b c + 72320a b c +--R + +--R 8 +--R - 25200a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 399360a b c - 289280a b c + 460160a b c - 90720a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (- 829440a b c + 691200a b c - 120960a b )x +--R + +--R 6 2 5 3 4 5 +--R (- 368640a b c + 307200a b c - 53760a b )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c + 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 3 5 2 2 4 2 +--R (1474560a b c + 614400a b c )x + (1474560a c + 2580480a b c )x +--R + +--R 3 4 4 4 +--R 3932160a b c x + 1966080a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c - 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c - 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 +--R (- 3686400a b c - 1536000a b c )x +--R + +--R 4 5 3 2 4 2 4 4 5 4 +--R (- 2457600a c - 4300800a b c )x - 4915200a b c x - 1966080a c +--R * +--R +-+ +--R \|c +--R , +--R +--R 4 4 3 3 3 2 5 2 7 +--R 23040a b c + 38400a b c - 37440a b c + 2400a b c +--R + +--R 9 +--R 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (276480a b c - 115200a b c - 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (276480a b c + 253440a b c - 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c - 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R - 307200a b c + 53760a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c + 19200a b c + 14880a b c - 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c - 192000a b c + 187200a b c - 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (- 691200a b c + 288000a b c + 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (- 460800a b c - 422400a b c + 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c + 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R 307200a b c - 53760a b +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 6 3 5 5 4 9 +--R (- 30720a b c - 15360a b c - 384b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (- 61440a c - 157440a b c - 21120a b c - 48b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (- 386560a b c - 173440a b c - 288a b c + 56b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (- 266240a c - 499840a b c + 480a b c + 232a b c - 70b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (- 587520a b c + 3840a b c - 3744a b c + 240a b c + 105b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 245760a c + 76800a b c - 35200a b c - 12800a b c +--R + +--R 8 +--R 4200a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (107520a b c + 83200a b c - 128320a b c + 25200a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (322560a b c - 268800a b c + 47040a b )x +--R + +--R 6 2 5 3 4 5 +--R (184320a b c - 153600a b c + 26880a b )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 2 7 2 6 4 5 10 +--R (12288a c + 30720a b c + 3840b c )x +--R + +--R 2 6 3 5 5 4 9 +--R (161280a b c + 96000a b c + 4320b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (163840a c + 464640a b c + 73600a b c - 80b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (753920a b c + 365120a b c - 720a b c + 140b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (389120a c + 757120a b c + 2400a b c + 1160a b c - 350b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (679680a b c - 43520a b c + 47904a b c - 4960a b c - 945b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 245760a c - 245760a b c + 118400a b c + 36160a b c +--R + +--R 8 +--R - 12600a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 199680a b c - 144640a b c + 230080a b c - 45360a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (- 414720a b c + 345600a b c - 60480a b )x +--R + +--R 6 2 5 3 4 5 +--R (- 184320a b c + 153600a b c - 26880a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R 2 6 2 5 4 4 4 +--R (61440a c + 153600a b c + 19200b c )x +--R + +--R 2 5 3 4 3 3 5 2 2 4 2 +--R (737280a b c + 307200a b c )x + (737280a c + 1290240a b c )x +--R + +--R 3 4 4 4 +--R 1966080a b c x + 983040a c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 6 3 5 5 4 5 +--R (- 153600a b c - 76800a b c - 1920b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 307200a c - 768000a b c - 96000a b c )x +--R + +--R 3 5 2 3 4 3 +--R (- 1843200a b c - 768000a b c )x +--R + +--R 4 5 3 2 4 2 4 4 5 4 +--R (- 1228800a c - 2150400a b c )x - 2457600a b c x - 983040a c +--R * +--R +---+ +--R \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 45 + +--S 46 of 486 +m0308a:= a0308.1-r0308 +--R +--R +--R (42) +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (23040a b c + 38400a b c - 37440a b c + 2400a b c + 1050b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (276480a b c - 115200a b c - 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (276480a b c + 253440a b c - 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c - 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R - 307200a b c + 53760a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c + 19200a b c + 14880a b c - 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c - 192000a b c + 187200a b c - 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (- 691200a b c + 288000a b c + 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (- 460800a b c - 422400a b c + 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c + 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R 307200a b c - 53760a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 4 4 3 3 3 2 5 2 7 +--R - 23040a b c - 38400a b c + 37440a b c - 2400a b c +--R + +--R 9 +--R - 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c + 115200a b c + 55680a b c - 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c - 253440a b c + 362880a b c - 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (- 737280a b c + 614400a b c - 107520a b )x - 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c - 53760a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (57600a b c - 19200a b c - 14880a b c + 3600a b c + 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R 115200a b c + 192000a b c - 187200a b c + 12000a b c +--R + +--R 9 +--R 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c - 288000a b c - 139200a b c + 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c + 422400a b c - 604800a b c + 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (921600a b c - 768000a b c + 134400a b )x + 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c + 53760a b +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 4 +--R (- 16384a c - 11520a b c + 61760a b c - 7600a b c - 2100a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 196608a b c + 271360a b c + 66560a b c - 33600a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (- 196608a c + 9216a b c + 537600a b c - 141120a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (- 524288a b c + 942080a b c - 215040a b )x - 262144a c +--R + +--R 6 2 5 4 +--R 471040a b c - 107520a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (40960a b c - 53120a b c - 19488a b c + 7480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 4 +--R (81920a c + 57600a b c - 308800a b c + 38000a b c + 10500a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (491520a b c - 678400a b c - 166400a b c + 84000a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (327680a c - 15360a b c - 896000a b c + 235200a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (655360a b c - 1177600a b c + 268800a b )x + 262144a c +--R + +--R 6 2 5 4 +--R - 471040a b c + 107520a b +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c + 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 3 5 2 2 4 2 +--R (1474560a b c + 614400a b c )x + (1474560a c + 2580480a b c )x +--R + +--R 3 4 4 4 +--R 3932160a b c x + 1966080a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c - 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c - 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 +--R (- 3686400a b c - 1536000a b c )x +--R + +--R 4 5 3 2 4 2 4 4 5 4 +--R (- 2457600a c - 4300800a b c )x - 4915200a b c x - 1966080a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 46 + +--S 47 of 486 +d0308a:= D(m0308a,x) +--R +--R +--R (43) 0 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 486 +m0308b:= a0308.2-r0308 +--R +--R +--R (44) +--R 4 4 3 3 3 2 5 2 7 +--R - 23040a b c - 38400a b c + 37440a b c - 2400a b c +--R + +--R 9 +--R - 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c + 115200a b c + 55680a b c - 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c - 253440a b c + 362880a b c - 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (- 737280a b c + 614400a b c - 107520a b )x - 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c - 53760a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (57600a b c - 19200a b c - 14880a b c + 3600a b c + 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R 115200a b c + 192000a b c - 187200a b c + 12000a b c +--R + +--R 9 +--R 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c - 288000a b c - 139200a b c + 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c + 422400a b c - 604800a b c + 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (921600a b c - 768000a b c + 134400a b )x + 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c + 53760a b +--R * +--R +---+ +--R \|- c +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (46080a b c + 76800a b c - 74880a b c + 4800a b c + 2100b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (552960a b c - 230400a b c - 111360a b c + 33600a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (552960a b c + 506880a b c - 725760a b c + 141120a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (1474560a b c - 1228800a b c + 215040a b )x + 737280a b c +--R + +--R 5 3 4 5 +--R - 614400a b c + 107520a b +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 4 2 4 3 4 3 2 6 2 8 +--R - 115200a b c + 38400a b c + 29760a b c - 7200a b c +--R + +--R 10 +--R - 210b +--R * +--R 5 +--R x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 230400a b c - 384000a b c + 374400a b c - 24000a b c +--R + +--R 9 +--R - 10500a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (- 1382400a b c + 576000a b c + 278400a b c - 84000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (- 921600a b c - 844800a b c + 1209600a b c - 235200a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 1843200a b c + 1536000a b c - 268800a b )x - 737280a b c +--R + +--R 6 3 5 5 +--R 614400a b c - 107520a b +--R * +--R +-+ +--R \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 4 +--R (- 16384a c - 11520a b c + 61760a b c - 7600a b c - 2100a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 196608a b c + 271360a b c + 66560a b c - 33600a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (- 196608a c + 9216a b c + 537600a b c - 141120a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (- 524288a b c + 942080a b c - 215040a b )x - 262144a c +--R + +--R 6 2 5 4 +--R 471040a b c - 107520a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (40960a b c - 53120a b c - 19488a b c + 7480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 4 +--R (81920a c + 57600a b c - 308800a b c + 38000a b c + 10500a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (491520a b c - 678400a b c - 166400a b c + 84000a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (327680a c - 15360a b c - 896000a b c + 235200a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (655360a b c - 1177600a b c + 268800a b )x + 262144a c +--R + +--R 6 2 5 4 +--R - 471040a b c + 107520a b +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c + 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 3 5 2 2 4 2 +--R (1474560a b c + 614400a b c )x + (1474560a c + 2580480a b c )x +--R + +--R 3 4 4 4 +--R 3932160a b c x + 1966080a c +--R * +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R \|- c \|a \|c \|c x + b x + a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c - 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c - 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 +--R (- 3686400a b c - 1536000a b c )x +--R + +--R 4 5 3 2 4 2 4 4 5 4 +--R (- 2457600a c - 4300800a b c )x - 4915200a b c x - 1966080a c +--R * +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 48 + +--S 49 of 486 +d0308b:= D(m0308b,x) +--R +--R +--R (45) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 486 +t0309:= x^2*(a+b*x+c*x^2)^(1/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (46) x \|c x + b x + a +--R Type: Expression(Integer) +--E 50 + +--S 51 of 486 +r0309:= 5/64*b^2*(b+2*c*x)*(a+b*x+c*x^2)^(1/2)/c^3-1/16*a*(b+2*c*x)*_ + (a+b*x+c*x^2)^(1/2)/c^2-5/24*b*(a+b*x+c*x^2)^(3/2)/c^2+1/4*x*_ + (a+b*x+c*x^2)^(3/2)/c-5/128*b^4*atanh(2*c^(1/2)*_ + (a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(7/2)+1/32*a*(6*b^2-4*a*c)*_ + atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(5/2) +--R +--R +--R (47) +--R +--------------+ +--R +-+ | 2 +--R 2 2 2 4 2\|c \|c x + b x + a +--R (- 48a c + 72a b c - 15b )atanh(----------------------) +--R 2c x + b +--R + +--R 3 3 2 2 2 2 3 +-+ +--R (96c x + 16b c x + (48a c - 20b c)x - 104a b c + 30b )\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R / +--R 3 +-+ +--R 384c \|c +--R Type: Expression(Integer) +--E 51 + +--S 52 of 486 +a0309:= integrate(t0309,x) +--R +--R +--R (48) +--R [ +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c - 768a b c - 4800a b c + 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (9216a b c - 13824a b c + 2880a b )x + 6144a c - 9216a b c +--R + +--R 3 4 +--R 1920a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (- 768a c + 1440a b c - 288a b c - 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (- 12288a b c + 18432a b c - 3840a b )x - 6144a c + 9216a b c +--R + +--R 4 4 +--R - 1920a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 5 2 4 4 3 7 +--R (- 1536a c - 2304a b c - 96b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (- 12544a b c - 3456a b c - 16b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (- 13056a c - 18240a b c - 80a b c + 20b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 31104a b c + 480a b c + 24a b c - 30b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (- 18432a c + 768a b c + 2816a b c - 720a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 7680a b c + 11520a b c - 2400a b )x +--R + +--R 5 2 4 2 3 4 +--R (- 6144a c + 9216a b c - 1920a b )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 5 3 4 8 2 5 2 4 4 3 7 +--R (3072a b c + 768b c )x + (6144a c + 11264a b c + 896b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (30208a b c + 9984a b c - 32b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (21504a c + 31488a b c - 320a b c + 80b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (42624a b c - 4896a b c + 152a b c + 210b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (21504a c - 2304a b c - 6464a b c + 1680a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (10752a b c - 16128a b c + 3360a b )x +--R + +--R 5 2 4 2 3 4 +--R (6144a c - 9216a b c + 1920a b )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c + 3072b c )x + (24576a c + 30720a b c )x +--R + +--R 2 3 3 3 +--R 73728a b c x + 49152a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 +--R (- 6144a c - 9216a b c - 384b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 49152a b c - 12288a b c )x + (- 49152a c - 61440a b c )x +--R + +--R 3 3 4 3 +--R - 98304a b c x - 49152a c +--R * +--R +-+ +--R \|c +--R , +--R +--R 3 3 2 3 2 5 7 3 +--R (- 1536a b c + 1920a b c + 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 3072a c + 768a b c + 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c + 13824a b c - 2880a b )x - 6144a c + 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c + 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (6144a b c - 7680a b c - 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (6144a c - 1536a b c - 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c - 18432a b c + 3840a b )x + 6144a c - 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 5 2 4 4 3 7 +--R (- 768a c - 1152a b c - 48b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (- 6272a b c - 1728a b c - 8b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (- 6528a c - 9120a b c - 40a b c + 10b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 15552a b c + 240a b c + 12a b c - 15b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (- 9216a c + 384a b c + 1408a b c - 360a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 3840a b c + 5760a b c - 1200a b )x +--R + +--R 5 2 4 2 3 4 +--R (- 3072a c + 4608a b c - 960a b )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 5 3 4 8 2 5 2 4 4 3 7 +--R (1536a b c + 384b c )x + (3072a c + 5632a b c + 448b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (15104a b c + 4992a b c - 16b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (10752a c + 15744a b c - 160a b c + 40b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (21312a b c - 2448a b c + 76a b c + 105b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (10752a c - 1152a b c - 3232a b c + 840a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (5376a b c - 8064a b c + 1680a b )x +--R + +--R 5 2 4 2 3 4 +--R (3072a c - 4608a b c + 960a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (6144a b c + 1536b c )x + (12288a c + 15360a b c )x +--R + +--R 2 3 3 3 +--R 36864a b c x + 24576a c +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 +--R (- 3072a c - 4608a b c - 192b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 24576a b c - 6144a b c )x + (- 24576a c - 30720a b c )x +--R + +--R 3 3 4 3 +--R - 49152a b c x - 24576a c +--R * +--R +---+ +--R \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 52 + +--S 53 of 486 +m0309a:= a0309.1-r0309 +--R +--R +--R (49) +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c - 768a b c - 4800a b c + 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (9216a b c - 13824a b c + 2880a b )x + 6144a c - 9216a b c +--R + +--R 3 4 +--R 1920a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (- 768a c + 1440a b c - 288a b c - 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (- 12288a b c + 18432a b c - 3840a b )x - 6144a c + 9216a b c +--R + +--R 4 4 +--R - 1920a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c - 768a b c - 4800a b c + 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (9216a b c - 13824a b c + 2880a b )x + 6144a c - 9216a b c +--R + +--R 3 4 +--R 1920a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (- 768a c + 1440a b c - 288a b c - 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (- 12288a b c + 18432a b c - 3840a b )x - 6144a c + 9216a b c +--R + +--R 4 4 +--R - 1920a b +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 3 2 2 2 4 6 3 +--R (- 3328a b c + 128a b c + 240a b )x +--R + +--R 4 2 3 3 2 5 2 4 2 3 4 +--R (- 6656a b c - 6400a b c + 2400a b )x + (- 19968a b c + 5760a b )x +--R + +--R 5 4 3 +--R - 13312a b c + 3840a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 4 +--R (1664a b c + 2016a b c - 616a b c - 30b )x +--R + +--R 3 2 2 2 4 6 3 +--R (13312a b c - 512a b c - 960a b )x +--R + +--R 4 2 3 3 2 5 2 4 2 3 4 +--R (13312a b c + 12800a b c - 4800a b )x + (26624a b c - 7680a b )x +--R + +--R 5 4 3 +--R 13312a b c - 3840a b +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c + 3072b c )x + (24576a c + 30720a b c )x +--R + +--R 2 3 3 3 +--R 73728a b c x + 49152a c +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 +--R (- 6144a c - 9216a b c - 384b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 49152a b c - 12288a b c )x + (- 49152a c - 61440a b c )x +--R + +--R 3 3 4 3 +--R - 98304a b c x - 49152a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 53 + +--S 54 of 486 +d0309a:= D(m0309a,x) +--R +--R +--R (50) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 486 +m0309b:= a0309.2-r0309 +--R +--R +--R (51) +--R 3 3 2 3 2 5 7 3 +--R (1536a b c - 1920a b c - 96a b c + 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c - 768a b c - 4800a b c + 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (9216a b c - 13824a b c + 2880a b )x + 6144a c - 9216a b c +--R + +--R 3 4 +--R 1920a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (- 768a c + 1440a b c - 288a b c - 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c + 7680a b c + 384a b c - 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (- 12288a b c + 18432a b c - 3840a b )x - 6144a c + 9216a b c +--R + +--R 4 4 +--R - 1920a b +--R * +--R +---+ +--R \|- c +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 3 3 2 3 2 5 7 3 +--R (- 3072a b c + 3840a b c + 192a b c - 240b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 6144a c + 1536a b c + 9600a b c - 2400a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 18432a b c + 27648a b c - 5760a b )x - 12288a c + 18432a b c +--R + +--R 3 4 +--R - 3840a b +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 4 4 2 4 2 6 8 4 +--R (1536a c - 2880a b c + 576a b c + 30b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (12288a b c - 15360a b c - 768a b c + 960a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (12288a c - 3072a b c - 19200a b c + 4800a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (24576a b c - 36864a b c + 7680a b )x + 12288a c - 18432a b c +--R + +--R 4 4 +--R 3840a b +--R * +--R +-+ +--R \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 2 2 2 4 6 3 +--R (- 3328a b c + 128a b c + 240a b )x +--R + +--R 4 2 3 3 2 5 2 4 2 3 4 +--R (- 6656a b c - 6400a b c + 2400a b )x + (- 19968a b c + 5760a b )x +--R + +--R 5 4 3 +--R - 13312a b c + 3840a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 5 7 4 +--R (1664a b c + 2016a b c - 616a b c - 30b )x +--R + +--R 3 2 2 2 4 6 3 +--R (13312a b c - 512a b c - 960a b )x +--R + +--R 4 2 3 3 2 5 2 4 2 3 4 +--R (13312a b c + 12800a b c - 4800a b )x + (26624a b c - 7680a b )x +--R + +--R 5 4 3 +--R 13312a b c - 3840a b +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c + 3072b c )x + (24576a c + 30720a b c )x +--R + +--R 2 3 3 3 +--R 73728a b c x + 49152a c +--R * +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R \|- c \|a \|c \|c x + b x + a +--R + +--R 2 5 2 4 4 3 4 +--R (- 6144a c - 9216a b c - 384b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 49152a b c - 12288a b c )x + (- 49152a c - 61440a b c )x +--R + +--R 3 3 4 3 +--R - 98304a b c x - 49152a c +--R * +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 55 + +--S 56 of 486 +d0309b:= D(m0309b,x) +--R +--R +--R (52) 0 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 486 +t0310:= x*(a+b*x+c*x^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (53) x\|c x + b x + a +--R Type: Expression(Integer) +--E 57 + +--S 58 of 486 +r0310:= -1/8*b*(b+2*c*x)*(a+b*x+c*x^2)^(1/2)/c^2+1/3*(a+b*x+c*x^2)^(3/2)/c+_ + 1/16*b*(b^2-4*a*c)*atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (b+2*c*x))/c^(5/2) +--R +--R +--R (54) +--R +--------------+ +--R +-+ | 2 +--R 3 2\|c \|c x + b x + a +--R (- 12a b c + 3b )atanh(----------------------) +--R 2c x + b +--R + +--R +--------------+ +--R 2 2 2 +-+ | 2 +--R (16c x + 4b c x + 16a c - 6b )\|c \|c x + b x + a +--R / +--R 2 +-+ +--R 48c \|c +--R Type: Expression(Integer) +--E 58 + +--S 59 of 486 +a0310:= integrate(t0310,x) +--R +--R +--R (55) +--R [ +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96a b )x + 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c + 24a b c + 3b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 288a b c - 144a b c + 54a b )x + (- 576a b c + 144a b )x +--R + +--R 4 3 3 +--R - 384a b c + 96a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 3 3 2 5 2 3 2 2 4 4 +--R (- 192a b c - 16b c )x + (- 384a c - 336a b c - 4b c)x +--R + +--R 2 2 3 5 3 +--R (- 1056a b c - 16a b c + 6b )x +--R + +--R 3 2 2 2 4 2 3 2 3 +--R (- 768a c - 288a b c + 72a b )x + (- 384a b c + 96a b )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 4 2 3 6 3 3 2 5 +--R (128a c + 96b c )x + (672a b c + 120b c )x +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (768a c + 816a b c - 12b c)x + (1632a b c + 64a b c - 30b )x +--R + +--R 3 2 2 2 4 2 3 2 3 +--R (768a c + 480a b c - 120a b )x + (384a b c - 96a b )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 3 2 2 2 2 2 2 +-+ +-+ +--R ((384a c + 288b c )x + 1536a b c x + 1536a c )\|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c - 48b c )x + (- 1152a c - 864a b c )x - 2304a b c x +--R + +--R 3 2 +--R - 1536a c +--R * +--R +-+ +--R \|c +--R , +--R +--R 2 2 3 5 2 2 2 4 +--R (- 96a b c - 48a b c + 18b )x + (- 384a b c + 96a b )x +--R + +--R 3 2 3 +--R - 384a b c + 96a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 3 3 2 2 3 5 2 +--R (144a b c - 24a b c - 3b )x + (288a b c + 144a b c - 54a b )x +--R + +--R 3 2 2 4 4 3 3 +--R (576a b c - 144a b )x + 384a b c - 96a b +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 3 2 5 2 3 2 2 4 4 +--R (- 96a b c - 8b c )x + (- 192a c - 168a b c - 2b c)x +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (- 528a b c - 8a b c + 3b )x + (- 384a c - 144a b c + 36a b )x +--R + +--R 3 2 3 +--R (- 192a b c + 48a b )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- c \|c x + b x + a +--R + +--R 4 2 3 6 3 3 2 5 +--R (64a c + 48b c )x + (336a b c + 60b c )x +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (384a c + 408a b c - 6b c)x + (816a b c + 32a b c - 15b )x +--R + +--R 3 2 2 2 4 2 3 2 3 +--R (384a c + 240a b c - 60a b )x + (192a b c - 48a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +--R ((192a c + 144b c )x + 768a b c x + 768a c )\|- c \|a +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 288a b c - 24b c )x + (- 576a c - 432a b c )x - 1152a b c x +--R + +--R 3 2 +--R - 768a c +--R * +--R +---+ +--R \|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 59 + +--S 60 of 486 +m0310a:= a0310.1-r0310 +--R +--R +--R (56) +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96a b )x + 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 3 3 2 2 3 5 2 +--R (- 144a b c + 24a b c + 3b )x + (- 288a b c - 144a b c + 54a b )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 576a b c + 144a b )x - 384a b c + 96a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R - 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96a b )x + 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 3 3 2 2 3 5 2 +--R (- 144a b c + 24a b c + 3b )x + (- 288a b c - 144a b c + 54a b )x +--R + +--R 3 2 2 4 4 3 3 +--R (- 576a b c + 144a b )x - 384a b c + 96a b +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 3 2 2 2 4 2 3 2 3 4 +--R (128a c + 48a b c - 36a b )x + (512a b c - 192a b )x + 512a c +--R + +--R 3 2 +--R - 192a b +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|c x + b x + a +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (- 192a b c + 56a b c + 6b )x + (- 384a c - 144a b c + 108a b )x +--R + +--R 3 2 3 4 3 2 +--R (- 768a b c + 288a b )x - 512a c + 192a b +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +-+ +-+ | 2 +--R ((384a c + 288b c )x + 1536a b c x + 1536a c )\|a \|c \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c - 48b c )x + (- 1152a c - 864a b c )x - 2304a b c x +--R + +--R 3 2 +--R - 1536a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 60 + +--S 61 of 486 +d0310a:= D(m0310a,x) +--R +--R +--R (57) 0 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 486 +m0310b:= a0310.2-r0310 +--R +--R +--R (58) +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c + 48a b c - 18b )x + (384a b c - 96a b )x + 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|a \|c x + b x + a +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c + 24a b c + 3b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 288a b c - 144a b c + 54a b )x + (- 576a b c + 144a b )x +--R + +--R 4 3 3 +--R - 384a b c + 96a b +--R * +--R +---+ +--R \|- c +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R 2 2 3 5 2 2 2 4 +--R (- 192a b c - 96a b c + 36b )x + (- 768a b c + 192a b )x +--R + +--R 3 2 3 +--R - 768a b c + 192a b +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|a \|c \|c x + b x + a +--R + +--R 2 2 2 4 6 3 +--R (288a b c - 48a b c - 6b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (576a b c + 288a b c - 108a b )x + (1152a b c - 288a b )x +--R + +--R 4 3 3 +--R 768a b c - 192a b +--R * +--R +-+ +--R \|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 3 2 2 2 4 2 3 2 3 4 +--R (128a c + 48a b c - 36a b )x + (512a b c - 192a b )x + 512a c +--R + +--R 3 2 +--R - 192a b +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- c \|c \|c x + b x + a +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (- 192a b c + 56a b c + 6b )x + (- 384a c - 144a b c + 108a b )x +--R + +--R 3 2 3 4 3 2 +--R (- 768a b c + 288a b )x - 512a c + 192a b +--R * +--R +---+ +-+ +-+ +--R \|- c \|a \|c +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +-+ +--R ((384a c + 288b c )x + 1536a b c x + 1536a c )\|- c \|a \|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c - 48b c )x + (- 1152a c - 864a b c )x - 2304a b c x +--R + +--R 3 2 +--R - 1536a c +--R * +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 62 + +--S 63 of 486 +d0310b:= D(m0310b,x) +--R +--R +--R (59) 0 +--R Type: Expression(Integer) +--E 63 + +--S 64 of 486 +t0311:= (a+b*x+c*x^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (60) \|c x + b x + a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 486 +r0311:= 1/4*(b+2*c*x)*(a+b*x+c*x^2)^(1/2)/c-1/8*(b^2-4*a*c)*_ + atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(3/2) +--R +--R +--R (61) +--R +--------------+ +--R +-+ | 2 +--------------+ +--R 2 2\|c \|c x + b x + a +-+ | 2 +--R (4a c - b )atanh(----------------------) + (4c x + 2b)\|c \|c x + b x + a +--R 2c x + b +--R --------------------------------------------------------------------------- +--R +-+ +--R 8c\|c +--R Type: Expression(Integer) +--E 65 + +--S 66 of 486 +a0311:= integrate(t0311,x) +--R +--R +--R (62) +--R [ +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8a b )\|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (- 16a c + b )x + (- 32a b c + 8a b )x - 32a c + 8a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R 2 2 3 3 2 2 2 +-+ +--R ((- 16a c - 4b c)x + (- 40a b c - 2b )x + (- 32a c - 8a b )x)\|c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 4 2 2 3 3 2 +--R 16b c x + (32a c + 24b c)x + (56a b c + 6b )x +--R + +--R 2 2 +--R (32a c + 8a b )x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------------+ +--R +-+ +-+ | 2 +--R (32b c x + 64a c)\|a \|c \|c x + b x + a +--R + +--R 2 2 2 2 +-+ +--R ((- 32a c - 8b c)x - 64a b c x - 64a c)\|c +--R , +--R +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8a b )\|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (- 16a c + b )x + (- 32a b c + 8a b )x - 32a c + 8a b +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R 2 2 3 3 2 2 2 +---+ +--R ((- 8a c - 2b c)x + (- 20a b c - b )x + (- 16a c - 4a b )x)\|- c +--R * +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R + +--R 2 4 2 2 3 3 2 2 2 +--R (8b c x + (16a c + 12b c)x + (28a b c + 3b )x + (16a c + 4a b )x) +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------------+ +--R +---+ +-+ | 2 +--R (16b c x + 32a c)\|- c \|a \|c x + b x + a +--R + +--R 2 2 2 2 +---+ +--R ((- 16a c - 4b c)x - 32a b c x - 32a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 66 + +--S 67 of 486 +m0311a:= a0311.1-r0311 +--R +--R +--R (63) +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((16a b c - 4b )x + 32a c - 8a b )\|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (- 16a c + b )x + (- 32a b c + 8a b )x - 32a c + 8a b +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +--R + +--R +-+ +--R 2c x\|a +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|a \|c x + b x + a - b x - 2a +--R + +--R +--------------+ +--R 3 2 2 +-+ | 2 +--R ((- 16a b c + 4b )x - 32a c + 8a b )\|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (16a c - b )x + (32a b c - 8a b )x + 32a c - 8a b +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R +--------------+ +--R 2 2 +-+ | 2 +--R (8a b x + 16a b)\|c \|c x + b x + a +--R + +--R 3 2 2 2 +-+ +-+ +--R ((- 8a b c - 2b )x - 16a b x - 16a b)\|a \|c +--R / +--R +--------------+ +--R +-+ +-+ | 2 +--R (32b c x + 64a c)\|a \|c \|c x + b x + a +--R + +--R 2 2 2 2 +-+ +--R ((- 32a c - 8b c)x - 64a b c x - 64a c)\|c +--R Type: Expression(Integer) +--E 67 + +--S 68 of 486 +d0311a:= D(m0311a,x) +--R +--R +--R (64) 0 +--R Type: Expression(Integer) +--E 68 + +--S 69 of 486 +m0311b:= a0311.2-r0311 +--R +--R +--R (65) +--R +--------------+ +--R 3 2 2 +---+ +-+ | 2 +--R ((- 16a b c + 4b )x - 32a c + 8a b )\|- c \|a \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +---+ +--R ((16a c - b )x + (32a b c - 8a b )x + 32a c - 8a b )\|- c +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|c x + b x + a +--R atanh(----------------------) +--R 2c x + b +--R + +--R +--------------+ +--R 3 2 2 +-+ +-+ | 2 +--R ((32a b c - 8b )x + 64a c - 16a b )\|a \|c \|c x + b x + a +--R + +--R 2 2 4 2 2 3 3 2 2 +-+ +--R ((- 32a c + 2b )x + (- 64a b c + 16a b )x - 64a c + 16a b )\|c +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- c \|c x + b x + a - \|- c \|a +--R atan(------------------------------------) +--R c x +--R + +--R +--------------+ +--R 2 2 +---+ +-+ | 2 +--R (8a b x + 16a b)\|- c \|c \|c x + b x + a +--R + +--R 3 2 2 2 +---+ +-+ +-+ +--R ((- 8a b c - 2b )x - 16a b x - 16a b)\|- c \|a \|c +--R / +--R +--------------+ +--R +---+ +-+ +-+ | 2 +--R (32b c x + 64a c)\|- c \|a \|c \|c x + b x + a +--R + +--R 2 2 2 2 +---+ +-+ +--R ((- 32a c - 8b c)x - 64a b c x - 64a c)\|- c \|c +--R Type: Expression(Integer) +--E 69 + +--S 70 of 486 +d0311b:= D(m0311b,x) +--R +--R +--R (66) 0 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 486 +t0312:= x^3*(a+b*x-c*x^2)^(1/2) +--R +--R +--R +----------------+ +--R 3 | 2 +--R (67) x \|- c x + b x + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 486 +r0312:= -7/128*b^3*(b-2*c*x)*(a+b*x-c*x^2)^(1/2)/c^4-3/32*a*b*(b-2*c*x)*_ + (a+b*x-c*x^2)^(1/2)/c^3-7/48*b^2*(a+b*x-c*x^2)^(3/2)/c^3-2/15*a*_ + (a+b*x-c*x^2)^(3/2)/c^2-7/40*b*x*(a+b*x-c*x^2)^(3/2)/c^2-1/5*x^2*_ + (a+b*x-c*x^2)^(3/2)/c+7/256*b^5*atan(2*c^(1/2)*_ + (a+b*x-c*x^2)^(1/2)/(b-2*c*x))/c^(9/2)+3/64*a*b*(10/3*b^2+4*a*c)*_ + atan(2*c^(1/2)*(a+b*x-c*x^2)^(1/2)/(b-2*c*x))/c^(7/2) +--R +--R +--R (68) +--R +----------------+ +--R | 2 +-+ +--R 2 2 3 5 2\|- c x + b x + a \|c +--R (- 720a b c - 600a b c - 105b )atan(------------------------) +--R 2c x - b +--R + +--R 4 4 3 3 3 2 2 2 +--R 768c x - 96b c x + (- 256a c - 112b c )x +--R + +--R 2 3 2 2 2 4 +--R (- 464a b c - 140b c)x - 512a c - 920a b c - 210b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|c +--R / +--R 4 +-+ +--R 3840c \|c +--R Type: Expression(Integer) +--E 72 + +--S 73 of 486 +a0312:= integrate(t0312,x) +--R +--R +--R (69) +--R [ +--R 4 4 3 3 3 2 5 2 7 +--R 23040a b c - 38400a b c - 37440a b c - 2400a b c +--R + +--R 9 +--R 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c - 115200a b c + 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c + 253440a b c + 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c + 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c + 53760a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c - 19200a b c + 14880a b c + 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c + 192000a b c + 187200a b c + 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c + 288000a b c - 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c - 422400a b c - 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c - 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c - 53760a b +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 2 7 2 6 4 5 10 +--R (- 24576a c + 61440a b c - 7680b c )x +--R + +--R 2 6 3 5 5 4 9 +--R (322560a b c - 192000a b c + 8640b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (327680a c - 929280a b c + 147200a b c + 160b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (- 1507840a b c + 730240a b c + 1440a b c + 280b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (- 778240a c + 1514240a b c - 4800a b c + 2320a b c + 700b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (1359360a b c + 87040a b c + 95808a b c + 9920a b c - 1890b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 491520a c + 491520a b c + 236800a b c - 72320a b c +--R + +--R 8 +--R - 25200a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (399360a b c - 289280a b c - 460160a b c - 90720a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (- 829440a b c - 691200a b c - 120960a b )x +--R + +--R 6 2 5 3 4 5 +--R (- 368640a b c - 307200a b c - 53760a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 2 6 3 5 5 4 9 +--R (- 61440a b c + 30720a b c - 768b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (- 122880a c + 314880a b c - 42240a b c + 96b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (773120a b c - 346880a b c + 576a b c + 112b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (532480a c - 999680a b c - 960a b c + 464a b c + 140b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (- 1175040a b c - 7680a b c - 7488a b c - 480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 491520a c - 153600a b c - 70400a b c + 25600a b c +--R + +--R 8 +--R 8400a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 215040a b c + 166400a b c + 256640a b c + 50400a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (645120a b c + 537600a b c + 94080a b )x +--R + +--R 6 2 5 3 4 5 +--R (368640a b c + 307200a b c + 53760a b )x +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c - 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 +--R (- 1474560a b c + 614400a b c )x +--R + +--R 3 5 2 2 4 2 3 4 4 4 +--R (- 1474560a c + 2580480a b c )x + 3932160a b c x + 1966080a c +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c + 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c + 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 4 5 3 2 4 2 +--R (3686400a b c - 1536000a b c )x + (2457600a c - 4300800a b c )x +--R + +--R 4 4 5 4 +--R - 4915200a b c x - 1966080a c +--R * +--R +---+ +--R \|- c +--R , +--R +--R 4 4 3 3 3 2 5 2 7 +--R 23040a b c - 38400a b c - 37440a b c - 2400a b c +--R + +--R 9 +--R 1050b +--R * +--R 4 +--R x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c - 115200a b c + 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c + 253440a b c + 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c + 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c + 53760a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c - 19200a b c + 14880a b c + 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c + 192000a b c + 187200a b c + 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c + 288000a b c - 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c - 422400a b c - 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c - 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c - 53760a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 2 7 2 6 4 5 10 +--R (- 12288a c + 30720a b c - 3840b c )x +--R + +--R 2 6 3 5 5 4 9 +--R (161280a b c - 96000a b c + 4320b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (163840a c - 464640a b c + 73600a b c + 80b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (- 753920a b c + 365120a b c + 720a b c + 140b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 +--R - 389120a c + 757120a b c - 2400a b c + 1160a b c +--R + +--R 8 +--R 350b c +--R * +--R 6 +--R x +--R + +--R 4 4 3 3 3 2 5 2 7 +--R 679680a b c + 43520a b c + 47904a b c + 4960a b c +--R + +--R 9 +--R - 945b +--R * +--R 5 +--R x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 245760a c + 245760a b c + 118400a b c - 36160a b c +--R + +--R 8 +--R - 12600a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (199680a b c - 144640a b c - 230080a b c - 45360a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (- 414720a b c - 345600a b c - 60480a b )x +--R + +--R 6 2 5 3 4 5 +--R (- 184320a b c - 153600a b c - 26880a b )x +--R * +--R +-+ +--R \|a +--R + +--R 2 6 3 5 5 4 9 +--R (- 30720a b c + 15360a b c - 384b c )x +--R + +--R 3 6 2 2 5 4 4 6 3 8 +--R (- 61440a c + 157440a b c - 21120a b c + 48b c )x +--R + +--R 3 5 2 3 4 5 3 7 2 7 +--R (386560a b c - 173440a b c + 288a b c + 56b c )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 6 +--R (266240a c - 499840a b c - 480a b c + 232a b c + 70b c)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (- 587520a b c - 3840a b c - 3744a b c - 240a b c + 105b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 245760a c - 76800a b c - 35200a b c + 12800a b c +--R + +--R 8 +--R 4200a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 107520a b c + 83200a b c + 128320a b c + 25200a b )x +--R + +--R 5 2 2 4 4 3 6 2 +--R (322560a b c + 268800a b c + 47040a b )x +--R + +--R 6 2 5 3 4 5 +--R (184320a b c + 153600a b c + 26880a b )x +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R 2 6 2 5 4 4 4 +--R (61440a c - 153600a b c + 19200b c )x +--R + +--R 2 5 3 4 3 +--R (- 737280a b c + 307200a b c )x +--R + +--R 3 5 2 2 4 2 3 4 4 4 +--R (- 737280a c + 1290240a b c )x + 1966080a b c x + 983040a c +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 6 3 5 5 4 5 +--R (- 153600a b c + 76800a b c - 1920b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 307200a c + 768000a b c - 96000a b c )x +--R + +--R 3 5 2 3 4 3 4 5 3 2 4 2 +--R (1843200a b c - 768000a b c )x + (1228800a c - 2150400a b c )x +--R + +--R 4 4 5 4 +--R - 2457600a b c x - 983040a c +--R * +--R +-+ +--R \|c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 73 + +--S 74 of 486 +m0312a:= a0312.1-r0312 +--R +--R +--R (70) +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (23040a b c - 38400a b c - 37440a b c - 2400a b c + 1050b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c - 115200a b c + 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c + 253440a b c + 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c + 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c + 53760a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c - 19200a b c + 14880a b c + 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c + 192000a b c + 187200a b c + 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c + 288000a b c - 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c - 422400a b c - 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c - 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c - 53760a b +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (23040a b c - 38400a b c - 37440a b c - 2400a b c + 1050b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c - 115200a b c + 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c + 253440a b c + 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c + 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c + 53760a b +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 +--R - 57600a b c - 19200a b c + 14880a b c + 3600a b c +--R + +--R 10 +--R - 105b +--R * +--R 5 +--R x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c + 192000a b c + 187200a b c + 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c + 288000a b c - 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c - 422400a b c - 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c - 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c - 53760a b +--R * +--R +---+ +--R \|- c +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (40960a b c + 53120a b c - 19488a b c - 7480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 81920a c - 57600a b c - 308800a b c - 38000a b c +--R + +--R 8 +--R 10500a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 491520a b c - 678400a b c + 166400a b c + 84000a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (- 327680a c - 15360a b c + 896000a b c + 235200a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (655360a b c + 1177600a b c + 268800a b )x + 262144a c +--R + +--R 6 2 5 4 +--R 471040a b c + 107520a b +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 16384a c + 11520a b c + 61760a b c + 7600a b c +--R + +--R 8 +--R - 2100a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (196608a b c + 271360a b c - 66560a b c - 33600a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (196608a c + 9216a b c - 537600a b c - 141120a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (- 524288a b c - 942080a b c - 215040a b )x - 262144a c +--R + +--R 6 2 5 4 +--R - 471040a b c - 107520a b +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R * +--R +-+ +--R \|c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c - 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 +--R (- 1474560a b c + 614400a b c )x +--R + +--R 3 5 2 2 4 2 3 4 4 4 +--R (- 1474560a c + 2580480a b c )x + 3932160a b c x + 1966080a c +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c + 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c + 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 4 5 3 2 4 2 +--R (3686400a b c - 1536000a b c )x + (2457600a c - 4300800a b c )x +--R + +--R 4 4 5 4 +--R - 4915200a b c x - 1966080a c +--R * +--R +---+ +--R \|- c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 74 + +--S 75 of 486 +d0312a:= D(m0312a,x) +--R +--R +--R (71) 0 +--R Type: Expression(Integer) +--E 75 + +--S 76 of 486 +m0312b:= a0312.2-r0312 +--R +--R +--R (72) +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (46080a b c - 76800a b c - 74880a b c - 4800a b c + 2100b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 552960a b c - 230400a b c + 111360a b c + 33600a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 552960a b c + 506880a b c + 725760a b c + 141120a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (1474560a b c + 1228800a b c + 215040a b )x + 737280a b c +--R + +--R 5 3 4 5 +--R 614400a b c + 107520a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 115200a b c - 38400a b c + 29760a b c + 7200a b c - 210b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 230400a b c + 384000a b c + 374400a b c + 24000a b c +--R + +--R 9 +--R - 10500a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (1382400a b c + 576000a b c - 278400a b c - 84000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (921600a b c - 844800a b c - 1209600a b c - 235200a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 1843200a b c - 1536000a b c - 268800a b )x - 737280a b c +--R + +--R 6 3 5 5 +--R - 614400a b c - 107520a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 4 4 3 3 3 2 5 2 7 9 4 +--R (23040a b c - 38400a b c - 37440a b c - 2400a b c + 1050b )x +--R + +--R 4 2 3 3 4 2 2 6 8 3 +--R (- 276480a b c - 115200a b c + 55680a b c + 16800a b )x +--R + +--R 5 3 4 3 2 3 5 2 7 2 +--R (- 276480a b c + 253440a b c + 362880a b c + 70560a b )x +--R + +--R 5 2 2 4 4 3 6 6 2 +--R (737280a b c + 614400a b c + 107520a b )x + 368640a b c +--R + +--R 5 3 4 5 +--R 307200a b c + 53760a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 2 4 3 4 3 2 6 2 8 10 5 +--R (- 57600a b c - 19200a b c + 14880a b c + 3600a b c - 105b )x +--R + +--R 5 4 4 3 3 3 5 2 2 7 +--R - 115200a b c + 192000a b c + 187200a b c + 12000a b c +--R + +--R 9 +--R - 5250a b +--R * +--R 4 +--R x +--R + +--R 5 2 3 4 4 2 3 6 2 8 3 +--R (691200a b c + 288000a b c - 139200a b c - 42000a b )x +--R + +--R 6 3 5 3 2 4 5 3 7 2 +--R (460800a b c - 422400a b c - 604800a b c - 117600a b )x +--R + +--R 6 2 2 5 4 4 6 7 2 +--R (- 921600a b c - 768000a b c - 134400a b )x - 368640a b c +--R + +--R 6 3 5 5 +--R - 307200a b c - 53760a b +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 4 4 3 3 3 2 5 2 7 9 5 +--R (40960a b c + 53120a b c - 19488a b c - 7480a b c + 210b )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R 81920a c - 57600a b c - 308800a b c - 38000a b c +--R + +--R 8 +--R 10500a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (- 491520a b c - 678400a b c + 166400a b c + 84000a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (- 327680a c - 15360a b c + 896000a b c + 235200a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (655360a b c + 1177600a b c + 268800a b )x + 262144a c +--R + +--R 6 2 5 4 +--R 471040a b c + 107520a b +--R * +--R +-+ +--R \|a +--R + +--R 5 4 4 2 3 3 4 2 2 6 +--R - 16384a c + 11520a b c + 61760a b c + 7600a b c +--R + +--R 8 +--R - 2100a b +--R * +--R 4 +--R x +--R + +--R 5 3 4 3 2 3 5 2 7 3 +--R (196608a b c + 271360a b c - 66560a b c - 33600a b )x +--R + +--R 6 3 5 2 2 4 4 3 6 2 +--R (196608a c + 9216a b c - 537600a b c - 141120a b )x +--R + +--R 6 2 5 3 4 5 7 2 +--R (- 524288a b c - 942080a b c - 215040a b )x - 262144a c +--R + +--R 6 2 5 4 +--R - 471040a b c - 107520a b +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R 2 6 2 5 4 4 4 +--R (122880a c - 307200a b c + 38400b c )x +--R + +--R 2 5 3 4 3 +--R (- 1474560a b c + 614400a b c )x +--R + +--R 3 5 2 2 4 2 3 4 4 4 +--R (- 1474560a c + 2580480a b c )x + 3932160a b c x + 1966080a c +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 6 3 5 5 4 5 +--R (- 307200a b c + 153600a b c - 3840b c )x +--R + +--R 3 6 2 2 5 4 4 4 +--R (- 614400a c + 1536000a b c - 192000a b c )x +--R + +--R 3 5 2 3 4 3 4 5 3 2 4 2 +--R (3686400a b c - 1536000a b c )x + (2457600a c - 4300800a b c )x +--R + +--R 4 4 5 4 +--R - 4915200a b c x - 1966080a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 76 + +--S 77 of 486 +d0312b:= D(m0312b,x) +--R +--R +--R (73) 0 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 486 +t0313:= x^2*(a+b*x-c*x^2)^(1/2) +--R +--R +--R +----------------+ +--R 2 | 2 +--R (74) x \|- c x + b x + a +--R Type: Expression(Integer) +--E 78 + +--S 79 of 486 +r0313:= -5/64*b^2*(b-2*c*x)*(a+b*x-c*x^2)^(1/2)/c^3-1/16*a*(b-2*c*x)*_ + (a+b*x-c*x^2)^(1/2)/c^2-5/24*b*(a+b*x-c*x^2)^(3/2)/c^2-1/4*x*_ + (a+b*x-c*x^2)^(3/2)/c+5/128*b^4*atan(2*c^(1/2)*_ + (a+b*x-c*x^2)^(1/2)/(b-2*c*x))/c^(7/2)+1/32*a*(6*b^2+4*a*c)*_ + atan(2*c^(1/2)*(a+b*x-c*x^2)^(1/2)/(b-2*c*x))/c^(5/2) +--R +--R +--R (75) +--R +----------------+ +--R | 2 +-+ +--R 2 2 2 4 2\|- c x + b x + a \|c +--R (- 48a c - 72a b c - 15b )atan(------------------------) +--R 2c x - b +--R + +--R 3 3 2 2 2 2 3 +--R (96c x - 16b c x + (- 48a c - 20b c)x - 104a b c - 30b ) +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|c +--R / +--R 3 +-+ +--R 384c \|c +--R Type: Expression(Integer) +--E 79 + +--S 80 of 486 +a0313:= integrate(t0313,x) +--R +--R +--R (76) +--R [ +--R 3 3 2 3 2 5 7 3 +--R (1536a b c + 1920a b c - 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 768a b c - 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c - 13824a b c - 2880a b )x - 6144a c - 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c - 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c - 7680a b c + 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 1536a b c + 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c + 18432a b c + 3840a b )x + 6144a c + 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 5 3 4 8 2 5 2 4 4 3 7 +--R (- 3072a b c + 768b c )x + (- 6144a c + 11264a b c - 896b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (30208a b c - 9984a b c - 32b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (21504a c - 31488a b c - 320a b c - 80b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 42624a b c - 4896a b c - 152a b c + 210b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (- 21504a c - 2304a b c + 6464a b c + 1680a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (10752a b c + 16128a b c + 3360a b )x +--R + +--R 5 2 4 2 3 4 +--R (6144a c + 9216a b c + 1920a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 2 5 2 4 4 3 7 +--R (1536a c - 2304a b c + 96b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (- 12544a b c + 3456a b c - 16b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (- 13056a c + 18240a b c - 80a b c - 20b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (31104a b c + 480a b c - 24a b c - 30b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (18432a c + 768a b c - 2816a b c - 720a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 7680a b c - 11520a b c - 2400a b )x +--R + +--R 5 2 4 2 3 4 +--R (- 6144a c - 9216a b c - 1920a b )x +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c - 3072b c )x + (24576a c - 30720a b c )x +--R + +--R 2 3 3 3 +--R - 73728a b c x - 49152a c +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 2 5 2 4 4 3 4 +--R (6144a c - 9216a b c + 384b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 49152a b c + 12288a b c )x + (- 49152a c + 61440a b c )x +--R + +--R 3 3 4 3 +--R 98304a b c x + 49152a c +--R * +--R +---+ +--R \|- c +--R , +--R +--R 3 3 2 3 2 5 7 3 +--R (1536a b c + 1920a b c - 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 768a b c - 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c - 13824a b c - 2880a b )x - 6144a c - 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c - 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c - 7680a b c + 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 1536a b c + 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c + 18432a b c + 3840a b )x + 6144a c + 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 5 3 4 8 +--R (- 1536a b c + 384b c )x +--R + +--R 2 5 2 4 4 3 7 +--R (- 3072a c + 5632a b c - 448b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (15104a b c - 4992a b c - 16b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (10752a c - 15744a b c - 160a b c - 40b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 21312a b c - 2448a b c - 76a b c + 105b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (- 10752a c - 1152a b c + 3232a b c + 840a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (5376a b c + 8064a b c + 1680a b )x +--R + +--R 5 2 4 2 3 4 +--R (3072a c + 4608a b c + 960a b )x +--R * +--R +-+ +--R \|a +--R + +--R 2 5 2 4 4 3 7 +--R (768a c - 1152a b c + 48b c )x +--R + +--R 2 4 3 3 5 2 6 +--R (- 6272a b c + 1728a b c - 8b c )x +--R + +--R 3 4 2 2 3 4 2 6 5 +--R (- 6528a c + 9120a b c - 40a b c - 10b c)x +--R + +--R 3 3 2 3 2 5 7 4 +--R (15552a b c + 240a b c - 12a b c - 15b )x +--R + +--R 4 3 3 2 2 2 4 6 3 +--R (9216a c + 384a b c - 1408a b c - 360a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 3840a b c - 5760a b c - 1200a b )x +--R + +--R 5 2 4 2 3 4 +--R (- 3072a c - 4608a b c - 960a b )x +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (6144a b c - 1536b c )x + (12288a c - 15360a b c )x +--R + +--R 2 3 3 3 +--R - 36864a b c x - 24576a c +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 5 2 4 4 3 4 2 4 3 3 3 +--R (3072a c - 4608a b c + 192b c )x + (- 24576a b c + 6144a b c )x +--R + +--R 3 4 2 2 3 2 3 3 4 3 +--R (- 24576a c + 30720a b c )x + 49152a b c x + 24576a c +--R * +--R +-+ +--R \|c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 80 + +--S 81 of 486 +m0313a:= a0313.1-r0313 +--R +--R +--R (77) +--R 3 3 2 3 2 5 7 3 +--R (1536a b c + 1920a b c - 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 768a b c - 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c - 13824a b c - 2880a b )x - 6144a c - 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c - 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c - 7680a b c + 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 1536a b c + 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c + 18432a b c + 3840a b )x + 6144a c + 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 3 3 2 3 2 5 7 3 +--R (1536a b c + 1920a b c - 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 768a b c - 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c - 13824a b c - 2880a b )x - 6144a c - 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c - 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c - 7680a b c + 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 1536a b c + 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c + 18432a b c + 3840a b )x + 6144a c + 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R +---+ +--R \|- c +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 1664a b c + 2016a b c + 616a b c - 30b )x +--R + +--R 3 2 2 2 4 6 3 +--R (13312a b c + 512a b c - 960a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (13312a b c - 12800a b c - 4800a b )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 26624a b c - 7680a b )x - 13312a b c - 3840a b +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 3 2 2 2 4 6 3 +--R (- 3328a b c - 128a b c + 240a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 6656a b c + 6400a b c + 2400a b )x +--R + +--R 4 2 3 4 5 4 3 +--R (19968a b c + 5760a b )x + 13312a b c + 3840a b +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R * +--R +-+ +--R \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c - 3072b c )x + (24576a c - 30720a b c )x +--R + +--R 2 3 3 3 +--R - 73728a b c x - 49152a c +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 2 5 2 4 4 3 4 +--R (6144a c - 9216a b c + 384b c )x +--R + +--R 2 4 3 3 3 3 4 2 2 3 2 +--R (- 49152a b c + 12288a b c )x + (- 49152a c + 61440a b c )x +--R + +--R 3 3 4 3 +--R 98304a b c x + 49152a c +--R * +--R +---+ +--R \|- c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 81 + +--S 82 of 486 +d0313a:= D(m0313a,x) +--R +--R +--R (78) 0 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 486 +m0313b:= a0313.2-r0313 +--R +--R +--R (79) +--R 3 3 2 3 2 5 7 3 +--R (3072a b c + 3840a b c - 192a b c - 240b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (6144a c + 1536a b c - 9600a b c - 2400a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 18432a b c - 27648a b c - 5760a b )x - 12288a c - 18432a b c +--R + +--R 3 4 +--R - 3840a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (1536a c - 2880a b c - 576a b c + 30b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 12288a b c - 15360a b c + 768a b c + 960a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 12288a c - 3072a b c + 19200a b c + 4800a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (24576a b c + 36864a b c + 7680a b )x + 12288a c + 18432a b c +--R + +--R 4 4 +--R 3840a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 3 3 2 3 2 5 7 3 +--R (1536a b c + 1920a b c - 96a b c - 120b )x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (3072a c + 768a b c - 4800a b c - 1200a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 +--R (- 9216a b c - 13824a b c - 2880a b )x - 6144a c - 9216a b c +--R + +--R 3 4 +--R - 1920a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 4 4 2 4 2 6 8 4 +--R (768a c - 1440a b c - 288a b c + 15b )x +--R + +--R 4 3 3 3 2 2 5 7 3 +--R (- 6144a b c - 7680a b c + 384a b c + 480a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 2 +--R (- 6144a c - 1536a b c + 9600a b c + 2400a b )x +--R + +--R 5 2 4 3 3 5 6 2 5 2 +--R (12288a b c + 18432a b c + 3840a b )x + 6144a c + 9216a b c +--R + +--R 4 4 +--R 1920a b +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 3 3 2 3 2 5 7 4 +--R (- 1664a b c + 2016a b c + 616a b c - 30b )x +--R + +--R 3 2 2 2 4 6 3 +--R (13312a b c + 512a b c - 960a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (13312a b c - 12800a b c - 4800a b )x +--R + +--R 4 2 3 4 5 4 3 +--R (- 26624a b c - 7680a b )x - 13312a b c - 3840a b +--R * +--R +-+ +--R \|a +--R + +--R 3 2 2 2 4 6 3 +--R (- 3328a b c - 128a b c + 240a b )x +--R + +--R 4 2 3 3 2 5 2 +--R (- 6656a b c + 6400a b c + 2400a b )x +--R + +--R 4 2 3 4 5 4 3 +--R (19968a b c + 5760a b )x + 13312a b c + 3840a b +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R 4 3 3 3 2 4 2 3 2 +--R (12288a b c - 3072b c )x + (24576a c - 30720a b c )x +--R + +--R 2 3 3 3 +--R - 73728a b c x - 49152a c +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 5 2 4 4 3 4 2 4 3 3 3 +--R (6144a c - 9216a b c + 384b c )x + (- 49152a b c + 12288a b c )x +--R + +--R 3 4 2 2 3 2 3 3 4 3 +--R (- 49152a c + 61440a b c )x + 98304a b c x + 49152a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 83 + +--S 84 of 486 +d0313b:= D(m0313b,x) +--R +--R +--R (80) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 486 +t0314:= x*(a+b*x-c*x^2)^(1/2) +--R +--R +--R +----------------+ +--R | 2 +--R (81) x\|- c x + b x + a +--R Type: Expression(Integer) +--E 85 + +--S 86 of 486 +r0314:= -1/8*b*(b-2*c*x)*(a+b*x-c*x^2)^(1/2)/c^2-1/3*(a+b*x-c*x^2)^(3/2)/c+_ + 1/16*b*(b^2+4*a*c)*atan(2*c^(1/2)*(a+b*x-c*x^2)^(1/2)/_ + (b-2*c*x))/c^(5/2) +--R +--R +--R (82) +--R +----------------+ +--R | 2 +-+ +--R 3 2\|- c x + b x + a \|c +--R (- 12a b c - 3b )atan(------------------------) +--R 2c x - b +--R + +--R +----------------+ +--R 2 2 2 | 2 +-+ +--R (16c x - 4b c x - 16a c - 6b )\|- c x + b x + a \|c +--R / +--R 2 +-+ +--R 48c \|c +--R Type: Expression(Integer) +--E 86 + +--S 87 of 486 +a0314:= integrate(t0314,x) +--R +--R +--R (83) +--R [ +--R 2 2 3 5 2 2 2 4 +--R (96a b c - 48a b c - 18b )x + (- 384a b c - 96a b )x +--R + +--R 3 2 3 +--R - 384a b c - 96a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c - 24a b c + 3b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 288a b c + 144a b c + 54a b )x + (576a b c + 144a b )x +--R + +--R 4 3 3 +--R 384a b c + 96a b +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 4 2 3 6 3 3 2 5 +--R (- 128a c + 96b c )x + (672a b c - 120b c )x +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (768a c - 816a b c - 12b c)x + (- 1632a b c + 64a b c + 30b )x +--R + +--R 3 2 2 2 4 2 3 2 3 +--R (- 768a c + 480a b c + 120a b )x + (384a b c + 96a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 3 3 2 5 2 3 2 2 4 4 +--R (- 192a b c + 16b c )x + (- 384a c + 336a b c - 4b c)x +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (1056a b c - 16a b c - 6b )x + (768a c - 288a b c - 72a b )x +--R + +--R 3 2 3 +--R (- 384a b c - 96a b )x +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R / +--R +----------------+ +--R 3 2 2 2 2 2 2 | 2 +--R ((384a c - 288b c )x - 1536a b c x - 1536a c )\|- c x + b x + a +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c + 48b c )x + (- 1152a c + 864a b c )x + 2304a b c x +--R + +--R 3 2 +--R 1536a c +--R * +--R +---+ +--R \|- c +--R , +--R +--R 2 2 3 5 2 2 2 4 +--R (96a b c - 48a b c - 18b )x + (- 384a b c - 96a b )x +--R + +--R 3 2 3 +--R - 384a b c - 96a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c - 24a b c + 3b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 288a b c + 144a b c + 54a b )x + (576a b c + 144a b )x +--R + +--R 4 3 3 +--R 384a b c + 96a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 4 2 3 6 3 3 2 5 +--R (- 64a c + 48b c )x + (336a b c - 60b c )x +--R + +--R 2 3 2 2 4 4 +--R (384a c - 408a b c - 6b c)x +--R + +--R 2 2 3 5 3 +--R (- 816a b c + 32a b c + 15b )x +--R + +--R 3 2 2 2 4 2 3 2 3 +--R (- 384a c + 240a b c + 60a b )x + (192a b c + 48a b )x +--R * +--R +-+ +--R \|a +--R + +--R 3 3 2 5 2 3 2 2 4 4 +--R (- 96a b c + 8b c )x + (- 192a c + 168a b c - 2b c)x +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (528a b c - 8a b c - 3b )x + (384a c - 144a b c - 36a b )x +--R + +--R 3 2 3 +--R (- 192a b c - 48a b )x +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R 3 2 2 2 2 2 2 | 2 +-+ +--R ((192a c - 144b c )x - 768a b c x - 768a c )\|- c x + b x + a \|a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 288a b c + 24b c )x + (- 576a c + 432a b c )x + 1152a b c x +--R + +--R 3 2 +--R 768a c +--R * +--R +-+ +--R \|c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 87 + +--S 88 of 486 +m0314a:= a0314.1-r0314 +--R +--R +--R (84) +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c - 48a b c - 18b )x + (- 384a b c - 96a b )x - 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 2 2 4 6 3 3 2 2 3 5 2 +--R (- 144a b c - 24a b c + 3b )x + (- 288a b c + 144a b c + 54a b )x +--R + +--R 3 2 2 4 4 3 3 +--R (576a b c + 144a b )x + 384a b c + 96a b +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c - 48a b c - 18b )x + (- 384a b c - 96a b )x - 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +----------------+ +--R | 2 +---+ +-+ +--R \|- c x + b x + a \|- c \|a +--R + +--R 2 2 2 4 6 3 +--R (- 144a b c - 24a b c + 3b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 288a b c + 144a b c + 54a b )x + (576a b c + 144a b )x +--R + +--R 4 3 3 +--R 384a b c + 96a b +--R * +--R +---+ +--R \|- c +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (192a b c + 56a b c - 6b )x + (384a c - 144a b c - 108a b )x +--R + +--R 3 2 3 4 3 2 +--R (- 768a b c - 288a b )x - 512a c - 192a b +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 3 2 2 2 4 2 3 2 3 4 +--R (- 128a c + 48a b c + 36a b )x + (512a b c + 192a b )x + 512a c +--R + +--R 3 2 +--R 192a b +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R 3 2 2 2 2 2 2 | 2 +--R ((384a c - 288b c )x - 1536a b c x - 1536a c )\|- c x + b x + a +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c + 48b c )x + (- 1152a c + 864a b c )x + 2304a b c x +--R + +--R 3 2 +--R 1536a c +--R * +--R +---+ +--R \|- c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 88 + +--S 89 of 486 +d0314a:= D(m0314a,x) +--R +--R +--R (85) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 486 +m0314b:= a0314.2-r0314 +--R +--R +--R (86) +--R 2 2 3 5 2 2 2 4 +--R (192a b c - 96a b c - 36b )x + (- 768a b c - 192a b )x +--R + +--R 3 2 3 +--R - 768a b c - 192a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 2 2 4 6 3 +--R (- 288a b c - 48a b c + 6b )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 576a b c + 288a b c + 108a b )x + (1152a b c + 288a b )x +--R + +--R 4 3 3 +--R 768a b c + 192a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 2 2 3 5 2 2 2 4 3 +--R (96a b c - 48a b c - 18b )x + (- 384a b c - 96a b )x - 384a b c +--R + +--R 2 3 +--R - 96a b +--R * +--R +----------------+ +--R | 2 +-+ +--R \|- c x + b x + a \|a +--R + +--R 2 2 2 4 6 3 3 2 2 3 5 2 +--R (- 144a b c - 24a b c + 3b )x + (- 288a b c + 144a b c + 54a b )x +--R + +--R 3 2 2 4 4 3 3 +--R (576a b c + 144a b )x + 384a b c + 96a b +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (192a b c + 56a b c - 6b )x + (384a c - 144a b c - 108a b )x +--R + +--R 3 2 3 4 3 2 +--R (- 768a b c - 288a b )x - 512a c - 192a b +--R * +--R +-+ +--R \|a +--R + +--R 3 2 2 2 4 2 3 2 3 4 +--R (- 128a c + 48a b c + 36a b )x + (512a b c + 192a b )x + 512a c +--R + +--R 3 2 +--R 192a b +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R 3 2 2 2 2 2 2 | 2 +-+ +--R ((384a c - 288b c )x - 1536a b c x - 1536a c )\|- c x + b x + a \|a +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576a b c + 48b c )x + (- 1152a c + 864a b c )x + 2304a b c x +--R + +--R 3 2 +--R 1536a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 90 + +--S 91 of 486 +d0314b:= D(m0314b,x) +--R +--R +--R (87) 0 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 486 +t0315:= (a+b*x-c*x^2)^(1/2) +--R +--R +--R +----------------+ +--R | 2 +--R (88) \|- c x + b x + a +--R Type: Expression(Integer) +--E 92 + +--S 93 of 486 +r0315:= -1/4*(b-2*c*x)*(a+b*x-c*x^2)^(1/2)/c+1/8*(b^2+4*a*c)*_ + atan(2*c^(1/2)*(a+b*x-c*x^2)^(1/2)/(b-2*c*x))/c^(3/2) +--R +--R +--R (89) +--R +----------------+ +--R | 2 +-+ +--R 2 2\|- c x + b x + a \|c +--R (- 4a c - b )atan(------------------------) +--R 2c x - b +--R + +--R +----------------+ +--R | 2 +-+ +--R (4c x - 2b)\|- c x + b x + a \|c +--R / +--R +-+ +--R 8c\|c +--R Type: Expression(Integer) +--E 93 + +--S 94 of 486 +a0315:= integrate(t0315,x) +--R +--R +--R (90) +--R [ +--R +----------------+ +--R 3 2 2 | 2 +-+ +--R ((16a b c + 4b )x + 32a c + 8a b )\|- c x + b x + a \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (16a c - b )x + (- 32a b c - 8a b )x - 32a c - 8a b +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R 2 4 2 2 3 3 2 +--R - 16b c x + (- 32a c + 24b c)x + (56a b c - 6b )x +--R + +--R 2 2 +--R (32a c - 8a b )x +--R * +--R +---+ +-+ +--R \|- c \|a +--R + +--R 2 2 3 3 2 2 2 +--R ((16a c - 4b c)x + (- 40a b c + 2b )x + (- 32a c + 8a b )x) +--R * +--R +----------------+ +--R | 2 +---+ +--R \|- c x + b x + a \|- c +--R / +--R +----------------+ +--R | 2 +---+ +-+ +--R (32b c x + 64a c)\|- c x + b x + a \|- c \|a +--R + +--R 2 2 2 2 +---+ +--R ((32a c - 8b c)x - 64a b c x - 64a c)\|- c +--R , +--R +--R +----------------+ +--R 3 2 2 | 2 +-+ +--R ((16a b c + 4b )x + 32a c + 8a b )\|- c x + b x + a \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (16a c - b )x + (- 32a b c - 8a b )x - 32a c - 8a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R 2 4 2 2 3 3 2 +--R - 8b c x + (- 16a c + 12b c)x + (28a b c - 3b )x +--R + +--R 2 2 +--R (16a c - 4a b )x +--R * +--R +-+ +--R \|a +--R + +--R 2 2 3 3 2 2 2 +--R ((8a c - 2b c)x + (- 20a b c + b )x + (- 16a c + 4a b )x) +--R * +--R +----------------+ +--R | 2 +--R \|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R | 2 +-+ 2 2 2 +--R (16b c x + 32a c)\|- c x + b x + a \|a + (16a c - 4b c)x +--R + +--R 2 +--R - 32a b c x - 32a c +--R * +--R +-+ +--R \|c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 94 + +--S 95 of 486 +m0315a:= a0315.1-r0315 +--R +--R +--R (91) +--R +----------------+ +--R 3 2 2 | 2 +-+ +--R ((16a b c + 4b )x + 32a c + 8a b )\|- c x + b x + a \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (16a c - b )x + (- 32a b c - 8a b )x - 32a c - 8a b +--R * +--R +-+ +--R \|c +--R * +--R log +--R +----------------+ +--R | 2 +---+ +-+ +--R (2\|- c x + b x + a \|- c - 2c x)\|a +--R + +--R +----------------+ +--R 2 +---+ | 2 +--R (2c x - b x - 2a)\|- c + 2c x\|- c x + b x + a +--R / +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|a - b x - 2a +--R + +--R +----------------+ +--R 3 2 2 | 2 +---+ +-+ +--R ((16a b c + 4b )x + 32a c + 8a b )\|- c x + b x + a \|- c \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +---+ +--R ((16a c - b )x + (- 32a b c - 8a b )x - 32a c - 8a b )\|- c +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 3 2 2 2 +---+ +-+ +--R ((- 8a b c + 2b )x + 16a b x + 16a b)\|- c \|a +--R + +--R +----------------+ +--R 2 2 | 2 +---+ +--R (- 8a b x - 16a b)\|- c x + b x + a \|- c +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R | 2 +---+ +-+ +--R (32b c x + 64a c)\|- c x + b x + a \|- c \|a +--R + +--R 2 2 2 2 +---+ +--R ((32a c - 8b c)x - 64a b c x - 64a c)\|- c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 95 + +--S 96 of 486 +d0315a:= D(m0315a,x) +--R +--R +--R (92) 0 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 486 +m0315b:= a0315.2-r0315 +--R +--R +--R (93) +--R +----------------+ +--R 3 2 2 | 2 +-+ +--R ((32a b c + 8b )x + 64a c + 16a b )\|- c x + b x + a \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (32a c - 2b )x + (- 64a b c - 16a b )x - 64a c - 16a b +--R * +--R +----------------+ +--R +-+ | 2 +-+ +--R (\|a - \|- c x + b x + a )\|c +--R atan(--------------------------------) +--R c x +--R + +--R +----------------+ +--R 3 2 2 | 2 +-+ +--R ((16a b c + 4b )x + 32a c + 8a b )\|- c x + b x + a \|a +--R + +--R 2 2 4 2 2 3 3 2 2 +--R (16a c - b )x + (- 32a b c - 8a b )x - 32a c - 8a b +--R * +--R +----------------+ +--R | 2 +-+ +--R 2\|- c x + b x + a \|c +--R atan(------------------------) +--R 2c x - b +--R + +--R 3 2 2 2 +-+ +--R ((- 8a b c + 2b )x + 16a b x + 16a b)\|a +--R + +--R +----------------+ +--R 2 2 | 2 +--R (- 8a b x - 16a b)\|- c x + b x + a +--R * +--R +-+ +--R \|c +--R / +--R +----------------+ +--R | 2 +-+ 2 2 2 +--R (32b c x + 64a c)\|- c x + b x + a \|a + (32a c - 8b c)x +--R + +--R 2 +--R - 64a b c x - 64a c +--R * +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 97 + +--S 98 of 486 +d0315b:= D(m0315b,x) +--R +--R +--R (94) 0 +--R Type: Expression(Integer) +--E 98 + +--S 99 of 486 +t0316:= 1/(b*x-b^2*x^2)^(1/2) +--R +--R +--R 1 +--R (95) --------------- +--R +------------+ +--R | 2 2 +--R \|- b x + b x +--R Type: Expression(Integer) +--E 99 + +--S 100 of 486 +r0316:= asin(-1+2*b*x)/b +--R +--R +--R asin(2b x - 1) +--R (96) -------------- +--R b +--R Type: Expression(Integer) +--E 100 + +--S 101 of 486 +a0316:= integrate(t0316,x) +--R +--R +--R +------------+ +--R | 2 2 +--R \|- b x + b x +--R 2atan(---------------) +--R b x +--R (97) - ---------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 101 + +--S 102 of 486 +m0316:= a0316-r0316 +--R +--R +--R +------------+ +--R | 2 2 +--R \|- b x + b x +--R - 2atan(---------------) - asin(2b x - 1) +--R b x +--R (98) ----------------------------------------- +--R b +--R Type: Expression(Integer) +--E 102 + +--S 103 of 486 +d0316:= D(m0316,x) +--R +--R +--R +------------+ +--------------+ +--R | 2 2 | 2 2 +--R - 2\|- b x + b x + \|- 4b x + 4b x +--R (99) -------------------------------------- +--R +--------------+ +------------+ +--R | 2 2 | 2 2 +--R \|- 4b x + 4b x \|- b x + b x +--R Type: Expression(Integer) +--E 103 + +--S 104 of 486 +t0317:= 1/(b*x+b^2*x^2)^(1/2) +--R +--R +--R 1 +--R (100) ------------- +--R +----------+ +--R | 2 2 +--R \|b x + b x +--R Type: Expression(Integer) +--E 104 + +--S 105 of 486 +r0317:= atanh(2*(b*x*(1+b*x))^(1/2)/(1+2*b*x))/b +--R +--R +--R +----------+ +--R | 2 2 +--R 2\|b x + b x +--R atanh(--------------) +--R 2b x + 1 +--R (101) --------------------- +--R b +--R Type: Expression(Integer) +--E 105 + +--S 106 of 486 +a0317:= integrate(t0317,x) +--R +--R +--R +----------+ +--R | 2 2 +--R log(2\|b x + b x - 2b x - 1) +--R (102) - ------------------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 106 + +--S 107 of 486 +m0317:= a0317-r0317 +--R +--R +--R +----------+ +--R +----------+ | 2 2 +--R | 2 2 2\|b x + b x +--R - log(2\|b x + b x - 2b x - 1) - atanh(--------------) +--R 2b x + 1 +--R (103) -------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 107 + +--S 108 of 486 +d0317:= D(m0317,x) +--R +--R +--R (104) 0 +--R Type: Expression(Integer) +--E 108 + +--S 109 of 486 +t0318:= 2/((4*c+b^2)/c+4*b*x+4*c*x^2)^(1/2) +--R +--R +--R 2 +--R (105) --------------------------- +--R +------------------------+ +--R | 2 2 2 +--R |4c x + 4b c x + 4c + b +--R |------------------------ +--R \| c +--R Type: Expression(Integer) +--E 109 + +--S 110 of 486 +r0318:= asinh(1/2*(b+2*c*x)/c^(1/2))/c^(1/2) +--R +--R +--R 2c x + b +--R asinh(--------) +--R +-+ +--R 2\|c +--R (106) --------------- +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 110 + +--S 111 of 486 +a0318:= integrate(t0318,x) +--R +--R +--R (107) +--R [ +--R log +--R +-------+ +------------------------+ +--R | 2 | 2 2 2 +--R |4c + b +-+ 2 |4c x + 4b c x + 4c + b +--R (c |------- \|c - 2c x) |------------------------ +--R \| c \| c +--R + +--R +-------+ +--R | 2 +--R 2 2 2 +-+ 2 |4c + b +--R (- 4c x - 2b c x - 4c - b )\|c + 2c x |------- +--R \| c +--R / +--R +-------+ +------------------------+ +--R | 2 | 2 2 2 +--R |4c + b |4c x + 4b c x + 4c + b 2 +--R c |------- |------------------------ - 2b c x - 4c - b +--R \| c \| c +--R / +--R +-+ +--R \|c +--R , +--R +------------------------+ +-------+ +--R | 2 2 2 | 2 +--R +---+ |4c x + 4b c x + 4c + b +---+ |4c + b +--R \|- c |------------------------ - \|- c |------- +--R \| c \| c +--R 2atan(----------------------------------------------------) +--R 2c x +--R -----------------------------------------------------------] +--R +---+ +--R \|- c +--R Type: Union(List(Expression(Integer)),...) +--E 111 + +--S 112 of 486 +m0318a:= a0318.1-r0318 +--R +--R +--R (108) +--R log +--R +-------+ +------------------------+ +--R | 2 | 2 2 2 +--R |4c + b +-+ 2 |4c x + 4b c x + 4c + b +--R (c |------- \|c - 2c x) |------------------------ +--R \| c \| c +--R + +--R +-------+ +--R | 2 +--R 2 2 2 +-+ 2 |4c + b +--R (- 4c x - 2b c x - 4c - b )\|c + 2c x |------- +--R \| c +--R / +--R +-------+ +------------------------+ +--R | 2 | 2 2 2 +--R |4c + b |4c x + 4b c x + 4c + b 2 +--R c |------- |------------------------ - 2b c x - 4c - b +--R \| c \| c +--R + +--R 2c x + b +--R - asinh(--------) +--R +-+ +--R 2\|c +--R / +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 112 + +--S 113 of 486 +d0318a:= D(m0318a,x) +--R +--R +--R (109) +--R 4 3 4 2 3 2 3 3 2 3 +--R - 8b c x + (- 24c - 12b c )x + (- 32b c - 8b c )x - 32c +--R + +--R 2 2 4 +--R - 16b c - 2b c +--R * +--R +-------+ +--R | 2 +--R |4c + b +-+ +--R |------- \|c +--R \| c +--R + +--R 5 2 4 3 4 3 3 2 4 2 3 4 2 +--R (16c + 8b c )x + (48b c + 12b c )x + (64c + 32b c + 4b c )x +--R * +--R +------------------------+ +--R | 2 2 2 +--R |4c x + 4b c x + 4c + b +--R |------------------------ +--R \| 4c +--R + +--R 5 2 4 4 4 3 3 3 +--R (- 16c - 8b c )x + (- 56b c - 16b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 3 +--R (- 80c - 76b c - 14b c )x + (- 96b c - 48b c - 6b c)x - 64c +--R + +--R 2 2 4 6 +--R - 48b c - 12b c - b +--R * +--R +-+ +--R \|c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R 8b c x + (24c + 16b c )x + (40b c + 10b c )x +--R + +--R 4 2 3 4 2 +--R (32c + 16b c + 2b c )x +--R * +--R +-------+ +--R | 2 +--R |4c + b +--R |------- +--R \| c +--R * +--R +------------------------+ +--R | 2 2 2 +--R |4c x + 4b c x + 4c + b +--R |------------------------ +--R \| c +--R + +--R 5 2 4 4 4 3 3 3 +--R (32c + 16b c )x + (112b c + 32b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 +--R (160c + 152b c + 28b c )x + (192b c + 96b c + 12b c)x +--R + +--R 3 2 2 4 6 +--R 128c + 96b c + 24b c + 2b +--R * +--R +-+ +--R \|c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R - 16b c x + (- 48c - 32b c )x + (- 80b c - 20b c )x +--R + +--R 4 2 3 4 2 +--R (- 64c - 32b c - 4b c )x +--R * +--R +-------+ +--R | 2 +--R |4c + b +--R |------- +--R \| c +--R * +--R +------------------------+ +--R | 2 2 2 +--R |4c x + 4b c x + 4c + b +--R |------------------------ +--R \| 4c +--R + +--R 5 5 5 2 4 4 4 3 3 3 +--R 16b c x + (48c + 40b c )x + (128b c + 44b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 3 +--R (112c + 132b c + 26b c )x + (128b c + 64b c + 8b c)x + 64c +--R + +--R 2 2 4 6 +--R 48b c + 12b c + b +--R * +--R +-------+ +--R | 2 +--R |4c + b +-+ +--R |------- \|c +--R \| c +--R + +--R 6 2 5 5 5 3 4 4 +--R (- 32c - 16b c )x + (- 128b c - 40b c )x +--R + +--R 5 2 4 4 3 3 4 3 3 5 2 2 +--R (- 160c - 184b c - 36b c )x + (- 224b c - 112b c - 14b c )x +--R + +--R 4 2 3 4 2 6 +--R (- 128c - 96b c - 24b c - 2b c)x +--R / +--R 5 2 4 4 4 3 3 3 +--R (16c + 8b c )x + (56b c + 16b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 3 +--R (80c + 76b c + 14b c )x + (96b c + 48b c + 6b c)x + 64c +--R + +--R 2 2 4 6 +--R 48b c + 12b c + b +--R * +--R +-+ +--R \|c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R - 8b c x + (- 24c - 16b c )x + (- 40b c - 10b c )x +--R + +--R 4 2 3 4 2 +--R (- 32c - 16b c - 2b c )x +--R * +--R +-------+ +--R | 2 +--R |4c + b +--R |------- +--R \| c +--R * +--R +------------------------+ +------------------------+ +--R | 2 2 2 | 2 2 2 +--R |4c x + 4b c x + 4c + b |4c x + 4b c x + 4c + b +--R |------------------------ |------------------------ +--R \| 4c \| c +--R + +--R 5 5 5 2 4 4 4 3 3 3 +--R - 16b c x + (- 48c - 40b c )x + (- 128b c - 44b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 +--R (- 112c - 132b c - 26b c )x + (- 128b c - 64b c - 8b c)x +--R + +--R 3 2 2 4 6 +--R - 64c - 48b c - 12b c - b +--R * +--R +-------+ +--R | 2 +--R |4c + b +-+ +--R |------- \|c +--R \| c +--R + +--R 6 2 5 5 5 3 4 4 +--R (32c + 16b c )x + (128b c + 40b c )x +--R + +--R 5 2 4 4 3 3 4 3 3 5 2 2 +--R (160c + 184b c + 36b c )x + (224b c + 112b c + 14b c )x +--R + +--R 4 2 3 4 2 6 +--R (128c + 96b c + 24b c + 2b c)x +--R * +--R +------------------------+ +--R | 2 2 2 +--R |4c x + 4b c x + 4c + b +--R |------------------------ +--R \| 4c +--R Type: Expression(Integer) +--E 113 + +--S 114 of 486 +m0318b:= a0318.2-r0318 +--R +--R +--R (110) +--R +------------------------+ +-------+ +--R | 2 2 2 | 2 +--R +---+ |4c x + 4b c x + 4c + b +---+ |4c + b +--R \|- c |------------------------ - \|- c |------- +--R +-+ \| c \| c +--R 2\|c atan(----------------------------------------------------) +--R 2c x +--R + +--R +---+ 2c x + b +--R - \|- c asinh(--------) +--R +-+ +--R 2\|c +--R / +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 114 + +--S 115 of 486 +d0318b:= D(m0318b,x) +--R +--R +--R +------------------------+ +------------------------+ +--R | 2 2 2 | 2 2 2 +--R |4c x + 4b c x + 4c + b |4c x + 4b c x + 4c + b +--R - |------------------------ + 2 |------------------------ +--R \| c \| 4c +--R (111) ------------------------------------------------------------ +--R +------------------------+ +------------------------+ +--R | 2 2 2 | 2 2 2 +--R |4c x + 4b c x + 4c + b |4c x + 4b c x + 4c + b +--R |------------------------ |------------------------ +--R \| 4c \| c +--R Type: Expression(Integer) +--E 115 + +--S 116 of 486 +t0319:= 2/((4*c-b^2)/c+4*b*x-4*c*x^2)^(1/2) +--R +--R +--R 2 +--R (112) ----------------------------- +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| c +--R Type: Expression(Integer) +--E 116 + +--S 117 of 486 +r0319:= -asin(1/2*(b-2*c*x)/c^(1/2))/c^(1/2) +--R +--R +--R 2c x - b +--R asin(--------) +--R +-+ +--R 2\|c +--R (113) -------------- +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 117 + +--S 118 of 486 +a0319:= integrate(t0319,x) +--R +--R +--R (114) +--R [ +--R log +--R +--------------------------+ +-------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + 4c - b +---+ 2 |4c - b +--R (c |-------------------------- \|- c - 2c x) |------- +--R \| c \| c +--R + +--R +--------------------------+ +--R | 2 2 2 +--R 2 2 2 +---+ 2 |- 4c x + 4b c x + 4c - b +--R (4c x - 2b c x - 4c + b )\|- c + 2c x |-------------------------- +--R \| c +--R / +--R +--------------------------+ +-------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + 4c - b |4c - b 2 +--R c |-------------------------- |------- - 2b c x - 4c + b +--R \| c \| c +--R / +--R +---+ +--R \|- c +--R , +--R +-------+ +--------------------------+ +--R | 2 | 2 2 2 +--R |4c - b |- 4c x + 4b c x + 4c - b +-+ +--R ( |------- - |-------------------------- )\|c +--R \| c \| c +--R 2atan(------------------------------------------------) +--R 2c x +--R -------------------------------------------------------] +--R +-+ +--R \|c +--R Type: Union(List(Expression(Integer)),...) +--E 118 + +--S 119 of 486 +m0319a:= a0319.1-r0319 +--R +--R +--R (115) +--R +-+ +--R \|c +--R * +--R log +--R +--------------------------+ +-------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + 4c - b +---+ 2 |4c - b +--R (c |-------------------------- \|- c - 2c x) |------- +--R \| c \| c +--R + +--R 2 2 2 +---+ +--R (4c x - 2b c x - 4c + b )\|- c +--R + +--R +--------------------------+ +--R | 2 2 2 +--R 2 |- 4c x + 4b c x + 4c - b +--R 2c x |-------------------------- +--R \| c +--R / +--R +--------------------------+ +-------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + 4c - b |4c - b 2 +--R c |-------------------------- |------- - 2b c x - 4c + b +--R \| c \| c +--R + +--R +---+ 2c x - b +--R - \|- c asin(--------) +--R +-+ +--R 2\|c +--R / +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 119 + +--S 120 of 486 +d0319a:= D(m0319a,x) +--R +--R +--R (116) +--R 4 3 4 2 3 2 3 3 2 3 +--R - 8b c x + (- 24c + 12b c )x + (32b c - 8b c )x + 32c +--R + +--R 2 2 4 +--R - 16b c + 2b c +--R * +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +--R |-------------------------- |-------------------------- +--R \| c \| 4c +--R + +--R 5 5 5 2 4 4 4 3 3 3 +--R - 16b c x + (- 48c + 40b c )x + (128b c - 44b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 +--R (112c - 132b c + 26b c )x + (- 128b c + 64b c - 8b c)x +--R + +--R 3 2 2 4 6 +--R - 64c + 48b c - 12b c + b +--R * +--R +---+ +--R \|- c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R 16b c x + (48c - 32b c )x + (- 80b c + 20b c )x +--R + +--R 4 2 3 4 2 +--R (- 64c + 32b c - 4b c )x +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| 4c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R - 8b c x + (- 24c + 16b c )x + (40b c - 10b c )x +--R + +--R 4 2 3 4 2 +--R (32c - 16b c + 2b c )x +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| c +--R * +--R +-------+ +--R | 2 +--R |4c - b +--R |------- +--R \| c +--R + +--R 5 2 4 4 4 3 3 3 +--R (- 32c + 16b c )x + (112b c - 32b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 +--R (160c - 152b c + 28b c )x + (- 192b c + 96b c - 12b c)x +--R + +--R 3 2 2 4 6 +--R - 128c + 96b c - 24b c + 2b +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| 4c +--R + +--R 5 2 4 4 4 3 3 3 +--R (16c - 8b c )x + (- 56b c + 16b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 3 +--R (- 80c + 76b c - 14b c )x + (96b c - 48b c + 6b c)x + 64c +--R + +--R 2 2 4 6 +--R - 48b c + 12b c - b +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| c +--R * +--R +---+ +--R \|- c +--R + +--R 5 2 4 3 4 3 3 2 4 2 3 4 2 +--R ((- 16c + 8b c )x + (48b c - 12b c )x + (64c - 32b c + 4b c )x) +--R * +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +--R |-------------------------- |-------------------------- +--R \| c \| 4c +--R + +--R 6 2 5 5 5 3 4 4 5 2 4 4 3 3 +--R (- 32c + 16b c )x + (128b c - 40b c )x + (160c - 184b c + 36b c )x +--R + +--R 4 3 3 5 2 2 4 2 3 4 2 6 +--R (- 224b c + 112b c - 14b c )x + (- 128c + 96b c - 24b c + 2b c)x +--R / +--R 5 5 5 2 4 4 4 3 3 3 +--R 16b c x + (48c - 40b c )x + (- 128b c + 44b c )x +--R + +--R 4 2 3 4 2 2 3 3 2 5 +--R (- 112c + 132b c - 26b c )x + (128b c - 64b c + 8b c)x +--R + +--R 3 2 2 4 6 +--R 64c - 48b c + 12b c - b +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +---+ +--R |-------------------------- \|- c +--R \| 4c +--R + +--R 5 4 5 2 4 3 4 3 3 2 +--R 8b c x + (24c - 16b c )x + (- 40b c + 10b c )x +--R + +--R 4 2 3 4 2 +--R (- 32c + 16b c - 2b c )x +--R * +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +--R |-------------------------- |-------------------------- +--R \| c \| 4c +--R * +--R +-------+ +--R | 2 +--R |4c - b +--R |------- +--R \| c +--R + +--R 5 2 4 4 4 3 3 3 4 2 3 4 2 2 +--R (- 16c + 8b c )x + (56b c - 16b c )x + (80c - 76b c + 14b c )x +--R + +--R 3 3 2 5 3 2 2 4 6 +--R (- 96b c + 48b c - 6b c)x - 64c + 48b c - 12b c + b +--R * +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +---+ +--R |-------------------------- |-------------------------- \|- c +--R \| c \| 4c +--R + +--R 6 2 5 5 5 3 4 4 +--R (32c - 16b c )x + (- 128b c + 40b c )x +--R + +--R 5 2 4 4 3 3 4 3 3 5 2 2 +--R (- 160c + 184b c - 36b c )x + (224b c - 112b c + 14b c )x +--R + +--R 4 2 3 4 2 6 +--R (128c - 96b c + 24b c - 2b c)x +--R * +--R +--------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + 4c - b +--R |-------------------------- +--R \| 4c +--R Type: Expression(Integer) +--E 120 + +--S 121 of 486 +m0319b:= a0319.2-r0319 +--R +--R +--R (117) +--R +-------+ +--------------------------+ +--R | 2 | 2 2 2 +--R |4c - b |- 4c x + 4b c x + 4c - b +-+ +--R ( |------- - |-------------------------- )\|c +--R \| c \| c 2c x - b +--R 2atan(------------------------------------------------) - asin(--------) +--R 2c x +-+ +--R 2\|c +--R ------------------------------------------------------------------------ +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 121 + +--S 122 of 486 +d0319b:= D(m0319b,x) +--R +--R +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +--R 2 |-------------------------- - |-------------------------- +--R \| 4c \| c +--R (118) -------------------------------------------------------------- +--R +--------------------------+ +--------------------------+ +--R | 2 2 2 | 2 2 2 +--R |- 4c x + 4b c x + 4c - b |- 4c x + 4b c x + 4c - b +--R |-------------------------- |-------------------------- +--R \| c \| 4c +--R Type: Expression(Integer) +--E 122 + +--S 123 of 486 +t0320:= 2/((c-b^2)/c+4*b*x-4*c*x^2)^(1/2) +--R +--R +--R 2 +--R (119) ---------------------------- +--R +-------------------------+ +--R | 2 2 2 +--R |- 4c x + 4b c x + c - b +--R |------------------------- +--R \| c +--R Type: Expression(Integer) +--E 123 + +--S 124 of 486 +r0320:= -asin((b-2*c*x)/c^(1/2))/c^(1/2) +--R +--R +--R 2c x - b +--R asin(--------) +--R +-+ +--R \|c +--R (120) -------------- +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 124 + +--S 125 of 486 +a0320:= integrate(t0320,x) +--R +--R +--R (121) +--R [ +--R log +--R +-------------------------+ +------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + c - b +---+ 2 |c - b +--R (c |------------------------- \|- c - 2c x) |------ +--R \| c \| c +--R + +--R +-------------------------+ +--R | 2 2 2 +--R 2 2 2 +---+ 2 |- 4c x + 4b c x + c - b +--R (4c x - 2b c x - c + b )\|- c + 2c x |------------------------- +--R \| c +--R / +--R +-------------------------+ +------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + c - b |c - b 2 +--R c |------------------------- |------ - 2b c x - c + b +--R \| c \| c +--R / +--R +---+ +--R \|- c +--R , +--R +------+ +-------------------------+ +--R | 2 | 2 2 2 +--R |c - b |- 4c x + 4b c x + c - b +-+ +--R ( |------ - |------------------------- )\|c +--R \| c \| c +--R 2atan(----------------------------------------------) +--R 2c x +--R -----------------------------------------------------] +--R +-+ +--R \|c +--R Type: Union(List(Expression(Integer)),...) +--E 125 + +--S 126 of 486 +m0320a:= a0320.1-r0320 +--R +--R +--R (122) +--R +-+ +--R \|c +--R * +--R log +--R +-------------------------+ +------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + c - b +---+ 2 |c - b +--R (c |------------------------- \|- c - 2c x) |------ +--R \| c \| c +--R + +--R +-------------------------+ +--R | 2 2 2 +--R 2 2 2 +---+ 2 |- 4c x + 4b c x + c - b +--R (4c x - 2b c x - c + b )\|- c + 2c x |------------------------- +--R \| c +--R / +--R +-------------------------+ +------+ +--R | 2 2 2 | 2 +--R |- 4c x + 4b c x + c - b |c - b 2 +--R c |------------------------- |------ - 2b c x - c + b +--R \| c \| c +--R + +--R +---+ 2c x - b +--R - \|- c asin(--------) +--R +-+ +--R \|c +--R / +--R +---+ +-+ +--R \|- c \|c +--R Type: Expression(Integer) +--E 126 + +--S 127 of 486 +d0320a:= D(m0320a,x) +--R +--R +--R (123) 0 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 486 +m0320b:= a0320.2-r0320 +--R +--R +--R (124) +--R +------+ +-------------------------+ +--R | 2 | 2 2 2 +--R |c - b |- 4c x + 4b c x + c - b +-+ +--R ( |------ - |------------------------- )\|c +--R \| c \| c 2c x - b +--R 2atan(----------------------------------------------) - asin(--------) +--R 2c x +-+ +--R \|c +--R ---------------------------------------------------------------------- +--R +-+ +--R \|c +--R Type: Expression(Integer) +--E 128 + +--S 129 of 486 +d0320b:= D(m0320b,x) +--R +--R +--R (125) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 486 +t0321:= (-(-2+3*x)^2)^(1/2) +--R +--R +--R +---------------+ +--R | 2 +--R (126) \|- 9x + 12x - 4 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 486 +r0321:= -1/6*(2-3*x)*(-(2-3*x)^2)^(1/2) +--R +--R +--R +---------------+ +--R | 2 +--R (3x - 2)\|- 9x + 12x - 4 +--R (127) -------------------------- +--R 6 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 486 +a0321:= integrate(t0321,x) +--R +--R +--R 2 +---+ +--R (3x - 4x)\|- 1 +--R (128) ---------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 132 + +--S 133 of 486 +m0321:= a0321-r0321 +--R +--R +--R +---------------+ +--R | 2 2 +---+ +--R (- 3x + 2)\|- 9x + 12x - 4 + (9x - 12x)\|- 1 +--R (129) ------------------------------------------------ +--R 6 +--R Type: Expression(Integer) +--E 133 + +--S 134 of 486 +d0321:= D(m0321,x) +--R +--R +--R +---------------+ +--R +---+ | 2 2 +--R (3x - 2)\|- 1 \|- 9x + 12x - 4 + 9x - 12x + 4 +--R (130) ------------------------------------------------ +--R +---------------+ +--R | 2 +--R \|- 9x + 12x - 4 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 486 +t0322:= (-(2+3*x)^2)^(1/2) +--R +--R +--R +---------------+ +--R | 2 +--R (131) \|- 9x - 12x - 4 +--R Type: Expression(Integer) +--E 135 + +--S 136 of 486 +r0322:= 1/6*(2+3*x)*(-(2+3*x)^2)^(1/2) +--R +--R +--R +---------------+ +--R | 2 +--R (3x + 2)\|- 9x - 12x - 4 +--R (132) -------------------------- +--R 6 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 486 +a0322:= integrate(t0322,x) +--R +--R +--R 2 +---+ +--R (3x + 4x)\|- 1 +--R (133) ---------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 137 + +--S 138 of 486 +m0322:= a0322-r0322 +--R +--R +--R +---------------+ +--R | 2 2 +---+ +--R (- 3x - 2)\|- 9x - 12x - 4 + (9x + 12x)\|- 1 +--R (134) ------------------------------------------------ +--R 6 +--R Type: Expression(Integer) +--E 138 + +--S 139 of 486 +d0322:= D(m0322,x) +--R +--R +--R +---------------+ +--R +---+ | 2 2 +--R (3x + 2)\|- 1 \|- 9x - 12x - 4 + 9x + 12x + 4 +--R (135) ------------------------------------------------ +--R +---------------+ +--R | 2 +--R \|- 9x - 12x - 4 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 486 +t0323:= x/(-(-a+b*x)^2)^(1/2) +--R +--R +--R x +--R (136) ----------------------- +--R +--------------------+ +--R | 2 2 2 +--R \|- b x + 2a b x - a +--R Type: Expression(Integer) +--E 140 + +--S 141 of 486 +r0323:= -(-(-a+b*x)^2)^(1/2)/b^2-a*(a-b*x)*log(a-b*x)/b^2/(-(a-b*x)^2)^(1/2) +--R +--R +--R 2 2 2 2 +--R (a b x - a )log(- b x + a) + b x - 2a b x + a +--R (137) ----------------------------------------------- +--R +--------------------+ +--R 2 | 2 2 2 +--R b \|- b x + 2a b x - a +--R Type: Expression(Integer) +--E 141 + +--S 142 of 486 +a0323:= integrate(t0323,x) +--R +--R +--R b x - a +--R a log(-------) + b x +--R b +--R (138) -------------------- +--R 2 +---+ +--R b \|- 1 +--R Type: Union(Expression(Integer),...) +--E 142 + +--S 143 of 486 +m0323:= a0323-r0323 +--R +--R +--R (139) +--R +--------------------+ +--R b x - a | 2 2 2 +--R (a log(-------) + b x)\|- b x + 2a b x - a +--R b +--R + +--R 2 +---+ 2 2 2 +---+ +--R (- a b x + a )\|- 1 log(- b x + a) + (- b x + 2a b x - a )\|- 1 +--R / +--R +--------------------+ +--R 2 +---+ | 2 2 2 +--R b \|- 1 \|- b x + 2a b x - a +--R Type: Expression(Integer) +--E 143 + +--S 144 of 486 +d0323:= D(m0323,x) +--R +--R +--R +--------------------+ +--R +---+ | 2 2 2 2 +--R - x\|- 1 \|- b x + 2a b x - a - b x + a x +--R (140) --------------------------------------------- +--R +--------------------+ +--R | 2 2 2 +--R (b x - a)\|- b x + 2a b x - a +--R Type: Expression(Integer) +--E 144 + +--S 145 of 486 +t0324:= x/(-(a+b*x)^2)^(1/2) +--R +--R +--R x +--R (141) ----------------------- +--R +--------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a +--R Type: Expression(Integer) +--E 145 + +--S 146 of 486 +r0324:= -(-(a+b*x)^2)^(1/2)/b^2-a*(a+b*x)*log(a+b*x)/b^2/(-(a+b*x)^2)^(1/2) +--R +--R +--R 2 2 2 2 +--R (- a b x - a )log(b x + a) + b x + 2a b x + a +--R (142) ----------------------------------------------- +--R +--------------------+ +--R 2 | 2 2 2 +--R b \|- b x - 2a b x - a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 486 +a0324:= integrate(t0324,x) +--R +--R +--R b x + a +--R - a log(-------) + b x +--R b +--R (143) ---------------------- +--R 2 +---+ +--R b \|- 1 +--R Type: Union(Expression(Integer),...) +--E 147 + +--S 148 of 486 +m0324:= a0324-r0324 +--R +--R +--R (144) +--R +--------------------+ +--R b x + a | 2 2 2 +--R (- a log(-------) + b x)\|- b x - 2a b x - a +--R b +--R + +--R 2 +---+ 2 2 2 +---+ +--R (a b x + a )\|- 1 log(b x + a) + (- b x - 2a b x - a )\|- 1 +--R / +--R +--------------------+ +--R 2 +---+ | 2 2 2 +--R b \|- 1 \|- b x - 2a b x - a +--R Type: Expression(Integer) +--E 148 + +--S 149 of 486 +d0324:= D(m0324,x) +--R +--R +--R +--------------------+ +--R +---+ | 2 2 2 2 +--R - x\|- 1 \|- b x - 2a b x - a - b x - a x +--R (145) --------------------------------------------- +--R +--------------------+ +--R | 2 2 2 +--R (b x + a)\|- b x - 2a b x - a +--R Type: Expression(Integer) +--E 149 + +--S 150 of 486 +t0325:= 1/x/((2+3*x)^2)^(1/2) +--R +--R +--R 1 +--R (146) ----------------- +--R +-------------+ +--R | 2 +--R x\|9x + 12x + 4 +--R Type: Expression(Integer) +--E 150 + +--S 151 of 486 +r0325:= -atanh(1+3*x)*cos(2+3*x) +--R +--R +--R (147) - atanh(3x + 1)cos(3x + 2) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 486 +a0325:= integrate(t0325,x) +--R +--R +--R - log(3x + 2) + log(x) +--R (148) ---------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 152 + +--S 153 of 486 +m0325:= a0325-r0325 +--R +--R +--R - log(3x + 2) + log(x) + 2atanh(3x + 1)cos(3x + 2) +--R (149) -------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 153 + +--S 154 of 486 +d0325:= D(m0325,x) +--R +--R +--R 2 +--R (- 9x - 6x)atanh(3x + 1)sin(3x + 2) - cos(3x + 2) + 1 +--R (150) ------------------------------------------------------ +--R 2 +--R 3x + 2x +--R Type: Expression(Integer) +--E 154 + +--S 155 of 486 +t0326:= 1/x/((-2+3*x)^2)^(1/2) +--R +--R +--R 1 +--R (151) ----------------- +--R +-------------+ +--R | 2 +--R x\|9x - 12x + 4 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 486 +r0326:= -cos(-2+3*x)*atanh(-1+3*x) +--R +--R +--R (152) - atanh(3x - 1)cos(3x - 2) +--R Type: Expression(Integer) +--E 156 + +--S 157 of 486 +a0326:= integrate(t0326,x) +--R +--R +--R log(3x - 2) - log(x) +--R (153) -------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 157 + +--S 158 of 486 +m0326:= a0326-r0326 +--R +--R +--R log(3x - 2) - log(x) + 2atanh(3x - 1)cos(3x - 2) +--R (154) ------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 158 + +--S 159 of 486 +d0326:= D(m0326,x) +--R +--R +--R 2 +--R (- 9x + 6x)atanh(3x - 1)sin(3x - 2) - cos(3x - 2) + 1 +--R (155) ------------------------------------------------------ +--R 2 +--R 3x - 2x +--R Type: Expression(Integer) +--E 159 + +--S 160 of 486 +t0327:= 1/x/(-(-2+3*x)^2)^(1/2) +--R +--R +--R 1 +--R (156) ------------------- +--R +---------------+ +--R | 2 +--R x\|- 9x + 12x - 4 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 486 +r0327:= (2-3*x)*atanh(-1+3*x)/(-(2-3*x)^2)^(1/2) +--R +--R +--R (- 3x + 2)atanh(3x - 1) +--R (157) ----------------------- +--R +---------------+ +--R | 2 +--R \|- 9x + 12x - 4 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 486 +a0327:= integrate(t0327,x) +--R +--R +--R +---+ +---+ 3x - 2 +--R \|- 1 log(x) - \|- 1 log(------) +--R 3 +--R (158) -------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 162 + +--S 163 of 486 +m0327:= a0327-r0327 +--R +--R +--R (159) +--R +---------------+ +--R +---+ +---+ 3x - 2 | 2 +--R (\|- 1 log(x) - \|- 1 log(------))\|- 9x + 12x - 4 + (6x - 4)atanh(3x - 1) +--R 3 +--R ---------------------------------------------------------------------------- +--R +---------------+ +--R | 2 +--R 2\|- 9x + 12x - 4 +--R Type: Expression(Integer) +--E 163 + +--S 164 of 486 +d0327:= D(m0327,x) +--R +--R +--R +---------------+ +--R +---+ | 2 +--R - \|- 1 \|- 9x + 12x - 4 - 3x + 2 +--R (160) ----------------------------------- +--R +---------------+ +--R 2 | 2 +--R (3x - 2x)\|- 9x + 12x - 4 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 486 +t0328:= (a+b*x)*(c+d*x+e*x^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (161) (b x + a)\|e x + d x + c +--R Type: Expression(Integer) +--E 165 + +--S 166 of 486 +r0328:= -1/8*(b*d-2*a*e)*(d+2*e*x)*(c+d*x+e*x^2)^(1/2)/e^2+1/3*b*_ + (c+d*x+e*x^2)^(3/2)/e+1/16*(b*d-2*a*e)*(d^2-4*c*e)*_ + atanh(2*e^(1/2)*(c+d*x+e*x^2)^(1/2)/(d+2*e*x))/e^(5/2) +--R +--R +--R (162) +--R +--------------+ +--R +-+ | 2 +--R 2 2 3 2\|e \|e x + d x + c +--R (24a c e + (- 6a d - 12b c d)e + 3b d )atanh(----------------------) +--R 2e x + d +--R + +--R 2 2 2 2 +-+ +--R (16b e x + (24a e + 4b d e)x + (12a d + 16b c)e - 6b d )\|e +--R * +--R +--------------+ +--R | 2 +--R \|e x + d x + c +--R / +--R 2 +-+ +--R 48e \|e +--R Type: Expression(Integer) +--E 166 + +--S 167 of 486 +a0328:= integrate(t0328,x) +--R +--R +--R (163) +--R [ +--R 2 3 2 2 2 4 3 +--R 192a c e + (96a c d - 96b c d)e + (- 36a d - 48b c d )e +--R + +--R 5 +--R 18b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (768a c d e + (- 192a c d - 384b c d )e + 96b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R 768a c e + (- 192a c d - 384b c d)e + 96b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|e x + d x + c +--R + +--R 2 3 3 2 2 2 5 4 +--R - 288a c d e + (48a c d + 144b c d )e + (6a d - 24b c d )e +--R + +--R 6 +--R - 3b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 +--R - 576a c e + (- 288a c d + 288b c d)e +--R + +--R 4 2 3 5 +--R (108a c d + 144b c d )e - 54b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 +--R (- 1152a c d e + (288a c d + 576b c d )e - 144b c d )x +--R + +--R 4 2 3 2 4 3 3 +--R - 768a c e + (192a c d + 384b c d)e - 96b c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|c \|e - 2e x)\|e x + d x + c + (- 2e x - d x - 2c)\|e +--R + +--R +-+ +--R 2e x\|c +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|e x + d x + c - d x - 2c +--R + +--R 3 3 2 5 +--R (- 192b c d e - 16b d e )x +--R + +--R 2 3 3 2 2 4 4 +--R ((- 288a c d - 384b c )e + (- 24a d - 336b c d )e - 4b d e)x +--R + +--R 2 3 2 2 2 +--R - 576a c e + (- 576a c d - 1056b c d)e +--R + +--R 4 3 5 +--R (- 12a d - 16b c d )e + 6b d +--R * +--R 3 +--R x +--R + +--R 2 3 2 3 2 2 +--R (- 1344a c d - 768b c )e + (- 144a c d - 288b c d )e +--R + +--R 4 +--R 72b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 2 3 2 3 +--R (- 768a c e + (- 192a c d - 384b c d)e + 96b c d )x +--R * +--R +--------------+ +--R +-+ | 2 +--R \|e \|e x + d x + c +--R + +--R 4 2 3 6 +--R (128b c e + 96b d e )x +--R + +--R 4 2 3 3 2 5 +--R (192a c e + (144a d + 672b c d)e + 120b d e )x +--R + +--R 2 3 3 2 2 4 4 +--R ((1056a c d + 768b c )e + (216a d + 816b c d )e - 12b d e)x +--R + +--R 2 3 2 2 2 4 3 +--R 960a c e + (1248a c d + 1632b c d)e + (60a d + 64b c d )e +--R + +--R 5 +--R - 30b d +--R * +--R 3 +--R x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((1728a c d + 768b c )e + (240a c d + 480b c d )e - 120b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (768a c e + (192a c d + 384b c d)e - 96b c d )x +--R * +--R +-+ +-+ +--R \|c \|e +--R / +--R 3 2 2 2 2 2 2 +-+ +-+ +--R ((384c e + 288d e )x + 1536c d e x + 1536c e )\|c \|e +--R * +--R +--------------+ +--R | 2 +--R \|e x + d x + c +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576c d e - 48d e )x + (- 1152c e - 864c d e )x - 2304c d e x +--R + +--R 3 2 +--R - 1536c e +--R * +--R +-+ +--R \|e +--R , +--R +--R 2 3 2 2 2 4 3 +--R 192a c e + (96a c d - 96b c d)e + (- 36a d - 48b c d )e +--R + +--R 5 +--R 18b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (768a c d e + (- 192a c d - 384b c d )e + 96b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R 768a c e + (- 192a c d - 384b c d)e + 96b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|e x + d x + c +--R + +--R 2 3 3 2 2 2 5 4 +--R - 288a c d e + (48a c d + 144b c d )e + (6a d - 24b c d )e +--R + +--R 6 +--R - 3b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 +--R - 576a c e + (- 288a c d + 288b c d)e +--R + +--R 4 2 3 5 +--R (108a c d + 144b c d )e - 54b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 +--R (- 1152a c d e + (288a c d + 576b c d )e - 144b c d )x +--R + +--R 4 2 3 2 4 3 3 +--R - 768a c e + (192a c d + 384b c d)e - 96b c d +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- e \|e x + d x + c - \|- e \|c +--R atan(------------------------------------) +--R e x +--R + +--R 3 3 2 5 +--R (- 96b c d e - 8b d e )x +--R + +--R 2 3 3 2 2 4 4 +--R ((- 144a c d - 192b c )e + (- 12a d - 168b c d )e - 2b d e)x +--R + +--R 2 3 2 2 2 4 3 +--R - 288a c e + (- 288a c d - 528b c d)e + (- 6a d - 8b c d )e +--R + +--R 5 +--R 3b d +--R * +--R 3 +--R x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((- 672a c d - 384b c )e + (- 72a c d - 144b c d )e + 36b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (- 384a c e + (- 96a c d - 192b c d)e + 48b c d )x +--R * +--R +--------------+ +--R +---+ | 2 +--R \|- e \|e x + d x + c +--R + +--R 4 2 3 6 +--R (64b c e + 48b d e )x +--R + +--R 4 2 3 3 2 5 +--R (96a c e + (72a d + 336b c d)e + 60b d e )x +--R + +--R 2 3 3 2 2 4 4 +--R ((528a c d + 384b c )e + (108a d + 408b c d )e - 6b d e)x +--R + +--R 2 3 2 2 2 4 3 +--R 480a c e + (624a c d + 816b c d)e + (30a d + 32b c d )e +--R + +--R 5 +--R - 15b d +--R * +--R 3 +--R x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((864a c d + 384b c )e + (120a c d + 240b c d )e - 60b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R (384a c e + (96a c d + 192b c d)e - 48b c d )x +--R * +--R +---+ +-+ +--R \|- e \|c +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +--R ((192c e + 144d e )x + 768c d e x + 768c e )\|- e \|c +--R * +--R +--------------+ +--R | 2 +--R \|e x + d x + c +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 288c d e - 24d e )x + (- 576c e - 432c d e )x - 1152c d e x +--R + +--R 3 2 +--R - 768c e +--R * +--R +---+ +--R \|- e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 167 + +--S 168 of 486 +m0328a:= a0328.1-r0328 +--R +--R +--R (164) +--R 2 3 2 2 2 4 3 +--R 192a c e + (96a c d - 96b c d)e + (- 36a d - 48b c d )e +--R + +--R 5 +--R 18b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (768a c d e + (- 192a c d - 384b c d )e + 96b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R 768a c e + (- 192a c d - 384b c d)e + 96b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|e x + d x + c +--R + +--R 2 3 3 2 2 2 5 4 +--R - 288a c d e + (48a c d + 144b c d )e + (6a d - 24b c d )e +--R + +--R 6 +--R - 3b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 +--R - 576a c e + (- 288a c d + 288b c d)e +--R + +--R 4 2 3 5 +--R (108a c d + 144b c d )e - 54b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 4 2 +--R (- 1152a c d e + (288a c d + 576b c d )e - 144b c d )x - 768a c e +--R + +--R 3 2 4 3 3 +--R (192a c d + 384b c d)e - 96b c d +--R * +--R log +--R +--------------+ +--R +-+ +-+ | 2 2 +-+ +--R (2\|c \|e - 2e x)\|e x + d x + c + (- 2e x - d x - 2c)\|e +--R + +--R +-+ +--R 2e x\|c +--R / +--R +--------------+ +--R +-+ | 2 +--R 2\|c \|e x + d x + c - d x - 2c +--R + +--R 2 3 2 2 2 4 3 +--R - 192a c e + (- 96a c d + 96b c d)e + (36a d + 48b c d )e +--R + +--R 5 +--R - 18b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (- 768a c d e + (192a c d + 384b c d )e - 96b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R - 768a c e + (192a c d + 384b c d)e - 96b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|c \|e x + d x + c +--R + +--R 2 3 3 2 2 2 5 4 +--R 288a c d e + (- 48a c d - 144b c d )e + (- 6a d + 24b c d )e +--R + +--R 6 +--R 3b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 4 2 3 +--R 576a c e + (288a c d - 288b c d)e + (- 108a c d - 144b c d )e +--R + +--R 5 +--R 54b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 4 2 +--R (1152a c d e + (- 288a c d - 576b c d )e + 144b c d )x + 768a c e +--R + +--R 3 2 4 3 3 +--R (- 192a c d - 384b c d)e + 96b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|e \|e x + d x + c +--R atanh(----------------------) +--R 2e x + d +--R + +--R 2 3 2 3 2 2 4 2 +--R ((96a c d + 128b c )e + (72a c d + 48b c d )e - 36b c d )x +--R + +--R 2 2 3 2 3 3 4 +--R ((384a c d + 512b c d)e - 192b c d )x + (384a c d + 512b c )e +--R + +--R 3 2 +--R - 192b c d +--R * +--R +--------------+ +--R +-+ | 2 +--R \|e \|e x + d x + c +--R + +--R 2 2 2 4 3 5 3 +--R ((- 144a c d - 192b c d)e + (- 12a d + 56b c d )e + 6b d )x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((- 288a c d - 384b c )e + (- 216a c d - 144b c d )e + 108b c d )x +--R + +--R 2 2 3 2 3 3 4 +--R ((- 576a c d - 768b c d)e + 288b c d )x + (- 384a c d - 512b c )e +--R + +--R 3 2 +--R 192b c d +--R * +--R +-+ +-+ +--R \|c \|e +--R / +--R +--------------+ +--R 3 2 2 2 2 2 2 +-+ +-+ | 2 +--R ((384c e + 288d e )x + 1536c d e x + 1536c e )\|c \|e \|e x + d x + c +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576c d e - 48d e )x + (- 1152c e - 864c d e )x - 2304c d e x +--R + +--R 3 2 +--R - 1536c e +--R * +--R +-+ +--R \|e +--R Type: Expression(Integer) +--E 168 + +--S 169 of 486 +d0328a:= D(m0328a,x) +--R +--R +--R (165) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 486 +m0328b:= a0328.2-r0328 +--R +--R +--R (166) +--R 2 3 2 2 2 4 3 +--R - 192a c e + (- 96a c d + 96b c d)e + (36a d + 48b c d )e +--R + +--R 5 +--R - 18b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (- 768a c d e + (192a c d + 384b c d )e - 96b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R - 768a c e + (192a c d + 384b c d)e - 96b c d +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- e \|c \|e x + d x + c +--R + +--R 2 3 3 2 2 2 +--R 288a c d e + (- 48a c d - 144b c d )e +--R + +--R 5 4 6 +--R (- 6a d + 24b c d )e + 3b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 +--R 576a c e + (288a c d - 288b c d)e +--R + +--R 4 2 3 5 +--R (- 108a c d - 144b c d )e + 54b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 +--R (1152a c d e + (- 288a c d - 576b c d )e + 144b c d )x +--R + +--R 4 2 3 2 4 3 3 +--R 768a c e + (- 192a c d - 384b c d)e + 96b c d +--R * +--R +---+ +--R \|- e +--R * +--R +--------------+ +--R +-+ | 2 +--R 2\|e \|e x + d x + c +--R atanh(----------------------) +--R 2e x + d +--R + +--R 2 3 2 2 2 4 3 +--R 384a c e + (192a c d - 192b c d)e + (- 72a d - 96b c d )e +--R + +--R 5 +--R 36b d +--R * +--R 2 +--R x +--R + +--R 2 2 3 2 2 4 +--R (1536a c d e + (- 384a c d - 768b c d )e + 192b c d )x +--R + +--R 3 2 2 2 3 2 3 +--R 1536a c e + (- 384a c d - 768b c d)e + 192b c d +--R * +--R +--------------+ +--R +-+ +-+ | 2 +--R \|c \|e \|e x + d x + c +--R + +--R 2 3 3 2 2 2 +--R - 576a c d e + (96a c d + 288b c d )e +--R + +--R 5 4 6 +--R (12a d - 48b c d )e - 6b d +--R * +--R 3 +--R x +--R + +--R 3 3 2 2 3 2 +--R - 1152a c e + (- 576a c d + 576b c d)e +--R + +--R 4 2 3 5 +--R (216a c d + 288b c d )e - 108b c d +--R * +--R 2 +--R x +--R + +--R 3 2 2 3 3 2 2 4 +--R (- 2304a c d e + (576a c d + 1152b c d )e - 288b c d )x +--R + +--R 4 2 3 2 4 3 3 +--R - 1536a c e + (384a c d + 768b c d)e - 192b c d +--R * +--R +-+ +--R \|e +--R * +--R +--------------+ +--R +---+ | 2 +---+ +-+ +--R \|- e \|e x + d x + c - \|- e \|c +--R atan(------------------------------------) +--R e x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((96a c d + 128b c )e + (72a c d + 48b c d )e - 36b c d )x +--R + +--R 2 2 3 2 3 3 4 +--R ((384a c d + 512b c d)e - 192b c d )x + (384a c d + 512b c )e +--R + +--R 3 2 +--R - 192b c d +--R * +--R +--------------+ +--R +---+ +-+ | 2 +--R \|- e \|e \|e x + d x + c +--R + +--R 2 2 2 4 3 5 3 +--R ((- 144a c d - 192b c d)e + (- 12a d + 56b c d )e + 6b d )x +--R + +--R 2 3 2 3 2 2 4 2 +--R ((- 288a c d - 384b c )e + (- 216a c d - 144b c d )e + 108b c d )x +--R + +--R 2 2 3 2 3 3 4 +--R ((- 576a c d - 768b c d)e + 288b c d )x + (- 384a c d - 512b c )e +--R + +--R 3 2 +--R 192b c d +--R * +--R +---+ +-+ +-+ +--R \|- e \|c \|e +--R / +--R 3 2 2 2 2 2 2 +---+ +-+ +-+ +--R ((384c e + 288d e )x + 1536c d e x + 1536c e )\|- e \|c \|e +--R * +--R +--------------+ +--R | 2 +--R \|e x + d x + c +--R + +--R 3 3 2 3 2 3 2 2 2 2 2 +--R (- 576c d e - 48d e )x + (- 1152c e - 864c d e )x - 2304c d e x +--R + +--R 3 2 +--R - 1536c e +--R * +--R +---+ +-+ +--R \|- e \|e +--R Type: Expression(Integer) +--E 170 + +--S 171 of 486 +d0328b:= D(m0328b,x) +--R +--R +--R (167) 0 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 486 +t0329:= 1/(x+(-3-4*x-x^2)^(1/2)) +--R +--R +--R 1 +--R (168) -------------------- +--R +-------------+ +--R | 2 +--R \|- x - 4x - 3 + x +--R Type: Expression(Integer) +--E 172 + +--S 173 of 486 +r0329:= -atan((-1-x)^(1/2)/(3+x)^(1/2))-2^(1/2)*atan(1/2*(1-3*(-1-x)^(1/2)/_ + (3+x)^(1/2))*2^(1/2))-1/2*log(2/(3+x))+1/2*log(1-3*(1+x)/_ + (3+x)-2*(-1-x)^(1/2)/(3+x)^(1/2)) +--R +--R +--R (169) +--R +-----+ +-------+ +--R - 2x\|x + 3 + (- 2x - 6)\|- x - 1 +--R log(-----------------------------------) +--R +-----+ +--R (x + 3)\|x + 3 +--R + +--R +-+ +-----+ +-+ +-------+ +-------+ +--R +-+ \|2 \|x + 3 - 3\|2 \|- x - 1 \|- x - 1 +--R - 2\|2 atan(------------------------------) - 2atan(----------) +--R +-----+ +-----+ +--R 2\|x + 3 \|x + 3 +--R + +--R 2 +--R - log(-----) +--R x + 3 +--R / +--R 2 +--R Type: Expression(Integer) +--E 173 + +--S 174 of 486 +a0329:= integrate(t0329,x) +--R +--R +--R (170) +--R +-------------+ +--R | 2 +--R +-+ 2x\|- x - 4x - 3 - 4x - 3 +--R \|2 log(---------------------------) +--R 2 +--R x +--R + +--R +-------------+ +-------------+ +--R | 2 | 2 +--R +-+ - 2x\|- x - 4x - 3 - 4x - 3 +-+ \|- x - 4x - 3 +--R - \|2 log(-----------------------------) - 4\|2 atan(----------------) +--R 2 x + 2 +--R x +--R + +--R +-+ +-+ +--R (2x + 3)\|2 (2x + 3)\|2 +--R - 4atan(---------------------) - 4atan(---------------------) +--R +-------------+ +-------------+ +--R | 2 | 2 +--R 3\|- x - 4x - 3 - x 3\|- x - 4x - 3 + x +--R + +--R +-+ +--R +-+ 2 (2x + 2)\|2 +--R 2\|2 log(2x + 4x + 3) + 4atan(------------) +--R 2 +--R 2x + 4x + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 174 + +--S 175 of 486 +m0329:= a0329-r0329 +--R +--R +--R (171) +--R +-------------+ +--R | 2 +--R +-+ 2x\|- x - 4x - 3 - 4x - 3 +--R \|2 log(---------------------------) +--R 2 +--R x +--R + +--R +-----+ +-------+ +--R +-+ - 2x\|x + 3 + (- 2x - 6)\|- x - 1 +--R - 4\|2 log(-----------------------------------) +--R +-----+ +--R (x + 3)\|x + 3 +--R + +--R +-------------+ +-------------+ +--R | 2 | 2 +--R +-+ - 2x\|- x - 4x - 3 - 4x - 3 +-+ \|- x - 4x - 3 +--R - \|2 log(-----------------------------) - 4\|2 atan(----------------) +--R 2 x + 2 +--R x +--R + +--R +-+ +-----+ +-+ +-------+ +-+ +--R \|2 \|x + 3 - 3\|2 \|- x - 1 (2x + 3)\|2 +--R 16atan(------------------------------) - 4atan(---------------------) +--R +-----+ +-------------+ +--R 2\|x + 3 | 2 +--R 3\|- x - 4x - 3 - x +--R + +--R +-+ +-------+ +--R (2x + 3)\|2 +-+ \|- x - 1 +--R - 4atan(---------------------) + 8\|2 atan(----------) +--R +-------------+ +-----+ +--R | 2 \|x + 3 +--R 3\|- x - 4x - 3 + x +--R + +--R +-+ +--R +-+ 2 +-+ 2 (2x + 2)\|2 +--R 2\|2 log(2x + 4x + 3) + 4\|2 log(-----) + 4atan(------------) +--R x + 3 2 +--R 2x + 4x + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 175 + +--S 176 of 486 +d0329:= D(m0329,x) +--R +--R +--R (172) +--R +-------------+ +--R | 2 2 +-------+ +-----+ +--R (x\|- x - 4x - 3 + x + 4x + 3)\|- x - 1 \|x + 3 +--R + +--R +-------------+ +--R 2 | 2 3 2 +--R (- x - 4x - 3)\|- x - 4x - 3 + x + 4x + 3x +--R / +--R +-------------+ +--R 2 | 2 +-------+ +-----+ +--R (2x + 4x + 3)\|- x - 4x - 3 \|- x - 1 \|x + 3 +--R + +--R +-------------+ +--R 3 2 | 2 +--R (2x + 4x + 3x)\|- x - 4x - 3 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 486 +t0330:= 1/(x+(3-2*x-x^2)^(1/2)) +--R +--R +--R 1 +--R (173) -------------------- +--R +-------------+ +--R | 2 +--R \|- x - 2x + 3 + x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 486 +r0330:= atan((3^(1/2)-(3-2*x-x^2)^(1/2))/x)-1/7*atanh(1/7*(1+3^(1/2)-_ + 3^(1/2)*(3^(1/2)-(3-2*x-x^2)^(1/2))/x)*7^(1/2))*7^(1/2)-_ + 1/2*log(1+(3^(1/2)-(3-2*x-x^2)^(1/2))^2/x^2)+1/2*log(2-3^(1/2)-_ + 2*(1+3^(1/2))*(3^(1/2)-(3-2*x-x^2)^(1/2))/x+3^(1/2)*(3^(1/2)-_ + (3-2*x-x^2)^(1/2))^2/x^2) +--R +--R +--R (174) +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R (2x\|3 + 2x - 6)\|- x - 2x + 3 + (- 2x - 4x + 6)\|3 + 2x - 6x +--R 7log(-------------------------------------------------------------------) +--R 2 +--R x +--R + +--R +-------------+ +--R +-+ | 2 +--R - 2\|3 \|- x - 2x + 3 - 2x + 6 +--R - 7log(--------------------------------) +--R 2 +--R x +--R + +--R +-------------+ +--R +-+ +-+ | 2 +-+ +-+ +--R +-+ \|3 \|7 \|- x - 2x + 3 + (x\|3 + x - 3)\|7 +--R - 2\|7 atanh(----------------------------------------------) +--R 7x +--R + +--R +-------------+ +--R | 2 +-+ +--R \|- x - 2x + 3 - \|3 +--R - 14atan(-----------------------) +--R x +--R / +--R 14 +--R Type: Expression(Integer) +--E 178 + +--S 179 of 486 +a0330:= integrate(t0330,x) +--R +--R +--R (175) +--R +-+ +--R \|7 +--R * +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 + 3x)\|- x - 2x + 3 + (x - 3x)\|3 - 3x - 6x + 9 +--R log(-----------------------------------------------------------------) +--R 2 +--R x +--R + +--R - +--R +-+ +--R \|7 +--R * +--R log +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 - 3x)\|- x - 2x + 3 + (- x + 3x)\|3 - 3x +--R + +--R - 6x + 9 +--R / +--R 2 +--R x +--R + +--R log +--R +-------------+ +--R +-+ +-+ +-+ | 2 +--R (((x - 3)\|3 - 3x)\|7 + 7x\|3 )\|- x - 2x + 3 +--R + +--R 2 +-+ 2 +-+ 2 +-+ 2 +--R ((- x + 3x)\|3 + 4x - 6x + 9)\|7 - 7x \|3 + 7x - 21x +--R / +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 - 3x)\|- x - 2x + 3 + (- x + 3x)\|3 - 3x - 6x + 9 +--R + +--R log +--R +-------------+ +--R +-+ +-+ +-+ | 2 +--R (((x - 3)\|3 + 3x)\|7 - 7x\|3 )\|- x - 2x + 3 +--R + +--R 2 +-+ 2 +-+ 2 +-+ 2 +--R ((x - 3x)\|3 + 4x - 6x + 9)\|7 - 7x \|3 - 7x + 21x +--R / +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 + 3x)\|- x - 2x + 3 + (x - 3x)\|3 - 3x - 6x + 9 +--R + +--R +-------------+ +--R | 2 +-+ 2 +-+ +--R +-+ \|- x - 2x + 3 - \|3 (2x + 2x + 4)\|7 + 14x + 7 +--R - 4\|7 atan(-----------------------) + log(----------------------------) +--R x 2 +--R 2x + 2x - 3 +--R + +--R +-+ 2 +--R \|7 log(2x + 2x - 3) +--R / +--R +-+ +--R 4\|7 +--R Type: Union(Expression(Integer),...) +--E 179 + +--S 180 of 486 +m0330:= a0330-r0330 +--R +--R +--R (176) +--R - +--R +-+ +--R 2\|7 +--R * +--R log +--R +-------------+ +--R +-+ | 2 2 +-+ +--R (2x\|3 + 2x - 6)\|- x - 2x + 3 + (- 2x - 4x + 6)\|3 +--R + +--R 2 +--R 2x - 6x +--R / +--R 2 +--R x +--R + +--R +-+ +--R \|7 +--R * +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 + 3x)\|- x - 2x + 3 + (x - 3x)\|3 - 3x - 6x + 9 +--R log(-----------------------------------------------------------------) +--R 2 +--R x +--R + +--R - +--R +-+ +--R \|7 +--R * +--R log +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 - 3x)\|- x - 2x + 3 + (- x + 3x)\|3 - 3x +--R + +--R - 6x + 9 +--R / +--R 2 +--R x +--R + +--R log +--R +-------------+ +--R +-+ +-+ +-+ | 2 +--R (((x - 3)\|3 - 3x)\|7 + 7x\|3 )\|- x - 2x + 3 +--R + +--R 2 +-+ 2 +-+ 2 +-+ 2 +--R ((- x + 3x)\|3 + 4x - 6x + 9)\|7 - 7x \|3 + 7x - 21x +--R / +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 - 3x)\|- x - 2x + 3 + (- x + 3x)\|3 - 3x - 6x + 9 +--R + +--R log +--R +-------------+ +--R +-+ +-+ +-+ | 2 +--R (((x - 3)\|3 + 3x)\|7 - 7x\|3 )\|- x - 2x + 3 +--R + +--R 2 +-+ 2 +-+ 2 +-+ 2 +--R ((x - 3x)\|3 + 4x - 6x + 9)\|7 - 7x \|3 - 7x + 21x +--R / +--R +-------------+ +--R +-+ | 2 2 +-+ 2 +--R ((x - 3)\|3 + 3x)\|- x - 2x + 3 + (x - 3x)\|3 - 3x - 6x + 9 +--R + +--R +-------------+ +--R +-+ | 2 +--R +-+ - 2\|3 \|- x - 2x + 3 - 2x + 6 +--R 2\|7 log(--------------------------------) +--R 2 +--R x +--R + +--R +-------------+ +--R +-+ +-+ | 2 +-+ +-+ +--R \|3 \|7 \|- x - 2x + 3 + (x\|3 + x - 3)\|7 +--R 4atanh(----------------------------------------------) +--R 7x +--R + +--R 2 +-+ +--R (2x + 2x + 4)\|7 + 14x + 7 +-+ 2 +--R log(----------------------------) + \|7 log(2x + 2x - 3) +--R 2 +--R 2x + 2x - 3 +--R / +--R +-+ +--R 4\|7 +--R Type: Expression(Integer) +--E 180 + +--S 181 of 486 +d0330:= D(m0330,x) +--R +--R +--R (177) 0 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 486 +t0331:= (a+b*x+c*x^2)^(1/2)/(d+e*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R \|c x + b x + a +--R (178) ----------------- +--R 2 +--R e x + d +--R Type: Expression(Integer) +--E 182 + +--S 183 of 486 +r0331:= -1/2*(-2*c^(1/2)*atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (b+2*c*x))*d^(1/2)+(c*d-b*d^(1/2)*(-e)^(1/2)-a*e)^(1/2)*_ + atanh(2*(c*d-b*d^(1/2)*(-e)^(1/2)-a*e)^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (b*d^(1/2)-2*a*(-e)^(1/2)+2*x*c*d^(1/2)-x*b*(-e)^(1/2)))+_ + (c*d+b*d^(1/2)*(-e)^(1/2)-a*e)^(1/2)*atanh(2*(c*d+b*d^(1/2)*_ + (-e)^(1/2)-a*e)^(1/2)*(a+b*x+c*x^2)^(1/2)/(b*d^(1/2)+2*a*_ + (-e)^(1/2)+2*x*c*d^(1/2)+x*b*(-e)^(1/2))))/d^(1/2)/e +--R +--R +--R (179) +--R - +--R +-----------------------+ +--R | +---+ +-+ +--R \|b\|- e \|d - a e + c d +--R * +--R +--------------+ +-----------------------+ +--R | 2 | +---+ +-+ +--R 2\|c x + b x + a \|b\|- e \|d - a e + c d +--R atanh(--------------------------------------------) +--R +-+ +---+ +--R (2c x + b)\|d + (b x + 2a)\|- e +--R + +--R - +--R +-------------------------+ +--R | +---+ +-+ +--R \|- b\|- e \|d - a e + c d +--R * +--R +--------------+ +-------------------------+ +--R | 2 | +---+ +-+ +--R 2\|c x + b x + a \|- b\|- e \|d - a e + c d +--R atanh(----------------------------------------------) +--R +-+ +---+ +--R (2c x + b)\|d + (- b x - 2a)\|- e +--R + +--R +--------------+ +--R +-+ | 2 +--R +-+ +-+ 2\|c \|c x + b x + a +--R 2\|c \|d atanh(----------------------) +--R 2c x + b +--R / +--R +-+ +--R 2e\|d +--R Type: Expression(Integer) +--E 183 + +--S 184 of 486 too expensive to compute during test +--a0331:= integrate(t0331,x) +-- +-- +-- (180) +-- [ +-- - +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- - +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-+ +-- 2\|c +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-+ 2 +-- (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x +-- + +-- - 2a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- / +-- 2e +-- , +-- +-- - +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- - +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- | \| 4d e +-- e |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +--------------+ +-- | 2 +-+ +-- +---+ \|c x + b x + a - \|a +-- 4\|- c atan(------------------------) +-- +---+ +-- x\|- c +-- / +-- 2e +-- ] +-- Type: Union(List Expression Integer,...) +--E 184 + +--S 185 of 486 +--m0331a:= a0331.1-r0331 +-- +-- +-- (181) +-- - +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- - +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------+ +-- | +---+ +-+ +-- \|b\|- e \|d - a e + c d +-- * +-- +--------------+ +-----------------------+ +-- | 2 | +---+ +-+ +-- 2\|c x + b x + a \|b\|- e \|d - a e + c d +-- atanh(--------------------------------------------) +-- +-+ +---+ +-- (2c x + b)\|d + (b x + 2a)\|- e +-- + +-- +-------------------------+ +-- | +---+ +-+ +-- \|- b\|- e \|d - a e + c d +-- * +-- +--------------+ +-------------------------+ +-- | 2 | +---+ +-+ +-- 2\|c x + b x + a \|- b\|- e \|d - a e + c d +-- atanh(----------------------------------------------) +-- +-+ +---+ +-- (2c x + b)\|d + (- b x - 2a)\|- e +-- + +-- +-+ +-+ +-- 2\|c \|d +-- * +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-+ 2 +-- (- 2x\|c + 2\|a )\|c x + b x + a + 2x\|a \|c - 2c x - b x - 2a +-- log(-------------------------------------------------------------------) +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- +--------------+ +-- +-+ | 2 +-- +-+ +-+ 2\|c \|c x + b x + a +-- - 2\|c \|d atanh(----------------------) +-- 2c x + b +-- / +-- +-+ +-- 2e\|d +-- Type: Expression Integer +--E 185 + +--S 186 of 486 +--d0331a:= D(m0331a,x) +-- +-- +-- (182) 0 +-- Type: Expression Integer +--E 186 + +--S 187 of 486 +--m0331b:= a0331.2-r0331 +-- +-- +-- (183) +-- - +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- - +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |----------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +-----------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |- 2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |----------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (- 2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +-- +-+ | \| 4d e +-- e\|d |--------------------------- +-- | 2 +-- \| d e +-- * +-- log +-- +---------------------------+ +-- | +-------+ +-- | | 2 +-- | 2 | b +-- |2d e |- ----- - a e + c d +-- | | 3 +--------------+ +-- | \| 4d e | 2 +-- - b e x |--------------------------- + b\|c x + b x + a +-- | 2 +-- \| d e +-- + +-- +-------+ +-- | 2 +-- 2 | b +-+ +-- (2e x |- ----- - b)\|a +-- | 3 +-- \| 4d e +-- / +-- x +-- + +-- +-----------------------+ +-- | +---+ +-+ +-- \|b\|- e \|d - a e + c d +-- * +-- +--------------+ +-----------------------+ +-- | 2 | +---+ +-+ +-- 2\|c x + b x + a \|b\|- e \|d - a e + c d +-- atanh(--------------------------------------------) +-- +-+ +---+ +-- (2c x + b)\|d + (b x + 2a)\|- e +-- + +-- +-------------------------+ +-- | +---+ +-+ +-- \|- b\|- e \|d - a e + c d +-- * +-- +--------------+ +-------------------------+ +-- | 2 | +---+ +-+ +-- 2\|c x + b x + a \|- b\|- e \|d - a e + c d +-- atanh(----------------------------------------------) +-- +-+ +---+ +-- (2c x + b)\|d + (- b x - 2a)\|- e +-- + +-- +--------------+ +-- +-+ | 2 +-- +-+ +-+ 2\|c \|c x + b x + a +-- - 2\|c \|d atanh(----------------------) +-- 2c x + b +-- + +-- +--------------+ +-- | 2 +-+ +-- +---+ +-+ \|c x + b x + a - \|a +-- 4\|- c \|d atan(------------------------) +-- +---+ +-- x\|- c +-- / +-- +-+ +-- 2e\|d +-- Type: Expression Integer +--E 187 + +--S 188 of 486 +--d0331b:= D(m0331b,x) +-- +-- +-- (184) 0 +-- Type: Expression Integer +--E 188 + +--S 189 of 486 +t0332:= x*(a+b*x+c*x^2)^(1/2)/(d+e*x^2) +--R +--R +--R +--------------+ +--R | 2 +--R x\|c x + b x + a +--R (180) ------------------ +--R 2 +--R e x + d +--R Type: Expression(Integer) +--E 189 + +--S 190 of 486 +r0332:= (a+b*x+c*x^2)^(1/2)/e+1/2*b*atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (b+2*c*x))/c^(1/2)/e+1/2*(-c*d-b*d^(1/2)*(-e)^(1/2)+a*e)^(1/2)*_ + atanh(2*e^(1/2)*(-c*d-b*d^(1/2)*(-e)^(1/2)+a*e)^(1/2)*_ + (a+b*x+c*x^2)^(1/2)/(b*d^(1/2)*(-e)^(1/2)-2*a*e+(2*c*d^(1/2)*_ + (-e)^(1/2)-b*e)*x))/e^(3/2)-1/2*(-c*d+b*d^(1/2)*(-e)^(1/2)+_ + a*e)^(1/2)*atanh(2*e^(1/2)*(-c*d+b*d^(1/2)*(-e)^(1/2)+a*e)^(1/2)_ + *(a+b*x+c*x^2)^(1/2)/(b*d^(1/2)*(-e)^(1/2)+2*a*e+_ + (2*c*d^(1/2)*(-e)^(1/2)+b*e)*x))/e^(3/2) +--R +--R +--R (181) +--R - +--R +-----------------------+ +--R +-+ | +---+ +-+ +--R \|c \|b\|- e \|d + a e - c d +--R * +--R +--------------+ +-----------------------+ +--R +-+ | 2 | +---+ +-+ +--R 2\|e \|c x + b x + a \|b\|- e \|d + a e - c d +--R atanh(------------------------------------------------) +--R +---+ +-+ +--R (2c x + b)\|- e \|d + b e x + 2a e +--R + +--R +-------------------------+ +--R +-+ | +---+ +-+ +--R \|c \|- b\|- e \|d + a e - c d +--R * +--R +--------------+ +-------------------------+ +--R +-+ | 2 | +---+ +-+ +--R 2\|e \|c x + b x + a \|- b\|- e \|d + a e - c d +--R atanh(--------------------------------------------------) +--R +---+ +-+ +--R (2c x + b)\|- e \|d - b e x - 2a e +--R + +--R +--------------+ +--R +-+ | 2 +--------------+ +--R +-+ 2\|c \|c x + b x + a +-+ +-+ | 2 +--R b\|e atanh(----------------------) + 2\|c \|e \|c x + b x + a +--R 2c x + b +--R / +--R +-+ +-+ +--R 2e\|c \|e +--R Type: Expression(Integer) +--E 190 + +--S 191 of 486 too expensive to compute during test +--a0332:= integrate(t0332,x) +-- +-- +-- (187) +-- [ +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (2e\|a \|c \|c x + b x + a + (- b e x - 2a e)\|c ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (- 2e\|a \|c \|c x + b x + a + (b e x + 2a e)\|c ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (2e\|a \|c \|c x + b x + a + (- b e x - 2a e)\|c ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (- 2e\|a \|c \|c x + b x + a + (b e x + 2a e)\|c ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |----------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ | 2 2 +-- (2b\|a \|c x + b x + a - b x - 2a b) +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- +--------------+ +-- +-+ | 2 2 +-+ +-+ +-- - 2b x\|c \|c x + b x + a + (4c x + 2b x)\|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- 4e\|a \|c \|c x + b x + a + (- 2b e x - 4a e)\|c +-- , +-- +-- +--------------+ +-- +---+ +-+ | 2 +---+ +-- (2e\|- c \|a \|c x + b x + a + (- b e x - 2a e)\|- c ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ | 2 +---+ +-- (- 2e\|- c \|a \|c x + b x + a + (b e x + 2a e)\|- c ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ | 2 +---+ +-- (2e\|- c \|a \|c x + b x + a + (- b e x - 2a e)\|- c ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ | 2 +---+ +-- (- 2e\|- c \|a \|c x + b x + a + (b e x + 2a e)\|- c ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |----------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ | 2 2 +-- (4b\|a \|c x + b x + a - 2b x - 4a b) +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- +--------------+ +-- +---+ | 2 2 +---+ +-+ +-- - 2b x\|- c \|c x + b x + a + (4c x + 2b x)\|- c \|a +-- / +-- +--------------+ +-- +---+ +-+ | 2 +---+ +-- 4e\|- c \|a \|c x + b x + a + (- 2b e x - 4a e)\|- c +-- ] +-- Type: Union(List Expression Integer,...) +--E 191 + +--S 192 of 486 +--m0332a:= a0332.1-r0332 +-- +-- +-- (188) +-- +--------------+ +-- +-+ +-+ +-+ | 2 +-+ +-+ +-- (2e\|a \|c \|e \|c x + b x + a + (- b e x - 2a e)\|c \|e ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ +-+ | 2 +-+ +-+ +-- (- 2e\|a \|c \|e \|c x + b x + a + (b e x + 2a e)\|c \|e ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |------------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ +-+ | 2 +-+ +-+ +-- (2e\|a \|c \|e \|c x + b x + a + (- b e x - 2a e)\|c \|e ) +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ +-+ | 2 +-+ +-+ +-- (- 2e\|a \|c \|e \|c x + b x + a + (b e x + 2a e)\|c \|e ) +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- - 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (2\|a \|c \|c x + b x + a + (- b x - 2a)\|c ) +-- * +-- +-----------------------+ +-- | +---+ +-+ +-- \|b\|- e \|d + a e - c d +-- * +-- +--------------+ +-----------------------+ +-- +-+ | 2 | +---+ +-+ +-- 2\|e \|c x + b x + a \|b\|- e \|d + a e - c d +-- atanh(------------------------------------------------) +-- +---+ +-+ +-- (2c x + b)\|- e \|d + b e x + 2a e +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-- (- 2\|a \|c \|c x + b x + a + (b x + 2a)\|c ) +-- * +-- +-------------------------+ +-- | +---+ +-+ +-- \|- b\|- e \|d + a e - c d +-- * +-- +--------------+ +-------------------------+ +-- +-+ | 2 | +---+ +-+ +-- 2\|e \|c x + b x + a \|- b\|- e \|d + a e - c d +-- atanh(--------------------------------------------------) +-- +---+ +-+ +-- (2c x + b)\|- e \|d - b e x - 2a e +-- + +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2b\|a \|e \|c x + b x + a + (- b x - 2a b)\|e ) +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c - 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (- 2b\|a \|e \|c x + b x + a + (b x + 2a b)\|e ) +-- * +-- +--------------+ +-- +-+ | 2 +-- 2\|c \|c x + b x + a +-- atanh(----------------------) +-- 2c x + b +-- + +-- +--------------+ +-- +-+ +-+ | 2 +-+ +-+ +-+ +-- 4a\|c \|e \|c x + b x + a + (- 2b x - 4a)\|a \|c \|e +-- / +-- +--------------+ +-- +-+ +-+ +-+ | 2 +-+ +-+ +-- 4e\|a \|c \|e \|c x + b x + a + (- 2b e x - 4a e)\|c \|e +-- Type: Expression Integer +--E 192 + +--S 193 of 486 +--d0332a:= D(m0332a,x) +-- +-- +-- (189) 0 +-- Type: Expression Integer +--E 193 + +--S 194 of 486 +--m0332b:= a0332.2-r0332 +-- +-- +-- (190) +-- +--------------+ +-- +---+ +-+ +-+ +-+ | 2 +-- 2e\|- c \|a \|c \|e \|c x + b x + a +-- + +-- +---+ +-+ +-+ +-- (- b e x - 2a e)\|- c \|c \|e +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ +-+ +-+ | 2 +-- - 2e\|- c \|a \|c \|e \|c x + b x + a +-- + +-- +---+ +-+ +-+ +-- (b e x + 2a e)\|- c \|c \|e +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- 2e x |- --- |------------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ +-+ +-+ | 2 +-- 2e\|- c \|a \|c \|e \|c x + b x + a +-- + +-- +---+ +-+ +-+ +-- (- b e x - 2a e)\|- c \|c \|e +-- * +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |- 2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |------------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-------------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |- 2e |- --- + a e - c d +-- | 2 | | 5 +-- 4 | b d | \| 4e +-- - 2e x |- --- |------------------------- +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- +--------------+ | 2 +-- | 2 3 | b d +-+ +-- b d\|c x + b x + a + (2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ +-+ +-+ | 2 +-- - 2e\|- c \|a \|c \|e \|c x + b x + a +-- + +-- +---+ +-+ +-+ +-- (b e x + 2a e)\|- c \|c \|e +-- * +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- |2e |- --- + a e - c d +-- | | 5 +-- | \| 4e +-- |----------------------- +-- | 3 +-- \| e +-- * +-- log +-- +-----------------------+ +-- | +-----+ +-- | | 2 +-- | 3 | b d +-- +-----+ |2e |- --- + a e - c d +-- | 2 | | 5 +--------------+ +-- 4 | b d | \| 4e | 2 +-- - 2e x |- --- |----------------------- + b d\|c x + b x + a +-- | 5 | 3 +-- \| 4e \| e +-- + +-- +-----+ +-- | 2 +-- 3 | b d +-+ +-- (- 2e x |- --- - b d)\|a +-- | 5 +-- \| 4e +-- / +-- x +-- + +-- +--------------+ +-- +---+ +-+ +-+ | 2 +---+ +-+ +-- (2\|- c \|a \|c \|c x + b x + a + (- b x - 2a)\|- c \|c ) +-- * +-- +-----------------------+ +-- | +---+ +-+ +-- \|b\|- e \|d + a e - c d +-- * +-- +--------------+ +-----------------------+ +-- +-+ | 2 | +---+ +-+ +-- 2\|e \|c x + b x + a \|b\|- e \|d + a e - c d +-- atanh(------------------------------------------------) +-- +---+ +-+ +-- (2c x + b)\|- e \|d + b e x + 2a e +-- + +-- +--------------+ +-- +---+ +-+ +-+ | 2 +---+ +-+ +-- (- 2\|- c \|a \|c \|c x + b x + a + (b x + 2a)\|- c \|c ) +-- * +-- +-------------------------+ +-- | +---+ +-+ +-- \|- b\|- e \|d + a e - c d +-- * +-- +--------------+ +-------------------------+ +-- +-+ | 2 | +---+ +-+ +-- 2\|e \|c x + b x + a \|- b\|- e \|d + a e - c d +-- atanh(--------------------------------------------------) +-- +---+ +-+ +-- (2c x + b)\|- e \|d - b e x - 2a e +-- + +-- +--------------+ +-- +---+ +-+ +-+ | 2 2 +---+ +-+ +-- (- 2b\|- c \|a \|e \|c x + b x + a + (b x + 2a b)\|- c \|e ) +-- * +-- +--------------+ +-- +-+ | 2 +-- 2\|c \|c x + b x + a +-- atanh(----------------------) +-- 2c x + b +-- + +-- +--------------+ +-- +-+ +-+ +-+ | 2 2 +-+ +-+ +-- (4b\|a \|c \|e \|c x + b x + a + (- 2b x - 4a b)\|c \|e ) +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- +--------------+ +-- +---+ +-+ +-+ | 2 +---+ +-+ +-+ +-+ +-- 4a\|- c \|c \|e \|c x + b x + a + (- 2b x - 4a)\|- c \|a \|c \|e +-- / +-- +--------------+ +-- +---+ +-+ +-+ +-+ | 2 +---+ +-+ +-+ +-- 4e\|- c \|a \|c \|e \|c x + b x + a + (- 2b e x - 4a e)\|- c \|c \|e +-- Type: Expression Integer +--E 194 + +--S 195 of 486 +--d0332b:= D(m0332b,x) +-- +-- +-- (191) 0 +-- Type: Expression Integer +--E 195 + +--S 196 of 486 +t0333:= (a+b*x+c*x^2)^(3/2)/(1-x^2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (- c x - b x - a)\|c x + b x + a +--R (182) ----------------------------------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 486 +r0333:= -5/4*b*(a+b*x+c*x^2)^(1/2)-1/2*c*x*(a+b*x+c*x^2)^(1/2)-_ + 1/2*(a-b+c)^(3/2)*atanh(2*(a-b+c)^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (2*a-b+(b-2*c)*x))+1/4*(b-2*c)*(-b+c)*atanh(2*c^(1/2)*_ + (a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(1/2)-1/4*(b+c)*(b+2*c)*_ + atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/(b+2*c*x))/c^(1/2)+_ + 1/8*(b^2-12*a*c)*atanh(2*c^(1/2)*(a+b*x+c*x^2)^(1/2)/_ + (b+2*c*x))/c^(1/2)+1/2*(a+b+c)^(3/2)*atanh(2*(a+b+c)^(1/2)*_ + (a+b*x+c*x^2)^(1/2)/(2*a+b+(b+2*c)*x)) +--R +--R +--R (183) +--R +--------------+ +--R +---------+ | 2 +--R +-+ +---------+ 2\|c + b + a \|c x + b x + a +--R (4c + 4b + 4a)\|c \|c + b + a atanh(------------------------------) +--R (2c + b)x + b + 2a +--R + +--R +--------------+ +--R +-+ | 2 +--R 2 2 2\|c \|c x + b x + a +--R (- 8c - 12a c - 3b )atanh(----------------------) +--R 2c x + b +--R + +--R +--------------+ +--R +---------+ | 2 +--R +---------+ +-+ 2\|c - b + a \|c x + b x + a +--R (4c - 4b + 4a)\|c - b + a \|c atanh(------------------------------) +--R (2c - b)x + b - 2a +--R + +--R +--------------+ +--R +-+ | 2 +--R (- 4c x - 10b)\|c \|c x + b x + a +--R / +--R +-+ +--R 8\|c +--R Type: Expression(Integer) +--E 197 + +--S 198 of 486 too expensive to compute during test +--a0333:= integrate(t0333,x) +-- +-- +-- (194) +-- [ +-- 2 2 +-+ +-+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-+ +---------+ +-- ((16b c - 16b + 16a b)x + 32a c - 32a b + 32a )\|a \|c - b + a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b + 16a b - 16a )c + 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c + 32a b - 32a b)x - 32a c + 32a b - 32a +-- * +-- +---------+ +-+ +-- \|c - b + a \|c +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (- 2x\|c - b + a + (2x + 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x + 2x)\|a \|c - b + a + (- 2c + b - 2a)x + (- b - 2a)x +-- + +-- - 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x + 2)\|a \|c x + b x + a - b x + (- b - 2a)x - 2a +-- + +-- 2 2 3 3 2 2 2 +-+ +-- ((16a c + 4b c)x + (72a b c + 10b )x + (32a c + 40a b )x)\|c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 16b c x + (- 32a c - 56b c)x + (- 88a b c - 30b )x +-- + +-- 2 2 +-- (- 32a c - 40a b )x +-- * +-- +-+ +-+ +-- \|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- , +-- +-- 2 2 +-+ +-+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-----------+ +-- ((32b c - 32b + 32a b)x + 64a c - 64a b + 64a )\|- c + b - a +-- * +-- +--------------+ +-- +-+ +-+ | 2 +-- \|a \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 32a c + (- 8b + 32a b - 32a )c + 8b - 8a b )x +-- + +-- 2 2 2 2 3 +-- (- 64a b c + 64a b - 64a b)x - 64a c + 64a b - 64a +-- * +-- +-----------+ +-+ +-- \|- c + b - a \|c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (- x - 1)\|a +-- atan(---------------------------------) +-- +-----------+ +-- x\|- c + b - a +-- + +-- 2 2 3 3 2 2 2 +-+ +-- ((16a c + 4b c)x + (72a b c + 10b )x + (32a c + 40a b )x)\|c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 16b c x + (- 32a c - 56b c)x + (- 88a b c - 30b )x +-- + +-- 2 2 +-- (- 32a c - 40a b )x +-- * +-- +-+ +-+ +-- \|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- , +-- +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-+ +---------+ +-- ((16b c - 16b + 16a b)x + 32a c - 32a b + 32a )\|a \|c - b + a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b + 16a b - 16a )c + 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c + 32a b - 32a b)x - 32a c + 32a b - 32a +-- * +-- +---------+ +-+ +-- \|c - b + a \|c +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (- 2x\|c - b + a + (2x + 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x + 2x)\|a \|c - b + a + (- 2c + b - 2a)x + (- b - 2a)x +-- + +-- - 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x + 2)\|a \|c x + b x + a - b x + (- b - 2a)x - 2a +-- + +-- 2 2 +-----------+ +-- ((32b c + 32b + 32a b)x + 64a c + 64a b + 64a )\|- c - b - a +-- * +-- +--------------+ +-- +-+ +-+ | 2 +-- \|a \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 32a c + (- 8b - 32a b - 32a )c - 8b - 8a b )x +-- + +-- 2 2 2 2 3 +-- (- 64a b c - 64a b - 64a b)x - 64a c - 64a b - 64a +-- * +-- +-----------+ +-+ +-- \|- c - b - a \|c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (x - 1)\|a +-- atan(-------------------------------) +-- +-----------+ +-- x\|- c - b - a +-- + +-- 2 2 3 3 2 2 2 +-+ +-- ((16a c + 4b c)x + (72a b c + 10b )x + (32a c + 40a b )x)\|c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 16b c x + (- 32a c - 56b c)x + (- 88a b c - 30b )x +-- + +-- 2 2 +-- (- 32a c - 40a b )x +-- * +-- +-+ +-+ +-- \|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- , +-- +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-----------+ +-- ((32b c + 32b + 32a b)x + 64a c + 64a b + 64a )\|- c - b - a +-- * +-- +--------------+ +-- +-+ +-+ | 2 +-- \|a \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 32a c + (- 8b - 32a b - 32a )c - 8b - 8a b )x +-- + +-- 2 2 2 2 3 +-- (- 64a b c - 64a b - 64a b)x - 64a c - 64a b - 64a +-- * +-- +-----------+ +-+ +-- \|- c - b - a \|c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (x - 1)\|a +-- atan(-------------------------------) +-- +-----------+ +-- x\|- c - b - a +-- + +-- 2 2 +-----------+ +-- ((32b c - 32b + 32a b)x + 64a c - 64a b + 64a )\|- c + b - a +-- * +-- +--------------+ +-- +-+ +-+ | 2 +-- \|a \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 32a c + (- 8b + 32a b - 32a )c + 8b - 8a b )x +-- + +-- 2 2 2 2 3 +-- (- 64a b c + 64a b - 64a b)x - 64a c + 64a b - 64a +-- * +-- +-----------+ +-+ +-- \|- c + b - a \|c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (- x - 1)\|a +-- atan(---------------------------------) +-- +-----------+ +-- x\|- c + b - a +-- + +-- 2 2 3 3 2 2 2 +-+ +-- ((16a c + 4b c)x + (72a b c + 10b )x + (32a c + 40a b )x)\|c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 16b c x + (- 32a c - 56b c)x + (- 88a b c - 30b )x +-- + +-- 2 2 +-- (- 32a c - 40a b )x +-- * +-- +-+ +-+ +-- \|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- , +-- +-- 2 2 +---+ +-+ +-- ((8b c + 8b + 8a b)x + 16a c + 16a b + 16a )\|- c \|a +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 8a c + (- 2b - 8a b - 8a )c - 2b - 2a b )x +-- + +-- 2 2 2 2 3 +-- (- 16a b c - 16a b - 16a b)x - 16a c - 16a b - 16a +-- * +-- +---+ +---------+ +-- \|- c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 2 +---+ +-+ +-- ((8b c - 8b + 8a b)x + 16a c - 16a b + 16a )\|- c \|a +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c - b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 8a c + (- 2b + 8a b - 8a )c + 2b - 2a b )x +-- + +-- 2 2 2 2 3 +-- (- 16a b c + 16a b - 16a b)x - 16a c + 16a b - 16a +-- * +-- +---+ +---------+ +-- \|- c \|c - b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (- 2x\|c - b + a + (2x + 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x + 2x)\|a \|c - b + a + (- 2c + b - 2a)x + (- b - 2a)x +-- + +-- - 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x + 2)\|a \|c x + b x + a - b x + (- b - 2a)x - 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((- 32b c - 48a b c - 12b )x - 64a c - 96a c - 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (32a c + (8b + 48a )c + 24a b c + 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (64a b c + 96a b c + 24a b )x + 64a c + 96a c + 24a b +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- 2 2 3 3 2 2 2 +---+ +-- ((8a c + 2b c)x + (36a b c + 5b )x + (16a c + 20a b )x)\|- c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 8b c x + (- 16a c - 28b c)x + (- 44a b c - 15b )x +-- + +-- 2 2 +-- (- 16a c - 20a b )x +-- * +-- +---+ +-+ +-- \|- c \|a +-- / +-- +--------------+ +-- +---+ +-+ | 2 +-- (16b x + 32a)\|- c \|a \|c x + b x + a +-- + +-- 2 2 2 +---+ +-- ((- 16a c - 4b )x - 32a b x - 32a )\|- c +-- , +-- +-- 2 2 +---+ +-+ +-- ((8b c + 8b + 8a b)x + 16a c + 16a b + 16a )\|- c \|a +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 8a c + (- 2b - 8a b - 8a )c - 2b - 2a b )x +-- + +-- 2 2 2 2 3 +-- (- 16a b c - 16a b - 16a b)x - 16a c - 16a b - 16a +-- * +-- +---+ +---------+ +-- \|- c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((- 32b c - 48a b c - 12b )x - 64a c - 96a c - 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (32a c + (8b + 48a )c + 24a b c + 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (64a b c + 96a b c + 24a b )x + 64a c + 96a c + 24a b +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- 2 2 +---+ +-- ((16b c - 16b + 16a b)x + 32a c - 32a b + 32a )\|- c +-- * +-- +--------------+ +-- +-----------+ +-+ | 2 +-- \|- c + b - a \|a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b + 16a b - 16a )c + 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c + 32a b - 32a b)x - 32a c + 32a b - 32a +-- * +-- +---+ +-----------+ +-- \|- c \|- c + b - a +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (- x - 1)\|a +-- atan(---------------------------------) +-- +-----------+ +-- x\|- c + b - a +-- + +-- 2 2 3 3 2 2 2 +---+ +-- ((8a c + 2b c)x + (36a b c + 5b )x + (16a c + 20a b )x)\|- c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 8b c x + (- 16a c - 28b c)x + (- 44a b c - 15b )x +-- + +-- 2 2 +-- (- 16a c - 20a b )x +-- * +-- +---+ +-+ +-- \|- c \|a +-- / +-- +--------------+ +-- +---+ +-+ | 2 +-- (16b x + 32a)\|- c \|a \|c x + b x + a +-- + +-- 2 2 2 +---+ +-- ((- 16a c - 4b )x - 32a b x - 32a )\|- c +-- , +-- +-- 2 2 +---+ +-+ +-- ((8b c - 8b + 8a b)x + 16a c - 16a b + 16a )\|- c \|a +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c - b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 8a c + (- 2b + 8a b - 8a )c + 2b - 2a b )x +-- + +-- 2 2 2 2 3 +-- (- 16a b c + 16a b - 16a b)x - 16a c + 16a b - 16a +-- * +-- +---+ +---------+ +-- \|- c \|c - b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (- 2x\|c - b + a + (2x + 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x + 2x)\|a \|c - b + a + (- 2c + b - 2a)x + (- b - 2a)x +-- + +-- - 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x + 2)\|a \|c x + b x + a - b x + (- b - 2a)x - 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((- 32b c - 48a b c - 12b )x - 64a c - 96a c - 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (32a c + (8b + 48a )c + 24a b c + 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (64a b c + 96a b c + 24a b )x + 64a c + 96a c + 24a b +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- 2 2 +-----------+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|- c - b - a +-- * +-- +--------------+ +-- +---+ +-+ | 2 +-- \|- c \|a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-----------+ +---+ +-- \|- c - b - a \|- c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (x - 1)\|a +-- atan(-------------------------------) +-- +-----------+ +-- x\|- c - b - a +-- + +-- 2 2 3 3 2 2 2 +---+ +-- ((8a c + 2b c)x + (36a b c + 5b )x + (16a c + 20a b )x)\|- c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 8b c x + (- 16a c - 28b c)x + (- 44a b c - 15b )x +-- + +-- 2 2 +-- (- 16a c - 20a b )x +-- * +-- +---+ +-+ +-- \|- c \|a +-- / +-- +--------------+ +-- +---+ +-+ | 2 +-- (16b x + 32a)\|- c \|a \|c x + b x + a +-- + +-- 2 2 2 +---+ +-- ((- 16a c - 4b )x - 32a b x - 32a )\|- c +-- , +-- +-- 2 3 2 2 2 +-+ +-- ((- 32b c - 48a b c - 12b )x - 64a c - 96a c - 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (32a c + (8b + 48a )c + 24a b c + 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (64a b c + 96a b c + 24a b )x + 64a c + 96a c + 24a b +-- * +-- +--------------+ +-- +---+ | 2 +---+ +-+ +-- \|- c \|c x + b x + a - \|- c \|a +-- atan(------------------------------------) +-- c x +-- + +-- 2 2 +-----------+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|- c - b - a +-- * +-- +--------------+ +-- +---+ +-+ | 2 +-- \|- c \|a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-----------+ +---+ +-- \|- c - b - a \|- c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (x - 1)\|a +-- atan(-------------------------------) +-- +-----------+ +-- x\|- c - b - a +-- + +-- 2 2 +---+ +-- ((16b c - 16b + 16a b)x + 32a c - 32a b + 32a )\|- c +-- * +-- +--------------+ +-- +-----------+ +-+ | 2 +-- \|- c + b - a \|a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b + 16a b - 16a )c + 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c + 32a b - 32a b)x - 32a c + 32a b - 32a +-- * +-- +---+ +-----------+ +-- \|- c \|- c + b - a +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (- x - 1)\|a +-- atan(---------------------------------) +-- +-----------+ +-- x\|- c + b - a +-- + +-- 2 2 3 3 2 2 2 +---+ +-- ((8a c + 2b c)x + (36a b c + 5b )x + (16a c + 20a b )x)\|- c +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 2 4 2 2 3 3 2 +-- - 8b c x + (- 16a c - 28b c)x + (- 44a b c - 15b )x +-- + +-- 2 2 +-- (- 16a c - 20a b )x +-- * +-- +---+ +-+ +-- \|- c \|a +-- / +-- +--------------+ +-- +---+ +-+ | 2 +-- (16b x + 32a)\|- c \|a \|c x + b x + a +-- + +-- 2 2 2 +---+ +-- ((- 16a c - 4b )x - 32a b x - 32a )\|- c +-- ] +-- Type: Union(List Expression Integer,...) +--E 198 + +--S 199 of 486 +-m0333a:= a0333.1-r0333 +-- +-- +-- (195) +-- 2 2 +-+ +-+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-+ +---------+ +-- ((16b c - 16b + 16a b)x + 32a c - 32a b + 32a )\|a \|c - b + a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b + 16a b - 16a )c + 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c + 32a b - 32a b)x - 32a c + 32a b - 32a +-- * +-- +---------+ +-+ +-- \|c - b + a \|c +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (- 2x\|c - b + a + (2x + 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x + 2x)\|a \|c - b + a + (- 2c + b - 2a)x + (- b - 2a)x - 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x + 2)\|a \|c x + b x + a - b x + (- b - 2a)x - 2a +-- + +-- 2 2 +-+ +-+ +-- ((- 16b c - 16b - 16a b)x - 32a c - 32a b - 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (16a c + (4b + 16a b + 16a )c + 4b + 4a b )x +-- + +-- 2 2 2 2 3 +-- (32a b c + 32a b + 32a b)x + 32a c + 32a b + 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- +--------------+ +-- +---------+ | 2 +-- 2\|c + b + a \|c x + b x + a +-- atanh(------------------------------) +-- (2c + b)x + b + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- +--------------+ +-- +-+ | 2 +-- 2\|c \|c x + b x + a +-- atanh(----------------------) +-- 2c x + b +-- + +-- 2 2 +-+ +---------+ +-- ((- 16b c + 16b - 16a b)x - 32a c + 32a b - 32a )\|a \|c - b + a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (16a c + (4b - 16a b + 16a )c - 4b + 4a b )x +-- + +-- 2 2 2 2 3 +-- (32a b c - 32a b + 32a b)x + 32a c - 32a b + 32a +-- * +-- +---------+ +-+ +-- \|c - b + a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- 2\|c - b + a \|c x + b x + a +-- atanh(------------------------------) +-- (2c - b)x + b - 2a +-- + +-- +--------------+ +-- 2 2 +-+ | 2 +-- (- 40a b x - 80a b)\|c \|c x + b x + a +-- + +-- 3 2 2 2 +-+ +-+ +-- ((40a b c + 10b )x + 80a b x + 80a b)\|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- Type: Expression(Integer) +--E 199 + +--S 200 of 486 +--d0333a:= D(m0333a,x) +-- +-- +-- (196) 0 +-- Type: Expression Integer +--E 200 + +--S 201 of 486 +--m0333b:= a0333.2-r0333 +-- +-- +-- (197) +-- 2 2 +-+ +-+ +-- ((16b c + 16b + 16a b)x + 32a c + 32a b + 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 16a c + (- 4b - 16a b - 16a )c - 4b - 4a b )x +-- + +-- 2 2 2 2 3 +-- (- 32a b c - 32a b - 32a b)x - 32a c - 32a b - 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- log +-- +--------------+ +-- +---------+ +-+ | 2 +-- (2x\|c + b + a + (2x - 2)\|a )\|c x + b x + a +-- + +-- 2 +-+ +---------+ 2 +-- (2x - 2x)\|a \|c + b + a + (2c + b + 2a)x + (b - 2a)x + 2a +-- / +-- +--------------+ +-- +-+ | 2 2 +-- (2x - 2)\|a \|c x + b x + a - b x + (b - 2a)x + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- log +-- +--------------+ +-- +-+ +-+ | 2 2 +-+ +-- (2\|a \|c + 2c x)\|c x + b x + a + (- 2c x - b x - 2a)\|c +-- + +-- +-+ +-- - 2c x\|a +-- / +-- +--------------+ +-- +-+ | 2 +-- 2\|a \|c x + b x + a - b x - 2a +-- + +-- 2 2 +-+ +-+ +-- ((- 16b c - 16b - 16a b)x - 32a c - 32a b - 32a )\|a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- \|c + b + a \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (16a c + (4b + 16a b + 16a )c + 4b + 4a b )x +-- + +-- 2 2 2 2 3 +-- (32a b c + 32a b + 32a b)x + 32a c + 32a b + 32a +-- * +-- +-+ +---------+ +-- \|c \|c + b + a +-- * +-- +--------------+ +-- +---------+ | 2 +-- 2\|c + b + a \|c x + b x + a +-- atanh(------------------------------) +-- (2c + b)x + b + 2a +-- + +-- 2 3 2 2 2 +-+ +-- ((32b c + 48a b c + 12b )x + 64a c + 96a c + 24a b )\|a +-- * +-- +--------------+ +-- | 2 +-- \|c x + b x + a +-- + +-- 3 2 2 2 2 4 2 +-- (- 32a c + (- 8b - 48a )c - 24a b c - 3b )x +-- + +-- 2 2 3 2 2 3 2 2 +-- (- 64a b c - 96a b c - 24a b )x - 64a c - 96a c - 24a b +-- * +-- +--------------+ +-- +-+ | 2 +-- 2\|c \|c x + b x + a +-- atanh(----------------------) +-- 2c x + b +-- + +-- 2 2 +-+ +---------+ +-- ((- 16b c + 16b - 16a b)x - 32a c + 32a b - 32a )\|a \|c - b + a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (16a c + (4b - 16a b + 16a )c - 4b + 4a b )x +-- + +-- 2 2 2 2 3 +-- (32a b c - 32a b + 32a b)x + 32a c - 32a b + 32a +-- * +-- +---------+ +-+ +-- \|c - b + a \|c +-- * +-- +--------------+ +-- +---------+ | 2 +-- 2\|c - b + a \|c x + b x + a +-- atanh(------------------------------) +-- (2c - b)x + b - 2a +-- + +-- 2 2 +-----------+ +-+ +-- ((32b c - 32b + 32a b)x + 64a c - 64a b + 64a )\|- c + b - a \|a +-- * +-- +--------------+ +-- +-+ | 2 +-- \|c \|c x + b x + a +-- + +-- 2 2 2 3 2 2 +-- (- 32a c + (- 8b + 32a b - 32a )c + 8b - 8a b )x +-- + +-- 2 2 2 2 3 +-- (- 64a b c + 64a b - 64a b)x - 64a c + 64a b - 64a +-- * +-- +-----------+ +-+ +-- \|- c + b - a \|c +-- * +-- +--------------+ +-- | 2 +-+ +-- \|c x + b x + a + (- x - 1)\|a +-- atan(---------------------------------) +-- +-----------+ +-- x\|- c + b - a +-- + +-- +--------------+ +-- 2 2 +-+ | 2 +-- (- 40a b x - 80a b)\|c \|c x + b x + a +-- + +-- 3 2 2 2 +-+ +-+ +-- ((40a b c + 10b )x + 80a b x + 80a b)\|a \|c +-- / +-- +--------------+ +-- +-+ +-+ | 2 +-- (32b x + 64a)\|a \|c \|c x + b x + a +-- + +-- 2 2 2 +-+ +-- ((- 32a c - 8b )x - 64a b x - 64a )\|c +-- Type: Expression(Integer) +--E 201 + +--S 202 of 486 +--d0333b:= D(m0333b,x) +-- +-- +-- (198) 0 +-- Type: Expression(Integer) +--E 202 + +--S 203 of 486 +t0334:= x^(-1-n*q-p*(1+q))*(x^n*(a+b*x^p))^q +--R +--R +--R (- p - n)q - p - 1 n p n q +--R (184) x (b x x + a x ) +--R Type: Expression(Integer) +--E 203 + +--S 204 of 486 +r0334:= -x^(-n-n*q-p*(1+q))*(x^n*(a+b*x^p))^(1+q)/a/p/(1+q) +--R +--R +--R (- p - n)q - p - n n p n q + 1 +--R x (b x x + a x ) +--R (185) - --------------------------------------- +--R a p q + a p +--R Type: Expression(Integer) +--E 204 + +--S 205 of 486 +a0334:= integrate(t0334,x) +--R +--R +--R x +--R ++ (- p - n)q - p - 1 n p n q +--R (186) | %V (b %V %V + a %V ) d%V +--R ++ +--R Type: Union(Expression(Integer),...) +--E 205 + +--S 206 of 486 +m0334:= a0334-r0334 +--R +--R +--R (187) +--R x +--R ++ (- p - n)q - p - 1 n p n q +--R (a p q + a p) | %V (b %V %V + a %V ) d%V +--R ++ +--R + +--R (- p - n)q - p - n n p n q + 1 +--R x (b x x + a x ) +--R / +--R a p q + a p +--R Type: Expression(Integer) +--E 206 + +--S 207 of 486 +d0334:= D(m0334,x) +--R +--R +--R (188) +--R (- p - n)q - p - n - 1 n p n q + 1 +--R (- p - n)x (b x x + a x ) +--R + +--R (- p - n)q - p - n n - 1 p (- p - n)q - p - n n p - 1 +--R b n x x x + b p x x x +--R + +--R (- p - n)q - p - n n - 1 (- p - n)q - p - 1 +--R a n x x + a p x +--R * +--R n p n q +--R (b x x + a x ) +--R / +--R a p +--R Type: Expression(Integer) +--E 207 + +--S 208 of 486 +t0335:= x^(-1+n-p*(1+q))*(a*x^n+b*x^p)^q +--R +--R +--R - p q - p + n - 1 p n q +--R (189) x (b x + a x ) +--R Type: Expression(Integer) +--E 208 + +--S 209 of 486 +r0335:= (x^n*(a+b*x^(-n+p)))^(1+q)/(x^(p*(1+q)))/a/(n-p)/(1+q) +--R +--R +--R n p - n n q + 1 +--R (b x x + a x ) +--R (190) - ---------------------------------- +--R p q + p +--R ((a p - a n)q + a p - a n)x +--R Type: Expression(Integer) +--E 209 + +--S 210 of 486 +a0335:= integrate(t0335,x) +--R +--R +--R x +--R ++ - p q - p + n - 1 p n q +--R (191) | %V (b %V + a %V ) d%V +--R ++ +--R Type: Union(Expression(Integer),...) +--E 210 + +--S 211 of 486 +m0335:= a0335-r0335 +--R +--R +--R (192) +--R p q + p +--R ((a p - a n)q + a p - a n)x +--R * +--R x +--R ++ - p q - p + n - 1 p n q +--R | %V (b %V + a %V ) d%V +--R ++ +--R + +--R n p - n n q + 1 +--R (b x x + a x ) +--R / +--R p q + p +--R ((a p - a n)q + a p - a n)x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 486 +d0335:= D(m0335,x) +--R +--R +--R (193) +--R - p q - p + n - 1 p q + p 2 p n q +--R (a p - a n)x (x ) (b x + a x ) +--R + +--R p q + p - 1 n p - n n q + 1 +--R - p x (b x x + a x ) +--R + +--R n - 1 p - n n p - n - 1 n - 1 p q + p +--R (b n x x + (b p - b n)x x + a n x )x +--R * +--R n p - n n q +--R (b x x + a x ) +--R / +--R p q + p 2 +--R (a p - a n)(x ) +--R Type: Expression(Integer) +--E 212 + +--S 213 of 486 +t0336:= 1/2*x^(-1+m)*(2*a*m+b*(2*m-n)*x^n)/(a+b*x^n)^(3/2) +--R +--R +--R m - 1 n m - 1 +--R (- b n + 2b m)x x + 2a m x +--R (194) ------------------------------------ +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 213 + +--S 214 of 486 +r0336:= x^m/(a+b*x^n)^(1/2) +--R +--R +--R m +--R x +--R (195) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 486 +a0336:= integrate(t0336,x) +--R +--R +--R +----------------+ +--R (m - 1)log(x) | n log(x) +--R x %e \|b %e + a +--R (196) ------------------------------------ +--R n log(x) +--R b %e + a +--R Type: Union(Expression(Integer),...) +--E 215 + +--S 216 of 486 +m0336:= a0336-r0336 +--R +--R +--R (197) +--R +--------+ +----------------+ +--R (m - 1)log(x) | n | n log(x) m n log(x) m +--R x %e \|b x + a \|b %e + a - b x %e - a x +--R ----------------------------------------------------------------------- +--R +--------+ +--R n log(x) | n +--R (b %e + a)\|b x + a +--R Type: Expression(Integer) +--E 216 + +--S 217 of 486 +d0336:= D(m0336,x) +--R +--R +--R (198) +--R 2 m - 1 n 2 m n - 1 m - 1 n log(x) +--R (- 2b m x x + b n x x - 2a b m x )%e +--R + +--R m - 1 n m n - 1 2 m - 1 +--R - 2a b m x x + a b n x x - 2a m x +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R 2 2 n (m - 1)log(x) n log(x) +--R ((- b n + 2b m)x - a b n + 2a b m)%e %e +--R + +--R n 2 (m - 1)log(x) +--R (2a b m x + 2a m)%e +--R * +--R +--------+ +--R | n +--R \|b x + a +--R / +--R +--------+ +----------------+ +--R 2 n n log(x) n 2 | n | n log(x) +--R ((2b x + 2a b)%e + 2a b x + 2a )\|b x + a \|b %e + a +--R Type: Expression(Integer) +--E 217 + +--S 218 of 486 +t0337:= -1/2*b*n*x^(-1+m+n)/(a+b*x^n)^(3/2)+m*x^(-1+m)/(a+b*x^n)^(1/2) +--R +--R +--R n + m - 1 m - 1 n m - 1 +--R - b n x + 2b m x x + 2a m x +--R (199) ---------------------------------------------- +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 218 + +--S 219 of 486 +r0337:= x^m/(a+b*x^n)^(1/2) +--R +--R +--R m +--R x +--R (200) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 486 +--a0337:= integrate(t0337,x) +--E 220 + +--S 221 of 486 +--m0337:= a0337-r0337 +--E 221 + +--S 222 of 486 +--d0337:= D(m0337,x) +-- 2 >> Error detected within library code: +-- integrate: implementation incomplete (constant residues) +--E 222 + +--S 223 of 486 +t0338:= a*(2+m)*x^(1+m)/(a+b*x^2)^(1/2)+b*(3+m)*x^(3+m)/(a+b*x^2)^(1/2) +--R +--R +--R m + 3 m + 1 +--R (b m + 3b)x + (a m + 2a)x +--R (201) ----------------------------------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 223 + +--S 224 of 486 +r0338:= x^(2+m)*(a+b*x^2)^(1/2) +--R +--R +--R +--------+ +--R m + 2 | 2 +--R (202) x \|b x + a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 486 +a0338:= integrate(t0338,x) +--R +--R +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R (203) ---------------------------------------------------------------- +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Union(Expression(Integer),...) +--E 225 + +--S 226 of 486 +m0338:= a0338-r0338 +--R +--R +--R (204) +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R + +--R +--------+ +--R 2 m + 2 | 2 2 m + 2 +-+ +--R (b x + 2a)x \|b x + a + (- 2b x - 2a)x \|a +--R / +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 486 +d0338:= D(m0338,x) +--R +--R +--R (205) +--R 2 (m + 1)log(x) m + 2 +--R ((b m + 3b)x + a m + 2a)%e - b x x +--R + +--R 2 m + 1 +--R ((- b m - 2b)x - a m - 2a)x +--R / +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 227 + +--S 228 of 486 +t0339:= 1/2/(a+b*x^n)^(3/2)/x*(2*x^m*a*m+2*x^(m+n)*m*b-x^(m+n)*b*n) +--R +--R +--R n + m m +--R (- b n + 2b m)x + 2a m x +--R (206) ------------------------------ +--R +--------+ +--R n | n +--R (2b x x + 2a x)\|b x + a +--R Type: Expression(Integer) +--E 228 + +--S 229 of 486 +r0339:= x^m/(a+b*x^n)^(1/2) +--R +--R +--R m +--R x +--R (207) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 486 +--a0339:= integrate(t0339,x) +--E 230 + +--S 231 of 486 +--m0339:= a0339-r0339 +--E 231 + +--S 232 of 486 +--d0339:= D(m0339,x) +-- 2 >> Error detected within library code: +-- integrate: implementation incomplete (constant residues) +--E 232 + +--S 233 of 486 +t0340:= x^m*m/x/(a+b*x^n)^(1/2)-1/2*x^m/(a+b*x^n)^(3/2)*b*x^n*n/x +--R +--R +--R m n m +--R (- b n + 2b m)x x + 2a m x +--R (208) ---------------------------- +--R +--------+ +--R n | n +--R (2b x x + 2a x)\|b x + a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 486 +r0340:= x^m/(a+b*x^n)^(1/2) +--R +--R +--R m +--R x +--R (209) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 234 + +--S 235 of 486 +a0340:= integrate(t0340,x) +--R +--R +--R +----------------+ +--R m log(x) | n log(x) +--R %e \|b %e + a +--R (210) ----------------------------- +--R n log(x) +--R b %e + a +--R Type: Union(Expression(Integer),...) +--E 235 + +--S 236 of 486 +m0340:= a0340-r0340 +--R +--R +--R +--------+ +----------------+ +--R m log(x) | n | n log(x) m n log(x) m +--R %e \|b x + a \|b %e + a - b x %e - a x +--R (211) ---------------------------------------------------------------- +--R +--------+ +--R n log(x) | n +--R (b %e + a)\|b x + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 486 +d0340:= D(m0340,x) +--R +--R +--R (212) +--R 2 m - 1 n 2 m n - 1 m - 1 n log(x) +--R (- 2b m x x x + b n x x x - 2a b m x x )%e +--R + +--R m - 1 n m n - 1 2 m - 1 +--R - 2a b m x x x + a b n x x x - 2a m x x +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R 2 2 n m log(x) n log(x) +--R ((- b n + 2b m)x - a b n + 2a b m)%e %e +--R + +--R n 2 m log(x) +--R (2a b m x + 2a m)%e +--R * +--R +--------+ +--R | n +--R \|b x + a +--R / +--R +--------+ +--R 2 n n log(x) n 2 | n +--R ((2b x x + 2a b x)%e + 2a b x x + 2a x)\|b x + a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R Type: Expression(Integer) +--E 237 + +--S 238 of 486 +t0341:= (x^(-2+2*n)*(a+b*x^n))^(1/2) +--R +--R +--R +-----------------+ +--R | n 2n - 2 +--R (213) \|(b x + a)x +--R Type: Expression(Integer) +--E 238 + +--S 239 of 486 +r0341:= 2/3*x^(3-3*n)*((a+b*x^n)/(x^(2-2*n)))^(3/2)/b/n +--R +--R +--R +---------+ +--R | n +--R - 3n + 3 n - 3n + 3 | b x + a +--R (2b x x + 2a x ) |--------- +--R | - 2n + 2 +--R \|x +--R (214) ------------------------------------------- +--R - 2n + 2 +--R 3b n x +--R Type: Expression(Integer) +--E 239 + +--S 240 of 486 +a0341:= integrate(t0341,x) +--R +--R +--R +----------------+ +--R n log(x) | n log(x) +--R (2b %e + 2a)\|b %e + a +--R (215) --------------------------------------- +--R 3b n +--R Type: Union(Expression(Integer),...) +--E 240 + +--S 241 of 486 +m0341:= a0341-r0341 +--R +--R +--R (216) +--R +----------------+ +--R - 2n + 2 n log(x) - 2n + 2 | n log(x) +--R (2b x %e + 2a x )\|b %e + a +--R + +--R +---------+ +--R | n +--R - 3n + 3 n - 3n + 3 | b x + a +--R (- 2b x x - 2a x ) |--------- +--R | - 2n + 2 +--R \|x +--R / +--R - 2n + 2 +--R 3b n x +--R Type: Expression(Integer) +--E 241 + +--S 242 of 486 +d0341:= D(m0341,x) +--R +--R +--R (217) +--R 2 2 - 3n + 3 - 2n + 1 - 2n + 2 2 +--R (- 2b n + 2b )x x x (x ) +--R + +--R 2 2 - 4n + 4 - 3n + 2 - 2n + 2 +--R (6b n - 6b )x x x x +--R + +--R 2 2 - 4n + 4 - 3n + 3 - 2n + 1 +--R (- 4b n + 4b )x x x x +--R * +--R n 2 +--R (x ) +--R + +--R 2 - 3n + 3 - 2n + 2 3 +--R - b n x x (x ) +--R + +--R 2 - 4n + 4 - 3n + 3 - 2n + 2 +--R - 2b n x x x x +--R * +--R n - 1 +--R x +--R + +--R - 3n + 3 - 2n + 1 - 2n + 2 2 +--R (- 4a b n + 4a b)x x x (x ) +--R + +--R - 4n + 4 - 3n + 2 - 2n + 2 +--R (12a b n - 12a b)x x x x +--R + +--R - 4n + 4 - 3n + 3 - 2n + 1 +--R (- 8a b n + 8a b)x x x x +--R * +--R n +--R x +--R + +--R - 3n + 3 - 2n + 2 3 +--R - a b n x x (x ) +--R + +--R - 4n + 4 - 3n + 3 - 2n + 2 +--R - 2a b n x x x x +--R * +--R n - 1 +--R x +--R + +--R 2 2 - 3n + 3 - 2n + 1 - 2n + 2 2 +--R (- 2a n + 2a )x x x (x ) +--R + +--R 2 2 - 4n + 4 - 3n + 2 - 2n + 2 +--R (6a n - 6a )x x x x +--R + +--R 2 2 - 4n + 4 - 3n + 3 - 2n + 1 +--R (- 4a n + 4a )x x x x +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R 2 - 4n + 4 - 2n + 2 3 n log(x) 2 +--R 3b n x (x ) (%e ) +--R + +--R - 4n + 4 - 2n + 2 3 n log(x) +--R 3a b n x (x ) %e +--R * +--R +---------+ +--R | n +--R | b x + a +--R |--------- +--R | - 2n + 2 +--R \|x +--R / +--R +---------+ +--R | n +----------------+ +--R - 4n + 4 - 2n + 2 3 | b x + a | n log(x) +--R 3b n x x (x ) |--------- \|b %e + a +--R | - 2n + 2 +--R \|x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 486 +t0342:= (x^(-3+3*n)*(a+b*x^n))^(1/3) +--R +--R +--R +-----------------+ +--R 3| n 3n - 3 +--R (218) \|(b x + a)x +--R Type: Expression(Integer) +--E 243 + +--S 244 of 486 +r0342:= 3/4*x^(4-4*n)*((a+b*x^n)/(x^(3-3*n)))^(4/3)/b/n +--R +--R +--R +---------+ +--R | n +--R - 4n + 4 n - 4n + 4 | b x + a +--R (3b x x + 3a x ) |--------- +--R 3| - 3n + 3 +--R \|x +--R (219) ------------------------------------------- +--R - 3n + 3 +--R 4b n x +--R Type: Expression(Integer) +--E 244 + +--S 245 of 486 +a0342:= integrate(t0342,x) +--R +--R +--R +----------------+ +--R n log(x) 3| n log(x) +--R (3b %e + 3a)\|b %e + a +--R (220) --------------------------------------- +--R 4b n +--R Type: Union(Expression(Integer),...) +--E 245 + +--S 246 of 486 +m0342:= a0342-r0342 +--R +--R +--R (221) +--R +----------------+ +--R - 3n + 3 n log(x) - 3n + 3 3| n log(x) +--R (3b x %e + 3a x )\|b %e + a +--R + +--R +---------+ +--R | n +--R - 4n + 4 n - 4n + 4 | b x + a +--R (- 3b x x - 3a x ) |--------- +--R 3| - 3n + 3 +--R \|x +--R / +--R - 3n + 3 +--R 4b n x +--R Type: Expression(Integer) +--E 246 + +--S 247 of 486 +d0342:= D(m0342,x) +--R +--R +--R (222) +--R 2 2 - 4n + 4 - 3n + 2 - 3n + 3 2 +--R (- 3b n + 3b )x x x (x ) +--R + +--R 2 2 - 6n + 6 - 4n + 3 - 3n + 3 +--R (12b n - 12b )x x x x +--R + +--R 2 2 - 6n + 6 - 4n + 4 - 3n + 2 +--R (- 9b n + 9b )x x x x +--R * +--R n 2 +--R (x ) +--R + +--R 2 - 4n + 4 - 3n + 3 3 +--R - b n x x (x ) +--R + +--R 2 - 6n + 6 - 4n + 4 - 3n + 3 +--R - 3b n x x x x +--R * +--R n - 1 +--R x +--R + +--R - 4n + 4 - 3n + 2 - 3n + 3 2 +--R (- 6a b n + 6a b)x x x (x ) +--R + +--R - 6n + 6 - 4n + 3 - 3n + 3 +--R (24a b n - 24a b)x x x x +--R + +--R - 6n + 6 - 4n + 4 - 3n + 2 +--R (- 18a b n + 18a b)x x x x +--R * +--R n +--R x +--R + +--R - 4n + 4 - 3n + 3 3 +--R - a b n x x (x ) +--R + +--R - 6n + 6 - 4n + 4 - 3n + 3 +--R - 3a b n x x x x +--R * +--R n - 1 +--R x +--R + +--R 2 2 - 4n + 4 - 3n + 2 - 3n + 3 2 +--R (- 3a n + 3a )x x x (x ) +--R + +--R 2 2 - 6n + 6 - 4n + 3 - 3n + 3 +--R (12a n - 12a )x x x x +--R + +--R 2 2 - 6n + 6 - 4n + 4 - 3n + 2 +--R (- 9a n + 9a )x x x x +--R * +--R +----------------+2 +--R 3| n log(x) +--R \|b %e + a +--R + +--R 2 - 6n + 6 - 3n + 3 3 n log(x) 2 +--R 4b n x (x ) (%e ) +--R + +--R - 6n + 6 - 3n + 3 3 n log(x) +--R 4a b n x (x ) %e +--R * +--R +---------+2 +--R | n +--R | b x + a +--R |--------- +--R 3| - 3n + 3 +--R \|x +--R / +--R +---------+2 +--R | n +----------------+2 +--R - 6n + 6 - 3n + 3 3 | b x + a 3| n log(x) +--R 4b n x x (x ) |--------- \|b %e + a +--R 3| - 3n + 3 +--R \|x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 486 +t0343:= (x^(-4+4*n)*(a+b*x^n))^(1/4) +--R +--R +--R +-----------------+ +--R 4| n 4n - 4 +--R (223) \|(b x + a)x +--R Type: Expression(Integer) +--E 248 + +--S 249 of 486 +r0343:= 4/5*x^(5-5*n)*((a+b*x^n)/(x^(4-4*n)))^(5/4)/b/n +--R +--R +--R +---------+ +--R | n +--R - 5n + 5 n - 5n + 5 | b x + a +--R (4b x x + 4a x ) |--------- +--R 4| - 4n + 4 +--R \|x +--R (224) ------------------------------------------- +--R - 4n + 4 +--R 5b n x +--R Type: Expression(Integer) +--E 249 + +--S 250 of 486 +a0343:= integrate(t0343,x) +--R +--R +--R +----------------+ +--R n log(x) 4| n log(x) +--R (4b %e + 4a)\|b %e + a +--R (225) --------------------------------------- +--R 5b n +--R Type: Union(Expression(Integer),...) +--E 250 + +--S 251 of 486 +m0343:= a0343-r0343 +--R +--R +--R (226) +--R +----------------+ +--R - 4n + 4 n log(x) - 4n + 4 4| n log(x) +--R (4b x %e + 4a x )\|b %e + a +--R + +--R +---------+ +--R | n +--R - 5n + 5 n - 5n + 5 | b x + a +--R (- 4b x x - 4a x ) |--------- +--R 4| - 4n + 4 +--R \|x +--R / +--R - 4n + 4 +--R 5b n x +--R Type: Expression(Integer) +--E 251 + +--S 252 of 486 +d0343:= D(m0343,x) +--R +--R +--R (227) +--R 2 2 - 5n + 5 - 4n + 3 - 4n + 4 2 +--R (- 4b n + 4b )x x x (x ) +--R + +--R 2 2 - 8n + 8 - 5n + 4 - 4n + 4 +--R (20b n - 20b )x x x x +--R + +--R 2 2 - 8n + 8 - 5n + 5 - 4n + 3 +--R (- 16b n + 16b )x x x x +--R * +--R n 2 +--R (x ) +--R + +--R 2 - 5n + 5 - 4n + 4 3 +--R - b n x x (x ) +--R + +--R 2 - 8n + 8 - 5n + 5 - 4n + 4 +--R - 4b n x x x x +--R * +--R n - 1 +--R x +--R + +--R - 5n + 5 - 4n + 3 - 4n + 4 2 +--R (- 8a b n + 8a b)x x x (x ) +--R + +--R - 8n + 8 - 5n + 4 - 4n + 4 +--R (40a b n - 40a b)x x x x +--R + +--R - 8n + 8 - 5n + 5 - 4n + 3 +--R (- 32a b n + 32a b)x x x x +--R * +--R n +--R x +--R + +--R - 5n + 5 - 4n + 4 3 +--R - a b n x x (x ) +--R + +--R - 8n + 8 - 5n + 5 - 4n + 4 +--R - 4a b n x x x x +--R * +--R n - 1 +--R x +--R + +--R 2 2 - 5n + 5 - 4n + 3 - 4n + 4 2 +--R (- 4a n + 4a )x x x (x ) +--R + +--R 2 2 - 8n + 8 - 5n + 4 - 4n + 4 +--R (20a n - 20a )x x x x +--R + +--R 2 2 - 8n + 8 - 5n + 5 - 4n + 3 +--R (- 16a n + 16a )x x x x +--R * +--R +----------------+3 +--R 4| n log(x) +--R \|b %e + a +--R + +--R 2 - 8n + 8 - 4n + 4 3 n log(x) 2 +--R 5b n x (x ) (%e ) +--R + +--R - 8n + 8 - 4n + 4 3 n log(x) +--R 5a b n x (x ) %e +--R * +--R +---------+3 +--R | n +--R | b x + a +--R |--------- +--R 4| - 4n + 4 +--R \|x +--R / +--R +---------+3 +--R | n +----------------+3 +--R - 8n + 8 - 4n + 4 3 | b x + a 4| n log(x) +--R 5b n x x (x ) |--------- \|b %e + a +--R 4| - 4n + 4 +--R \|x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 486 +t0344:= (x^(p*(-1+n))*(a+b*x^n))^(1/p) +--R +--R +--R 1 +--R - +--R n (n - 1)p p +--R (228) ((b x + a)x ) +--R Type: Expression(Integer) +--E 253 + +--S 254 of 486 +r0344:= x^((1-n)*(p+1))*((a+b*x^n)/(x^((1-n)*p)))^(1+1/p)/b/n/(1+1/p) +--R +--R +--R p + 1 +--R ----- +--R n p +--R (- n + 1)p - n + 1 b x + a +--R p x (-----------) +--R (- n + 1)p +--R x +--R (229) --------------------------------------- +--R b n p + b n +--R Type: Expression(Integer) +--E 254 + +--S 255 of 486 +a0344:= integrate(t0344,x) +--R +--R +--R 1 +--R x - +--R ++ n (n - 1)p p +--R (230) | ((b %V + a)%V ) d%V +--R ++ +--R Type: Union(Expression(Integer),...) +--E 255 + +--S 256 of 486 +m0344:= a0344-r0344 +--R +--R +--R (231) +--R 1 +--R x - +--R ++ n (n - 1)p p +--R (b n p + b n) | ((b %V + a)%V ) d%V +--R ++ +--R + +--R p + 1 +--R ----- +--R n p +--R (- n + 1)p - n + 1 b x + a +--R - p x (-----------) +--R (- n + 1)p +--R x +--R / +--R b n p + b n +--R Type: Expression(Integer) +--E 256 + +--S 257 of 486 +d0344:= D(m0344,x) +--R +--R +--R (232) +--R 1 +--R - +--R (- 2n + 2)p n (n - 1)p p +--R b n x ((b x + a)x ) +--R + +--R p + 1 +--R ----- +--R n p +--R (- 2n + 2)p (- n + 1)p - n b x + a +--R (n - 1)p x x (-----------) +--R (- n + 1)p +--R x +--R + +--R (- n + 1)p - n + 1 (- n + 1)p - 1 n +--R (- b n + b)p x x x +--R + +--R (- n + 1)p - n + 1 (- n + 1)p n - 1 +--R - b n x x x +--R + +--R (- n + 1)p - n + 1 (- n + 1)p - 1 +--R (- a n + a)p x x +--R * +--R 1 +--R - +--R n p +--R b x + a +--R (-----------) +--R (- n + 1)p +--R x +--R / +--R (- 2n + 2)p +--R b n x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 486 +t0345:= (x^((-1+n)/p)*(a+b*x^n))^p +--R +--R +--R n - 1 n - 1 p +--R ----- ----- +--R p n p +--R (233) (b x x + a x ) +--R Type: Expression(Integer) +--E 258 + +--S 259 of 486 +r0345:= 1/b/n/(p+1)*(x^((-1+n)/p)*(a+b*x^n))^p*(a*x^(1-n)+b*x) +--R +--R +--R n - 1 n - 1 p +--R ----- ----- +--R - n + 1 p n p +--R (a x + b x)(b x x + a x ) +--R (234) ------------------------------------------ +--R b n p + b n +--R Type: Expression(Integer) +--E 259 + +--S 260 of 486 +a0345:= integrate(t0345,x) +--R +--R +--R n - 1 n - 1 p +--R x ----- ----- +--R ++ p n p +--R (235) | (b %V %V + a %V ) d%V +--R ++ +--R Type: Union(Expression(Integer),...) +--E 260 + +--S 261 of 486 +m0345:= a0345-r0345 +--R +--R +--R (236) +--R n - 1 n - 1 p +--R x ----- ----- +--R ++ p n p +--R (b n p + b n) | (b %V %V + a %V ) d%V +--R ++ +--R + +--R n - 1 n - 1 p +--R ----- ----- +--R - n + 1 p n p +--R (- a x - b x)(b x x + a x ) +--R / +--R b n p + b n +--R Type: Expression(Integer) +--E 261 + +--S 262 of 486 +d0345:= D(m0345,x) +--R +--R +--R (237) +--R n - 1 n - 1 p +--R ----- ----- +--R - n p n p +--R ((a n - a)x + b n p + b n - b)(b x x + a x ) +--R + +--R - p + n - 1 +--R ----------- +--R - n + 1 2 2 p n +--R ((- a b n + a b)x + (- b n + b )x)x x +--R + +--R n - 1 +--R ----- +--R - n + 1 2 p n - 1 +--R (- a b n p x - b n p x)x x +--R + +--R - p + n - 1 +--R ----------- +--R 2 2 - n + 1 p +--R ((- a n + a )x + (- a b n + a b)x)x +--R * +--R n - 1 n - 1 p - 1 +--R ----- ----- +--R p n p +--R (b x x + a x ) +--R / +--R b n p + b n +--R Type: Expression(Integer) +--E 262 + +--S 263 of 486 +t0346:= 1/(a+b/x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R 1 +--R (238) ---------------------- +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|d x + c +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 263 + +--S 264 of 486 +r0346:= (b+a*x^2)^(1/2)*atanh(d^(1/2)*(b+a*x^2)^(1/2)/a^(1/2)/_ + (c+d*x^2)^(1/2))/a^(1/2)/d^(1/2)/(a+b/x^2)^(1/2)/x +--R +--R +--R +--------+ +--R +--------+ +-+ | 2 +--R | 2 \|d \|a x + b +--R \|a x + b atanh(---------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|d x + c +--R (239) --------------------------------- +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R x\|a |-------- \|d +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 486 +--a0346:= integrate(t0346,x) +--E 265 + +--S 266 of 486 +--m0346:= a0346-r0346 +--E 266 + +--S 267 of 486 +--d0346:= D(m0346,x) +--E 267 + +--S 268 of 486 +t0347:= x^m/(a+b*x^(2+2*m)) +--R +--R +--R m +--R x +--R (240) ------------- +--R 2m + 2 +--R b x + a +--R Type: Expression(Integer) +--E 268 + +--S 269 of 486 +r0347:= atan(b^(1/2)*x^(1+m)/a^(1/2))/a^(1/2)/b^(1/2)/(1+m) +--R +--R +--R m + 1 +-+ +--R x \|b +--R atan(----------) +--R +-+ +--R \|a +--R (241) ---------------- +--R +-+ +-+ +--R (m + 1)\|a \|b +--R Type: Expression(Integer) +--E 269 + +--S 270 of 486 +a0347:= integrate(t0347,x) +--R +--R +--R (242) +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R [--------------------------------------------------------------, +--R +-----+ +--R (2m + 2)\|- a b +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R -----------------------] +--R +---+ +--R (m + 1)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 270 + +--S 271 of 486 +m0347a:= a0347.1-r0347 +--R +--R +--R (243) +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R +-+ +-+ b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R \|a \|b log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R m + 1 +-+ +--R +-----+ x \|b +--R - 2\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R (2m + 2)\|- a b \|a \|b +--R Type: Expression(Integer) +--E 271 + +--S 272 of 486 +d0347a:= D(m0347a,x) +--R +--R +--R 2 m m log(x) 2 m + 1 2 m log(x) m +--R - b x x (%e ) + (b (x ) + a)%e - a x +--R (244) ---------------------------------------------------------- +--R 2 2 m + 1 2 2 m log(x) 2 m + 1 2 2 +--R (b x (x ) + a b x )(%e ) + a b (x ) + a +--R Type: Expression(Integer) +--E 272 + +--S 273 of 486 +m0347b:= a0347.2-r0347 +--R +--R +--R +---+ m log(x) m + 1 +-+ +--R +-+ +-+ x\|a b %e +---+ x \|b +--R \|a \|b atan(-----------------) - \|a b atan(----------) +--R a +-+ +--R \|a +--R (245) -------------------------------------------------------- +--R +-+ +-+ +---+ +--R (m + 1)\|a \|b \|a b +--R Type: Expression(Integer) +--E 273 + +--S 274 of 486 +d0347b:= D(m0347b,x) +--R +--R +--R 2 m m log(x) 2 m + 1 2 m log(x) m +--R - b x x (%e ) + (b (x ) + a)%e - a x +--R (246) ---------------------------------------------------------- +--R 2 2 m + 1 2 2 m log(x) 2 m + 1 2 2 +--R (b x (x ) + a b x )(%e ) + a b (x ) + a +--R Type: Expression(Integer) +--E 274 + +--S 275 of 486 +t0348:= x^m/(a+b*x^(2+2*m))^2 +--R +--R +--R m +--R x +--R (247) -------------------------------- +--R 2 2m + 2 2 2m + 2 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 486 +r0348:= 1/2*x^(1+m)/a/(1+m)/(a+b*x^(2+2*m))+1/2*atan(b^(1/2)*x^(1+m)/_ + a^(1/2))/a^(3/2)/b^(1/2)/(1+m) +--R +--R +--R m + 1 +-+ +--R 2m + 2 x \|b m + 1 +-+ +-+ +--R (b x + a)atan(----------) + x \|a \|b +--R +-+ +--R \|a +--R (248) ------------------------------------------------ +--R 2m + 2 2 2 +-+ +-+ +--R ((2a b m + 2a b)x + 2a m + 2a )\|a \|b +--R Type: Expression(Integer) +--E 276 + +--S 277 of 486 +a0348:= integrate(t0348,x) +--R +--R +--R (249) +--R [ +--R 2 m log(x) 2 +--R (b x (%e ) + a) +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R +-----+ m log(x) +--R 2x\|- a b %e +--R / +--R 2 +-----+ m log(x) 2 2 2 +-----+ +--R (4a b m + 4a b)x \|- a b (%e ) + (4a m + 4a )\|- a b +--R , +--R +---+ m log(x) +--R 2 m log(x) 2 x\|a b %e +---+ m log(x) +--R (b x (%e ) + a)atan(-----------------) + x\|a b %e +--R a +--R ------------------------------------------------------------------] +--R 2 +---+ m log(x) 2 2 2 +---+ +--R (2a b m + 2a b)x \|a b (%e ) + (2a m + 2a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 277 + +--S 278 of 486 +m0348a:= a0348.1-r0348 +--R +--R +--R (250) +--R 2 2 2m + 2 2 +-+ +-+ m log(x) 2 +--R (b x x + a b x )\|a \|b (%e ) +--R + +--R 2m + 2 2 +-+ +-+ +--R (a b x + a )\|a \|b +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 +-----+ x \|b +--R (- 2b x x - 2a b x )\|- a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 +-----+ +-+ +-+ +--R - 2b x x \|- a b \|a \|b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2m + 2 +-----+ +-+ +-+ m log(x) +--R (2b x x + 2a x)\|- a b \|a \|b %e +--R + +--R m + 1 +-+ +--R 2m + 2 2 +-----+ x \|b m + 1 +-----+ +-+ +-+ +--R (- 2a b x - 2a )\|- a b atan(----------) - 2a x \|- a b \|a \|b +--R +-+ +--R \|a +--R / +--R 2 2 2 2m + 2 2 2 2 +-----+ +-+ +-+ +--R ((4a b m + 4a b )x x + (4a b m + 4a b)x )\|- a b \|a \|b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2 2m + 2 3 3 +-----+ +-+ +-+ +--R ((4a b m + 4a b)x + 4a m + 4a )\|- a b \|a \|b +--R Type: Expression(Integer) +--E 278 + +--S 279 of 486 +d0348a:= D(m0348a,x) +--R +--R +--R (251) +--R 4 4 m 2m + 2 2 4 4 m m + 1 2 3 4 m 2m + 2 +--R - b x x (x ) + (- b x x (x ) - 3a b x x )x +--R + +--R 4 4 m + 1 3 3 4 m + 1 2m + 1 3 4 m m + 1 2 2 2 4 m +--R (2b x (x ) + 2a b x x )x - a b x x (x ) - 2a b x x +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 3 2 m 2m + 2 2 3 2 m m + 1 2 2 2 2 m 2m + 2 +--R - 2a b x x (x ) + (- 2a b x x (x ) - 6a b x x )x +--R + +--R 3 2 m + 1 3 2 2 2 m + 1 2m + 1 2 2 2 m m + 1 2 +--R (4a b x (x ) + 4a b x x )x - 2a b x x (x ) +--R + +--R 3 2 m +--R - 4a b x x +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 3 m + 1 2 2 2 2m + 2 2 2 2 m + 1 2 3 2m + 2 +--R (2a b (x ) + 2a b )(x ) + (4a b (x ) + 4a b)x +--R + +--R 3 m + 1 2 4 +--R 2a b (x ) + 2a +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m 2m + 2 2 2 2 m m + 1 2 3 m 2m + 2 +--R - a b x (x ) + (- a b x (x ) - 3a b x )x +--R + +--R 2 2 m + 1 3 3 m + 1 2m + 1 3 m m + 1 2 4 m +--R (2a b (x ) + 2a b x )x - a b x (x ) - 2a x +--R / +--R 5 4 m + 1 2 2 4 4 2m + 2 2 +--R (2a b x (x ) + 2a b x )(x ) +--R + +--R 2 4 4 m + 1 2 3 3 4 2m + 2 3 3 4 m + 1 2 4 2 4 +--R (4a b x (x ) + 4a b x )x + 2a b x (x ) + 2a b x +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 2 4 2 m + 1 2 3 3 2 2m + 2 2 +--R (4a b x (x ) + 4a b x )(x ) +--R + +--R 3 3 2 m + 1 2 4 2 2 2m + 2 4 2 2 m + 1 2 5 2 +--R (8a b x (x ) + 8a b x )x + 4a b x (x ) + 4a b x +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 3 3 m + 1 2 4 2 2m + 2 2 4 2 m + 1 2 5 2m + 2 +--R (2a b (x ) + 2a b )(x ) + (4a b (x ) + 4a b)x +--R + +--R 5 m + 1 2 6 +--R 2a b (x ) + 2a +--R Type: Expression(Integer) +--E 279 + +--S 280 of 486 +m0348b:= a0348.2-r0348 +--R +--R +--R (252) +--R 2 2 2m + 2 2 +-+ +-+ m log(x) 2 +--R (b x x + a b x )\|a \|b (%e ) +--R + +--R 2m + 2 2 +-+ +-+ +--R (a b x + a )\|a \|b +--R * +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 +---+ x \|b +--R (- b x x - a b x )\|a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 +-+ +-+ +---+ +--R - b x x \|a \|b \|a b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2m + 2 +-+ +-+ +---+ m log(x) +--R (b x x + a x)\|a \|b \|a b %e +--R + +--R m + 1 +-+ +--R 2m + 2 2 +---+ x \|b m + 1 +-+ +-+ +---+ +--R (- a b x - a )\|a b atan(----------) - a x \|a \|b \|a b +--R +-+ +--R \|a +--R / +--R 2 2 2 2m + 2 2 2 2 +-+ +-+ +---+ +--R ((2a b m + 2a b )x x + (2a b m + 2a b)x )\|a \|b \|a b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2 2m + 2 3 3 +-+ +-+ +---+ +--R ((2a b m + 2a b)x + 2a m + 2a )\|a \|b \|a b +--R Type: Expression(Integer) +--E 280 + +--S 281 of 486 +d0348b:= D(m0348b,x) +--R +--R +--R (253) +--R 4 4 m 2m + 2 2 4 4 m m + 1 2 3 4 m 2m + 2 +--R - b x x (x ) + (- b x x (x ) - 3a b x x )x +--R + +--R 4 4 m + 1 3 3 4 m + 1 2m + 1 3 4 m m + 1 2 2 2 4 m +--R (2b x (x ) + 2a b x x )x - a b x x (x ) - 2a b x x +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 3 2 m 2m + 2 2 3 2 m m + 1 2 2 2 2 m 2m + 2 +--R - 2a b x x (x ) + (- 2a b x x (x ) - 6a b x x )x +--R + +--R 3 2 m + 1 3 2 2 2 m + 1 2m + 1 2 2 2 m m + 1 2 +--R (4a b x (x ) + 4a b x x )x - 2a b x x (x ) +--R + +--R 3 2 m +--R - 4a b x x +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 3 m + 1 2 2 2 2m + 2 2 2 2 m + 1 2 3 2m + 2 +--R (2a b (x ) + 2a b )(x ) + (4a b (x ) + 4a b)x +--R + +--R 3 m + 1 2 4 +--R 2a b (x ) + 2a +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m 2m + 2 2 2 2 m m + 1 2 3 m 2m + 2 +--R - a b x (x ) + (- a b x (x ) - 3a b x )x +--R + +--R 2 2 m + 1 3 3 m + 1 2m + 1 3 m m + 1 2 4 m +--R (2a b (x ) + 2a b x )x - a b x (x ) - 2a x +--R / +--R 5 4 m + 1 2 2 4 4 2m + 2 2 +--R (2a b x (x ) + 2a b x )(x ) +--R + +--R 2 4 4 m + 1 2 3 3 4 2m + 2 3 3 4 m + 1 2 4 2 4 +--R (4a b x (x ) + 4a b x )x + 2a b x (x ) + 2a b x +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 2 4 2 m + 1 2 3 3 2 2m + 2 2 +--R (4a b x (x ) + 4a b x )(x ) +--R + +--R 3 3 2 m + 1 2 4 2 2 2m + 2 4 2 2 m + 1 2 5 2 +--R (8a b x (x ) + 8a b x )x + 4a b x (x ) + 4a b x +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 3 3 m + 1 2 4 2 2m + 2 2 4 2 m + 1 2 5 2m + 2 +--R (2a b (x ) + 2a b )(x ) + (4a b (x ) + 4a b)x +--R + +--R 5 m + 1 2 6 +--R 2a b (x ) + 2a +--R Type: Expression(Integer) +--E 281 + +--S 282 of 486 +t0349:= x^n*(1+x^(1+n))^(1/2) +--R +--R +--R +----------+ +--R n | n + 1 +--R (254) x \|x + 1 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 486 +r0349:= 2*(1+x^(1+n))^(3/2)/(3+3*n) +--R +--R +--R +----------+ +--R n + 1 | n + 1 +--R (2x + 2)\|x + 1 +--R (255) -------------------------- +--R 3n + 3 +--R Type: Expression(Integer) +--E 283 + +--S 284 of 486 +a0349:= integrate(t0349,x) +--R +--R +--R +-------------------+ +--R (n + 1)log(x) | (n + 1)log(x) +--R (2%e + 2)\|%e + 1 +--R (256) -------------------------------------------- +--R 3n + 3 +--R Type: Union(Expression(Integer),...) +--E 284 + +--S 285 of 486 +m0349:= a0349-r0349 +--R +--R +--R (257) +--R +-------------------+ +----------+ +--R (n + 1)log(x) | (n + 1)log(x) n + 1 | n + 1 +--R (2%e + 2)\|%e + 1 + (- 2x - 2)\|x + 1 +--R --------------------------------------------------------------------------- +--R 3n + 3 +--R Type: Expression(Integer) +--E 285 + +--S 286 of 486 +d0349:= D(m0349,x) +--R +--R +--R (258) +--R +-------------------+ +--R n n + 1 n | (n + 1)log(x) +--R (- x x x - x x )\|%e + 1 +--R + +--R +----------+ +--R (n + 1)log(x) 2 (n + 1)log(x) | n + 1 +--R ((%e ) + %e )\|x + 1 +--R / +--R +----------+ +-------------------+ +--R | n + 1 | (n + 1)log(x) +--R x\|x + 1 \|%e + 1 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 486 +t0350:= x^n*(a^2+x^(1+n))^(1/2) +--R +--R +--R +-----------+ +--R n | n + 1 2 +--R (259) x \|x + a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 486 +r0350:= 2*(a^2+x^(1+n))^(3/2)/(3+3*n) +--R +--R +--R +-----------+ +--R n + 1 2 | n + 1 2 +--R (2x + 2a )\|x + a +--R (260) ----------------------------- +--R 3n + 3 +--R Type: Expression(Integer) +--E 288 + +--S 289 of 486 +a0350:= integrate(t0350,x) +--R +--R +--R +--------------------+ +--R (n + 1)log(x) 2 | (n + 1)log(x) 2 +--R (2%e + 2a )\|%e + a +--R (261) ----------------------------------------------- +--R 3n + 3 +--R Type: Union(Expression(Integer),...) +--E 289 + +--S 290 of 486 +m0350:= a0350-r0350 +--R +--R +--R (262) +--R +--------------------+ +--R (n + 1)log(x) 2 | (n + 1)log(x) 2 +--R (2%e + 2a )\|%e + a +--R + +--R +-----------+ +--R n + 1 2 | n + 1 2 +--R (- 2x - 2a )\|x + a +--R / +--R 3n + 3 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 486 +d0350:= D(m0350,x) +--R +--R +--R (263) +--R +--------------------+ +--R n n + 1 2 n | (n + 1)log(x) 2 +--R (- x x x - a x x )\|%e + a +--R + +--R +-----------+ +--R (n + 1)log(x) 2 2 (n + 1)log(x) | n + 1 2 +--R ((%e ) + a %e )\|x + a +--R / +--R +-----------+ +--------------------+ +--R | n + 1 2 | (n + 1)log(x) 2 +--R x\|x + a \|%e + a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 486 +t0351:= x/(4-x^2+(4-x^2)^(1/2)) +--R +--R +--R x +--R (264) -------------------- +--R +--------+ +--R | 2 2 +--R \|- x + 4 - x + 4 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 486 +r0351:= -log(1+(4-x^2)^(1/2)) +--R +--R +--R +--------+ +--R | 2 +--R (265) - log(\|- x + 4 + 1) +--R Type: Expression(Integer) +--E 293 + +--S 294 of 486 +a0351:94= integrate(t0351,x) +--R +--R +--RDaly Bug +--R Category, domain or package constructor = is not available. +--E 294 + +--S 295 of 486 +m0351:= a0351-r0351 +--R +--R +--R +--------+ +--R | 2 +--R (266) log(\|- x + 4 + 1) + a0351 +--R Type: Expression(Integer) +--E 295 + +--S 296 of 486 +d0351:= D(m0351,x) +--R +--R +--R x +--R (267) - -------------------- +--R +--------+ +--R | 2 2 +--R \|- x + 4 - x + 4 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 486 +t0352:= ((b-x)*(-a+x))^(1/2) +--R +--R +--R +---------------------+ +--R | 2 +--R (268) \|- x + (b + a)x - a b +--R Type: Expression(Integer) +--E 297 + +--S 298 of 486 +r0352:= -1/4*(a+b-2*x)*(-a*b+a*x+b*x-x^2)^(1/2)-1/8*(4*a*b-(a+b)^2)*_ + atan(2*(-a*b+a*x+b*x-x^2)^(1/2)/(a+b-2*x)) +--R +--R +--R (269) +--R +---------------------+ +--R | 2 +--R 2 2 2\|- x + (b + a)x - a b +--R (- b + 2a b - a )atan(-------------------------) +--R 2x - b - a +--R + +--R +---------------------+ +--R | 2 +--R (4x - 2b - 2a)\|- x + (b + a)x - a b +--R / +--R 8 +--R Type: Expression(Integer) +--E 298 + +--S 299 of 486 +a0352:= integrate(t0352,x) +--R +--R +--R (270) +--R 3 2 2 3 3 2 2 3 +--R ((4b - 4a b - 4a b + 4a )x - 8a b + 16a b - 8a b) +--R * +--R +---------------------+ +--R | 2 +-----+ +--R \|- x + (b + a)x - a b \|- a b +--R + +--R 4 3 2 2 3 4 2 +--R (- b - 4a b + 10a b - 4a b - a )x +--R + +--R 4 2 3 3 2 4 2 4 3 3 4 2 +--R (8a b - 8a b - 8a b + 8a b)x - 8a b + 16a b - 8a b +--R * +--R +---------------------+ +--R +-----+ | 2 +--R \|- a b - \|- x + (b + a)x - a b +--R atan(-----------------------------------) +--R x +--R + +--R 4 2 2 3 +--R (- 8b - 8a)x + (12b + 40a b + 12a )x +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 3b - 37a b - 37a b - 3a )x + (4a b + 24a b + 4a b)x +--R * +--R +-----+ +--R \|- a b +--R + +--R 2 2 3 3 2 2 3 2 +--R (- 2b - 12a b - 2a )x + (b + 23a b + 23a b + a )x +--R + +--R 3 2 2 3 +--R (- 4a b - 24a b - 4a b)x +--R * +--R +---------------------+ +--R | 2 +--R \|- x + (b + a)x - a b +--R / +--R +---------------------+ +--R | 2 +-----+ +--R ((16b + 16a)x - 32a b)\|- x + (b + a)x - a b \|- a b +--R + +--R 2 2 2 2 2 2 2 +--R (- 4b - 24a b - 4a )x + (32a b + 32a b)x - 32a b +--R Type: Union(Expression(Integer),...) +--E 299 + +--S 300 of 486 +m0352:= a0352-r0352 +--R +--R +--R (271) +--R 3 2 2 3 3 2 2 3 +--R ((8b - 8a b - 8a b + 8a )x - 16a b + 32a b - 16a b) +--R * +--R +---------------------+ +--R | 2 +-----+ +--R \|- x + (b + a)x - a b \|- a b +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b - 8a b + 20a b - 8a b - 2a )x +--R + +--R 4 2 3 3 2 4 2 4 3 3 4 2 +--R (16a b - 16a b - 16a b + 16a b)x - 16a b + 32a b - 16a b +--R * +--R +---------------------+ +--R +-----+ | 2 +--R \|- a b - \|- x + (b + a)x - a b +--R atan(-----------------------------------) +--R x +--R + +--R 3 2 2 3 3 2 2 3 +--R ((4b - 4a b - 4a b + 4a )x - 8a b + 16a b - 8a b) +--R * +--R +---------------------+ +--R | 2 +-----+ +--R \|- x + (b + a)x - a b \|- a b +--R + +--R 4 3 2 2 3 4 2 +--R (- b - 4a b + 10a b - 4a b - a )x +--R + +--R 4 2 3 3 2 4 2 4 3 3 4 2 +--R (8a b - 8a b - 8a b + 8a b)x - 8a b + 16a b - 8a b +--R * +--R +---------------------+ +--R | 2 +--R 2\|- x + (b + a)x - a b +--R atan(-------------------------) +--R 2x - b - a +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (2b + 14a b + 14a b + 2a )x + (- 16a b - 32a b - 16a b)x +--R + +--R 2 3 3 2 +--R 16a b + 16a b +--R * +--R +-----+ +--R \|- a b +--R + +--R +---------------------+ +--R 3 2 2 3 2 3 3 2 | 2 +--R ((8a b + 16a b + 8a b)x - 16a b - 16a b )\|- x + (b + a)x - a b +--R / +--R +---------------------+ +--R | 2 +-----+ +--R ((32b + 32a)x - 64a b)\|- x + (b + a)x - a b \|- a b +--R + +--R 2 2 2 2 2 2 2 +--R (- 8b - 48a b - 8a )x + (64a b + 64a b)x - 64a b +--R Type: Expression(Integer) +--E 300 + +--S 301 of 486 +d0352:= D(m0352,x) +--R +--R +--R (272) 0 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 486 +t0353:= 1/((1+x)^(1/4)+(1+x)^(1/2)) +--R +--R +--R 1 +--R (273) ------------------- +--R 4+-----+ +-----+ +--R \|x + 1 + \|x + 1 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 486 +r0353:= -4*(1+x)^(1/4)+2*(1+x)^(1/2)+4*log(1+(1+x)^(1/4)) +--R +--R +--R 4+-----+ 4+-----+ +-----+ +--R (274) 4log(\|x + 1 + 1) - 4\|x + 1 + 2\|x + 1 +--R Type: Expression(Integer) +--E 303 + +--S 304 of 486 +a0353:= integrate(t0353,x) +--R +--R +--R 4+-----+ 4+-----+2 4+-----+ +--R (275) 4log(\|x + 1 + 1) + 2\|x + 1 - 4\|x + 1 +--R Type: Union(Expression(Integer),...) +--E 304 + +--S 305 of 486 +m0353:= a0353-r0353 +--R +--R +--R 4+-----+2 +-----+ +--R (276) 2\|x + 1 - 2\|x + 1 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 486 +d0353:= D(m0353,x) +--R +--R +--R 4+-----+2 +-----+ +--R - \|x + 1 + \|x + 1 +--R (277) ---------------------- +--R +-----+4+-----+2 +--R \|x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 486 +t0354:= 1/(1+x^(2/3)) +--R +--R +--R 1 +--R (278) --------- +--R 3+-+2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 486 +r0354:= 3*x^(1/3)-3*atan(x^(1/3)) +--R +--R +--R 3+-+ 3+-+ +--R (279) - 3atan(\|x ) + 3\|x +--R Type: Expression(Integer) +--E 308 + +--S 309 of 486 +a0354:= integrate(t0354,x) +--R +--R +--R 3+-+ 3+-+ +--R (280) - 3atan(\|x ) + 3\|x +--R Type: Union(Expression(Integer),...) +--E 309 + +--S 310 of 486 +m0354:= a0354-r0354 +--R +--R +--R (281) 0 +--R Type: Expression(Integer) +--E 310 + +--S 311 of 486 +d0354:= D(m0354,x) +--R +--R +--R (282) 0 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 486 +t0355:= 1/(1+x^(1/5)) +--R +--R +--R 1 +--R (283) -------- +--R 5+-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 486 +r0355:= -5*x^(1/5)+5/2*x^(2/5)-5/3*x^(3/5)+5/4*x^(4/5)+5*log(1+x^(1/5)) +--R +--R +--R 5+-+ 5+-+4 5+-+3 5+-+2 5+-+ +--R 60log(\|x + 1) + 15\|x - 20\|x + 30\|x - 60\|x +--R (284) ------------------------------------------------------ +--R 12 +--R Type: Expression(Integer) +--E 313 + +--S 314 of 486 +a0355:= integrate(t0355,x) +--R +--R +--R 5+-+ 5+-+4 5+-+3 5+-+2 5+-+ +--R 60log(\|x + 1) + 15\|x - 20\|x + 30\|x - 60\|x +--R (285) ------------------------------------------------------ +--R 12 +--R Type: Union(Expression(Integer),...) +--E 314 + +--S 315 of 486 +m0355:= a0355-r0355 +--R +--R +--R (286) 0 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 486 +d0355:= D(m0355,x) +--R +--R +--R (287) 0 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 486 +t0356:= (1+x^(1/2))/(1+x^(1/3))/x^(1/2) +--R +--R +--R +-+ +--R \|x + 1 +--R (288) --------------- +--R +-+3+-+ +-+ +--R \|x \|x + \|x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 486 +r0356:= 6*x^(1/6)-3*x^(1/3)+3/2*x^(2/3)-6*atan(x^(1/6))+3*log(1+x^(1/3)) +--R +--R +--R 3+-+ 6+-+ 6+-+ 3+-+2 3+-+ +--R 6log(\|x + 1) - 12atan(\|x ) + 12\|x + 3\|x - 6\|x +--R (289) ------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 318 + +--S 319 of 486 +a0356:= integrate(t0356,x) +--R +--R +--R 6+-+2 6+-+ 6+-+4 6+-+2 6+-+ +--R 6log(\|x + 1) - 12atan(\|x ) + 3\|x - 6\|x + 12\|x +--R (290) --------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 486 +m0356:= a0356-r0356 +--R +--R +--R 6+-+2 3+-+ 6+-+4 6+-+2 3+-+2 3+-+ +--R 6log(\|x + 1) - 6log(\|x + 1) + 3\|x - 6\|x - 3\|x + 6\|x +--R (291) ------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 486 +d0356:= D(m0356,x) +--R +--R +--R 6+-+2 3+-+ +--R - \|x + \|x +--R (292) -------------------------- +--R 3+-+ 6+-+2 3+-+ +--R (\|x + 1)\|x + \|x + 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 486 +t0357:= 1/(1+x^(1/3)) +--R +--R +--R 1 +--R (293) -------- +--R 3+-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 486 +r0357:= -3*x^(1/3)+3/2*x^(2/3)+3*log(1+x^(1/3)) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 6log(\|x + 1) + 3\|x - 6\|x +--R (294) ------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 486 +a0357:= integrate(t0357,x) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 6log(\|x + 1) + 3\|x - 6\|x +--R (295) ------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 324 + +--S 325 of 486 +m0357:= a0357-r0357 +--R +--R +--R (296) 0 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 486 +d0357:= D(m0357,x) +--R +--R +--R (297) 0 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 486 +t0358:= 1/(-7+2*x+5*x^2)^(1/2)/(8+12*x+5*x^2) +--R +--R +--R 1 +--R (298) ------------------------------ +--R +------------+ +--R 2 | 2 +--R (5x + 12x + 8)\|5x + 2x - 7 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 486 +r0358:= (1/20+1/10*%i)*atan((40+20*%i)*(-7+2*x+5*x^2)^(1/2)/(-164+8*%i+_ + (-100+40*%i)*x))-(1/10+1/20*%i)*atanh((20+40*%i)*(-7+2*x+_ + 5*x^2)^(1/2)/(-164-8*%i-(100+40*%i)*x)) +--R +--R +--R (299) +--R +------------+ +--R 9 8 | 2 +--R (-- + -- %i)\|5x + 2x - 7 +--R 1 1 29 29 +--R (-- + -- %i)atanh(---------------------------) +--R 10 20 209 72 +--R x + --- - --- %i +--R 145 145 +--R + +--R +------------+ +--R 8 9 | 2 +--R (-- + -- %i)\|5x + 2x - 7 +--R 1 1 29 29 +--R (- -- - -- %i)atan(---------------------------) +--R 20 10 209 72 +--R x + --- + --- %i +--R 145 145 +--R Type: Expression(Complex(Fraction(Integer))) +--E 328 + +--S 329 of 486 +a0358:= integrate(t0358,x) +--R +--R +--R (300) +--R +------------+ +--R | 2 2 +--R (5x + 5)\|5x + 2x - 7 + 15x + 26x + 9 +--R log(----------------------------------------) +--R 2 +--R x +--R + +--R +------------+ +--R | 2 2 +--R (- 5x - 5)\|5x + 2x - 7 + 15x + 26x + 9 +--R - log(------------------------------------------) +--R 2 +--R x +--R + +--R +------------+ +------------+ +--R | 2 | 2 +--R 5\|5x + 2x - 7 - x + 7 5\|5x + 2x - 7 + x - 7 +--R atan(---------------------------) - atan(---------------------------) +--R +------------+ +------------+ +--R | 2 | 2 +--R 5\|5x + 2x - 7 - 17x - 25 5\|5x + 2x - 7 + 17x + 25 +--R / +--R 20 +--R Type: Union(Expression(Integer),...) +--E 329 + +--S 330 of 486 +m0358:= a0358-r0358 +--R +--R +--R (301) +--R +------------+ +--R | 2 2 +--R 1 (5x + 5)\|5x + 2x - 7 + 15x + 26x + 9 +--R -- log(----------------------------------------) +--R 20 2 +--R x +--R + +--R +------------+ +--R | 2 2 +--R 1 (- 5x - 5)\|5x + 2x - 7 + 15x + 26x + 9 +--R - -- log(------------------------------------------) +--R 20 2 +--R x +--R + +--R +------------+ +--R 9 8 | 2 +--R (-- + -- %i)\|5x + 2x - 7 +--R 1 1 29 29 +--R (- -- - -- %i)atanh(---------------------------) +--R 10 20 209 72 +--R x + --- - --- %i +--R 145 145 +--R + +--R +------------+ +--R 8 9 | 2 +--R (-- + -- %i)\|5x + 2x - 7 +--R 1 1 29 29 +--R (-- + -- %i)atan(---------------------------) +--R 20 10 209 72 +--R x + --- + --- %i +--R 145 145 +--R + +--R +------------+ +------------+ +--R | 2 1 7 | 2 1 7 +--R \|5x + 2x - 7 - - x + - \|5x + 2x - 7 + - x - - +--R 1 5 5 1 5 5 +--R -- atan(--------------------------) - -- atan(--------------------------) +--R 20 +------------+ 20 +------------+ +--R | 2 17 | 2 17 +--R \|5x + 2x - 7 - -- x - 5 \|5x + 2x - 7 + -- x + 5 +--R 5 5 +--R Type: Expression(Complex(Fraction(Integer))) +--E 330 + +--S 331 of 486 +d0358:= D(m0358,x) +--R +--R +--R (302) 0 +--R Type: Expression(Complex(Fraction(Integer))) +--E 331 + +--S 332 of 486 +t0359:= (x^(1/6)+(x^3)^(1/5))/x^(1/2) +--R +--R +--R +--+ +--R 5| 3 6+-+ +--R \|x + \|x +--R (303) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 332 + +--S 333 of 486 +r0359:= 3/2*x^(2/3)+10/11*x^(1/2)*(x^3)^(1/5) +--R +--R +--R +--+ +--R +-+5| 3 3+-+2 +--R 20\|x \|x + 33\|x +--R (304) --------------------- +--R 22 +--R Type: Expression(Integer) +--E 333 + +--S 334 of 486 +--a0359:= integrate(t0359,x) +--E 334 + +--S 335 of 486 +--m0359:= a0359-r0359 +--E 335 + +--S 336 of 486 +--d0359:= D(m0359,x) +--E 336 + +--S 337 of 486 +t0360:= 1/(4+x+(1+x)^(1/2)) +--R +--R +--R 1 +--R (305) ---------------- +--R +-----+ +--R \|x + 1 + x + 4 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 486 +r0360:= -2/11*atan(1/11*(1+2*(1+x)^(1/2))*11^(1/2))*11^(1/2)+_ + log(4+x+(1+x)^(1/2)) +--R +--R +--R +--+ +-----+ +--+ +--R +-----+ +--+ 2\|11 \|x + 1 + \|11 +--R 11log(\|x + 1 + x + 4) - 2\|11 atan(----------------------) +--R 11 +--R (306) ------------------------------------------------------------ +--R 11 +--R Type: Expression(Integer) +--E 338 + +--S 339 of 486 +a0360:= integrate(t0360,x) +--R +--R +--R +--+ +-----+ +--+ +--R +--+ +-----+ 2\|11 \|x + 1 + \|11 +--R \|11 log(\|x + 1 + x + 4) - 2atan(----------------------) +--R 11 +--R (307) ---------------------------------------------------------- +--R +--+ +--R \|11 +--R Type: Union(Expression(Integer),...) +--E 339 + +--S 340 of 486 +m0360:= a0360-r0360 +--R +--R +--R (308) 0 +--R Type: Expression(Integer) +--E 340 + +--S 341 of 486 +d0360:= D(m0360,x) +--R +--R +--R (309) 0 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 486 +t0361:= 1/(-1/x^(1/3)+x^(1/2)) +--R +--R +--R 3+-+ +--R \|x +--R (310) ------------ +--R +-+3+-+ +--R \|x \|x - 1 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 486 +r0361:= 2*x^(1/2)+6*2^(1/2)/(25+5*5^(1/2))^(1/2)*atan((1-5^(1/2)+_ + 4*x^(1/6))/(10+2*5^(1/2))^(1/2))-6*2^(1/2)/(25-5*5^(1/2))^(1/2)*_ + atan((1+5^(1/2)+4*x^(1/6))/(10-2*5^(1/2))^(1/2))+6/5*log(1-x^(1/6))-_ + 3/10*(5^(1/2)+1)*log(2+(1-5^(1/2))*x^(1/6)+2*x^(1/3))-_ + 3/10*(1-5^(1/2))*log(2+(5^(1/2)+1)*x^(1/6)+2*x^(1/3)) +--R +--R +--R (311) +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (15\|5 - 15)log((\|5 + 1)\|x + 2\|x + 2) + 60log(- \|x + 1) +--R + +--R +-+ +-+ 6+-+ 3+-+ +--R (- 15\|5 - 15)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +------------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x + \|5 + 1 +--R (- 3\|2 \|5 - 15\|2 )\|- 5\|5 + 25 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x - \|5 + 1 +-+ +--R (- 3\|2 \|5 + 15\|2 )\|5\|5 + 25 atan(----------------) + 100\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 50 +--R Type: Expression(Integer) +--E 343 + +--S 344 of 486 +a0361:= integrate(t0361,x) +--R +--R +--R (312) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--I - 5%%KV1 - 5%%KV0 - 6 +--R * +--R log +--I (5%%KV1 + 5%%KV0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%KV1 + 25%%KV0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--I - 5%%KV1 - 5%%KV0 - 6 +--R * +--R log +--I (- 5%%KV1 - 5%%KV0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%KV1 + 25%%KV0 + 72\|x + 36 +--R + +--R 2 6+-+ 6+-+ +--I 10%%KV1 log(- 25%%KV1 + 36\|x ) + 12log(\|x - 1) +--R + +--R 2 6+-+ 6+-+3 +--I 10%%KV0 log(- 25%%KV0 + 36\|x ) + 20\|x +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 344 + +--S 345 of 486 +m0361:= a0361-r0361 +--R +--R +--R (313) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I 5\|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--I - 25%%KV1 - 25%%KV0 - 30 +--R * +--R log +--I (5%%KV1 + 5%%KV0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%KV1 + 25%%KV0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - 5\|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--I - 25%%KV1 - 25%%KV0 - 30 +--R * +--R log +--I (- 5%%KV1 - 5%%KV0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KV1 + (- 50%%KV0 - 60)%%KV1 - 75%%KV0 - 60%%KV0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%KV1 + 25%%KV0 + 72\|x + 36 +--R + +--R 2 6+-+ +--I 50%%KV1 log(- 25%%KV1 + 36\|x ) +--R + +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (- 15\|5 + 15)log((\|5 + 1)\|x + 2\|x + 2) + 60log(\|x - 1) +--R + +--R 6+-+ +-+ +-+ 6+-+ 3+-+ +--R - 60log(- \|x + 1) + (15\|5 + 15)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R 2 6+-+ +--I 50%%KV0 log(- 25%%KV0 + 36\|x ) +--R + +--R +------------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x + \|5 + 1 +--R (3\|2 \|5 + 15\|2 )\|- 5\|5 + 25 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x - \|5 + 1 6+-+3 +--R (3\|2 \|5 - 15\|2 )\|5\|5 + 25 atan(----------------) + 100\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R + +--R +-+ +--R - 100\|x +--R / +--R 50 +--R Type: Expression(Integer) +--E 345 + +--S 346 of 486 +d0361:= D(m0361,x) +--R +--R +--R (314) +--R +-+ +-+ +-+ +-+3+-+2 2 +-+ +-+ 2 +-+ +-+ 6+-+5 +--R ((2x\|2 \|5 - 10x\|2 )\|x \|x + (x \|2 \|5 - 5x \|2 )\|x )\|x +--R + +--R +-+ +-+ +-+ +-+3+-+2 +--R (x\|2 \|5 - 5x\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((x + 4x)\|2 \|5 + (- 5x - 10x)\|2 )\|x \|x +--R * +--R 6+-+4 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((- x - x)\|2 \|5 + (5x - 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((- 4x - 5x)\|2 \|5 + (10x + 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +--R (x \|2 \|5 - 5x \|2 )\|x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((x - 3x)\|2 \|5 + (5x + 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((5x + x)\|2 \|5 + (- 5x - 5x)\|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((- x - 3x )\|2 \|5 + (5x + 5x )\|2 )\|x +--R * +--R 6+-+2 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((3x + 5x)\|2 \|5 + (- 5x - 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((- x + 2x)\|2 \|5 + 5x \|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((3x + 3x )\|2 \|5 + (- 5x - 5x )\|2 )\|x +--R * +--R 6+-+ +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((- 5x - 2x)\|2 \|5 + (5x + 10x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ +-+ +-+3+-+ +--R ((- 2x - x)\|2 \|5 + 5x\|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((- 3x - x )\|2 \|5 + (5x + 5x )\|2 )\|x +--R * +--R +----------+ +----------+ +--R | +-+ | +-+ +--R \|2\|5 + 10 \|5\|5 + 25 +--R + +--R +------------+ +------------+ +--R +-+ +-+ +-+ | +-+ | +-+ +--R (2x\|2 \|5 + 10x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 + 400x +--R + +--R - 80 +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R - 800x + 800x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 +-+ 3 2 3+-+ +--R ((- 40x - 80x)\|x - 400x - 800x + 400x)\|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ 2 +--R ((x \|2 \|5 + 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 + 80x - 80x) +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R 400x +--R * +--R 6+-+5 +--R \|x +--R + +--R +------------+ +------------+ +--R +-+ +-+ +-+ | +-+ | +-+ 2 +--R (x\|2 \|5 + 5x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 - 80x +--R + +--R - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 400x - 1600x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((x + 4x)\|2 \|5 + (5x + 10x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 80x - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 400x - 800x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 +-+ 3 +--R 80x \|x - 800x +--R * +--R 6+-+4 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- x - x)\|2 \|5 + (- 5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 160x - 240x +--R * +--R +-+ +--R \|x +--R + +--R 3 +--R 800x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- 4x - 5x)\|2 \|5 + (- 10x - 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R - 320x - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 +--R 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ 2 +-+ +--R ((x \|2 \|5 + 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 - 80x )\|x +--R + +--R 4 +--R 400x +--R * +--R 6+-+3 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((x - 3x)\|2 \|5 + (- 5x - 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 640x - 240x +--R * +--R +-+3+-+2 +--R \|x \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((5x + x)\|2 \|5 + (5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 400x + 480x - 80x +--R * +--R +-+3+-+ +--R \|x \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((- x - 3x )\|2 \|5 + (- 5x - 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 80x - 80x +--R * +--R +-+ +--R \|x +--R * +--R 6+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((3x + 5x)\|2 \|5 + (5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 1040x - 240x +--R * +--R +-+3+-+2 +--R \|x \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ +--R ((- x + 2x)\|2 \|5 - 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 480x - 120x +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R - 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((3x + 3x )\|2 \|5 + (5x + 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 480x - 80x +--R * +--R +-+ +--R \|x +--R * +--R 6+-+ +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- 5x - 2x)\|2 \|5 + (- 5x - 10x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 800x + 240x - 320x +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R 400x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ +-+ | +-+ | +-+ +--R ((- 2x - x)\|2 \|5 - 5x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 160x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 800x + 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((- 3x - x )\|2 \|5 + (- 5x - 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 4 3 2 +--R - 400x + 80x - 80x +--R * +--R +-+ +--R \|x +--R / +--R 2 +-+3+-+2 3 2 +-+3+-+ 2 +-+ +--R ((800x - 800x)\|x \|x + (400x + 800x - 400x)\|x \|x - 400x \|x ) +--R * +--R 6+-+5 +--R \|x +--R + +--R 3 2 +-+3+-+2 3 2 +-+3+-+ 3 +-+ +--R ((- 400x + 1600x )\|x \|x + (- 400x + 800x )\|x \|x + 800x \|x ) +--R * +--R 6+-+4 +--R \|x +--R + +--R 3 +-+3+-+2 3 +-+3+-+ 4 +-+ 6+-+3 2 +-+3+-+6+-+ +--R (- 800x \|x \|x - 400x \|x \|x - 400x \|x )\|x + 400x \|x \|x \|x +--R + +--R 2 +-+3+-+2 3 2 +-+3+-+ +--R - 400x \|x \|x + (- 800x - 400x )\|x \|x +--R Type: Expression(Integer) +--E 346 + +--S 347 of 486 +t0362:= x^(1/2)/(-1/x^(1/3)+x^(1/2)) +--R +--R +--R +-+3+-+ +--R \|x \|x +--R (315) ------------ +--R +-+3+-+ +--R \|x \|x - 1 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 486 +r0362:= 6*x^(1/6)+x-3/5*(10+2*5^(1/2))^(1/2)*atan((1-5^(1/2)+_ + 4*x^(1/6))/(10+2*5^(1/2))^(1/2))-3/5*(10-2*5^(1/2))^(1/2)*_ + atan((1+5^(1/2)+4*x^(1/6))/(10-2*5^(1/2))^(1/2))+_ + 6/5*log(1-x^(1/6))-3/10*(1-5^(1/2))*log(2+(1-5^(1/2))*x^(1/6)+_ + 2*x^(1/3))-3/10*(5^(1/2)+1)*log(2+(5^(1/2)+1)*x^(1/6)+2*x^(1/3)) +--R +--R +--R (316) +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (- 3\|5 - 3)log((\|5 + 1)\|x + 2\|x + 2) + 12log(- \|x + 1) +--R + +--R +-+ +-+ 6+-+ 3+-+ +--R (3\|5 - 3)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +------------+ 6+-+ +-+ +--R | +-+ 4\|x + \|5 + 1 +--R - 6\|- 2\|5 + 10 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 6+-+ +--R - 6\|2\|5 + 10 atan(----------------) + 60\|x + 10x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 10 +--R Type: Expression(Integer) +--E 348 + +--S 349 of 486 +a0362:= integrate(t0362,x) +--R +--R +--R (317) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--I - 5%%KW1 - 5%%KW0 - 6 +--R * +--R log +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--R 6+-+ +--I 5%%KW1 + 5%%KW0 + 12\|x + 6 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--I - 5%%KW1 - 5%%KW0 - 6 +--R * +--R log +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--R 6+-+ +--I 5%%KW1 + 5%%KW0 + 12\|x + 6 +--R + +--R 6+-+ 6+-+ +--I 10%%KW1 log(- 5%%KW1 + 6\|x ) + 12log(\|x - 1) +--R + +--R 6+-+ 6+-+ +--I 10%%KW0 log(- 5%%KW0 + 6\|x ) + 60\|x + 10x +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 349 + +--S 350 of 486 +m0362:= a0362-r0362 +--R +--R +--R (318) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--I - 5%%KW1 - 5%%KW0 - 6 +--R * +--R log +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--R 6+-+ +--I 5%%KW1 + 5%%KW0 + 12\|x + 6 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--I - 5%%KW1 - 5%%KW0 - 6 +--R * +--R log +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%KW1 + (- 50%%KW0 - 60)%%KW1 - 75%%KW0 - 60%%KW0 - 108 +--R + +--R 6+-+ +--I 5%%KW1 + 5%%KW0 + 12\|x + 6 +--R + +--R 6+-+ +--I 10%%KW1 log(- 5%%KW1 + 6\|x ) +--R + +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (3\|5 + 3)log((\|5 + 1)\|x + 2\|x + 2) + 12log(\|x - 1) +--R + +--R 6+-+ +-+ +-+ 6+-+ 3+-+ +--R - 12log(- \|x + 1) + (- 3\|5 + 3)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +------------+ 6+-+ +-+ +--R 6+-+ | +-+ 4\|x + \|5 + 1 +--I 10%%KW0 log(- 5%%KW0 + 6\|x ) + 6\|- 2\|5 + 10 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 +--R 6\|2\|5 + 10 atan(----------------) +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 10 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 486 +d0362:= D(m0362,x) +--R +--R +--R (319) +--R 3+-+2 3+-+ 2 6+-+5 +--R ((- 4x - 6)\|x + (- 3x - 7)\|x - 3x - 2x)\|x +--R + +--R 3+-+2 3+-+ 2 6+-+4 +--R ((6x - 1)\|x + (7x + 2)\|x + 2x - 2x)\|x +--R + +--R 3+-+2 3+-+ 2 6+-+3 +--R ((x + 7)\|x - x\|x + 2x + 3x)\|x +--R + +--R 3+-+2 2 3+-+ 2 6+-+2 +--R ((- 10x - 2)\|x + (- x - 2x)\|x - 3x - 2x)\|x +--R + +--R 2 3+-+2 2 3+-+ 2 6+-+ 2 3+-+2 +--R ((3x + 3x)\|x + (2x + 3x)\|x + 2x )\|x + (- x + 4x)\|x +--R + +--R 2 3+-+ 2 +--R (- 3x + 3x)\|x + 3x +--R / +--R 3+-+6+-+4 3+-+2 2 3+-+ 6+-+3 +--R 10x\|x \|x + (- 10x \|x + (- 20x - 10x)\|x )\|x +--R + +--R 2 3+-+2 3 2 3+-+ 2 6+-+2 +--R ((20x - 20x)\|x + (10x + 20x - 10x)\|x - 10x )\|x +--R + +--R 3 2 3+-+2 3 2 3+-+ 3 6+-+ 3 3+-+2 +--R ((- 10x + 40x )\|x + (- 10x + 20x )\|x + 20x )\|x - 20x \|x +--R + +--R 3 3+-+ 4 +--R - 10x \|x - 10x +--R Type: Expression(Integer) +--E 351 + +--S 352 of 486 +t0363:= 1/(1+2*x)/(x+x^2)^(1/2) +--R +--R +--R 1 +--R (320) ----------------- +--R +------+ +--R | 2 +--R (2x + 1)\|x + x +--R Type: Expression(Integer) +--E 352 + +--S 353 of 486 +r0363:= atan(2*(x+x^2)^(1/2)) +--R +--R +--R +------+ +--R | 2 +--R (321) atan(2\|x + x ) +--R Type: Expression(Integer) +--E 353 + +--S 354 of 486 +a0363:= integrate(t0363,x) +--R +--R +--R +------+ +--R | 2 +--R (322) 2atan(2\|x + x - 2x - 1) +--R Type: Union(Expression(Integer),...) +--E 354 + +--S 355 of 486 +m0363:= a0363-r0363 +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (323) - atan(2\|x + x ) + 2atan(2\|x + x - 2x - 1) +--R Type: Expression(Integer) +--E 355 + +--S 356 of 486 +d0363:= D(m0363,x) +--R +--R +--R (324) 0 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 486 +t0364:= 1/(2+(1+x^(1/2))^(1/2))^(1/2) +--R +--R +--R 1 +--R (325) ------------------ +--R +---------------+ +--R | +--------+ +--R | | +-+ +--R \|\|\|x + 1 + 2 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 486 +r0364:= -48*(2+(1+x^(1/2))^(1/2))^(1/2)+88/3*(2+(1+x^(1/2))^(1/2))^(3/2)-_ + 48/5*(2+(1+x^(1/2))^(1/2))^(5/2)+8/7*(2+(1+x^(1/2))^(1/2))^(7/2) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((120\|x + 608)\|\|x + 1 - 288\|x - 2240)\|\|\|x + 1 + 2 +--R (326) --------------------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 486 +a0364:= integrate(t0364,x) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((120\|x + 608)\|\|x + 1 - 288\|x - 2240)\|\|\|x + 1 + 2 +--R (327) --------------------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 359 + +--S 360 of 486 +m0364:= a0364-r0364 +--R +--R +--R (328) 0 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 486 +d0364:= D(m0364,x) +--R +--R +--R (329) 0 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 486 +t0365:= x^(1/2)/(-1+x) +--R +--R +--R +-+ +--R \|x +--R (330) ----- +--R x - 1 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 486 +r0365:= 2*x^(1/2)-2*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (331) - 2atanh(\|x ) + 2\|x +--R Type: Expression(Integer) +--E 363 + +--S 364 of 486 +a0365:= integrate(t0365,x) +--R +--R +--R +-+ +-+ +-+ +--R (332) - log(\|x + 1) + log(\|x - 1) + 2\|x +--R Type: Union(Expression(Integer),...) +--E 364 + +--S 365 of 486 +m0365:= a0365-r0365 +--R +--R +--R +-+ +-+ +-+ +--R (333) - log(\|x + 1) + log(\|x - 1) + 2atanh(\|x ) +--R Type: Expression(Integer) +--E 365 + +--S 366 of 486 +d0365:= D(m0365,x) +--R +--R +--R (334) 0 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 486 +t0366:= 3/(4+x^(1/3)) +--R +--R +--R 3 +--R (335) -------- +--R 3+-+ +--R \|x + 4 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 486 +r0366:= -36*x^(1/3)+9/2*x^(2/3)+144*log(4+x^(1/3)) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 288log(\|x + 4) + 9\|x - 72\|x +--R (336) ---------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 486 +a0366:= integrate(t0366,x) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 288log(\|x + 4) + 9\|x - 72\|x +--R (337) ---------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 369 + +--S 370 of 486 +m0366:= a0366-r0366 +--R +--R +--R (338) 0 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 486 +d0366:= D(m0366,x) +--R +--R +--R (339) 0 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 486 +t0367:= (1+(-3+x)^(1/2))^(1/3) +--R +--R +--R +------------+ +--R 3| +-----+ +--R (340) \|\|x - 3 + 1 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 486 +r0367:= -9/14*(1+(-3+x)^(1/2))^(4/3)+6/7*(1+(-3+x)^(1/2))^(4/3)*(-3+x)^(1/2) +--R +--R +--R +------------+ +--R +-----+ 3| +-----+ +--R (3\|x - 3 + 12x - 45)\|\|x - 3 + 1 +--R (341) ------------------------------------- +--R 14 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 486 +a0367:= integrate(t0367,x) +--R +--R +--R +------------+ +--R +-----+ 3| +-----+ +--R (3\|x - 3 + 12x - 45)\|\|x - 3 + 1 +--R (342) ------------------------------------- +--R 14 +--R Type: Union(Expression(Integer),...) +--E 374 + +--S 375 of 486 +m0367:= a0367-r0367 +--R +--R +--R (343) 0 +--R Type: Expression(Integer) +--E 375 + +--S 376 of 486 +d0367:= D(m0367,x) +--R +--R +--R (344) 0 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 486 +t0368:= (1+x^(1/2)+x)^(1/2) +--R +--R +--R +------------+ +--R | +-+ +--R (345) \|\|x + x + 1 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 486 +r0368:= -1/4*(1+2*x^(1/2))*(1+x^(1/2)+x)^(1/2)+2/3*(1+x^(1/2)+x)^(3/2)-3/8*_ + asinh(1/3*(1+2*x^(1/2))*3^(1/2)) +--R +--R +--R +------------+ +-+ +-+ +-+ +--R +-+ | +-+ 2\|3 \|x + \|3 +--R (4\|x + 16x + 10)\|\|x + x + 1 - 9asinh(----------------) +--R 3 +--R (346) ------------------------------------------------------------ +--R 24 +--R Type: Expression(Integer) +--E 378 + +--S 379 of 486 +a0368:= integrate(t0368,x) +--R +--R +--R (347) +--R +------------+ +--R +-+ | +-+ +-+ +--R - 9log((8\|x + 4)\|\|x + x + 1 + 8\|x + 8x + 5) +--R + +--R +------------+ +--R +-+ | +-+ +--R (8\|x + 32x + 20)\|\|x + x + 1 +--R / +--R 48 +--R Type: Union(Expression(Integer),...) +--E 379 + +--S 380 of 486 +m0368:= a0368-r0368 +--R +--R +--R (348) +--R +------------+ +--R +-+ | +-+ +-+ +--R - 3log((8\|x + 4)\|\|x + x + 1 + 8\|x + 8x + 5) +--R + +--R +-+ +-+ +-+ +--R 2\|3 \|x + \|3 +--R 6asinh(----------------) +--R 3 +--R / +--R 16 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 486 +d0368:= D(m0368,x) +--R +--R +--R +--------------+ +------------+ +--R | +-+ | +-+ +--R - 3\|4\|x + 4x + 4 + 6\|\|x + x + 1 +--R (349) --------------------------------------- +--R +------------+ +--------------+ +--R +-+ | +-+ | +-+ +--R 16\|x \|\|x + x + 1 \|4\|x + 4x + 4 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 486 +t0369:= (1+x+(1+x)^(1/2))^(1/2) +--R +--R +--R +----------------+ +--R | +-----+ +--R (350) \|\|x + 1 + x + 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 486 +r0369:= 2/3*(1+x+(1+x)^(1/2))^(3/2)-1/4*(1+x+(1+x)^(1/2))^(1/2)*_ + (1+2*(1+x)^(1/2))+1/8*atanh(2*(1+x+(1+x)^(1/2))^(1/2)/_ + (1+2*(1+x)^(1/2))) +--R +--R +--R (351) +--R +----------------+ +--R | +-----+ +----------------+ +--R 2\|\|x + 1 + x + 1 +-----+ | +-----+ +--R 3atanh(--------------------) + (4\|x + 1 + 16x + 10)\|\|x + 1 + x + 1 +--R +-----+ +--R 2\|x + 1 + 1 +--R ------------------------------------------------------------------------ +--R 24 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 486 +a0369:= integrate(t0369,x) +--R +--R +--R (352) +--R +----------------+ +--R +-----+ | +-----+ +-----+ +--R - 3log((- 8\|x + 1 - 4)\|\|x + 1 + x + 1 + 8\|x + 1 + 8x + 9) +--R + +--R +----------------+ +--R +-----+ | +-----+ +--R (8\|x + 1 + 32x + 20)\|\|x + 1 + x + 1 +--R / +--R 48 +--R Type: Union(Expression(Integer),...) +--E 384 + +--S 385 of 486 +m0369:= a0369-r0369 +--R +--R +--R (353) +--R +----------------+ +--R +-----+ | +-----+ +-----+ +--R - log((- 8\|x + 1 - 4)\|\|x + 1 + x + 1 + 8\|x + 1 + 8x + 9) +--R + +--R +----------------+ +--R | +-----+ +--R 2\|\|x + 1 + x + 1 +--R - 2atanh(--------------------) +--R +-----+ +--R 2\|x + 1 + 1 +--R / +--R 16 +--R Type: Expression(Integer) +--E 385 + +--S 386 of 486 +d0369:= D(m0369,x) +--R +--R +--R (354) 0 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 486 +t0370:= (2*x+(-1+2*x)^(1/2))^(1/2) +--R +--R +--R +--------------+ +--R | +------+ +--R (355) \|\|2x - 1 + 2x +--R Type: Expression(Integer) +--E 387 + +--S 388 of 486 +r0370:= 1/3*(2*x+(-1+2*x)^(1/2))^(3/2)-1/8*(2*x+(-1+2*x)^(1/2))^(1/2)*_ + (1+2*(-1+2*x)^(1/2))-3/16*asinh(1/3*(1+2*(-1+2*x)^(1/2))*3^(1/2)) +--R +--R +--R (356) +--R +--------------+ +-+ +------+ +-+ +--R +------+ | +------+ 2\|3 \|2x - 1 + \|3 +--R (4\|2x - 1 + 32x - 6)\|\|2x - 1 + 2x - 9asinh(---------------------) +--R 3 +--R ----------------------------------------------------------------------- +--R 48 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 486 +a0370:= integrate(t0370,x) +--R +--R +--R (357) +--R +--------------+ +--R +------+ | +------+ +------+ +--R - 9log((- 8\|2x - 1 - 4)\|\|2x - 1 + 2x - 8\|2x - 1 - 16x + 3) +--R + +--R +--------------+ +--R +------+ | +------+ +--R (8\|2x - 1 + 64x - 12)\|\|2x - 1 + 2x +--R / +--R 96 +--R Type: Union(Expression(Integer),...) +--E 389 + +--S 390 of 486 +m0370:= a0370-r0370 +--R +--R +--R (358) +--R +--------------+ +--R +------+ | +------+ +------+ +--R - 3log((- 8\|2x - 1 - 4)\|\|2x - 1 + 2x - 8\|2x - 1 - 16x + 3) +--R + +--R +-+ +------+ +-+ +--R 2\|3 \|2x - 1 + \|3 +--R 6asinh(---------------------) +--R 3 +--R / +--R 32 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 486 +d0370:= D(m0370,x) +--R +--R +--R +---------------+ +--------------+ +--R | +------+ | +------+ +--R - 3\|4\|2x - 1 + 8x + 6\|\|2x - 1 + 2x +--R (359) ---------------------------------------------- +--R +--------------+ +---------------+ +--R +------+ | +------+ | +------+ +--R 16\|2x - 1 \|\|2x - 1 + 2x \|4\|2x - 1 + 8x +--R Type: Expression(Integer) +--E 391 + +--S 392 of 486 +t0371:= ((-1+x)^(1/2)+x)^(1/2) +--R +--R +--R +------------+ +--R | +-----+ +--R (360) \|\|x - 1 + x +--R Type: Expression(Integer) +--E 392 + +--S 393 of 486 +r0371:= -1/4*(1+2*(-1+x)^(1/2))*((-1+x)^(1/2)+x)^(1/2)+_ + 2/3*((-1+x)^(1/2)+x)^(3/2)-3/8*asinh(1/3*(1+2*(-1+x)^(1/2))*3^(1/2)) +--R +--R +--R +------------+ +-+ +-----+ +-+ +--R +-----+ | +-----+ 2\|3 \|x - 1 + \|3 +--R (4\|x - 1 + 16x - 6)\|\|x - 1 + x - 9asinh(--------------------) +--R 3 +--R (361) ------------------------------------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 486 +a0371:= integrate(t0371,x) +--R +--R +--R (362) +--R +------------+ +--R +-----+ | +-----+ +-----+ +--R - 9log((- 8\|x - 1 - 4)\|\|x - 1 + x - 8\|x - 1 - 8x + 3) +--R + +--R +------------+ +--R +-----+ | +-----+ +--R (8\|x - 1 + 32x - 12)\|\|x - 1 + x +--R / +--R 48 +--R Type: Union(Expression(Integer),...) +--E 394 + +--S 395 of 486 +m0371:= a0371-r0371 +--R +--R +--R (363) +--R +------------+ +--R +-----+ | +-----+ +-----+ +--R - 3log((- 8\|x - 1 - 4)\|\|x - 1 + x - 8\|x - 1 - 8x + 3) +--R + +--R +-+ +-----+ +-+ +--R 2\|3 \|x - 1 + \|3 +--R 6asinh(--------------------) +--R 3 +--R / +--R 16 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 486 +d0371:= D(m0371,x) +--R +--R +--R +--------------+ +------------+ +--R | +-----+ | +-----+ +--R - 3\|4\|x - 1 + 4x + 6\|\|x - 1 + x +--R (364) ------------------------------------------ +--R +------------+ +--------------+ +--R +-----+ | +-----+ | +-----+ +--R 16\|x - 1 \|\|x - 1 + x \|4\|x - 1 + 4x +--R Type: Expression(Integer) +--E 396 + +--S 397 of 486 +t0372:= 1/(3+(-1+2*x)^(1/2))^(1/2) +--R +--R +--R 1 +--R (365) ---------------- +--R +-------------+ +--R | +------+ +--R \|\|2x - 1 + 3 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 486 +r0372:= -4*(3+(-1+2*x)^(1/2))^(1/2)+2/3*(-1+2*x)^(1/2)*(3+(-1+2*x)^(1/2))^(1/2) +--R +--R +--R +-------------+ +--R +------+ | +------+ +--R (2\|2x - 1 - 12)\|\|2x - 1 + 3 +--R (366) --------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 486 +a0372:= integrate(t0372,x) +--R +--R +--R +-------------+ +--R +------+ | +------+ +--R (2\|2x - 1 - 12)\|\|2x - 1 + 3 +--R (367) --------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 486 +m0372:= a0372-r0372 +--R +--R +--R (368) 0 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 486 +d0372:= D(m0372,x) +--R +--R +--R (369) 0 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 486 +t0373:= 1/(x+(1+x)^(1/2))^(1/2) +--R +--R +--R 1 +--R (370) --------------- +--R +------------+ +--R | +-----+ +--R \|\|x + 1 + x +--R Type: Expression(Integer) +--E 402 + +--S 403 of 486 +r0373:= 2*(x+(1+x)^(1/2))^(1/2)-_ + atanh(2*(x+(1+x)^(1/2))^(1/2)/(1+2*(1+x)^(1/2))) +--R +--R +--R +------------+ +--R | +-----+ +------------+ +--R 2\|\|x + 1 + x | +-----+ +--R (371) - atanh(----------------) + 2\|\|x + 1 + x +--R +-----+ +--R 2\|x + 1 + 1 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 486 +a0373:= integrate(t0373,x) +--R +--R +--R (372) +--R +------------+ +------------+ +--R +-----+ | +-----+ +-----+ | +-----+ +--R - log((8\|x + 1 + 4)\|\|x + 1 + x + 8\|x + 1 + 8x + 5) + 4\|\|x + 1 + x +--R ----------------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 404 + +--S 405 of 486 +m0373:= a0373-r0373 +--R +--R +--R (373) +--R +------------+ +--R +-----+ | +-----+ +-----+ +--R - log((8\|x + 1 + 4)\|\|x + 1 + x + 8\|x + 1 + 8x + 5) +--R + +--R +------------+ +--R | +-----+ +--R 2\|\|x + 1 + x +--R 2atanh(----------------) +--R +-----+ +--R 2\|x + 1 + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 486 +d0373:= D(m0373,x) +--R +--R +--R (374) 0 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 486 +t0374:= 1/(1+x+(-1+2*x)^(1/2))^(1/2) +--R +--R +--R 1 +--R (375) -------------------- +--R +-----------------+ +--R | +------+ +--R \|\|2x - 1 + x + 1 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 486 +r0374:= 2*(1+x+(-1+2*x)^(1/2))^(1/2)-2^(1/2)*_ + asinh(1/2*(1+(-1+2*x)^(1/2))*2^(1/2)) +--R +--R +--R +-----------------+ +-+ +------+ +-+ +--R | +------+ +-+ \|2 \|2x - 1 + \|2 +--R (376) 2\|\|2x - 1 + x + 1 - \|2 asinh(--------------------) +--R 2 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 486 +a0374:= integrate(t0374,x) +--R +--R +--R (377) +--R - +--R +-+ +--R \|2 +--R * +--R +-----------------+ +--R +-+ +------+ +-+ | +------+ +------+ +--R log((\|2 \|2x - 1 + \|2 )\|\|2x - 1 + x + 1 + 2\|2x - 1 + 2x + 1) +--R + +--R +-----------------+ +--R | +------+ +--R 4\|\|2x - 1 + x + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 409 + +--S 410 of 486 +m0374:= a0374-r0374 +--R +--R +--R (378) +--R - +--R +-+ +--R \|2 +--R * +--R +-----------------+ +--R +-+ +------+ +-+ | +------+ +------+ +--R log((\|2 \|2x - 1 + \|2 )\|\|2x - 1 + x + 1 + 2\|2x - 1 + 2x + 1) +--R + +--R +-+ +------+ +-+ +--R +-+ \|2 \|2x - 1 + \|2 +--R 2\|2 asinh(--------------------) +--R 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 410 + +--S 411 of 486 +d0374:= D(m0374,x) +--R +--R +--R (379) 0 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 486 +t0375:= (3*x+(-7+8*x)^(1/2))^(1/2) +--R +--R +--R +--------------+ +--R | +------+ +--R (380) \|\|8x - 7 + 3x +--R Type: Expression(Integer) +--E 412 + +--S 413 of 486 +r0375:= 2/9*(3*x+(-7+8*x)^(1/2))^(3/2)-1/18*(3*x+(-7+8*x)^(1/2))^(1/2)*_ + (4+3*(-7+8*x)^(1/2))-47/216*asinh(1/47*(4+3*(-7+8*x)^(1/2))*_ + 47^(1/2))*6^(1/2) +--R +--R +--R (381) +--R +--------------+ +--R +------+ | +------+ +--R (12\|8x - 7 + 144x - 48)\|\|8x - 7 + 3x +--R + +--R +--+ +------+ +--+ +--R +-+ 3\|47 \|8x - 7 + 4\|47 +--R - 47\|6 asinh(------------------------) +--R 47 +--R / +--R 216 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 486 +a0375:= integrate(t0375,x) +--R +--R +--R (382) +--R - +--R +-+ +--R 47\|6 +--R * +--R log +--R +--------------+ +--R +-+ +------+ +-+ | +------+ +------+ +--R (- 12\|6 \|8x - 7 - 16\|6 )\|\|8x - 7 + 3x - 48\|8x - 7 +--R + +--R - 144x + 47 +--R + +--R +--------------+ +--R +------+ | +------+ +--R (24\|8x - 7 + 288x - 96)\|\|8x - 7 + 3x +--R / +--R 432 +--R Type: Union(Expression(Integer),...) +--E 414 + +--S 415 of 486 +m0375:= a0375-r0375 +--R +--R +--R (383) +--R - +--R +-+ +--R 47\|6 +--R * +--R log +--R +--------------+ +--R +-+ +------+ +-+ | +------+ +------+ +--R (- 12\|6 \|8x - 7 - 16\|6 )\|\|8x - 7 + 3x - 48\|8x - 7 +--R + +--R - 144x + 47 +--R + +--R +--+ +------+ +--+ +--R +-+ 3\|47 \|8x - 7 + 4\|47 +--R 94\|6 asinh(------------------------) +--R 47 +--R / +--R 432 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 486 +d0375:= D(m0375,x) +--R +--R +--R (384) +--R +--------------+ +--R +-+ +------+ +-+ | +------+ +--R (- 752\|6 \|8x - 7 + (- 4512x + 3948)\|6 )\|\|8x - 7 + 3x +--R + +--R +------+ +--R (- 6768x + 2209)\|8x - 7 - 18048x + 15792 +--R * +--R +-----------------+ +--R | +------+ +--R \|24\|8x - 7 + 72x +--R + +--R +--------------+ +--R +-+ +------+ +-+ | +------+ +--R ((13536x - 4418)\|6 \|8x - 7 + (36096x - 31584)\|6 )\|\|8x - 7 + 3x +--R + +--R +------+ 2 +--R (81216x - 47376)\|8x - 7 + 162432x - 69936x - 63168 +--R / +--R +--------------+ +--R +------+ 2 | +------+ +--R ((13824x - 12096)\|8x - 7 + 41472x - 49824x + 11844)\|\|8x - 7 + 3x +--R + +--R 2 +-+ +------+ 2 +-+ +--R (10368x - 4464x - 4032)\|6 \|8x - 7 + (41472x - 60480x + 21168)\|6 +--R * +--R +-----------------+ +--R | +------+ +--R \|24\|8x - 7 + 72x +--R Type: Expression(Integer) +--E 416 + +--S 417 of 486 +t0376:= (1+(1+x^2)^(1/2))^(1/2) +--R +--R +--R +-------------+ +--R | +------+ +--R | | 2 +--R (385) \|\|x + 1 + 1 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 486 +r0376:= 2/3*(-1+x^2+(1+x^2)^(1/2))*(1+(1+x^2)^(1/2))^(1/2)/x +--R +--R +--R +-------------+ +--R +------+ | +------+ +--R | 2 2 | | 2 +--R (2\|x + 1 + 2x - 2)\|\|x + 1 + 1 +--R (386) -------------------------------------- +--R 3x +--R Type: Expression(Integer) +--E 418 + +--S 419 of 486 +a0376:= integrate(t0376,x) +--R +--R +--R +-------------+ +--R +------+ | +------+ +--R | 2 2 | | 2 +--R (2\|x + 1 + 2x - 2)\|\|x + 1 + 1 +--R (387) -------------------------------------- +--R 3x +--R Type: Union(Expression(Integer),...) +--E 419 + +--S 420 of 486 +m0376:= a0376-r0376 +--R +--R +--R (388) 0 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 486 +d0376:= D(m0376,x) +--R +--R +--R (389) 0 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 486 +t0377:= (5+(25+x^2)^(1/2))^(1/2) +--R +--R +--R +--------------+ +--R | +-------+ +--R | | 2 +--R (390) \|\|x + 25 + 5 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 486 +r0377:= 2/3*(-25+x^2+5*(25+x^2)^(1/2))*(5+(25+x^2)^(1/2))^(1/2)/x +--R +--R +--R +--------------+ +--R +-------+ | +-------+ +--R | 2 2 | | 2 +--R (10\|x + 25 + 2x - 50)\|\|x + 25 + 5 +--R (391) ------------------------------------------ +--R 3x +--R Type: Expression(Integer) +--E 423 + +--S 424 of 486 +a0377:= integrate(t0377,x) +--R +--R +--R +--------------+ +--R +-------+ | +-------+ +--R | 2 2 | | 2 +--R (10\|x + 25 + 2x - 50)\|\|x + 25 + 5 +--R (392) ------------------------------------------ +--R 3x +--R Type: Union(Expression(Integer),...) +--E 424 + +--S 425 of 486 +m0377:= a0377-r0377 +--R +--R +--R (393) 0 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 486 +d0377:= D(m0377,x) +--R +--R +--R (394) 0 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 486 +t0378:= x^2*((1-x^3)/(1+x^3))^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R 2 |- x + 1 +--R (395) x |-------- +--R | 3 +--R \| x + 1 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 486 +r0378:= 1/3*((1-x^3)/(1+x^3))^(1/2)*(1+x^3)-2/3*atan(((1-x^3)/(1+x^3))^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |- x + 1 3 |- x + 1 +--R - 2atan( |-------- ) + (x + 1) |-------- +--R | 3 | 3 +--R \| x + 1 \| x + 1 +--R (396) ------------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 486 +a0378:= integrate(t0378,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 |- x + 1 +--R +--------+ (x + 1) |-------- - 1 +--R | 3 | 3 +--R 3 |- x + 1 \| x + 1 6 +--R ((- 2x - 2) |-------- + 2)atan(-----------------------) - x +--R | 3 3 +--R \| x + 1 x +--R (397) -------------------------------------------------------------- +--R +--------+ +--R | 3 +--R 3 |- x + 1 +--R (3x + 3) |-------- - 3 +--R | 3 +--R \| x + 1 +--R Type: Union(Expression(Integer),...) +--E 429 + +--S 430 of 486 +m0378:= a0378-r0378 +--R +--R +--R +--------+ +--R | 3 +--R 3 |- x + 1 +--R (x + 1) |-------- - 1 +--------+ +--R | 3 | 3 +--R \| x + 1 |- x + 1 +--R - 2atan(-----------------------) + 2atan( |-------- ) + 1 +--R 3 | 3 +--R x \| x + 1 +--R (398) --------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 486 +d0378:= D(m0378,x) +--R +--R +--R (399) 0 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 486 +t0379:= x^8*((1-x^3)/(1+x^3))^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R 8 |- x + 1 +--R (400) x |-------- +--R | 3 +--R \| x + 1 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 486 +r0379:= 2/9*(-(-1+x^3)/(1+x^3))^(1/2)+1/18*(-(-1+x^3)/(1+x^3))^(1/2)*x^3-_ + 1/18*(-(-1+x^3)/(1+x^3))^(1/2)*x^6+1/9*(-(-1+x^3)/_ + (1+x^3))^(1/2)*x^9-1/3*atan((-(-1+x^3)/(1+x^3))^(1/2)) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |- x + 1 9 6 3 |- x + 1 +--R - 6atan( |-------- ) + (2x - x + x + 4) |-------- +--R | 3 | 3 +--R \| x + 1 \| x + 1 +--R (401) ----------------------------------------------------- +--R 18 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 486 +a0379:= integrate(t0379,x) +--R +--R +--R (402) +--R +--------+ +--R | 3 +--R 9 6 3 |- x + 1 6 +--R ((- 6x - 6x + 24x + 24) |-------- + 18x - 24) +--R | 3 +--R \| x + 1 +--R * +--R +--------+ +--R | 3 +--R 3 |- x + 1 +--R (x + 1) |-------- - 1 +--R | 3 +--R \| x + 1 +--R atan(-----------------------) +--R 3 +--R x +--R + +--R +--------+ +--R | 3 +--R 15 12 9 6 3 |- x + 1 18 15 12 +--R (- 6x + 3x + 9x - 12x - 12x ) |-------- - 2x + 3x + 6x +--R | 3 +--R \| x + 1 +--R + +--R 9 3 +--R - 15x + 12x +--R / +--R +--------+ +--R | 3 +--R 9 6 3 |- x + 1 6 +--R (18x + 18x - 72x - 72) |-------- - 54x + 72 +--R | 3 +--R \| x + 1 +--R Type: Union(Expression(Integer),...) +--E 434 + +--S 435 of 486 +m0379:= a0379-r0379 +--R +--R +--R +--------+ +--R | 3 +--R 3 |- x + 1 +--R (x + 1) |-------- - 1 +--------+ +--R | 3 | 3 +--R \| x + 1 |- x + 1 +--R - 3atan(-----------------------) + 3atan( |-------- ) + 2 +--R 3 | 3 +--R x \| x + 1 +--R (403) --------------------------------------------------------- +--R 9 +--R Type: Expression(Integer) +--E 435 + +--S 436 of 486 +d0379:= D(m0379,x) +--R +--R +--R (404) 0 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 486 +t0380:= x^9*((5-7*x^5)/(7+5*x^5))^(1/2) +--R +--R +--R +---------+ +--R | 5 +--R 9 |- 7x + 5 +--R (405) x |--------- +--R | 5 +--R \| 5x + 7 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 486 +r0380:= -43/125*(-(-5+7*x^5)/(7+5*x^5))^(1/2)-37/350*(-(-5+7*x^5)/_ + (7+5*x^5))^(1/2)*x^5+1/10*(-(-5+7*x^5)/(7+5*x^5))^(1/2)*x^10+_ + 2257/30625*atan(1/7*35^(1/2)*(-(-5+7*x^5)/(7+5*x^5))^(1/2))*35^(1/2) +--R +--R +--R (406) +--R +---------+ +--R | 5 +--R +--+ |- 7x + 5 +--R \|35 |--------- +---------+ +--R | 5 | 5 +--R +--+ \| 5x + 7 10 5 |- 7x + 5 +--R 4514\|35 atan(-----------------) + (6125x - 6475x - 21070) |--------- +--R 7 | 5 +--R \| 5x + 7 +--R ------------------------------------------------------------------------- +--R 61250 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 486 +a0380:= integrate(t0380,x) +--R +--R +--R (407) +--R +---------+ +--R | 5 +--R 10 5 |- 7x + 5 +--R (18958800x - 28754180x - 77415100) |--------- +--R | 5 +--R \| 5x + 7 +--R + +--R 10 5 +--+ +--R (- 4879634x - 7583520x + 11059300)\|35 +--R * +--R +---------+ +--R | 5 +--R 5 +--+ |- 7x + 5 +--R (5x + 7)\|35 |--------- - 35 +--R | 5 +--R \| 5x + 7 +--R atan(-------------------------------) +--R 5 +--R 35x +--R + +--R +---------+ +--R | 5 +--R 20 15 10 5 |- 7x + 5 +--R (- 6621125x - 3290525x + 36018920x + 38707550x ) |--------- +--R | 5 +--R \| 5x + 7 +--R + +--R 20 15 10 5 +--+ +--R (- 1029000x + 4824050x + 700070x - 5529650x )\|35 +--R / +--R +---------+ +--R | 5 +--R 10 5 +--+ |- 7x + 5 10 +--R (7350000x - 11147500x - 30012500)\|35 |--------- - 66211250x +--R | 5 +--R \| 5x + 7 +--R + +--R 5 +--R - 102900000x + 150062500 +--R Type: Union(Expression(Integer),...) +--E 439 + +--S 440 of 486 +m0380:= a0380-r0380 +--R +--R +--R (408) +--R +---------+ +--R | 5 +--R 10 5 |- 7x + 5 +--R (9479400x - 14377090x - 38707550) |--------- +--R | 5 +--R \| 5x + 7 +--R + +--R 10 5 +--+ +--R (- 2439817x - 3791760x + 5529650)\|35 +--R * +--R +---------+ +--R | 5 +--R 5 +--+ |- 7x + 5 +--R (5x + 7)\|35 |--------- - 35 +--R | 5 +--R \| 5x + 7 +--R atan(-------------------------------) +--R 5 +--R 35x +--R + +--R +---------+ +--R | 5 +--R 10 5 |- 7x + 5 +--R (- 9479400x + 14377090x + 38707550) |--------- +--R | 5 +--R \| 5x + 7 +--R + +--R 10 5 +--+ +--R (2439817x + 3791760x - 5529650)\|35 +--R * +--R +---------+ +--R | 5 +--R +--+ |- 7x + 5 +--R \|35 |--------- +--R | 5 +--R \| 5x + 7 +--R atan(-----------------) +--R 7 +--R + +--R +---------+ +--R | 5 +--R 10 5 |- 7x + 5 +--R (- 6321000x + 9586850x + 25810750) |--------- +--R | 5 +--R \| 5x + 7 +--R + +--R 10 5 +--+ +--R (1626905x + 2528400x - 3687250)\|35 +--R / +--R +---------+ +--R | 5 +--R 10 5 +--+ |- 7x + 5 10 +--R (3675000x - 5573750x - 15006250)\|35 |--------- - 33105625x +--R | 5 +--R \| 5x + 7 +--R + +--R 5 +--R - 51450000x + 75031250 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 486 +d0380:= D(m0380,x) +--R +--R +--R (409) 0 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 486 +t0381:= (-1+x^3)/x^(1/2)/(1+x^2) +--R +--R +--R 3 +--R x - 1 +--R (410) ------------ +--R 2 +-+ +--R (x + 1)\|x +--R Type: Expression(Integer) +--E 442 + +--S 443 of 486 +r0381:= 2/3*x^(3/2)-atan(-1+2^(1/2)*x^(1/2))*2^(1/2)-_ + atan(1+2^(1/2)*x^(1/2))*2^(1/2) +--R +--R +--R +-+ +-+ +-+ +-+ +-+ +-+ +-+ +--R - 3\|2 atan(\|2 \|x + 1) - 3\|2 atan(\|2 \|x - 1) + 2x\|x +--R (411) ------------------------------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 486 +a0381:= integrate(t0381,x) +--R +--R +--R +-+ +-+ +--R +-+ \|2 \|x +-+ +--R 3\|2 atan(--------) + 2x\|x +--R x - 1 +--R (412) ---------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 444 + +--S 445 of 486 +m0381:= a0381-r0381 +--R +--R +--R +-+ +-+ +--R +-+ +-+ +-+ +-+ +-+ +-+ +-+ \|2 \|x +--R (413) \|2 atan(\|2 \|x + 1) + \|2 atan(\|2 \|x - 1) + \|2 atan(--------) +--R x - 1 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 486 +d0381:= D(m0381,x) +--R +--R +--R (414) 0 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 486 +t0382:= 1/(1+x^4)/(-x^2+(1+x^4)^(1/2))^(1/2) +--R +--R +--R 1 +--R (415) ------------------------- +--R +--------------+ +--R | +------+ +--R 4 | | 4 2 +--R (x + 1)\|\|x + 1 - x +--R Type: Expression(Integer) +--E 447 + +--S 448 of 486 +r0382:= acot((-x^2+(1+x^4)^(1/2))^(1/2)/x) +--R +--R +--R +--------------+ +--R | +------+ +--R | | 4 2 +--R \|\|x + 1 - x +--R (416) acot(-----------------) +--R x +--R Type: Expression(Integer) +--E 448 + + +--S 449 of 486 We get it correct but it takes too long +--a0382:= integrate(t0382,x) +--E 449 + +--S 450 of 486 +--m0382:= a0382-r0382 +--E 450 + +--S 451 of 486 +--d0382:= D(m0382,x) +--E 451 + +--S 452 of 486 +t0383:= (1+x^(7/2))/(1-x^2) +--R +--R +--R 3 +-+ +--R - x \|x - 1 +--R (417) ------------ +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 486 +r0383:= -2*x^(1/2)-2/5*x^(5/2)+atan(x^(1/2))+atanh(x^(1/2))+atanh(x) +--R +--R +--R +-+ +-+ 2 +-+ +--R 5atanh(\|x ) + 5atan(\|x ) + (- 2x - 10)\|x + 5atanh(x) +--R (418) --------------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 486 +a0383:= integrate(t0383,x) +--R +--R +--R +-+ +-+ 2 +-+ +--R - 10log(\|x - 1) + 10atan(\|x ) + (- 4x - 20)\|x + 5log(x + 1) +--R (419) ----------------------------------------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 454 + +--S 455 of 486 +m0383:= a0383-r0383 +--R +--R +--R +-+ +-+ +--R - 2log(\|x - 1) - 2atanh(\|x ) + log(x + 1) - 2atanh(x) +--R (420) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 486 +d0383:= D(m0383,x) +--R +--R +--R (421) 0 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 486 +t0384:= 1/(1+3*x^(1/2))/x +--R +--R +--R 1 +--R (422) ---------- +--R +-+ +--R 3x\|x + x +--R Type: Expression(Integer) +--E 457 + +--S 458 of 486 +r0384:= -2*log(3+1/x^(1/2)) +--R +--R +--R +-+ +--R 3\|x + 1 +--R (423) - 2log(---------) +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 458 + +--S 459 of 486 +a0384:= integrate(t0384,x) +--R +--R +--R +-+ +-+ +--R (424) - 2log(3\|x + 1) + 2log(\|x ) +--R Type: Union(Expression(Integer),...) +--E 459 + +--S 460 of 486 +m0384:= a0384-r0384 +--R +--R +--R +-+ +--R +-+ +-+ 3\|x + 1 +--R (425) - 2log(3\|x + 1) + 2log(\|x ) + 2log(---------) +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 460 + +--S 461 of 486 +d0384:= D(m0384,x) +--R +--R +--R (426) 0 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 486 +t0385:= (x+x^(5/2))^(1/2) +--R +--R +--R +----------+ +--R | 2 +-+ +--R (427) \|x \|x + x +--R Type: Expression(Integer) +--E 462 + +--S 463 of 486 +r0385:= 4/9*(x*(1+x^(3/2)))^(3/2)/x^(3/2) +--R +--R +--R +----------+ +--R +-+ | 2 +-+ +--R (4x\|x + 4)\|x \|x + x +--R (428) ------------------------- +--R +-+ +--R 9\|x +--R Type: Expression(Integer) +--E 463 + +--S 464 of 486 +a0385:= integrate(t0385,x) +--R +--R +--R +----------+ +--R +-+ 2 | 2 +-+ +--R (4\|x + 4x )\|x \|x + x +--R (429) -------------------------- +--R 9x +--R Type: Union(Expression(Integer),...) +--E 464 + +--S 465 of 486 +m0385:= a0385-r0385 +--R +--R +--R (430) 0 +--R Type: Expression(Integer) +--E 465 + +--S 466 of 486 +d0385:= D(m0385,x) +--R +--R +--R (431) 0 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 486 +t0386:= (x^(1/4)+x)^(1/2) +--R +--R +--R +--------+ +--R |4+-+ +--R (432) \|\|x + x +--R Type: Expression(Integer) +--E 467 + +--S 468 of 486 +r0386:= 1/3*((1+x^(3/4))*x^(1/4))^(1/2)*((1+x^(3/4))^(1/2)*x^(3/8)+_ + 2*(1+x^(3/4))^(1/2)*x^(9/8)-asinh(x^(3/8)))/(1+x^(3/4))^(1/2)/x^(1/8) +--R +--R +--R +--------+ +---------+ +--------+ +--R 8+-+3 8+-+ |4+-+ |4+-+3 8+-+3 |4+-+ +--R (\|x + 2x\|x )\|\|x + x \|\|x + 1 - asinh(\|x )\|\|x + x +--R (433) ----------------------------------------------------------------- +--R +---------+ +--R 8+-+ |4+-+3 +--R 3\|x \|\|x + 1 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 486 +--a0386:= integrate(t0386,x) +--E 469 + +--S 470 of 486 +--m0386:= a0386-r0386 +--E 470 + +--S 471 of 486 +--d0386:= D(m0386,x) +--E 471 + +--S 472 of 486 +t0387:= (a*x^m+b*x^(6*m+1))^5 +--R +--R +--R (434) +--R 5 6m + 1 5 4 m 6m + 1 4 2 3 m 2 6m + 1 3 +--R b (x ) + 5a b x (x ) + 10a b (x ) (x ) +--R + +--R 3 2 m 3 6m + 1 2 4 m 4 6m + 1 5 m 5 +--R 10a b (x ) (x ) + 5a b (x ) x + a (x ) +--R Type: Expression(Integer) +--E 472 + +--S 473 of 486 +r0387:= 1/6*(a+b*x^(1+5*m))^6/b/(1+5*m) +--R +--R +--R (435) +--R 6 5m + 1 6 5 5m + 1 5 2 4 5m + 1 4 3 3 5m + 1 3 +--R b (x ) + 6a b (x ) + 15a b (x ) + 20a b (x ) +--R + +--R 4 2 5m + 1 2 5 5m + 1 6 +--R 15a b (x ) + 6a b x + a +--R / +--R 30b m + 6b +--R Type: Expression(Integer) +--E 473 + +--S 474 of 486 +a0387:= integrate(t0387,x) +--R +--R +--R (436) +--R 5 6 m log(x) 30 4 5 m log(x) 25 2 3 4 m log(x) 20 +--R b x (%e ) + 6a b x (%e ) + 15a b x (%e ) +--R + +--R 3 2 3 m log(x) 15 4 2 m log(x) 10 5 m log(x) 5 +--R 20a b x (%e ) + 15a b x (%e ) + 6a x (%e ) +--R / +--R 30m + 6 +--R Type: Union(Expression(Integer),...) +--E 474 + +--S 475 of 486 +m0387:= a0387-r0387 +--R +--R +--R (437) +--R 6 6 m log(x) 30 5 5 m log(x) 25 2 4 4 m log(x) 20 +--R b x (%e ) + 6a b x (%e ) + 15a b x (%e ) +--R + +--R 3 3 3 m log(x) 15 4 2 2 m log(x) 10 5 m log(x) 5 +--R 20a b x (%e ) + 15a b x (%e ) + 6a b x (%e ) +--R + +--R 6 5m + 1 6 5 5m + 1 5 2 4 5m + 1 4 3 3 5m + 1 3 +--R - b (x ) - 6a b (x ) - 15a b (x ) - 20a b (x ) +--R + +--R 4 2 5m + 1 2 5 5m + 1 6 +--R - 15a b (x ) - 6a b x - a +--R / +--R 30b m + 6b +--R Type: Expression(Integer) +--E 475 + +--S 476 of 486 +d0387:= D(m0387,x) +--R +--R +--R (438) +--R 5 5 m log(x) 30 4 4 m log(x) 25 2 3 3 m log(x) 20 +--R b x (%e ) + 5a b x (%e ) + 10a b x (%e ) +--R + +--R 3 2 2 m log(x) 15 4 m log(x) 10 5 m log(x) 5 +--R 10a b x (%e ) + 5a b x (%e ) + a (%e ) +--R + +--R 5 5m 5m + 1 5 4 5m 5m + 1 4 2 3 5m 5m + 1 3 +--R - b x (x ) - 5a b x (x ) - 10a b x (x ) +--R + +--R 3 2 5m 5m + 1 2 4 5m 5m + 1 5 5m +--R - 10a b x (x ) - 5a b x x - a x +--R Type: Expression(Integer) +--E 476 + +--S 477 of 486 +t0388:= 1/(a*x^m+b*x^(1-2*m))^3 +--R +--R +--R 1 +--R (439) -------------------------------------------------------------------- +--R 3 m 3 2 - 2m + 1 m 2 2 - 2m + 1 2 m 3 - 2m + 1 3 +--R a (x ) + 3a b x (x ) + 3a b (x ) x + b (x ) +--R Type: Expression(Integer) +--E 477 + +--S 478 of 486 +r0388:= -1/2/b/(1-3*m)/(a+b*x^(1-3*m))^2 +--R +--R +--R (440) +--R 1 +--R --------------------------------------------------------------------- +--R 3 3 - 3m + 1 2 2 2 - 3m + 1 2 2 +--R (6b m - 2b )(x ) + (12a b m - 4a b )x + 6a b m - 2a b +--R Type: Expression(Integer) +--E 478 + +--S 479 of 486 +a0388:= integrate(t0388,x) +--R +--R +--R (441) +--R m log(x) 3 2 +--R - 2a x (%e ) - b x +--R / +--R 4 4 m log(x) 6 3 3 m log(x) 3 +--R (6a m - 2a )(%e ) + (12a b m - 4a b)x (%e ) +--R + +--R 2 2 2 2 2 +--R (6a b m - 2a b )x +--R Type: Union(Expression(Integer),...) +--E 479 + +--S 480 of 486 +m0388:= a0388-r0388 +--R +--R +--R (442) +--R 4 m log(x) 6 +--R - a (%e ) +--R + +--R 3 - 3m + 1 2 2 2 - 3m + 1 3 m log(x) 3 +--R (- 2a b x (x ) - 4a b x x - 4a b x)(%e ) +--R + +--R 4 2 - 3m + 1 2 3 2 - 3m + 1 2 2 2 +--R - b x (x ) - 2a b x x - 2a b x +--R / +--R 4 3 4 3 - 3m + 1 2 5 2 5 2 - 3m + 1 6 +--R (6a b m - 2a b )(x ) + (12a b m - 4a b )x + 6a b m +--R + +--R 6 +--R - 2a b +--R * +--R m log(x) 6 +--R (%e ) +--R + +--R 3 4 3 4 - 3m + 1 2 4 3 4 3 - 3m + 1 +--R (12a b m - 4a b )x (x ) + (24a b m - 8a b )x x +--R + +--R 5 2 5 2 +--R (12a b m - 4a b )x +--R * +--R m log(x) 3 +--R (%e ) +--R + +--R 2 5 2 5 2 - 3m + 1 2 3 4 3 4 2 - 3m + 1 +--R (6a b m - 2a b )x (x ) + (12a b m - 4a b )x x +--R + +--R 4 3 4 3 2 +--R (6a b m - 2a b )x +--R Type: Expression(Integer) +--E 480 + +--S 481 of 486 +d0388:= D(m0388,x) +--R +--R +--R (443) +--R 3 - 3m m log(x) 9 +--R - a x (%e ) +--R + +--R 3 - 3m + 1 3 2 - 3m + 1 2 2 - 3m + 1 2 - 3m +--R b (x ) + 3a b (x ) + 3a b x - 3a b x x +--R + +--R 3 +--R a +--R * +--R m log(x) 6 +--R (%e ) +--R + +--R 2 2 - 3m m log(x) 3 3 3 - 3m +--R - 3a b x x (%e ) - b x x +--R / +--R 3 3 - 3m + 1 3 4 2 - 3m + 1 2 5 - 3m + 1 6 m log(x) 9 +--R (a b (x ) + 3a b (x ) + 3a b x + a )(%e ) +--R + +--R 2 4 - 3m + 1 3 3 3 - 3m + 1 2 4 2 - 3m + 1 5 +--R (3a b x (x ) + 9a b x (x ) + 9a b x x + 3a b x) +--R * +--R m log(x) 6 +--R (%e ) +--R + +--R 5 2 - 3m + 1 3 2 4 2 - 3m + 1 2 3 3 2 - 3m + 1 +--R 3a b x (x ) + 9a b x (x ) + 9a b x x +--R + +--R 4 2 2 +--R 3a b x +--R * +--R m log(x) 3 +--R (%e ) +--R + +--R 6 3 - 3m + 1 3 5 3 - 3m + 1 2 2 4 3 - 3m + 1 3 3 3 +--R b x (x ) + 3a b x (x ) + 3a b x x + a b x +--R Type: Expression(Integer) +--E 481 + +--S 482 of 486 +t0389:= (1/x^3)^(1/3) +--R +--R +--R +--+ +--R | 1 +--R (444) |-- +--R 3| 3 +--R \|x +--R Type: Expression(Integer) +--E 482 + +--S 483 of 486 +r0389:= (1/x^3)^(1/3)*x*log(x) +--R +--R +--R +--+ +--R | 1 +--R (445) x log(x) |-- +--R 3| 3 +--R \|x +--R Type: Expression(Integer) +--E 483 + +--S 484 of 486 +a0389:= integrate(t0389,x) +--R +--R +--R (446) log(x) +--R Type: Union(Expression(Integer),...) +--E 484 + +--S 485 of 486 +m0389:= a0389-r0389 +--R +--R +--R +--+ +--R | 1 +--R (447) - x log(x) |-- + log(x) +--R 3| 3 +--R \|x +--R Type: Expression(Integer) +--E 485 + +--S 486 of 486 +d0389:= D(m0389,x) +--R +--R +--R +--+2 +--R 2 | 1 +--R x |-- - 1 +--R 3| 3 +--R \|x +--R (448) ------------ +--R +--+2 +--R 3 | 1 +--R x |-- +--R 3| 3 +--R \|x +--R Type: Expression(Integer) +--E 486 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richalgebraic300-399.input.pdf b/src/axiom-website/CATS/richalgebraic300-399.input.pdf new file mode 100644 index 0000000..d3e3369 Binary files /dev/null and b/src/axiom-website/CATS/richalgebraic300-399.input.pdf differ diff --git a/src/axiom-website/CATS/richalgebraic400-461.input.pamphlet b/src/axiom-website/CATS/richalgebraic400-461.input.pamphlet new file mode 100644 index 0000000..df05911 --- /dev/null +++ b/src/axiom-website/CATS/richalgebraic400-461.input.pamphlet @@ -0,0 +1,8135 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richalgebraic400-461.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic400-461.output +)spool richalgebraic400-461.output +)set message test on +)set message auto off +)clear all + +--S 1 of 324 +t0400:= 1/(x^3)^(1/3) +--R +--R +--R 1 +--R (1) ----- +--R +--+ +--R 3| 3 +--R \|x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 324 +r0400:= x*log(x)/(x^3)^(1/3) +--R +--R +--R x log(x) +--R (2) -------- +--R +--+ +--R 3| 3 +--R \|x +--R Type: Expression(Integer) +--E 2 + +--S 3 of 324 +a0400:= integrate(t0400,x) +--R +--R +--R (3) log(x) +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 324 +m0400:= a0400-r0400 +--R +--R +--R +--+ +--R 3| 3 +--R log(x)\|x - x log(x) +--R (4) ---------------------- +--R +--+ +--R 3| 3 +--R \|x +--R Type: Expression(Integer) +--E 4 + +--S 5 of 324 +d0400:= D(m0400,x) +--R +--R +--R +--+ +--R 3| 3 +--R \|x - x +--R (5) --------- +--R +--+ +--R 3| 3 +--R x\|x +--R Type: Expression(Integer) +--E 5 + +--S 6 of 324 +t0401:= (x^m)^(-1/m) +--R +--R +--R 1 +--R (6) - +--R x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 324 +r0401:= x*log(x)/((x^m)^(1/m)) +--R +--R +--R (7) log(x) +--R Type: Expression(Integer) +--E 7 + +--S 8 of 324 +a0401:= integrate(t0401,x) +--R +--R +--R (8) log(x) +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 324 +m0401:= a0401-r0401 +--R +--R +--R (9) 0 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 324 +d0401:= D(m0401,x) +--R +--R +--R (10) 0 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 324 +t0402:= (a*(b*x^m)^n)^(-1/m/n) +--R +--R +--R 1 +--R - --- +--R m n m n +--R (11) (a (b x ) ) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 324 +r0402:= x*log(x)*(a*(b*x^m)^n)^(-1/m/n) +--R +--R +--R 1 +--R - --- +--R m n m n +--R (12) x log(x)(a (b x ) ) +--R Type: Expression(Integer) +--E 12 + +--S 13 of 324 +a0402:= integrate(t0402,x) +--R +--R +--R - n log(b) - log(a) +--R ------------------- +--R m n +--R (13) log(x)%e +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 324 +m0402:= a0402-r0402 +--R +--R +--R 1 - n log(b) - log(a) +--R - --- ------------------- +--R m n m n m n +--R (14) - x log(x)(a (b x ) ) + log(x)%e +--R Type: Expression(Integer) +--E 14 + +--S 15 of 324 +d0402:= D(m0402,x) +--R +--R +--R (15) +--R 1 +--R - --- +--R m n m n +--R (- x log(x) - x)(a (b x ) ) +--R + +--R - m n - 1 - n log(b) - log(a) +--R --------- ------------------- +--R 2 m - 1 m n - 1 m n m n m n +--R a b x log(x)x (b x ) (a (b x ) ) + %e +--R / +--R x +--R Type: Expression(Integer) +--E 15 + +--S 16 of 324 +t0403:= x^(1/2)/(1+x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (16) -------- +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 324 +r0403:= x^(1/2)*(1+x)^(1/2)-asinh(x^(1/2)) +--R +--R +--R +-+ +-+ +-----+ +--R (17) - asinh(\|x ) + \|x \|x + 1 +--R Type: Expression(Integer) +--E 17 + + + +-- +-+ +-----+ +-+ +-----+ +-- - log(- 2\|x \|x + 1 - 2x - 1) + 2\|x \|x + 1 +-- (18) ----------------------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 18 of 324 ok to fail due to sign difference (see above) +a0403:= integrate(t0403,x) +--R +--R +--R +-+ +-----+ +-+ +-----+ +--R - log(2\|x \|x + 1 + 2x + 1) + 2\|x \|x + 1 +--R (18) --------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 18 + + + +-- +-+ +-----+ +-+ +-- - log(- 2\|x \|x + 1 - 2x - 1) + 2asinh(\|x ) +-- (19) ---------------------------------------------- +-- 2 +-- Type: Expression(Integer) + +--S 19 of 324 ok to fail due to sign difference (see above) +m0403:= a0403-r0403 +--R +--R +--R +-+ +-----+ +-+ +--R - log(2\|x \|x + 1 + 2x + 1) + 2asinh(\|x ) +--R (19) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 324 +d0403:= D(m0403,x) +--R +--R +--R (20) 0 +--R Type: Expression(Integer) +--E 20 + +--S 21 of 324 +t0404:= (-1+x)^(1/2)/x^(1/2) +--R +--R +--R +-----+ +--R \|x - 1 +--R (21) -------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 324 +r0404:= (-1+x)^(1/2)*x^(1/2)-asinh((-1+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +-+ +--R (22) - asinh(\|x - 1 ) + \|x - 1 \|x +--R Type: Expression(Integer) +--E 22 + + + +-- +-----+ +-+ +-----+ +-+ +-- - log(2\|x - 1 \|x + 2x - 1) + 2\|x - 1 \|x +-- (23) --------------------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 23 of 324 ok to fail due to sign difference (see above) +a0404:= integrate(t0404,x) +--R +--R +--R +-----+ +-+ +-----+ +-+ +--R - log(- 2\|x - 1 \|x - 2x + 1) + 2\|x - 1 \|x +--R (23) ----------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 23 + + + +-- +-----+ +-+ +-----+ +-- - log(2\|x - 1 \|x + 2x - 1) + 2asinh(\|x - 1 ) +-- (24) ------------------------------------------------ +-- 2 +-- Type: Expression(Integer) + +--S 24 of 324 ok to fail due to sign difference (see above) +m0404:= a0404-r0404 +--R +--R +--R +-----+ +-+ +-----+ +--R - log(- 2\|x - 1 \|x - 2x + 1) + 2asinh(\|x - 1 ) +--R (24) -------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 324 +d0404:= D(m0404,x) +--R +--R +--R (25) 0 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 324 +t0405:= (1+x^(1/2))^2/x^(1/2) +--R +--R +--R +-+ +--R 2\|x + x + 1 +--R (26) ------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 324 +r0405:= 2/3*(1+x^(1/2))^3 +--R +--R +--R +-+ +--R (2x + 6)\|x + 6x + 2 +--R (27) --------------------- +--R 3 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 324 +a0405:= integrate(t0405,x) +--R +--R +--R +-+ +--R (2x + 6)\|x + 6x +--R (28) ----------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 324 +m0405:= a0405-r0405 +--R +--R +--R 2 +--R (29) - - +--R 3 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 324 +d0405:= D(m0405,x) +--R +--R +--R (30) 0 +--R Type: Expression(Integer) +--E 30 + +--S 31 of 324 +t0406:= (1+x^(1/2))^3/x^(1/2) +--R +--R +--R +-+ +--R (x + 3)\|x + 3x + 1 +--R (31) -------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 324 +r0406:= 1/2*(1+x^(1/2))^4 +--R +--R +--R +-+ 2 +--R (4x + 4)\|x + x + 6x + 1 +--R (32) -------------------------- +--R 2 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 324 +a0406:= integrate(t0406,x) +--R +--R +--R +-+ 2 +--R (4x + 4)\|x + x + 6x +--R (33) ---------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 324 +m0406:= a0406-r0406 +--R +--R +--R 1 +--R (34) - - +--R 2 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 324 +d0406:= D(m0406,x) +--R +--R +--R (35) 0 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 324 +t0407:= (x/(1+x))^(1/2) +--R +--R +--R +-----+ +--R | x +--R (36) |----- +--R \|x + 1 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 324 +r0407:= x^(1/2)*(1+x)^(1/2)-asinh(x^(1/2)) +--R +--R +--R +-+ +-+ +-----+ +--R (37) - asinh(\|x ) + \|x \|x + 1 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 324 +a0407:= integrate(t0407,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R | x | x | x +--R - log( |----- + 1) + log( |----- - 1) + (2x + 2) |----- +--R \|x + 1 \|x + 1 \|x + 1 +--R (38) ---------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 324 +m0407:= a0407-r0407 +--R +--R +--R (39) +--R +-----+ +-----+ +--R | x | x +-+ +-+ +-----+ +--R - log( |----- + 1) + log( |----- - 1) + 2asinh(\|x ) - 2\|x \|x + 1 +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R | x +--R (2x + 2) |----- +--R \|x + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 324 +d0407:= D(m0407,x) +--R +--R +--R +-----+ +--R | x +-+ +-----+ +--R |----- \|x \|x + 1 - x +--R \|x + 1 +--R (40) ------------------------ +--R +-+ +-----+ +--R \|x \|x + 1 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 324 +t0408:= (-x/(1+x))^(1/2) +--R +--R +--R +-------+ +--R | x +--R (41) |- ----- +--R \| x + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 324 +r0408:= (-x/(1+x))^(1/2)*(1+x)-atan((-x/(1+x))^(1/2)) +--R +--R +--R +-------+ +-------+ +--R | x | x +--R (42) - atan( |- ----- ) + (x + 1) |- ----- +--R \| x + 1 \| x + 1 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 324 +a0408:= integrate(t0408,x) +--R +--R +--R +-------+ +-------+ +--R | x | x +--R (43) - atan( |- ----- ) + (x + 1) |- ----- +--R \| x + 1 \| x + 1 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 324 +m0408:= a0408-r0408 +--R +--R +--R (44) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 324 +d0408:= D(m0408,x) +--R +--R +--R (45) 0 +--R Type: Expression(Integer) +--E 45 + +--S 46 of 324 +t0409:= ((1+x)/x)^(1/2) +--R +--R +--R +-----+ +--R |x + 1 +--R (46) |----- +--R \| x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 324 +r0409:= x*((1+x)/x)^(1/2)+atanh(((1+x)/x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R |x + 1 |x + 1 +--R (47) atanh( |----- ) + x |----- +--R \| x \| x +--R Type: Expression(Integer) +--E 47 + +--S 48 of 324 +a0409:= integrate(t0409,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R log( |----- + 1) - log( |----- - 1) + 2x |----- +--R \| x \| x \| x +--R (48) -------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 324 +m0409:= a0409-r0409 +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R log( |----- + 1) - log( |----- - 1) - 2atanh( |----- ) +--R \| x \| x \| x +--R (49) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 324 +d0409:= D(m0409,x) +--R +--R +--R (50) 0 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 324 +t0410:= ((1-x)/x)^(1/2) +--R +--R +--R +-------+ +--R |- x + 1 +--R (51) |------- +--R \| x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 324 +r0410:= (-(-1+x)/x)^(1/2)*x-atan((-(-1+x)/x)^(1/2)) +--R +--R +--R +-------+ +-------+ +--R |- x + 1 |- x + 1 +--R (52) - atan( |------- ) + x |------- +--R \| x \| x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 324 +a0410:= integrate(t0410,x) +--R +--R +--R +-------+ +-------+ +--R |- x + 1 |- x + 1 +--R (53) - atan( |------- ) + x |------- +--R \| x \| x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 324 +m0410:= a0410-r0410 +--R +--R +--R (54) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 324 +d0410:= D(m0410,x) +--R +--R +--R (55) 0 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 324 +t0411:= ((-1+x)/x)^(1/2) +--R +--R +--R +-----+ +--R |x - 1 +--R (56) |----- +--R \| x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 324 +r0411:= (-1+x)^(1/2)*x^(1/2)-asinh((-1+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +-+ +--R (57) - asinh(\|x - 1 ) + \|x - 1 \|x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 324 +a0411:= integrate(t0411,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x - 1 |x - 1 |x - 1 +--R - log( |----- + 1) + log( |----- - 1) + 2x |----- +--R \| x \| x \| x +--R (58) ---------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 324 +m0411:= a0411-r0411 +--R +--R +--R (59) +--R +-----+ +-----+ +--R |x - 1 |x - 1 +-----+ +--R - log( |----- + 1) + log( |----- - 1) + 2asinh(\|x - 1 ) +--R \| x \| x +--R + +--R +-----+ +--R +-----+ +-+ |x - 1 +--R - 2\|x - 1 \|x + 2x |----- +--R \| x +--R / +--R 2 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 324 +d0411:= D(m0411,x) +--R +--R +--R +-----+ +--R |x - 1 +-----+ +-+ +--R |----- \|x - 1 \|x - x + 1 +--R \| x +--R (60) ---------------------------- +--R +-----+ +-+ +--R \|x - 1 \|x +--R Type: Expression(Integer) +--E 60 + +--S 61 of 324 +t0412:= (-x/(1+x))^(1/2)/x +--R +--R +--R +-------+ +--R | x +--R |- ----- +--R \| x + 1 +--R (61) ---------- +--R x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 324 +r0412:= 2*atan((-x/(1+x))^(1/2)) +--R +--R +--R +-------+ +--R | x +--R (62) 2atan( |- ----- ) +--R \| x + 1 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 324 +a0412:= integrate(t0412,x) +--R +--R +--R +-------+ +--R | x +--R (63) 2atan( |- ----- ) +--R \| x + 1 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 324 +m0412:= a0412-r0412 +--R +--R +--R (64) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 324 +d0412:= D(m0412,x) +--R +--R +--R (65) 0 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 324 +t0413:= ((1+x)/x)^(1/2)/x +--R +--R +--R +-----+ +--R |x + 1 +--R |----- +--R \| x +--R (66) -------- +--R x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 324 +r0413:= -2*((1+x)/x)^(1/2)+2*atanh(((1+x)/x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R |x + 1 |x + 1 +--R (67) 2atanh( |----- ) - 2 |----- +--R \| x \| x +--R Type: Expression(Integer) +--E 67 + +--S 68 of 324 +a0413:= integrate(t0413,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R (68) log( |----- + 1) - log( |----- - 1) - 2 |----- +--R \| x \| x \| x +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 324 +m0413:= a0413-r0413 +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R (69) log( |----- + 1) - log( |----- - 1) - 2atanh( |----- ) +--R \| x \| x \| x +--R Type: Expression(Integer) +--E 69 + +--S 70 of 324 +d0413:= D(m0413,x) +--R +--R +--R (70) 0 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 324 +t0414:= ((1-x)/(1+x))^(1/2)/(-1+x) +--R +--R +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x + 1 +--R (71) ---------- +--R x - 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 324 +r0414:= 2*atan((-(-1+x)/(1+x))^(1/2)) +--R +--R +--R +-------+ +--R |- x + 1 +--R (72) 2atan( |------- ) +--R \| x + 1 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 324 +a0414:= integrate(t0414,x) +--R +--R +--R +-------+ +--R |- x + 1 +--R (73) 2atan( |------- ) +--R \| x + 1 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 324 +m0414:= a0414-r0414 +--R +--R +--R (74) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 324 +d0414:= D(m0414,x) +--R +--R +--R (75) 0 +--R Type: Expression(Integer) +--E 75 + +--S 76 of 324 +t0415:= (2+(4+x^(1/2))^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +--------+ +--R | | +-+ +--R (76) \|\|\|x + 4 + 2 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 324 +r0415:= 64/5*(2+(4+x^(1/2))^(1/2))^(5/2)-48/7*(2+(4+x^(1/2))^(1/2))^(7/2)+_ + 8/9*(2+(4+x^(1/2))^(1/2))^(9/2) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((80\|x - 512)\|\|x + 4 + 32\|x + 280x - 1024)\|\|\|x + 4 + 2 +--R (77) -------------------------------------------------------------------- +--R 315 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 324 +a0415:= integrate(t0415,x) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((80\|x - 512)\|\|x + 4 + 32\|x + 280x - 1024)\|\|\|x + 4 + 2 +--R (78) -------------------------------------------------------------------- +--R 315 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 324 +m0415:= a0415-r0415 +--R +--R +--R (79) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 324 +d0415:= D(m0415,x) +--R +--R +--R (80) 0 +--R Type: Expression(Integer) +--E 80 + +--S 81 of 324 +t0416:= (2-(4+(-9+5*x)^(1/2))^(1/2))^(1/2) +--R +--R +--R +----------------------+ +--R | +-------------+ +--R | | +------+ +--R (81) \|- \|\|5x - 9 + 4 + 2 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 324 +r0416:= 64/25*(2-(4+(-9+5*x)^(1/2))^(1/2))^(5/2)-48/_ + 35*(2-(4+(-9+5*x)^(1/2))^(1/2))^(7/2)+8/45*_ + (2-(4+(-9+5*x)^(1/2))^(1/2))^(9/2) +--R +--R +--R (82) +--R +-------------+ +--R +------+ | +------+ +------+ +--R ((- 80\|5x - 9 + 512)\|\|5x - 9 + 4 + 32\|5x - 9 + 1400x - 3544) +--R * +--R +----------------------+ +--R | +-------------+ +--R | | +------+ +--R \|- \|\|5x - 9 + 4 + 2 +--R / +--R 1575 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 324 +a0416:= integrate(t0416,x) +--R +--R +--R (83) +--R +-------------+ +--R +------+ | +------+ +------+ +--R ((- 80\|5x - 9 + 512)\|\|5x - 9 + 4 + 32\|5x - 9 + 1400x - 3544) +--R * +--R +----------------------+ +--R | +-------------+ +--R | | +------+ +--R \|- \|\|5x - 9 + 4 + 2 +--R / +--R 1575 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 324 +m0416:= a0416-r0416 +--R +--R +--R (84) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 324 +d0416:= D(m0416,x) +--R +--R +--R (85) 0 +--R Type: Expression(Integer) +--E 85 + +--S 86 of 324 +t0417:= (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(1/2) +--R +--R +--R +----------------------+ +--R | +---------------+ +--R | | +--------+ +--R | | | +-+ +--R (86) \|\|\|\|x + 1 + 1 + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 324 +r0417:= -32/5*(1+(1+(1+x^(1/2))^(1/2))^(1/2))^(5/2)+48/7*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(7/2)+112/9*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(9/2)-320/11*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(11/2)+288/13*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(13/2)-112/15*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(15/2)+16/17*_ + (1+(1+(1+x^(1/2))^(1/2))^(1/2))^(17/2) +--R +--R +--R (87) +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((48048\|x - 74752)\|\|x + 1 - 56448\|x + 140032)\|\|\|x + 1 + 1 +--R + +--R +--------+ +--R +-+ | +-+ +-+ +--R (3696\|x - 20864)\|\|x + 1 + 73808\|x + 720720x - 450432 +--R * +--R +----------------------+ +--R | +---------------+ +--R | | +--------+ +--R | | | +-+ +--R \|\|\|\|x + 1 + 1 + 1 +--R / +--R 765765 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 324 +a0417:= integrate(t0417,x) +--R +--R +--R (88) +--R +---------------+ +--R +--------+ | +--------+ +--R +-+ | +-+ +-+ | | +-+ +--R ((48048\|x - 74752)\|\|x + 1 - 56448\|x + 140032)\|\|\|x + 1 + 1 +--R + +--R +--------+ +--R +-+ | +-+ +-+ +--R (3696\|x - 20864)\|\|x + 1 + 73808\|x + 720720x - 450432 +--R * +--R +----------------------+ +--R | +---------------+ +--R | | +--------+ +--R | | | +-+ +--R \|\|\|\|x + 1 + 1 + 1 +--R / +--R 765765 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 324 +m0417:= a0417-r0417 +--R +--R +--R (89) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 324 +d0417:= D(m0417,x) +--R +--R +--R (90) 0 +--R Type: Expression(Integer) +--E 90 + +--S 91 of 324 +t0418:= (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(1/2) +--R +--R +--R +-----------------------+ +--R | +----------------+ +--R | | +---------+ +--R | | | +-+ +--R (91) \|\|\|2\|x - 1 + 3 + 2 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 324 +r0418:= -16/3*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(3/2)+136/5*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(5/2)-480/7*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(7/2)+304/3*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(9/2)-760/11*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(11/2)+300/13*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(13/2)-56/15*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(15/2)+4/17*_ + (2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(17/2) +--R +--R +--R (92) +--R +---------+ +--R +-+ | +-+ +-+ +--R ((16016\|x + 108800)\|2\|x - 1 - 37632\|x - 475392) +--R * +--R +----------------+ +--R | +---------+ +--R | | +-+ +--R \|\|2\|x - 1 + 3 +--R + +--R +---------+ +--R +-+ | +-+ +-+ +--R (- 6776\|x + 13504)\|2\|x - 1 - 30744\|x + 240240x - 992640 +--R * +--R +-----------------------+ +--R | +----------------+ +--R | | +---------+ +--R | | | +-+ +--R \|\|\|2\|x - 1 + 3 + 2 +--R / +--R 255255 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 324 +a0418:= integrate(t0418,x) +--R +--R +--R (93) +--R +---------+ +--R +-+ | +-+ +-+ +--R ((16016\|x + 108800)\|2\|x - 1 - 37632\|x - 475392) +--R * +--R +----------------+ +--R | +---------+ +--R | | +-+ +--R \|\|2\|x - 1 + 3 +--R + +--R +---------+ +--R +-+ | +-+ +-+ +--R (- 6776\|x + 13504)\|2\|x - 1 - 30744\|x + 240240x - 992640 +--R * +--R +-----------------------+ +--R | +----------------+ +--R | | +---------+ +--R | | | +-+ +--R \|\|\|2\|x - 1 + 3 + 2 +--R / +--R 255255 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 324 +m0418:= a0418-r0418 +--R +--R +--R (94) 0 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 324 +d0418:= D(m0418,x) +--R +--R +--R (95) 0 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 324 +t0419:= x^3/(3*x^2-4*x^4)^(1/2) +--R +--R +--R 3 +--R x +--R (96) -------------- +--R +-----------+ +--R | 4 2 +--R \|- 4x + 3x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 324 +r0419:= -1/8*(3*x^2-4*x^4)^(1/2)+3/32*asin(-1+8/3*x^2) +--R +--R +--R +-----------+ 2 +--R | 4 2 8x - 3 +--R - 4\|- 4x + 3x + 3asin(-------) +--R 3 +--R (97) ---------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 324 +a0419:= integrate(t0419,x) +--R +--R +--R (98) +--R +---------+ +--R +---------+ | 2 +-+ +--R +-+ | 2 2 \|- 4x + 3 - \|3 +--R (- 3\|3 \|- 4x + 3 - 6x + 9)atan(-------------------) +--R 2x +--R + +--R +---------+ +--R 3 | 2 3 +-+ +--R (- 2x + 3x)\|- 4x + 3 + (4x - 3x)\|3 +--R / +--R +---------+ +--R +-+ | 2 2 +--R 8\|3 \|- 4x + 3 + 16x - 24 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 324 +m0419:= a0419-r0419 +--R +--R +--R (99) +--R +---------+ +--R +---------+ | 2 +-+ +--R +-+ | 2 2 \|- 4x + 3 - \|3 +--R (- 12\|3 \|- 4x + 3 - 24x + 36)atan(-------------------) +--R 2x +--R + +--R +-----------+ 2 +---------+ +--R +-+ | 4 2 +-+ 8x - 3 3 | 2 +--R (4\|3 \|- 4x + 3x - 3\|3 asin(-------) - 8x + 12x)\|- 4x + 3 +--R 3 +--R + +--R +-----------+ 2 +--R 2 | 4 2 2 8x - 3 3 +-+ +--R (8x - 12)\|- 4x + 3x + (- 6x + 9)asin(-------) + (16x - 12x)\|3 +--R 3 +--R / +--R +---------+ +--R +-+ | 2 2 +--R 32\|3 \|- 4x + 3 + 64x - 96 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 324 +d0419:= D(m0419,x) +--R +--R +--R (100) +--R +-------------+ +--R 4 2 +-+ | 4 2 5 3 +--R ((16x - 24x )\|3 \|- 64x + 48x - 24x + 144x - 108x) +--R * +--R +-----------+ +--R | 4 2 +--R \|- 4x + 3x +--R + +--R +-------------+ +--R 7 5 3 | 4 2 +--R (- 16x + 102x - 108x + 27x)\|- 64x + 48x +--R * +--R +---------+ +--R | 2 +--R \|- 4x + 3 +--R + +--R +-------------+ +--R 6 4 2 | 4 2 5 3 +-+ +--R ((16x - 96x + 72x )\|- 64x + 48x + (96x - 216x + 108x)\|3 ) +--R * +--R +-----------+ +--R | 4 2 +--R \|- 4x + 3x +--R + +--R +-------------+ +--R 7 5 3 +-+ | 4 2 +--R (64x - 168x + 126x - 27x)\|3 \|- 64x + 48x +--R / +--R +-------------+ +-----------+ +---------+ +--R 4 2 | 4 2 | 4 2 | 2 +--R (16x - 96x + 72)\|- 64x + 48x \|- 4x + 3x \|- 4x + 3 +--R + +--R +-------------+ +-----------+ +--R 4 2 +-+ | 4 2 | 4 2 +--R (- 64x + 144x - 72)\|3 \|- 64x + 48x \|- 4x + 3x +--R Type: Expression(Integer) +--E 100 + +--S 101 of 324 +t0420:= x^3/(-3*x^2-4*x^4)^(1/2) +--R +--R +--R 3 +--R x +--R (101) -------------- +--R +-----------+ +--R | 4 2 +--R \|- 4x - 3x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 324 +r0420:= -1/8*(-3*x^2-4*x^4)^(1/2)-3/32*asin(1+8/3*x^2) +--R +--R +--R +-----------+ 2 +--R | 4 2 8x + 3 +--R - 4\|- 4x - 3x - 3asin(-------) +--R 3 +--R (102) ---------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 324 +a0420:= integrate(t0420,x) +--R +--R +--R (103) +--R +---------+ +--R +---+ +---+ | 2 2 +---+ +--R (3\|- 3 \|- 1 \|- 4x - 3 + (6x + 9)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +---+ +--R \|- 4x - 3 + 2x\|- 1 - \|- 3 +--R log(--------------------------------) +--R x +--R + +--R +---------+ +--R +---+ +---+ | 2 2 +---+ +--R (- 3\|- 3 \|- 1 \|- 4x - 3 + (- 6x - 9)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +---+ +--R \|- 4x - 3 - 2x\|- 1 - \|- 3 +--R log(--------------------------------) +--R x +--R + +--R +---------+ +--R 3 | 2 3 +---+ +--R (- 4x - 6x)\|- 4x - 3 + (8x + 6x)\|- 3 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 16\|- 3 \|- 4x - 3 + 32x + 48 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 324 +m0420:= a0420-r0420 +--R +--R +--R (104) +--R +---------+ +--R +---+ +---+ | 2 2 +---+ +--R (6\|- 3 \|- 1 \|- 4x - 3 + (12x + 18)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +---+ +--R \|- 4x - 3 + 2x\|- 1 - \|- 3 +--R log(--------------------------------) +--R x +--R + +--R +---------+ +--R +---+ +---+ | 2 2 +---+ +--R (- 6\|- 3 \|- 1 \|- 4x - 3 + (- 12x - 18)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +---+ +--R \|- 4x - 3 - 2x\|- 1 - \|- 3 +--R log(--------------------------------) +--R x +--R + +--R +-----------+ 2 +---------+ +--R +---+ | 4 2 +---+ 8x + 3 3 | 2 +--R (4\|- 3 \|- 4x - 3x + 3\|- 3 asin(-------) - 8x - 12x)\|- 4x - 3 +--R 3 +--R + +--R +-----------+ 2 +--R 2 | 4 2 2 8x + 3 3 +---+ +--R (8x + 12)\|- 4x - 3x + (6x + 9)asin(-------) + (16x + 12x)\|- 3 +--R 3 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 32\|- 3 \|- 4x - 3 + 64x + 96 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 324 +d0420:= D(m0420,x) +--R +--R +--R (105) +--R +-------------+ +--R 6 4 2 | 4 2 +--R (- 120x - 360x - 216x )\|- 64x - 48x +--R + +--R 7 5 3 +---+ +--R (48x + 468x + 756x + 324x)\|- 3 +--R * +--R +-----------+ +--R | 4 2 +--R \|- 4x - 3x +--R + +--R +-------------+ +--R 9 7 5 3 +---+ | 4 2 +--R (- 32x - 324x - 621x - 405x - 81x)\|- 3 \|- 64x - 48x +--R * +--R +---------+ +--R | 2 +--R \|- 4x - 3 +--R + +--R +-------------+ +--R 8 6 4 2 +---+ | 4 2 7 5 +--R (32x + 312x + 504x + 216x )\|- 3 \|- 64x - 48x + 720x + 2700x +--R + +--R 3 +--R 2916x + 972x +--R * +--R +-----------+ +--R | 4 2 +--R \|- 4x - 3x +--R + +--R +-------------+ +--R 9 7 5 3 | 4 2 +--R (- 480x - 1980x - 2619x - 1377x - 243x)\|- 64x - 48x +--R / +--R +-------------+ +-----------+ +--R 6 4 2 +---+ | 4 2 | 4 2 +--R (32x + 312x + 504x + 216)\|- 3 \|- 64x - 48x \|- 4x - 3x +--R * +--R +---------+ +--R | 2 +--R \|- 4x - 3 +--R + +--R +-------------+ +-----------+ +--R 6 4 2 | 4 2 | 4 2 +--R (480x + 1800x + 1944x + 648)\|- 64x - 48x \|- 4x - 3x +--R Type: Expression(Integer) +--E 105 + +--S 106 of 324 +t0421:= 1/(-x^(3/5)+x) +--R +--R +--R 1 +--R (106) - --------- +--R 5+-+3 +--R \|x - x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 324 +r0421:= 5/2*log(-1+x^(2/5)) +--R +--R +--R 5+-+2 +--R 5log(\|x - 1) +--R (107) --------------- +--R 2 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 324 +a0421:= integrate(t0421,x) +--R +--R +--R 5+-+2 +--R 5log(\|x - 1) +--R (108) --------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 324 +m0421:= a0421-r0421 +--R +--R +--R (109) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 324 +d0421:= D(m0421,x) +--R +--R +--R (110) 0 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 324 +t0422:= 1/(x+x^(2^(1/2))) +--R +--R +--R 1 +--R (111) --------- +--R +-+ +--R \|2 +--R x + x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 324 +r0422:= -log(1+x^(-2^(1/2)+1))/(2^(1/2)-1) +--R +--R +--R +-+ +--R - \|2 + 1 +--R log(x + 1) +--R (112) - -------------------- +--R +-+ +--R \|2 - 1 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 324 +a0422:= integrate(t0422,x) +--R +--R +--R +-+ +--R +-+ \|2 log(x) +-+ +--R (113) (- \|2 - 1)log(%e + x) + (\|2 + 2)log(x) +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 324 +m0422:= a0422-r0422 +--R +--R +--R +-+ +-+ +--R \|2 log(x) - \|2 + 1 +-+ +--R - log(%e + x) + log(x + 1) + \|2 log(x) +--R (114) ----------------------------------------------------------- +--R +-+ +--R \|2 - 1 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 324 +d0422:= D(m0422,x) +--R +--R +--R +-+ +-+ +-+ +-+ +--R - \|2 \|2 log(x) - \|2 + 1 - \|2 +--R - x %e + x - x x + 1 +--R (115) --------------------------------------------------- +--R +-+ +-+ +-+ +--R - \|2 + 1 \|2 log(x) - \|2 + 1 +--R (x + 1)%e + x x + x +--R Type: Expression(Integer) +--E 115 + +--S 116 of 324 +t0423:= 1/(-x^(1/4)+x^(1/2)) +--R +--R +--R 1 +--R (116) - ----------- +--R 4+-+ +-+ +--R \|x - \|x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 324 +r0423:= 4*x^(1/4)+2*x^(1/2)+4*log(1-x^(1/4)) +--R +--R +--R 4+-+ 4+-+ +-+ +--R (117) 4log(- \|x + 1) + 4\|x + 2\|x +--R Type: Expression(Integer) +--E 117 + +--S 118 of 324 +a0423:= integrate(t0423,x) +--R +--R +--R 4+-+ 4+-+2 4+-+ +--R (118) 4log(\|x - 1) + 2\|x + 4\|x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 324 +m0423:= a0423-r0423 +--R +--R +--R 4+-+ 4+-+ 4+-+2 +-+ +--R (119) 4log(\|x - 1) - 4log(- \|x + 1) + 2\|x - 2\|x +--R Type: Expression(Integer) +--E 119 + +--S 120 of 324 +d0423:= D(m0423,x) +--R +--R +--R 4+-+2 +-+ +--R - \|x + \|x +--R (120) -------------- +--R +-+4+-+2 +--R \|x \|x +--R Type: Expression(Integer) +--E 120 + +--S 121 of 324 +t0424:= 1/(x^(1/4)+x^(1/3)) +--R +--R +--R 1 +--R (121) ----------- +--R 4+-+ 3+-+ +--R \|x + \|x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 324 +r0424:= -12*x^(1/12)+6*x^(1/6)-4*x^(1/4)+3*x^(1/3)-12/5*x^(5/12)+_ + 2*x^(1/2)-12/7*x^(7/12)+3/2*x^(2/3)+12*log(1+x^(1/12)) +--R +--R +--R (122) +--R 12+-+ 12+-+7 12+-+5 12+-+ 6+-+ 4+-+ +--R 840log( \|x + 1) - 120 \|x - 168 \|x - 840 \|x + 420\|x - 280\|x +--R + +--R 3+-+2 3+-+ +-+ +--R 105\|x + 210\|x + 140\|x +--R / +--R 70 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 324 +a0424:= integrate(t0424,x) +--R +--R +--R (123) +--R 12+-+ 12+-+8 12+-+7 12+-+6 12+-+5 +--R 840log( \|x + 1) + 105 \|x - 120 \|x + 140 \|x - 168 \|x +--R + +--R 12+-+4 12+-+3 12+-+2 12+-+ +--R 210 \|x - 280 \|x + 420 \|x - 840 \|x +--R / +--R 70 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 324 +m0424:= a0424-r0424 +--R +--R +--R (124) +--R 12+-+8 12+-+6 12+-+4 12+-+3 12+-+2 6+-+ 4+-+ +--R 3 \|x + 4 \|x + 6 \|x - 8 \|x + 12 \|x - 12\|x + 8\|x +--R + +--R 3+-+2 3+-+ +-+ +--R - 3\|x - 6\|x - 4\|x +--R / +--R 2 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 324 +d0424:= D(m0424,x) +--R +--R +--R (125) +--R 3+-+2 +-+3+-+ +-+ 4+-+3 +-+3+-+2 6+-+5 +-+3+-+2 4+-+3 +--R (((- \|x - \|x \|x - \|x )\|x + \|x \|x )\|x - \|x \|x \|x ) +--R * +--R 12+-+10 +--R \|x +--R + +--R +-+3+-+2 4+-+3 6+-+5 12+-+6 +-+3+-+2 4+-+3 6+-+5 12+-+4 +--R \|x \|x \|x \|x \| + \|x \|x \|x \|x \|x +--R + +--R +-+3+-+2 4+-+3 6+-+5 12+-+2 +-+3+-+2 4+-+3 6+-+5 12+-+ +-+3+-+2 4+-+3 6+-+5 +--R \|x \|x \|x \|x \| - \|x \|x \|x \|x \ + \|x \|x \|x \|x +--R / +--R +-+3+-+2 4+-+3 6+-+5 12+-+10 +--R \|x \|x \|x \|x \|x +--R Type: Expression(Integer) +--E 125 + +--S 126 of 324 +t0425:= 1/(x^(1/3)+x^(1/2)) +--R +--R +--R 1 +--R (126) ----------- +--R 3+-+ +-+ +--R \|x + \|x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 324 +r0425:= 6*x^(1/6)-3*x^(1/3)+2*x^(1/2)-6*log(1+x^(1/6)) +--R +--R +--R 6+-+ 6+-+ 3+-+ +-+ +--R (127) - 6log(\|x + 1) + 6\|x - 3\|x + 2\|x +--R Type: Expression(Integer) +--E 127 + +--S 128 of 324 +a0425:= integrate(t0425,x) +--R +--R +--R 6+-+ 6+-+3 6+-+2 6+-+ +--R (128) - 6log(\|x + 1) + 2\|x - 3\|x + 6\|x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 324 +m0425:= a0425-r0425 +--R +--R +--R 6+-+3 6+-+2 3+-+ +-+ +--R (129) 2\|x - 3\|x + 3\|x - 2\|x +--R Type: Expression(Integer) +--E 129 + +--S 130 of 324 +d0425:= D(m0425,x) +--R +--R +--R 3+-+2 +-+ 6+-+4 +-+3+-+2 6+-+ +-+3+-+2 +--R (- \|x + \|x )\|x + \|x \|x \|x - \|x \|x +--R (130) ------------------------------------------------- +--R +-+3+-+2 6+-+4 +--R \|x \|x \|x +--R Type: Expression(Integer) +--E 130 + +--S 131 of 324 +t0426:= 1/(x^(1/4)+x^(1/2)) +--R +--R +--R 1 +--R (131) ----------- +--R 4+-+ +-+ +--R \|x + \|x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 324 +r0426:= -4*x^(1/4)+2*x^(1/2)+4*log(1+x^(1/4)) +--R +--R +--R 4+-+ 4+-+ +-+ +--R (132) 4log(\|x + 1) - 4\|x + 2\|x +--R Type: Expression(Integer) +--E 132 + +--S 133 of 324 +a0426:= integrate(t0426,x) +--R +--R +--R 4+-+ 4+-+2 4+-+ +--R (133) 4log(\|x + 1) + 2\|x - 4\|x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 324 +m0426:= a0426-r0426 +--R +--R +--R 4+-+2 +-+ +--R (134) 2\|x - 2\|x +--R Type: Expression(Integer) +--E 134 + +--S 135 of 324 +d0426:= D(m0426,x) +--R +--R +--R 4+-+2 +-+ +--R - \|x + \|x +--R (135) -------------- +--R +-+4+-+2 +--R \|x \|x +--R Type: Expression(Integer) +--E 135 + +--S 136 of 324 +t0427:= (1+x^(2/3))/(-1+x^(2/3)) +--R +--R +--R 3+-+2 +--R \|x + 1 +--R (136) --------- +--R 3+-+2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 324 +r0427:= 6*x^(1/3)+x-6*atanh(x^(1/3)) +--R +--R +--R 3+-+ 3+-+ +--R (137) - 6atanh(\|x ) + 6\|x + x +--R Type: Expression(Integer) +--E 137 + +--S 138 of 324 +a0427:= integrate(t0427,x) +--R +--R +--R 3+-+ 3+-+ 3+-+ +--R (138) - 3log(\|x + 1) + 3log(\|x - 1) + 6\|x + x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 324 +m0427:= a0427-r0427 +--R +--R +--R 3+-+ 3+-+ 3+-+ +--R (139) - 3log(\|x + 1) + 3log(\|x - 1) + 6atanh(\|x ) +--R Type: Expression(Integer) +--E 139 + +--S 140 of 324 +d0427:= D(m0427,x) +--R +--R +--R (140) 0 +--R Type: Expression(Integer) +--E 140 + +--S 141 of 324 +t0428:= 1/((a+b*x^3)/x)^(1/2) +--R +--R +--R 1 +--R (141) ----------- +--R +--------+ +--R | 3 +--R |b x + a +--R |-------- +--R \| x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 324 +r0428:= 2/3*atanh(b^(1/2)*x/((a+b*x^3)/x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R 2atanh(-----------) +--R +--------+ +--R | 3 +--R |b x + a +--R |-------- +--R \| x +--R (142) ------------------- +--R +-+ +--R 3\|b +--R Type: Expression(Integer) +--E 142 + +--S 143 of 324 +a0428:= integrate(t0428,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 3 +--R |1 2 |1 |b x + a 3 +--R |- log(2b x |- |-------- - 2b x - a) +--R \|b \|b \| x +--R (143) - ----------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 324 +m0428:= a0428-r0428 +--R +--R +--R (144) +--R +--------+ +--R +-+ +-+ | 3 +-+ +--R |1 +-+ 2 |1 |b x + a 3 x\|b +--R - |- \|b log(2b x |- |-------- - 2b x - a) - 2atanh(-----------) +--R \|b \|b \| x +--------+ +--R | 3 +--R |b x + a +--R |-------- +--R \| x +--R --------------------------------------------------------------------- +--R +-+ +--R 3\|b +--R Type: Expression(Integer) +--E 144 + +--S 145 of 324 +d0428:= D(m0428,x) +--R +--R +--R (145) 0 +--R Type: Expression(Integer) +--E 145 + +--S 146 of 324 +t0429:= 1/((a+b*x^4)/x^2)^(1/2) +--R +--R +--R 1 +--R (146) ----------- +--R +--------+ +--R | 4 +--R |b x + a +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 324 +r0429:= 1/2*atanh(b^(1/2)*x/((a+b*x^4)/x^2)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 4 +--R |b x + a +--R |-------- +--R | 2 +--R \| x +--R (147) ------------------ +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 147 + +--S 148 of 324 +a0429:= integrate(t0429,x) +--R +--R +--R (148) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|b - b x )\|b x + a + (- b x - a)\|b + b x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|b x + a - a +--R [---------------------------------------------------------------, +--R +-+ +--R 2\|b +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R 2 +--R b x +--R ------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 148 + +--S 149 of 324 +m0429a:= a0429.1-r0429 +--R +--R +--R (149) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|b - b x )\|b x + a + (- b x - a)\|b + b x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 4 +--R |b x + a +--R |-------- +--R | 2 +--R \| x +--R / +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 149 + +--S 150 of 324 +d0429a:= D(m0429a,x) +--R +--R +--R (150) +--R +--------+ +--R | 4 +--R 5 +-+ +-+ 2 7 3 |b x + a +--R ((- 3b x - 4a x)\|a \|b + b x + 4a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 2 8 4 2 +-+ 2 6 2 +-+ +--R (- b x - 5a b x - 4a )\|b + (3b x + 4a b x )\|a +--R * +--R +--------+ +--R | 4 +--R \|b x + a +--R + +--R +--------+ +--R | 4 +--R 2 9 5 2 +-+ 2 7 3 +-+ |b x + a +--R ((b x + 5a b x + 4a x)\|b + (- 3b x - 4a b x )\|a ) |-------- +--R | 2 +--R \| x +--R + +--R 2 8 4 2 +-+ +-+ 3 10 2 6 2 2 +--R (3b x + 7a b x + 4a )\|a \|b - b x - 5a b x - 4a b x +--R / +--R +--------+ +--R | 4 +--R 2 8 4 2 +-+ 2 6 2 +-+ |b x + a +--R ((b x + 5a b x + 4a )\|b + (- 3b x - 4a b x )\|a ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|b x + a +--R + +--R +--------+ +--R | 4 +--R 2 8 4 2 +-+ +-+ 3 10 2 6 2 2 |b x + a +--R ((- 3b x - 7a b x - 4a )\|a \|b + b x + 5a b x + 4a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 150 + +--S 151 of 324 +m0429b:= a0429.2-r0429 +--R +--R +--R (151) +--R +--------+ +--R +-+ +---+ | 4 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ 2 +--R | 4 b x +--R |b x + a +--R |-------- +--R | 2 +--R \| x +--R ---------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 151 + +--S 152 of 324 +d0429b:= D(m0429b,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 |b x + a +--R - \|b x + a + x |-------- +--R | 2 +--R \| x +--R (152) ---------------------------- +--R +--------+ +--R | 4 +--------+ +--R |b x + a | 4 +--R |-------- \|b x + a +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 324 +t0430:= 1/((a+b*x^5)/x^3)^(1/2) +--R +--R +--R 1 +--R (153) ----------- +--R +--------+ +--R | 5 +--R |b x + a +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 153 + +--S 154 of 324 +r0430:= 2/5*atanh(b^(1/2)*x/((a+b*x^5)/x^3)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R 2atanh(-----------) +--R +--------+ +--R | 5 +--R |b x + a +--R |-------- +--R | 3 +--R \| x +--R (154) ------------------- +--R +-+ +--R 5\|b +--R Type: Expression(Integer) +--E 154 + +--S 155 of 324 +a0430:= integrate(t0430,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 5 +--R |1 3 |1 |b x + a 5 +--R |- log(- 2b x |- |-------- + 2b x + a) +--R \|b \|b \| x +--R (155) - ------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 155 + +--S 156 of 324 +m0430:= a0430-r0430 +--R +--R +--R (156) +--R +--------+ +--R +-+ +-+ | 5 +-+ +--R |1 +-+ 3 |1 |b x + a 5 x\|b +--R - |- \|b log(- 2b x |- |-------- + 2b x + a) - 2atanh(-----------) +--R \|b \|b \| x +--------+ +--R | 5 +--R |b x + a +--R |-------- +--R | 3 +--R \| x +--R ----------------------------------------------------------------------- +--R +-+ +--R 5\|b +--R Type: Expression(Integer) +--E 156 + +--S 157 of 324 +d0430:= D(m0430,x) +--R +--R +--R (157) +--R +--------+ +--------+ +--R +-+ | 5 | 5 +--R 4 |1 |b x + a 5 |b x + a +--R (- 2b x |- |-------- - 2b x - a) |-------- +--R \|b | 3 \| x +--R \| x +--R + +--R +--------+ +--R | 5 +-+ +--R 6 |b x + a 2 7 2 |1 +--R (2b x + a x) |-------- + (2b x + 2a b x ) |- +--R | 3 \|b +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 5 | 5 +-+ | 5 +--R 5 |b x + a |b x + a 2 7 2 |1 |b x + a +--R (2b x + a) |-------- |-------- + (- 2b x - 2a b x ) |- |-------- +--R | 3 \| x \|b | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 157 + +--S 158 of 324 +t0431:= 1/((a+b*x^n)/(x^(-2+n)))^(1/2) +--R +--R +--R 1 +--R (158) ----------- +--R +--------+ +--R | n +--R |b x + a +--R |-------- +--R | n - 2 +--R \| x +--R Type: Expression(Integer) +--E 158 + +--S 159 of 324 +r0431:= 2*atanh(b^(1/2)*x/(x^2*(x^(-n)*a+b))^(1/2))/b^(1/2)/n +--R +--R +--R +-+ +--R x\|b +--R 2atanh(------------------) +--R +---------------+ +--R | 2 - n 2 +--R \|a x x + b x +--R (159) -------------------------- +--R +-+ +--R n\|b +--R Type: Expression(Integer) +--E 159 + +--S 160 of 324 +a0431:= integrate(t0431,x) +--R +--R +--R (160) +--R +----------------+ +--R | n log(x) +--R n log(x) |b %e + a +-+ n log(x) +-+ +--R log(2b %e |---------------- + 2b\|b %e + a\|b ) +--R | n log(x) +--R \| %e +--R [----------------------------------------------------------------, +--R +-+ +--R n\|b +--R +----------------+ +--R | n log(x) +--R +---+ |b %e + a +--R \|- b |---------------- +--R | n log(x) +--R \| %e +--R 2atan(-------------------------) +--R b +--R --------------------------------] +--R +---+ +--R n\|- b +--R Type: Union(List(Expression(Integer)),...) +--E 160 + +--S 161 of 324 +m0431a:= a0431.1-r0431 +--R +--R +--R (161) +--R +----------------+ +--R | n log(x) +--R n log(x) |b %e + a +-+ n log(x) +-+ +--R log(2b %e |---------------- + 2b\|b %e + a\|b ) +--R | n log(x) +--R \| %e +--R + +--R +-+ +--R x\|b +--R - 2atanh(------------------) +--R +---------------+ +--R | 2 - n 2 +--R \|a x x + b x +--R / +--R +-+ +--R n\|b +--R Type: Expression(Integer) +--E 161 + +--S 162 of 324 +d0431a:= D(m0431a,x) +--R +--R +--R (162) +--R +---------------+ +--R - n n log(x) | 2 - n 2 2 - n - 1 +-+ n log(x) +--R 2b x %e \|a x x + b x - 2b x x \|b %e +--R + +--R 2 - n - 1 +-+ +--R - a x x \|b +--R * +--R +----------------+ +--R | n log(x) +--R |b %e + a +--R |---------------- +--R | n log(x) +--R \| %e +--R + +--R +---------------+ +--R - n +-+ n log(x) - n +-+ | 2 - n 2 +--R (2b x \|b %e + a x \|b )\|a x x + b x +--R + +--R 2 2 - n - 1 n log(x) 2 - n - 1 +--R - 2b x x %e - 2a b x x +--R / +--R +---------------+ +--R - n +-+ n log(x) - n +-+ | 2 - n 2 +--R (2b x x \|b %e + a x x \|b )\|a x x + b x +--R * +--R +----------------+ +--R | n log(x) +--R |b %e + a +--R |---------------- +--R | n log(x) +--R \| %e +--R + +--R +---------------+ +--R 2 - n n log(x) - n | 2 - n 2 +--R (2b x x %e + 2a b x x )\|a x x + b x +--R Type: Expression(Integer) +--E 162 + +--S 163 of 324 +m0431b:= a0431.2-r0431 +--R +--R +--R (163) +--R +----------------+ +--R | n log(x) +--R +---+ |b %e + a +--R \|- b |---------------- +--R | n log(x) +-+ +--R +-+ \| %e +---+ x\|b +--R 2\|b atan(-------------------------) - 2\|- b atanh(------------------) +--R b +---------------+ +--R | 2 - n 2 +--R \|a x x + b x +--R ----------------------------------------------------------------------- +--R +---+ +-+ +--R n\|- b \|b +--R Type: Expression(Integer) +--E 163 + +--S 164 of 324 +d0431b:= D(m0431b,x) +--R +--R +--R +----------------+ +--R | n log(x) +---------------+ +--R 2 - n - 1 |b %e + a - n | 2 - n 2 +--R - x x |---------------- + x \|a x x + b x +--R | n log(x) +--R \| %e +--R (164) -------------------------------------------------------- +--R +----------------+ +--R +---------------+ | n log(x) +--R - n | 2 - n 2 |b %e + a +--R x x \|a x x + b x |---------------- +--R | n log(x) +--R \| %e +--R Type: Expression(Integer) +--E 164 + +--S 165 of 324 +t0432:= 1/((a-b*x^3)/x)^(1/2) +--R +--R +--R 1 +--R (165) ------------- +--R +----------+ +--R | 3 +--R |- b x + a +--R |---------- +--R \| x +--R Type: Expression(Integer) +--E 165 + +--S 166 of 324 +r0432:= 2/3*atan(b^(1/2)*x/((a-b*x^3)/x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R 2atan(-------------) +--R +----------+ +--R | 3 +--R |- b x + a +--R |---------- +--R \| x +--R (166) -------------------- +--R +-+ +--R 3\|b +--R Type: Expression(Integer) +--E 166 + +--S 167 of 324 +a0432:= integrate(t0432,x) +--R +--R +--R +----------+ +--R +---+ | 3 +---+ +--R | 1 2 |- b x + a | 1 3 +--R |- - log(- 2b x |---------- |- - + 2b x - a) +--R \| b \| x \| b +--R (167) - ------------------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 167 + +--S 168 of 324 +m0432:= a0432-r0432 +--R +--R +--R (168) +--R +----------+ +--R +---+ | 3 +---+ +--R | 1 +-+ 2 |- b x + a | 1 3 +--R - |- - \|b log(- 2b x |---------- |- - + 2b x - a) +--R \| b \| x \| b +--R + +--R +-+ +--R x\|b +--R - 2atan(-------------) +--R +----------+ +--R | 3 +--R |- b x + a +--R |---------- +--R \| x +--R / +--R +-+ +--R 3\|b +--R Type: Expression(Integer) +--E 168 + +--S 169 of 324 +d0432:= D(m0432,x) +--R +--R +--R (169) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 324 +t0433:= 1/((a-b*x^4)/x^2)^(1/2) +--R +--R +--R 1 +--R (170) ------------- +--R +----------+ +--R | 4 +--R |- b x + a +--R |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 170 + +--S 171 of 324 +r0433:= 1/2*atan(b^(1/2)*x/((a-b*x^4)/x^2)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R atan(-------------) +--R +----------+ +--R | 4 +--R |- b x + a +--R |---------- +--R | 2 +--R \| x +--R (171) ------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 171 + +--S 172 of 324 +a0433:= integrate(t0433,x) +--R +--R +--R (172) +--R +----------+ +----------+ +--R | 4 +---+ 2 +-+ 4 +---+ 2 | 4 +--R (\|- b x + a \|- b - b x )\|a + (b x - a)\|- b + b x \|- b x + a +--R log(-----------------------------------------------------------------------) +--R +----------+ +--R | 4 +-+ +--R \|- b x + a \|a - a +--R [---------------------------------------------------------------------------- +--R +---+ +--R 2\|- b +--R , +--R +----------+ +--R +-+ | 4 +-+ +--R (\|a - \|- b x + a )\|b +--R atan(--------------------------) +--R 2 +--R b x +--R --------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 172 + +--S 173 of 324 +m0433a:= a0433.1-r0433 +--R +--R +--R (173) +--R +-+ +--R \|b +--R * +--R log +--R +----------+ +--R | 4 +---+ 2 +-+ 4 +---+ +--R (\|- b x + a \|- b - b x )\|a + (b x - a)\|- b +--R + +--R +----------+ +--R 2 | 4 +--R b x \|- b x + a +--R / +--R +----------+ +--R | 4 +-+ +--R \|- b x + a \|a - a +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b atan(-------------) +--R +----------+ +--R | 4 +--R |- b x + a +--R |---------- +--R | 2 +--R \| x +--R / +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 173 + +--S 174 of 324 +d0433a:= D(m0433a,x) +--R +--R +--R (174) +--R +----------+ +--R +----------+ | 4 +--R 5 | 4 |- b x + a 2 8 4 +--R (- 3b x + 4a x)\|- b x + a |---------- - 3b x + 7a b x +--R | 2 +--R \| x +--R + +--R 2 +--R - 4a +--R * +--R +---+ +--R \|- b +--R + +--R +----------+ +--R | 4 +----------+ +--R 2 7 3 |- b x + a 2 6 2 | 4 +--R (3b x - 4a b x ) |---------- + (- 3b x + 4a b x )\|- b x + a +--R | 2 +--R \| x +--R * +--R +-+ +--R \|a +--R + +--R +----------+ +--R | 4 +--R 2 9 5 2 |- b x + a +--R (- b x + 5a b x - 4a x) |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 8 4 2 | 4 +--R (b x - 5a b x + 4a )\|- b x + a +--R * +--R +---+ +--R \|- b +--R + +--R +----------+ +--R +----------+ | 4 +--R 2 7 3 | 4 |- b x + a 3 10 2 6 2 2 +--R (- b x + 4a b x )\|- b x + a |---------- - b x + 5a b x - 4a b x +--R | 2 +--R \| x +--R / +--R +----------+ +--R | 4 +--R 2 8 4 2 |- b x + a +---+ +--R (3b x - 7a b x + 4a ) |---------- \|- b +--R | 2 +--R \| x +--R + +--R +----------+ +--R +----------+ | 4 +--R 2 6 2 | 4 |- b x + a +--R (3b x - 4a b x )\|- b x + a |---------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|a +--R + +--R +----------+ +--R +----------+ | 4 +--R 2 8 4 2 | 4 |- b x + a +---+ +--R (- b x + 5a b x - 4a )\|- b x + a |---------- \|- b +--R | 2 +--R \| x +--R + +--R +----------+ +--R | 4 +--R 3 10 2 6 2 2 |- b x + a +--R (b x - 5a b x + 4a b x ) |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 174 + +--S 175 of 324 +m0433b:= a0433.2-r0433 +--R +--R +--R +----------+ +--R +-+ | 4 +-+ +-+ +--R (\|a - \|- b x + a )\|b x\|b +--R 2atan(--------------------------) - atan(-------------) +--R 2 +----------+ +--R b x | 4 +--R |- b x + a +--R |---------- +--R | 2 +--R \| x +--R (175) ------------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 175 + +--S 176 of 324 +d0433b:= D(m0433b,x) +--R +--R +--R +----------+ +--R | 4 +----------+ +--R |- b x + a | 4 +--R x |---------- - \|- b x + a +--R | 2 +--R \| x +--R (176) ------------------------------ +--R +----------+ +--R +----------+ | 4 +--R | 4 |- b x + a +--R \|- b x + a |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 324 +t0434:= 1/((a-b*x^5)/x^3)^(1/2) +--R +--R +--R 1 +--R (177) ------------- +--R +----------+ +--R | 5 +--R |- b x + a +--R |---------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 324 +r0434:= 2/5*atan(b^(1/2)*x/((a-b*x^5)/x^3)^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R 2atan(-------------) +--R +----------+ +--R | 5 +--R |- b x + a +--R |---------- +--R | 3 +--R \| x +--R (178) -------------------- +--R +-+ +--R 5\|b +--R Type: Expression(Integer) +--E 178 + +--S 179 of 324 +a0434:= integrate(t0434,x) +--R +--R +--R +----------+ +--R +---+ | 5 +---+ +--R | 1 3 |- b x + a | 1 5 +--R |- - log(2b x |---------- |- - - 2b x + a) +--R \| b \| x \| b +--R (179) - ----------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 179 + +--S 180 of 324 +m0434:= a0434-r0434 +--R +--R +--R (180) +--R +----------+ +--R +---+ | 5 +---+ +-+ +--R | 1 +-+ 3 |- b x + a | 1 5 x\|b +--R - |- - \|b log(2b x |---------- |- - - 2b x + a) - 2atan(-------------) +--R \| b \| x \| b +----------+ +--R | 5 +--R |- b x + a +--R |---------- +--R | 3 +--R \| x +--R ---------------------------------------------------------------------------- +--R +-+ +--R 5\|b +--R Type: Expression(Integer) +--E 180 + +--S 181 of 324 +d0434:= D(m0434,x) +--R +--R +--R (181) +--R +----------+ +----------+ +--R | 5 | 5 +---+ +--R 4 |- b x + a |- b x + a 2 7 2 | 1 +--R (- 2b x |---------- |---------- - 2b x + 2a b x ) |- - +--R \| x | 3 \| b +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 6 |- b x + a 5 |- b x + a +--R (2b x - a x) |---------- + (- 2b x + a) |---------- +--R | 3 \| x +--R \| x +--R / +--R +----------+ +--R | 5 +---+ +--R 2 7 2 |- b x + a | 1 +--R (2b x - 2a b x ) |---------- |- - +--R | 3 \| b +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 5 |- b x + a |- b x + a +--R (2b x - a) |---------- |---------- +--R \| x | 3 +--R \| x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 324 +t0435:= 1/((a-b*x^n)/(x^(-2+n)))^(1/2) +--R +--R +--R 1 +--R (182) ------------- +--R +----------+ +--R | n +--R |- b x + a +--R |---------- +--R | n - 2 +--R \| x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 324 +r0435:= 2*atan(b^(1/2)*x/(x^2*(x^(-n)*a-b))^(1/2))/b^(1/2)/n +--R +--R +--R +-+ +--R x\|b +--R 2atan(------------------) +--R +---------------+ +--R | 2 - n 2 +--R \|a x x - b x +--R (183) ------------------------- +--R +-+ +--R n\|b +--R Type: Expression(Integer) +--E 183 + +--S 184 of 324 +a0435:= integrate(t0435,x) +--R +--R +--R (184) +--R +------------------+ +--R | n log(x) +--R n log(x) |- b %e + a +---+ n log(x) +---+ +--R log(- 2b %e |------------------ - 2b\|- b %e + a\|- b ) +--R | n log(x) +--R \| %e +--R [------------------------------------------------------------------------, +--R +---+ +--R n\|- b +--R +------------------+ +--R | n log(x) +--R +-+ |- b %e + a +--R \|b |------------------ +--R | n log(x) +--R \| %e +--R 2atan(-------------------------) +--R b +--R - --------------------------------] +--R +-+ +--R n\|b +--R Type: Union(List(Expression(Integer)),...) +--E 184 + +--S 185 of 324 +m0435a:= a0435.1-r0435 +--R +--R +--R (185) +--R +-+ +--R \|b +--R * +--R +------------------+ +--R | n log(x) +--R n log(x) |- b %e + a +---+ n log(x) +---+ +--R log(- 2b %e |------------------ - 2b\|- b %e + a\|- b ) +--R | n log(x) +--R \| %e +--R + +--R +-+ +--R +---+ x\|b +--R - 2\|- b atan(------------------) +--R +---------------+ +--R | 2 - n 2 +--R \|a x x - b x +--R / +--R +---+ +-+ +--R n\|- b \|b +--R Type: Expression(Integer) +--E 185 + +--S 186 of 324 +d0435a:= D(m0435a,x) +--R +--R +--R (186) +--R +---------------+ +--R - n n log(x) | 2 - n 2 2 - n - 1 +---+ n log(x) +--R 2b x %e \|a x x - b x - 2b x x \|- b %e +--R + +--R 2 - n - 1 +---+ +--R a x x \|- b +--R * +--R +------------------+ +--R | n log(x) +--R |- b %e + a +--R |------------------ +--R | n log(x) +--R \| %e +--R + +--R +---------------+ +--R - n +---+ n log(x) - n +---+ | 2 - n 2 +--R (2b x \|- b %e - a x \|- b )\|a x x - b x +--R + +--R 2 2 - n - 1 n log(x) 2 - n - 1 +--R 2b x x %e - 2a b x x +--R / +--R +---------------+ +--R - n +---+ n log(x) - n +---+ | 2 - n 2 +--R (2b x x \|- b %e - a x x \|- b )\|a x x - b x +--R * +--R +------------------+ +--R | n log(x) +--R |- b %e + a +--R |------------------ +--R | n log(x) +--R \| %e +--R + +--R +---------------+ +--R 2 - n n log(x) - n | 2 - n 2 +--R (- 2b x x %e + 2a b x x )\|a x x - b x +--R Type: Expression(Integer) +--E 186 + +--S 187 of 324 +m0435b:= a0435.2-r0435 +--R +--R +--R +------------------+ +--R | n log(x) +--R +-+ |- b %e + a +--R \|b |------------------ +--R | n log(x) +-+ +--R \| %e x\|b +--R - 2atan(-------------------------) - 2atan(------------------) +--R b +---------------+ +--R | 2 - n 2 +--R \|a x x - b x +--R (187) -------------------------------------------------------------- +--R +-+ +--R n\|b +--R Type: Expression(Integer) +--E 187 + +--S 188 of 324 +d0435b:= D(m0435b,x) +--R +--R +--R +------------------+ +--R | n log(x) +---------------+ +--R 2 - n - 1 |- b %e + a - n | 2 - n 2 +--R - x x |------------------ + x \|a x x - b x +--R | n log(x) +--R \| %e +--R (188) ---------------------------------------------------------- +--R +------------------+ +--R +---------------+ | n log(x) +--R - n | 2 - n 2 |- b %e + a +--R x x \|a x x - b x |------------------ +--R | n log(x) +--R \| %e +--R Type: Expression(Integer) +--E 188 + +--S 189 of 324 +t0436:= ((a+b*x^2)/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |b x + a +--R (189) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 189 + +--S 190 of 324 +r0436:= (b+a/x^2)^(1/2)*x-a^(1/2)*atanh((b+a/x^2)^(1/2)*x/a^(1/2)) +--R +--R +--R +--------+ +--R | 2 +--R |b x + a +--R x |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x |b x + a +--R (190) - \|a atanh(------------) + x |-------- +--R +-+ | 2 +--R \|a \| x +--R Type: Expression(Integer) +--E 190 + +--S 191 of 324 +a0436:= integrate(t0436,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|b x + a - \|a 2 +-+ +--R (a\|b x + a - a\|a )log(------------------) + b x \|a +--R x +--R (191) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R Type: Union(Expression(Integer),...) +--E 191 + +--S 192 of 324 +m0436:= a0436-r0436 +--R +--R +--R (192) +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|b x + a - \|a +--R (a\|b x + a - a\|a )log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--R |b x + a +--R x |-------- +--------+ +--R +--------+ | 2 | 2 +--------+ +--R | 2 +-+ \| x +-+ |b x + a | 2 +--R (a\|b x + a - a\|a )atanh(------------) - x\|a |-------- \|b x + a +--R +-+ | 2 +--R \|a \| x +--R + +--R +--------+ +--R | 2 +--R |b x + a 2 +-+ +--R a x |-------- + b x \|a +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R Type: Expression(Integer) +--E 192 + +--S 193 of 324 +d0436:= D(m0436,x) +--R +--R +--R (193) +--R +--------+ +--R | 2 +--R 2 5 3 2 |b x + a 2 4 2 2 +-+ +--R ((- b x - 5a b x - 4a x) |-------- + (- 3b x - 7a b x - 4a )\|a ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |b x + a 3 6 2 4 2 2 3 +--R (3b x + 7a b x + 4a x)\|a |-------- + b x + 6a b x + 9a b x + 4a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 2 +-+ |b x + a | 2 +--R (3b x + 4a x )\|a |-------- \|b x + a +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |b x + a +--R (- b x - 5a b x - 4a x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 193 + +--S 194 of 324 +t0437:= ((a+b*x^n)/x^2)^(1/2) +--R +--R +--R +--------+ +--R | n +--R |b x + a +--R (194) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 194 + +--S 195 of 324 +r0437:= 2*x*((a+b*x^n)/x^2)^(1/2)*((a+b*x^n)^(1/2)-a^(1/2)*_ + atanh((a+b*x^n)^(1/2)/a^(1/2)))/n/(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--------+ +--------+ +--R | n | n | n +--------+ +--R +-+ |b x + a \|b x + a |b x + a | n +--R - 2x\|a |-------- atanh(-----------) + 2x |-------- \|b x + a +--R | 2 +-+ | 2 +--R \| x \|a \| x +--R (195) ---------------------------------------------------------------- +--R +--------+ +--R | n +--R n\|b x + a +--R Type: Expression(Integer) +--E 195 + +--S 196 of 324 +a0437:= integrate(t0437,x) +--R +--R +--R (196) +--R [ +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R | n log(x) +--R 2\|b %e + a +--R / +--R n +--R , +--R +----------------+ +--R | n log(x) +----------------+ +--R +---+ \|b %e + a | n log(x) +--R - 2\|- a atan(-------------------) + 2\|b %e + a +--R +---+ +--R \|- a +--R ---------------------------------------------------------] +--R n +--R Type: Union(List(Expression(Integer)),...) +--E 196 + +--S 197 of 324 +m0437a:= a0437.1-r0437 +--R +--R +--R (197) +--R +----------------+ +--R +--------+ +-+ | n log(x) n log(x) +--R +-+ | n - 2\|a \|b %e + a + b %e + 2a +--R \|a \|b x + a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--------+ +--R +--------+ +----------------+ | n | n +--R | n | n log(x) +-+ |b x + a \|b x + a +--R 2\|b x + a \|b %e + a + 2x\|a |-------- atanh(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R +--------+ +--R | n +--------+ +--R |b x + a | n +--R - 2x |-------- \|b x + a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +--R n\|b x + a +--R Type: Expression(Integer) +--E 197 + +--S 198 of 324 +d0437a:= D(m0437a,x) +--R +--R +--R (198) +--R +--------+ +--R | n +--R n n log(x) n |b x + a +--R (- b x %e - 2a x ) |-------- +--R | 2 +--R \| x +--R + +--R n - 1 n n - 1 +-+ +--R (- 2b x x - 2a x )\|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R n +-+ n log(x) n +-+ |b x + a +--R (2b x \|a %e + 2a x \|a ) |-------- +--R | 2 +--R \| x +--R + +--R 2 n - 1 n n - 1 n log(x) n - 1 n 2 n - 1 +--R (b x x + a b x )%e + 2a b x x + 2a x +--R / +--R +--------+ +--R | n +----------------+ +--R n +-+ |b x + a | n log(x) +--R 2x x \|a |-------- \|b %e + a +--R | 2 +--R \| x +--R + +--R +--------+ +--R | n +--R n n log(x) n |b x + a +--R (- b x x %e - 2a x x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 198 + +--S 199 of 324 +m0437b:= a0437.2-r0437 +--R +--R +--R (199) +--R +----------------+ +--R +--------+ | n log(x) +--R +---+ | n \|b %e + a +--R - 2\|- a \|b x + a atan(-------------------) +--R +---+ +--R \|- a +--R + +--R +--------+ +--------+ +--R +--------+ +----------------+ | n | n +--R | n | n log(x) +-+ |b x + a \|b x + a +--R 2\|b x + a \|b %e + a + 2x\|a |-------- atanh(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R +--------+ +--R | n +--------+ +--R |b x + a | n +--R - 2x |-------- \|b x + a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +--R n\|b x + a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 324 +d0437b:= D(m0437b,x) +--R +--R +--R (200) +--R +----------------+ +--R n - 1 n n - 1 | n log(x) +--R (- b x x - a x )\|b %e + a +--R + +--R +--------+ +--R | n +--R n n log(x) n |b x + a +--R (b x %e + a x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +----------------+ +--R n |b x + a | n log(x) +--R x x |-------- \|b %e + a +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 200 + +--S 201 of 324 +t0438:= ((-a+b*x^2)/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |b x - a +--R (201) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 201 + +--S 202 of 324 +r0438:= (b-a/x^2)^(1/2)*x-a^(1/2)*atan((b-a/x^2)^(1/2)*x/a^(1/2)) +--R +--R +--R +--------+ +--R | 2 +--R |b x - a +--R x |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x |b x - a +--R (202) - \|a atan(------------) + x |-------- +--R +-+ | 2 +--R \|a \| x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 324 +a0438:= integrate(t0438,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +---+ +--R | 2 +---+ \|b x - a - \|- a 2 +---+ +--R (- a\|b x - a + a\|- a )log(--------------------) + b x \|- a +--R x +--R (203) ---------------------------------------------------------------- +--R +--------+ +--R +---+ | 2 +--R \|- a \|b x - a + a +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 324 +m0438:= a0438-r0438 +--R +--R +--R (204) +--R +--------+ +--R +--------+ | 2 +---+ +--R | 2 +---+ \|b x - a - \|- a +--R (- a\|b x - a + a\|- a )log(--------------------) +--R x +--R + +--R +--------+ +--R | 2 +--R |b x - a +--R x |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 +-+ \| x +--R (\|- a \|a \|b x - a + a\|a )atan(------------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +---+ |b x - a | 2 |b x - a 2 +---+ +--R - x\|- a |-------- \|b x - a - a x |-------- + b x \|- a +--R | 2 | 2 +--R \| x \| x +--R / +--R +--------+ +--R +---+ | 2 +--R \|- a \|b x - a + a +--R Type: Expression(Integer) +--E 204 + +--S 205 of 324 +d0438:= D(m0438,x) +--R +--R +--R (205) +--R +--------+ +--R | 2 +--R 2 5 3 2 |b x - a +--R (- b x + 5a b x - 4a x) |-------- +--R | 2 +--R \| x +--R + +--R 2 4 2 2 +---+ +--R (- 3b x + 7a b x - 4a )\|- a +--R * +--R +--------+ +--R | 2 +--R \|b x - a +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +---+ |b x - a 3 6 2 4 2 2 3 +--R (3b x - 7a b x + 4a x)\|- a |-------- + b x - 6a b x + 9a b x - 4a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 2 +---+ |b x - a | 2 +--R (3b x - 4a x )\|- a |-------- \|b x - a +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |b x - a +--R (- b x + 5a b x - 4a x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 205 + +--S 206 of 324 +t0439:= ((-a+b*x^n)/x^2)^(1/2) +--R +--R +--R +--------+ +--R | n +--R |b x - a +--R (206) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 206 + +--S 207 of 324 +r0439:= 2*x*(-(a-b*x^n)/x^2)^(1/2)*((-a+b*x^n)^(1/2)-a^(1/2)*_ + atan((-a+b*x^n)^(1/2)/a^(1/2)))/n/(-a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--------+ +--------+ +--R | n | n | n +--------+ +--R +-+ |b x - a \|b x - a |b x - a | n +--R - 2x\|a |-------- atan(-----------) + 2x |-------- \|b x - a +--R | 2 +-+ | 2 +--R \| x \|a \| x +--R (207) --------------------------------------------------------------- +--R +--------+ +--R | n +--R n\|b x - a +--R Type: Expression(Integer) +--E 207 + +--S 208 of 324 +a0439:= integrate(t0439,x) +--R +--R +--R (208) +--R [ +--R +----------------+ +--R +---+ | n log(x) n log(x) +--R +---+ - 2\|- a \|b %e - a + b %e - 2a +--R \|- a log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R | n log(x) +--R 2\|b %e - a +--R / +--R n +--R , +--R +----------------+ +--R | n log(x) +----------------+ +--R +-+ \|b %e - a | n log(x) +--R - 2\|a atan(-------------------) + 2\|b %e - a +--R +-+ +--R \|a +--R -------------------------------------------------------] +--R n +--R Type: Union(List(Expression(Integer)),...) +--E 208 + +--S 209 of 324 +m0439a:= a0439.1-r0439 +--R +--R +--R (209) +--R +----------------+ +--R +--------+ +---+ | n log(x) n log(x) +--R +---+ | n - 2\|- a \|b %e - a + b %e - 2a +--R \|- a \|b x - a log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--------+ +--R +--------+ +----------------+ | n | n +--R | n | n log(x) +-+ |b x - a \|b x - a +--R 2\|b x - a \|b %e - a + 2x\|a |-------- atan(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R +--------+ +--R | n +--------+ +--R |b x - a | n +--R - 2x |-------- \|b x - a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +--R n\|b x - a +--R Type: Expression(Integer) +--E 209 + +--S 210 of 324 +d0439a:= D(m0439a,x) +--R +--R +--R (210) +--R +--------+ +--R | n +--R n n log(x) n |b x - a +--R (- b x %e + 2a x ) |-------- +--R | 2 +--R \| x +--R + +--R n - 1 n n - 1 +---+ +--R (- 2b x x + 2a x )\|- a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e - a +--R + +--R +--------+ +--R | n +--R n +---+ n log(x) n +---+ |b x - a +--R (2b x \|- a %e - 2a x \|- a ) |-------- +--R | 2 +--R \| x +--R + +--R 2 n - 1 n n - 1 n log(x) n - 1 n 2 n - 1 +--R (b x x - a b x )%e - 2a b x x + 2a x +--R / +--R +--------+ +--R | n +----------------+ +--R n +---+ |b x - a | n log(x) +--R 2x x \|- a |-------- \|b %e - a +--R | 2 +--R \| x +--R + +--R +--------+ +--R | n +--R n n log(x) n |b x - a +--R (- b x x %e + 2a x x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 210 + +--S 211 of 324 +m0439b:= a0439.2-r0439 +--R +--R +--R (211) +--R +----------------+ +--R +--------+ | n log(x) +--R +-+ | n \|b %e - a +--R - 2\|a \|b x - a atan(-------------------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R +--------+ +----------------+ | n | n +--R | n | n log(x) +-+ |b x - a \|b x - a +--R 2\|b x - a \|b %e - a + 2x\|a |-------- atan(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R +--------+ +--R | n +--------+ +--R |b x - a | n +--R - 2x |-------- \|b x - a +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +--R n\|b x - a +--R Type: Expression(Integer) +--E 211 + +--S 212 of 324 +d0439b:= D(m0439b,x) +--R +--R +--R (212) +--R +----------------+ +--R n - 1 n n - 1 | n log(x) +--R (- b x x + a x )\|b %e - a +--R + +--R +--------+ +--R | n +--R n n log(x) n |b x - a +--R (b x %e - a x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | n +----------------+ +--R n |b x - a | n log(x) +--R x x |-------- \|b %e - a +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 324 +t0440:= ((a+x)/(a-x))^(1/2) +--R +--R +--R +-------+ +--R |- x - a +--R (213) |------- +--R \| x - a +--R Type: Expression(Integer) +--E 213 + +--S 214 of 324 +r0440:= (-a+x)*((a+x)/(a-x))^(1/2)+2*a*atan(((a+x)/(a-x))^(1/2)) +--R +--R +--R +-------+ +-------+ +--R |- x - a |- x - a +--R (214) 2a atan( |------- ) + (x - a) |------- +--R \| x - a \| x - a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 324 +a0440:= integrate(t0440,x) +--R +--R +--R +-------+ +-------+ +--R |- x - a |- x - a +--R (215) 2a atan( |------- ) + (x - a) |------- +--R \| x - a \| x - a +--R Type: Union(Expression(Integer),...) +--E 215 + +--S 216 of 324 +m0440:= a0440-r0440 +--R +--R +--R (216) 0 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 324 +d0440:= D(m0440,x) +--R +--R +--R (217) 0 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 324 +t0441:= ((-a+x)/(a+x))^(1/2) +--R +--R +--R +-----+ +--R |x - a +--R (218) |----- +--R \|x + a +--R Type: Expression(Integer) +--E 218 + +--S 219 of 324 +r0441:= (-(a-x)/(a+x))^(1/2)*(a+x)-2*a*atanh((-(a-x)/(a+x))^(1/2)) +--R +--R +--R +-----+ +-----+ +--R |x - a |x - a +--R (219) - 2a atanh( |----- ) + (x + a) |----- +--R \|x + a \|x + a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 324 +a0441:= integrate(t0441,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x - a |x - a |x - a +--R (220) - a log( |----- + 1) + a log( |----- - 1) + (x + a) |----- +--R \|x + a \|x + a \|x + a +--R Type: Union(Expression(Integer),...) +--E 220 + +--S 221 of 324 +m0441:= a0441-r0441 +--R +--R +--R +-----+ +-----+ +-----+ +--R |x - a |x - a |x - a +--R (221) - a log( |----- + 1) + a log( |----- - 1) + 2a atanh( |----- ) +--R \|x + a \|x + a \|x + a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 324 +d0441:= D(m0441,x) +--R +--R +--R (222) 0 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 324 +t0442:= ((a+b*x)/(c+d*x))^(1/2) +--R +--R +--R +-------+ +--R |b x + a +--R (223) |------- +--R \|d x + c +--R Type: Expression(Integer) +--E 223 + +--S 224 of 324 +r0442:= ((a+b*x)/(c+d*x))^(1/2)*(c+d*x)/d-(b*c-a*d)*_ + atanh(d^(1/2)*((a+b*x)/(c+d*x))^(1/2)/b^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +-------+ +--R |b x + a +-+ +--R |------- \|d +-------+ +--R \|d x + c |b x + a +-+ +-+ +--R (a d - b c)atanh(--------------) + (d x + c) |------- \|b \|d +--R +-+ \|d x + c +--R \|b +--R (224) -------------------------------------------------------------- +--R +-+ +-+ +--R d\|b \|d +--R Type: Expression(Integer) +--E 224 + +--S 225 of 324 +a0442:= integrate(t0442,x) +--R +--R +--R (225) +--R [ +--R (a d - b c) +--R * +--R +-------+ +--R +---+ 2 |b x + a +--R log((2b d x + a d + b c)\|b d + (2b d x + 2b c d) |------- ) +--R \|d x + c +--R + +--R +-------+ +--R |b x + a +---+ +--R (2d x + 2c) |------- \|b d +--R \|d x + c +--R / +--R +---+ +--R 2d\|b d +--R , +--R +-------+ +--R +-----+ |b x + a +--R \|- b d |------- +-------+ +--R \|d x + c +-----+ |b x + a +--R (a d - b c)atan(------------------) + (d x + c)\|- b d |------- +--R b \|d x + c +--R -----------------------------------------------------------------] +--R +-----+ +--R d\|- b d +--R Type: Union(List(Expression(Integer)),...) +--E 225 + +--S 226 of 324 +m0442a:= a0442.1-r0442 +--R +--R +--R (226) +--R +-+ +-+ +--R (a d - b c)\|b \|d +--R * +--R +-------+ +--R +---+ 2 |b x + a +--R log((2b d x + a d + b c)\|b d + (2b d x + 2b c d) |------- ) +--R \|d x + c +--R + +--R +-------+ +--R |b x + a +-+ +--R |------- \|d +--R +---+ \|d x + c +--R (- 2a d + 2b c)\|b d atanh(--------------) +--R +-+ +--R \|b +--R / +--R +-+ +-+ +---+ +--R 2d\|b \|d \|b d +--R Type: Expression(Integer) +--E 226 + +--S 227 of 324 +d0442a:= D(m0442a,x) +--R +--R +--R (227) 0 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 324 +m0442b:= a0442.2-r0442 +--R +--R +--R (228) +--R +-------+ +--R |b x + a +-+ +--R |------- \|d +--R +-----+ \|d x + c +--R (- a d + b c)\|- b d atanh(--------------) +--R +-+ +--R \|b +--R + +--R +-------+ +--R +-----+ |b x + a +--R \|- b d |------- +--R +-+ +-+ \|d x + c +--R (a d - b c)\|b \|d atan(------------------) +--R b +--R / +--R +-----+ +-+ +-+ +--R d\|- b d \|b \|d +--R Type: Expression(Integer) +--E 228 + +--S 229 of 324 +d0442b:= D(m0442b,x) +--R +--R +--R (229) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 324 +t0443:= ((-1+5*x)/(1+7*x))^(1/2)/x^2 +--R +--R +--R +------+ +--R |5x - 1 +--R |------ +--R \|7x + 1 +--R (230) --------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 230 + +--S 231 of 324 +r0443:= -(-(1-5*x)/(1+7*x))^(1/2)*(1+7*x)/x+12*atan((-(1-5*x)/(1+7*x))^(1/2)) +--R +--R +--R +------+ +------+ +--R |5x - 1 |5x - 1 +--R 12x atan( |------ ) + (- 7x - 1) |------ +--R \|7x + 1 \|7x + 1 +--R (231) ----------------------------------------- +--R x +--R Type: Expression(Integer) +--E 231 + +--S 232 of 324 +a0443:= integrate(t0443,x) +--R +--R +--R +------+ +------+ +--R |5x - 1 |5x - 1 +--R 12x atan( |------ ) + (- 7x - 1) |------ +--R \|7x + 1 \|7x + 1 +--R (232) ----------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 232 + +--S 233 of 324 +m0443:= a0443-r0443 +--R +--R +--R (233) 0 +--R Type: Expression(Integer) +--E 233 + +--S 234 of 324 +d0443:= D(m0443,x) +--R +--R +--R (234) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 324 +t0444:= ((-1+x)/(5+3*x))^(1/2) +--R +--R +--R +------+ +--R | x - 1 +--R (235) |------ +--R \|3x + 5 +--R Type: Expression(Integer) +--E 235 + +--S 236 of 324 +r0444:= 1/3*(-(1-x)/(5+3*x))^(1/2)*(5+3*x)-8/9*_ + atanh(3^(1/2)*(-(1-x)/(5+3*x))^(1/2))*3^(1/2) +--R +--R +--R +------+ +------+ +--R +-+ +-+ | x - 1 | x - 1 +--R - 8\|3 atanh(\|3 |------ ) + (9x + 15) |------ +--R \|3x + 5 \|3x + 5 +--R (236) ------------------------------------------------ +--R 9 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 324 +a0444:= integrate(t0444,x) +--R +--R +--R +------+ +------+ +--R | x - 1 +-+ +-+ | x - 1 +--R 4log((9x + 15) |------ + (- 3x - 1)\|3 ) + (3x + 5)\|3 |------ +--R \|3x + 5 \|3x + 5 +--R (237) ----------------------------------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Union(Expression(Integer),...) +--E 237 + +--S 238 of 324 +m0444:= a0444-r0444 +--R +--R +--R +------+ +------+ +--R | x - 1 +-+ +-+ | x - 1 +--R 4log((9x + 15) |------ + (- 3x - 1)\|3 ) + 8atanh(\|3 |------ ) +--R \|3x + 5 \|3x + 5 +--R (238) ----------------------------------------------------------------- +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 238 + +--S 239 of 324 +d0444:= D(m0444,x) +--R +--R +--R (239) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 324 +t0445:= (1-x^(1/2))/(1+x^(1/4)) +--R +--R +--R +-+ +--R - \|x + 1 +--R (240) ---------- +--R 4+-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 240 + +--S 241 of 324 +r0445:= x-4/5*x^(5/4) +--R +--R +--R 4+-+ +--R - 4x\|x + 5x +--R (241) ------------- +--R 5 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 324 +a0445:= integrate(t0445,x) +--R +--R +--R 4+-+ +--R - 4x\|x + 5x +--R (242) ------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 324 +m0445:= a0445-r0445 +--R +--R +--R (243) 0 +--R Type: Expression(Integer) +--E 243 + +--S 244 of 324 +d0445:= D(m0445,x) +--R +--R +--R (244) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 324 +t0446:= (x^6)^(1/2)/x/(1-x^4) +--R +--R +--R +--+ +--R | 6 +--R \|x +--R (245) - ------ +--R 5 +--R x - x +--R Type: Expression(Integer) +--E 245 + +--S 246 of 324 +r0446:= -1/2*cos(x^3)*(atan(x)-atanh(x)) +--R +--R +--R 3 +--R (atanh(x) - atan(x))cos(x ) +--R (246) --------------------------- +--R 2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 324 +a0446:= integrate(t0446,x) +--R +--R +--R log(x + 1) - log(x - 1) - 2atan(x) +--R (247) ---------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 247 + +--S 248 of 324 +m0446:= a0446-r0446 +--R +--R +--R 3 +--R log(x + 1) - log(x - 1) + (- 2atanh(x) + 2atan(x))cos(x ) - 2atan(x) +--R (248) -------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 248 + +--S 249 of 324 +d0446:= D(m0446,x) +--R +--R +--R (249) +--R 6 2 6 2 3 2 3 2 +--R ((3x - 3x )atanh(x) + (- 3x + 3x )atan(x))sin(x ) + 2x cos(x ) - 2x +--R ---------------------------------------------------------------------- +--R 4 +--R 2x - 2 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 324 +t0447:= (x^6)^(1/2)/(x-x^5) +--R +--R +--R +--+ +--R | 6 +--R \|x +--R (250) - ------ +--R 5 +--R x - x +--R Type: Expression(Integer) +--E 250 + +--S 251 of 324 +r0447:= -1/2*cos(x^3)*(atan(x)-atanh(x)) +--R +--R +--R 3 +--R (atanh(x) - atan(x))cos(x ) +--R (251) --------------------------- +--R 2 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 324 +a0447:= integrate(t0447,x) +--R +--R +--R log(x + 1) - log(x - 1) - 2atan(x) +--R (252) ---------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 252 + +--S 253 of 324 +m0447:= a0447-r0447 +--R +--R +--R 3 +--R log(x + 1) - log(x - 1) + (- 2atanh(x) + 2atan(x))cos(x ) - 2atan(x) +--R (253) -------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 253 + +--S 254 of 324 +d0447:= D(m0447,x) +--R +--R +--R (254) +--R 6 2 6 2 3 2 3 2 +--R ((3x - 3x )atanh(x) + (- 3x + 3x )atan(x))sin(x ) + 2x cos(x ) - 2x +--R ---------------------------------------------------------------------- +--R 4 +--R 2x - 2 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 324 +t0448:= (x^6)^(3/2)/x/(1-x^4) +--R +--R +--R +--+ +--R 5 | 6 +--R x \|x +--R (255) - ------- +--R 4 +--R x - 1 +--R Type: Expression(Integer) +--E 255 + +--S 256 of 324 +r0448:= 1/10*cos(x^3)*(-10*x-2*x^5+5*atan(x)+5*atanh(x)) +--R +--R +--R 5 3 +--R (5atanh(x) + 5atan(x) - 2x - 10x)cos(x ) +--R (256) ----------------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 324 +a0448:= integrate(t0448,x) +--R +--R +--R 5 +--R 5log(x + 1) - 5log(x - 1) + 10atan(x) - 4x - 20x +--R (257) ------------------------------------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 257 + +--S 258 of 324 +m0448:= a0448-r0448 +--R +--R +--R (258) +--R 5 3 +--R 5log(x + 1) - 5log(x - 1) + (- 10atanh(x) - 10atan(x) + 4x + 20x)cos(x ) +--R + +--R 5 +--R 10atan(x) - 4x - 20x +--R / +--R 20 +--R Type: Expression(Integer) +--E 258 + +--S 259 of 324 +d0448:= D(m0448,x) +--R +--R +--R (259) +--R 6 2 6 2 11 7 3 +--R ((15x - 15x )atanh(x) + (15x - 15x )atan(x) - 6x - 24x + 30x ) +--R * +--R 3 +--R sin(x ) +--R + +--R 8 3 8 +--R 10x cos(x ) - 10x +--R / +--R 4 +--R 10x - 10 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 324 +t0449:= (x^3)^(1/2)/(x-x^3) +--R +--R +--R +--+ +--R | 3 +--R \|x +--R (260) - ------ +--R 3 +--R x - x +--R Type: Expression(Integer) +--E 260 + +--S 261 of 324 +r0449:= -(x^3)^(1/2)*(atan(x^(1/2))-atanh(x^(1/2)))/x^(3/2) +--R +--R +--R +--+ +--+ +--R | 3 +-+ | 3 +-+ +--R \|x atanh(\|x ) - \|x atan(\|x ) +--R (261) ---------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 261 + +--S 262 of 324 +a0449:= integrate(t0449,x) +--R +--R +--R +-+ +-+ +-+ +--R log(\|x + 1) - log(\|x - 1) - 2atan(\|x ) +--R (262) ------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 262 + +--S 263 of 324 +m0449:= a0449-r0449 +--R +--R +--R (263) +--R +--+ +--R +-+ +-+ +-+ +-+ | 3 +-+ +--R x\|x log(\|x + 1) - x\|x log(\|x - 1) - 2\|x atanh(\|x ) +--R + +--R +--+ +--R | 3 +-+ +-+ +--R (2\|x - 2x\|x )atan(\|x ) +--R / +--R +-+ +--R 2x\|x +--R Type: Expression(Integer) +--E 263 + +--S 264 of 324 +d0449:= D(m0449,x) +--R +--R +--R +--+ +--R | 3 2 +-+ +--R - x\|x + x \|x +--R (264) ----------------- +--R +--+ +--R 2 +-+ | 3 +--R (x - 1)\|x \|x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 324 +t0450:= (x^(1/2)-(x^3)^(1/2))/(x-x^3) +--R +--R +--R +--+ +--R | 3 +-+ +--R \|x - \|x +--R (265) ------------ +--R 3 +--R x - x +--R Type: Expression(Integer) +--E 265 + +--S 266 of 324 +r0450:= atan(x^(1/2))+(x^3)^(1/2)*(atan(x^(1/2))-_ + atanh(x^(1/2)))/x^(3/2)+atanh(x^(1/2)) +--R +--R +--R +--+ +--+ +--R | 3 +-+ +-+ | 3 +-+ +-+ +--R (- \|x + x\|x )atanh(\|x ) + (\|x + x\|x )atan(\|x ) +--R (266) -------------------------------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 266 + +--S 267 of 324 +a0450:= integrate(t0450,x) +--R +--R +--R +-+ +--R (267) 2atan(\|x ) +--R Type: Union(Expression(Integer),...) +--E 267 + +--S 268 of 324 +m0450:= a0450-r0450 +--R +--R +--R +--+ +--+ +--R | 3 +-+ +-+ | 3 +-+ +-+ +--R (\|x - x\|x )atanh(\|x ) + (- \|x + x\|x )atan(\|x ) +--R (268) -------------------------------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 268 + +--S 269 of 324 +d0450:= D(m0450,x) +--R +--R +--R +--+ +--R | 3 2 +-+ +--R x\|x - x \|x +--R (269) ----------------- +--R +--+ +--R 2 +-+ | 3 +--R (x - 1)\|x \|x +--R Type: Expression(Integer) +--E 269 + +--S 270 of 324 +t0451:= x^2/(-1+x^2+(1-x^2)^(1/2)) +--R +--R +--R 2 +--R x +--R (270) -------------------- +--R +--------+ +--R | 2 2 +--R \|- x + 1 + x - 1 +--R Type: Expression(Integer) +--E 270 + +--S 271 of 324 +r0451:= x+asin(x) +--R +--R +--R (271) asin(x) + x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 324 +a0451:= integrate(t0451,x) +--R +--R +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R (272) - 2atan(---------------) + x +--R x +--R Type: Union(Expression(Integer),...) +--E 272 + +--S 273 of 324 +m0451:= a0451-r0451 +--R +--R +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R (273) - 2atan(---------------) - asin(x) +--R x +--R Type: Expression(Integer) +--E 273 + +--S 274 of 324 +d0451:= D(m0451,x) +--R +--R +--R (274) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 324 +t0452:= x*(1+x)^(1/2)/(1+x^2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (275) --------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 324 +r0452:= 2*(1+x)^(1/2)+atan(((2+2*2^(1/2))^(1/2)-2*(1+x)^(1/2))/_ + (-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2)-_ + atan(((2+2*2^(1/2))^(1/2)+2*(1+x)^(1/2))/_ + (-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2)+_ + 1/4*(2+2^(1/2))*log(1+2^(1/2)+x-_ + (2+2*2^(1/2))^(1/2)*(1+x)^(1/2))/(1+2^(1/2))^(1/2)-_ + 1/4*(2+2^(1/2))*log(1+2^(1/2)+x+(2+2*2^(1/2))^(1/2)*_ + (1+x)^(1/2))/(1+2^(1/2))^(1/2) +--R +--R +--R (276) +--R +---------+ +---------+ +--R +-+ | +-+ +-----+ | +-+ +-+ +--R (- \|2 - 2)\|2\|2 + 2 log(\|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +---------+ +--R +-+ | +-+ +-----+ | +-+ +-+ +--R (\|2 + 2)\|2\|2 + 2 log(- \|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 + 2\|x + 1 +--R - 4\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 - 2\|x + 1 +--R 4\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +--------+ +---------+ +--R +-----+ | +-+ | +-+ +--R 8\|x + 1 \|\|2 + 1 \|2\|2 + 2 +--R / +--R +--------+ +---------+ +--R | +-+ | +-+ +--R 4\|\|2 + 1 \|2\|2 + 2 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 324 +a0452:= integrate(t0452,x) +--R +--R +--R (277) +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(- 2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +--R 2\|2 sin(---)atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 - \|2 cos(---) +--R 8 +--R + +--R 4+-+ %pi +--R \|2 sin(---) +--R 4+-+ %pi 8 +-----+ +--R 2\|2 sin(---)atan(-----------------------) + 4\|x + 1 +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 + \|2 cos(---) +--R 8 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 277 + +--S 278 of 324 +m0452:= a0452-r0452 +--R +--R +--R (278) +--R +---------+ +---------+ +--R +-+ | +-+ +-----+ | +-+ +-+ +--R (\|2 + 2)\|2\|2 + 2 log(\|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R - +--R +--------+ +---------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|2 cos(---)\|\|2 + 1 \|2\|2 + 2 +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R +--------+ +---------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|2 cos(---)\|\|2 + 1 \|2\|2 + 2 +--R 8 +--R * +--R 4+-+ %pi +-----+ 4+-+2 %pi 2 4+-+2 %pi 2 +--R log(- 2\|2 cos(---)\|x + 1 + \|2 sin(---) + \|2 cos(---) + x + 1) +--R 8 8 8 +--R + +--R +---------+ +---------+ +--R +-+ | +-+ +-----+ | +-+ +-+ +--R (- \|2 - 2)\|2\|2 + 2 log(- \|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 + 2\|x + 1 +--R 4\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 - 2\|x + 1 +--R - 4\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R 4+-+ %pi +--R +--------+ +---------+ \|2 sin(---) +--R 4+-+ %pi | +-+ | +-+ 8 +--R 4\|2 sin(---)\|\|2 + 1 \|2\|2 + 2 atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 - \|2 cos(---) +--R 8 +--R + +--R 4+-+ %pi +--R +--------+ +---------+ \|2 sin(---) +--R 4+-+ %pi | +-+ | +-+ 8 +--R 4\|2 sin(---)\|\|2 + 1 \|2\|2 + 2 atan(-----------------------) +--R 8 +-----+ 4+-+ %pi +--R \|x + 1 + \|2 cos(---) +--R 8 +--R / +--R +--------+ +---------+ +--R | +-+ | +-+ +--R 4\|\|2 + 1 \|2\|2 + 2 +--R Type: Expression(Integer) +--E 278 + +--S 279 of 324 +d0452:= D(m0452,x) +--R +--R +--R (279) +--R +-+ %pi 4 +--R ((8x + 16)\|2 + 8x + 24)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 2 +--R ((- 8x - 24x - 16)\|2 - 8x - 32x - 24)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (4x + 16x + 20x + 8)\|2 + 4x + 20x + 28x + 12 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 6 +--R ((32x + 64)\|2 + 32x + 96)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 4 +--R ((- 16x - 48x - 32)\|2 - 16x - 64x - 48)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((- 16x - 64x - 80x - 32)\|2 - 16x - 80x - 112x - 48) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (8x + 40x + 72x + 56x + 16)\|2 + 8x + 48x + 96x +--R + +--R 80x + 24 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 8 +--R ((48x + 96)\|2 + 48x + 144)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 6 +--R ((- 32x - 96x - 64)\|2 - 32x - 128x - 96)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((16x + 64x + 80x + 32)\|2 + 16x + 80x + 112x + 48) +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 16x - 80x - 144x - 112x - 32)\|2 - 16x - 96x +--R + +--R 2 +--R - 192x - 160x - 48 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (12x + 72x + 168x + 192x + 108x + 24)\|2 + 12x + 84x +--R + +--R 3 2 +--R 216x + 264x + 156x + 36 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 10 +--R ((32x + 64)\|2 + 32x + 96)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 8 +--R ((- 48x - 144x - 96)\|2 - 48x - 192x - 144)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((32x + 128x + 160x + 64)\|2 + 32x + 160x + 224x + 96) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (16x + 80x + 144x + 112x + 32)\|2 + 16x + 96x +--R + +--R 2 +--R 192x + 160x + 48 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 24x - 144x - 336x - 384x - 216x - 48)\|2 - 24x +--R + +--R 4 3 2 +--R - 168x - 432x - 528x - 312x - 72 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (4x + 28x + 80x + 120x + 100x + 44x + 8)\|2 + 4x +--R + +--R 5 4 3 2 +--R 32x + 100x + 160x + 140x + 64x + 12 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 12 +--R ((8x + 16)\|2 + 8x + 24)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 10 +--R ((- 24x - 72x - 48)\|2 - 24x - 96x - 72)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((60x + 240x + 300x + 120)\|2 + 60x + 300x + 420x + 180) +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 40x - 200x - 360x - 280x - 80)\|2 - 40x - 240x +--R + +--R 2 +--R - 480x - 400x - 120 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (30x + 180x + 420x + 480x + 270x + 60)\|2 + 30x + 210x +--R + +--R 3 2 +--R 540x + 660x + 390x + 90 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (- 6x - 42x - 120x - 180x - 150x - 66x - 12)\|2 - 6x +--R + +--R 5 4 3 2 +--R - 48x - 150x - 240x - 210x - 96x - 18 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 6 +--R (x + 8x + 27x + 50x + 55x + 36x + 13x + 2)\|2 + x + 9x +--R + +--R 5 4 3 2 +--R 33x + 65x + 75x + 51x + 19x + 3 +--R * +--R +---------+ +--R +-----+ | +-+ +--R \|x + 1 \|2\|2 - 2 +--R + +--R +-+ %pi 4 +--R ((- 24x + 8)\|2 - 32x + 16)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 2 +--R ((24x + 16x - 8)\|2 + 32x + 16x - 16)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 12x - 20x - 4x + 4)\|2 - 16x - 24x + 8 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 6 +--R ((- 96x + 32)\|2 - 128x + 64)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 4 +--R ((48x + 32x - 16)\|2 + 64x + 32x - 32)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 2 +--R ((48x + 80x + 16x - 16)\|2 + 64x + 96x - 32)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 24x - 64x - 48x + 8)\|2 - 32x - 80x - 48x + 16x +--R + +--R 16 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 8 +--R ((- 144x + 48)\|2 - 192x + 96)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 6 +--R ((96x + 64x - 32)\|2 + 128x + 64x - 64)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 4 +--R ((- 48x - 80x - 16x + 16)\|2 - 64x - 96x + 32)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (48x + 128x + 96x - 16)\|2 + 64x + 160x + 96x +--R + +--R - 32x - 32 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (- 36x - 132x - 168x - 72x + 12x + 12)\|2 - 48x - 168x +--R + +--R 3 2 +--R - 192x - 48x + 48x + 24 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 10 +--R ((- 96x + 32)\|2 - 128x + 64)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 8 +--R ((144x + 96x - 48)\|2 + 192x + 96x - 96)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((- 96x - 160x - 32x + 32)\|2 - 128x - 192x + 64) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 48x - 128x - 96x + 16)\|2 - 64x - 160x - 96x +--R + +--R 32x + 32 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (72x + 264x + 336x + 144x - 24x - 24)\|2 + 96x +--R + +--R 4 3 2 +--R 336x + 384x + 96x - 96x - 48 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (- 12x - 56x - 100x - 80x - 20x + 8x + 4)\|2 - 16x +--R + +--R 5 4 3 +--R - 72x - 120x - 80x + 24x + 8 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 12 +--R ((- 24x + 8)\|2 - 32x + 16)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 10 +--R ((72x + 48x - 24)\|2 + 96x + 48x - 48)\|2 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 8 +--R ((- 180x - 300x - 60x + 60)\|2 - 240x - 360x + 120)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (120x + 320x + 240x - 40)\|2 + 160x + 400x + 240x +--R + +--R - 80x - 80 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 90x - 330x - 420x - 180x + 30x + 30)\|2 - 120x +--R + +--R 4 3 2 +--R - 420x - 480x - 120x + 120x + 60 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (18x + 84x + 150x + 120x + 30x - 12x - 6)\|2 + 24x +--R + +--R 5 4 3 +--R 108x + 180x + 120x - 36x - 12 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 +--R (- 3x - 17x - 39x - 45x - 25x - 3x + 3x + 1)\|2 - 4x +--R + +--R 6 5 4 3 2 +--R - 22x - 48x - 50x - 20x + 6x + 8x + 2 +--R * +--R +--------+ +--R +-----+ | +-+ +--R \|x + 1 \|\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|2\|2 + 2 +--R + +--R 2 +-+ 2 %pi 4 +--R ((- 64x - 64)\|2 - 96x - 96)cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 4+-+2 +--R ((64x + 64x + 64x + 64)\|2 + 96x + 96x + 96x + 96)\|2 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 32x - 64x - 64x - 64x - 32)\|2 - 48x - 96x - 96x - 96x +--R + +--R - 48 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 +-+ 2 %pi 6 +--R ((- 256x - 256)\|2 - 384x - 384)cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((160x + 160x + 160x + 160)\|2 + 240x + 240x + 240x + 240) +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (64x + 128x + 128x + 128x + 64)\|2 + 96x + 192x + 192x +--R + +--R 192x + 96 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 48x - 144x - 192x - 192x - 144x - 48)\|2 - 72x +--R + +--R 4 3 2 +--R - 216x - 288x - 288x - 216x - 72 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 +-+ 2 %pi 8 +--R ((- 384x - 384)\|2 - 576x - 576)cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((288x + 288x + 288x + 288)\|2 + 432x + 432x + 432x + 432) +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 96x - 192x - 192x - 192x - 96)\|2 - 144x - 288x +--R + +--R 2 +--R - 288x - 288x - 144 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (48x + 144x + 192x + 192x + 144x + 48)\|2 + 72x + 216x +--R + +--R 3 2 +--R 288x + 288x + 216x + 72 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (- 48x - 192x - 336x - 384x - 336x - 192x - 48)\|2 - 72x +--R + +--R 5 4 3 2 +--R - 288x - 504x - 576x - 504x - 288x - 72 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 +-+ 2 %pi 10 +--R ((- 256x - 256)\|2 - 384x - 384)cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((352x + 352x + 352x + 352)\|2 + 528x + 528x + 528x + 528) +--R * +--R 4+-+2 %pi 8 +--R \|2 cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 256x - 512x - 512x - 512x - 256)\|2 - 384x - 768x +--R + +--R 2 +--R - 768x - 768x - 384 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (- 32x - 96x - 128x - 128x - 96x - 32)\|2 - 48x - 144x +--R + +--R 3 2 +--R - 192x - 192x - 144x - 48 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (64x + 256x + 448x + 512x + 448x + 256x + 64)\|2 + 96x +--R + +--R 5 4 3 2 +--R 384x + 672x + 768x + 672x + 384x + 96 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ +--R (- 8x - 40x - 88x - 120x - 120x - 88x - 40x - 8)\|2 +--R + +--R 7 6 5 4 3 2 +--R - 12x - 60x - 132x - 180x - 180x - 132x - 60x - 12 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 +-+ 2 %pi 12 +--R ((- 64x - 64)\|2 - 96x - 96)cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((160x + 160x + 160x + 160)\|2 + 240x + 240x + 240x + 240) +--R * +--R 4+-+2 %pi 10 +--R \|2 cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 320x - 640x - 640x - 640x - 320)\|2 - 480x - 960x +--R + +--R 2 +--R - 960x - 960x - 480 +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (160x + 480x + 640x + 640x + 480x + 160)\|2 + 240x + 720x +--R + +--R 3 2 +--R 960x + 960x + 720x + 240 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (- 80x - 320x - 560x - 640x - 560x - 320x - 80)\|2 - 120x +--R + +--R 5 4 3 2 +--R - 480x - 840x - 960x - 840x - 480x - 120 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 +--R (8x + 40x + 88x + 120x + 120x + 88x + 40x + 8)\|2 + 12x +--R + +--R 6 5 4 3 2 +--R 60x + 132x + 180x + 180x + 132x + 60x + 12 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R * +--R +-----+ +--R \|x + 1 +--R / +--R 3 2 +-+ 3 2 %pi 4 +--R ((64x + 64x + 64x + 64)\|2 + 96x + 96x + 96x + 96)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 64x - 128x - 128x - 128x - 64)\|2 - 96x - 192x - 192x +--R + +--R - 192x - 96 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 3 +--R (32x + 96x + 128x + 128x + 96x + 32)\|2 + 48x + 144x + 192x +--R + +--R 2 +--R 192x + 144x + 48 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((256x + 256x + 256x + 256)\|2 + 384x + 384x + 384x + 384) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 128x - 256x - 256x - 256x - 128)\|2 - 192x - 384x +--R + +--R 2 +--R - 384x - 384x - 192 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 128x - 384x - 512x - 512x - 384x - 128)\|2 - 192x +--R + +--R 4 3 2 +--R - 576x - 768x - 768x - 576x - 192 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (64x + 256x + 448x + 512x + 448x + 256x + 64)\|2 + 96x +--R + +--R 5 4 3 2 +--R 384x + 672x + 768x + 672x + 384x + 96 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((384x + 384x + 384x + 384)\|2 + 576x + 576x + 576x + 576) +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 256x - 512x - 512x - 512x - 256)\|2 - 384x - 768x +--R + +--R 2 +--R - 768x - 768x - 384 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (128x + 384x + 512x + 512x + 384x + 128)\|2 + 192x + 576x +--R + +--R 3 2 +--R 768x + 768x + 576x + 192 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ +--R (- 128x - 512x - 896x - 1024x - 896x - 512x - 128)\|2 +--R + +--R 6 5 4 3 2 +--R - 192x - 768x - 1344x - 1536x - 1344x - 768x - 192 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ +--R (96x + 480x + 1056x + 1440x + 1440x + 1056x + 480x + 96)\|2 +--R + +--R 7 6 5 4 3 2 +--R 144x + 720x + 1584x + 2160x + 2160x + 1584x + 720x + 144 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((256x + 256x + 256x + 256)\|2 + 384x + 384x + 384x + 384) +--R * +--R %pi 10 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 384x - 768x - 768x - 768x - 384)\|2 - 576x - 1152x +--R + +--R 2 +--R - 1152x - 1152x - 576 +--R * +--R 4+-+2 %pi 8 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (256x + 768x + 1024x + 1024x + 768x + 256)\|2 + 384x +--R + +--R 4 3 2 +--R 1152x + 1536x + 1536x + 1152x + 384 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (128x + 512x + 896x + 1024x + 896x + 512x + 128)\|2 + 192x +--R + +--R 5 4 3 2 +--R 768x + 1344x + 1536x + 1344x + 768x + 192 +--R * +--R 4+-+2 %pi 4 +--R \|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 192x - 960x - 2112x - 2880x - 2880x - 2112x - 960x +--R + +--R - 192 +--R * +--R +-+ +--R \|2 +--R + +--R 7 6 5 4 3 2 +--R - 288x - 1440x - 3168x - 4320x - 4320x - 3168x - 1440x - 288 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 32x + 192x + 512x + 832x + 960x + 832x + 512x + 192x +--R + +--R 32 +--R * +--R +-+ +--R \|2 +--R + +--R 8 7 6 5 4 3 2 +--R 48x + 288x + 768x + 1248x + 1440x + 1248x + 768x + 288x + 48 +--R * +--R 4+-+2 +--R \|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 12 +--R ((64x + 64x + 64x + 64)\|2 + 96x + 96x + 96x + 96)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 192x - 384x - 384x - 384x - 192)\|2 - 288x - 576x - 576x +--R + +--R - 576x - 288 +--R * +--R 4+-+2 %pi 10 +--R \|2 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (480x + 1440x + 1920x + 1920x + 1440x + 480)\|2 + 720x + 2160x +--R + +--R 3 2 +--R 2880x + 2880x + 2160x + 720 +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ +--R (- 320x - 1280x - 2240x - 2560x - 2240x - 1280x - 320)\|2 +--R + +--R 6 5 4 3 2 +--R - 480x - 1920x - 3360x - 3840x - 3360x - 1920x - 480 +--R * +--R 4+-+2 %pi 6 +--R \|2 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (240x + 1200x + 2640x + 3600x + 3600x + 2640x + 1200x + 240) +--R * +--R +-+ +--R \|2 +--R + +--R 7 6 5 4 3 2 +--R 360x + 1800x + 3960x + 5400x + 5400x + 3960x + 1800x + 360 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R - 48x - 288x - 768x - 1248x - 1440x - 1248x - 768x - 288x +--R + +--R - 48 +--R * +--R +-+ +--R \|2 +--R + +--R 8 7 6 5 4 3 2 +--R - 72x - 432x - 1152x - 1872x - 2160x - 1872x - 1152x - 432x - 72 +--R * +--R 4+-+2 %pi 2 +--R \|2 cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 2 +--R (8x + 56x + 176x + 336x + 448x + 448x + 336x + 176x + 56x + 8) +--R * +--R +-+ +--R \|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R 12x + 84x + 264x + 504x + 672x + 672x + 504x + 264x + 84x + 12 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 324 +t0453:= 1/(1+2*x/(1+x^2))^(1/2) +--R +--R +--R 1 +--R (280) -------------- +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R Type: Expression(Integer) +--E 280 + +--S 281 of 324 +r0453:= (1+x)*((1+x^2)^(1/2)-asinh(x)+2*2^(1/2)*_ + atanh(1/2*(-1+tanh(1/2*asinh(x)))*2^(1/2)))/_ + (1+x^2)^(1/2)/((1+x)^2/(1+x^2))^(1/2) +--R +--R +--R (281) +--R +-+ asinh(x) +-+ +--R \|2 tanh(--------) - \|2 +------+ +--R +-+ 2 | 2 +--R (2x + 2)\|2 atanh(-------------------------) + (x + 1)\|x + 1 +--R 2 +--R + +--R (- x - 1)asinh(x) +--R / +--R +-----------+ +--R | 2 +------+ +--R |x + 2x + 1 | 2 +--R |----------- \|x + 1 +--R | 2 +--R \| x + 1 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 324 +a0453:= integrate(t0453,x) +--R +--R +--R (282) +--R +------+ +------+ +--R | 2 | 2 +--R (\|x + 1 - x)log(\|x + 1 - x) +--R + +--R +------+ +--R +-+ | 2 +-+ +--R (\|2 \|x + 1 - x\|2 ) +--R * +--R +------+ +--R +-+ | 2 +-+ 2 +--R (\|2 + x + 1)\|x + 1 + (- x - 1)\|2 - x - x - 2 +--R log(----------------------------------------------------) +--R +------+ +--R | 2 2 +--R (x + 1)\|x + 1 - x - x +--R + +--R +------+ +--R | 2 2 +--R - x\|x + 1 + x + 1 +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 282 + +--S 283 of 324 +m0453:= a0453-r0453 +--R +--R +--R (283) +--R +------+ +--R +-+ | 2 2 +-+ +--R ((2x + 2)\|2 \|x + 1 + (- 2x - 2x)\|2 ) +--R * +--R +-+ asinh(x) +-+ +--R \|2 tanh(--------) - \|2 +--R 2 +--R atanh(-------------------------) +--R 2 +--R + +--R +-----------+ +-----------+ +--R | 2 +------+ | 2 +------+ +--R |x + 2x + 1 | 2 2 |x + 2x + 1 | 2 +--R (x |----------- \|x + 1 + (- x - 1) |----------- )log(\|x + 1 - x) +--R | 2 | 2 +--R \| x + 1 \| x + 1 +--R + +--R +-----------+ +-----------+ +--R | 2 +------+ | 2 +--R +-+ |x + 2x + 1 | 2 2 +-+ |x + 2x + 1 +--R (x\|2 |----------- \|x + 1 + (- x - 1)\|2 |----------- ) +--R | 2 | 2 +--R \| x + 1 \| x + 1 +--R * +--R +------+ +--R +-+ | 2 +-+ 2 +--R (\|2 + x + 1)\|x + 1 + (- x - 1)\|2 - x - x - 2 +--R log(----------------------------------------------------) +--R +------+ +--R | 2 2 +--R (x + 1)\|x + 1 - x - x +--R + +--R +-----------+ +--R | 2 +------+ +--R 2 |x + 2x + 1 2 | 2 +--R ((- x - 1) |----------- + (- x - 1)asinh(x) - x - x)\|x + 1 +--R | 2 +--R \| x + 1 +--R + +--R +-----------+ +--R | 2 +--R 3 |x + 2x + 1 2 3 2 +--R (x + x) |----------- + (x + x)asinh(x) + x + x + x + 1 +--R | 2 +--R \| x + 1 +--R / +--R +-----------+ +-----------+ +--R | 2 +------+ | 2 +--R |x + 2x + 1 | 2 2 |x + 2x + 1 +--R x |----------- \|x + 1 + (- x - 1) |----------- +--R | 2 | 2 +--R \| x + 1 \| x + 1 +--R Type: Expression(Integer) +--E 283 + +--S 284 of 324 +d0453:= D(m0453,x) +--R +--R +--R (284) +--R 8 7 6 5 4 3 2 +--R (- 16x - 8x - 44x - 20x - 41x - 16x - 14x - 4x - 1) +--R * +--R +-+ +--R \|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 16x - 16x - 60x - 44x - 81x - 41x - 46x - 14x - 9x +--R + +--R - 1 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (- 16x - 56x - 92x - 108x - 97x - 60x - 26x - 8x - 1)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 16x - 64x - 132x - 192x - 205x - 164x - 100x - 42x +--R + +--R - 11x - 2 +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R (16x + 8x + 52x + 24x + 61x + 25x + 30x + 10x + 5x + 1) +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R 16x + 16x + 68x + 52x + 109x + 61x + 80x + 30x + 25x +--R + +--R 5x + 2 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R 16x + 56x + 100x + 136x + 141x + 107x + 64x + 28x + 7x +--R + +--R 1 +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R 16x + 64x + 140x + 224x + 269x + 252x + 187x + 104x + 43x +--R + +--R 12x + 1 +--R * +--R asinh(x) 2 +--R tanh(--------) +--R 2 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (32x + 16x + 88x + 40x + 82x + 32x + 28x + 8x + 2)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R 32x + 32x + 120x + 88x + 162x + 82x + 92x + 28x + 18x +--R + +--R 2 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (32x + 48x + 24x + 8x - 30x - 44x - 24x - 12x - 2)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R 32x + 64x + 72x + 48x - 22x - 60x - 68x - 48x - 14x - 4 +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 32x - 16x - 104x - 48x - 122x - 50x - 60x - 20x +--R + +--R - 10x - 2 +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 32x - 32x - 136x - 104x - 218x - 122x - 160x - 60x +--R + +--R 2 +--R - 50x - 10x - 4 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R (- 32x - 48x - 40x - 32x + 22x + 46x + 40x + 32x + 10x + 2) +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R - 32x - 64x - 88x - 80x - 10x + 44x + 86x + 80x + 42x + 20x +--R + +--R 2 +--R * +--R asinh(x) +--R tanh(--------) +--R 2 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (16x + 8x + 44x + 20x + 41x + 16x + 14x + 4x + 1)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R 16x + 16x + 60x + 44x + 81x + 41x + 46x + 14x + 9x + 1 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 8 7 6 5 4 3 2 +-+ 9 +--R (16x + 56x + 92x + 108x + 97x + 60x + 26x + 8x + 1)\|2 + 16x +--R + +--R 8 7 6 5 4 3 2 +--R 64x + 132x + 192x + 205x + 164x + 100x + 42x + 11x + 2 +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +-+ +--R (- 16x - 8x - 52x - 24x - 61x - 25x - 30x - 10x - 5x - 1)\|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R - 16x - 16x - 68x - 52x - 109x - 61x - 80x - 30x - 25x - 5x +--R + +--R - 2 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R (- 16x - 56x - 100x - 136x - 141x - 107x - 64x - 28x - 7x - 1) +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R - 16x - 64x - 140x - 224x - 269x - 252x - 187x - 104x - 43x +--R + +--R - 12x - 1 +--R / +--R 8 7 6 5 4 3 2 +-+ +--R (16x + 24x + 44x + 52x + 41x + 34x + 14x + 6x + 1)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R 16x + 32x + 68x + 88x + 93x + 82x + 48x + 28x + 7x + 2 +--R * +--R +-----------+ +--R | 2 +------+ +--R |x + 2x + 1 | 2 +--R |----------- \|x + 1 +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 16x - 24x - 52x - 64x - 61x - 57x - 30x - 18x - 5x +--R + +--R - 1 +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 16x - 32x - 76x - 104x - 125x - 122x - 87x - 60x +--R + +--R 2 +--R - 23x - 10x - 1 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R * +--R asinh(x) 2 +--R tanh(--------) +--R 2 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (- 32x - 48x - 88x - 104x - 82x - 68x - 28x - 12x - 2)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 32x - 64x - 136x - 176x - 186x - 164x - 96x - 56x - 14x +--R + +--R - 4 +--R * +--R +-----------+ +--R | 2 +------+ +--R |x + 2x + 1 | 2 +--R |----------- \|x + 1 +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +--R 32x + 48x + 104x + 128x + 122x + 114x + 60x + 36x +--R + +--R 10x + 2 +--R * +--R +-+ +--R \|2 +--R + +--R 10 9 8 7 6 5 4 3 +--R 32x + 64x + 152x + 208x + 250x + 244x + 174x + 120x +--R + +--R 2 +--R 46x + 20x + 2 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R * +--R asinh(x) +--R tanh(--------) +--R 2 +--R + +--R 8 7 6 5 4 3 2 +-+ +--R (- 16x - 24x - 44x - 52x - 41x - 34x - 14x - 6x - 1)\|2 +--R + +--R 9 8 7 6 5 4 3 2 +--R - 16x - 32x - 68x - 88x - 93x - 82x - 48x - 28x - 7x - 2 +--R * +--R +-----------+ +--R | 2 +------+ +--R |x + 2x + 1 | 2 +--R |----------- \|x + 1 +--R | 2 +--R \| x + 1 +--R + +--R 9 8 7 6 5 4 3 2 +-+ +--R (16x + 24x + 52x + 64x + 61x + 57x + 30x + 18x + 5x + 1)\|2 +--R + +--R 10 9 8 7 6 5 4 3 2 +--R 16x + 32x + 76x + 104x + 125x + 122x + 87x + 60x + 23x +--R + +--R 10x + 1 +--R * +--R +-----------+ +--R | 2 +--R |x + 2x + 1 +--R |----------- +--R | 2 +--R \| x + 1 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 324 +t0454:= x/(1+x)/((2+x)/(3+x))^(1/2) +--R +--R +--R x +--R (285) --------------- +--R +-----+ +--R |x + 2 +--R (x + 1) |----- +--R \|x + 3 +--R Type: Expression(Integer) +--E 285 + +--S 286 of 324 +r0454:= (2+x)^(1/2)*(3+x)^(1/2)-atanh(((2+x)/(3+x))^(1/2))+2*2^(1/2)*_ + atanh(2^(1/2)*((2+x)/(3+x))^(1/2)) +--R +--R +--R +-----+ +-----+ +--R +-+ +-+ |x + 2 |x + 2 +-----+ +-----+ +--R (286) 2\|2 atanh(\|2 |----- ) - atanh( |----- ) + \|x + 2 \|x + 3 +--R \|x + 3 \|x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 324 +a0454:= integrate(t0454,x) +--R +--R +--R (287) +--R +-----+ +--R +-+ |x + 2 +--R (2x + 6)\|2 |----- + 3x + 7 +-----+ +--R +-+ \|x + 3 |x + 2 +--R 2\|2 log(-----------------------------) - log( |----- + 1) +--R x + 1 \|x + 3 +--R + +--R +-----+ +-----+ +--R |x + 2 |x + 2 +--R log( |----- - 1) + (2x + 6) |----- +--R \|x + 3 \|x + 3 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 287 + +--S 288 of 324 +m0454:= a0454-r0454 +--R +--R +--R (288) +--R +-----+ +--R +-+ |x + 2 +--R (2x + 6)\|2 |----- + 3x + 7 +-----+ +--R +-+ \|x + 3 |x + 2 +--R 2\|2 log(-----------------------------) - log( |----- + 1) +--R x + 1 \|x + 3 +--R + +--R +-----+ +-----+ +-----+ +--R |x + 2 +-+ +-+ |x + 2 |x + 2 +--R log( |----- - 1) - 4\|2 atanh(\|2 |----- ) + 2atanh( |----- ) +--R \|x + 3 \|x + 3 \|x + 3 +--R + +--R +-----+ +--R +-----+ +-----+ |x + 2 +--R - 2\|x + 2 \|x + 3 + (2x + 6) |----- +--R \|x + 3 +--R / +--R 2 +--R Type: Expression(Integer) +--E 288 + +--S 289 of 324 +d0454:= D(m0454,x) +--R +--R +--R +-----+ +--R +-----+ +-----+ 2 |x + 2 +--R (2x + 5)\|x + 2 \|x + 3 + (- 2x - 11x - 15) |----- +--R \|x + 3 +--R (289) ----------------------------------------------------- +--R +-----+ +--R |x + 2 +-----+ +-----+ +--R (2x + 6) |----- \|x + 2 \|x + 3 +--R \|x + 3 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 324 +t0455:= (x^(1/2)+x)^(1/2) +--R +--R +--R +--------+ +--R | +-+ +--R (290) \|\|x + x +--R Type: Expression(Integer) +--E 290 + +--S 291 of 324 +r0455:= -1/4*(1+2*x^(1/2))*(x^(1/2)+x)^(1/2)+2/3*(x^(1/2)+x)^(3/2)+_ + 1/8*atanh(2*(x^(1/2)+x)^(1/2)/(1+2*x^(1/2))) +--R +--R +--R +--------+ +--R | +-+ +--------+ +--R 2\|\|x + x +-+ | +-+ +--R 3atanh(------------) + (4\|x + 16x - 6)\|\|x + x +--R +-+ +--R 2\|x + 1 +--R (291) --------------------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 324 +a0455:= integrate(t0455,x) +--R +--R +--R (292) +--R +--------+ +--R +-+ | +-+ +-+ +--R - 3log((8\|x + 4)\|\|x + x - 8\|x - 8x - 1) +--R + +--R +--------+ +--R +-+ | +-+ +--R (8\|x + 32x - 12)\|\|x + x +--R / +--R 48 +--R Type: Union(Expression(Integer),...) +--E 292 + +--S 293 of 324 +m0455:= a0455-r0455 +--R +--R +--R (293) +--R +--------+ +--R +--------+ | +-+ +--R +-+ | +-+ +-+ 2\|\|x + x +--R - log((8\|x + 4)\|\|x + x - 8\|x - 8x - 1) - 2atanh(------------) +--R +-+ +--R 2\|x + 1 +--R --------------------------------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 293 + +--S 294 of 324 +d0455:= D(m0455,x) +--R +--R +--R (294) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 324 +t0456:= (x-(-4+x^2)^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +------+ +--R | | 2 +--R (295) \|- \|x - 4 + x +--R Type: Expression(Integer) +--E 295 + +--S 296 of 324 +r0456:= 2/3*(x-(-4+x^2)^(1/2))^(1/2)*(2*x+(-4+x^2)^(1/2)) +--R +--R +--R +---------------+ +--R +------+ | +------+ +--R | 2 | | 2 +--R (2\|x - 4 + 4x)\|- \|x - 4 + x +--R (296) ----------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 324 +a0456:= integrate(t0456,x) +--R +--R +--R +------+ +--R | 2 2 +--R - 2x\|x - 4 + 2x + 8 +--R (297) ----------------------- +--R +---------------+ +--R | +------+ +--R | | 2 +--R 3\|- \|x - 4 + x +--R Type: Union(Expression(Integer),...) +--E 297 + +--S 298 of 324 +m0456:= a0456-r0456 +--R +--R +--R (298) 0 +--R Type: Expression(Integer) +--E 298 + +--S 299 of 324 +d0456:= D(m0456,x) +--R +--R +--R (299) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 324 +t0457:= (1+(1-x^2)^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +--------+ +--R | | 2 +--R (300) \|\|- x + 1 + 1 +--R Type: Expression(Integer) +--E 300 + +--S 301 of 324 +r0457:= 2/3*(1+x^2-(1-x^2)^(1/2))*(1+(1-x^2)^(1/2))^(1/2)/x +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R | 2 2 | | 2 +--R (- 2\|- x + 1 + 2x + 2)\|\|- x + 1 + 1 +--R (301) -------------------------------------------- +--R 3x +--R Type: Expression(Integer) +--E 301 + +--S 302 of 324 +a0457:= integrate(t0457,x) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R | 2 2 | | 2 +--R (- 2\|- x + 1 + 2x + 2)\|\|- x + 1 + 1 +--R (302) -------------------------------------------- +--R 3x +--R Type: Union(Expression(Integer),...) +--E 302 + +--S 303 of 324 +m0457:= a0457-r0457 +--R +--R +--R (303) 0 +--R Type: Expression(Integer) +--E 303 + +--S 304 of 324 +d0457:= D(m0457,x) +--R +--R +--R (304) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 324 +t0458:= (1-x^(1/2)-x)^(1/2) +--R +--R +--R +--------------+ +--R | +-+ +--R (305) \|- \|x - x + 1 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 324 +r0458:= -1/4*(1+2*x^(1/2))*(1-x^(1/2)-x)^(1/2)-2/3*(1-x^(1/2)-x)^(3/2)-5/8*_ + asin(1/5*(1+2*x^(1/2))*5^(1/2)) +--R +--R +--R +--------------+ +-+ +-+ +-+ +--R +-+ | +-+ 2\|5 \|x + \|5 +--R (4\|x + 16x - 22)\|- \|x - x + 1 - 15asin(----------------) +--R 5 +--R (306) -------------------------------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 324 +a0458:= integrate(t0458,x) +--R +--R +--R (307) +--R +-+ +--------------+ +--R 8\|x + 8x - 3 +-+ | +-+ +--R - 15atan(----------------------------) + (8\|x + 32x - 44)\|- \|x - x + 1 +--R +--------------+ +--R +-+ | +-+ +--R (8\|x + 4)\|- \|x - x + 1 +--R ---------------------------------------------------------------------------- +--R 48 +--R Type: Union(Expression(Integer),...) +--E 307 + +--S 308 of 324 +m0458:= a0458-r0458 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 8\|x + 8x - 3 2\|5 \|x + \|5 +--R - 5atan(----------------------------) + 10asin(----------------) +--R +--------------+ 5 +--R +-+ | +-+ +--R (8\|x + 4)\|- \|x - x + 1 +--R (308) ---------------------------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 308 + +--S 309 of 324 +d0458:= D(m0458,x) +--R +--R +--R (309) +--R +--------------+ +--R 2 +-+ 2 | +-+ +--R ((40x + 10x - 10)\|x + 80x - 30x)\|- \|x - x + 1 +--R + +--R +----------------+ +--R 2 +-+ 2 | +-+ +--R ((- 20x - 5x + 5)\|x - 40x + 15x)\|- 4\|x - 4x + 4 +--R / +--R +----------------+ +--------------+ +--R 2 +-+ 3 2 | +-+ | +-+ +--R ((128x - 48x)\|x + 64x + 16x - 16x)\|- 4\|x - 4x + 4 \|- \|x - x + 1 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 324 +t0459:= 1/((-1-x)/x)^(1/2) +--R +--R +--R 1 +--R (310) ---------- +--R +-------+ +--R |- x - 1 +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 310 + +--S 311 of 324 +r0459:= -x*(-(1+x)/x)^(1/2)+atan((-(1+x)/x)^(1/2)) +--R +--R +--R +-------+ +-------+ +--R |- x - 1 |- x - 1 +--R (311) atan( |------- ) - x |------- +--R \| x \| x +--R Type: Expression(Integer) +--E 311 + +--S 312 of 324 +a0459:= integrate(t0459,x) +--R +--R +--R +-------+ +-------+ +--R |- x - 1 |- x - 1 +--R (312) atan( |------- ) - x |------- +--R \| x \| x +--R Type: Union(Expression(Integer),...) +--E 312 + +--S 313 of 324 +m0459:= a0459-r0459 +--R +--R +--R (313) 0 +--R Type: Expression(Integer) +--E 313 + +--S 314 of 324 +d0459:= D(m0459,x) +--R +--R +--R (314) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 324 +t0460:= (x+x^2)^(3/2)/(1+x^2) +--R +--R +--R +------+ +--R 2 | 2 +--R (x + x)\|x + x +--R (315) ----------------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 324 +r0460:= 5/4*(x+x^2)^(1/2)+1/2*x*(x+x^2)^(1/2)-5/4*_ + atanh((x*(1+x))^(1/2)/x)+1/2*(1-%i)^(3/2)*_ + atanh(2*(1-%i)^(1/2)*(x+x^2)^(1/2)/(1+(2-%i)*x))+1/2*(1+%i)^(3/2)*_ + atanh(2*(1+%i)^(1/2)*(x+x^2)^(1/2)/(1+(2+%i)*x)) +--R +--R +--R (316) +--R +------+ +--R +------+ | 2 +--R +------+ 2\|1 + %i \|x + x +--R (2 + 2%i)\|1 + %i atanh(-------------------) +--R (2 + %i)x + 1 +--R + +--R +------+ +------+ +--R +------+ | 2 | 2 +--R +------+ 2%i\|1 - %i \|x + x \|x + x +--R (2 - 2%i)\|1 - %i atanh(---------------------) - 5atanh(---------) +--R (1 + 2%i)x + %i x +--R + +--R +------+ +--R | 2 +--R (2x + 5)\|x + x +--R / +--R 4 +--R Type: Expression(Complex(Integer)) +--E 316 + +--S 317 of 324 +a0460:= integrate(t0460,x) +--R +--R +--R (317) +--R +------+ +--R 4+-+ %pi | 2 2 4+-+ %pi +--R ((- 128x - 64)\|8 cos(---)\|x + x + (128x + 128x + 16)\|8 cos(---)) +--R 8 8 +--R * +--R log +--R +------+ +--R 4+-+ %pi 4+-+ %pi | 2 4+-+2 %pi 2 +--R (2\|8 sin(---) + 2\|8 cos(---) - 4x)\|x + x + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+ %pi 4+-+2 %pi 2 4+-+ %pi +--R (- 2x + 2)\|8 sin(---) + \|8 cos(---) + (- 2x - 2)\|8 cos(---) +--R 8 8 8 +--R + +--R 2 +--R 4x + 2x + 2 +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R ((160x + 80)\|x + x - 160x - 160x - 20)log(2\|x + x - 2x - 1) +--R + +--R +------+ +--R 4+-+ %pi | 2 2 4+-+ %pi +--R ((128x + 64)\|8 cos(---)\|x + x + (- 128x - 128x - 16)\|8 cos(---)) +--R 8 8 +--R * +--R log +--R +------+ +--R 4+-+ %pi 4+-+ %pi | 2 4+-+2 %pi 2 +--R (- 2\|8 sin(---) - 2\|8 cos(---) - 4x)\|x + x + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+ %pi 4+-+2 %pi 2 4+-+ %pi 2 +--R (2x - 2)\|8 sin(---) + \|8 cos(---) + (2x + 2)\|8 cos(---) + 4x +--R 8 8 8 +--R + +--R 2x + 2 +--R + +--R +------+ +--R 4+-+ %pi | 2 2 4+-+ %pi +--R ((256x + 128)\|8 sin(---)\|x + x + (- 256x - 256x - 32)\|8 sin(---)) +--R 8 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) - \|8 cos(---) + 2 +--R 8 8 +--R atan(---------------------------------------------) +--R +------+ +--R | 2 4+-+ %pi 4+-+ %pi +--R 2\|x + x + \|8 sin(---) + \|8 cos(---) - 2x +--R 8 8 +--R + +--R +------+ +--R 4+-+ %pi | 2 2 4+-+ %pi +--R ((256x + 128)\|8 sin(---)\|x + x + (- 256x - 256x - 32)\|8 sin(---)) +--R 8 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) - \|8 cos(---) - 2 +--R 8 8 +--R atan(---------------------------------------------) +--R +------+ +--R | 2 4+-+ %pi 4+-+ %pi +--R 2\|x + x - \|8 sin(---) - \|8 cos(---) - 2x +--R 8 8 +--R + +--R +------+ +--R 3 2 | 2 4 3 2 +--R (- 128x - 448x - 264x - 4)\|x + x + 128x + 512x + 472x + 88x - 9 +--R / +--R +------+ +--R | 2 2 +--R (256x + 128)\|x + x - 256x - 256x - 32 +--R Type: Union(Expression(Integer),...) +--E 317 + +--S 318 of 324 +m0460:= a0460-r0460 +--R +--R +--R (318) +--R - +--R 4+-+ %pi +--R 16\|8 cos(---) +--R 8 +--R * +--R log +--R +------+ +--R 4+-+ %pi 4+-+ %pi | 2 4+-+2 %pi 2 +--R (2\|8 sin(---) + 2\|8 cos(---) - 4x)\|x + x + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+ %pi 4+-+2 %pi 2 +--R (- 2x + 2)\|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R 4+-+ %pi 2 +--R (- 2x - 2)\|8 cos(---) + 4x + 2x + 2 +--R 8 +--R + +--R +------+ +--R | 2 +--R 20log(2\|x + x - 2x - 1) +--R + +--R 4+-+ %pi +--R 16\|8 cos(---) +--R 8 +--R * +--R log +--R +------+ +--R 4+-+ %pi 4+-+ %pi | 2 4+-+2 %pi 2 +--R (- 2\|8 sin(---) - 2\|8 cos(---) - 4x)\|x + x + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+ %pi 4+-+2 %pi 2 4+-+ %pi 2 +--R (2x - 2)\|8 sin(---) + \|8 cos(---) + (2x + 2)\|8 cos(---) + 4x +--R 8 8 8 +--R + +--R 2x + 2 +--R + +--R +------+ +--R +------+ | 2 +--R +------+ 2\|1 + %i \|x + x +--R (- 16 - 16%i)\|1 + %i atanh(-------------------) +--R (2 + %i)x + 1 +--R + +--R +------+ +------+ +--R +------+ | 2 | 2 +--R +------+ 2%i\|1 - %i \|x + x \|x + x +--R (- 16 + 16%i)\|1 - %i atanh(---------------------) + 40atanh(---------) +--R (1 + 2%i)x + %i x +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) - \|8 cos(---) + 2 +--R 4+-+ %pi 8 8 +--R 32\|8 sin(---)atan(---------------------------------------------) +--R 8 +------+ +--R | 2 4+-+ %pi 4+-+ %pi +--R 2\|x + x + \|8 sin(---) + \|8 cos(---) - 2x +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) - \|8 cos(---) - 2 +--R 4+-+ %pi 8 8 +--R 32\|8 sin(---)atan(---------------------------------------------) + 9 +--R 8 +------+ +--R | 2 4+-+ %pi 4+-+ %pi +--R 2\|x + x - \|8 sin(---) - \|8 cos(---) - 2x +--R 8 8 +--R / +--R 32 +--R Type: Expression(Complex(Integer)) +--E 318 + +--S 319 of 324 +d0460:= D(m0460,x) +--R +--R +--R (319) +--R 3 2 %pi 12 3 2 %pi %pi 11 +--R (- 16x - 8x - 8)sin(---) + (- 64x - 32x - 32)cos(---)sin(---) +--R 8 8 8 +--R + +--R 3 2 %pi 2 +--R (- 160x - 80x - 80)cos(---) +--R 8 +--R + +--R 5 3 2 4+-+2 +--R (48x - 10x + 18x - 26x + 2)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 3 +--R (- 320x - 160x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (160x - 64x - 124x - 4x - 124x - 4)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 4 +--R (- 496x - 248x - 248)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 7 +--R (592x + 128x - 166x + 110x - 214x - 34)\|8 cos(---) - 128x +--R 8 +--R + +--R 6 5 4 3 2 +--R 1088x + 1336x + 460x + 664x + 168x - 4 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 5 +--R (- 640x - 320x - 320)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (1152x + 512x - 112x + 304x - 240x - 80)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 2048x + 1024x + 2944x + 192x + 1024x + 320x - 128x) +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 6 +--R (- 704x - 352x - 352)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (1696x + 1024x + 52x + 540x - 172x - 132)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 7168x - 1536x + 4672x - 1696x - 160x - 160x - 864x) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R - 128x - 896x - 544x + 768x + 471x + 359x + 248x +--R + +--R 2 +--R - 24x + x + 1 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 7 +--R (- 640x - 320x - 320)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (2112x + 1664x + 424x + 856x + 40x - 168)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 11264x - 512x + 15168x + 6816x + 4864x + 1984x +--R + +--R - 1344x - 96 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 1792x - 256x - 1472x + 3904x + 4934x + 3310x + 1680x +--R + +--R 2 +--R 144x - 22x + 2 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 8 +--R (- 496x - 248x - 248)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (1888x + 1792x + 652x + 900x + 236x - 156)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 23296x - 22144x + 5072x + 4424x + 4976x + 5264x +--R + +--R - 160x - 248 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 1408x - 13696x - 29344x - 20224x - 8797x - 1205x +--R + +--R 3 2 +--R 2552x + 840x - 11x - 3 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 4096x - 13824x - 24320x - 23040x - 14608x - 5924x +--R + +--R 4 3 2 +--R - 384x + 40x + 16x - 4x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 9 +--R (- 320x - 160x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 7 +--R (1408x + 1536x + 688x + 784x + 304x - 112)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 18432x - 27648x - 8320x - 576x + 1920x + 4672x +--R + +--R 1280x - 256 +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 17920x + 19968x - 13184x - 25728x - 18916x - 11796x +--R + +--R 3 2 +--R - 2400x + 672x + 68x - 12 +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R 16384x + 90112x + 156672x + 124416x + 59968x + 15584x +--R + +--R 5 4 3 2 +--R - 5424x - 2560x + 736x + 288x + 16x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 10 +--R (- 160x - 80x - 80)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 8 +--R (816x + 1024x + 534x + 530x + 262x - 62)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 13312x - 25088x - 16192x - 8928x - 3552x + 1696x +--R + +--R 1248x - 128 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 11904x + 28032x + 18336x - 512x - 6267x - 6923x +--R + +--R 3 2 +--R - 3656x - 280x + 83x - 13 +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 +--R - 57344x - 77824x + 66048x + 186624x + 172320x +--R + +--R 6 5 4 3 2 +--R 107408x + 40024x + 5120x + 336x + 368x + 56x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 +--R - 4096x - 16384x - 32256x - 36352x - 27408x +--R + +--R 8 7 6 5 4 3 2 +--R - 15840x - 6890x - 2446x - 648x - 128x - 14x - 2x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 11 +--R (- 64x - 32x - 32)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 9 +--R (288x + 448x + 276x + 236x + 148x - 20)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 5120x - 11776x - 10048x - 6560x - 3712x - 320x + 448x +--R + +--R - 32 +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 6912x + 19200x + 20288x + 12096x + 4782x - 298x +--R + +--R 3 2 +--R - 1488x - 400x + 34x - 6 +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 +--R - 32768x - 114688x - 139264x - 60416x + 11648x +--R + +--R 6 5 4 3 2 +--R 36160x + 31408x + 12288x + 1952x + 192x + 48x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 8192x + 16384x - 5120x - 41984x - 57568x - 47872x +--R + +--R 7 6 5 4 3 2 +--R - 27964x - 12084x - 3952x - 928x - 148x - 12x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 12 +--R (- 16x - 8x - 8)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 10 +--R (80x + 128x + 90x + 78x + 42x - 2)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 1152x - 3520x - 3848x - 2836x - 1928x - 568x + 32x - 4) +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 1152x + 4992x + 7968x + 7168x + 4913x + 2409x + 472x +--R + +--R 2 +--R - 24x + 7x - 1 +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 8192x - 32768x - 60416x - 65024x - 46624x - 24640x +--R + +--R 5 4 3 +--R - 8436x - 960x + 136x + 12x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 4096x + 16384x + 28160x + 26112x + 14352x + 4448x +--R + +--R 7 6 5 4 3 2 +--R - 166x - 890x - 504x - 176x - 34x - 6x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 16384x + 49152x + 71680x + 69632x + 48704x + 25664x +--R + +--R 7 6 5 4 3 +--R 10312x + 3104x + 688x + 96x + 8x +--R * +--R +------+ +--R | 2 +--R \|x + x +--R + +--R 4 3 2 %pi 12 +--R (16x + 16x + 16x + 16x)sin(---) +--R 8 +--R + +--R 4 3 2 %pi %pi 11 +--R (64x + 64x + 64x + 64x)cos(---)sin(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (160x + 160x + 160x + 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 4+-+2 +--R (- 48x - 24x + 16x - 16x + 8x)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (320x + 320x + 320x + 320x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi +--R (- 160x - 16x + 176x + 48x + 80x + 64x)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (496x + 496x + 496x + 496x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 2 8 +--R (- 592x - 424x + 176x - 48x + 128x + 184x)\|8 cos(---) + 128x +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 1024x - 1896x - 984x - 800x - 480x + 72x - 8x +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (640x + 640x + 640x + 640x)cos(---) +--R 8 +--R + +--R 6 5 3 2 4+-+2 %pi 3 +--R (- 1152x - 1088x - 256x + 128x + 320x)\|8 cos(---) +--R 8 +--R + +--R 8 6 5 4 3 2 %pi +--R (2048x - 3712x - 1408x - 896x - 896x + 256x )cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (704x + 704x + 704x + 704x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 4 +--R (- 1696x - 1872x - 352x - 544x + 64x + 432x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (7168x + 5120x - 4800x - 384x + 1408x - 128x + 1088x + 256x) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 3 +--R 128x + 960x + 976x - 600x - 872x - 496x - 416x - 56x +--R + +--R 2 +--R - 8x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 7 +--R (640x + 640x + 640x + 640x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 5 +--R (- 2112x - 2720x - 992x - 992x - 160x + 448x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 11264x + 6144x - 16320x - 13760x - 6784x - 4224x + 832x +--R + +--R 832x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 1792x - 640x + 1824x - 3312x - 6984x - 5256x - 2976x +--R + +--R 3 2 +--R - 720x + 8x + 8x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 8 +--R (496x + 496x + 496x + 496x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 6 +--R (- 1888x - 2736x - 1312x - 1120x - 320x + 336x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 23296x + 33792x + 3088x - 8272x - 6080x - 7744x - 1488x +--R + +--R 1040x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 1408x + 12992x + 36368x + 33096x + 16152x + 4336x +--R + +--R 4 3 2 +--R - 2528x - 2008x - 136x + 32x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 5 +--R 4096x + 15872x + 30720x + 33728x + 23792x + 11440x + 2304x +--R + +--R 4 3 2 +--R - 128x + 16x + 16x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 9 +--R (320x + 320x + 320x + 320x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 7 +--R (- 1408x - 2240x - 1280x - 1024x - 384x + 192x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 18432x + 36864x + 19840x + 2432x - 1664x - 5760x - 2560x +--R + +--R 512x +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 17920x - 28928x + 5440x + 33696x + 29584x + 19152x +--R + +--R 4 3 2 +--R 6848x - 288x - 272x + 48x +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R - 16384x - 98304x - 199680x - 192512x - 107584x - 36736x +--R + +--R 6 5 4 3 2 +--R 1344x + 5632x - 192x - 640x - 64x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 10 +--R (160x + 160x + 160x + 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 8 +--R (- 816x - 1432x - 944x - 720x - 320x + 72x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (13312x + 31744x + 27072x + 14720x + 7040x - 640x - 1600x ) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 11904x - 33984x - 30864x - 5896x + 7528x + 9616x +--R + +--R 4 3 2 +--R 6560x + 1496x - 56x + 32x +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 57344x + 106496x - 34304x - 225792x - 254752x - 175840x +--R + +--R 6 5 4 3 2 +--R - 80320x - 17664x - 1120x - 544x - 192x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R 4096x + 18432x + 39936x + 50688x + 42416x + 26488x +--R + +--R 8 7 6 5 4 +--R 12760x + 4816x + 1472x + 312x + 56x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 11 +--R (64x + 64x + 64x + 64x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 9 +--R (- 288x - 592x - 464x - 336x - 176x )\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 5120x + 14336x + 15296x + 10432x + 6272x + 1664x - 320x +--R + +--R - 64x +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 6912x - 22656x - 29024x - 20272x - 9224x - 1288x +--R + +--R 4 3 2 +--R 1888x + 1008x + 72x + 8x +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 32768x + 131072x + 192512x + 117760x + 7040x - 44416x +--R + +--R 6 5 4 3 2 +--R - 47232x - 24576x - 5760x - 640x - 128x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 8192x - 20480x - 2048x + 46080x + 77216x + 72144x +--R + +--R 8 7 6 5 4 3 +--R 46848x + 22384x + 8128x + 2192x + 416x + 48x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 12 +--R (16x + 16x + 16x + 16x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 10 +--R (- 80x - 168x - 144x - 112x - 64x - 8x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (1152x + 4096x + 5464x + 4392x + 3040x + 1312x + 136x - 8x) +--R * +--R %pi 8 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 1152x - 5568x - 10320x - 10600x - 7768x - 4304x - 1312x +--R + +--R 3 2 +--R - 72x + 8x +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 6 +--R 8192x + 36864x + 75776x + 91648x + 73312x + 42544x + 17360x +--R + +--R 5 4 3 2 +--R 3584x - 32x - 48x - 16x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 4096x - 18432x - 35840x - 38400x - 24752x - 9592x +--R + +--R 8 7 6 5 4 3 +--R - 1160x + 1152x + 864x + 360x + 88x + 16x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 16384x - 57344x - 94208x - 100352x - 76992x - 44320x +--R + +--R 8 7 6 5 4 +--R - 19616x - 6592x - 1664x - 288x - 32x +--R / +--R 5 4+-+2 %pi 10 5 4+-+2 %pi %pi 9 +--R (16x - 16x)\|8 sin(---) + (64x - 64x)\|8 cos(---)sin(---) +--R 8 8 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 7 6 +--R (208x + 96x + 96x + 96x - 112x)\|8 cos(---) - 192x + 224x +--R 8 +--R + +--R 5 4 3 2 +--R 192x + 192x + 384x - 32x +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (384x + 256x + 256x + 256x - 128x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi +--R (- 1280x - 384x - 384x - 512x + 768x - 128x - 128x)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (544x + 448x + 448x + 448x - 96x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 3584x - 2304x - 1536x - 2048x + 1536x + 256x - 512x) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 2 +--R 256x - 128x + 80x + 296x + 40x + 416x + 208x - 8x +--R + +--R - 8x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (640x + 640x + 640x + 640x )\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 5888x - 5248x - 2432x - 3072x + 2816x + 2176x - 640x) +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 1792x + 1024x + 528x + 1168x - 544x + 192x + 688x +--R + +--R 2 +--R 48x - 32x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (544x + 640x + 640x + 640x + 96x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi 4 +--R (- 8832x - 13248x - 9856x - 9856x - 1024x + 3392x )cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 3840x + 2432x - 1680x - 1752x - 5304x - 3936x + 176x +--R + +--R 2 +--R 248x - 40x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 5 +--R - 2304x - 1664x - 3360x - 5296x - 2624x - 2992x - 1248x +--R + +--R 4 3 2 +--R 688x + 320x + 48x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 7 +--R (384x + 512x + 512x + 512x + 128x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 5888x - 12416x - 11392x - 10752x - 4864x + 1664x +--R + +--R 640x +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 8704x + 17408x + 15328x + 13472x + 4992x - 3712x +--R + +--R 3 2 +--R - 1632x + 224x +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 9216x + 1536x + 23424x + 28992x + 38144x + 27968x +--R + +--R 5 4 3 2 +--R 6272x + 704x + 768x + 192x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 8 +--R (208x + 320x + 320x + 320x + 112x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 3584x - 8448x - 9216x - 8704x - 5120x - 256x + 512x) +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 +--R 3840x + 12928x + 16688x + 15864x + 11960x + 2912x +--R + +--R 3 2 +--R - 848x - 24x + 40x +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 +--R - 38400x - 96000x - 111296x - 104992x - 65792x +--R + +--R 6 5 4 3 2 +--R - 8608x + 6848x + 544x - 256x + 160x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 1024x - 1024x - 5824x - 9856x - 13036x - 11580x +--R + +--R 7 6 5 4 3 2 +--R - 6868x - 2820x - 660x - 68x + 20x + 4x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 9 +--R (64x + 128x + 128x + 128x + 64x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 1280x - 3456x - 4224x - 4096x - 2816x - 640x + 128x) +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 +--R 1792x + 6144x + 9488x + 9936x + 8096x + 3776x + 432x +--R + +--R 2 +--R - 16x + 32x +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 9216x - 47616x - 87168x - 100032x - 91648x - 53696x +--R + +--R 5 4 3 2 +--R - 14208x - 1344x - 512x - 64x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 10240x + 30720x + 48256x + 57600x + 50376x + 30408x +--R + +--R 7 6 5 4 3 2 +--R 12920x + 3576x + 568x + 56x + 8x + 8x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 10 +--R (16x + 32x + 32x + 32x + 16x)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi 8 +--R (- 192x - 800x - 1088x - 1088x - 896x - 288x )cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 2 +--R 256x + 1152x + 2320x + 2744x + 2520x + 1632x + 464x + 40x +--R + +--R 8x +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 11 10 9 8 7 6 +--R - 2304x - 9856x - 21792x - 30896x - 31424x - 24368x +--R + +--R 5 4 3 2 +--R - 12512x - 3408x - 576x - 80x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 13 12 11 10 9 8 +--R 1024x + 7168x + 16704x + 24448x + 27668x + 23012x +--R + +--R 7 6 5 4 3 2 +--R 13836x + 6140x + 1900x + 412x + 52x + 4x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 15 14 13 12 11 10 +--R - 8192x - 28672x - 55296x - 78848x - 85600x - 72336x +--R + +--R 9 8 7 6 5 4 3 +--R - 48304x - 25456x - 10640x - 3440x - 848x - 144x - 16x +--R * +--R +------+ +--R | 2 +--R \|x + x +--R + +--R 4 3 2 %pi 12 +--R (8x + 8x + 8x + 8x)sin(---) +--R 8 +--R + +--R 4 3 2 %pi %pi 11 +--R (32x + 32x + 32x + 32x)cos(---)sin(---) +--R 8 8 +--R + +--R 4 3 2 %pi 2 +--R (80x + 80x + 80x + 80x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 +--R (- 16x - 8x - 8x - 8x + 8x )\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (160x + 160x + 160x + 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi +--R (- 64x - 32x - 16x - 16x + 48x + 16x)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (248x + 248x + 248x + 248x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 2 8 +--R (- 208x - 200x - 136x - 136x + 72x + 64x)\|8 cos(---) + 192x +--R 8 +--R + +--R 7 6 5 4 3 2 +--R - 128x - 328x - 248x - 432x - 112x + 88x + 8x +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (320x + 320x + 320x + 320x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 3 +--R (- 384x - 448x - 320x - 320x + 64x + 128x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 %pi +--R (1280x + 1024x + 416x + 736x - 512x - 256x + 352x + 32x)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (352x + 352x + 352x + 352x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 4 +--R (- 544x - 720x - 528x - 528x + 16x + 192x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (3584x + 4096x + 2240x + 2752x - 704x - 1216x + 640x + 128x) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 10 8 7 6 5 4 3 4+-+2 +--R (- 256x + 16x - 368x - 160x - 416x - 432x - 48x )\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 7 +--R (320x + 320x + 320x + 320x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 5 +--R (- 640x - 960x - 736x - 736x - 96x + 224x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (5888x + 8192x + 4320x + 4000x - 1536x - 3840x + 32x + 352x) +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 1792x - 1920x - 816x - 1416x + 32x + 184x - 912x +--R + +--R 3 2 +--R - 312x + 32x + 8x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 8 +--R (248x + 248x + 248x + 248x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 6 +--R (- 544x - 912x - 720x - 720x - 176x + 192x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 8832x + 17664x + 15376x + 13680x + 5344x - 3488x - 1200x +--R + +--R 496x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 3840x - 4352x + 944x + 2656x + 5968x + 6464x + 1200x +--R + +--R 3 2 +--R - 512x + 16x + 32x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 6 +--R 2304x + 2816x + 3904x + 6912x + 4866x + 3850x + 2614x +--R + +--R 5 4 3 2 +--R - 386x - 642x - 138x + 10x + 2x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 9 +--R (160x + 160x + 160x + 160x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 7 +--R (- 384x - 704x - 576x - 576x - 192x + 128x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 5888x + 15360x + 16864x + 15264x + 9728x + 256x - 1248x +--R + +--R 352x +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 8704x - 21760x - 22944x - 19504x - 10560x + 2384x +--R + +--R 4 3 2 +--R 3616x + 176x - 64x + 48x +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 9216x + 3072x - 25344x - 39936x - 50168x - 44568x +--R + +--R 6 5 4 3 2 +--R - 16616x - 2056x - 1032x - 488x - 24x + 8x +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 10 +--R (80x + 80x + 80x + 80x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 8 +--R (- 208x - 424x - 360x - 360x - 152x + 64x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R 3584x + 10240x + 12992x + 12480x + 9024x + 2368x - 384x +--R + +--R 128x +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 3840x - 14848x - 22672x - 22832x - 18464x - 7552x +--R + +--R 4 3 2 +--R 304x + 464x - 64x + 32x +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 38400x + 115200x + 154496x + 151040x + 108876x + 32636x +--R + +--R 6 5 4 3 2 +--R - 6716x - 3340x + 436x - 124x - 68x + 12x +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 1024x + 512x + 6464x + 12576x + 17340x + 17162x +--R + +--R 8 7 6 5 4 3 2 +--R 11466x + 5358x + 1606x + 246x - 10x - 14x - 2x +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 11 +--R (32x + 32x + 32x + 32x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 9 +--R (- 64x - 160x - 144x - 144x - 80x + 16x)\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (1280x + 4096x + 5792x + 5856x + 4608x + 1792x + 96x + 32x) +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 +--R - 1792x - 7040x - 12336x - 14024x - 12192x - 6984x +--R + +--R 4 3 2 +--R - 1680x + 8x - 32x + 8x +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 +--R 9216x + 52224x + 109824x + 138240x + 133384x + 90856x +--R + +--R 6 5 4 3 2 +--R 33560x + 5112x + 760x + 280x - 24x + 8x +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 10240x - 35840x - 62336x - 78528x - 74664x - 50492x +--R + +--R 8 7 6 5 4 3 2 +--R - 24172x - 7988x - 1620x - 196x - 20x - 12x - 4x +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 4 3 2 %pi 12 +--R (8x + 8x + 8x + 8x)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 10 +--R (- 16x - 40x - 40x - 40x - 24x )\|8 cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 %pi 8 +--R (192x + 896x + 1464x + 1544x + 1360x + 656x + 88x + 8x)cos(---) +--R 8 +--R + +--R 10 9 8 7 6 5 4 +--R - 256x - 1280x - 2864x - 3776x - 3664x - 2656x - 1072x +--R + +--R 3 2 +--R - 160x - 16x +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 12 11 10 9 8 7 6 +--R 2304x + 11008x + 26432x + 40704x + 44674x + 37258x + 22070x +--R + +--R 5 4 3 2 +--R 7806x + 1534x + 246x + 10x + 2x +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 14 13 12 11 10 9 +--R - 1024x - 7680x - 20160x - 31968x - 38212x - 34582x +--R + +--R 8 7 6 5 4 3 2 +--R - 22934x - 11282x - 4026x - 1002x - 170x - 14x - 2x +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 16 15 14 13 12 11 +--R 8192x + 32768x + 68608x + 103424x + 119584x + 107840x +--R + +--R 10 9 8 7 6 5 4 3 +--R 77156x + 43892x + 19884x + 7100x + 1948x + 396x + 52x + 4x +--R Type: Expression(Complex(Integer)) +--E 319 + +--S 320 of 324 +t0461:= x^(1/3)/(-1+x^(5/6)) +--R +--R +--R 3+-+ +--R \|x +--R (320) --------- +--R 6+-+5 +--R \|x - 1 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 324 +r0461:= 2*x^(1/2)+6*2^(1/2)/(25+5*5^(1/2))^(1/2)*_ + atan((1-5^(1/2)+4*x^(1/6))/(10+2*5^(1/2))^(1/2))-_ + 6*2^(1/2)/(25-5*5^(1/2))^(1/2)*_ + atan((1+5^(1/2)+4*x^(1/6))/(10-2*5^(1/2))^(1/2))+_ + 6/5*log(1-x^(1/6))-3/10*(5^(1/2)+1)*log(2+(1-5^(1/2))*x^(1/6)+_ + 2*x^(1/3))-3/10*(1-5^(1/2))*log(2+(5^(1/2)+1)*x^(1/6)+2*x^(1/3)) +--R +--R +--R (321) +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (15\|5 - 15)log((\|5 + 1)\|x + 2\|x + 2) + 60log(- \|x + 1) +--R + +--R +-+ +-+ 6+-+ 3+-+ +--R (- 15\|5 - 15)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +------------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x + \|5 + 1 +--R (- 3\|2 \|5 - 15\|2 )\|- 5\|5 + 25 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x - \|5 + 1 +-+ +--R (- 3\|2 \|5 + 15\|2 )\|5\|5 + 25 atan(----------------) + 100\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 50 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 324 +a0461:= integrate(t0461,x) +--R +--R +--R (322) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--I - 5%%EX1 - 5%%EX0 - 6 +--R * +--R log +--I (5%%EX1 + 5%%EX0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%EX1 + 25%%EX0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--I - 5%%EX1 - 5%%EX0 - 6 +--R * +--R log +--I (- 5%%EX1 - 5%%EX0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%EX1 + 25%%EX0 + 72\|x + 36 +--R + +--R 2 6+-+ 6+-+ +--I 10%%EX1 log(- 25%%EX1 + 36\|x ) + 12log(\|x - 1) +--R + +--R 2 6+-+ 6+-+3 +--I 10%%EX0 log(- 25%%EX0 + 36\|x ) + 20\|x +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 322 + +--S 323 of 324 +m0461:= a0461-r0461 +--R +--R +--R (323) +--R +-------------------------------------------------------------+ +--R | 2 2 +--I 5\|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--I - 25%%EX1 - 25%%EX0 - 30 +--R * +--R log +--I (5%%EX1 + 5%%EX0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%EX1 + 25%%EX0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--I - 5\|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--I - 25%%EX1 - 25%%EX0 - 30 +--R * +--R log +--I (- 5%%EX1 - 5%%EX0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%EX1 + (- 50%%EX0 - 60)%%EX1 - 75%%EX0 - 60%%EX0 - 108 +--R + +--R 2 2 6+-+ +--I 25%%EX1 + 25%%EX0 + 72\|x + 36 +--R + +--R 2 6+-+ +--I 50%%EX1 log(- 25%%EX1 + 36\|x ) +--R + +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (- 15\|5 + 15)log((\|5 + 1)\|x + 2\|x + 2) + 60log(\|x - 1) +--R + +--R 6+-+ +-+ +-+ 6+-+ 3+-+ +--R - 60log(- \|x + 1) + (15\|5 + 15)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R 2 6+-+ +--I 50%%EX0 log(- 25%%EX0 + 36\|x ) +--R + +--R +------------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x + \|5 + 1 +--R (3\|2 \|5 + 15\|2 )\|- 5\|5 + 25 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +----------+ 6+-+ +-+ +--R +-+ +-+ +-+ | +-+ 4\|x - \|5 + 1 6+-+3 +--R (3\|2 \|5 - 15\|2 )\|5\|5 + 25 atan(----------------) + 100\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R + +--R +-+ +--R - 100\|x +--R / +--R 50 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 324 +d0461:= D(m0461,x) +--R +--R +--R (324) +--R +-+ +-+ +-+ +-+3+-+2 2 +-+ +-+ 2 +-+ +-+ 6+-+5 +--R ((2x\|2 \|5 - 10x\|2 )\|x \|x + (x \|2 \|5 - 5x \|2 )\|x )\|x +--R + +--R +-+ +-+ +-+ +-+3+-+2 +--R (x\|2 \|5 - 5x\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((x + 4x)\|2 \|5 + (- 5x - 10x)\|2 )\|x \|x +--R * +--R 6+-+4 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((- x - x)\|2 \|5 + (5x - 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((- 4x - 5x)\|2 \|5 + (10x + 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +--R (x \|2 \|5 - 5x \|2 )\|x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((x - 3x)\|2 \|5 + (5x + 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((5x + x)\|2 \|5 + (- 5x - 5x)\|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((- x - 3x )\|2 \|5 + (5x + 5x )\|2 )\|x +--R * +--R 6+-+2 +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((3x + 5x)\|2 \|5 + (- 5x - 5x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+ +--R ((- x + 2x)\|2 \|5 + 5x \|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((3x + 3x )\|2 \|5 + (- 5x - 5x )\|2 )\|x +--R * +--R 6+-+ +--R \|x +--R + +--R 2 +-+ +-+ 2 +-+ +-+3+-+2 +--R ((- 5x - 2x)\|2 \|5 + (5x + 10x)\|2 )\|x \|x +--R + +--R 2 +-+ +-+ +-+ +-+3+-+ +--R ((- 2x - x)\|2 \|5 + 5x\|2 )\|x \|x +--R + +--R 3 2 +-+ +-+ 3 2 +-+ +-+ +--R ((- 3x - x )\|2 \|5 + (5x + 5x )\|2 )\|x +--R * +--R +----------+ +----------+ +--R | +-+ | +-+ +--R \|2\|5 + 10 \|5\|5 + 25 +--R + +--R +------------+ +------------+ +--R +-+ +-+ +-+ | +-+ | +-+ +--R (2x\|2 \|5 + 10x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 + 400x +--R + +--R - 80 +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R - 800x + 800x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 +-+ 3 2 3+-+ +--R ((- 40x - 80x)\|x - 400x - 800x + 400x)\|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ 2 +--R ((x \|2 \|5 + 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 + 80x - 80x) +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R 400x +--R * +--R 6+-+5 +--R \|x +--R + +--R +------------+ +------------+ +--R +-+ +-+ +-+ | +-+ | +-+ 2 +--R (x\|2 \|5 + 5x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 - 80x +--R + +--R - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 400x - 1600x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((x + 4x)\|2 \|5 + (5x + 10x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 80x - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 400x - 800x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 +-+ 3 +--R 80x \|x - 800x +--R * +--R 6+-+4 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- x - x)\|2 \|5 + (- 5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 160x - 240x +--R * +--R +-+ +--R \|x +--R + +--R 3 +--R 800x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- 4x - 5x)\|2 \|5 + (- 10x - 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R - 320x - 80x +--R * +--R +-+ +--R \|x +--R + +--R 3 +--R 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ 2 +-+ +--R ((x \|2 \|5 + 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 - 80x )\|x +--R + +--R 4 +--R 400x +--R * +--R 6+-+3 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((x - 3x)\|2 \|5 + (- 5x - 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 2 +--R 640x - 240x +--R * +--R +-+3+-+2 +--R \|x \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((5x + x)\|2 \|5 + (5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 400x + 480x - 80x +--R * +--R +-+3+-+ +--R \|x \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((- x - 3x )\|2 \|5 + (- 5x - 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 80x - 80x +--R * +--R +-+ +--R \|x +--R * +--R 6+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((3x + 5x)\|2 \|5 + (5x + 5x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 1040x - 240x +--R * +--R +-+3+-+2 +--R \|x \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ | +-+ +--R ((- x + 2x)\|2 \|5 - 5x \|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 480x - 120x +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R - 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((3x + 3x )\|2 \|5 + (5x + 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R 480x - 80x +--R * +--R +-+ +--R \|x +--R * +--R 6+-+ +--R \|x +--R + +--R +------------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +--R ((- 5x - 2x)\|2 \|5 + (- 5x - 10x)\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 800x + 240x - 320x +--R * +--R +-+ +--R \|x +--R + +--R 2 +--R 400x +--R * +--R 3+-+2 +--R \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ +-+ +-+ | +-+ | +-+ +--R ((- 2x - x)\|2 \|5 - 5x\|2 )\|- 5\|5 + 25 \|- 2\|5 + 10 +--R + +--R 3 2 +--R - 400x + 160x +--R * +--R +-+ +--R \|x +--R + +--R 3 2 +--R 800x + 400x +--R * +--R 3+-+ +--R \|x +--R + +--R +------------+ +--R 3 2 +-+ +-+ 3 2 +-+ | +-+ +--R ((- 3x - x )\|2 \|5 + (- 5x - 5x )\|2 )\|- 5\|5 + 25 +--R * +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R 4 3 2 +--R - 400x + 80x - 80x +--R * +--R +-+ +--R \|x +--R / +--R 2 +-+3+-+2 3 2 +-+3+-+ 2 +-+ +--R ((800x - 800x)\|x \|x + (400x + 800x - 400x)\|x \|x - 400x \|x ) +--R * +--R 6+-+5 +--R \|x +--R + +--R 3 2 +-+3+-+2 3 2 +-+3+-+ 3 +-+ +--R ((- 400x + 1600x )\|x \|x + (- 400x + 800x )\|x \|x + 800x \|x ) +--R * +--R 6+-+4 +--R \|x +--R + +--R 3 +-+3+-+2 3 +-+3+-+ 4 +-+ 6+-+3 2 +-+3+-+6+-+ +--R (- 800x \|x \|x - 400x \|x \|x - 400x \|x )\|x + 400x \|x \|x \|x +--R + +--R 2 +-+3+-+2 3 2 +-+3+-+ +--R - 400x \|x \|x + (- 800x - 400x )\|x \|x +--R Type: Expression(Integer) +--E 324 + +)spool + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richalgebraic400-461.input.pdf b/src/axiom-website/CATS/richalgebraic400-461.input.pdf new file mode 100644 index 0000000..9b354e1 Binary files /dev/null and b/src/axiom-website/CATS/richalgebraic400-461.input.pdf differ diff --git a/src/axiom-website/CATS/richerror000-078.input.pamphlet b/src/axiom-website/CATS/richerror000-078.input.pamphlet new file mode 100644 index 0000000..e14c561 --- /dev/null +++ b/src/axiom-website/CATS/richerror000-078.input.pamphlet @@ -0,0 +1,4012 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richerror000-078.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richerror000-078.output +)spool richerror000-078.output +)set message auto off +)clear all + +--S 1 of 395 +t0000:= erf(b*x)^2/x^7 +--R +--R +--R 2 +--R erf(b x) +--R (1) --------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 395 +r0000:= -1/15*b^2/(exp(1)^(2*b^2*x^2))/%pi/x^4+2/9*b^4/_ + (exp(1)^(2*b^2*x^2))/%pi/x^2-2/45*b*(3-2*b^2*x^2+_ + 4*b^4*x^4)*erf(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/_ + x^5-4/45*b^6*erf(b*x)^2-1/6*erf(b*x)^2/x^6+_ + 28/45*b^6*Ei(-2*b^2*x^2)/%pi +--R +--R +--R (2) +--R 2 2 2 2 +--R 6 6 2 6 6 2 2 b x 2b x +--R ((- 8b %pi x - 15%pi)erf(b x) + 56b x Ei(- 2b x ))%e %e +--R + +--R 2 2 +--R 4 4 2 2 b x +--R (20b x - 6b x )%e +--R * +--R +---+ +--R \|%pi +--R + +--R 2 2 +--R 5 5 3 3 2b x +--R (- 16b %pi x + 8b %pi x - 12b %pi x)erf(b x)%e +--R / +--R 2 2 2 2 +--R 6 b x 2b x +---+ +--R 90%pi x %e %e \|%pi +--R Type: Expression(Integer) +--E 2 + +--S 3 of 395 +a0000:= integrate(t0000,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 3 + +--S 4 of 395 +--m0000:= a0000-r0000 +--E 4 + +--S 5 of 395 +--d0000:= D(m0000,x) +--E 5 + +--S 6 of 395 +t0001:= erf(b*x)^2/x^5 +--R +--R +--R 2 +--R erf(b x) +--R (3) --------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 395 +r0001:= -1/3*b^2/(exp(1)^(2*b^2*x^2))/%pi/x^2-_ + 1/3*b*(1-2*b^2*x^2)*erf(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x^3+_ + 1/3*b^4*erf(b*x)^2-1/4*erf(b*x)^2/x^4-4/3*b^4*Ei(-2*b^2*x^2)/%pi +--R +--R +--R (4) +--R 2 2 2 2 +--R 4 4 2 4 4 2 2 b x 2b x +--R ((4b %pi x - 3%pi)erf(b x) - 16b x Ei(- 2b x ))%e %e +--R + +--R 2 2 +--R 2 2 b x +--R - 4b x %e +--R * +--R +---+ +--R \|%pi +--R + +--R 2 2 +--R 3 3 2b x +--R (8b %pi x - 4b %pi x)erf(b x)%e +--R / +--R 2 2 2 2 +--R 4 b x 2b x +---+ +--R 12%pi x %e %e \|%pi +--R Type: Expression(Integer) +--E 7 + +--S 8 of 395 +a0001:= integrate(t0001,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 8 + +--S 9 of 395 +--m0001:= a0001-r0001 +--E 9 + +--S 10 of 395 +--d0001:= D(m0001,x) +--E 10 + +--S 11 of 395 +t0002:= erf(b*x)^2/x^3 +--R +--R +--R 2 +--R erf(b x) +--R (5) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 395 +r0002:= -2*b*erf(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x-b^2*erf(b*x)^2-_ + 1/2*erf(b*x)^2/x^2+2*b^2*Ei(-2*b^2*x^2)/%pi +--R +--R +--R (6) +--R 2 2 +--R 2 2 2 2 2 2 2 b x +---+ +--R ((- 2b %pi x - %pi)erf(b x) + 4b x Ei(- 2b x ))%e \|%pi +--R + +--R - 4b %pi x erf(b x) +--R / +--R 2 2 +--R 2 b x +---+ +--R 2%pi x %e \|%pi +--R Type: Expression(Integer) +--E 12 + +--S 13 of 395 +a0002:= integrate(t0002,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 13 + +--S 14 of 395 +--m0002:= a0002-r0002 +--E 14 + +--S 15 of 395 +--d0002:= D(m0002,x) +--E 15 + +--S 16 of 395 +t0003:= x*erf(b*x)^2 +--R +--R +--R 2 +--R (7) x erf(b x) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 395 +r0003:= 1/2/(exp(1)^(2*b^2*x^2))/b^2/%pi+x*erf(b*x)/(exp(1)^(b^2*x^2))/_ + b/%pi^(1/2)-1/4*erf(b*x)^2/b^2+1/2*x^2*erf(b*x)^2 +--R +--R +--R (8) +--R 2 2 2 2 2 2 +--R 2 2 2 b x 2b x b x +---+ +--R ((2b %pi x - %pi)erf(b x) %e %e + 2%e )\|%pi +--R + +--R 2 2 +--R 2b x +--R 4b %pi x erf(b x)%e +--R / +--R 2 2 2 2 +--R 2 b x 2b x +---+ +--R 4b %pi %e %e \|%pi +--R Type: Expression(Integer) +--E 17 + +--S 18 of 395 +a0003:= integrate(t0003,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 18 + +--S 19 of 395 +--m0003:= a0003-r0003 +--E 19 + +--S 20 of 395 +--d0003:= D(m0003,x) +--E 20 + +--S 21 of 395 +t0004:= x^3*erf(b*x)^2 +--R +--R +--R 3 2 +--R (9) x erf(b x) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 395 +r0004:= 1/2/(exp(1)^(2*b^2*x^2))/b^4/%pi+1/4*x^2/(exp(1)^(2*b^2*x^2))/b^2/%pi+_ + 1/4*x*(3+2*b^2*x^2)*erf(b*x)/(exp(1)^(b^2*x^2))/b^3/%pi^(1/2)-_ + 3/16*erf(b*x)^2/b^4+1/4*x^4*erf(b*x)^2 +--R +--R +--R (10) +--R 2 2 2 2 2 2 +--R 4 4 2 b x 2b x 2 2 b x +---+ +--R ((4b %pi x - 3%pi)erf(b x) %e %e + (4b x + 8)%e )\|%pi +--R + +--R 2 2 +--R 3 3 2b x +--R (8b %pi x + 12b %pi x)erf(b x)%e +--R / +--R 2 2 2 2 +--R 4 b x 2b x +---+ +--R 16b %pi %e %e \|%pi +--R Type: Expression(Integer) +--E 22 + +--S 23 of 395 +a0004:= integrate(t0004,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 23 + +--S 24 of 395 +--m0004:= a0004-r0004 +--E 24 + +--S 25 of 395 +--d0004:= D(m0004,x) +--E 25 + +--S 26 of 395 +t0005:= x^5*erf(b*x)^2 +--R +--R +--R 5 2 +--R (11) x erf(b x) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 395 +r0005:= 11/12/(exp(1)^(2*b^2*x^2))/b^6/%pi+7/12*x^2/(exp(1)^(2*b^2*x^2))/_ + b^4/%pi+1/6*x^4/(exp(1)^(2*b^2*x^2))/b^2/%pi+1/12*x*(15+10*b^2*x^2+_ + 4*b^4*x^4)*erf(b*x)/(exp(1)^(b^2*x^2))/b^5/%pi^(1/2)-_ + 5/16*erf(b*x)^2/b^6+1/6*x^6*erf(b*x)^2 +--R +--R +--R (12) +--R 2 2 2 2 +--R 6 6 2 b x 2b x +--R (8b %pi x - 15%pi)erf(b x) %e %e +--R + +--R 2 2 +--R 4 4 2 2 b x +--R (8b x + 28b x + 44)%e +--R * +--R +---+ +--R \|%pi +--R + +--R 2 2 +--R 5 5 3 3 2b x +--R (16b %pi x + 40b %pi x + 60b %pi x)erf(b x)%e +--R / +--R 2 2 2 2 +--R 6 b x 2b x +---+ +--R 48b %pi %e %e \|%pi +--R Type: Expression(Integer) +--E 27 + +--S 28 of 395 +a0005:= integrate(t0005,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 28 + +--S 29 of 395 +--m0005:= a0005-r0005 +--E 29 + +--S 30 of 395 +--d0005:= D(m0005,x) +--E 30 + +--S 31 of 395 +t0006:= x*erf(a+b*x)^2 +--R +--R +--R 2 +--R (13) x erf(b x + a) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 395 +r0006:= 1/4/b^2*(2/(exp(1)^(2*(a+b*x)^2))/%pi-_ + 4*(a-b*x)*erf(a+b*x)/exp((a+b*x)^2)/%pi^(1/2)-erf(a+b*x)^2-_ + 4*a*(a+b*x)*erf(a+b*x)^2+2*(a+b*x)^2*erf(a+b*x)^2+_ + 4*a*2^(1/2)/%pi^(1/2)*erf(2^(1/2)*(a+b*x))) +--R +--R +--R (14) +--R 2 2 2 +--R 2 2 2 2 b x + 2a b x + a +--R (2b %pi x + (- 2a - 1)%pi)erf(b x + a) %e +--R * +--R 2 2 2 +--R 2b x + 4a b x + 2a +--R %e +--R + +--R 2 2 2 +--R b x + 2a b x + a +--R 2%e +--R * +--R +---+ +--R \|%pi +--R + +--R 2 2 2 +--R +-+ +-+ b x + 2a b x + a +--R 4a %pi\|2 erf((b x + a)\|2 )%e +--R + +--R (4b %pi x - 4a %pi)erf(b x + a) +--R * +--R 2 2 2 +--R 2b x + 4a b x + 2a +--R %e +--R / +--R 2 2 2 2 2 2 +--R 2 b x + 2a b x + a 2b x + 4a b x + 2a +---+ +--R 4b %pi %e %e \|%pi +--R Type: Expression(Integer) +--E 32 + +--S 33 of 395 +a0006:= integrate(t0006,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 33 + +--S 34 of 395 +--m0006:= a0006-r0006 +--E 34 + +--S 35 of 395 +--d0006:= D(m0006,x) +--E 35 + +--S 36 of 395 +t0007:= x^2*erf(a+b*x)^2 +--R +--R +--R 2 2 +--R (15) x erf(b x + a) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 395 +r0007:= -1/6/b^3*(4*a/(exp(1)^(2*(a+b*x)^2))/%pi-_ + 2*b*x/(exp(1)^(2*(a+b*x)^2))/%pi-_ + 4*(1+a^2-a*b*x+b^2*x^2)*erf(a+b*x)/exp((a+b*x)^2)/%pi^(1/2)-_ + 3*a*erf(a+b*x)^2-6*a^2*(a+b*x)*erf(a+b*x)^2+_ + 6*a*(a+b*x)^2*erf(a+b*x)^2-2*(a+b*x)^3*erf(a+b*x)^2+_ + 1/2*(5+12*a^2)*erf(2^(1/2)*(a+b*x))*2^(1/2)/%pi^(1/2)) +--R +--R +--R (16) +--R 2 2 2 +--R 3 3 3 2 b x + 2a b x + a +--R (4b %pi x + (4a + 6a)%pi)erf(b x + a) %e +--R * +--R 2 2 2 +--R 2b x + 4a b x + 2a +--R %e +--R + +--R 2 2 2 +--R b x + 2a b x + a +--R (4b x - 8a)%e +--R * +--R +---+ +--R \|%pi +--R + +--R 2 2 2 +--R 2 +-+ +-+ b x + 2a b x + a +--R (- 12a - 5)%pi\|2 erf((b x + a)\|2 )%e +--R + +--R 2 2 2 +--R (8b %pi x - 8a b %pi x + (8a + 8)%pi)erf(b x + a) +--R * +--R 2 2 2 +--R 2b x + 4a b x + 2a +--R %e +--R / +--R 2 2 2 2 2 2 +--R 3 b x + 2a b x + a 2b x + 4a b x + 2a +---+ +--R 12b %pi %e %e \|%pi +--R Type: Expression(Integer) +--E 37 + +--S 38 of 395 +a0007:= integrate(t0007,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 38 + +--S 39 of 395 +--m0007:= a0007-r0007 +--E 39 + +--S 40 of 395 +--d0007:= D(m0007,x) +--E 40 + +--S 41 of 395 +t0008:= exp(1)^(-b^2*x^2)*erf(b*x)/x^8 +--R +--R +--R 2 2 +--R - b x +--R erf(b x)%e +--R (17) ---------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 395 +r0008:= -1/21*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^6+_ + 8/105*b^3/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^4-_ + 4/21*b^5/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-1/105*(15-6*b^2*x^2+_ + 4*b^4*x^4-8*b^6*x^6)*erf(b*x)/(exp(1)^(b^2*x^2))/x^7+_ + 4/105*b^7*%pi^(1/2)*erf(b*x)^2-16/35*b^7*Ei(-2*b^2*x^2)/%pi^(1/2) +--R +--R +--R (18) +--R 2 2 +--R 6 6 4 4 2 2 2b x +---+ +--R (8b x - 4b x + 6b x - 15)erf(b x)%e \|%pi +--R + +--R 2 2 2 2 +--R 7 7 2 7 7 2 2 b x 2b x +--R (4b %pi x erf(b x) - 48b x Ei(- 2b x ))%e %e +--R + +--R 2 2 +--R 5 5 3 3 b x +--R (- 20b x + 8b x - 5b x)%e +--R / +--R 2 2 2 2 +--R 7 b x 2b x +---+ +--R 105x %e %e \|%pi +--R Type: Expression(Integer) +--E 42 + +--S 43 of 395 +a0008:= integrate(t0008,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 43 + +--S 44 of 395 +--m0008:= a0008-r0008 +--E 44 + +--S 45 of 395 +--d0008:= D(m0008,x) +--E 45 + +--S 46 of 395 +t0009:= exp(1)^(-b^2*x^2)*erf(b*x)/x^6 +--R +--R +--R 2 2 +--R - b x +--R erf(b x)%e +--R (19) ---------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 395 +r0009:= -1/10*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^4+_ + 1/3*b^3/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-_ + 1/15*(3-2*b^2*x^2+4*b^4*x^4)*erf(b*x)/(exp(1)^(b^2*x^2))/x^5-_ + 2/15*b^5*%pi^(1/2)*erf(b*x)^2+14/15*b^5*Ei(-2*b^2*x^2)/%pi^(1/2) +--R +--R +--R (20) +--R 2 2 +--R 4 4 2 2 2b x +---+ +--R (- 8b x + 4b x - 6)erf(b x)%e \|%pi +--R + +--R 2 2 2 2 +--R 5 5 2 5 5 2 2 b x 2b x +--R (- 4b %pi x erf(b x) + 28b x Ei(- 2b x ))%e %e +--R + +--R 2 2 +--R 3 3 b x +--R (10b x - 3b x)%e +--R / +--R 2 2 2 2 +--R 5 b x 2b x +---+ +--R 30x %e %e \|%pi +--R Type: Expression(Integer) +--E 47 + +--S 48 of 395 +a0009:= integrate(t0009,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 48 + +--S 49 of 395 +--m0009:= a0009-r0009 +--E 49 + +--S 50 of 395 +--d0009:= D(m0009,x) +--E 50 + +--S 51 of 395 +t0010:= exp(1)^(-b^2*x^2)*erf(b*x)/x^4 +--R +--R +--R 2 2 +--R - b x +--R erf(b x)%e +--R (21) ---------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 395 +r0010:= -1/3*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-_ + 1/3*(1-2*b^2*x^2)*erf(b*x)/(exp(1)^(b^2*x^2))/x^3+_ + 1/3*b^3*%pi^(1/2)*erf(b*x)^2-4/3*b^3*Ei(-2*b^2*x^2)/%pi^(1/2) +--R +--R +--R (22) +--R 2 2 +--R 2 2 2b x +---+ +--R (2b x - 1)erf(b x)%e \|%pi +--R + +--R 2 2 2 2 2 2 +--R 3 3 2 3 3 2 2 b x 2b x b x +--R (b %pi x erf(b x) - 4b x Ei(- 2b x ))%e %e - b x %e +--R / +--R 2 2 2 2 +--R 3 b x 2b x +---+ +--R 3x %e %e \|%pi +--R Type: Expression(Integer) +--E 52 + +--S 53 of 395 +a0010:= integrate(t0010,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 53 + +--S 54 of 395 +--m0010:= a0010-r0010 +--E 54 + +--S 55 of 395 +--d0010:= D(m0010,x) +--E 55 + +--S 56 of 395 +t0011:= exp(1)^(-b^2*x^2)*erf(b*x)/x^2 +--R +--R +--R 2 2 +--R - b x +--R erf(b x)%e +--R (23) ---------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 395 +r0011:= -erf(b*x)/(exp(1)^(b^2*x^2))/x-1/2*b*%pi^(1/2)*erf(b*x)^2+_ + b*Ei(-2*b^2*x^2)/%pi^(1/2) +--R +--R +--R 2 2 +--R +---+ 2 2 2 b x +--R - 2erf(b x)\|%pi + (- b %pi x erf(b x) + 2b x Ei(- 2b x ))%e +--R (24) ------------------------------------------------------------------ +--R 2 2 +--R b x +---+ +--R 2x %e \|%pi +--R Type: Expression(Integer) +--E 57 + +--S 58 of 395 +a0011:= integrate(t0011,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 58 + +--S 59 of 395 +--m0011:= a0011-r0011 +--E 59 + +--S 60 of 395 +--d0011:= D(m0011,x) +--E 60 + +--S 61 of 395 +t0012:= x^2*exp(1)^(-b^2*x^2)*erf(b*x) +--R +--R +--R 2 2 +--R 2 - b x +--R (25) x erf(b x)%e +--R Type: Expression(Integer) +--E 61 + +--S 62 of 395 +r0012:= 1/8*exp(-2*b^2*x^2)*(-2-4*x*erf(b*x)*exp(b^2*x^2)*b*%pi^(1/2)+_ + %pi*erf(b*x)^2*exp(2*b^2*x^2))/b^3/%pi^(1/2) +--R +--R +--R (26) +--R 2 2 2 2 2 2 2 2 +--R - 2b x b x +---+ 2 - 2b x 2b x +--R - 4b x erf(b x)%e %e \|%pi + %pi erf(b x) %e %e +--R + +--R 2 2 +--R - 2b x +--R - 2%e +--R / +--R 3 +---+ +--R 8b \|%pi +--R Type: Expression(Integer) +--E 62 + +--S 63 of 395 +a0012:= integrate(t0012,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 63 + +--S 64 of 395 +--m0012:= a0012-r0012 +--E 64 + +--S 65 of 395 +--d0012:= D(m0012,x) +--E 65 + +--S 66 of 395 +t0013:= x^4*exp(1)^(-b^2*x^2)*erf(b*x) +--R +--R +--R 2 2 +--R 4 - b x +--R (27) x erf(b x)%e +--R Type: Expression(Integer) +--E 66 + +--S 67 of 395 +r0013:= 1/16*exp(-2*b^2*x^2)*(-8-4*b^2*x^2-_ + 12*x*erf(b*x)*exp(b^2*x^2)*b*%pi^(1/2)-_ + 8*x^3*erf(b*x)*exp(b^2*x^2)*b^3*%pi^(1/2)+_ + 3*%pi*erf(b*x)^2*exp(2*b^2*x^2))/b^5/%pi^(1/2) +--R +--R +--R (28) +--R 2 2 2 2 +--R 3 3 - 2b x b x +---+ +--R (- 8b x - 12b x)erf(b x)%e %e \|%pi +--R + +--R 2 2 2 2 2 2 +--R 2 - 2b x 2b x 2 2 - 2b x +--R 3%pi erf(b x) %e %e + (- 4b x - 8)%e +--R / +--R 5 +---+ +--R 16b \|%pi +--R Type: Expression(Integer) +--E 67 + +--S 68 of 395 +a0013:= integrate(t0013,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 68 + +--S 69 of 395 +--m0013:= a0013-r0013 +--E 69 + +--S 70 of 395 +--d0013:= D(m0013,x) +--E 70 + +--S 71 of 395 +t0014:= x^6*exp(1)^(-b^2*x^2)*erf(b*x) +--R +--R +--R 2 2 +--R 6 - b x +--R (29) x erf(b x)%e +--R Type: Expression(Integer) +--E 71 + +--S 72 of 395 +r0014:= 1/32*exp(-2*b^2*x^2)*(-44-28*b^2*x^2-8*b^4*x^4-_ + 60*x*erf(b*x)*exp(b^2*x^2)*b*%pi^(1/2)-_ + 40*x^3*erf(b*x)*exp(b^2*x^2)*b^3*%pi^(1/2)-_ + 16*x^5*erf(b*x)*exp(b^2*x^2)*b^5*%pi^(1/2)+_ + 15*%pi*erf(b*x)^2*exp(2*b^2*x^2))/b^7/%pi^(1/2) +--R +--R +--R (30) +--R 2 2 2 2 +--R 5 5 3 3 - 2b x b x +---+ +--R (- 16b x - 40b x - 60b x)erf(b x)%e %e \|%pi +--R + +--R 2 2 2 2 2 2 +--R 2 - 2b x 2b x 4 4 2 2 - 2b x +--R 15%pi erf(b x) %e %e + (- 8b x - 28b x - 44)%e +--R / +--R 7 +---+ +--R 32b \|%pi +--R Type: Expression(Integer) +--E 72 + +--S 73 of 395 +a0014:= integrate(t0014,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 73 + +--S 74 of 395 +--m0014:= a0014-r0014 +--E 74 + +--S 75 of 395 +--d0014:= D(m0014,x) +--E 75 + +--S 76 of 395 +t0015:= erfc(b*x)^2/x^7 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 76 + +--S 77 of 395 +r0015:= -1/15*b^2/(exp(1)^(2*b^2*x^2))/%pi/x^4+_ + 2/9*b^4/(exp(1)^(2*b^2*x^2))/%pi/x^2+_ + 2/15*b*erfc(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x^5-_ + 4/45*b^3*erfc(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x^3+_ + 8/45*b^5*erfc(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x-4/_ + 45*b^6*erfc(b*x)^2-1/6*erfc(b*x)^2/x^6+28/45*b^6*Ei(-2*b^2*x^2)/%pi +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 395 +--a0015:= integrate(t0015,x) +--E 78 + +--S 79 of 395 +--m0015:= a0015-r0015 +--E 79 + +--S 80 of 395 +--d0015:= D(m0015,x) +--E 80 + +--S 81 of 395 +t0016:= erfc(b*x)^2/x^5 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 81 + +--S 82 of 395 +r0016:= -1/3*b^2/(exp(1)^(2*b^2*x^2))/%pi/x^2+1/3*b*erfc(b*x)/_ + (exp(1)^(b^2*x^2))/%pi^(1/2)/x^3-2/3*b^3*erfc(b*x)/_ + (exp(1)^(b^2*x^2))/%pi^(1/2)/x+1/3*b^4*erfc(b*x)^2-_ + 1/4*erfc(b*x)^2/x^4-4/3*b^4*Ei(-2*b^2*x^2)/%pi +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 395 +--a0016:= integrate(t0016,x) +--E 83 + +--S 84 of 395 +--m0016:= a0016-r0016 +--E 84 + +--S 85 of 395 +--d0016:= D(m0016,x) +--E 85 + +--S 86 of 395 +t0017:= erfc(b*x)^2/x^3 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 86 + +--S 87 of 395 +r0017:= 2*b*erfc(b*x)/(exp(1)^(b^2*x^2))/%pi^(1/2)/x-b^2*erfc(b*x)^2-_ + 1/2*erfc(b*x)^2/x^2+2*b^2*Ei(-2*b^2*x^2)/%pi +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 395 +--a0017:= integrate(t0017,x) +--E 88 + +--S 89 of 395 +--m0017:= a0017-r0017 +--E 89 + +--S 90 of 395 +--d0017:= D(m0017,x) +--E 90 + +--S 91 of 395 +t0018:= erfc(b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 91 + +--S 92 of 395 +r0018:= -2^(1/2)/%pi^(1/2)*erf(2^(1/2)*b*x)/b-2*erfc(b*x)/_ + (exp(1)^(b^2*x^2))/b/%pi^(1/2)+x*erfc(b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 395 +--a0018:= integrate(t0018,x) +--E 93 + +--S 94 of 395 +--m0018:= a0018-r0018 +--E 94 + +--S 95 of 395 +--d0018:= D(m0018,x) +--E 95 + +--S 96 of 395 +t0019:= x*erfc(b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 96 + +--S 97 of 395 +r0019:= 1/2/(exp(1)^(2*b^2*x^2))/b^2/%pi-x*erfc(b*x)/_ + (exp(1)^(b^2*x^2))/b/%pi^(1/2)-1/4*erfc(b*x)^2/b^2+1/2*x^2*erfc(b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 395 +--a0019:= integrate(t0019,x) +--E 98 + +--S 99 of 395 +--m0019:= a0019-r0019 +--E 99 + +--S 100 of 395 +--d0019:= D(m0019,x) +--E 100 + +--S 101 of 395 +t0020:= x^3*erfc(b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 101 + +--S 102 of 395 +r0020:= 1/2/(exp(1)^(2*b^2*x^2))/b^4/%pi+1/4*x^2/_ + (exp(1)^(2*b^2*x^2))/b^2/%pi-3/4*x*erfc(b*x)/_ + (exp(1)^(b^2*x^2))/b^3/%pi^(1/2)-1/2*x^3*erfc(b*x)/_ + (exp(1)^(b^2*x^2))/b/%pi^(1/2)-3/16*erfc(b*x)^2/b^4+1/4*x^4*erfc(b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 395 +--a0020:= integrate(t0020,x) +--E 103 + +--S 104 of 395 +--m0020:= a0020-r0020 +--E 104 + +--S 105 of 395 +--d0020:= D(m0020,x) +--E 105 + +--S 106 of 395 +t0021:= x^5*erfc(b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 106 + +--S 107 of 395 +r0021:= 11/12/(exp(1)^(2*b^2*x^2))/b^6/%pi+7/12*x^2/_ + (exp(1)^(2*b^2*x^2))/b^4/%pi+1/6*x^4/(exp(1)^(2*b^2*x^2))/b^2/%pi-_ + 5/4*x*erfc(b*x)/(exp(1)^(b^2*x^2))/b^5/%pi^(1/2)-_ + 5/6*x^3*erfc(b*x)/(exp(1)^(b^2*x^2))/b^3/%pi^(1/2)-_ + 1/3*x^5*erfc(b*x)/(exp(1)^(b^2*x^2))/b/%pi^(1/2)-_ + 5/16*erfc(b*x)^2/b^6+1/6*x^6*erfc(b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 395 +--a0021:= integrate(t0021,x) +--E 108 + +--S 109 of 395 +--m0021:= a0021-r0021 +--E 109 + +--S 110 of 395 +--d0021:= D(m0021,x) +--E 110 + +--S 111 of 395 +t0022:= erfc(a+b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 111 + +--S 112 of 395 +r0022:= -2^(1/2)/%pi^(1/2)*erf(2^(1/2)*(a+b*x))/b-_ + 2*erfc(a+b*x)/exp((a+b*x)^2)/b/%pi^(1/2)+(a+b*x)*erfc(a+b*x)^2/b +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 112 + +--S 113 of 395 +--a0022:= integrate(t0022,x) +--E 113 + +--S 114 of 395 +--m0022:= a0022-r0022 +--E 114 + +--S 115 of 395 +--d0022:= D(m0022,x) +--E 115 + +--S 116 of 395 +t0023:= x*erfc(a+b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 116 + +--S 117 of 395 +r0023:= 1/4/b^2*(2/(exp(1)^(2*(a+b*x)^2))/%pi+4*a*2^(1/2)/%pi^(1/2)*_ + erf(2^(1/2)*(a+b*x))+erfc(a+b*x)*(4*a/exp((a+b*x)^2)/%pi^(1/2)-_ + erfc(a+b*x)-4*b*x/exp((a+b*x)^2)/%pi^(1/2)-_ + 4*a*(a+b*x)*erfc(a+b*x)+2*(a+b*x)^2*erfc(a+b*x))) +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 395 +--a0023:= integrate(t0023,x) +--E 118 + +--S 119 of 395 +--m0023:= a0023-r0023 +--E 119 + +--S 120 of 395 +--d0023:= D(m0023,x) +--E 120 + +--S 121 of 395 +t0024:= x^2*erfc(a+b*x)^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 121 + +--S 122 of 395 +r0024:= -1/6/b^3*(4*a/(exp(1)^(2*(a+b*x)^2))/%pi+_ + 1/2*(5+12*a^2)*erf(2^(1/2)*(a+b*x))*2^(1/2)/%pi^(1/2)+_ + 4*erfc(a+b*x)/exp((a+b*x)^2)/%pi^(1/2)+_ + 4*(a+b*x)^2*erfc(a+b*x)/exp((a+b*x)^2)/%pi^(1/2)-_ + 3*a*erfc(a+b*x)^2-6*a^2*(a+b*x)*erfc(a+b*x)^2+_ + 6*a*(a+b*x)^2*erfc(a+b*x)^2-2*(a+b*x)^3*erfc(a+b*x)^2-_ + 2*b*x*(exp(1)^(-2*(a+b*x)^2)+_ + 6*a*%pi^(1/2)*erfc(a+b*x)/exp((a+b*x)^2))/%pi) +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 395 +--a0024:= integrate(t0024,x) +--E 123 + +--S 124 of 395 +--m0024:= a0024-r0024 +--E 124 + +--S 125 of 395 +--d0024:= D(m0024,x) +--E 125 + +--S 126 of 395 +t0025:= exp(1)^(-b^2*x^2)*erfc(b*x)/x^8 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 126 + +--S 127 of 395 +r0025:= 1/21*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^6-_ + 8/105*b^3/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^4+_ + 4/21*b^5/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-_ + 1/7*erfc(b*x)/(exp(1)^(b^2*x^2))/x^7+_ + 2/35*b^2*erfc(b*x)/(exp(1)^(b^2*x^2))/x^5-_ + 4/105*b^4*erfc(b*x)/(exp(1)^(b^2*x^2))/x^3+_ + 8/105*b^6*erfc(b*x)/(exp(1)^(b^2*x^2))/x-_ + 4/105*b^7*%pi^(1/2)*erfc(b*x)^2+16/35*b^7*Ei(-2*b^2*x^2)/%pi^(1/2) +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 395 +--a0025:= integrate(t0025,x) +--E 128 + +--S 129 of 395 +--m0025:= a0025-r0025 +--E 129 + +--S 130 of 395 +--d0025:= D(m0025,x) +--E 130 + +--S 131 of 395 +t0026:= exp(1)^(-b^2*x^2)*erfc(b*x)/x^6 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 131 + +--S 132 of 395 +r0026:= 1/10*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^4-_ + 1/3*b^3/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-_ + 1/5*erfc(b*x)/(exp(1)^(b^2*x^2))/x^5+_ + 2/15*b^2*erfc(b*x)/(exp(1)^(b^2*x^2))/x^3-_ + 4/15*b^4*erfc(b*x)/(exp(1)^(b^2*x^2))/x+_ + 2/15*b^5*%pi^(1/2)*erfc(b*x)^2-14/15*b^5*Ei(-2*b^2*x^2)/%pi^(1/2) +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 395 +--a0026:= integrate(t0026,x) +--E 133 + +--S 134 of 395 +--m0026:= a0026-r0026 +--E 134 + +--S 135 of 395 +--d0026:= D(m0026,x) +--E 135 + +--S 136 of 395 +t0027:= exp(1)^(-b^2*x^2)*erfc(b*x)/x^4 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 136 + +--S 137 of 395 +r0027:= 1/3*b/(exp(1)^(2*b^2*x^2))/%pi^(1/2)/x^2-_ + 1/3*erfc(b*x)/(exp(1)^(b^2*x^2))/x^3+_ + 2/3*b^2*erfc(b*x)/(exp(1)^(b^2*x^2))/x-_ + 1/3*b^3*%pi^(1/2)*erfc(b*x)^2+4/3*b^3*Ei(-2*b^2*x^2)/%pi^(1/2) +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 137 + +--S 138 of 395 +--a0027:= integrate(t0027,x) +--E 138 + +--S 139 of 395 +--m0027:= a0027-r0027 +--E 139 + +--S 140 of 395 +--d0027:= D(m0027,x) +--E 140 + +--S 141 of 395 +t0028:= exp(1)^(-b^2*x^2)*erfc(b*x)/x^2 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 141 + +--S 142 of 395 +r0028:= -erfc(b*x)/(exp(1)^(b^2*x^2))/x+_ + 1/2*b*%pi^(1/2)*erfc(b*x)^2-b*Ei(-2*b^2*x^2)/%pi^(1/2) +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 142 + +--S 143 of 395 +--a0028:= integrate(t0028,x) +--E 143 + +--S 144 of 395 +--m0028:= a0028-r0028 +--E 144 + +--S 145 of 395 +--d0028:= D(m0028,x) +--E 145 + +--S 146 of 395 +t0029:= x^2*exp(1)^(-b^2*x^2)*erfc(b*x) +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 146 + +--S 147 of 395 +r0029:= 1/4/(exp(1)^(2*b^2*x^2))/b^3/%pi^(1/2)-_ + 1/2*x*erfc(b*x)/(exp(1)^(b^2*x^2))/b^2-1/8*%pi^(1/2)*erfc(b*x)^2/b^3 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 395 +--a0029:= integrate(t0029,x) +--E 148 + +--S 149 of 395 +--m0029:= a0029-r0029 +--E 149 + +--S 150 of 395 +--d0029:= D(m0029,x) +--E 150 + +--S 151 of 395 +t0030:= x^4*exp(1)^(-b^2*x^2)*erfc(b*x) +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 151 + +--S 152 of 395 +r0030:= 1/2/(exp(1)^(2*b^2*x^2))/b^5/%pi^(1/2)+_ + 1/4*x^2/(exp(1)^(2*b^2*x^2))/b^3/%pi^(1/2)-_ + 3/4*x*erfc(b*x)/(exp(1)^(b^2*x^2))/b^4-_ + 1/2*x^3*erfc(b*x)/(exp(1)^(b^2*x^2))/b^2-_ + 3/16*%pi^(1/2)*erfc(b*x)^2/b^5 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 152 + +--S 153 of 395 +--a0030:= integrate(t0030,x) +--E 153 + +--S 154 of 395 +--m0030:= a0030-r0030 +--E 154 + +--S 155 of 395 +--d0030:= D(m0030,x) +--E 155 + +--S 156 of 395 +t0031:= x^6*exp(1)^(-b^2*x^2)*erfc(b*x) +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 156 + +--S 157 of 395 +r0031:= 11/8/(exp(1)^(2*b^2*x^2))/b^7/%pi^(1/2)+_ + 7/8*x^2/(exp(1)^(2*b^2*x^2))/b^5/%pi^(1/2)+_ + 1/4*x^4/(exp(1)^(2*b^2*x^2))/b^3/%pi^(1/2)-_ + 15/8*x*erfc(b*x)/(exp(1)^(b^2*x^2))/b^6-_ + 5/4*x^3*erfc(b*x)/(exp(1)^(b^2*x^2))/b^4-_ + 1/2*x^5*erfc(b*x)/(exp(1)^(b^2*x^2))/b^2-_ + 15/32*%pi^(1/2)*erfc(b*x)^2/b^7 +--R +--R There are no library operations named erfc +--R Use HyperDoc Browse or issue +--R )what op erfc +--R to learn if there is any operation containing " erfc " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfc +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 157 + +--S 158 of 395 +--a0031:= integrate(t0031,x) +--E 158 + +--S 159 of 395 +--m0031:= a0031-r0031 +--E 159 + +--S 160 of 395 +--d0031:= D(m0031,x) +--E 160 + +--S 161 of 395 +t0032:= erfi(b*x)^2/x^7 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 161 + +--S 162 of 395 +r0032:= -1/15*b^2*exp(1)^(2*b^2*x^2)/%pi/x^4-_ + 2/9*b^4*exp(1)^(2*b^2*x^2)/%pi/x^2-_ + 2/45*b*exp(1)^(b^2*x^2)*(3+2*b^2*x^2+4*b^4*x^4)*_ + erfi(b*x)/%pi^(1/2)/x^5+4/45*b^6*erfi(b*x)^2-_ + 1/6*erfi(b*x)^2/x^6+28/45*b^6*Ei(2*b^2*x^2)/%pi +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 395 +--a0032:= integrate(t0032,x) +--E 163 + +--S 164 of 395 +--m0032:= a0032-r0032 +--E 164 + +--S 165 of 395 +--d0032:= D(m0032,x) +--E 165 + +--S 166 of 395 +t0033:= erfi(b*x)^2/x^5 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 166 + +--S 167 of 395 +r0033:= -1/3*b^2*exp(1)^(2*b^2*x^2)/%pi/x^2-_ + 1/3*b*exp(1)^(b^2*x^2)*(1+2*b^2*x^2)*erfi(b*x)/%pi^(1/2)/x^3+_ + 1/3*b^4*erfi(b*x)^2-1/4*erfi(b*x)^2/x^4+4/3*b^4*Ei(2*b^2*x^2)/%pi +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 167 + +--S 168 of 395 +--a0033:= integrate(t0033,x) +--E 168 + +--S 169 of 395 +--m0033:= a0033-r0033 +--E 169 + +--S 170 of 395 +--d0033:= D(m0033,x) +--E 170 + +--S 171 of 395 +t0034:= erfi(b*x)^2/x^3 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 171 + +--S 172 of 395 +r0034:= -2*b*exp(1)^(b^2*x^2)*erfi(b*x)/%pi^(1/2)/x+_ + b^2*erfi(b*x)^2-1/2*erfi(b*x)^2/x^2+2*b^2*Ei(2*b^2*x^2)/%pi +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 172 + +--S 173 of 395 +--a0034:= integrate(t0034,x) +--E 173 + +--S 174 of 395 +--m0034:= a0034-r0034 +--E 174 + +--S 175 of 395 +--d0034:= D(m0034,x) +--E 175 + +--S 176 of 395 +t0035:= erfi(b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 176 + +--S 177 of 395 +r0035:= (-2*exp(b^2*x^2)*erfi(b*x)+x*erfi(b*x)^2*b*%pi^(1/2)+_ + 2^(1/2)*erfi(2^(1/2)*b*x))/b/%pi^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 177 + +--S 178 of 395 +--a0035:= integrate(t0035,x) +--E 178 + +--S 179 of 395 +--m0035:= a0035-r0035 +--E 179 + +--S 180 of 395 +--d0035:= D(m0035,x) +--E 180 + +--S 181 of 395 +t0036:= x*erfi(b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 181 + +--S 182 of 395 +r0036:= 1/2*exp(1)^(2*b^2*x^2)/b^2/%pi-_ + exp(1)^(b^2*x^2)*x*erfi(b*x)/b/%pi^(1/2)+_ + 1/4*erfi(b*x)^2/b^2+1/2*x^2*erfi(b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 182 + +--S 183 of 395 +--a0036:= integrate(t0036,x) +--E 183 + +--S 184 of 395 +--m0036:= a0036-r0036 +--E 184 + +--S 185 of 395 +--d0036:= D(m0036,x) +--E 185 + +--S 186 of 395 +t0037:= x^2*erfi(b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 186 + +--S 187 of 395 +r0037:= 1/3*exp(1)^(2*b^2*x^2)*x/b^2/%pi+_ + 2/3*exp(1)^(b^2*x^2)*(1-b^2*x^2)*erfi(b*x)/b^3/%pi^(1/2)+_ + 1/3*x^3*erfi(b*x)^2-5/12*erfi(2^(1/2)*b*x)/b^3*2^(1/2)/%pi^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 187 + +--S 188 of 395 +--a0037:= integrate(t0037,x) +--E 188 + +--S 189 of 395 +--m0037:= a0037-r0037 +--E 189 + +--S 190 of 395 +--d0037:= D(m0037,x) +--E 190 + +--S 191 of 395 +t0038:= x^3*erfi(b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 191 + +--S 192 of 395 +r0038:= -1/2*exp(1)^(2*b^2*x^2)/b^4/%pi+1/4*exp(1)^(2*b^2*x^2)*x^2/b^2/%pi+_ + 1/4*exp(1)^(b^2*x^2)*x*(3-2*b^2*x^2)*erfi(b*x)/b^3/%pi^(1/2)-_ + 3/16*erfi(b*x)^2/b^4+1/4*x^4*erfi(b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 192 + +--S 193 of 395 +--a0038:= integrate(t0038,x) +--E 193 + +--S 194 of 395 +--m0038:= a0038-r0038 +--E 194 + +--S 195 of 395 +--d0038:= D(m0038,x) +--E 195 + +--S 196 of 395 +t0039:= x^4*erfi(b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 196 + +--S 197 of 395 +r0039:= -11/20*exp(1)^(2*b^2*x^2)*x/b^4/%pi+_ + 1/5*exp(1)^(2*b^2*x^2)*x^3/b^2/%pi-_ + 2/5*exp(1)^(b^2*x^2)*(2-2*b^2*x^2+b^4*x^4)*erfi(b*x)/b^5/%pi^(1/2)+_ + 1/5*x^5*erfi(b*x)^2+43/80*erfi(2^(1/2)*b*x)/b^5*2^(1/2)/%pi^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 197 + +--S 198 of 395 +--a0039:= integrate(t0039,x) +--E 198 + +--S 199 of 395 +--m0039:= a0039-r0039 +--E 199 + +--S 200 of 395 +--d0039:= D(m0039,x) +--E 200 + +--S 201 of 395 +t0040:= x^5*erfi(b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 201 + +--S 202 of 395 +r0040:= 11/12*exp(1)^(2*b^2*x^2)/b^6/%pi-_ + 7/12*exp(1)^(2*b^2*x^2)*x^2/b^4/%pi+_ + 1/6*exp(1)^(2*b^2*x^2)*x^4/b^2/%pi-_ + 1/12*exp(1)^(b^2*x^2)*x*(15-10*b^2*x^2+_ + 4*b^4*x^4)*erfi(b*x)/b^5/%pi^(1/2)+5/16*erfi(b*x)^2/b^6+_ + 1/6*x^6*erfi(b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 202 + +--S 203 of 395 +--a0040:= integrate(t0040,x) +--E 203 + +--S 204 of 395 +--m0040:= a0040-r0040 +--E 204 + +--S 205 of 395 +--d0040:= D(m0040,x) +--E 205 + +--S 206 of 395 +t0041:= x^6*erfi(b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 206 + +--S 207 of 395 +r0041:= 21/16*exp(1)^(2*b^2*x^2)*x/b^6/%pi-_ + 17/28*exp(1)^(2*b^2*x^2)*x^3/b^4/%pi+_ + 1/7*exp(1)^(2*b^2*x^2)*x^5/b^2/%pi+_ + 2/7*exp(1)^(b^2*x^2)*(6-6*b^2*x^2+3*b^4*x^4-_ + b^6*x^6)*erfi(b*x)/b^7/%pi^(1/2)+1/7*x^7*erfi(b*x)^2-_ + 531/448*erfi(2^(1/2)*b*x)/b^7*2^(1/2)/%pi^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 207 + +--S 208 of 395 +--a0041:= integrate(t0041,x) +--E 208 + +--S 209 of 395 +--m0041:= a0041-r0041 +--E 209 + +--S 210 of 395 +--d0041:= D(m0041,x) +--E 210 + +--S 211 of 395 +t0042:= erfi(a+b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 395 +r0042:= -2*exp((a+b*x)^2)*erfi(a+b*x)/b/%pi^(1/2)+(a+b*x)*_ + erfi(a+b*x)^2/b+2^(1/2)/%pi^(1/2)*erfi(2^(1/2)*(a+b*x))/b +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 212 + +--S 213 of 395 +--a0042:= integrate(t0042,x) +--E 213 + +--S 214 of 395 +--m0042:= a0042-r0042 +--E 214 + +--S 215 of 395 +--d0042:= D(m0042,x) +--E 215 + +--S 216 of 395 +t0043:= x*erfi(a+b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 216 + +--S 217 of 395 +r0043:= 1/4/b^2*(2*exp(1)^(2*(a+b*x)^2)/%pi+_ + 4*exp((a+b*x)^2)*(a-b*x)*erfi(a+b*x)/%pi^(1/2)+_ + erfi(a+b*x)^2-4*a*(a+b*x)*erfi(a+b*x)^2+_ + 2*(a+b*x)^2*erfi(a+b*x)^2-4*a*2^(1/2)/%pi^(1/2)*erfi(2^(1/2)*(a+b*x))) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 217 + +--S 218 of 395 +--a0043:= integrate(t0043,x) +--E 218 + +--S 219 of 395 +--m0043:= a0043-r0043 +--E 219 + +--S 220 of 395 +--d0043:= D(m0043,x) +--E 220 + +--S 221 of 395 +t0044:= x^2*erfi(a+b*x)^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 221 + +--S 222 of 395 +r0044:= -1/6/b^3*(4*a*exp(1)^(2*(a+b*x)^2)/%pi-_ + 2*b*exp(1)^(2*(a+b*x)^2)*x/%pi-_ + 4*exp((a+b*x)^2)*(1-a^2+a*b*x-b^2*x^2)*erfi(a+b*x)/%pi^(1/2)+_ + 3*a*erfi(a+b*x)^2-6*a^2*(a+b*x)*erfi(a+b*x)^2+_ + 6*a*(a+b*x)^2*erfi(a+b*x)^2-2*(a+b*x)^3*erfi(a+b*x)^2+_ + 1/2*(5-12*a^2)*erfi(2^(1/2)*(a+b*x))*2^(1/2)/%pi^(1/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 222 + +--S 223 of 395 +--a0044:= integrate(t0044,x) +--E 223 + +--S 224 of 395 +--m0044:= a0044-r0044 +--E 224 + +--S 225 of 395 +--d0044:= D(m0044,x) +--E 225 + +--S 226 of 395 +t0045:= exp(1)^(b^2*x^2)*erfi(b*x)/x^8 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 226 + +--S 227 of 395 +r0045:= -1/21*b*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^6-_ + 8/105*b^3*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^4-_ + 4/21*b^5*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^2-_ + 1/105*exp(1)^(b^2*x^2)*(15+6*b^2*x^2+4*b^4*x^4+_ + 8*b^6*x^6)*erfi(b*x)/x^7+4/105*b^7*%pi^(1/2)*erfi(b*x)^2+_ + 16/35*b^7*Ei(2*b^2*x^2)/%pi^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 395 +--a0045:= integrate(t0045,x) +--E 228 + +--S 229 of 395 +--m0045:= a0045-r0045 +--E 229 + +--S 230 of 395 +--d0045:= D(m0045,x) +--E 230 + +--S 231 of 395 +t0046:= exp(1)^(b^2*x^2)*erfi(b*x)/x^6 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 231 + +--S 232 of 395 +r0046:= -1/10*b*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^4-_ + 1/3*b^3*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^2-_ + 1/15*exp(1)^(b^2*x^2)*(3+2*b^2*x^2+4*b^4*x^4)*erfi(b*x)/x^5+_ + 2/15*b^5*%pi^(1/2)*erfi(b*x)^2+14/15*b^5*Ei(2*b^2*x^2)/%pi^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 232 + +--S 233 of 395 +--a0046:= integrate(t0046,x) +--E 233 + +--S 234 of 395 +--m0046:= a0046-r0046 +--E 234 + +--S 235 of 395 +--d0046:= D(m0046,x) +--E 235 + +--S 236 of 395 +t0047:= exp(1)^(b^2*x^2)*erfi(b*x)/x^4 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 236 + +--S 237 of 395 +r0047:= -1/3*b*exp(1)^(2*b^2*x^2)/%pi^(1/2)/x^2-_ + 1/3*exp(1)^(b^2*x^2)*(1+2*b^2*x^2)*erfi(b*x)/x^3+_ + 1/3*b^3*%pi^(1/2)*erfi(b*x)^2+4/3*b^3*Ei(2*b^2*x^2)/%pi^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 395 +--a0047:= integrate(t0047,x) +--E 238 + +--S 239 of 395 +--m0047:= a0047-r0047 +--E 239 + +--S 240 of 395 +--d0047:= D(m0047,x) +--E 240 + +--S 241 of 395 +t0048:= exp(1)^(b^2*x^2)*erfi(b*x)/x^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 241 + +--S 242 of 395 +r0048:= -exp(1)^(b^2*x^2)*erfi(b*x)/x+_ + 1/2*b*%pi^(1/2)*erfi(b*x)^2+b*Ei(2*b^2*x^2)/%pi^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 242 + +--S 243 of 395 +--a0048:= integrate(t0048,x) +--E 243 + +--S 244 of 395 +--m0048:= a0048-r0048 +--E 244 + +--S 245 of 395 +--d0048:= D(m0048,x) +--E 245 + +--S 246 of 395 +t0049:= x*exp(1)^(b^2*x^2)*erfi(b*x) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 246 + +--S 247 of 395 +r0049:= -1/4*(-2*exp(b^2*x^2)*erfi(b*x)+erfi(2^(1/2)*b*x)*2^(1/2))/b^2 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 247 + +--S 248 of 395 +--a0049:= integrate(t0049,x) +--E 248 + +--S 249 of 395 +--m0049:= a0049-r0049 +--E 249 + +--S 250 of 395 +--d0049:= D(m0049,x) +--E 250 + +--S 251 of 395 +t0050:= x^2*exp(1)^(b^2*x^2)*erfi(b*x) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 251 + +--S 252 of 395 +r0050:= -1/8*(2*exp(2*b^2*x^2)-4*exp(b^2*x^2)*x*erfi(b*x)*b*%pi^(1/2)+_ + %pi*erfi(b*x)^2)/b^3/%pi^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 252 + +--S 253 of 395 +--a0050:= integrate(t0050,x) +--E 253 + +--S 254 of 395 +--m0050:= a0050-r0050 +--E 254 + +--S 255 of 395 +--d0050:= D(m0050,x) +--E 255 + +--S 256 of 395 +t0051:= x^3*exp(1)^(b^2*x^2)*erfi(b*x) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 256 + +--S 257 of 395 +r0051:= -1/4*exp(1)^(2*b^2*x^2)*x/b^3/%pi^(1/2)-_ + 1/2*exp(1)^(b^2*x^2)*(1-b^2*x^2)*erfi(b*x)/b^4+_ + 5/16*erfi(2^(1/2)*b*x)*2^(1/2)/b^4 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 257 + +--S 258 of 395 +--a0051:= integrate(t0051,x) +--E 258 + +--S 259 of 395 +--m0051:= a0051-r0051 +--E 259 + +--S 260 of 395 +--d0051:= D(m0051,x) +--E 260 + +--S 261 of 395 +t0052:= x^4*exp(1)^(b^2*x^2)*erfi(b*x) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 261 + +--S 262 of 395 +r0052:= -1/16*(-8*exp(2*b^2*x^2)+4*exp(2*b^2*x^2)*x^2*b^2+_ + 12*exp(b^2*x^2)*x*erfi(b*x)*b*%pi^(1/2)-_ + 8*exp(b^2*x^2)*x^3*erfi(b*x)*b^3*%pi^(1/2)-_ + 3*%pi*erfi(b*x)^2)/b^5/%pi^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 262 + +--S 263 of 395 +--a0052:= integrate(t0052,x) +--E 263 + +--S 264 of 395 +--m0052:= a0052-r0052 +--E 264 + +--S 265 of 395 +--d0052:= D(m0052,x) +--E 265 + +--S 266 of 395 +t0053:= x^5*exp(1)^(b^2*x^2)*erfi(b*x) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 266 + +--S 267 of 395 +r0053:= 11/16*exp(1)^(2*b^2*x^2)*x/b^5/%pi^(1/2)-_ + 1/4*exp(1)^(2*b^2*x^2)*x^3/b^3/%pi^(1/2)+_ + 1/2*exp(1)^(b^2*x^2)*(2-2*b^2*x^2+b^4*x^4)*erfi(b*x)/b^6-_ + 43/64*erfi(2^(1/2)*b*x)*2^(1/2)/b^6 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 395 +--a0053:= integrate(t0053,x) +--E 268 + +--S 269 of 395 +--m0053:= a0053-r0053 +--E 269 + +--S 270 of 395 +--d0053:= D(m0053,x) +--E 270 + +--S 271 of 395 +t0054:= x^6*exp(1)^(b^2*x^2)*erfi(b*x) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 271 + +--S 272 of 395 +r0054:= -11/8*exp(1)^(2*b^2*x^2)/b^7/%pi^(1/2)+_ + 7/8*exp(1)^(2*b^2*x^2)*x^2/b^5/%pi^(1/2)-_ + 1/4*exp(1)^(2*b^2*x^2)*x^4/b^3/%pi^(1/2)+_ + 1/8*exp(1)^(b^2*x^2)*x*(15-10*b^2*x^2+4*b^4*x^4)*erfi(b*x)/b^6-_ + 15/32*%pi^(1/2)*erfi(b*x)^2/b^7 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 272 + +--S 273 of 395 +--a0054:= integrate(t0054,x) +--E 273 + +--S 274 of 395 +--m0054:= a0054-r0054 +--E 274 + +--S 275 of 395 +--d0054:= D(m0054,x) +--E 275 + +--S 276 of 395 +t0055:= FresnelS(b*x)^2/x^9 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 276 + +--S 277 of 395 +r0055:= -1/336*b^2/x^6+1/1680*b^6*%pi^2/x^2+1/336*b^2*cos(b^2*%pi*x^2)/x^6-_ + 1/336*b^6*%pi^2*cos(b^2*%pi*x^2)/x^2+_ + 1/840*b^8*%pi^4*FresnelS(b*x)^2-1/8*FresnelS(b*x)^2/x^8-_ + 1/420*b*FresnelS(b*x)*(b^2*%pi*_ + x^2*(3-b^4*%pi^2*x^4)*cos(1/2*b^2*%pi*x^2)+_ + (15-b^4*%pi^2*x^4)*sin(1/2*b^2*%pi*x^2))/x^7-_ + 1/420*b^4*%pi*sin(b^2*%pi*x^2)/x^4-1/280*b^8*%pi^3*Si(b^2*%pi*x^2) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 277 + +--S 278 of 395 +--a0055:= integrate(t0055,x) +--E 278 + +--S 279 of 395 +--m0055:= a0055-r0055 +--E 279 + +--S 280 of 395 +--d0055:= D(m0055,x) +--E 280 + +--S 281 of 395 +t0056:= FresnelS(b*x)^2/x^5 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 281 + +--S 282 of 395 +r0056:= -1/24*(b^2*x^2-b^2*cos(b^2*%pi*x^2)*x^2+2*b^4*%pi^2*_ + FresnelS(b*x)^2*x^4+6*FresnelS(b*x)^2+4*b^3*_ + FresnelS(b*x)*x^3*%pi*cos(1/2*b^2*%pi*x^2)+4*_ + FresnelS(b*x)*sin(1/2*b^2*%pi*x^2)*b*x-_ + 2*b^4*%pi*Si(b^2*%pi*x^2)*x^4)/x^4 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 395 +--a0056:= integrate(t0056,x) +--E 283 + +--S 284 of 395 +--m0056:= a0056-r0056 +--E 284 + +--S 285 of 395 +--d0056:= D(m0056,x) +--E 285 + +--S 286 of 395 +t0057:= x^3*FresnelS(b*x)^2 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 286 + +--S 287 of 395 +r0057:= 1/8*(3*b^2*%pi*x^2+x^2*cos(b^2*%pi*x^2)*b^2*%pi+_ + 6*FresnelS(b*x)^2*%pi+2*x^4*FresnelS(b*x)^2*b^4*%pi^3+_ + 4*x^3*FresnelS(b*x)*b^3*%pi^2*cos(1/2*b^2*%pi*x^2)-_ + 12*x*FresnelS(b*x)*b*%pi*sin(1/2*b^2*%pi*x^2)-_ + 4*sin(b^2*%pi*x^2))/b^4/%pi^3 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 287 + +--S 288 of 395 +--a0057:= integrate(t0057,x) +--E 288 + +--S 289 of 395 +--m0057:= a0057-r0057 +--E 289 + +--S 290 of 395 +--d0057:= D(m0057,x) +--E 290 + +--S 291 of 395 +t0058:= x^7*FresnelS(b*x)^2 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 291 + +--S 292 of 395 +r0058:= -105/16*x^2/b^6/%pi^4+7/48*x^6/b^2/%pi^2-_ + 55/16*x^2*cos(b^2*%pi*x^2)/b^6/%pi^4+_ + 1/16*x^6*cos(b^2*%pi*x^2)/b^2/%pi^2-_ + 105/8*FresnelS(b*x)^2/b^8/%pi^4+1/8*x^8*FresnelS(b*x)^2-_ + 1/4*x*FresnelS(b*x)*(b^2*%pi*x^2*(35-b^4*%pi^2*x^4)*_ + cos(1/2*b^2*%pi*x^2)-7*(15-b^4*%pi^2*x^4)*_ + sin(1/2*b^2*%pi*x^2))/b^7/%pi^4+10*sin(b^2*%pi*x^2)/b^8/%pi^5-_ + 5/8*x^4*sin(b^2*%pi*x^2)/b^4/%pi^3 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 292 + +--S 293 of 395 +--a0058:= integrate(t0058,x) +--E 293 + +--S 294 of 395 +--m0058:= a0058-r0058 +--E 294 + +--S 295 of 395 +--d0058:= D(m0058,x) +--E 295 + +--S 296 of 395 +t0059:= sin(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x^8 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 296 + +--S 297 of 395 +r0059:= -1/84*b/x^6+1/420*b^5*%pi^2/x^2+1/84*b*cos(b^2*%pi*x^2)/x^6-_ + 1/84*b^5*%pi^2*cos(b^2*%pi*x^2)/x^2+1/210*b^7*%pi^4*FresnelS(b*x)^2-_ + 1/105*FresnelS(b*x)*(b^2*%pi*x^2*(3-b^4*%pi^2*x^4)*_ + cos(1/2*b^2*%pi*x^2)+(15-b^4*%pi^2*x^4)*_ + sin(1/2*b^2*%pi*x^2))/x^7-1/105*b^3*%pi*_ + sin(b^2*%pi*x^2)/x^4-1/70*b^7*%pi^3*Si(b^2*%pi*x^2) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 297 + +--S 298 of 395 +--a0059:= integrate(t0059,x) +--E 298 + +--S 299 of 395 +--m0059:= a0059-r0059 +--E 299 + +--S 300 of 395 +--d0059:= D(m0059,x) +--E 300 + +--S 301 of 395 +t0060:= sin(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x^4 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 301 + +--S 302 of 395 +r0060:= -1/12*(b*x-x*cos(b^2*%pi*x^2)*b+2*x^3*FresnelS(b*x)^2*b^3*%pi^2+_ + 4*FresnelS(b*x)*b^2*%pi*x^2*cos(1/2*b^2*%pi*x^2)+_ + 4*sin(1/2*b^2*%pi*x^2)*FresnelS(b*x)-_ + 2*b^3*%pi*Si(b^2*%pi*x^2)*x^3)/x^3 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 302 + +--S 303 of 395 +--a0060:= integrate(t0060,x) +--E 303 + +--S 304 of 395 +--m0060:= a0060-r0060 +--E 304 + +--S 305 of 395 +--d0060:= D(m0060,x) +--E 305 + +--S 306 of 395 +t0061:= x^4*sin(1/2*b^2*%pi*x^2)*FresnelS(b*x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 306 + +--S 307 of 395 +r0061:= -1/4*(3*b^2*%pi*x^2+x^2*cos(b^2*%pi*x^2)*b^2*%pi+_ + 6*FresnelS(b*x)^2*%pi+4*x^3*FresnelS(b*x)*_ + b^3*%pi^2*cos(1/2*b^2*%pi*x^2)-12*x*FresnelS(b*x)*b*%pi*_ + sin(1/2*b^2*%pi*x^2)-4*sin(b^2*%pi*x^2))/b^5/%pi^3 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 307 + +--S 308 of 395 +--a0061:= integrate(t0061,x) +--E 308 + +--S 309 of 395 +--m0061:= a0061-r0061 +--E 309 + +--S 310 of 395 +--d0061:= D(m0061,x) +--E 310 + +--S 311 of 395 +t0062:= cos(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x^10 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 311 + +--S 312 of 395 +r0062:= 1/756*b^3*%pi/x^6-1/3780*b^7*%pi^3/x^2-_ + 11/3024*b^3*%pi*cos(b^2*%pi*x^2)/x^6+_ + 5/2016*b^7*%pi^3*cos(b^2*%pi*x^2)/x^2-_ + 1/1890*b^9*%pi^5*FresnelS(b*x)^2-_ + 1/945*FresnelS(b*x)*((105-3*b^4*%pi^2*x^4+b^8*%pi^4*x^8)*_ + cos(1/2*b^2*%pi*x^2)-b^2*%pi*x^2*(15-b^4*%pi^2*x^4)*_ + sin(1/2*b^2*%pi*x^2))/x^9-1/144*b*sin(b^2*%pi*x^2)/x^8+_ + 67/30240*b^5*%pi^2*sin(b^2*%pi*x^2)/x^4+_ + 83/30240*b^9*%pi^4*Si(b^2*%pi*x^2) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 312 + +--S 313 of 395 +--a0062:= integrate(t0062,x) +--E 313 + +--S 314 of 395 +--m0062:= a0062-r0062 +--E 314 + +--S 315 of 395 +--d0062:= D(m0062,x) +--E 315 + +--S 316 of 395 +t0063:= cos(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x^6 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 316 + +--S 317 of 395 +r0063:= 1/60*b^3*%pi/x^2-1/24*b^3*%pi*cos(b^2*%pi*x^2)/x^2+_ + 1/30*b^5*%pi^3*FresnelS(b*x)^2-1/15*FresnelS(b*x)*_ + ((3-b^4*%pi^2*x^4)*cos(1/2*b^2*%pi*x^2)-b^2*%pi*x^2*_ + sin(1/2*b^2*%pi*x^2))/x^5-1/40*b*sin(b^2*%pi*x^2)/x^4-_ + 7/120*b^5*%pi^2*Si(b^2*%pi*x^2) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 317 + +--S 318 of 395 +--a0063:= integrate(t0063,x) +--E 318 + +--S 319 of 395 +--m0063:= a0063-r0063 +--E 319 + +--S 320 of 395 +--d0063:= D(m0063,x) +--E 320 + +--S 321 of 395 +t0064:= cos(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x^2 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 321 + +--S 322 of 395 +r0064:= -cos(1/2*b^2*%pi*x^2)*FresnelS(b*x)/x-_ + 1/2*b*%pi*FresnelS(b*x)^2+1/4*b*Si(b^2*%pi*x^2) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 322 + +--S 323 of 395 +--a0064:= integrate(t0064,x) +--E 323 + +--S 324 of 395 +--m0064:= a0064-r0064 +--E 324 + +--S 325 of 395 +--d0064:= D(m0064,x) +--E 325 + +--S 326 of 395 +t0065:= x^2*cos(1/2*b^2*%pi*x^2)*FresnelS(b*x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 326 + +--S 327 of 395 +r0065:= 1/4*(-b^2*%pi*x^2-2*FresnelS(b*x)^2*%pi+_ + 4*x*FresnelS(b*x)*b*%pi*sin(1/2*b^2*%pi*x^2)+_ + sin(b^2*%pi*x^2))/b^3/%pi^2 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 327 + +--S 328 of 395 +--a0065:= integrate(t0065,x) +--E 328 + +--S 329 of 395 +--m0065:= a0065-r0065 +--E 329 + +--S 330 of 395 +--d0065:= D(m0065,x) +--E 330 + +--S 331 of 395 +t0066:= x^6*cos(1/2*b^2*%pi*x^2)*FresnelS(b*x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 331 + +--S 332 of 395 +r0066:= 1/12*(45*b^2*%pi*x^2-x^6*b^6*%pi^3+_ + 21*x^2*cos(b^2*%pi*x^2)*b^2*%pi+90*FresnelS(b*x)^2*%pi+_ + 60*x^3*FresnelS(b*x)*b^3*%pi^2*cos(1/2*b^2*%pi*x^2)-_ + 180*x*FresnelS(b*x)*b*%pi*sin(1/2*b^2*%pi*x^2)+_ + 12*x^5*FresnelS(b*x)*b^5*%pi^3*sin(1/2*b^2*%pi*x^2)-_ + 66*sin(b^2*%pi*x^2)+3*x^4*sin(b^2*%pi*x^2)*b^4*%pi^2)/b^7/%pi^4 +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 332 + +--S 333 of 395 +--a0066:= integrate(t0066,x) +--E 333 + +--S 334 of 395 +--m0066:= a0066-r0066 +--E 334 + +--S 335 of 395 +--d0066:= D(m0066,x) +--E 335 + +--S 336 of 395 +t0067:= FresnelC(b*x)^2/x^9 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 336 + +--S 337 of 395 +r0067:= -1/336*b^2/x^6+1/1680*b^6*%pi^2/x^2-_ + 1/336*b^2*cos(b^2*%pi*x^2)/x^6+1/336*b^6*%pi^2*cos(b^2*%pi*x^2)/x^2+_ + 1/840*b^8*%pi^4*FresnelC(b*x)^2-1/8*FresnelC(b*x)^2/x^8-_ + 1/420*b*FresnelC(b*x)*((15-b^4*%pi^2*x^4)*cos(1/2*b^2*%pi*x^2)-_ + b^2*%pi*x^2*(3-b^4*%pi^2*x^4)*sin(1/2*b^2*%pi*x^2))/x^7+_ + 1/420*b^4*%pi*sin(b^2*%pi*x^2)/x^4+1/280*b^8*%pi^3*Si(b^2*%pi*x^2) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 337 + +--S 338 of 395 +--a0067:= integrate(t0067,x) +--E 338 + +--S 339 of 395 +--m0067:= a0067-r0067 +--E 339 + +--S 340 of 395 +--d0067:= D(m0067,x) +--E 340 + +--S 341 of 395 +t0068:= FresnelC(b*x)^2/x^5 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 341 + +--S 342 of 395 +r0068:= -1/24*(b^2*x^2+b^2*cos(b^2*%pi*x^2)*x^2+2*b^4*%pi^2*_ + FresnelC(b*x)^2*x^4+6*FresnelC(b*x)^2+4*FresnelC(b*x)*_ + cos(1/2*b^2*%pi*x^2)*b*x-4*b^3*FresnelC(b*x)*x^3*%pi*_ + sin(1/2*b^2*%pi*x^2)+2*b^4*%pi*Si(b^2*%pi*x^2)*x^4)/x^4 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 342 + +--S 343 of 395 +--a0068:= integrate(t0068,x) +--E 343 + +--S 344 of 395 +--m0068:= a0068-r0068 +--E 344 + +--S 345 of 395 +--d0068:= D(m0068,x) +--E 345 + +--S 346 of 395 +t0069:= x^3*FresnelC(b*x)^2 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 346 + +--S 347 of 395 +r0069:= -1/8*(-3*b^2*%pi*x^2+x^2*cos(b^2*%pi*x^2)*b^2*%pi-_ + 6*FresnelC(b*x)^2*%pi-2*x^4*FresnelC(b*x)^2*b^4*%pi^3+_ + 12*x*FresnelC(b*x)*b*%pi*cos(1/2*b^2*%pi*x^2)+_ + 4*x^3*FresnelC(b*x)*b^3*%pi^2*sin(1/2*b^2*%pi*x^2)-_ + 4*sin(b^2*%pi*x^2))/b^4/%pi^3 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 347 + +--S 348 of 395 +--a0069:= integrate(t0069,x) +--E 348 + +--S 349 of 395 +--m0069:= a0069-r0069 +--E 349 + +--S 350 of 395 +--d0069:= D(m0069,x) +--E 350 + +--S 351 of 395 +t0070:= x^7*FresnelC(b*x)^2 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 351 + +--S 352 of 395 +r0070:= -105/16*x^2/b^6/%pi^4+7/48*x^6/b^2/%pi^2+_ + 55/16*x^2*cos(b^2*%pi*x^2)/b^6/%pi^4-_ + 1/16*x^6*cos(b^2*%pi*x^2)/b^2/%pi^2-105/8*FresnelC(b*x)^2/b^8/%pi^4+_ + 1/8*x^8*FresnelC(b*x)^2+1/4*x*FresnelC(b*x)*_ + (7*(15-b^4*%pi^2*x^4)*cos(1/2*b^2*%pi*x^2)+_ + b^2*%pi*x^2*(35-b^4*%pi^2*x^4)*sin(1/2*b^2*%pi*x^2))/b^7/%pi^4-_ + 10*sin(b^2*%pi*x^2)/b^8/%pi^5+5/8*x^4*sin(b^2*%pi*x^2)/b^4/%pi^3 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 352 + +--S 353 of 395 +--a0070:= integrate(t0070,x) +--E 353 + +--S 354 of 395 +--m0070:= a0070-r0070 +--E 354 + +--S 355 of 395 +--d0070:= D(m0070,x) +--E 355 + +--S 356 of 395 +t0071:= sin(1/2*b^2*%pi*x^2)*FresnelC(b*x)/x^10 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 356 + +--S 357 of 395 +r0071:= -1/756*b^3*%pi/x^6+1/3780*b^7*%pi^3/x^2-_ + 11/3024*b^3*%pi*cos(b^2*%pi*x^2)/x^6+_ + 5/2016*b^7*%pi^3*cos(b^2*%pi*x^2)/x^2+_ + 1/1890*b^9*%pi^5*FresnelC(b*x)^2-_ + 1/945*FresnelC(b*x)*(b^2*%pi*x^2*(15-b^4*%pi^2*x^4)*_ + cos(1/2*b^2*%pi*x^2)+(105-3*b^4*%pi^2*x^4+b^8*%pi^4*x^8)*_ + sin(1/2*b^2*%pi*x^2))/x^9-1/144*b*sin(b^2*%pi*x^2)/x^8+_ + 67/30240*b^5*%pi^2*sin(b^2*%pi*x^2)/x^4+83/30240*_ + b^9*%pi^4*Si(b^2*%pi*x^2) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 357 + +--S 358 of 395 +--a0071:= integrate(t0071,x) +--E 358 + +--S 359 of 395 +--m0071:= a0071-r0071 +--E 359 + +--S 360 of 395 +--d0071:= D(m0071,x) +--E 360 + +--S 361 of 395 +t0072:= sin(1/2*b^2*%pi*x^2)*FresnelC(b*x)/x^6 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 361 + +--S 362 of 395 +r0072:= -1/60*b^3*%pi/x^2-1/24*b^3*%pi*cos(b^2*%pi*x^2)/x^2-_ + 1/30*b^5*%pi^3*FresnelC(b*x)^2-_ + 1/15*FresnelC(b*x)*(b^2*%pi*x^2*cos(1/2*b^2*%pi*x^2)+_ + (3-b^4*%pi^2*x^4)*sin(1/2*b^2*%pi*x^2))/x^5-_ + 1/40*b*sin(b^2*%pi*x^2)/x^4-7/120*b^5*%pi^2*Si(b^2*%pi*x^2) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 362 + +--S 363 of 395 +--a0072:= integrate(t0072,x) +--E 363 + +--S 364 of 395 +--m0072:= a0072-r0072 +--E 364 + +--S 365 of 395 +--d0072:= D(m0072,x) +--E 365 + +--S 366 of 395 +t0073:= sin(1/2*b^2*%pi*x^2)*FresnelC(b*x)/x^2 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 366 + +--S 367 of 395 +r0073:= 1/2*b*%pi*FresnelC(b*x)^2-FresnelC(b*x)*sin(1/2*b^2*%pi*x^2)/x+_ + 1/4*b*Si(b^2*%pi*x^2) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 367 + +--S 368 of 395 +--a0073:= integrate(t0073,x) +--E 368 + +--S 369 of 395 +--m0073:= a0073-r0073 +--E 369 + +--S 370 of 395 +--d0073:= D(m0073,x) +--E 370 + +--S 371 of 395 +t0074:= x^2*sin(1/2*b^2*%pi*x^2)*FresnelC(b*x) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 371 + +--S 372 of 395 +r0074:= -1/4*(-b^2*%pi*x^2+4*x*FresnelC(b*x)*b*%pi*cos(1/2*b^2*%pi*x^2)-_ + 2*FresnelC(b*x)^2*%pi-sin(b^2*%pi*x^2))/b^3/%pi^2 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 372 + +--S 373 of 395 +--a0074:= integrate(t0074,x) +--E 373 + +--S 374 of 395 +--m0074:= a0074-r0074 +--E 374 + +--S 375 of 395 +--d0074:= D(m0074,x) +--E 375 + +--S 376 of 395 +t0075:= x^6*sin(1/2*b^2*%pi*x^2)*FresnelC(b*x) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 376 + +--S 377 of 395 +r0075:= -1/12*(45*b^2*%pi*x^2-x^6*b^6*%pi^3-21*x^2*cos(b^2*%pi*x^2)*b^2*%pi+_ + 90*FresnelC(b*x)^2*%pi-180*x*FresnelC(b*x)*b*_ + %pi*cos(1/2*b^2*%pi*x^2)+12*x^5*FresnelC(b*x)*b^5*%pi^3*_ + cos(1/2*b^2*%pi*x^2)-60*x^3*FresnelC(b*x)*b^3*%pi^2*_ + sin(1/2*b^2*%pi*x^2)+66*sin(b^2*%pi*x^2)-_ + 3*x^4*sin(b^2*%pi*x^2)*b^4*%pi^2)/b^7/%pi^4 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 377 + +--S 378 of 395 +--a0075:= integrate(t0075,x) +--E 378 + +--S 379 of 395 +--m0075:= a0075-r0075 +--E 379 + +--S 380 of 395 +--d0075:= D(m0075,x) +--E 380 + +--S 381 of 395 +t0076:= cos(1/2*b^2*%pi*x^2)*FresnelC(b*x)/x^8 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 381 + +--S 382 of 395 +r0076:= -1/84*b/x^6+1/420*b^5*%pi^2/x^2-1/84*b*cos(b^2*%pi*x^2)/x^6+_ + 1/84*b^5*%pi^2*cos(b^2*%pi*x^2)/x^2+1/210*b^7*%pi^4*FresnelC(b*x)^2-_ + 1/105*FresnelC(b*x)*((15-b^4*%pi^2*x^4)*cos(1/2*b^2*%pi*x^2)-_ + b^2*%pi*x^2*(3-b^4*%pi^2*x^4)*sin(1/2*b^2*%pi*x^2))/x^7+_ + 1/105*b^3*%pi*sin(b^2*%pi*x^2)/x^4+1/70*b^7*%pi^3*Si(b^2*%pi*x^2) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 382 + +--S 383 of 395 +--a0076:= integrate(t0076,x) +--E 383 + +--S 384 of 395 +--m0076:= a0076-r0076 +--E 384 + +--S 385 of 395 +--d0076:= D(m0076,x) +--E 385 + +--S 386 of 395 +t0077:= cos(1/2*b^2*%pi*x^2)*FresnelC(b*x)/x^4 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 386 + +--S 387 of 395 +r0077:= -1/12*(b*x+x*cos(b^2*%pi*x^2)*b+2*x^3*FresnelC(b*x)^2*b^3*%pi^2+_ + 4*cos(1/2*b^2*%pi*x^2)*FresnelC(b*x)-4*FresnelC(b*x)*b^2*%pi*x^2*_ + sin(1/2*b^2*%pi*x^2)+2*b^3*%pi*Si(b^2*%pi*x^2)*x^3)/x^3 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 387 + +--S 388 of 395 +--a0077:= integrate(t0077,x) +--E 388 + +--S 389 of 395 +--m0077:= a0077-r0077 +--E 389 + +--S 390 of 395 +--d0077:= D(m0077,x) +--E 390 + +--S 391 of 395 +t0078:= x^4*cos(1/2*b^2*%pi*x^2)*FresnelC(b*x) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 391 + +--S 392 of 395 +r0078:= 1/4*(-3*b^2*%pi*x^2+x^2*cos(b^2*%pi*x^2)*b^2*%pi-_ + 6*FresnelC(b*x)^2*%pi+12*x*FresnelC(b*x)*b*%pi*_ + cos(1/2*b^2*%pi*x^2)+4*x^3*FresnelC(b*x)*_ + b^3*%pi^2*sin(1/2*b^2*%pi*x^2)-4*sin(b^2*%pi*x^2))/b^5/%pi^3 +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 392 + +--S 393 of 395 +--a0078:= integrate(t0078,x) +--E 393 + +--S 394 of 395 +--m0078:= a0078-r0078 +--E 394 + +--S 395 of 395 +--d0078:= D(m0078,x) +--E 395 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richerror000-078.input.pdf b/src/axiom-website/CATS/richerror000-078.input.pdf new file mode 100644 index 0000000..d49c5ed Binary files /dev/null and b/src/axiom-website/CATS/richerror000-078.input.pdf differ diff --git a/src/axiom-website/CATS/richexponential.input.pamphlet b/src/axiom-website/CATS/richexponential.input.pamphlet new file mode 100644 index 0000000..b34ae9d --- /dev/null +++ b/src/axiom-website/CATS/richexponential.input.pamphlet @@ -0,0 +1,8679 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richexponential.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richexponential.output +)spool richexponential.output +)set message auto off +)clear all + +--S 1 of 578 +t0000:= exp(1)^(a+b*x)/x +--R +--R +--R b x + a +--R %e +--R (1) --------- +--R x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 578 +r0000:= exp(a)*Ei(b*x) +--R +--R +--R a +--R (2) Ei(b x)%e +--R Type: Expression(Integer) +--E 2 + +--S 3 of 578 +a0000:= integrate(t0000,x) +--R +--R +--R x %A b + a +--R ++ %e +--R (3) | ---------- d%A +--R ++ %A +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 578 +m0000:= a0000-r0000 +--R +--R +--R x %A b + a +--R ++ %e a +--R (4) | ---------- d%A - Ei(b x)%e +--R ++ %A +--R Type: Expression(Integer) +--E 4 + +--S 5 of 578 +d0000:= D(m0000,x) +--R +--R +--R b x + a a b x +--R %e - %e %e +--R (5) -------------------- +--R x +--R Type: Expression(Integer) +--E 5 + +--S 6 of 578 +t0001:= x^3*exp((a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R 3 b x + 3a b x + 3a b x + a +--R (6) x %e +--R Type: Expression(Integer) +--E 6 + +--S 7 of 578 +r0001:= -2/3*a*exp((a+b*x)^3)/b^4+1/3*exp((a+b*x)^3)*x/b^3+_ + 1/9*(1+3*a^3)*(a+b*x)*Gamma(1/3,-(a+b*x)^3)/b^4/(-(a+b*x)^3)^(1/3)_ + -a^2*(a+b*x)^2*Gamma(2/3,-(a+b*x)^3)/b^4/(-(a+b*x)^3)^(2/3) +--R +--R +--R (7) +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (3b x - 6a)%e +--R * +--R +------------------------------+2 +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 3 4 _ 1 3 3 2 2 2 3 +--R ((3a + 1)b x + 3a + a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 3 4 _ 2 3 3 2 2 2 3 +--R (- 9a b x - 18a b x - 9a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 4 3| 3 3 2 2 2 3 +--R 9b \|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 7 + +--S 8 of 578 +a0001:= integrate(t0001,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ 3 %A b + 3%A a b + 3%A a b + a +--R (8) | %A %e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 578 +m0001:= a0001-r0001 +--R +--R +--R (9) +--R +------------------------------+2 +--R 4 3| 3 3 2 2 2 3 +--R 9b \|- b x - 3a b x - 3a b x - a +--R * +--R x 3 3 2 2 2 3 +--R ++ 3 %A b + 3%A a b + 3%A a b + a +--R | %A %e d%A +--R ++ +--R + +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (- 3b x + 6a)%e +--R * +--R +------------------------------+2 +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 3 4 _ 1 3 3 2 2 2 3 +--R ((- 3a - 1)b x - 3a - a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 3 4 _ 2 3 3 2 2 2 3 +--R (9a b x + 18a b x + 9a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 4 3| 3 3 2 2 2 3 +--R 9b \|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 9 + +--S 10 of 578 +d0001:= D(m0001,x) +--R +--R +--R (10) 0 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 578 +t0002:= x^2*exp((a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R 2 b x + 3a b x + 3a b x + a +--R (11) x %e +--R Type: Expression(Integer) +--E 11 + +--S 12 of 578 +r0002:= 1/3*exp((a+b*x)^3)/b^3-1/3*a^2*(a+b*x)*_ + Gamma(1/3,-(a+b*x)^3)/b^3/(-(a+b*x)^3)^(1/3)+2/3*a*(a+b*x)^2*_ + Gamma(2/3,-(a+b*x)^3)/b^3/(-(a+b*x)^3)^(2/3) +--R +--R +--R (12) +--R 3 3 2 2 2 3 +------------------------------+2 +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R %e \|- b x - 3a b x - 3a b x - a +--R + +--R 2 3 _ 1 3 3 2 2 2 3 +--R (- a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 3 _ 2 3 3 2 2 2 3 +--R (2a b x + 4a b x + 2a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 12 + +--S 13 of 578 +a0002:= integrate(t0002,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ 2 %A b + 3%A a b + 3%A a b + a +--R (13) | %A %e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 578 +m0002:= a0002-r0002 +--R +--R +--R (14) +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R * +--R x 3 3 2 2 2 3 +--R ++ 2 %A b + 3%A a b + 3%A a b + a +--R | %A %e d%A +--R ++ +--R + +--R 3 3 2 2 2 3 +------------------------------+2 +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R - %e \|- b x - 3a b x - 3a b x - a +--R + +--R 2 3 _ 1 3 3 2 2 2 3 +--R (a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 3 _ 2 3 3 2 2 2 3 +--R (- 2a b x - 4a b x - 2a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 14 + +--S 15 of 578 +d0002:= D(m0002,x) +--R +--R +--R (15) 0 +--R Type: Expression(Integer) +--E 15 + +--S 16 of 578 +t0003:= x*exp((a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (16) x %e +--R Type: Expression(Integer) +--E 16 + +--S 17 of 578 +r0003:= 1/3*a*(a+b*x)*_ + Gamma(1/3,-(a+b*x)^3)/b^2/(-(a+b*x)^3)^(1/3)-1/3*(a+b*x)^2*_ + Gamma(2/3,-(a+b*x)^3)/b^2/(-(a+b*x)^3)^(2/3) +--R +--R +--R (17) +--R 2 _ 1 3 3 2 2 2 3 +--R (a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (- b x - 2a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 17 + +--S 18 of 578 +a0003:= integrate(t0003,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R (18) | %A %e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 578 +m0003:= a0003-r0003 +--R +--R +--R (19) +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R * +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R | %A %e d%A +--R ++ +--R + +--R 2 _ 1 3 3 2 2 2 3 +--R (- a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 578 +d0003:= D(m0003,x) +--R +--R +--R (20) 0 +--R Type: Expression(Integer) +--E 20 + +--S 21 of 578 +t0004:= exp((a+b*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (21) %e +--R Type: Expression(Integer) +--E 21 + +--S 22 of 578 +r0004:= -1/3*(a+b*x)*Gamma(1/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(1/3) +--R +--R +--R _ 1 3 3 2 2 2 3 +--R (- b x - a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R (22) ----------------------------------------------- +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3b\|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 22 + +--S 23 of 578 +a0004:= integrate(t0004,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R (23) | %e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 578 +m0004:= a0004-r0004 +--R +--R +--R (24) +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3b\|- b x - 3a b x - 3a b x - a +--R * +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R | %e d%A +--R ++ +--R + +--R _ 1 3 3 2 2 2 3 +--R (b x + a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3b\|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 24 + +--S 25 of 578 +d0004:= D(m0004,x) +--R +--R +--R (25) 0 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 578 +t0005:= exp(1)^(a+b*x)/(a+b*x) +--R +--R +--R b x + a +--R %e +--R (26) --------- +--R b x + a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 578 +r0005:= Ei(a+b*x)/b +--R +--R +--R Ei(b x + a) +--R (27) ----------- +--R b +--R Type: Expression(Integer) +--E 27 + +--S 28 of 578 +a0005:= integrate(t0005,x) +--R +--R +--R Ei(b x + a) +--R (28) ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 578 +m0005:= a0005-r0005 +--R +--R +--R (29) 0 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 578 +d0005:= D(m0005,x) +--R +--R +--R (30) 0 +--R Type: Expression(Integer) +--E 30 + +--S 31 of 578 +t0006:= exp((a+b*x)^3)*(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R 3 3 2 2 2 3 b x + 3a b x + 3a b x + a +--R (31) (b x + 3a b x + 3a b x + a )%e +--R Type: Expression(Integer) +--E 31 + +--S 32 of 578 +r0006:= 1/3*exp((a+b*x)^3)*(a+b*x)/b+1/9*(a+b*x)*_ + Gamma(1/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(1/3) +--R +--R +--R (32) +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (3b x + 3a)%e +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R _ 1 3 3 2 2 2 3 +--R (b x + a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 9b\|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 32 + +--S 33 of 578 +a0006:= integrate(t0006,x) +--R +--R +--R (33) +--R x 3 3 2 2 2 3 +--R ++ 3 3 2 2 2 3 %A b + 3%A a b + 3%A a b + a +--R | (%A b + 3%A a b + 3%A a b + a )%e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 578 +m0006:= a0006-r0006 +--R +--R +--R (34) +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 9b\|- b x - 3a b x - 3a b x - a +--R * +--R INTSIGN +--R , +--R x +--R , +--R 3 3 2 2 2 3 +--R 3 3 2 2 2 3 %A b + 3%A a b + 3%A a b + a +--R (%A b + 3%A a b + 3%A a b + a )%e +--R * +--R d%A +--R + +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (- 3b x - 3a)%e +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- b x - 3a b x - 3a b x - a +--R + +--R _ 1 3 3 2 2 2 3 +--R (- b x - a)| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 9b\|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 578 +d0006:= D(m0006,x) +--R +--R +--R (35) 0 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 578 +t0007:= exp((a+b*x)^3)*(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (36) (b x + a)%e +--R Type: Expression(Integer) +--E 36 + +--S 37 of 578 +r0007:= -1/3*(a+b*x)^2*Gamma(2/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(2/3) +--R +--R +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (- b x - 2a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R (37) ---------------------------------------------------------- +--R +------------------------------+2 +--R 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 578 +a0007:= integrate(t0007,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R (38) | (%A b + a)%e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 578 +m0007:= a0007-r0007 +--R +--R +--R (39) +--R +------------------------------+2 +--R 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R * +--R x 3 3 2 2 2 3 +--R ++ %A b + 3%A a b + 3%A a b + a +--R | (%A b + a)%e d%A +--R ++ +--R + +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (b x + 2a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 3| 3 3 2 2 2 3 +--R 3b \|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 39 + +--S 40 of 578 +d0007:= D(m0007,x) +--R +--R +--R (40) 0 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 578 +t0008:= exp((a+b*x)^3)/(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R %e +--R (41) ------------------------------ +--R b x + a +--R Type: Expression(Integer) +--E 41 + +--S 42 of 578 +r0008:= 1/3*Ei((a+b*x)^3)/b +--R +--R +--R 3 3 2 2 2 3 +--R Ei(b x + 3a b x + 3a b x + a ) +--R (42) -------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 42 + +--S 43 of 578 +a0008:= integrate(t0008,x) +--R +--R +--R 3 3 2 2 2 3 +--R Ei(b x + 3a b x + 3a b x + a ) +--R (43) -------------------------------- +--R 3b +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 578 +m0008:= a0008-r0008 +--R +--R +--R (44) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 578 +d0008:= D(m0008,x) +--R +--R +--R (45) 0 +--R Type: Expression(Integer) +--E 45 + +--S 46 of 578 +t0009:= exp((a+b*x)^3)/(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R %e +--R (46) ------------------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 578 +r0009:= -exp((a+b*x)^3)/b/(a+b*x)-(a+b*x)^2*_ + Gamma(2/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(2/3) +--R +--R +--R (47) +--R 3 3 2 2 2 3 +------------------------------+2 +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R - %e \|- b x - 3a b x - 3a b x - a +--R + +--R 3 3 2 2 2 3 _ 2 3 3 2 2 2 3 +--R (- b x - 3a b x - 3a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R (b x + a b)\|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 47 + +--S 48 of 578 +a0009:= integrate(t0009,x) +--R +--R +--R 3 3 2 2 2 3 +--R x %A b + 3%A a b + 3%A a b + a +--R ++ %e +--R (48) | --------------------------------- d%A +--R ++ 2 2 2 +--R %A b + 2%A a b + a +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 578 +m0009:= a0009-r0009 +--R +--R +--R (49) +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R (b x + a b)\|- b x - 3a b x - 3a b x - a +--R * +--R 3 3 2 2 2 3 +--R x %A b + 3%A a b + 3%A a b + a +--R ++ %e +--R | --------------------------------- d%A +--R ++ 2 2 2 +--R %A b + 2%A a b + a +--R + +--R 3 3 2 2 2 3 +------------------------------+2 +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R %e \|- b x - 3a b x - 3a b x - a +--R + +--R 3 3 2 2 2 3 _ 2 3 3 2 2 2 3 +--R (b x + 3a b x + 3a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R (b x + a b)\|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 578 +d0009:= D(m0009,x) +--R +--R +--R (50) 0 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 578 +t0010:= exp((a+b*x)^3)/(a+b*x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R %e +--R (51) ------------------------------ +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 578 +r0010:= -1/2*exp((a+b*x)^3)/b/(a+b*x)^2-1/2*(a+b*x)*_ + Gamma(1/3,-(a+b*x)^3)/b/(-(a+b*x)^3)^(1/3) +--R +--R +--R (52) +--R 3 3 2 2 2 3 +------------------------------+ +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R - %e \|- b x - 3a b x - 3a b x - a +--R + +--R 3 3 2 2 2 3 _ 1 3 3 2 2 2 3 +--R (- b x - 3a b x - 3a b x - a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+ +--R 3 2 2 2 3| 3 3 2 2 2 3 +--R (2b x + 4a b x + 2a b)\|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 578 +a0010:= integrate(t0010,x) +--R +--R +--R 3 3 2 2 2 3 +--R x %A b + 3%A a b + 3%A a b + a +--R ++ %e +--R (53) | --------------------------------- d%A +--R ++ 3 3 2 2 2 3 +--R %A b + 3%A a b + 3%A a b + a +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 578 +m0010:= a0010-r0010 +--R +--R +--R (54) +--R +------------------------------+ +--R 3 2 2 2 3| 3 3 2 2 2 3 +--R (2b x + 4a b x + 2a b)\|- b x - 3a b x - 3a b x - a +--R * +--R 3 3 2 2 2 3 +--R x %A b + 3%A a b + 3%A a b + a +--R ++ %e +--R | --------------------------------- d%A +--R ++ 3 3 2 2 2 3 +--R %A b + 3%A a b + 3%A a b + a +--R + +--R 3 3 2 2 2 3 +------------------------------+ +--R b x + 3a b x + 3a b x + a 3| 3 3 2 2 2 3 +--R %e \|- b x - 3a b x - 3a b x - a +--R + +--R 3 3 2 2 2 3 _ 1 3 3 2 2 2 3 +--R (b x + 3a b x + 3a b x + a )| (-,- b x - 3a b x - 3a b x - a ) +--R 3 +--R / +--R +------------------------------+ +--R 3 2 2 2 3| 3 3 2 2 2 3 +--R (2b x + 4a b x + 2a b)\|- b x - 3a b x - 3a b x - a +--R Type: Expression(Integer) +--E 54 + +--S 55 of 578 +d0010:= D(m0010,x) +--R +--R +--R (55) 0 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 578 +t0011:= x^m*exp(1)^(x^n) +--R +--R +--R n +--R m x +--R (56) x %e +--R Type: Expression(Integer) +--E 56 + +--S 57 of 578 +r0011:= -x^(1+m)*Gamma((1+m)/n,-x^n)*(-x^n)^(-(1+m)/n)/n +--R +--R +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R x (- x ) | (-----,- x ) +--R n +--R (57) - --------------------------------- +--R n +--R Type: Expression(Integer) +--E 57 + +--S 58 of 578 +a0011:= integrate(t0011,x) +--R +--R +--R x n +--R ++ m %A +--R (58) | %A %e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 578 +m0011:= a0011-r0011 +--R +--R +--R - m - 1 +--R x n ------- +--R ++ m %A m + 1 n n _ m + 1 n +--R n | %A %e d%A + x (- x ) | (-----,- x ) +--R ++ n +--R (59) ------------------------------------------------------ +--R n +--R Type: Expression(Integer) +--E 59 + +--S 60 of 578 +d0011:= D(m0011,x) +--R +--R +--R (60) +--R - m - 1 - n - m - 1 +--R ------- ----------- +--R m n n m + 1 n - 1 n n +--R ((m + 1)x (- x ) + (m + 1)x x (- x ) ) +--R * +--R _ m + 1 n +--R | (-----,- x ) +--R n +--R + +--R - n + m + 1 - m - 1 +--R n ----------- ------- n +--R m + 1 n - 1 x n n n n m x +--R n x x %e (- x ) (- x ) + n x %e +--R / +--R n +--R Type: Expression(Integer) +--E 60 + +--S 61 of 578 +t0012:= x^m*f^(x^n) +--R +--R +--R n +--R m x +--R (61) x f +--R Type: Expression(Integer) +--E 61 + +--S 62 of 578 +r0012:= -x^(1+m)*Gamma((1+m)/n,-x^n*log(f))*(-x^n*log(f))^(-(1+m)/n)/n +--R +--R +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R x (- log(f)x ) | (-----,- log(f)x ) +--R n +--R (62) - --------------------------------------------- +--R n +--R Type: Expression(Integer) +--E 62 + +--S 63 of 578 +a0012:= integrate(t0012,x) +--R +--R +--R x n +--R ++ m %A +--R (63) | %A f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 578 +m0012:= a0012-r0012 +--R +--R +--R - m - 1 +--R x n ------- +--R ++ m %A m + 1 n n _ m + 1 n +--R n | %A f d%A + x (- log(f)x ) | (-----,- log(f)x ) +--R ++ n +--R (64) ----------------------------------------------------------------- +--R n +--R Type: Expression(Integer) +--E 64 + +--S 65 of 578 +d0012:= D(m0012,x) +--R +--R +--R (65) +--R - m - 1 +--R ------- +--R m n n +--R (m + 1)x (- log(f)x ) +--R + +--R - n - m - 1 +--R ----------- +--R m + 1 n - 1 n n +--R (m + 1)log(f)x x (- log(f)x ) +--R * +--R _ m + 1 n +--R | (-----,- log(f)x ) +--R n +--R + +--R n +--R m x +--R n x f +--R + +--R - n + m + 1 - m - 1 +--R n ----------- ------- +--R m + 1 n - 1 log(f)x n n n n +--R n log(f)x x %e (- log(f)x ) (- log(f)x ) +--R / +--R n +--R Type: Expression(Integer) +--E 65 + +--S 66 of 578 +t0013:= (a+b*x)^m*exp(1)^((a+b*x)^n) +--R +--R +--R n +--R m (b x + a) +--R (66) (b x + a) %e +--R Type: Expression(Integer) +--E 66 + +--S 67 of 578 +r0013:= -(a+b*x)^(1+m)*Gamma((1+m)/n,-(a+b*x)^n)*(-(a+b*x)^n)^(-(1+m)/n)/b/n +--R +--R +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R (b x + a) (- (b x + a) ) | (-----,- (b x + a) ) +--R n +--R (67) - --------------------------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 67 + +--S 68 of 578 +a0013:= integrate(t0013,x) +--R +--R +--R x n +--R ++ m (%A b + a) +--R (68) | (%A b + a) %e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 578 +m0013:= a0013-r0013 +--R +--R +--R (69) +--R x n +--R ++ m (%A b + a) +--R b n | (%A b + a) %e d%A +--R ++ +--R + +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R (b x + a) (- (b x + a) ) | (-----,- (b x + a) ) +--R n +--R / +--R b n +--R Type: Expression(Integer) +--E 69 + +--S 70 of 578 +d0013:= D(m0013,x) +--R +--R +--R (70) +--R - m - 1 +--R ------- +--R m n n +--R (m + 1)(b x + a) (- (b x + a) ) +--R + +--R - n - m - 1 +--R ----------- +--R m + 1 n - 1 n n +--R (m + 1)(b x + a) (b x + a) (- (b x + a) ) +--R * +--R _ m + 1 n +--R | (-----,- (b x + a) ) +--R n +--R + +--R - n + m + 1 +--R n ----------- +--R m + 1 n - 1 (b x + a) n n +--R n (b x + a) (b x + a) %e (- (b x + a) ) +--R * +--R - m - 1 +--R ------- +--R n n +--R (- (b x + a) ) +--R + +--R n +--R m (b x + a) +--R n (b x + a) %e +--R / +--R n +--R Type: Expression(Integer) +--E 70 + +--S 71 of 578 +t0014:= (a+b*x)^m*f^((a+b*x)^n) +--R +--R +--R n +--R m (b x + a) +--R (71) (b x + a) f +--R Type: Expression(Integer) +--E 71 + +--S 72 of 578 +r0014:= -(a+b*x)^(1+m)*_ + Gamma((1+m)/n,-(a+b*x)^n*log(f))*(-(a+b*x)^n*log(f))^(-(1+m)/n)/b/n +--R +--R +--R (72) +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R (b x + a) (- log(f)(b x + a) ) | (-----,- log(f)(b x + a) ) +--R n +--R - --------------------------------------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 72 + +--S 73 of 578 +a0014:= integrate(t0014,x) +--R +--R +--R x n +--R ++ m (%A b + a) +--R (73) | (%A b + a) f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 578 +m0014:= a0014-r0014 +--R +--R +--R (74) +--R x n +--R ++ m (%A b + a) +--R b n | (%A b + a) f d%A +--R ++ +--R + +--R - m - 1 +--R ------- +--R m + 1 n n _ m + 1 n +--R (b x + a) (- log(f)(b x + a) ) | (-----,- log(f)(b x + a) ) +--R n +--R / +--R b n +--R Type: Expression(Integer) +--E 74 + +--S 75 of 578 +d0014:= D(m0014,x) +--R +--R +--R (75) +--R - m - 1 +--R ------- +--R m n n +--R (m + 1)(b x + a) (- log(f)(b x + a) ) +--R + +--R m + 1 n - 1 +--R (m + 1)log(f)(b x + a) (b x + a) +--R * +--R - n - m - 1 +--R ----------- +--R n n +--R (- log(f)(b x + a) ) +--R * +--R _ m + 1 n +--R | (-----,- log(f)(b x + a) ) +--R n +--R + +--R n +--R m (b x + a) +--R n (b x + a) f +--R + +--R n +--R m + 1 n - 1 log(f)(b x + a) +--R n log(f)(b x + a) (b x + a) %e +--R * +--R - n + m + 1 - m - 1 +--R ----------- ------- +--R n n n n +--R (- log(f)(b x + a) ) (- log(f)(b x + a) ) +--R / +--R n +--R Type: Expression(Integer) +--E 75 + +--S 76 of 578 +t0015:= exp(1)^(c+d*x)/(a+b*x)^2 +--R +--R +--R d x + c +--R %e +--R (76) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 578 +r0015:= -exp(1)^(c+d*x)/b/(a+b*x)+d*exp(1)^(c-a*d/b)*Ei(d*(a+b*x)/b)/b^2 +--R +--R +--R - a d + b c +--R ----------- +--R d x + c b d x + a d b +--R - b %e + (b d x + a d)Ei(-----------)%e +--R b +--R (77) --------------------------------------------------------- +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 77 + +--S 78 of 578 +a0015:= integrate(t0015,x) +--R +--R +--R x %A d + c +--R ++ %e +--R (78) | -------------------- d%A +--R ++ 2 2 2 +--R %A b + 2%A a b + a +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 578 +m0015:= a0015-r0015 +--R +--R +--R (79) +--R x %A d + c +--R 3 2 ++ %e d x + c +--R (b x + a b ) | -------------------- d%A + b %e +--R ++ 2 2 2 +--R %A b + 2%A a b + a +--R + +--R - a d + b c +--R ----------- +--R b d x + a d b +--R (- b d x - a d)Ei(-----------)%e +--R b +--R / +--R 3 2 +--R b x + a b +--R Type: Expression(Integer) +--E 79 + +--S 80 of 578 +d0015:= D(m0015,x) +--R +--R +--R - a d + b c b d x + a d +--R ----------- ----------- +--R b b d x + c +--R - d %e %e + d %e +--R (80) -------------------------------------------- +--R 2 +--R b x + a b +--R Type: Expression(Integer) +--E 80 + +--S 81 of 578 +t0016:= exp(1)^(c+d*x)/(a+b*x)^3 +--R +--R +--R d x + c +--R %e +--R (81) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 578 +r0016:= -1/2*exp(1)^(c+d*x)/b/(a+b*x)^2-1/2*d*_ + exp(1)^(c+d*x)/b^2/(a+b*x)+1/2*d^2*exp(1)^(c-a*d/b)*_ + Ei(d*(a+b*x)/b)/b^3 +--R +--R +--R (82) +--R 2 2 d x + c +--R (- b d x - a b d - b )%e +--R + +--R - a d + b c +--R ----------- +--R 2 2 2 2 2 2 b d x + a d b +--R (b d x + 2a b d x + a d )Ei(-----------)%e +--R b +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 82 + +--S 83 of 578 +a0016:= integrate(t0016,x) +--R +--R +--R x %A d + c +--R ++ %e +--R (83) | ------------------------------- d%A +--R ++ 3 3 2 2 2 3 +--R %A b + 3%A a b + 3%A a b + a +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 578 +m0016:= a0016-r0016 +--R +--R +--R (84) +--R x %A d + c +--R 5 2 4 2 3 ++ %e +--R (2b x + 4a b x + 2a b ) | ------------------------------- d%A +--R ++ 3 3 2 2 2 3 +--R %A b + 3%A a b + 3%A a b + a +--R + +--R 2 2 d x + c +--R (b d x + a b d + b )%e +--R + +--R - a d + b c +--R ----------- +--R 2 2 2 2 2 2 b d x + a d b +--R (- b d x - 2a b d x - a d )Ei(-----------)%e +--R b +--R / +--R 5 2 4 2 3 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 84 + +--S 85 of 578 +d0016:= D(m0016,x) +--R +--R +--R - a d + b c b d x + a d +--R ----------- ----------- +--R 2 b b 2 d x + c +--R - d %e %e + d %e +--R (85) -------------------------------------------- +--R 3 2 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 85 + +--S 86 of 578 +t0017:= exp((c+d*x)^2)*(a+b*x)^2 +--R +--R +--R 2 2 2 +--R 2 2 2 d x + 2c d x + c +--R (86) (b x + 2a b x + a )%e +--R Type: Expression(Integer) +--E 86 + +--S 87 of 578 +r0017:= -b*(1/2*b*c-a*d)*_ + exp((c+d*x)^2)/d^3+1/2*b^2*_ + exp((c+d*x)^2)*x/d^2-1/4*(b^2*(1-2*c^2)+4*a*b*c*d-2*a^2*d^2)*_ + %pi^(1/2)*erfi(c+d*x)/d^3 +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 578 +a0017:= integrate(t0017,x) +--R +--R +--R x 2 2 2 +--R ++ 2 2 2 %A d + 2%A c d + c +--R (87) | (%A b + 2%A a b + a )%e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 578 +m0017:= a0017-r0017 +--R +--R +--R x 2 2 2 +--R ++ 2 2 2 %A d + 2%A c d + c +--R (88) | (%A b + 2%A a b + a )%e d%A - r0017 +--R ++ +--R Type: Expression(Integer) +--E 89 + +--S 90 of 578 +d0017:= D(m0017,x) +--R +--R +--R 2 2 2 +--R 2 2 2 d x + 2c d x + c +--R (89) (b x + 2a b x + a )%e +--R Type: Expression(Integer) +--E 90 + +--S 91 of 578 +t0018:= exp((c+d*x)^3)*(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R 2 2 2 d x + 3c d x + 3c d x + c +--R (90) (b x + 2a b x + a )%e +--R Type: Expression(Integer) +--E 91 + +--S 92 of 578 +r0018:= 1/3*b^2*exp((c+d*x)^3)/d^3-1/3*(b*c-a*d)^2*(c+d*x)*_ + Gamma(1/3,-(c+d*x)^3)/d^3/(-(c+d*x)^3)^(1/3)+_ + 2/3*b*(b*c-a*d)*(c+d*x)^2*_ + Gamma(2/3,-(c+d*x)^3)/d^3/(-(c+d*x)^3)^(2/3) +--R +--R +--R (91) +--R 3 3 2 2 2 3 +------------------------------+2 +--R 2 d x + 3c d x + 3c d x + c 3| 3 3 2 2 2 3 +--R b %e \|- d x - 3c d x - 3c d x - c +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((- a d + 2a b c d - b c d)x - a c d + 2a b c d - b c ) +--R * +--R +------------------------------+ +--R _ 1 3 3 2 2 2 3 3| 3 3 2 2 2 3 +--R | (-,- d x - 3c d x - 3c d x - c )\|- d x - 3c d x - 3c d x - c +--R 3 +--R + +--R 3 2 2 2 2 2 2 2 2 3 +--R ((- 2a b d + 2b c d )x + (- 4a b c d + 4b c d)x - 2a b c d + 2b c ) +--R * +--R _ 2 3 3 2 2 2 3 +--R | (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R / +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R Type: Expression(Integer) +--E 92 + +--S 93 of 578 +a0018:= integrate(t0018,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ 2 2 2 %A d + 3%A c d + 3%A c d + c +--R (92) | (%A b + 2%A a b + a )%e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 578 +m0018:= a0018-r0018 +--R +--R +--R (93) +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R * +--R x 3 3 2 2 2 3 +--R ++ 2 2 2 %A d + 3%A c d + 3%A c d + c +--R | (%A b + 2%A a b + a )%e d%A +--R ++ +--R + +--R 3 3 2 2 2 3 +------------------------------+2 +--R 2 d x + 3c d x + 3c d x + c 3| 3 3 2 2 2 3 +--R - b %e \|- d x - 3c d x - 3c d x - c +--R + +--R 2 3 2 2 2 2 2 2 2 3 +--R ((a d - 2a b c d + b c d)x + a c d - 2a b c d + b c ) +--R * +--R +------------------------------+ +--R _ 1 3 3 2 2 2 3 3| 3 3 2 2 2 3 +--R | (-,- d x - 3c d x - 3c d x - c )\|- d x - 3c d x - 3c d x - c +--R 3 +--R + +--R 3 2 2 2 2 2 2 2 2 3 +--R ((2a b d - 2b c d )x + (4a b c d - 4b c d)x + 2a b c d - 2b c ) +--R * +--R _ 2 3 3 2 2 2 3 +--R | (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R / +--R +------------------------------+2 +--R 3 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R Type: Expression(Integer) +--E 94 + +--S 95 of 578 +d0018:= D(m0018,x) +--R +--R +--R (94) 0 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 578 +t0019:= exp((c+d*x)^3)*(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (95) (b x + a)%e +--R Type: Expression(Integer) +--E 96 + +--S 97 of 578 +r0019:= 1/3*(b*c-a*d)*(c+d*x)*_ + Gamma(1/3,-(c+d*x)^3)/d^2/(-(c+d*x)^3)^(1/3)-_ + 1/3*b*(c+d*x)^2*_ + Gamma(2/3,-(c+d*x)^3)/d^2/(-(c+d*x)^3)^(2/3) +--R +--R +--R (96) +--R 2 2 _ 1 3 3 2 2 2 3 +--R ((- a d + b c d)x - a c d + b c )| (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- d x - 3c d x - 3c d x - c +--R + +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (- b d x - 2b c d x - b c )| (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R Type: Expression(Integer) +--E 97 + +--S 98 of 578 +a0019:= integrate(t0019,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ %A d + 3%A c d + 3%A c d + c +--R (97) | (%A b + a)%e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 578 +m0019:= a0019-r0019 +--R +--R +--R (98) +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R * +--R x 3 3 2 2 2 3 +--R ++ %A d + 3%A c d + 3%A c d + c +--R | (%A b + a)%e d%A +--R ++ +--R + +--R 2 2 _ 1 3 3 2 2 2 3 +--R ((a d - b c d)x + a c d - b c )| (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R * +--R +------------------------------+ +--R 3| 3 3 2 2 2 3 +--R \|- d x - 3c d x - 3c d x - c +--R + +--R 2 2 2 _ 2 3 3 2 2 2 3 +--R (b d x + 2b c d x + b c )| (-,- d x - 3c d x - 3c d x - c ) +--R 3 +--R / +--R +------------------------------+2 +--R 2 3| 3 3 2 2 2 3 +--R 3d \|- d x - 3c d x - 3c d x - c +--R Type: Expression(Integer) +--E 99 + +--S 100 of 578 +d0019:= D(m0019,x) +--R +--R +--R (99) 0 +--R Type: Expression(Integer) +--E 100 + +--S 101 of 578 +t0020:= x^2*exp(1)^(a+b*x)/(c+d*x^2) +--R +--R +--R 2 b x + a +--R x %e +--R (100) ----------- +--R 2 +--R d x + c +--R Type: Expression(Integer) +--E 101 + +--S 102 of 578 +r0020:= exp(1)^(a+b*x)/b/d-1/2*c^(1/2)*_ + exp(1)^(a+b*c^(1/2)/(-d)^(1/2))*_ + Ei(-b*(c^(1/2)-(-d)^(1/2)*x)/(-d)^(1/2))/(-d)^(3/2)+1/2*c^(1/2)*_ + exp(1)^(a-b*c^(1/2)/(-d)^(1/2))*_ + Ei(b*(c^(1/2)+(-d)^(1/2)*x)/(-d)^(1/2))/(-d)^(3/2) +--R +--R +--R (101) +--R +-+ +---+ +--R b\|c + a\|- d +--R --------------- +--R +-+ +---+ +---+ +--R +-+ - b\|c + b x\|- d \|- d +--R b\|c Ei(-------------------)%e +--R +---+ +--R \|- d +--R + +--R +-+ +---+ +--R - b\|c + a\|- d +--R ----------------- +--R +-+ +---+ +---+ +--R +-+ b\|c + b x\|- d \|- d b x + a +---+ +--R - b\|c Ei(-----------------)%e + 2%e \|- d +--R +---+ +--R \|- d +--R / +--R +---+ +--R 2b d\|- d +--R Type: Expression(Integer) +--E 102 + +--S 103 of 578 +a0020:= integrate(t0020,x) +--R +--R +--R x 2 %A b + a +--R ++ %A %e +--R (102) | ------------- d%A +--R ++ 2 +--R %A d + c +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 578 +m0020:= a0020-r0020 +--R +--R +--R (103) +--R x 2 %A b + a +--R +---+ ++ %A %e +--R 2b d\|- d | ------------- d%A +--R ++ 2 +--R %A d + c +--R + +--R +-+ +---+ +--R b\|c + a\|- d +--R --------------- +--R +-+ +---+ +---+ +--R +-+ - b\|c + b x\|- d \|- d +--R - b\|c Ei(-------------------)%e +--R +---+ +--R \|- d +--R + +--R +-+ +---+ +--R - b\|c + a\|- d +--R ----------------- +--R +-+ +---+ +---+ +--R +-+ b\|c + b x\|- d \|- d b x + a +---+ +--R b\|c Ei(-----------------)%e - 2%e \|- d +--R +---+ +--R \|- d +--R / +--R +---+ +--R 2b d\|- d +--R Type: Expression(Integer) +--E 104 + +--S 105 of 578 +d0020:= D(m0020,x) +--R +--R +--R (104) +--R +-+ +---+ +-+ +---+ +--R - b\|c + a\|- d b\|c + b x\|- d +--R ----------------- ----------------- +--R +---+ +---+ +--R +---+ +-+ \|- d \|- d +--R (- x\|- d \|c + c)%e %e +--R + +--R +-+ +---+ +-+ +---+ +--R - b\|c + b x\|- d b\|c + a\|- d +--R ------------------- --------------- +--R +---+ +---+ +--R +---+ +-+ \|- d \|- d b x + a +--R (x\|- d \|c + c)%e %e - 2c %e +--R / +--R 2 2 +--R 2d x + 2c d +--R Type: Expression(Integer) +--E 105 + +--S 106 of 578 +t0021:= 1/(a+b*exp(1)^(c-d*x)) +--R +--R +--R 1 +--R (105) ----------------- +--R - d x + c +--R b %e + a +--R Type: Expression(Integer) +--E 106 + +--S 107 of 578 +r0021:= log(b+a*exp(-c+d*x))/a/d +--R +--R +--R d x - c +--R log(a %e + b) +--R (106) -------------------- +--R a d +--R Type: Expression(Integer) +--E 107 + +--S 108 of 578 +a0021:= integrate(t0021,x) +--R +--R +--R - d x + c +--R log(b %e + a) + d x +--R (107) ---------------------------- +--R a d +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 578 +m0021:= a0021-r0021 +--R +--R +--R d x - c - d x + c +--R - log(a %e + b) + log(b %e + a) + d x +--R (108) ----------------------------------------------------- +--R a d +--R Type: Expression(Integer) +--E 109 + +--S 110 of 578 +d0021:= D(m0021,x) +--R +--R +--R - d x + c d x - c +--R - b %e %e + b +--R (109) ----------------------------------------------------- +--R - d x + c 2 d x - c 2 - d x + c +--R (a b %e + a )%e + b %e + a b +--R Type: Expression(Integer) +--E 110 + +--S 111 of 578 +t0022:= 1/(a+b*exp(1)^(c-d*x))^2 +--R +--R +--R 1 +--R (110) ---------------------------------------- +--R 2 - d x + c 2 - d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 111 + +--S 112 of 578 +r0022:= -1/a/d/(a+b*exp(1)^(c-d*x))+log(b+a*exp(1)^(-c+d*x))/a^2/d +--R +--R +--R - d x + c d x - c +--R (b %e + a)log(a %e + b) - a +--R (111) ------------------------------------------- +--R 2 - d x + c 3 +--R a b d %e + a d +--R Type: Expression(Integer) +--E 112 + +--S 113 of 578 +a0022:= integrate(t0022,x) +--R +--R +--R (112) +--R - d x + c - d x + c - d x + c +--R (b %e + a)log(b %e + a) + b d x %e + a d x - a +--R ------------------------------------------------------------------------- +--R 2 - d x + c 3 +--R a b d %e + a d +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 578 +m0022:= a0022-r0022 +--R +--R +--R d x - c - d x + c +--R - log(a %e + b) + log(b %e + a) + d x +--R (113) ----------------------------------------------------- +--R 2 +--R a d +--R Type: Expression(Integer) +--E 114 + +--S 115 of 578 +d0022:= D(m0022,x) +--R +--R +--R - d x + c d x - c +--R - b %e %e + b +--R (114) ------------------------------------------------------- +--R 2 - d x + c 3 d x - c 2 - d x + c 2 +--R (a b %e + a )%e + a b %e + a b +--R Type: Expression(Integer) +--E 115 + +--S 116 of 578 +t0023:= 1/(a+b*exp(1)^(-c-d*x)) +--R +--R +--R 1 +--R (115) ----------------- +--R - d x - c +--R b %e + a +--R Type: Expression(Integer) +--E 116 + +--S 117 of 578 +r0023:= log(b+a*exp(c+d*x))/a/d +--R +--R +--R d x + c +--R log(a %e + b) +--R (116) -------------------- +--R a d +--R Type: Expression(Integer) +--E 117 + +--S 118 of 578 +a0023:= integrate(t0023,x) +--R +--R +--R - d x - c +--R log(b %e + a) + d x +--R (117) ---------------------------- +--R a d +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 578 +m0023:= a0023-r0023 +--R +--R +--R d x + c - d x - c +--R - log(a %e + b) + log(b %e + a) + d x +--R (118) ----------------------------------------------------- +--R a d +--R Type: Expression(Integer) +--E 119 + +--S 120 of 578 +d0023:= D(m0023,x) +--R +--R +--R - d x - c d x + c +--R - b %e %e + b +--R (119) ----------------------------------------------------- +--R - d x - c 2 d x + c 2 - d x - c +--R (a b %e + a )%e + b %e + a b +--R Type: Expression(Integer) +--E 120 + +--S 121 of 578 +t0024:= 1/(a+b*exp(1)^(-c-d*x))^2 +--R +--R +--R 1 +--R (120) ---------------------------------------- +--R 2 - d x - c 2 - d x - c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 578 +r0024:= -1/a/d/(a+b*exp(1)^(-c-d*x))+log(b+a*exp(1)^(c+d*x))/a^2/d +--R +--R +--R - d x - c d x + c +--R (b %e + a)log(a %e + b) - a +--R (121) ------------------------------------------- +--R 2 - d x - c 3 +--R a b d %e + a d +--R Type: Expression(Integer) +--E 122 + +--S 123 of 578 +a0024:= integrate(t0024,x) +--R +--R +--R (122) +--R - d x - c - d x - c - d x - c +--R (b %e + a)log(b %e + a) + b d x %e + a d x - a +--R ------------------------------------------------------------------------- +--R 2 - d x - c 3 +--R a b d %e + a d +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 578 +m0024:= a0024-r0024 +--R +--R +--R d x + c - d x - c +--R - log(a %e + b) + log(b %e + a) + d x +--R (123) ----------------------------------------------------- +--R 2 +--R a d +--R Type: Expression(Integer) +--E 124 + +--S 125 of 578 +d0024:= D(m0024,x) +--R +--R +--R - d x - c d x + c +--R - b %e %e + b +--R (124) ------------------------------------------------------- +--R 2 - d x - c 3 d x + c 2 - d x - c 2 +--R (a b %e + a )%e + a b %e + a b +--R Type: Expression(Integer) +--E 125 + +--S 126 of 578 +t0025:= 1/(a+b*exp(1)^(-c-d*x))^3 +--R +--R +--R 1 +--R (125) -------------------------------------------------------------- +--R 3 - d x - c 3 2 - d x - c 2 2 - d x - c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 578 +r0025:= -1/2/a/d/(a+b*exp(1)^(-c-d*x))^2-1/a^2/d/(a+b*exp(1)^(-c-d*x))+_ + log(b+a*exp(1)^(c+d*x))/a^3/d +--R +--R +--R (126) +--R 2 - d x - c 2 - d x - c 2 d x + c +--R (2b (%e ) + 4a b %e + 2a )log(a %e + b) +--R + +--R - d x - c 2 +--R - 2a b %e - 3a +--R / +--R 3 2 - d x - c 2 4 - d x - c 5 +--R 2a b d (%e ) + 4a b d %e + 2a d +--R Type: Expression(Integer) +--E 127 + +--S 128 of 578 +a0025:= integrate(t0025,x) +--R +--R +--R (127) +--R 2 - d x - c 2 - d x - c 2 - d x - c +--R (2b (%e ) + 4a b %e + 2a )log(b %e + a) +--R + +--R 2 - d x - c 2 - d x - c 2 2 +--R 2b d x (%e ) + (4a b d x - 2a b)%e + 2a d x - 3a +--R / +--R 3 2 - d x - c 2 4 - d x - c 5 +--R 2a b d (%e ) + 4a b d %e + 2a d +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 578 +m0025:= a0025-r0025 +--R +--R +--R d x + c - d x - c +--R - log(a %e + b) + log(b %e + a) + d x +--R (128) ----------------------------------------------------- +--R 3 +--R a d +--R Type: Expression(Integer) +--E 129 + +--S 130 of 578 +d0025:= D(m0025,x) +--R +--R +--R - d x - c d x + c +--R - b %e %e + b +--R (129) ------------------------------------------------------- +--R 3 - d x - c 4 d x + c 2 2 - d x - c 3 +--R (a b %e + a )%e + a b %e + a b +--R Type: Expression(Integer) +--E 130 + +--S 131 of 578 +t0026:= x/(a+b*exp(1)^(c+d*x)) +--R +--R +--R x +--R (130) --------------- +--R d x + c +--R b %e + a +--R Type: Expression(Integer) +--E 131 + +--S 132 of 578 +r0026:= -1/2*(-d^2*x^2+2*x*log((a+b*exp(c+d*x))/a)*d+2*_ + polylog(2,-b*exp(c+d*x)/a))/a/d^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 578 +a0026:= integrate(t0026,x) +--R +--R +--R x +--R ++ %A +--R (131) | ---------------- d%A +--R ++ %A d + c +--R b %e + a +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 578 +m0026:= a0026-r0026 +--R +--R +--R x +--R ++ %A +--R (132) | ---------------- d%A - r0026 +--R ++ %A d + c +--R b %e + a +--R Type: Expression(Integer) +--E 134 + +--S 135 of 578 +d0026:= D(m0026,x) +--R +--R +--R x +--R (133) --------------- +--R d x + c +--R b %e + a +--R Type: Expression(Integer) +--E 135 + +--S 136 of 578 +t0027:= x^2/(a+b*exp(1)^(c+d*x)) +--R +--R +--R 2 +--R x +--R (134) --------------- +--R d x + c +--R b %e + a +--R Type: Expression(Integer) +--E 136 + +--S 137 of 578 +r0027:= 1/3*(d^3*x^3-3*x^2*log((a+b*exp(c+d*x))/a)*d^2-6*x*_ + polylog(2,-b*exp(c+d*x)/a)*d+6*_ + polylog(3,-b*exp(c+d*x)/a))/a/d^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 137 + +--S 138 of 578 +a0027:= integrate(t0027,x) +--R +--R +--R x 2 +--R ++ %A +--R (135) | ---------------- d%A +--R ++ %A d + c +--R b %e + a +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 578 +m0027:= a0027-r0027 +--R +--R +--R x 2 +--R ++ %A +--R (136) | ---------------- d%A - r0027 +--R ++ %A d + c +--R b %e + a +--R Type: Expression(Integer) +--E 139 + +--S 140 of 578 +d0027:= D(m0027,x) +--R +--R +--R 2 +--R x +--R (137) --------------- +--R d x + c +--R b %e + a +--R Type: Expression(Integer) +--E 140 + +--S 141 of 578 +t0028:= x^3/(a+b*exp(1)^(c+d*x)) +--R +--R +--R 3 +--R x +--R (138) --------------- +--R d x + c +--R b %e + a +--R Type: Expression(Integer) +--E 141 + +--S 142 of 578 +r0028:= 1/4*(x^4*d^4-4*x^3*log((a+b*exp(c+d*x))/a)*d^3-12*x^2*_ + polylog(2,-b*exp(c+d*x)/a)*d^2+24*x*_ + polylog(3,-b*exp(c+d*x)/a)*d-24*_ + polylog(4,-b*exp(c+d*x)/a))/a/d^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 142 + +--S 143 of 578 +a0028:= integrate(t0028,x) +--R +--R +--R x 3 +--R ++ %A +--R (139) | ---------------- d%A +--R ++ %A d + c +--R b %e + a +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 578 +m0028:= a0028-r0028 +--R +--R +--R x 3 +--R ++ %A +--R (140) | ---------------- d%A - r0028 +--R ++ %A d + c +--R b %e + a +--R Type: Expression(Integer) +--E 144 + +--S 145 of 578 +d0028:= D(m0028,x) +--R +--R +--R 3 +--R x +--R (141) --------------- +--R d x + c +--R b %e + a +--R Type: Expression(Integer) +--E 145 + +--S 146 of 578 +t0029:= x/(a+b*exp(1)^(c+d*x))^2 +--R +--R +--R x +--R (142) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 578 +r0029:= -x/a^2/d+x/a/d/(a+b*exp(1)^(c+d*x))+1/2*x^2/a^2+_ + log(a+b*exp(1)^(c+d*x))/a^2/d^2-_ + x*log(1+b*exp(1)^(c+d*x)/a)/a^2/d-_ + polylog(2,-b*exp(1)^(c+d*x)/a)/a^2/d^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 578 +a0029:= integrate(t0029,x) +--R +--R +--R x +--R ++ %A +--R (143) | -------------------------------------- d%A +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 578 +m0029:= a0029-r0029 +--R +--R +--R x +--R ++ %A +--R (144) | -------------------------------------- d%A - r0029 +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 149 + +--S 150 of 578 +d0029:= D(m0029,x) +--R +--R +--R x +--R (145) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 578 +t0030:= x^2/(a+b*exp(1)^(c+d*x))^2 +--R +--R +--R 2 +--R x +--R (146) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 151 + +--S 152 of 578 +r0030:= -x^2/a^2/d+x^2/a/d/(a+b*exp(1)^(c+d*x))+_ + 1/3*x^3/a^2+2*x*log(1+b*exp(1)^(c+d*x)/a)/a^2/d^2-_ + x^2*log(1+b*exp(1)^(c+d*x)/a)/a^2/d+_ + 2*(1-d*x)*polylog(2,-b*exp(1)^(c+d*x)/a)/a^2/d^3+_ + 2*polylog(3,-b*exp(1)^(c+d*x)/a)/a^2/d^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 152 + +--S 153 of 578 +a0030:= integrate(t0030,x) +--R +--R +--R x 2 +--R ++ %A +--R (147) | -------------------------------------- d%A +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 578 +m0030:= a0030-r0030 +--R +--R +--R x 2 +--R ++ %A +--R (148) | -------------------------------------- d%A - r0030 +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 154 + +--S 155 of 578 +d0030:= D(m0030,x) +--R +--R +--R 2 +--R x +--R (149) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 155 + +--S 156 of 578 +t0031:= x^3/(a+b*exp(1)^(c+d*x))^2 +--R +--R +--R 3 +--R x +--R (150) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 578 +r0031:= -x^3/a^2/d+x^3/a/d/(a+b*exp(1)^(c+d*x))+1/4*x^4/a^2+_ + 3*x^2*log(1+b*exp(1)^(c+d*x)/a)/a^2/d^2-_ + x^3*log(1+b*exp(1)^(c+d*x)/a)/a^2/d+3*x*(2-d*x)*_ + polylog(2,-b*exp(1)^(c+d*x)/a)/a^2/d^3-6*(1-d*x)*_ + polylog(3,-b*exp(1)^(c+d*x)/a)/a^2/d^4-6*_ + polylog(4,-b*exp(1)^(c+d*x)/a)/a^2/d^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 157 + +--S 158 of 578 +a0031:= integrate(t0031,x) +--R +--R +--R x 3 +--R ++ %A +--R (151) | -------------------------------------- d%A +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 578 +m0031:= a0031-r0031 +--R +--R +--R x 3 +--R ++ %A +--R (152) | -------------------------------------- d%A - r0031 +--R ++ 2 %A d + c 2 %A d + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 159 + +--S 160 of 578 +d0031:= D(m0031,x) +--R +--R +--R 3 +--R x +--R (153) ------------------------------------ +--R 2 d x + c 2 d x + c 2 +--R b (%e ) + 2a b %e + a +--R Type: Expression(Integer) +--E 160 + +--S 161 of 578 +t0032:= x/(a+b*exp(1)^(c+d*x))^3 +--R +--R +--R x +--R (154) -------------------------------------------------------- +--R 3 d x + c 3 2 d x + c 2 2 d x + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 578 +r0032:= -1/2/a^2/d^2/(a+b*exp(1)^(c+d*x))-3/2*x/a^3/d+1/2*x^2/a^3+_ + 1/2*x*(2*a/d/(a+b*exp(1)^(c+d*x))+(a^2/(a+b*exp(1)^(c+d*x))^2-_ + 2*log(a+b*exp(1)^(c+d*x)))/d)/a^3+3/2*_ + log(a+b*exp(1)^(c+d*x))/a^3/d^2+x*_ + log(a+b*exp(1)^(c+d*x))/a^3/d-x*log(1+b*exp(1)^(c+d*x)/a)/a^3/d-_ + polylog(2,-b*exp(1)^(c+d*x)/a)/a^3/d^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 578 +a0032:= integrate(t0032,x) +--R +--R +--R (155) +--R x +--R ++ %A +--R | ----------------------------------------------------------- d%A +--R ++ 3 %A d + c 3 2 %A d + c 2 2 %A d + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 578 +m0032:= a0032-r0032 +--R +--R +--R (156) +--R x +--R ++ %A +--R | ----------------------------------------------------------- d%A - r0032 +--R ++ 3 %A d + c 3 2 %A d + c 2 2 %A d + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression(Integer) +--E 164 + +--S 165 of 578 +d0032:= D(m0032,x) +--R +--R +--R x +--R (157) -------------------------------------------------------- +--R 3 d x + c 3 2 d x + c 2 2 d x + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression(Integer) +--E 165 + +--S 166 of 578 +t0033:= x^2/(a+b*exp(1)^(c+d*x))^3 +--R +--R +--R 2 +--R x +--R (158) -------------------------------------------------------- +--R 3 d x + c 3 2 d x + c 2 2 d x + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 578 +r0033:= x/a^3/d^2-x/a^2/d^2/(a+b*exp(1)^(c+d*x))-3/2*x^2/a^3/d+1/3*x^3/a^3+_ + 1/2*x^2*(2*a/d/(a+b*exp(1)^(c+d*x))+(a^2/(a+b*exp(1)^(c+d*x))^2-_ + 2*log(a+b*exp(1)^(c+d*x)))/d)/a^3-log(a+b*exp(1)^(c+d*x))/a^3/d^3+_ + x^2*log(a+b*exp(1)^(c+d*x))/a^3/d+3*x*_ + log(1+b*exp(1)^(c+d*x)/a)/a^3/d^2-x^2*log(1+b*exp(1)^(c+d*x)/a)/a^3/d+_ + (3-2*d*x)*polylog(2,-b*exp(1)^(c+d*x)/a)/a^3/d^3+2*_ + polylog(3,-b*exp(1)^(c+d*x)/a)/a^3/d^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 167 + +--S 168 of 578 +a0033:= integrate(t0033,x) +--R +--R +--R (159) +--R x 2 +--R ++ %A +--R | ----------------------------------------------------------- d%A +--R ++ 3 %A d + c 3 2 %A d + c 2 2 %A d + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 578 +m0033:= a0033-r0033 +--R +--R +--R (160) +--R x 2 +--R ++ %A +--R | ----------------------------------------------------------- d%A - r0033 +--R ++ 3 %A d + c 3 2 %A d + c 2 2 %A d + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression(Integer) +--E 169 + +--S 170 of 578 +d0033:= D(m0033,x) +--R +--R +--R 2 +--R x +--R (161) -------------------------------------------------------- +--R 3 d x + c 3 2 d x + c 2 2 d x + c 3 +--R b (%e ) + 3a b (%e ) + 3a b %e + a +--R Type: Expression(Integer) +--E 170 + +--S 171 of 578 +t0034:= (exp(1)^(a+b*x))^(1/2)/x +--R +--R +--R +---------+ +--R | b x + a +--R \|%e +--R (162) ------------ +--R x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 578 +r0034:= exp(a+b*x)^(1/2)*Ei(1/2*b*x)*exp(-1/2*b*x) +--R +--R +--R b x +--R - --- +---------+ +--R b x 2 | b x + a +--R (163) Ei(---)%e \|%e +--R 2 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 578 +a0034:= integrate(t0034,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 173 + +--S 174 of 578 +m0034:= a0034-r0034 +--R +--R +--R b x +--R - --- +---------+ +--R b x 2 | b x + a +--R (164) - Ei(---)%e \|%e + a0034 +--R 2 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 578 +d0034:= D(m0034,x) +--R +--R +--R b x b x +--R - --- --- +---------+ +--R 2 2 | b x + a +--R %e %e \|%e +--R (165) - ------------------------ +--R x +--R Type: Expression(Integer) +--E 175 + +--S 176 of 578 +t0035:= (exp(1)^(a+b*x))^(1/2)/x^2 +--R +--R +--R +---------+ +--R | b x + a +--R \|%e +--R (166) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 578 +r0035:= 1/2*exp(-1/2*a-1/2*b*x)*exp(a+b*x)^(1/2)*(-2*exp(1/2*a+1/2*b*x)+_ + b*exp(1/2*a)*Ei(1/2*b*x)*x)/x +--R +--R +--R - b x - a b x + a - b x - a a +--R --------- ------- --------- - +---------+ +--R 2 2 b x 2 2 | b x + a +--R (- 2%e %e + b x Ei(---)%e %e )\|%e +--R 2 +--R (167) ----------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 578 +a0035:= integrate(t0035,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 178 + +--S 179 of 578 +m0035:= a0035-r0035 +--R +--R +--R (168) +--R - b x - a b x + a - b x - a a +--R --------- ------- --------- - +---------+ +--R 2 2 b x 2 2 | b x + a +--R (2%e %e - b x Ei(---)%e %e )\|%e + 2a0035 x +--R 2 +--R -------------------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 179 + +--S 180 of 578 +d0035:= D(m0035,x) +--R +--R +--R - b x - a b x + a - b x - a a b x +--R --------- ------- --------- - --- +--R 2 2 2 2 2 b x + a +--R ((b x - 2)%e %e - b x %e %e %e )%e +--R (169) ------------------------------------------------------------------ +--R +---------+ +--R 2 | b x + a +--R 2x \|%e +--R Type: Expression(Integer) +--E 180 + +--S 181 of 578 +t0036:= (exp(1)^(a+b*x))^(1/2)/x^3 +--R +--R +--R +---------+ +--R | b x + a +--R \|%e +--R (170) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 578 +r0036:= 1/8*exp(-1/2*a-1/2*b*x)*exp(a+b*x)^(1/2)*(-4*exp(1/2*a+1/2*b*x)-_ + 2*b*exp(1/2*a+1/2*b*x)*x+b^2*exp(1/2*a)*Ei(1/2*b*x)*x^2)/x^2 +--R +--R +--R (171) +--R - b x - a b x + a - b x - a a +--R --------- ------- --------- - +---------+ +--R 2 2 2 2 b x 2 2 | b x + a +--R ((- 2b x - 4)%e %e + b x Ei(---)%e %e )\|%e +--R 2 +--R -------------------------------------------------------------------------- +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 578 +a0036:= integrate(t0036,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 183 + +--S 184 of 578 +m0036:= a0036-r0036 +--R +--R +--R (172) +--R - b x - a b x + a - b x - a a +--R --------- ------- --------- - +---------+ +--R 2 2 2 2 b x 2 2 | b x + a +--R ((2b x + 4)%e %e - b x Ei(---)%e %e )\|%e +--R 2 +--R + +--R 2 +--R 8a0036 x +--R / +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 184 + +--S 185 of 578 +d0036:= D(m0036,x) +--R +--R +--R - b x - a b x + a - b x - a a b x +--R --------- ------- --------- - --- +--R 2 2 2 2 2 2 2 2 2 b x + a +--R ((b x - 8)%e %e - b x %e %e %e )%e +--R (173) ------------------------------------------------------------------- +--R +---------+ +--R 3 | b x + a +--R 8x \|%e +--R Type: Expression(Integer) +--E 185 + +--S 186 of 578 +t0037:= f^(a+b*(c+d*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R (174) f +--R Type: Expression(Integer) +--E 186 + +--S 187 of 578 +r0037:= -1/3*f^a*(c+d*x)*Gamma(1/3,-b*(c+d*x)^3*log(f))/d/_ + (-b*(c+d*x)^3*log(f))^(1/3) +--R +--R +--R a _ 1 3 3 2 2 2 3 +--R (- d x - c)f | (-,(- b d x - 3b c d x - 3b c d x - b c )log(f)) +--R 3 +--R (175) ----------------------------------------------------------------- +--R +----------------------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3d\|(- b d x - 3b c d x - 3b c d x - b c )log(f) +--R Type: Expression(Integer) +--E 187 + +--S 188 of 578 +a0037:= integrate(t0037,x) +--R +--R +--R x 3 3 2 2 2 3 +--R ++ %A b d + 3%A b c d + 3%A b c d + b c + a +--R (176) | f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 578 +m0037:= a0037-r0037 +--R +--R +--R (177) +--R +----------------------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3d\|(- b d x - 3b c d x - 3b c d x - b c )log(f) +--R * +--R x 3 3 2 2 2 3 +--R ++ %A b d + 3%A b c d + 3%A b c d + b c + a +--R | f d%A +--R ++ +--R + +--R a _ 1 3 3 2 2 2 3 +--R (d x + c)f | (-,(- b d x - 3b c d x - 3b c d x - b c )log(f)) +--R 3 +--R / +--R +----------------------------------------------+ +--R 3| 3 3 2 2 2 3 +--R 3d\|(- b d x - 3b c d x - 3b c d x - b c )log(f) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 578 +d0037:= D(m0037,x) +--R +--R +--R (178) +--R 3 3 2 2 2 3 +--R a (b d x + 3b c d x + 3b c d x + b c )log(f) +--R - f %e +--R + +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R f +--R Type: Expression(Integer) +--E 190 + +--S 191 of 578 +t0038:= f^(a+b*(c+d*x)^n) +--R +--R +--R n +--R b (d x + c) + a +--R (179) f +--R Type: Expression(Integer) +--E 191 + +--S 192 of 578 +r0038:= -f^a*(c+d*x)*Gamma(1/n,-b*(c+d*x)^n*log(f))/_ + ((-b*(c+d*x)^n*log(f))^(1/n))/d/n +--R +--R +--R a _ 1 n +--R (- d x - c)f | (-,- b log(f)(d x + c) ) +--R n +--R (180) --------------------------------------- +--R 1 +--R - +--R n n +--R d n (- b log(f)(d x + c) ) +--R Type: Expression(Integer) +--E 192 + +--S 193 of 578 +a0038:= integrate(t0038,x) +--R +--R +--R x n +--R ++ b (%A d + c) + a +--R (181) | f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 578 +m0038:= a0038-r0038 +--R +--R +--R (182) +--R 1 +--R - x n +--R n n ++ b (%A d + c) + a +--R d n (- b log(f)(d x + c) ) | f d%A +--R ++ +--R + +--R a _ 1 n +--R (d x + c)f | (-,- b log(f)(d x + c) ) +--R n +--R / +--R 1 +--R - +--R n n +--R d n (- b log(f)(d x + c) ) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 578 +d0038:= D(m0038,x) +--R +--R +--R (183) +--R 1 +--R - +--R a n n +--R f (- b log(f)(d x + c) ) +--R + +--R - n + 1 +--R ------- +--R a n - 1 n n +--R (b d x + b c)log(f)f (d x + c) (- b log(f)(d x + c) ) +--R * +--R _ 1 n +--R | (-,- b log(f)(d x + c) ) +--R n +--R + +--R 1 2 +--R - n +--R n n b (d x + c) + a +--R n ((- b log(f)(d x + c) ) ) f +--R + +--R n +--R a n - 1 b log(f)(d x + c) +--R (b d n x + b c n)log(f)f (d x + c) %e +--R * +--R - n + 1 1 +--R ------- - +--R n n n n +--R (- b log(f)(d x + c) ) (- b log(f)(d x + c) ) +--R / +--R 1 2 +--R - +--R n n +--R n ((- b log(f)(d x + c) ) ) +--R Type: Expression(Integer) +--E 195 + +--S 196 of 578 +t0039:= f^(a+b*(c+d*x)^(1/2)) +--R +--R +--R +-------+ +--R b\|d x + c + a +--R (184) f +--R Type: Expression(Integer) +--E 196 + +--S 197 of 578 +r0039:= 2*f^(a+b*(c+d*x)^(1/2))*(-1+(c+d*x)^(1/2)*b*log(f))/b^2/d/log(f)^2 +--R +--R +--R +-------+ +--R +-------+ b\|d x + c + a +--R (2b log(f)\|d x + c - 2)f +--R (185) ----------------------------------------- +--R 2 2 +--R b d log(f) +--R Type: Expression(Integer) +--E 197 + +--S 198 of 578 +a0039:= integrate(t0039,x) +--R +--R +--R +-------+ +--R +-------+ b log(f)\|d x + c + a log(f) +--R (2b log(f)\|d x + c - 2)%e +--R (186) -------------------------------------------------------- +--R 2 2 +--R b d log(f) +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 578 +m0039:= a0039-r0039 +--R +--R +--R (187) +--R +-------+ +--R +-------+ b\|d x + c + a +--R (- 2b log(f)\|d x + c + 2)f +--R + +--R +-------+ +--R +-------+ b log(f)\|d x + c + a log(f) +--R (2b log(f)\|d x + c - 2)%e +--R / +--R 2 2 +--R b d log(f) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 578 +d0039:= D(m0039,x) +--R +--R +--R +-------+ +-------+ +--R b\|d x + c + a b log(f)\|d x + c + a log(f) +--R (188) - f + %e +--R Type: Expression(Integer) +--E 200 + +--S 201 of 578 +t0040:= f^(a+b*(c+d*x)^(1/3)) +--R +--R +--R 3+-------+ +--R b\|d x + c + a +--R (189) f +--R Type: Expression(Integer) +--E 201 + +--S 202 of 578 +r0040:= 3*f^(a+b*(c+d*x)^(1/3))*(2-2*(c+d*x)^(1/3)*b*log(f)+_ + (c+d*x)^(2/3)*b^2*log(f)^2)/b^3/d/log(f)^3 +--R +--R +--R 3+-------+ +--R 2 2 3+-------+2 3+-------+ b\|d x + c + a +--R (3b log(f) \|d x + c - 6b log(f)\|d x + c + 6)f +--R (190) ----------------------------------------------------------------- +--R 3 3 +--R b d log(f) +--R Type: Expression(Integer) +--E 202 + +--S 203 of 578 +a0040:= integrate(t0040,x) +--R +--R +--R (191) +--R 2 2 3+-------+2 3+-------+ +--R (3b log(f) \|d x + c - 6b log(f)\|d x + c + 6) +--R * +--R 3+-------+ +--R b log(f)\|d x + c + a log(f) +--R %e +--R / +--R 3 3 +--R b d log(f) +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 578 +m0040:= a0040-r0040 +--R +--R +--R (192) +--R 3+-------+ +--R 2 2 3+-------+2 3+-------+ b\|d x + c + a +--R (- 3b log(f) \|d x + c + 6b log(f)\|d x + c - 6)f +--R + +--R 2 2 3+-------+2 3+-------+ +--R (3b log(f) \|d x + c - 6b log(f)\|d x + c + 6) +--R * +--R 3+-------+ +--R b log(f)\|d x + c + a log(f) +--R %e +--R / +--R 3 3 +--R b d log(f) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 578 +d0040:= D(m0040,x) +--R +--R +--R 3+-------+ 3+-------+ +--R b\|d x + c + a b log(f)\|d x + c + a log(f) +--R (193) - f + %e +--R Type: Expression(Integer) +--E 205 + +--S 206 of 578 +t0041:= x^3*exp(1)^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 3 c x + b x + a +--R (194) x %e +--R Type: Expression(Integer) +--E 206 + +--S 207 of 578 +r0041:= 1/8*b^2*exp(1)^(a+b*x+c*x^2)/c^3-1/2*exp(1)^(a+b*x+c*x^2)/c^2-_ + 1/4*b*exp(1)^(a+b*x+c*x^2)*x/c^2+1/2*exp(1)^(a+b*x+c*x^2)*x^2/c-_ + 1/16*b*(b^2-6*c)*exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)/c^(1/2))/c^(7/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 207 + +--S 208 of 578 +a0041:= integrate(t0041,x) +--R +--R +--R x 2 +--R ++ 3 %A c + %A b + a +--R (195) | %A %e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 578 +m0041:= a0041-r0041 +--R +--R +--R x 2 +--R ++ 3 %A c + %A b + a +--R (196) | %A %e d%A - r0041 +--R ++ +--R Type: Expression(Integer) +--E 209 + +--S 210 of 578 +d0041:= D(m0041,x) +--R +--R +--R 2 +--R 3 c x + b x + a +--R (197) x %e +--R Type: Expression(Integer) +--E 210 + +--S 211 of 578 +t0042:= x^2*exp(1)^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (198) x %e +--R Type: Expression(Integer) +--E 211 + +--S 212 of 578 +r0042:= -1/4*b*exp(1)^(a+b*x+c*x^2)/c^2+1/2*exp(1)^(a+b*x+c*x^2)*x/c+_ + 1/8*(b^2-2*c)*exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)/c^(1/2))/c^(5/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 212 + +--S 213 of 578 +a0042:= integrate(t0042,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (199) | %A %e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 578 +m0042:= a0042-r0042 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (200) | %A %e d%A - r0042 +--R ++ +--R Type: Expression(Integer) +--E 214 + +--S 215 of 578 +d0042:= D(m0042,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (201) x %e +--R Type: Expression(Integer) +--E 215 + +--S 216 of 578 +t0043:= x^3*exp(1)^((a+b*x)*(c+d*x)) +--R +--R +--R 2 +--R 3 b d x + (a d + b c)x + a c +--R (202) x %e +--R Type: Expression(Integer) +--E 216 + +--S 217 of 578 +r0043:= -1/2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)/b^2/d^2+_ + 1/8*(b*c+a*d)^2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)/b^3/d^3-_ + 1/4*(b*c+a*d)*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)*x/b^2/d^2+_ + 1/2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)*x^2/b/d-_ + 1/16*(b^3*c^3-3*b^2*c*(2-a*c)*d-3*a*b*(2-a*c)*d^2+_ + a^3*d^3)*%pi^(1/2)*erfi(1/2*(b*c+a*d+2*b*x*d)/b^(1/2)/d^(1/2))/_ + (exp(1)^(1/4*(b*c-a*d)^2/b/d))/b^(7/2)/d^(7/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 217 + +--S 218 of 578 +a0043:= integrate(t0043,x) +--R +--R +--R x 2 +--R ++ 3 (%A b + %A a)d + (%A b + a)c +--R (203) | %A %e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 578 +m0043:= a0043-r0043 +--R +--R +--R x 2 +--R ++ 3 (%A b + %A a)d + (%A b + a)c +--R (204) | %A %e d%A - r0043 +--R ++ +--R Type: Expression(Integer) +--E 219 + +--S 220 of 578 +d0043:= D(m0043,x) +--R +--R +--R 2 +--R 3 b d x + (a d + b c)x + a c +--R (205) x %e +--R Type: Expression(Integer) +--E 220 + +--S 221 of 578 +t0044:= x^2*exp(1)^((a+b*x)*(c+d*x)) +--R +--R +--R 2 +--R 2 b d x + (a d + b c)x + a c +--R (206) x %e +--R Type: Expression(Integer) +--E 221 + +--S 222 of 578 +r0044:= -1/4*(b*c+a*d)*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)/b^2/d^2+_ + 1/2*exp(1)^(a*c+(b*c+a*d)*x+b*d*x^2)*x/b/d+_ + 1/8*(b^2*c^2-2*b*(1-a*c)*d+a^2*d^2)*%pi^(1/2)*_ + erfi(1/2*(b*c+a*d+2*b*x*d)/b^(1/2)/d^(1/2))/_ + (exp(1)^(1/4*(b*c-a*d)^2/b/d))/b^(5/2)/d^(5/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 222 + +--S 223 of 578 +a0044:= integrate(t0044,x) +--R +--R +--R x 2 +--R ++ 2 (%A b + %A a)d + (%A b + a)c +--R (207) | %A %e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 578 +m0044:= a0044-r0044 +--R +--R +--R x 2 +--R ++ 2 (%A b + %A a)d + (%A b + a)c +--R (208) | %A %e d%A - r0044 +--R ++ +--R Type: Expression(Integer) +--E 224 + +--S 225 of 578 +d0044:= D(m0044,x) +--R +--R +--R 2 +--R 2 b d x + (a d + b c)x + a c +--R (209) x %e +--R Type: Expression(Integer) +--E 225 + +--S 226 of 578 +t0045:= x^3*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 3 c x + b x + a +--R (210) x f +--R Type: Expression(Integer) +--E 226 + +--S 227 of 578 +r0045:= -1/2*f^(a+b*x+c*x^2)/c^2/log(f)^2+1/8*b^2*f^(a+b*x+c*x^2)/c^3/log(f)-_ + 1/4*b*f^(a+b*x+c*x^2)*x/c^2/log(f)+1/2*f^(a+b*x+c*x^2)*x^2/c/log(f)+_ + 1/16*b*f^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*log(f)^(1/2)/c^(1/2))*_ + (6*c-b^2*log(f))/c^(7/2)/log(f)^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 578 +a0045:= integrate(t0045,x) +--R +--R +--R x 2 +--R ++ 3 %A c + %A b + a +--R (211) | %A f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 578 +m0045:= a0045-r0045 +--R +--R +--R x 2 +--R ++ 3 %A c + %A b + a +--R (212) | %A f d%A - r0045 +--R ++ +--R Type: Expression(Integer) +--E 229 + +--S 230 of 578 +d0045:= D(m0045,x) +--R +--R +--R 2 +--R 3 c x + b x + a +--R (213) x f +--R Type: Expression(Integer) +--E 230 + +--S 231 of 578 +t0046:= x^2*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (214) x f +--R Type: Expression(Integer) +--E 231 + +--S 232 of 578 +r0046:= -1/4*b*f^(a+b*x+c*x^2)/c^2/log(f)+1/2*f^(a+b*x+c*x^2)*x/c/log(f)-_ + 1/8*f^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)*_ + log(f)^(1/2)/c^(1/2))*(2*c-b^2*log(f))/c^(5/2)/log(f)^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 232 + +--S 233 of 578 +a0046:= integrate(t0046,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (215) | %A f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 578 +m0046:= a0046-r0046 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (216) | %A f d%A - r0046 +--R ++ +--R Type: Expression(Integer) +--E 234 + +--S 235 of 578 +d0046:= D(m0046,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (217) x f +--R Type: Expression(Integer) +--E 235 + +--S 236 of 578 +t0047:= (d+e*x)^3*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 3 3 2 2 2 3 c x + b x + a +--R (218) (e x + 3d e x + 3d e x + d )f +--R Type: Expression(Integer) +--E 236 + +--S 237 of 578 +r0047:= -1/2*e^3*f^(a+b*x+c*x^2)/c^2/log(f)^2+_ + 1/8*e*(2*c*d-b*e)^2*f^(a+b*x+c*x^2)/c^3/log(f)+_ + 1/4*e*(2*c*d-b*e)*f^(a+b*x+c*x^2)*(d+e*x)/c^2/log(f)+_ + 1/2*e*f^(a+b*x+c*x^2)*(d+e*x)^2/c/log(f)-_ + 1/16*(2*c*d-b*e)*f^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*log(f)^(1/2)/c^(1/2))*_ + (6*c*e^2-(2*c*d-b*e)^2*log(f))/c^(7/2)/log(f)^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 578 +a0047:= integrate(t0047,x) +--R +--R +--R x 2 +--R ++ 3 3 2 2 2 3 %A c + %A b + a +--R (219) | (%A e + 3%A d e + 3%A d e + d )f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 578 +m0047:= a0047-r0047 +--R +--R +--R x 2 +--R ++ 3 3 2 2 2 3 %A c + %A b + a +--R (220) | (%A e + 3%A d e + 3%A d e + d )f d%A - r0047 +--R ++ +--R Type: Expression(Integer) +--E 239 + +--S 240 of 578 +d0047:= D(m0047,x) +--R +--R +--R 2 +--R 3 3 2 2 2 3 c x + b x + a +--R (221) (e x + 3d e x + 3d e x + d )f +--R Type: Expression(Integer) +--E 240 + +--S 241 of 578 +t0048:= (d+e*x)^2*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2 2 2 c x + b x + a +--R (222) (e x + 2d e x + d )f +--R Type: Expression(Integer) +--E 241 + +--S 242 of 578 +r0048:= 1/4*e*(4*c*d-b*e)*f^(a+b*x+c*x^2)/c^2/log(f)+_ + 1/2*e^2*f^(a+b*x+c*x^2)*x/c/log(f)-_ + 1/8*f^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*log(f)^(1/2)/c^(1/2))*_ + (2*c*e^2-(2*c*d-b*e)^2*log(f))/c^(5/2)/log(f)^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 242 + +--S 243 of 578 +a0048:= integrate(t0048,x) +--R +--R +--R x 2 +--R ++ 2 2 2 %A c + %A b + a +--R (223) | (%A e + 2%A d e + d )f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 578 +m0048:= a0048-r0048 +--R +--R +--R x 2 +--R ++ 2 2 2 %A c + %A b + a +--R (224) | (%A e + 2%A d e + d )f d%A - r0048 +--R ++ +--R Type: Expression(Integer) +--E 244 + +--S 245 of 578 +d0048:= D(m0048,x) +--R +--R +--R 2 +--R 2 2 2 c x + b x + a +--R (225) (e x + 2d e x + d )f +--R Type: Expression(Integer) +--E 245 + +--S 246 of 578 +t0049:= (d+e*x)*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R c x + b x + a +--R (226) (e x + d)f +--R Type: Expression(Integer) +--E 246 + +--S 247 of 578 +r0049:= 1/2*e*f^(a+b*x+c*x^2)/c/log(f)+1/4*(2*c*d-b*e)*_ + f^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)*_ + log(f)^(1/2)/c^(1/2))/c^(3/2)/log(f)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 247 + +--S 248 of 578 +a0049:= integrate(t0049,x) +--R +--R +--R x 2 +--R ++ %A c + %A b + a +--R (227) | (%A e + d)f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 578 +m0049:= a0049-r0049 +--R +--R +--R x 2 +--R ++ %A c + %A b + a +--R (228) | (%A e + d)f d%A - r0049 +--R ++ +--R Type: Expression(Integer) +--E 249 + +--S 250 of 578 +d0049:= D(m0049,x) +--R +--R +--R 2 +--R c x + b x + a +--R (229) (e x + d)f +--R Type: Expression(Integer) +--E 250 + +--S 251 of 578 +t0050:= (b+2*c*x)^2*f^(a+b*x+c*x^2) +--R +--R +--R 2 +--R 2 2 2 c x + b x + a +--R (230) (4c x + 4b c x + b )f +--R Type: Expression(Integer) +--E 251 + +--S 252 of 578 +r0050:= -c^(1/2)*f^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)*_ + log(f)^(1/2)/c^(1/2))/log(f)^(3/2)+f^(a+b*x+c*x^2)*(b+2*c*x)/log(f) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 252 + +--S 253 of 578 +a0050:= integrate(t0050,x) +--R +--R +--R x 2 +--R ++ 2 2 2 %A c + %A b + a +--R (231) | (4%A c + 4%A b c + b )f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 578 +m0050:= a0050-r0050 +--R +--R +--R x 2 +--R ++ 2 2 2 %A c + %A b + a +--R (232) | (4%A c + 4%A b c + b )f d%A - r0050 +--R ++ +--R Type: Expression(Integer) +--E 254 + +--S 255 of 578 +d0050:= D(m0050,x) +--R +--R +--R 2 +--R 2 2 2 c x + b x + a +--R (233) (4c x + 4b c x + b )f +--R Type: Expression(Integer) +--E 255 + +--S 256 of 578 +t0051:= f^(a+b*x^n)*g^(c+d*x^n) +--R +--R +--R n n +--R b x + a d x + c +--R (234) f g +--R Type: Expression(Integer) +--E 256 + +--S 257 of 578 +r0051:= -f^a*g^c*x*Gamma(1/n,-x^n*(b*log(f)+d*log(g)))/_ + ((-x^n*(b*log(f)+d*log(g)))^(1/n))/n +--R +--R +--R a c _ 1 n +--R x f g | (-,(- d log(g) - b log(f))x ) +--R n +--R (235) - ------------------------------------- +--R 1 +--R - +--R n n +--R n ((- d log(g) - b log(f))x ) +--R Type: Expression(Integer) +--E 257 + +--S 258 of 578 +a0051:= integrate(t0051,x) +--R +--R +--R x n n +--R ++ b %A + a d %A + c +--R (236) | f g d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 578 +m0051:= a0051-r0051 +--R +--R +--R (237) +--R 1 +--R - x n n +--R n n ++ b %A + a d %A + c +--R n ((- d log(g) - b log(f))x ) | f g d%A +--R ++ +--R + +--R a c _ 1 n +--R x f g | (-,(- d log(g) - b log(f))x ) +--R n +--R / +--R 1 +--R - +--R n n +--R n ((- d log(g) - b log(f))x ) +--R Type: Expression(Integer) +--E 259 + +--S 260 of 578 +d0051:= D(m0051,x) +--R +--R +--R (238) +--R 1 +--R - +--R a c n n +--R f g ((- d log(g) - b log(f))x ) +--R + +--R - n + 1 +--R ------- +--R a c n - 1 n n +--R (d x log(g) + b x log(f))f g x ((- d log(g) - b log(f))x ) +--R * +--R _ 1 n +--R | (-,(- d log(g) - b log(f))x ) +--R n +--R + +--R 1 2 +--R - n n +--R n n b x + a d x + c +--R n (((- d log(g) - b log(f))x ) ) f g +--R + +--R n +--R a c n - 1 (d log(g) + b log(f))x +--R (d n x log(g) + b n x log(f))f g x %e +--R * +--R - n + 1 1 +--R ------- - +--R n n n n +--R ((- d log(g) - b log(f))x ) ((- d log(g) - b log(f))x ) +--R / +--R 1 2 +--R - +--R n n +--R n (((- d log(g) - b log(f))x ) ) +--R Type: Expression(Integer) +--E 260 + +--S 261 of 578 +t0052:= exp(1)^(4*x)/(a+b*exp(1)^(2*x))^(2/3) +--R +--R +--R 4x +--R %e +--R (239) -------------- +--R +----------+2 +--R 3| 2x +--R \|b %e + a +--R Type: Expression(Integer) +--E 261 + +--S 262 of 578 +r0052:= 3/8*(a+b*exp(2*x))^(1/3)*(-3*a+b*exp(2*x))/b^2 +--R +--R +--R +----------+ +--R 2x 3| 2x +--R (3b %e - 9a)\|b %e + a +--R (240) --------------------------- +--R 2 +--R 8b +--R Type: Expression(Integer) +--E 262 + +--S 263 of 578 +a0052:= integrate(t0052,x) +--R +--R +--R +----------+ +--R 2x 3| 2x +--R (3b %e - 9a)\|b %e + a +--R (241) --------------------------- +--R 2 +--R 8b +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 578 +m0052:= a0052-r0052 +--R +--R +--R (242) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 578 +d0052:= D(m0052,x) +--R +--R +--R (243) 0 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 578 +t0053:= f^(a+b*x)/(c+d*f^(e+2*b*x)) +--R +--R +--R b x + a +--R f +--R (244) --------------- +--R 2b x + e +--R d f + c +--R Type: Expression(Integer) +--E 266 + +--S 267 of 578 +r0053:= f^(a-1/2*e)*_ + arctan(d^(1/2)*f^(1/2*e+b*x)/c^(1/2))/b/c^(1/2)/d^(1/2)/log(f) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 578 +a0053:= integrate(t0053,x) +--R +--R +--R (245) +--R [ +--R log +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R (d %e (%e ) - c) +--R * +--R +----------------------+ +--R | (e - 2a)log(f) +--R \|- c d %e +--R + +--R (e - 2a)log(f) (b x + a)log(f) +--R 2c d %e %e +--R / +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R d %e (%e ) + c +--R / +--R +----------------------+ +--R | (e - 2a)log(f) +--R 2b log(f)\|- c d %e +--R , +--R +--------------------+ +--R (b x + a)log(f) | (e - 2a)log(f) +--R %e \|c d %e +--R atan(----------------------------------------) +--R c +--R ----------------------------------------------] +--R +--------------------+ +--R | (e - 2a)log(f) +--R b log(f)\|c d %e +--R Type: Union(List(Expression(Integer)),...) +--E 268 + +--S 269 of 578 +m0053a:= a0053.1-r0053 +--R +--R +--R (246) +--R log +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R (d %e (%e ) - c) +--R * +--R +----------------------+ +--R | (e - 2a)log(f) +--R \|- c d %e +--R + +--R (e - 2a)log(f) (b x + a)log(f) +--R 2c d %e %e +--R / +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R d %e (%e ) + c +--R + +--R +----------------------+ +--R | (e - 2a)log(f) +--R - 2b r0053 log(f)\|- c d %e +--R / +--R +----------------------+ +--R | (e - 2a)log(f) +--R 2b log(f)\|- c d %e +--R Type: Expression(Integer) +--E 269 + +--S 270 of 578 +d0053a:= D(m0053a,x) +--R +--R +--R (b x + a)log(f) +--R %e +--R (247) ------------------------------------------ +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R d %e (%e ) + c +--R Type: Expression(Integer) +--E 270 + +--S 271 of 578 +m0053b:= a0053.2-r0053 +--R +--R +--R (248) +--R +--------------------+ +--R (b x + a)log(f) | (e - 2a)log(f) +--R %e \|c d %e +--R atan(----------------------------------------) +--R c +--R + +--R +--------------------+ +--R | (e - 2a)log(f) +--R - b r0053 log(f)\|c d %e +--R / +--R +--------------------+ +--R | (e - 2a)log(f) +--R b log(f)\|c d %e +--R Type: Expression(Integer) +--E 271 + +--S 272 of 578 +d0053b:= D(m0053b,x) +--R +--R +--R (b x + a)log(f) +--R %e +--R (249) ------------------------------------------ +--R (e - 2a)log(f) (b x + a)log(f) 2 +--R d %e (%e ) + c +--R Type: Expression(Integer) +--E 272 + +--S 273 of 578 +t0054:= f^(a+2*b*x)/(c+d*f^(e+2*b*x)) +--R +--R +--R 2b x + a +--R f +--R (250) --------------- +--R 2b x + e +--R d f + c +--R Type: Expression(Integer) +--E 273 + +--S 274 of 578 +r0054:= 1/2*f^(a-e)*log(c+d*f^(e+2*b*x))/b/d/log(f) +--R +--R +--R - e + a 2b x + e +--R f log(d f + c) +--R (251) ---------------------------- +--R 2b d log(f) +--R Type: Expression(Integer) +--E 274 + +--S 275 of 578 +a0054:= integrate(t0054,x) +--R +--R +--R (- e + a)log(f) (2b x + e)log(f) +--R %e log(d %e + c) +--R (252) ---------------------------------------------- +--R 2b d log(f) +--R Type: Union(Expression(Integer),...) +--E 275 + +--S 276 of 578 +m0054:= a0054-r0054 +--R +--R +--R (253) +--R (- e + a)log(f) (2b x + e)log(f) - e + a 2b x + e +--R %e log(d %e + c) - f log(d f + c) +--R ----------------------------------------------------------------------------- +--R 2b d log(f) +--R Type: Expression(Integer) +--E 276 + +--S 277 of 578 +d0054:= D(m0054,x) +--R +--R +--R (254) +--R 2b x + e (- e + a)log(f) - e + a 2b x + e +--R ((d f + c)%e - d f f ) +--R * +--R (2b x + e)log(f) +--R %e +--R + +--R - e + a 2b x + e +--R - c f f +--R / +--R 2 2b x + e (2b x + e)log(f) 2b x + e 2 +--R (d f + c d)%e + c d f + c +--R Type: Expression(Integer) +--E 277 + +--S 278 of 578 +t0055:= f^(a+3*b*x)/(c+d*f^(e+2*b*x)) +--R +--R +--R 3b x + a +--R f +--R (255) --------------- +--R 2b x + e +--R d f + c +--R Type: Expression(Integer) +--E 278 + +--S 279 of 578 +r0055:= -(-f^(a-e+b*x)*d^(1/2)+c^(1/2)*f^(a-2*e)*(f^e)^(1/2)*_ + arctan(d^(1/2)*f^(b*x)*(f^e)^(1/2)/c^(1/2)))/b/d^(3/2)/log(f) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 279 + +--S 280 of 578 +a0055:= integrate(t0055,x) +--R +--R +--R (256) +--R [ +--R (- 3e + 2a)log(f) +--R +---+ ----------------- +--R | c 2 +--R |- - %e +--R \| d +--R * +--R (2b x + e)log(f) 2 (2b x + e)log(f) +--R ---------------- +---+ ---------------- +--R 2 | c 2 +--R d (%e ) - 2d |- - %e - c +--R \| d +--R log(--------------------------------------------------------) +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R + +--R (- 3e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R 2%e %e +--R / +--R 2b d log(f) +--R , +--R +--R (2b x + e)log(f) +--R (- 3e + 2a)log(f) ---------------- +--R +-+ ----------------- 2 +--R |c 2 %e +--R - |- %e atan(------------------) +--R \|d +-+ +--R |c +--R |- +--R \|d +--R + +--R (- 3e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R %e %e +--R / +--R b d log(f) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 280 + +--S 281 of 578 +m0055a:= a0055.1-r0055 +--R +--R +--R (257) +--R (- 3e + 2a)log(f) +--R +---+ ----------------- +--R | c 2 +--R |- - %e +--R \| d +--R * +--R (2b x + e)log(f) 2 (2b x + e)log(f) +--R ---------------- +---+ ---------------- +--R 2 | c 2 +--R d (%e ) - 2d |- - %e - c +--R \| d +--R log(--------------------------------------------------------) +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R + +--R (- 3e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R 2%e %e - 2b d r0055 log(f) +--R / +--R 2b d log(f) +--R Type: Expression(Integer) +--E 281 + +--S 282 of 578 +d0055a:= D(m0055a,x) +--R +--R +--R (- 3e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R %e (%e ) +--R (258) ---------------------------------------- +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R Type: Expression(Integer) +--E 282 + +--S 283 of 578 +m0055b:= a0055.2-r0055 +--R +--R +--R (259) +--R (2b x + e)log(f) +--R (- 3e + 2a)log(f) ---------------- +--R +-+ ----------------- 2 +--R |c 2 %e +--R - |- %e atan(------------------) +--R \|d +-+ +--R |c +--R |- +--R \|d +--R + +--R (- 3e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R %e %e - b d r0055 log(f) +--R / +--R b d log(f) +--R Type: Expression(Integer) +--E 283 + +--S 284 of 578 +d0055b:= D(m0055b,x) +--R +--R +--R (- 3e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R %e (%e ) +--R (260) ---------------------------------------- +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R Type: Expression(Integer) +--E 284 + +--S 285 of 578 +t0056:= f^(a+5*b*x)/(c+d*f^(e+2*b*x)) +--R +--R +--R 5b x + a +--R f +--R (261) --------------- +--R 2b x + e +--R d f + c +--R Type: Expression(Integer) +--E 285 + +--S 286 of 578 +r0056:= -1/3/d^(5/2)*(3*c*f^(a-2*e+b*x)*d^(1/2)-f^(a-e+3*b*x)*d^(3/2)-_ + 3*c^(3/2)*f^(a-3*e)*(f^e)^(1/2)*_ + arctan(d^(1/2)*f^(b*x)*(f^e)^(1/2)/c^(1/2)))/b/log(f) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 286 + +--S 287 of 578 +a0056:= integrate(t0056,x) +--R +--R +--R (262) +--R [ +--R (- 5e + 2a)log(f) +--R +---+ ----------------- +--R | c 2 +--R 3c |- - %e +--R \| d +--R * +--R (2b x + e)log(f) 2 (2b x + e)log(f) +--R ---------------- +---+ ---------------- +--R 2 | c 2 +--R d (%e ) + 2d |- - %e - c +--R \| d +--R log(--------------------------------------------------------) +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R 2d %e (%e ) +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R - 6c %e %e +--R / +--R 2 +--R 6b d log(f) +--R , +--R +--R (2b x + e)log(f) +--R (- 5e + 2a)log(f) ---------------- +--R +-+ ----------------- 2 +--R |c 2 %e +--R 3c |- %e atan(------------------) +--R \|d +-+ +--R |c +--R |- +--R \|d +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R d %e (%e ) +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 +--R - 3c %e %e +--R / +--R 2 +--R 3b d log(f) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 287 + +--S 288 of 578 +m0056a:= a0056.1-r0056 +--R +--R +--R (263) +--R (- 5e + 2a)log(f) +--R +---+ ----------------- +--R | c 2 +--R 3c |- - %e +--R \| d +--R * +--R (2b x + e)log(f) 2 (2b x + e)log(f) +--R ---------------- +---+ ---------------- +--R 2 | c 2 +--R d (%e ) + 2d |- - %e - c +--R \| d +--R log(--------------------------------------------------------) +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R 2d %e (%e ) +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 2 +--R - 6c %e %e - 6b d r0056 log(f) +--R / +--R 2 +--R 6b d log(f) +--R Type: Expression(Integer) +--E 288 + +--S 289 of 578 +d0056a:= D(m0056a,x) +--R +--R +--R (- 5e + 2a)log(f) (2b x + e)log(f) 5 +--R ----------------- ---------------- +--R 2 2 +--R %e (%e ) +--R (264) ---------------------------------------- +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R Type: Expression(Integer) +--E 289 + +--S 290 of 578 +m0056b:= a0056.2-r0056 +--R +--R +--R (265) +--R (2b x + e)log(f) +--R (- 5e + 2a)log(f) ---------------- +--R +-+ ----------------- 2 +--R |c 2 %e +--R 3c |- %e atan(------------------) +--R \|d +-+ +--R |c +--R |- +--R \|d +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) 3 +--R ----------------- ---------------- +--R 2 2 +--R d %e (%e ) +--R + +--R (- 5e + 2a)log(f) (2b x + e)log(f) +--R ----------------- ---------------- +--R 2 2 2 +--R - 3c %e %e - 3b d r0056 log(f) +--R / +--R 2 +--R 3b d log(f) +--R Type: Expression(Integer) +--E 290 + +--S 291 of 578 +d0056b:= D(m0056b,x) +--R +--R +--R (- 5e + 2a)log(f) (2b x + e)log(f) 5 +--R ----------------- ---------------- +--R 2 2 +--R %e (%e ) +--R (266) ---------------------------------------- +--R (2b x + e)log(f) 2 +--R ---------------- +--R 2 +--R d (%e ) + c +--R Type: Expression(Integer) +--E 291 + +--S 292 of 578 +t0057:= x*exp(x)/(1+exp(1)^(2*x)) +--R +--R +--R x +--R x %e +--R (267) -------- +--R 2x +--R %e + 1 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 578 +r0057:= x*arctan(exp(x))-_ + 1/2*%i*polylog(2,-%i*exp(x))+_ + 1/2*%i*polylog(2,%i*exp(x)) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 293 + +--S 294 of 578 +a0057:= integrate(t0057,x) +--R +--R +--R x %A +--R ++ %A %e +--R (268) | --------- d%A +--R ++ 2%A +--R %e + 1 +--R Type: Union(Expression(Integer),...) +--E 294 + +--S 295 of 578 +m0057:= a0057-r0057 +--R +--R +--R x %A +--R ++ %A %e +--R (269) | --------- d%A - r0057 +--R ++ 2%A +--R %e + 1 +--R Type: Expression(Integer) +--E 295 + +--S 296 of 578 +d0057:= D(m0057,x) +--R +--R +--R x +--R x %e +--R (270) -------- +--R 2x +--R %e + 1 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 578 +t0058:= x^2*exp(x)/(1+exp(1)^(2*x)) +--R +--R +--R 2 x +--R x %e +--R (271) -------- +--R 2x +--R %e + 1 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 578 +r0058:= x^2*arctan(exp(x))-%i*x*_ + polylog(2,-%i*exp(x))+%i*x*polylog(2,%i*exp(x))+_ + %i*polylog(3,-%i*exp(x))-%i*polylog(3,%i*exp(x)) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 298 + +--S 299 of 578 +a0058:= integrate(t0058,x) +--R +--R +--R x 2 %A +--R ++ %A %e +--R (272) | --------- d%A +--R ++ 2%A +--R %e + 1 +--R Type: Union(Expression(Integer),...) +--E 299 + +--S 300 of 578 +m0058:= a0058-r0058 +--R +--R +--R x 2 %A +--R ++ %A %e +--R (273) | --------- d%A - r0058 +--R ++ 2%A +--R %e + 1 +--R Type: Expression(Integer) +--E 300 + +--S 301 of 578 +d0058:= D(m0058,x) +--R +--R +--R 2 x +--R x %e +--R (274) -------- +--R 2x +--R %e + 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 578 +t0059:= x^3*exp(x)/(1+exp(1)^(2*x)) +--R +--R +--R 3 x +--R x %e +--R (275) -------- +--R 2x +--R %e + 1 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 578 +r0059:= x^3*arctan(exp(x))-3/2*%i*x^2*polylog(2,-%i*exp(x))+_ + 3/2*%i*x^2*polylog(2,%i*exp(x))+_ + 3*%i*x*polylog(3,-%i*exp(x))-_ + 3*%i*x*polylog(3,%i*exp(x))-_ + 3*%i*polylog(4,-%i*exp(x))+_ + 3*%i*polylog(4,%i*exp(x)) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 303 + +--S 304 of 578 +a0059:= integrate(t0059,x) +--R +--R +--R x 3 %A +--R ++ %A %e +--R (276) | --------- d%A +--R ++ 2%A +--R %e + 1 +--R Type: Union(Expression(Integer),...) +--E 304 + +--S 305 of 578 +m0059:= a0059-r0059 +--R +--R +--R x 3 %A +--R ++ %A %e +--R (277) | --------- d%A - r0059 +--R ++ 2%A +--R %e + 1 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 578 +d0059:= D(m0059,x) +--R +--R +--R 3 x +--R x %e +--R (278) -------- +--R 2x +--R %e + 1 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 578 +t0060:= x*exp(x)/(1-exp(1)^(2*x)) +--R +--R +--R x +--R x %e +--R (279) - -------- +--R 2x +--R %e - 1 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 578 +r0060:= x*arctanh(exp(x))+1/2*polylog(2,-exp(x))-1/2*polylog(2,exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 308 + +--S 309 of 578 +a0060:= integrate(t0060,x) +--R +--R +--R x %A +--R ++ %A %e +--R (280) | - --------- d%A +--R ++ 2%A +--R %e - 1 +--R Type: Union(Expression(Integer),...) +--E 309 + +--S 310 of 578 +m0060:= a0060-r0060 +--R +--R +--R x %A +--R ++ %A %e +--R (281) | - --------- d%A - r0060 +--R ++ 2%A +--R %e - 1 +--R Type: Expression(Integer) +--E 310 + +--S 311 of 578 +d0060:= D(m0060,x) +--R +--R +--R x +--R x %e +--R (282) - -------- +--R 2x +--R %e - 1 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 578 +t0061:= x^2*exp(x)/(1-exp(1)^(2*x)) +--R +--R +--R 2 x +--R x %e +--R (283) - -------- +--R 2x +--R %e - 1 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 578 +r0061:= x^2*arctanh(exp(x))+x*polylog(2,-exp(x))-_ + x*polylog(2,exp(x))-_ + polylog(3,-exp(x))+polylog(3,exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 313 + +--S 314 of 578 +a0061:= integrate(t0061,x) +--R +--R +--R x 2 %A +--R ++ %A %e +--R (284) | - --------- d%A +--R ++ 2%A +--R %e - 1 +--R Type: Union(Expression(Integer),...) +--E 314 + +--S 315 of 578 +m0061:= a0061-r0061 +--R +--R +--R x 2 %A +--R ++ %A %e +--R (285) | - --------- d%A - r0061 +--R ++ 2%A +--R %e - 1 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 578 +d0061:= D(m0061,x) +--R +--R +--R 2 x +--R x %e +--R (286) - -------- +--R 2x +--R %e - 1 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 578 +t0062:= x^3*exp(x)/(1-exp(1)^(2*x)) +--R +--R +--R 3 x +--R x %e +--R (287) - -------- +--R 2x +--R %e - 1 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 578 +r0062:= x^3*arctanh(exp(x))+3/2*x^2*polylog(2,-exp(x))-_ + 3/2*x^2*polylog(2,exp(x))-3*x*polylog(3,-exp(x))+_ + 3*x*polylog(3,exp(x))+3*polylog(4,-exp(x))-3*polylog(4,exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 318 + +--S 319 of 578 +a0062:= integrate(t0062,x) +--R +--R +--R x 3 %A +--R ++ %A %e +--R (288) | - --------- d%A +--R ++ 2%A +--R %e - 1 +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 578 +m0062:= a0062-r0062 +--R +--R +--R x 3 %A +--R ++ %A %e +--R (289) | - --------- d%A - r0062 +--R ++ 2%A +--R %e - 1 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 578 +d0062:= D(m0062,x) +--R +--R +--R 3 x +--R x %e +--R (290) - -------- +--R 2x +--R %e - 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 578 +t0063:= f^x/(a+b*f^(2*x)) +--R +--R +--R x +--R f +--R (291) --------- +--R 2x +--R b f + a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 578 +r0063:= arctan(b^(1/2)*f^x/a^(1/2))/a^(1/2)/b^(1/2)/log(f) +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 323 + +--S 324 of 578 +a0063:= integrate(t0063,x) +--R +--R +--R (292) +--R +-----+ x log(f) 2 x log(f) +-----+ +--R b\|- a b (%e ) + 2a b %e - a\|- a b +--R log(----------------------------------------------------) +--R x log(f) 2 +--R b (%e ) + a +--R [---------------------------------------------------------, +--R +-----+ +--R 2log(f)\|- a b +--R +---+ x log(f) +--R \|a b %e +--R atan(----------------) +--R a +--R ----------------------] +--R +---+ +--R log(f)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 324 + +--S 325 of 578 +m0063a:= a0063.1-r0063 +--R +--R +--R (293) +--R +-----+ x log(f) 2 x log(f) +-----+ +--R b\|- a b (%e ) + 2a b %e - a\|- a b +--R log(----------------------------------------------------) +--R x log(f) 2 +--R b (%e ) + a +--R + +--R +-----+ +--R - 2r0063 log(f)\|- a b +--R / +--R +-----+ +--R 2log(f)\|- a b +--R Type: Expression(Integer) +--E 325 + +--S 326 of 578 +d0063a:= D(m0063a,x) +--R +--R +--R x log(f) +--R %e +--R (294) ------------------- +--R x log(f) 2 +--R b (%e ) + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 578 +m0063b:= a0063.2-r0063 +--R +--R +--R +---+ x log(f) +--R \|a b %e +---+ +--R atan(----------------) - r0063 log(f)\|a b +--R a +--R (295) ------------------------------------------- +--R +---+ +--R log(f)\|a b +--R Type: Expression(Integer) +--E 327 + +--S 328 of 578 +d0063b:= D(m0063b,x) +--R +--R +--R x log(f) +--R %e +--R (296) ------------------- +--R x log(f) 2 +--R b (%e ) + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 578 +t0064:= x*f^x/(a+b*f^(2*x)) +--R +--R +--R x +--R x f +--R (297) --------- +--R 2x +--R b f + a +--R Type: Expression(Integer) +--E 329 + +--S 330 of 578 +r0064:= 1/2*(2*x*arctan(b^(1/2)*f^x/a^(1/2))*log(f)-_ + %i*polylog(2,-%i*b^(1/2)*f^x/a^(1/2))+_ + %i*polylog(2,%i*b^(1/2)*f^x/a^(1/2)))/a^(1/2)/b^(1/2)/log(f)^2 +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 330 + +--S 331 of 578 +a0064:= integrate(t0064,x) +--R +--R +--R x %A +--R ++ %A f +--R (298) | ---------- d%A +--R ++ 2%A +--R b f + a +--R Type: Union(Expression(Integer),...) +--E 331 + +--S 332 of 578 +m0064:= a0064-r0064 +--R +--R +--R x %A +--R ++ %A f +--R (299) | ---------- d%A - r0064 +--R ++ 2%A +--R b f + a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 578 +d0064:= D(m0064,x) +--R +--R +--R x +--R x f +--R (300) --------- +--R 2x +--R b f + a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 578 +t0065:= x^2*f^x/(a+b*f^(2*x)) +--R +--R +--R 2 x +--R x f +--R (301) --------- +--R 2x +--R b f + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 578 +r0065:= (x^2*arctan(b^(1/2)*f^x/a^(1/2))*log(f)^2-_ + %i*x*polylog(2,-%i*b^(1/2)*f^x/a^(1/2))*log(f)+_ + %i*x*polylog(2,%i*b^(1/2)*f^x/a^(1/2))*log(f)+_ + %i*polylog(3,-%i*b^(1/2)*f^x/a^(1/2))-_ + %i*polylog(3,%i*b^(1/2)*f^x/a^(1/2)))/a^(1/2)/b^(1/2)/log(f)^3 +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 335 + +--S 336 of 578 +a0065:= integrate(t0065,x) +--R +--R +--R x 2 %A +--R ++ %A f +--R (302) | ---------- d%A +--R ++ 2%A +--R b f + a +--R Type: Union(Expression(Integer),...) +--E 336 + +--S 337 of 578 +m0065:= a0065-r0065 +--R +--R +--R x 2 %A +--R ++ %A f +--R (303) | ---------- d%A - r0065 +--R ++ 2%A +--R b f + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 578 +d0065:= D(m0065,x) +--R +--R +--R 2 x +--R x f +--R (304) --------- +--R 2x +--R b f + a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 578 +t0066:= x^3*f^x/(a+b*f^(2*x)) +--R +--R +--R 3 x +--R x f +--R (305) --------- +--R 2x +--R b f + a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 578 +r0066:= 1/2*(2*x^3*arctan(b^(1/2)*f^x/a^(1/2))*log(f)^3-_ + 3*%i*x^2*polylog(2,-%i*b^(1/2)*f^x/a^(1/2))*log(f)^2+_ + 3*%i*x^2*polylog(2,%i*b^(1/2)*f^x/a^(1/2))*log(f)^2+_ + 6*%i*x*polylog(3,-%i*b^(1/2)*f^x/a^(1/2))*log(f)-_ + 6*%i*x*polylog(3,%i*b^(1/2)*f^x/a^(1/2))*log(f)-_ + 6*%i*polylog(4,-%i*b^(1/2)*f^x/a^(1/2))+_ + 6*%i*polylog(4,%i*b^(1/2)*f^x/a^(1/2)))/a^(1/2)/b^(1/2)/log(f)^4 +--R +--R There are no library operations named arctan +--R Use HyperDoc Browse or issue +--R )what op arctan +--R to learn if there is any operation containing " arctan " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctan with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 340 + +--S 341 of 578 +a0066:= integrate(t0066,x) +--R +--R +--R x 3 %A +--R ++ %A f +--R (306) | ---------- d%A +--R ++ 2%A +--R b f + a +--R Type: Union(Expression(Integer),...) +--E 341 + +--S 342 of 578 +m0066:= a0066-r0066 +--R +--R +--R x 3 %A +--R ++ %A f +--R (307) | ---------- d%A - r0066 +--R ++ 2%A +--R b f + a +--R Type: Expression(Integer) +--E 342 + +--S 343 of 578 +d0066:= D(m0066,x) +--R +--R +--R 3 x +--R x f +--R (308) --------- +--R 2x +--R b f + a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 578 +t0067:= x/(3+3*exp(x)+exp(1)^(2*x)) +--R +--R +--R x +--R (309) --------------- +--R 2x x +--R %e + 3%e + 3 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 578 +r0067:= -1/3*%i*x^2*3^(1/2)/(3-%i*3^(1/2))+_ + 1/3*%i*x^2*3^(1/2)/(3+%i*3^(1/2))+_ + 2/3*%i*x*log(1+2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_ + 2/3*%i*x*log(1+2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))+_ + 2/3*%i*polylog(2,-2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_ + 2/3*%i*polylog(2,-2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 345 + +--S 346 of 578 +a0067:= integrate(t0067,x) +--R +--R +--R x +--R ++ %A +--R (310) | ----------------- d%A +--R ++ 2%A %A +--R %e + 3%e + 3 +--R Type: Union(Expression(Integer),...) +--E 346 + +--S 347 of 578 +m0067:= a0067-r0067 +--R +--R +--R x +--R ++ %A +--R (311) | ----------------- d%A - r0067 +--R ++ 2%A %A +--R %e + 3%e + 3 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 578 +d0067:= D(m0067,x) +--R +--R +--R x +--R (312) --------------- +--R 2x x +--R %e + 3%e + 3 +--R Type: Expression(Integer) +--E 348 + +--S 349 of 578 +t0068:= x/(a+b*exp(x)+c*exp(1)^(2*x)) +--R +--R +--R x +--R (313) ------------------ +--R 2x x +--R c %e + b %e + a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 578 +r0068:= c*x^2/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_ + c*x^2/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 2*c*x*log(1+2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/_ + (b-(b^2-4*a*c)^(1/2))+2*c*x*log(1+2*c*exp(x)/_ + (b+(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 2*c*polylog(2,-2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))+_ + 2*c*polylog(2,-2*c*exp(x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 350 + +--S 351 of 578 +a0068:= integrate(t0068,x) +--R +--R +--R x +--R ++ %A +--R (314) | -------------------- d%A +--R ++ 2%A %A +--R c %e + b %e + a +--R Type: Union(Expression(Integer),...) +--E 351 + +--S 352 of 578 +m0068:= a0068-r0068 +--R +--R +--R x +--R ++ %A +--R (315) | -------------------- d%A - r0068 +--R ++ 2%A %A +--R c %e + b %e + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 578 +d0068:= D(m0068,x) +--R +--R +--R x +--R (316) ------------------ +--R 2x x +--R c %e + b %e + a +--R Type: Expression(Integer) +--E 353 + +--S 354 of 578 +t0069:= x^2/(-1+exp(x)+exp(1)^(2*x)) +--R +--R +--R 2 +--R x +--R (317) -------------- +--R 2x x +--R %e + %e - 1 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 578 +r0069:= 2/15*x^3*5^(1/2)/(1-5^(1/2))-2/15*x^3*5^(1/2)/(5^(1/2)+1)-_ + 2/5*x^2*log(1+2*exp(x)/(1-5^(1/2)))*5^(1/2)/(1-5^(1/2))+_ + 2/5*x^2*log(1+2*exp(x)/(5^(1/2)+1))*5^(1/2)/(5^(1/2)+1)-_ + 4/5*x*polylog(2,-2*exp(x)/(1-5^(1/2)))*5^(1/2)/(1-5^(1/2))+_ + 4/5*x*polylog(2,-2*exp(x)/(5^(1/2)+1))*5^(1/2)/(5^(1/2)+1)+_ + 4/5*polylog(3,-2*exp(x)/(1-5^(1/2)))*5^(1/2)/(1-5^(1/2))-_ + 4/5*polylog(3,-2*exp(x)/(5^(1/2)+1))*5^(1/2)/(5^(1/2)+1) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 355 + +--S 356 of 578 +a0069:= integrate(t0069,x) +--R +--R +--R x 2 +--R ++ %A +--R (318) | ---------------- d%A +--R ++ 2%A %A +--R %e + %e - 1 +--R Type: Union(Expression(Integer),...) +--E 356 + +--S 357 of 578 +m0069:= a0069-r0069 +--R +--R +--R x 2 +--R ++ %A +--R (319) | ---------------- d%A - r0069 +--R ++ 2%A %A +--R %e + %e - 1 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 578 +d0069:= D(m0069,x) +--R +--R +--R 2 +--R x +--R (320) -------------- +--R 2x x +--R %e + %e - 1 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 578 +t0070:= x^2/(3+3*exp(x)+exp(1)^(2*x)) +--R +--R +--R 2 +--R x +--R (321) --------------- +--R 2x x +--R %e + 3%e + 3 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 578 +r0070:= -2/9*%i*x^3*3^(1/2)/(3-%i*3^(1/2))+2/9*%i*x^3*3^(1/2)/(3+%i*3^(1/2))+_ + 2/3*%i*x^2*log(1+2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_ + 2/3*%i*x^2*log(1+2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))+_ + 4/3*%i*x*polylog(2,-2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))-_ + 4/3*%i*x*polylog(2,-2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2))-_ + 4/3*%i*polylog(3,-2*exp(x)/(3-%i*3^(1/2)))*3^(1/2)/(3-%i*3^(1/2))+_ + 4/3*%i*polylog(3,-2*exp(x)/(3+%i*3^(1/2)))*3^(1/2)/(3+%i*3^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 360 + +--S 361 of 578 +a0070:= integrate(t0070,x) +--R +--R +--R x 2 +--R ++ %A +--R (322) | ----------------- d%A +--R ++ 2%A %A +--R %e + 3%e + 3 +--R Type: Union(Expression(Integer),...) +--E 361 + +--S 362 of 578 +m0070:= a0070-r0070 +--R +--R +--R x 2 +--R ++ %A +--R (323) | ----------------- d%A - r0070 +--R ++ 2%A %A +--R %e + 3%e + 3 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 578 +d0070:= D(m0070,x) +--R +--R +--R 2 +--R x +--R (324) --------------- +--R 2x x +--R %e + 3%e + 3 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 578 +t0071:= x^2/(a+b*exp(x)+c*exp(1)^(2*x)) +--R +--R +--R 2 +--R x +--R (325) ------------------ +--R 2x x +--R c %e + b %e + a +--R Type: Expression(Integer) +--E 364 + +--S 365 of 578 +r0071:= 2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_ + 2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 2*c*x^2*log(1+2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))+2*c*x^2*log(1+2*c*exp(x)/_ + (b+(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 4*c*x*polylog(2,-2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))+_ + 4*c*x*polylog(2,-2*c*exp(x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))+_ + 4*c*polylog(3,-2*c*exp(x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_ + 4*c*polylog(3,-2*c*exp(x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 365 + +--S 366 of 578 +a0071:= integrate(t0071,x) +--R +--R +--R x 2 +--R ++ %A +--R (326) | -------------------- d%A +--R ++ 2%A %A +--R c %e + b %e + a +--R Type: Union(Expression(Integer),...) +--E 366 + +--S 367 of 578 +m0071:= a0071-r0071 +--R +--R +--R x 2 +--R ++ %A +--R (327) | -------------------- d%A - r0071 +--R ++ 2%A %A +--R c %e + b %e + a +--R Type: Expression(Integer) +--E 367 + +--S 368 of 578 +d0071:= D(m0071,x) +--R +--R +--R 2 +--R x +--R (328) ------------------ +--R 2x x +--R c %e + b %e + a +--R Type: Expression(Integer) +--E 368 + +--S 369 of 578 +t0072:= 1/(1+2*f^(c+d*x)+f^(2*c+2*d*x)) +--R +--R +--R 1 +--R (329) -------------------------- +--R 2d x + 2c d x + c +--R f + 2f + 1 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 578 +r0072:= x+1/d/(1+f^(c+d*x))/log(f)-log(1+f^(c+d*x))/d/log(f) +--R +--R +--R (330) +--R d x + c d x + c d x + c +--R (- f - 1)log(f + 1) + d x log(f)f + d x log(f) + 1 +--R ----------------------------------------------------------------------- +--R d x + c +--R d log(f)f + d log(f) +--R Type: Expression(Integer) +--E 370 + +--S 371 of 578 +a0072:= integrate(t0072,x) +--R +--R +--R (331) +--R (d x + c)log(f) (d x + c)log(f) +--R (- %e - 1)log(%e + 1) +--R + +--R (d x + c)log(f) +--R d x log(f)%e + d x log(f) + 1 +--R / +--R (d x + c)log(f) +--R d log(f)%e + d log(f) +--R Type: Union(Expression(Integer),...) +--E 371 + +--S 372 of 578 +m0072:= a0072-r0072 +--R +--R +--R (332) +--R d x + c (d x + c)log(f) d x + c +--R ((- f - 1)%e - f - 1) +--R * +--R (d x + c)log(f) +--R log(%e + 1) +--R + +--R d x + c (d x + c)log(f) d x + c d x + c +--R ((f + 1)%e + f + 1)log(f + 1) +--R + +--R (d x + c)log(f) d x + c +--R - %e + f +--R / +--R d x + c (d x + c)log(f) d x + c +--R (d log(f)f + d log(f))%e + d log(f)f +--R + +--R d log(f) +--R Type: Expression(Integer) +--E 372 + +--S 373 of 578 +d0072:= D(m0072,x) +--R +--R +--R (333) +--R (d x + c)log(f) 2 (d x + c)log(f) d x + c 2 d x + c +--R - (%e ) - 2%e + (f ) + 2f +--R / +--R d x + c 2 d x + c (d x + c)log(f) 2 +--R ((f ) + 2f + 1)(%e ) +--R + +--R d x + c 2 d x + c (d x + c)log(f) d x + c 2 d x + c +--R (2(f ) + 4f + 2)%e + (f ) + 2f +--R + +--R 1 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 578 +t0073:= 1/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x)) +--R +--R +--R 1 +--R (334) ----------------------------- +--R 2d x + 2c d x + c +--R c f + b f + a +--R Type: Expression(Integer) +--E 374 + +--S 375 of 578 +r0073:= x/a+b*arctanh((b+2*c*f^(c+d*x))/(b^2-4*a*c)^(1/2))/a/_ + (b^2-4*a*c)^(1/2)/d/log(f)-1/2*log(a+b*f^(c+d*x)+_ + c*f^(2*c+2*d*x))/a/d/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 375 + +--S 376 of 578 +a0073:= integrate(t0073,x) +--R +--R +--R (335) +--R [ +--R +-----------+ +--R | 2 (d x + c)log(f) 2 (d x + c)log(f) +--R - \|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 | 2 (d x + c)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (d x + c)log(f) +--R (2b c\|- 4a c + b - 8a c + 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b - 4a b c + b +--R / +--R (d x + c)log(f) 2 (d x + c)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R 2d x log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a d log(f)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 (d x + c)log(f) 2 (d x + c)log(f) +--R - \|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (d x + c)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R - 2b atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R 2d x log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a d log(f)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 376 + +--S 377 of 578 +m0073:= a0073-r0073 +--R +--R There are 12 exposed and 3 unexposed library operations named - +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op - +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named - +--R with argument type(s) +--R List(Expression(Integer)) +--R Variable(r0073) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 377 + +--S 378 of 578 +d0073:= D(m0073,x) +--R +--R +--R (336) 0 +--R Type: Polynomial(Integer) +--E 378 + +--S 379 of 578 +t0074:= x/(1+2*f^(c+d*x)+f^(2*c+2*d*x)) +--R +--R +--R x +--R (337) -------------------------- +--R 2d x + 2c d x + c +--R f + 2f + 1 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 578 +r0074:= 1/2*x^2-x/d/log(f)+log(1+f^(c+d*x))/d^2/log(f)^2+_ + x*(1/d/(1+f^(c+d*x))/log(f)-log(1+f^(c+d*x))/d/log(f))-_ + polylog(2,-f^(c+d*x))/d^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 380 + +--S 381 of 578 +a0074:= integrate(t0074,x) +--R +--R +--R x +--R ++ %A +--R (338) | ---------------------------- d%A +--R ++ 2%A d + 2c %A d + c +--R f + 2f + 1 +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 578 +m0074:= a0074-r0074 +--R +--R +--R x +--R ++ %A +--R (339) | ---------------------------- d%A - r0074 +--R ++ 2%A d + 2c %A d + c +--R f + 2f + 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 578 +d0074:= D(m0074,x) +--R +--R +--R x +--R (340) -------------------------- +--R 2d x + 2c d x + c +--R f + 2f + 1 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 578 +t0075:= x/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x)) +--R +--R +--R x +--R (341) ----------------------------- +--R 2d x + 2c d x + c +--R c f + b f + a +--R Type: Expression(Integer) +--E 384 + +--S 385 of 578 +r0075:= c*x^2/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_ + c*x^2/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 2*c*x*log(1+2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d/log(f)+_ + 2*c*x*log(1+2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d/log(f)-_ + 2*c*polylog(2,-2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d^2/log(f)^2+_ + 2*c*polylog(2,-2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 385 + +--S 386 of 578 +a0075:= integrate(t0075,x) +--R +--R +--R x +--R ++ %A +--R (342) | ------------------------------- d%A +--R ++ 2%A d + 2c %A d + c +--R c f + b f + a +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 578 +m0075:= a0075-r0075 +--R +--R +--R x +--R ++ %A +--R (343) | ------------------------------- d%A - r0075 +--R ++ 2%A d + 2c %A d + c +--R c f + b f + a +--R Type: Expression(Integer) +--E 387 + +--S 388 of 578 +d0075:= D(m0075,x) +--R +--R +--R x +--R (344) ----------------------------- +--R 2d x + 2c d x + c +--R c f + b f + a +--R Type: Expression(Integer) +--E 388 + +--S 389 of 578 +t0076:= x^2/(1+2*f^(c+d*x)+f^(2*c+2*d*x)) +--R +--R +--R 2 +--R x +--R (345) -------------------------- +--R 2d x + 2c d x + c +--R f + 2f + 1 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 578 +r0076:= 1/3*x^3-x^2/d/log(f)+2*x*log(1+f^(c+d*x))/d^2/log(f)^2+_ + x^2*(1/d/(1+f^(c+d*x))/log(f)-log(1+f^(c+d*x))/d/log(f))+_ + 2*(1-d*x*log(f))*polylog(2,-f^(c+d*x))/d^3/log(f)^3+_ + 2*polylog(3,-f^(c+d*x))/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 390 + +--S 391 of 578 +a0076:= integrate(t0076,x) +--R +--R +--R x 2 +--R ++ %A +--R (346) | ---------------------------- d%A +--R ++ 2%A d + 2c %A d + c +--R f + 2f + 1 +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 578 +m0076:= a0076-r0076 +--R +--R +--R x 2 +--R ++ %A +--R (347) | ---------------------------- d%A - r0076 +--R ++ 2%A d + 2c %A d + c +--R f + 2f + 1 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 578 +d0076:= D(m0076,x) +--R +--R +--R 2 +--R x +--R (348) -------------------------- +--R 2d x + 2c d x + c +--R f + 2f + 1 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 578 +t0077:= x^2/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x)) +--R +--R +--R 2 +--R x +--R (349) ----------------------------- +--R 2d x + 2c d x + c +--R c f + b f + a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 578 +r0077:= 2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))-_ + 2/3*c*x^3/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))-_ + 2*c*x^2*log(1+2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d/log(f)+_ + 2*c*x^2*log(1+2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d/log(f)-_ + 4*c*x*polylog(2,-2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d^2/log(f)^2+_ + 4*c*x*polylog(2,-2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d^2/log(f)^2+_ + 4*c*polylog(3,-2*c*f^(c+d*x)/(b-(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/d^3/log(f)^3-_ + 4*c*polylog(3,-2*c*f^(c+d*x)/(b+(b^2-4*a*c)^(1/2)))/_ + (b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 395 + +--S 396 of 578 +a0077:= integrate(t0077,x) +--R +--R +--R x 2 +--R ++ %A +--R (350) | ------------------------------- d%A +--R ++ 2%A d + 2c %A d + c +--R c f + b f + a +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 578 +m0077:= a0077-r0077 +--R +--R +--R x 2 +--R ++ %A +--R (351) | ------------------------------- d%A - r0077 +--R ++ 2%A d + 2c %A d + c +--R c f + b f + a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 578 +d0077:= D(m0077,x) +--R +--R +--R 2 +--R x +--R (352) ----------------------------- +--R 2d x + 2c d x + c +--R c f + b f + a +--R Type: Expression(Integer) +--E 398 + +--S 399 of 578 +t0078:= 1/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x)) +--R +--R +--R 1 +--R (353) ----------------------------- +--R 2h x + 2g h x + g +--R c f + b f + a +--R Type: Expression(Integer) +--E 399 + +--S 400 of 578 +r0078:= x/a+b*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/a/_ + (b^2-4*a*c)^(1/2)/h/log(f)-1/2*log(a+b*f^(g+h*x)+_ + c*f^(2*g+2*h*x))/a/h/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 400 + +--S 401 of 578 +a0078:= integrate(t0078,x) +--R +--R +--R (354) +--R [ +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b - 8a c + 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b - 4a b c + b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R 2h x log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R - 2b atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R 2h x log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 401 + +--S 402 of 578 +m0078a:= a0078.1-r0078 +--R +--R +--R (355) +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b - 8a c + 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b - 4a b c + b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R (2h x - 2a h r0078)log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R Type: Expression(Integer) +--E 402 + +--S 403 of 578 +d0078a:= D(m0078a,x) +--R +--R +--R 1 +--R (356) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 578 +m0078b:= a0078.2-r0078 +--R +--R +--R (357) +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R - 2b atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (2h x - 2a h r0078)log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R Type: Expression(Integer) +--E 404 + +--S 405 of 578 +d0078b:= D(m0078b,x) +--R +--R +--R 1 +--R (358) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression(Integer) +--E 405 + +--S 406 of 578 +t0079:= 1/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x)) +--R +--R +--R 1 +--R (359) ----------------------------- +--R 2h x + 2g h x + g +--R c f + b f + a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 578 +r0079:= x/a+b*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/a/_ + (b^2-4*a*c)^(1/2)/h/log(f)-1/2*log(a+b*f^(g+h*x)+_ + c*f^(2*g+2*h*x))/a/h/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 407 + +--S 408 of 578 +a0079:= integrate(t0079,x) +--R +--R +--R (360) +--R [ +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b - 8a c + 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b - 4a b c + b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R 2h x log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R - 2b atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R 2h x log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 408 + +--S 409 of 578 +m0079a:= a0079.1-r0079 +--R +--R +--R (361) +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R b +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b - 8a c + 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b - 4a b c + b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R (2h x - 2a h r0079)log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R Type: Expression(Integer) +--E 409 + +--S 410 of 578 +d0079a:= D(m0079a,x) +--R +--R +--R 1 +--R (362) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 578 +m0079b:= a0079.2-r0079 +--R +--R +--R (363) +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - \|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R - 2b atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (2h x - 2a h r0079)log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R Type: Expression(Integer) +--E 411 + +--S 412 of 578 +d0079b:= D(m0079b,x) +--R +--R +--R 1 +--R (364) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression(Integer) +--E 412 + +--S 413 of 578 +t0080:= (d+e*f^(g+h*x))/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x)) +--R +--R +--R h x + g +--R e f + d +--R (365) ----------------------------- +--R 2h x + 2g h x + g +--R c f + b f + a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 578 +r0080:= d*x/a+(b*d-2*a*e)*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/_ + a/(b^2-4*a*c)^(1/2)/h/log(f)-1/2*d*log(a+b*f^(g+h*x)+_ + c*f^(2*g+2*h*x))/a/h/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 414 + +--S 415 of 578 +a0080:= integrate(t0080,x) +--R +--R +--R (366) +--R [ +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R (2a e - b d) +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b + 8a c - 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b + 4a b c - b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R 2d h x log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R (4a e - 2b d)atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R 2d h x log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 415 + +--S 416 of 578 +m0080a:= a0080.1-r0080 +--R +--R +--R (367) +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R (2a e - b d) +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b + 8a c - 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b + 4a b c - b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R (2d h x - 2a h r0080)log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R Type: Expression(Integer) +--E 416 + +--S 417 of 578 +d0080a:= D(m0080a,x) +--R +--R +--R (h x + g)log(f) +--R e %e + d +--R (368) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression(Integer) +--E 417 + +--S 418 of 578 +m0080b:= a0080.2-r0080 +--R +--R +--R (369) +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R (4a e - 2b d)atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (2d h x - 2a h r0080)log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R Type: Expression(Integer) +--E 418 + +--S 419 of 578 +d0080b:= D(m0080b,x) +--R +--R +--R (h x + g)log(f) +--R e %e + d +--R (370) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 578 +t0081:= (d+e*f^(g+h*x))/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x)) +--R +--R +--R h x + g +--R e f + d +--R (371) ----------------------------- +--R 2h x + 2g h x + g +--R c f + b f + a +--R Type: Expression(Integer) +--E 420 + +--S 421 of 578 +r0081:= d*x/a+(b*d-2*a*e)*arctanh((b+2*c*f^(g+h*x))/(b^2-4*a*c)^(1/2))/_ + a/(b^2-4*a*c)^(1/2)/h/log(f)-1/2*d*log(a+b*f^(g+h*x)+_ + c*f^(2*g+2*h*x))/a/h/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 421 + +--S 422 of 578 +a0081:= integrate(t0081,x) +--R +--R +--R (372) +--R [ +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R (2a e - b d) +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b + 8a c - 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b + 4a b c - b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R 2d h x log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R (4a e - 2b d)atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R 2d h x log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 422 + +--S 423 of 578 +m0081a:= a0081.1-r0081 +--R +--R +--R (373) +--R +-----------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|- 4a c + b log(c (%e ) + b %e + a) +--R + +--R (2a e - b d) +--R * +--R log +--R +-----------+ +--R 2 | 2 (h x + g)log(f) 2 +--R 2c \|- 4a c + b (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (h x + g)log(f) +--R (2b c\|- 4a c + b + 8a c - 2b c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2a c + b )\|- 4a c + b + 4a b c - b +--R / +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R + +--R +-----------+ +--R | 2 +--R (2d h x - 2a h r0081)log(f)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a h log(f)\|- 4a c + b +--R Type: Expression(Integer) +--E 423 + +--S 424 of 578 +d0081a:= D(m0081a,x) +--R +--R +--R (h x + g)log(f) +--R e %e + d +--R (374) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 578 +m0081b:= a0081.2-r0081 +--R +--R +--R (375) +--R +---------+ +--R | 2 (h x + g)log(f) 2 (h x + g)log(f) +--R - d\|4a c - b log(c (%e ) + b %e + a) +--R + +--R +---------+ +---------+ +--R | 2 (h x + g)log(f) | 2 +--R 2c\|4a c - b %e + b\|4a c - b +--R (4a e - 2b d)atan(-----------------------------------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R | 2 +--R (2d h x - 2a h r0081)log(f)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a h log(f)\|4a c - b +--R Type: Expression(Integer) +--E 425 + +--S 426 of 578 +d0081b:= D(m0081b,x) +--R +--R +--R (h x + g)log(f) +--R e %e + d +--R (376) ------------------------------------------------ +--R (h x + g)log(f) 2 (h x + g)log(f) +--R c (%e ) + b %e + a +--R Type: Expression(Integer) +--E 426 + +--S 427 of 578 +t0082:= x^2/(2+f^(-c-d*x)+f^(c+d*x)) +--R +--R +--R 2 +--R x +--R (377) ------------------------- +--R d x + c - d x - c +--R f + f + 2 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 578 +r0082:= x^2/d/log(f)-x^2/d/(1+f^(c+d*x))/log(f)-_ + 2*x*log(1+f^(c+d*x))/d^2/log(f)^2-_ + 2*polylog(2,-f^(c+d*x))/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 428 + +--S 429 of 578 +a0082:= integrate(t0082,x) +--R +--R +--R x 2 +--R ++ %A +--R (378) | --------------------------- d%A +--R ++ %A d + c - %A d - c +--R f + f + 2 +--R Type: Union(Expression(Integer),...) +--E 429 + +--S 430 of 578 +m0082:= a0082-r0082 +--R +--R +--R x 2 +--R ++ %A +--R (379) | --------------------------- d%A - r0082 +--R ++ %A d + c - %A d - c +--R f + f + 2 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 578 +d0082:= D(m0082,x) +--R +--R +--R 2 +--R x +--R (380) ------------------------- +--R d x + c - d x - c +--R f + f + 2 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 578 +t0083:= 1/(1-exp(1)^(-x)+2*exp(x)) +--R +--R +--R 1 +--R (381) ---------------- +--R x - x +--R 2%e - %e + 1 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 578 +r0083:= -2/3*arctanh(1/3+4/3*exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 433 + +--S 434 of 578 +a0083:= integrate(t0083,x) +--R +--R +--R x x +--R log(2%e - 1) - log(%e + 1) +--R (382) ---------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 434 + +--S 435 of 578 +m0083:= a0083-r0083 +--R +--R +--R x x +--R log(2%e - 1) - log(%e + 1) - 3r0083 +--R (383) ------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 435 + +--S 436 of 578 +d0083:= D(m0083,x) +--R +--R +--R x +--R %e +--R (384) ----------------- +--R x 2 x +--R 2(%e ) + %e - 1 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 578 +t0084:= x^2/(a+b*exp(1)^(-x)+c*exp(x)) +--R +--R +--R 2 +--R x +--R (385) ------------------- +--R x - x +--R c %e + b %e + a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 578 +r0084:= (x^2*log(-(a-(a^2-4*b*c)^(1/2)+2*c*exp(x))/(-a+(a^2-4*b*c)^(1/2)))-_ + x^2*log((a+(a^2-4*b*c)^(1/2)+2*c*exp(x))/(a+(a^2-4*b*c)^(1/2)))+_ + 2*x*polylog(2,2*c*exp(x)/(-a+(a^2-4*b*c)^(1/2)))-_ + 2*x*polylog(2,-2*c*exp(x)/(a+(a^2-4*b*c)^(1/2)))-_ + 2*polylog(3,2*c*exp(x)/(-a+(a^2-4*b*c)^(1/2)))+_ + 2*polylog(3,-2*c*exp(x)/(a+(a^2-4*b*c)^(1/2))))/(a^2-4*b*c)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 438 + +--S 439 of 578 +a0084:= integrate(t0084,x) +--R +--R +--R x 2 +--R ++ %A +--R (386) | --------------------- d%A +--R ++ %A - %A +--R c %e + b %e + a +--R Type: Union(Expression(Integer),...) +--E 439 + +--S 440 of 578 +m0084:= a0084-r0084 +--R +--R +--R x 2 +--R ++ %A +--R (387) | --------------------- d%A - r0084 +--R ++ %A - %A +--R c %e + b %e + a +--R Type: Expression(Integer) +--E 440 + +--S 441 of 578 +d0084:= D(m0084,x) +--R +--R +--R 2 +--R x +--R (388) ------------------- +--R x - x +--R c %e + b %e + a +--R Type: Expression(Integer) +--E 441 + +--S 442 of 578 +t0085:= 1/(a+b*f^(-c-d*x)+c*f^(c+d*x)) +--R +--R +--R 1 +--R (389) ----------------------------- +--R d x + c - d x - c +--R c f + b f + a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 578 +r0085:= -2*arctanh((a+2*c*f^(c+d*x))/(a^2-4*b*c)^(1/2))/_ + (a^2-4*b*c)^(1/2)/d/log(f) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 443 + +--S 444 of 578 +a0085:= integrate(t0085,x) +--R +--R +--R (390) +--R [ +--R log +--R +-----------+ +--R 2 | 2 (d x + c)log(f) 2 +--R 2c \|- 4b c + a (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (d x + c)log(f) +--R (2a c\|- 4b c + a + 8b c - 2a c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2b c + a )\|- 4b c + a + 4a b c - a +--R / +--R (d x + c)log(f) 2 (d x + c)log(f) +--R c (%e ) + a %e + b +--R / +--R +-----------+ +--R | 2 +--R d log(f)\|- 4b c + a +--R , +--R +---------+ +---------+ +--R | 2 (d x + c)log(f) | 2 +--R 2c\|4b c - a %e + a\|4b c - a +--R 2atan(-----------------------------------------------) +--R 2 +--R 4b c - a +--R ------------------------------------------------------] +--R +---------+ +--R | 2 +--R d log(f)\|4b c - a +--R Type: Union(List(Expression(Integer)),...) +--E 444 + +--S 445 of 578 +m0085a:= a0085.1-r0085 +--R +--R +--R (391) +--R log +--R +-----------+ +--R 2 | 2 (d x + c)log(f) 2 +--R 2c \|- 4b c + a (%e ) +--R + +--R +-----------+ +--R | 2 2 2 (d x + c)log(f) +--R (2a c\|- 4b c + a + 8b c - 2a c)%e +--R + +--R +-----------+ +--R 2 | 2 3 +--R (- 2b c + a )\|- 4b c + a + 4a b c - a +--R / +--R (d x + c)log(f) 2 (d x + c)log(f) +--R c (%e ) + a %e + b +--R + +--R +-----------+ +--R | 2 +--R - d r0085 log(f)\|- 4b c + a +--R / +--R +-----------+ +--R | 2 +--R d log(f)\|- 4b c + a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 578 +d0085a:= D(m0085a,x) +--R +--R +--R (d x + c)log(f) +--R %e +--R (392) ------------------------------------------------ +--R (d x + c)log(f) 2 (d x + c)log(f) +--R c (%e ) + a %e + b +--R Type: Expression(Integer) +--E 446 + +--S 447 of 578 +m0085b:= a0085.2-r0085 +--R +--R +--R (393) +--R +---------+ +---------+ +--R | 2 (d x + c)log(f) | 2 +--R 2c\|4b c - a %e + a\|4b c - a +--R 2atan(-----------------------------------------------) +--R 2 +--R 4b c - a +--R + +--R +---------+ +--R | 2 +--R - d r0085 log(f)\|4b c - a +--R / +--R +---------+ +--R | 2 +--R d log(f)\|4b c - a +--R Type: Expression(Integer) +--E 447 + +--S 448 of 578 +d0085b:= D(m0085b,x) +--R +--R +--R (d x + c)log(f) +--R %e +--R (394) ------------------------------------------------ +--R (d x + c)log(f) 2 (d x + c)log(f) +--R c (%e ) + a %e + b +--R Type: Expression(Integer) +--E 448 + +--S 449 of 578 +t0086:= x/(a+b*f^(-c-d*x)+c*f^(c+d*x)) +--R +--R +--R x +--R (395) ----------------------------- +--R d x + c - d x - c +--R c f + b f + a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 578 +r0086:= (x*log(-(a-(a^2-4*b*c)^(1/2)+2*c*f^(c+d*x))/_ + (-a+(a^2-4*b*c)^(1/2)))*d*log(f)-x*log((a+(a^2-4*b*c)^(1/2)+_ + 2*c*f^(c+d*x))/(a+(a^2-4*b*c)^(1/2)))*d*log(f)+_ + polylog(2,2*c*f^(c+d*x)/(-a+(a^2-4*b*c)^(1/2)))-_ + polylog(2,-2*c*f^(c+d*x)/(a+(a^2-4*b*c)^(1/2))))/_ + (a^2-4*b*c)^(1/2)/d^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 450 + +--S 451 of 578 +a0086:= integrate(t0086,x) +--R +--R +--R x +--R ++ %A +--R (396) | ------------------------------- d%A +--R ++ %A d + c - %A d - c +--R c f + b f + a +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 578 +m0086:= a0086-r0086 +--R +--R +--R x +--R ++ %A +--R (397) | ------------------------------- d%A - r0086 +--R ++ %A d + c - %A d - c +--R c f + b f + a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 578 +d0086:= D(m0086,x) +--R +--R +--R x +--R (398) ----------------------------- +--R d x + c - d x - c +--R c f + b f + a +--R Type: Expression(Integer) +--E 453 + +--S 454 of 578 +t0087:= x^2/(a+b*f^(-c-d*x)+c*f^(c+d*x)) +--R +--R +--R 2 +--R x +--R (399) ----------------------------- +--R d x + c - d x - c +--R c f + b f + a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 578 +r0087:= (x^2*log(-(a-(a^2-4*b*c)^(1/2)+2*c*f^(c+d*x))/_ + (-a+(a^2-4*b*c)^(1/2)))*d^2*log(f)^2-_ + x^2*log((a+(a^2-4*b*c)^(1/2)+2*c*f^(c+d*x))/_ + (a+(a^2-4*b*c)^(1/2)))*d^2*log(f)^2+_ + 2*x*polylog(2,2*c*f^(c+d*x)/(-a+(a^2-4*b*c)^(1/2)))*d*log(f)-_ + 2*x*polylog(2,-2*c*f^(c+d*x)/(a+(a^2-4*b*c)^(1/2)))*d*log(f)-_ + 2*polylog(3,2*c*f^(c+d*x)/(-a+(a^2-4*b*c)^(1/2)))+_ + 2*polylog(3,-2*c*f^(c+d*x)/(a+(a^2-4*b*c)^(1/2))))/_ + (a^2-4*b*c)^(1/2)/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 455 + +--S 456 of 578 +a0087:= integrate(t0087,x) +--R +--R +--R x 2 +--R ++ %A +--R (400) | ------------------------------- d%A +--R ++ %A d + c - %A d - c +--R c f + b f + a +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 578 +m0087:= a0087-r0087 +--R +--R +--R x 2 +--R ++ %A +--R (401) | ------------------------------- d%A - r0087 +--R ++ %A d + c - %A d - c +--R c f + b f + a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 578 +d0087:= D(m0087,x) +--R +--R +--R 2 +--R x +--R (402) ----------------------------- +--R d x + c - d x - c +--R c f + b f + a +--R Type: Expression(Integer) +--E 458 + +--S 459 of 578 +t0088:= f^(a+b*x+c*x^2)*g^(d+e*x+f*x^2) +--R +--R +--R 2 2 +--R c x + b x + a f x + e x + d +--R (403) f g +--R Type: Expression(Integer) +--E 459 + +--S 460 of 578 +r0088:= 1/2*f^a*g^d*%pi^(1/2)*erfi(1/2*(b*log(f)+e*log(g)+_ + 2*x*c*log(f)+2*x*f*log(g))/(c*log(f)+f*log(g))^(1/2))/(c*log(f)+_ + f*log(g))^(1/2)*exp(-1/4*(b*log(f)+e*log(g))^2/(c*log(f)+f*log(g))) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 460 + +--S 461 of 578 +a0088:= integrate(t0088,x) +--R +--R +--R x 2 2 +--R ++ %A c + %A b + a %A f + %A e + d +--R (404) | f g d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 578 +m0088:= a0088-r0088 +--R +--R +--R x 2 2 +--R ++ %A c + %A b + a %A f + %A e + d +--R (405) | f g d%A - r0088 +--R ++ +--R Type: Expression(Integer) +--E 462 + +--S 463 of 578 +d0088:= D(m0088,x) +--R +--R +--R 2 2 +--R c x + b x + a f x + e x + d +--R (406) f g +--R Type: Expression(Integer) +--E 463 + +--S 464 of 578 +t0089:= exp(x)*sin(a+b*x+c*x^2) +--R +--R +--R x 2 +--R (407) %e sin(c x + b x + a) +--R Type: Expression(Integer) +--E 464 + +--S 465 of 578 +r0089:= 1/4*(-1)^(3/4)*exp(1)^(%i*a+1/4*%i*(1+%i*b)^2/c)*%pi^(1/2)*_ + erf(1/2*(-1)^(1/4)*(1+%i*b+2*%i*c*x)/c^(1/2))/c^(1/2)+_ + 1/4*(-1)^(3/4)*exp(1)^(-%i*a-1/4*%i*(1-%i*b)^2/c)*%pi^(1/2)*_ + erfi(1/2*(-1)^(1/4)*(1-%i*b-2*%i*c*x)/c^(1/2))/c^(1/2) +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R AlgebraicNumber +--R Polynomial(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 465 + +--S 466 of 578 +a0089:= integrate(t0089,x) +--R +--R +--R x +--R ++ %A 2 +--R (408) | %e sin(%A c + %A b + a)d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 578 +m0089:= a0089-r0089 +--R +--R +--R x +--R ++ %A 2 +--R (409) | %e sin(%A c + %A b + a)d%A - r0089 +--R ++ +--R Type: Expression(Integer) +--E 467 + +--S 468 of 578 +d0089:= D(m0089,x) +--R +--R +--R x 2 +--R (410) %e sin(c x + b x + a) +--R Type: Expression(Integer) +--E 468 + +--S 469 of 578 +t0090:= exp(x)*cos(a+b*x+c*x^2) +--R +--R +--R 2 x +--R (411) cos(c x + b x + a)%e +--R Type: Expression(Integer) +--E 469 + +--S 470 of 578 +r0090:= (-1/8-1/8*%i)*2^(1/2)*%pi^(1/2)*(exp(1/4*%i*(4*a*c+1+2*%i*b-b^2)/c)*_ + erf((1/4+1/4*%i)*2^(1/2)*(1+%i*b+2*%i*c*x)/c^(1/2))+_ + %i*exp(1/4*%i*(-4*a*c-1+2*%i*b+b^2)/c)*_ + erf(1/4*2^(1/2)*(%i*b+2*%i*c*x-1+%i+b+2*c*x)/c^(1/2)))/c^(1/2) +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R AlgebraicNumber +--R Polynomial(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 470 + +--S 471 of 578 +a0090:= integrate(t0090,x) +--R +--R +--R x +--R ++ 2 %A +--R (412) | cos(%A c + %A b + a)%e d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 578 +m0090:= a0090-r0090 +--R +--R +--R x +--R ++ 2 %A +--R (413) | cos(%A c + %A b + a)%e d%A - r0090 +--R ++ +--R Type: Expression(Integer) +--E 472 + +--S 473 of 578 +d0090:= D(m0090,x) +--R +--R +--R 2 x +--R (414) cos(c x + b x + a)%e +--R Type: Expression(Integer) +--E 473 + +--S 474 of 578 +t0091:= f^(a+b*x+c*x^2)*sin(c+d*x+e*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (415) sin(e x + d x + c)f +--R Type: Expression(Integer) +--E 474 + +--S 475 of 578 +r0091:= 1/4*%i*exp(1)^(-%i*c+(%i*d-b*log(f))^2/(4*%i*e-4*c*log(f)))*f^a*_ + %pi^(1/2)*erf(1/2*(%i*d-b*log(f)+2*x*(%i*e-c*log(f)))/_ + (%i*e-c*log(f))^(1/2))/(%i*e-c*log(f))^(1/2)-_ + 1/4*%i*exp(1)^(%i*c-(%i*d+b*log(f))^2/(4*%i*e+4*c*log(f)))*f^a*_ + %pi^(1/2)*erfi(1/2*(%i*d+b*log(f)+2*x*(%i*e+c*log(f)))/_ + (%i*e+c*log(f))^(1/2))/(%i*e+c*log(f))^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 475 + +--S 476 of 578 +a0091:= integrate(t0091,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (416) | sin(%A e + %A d + c)f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 578 +m0091:= a0091-r0091 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (417) | sin(%A e + %A d + c)f d%A - r0091 +--R ++ +--R Type: Expression(Integer) +--E 477 + +--S 478 of 578 +d0091:= D(m0091,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (418) sin(e x + d x + c)f +--R Type: Expression(Integer) +--E 478 + +--S 479 of 578 +t0092:= f^(a+b*x+c*x^2)*cos(c+d*x+e*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (419) cos(e x + d x + c)f +--R Type: Expression(Integer) +--E 479 + +--S 480 of 578 +r0092:= 1/4*exp(1)^(-%i*c+(%i*d-b*log(f))^2/(4*%i*e-4*c*log(f)))*f^a*_ + %pi^(1/2)*erf(1/2*(%i*d-b*log(f)+2*x*(%i*e-c*log(f)))/_ + (%i*e-c*log(f))^(1/2))/(%i*e-c*log(f))^(1/2)+_ + 1/4*exp(1)^(%i*c-(%i*d+b*log(f))^2/(4*%i*e+4*c*log(f)))*f^a*_ + %pi^(1/2)*erfi(1/2*(%i*d+b*log(f)+2*x*(%i*e+c*log(f)))/_ + (%i*e+c*log(f))^(1/2))/(%i*e+c*log(f))^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 480 + +--S 481 of 578 +a0092:= integrate(t0092,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (420) | cos(%A e + %A d + c)f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 578 +m0092:= a0092-r0092 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (421) | cos(%A e + %A d + c)f d%A - r0092 +--R ++ +--R Type: Expression(Integer) +--E 482 + +--S 483 of 578 +d0092:= D(m0092,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (422) cos(e x + d x + c)f +--R Type: Expression(Integer) +--E 483 + +--S 484 of 578 +t0093:= exp(1)^(2*x)*cos(exp(x)) +--R +--R +--R 2x x +--R (423) %e cos(%e ) +--R Type: Expression(Integer) +--E 484 + +--S 485 of 578 +r0093:= cos(exp(x))+exp(x)*sin(exp(x)) +--R +--R +--R x x x +--R (424) %e sin(%e ) + cos(%e ) +--R Type: Expression(Integer) +--E 485 + +--S 486 of 578 +a0093:= integrate(t0093,x) +--R +--R +--R x x x +--R (425) %e sin(%e ) + cos(%e ) +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 578 +m0093:= a0093-r0093 +--R +--R +--R (426) 0 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 578 +d0093:= D(m0093,x) +--R +--R +--R (427) 0 +--R Type: Expression(Integer) +--E 488 + +--S 489 of 578 +t0094:= exp(x)*sec(exp(x)) +--R +--R +--R x x +--R (428) %e sec(%e ) +--R Type: Expression(Integer) +--E 489 + +--S 490 of 578 +r0094:= arctanh(sin(exp(x))) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 490 + +--S 491 of 578 +a0094:= integrate(t0094,x) +--R +--R +--R x x +--R log(sin(%e ) + 1) - log(sin(%e ) - 1) +--R (429) ------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 578 +m0094:= a0094-r0094 +--R +--R +--R x x +--R log(sin(%e ) + 1) - log(sin(%e ) - 1) - 2r0094 +--R (430) ---------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 578 +d0094:= D(m0094,x) +--R +--R +--R x x +--R %e cos(%e ) +--R (431) - ------------- +--R x 2 +--R sin(%e ) - 1 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 578 +t0095:= (cos(x)+sin(x))/(exp(1)^(-x)+sin(x)) +--R +--R +--R sin(x) + cos(x) +--R (432) --------------- +--R - x +--R sin(x) + %e +--R Type: Expression(Integer) +--E 494 + +--S 495 of 578 +r0095:= log(1+exp(x)*sin(x)) +--R +--R +--R x +--R (433) log(%e sin(x) + 1) +--R Type: Expression(Integer) +--E 495 + +--S 496 of 578 +a0095:= integrate(t0095,x) +--R +--R +--R - x - x 2 2 +--R log(2%e sin(x) + (%e ) - cos(x) + 1) + 2x +--R (434) ----------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 578 +m0095:= a0095-r0095 +--R +--R +--R (435) +--R x - x - x 2 2 +--R - 2log(%e sin(x) + 1) + log(2%e sin(x) + (%e ) - cos(x) + 1) + 2x +--R ----------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 578 +d0095:= D(m0095,x) +--R +--R +--R (436) +--R - x x 2 +--R (- %e + cos(x))%e sin(x) +--R + +--R - x 2 - x x - x +--R ((- (%e ) - cos(x)%e )%e + %e + cos(x))sin(x) +--R + +--R - x 2 3 x - x 2 +--R (- cos(x)(%e ) + cos(x) - cos(x))%e + cos(x)%e - cos(x) + 1 +--R / +--R - x x 2 - x 2 2 x - x +--R 2%e %e sin(x) + (((%e ) - cos(x) + 1)%e + 2%e )sin(x) +--R + +--R - x 2 2 +--R (%e ) - cos(x) + 1 +--R Type: Expression(Integer) +--E 498 + +--S 499 of 578 +t0096:= exp(x)*cosh(x)*sinh(x)^2 +--R +--R +--R x 2 +--R (437) cosh(x)%e sinh(x) +--R Type: Expression(Integer) +--E 499 + +--S 500 of 578 +r0096:= -1/16*exp(-2*x)-1/16*exp(2*x)+1/32*exp(4*x)-1/8*x +--R +--R +--R 4x 2x - 2x +--R %e - 2%e - 2%e - 4x +--R (438) --------------------------- +--R 32 +--R Type: Expression(Integer) +--E 500 + +--S 501 of 578 +a0096:= integrate(t0096,x) +--R +--R +--R (439) +--R 3 2 2 3 +--R - 3sinh(x) + 3cosh(x)sinh(x) + (- 9cosh(x) - 4x + 2)sinh(x) + cosh(x) +--R + +--R (4x + 2)cosh(x) +--R / +--R 32sinh(x) - 32cosh(x) +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 578 +m0096:= a0096-r0096 +--R +--R +--R (440) +--R 3 2 +--R - 3sinh(x) + 3cosh(x)sinh(x) +--R + +--R 4x 2x - 2x 2 4x +--R (- %e + 2%e + 2%e - 9cosh(x) + 2)sinh(x) + cosh(x)%e +--R + +--R 2x - 2x 3 +--R - 2cosh(x)%e - 2cosh(x)%e + cosh(x) + 2cosh(x) +--R / +--R 32sinh(x) - 32cosh(x) +--R Type: Expression(Integer) +--E 502 + +--S 503 of 578 +d0096:= D(m0096,x) +--R +--R +--R (441) +--R 2 4x 2x - 2x 4x +--R - 6cosh(x)sinh(x) + (- %e + %e - %e + 1)sinh(x) + cosh(x)%e +--R + +--R 2x - 2x 3 +--R - cosh(x)%e + cosh(x)%e - 2cosh(x) + cosh(x) +--R / +--R 8sinh(x) - 8cosh(x) +--R Type: Expression(Integer) +--E 503 + +--S 504 of 578 +t0097:= f^(a+b*x+c*x^2)*sinh(c+d*x+e*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (442) sinh(e x + d x + c)f +--R Type: Expression(Integer) +--E 504 + +--S 505 of 578 +r0097:= -1/4*exp(1)^(-c+(d-b*log(f))^2/(4*e-4*c*log(f)))*f^a*_ + %pi^(1/2)*erf(1/2*(d-b*log(f)+2*x*(e-c*log(f)))/(e-c*log(f))^(1/2))/_ + (e-c*log(f))^(1/2)+1/4*exp(1)^(c-(d+b*log(f))^2/(4*e+4*c*log(f)))*_ + f^a*%pi^(1/2)*erfi(1/2*(d+b*log(f)+2*x*(e+c*log(f)))/_ + (e+c*log(f))^(1/2))/(e+c*log(f))^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 505 + +--S 506 of 578 +a0097:= integrate(t0097,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (443) | sinh(%A e + %A d + c)f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 578 +m0097:= a0097-r0097 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (444) | sinh(%A e + %A d + c)f d%A - r0097 +--R ++ +--R Type: Expression(Integer) +--E 507 + +--S 508 of 578 +d0097:= D(m0097,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (445) sinh(e x + d x + c)f +--R Type: Expression(Integer) +--E 508 + +--S 509 of 578 +t0098:= f^(a+b*x+c*x^2)*cosh(c+d*x+e*x^2) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (446) cosh(e x + d x + c)f +--R Type: Expression(Integer) +--E 509 + +--S 510 of 578 +r0098:= 1/4*exp(1)^(-c+(d-b*log(f))^2/(4*e-4*c*log(f)))*f^a*_ + %pi^(1/2)*erf(1/2*(d-b*log(f)+2*x*(e-c*log(f)))/_ + (e-c*log(f))^(1/2))/(e-c*log(f))^(1/2)+_ + 1/4*exp(1)^(c-(d+b*log(f))^2/(4*e+4*c*log(f)))*f^a*_ + %pi^(1/2)*erfi(1/2*(d+b*log(f)+2*x*(e+c*log(f)))/_ + (e+c*log(f))^(1/2))/(e+c*log(f))^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 510 + +--S 511 of 578 +a0098:= integrate(t0098,x) +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (447) | cosh(%A e + %A d + c)f d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 511 + +--S 512 of 578 +m0098:= a0098-r0098 +--R +--R +--R x 2 +--R ++ 2 %A c + %A b + a +--R (448) | cosh(%A e + %A d + c)f d%A - r0098 +--R ++ +--R Type: Expression(Integer) +--E 512 + +--S 513 of 578 +d0098:= D(m0098,x) +--R +--R +--R 2 +--R 2 c x + b x + a +--R (449) cosh(e x + d x + c)f +--R Type: Expression(Integer) +--E 513 + +--S 514 of 578 +t0099:= 1/exp(x)/(1-exp(1)^(-2*x))^(1/2) +--R +--R +--R 1 +--R (450) ------------------ +--R +------------+ +--R x | - 2x +--R %e \|- %e + 1 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 578 +r0099:= -arcsin(exp(-x)) +--R +--R There are no library operations named arcsin +--R Use HyperDoc Browse or issue +--R )what op arcsin +--R to learn if there is any operation containing " arcsin " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arcsin with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 515 + +--S 516 of 578 +a0099:= integrate(t0099,x) +--R +--R +--R +----------+ +--R | x 2 x +--R (451) 2atan(\|(%e ) - 1 - %e ) +--R Type: Union(Expression(Integer),...) +--E 516 + +--S 517 of 578 +m0099:= a0099-r0099 +--R +--R +--R +----------+ +--R | x 2 x +--R (452) 2atan(\|(%e ) - 1 - %e ) - r0099 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 578 +d0099:= D(m0099,x) +--R +--R +--R 1 +--R (453) ------------- +--R +----------+ +--R | x 2 +--R \|(%e ) - 1 +--R Type: Expression(Integer) +--E 518 + +--S 519 of 578 +t0100:= exp(x)/(-4+exp(1)^(2*x)) +--R +--R +--R x +--R %e +--R (454) -------- +--R 2x +--R %e - 4 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 578 +r0100:= -1/2*arctanh(1/2*exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 520 + +--S 521 of 578 +a0100:= integrate(t0100,x) +--R +--R +--R x x +--R - log(%e + 2) + log(%e - 2) +--R (455) ----------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 521 + +--S 522 of 578 +m0100:= a0100-r0100 +--R +--R +--R x x +--R - log(%e + 2) + log(%e - 2) - 4r0100 +--R (456) -------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 578 +d0100:= D(m0100,x) +--R +--R +--R x +--R %e +--R (457) ---------- +--R x 2 +--R (%e ) - 4 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 578 +t0101:= (exp(1)^(-2*x)+exp(1)^(2*x))/(-exp(1)^(-2*x)+exp(1)^(2*x)) +--R +--R +--R 2x - 2x +--R %e + %e +--R (458) ------------- +--R 2x - 2x +--R %e - %e +--R Type: Expression(Integer) +--E 524 + +--S 525 of 578 +r0101:= 1/2*log(-exp(-2*x)+exp(2*x)) +--R +--R +--R 2x - 2x +--R log(%e - %e ) +--R (459) ------------------ +--R 2 +--R Type: Expression(Integer) +--E 525 + +--S 526 of 578 +a0101:= integrate(t0101,x) +--R +--R +--R 2x 2 +--R log((%e ) - 1) - 2x +--R (460) --------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 526 + +--S 527 of 578 +m0101:= a0101-r0101 +--R +--R +--R 2x 2 2x - 2x +--R log((%e ) - 1) - log(%e - %e ) - 2x +--R (461) ------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 578 +d0101:= D(m0101,x) +--R +--R +--R - 2x 2x 2 2x +--R - 2%e (%e ) + 2%e +--R (462) --------------------------------------- +--R 2x 3 - 2x 2x 2 2x - 2x +--R (%e ) - %e (%e ) - %e + %e +--R Type: Expression(Integer) +--E 528 + +--S 529 of 578 +t0102:= exp(x)/(16-exp(1)^(2*x)) +--R +--R +--R x +--R %e +--R (463) - --------- +--R 2x +--R %e - 16 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 578 +r0102:= 1/4*arctanh(1/4*exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 530 + +--S 531 of 578 +a0102:= integrate(t0102,x) +--R +--R +--R x x +--R log(%e + 4) - log(%e - 4) +--R (464) --------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 531 + +--S 532 of 578 +m0102:= a0102-r0102 +--R +--R +--R x x +--R log(%e + 4) - log(%e - 4) - 8r0102 +--R (465) ------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 532 + +--S 533 of 578 +d0102:= D(m0102,x) +--R +--R +--R x +--R %e +--R (466) - ----------- +--R x 2 +--R (%e ) - 16 +--R Type: Expression(Integer) +--E 533 + +--S 534 of 578 +t0103:= exp(1)^(4*x)/(16+exp(1)^(8*x))^(1/2) +--R +--R +--R 4x +--R %e +--R (467) ------------ +--R +---------+ +--R | 8x +--R \|%e + 16 +--R Type: Expression(Integer) +--E 534 + +--S 535 of 578 +r0103:= 1/4*arcsinh(1/4*exp(4*x)) +--R +--R There are no library operations named arcsinh +--R Use HyperDoc Browse or issue +--R )what op arcsinh +--R to learn if there is any operation containing " arcsinh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arcsinh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 535 + +--S 536 of 578 +a0103:= integrate(t0103,x) +--R +--R +--R +------------+ +--R | 4x 2 4x +--R log(\|(%e ) + 16 - %e ) +--R (468) - --------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 536 + +--S 537 of 578 +m0103:= a0103-r0103 +--R +--R +--R +------------+ +--R | 4x 2 4x +--R - log(\|(%e ) + 16 - %e ) - 4r0103 +--R (469) -------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 537 + +--S 538 of 578 +d0103:= D(m0103,x) +--R +--R +--R 4x +--R %e +--R (470) --------------- +--R +------------+ +--R | 4x 2 +--R \|(%e ) + 16 +--R Type: Expression(Integer) +--E 538 + +--S 539 of 578 +t0104:= 1/exp(x)/(1+2*exp(x)) +--R +--R +--R 1 +--R (471) ------------- +--R x 2 x +--R 2(%e ) + %e +--R Type: Expression(Integer) +--E 539 + +--S 540 of 578 +r0104:= -exp(-x)+2*log(2+exp(-x)) +--R +--R +--R - x - x +--R (472) 2log(%e + 2) - %e +--R Type: Expression(Integer) +--E 540 + +--S 541 of 578 +a0104:= integrate(t0104,x) +--R +--R +--R x x x +--R 2%e log(2%e + 1) - 2x %e - 1 +--R (473) ------------------------------ +--R x +--R %e +--R Type: Union(Expression(Integer),...) +--E 541 + +--S 542 of 578 +m0104:= a0104-r0104 +--R +--R +--R x x x - x - x x +--R 2%e log(2%e + 1) - 2%e log(%e + 2) + (%e - 2x)%e - 1 +--R (474) ------------------------------------------------------------ +--R x +--R %e +--R Type: Expression(Integer) +--E 542 + +--S 543 of 578 +d0104:= D(m0104,x) +--R +--R +--R - x 2 x 2 - x 2 x - x +--R - 2(%e ) (%e ) - (%e ) %e + %e + 2 +--R (475) ------------------------------------------- +--R - x x 2 - x x +--R (2%e + 4)(%e ) + (%e + 2)%e +--R Type: Expression(Integer) +--E 543 + +--S 544 of 578 +t0105:= exp(x)*sec(-1+exp(x))^3 +--R +--R +--R x x 3 +--R (476) %e sec(%e - 1) +--R Type: Expression(Integer) +--E 544 + +--S 545 of 578 +r0105:= 1/2*arctanh(sin(-1+exp(x)))+1/2*sec(-1+exp(x))*tan(-1+exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 545 + +--S 546 of 578 +a0105:= integrate(t0105,x) +--R +--R +--R (477) +--R x 2 x x 2 x +--R cos(%e - 1) log(sin(%e - 1) + 1) - cos(%e - 1) log(sin(%e - 1) - 1) +--R + +--R x +--R 2sin(%e - 1) +--R / +--R x 2 +--R 4cos(%e - 1) +--R Type: Union(Expression(Integer),...) +--E 546 + +--S 547 of 578 +m0105:= a0105-r0105 +--R +--R +--R (478) +--R x 2 x x 2 x +--R cos(%e - 1) log(sin(%e - 1) + 1) - cos(%e - 1) log(sin(%e - 1) - 1) +--R + +--R x x 2 +--R 2sin(%e - 1) - 4r0105 cos(%e - 1) +--R / +--R x 2 +--R 4cos(%e - 1) +--R Type: Expression(Integer) +--E 547 + +--S 548 of 578 +d0105:= D(m0105,x) +--R +--R +--R (479) +--R x x 4 x x 2 x x 2 +--R 2%e sin(%e - 1) + (%e cos(%e - 1) - 2%e )sin(%e - 1) +--R + +--R x x 4 x x 2 +--R - %e cos(%e - 1) - %e cos(%e - 1) +--R / +--R x 3 x 2 x 3 +--R 2cos(%e - 1) sin(%e - 1) - 2cos(%e - 1) +--R Type: Expression(Integer) +--E 548 + +--S 549 of 578 +t0106:= exp(x)/(2+3*exp(x)+exp(1)^(2*x)) +--R +--R +--R x +--R %e +--R (480) --------------- +--R 2x x +--R %e + 3%e + 2 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 578 +r0106:= -2*arctanh(3+2*exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 550 + +--S 551 of 578 +a0106:= integrate(t0106,x) +--R +--R +--R x x +--R (481) - log(%e + 2) + log(%e + 1) +--R Type: Union(Expression(Integer),...) +--E 551 + +--S 552 of 578 +m0106:= a0106-r0106 +--R +--R +--R x x +--R (482) - log(%e + 2) + log(%e + 1) - r0106 +--R Type: Expression(Integer) +--E 552 + +--S 553 of 578 +d0106:= D(m0106,x) +--R +--R +--R x +--R %e +--R (483) ----------------- +--R x 2 x +--R (%e ) + 3%e + 2 +--R Type: Expression(Integer) +--E 553 + +--S 554 of 578 +t0107:= 2^x/(1+4^x)^(1/2) +--R +--R +--R x +--R 2 +--R (484) --------- +--R +------+ +--R | x +--R \|4 + 1 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 578 +r0107:= arcsinh(2^x)/log(2) +--R +--R There are no library operations named arcsinh +--R Use HyperDoc Browse or issue +--R )what op arcsinh +--R to learn if there is any operation containing " arcsinh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arcsinh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 555 + +--S 556 of 578 +a0107:= integrate(t0107,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 556 + +--S 557 of 578 +m0107:= a0107-r0107 +--R +--R +--R (485) - r0107 + a0107 +--R Type: Polynomial(Integer) +--E 557 + +--S 558 of 578 +d0107:= D(m0107,x) +--R +--R +--R (486) 0 +--R Type: Polynomial(Integer) +--E 558 + +--S 559 of 578 +t0108:= exp(1)^(3*x)/(-1+exp(1)^(2*x)) +--R +--R +--R 3x +--R %e +--R (487) -------- +--R 2x +--R %e - 1 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 578 +r0108:= exp(x)-arctanh(exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 560 + +--S 561 of 578 +a0108:= integrate(t0108,x) +--R +--R +--R x x x +--R - log(%e + 1) + log(%e - 1) + 2%e +--R (488) ------------------------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 561 + +--S 562 of 578 +m0108:= a0108-r0108 +--R +--R +--R x x x +--R - log(%e + 1) + log(%e - 1) + 2%e - 2r0108 +--R (489) --------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 578 +d0108:= D(m0108,x) +--R +--R +--R x 3 +--R (%e ) +--R (490) ---------- +--R x 2 +--R (%e ) - 1 +--R Type: Expression(Integer) +--E 563 + +--S 564 of 578 +t0109:= exp((a+x)^2)/x^2-2*a*exp((a+x)^2)/x +--R +--R +--R 2 2 +--R x + 2a x + a +--R (- 2a x + 1)%e +--R (491) ---------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 564 + +--S 565 of 578 +r0109:= -exp((a+x)^2)/x+%pi^(1/2)*erfi(a+x) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 565 + +--S 566 of 578 +a0109:= integrate(t0109,x) +--R +--R +--R 2 2 +--R x a + 2%A a + %A +--R ++ (- 2%A a + 1)%e +--R (492) | ------------------------------- d%A +--R ++ 2 +--R %A +--R Type: Union(Expression(Integer),...) +--E 566 + +--S 567 of 578 +m0109:= a0109-r0109 +--R +--R +--R 2 2 +--R x a + 2%A a + %A +--R ++ (- 2%A a + 1)%e +--R (493) | ------------------------------- d%A - r0109 +--R ++ 2 +--R %A +--R Type: Expression(Integer) +--E 567 + +--S 568 of 578 +d0109:= D(m0109,x) +--R +--R +--R 2 2 +--R x + 2a x + a +--R (- 2a x + 1)%e +--R (494) ---------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 568 + +--S 569 of 578 +t0110:= 1/(-exp(x)+exp(1)^(3*x)) +--R +--R +--R 1 +--R (495) ---------- +--R 3x x +--R %e - %e +--R Type: Expression(Integer) +--E 569 + +--S 570 of 578 +r0110:= exp(-x)-arctanh(exp(x)) +--R +--R There are no library operations named arctanh +--R Use HyperDoc Browse or issue +--R )what op arctanh +--R to learn if there is any operation containing " arctanh " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R arctanh with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 570 + +--S 571 of 578 +a0110:= integrate(t0110,x) +--R +--R +--R x x x x +--R - %e log(%e + 1) + %e log(%e - 1) + 2 +--R (496) --------------------------------------- +--R x +--R 2%e +--R Type: Union(Expression(Integer),...) +--E 571 + +--S 572 of 578 +m0110:= a0110-r0110 +--R +--R +--R x x x x x +--R - %e log(%e + 1) + %e log(%e - 1) - 2r0110 %e + 2 +--R (497) ---------------------------------------------------- +--R x +--R 2%e +--R Type: Expression(Integer) +--E 572 + +--S 573 of 578 +d0110:= D(m0110,x) +--R +--R +--R 1 +--R (498) ------------ +--R x 3 x +--R (%e ) - %e +--R Type: Expression(Integer) +--E 573 + +--S 574 of 578 +t0111:= 10^(x^(1/2))/x^(1/2) +--R +--R +--R +-+ +--R \|x +--R 10 +--R (499) ------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 574 + +--S 575 of 578 +r0111:= 2^(1+x^(1/2))*5^(x^(1/2))/log(10) +--R +--R +--R +-+ +-+ +--R \|x + 1 \|x +--R 2 5 +--R (500) -------------- +--R log(10) +--R Type: Expression(Integer) +--E 575 + +--S 576 of 578 +a0111:= integrate(t0111,x) +--R +--R +--R +-+ +--R log(10)\|x +--R 2%e +--R (501) -------------- +--R log(10) +--R Type: Union(Expression(Integer),...) +--E 576 + +--S 577 of 578 +m0111:= a0111-r0111 +--R +--R +--R +-+ +-+ +-+ +--R \|x + 1 \|x log(10)\|x +--R - 2 5 + 2%e +--R (502) --------------------------------- +--R log(10) +--R Type: Expression(Integer) +--E 577 + +--S 578 of 578 +d0111:= D(m0111,x) +--R +--R +--R +-+ +-+ +-+ +--R \|x + 1 \|x log(10)\|x +--R (- log(5) - log(2))2 5 + 2log(10)%e +--R (503) --------------------------------------------------------- +--R +-+ +--R 2log(10)\|x +--R Type: Expression(Integer) +--E 578 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richexponential.input.pdf b/src/axiom-website/CATS/richexponential.input.pdf new file mode 100644 index 0000000..4bbdbf6 Binary files /dev/null and b/src/axiom-website/CATS/richexponential.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper000-099.input.pamphlet b/src/axiom-website/CATS/richhyper000-099.input.pamphlet new file mode 100644 index 0000000..0a5a784 --- /dev/null +++ b/src/axiom-website/CATS/richhyper000-099.input.pamphlet @@ -0,0 +1,67641 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper000-099.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper000-099.output +)spool richhyper000-099.output +)set message auto off +)clear all + +--S 1 of 510 +t0000:= sinh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (1) \|sinh(b x + a) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 510 +r0000:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + sinh(a+b*x)^(1/2)/b/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 510 +a0000:= integrate(t0000,x) +--R +--R +--R x +--R ++ +--------------+ +--R (2) | \|sinh(%N b + a) d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 510 +m0000:= a0000-r0000 +--R +--R +--R x +--R ++ +--------------+ +--R (3) | \|sinh(%N b + a) d%N - r0000 +--R ++ +--R Type: Expression(Integer) +--E 4 + +--S 5 of 510 +d0000:= D(m0000,x) +--R +--R +--R +-------------+ +--R (4) \|sinh(b x + a) +--R Type: Expression(Integer) +--E 5 + +--S 6 of 510 +t0001:= sinh(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (5) sinh(b x + a)\|sinh(b x + a) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 510 +r0001:= 2/3*(%i*EllipticF(-1/4*%pi+1/2*%i*a+1/2*%i*b*x,2)*_ + (%i*sinh(a+b*x))^(1/2)+cosh(a+b*x)*sinh(a+b*x))/sinh(a+b*x)^(1/2)/b +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Expression(Complex(Integer)) +--R Polynomial(Complex(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 510 +a0001:= integrate(t0001,x) +--R +--R +--R x +--R ++ +--------------+ +--R (6) | sinh(%N b + a)\|sinh(%N b + a) d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 510 +m0001:= a0001-r0001 +--R +--R +--R x +--R ++ +--------------+ +--R (7) | sinh(%N b + a)\|sinh(%N b + a) d%N - r0001 +--R ++ +--R Type: Expression(Integer) +--E 9 + +--S 10 of 510 +d0001:= D(m0001,x) +--R +--R +--R +-------------+ +--R (8) sinh(b x + a)\|sinh(b x + a) +--R Type: Expression(Integer) +--E 10 + +--S 11 of 510 +t0002:= sinh(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (9) sinh(b x + a) \|sinh(b x + a) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 510 +r0002:= 6/5*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + sinh(a+b*x)^(1/2)/b/(%i*sinh(a+b*x))^(1/2)+_ + 2/5*cosh(a+b*x)*sinh(a+b*x)^(3/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 510 +a0002:= integrate(t0002,x) +--R +--R +--R x +--R ++ 2 +--------------+ +--R (10) | sinh(%N b + a) \|sinh(%N b + a) d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 510 +m0002:= a0002-r0002 +--R +--R +--R x +--R ++ 2 +--------------+ +--R (11) | sinh(%N b + a) \|sinh(%N b + a) d%N - r0002 +--R ++ +--R Type: Expression(Integer) +--E 14 + +--S 15 of 510 +d0002:= D(m0002,x) +--R +--R +--R 2 +-------------+ +--R (12) sinh(b x + a) \|sinh(b x + a) +--R Type: Expression(Integer) +--E 15 + +--S 16 of 510 +t0003:= 1/sinh(a+b*x)^(1/2) +--R +--R +--R 1 +--R (13) ---------------- +--R +-------------+ +--R \|sinh(b x + a) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 510 +r0003:= -2*%i*EllipticF(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + (%i*sinh(a+b*x))^(1/2)/b/sinh(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 510 +a0003:= integrate(t0003,x) +--R +--R +--R x +--R ++ 1 +--R (14) | ----------------- d%N +--R ++ +--------------+ +--R \|sinh(%N b + a) +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 510 +m0003:= a0003-r0003 +--R +--R +--R x +--R ++ 1 +--R (15) | ----------------- d%N - r0003 +--R ++ +--------------+ +--R \|sinh(%N b + a) +--R Type: Expression(Integer) +--E 19 + +--S 20 of 510 +d0003:= D(m0003,x) +--R +--R +--R 1 +--R (16) ---------------- +--R +-------------+ +--R \|sinh(b x + a) +--R Type: Expression(Integer) +--E 20 + +--S 21 of 510 +t0004:= 1/sinh(a+b*x)^(3/2) +--R +--R +--R 1 +--R (17) ----------------------------- +--R +-------------+ +--R sinh(b x + a)\|sinh(b x + a) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 510 +r0004:= -2*cosh(a+b*x)/b/sinh(a+b*x)^(1/2)-_ + 2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + sinh(a+b*x)^(1/2)/b/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 510 +a0004:= integrate(t0004,x) +--R +--R +--R x +--R ++ 1 +--R (18) | ------------------------------- d%N +--R ++ +--------------+ +--R sinh(%N b + a)\|sinh(%N b + a) +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 510 +m0004:= a0004-r0004 +--R +--R +--R x +--R ++ 1 +--R (19) | ------------------------------- d%N - r0004 +--R ++ +--------------+ +--R sinh(%N b + a)\|sinh(%N b + a) +--R Type: Expression(Integer) +--E 24 + +--S 25 of 510 +d0004:= D(m0004,x) +--R +--R +--R 1 +--R (20) ----------------------------- +--R +-------------+ +--R sinh(b x + a)\|sinh(b x + a) +--R Type: Expression(Integer) +--E 25 + +--S 26 of 510 +t0005:= 1/sinh(a+b*x)^(5/2) +--R +--R +--R 1 +--R (21) ------------------------------ +--R 2 +-------------+ +--R sinh(b x + a) \|sinh(b x + a) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 510 +r0005:= 2/3*(-cosh(a+b*x)+%i*EllipticF(-1/4*%pi+1/2*%i*a+1/2*%i*b*x,2)*_ + (%i*sinh(a+b*x))^(1/2)*sinh(a+b*x))/b/sinh(a+b*x)^(3/2) +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Expression(Complex(Integer)) +--R Polynomial(Complex(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 510 +a0005:= integrate(t0005,x) +--R +--R +--R x +--R ++ 1 +--R (22) | -------------------------------- d%N +--R ++ 2 +--------------+ +--R sinh(%N b + a) \|sinh(%N b + a) +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 510 +m0005:= a0005-r0005 +--R +--R +--R x +--R ++ 1 +--R (23) | -------------------------------- d%N - r0005 +--R ++ 2 +--------------+ +--R sinh(%N b + a) \|sinh(%N b + a) +--R Type: Expression(Integer) +--E 29 + +--S 30 of 510 +d0005:= D(m0005,x) +--R +--R +--R 1 +--R (24) ------------------------------ +--R 2 +-------------+ +--R sinh(b x + a) \|sinh(b x + a) +--R Type: Expression(Integer) +--E 30 + +--S 31 of 510 +t0006:= sinh(a+b*x^n)/x +--R +--R +--R n +--R sinh(b x + a) +--R (25) -------------- +--R x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 510 +r0006:= (Chi(b*x^n)*sinh(a)+cosh(a)*Shi(b*x^n))/n +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 510 +a0006:= integrate(t0006,x) +--R +--R +--R x n +--R ++ sinh(b %N + a) +--R (26) | --------------- d%N +--R ++ %N +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 510 +m0006:= a0006-r0006 +--R +--R +--R x n +--R ++ sinh(b %N + a) +--R (27) | --------------- d%N - r0006 +--R ++ %N +--R Type: Expression(Integer) +--E 34 + +--S 35 of 510 +d0006:= D(m0006,x) +--R +--R +--R n +--R sinh(b x + a) +--R (28) -------------- +--R x +--R Type: Expression(Integer) +--E 35 + +--S 36 of 510 +t0007:= sinh(a+b*x)/x^2 +--R +--R +--R sinh(b x + a) +--R (29) ------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 510 +r0007:= b*cosh(a)*Chi(b*x)-sinh(a+b*x)/x+b*sinh(a)*Shi(b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 510 +a0007:= integrate(t0007,x) +--R +--R +--R x +--R ++ sinh(%N b + a) +--R (30) | -------------- d%N +--R ++ 2 +--R %N +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 510 +m0007:= a0007-r0007 +--R +--R +--R x +--R ++ sinh(%N b + a) +--R (31) | -------------- d%N - r0007 +--R ++ 2 +--R %N +--R Type: Expression(Integer) +--E 39 + +--S 40 of 510 +d0007:= D(m0007,x) +--R +--R +--R sinh(b x + a) +--R (32) ------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 40 + +--S 41 of 510 +t0008:= sinh(a+b*x)^3/x^2 +--R +--R +--R 3 +--R sinh(b x + a) +--R (33) -------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 510 +r0008:= -1/4*(3*b*cosh(a)*Chi(b*x)*x-3*b*cosh(3*a)*Chi(3*b*x)*x-_ + 3*sinh(a+b*x)+sinh(3*a+3*b*x)+3*b*sinh(a)*Shi(b*x)*x-_ + 3*b*sinh(3*a)*Shi(3*b*x)*x)/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 of 510 +a0008:= integrate(t0008,x) +--R +--R +--R x 3 +--R ++ sinh(%N b + a) +--R (34) | --------------- d%N +--R ++ 2 +--R %N +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 510 +m0008:= a0008-r0008 +--R +--R +--R x 3 +--R ++ sinh(%N b + a) +--R (35) | --------------- d%N - r0008 +--R ++ 2 +--R %N +--R Type: Expression(Integer) +--E 44 + +--S 45 of 510 +d0008:= D(m0008,x) +--R +--R +--R 3 +--R sinh(b x + a) +--R (36) -------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 45 + +--S 46 of 510 +t0009:= sinh(a+b*x)/x^3 +--R +--R +--R sinh(b x + a) +--R (37) ------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 510 +r0009:= 1/2*(-b*cosh(a+b*x)*x+b^2*Chi(b*x)*sinh(a)*x^2-_ + sinh(a+b*x)+b^2*cosh(a)*Shi(b*x)*x^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 47 + +--S 48 of 510 +a0009:= integrate(t0009,x) +--R +--R +--R x +--R ++ sinh(%N b + a) +--R (38) | -------------- d%N +--R ++ 3 +--R %N +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 510 +m0009:= a0009-r0009 +--R +--R +--R x +--R ++ sinh(%N b + a) +--R (39) | -------------- d%N - r0009 +--R ++ 3 +--R %N +--R Type: Expression(Integer) +--E 49 + +--S 50 of 510 +d0009:= D(m0009,x) +--R +--R +--R sinh(b x + a) +--R (40) ------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 50 + +--S 51 of 510 +t0010:= sinh(a+b*x)^2/x^3 +--R +--R +--R 2 +--R sinh(b x + a) +--R (41) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 510 +r0010:= b^2*cosh(2*a)*Chi(2*b*x)-b*cosh(a+b*x)*sinh(a+b*x)/x-_ + 1/2*sinh(a+b*x)^2/x^2+b^2*sinh(2*a)*Shi(2*b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 510 +a0010:= integrate(t0010,x) +--R +--R +--R x 2 +--R ++ sinh(%N b + a) +--R (42) | --------------- d%N +--R ++ 3 +--R %N +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 510 +m0010:= a0010-r0010 +--R +--R +--R x 2 +--R ++ sinh(%N b + a) +--R (43) | --------------- d%N - r0010 +--R ++ 3 +--R %N +--R Type: Expression(Integer) +--E 54 + +--S 55 of 510 +d0010:= D(m0010,x) +--R +--R +--R 2 +--R sinh(b x + a) +--R (44) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 55 + +--S 56 of 510 +t0011:= sinh(a+b*x)^3/x^3 +--R +--R +--R 3 +--R sinh(b x + a) +--R (45) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 510 +r0011:= -3/8*b^2*Chi(b*x)*sinh(a)+9/8*b^2*Chi(3*b*x)*sinh(3*a)-_ + 3/2*b*cosh(a+b*x)*sinh(a+b*x)^2/x-1/2*sinh(a+b*x)^3/x^2-_ + 3/8*b^2*cosh(a)*Shi(b*x)+9/8*b^2*cosh(3*a)*Shi(3*b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 510 +a0011:= integrate(t0011,x) +--R +--R +--R x 3 +--R ++ sinh(%N b + a) +--R (46) | --------------- d%N +--R ++ 3 +--R %N +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 510 +m0011:= a0011-r0011 +--R +--R +--R x 3 +--R ++ sinh(%N b + a) +--R (47) | --------------- d%N - r0011 +--R ++ 3 +--R %N +--R Type: Expression(Integer) +--E 59 + +--S 60 of 510 +d0011:= D(m0011,x) +--R +--R +--R 3 +--R sinh(b x + a) +--R (48) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 60 + +--S 61 of 510 +t0012:= sinh(x)^(1/2) +--R +--R +--R +-------+ +--R (49) \|sinh(x) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 510 +r0012:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*x,2)*sinh(x)^(1/2)/(%i*sinh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 510 +a0012:= integrate(t0012,x) +--R +--R +--R x +--R ++ +--------+ +--R (50) | \|sinh(%N) d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 510 +m0012:= a0012-r0012 +--R +--R +--R x +--R ++ +--------+ +--R (51) | \|sinh(%N) d%N - r0012 +--R ++ +--R Type: Expression(Integer) +--E 64 + +--S 65 of 510 +d0012:= D(m0012,x) +--R +--R +--R +-------+ +--R (52) \|sinh(x) +--R Type: Expression(Integer) +--E 65 + +--S 66 of 510 +t0013:= (sinh(x)^3)^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R (53) \|sinh(x) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 510 +r0013:= -2/3*csch(x)^2*(sinh(x)^3)^(1/2)*(-%i*EllipticF(-1/4*%pi+_ + 1/2*%i*x,2)*(%i*sinh(x))^(1/2)-cosh(x)*sinh(x)) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 of 510 +a0013:= integrate(t0013,x) +--R +--R +--R x +---------+ +--R ++ | 3 +--R (54) | \|sinh(%N) d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 510 +m0013:= a0013-r0013 +--R +--R +--R x +---------+ +--R ++ | 3 +--R (55) | \|sinh(%N) d%N - r0013 +--R ++ +--R Type: Expression(Integer) +--E 69 + +--S 70 of 510 +d0013:= D(m0013,x) +--R +--R +--R +--------+ +--R | 3 +--R (56) \|sinh(x) +--R Type: Expression(Integer) +--E 70 + +--S 71 of 510 +t0014:= (sinh(x)^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (57) \|sinh(x) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 510 +r0014:= -1/2*csch(x)^2*(sinh(x)^4)^(1/2)*(x-cosh(x)*sinh(x)) +--R +--R +--R +--------+ +--R 2 2 | 4 +--R (cosh(x)csch(x) sinh(x) - x csch(x) )\|sinh(x) +--R (58) ------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 510 +a0014:= integrate(t0014,x) +--R +--R +--R cosh(x)sinh(x) - x +--R (59) ------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 510 +m0014:= a0014-r0014 +--R +--R +--R (60) +--R +--------+ +--R 2 2 | 4 +--R (- cosh(x)csch(x) sinh(x) + x csch(x) )\|sinh(x) + cosh(x)sinh(x) - x +--R ----------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 510 +d0014:= D(m0014,x) +--R +--R +--R (61) +--R +--------+ +--R 2 2 | 4 2 6 +--R (sinh(x) + cosh(x) - 1)\|sinh(x) - csch(x) sinh(x) +--R + +--R 2 5 +--R 2cosh(x)coth(x)csch(x) sinh(x) +--R + +--R 2 2 4 2 3 +--R (- 2x coth(x) - 3cosh(x) + 1)csch(x) sinh(x) + 2x cosh(x)csch(x) sinh(x) +--R / +--R +--------+ +--R | 4 +--R 2\|sinh(x) +--R Type: Expression(Integer) +--E 75 + +--S 76 of 510 +t0015:= 1/(a+b*sinh(c+d*x))^2 +--R +--R +--R 1 +--R (62) ------------------------------------------ +--R 2 2 2 +--R b sinh(d x + c) + 2a b sinh(d x + c) + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 510 +r0015:= -2*a*atanh((b-a*tanh(1/2*c+1/2*d*x))/(a^2+b^2)^(1/2))/_ + (a^2+b^2)^(3/2)/d-b*cosh(c+d*x)/(a^2+b^2)/d/(a+b*sinh(c+d*x)) +--R +--R +--R (63) +--R d x + c +--R a tanh(-------) - b +--R 2 2 +--R (2a b sinh(d x + c) + 2a )atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R | 2 2 +--R - b cosh(d x + c)\|b + a +--R / +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b + a b)d sinh(d x + c) + (a b + a )d)\|b + a +--R Type: Expression(Integer) +--E 77 + +--S 78 of 510 +a0015:= integrate(t0015,x) +--R +--R +--R (64) +--R 2 2 +--R a b sinh(d x + c) + (2a b cosh(d x + c) + 2a )sinh(d x + c) +--R + +--R 2 2 +--R a b cosh(d x + c) + 2a cosh(d x + c) - a b +--R * +--R log +--R 2 2 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a b)sinh(d x + c) +--R + +--R 2 2 2 2 +--R b cosh(d x + c) + 2a b cosh(d x + c) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 +--R (- 2b - 2a b)sinh(d x + c) + (- 2b - 2a b)cosh(d x + c) +--R + +--R 2 3 +--R - 2a b - 2a +--R / +--R 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R 2 +--R b cosh(d x + c) + 2a cosh(d x + c) - b +--R + +--R +-------+ +--R | 2 2 +--R (2a sinh(d x + c) + 2a cosh(d x + c) - 2b)\|b + a +--R / +--R 3 2 2 +--R (b + a b)d sinh(d x + c) +--R + +--R 3 2 2 3 +--R ((2b + 2a b)d cosh(d x + c) + (2a b + 2a )d)sinh(d x + c) +--R + +--R 3 2 2 2 3 3 2 +--R (b + a b)d cosh(d x + c) + (2a b + 2a )d cosh(d x + c) + (- b - a b)d +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 510 +m0015:= a0015-r0015 +--R +--R +--R (65) +--R 2 3 2 2 2 +--R a b sinh(d x + c) + (2a b cosh(d x + c) + 3a b)sinh(d x + c) +--R + +--R 2 2 2 2 3 +--R (a b cosh(d x + c) + 4a b cosh(d x + c) - a b + 2a )sinh(d x + c) +--R + +--R 2 2 3 2 +--R a b cosh(d x + c) + 2a cosh(d x + c) - a b +--R * +--R log +--R 2 2 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a b)sinh(d x + c) +--R + +--R 2 2 2 2 +--R b cosh(d x + c) + 2a b cosh(d x + c) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 +--R (- 2b - 2a b)sinh(d x + c) + (- 2b - 2a b)cosh(d x + c) +--R + +--R 2 3 +--R - 2a b - 2a +--R / +--R 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R 2 +--R b cosh(d x + c) + 2a cosh(d x + c) - b +--R + +--R 2 3 2 2 2 +--R - 2a b sinh(d x + c) + (- 4a b cosh(d x + c) - 6a b)sinh(d x + c) +--R + +--R 2 2 2 2 3 +--R (- 2a b cosh(d x + c) - 8a b cosh(d x + c) + 2a b - 4a ) +--R * +--R sinh(d x + c) +--R + +--R 2 2 3 2 +--R - 2a b cosh(d x + c) - 4a cosh(d x + c) + 2a b +--R * +--R d x + c +--R a tanh(-------) - b +--R 2 +--R atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 +--R (b cosh(d x + c) + 2a b)sinh(d x + c) +--R + +--R 2 2 2 2 +--R (2b cosh(d x + c) + 4a b cosh(d x + c) - 2b + 2a )sinh(d x + c) +--R + +--R 2 3 2 2 2 +--R b cosh(d x + c) + 2a b cosh(d x + c) + (- b + 2a )cosh(d x + c) +--R + +--R - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 2 3 +--R (b + a b )d sinh(d x + c) +--R + +--R 4 2 2 3 3 2 +--R ((2b + 2a b )d cosh(d x + c) + (3a b + 3a b)d)sinh(d x + c) +--R + +--R 4 2 2 2 3 3 +--R (b + a b )d cosh(d x + c) + (4a b + 4a b)d cosh(d x + c) +--R + +--R 4 2 2 4 +--R (- b + a b + 2a )d +--R * +--R sinh(d x + c) +--R + +--R 3 3 2 2 2 4 +--R (a b + a b)d cosh(d x + c) + (2a b + 2a )d cosh(d x + c) +--R + +--R 3 3 +--R (- a b - a b)d +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 79 + +--S 80 of 510 +d0015:= D(m0015,x) +--R +--R +--R (66) +--R 2 3 5 +--R - a b sinh(d x + c) +--R + +--R 4 2 2 3 4 3 2 +--R (- a b cosh(d x + c) - 4a b cosh(d x + c) + 4a b - a b ) +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 4 3 2 3 2 +--R - 4a b cosh(d x + c) - 10a b cosh(d x + c) +--R + +--R 4 3 2 2 3 +--R (8a b - 8a b )cosh(d x + c) + 10a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 4 2 3 3 +--R - 6a b cosh(d x + c) - 16a b cosh(d x + c) +--R + +--R 4 3 2 2 2 3 4 +--R (6a b - 18a b )cosh(d x + c) + (20a b - 4a b)cosh(d x + c) +--R + +--R 3 2 +--R 10a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 5 2 3 4 +--R - 4a b cosh(d x + c) - 13a b cosh(d x + c) +--R + +--R 4 3 2 3 2 3 4 2 +--R (4a b - 16a b )cosh(d x + c) + (14a b - 8a b)cosh(d x + c) +--R + +--R 3 2 2 3 4 +--R 16a b cosh(d x + c) - a b + 4a b +--R * +--R sinh(d x + c) +--R + +--R 4 6 2 3 5 +--R - a b cosh(d x + c) - 4a b cosh(d x + c) +--R + +--R 4 3 2 4 2 3 4 3 +--R (2a b - 5a b )cosh(d x + c) + (4a b - 4a b)cosh(d x + c) +--R + +--R 4 3 2 2 4 3 2 +--R (- a b + 6a b )cosh(d x + c) + 4a b cosh(d x + c) - a b +--R * +--R d x + c 2 +--R tanh(-------) +--R 2 +--R + +--R 5 6 5 4 5 +--R - 2b sinh(d x + c) + (- 8b cosh(d x + c) - 10a b )sinh(d x + c) +--R + +--R 5 2 4 5 2 3 +--R (- 10b cosh(d x + c) - 32a b cosh(d x + c) - 4b - 24a b ) +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 4 2 5 2 3 4 +--R - 28a b cosh(d x + c) + (- 8b - 56a b )cosh(d x + c) - 4a b +--R + +--R 3 2 +--R - 24a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 5 4 4 3 +--R 10b cosh(d x + c) + 8a b cosh(d x + c) +--R + +--R 5 2 3 2 4 3 2 +--R (- 8b - 32a b )cosh(d x + c) + (- 16a b - 48a b )cosh(d x + c) +--R + +--R 5 4 +--R - 2b - 8a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 5 4 4 +--R 8b cosh(d x + c) + 22a b cosh(d x + c) +--R + +--R 5 2 3 3 4 3 2 2 +--R (- 8b + 8a b )cosh(d x + c) + (- 20a b - 24a b )cosh(d x + c) +--R + +--R 2 3 4 4 +--R (- 8a b - 16a b)cosh(d x + c) - 2a b +--R * +--R sinh(d x + c) +--R + +--R 5 6 4 5 +--R 2b cosh(d x + c) + 8a b cosh(d x + c) +--R + +--R 5 2 3 4 4 3 +--R (- 4b + 8a b )cosh(d x + c) - 8a b cosh(d x + c) +--R + +--R 5 2 3 4 2 +--R (2b - 8a b - 8a b)cosh(d x + c) +--R * +--R d x + c +--R tanh(-------) +--R 2 +--R + +--R 2 3 5 +--R a b sinh(d x + c) +--R + +--R 4 2 2 3 4 3 2 4 +--R (a b cosh(d x + c) + 4a b cosh(d x + c) - 4a b + a b )sinh(d x + c) +--R + +--R 4 3 2 3 2 +--R 4a b cosh(d x + c) + 10a b cosh(d x + c) +--R + +--R 4 3 2 2 3 +--R (- 8a b + 8a b )cosh(d x + c) - 10a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 4 2 3 3 +--R 6a b cosh(d x + c) + 16a b cosh(d x + c) +--R + +--R 4 3 2 2 2 3 4 +--R (- 6a b + 18a b )cosh(d x + c) + (- 20a b + 4a b)cosh(d x + c) +--R + +--R 3 2 +--R - 10a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 5 2 3 4 +--R 4a b cosh(d x + c) + 13a b cosh(d x + c) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 4a b + 16a b )cosh(d x + c) + (- 14a b + 8a b)cosh(d x + c) +--R + +--R 3 2 2 3 4 +--R - 16a b cosh(d x + c) + a b - 4a b +--R * +--R sinh(d x + c) +--R + +--R 4 6 2 3 5 +--R a b cosh(d x + c) + 4a b cosh(d x + c) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 2a b + 5a b )cosh(d x + c) + (- 4a b + 4a b)cosh(d x + c) +--R + +--R 4 3 2 2 4 3 2 +--R (a b - 6a b )cosh(d x + c) - 4a b cosh(d x + c) + a b +--R / +--R 6 3 4 6 +--R (a b + a b )sinh(d x + c) +--R + +--R 6 3 4 2 5 4 3 5 +--R ((4a b + 4a b )cosh(d x + c) + 6a b + 6a b )sinh(d x + c) +--R + +--R 6 3 4 2 2 5 4 3 +--R (6a b + 6a b )cosh(d x + c) + (20a b + 20a b )cosh(d x + c) +--R + +--R 6 3 4 5 2 +--R - 2a b + 11a b + 13a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 6 3 4 3 2 5 4 3 2 +--R (4a b + 4a b )cosh(d x + c) + (24a b + 24a b )cosh(d x + c) +--R + +--R 6 3 4 5 2 2 5 4 3 6 +--R (- 4a b + 32a b + 36a b )cosh(d x + c) - 8a b + 4a b + 12a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 3 4 4 2 5 4 3 3 +--R (a b + a b )cosh(d x + c) + (12a b + 12a b )cosh(d x + c) +--R + +--R 6 3 4 5 2 2 +--R (- 2a b + 32a b + 34a b )cosh(d x + c) +--R + +--R 2 5 4 3 6 6 3 4 5 2 +--R (- 12a b + 16a b + 28a b)cosh(d x + c) + a b - 9a b - 6a b +--R + +--R 7 +--R 4a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 5 4 3 4 3 4 5 2 3 +--R (2a b + 2a b )cosh(d x + c) + (12a b + 12a b )cosh(d x + c) +--R + +--R 2 5 4 3 6 2 +--R (- 4a b + 16a b + 20a b)cosh(d x + c) +--R + +--R 3 4 5 2 7 2 5 4 3 6 +--R (- 12a b - 4a b + 8a )cosh(d x + c) + 2a b - 2a b - 4a b +--R * +--R sinh(d x + c) +--R + +--R 3 4 5 2 4 4 3 6 3 +--R (a b + a b )cosh(d x + c) + (4a b + 4a b)cosh(d x + c) +--R + +--R 3 4 5 2 7 2 4 3 6 +--R (- 2a b + 2a b + 4a )cosh(d x + c) + (- 4a b - 4a b)cosh(d x + c) +--R + +--R 3 4 5 2 +--R a b + a b +--R * +--R d x + c 2 +--R tanh(-------) +--R 2 +--R + +--R 7 2 5 6 +--R (- 2b - 2a b )sinh(d x + c) +--R + +--R 7 2 5 6 3 4 5 +--R ((- 8b - 8a b )cosh(d x + c) - 12a b - 12a b )sinh(d x + c) +--R + +--R 7 2 5 2 +--R (- 12b - 12a b )cosh(d x + c) +--R + +--R 6 3 4 7 2 5 4 3 +--R (- 40a b - 40a b )cosh(d x + c) + 4b - 22a b - 26a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 7 2 5 3 6 3 4 2 +--R (- 8b - 8a b )cosh(d x + c) + (- 48a b - 48a b )cosh(d x + c) +--R + +--R 7 2 5 4 3 6 3 4 5 2 +--R (8b - 64a b - 72a b )cosh(d x + c) + 16a b - 8a b - 24a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 7 2 5 4 6 3 4 3 +--R (- 2b - 2a b )cosh(d x + c) + (- 24a b - 24a b )cosh(d x + c) +--R + +--R 7 2 5 4 3 2 +--R (4b - 64a b - 68a b )cosh(d x + c) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (24a b - 32a b - 56a b )cosh(d x + c) - 2b + 18a b + 12a b +--R + +--R 6 +--R - 8a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 6 3 4 4 +--R (- 4a b - 4a b )cosh(d x + c) +--R + +--R 2 5 4 3 3 +--R (- 24a b - 24a b )cosh(d x + c) +--R + +--R 6 3 4 5 2 2 +--R (8a b - 32a b - 40a b )cosh(d x + c) +--R + +--R 2 5 4 3 6 6 3 4 5 2 +--R (24a b + 8a b - 16a b)cosh(d x + c) - 4a b + 4a b + 8a b +--R * +--R sinh(d x + c) +--R + +--R 2 5 4 3 4 3 4 5 2 3 +--R (- 2a b - 2a b )cosh(d x + c) + (- 8a b - 8a b )cosh(d x + c) +--R + +--R 2 5 4 3 6 2 3 4 5 2 +--R (4a b - 4a b - 8a b)cosh(d x + c) + (8a b + 8a b )cosh(d x + c) +--R + +--R 2 5 4 3 +--R - 2a b - 2a b +--R * +--R d x + c +--R tanh(-------) +--R 2 +--R + +--R 6 3 4 6 +--R (- a b - a b )sinh(d x + c) +--R + +--R 6 3 4 2 5 4 3 5 +--R ((- 4a b - 4a b )cosh(d x + c) - 6a b - 6a b )sinh(d x + c) +--R + +--R 6 3 4 2 2 5 4 3 +--R (- 6a b - 6a b )cosh(d x + c) + (- 20a b - 20a b )cosh(d x + c) +--R + +--R 6 3 4 5 2 +--R 2a b - 11a b - 13a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 6 3 4 3 2 5 4 3 2 +--R (- 4a b - 4a b )cosh(d x + c) + (- 24a b - 24a b )cosh(d x + c) +--R + +--R 6 3 4 5 2 2 5 4 3 6 +--R (4a b - 32a b - 36a b )cosh(d x + c) + 8a b - 4a b - 12a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 3 4 4 2 5 4 3 3 +--R (- a b - a b )cosh(d x + c) + (- 12a b - 12a b )cosh(d x + c) +--R + +--R 6 3 4 5 2 2 +--R (2a b - 32a b - 34a b )cosh(d x + c) +--R + +--R 2 5 4 3 6 6 3 4 5 2 7 +--R (12a b - 16a b - 28a b)cosh(d x + c) - a b + 9a b + 6a b - 4a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 5 4 3 4 3 4 5 2 3 +--R (- 2a b - 2a b )cosh(d x + c) + (- 12a b - 12a b )cosh(d x + c) +--R + +--R 2 5 4 3 6 2 +--R (4a b - 16a b - 20a b)cosh(d x + c) +--R + +--R 3 4 5 2 7 2 5 4 3 6 +--R (12a b + 4a b - 8a )cosh(d x + c) - 2a b + 2a b + 4a b +--R * +--R sinh(d x + c) +--R + +--R 3 4 5 2 4 4 3 6 3 +--R (- a b - a b )cosh(d x + c) + (- 4a b - 4a b)cosh(d x + c) +--R + +--R 3 4 5 2 7 2 4 3 6 3 4 +--R (2a b - 2a b - 4a )cosh(d x + c) + (4a b + 4a b)cosh(d x + c) - a b +--R + +--R 5 2 +--R - a b +--R Type: Expression(Integer) +--E 80 + +--S 81 of 510 +t0016:= 1/(a+b*sinh(c+d*x))^3 +--R +--R +--R 1 +--R (67) ---------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R b sinh(d x + c) + 3a b sinh(d x + c) + 3a b sinh(d x + c) + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 510 +r0016:= -(-b^2+2*a^2)*atanh((b-a*tanh(1/2*c+1/2*d*x))/(a^2+b^2)^(1/2))/_ + (a^2+b^2)^(5/2)/d-1/2*b*cosh(c+d*x)/(a^2+b^2)/d/(a+b*sinh(c+d*x))^2-_ + 3/2*a*b*cosh(c+d*x)/(a^2+b^2)^2/d/(a+b*sinh(c+d*x)) +--R +--R +--R (68) +--R 4 2 2 2 3 3 2 2 +--R (- 2b + 4a b )sinh(d x + c) + (- 4a b + 8a b)sinh(d x + c) - 2a b +--R + +--R 4 +--R 4a +--R * +--R d x + c +--R a tanh(-------) - b +--R 2 +--R atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 3 2 | 2 2 +--R (- 3a b cosh(d x + c)sinh(d x + c) + (- b - 4a b)cosh(d x + c))\|b + a +--R / +--R 6 2 4 4 2 2 +--R (2b + 4a b + 2a b )d sinh(d x + c) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (4a b + 8a b + 4a b)d sinh(d x + c) + (2a b + 4a b + 2a )d +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 82 + +--S 83 of 510 +a0016:= integrate(t0016,x) +--R +--R +--R (69) +--R 4 2 2 4 +--R (b - 2a b )sinh(d x + c) +--R + +--R 4 2 2 3 3 3 +--R ((4b - 8a b )cosh(d x + c) + 4a b - 8a b)sinh(d x + c) +--R + +--R 4 2 2 2 3 3 +--R (6b - 12a b )cosh(d x + c) + (12a b - 24a b)cosh(d x + c) +--R + +--R 4 2 2 4 +--R - 2b + 8a b - 8a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 2 2 3 3 3 2 +--R (4b - 8a b )cosh(d x + c) + (12a b - 24a b)cosh(d x + c) +--R + +--R 4 2 2 4 3 3 +--R (- 4b + 16a b - 16a )cosh(d x + c) - 4a b + 8a b +--R * +--R sinh(d x + c) +--R + +--R 4 2 2 4 3 3 3 +--R (b - 2a b )cosh(d x + c) + (4a b - 8a b)cosh(d x + c) +--R + +--R 4 2 2 4 2 3 3 +--R (- 2b + 8a b - 8a )cosh(d x + c) + (- 4a b + 8a b)cosh(d x + c) +--R + +--R 4 2 2 +--R b - 2a b +--R * +--R log +--R 2 2 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a b)sinh(d x + c) +--R + +--R 2 2 2 2 +--R b cosh(d x + c) + 2a b cosh(d x + c) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 +--R (2b + 2a b)sinh(d x + c) + (2b + 2a b)cosh(d x + c) + 2a b +--R + +--R 3 +--R 2a +--R / +--R 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R 2 +--R b cosh(d x + c) + 2a cosh(d x + c) - b +--R + +--R 3 2 3 +--R (- 2b + 4a b)sinh(d x + c) +--R + +--R 3 2 2 3 2 +--R ((- 6b + 12a b)cosh(d x + c) - 6a b + 12a )sinh(d x + c) +--R + +--R 3 2 2 2 3 +--R (- 6b + 12a b)cosh(d x + c) + (- 12a b + 24a )cosh(d x + c) +--R + +--R 3 2 +--R - 2b - 20a b +--R * +--R sinh(d x + c) +--R + +--R 3 2 3 2 3 2 +--R (- 2b + 4a b)cosh(d x + c) + (- 6a b + 12a )cosh(d x + c) +--R + +--R 3 2 2 +--R (- 2b - 20a b)cosh(d x + c) + 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 6 2 4 4 2 4 +--R (2b + 4a b + 2a b )d sinh(d x + c) +--R + +--R 6 2 4 4 2 5 3 3 5 +--R ((8b + 16a b + 8a b )d cosh(d x + c) + (8a b + 16a b + 8a b)d) +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 2 4 4 2 2 +--R (12b + 24a b + 12a b )d cosh(d x + c) +--R + +--R 5 3 3 5 6 4 2 6 +--R (24a b + 48a b + 24a b)d cosh(d x + c) + (- 4b + 12a b + 8a )d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 6 2 4 4 2 3 +--R (8b + 16a b + 8a b )d cosh(d x + c) +--R + +--R 5 3 3 5 2 +--R (24a b + 48a b + 24a b)d cosh(d x + c) +--R + +--R 6 4 2 6 5 3 3 5 +--R (- 8b + 24a b + 16a )d cosh(d x + c) + (- 8a b - 16a b - 8a b)d +--R * +--R sinh(d x + c) +--R + +--R 6 2 4 4 2 4 +--R (2b + 4a b + 2a b )d cosh(d x + c) +--R + +--R 5 3 3 5 3 +--R (8a b + 16a b + 8a b)d cosh(d x + c) +--R + +--R 6 4 2 6 2 +--R (- 4b + 12a b + 8a )d cosh(d x + c) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 8a b - 16a b - 8a b)d cosh(d x + c) + (2b + 4a b + 2a b )d +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 510 +m0016:= a0016-r0016 +--R +--R +--R (70) +--R 6 2 4 6 +--R (b - 2a b )sinh(d x + c) +--R + +--R 6 2 4 5 3 3 5 +--R ((4b - 8a b )cosh(d x + c) + 6a b - 12a b )sinh(d x + c) +--R + +--R 6 2 4 2 5 3 3 +--R (6b - 12a b )cosh(d x + c) + (20a b - 40a b )cosh(d x + c) +--R + +--R 6 2 4 4 2 +--R - 2b + 17a b - 26a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 6 2 4 3 5 3 3 2 +--R (4b - 8a b )cosh(d x + c) + (24a b - 48a b )cosh(d x + c) +--R + +--R 6 2 4 4 2 5 3 3 5 +--R (- 4b + 44a b - 72a b )cosh(d x + c) - 8a b + 28a b - 24a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 2 4 4 5 3 3 3 +--R (b - 2a b )cosh(d x + c) + (12a b - 24a b )cosh(d x + c) +--R + +--R 6 2 4 4 2 2 +--R (- 2b + 38a b - 68a b )cosh(d x + c) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 12a b + 52a b - 56a b)cosh(d x + c) + b - 12a b + 24a b +--R + +--R 6 +--R - 8a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (2a b - 4a b )cosh(d x + c) + (12a b - 24a b )cosh(d x + c) +--R + +--R 5 3 3 5 2 +--R (- 4a b + 28a b - 40a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (- 12a b + 32a b - 16a )cosh(d x + c) + 2a b - 8a b + 8a b +--R * +--R sinh(d x + c) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (a b - 2a b )cosh(d x + c) + (4a b - 8a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 2 3 3 5 +--R (- 2a b + 8a b - 8a )cosh(d x + c) + (- 4a b + 8a b)cosh(d x + c) +--R + +--R 2 4 4 2 +--R a b - 2a b +--R * +--R log +--R 2 2 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a b)sinh(d x + c) +--R + +--R 2 2 2 2 +--R b cosh(d x + c) + 2a b cosh(d x + c) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 +--R (2b + 2a b)sinh(d x + c) + (2b + 2a b)cosh(d x + c) + 2a b +--R + +--R 3 +--R 2a +--R / +--R 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R 2 +--R b cosh(d x + c) + 2a cosh(d x + c) - b +--R + +--R 6 2 4 6 +--R (2b - 4a b )sinh(d x + c) +--R + +--R 6 2 4 5 3 3 5 +--R ((8b - 16a b )cosh(d x + c) + 12a b - 24a b )sinh(d x + c) +--R + +--R 6 2 4 2 5 3 3 +--R (12b - 24a b )cosh(d x + c) + (40a b - 80a b )cosh(d x + c) +--R + +--R 6 2 4 4 2 +--R - 4b + 34a b - 52a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 6 2 4 3 5 3 3 2 +--R (8b - 16a b )cosh(d x + c) + (48a b - 96a b )cosh(d x + c) +--R + +--R 6 2 4 4 2 5 3 3 5 +--R (- 8b + 88a b - 144a b )cosh(d x + c) - 16a b + 56a b - 48a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 2 4 4 5 3 3 3 +--R (2b - 4a b )cosh(d x + c) + (24a b - 48a b )cosh(d x + c) +--R + +--R 6 2 4 4 2 2 +--R (- 4b + 76a b - 136a b )cosh(d x + c) +--R + +--R 5 3 3 5 6 2 4 +--R (- 24a b + 104a b - 112a b)cosh(d x + c) + 2b - 24a b +--R + +--R 4 2 6 +--R 48a b - 16a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (4a b - 8a b )cosh(d x + c) + (24a b - 48a b )cosh(d x + c) +--R + +--R 5 3 3 5 2 +--R (- 8a b + 56a b - 80a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (- 24a b + 64a b - 32a )cosh(d x + c) + 4a b - 16a b + 16a b +--R * +--R sinh(d x + c) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (2a b - 4a b )cosh(d x + c) + (8a b - 16a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 2 +--R (- 4a b + 16a b - 16a )cosh(d x + c) +--R + +--R 3 3 5 2 4 4 2 +--R (- 8a b + 16a b)cosh(d x + c) + 2a b - 4a b +--R * +--R d x + c +--R a tanh(-------) - b +--R 2 +--R atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 5 2 3 5 +--R (3a b cosh(d x + c) - 2b + 4a b )sinh(d x + c) +--R + +--R 4 2 5 2 3 4 +--R 12a b cosh(d x + c) + (- 5b + 28a b )cosh(d x + c) - 10a b +--R + +--R 3 2 +--R 20a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 4 3 5 2 3 2 +--R 18a b cosh(d x + c) + (- 2b + 64a b )cosh(d x + c) +--R + +--R 4 3 2 5 2 3 4 +--R (- 26a b + 76a b )cosh(d x + c) - 2b - 34a b + 28a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 4 5 2 3 3 +--R 12a b cosh(d x + c) + (4b + 64a b )cosh(d x + c) +--R + +--R 4 3 2 2 +--R (- 18a b + 108a b )cosh(d x + c) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 4b - 66a b + 76a b)cosh(d x + c) + 2a b - 46a b + 12a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 5 5 2 3 4 +--R 3a b cosh(d x + c) + (4b + 28a b )cosh(d x + c) +--R + +--R 4 3 2 3 +--R (2a b + 68a b )cosh(d x + c) +--R + +--R 5 2 3 4 2 +--R (- 4b - 38a b + 68a b)cosh(d x + c) +--R + +--R 4 3 2 5 2 3 4 +--R (- 5a b - 68a b + 24a )cosh(d x + c) + 10a b - 20a b +--R * +--R sinh(d x + c) +--R + +--R 5 2 3 5 4 3 2 4 +--R (b + 4a b )cosh(d x + c) + (4a b + 16a b )cosh(d x + c) +--R + +--R 5 2 3 4 3 +--R (- 2b - 6a b + 20a b)cosh(d x + c) +--R + +--R 4 3 2 5 2 +--R (- 4a b - 22a b + 12a )cosh(d x + c) +--R + +--R 5 2 3 4 3 2 +--R (b + 2a b - 20a b)cosh(d x + c) + 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 8 2 6 4 4 6 +--R (2b + 4a b + 2a b )d sinh(d x + c) +--R + +--R 8 2 6 4 4 7 3 5 5 3 +--R ((8b + 16a b + 8a b )d cosh(d x + c) + (12a b + 24a b + 12a b )d) +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 2 6 4 4 2 +--R (12b + 24a b + 12a b )d cosh(d x + c) +--R + +--R 7 3 5 5 3 +--R (40a b + 80a b + 40a b )d cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 +--R (- 4b + 18a b + 48a b + 26a b )d +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 2 6 4 4 3 +--R (8b + 16a b + 8a b )d cosh(d x + c) +--R + +--R 7 3 5 5 3 2 +--R (48a b + 96a b + 48a b )d cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 +--R (- 8b + 56a b + 136a b + 72a b )d cosh(d x + c) +--R + +--R 7 3 5 5 3 7 +--R (- 16a b - 8a b + 32a b + 24a b)d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 8 2 6 4 4 4 +--R (2b + 4a b + 2a b )d cosh(d x + c) +--R + +--R 7 3 5 5 3 3 +--R (24a b + 48a b + 24a b )d cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 4b + 60a b + 132a b + 68a b )d cosh(d x + c) +--R + +--R 7 3 5 5 3 7 +--R (- 24a b + 8a b + 88a b + 56a b)d cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 +--R (2b - 16a b - 30a b - 4a b + 8a )d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 7 3 5 5 3 4 +--R (4a b + 8a b + 4a b )d cosh(d x + c) +--R + +--R 2 6 4 4 6 2 3 +--R (24a b + 48a b + 24a b )d cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (- 8a b + 24a b + 72a b + 40a b)d cosh(d x + c) +--R + +--R 2 6 4 4 6 2 8 +--R (- 24a b - 32a b + 8a b + 16a )d cosh(d x + c) +--R + +--R 7 5 3 7 +--R (4a b - 12a b - 8a b)d +--R * +--R sinh(d x + c) +--R + +--R 2 6 4 4 6 2 4 +--R (2a b + 4a b + 2a b )d cosh(d x + c) +--R + +--R 3 5 5 3 7 3 +--R (8a b + 16a b + 8a b)d cosh(d x + c) +--R + +--R 2 6 6 2 8 2 +--R (- 4a b + 12a b + 8a )d cosh(d x + c) +--R + +--R 3 5 5 3 7 2 6 4 4 6 2 +--R (- 8a b - 16a b - 8a b)d cosh(d x + c) + (2a b + 4a b + 2a b )d +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 84 + +--S 85 of 510 +d0016:= D(m0016,x) +--R +--R +--R (71) +--R 8 2 6 9 +--R (b + a b )sinh(d x + c) +--R + +--R 8 2 6 7 3 5 8 +--R ((6b + 6a b )cosh(d x + c) + 10a b + 7a b )sinh(d x + c) +--R + +--R 8 2 6 2 7 3 5 +--R (15b + 12a b )cosh(d x + c) + (54a b + 36a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 +--R - 3b + 37a b + 16a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 8 2 6 3 7 3 5 2 +--R (20b + 2a b )cosh(d x + c) + (118a b + 52a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 7 3 5 5 3 +--R (- 12b + 180a b + 66a b )cosh(d x + c) - 8a b + 98a b + 22a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 2 6 4 7 3 5 3 +--R (15b - 30a b )cosh(d x + c) + (128a b - 40a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 2 +--R (- 18b + 351a b + 36a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 8 2 6 +--R (- 36a b + 390a b + 48a b )cosh(d x + c) + 3b - 21a b +--R + +--R 4 4 6 2 +--R 164a b + 20a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 2 6 5 7 3 5 4 +--R (6b - 54a b )cosh(d x + c) + (60a b - 210a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 3 +--R (- 12b + 332a b - 226a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 2 +--R (- 54a b + 636a b - 90a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 7 3 5 +--R (6b - 66a b + 570a b + 12a b )cosh(d x + c) + 18a b - 42a b +--R + +--R 5 3 7 +--R 158a b + 8a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 2 6 6 7 3 5 5 +--R (b - 44a b )cosh(d x + c) + (- 10a b - 268a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 4 +--R (- 3b + 123a b - 504a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 3 +--R (- 20a b + 540a b - 400a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 2 +--R (3b - 66a b + 800a b - 136a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (30a b - 96a b + 504a b )cosh(d x + c) - b + 35a b - 44a b +--R + +--R 6 2 +--R 88a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 6 7 7 3 5 6 +--R - 18a b cosh(d x + c) + (- 26a b - 164a b )cosh(d x + c) +--R + +--R 2 6 4 4 5 +--R (- 36a b - 450a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 4 +--R (24a b + 234a b - 510a b )cosh(d x + c) +--R + +--R 2 6 4 4 6 2 3 +--R (6a b + 596a b - 280a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (6a b - 72a b + 612a b - 48a b)cosh(d x + c) +--R + +--R 2 6 4 4 6 2 7 3 5 +--R (48a b - 90a b + 240a b )cosh(d x + c) - 4a b + 26a b +--R + +--R 5 3 7 +--R - 30a b + 24a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 6 8 7 3 5 7 +--R - 3a b cosh(d x + c) + (- 12a b - 48a b )cosh(d x + c) +--R + +--R 2 6 4 4 6 +--R (- 47a b - 188a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 5 +--R (24a b + 30a b - 288a b )cosh(d x + c) +--R + +--R 2 6 4 4 6 2 4 +--R (51a b + 252a b - 204a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 3 +--R (- 12a b - 12a b + 344a b - 64a b)cosh(d x + c) +--R + +--R 2 6 4 4 6 2 2 +--R (3a b - 72a b + 216a b )cosh(d x + c) +--R + +--R 3 5 5 3 7 2 6 4 4 6 2 +--R (30a b - 48a b + 48a b)cosh(d x + c) - 4a b + 8a b - 12a b +--R * +--R sinh(d x + c) +--R + +--R 7 3 5 8 2 6 4 4 7 +--R (- 2a b - 5a b )cosh(d x + c) + (- 12a b - 30a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 6 +--R (6a b - 8a b - 62a b )cosh(d x + c) +--R + +--R 2 6 4 4 6 2 5 +--R (24a b + 50a b - 52a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 4 +--R (- 6a b + 6a b + 78a b - 24a b)cosh(d x + c) +--R + +--R 2 6 4 4 6 2 3 +--R (- 12a b - 26a b + 64a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b + 8a b - 18a b + 24a b)cosh(d x + c) +--R + +--R 4 4 6 2 3 5 5 3 +--R (6a b - 12a b )cosh(d x + c) - a b + 2a b +--R * +--R d x + c 2 +--R tanh(-------) +--R 2 +--R + +--R 7 9 +--R - 6a b sinh(d x + c) +--R + +--R 7 8 2 6 8 +--R (- 36a b cosh(d x + c) - 2b - 50a b )sinh(d x + c) +--R + +--R 7 2 8 2 6 7 +--R - 84a b cosh(d x + c) + (- 12b - 264a b )cosh(d x + c) + 4a b +--R + +--R 3 5 +--R - 164a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 7 3 8 2 6 2 +--R - 84a b cosh(d x + c) + (- 26b - 524a b )cosh(d x + c) +--R + +--R 3 5 8 2 6 4 4 +--R - 756a b cosh(d x + c) - 26b + 14a b - 296a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 2 6 3 +--R (- 16b - 400a b )cosh(d x + c) +--R + +--R 7 3 5 2 +--R (- 36a b - 1260a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 7 3 5 +--R (- 72b + 36a b - 1152a b )cosh(d x + c) - 84a b + 32a b +--R + +--R 5 3 +--R - 304a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 7 5 8 2 6 4 +--R 84a b cosh(d x + c) + (30b + 120a b )cosh(d x + c) +--R + +--R 7 3 5 3 +--R (- 40a b - 700a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 2 +--R (- 72b - 42a b - 1560a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 8 2 6 +--R (- 228a b + 24a b - 1008a b )cosh(d x + c) - 6b - 126a b +--R + +--R 4 4 6 2 +--R 56a b - 160a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 7 6 8 2 6 5 +--R 84a b cosh(d x + c) + (68b + 440a b )cosh(d x + c) +--R + +--R 7 3 5 4 +--R (60a b + 420a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 3 +--R (- 56b - 184a b - 608a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 2 +--R (- 228a b - 208a b - 1120a b )cosh(d x + c) +--R + +--R 8 2 6 6 2 7 3 5 +--R (- 12b - 288a b - 480a b )cosh(d x + c) - 12a b - 116a b +--R + +--R 5 3 7 +--R 32a b - 32a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 7 7 8 2 6 6 +--R 36a b cosh(d x + c) + (58b + 316a b )cosh(d x + c) +--R + +--R 7 3 5 5 +--R (144a b + 756a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 4 +--R (- 66b - 150a b + 456a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 3 +--R (- 156a b - 448a b - 352a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 2 +--R (6b - 216a b - 288a b - 480a b )cosh(d x + c) +--R + +--R 7 3 5 7 8 2 6 4 4 +--R (- 24a b - 180a b - 96a b)cosh(d x + c) + 2b + 2a b - 48a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 7 8 8 2 6 7 +--R 6a b cosh(d x + c) + (24b + 96a b )cosh(d x + c) +--R + +--R 7 3 5 6 +--R (100a b + 364a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 5 +--R (- 48b - 12a b + 480a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 4 +--R (- 120a b - 336a b + 144a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 3 +--R (24b - 72a b - 352a b - 160a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (12a b - 36a b - 96a b - 96a b)cosh(d x + c) +--R + +--R 2 6 4 4 7 3 5 +--R (- 12a b - 48a b )cosh(d x + c) + 2a b + 8a b +--R * +--R sinh(d x + c) +--R + +--R 8 2 6 8 7 3 5 7 +--R (4b + 10a b )cosh(d x + c) + (24a b + 60a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 +--R (- 12b + 18a b + 120a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 5 +--R (- 48a b - 88a b + 80a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 4 +--R (12b - 18a b - 120a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 3 +--R (24a b + 28a b - 64a b - 32a b)cosh(d x + c) +--R + +--R 8 2 6 2 +--R (- 4b - 10a b )cosh(d x + c) +--R * +--R d x + c +--R tanh(-------) +--R 2 +--R + +--R 8 2 6 9 +--R (- b - a b )sinh(d x + c) +--R + +--R 8 2 6 7 3 5 8 +--R ((- 6b - 6a b )cosh(d x + c) - 10a b - 7a b )sinh(d x + c) +--R + +--R 8 2 6 2 7 3 5 +--R (- 15b - 12a b )cosh(d x + c) + (- 54a b - 36a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 +--R 3b - 37a b - 16a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 8 2 6 3 7 3 5 2 +--R (- 20b - 2a b )cosh(d x + c) + (- 118a b - 52a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 7 3 5 5 3 +--R (12b - 180a b - 66a b )cosh(d x + c) + 8a b - 98a b - 22a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 2 6 4 7 3 5 3 +--R (- 15b + 30a b )cosh(d x + c) + (- 128a b + 40a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 2 +--R (18b - 351a b - 36a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (36a b - 390a b - 48a b )cosh(d x + c) - 3b + 21a b - 164a b +--R + +--R 6 2 +--R - 20a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 2 6 5 7 3 5 4 +--R (- 6b + 54a b )cosh(d x + c) + (- 60a b + 210a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 3 +--R (12b - 332a b + 226a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 2 +--R (54a b - 636a b + 90a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 7 3 5 +--R (- 6b + 66a b - 570a b - 12a b )cosh(d x + c) - 18a b + 42a b +--R + +--R 5 3 7 +--R - 158a b - 8a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 2 6 6 7 3 5 5 +--R (- b + 44a b )cosh(d x + c) + (10a b + 268a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 4 +--R (3b - 123a b + 504a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 3 +--R (20a b - 540a b + 400a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 3b + 66a b - 800a b + 136a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (- 30a b + 96a b - 504a b )cosh(d x + c) + b - 35a b + 44a b +--R + +--R 6 2 +--R - 88a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 6 7 7 3 5 6 +--R 18a b cosh(d x + c) + (26a b + 164a b )cosh(d x + c) +--R + +--R 2 6 4 4 5 +--R (36a b + 450a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 4 +--R (- 24a b - 234a b + 510a b )cosh(d x + c) +--R + +--R 2 6 4 4 6 2 3 +--R (- 6a b - 596a b + 280a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b + 72a b - 612a b + 48a b)cosh(d x + c) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 +--R (- 48a b + 90a b - 240a b )cosh(d x + c) + 4a b - 26a b + 30a b +--R + +--R 7 +--R - 24a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 6 8 7 3 5 7 +--R 3a b cosh(d x + c) + (12a b + 48a b )cosh(d x + c) +--R + +--R 2 6 4 4 6 +--R (47a b + 188a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 5 +--R (- 24a b - 30a b + 288a b )cosh(d x + c) +--R + +--R 2 6 4 4 6 2 4 +--R (- 51a b - 252a b + 204a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 3 +--R (12a b + 12a b - 344a b + 64a b)cosh(d x + c) +--R + +--R 2 6 4 4 6 2 2 +--R (- 3a b + 72a b - 216a b )cosh(d x + c) +--R + +--R 3 5 5 3 7 2 6 4 4 6 2 +--R (- 30a b + 48a b - 48a b)cosh(d x + c) + 4a b - 8a b + 12a b +--R * +--R sinh(d x + c) +--R + +--R 7 3 5 8 2 6 4 4 7 +--R (2a b + 5a b )cosh(d x + c) + (12a b + 30a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 6 +--R (- 6a b + 8a b + 62a b )cosh(d x + c) +--R + +--R 2 6 4 4 6 2 5 +--R (- 24a b - 50a b + 52a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b - 6a b - 78a b + 24a b)cosh(d x + c) +--R + +--R 2 6 4 4 6 2 3 +--R (12a b + 26a b - 64a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (- 2a b - 8a b + 18a b - 24a b)cosh(d x + c) +--R + +--R 4 4 6 2 3 5 5 3 +--R (- 6a b + 12a b )cosh(d x + c) + a b - 2a b +--R / +--R 10 3 8 5 6 9 +--R (2a b + 4a b + 2a b )sinh(d x + c) +--R + +--R 10 3 8 5 6 2 9 4 7 +--R (12a b + 24a b + 12a b )cosh(d x + c) + 18a b + 36a b +--R + +--R 6 5 +--R 18a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (30a b + 60a b + 30a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 10 3 8 +--R (96a b + 192a b + 96a b )cosh(d x + c) - 6a b + 54a b +--R + +--R 5 6 7 4 +--R 126a b + 66a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 3 +--R (40a b + 80a b + 40a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 2 +--R (210a b + 420a b + 210a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 9 +--R (- 24a b + 264a b + 600a b + 312a b )cosh(d x + c) - 42a b +--R + +--R 4 7 6 5 8 3 +--R 42a b + 210a b + 126a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 4 +--R (30a b + 60a b + 30a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 3 +--R (240a b + 480a b + 240a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 +--R (- 36a b + 522a b + 1152a b + 594a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (- 144a b + 240a b + 912a b + 528a b )cosh(d x + c) + 6a b +--R + +--R 3 8 5 6 7 4 9 2 +--R - 102a b - 90a b + 150a b + 132a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 5 +--R (12a b + 24a b + 12a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 4 +--R (150a b + 300a b + 150a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 24a b + 528a b + 1128a b + 576a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 2 +--R (- 180a b + 510a b + 1560a b + 870a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (12a b - 312a b - 168a b + 648a b + 492a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R 30a b - 90a b - 198a b - 6a b + 72a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 6 +--R (2a b + 4a b + 2a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 5 +--R (48a b + 96a b + 48a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 4 +--R (- 6a b + 282a b + 582a b + 294a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (- 96a b + 512a b + 1312a b + 704a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (6a b - 336a b + 6a b + 1044a b + 696a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (48a b - 288a b - 480a b + 96a b + 240a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 11 +--R - 2a b + 50a b + 10a b - 122a b - 64a b + 16a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 9 4 7 6 5 6 +--R (6a b + 12a b + 6a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 5 +--R (72a b + 144a b + 72a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 4 +--R (- 18a b + 246a b + 546a b + 282a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (- 144a b + 168a b + 768a b + 456a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (18a b - 288a b - 342a b + 252a b + 288a b)cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 11 +--R (72a b - 72a b - 312a b - 120a b + 48a )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R - 6a b + 30a b + 54a b - 6a b - 24a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 8 5 6 7 4 6 +--R (6a b + 12a b + 6a b )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 5 +--R (48a b + 96a b + 48a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 4 +--R (- 18a b + 96a b + 246a b + 132a b )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 10 3 +--R (- 96a b - 48a b + 192a b + 144a b)cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 11 2 +--R (18a b - 108a b - 222a b - 48a b + 48a )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 10 3 8 7 4 +--R (48a b + 48a b - 48a b - 48a b)cosh(d x + c) - 6a b + 18a b +--R + +--R 9 2 +--R 12a b +--R * +--R sinh(d x + c) +--R + +--R 4 7 6 5 8 3 6 +--R (2a b + 4a b + 2a b )cosh(d x + c) +--R + +--R 5 6 7 4 9 2 5 +--R (12a b + 24a b + 12a b )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 10 4 +--R (- 6a b + 12a b + 42a b + 24a b)cosh(d x + c) +--R + +--R 5 6 7 4 9 2 11 3 +--R (- 24a b - 32a b + 8a b + 16a )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 10 2 +--R (6a b - 12a b - 42a b - 24a b)cosh(d x + c) +--R + +--R 5 6 7 4 9 2 4 7 6 5 8 3 +--R (12a b + 24a b + 12a b )cosh(d x + c) - 2a b - 4a b - 2a b +--R * +--R d x + c 2 +--R tanh(-------) +--R 2 +--R + +--R 11 2 9 4 7 9 +--R (- 4b - 8a b - 4a b )sinh(d x + c) +--R + +--R 11 2 9 4 7 10 3 8 +--R (- 24b - 48a b - 24a b )cosh(d x + c) - 36a b - 72a b +--R + +--R 5 6 +--R - 36a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 11 2 9 4 7 2 +--R (- 60b - 120a b - 60a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 11 2 9 +--R (- 192a b - 384a b - 192a b )cosh(d x + c) + 12b - 108a b +--R + +--R 4 7 6 5 +--R - 252a b - 132a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 11 2 9 4 7 3 +--R (- 80b - 160a b - 80a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (- 420a b - 840a b - 420a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 10 +--R (48b - 528a b - 1200a b - 624a b )cosh(d x + c) + 84a b +--R + +--R 3 8 5 6 7 4 +--R - 84a b - 420a b - 252a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 11 2 9 4 7 4 +--R (- 60b - 120a b - 60a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 3 +--R (- 480a b - 960a b - 480a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 2 +--R (72b - 1044a b - 2304a b - 1188a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 11 +--R (288a b - 480a b - 1824a b - 1056a b )cosh(d x + c) - 12b +--R + +--R 2 9 4 7 6 5 8 3 +--R 204a b + 180a b - 300a b - 264a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 11 2 9 4 7 5 +--R (- 24b - 48a b - 24a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 4 +--R (- 300a b - 600a b - 300a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 3 +--R (48b - 1056a b - 2256a b - 1152a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 +--R (360a b - 1020a b - 3120a b - 1740a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 +--R (- 24b + 624a b + 336a b - 1296a b - 984a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R - 60a b + 180a b + 396a b + 12a b - 144a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 11 2 9 4 7 6 +--R (- 4b - 8a b - 4a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 5 +--R (- 96a b - 192a b - 96a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 4 +--R (12b - 564a b - 1164a b - 588a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (192a b - 1024a b - 2624a b - 1408a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 2 +--R (- 12b + 672a b - 12a b - 2088a b - 1392a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (- 96a b + 576a b + 960a b - 192a b - 480a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 10 +--R 4b - 100a b - 20a b + 244a b + 128a b - 32a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 6 +--R (- 12a b - 24a b - 12a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 5 +--R (- 144a b - 288a b - 144a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 4 +--R (36a b - 492a b - 1092a b - 564a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (288a b - 336a b - 1536a b - 912a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (- 36a b + 576a b + 684a b - 504a b - 576a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (- 144a b + 144a b + 624a b + 240a b - 96a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R 12a b - 60a b - 108a b + 12a b + 48a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 9 4 7 6 5 6 +--R (- 12a b - 24a b - 12a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 5 +--R (- 96a b - 192a b - 96a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 4 +--R (36a b - 192a b - 492a b - 264a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (192a b + 96a b - 384a b - 288a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (- 36a b + 216a b + 444a b + 96a b - 96a b)cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 2 9 +--R (- 96a b - 96a b + 96a b + 96a b )cosh(d x + c) + 12a b +--R + +--R 6 5 8 3 +--R - 36a b - 24a b +--R * +--R sinh(d x + c) +--R + +--R 3 8 5 6 7 4 6 +--R (- 4a b - 8a b - 4a b )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 5 +--R (- 24a b - 48a b - 24a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 4 +--R (12a b - 24a b - 84a b - 48a b )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 10 3 +--R (48a b + 64a b - 16a b - 32a b)cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 2 +--R (- 12a b + 24a b + 84a b + 48a b )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 3 8 5 6 7 4 +--R (- 24a b - 48a b - 24a b )cosh(d x + c) + 4a b + 8a b + 4a b +--R * +--R d x + c +--R tanh(-------) +--R 2 +--R + +--R 10 3 8 5 6 9 +--R (- 2a b - 4a b - 2a b )sinh(d x + c) +--R + +--R 10 3 8 5 6 2 9 4 7 6 5 +--R ((- 12a b - 24a b - 12a b )cosh(d x + c) - 18a b - 36a b - 18a b ) +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (- 30a b - 60a b - 30a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 10 3 8 +--R (- 96a b - 192a b - 96a b )cosh(d x + c) + 6a b - 54a b +--R + +--R 5 6 7 4 +--R - 126a b - 66a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 3 +--R (- 40a b - 80a b - 40a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 2 +--R (- 210a b - 420a b - 210a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 9 +--R (24a b - 264a b - 600a b - 312a b )cosh(d x + c) + 42a b +--R + +--R 4 7 6 5 8 3 +--R - 42a b - 210a b - 126a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 4 +--R (- 30a b - 60a b - 30a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 3 +--R (- 240a b - 480a b - 240a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 +--R (36a b - 522a b - 1152a b - 594a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (144a b - 240a b - 912a b - 528a b )cosh(d x + c) - 6a b +--R + +--R 3 8 5 6 7 4 9 2 +--R 102a b + 90a b - 150a b - 132a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 5 +--R (- 12a b - 24a b - 12a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 4 +--R (- 150a b - 300a b - 150a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (24a b - 528a b - 1128a b - 576a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 2 +--R (180a b - 510a b - 1560a b - 870a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (- 12a b + 312a b + 168a b - 648a b - 492a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R - 30a b + 90a b + 198a b + 6a b - 72a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 6 +--R (- 2a b - 4a b - 2a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 5 +--R (- 48a b - 96a b - 48a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 4 +--R (6a b - 282a b - 582a b - 294a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (96a b - 512a b - 1312a b - 704a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (- 6a b + 336a b - 6a b - 1044a b - 696a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (- 48a b + 288a b + 480a b - 96a b - 240a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 11 +--R 2a b - 50a b - 10a b + 122a b + 64a b - 16a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 9 4 7 6 5 6 +--R (- 6a b - 12a b - 6a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 5 +--R (- 72a b - 144a b - 72a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 4 +--R (18a b - 246a b - 546a b - 282a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (144a b - 168a b - 768a b - 456a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (- 18a b + 288a b + 342a b - 252a b - 288a b)cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 11 2 9 +--R (- 72a b + 72a b + 312a b + 120a b - 48a )cosh(d x + c) + 6a b +--R + +--R 4 7 6 5 8 3 10 +--R - 30a b - 54a b + 6a b + 24a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 8 5 6 7 4 6 +--R (- 6a b - 12a b - 6a b )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 5 +--R (- 48a b - 96a b - 48a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 4 +--R (18a b - 96a b - 246a b - 132a b )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 10 3 +--R (96a b + 48a b - 192a b - 144a b)cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 11 2 +--R (- 18a b + 108a b + 222a b + 48a b - 48a )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 10 3 8 7 4 +--R (- 48a b - 48a b + 48a b + 48a b)cosh(d x + c) + 6a b - 18a b +--R + +--R 9 2 +--R - 12a b +--R * +--R sinh(d x + c) +--R + +--R 4 7 6 5 8 3 6 +--R (- 2a b - 4a b - 2a b )cosh(d x + c) +--R + +--R 5 6 7 4 9 2 5 +--R (- 12a b - 24a b - 12a b )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 10 4 +--R (6a b - 12a b - 42a b - 24a b)cosh(d x + c) +--R + +--R 5 6 7 4 9 2 11 3 +--R (24a b + 32a b - 8a b - 16a )cosh(d x + c) +--R + +--R 4 7 6 5 8 3 10 2 +--R (- 6a b + 12a b + 42a b + 24a b)cosh(d x + c) +--R + +--R 5 6 7 4 9 2 4 7 6 5 8 3 +--R (- 12a b - 24a b - 12a b )cosh(d x + c) + 2a b + 4a b + 2a b +--R Type: Expression(Integer) +--E 85 + +--S 86 of 510 +t0017:= 1/(a+b*sinh(c+d*x))^4 +--R +--R +--R (72) +--R 1 +--R / +--R 4 4 3 3 2 2 2 +--R b sinh(d x + c) + 4a b sinh(d x + c) + 6a b sinh(d x + c) +--R + +--R 3 4 +--R 4a b sinh(d x + c) + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 510 +r0017:= -a*(-3*b^2+2*a^2)*atanh((b-a*tanh(1/2*c+1/2*d*x))/_ + (a^2+b^2)^(1/2))/(a^2+b^2)^(7/2)/d-1/3*b*cosh(c+d*x)/_ + (a^2+b^2)/d/(a+b*sinh(c+d*x))^3-5/6*a*b*cosh(c+d*x)/_ + (a^2+b^2)^2/d/(a+b*sinh(c+d*x))^2-1/6*b*(11*a^2-4*b^2)*_ + cosh(c+d*x)/(a^2+b^2)^3/d/(a+b*sinh(c+d*x)) +--R +--R +--R (73) +--R 5 3 3 3 2 4 4 2 2 +--R (- 18a b + 12a b )sinh(d x + c) + (- 54a b + 36a b )sinh(d x + c) +--R + +--R 3 3 5 4 2 6 +--R (- 54a b + 36a b)sinh(d x + c) - 18a b + 12a +--R * +--R d x + c +--R a tanh(-------) - b +--R 2 +--R atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 5 2 3 2 +--R (4b - 11a b )cosh(d x + c)sinh(d x + c) +--R + +--R 4 3 2 +--R (3a b - 27a b )cosh(d x + c)sinh(d x + c) +--R + +--R 5 2 3 4 +--R (- 2b - 5a b - 18a b)cosh(d x + c) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 9 2 7 4 5 6 3 3 +--R (6b + 18a b + 18a b + 6a b )d sinh(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (18a b + 54a b + 54a b + 18a b )d sinh(d x + c) +--R + +--R 2 7 4 5 6 3 8 +--R (18a b + 54a b + 54a b + 18a b)d sinh(d x + c) +--R + +--R 3 6 5 4 7 2 9 +--R (6a b + 18a b + 18a b + 6a )d +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 510 +a0017:= integrate(t0017,x) +--R +--R +--R (74) +--R 5 3 3 6 +--R (9a b - 6a b )sinh(d x + c) +--R + +--R 5 3 3 2 4 4 2 5 +--R ((54a b - 36a b )cosh(d x + c) + 54a b - 36a b )sinh(d x + c) +--R + +--R 5 3 3 2 +--R (135a b - 90a b )cosh(d x + c) +--R + +--R 2 4 4 2 5 3 3 5 +--R (270a b - 180a b )cosh(d x + c) - 27a b + 126a b - 72a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 5 3 3 3 +--R (180a b - 120a b )cosh(d x + c) +--R + +--R 2 4 4 2 2 +--R (540a b - 360a b )cosh(d x + c) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 108a b + 504a b - 288a b)cosh(d x + c) - 108a b + 144a b +--R + +--R 6 +--R - 48a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 5 3 3 4 +--R (135a b - 90a b )cosh(d x + c) +--R + +--R 2 4 4 2 3 +--R (540a b - 360a b )cosh(d x + c) +--R + +--R 5 3 3 5 2 +--R (- 162a b + 756a b - 432a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 5 3 3 +--R (- 324a b + 432a b - 144a )cosh(d x + c) + 27a b - 126a b +--R + +--R 5 +--R 72a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 3 3 5 +--R (54a b - 36a b )cosh(d x + c) +--R + +--R 2 4 4 2 4 +--R (270a b - 180a b )cosh(d x + c) +--R + +--R 5 3 3 5 3 +--R (- 108a b + 504a b - 288a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 2 +--R (- 324a b + 432a b - 144a )cosh(d x + c) +--R + +--R 5 3 3 5 2 4 4 2 +--R (54a b - 252a b + 144a b)cosh(d x + c) + 54a b - 36a b +--R * +--R sinh(d x + c) +--R + +--R 5 3 3 6 2 4 4 2 5 +--R (9a b - 6a b )cosh(d x + c) + (54a b - 36a b )cosh(d x + c) +--R + +--R 5 3 3 5 4 +--R (- 27a b + 126a b - 72a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 3 +--R (- 108a b + 144a b - 48a )cosh(d x + c) +--R + +--R 5 3 3 5 2 +--R (27a b - 126a b + 72a b)cosh(d x + c) +--R + +--R 2 4 4 2 5 3 3 +--R (54a b - 36a b )cosh(d x + c) - 9a b + 6a b +--R * +--R log +--R 2 2 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a b)sinh(d x + c) +--R + +--R 2 2 2 2 +--R b cosh(d x + c) + 2a b cosh(d x + c) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 +--R (2b + 2a b)sinh(d x + c) + (2b + 2a b)cosh(d x + c) + 2a b +--R + +--R 3 +--R 2a +--R / +--R 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R 2 +--R b cosh(d x + c) + 2a cosh(d x + c) - b +--R + +--R 4 3 2 5 +--R (- 18a b + 12a b )sinh(d x + c) +--R + +--R 4 3 2 2 3 4 4 +--R ((- 90a b + 60a b )cosh(d x + c) - 90a b + 60a b)sinh(d x + c) +--R + +--R 4 3 2 2 +--R (- 180a b + 120a b )cosh(d x + c) +--R + +--R 2 3 4 4 3 2 5 +--R (- 360a b + 240a b)cosh(d x + c) + 48a b - 164a b + 88a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 3 +--R (- 180a b + 120a b )cosh(d x + c) +--R + +--R 2 3 4 2 +--R (- 540a b + 360a b)cosh(d x + c) +--R + +--R 4 3 2 5 5 2 3 4 +--R (144a b - 492a b + 264a )cosh(d x + c) - 24b + 72a b - 204a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 3 2 4 +--R (- 90a b + 60a b )cosh(d x + c) +--R + +--R 2 3 4 3 +--R (- 360a b + 240a b)cosh(d x + c) +--R + +--R 4 3 2 5 2 +--R (144a b - 492a b + 264a )cosh(d x + c) +--R + +--R 5 2 3 4 4 3 2 +--R (- 48b + 144a b - 408a b)cosh(d x + c) - 30a b + 120a b +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 5 2 3 4 4 +--R (- 18a b + 12a b )cosh(d x + c) + (- 90a b + 60a b)cosh(d x + c) +--R + +--R 4 3 2 5 3 +--R (48a b - 164a b + 88a )cosh(d x + c) +--R + +--R 5 2 3 4 2 +--R (- 24b + 72a b - 204a b)cosh(d x + c) +--R + +--R 4 3 2 5 2 3 +--R (- 30a b + 120a b )cosh(d x + c) + 8b - 22a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 9 2 7 4 5 6 3 6 +--R (6b + 18a b + 18a b + 6a b )d sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 +--R (36b + 108a b + 108a b + 36a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (36a b + 108a b + 108a b + 36a b )d +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 2 +--R (90b + 270a b + 270a b + 90a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (180a b + 540a b + 540a b + 180a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (- 18b + 18a b + 162a b + 198a b + 72a b)d +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 3 +--R (120b + 360a b + 360a b + 120a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (360a b + 1080a b + 1080a b + 360a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (- 72b + 72a b + 648a b + 792a b + 288a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 +--R (- 72a b - 168a b - 72a b + 72a b + 48a )d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 4 +--R (90b + 270a b + 270a b + 90a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 3 +--R (360a b + 1080a b + 1080a b + 360a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (- 108b + 108a b + 972a b + 1188a b + 432a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 +--R (- 216a b - 504a b - 216a b + 216a b + 144a )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (18b - 18a b - 162a b - 198a b - 72a b)d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 5 +--R (36b + 108a b + 108a b + 36a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 4 +--R (180a b + 540a b + 540a b + 180a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (- 72b + 72a b + 648a b + 792a b + 288a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (- 216a b - 504a b - 216a b + 216a b + 144a )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (36b - 36a b - 324a b - 396a b - 144a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (36a b + 108a b + 108a b + 36a b )d +--R * +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 6 +--R (6b + 18a b + 18a b + 6a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 5 +--R (36a b + 108a b + 108a b + 36a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (- 18b + 18a b + 162a b + 198a b + 72a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 72a b - 168a b - 72a b + 72a b + 48a )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (18b - 18a b - 162a b - 198a b - 72a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (36a b + 108a b + 108a b + 36a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 +--R (- 6b - 18a b - 18a b - 6a b )d +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 510 +m0017:= a0017-r0017 +--R +--R +--R (75) +--R 8 3 6 9 +--R (9a b - 6a b )sinh(d x + c) +--R + +--R 8 3 6 2 7 4 5 8 +--R ((54a b - 36a b )cosh(d x + c) + 81a b - 54a b )sinh(d x + c) +--R + +--R 8 3 6 2 +--R (135a b - 90a b )cosh(d x + c) +--R + +--R 2 7 4 5 8 3 6 5 4 +--R (432a b - 288a b )cosh(d x + c) - 27a b + 315a b - 198a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 8 3 6 3 +--R (180a b - 120a b )cosh(d x + c) +--R + +--R 2 7 4 5 2 +--R (945a b - 630a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 2 7 4 5 +--R (- 108a b + 1476a b - 936a b )cosh(d x + c) - 189a b + 693a b +--R + +--R 6 3 +--R - 378a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 3 6 4 +--R (135a b - 90a b )cosh(d x + c) +--R + +--R 2 7 4 5 3 +--R (1080a b - 720a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 2 +--R (- 162a b + 2781a b - 1782a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 3 6 +--R (- 648a b + 2808a b - 1584a b )cosh(d x + c) + 27a b - 531a b +--R + +--R 5 4 7 2 +--R 936a b - 396a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 3 6 5 +--R (54a b - 36a b )cosh(d x + c) +--R + +--R 2 7 4 5 4 +--R (675a b - 450a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 3 +--R (- 108a b + 2664a b - 1728a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 2 +--R (- 810a b + 4455a b - 2610a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 7 +--R (54a b - 1548a b + 3222a b - 1476a b )cosh(d x + c) + 135a b +--R + +--R 4 5 6 3 8 +--R - 765a b + 774a b - 216a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 3 6 6 2 7 4 5 5 +--R (9a b - 6a b )cosh(d x + c) + (216a b - 144a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 4 +--R (- 27a b + 1341a b - 882a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 3 +--R (- 432a b + 3456a b - 2112a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (27a b - 1584a b + 4176a b - 2088a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 8 +--R (216a b - 1872a b + 2232a b - 720a b)cosh(d x + c) - 9a b +--R + +--R 3 6 5 4 7 2 9 +--R 249a b - 594a b + 360a b - 48a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 7 4 5 6 +--R (27a b - 18a b )cosh(d x + c) +--R + +--R 3 6 5 4 5 +--R (324a b - 216a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 4 +--R (- 81a b + 1323a b - 846a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 3 +--R (- 648a b + 2484a b - 1368a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 2 +--R (81a b - 1512a b + 2268a b - 864a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 2 7 +--R (324a b - 1188a b + 864a b - 144a )cosh(d x + c) - 27a b +--R + +--R 4 5 6 3 8 +--R 207a b - 234a b + 72a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 6 5 4 6 +--R (27a b - 18a b )cosh(d x + c) +--R + +--R 4 5 6 3 5 +--R (216a b - 144a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 4 +--R (- 81a b + 648a b - 396a b )cosh(d x + c) +--R + +--R 4 5 6 3 8 3 +--R (- 432a b + 936a b - 432a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 2 +--R (81a b - 702a b + 648a b - 144a )cosh(d x + c) +--R + +--R 4 5 6 3 8 3 6 5 4 +--R (216a b - 360a b + 144a b)cosh(d x + c) - 27a b + 72a b +--R + +--R 7 2 +--R - 36a b +--R * +--R sinh(d x + c) +--R + +--R 4 5 6 3 6 5 4 7 2 5 +--R (9a b - 6a b )cosh(d x + c) + (54a b - 36a b )cosh(d x + c) +--R + +--R 4 5 6 3 8 4 +--R (- 27a b + 126a b - 72a b)cosh(d x + c) +--R + +--R 5 4 7 2 9 3 +--R (- 108a b + 144a b - 48a )cosh(d x + c) +--R + +--R 4 5 6 3 8 2 +--R (27a b - 126a b + 72a b)cosh(d x + c) +--R + +--R 5 4 7 2 4 5 6 3 +--R (54a b - 36a b )cosh(d x + c) - 9a b + 6a b +--R * +--R log +--R 2 2 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a b)sinh(d x + c) +--R + +--R 2 2 2 2 +--R b cosh(d x + c) + 2a b cosh(d x + c) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 +--R (2b + 2a b)sinh(d x + c) + (2b + 2a b)cosh(d x + c) + 2a b +--R + +--R 3 +--R 2a +--R / +--R 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R 2 +--R b cosh(d x + c) + 2a cosh(d x + c) - b +--R + +--R 8 3 6 9 +--R (18a b - 12a b )sinh(d x + c) +--R + +--R 8 3 6 2 7 4 5 8 +--R ((108a b - 72a b )cosh(d x + c) + 162a b - 108a b )sinh(d x + c) +--R + +--R 8 3 6 2 +--R (270a b - 180a b )cosh(d x + c) +--R + +--R 2 7 4 5 8 3 6 5 4 +--R (864a b - 576a b )cosh(d x + c) - 54a b + 630a b - 396a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 8 3 6 3 +--R (360a b - 240a b )cosh(d x + c) +--R + +--R 2 7 4 5 2 +--R (1890a b - 1260a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 2 7 +--R (- 216a b + 2952a b - 1872a b )cosh(d x + c) - 378a b +--R + +--R 4 5 6 3 +--R 1386a b - 756a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 3 6 4 +--R (270a b - 180a b )cosh(d x + c) +--R + +--R 2 7 4 5 3 +--R (2160a b - 1440a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 2 +--R (- 324a b + 5562a b - 3564a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 +--R (- 1296a b + 5616a b - 3168a b )cosh(d x + c) + 54a b +--R + +--R 3 6 5 4 7 2 +--R - 1062a b + 1872a b - 792a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 3 6 5 +--R (108a b - 72a b )cosh(d x + c) +--R + +--R 2 7 4 5 4 +--R (1350a b - 900a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 3 +--R (- 216a b + 5328a b - 3456a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 2 +--R (- 1620a b + 8910a b - 5220a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 7 +--R (108a b - 3096a b + 6444a b - 2952a b )cosh(d x + c) + 270a b +--R + +--R 4 5 6 3 8 +--R - 1530a b + 1548a b - 432a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 3 6 6 +--R (18a b - 12a b )cosh(d x + c) +--R + +--R 2 7 4 5 5 +--R (432a b - 288a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 4 +--R (- 54a b + 2682a b - 1764a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 3 +--R (- 864a b + 6912a b - 4224a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (54a b - 3168a b + 8352a b - 4176a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 8 +--R (432a b - 3744a b + 4464a b - 1440a b)cosh(d x + c) - 18a b +--R + +--R 3 6 5 4 7 2 9 +--R 498a b - 1188a b + 720a b - 96a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 7 4 5 6 +--R (54a b - 36a b )cosh(d x + c) +--R + +--R 3 6 5 4 5 +--R (648a b - 432a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 4 +--R (- 162a b + 2646a b - 1692a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 3 +--R (- 1296a b + 4968a b - 2736a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 2 +--R (162a b - 3024a b + 4536a b - 1728a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 2 7 +--R (648a b - 2376a b + 1728a b - 288a )cosh(d x + c) - 54a b +--R + +--R 4 5 6 3 8 +--R 414a b - 468a b + 144a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 6 5 4 6 +--R (54a b - 36a b )cosh(d x + c) +--R + +--R 4 5 6 3 5 +--R (432a b - 288a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 4 +--R (- 162a b + 1296a b - 792a b )cosh(d x + c) +--R + +--R 4 5 6 3 8 3 +--R (- 864a b + 1872a b - 864a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 2 +--R (162a b - 1404a b + 1296a b - 288a )cosh(d x + c) +--R + +--R 4 5 6 3 8 3 6 5 4 +--R (432a b - 720a b + 288a b)cosh(d x + c) - 54a b + 144a b +--R + +--R 7 2 +--R - 72a b +--R * +--R sinh(d x + c) +--R + +--R 4 5 6 3 6 5 4 7 2 5 +--R (18a b - 12a b )cosh(d x + c) + (108a b - 72a b )cosh(d x + c) +--R + +--R 4 5 6 3 8 4 +--R (- 54a b + 252a b - 144a b)cosh(d x + c) +--R + +--R 5 4 7 2 9 3 +--R (- 216a b + 288a b - 96a )cosh(d x + c) +--R + +--R 4 5 6 3 8 2 +--R (54a b - 252a b + 144a b)cosh(d x + c) +--R + +--R 5 4 7 2 4 5 6 3 +--R (108a b - 72a b )cosh(d x + c) - 18a b + 12a b +--R * +--R d x + c +--R a tanh(-------) - b +--R 2 +--R atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 8 2 6 7 3 5 8 +--R ((- 4b + 11a b )cosh(d x + c) - 18a b + 12a b )sinh(d x + c) +--R + +--R 8 2 6 2 +--R (- 24b + 66a b )cosh(d x + c) +--R + +--R 7 3 5 2 6 4 4 +--R (- 117a b + 153a b )cosh(d x + c) - 144a b + 96a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 8 2 6 3 +--R (- 60b + 165a b )cosh(d x + c) +--R + +--R 7 3 5 2 +--R (- 318a b + 612a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 7 3 5 +--R (14b - 724a b + 732a b )cosh(d x + c) + 48a b - 488a b +--R + +--R 5 3 +--R 304a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 2 6 4 +--R (- 80b + 220a b )cosh(d x + c) +--R + +--R 7 3 5 3 +--R (- 465a b + 1185a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 2 +--R (60b - 1464a b + 2166a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 8 2 6 +--R (213a b - 2093a b + 1684a b )cosh(d x + c) - 24b + 216a b +--R + +--R 4 4 6 2 +--R - 984a b + 456a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 2 6 5 +--R (- 60b + 165a b )cosh(d x + c) +--R + +--R 7 3 5 4 +--R (- 390a b + 1260a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 3 +--R (102b - 1491a b + 3282a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 2 +--R (384a b - 3462a b + 3804a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 7 +--R (- 66b + 702a b - 3528a b + 2004a b )cosh(d x + c) - 102a b +--R + +--R 3 5 5 3 7 +--R 480a b - 1194a b + 324a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 2 6 6 +--R (- 24b + 66a b )cosh(d x + c) +--R + +--R 7 3 5 5 +--R (- 183a b + 747a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 4 +--R (88b - 764a b + 2748a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 3 +--R (366a b - 2678a b + 4456a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 72b + 810a b - 4764a b + 3504a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 8 +--R (- 231a b + 1123a b - 3560a b + 1176a b)cosh(d x + c) + 8b +--R + +--R 2 6 4 4 6 2 8 +--R - 184a b + 624a b - 776a b + 88a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 8 2 6 7 +--R (- 4b + 11a b )cosh(d x + c) +--R + +--R 7 3 5 6 +--R (- 42a b + 228a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 5 +--R (42b - 150a b + 1248a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 4 +--R (204a b - 872a b + 2824a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 48b + 387a b - 2892a b + 3048a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (- 186a b + 816a b - 3804a b + 1584a b)cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 +--R (10b - 272a b + 1092a b - 1932a b + 264a )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 +--R 24a b - 180a b + 432a b - 204a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 7 3 5 7 +--R (- 3a b + 27a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 +--R (12b + 12a b + 270a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 5 +--R (69a b - 21a b + 900a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 24b + 72a b - 684a b + 1320a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 3 +--R (- 81a b + 129a b - 1704a b + 936a b)cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (12b - 108a b + 510a b - 1536a b + 264a )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 6 +--R (15a b - 135a b + 612a b - 408a b)cosh(d x + c) + 24a b +--R + +--R 4 4 6 2 +--R - 96a b + 120a b +--R * +--R sinh(d x + c) +--R + +--R 8 2 6 4 4 7 +--R (2b + 5a b + 18a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 6 +--R (12a b + 30a b + 108a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 6b + 9a b - 12a b + 228a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 4 +--R (- 24a b - 44a b - 266a b + 204a b)cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (6b - 9a b + 42a b - 380a b + 88a )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (12a b + 6a b + 180a b - 204a b)cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 3 5 5 3 +--R (- 2b - 5a b - 48a b + 120a b )cosh(d x + c) + 8a b - 22a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 12 2 10 4 8 6 6 9 +--R (6b + 18a b + 18a b + 6a b )d sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 +--R (36b + 108a b + 108a b + 36a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 +--R (54a b + 162a b + 162a b + 54a b )d +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 2 +--R (90b + 270a b + 270a b + 90a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 +--R (288a b + 864a b + 864a b + 288a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (- 18b + 144a b + 540a b + 576a b + 198a b )d +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 3 +--R (120b + 360a b + 360a b + 120a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 2 +--R (630a b + 1890a b + 1890a b + 630a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (- 72b + 720a b + 2592a b + 2736a b + 936a b )d cosh(d x + c) +--R + +--R 11 5 7 7 5 9 3 +--R (- 126a b + 756a b + 1008a b + 378a b )d +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 4 +--R (90b + 270a b + 270a b + 90a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 3 +--R (720a b + 2160a b + 2160a b + 720a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (- 108b + 1458a b + 5022a b + 5238a b + 1782a b )d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (- 432a b + 288a b + 3456a b + 4320a b + 1584a b )d +--R * +--R cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (18b - 288a b - 576a b + 180a b + 846a b + 396a b )d +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 5 +--R (36b + 108a b + 108a b + 36a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 4 +--R (450a b + 1350a b + 1350a b + 450a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (- 72b + 1512a b + 4968a b + 5112a b + 1728a b )d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (- 540a b + 990a b + 6210a b + 7290a b + 2610a b )d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (36b - 900a b - 1440a b + 1440a b + 3420a b + 1476a b )d +--R * +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (90a b - 180a b - 864a b - 612a b + 198a b + 216a b)d +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 6 +--R (6b + 18a b + 18a b + 6a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 5 +--R (144a b + 432a b + 432a b + 144a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (- 18b + 828a b + 2592a b + 2628a b + 882a b )d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (- 288a b + 1248a b + 5472a b + 6048a b + 2112a b )d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (18b - 990a b - 990a b + 3150a b + 5220a b + 2088a b )d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (144a b - 720a b - 2304a b - 1152a b + 1008a b + 720a b)d +--R * +--R cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 12 +--R (- 6b + 144a b + 180a b - 336a b - 558a b - 144a b + 48a )d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 11 3 9 5 7 7 5 6 +--R (18a b + 54a b + 54a b + 18a b )d cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 5 +--R (216a b + 648a b + 648a b + 216a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (- 54a b + 684a b + 2376a b + 2484a b + 846a b )d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (- 432a b + 72a b + 2808a b + 3672a b + 1368a b )d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (54a b - 810a b - 1890a b - 270a b + 1620a b + 864a b)d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 10 6 6 8 4 10 2 12 +--R (216a b - 1152a b - 1296a b - 216a b + 144a )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (- 18a b + 72a b + 252a b + 144a b - 90a b - 72a b)d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 6 +--R (18a b + 54a b + 54a b + 18a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 5 +--R (144a b + 432a b + 432a b + 144a b )d cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (- 54a b + 234a b + 1026a b + 1134a b + 396a b )d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 11 +--R (- 288a b - 432a b + 432a b + 1008a b + 432a b)d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 12 2 +--R (54a b - 270a b - 990a b - 810a b + 144a )d cosh(d x + c) +--R + +--R 3 9 5 7 9 3 11 +--R (144a b + 288a b - 288a b - 144a b)d cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (- 18a b - 18a b + 54a b + 90a b + 36a b )d +--R * +--R sinh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 6 +--R (6a b + 18a b + 18a b + 6a b )d cosh(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 5 +--R (36a b + 108a b + 108a b + 36a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 11 4 +--R (- 18a b + 18a b + 162a b + 198a b + 72a b)d cosh(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 12 3 +--R (- 72a b - 168a b - 72a b + 72a b + 48a )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 11 2 +--R (18a b - 18a b - 162a b - 198a b - 72a b)d cosh(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 +--R (36a b + 108a b + 108a b + 36a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 +--R (- 6a b - 18a b - 18a b - 6a b )d +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 89 + +--S 90 of 510 +d0017:= D(m0017,x) +--R +--R +--R (76) +--R 10 3 8 12 +--R (5a b + 5a b )sinh(d x + c) +--R + +--R 10 3 8 2 9 4 7 11 +--R ((40a b + 40a b )cosh(d x + c) + 69a b + 54a b )sinh(d x + c) +--R + +--R 10 3 8 2 +--R (144a b + 129a b )cosh(d x + c) +--R + +--R 2 9 4 7 10 3 8 5 6 +--R (512a b + 392a b )cosh(d x + c) - 18a b + 388a b + 241a b +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 10 3 8 3 +--R (312a b + 192a b )cosh(d x + c) +--R + +--R 2 9 4 7 2 +--R (1682a b + 1112a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 2 9 +--R (- 104a b + 2672a b + 1576a b )cosh(d x + c) - 218a b +--R + +--R 4 7 6 5 +--R 1169a b + 562a b +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 10 3 8 4 +--R (462a b + 42a b )cosh(d x + c) +--R + +--R 2 9 4 7 3 +--R (3232a b + 1312a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (- 266a b + 8046a b + 3857a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 10 +--R (- 1168a b + 7504a b + 3272a b )cosh(d x + c) + 118a b +--R + +--R 3 8 5 6 7 4 +--R - 778a b + 2365a b + 786a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 10 3 8 5 +--R (504a b - 336a b )cosh(d x + c) +--R + +--R 2 9 4 7 4 +--R (4046a b - 364a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 3 +--R (- 432a b + 13840a b + 3232a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 2 +--R (- 2684a b + 20884a b + 6648a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 +--R (456a b - 4112a b + 13688a b + 3856a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 +--R 622a b - 1592a b + 3440a b + 704a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 10 3 8 6 +--R (420a b - 630a b )cosh(d x + c) +--R + +--R 2 9 4 7 5 +--R (3472a b - 3248a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 4 +--R (- 568a b + 14800a b - 3742a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 3 +--R (- 3616a b + 32608a b + 2624a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 +--R (684a b - 9078a b + 34420a b + 5752a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 +--R (2304a b - 7840a b + 17728a b + 2672a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R - 8a b + 1564a b - 2302a b + 3440a b + 384a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 10 3 8 7 +--R (264a b - 576a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 +--R (2072a b - 4648a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 5 +--R (- 664a b + 9840a b - 12176a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 4 +--R (- 3488a b + 30446a b - 11636a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (584a b - 10832a b + 48520a b - 2224a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 2 +--R (3336a b - 15844a b + 39504a b + 1984a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (8a b + 5312a b - 9848a b + 16144a b + 1056a b ) +--R * +--R cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R - 96a b + 2414a b - 2276a b + 2240a b + 96a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 10 3 8 8 +--R (117a b - 303a b )cosh(d x + c) +--R + +--R 2 9 4 7 7 +--R (832a b - 3488a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 6 +--R (- 624a b + 3572a b - 13654a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 5 +--R (- 2848a b + 16064a b - 23088a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 4 +--R (510a b - 7630a b + 40550a b - 17460a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (2672a b - 16144a b + 49488a b - 5616a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 2 +--R (6876a b - 17002a b + 32000a b - 192a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (- 80a b + 7216a b - 8416a b + 9680a b + 192a b) +--R * +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R - 3a b - 355a b + 2266a b - 1420a b + 912a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 10 3 8 9 +--R (32a b - 88a b )cosh(d x + c) +--R + +--R 2 9 4 7 8 +--R (197a b - 1498a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 +--R (- 416a b + 176a b - 8288a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 6 +--R (- 1988a b + 3044a b - 20168a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 5 +--R (528a b - 3408a b + 18760a b - 23504a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 4 +--R (1854a b - 7648a b + 37264a b - 13504a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (- 128a b + 4336a b - 14224a b + 34784a b - 3648a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (- 68a b + 7612a b - 12312a b + 16896a b - 192a b) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (- 16a b - 440a b + 5864a b - 4656a b + 3456a b ) +--R * +--R cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R 5a b - 550a b + 1152a b - 576a b + 192a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 10 3 8 10 +--R (4a b - 11a b )cosh(d x + c) +--R + +--R 2 9 4 7 9 +--R (16a b - 344a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 8 +--R (- 182a b - 420a b - 2803a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 7 +--R (- 1024a b - 1376a b - 9472a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 6 +--R (376a b - 1162a b + 3108a b - 15304a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 5 +--R (1392a b - 352a b + 16224a b - 12272a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (- 220a b + 1652a b - 4754a b + 22192a b - 4992a b ) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (- 352a b + 2944a b - 8768a b + 15008a b - 768a b) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (20a b - 99a b + 4900a b - 5880a b + 4896a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (- 32a b - 680a b + 2592a b - 1584a b + 576a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R 2a b + 40a b - 355a b + 288a b - 144a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 9 4 7 10 +--R (- 2a b - 32a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 9 +--R (- 48a b - 160a b - 472a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 +--R (- 326a b - 887a b - 2286a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 7 +--R (144a b - 368a b - 840a b - 5008a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 6 +--R (700a b + 988a b + 3376a b - 5312a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (- 144a b + 624a b + 584a b + 7952a b - 2784a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (- 412a b - 106a b - 2884a b + 6848a b - 672a b) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 3 +--R (48a b - 80a b + 1128a b - 3472a b + 3072a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (38a b - 4a b + 1872a b - 1440a b + 576a b)cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 2 9 +--R (- 16a b - 400a b + 528a b - 288a b )cosh(d x + c) + 2a b +--R + +--R 4 7 6 5 8 3 +--R 41a b - 78a b + 48a b +--R * +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 10 +--R (- 6a b - 18a b - 27a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 9 +--R (- 48a b - 144a b - 216a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 8 +--R (24a b - 72a b - 315a b - 654a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 7 +--R (144a b + 240a b + 144a b - 912a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 6 +--R (- 36a b + 180a b + 570a b + 1248a b - 576a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 5 +--R (- 144a b - 240a b - 288a b + 1296a b - 192a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 4 +--R (24a b - 72a b - 174a b - 828a b + 720a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 3 +--R (48a b + 144a b + 432a b - 432a b + 192a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (- 6a b - 18a b - 63a b + 240a b - 144a b )cosh(d x + c) +--R + +--R 6 5 8 3 5 6 7 4 +--R (- 72a b + 48a b )cosh(d x + c) + 9a b - 6a b +--R * +--R d x + c 2 +--R tanh(-------) +--R 2 +--R + +--R 11 2 9 12 +--R (8b - 22a b )sinh(d x + c) +--R + +--R 11 2 9 10 3 8 11 +--R ((64b - 176a b )cosh(d x + c) + 78a b - 252a b )sinh(d x + c) +--R + +--R 11 2 9 2 +--R (216b - 594a b )cosh(d x + c) +--R + +--R 10 3 8 11 2 9 4 7 +--R (560a b - 1840a b )cosh(d x + c) - 36b + 388a b - 1226a b +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 11 2 9 3 +--R (384b - 1056a b )cosh(d x + c) +--R + +--R 10 3 8 2 +--R (1676a b - 5584a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 10 +--R (- 224b + 2432a b - 8144a b )cosh(d x + c) - 284a b +--R + +--R 3 8 5 6 +--R 1382a b - 3284a b +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 11 2 9 4 +--R (336b - 924a b )cosh(d x + c) +--R + +--R 10 3 8 3 +--R (2608a b - 8672a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 2 +--R (- 548b + 6228a b - 22114a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 11 +--R (- 1552a b + 7456a b - 19792a b )cosh(d x + c) - 128b +--R + +--R 2 9 4 7 6 5 +--R - 1540a b + 3064a b - 5424a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 10 3 8 4 +--R (1988a b - 5992a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 3 +--R (- 576b + 8128a b - 29696a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (- 3272a b + 15832a b - 47856a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 +--R (- 480b - 6752a b + 14816a b - 29312a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 +--R - 380a b - 4304a b + 4208a b - 5728a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 11 2 9 6 +--R (- 336b + 924a b )cosh(d x + c) +--R + +--R 10 3 8 5 +--R (112a b + 1792a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 4 +--R (56b + 5320a b - 15316a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 3 +--R (- 2848a b + 16096a b - 54976a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 2 +--R (- 720b - 11220a b + 26704a b - 62336a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 +--R (- 1584a b - 16576a b + 17968a b - 27520a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 +--R - 56b - 272a b - 6556a b + 3776a b - 3744a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 11 2 9 7 +--R (- 384b + 1056a b )cosh(d x + c) +--R + +--R 10 3 8 6 +--R (- 1120a b + 7280a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 5 +--R (896b + 1344a b + 10528a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 4 +--R (496a b + 7508a b - 19448a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 3 +--R (- 736b - 8000a b + 19744a b - 60352a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 +--R (- 2784a b - 23608a b + 26544a b - 50912a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 +--R (- 160b - 1888a b - 22784a b + 13216a b - 16128a b ) +--R * +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R - 240a b + 212a b - 5960a b + 2144a b - 1344a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 11 2 9 8 +--R (- 216b + 594a b )cosh(d x + c) +--R + +--R 10 3 8 7 +--R (- 944a b + 6496a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 +--R (1176b + 392a b + 22316a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 5 +--R (3536a b + 2432a b + 24096a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 4 +--R (- 912b - 796a b + 1664a b - 13152a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 3184a b - 15232a b + 10512a b - 41280a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 +--R (- 72b - 4200a b - 28708a b + 13472a b - 26208a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (- 560a b - 992a b - 18160a b + 5696a b - 5376a b ) +--R * +--R cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 10 +--R 24b - 310a b + 568a b - 3280a b + 576a b - 192a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 11 2 9 9 +--R (- 64b + 176a b )cosh(d x + c) +--R + +--R 10 3 8 8 +--R (- 322a b + 2948a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 7 +--R (832b + 1088a b + 15616a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 6 +--R (3688a b + 3896a b + 33808a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 5 +--R (- 1056b + 2496a b - 3680a b + 26368a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 4 +--R (- 3276a b - 5728a b - 11312a b - 5920a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 +--R (256b - 4352a b - 16192a b - 3136a b - 18432a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (- 152a b - 2936a b - 18864a b + 2496a b - 8064a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 10 +--R (32b - 560a b + 32a b - 8256a b + 1152a b - 768a b) +--R * +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 +--R 62a b - 100a b + 624a b - 864a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 11 2 9 10 +--R (- 8b + 22a b )cosh(d x + c) +--R + +--R 10 3 8 9 +--R (- 32a b + 688a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 8 +--R (364b + 948a b + 5534a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 +--R (2048a b + 4192a b + 17984a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 6 +--R (- 752b + 1892a b + 1200a b + 25856a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 5 +--R (- 2784a b - 3616a b - 12720a b + 13312a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 +--R (440b - 2656a b - 5828a b - 14720a b - 3168a b ) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (704a b - 1568a b - 6944a b - 5248a b - 5376a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 10 +--R (- 40b - 234a b - 1088a b - 5952a b - 1152a b) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 11 +--R (64a b - 80a b + 528a b - 1728a b )cosh(d x + c) - 4b +--R + +--R 2 9 4 7 6 5 +--R 28a b - 10a b + 288a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 10 3 8 10 +--R (4a b + 64a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 9 +--R (96b + 320a b + 944a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 8 +--R (652a b + 1846a b + 4524a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 7 +--R (- 288b + 736a b + 2400a b + 9536a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 6 +--R (- 1400a b - 2264a b - 3824a b + 8800a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 +--R (288b - 1248a b - 3328a b - 9568a b + 2304a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (824a b + 644a b - 136a b - 5920a b - 1344a b ) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 10 +--R (- 96b + 160a b - 96a b - 256a b - 1152a b - 768a b) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 +--R (- 76a b - 280a b - 528a b - 864a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 10 3 8 5 6 +--R (32a b + 80a b + 288a b )cosh(d x + c) - 4a b - 10a b - 36a b +--R * +--R sinh(d x + c) +--R + +--R 11 2 9 4 7 10 +--R (12b + 36a b + 54a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 9 +--R (96a b + 288a b + 432a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 +--R (- 48b + 144a b + 648a b + 1296a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 7 +--R (- 288a b - 480a b - 144a b + 1728a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 6 +--R (72b - 360a b - 1212a b - 2016a b + 864a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 5 +--R (288a b + 480a b + 144a b - 1728a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 10 +--R (- 48b + 144a b + 456a b + 720a b - 576a b - 192a b) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 3 8 5 6 3 +--R (- 96a b - 288a b - 432a b )cosh(d x + c) +--R + +--R 11 2 9 4 7 2 +--R (12b + 36a b + 54a b )cosh(d x + c) +--R * +--R d x + c +--R tanh(-------) +--R 2 +--R + +--R 10 3 8 12 +--R (- 5a b - 5a b )sinh(d x + c) +--R + +--R 10 3 8 2 9 4 7 11 +--R ((- 40a b - 40a b )cosh(d x + c) - 69a b - 54a b )sinh(d x + c) +--R + +--R 10 3 8 2 +--R (- 144a b - 129a b )cosh(d x + c) +--R + +--R 2 9 4 7 10 3 8 5 6 +--R (- 512a b - 392a b )cosh(d x + c) + 18a b - 388a b - 241a b +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 10 3 8 3 +--R (- 312a b - 192a b )cosh(d x + c) +--R + +--R 2 9 4 7 2 +--R (- 1682a b - 1112a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 2 9 4 7 +--R (104a b - 2672a b - 1576a b )cosh(d x + c) + 218a b - 1169a b +--R + +--R 6 5 +--R - 562a b +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 10 3 8 4 +--R (- 462a b - 42a b )cosh(d x + c) +--R + +--R 2 9 4 7 3 +--R (- 3232a b - 1312a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (266a b - 8046a b - 3857a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 10 3 8 +--R (1168a b - 7504a b - 3272a b )cosh(d x + c) - 118a b + 778a b +--R + +--R 5 6 7 4 +--R - 2365a b - 786a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 10 3 8 5 +--R (- 504a b + 336a b )cosh(d x + c) +--R + +--R 2 9 4 7 4 +--R (- 4046a b + 364a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 3 +--R (432a b - 13840a b - 3232a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 2 +--R (2684a b - 20884a b - 6648a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 9 +--R (- 456a b + 4112a b - 13688a b - 3856a b )cosh(d x + c) - 622a b +--R + +--R 4 7 6 5 8 3 +--R 1592a b - 3440a b - 704a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 10 3 8 6 +--R (- 420a b + 630a b )cosh(d x + c) +--R + +--R 2 9 4 7 5 +--R (- 3472a b + 3248a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 4 +--R (568a b - 14800a b + 3742a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 3 +--R (3616a b - 32608a b - 2624a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 +--R (- 684a b + 9078a b - 34420a b - 5752a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (- 2304a b + 7840a b - 17728a b - 2672a b )cosh(d x + c) + 8a b +--R + +--R 3 8 5 6 7 4 9 2 +--R - 1564a b + 2302a b - 3440a b - 384a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 10 3 8 7 +--R (- 264a b + 576a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 +--R (- 2072a b + 4648a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 5 +--R (664a b - 9840a b + 12176a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 4 +--R (3488a b - 30446a b + 11636a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 584a b + 10832a b - 48520a b + 2224a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 2 +--R (- 3336a b + 15844a b - 39504a b - 1984a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (- 8a b - 5312a b + 9848a b - 16144a b - 1056a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R 96a b - 2414a b + 2276a b - 2240a b - 96a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 10 3 8 8 +--R (- 117a b + 303a b )cosh(d x + c) +--R + +--R 2 9 4 7 7 +--R (- 832a b + 3488a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 6 +--R (624a b - 3572a b + 13654a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 5 +--R (2848a b - 16064a b + 23088a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 4 +--R (- 510a b + 7630a b - 40550a b + 17460a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (- 2672a b + 16144a b - 49488a b + 5616a b )cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 2 +--R (- 6876a b + 17002a b - 32000a b + 192a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (80a b - 7216a b + 8416a b - 9680a b - 192a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R 3a b + 355a b - 2266a b + 1420a b - 912a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 10 3 8 9 +--R (- 32a b + 88a b )cosh(d x + c) +--R + +--R 2 9 4 7 8 +--R (- 197a b + 1498a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 +--R (416a b - 176a b + 8288a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 6 +--R (1988a b - 3044a b + 20168a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 5 +--R (- 528a b + 3408a b - 18760a b + 23504a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 4 +--R (- 1854a b + 7648a b - 37264a b + 13504a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (128a b - 4336a b + 14224a b - 34784a b + 3648a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (68a b - 7612a b + 12312a b - 16896a b + 192a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (16a b + 440a b - 5864a b + 4656a b - 3456a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R - 5a b + 550a b - 1152a b + 576a b - 192a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 10 3 8 10 +--R (- 4a b + 11a b )cosh(d x + c) +--R + +--R 2 9 4 7 9 +--R (- 16a b + 344a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 8 +--R (182a b + 420a b + 2803a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 7 +--R (1024a b + 1376a b + 9472a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 6 +--R (- 376a b + 1162a b - 3108a b + 15304a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 5 +--R (- 1392a b + 352a b - 16224a b + 12272a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 4 +--R (220a b - 1652a b + 4754a b - 22192a b + 4992a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 3 +--R (352a b - 2944a b + 8768a b - 15008a b + 768a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (- 20a b + 99a b - 4900a b + 5880a b - 4896a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (32a b + 680a b - 2592a b + 1584a b - 576a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R - 2a b - 40a b + 355a b - 288a b + 144a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 9 4 7 10 +--R (2a b + 32a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 9 +--R (48a b + 160a b + 472a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 +--R (326a b + 887a b + 2286a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 7 +--R (- 144a b + 368a b + 840a b + 5008a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 6 +--R (- 700a b - 988a b - 3376a b + 5312a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 5 +--R (144a b - 624a b - 584a b - 7952a b + 2784a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 4 +--R (412a b + 106a b + 2884a b - 6848a b + 672a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 3 +--R (- 48a b + 80a b - 1128a b + 3472a b - 3072a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (- 38a b + 4a b - 1872a b + 1440a b - 576a b)cosh(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 2 9 4 7 +--R (16a b + 400a b - 528a b + 288a b )cosh(d x + c) - 2a b - 41a b +--R + +--R 6 5 8 3 +--R 78a b - 48a b +--R * +--R sinh(d x + c) +--R + +--R 10 3 8 5 6 10 +--R (6a b + 18a b + 27a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 9 +--R (48a b + 144a b + 216a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 8 +--R (- 24a b + 72a b + 315a b + 654a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 7 +--R (- 144a b - 240a b - 144a b + 912a b )cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 6 +--R (36a b - 180a b - 570a b - 1248a b + 576a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 5 +--R (144a b + 240a b + 288a b - 1296a b + 192a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 4 +--R (- 24a b + 72a b + 174a b + 828a b - 720a b )cosh(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 3 +--R (- 48a b - 144a b - 432a b + 432a b - 192a b)cosh(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (6a b + 18a b + 63a b - 240a b + 144a b )cosh(d x + c) +--R + +--R 6 5 8 3 5 6 7 4 +--R (72a b - 48a b )cosh(d x + c) - 9a b + 6a b +--R / +--R 14 3 12 5 10 7 8 12 +--R (6a b + 18a b + 18a b + 6a b )sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 2 13 +--R (48a b + 144a b + 144a b + 48a b )cosh(d x + c) + 72a b +--R + +--R 4 11 6 9 8 7 +--R 216a b + 216a b + 72a b +--R * +--R 11 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 2 +--R (168a b + 504a b + 504a b + 168a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 +--R (528a b + 1584a b + 1584a b + 528a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 24a b + 300a b + 1044a b + 1092a b + 372a b +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 3 +--R (336a b + 1008a b + 1008a b + 336a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 2 +--R (1680a b + 5040a b + 5040a b + 1680a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (- 144a b + 2064a b + 7056a b + 7344a b + 2496a b ) +--R * +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 240a b + 360a b + 2520a b + 3000a b + 1080a b +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 4 +--R (420a b + 1260a b + 1260a b + 420a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 3 +--R (3024a b + 9072a b + 9072a b + 3024a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (- 360a b + 6120a b + 20520a b + 21240a b + 7200a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (- 1296a b + 2736a b + 15984a b + 18576a b + 6624a b ) +--R * +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R 36a b - 900a b - 990a b + 2790a b + 4770a b + 1926a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 5 +--R (336a b + 1008a b + 1008a b + 336a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 4 +--R (3360a b + 10080a b + 10080a b + 3360a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (- 480a b + 10176a b + 33408a b + 34368a b + 11616a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (- 2880a b + 8640a b + 43200a b + 48960a b + 17280a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 144a b - 4464a b - 3456a b + 17856a b + 27504a b +--R + +--R 11 4 +--R 10800a b +--R * +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R 288a b - 1440a b - 3888a b - 144a b + 4176a b + 2160a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 6 +--R (168a b + 504a b + 504a b + 168a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 5 +--R (2352a b + 7056a b + 7056a b + 2352a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (- 360a b + 10320a b + 33120a b + 33840a b + 11400a b ) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (- 3360a b + 14784a b + 64512a b + 71232a b + 24864a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 216a b - 9000a b - 2880a b + 47520a b + 66600a b +--R + +--R 11 4 +--R 25416a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R 1008a b - 7056a b - 16128a b + 4032a b + 23184a b +--R + +--R 12 3 +--R 11088a b +--R * +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 24a b + 864a b - 360a b - 5016a b - 3888a b + 1368a b +--R + +--R 13 2 +--R 1488a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 7 +--R (48a b + 144a b + 144a b + 48a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 6 +--R (1008a b + 3024a b + 3024a b + 1008a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (- 144a b + 6480a b + 20304a b + 20592a b + 6912a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (- 2160a b + 14880a b + 57600a b + 61920a b + 21360a b ) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 144a b - 9360a b + 3456a b + 67968a b + 87408a b +--R + +--R 11 4 +--R 32400a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R 1296a b - 13680a b - 25344a b + 19008a b + 52848a b +--R + +--R 12 3 +--R 23472a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 48a b + 2736a b - 3744a b - 21120a b - 12816a b +--R + +--R 11 4 13 2 +--R 8784a b + 7008a b +--R * +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 144a b + 1152a b + 1872a b - 2160a b - 4032a b +--R + +--R 12 3 14 +--R - 720a b + 576a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 8 +--R (6a b + 18a b + 18a b + 6a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 7 +--R (240a b + 720a b + 720a b + 240a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (- 24a b + 2424a b + 7416a b + 7464a b + 2496a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (- 720a b + 8880a b + 30960a b + 32400a b + 11040a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 36a b - 5220a b + 8160a b + 56160a b + 66780a b +--R + +--R 11 4 +--R 24036a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R 720a b - 13200a b - 17664a b + 33408a b + 63408a b +--R + +--R 12 3 +--R 26256a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 24a b + 3096a b - 9360a b - 33600a b - 13320a b +--R + +--R 11 4 13 2 +--R 21096a b + 13296a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 240a b + 3600a b + 3456a b - 11136a b - 14544a b +--R + +--R 12 3 14 +--R - 1296a b + 2496a b +--R * +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R 6a b - 318a b + 486a b + 2370a b + 1020a b - 1404a b +--R + +--R 13 2 15 +--R - 768a b + 96a +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 8 +--R (24a b + 72a b + 72a b + 24a b )cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 7 +--R (480a b + 1440a b + 1440a b + 480a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (- 96a b + 2976a b + 9504a b + 9696a b + 3264a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R (- 1440a b + 6000a b + 26640a b + 29520a b + 10320a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R 144a b - 6480a b - 3840a b + 28800a b + 42480a b +--R + +--R 12 3 +--R 16464a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R 1440a b - 9600a b - 24576a b - 1728a b + 24672a b +--R + +--R 13 2 +--R 12864a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 13 4 11 8 7 10 5 12 3 +--R - 96a b + 3744a b - 19200a b - 18720a b + 864a b +--R + +--R 14 +--R 4224a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R - 480a b + 2160a b + 5904a b + 336a b - 5616a b +--R + +--R 13 2 15 +--R - 2304a b + 384a +--R * +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R 24a b - 312a b - 360a b + 840a b + 1200a b + 144a b +--R + +--R 14 +--R - 192a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 8 +--R (36a b + 108a b + 108a b + 36a b )cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 7 +--R (480a b + 1440a b + 1440a b + 480a b )cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R (- 144a b + 1944a b + 6696a b + 6984a b + 2376a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R (- 1440a b + 1296a b + 12528a b + 15408a b + 5616a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R 216a b - 4320a b - 7680a b + 5040a b + 14760a b +--R + +--R 13 2 +--R 6576a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R 1440a b - 2880a b - 13824a b - 9792a b + 3168a b +--R + +--R 14 +--R 3456a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R - 144a b + 2376a b + 3960a b - 3240a b - 7560a b +--R + +--R 13 2 15 +--R - 2304a b + 576a +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R - 480a b + 144a b + 2736a b + 2544a b - 144a b +--R + +--R 14 +--R - 576a b +--R * +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R 36a b - 108a b - 396a b - 180a b + 216a b + 144a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 8 +--R (24a b + 72a b + 72a b + 24a b )cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 7 +--R (240a b + 720a b + 720a b + 240a b )cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R (- 96a b + 624a b + 2448a b + 2640a b + 912a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 +--R (- 720a b - 528a b + 2736a b + 4176a b + 1632a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R 144a b - 1440a b - 3840a b - 1440a b + 2160a b +--R + +--R 14 +--R 1344a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 15 +--R (720a b + 240a b - 3216a b - 3888a b - 768a b + 384a ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R - 96a b + 720a b + 2160a b + 1200a b - 720a b +--R + +--R 14 +--R - 576a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 +--R (- 240a b - 432a b + 144a b + 624a b + 288a b ) +--R * +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R 24a b + 24a b - 72a b - 120a b - 48a b +--R * +--R sinh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 8 +--R (6a b + 18a b + 18a b + 6a b )cosh(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 7 +--R (48a b + 144a b + 144a b + 48a b )cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 6 +--R (- 24a b + 72a b + 360a b + 408a b + 144a b )cosh(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 14 5 +--R (- 144a b - 240a b + 144a b + 432a b + 192a b)cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 15 4 +--R (36a b - 180a b - 660a b - 540a b + 96a )cosh(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 14 3 +--R (144a b + 240a b - 144a b - 432a b - 192a b)cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 2 +--R (- 24a b + 72a b + 360a b + 408a b + 144a b )cosh(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 5 10 +--R (- 48a b - 144a b - 144a b - 48a b )cosh(d x + c) + 6a b +--R + +--R 7 8 9 6 11 4 +--R 18a b + 18a b + 6a b +--R * +--R d x + c 2 +--R tanh(-------) +--R 2 +--R + +--R 15 2 13 4 11 6 9 12 +--R (- 12b - 36a b - 36a b - 12a b )sinh(d x + c) +--R + +--R 15 2 13 4 11 6 9 14 +--R (- 96b - 288a b - 288a b - 96a b )cosh(d x + c) - 144a b +--R + +--R 3 12 5 10 7 8 +--R - 432a b - 432a b - 144a b +--R * +--R 11 +--R sinh(d x + c) +--R + +--R 15 2 13 4 11 6 9 2 +--R (- 336b - 1008a b - 1008a b - 336a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 +--R (- 1056a b - 3168a b - 3168a b - 1056a b )cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R 48b - 600a b - 2088a b - 2184a b - 744a b +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 15 2 13 4 11 6 9 3 +--R (- 672b - 2016a b - 2016a b - 672a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 2 +--R (- 3360a b - 10080a b - 10080a b - 3360a b )cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R (288b - 4128a b - 14112a b - 14688a b - 4992a b ) +--R * +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 480a b - 720a b - 5040a b - 6000a b - 2160a b +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 15 2 13 4 11 6 9 4 +--R (- 840b - 2520a b - 2520a b - 840a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 3 +--R (- 6048a b - 18144a b - 18144a b - 6048a b )cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R (720b - 12240a b - 41040a b - 42480a b - 14400a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (2592a b - 5472a b - 31968a b - 37152a b - 13248a b ) +--R * +--R cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R - 72b + 1800a b + 1980a b - 5580a b - 9540a b - 3852a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 15 2 13 4 11 6 9 5 +--R (- 672b - 2016a b - 2016a b - 672a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 4 +--R (- 6720a b - 20160a b - 20160a b - 6720a b )cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R (960b - 20352a b - 66816a b - 68736a b - 23232a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (5760a b - 17280a b - 86400a b - 97920a b - 34560a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R - 288b + 8928a b + 6912a b - 35712a b - 55008a b +--R + +--R 10 5 +--R - 21600a b +--R * +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 576a b + 2880a b + 7776a b + 288a b - 8352a b - 4320a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 15 2 13 4 11 6 9 6 +--R (- 336b - 1008a b - 1008a b - 336a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 5 +--R (- 4704a b - 14112a b - 14112a b - 4704a b )cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R (720b - 20640a b - 66240a b - 67680a b - 22800a b ) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (6720a b - 29568a b - 129024a b - 142464a b - 49728a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R - 432b + 18000a b + 5760a b - 95040a b - 133200a b +--R + +--R 10 5 +--R - 50832a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 2016a b + 14112a b + 32256a b - 8064a b - 46368a b +--R + +--R 11 4 +--R - 22176a b +--R * +--R cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R 48b - 1728a b + 720a b + 10032a b + 7776a b - 2736a b +--R + +--R 12 3 +--R - 2976a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 15 2 13 4 11 6 9 7 +--R (- 96b - 288a b - 288a b - 96a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 6 +--R (- 2016a b - 6048a b - 6048a b - 2016a b )cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R (288b - 12960a b - 40608a b - 41184a b - 13824a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (4320a b - 29760a b - 115200a b - 123840a b - 42720a b ) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R - 288b + 18720a b - 6912a b - 135936a b - 174816a b +--R + +--R 10 5 +--R - 64800a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 +--R - 2592a b + 27360a b + 50688a b - 38016a b +--R + +--R 9 6 11 4 +--R - 105696a b - 46944a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R 96b - 5472a b + 7488a b + 42240a b + 25632a b +--R + +--R 10 5 12 3 +--R - 17568a b - 14016a b +--R * +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 288a b - 2304a b - 3744a b + 4320a b + 8064a b +--R + +--R 11 4 13 2 +--R 1440a b - 1152a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 +--R (- 12b - 36a b - 36a b - 12a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 7 +--R (- 480a b - 1440a b - 1440a b - 480a b )cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R (48b - 4848a b - 14832a b - 14928a b - 4992a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (1440a b - 17760a b - 61920a b - 64800a b - 22080a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R - 72b + 10440a b - 16320a b - 112320a b - 133560a b +--R + +--R 10 5 +--R - 48072a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 +--R - 1440a b + 26400a b + 35328a b - 66816a b +--R + +--R 9 6 11 4 +--R - 126816a b - 52512a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R 48b - 6192a b + 18720a b + 67200a b + 26640a b +--R + +--R 10 5 12 3 +--R - 42192a b - 26592a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 480a b - 7200a b - 6912a b + 22272a b + 29088a b +--R + +--R 11 4 13 2 +--R 2592a b - 4992a b +--R * +--R cosh(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R - 12b + 636a b - 972a b - 4740a b - 2040a b + 2808a b +--R + +--R 12 3 14 +--R 1536a b - 192a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 8 +--R (- 48a b - 144a b - 144a b - 48a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 7 +--R (- 960a b - 2880a b - 2880a b - 960a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (192a b - 5952a b - 19008a b - 19392a b - 6528a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (2880a b - 12000a b - 53280a b - 59040a b - 20640a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 288a b + 12960a b + 7680a b - 57600a b - 84960a b +--R + +--R 11 4 +--R - 32928a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 2880a b + 19200a b + 49152a b + 3456a b - 49344a b +--R + +--R 12 3 +--R - 25728a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 14 3 12 7 8 9 6 11 4 +--R 192a b - 7488a b + 38400a b + 37440a b - 1728a b +--R + +--R 13 2 +--R - 8448a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R 960a b - 4320a b - 11808a b - 672a b + 11232a b +--R + +--R 12 3 14 +--R 4608a b - 768a b +--R * +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 48a b + 624a b + 720a b - 1680a b - 2400a b - 288a b +--R + +--R 13 2 +--R 384a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 8 +--R (- 72a b - 216a b - 216a b - 72a b )cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 7 +--R (- 960a b - 2880a b - 2880a b - 960a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (288a b - 3888a b - 13392a b - 13968a b - 4752a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R (2880a b - 2592a b - 25056a b - 30816a b - 11232a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 432a b + 8640a b + 15360a b - 10080a b - 29520a b +--R + +--R 12 3 +--R - 13152a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R - 2880a b + 5760a b + 27648a b + 19584a b - 6336a b +--R + +--R 13 2 +--R - 6912a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R 288a b - 4752a b - 7920a b + 6480a b + 15120a b +--R + +--R 12 3 14 +--R 4608a b - 1152a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R 960a b - 288a b - 5472a b - 5088a b + 288a b +--R + +--R 13 2 +--R 1152a b +--R * +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 72a b + 216a b + 792a b + 360a b - 432a b - 288a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 8 +--R (- 48a b - 144a b - 144a b - 48a b )cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 7 +--R (- 480a b - 1440a b - 1440a b - 480a b )cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R (192a b - 1248a b - 4896a b - 5280a b - 1824a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R (1440a b + 1056a b - 5472a b - 8352a b - 3264a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R - 288a b + 2880a b + 7680a b + 2880a b - 4320a b +--R + +--R 13 2 +--R - 2688a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R - 1440a b - 480a b + 6432a b + 7776a b + 1536a b +--R + +--R 14 +--R - 768a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R 192a b - 1440a b - 4320a b - 2400a b + 1440a b +--R + +--R 13 2 +--R 1152a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R (480a b + 864a b - 288a b - 1248a b - 576a b ) +--R * +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R - 48a b - 48a b + 144a b + 240a b + 96a b +--R * +--R sinh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 8 +--R (- 12a b - 36a b - 36a b - 12a b )cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 7 +--R (- 96a b - 288a b - 288a b - 96a b )cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 6 +--R (48a b - 144a b - 720a b - 816a b - 288a b )cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 5 +--R (288a b + 480a b - 288a b - 864a b - 384a b )cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 14 4 +--R (- 72a b + 360a b + 1320a b + 1080a b - 192a b)cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 3 +--R (- 288a b - 480a b + 288a b + 864a b + 384a b )cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 2 +--R (48a b - 144a b - 720a b - 816a b - 288a b )cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 4 11 +--R (96a b + 288a b + 288a b + 96a b )cosh(d x + c) - 12a b +--R + +--R 6 9 8 7 10 5 +--R - 36a b - 36a b - 12a b +--R * +--R d x + c +--R tanh(-------) +--R 2 +--R + +--R 14 3 12 5 10 7 8 12 +--R (- 6a b - 18a b - 18a b - 6a b )sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 2 13 +--R (- 48a b - 144a b - 144a b - 48a b )cosh(d x + c) - 72a b +--R + +--R 4 11 6 9 8 7 +--R - 216a b - 216a b - 72a b +--R * +--R 11 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 2 +--R (- 168a b - 504a b - 504a b - 168a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 14 +--R (- 528a b - 1584a b - 1584a b - 528a b )cosh(d x + c) + 24a b +--R + +--R 3 12 5 10 7 8 9 6 +--R - 300a b - 1044a b - 1092a b - 372a b +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 3 +--R (- 336a b - 1008a b - 1008a b - 336a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 2 +--R (- 1680a b - 5040a b - 5040a b - 1680a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (144a b - 2064a b - 7056a b - 7344a b - 2496a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R 240a b - 360a b - 2520a b - 3000a b - 1080a b +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 4 +--R (- 420a b - 1260a b - 1260a b - 420a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 3 +--R (- 3024a b - 9072a b - 9072a b - 3024a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (360a b - 6120a b - 20520a b - 21240a b - 7200a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (1296a b - 2736a b - 15984a b - 18576a b - 6624a b ) +--R * +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 36a b + 900a b + 990a b - 2790a b - 4770a b - 1926a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 5 +--R (- 336a b - 1008a b - 1008a b - 336a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 4 +--R (- 3360a b - 10080a b - 10080a b - 3360a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (480a b - 10176a b - 33408a b - 34368a b - 11616a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (2880a b - 8640a b - 43200a b - 48960a b - 17280a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 144a b + 4464a b + 3456a b - 17856a b - 27504a b +--R + +--R 11 4 +--R - 10800a b +--R * +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 288a b + 1440a b + 3888a b + 144a b - 4176a b - 2160a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 6 +--R (- 168a b - 504a b - 504a b - 168a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 5 +--R (- 2352a b - 7056a b - 7056a b - 2352a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (360a b - 10320a b - 33120a b - 33840a b - 11400a b ) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (3360a b - 14784a b - 64512a b - 71232a b - 24864a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 216a b + 9000a b + 2880a b - 47520a b - 66600a b +--R + +--R 11 4 +--R - 25416a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 1008a b + 7056a b + 16128a b - 4032a b - 23184a b +--R + +--R 12 3 +--R - 11088a b +--R * +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R 24a b - 864a b + 360a b + 5016a b + 3888a b - 1368a b +--R + +--R 13 2 +--R - 1488a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 7 +--R (- 48a b - 144a b - 144a b - 48a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 6 +--R (- 1008a b - 3024a b - 3024a b - 1008a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (144a b - 6480a b - 20304a b - 20592a b - 6912a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (2160a b - 14880a b - 57600a b - 61920a b - 21360a b ) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 144a b + 9360a b - 3456a b - 67968a b - 87408a b +--R + +--R 11 4 +--R - 32400a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 1296a b + 13680a b + 25344a b - 19008a b - 52848a b +--R + +--R 12 3 +--R - 23472a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 48a b - 2736a b + 3744a b + 21120a b + 12816a b +--R + +--R 11 4 13 2 +--R - 8784a b - 7008a b +--R * +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R 144a b - 1152a b - 1872a b + 2160a b + 4032a b + 720a b +--R + +--R 14 +--R - 576a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 14 3 12 5 10 7 8 8 +--R (- 6a b - 18a b - 18a b - 6a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 7 +--R (- 240a b - 720a b - 720a b - 240a b )cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 6 +--R (24a b - 2424a b - 7416a b - 7464a b - 2496a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (720a b - 8880a b - 30960a b - 32400a b - 11040a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 36a b + 5220a b - 8160a b - 56160a b - 66780a b +--R + +--R 11 4 +--R - 24036a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 720a b + 13200a b + 17664a b - 33408a b - 63408a b +--R + +--R 12 3 +--R - 26256a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 24a b - 3096a b + 9360a b + 33600a b + 13320a b +--R + +--R 11 4 13 2 +--R - 21096a b - 13296a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R 240a b - 3600a b - 3456a b + 11136a b + 14544a b +--R + +--R 12 3 14 +--R 1296a b - 2496a b +--R * +--R cosh(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 6a b + 318a b - 486a b - 2370a b - 1020a b + 1404a b +--R + +--R 13 2 15 +--R 768a b - 96a +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 8 +--R (- 24a b - 72a b - 72a b - 24a b )cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 7 +--R (- 480a b - 1440a b - 1440a b - 480a b )cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 6 +--R (96a b - 2976a b - 9504a b - 9696a b - 3264a b )cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R (1440a b - 6000a b - 26640a b - 29520a b - 10320a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 144a b + 6480a b + 3840a b - 28800a b - 42480a b +--R + +--R 12 3 +--R - 16464a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R - 1440a b + 9600a b + 24576a b + 1728a b - 24672a b +--R + +--R 13 2 +--R - 12864a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 13 4 11 8 7 10 5 12 3 +--R 96a b - 3744a b + 19200a b + 18720a b - 864a b +--R + +--R 14 +--R - 4224a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R 480a b - 2160a b - 5904a b - 336a b + 5616a b + 2304a b +--R + +--R 15 +--R - 384a +--R * +--R cosh(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 24a b + 312a b + 360a b - 840a b - 1200a b - 144a b +--R + +--R 14 +--R 192a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 8 +--R (- 36a b - 108a b - 108a b - 36a b )cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 7 +--R (- 480a b - 1440a b - 1440a b - 480a b )cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R (144a b - 1944a b - 6696a b - 6984a b - 2376a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R (1440a b - 1296a b - 12528a b - 15408a b - 5616a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R - 216a b + 4320a b + 7680a b - 5040a b - 14760a b +--R + +--R 13 2 +--R - 6576a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R - 1440a b + 2880a b + 13824a b + 9792a b - 3168a b +--R + +--R 14 +--R - 3456a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R 144a b - 2376a b - 3960a b + 3240a b + 7560a b +--R + +--R 13 2 15 +--R 2304a b - 576a +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R (480a b - 144a b - 2736a b - 2544a b + 144a b + 576a b) +--R * +--R cosh(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R - 36a b + 108a b + 396a b + 180a b - 216a b - 144a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 8 +--R (- 24a b - 72a b - 72a b - 24a b )cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 7 +--R (- 240a b - 720a b - 720a b - 240a b )cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 6 +--R (96a b - 624a b - 2448a b - 2640a b - 912a b )cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 5 +--R (720a b + 528a b - 2736a b - 4176a b - 1632a b )cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R - 144a b + 1440a b + 3840a b + 1440a b - 2160a b +--R + +--R 14 +--R - 1344a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 15 +--R (- 720a b - 240a b + 3216a b + 3888a b + 768a b - 384a ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R (96a b - 720a b - 2160a b - 1200a b + 720a b + 576a b) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 +--R (240a b + 432a b - 144a b - 624a b - 288a b )cosh(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R - 24a b - 24a b + 72a b + 120a b + 48a b +--R * +--R sinh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 8 +--R (- 6a b - 18a b - 18a b - 6a b )cosh(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 7 +--R (- 48a b - 144a b - 144a b - 48a b )cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 6 +--R (24a b - 72a b - 360a b - 408a b - 144a b )cosh(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 14 5 +--R (144a b + 240a b - 144a b - 432a b - 192a b)cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 15 4 +--R (- 36a b + 180a b + 660a b + 540a b - 96a )cosh(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 14 3 +--R (- 144a b - 240a b + 144a b + 432a b + 192a b)cosh(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 13 2 2 +--R (24a b - 72a b - 360a b - 408a b - 144a b )cosh(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 5 10 7 8 +--R (48a b + 144a b + 144a b + 48a b )cosh(d x + c) - 6a b - 18a b +--R + +--R 9 6 11 4 +--R - 18a b - 6a b +--R Type: Expression(Integer) +--E 90 + +--S 91 of 510 +t0018:= 1/(1+%i*sinh(c+d*x))^4 +--R +--R +--R (77) +--R 1 +--R ----------------------------------------------------------------------------- +--R 4 3 2 +--R sinh(d x + c) - 4%i sinh(d x + c) - 6sinh(d x + c) + 4%i sinh(d x + c) + 1 +--R Type: Expression(Complex(Integer)) +--E 91 + +--S 92 of 510 +r0018:= 1/35*cosh(c+d*x)*(35+35*%i*sinh(c+d*x)-25*cosh(c+d*x)^2-_ + 10*%i*sinh(c+d*x)*cosh(c+d*x)^2+2*cosh(c+d*x)^4)/d/_ + (-%i+sinh(c+d*x))/(1+%i*sinh(c+d*x))^4 +--R +--R +--R (78) +--R 3 +--R (- 10%i cosh(d x + c) + 35%i cosh(d x + c))sinh(d x + c) +--R + +--R 5 3 +--R 2cosh(d x + c) - 25cosh(d x + c) + 35cosh(d x + c) +--R / +--R 5 4 3 +--R 35d sinh(d x + c) - 175%i d sinh(d x + c) - 350d sinh(d x + c) +--R + +--R 2 +--R 350%i d sinh(d x + c) + 175d sinh(d x + c) - 35%i d +--R Type: Expression(Complex(Integer)) +--E 92 + +--S 93 of 510 +a0018:= integrate(t0018,x) +--R +--R +--R (79) +--R 2 +--R - 140sinh(d x + c) + (- 280cosh(d x + c) + 88%i)sinh(d x + c) +--R + +--R 2 +--R - 140cosh(d x + c) + 80%i cosh(d x + c) + 28 +--R / +--R 6 5 +--R 35d sinh(d x + c) + (210d cosh(d x + c) - 245%i d)sinh(d x + c) +--R + +--R 2 4 +--R (525d cosh(d x + c) - 1225%i d cosh(d x + c) - 735d)sinh(d x + c) +--R + +--R 3 2 +--R 700d cosh(d x + c) - 2450%i d cosh(d x + c) - 2940d cosh(d x + c) +--R + +--R 1225%i d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 525d cosh(d x + c) - 2450%i d cosh(d x + c) - 4410d cosh(d x + c) +--R + +--R 3675%i d cosh(d x + c) + 1225d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 210d cosh(d x + c) - 1225%i d cosh(d x + c) - 2940d cosh(d x + c) +--R + +--R 2 +--R 3675%i d cosh(d x + c) + 2450d cosh(d x + c) - 770%i d +--R * +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 35d cosh(d x + c) - 245%i d cosh(d x + c) - 735d cosh(d x + c) +--R + +--R 3 2 +--R 1225%i d cosh(d x + c) + 1225d cosh(d x + c) - 700%i d cosh(d x + c) +--R + +--R - 245d +--R Type: Union(Expression(Complex(Integer)),...) +--E 93 + +--S 94 of 510 +m0018:= a0018-r0018 +--R +--R +--R (80) +--R 3 7 +--R (10%i cosh(d x + c) - 35%i cosh(d x + c) - 140)sinh(d x + c) +--R + +--R 5 4 3 +--R - 2cosh(d x + c) + 60%i cosh(d x + c) + 95cosh(d x + c) +--R + +--R 2 +--R - 210%i cosh(d x + c) - 560cosh(d x + c) + 788%i +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R - 12cosh(d x + c) + 164%i cosh(d x + c) + 500cosh(d x + c) +--R + +--R 3 2 +--R - 910%i cosh(d x + c) - 1575cosh(d x + c) + 2460%i cosh(d x + c) +--R + +--R 1868 +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 7 6 5 +--R - 30cosh(d x + c) + 270%i cosh(d x + c) + 1117cosh(d x + c) +--R + +--R 4 3 2 +--R - 2415%i cosh(d x + c) - 3850cosh(d x + c) + 4865%i cosh(d x + c) +--R + +--R 5160cosh(d x + c) - 2420%i +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 7 6 +--R - 40cosh(d x + c) + 290%i cosh(d x + c) + 1368cosh(d x + c) +--R + +--R 5 4 3 +--R - 3605%i cosh(d x + c) - 6300cosh(d x + c) + 8085%i cosh(d x + c) +--R + +--R 2 +--R 8015cosh(d x + c) - 6050%i cosh(d x + c) - 1860 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 9 8 7 +--R - 30cosh(d x + c) + 200%i cosh(d x + c) + 977cosh(d x + c) +--R + +--R 6 5 4 +--R - 3010%i cosh(d x + c) - 6020cosh(d x + c) + 8715%i cosh(d x + c) +--R + +--R 3 2 +--R 9180cosh(d x + c) - 7525%i cosh(d x + c) - 4195cosh(d x + c) + 860%i +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 10 9 8 +--R - 12cosh(d x + c) + 80%i cosh(d x + c) + 388cosh(d x + c) +--R + +--R 7 6 5 +--R - 1330%i cosh(d x + c) - 3045cosh(d x + c) + 4979%i cosh(d x + c) +--R + +--R 4 3 2 +--R 6115cosh(d x + c) - 5520%i cosh(d x + c) - 3850cosh(d x + c) +--R + +--R 1695%i cosh(d x + c) + 228 +--R * +--R sinh(d x + c) +--R + +--R 11 10 9 +--R - 2cosh(d x + c) + 14%i cosh(d x + c) + 67cosh(d x + c) +--R + +--R 8 7 6 +--R - 245%i cosh(d x + c) - 630cosh(d x + c) + 1160%i cosh(d x + c) +--R + +--R 5 4 3 +--R 1624cosh(d x + c) - 1725%i cosh(d x + c) - 1400cosh(d x + c) +--R + +--R 2 +--R 840%i cosh(d x + c) + 325cosh(d x + c) - 28%i +--R / +--R 11 10 +--R 35d sinh(d x + c) + (210d cosh(d x + c) - 420%i d)sinh(d x + c) +--R + +--R 2 9 +--R (525d cosh(d x + c) - 2275%i d cosh(d x + c) - 2310d)sinh(d x + c) +--R + +--R 3 2 +--R 700d cosh(d x + c) - 5075%i d cosh(d x + c) - 11165d cosh(d x + c) +--R + +--R 7700%i d +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 525d cosh(d x + c) - 5950%i d cosh(d x + c) - 21910d cosh(d x + c) +--R + +--R 32725%i d cosh(d x + c) + 17325d +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 210d cosh(d x + c) - 3850%i d cosh(d x + c) - 22190d cosh(d x + c) +--R + +--R 2 +--R 55475%i d cosh(d x + c) + 63525d cosh(d x + c) - 27755%i d +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 35d cosh(d x + c) - 1295%i d cosh(d x + c) - 12110d cosh(d x + c) +--R + +--R 3 2 +--R 47425%i d cosh(d x + c) + 90825d cosh(d x + c) +--R + +--R - 85435%i d cosh(d x + c) - 32515d +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 6 5 +--R - 175%i d cosh(d x + c) - 3325d cosh(d x + c) +--R + +--R 4 3 +--R 21175%i d cosh(d x + c) + 63525d cosh(d x + c) +--R + +--R 2 +--R - 99750%i d cosh(d x + c) - 80675d cosh(d x + c) + 28035%i d +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 6 5 +--R - 350d cosh(d x + c) + 4550%i d cosh(d x + c) +--R + +--R 4 3 +--R 22225d cosh(d x + c) - 54600%i d cosh(d x + c) +--R + +--R 2 +--R - 73500d cosh(d x + c) + 52815%i d cosh(d x + c) + 17500d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 5 +--R 350%i d cosh(d x + c) + 3500d cosh(d x + c) +--R + +--R 4 3 +--R - 14000%i d cosh(d x + c) - 29400d cosh(d x + c) +--R + +--R 2 +--R 35035%i d cosh(d x + c) + 22925d cosh(d x + c) - 7525%i d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 175d cosh(d x + c) - 1435%i d cosh(d x + c) - 4900d cosh(d x + c) +--R + +--R 3 2 +--R 9065%i d cosh(d x + c) + 9800d cosh(d x + c) +--R + +--R - 5950%i d cosh(d x + c) - 1995d +--R * +--R sinh(d x + c) +--R + +--R 6 5 4 +--R - 35%i d cosh(d x + c) - 245d cosh(d x + c) + 735%i d cosh(d x + c) +--R + +--R 3 2 +--R 1225d cosh(d x + c) - 1225%i d cosh(d x + c) - 700d cosh(d x + c) +--R + +--R 245%i d +--R Type: Expression(Complex(Integer)) +--E 94 + +--S 95 of 510 +d0018:= D(m0018,x) +--R +--R +--R (81) +--R 2 15 +--R (30%i cosh(d x + c) - 35%i)sinh(d x + c) +--R + +--R 4 3 2 +--R - 10cosh(d x + c) + 360%i cosh(d x + c) + 525cosh(d x + c) +--R + +--R - 420%i cosh(d x + c) +--R * +--R 14 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R - 120cosh(d x + c) + 2090%i cosh(d x + c) + 5880cosh(d x + c) +--R + +--R 2 +--R - 6445%i cosh(d x + c) - 1750cosh(d x + c) - 2548%i +--R * +--R 13 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R - 650cosh(d x + c) + 7780%i cosh(d x + c) + 30405cosh(d x + c) +--R + +--R 3 2 +--R - 50390%i cosh(d x + c) - 35315cosh(d x + c) - 7490%i cosh(d x + c) +--R + +--R - 17696 +--R * +--R 12 +--R sinh(d x + c) +--R + +--R 7 6 5 +--R - 2080cosh(d x + c) + 20430%i cosh(d x + c) + 95500cosh(d x + c) +--R + +--R 4 3 +--R - 216035%i cosh(d x + c) - 247030cosh(d x + c) +--R + +--R 2 +--R 95018%i cosh(d x + c) - 76482cosh(d x + c) + 61320%i +--R * +--R 11 +--R sinh(d x + c) +--R + +--R 8 7 6 +--R - 4290cosh(d x + c) + 38720%i cosh(d x + c) + 199925cosh(d x + c) +--R + +--R 5 4 +--R - 571320%i cosh(d x + c) - 909580cosh(d x + c) +--R + +--R 3 2 +--R 749210%i cosh(d x + c) + 114153cosh(d x + c) +--R + +--R 266602%i cosh(d x + c) + 130074 +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 9 8 7 +--R - 5720cosh(d x + c) + 51370%i cosh(d x + c) + 282700cosh(d x + c) +--R + +--R 6 5 +--R - 974565%i cosh(d x + c) - 2010540cosh(d x + c) +--R + +--R 4 3 +--R 2447850%i cosh(d x + c) + 1491790cosh(d x + c) +--R + +--R 2 +--R 22890%i cosh(d x + c) + 517188cosh(d x + c) - 174202%i +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 10 9 8 +--R - 4290cosh(d x + c) + 41580%i cosh(d x + c) + 245685cosh(d x + c) +--R + +--R 7 6 +--R - 1023090%i cosh(d x + c) - 2694475cosh(d x + c) +--R + +--R 5 4 +--R 4406852%i cosh(d x + c) + 4321335cosh(d x + c) +--R + +--R 3 2 +--R - 2007880%i cosh(d x + c) + 235547cosh(d x + c) +--R + +--R - 578578%i cosh(d x + c) - 127918 +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 10 9 +--R 5610%i cosh(d x + c) + 56760cosh(d x + c) +--R + +--R 8 7 +--R - 432705%i cosh(d x + c) - 1772540cosh(d x + c) +--R + +--R 6 5 +--R 4118120%i cosh(d x + c) + 5806024cosh(d x + c) +--R + +--R 4 3 +--R - 4807440%i cosh(d x + c) - 1787962cosh(d x + c) +--R + +--R 2 +--R - 202762%i cosh(d x + c) - 257880cosh(d x + c) - 7084%i +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 12 11 10 +--R 4290cosh(d x + c) - 35640%i cosh(d x + c) - 179025cosh(d x + c) +--R + +--R 9 8 +--R 509980%i cosh(d x + c) + 664160cosh(d x + c) +--R + +--R 7 6 +--R 167048%i cosh(d x + c) + 1989078cosh(d x + c) +--R + +--R 5 4 +--R - 3237820%i cosh(d x + c) - 2502618cosh(d x + c) +--R + +--R 3 2 +--R 837102%i cosh(d x + c) + 179473cosh(d x + c) +--R + +--R - 265118%i cosh(d x + c) - 137900 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 13 12 11 +--R 5720cosh(d x + c) - 54450%i cosh(d x + c) - 303600cosh(d x + c) +--R + +--R 10 9 +--R 1134465%i cosh(d x + c) + 2842210cosh(d x + c) +--R + +--R 8 7 +--R - 4873820%i cosh(d x + c) - 5876472cosh(d x + c) +--R + +--R 6 5 +--R 5074732%i cosh(d x + c) + 3233082cosh(d x + c) +--R + +--R 4 3 +--R - 1577842%i cosh(d x + c) - 320320cosh(d x + c) +--R + +--R 2 +--R - 530658%i cosh(d x + c) - 578718cosh(d x + c) + 174811%i +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 14 13 12 +--R 4290cosh(d x + c) - 44740%i cosh(d x + c) - 264825cosh(d x + c) +--R + +--R 11 10 +--R 1092230%i cosh(d x + c) + 3216535cosh(d x + c) +--R + +--R 9 8 +--R - 6883590%i cosh(d x + c) - 10987270cosh(d x + c) +--R + +--R 7 6 +--R 13364640%i cosh(d x + c) + 12505620cosh(d x + c) +--R + +--R 5 4 +--R - 8924370%i cosh(d x + c) - 4528885cosh(d x + c) +--R + +--R 3 2 +--R 1082750%i cosh(d x + c) - 493990cosh(d x + c) +--R + +--R 511252%i cosh(d x + c) + 123578 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 15 14 13 +--R 2080cosh(d x + c) - 23510%i cosh(d x + c) - 146820cosh(d x + c) +--R + +--R 12 11 +--R 646855%i cosh(d x + c) + 2102450cosh(d x + c) +--R + +--R 10 9 +--R - 5116930%i cosh(d x + c) - 9504470cosh(d x + c) +--R + +--R 8 7 +--R 13725640%i cosh(d x + c) + 15572570cosh(d x + c) +--R + +--R 6 5 +--R - 13854610%i cosh(d x + c) - 9453408cosh(d x + c) +--R + +--R 4 3 +--R 4575200%i cosh(d x + c) + 1154860cosh(d x + c) +--R + +--R 2 +--R 210628%i cosh(d x + c) + 261282cosh(d x + c) - 54425%i +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 16 15 14 +--R 650cosh(d x + c) - 7920%i cosh(d x + c) - 52145cosh(d x + c) +--R + +--R 13 12 +--R 242560%i cosh(d x + c) + 849100cosh(d x + c) +--R + +--R 11 10 +--R - 2274770%i cosh(d x + c) - 4732575cosh(d x + c) +--R + +--R 9 8 +--R 7767650%i cosh(d x + c) + 10177000cosh(d x + c) +--R + +--R 7 6 +--R - 10681650%i cosh(d x + c) - 8914185cosh(d x + c) +--R + +--R 5 4 +--R 5761206%i cosh(d x + c) + 2683390cosh(d x + c) +--R + +--R 3 2 +--R - 724468%i cosh(d x + c) + 12103cosh(d x + c) +--R + +--R - 75880%i cosh(d x + c) - 14210 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 17 16 15 +--R 120cosh(d x + c) - 1570%i cosh(d x + c) - 10900cosh(d x + c) +--R + +--R 14 13 +--R 53265%i cosh(d x + c) + 198240cosh(d x + c) +--R + +--R 12 11 +--R - 574250%i cosh(d x + c) - 1311110cosh(d x + c) +--R + +--R 10 9 +--R 2390890%i cosh(d x + c) + 3523810cosh(d x + c) +--R + +--R 8 7 +--R - 4226600%i cosh(d x + c) - 4123512cosh(d x + c) +--R + +--R 6 5 +--R 3239182%i cosh(d x + c) + 1995050cosh(d x + c) +--R + +--R 4 3 +--R - 906607%i cosh(d x + c) - 261898cosh(d x + c) +--R + +--R 2 +--R 23975%i cosh(d x + c) - 9800cosh(d x + c) + 1715%i +--R * +--R sinh(d x + c) +--R + +--R 18 17 16 +--R 10cosh(d x + c) - 140%i cosh(d x + c) - 1025cosh(d x + c) +--R + +--R 15 14 13 +--R 5250%i cosh(d x + c) + 20615cosh(d x + c) - 63820%i cosh(d x + c) +--R + +--R 12 11 +--R - 157745cosh(d x + c) + 314840%i cosh(d x + c) +--R + +--R 10 9 8 +--R 513065cosh(d x + c) - 688520%i cosh(d x + c) - 763605cosh(d x + c) +--R + +--R 7 6 5 +--R 697802%i cosh(d x + c) + 519732cosh(d x + c) - 307552%i cosh(d x + c) +--R + +--R 4 3 2 +--R - 137907cosh(d x + c) + 42140%i cosh(d x + c) + 6860cosh(d x + c) +--R / +--R 18 17 +--R 35sinh(d x + c) + (420cosh(d x + c) - 700%i)sinh(d x + c) +--R + +--R 2 16 +--R (2310cosh(d x + c) - 7910%i cosh(d x + c) - 6650)sinh(d x + c) +--R + +--R 3 2 +--R 7700cosh(d x + c) - 40810%i cosh(d x + c) - 70490cosh(d x + c) +--R + +--R 39900%i +--R * +--R 15 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 17325cosh(d x + c) - 127050%i cosh(d x + c) - 339675cosh(d x + c) +--R + +--R 395010%i cosh(d x + c) + 169575 +--R * +--R 14 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 27720cosh(d x + c) - 265650%i cosh(d x + c) - 982800cosh(d x + c) +--R + +--R 2 +--R 1769040%i cosh(d x + c) + 1560090cosh(d x + c) - 542710%i +--R * +--R 13 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 32340cosh(d x + c) - 392700%i cosh(d x + c) - 1898925cosh(d x + c) +--R + +--R 3 2 +--R 4730110%i cosh(d x + c) + 6456345cosh(d x + c) +--R + +--R - 4612790%i cosh(d x + c) - 1357510 +--R * +--R 12 +--R sinh(d x + c) +--R + +--R 7 6 5 +--R 27720cosh(d x + c) - 420420%i cosh(d x + c) - 2576700cosh(d x + c) +--R + +--R 4 3 +--R 8390340%i cosh(d x + c) + 15848420cosh(d x + c) +--R + +--R 2 +--R - 17522190%i cosh(d x + c) - 10585540cosh(d x + c) + 2718590%i +--R * +--R 11 +--R sinh(d x + c) +--R + +--R 8 7 6 +--R 17325cosh(d x + c) - 328020%i cosh(d x + c) - 2512230cosh(d x + c) +--R + +--R 5 4 +--R 10371060%i cosh(d x + c) + 25610515cosh(d x + c) +--R + +--R 3 2 +--R - 39179910%i cosh(d x + c) - 36613010cosh(d x + c) +--R + +--R 19284790%i cosh(d x + c) + 4428060 +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 9 8 7 +--R 7700cosh(d x + c) - 184800%i cosh(d x + c) - 1768200cosh(d x + c) +--R + +--R 6 5 +--R 9125760%i cosh(d x + c) + 28576100cosh(d x + c) +--R + +--R 4 3 +--R - 57151850%i cosh(d x + c) - 73877300cosh(d x + c) +--R + +--R 2 +--R 60145190%i cosh(d x + c) + 28280980cosh(d x + c) - 5923190%i +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 10 9 8 +--R 2310cosh(d x + c) - 73150%i cosh(d x + c) - 888300cosh(d x + c) +--R + +--R 7 6 +--R 5731740%i cosh(d x + c) + 22447390cosh(d x + c) +--R + +--R 5 4 +--R - 56935620%i cosh(d x + c) - 96198550cosh(d x + c) +--R + +--R 3 2 +--R 108267810%i cosh(d x + c) + 78585570cosh(d x + c) +--R + +--R - 33629050%i cosh(d x + c) - 6536565 +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 11 10 9 +--R 420cosh(d x + c) - 19250%i cosh(d x + c) - 309050cosh(d x + c) +--R + +--R 8 7 +--R 2533860%i cosh(d x + c) + 12414920cosh(d x + c) +--R + +--R 6 5 +--R - 39395160%i cosh(d x + c) - 84413210cosh(d x + c) +--R + +--R 4 3 +--R 124124490%i cosh(d x + c) + 124418980cosh(d x + c) +--R + +--R 2 +--R - 82027610%i cosh(d x + c) - 32472370cosh(d x + c) + 5948880%i +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 12 11 10 +--R 35cosh(d x + c) - 3010%i cosh(d x + c) - 70175cosh(d x + c) +--R + +--R 9 8 +--R 762090%i cosh(d x + c) + 4749745cosh(d x + c) +--R + +--R 7 6 +--R - 18867100%i cosh(d x + c) - 50586725cosh(d x + c) +--R + +--R 5 4 +--R 94313100%i cosh(d x + c) + 123418120cosh(d x + c) +--R + +--R 3 2 +--R - 112186830%i cosh(d x + c) - 68234355cosh(d x + c) +--R + +--R 25347630%i cosh(d x + c) + 4439435 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 12 11 +--R - 210%i cosh(d x + c) - 9240cosh(d x + c) +--R + +--R 10 9 +--R 146160%i cosh(d x + c) + 1208690cosh(d x + c) +--R + +--R 8 7 +--R - 6113310%i cosh(d x + c) - 20527920cosh(d x + c) +--R + +--R 6 5 +--R 47891270%i cosh(d x + c) + 79421790cosh(d x + c) +--R + +--R 4 3 +--R - 94134530%i cosh(d x + c) - 78761760cosh(d x + c) +--R + +--R 2 +--R 44788800%i cosh(d x + c) + 15811250cosh(d x + c) - 2683450%i +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 12 11 +--R - 525cosh(d x + c) + 15750%i cosh(d x + c) +--R + +--R 10 9 +--R 190225cosh(d x + c) - 1278550%i cosh(d x + c) +--R + +--R 8 7 +--R - 5471025cosh(d x + c) + 15990100%i cosh(d x + c) +--R + +--R 6 5 +--R 33176535cosh(d x + c) - 49791700%i cosh(d x + c) +--R + +--R 4 3 +--R - 54226200cosh(d x + c) + 42292250%i cosh(d x + c) +--R + +--R 2 +--R 22749265cosh(d x + c) - 7717570%i cosh(d x + c) - 1286040 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 12 11 +--R 700%i cosh(d x + c) + 16100cosh(d x + c) +--R + +--R 10 9 +--R - 158410%i cosh(d x + c) - 901950cosh(d x + c) +--R + +--R 8 7 +--R 3361400%i cosh(d x + c) + 8738240cosh(d x + c) +--R + +--R 6 5 +--R - 16400440%i cosh(d x + c) - 22588650cosh(d x + c) +--R + +--R 4 3 +--R 22877750%i cosh(d x + c) + 16813860cosh(d x + c) +--R + +--R 2 +--R - 8642830%i cosh(d x + c) - 2845360cosh(d x + c) + 471590%i +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 12 11 10 +--R 525cosh(d x + c) - 9870%i cosh(d x + c) - 82425cosh(d x + c) +--R + +--R 9 8 +--R 409150%i cosh(d x + c) + 1356810cosh(d x + c) +--R + +--R 7 6 +--R - 3190320%i cosh(d x + c) - 5491045cosh(d x + c) +--R + +--R 5 4 +--R 7021560%i cosh(d x + c) + 6681640cosh(d x + c) +--R + +--R 3 2 +--R - 4671170%i cosh(d x + c) - 2315040cosh(d x + c) +--R + +--R 745850%i cosh(d x + c) + 124495 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 12 11 +--R - 210%i cosh(d x + c) - 3360cosh(d x + c) +--R + +--R 10 9 +--R 24500%i cosh(d x + c) + 108290cosh(d x + c) +--R + +--R 8 7 +--R - 324870%i cosh(d x + c) - 700280cosh(d x + c) +--R + +--R 6 5 +--R 1117830%i cosh(d x + c) + 1340150cosh(d x + c) +--R + +--R 4 3 +--R - 1208830%i cosh(d x + c) - 810460cosh(d x + c) +--R + +--R 2 +--R 390250%i cosh(d x + c) + 123900cosh(d x + c) - 21070%i +--R * +--R sinh(d x + c) +--R + +--R 12 11 10 +--R - 35cosh(d x + c) + 490%i cosh(d x + c) + 3185cosh(d x + c) +--R + +--R 9 8 7 +--R - 12740%i cosh(d x + c) - 35035cosh(d x + c) + 70000%i cosh(d x + c) +--R + +--R 6 5 4 +--R 104615cosh(d x + c) - 118580%i cosh(d x + c) - 102165cosh(d x + c) +--R + +--R 3 2 +--R 66150%i cosh(d x + c) + 31150cosh(d x + c) - 9800%i cosh(d x + c) - 1715 +--R Type: Expression(Complex(Integer)) +--E 95 + +--S 96 of 510 +t0019:= 1/(1-%i*sinh(c+d*x))^3 +--R +--R +--R %i +--R (82) - --------------------------------------------------------- +--R 3 2 +--R sinh(d x + c) + 3%i sinh(d x + c) - 3sinh(d x + c) - %i +--R Type: Expression(Complex(Integer)) +--E 96 + +--S 97 of 510 +r0019:= -1/5*%i*cosh(c+d*x)/d/(1-%i*sinh(c+d*x))^3-_ + 2/15*%i*cosh(c+d*x)/d/(1-%i*sinh(c+d*x))^2+_ + 2/15*cosh(c+d*x)/d/(%i+sinh(c+d*x)) +--R +--R +--R (83) +--R 2 2 2 +--R -- cosh(d x + c)sinh(d x + c) + - %i cosh(d x + c)sinh(d x + c) +--R 15 5 +--R + +--R 7 +--R - -- cosh(d x + c) +--R 15 +--R / +--R 3 2 +--R d sinh(d x + c) + 3%i d sinh(d x + c) - 3d sinh(d x + c) - %i d +--R Type: Expression(Complex(Fraction(Integer))) +--E 97 + +--S 98 of 510 +a0019:= integrate(t0019,x) +--R +--R +--R (84) +--R 44%i sinh(d x + c) + 36%i cosh(d x + c) - 20 +--R / +--R 4 3 +--R 15d sinh(d x + c) + (60d cosh(d x + c) + 75%i d)sinh(d x + c) +--R + +--R 2 2 +--R (90d cosh(d x + c) + 225%i d cosh(d x + c) - 150d)sinh(d x + c) +--R + +--R 3 2 +--R 60d cosh(d x + c) + 225%i d cosh(d x + c) - 300d cosh(d x + c) +--R + +--R - 165%i d +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 15d cosh(d x + c) + 75%i d cosh(d x + c) - 150d cosh(d x + c) +--R + +--R - 135%i d cosh(d x + c) + 75d +--R Type: Union(Expression(Complex(Integer)),...) +--E 98 + +--S 99 of 510 +m0019:= a0019-r0019 +--R +--R +--R (85) +--R 2 6 +--R - -- cosh(d x + c)sinh(d x + c) +--R 15 +--R + +--R 8 2 16 5 +--R (- -- cosh(d x + c) - -- %i cosh(d x + c))sinh(d x + c) +--R 15 15 +--R + +--R 4 3 18 2 19 44 +--R (- - cosh(d x + c) - -- %i cosh(d x + c) + -- cosh(d x + c) + -- %i) +--R 5 5 5 15 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 4 22 3 158 2 +--R - -- cosh(d x + c) - -- %i cosh(d x + c) + --- cosh(d x + c) +--R 15 5 15 +--R + +--R 51 152 +--R -- %i cosh(d x + c) - --- +--R 5 15 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 5 34 4 152 3 +--R - -- cosh(d x + c) - -- %i cosh(d x + c) + --- cosh(d x + c) +--R 15 15 15 +--R + +--R 81 2 254 64 +--R -- %i cosh(d x + c) - --- cosh(d x + c) - -- %i +--R 5 15 5 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 5 58 4 3 +--R - - %i cosh(d x + c) + -- cosh(d x + c) + 11%i cosh(d x + c) +--R 5 15 +--R + +--R 194 2 43 104 +--R - --- cosh(d x + c) - -- %i cosh(d x + c) + --- +--R 15 3 15 +--R * +--R sinh(d x + c) +--R + +--R 7 5 7 4 14 3 +--R -- cosh(d x + c) + - %i cosh(d x + c) - -- cosh(d x + c) +--R 15 3 3 +--R + +--R 21 2 71 4 +--R - -- %i cosh(d x + c) + -- cosh(d x + c) + - %i +--R 5 15 3 +--R / +--R 7 6 +--R d sinh(d x + c) + (4d cosh(d x + c) + 8%i d)sinh(d x + c) +--R + +--R 2 5 +--R (6d cosh(d x + c) + 27%i d cosh(d x + c) - 28d)sinh(d x + c) +--R + +--R 3 2 +--R 4d cosh(d x + c) + 33%i d cosh(d x + c) - 77d cosh(d x + c) +--R + +--R - 57%i d +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R d cosh(d x + c) + 17%i d cosh(d x + c) - 73d cosh(d x + c) +--R + +--R - 118%i d cosh(d x + c) + 73d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 3%i d cosh(d x + c) - 27d cosh(d x + c) - 81%i d cosh(d x + c) +--R + +--R 102d cosh(d x + c) + 58%i d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - 3d cosh(d x + c) - 19%i d cosh(d x + c) + 45d cosh(d x + c) +--R + +--R 47%i d cosh(d x + c) - 26d +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - %i d cosh(d x + c) + 5d cosh(d x + c) + 10%i d cosh(d x + c) +--R + +--R - 9d cosh(d x + c) - 5%i d +--R Type: Expression(Complex(Fraction(Integer))) +--E 99 + +--S 100 of 510 +d0019:= D(m0019,x) +--R +--R +--R (86) +--R 2 12 16 28 11 +--R - -- sinh(d x + c) + (- -- cosh(d x + c) - -- %i)sinh(d x + c) +--R 15 15 15 +--R + +--R 18 2 68 61 10 +--R (- -- cosh(d x + c) - -- %i cosh(d x + c) + --)sinh(d x + c) +--R 5 5 5 +--R + +--R 32 3 616 2 1204 +--R - -- cosh(d x + c) - --- %i cosh(d x + c) + ---- cosh(d x + c) +--R 5 15 15 +--R + +--R 601 +--R --- %i +--R 15 +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 28 4 944 3 3209 2 +--R - -- cosh(d x + c) - --- %i cosh(d x + c) + ---- cosh(d x + c) +--R 5 15 15 +--R + +--R 1226 317 +--R ---- %i cosh(d x + c) - --- +--R 5 5 +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 616 4 4108 3 +--R - --- %i cosh(d x + c) + ---- cosh(d x + c) +--R 15 15 +--R + +--R 1748 2 5848 301 +--R ---- %i cosh(d x + c) - ---- cosh(d x + c) - --- %i +--R 3 15 15 +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 28 6 56 5 322 4 +--R -- cosh(d x + c) + -- %i cosh(d x + c) + --- cosh(d x + c) +--R 5 3 3 +--R + +--R 2984 3 12466 2 3688 +--R ---- %i cosh(d x + c) - ----- cosh(d x + c) - ---- %i cosh(d x + c) +--R 5 15 15 +--R + +--R 428 +--R - --- +--R 5 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 32 7 896 6 2492 5 +--R -- cosh(d x + c) + --- %i cosh(d x + c) - ---- cosh(d x + c) +--R 5 15 15 +--R + +--R 26 4 3 6847 2 +--R -- %i cosh(d x + c) - 556cosh(d x + c) - ---- %i cosh(d x + c) +--R 3 15 +--R + +--R 2422 1862 +--R - ---- cosh(d x + c) - ---- %i +--R 15 15 +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 18 8 784 7 4186 6 +--R -- cosh(d x + c) + --- %i cosh(d x + c) - ---- cosh(d x + c) +--R 5 15 15 +--R + +--R 9424 5 4 1074 3 +--R - ---- %i cosh(d x + c) + 564cosh(d x + c) + ---- %i cosh(d x + c) +--R 15 5 +--R + +--R 5452 2 6106 547 +--R - ---- cosh(d x + c) - ---- %i cosh(d x + c) + --- +--R 15 15 15 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 16 9 356 8 2876 7 +--R -- cosh(d x + c) + --- %i cosh(d x + c) - ---- cosh(d x + c) +--R 15 15 15 +--R + +--R 10372 6 19184 5 +--R - ----- %i cosh(d x + c) + ----- cosh(d x + c) +--R 15 15 +--R + +--R 20393 4 16504 3 +--R ----- %i cosh(d x + c) - ----- cosh(d x + c) +--R 15 15 +--R + +--R 2504 2 1492 757 +--R - ---- %i cosh(d x + c) + ---- cosh(d x + c) - --- %i +--R 3 5 15 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 10 28 9 1057 8 +--R -- cosh(d x + c) + -- %i cosh(d x + c) - ---- cosh(d x + c) +--R 15 5 15 +--R + +--R 1072 7 4734 6 +--R - ---- %i cosh(d x + c) + ---- cosh(d x + c) +--R 3 5 +--R + +--R 22136 5 22904 4 +--R ----- %i cosh(d x + c) - ----- cosh(d x + c) +--R 15 15 +--R + +--R 17864 3 9982 2 +--R - ----- %i cosh(d x + c) + ---- cosh(d x + c) +--R 15 15 +--R + +--R 488 139 +--R --- %i cosh(d x + c) + --- +--R 5 3 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 8 10 40 9 1403 8 +--R -- %i cosh(d x + c) - -- cosh(d x + c) - ---- %i cosh(d x + c) +--R 15 3 15 +--R + +--R 4924 7 2039 6 13714 5 +--R ---- cosh(d x + c) + ---- %i cosh(d x + c) - ----- cosh(d x + c) +--R 15 3 15 +--R + +--R 13138 4 1832 3 +--R - ----- %i cosh(d x + c) + ---- cosh(d x + c) +--R 15 3 +--R + +--R 4163 2 34 35 +--R ---- %i cosh(d x + c) - -- cosh(d x + c) + -- %i +--R 15 3 3 +--R * +--R sinh(d x + c) +--R + +--R 10 9 8 +--R - cosh(d x + c) - 10%i cosh(d x + c) + 45cosh(d x + c) +--R + +--R 7 6 710 5 +--R 118%i cosh(d x + c) - 200cosh(d x + c) - --- %i cosh(d x + c) +--R 3 +--R + +--R 623 4 386 3 155 2 +--R --- cosh(d x + c) + --- %i cosh(d x + c) - --- cosh(d x + c) +--R 3 3 3 +--R / +--R 12 11 +--R sinh(d x + c) + (8cosh(d x + c) + 14%i)sinh(d x + c) +--R + +--R 2 10 +--R (28cosh(d x + c) + 102%i cosh(d x + c) - 91)sinh(d x + c) +--R + +--R 3 2 +--R (56cosh(d x + c) + 322%i cosh(d x + c) - 598cosh(d x + c) - 366%i) +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 70cosh(d x + c) + 574%i cosh(d x + c) - 1683cosh(d x + c) +--R + +--R - 2138%i cosh(d x + c) + 1019 +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 56cosh(d x + c) + 630%i cosh(d x + c) - 2636cosh(d x + c) +--R + +--R 2 +--R - 5276%i cosh(d x + c) + 5192cosh(d x + c) + 2072%i +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 28cosh(d x + c) + 434%i cosh(d x + c) - 2495cosh(d x + c) +--R + +--R 3 2 +--R - 7120%i cosh(d x + c) + 10994cosh(d x + c) + 8996%i cosh(d x + c) +--R + +--R - 3154 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 7 6 5 +--R 8cosh(d x + c) + 182%i cosh(d x + c) - 1446cosh(d x + c) +--R + +--R 4 3 +--R - 5674%i cosh(d x + c) + 12460cosh(d x + c) +--R + +--R 2 +--R 15904%i cosh(d x + c) - 11332cosh(d x + c) - 3616%i +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 7 6 +--R cosh(d x + c) + 42%i cosh(d x + c) - 493cosh(d x + c) +--R + +--R 5 4 3 +--R - 2682%i cosh(d x + c) + 8096cosh(d x + c) + 14636%i cosh(d x + c) +--R + +--R 2 +--R - 16152cosh(d x + c) - 10348%i cosh(d x + c) + 3091 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 7 6 +--R 4%i cosh(d x + c) - 88cosh(d x + c) - 712%i cosh(d x + c) +--R + +--R 5 4 3 +--R 2988cosh(d x + c) + 7414%i cosh(d x + c) - 11524cosh(d x + c) +--R + +--R 2 +--R - 11348%i cosh(d x + c) + 6688cosh(d x + c) + 1914%i +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 8 7 6 +--R - 6cosh(d x + c) - 92%i cosh(d x + c) + 578cosh(d x + c) +--R + +--R 5 4 3 +--R 1998%i cosh(d x + c) - 4251cosh(d x + c) - 5856%i cosh(d x + c) +--R + +--R 2 +--R 5266cosh(d x + c) + 2902%i cosh(d x + c) - 811 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 8 7 6 +--R - 4%i cosh(d x + c) + 48cosh(d x + c) + 250%i cosh(d x + c) +--R + +--R 5 4 3 +--R - 742cosh(d x + c) - 1394%i cosh(d x + c) + 1740cosh(d x + c) +--R + +--R 2 +--R 1454%i cosh(d x + c) - 758cosh(d x + c) - 210%i +--R * +--R sinh(d x + c) +--R + +--R 8 7 6 +--R cosh(d x + c) + 10%i cosh(d x + c) - 45cosh(d x + c) +--R + +--R 5 4 3 +--R - 118%i cosh(d x + c) + 200cosh(d x + c) + 230%i cosh(d x + c) +--R + +--R 2 +--R - 181cosh(d x + c) - 90%i cosh(d x + c) + 25 +--R Type: Expression(Complex(Fraction(Integer))) +--E 100 + +--S 101 of 510 +t0020:= 1/(1-%i*sinh(c+d*x))^4 +--R +--R +--R (87) +--R 1 +--R ----------------------------------------------------------------------------- +--R 4 3 2 +--R sinh(d x + c) + 4%i sinh(d x + c) - 6sinh(d x + c) - 4%i sinh(d x + c) + 1 +--R Type: Expression(Complex(Integer)) +--E 101 + +--S 102 of 510 +r0020:= 1/35*cosh(c+d*x)*(35-35*%i*sinh(c+d*x)-25*cosh(c+d*x)^2+_ + 10*%i*sinh(c+d*x)*cosh(c+d*x)^2+2*cosh(c+d*x)^4)/d/_ + (-1+%i*sinh(c+d*x))^4/(%i+sinh(c+d*x)) +--R +--R +--R (88) +--R 3 5 +--R (10%i cosh(d x + c) - 35%i cosh(d x + c))sinh(d x + c) + 2cosh(d x + c) +--R + +--R 3 +--R - 25cosh(d x + c) + 35cosh(d x + c) +--R / +--R 5 4 3 +--R 35d sinh(d x + c) + 175%i d sinh(d x + c) - 350d sinh(d x + c) +--R + +--R 2 +--R - 350%i d sinh(d x + c) + 175d sinh(d x + c) + 35%i d +--R Type: Expression(Complex(Integer)) +--E 102 + +--S 103 of 510 +a0020:= integrate(t0020,x) +--R +--R +--R (89) +--R 2 +--R - 140sinh(d x + c) + (- 280cosh(d x + c) - 88%i)sinh(d x + c) +--R + +--R 2 +--R - 140cosh(d x + c) - 80%i cosh(d x + c) + 28 +--R / +--R 6 5 +--R 35d sinh(d x + c) + (210d cosh(d x + c) + 245%i d)sinh(d x + c) +--R + +--R 2 4 +--R (525d cosh(d x + c) + 1225%i d cosh(d x + c) - 735d)sinh(d x + c) +--R + +--R 3 2 +--R 700d cosh(d x + c) + 2450%i d cosh(d x + c) - 2940d cosh(d x + c) +--R + +--R - 1225%i d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 525d cosh(d x + c) + 2450%i d cosh(d x + c) - 4410d cosh(d x + c) +--R + +--R - 3675%i d cosh(d x + c) + 1225d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 210d cosh(d x + c) + 1225%i d cosh(d x + c) - 2940d cosh(d x + c) +--R + +--R 2 +--R - 3675%i d cosh(d x + c) + 2450d cosh(d x + c) + 770%i d +--R * +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 35d cosh(d x + c) + 245%i d cosh(d x + c) - 735d cosh(d x + c) +--R + +--R 3 2 +--R - 1225%i d cosh(d x + c) + 1225d cosh(d x + c) + 700%i d cosh(d x + c) +--R + +--R - 245d +--R Type: Union(Expression(Complex(Integer)),...) +--E 103 + +--S 104 of 510 +m0020:= a0020-r0020 +--R +--R +--R (90) +--R 3 7 +--R (- 10%i cosh(d x + c) + 35%i cosh(d x + c) - 140)sinh(d x + c) +--R + +--R 5 4 3 +--R - 2cosh(d x + c) - 60%i cosh(d x + c) + 95cosh(d x + c) +--R + +--R 2 +--R 210%i cosh(d x + c) - 560cosh(d x + c) - 788%i +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R - 12cosh(d x + c) - 164%i cosh(d x + c) + 500cosh(d x + c) +--R + +--R 3 2 +--R 910%i cosh(d x + c) - 1575cosh(d x + c) - 2460%i cosh(d x + c) + 1868 +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 7 6 5 +--R - 30cosh(d x + c) - 270%i cosh(d x + c) + 1117cosh(d x + c) +--R + +--R 4 3 2 +--R 2415%i cosh(d x + c) - 3850cosh(d x + c) - 4865%i cosh(d x + c) +--R + +--R 5160cosh(d x + c) + 2420%i +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 7 6 +--R - 40cosh(d x + c) - 290%i cosh(d x + c) + 1368cosh(d x + c) +--R + +--R 5 4 3 +--R 3605%i cosh(d x + c) - 6300cosh(d x + c) - 8085%i cosh(d x + c) +--R + +--R 2 +--R 8015cosh(d x + c) + 6050%i cosh(d x + c) - 1860 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 9 8 7 +--R - 30cosh(d x + c) - 200%i cosh(d x + c) + 977cosh(d x + c) +--R + +--R 6 5 4 +--R 3010%i cosh(d x + c) - 6020cosh(d x + c) - 8715%i cosh(d x + c) +--R + +--R 3 2 +--R 9180cosh(d x + c) + 7525%i cosh(d x + c) - 4195cosh(d x + c) - 860%i +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 10 9 8 +--R - 12cosh(d x + c) - 80%i cosh(d x + c) + 388cosh(d x + c) +--R + +--R 7 6 5 +--R 1330%i cosh(d x + c) - 3045cosh(d x + c) - 4979%i cosh(d x + c) +--R + +--R 4 3 2 +--R 6115cosh(d x + c) + 5520%i cosh(d x + c) - 3850cosh(d x + c) +--R + +--R - 1695%i cosh(d x + c) + 228 +--R * +--R sinh(d x + c) +--R + +--R 11 10 9 +--R - 2cosh(d x + c) - 14%i cosh(d x + c) + 67cosh(d x + c) +--R + +--R 8 7 6 +--R 245%i cosh(d x + c) - 630cosh(d x + c) - 1160%i cosh(d x + c) +--R + +--R 5 4 3 +--R 1624cosh(d x + c) + 1725%i cosh(d x + c) - 1400cosh(d x + c) +--R + +--R 2 +--R - 840%i cosh(d x + c) + 325cosh(d x + c) + 28%i +--R / +--R 11 10 +--R 35d sinh(d x + c) + (210d cosh(d x + c) + 420%i d)sinh(d x + c) +--R + +--R 2 9 +--R (525d cosh(d x + c) + 2275%i d cosh(d x + c) - 2310d)sinh(d x + c) +--R + +--R 3 2 +--R 700d cosh(d x + c) + 5075%i d cosh(d x + c) - 11165d cosh(d x + c) +--R + +--R - 7700%i d +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 525d cosh(d x + c) + 5950%i d cosh(d x + c) - 21910d cosh(d x + c) +--R + +--R - 32725%i d cosh(d x + c) + 17325d +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 210d cosh(d x + c) + 3850%i d cosh(d x + c) - 22190d cosh(d x + c) +--R + +--R 2 +--R - 55475%i d cosh(d x + c) + 63525d cosh(d x + c) + 27755%i d +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 35d cosh(d x + c) + 1295%i d cosh(d x + c) - 12110d cosh(d x + c) +--R + +--R 3 2 +--R - 47425%i d cosh(d x + c) + 90825d cosh(d x + c) +--R + +--R 85435%i d cosh(d x + c) - 32515d +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 6 5 +--R 175%i d cosh(d x + c) - 3325d cosh(d x + c) +--R + +--R 4 3 +--R - 21175%i d cosh(d x + c) + 63525d cosh(d x + c) +--R + +--R 2 +--R 99750%i d cosh(d x + c) - 80675d cosh(d x + c) - 28035%i d +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 6 5 +--R - 350d cosh(d x + c) - 4550%i d cosh(d x + c) +--R + +--R 4 3 +--R 22225d cosh(d x + c) + 54600%i d cosh(d x + c) +--R + +--R 2 +--R - 73500d cosh(d x + c) - 52815%i d cosh(d x + c) + 17500d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 5 +--R - 350%i d cosh(d x + c) + 3500d cosh(d x + c) +--R + +--R 4 3 +--R 14000%i d cosh(d x + c) - 29400d cosh(d x + c) +--R + +--R 2 +--R - 35035%i d cosh(d x + c) + 22925d cosh(d x + c) + 7525%i d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 175d cosh(d x + c) + 1435%i d cosh(d x + c) - 4900d cosh(d x + c) +--R + +--R 3 2 +--R - 9065%i d cosh(d x + c) + 9800d cosh(d x + c) +--R + +--R 5950%i d cosh(d x + c) - 1995d +--R * +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 35%i d cosh(d x + c) - 245d cosh(d x + c) - 735%i d cosh(d x + c) +--R + +--R 3 2 +--R 1225d cosh(d x + c) + 1225%i d cosh(d x + c) - 700d cosh(d x + c) +--R + +--R - 245%i d +--R Type: Expression(Complex(Integer)) +--E 104 + +--S 105 of 510 +d0020:= D(m0020,x) +--R +--R +--R (91) +--R 2 15 +--R (- 30%i cosh(d x + c) + 35%i)sinh(d x + c) +--R + +--R 4 3 2 +--R - 10cosh(d x + c) - 360%i cosh(d x + c) + 525cosh(d x + c) +--R + +--R 420%i cosh(d x + c) +--R * +--R 14 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R - 120cosh(d x + c) - 2090%i cosh(d x + c) + 5880cosh(d x + c) +--R + +--R 2 +--R 6445%i cosh(d x + c) - 1750cosh(d x + c) + 2548%i +--R * +--R 13 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R - 650cosh(d x + c) - 7780%i cosh(d x + c) + 30405cosh(d x + c) +--R + +--R 3 2 +--R 50390%i cosh(d x + c) - 35315cosh(d x + c) + 7490%i cosh(d x + c) +--R + +--R - 17696 +--R * +--R 12 +--R sinh(d x + c) +--R + +--R 7 6 5 +--R - 2080cosh(d x + c) - 20430%i cosh(d x + c) + 95500cosh(d x + c) +--R + +--R 4 3 +--R 216035%i cosh(d x + c) - 247030cosh(d x + c) +--R + +--R 2 +--R - 95018%i cosh(d x + c) - 76482cosh(d x + c) - 61320%i +--R * +--R 11 +--R sinh(d x + c) +--R + +--R 8 7 6 +--R - 4290cosh(d x + c) - 38720%i cosh(d x + c) + 199925cosh(d x + c) +--R + +--R 5 4 +--R 571320%i cosh(d x + c) - 909580cosh(d x + c) +--R + +--R 3 2 +--R - 749210%i cosh(d x + c) + 114153cosh(d x + c) +--R + +--R - 266602%i cosh(d x + c) + 130074 +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 9 8 7 +--R - 5720cosh(d x + c) - 51370%i cosh(d x + c) + 282700cosh(d x + c) +--R + +--R 6 5 +--R 974565%i cosh(d x + c) - 2010540cosh(d x + c) +--R + +--R 4 3 +--R - 2447850%i cosh(d x + c) + 1491790cosh(d x + c) +--R + +--R 2 +--R - 22890%i cosh(d x + c) + 517188cosh(d x + c) + 174202%i +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 10 9 8 +--R - 4290cosh(d x + c) - 41580%i cosh(d x + c) + 245685cosh(d x + c) +--R + +--R 7 6 +--R 1023090%i cosh(d x + c) - 2694475cosh(d x + c) +--R + +--R 5 4 +--R - 4406852%i cosh(d x + c) + 4321335cosh(d x + c) +--R + +--R 3 2 +--R 2007880%i cosh(d x + c) + 235547cosh(d x + c) +--R + +--R 578578%i cosh(d x + c) - 127918 +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 10 9 +--R - 5610%i cosh(d x + c) + 56760cosh(d x + c) +--R + +--R 8 7 +--R 432705%i cosh(d x + c) - 1772540cosh(d x + c) +--R + +--R 6 5 +--R - 4118120%i cosh(d x + c) + 5806024cosh(d x + c) +--R + +--R 4 3 +--R 4807440%i cosh(d x + c) - 1787962cosh(d x + c) +--R + +--R 2 +--R 202762%i cosh(d x + c) - 257880cosh(d x + c) + 7084%i +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 12 11 10 +--R 4290cosh(d x + c) + 35640%i cosh(d x + c) - 179025cosh(d x + c) +--R + +--R 9 8 +--R - 509980%i cosh(d x + c) + 664160cosh(d x + c) +--R + +--R 7 6 +--R - 167048%i cosh(d x + c) + 1989078cosh(d x + c) +--R + +--R 5 4 +--R 3237820%i cosh(d x + c) - 2502618cosh(d x + c) +--R + +--R 3 2 +--R - 837102%i cosh(d x + c) + 179473cosh(d x + c) +--R + +--R 265118%i cosh(d x + c) - 137900 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 13 12 11 +--R 5720cosh(d x + c) + 54450%i cosh(d x + c) - 303600cosh(d x + c) +--R + +--R 10 9 +--R - 1134465%i cosh(d x + c) + 2842210cosh(d x + c) +--R + +--R 8 7 +--R 4873820%i cosh(d x + c) - 5876472cosh(d x + c) +--R + +--R 6 5 +--R - 5074732%i cosh(d x + c) + 3233082cosh(d x + c) +--R + +--R 4 3 +--R 1577842%i cosh(d x + c) - 320320cosh(d x + c) +--R + +--R 2 +--R 530658%i cosh(d x + c) - 578718cosh(d x + c) - 174811%i +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 14 13 12 +--R 4290cosh(d x + c) + 44740%i cosh(d x + c) - 264825cosh(d x + c) +--R + +--R 11 10 +--R - 1092230%i cosh(d x + c) + 3216535cosh(d x + c) +--R + +--R 9 8 +--R 6883590%i cosh(d x + c) - 10987270cosh(d x + c) +--R + +--R 7 6 +--R - 13364640%i cosh(d x + c) + 12505620cosh(d x + c) +--R + +--R 5 4 +--R 8924370%i cosh(d x + c) - 4528885cosh(d x + c) +--R + +--R 3 2 +--R - 1082750%i cosh(d x + c) - 493990cosh(d x + c) +--R + +--R - 511252%i cosh(d x + c) + 123578 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 15 14 13 +--R 2080cosh(d x + c) + 23510%i cosh(d x + c) - 146820cosh(d x + c) +--R + +--R 12 11 +--R - 646855%i cosh(d x + c) + 2102450cosh(d x + c) +--R + +--R 10 9 +--R 5116930%i cosh(d x + c) - 9504470cosh(d x + c) +--R + +--R 8 7 +--R - 13725640%i cosh(d x + c) + 15572570cosh(d x + c) +--R + +--R 6 5 +--R 13854610%i cosh(d x + c) - 9453408cosh(d x + c) +--R + +--R 4 3 +--R - 4575200%i cosh(d x + c) + 1154860cosh(d x + c) +--R + +--R 2 +--R - 210628%i cosh(d x + c) + 261282cosh(d x + c) + 54425%i +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 16 15 14 +--R 650cosh(d x + c) + 7920%i cosh(d x + c) - 52145cosh(d x + c) +--R + +--R 13 12 +--R - 242560%i cosh(d x + c) + 849100cosh(d x + c) +--R + +--R 11 10 +--R 2274770%i cosh(d x + c) - 4732575cosh(d x + c) +--R + +--R 9 8 +--R - 7767650%i cosh(d x + c) + 10177000cosh(d x + c) +--R + +--R 7 6 +--R 10681650%i cosh(d x + c) - 8914185cosh(d x + c) +--R + +--R 5 4 +--R - 5761206%i cosh(d x + c) + 2683390cosh(d x + c) +--R + +--R 3 2 +--R 724468%i cosh(d x + c) + 12103cosh(d x + c) + 75880%i cosh(d x + c) +--R + +--R - 14210 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 17 16 15 +--R 120cosh(d x + c) + 1570%i cosh(d x + c) - 10900cosh(d x + c) +--R + +--R 14 13 +--R - 53265%i cosh(d x + c) + 198240cosh(d x + c) +--R + +--R 12 11 +--R 574250%i cosh(d x + c) - 1311110cosh(d x + c) +--R + +--R 10 9 +--R - 2390890%i cosh(d x + c) + 3523810cosh(d x + c) +--R + +--R 8 7 +--R 4226600%i cosh(d x + c) - 4123512cosh(d x + c) +--R + +--R 6 5 +--R - 3239182%i cosh(d x + c) + 1995050cosh(d x + c) +--R + +--R 4 3 +--R 906607%i cosh(d x + c) - 261898cosh(d x + c) +--R + +--R 2 +--R - 23975%i cosh(d x + c) - 9800cosh(d x + c) - 1715%i +--R * +--R sinh(d x + c) +--R + +--R 18 17 16 +--R 10cosh(d x + c) + 140%i cosh(d x + c) - 1025cosh(d x + c) +--R + +--R 15 14 13 +--R - 5250%i cosh(d x + c) + 20615cosh(d x + c) + 63820%i cosh(d x + c) +--R + +--R 12 11 +--R - 157745cosh(d x + c) - 314840%i cosh(d x + c) +--R + +--R 10 9 8 +--R 513065cosh(d x + c) + 688520%i cosh(d x + c) - 763605cosh(d x + c) +--R + +--R 7 6 +--R - 697802%i cosh(d x + c) + 519732cosh(d x + c) +--R + +--R 5 4 3 +--R 307552%i cosh(d x + c) - 137907cosh(d x + c) - 42140%i cosh(d x + c) +--R + +--R 2 +--R 6860cosh(d x + c) +--R / +--R 18 17 +--R 35sinh(d x + c) + (420cosh(d x + c) + 700%i)sinh(d x + c) +--R + +--R 2 16 +--R (2310cosh(d x + c) + 7910%i cosh(d x + c) - 6650)sinh(d x + c) +--R + +--R 3 2 +--R 7700cosh(d x + c) + 40810%i cosh(d x + c) - 70490cosh(d x + c) +--R + +--R - 39900%i +--R * +--R 15 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 17325cosh(d x + c) + 127050%i cosh(d x + c) - 339675cosh(d x + c) +--R + +--R - 395010%i cosh(d x + c) + 169575 +--R * +--R 14 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 27720cosh(d x + c) + 265650%i cosh(d x + c) - 982800cosh(d x + c) +--R + +--R 2 +--R - 1769040%i cosh(d x + c) + 1560090cosh(d x + c) + 542710%i +--R * +--R 13 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 32340cosh(d x + c) + 392700%i cosh(d x + c) - 1898925cosh(d x + c) +--R + +--R 3 2 +--R - 4730110%i cosh(d x + c) + 6456345cosh(d x + c) +--R + +--R 4612790%i cosh(d x + c) - 1357510 +--R * +--R 12 +--R sinh(d x + c) +--R + +--R 7 6 5 +--R 27720cosh(d x + c) + 420420%i cosh(d x + c) - 2576700cosh(d x + c) +--R + +--R 4 3 +--R - 8390340%i cosh(d x + c) + 15848420cosh(d x + c) +--R + +--R 2 +--R 17522190%i cosh(d x + c) - 10585540cosh(d x + c) - 2718590%i +--R * +--R 11 +--R sinh(d x + c) +--R + +--R 8 7 6 +--R 17325cosh(d x + c) + 328020%i cosh(d x + c) - 2512230cosh(d x + c) +--R + +--R 5 4 +--R - 10371060%i cosh(d x + c) + 25610515cosh(d x + c) +--R + +--R 3 2 +--R 39179910%i cosh(d x + c) - 36613010cosh(d x + c) +--R + +--R - 19284790%i cosh(d x + c) + 4428060 +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 9 8 7 +--R 7700cosh(d x + c) + 184800%i cosh(d x + c) - 1768200cosh(d x + c) +--R + +--R 6 5 +--R - 9125760%i cosh(d x + c) + 28576100cosh(d x + c) +--R + +--R 4 3 +--R 57151850%i cosh(d x + c) - 73877300cosh(d x + c) +--R + +--R 2 +--R - 60145190%i cosh(d x + c) + 28280980cosh(d x + c) + 5923190%i +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 10 9 8 +--R 2310cosh(d x + c) + 73150%i cosh(d x + c) - 888300cosh(d x + c) +--R + +--R 7 6 +--R - 5731740%i cosh(d x + c) + 22447390cosh(d x + c) +--R + +--R 5 4 +--R 56935620%i cosh(d x + c) - 96198550cosh(d x + c) +--R + +--R 3 2 +--R - 108267810%i cosh(d x + c) + 78585570cosh(d x + c) +--R + +--R 33629050%i cosh(d x + c) - 6536565 +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 11 10 9 +--R 420cosh(d x + c) + 19250%i cosh(d x + c) - 309050cosh(d x + c) +--R + +--R 8 7 +--R - 2533860%i cosh(d x + c) + 12414920cosh(d x + c) +--R + +--R 6 5 +--R 39395160%i cosh(d x + c) - 84413210cosh(d x + c) +--R + +--R 4 3 +--R - 124124490%i cosh(d x + c) + 124418980cosh(d x + c) +--R + +--R 2 +--R 82027610%i cosh(d x + c) - 32472370cosh(d x + c) - 5948880%i +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 12 11 10 +--R 35cosh(d x + c) + 3010%i cosh(d x + c) - 70175cosh(d x + c) +--R + +--R 9 8 +--R - 762090%i cosh(d x + c) + 4749745cosh(d x + c) +--R + +--R 7 6 +--R 18867100%i cosh(d x + c) - 50586725cosh(d x + c) +--R + +--R 5 4 +--R - 94313100%i cosh(d x + c) + 123418120cosh(d x + c) +--R + +--R 3 2 +--R 112186830%i cosh(d x + c) - 68234355cosh(d x + c) +--R + +--R - 25347630%i cosh(d x + c) + 4439435 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 12 11 +--R 210%i cosh(d x + c) - 9240cosh(d x + c) +--R + +--R 10 9 +--R - 146160%i cosh(d x + c) + 1208690cosh(d x + c) +--R + +--R 8 7 +--R 6113310%i cosh(d x + c) - 20527920cosh(d x + c) +--R + +--R 6 5 +--R - 47891270%i cosh(d x + c) + 79421790cosh(d x + c) +--R + +--R 4 3 +--R 94134530%i cosh(d x + c) - 78761760cosh(d x + c) +--R + +--R 2 +--R - 44788800%i cosh(d x + c) + 15811250cosh(d x + c) + 2683450%i +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 12 11 +--R - 525cosh(d x + c) - 15750%i cosh(d x + c) +--R + +--R 10 9 +--R 190225cosh(d x + c) + 1278550%i cosh(d x + c) +--R + +--R 8 7 +--R - 5471025cosh(d x + c) - 15990100%i cosh(d x + c) +--R + +--R 6 5 +--R 33176535cosh(d x + c) + 49791700%i cosh(d x + c) +--R + +--R 4 3 +--R - 54226200cosh(d x + c) - 42292250%i cosh(d x + c) +--R + +--R 2 +--R 22749265cosh(d x + c) + 7717570%i cosh(d x + c) - 1286040 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 12 11 +--R - 700%i cosh(d x + c) + 16100cosh(d x + c) +--R + +--R 10 9 +--R 158410%i cosh(d x + c) - 901950cosh(d x + c) +--R + +--R 8 7 +--R - 3361400%i cosh(d x + c) + 8738240cosh(d x + c) +--R + +--R 6 5 +--R 16400440%i cosh(d x + c) - 22588650cosh(d x + c) +--R + +--R 4 3 +--R - 22877750%i cosh(d x + c) + 16813860cosh(d x + c) +--R + +--R 2 +--R 8642830%i cosh(d x + c) - 2845360cosh(d x + c) - 471590%i +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 12 11 10 +--R 525cosh(d x + c) + 9870%i cosh(d x + c) - 82425cosh(d x + c) +--R + +--R 9 8 +--R - 409150%i cosh(d x + c) + 1356810cosh(d x + c) +--R + +--R 7 6 +--R 3190320%i cosh(d x + c) - 5491045cosh(d x + c) +--R + +--R 5 4 +--R - 7021560%i cosh(d x + c) + 6681640cosh(d x + c) +--R + +--R 3 2 +--R 4671170%i cosh(d x + c) - 2315040cosh(d x + c) +--R + +--R - 745850%i cosh(d x + c) + 124495 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 12 11 10 +--R 210%i cosh(d x + c) - 3360cosh(d x + c) - 24500%i cosh(d x + c) +--R + +--R 9 8 7 +--R 108290cosh(d x + c) + 324870%i cosh(d x + c) - 700280cosh(d x + c) +--R + +--R 6 5 +--R - 1117830%i cosh(d x + c) + 1340150cosh(d x + c) +--R + +--R 4 3 +--R 1208830%i cosh(d x + c) - 810460cosh(d x + c) +--R + +--R 2 +--R - 390250%i cosh(d x + c) + 123900cosh(d x + c) + 21070%i +--R * +--R sinh(d x + c) +--R + +--R 12 11 10 +--R - 35cosh(d x + c) - 490%i cosh(d x + c) + 3185cosh(d x + c) +--R + +--R 9 8 7 +--R 12740%i cosh(d x + c) - 35035cosh(d x + c) - 70000%i cosh(d x + c) +--R + +--R 6 5 4 +--R 104615cosh(d x + c) + 118580%i cosh(d x + c) - 102165cosh(d x + c) +--R + +--R 3 2 +--R - 66150%i cosh(d x + c) + 31150cosh(d x + c) + 9800%i cosh(d x + c) +--R + +--R - 1715 +--R Type: Expression(Complex(Integer)) +--E 105 + +--S 106 of 510 +t0021:= (a+b*sinh(c+d*x))^(1/2) +--R +--R +--R +-------------------+ +--R (92) \|b sinh(d x + c) + a +--R Type: Expression(Integer) +--E 106 + +--S 107 of 510 +r0021:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(c+d*x),2*%i*b/(a-%i*b))*_ + (a+b*sinh(c+d*x))^(1/2)/d/((a+b*sinh(c+d*x))/(a-%i*b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 510 +a0021:= integrate(t0021,x) +--R +--R +--R x +--R ++ +--------------------+ +--R (93) | \|b sinh(%N d + c) + a d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 510 +m0021:= a0021-r0021 +--R +--R +--R x +--R ++ +--------------------+ +--R (94) | \|b sinh(%N d + c) + a d%N - r0021 +--R ++ +--R Type: Expression(Integer) +--E 109 + +--S 110 of 510 +d0021:= D(m0021,x) +--R +--R +--R +-------------------+ +--R (95) \|b sinh(d x + c) + a +--R Type: Expression(Integer) +--E 110 + +--S 111 of 510 +t0022:= (a+b*sinh(x))^(3/2) +--R +--R +--R +-------------+ +--R (96) (b sinh(x) + a)\|b sinh(x) + a +--R Type: Expression(Integer) +--E 111 + +--S 112 of 510 +r0022:= -2/3*(-4*a*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))+_ + a*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))+b*cosh(x)*_ + ((a+b*sinh(x))/(a+b))^(1/2)-b*EllipticF(-1/4*%pi+_ + 1/2*x,2*b/(a+b)))*(a+b*sinh(x))^(1/2)/((a+b*sinh(x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 112 + +--S 113 of 510 +a0022:= integrate(t0022,x) +--R +--R +--R x +--R ++ +--------------+ +--R (97) | (b sinh(%N) + a)\|b sinh(%N) + a d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 510 +m0022:= a0022-r0022 +--R +--R +--R x +--R ++ +--------------+ +--R (98) | (b sinh(%N) + a)\|b sinh(%N) + a d%N - r0022 +--R ++ +--R Type: Expression(Integer) +--E 114 + +--S 115 of 510 +d0022:= D(m0022,x) +--R +--R +--R +-------------+ +--R (99) (b sinh(x) + a)\|b sinh(x) + a +--R Type: Expression(Integer) +--E 115 + +--S 116 of 510 +t0023:= 1/(a+b*sinh(x))^(1/2) +--R +--R +--R 1 +--R (100) ---------------- +--R +-------------+ +--R \|b sinh(x) + a +--R Type: Expression(Integer) +--E 116 + +--S 117 of 510 +r0023:= -2*%i*EllipticF(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*_ + ((a+b*sinh(x))/(a-%i*b))^(1/2)/(a+b*sinh(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 510 +a0023:= integrate(t0023,x) +--R +--R +--R x +--R ++ 1 +--R (101) | ----------------- d%N +--R ++ +--------------+ +--R \|b sinh(%N) + a +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 510 +m0023:= a0023-r0023 +--R +--R +--R x +--R ++ 1 +--R (102) | ----------------- d%N - r0023 +--R ++ +--------------+ +--R \|b sinh(%N) + a +--R Type: Expression(Integer) +--E 119 + +--S 120 of 510 +d0023:= D(m0023,x) +--R +--R +--R 1 +--R (103) ---------------- +--R +-------------+ +--R \|b sinh(x) + a +--R Type: Expression(Integer) +--E 120 + +--S 121 of 510 +t0024:= 1/(a+b*sinh(x))^(3/2) +--R +--R +--R 1 +--R (104) ------------------------------- +--R +-------------+ +--R (b sinh(x) + a)\|b sinh(x) + a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 510 +r0024:= -2*b*cosh(x)/(a^2+b^2)/(a+b*sinh(x))^(1/2)-2*%i*EllipticE(-1/4*%pi+_ + 1/2*%i*x,2*%i*b/(a-%i*b))*(a+b*sinh(x))^(1/2)/(a^2+b^2)/_ + ((a+b*sinh(x))/(a-%i*b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 510 +a0024:= integrate(t0024,x) +--R +--R +--R x +--R ++ 1 +--R (105) | --------------------------------- d%N +--R ++ +--------------+ +--R (b sinh(%N) + a)\|b sinh(%N) + a +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 510 +m0024:= a0024-r0024 +--R +--R +--R x +--R ++ 1 +--R (106) | --------------------------------- d%N - r0024 +--R ++ +--------------+ +--R (b sinh(%N) + a)\|b sinh(%N) + a +--R Type: Expression(Integer) +--E 124 + +--S 125 of 510 +d0024:= D(m0024,x) +--R +--R +--R 1 +--R (107) ------------------------------- +--R +-------------+ +--R (b sinh(x) + a)\|b sinh(x) + a +--R Type: Expression(Integer) +--E 125 + +--S 126 of 510 +t0025:= 1/(a+b*sinh(x))^(5/2) +--R +--R +--R 1 +--R (108) ------------------------------------------------ +--R 2 2 2 +-------------+ +--R (b sinh(x) + 2a b sinh(x) + a )\|b sinh(x) + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 510 +r0025:= -2/3*b*cosh(x)/(a^2+b^2)/(a+b*sinh(x))^(3/2)-8/3*a*b*_ + cosh(x)/(a^2+b^2)^2/(a+b*sinh(x))^(1/2)-8/3*%i*a*_ + EllipticE(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*(a+b*sinh(x))^(1/2)/_ + (a^2+b^2)^2/((a+b*sinh(x))/(a-%i*b))^(1/2)+2/3*%i*_ + EllipticF(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*((a+b*sinh(x))/_ + (a-%i*b))^(1/2)/(a^2+b^2)/(a+b*sinh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 510 +a0025:= integrate(t0025,x) +--R +--R +--R x +--R ++ 1 +--R (109) | --------------------------------------------------- d%N +--R ++ 2 2 2 +--------------+ +--R (b sinh(%N) + 2a b sinh(%N) + a )\|b sinh(%N) + a +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 510 +m0025:= a0025-r0025 +--R +--R +--R (110) +--R x +--R ++ 1 +--R | --------------------------------------------------- d%N - r0025 +--R ++ 2 2 2 +--------------+ +--R (b sinh(%N) + 2a b sinh(%N) + a )\|b sinh(%N) + a +--R Type: Expression(Integer) +--E 129 + +--S 130 of 510 +d0025:= D(m0025,x) +--R +--R +--R 1 +--R (111) ------------------------------------------------ +--R 2 2 2 +-------------+ +--R (b sinh(x) + 2a b sinh(x) + a )\|b sinh(x) + a +--R Type: Expression(Integer) +--E 130 + +--S 131 of 510 +t0026:= (a+%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R +----------------------+ +--R (112) \|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 131 + +--S 132 of 510 +r0026:= 2*%i*a*cosh(c+d*x)/d/(a+%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R 2%i a cosh(d x + c) +--R (113) -------------------------- +--R +----------------------+ +--R d\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 132 + +--S 133 of 510 +a0026:= integrate(t0026,x) +--R +--R +--R (114) +--R %i a sinh(d x + c) + %i a cosh(d x + c) - a +--R --------------------------------------------------------------------- +--R +-------------------------------+ +--R | %i a +--R (d sinh(d x + c) + d cosh(d x + c)) |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Union(Expression(Complex(Integer)),...) +--E 133 + +--S 134 of 510 +m0026:= a0026-r0026 +--R +--R +--R (115) +--R +----------------------+ +--R (%i a sinh(d x + c) + %i a cosh(d x + c) - a)\|%i a sinh(d x + c) + a +--R + +--R 2 +--R (- 2%i a cosh(d x + c)sinh(d x + c) - 2%i a cosh(d x + c) ) +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R +-------------------------------+ +--R | %i a +--R (d sinh(d x + c) + d cosh(d x + c)) |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 134 + +--S 135 of 510 +d0026:= D(m0026,x) +--R +--R +--R (116) +--R 2 +--R %i a sinh(d x + c) + (%i a cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R a cosh(d x + c) - %i a +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R + +--R 3 2 +--R - 4%i a sinh(d x + c) + (- 4%i a cosh(d x + c) - 4a)sinh(d x + c) +--R + +--R 2 +--R (2%i a cosh(d x + c) - 4a cosh(d x + c))sinh(d x + c) +--R + +--R 3 +--R 2%i a cosh(d x + c) +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2 +--R 2sinh(d x + c) + (2cosh(d x + c) - 2%i)sinh(d x + c) +--R + +--R - 2%i cosh(d x + c) +--R * +--R +-------------------------------+ +--R | %i a +----------------------+ +--R |------------------------------- \|%i a sinh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Complex(Integer)) +--E 135 + +--S 136 of 510 +t0027:= (a+%i*a*sinh(c+d*x))^(3/2) +--R +--R +--R +----------------------+ +--R (117) (%i a sinh(d x + c) + a)\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 136 + +--S 137 of 510 +r0027:= 2/3*%i*a^2*cosh(c+d*x)*(5+%i*sinh(c+d*x))/(a*(1+%i*sinh(c+d*x)))^(1/2)/d +--R +--R +--R - 2cosh(d x + c)sinh(d x + c) + 10%i cosh(d x + c) 2 +--R (118) -------------------------------------------------- a +--R +----------------------+ +--R 3d\|%i a sinh(d x + c) + a +--R Type: UnivariatePolynomial(a,Expression(Complex(Integer))) +--E 137 + +--S 138 of 510 +a0027:= integrate(t0027,x) +--R +--R +--R (119) +--R 2 3 2 2 2 +--R - a sinh(d x + c) + (- 3a cosh(d x + c) + 9%i a )sinh(d x + c) +--R + +--R 2 2 2 2 +--R (- 3a cosh(d x + c) + 18%i a cosh(d x + c) - 9a )sinh(d x + c) +--R + +--R 2 3 2 2 2 2 +--R - a cosh(d x + c) + 9%i a cosh(d x + c) - 9a cosh(d x + c) + %i a +--R / +--R 2 2 +--R (6d sinh(d x + c) + 12d cosh(d x + c)sinh(d x + c) + 6d cosh(d x + c) ) +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Union(Expression(Complex(Integer)),...) +--E 138 + +--S 139 of 510 +m0027:= a0027-r0027 +--R +--R +--R (120) +--R 3 2 +--R - sinh(d x + c) + (- 3cosh(d x + c) + 9%i)sinh(d x + c) +--R + +--R 2 +--R (- 3cosh(d x + c) + 18%i cosh(d x + c) - 9)sinh(d x + c) +--R + +--R 3 2 +--R - cosh(d x + c) + 9%i cosh(d x + c) - 9cosh(d x + c) + %i +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R + +--R 3 +--R 4cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 +--R (8cosh(d x + c) - 20%i cosh(d x + c))sinh(d x + c) +--R + +--R 3 2 +--R (4cosh(d x + c) - 40%i cosh(d x + c) )sinh(d x + c) +--R + +--R 3 +--R - 20%i cosh(d x + c) +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2 +--R 6d sinh(d x + c) + 12d cosh(d x + c)sinh(d x + c) +--R + +--R 2 +--R 6d cosh(d x + c) +--R * +--R +-------------------------------+ +--R | %i a +----------------------+ +--R |------------------------------- \|%i a sinh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R * +--R 2 +--R a +--R Type: UnivariatePolynomial(a,Expression(Complex(Integer))) +--E 139 + +--S 140 of 510 +d0027:= D(m0027,x) +--R +--R +--R (121) +--R 4 3 +--R - 3sinh(d x + c) + (- 9cosh(d x + c) + 12%i)sinh(d x + c) +--R + +--R 2 2 +--R (- 9cosh(d x + c) + 27%i cosh(d x + c) + 18)sinh(d x + c) +--R + +--R 3 2 +--R - 3cosh(d x + c) + 18%i cosh(d x + c) + 27cosh(d x + c) +--R + +--R - 12%i +--R * +--R sinh(d x + c) +--R + +--R 3 2 +--R 3%i cosh(d x + c) + 9cosh(d x + c) - 9%i cosh(d x + c) - 3 +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R + +--R 5 4 +--R 8sinh(d x + c) + (16cosh(d x + c) - 48%i)sinh(d x + c) +--R + +--R 2 3 +--R (12cosh(d x + c) - 96%i cosh(d x + c) - 40)sinh(d x + c) +--R + +--R 3 2 +--R (8cosh(d x + c) - 36%i cosh(d x + c) - 80cosh(d x + c)) +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R (4cosh(d x + c) + 24%i cosh(d x + c) - 40cosh(d x + c) ) +--R * +--R sinh(d x + c) +--R + +--R 4 +--R 12%i cosh(d x + c) +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 3 2 +--R 12sinh(d x + c) + (24cosh(d x + c) - 12%i)sinh(d x + c) +--R + +--R 2 +--R (12cosh(d x + c) - 24%i cosh(d x + c))sinh(d x + c) +--R + +--R 2 +--R - 12%i cosh(d x + c) +--R * +--R +-------------------------------+ +--R | %i a +----------------------+ +--R |------------------------------- \|%i a sinh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R * +--R 2 +--R a +--R + +--R 3 2 +--R - sinh(d x + c) + (- 3cosh(d x + c) + 9%i)sinh(d x + c) +--R + +--R 2 +--R (- 3cosh(d x + c) + 18%i cosh(d x + c) - 9)sinh(d x + c) +--R + +--R 3 2 +--R - cosh(d x + c) + 9%i cosh(d x + c) - 9cosh(d x + c) + %i +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R + +--R 3 +--R 4cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 +--R (8cosh(d x + c) - 20%i cosh(d x + c))sinh(d x + c) +--R + +--R 3 2 +--R (4cosh(d x + c) - 40%i cosh(d x + c) )sinh(d x + c) +--R + +--R 3 +--R - 20%i cosh(d x + c) +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2 +--R 3d sinh(d x + c) + 6d cosh(d x + c)sinh(d x + c) +--R + +--R 2 +--R 3d cosh(d x + c) +--R * +--R +-------------------------------+ +--R | %i a +----------------------+ +--R |------------------------------- \|%i a sinh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R * +--R a +--R Type: UnivariatePolynomial(a,Expression(Complex(Integer))) +--E 140 + +--S 141 of 510 +t0028:= (a+%i*a*sinh(c+d*x))^(5/2) +--R +--R +--R (122) +--R 2 2 2 2 +----------------------+ +--R (- a sinh(d x + c) + 2%i a sinh(d x + c) + a )\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 141 + +--S 142 of 510 +r0028:= -2/15*%i*cosh(c+d*x)*(-46-14*%i*sinh(c+d*x)+_ + 3*cosh(c+d*x)^2)*a^3/(a*(1+%i*sinh(c+d*x)))^(1/2)/d +--R +--R +--R (123) +--R 28 3 2 3 3 +--R - -- a cosh(d x + c)sinh(d x + c) - - %i a cosh(d x + c) +--R 15 5 +--R + +--R 92 3 +--R -- %i a cosh(d x + c) +--R 15 +--R / +--R +----------------------+ +--R d\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 142 + +--S 143 of 510 +a0028:= integrate(t0028,x) +--R +--R +--R (124) +--R 3 5 3 3 4 +--R - 3%i a sinh(d x + c) + (- 15%i a cosh(d x + c) - 25a )sinh(d x + c) +--R + +--R 3 2 3 3 3 +--R (- 30%i a cosh(d x + c) - 100a cosh(d x + c) + 150%i a )sinh(d x + c) +--R + +--R 3 3 3 2 3 +--R - 30%i a cosh(d x + c) - 150a cosh(d x + c) + 450%i a cosh(d x + c) +--R + +--R 3 +--R - 150a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 4 3 3 +--R - 15%i a cosh(d x + c) - 100a cosh(d x + c) +--R + +--R 3 2 3 3 +--R 450%i a cosh(d x + c) - 300a cosh(d x + c) + 25%i a +--R * +--R sinh(d x + c) +--R + +--R 3 5 3 4 3 3 +--R - 3%i a cosh(d x + c) - 25a cosh(d x + c) + 150%i a cosh(d x + c) +--R + +--R 3 2 3 3 +--R - 150a cosh(d x + c) + 25%i a cosh(d x + c) + 3a +--R / +--R 3 2 +--R 60d sinh(d x + c) + 180d cosh(d x + c)sinh(d x + c) +--R + +--R 2 3 +--R 180d cosh(d x + c) sinh(d x + c) + 60d cosh(d x + c) +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Union(Expression(Complex(Integer)),...) +--E 143 + +--S 144 of 510 +m0028:= a0028-r0028 +--R +--R +--R (125) +--R 1 3 5 +--R - -- %i a sinh(d x + c) +--R 20 +--R + +--R 1 3 5 3 4 +--R (- - %i a cosh(d x + c) - -- a )sinh(d x + c) +--R 4 12 +--R + +--R 1 3 2 5 3 5 3 3 +--R (- - %i a cosh(d x + c) - - a cosh(d x + c) + - %i a )sinh(d x + c) +--R 2 3 2 +--R + +--R 1 3 3 5 3 2 +--R - - %i a cosh(d x + c) - - a cosh(d x + c) +--R 2 2 +--R + +--R 15 3 5 3 +--R -- %i a cosh(d x + c) - - a +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 1 3 4 5 3 3 +--R - - %i a cosh(d x + c) - - a cosh(d x + c) +--R 4 3 +--R + +--R 15 3 2 3 5 3 +--R -- %i a cosh(d x + c) - 5a cosh(d x + c) + -- %i a +--R 2 12 +--R * +--R sinh(d x + c) +--R + +--R 1 3 5 5 3 4 +--R - -- %i a cosh(d x + c) - -- a cosh(d x + c) +--R 20 12 +--R + +--R 5 3 3 5 3 2 5 3 +--R - %i a cosh(d x + c) - - a cosh(d x + c) + -- %i a cosh(d x + c) +--R 2 2 12 +--R + +--R 1 3 +--R -- a +--R 20 +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R + +--R 28 3 4 +--R -- a cosh(d x + c)sinh(d x + c) +--R 15 +--R + +--R 2 3 3 28 3 2 +--R - %i a cosh(d x + c) + -- a cosh(d x + c) +--R 5 5 +--R + +--R 92 3 +--R - -- %i a cosh(d x + c) +--R 15 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 3 4 28 3 3 +--R - %i a cosh(d x + c) + -- a cosh(d x + c) +--R 5 5 +--R + +--R 92 3 2 +--R - -- %i a cosh(d x + c) +--R 5 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 6 3 5 28 3 4 +--R - %i a cosh(d x + c) + -- a cosh(d x + c) +--R 5 15 +--R + +--R 92 3 3 +--R - -- %i a cosh(d x + c) +--R 5 +--R * +--R sinh(d x + c) +--R + +--R 2 3 6 92 3 4 +--R - %i a cosh(d x + c) - -- %i a cosh(d x + c) +--R 5 15 +--R * +--R +-----------------------------+ +--R | 1 +--R | - %i a +--R | 2 +--R |----------------------------- +--R \|sinh(d x + c) + cosh(d x + c) +--R / +--R 3 2 +--R d sinh(d x + c) + 3d cosh(d x + c)sinh(d x + c) +--R + +--R 2 3 +--R 3d cosh(d x + c) sinh(d x + c) + d cosh(d x + c) +--R * +--R +-----------------------------+ +--R | 1 +--R | - %i a +--R | 2 +----------------------+ +--R |----------------------------- \|%i a sinh(d x + c) + a +--R \|sinh(d x + c) + cosh(d x + c) +--R Type: Expression(Complex(Fraction(Integer))) +--E 144 + +--S 145 of 510 +d0028:= D(m0028,x) +--R +--R +--R (126) +--R 1 3 6 +--R - - %i a sinh(d x + c) +--R 8 +--R + +--R 5 3 3 3 5 +--R (- - %i a cosh(d x + c) - - a )sinh(d x + c) +--R 8 4 +--R + +--R 5 3 2 25 3 15 3 +--R (- - %i a cosh(d x + c) - -- a cosh(d x + c) + -- %i a ) +--R 4 8 8 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 5 3 3 3 2 +--R - - %i a cosh(d x + c) - 5a cosh(d x + c) +--R 4 +--R + +--R 25 3 5 3 +--R -- %i a cosh(d x + c) + - a +--R 4 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 5 3 4 15 3 3 +--R - - %i a cosh(d x + c) - -- a cosh(d x + c) +--R 8 4 +--R + +--R 15 3 2 25 3 15 3 +--R -- %i a cosh(d x + c) + -- a cosh(d x + c) - -- %i a +--R 2 4 8 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 1 3 5 5 3 4 +--R - - %i a cosh(d x + c) - - a cosh(d x + c) +--R 8 4 +--R + +--R 15 3 3 3 2 +--R -- %i a cosh(d x + c) + 5a cosh(d x + c) +--R 4 +--R + +--R 25 3 3 3 +--R - -- %i a cosh(d x + c) - - a +--R 8 4 +--R * +--R sinh(d x + c) +--R + +--R 1 3 5 5 3 4 5 3 3 +--R - - a cosh(d x + c) + - %i a cosh(d x + c) + - a cosh(d x + c) +--R 8 8 4 +--R + +--R 5 3 2 5 3 1 3 +--R - - %i a cosh(d x + c) - - a cosh(d x + c) + - %i a +--R 4 8 8 +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R + +--R 28 3 6 +--R -- a sinh(d x + c) +--R 15 +--R + +--R 6 3 2 28 3 3 5 +--R (- %i a cosh(d x + c) + -- a cosh(d x + c) - 8%i a )sinh(d x + c) +--R 5 5 +--R + +--R 18 3 3 116 3 2 +--R -- %i a cosh(d x + c) + --- a cosh(d x + c) +--R 5 15 +--R + +--R 3 92 3 +--R - 24%i a cosh(d x + c) - -- a +--R 15 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 17 3 4 124 3 3 +--R -- %i a cosh(d x + c) + --- a cosh(d x + c) +--R 5 15 +--R + +--R 114 3 2 92 3 +--R - --- %i a cosh(d x + c) - -- a cosh(d x + c) +--R 5 5 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 3 5 32 3 4 +--R - %i a cosh(d x + c) + -- a cosh(d x + c) +--R 5 5 +--R + +--R 22 3 3 92 3 2 +--R - -- %i a cosh(d x + c) - -- a cosh(d x + c) +--R 5 5 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 3 6 32 3 5 +--R - - %i a cosh(d x + c) + -- a cosh(d x + c) +--R 5 15 +--R + +--R 18 3 4 92 3 3 +--R -- %i a cosh(d x + c) - -- a cosh(d x + c) +--R 5 15 +--R * +--R sinh(d x + c) +--R + +--R 1 3 7 6 3 5 +--R - - %i a cosh(d x + c) + - %i a cosh(d x + c) +--R 5 5 +--R * +--R +-----------------------------+ +--R | 1 +--R | - %i a +--R | 2 +--R |----------------------------- +--R \|sinh(d x + c) + cosh(d x + c) +--R / +--R 4 3 +--R sinh(d x + c) + (3cosh(d x + c) - %i)sinh(d x + c) +--R + +--R 2 2 +--R (3cosh(d x + c) - 3%i cosh(d x + c))sinh(d x + c) +--R + +--R 3 2 3 +--R (cosh(d x + c) - 3%i cosh(d x + c) )sinh(d x + c) - %i cosh(d x + c) +--R * +--R +-----------------------------+ +--R | 1 +--R | - %i a +--R | 2 +----------------------+ +--R |----------------------------- \|%i a sinh(d x + c) + a +--R \|sinh(d x + c) + cosh(d x + c) +--R Type: Expression(Complex(Fraction(Integer))) +--E 145 + +--S 146 of 510 +t0029:= 1/(a+%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (127) ------------------------- +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 146 + +--S 147 of 510 +r0029:= 2*atan(sinh(1/2*c+1/4*%i*%pi+1/2*d*x))*_ + cosh(1/2*c+1/4*%i*%pi+1/2*d*x)/d/(a+%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R 2cosh(------------------)atan(sinh(------------------)) +--R 4 4 +--R (128) ------------------------------------------------------- +--R +----------------------+ +--R d\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 147 + +--S 148 of 510 +a0029:= integrate(t0029,x) +--R +--R +--R (129) +--R [ +--R +-+ +--R |2 +--R %i |- +--R \|a +--R * +--R log +--R +-+ +--R |2 +--R (- 2sinh(d x + c) - 2cosh(d x + c)) |- +--R \|a +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R - sinh(d x + c) - cosh(d x + c) - %i +--R / +--R sinh(d x + c) + cosh(d x + c) - %i +--R / +--R d +--R , +--R +-------------------------------+ +--R | %i a +--R +-+ 2%i |------------------------------- +--R |2 \|2sinh(d x + c) + 2cosh(d x + c) +--R 2 |- atan(-------------------------------------) +--R \|a +-+ +--R |2 +--R a |- +--R \|a +--R ------------------------------------------------] +--R d +--R Type: Union(List(Expression(Complex(Integer))),...) +--E 148 + +--S 149 of 510 +m0029a:= a0029.1-r0029 +--R +--R +--R (130) +--R +-+ +--R |2 +----------------------+ +--R %i |- \|%i a sinh(d x + c) + a +--R \|a +--R * +--R log +--R +-+ +--R |2 +--R (- 2sinh(d x + c) - 2cosh(d x + c)) |- +--R \|a +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R - sinh(d x + c) - cosh(d x + c) - %i +--R / +--R sinh(d x + c) + cosh(d x + c) - %i +--R + +--R 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R - 2cosh(------------------)atan(sinh(------------------)) +--R 4 4 +--R / +--R +----------------------+ +--R d\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 149 + +--S 150 of 510 +d0029a:= D(m0029a,x) +--R +--R +--R (131) +--R 2d x + %i %pi + 2c 2 2 +--R (2sinh(------------------) + 2)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (2cosh(d x + c) - 2%i)sinh(------------------) +--R 4 +--R + +--R 2cosh(d x + c) - 2%i +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R - 2%i cosh(d x + c)sinh(------------------) - 2%i cosh(d x + c) +--R 4 +--R * +--R +-+ +-------------------------------+ +--R |2 | %i a +--R |- |------------------------------- +--R \|a \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R (sinh(------------------) + 1)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (cosh(d x + c)sinh(------------------) + cosh(d x + c))sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (- %i cosh(d x + c) + 1)sinh(------------------) - %i cosh(d x + c) +--R 4 +--R + +--R 1 +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (- sinh(------------------) - sinh(------------------)) +--R 4 4 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 +--R (- 2cosh(d x + c) + %i)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c 2 +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R (- 2cosh(d x + c) + %i)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 +--R (- cosh(d x + c) + 2%i cosh(d x + c) - 1) +--R * +--R 2d x + %i %pi + 2c 3 +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R 2cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c 2 +--R sinh(------------------) +--R 4 +--R + +--R 2 +--R (- cosh(d x + c) + 2%i cosh(d x + c) - 1) +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R 2cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2 2d x + %i %pi + 2c 3 +--R (%i cosh(d x + c) + %i)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 3 +--R cosh(------------------)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c 2 +--R sinh(------------------) +--R 4 +--R + +--R 2 2d x + %i %pi + 2c +--R (%i cosh(d x + c) + %i)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 3 +--R cosh(------------------)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c +--R atan(sinh(------------------)) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 3 +--R - cosh(------------------) sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R - 2cosh(------------------) cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R %i cosh(------------------) +--R 4 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R - cosh(------------------) cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R 2%i cosh(------------------) cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R - cosh(------------------) +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R %i cosh(------------------) cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R %i cosh(------------------) +--R 4 +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (- %i a sinh(------------------) - %i a sinh(------------------)) +--R 4 4 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 +--R (- %i a cosh(d x + c) - 2a)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R %i a cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c 2 +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R (- %i a cosh(d x + c) - 2a)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R %i a cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 +--R (- a cosh(d x + c) + %i a)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R %i a cosh(------------------)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R a cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c 2 +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R (- a cosh(d x + c) + %i a)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R %i a cosh(------------------)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R a cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R +-+ +--R |2 2d x + %i %pi + 2c +--R |- atan(sinh(------------------)) +--R \|a 4 +--R + +--R 2d x + %i %pi + 2c 2 2 +--R - %i a cosh(------------------) sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R - %i a cosh(------------------) cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R - 2a cosh(------------------) +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R - a cosh(------------------) cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R %i a cosh(------------------) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 2d x + %i %pi + 2c 2 3 +--R (sinh(------------------) + 1)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (2cosh(d x + c) - %i)sinh(------------------) + 2cosh(d x + c) +--R 4 +--R + +--R - %i +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 +--R (cosh(d x + c) - 2%i cosh(d x + c) + 1) +--R * +--R 2d x + %i %pi + 2c 2 +--R sinh(------------------) +--R 4 +--R + +--R 2 +--R cosh(d x + c) - 2%i cosh(d x + c) + 1 +--R * +--R sinh(d x + c) +--R + +--R 2 2d x + %i %pi + 2c 2 +--R (- %i cosh(d x + c) - %i)sinh(------------------) +--R 4 +--R + +--R 2 +--R - %i cosh(d x + c) - %i +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R (%i a sinh(------------------) + %i a)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (%i a cosh(d x + c) + 2a)sinh(------------------) +--R 4 +--R + +--R %i a cosh(d x + c) + 2a +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R (a cosh(d x + c) - %i a)sinh(------------------) + a cosh(d x + c) +--R 4 +--R + +--R - %i a +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 150 + +--S 151 of 510 +m0029b:= a0029.2-r0029 +--R +--R +--R (132) +--R +-------------------------------+ +--R | %i a +--R +-+ 2%i |------------------------------- +--R |2 +----------------------+ \|2sinh(d x + c) + 2cosh(d x + c) +--R 2 |- \|%i a sinh(d x + c) + a atan(-------------------------------------) +--R \|a +-+ +--R |2 +--R a |- +--R \|a +--R + +--R 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R - 2cosh(------------------)atan(sinh(------------------)) +--R 4 4 +--R / +--R +----------------------+ +--R d\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 151 + +--S 152 of 510 +d0029b:= D(m0029b,x) +--R +--R +--R (133) +--R 2d x + %i %pi + 2c 2 +--R (sinh(------------------) + 1)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R - %i sinh(------------------) - %i +--R 4 +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (- sinh(------------------) - sinh(------------------)) +--R 4 4 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 +--R (- cosh(d x + c) + 2%i)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c 2 +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R (- cosh(d x + c) + 2%i)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 +--R (%i cosh(d x + c) + 1)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R cosh(------------------)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R - %i cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c 2 +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R (%i cosh(d x + c) + 1)sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R cosh(------------------)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R - %i cosh(------------------)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c +--R atan(sinh(------------------)) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 2 +--R - cosh(------------------) sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R - cosh(------------------) cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R 2%i cosh(------------------) +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2d x + %i %pi + 2c 2 +--R %i cosh(------------------) cosh(d x + c) + cosh(------------------) +--R 4 4 +--R * +--R +-------------------------------+ +--R | %i a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2d x + %i %pi + 2c 2 2 +--R (sinh(------------------) + 1)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (cosh(d x + c) - 2%i)sinh(------------------) + cosh(d x + c) +--R 4 +--R + +--R - 2%i +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R (- %i cosh(d x + c) - 1)sinh(------------------) - %i cosh(d x + c) - 1 +--R 4 +--R * +--R +-------------------------------+ +--R | %i a +----------------------+ +--R |------------------------------- \|%i a sinh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Complex(Integer)) +--E 152 + +--S 153 of 510 +t0030:= 1/(a+%i*a*sinh(c+d*x))^(3/2) +--R +--R +--R %i +--R (134) - ------------------------------------------------- +--R +----------------------+ +--R (a sinh(d x + c) - %i a)\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 153 + +--S 154 of 510 +r0030:= 1/2*%i*cosh(c+d*x)/d/(a+%i*a*sinh(c+d*x))^(3/2)+_ + 1/2*atan(sinh(1/2*c+1/4*%i*%pi+1/2*d*x))*_ + cosh(1/2*c+1/4*%i*%pi+1/2*d*x)/a/d/(a+%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R (135) +--R 1 1 1 1 +--R - cosh(- d x + - %i %pi + - c)sinh(d x + c) +--R 2 2 4 2 +--R + +--R 1 1 1 1 +--R - - %i cosh(- d x + - %i %pi + - c) +--R 2 2 4 2 +--R * +--R 1 1 1 +--R atan(sinh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 1 +--R - cosh(d x + c) +--R 2 +--R / +--R +----------------------+ +--R (a d sinh(d x + c) - %i a d)\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 154 + +--S 155 of 510 +a0030:= integrate(t0030,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 155 + +--S 156 of 510 +m0030:= a0030-r0030 +--R +--R +--R (136) +--R +----------------------+ +--R (a a0030 d sinh(d x + c) - %i a a0030 d)\|%i a sinh(d x + c) + a +--R + +--R 1 1 1 1 +--R - - cosh(- d x + - %i %pi + - c)sinh(d x + c) +--R 2 2 4 2 +--R + +--R 1 1 1 1 +--R - %i cosh(- d x + - %i %pi + - c) +--R 2 2 4 2 +--R * +--R 1 1 1 +--R atan(sinh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 1 +--R - - cosh(d x + c) +--R 2 +--R / +--R +----------------------+ +--R (a d sinh(d x + c) - %i a d)\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 156 + +--S 157 of 510 +d0030:= D(m0030,x) +--R +--R +--R (137) +--R 1 1 1 1 3 +--R - - sinh(- d x + - %i %pi + - c) +--R 4 2 4 2 +--R + +--R 1 1 1 1 +--R - - sinh(- d x + - %i %pi + - c) +--R 4 2 4 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 1 1 1 1 3 +--R - %i sinh(- d x + - %i %pi + - c) +--R 2 2 4 2 +--R + +--R 1 1 1 1 +--R - cosh(- d x + - %i %pi + - c)cosh(d x + c) +--R 4 2 4 2 +--R * +--R 1 1 1 2 +--R sinh(- d x + - %i %pi + - c) +--R 2 4 2 +--R + +--R 1 1 1 1 +--R - %i sinh(- d x + - %i %pi + - c) +--R 2 2 4 2 +--R + +--R 1 1 1 1 +--R - cosh(- d x + - %i %pi + - c)cosh(d x + c) +--R 4 2 4 2 +--R * +--R sinh(d x + c) +--R + +--R 1 1 1 1 3 +--R - sinh(- d x + - %i %pi + - c) +--R 4 2 4 2 +--R + +--R - +--R 1 1 1 1 +--R - %i cosh(- d x + - %i %pi + - c)cosh(d x + c) +--R 4 2 4 2 +--R * +--R 1 1 1 2 +--R sinh(- d x + - %i %pi + - c) +--R 2 4 2 +--R + +--R 1 1 1 1 +--R - sinh(- d x + - %i %pi + - c) +--R 4 2 4 2 +--R + +--R 1 1 1 1 +--R - - %i cosh(- d x + - %i %pi + - c)cosh(d x + c) +--R 4 2 4 2 +--R * +--R 1 1 1 +--R atan(sinh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 1 1 1 1 2 1 1 1 1 2 +--R - - sinh(- d x + - %i %pi + - c) - - cosh(- d x + - %i %pi + - c) +--R 2 2 4 2 4 2 4 2 +--R + +--R 1 +--R - - +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 1 1 1 1 2 +--R - %i sinh(- d x + - %i %pi + - c) +--R 2 2 4 2 +--R + +--R 1 1 1 1 2 1 +--R - %i cosh(- d x + - %i %pi + - c) + - %i +--R 2 2 4 2 2 +--R * +--R sinh(d x + c) +--R + +--R 3 2 1 1 1 2 3 2 +--R - cosh(d x + c) sinh(- d x + - %i %pi + - c) + - cosh(d x + c) +--R 4 2 4 2 4 +--R + +--R 1 1 1 1 2 +--R - cosh(- d x + - %i %pi + - c) +--R 4 2 4 2 +--R / +--R 1 1 1 2 2 +--R (a sinh(- d x + - %i %pi + - c) + a)sinh(d x + c) +--R 2 4 2 +--R + +--R 1 1 1 2 +--R (- 2%i a sinh(- d x + - %i %pi + - c) - 2%i a)sinh(d x + c) +--R 2 4 2 +--R + +--R 1 1 1 2 +--R - a sinh(- d x + - %i %pi + - c) - a +--R 2 4 2 +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 157 + +--S 158 of 510 +t0031:= 1/(a+%i*a*sinh(c+d*x))^(5/2) +--R +--R +--R (138) +--R 1 +--R - ---------------------------------------------------------------------- +--R 2 2 2 2 +----------------------+ +--R (a sinh(d x + c) - 2%i a sinh(d x + c) - a )\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 158 + +--S 159 of 510 +r0031:= 1/4*%i*cosh(c+d*x)/d/(a+%i*a*sinh(c+d*x))^(5/2)+_ + 3/16*%i*cosh(c+d*x)/a/d/(a+%i*a*sinh(c+d*x))^(3/2)+_ + 3/16*atan(sinh(1/2*c+1/4*%i*%pi+1/2*d*x))*_ + cosh(1/2*c+1/4*%i*%pi+1/2*d*x)/a^2/d/(a+%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R (139) +--R 3 1 1 1 2 +--R -- cosh(- d x + - %i %pi + - c)sinh(d x + c) +--R 16 2 4 2 +--R + +--R 3 1 1 1 +--R - - %i cosh(- d x + - %i %pi + - c)sinh(d x + c) +--R 8 2 4 2 +--R + +--R 3 1 1 1 +--R - -- cosh(- d x + - %i %pi + - c) +--R 16 2 4 2 +--R * +--R 1 1 1 +--R atan(sinh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 3 7 +--R -- cosh(d x + c)sinh(d x + c) - -- %i cosh(d x + c) +--R 16 16 +--R / +--R 2 2 2 2 +----------------------+ +--R (a d sinh(d x + c) - 2%i a d sinh(d x + c) - a d)\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 159 + +--S 160 of 510 +a0031:= integrate(t0031,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 160 + +--S 161 of 510 +m0031:= a0031-r0031 +--R +--R +--R (140) +--R 2 2 2 2 +--R (a a0031 d sinh(d x + c) - 2%i a a0031 d sinh(d x + c) - a a0031 d) +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R + +--R 3 1 1 1 2 +--R - -- cosh(- d x + - %i %pi + - c)sinh(d x + c) +--R 16 2 4 2 +--R + +--R 3 1 1 1 +--R - %i cosh(- d x + - %i %pi + - c)sinh(d x + c) +--R 8 2 4 2 +--R + +--R 3 1 1 1 +--R -- cosh(- d x + - %i %pi + - c) +--R 16 2 4 2 +--R * +--R 1 1 1 +--R atan(sinh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 3 7 +--R - -- cosh(d x + c)sinh(d x + c) + -- %i cosh(d x + c) +--R 16 16 +--R / +--R 2 2 2 2 +----------------------+ +--R (a d sinh(d x + c) - 2%i a d sinh(d x + c) - a d)\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 161 + +--S 162 of 510 +d0031:= D(m0031,x) +--R +--R +--R (141) +--R 3 1 1 1 3 +--R - -- sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 3 1 1 1 +--R - -- sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 9 1 1 1 3 +--R -- %i sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 3 1 1 1 +--R -- cosh(- d x + - %i %pi + - c)cosh(d x + c) +--R 32 2 4 2 +--R * +--R 1 1 1 2 +--R sinh(- d x + - %i %pi + - c) +--R 2 4 2 +--R + +--R 9 1 1 1 +--R -- %i sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 3 1 1 1 +--R -- cosh(- d x + - %i %pi + - c)cosh(d x + c) +--R 32 2 4 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 9 1 1 1 3 +--R -- sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R - +--R 3 1 1 1 +--R -- %i cosh(- d x + - %i %pi + - c)cosh(d x + c) +--R 16 2 4 2 +--R * +--R 1 1 1 2 +--R sinh(- d x + - %i %pi + - c) +--R 2 4 2 +--R + +--R 9 1 1 1 +--R -- sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 3 1 1 1 +--R - -- %i cosh(- d x + - %i %pi + - c)cosh(d x + c) +--R 16 2 4 2 +--R * +--R sinh(d x + c) +--R + +--R 3 1 1 1 3 +--R - -- %i sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R - +--R 3 1 1 1 +--R -- cosh(- d x + - %i %pi + - c)cosh(d x + c) +--R 32 2 4 2 +--R * +--R 1 1 1 2 +--R sinh(- d x + - %i %pi + - c) +--R 2 4 2 +--R + +--R 3 1 1 1 +--R - -- %i sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 3 1 1 1 +--R - -- cosh(- d x + - %i %pi + - c)cosh(d x + c) +--R 32 2 4 2 +--R * +--R 1 1 1 +--R atan(sinh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 3 1 1 1 2 3 1 1 1 2 +--R - -- sinh(- d x + - %i %pi + - c) - -- cosh(- d x + - %i %pi + - c) +--R 16 2 4 2 32 2 4 2 +--R + +--R 3 +--R - -- +--R 16 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 5 1 1 1 2 +--R - %i sinh(- d x + - %i %pi + - c) +--R 8 2 4 2 +--R + +--R 9 1 1 1 2 5 +--R -- %i cosh(- d x + - %i %pi + - c) + - %i +--R 32 2 4 2 8 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 9 2 7 1 1 1 2 +--R (-- cosh(d x + c) + --)sinh(- d x + - %i %pi + - c) +--R 32 16 2 4 2 +--R + +--R 9 2 9 1 1 1 2 7 +--R -- cosh(d x + c) + -- cosh(- d x + - %i %pi + - c) + -- +--R 32 32 2 4 2 16 +--R * +--R sinh(d x + c) +--R + +--R 29 2 1 1 1 2 +--R - -- %i cosh(d x + c) sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 29 2 3 1 1 1 2 +--R - -- %i cosh(d x + c) - -- %i cosh(- d x + - %i %pi + - c) +--R 32 32 2 4 2 +--R / +--R 2 1 1 1 2 2 3 +--R (a sinh(- d x + - %i %pi + - c) + a )sinh(d x + c) +--R 2 4 2 +--R + +--R 2 1 1 1 2 2 2 +--R (- 3%i a sinh(- d x + - %i %pi + - c) - 3%i a )sinh(d x + c) +--R 2 4 2 +--R + +--R 2 1 1 1 2 2 +--R (- 3a sinh(- d x + - %i %pi + - c) - 3a )sinh(d x + c) +--R 2 4 2 +--R + +--R 2 1 1 1 2 2 +--R %i a sinh(- d x + - %i %pi + - c) + %i a +--R 2 4 2 +--R * +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 162 + +--S 163 of 510 +t0032:= (a-%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R +------------------------+ +--R (142) \|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 163 + +--S 164 of 510 +r0032:= -2*%i*a*cosh(c+d*x)/d/(a-%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R 2%i a cosh(d x + c) +--R (143) - ---------------------------- +--R +------------------------+ +--R d\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 164 + +--S 165 of 510 +a0032:= integrate(t0032,x) +--R +--R +--R (144) +--R - %i a sinh(d x + c) - %i a cosh(d x + c) - a +--R ----------------------------------------------------------------------- +--R +---------------------------------+ +--R | %i a +--R (d sinh(d x + c) + d cosh(d x + c)) |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R Type: Union(Expression(Complex(Integer)),...) +--E 165 + +--S 166 of 510 +m0032:= a0032-r0032 +--R +--R +--R (145) +--R 2 +--R (2%i a cosh(d x + c)sinh(d x + c) + 2%i a cosh(d x + c) ) +--R * +--R +---------------------------------+ +--R | %i a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R +------------------------+ +--R (- %i a sinh(d x + c) - %i a cosh(d x + c) - a)\|- %i a sinh(d x + c) + a +--R / +--R +------------------------+ +--R (d sinh(d x + c) + d cosh(d x + c))\|- %i a sinh(d x + c) + a +--R * +--R +---------------------------------+ +--R | %i a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Complex(Integer)) +--E 166 + +--S 167 of 510 +d0032:= D(m0032,x) +--R +--R +--R (146) +--R 3 2 +--R 4%i a sinh(d x + c) + (4%i a cosh(d x + c) - 4a)sinh(d x + c) +--R + +--R 2 +--R (- 2%i a cosh(d x + c) - 4a cosh(d x + c))sinh(d x + c) +--R + +--R 3 +--R - 2%i a cosh(d x + c) +--R * +--R +---------------------------------+ +--R | %i a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R 2 +--R - %i a sinh(d x + c) + (- %i a cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R a cosh(d x + c) + %i a +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R / +--R 2 +--R 2sinh(d x + c) + (2cosh(d x + c) + 2%i)sinh(d x + c) +--R + +--R 2%i cosh(d x + c) +--R * +--R +---------------------------------+ +--R +------------------------+ | %i a +--R \|- %i a sinh(d x + c) + a |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Complex(Integer)) +--E 167 + +--S 168 of 510 +t0033:= (a-%i*a*sinh(c+d*x))^(3/2) +--R +--R +--R +------------------------+ +--R (147) (- %i a sinh(d x + c) + a)\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 168 + +--S 169 of 510 +r0033:= 2/3*%i*cosh(c+d*x)*a^2*(-5+%i*sinh(c+d*x))/(-a*(-1+%i*sinh(c+d*x)))^(1/2)/d +--R +--R +--R 2 2 10 2 +--R - - a cosh(d x + c)sinh(d x + c) - -- %i a cosh(d x + c) +--R 3 3 +--R (148) -------------------------------------------------------- +--R +------------------------+ +--R d\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 169 + +--S 170 of 510 +a0033:= integrate(t0033,x) +--R +--R +--R (149) +--R 2 3 2 2 2 +--R - a sinh(d x + c) + (- 3a cosh(d x + c) - 9%i a )sinh(d x + c) +--R + +--R 2 2 2 2 +--R (- 3a cosh(d x + c) - 18%i a cosh(d x + c) - 9a )sinh(d x + c) +--R + +--R 2 3 2 2 2 2 +--R - a cosh(d x + c) - 9%i a cosh(d x + c) - 9a cosh(d x + c) - %i a +--R / +--R 2 2 +--R (6d sinh(d x + c) + 12d cosh(d x + c)sinh(d x + c) + 6d cosh(d x + c) ) +--R * +--R +---------------------------------+ +--R | %i a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R Type: Union(Expression(Complex(Integer)),...) +--E 170 + +--S 171 of 510 +m0033:= a0033-r0033 +--R +--R +--R (150) +--R 2 2 3 +--R - a cosh(d x + c)sinh(d x + c) +--R 3 +--R + +--R 4 2 2 10 2 2 +--R (- a cosh(d x + c) + -- %i a cosh(d x + c))sinh(d x + c) +--R 3 3 +--R + +--R 2 2 3 20 2 2 +--R (- a cosh(d x + c) + -- %i a cosh(d x + c) )sinh(d x + c) +--R 3 3 +--R + +--R 10 2 3 +--R -- %i a cosh(d x + c) +--R 3 +--R * +--R +-------------------------------+ +--R | 1 +--R | - %i a +--R | 2 +--R |- ----------------------------- +--R \| sinh(d x + c) + cosh(d x + c) +--R + +--R 1 2 3 1 2 3 2 2 +--R - - a sinh(d x + c) + (- - a cosh(d x + c) - - %i a )sinh(d x + c) +--R 6 2 2 +--R + +--R 1 2 2 2 3 2 +--R (- - a cosh(d x + c) - 3%i a cosh(d x + c) - - a )sinh(d x + c) +--R 2 2 +--R + +--R 1 2 3 3 2 2 3 2 +--R - - a cosh(d x + c) - - %i a cosh(d x + c) - - a cosh(d x + c) +--R 6 2 2 +--R + +--R 1 2 +--R - - %i a +--R 6 +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R / +--R 2 2 +--R (d sinh(d x + c) + 2d cosh(d x + c)sinh(d x + c) + d cosh(d x + c) ) +--R * +--R +-------------------------------+ +--R | 1 +--R | - %i a +--R +------------------------+ | 2 +--R \|- %i a sinh(d x + c) + a |- ----------------------------- +--R \| sinh(d x + c) + cosh(d x + c) +--R Type: Expression(Complex(Fraction(Integer))) +--E 171 + +--S 172 of 510 +d0033:= D(m0033,x) +--R +--R +--R (151) +--R 2 2 5 4 2 2 4 +--R - a sinh(d x + c) + (- a cosh(d x + c) + 4%i a )sinh(d x + c) +--R 3 3 +--R + +--R 2 2 2 10 2 3 +--R (a cosh(d x + c) + 8%i a cosh(d x + c) - -- a )sinh(d x + c) +--R 3 +--R + +--R 2 2 3 2 2 20 2 +--R (- a cosh(d x + c) + 3%i a cosh(d x + c) - -- a cosh(d x + c)) +--R 3 3 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 1 2 4 2 3 10 2 2 +--R (- a cosh(d x + c) - 2%i a cosh(d x + c) - -- a cosh(d x + c) ) +--R 3 3 +--R * +--R sinh(d x + c) +--R + +--R 2 4 +--R - %i a cosh(d x + c) +--R * +--R +-------------------------------+ +--R | 1 +--R | - %i a +--R | 2 +--R |- ----------------------------- +--R \| sinh(d x + c) + cosh(d x + c) +--R + +--R 1 2 4 3 2 2 3 +--R - - a sinh(d x + c) + (- - a cosh(d x + c) - %i a )sinh(d x + c) +--R 4 4 +--R + +--R 3 2 2 9 2 3 2 2 +--R (- - a cosh(d x + c) - - %i a cosh(d x + c) + - a )sinh(d x + c) +--R 4 4 2 +--R + +--R 1 2 3 3 2 2 9 2 +--R - - a cosh(d x + c) - - %i a cosh(d x + c) + - a cosh(d x + c) +--R 4 2 4 +--R + +--R 2 +--R %i a +--R * +--R sinh(d x + c) +--R + +--R 1 2 3 3 2 2 3 2 +--R - - %i a cosh(d x + c) + - a cosh(d x + c) + - %i a cosh(d x + c) +--R 4 4 4 +--R + +--R 1 2 +--R - - a +--R 4 +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R / +--R 3 2 +--R sinh(d x + c) + (2cosh(d x + c) + %i)sinh(d x + c) +--R + +--R 2 2 +--R (cosh(d x + c) + 2%i cosh(d x + c))sinh(d x + c) + %i cosh(d x + c) +--R * +--R +-------------------------------+ +--R | 1 +--R | - %i a +--R +------------------------+ | 2 +--R \|- %i a sinh(d x + c) + a |- ----------------------------- +--R \| sinh(d x + c) + cosh(d x + c) +--R Type: Expression(Complex(Fraction(Integer))) +--E 172 + +--S 173 of 510 +t0034:= (a-%i*a*sinh(c+d*x))^(5/2) +--R +--R +--R (152) +--R 2 2 2 2 +------------------------+ +--R (- a sinh(d x + c) - 2%i a sinh(d x + c) + a )\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 173 + +--S 174 of 510 +r0034:= 2/15*%i*cosh(c+d*x)*(-46+14*%i*sinh(c+d*x)+_ + 3*cosh(c+d*x)^2)*a^3/(-a*(-1+%i*sinh(c+d*x)))^(1/2)/d +--R +--R +--R (153) +--R 28 3 2 3 3 +--R - -- a cosh(d x + c)sinh(d x + c) + - %i a cosh(d x + c) +--R 15 5 +--R + +--R 92 3 +--R - -- %i a cosh(d x + c) +--R 15 +--R / +--R +------------------------+ +--R d\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 174 + +--S 175 of 510 +a0034:= integrate(t0034,x) +--R +--R +--R (154) +--R 3 5 3 3 4 +--R 3%i a sinh(d x + c) + (15%i a cosh(d x + c) - 25a )sinh(d x + c) +--R + +--R 3 2 3 3 3 +--R (30%i a cosh(d x + c) - 100a cosh(d x + c) - 150%i a )sinh(d x + c) +--R + +--R 3 3 3 2 3 +--R 30%i a cosh(d x + c) - 150a cosh(d x + c) - 450%i a cosh(d x + c) +--R + +--R 3 +--R - 150a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 4 3 3 3 2 +--R 15%i a cosh(d x + c) - 100a cosh(d x + c) - 450%i a cosh(d x + c) +--R + +--R 3 3 +--R - 300a cosh(d x + c) - 25%i a +--R * +--R sinh(d x + c) +--R + +--R 3 5 3 4 3 3 +--R 3%i a cosh(d x + c) - 25a cosh(d x + c) - 150%i a cosh(d x + c) +--R + +--R 3 2 3 3 +--R - 150a cosh(d x + c) - 25%i a cosh(d x + c) + 3a +--R / +--R 3 2 +--R 60d sinh(d x + c) + 180d cosh(d x + c)sinh(d x + c) +--R + +--R 2 3 +--R 180d cosh(d x + c) sinh(d x + c) + 60d cosh(d x + c) +--R * +--R +---------------------------------+ +--R | %i a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R Type: Union(Expression(Complex(Integer)),...) +--E 175 + +--S 176 of 510 +m0034:= a0034-r0034 +--R +--R +--R (155) +--R 28 3 4 +--R -- a cosh(d x + c)sinh(d x + c) +--R 15 +--R + +--R 2 3 3 28 3 2 +--R - - %i a cosh(d x + c) + -- a cosh(d x + c) +--R 5 5 +--R + +--R 92 3 +--R -- %i a cosh(d x + c) +--R 15 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 3 4 28 3 3 +--R - - %i a cosh(d x + c) + -- a cosh(d x + c) +--R 5 5 +--R + +--R 92 3 2 +--R -- %i a cosh(d x + c) +--R 5 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 6 3 5 28 3 4 +--R - - %i a cosh(d x + c) + -- a cosh(d x + c) +--R 5 15 +--R + +--R 92 3 3 +--R -- %i a cosh(d x + c) +--R 5 +--R * +--R sinh(d x + c) +--R + +--R 2 3 6 92 3 4 +--R - - %i a cosh(d x + c) + -- %i a cosh(d x + c) +--R 5 15 +--R * +--R +-------------------------------+ +--R | 1 +--R | - %i a +--R | 2 +--R |- ----------------------------- +--R \| sinh(d x + c) + cosh(d x + c) +--R + +--R 1 3 5 1 3 5 3 4 +--R -- %i a sinh(d x + c) + (- %i a cosh(d x + c) - -- a )sinh(d x + c) +--R 20 4 12 +--R + +--R 1 3 2 5 3 5 3 3 +--R (- %i a cosh(d x + c) - - a cosh(d x + c) - - %i a )sinh(d x + c) +--R 2 3 2 +--R + +--R 1 3 3 5 3 2 +--R - %i a cosh(d x + c) - - a cosh(d x + c) +--R 2 2 +--R + +--R 15 3 5 3 +--R - -- %i a cosh(d x + c) - - a +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 1 3 4 5 3 3 +--R - %i a cosh(d x + c) - - a cosh(d x + c) +--R 4 3 +--R + +--R 15 3 2 3 5 3 +--R - -- %i a cosh(d x + c) - 5a cosh(d x + c) - -- %i a +--R 2 12 +--R * +--R sinh(d x + c) +--R + +--R 1 3 5 5 3 4 5 3 3 +--R -- %i a cosh(d x + c) - -- a cosh(d x + c) - - %i a cosh(d x + c) +--R 20 12 2 +--R + +--R 5 3 2 5 3 1 3 +--R - - a cosh(d x + c) - -- %i a cosh(d x + c) + -- a +--R 2 12 20 +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R / +--R 3 2 +--R d sinh(d x + c) + 3d cosh(d x + c)sinh(d x + c) +--R + +--R 2 3 +--R 3d cosh(d x + c) sinh(d x + c) + d cosh(d x + c) +--R * +--R +-------------------------------+ +--R | 1 +--R | - %i a +--R +------------------------+ | 2 +--R \|- %i a sinh(d x + c) + a |- ----------------------------- +--R \| sinh(d x + c) + cosh(d x + c) +--R Type: Expression(Complex(Fraction(Integer))) +--E 176 + +--S 177 of 510 +d0034:= D(m0034,x) +--R +--R +--R (156) +--R 28 3 6 +--R -- a sinh(d x + c) +--R 15 +--R + +--R 6 3 2 28 3 3 5 +--R (- - %i a cosh(d x + c) + -- a cosh(d x + c) + 8%i a )sinh(d x + c) +--R 5 5 +--R + +--R 18 3 3 116 3 2 +--R - -- %i a cosh(d x + c) + --- a cosh(d x + c) +--R 5 15 +--R + +--R 3 92 3 +--R 24%i a cosh(d x + c) - -- a +--R 15 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 17 3 4 124 3 3 +--R - -- %i a cosh(d x + c) + --- a cosh(d x + c) +--R 5 15 +--R + +--R 114 3 2 92 3 +--R --- %i a cosh(d x + c) - -- a cosh(d x + c) +--R 5 5 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 3 5 32 3 4 +--R - - %i a cosh(d x + c) + -- a cosh(d x + c) +--R 5 5 +--R + +--R 22 3 3 92 3 2 +--R -- %i a cosh(d x + c) - -- a cosh(d x + c) +--R 5 5 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 3 6 32 3 5 +--R - %i a cosh(d x + c) + -- a cosh(d x + c) +--R 5 15 +--R + +--R 18 3 4 92 3 3 +--R - -- %i a cosh(d x + c) - -- a cosh(d x + c) +--R 5 15 +--R * +--R sinh(d x + c) +--R + +--R 1 3 7 6 3 5 +--R - %i a cosh(d x + c) - - %i a cosh(d x + c) +--R 5 5 +--R * +--R +-------------------------------+ +--R | 1 +--R | - %i a +--R | 2 +--R |- ----------------------------- +--R \| sinh(d x + c) + cosh(d x + c) +--R + +--R 1 3 6 5 3 3 3 5 +--R - %i a sinh(d x + c) + (- %i a cosh(d x + c) - - a )sinh(d x + c) +--R 8 8 4 +--R + +--R 5 3 2 25 3 15 3 4 +--R (- %i a cosh(d x + c) - -- a cosh(d x + c) - -- %i a )sinh(d x + c) +--R 4 8 8 +--R + +--R 5 3 3 3 2 25 3 +--R - %i a cosh(d x + c) - 5a cosh(d x + c) - -- %i a cosh(d x + c) +--R 4 4 +--R + +--R 5 3 +--R - a +--R 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 5 3 4 15 3 3 +--R - %i a cosh(d x + c) - -- a cosh(d x + c) +--R 8 4 +--R + +--R 15 3 2 25 3 15 3 +--R - -- %i a cosh(d x + c) + -- a cosh(d x + c) + -- %i a +--R 2 4 8 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 1 3 5 5 3 4 +--R - %i a cosh(d x + c) - - a cosh(d x + c) +--R 8 4 +--R + +--R 15 3 3 3 2 +--R - -- %i a cosh(d x + c) + 5a cosh(d x + c) +--R 4 +--R + +--R 25 3 3 3 +--R -- %i a cosh(d x + c) - - a +--R 8 4 +--R * +--R sinh(d x + c) +--R + +--R 1 3 5 5 3 4 5 3 3 +--R - - a cosh(d x + c) - - %i a cosh(d x + c) + - a cosh(d x + c) +--R 8 8 4 +--R + +--R 5 3 2 5 3 1 3 +--R - %i a cosh(d x + c) - - a cosh(d x + c) - - %i a +--R 4 8 8 +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R / +--R 4 3 +--R sinh(d x + c) + (3cosh(d x + c) + %i)sinh(d x + c) +--R + +--R 2 2 +--R (3cosh(d x + c) + 3%i cosh(d x + c))sinh(d x + c) +--R + +--R 3 2 3 +--R (cosh(d x + c) + 3%i cosh(d x + c) )sinh(d x + c) + %i cosh(d x + c) +--R * +--R +-------------------------------+ +--R | 1 +--R | - %i a +--R +------------------------+ | 2 +--R \|- %i a sinh(d x + c) + a |- ----------------------------- +--R \| sinh(d x + c) + cosh(d x + c) +--R Type: Expression(Complex(Fraction(Integer))) +--E 177 + +--S 178 of 510 +t0035:= 1/(a-%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (157) --------------------------- +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 178 + +--S 179 of 510 +r0035:= -2*atanh(cosh(1/2*c+1/4*%i*%pi+1/2*d*x))*_ + sinh(1/2*c+1/4*%i*%pi+1/2*d*x)/d/(a-%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R 2sinh(------------------)atanh(cosh(------------------)) +--R 4 4 +--R (158) - -------------------------------------------------------- +--R +------------------------+ +--R d\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 179 + +--S 180 of 510 +a0035:= integrate(t0035,x) +--R +--R +--R (159) +--R [ +--R +-+ +--R |2 +--R %i |- +--R \|a +--R * +--R log +--R +-+ +--R |2 +--R (2sinh(d x + c) + 2cosh(d x + c)) |- +--R \|a +--R * +--R +---------------------------------+ +--R | %i a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R - sinh(d x + c) - cosh(d x + c) + %i +--R / +--R sinh(d x + c) + cosh(d x + c) + %i +--R / +--R d +--R , +--R +---------------------------------+ +--R | %i a +--R +-+ 2%i |- ------------------------------- +--R |2 \| 2sinh(d x + c) + 2cosh(d x + c) +--R 2 |- atan(---------------------------------------) +--R \|a +-+ +--R |2 +--R a |- +--R \|a +--R - --------------------------------------------------] +--R d +--R Type: Union(List(Expression(Complex(Integer))),...) +--E 180 + +--S 181 of 510 +m0035a:= a0035.1-r0035 +--R +--R +--R (160) +--R +-+ +--R |2 +------------------------+ +--R %i |- \|- %i a sinh(d x + c) + a +--R \|a +--R * +--R log +--R +-+ +--R |2 +--R (2sinh(d x + c) + 2cosh(d x + c)) |- +--R \|a +--R * +--R +---------------------------------+ +--R | %i a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R - sinh(d x + c) - cosh(d x + c) + %i +--R / +--R sinh(d x + c) + cosh(d x + c) + %i +--R + +--R 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R 2sinh(------------------)atanh(cosh(------------------)) +--R 4 4 +--R / +--R +------------------------+ +--R d\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 181 + +--S 182 of 510 +d0035a:= D(m0035a,x) +--R +--R +--R (161) +--R 2d x + %i %pi + 2c 2 2 +--R (- 2cosh(------------------) + 2)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (- 2cosh(------------------) + 2)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R - 2%i cosh(------------------) + 2%i +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R (- 2%i cosh(------------------) + 2%i)cosh(d x + c) +--R 4 +--R * +--R +-+ +--R |2 +------------------------+ +--R |- \|- %i a sinh(d x + c) + a +--R \|a +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (cosh(------------------) - cosh(------------------)) +--R 4 4 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R (- cosh(------------------) + 1)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (2cosh(------------------) - 2cosh(------------------)) +--R 4 4 +--R * +--R cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R %i cosh(------------------) - %i cosh(------------------) +--R 4 4 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R (- 2cosh(------------------) + 2)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (cosh(------------------) - cosh(------------------)) +--R 4 4 +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 +--R 2%i cosh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R - 2%i cosh(------------------) +--R 4 +--R * +--R cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R cosh(------------------) - cosh(------------------) +--R 4 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 3 +--R (- cosh(------------------) + 1)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (- cosh(------------------) + 1)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (%i cosh(------------------) - %i cosh(------------------)) +--R 4 4 +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R %i cosh(------------------) - %i cosh(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c +--R atanh(cosh(------------------)) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 3 +--R - sinh(------------------) sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 2 +--R (- 2cosh(d x + c) - %i)sinh(------------------) sinh(d x + c) +--R 4 +--R + +--R 2 2d x + %i %pi + 2c 2 +--R (- cosh(d x + c) - 2%i cosh(d x + c) - 1)sinh(------------------) +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2 2d x + %i %pi + 2c 2 +--R (- %i cosh(d x + c) - %i)sinh(------------------) +--R 4 +--R * +--R +---------------------------------+ +--R | %i a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R (cosh(------------------) - 1)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (cosh(------------------) - 1)cosh(d x + c)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (%i cosh(------------------) - %i)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R cosh(------------------) - 1 +--R 4 +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (%i a cosh(------------------) - %i a cosh(------------------)) +--R 4 4 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R (- %i a cosh(------------------) + %i a)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 3 +--R %i a cosh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c +--R - %i a cosh(------------------) +--R 4 +--R * +--R cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R - 2a cosh(------------------) + 2a cosh(------------------) +--R 4 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R (- %i a cosh(------------------) + %i a)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (a cosh(------------------) - a)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (- a cosh(------------------) + a cosh(------------------)) +--R 4 4 +--R * +--R cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R - %i a cosh(------------------) + %i a cosh(------------------) +--R 4 4 +--R * +--R +-+ +--R |2 2d x + %i %pi + 2c +--R |- atanh(cosh(------------------)) +--R \|a 4 +--R + +--R 2d x + %i %pi + 2c 2 2 +--R - %i a sinh(------------------) sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (- %i a cosh(d x + c) + 2a)sinh(------------------) sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (a cosh(d x + c) + %i a)sinh(------------------) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 2d x + %i %pi + 2c 2 3 +--R (cosh(------------------) - 1)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (2cosh(------------------) - 2)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R %i cosh(------------------) - %i +--R 4 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R (cosh(------------------) - 1)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (2%i cosh(------------------) - 2%i)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R cosh(------------------) - 1 +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R (%i cosh(------------------) - %i)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R %i cosh(------------------) - %i +--R 4 +--R * +--R +---------------------------------+ +--R +------------------------+ | %i a +--R \|- %i a sinh(d x + c) + a |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R (%i a cosh(------------------) - %i a)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (%i a cosh(------------------) - %i a)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R - 2a cosh(------------------) + 2a +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R (- a cosh(------------------) + a)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R - %i a cosh(------------------) + %i a +--R 4 +--R * +--R +-+ +--R |2 +------------------------+ +--R |- \|- %i a sinh(d x + c) + a +--R \|a +--R Type: Expression(Complex(Integer)) +--E 182 + +--S 183 of 510 +m0035b:= a0035.2-r0035 +--R +--R +--R (162) +--R - +--R +-+ +--R |2 +------------------------+ +--R 2 |- \|- %i a sinh(d x + c) + a +--R \|a +--R * +--R +---------------------------------+ +--R | %i a +--R 2%i |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R atan(---------------------------------------) +--R +-+ +--R |2 +--R a |- +--R \|a +--R + +--R 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R 2sinh(------------------)atanh(cosh(------------------)) +--R 4 4 +--R / +--R +------------------------+ +--R d\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 183 + +--S 184 of 510 +d0035b:= D(m0035b,x) +--R +--R +--R (163) +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (cosh(------------------) - cosh(------------------)) +--R 4 4 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R (- cosh(------------------) + 1)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (cosh(------------------) - cosh(------------------)) +--R 4 4 +--R * +--R cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R 2%i cosh(------------------) - 2%i cosh(------------------) +--R 4 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 2 +--R (- cosh(------------------) + 1)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (- %i cosh(------------------) + %i)cosh(d x + c) +--R 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R (%i cosh(------------------) - %i cosh(------------------)) +--R 4 4 +--R * +--R cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R - cosh(------------------) + cosh(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c +--R atanh(cosh(------------------)) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 2 +--R - sinh(------------------) sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (- cosh(d x + c) - 2%i)sinh(------------------) sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (- %i cosh(d x + c) + 1)sinh(------------------) +--R 4 +--R * +--R +---------------------------------+ +--R | %i a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R (cosh(------------------) - 1)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R %i cosh(------------------) - %i +--R 4 +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R / +--R 2d x + %i %pi + 2c 2 2 +--R (cosh(------------------) - 1)sinh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R (cosh(------------------) - 1)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R 2%i cosh(------------------) - 2%i +--R 4 +--R * +--R sinh(d x + c) +--R + +--R 2d x + %i %pi + 2c 2 +--R (%i cosh(------------------) - %i)cosh(d x + c) +--R 4 +--R + +--R 2d x + %i %pi + 2c 2 +--R - cosh(------------------) + 1 +--R 4 +--R * +--R +---------------------------------+ +--R +------------------------+ | %i a +--R \|- %i a sinh(d x + c) + a |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Complex(Integer)) +--E 184 + +--S 185 of 510 +t0036:= 1/(a-%i*a*sinh(c+d*x))^(3/2) +--R +--R +--R %i +--R (164) --------------------------------------------------- +--R +------------------------+ +--R (a sinh(d x + c) + %i a)\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 185 + +--S 186 of 510 +r0036:= -1/2*%i*cosh(c+d*x)/d/(a-%i*a*sinh(c+d*x))^(3/2)-_ + 1/2*atanh(cosh(1/2*c+1/4*%i*%pi+1/2*d*x))*_ + sinh(1/2*c+1/4*%i*%pi+1/2*d*x)/a/d/(a-%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R (165) +--R 1 1 1 1 +--R - - sinh(- d x + - %i %pi + - c)sinh(d x + c) +--R 2 2 4 2 +--R + +--R 1 1 1 1 +--R - - %i sinh(- d x + - %i %pi + - c) +--R 2 2 4 2 +--R * +--R 1 1 1 +--R atanh(cosh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 1 +--R - cosh(d x + c) +--R 2 +--R / +--R +------------------------+ +--R (a d sinh(d x + c) + %i a d)\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 186 + +--S 187 of 510 +a0036:= integrate(t0036,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 187 + +--S 188 of 510 +m0036:= a0036-r0036 +--R +--R +--R (166) +--R +------------------------+ +--R (a a0036 d sinh(d x + c) + %i a a0036 d)\|- %i a sinh(d x + c) + a +--R + +--R 1 1 1 1 +--R - sinh(- d x + - %i %pi + - c)sinh(d x + c) +--R 2 2 4 2 +--R + +--R 1 1 1 1 +--R - %i sinh(- d x + - %i %pi + - c) +--R 2 2 4 2 +--R * +--R 1 1 1 +--R atanh(cosh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 1 +--R - - cosh(d x + c) +--R 2 +--R / +--R +------------------------+ +--R (a d sinh(d x + c) + %i a d)\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 188 + +--S 189 of 510 +d0036:= D(m0036,x) +--R +--R +--R (167) +--R 1 1 1 1 3 1 1 1 1 +--R (- cosh(- d x + - %i %pi + - c) - - cosh(- d x + - %i %pi + - c)) +--R 4 2 4 2 4 2 4 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 1 1 1 1 2 1 +--R (- - cosh(- d x + - %i %pi + - c) + -)cosh(d x + c) +--R 4 2 4 2 4 +--R * +--R 1 1 1 +--R sinh(- d x + - %i %pi + - c) +--R 2 4 2 +--R + +--R 1 1 1 1 3 +--R - %i cosh(- d x + - %i %pi + - c) +--R 2 2 4 2 +--R + +--R 1 1 1 1 +--R - - %i cosh(- d x + - %i %pi + - c) +--R 2 2 4 2 +--R * +--R sinh(d x + c) +--R + +--R 1 1 1 1 2 1 +--R (- - %i cosh(- d x + - %i %pi + - c) + - %i)cosh(d x + c) +--R 4 2 4 2 4 +--R * +--R 1 1 1 +--R sinh(- d x + - %i %pi + - c) +--R 2 4 2 +--R + +--R 1 1 1 1 3 1 1 1 1 +--R - - cosh(- d x + - %i %pi + - c) + - cosh(- d x + - %i %pi + - c) +--R 4 2 4 2 4 2 4 2 +--R * +--R 1 1 1 +--R atanh(cosh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 1 1 1 1 2 1 1 1 1 2 +--R - - sinh(- d x + - %i %pi + - c) - - cosh(- d x + - %i %pi + - c) +--R 4 2 4 2 2 2 4 2 +--R + +--R 1 +--R - +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 1 1 1 1 2 +--R - - %i sinh(- d x + - %i %pi + - c) +--R 2 2 4 2 +--R + +--R 1 1 1 1 2 1 +--R - - %i cosh(- d x + - %i %pi + - c) + - %i +--R 2 2 4 2 2 +--R * +--R sinh(d x + c) +--R + +--R 1 1 1 1 2 +--R - sinh(- d x + - %i %pi + - c) +--R 4 2 4 2 +--R + +--R 3 1 1 1 2 3 2 +--R (- cosh(- d x + - %i %pi + - c) - -)cosh(d x + c) +--R 4 2 4 2 4 +--R / +--R 1 1 1 2 2 +--R (a cosh(- d x + - %i %pi + - c) - a)sinh(d x + c) +--R 2 4 2 +--R + +--R 1 1 1 2 +--R (2%i a cosh(- d x + - %i %pi + - c) - 2%i a)sinh(d x + c) +--R 2 4 2 +--R + +--R 1 1 1 2 +--R - a cosh(- d x + - %i %pi + - c) + a +--R 2 4 2 +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 189 + +--S 190 of 510 +t0037:= 1/(a-%i*a*sinh(c+d*x))^(5/2) +--R +--R +--R (168) +--R 1 +--R - ------------------------------------------------------------------------ +--R 2 2 2 2 +------------------------+ +--R (a sinh(d x + c) + 2%i a sinh(d x + c) - a )\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 190 + +--S 191 of 510 +r0037:= -1/4*%i*cosh(c+d*x)/d/(a-%i*a*sinh(c+d*x))^(5/2)-_ + 3/16*%i*cosh(c+d*x)/a/d/(a-%i*a*sinh(c+d*x))^(3/2)-_ + 3/16*atanh(cosh(1/2*c+1/4*%i*%pi+1/2*d*x))*_ + sinh(1/2*c+1/4*%i*%pi+1/2*d*x)/a^2/d/(a-%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R (169) +--R 3 1 1 1 2 +--R - -- sinh(- d x + - %i %pi + - c)sinh(d x + c) +--R 16 2 4 2 +--R + +--R 3 1 1 1 +--R - - %i sinh(- d x + - %i %pi + - c)sinh(d x + c) +--R 8 2 4 2 +--R + +--R 3 1 1 1 +--R -- sinh(- d x + - %i %pi + - c) +--R 16 2 4 2 +--R * +--R 1 1 1 +--R atanh(cosh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 3 7 +--R -- cosh(d x + c)sinh(d x + c) + -- %i cosh(d x + c) +--R 16 16 +--R / +--R 2 2 2 2 +--R (a d sinh(d x + c) + 2%i a d sinh(d x + c) - a d) +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 191 + +--S 192 of 510 +a0037:= integrate(t0037,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 192 + +--S 193 of 510 +m0037:= a0037-r0037 +--R +--R +--R (170) +--R 2 2 2 2 +--R (a a0037 d sinh(d x + c) + 2%i a a0037 d sinh(d x + c) - a a0037 d) +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R + +--R 3 1 1 1 2 +--R -- sinh(- d x + - %i %pi + - c)sinh(d x + c) +--R 16 2 4 2 +--R + +--R 3 1 1 1 +--R - %i sinh(- d x + - %i %pi + - c)sinh(d x + c) +--R 8 2 4 2 +--R + +--R 3 1 1 1 +--R - -- sinh(- d x + - %i %pi + - c) +--R 16 2 4 2 +--R * +--R 1 1 1 +--R atanh(cosh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 3 7 +--R - -- cosh(d x + c)sinh(d x + c) - -- %i cosh(d x + c) +--R 16 16 +--R / +--R 2 2 2 2 +--R (a d sinh(d x + c) + 2%i a d sinh(d x + c) - a d) +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 193 + +--S 194 of 510 +d0037:= D(m0037,x) +--R +--R +--R (171) +--R 3 1 1 1 3 +--R -- cosh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 3 1 1 1 +--R - -- cosh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 1 1 1 2 3 +--R (- -- cosh(- d x + - %i %pi + - c) + --)cosh(d x + c) +--R 32 2 4 2 32 +--R * +--R 1 1 1 +--R sinh(- d x + - %i %pi + - c) +--R 2 4 2 +--R + +--R 9 1 1 1 3 +--R -- %i cosh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 9 1 1 1 +--R - -- %i cosh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 1 1 1 2 3 +--R (- -- %i cosh(- d x + - %i %pi + - c) + -- %i)cosh(d x + c) +--R 16 2 4 2 16 +--R * +--R 1 1 1 +--R sinh(- d x + - %i %pi + - c) +--R 2 4 2 +--R + +--R 9 1 1 1 3 +--R - -- cosh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 9 1 1 1 +--R -- cosh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R * +--R sinh(d x + c) +--R + +--R 3 1 1 1 2 3 +--R (-- cosh(- d x + - %i %pi + - c) - --)cosh(d x + c) +--R 32 2 4 2 32 +--R * +--R 1 1 1 +--R sinh(- d x + - %i %pi + - c) +--R 2 4 2 +--R + +--R 3 1 1 1 3 +--R - -- %i cosh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 3 1 1 1 +--R -- %i cosh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R * +--R 1 1 1 +--R atanh(cosh(- d x + - %i %pi + - c)) +--R 2 4 2 +--R + +--R 3 1 1 1 2 3 1 1 1 2 +--R - -- sinh(- d x + - %i %pi + - c) - -- cosh(- d x + - %i %pi + - c) +--R 32 2 4 2 16 2 4 2 +--R + +--R 3 +--R -- +--R 16 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 9 1 1 1 2 +--R - -- %i sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 5 1 1 1 2 5 +--R - - %i cosh(- d x + - %i %pi + - c) + - %i +--R 8 2 4 2 8 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 9 1 1 1 2 +--R -- sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 9 1 1 1 2 9 2 +--R (-- cosh(- d x + - %i %pi + - c) - --)cosh(d x + c) +--R 32 2 4 2 32 +--R + +--R 7 1 1 1 2 7 +--R -- cosh(- d x + - %i %pi + - c) - -- +--R 16 2 4 2 16 +--R * +--R sinh(d x + c) +--R + +--R 3 1 1 1 2 +--R -- %i sinh(- d x + - %i %pi + - c) +--R 32 2 4 2 +--R + +--R 29 1 1 1 2 29 2 +--R (-- %i cosh(- d x + - %i %pi + - c) - -- %i)cosh(d x + c) +--R 32 2 4 2 32 +--R / +--R 2 1 1 1 2 2 3 +--R (a cosh(- d x + - %i %pi + - c) - a )sinh(d x + c) +--R 2 4 2 +--R + +--R 2 1 1 1 2 2 2 +--R (3%i a cosh(- d x + - %i %pi + - c) - 3%i a )sinh(d x + c) +--R 2 4 2 +--R + +--R 2 1 1 1 2 2 +--R (- 3a cosh(- d x + - %i %pi + - c) + 3a )sinh(d x + c) +--R 2 4 2 +--R + +--R 2 1 1 1 2 2 +--R - %i a cosh(- d x + - %i %pi + - c) + %i a +--R 2 4 2 +--R * +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Fraction(Integer))) +--E 194 + +--S 195 of 510 +t0038:= (b*sinh(c+d*x))^(1/2) +--R +--R +--R +---------------+ +--R (172) \|b sinh(d x + c) +--R Type: Expression(Integer) +--E 195 + +--S 196 of 510 +r0038:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(c+d*x),2)*_ + (b*sinh(c+d*x))^(1/2)/d/(%i*sinh(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 196 + +--S 197 of 510 +a0038:= integrate(t0038,x) +--R +--R +--R x +--R ++ +----------------+ +--R (173) | \|b sinh(%N d + c) d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 197 + +--S 198 of 510 +m0038:= a0038-r0038 +--R +--R +--R x +--R ++ +----------------+ +--R (174) | \|b sinh(%N d + c) d%N - r0038 +--R ++ +--R Type: Expression(Integer) +--E 198 + +--S 199 of 510 +d0038:= D(m0038,x) +--R +--R +--R +---------------+ +--R (175) \|b sinh(d x + c) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 510 +t0039:= (b*sinh(c+d*x))^(3/2) +--R +--R +--R +---------------+ +--R (176) b sinh(d x + c)\|b sinh(d x + c) +--R Type: Expression(Integer) +--E 200 + +--S 201 of 510 +r0039:= 2/3*b^2*(%i*EllipticF(-1/4*%pi+1/2*%i*c+1/2*%i*d*x,2)*_ + (%i*sinh(c+d*x))^(1/2)+cosh(c+d*x)*sinh(c+d*x))/(b*sinh(c+d*x))^(1/2)/d +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Expression(Complex(Integer)) +--R Polynomial(Complex(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 201 + +--S 202 of 510 +a0039:= integrate(t0039,x) +--R +--R +--R x +--R ++ +----------------+ +--R (177) | b sinh(%N d + c)\|b sinh(%N d + c) d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 202 + +--S 203 of 510 +m0039:= a0039-r0039 +--R +--R +--R x +--R ++ +----------------+ +--R (178) | b sinh(%N d + c)\|b sinh(%N d + c) d%N - r0039 +--R ++ +--R Type: Expression(Integer) +--E 203 + +--S 204 of 510 +d0039:= D(m0039,x) +--R +--R +--R +---------------+ +--R (179) b sinh(d x + c)\|b sinh(d x + c) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 510 +t0040:= (b*sinh(c+d*x))^(5/2) +--R +--R +--R 2 2 +---------------+ +--R (180) b sinh(d x + c) \|b sinh(d x + c) +--R Type: Expression(Integer) +--E 205 + +--S 206 of 510 +r0040:= 6/5*%i*b^2*EllipticE(-1/4*%pi+1/2*%i*(c+d*x),2)*_ + (b*sinh(c+d*x))^(1/2)/d/(%i*sinh(c+d*x))^(1/2)+_ + 2/5*b*cosh(c+d*x)*(b*sinh(c+d*x))^(3/2)/d +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 206 + +--S 207 of 510 +a0040:= integrate(t0040,x) +--R +--R +--R x +--R ++ 2 2 +----------------+ +--R (181) | b sinh(%N d + c) \|b sinh(%N d + c) d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 207 + +--S 208 of 510 +m0040:= a0040-r0040 +--R +--R +--R x +--R ++ 2 2 +----------------+ +--R (182) | b sinh(%N d + c) \|b sinh(%N d + c) d%N - r0040 +--R ++ +--R Type: Expression(Integer) +--E 208 + +--S 209 of 510 +d0040:= D(m0040,x) +--R +--R +--R 2 2 +---------------+ +--R (183) b sinh(d x + c) \|b sinh(d x + c) +--R Type: Expression(Integer) +--E 209 + +--S 210 of 510 +t0041:= 1/(b*sinh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (184) ------------------ +--R +---------------+ +--R \|b sinh(d x + c) +--R Type: Expression(Integer) +--E 210 + +--S 211 of 510 +r0041:= -2*%i*EllipticF(-1/4*%pi+1/2*%i*(c+d*x),2)*(%i*sinh(c+d*x))^(1/2)/_ + d/(b*sinh(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 510 +a0041:= integrate(t0041,x) +--R +--R +--R x +--R ++ 1 +--R (185) | ------------------- d%N +--R ++ +----------------+ +--R \|b sinh(%N d + c) +--R Type: Union(Expression(Integer),...) +--E 212 + +--S 213 of 510 +m0041:= a0041-r0041 +--R +--R +--R x +--R ++ 1 +--R (186) | ------------------- d%N - r0041 +--R ++ +----------------+ +--R \|b sinh(%N d + c) +--R Type: Expression(Integer) +--E 213 + +--S 214 of 510 +d0041:= D(m0041,x) +--R +--R +--R 1 +--R (187) ------------------ +--R +---------------+ +--R \|b sinh(d x + c) +--R Type: Expression(Integer) +--E 214 + +--S 215 of 510 +t0042:= 1/(b*sinh(c+d*x))^(3/2) +--R +--R +--R 1 +--R (188) --------------------------------- +--R +---------------+ +--R b sinh(d x + c)\|b sinh(d x + c) +--R Type: Expression(Integer) +--E 215 + +--S 216 of 510 +r0042:= -2*cosh(c+d*x)/b/d/(b*sinh(c+d*x))^(1/2)-_ + 2*%i*EllipticE(-1/4*%pi+1/2*%i*(c+d*x),2)*_ + (b*sinh(c+d*x))^(1/2)/b^2/d/(%i*sinh(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 216 + +--S 217 of 510 +a0042:= integrate(t0042,x) +--R +--R +--R x +--R ++ 1 +--R (189) | ----------------------------------- d%N +--R ++ +----------------+ +--R b sinh(%N d + c)\|b sinh(%N d + c) +--R Type: Union(Expression(Integer),...) +--E 217 + +--S 218 of 510 +m0042:= a0042-r0042 +--R +--R +--R x +--R ++ 1 +--R (190) | ----------------------------------- d%N - r0042 +--R ++ +----------------+ +--R b sinh(%N d + c)\|b sinh(%N d + c) +--R Type: Expression(Integer) +--E 218 + +--S 219 of 510 +d0042:= D(m0042,x) +--R +--R +--R 1 +--R (191) --------------------------------- +--R +---------------+ +--R b sinh(d x + c)\|b sinh(d x + c) +--R Type: Expression(Integer) +--E 219 + +--S 220 of 510 +t0043:= 1/(b*sinh(c+d*x))^(5/2) +--R +--R +--R 1 +--R (192) ---------------------------------- +--R 2 2 +---------------+ +--R b sinh(d x + c) \|b sinh(d x + c) +--R Type: Expression(Integer) +--E 220 + +--S 221 of 510 +r0043:= 2/3/b^2*(-cosh(c+d*x)+%i*EllipticF(-1/4*%pi+1/2*%i*c+_ + 1/2*%i*d*x,2)*(%i*sinh(c+d*x))^(1/2)*sinh(c+d*x))/d/_ + sinh(c+d*x)/(b*sinh(c+d*x))^(1/2) +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Expression(Complex(Integer)) +--R Polynomial(Complex(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 221 + +--S 222 of 510 +a0043:= integrate(t0043,x) +--R +--R +--R x +--R ++ 1 +--R (193) | ------------------------------------ d%N +--R ++ 2 2 +----------------+ +--R b sinh(%N d + c) \|b sinh(%N d + c) +--R Type: Union(Expression(Integer),...) +--E 222 + +--S 223 of 510 +m0043:= a0043-r0043 +--R +--R +--R x +--R ++ 1 +--R (194) | ------------------------------------ d%N - r0043 +--R ++ 2 2 +----------------+ +--R b sinh(%N d + c) \|b sinh(%N d + c) +--R Type: Expression(Integer) +--E 223 + +--S 224 of 510 +d0043:= D(m0043,x) +--R +--R +--R 1 +--R (195) ---------------------------------- +--R 2 2 +---------------+ +--R b sinh(d x + c) \|b sinh(d x + c) +--R Type: Expression(Integer) +--E 224 + +--S 225 of 510 +t0044:= x^2/(a+b*sinh(x)) +--R +--R +--R 2 +--R x +--R (196) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 225 + +--S 226 of 510 +r0044:= -(-x^2*log((-a+(a^2+b^2)^(1/2)-b*exp(x))/((a^2+b^2)^(1/2)-a))+_ + x^2*log((a+(a^2+b^2)^(1/2)+b*exp(x))/(a+(a^2+b^2)^(1/2)))-_ + 2*x*polylog(2,b*exp(x)/((a^2+b^2)^(1/2)-a))+2*x*_ + polylog(2,-b*exp(x)/(a+(a^2+b^2)^(1/2)))+2*_ + polylog(3,b*exp(x)/((a^2+b^2)^(1/2)-a))-2*_ + polylog(3,-b*exp(x)/(a+(a^2+b^2)^(1/2))))/(a^2+b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 226 + +--S 227 of 510 +a0044:= integrate(t0044,x) +--R +--R +--R x 2 +--R ++ %N +--R (197) | -------------- d%N +--R ++ b sinh(%N) + a +--R Type: Union(Expression(Integer),...) +--E 227 + +--S 228 of 510 +m0044:= a0044-r0044 +--R +--R +--R x 2 +--R ++ %N +--R (198) | -------------- d%N - r0044 +--R ++ b sinh(%N) + a +--R Type: Expression(Integer) +--E 228 + +--S 229 of 510 +d0044:= D(m0044,x) +--R +--R +--R 2 +--R x +--R (199) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 510 +t0045:= x^3/(a+b*sinh(x)) +--R +--R +--R 3 +--R x +--R (200) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 230 + +--S 231 of 510 +r0045:= (x^3*log((-a+(a^2+b^2)^(1/2)-b*exp(x))/((a^2+b^2)^(1/2)-a))-_ + x^3*log((a+(a^2+b^2)^(1/2)+b*exp(x))/(a+(a^2+b^2)^(1/2)))+_ + 3*x^2*polylog(2,b*exp(x)/((a^2+b^2)^(1/2)-a))-_ + 3*x^2*polylog(2,-b*exp(x)/(a+(a^2+b^2)^(1/2)))-_ + 6*x*polylog(3,b*exp(x)/((a^2+b^2)^(1/2)-a))+_ + 6*x*polylog(3,-b*exp(x)/(a+(a^2+b^2)^(1/2)))+_ + 6*polylog(4,b*exp(x)/((a^2+b^2)^(1/2)-a))-_ + 6*polylog(4,-b*exp(x)/(a+(a^2+b^2)^(1/2))))/(a^2+b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 231 + +--S 232 of 510 +a0045:= integrate(t0045,x) +--R +--R +--R x 3 +--R ++ %N +--R (201) | -------------- d%N +--R ++ b sinh(%N) + a +--R Type: Union(Expression(Integer),...) +--E 232 + +--S 233 of 510 +m0045:= a0045-r0045 +--R +--R +--R x 3 +--R ++ %N +--R (202) | -------------- d%N - r0045 +--R ++ b sinh(%N) + a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 510 +d0045:= D(m0045,x) +--R +--R +--R 3 +--R x +--R (203) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 234 + +--S 235 of 510 +t0046:= x/(1+%i*sinh(x)) +--R +--R +--R %i x +--R (204) - ------------ +--R sinh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 235 + +--S 236 of 510 +r0046:= -2*log(cos(-1/4*%pi+1/2*%i*x))+%i*x*cot(1/4*%pi+1/2*%i*x) +--R +--R +--R 2%i x - %pi 2%i x + %pi +--R (205) - 2log(cos(-----------)) + %i x cot(-----------) +--R 4 4 +--R Type: Expression(Complex(Integer)) +--E 236 + +--S 237 of 510 +a0046:= integrate(t0046,x) +--R +--R +--R (206) +--R (- 2sinh(x) - 2cosh(x) + 2%i)log(sinh(x) + cosh(x) - %i) + 2x sinh(x) +--R + +--R 2x cosh(x) +--R / +--R sinh(x) + cosh(x) - %i +--R Type: Union(Expression(Complex(Integer)),...) +--E 237 + +--S 238 of 510 +m0046:= a0046-r0046 +--R +--R +--R (207) +--R (- 2sinh(x) - 2cosh(x) + 2%i)log(sinh(x) + cosh(x) - %i) +--R + +--R 2%i x - %pi +--R (2sinh(x) + 2cosh(x) - 2%i)log(cos(-----------)) +--R 4 +--R + +--R 2%i x + %pi +--R (- %i x cot(-----------) + 2x)sinh(x) +--R 4 +--R + +--R 2%i x + %pi +--R (- %i x cosh(x) - x)cot(-----------) + 2x cosh(x) +--R 4 +--R / +--R sinh(x) + cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 238 + +--S 239 of 510 +d0046:= D(m0046,x) +--R +--R +--R (208) +--R 2%i x - %pi 2%i x - %pi 2%i x + %pi 2 +--R - 2%i sin(-----------) - x cos(-----------)cot(-----------) +--R 4 4 4 +--R + +--R 2%i x - %pi 2%i x + %pi 2%i x - %pi +--R - 2%i cos(-----------)cot(-----------) - x cos(-----------) +--R 4 4 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 2%i x - %pi +--R (- 4%i cosh(x) - 4)sin(-----------) +--R 4 +--R + +--R 2%i x - %pi 2%i x - %pi +--R (- 2x cos(-----------)cosh(x) + 2%i x cos(-----------)) +--R 4 4 +--R * +--R 2%i x + %pi 2 +--R cot(-----------) +--R 4 +--R + +--R 2%i x - %pi 2%i x - %pi 2%i x + %pi +--R (- 4%i cos(-----------)cosh(x) - 4cos(-----------))cot(-----------) +--R 4 4 4 +--R + +--R 2%i x - %pi 2%i x - %pi +--R - 2x cos(-----------)cosh(x) - 2%i x cos(-----------) +--R 4 4 +--R * +--R sinh(x) +--R + +--R 2 2%i x - %pi +--R (- 2%i cosh(x) - 4cosh(x) + 2%i)sin(-----------) +--R 4 +--R + +--R 2%i x - %pi 2 2%i x - %pi +--R - x cos(-----------)cosh(x) + 2%i x cos(-----------)cosh(x) +--R 4 4 +--R + +--R 2%i x - %pi +--R x cos(-----------) +--R 4 +--R * +--R 2%i x + %pi 2 +--R cot(-----------) +--R 4 +--R + +--R 2%i x - %pi 2 2%i x - %pi +--R - 2%i cos(-----------)cosh(x) - 4cos(-----------)cosh(x) +--R 4 4 +--R + +--R 2%i x - %pi +--R 2%i cos(-----------) +--R 4 +--R * +--R 2%i x + %pi +--R cot(-----------) +--R 4 +--R + +--R 2%i x - %pi 2 2%i x - %pi +--R - x cos(-----------)cosh(x) - 2%i x cos(-----------)cosh(x) +--R 4 4 +--R + +--R 2%i x - %pi +--R x cos(-----------) +--R 4 +--R / +--R 2%i x - %pi 2 +--R 2cos(-----------)sinh(x) +--R 4 +--R + +--R 2%i x - %pi 2%i x - %pi +--R (4cos(-----------)cosh(x) - 4%i cos(-----------))sinh(x) +--R 4 4 +--R + +--R 2%i x - %pi 2 2%i x - %pi 2%i x - %pi +--R 2cos(-----------)cosh(x) - 4%i cos(-----------)cosh(x) - 2cos(-----------) +--R 4 4 4 +--R Type: Expression(Complex(Integer)) +--E 239 + +--S 240 of 510 +t0047:= x/(1-%i*sinh(x)) +--R +--R +--R %i x +--R (209) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 240 + +--S 241 of 510 +r0047:= -2*log(cos(1/4*%pi+1/2*%i*x))-%i*x*tan(1/4*%pi+1/2*%i*x) +--R +--R +--R 2%i x + %pi 2%i x + %pi +--R (210) - 2log(cos(-----------)) - %i x tan(-----------) +--R 4 4 +--R Type: Expression(Complex(Integer)) +--E 241 + +--S 242 of 510 +a0047:= integrate(t0047,x) +--R +--R +--R (211) +--R (- 2sinh(x) - 2cosh(x) - 2%i)log(sinh(x) + cosh(x) + %i) + 2x sinh(x) +--R + +--R 2x cosh(x) +--R / +--R sinh(x) + cosh(x) + %i +--R Type: Union(Expression(Complex(Integer)),...) +--E 242 + +--S 243 of 510 +m0047:= a0047-r0047 +--R +--R +--R (212) +--R (- 2sinh(x) - 2cosh(x) - 2%i)log(sinh(x) + cosh(x) + %i) +--R + +--R 2%i x + %pi +--R (2sinh(x) + 2cosh(x) + 2%i)log(cos(-----------)) +--R 4 +--R + +--R 2%i x + %pi +--R (%i x sinh(x) + %i x cosh(x) - x)tan(-----------) + 2x sinh(x) + 2x cosh(x) +--R 4 +--R / +--R sinh(x) + cosh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 243 + +--S 244 of 510 +d0047:= D(m0047,x) +--R +--R +--R (213) +--R 2%i x + %pi 2 +--R - x cos(-----------)sinh(x) +--R 4 +--R + +--R 2%i x + %pi 2%i x + %pi +--R (- 2x cos(-----------)cosh(x) - 2%i x cos(-----------))sinh(x) +--R 4 4 +--R + +--R 2%i x + %pi 2 2%i x + %pi +--R - x cos(-----------)cosh(x) - 2%i x cos(-----------)cosh(x) +--R 4 4 +--R + +--R 2%i x + %pi +--R x cos(-----------) +--R 4 +--R * +--R 2%i x + %pi 2 +--R tan(-----------) +--R 4 +--R + +--R 2%i x + %pi 2 +--R 2%i cos(-----------)sinh(x) +--R 4 +--R + +--R 2%i x + %pi 2%i x + %pi +--R (4%i cos(-----------)cosh(x) - 4cos(-----------))sinh(x) +--R 4 4 +--R + +--R 2%i x + %pi 2 2%i x + %pi +--R 2%i cos(-----------)cosh(x) - 4cos(-----------)cosh(x) +--R 4 4 +--R + +--R 2%i x + %pi +--R - 2%i cos(-----------) +--R 4 +--R * +--R 2%i x + %pi +--R tan(-----------) +--R 4 +--R + +--R 2%i x + %pi 2%i x + %pi 2 +--R (- 2%i sin(-----------) - x cos(-----------))sinh(x) +--R 4 4 +--R + +--R 2%i x + %pi 2%i x + %pi +--R (- 4%i cosh(x) + 4)sin(-----------) - 2x cos(-----------)cosh(x) +--R 4 4 +--R + +--R 2%i x + %pi +--R 2%i x cos(-----------) +--R 4 +--R * +--R sinh(x) +--R + +--R 2 2%i x + %pi +--R (- 2%i cosh(x) + 4cosh(x) + 2%i)sin(-----------) +--R 4 +--R + +--R 2%i x + %pi 2 2%i x + %pi +--R - x cos(-----------)cosh(x) + 2%i x cos(-----------)cosh(x) +--R 4 4 +--R + +--R 2%i x + %pi +--R x cos(-----------) +--R 4 +--R / +--R 2%i x + %pi 2 +--R 2cos(-----------)sinh(x) +--R 4 +--R + +--R 2%i x + %pi 2%i x + %pi +--R (4cos(-----------)cosh(x) + 4%i cos(-----------))sinh(x) +--R 4 4 +--R + +--R 2%i x + %pi 2 2%i x + %pi 2%i x + %pi +--R 2cos(-----------)cosh(x) + 4%i cos(-----------)cosh(x) - 2cos(-----------) +--R 4 4 4 +--R Type: Expression(Complex(Integer)) +--E 244 + +--S 245 of 510 +t0048:= x/(a+b*sinh(x))^2 +--R +--R +--R x +--R (214) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 245 + +--S 246 of 510 +r0048:= a*x*log(1+b*exp(x)/(a-(a^2+b^2)^(1/2)))/(a^2+b^2)^(3/2)-_ + a*x*log(1+b*exp(x)/(a+(a^2+b^2)^(1/2)))/(a^2+b^2)^(3/2)+_ + log(a+b*sinh(x))/(a^2+b^2)+a*polylog(2,-b*exp(x)/_ + (a-(a^2+b^2)^(1/2)))/(a^2+b^2)^(3/2)-_ + a*polylog(2,-b*exp(x)/(a+(a^2+b^2)^(1/2)))/(a^2+b^2)^(3/2)-_ + b*x*cosh(x)/(a^2+b^2)/(a+b*sinh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 246 + +--S 247 of 510 +a0048:= integrate(t0048,x) +--R +--R +--R x +--R ++ %N +--R (215) | -------------------------------- d%N +--R ++ 2 2 2 +--R b sinh(%N) + 2a b sinh(%N) + a +--R Type: Union(Expression(Integer),...) +--E 247 + +--S 248 of 510 +m0048:= a0048-r0048 +--R +--R +--R x +--R ++ %N +--R (216) | -------------------------------- d%N - r0048 +--R ++ 2 2 2 +--R b sinh(%N) + 2a b sinh(%N) + a +--R Type: Expression(Integer) +--E 248 + +--S 249 of 510 +d0048:= D(m0048,x) +--R +--R +--R x +--R (217) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 249 + +--S 250 of 510 +t0049:= x*(a+%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R +----------------------+ +--R (218) x\|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 250 + +--S 251 of 510 +r0049:= -2*2^(1/2)*(a*cosh(1/2*c+1/4*%i*%pi+1/2*d*x)^2)^(1/2)*_ + sech(1/2*c+1/4*%i*%pi+1/2*d*x)*(2*cosh(1/2*c+1/4*%i*%pi+1/2*d*x)-_ + d*x*sinh(1/2*c+1/4*%i*%pi+1/2*d*x))/d^2 +--R +--R +--R (219) +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R 2d x\|2 sech(------------------)sinh(------------------) +--R 4 4 +--R + +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R - 4\|2 cosh(------------------)sech(------------------) +--R 4 4 +--R * +--R +---------------------------+ +--R | 2d x + %i %pi + 2c 2 +--R |a cosh(------------------) +--R \| 4 +--R / +--R 2 +--R d +--R Type: Expression(Complex(Integer)) +--E 251 + +--S 252 of 510 +a0049:= integrate(t0049,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 252 + +--S 253 of 510 +m0049:= a0049-r0049 +--R +--R +--R (220) +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R - 2d x\|2 sech(------------------)sinh(------------------) +--R 4 4 +--R + +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R 4\|2 cosh(------------------)sech(------------------) +--R 4 4 +--R * +--R +---------------------------+ +--R | 2d x + %i %pi + 2c 2 +--R |a cosh(------------------) +--R \| 4 +--R + +--R 2 +--R a0049 d +--R / +--R 2 +--R d +--R Type: Expression(Complex(Integer)) +--E 253 + +--S 254 of 510 +d0049:= D(m0049,x) +--R +--R +--R (221) +--R +-+ 2d x + %i %pi + 2c 2 2d x + %i %pi + 2c +--R a d x\|2 cosh(------------------) sech(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R +-+ 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R - 2a\|2 cosh(------------------) sech(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c +--R tanh(------------------) +--R 4 +--R + +--R - +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R a d x\|2 cosh(------------------)sech(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c 2 +--R sinh(------------------) +--R 4 +--R + +--R +-+ 2d x + %i %pi + 2c 2 2d x + %i %pi + 2c +--R 2a\|2 cosh(------------------) sech(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R +-+ 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R - a d x\|2 cosh(------------------) sech(------------------) +--R 4 4 +--R / +--R +---------------------------+ +--R | 2d x + %i %pi + 2c 2 +--R d |a cosh(------------------) +--R \| 4 +--R Type: Expression(Complex(Integer)) +--E 254 + +--S 255 of 510 +t0050:= x^2*(a+%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R 2 +----------------------+ +--R (222) x \|%i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 255 + +--S 256 of 510 +r0050:= -2*2^(1/2)*(a*cosh(1/2*c+1/4*%i*%pi+1/2*d*x)^2)^(1/2)*_ + sech(1/2*c+1/4*%i*%pi+1/2*d*x)*(4*d*x*cosh(1/2*c+1/4*%i*%pi+1/2*d*x)-_ + (8+d^2*x^2)*sinh(1/2*c+1/4*%i*%pi+1/2*d*x))/d^3 +--R +--R +--R (223) +--R 2 2 +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R (2d x + 16)\|2 sech(------------------)sinh(------------------) +--R 4 4 +--R + +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R - 8d x\|2 cosh(------------------)sech(------------------) +--R 4 4 +--R * +--R +---------------------------+ +--R | 2d x + %i %pi + 2c 2 +--R |a cosh(------------------) +--R \| 4 +--R / +--R 3 +--R d +--R Type: Expression(Complex(Integer)) +--E 256 + +--S 257 of 510 +a0050:= integrate(t0050,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 257 + +--S 258 of 510 +m0050:= a0050-r0050 +--R +--R +--R (224) +--R 2 2 +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R (- 2d x - 16)\|2 sech(------------------)sinh(------------------) +--R 4 4 +--R + +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R 8d x\|2 cosh(------------------)sech(------------------) +--R 4 4 +--R * +--R +---------------------------+ +--R | 2d x + %i %pi + 2c 2 +--R |a cosh(------------------) +--R \| 4 +--R + +--R 3 +--R a0050 d +--R / +--R 3 +--R d +--R Type: Expression(Complex(Integer)) +--E 258 + +--S 259 of 510 +d0050:= D(m0050,x) +--R +--R +--R (225) +--R 2 2 +-+ 2d x + %i %pi + 2c 2 2d x + %i %pi + 2c +--R (a d x + 8a)\|2 cosh(------------------) sech(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R +-+ 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R - 4a d x\|2 cosh(------------------) sech(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c +--R tanh(------------------) +--R 4 +--R + +--R 2 2 +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R (- a d x - 8a)\|2 cosh(------------------)sech(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c 2 +--R sinh(------------------) +--R 4 +--R + +--R +-+ 2d x + %i %pi + 2c 2 2d x + %i %pi + 2c +--R 4a d x\|2 cosh(------------------) sech(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R + +--R 2 2 +-+ 2d x + %i %pi + 2c 3 2d x + %i %pi + 2c +--R - a d x \|2 cosh(------------------) sech(------------------) +--R 4 4 +--R / +--R +---------------------------+ +--R 2 | 2d x + %i %pi + 2c 2 +--R d |a cosh(------------------) +--R \| 4 +--R Type: Expression(Complex(Integer)) +--E 259 + +--S 260 of 510 +t0051:= (a+%i*a*sinh(c+d*x))^(1/2)/x +--R +--R +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R (226) ------------------------- +--R x +--R Type: Expression(Complex(Integer)) +--E 260 + +--S 261 of 510 +r0051:= 2^(1/2)*(a*cosh(1/2*c+1/4*%i*%pi+1/2*d*x)^2)^(1/2)*_ + sech(1/2*c+1/4*%i*%pi+1/2*d*x)*(cosh(1/2*c+1/4*%i*%pi)*_ + Chi(1/2*d*x)+sinh(1/2*c+1/4*%i*%pi)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 261 + +--S 262 of 510 +a0051:= integrate(t0051,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 262 + +--S 263 of 510 +m0051:= a0051-r0051 +--R +--R +--R (227) - r0051 + a0051 +--R Type: Polynomial(Integer) +--E 263 + +--S 264 of 510 +d0051:= D(m0051,x) +--R +--R +--R (228) 0 +--R Type: Polynomial(Integer) +--E 264 + +--S 265 of 510 +t0052:= (a+%i*a*sinh(c+d*x))^(1/2)/x^2 +--R +--R +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R (229) ------------------------- +--R 2 +--R x +--R Type: Expression(Complex(Integer)) +--E 265 + +--S 266 of 510 +r0052:= -1/2*2^(1/2)*(a*cosh(1/2*c+1/4*%i*%pi+1/2*d*x)^2)^(1/2)*_ + sech(1/2*c+1/4*%i*%pi+1/2*d*x)*(2*cosh(1/2*c+1/4*%i*%pi+1/2*d*x)/x-_ + d*Chi(1/2*d*x)*sinh(1/2*c+1/4*%i*%pi)-_ + d*cosh(1/2*c+1/4*%i*%pi)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 266 + +--S 267 of 510 +a0052:= integrate(t0052,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 267 + +--S 268 of 510 +m0052:= a0052-r0052 +--R +--R +--R (230) - r0052 + a0052 +--R Type: Polynomial(Integer) +--E 268 + +--S 269 of 510 +d0052:= D(m0052,x) +--R +--R +--R (231) 0 +--R Type: Polynomial(Integer) +--E 269 + +--S 270 of 510 +t0053:= (a+%i*a*sinh(c+d*x))^(1/2)/x^3 +--R +--R +--R +----------------------+ +--R \|%i a sinh(d x + c) + a +--R (232) ------------------------- +--R 3 +--R x +--R Type: Expression(Complex(Integer)) +--E 270 + +--S 271 of 510 +r0053:= -1/8*2^(1/2)*(a*cosh(1/2*c+1/4*%i*%pi+1/2*d*x)^2)^(1/2)*_ + sech(1/2*c+1/4*%i*%pi+1/2*d*x)*(4*cosh(1/2*c+1/4*%i*%pi+_ + 1/2*d*x)/x^2-d^2*cosh(1/2*c+1/4*%i*%pi)*Chi(1/2*d*x)+_ + 2*d*sinh(1/2*c+1/4*%i*%pi+1/2*d*x)/x-_ + d^2*sinh(1/2*c+1/4*%i*%pi)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 271 + +--S 272 of 510 +a0053:= integrate(t0053,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 272 + +--S 273 of 510 +m0053:= a0053-r0053 +--R +--R +--R (233) - r0053 + a0053 +--R Type: Polynomial(Integer) +--E 273 + +--S 274 of 510 +d0053:= D(m0053,x) +--R +--R +--R (234) 0 +--R Type: Polynomial(Integer) +--E 274 + +--S 275 of 510 +t0054:= x*(a-%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R +------------------------+ +--R (235) x\|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 275 + +--S 276 of 510 +r0054:= -2*%i*2^(1/2)*(-a*sinh(1/2*c+1/4*%i*%pi+1/2*d*x)^2)^(1/2)*_ + csch(1/2*c+1/4*%i*%pi+1/2*d*x)*(-2*%i*sinh(1/2*c+1/4*%i*%pi+_ + 1/2*d*x)+%i*d*x*cosh(1/2*c+1/4*%i*%pi+1/2*d*x))/d^2 +--R +--R +--R (236) +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R - 4\|2 csch(------------------)sinh(------------------) +--R 4 4 +--R + +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R 2d x\|2 cosh(------------------)csch(------------------) +--R 4 4 +--R * +--R +-----------------------------+ +--R | 2d x + %i %pi + 2c 2 +--R |- a sinh(------------------) +--R \| 4 +--R / +--R 2 +--R d +--R Type: Expression(Complex(Integer)) +--E 276 + +--S 277 of 510 +a0054:= integrate(t0054,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 277 + +--S 278 of 510 +m0054:= a0054-r0054 +--R +--R +--R (237) +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R 4\|2 csch(------------------)sinh(------------------) +--R 4 4 +--R + +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R - 2d x\|2 cosh(------------------)csch(------------------) +--R 4 4 +--R * +--R +-----------------------------+ +--R | 2d x + %i %pi + 2c 2 +--R |- a sinh(------------------) +--R \| 4 +--R + +--R 2 +--R a0054 d +--R / +--R 2 +--R d +--R Type: Expression(Complex(Integer)) +--E 278 + +--S 279 of 510 +d0054:= D(m0054,x) +--R +--R +--R (238) +--R +-+ 2d x + %i %pi + 2c +-+ 2d x + %i %pi + 2c +--R (2a\|2 coth(------------------) + a d x\|2 )csch(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c 3 +--R sinh(------------------) +--R 4 +--R + +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R - a d x\|2 cosh(------------------)coth(------------------) +--R 4 4 +--R + +--R +-+ 2d x + %i %pi + 2c +--R - 2a\|2 cosh(------------------) +--R 4 +--R * +--R 2d x + %i %pi + 2c 2d x + %i %pi + 2c 2 +--R csch(------------------)sinh(------------------) +--R 4 4 +--R + +--R +-+ 2d x + %i %pi + 2c 2 2d x + %i %pi + 2c +--R a d x\|2 cosh(------------------) csch(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R / +--R +-----------------------------+ +--R | 2d x + %i %pi + 2c 2 +--R d |- a sinh(------------------) +--R \| 4 +--R Type: Expression(Complex(Integer)) +--E 279 + +--S 280 of 510 +t0055:= x^2*(a-%i*a*sinh(c+d*x))^(1/2) +--R +--R +--R 2 +------------------------+ +--R (239) x \|- %i a sinh(d x + c) + a +--R Type: Expression(Complex(Integer)) +--E 280 + +--S 281 of 510 +r0055:= -2*%i*2^(1/2)*(-a*sinh(1/2*c+1/4*%i*%pi+1/2*d*x)^2)^(1/2)*_ + csch(1/2*c+1/4*%i*%pi+1/2*d*x)*(-4*%i*d*x*sinh(1/2*c+_ + 1/4*%i*%pi+1/2*d*x)+%i*(8+d^2*x^2)*cosh(1/2*c+1/4*%i*%pi+1/2*d*x))/d^3 +--R +--R +--R (240) +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R - 8d x\|2 csch(------------------)sinh(------------------) +--R 4 4 +--R + +--R 2 2 +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R (2d x + 16)\|2 cosh(------------------)csch(------------------) +--R 4 4 +--R * +--R +-----------------------------+ +--R | 2d x + %i %pi + 2c 2 +--R |- a sinh(------------------) +--R \| 4 +--R / +--R 3 +--R d +--R Type: Expression(Complex(Integer)) +--E 281 + +--S 282 of 510 +a0055:= integrate(t0055,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 282 + +--S 283 of 510 +m0055:= a0055-r0055 +--R +--R +--R (241) +--R +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R 8d x\|2 csch(------------------)sinh(------------------) +--R 4 4 +--R + +--R 2 2 +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R (- 2d x - 16)\|2 cosh(------------------)csch(------------------) +--R 4 4 +--R * +--R +-----------------------------+ +--R | 2d x + %i %pi + 2c 2 +--R |- a sinh(------------------) +--R \| 4 +--R + +--R 3 +--R a0055 d +--R / +--R 3 +--R d +--R Type: Expression(Complex(Integer)) +--E 283 + +--S 284 of 510 +d0055:= D(m0055,x) +--R +--R +--R (242) +--R +-+ 2d x + %i %pi + 2c 2 2 +-+ +--R (4a d x\|2 coth(------------------) + a d x \|2 ) +--R 4 +--R * +--R 2d x + %i %pi + 2c 2d x + %i %pi + 2c 3 +--R csch(------------------)sinh(------------------) +--R 4 4 +--R + +--R 2 2 +-+ 2d x + %i %pi + 2c 2d x + %i %pi + 2c +--R (- a d x - 8a)\|2 cosh(------------------)coth(------------------) +--R 4 4 +--R + +--R +-+ 2d x + %i %pi + 2c +--R - 4a d x\|2 cosh(------------------) +--R 4 +--R * +--R 2d x + %i %pi + 2c 2d x + %i %pi + 2c 2 +--R csch(------------------)sinh(------------------) +--R 4 4 +--R + +--R 2 2 +-+ 2d x + %i %pi + 2c 2 2d x + %i %pi + 2c +--R (a d x + 8a)\|2 cosh(------------------) csch(------------------) +--R 4 4 +--R * +--R 2d x + %i %pi + 2c +--R sinh(------------------) +--R 4 +--R / +--R +-----------------------------+ +--R 2 | 2d x + %i %pi + 2c 2 +--R d |- a sinh(------------------) +--R \| 4 +--R Type: Expression(Complex(Integer)) +--E 284 + +--S 285 of 510 +t0056:= (a-%i*a*sinh(c+d*x))^(1/2)/x +--R +--R +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R (243) --------------------------- +--R x +--R Type: Expression(Complex(Integer)) +--E 285 + +--S 286 of 510 +r0056:= %i*2^(1/2)*(-a*sinh(1/2*c+1/4*%i*%pi+1/2*d*x)^2)^(1/2)*_ + csch(1/2*c+1/4*%i*%pi+1/2*d*x)*(-%i*sinh(1/2*c+1/4*%i*%pi)*_ + Chi(1/2*d*x)-%i*cosh(1/2*c+1/4*%i*%pi)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 286 + +--S 287 of 510 +a0056:= integrate(t0056,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 287 + +--S 288 of 510 +m0056:= a0056-r0056 +--R +--R +--R (244) - r0056 + a0056 +--R Type: Polynomial(Integer) +--E 288 + +--S 289 of 510 +d0056:= D(m0056,x) +--R +--R +--R (245) 0 +--R Type: Polynomial(Integer) +--E 289 + +--S 290 of 510 +t0057:= (a-%i*a*sinh(c+d*x))^(1/2)/x^2 +--R +--R +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R (246) --------------------------- +--R 2 +--R x +--R Type: Expression(Complex(Integer)) +--E 290 + +--S 291 of 510 +r0057:= -1/2*%i*2^(1/2)*(-a*sinh(1/2*c+1/4*%i*%pi+1/2*d*x)^2)^(1/2)*_ + csch(1/2*c+1/4*%i*%pi+1/2*d*x)*(-2*%i*sinh(1/2*c+1/4*%i*%pi+_ + 1/2*d*x)/x+%i*d*Chi(1/2*d*x)*cosh(1/2*c+1/4*%i*%pi)+_ + %i*d*sinh(1/2*c+1/4*%i*%pi)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 291 + +--S 292 of 510 +a0057:= integrate(t0057,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 292 + +--S 293 of 510 +m0057:= a0057-r0057 +--R +--R +--R (247) - r0057 + a0057 +--R Type: Polynomial(Integer) +--E 293 + +--S 294 of 510 +d0057:= D(m0057,x) +--R +--R +--R (248) 0 +--R Type: Polynomial(Integer) +--E 294 + +--S 295 of 510 +t0058:= (a-%i*a*sinh(c+d*x))^(1/2)/x^3 +--R +--R +--R +------------------------+ +--R \|- %i a sinh(d x + c) + a +--R (249) --------------------------- +--R 3 +--R x +--R Type: Expression(Complex(Integer)) +--E 295 + +--S 296 of 510 +r0058:= -1/8*%i*2^(1/2)*(-a*sinh(1/2*c+1/4*%i*%pi+1/2*d*x)^2)^(1/2)*_ + csch(1/2*c+1/4*%i*%pi+1/2*d*x)*(-4*%i*sinh(1/2*c+1/4*%i*%pi+_ + 1/2*d*x)/x^2+%i*d^2*sinh(1/2*c+1/4*%i*%pi)*Chi(1/2*d*x)-_ + 2*%i*d*cosh(1/2*c+1/4*%i*%pi+1/2*d*x)/x+_ + %i*d^2*cosh(1/2*c+1/4*%i*%pi)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 296 + +--S 297 of 510 +a0058:= integrate(t0058,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 297 + +--S 298 of 510 +m0058:= a0058-r0058 +--R +--R +--R (250) - r0058 + a0058 +--R Type: Polynomial(Integer) +--E 298 + +--S 299 of 510 +d0058:= D(m0058,x) +--R +--R +--R (251) 0 +--R Type: Polynomial(Integer) +--E 299 + +--S 300 of 510 +t0059:= 1/(a+b*sinh(x)^2) +--R +--R +--R 1 +--R (252) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 300 + +--S 301 of 510 +r0059:= atan((-a+b)^(1/2)*tanh(x)/a^(1/2))/a^(1/2)/(-a+b)^(1/2) +--R +--R +--R +-----+ +--R tanh(x)\|b - a +--R atan(---------------) +--R +-+ +--R \|a +--R (253) --------------------- +--R +-+ +-----+ +--R \|a \|b - a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 510 +a0059:= integrate(t0059,x) +--R +--R +--R (254) +--R [ +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R * +--R +----------+ +--R | 2 +--R \|- a b + a +--R + +--R 2 2 2 2 2 +--R (4a b - 4a b)sinh(x) + (8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (4a b - 4a b)cosh(x) - 4a b + 12a b - 8a +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R / +--R +----------+ +--R | 2 +--R 2\|- a b + a +--R , +--R +--------+ +--R 2 2 | 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a)\|a b - a +--R atan(-----------------------------------------------------------------) +--R 2 +--R 2a b - 2a +--R -----------------------------------------------------------------------] +--R +--------+ +--R | 2 +--R \|a b - a +--R Type: Union(List(Expression(Integer)),...) +--E 302 + +--S 303 of 510 +m0059a:= a0059.1-r0059 +--R +--R +--R (255) +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R * +--R +----------+ +--R | 2 +--R \|- a b + a +--R + +--R 2 2 2 2 2 +--R (4a b - 4a b)sinh(x) + (8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (4a b - 4a b)cosh(x) - 4a b + 12a b - 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R +----------+ +-----+ +--R | 2 tanh(x)\|b - a +--R - 2\|- a b + a atan(---------------) +--R +-+ +--R \|a +--R / +--R +----------+ +--R | 2 +-+ +-----+ +--R 2\|- a b + a \|a \|b - a +--R Type: Expression(Integer) +--E 303 + +--S 304 of 510 +d0059a:= D(m0059a,x) +--R +--R +--R (256) +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (- 4b cosh(x) + 4b cosh(x))sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 2 4 2 3 +--R (b - a b)sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a b)cosh(x) - 2b + 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b - 4a b)cosh(x) + (- 4b + 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b - a b)cosh(x) + (- 2b + 6a b - 4a )cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) - 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (- 4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (- 2a b + 4a )cosh(x) + a b +--R Type: Expression(Integer) +--E 304 + +--S 305 of 510 +m0059b:= a0059.2-r0059 +--R +--R +--R (257) +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R +--------+ +--R 2 2 | 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a)\|a b - a +--R atan(-----------------------------------------------------------------) +--R 2 +--R 2a b - 2a +--R + +--R +--------+ +-----+ +--R | 2 tanh(x)\|b - a +--R - \|a b - a atan(---------------) +--R +-+ +--R \|a +--R / +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|a b - a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 510 +d0059b:= D(m0059b,x) +--R +--R +--R (258) +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (- 4b cosh(x) + 4b cosh(x))sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 2 4 2 3 +--R (b - a b)sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a b)cosh(x) - 2b + 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b - 4a b)cosh(x) + (- 4b + 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b - a b)cosh(x) + (- 2b + 6a b - 4a )cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) - 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (- 4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (- 2a b + 4a )cosh(x) + a b +--R Type: Expression(Integer) +--E 306 + +--S 307 of 510 +t0060:= 1/(a+b*sinh(x)^2)^2 +--R +--R +--R 1 +--R (259) ------------------------------- +--R 2 4 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 510 +r0060:= -1/2*(2*a-b)*atan((-a+b)^(1/2)*tanh(x)/a^(1/2))/a^(3/2)/(-a+b)^(3/2)-_ + 1/2*b*tanh(x)/a/(a-b)/(a-(a-b)*tanh(x)^2) +--R +--R +--R (260) +--R +-----+ +--R 2 2 2 2 tanh(x)\|b - a +--R ((b - 3a b + 2a )tanh(x) + a b - 2a )atan(---------------) +--R +-+ +--R \|a +--R + +--R +-+ +-----+ +--R b tanh(x)\|a \|b - a +--R / +--R 2 2 3 2 2 3 +-+ +-----+ +--R ((2a b - 4a b + 2a )tanh(x) + 2a b - 2a )\|a \|b - a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 510 +a0060:= integrate(t0060,x) +--R +--R +--R (261) +--R [ +--R 2 4 2 3 +--R (b - 2a b)sinh(x) + (4b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 12a b)cosh(x) - 2b + 8a b - 8a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b - 8a b)cosh(x) + (- 4b + 16a b - 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b - 2a b)cosh(x) + (- 2b + 8a b - 8a )cosh(x) + b - 2a b +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R * +--R +----------+ +--R | 2 +--R \|- a b + a +--R + +--R 2 2 2 2 2 +--R (4a b - 4a b)sinh(x) + (8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (4a b - 4a b)cosh(x) - 4a b + 12a b - 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 2 +--R (4b - 8a)sinh(x) + (8b - 16a)cosh(x)sinh(x) + (4b - 8a)cosh(x) +--R + +--R - 4b +--R * +--R +----------+ +--R | 2 +--R \|- a b + a +--R / +--R 2 2 4 2 2 3 +--R (4a b - 4a b)sinh(x) + (16a b - 16a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((24a b - 24a b)cosh(x) - 8a b + 24a b - 16a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((16a b - 16a b)cosh(x) + (- 16a b + 48a b - 32a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 +--R (4a b - 4a b)cosh(x) + (- 8a b + 24a b - 16a )cosh(x) + 4a b +--R + +--R 2 +--R - 4a b +--R * +--R +----------+ +--R | 2 +--R \|- a b + a +--R , +--R +--R 2 4 2 3 +--R (b - 2a b)sinh(x) + (4b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 12a b)cosh(x) - 2b + 8a b - 8a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b - 8a b)cosh(x) + (- 4b + 16a b - 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b - 2a b)cosh(x) + (- 2b + 8a b - 8a )cosh(x) + b - 2a b +--R * +--R +--------+ +--R 2 2 | 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a)\|a b - a +--R atan(-----------------------------------------------------------------) +--R 2 +--R 2a b - 2a +--R + +--R 2 2 +--R (2b - 4a)sinh(x) + (4b - 8a)cosh(x)sinh(x) + (2b - 4a)cosh(x) +--R + +--R - 2b +--R * +--R +--------+ +--R | 2 +--R \|a b - a +--R / +--R 2 2 4 2 2 3 +--R (2a b - 2a b)sinh(x) + (8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((12a b - 12a b)cosh(x) - 4a b + 12a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((8a b - 8a b)cosh(x) + (- 8a b + 24a b - 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 2 +--R (2a b - 2a b)cosh(x) + (- 4a b + 12a b - 8a )cosh(x) + 2a b - 2a b +--R * +--R +--------+ +--R | 2 +--R \|a b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 309 + +--S 310 of 510 +m0060a:= a0060.1-r0060 +--R +--R +--R (262) +--R 3 2 2 4 +--R (b - 3a b + 2a b)sinh(x) +--R + +--R 3 2 2 3 +--R (4b - 12a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 +--R ((6b - 18a b + 12a b)cosh(x) - 2b + 10a b - 16a b + 8a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (4b - 12a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 20a b - 32a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 4 +--R (b - 3a b + 2a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 2b + 10a b - 16a b + 8a )cosh(x) + b - 3a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (a b - 2a b)sinh(x) + (4a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((6a b - 12a b)cosh(x) - 2a b + 8a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((4a b - 8a b)cosh(x) + (- 4a b + 16a b - 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 2 +--R (a b - 2a b)cosh(x) + (- 2a b + 8a b - 8a )cosh(x) + a b - 2a b +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R * +--R +----------+ +--R | 2 +--R \|- a b + a +--R + +--R 2 2 2 2 2 +--R (4a b - 4a b)sinh(x) + (8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (4a b - 4a b)cosh(x) - 4a b + 12a b - 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 3 2 2 4 +--R (- 2b + 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 +--R (- 8b + 24a b - 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 12b + 36a b - 24a b)cosh(x) + 4b - 20a b + 32a b +--R + +--R 3 +--R - 16a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 8b + 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 3 +--R (8b - 40a b + 64a b - 32a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 2b + 6a b - 4a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (4b - 20a b + 32a b - 16a )cosh(x) - 2b + 6a b - 4a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b + 4a b)sinh(x) + (- 8a b + 16a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((- 12a b + 24a b)cosh(x) + 4a b - 16a b + 16a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 8a b + 16a b)cosh(x) + (8a b - 32a b + 32a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 +--R (- 2a b + 4a b)cosh(x) + (4a b - 16a b + 16a )cosh(x) - 2a b +--R + +--R 2 +--R 4a b +--R * +--R +----------+ +-----+ +--R | 2 tanh(x)\|b - a +--R \|- a b + a atan(---------------) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 +--R (4b - 12a b + 8a )sinh(x) + (8b - 24a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4b - 12a b + 8a )cosh(x) - 4b + 4a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 12b cosh(x) + 4b - 8a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (- 8b cosh(x) + (8b - 16a b)cosh(x))sinh(x) - 2b cosh(x) +--R + +--R 2 2 2 +--R (4b - 8a b)cosh(x) - 2b +--R * +--R tanh(x) +--R + +--R 2 2 2 +--R (4a b - 8a )sinh(x) + (8a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 +--R (4a b - 8a )cosh(x) - 4a b +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- a b + a \|a \|b - a +--R / +--R 3 2 2 3 4 +--R (4a b - 8a b + 4a b)sinh(x) +--R + +--R 3 2 2 3 3 +--R (16a b - 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (24a b - 48a b + 24a b)cosh(x) - 8a b + 32a b - 40a b +--R + +--R 4 +--R 16a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (16a b - 32a b + 16a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 16a b + 64a b - 80a b + 32a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (4a b - 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (- 8a b + 32a b - 40a b + 16a )cosh(x) + 4a b - 8a b + 4a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (4a b - 4a b)sinh(x) + (16a b - 16a b)cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((24a b - 24a b)cosh(x) - 8a b + 24a b - 16a )sinh(x) +--R + +--R 2 2 3 3 2 2 3 4 +--R ((16a b - 16a b)cosh(x) + (- 16a b + 48a b - 32a )cosh(x))sinh(x) +--R + +--R 2 2 3 4 2 2 3 4 2 2 2 3 +--R (4a b - 4a b)cosh(x) + (- 8a b + 24a b - 16a )cosh(x) + 4a b - 4a b +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- a b + a \|a \|b - a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 510 +d0060a:= D(m0060a,x) +--R +--R +--R (263) +--R 2 8 2 7 +--R - b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (- 28b cosh(x) + 4b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (- 56b cosh(x) + (24b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- 70b cosh(x) + (60b - 120a b)cosh(x) + 10b - 16a b)sinh(x) +--R + +--R 2 5 2 3 2 +--R (- 56b cosh(x) + (80b - 160a b)cosh(x) + (40b - 64a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R - 28b cosh(x) + (60b - 120a b)cosh(x) + (60b - 96a b)cosh(x) +--R + +--R 2 +--R 4b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R - 8b cosh(x) + (24b - 48a b)cosh(x) + (40b - 64a b)cosh(x) +--R + +--R 2 +--R (8b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R - b cosh(x) + (4b - 8a b)cosh(x) + (10b - 16a b)cosh(x) +--R + +--R 2 2 2 +--R (4b - 8a b)cosh(x) - b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 8 2 7 +--R 2b sinh(x) + 16b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (56b cosh(x) - 8b + 16a b)sinh(x) +--R + +--R 2 3 2 5 +--R (112b cosh(x) + (- 48b + 96a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (140b cosh(x) + (- 120b + 240a b)cosh(x) + 12b )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (112b cosh(x) + (- 160b + 320a b)cosh(x) + 48b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R 56b cosh(x) + (- 120b + 240a b)cosh(x) + 72b cosh(x) - 8b +--R + +--R 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R 16b cosh(x) + (- 48b + 96a b)cosh(x) + 48b cosh(x) +--R + +--R 2 +--R (- 16b + 32a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R 2b cosh(x) + (- 8b + 16a b)cosh(x) + 12b cosh(x) +--R + +--R 2 2 2 +--R (- 8b + 16a b)cosh(x) + 2b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 8 2 7 2 2 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) + 4b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (- 56b cosh(x) + (24b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- 70b cosh(x) + (60b - 120a b)cosh(x) - 6b + 16a b)sinh(x) +--R + +--R 2 5 2 3 2 +--R (- 56b cosh(x) + (80b - 160a b)cosh(x) + (- 24b + 64a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R - 28b cosh(x) + (60b - 120a b)cosh(x) + (- 36b + 96a b)cosh(x) +--R + +--R 2 +--R 4b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R - 8b cosh(x) + (24b - 48a b)cosh(x) + (- 24b + 64a b)cosh(x) +--R + +--R 2 +--R (8b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R - b cosh(x) + (4b - 8a b)cosh(x) + (- 6b + 16a b)cosh(x) +--R + +--R 2 2 2 +--R (4b - 8a b)cosh(x) - b +--R / +--R 4 3 2 2 8 4 3 2 2 7 +--R (b - 2a b + a b )sinh(x) + (8b - 16a b + 8a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 3 +--R ((28b - 56a b + 28a b )cosh(x) - 4b + 16a b - 20a b + 8a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 +--R (56b - 112a b + 56a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 24b + 96a b - 120a b + 48a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 4 +--R (70b - 140a b + 70a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 60b + 240a b - 300a b + 120a b)cosh(x) + 6b - 28a b +--R + +--R 2 2 3 4 +--R 54a b - 48a b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 5 +--R (56b - 112a b + 56a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 80b + 320a b - 400a b + 160a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (24b - 112a b + 216a b - 192a b + 64a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 6 +--R (28b - 56a b + 28a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 60b + 240a b - 300a b + 120a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 +--R (36b - 168a b + 324a b - 288a b + 96a )cosh(x) - 4b + 16a b +--R + +--R 2 2 3 +--R - 20a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 7 +--R (8b - 16a b + 8a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 24b + 96a b - 120a b + 48a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (24b - 112a b + 216a b - 192a b + 64a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 8b + 32a b - 40a b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 8 +--R (b - 2a b + a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 4b + 16a b - 20a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (6b - 28a b + 54a b - 48a b + 16a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (- 4b + 16a b - 20a b + 8a b)cosh(x) + b - 2a b + a b +--R * +--R 4 +--R tanh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (2a b - 2a b )sinh(x) + (16a b - 16a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 6 +--R ((56a b - 56a b )cosh(x) - 8a b + 24a b - 16a b)sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((112a b - 112a b )cosh(x) + (- 48a b + 144a b - 96a b)cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140a b - 140a b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 120a b + 360a b - 240a b)cosh(x) + 12a b - 44a b + 64a b +--R + +--R 4 +--R - 32a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112a b - 112a b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 160a b + 480a b - 320a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (48a b - 176a b + 256a b - 128a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56a b - 56a b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 120a b + 360a b - 240a b)cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 +--R (72a b - 264a b + 384a b - 192a )cosh(x) - 8a b + 24a b +--R + +--R 3 +--R - 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 3 5 +--R (16a b - 16a b )cosh(x) + (- 48a b + 144a b - 96a b)cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (48a b - 176a b + 256a b - 128a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 16a b + 48a b - 32a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 3 6 +--R (2a b - 2a b )cosh(x) + (- 8a b + 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (12a b - 44a b + 64a b - 32a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 8a b + 24a b - 16a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 8 2 2 7 +--R a b sinh(x) + 8a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 6 +--R (28a b cosh(x) - 4a b + 8a b)sinh(x) +--R + +--R 2 2 3 2 2 3 5 +--R (56a b cosh(x) + (- 24a b + 48a b)cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 2 3 4 +--R (70a b cosh(x) + (- 60a b + 120a b)cosh(x) + 6a b - 16a b + 16a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 3 +--R 56a b cosh(x) + (- 80a b + 160a b)cosh(x) +--R + +--R 2 2 3 4 +--R (24a b - 64a b + 64a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 2 3 4 +--R 28a b cosh(x) + (- 60a b + 120a b)cosh(x) +--R + +--R 2 2 3 4 2 2 2 3 +--R (36a b - 96a b + 96a )cosh(x) - 4a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 3 5 +--R 8a b cosh(x) + (- 24a b + 48a b)cosh(x) +--R + +--R 2 2 3 4 3 2 2 3 +--R (24a b - 64a b + 64a )cosh(x) + (- 8a b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 3 6 2 2 3 4 4 +--R a b cosh(x) + (- 4a b + 8a b)cosh(x) + (6a b - 16a b + 16a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 4a b + 8a b)cosh(x) + a b +--R Type: Expression(Integer) +--E 311 + +--S 312 of 510 +m0060b:= a0060.2-r0060 +--R +--R +--R (264) +--R 3 2 2 4 +--R (b - 3a b + 2a b)sinh(x) +--R + +--R 3 2 2 3 +--R (4b - 12a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 +--R ((6b - 18a b + 12a b)cosh(x) - 2b + 10a b - 16a b + 8a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (4b - 12a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 20a b - 32a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 4 +--R (b - 3a b + 2a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 2b + 10a b - 16a b + 8a )cosh(x) + b - 3a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (a b - 2a b)sinh(x) + (4a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((6a b - 12a b)cosh(x) - 2a b + 8a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((4a b - 8a b)cosh(x) + (- 4a b + 16a b - 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 2 +--R (a b - 2a b)cosh(x) + (- 2a b + 8a b - 8a )cosh(x) + a b - 2a b +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R +--------+ +--R 2 2 | 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a)\|a b - a +--R atan(-----------------------------------------------------------------) +--R 2 +--R 2a b - 2a +--R + +--R 3 2 2 4 +--R (- b + 3a b - 2a b)sinh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 12a b - 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 +--R ((- 6b + 18a b - 12a b)cosh(x) + 2b - 10a b + 16a b - 8a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 12a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 +--R (4b - 20a b + 32a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- b + 3a b - 2a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (2b - 10a b + 16a b - 8a )cosh(x) - b + 3a b - 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (- a b + 2a b)sinh(x) + (- 4a b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6a b + 12a b)cosh(x) + 2a b - 8a b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 4a b + 8a b)cosh(x) + (4a b - 16a b + 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 2 +--R (- a b + 2a b)cosh(x) + (2a b - 8a b + 8a )cosh(x) - a b + 2a b +--R * +--R +--------+ +-----+ +--R | 2 tanh(x)\|b - a +--R \|a b - a atan(---------------) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 +--R (2b - 6a b + 4a )sinh(x) + (4b - 12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (2b - 6a b + 4a )cosh(x) - 2b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 6b cosh(x) + 2b - 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (- 4b cosh(x) + (4b - 8a b)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 2 2 +--R (2b - 4a b)cosh(x) - b +--R * +--R tanh(x) +--R + +--R 2 2 2 +--R (2a b - 4a )sinh(x) + (4a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 +--R (2a b - 4a )cosh(x) - 2a b +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|a b - a +--R / +--R 3 2 2 3 4 +--R (2a b - 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 3 3 +--R (8a b - 16a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (12a b - 24a b + 12a b)cosh(x) - 4a b + 16a b - 20a b +--R + +--R 4 +--R 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (8a b - 16a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 8a b + 32a b - 40a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (2a b - 4a b + 2a b)cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (- 4a b + 16a b - 20a b + 8a )cosh(x) + 2a b - 4a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (2a b - 2a b)sinh(x) + (8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((12a b - 12a b)cosh(x) - 4a b + 12a b - 8a )sinh(x) +--R + +--R 2 2 3 3 2 2 3 4 +--R ((8a b - 8a b)cosh(x) + (- 8a b + 24a b - 16a )cosh(x))sinh(x) +--R + +--R 2 2 3 4 2 2 3 4 2 2 2 3 +--R (2a b - 2a b)cosh(x) + (- 4a b + 12a b - 8a )cosh(x) + 2a b - 2a b +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|a b - a +--R Type: Expression(Integer) +--E 312 + +--S 313 of 510 +d0060b:= D(m0060b,x) +--R +--R +--R (265) +--R 2 8 2 7 +--R - b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (- 28b cosh(x) + 4b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (- 56b cosh(x) + (24b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- 70b cosh(x) + (60b - 120a b)cosh(x) + 10b - 16a b)sinh(x) +--R + +--R 2 5 2 3 2 +--R (- 56b cosh(x) + (80b - 160a b)cosh(x) + (40b - 64a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R - 28b cosh(x) + (60b - 120a b)cosh(x) + (60b - 96a b)cosh(x) +--R + +--R 2 +--R 4b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R - 8b cosh(x) + (24b - 48a b)cosh(x) + (40b - 64a b)cosh(x) +--R + +--R 2 +--R (8b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R - b cosh(x) + (4b - 8a b)cosh(x) + (10b - 16a b)cosh(x) +--R + +--R 2 2 2 +--R (4b - 8a b)cosh(x) - b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 8 2 7 +--R 2b sinh(x) + 16b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (56b cosh(x) - 8b + 16a b)sinh(x) +--R + +--R 2 3 2 5 +--R (112b cosh(x) + (- 48b + 96a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (140b cosh(x) + (- 120b + 240a b)cosh(x) + 12b )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (112b cosh(x) + (- 160b + 320a b)cosh(x) + 48b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R 56b cosh(x) + (- 120b + 240a b)cosh(x) + 72b cosh(x) - 8b +--R + +--R 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R 16b cosh(x) + (- 48b + 96a b)cosh(x) + 48b cosh(x) +--R + +--R 2 +--R (- 16b + 32a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R 2b cosh(x) + (- 8b + 16a b)cosh(x) + 12b cosh(x) +--R + +--R 2 2 2 +--R (- 8b + 16a b)cosh(x) + 2b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 8 2 7 2 2 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) + 4b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (- 56b cosh(x) + (24b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- 70b cosh(x) + (60b - 120a b)cosh(x) - 6b + 16a b)sinh(x) +--R + +--R 2 5 2 3 2 +--R (- 56b cosh(x) + (80b - 160a b)cosh(x) + (- 24b + 64a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R - 28b cosh(x) + (60b - 120a b)cosh(x) + (- 36b + 96a b)cosh(x) +--R + +--R 2 +--R 4b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R - 8b cosh(x) + (24b - 48a b)cosh(x) + (- 24b + 64a b)cosh(x) +--R + +--R 2 +--R (8b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R - b cosh(x) + (4b - 8a b)cosh(x) + (- 6b + 16a b)cosh(x) +--R + +--R 2 2 2 +--R (4b - 8a b)cosh(x) - b +--R / +--R 4 3 2 2 8 4 3 2 2 7 +--R (b - 2a b + a b )sinh(x) + (8b - 16a b + 8a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 3 +--R ((28b - 56a b + 28a b )cosh(x) - 4b + 16a b - 20a b + 8a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 +--R (56b - 112a b + 56a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 24b + 96a b - 120a b + 48a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 4 +--R (70b - 140a b + 70a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 60b + 240a b - 300a b + 120a b)cosh(x) + 6b - 28a b +--R + +--R 2 2 3 4 +--R 54a b - 48a b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 5 +--R (56b - 112a b + 56a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 80b + 320a b - 400a b + 160a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (24b - 112a b + 216a b - 192a b + 64a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 6 +--R (28b - 56a b + 28a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 60b + 240a b - 300a b + 120a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 +--R (36b - 168a b + 324a b - 288a b + 96a )cosh(x) - 4b + 16a b +--R + +--R 2 2 3 +--R - 20a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 7 +--R (8b - 16a b + 8a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 24b + 96a b - 120a b + 48a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (24b - 112a b + 216a b - 192a b + 64a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 8b + 32a b - 40a b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 8 +--R (b - 2a b + a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 4b + 16a b - 20a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (6b - 28a b + 54a b - 48a b + 16a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (- 4b + 16a b - 20a b + 8a b)cosh(x) + b - 2a b + a b +--R * +--R 4 +--R tanh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (2a b - 2a b )sinh(x) + (16a b - 16a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 6 +--R ((56a b - 56a b )cosh(x) - 8a b + 24a b - 16a b)sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((112a b - 112a b )cosh(x) + (- 48a b + 144a b - 96a b)cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140a b - 140a b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 120a b + 360a b - 240a b)cosh(x) + 12a b - 44a b + 64a b +--R + +--R 4 +--R - 32a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112a b - 112a b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 160a b + 480a b - 320a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (48a b - 176a b + 256a b - 128a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56a b - 56a b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 120a b + 360a b - 240a b)cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 +--R (72a b - 264a b + 384a b - 192a )cosh(x) - 8a b + 24a b +--R + +--R 3 +--R - 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 3 5 +--R (16a b - 16a b )cosh(x) + (- 48a b + 144a b - 96a b)cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (48a b - 176a b + 256a b - 128a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 16a b + 48a b - 32a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 3 6 +--R (2a b - 2a b )cosh(x) + (- 8a b + 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (12a b - 44a b + 64a b - 32a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 8a b + 24a b - 16a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 8 2 2 7 +--R a b sinh(x) + 8a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 6 +--R (28a b cosh(x) - 4a b + 8a b)sinh(x) +--R + +--R 2 2 3 2 2 3 5 +--R (56a b cosh(x) + (- 24a b + 48a b)cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 2 3 4 +--R (70a b cosh(x) + (- 60a b + 120a b)cosh(x) + 6a b - 16a b + 16a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 3 +--R 56a b cosh(x) + (- 80a b + 160a b)cosh(x) +--R + +--R 2 2 3 4 +--R (24a b - 64a b + 64a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 2 3 4 +--R 28a b cosh(x) + (- 60a b + 120a b)cosh(x) +--R + +--R 2 2 3 4 2 2 2 3 +--R (36a b - 96a b + 96a )cosh(x) - 4a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 3 5 +--R 8a b cosh(x) + (- 24a b + 48a b)cosh(x) +--R + +--R 2 2 3 4 3 2 2 3 +--R (24a b - 64a b + 64a )cosh(x) + (- 8a b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 3 6 2 2 3 4 4 +--R a b cosh(x) + (- 4a b + 8a b)cosh(x) + (6a b - 16a b + 16a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 4a b + 8a b)cosh(x) + a b +--R Type: Expression(Integer) +--E 313 + +--S 314 of 510 +t0061:= 1/(a+b*sinh(x)^2)^3 +--R +--R +--R 1 +--R (266) ----------------------------------------------- +--R 3 6 2 4 2 2 3 +--R b sinh(x) + 3a b sinh(x) + 3a b sinh(x) + a +--R Type: Expression(Integer) +--E 314 + +--S 315 of 510 +r0061:= 1/8*(8*a^2-8*a*b+3*b^2)*atanh((a-b)^(1/2)*_ + tanh(x)/a^(1/2))/a^(5/2)/(a-b)^(5/2)-_ + a*tanh(x)/(a-b)^2/(a-(a-b)*tanh(x)^2)^2+_ + 1/4*b^2*tanh(x)/a/(a-b)^2/(a-(a-b)*tanh(x)^2)^2+_ + tanh(x)^3/(a-b)/(a-(a-b)*tanh(x)^2)^2+_ + 1/8*(8*a^2-8*a*b+3*b^2)*tanh(x)/a^2/(a-b)^2/(a-(a-b)*tanh(x)^2) +--R +--R +--R (267) +--R 4 3 2 2 3 4 4 +--R (3b - 14a b + 27a b - 24a b + 8a )tanh(x) +--R + +--R 3 2 2 3 4 2 2 2 3 4 +--R (6a b - 22a b + 32a b - 16a )tanh(x) + 3a b - 8a b + 8a +--R * +--R +-------+ +--R tanh(x)\|- b + a +--R atanh(-----------------) +--R +-+ +--R \|a +--R + +--R 3 2 2 3 2 2 +-------+ +-+ +--R ((3b - 11a b + 8a b)tanh(x) + (5a b - 8a b)tanh(x))\|- b + a \|a +--R / +--R 2 4 3 3 4 2 5 6 4 +--R (8a b - 32a b + 48a b - 32a b + 8a )tanh(x) +--R + +--R 3 3 4 2 5 6 2 4 2 5 6 +--R (16a b - 48a b + 48a b - 16a )tanh(x) + 8a b - 16a b + 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R Type: Expression(Integer) +--E 315 + +--S 316 of 510 +a0061:= integrate(t0061,x) +--R +--R +--R (268) +--R [ +--R 4 3 2 2 8 +--R (3b - 8a b + 8a b )sinh(x) +--R + +--R 4 3 2 2 7 +--R (24b - 64a b + 64a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (84b - 224a b + 224a b )cosh(x) - 12b + 56a b - 96a b +--R + +--R 3 +--R 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 +--R (168b - 448a b + 448a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 72b + 336a b - 576a b + 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 4 +--R (210b - 560a b + 560a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 180b + 840a b - 1440a b + 960a b)cosh(x) + 18b - 96a b +--R + +--R 2 2 3 4 +--R 224a b - 256a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 5 +--R (168b - 448a b + 448a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 240b + 1120a b - 1920a b + 1280a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (72b - 384a b + 896a b - 1024a b + 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 6 +--R (84b - 224a b + 224a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 180b + 840a b - 1440a b + 960a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (108b - 576a b + 1344a b - 1536a b + 768a )cosh(x) - 12b +--R + +--R 3 2 2 3 +--R 56a b - 96a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 7 +--R (24b - 64a b + 64a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 72b + 336a b - 576a b + 384a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (72b - 384a b + 896a b - 1024a b + 512a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 24b + 112a b - 192a b + 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 8 +--R (3b - 8a b + 8a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 12b + 56a b - 96a b + 64a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (18b - 96a b + 224a b - 256a b + 128a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (- 12b + 56a b - 96a b + 64a b)cosh(x) + 3b - 8a b + 8a b +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R * +--R +----------+ +--R | 2 +--R \|- a b + a +--R + +--R 2 2 2 2 2 +--R (4a b - 4a b)sinh(x) + (8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (4a b - 4a b)cosh(x) - 4a b + 12a b - 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 3 2 2 6 +--R (12b - 32a b + 32a b)sinh(x) +--R + +--R 3 2 2 5 +--R (72b - 192a b + 192a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (180b - 480a b + 480a b)cosh(x) - 36b + 168a b - 288a b +--R + +--R 3 +--R 192a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (240b - 640a b + 640a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 144b + 672a b - 1152a b + 768a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (180b - 480a b + 480a b)cosh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 216b + 1008a b - 1728a b + 1152a )cosh(x) + 36b +--R + +--R 2 2 +--R - 160a b + 160a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (72b - 192a b + 192a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 144b + 672a b - 1152a b + 768a )cosh(x) +--R + +--R 3 2 2 +--R (72b - 320a b + 320a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 +--R (12b - 32a b + 32a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 36b + 168a b - 288a b + 192a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (36b - 160a b + 160a b)cosh(x) - 12b + 24a b +--R * +--R +----------+ +--R | 2 +--R \|- a b + a +--R / +--R 2 4 3 3 4 2 8 +--R (16a b - 32a b + 16a b )sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (128a b - 256a b + 128a b )cosh(x)sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (448a b - 896a b + 448a b )cosh(x) - 64a b + 256a b +--R + +--R 4 2 5 +--R - 320a b + 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (896a b - 1792a b + 896a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 384a b + 1536a b - 1920a b + 768a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (1120a b - 2240a b + 1120a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (- 960a b + 3840a b - 4800a b + 1920a b)cosh(x) + 96a b +--R + +--R 3 3 4 2 5 6 +--R - 448a b + 864a b - 768a b + 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (896a b - 1792a b + 896a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 1280a b + 5120a b - 6400a b + 2560a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (384a b - 1792a b + 3456a b - 3072a b + 1024a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (448a b - 896a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 960a b + 3840a b - 4800a b + 1920a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (576a b - 2688a b + 5184a b - 4608a b + 1536a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R - 64a b + 256a b - 320a b + 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (128a b - 256a b + 128a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 384a b + 1536a b - 1920a b + 768a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (384a b - 1792a b + 3456a b - 3072a b + 1024a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 128a b + 512a b - 640a b + 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (16a b - 32a b + 16a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 64a b + 256a b - 320a b + 128a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (96a b - 448a b + 864a b - 768a b + 256a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 +--R (- 64a b + 256a b - 320a b + 128a b)cosh(x) + 16a b - 32a b +--R + +--R 4 2 +--R 16a b +--R * +--R +----------+ +--R | 2 +--R \|- a b + a +--R , +--R +--R 4 3 2 2 8 +--R (3b - 8a b + 8a b )sinh(x) +--R + +--R 4 3 2 2 7 +--R (24b - 64a b + 64a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (84b - 224a b + 224a b )cosh(x) - 12b + 56a b - 96a b +--R + +--R 3 +--R 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 +--R (168b - 448a b + 448a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 72b + 336a b - 576a b + 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 4 +--R (210b - 560a b + 560a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 180b + 840a b - 1440a b + 960a b)cosh(x) + 18b - 96a b +--R + +--R 2 2 3 4 +--R 224a b - 256a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 5 +--R (168b - 448a b + 448a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 240b + 1120a b - 1920a b + 1280a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (72b - 384a b + 896a b - 1024a b + 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 6 +--R (84b - 224a b + 224a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 180b + 840a b - 1440a b + 960a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (108b - 576a b + 1344a b - 1536a b + 768a )cosh(x) - 12b +--R + +--R 3 2 2 3 +--R 56a b - 96a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 7 +--R (24b - 64a b + 64a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 72b + 336a b - 576a b + 384a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (72b - 384a b + 896a b - 1024a b + 512a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 24b + 112a b - 192a b + 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 8 +--R (3b - 8a b + 8a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 12b + 56a b - 96a b + 64a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (18b - 96a b + 224a b - 256a b + 128a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (- 12b + 56a b - 96a b + 64a b)cosh(x) + 3b - 8a b + 8a b +--R * +--R +--------+ +--R 2 2 | 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a)\|a b - a +--R atan(-----------------------------------------------------------------) +--R 2 +--R 2a b - 2a +--R + +--R 3 2 2 6 +--R (6b - 16a b + 16a b)sinh(x) +--R + +--R 3 2 2 5 +--R (36b - 96a b + 96a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (90b - 240a b + 240a b)cosh(x) - 18b + 84a b - 144a b +--R + +--R 3 +--R 96a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (120b - 320a b + 320a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 72b + 336a b - 576a b + 384a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (90b - 240a b + 240a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 108b + 504a b - 864a b + 576a )cosh(x) + 18b - 80a b +--R + +--R 2 +--R 80a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (36b - 96a b + 96a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 72b + 336a b - 576a b + 384a )cosh(x) +--R + +--R 3 2 2 +--R (36b - 160a b + 160a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 +--R (6b - 16a b + 16a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 18b + 84a b - 144a b + 96a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (18b - 80a b + 80a b)cosh(x) - 6b + 12a b +--R * +--R +--------+ +--R | 2 +--R \|a b - a +--R / +--R 2 4 3 3 4 2 8 +--R (8a b - 16a b + 8a b )sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (64a b - 128a b + 64a b )cosh(x)sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (224a b - 448a b + 224a b )cosh(x) - 32a b + 128a b +--R + +--R 4 2 5 +--R - 160a b + 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (448a b - 896a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 192a b + 768a b - 960a b + 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (560a b - 1120a b + 560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (- 480a b + 1920a b - 2400a b + 960a b)cosh(x) + 48a b +--R + +--R 3 3 4 2 5 6 +--R - 224a b + 432a b - 384a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (448a b - 896a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 640a b + 2560a b - 3200a b + 1280a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (192a b - 896a b + 1728a b - 1536a b + 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (224a b - 448a b + 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 480a b + 1920a b - 2400a b + 960a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (288a b - 1344a b + 2592a b - 2304a b + 768a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R - 32a b + 128a b - 160a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (64a b - 128a b + 64a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 192a b + 768a b - 960a b + 384a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (192a b - 896a b + 1728a b - 1536a b + 512a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 64a b + 256a b - 320a b + 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (8a b - 16a b + 8a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 32a b + 128a b - 160a b + 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (48a b - 224a b + 432a b - 384a b + 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 4 2 +--R (- 32a b + 128a b - 160a b + 64a b)cosh(x) + 8a b - 16a b + 8a b +--R * +--R +--------+ +--R | 2 +--R \|a b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 316 + +--S 317 of 510 +m0061a:= a0061.1-r0061 +--R +--R +--R (269) +--R 6 5 2 4 3 3 4 2 8 +--R (3b - 14a b + 27a b - 24a b + 8a b )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (24b - 112a b + 216a b - 192a b + 64a b )cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (84b - 392a b + 756a b - 672a b + 224a b )cosh(x) - 12b +--R + +--R 5 2 4 3 3 4 2 5 +--R 80a b - 220a b + 312a b - 224a b + 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (168b - 784a b + 1512a b - 1344a b + 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 72b + 480a b - 1320a b + 1872a b - 1344a b +--R + +--R 5 +--R 384a b +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (210b - 980a b + 1890a b - 1680a b + 560a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 180b + 1200a b - 3300a b + 4680a b - 3360a b +--R + +--R 5 +--R 960a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 18b - 132a b + 434a b - 800a b + 864a b - 512a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (168b - 784a b + 1512a b - 1344a b + 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 240b + 1600a b - 4400a b + 6240a b - 4480a b +--R + +--R 5 +--R 1280a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 72b - 528a b + 1736a b - 3200a b + 3456a b - 2048a b +--R + +--R 6 +--R 512a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (84b - 392a b + 756a b - 672a b + 224a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 180b + 1200a b - 3300a b + 4680a b - 3360a b +--R + +--R 5 +--R 960a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 108b - 792a b + 2604a b - 4800a b + 5184a b +--R + +--R 5 6 +--R - 3072a b + 768a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 12b + 80a b - 220a b + 312a b - 224a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (24b - 112a b + 216a b - 192a b + 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 72b + 480a b - 1320a b + 1872a b - 1344a b +--R + +--R 5 +--R 384a b +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 72b - 528a b + 1736a b - 3200a b + 3456a b - 2048a b +--R + +--R 6 +--R 512a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 24b + 160a b - 440a b + 624a b - 448a b + 128a b) +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (3b - 14a b + 27a b - 24a b + 8a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b + 80a b - 220a b + 312a b - 224a b + 64a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (18b - 132a b + 434a b - 800a b + 864a b - 512a b + 128a ) +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 12b + 80a b - 220a b + 312a b - 224a b + 64a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 3b - 14a b + 27a b - 24a b + 8a b +--R * +--R 4 +--R tanh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (6a b - 22a b + 32a b - 16a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (48a b - 176a b + 256a b - 128a b )cosh(x)sinh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (168a b - 616a b + 896a b - 448a b )cosh(x) - 24a b +--R + +--R 2 4 3 3 4 2 5 +--R 136a b - 304a b + 320a b - 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (336a b - 1232a b + 1792a b - 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 144a b + 816a b - 1824a b + 1920a b - 768a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (420a b - 1540a b + 2240a b - 1120a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 360a b + 2040a b - 4560a b + 4800a b - 1920a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 36a b - 228a b + 640a b - 960a b + 768a b - 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (336a b - 1232a b + 1792a b - 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 480a b + 2720a b - 6080a b + 6400a b - 2560a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 144a b - 912a b + 2560a b - 3840a b + 3072a b +--R + +--R 6 +--R - 1024a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (168a b - 616a b + 896a b - 448a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 360a b + 2040a b - 4560a b + 4800a b - 1920a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 216a b - 1368a b + 3840a b - 5760a b + 4608a b +--R + +--R 6 +--R - 1536a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 24a b + 136a b - 304a b + 320a b - 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (48a b - 176a b + 256a b - 128a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 144a b + 816a b - 1824a b + 1920a b - 768a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 144a b - 912a b + 2560a b - 3840a b + 3072a b +--R + +--R 6 +--R - 1024a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 48a b + 272a b - 608a b + 640a b - 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (6a b - 22a b + 32a b - 16a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 24a b + 136a b - 304a b + 320a b - 128a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (36a b - 228a b + 640a b - 960a b + 768a b - 256a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 5 +--R (- 24a b + 136a b - 304a b + 320a b - 128a b)cosh(x) + 6a b +--R + +--R 2 4 3 3 4 2 +--R - 22a b + 32a b - 16a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (3a b - 8a b + 8a b )sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (24a b - 64a b + 64a b )cosh(x)sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 4 2 +--R (84a b - 224a b + 224a b )cosh(x) - 12a b + 56a b - 96a b +--R + +--R 5 +--R 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (168a b - 448a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 72a b + 336a b - 576a b + 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (210a b - 560a b + 560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (- 180a b + 840a b - 1440a b + 960a b)cosh(x) + 18a b +--R + +--R 3 3 4 2 5 6 +--R - 96a b + 224a b - 256a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (168a b - 448a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 240a b + 1120a b - 1920a b + 1280a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (72a b - 384a b + 896a b - 1024a b + 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (84a b - 224a b + 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 180a b + 840a b - 1440a b + 960a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 2 4 +--R (108a b - 576a b + 1344a b - 1536a b + 768a )cosh(x) - 12a b +--R + +--R 3 3 4 2 5 +--R 56a b - 96a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (24a b - 64a b + 64a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 72a b + 336a b - 576a b + 384a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (72a b - 384a b + 896a b - 1024a b + 512a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 24a b + 112a b - 192a b + 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (3a b - 8a b + 8a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b + 56a b - 96a b + 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (18a b - 96a b + 224a b - 256a b + 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 4 2 +--R (- 12a b + 56a b - 96a b + 64a b)cosh(x) + 3a b - 8a b + 8a b +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R * +--R +----------+ +--R | 2 +--R \|- a b + a +--R + +--R 2 2 2 2 2 +--R (4a b - 4a b)sinh(x) + (8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (4a b - 4a b)cosh(x) - 4a b + 12a b - 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (- 6b + 28a b - 54a b + 48a b - 16a b )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (- 48b + 224a b - 432a b + 384a b - 128a b )cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- 168b + 784a b - 1512a b + 1344a b - 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 24b - 160a b + 440a b - 624a b + 448a b - 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 336b + 1568a b - 3024a b + 2688a b - 896a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (144b - 960a b + 2640a b - 3744a b + 2688a b - 768a b) +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 420b + 1960a b - 3780a b + 3360a b - 1120a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 360b - 2400a b + 6600a b - 9360a b + 6720a b +--R + +--R 5 +--R - 1920a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 36b + 264a b - 868a b + 1600a b - 1728a b + 1024a b +--R + +--R 6 +--R - 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 336b + 1568a b - 3024a b + 2688a b - 896a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 480b - 3200a b + 8800a b - 12480a b + 8960a b +--R + +--R 5 +--R - 2560a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 144b + 1056a b - 3472a b + 6400a b - 6912a b +--R + +--R 5 6 +--R 4096a b - 1024a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 168b + 784a b - 1512a b + 1344a b - 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 360b - 2400a b + 6600a b - 9360a b + 6720a b +--R + +--R 5 +--R - 1920a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 216b + 1584a b - 5208a b + 9600a b - 10368a b +--R + +--R 5 6 +--R 6144a b - 1536a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 24b - 160a b + 440a b - 624a b + 448a b - 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (- 48b + 224a b - 432a b + 384a b - 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (144b - 960a b + 2640a b - 3744a b + 2688a b - 768a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 144b + 1056a b - 3472a b + 6400a b - 6912a b +--R + +--R 5 6 +--R 4096a b - 1024a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (48b - 320a b + 880a b - 1248a b + 896a b - 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (- 6b + 28a b - 54a b + 48a b - 16a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (24b - 160a b + 440a b - 624a b + 448a b - 128a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 36b + 264a b - 868a b + 1600a b - 1728a b + 1024a b +--R + +--R 6 +--R - 256a +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (24b - 160a b + 440a b - 624a b + 448a b - 128a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 6b + 28a b - 54a b + 48a b - 16a b +--R * +--R 4 +--R tanh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (- 12a b + 44a b - 64a b + 32a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 96a b + 352a b - 512a b + 256a b )cosh(x)sinh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 336a b + 1232a b - 1792a b + 896a b )cosh(x) + 48a b +--R + +--R 2 4 3 3 4 2 5 +--R - 272a b + 608a b - 640a b + 256a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 672a b + 2464a b - 3584a b + 1792a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (288a b - 1632a b + 3648a b - 3840a b + 1536a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 840a b + 3080a b - 4480a b + 2240a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (720a b - 4080a b + 9120a b - 9600a b + 3840a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 72a b + 456a b - 1280a b + 1920a b - 1536a b + 512a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 672a b + 2464a b - 3584a b + 1792a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (960a b - 5440a b + 12160a b - 12800a b + 5120a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 288a b + 1824a b - 5120a b + 7680a b - 6144a b +--R + +--R 6 +--R 2048a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 336a b + 1232a b - 1792a b + 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (720a b - 4080a b + 9120a b - 9600a b + 3840a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 432a b + 2736a b - 7680a b + 11520a b - 9216a b +--R + +--R 6 +--R 3072a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 48a b - 272a b + 608a b - 640a b + 256a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 96a b + 352a b - 512a b + 256a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (288a b - 1632a b + 3648a b - 3840a b + 1536a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 288a b + 1824a b - 5120a b + 7680a b - 6144a b +--R + +--R 6 +--R 2048a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (96a b - 544a b + 1216a b - 1280a b + 512a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (- 12a b + 44a b - 64a b + 32a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (48a b - 272a b + 608a b - 640a b + 256a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 72a b + 456a b - 1280a b + 1920a b - 1536a b + 512a ) +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 5 +--R (48a b - 272a b + 608a b - 640a b + 256a b)cosh(x) - 12a b +--R + +--R 2 4 3 3 4 2 +--R 44a b - 64a b + 32a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 6a b + 16a b - 16a b )sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 48a b + 128a b - 128a b )cosh(x)sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (- 168a b + 448a b - 448a b )cosh(x) + 24a b - 112a b +--R + +--R 4 2 5 +--R 192a b - 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (- 336a b + 896a b - 896a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (144a b - 672a b + 1152a b - 768a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 420a b + 1120a b - 1120a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (360a b - 1680a b + 2880a b - 1920a b)cosh(x) - 36a b +--R + +--R 3 3 4 2 5 6 +--R 192a b - 448a b + 512a b - 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 336a b + 896a b - 896a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (480a b - 2240a b + 3840a b - 2560a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 144a b + 768a b - 1792a b + 2048a b - 1024a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (- 168a b + 448a b - 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (360a b - 1680a b + 2880a b - 1920a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (- 216a b + 1152a b - 2688a b + 3072a b - 1536a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R 24a b - 112a b + 192a b - 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 48a b + 128a b - 128a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (144a b - 672a b + 1152a b - 768a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 144a b + 768a b - 1792a b + 2048a b - 1024a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (48a b - 224a b + 384a b - 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 6a b + 16a b - 16a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (24a b - 112a b + 192a b - 128a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 36a b + 192a b - 448a b + 512a b - 256a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 4 2 +--R (24a b - 112a b + 192a b - 128a b)cosh(x) - 6a b + 16a b - 16a b +--R * +--R +----------+ +-------+ +--R | 2 tanh(x)\|- b + a +--R \|- a b + a atanh(-----------------) +--R +-+ +--R \|a +--R + +--R 5 4 2 3 3 2 4 6 +--R (12b - 56a b + 108a b - 96a b + 32a b)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (72b - 336a b + 648a b - 576a b + 192a b)cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (180b - 840a b + 1620a b - 1440a b + 480a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R - 36b + 240a b - 660a b + 936a b - 672a b + 192a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (240b - 1120a b + 2160a b - 1920a b + 640a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 144b + 960a b - 2640a b + 3744a b - 2688a b + 768a ) +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (180b - 840a b + 1620a b - 1440a b + 480a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 216b + 1440a b - 3960a b + 5616a b - 4032a b +--R + +--R 5 +--R 1152a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 36b - 232a b + 516a b - 480a b + 160a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (72b - 336a b + 648a b - 576a b + 192a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 144b + 960a b - 2640a b + 3744a b - 2688a b + 768a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (72b - 464a b + 1032a b - 960a b + 320a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (12b - 56a b + 108a b - 96a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 36b + 240a b - 660a b + 936a b - 672a b + 192a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (36b - 232a b + 516a b - 480a b + 160a b)cosh(x) - 12b +--R + +--R 4 2 3 3 2 +--R 48a b - 60a b + 24a b +--R * +--R 4 +--R tanh(x) +--R + +--R 5 4 2 3 8 +--R (- 6b + 22a b - 16a b )sinh(x) +--R + +--R 5 4 2 3 7 +--R (- 48b + 176a b - 128a b )cosh(x)sinh(x) +--R + +--R 5 4 2 3 2 5 4 +--R (- 168b + 616a b - 448a b )cosh(x) + 24b - 136a b +--R + +--R 2 3 3 2 +--R 240a b - 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 +--R (- 336b + 1232a b - 896a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (144b - 816a b + 1440a b - 768a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 4 +--R (- 420b + 1540a b - 1120a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 +--R (360b - 2040a b + 3600a b - 1920a b )cosh(x) - 36b +--R + +--R 4 2 3 3 2 4 +--R 228a b - 544a b + 608a b - 256a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 5 +--R (- 336b + 1232a b - 896a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (480b - 2720a b + 4800a b - 2560a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 144b + 912a b - 2176a b + 2432a b - 1024a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 6 +--R (- 168b + 616a b - 448a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (360b - 2040a b + 3600a b - 1920a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 216b + 1368a b - 3264a b + 3648a b - 1536a b)cosh(x) +--R + +--R 5 4 2 3 3 2 +--R 24b - 136a b + 240a b - 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 7 +--R (- 48b + 176a b - 128a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (144b - 816a b + 1440a b - 768a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 144b + 912a b - 2176a b + 2432a b - 1024a b)cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (48b - 272a b + 480a b - 256a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 8 +--R (- 6b + 22a b - 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (24b - 136a b + 240a b - 128a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 36b + 228a b - 544a b + 608a b - 256a b)cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (24b - 136a b + 240a b - 128a b )cosh(x) - 6b + 22a b +--R + +--R 2 3 +--R - 16a b +--R * +--R 3 +--R tanh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (24a b - 88a b + 128a b - 64a b)sinh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (144a b - 528a b + 768a b - 384a b)cosh(x)sinh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (360a b - 1320a b + 1920a b - 960a b)cosh(x) - 72a b +--R + +--R 2 3 3 2 4 5 +--R 408a b - 912a b + 960a b - 384a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (480a b - 1760a b + 2560a b - 1280a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 288a b + 1632a b - 3648a b + 3840a b - 1536a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (360a b - 1320a b + 1920a b - 960a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 432a b + 2448a b - 5472a b + 5760a b - 2304a )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R 72a b - 392a b + 640a b - 320a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (144a b - 528a b + 768a b - 384a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 288a b + 1632a b - 3648a b + 3840a b - 1536a )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (144a b - 784a b + 1280a b - 640a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (24a b - 88a b + 128a b - 64a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 72a b + 408a b - 912a b + 960a b - 384a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 2 3 +--R (72a b - 392a b + 640a b - 320a b)cosh(x) - 24a b + 72a b +--R + +--R 3 2 +--R - 48a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 2 3 8 4 2 3 7 +--R (- 10a b + 16a b )sinh(x) + (- 80a b + 128a b )cosh(x)sinh(x) +--R + +--R 4 2 3 2 4 2 3 3 2 +--R ((- 280a b + 448a b )cosh(x) + 40a b - 144a b + 128a b ) +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 +--R (- 560a b + 896a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (240a b - 864a b + 768a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 4 +--R (- 700a b + 1120a b )cosh(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (600a b - 2160a b + 1920a b )cosh(x) - 60a b + 256a b +--R + +--R 3 2 4 +--R - 416a b + 256a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 5 +--R (- 560a b + 896a b )cosh(x) +--R + +--R 4 2 3 3 2 3 +--R (800a b - 2880a b + 2560a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 240a b + 1024a b - 1664a b + 1024a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 6 +--R (- 280a b + 448a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (600a b - 2160a b + 1920a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (- 360a b + 1536a b - 2496a b + 1536a b)cosh(x) + 40a b +--R + +--R 2 3 3 2 +--R - 144a b + 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 7 +--R (- 80a b + 128a b )cosh(x) +--R + +--R 4 2 3 3 2 5 +--R (240a b - 864a b + 768a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 240a b + 1024a b - 1664a b + 1024a b)cosh(x) +--R + +--R 4 2 3 3 2 +--R (80a b - 288a b + 256a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 8 +--R (- 10a b + 16a b )cosh(x) +--R + +--R 4 2 3 3 2 6 +--R (40a b - 144a b + 128a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 60a b + 256a b - 416a b + 256a b)cosh(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (40a b - 144a b + 128a b )cosh(x) - 10a b + 16a b +--R * +--R tanh(x) +--R + +--R 2 3 3 2 4 6 +--R (12a b - 32a b + 32a b)sinh(x) +--R + +--R 2 3 3 2 4 5 +--R (72a b - 192a b + 192a b)cosh(x)sinh(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 +--R (180a b - 480a b + 480a b)cosh(x) - 36a b + 168a b - 288a b +--R + +--R 5 +--R 192a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 +--R (240a b - 640a b + 640a b)cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (- 144a b + 672a b - 1152a b + 768a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 4 4 +--R (180a b - 480a b + 480a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 2 3 +--R (- 216a b + 1008a b - 1728a b + 1152a )cosh(x) + 36a b +--R + +--R 3 2 4 +--R - 160a b + 160a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 4 5 +--R (72a b - 192a b + 192a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 144a b + 672a b - 1152a b + 768a )cosh(x) +--R + +--R 2 3 3 2 4 +--R (72a b - 320a b + 320a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3 2 4 6 +--R (12a b - 32a b + 32a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 36a b + 168a b - 288a b + 192a )cosh(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 +--R (36a b - 160a b + 160a b)cosh(x) - 12a b + 24a b +--R * +--R +----------+ +--R | 2 +-------+ +-+ +--R \|- a b + a \|- b + a \|a +--R / +--R 2 6 3 5 4 4 5 3 6 2 8 +--R (16a b - 64a b + 96a b - 64a b + 16a b )sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (128a b - 512a b + 768a b - 512a b + 128a b )cosh(x)sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (448a b - 1792a b + 2688a b - 1792a b + 448a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 64a b + 384a b - 896a b + 1024a b - 576a b + 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 3 +--R (896a b - 3584a b + 5376a b - 3584a b + 896a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 384a b + 2304a b - 5376a b + 6144a b - 3456a b +--R + +--R 7 +--R 768a b +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 4 +--R (1120a b - 4480a b + 6720a b - 4480a b + 1120a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 960a b + 5760a b - 13440a b + 15360a b - 8640a b +--R + +--R 7 +--R 1920a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 96a b - 640a b + 1856a b - 2944a b + 2656a b - 1280a b +--R + +--R 8 +--R 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 5 +--R (896a b - 3584a b + 5376a b - 3584a b + 896a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 1280a b + 7680a b - 17920a b + 20480a b - 11520a b +--R + +--R 7 +--R 2560a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 384a b - 2560a b + 7424a b - 11776a b + 10624a b +--R + +--R 7 8 +--R - 5120a b + 1024a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 6 +--R (448a b - 1792a b + 2688a b - 1792a b + 448a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 960a b + 5760a b - 13440a b + 15360a b - 8640a b +--R + +--R 7 +--R 1920a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 576a b - 3840a b + 11136a b - 17664a b + 15936a b +--R + +--R 7 8 +--R - 7680a b + 1536a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 64a b + 384a b - 896a b + 1024a b - 576a b + 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (128a b - 512a b + 768a b - 512a b + 128a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 384a b + 2304a b - 5376a b + 6144a b - 3456a b +--R + +--R 7 +--R 768a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 384a b - 2560a b + 7424a b - 11776a b + 10624a b +--R + +--R 7 8 +--R - 5120a b + 1024a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 128a b + 768a b - 1792a b + 2048a b - 1152a b +--R + +--R 7 +--R 256a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 8 +--R (16a b - 64a b + 96a b - 64a b + 16a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (- 64a b + 384a b - 896a b + 1024a b - 576a b + 128a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 96a b - 640a b + 1856a b - 2944a b + 2656a b - 1280a b +--R + +--R 8 +--R 256a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (- 64a b + 384a b - 896a b + 1024a b - 576a b + 128a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 16a b - 64a b + 96a b - 64a b + 16a b +--R * +--R 4 +--R tanh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 +--R (32a b - 96a b + 96a b - 32a b )sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (256a b - 768a b + 768a b - 256a b )cosh(x)sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 3 5 +--R (896a b - 2688a b + 2688a b - 896a b )cosh(x) - 128a b +--R + +--R 4 4 5 3 6 2 7 +--R 640a b - 1152a b + 896a b - 256a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 3 +--R (1792a b - 5376a b + 5376a b - 1792a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 768a b + 3840a b - 6912a b + 5376a b - 1536a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 4 +--R (2240a b - 6720a b + 6720a b - 2240a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 1920a b + 9600a b - 17280a b + 13440a b - 3840a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R 192a b - 1088a b + 2624a b - 3264a b + 2048a b - 512a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 5 +--R (1792a b - 5376a b + 5376a b - 1792a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 2560a b + 12800a b - 23040a b + 17920a b - 5120a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 768a b - 4352a b + 10496a b - 13056a b + 8192a b +--R + +--R 8 +--R - 2048a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 6 +--R (896a b - 2688a b + 2688a b - 896a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 1920a b + 9600a b - 17280a b + 13440a b - 3840a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 1152a b - 6528a b + 15744a b - 19584a b + 12288a b +--R + +--R 8 +--R - 3072a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R - 128a b + 640a b - 1152a b + 896a b - 256a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (256a b - 768a b + 768a b - 256a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 5 +--R (- 768a b + 3840a b - 6912a b + 5376a b - 1536a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 768a b - 4352a b + 10496a b - 13056a b + 8192a b +--R + +--R 8 +--R - 2048a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 256a b + 1280a b - 2304a b + 1792a b - 512a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 +--R (32a b - 96a b + 96a b - 32a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 6 +--R (- 128a b + 640a b - 1152a b + 896a b - 256a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (192a b - 1088a b + 2624a b - 3264a b + 2048a b - 512a ) +--R * +--R 4 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 2 +--R (- 128a b + 640a b - 1152a b + 896a b - 256a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R 32a b - 96a b + 96a b - 32a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 4 5 3 6 2 8 +--R (16a b - 32a b + 16a b )sinh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (128a b - 256a b + 128a b )cosh(x)sinh(x) +--R + +--R 4 4 5 3 6 2 2 4 4 5 3 6 2 +--R (448a b - 896a b + 448a b )cosh(x) - 64a b + 256a b - 320a b +--R + +--R 7 +--R 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 3 +--R (896a b - 1792a b + 896a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (- 384a b + 1536a b - 1920a b + 768a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 4 +--R (1120a b - 2240a b + 1120a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 4 4 +--R (- 960a b + 3840a b - 4800a b + 1920a b)cosh(x) + 96a b +--R + +--R 5 3 6 2 7 8 +--R - 448a b + 864a b - 768a b + 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 5 +--R (896a b - 1792a b + 896a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (- 1280a b + 5120a b - 6400a b + 2560a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (384a b - 1792a b + 3456a b - 3072a b + 1024a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 6 +--R (448a b - 896a b + 448a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (- 960a b + 3840a b - 4800a b + 1920a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 2 4 4 +--R (576a b - 2688a b + 5184a b - 4608a b + 1536a )cosh(x) - 64a b +--R + +--R 5 3 6 2 7 +--R 256a b - 320a b + 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (128a b - 256a b + 128a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (- 384a b + 1536a b - 1920a b + 768a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 3 +--R (384a b - 1792a b + 3456a b - 3072a b + 1024a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (- 128a b + 512a b - 640a b + 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 8 +--R (16a b - 32a b + 16a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 6 +--R (- 64a b + 256a b - 320a b + 128a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (96a b - 448a b + 864a b - 768a b + 256a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 4 4 5 3 +--R (- 64a b + 256a b - 320a b + 128a b)cosh(x) + 16a b - 32a b +--R + +--R 6 2 +--R 16a b +--R * +--R +----------+ +--R | 2 +-------+ +-+ +--R \|- a b + a \|- b + a \|a +--R Type: Expression(Integer) +--E 317 + +--S 318 of 510 +d0061a:= D(m0061a,x) +--R +--R +--R (270) +--R 3 12 3 11 +--R b sinh(x) + 12b cosh(x)sinh(x) +--R + +--R 3 2 3 2 10 +--R (66b cosh(x) - 6b + 12a b )sinh(x) +--R + +--R 3 3 3 2 9 +--R (220b cosh(x) + (- 60b + 120a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R 495b cosh(x) + (- 270b + 540a b )cosh(x) + 15b - 48a b +--R + +--R 2 +--R 48a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 5 3 2 3 +--R 792b cosh(x) + (- 720b + 1440a b )cosh(x) +--R + +--R 3 2 2 +--R (120b - 384a b + 384a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 6 3 2 4 +--R 924b cosh(x) + (- 1260b + 2520a b )cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (420b - 1344a b + 1344a b)cosh(x) + 44b - 120a b + 96a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 7 3 2 5 +--R 792b cosh(x) + (- 1512b + 3024a b )cosh(x) +--R + +--R 3 2 2 3 +--R (840b - 2688a b + 2688a b)cosh(x) +--R + +--R 3 2 2 +--R (264b - 720a b + 576a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 8 3 2 6 +--R 495b cosh(x) + (- 1260b + 2520a b )cosh(x) +--R + +--R 3 2 2 4 +--R (1050b - 3360a b + 3360a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (660b - 1800a b + 1440a b)cosh(x) + 15b - 48a b + 48a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 9 3 2 7 +--R 220b cosh(x) + (- 720b + 1440a b )cosh(x) +--R + +--R 3 2 2 5 +--R (840b - 2688a b + 2688a b)cosh(x) +--R + +--R 3 2 2 3 +--R (880b - 2400a b + 1920a b)cosh(x) +--R + +--R 3 2 2 +--R (60b - 192a b + 192a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 10 3 2 8 +--R 66b cosh(x) + (- 270b + 540a b )cosh(x) +--R + +--R 3 2 2 6 +--R (420b - 1344a b + 1344a b)cosh(x) +--R + +--R 3 2 2 4 +--R (660b - 1800a b + 1440a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (90b - 288a b + 288a b)cosh(x) - 6b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 11 3 2 9 +--R 12b cosh(x) + (- 60b + 120a b )cosh(x) +--R + +--R 3 2 2 7 +--R (120b - 384a b + 384a b)cosh(x) +--R + +--R 3 2 2 5 +--R (264b - 720a b + 576a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (60b - 192a b + 192a b)cosh(x) + (- 12b + 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 12 3 2 10 +--R b cosh(x) + (- 6b + 12a b )cosh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (15b - 48a b + 48a b)cosh(x) + (44b - 120a b + 96a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (15b - 48a b + 48a b)cosh(x) + (- 6b + 12a b )cosh(x) + b +--R * +--R 6 +--R tanh(x) +--R + +--R 3 12 3 11 +--R - 3b sinh(x) - 36b cosh(x)sinh(x) +--R + +--R 3 2 3 2 10 +--R (- 198b cosh(x) + 18b - 36a b )sinh(x) +--R + +--R 3 3 3 2 9 +--R (- 660b cosh(x) + (180b - 360a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R - 1485b cosh(x) + (810b - 1620a b )cosh(x) - 45b + 144a b +--R + +--R 2 +--R - 144a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 5 3 2 3 +--R - 2376b cosh(x) + (2160b - 4320a b )cosh(x) +--R + +--R 3 2 2 +--R (- 360b + 1152a b - 1152a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 6 3 2 4 +--R - 2772b cosh(x) + (3780b - 7560a b )cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 1260b + 4032a b - 4032a b)cosh(x) + 60b - 24a b - 96a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 7 3 2 5 +--R - 2376b cosh(x) + (4536b - 9072a b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2520b + 8064a b - 8064a b)cosh(x) +--R + +--R 3 2 2 +--R (360b - 144a b - 576a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 8 3 2 6 +--R - 1485b cosh(x) + (3780b - 7560a b )cosh(x) +--R + +--R 3 2 2 4 +--R (- 3150b + 10080a b - 10080a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (900b - 360a b - 1440a b)cosh(x) - 45b + 144a b - 144a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 9 3 2 7 +--R - 660b cosh(x) + (2160b - 4320a b )cosh(x) +--R + +--R 3 2 2 5 +--R (- 2520b + 8064a b - 8064a b)cosh(x) +--R + +--R 3 2 2 3 +--R (1200b - 480a b - 1920a b)cosh(x) +--R + +--R 3 2 2 +--R (- 180b + 576a b - 576a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 10 3 2 8 +--R - 198b cosh(x) + (810b - 1620a b )cosh(x) +--R + +--R 3 2 2 6 +--R (- 1260b + 4032a b - 4032a b)cosh(x) +--R + +--R 3 2 2 4 +--R (900b - 360a b - 1440a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 270b + 864a b - 864a b)cosh(x) + 18b - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 11 3 2 9 +--R - 36b cosh(x) + (180b - 360a b )cosh(x) +--R + +--R 3 2 2 7 +--R (- 360b + 1152a b - 1152a b)cosh(x) +--R + +--R 3 2 2 5 +--R (360b - 144a b - 576a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 180b + 576a b - 576a b)cosh(x) + (36b - 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 12 3 2 10 +--R - 3b cosh(x) + (18b - 36a b )cosh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (- 45b + 144a b - 144a b)cosh(x) + (60b - 24a b - 96a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (- 45b + 144a b - 144a b)cosh(x) + (18b - 36a b )cosh(x) - 3b +--R * +--R 4 +--R tanh(x) +--R + +--R 3 12 3 11 +--R 3b sinh(x) + 36b cosh(x)sinh(x) +--R + +--R 3 2 3 2 10 +--R (198b cosh(x) - 18b + 36a b )sinh(x) +--R + +--R 3 3 3 2 9 +--R (660b cosh(x) + (- 180b + 360a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R 1485b cosh(x) + (- 810b + 1620a b )cosh(x) + 45b - 144a b +--R + +--R 2 +--R 144a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 5 3 2 3 +--R 2376b cosh(x) + (- 2160b + 4320a b )cosh(x) +--R + +--R 3 2 2 +--R (360b - 1152a b + 1152a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 6 3 2 4 +--R 2772b cosh(x) + (- 3780b + 7560a b )cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (1260b - 4032a b + 4032a b)cosh(x) - 60b + 216a b - 96a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 7 3 2 5 +--R 2376b cosh(x) + (- 4536b + 9072a b )cosh(x) +--R + +--R 3 2 2 3 +--R (2520b - 8064a b + 8064a b)cosh(x) +--R + +--R 3 2 2 +--R (- 360b + 1296a b - 576a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 8 3 2 6 +--R 1485b cosh(x) + (- 3780b + 7560a b )cosh(x) +--R + +--R 3 2 2 4 +--R (3150b - 10080a b + 10080a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 900b + 3240a b - 1440a b)cosh(x) + 45b - 144a b + 144a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 9 3 2 7 +--R 660b cosh(x) + (- 2160b + 4320a b )cosh(x) +--R + +--R 3 2 2 5 +--R (2520b - 8064a b + 8064a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 1200b + 4320a b - 1920a b)cosh(x) +--R + +--R 3 2 2 +--R (180b - 576a b + 576a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 10 3 2 8 +--R 198b cosh(x) + (- 810b + 1620a b )cosh(x) +--R + +--R 3 2 2 6 +--R (1260b - 4032a b + 4032a b)cosh(x) +--R + +--R 3 2 2 4 +--R (- 900b + 3240a b - 1440a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (270b - 864a b + 864a b)cosh(x) - 18b + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 11 3 2 9 +--R 36b cosh(x) + (- 180b + 360a b )cosh(x) +--R + +--R 3 2 2 7 +--R (360b - 1152a b + 1152a b)cosh(x) +--R + +--R 3 2 2 5 +--R (- 360b + 1296a b - 576a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (180b - 576a b + 576a b)cosh(x) + (- 36b + 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 12 3 2 10 +--R 3b cosh(x) + (- 18b + 36a b )cosh(x) +--R + +--R 3 2 2 8 +--R (45b - 144a b + 144a b)cosh(x) +--R + +--R 3 2 2 6 +--R (- 60b + 216a b - 96a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (45b - 144a b + 144a b)cosh(x) + (- 18b + 36a b )cosh(x) + 3b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 12 3 11 +--R - b sinh(x) - 12b cosh(x)sinh(x) +--R + +--R 3 2 3 2 10 +--R (- 66b cosh(x) + 6b - 12a b )sinh(x) +--R + +--R 3 3 3 2 9 +--R (- 220b cosh(x) + (60b - 120a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 3 2 2 +--R (- 495b cosh(x) + (270b - 540a b )cosh(x) - 15b + 48a b - 48a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 5 3 2 3 +--R - 792b cosh(x) + (720b - 1440a b )cosh(x) +--R + +--R 3 2 2 +--R (- 120b + 384a b - 384a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 6 3 2 4 +--R - 924b cosh(x) + (1260b - 2520a b )cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 420b + 1344a b - 1344a b)cosh(x) + 20b - 72a b + 96a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 7 3 2 5 +--R - 792b cosh(x) + (1512b - 3024a b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 840b + 2688a b - 2688a b)cosh(x) +--R + +--R 3 2 2 +--R (120b - 432a b + 576a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 8 3 2 6 +--R - 495b cosh(x) + (1260b - 2520a b )cosh(x) +--R + +--R 3 2 2 4 +--R (- 1050b + 3360a b - 3360a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (300b - 1080a b + 1440a b)cosh(x) - 15b + 48a b - 48a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 9 3 2 7 +--R - 220b cosh(x) + (720b - 1440a b )cosh(x) +--R + +--R 3 2 2 5 +--R (- 840b + 2688a b - 2688a b)cosh(x) +--R + +--R 3 2 2 3 +--R (400b - 1440a b + 1920a b)cosh(x) +--R + +--R 3 2 2 +--R (- 60b + 192a b - 192a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 10 3 2 8 +--R - 66b cosh(x) + (270b - 540a b )cosh(x) +--R + +--R 3 2 2 6 +--R (- 420b + 1344a b - 1344a b)cosh(x) +--R + +--R 3 2 2 4 +--R (300b - 1080a b + 1440a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 90b + 288a b - 288a b)cosh(x) + 6b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 11 3 2 9 +--R - 12b cosh(x) + (60b - 120a b )cosh(x) +--R + +--R 3 2 2 7 +--R (- 120b + 384a b - 384a b)cosh(x) +--R + +--R 3 2 2 5 +--R (120b - 432a b + 576a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 60b + 192a b - 192a b)cosh(x) + (12b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 12 3 2 10 +--R - b cosh(x) + (6b - 12a b )cosh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (- 15b + 48a b - 48a b)cosh(x) + (20b - 72a b + 96a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (- 15b + 48a b - 48a b)cosh(x) + (6b - 12a b )cosh(x) - b +--R / +--R 6 5 2 4 3 3 12 +--R (b - 3a b + 3a b - a b )sinh(x) +--R + +--R 6 5 2 4 3 3 11 +--R (12b - 36a b + 36a b - 12a b )cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (66b - 198a b + 198a b - 66a b )cosh(x) - 6b + 30a b +--R + +--R 2 4 3 3 4 2 +--R - 54a b + 42a b - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (220b - 660a b + 660a b - 220a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 60b + 300a b - 540a b + 420a b - 120a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (495b - 1485a b + 1485a b - 495a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- 270b + 1350a b - 2430a b + 1890a b - 540a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 15b - 93a b + 237a b - 303a b + 192a b - 48a b +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (792b - 2376a b + 2376a b - 792a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 720b + 3600a b - 6480a b + 5040a b - 1440a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (120b - 744a b + 1896a b - 2424a b + 1536a b - 384a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 6 +--R (924b - 2772a b + 2772a b - 924a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 1260b + 6300a b - 11340a b + 8820a b - 2520a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (420b - 2604a b + 6636a b - 8484a b + 5376a b - 1344a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R - 20b + 132a b - 372a b + 588a b - 552a b + 288a b - 64a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 7 +--R (792b - 2376a b + 2376a b - 792a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 1512b + 7560a b - 13608a b + 10584a b - 3024a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 840b - 5208a b + 13272a b - 16968a b + 10752a b +--R + +--R 5 +--R - 2688a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 120b + 792a b - 2232a b + 3528a b - 3312a b + 1728a b +--R + +--R 6 +--R - 384a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 8 +--R (495b - 1485a b + 1485a b - 495a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 1260b + 6300a b - 11340a b + 8820a b - 2520a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 1050b - 6510a b + 16590a b - 21210a b + 13440a b +--R + +--R 5 +--R - 3360a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 300b + 1980a b - 5580a b + 8820a b - 8280a b + 4320a b +--R + +--R 6 +--R - 960a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 15b - 93a b + 237a b - 303a b + 192a b - 48a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 9 +--R (220b - 660a b + 660a b - 220a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (- 720b + 3600a b - 6480a b + 5040a b - 1440a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 840b - 5208a b + 13272a b - 16968a b + 10752a b +--R + +--R 5 +--R - 2688a b +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 400b + 2640a b - 7440a b + 11760a b - 11040a b +--R + +--R 5 6 +--R 5760a b - 1280a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (60b - 372a b + 948a b - 1212a b + 768a b - 192a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 10 +--R (66b - 198a b + 198a b - 66a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (- 270b + 1350a b - 2430a b + 1890a b - 540a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (420b - 2604a b + 6636a b - 8484a b + 5376a b - 1344a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 300b + 1980a b - 5580a b + 8820a b - 8280a b + 4320a b +--R + +--R 6 +--R - 960a +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (90b - 558a b + 1422a b - 1818a b + 1152a b - 288a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 6b + 30a b - 54a b + 42a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 11 +--R (12b - 36a b + 36a b - 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 9 +--R (- 60b + 300a b - 540a b + 420a b - 120a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (120b - 744a b + 1896a b - 2424a b + 1536a b - 384a b) +--R * +--R 7 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 120b + 792a b - 2232a b + 3528a b - 3312a b + 1728a b +--R + +--R 6 +--R - 384a +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (60b - 372a b + 948a b - 1212a b + 768a b - 192a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 12b + 60a b - 108a b + 84a b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 5 2 4 3 3 12 +--R (b - 3a b + 3a b - a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 10 +--R (- 6b + 30a b - 54a b + 42a b - 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (15b - 93a b + 237a b - 303a b + 192a b - 48a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 20b + 132a b - 372a b + 588a b - 552a b + 288a b - 64a ) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (15b - 93a b + 237a b - 303a b + 192a b - 48a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 5 +--R (- 6b + 30a b - 54a b + 42a b - 12a b )cosh(x) + b - 3a b +--R + +--R 2 4 3 3 +--R 3a b - a b +--R * +--R 6 +--R tanh(x) +--R + +--R 5 2 4 3 3 12 +--R (3a b - 6a b + 3a b )sinh(x) +--R + +--R 5 2 4 3 3 11 +--R (36a b - 72a b + 36a b )cosh(x)sinh(x) +--R + +--R 5 2 4 3 3 2 5 2 4 3 3 +--R (198a b - 396a b + 198a b )cosh(x) - 18a b + 72a b - 90a b +--R + +--R 4 2 +--R 36a b +--R * +--R 10 +--R sinh(x) +--R + +--R 5 2 4 3 3 3 +--R (660a b - 1320a b + 660a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 180a b + 720a b - 900a b + 360a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 +--R (1485a b - 2970a b + 1485a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 810a b + 3240a b - 4050a b + 1620a b )cosh(x) + 45a b +--R + +--R 2 4 3 3 4 2 5 +--R - 234a b + 477a b - 432a b + 144a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 5 +--R (2376a b - 4752a b + 2376a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 2160a b + 8640a b - 10800a b + 4320a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (360a b - 1872a b + 3816a b - 3456a b + 1152a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 2 4 3 3 6 +--R (2772a b - 5544a b + 2772a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 3780a b + 15120a b - 18900a b + 7560a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (1260a b - 6552a b + 13356a b - 12096a b + 4032a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 60a b + 336a b - 780a b + 984a b - 672a b + 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 4 3 3 7 +--R (2376a b - 4752a b + 2376a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 4536a b + 18144a b - 22680a b + 9072a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (2520a b - 13104a b + 26712a b - 24192a b + 8064a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 360a b + 2016a b - 4680a b + 5904a b - 4032a b + 1152a ) +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 4 3 3 8 +--R (1485a b - 2970a b + 1485a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 3780a b + 15120a b - 18900a b + 7560a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (3150a b - 16380a b + 33390a b - 30240a b + 10080a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 900a b + 5040a b - 11700a b + 14760a b - 10080a b +--R + +--R 6 +--R 2880a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 45a b - 234a b + 477a b - 432a b + 144a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 4 3 3 9 +--R (660a b - 1320a b + 660a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 2160a b + 8640a b - 10800a b + 4320a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (2520a b - 13104a b + 26712a b - 24192a b + 8064a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 1200a b + 6720a b - 15600a b + 19680a b - 13440a b +--R + +--R 6 +--R 3840a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (180a b - 936a b + 1908a b - 1728a b + 576a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 10 +--R (198a b - 396a b + 198a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (- 810a b + 3240a b - 4050a b + 1620a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (1260a b - 6552a b + 13356a b - 12096a b + 4032a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 900a b + 5040a b - 11700a b + 14760a b - 10080a b +--R + +--R 6 +--R 2880a +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (270a b - 1404a b + 2862a b - 2592a b + 864a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R - 18a b + 72a b - 90a b + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 11 +--R (36a b - 72a b + 36a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 9 +--R (- 180a b + 720a b - 900a b + 360a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (360a b - 1872a b + 3816a b - 3456a b + 1152a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 360a b + 2016a b - 4680a b + 5904a b - 4032a b + 1152a ) +--R * +--R 5 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (180a b - 936a b + 1908a b - 1728a b + 576a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 36a b + 144a b - 180a b + 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 12 +--R (3a b - 6a b + 3a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 10 +--R (- 18a b + 72a b - 90a b + 36a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 8 +--R (45a b - 234a b + 477a b - 432a b + 144a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 60a b + 336a b - 780a b + 984a b - 672a b + 192a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (45a b - 234a b + 477a b - 432a b + 144a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 2 4 3 3 +--R (- 18a b + 72a b - 90a b + 36a b )cosh(x) + 3a b - 6a b + 3a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 4 3 3 12 2 4 3 3 11 +--R (3a b - 3a b )sinh(x) + (36a b - 36a b )cosh(x)sinh(x) +--R + +--R 2 4 3 3 2 2 4 3 3 4 2 10 +--R ((198a b - 198a b )cosh(x) - 18a b + 54a b - 36a b )sinh(x) +--R + +--R 2 4 3 3 3 +--R (660a b - 660a b )cosh(x) +--R + +--R 2 4 3 3 4 2 +--R (- 180a b + 540a b - 360a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 4 3 3 4 +--R (1485a b - 1485a b )cosh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (- 810a b + 2430a b - 1620a b )cosh(x) + 45a b - 189a b +--R + +--R 4 2 5 +--R 288a b - 144a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 4 3 3 5 +--R (2376a b - 2376a b )cosh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (- 2160a b + 6480a b - 4320a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (360a b - 1512a b + 2304a b - 1152a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 4 3 3 6 +--R (2772a b - 2772a b )cosh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 3780a b + 11340a b - 7560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (1260a b - 5292a b + 8064a b - 4032a b)cosh(x) - 60a b +--R + +--R 3 3 4 2 5 6 +--R 276a b - 504a b + 480a b - 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 7 +--R (2376a b - 2376a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 4536a b + 13608a b - 9072a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (2520a b - 10584a b + 16128a b - 8064a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 360a b + 1656a b - 3024a b + 2880a b - 1152a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 8 +--R (1485a b - 1485a b )cosh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (- 3780a b + 11340a b - 7560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (3150a b - 13230a b + 20160a b - 10080a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (- 900a b + 4140a b - 7560a b + 7200a b - 2880a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R 45a b - 189a b + 288a b - 144a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 9 +--R (660a b - 660a b )cosh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 2160a b + 6480a b - 4320a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (2520a b - 10584a b + 16128a b - 8064a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 1200a b + 5520a b - 10080a b + 9600a b - 3840a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (180a b - 756a b + 1152a b - 576a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 10 +--R (198a b - 198a b )cosh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 810a b + 2430a b - 1620a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (1260a b - 5292a b + 8064a b - 4032a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 900a b + 4140a b - 7560a b + 7200a b - 2880a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (270a b - 1134a b + 1728a b - 864a b)cosh(x) - 18a b +--R + +--R 3 3 4 2 +--R 54a b - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 11 +--R (36a b - 36a b )cosh(x) +--R + +--R 2 4 3 3 4 2 9 +--R (- 180a b + 540a b - 360a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (360a b - 1512a b + 2304a b - 1152a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 360a b + 1656a b - 3024a b + 2880a b - 1152a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (180a b - 756a b + 1152a b - 576a b)cosh(x) +--R + +--R 2 4 3 3 4 2 +--R (- 36a b + 108a b - 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 12 2 4 3 3 4 2 10 +--R (3a b - 3a b )cosh(x) + (- 18a b + 54a b - 36a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (45a b - 189a b + 288a b - 144a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 60a b + 276a b - 504a b + 480a b - 192a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (45a b - 189a b + 288a b - 144a b)cosh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (- 18a b + 54a b - 36a b )cosh(x) + 3a b - 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 3 12 3 3 11 +--R a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 4 2 10 +--R (66a b cosh(x) - 6a b + 12a b )sinh(x) +--R + +--R 3 3 3 3 3 4 2 9 +--R (220a b cosh(x) + (- 60a b + 120a b )cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 4 2 2 3 3 4 2 +--R 495a b cosh(x) + (- 270a b + 540a b )cosh(x) + 15a b - 48a b +--R + +--R 5 +--R 48a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 3 5 3 3 4 2 3 +--R 792a b cosh(x) + (- 720a b + 1440a b )cosh(x) +--R + +--R 3 3 4 2 5 +--R (120a b - 384a b + 384a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 3 6 3 3 4 2 4 +--R 924a b cosh(x) + (- 1260a b + 2520a b )cosh(x) +--R + +--R 3 3 4 2 5 2 3 3 4 2 5 6 +--R (420a b - 1344a b + 1344a b)cosh(x) - 20a b + 72a b - 96a b + 64a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 7 3 3 4 2 5 +--R 792a b cosh(x) + (- 1512a b + 3024a b )cosh(x) +--R + +--R 3 3 4 2 5 3 +--R (840a b - 2688a b + 2688a b)cosh(x) +--R + +--R 3 3 4 2 5 6 +--R (- 120a b + 432a b - 576a b + 384a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 3 8 3 3 4 2 6 +--R 495a b cosh(x) + (- 1260a b + 2520a b )cosh(x) +--R + +--R 3 3 4 2 5 4 +--R (1050a b - 3360a b + 3360a b)cosh(x) +--R + +--R 3 3 4 2 5 6 2 3 3 4 2 +--R (- 300a b + 1080a b - 1440a b + 960a )cosh(x) + 15a b - 48a b +--R + +--R 5 +--R 48a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 9 3 3 4 2 7 +--R 220a b cosh(x) + (- 720a b + 1440a b )cosh(x) +--R + +--R 3 3 4 2 5 5 +--R (840a b - 2688a b + 2688a b)cosh(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- 400a b + 1440a b - 1920a b + 1280a )cosh(x) +--R + +--R 3 3 4 2 5 +--R (60a b - 192a b + 192a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 10 3 3 4 2 8 +--R 66a b cosh(x) + (- 270a b + 540a b )cosh(x) +--R + +--R 3 3 4 2 5 6 +--R (420a b - 1344a b + 1344a b)cosh(x) +--R + +--R 3 3 4 2 5 6 4 +--R (- 300a b + 1080a b - 1440a b + 960a )cosh(x) +--R + +--R 3 3 4 2 5 2 3 3 4 2 +--R (90a b - 288a b + 288a b)cosh(x) - 6a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 11 3 3 4 2 9 +--R 12a b cosh(x) + (- 60a b + 120a b )cosh(x) +--R + +--R 3 3 4 2 5 7 +--R (120a b - 384a b + 384a b)cosh(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 120a b + 432a b - 576a b + 384a )cosh(x) +--R + +--R 3 3 4 2 5 3 3 3 4 2 +--R (60a b - 192a b + 192a b)cosh(x) + (- 12a b + 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 12 3 3 4 2 10 +--R a b cosh(x) + (- 6a b + 12a b )cosh(x) +--R + +--R 3 3 4 2 5 8 +--R (15a b - 48a b + 48a b)cosh(x) +--R + +--R 3 3 4 2 5 6 6 +--R (- 20a b + 72a b - 96a b + 64a )cosh(x) +--R + +--R 3 3 4 2 5 4 3 3 4 2 2 3 3 +--R (15a b - 48a b + 48a b)cosh(x) + (- 6a b + 12a b )cosh(x) + a b +--R Type: Expression(Integer) +--E 318 + +--S 319 of 510 +m0061b:= a0061.2-r0061 +--R +--R +--R (271) +--R 6 5 2 4 3 3 4 2 8 +--R (- 3b + 14a b - 27a b + 24a b - 8a b )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (- 24b + 112a b - 216a b + 192a b - 64a b )cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- 84b + 392a b - 756a b + 672a b - 224a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 12b - 80a b + 220a b - 312a b + 224a b - 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 168b + 784a b - 1512a b + 1344a b - 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (72b - 480a b + 1320a b - 1872a b + 1344a b - 384a b) +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 210b + 980a b - 1890a b + 1680a b - 560a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 180b - 1200a b + 3300a b - 4680a b + 3360a b +--R + +--R 5 +--R - 960a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R - 18b + 132a b - 434a b + 800a b - 864a b + 512a b - 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 168b + 784a b - 1512a b + 1344a b - 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 240b - 1600a b + 4400a b - 6240a b + 4480a b +--R + +--R 5 +--R - 1280a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 72b + 528a b - 1736a b + 3200a b - 3456a b +--R + +--R 5 6 +--R 2048a b - 512a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 84b + 392a b - 756a b + 672a b - 224a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 180b - 1200a b + 3300a b - 4680a b + 3360a b +--R + +--R 5 +--R - 960a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 108b + 792a b - 2604a b + 4800a b - 5184a b +--R + +--R 5 6 +--R 3072a b - 768a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 12b - 80a b + 220a b - 312a b + 224a b - 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (- 24b + 112a b - 216a b + 192a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (72b - 480a b + 1320a b - 1872a b + 1344a b - 384a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 72b + 528a b - 1736a b + 3200a b - 3456a b +--R + +--R 5 6 +--R 2048a b - 512a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (24b - 160a b + 440a b - 624a b + 448a b - 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (- 3b + 14a b - 27a b + 24a b - 8a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (12b - 80a b + 220a b - 312a b + 224a b - 64a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 18b + 132a b - 434a b + 800a b - 864a b + 512a b +--R + +--R 6 +--R - 128a +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (12b - 80a b + 220a b - 312a b + 224a b - 64a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 3b + 14a b - 27a b + 24a b - 8a b +--R * +--R 4 +--R tanh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (- 6a b + 22a b - 32a b + 16a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 48a b + 176a b - 256a b + 128a b )cosh(x)sinh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 168a b + 616a b - 896a b + 448a b )cosh(x) + 24a b +--R + +--R 2 4 3 3 4 2 5 +--R - 136a b + 304a b - 320a b + 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 336a b + 1232a b - 1792a b + 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (144a b - 816a b + 1824a b - 1920a b + 768a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 420a b + 1540a b - 2240a b + 1120a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (360a b - 2040a b + 4560a b - 4800a b + 1920a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 36a b + 228a b - 640a b + 960a b - 768a b + 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 336a b + 1232a b - 1792a b + 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (480a b - 2720a b + 6080a b - 6400a b + 2560a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 144a b + 912a b - 2560a b + 3840a b - 3072a b +--R + +--R 6 +--R 1024a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 168a b + 616a b - 896a b + 448a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (360a b - 2040a b + 4560a b - 4800a b + 1920a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 216a b + 1368a b - 3840a b + 5760a b - 4608a b +--R + +--R 6 +--R 1536a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 24a b - 136a b + 304a b - 320a b + 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 48a b + 176a b - 256a b + 128a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (144a b - 816a b + 1824a b - 1920a b + 768a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 144a b + 912a b - 2560a b + 3840a b - 3072a b +--R + +--R 6 +--R 1024a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (48a b - 272a b + 608a b - 640a b + 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (- 6a b + 22a b - 32a b + 16a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (24a b - 136a b + 304a b - 320a b + 128a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (- 36a b + 228a b - 640a b + 960a b - 768a b + 256a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 5 +--R (24a b - 136a b + 304a b - 320a b + 128a b)cosh(x) - 6a b +--R + +--R 2 4 3 3 4 2 +--R 22a b - 32a b + 16a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 3a b + 8a b - 8a b )sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 24a b + 64a b - 64a b )cosh(x)sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 4 2 +--R (- 84a b + 224a b - 224a b )cosh(x) + 12a b - 56a b + 96a b +--R + +--R 5 +--R - 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (- 168a b + 448a b - 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (72a b - 336a b + 576a b - 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 210a b + 560a b - 560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 +--R (180a b - 840a b + 1440a b - 960a b)cosh(x) - 18a b + 96a b +--R + +--R 4 2 5 6 +--R - 224a b + 256a b - 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 168a b + 448a b - 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (240a b - 1120a b + 1920a b - 1280a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 72a b + 384a b - 896a b + 1024a b - 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (- 84a b + 224a b - 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (180a b - 840a b + 1440a b - 960a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (- 108a b + 576a b - 1344a b + 1536a b - 768a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R 12a b - 56a b + 96a b - 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 24a b + 64a b - 64a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (72a b - 336a b + 576a b - 384a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 72a b + 384a b - 896a b + 1024a b - 512a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (24a b - 112a b + 192a b - 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 3a b + 8a b - 8a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (12a b - 56a b + 96a b - 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 18a b + 96a b - 224a b + 256a b - 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 4 2 +--R (12a b - 56a b + 96a b - 64a b)cosh(x) - 3a b + 8a b - 8a b +--R * +--R +--------+ +-------+ +--R | 2 tanh(x)\|- b + a +--R \|a b - a atanh(-----------------) +--R +-+ +--R \|a +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (3b - 14a b + 27a b - 24a b + 8a b )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (24b - 112a b + 216a b - 192a b + 64a b )cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (84b - 392a b + 756a b - 672a b + 224a b )cosh(x) - 12b +--R + +--R 5 2 4 3 3 4 2 5 +--R 80a b - 220a b + 312a b - 224a b + 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (168b - 784a b + 1512a b - 1344a b + 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 72b + 480a b - 1320a b + 1872a b - 1344a b +--R + +--R 5 +--R 384a b +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (210b - 980a b + 1890a b - 1680a b + 560a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 180b + 1200a b - 3300a b + 4680a b - 3360a b +--R + +--R 5 +--R 960a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 18b - 132a b + 434a b - 800a b + 864a b - 512a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (168b - 784a b + 1512a b - 1344a b + 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 240b + 1600a b - 4400a b + 6240a b - 4480a b +--R + +--R 5 +--R 1280a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 72b - 528a b + 1736a b - 3200a b + 3456a b - 2048a b +--R + +--R 6 +--R 512a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (84b - 392a b + 756a b - 672a b + 224a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 180b + 1200a b - 3300a b + 4680a b - 3360a b +--R + +--R 5 +--R 960a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 108b - 792a b + 2604a b - 4800a b + 5184a b +--R + +--R 5 6 +--R - 3072a b + 768a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 12b + 80a b - 220a b + 312a b - 224a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (24b - 112a b + 216a b - 192a b + 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 72b + 480a b - 1320a b + 1872a b - 1344a b +--R + +--R 5 +--R 384a b +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 72b - 528a b + 1736a b - 3200a b + 3456a b - 2048a b +--R + +--R 6 +--R 512a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 24b + 160a b - 440a b + 624a b - 448a b + 128a b) +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (3b - 14a b + 27a b - 24a b + 8a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b + 80a b - 220a b + 312a b - 224a b + 64a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (18b - 132a b + 434a b - 800a b + 864a b - 512a b + 128a ) +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 12b + 80a b - 220a b + 312a b - 224a b + 64a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 3b - 14a b + 27a b - 24a b + 8a b +--R * +--R 4 +--R tanh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (6a b - 22a b + 32a b - 16a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (48a b - 176a b + 256a b - 128a b )cosh(x)sinh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (168a b - 616a b + 896a b - 448a b )cosh(x) - 24a b +--R + +--R 2 4 3 3 4 2 5 +--R 136a b - 304a b + 320a b - 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (336a b - 1232a b + 1792a b - 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 144a b + 816a b - 1824a b + 1920a b - 768a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (420a b - 1540a b + 2240a b - 1120a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 360a b + 2040a b - 4560a b + 4800a b - 1920a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 36a b - 228a b + 640a b - 960a b + 768a b - 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (336a b - 1232a b + 1792a b - 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 480a b + 2720a b - 6080a b + 6400a b - 2560a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 144a b - 912a b + 2560a b - 3840a b + 3072a b +--R + +--R 6 +--R - 1024a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (168a b - 616a b + 896a b - 448a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 360a b + 2040a b - 4560a b + 4800a b - 1920a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 216a b - 1368a b + 3840a b - 5760a b + 4608a b +--R + +--R 6 +--R - 1536a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 24a b + 136a b - 304a b + 320a b - 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (48a b - 176a b + 256a b - 128a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 144a b + 816a b - 1824a b + 1920a b - 768a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 144a b - 912a b + 2560a b - 3840a b + 3072a b +--R + +--R 6 +--R - 1024a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 48a b + 272a b - 608a b + 640a b - 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (6a b - 22a b + 32a b - 16a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 24a b + 136a b - 304a b + 320a b - 128a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (36a b - 228a b + 640a b - 960a b + 768a b - 256a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 5 +--R (- 24a b + 136a b - 304a b + 320a b - 128a b)cosh(x) + 6a b +--R + +--R 2 4 3 3 4 2 +--R - 22a b + 32a b - 16a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (3a b - 8a b + 8a b )sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (24a b - 64a b + 64a b )cosh(x)sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 4 2 +--R (84a b - 224a b + 224a b )cosh(x) - 12a b + 56a b - 96a b +--R + +--R 5 +--R 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (168a b - 448a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 72a b + 336a b - 576a b + 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (210a b - 560a b + 560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (- 180a b + 840a b - 1440a b + 960a b)cosh(x) + 18a b +--R + +--R 3 3 4 2 5 6 +--R - 96a b + 224a b - 256a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (168a b - 448a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 240a b + 1120a b - 1920a b + 1280a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (72a b - 384a b + 896a b - 1024a b + 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (84a b - 224a b + 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 180a b + 840a b - 1440a b + 960a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 2 4 +--R (108a b - 576a b + 1344a b - 1536a b + 768a )cosh(x) - 12a b +--R + +--R 3 3 4 2 5 +--R 56a b - 96a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (24a b - 64a b + 64a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 72a b + 336a b - 576a b + 384a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (72a b - 384a b + 896a b - 1024a b + 512a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 24a b + 112a b - 192a b + 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (3a b - 8a b + 8a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b + 56a b - 96a b + 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (18a b - 96a b + 224a b - 256a b + 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 4 2 +--R (- 12a b + 56a b - 96a b + 64a b)cosh(x) + 3a b - 8a b + 8a b +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R * +--R +--------+ +--R 2 2 | 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a)\|a b - a +--R atan(-----------------------------------------------------------------) +--R 2 +--R 2a b - 2a +--R + +--R 5 4 2 3 3 2 4 6 +--R (6b - 28a b + 54a b - 48a b + 16a b)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (36b - 168a b + 324a b - 288a b + 96a b)cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (90b - 420a b + 810a b - 720a b + 240a b)cosh(x) - 18b +--R + +--R 4 2 3 3 2 4 5 +--R 120a b - 330a b + 468a b - 336a b + 96a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (120b - 560a b + 1080a b - 960a b + 320a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 72b + 480a b - 1320a b + 1872a b - 1344a b + 384a ) +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (90b - 420a b + 810a b - 720a b + 240a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 108b + 720a b - 1980a b + 2808a b - 2016a b + 576a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 18b - 116a b + 258a b - 240a b + 80a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (36b - 168a b + 324a b - 288a b + 96a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 72b + 480a b - 1320a b + 1872a b - 1344a b + 384a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (36b - 232a b + 516a b - 480a b + 160a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (6b - 28a b + 54a b - 48a b + 16a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 18b + 120a b - 330a b + 468a b - 336a b + 96a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (18b - 116a b + 258a b - 240a b + 80a b)cosh(x) - 6b +--R + +--R 4 2 3 3 2 +--R 24a b - 30a b + 12a b +--R * +--R 4 +--R tanh(x) +--R + +--R 5 4 2 3 8 +--R (- 3b + 11a b - 8a b )sinh(x) +--R + +--R 5 4 2 3 7 +--R (- 24b + 88a b - 64a b )cosh(x)sinh(x) +--R + +--R 5 4 2 3 2 5 4 +--R (- 84b + 308a b - 224a b )cosh(x) + 12b - 68a b +--R + +--R 2 3 3 2 +--R 120a b - 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 +--R (- 168b + 616a b - 448a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (72b - 408a b + 720a b - 384a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 4 +--R (- 210b + 770a b - 560a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 +--R (180b - 1020a b + 1800a b - 960a b )cosh(x) - 18b +--R + +--R 4 2 3 3 2 4 +--R 114a b - 272a b + 304a b - 128a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 5 +--R (- 168b + 616a b - 448a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (240b - 1360a b + 2400a b - 1280a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 72b + 456a b - 1088a b + 1216a b - 512a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 6 +--R (- 84b + 308a b - 224a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (180b - 1020a b + 1800a b - 960a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 108b + 684a b - 1632a b + 1824a b - 768a b)cosh(x) +--R + +--R 5 4 2 3 3 2 +--R 12b - 68a b + 120a b - 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 7 +--R (- 24b + 88a b - 64a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (72b - 408a b + 720a b - 384a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 72b + 456a b - 1088a b + 1216a b - 512a b)cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (24b - 136a b + 240a b - 128a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 8 +--R (- 3b + 11a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (12b - 68a b + 120a b - 64a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 18b + 114a b - 272a b + 304a b - 128a b)cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 2 3 +--R (12b - 68a b + 120a b - 64a b )cosh(x) - 3b + 11a b - 8a b +--R * +--R 3 +--R tanh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (12a b - 44a b + 64a b - 32a b)sinh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (72a b - 264a b + 384a b - 192a b)cosh(x)sinh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (180a b - 660a b + 960a b - 480a b)cosh(x) - 36a b +--R + +--R 2 3 3 2 4 5 +--R 204a b - 456a b + 480a b - 192a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (240a b - 880a b + 1280a b - 640a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 144a b + 816a b - 1824a b + 1920a b - 768a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (180a b - 660a b + 960a b - 480a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 216a b + 1224a b - 2736a b + 2880a b - 1152a )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R 36a b - 196a b + 320a b - 160a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (72a b - 264a b + 384a b - 192a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 144a b + 816a b - 1824a b + 1920a b - 768a )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (72a b - 392a b + 640a b - 320a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (12a b - 44a b + 64a b - 32a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 36a b + 204a b - 456a b + 480a b - 192a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 2 3 +--R (36a b - 196a b + 320a b - 160a b)cosh(x) - 12a b + 36a b +--R + +--R 3 2 +--R - 24a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 2 3 8 4 2 3 7 +--R (- 5a b + 8a b )sinh(x) + (- 40a b + 64a b )cosh(x)sinh(x) +--R + +--R 4 2 3 2 4 2 3 3 2 +--R ((- 140a b + 224a b )cosh(x) + 20a b - 72a b + 64a b ) +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 +--R (- 280a b + 448a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (120a b - 432a b + 384a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 4 +--R (- 350a b + 560a b )cosh(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (300a b - 1080a b + 960a b )cosh(x) - 30a b + 128a b +--R + +--R 3 2 4 +--R - 208a b + 128a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 5 +--R (- 280a b + 448a b )cosh(x) +--R + +--R 4 2 3 3 2 3 +--R (400a b - 1440a b + 1280a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 120a b + 512a b - 832a b + 512a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 6 +--R (- 140a b + 224a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (300a b - 1080a b + 960a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (- 180a b + 768a b - 1248a b + 768a b)cosh(x) + 20a b +--R + +--R 2 3 3 2 +--R - 72a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 7 +--R (- 40a b + 64a b )cosh(x) +--R + +--R 4 2 3 3 2 5 +--R (120a b - 432a b + 384a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 120a b + 512a b - 832a b + 512a b)cosh(x) +--R + +--R 4 2 3 3 2 +--R (40a b - 144a b + 128a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 8 4 2 3 3 2 6 +--R (- 5a b + 8a b )cosh(x) + (20a b - 72a b + 64a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 30a b + 128a b - 208a b + 128a b)cosh(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (20a b - 72a b + 64a b )cosh(x) - 5a b + 8a b +--R * +--R tanh(x) +--R + +--R 2 3 3 2 4 6 +--R (6a b - 16a b + 16a b)sinh(x) +--R + +--R 2 3 3 2 4 5 +--R (36a b - 96a b + 96a b)cosh(x)sinh(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 +--R (90a b - 240a b + 240a b)cosh(x) - 18a b + 84a b - 144a b +--R + +--R 5 +--R 96a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 +--R (120a b - 320a b + 320a b)cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (- 72a b + 336a b - 576a b + 384a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 4 4 +--R (90a b - 240a b + 240a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 +--R (- 108a b + 504a b - 864a b + 576a )cosh(x) + 18a b - 80a b +--R + +--R 4 +--R 80a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 4 5 +--R (36a b - 96a b + 96a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 72a b + 336a b - 576a b + 384a )cosh(x) +--R + +--R 2 3 3 2 4 +--R (36a b - 160a b + 160a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3 2 4 6 +--R (6a b - 16a b + 16a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 18a b + 84a b - 144a b + 96a )cosh(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 +--R (18a b - 80a b + 80a b)cosh(x) - 6a b + 12a b +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|a b - a +--R / +--R 2 6 3 5 4 4 5 3 6 2 8 +--R (8a b - 32a b + 48a b - 32a b + 8a b )sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (64a b - 256a b + 384a b - 256a b + 64a b )cosh(x)sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (224a b - 896a b + 1344a b - 896a b + 224a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 32a b + 192a b - 448a b + 512a b - 288a b + 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 3 +--R (448a b - 1792a b + 2688a b - 1792a b + 448a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 192a b + 1152a b - 2688a b + 3072a b - 1728a b +--R + +--R 7 +--R 384a b +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 4 +--R (560a b - 2240a b + 3360a b - 2240a b + 560a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 480a b + 2880a b - 6720a b + 7680a b - 4320a b +--R + +--R 7 +--R 960a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R 48a b - 320a b + 928a b - 1472a b + 1328a b - 640a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 5 +--R (448a b - 1792a b + 2688a b - 1792a b + 448a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 640a b + 3840a b - 8960a b + 10240a b - 5760a b +--R + +--R 7 +--R 1280a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 192a b - 1280a b + 3712a b - 5888a b + 5312a b +--R + +--R 7 8 +--R - 2560a b + 512a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 6 +--R (224a b - 896a b + 1344a b - 896a b + 224a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 480a b + 2880a b - 6720a b + 7680a b - 4320a b +--R + +--R 7 +--R 960a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 288a b - 1920a b + 5568a b - 8832a b + 7968a b +--R + +--R 7 8 +--R - 3840a b + 768a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 32a b + 192a b - 448a b + 512a b - 288a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (64a b - 256a b + 384a b - 256a b + 64a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 192a b + 1152a b - 2688a b + 3072a b - 1728a b +--R + +--R 7 +--R 384a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 192a b - 1280a b + 3712a b - 5888a b + 5312a b +--R + +--R 7 8 +--R - 2560a b + 512a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (- 64a b + 384a b - 896a b + 1024a b - 576a b + 128a b) +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 8 +--R (8a b - 32a b + 48a b - 32a b + 8a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 6 +--R (- 32a b + 192a b - 448a b + 512a b - 288a b + 64a b)cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 48a b - 320a b + 928a b - 1472a b + 1328a b - 640a b +--R + +--R 8 +--R 128a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (- 32a b + 192a b - 448a b + 512a b - 288a b + 64a b)cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 8a b - 32a b + 48a b - 32a b + 8a b +--R * +--R 4 +--R tanh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 +--R (16a b - 48a b + 48a b - 16a b )sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (128a b - 384a b + 384a b - 128a b )cosh(x)sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 3 5 +--R (448a b - 1344a b + 1344a b - 448a b )cosh(x) - 64a b +--R + +--R 4 4 5 3 6 2 7 +--R 320a b - 576a b + 448a b - 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 3 +--R (896a b - 2688a b + 2688a b - 896a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 384a b + 1920a b - 3456a b + 2688a b - 768a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 4 +--R (1120a b - 3360a b + 3360a b - 1120a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 2 +--R (- 960a b + 4800a b - 8640a b + 6720a b - 1920a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R 96a b - 544a b + 1312a b - 1632a b + 1024a b - 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 5 +--R (896a b - 2688a b + 2688a b - 896a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 1280a b + 6400a b - 11520a b + 8960a b - 2560a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (384a b - 2176a b + 5248a b - 6528a b + 4096a b - 1024a ) +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 6 +--R (448a b - 1344a b + 1344a b - 448a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 4 +--R (- 960a b + 4800a b - 8640a b + 6720a b - 1920a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (576a b - 3264a b + 7872a b - 9792a b + 6144a b - 1536a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R - 64a b + 320a b - 576a b + 448a b - 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (128a b - 384a b + 384a b - 128a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 5 +--R (- 384a b + 1920a b - 3456a b + 2688a b - 768a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (384a b - 2176a b + 5248a b - 6528a b + 4096a b - 1024a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 128a b + 640a b - 1152a b + 896a b - 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 +--R (16a b - 48a b + 48a b - 16a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 6 +--R (- 64a b + 320a b - 576a b + 448a b - 128a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (96a b - 544a b + 1312a b - 1632a b + 1024a b - 256a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 2 3 5 +--R (- 64a b + 320a b - 576a b + 448a b - 128a b)cosh(x) + 16a b +--R + +--R 4 4 5 3 6 2 +--R - 48a b + 48a b - 16a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 4 5 3 6 2 8 +--R (8a b - 16a b + 8a b )sinh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (64a b - 128a b + 64a b )cosh(x)sinh(x) +--R + +--R 4 4 5 3 6 2 2 4 4 5 3 6 2 +--R (224a b - 448a b + 224a b )cosh(x) - 32a b + 128a b - 160a b +--R + +--R 7 +--R 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 3 +--R (448a b - 896a b + 448a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (- 192a b + 768a b - 960a b + 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 4 +--R (560a b - 1120a b + 560a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 4 4 +--R (- 480a b + 1920a b - 2400a b + 960a b)cosh(x) + 48a b +--R + +--R 5 3 6 2 7 8 +--R - 224a b + 432a b - 384a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 5 +--R (448a b - 896a b + 448a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (- 640a b + 2560a b - 3200a b + 1280a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (192a b - 896a b + 1728a b - 1536a b + 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 6 +--R (224a b - 448a b + 224a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (- 480a b + 1920a b - 2400a b + 960a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 2 4 4 +--R (288a b - 1344a b + 2592a b - 2304a b + 768a )cosh(x) - 32a b +--R + +--R 5 3 6 2 7 +--R 128a b - 160a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (64a b - 128a b + 64a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (- 192a b + 768a b - 960a b + 384a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 3 +--R (192a b - 896a b + 1728a b - 1536a b + 512a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (- 64a b + 256a b - 320a b + 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 8 +--R (8a b - 16a b + 8a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 6 +--R (- 32a b + 128a b - 160a b + 64a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (48a b - 224a b + 432a b - 384a b + 128a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 4 4 5 3 6 2 +--R (- 32a b + 128a b - 160a b + 64a b)cosh(x) + 8a b - 16a b + 8a b +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|a b - a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 510 +d0061b:= D(m0061b,x) +--R +--R +--R (272) +--R 3 12 3 11 +--R b sinh(x) + 12b cosh(x)sinh(x) +--R + +--R 3 2 3 2 10 +--R (66b cosh(x) - 6b + 12a b )sinh(x) +--R + +--R 3 3 3 2 9 +--R (220b cosh(x) + (- 60b + 120a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R 495b cosh(x) + (- 270b + 540a b )cosh(x) + 15b - 48a b +--R + +--R 2 +--R 48a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 5 3 2 3 +--R 792b cosh(x) + (- 720b + 1440a b )cosh(x) +--R + +--R 3 2 2 +--R (120b - 384a b + 384a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 6 3 2 4 +--R 924b cosh(x) + (- 1260b + 2520a b )cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (420b - 1344a b + 1344a b)cosh(x) + 44b - 120a b + 96a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 7 3 2 5 +--R 792b cosh(x) + (- 1512b + 3024a b )cosh(x) +--R + +--R 3 2 2 3 +--R (840b - 2688a b + 2688a b)cosh(x) +--R + +--R 3 2 2 +--R (264b - 720a b + 576a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 8 3 2 6 +--R 495b cosh(x) + (- 1260b + 2520a b )cosh(x) +--R + +--R 3 2 2 4 +--R (1050b - 3360a b + 3360a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (660b - 1800a b + 1440a b)cosh(x) + 15b - 48a b + 48a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 9 3 2 7 +--R 220b cosh(x) + (- 720b + 1440a b )cosh(x) +--R + +--R 3 2 2 5 +--R (840b - 2688a b + 2688a b)cosh(x) +--R + +--R 3 2 2 3 +--R (880b - 2400a b + 1920a b)cosh(x) +--R + +--R 3 2 2 +--R (60b - 192a b + 192a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 10 3 2 8 +--R 66b cosh(x) + (- 270b + 540a b )cosh(x) +--R + +--R 3 2 2 6 +--R (420b - 1344a b + 1344a b)cosh(x) +--R + +--R 3 2 2 4 +--R (660b - 1800a b + 1440a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (90b - 288a b + 288a b)cosh(x) - 6b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 11 3 2 9 +--R 12b cosh(x) + (- 60b + 120a b )cosh(x) +--R + +--R 3 2 2 7 +--R (120b - 384a b + 384a b)cosh(x) +--R + +--R 3 2 2 5 +--R (264b - 720a b + 576a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (60b - 192a b + 192a b)cosh(x) + (- 12b + 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 12 3 2 10 +--R b cosh(x) + (- 6b + 12a b )cosh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (15b - 48a b + 48a b)cosh(x) + (44b - 120a b + 96a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (15b - 48a b + 48a b)cosh(x) + (- 6b + 12a b )cosh(x) + b +--R * +--R 6 +--R tanh(x) +--R + +--R 3 12 3 11 +--R - 3b sinh(x) - 36b cosh(x)sinh(x) +--R + +--R 3 2 3 2 10 +--R (- 198b cosh(x) + 18b - 36a b )sinh(x) +--R + +--R 3 3 3 2 9 +--R (- 660b cosh(x) + (180b - 360a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R - 1485b cosh(x) + (810b - 1620a b )cosh(x) - 45b + 144a b +--R + +--R 2 +--R - 144a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 5 3 2 3 +--R - 2376b cosh(x) + (2160b - 4320a b )cosh(x) +--R + +--R 3 2 2 +--R (- 360b + 1152a b - 1152a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 6 3 2 4 +--R - 2772b cosh(x) + (3780b - 7560a b )cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 1260b + 4032a b - 4032a b)cosh(x) + 60b - 24a b - 96a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 7 3 2 5 +--R - 2376b cosh(x) + (4536b - 9072a b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2520b + 8064a b - 8064a b)cosh(x) +--R + +--R 3 2 2 +--R (360b - 144a b - 576a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 8 3 2 6 +--R - 1485b cosh(x) + (3780b - 7560a b )cosh(x) +--R + +--R 3 2 2 4 +--R (- 3150b + 10080a b - 10080a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (900b - 360a b - 1440a b)cosh(x) - 45b + 144a b - 144a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 9 3 2 7 +--R - 660b cosh(x) + (2160b - 4320a b )cosh(x) +--R + +--R 3 2 2 5 +--R (- 2520b + 8064a b - 8064a b)cosh(x) +--R + +--R 3 2 2 3 +--R (1200b - 480a b - 1920a b)cosh(x) +--R + +--R 3 2 2 +--R (- 180b + 576a b - 576a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 10 3 2 8 +--R - 198b cosh(x) + (810b - 1620a b )cosh(x) +--R + +--R 3 2 2 6 +--R (- 1260b + 4032a b - 4032a b)cosh(x) +--R + +--R 3 2 2 4 +--R (900b - 360a b - 1440a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 270b + 864a b - 864a b)cosh(x) + 18b - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 11 3 2 9 +--R - 36b cosh(x) + (180b - 360a b )cosh(x) +--R + +--R 3 2 2 7 +--R (- 360b + 1152a b - 1152a b)cosh(x) +--R + +--R 3 2 2 5 +--R (360b - 144a b - 576a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 180b + 576a b - 576a b)cosh(x) + (36b - 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 12 3 2 10 +--R - 3b cosh(x) + (18b - 36a b )cosh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (- 45b + 144a b - 144a b)cosh(x) + (60b - 24a b - 96a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (- 45b + 144a b - 144a b)cosh(x) + (18b - 36a b )cosh(x) - 3b +--R * +--R 4 +--R tanh(x) +--R + +--R 3 12 3 11 +--R 3b sinh(x) + 36b cosh(x)sinh(x) +--R + +--R 3 2 3 2 10 +--R (198b cosh(x) - 18b + 36a b )sinh(x) +--R + +--R 3 3 3 2 9 +--R (660b cosh(x) + (- 180b + 360a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R 1485b cosh(x) + (- 810b + 1620a b )cosh(x) + 45b - 144a b +--R + +--R 2 +--R 144a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 5 3 2 3 +--R 2376b cosh(x) + (- 2160b + 4320a b )cosh(x) +--R + +--R 3 2 2 +--R (360b - 1152a b + 1152a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 6 3 2 4 +--R 2772b cosh(x) + (- 3780b + 7560a b )cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (1260b - 4032a b + 4032a b)cosh(x) - 60b + 216a b - 96a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 7 3 2 5 +--R 2376b cosh(x) + (- 4536b + 9072a b )cosh(x) +--R + +--R 3 2 2 3 +--R (2520b - 8064a b + 8064a b)cosh(x) +--R + +--R 3 2 2 +--R (- 360b + 1296a b - 576a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 8 3 2 6 +--R 1485b cosh(x) + (- 3780b + 7560a b )cosh(x) +--R + +--R 3 2 2 4 +--R (3150b - 10080a b + 10080a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 900b + 3240a b - 1440a b)cosh(x) + 45b - 144a b + 144a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 9 3 2 7 +--R 660b cosh(x) + (- 2160b + 4320a b )cosh(x) +--R + +--R 3 2 2 5 +--R (2520b - 8064a b + 8064a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 1200b + 4320a b - 1920a b)cosh(x) +--R + +--R 3 2 2 +--R (180b - 576a b + 576a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 10 3 2 8 +--R 198b cosh(x) + (- 810b + 1620a b )cosh(x) +--R + +--R 3 2 2 6 +--R (1260b - 4032a b + 4032a b)cosh(x) +--R + +--R 3 2 2 4 +--R (- 900b + 3240a b - 1440a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (270b - 864a b + 864a b)cosh(x) - 18b + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 11 3 2 9 +--R 36b cosh(x) + (- 180b + 360a b )cosh(x) +--R + +--R 3 2 2 7 +--R (360b - 1152a b + 1152a b)cosh(x) +--R + +--R 3 2 2 5 +--R (- 360b + 1296a b - 576a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (180b - 576a b + 576a b)cosh(x) + (- 36b + 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 12 3 2 10 +--R 3b cosh(x) + (- 18b + 36a b )cosh(x) +--R + +--R 3 2 2 8 +--R (45b - 144a b + 144a b)cosh(x) +--R + +--R 3 2 2 6 +--R (- 60b + 216a b - 96a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (45b - 144a b + 144a b)cosh(x) + (- 18b + 36a b )cosh(x) + 3b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 12 3 11 +--R - b sinh(x) - 12b cosh(x)sinh(x) +--R + +--R 3 2 3 2 10 +--R (- 66b cosh(x) + 6b - 12a b )sinh(x) +--R + +--R 3 3 3 2 9 +--R (- 220b cosh(x) + (60b - 120a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 3 2 2 +--R (- 495b cosh(x) + (270b - 540a b )cosh(x) - 15b + 48a b - 48a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 5 3 2 3 +--R - 792b cosh(x) + (720b - 1440a b )cosh(x) +--R + +--R 3 2 2 +--R (- 120b + 384a b - 384a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 6 3 2 4 +--R - 924b cosh(x) + (1260b - 2520a b )cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 420b + 1344a b - 1344a b)cosh(x) + 20b - 72a b + 96a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 7 3 2 5 +--R - 792b cosh(x) + (1512b - 3024a b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 840b + 2688a b - 2688a b)cosh(x) +--R + +--R 3 2 2 +--R (120b - 432a b + 576a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 8 3 2 6 +--R - 495b cosh(x) + (1260b - 2520a b )cosh(x) +--R + +--R 3 2 2 4 +--R (- 1050b + 3360a b - 3360a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (300b - 1080a b + 1440a b)cosh(x) - 15b + 48a b - 48a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 9 3 2 7 +--R - 220b cosh(x) + (720b - 1440a b )cosh(x) +--R + +--R 3 2 2 5 +--R (- 840b + 2688a b - 2688a b)cosh(x) +--R + +--R 3 2 2 3 +--R (400b - 1440a b + 1920a b)cosh(x) +--R + +--R 3 2 2 +--R (- 60b + 192a b - 192a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 10 3 2 8 +--R - 66b cosh(x) + (270b - 540a b )cosh(x) +--R + +--R 3 2 2 6 +--R (- 420b + 1344a b - 1344a b)cosh(x) +--R + +--R 3 2 2 4 +--R (300b - 1080a b + 1440a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 90b + 288a b - 288a b)cosh(x) + 6b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 11 3 2 9 +--R - 12b cosh(x) + (60b - 120a b )cosh(x) +--R + +--R 3 2 2 7 +--R (- 120b + 384a b - 384a b)cosh(x) +--R + +--R 3 2 2 5 +--R (120b - 432a b + 576a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 60b + 192a b - 192a b)cosh(x) + (12b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 12 3 2 10 +--R - b cosh(x) + (6b - 12a b )cosh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (- 15b + 48a b - 48a b)cosh(x) + (20b - 72a b + 96a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (- 15b + 48a b - 48a b)cosh(x) + (6b - 12a b )cosh(x) - b +--R / +--R 6 5 2 4 3 3 12 +--R (b - 3a b + 3a b - a b )sinh(x) +--R + +--R 6 5 2 4 3 3 11 +--R (12b - 36a b + 36a b - 12a b )cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (66b - 198a b + 198a b - 66a b )cosh(x) - 6b + 30a b +--R + +--R 2 4 3 3 4 2 +--R - 54a b + 42a b - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (220b - 660a b + 660a b - 220a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 60b + 300a b - 540a b + 420a b - 120a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (495b - 1485a b + 1485a b - 495a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- 270b + 1350a b - 2430a b + 1890a b - 540a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 15b - 93a b + 237a b - 303a b + 192a b - 48a b +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (792b - 2376a b + 2376a b - 792a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 720b + 3600a b - 6480a b + 5040a b - 1440a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (120b - 744a b + 1896a b - 2424a b + 1536a b - 384a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 6 +--R (924b - 2772a b + 2772a b - 924a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 1260b + 6300a b - 11340a b + 8820a b - 2520a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (420b - 2604a b + 6636a b - 8484a b + 5376a b - 1344a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R - 20b + 132a b - 372a b + 588a b - 552a b + 288a b - 64a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 7 +--R (792b - 2376a b + 2376a b - 792a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 1512b + 7560a b - 13608a b + 10584a b - 3024a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 840b - 5208a b + 13272a b - 16968a b + 10752a b +--R + +--R 5 +--R - 2688a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 120b + 792a b - 2232a b + 3528a b - 3312a b + 1728a b +--R + +--R 6 +--R - 384a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 8 +--R (495b - 1485a b + 1485a b - 495a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 1260b + 6300a b - 11340a b + 8820a b - 2520a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 1050b - 6510a b + 16590a b - 21210a b + 13440a b +--R + +--R 5 +--R - 3360a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 300b + 1980a b - 5580a b + 8820a b - 8280a b + 4320a b +--R + +--R 6 +--R - 960a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 15b - 93a b + 237a b - 303a b + 192a b - 48a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 9 +--R (220b - 660a b + 660a b - 220a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (- 720b + 3600a b - 6480a b + 5040a b - 1440a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 840b - 5208a b + 13272a b - 16968a b + 10752a b +--R + +--R 5 +--R - 2688a b +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 400b + 2640a b - 7440a b + 11760a b - 11040a b +--R + +--R 5 6 +--R 5760a b - 1280a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (60b - 372a b + 948a b - 1212a b + 768a b - 192a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 10 +--R (66b - 198a b + 198a b - 66a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (- 270b + 1350a b - 2430a b + 1890a b - 540a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (420b - 2604a b + 6636a b - 8484a b + 5376a b - 1344a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 300b + 1980a b - 5580a b + 8820a b - 8280a b + 4320a b +--R + +--R 6 +--R - 960a +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (90b - 558a b + 1422a b - 1818a b + 1152a b - 288a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 6b + 30a b - 54a b + 42a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 11 +--R (12b - 36a b + 36a b - 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 9 +--R (- 60b + 300a b - 540a b + 420a b - 120a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (120b - 744a b + 1896a b - 2424a b + 1536a b - 384a b) +--R * +--R 7 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 120b + 792a b - 2232a b + 3528a b - 3312a b + 1728a b +--R + +--R 6 +--R - 384a +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (60b - 372a b + 948a b - 1212a b + 768a b - 192a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 12b + 60a b - 108a b + 84a b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 5 2 4 3 3 12 +--R (b - 3a b + 3a b - a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 10 +--R (- 6b + 30a b - 54a b + 42a b - 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (15b - 93a b + 237a b - 303a b + 192a b - 48a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 20b + 132a b - 372a b + 588a b - 552a b + 288a b - 64a ) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (15b - 93a b + 237a b - 303a b + 192a b - 48a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 5 +--R (- 6b + 30a b - 54a b + 42a b - 12a b )cosh(x) + b - 3a b +--R + +--R 2 4 3 3 +--R 3a b - a b +--R * +--R 6 +--R tanh(x) +--R + +--R 5 2 4 3 3 12 +--R (3a b - 6a b + 3a b )sinh(x) +--R + +--R 5 2 4 3 3 11 +--R (36a b - 72a b + 36a b )cosh(x)sinh(x) +--R + +--R 5 2 4 3 3 2 5 2 4 3 3 +--R (198a b - 396a b + 198a b )cosh(x) - 18a b + 72a b - 90a b +--R + +--R 4 2 +--R 36a b +--R * +--R 10 +--R sinh(x) +--R + +--R 5 2 4 3 3 3 +--R (660a b - 1320a b + 660a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 180a b + 720a b - 900a b + 360a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 +--R (1485a b - 2970a b + 1485a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 810a b + 3240a b - 4050a b + 1620a b )cosh(x) + 45a b +--R + +--R 2 4 3 3 4 2 5 +--R - 234a b + 477a b - 432a b + 144a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 5 +--R (2376a b - 4752a b + 2376a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 2160a b + 8640a b - 10800a b + 4320a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (360a b - 1872a b + 3816a b - 3456a b + 1152a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 2 4 3 3 6 +--R (2772a b - 5544a b + 2772a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 3780a b + 15120a b - 18900a b + 7560a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (1260a b - 6552a b + 13356a b - 12096a b + 4032a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 60a b + 336a b - 780a b + 984a b - 672a b + 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 4 3 3 7 +--R (2376a b - 4752a b + 2376a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 4536a b + 18144a b - 22680a b + 9072a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (2520a b - 13104a b + 26712a b - 24192a b + 8064a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 360a b + 2016a b - 4680a b + 5904a b - 4032a b + 1152a ) +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 4 3 3 8 +--R (1485a b - 2970a b + 1485a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 3780a b + 15120a b - 18900a b + 7560a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (3150a b - 16380a b + 33390a b - 30240a b + 10080a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 900a b + 5040a b - 11700a b + 14760a b - 10080a b +--R + +--R 6 +--R 2880a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 45a b - 234a b + 477a b - 432a b + 144a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 4 3 3 9 +--R (660a b - 1320a b + 660a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 2160a b + 8640a b - 10800a b + 4320a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (2520a b - 13104a b + 26712a b - 24192a b + 8064a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 1200a b + 6720a b - 15600a b + 19680a b - 13440a b +--R + +--R 6 +--R 3840a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (180a b - 936a b + 1908a b - 1728a b + 576a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 10 +--R (198a b - 396a b + 198a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (- 810a b + 3240a b - 4050a b + 1620a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (1260a b - 6552a b + 13356a b - 12096a b + 4032a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 900a b + 5040a b - 11700a b + 14760a b - 10080a b +--R + +--R 6 +--R 2880a +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (270a b - 1404a b + 2862a b - 2592a b + 864a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R - 18a b + 72a b - 90a b + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 11 +--R (36a b - 72a b + 36a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 9 +--R (- 180a b + 720a b - 900a b + 360a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (360a b - 1872a b + 3816a b - 3456a b + 1152a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 360a b + 2016a b - 4680a b + 5904a b - 4032a b + 1152a ) +--R * +--R 5 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (180a b - 936a b + 1908a b - 1728a b + 576a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 36a b + 144a b - 180a b + 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 12 +--R (3a b - 6a b + 3a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 10 +--R (- 18a b + 72a b - 90a b + 36a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 8 +--R (45a b - 234a b + 477a b - 432a b + 144a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 60a b + 336a b - 780a b + 984a b - 672a b + 192a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (45a b - 234a b + 477a b - 432a b + 144a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 2 4 3 3 +--R (- 18a b + 72a b - 90a b + 36a b )cosh(x) + 3a b - 6a b + 3a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 4 3 3 12 2 4 3 3 11 +--R (3a b - 3a b )sinh(x) + (36a b - 36a b )cosh(x)sinh(x) +--R + +--R 2 4 3 3 2 2 4 3 3 4 2 10 +--R ((198a b - 198a b )cosh(x) - 18a b + 54a b - 36a b )sinh(x) +--R + +--R 2 4 3 3 3 +--R (660a b - 660a b )cosh(x) +--R + +--R 2 4 3 3 4 2 +--R (- 180a b + 540a b - 360a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 4 3 3 4 +--R (1485a b - 1485a b )cosh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (- 810a b + 2430a b - 1620a b )cosh(x) + 45a b - 189a b +--R + +--R 4 2 5 +--R 288a b - 144a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 4 3 3 5 +--R (2376a b - 2376a b )cosh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (- 2160a b + 6480a b - 4320a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (360a b - 1512a b + 2304a b - 1152a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 4 3 3 6 +--R (2772a b - 2772a b )cosh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 3780a b + 11340a b - 7560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (1260a b - 5292a b + 8064a b - 4032a b)cosh(x) - 60a b +--R + +--R 3 3 4 2 5 6 +--R 276a b - 504a b + 480a b - 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 7 +--R (2376a b - 2376a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 4536a b + 13608a b - 9072a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (2520a b - 10584a b + 16128a b - 8064a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 360a b + 1656a b - 3024a b + 2880a b - 1152a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 8 +--R (1485a b - 1485a b )cosh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (- 3780a b + 11340a b - 7560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (3150a b - 13230a b + 20160a b - 10080a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (- 900a b + 4140a b - 7560a b + 7200a b - 2880a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R 45a b - 189a b + 288a b - 144a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 9 +--R (660a b - 660a b )cosh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 2160a b + 6480a b - 4320a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (2520a b - 10584a b + 16128a b - 8064a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 1200a b + 5520a b - 10080a b + 9600a b - 3840a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (180a b - 756a b + 1152a b - 576a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 10 +--R (198a b - 198a b )cosh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 810a b + 2430a b - 1620a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (1260a b - 5292a b + 8064a b - 4032a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 900a b + 4140a b - 7560a b + 7200a b - 2880a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (270a b - 1134a b + 1728a b - 864a b)cosh(x) - 18a b +--R + +--R 3 3 4 2 +--R 54a b - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 11 +--R (36a b - 36a b )cosh(x) +--R + +--R 2 4 3 3 4 2 9 +--R (- 180a b + 540a b - 360a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (360a b - 1512a b + 2304a b - 1152a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 360a b + 1656a b - 3024a b + 2880a b - 1152a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (180a b - 756a b + 1152a b - 576a b)cosh(x) +--R + +--R 2 4 3 3 4 2 +--R (- 36a b + 108a b - 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 12 2 4 3 3 4 2 10 +--R (3a b - 3a b )cosh(x) + (- 18a b + 54a b - 36a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (45a b - 189a b + 288a b - 144a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 60a b + 276a b - 504a b + 480a b - 192a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (45a b - 189a b + 288a b - 144a b)cosh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (- 18a b + 54a b - 36a b )cosh(x) + 3a b - 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 3 12 3 3 11 +--R a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 4 2 10 +--R (66a b cosh(x) - 6a b + 12a b )sinh(x) +--R + +--R 3 3 3 3 3 4 2 9 +--R (220a b cosh(x) + (- 60a b + 120a b )cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 4 2 2 3 3 4 2 +--R 495a b cosh(x) + (- 270a b + 540a b )cosh(x) + 15a b - 48a b +--R + +--R 5 +--R 48a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 3 5 3 3 4 2 3 +--R 792a b cosh(x) + (- 720a b + 1440a b )cosh(x) +--R + +--R 3 3 4 2 5 +--R (120a b - 384a b + 384a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 3 6 3 3 4 2 4 +--R 924a b cosh(x) + (- 1260a b + 2520a b )cosh(x) +--R + +--R 3 3 4 2 5 2 3 3 4 2 5 6 +--R (420a b - 1344a b + 1344a b)cosh(x) - 20a b + 72a b - 96a b + 64a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 7 3 3 4 2 5 +--R 792a b cosh(x) + (- 1512a b + 3024a b )cosh(x) +--R + +--R 3 3 4 2 5 3 +--R (840a b - 2688a b + 2688a b)cosh(x) +--R + +--R 3 3 4 2 5 6 +--R (- 120a b + 432a b - 576a b + 384a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 3 8 3 3 4 2 6 +--R 495a b cosh(x) + (- 1260a b + 2520a b )cosh(x) +--R + +--R 3 3 4 2 5 4 +--R (1050a b - 3360a b + 3360a b)cosh(x) +--R + +--R 3 3 4 2 5 6 2 3 3 4 2 +--R (- 300a b + 1080a b - 1440a b + 960a )cosh(x) + 15a b - 48a b +--R + +--R 5 +--R 48a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 9 3 3 4 2 7 +--R 220a b cosh(x) + (- 720a b + 1440a b )cosh(x) +--R + +--R 3 3 4 2 5 5 +--R (840a b - 2688a b + 2688a b)cosh(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- 400a b + 1440a b - 1920a b + 1280a )cosh(x) +--R + +--R 3 3 4 2 5 +--R (60a b - 192a b + 192a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 10 3 3 4 2 8 +--R 66a b cosh(x) + (- 270a b + 540a b )cosh(x) +--R + +--R 3 3 4 2 5 6 +--R (420a b - 1344a b + 1344a b)cosh(x) +--R + +--R 3 3 4 2 5 6 4 +--R (- 300a b + 1080a b - 1440a b + 960a )cosh(x) +--R + +--R 3 3 4 2 5 2 3 3 4 2 +--R (90a b - 288a b + 288a b)cosh(x) - 6a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 11 3 3 4 2 9 +--R 12a b cosh(x) + (- 60a b + 120a b )cosh(x) +--R + +--R 3 3 4 2 5 7 +--R (120a b - 384a b + 384a b)cosh(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 120a b + 432a b - 576a b + 384a )cosh(x) +--R + +--R 3 3 4 2 5 3 3 3 4 2 +--R (60a b - 192a b + 192a b)cosh(x) + (- 12a b + 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 12 3 3 4 2 10 +--R a b cosh(x) + (- 6a b + 12a b )cosh(x) +--R + +--R 3 3 4 2 5 8 +--R (15a b - 48a b + 48a b)cosh(x) +--R + +--R 3 3 4 2 5 6 6 +--R (- 20a b + 72a b - 96a b + 64a )cosh(x) +--R + +--R 3 3 4 2 5 4 3 3 4 2 2 3 3 +--R (15a b - 48a b + 48a b)cosh(x) + (- 6a b + 12a b )cosh(x) + a b +--R Type: Expression(Integer) +--E 320 + +--S 321 of 510 +t0062:= 1/(1-sinh(x)^2) +--R +--R +--R 1 +--R (273) - ------------ +--R 2 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 510 +r0062:= 1/2*atanh(2^(1/2)*tanh(x))*2^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 atanh(\|2 tanh(x)) +--R (274) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 510 +a0062:= integrate(t0062,x) +--R +--R +--R (275) +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 510 +m0062:= a0062-r0062 +--R +--R +--R (276) +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ +--R - 2atanh(\|2 tanh(x)) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 510 +d0062:= D(m0062,x) +--R +--R +--R (277) +--R +-+ 4 +-+ 3 +--R (3\|2 - 4)sinh(x) + (16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 42\|2 + 56)cosh(x) - 6\|2 + 8)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((16\|2 - 24)cosh(x) + (16\|2 - 24)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (3\|2 - 4)cosh(x) + (- 6\|2 + 8)cosh(x) - 9\|2 + 12 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (3\|2 - 4)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((30\|2 - 40)cosh(x) - 12\|2 + 16)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 16\|2 + 24)cosh(x) + (16\|2 - 24)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (3\|2 - 4)cosh(x) + (- 12\|2 + 16)cosh(x) + 9\|2 - 12 +--R / +--R +-+ 4 +-+ 3 +--R (18\|2 - 24)sinh(x) + (- 32\|2 + 48)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((36\|2 - 48)cosh(x) - 60\|2 + 80)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 32\|2 + 48)cosh(x) + (96\|2 - 144)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (18\|2 - 24)cosh(x) + (- 60\|2 + 80)cosh(x) + 18\|2 - 24 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 9\|2 + 12)sinh(x) + (16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 18\|2 + 24)cosh(x) + 30\|2 - 40)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((16\|2 - 24)cosh(x) + (- 48\|2 + 72)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 9\|2 + 12)cosh(x) + (30\|2 - 40)cosh(x) - 9\|2 + 12 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 510 +t0063:= 1/(1-sinh(x)^2)^2 +--R +--R +--R 1 +--R (278) ------------------------ +--R 4 2 +--R sinh(x) - 2sinh(x) + 1 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 510 +r0063:= 3/8*atanh(2^(1/2)*tanh(x))*2^(1/2)+tanh(x)/(4-8*tanh(x)^2) +--R +--R +--R +-+ 2 +-+ +-+ +--R (6\|2 tanh(x) - 3\|2 )atanh(\|2 tanh(x)) - 2tanh(x) +--R (279) ---------------------------------------------------- +--R 2 +--R 16tanh(x) - 8 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 510 +a0063:= integrate(t0063,x) +--R +--R +--R (280) +--R 4 3 2 2 +--R 3sinh(x) + 12cosh(x)sinh(x) + (18cosh(x) - 18)sinh(x) +--R + +--R 3 4 2 +--R (12cosh(x) - 36cosh(x))sinh(x) + 3cosh(x) - 18cosh(x) + 3 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R - 12\|2 sinh(x) - 24\|2 cosh(x)sinh(x) - 12\|2 cosh(x) + 4\|2 +--R / +--R +-+ 4 +-+ 3 +-+ 2 +-+ 2 +--R 8\|2 sinh(x) + 32\|2 cosh(x)sinh(x) + (48\|2 cosh(x) - 48\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (32\|2 cosh(x) - 96\|2 cosh(x))sinh(x) + 8\|2 cosh(x) - 48\|2 cosh(x) +--R + +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 510 +m0063:= a0063-r0063 +--R +--R +--R (281) +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) - 36)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) - 72cosh(x))sinh(x) + 6cosh(x) - 36cosh(x) + 6 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 3sinh(x) - 12cosh(x)sinh(x) + (- 18cosh(x) + 18)sinh(x) +--R + +--R 3 4 2 +--R (- 12cosh(x) + 36cosh(x))sinh(x) - 3cosh(x) + 18cosh(x) - 3 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R 4 3 2 2 +--R - 12sinh(x) - 48cosh(x)sinh(x) + (- 72cosh(x) + 72)sinh(x) +--R + +--R 3 4 2 +--R (- 48cosh(x) + 144cosh(x))sinh(x) - 12cosh(x) + 72cosh(x) - 12 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) - 36)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) - 72cosh(x))sinh(x) + 6cosh(x) - 36cosh(x) + 6 +--R * +--R +-+ +--R atanh(\|2 tanh(x)) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- 24\|2 sinh(x) - 48\|2 cosh(x)sinh(x) - 24\|2 cosh(x) + 8\|2 ) +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|2 cosh(x) - 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8\|2 cosh(x) - 24\|2 cosh(x))sinh(x) + 2\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 12\|2 cosh(x) + 2\|2 +--R * +--R tanh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R 12\|2 sinh(x) + 24\|2 cosh(x)sinh(x) + 12\|2 cosh(x) - 4\|2 +--R / +--R +-+ 4 +-+ 3 +--R 16\|2 sinh(x) + 64\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (96\|2 cosh(x) - 96\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (64\|2 cosh(x) - 192\|2 cosh(x))sinh(x) + 16\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 96\|2 cosh(x) + 16\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 8\|2 sinh(x) - 32\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 48\|2 cosh(x) + 48\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 32\|2 cosh(x) + 96\|2 cosh(x))sinh(x) - 8\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 48\|2 cosh(x) - 8\|2 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 510 +d0063:= D(m0063,x) +--R +--R +--R (282) +--R +-+ 12 +-+ 11 +--R (18\|2 - 24)sinh(x) + (176\|2 - 240)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((652\|2 - 912)cosh(x) - 48\|2 + 64)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((1072\|2 - 1584)cosh(x) + (- 1056\|2 + 1520)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (302\|2 - 744)cosh(x) + (- 3504\|2 + 5312)cosh(x) + 378\|2 +--R + +--R - 504 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 1760\|2 + 1824)cosh(x) + (- 2304\|2 + 4672)cosh(x) +--R + +--R +-+ +--R (2624\|2 - 3744)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 2968\|2 + 3360)cosh(x) + (6624\|2 - 6400)cosh(x) +--R + +--R +-+ 2 +-+ +--R (1928\|2 - 3552)cosh(x) - 912\|2 + 1216 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 1760\|2 + 1824)cosh(x) + (12864\|2 - 14432)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 9856\|2 + 11424)cosh(x) + (- 672\|2 + 544)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (302\|2 - 744)cosh(x) + (6624\|2 - 6400)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 19076\|2 + 23472)cosh(x) + (8784\|2 - 13376)cosh(x) +--R + +--R +-+ +--R - 954\|2 + 1272 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (1072\|2 - 1584)cosh(x) + (- 2304\|2 + 4672)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 9856\|2 + 11424)cosh(x) + (17088\|2 - 25408)cosh(x) +--R + +--R +-+ +--R (- 3568\|2 + 4752)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (652\|2 - 912)cosh(x) + (- 3504\|2 + 5312)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (1928\|2 - 3552)cosh(x) + (8784\|2 - 13376)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 5364\|2 + 7152)cosh(x) + 384\|2 - 512 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (176\|2 - 240)cosh(x) + (- 1056\|2 + 1520)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (2624\|2 - 3744)cosh(x) + (- 672\|2 + 544)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 3568\|2 + 4752)cosh(x) + (960\|2 - 1296)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (18\|2 - 24)cosh(x) + (- 48\|2 + 64)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (378\|2 - 504)cosh(x) + (- 912\|2 + 1216)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 954\|2 + 1272)cosh(x) + (384\|2 - 512)cosh(x) - 18\|2 + 24 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 11 +--R (- 64\|2 + 96)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 368\|2 + 576)cosh(x) - 228\|2 + 304)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 704\|2 + 1248)cosh(x) + (- 240\|2 + 128)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 64\|2 + 768)cosh(x) + (1164\|2 - 2704)cosh(x) + 1044\|2 +--R + +--R - 1392 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (1792\|2 - 1344)cosh(x) + (384\|2 - 3584)cosh(x) +--R + +--R +-+ +--R (2208\|2 - 2304)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (2912\|2 - 2688)cosh(x) + (- 7080\|2 + 4448)cosh(x) +--R + +--R +-+ 2 +-+ +--R (3792\|2 - 2112)cosh(x) - 1800\|2 + 2400 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (1792\|2 - 1344)cosh(x) + (- 12576\|2 + 11008)cosh(x) +--R + +--R +-+ 3 +-+ +--R (12000\|2 - 9984)cosh(x) + (- 6144\|2 + 7872)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 64\|2 + 768)cosh(x) + (- 7080\|2 + 4448)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (18744\|2 - 17568)cosh(x) + (- 13272\|2 + 16800)cosh(x) +--R + +--R +-+ +--R 2376\|2 - 3168 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 704\|2 + 1248)cosh(x) + (384\|2 - 3584)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (12000\|2 - 9984)cosh(x) + (- 17856\|2 + 22656)cosh(x) +--R + +--R +-+ +--R (6560\|2 - 8544)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 368\|2 + 576)cosh(x) + (1164\|2 - 2704)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (3792\|2 - 2112)cosh(x) + (- 13272\|2 + 16800)cosh(x) +--R + +--R +-+ 2 +-+ +--R (8640\|2 - 11136)cosh(x) - 660\|2 + 880 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 64\|2 + 96)cosh(x) + (- 240\|2 + 128)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (2208\|2 - 2304)cosh(x) + (- 6144\|2 + 7872)cosh(x) +--R + +--R +-+ 3 +-+ +--R (6560\|2 - 8544)cosh(x) + (- 1296\|2 + 1728)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 228\|2 + 304)cosh(x) + (1044\|2 - 1392)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 1800\|2 + 2400)cosh(x) + (2376\|2 - 3168)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 660\|2 + 880)cosh(x) + 36\|2 - 48 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 9\|2 + 12)sinh(x) + (- 40\|2 + 48)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 50\|2 + 24)cosh(x) + 195\|2 - 260)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 8\|2 - 144)cosh(x) + (708\|2 - 856)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 103\|2 - 204)cosh(x) + (879\|2 - 628)cosh(x) - 972\|2 + 1296) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 464\|2 + 96)cosh(x) + (864\|2 + 352)cosh(x) +--R + +--R +-+ +--R (- 2968\|2 + 3600)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 700\|2 + 336)cosh(x) + (1998\|2 - 136)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 3808\|2 + 3360)cosh(x) + 1806\|2 - 2408 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 464\|2 + 96)cosh(x) + (3000\|2 - 1040)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 4072\|2 + 1776)cosh(x) + (4944\|2 - 6176)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 103\|2 - 204)cosh(x) + (1998\|2 - 136)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 4520\|2 + 1440)cosh(x) + (5562\|2 - 5912)cosh(x) - 1305\|2 +--R + +--R 1740 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 8\|2 - 144)cosh(x) + (864\|2 + 352)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 4072\|2 + 1776)cosh(x) + (4848\|2 - 4288)cosh(x) +--R + +--R +-+ +--R (- 3136\|2 + 4032)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 50\|2 + 24)cosh(x) + (879\|2 - 628)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 3808\|2 + 3360)cosh(x) + (5562\|2 - 5912)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 3798\|2 + 4776)cosh(x) + 303\|2 - 404 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 40\|2 + 48)cosh(x) + (708\|2 - 856)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 2968\|2 + 3600)cosh(x) + (4944\|2 - 6176)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 3136\|2 + 4032)cosh(x) + (492\|2 - 648)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 9\|2 + 12)cosh(x) + (195\|2 - 260)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 972\|2 + 1296)cosh(x) + (1806\|2 - 2408)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 1305\|2 + 1740)cosh(x) + (303\|2 - 404)cosh(x) - 18\|2 + 24 +--R / +--R +-+ 12 +-+ 11 +--R (72\|2 - 96)sinh(x) + (448\|2 - 576)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((1136\|2 - 1344)cosh(x) - 1104\|2 + 1472)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((1472\|2 - 1344)cosh(x) + (- 5184\|2 + 6592)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (952\|2 + 96)cosh(x) + (- 9360\|2 + 10432)cosh(x) + 5688\|2 +--R + +--R - 7584 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (128\|2 + 1920)cosh(x) + (- 7680\|2 + 4352)cosh(x) +--R + +--R +-+ +--R (19328\|2 - 24192)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 224\|2 + 2688)cosh(x) + (- 1824\|2 - 7808)cosh(x) +--R + +--R +-+ 2 +-+ +--R (22880\|2 - 22656)cosh(x) - 10848\|2 + 14464 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (128\|2 + 1920)cosh(x) + (1152\|2 - 13696)cosh(x) +--R + +--R +-+ 3 +-+ +--R (8576\|2 + 5760)cosh(x) + (- 27264\|2 + 33664)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (952\|2 + 96)cosh(x) + (- 1824\|2 - 7808)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 1328\|2 + 23616)cosh(x) + (- 17952\|2 + 13696)cosh(x) +--R + +--R +-+ +--R 5688\|2 - 7584 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (1472\|2 - 1344)cosh(x) + (- 7680\|2 + 4352)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (8576\|2 + 5760)cosh(x) + (- 3072\|2 - 11008)cosh(x) +--R + +--R +-+ +--R (11968\|2 - 15168)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (1136\|2 - 1344)cosh(x) + (- 9360\|2 + 10432)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (22880\|2 - 22656)cosh(x) + (- 17952\|2 + 13696)cosh(x) +--R + +--R +-+ 2 +-+ +--R (13104\|2 - 15936)cosh(x) - 1104\|2 + 1472 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (448\|2 - 576)cosh(x) + (- 5184\|2 + 6592)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (19328\|2 - 24192)cosh(x) + (- 27264\|2 + 33664)cosh(x) +--R + +--R +-+ 3 +-+ +--R (11968\|2 - 15168)cosh(x) + (- 1344\|2 + 1728)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (72\|2 - 96)cosh(x) + (- 1104\|2 + 1472)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (5688\|2 - 7584)cosh(x) + (- 10848\|2 + 14464)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (5688\|2 - 7584)cosh(x) + (- 1104\|2 + 1472)cosh(x) + 72\|2 - 96 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 72\|2 + 96)sinh(x) + (- 448\|2 + 576)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 1136\|2 + 1344)cosh(x) + 1104\|2 - 1472)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 1472\|2 + 1344)cosh(x) + (5184\|2 - 6592)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 952\|2 - 96)cosh(x) + (9360\|2 - 10432)cosh(x) - 5688\|2 +--R + +--R 7584 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 128\|2 - 1920)cosh(x) + (7680\|2 - 4352)cosh(x) +--R + +--R +-+ +--R (- 19328\|2 + 24192)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (224\|2 - 2688)cosh(x) + (1824\|2 + 7808)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 22880\|2 + 22656)cosh(x) + 10848\|2 - 14464 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 128\|2 - 1920)cosh(x) + (- 1152\|2 + 13696)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 8576\|2 - 5760)cosh(x) + (27264\|2 - 33664)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 952\|2 - 96)cosh(x) + (1824\|2 + 7808)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (1328\|2 - 23616)cosh(x) + (17952\|2 - 13696)cosh(x) +--R + +--R +-+ +--R - 5688\|2 + 7584 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 1472\|2 + 1344)cosh(x) + (7680\|2 - 4352)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 8576\|2 - 5760)cosh(x) + (3072\|2 + 11008)cosh(x) +--R + +--R +-+ +--R (- 11968\|2 + 15168)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 1136\|2 + 1344)cosh(x) + (9360\|2 - 10432)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 22880\|2 + 22656)cosh(x) + (17952\|2 - 13696)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 13104\|2 + 15936)cosh(x) + 1104\|2 - 1472 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 448\|2 + 576)cosh(x) + (5184\|2 - 6592)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 19328\|2 + 24192)cosh(x) + (27264\|2 - 33664)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 11968\|2 + 15168)cosh(x) + (1344\|2 - 1728)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 72\|2 + 96)cosh(x) + (1104\|2 - 1472)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 5688\|2 + 7584)cosh(x) + (10848\|2 - 14464)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 5688\|2 + 7584)cosh(x) + (1104\|2 - 1472)cosh(x) - 72\|2 + 96 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (18\|2 - 24)sinh(x) + (112\|2 - 144)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((284\|2 - 336)cosh(x) - 276\|2 + 368)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((368\|2 - 336)cosh(x) + (- 1296\|2 + 1648)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (238\|2 + 24)cosh(x) + (- 2340\|2 + 2608)cosh(x) + 1422\|2 +--R + +--R - 1896 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (32\|2 + 480)cosh(x) + (- 1920\|2 + 1088)cosh(x) +--R + +--R +-+ +--R (4832\|2 - 6048)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 56\|2 + 672)cosh(x) + (- 456\|2 - 1952)cosh(x) +--R + +--R +-+ 2 +-+ +--R (5720\|2 - 5664)cosh(x) - 2712\|2 + 3616 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (32\|2 + 480)cosh(x) + (288\|2 - 3424)cosh(x) +--R + +--R +-+ 3 +-+ +--R (2144\|2 + 1440)cosh(x) + (- 6816\|2 + 8416)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (238\|2 + 24)cosh(x) + (- 456\|2 - 1952)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 332\|2 + 5904)cosh(x) + (- 4488\|2 + 3424)cosh(x) + 1422\|2 +--R + +--R - 1896 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (368\|2 - 336)cosh(x) + (- 1920\|2 + 1088)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (2144\|2 + 1440)cosh(x) + (- 768\|2 - 2752)cosh(x) +--R + +--R +-+ +--R (2992\|2 - 3792)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (284\|2 - 336)cosh(x) + (- 2340\|2 + 2608)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (5720\|2 - 5664)cosh(x) + (- 4488\|2 + 3424)cosh(x) +--R + +--R +-+ 2 +-+ +--R (3276\|2 - 3984)cosh(x) - 276\|2 + 368 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (112\|2 - 144)cosh(x) + (- 1296\|2 + 1648)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (4832\|2 - 6048)cosh(x) + (- 6816\|2 + 8416)cosh(x) +--R + +--R +-+ 3 +-+ +--R (2992\|2 - 3792)cosh(x) + (- 336\|2 + 432)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (18\|2 - 24)cosh(x) + (- 276\|2 + 368)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (1422\|2 - 1896)cosh(x) + (- 2712\|2 + 3616)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (1422\|2 - 1896)cosh(x) + (- 276\|2 + 368)cosh(x) + 18\|2 - 24 +--R Type: Expression(Integer) +--E 330 + +--S 331 of 510 +t0064:= 1/(1-sinh(x)^2)^3 +--R +--R +--R 1 +--R (283) - ------------------------------------ +--R 6 4 2 +--R sinh(x) - 3sinh(x) + 3sinh(x) - 1 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 510 +r0064:= 19/64*atanh(2^(1/2)*tanh(x))*2^(1/2)+_ + 1/16*tanh(x)/(-1+2*tanh(x)^2)^2-11*tanh(x)/(-32+64*tanh(x)^2) +--R +--R +--R (284) +--R +-+ 4 +-+ 2 +-+ +-+ 3 +--R (76\|2 tanh(x) - 76\|2 tanh(x) + 19\|2 )atanh(\|2 tanh(x)) - 44tanh(x) +--R + +--R 26tanh(x) +--R / +--R 4 2 +--R 256tanh(x) - 256tanh(x) + 64 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 510 +a0064:= integrate(t0064,x) +--R +--R +--R (285) +--R 8 7 2 6 +--R 19sinh(x) + 152cosh(x)sinh(x) + (532cosh(x) - 228)sinh(x) +--R + +--R 3 5 +--R (1064cosh(x) - 1368cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1330cosh(x) - 3420cosh(x) + 722)sinh(x) +--R + +--R 5 3 3 +--R (1064cosh(x) - 4560cosh(x) + 2888cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (532cosh(x) - 3420cosh(x) + 4332cosh(x) - 228)sinh(x) +--R + +--R 7 5 3 +--R (152cosh(x) - 1368cosh(x) + 2888cosh(x) - 456cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 19cosh(x) - 228cosh(x) + 722cosh(x) - 228cosh(x) + 19 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ 6 +-+ 5 +--R - 76\|2 sinh(x) - 456\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (- 1140\|2 cosh(x) + 684\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (- 1520\|2 cosh(x) + 2736\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 1140\|2 cosh(x) + 4104\|2 cosh(x) - 356\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 456\|2 cosh(x) + 2736\|2 cosh(x) - 712\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 76\|2 cosh(x) + 684\|2 cosh(x) - 356\|2 cosh(x) + 36\|2 +--R / +--R +-+ 8 +-+ 7 +--R 64\|2 sinh(x) + 512\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (1792\|2 cosh(x) - 768\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (3584\|2 cosh(x) - 4608\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (4480\|2 cosh(x) - 11520\|2 cosh(x) + 2432\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (3584\|2 cosh(x) - 15360\|2 cosh(x) + 9728\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (1792\|2 cosh(x) - 11520\|2 cosh(x) + 14592\|2 cosh(x) - 768\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 512\|2 cosh(x) - 4608\|2 cosh(x) + 9728\|2 cosh(x) +--R + +--R +-+ +--R - 1536\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 64\|2 cosh(x) - 768\|2 cosh(x) + 2432\|2 cosh(x) - 768\|2 cosh(x) +--R + +--R +-+ +--R 64\|2 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 510 +m0064:= a0064-r0064 +--R +--R +--R (286) +--R 8 7 2 6 +--R 76sinh(x) + 608cosh(x)sinh(x) + (2128cosh(x) - 912)sinh(x) +--R + +--R 3 5 +--R (4256cosh(x) - 5472cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (5320cosh(x) - 13680cosh(x) + 2888)sinh(x) +--R + +--R 5 3 3 +--R (4256cosh(x) - 18240cosh(x) + 11552cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (2128cosh(x) - 13680cosh(x) + 17328cosh(x) - 912)sinh(x) +--R + +--R 7 5 3 +--R (608cosh(x) - 5472cosh(x) + 11552cosh(x) - 1824cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 76cosh(x) - 912cosh(x) + 2888cosh(x) - 912cosh(x) + 76 +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 +--R - 76sinh(x) - 608cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 2128cosh(x) + 912)sinh(x) +--R + +--R 3 5 +--R (- 4256cosh(x) + 5472cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 5320cosh(x) + 13680cosh(x) - 2888)sinh(x) +--R + +--R 5 3 3 +--R (- 4256cosh(x) + 18240cosh(x) - 11552cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 2128cosh(x) + 13680cosh(x) - 17328cosh(x) + 912)sinh(x) +--R + +--R 7 5 3 +--R (- 608cosh(x) + 5472cosh(x) - 11552cosh(x) + 1824cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - 76cosh(x) + 912cosh(x) - 2888cosh(x) + 912cosh(x) - 76 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 19sinh(x) + 152cosh(x)sinh(x) + (532cosh(x) - 228)sinh(x) +--R + +--R 3 5 +--R (1064cosh(x) - 1368cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1330cosh(x) - 3420cosh(x) + 722)sinh(x) +--R + +--R 5 3 3 +--R (1064cosh(x) - 4560cosh(x) + 2888cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (532cosh(x) - 3420cosh(x) + 4332cosh(x) - 228)sinh(x) +--R + +--R 7 5 3 +--R (152cosh(x) - 1368cosh(x) + 2888cosh(x) - 456cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 19cosh(x) - 228cosh(x) + 722cosh(x) - 228cosh(x) + 19 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R 8 7 +--R - 152sinh(x) - 1216cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 4256cosh(x) + 1824)sinh(x) +--R + +--R 3 5 +--R (- 8512cosh(x) + 10944cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 10640cosh(x) + 27360cosh(x) - 5776)sinh(x) +--R + +--R 5 3 3 +--R (- 8512cosh(x) + 36480cosh(x) - 23104cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 4256cosh(x) + 27360cosh(x) - 34656cosh(x) + 1824)sinh(x) +--R + +--R 7 5 3 +--R (- 1216cosh(x) + 10944cosh(x) - 23104cosh(x) + 3648cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - 152cosh(x) + 1824cosh(x) - 5776cosh(x) + 1824cosh(x) - 152 +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 152sinh(x) + 1216cosh(x)sinh(x) + (4256cosh(x) - 1824)sinh(x) +--R + +--R 3 5 +--R (8512cosh(x) - 10944cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (10640cosh(x) - 27360cosh(x) + 5776)sinh(x) +--R + +--R 5 3 3 +--R (8512cosh(x) - 36480cosh(x) + 23104cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (4256cosh(x) - 27360cosh(x) + 34656cosh(x) - 1824)sinh(x) +--R + +--R 7 5 3 +--R (1216cosh(x) - 10944cosh(x) + 23104cosh(x) - 3648cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R 152cosh(x) - 1824cosh(x) + 5776cosh(x) - 1824cosh(x) + 152 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 38sinh(x) - 304cosh(x)sinh(x) + (- 1064cosh(x) + 456)sinh(x) +--R + +--R 3 5 +--R (- 2128cosh(x) + 2736cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 2660cosh(x) + 6840cosh(x) - 1444)sinh(x) +--R + +--R 5 3 3 +--R (- 2128cosh(x) + 9120cosh(x) - 5776cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 1064cosh(x) + 6840cosh(x) - 8664cosh(x) + 456)sinh(x) +--R + +--R 7 5 3 +--R (- 304cosh(x) + 2736cosh(x) - 5776cosh(x) + 912cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 38cosh(x) + 456cosh(x) - 1444cosh(x) + 456cosh(x) - 38 +--R * +--R +-+ +--R atanh(\|2 tanh(x)) +--R + +--R +-+ 6 +-+ 5 +--R - 304\|2 sinh(x) - 1824\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (- 4560\|2 cosh(x) + 2736\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (- 6080\|2 cosh(x) + 10944\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 4560\|2 cosh(x) + 16416\|2 cosh(x) - 1424\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 1824\|2 cosh(x) + 10944\|2 cosh(x) - 2848\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 304\|2 cosh(x) + 2736\|2 cosh(x) - 1424\|2 cosh(x) + 144\|2 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 44\|2 sinh(x) + 352\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (1232\|2 cosh(x) - 528\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (2464\|2 cosh(x) - 3168\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (3080\|2 cosh(x) - 7920\|2 cosh(x) + 1672\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (2464\|2 cosh(x) - 10560\|2 cosh(x) + 6688\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (1232\|2 cosh(x) - 7920\|2 cosh(x) + 10032\|2 cosh(x) - 528\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 352\|2 cosh(x) - 3168\|2 cosh(x) + 6688\|2 cosh(x) +--R + +--R +-+ +--R - 1056\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 44\|2 cosh(x) - 528\|2 cosh(x) + 1672\|2 cosh(x) - 528\|2 cosh(x) +--R + +--R +-+ +--R 44\|2 +--R * +--R 3 +--R tanh(x) +--R + +--R +-+ 6 +-+ 5 +--R 304\|2 sinh(x) + 1824\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (4560\|2 cosh(x) - 2736\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (6080\|2 cosh(x) - 10944\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (4560\|2 cosh(x) - 16416\|2 cosh(x) + 1424\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (1824\|2 cosh(x) - 10944\|2 cosh(x) + 2848\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 304\|2 cosh(x) - 2736\|2 cosh(x) + 1424\|2 cosh(x) - 144\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 26\|2 sinh(x) - 208\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 728\|2 cosh(x) + 312\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 1456\|2 cosh(x) + 1872\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 1820\|2 cosh(x) + 4680\|2 cosh(x) - 988\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 1456\|2 cosh(x) + 6240\|2 cosh(x) - 3952\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 728\|2 cosh(x) + 4680\|2 cosh(x) - 5928\|2 cosh(x) + 312\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 208\|2 cosh(x) + 1872\|2 cosh(x) - 3952\|2 cosh(x) +--R + +--R +-+ +--R 624\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 26\|2 cosh(x) + 312\|2 cosh(x) - 988\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 312\|2 cosh(x) - 26\|2 +--R * +--R tanh(x) +--R + +--R +-+ 6 +-+ 5 +--R - 76\|2 sinh(x) - 456\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (- 1140\|2 cosh(x) + 684\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (- 1520\|2 cosh(x) + 2736\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 1140\|2 cosh(x) + 4104\|2 cosh(x) - 356\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 456\|2 cosh(x) + 2736\|2 cosh(x) - 712\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 76\|2 cosh(x) + 684\|2 cosh(x) - 356\|2 cosh(x) + 36\|2 +--R / +--R +-+ 8 +-+ 7 +--R 256\|2 sinh(x) + 2048\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (7168\|2 cosh(x) - 3072\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (14336\|2 cosh(x) - 18432\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (17920\|2 cosh(x) - 46080\|2 cosh(x) + 9728\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (14336\|2 cosh(x) - 61440\|2 cosh(x) + 38912\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 7168\|2 cosh(x) - 46080\|2 cosh(x) + 58368\|2 cosh(x) +--R + +--R +-+ +--R - 3072\|2 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 2048\|2 cosh(x) - 18432\|2 cosh(x) + 38912\|2 cosh(x) +--R + +--R +-+ +--R - 6144\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 256\|2 cosh(x) - 3072\|2 cosh(x) + 9728\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 3072\|2 cosh(x) + 256\|2 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 256\|2 sinh(x) - 2048\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 7168\|2 cosh(x) + 3072\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 14336\|2 cosh(x) + 18432\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 17920\|2 cosh(x) + 46080\|2 cosh(x) - 9728\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 14336\|2 cosh(x) + 61440\|2 cosh(x) - 38912\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 7168\|2 cosh(x) + 46080\|2 cosh(x) - 58368\|2 cosh(x) +--R + +--R +-+ +--R 3072\|2 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 2048\|2 cosh(x) + 18432\|2 cosh(x) - 38912\|2 cosh(x) +--R + +--R +-+ +--R 6144\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 256\|2 cosh(x) + 3072\|2 cosh(x) - 9728\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 3072\|2 cosh(x) - 256\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 64\|2 sinh(x) + 512\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (1792\|2 cosh(x) - 768\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (3584\|2 cosh(x) - 4608\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (4480\|2 cosh(x) - 11520\|2 cosh(x) + 2432\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (3584\|2 cosh(x) - 15360\|2 cosh(x) + 9728\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (1792\|2 cosh(x) - 11520\|2 cosh(x) + 14592\|2 cosh(x) - 768\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 512\|2 cosh(x) - 4608\|2 cosh(x) + 9728\|2 cosh(x) +--R + +--R +-+ +--R - 1536\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 64\|2 cosh(x) - 768\|2 cosh(x) + 2432\|2 cosh(x) - 768\|2 cosh(x) +--R + +--R +-+ +--R 64\|2 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 510 +d0064:= D(m0064,x) +--R +--R +--R (287) +--R +-+ 16 +-+ 15 +--R (312\|2 - 416)sinh(x) + (4000\|2 - 5376)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R ((22464\|2 - 30464)cosh(x) - 3768\|2 + 5024)sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R ((71392\|2 - 98048)cosh(x) + (- 47264\|2 + 64320)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +--R (134944\|2 - 189824)cosh(x) + (- 236776\|2 + 328160)cosh(x) +--R + +--R +-+ +--R 8520\|2 - 11360 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (130464\|2 - 197888)cosh(x) + (- 606784\|2 + 863360)cosh(x) +--R + +--R +-+ +--R (152736\|2 - 215552)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 26048\|2 - 8448)cosh(x) + (- 752888\|2 + 1148064)cosh(x) +--R + +--R +-+ 2 +-+ +--R (698448\|2 - 1021376)cosh(x) - 32184\|2 + 42912 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 271392\|2 + 301312)cosh(x) + (3744\|2 + 260288)cosh(x) +--R + +--R +-+ 3 +-+ +--R (1196064\|2 - 1899008)cosh(x) + (- 258720\|2 + 363072)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 394416\|2 + 458304)cosh(x) + (1484952\|2 - 1612320)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 50376\|2 - 551328)cosh(x) + (- 440664\|2 + 693024)cosh(x) +--R + +--R +-+ +--R 75960\|2 - 101280 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 271392\|2 + 301312)cosh(x) + (2283648\|2 - 2638080)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 3302592\|2 + 3523584)cosh(x) + (921216\|2 - 957696)cosh(x) +--R + +--R +-+ +--R (183264\|2 - 215808)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 26048\|2 - 8448)cosh(x) + (1484952\|2 - 1612320)cosh(x) +--R + +--R +-+ 6 +--R (- 5220768\|2 + 5986176)cosh(x) +--R + +--R +-+ 4 +--R (4315920\|2 - 5331648)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 788448\|2 + 1251456)cosh(x) + 74520\|2 - 99360 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (130464\|2 - 197888)cosh(x) + (3744\|2 + 260288)cosh(x) +--R + +--R +-+ 7 +--R (- 3302592\|2 + 3523584)cosh(x) +--R + +--R +-+ 5 +--R (6361152\|2 - 8002176)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 3587808\|2 + 5327616)cosh(x) + (437024\|2 - 582720)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +--R (134944\|2 - 189824)cosh(x) +--R + +--R +-+ 10 +--R (- 752888\|2 + 1148064)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 50376\|2 - 551328)cosh(x) + (4315920\|2 - 5331648)cosh(x) +--R + +--R +-+ 4 +--R (- 5384112\|2 + 7923264)cosh(x) +--R + +--R +-+ 2 +-+ +--R (1117672\|2 - 1493472)cosh(x) - 41640\|2 + 55520 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +--R (71392\|2 - 98048)cosh(x) + (- 606784\|2 + 863360)cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R (1196064\|2 - 1899008)cosh(x) + (921216\|2 - 957696)cosh(x) +--R + +--R +-+ 5 +--R (- 3587808\|2 + 5327616)cosh(x) +--R + +--R +-+ 3 +-+ +--R (1510336\|2 - 2020224)cosh(x) + (- 196640\|2 + 264704)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R (22464\|2 - 30464)cosh(x) + (- 236776\|2 + 328160)cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R (698448\|2 - 1021376)cosh(x) + (- 440664\|2 + 693024)cosh(x) +--R + +--R +-+ 6 +--R (- 788448\|2 + 1251456)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (1117672\|2 - 1493472)cosh(x) + (- 311088\|2 + 419904)cosh(x) +--R + +--R +-+ +--R 4440\|2 - 5920 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R (4000\|2 - 5376)cosh(x) + (- 47264\|2 + 64320)cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R (152736\|2 - 215552)cosh(x) + (- 258720\|2 + 363072)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (183264\|2 - 215808)cosh(x) + (437024\|2 - 582720)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 196640\|2 + 264704)cosh(x) + (12320\|2 - 16704)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R (312\|2 - 416)cosh(x) + (- 3768\|2 + 5024)cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R (8520\|2 - 11360)cosh(x) + (- 32184\|2 + 42912)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (75960\|2 - 101280)cosh(x) + (74520\|2 - 99360)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 41640\|2 + 55520)cosh(x) + (4440\|2 - 5920)cosh(x) - 144\|2 +--R + +--R 192 +--R * +--R 6 +--R tanh(x) +--R + +--R +-+ 16 +-+ 15 +--R (- 252\|2 + 336)sinh(x) + (- 3792\|2 + 5184)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R ((- 23616\|2 + 33024)cosh(x) + 1044\|2 - 1392)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 80112\|2 + 115392)cosh(x) + (31440\|2 - 45216)cosh(x)) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 155856\|2 + 237504)cosh(x) + (207132\|2 - 308688)cosh(x) +--R + +--R +-+ +--R 24372\|2 - 32496 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 142416\|2 + 261696)cosh(x) + (592800\|2 - 937536)cosh(x) +--R + +--R +-+ +--R (31536\|2 - 13632)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (78144\|2 + 25344)cosh(x) + (707124\|2 - 1351152)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 266328\|2 + 581664)cosh(x) - 89964\|2 + 119952 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (422928\|2 - 382272)cosh(x) + (- 353232\|2 - 315744)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 504720\|2 + 1490880)cosh(x) + (- 392112\|2 + 458208)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (596376\|2 - 592416)cosh(x) + (- 2389860\|2 + 2054448)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (1315980\|2 + 42480)cosh(x) + (- 1153404\|2 + 1112400)cosh(x) +--R + +--R +-+ +--R 115452\|2 - 153936 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (422928\|2 - 382272)cosh(x) + (- 3491136\|2 + 3383424)cosh(x) +--R + +--R +-+ 5 +--R (5634144\|2 - 4770432)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 3576384\|2 + 3507840)cosh(x) + (768528\|2 - 1012032)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (78144\|2 + 25344)cosh(x) + (- 2389860\|2 + 2054448)cosh(x) +--R + +--R +-+ 6 +--R (8173872\|2 - 7769664)cosh(x) +--R + +--R +-+ 4 +--R (- 7949592\|2 + 8352288)cosh(x) +--R + +--R +-+ 2 +-+ +--R (3036528\|2 - 4030272)cosh(x) - 250020\|2 + 333360 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +--R (- 142416\|2 + 261696)cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 353232\|2 - 315744)cosh(x) + (5634144\|2 - 4770432)cosh(x) +--R + +--R +-+ 5 +--R (- 10448928\|2 + 11237184)cosh(x) +--R + +--R +-+ 3 +-+ +--R (7076592\|2 - 9475776)cosh(x) + (- 1174800\|2 + 1543968)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +--R (- 155856\|2 + 237504)cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R (707124\|2 - 1351152)cosh(x) + (1315980\|2 + 42480)cosh(x) +--R + +--R +-+ 6 +--R (- 7949592\|2 + 8352288)cosh(x) +--R + +--R +-+ 4 +--R (9386280\|2 - 12607200)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2538780\|2 + 3302352)cosh(x) + 99612\|2 - 132816 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +--R (- 80112\|2 + 115392)cosh(x) + (592800\|2 - 937536)cosh(x) +--R + +--R +-+ 9 +--R (- 504720\|2 + 1490880)cosh(x) +--R + +--R +-+ 7 +--R (- 3576384\|2 + 3507840)cosh(x) +--R + +--R +-+ 5 +--R (7076592\|2 - 9475776)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 3228000\|2 + 4183488)cosh(x) + (395664\|2 - 527808)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R (- 23616\|2 + 33024)cosh(x) + (207132\|2 - 308688)cosh(x) +--R + +--R +-+ 10 +--R (- 266328\|2 + 581664)cosh(x) +--R + +--R +-+ 8 +--R (- 1153404\|2 + 1112400)cosh(x) +--R + +--R +-+ 6 +--R (3036528\|2 - 4030272)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 2538780\|2 + 3302352)cosh(x) + (595368\|2 - 794592)cosh(x) +--R + +--R +-+ +--R - 11268\|2 + 15024 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R (- 3792\|2 + 5184)cosh(x) + (31440\|2 - 45216)cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R (31536\|2 - 13632)cosh(x) + (- 392112\|2 + 458208)cosh(x) +--R + +--R +-+ 7 +--R (768528\|2 - 1012032)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 1174800\|2 + 1543968)cosh(x) + (395664\|2 - 527808)cosh(x) +--R + +--R +-+ +--R (- 25104\|2 + 33696)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R (- 252\|2 + 336)cosh(x) + (1044\|2 - 1392)cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R (24372\|2 - 32496)cosh(x) + (- 89964\|2 + 119952)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (115452\|2 - 153936)cosh(x) + (- 250020\|2 + 333360)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (99612\|2 - 132816)cosh(x) + (- 11268\|2 + 15024)cosh(x) +--R + +--R +-+ +--R 432\|2 - 576 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 16 +-+ 15 +--R (- 90\|2 + 120)sinh(x) + (- 312\|2 + 288)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R ((1728\|2 - 3840)cosh(x) + 4086\|2 - 5448)sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R ((13080\|2 - 26016)cosh(x) + (23736\|2 - 28656)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +--R (31368\|2 - 71520)cosh(x) + (44466\|2 - 29208)cosh(x) +--R + +--R +-+ +--R - 49338\|2 + 65784 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (17928\|2 - 95712)cosh(x) + (20976\|2 + 111264)cosh(x) +--R + +--R +-+ +--R (- 276408\|2 + 343776)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 78144\|2 - 25344)cosh(x) + (68646\|2 + 304632)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 648180\|2 + 659568)cosh(x) + 183222\|2 - 244296 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 227304\|2 + 121440)cosh(x) + (524232\|2 + 83184)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 1037016\|2 + 612192)cosh(x) + (976248\|2 - 1231920)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 302940\|2 + 201168)cosh(x) + (1357362\|2 - 663192)cosh(x) +--R + +--R +-+ 4 +--R (- 1898406\|2 + 763272)cosh(x) +--R + +--R +-+ 2 +-+ +--R (2391102\|2 - 2708136)cosh(x) - 287118\|2 + 382824 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 227304\|2 + 121440)cosh(x) + (1811232\|2 - 1118016)cosh(x) +--R + +--R +-+ 5 +--R (- 3497328\|2 + 1870272)cosh(x) +--R + +--R +-+ 3 +-+ +--R (3982752\|2 - 3825216)cosh(x) + (- 1427688\|2 + 1841760)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 78144\|2 - 25344)cosh(x) + (1357362\|2 - 663192)cosh(x) +--R + +--R +-+ 6 +--R (- 4429656\|2 + 2675232)cosh(x) +--R + +--R +-+ 4 +--R (5450508\|2 - 4530960)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 3372120\|2 + 4168224)cosh(x) + 263250\|2 - 351000 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (17928\|2 - 95712)cosh(x) + (524232\|2 + 83184)cosh(x) +--R + +--R +-+ 7 +--R (- 3497328\|2 + 1870272)cosh(x) +--R + +--R +-+ 5 +--R (6131664\|2 - 4852512)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 5233176\|2 + 6222240)cosh(x) + (1106664\|2 - 1441872)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (31368\|2 - 71520)cosh(x) + (68646\|2 + 304632)cosh(x) +--R + +--R +-+ 8 +--R (- 1898406\|2 + 763272)cosh(x) +--R + +--R +-+ 6 +--R (5450508\|2 - 4530960)cosh(x) +--R + +--R +-+ 4 +--R (- 6003252\|2 + 7025904)cosh(x) +--R + +--R +-+ 2 +-+ +--R (2131662\|2 - 2713320)cosh(x) - 86958\|2 + 115944 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +--R (13080\|2 - 26016)cosh(x) + (20976\|2 + 111264)cosh(x) +--R + +--R +-+ 9 +--R (- 1037016\|2 + 612192)cosh(x) +--R + +--R +-+ 7 +--R (3982752\|2 - 3825216)cosh(x) +--R + +--R +-+ 5 +--R (- 5233176\|2 + 6222240)cosh(x) +--R + +--R +-+ 3 +-+ +--R (2576496\|2 - 3244896)cosh(x) + (- 298536\|2 + 394656)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R (1728\|2 - 3840)cosh(x) + (44466\|2 - 29208)cosh(x) +--R + +--R +-+ 10 +--R (- 648180\|2 + 659568)cosh(x) +--R + +--R +-+ 8 +--R (2391102\|2 - 2708136)cosh(x) +--R + +--R +-+ 6 +--R (- 3372120\|2 + 4168224)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (2131662\|2 - 2713320)cosh(x) + (- 426420\|2 + 562032)cosh(x) +--R + +--R +-+ +--R 10242\|2 - 13656 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R (- 312\|2 + 288)cosh(x) + (23736\|2 - 28656)cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 276408\|2 + 343776)cosh(x) + (976248\|2 - 1231920)cosh(x) +--R + +--R +-+ 7 +--R (- 1427688\|2 + 1841760)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (1106664\|2 - 1441872)cosh(x) + (- 298536\|2 + 394656)cosh(x) +--R + +--R +-+ +--R (19176\|2 - 25488)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R (- 90\|2 + 120)cosh(x) + (4086\|2 - 5448)cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 49338\|2 + 65784)cosh(x) + (183222\|2 - 244296)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 287118\|2 + 382824)cosh(x) + (263250\|2 - 351000)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 86958\|2 + 115944)cosh(x) + (10242\|2 - 13656)cosh(x) +--R + +--R +-+ +--R - 432\|2 + 576 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 16 +-+ 15 +--R (87\|2 - 116)sinh(x) + (788\|2 - 1008)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R ((3072\|2 - 3584)cosh(x) - 2217\|2 + 2956)sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R ((6812\|2 - 6224)cosh(x) + (- 17108\|2 + 21864)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +--R (10292\|2 - 3824)cosh(x) + (- 56755\|2 + 66052)cosh(x) +--R + +--R +-+ +--R 20607\|2 - 27476 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (14772\|2 + 4240)cosh(x) + (- 109288\|2 + 100624)cosh(x) +--R + +--R +-+ +--R (132948\|2 - 169616)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (26048\|2 + 8448)cosh(x) + (- 152177\|2 + 72876)cosh(x) +--R + +--R +-+ 2 +-+ +--R (368478\|2 - 426728)cosh(x) - 76617\|2 + 102156 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (43164\|2 + 2992)cosh(x) + (- 203244\|2 + 11032)cosh(x) +--R + +--R +-+ 3 +-+ +--R (602628\|2 - 554576)cosh(x) + (- 422772\|2 + 539592)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (52074\|2 - 1848)cosh(x) + (- 280371\|2 - 10812)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (729873\|2 - 388716)cosh(x) + (- 1003317\|2 + 1168668)cosh(x) +--R + +--R +-+ +--R 124317\|2 - 165756 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (43164\|2 + 2992)cosh(x) + (- 323760\|2 - 4896)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (809640\|2 - 140064)cosh(x) + (- 1395312\|2 + 1327968)cosh(x) +--R + +--R +-+ +--R (585756\|2 - 752208)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (26048\|2 + 8448)cosh(x) + (- 280371\|2 - 10812)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (852516\|2 - 42672)cosh(x) + (- 1400322\|2 + 873432)cosh(x) +--R + +--R +-+ 2 +-+ +--R (1179972\|2 - 1412400)cosh(x) - 89955\|2 + 119940 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (14772\|2 + 4240)cosh(x) + (- 203244\|2 + 11032)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (809640\|2 - 140064)cosh(x) + (- 1324344\|2 + 553392)cosh(x) +--R + +--R +-+ 3 +-+ +--R (1437156\|2 - 1531824)cosh(x) + (- 357532\|2 + 463608)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (10292\|2 - 3824)cosh(x) + (- 152177\|2 + 72876)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (729873\|2 - 388716)cosh(x) + (- 1400322\|2 + 873432)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (1437246\|2 - 1411752)cosh(x) + (- 642701\|2 + 806268)cosh(x) +--R + +--R +-+ +--R 26877\|2 - 35836 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +--R (6812\|2 - 6224)cosh(x) + (- 109288\|2 + 100624)cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R (602628\|2 - 554576)cosh(x) + (- 1395312\|2 + 1327968)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (1437156\|2 - 1531824)cosh(x) + (- 750248\|2 + 925200)cosh(x) +--R + +--R +-+ +--R (83324\|2 - 109360)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R (3072\|2 - 3584)cosh(x) + (- 56755\|2 + 66052)cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R (368478\|2 - 426728)cosh(x) + (- 1003317\|2 + 1168668)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (1179972\|2 - 1412400)cosh(x) + (- 642701\|2 + 806268)cosh(x) +--R + +--R +-+ 2 +-+ +--R (113982\|2 - 148584)cosh(x) - 3243\|2 + 4324 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R (788\|2 - 1008)cosh(x) + (- 17108\|2 + 21864)cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R (132948\|2 - 169616)cosh(x) + (- 422772\|2 + 539592)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (585756\|2 - 752208)cosh(x) + (- 357532\|2 + 463608)cosh(x) +--R + +--R +-+ 3 +-+ +--R (83324\|2 - 109360)cosh(x) + (- 5404\|2 + 7128)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R (87\|2 - 116)cosh(x) + (- 2217\|2 + 2956)cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R (20607\|2 - 27476)cosh(x) + (- 76617\|2 + 102156)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (124317\|2 - 165756)cosh(x) + (- 89955\|2 + 119940)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (26877\|2 - 35836)cosh(x) + (- 3243\|2 + 4324)cosh(x) + 144\|2 - 192 +--R / +--R +-+ 16 +-+ 15 +--R (1152\|2 - 1536)sinh(x) + (11776\|2 - 15360)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R ((53760\|2 - 67584)cosh(x) - 24576\|2 + 32768)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((143872\|2 - 168960)cosh(x) + (- 210432\|2 + 273408)cosh(x)) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +--R (248320\|2 - 251904)cosh(x) + (- 789504\|2 + 978944)cosh(x) +--R + +--R +-+ +--R 198144\|2 - 264192 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (284160\|2 - 187392)cosh(x) + (- 1692672\|2 + 1906688)cosh(x) +--R + +--R +-+ +--R (1390080\|2 - 1797120)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (208384\|2 + 67584)cosh(x) + (- 2251776\|2 + 1978368)cosh(x) +--R + +--R +-+ 2 +-+ +--R (4167168\|2 - 5068800)cosh(x) - 737280\|2 + 983040 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (84480\|2 + 371712)cosh(x) + (- 1853952\|2 + 398336)cosh(x) +--R + +--R +-+ 3 +-+ +--R (6876672\|2 - 7240704)cosh(x) + (- 4161024\|2 + 5348352)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (25344\|2 + 506880)cosh(x) + (- 866304\|2 - 1941504)cosh(x) +--R + +--R +-+ 4 +--R (6615552\|2 - 4184064)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 9676800\|2 + 11476992)cosh(x) + 1223424\|2 - 1631232 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (84480\|2 + 371712)cosh(x) + (- 350208\|2 - 3059712)cosh(x) +--R + +--R +-+ 5 +--R (3628032\|2 + 2746368)cosh(x) +--R + +--R +-+ 3 +--R (- 11704320\|2 + 11046912)cosh(x) +--R + +--R +-+ +--R (5564928\|2 - 7123968)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (208384\|2 + 67584)cosh(x) + (- 866304\|2 - 1941504)cosh(x) +--R + +--R +-+ 6 +--R (1827840\|2 + 6451200)cosh(x) +--R + +--R +-+ 4 +--R (- 7870464\|2 + 1892352)cosh(x) +--R + +--R +-+ 2 +-+ +--R (9887232\|2 - 11483136)cosh(x) - 737280\|2 + 983040 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (284160\|2 - 187392)cosh(x) + (- 1853952\|2 + 398336)cosh(x) +--R + +--R +-+ 7 +--R (3628032\|2 + 2746368)cosh(x) +--R + +--R +-+ 5 +--R (- 4838400\|2 - 4085760)cosh(x) +--R + +--R +-+ 3 +-+ +--R (9039360\|2 - 7916544)cosh(x) + (- 2769408\|2 + 3572736)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +--R (248320\|2 - 251904)cosh(x) +--R + +--R +-+ 10 +--R (- 2251776\|2 + 1978368)cosh(x) +--R + +--R +-+ 8 +--R (6615552\|2 - 4184064)cosh(x) +--R + +--R +-+ 6 +--R (- 7870464\|2 + 1892352)cosh(x) +--R + +--R +-+ 4 +--R (6987264\|2 - 3852288)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 4598784\|2 + 5664768)cosh(x) + 198144\|2 - 264192 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +--R (143872\|2 - 168960)cosh(x) +--R + +--R +-+ 11 +--R (- 1692672\|2 + 1906688)cosh(x) +--R + +--R +-+ 9 +--R (6876672\|2 - 7240704)cosh(x) +--R + +--R +-+ 7 +--R (- 11704320\|2 + 11046912)cosh(x) +--R + +--R +-+ 5 +--R (9039360\|2 - 7916544)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 5133312\|2 + 6150144)cosh(x) + (537088\|2 - 697344)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R (53760\|2 - 67584)cosh(x) + (- 789504\|2 + 978944)cosh(x) +--R + +--R +-+ 10 +--R (4167168\|2 - 5068800)cosh(x) +--R + +--R +-+ 8 +--R (- 9676800\|2 + 11476992)cosh(x) +--R + +--R +-+ 6 +--R (9887232\|2 - 11483136)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 4598784\|2 + 5664768)cosh(x) + (686592\|2 - 878592)cosh(x) +--R + +--R +-+ +--R - 24576\|2 + 32768 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R (11776\|2 - 15360)cosh(x) + (- 210432\|2 + 273408)cosh(x) +--R + +--R +-+ 11 +--R (1390080\|2 - 1797120)cosh(x) +--R + +--R +-+ 9 +--R (- 4161024\|2 + 5348352)cosh(x) +--R + +--R +-+ 7 +--R (5564928\|2 - 7123968)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 2769408\|2 + 3572736)cosh(x) + (537088\|2 - 697344)cosh(x) +--R + +--R +-+ +--R (- 35328\|2 + 46080)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R (1152\|2 - 1536)cosh(x) + (- 24576\|2 + 32768)cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R (198144\|2 - 264192)cosh(x) + (- 737280\|2 + 983040)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (1223424\|2 - 1631232)cosh(x) + (- 737280\|2 + 983040)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (198144\|2 - 264192)cosh(x) + (- 24576\|2 + 32768)cosh(x) +--R + +--R +-+ +--R 1152\|2 - 1536 +--R * +--R 6 +--R tanh(x) +--R + +--R +-+ 16 +-+ 15 +--R (- 1728\|2 + 2304)sinh(x) + (- 17664\|2 + 23040)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R ((- 80640\|2 + 101376)cosh(x) + 36864\|2 - 49152)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 215808\|2 + 253440)cosh(x) + (315648\|2 - 410112)cosh(x)) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 372480\|2 + 377856)cosh(x) + (1184256\|2 - 1468416)cosh(x) +--R + +--R +-+ +--R - 297216\|2 + 396288 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 426240\|2 + 281088)cosh(x) + (2539008\|2 - 2860032)cosh(x) +--R + +--R +-+ +--R (- 2085120\|2 + 2695680)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 312576\|2 - 101376)cosh(x) + (3377664\|2 - 2967552)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 6250752\|2 + 7603200)cosh(x) + 1105920\|2 - 1474560 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 126720\|2 - 557568)cosh(x) + (2780928\|2 - 597504)cosh(x) +--R + +--R +-+ 3 +--R (- 10315008\|2 + 10861056)cosh(x) +--R + +--R +-+ +--R (6241536\|2 - 8022528)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 38016\|2 - 760320)cosh(x) + (1299456\|2 + 2912256)cosh(x) +--R + +--R +-+ 4 +--R (- 9923328\|2 + 6276096)cosh(x) +--R + +--R +-+ 2 +-+ +--R (14515200\|2 - 17215488)cosh(x) - 1835136\|2 + 2446848 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 126720\|2 - 557568)cosh(x) + (525312\|2 + 4589568)cosh(x) +--R + +--R +-+ 5 +--R (- 5442048\|2 - 4119552)cosh(x) +--R + +--R +-+ 3 +--R (17556480\|2 - 16570368)cosh(x) +--R + +--R +-+ +--R (- 8347392\|2 + 10685952)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +--R (- 312576\|2 - 101376)cosh(x) +--R + +--R +-+ 8 +--R (1299456\|2 + 2912256)cosh(x) +--R + +--R +-+ 6 +--R (- 2741760\|2 - 9676800)cosh(x) +--R + +--R +-+ 4 +--R (11805696\|2 - 2838528)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 14830848\|2 + 17224704)cosh(x) + 1105920\|2 - 1474560 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 426240\|2 + 281088)cosh(x) + (2780928\|2 - 597504)cosh(x) +--R + +--R +-+ 7 +--R (- 5442048\|2 - 4119552)cosh(x) +--R + +--R +-+ 5 +--R (7257600\|2 + 6128640)cosh(x) +--R + +--R +-+ 3 +--R (- 13559040\|2 + 11874816)cosh(x) +--R + +--R +-+ +--R (4154112\|2 - 5359104)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +--R (- 372480\|2 + 377856)cosh(x) +--R + +--R +-+ 10 +--R (3377664\|2 - 2967552)cosh(x) +--R + +--R +-+ 8 +--R (- 9923328\|2 + 6276096)cosh(x) +--R + +--R +-+ 6 +--R (11805696\|2 - 2838528)cosh(x) +--R + +--R +-+ 4 +--R (- 10480896\|2 + 5778432)cosh(x) +--R + +--R +-+ 2 +-+ +--R (6898176\|2 - 8497152)cosh(x) - 297216\|2 + 396288 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +--R (- 215808\|2 + 253440)cosh(x) +--R + +--R +-+ 11 +--R (2539008\|2 - 2860032)cosh(x) +--R + +--R +-+ 9 +--R (- 10315008\|2 + 10861056)cosh(x) +--R + +--R +-+ 7 +--R (17556480\|2 - 16570368)cosh(x) +--R + +--R +-+ 5 +--R (- 13559040\|2 + 11874816)cosh(x) +--R + +--R +-+ 3 +-+ +--R (7699968\|2 - 9225216)cosh(x) + (- 805632\|2 + 1046016)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +--R (- 80640\|2 + 101376)cosh(x) +--R + +--R +-+ 12 +--R (1184256\|2 - 1468416)cosh(x) +--R + +--R +-+ 10 +--R (- 6250752\|2 + 7603200)cosh(x) +--R + +--R +-+ 8 +--R (14515200\|2 - 17215488)cosh(x) +--R + +--R +-+ 6 +--R (- 14830848\|2 + 17224704)cosh(x) +--R + +--R +-+ 4 +--R (6898176\|2 - 8497152)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 1029888\|2 + 1317888)cosh(x) + 36864\|2 - 49152 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R (- 17664\|2 + 23040)cosh(x) + (315648\|2 - 410112)cosh(x) +--R + +--R +-+ 11 +--R (- 2085120\|2 + 2695680)cosh(x) +--R + +--R +-+ 9 +--R (6241536\|2 - 8022528)cosh(x) +--R + +--R +-+ 7 +--R (- 8347392\|2 + 10685952)cosh(x) +--R + +--R +-+ 5 +--R (4154112\|2 - 5359104)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 805632\|2 + 1046016)cosh(x) + (52992\|2 - 69120)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R (- 1728\|2 + 2304)cosh(x) + (36864\|2 - 49152)cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 297216\|2 + 396288)cosh(x) + (1105920\|2 - 1474560)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 1835136\|2 + 2446848)cosh(x) + (1105920\|2 - 1474560)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 297216\|2 + 396288)cosh(x) + (36864\|2 - 49152)cosh(x) +--R + +--R +-+ +--R - 1728\|2 + 2304 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 16 +-+ 15 +--R (864\|2 - 1152)sinh(x) + (8832\|2 - 11520)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R ((40320\|2 - 50688)cosh(x) - 18432\|2 + 24576)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((107904\|2 - 126720)cosh(x) + (- 157824\|2 + 205056)cosh(x)) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +--R (186240\|2 - 188928)cosh(x) + (- 592128\|2 + 734208)cosh(x) +--R + +--R +-+ +--R 148608\|2 - 198144 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (213120\|2 - 140544)cosh(x) + (- 1269504\|2 + 1430016)cosh(x) +--R + +--R +-+ +--R (1042560\|2 - 1347840)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (156288\|2 + 50688)cosh(x) + (- 1688832\|2 + 1483776)cosh(x) +--R + +--R +-+ 2 +-+ +--R (3125376\|2 - 3801600)cosh(x) - 552960\|2 + 737280 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (63360\|2 + 278784)cosh(x) + (- 1390464\|2 + 298752)cosh(x) +--R + +--R +-+ 3 +-+ +--R (5157504\|2 - 5430528)cosh(x) + (- 3120768\|2 + 4011264)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (19008\|2 + 380160)cosh(x) + (- 649728\|2 - 1456128)cosh(x) +--R + +--R +-+ 4 +--R (4961664\|2 - 3138048)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 7257600\|2 + 8607744)cosh(x) + 917568\|2 - 1223424 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (63360\|2 + 278784)cosh(x) + (- 262656\|2 - 2294784)cosh(x) +--R + +--R +-+ 5 +--R (2721024\|2 + 2059776)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 8778240\|2 + 8285184)cosh(x) + (4173696\|2 - 5342976)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (156288\|2 + 50688)cosh(x) + (- 649728\|2 - 1456128)cosh(x) +--R + +--R +-+ 6 +--R (1370880\|2 + 4838400)cosh(x) +--R + +--R +-+ 4 +--R (- 5902848\|2 + 1419264)cosh(x) +--R + +--R +-+ 2 +-+ +--R (7415424\|2 - 8612352)cosh(x) - 552960\|2 + 737280 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (213120\|2 - 140544)cosh(x) + (- 1390464\|2 + 298752)cosh(x) +--R + +--R +-+ 7 +--R (2721024\|2 + 2059776)cosh(x) +--R + +--R +-+ 5 +--R (- 3628800\|2 - 3064320)cosh(x) +--R + +--R +-+ 3 +-+ +--R (6779520\|2 - 5937408)cosh(x) + (- 2077056\|2 + 2679552)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +--R (186240\|2 - 188928)cosh(x) +--R + +--R +-+ 10 +--R (- 1688832\|2 + 1483776)cosh(x) +--R + +--R +-+ 8 +--R (4961664\|2 - 3138048)cosh(x) +--R + +--R +-+ 6 +--R (- 5902848\|2 + 1419264)cosh(x) +--R + +--R +-+ 4 +--R (5240448\|2 - 2889216)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 3449088\|2 + 4248576)cosh(x) + 148608\|2 - 198144 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +--R (107904\|2 - 126720)cosh(x) +--R + +--R +-+ 11 +--R (- 1269504\|2 + 1430016)cosh(x) +--R + +--R +-+ 9 +--R (5157504\|2 - 5430528)cosh(x) +--R + +--R +-+ 7 +--R (- 8778240\|2 + 8285184)cosh(x) +--R + +--R +-+ 5 +--R (6779520\|2 - 5937408)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 3849984\|2 + 4612608)cosh(x) + (402816\|2 - 523008)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R (40320\|2 - 50688)cosh(x) + (- 592128\|2 + 734208)cosh(x) +--R + +--R +-+ 10 +--R (3125376\|2 - 3801600)cosh(x) +--R + +--R +-+ 8 +--R (- 7257600\|2 + 8607744)cosh(x) +--R + +--R +-+ 6 +--R (7415424\|2 - 8612352)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 3449088\|2 + 4248576)cosh(x) + (514944\|2 - 658944)cosh(x) +--R + +--R +-+ +--R - 18432\|2 + 24576 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R (8832\|2 - 11520)cosh(x) + (- 157824\|2 + 205056)cosh(x) +--R + +--R +-+ 11 +--R (1042560\|2 - 1347840)cosh(x) +--R + +--R +-+ 9 +--R (- 3120768\|2 + 4011264)cosh(x) +--R + +--R +-+ 7 +--R (4173696\|2 - 5342976)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 2077056\|2 + 2679552)cosh(x) + (402816\|2 - 523008)cosh(x) +--R + +--R +-+ +--R (- 26496\|2 + 34560)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R (864\|2 - 1152)cosh(x) + (- 18432\|2 + 24576)cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R (148608\|2 - 198144)cosh(x) + (- 552960\|2 + 737280)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (917568\|2 - 1223424)cosh(x) + (- 552960\|2 + 737280)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (148608\|2 - 198144)cosh(x) + (- 18432\|2 + 24576)cosh(x) +--R + +--R +-+ +--R 864\|2 - 1152 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 16 +-+ 15 +--R (- 144\|2 + 192)sinh(x) + (- 1472\|2 + 1920)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R ((- 6720\|2 + 8448)cosh(x) + 3072\|2 - 4096)sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R ((- 17984\|2 + 21120)cosh(x) + (26304\|2 - 34176)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 31040\|2 + 31488)cosh(x) + (98688\|2 - 122368)cosh(x) +--R + +--R +-+ +--R - 24768\|2 + 33024 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 35520\|2 + 23424)cosh(x) + (211584\|2 - 238336)cosh(x) +--R + +--R +-+ +--R (- 173760\|2 + 224640)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 26048\|2 - 8448)cosh(x) + (281472\|2 - 247296)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 520896\|2 + 633600)cosh(x) + 92160\|2 - 122880 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 10560\|2 - 46464)cosh(x) + (231744\|2 - 49792)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 859584\|2 + 905088)cosh(x) + (520128\|2 - 668544)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 3168\|2 - 63360)cosh(x) + (108288\|2 + 242688)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 826944\|2 + 523008)cosh(x) + (1209600\|2 - 1434624)cosh(x) +--R + +--R +-+ +--R - 152928\|2 + 203904 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 10560\|2 - 46464)cosh(x) + (43776\|2 + 382464)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 453504\|2 - 343296)cosh(x) + (1463040\|2 - 1380864)cosh(x) +--R + +--R +-+ +--R (- 695616\|2 + 890496)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 26048\|2 - 8448)cosh(x) + (108288\|2 + 242688)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 228480\|2 - 806400)cosh(x) + (983808\|2 - 236544)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 1235904\|2 + 1435392)cosh(x) + 92160\|2 - 122880 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 35520\|2 + 23424)cosh(x) + (231744\|2 - 49792)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 453504\|2 - 343296)cosh(x) + (604800\|2 + 510720)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 1129920\|2 + 989568)cosh(x) + (346176\|2 - 446592)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 31040\|2 + 31488)cosh(x) + (281472\|2 - 247296)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 826944\|2 + 523008)cosh(x) + (983808\|2 - 236544)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 873408\|2 + 481536)cosh(x) + (574848\|2 - 708096)cosh(x) +--R + +--R +-+ +--R - 24768\|2 + 33024 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +--R (- 17984\|2 + 21120)cosh(x) + (211584\|2 - 238336)cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 859584\|2 + 905088)cosh(x) + (1463040\|2 - 1380864)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 1129920\|2 + 989568)cosh(x) + (641664\|2 - 768768)cosh(x) +--R + +--R +-+ +--R (- 67136\|2 + 87168)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R (- 6720\|2 + 8448)cosh(x) + (98688\|2 - 122368)cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 520896\|2 + 633600)cosh(x) + (1209600\|2 - 1434624)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 1235904\|2 + 1435392)cosh(x) + (574848\|2 - 708096)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 85824\|2 + 109824)cosh(x) + 3072\|2 - 4096 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R (- 1472\|2 + 1920)cosh(x) + (26304\|2 - 34176)cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 173760\|2 + 224640)cosh(x) + (520128\|2 - 668544)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 695616\|2 + 890496)cosh(x) + (346176\|2 - 446592)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 67136\|2 + 87168)cosh(x) + (4416\|2 - 5760)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R (- 144\|2 + 192)cosh(x) + (3072\|2 - 4096)cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 24768\|2 + 33024)cosh(x) + (92160\|2 - 122880)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 152928\|2 + 203904)cosh(x) + (92160\|2 - 122880)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 24768\|2 + 33024)cosh(x) + (3072\|2 - 4096)cosh(x) - 144\|2 + 192 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 510 +t0065:= (1-sinh(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (288) \|- sinh(x) + 1 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 510 +r0065:= x +--R +--R +--R (289) x +--R Type: Variable(x) +--E 337 + +--S 338 of 510 +a0065:= integrate(t0065,x) +--R +--R +--R x +---------------+ +--R ++ | 2 +--R (290) | \|- sinh(%N) + 1 d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 510 +m0065:= a0065-r0065 +--R +--R +--R x +---------------+ +--R ++ | 2 +--R (291) | \|- sinh(%N) + 1 d%N - x +--R ++ +--R Type: Expression(Integer) +--E 339 + +--S 340 of 510 +d0065:= D(m0065,x) +--R +--R +--R +--------------+ +--R | 2 +--R (292) \|- sinh(x) + 1 - 1 +--R Type: Expression(Integer) +--E 340 + +--S 341 of 510 +t0066:= (-1+sinh(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (293) \|sinh(x) - 1 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 510 +r0066:= (-3+cosh(2*x))^(1/2)*x/(3-cosh(2*x))^(1/2) +--R +--R +--R +------------+ +--R x\|cosh(2x) - 3 +--R (294) ----------------- +--R +--------------+ +--R \|- cosh(2x) + 3 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 510 +a0066:= integrate(t0066,x) +--R +--R +--R x +-------------+ +--R ++ | 2 +--R (295) | \|sinh(%N) - 1 d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 510 +m0066:= a0066-r0066 +--R +--R +--R x +-------------+ +--R +--------------+ ++ | 2 +------------+ +--R \|- cosh(2x) + 3 | \|sinh(%N) - 1 d%N - x\|cosh(2x) - 3 +--R ++ +--R (296) ------------------------------------------------------------- +--R +--------------+ +--R \|- cosh(2x) + 3 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 510 +d0066:= D(m0066,x) +--R +--R +--R +------------+ +--R +--------------+ +------------+ | 2 +--R \|- cosh(2x) + 3 \|cosh(2x) - 3 \|sinh(x) - 1 - cosh(2x) + 3 +--R (297) -------------------------------------------------------------- +--R +--------------+ +------------+ +--R \|- cosh(2x) + 3 \|cosh(2x) - 3 +--R Type: Expression(Integer) +--E 345 + +--S 346 of 510 +t0067:= (a+b*sinh(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (298) \|b sinh(x) + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 510 +r0067:= -%i*(2*a-b+b*cosh(2*x))^(1/2)*_ + EllipticE(%i*x,b/a)/((2*a-b+b*cosh(2*x))/a)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Integer)) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 347 + +--S 348 of 510 +a0067:= integrate(t0067,x) +--R +--R +--R x +---------------+ +--R ++ | 2 +--R (299) | \|b sinh(%N) + a d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 510 +m0067:= a0067-r0067 +--R +--R +--R x +---------------+ +--R ++ | 2 +--R (300) | \|b sinh(%N) + a d%N - r0067 +--R ++ +--R Type: Expression(Integer) +--E 349 + +--S 350 of 510 +d0067:= D(m0067,x) +--R +--R +--R +--------------+ +--R | 2 +--R (301) \|b sinh(x) + a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 510 +t0068:= 1/(1-sinh(x)^2)^(1/2) +--R +--R +--R 1 +--R (302) ----------------- +--R +--------------+ +--R | 2 +--R \|- sinh(x) + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 510 +r0068:= atan(x) +--R +--R +--R (303) atan(x) +--R Type: Expression(Integer) +--E 352 + +--S 353 of 510 +a0068:= integrate(t0068,x) +--R +--R +--R x +--R ++ 1 +--R (304) | ------------------ d%N +--R ++ +---------------+ +--R | 2 +--R \|- sinh(%N) + 1 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 510 +m0068:= a0068-r0068 +--R +--R +--R x +--R ++ 1 +--R (305) | ------------------ d%N - atan(x) +--R ++ +---------------+ +--R | 2 +--R \|- sinh(%N) + 1 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 510 +d0068:= D(m0068,x) +--R +--R +--R +--------------+ +--R | 2 2 +--R - \|- sinh(x) + 1 + x + 1 +--R (306) ---------------------------- +--R +--------------+ +--R 2 | 2 +--R (x + 1)\|- sinh(x) + 1 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 510 +t0069:= 1/(-1+sinh(x)^2)^(1/2) +--R +--R +--R 1 +--R (307) --------------- +--R +------------+ +--R | 2 +--R \|sinh(x) - 1 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 510 +r0069:= (3-cosh(2*x))^(1/2)*atan(x)/(-3+cosh(2*x))^(1/2) +--R +--R +--R +--------------+ +--R atan(x)\|- cosh(2x) + 3 +--R (308) ------------------------ +--R +------------+ +--R \|cosh(2x) - 3 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 510 +a0069:= integrate(t0069,x) +--R +--R +--R x +--R ++ 1 +--R (309) | ---------------- d%N +--R ++ +-------------+ +--R | 2 +--R \|sinh(%N) - 1 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 510 +m0069:= a0069-r0069 +--R +--R +--R x +--R +------------+ ++ 1 +--------------+ +--R \|cosh(2x) - 3 | ---------------- d%N - atan(x)\|- cosh(2x) + 3 +--R ++ +-------------+ +--R | 2 +--R \|sinh(%N) - 1 +--R (310) -------------------------------------------------------------------- +--R +------------+ +--R \|cosh(2x) - 3 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 510 +d0069:= D(m0069,x) +--R +--R +--R (311) +--R +------------+ +--R | 2 2 +--------------+ +------------+ +--R (cosh(2x) - 3)\|sinh(x) - 1 + (x + 1)\|- cosh(2x) + 3 \|cosh(2x) - 3 +--R ------------------------------------------------------------------------ +--R +------------+ +--R 2 +--------------+ +------------+ | 2 +--R (x + 1)\|- cosh(2x) + 3 \|cosh(2x) - 3 \|sinh(x) - 1 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 510 +t0070:= 1/(a+b*sinh(x)^2)^(1/2) +--R +--R +--R 1 +--R (312) ----------------- +--R +--------------+ +--R | 2 +--R \|b sinh(x) + a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 510 +r0070:= -%i*((2*a-b+b*cosh(2*x))/a)^(1/2)*_ + EllipticF(%i*x,b/a)/(2*a-b+b*cosh(2*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Integer)) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 362 + +--S 363 of 510 +a0070:= integrate(t0070,x) +--R +--R +--R x +--R ++ 1 +--R (313) | ------------------ d%N +--R ++ +---------------+ +--R | 2 +--R \|b sinh(%N) + a +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 510 +m0070:= a0070-r0070 +--R +--R +--R x +--R ++ 1 +--R (314) | ------------------ d%N - r0070 +--R ++ +---------------+ +--R | 2 +--R \|b sinh(%N) + a +--R Type: Expression(Integer) +--E 364 + +--S 365 of 510 +d0070:= D(m0070,x) +--R +--R +--R 1 +--R (315) ----------------- +--R +--------------+ +--R | 2 +--R \|b sinh(x) + a +--R Type: Expression(Integer) +--E 365 + +--S 366 of 510 +t0071:= x/(a+b*sinh(x)^2) +--R +--R +--R x +--R (316) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 366 + +--S 367 of 510 +r0071:= -1/4*(-2*x*log((-2*a+2*a^(1/2)*(a-b)^(1/2)+b-_ + b*exp(2*x))/(-2*a+2*a^(1/2)*(a-b)^(1/2)+b))+_ + 2*x*log((2*a+2*a^(1/2)*(a-b)^(1/2)-b+b*exp(2*x))/_ + (2*a+2*a^(1/2)*(a-b)^(1/2)-b))-_ + polylog(2,b*exp(2*x)/(-2*a+2*a^(1/2)*(a-b)^(1/2)+b))+_ + polylog(2,-1/(2*a+2*a^(1/2)*(a-b)^(1/2)-b)*b*_ + exp(2*x)))/a^(1/2)/(a-b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 367 + +--S 368 of 510 +a0071:= integrate(t0071,x) +--R +--R +--R x +--R ++ %N +--R (317) | --------------- d%N +--R ++ 2 +--R b sinh(%N) + a +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 510 +m0071:= a0071-r0071 +--R +--R +--R x +--R ++ %N +--R (318) | --------------- d%N - r0071 +--R ++ 2 +--R b sinh(%N) + a +--R Type: Expression(Integer) +--E 369 + +--S 370 of 510 +d0071:= D(m0071,x) +--R +--R +--R x +--R (319) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 370 + +--S 371 of 510 +t0072:= x^2/(a+b*sinh(x)^2) +--R +--R +--R 2 +--R x +--R (320) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 371 + +--S 372 of 510 +r0072:= -1/4*(-2*x^2*log((-2*a+2*a^(1/2)*(a-b)^(1/2)+b-_ + b*exp(2*x))/(-2*a+2*a^(1/2)*(a-b)^(1/2)+b))+_ + 2*x^2*log((2*a+2*a^(1/2)*(a-b)^(1/2)-b+_ + b*exp(2*x))/(2*a+2*a^(1/2)*(a-b)^(1/2)-b))-_ + 2*x*polylog(2,b*exp(2*x)/(-2*a+2*a^(1/2)*(a-b)^(1/2)+b))+_ + 2*x*polylog(2,-1/(2*a+2*a^(1/2)*(a-b)^(1/2)-b)*b*exp(2*x))+_ + polylog(3,b*exp(2*x)/(-2*a+2*a^(1/2)*(a-b)^(1/2)+b))-_ + polylog(3,-1/(2*a+2*a^(1/2)*(a-b)^(1/2)-b)*_ + b*exp(2*x)))/a^(1/2)/(a-b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 372 + +--S 373 of 510 +a0072:= integrate(t0072,x) +--R +--R +--R x 2 +--R ++ %N +--R (321) | --------------- d%N +--R ++ 2 +--R b sinh(%N) + a +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 510 +m0072:= a0072-r0072 +--R +--R +--R x 2 +--R ++ %N +--R (322) | --------------- d%N - r0072 +--R ++ 2 +--R b sinh(%N) + a +--R Type: Expression(Integer) +--E 374 + +--S 375 of 510 +d0072:= D(m0072,x) +--R +--R +--R 2 +--R x +--R (323) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 375 + +--S 376 of 510 +t0073:= x^3/(a+b*sinh(x)^2) +--R +--R +--R 3 +--R x +--R (324) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 376 + +--S 377 of 510 +r0073:= -1/8*(-4*x^3*log((-2*a+2*a^(1/2)*(a-b)^(1/2)+b-b*exp(2*x))/_ + (-2*a+2*a^(1/2)*(a-b)^(1/2)+b))+4*x^3*log((2*a+2*a^(1/2)*_ + (a-b)^(1/2)-b+b*exp(2*x))/(2*a+2*a^(1/2)*(a-b)^(1/2)-b))-_ + 6*x^2*polylog(2,b*exp(2*x)/(-2*a+2*a^(1/2)*(a-b)^(1/2)+b))+_ + 6*x^2*polylog(2,-1/(2*a+2*a^(1/2)*(a-b)^(1/2)-b)*b*exp(2*x))+_ + 6*x*polylog(3,b*exp(2*x)/(-2*a+2*a^(1/2)*(a-b)^(1/2)+b))-_ + 6*x*polylog(3,-1/(2*a+2*a^(1/2)*(a-b)^(1/2)-b)*b*exp(2*x))-_ + 3*polylog(4,b*exp(2*x)/(-2*a+2*a^(1/2)*(a-b)^(1/2)+b))+_ + 3*polylog(4,-1/(2*a+2*a^(1/2)*(a-b)^(1/2)-b)*_ + b*exp(2*x)))/a^(1/2)/(a-b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 377 + +--S 378 of 510 +a0073:= integrate(t0073,x) +--R +--R +--R x 3 +--R ++ %N +--R (325) | --------------- d%N +--R ++ 2 +--R b sinh(%N) + a +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 510 +m0073:= a0073-r0073 +--R +--R +--R x 3 +--R ++ %N +--R (326) | --------------- d%N - r0073 +--R ++ 2 +--R b sinh(%N) + a +--R Type: Expression(Integer) +--E 379 + +--S 380 of 510 +d0073:= D(m0073,x) +--R +--R +--R 3 +--R x +--R (327) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 380 + +--S 381 of 510 +t0074:= 1/(a+b*sinh(x)^3) +--R +--R +--R 1 +--R (328) -------------- +--R 3 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 381 + +--S 382 of 510 +r0074:= -2/3*atanh((b^(1/3)-a^(1/3)*tanh(1/2*x))/(a^(2/3)+b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)+b^(2/3))^(1/2)-2/3*atanh(((-1)^(2/3)*b^(1/3)-_ + a^(1/3)*tanh(1/2*x))/(a^(2/3)-(-1)^(1/3)*b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-(-1)^(1/3)*b^(2/3))^(1/2)+_ + 2/3*atanh(((-1)^(1/3)*b^(1/3)+_ + a^(1/3)*tanh(1/2*x))/(a^(2/3)+(-1)^(2/3)*b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)+(-1)^(2/3)*b^(2/3))^(1/2) +--R +--R +--R (329) +--R - +--R +-------------+ +--------------------+ +--R |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 2\|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+2 3+-+ x 3+-+ +--R \|- 1 \|b - tanh(-)\|a +--R 2 +--R atanh(-------------------------) +--R +---------------------+ +--R | 3+---+3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +---------------------+ +--------------------+ +--R | 3+---+3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+-+ x 3+-+ +--R \|b - tanh(-)\|a +--R 2 +--R atanh(------------------) +--R +-------------+ +--R |3+-+2 3+-+2 +--R \|\|b + \|a +--R + +--R 3+---+3+-+ x 3+-+ +--R +---------------------+ +-------------+ \|- 1 \|b + tanh(-)\|a +--R | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 2 +--R 2\|- \|- 1 \|b + \|a \|\|b + \|a atanh(------------------------) +--R +--------------------+ +--R |3+---+2 3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +---------------------+ +-------------+ +--------------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 382 + +--S 383 of 510 +a0074:= integrate(t0074,x) +--R +--R +--R (330) +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b + 486a )%%ER0 - 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b + 486a )%%ER0 + (27a b - 135a )%%ER0 + 9a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (- 162a b - 162a )%%ER0 +--R * +--R ROOT +--R 2 4 4 2 6 2 2 2 4 +--I (- 81a b - 162a b - 81a )%%ER0 + (18a b + 18a )%%ER0 +--R + +--R 2 2 +--R - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%ER0 + 54a %%ER0 + 4b sinh(x) + 4b cosh(x) - 4a +--R + +--R - +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b + 486a )%%ER0 - 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b - 486a )%%ER0 + (- 27a b + 135a )%%ER0 - 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (162a b + 162a )%%ER0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%ER0 + 54a %%ER0 + 4b sinh(x) + 4b cosh(x) +--R + +--R - 4a +--R + +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b - 486a )%%ER0 + 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b + 486a )%%ER0 + (27a b - 135a )%%ER0 + 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (162a b + 162a )%%ER0 +--R * +--R ROOT +--R 2 4 4 2 6 2 2 2 4 +--I (- 81a b - 162a b - 81a )%%ER0 + (18a b + 18a )%%ER0 +--R + +--R 2 2 +--R - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%ER0 + 54a %%ER0 + 4b sinh(x) + 4b cosh(x) - 4a +--R + +--R - +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b - 486a )%%ER0 + 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b - 486a )%%ER0 + (- 27a b + 135a )%%ER0 - 9a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (- 162a b - 162a )%%ER0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%ER0 + 54a %%ER0 + 4b sinh(x) + 4b cosh(x) +--R + +--R - 4a +--R + +--R - +--R +------+ +--I \|4%%ER0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--I ((486a b + 486a )%%ER0 + (27a b - 135a )%%ER0 + 9a ) +--R * +--R +------+ +--I \|4%%ER0 +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%ER0 - 54a %%ER0 + 2b sinh(x) + 2b cosh(x) +--R + +--R 4a +--R + +--R +------+ +--I \|4%%ER0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--I ((- 486a b - 486a )%%ER0 + (- 27a b + 135a )%%ER0 - 9a ) +--R * +--R +------+ +--I \|4%%ER0 +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%ER0 - 54a %%ER0 + 2b sinh(x) + 2b cosh(x) + 4a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 510 +m0074:= a0074-r0074 +--R +--R +--R (331) +--R +---------------------+ +-------------+ +--------------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b + 486a )%%ER0 - 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b + 486a )%%ER0 + (27a b - 135a )%%ER0 + 9a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (- 162a b - 162a )%%ER0 +--R * +--R ROOT +--R 2 4 4 2 6 2 2 2 4 +--I (- 81a b - 162a b - 81a )%%ER0 + (18a b + 18a )%%ER0 +--R + +--R 2 2 +--R - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%ER0 + 54a %%ER0 + 4b sinh(x) + 4b cosh(x) - 4a +--R + +--R - +--R +---------------------+ +-------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--R |3+---+2 3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b + 486a )%%ER0 - 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b - 486a )%%ER0 + (- 27a b + 135a )%%ER0 - 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (162a b + 162a )%%ER0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%ER0 + 54a %%ER0 + 4b sinh(x) + 4b cosh(x) +--R + +--R - 4a +--R + +--R +---------------------+ +-------------+ +--------------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b - 486a )%%ER0 + 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b + 486a )%%ER0 + (27a b - 135a )%%ER0 + 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (162a b + 162a )%%ER0 +--R * +--R ROOT +--R 2 4 4 2 6 2 2 2 4 +--I (- 81a b - 162a b - 81a )%%ER0 + (18a b + 18a )%%ER0 +--R + +--R 2 2 +--R - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%ER0 + 54a %%ER0 + 4b sinh(x) + 4b cosh(x) - 4a +--R + +--R - +--R +---------------------+ +-------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--R |3+---+2 3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b - 486a )%%ER0 + 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b - 486a )%%ER0 + (- 27a b + 135a )%%ER0 - 9a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%ER0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (- 162a b - 162a )%%ER0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%ER0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%ER0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%ER0 + 54a %%ER0 + 4b sinh(x) + 4b cosh(x) +--R + +--R - 4a +--R + +--R - +--R +---------------------+ +-------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--R |3+---+2 3+-+2 3+-+2 +------+ +--I \|\|- 1 \|b + \|a \|4%%ER0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--I ((486a b + 486a )%%ER0 + (27a b - 135a )%%ER0 + 9a ) +--R * +--R +------+ +--I \|4%%ER0 +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%ER0 - 54a %%ER0 + 2b sinh(x) + 2b cosh(x) +--R + +--R 4a +--R + +--R +---------------------+ +-------------+ +--------------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%ER0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--I ((- 486a b - 486a )%%ER0 + (- 27a b + 135a )%%ER0 - 9a ) +--R * +--R +------+ +--I \|4%%ER0 +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%ER0 - 54a %%ER0 + 2b sinh(x) + 2b cosh(x) + 4a +--R + +--R 3+---+2 3+-+ x 3+-+ +--R +-------------+ +--------------------+ \|- 1 \|b - tanh(-)\|a +--R |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 2 +--R 4\|\|b + \|a \|\|- 1 \|b + \|a atanh(-------------------------) +--R +---------------------+ +--R | 3+---+3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R 3+-+ x 3+-+ +--R +---------------------+ +--------------------+ \|b - tanh(-)\|a +--R | 3+---+3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 2 +--R 4\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atanh(------------------) +--R +-------------+ +--R |3+-+2 3+-+2 +--R \|\|b + \|a +--R + +--R 3+---+3+-+ x 3+-+ +--R +---------------------+ +-------------+ \|- 1 \|b + tanh(-)\|a +--R | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 2 +--R - 4\|- \|- 1 \|b + \|a \|\|b + \|a atanh(------------------------) +--R +--------------------+ +--R |3+---+2 3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +---------------------+ +-------------+ +--------------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 6\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 384 + +--S 385 of 510 +d0074:= D(m0074,x) +--R +--R +--R (332) +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 9a b \|- 1 - 9a b\|- 1 + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 60a b \|- 1 + 60a b\|- 1 - 60a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (36a b \|- 1 - 36a b\|- 1 + 36a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (54a b \|- 1 - 54a b\|- 1 + 54a b)cosh(x) - 9a b \|- 1 +--R + +--R 2 3+---+ 2 +--R 9a b\|- 1 - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (36a b \|- 1 - 36a b\|- 1 + 36a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (9a b \|- 1 - 9a b\|- 1 + 9a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cosh(x) + 3a b \|- 1 +--R + +--R 2 3+---+ 2 +--R - 3a b\|- 1 + 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (12a b \|- 1 - 12a b \|- 1 + 12a b )sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (180a b \|- 1 - 180a b \|- 1 + 180a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 36a b \|- 1 + 36a b \|- 1 - 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (240a b \|- 1 - 240a b \|- 1 + 240a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 48a b \|- 1 + 48a b\|- 1 - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (180a b \|- 1 - 180a b \|- 1 + 180a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 36a b \|- 1 - 36a b \|- 1 + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (12a b \|- 1 - 12a b \|- 1 + 12a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 48a b \|- 1 + 48a b\|- 1 - 48a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) - 12a b \|- 1 +--R + +--R 2 3+---+ 2 +--R 12a b \|- 1 - 12a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R ((- 4b + 5a b)\|- 1 + (4b - 5a b)\|- 1 - 4b + 5a b)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((- 24b + 30a b)\|- 1 + (24b - 30a b)\|- 1 - 24b + 30a b) +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 60b + 75a b)\|- 1 + (60b - 75a b)\|- 1 - 60b +--R + +--R 2 +--R 75a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (12b - 15a b)\|- 1 + (- 12b + 15a b)\|- 1 + 12b - 15a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 80b + 100a b)\|- 1 + (80b - 100a b)\|- 1 - 80b +--R + +--R 2 +--R 100a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (48b - 60a b)\|- 1 + (- 48b + 60a b)\|- 1 + 48b +--R + +--R 2 +--R - 60a b +--R * +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 +--R (64a b + 64a )\|- 1 + (- 64a b - 64a )\|- 1 + 64a b +--R + +--R 3 +--R 64a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 60b + 75a b)\|- 1 + (60b - 75a b)\|- 1 - 60b +--R + +--R 2 +--R 75a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (72b - 90a b)\|- 1 + (- 72b + 90a b)\|- 1 + 72b +--R + +--R 2 +--R - 90a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ +--R (192a b + 192a )\|- 1 + (- 192a b - 192a )\|- 1 +--R + +--R 2 3 +--R 192a b + 192a +--R * +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 12b + 15a b)\|- 1 + (12b - 15a b)\|- 1 - 12b + 15a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 24b + 30a b)\|- 1 + (24b - 30a b)\|- 1 - 24b +--R + +--R 2 +--R 30a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (48b - 60a b)\|- 1 + (- 48b + 60a b)\|- 1 + 48b +--R + +--R 2 +--R - 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ +--R (192a b + 192a )\|- 1 + (- 192a b - 192a )\|- 1 +--R + +--R 2 3 +--R 192a b + 192a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 24b + 30a b)\|- 1 + (24b - 30a b)\|- 1 - 24b +--R + +--R 2 +--R 30a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R ((- 4b + 5a b)\|- 1 + (4b - 5a b)\|- 1 - 4b + 5a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((12b - 15a b)\|- 1 + (- 12b + 15a b)\|- 1 + 12b - 15a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 +--R (64a b + 64a )\|- 1 + (- 64a b - 64a )\|- 1 + 64a b +--R + +--R 3 +--R 64a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((- 12b + 15a b)\|- 1 + (12b - 15a b)\|- 1 - 12b + 15a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (4b - 5a b)\|- 1 + (- 4b + 5a b)\|- 1 + 4b - 5a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 24a b \|- 1 + 24a b \|- 1 - 24a b )sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 360a b \|- 1 + 360a b \|- 1 - 360a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 72a b \|- 1 - 72a b \|- 1 + 72a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 480a b \|- 1 + 480a b \|- 1 - 480a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (288a b \|- 1 - 288a b \|- 1 + 288a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 96a b \|- 1 + 96a b\|- 1 - 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 360a b \|- 1 + 360a b \|- 1 - 360a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (432a b \|- 1 - 432a b \|- 1 + 432a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 288a b \|- 1 + 288a b\|- 1 - 288a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 72a b \|- 1 + 72a b \|- 1 - 72a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (288a b \|- 1 - 288a b \|- 1 + 288a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 288a b \|- 1 + 288a b\|- 1 - 288a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 24a b \|- 1 + 24a b \|- 1 - 24a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 96a b \|- 1 + 96a b\|- 1 - 96a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) + 24a b \|- 1 +--R + +--R 2 3+---+ 2 +--R - 24a b \|- 1 + 24a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R ((4b - 5a b)\|- 1 + (- 4b + 5a b)\|- 1 + 4b - 5a b)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((24b - 30a b)\|- 1 + (- 24b + 30a b)\|- 1 + 24b - 30a b) +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (60b - 75a b)\|- 1 + (- 60b + 75a b)\|- 1 + 60b +--R + +--R 2 +--R - 75a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 12b + 15a b)\|- 1 + (12b - 15a b)\|- 1 - 12b + 15a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (80b - 100a b)\|- 1 + (- 80b + 100a b)\|- 1 + 80b +--R + +--R 2 +--R - 100a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 48b + 60a b)\|- 1 + (48b - 60a b)\|- 1 - 48b +--R + +--R 2 +--R 60a b +--R * +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 +--R (- 64a b - 64a )\|- 1 + (64a b + 64a )\|- 1 - 64a b +--R + +--R 3 +--R - 64a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (60b - 75a b)\|- 1 + (- 60b + 75a b)\|- 1 + 60b +--R + +--R 2 +--R - 75a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 72b + 90a b)\|- 1 + (72b - 90a b)\|- 1 - 72b +--R + +--R 2 +--R 90a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ +--R (- 192a b - 192a )\|- 1 + (192a b + 192a )\|- 1 +--R + +--R 2 3 +--R - 192a b - 192a +--R * +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (12b - 15a b)\|- 1 + (- 12b + 15a b)\|- 1 + 12b - 15a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (24b - 30a b)\|- 1 + (- 24b + 30a b)\|- 1 + 24b +--R + +--R 2 +--R - 30a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 48b + 60a b)\|- 1 + (48b - 60a b)\|- 1 - 48b +--R + +--R 2 +--R 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ +--R (- 192a b - 192a )\|- 1 + (192a b + 192a )\|- 1 +--R + +--R 2 3 +--R - 192a b - 192a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (24b - 30a b)\|- 1 + (- 24b + 30a b)\|- 1 + 24b +--R + +--R 2 +--R - 30a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R ((4b - 5a b)\|- 1 + (- 4b + 5a b)\|- 1 + 4b - 5a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((- 12b + 15a b)\|- 1 + (12b - 15a b)\|- 1 - 12b + 15a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 +--R (- 64a b - 64a )\|- 1 + (64a b + 64a )\|- 1 - 64a b +--R + +--R 3 +--R - 64a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((12b - 15a b)\|- 1 + (- 12b + 15a b)\|- 1 + 12b - 15a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 4b + 5a b)\|- 1 + (4b - 5a b)\|- 1 - 4b + 5a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (12a b \|- 1 - 12a b \|- 1 + 12a b )sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (180a b \|- 1 - 180a b \|- 1 + 180a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 36a b \|- 1 + 36a b \|- 1 - 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (240a b \|- 1 - 240a b \|- 1 + 240a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 48a b \|- 1 + 48a b\|- 1 - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (180a b \|- 1 - 180a b \|- 1 + 180a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 36a b \|- 1 - 36a b \|- 1 + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (12a b \|- 1 - 12a b \|- 1 + 12a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 48a b \|- 1 + 48a b\|- 1 - 48a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) - 12a b \|- 1 +--R + +--R 2 3+---+ 2 +--R 12a b \|- 1 - 12a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (3a b \|- 1 - 3a b\|- 1 + 3a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (45a b \|- 1 - 45a b\|- 1 + 45a b)cosh(x) - 9a b \|- 1 +--R + +--R 2 3+---+ 2 +--R 9a b\|- 1 - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (60a b \|- 1 - 60a b\|- 1 + 60a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (45a b \|- 1 - 45a b\|- 1 + 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cosh(x) + 9a b \|- 1 +--R + +--R 2 3+---+ 2 +--R - 9a b\|- 1 + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (3a b \|- 1 - 3a b\|- 1 + 3a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (9a b \|- 1 - 9a b\|- 1 + 9a b)cosh(x) - 3a b \|- 1 +--R + +--R 2 3+---+ 2 +--R 3a b\|- 1 - 3a b +--R * +--R 3+-+2 3+-+2 +--R \|a \|b +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 9a b \|- 1 - 9a b \|- 1 + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 60a b \|- 1 + 60a b \|- 1 - 60a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 9a b \|- 1 + 9a b \|- 1 - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) + 3a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 3a b \|- 1 + 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((4a b + 4a b)\|- 1 + (- 4a b - 4a b)\|- 1 + 4a b + 4a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (24a b + 24a b)\|- 1 + (- 24a b - 24a b)\|- 1 + 24a b +--R + +--R 3 +--R 24a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (60a b + 60a b)\|- 1 + (- 60a b - 60a b)\|- 1 +--R + +--R 3 3 +--R 60a b + 60a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 12a b)\|- 1 + (12a b + 12a b)\|- 1 - 12a b +--R + +--R 3 +--R - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (80a b + 80a b)\|- 1 + (- 80a b - 80a b)\|- 1 +--R + +--R 3 3 +--R 80a b + 80a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 48a b - 48a b)\|- 1 + (48a b + 48a b)\|- 1 +--R + +--R 3 3 +--R - 48a b - 48a b +--R * +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 16a b - 16a )\|- 1 + (16a b + 16a )\|- 1 - 16a b +--R + +--R 4 +--R - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (60a b + 60a b)\|- 1 + (- 60a b - 60a b)\|- 1 +--R + +--R 3 3 +--R 60a b + 60a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 72a b - 72a b)\|- 1 + (72a b + 72a b)\|- 1 +--R + +--R 3 3 +--R - 72a b - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 4 +--R - 48a +--R * +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 12a b)\|- 1 + (- 12a b - 12a b)\|- 1 + 12a b +--R + +--R 3 +--R 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (24a b + 24a b)\|- 1 + (- 24a b - 24a b)\|- 1 +--R + +--R 3 3 +--R 24a b + 24a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 48a b - 48a b)\|- 1 + (48a b + 48a b)\|- 1 +--R + +--R 3 3 +--R - 48a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 4 +--R - 48a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (24a b + 24a b)\|- 1 + (- 24a b - 24a b)\|- 1 +--R + +--R 3 3 +--R 24a b + 24a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((4a b + 4a b)\|- 1 + (- 4a b - 4a b)\|- 1 + 4a b + 4a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 12a b)\|- 1 + (12a b + 12a b)\|- 1 - 12a b +--R + +--R 3 +--R - 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 16a b - 16a )\|- 1 + (16a b + 16a )\|- 1 - 16a b +--R + +--R 4 +--R - 16a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 12a b)\|- 1 + (- 12a b - 12a b)\|- 1 + 12a b +--R + +--R 3 +--R 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R (- 4a b - 4a b)\|- 1 + (4a b + 4a b)\|- 1 - 4a b - 4a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 9a b \|- 1 - 9a b \|- 1 + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 60a b \|- 1 + 60a b \|- 1 - 60a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R 192a b \|- 1 - 192a b\|- 1 + 192a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (576a b \|- 1 - 576a b\|- 1 + 576a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 9a b \|- 1 + 9a b \|- 1 - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (576a b \|- 1 - 576a b\|- 1 + 576a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (192a b \|- 1 - 192a b\|- 1 + 192a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) + 3a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 3a b \|- 1 + 3a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((- 8a b - 8a b)\|- 1 + (8a b + 8a b)\|- 1 - 8a b - 8a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 48a b - 48a b)\|- 1 + (48a b + 48a b)\|- 1 - 48a b +--R + +--R 3 +--R - 48a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 120a b - 120a b)\|- 1 + (120a b + 120a b)\|- 1 +--R + +--R 3 3 +--R - 120a b - 120a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (24a b + 24a b)\|- 1 + (- 24a b - 24a b)\|- 1 + 24a b +--R + +--R 3 +--R 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 160a b - 160a b)\|- 1 + (160a b + 160a b)\|- 1 +--R + +--R 3 3 +--R - 160a b - 160a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (96a b + 96a b)\|- 1 + (- 96a b - 96a b)\|- 1 +--R + +--R 3 3 +--R 96a b + 96a b +--R * +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 160a b + 32a )\|- 1 + (160a b - 32a )\|- 1 - 160a b +--R + +--R 4 +--R 32a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 120a b - 120a b)\|- 1 + (120a b + 120a b)\|- 1 +--R + +--R 3 3 +--R - 120a b - 120a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (144a b + 144a b)\|- 1 + (- 144a b - 144a b)\|- 1 +--R + +--R 3 3 +--R 144a b + 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (- 480a b + 96a )\|- 1 + (480a b - 96a )\|- 1 +--R + +--R 2 2 4 +--R - 480a b + 96a +--R * +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 24a b - 24a b)\|- 1 + (24a b + 24a b)\|- 1 - 24a b +--R + +--R 3 +--R - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 48a b - 48a b)\|- 1 + (48a b + 48a b)\|- 1 +--R + +--R 3 3 +--R - 48a b - 48a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (96a b + 96a b)\|- 1 + (- 96a b - 96a b)\|- 1 +--R + +--R 3 3 +--R 96a b + 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (- 480a b + 96a )\|- 1 + (480a b - 96a )\|- 1 +--R + +--R 2 2 4 +--R - 480a b + 96a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 48a b - 48a b)\|- 1 + (48a b + 48a b)\|- 1 +--R + +--R 3 3 +--R - 48a b - 48a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((- 8a b - 8a b)\|- 1 + (8a b + 8a b)\|- 1 - 8a b - 8a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (24a b + 24a b)\|- 1 + (- 24a b - 24a b)\|- 1 + 24a b +--R + +--R 3 +--R 24a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 160a b + 32a )\|- 1 + (160a b - 32a )\|- 1 - 160a b +--R + +--R 4 +--R 32a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 24a b - 24a b)\|- 1 + (24a b + 24a b)\|- 1 - 24a b +--R + +--R 3 +--R - 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R (8a b + 8a b)\|- 1 + (- 8a b - 8a b)\|- 1 + 8a b + 8a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 9a b \|- 1 + 9a b \|- 1 - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (60a b \|- 1 - 60a b \|- 1 + 60a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R - 192a b \|- 1 + 192a b\|- 1 - 192a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 576a b \|- 1 + 576a b\|- 1 - 576a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 9a b \|- 1 - 9a b \|- 1 + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 576a b \|- 1 + 576a b\|- 1 - 576a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 192a b \|- 1 + 192a b\|- 1 - 192a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) - 3a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 3a b \|- 1 - 3a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((4a b + 4a b)\|- 1 + (- 4a b - 4a b)\|- 1 + 4a b + 4a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (24a b + 24a b)\|- 1 + (- 24a b - 24a b)\|- 1 + 24a b +--R + +--R 3 +--R 24a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (60a b + 60a b)\|- 1 + (- 60a b - 60a b)\|- 1 +--R + +--R 3 3 +--R 60a b + 60a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 12a b)\|- 1 + (12a b + 12a b)\|- 1 - 12a b +--R + +--R 3 +--R - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (80a b + 80a b)\|- 1 + (- 80a b - 80a b)\|- 1 +--R + +--R 3 3 +--R 80a b + 80a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 48a b - 48a b)\|- 1 + (48a b + 48a b)\|- 1 +--R + +--R 3 3 +--R - 48a b - 48a b +--R * +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 16a b - 16a )\|- 1 + (16a b + 16a )\|- 1 - 16a b +--R + +--R 4 +--R - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (60a b + 60a b)\|- 1 + (- 60a b - 60a b)\|- 1 +--R + +--R 3 3 +--R 60a b + 60a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 72a b - 72a b)\|- 1 + (72a b + 72a b)\|- 1 +--R + +--R 3 3 +--R - 72a b - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 4 +--R - 48a +--R * +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 12a b)\|- 1 + (- 12a b - 12a b)\|- 1 + 12a b +--R + +--R 3 +--R 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (24a b + 24a b)\|- 1 + (- 24a b - 24a b)\|- 1 +--R + +--R 3 3 +--R 24a b + 24a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 48a b - 48a b)\|- 1 + (48a b + 48a b)\|- 1 +--R + +--R 3 3 +--R - 48a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 4 +--R - 48a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (24a b + 24a b)\|- 1 + (- 24a b - 24a b)\|- 1 +--R + +--R 3 3 +--R 24a b + 24a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((4a b + 4a b)\|- 1 + (- 4a b - 4a b)\|- 1 + 4a b + 4a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 12a b)\|- 1 + (12a b + 12a b)\|- 1 - 12a b +--R + +--R 3 +--R - 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 16a b - 16a )\|- 1 + (16a b + 16a )\|- 1 - 16a b +--R + +--R 4 +--R - 16a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 12a b)\|- 1 + (- 12a b - 12a b)\|- 1 + 12a b +--R + +--R 3 +--R 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R (- 4a b - 4a b)\|- 1 + (4a b + 4a b)\|- 1 - 4a b - 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) - 9a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 9a b \|- 1 - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (60a b \|- 1 - 60a b \|- 1 + 60a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) + 9a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 9a b \|- 1 + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) - 3a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 3a b \|- 1 - 3a b +--R * +--R 3+-+ +--R \|b +--R + +--R 3 3 6 3 3 5 +--R (- 3a b - 3a b)sinh(x) + (- 18a b - 18a b)cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 4 +--R ((- 45a b - 45a b)cosh(x) + 9a b + 9a b)sinh(x) +--R + +--R 3 3 3 3 3 3 +--R ((- 60a b - 60a b)cosh(x) + (36a b + 36a b)cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 3 +--R (- 45a b - 45a b)cosh(x) + (54a b + 54a b)cosh(x) - 9a b +--R + +--R 3 +--R - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 3 3 3 +--R (- 18a b - 18a b)cosh(x) + (36a b + 36a b)cosh(x) +--R + +--R 3 3 +--R (- 18a b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 6 3 3 4 +--R (- 3a b - 3a b)cosh(x) + (9a b + 9a b)cosh(x) +--R + +--R 3 3 2 3 3 +--R (- 9a b - 9a b)cosh(x) + 3a b + 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (12a b \|- 1 - 12a b \|- 1 + 12a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (180a b \|- 1 - 180a b \|- 1 + 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 36a b \|- 1 + 36a b \|- 1 - 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (240a b \|- 1 - 240a b \|- 1 + 240a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R - 48a b \|- 1 + 48a b\|- 1 - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (180a b \|- 1 - 180a b \|- 1 + 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 36a b \|- 1 - 36a b \|- 1 + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (12a b \|- 1 - 12a b \|- 1 + 12a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 48a b \|- 1 + 48a b\|- 1 - 48a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) - 12a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 12a b \|- 1 - 12a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 3 3+---+2 3 3+---+ 3 3 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 3a b + 9a b)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 18a b + 54a b)cosh(x)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (- 180a b \|- 1 + 180a b \|- 1 - 45a b + 135a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R 36a b \|- 1 - 36a b \|- 1 + 9a b - 27a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 3 +--R (- 240a b \|- 1 + 240a b \|- 1 - 60a b + 180a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (144a b \|- 1 - 144a b \|- 1 + 36a b - 108a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 192a b \|- 1 - 192a b \|- 1 + 192a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 4 +--R (- 180a b \|- 1 + 180a b \|- 1 - 45a b + 135a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (216a b \|- 1 - 216a b \|- 1 + 54a b - 162a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (576a b \|- 1 - 576a b \|- 1 + 576a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R - 36a b \|- 1 + 36a b \|- 1 - 9a b + 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 18a b + 54a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 3 +--R (144a b \|- 1 - 144a b \|- 1 + 36a b - 108a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (576a b \|- 1 - 576a b \|- 1 + 576a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 72a b \|- 1 + 72a b \|- 1 - 18a b + 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 3a b + 9a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 4 +--R (36a b \|- 1 - 36a b \|- 1 + 9a b - 27a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (192a b \|- 1 - 192a b \|- 1 + 192a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 9a b + 27a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R 12a b \|- 1 - 12a b \|- 1 + 3a b - 9a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 24a b \|- 1 + 24a b \|- 1 - 24a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 360a b \|- 1 + 360a b \|- 1 - 360a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 72a b \|- 1 - 72a b \|- 1 + 72a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 480a b \|- 1 + 480a b \|- 1 - 480a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (288a b \|- 1 - 288a b \|- 1 + 288a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R 96a b \|- 1 - 96a b\|- 1 - 192a b - 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 360a b \|- 1 + 360a b \|- 1 - 360a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (432a b \|- 1 - 432a b \|- 1 + 432a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (288a b \|- 1 - 288a b\|- 1 - 576a b - 288a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 72a b \|- 1 + 72a b \|- 1 - 72a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (288a b \|- 1 - 288a b \|- 1 + 288a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (288a b \|- 1 - 288a b\|- 1 - 576a b - 288a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 24a b \|- 1 + 24a b \|- 1 - 24a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 3 +--R (96a b \|- 1 - 96a b\|- 1 - 192a b - 96a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) + 24a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 24a b \|- 1 + 24a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 3 3+---+2 3 3+---+ 3 3 6 +--R (12a b \|- 1 - 12a b \|- 1 + 3a b - 9a b)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 5 +--R (72a b \|- 1 - 72a b \|- 1 + 18a b - 54a b)cosh(x)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (180a b \|- 1 - 180a b \|- 1 + 45a b - 135a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R - 36a b \|- 1 + 36a b \|- 1 - 9a b + 27a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 3 +--R (240a b \|- 1 - 240a b \|- 1 + 60a b - 180a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 144a b \|- 1 + 144a b \|- 1 - 36a b + 108a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 192a b \|- 1 + 192a b \|- 1 - 192a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 4 +--R (180a b \|- 1 - 180a b \|- 1 + 45a b - 135a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 54a b + 162a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 576a b \|- 1 + 576a b \|- 1 - 576a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R 36a b \|- 1 - 36a b \|- 1 + 9a b - 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 5 +--R (72a b \|- 1 - 72a b \|- 1 + 18a b - 54a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 3 +--R (- 144a b \|- 1 + 144a b \|- 1 - 36a b + 108a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 576a b \|- 1 + 576a b \|- 1 - 576a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (72a b \|- 1 - 72a b \|- 1 + 18a b - 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 6 +--R (12a b \|- 1 - 12a b \|- 1 + 3a b - 9a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 4 +--R (- 36a b \|- 1 + 36a b \|- 1 - 9a b + 27a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 192a b \|- 1 + 192a b \|- 1 - 192a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (36a b \|- 1 - 36a b \|- 1 + 9a b - 27a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R - 12a b \|- 1 + 12a b \|- 1 - 3a b + 9a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (12a b \|- 1 - 12a b \|- 1 + 12a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (180a b \|- 1 - 180a b \|- 1 + 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 36a b \|- 1 + 36a b \|- 1 - 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (240a b \|- 1 - 240a b \|- 1 + 240a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R - 48a b \|- 1 + 48a b\|- 1 - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (180a b \|- 1 - 180a b \|- 1 + 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 36a b \|- 1 - 36a b \|- 1 + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (12a b \|- 1 - 12a b \|- 1 + 12a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 48a b \|- 1 + 48a b\|- 1 - 48a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) - 12a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 12a b \|- 1 - 12a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 6 3 3 5 +--R (3a b + 3a b)sinh(x) + (18a b + 18a b)cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 4 +--R ((45a b + 45a b)cosh(x) - 9a b - 9a b)sinh(x) +--R + +--R 3 3 3 3 3 3 +--R ((60a b + 60a b)cosh(x) + (- 36a b - 36a b)cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 3 +--R (45a b + 45a b)cosh(x) + (- 54a b - 54a b)cosh(x) + 9a b +--R + +--R 3 +--R 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 3 3 3 +--R (18a b + 18a b)cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 3 3 +--R (18a b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 6 3 3 4 +--R (3a b + 3a b)cosh(x) + (- 9a b - 9a b)cosh(x) +--R + +--R 3 3 2 3 3 +--R (9a b + 9a b)cosh(x) - 3a b - 3a b +--R * +--R 3+-+ +--R \|a +--R / +--R 3 3+---+2 3 3+---+ 3 6 +--R (3a b \|- 1 - 3a b\|- 1 + 3a b)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 5 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 +--R (45a b \|- 1 - 45a b\|- 1 + 45a b)cosh(x) - 9a b \|- 1 +--R + +--R 3 3+---+ 3 +--R 9a b\|- 1 - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (60a b \|- 1 - 60a b\|- 1 + 60a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 3+---+2 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x) + 24a \|- 1 +--R + +--R 4 3+---+ 4 +--R - 24a \|- 1 + 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 +--R (45a b \|- 1 - 45a b\|- 1 + 45a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 3+---+2 +--R (72a \|- 1 - 72a \|- 1 + 72a )cosh(x) + 9a b \|- 1 +--R + +--R 3 3+---+ 3 +--R - 9a b\|- 1 + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 5 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (72a \|- 1 - 72a \|- 1 + 72a )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 6 +--R (3a b \|- 1 - 3a b\|- 1 + 3a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 +--R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (24a \|- 1 - 24a \|- 1 + 24a )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 +--R (9a b \|- 1 - 9a b\|- 1 + 9a b)cosh(x) - 3a b \|- 1 +--R + +--R 3 3+---+ 3 +--R 3a b\|- 1 - 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 270a b \|- 1 + 270a b \|- 1 - 270a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 54a b \|- 1 - 54a b \|- 1 + 54a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 360a b \|- 1 + 360a b \|- 1 - 360a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R - 144a b \|- 1 + 144a b\|- 1 - 144a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 270a b \|- 1 + 270a b \|- 1 - 270a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (324a b \|- 1 - 324a b \|- 1 + 324a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 54a b \|- 1 + 54a b \|- 1 - 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) + 18a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 18a b \|- 1 + 18a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 3a b)\|- 1 + (- 12a b - 3a b)\|- 1 + 12a b +--R + +--R 3 +--R 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (72a b + 18a b)\|- 1 + (- 72a b - 18a b)\|- 1 + 72a b +--R + +--R 3 +--R 18a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (180a b + 45a b)\|- 1 + (- 180a b - 45a b)\|- 1 +--R + +--R 3 3 +--R 180a b + 45a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 36a b - 9a b)\|- 1 + (36a b + 9a b)\|- 1 - 36a b +--R + +--R 3 +--R - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (240a b + 60a b)\|- 1 + (- 240a b - 60a b)\|- 1 +--R + +--R 3 3 +--R 240a b + 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 144a b - 36a b)\|- 1 + (144a b + 36a b)\|- 1 +--R + +--R 3 3 +--R - 144a b - 36a b +--R * +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (96a b + 24a )\|- 1 + (- 96a b - 24a )\|- 1 + 96a b +--R + +--R 4 +--R 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (180a b + 45a b)\|- 1 + (- 180a b - 45a b)\|- 1 +--R + +--R 3 3 +--R 180a b + 45a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 216a b - 54a b)\|- 1 + (216a b + 54a b)\|- 1 +--R + +--R 3 3 +--R - 216a b - 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (288a b + 72a )\|- 1 + (- 288a b - 72a )\|- 1 +--R + +--R 2 2 4 +--R 288a b + 72a +--R * +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (36a b + 9a b)\|- 1 + (- 36a b - 9a b)\|- 1 + 36a b +--R + +--R 3 +--R 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (72a b + 18a b)\|- 1 + (- 72a b - 18a b)\|- 1 +--R + +--R 3 3 +--R 72a b + 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 144a b - 36a b)\|- 1 + (144a b + 36a b)\|- 1 +--R + +--R 3 3 +--R - 144a b - 36a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (288a b + 72a )\|- 1 + (- 288a b - 72a )\|- 1 +--R + +--R 2 2 4 +--R 288a b + 72a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (72a b + 18a b)\|- 1 + (- 72a b - 18a b)\|- 1 +--R + +--R 3 3 +--R 72a b + 18a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 3a b)\|- 1 + (- 12a b - 3a b)\|- 1 + 12a b +--R + +--R 3 +--R 3a b +--R * +--R 6 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 36a b - 9a b)\|- 1 + (36a b + 9a b)\|- 1 - 36a b +--R + +--R 3 +--R - 9a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (96a b + 24a )\|- 1 + (- 96a b - 24a )\|- 1 + 96a b +--R + +--R 4 +--R 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (36a b + 9a b)\|- 1 + (- 36a b - 9a b)\|- 1 + 36a b +--R + +--R 3 +--R 9a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R (- 12a b - 3a b)\|- 1 + (12a b + 3a b)\|- 1 - 12a b - 3a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (12a b \|- 1 - 12a b \|- 1 + 12a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (180a b \|- 1 - 180a b \|- 1 + 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 36a b \|- 1 + 36a b \|- 1 - 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (240a b \|- 1 - 240a b \|- 1 + 240a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R 96a b \|- 1 - 96a b\|- 1 + 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (180a b \|- 1 - 180a b \|- 1 + 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (288a b \|- 1 - 288a b\|- 1 + 288a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 36a b \|- 1 - 36a b \|- 1 + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 144a b \|- 1 + 144a b \|- 1 - 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (288a b \|- 1 - 288a b\|- 1 + 288a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (12a b \|- 1 - 12a b \|- 1 + 12a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (96a b \|- 1 - 96a b\|- 1 + 96a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) - 12a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 12a b \|- 1 - 12a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 3a b)\|- 1 + (12a b + 3a b)\|- 1 - 12a b +--R + +--R 3 +--R - 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 72a b - 18a b)\|- 1 + (72a b + 18a b)\|- 1 - 72a b +--R + +--R 3 +--R - 18a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 180a b - 45a b)\|- 1 + (180a b + 45a b)\|- 1 +--R + +--R 3 3 +--R - 180a b - 45a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (36a b + 9a b)\|- 1 + (- 36a b - 9a b)\|- 1 + 36a b +--R + +--R 3 +--R 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 240a b - 60a b)\|- 1 + (240a b + 60a b)\|- 1 +--R + +--R 3 3 +--R - 240a b - 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (144a b + 36a b)\|- 1 + (- 144a b - 36a b)\|- 1 +--R + +--R 3 3 +--R 144a b + 36a b +--R * +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 96a b - 24a )\|- 1 + (96a b + 24a )\|- 1 - 96a b +--R + +--R 4 +--R - 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 180a b - 45a b)\|- 1 + (180a b + 45a b)\|- 1 +--R + +--R 3 3 +--R - 180a b - 45a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (216a b + 54a b)\|- 1 + (- 216a b - 54a b)\|- 1 +--R + +--R 3 3 +--R 216a b + 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (- 288a b - 72a )\|- 1 + (288a b + 72a )\|- 1 +--R + +--R 2 2 4 +--R - 288a b - 72a +--R * +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 36a b - 9a b)\|- 1 + (36a b + 9a b)\|- 1 - 36a b +--R + +--R 3 +--R - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 72a b - 18a b)\|- 1 + (72a b + 18a b)\|- 1 +--R + +--R 3 3 +--R - 72a b - 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (144a b + 36a b)\|- 1 + (- 144a b - 36a b)\|- 1 +--R + +--R 3 3 +--R 144a b + 36a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (- 288a b - 72a )\|- 1 + (288a b + 72a )\|- 1 +--R + +--R 2 2 4 +--R - 288a b - 72a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 72a b - 18a b)\|- 1 + (72a b + 18a b)\|- 1 +--R + +--R 3 3 +--R - 72a b - 18a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 3a b)\|- 1 + (12a b + 3a b)\|- 1 - 12a b +--R + +--R 3 +--R - 3a b +--R * +--R 6 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (36a b + 9a b)\|- 1 + (- 36a b - 9a b)\|- 1 + 36a b +--R + +--R 3 +--R 9a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 96a b - 24a )\|- 1 + (96a b + 24a )\|- 1 - 96a b +--R + +--R 4 +--R - 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 36a b - 9a b)\|- 1 + (36a b + 9a b)\|- 1 - 36a b +--R + +--R 3 +--R - 9a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R (12a b + 3a b)\|- 1 + (- 12a b - 3a b)\|- 1 + 12a b + 3a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 270a b \|- 1 + 270a b \|- 1 - 270a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 54a b \|- 1 - 54a b \|- 1 + 54a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 360a b \|- 1 + 360a b \|- 1 - 360a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R - 144a b \|- 1 + 144a b\|- 1 - 144a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 270a b \|- 1 + 270a b \|- 1 - 270a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (324a b \|- 1 - 324a b \|- 1 + 324a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 54a b \|- 1 + 54a b \|- 1 - 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) + 18a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 18a b \|- 1 + 18a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3+---+2 3 3+---+ 3 6 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 5 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) + 9a b \|- 1 +--R + +--R 3 3+---+ 3 +--R - 9a b\|- 1 + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 60a b \|- 1 + 60a b\|- 1 - 60a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 3+---+2 +--R (36a b \|- 1 - 36a b\|- 1 + 36a b)cosh(x) - 24a \|- 1 +--R + +--R 4 3+---+ 4 +--R 24a \|- 1 - 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (54a b \|- 1 - 54a b\|- 1 + 54a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 3+---+2 +--R (- 72a \|- 1 + 72a \|- 1 - 72a )cosh(x) - 9a b \|- 1 +--R + +--R 3 3+---+ 3 +--R 9a b\|- 1 - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 5 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (36a b \|- 1 - 36a b\|- 1 + 36a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (- 72a \|- 1 + 72a \|- 1 - 72a )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 6 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 +--R (9a b \|- 1 - 9a b\|- 1 + 9a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (- 24a \|- 1 + 24a \|- 1 - 24a )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 +--R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cosh(x) + 3a b \|- 1 +--R + +--R 3 3+---+ 3 +--R - 3a b\|- 1 + 3a b +--R * +--R 3+-+2 3+-+2 +--R \|a \|b +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R - 9a b \|- 1 + 9a b \|- 1 - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (60a b \|- 1 - 60a b \|- 1 + 60a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R 24a b \|- 1 - 24a b\|- 1 + 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 2 3+---+2 +--R (72a b \|- 1 - 72a b\|- 1 + 72a b)cosh(x) + 9a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R - 9a b \|- 1 + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (72a b \|- 1 - 72a b\|- 1 + 72a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (24a b \|- 1 - 24a b\|- 1 + 24a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) - 3a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R 3a b \|- 1 - 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R ((- 6a b - 6a b)\|- 1 + (6a b + 6a b)\|- 1 - 6a b - 6a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 36a b - 36a b)\|- 1 + (36a b + 36a b)\|- 1 - 36a b +--R + +--R 4 +--R - 36a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 90a b - 90a b)\|- 1 + (90a b + 90a b)\|- 1 +--R + +--R 2 3 4 +--R - 90a b - 90a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 18a b +--R + +--R 4 +--R 18a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 120a b - 120a b)\|- 1 + (120a b + 120a b)\|- 1 +--R + +--R 2 3 4 +--R - 120a b - 120a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (72a b + 72a b)\|- 1 + (- 72a b - 72a b)\|- 1 +--R + +--R 2 3 4 +--R 72a b + 72a b +--R * +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 5 +--R - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 90a b - 90a b)\|- 1 + (90a b + 90a b)\|- 1 +--R + +--R 2 3 4 +--R - 90a b - 90a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (108a b + 108a b)\|- 1 + (- 108a b - 108a b)\|- 1 +--R + +--R 2 3 4 +--R 108a b + 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 144a b - 144a )\|- 1 + (144a b + 144a )\|- 1 +--R + +--R 3 2 5 +--R - 144a b - 144a +--R * +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 18a b - 18a b)\|- 1 + (18a b + 18a b)\|- 1 - 18a b +--R + +--R 4 +--R - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 36a b - 36a b)\|- 1 + (36a b + 36a b)\|- 1 +--R + +--R 2 3 4 +--R - 36a b - 36a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (72a b + 72a b)\|- 1 + (- 72a b - 72a b)\|- 1 +--R + +--R 2 3 4 +--R 72a b + 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 144a b - 144a )\|- 1 + (144a b + 144a )\|- 1 +--R + +--R 3 2 5 +--R - 144a b - 144a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 36a b - 36a b)\|- 1 + (36a b + 36a b)\|- 1 +--R + +--R 2 3 4 +--R - 36a b - 36a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R ((- 6a b - 6a b)\|- 1 + (6a b + 6a b)\|- 1 - 6a b - 6a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 18a b +--R + +--R 4 +--R 18a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 5 +--R - 48a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 18a b - 18a b)\|- 1 + (18a b + 18a b)\|- 1 - 18a b +--R + +--R 4 +--R - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R (6a b + 6a b)\|- 1 + (- 6a b - 6a b)\|- 1 + 6a b + 6a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (27a b \|- 1 - 27a b \|- 1 + 27a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (162a b \|- 1 - 162a b \|- 1 + 162a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (405a b \|- 1 - 405a b \|- 1 + 405a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R - 81a b \|- 1 + 81a b \|- 1 - 81a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (540a b \|- 1 - 540a b \|- 1 + 540a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 324a b \|- 1 + 324a b \|- 1 - 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R 216a b \|- 1 - 216a b\|- 1 + 216a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (405a b \|- 1 - 405a b \|- 1 + 405a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (- 486a b \|- 1 + 486a b \|- 1 - 486a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R (648a b \|- 1 - 648a b\|- 1 + 648a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R 81a b \|- 1 - 81a b \|- 1 + 81a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (162a b \|- 1 - 162a b \|- 1 + 162a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 324a b \|- 1 + 324a b \|- 1 - 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (648a b \|- 1 - 648a b\|- 1 + 648a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (162a b \|- 1 - 162a b \|- 1 + 162a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (27a b \|- 1 - 27a b \|- 1 + 27a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 81a b \|- 1 + 81a b \|- 1 - 81a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (216a b \|- 1 - 216a b\|- 1 + 216a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (81a b \|- 1 - 81a b \|- 1 + 81a b )cosh(x) - 27a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R 27a b \|- 1 - 27a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 12a b + 12a b)\|- 1 + (12a b - 12a b)\|- 1 - 12a b +--R + +--R 4 +--R 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 72a b + 72a b)\|- 1 + (72a b - 72a b)\|- 1 - 72a b +--R + +--R 4 +--R 72a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 180a b + 180a b)\|- 1 + (180a b - 180a b)\|- 1 +--R + +--R 2 3 4 +--R - 180a b + 180a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (36a b - 36a b)\|- 1 + (- 36a b + 36a b)\|- 1 + 36a b +--R + +--R 4 +--R - 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 240a b + 240a b)\|- 1 + (240a b - 240a b)\|- 1 +--R + +--R 2 3 4 +--R - 240a b + 240a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (144a b - 144a b)\|- 1 + (- 144a b + 144a b)\|- 1 +--R + +--R 2 3 4 +--R 144a b - 144a b +--R * +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 96a b + 96a )\|- 1 + (96a b - 96a )\|- 1 - 96a b +--R + +--R 5 +--R 96a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 180a b + 180a b)\|- 1 + (180a b - 180a b)\|- 1 +--R + +--R 2 3 4 +--R - 180a b + 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (216a b - 216a b)\|- 1 + (- 216a b + 216a b)\|- 1 +--R + +--R 2 3 4 +--R 216a b - 216a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 288a b + 288a )\|- 1 + (288a b - 288a )\|- 1 +--R + +--R 3 2 5 +--R - 288a b + 288a +--R * +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 36a b + 36a b)\|- 1 + (36a b - 36a b)\|- 1 - 36a b +--R + +--R 4 +--R 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 72a b + 72a b)\|- 1 + (72a b - 72a b)\|- 1 +--R + +--R 2 3 4 +--R - 72a b + 72a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (144a b - 144a b)\|- 1 + (- 144a b + 144a b)\|- 1 +--R + +--R 2 3 4 +--R 144a b - 144a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 288a b + 288a )\|- 1 + (288a b - 288a )\|- 1 +--R + +--R 3 2 5 +--R - 288a b + 288a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 72a b + 72a b)\|- 1 + (72a b - 72a b)\|- 1 +--R + +--R 2 3 4 +--R - 72a b + 72a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 12a b + 12a b)\|- 1 + (12a b - 12a b)\|- 1 - 12a b +--R + +--R 4 +--R 12a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (36a b - 36a b)\|- 1 + (- 36a b + 36a b)\|- 1 + 36a b +--R + +--R 4 +--R - 36a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 96a b + 96a )\|- 1 + (96a b - 96a )\|- 1 - 96a b +--R + +--R 5 +--R 96a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 36a b + 36a b)\|- 1 + (36a b - 36a b)\|- 1 - 36a b +--R + +--R 4 +--R 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R (12a b - 12a b)\|- 1 + (- 12a b + 12a b)\|- 1 + 12a b - 12a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 27a b \|- 1 + 27a b \|- 1 - 27a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 162a b \|- 1 + 162a b \|- 1 - 162a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (- 405a b \|- 1 + 405a b \|- 1 - 405a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R 81a b \|- 1 - 81a b \|- 1 + 81a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 540a b \|- 1 + 540a b \|- 1 - 540a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (324a b \|- 1 - 324a b \|- 1 + 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R - 216a b \|- 1 + 216a b\|- 1 - 216a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 405a b \|- 1 + 405a b \|- 1 - 405a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (486a b \|- 1 - 486a b \|- 1 + 486a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R (- 648a b \|- 1 + 648a b\|- 1 - 648a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R - 81a b \|- 1 + 81a b \|- 1 - 81a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 162a b \|- 1 + 162a b \|- 1 - 162a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (324a b \|- 1 - 324a b \|- 1 + 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (- 648a b \|- 1 + 648a b\|- 1 - 648a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 162a b \|- 1 + 162a b \|- 1 - 162a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 27a b \|- 1 + 27a b \|- 1 - 27a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (81a b \|- 1 - 81a b \|- 1 + 81a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (- 81a b \|- 1 + 81a b \|- 1 - 81a b )cosh(x) + 27a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R - 27a b \|- 1 + 27a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R ((- 6a b - 6a b)\|- 1 + (6a b + 6a b)\|- 1 - 6a b - 6a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 36a b - 36a b)\|- 1 + (36a b + 36a b)\|- 1 - 36a b +--R + +--R 4 +--R - 36a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 90a b - 90a b)\|- 1 + (90a b + 90a b)\|- 1 +--R + +--R 2 3 4 +--R - 90a b - 90a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 18a b +--R + +--R 4 +--R 18a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 120a b - 120a b)\|- 1 + (120a b + 120a b)\|- 1 +--R + +--R 2 3 4 +--R - 120a b - 120a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (72a b + 72a b)\|- 1 + (- 72a b - 72a b)\|- 1 +--R + +--R 2 3 4 +--R 72a b + 72a b +--R * +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 5 +--R - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 90a b - 90a b)\|- 1 + (90a b + 90a b)\|- 1 +--R + +--R 2 3 4 +--R - 90a b - 90a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (108a b + 108a b)\|- 1 + (- 108a b - 108a b)\|- 1 +--R + +--R 2 3 4 +--R 108a b + 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 144a b - 144a )\|- 1 + (144a b + 144a )\|- 1 +--R + +--R 3 2 5 +--R - 144a b - 144a +--R * +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 18a b - 18a b)\|- 1 + (18a b + 18a b)\|- 1 - 18a b +--R + +--R 4 +--R - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 36a b - 36a b)\|- 1 + (36a b + 36a b)\|- 1 +--R + +--R 2 3 4 +--R - 36a b - 36a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (72a b + 72a b)\|- 1 + (- 72a b - 72a b)\|- 1 +--R + +--R 2 3 4 +--R 72a b + 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 144a b - 144a )\|- 1 + (144a b + 144a )\|- 1 +--R + +--R 3 2 5 +--R - 144a b - 144a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 36a b - 36a b)\|- 1 + (36a b + 36a b)\|- 1 +--R + +--R 2 3 4 +--R - 36a b - 36a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R ((- 6a b - 6a b)\|- 1 + (6a b + 6a b)\|- 1 - 6a b - 6a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 18a b +--R + +--R 4 +--R 18a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 5 +--R - 48a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 18a b - 18a b)\|- 1 + (18a b + 18a b)\|- 1 - 18a b +--R + +--R 4 +--R - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R (6a b + 6a b)\|- 1 + (- 6a b - 6a b)\|- 1 + 6a b + 6a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) + 9a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R - 9a b \|- 1 + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 60a b \|- 1 + 60a b \|- 1 - 60a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 3+---+2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) - 24a b \|- 1 +--R + +--R 4 3+---+ 4 +--R 24a b\|- 1 - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 2 3+---+2 +--R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cosh(x) - 9a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R 9a b \|- 1 - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) + 3a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R - 3a b \|- 1 + 3a b +--R * +--R 3+-+ +--R \|b +--R + +--R 2 3 4 6 2 3 4 5 +--R (3a b + 3a b)sinh(x) + (18a b + 18a b)cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R ((45a b + 45a b)cosh(x) - 9a b - 9a b)sinh(x) +--R + +--R 2 3 4 3 2 3 4 3 2 +--R (60a b + 60a b)cosh(x) + (- 36a b - 36a b)cosh(x) + 24a b +--R + +--R 5 +--R 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 4 2 3 4 2 +--R (45a b + 45a b)cosh(x) + (- 54a b - 54a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (72a b + 72a )cosh(x) + 9a b + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 5 2 3 4 3 +--R (18a b + 18a b)cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 3 2 5 2 2 3 4 +--R (72a b + 72a )cosh(x) + (18a b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 6 2 3 4 4 +--R (3a b + 3a b)cosh(x) + (- 9a b - 9a b)cosh(x) +--R + +--R 3 2 5 3 2 3 4 2 2 3 4 +--R (24a b + 24a )cosh(x) + (9a b + 9a b)cosh(x) - 3a b - 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (- 270a b \|- 1 + 270a b \|- 1 - 270a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R 54a b \|- 1 - 54a b \|- 1 + 54a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 360a b \|- 1 + 360a b \|- 1 - 360a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R - 144a b \|- 1 + 144a b\|- 1 - 144a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 270a b \|- 1 + 270a b \|- 1 - 270a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (324a b \|- 1 - 324a b \|- 1 + 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R - 54a b \|- 1 + 54a b \|- 1 - 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) + 18a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R - 18a b \|- 1 + 18a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 6 +--R (36a b \|- 1 - 36a b \|- 1 + 27a b - 9a b)sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 5 +--R (216a b \|- 1 - 216a b \|- 1 + 162a b - 54a b)cosh(x)sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (540a b \|- 1 - 540a b \|- 1 + 405a b - 135a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R - 108a b \|- 1 + 108a b \|- 1 - 81a b + 27a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 +--R (720a b \|- 1 - 720a b \|- 1 + 540a b - 180a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R (- 432a b \|- 1 + 432a b \|- 1 - 324a b + 108a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R 288a b \|- 1 - 288a b \|- 1 + 216a b - 72a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 4 +--R (540a b \|- 1 - 540a b \|- 1 + 405a b - 135a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (- 648a b \|- 1 + 648a b \|- 1 - 486a b + 162a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (864a b \|- 1 - 864a b \|- 1 + 648a b - 216a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R 108a b \|- 1 - 108a b \|- 1 + 81a b - 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 5 +--R (216a b \|- 1 - 216a b \|- 1 + 162a b - 54a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 +--R (- 432a b \|- 1 + 432a b \|- 1 - 324a b + 108a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 +--R (864a b \|- 1 - 864a b \|- 1 + 648a b - 216a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R (216a b \|- 1 - 216a b \|- 1 + 162a b - 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 6 +--R (36a b \|- 1 - 36a b \|- 1 + 27a b - 9a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 4 +--R (- 108a b \|- 1 + 108a b \|- 1 - 81a b + 27a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 +--R (288a b \|- 1 - 288a b \|- 1 + 216a b - 72a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (108a b \|- 1 - 108a b \|- 1 + 81a b - 27a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R - 36a b \|- 1 + 36a b \|- 1 - 27a b + 9a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 6 +--R (36a b \|- 1 - 36a b \|- 1 - 24a b + 12a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (216a b \|- 1 - 216a b \|- 1 - 144a b + 72a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 2 +--R (540a b \|- 1 - 540a b \|- 1 - 360a b + 180a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R - 108a b \|- 1 + 108a b \|- 1 + 72a b - 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 3 +--R (720a b \|- 1 - 720a b \|- 1 - 480a b + 240a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (- 432a b \|- 1 + 432a b \|- 1 + 288a b - 144a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 2 3 4 +--R 288a b \|- 1 - 288a b\|- 1 - 192a b + 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 4 +--R (540a b \|- 1 - 540a b \|- 1 - 360a b + 180a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (- 648a b \|- 1 + 648a b \|- 1 + 432a b - 216a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 2 3 4 +--R (864a b \|- 1 - 864a b\|- 1 - 576a b + 288a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R 108a b \|- 1 - 108a b \|- 1 - 72a b + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 5 +--R (216a b \|- 1 - 216a b \|- 1 - 144a b + 72a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (- 432a b \|- 1 + 432a b \|- 1 + 288a b - 144a b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 2 3 4 2 +--R (864a b \|- 1 - 864a b\|- 1 - 576a b + 288a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (216a b \|- 1 - 216a b \|- 1 - 144a b + 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 6 +--R (36a b \|- 1 - 36a b \|- 1 - 24a b + 12a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 4 +--R (- 108a b \|- 1 + 108a b \|- 1 + 72a b - 36a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 2 3 4 3 +--R (288a b \|- 1 - 288a b\|- 1 - 192a b + 96a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 2 +--R (108a b \|- 1 - 108a b \|- 1 - 72a b + 36a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R - 36a b \|- 1 + 36a b \|- 1 + 24a b - 12a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 6 +--R (- 36a b \|- 1 + 36a b \|- 1 - 27a b + 9a b)sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R (- 216a b \|- 1 + 216a b \|- 1 - 162a b + 54a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (- 540a b \|- 1 + 540a b \|- 1 - 405a b + 135a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R 108a b \|- 1 - 108a b \|- 1 + 81a b - 27a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 +--R (- 720a b \|- 1 + 720a b \|- 1 - 540a b + 180a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R (432a b \|- 1 - 432a b \|- 1 + 324a b - 108a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R - 288a b \|- 1 + 288a b \|- 1 - 216a b + 72a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 4 +--R (- 540a b \|- 1 + 540a b \|- 1 - 405a b + 135a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (648a b \|- 1 - 648a b \|- 1 + 486a b - 162a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 864a b \|- 1 + 864a b \|- 1 - 648a b + 216a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R - 108a b \|- 1 + 108a b \|- 1 - 81a b + 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 5 +--R (- 216a b \|- 1 + 216a b \|- 1 - 162a b + 54a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 +--R (432a b \|- 1 - 432a b \|- 1 + 324a b - 108a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 +--R (- 864a b \|- 1 + 864a b \|- 1 - 648a b + 216a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R (- 216a b \|- 1 + 216a b \|- 1 - 162a b + 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 6 +--R (- 36a b \|- 1 + 36a b \|- 1 - 27a b + 9a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 4 +--R (108a b \|- 1 - 108a b \|- 1 + 81a b - 27a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 +--R (- 288a b \|- 1 + 288a b \|- 1 - 216a b + 72a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (- 108a b \|- 1 + 108a b \|- 1 - 81a b + 27a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R 36a b \|- 1 - 36a b \|- 1 + 27a b - 9a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (- 270a b \|- 1 + 270a b \|- 1 - 270a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R 54a b \|- 1 - 54a b \|- 1 + 54a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 360a b \|- 1 + 360a b \|- 1 - 360a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R - 144a b \|- 1 + 144a b\|- 1 - 144a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 270a b \|- 1 + 270a b \|- 1 - 270a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (324a b \|- 1 - 324a b \|- 1 + 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R - 54a b \|- 1 + 54a b \|- 1 - 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 108a b \|- 1 + 108a b \|- 1 - 108a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) + 18a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R - 18a b \|- 1 + 18a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 3a b - 3a b)sinh(x) + (- 18a b - 18a b)cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R ((- 45a b - 45a b)cosh(x) + 9a b + 9a b)sinh(x) +--R + +--R 2 3 4 3 2 3 4 3 2 +--R (- 60a b - 60a b)cosh(x) + (36a b + 36a b)cosh(x) - 24a b +--R + +--R 5 +--R - 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 4 2 3 4 2 +--R (- 45a b - 45a b)cosh(x) + (54a b + 54a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 72a b - 72a )cosh(x) - 9a b - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 5 2 3 4 3 +--R (- 18a b - 18a b)cosh(x) + (36a b + 36a b)cosh(x) +--R + +--R 3 2 5 2 2 3 4 +--R (- 72a b - 72a )cosh(x) + (- 18a b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 6 2 3 4 4 +--R (- 3a b - 3a b)cosh(x) + (9a b + 9a b)cosh(x) +--R + +--R 3 2 5 3 2 3 4 2 2 3 4 +--R (- 24a b - 24a )cosh(x) + (- 9a b - 9a b)cosh(x) + 3a b + 3a b +--R * +--R 3+-+ +--R \|a +--R Type: Expression(Integer) +--E 385 + +--S 386 of 510 +t0075:= 1/(a+b*sinh(x)^4) +--R +--R +--R 1 +--R (333) -------------- +--R 4 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 386 + +--S 387 of 510 +r0075:= 1/2*atan((-a^(1/2)+(-b)^(1/2))^(1/2)*tanh(x)/a^(1/4))/a^(3/4)/_ + (-a^(1/2)+(-b)^(1/2))^(1/2)+1/2*atanh((a^(1/2)+_ + (-b)^(1/2))^(1/2)*tanh(x)/a^(1/4))/a^(3/4)/(a^(1/2)+(-b)^(1/2))^(1/2) +--R +--R +--R (334) +--R +-------------+ +--R +---------------+ | +-+ +---+ +--R | +-+ +---+ tanh(x)\|\|a + \|- b +--R \|- \|a + \|- b atanh(-----------------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+ +--R +-------------+ | +-+ +---+ +--R | +-+ +---+ tanh(x)\|- \|a + \|- b +--R \|\|a + \|- b atan(-------------------------) +--R 4+-+ +--R \|a +--R / +--R +---------------+ +-------------+ +--R 4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|a \|- \|a + \|- b \|\|a + \|- b +--R Type: Expression(Integer) +--E 387 + +--S 388 of 510 +a0075:= integrate(t0075,x) +--R +--R +--R (335) +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((32a b + 32a ) |- ---------------------- + 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (- 16a b - 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((32a b + 32a ) |- ---------------------- - 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (16a b + 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((- 32a b - 32a ) |- ---------------------- + 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (16a b + 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R - +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((- 32a b - 32a ) |- ---------------------- - 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (- 16a b - 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 510 +m0075:= a0075-r0075 +--R +--R +--R (336) +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R +---------------+ | | 3 2 4 5 +--R 4+-+3 | +-+ +---+ | \| 64a b + 128a b + 64a +--R \|a \|- \|a + \|- b |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((32a b + 32a ) |- ---------------------- + 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (- 16a b - 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R - +--R +---------------+ +--R 4+-+3 | +-+ +---+ +--R \|a \|- \|a + \|- b +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +-------------+ +--R | \| 64a b + 128a b + 64a | +-+ +---+ +--R |--------------------------------------------- \|\|a + \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((32a b + 32a ) |- ---------------------- - 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (16a b + 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R +---------------+ | | 3 2 4 5 +--R 4+-+3 | +-+ +---+ | \| 64a b + 128a b + 64a +--R \|a \|- \|a + \|- b |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((- 32a b - 32a ) |- ---------------------- + 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (16a b + 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R - +--R +---------------+ +--R 4+-+3 | +-+ +---+ +--R \|a \|- \|a + \|- b +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +-------------+ +--R | \| 64a b + 128a b + 64a | +-+ +---+ +--R |------------------------------------------- \|\|a + \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((- 32a b - 32a ) |- ---------------------- - 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (- 16a b - 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R +-------------+ +--R +---------------+ | +-+ +---+ +--R | +-+ +---+ tanh(x)\|\|a + \|- b +--R - \|- \|a + \|- b atanh(-----------------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+ +--R +-------------+ | +-+ +---+ +--R | +-+ +---+ tanh(x)\|- \|a + \|- b +--R - \|\|a + \|- b atan(-------------------------) +--R 4+-+ +--R \|a +--R / +--R +---------------+ +-------------+ +--R 4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|a \|- \|a + \|- b \|\|a + \|- b +--R Type: Expression(Integer) +--E 389 + +--S 390 of 510 +d0075:= D(m0075,x) +--R +--R +--R (337) +--R 4 3 +--R (16b + 16a)sinh(x) + (64b + 64a)cosh(x)sinh(x) +--R + +--R 2 2 3 +--R (96b + 96a)cosh(x) sinh(x) + (64b + 64a)cosh(x) sinh(x) +--R + +--R 4 +--R (16b + 16a)cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) - 4b)sinh(x) +--R + +--R 3 5 +--R (56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70b cosh(x) - 60b cosh(x) + 6b + 16a)sinh(x) +--R + +--R 5 3 3 +--R (56b cosh(x) - 80b cosh(x) + (24b + 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28b cosh(x) - 60b cosh(x) + (36b + 96a)cosh(x) - 4b)sinh(x) +--R + +--R 7 5 3 +--R (8b cosh(x) - 24b cosh(x) + (24b + 64a)cosh(x) - 8b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) - 4b cosh(x) + (6b + 16a)cosh(x) - 4b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) + 4b)sinh(x) +--R + +--R 3 5 +--R (- 56b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70b cosh(x) + 60b cosh(x) - 6b)sinh(x) +--R + +--R 5 3 3 +--R (- 56b cosh(x) + 80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28b cosh(x) + 60b cosh(x) - 36b cosh(x) + 4b)sinh(x) +--R + +--R 7 5 3 +--R (- 8b cosh(x) + 24b cosh(x) - 24b cosh(x) + 8b cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - b cosh(x) + 4b cosh(x) - 6b cosh(x) + 4b cosh(x) - b +--R * +--R 4+-+2 +--R \|a +--R + +--R 8 7 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) + 4b)sinh(x) +--R + +--R 3 5 +--R (- 56b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70b cosh(x) + 60b cosh(x) - 6b - 16a)sinh(x) +--R + +--R 5 3 3 +--R (- 56b cosh(x) + 80b cosh(x) + (- 24b - 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 28b cosh(x) + 60b cosh(x) + (- 36b - 96a)cosh(x) + 4b) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R - 8b cosh(x) + 24b cosh(x) + (- 24b - 64a)cosh(x) +--R + +--R 8b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - b cosh(x) + 4b cosh(x) + (- 6b - 16a)cosh(x) + 4b cosh(x) - b +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) - 4b)sinh(x) +--R + +--R 3 5 +--R (56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70b cosh(x) - 60b cosh(x) + 6b - 16a)sinh(x) +--R + +--R 5 3 3 +--R (56b cosh(x) - 80b cosh(x) + (24b - 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28b cosh(x) - 60b cosh(x) + (36b - 96a)cosh(x) - 4b)sinh(x) +--R + +--R 7 5 3 +--R (8b cosh(x) - 24b cosh(x) + (24b - 64a)cosh(x) - 8b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) - 4b cosh(x) + (6b - 16a)cosh(x) - 4b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R * +--R +-+ +--R \|a +--R / +--R 2 8 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b + 28a b)cosh(x) - 4b - 4a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b + 56a b)cosh(x) + (- 24b - 24a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (70b + 70a b)cosh(x) + (- 60b - 60a b)cosh(x) + 6b +--R + +--R 2 +--R 22a b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (56b + 56a b)cosh(x) + (- 80b - 80a b)cosh(x) +--R + +--R 2 2 +--R (24b + 88a b + 64a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (28b + 28a b)cosh(x) + (- 60b - 60a b)cosh(x) +--R + +--R 2 2 2 2 +--R (36b + 132a b + 96a )cosh(x) - 4b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (8b + 8a b)cosh(x) + (- 24b - 24a b)cosh(x) +--R + +--R 2 2 3 2 +--R (24b + 88a b + 64a )cosh(x) + (- 8b - 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 +--R (b + a b)cosh(x) + (- 4b - 4a b)cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (6b + 22a b + 16a )cosh(x) + (- 4b - 4a b)cosh(x) + b + a b +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R a b sinh(x) + 8a b cosh(x)sinh(x) + (28a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 5 +--R (56a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 4 2 2 4 +--R (70a b cosh(x) - 60a b cosh(x) + 6a b + 16a )sinh(x) +--R + +--R 5 3 2 3 +--R (56a b cosh(x) - 80a b cosh(x) + (24a b + 64a )cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28a b cosh(x) - 60a b cosh(x) + (36a b + 96a )cosh(x) - 4a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 2 3 +--R 8a b cosh(x) - 24a b cosh(x) + (24a b + 64a )cosh(x) +--R + +--R - 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 2 4 2 +--R a b cosh(x) - 4a b cosh(x) + (6a b + 16a )cosh(x) - 4a b cosh(x) +--R + +--R a b +--R * +--R 4+-+2 +--R \|a +--R + +--R 8 7 +--R - 2a b sinh(x) - 16a b cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 56a b cosh(x) + 8a b)sinh(x) +--R + +--R 3 5 +--R (- 112a b cosh(x) + 48a b cosh(x))sinh(x) +--R + +--R 4 2 2 4 +--R (- 140a b cosh(x) + 120a b cosh(x) - 12a b - 32a )sinh(x) +--R + +--R 5 3 2 +--R (- 112a b cosh(x) + 160a b cosh(x) + (- 48a b - 128a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 2 +--R - 56a b cosh(x) + 120a b cosh(x) + (- 72a b - 192a )cosh(x) +--R + +--R 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 2 3 +--R - 16a b cosh(x) + 48a b cosh(x) + (- 48a b - 128a )cosh(x) +--R + +--R 16a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 2 4 +--R - 2a b cosh(x) + 8a b cosh(x) + (- 12a b - 32a )cosh(x) +--R + +--R 2 +--R 8a b cosh(x) - 2a b +--R * +--R 2 +-+ +--R tanh(x) \|a +--R Type: Expression(Integer) +--E 390 + +--S 391 of 510 +t0076:= 1/(a+b*sinh(x)^5) +--R +--R +--R 1 +--R (338) -------------- +--R 5 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 391 + +--S 392 of 510 +r0076:= -2/5*atanh((b^(1/5)-a^(1/5)*tanh(1/2*x))/(a^(2/5)+b^(2/5))^(1/2))/_ + a^(4/5)/(a^(2/5)+b^(2/5))^(1/2)-2/5*atanh(((-1)^(2/5)*b^(1/5)-_ + a^(1/5)*tanh(1/2*x))/(a^(2/5)+(-1)^(4/5)*b^(2/5))^(1/2))/_ + a^(4/5)/(a^(2/5)+(-1)^(4/5)*b^(2/5))^(1/2)-2/5*atanh(((-1)^(4/5)*_ + b^(1/5)-a^(1/5)*tanh(1/2*x))/(a^(2/5)-(-1)^(3/5)*b^(2/5))^(1/2))/_ + a^(4/5)/(a^(2/5)-(-1)^(3/5)*b^(2/5))^(1/2)+_ + 2/5*atanh(((-1)^(1/5)*b^(1/5)+a^(1/5)*tanh(1/2*x))/(a^(2/5)+_ + (-1)^(2/5)*b^(2/5))^(1/2))/a^(4/5)/(a^(2/5)+(-1)^(2/5)*_ + b^(2/5))^(1/2)+2/5*atanh(((-1)^(3/5)*b^(1/5)+a^(1/5)*_ + tanh(1/2*x))/(a^(2/5)-(-1)^(1/5)*b^(2/5))^(1/2))/_ + a^(4/5)/(a^(2/5)-(-1)^(1/5)*b^(2/5))^(1/2) +--R +--R +--R (339) +--R - +--R +---------------------+ +-------------+ +--------------------+ +--R | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 |5+---+2 5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+4 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b - tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +----------------------+ +--R | 5+---+3 5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +-------------+ +--------------------+ +--R | 5+---+3 5+-+2 5+-+2 |5+-+2 5+-+2 |5+---+2 5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+3 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b + tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +---------------------+ +--R | 5+---+5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +---------------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +--------------------+ +--------------------+ +--R |5+---+2 5+-+2 5+-+2 |5+---+4 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+-+ x 5+-+ +--R \|b - tanh(-)\|a +--R 2 +--R atanh(------------------) +--R +-------------+ +--R |5+-+2 5+-+2 +--R \|\|b + \|a +--R + +--R +----------------------+ +---------------------+ +-------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R 5+---+5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b + tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(------------------------) +--R +--------------------+ +--R |5+---+2 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +---------------------+ +-------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R 5+---+2 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b - tanh(-)\|a +--R |5+---+2 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +--------------------+ +--R |5+---+4 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------------+ +-------------+ +--R 5+-+4 | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 5\|a \|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--------------------+ +--R |5+---+2 5+-+2 5+-+2 |5+---+4 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 392 + +--S 393 of 510 +a0076:= integrate(t0076,x) +--R +--R +--R (340) +--R ROOT +--R 2 2 +--R (10b + 10a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET2 +--R + +--R 2 4 4 2 6 +--I (- 250a b - 500a b - 250a )%%ET1 +--R + +--R 2 4 4 2 6 2 2 4 +--I (- 250a b - 500a b - 250a )%%ET0 + 50a b + 50a +--R * +--I %%ET2 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET1 +--R + +--R 2 4 4 2 6 2 2 4 +--I ((- 250a b - 500a b - 250a )%%ET0 + 50a b + 50a ) +--R * +--I %%ET1 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET0 +--R + +--R 2 2 4 2 2 +--I (50a b + 50a )%%ET0 - 8b - 3a +--R / +--R 2 4 4 2 6 +--R 125a b + 250a b + 125a +--R + +--R 2 2 2 2 +--I (- 10b - 10a )%%ET2 + (- 10b - 10a )%%ET1 +--R + +--R 2 2 +--I (- 10b - 10a )%%ET0 + 2 +--R / +--R 2 2 +--R 5b + 5a +--R * +--R log +--R 8 2 10 6 2 +--I (11718750a b + 11718750a )%%ET0 - 234375a b +--R + +--R 8 +--R - 234375a +--R * +--I %%ET1 +--R + +--R 6 2 8 4 2 6 +--I (- 234375a b - 234375a )%%ET0 + 3125a b + 3125a +--R * +--I %%ET2 +--R + +--R 6 2 8 4 2 6 +--I ((- 234375a b - 234375a )%%ET0 + 3125a b + 3125a )%%ET1 +--R + +--R 4 2 6 +--I (3125a b + 3125a )%%ET0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET2 +--R + +--R 2 4 4 2 6 +--I (- 250a b - 500a b - 250a )%%ET1 +--R + +--R 2 4 4 2 6 2 2 4 +--I (- 250a b - 500a b - 250a )%%ET0 + 50a b + 50a +--R * +--I %%ET2 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET1 +--R + +--R 2 4 4 2 6 2 2 +--I (- 250a b - 500a b - 250a )%%ET0 + 50a b +--R + +--R 4 +--R 50a +--R * +--I %%ET1 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET0 +--R + +--R 2 2 4 2 2 +--I (50a b + 50a )%%ET0 - 8b - 3a +--R / +--R 2 4 4 2 6 +--R 125a b + 250a b + 125a +--R + +--R 8 2 10 6 2 +--I (11718750a b + 11718750a )%%ET0 - 234375a b +--R + +--R 8 +--R - 234375a +--R * +--I %%ET1 +--R + +--R 6 2 8 4 2 6 +--I (- 234375a b - 234375a )%%ET0 + 3125a b + 3125a +--R * +--R 2 +--I %%ET2 +--R + +--R 8 2 10 6 2 +--I (11718750a b + 11718750a )%%ET0 - 234375a b +--R + +--R 8 +--R - 234375a +--R * +--R 2 +--I %%ET1 +--R + +--R 8 2 10 2 +--I (11718750a b + 11718750a )%%ET0 +--R + +--R 6 2 8 6 +--I (- 234375a b - 2578125a )%%ET0 + 46875a +--R * +--I %%ET1 +--R + +--R 6 2 8 2 6 4 +--I (- 234375a b - 234375a )%%ET0 + 46875a %%ET0 - 625a +--R * +--I %%ET2 +--R + +--R 6 2 8 4 2 6 2 +--I ((- 234375a b - 234375a )%%ET0 + 3125a b + 3125a )%%ET1 +--R + +--R 6 2 8 2 6 4 +--I ((- 234375a b - 234375a )%%ET0 + 46875a %%ET0 - 625a )%%ET1 +--R + +--R 4 2 6 2 4 +--I (3125a b + 3125a )%%ET0 - 625a %%ET0 +--R * +--R ROOT +--R 2 2 +--R (10b + 10a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET2 +--R + +--R 2 4 4 2 6 +--I (- 250a b - 500a b - 250a )%%ET1 +--R + +--R 2 4 4 2 6 2 2 +--I (- 250a b - 500a b - 250a )%%ET0 + 50a b +--R + +--R 4 +--R 50a +--R * +--I %%ET2 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET1 +--R + +--R 2 4 4 2 6 2 2 +--I (- 250a b - 500a b - 250a )%%ET0 + 50a b +--R + +--R 4 +--R 50a +--R * +--I %%ET1 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET0 +--R + +--R 2 2 4 2 2 +--I (50a b + 50a )%%ET0 - 8b - 3a +--R / +--R 2 4 4 2 6 +--R 125a b + 250a b + 125a +--R + +--R 2 2 2 2 +--I (- 10b - 10a )%%ET2 + (- 10b - 10a )%%ET1 +--R + +--R 2 2 +--I (- 10b - 10a )%%ET0 + 2 +--R / +--R 2 2 +--R 5b + 5a +--R + +--R 7 2 9 5 2 7 +--I ((- 2343750a b - 2343750a )%%ET0 + 31250a b + 31250a ) +--R * +--I %%ET1 +--R + +--R 5 2 7 +--I (31250a b + 31250a )%%ET0 +--R * +--I %%ET2 +--R + +--R 5 2 7 +--I (31250a b + 31250a )%%ET0 %%ET1 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET2 +--R + +--R 2 4 4 2 6 +--I (- 250a b - 500a b - 250a )%%ET1 +--R + +--R 2 4 4 2 6 2 2 4 +--I (- 250a b - 500a b - 250a )%%ET0 + 50a b + 50a +--R * +--I %%ET2 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET1 +--R + +--R 2 4 4 2 6 2 2 4 +--I ((- 250a b - 500a b - 250a )%%ET0 + 50a b + 50a )%%ET1 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%ET0 +--R + +--R 2 2 4 2 2 +--I (50a b + 50a )%%ET0 - 8b - 3a +--R / +--R 2 4 4 2 6 +--R 125a b + 250a b + 125a +--R + +--R 7 2 9 5 2 7 +--I ((- 2343750a b - 2343750a )%%ET0 + 31250a b + 31250a )%%ET1 +--R + +--R 5 2 7 +--I (31250a b + 31250a )%%ET0 +--R * +--R 2 +--I %%ET2 +--R + +--R 7 2 9 5 2 7 2 +--I ((- 2343750a b - 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2109375a )%%ET0 +--R + +--R 4 2 6 2 4 2 +--I (3125a b + 143750a )%%ET0 - 4375a %%ET0 + 50a +--R * +--R +------+ +--I \|4%%ET0 +--R + +--R 7 2 9 4 5 2 7 3 +--I (2343750a b + 2343750a )%%ET0 + (31250a b - 437500a )%%ET0 +--R + +--R 5 2 3 +--I 31250a %%ET0 - 1000a %%ET0 + 2b sinh(x) + 2b cosh(x) + 12a +--R + +--R +----------------------+ +---------------------+ +-------------+ +--R 5+-+4 | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 5\|a \|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--------------------+ +--R |5+---+2 5+-+2 5+-+2 |5+---+4 5+-+2 5+-+2 +------+ +--I \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a \|4%%ET0 +--R * +--R log +--R 8 2 10 4 +--I (- 11718750a b - 11718750a )%%ET0 +--R + +--R 6 2 8 3 +--I (- 234375a b + 2109375a )%%ET0 +--R + +--R 4 2 6 2 4 2 +--I (- 3125a b - 143750a )%%ET0 + 4375a %%ET0 - 50a +--R * +--R +------+ +--I \|4%%ET0 +--R + +--R 7 2 9 4 5 2 7 3 +--I (2343750a b + 2343750a )%%ET0 + (31250a b - 437500a )%%ET0 +--R + +--R 5 2 3 +--I 31250a %%ET0 - 1000a %%ET0 + 2b sinh(x) + 2b cosh(x) + 12a +--R + +--R +---------------------+ +-------------+ +--------------------+ +--R | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 |5+---+2 5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+4 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b - tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +----------------------+ +--R | 5+---+3 5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +-------------+ +--------------------+ +--R | 5+---+3 5+-+2 5+-+2 |5+-+2 5+-+2 |5+---+2 5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+3 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b + tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +---------------------+ +--R | 5+---+5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +---------------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R 5+-+ x 5+-+ +--R +--------------------+ +--------------------+ \|b - tanh(-)\|a +--R |5+---+2 5+-+2 5+-+2 |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a atanh(------------------) +--R +-------------+ +--R |5+-+2 5+-+2 +--R \|\|b + \|a +--R + +--R - +--R +----------------------+ +---------------------+ +-------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R 5+---+5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b + tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(------------------------) +--R +--------------------+ +--R |5+---+2 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R + +--R +----------------------+ +---------------------+ +-------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R 5+---+2 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b - tanh(-)\|a +--R |5+---+2 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +--------------------+ +--R |5+---+4 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------------+ +-------------+ +--R 5+-+4 | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 10\|a \|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--------------------+ +--R |5+---+2 5+-+2 5+-+2 |5+---+4 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 510 +--d0076:= D(m0076,x) +--E 395 + +--S 396 of 510 +t0077:= 1/(a+b*sinh(x)^6) +--R +--R +--R 1 +--R (342) -------------- +--R 6 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 396 + +--S 397 of 510 +r0077:= 1/3*atan((-a^(1/3)+b^(1/3))^(1/2)*tanh(x)/a^(1/6))/a^(5/6)/_ + (-a^(1/3)+b^(1/3))^(1/2)+1/3*atan((-a^(1/3)+(-1)^(2/3)*_ + b^(1/3))^(1/2)*tanh(x)/a^(1/6))/a^(5/6)/(-a^(1/3)+_ + (-1)^(2/3)*b^(1/3))^(1/2)+1/3*atanh((a^(1/3)+_ + (-1)^(1/3)*b^(1/3))^(1/2)*tanh(x)/a^(1/6))/a^(5/6)/(a^(1/3)+_ + (-1)^(1/3)*b^(1/3))^(1/2) +--R +--R +--R (343) +--R +-----------------+ +--R +-----------+ +------------------+ |3+---+3+-+ 3+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|\|- 1 \|b + \|a +--R \|\|b - \|a \|\|- 1 \|b - \|a atanh(---------------------------) +--R 6+-+ +--R \|a +--R + +--R +------------------+ +--R +-----------+ +-----------------+ |3+---+2 3+-+ 3+-+ +--R |3+-+ 3+-+ |3+---+3+-+ 3+-+ tanh(x)\|\|- 1 \|b - \|a +--R \|\|b - \|a \|\|- 1 \|b + \|a atan(----------------------------) +--R 6+-+ +--R \|a +--R + +--R +-----------+ +--R +-----------------+ +------------------+ |3+-+ 3+-+ +--R |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|\|b - \|a +--R \|\|- 1 \|b + \|a \|\|- 1 \|b - \|a atan(---------------------) +--R 6+-+ +--R \|a +--R / +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|\|b - \|a \|\|- 1 \|b + \|a \|\|- 1 \|b - \|a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 510 +a0077:= integrate(t0077,x) +--R +--R +--R (344) +--R - +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EU0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%EU0 + 4b - 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144a )%%EU0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R - +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|\|b - \|a \|\|- 1 \|b + \|a \|\|- 1 \|b - \|a +--R * +--R +------+ +--I \|4%%EU0 +--R * +--R log +--R 5 6 2 3 4 +--I (- 7776a b + 7776a )%%EU0 + (- 216a b - 432a )%%EU0 - 6a b +--R + +--R 2 +--R 6a +--R * +--R +------+ +--I \|4%%EU0 +--R + +--R 4 5 2 2 3 +--I (- 2592a b + 2592a )%%EU0 + (- 72a b - 144a )%%EU0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R +-----------------+ +--R +-----------+ +------------------+ |3+---+3+-+ 3+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|\|- 1 \|b + \|a +--R - 2\|\|b - \|a \|\|- 1 \|b - \|a atanh(---------------------------) +--R 6+-+ +--R \|a +--R + +--R +------------------+ +--R +-----------+ +-----------------+ |3+---+2 3+-+ 3+-+ +--R |3+-+ 3+-+ |3+---+3+-+ 3+-+ tanh(x)\|\|- 1 \|b - \|a +--R - 2\|\|b - \|a \|\|- 1 \|b + \|a atan(----------------------------) +--R 6+-+ +--R \|a +--R + +--R +-----------+ +--R +-----------------+ +------------------+ |3+-+ 3+-+ +--R |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|\|b - \|a +--R - 2\|\|- 1 \|b + \|a \|\|- 1 \|b - \|a atan(---------------------) +--R 6+-+ +--R \|a +--R / +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 6\|a \|\|b - \|a \|\|- 1 \|b + \|a \|\|- 1 \|b - \|a +--R Type: Expression(Integer) +--E 399 + +--S 400 of 510 +--d0077:= D(m0077,x) +--E 400 + +--S 401 of 510 +t0078:= 1/(a+b*sinh(x)^8) +--R +--R +--R 1 +--R (346) -------------- +--R 8 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 510 +r0078:= 1/4*atanh((a^(1/4)+(-b)^(1/4))^(1/2)*tanh(x)/a^(1/8))/a^(7/8)/_ + (a^(1/4)+(-b)^(1/4))^(1/2)+1/4*atanh((a^(1/2)-a^(1/4)*_ + (-b)^(1/4))^(1/2)*tanh(x)/a^(1/4))/a^(3/4)/(a^(1/2)-_ + a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atanh((a^(1/2)-%i*a^(1/4)*_ + (-b)^(1/4))^(1/2)*tanh(x)/a^(1/4))/a^(3/4)/(a^(1/2)-_ + %i*a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atanh((a^(1/2)+_ + %i*a^(1/4)*(-b)^(1/4))^(1/2)*tanh(x)/a^(1/4))/a^(3/4)/_ + (a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2) +--R +--R +--R (347) +--R +-------------------+ +---------------------+ +-------------+ +--R 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R tanh(x)\|%i\|- b \|a + \|a +--R atanh(-----------------------------) +--R 4+-+ +--R \|a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +--R +-------------------+ |4+-+ 4+---+ +--R | 4+---+4+-+ +-+ tanh(x)\|\|a + \|- b +--R \|%i\|- b \|a + \|a atanh(-----------------------) +--R 8+-+ +--R \|a +--R + +--R +-------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R +---------------------+ +--R | 4+---+4+-+ +-+ +--R tanh(x)\|- %i\|- b \|a + \|a +--R atanh(-------------------------------) +--R 4+-+ +--R \|a +--R + +--R +---------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- %i\|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R tanh(x)\|- \|- b \|a + \|a +--R atanh(-----------------------------) +--R 4+-+ +--R \|a +--R / +--R +-------------------+ +---------------------+ +-------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R 4\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R Type: Expression(Complex(Integer)) +--E 402 + +--S 403 of 510 +a0078:= integrate(t0078,x) +--R +--R +--R (348) +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%EV0 + 64a b + 64a ) +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EV1 + (- 16a b - 16a )%%EV0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b + 1048576a )%%EV0 - 16384a b - 16384a )%%EV1 +--R + +--R 5 6 3 4 +--I (- 16384a b - 16384a )%%EV0 + 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b + 1048576a )%%EV0 - 16384a b - 16384a )%%EV1 +--R + +--R 7 8 2 6 3 +--I (1048576a b + 1048576a )%%EV0 - 65536a %%EV0 - 256a b +--R + +--R 4 +--R 768a +--R * +--I %%EV1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b - 16384a )%%EV0 + (- 256a b + 768a )%%EV0 + 8a b +--R + +--R 2 +--R - 8a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EV1 + (- 16a b - 16a )%%EV0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b - 262144a )%%EV0 + 4096a b + 4096a )%%EV1 +--R + +--R 4 5 2 3 +--I (4096a b + 4096a )%%EV0 - 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%EV0 + 64a b + 64a ) +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((- 262144a b - 262144a )%%EV0 + 4096a b + 4096a )%%EV1 +--R + +--R 6 7 2 5 2 3 +--I ((- 262144a b - 262144a )%%EV0 + 16384a %%EV0 + 64a b - 192a ) +--R * +--I %%EV1 +--R + +--R 4 5 2 2 3 2 +--I (4096a b + 4096a )%%EV0 + (64a b - 192a )%%EV0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R - +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EV1 + (- 16a b - 16a )%%EV0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b + 1048576a )%%EV0 - 16384a b - 16384a ) +--R * +--I %%EV1 +--R + +--R 5 6 3 4 +--I (- 16384a b - 16384a )%%EV0 + 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 +--I ((- 1048576a b - 1048576a )%%EV0 + 16384a b + 16384a ) +--R * +--R 2 +--I %%EV1 +--R + +--R 7 8 2 6 +--I (- 1048576a b - 1048576a )%%EV0 + 65536a %%EV0 +--R + +--R 3 4 +--R 256a b - 768a +--R * +--I %%EV1 +--R + +--R 5 6 2 3 4 +--I (16384a b + 16384a )%%EV0 + (256a b - 768a )%%EV0 - 8a b +--R + +--R 2 +--R 8a +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EV0 +--R + +--R 2 3 +--R 64a b + 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EV1 + (- 16a b - 16a )%%EV0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((262144a b + 262144a )%%EV0 - 4096a b - 4096a )%%EV1 +--R + +--R 4 5 2 3 +--I (- 4096a b - 4096a )%%EV0 + 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((- 262144a b - 262144a )%%EV0 + 4096a b + 4096a )%%EV1 +--R + +--R 6 7 2 5 2 +--I (- 262144a b - 262144a )%%EV0 + 16384a %%EV0 + 64a b +--R + +--R 3 +--R - 192a +--R * +--I %%EV1 +--R + +--R 4 5 2 2 3 2 +--I (4096a b + 4096a )%%EV0 + (64a b - 192a )%%EV0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%EV0 + 64a b + 64a ) +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EV1 + (- 16a b - 16a )%%EV0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 6 +--I ((- 1048576a b - 1048576a )%%EV0 + 16384a b + 16384a ) +--R * +--I %%EV1 +--R + +--R 5 6 3 4 +--I (16384a b + 16384a )%%EV0 - 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b + 1048576a )%%EV0 - 16384a b - 16384a )%%EV1 +--R + +--R 7 8 2 6 3 +--I (1048576a b + 1048576a )%%EV0 - 65536a %%EV0 - 256a b +--R + +--R 4 +--R 768a +--R * +--I %%EV1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b - 16384a )%%EV0 + (- 256a b + 768a )%%EV0 + 8a b +--R + +--R 2 +--R - 8a +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EV1 + (- 16a b - 16a )%%EV0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((262144a b + 262144a )%%EV0 - 4096a b - 4096a )%%EV1 +--R + +--R 4 5 2 3 +--I (- 4096a b - 4096a )%%EV0 + 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%EV0 + 64a b + 64a ) +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((- 262144a b - 262144a )%%EV0 + 4096a b + 4096a )%%EV1 +--R + +--R 6 7 2 5 2 3 +--I ((- 262144a b - 262144a )%%EV0 + 16384a %%EV0 + 64a b - 192a ) +--R * +--I %%EV1 +--R + +--R 4 5 2 2 3 2 +--I (4096a b + 4096a )%%EV0 + (64a b - 192a )%%EV0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R - +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EV1 + (- 16a b - 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262144a )%%EV0 + 16384a %%EV0 + 64a b - 192a ) +--R * +--I %%EV1 +--R + +--R 4 5 2 2 3 2 +--I (4096a b + 4096a )%%EV0 + (64a b - 192a )%%EV0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EV1 + (- 16a b - 16a )%%EV0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 +--I (- 1048576a b - 1048576a )%%EV0 + 16384a b +--R + +--R 6 +--R 16384a +--R * +--I %%EV1 +--R + +--R 5 6 3 4 +--I (16384a b + 16384a )%%EV0 - 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 +--I ((- 1048576a b - 1048576a )%%EV0 + 16384a b + 16384a ) +--R * +--R 2 +--I %%EV1 +--R + +--R 7 8 2 6 +--I (- 1048576a b - 1048576a )%%EV0 + 65536a %%EV0 +--R + +--R 3 4 +--R 256a b - 768a +--R * +--I %%EV1 +--R + +--R 5 6 2 3 4 +--I (16384a b + 16384a )%%EV0 + (256a b - 768a )%%EV0 - 8a b +--R + +--R 2 +--R 8a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EV0 +--R + +--R 2 3 +--R 64a b + 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EV1 + (- 16a b - 16a )%%EV0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b - 262144a )%%EV0 + 4096a b + 4096a )%%EV1 +--R + +--R 4 5 2 3 +--I (4096a b + 4096a )%%EV0 - 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EV0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%EV1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EV0 +--R + +--R 2 3 +--I (64a b + 64a )%%EV0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((- 262144a b - 262144a )%%EV0 + 4096a b + 4096a )%%EV1 +--R + +--R 6 7 2 5 2 +--I (- 262144a b - 262144a )%%EV0 + 16384a %%EV0 + 64a b +--R + +--R 3 +--R - 192a +--R * +--I %%EV1 +--R + +--R 4 5 2 2 3 2 +--I (4096a b + 4096a )%%EV0 + (64a b - 192a )%%EV0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%EV1 +--R * +--R log +--R 7 8 5 6 2 +--I ((2097152a b + 2097152a )%%EV0 - 32768a b - 32768a )%%EV1 +--R + +--R 7 8 2 6 3 +--I (2097152a b + 2097152a )%%EV0 - 131072a %%EV0 - 512a b +--R + +--R 4 +--R 1536a +--R * +--I %%EV1 +--R + +--R 7 8 3 6 2 +--I (2097152a b + 2097152a )%%EV0 - 131072a %%EV0 +--R + +--R 4 2 +--I 3072a %%EV0 - 8a b - 24a +--R * +--R +------+ +--I \|4%%EV1 +--R + +--R 6 7 4 5 2 +--I ((524288a b + 524288a )%%EV0 - 8192a b - 8192a )%%EV1 +--R + +--R 6 7 2 5 2 +--I (524288a b + 524288a )%%EV0 - 32768a %%EV0 - 128a b +--R + +--R 3 +--R 384a +--R * +--I %%EV1 +--R + +--R 6 7 3 5 2 3 +--I (524288a b + 524288a )%%EV0 - 32768a %%EV0 + 768a %%EV0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b - 6a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%EV1 +--R * +--R log +--R 7 8 5 6 2 +--I ((- 2097152a b - 2097152a )%%EV0 + 32768a b + 32768a )%%EV1 +--R + +--R 7 8 2 6 3 +--I (- 2097152a b - 2097152a )%%EV0 + 131072a %%EV0 + 512a b +--R + +--R 4 +--R - 1536a +--R * +--I %%EV1 +--R + +--R 7 8 3 6 2 +--I (- 2097152a b - 2097152a )%%EV0 + 131072a %%EV0 +--R + +--R 4 2 +--I - 3072a %%EV0 + 8a b + 24a +--R * +--R +------+ +--I \|4%%EV1 +--R + +--R 6 7 4 5 2 +--I ((524288a b + 524288a )%%EV0 - 8192a b - 8192a )%%EV1 +--R + +--R 6 7 2 5 2 3 +--I ((524288a b + 524288a )%%EV0 - 32768a %%EV0 - 128a b + 384a ) +--R * +--I %%EV1 +--R + +--R 6 7 3 5 2 3 +--I (524288a b + 524288a )%%EV0 - 32768a %%EV0 + 768a %%EV0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b - 6a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%EV0 +--R * +--R log +--R 7 8 3 5 6 2 +--I (2097152a b + 2097152a )%%EV0 + (32768a b - 98304a )%%EV0 +--R + +--R 3 4 2 +--I (512a b + 1536a )%%EV0 + 8a b - 8a +--R * +--R +------+ +--I \|4%%EV0 +--R + +--R 6 7 3 4 5 2 +--I (- 524288a b - 524288a )%%EV0 + (- 8192a b + 24576a )%%EV0 +--R + +--R 2 3 2 +--I (- 128a b - 384a )%%EV0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) - b + 2a +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%EV0 +--R * +--R log +--R 7 8 3 +--I (- 2097152a b - 2097152a )%%EV0 +--R + +--R 5 6 2 3 4 +--I (- 32768a b + 98304a )%%EV0 + (- 512a b - 1536a )%%EV0 +--R + +--R 2 +--R - 8a b + 8a +--R * +--R +------+ +--I \|4%%EV0 +--R + +--R 6 7 3 4 5 2 +--I (- 524288a b - 524288a )%%EV0 + (- 8192a b + 24576a )%%EV0 +--R + +--R 2 3 2 +--I (- 128a b - 384a )%%EV0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) - b + 2a +--R + +--R - +--R +-------------------+ +---------------------+ +-------------+ +--R 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R tanh(x)\|%i\|- b \|a + \|a +--R atanh(-----------------------------) +--R 4+-+ +--R \|a +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +--R +-------------------+ |4+-+ 4+---+ +--R | 4+---+4+-+ +-+ tanh(x)\|\|a + \|- b +--R \|%i\|- b \|a + \|a atanh(-----------------------) +--R 8+-+ +--R \|a +--R + +--R - +--R +-------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R +---------------------+ +--R | 4+---+4+-+ +-+ +--R tanh(x)\|- %i\|- b \|a + \|a +--R atanh(-------------------------------) +--R 4+-+ +--R \|a +--R + +--R - +--R +---------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- %i\|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R tanh(x)\|- \|- b \|a + \|a +--R atanh(-----------------------------) +--R 4+-+ +--R \|a +--R / +--R +-------------------+ +---------------------+ +-------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R 4\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R Type: Expression(Complex(Integer)) +--E 404 + +--S 405 of 510 +--d0078:= D(m0078,x) +--E 405 + +--S 406 of 510 +t0079:= 1/(a-b*sinh(x)^3) +--R +--R +--R 1 +--R (350) - -------------- +--R 3 +--R b sinh(x) - a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 510 +r0079:= -2/3*atanh(((-1)^(1/3)*b^(1/3)-a^(1/3)*tanh(1/2*x))/(a^(2/3)+_ + (-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)+_ + (-1)^(2/3)*b^(2/3))^(1/2)+2/3*atanh((b^(1/3)+_ + a^(1/3)*tanh(1/2*x))/(a^(2/3)+b^(2/3))^(1/2))/a^(2/3)/_ + (a^(2/3)+b^(2/3))^(1/2)+2/3*atanh(((-1)^(2/3)*b^(1/3)+_ + a^(1/3)*tanh(1/2*x))/(a^(2/3)-(-1)^(1/3)*b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-(-1)^(1/3)*b^(2/3))^(1/2) +--R +--R +--R (351) +--R 3+---+2 3+-+ x 3+-+ +--R +-------------+ +--------------------+ \|- 1 \|b + tanh(-)\|a +--R |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 2 +--R 2\|\|b + \|a \|\|- 1 \|b + \|a atanh(-------------------------) +--R +---------------------+ +--R | 3+---+3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R 3+-+ x 3+-+ +--R +---------------------+ +--------------------+ \|b + tanh(-)\|a +--R | 3+---+3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 2 +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atanh(------------------) +--R +-------------+ +--R |3+-+2 3+-+2 +--R \|\|b + \|a +--R + +--R 3+---+3+-+ x 3+-+ +--R +---------------------+ +-------------+ \|- 1 \|b - tanh(-)\|a +--R | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 2 +--R - 2\|- \|- 1 \|b + \|a \|\|b + \|a atanh(------------------------) +--R +--------------------+ +--R |3+---+2 3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +---------------------+ +-------------+ +--------------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 407 + +--S 408 of 510 +a0079:= integrate(t0079,x) +--R +--R +--R (352) +--R - +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b + 486a )%%EW0 - 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b + 486a )%%EW0 + (27a b - 135a )%%EW0 + 9a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (162a b + 162a )%%EW0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%EW0 - 54a %%EW0 + 4b sinh(x) + 4b cosh(x) +--R + +--R 4a +--R + +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b + 486a )%%EW0 - 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b - 486a )%%EW0 + (- 27a b + 135a )%%EW0 - 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (- 162a b - 162a )%%EW0 +--R * +--R ROOT +--R 2 4 4 2 6 2 2 2 4 +--I (- 81a b - 162a b - 81a )%%EW0 + (18a b + 18a )%%EW0 +--R + +--R 2 2 +--R - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%EW0 - 54a %%EW0 + 4b sinh(x) + 4b cosh(x) + 4a +--R + +--R - +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b - 486a )%%EW0 + 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b + 486a )%%EW0 + (27a b - 135a )%%EW0 + 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (- 162a b - 162a )%%EW0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%EW0 - 54a %%EW0 + 4b sinh(x) + 4b cosh(x) +--R + +--R 4a +--R + +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b - 486a )%%EW0 + 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b - 486a )%%EW0 + (- 27a b + 135a )%%EW0 - 9a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (162a b + 162a )%%EW0 +--R * +--R ROOT +--R 2 4 4 2 6 2 2 2 4 +--I (- 81a b - 162a b - 81a )%%EW0 + (18a b + 18a )%%EW0 +--R + +--R 2 2 +--R - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%EW0 - 54a %%EW0 + 4b sinh(x) + 4b cosh(x) + 4a +--R + +--R +------+ +--I \|4%%EW0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +------+ +--I ((486a b + 486a )%%EW0 + (27a b - 135a )%%EW0 + 9a )\|4%%EW0 +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%EW0 + 54a %%EW0 + 2b sinh(x) + 2b cosh(x) - 4a +--R + +--R - +--R +------+ +--I \|4%%EW0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--I ((- 486a b - 486a )%%EW0 + (- 27a b + 135a )%%EW0 - 9a ) +--R * +--R +------+ +--I \|4%%EW0 +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%EW0 + 54a %%EW0 + 2b sinh(x) + 2b cosh(x) +--R + +--R - 4a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 510 +m0079:= a0079-r0079 +--R +--R +--R (353) +--R - +--R +---------------------+ +-------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--R |3+---+2 3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b + 486a )%%EW0 - 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b + 486a )%%EW0 + (27a b - 135a )%%EW0 + 9a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (162a b + 162a )%%EW0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%EW0 - 54a %%EW0 + 4b sinh(x) + 4b cosh(x) +--R + +--R 4a +--R + +--R +---------------------+ +-------------+ +--------------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b + 486a )%%EW0 - 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b - 486a )%%EW0 + (- 27a b + 135a )%%EW0 - 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (- 162a b - 162a )%%EW0 +--R * +--R ROOT +--R 2 4 4 2 6 2 2 2 4 +--I (- 81a b - 162a b - 81a )%%EW0 + (18a b + 18a )%%EW0 +--R + +--R 2 2 +--R - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%EW0 - 54a %%EW0 + 4b sinh(x) + 4b cosh(x) + 4a +--R + +--R - +--R +---------------------+ +-------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--R |3+---+2 3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b - 486a )%%EW0 + 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b + 486a )%%EW0 + (27a b - 135a )%%EW0 + 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (- 162a b - 162a )%%EW0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%EW0 - 54a %%EW0 + 4b sinh(x) + 4b cosh(x) +--R + +--R 4a +--R + +--R +---------------------+ +-------------+ +--------------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b - 486a )%%EW0 + 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b - 486a )%%EW0 + (- 27a b + 135a )%%EW0 - 9a +--R * +--R ROOT +--R 2 2 +--R (6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b - 162a b - 81a )%%EW0 +--R + +--R 2 2 4 2 2 +--I (18a b + 18a )%%EW0 - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 2 2 +--I (- 6b - 6a )%%EW0 + 2 +--R / +--R 2 2 +--R 3b + 3a +--R + +--R 3 2 5 +--I (162a b + 162a )%%EW0 +--R * +--R ROOT +--R 2 4 4 2 6 2 2 2 4 +--I (- 81a b - 162a b - 81a )%%EW0 + (18a b + 18a )%%EW0 +--R + +--R 2 2 +--R - 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b + 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b + 162a )%%EW0 - 54a %%EW0 + 4b sinh(x) + 4b cosh(x) + 4a +--R + +--R +---------------------+ +-------------+ +--------------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%EW0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +------+ +--I ((486a b + 486a )%%EW0 + (27a b - 135a )%%EW0 + 9a )\|4%%EW0 +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%EW0 + 54a %%EW0 + 2b sinh(x) + 2b cosh(x) - 4a +--R + +--R - +--R +---------------------+ +-------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--R |3+---+2 3+-+2 3+-+2 +------+ +--I \|\|- 1 \|b + \|a \|4%%EW0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--I ((- 486a b - 486a )%%EW0 + (- 27a b + 135a )%%EW0 - 9a ) +--R * +--R +------+ +--I \|4%%EW0 +--R + +--R 3 2 5 2 3 +--I (- 162a b - 162a )%%EW0 + 54a %%EW0 + 2b sinh(x) + 2b cosh(x) +--R + +--R - 4a +--R + +--R - +--R +-------------+ +--------------------+ +--R |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 4\|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+2 3+-+ x 3+-+ +--R \|- 1 \|b + tanh(-)\|a +--R 2 +--R atanh(-------------------------) +--R +---------------------+ +--R | 3+---+3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +---------------------+ +--------------------+ +--R | 3+---+3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 4\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+-+ x 3+-+ +--R \|b + tanh(-)\|a +--R 2 +--R atanh(------------------) +--R +-------------+ +--R |3+-+2 3+-+2 +--R \|\|b + \|a +--R + +--R 3+---+3+-+ x 3+-+ +--R +---------------------+ +-------------+ \|- 1 \|b - tanh(-)\|a +--R | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 2 +--R 4\|- \|- 1 \|b + \|a \|\|b + \|a atanh(------------------------) +--R +--------------------+ +--R |3+---+2 3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +---------------------+ +-------------+ +--------------------+ +--R 3+-+2 | 3+---+3+-+2 3+-+2 |3+-+2 3+-+2 |3+---+2 3+-+2 3+-+2 +--R 6\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 510 +d0079:= D(m0079,x) +--R +--R +--R (354) +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 9a b \|- 1 - 9a b\|- 1 + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 60a b \|- 1 + 60a b\|- 1 - 60a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (36a b \|- 1 - 36a b\|- 1 + 36a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (54a b \|- 1 - 54a b\|- 1 + 54a b)cosh(x) - 9a b \|- 1 +--R + +--R 2 3+---+ 2 +--R 9a b\|- 1 - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (36a b \|- 1 - 36a b\|- 1 + 36a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (9a b \|- 1 - 9a b\|- 1 + 9a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cosh(x) + 3a b \|- 1 +--R + +--R 2 3+---+ 2 +--R - 3a b\|- 1 + 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 12a b )sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 180a b \|- 1 + 180a b \|- 1 - 180a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 36a b \|- 1 - 36a b \|- 1 + 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 240a b \|- 1 + 240a b \|- 1 - 240a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 48a b \|- 1 + 48a b\|- 1 - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 180a b \|- 1 + 180a b \|- 1 - 180a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 36a b \|- 1 + 36a b \|- 1 - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 12a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 48a b \|- 1 + 48a b\|- 1 - 48a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) + 12a b \|- 1 +--R + +--R 2 3+---+ 2 +--R - 12a b \|- 1 + 12a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R ((- 4b + 5a b)\|- 1 + (4b - 5a b)\|- 1 - 4b + 5a b)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((- 24b + 30a b)\|- 1 + (24b - 30a b)\|- 1 - 24b + 30a b) +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 60b + 75a b)\|- 1 + (60b - 75a b)\|- 1 - 60b +--R + +--R 2 +--R 75a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (12b - 15a b)\|- 1 + (- 12b + 15a b)\|- 1 + 12b - 15a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 80b + 100a b)\|- 1 + (80b - 100a b)\|- 1 - 80b +--R + +--R 2 +--R 100a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (48b - 60a b)\|- 1 + (- 48b + 60a b)\|- 1 + 48b +--R + +--R 2 +--R - 60a b +--R * +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 +--R (- 64a b - 64a )\|- 1 + (64a b + 64a )\|- 1 - 64a b +--R + +--R 3 +--R - 64a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 60b + 75a b)\|- 1 + (60b - 75a b)\|- 1 - 60b +--R + +--R 2 +--R 75a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (72b - 90a b)\|- 1 + (- 72b + 90a b)\|- 1 + 72b +--R + +--R 2 +--R - 90a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ +--R (- 192a b - 192a )\|- 1 + (192a b + 192a )\|- 1 +--R + +--R 2 3 +--R - 192a b - 192a +--R * +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 12b + 15a b)\|- 1 + (12b - 15a b)\|- 1 - 12b + 15a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 24b + 30a b)\|- 1 + (24b - 30a b)\|- 1 - 24b +--R + +--R 2 +--R 30a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (48b - 60a b)\|- 1 + (- 48b + 60a b)\|- 1 + 48b +--R + +--R 2 +--R - 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ +--R (- 192a b - 192a )\|- 1 + (192a b + 192a )\|- 1 +--R + +--R 2 3 +--R - 192a b - 192a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 24b + 30a b)\|- 1 + (24b - 30a b)\|- 1 - 24b +--R + +--R 2 +--R 30a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R ((- 4b + 5a b)\|- 1 + (4b - 5a b)\|- 1 - 4b + 5a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((12b - 15a b)\|- 1 + (- 12b + 15a b)\|- 1 + 12b - 15a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 +--R (- 64a b - 64a )\|- 1 + (64a b + 64a )\|- 1 - 64a b +--R + +--R 3 +--R - 64a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((- 12b + 15a b)\|- 1 + (12b - 15a b)\|- 1 - 12b + 15a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (4b - 5a b)\|- 1 + (- 4b + 5a b)\|- 1 + 4b - 5a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (24a b \|- 1 - 24a b \|- 1 + 24a b )sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (360a b \|- 1 - 360a b \|- 1 + 360a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 72a b \|- 1 + 72a b \|- 1 - 72a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (480a b \|- 1 - 480a b \|- 1 + 480a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 96a b \|- 1 + 96a b\|- 1 - 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (360a b \|- 1 - 360a b \|- 1 + 360a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 432a b \|- 1 + 432a b \|- 1 - 432a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 288a b \|- 1 + 288a b\|- 1 - 288a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 72a b \|- 1 - 72a b \|- 1 + 72a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 288a b \|- 1 + 288a b\|- 1 - 288a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (24a b \|- 1 - 24a b \|- 1 + 24a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 96a b \|- 1 + 96a b\|- 1 - 96a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) - 24a b \|- 1 +--R + +--R 2 3+---+ 2 +--R 24a b \|- 1 - 24a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R ((4b - 5a b)\|- 1 + (- 4b + 5a b)\|- 1 + 4b - 5a b)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((24b - 30a b)\|- 1 + (- 24b + 30a b)\|- 1 + 24b - 30a b) +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (60b - 75a b)\|- 1 + (- 60b + 75a b)\|- 1 + 60b +--R + +--R 2 +--R - 75a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 12b + 15a b)\|- 1 + (12b - 15a b)\|- 1 - 12b + 15a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (80b - 100a b)\|- 1 + (- 80b + 100a b)\|- 1 + 80b +--R + +--R 2 +--R - 100a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 48b + 60a b)\|- 1 + (48b - 60a b)\|- 1 - 48b +--R + +--R 2 +--R 60a b +--R * +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 +--R (64a b + 64a )\|- 1 + (- 64a b - 64a )\|- 1 + 64a b +--R + +--R 3 +--R 64a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (60b - 75a b)\|- 1 + (- 60b + 75a b)\|- 1 + 60b +--R + +--R 2 +--R - 75a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 72b + 90a b)\|- 1 + (72b - 90a b)\|- 1 - 72b +--R + +--R 2 +--R 90a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ +--R (192a b + 192a )\|- 1 + (- 192a b - 192a )\|- 1 +--R + +--R 2 3 +--R 192a b + 192a +--R * +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (12b - 15a b)\|- 1 + (- 12b + 15a b)\|- 1 + 12b - 15a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (24b - 30a b)\|- 1 + (- 24b + 30a b)\|- 1 + 24b +--R + +--R 2 +--R - 30a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (- 48b + 60a b)\|- 1 + (48b - 60a b)\|- 1 - 48b +--R + +--R 2 +--R 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ +--R (192a b + 192a )\|- 1 + (- 192a b - 192a )\|- 1 +--R + +--R 2 3 +--R 192a b + 192a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 +--R (24b - 30a b)\|- 1 + (- 24b + 30a b)\|- 1 + 24b +--R + +--R 2 +--R - 30a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R ((4b - 5a b)\|- 1 + (- 4b + 5a b)\|- 1 + 4b - 5a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((- 12b + 15a b)\|- 1 + (12b - 15a b)\|- 1 - 12b + 15a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 +--R (64a b + 64a )\|- 1 + (- 64a b - 64a )\|- 1 + 64a b +--R + +--R 3 +--R 64a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R ((12b - 15a b)\|- 1 + (- 12b + 15a b)\|- 1 + 12b - 15a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 4b + 5a b)\|- 1 + (4b - 5a b)\|- 1 - 4b + 5a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 12a b )sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 180a b \|- 1 + 180a b \|- 1 - 180a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 36a b \|- 1 - 36a b \|- 1 + 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 240a b \|- 1 + 240a b \|- 1 - 240a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 48a b \|- 1 + 48a b\|- 1 - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 180a b \|- 1 + 180a b \|- 1 - 180a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 36a b \|- 1 + 36a b \|- 1 - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 12a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 48a b \|- 1 + 48a b\|- 1 - 48a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) + 12a b \|- 1 +--R + +--R 2 3+---+ 2 +--R - 12a b \|- 1 + 12a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (3a b \|- 1 - 3a b\|- 1 + 3a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (45a b \|- 1 - 45a b\|- 1 + 45a b)cosh(x) - 9a b \|- 1 +--R + +--R 2 3+---+ 2 +--R 9a b\|- 1 - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (60a b \|- 1 - 60a b\|- 1 + 60a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (45a b \|- 1 - 45a b\|- 1 + 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cosh(x) + 9a b \|- 1 +--R + +--R 2 3+---+ 2 +--R - 9a b\|- 1 + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (3a b \|- 1 - 3a b\|- 1 + 3a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (9a b \|- 1 - 9a b\|- 1 + 9a b)cosh(x) - 3a b \|- 1 +--R + +--R 2 3+---+ 2 +--R 3a b\|- 1 - 3a b +--R * +--R 3+-+2 3+-+2 +--R \|a \|b +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 9a b \|- 1 - 9a b \|- 1 + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 60a b \|- 1 + 60a b \|- 1 - 60a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 9a b \|- 1 + 9a b \|- 1 - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) + 3a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 3a b \|- 1 + 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((- 4a b - 4a b)\|- 1 + (4a b + 4a b)\|- 1 - 4a b - 4a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 24a b - 24a b)\|- 1 + (24a b + 24a b)\|- 1 - 24a b +--R + +--R 3 +--R - 24a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 60a b - 60a b)\|- 1 + (60a b + 60a b)\|- 1 +--R + +--R 3 3 +--R - 60a b - 60a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 12a b)\|- 1 + (- 12a b - 12a b)\|- 1 + 12a b +--R + +--R 3 +--R 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 80a b - 80a b)\|- 1 + (80a b + 80a b)\|- 1 +--R + +--R 3 3 +--R - 80a b - 80a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (48a b + 48a b)\|- 1 + (- 48a b - 48a b)\|- 1 +--R + +--R 3 3 +--R 48a b + 48a b +--R * +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 16a b - 16a )\|- 1 + (16a b + 16a )\|- 1 - 16a b +--R + +--R 4 +--R - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 60a b - 60a b)\|- 1 + (60a b + 60a b)\|- 1 +--R + +--R 3 3 +--R - 60a b - 60a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (72a b + 72a b)\|- 1 + (- 72a b - 72a b)\|- 1 +--R + +--R 3 3 +--R 72a b + 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 4 +--R - 48a +--R * +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 12a b)\|- 1 + (12a b + 12a b)\|- 1 - 12a b +--R + +--R 3 +--R - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 24a b - 24a b)\|- 1 + (24a b + 24a b)\|- 1 +--R + +--R 3 3 +--R - 24a b - 24a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (48a b + 48a b)\|- 1 + (- 48a b - 48a b)\|- 1 +--R + +--R 3 3 +--R 48a b + 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 4 +--R - 48a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 24a b - 24a b)\|- 1 + (24a b + 24a b)\|- 1 +--R + +--R 3 3 +--R - 24a b - 24a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((- 4a b - 4a b)\|- 1 + (4a b + 4a b)\|- 1 - 4a b - 4a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 12a b)\|- 1 + (- 12a b - 12a b)\|- 1 + 12a b +--R + +--R 3 +--R 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 16a b - 16a )\|- 1 + (16a b + 16a )\|- 1 - 16a b +--R + +--R 4 +--R - 16a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 12a b)\|- 1 + (12a b + 12a b)\|- 1 - 12a b +--R + +--R 3 +--R - 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R (4a b + 4a b)\|- 1 + (- 4a b - 4a b)\|- 1 + 4a b + 4a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 9a b \|- 1 - 9a b \|- 1 + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 60a b \|- 1 + 60a b \|- 1 - 60a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R - 192a b \|- 1 + 192a b\|- 1 - 192a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 576a b \|- 1 + 576a b\|- 1 - 576a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 9a b \|- 1 + 9a b \|- 1 - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 576a b \|- 1 + 576a b\|- 1 - 576a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 192a b \|- 1 + 192a b\|- 1 - 192a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) + 3a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 3a b \|- 1 + 3a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((8a b + 8a b)\|- 1 + (- 8a b - 8a b)\|- 1 + 8a b + 8a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (48a b + 48a b)\|- 1 + (- 48a b - 48a b)\|- 1 + 48a b +--R + +--R 3 +--R 48a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (120a b + 120a b)\|- 1 + (- 120a b - 120a b)\|- 1 +--R + +--R 3 3 +--R 120a b + 120a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 24a b - 24a b)\|- 1 + (24a b + 24a b)\|- 1 - 24a b +--R + +--R 3 +--R - 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (160a b + 160a b)\|- 1 + (- 160a b - 160a b)\|- 1 +--R + +--R 3 3 +--R 160a b + 160a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 96a b - 96a b)\|- 1 + (96a b + 96a b)\|- 1 +--R + +--R 3 3 +--R - 96a b - 96a b +--R * +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 160a b + 32a )\|- 1 + (160a b - 32a )\|- 1 - 160a b +--R + +--R 4 +--R 32a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (120a b + 120a b)\|- 1 + (- 120a b - 120a b)\|- 1 +--R + +--R 3 3 +--R 120a b + 120a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 144a b - 144a b)\|- 1 + (144a b + 144a b)\|- 1 +--R + +--R 3 3 +--R - 144a b - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (- 480a b + 96a )\|- 1 + (480a b - 96a )\|- 1 +--R + +--R 2 2 4 +--R - 480a b + 96a +--R * +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (24a b + 24a b)\|- 1 + (- 24a b - 24a b)\|- 1 + 24a b +--R + +--R 3 +--R 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (48a b + 48a b)\|- 1 + (- 48a b - 48a b)\|- 1 +--R + +--R 3 3 +--R 48a b + 48a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 96a b - 96a b)\|- 1 + (96a b + 96a b)\|- 1 +--R + +--R 3 3 +--R - 96a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (- 480a b + 96a )\|- 1 + (480a b - 96a )\|- 1 +--R + +--R 2 2 4 +--R - 480a b + 96a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (48a b + 48a b)\|- 1 + (- 48a b - 48a b)\|- 1 +--R + +--R 3 3 +--R 48a b + 48a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((8a b + 8a b)\|- 1 + (- 8a b - 8a b)\|- 1 + 8a b + 8a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 24a b - 24a b)\|- 1 + (24a b + 24a b)\|- 1 - 24a b +--R + +--R 3 +--R - 24a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 160a b + 32a )\|- 1 + (160a b - 32a )\|- 1 - 160a b +--R + +--R 4 +--R 32a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (24a b + 24a b)\|- 1 + (- 24a b - 24a b)\|- 1 + 24a b +--R + +--R 3 +--R 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R (- 8a b - 8a b)\|- 1 + (8a b + 8a b)\|- 1 - 8a b - 8a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 9a b \|- 1 + 9a b \|- 1 - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (60a b \|- 1 - 60a b \|- 1 + 60a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R 192a b \|- 1 - 192a b\|- 1 + 192a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (576a b \|- 1 - 576a b\|- 1 + 576a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 9a b \|- 1 - 9a b \|- 1 + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (576a b \|- 1 - 576a b\|- 1 + 576a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (192a b \|- 1 - 192a b\|- 1 + 192a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) - 3a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 3a b \|- 1 - 3a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((- 4a b - 4a b)\|- 1 + (4a b + 4a b)\|- 1 - 4a b - 4a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 24a b - 24a b)\|- 1 + (24a b + 24a b)\|- 1 - 24a b +--R + +--R 3 +--R - 24a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 60a b - 60a b)\|- 1 + (60a b + 60a b)\|- 1 +--R + +--R 3 3 +--R - 60a b - 60a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 12a b)\|- 1 + (- 12a b - 12a b)\|- 1 + 12a b +--R + +--R 3 +--R 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 80a b - 80a b)\|- 1 + (80a b + 80a b)\|- 1 +--R + +--R 3 3 +--R - 80a b - 80a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (48a b + 48a b)\|- 1 + (- 48a b - 48a b)\|- 1 +--R + +--R 3 3 +--R 48a b + 48a b +--R * +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 16a b - 16a )\|- 1 + (16a b + 16a )\|- 1 - 16a b +--R + +--R 4 +--R - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 60a b - 60a b)\|- 1 + (60a b + 60a b)\|- 1 +--R + +--R 3 3 +--R - 60a b - 60a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (72a b + 72a b)\|- 1 + (- 72a b - 72a b)\|- 1 +--R + +--R 3 3 +--R 72a b + 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 4 +--R - 48a +--R * +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 12a b)\|- 1 + (12a b + 12a b)\|- 1 - 12a b +--R + +--R 3 +--R - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 24a b - 24a b)\|- 1 + (24a b + 24a b)\|- 1 +--R + +--R 3 3 +--R - 24a b - 24a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (48a b + 48a b)\|- 1 + (- 48a b - 48a b)\|- 1 +--R + +--R 3 3 +--R 48a b + 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 4 +--R - 48a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 24a b - 24a b)\|- 1 + (24a b + 24a b)\|- 1 +--R + +--R 3 3 +--R - 24a b - 24a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R ((- 4a b - 4a b)\|- 1 + (4a b + 4a b)\|- 1 - 4a b - 4a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 12a b)\|- 1 + (- 12a b - 12a b)\|- 1 + 12a b +--R + +--R 3 +--R 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 16a b - 16a )\|- 1 + (16a b + 16a )\|- 1 - 16a b +--R + +--R 4 +--R - 16a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 12a b)\|- 1 + (12a b + 12a b)\|- 1 - 12a b +--R + +--R 3 +--R - 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R (4a b + 4a b)\|- 1 + (- 4a b - 4a b)\|- 1 + 4a b + 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) - 9a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 9a b \|- 1 - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (60a b \|- 1 - 60a b \|- 1 + 60a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) + 9a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 9a b \|- 1 + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) - 3a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 3a b \|- 1 - 3a b +--R * +--R 3+-+ +--R \|b +--R + +--R 3 3 6 3 3 5 +--R (- 3a b - 3a b)sinh(x) + (- 18a b - 18a b)cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 4 +--R ((- 45a b - 45a b)cosh(x) + 9a b + 9a b)sinh(x) +--R + +--R 3 3 3 3 3 3 +--R ((- 60a b - 60a b)cosh(x) + (36a b + 36a b)cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 3 +--R (- 45a b - 45a b)cosh(x) + (54a b + 54a b)cosh(x) - 9a b +--R + +--R 3 +--R - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 3 3 3 +--R (- 18a b - 18a b)cosh(x) + (36a b + 36a b)cosh(x) +--R + +--R 3 3 +--R (- 18a b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 6 3 3 4 +--R (- 3a b - 3a b)cosh(x) + (9a b + 9a b)cosh(x) +--R + +--R 3 3 2 3 3 +--R (- 9a b - 9a b)cosh(x) + 3a b + 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 12a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 180a b \|- 1 + 180a b \|- 1 - 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 36a b \|- 1 - 36a b \|- 1 + 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 240a b \|- 1 + 240a b \|- 1 - 240a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R - 48a b \|- 1 + 48a b\|- 1 - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 180a b \|- 1 + 180a b \|- 1 - 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 36a b \|- 1 + 36a b \|- 1 - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 12a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 48a b \|- 1 + 48a b\|- 1 - 48a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) + 12a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 12a b \|- 1 + 12a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 3 3+---+2 3 3+---+ 3 3 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 3a b + 9a b)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 18a b + 54a b)cosh(x)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (- 180a b \|- 1 + 180a b \|- 1 - 45a b + 135a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R 36a b \|- 1 - 36a b \|- 1 + 9a b - 27a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 3 +--R (- 240a b \|- 1 + 240a b \|- 1 - 60a b + 180a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (144a b \|- 1 - 144a b \|- 1 + 36a b - 108a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 192a b \|- 1 + 192a b \|- 1 - 192a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 4 +--R (- 180a b \|- 1 + 180a b \|- 1 - 45a b + 135a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (216a b \|- 1 - 216a b \|- 1 + 54a b - 162a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 576a b \|- 1 + 576a b \|- 1 - 576a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R - 36a b \|- 1 + 36a b \|- 1 - 9a b + 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 18a b + 54a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 3 +--R (144a b \|- 1 - 144a b \|- 1 + 36a b - 108a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 576a b \|- 1 + 576a b \|- 1 - 576a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 72a b \|- 1 + 72a b \|- 1 - 18a b + 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 3a b + 9a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 4 +--R (36a b \|- 1 - 36a b \|- 1 + 9a b - 27a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 192a b \|- 1 + 192a b \|- 1 - 192a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 9a b + 27a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R 12a b \|- 1 - 12a b \|- 1 + 3a b - 9a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (24a b \|- 1 - 24a b \|- 1 + 24a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (360a b \|- 1 - 360a b \|- 1 + 360a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 72a b \|- 1 + 72a b \|- 1 - 72a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (480a b \|- 1 - 480a b \|- 1 + 480a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R 96a b \|- 1 - 96a b\|- 1 - 192a b - 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (360a b \|- 1 - 360a b \|- 1 + 360a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 432a b \|- 1 + 432a b \|- 1 - 432a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (288a b \|- 1 - 288a b\|- 1 - 576a b - 288a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 72a b \|- 1 - 72a b \|- 1 + 72a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 288a b \|- 1 + 288a b \|- 1 - 288a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (288a b \|- 1 - 288a b\|- 1 - 576a b - 288a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (24a b \|- 1 - 24a b \|- 1 + 24a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 3 +--R (96a b \|- 1 - 96a b\|- 1 - 192a b - 96a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (72a b \|- 1 - 72a b \|- 1 + 72a b )cosh(x) - 24a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 24a b \|- 1 - 24a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 3 3+---+2 3 3+---+ 3 3 6 +--R (12a b \|- 1 - 12a b \|- 1 + 3a b - 9a b)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 5 +--R (72a b \|- 1 - 72a b \|- 1 + 18a b - 54a b)cosh(x)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (180a b \|- 1 - 180a b \|- 1 + 45a b - 135a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R - 36a b \|- 1 + 36a b \|- 1 - 9a b + 27a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 3 +--R (240a b \|- 1 - 240a b \|- 1 + 60a b - 180a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 144a b \|- 1 + 144a b \|- 1 - 36a b + 108a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 192a b \|- 1 - 192a b \|- 1 + 192a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 4 +--R (180a b \|- 1 - 180a b \|- 1 + 45a b - 135a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 54a b + 162a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (576a b \|- 1 - 576a b \|- 1 + 576a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R 36a b \|- 1 - 36a b \|- 1 + 9a b - 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 5 +--R (72a b \|- 1 - 72a b \|- 1 + 18a b - 54a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 3 +--R (- 144a b \|- 1 + 144a b \|- 1 - 36a b + 108a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (576a b \|- 1 - 576a b \|- 1 + 576a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (72a b \|- 1 - 72a b \|- 1 + 18a b - 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 6 +--R (12a b \|- 1 - 12a b \|- 1 + 3a b - 9a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 4 +--R (- 36a b \|- 1 + 36a b \|- 1 - 9a b + 27a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (192a b \|- 1 - 192a b \|- 1 + 192a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 2 +--R (36a b \|- 1 - 36a b \|- 1 + 9a b - 27a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R - 12a b \|- 1 + 12a b \|- 1 - 3a b + 9a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 12a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 180a b \|- 1 + 180a b \|- 1 - 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 36a b \|- 1 - 36a b \|- 1 + 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 240a b \|- 1 + 240a b \|- 1 - 240a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R - 48a b \|- 1 + 48a b\|- 1 - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 180a b \|- 1 + 180a b \|- 1 - 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 36a b \|- 1 + 36a b \|- 1 - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 12a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 48a b \|- 1 + 48a b\|- 1 - 48a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) + 12a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 12a b \|- 1 + 12a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 6 3 3 5 +--R (3a b + 3a b)sinh(x) + (18a b + 18a b)cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 4 +--R ((45a b + 45a b)cosh(x) - 9a b - 9a b)sinh(x) +--R + +--R 3 3 3 3 3 3 +--R ((60a b + 60a b)cosh(x) + (- 36a b - 36a b)cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 3 +--R (45a b + 45a b)cosh(x) + (- 54a b - 54a b)cosh(x) + 9a b +--R + +--R 3 +--R 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 3 3 3 +--R (18a b + 18a b)cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 3 3 +--R (18a b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 6 3 3 4 +--R (3a b + 3a b)cosh(x) + (- 9a b - 9a b)cosh(x) +--R + +--R 3 3 2 3 3 +--R (9a b + 9a b)cosh(x) - 3a b - 3a b +--R * +--R 3+-+ +--R \|a +--R / +--R 3 3+---+2 3 3+---+ 3 6 +--R (3a b \|- 1 - 3a b\|- 1 + 3a b)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 5 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 +--R (45a b \|- 1 - 45a b\|- 1 + 45a b)cosh(x) - 9a b \|- 1 +--R + +--R 3 3+---+ 3 +--R 9a b\|- 1 - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (60a b \|- 1 - 60a b\|- 1 + 60a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 3+---+2 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x) - 24a \|- 1 +--R + +--R 4 3+---+ 4 +--R 24a \|- 1 - 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 +--R (45a b \|- 1 - 45a b\|- 1 + 45a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 54a b \|- 1 + 54a b\|- 1 - 54a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 3+---+2 +--R (- 72a \|- 1 + 72a \|- 1 - 72a )cosh(x) + 9a b \|- 1 +--R + +--R 3 3+---+ 3 +--R - 9a b\|- 1 + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 5 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (- 72a \|- 1 + 72a \|- 1 - 72a )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 6 +--R (3a b \|- 1 - 3a b\|- 1 + 3a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 +--R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (- 24a \|- 1 + 24a \|- 1 - 24a )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 +--R (9a b \|- 1 - 9a b\|- 1 + 9a b)cosh(x) - 3a b \|- 1 +--R + +--R 3 3+---+ 3 +--R 3a b\|- 1 - 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (270a b \|- 1 - 270a b \|- 1 + 270a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 54a b \|- 1 + 54a b \|- 1 - 54a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (360a b \|- 1 - 360a b \|- 1 + 360a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R - 144a b \|- 1 + 144a b\|- 1 - 144a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (270a b \|- 1 - 270a b \|- 1 + 270a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 324a b \|- 1 + 324a b \|- 1 - 324a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 54a b \|- 1 - 54a b \|- 1 + 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) - 18a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 18a b \|- 1 - 18a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 3a b)\|- 1 + (- 12a b - 3a b)\|- 1 + 12a b +--R + +--R 3 +--R 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (72a b + 18a b)\|- 1 + (- 72a b - 18a b)\|- 1 + 72a b +--R + +--R 3 +--R 18a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (180a b + 45a b)\|- 1 + (- 180a b - 45a b)\|- 1 +--R + +--R 3 3 +--R 180a b + 45a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 36a b - 9a b)\|- 1 + (36a b + 9a b)\|- 1 - 36a b +--R + +--R 3 +--R - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (240a b + 60a b)\|- 1 + (- 240a b - 60a b)\|- 1 +--R + +--R 3 3 +--R 240a b + 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 144a b - 36a b)\|- 1 + (144a b + 36a b)\|- 1 +--R + +--R 3 3 +--R - 144a b - 36a b +--R * +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 96a b - 24a )\|- 1 + (96a b + 24a )\|- 1 - 96a b +--R + +--R 4 +--R - 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (180a b + 45a b)\|- 1 + (- 180a b - 45a b)\|- 1 +--R + +--R 3 3 +--R 180a b + 45a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 216a b - 54a b)\|- 1 + (216a b + 54a b)\|- 1 +--R + +--R 3 3 +--R - 216a b - 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (- 288a b - 72a )\|- 1 + (288a b + 72a )\|- 1 +--R + +--R 2 2 4 +--R - 288a b - 72a +--R * +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (36a b + 9a b)\|- 1 + (- 36a b - 9a b)\|- 1 + 36a b +--R + +--R 3 +--R 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (72a b + 18a b)\|- 1 + (- 72a b - 18a b)\|- 1 +--R + +--R 3 3 +--R 72a b + 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 144a b - 36a b)\|- 1 + (144a b + 36a b)\|- 1 +--R + +--R 3 3 +--R - 144a b - 36a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (- 288a b - 72a )\|- 1 + (288a b + 72a )\|- 1 +--R + +--R 2 2 4 +--R - 288a b - 72a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (72a b + 18a b)\|- 1 + (- 72a b - 18a b)\|- 1 +--R + +--R 3 3 +--R 72a b + 18a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (12a b + 3a b)\|- 1 + (- 12a b - 3a b)\|- 1 + 12a b +--R + +--R 3 +--R 3a b +--R * +--R 6 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 36a b - 9a b)\|- 1 + (36a b + 9a b)\|- 1 - 36a b +--R + +--R 3 +--R - 9a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (- 96a b - 24a )\|- 1 + (96a b + 24a )\|- 1 - 96a b +--R + +--R 4 +--R - 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (36a b + 9a b)\|- 1 + (- 36a b - 9a b)\|- 1 + 36a b +--R + +--R 3 +--R 9a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R (- 12a b - 3a b)\|- 1 + (12a b + 3a b)\|- 1 - 12a b - 3a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 12a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 180a b \|- 1 + 180a b \|- 1 - 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 36a b \|- 1 - 36a b \|- 1 + 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 240a b \|- 1 + 240a b \|- 1 - 240a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R 96a b \|- 1 - 96a b\|- 1 + 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 180a b \|- 1 + 180a b \|- 1 - 180a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (216a b \|- 1 - 216a b \|- 1 + 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (288a b \|- 1 - 288a b\|- 1 + 288a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 36a b \|- 1 + 36a b \|- 1 - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (144a b \|- 1 - 144a b \|- 1 + 144a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (288a b \|- 1 - 288a b\|- 1 + 288a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 72a b \|- 1 + 72a b \|- 1 - 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (- 12a b \|- 1 + 12a b \|- 1 - 12a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (96a b \|- 1 - 96a b\|- 1 + 96a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) + 12a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R - 12a b \|- 1 + 12a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 3a b)\|- 1 + (12a b + 3a b)\|- 1 - 12a b +--R + +--R 3 +--R - 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 72a b - 18a b)\|- 1 + (72a b + 18a b)\|- 1 - 72a b +--R + +--R 3 +--R - 18a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 180a b - 45a b)\|- 1 + (180a b + 45a b)\|- 1 +--R + +--R 3 3 +--R - 180a b - 45a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (36a b + 9a b)\|- 1 + (- 36a b - 9a b)\|- 1 + 36a b +--R + +--R 3 +--R 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 240a b - 60a b)\|- 1 + (240a b + 60a b)\|- 1 +--R + +--R 3 3 +--R - 240a b - 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (144a b + 36a b)\|- 1 + (- 144a b - 36a b)\|- 1 +--R + +--R 3 3 +--R 144a b + 36a b +--R * +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (96a b + 24a )\|- 1 + (- 96a b - 24a )\|- 1 + 96a b +--R + +--R 4 +--R 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 180a b - 45a b)\|- 1 + (180a b + 45a b)\|- 1 +--R + +--R 3 3 +--R - 180a b - 45a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (216a b + 54a b)\|- 1 + (- 216a b - 54a b)\|- 1 +--R + +--R 3 3 +--R 216a b + 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (288a b + 72a )\|- 1 + (- 288a b - 72a )\|- 1 +--R + +--R 2 2 4 +--R 288a b + 72a +--R * +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 36a b - 9a b)\|- 1 + (36a b + 9a b)\|- 1 - 36a b +--R + +--R 3 +--R - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 72a b - 18a b)\|- 1 + (72a b + 18a b)\|- 1 +--R + +--R 3 3 +--R - 72a b - 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (144a b + 36a b)\|- 1 + (- 144a b - 36a b)\|- 1 +--R + +--R 3 3 +--R 144a b + 36a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ +--R (288a b + 72a )\|- 1 + (- 288a b - 72a )\|- 1 +--R + +--R 2 2 4 +--R 288a b + 72a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ +--R (- 72a b - 18a b)\|- 1 + (72a b + 18a b)\|- 1 +--R + +--R 3 3 +--R - 72a b - 18a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 12a b - 3a b)\|- 1 + (12a b + 3a b)\|- 1 - 12a b +--R + +--R 3 +--R - 3a b +--R * +--R 6 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (36a b + 9a b)\|- 1 + (- 36a b - 9a b)\|- 1 + 36a b +--R + +--R 3 +--R 9a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3+---+2 2 2 4 3+---+ 2 2 +--R (96a b + 24a )\|- 1 + (- 96a b - 24a )\|- 1 + 96a b +--R + +--R 4 +--R 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 +--R (- 36a b - 9a b)\|- 1 + (36a b + 9a b)\|- 1 - 36a b +--R + +--R 3 +--R - 9a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 3+---+2 3 3 3+---+ 3 3 +--R (12a b + 3a b)\|- 1 + (- 12a b - 3a b)\|- 1 + 12a b + 3a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (270a b \|- 1 - 270a b \|- 1 + 270a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R - 54a b \|- 1 + 54a b \|- 1 - 54a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (360a b \|- 1 - 360a b \|- 1 + 360a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R - 144a b \|- 1 + 144a b\|- 1 - 144a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (270a b \|- 1 - 270a b \|- 1 + 270a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 +--R (- 324a b \|- 1 + 324a b \|- 1 - 324a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R 54a b \|- 1 - 54a b \|- 1 + 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 5 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 3 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 6 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 4 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 2 2 2 3+---+2 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) - 18a b \|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R 18a b \|- 1 - 18a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3+---+2 3 3+---+ 3 6 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 5 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x)sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) + 9a b \|- 1 +--R + +--R 3 3+---+ 3 +--R - 9a b\|- 1 + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (- 60a b \|- 1 + 60a b\|- 1 - 60a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 3+---+2 +--R (36a b \|- 1 - 36a b\|- 1 + 36a b)cosh(x) + 24a \|- 1 +--R + +--R 4 3+---+ 4 +--R - 24a \|- 1 + 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 +--R (54a b \|- 1 - 54a b\|- 1 + 54a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 3+---+2 +--R (72a \|- 1 - 72a \|- 1 + 72a )cosh(x) - 9a b \|- 1 +--R + +--R 3 3+---+ 3 +--R 9a b\|- 1 - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 5 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 3 +--R (36a b \|- 1 - 36a b\|- 1 + 36a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (72a \|- 1 - 72a \|- 1 + 72a )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 +--R (- 18a b \|- 1 + 18a b\|- 1 - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 6 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 4 +--R (9a b \|- 1 - 9a b\|- 1 + 9a b)cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (24a \|- 1 - 24a \|- 1 + 24a )cosh(x) +--R + +--R 3 3+---+2 3 3+---+ 3 2 3 3+---+2 +--R (- 9a b \|- 1 + 9a b\|- 1 - 9a b)cosh(x) + 3a b \|- 1 +--R + +--R 3 3+---+ 3 +--R - 3a b\|- 1 + 3a b +--R * +--R 3+-+2 3+-+2 +--R \|a \|b +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R - 9a b \|- 1 + 9a b \|- 1 - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (60a b \|- 1 - 60a b \|- 1 + 60a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R - 24a b \|- 1 + 24a b\|- 1 - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (45a b \|- 1 - 45a b \|- 1 + 45a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 2 3+---+2 +--R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cosh(x) + 9a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R - 9a b \|- 1 + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 36a b \|- 1 + 36a b \|- 1 - 36a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (- 72a b \|- 1 + 72a b\|- 1 - 72a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (3a b \|- 1 - 3a b \|- 1 + 3a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (- 24a b \|- 1 + 24a b\|- 1 - 24a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) - 3a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R 3a b \|- 1 - 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R ((6a b + 6a b)\|- 1 + (- 6a b - 6a b)\|- 1 + 6a b + 6a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (36a b + 36a b)\|- 1 + (- 36a b - 36a b)\|- 1 + 36a b +--R + +--R 4 +--R 36a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (90a b + 90a b)\|- 1 + (- 90a b - 90a b)\|- 1 +--R + +--R 2 3 4 +--R 90a b + 90a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 18a b - 18a b)\|- 1 + (18a b + 18a b)\|- 1 - 18a b +--R + +--R 4 +--R - 18a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (120a b + 120a b)\|- 1 + (- 120a b - 120a b)\|- 1 +--R + +--R 2 3 4 +--R 120a b + 120a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 72a b - 72a b)\|- 1 + (72a b + 72a b)\|- 1 +--R + +--R 2 3 4 +--R - 72a b - 72a b +--R * +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 5 +--R - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (90a b + 90a b)\|- 1 + (- 90a b - 90a b)\|- 1 +--R + +--R 2 3 4 +--R 90a b + 90a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 108a b - 108a b)\|- 1 + (108a b + 108a b)\|- 1 +--R + +--R 2 3 4 +--R - 108a b - 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 144a b - 144a )\|- 1 + (144a b + 144a )\|- 1 +--R + +--R 3 2 5 +--R - 144a b - 144a +--R * +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 18a b +--R + +--R 4 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (36a b + 36a b)\|- 1 + (- 36a b - 36a b)\|- 1 +--R + +--R 2 3 4 +--R 36a b + 36a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 72a b - 72a b)\|- 1 + (72a b + 72a b)\|- 1 +--R + +--R 2 3 4 +--R - 72a b - 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 144a b - 144a )\|- 1 + (144a b + 144a )\|- 1 +--R + +--R 3 2 5 +--R - 144a b - 144a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (36a b + 36a b)\|- 1 + (- 36a b - 36a b)\|- 1 +--R + +--R 2 3 4 +--R 36a b + 36a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R ((6a b + 6a b)\|- 1 + (- 6a b - 6a b)\|- 1 + 6a b + 6a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 18a b - 18a b)\|- 1 + (18a b + 18a b)\|- 1 - 18a b +--R + +--R 4 +--R - 18a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 5 +--R - 48a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 18a b +--R + +--R 4 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R (- 6a b - 6a b)\|- 1 + (6a b + 6a b)\|- 1 - 6a b - 6a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (27a b \|- 1 - 27a b \|- 1 + 27a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (162a b \|- 1 - 162a b \|- 1 + 162a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (405a b \|- 1 - 405a b \|- 1 + 405a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R - 81a b \|- 1 + 81a b \|- 1 - 81a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (540a b \|- 1 - 540a b \|- 1 + 540a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 324a b \|- 1 + 324a b \|- 1 - 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R - 216a b \|- 1 + 216a b\|- 1 - 216a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (405a b \|- 1 - 405a b \|- 1 + 405a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (- 486a b \|- 1 + 486a b \|- 1 - 486a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R (- 648a b \|- 1 + 648a b\|- 1 - 648a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R 81a b \|- 1 - 81a b \|- 1 + 81a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (162a b \|- 1 - 162a b \|- 1 + 162a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 324a b \|- 1 + 324a b \|- 1 - 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (- 648a b \|- 1 + 648a b\|- 1 - 648a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (162a b \|- 1 - 162a b \|- 1 + 162a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (27a b \|- 1 - 27a b \|- 1 + 27a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 81a b \|- 1 + 81a b \|- 1 - 81a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (81a b \|- 1 - 81a b \|- 1 + 81a b )cosh(x) - 27a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R 27a b \|- 1 - 27a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (12a b - 12a b)\|- 1 + (- 12a b + 12a b)\|- 1 + 12a b +--R + +--R 4 +--R - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (72a b - 72a b)\|- 1 + (- 72a b + 72a b)\|- 1 + 72a b +--R + +--R 4 +--R - 72a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (180a b - 180a b)\|- 1 + (- 180a b + 180a b)\|- 1 +--R + +--R 2 3 4 +--R 180a b - 180a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 36a b + 36a b)\|- 1 + (36a b - 36a b)\|- 1 - 36a b +--R + +--R 4 +--R 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (240a b - 240a b)\|- 1 + (- 240a b + 240a b)\|- 1 +--R + +--R 2 3 4 +--R 240a b - 240a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 144a b + 144a b)\|- 1 + (144a b - 144a b)\|- 1 +--R + +--R 2 3 4 +--R - 144a b + 144a b +--R * +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 96a b + 96a )\|- 1 + (96a b - 96a )\|- 1 - 96a b +--R + +--R 5 +--R 96a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (180a b - 180a b)\|- 1 + (- 180a b + 180a b)\|- 1 +--R + +--R 2 3 4 +--R 180a b - 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 216a b + 216a b)\|- 1 + (216a b - 216a b)\|- 1 +--R + +--R 2 3 4 +--R - 216a b + 216a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 288a b + 288a )\|- 1 + (288a b - 288a )\|- 1 +--R + +--R 3 2 5 +--R - 288a b + 288a +--R * +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (36a b - 36a b)\|- 1 + (- 36a b + 36a b)\|- 1 + 36a b +--R + +--R 4 +--R - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (72a b - 72a b)\|- 1 + (- 72a b + 72a b)\|- 1 +--R + +--R 2 3 4 +--R 72a b - 72a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 144a b + 144a b)\|- 1 + (144a b - 144a b)\|- 1 +--R + +--R 2 3 4 +--R - 144a b + 144a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 288a b + 288a )\|- 1 + (288a b - 288a )\|- 1 +--R + +--R 3 2 5 +--R - 288a b + 288a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (72a b - 72a b)\|- 1 + (- 72a b + 72a b)\|- 1 +--R + +--R 2 3 4 +--R 72a b - 72a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (12a b - 12a b)\|- 1 + (- 12a b + 12a b)\|- 1 + 12a b +--R + +--R 4 +--R - 12a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 36a b + 36a b)\|- 1 + (36a b - 36a b)\|- 1 - 36a b +--R + +--R 4 +--R 36a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 96a b + 96a )\|- 1 + (96a b - 96a )\|- 1 - 96a b +--R + +--R 5 +--R 96a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (36a b - 36a b)\|- 1 + (- 36a b + 36a b)\|- 1 + 36a b +--R + +--R 4 +--R - 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R (- 12a b + 12a b)\|- 1 + (12a b - 12a b)\|- 1 - 12a b + 12a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 27a b \|- 1 + 27a b \|- 1 - 27a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 162a b \|- 1 + 162a b \|- 1 - 162a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (- 405a b \|- 1 + 405a b \|- 1 - 405a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R 81a b \|- 1 - 81a b \|- 1 + 81a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 540a b \|- 1 + 540a b \|- 1 - 540a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (324a b \|- 1 - 324a b \|- 1 + 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R 216a b \|- 1 - 216a b\|- 1 + 216a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 405a b \|- 1 + 405a b \|- 1 - 405a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (486a b \|- 1 - 486a b \|- 1 + 486a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R (648a b \|- 1 - 648a b\|- 1 + 648a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R - 81a b \|- 1 + 81a b \|- 1 - 81a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 162a b \|- 1 + 162a b \|- 1 - 162a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (324a b \|- 1 - 324a b \|- 1 + 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (648a b \|- 1 - 648a b\|- 1 + 648a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 162a b \|- 1 + 162a b \|- 1 - 162a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 27a b \|- 1 + 27a b \|- 1 - 27a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (81a b \|- 1 - 81a b \|- 1 + 81a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (216a b \|- 1 - 216a b\|- 1 + 216a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (- 81a b \|- 1 + 81a b \|- 1 - 81a b )cosh(x) + 27a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R - 27a b \|- 1 + 27a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R ((6a b + 6a b)\|- 1 + (- 6a b - 6a b)\|- 1 + 6a b + 6a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (36a b + 36a b)\|- 1 + (- 36a b - 36a b)\|- 1 + 36a b +--R + +--R 4 +--R 36a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (90a b + 90a b)\|- 1 + (- 90a b - 90a b)\|- 1 +--R + +--R 2 3 4 +--R 90a b + 90a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 18a b - 18a b)\|- 1 + (18a b + 18a b)\|- 1 - 18a b +--R + +--R 4 +--R - 18a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (120a b + 120a b)\|- 1 + (- 120a b - 120a b)\|- 1 +--R + +--R 2 3 4 +--R 120a b + 120a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 72a b - 72a b)\|- 1 + (72a b + 72a b)\|- 1 +--R + +--R 2 3 4 +--R - 72a b - 72a b +--R * +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 5 +--R - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (90a b + 90a b)\|- 1 + (- 90a b - 90a b)\|- 1 +--R + +--R 2 3 4 +--R 90a b + 90a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 108a b - 108a b)\|- 1 + (108a b + 108a b)\|- 1 +--R + +--R 2 3 4 +--R - 108a b - 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 144a b - 144a )\|- 1 + (144a b + 144a )\|- 1 +--R + +--R 3 2 5 +--R - 144a b - 144a +--R * +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 18a b +--R + +--R 4 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (36a b + 36a b)\|- 1 + (- 36a b - 36a b)\|- 1 +--R + +--R 2 3 4 +--R 36a b + 36a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (- 72a b - 72a b)\|- 1 + (72a b + 72a b)\|- 1 +--R + +--R 2 3 4 +--R - 72a b - 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ +--R (- 144a b - 144a )\|- 1 + (144a b + 144a )\|- 1 +--R + +--R 3 2 5 +--R - 144a b - 144a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ +--R (36a b + 36a b)\|- 1 + (- 36a b - 36a b)\|- 1 +--R + +--R 2 3 4 +--R 36a b + 36a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R ((6a b + 6a b)\|- 1 + (- 6a b - 6a b)\|- 1 + 6a b + 6a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (- 18a b - 18a b)\|- 1 + (18a b + 18a b)\|- 1 - 18a b +--R + +--R 4 +--R - 18a b +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 5 3+---+2 3 2 5 3+---+ 3 2 +--R (- 48a b - 48a )\|- 1 + (48a b + 48a )\|- 1 - 48a b +--R + +--R 5 +--R - 48a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 +--R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 18a b +--R + +--R 4 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 4 3+---+2 2 3 4 3+---+ 2 3 4 +--R (- 6a b - 6a b)\|- 1 + (6a b + 6a b)\|- 1 - 6a b - 6a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) + 9a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R - 9a b \|- 1 + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 60a b \|- 1 + 60a b \|- 1 - 60a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 3+---+2 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) + 24a b \|- 1 +--R + +--R 4 3+---+ 4 +--R - 24a b\|- 1 + 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 45a b \|- 1 + 45a b \|- 1 - 45a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 2 3+---+2 +--R (72a b \|- 1 - 72a b\|- 1 + 72a b)cosh(x) - 9a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R 9a b \|- 1 - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (36a b \|- 1 - 36a b \|- 1 + 36a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (72a b \|- 1 - 72a b\|- 1 + 72a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 18a b \|- 1 + 18a b \|- 1 - 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (- 3a b \|- 1 + 3a b \|- 1 - 3a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (9a b \|- 1 - 9a b \|- 1 + 9a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (24a b \|- 1 - 24a b\|- 1 + 24a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (- 9a b \|- 1 + 9a b \|- 1 - 9a b )cosh(x) + 3a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R - 3a b \|- 1 + 3a b +--R * +--R 3+-+ +--R \|b +--R + +--R 2 3 4 6 2 3 4 5 +--R (3a b + 3a b)sinh(x) + (18a b + 18a b)cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R ((45a b + 45a b)cosh(x) - 9a b - 9a b)sinh(x) +--R + +--R 2 3 4 3 2 3 4 3 2 +--R (60a b + 60a b)cosh(x) + (- 36a b - 36a b)cosh(x) - 24a b +--R + +--R 5 +--R - 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 4 2 3 4 2 +--R (45a b + 45a b)cosh(x) + (- 54a b - 54a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 72a b - 72a )cosh(x) + 9a b + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 5 2 3 4 3 +--R (18a b + 18a b)cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 3 2 5 2 2 3 4 +--R (- 72a b - 72a )cosh(x) + (18a b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 6 2 3 4 4 +--R (3a b + 3a b)cosh(x) + (- 9a b - 9a b)cosh(x) +--R + +--R 3 2 5 3 2 3 4 2 2 3 4 +--R (- 24a b - 24a )cosh(x) + (9a b + 9a b)cosh(x) - 3a b - 3a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (270a b \|- 1 - 270a b \|- 1 + 270a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R - 54a b \|- 1 + 54a b \|- 1 - 54a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (360a b \|- 1 - 360a b \|- 1 + 360a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R - 144a b \|- 1 + 144a b\|- 1 - 144a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (270a b \|- 1 - 270a b \|- 1 + 270a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (- 324a b \|- 1 + 324a b \|- 1 - 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R 54a b \|- 1 - 54a b \|- 1 + 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) - 18a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R 18a b \|- 1 - 18a b +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 6 +--R (36a b \|- 1 - 36a b \|- 1 + 27a b - 9a b)sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 5 +--R (216a b \|- 1 - 216a b \|- 1 + 162a b - 54a b)cosh(x)sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (540a b \|- 1 - 540a b \|- 1 + 405a b - 135a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R - 108a b \|- 1 + 108a b \|- 1 - 81a b + 27a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 +--R (720a b \|- 1 - 720a b \|- 1 + 540a b - 180a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R (- 432a b \|- 1 + 432a b \|- 1 - 324a b + 108a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R - 288a b \|- 1 + 288a b \|- 1 - 216a b + 72a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 4 +--R (540a b \|- 1 - 540a b \|- 1 + 405a b - 135a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (- 648a b \|- 1 + 648a b \|- 1 - 486a b + 162a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (- 864a b \|- 1 + 864a b \|- 1 - 648a b + 216a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R 108a b \|- 1 - 108a b \|- 1 + 81a b - 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 5 +--R (216a b \|- 1 - 216a b \|- 1 + 162a b - 54a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 +--R (- 432a b \|- 1 + 432a b \|- 1 - 324a b + 108a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 +--R (- 864a b \|- 1 + 864a b \|- 1 - 648a b + 216a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R (216a b \|- 1 - 216a b \|- 1 + 162a b - 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 6 +--R (36a b \|- 1 - 36a b \|- 1 + 27a b - 9a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 4 +--R (- 108a b \|- 1 + 108a b \|- 1 - 81a b + 27a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 +--R (- 288a b \|- 1 + 288a b \|- 1 - 216a b + 72a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (108a b \|- 1 - 108a b \|- 1 + 81a b - 27a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R - 36a b \|- 1 + 36a b \|- 1 - 27a b + 9a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 6 +--R (- 36a b \|- 1 + 36a b \|- 1 + 24a b - 12a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (- 216a b \|- 1 + 216a b \|- 1 + 144a b - 72a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (- 540a b \|- 1 + 540a b \|- 1 + 360a b - 180a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R 108a b \|- 1 - 108a b \|- 1 - 72a b + 36a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (- 720a b \|- 1 + 720a b \|- 1 + 480a b - 240a b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (432a b \|- 1 - 432a b \|- 1 - 288a b + 144a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 2 3 4 +--R 288a b \|- 1 - 288a b\|- 1 - 192a b + 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (- 540a b \|- 1 + 540a b \|- 1 + 360a b - 180a b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 2 +--R (648a b \|- 1 - 648a b \|- 1 - 432a b + 216a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 2 3 4 +--R (864a b \|- 1 - 864a b\|- 1 - 576a b + 288a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R - 108a b \|- 1 + 108a b \|- 1 + 72a b - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 5 +--R (- 216a b \|- 1 + 216a b \|- 1 + 144a b - 72a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 3 +--R (432a b \|- 1 - 432a b \|- 1 - 288a b + 144a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 2 3 4 2 +--R (864a b \|- 1 - 864a b\|- 1 - 576a b + 288a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R (- 216a b \|- 1 + 216a b \|- 1 + 144a b - 72a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 6 +--R (- 36a b \|- 1 + 36a b \|- 1 + 24a b - 12a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 4 +--R (108a b \|- 1 - 108a b \|- 1 - 72a b + 36a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 2 3 4 3 +--R (288a b \|- 1 - 288a b\|- 1 - 192a b + 96a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 2 +--R (- 108a b \|- 1 + 108a b \|- 1 + 72a b - 36a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 4 3 2 +--R 36a b \|- 1 - 36a b \|- 1 - 24a b + 12a b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 6 +--R (- 36a b \|- 1 + 36a b \|- 1 - 27a b + 9a b)sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R (- 216a b \|- 1 + 216a b \|- 1 - 162a b + 54a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (- 540a b \|- 1 + 540a b \|- 1 - 405a b + 135a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R 108a b \|- 1 - 108a b \|- 1 + 81a b - 27a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 +--R (- 720a b \|- 1 + 720a b \|- 1 - 540a b + 180a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R (432a b \|- 1 - 432a b \|- 1 + 324a b - 108a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R 288a b \|- 1 - 288a b \|- 1 + 216a b - 72a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 4 +--R (- 540a b \|- 1 + 540a b \|- 1 - 405a b + 135a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (648a b \|- 1 - 648a b \|- 1 + 486a b - 162a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (864a b \|- 1 - 864a b \|- 1 + 648a b - 216a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R - 108a b \|- 1 + 108a b \|- 1 - 81a b + 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 5 +--R (- 216a b \|- 1 + 216a b \|- 1 - 162a b + 54a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 3 +--R (432a b \|- 1 - 432a b \|- 1 + 324a b - 108a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 2 +--R (864a b \|- 1 - 864a b \|- 1 + 648a b - 216a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R (- 216a b \|- 1 + 216a b \|- 1 - 162a b + 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 6 +--R (- 36a b \|- 1 + 36a b \|- 1 - 27a b + 9a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 4 +--R (108a b \|- 1 - 108a b \|- 1 + 81a b - 27a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 3 +--R (288a b \|- 1 - 288a b \|- 1 + 216a b - 72a )cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 2 +--R (- 108a b \|- 1 + 108a b \|- 1 - 81a b + 27a b)cosh(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 4 +--R 36a b \|- 1 - 36a b \|- 1 + 27a b - 9a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x)sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (270a b \|- 1 - 270a b \|- 1 + 270a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R - 54a b \|- 1 + 54a b \|- 1 - 54a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (360a b \|- 1 - 360a b \|- 1 + 360a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R - 144a b \|- 1 + 144a b\|- 1 - 144a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (270a b \|- 1 - 270a b \|- 1 + 270a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 +--R (- 324a b \|- 1 + 324a b \|- 1 - 324a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R 54a b \|- 1 - 54a b \|- 1 + 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 5 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 3 +--R (- 216a b \|- 1 + 216a b \|- 1 - 216a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 2 +--R (- 432a b \|- 1 + 432a b\|- 1 - 432a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 +--R (108a b \|- 1 - 108a b \|- 1 + 108a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 6 +--R (18a b \|- 1 - 18a b \|- 1 + 18a b )cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 4 +--R (- 54a b \|- 1 + 54a b \|- 1 - 54a b )cosh(x) +--R + +--R 4 3+---+2 4 3+---+ 4 3 +--R (- 144a b \|- 1 + 144a b\|- 1 - 144a b)cosh(x) +--R + +--R 3 2 3+---+2 3 2 3+---+ 3 2 2 3 2 3+---+2 +--R (54a b \|- 1 - 54a b \|- 1 + 54a b )cosh(x) - 18a b \|- 1 +--R + +--R 3 2 3+---+ 3 2 +--R 18a b \|- 1 - 18a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 3a b - 3a b)sinh(x) + (- 18a b - 18a b)cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R ((- 45a b - 45a b)cosh(x) + 9a b + 9a b)sinh(x) +--R + +--R 2 3 4 3 2 3 4 3 2 +--R (- 60a b - 60a b)cosh(x) + (36a b + 36a b)cosh(x) + 24a b +--R + +--R 5 +--R 24a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 4 2 3 4 2 +--R (- 45a b - 45a b)cosh(x) + (54a b + 54a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (72a b + 72a )cosh(x) - 9a b - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 5 2 3 4 3 +--R (- 18a b - 18a b)cosh(x) + (36a b + 36a b)cosh(x) +--R + +--R 3 2 5 2 2 3 4 +--R (72a b + 72a )cosh(x) + (- 18a b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 6 2 3 4 4 +--R (- 3a b - 3a b)cosh(x) + (9a b + 9a b)cosh(x) +--R + +--R 3 2 5 3 2 3 4 2 2 3 4 +--R (24a b + 24a )cosh(x) + (- 9a b - 9a b)cosh(x) + 3a b + 3a b +--R * +--R 3+-+ +--R \|a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 510 +t0080:= 1/(a-b*sinh(x)^4) +--R +--R +--R 1 +--R (355) - -------------- +--R 4 +--R b sinh(x) - a +--R Type: Expression(Integer) +--E 411 + +--S 412 of 510 +r0080:= 1/2*atan((-a^(1/2)+b^(1/2))^(1/2)*tanh(x)/a^(1/4))/a^(3/4)/_ + (-a^(1/2)+b^(1/2))^(1/2)+1/2*atanh((a^(1/2)+b^(1/2))^(1/2)*_ + tanh(x)/a^(1/4))/a^(3/4)/(a^(1/2)+b^(1/2))^(1/2) +--R +--R +--R (356) +--R +-----------+ +--R +-----------+ | +-+ +-+ +--R | +-+ +-+ tanh(x)\|\|b + \|a +--R \|\|b - \|a atanh(---------------------) +--R 4+-+ +--R \|a +--R + +--R +-----------+ +--R +-----------+ | +-+ +-+ +--R | +-+ +-+ tanh(x)\|\|b - \|a +--R \|\|b + \|a atan(---------------------) +--R 4+-+ +--R \|a +--R / +--R +-----------+ +-----------+ +--R 4+-+3 | +-+ +-+ | +-+ +-+ +--R 2\|a \|\|b - \|a \|\|b + \|a +--R Type: Expression(Integer) +--E 412 + +--S 413 of 510 +a0080:= integrate(t0080,x) +--R +--R +--R (357) +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((32a b - 32a ) |---------------------- + 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (- 16a b + 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R - +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((32a b - 32a ) |---------------------- - 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (16a b - 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((- 32a b + 32a ) |---------------------- + 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (16a b - 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R - +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((- 32a b + 32a ) |---------------------- - 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (- 16a b + 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 510 +m0080:= a0080-r0080 +--R +--R +--R (358) +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +-----------+ +--R 4+-+3 | \|64a b - 128a b + 64a | +-+ +-+ +--R \|a |----------------------------------------- \|\|b - \|a +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((32a b - 32a ) |---------------------- + 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (- 16a b + 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R - +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +-----------+ +--R 4+-+3 | \|64a b - 128a b + 64a | +-+ +-+ +--R \|a |------------------------------------------- \|\|b - \|a +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((32a b - 32a ) |---------------------- - 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (16a b - 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +-----------+ +--R 4+-+3 | \|64a b - 128a b + 64a | +-+ +-+ +--R \|a |------------------------------------------- \|\|b - \|a +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((- 32a b + 32a ) |---------------------- + 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (16a b - 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R - +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +-----------+ +--R 4+-+3 | \|64a b - 128a b + 64a | +-+ +-+ +--R \|a |----------------------------------------- \|\|b - \|a +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((- 32a b + 32a ) |---------------------- - 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (- 16a b + 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b +--R + +--R +-----------+ +--R +-----------+ | +-+ +-+ +--R | +-+ +-+ tanh(x)\|\|b + \|a +--R - \|\|b - \|a atanh(---------------------) +--R 4+-+ +--R \|a +--R + +--R +-----------+ +--R +-----------+ | +-+ +-+ +--R | +-+ +-+ tanh(x)\|\|b - \|a +--R - \|\|b + \|a atan(---------------------) +--R 4+-+ +--R \|a +--R / +--R +-----------+ +-----------+ +--R 4+-+3 | +-+ +-+ | +-+ +-+ +--R 2\|a \|\|b - \|a \|\|b + \|a +--R Type: Expression(Integer) +--E 414 + +--S 415 of 510 +d0080:= D(m0080,x) +--R +--R +--R (359) +--R 4 3 +--R (- 16b + 16a)sinh(x) + (- 64b + 64a)cosh(x)sinh(x) +--R + +--R 2 2 3 +--R (- 96b + 96a)cosh(x) sinh(x) + (- 64b + 64a)cosh(x) sinh(x) +--R + +--R 4 +--R (- 16b + 16a)cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) + 4b)sinh(x) +--R + +--R 3 5 +--R (- 56b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70b cosh(x) + 60b cosh(x) - 6b + 16a)sinh(x) +--R + +--R 5 3 3 +--R (- 56b cosh(x) + 80b cosh(x) + (- 24b + 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 28b cosh(x) + 60b cosh(x) + (- 36b + 96a)cosh(x) + 4b) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R - 8b cosh(x) + 24b cosh(x) + (- 24b + 64a)cosh(x) +--R + +--R 8b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - b cosh(x) + 4b cosh(x) + (- 6b + 16a)cosh(x) + 4b cosh(x) - b +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) - 4b)sinh(x) +--R + +--R 3 5 +--R (56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70b cosh(x) - 60b cosh(x) + 6b)sinh(x) +--R + +--R 5 3 3 +--R (56b cosh(x) - 80b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28b cosh(x) - 60b cosh(x) + 36b cosh(x) - 4b)sinh(x) +--R + +--R 7 5 3 +--R (8b cosh(x) - 24b cosh(x) + 24b cosh(x) - 8b cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) - 4b cosh(x) + 6b cosh(x) - 4b cosh(x) + b +--R * +--R 4+-+2 +--R \|a +--R + +--R 8 7 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) - 4b)sinh(x) +--R + +--R 3 5 +--R (56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70b cosh(x) - 60b cosh(x) + 6b - 16a)sinh(x) +--R + +--R 5 3 3 +--R (56b cosh(x) - 80b cosh(x) + (24b - 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28b cosh(x) - 60b cosh(x) + (36b - 96a)cosh(x) - 4b)sinh(x) +--R + +--R 7 5 3 +--R (8b cosh(x) - 24b cosh(x) + (24b - 64a)cosh(x) - 8b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) - 4b cosh(x) + (6b - 16a)cosh(x) - 4b cosh(x) + b +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) + 4b)sinh(x) +--R + +--R 3 5 +--R (- 56b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70b cosh(x) + 60b cosh(x) - 6b - 16a)sinh(x) +--R + +--R 5 3 3 +--R (- 56b cosh(x) + 80b cosh(x) + (- 24b - 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 28b cosh(x) + 60b cosh(x) + (- 36b - 96a)cosh(x) + 4b) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R - 8b cosh(x) + 24b cosh(x) + (- 24b - 64a)cosh(x) +--R + +--R 8b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - b cosh(x) + 4b cosh(x) + (- 6b - 16a)cosh(x) + 4b cosh(x) - b +--R * +--R 2 +--R tanh(x) +--R * +--R +-+ +--R \|a +--R / +--R 2 8 2 7 +--R (b - a b)sinh(x) + (8b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b - 28a b)cosh(x) - 4b + 4a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b - 56a b)cosh(x) + (- 24b + 24a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (70b - 70a b)cosh(x) + (- 60b + 60a b)cosh(x) + 6b +--R + +--R 2 +--R - 22a b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (56b - 56a b)cosh(x) + (- 80b + 80a b)cosh(x) +--R + +--R 2 2 +--R (24b - 88a b + 64a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (28b - 28a b)cosh(x) + (- 60b + 60a b)cosh(x) +--R + +--R 2 2 2 2 +--R (36b - 132a b + 96a )cosh(x) - 4b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (8b - 8a b)cosh(x) + (- 24b + 24a b)cosh(x) +--R + +--R 2 2 3 2 +--R (24b - 88a b + 64a )cosh(x) + (- 8b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 +--R (b - a b)cosh(x) + (- 4b + 4a b)cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (6b - 22a b + 16a )cosh(x) + (- 4b + 4a b)cosh(x) + b - a b +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 +--R - a b sinh(x) - 8a b cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 28a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 5 +--R (- 56a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 4 2 2 4 +--R (- 70a b cosh(x) + 60a b cosh(x) - 6a b + 16a )sinh(x) +--R + +--R 5 3 2 3 +--R (- 56a b cosh(x) + 80a b cosh(x) + (- 24a b + 64a )cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R - 28a b cosh(x) + 60a b cosh(x) + (- 36a b + 96a )cosh(x) +--R + +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 2 3 +--R - 8a b cosh(x) + 24a b cosh(x) + (- 24a b + 64a )cosh(x) +--R + +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 2 4 +--R - a b cosh(x) + 4a b cosh(x) + (- 6a b + 16a )cosh(x) +--R + +--R 2 +--R 4a b cosh(x) - a b +--R * +--R 4+-+2 +--R \|a +--R + +--R 8 7 +--R 2a b sinh(x) + 16a b cosh(x)sinh(x) +--R + +--R 2 6 +--R (56a b cosh(x) - 8a b)sinh(x) +--R + +--R 3 5 +--R (112a b cosh(x) - 48a b cosh(x))sinh(x) +--R + +--R 4 2 2 4 +--R (140a b cosh(x) - 120a b cosh(x) + 12a b - 32a )sinh(x) +--R + +--R 5 3 2 3 +--R (112a b cosh(x) - 160a b cosh(x) + (48a b - 128a )cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56a b cosh(x) - 120a b cosh(x) + (72a b - 192a )cosh(x) - 8a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 2 3 +--R 16a b cosh(x) - 48a b cosh(x) + (48a b - 128a )cosh(x) +--R + +--R - 16a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 2 4 +--R 2a b cosh(x) - 8a b cosh(x) + (12a b - 32a )cosh(x) +--R + +--R 2 +--R - 8a b cosh(x) + 2a b +--R * +--R 2 +-+ +--R tanh(x) \|a +--R Type: Expression(Integer) +--E 415 + +--S 416 of 510 +t0081:= 1/(a-b*sinh(x)^5) +--R +--R +--R 1 +--R (360) - -------------- +--R 5 +--R b sinh(x) - a +--R Type: Expression(Integer) +--E 416 + +--S 417 of 510 +r0081:= -2/5*atanh(((-1)^(1/5)*b^(1/5)-a^(1/5)*tanh(1/2*x))/(a^(2/5)+_ + (-1)^(2/5)*b^(2/5))^(1/2))/a^(4/5)/(a^(2/5)+_ + (-1)^(2/5)*b^(2/5))^(1/2)-2/5*atanh(((-1)^(3/5)*b^(1/5)-_ + a^(1/5)*tanh(1/2*x))/(a^(2/5)-(-1)^(1/5)*b^(2/5))^(1/2))/_ + a^(4/5)/(a^(2/5)-(-1)^(1/5)*b^(2/5))^(1/2)+2/5*atanh((b^(1/5)+_ + a^(1/5)*tanh(1/2*x))/(a^(2/5)+b^(2/5))^(1/2))/a^(4/5)/(a^(2/5)+_ + b^(2/5))^(1/2)+2/5*atanh(((-1)^(2/5)*b^(1/5)+a^(1/5)*_ + tanh(1/2*x))/(a^(2/5)+(-1)^(4/5)*b^(2/5))^(1/2))/a^(4/5)/(a^(2/5)+_ + (-1)^(4/5)*b^(2/5))^(1/2)+2/5*atanh(((-1)^(4/5)*b^(1/5)+_ + a^(1/5)*tanh(1/2*x))/(a^(2/5)-(-1)^(3/5)*b^(2/5))^(1/2))/_ + a^(4/5)/(a^(2/5)-(-1)^(3/5)*b^(2/5))^(1/2) +--R +--R +--R (361) +--R +---------------------+ +-------------+ +--------------------+ +--R | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 |5+---+2 5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+4 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b + tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +----------------------+ +--R | 5+---+3 5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +-------------+ +--------------------+ +--R | 5+---+3 5+-+2 5+-+2 |5+-+2 5+-+2 |5+---+2 5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+3 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b - tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +---------------------+ +--R | 5+---+5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +---------------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R 5+-+ x 5+-+ +--R +--------------------+ +--------------------+ \|b + tanh(-)\|a +--R |5+---+2 5+-+2 5+-+2 |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a atanh(------------------) +--R +-------------+ +--R |5+-+2 5+-+2 +--R \|\|b + \|a +--R + +--R - +--R +----------------------+ +---------------------+ +-------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R 5+---+5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b - tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(------------------------) +--R +--------------------+ +--R |5+---+2 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R + +--R +----------------------+ +---------------------+ +-------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R 5+---+2 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b + tanh(-)\|a +--R |5+---+2 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +--------------------+ +--R |5+---+4 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------------+ +-------------+ +--R 5+-+4 | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 5\|a \|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--------------------+ +--R |5+---+2 5+-+2 5+-+2 |5+---+4 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 417 + +--S 418 of 510 +a0081:= integrate(t0081,x) +--R +--R +--R (362) +--R - +--R ROOT +--R 2 2 +--R (10b + 10a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY2 +--R + +--R 2 4 4 2 6 +--I (- 250a b - 500a b - 250a )%%EY1 +--R + +--R 2 4 4 2 6 2 2 4 +--I (- 250a b - 500a b - 250a )%%EY0 + 50a b + 50a +--R * +--I %%EY2 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY1 +--R + +--R 2 4 4 2 6 2 2 +--I (- 250a b - 500a b - 250a )%%EY0 + 50a b +--R + +--R 4 +--R 50a +--R * +--I %%EY1 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY0 +--R + +--R 2 2 4 2 2 +--I (50a b + 50a )%%EY0 - 8b - 3a +--R / +--R 2 4 4 2 6 +--R 125a b + 250a b + 125a +--R + +--R 2 2 2 2 +--I (- 10b - 10a )%%EY2 + (- 10b - 10a )%%EY1 +--R + +--R 2 2 +--I (- 10b - 10a )%%EY0 + 2 +--R / +--R 2 2 +--R 5b + 5a +--R * +--R log +--R 8 2 10 6 2 +--I (11718750a b + 11718750a )%%EY0 - 234375a b +--R + +--R 8 +--R - 234375a +--R * +--I %%EY1 +--R + +--R 6 2 8 4 2 6 +--I (- 234375a b - 234375a )%%EY0 + 3125a b + 3125a +--R * +--I %%EY2 +--R + +--R 6 2 8 4 2 6 +--I ((- 234375a b - 234375a )%%EY0 + 3125a b + 3125a ) +--R * +--I %%EY1 +--R + +--R 4 2 6 +--I (3125a b + 3125a )%%EY0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY2 +--R + +--R 2 4 4 2 6 +--I (- 250a b - 500a b - 250a )%%EY1 +--R + +--R 2 4 4 2 6 2 2 +--I (- 250a b - 500a b - 250a )%%EY0 + 50a b +--R + +--R 4 +--R 50a +--R * +--I %%EY2 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY1 +--R + +--R 2 4 4 2 6 2 2 +--I (- 250a b - 500a b - 250a )%%EY0 + 50a b +--R + +--R 4 +--R 50a +--R * +--I %%EY1 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY0 +--R + +--R 2 2 4 2 2 +--I (50a b + 50a )%%EY0 - 8b - 3a +--R / +--R 2 4 4 2 6 +--R 125a b + 250a b + 125a +--R + +--R 8 2 10 6 2 +--I (11718750a b + 11718750a )%%EY0 - 234375a b +--R + +--R 8 +--R - 234375a +--R * +--I %%EY1 +--R + +--R 6 2 8 4 2 6 +--I (- 234375a b - 234375a )%%EY0 + 3125a b + 3125a +--R * +--R 2 +--I %%EY2 +--R + +--R 8 2 10 6 2 +--I (11718750a b + 11718750a )%%EY0 - 234375a b +--R + +--R 8 +--R - 234375a +--R * +--R 2 +--I %%EY1 +--R + +--R 8 2 10 2 +--I (11718750a b + 11718750a )%%EY0 +--R + +--R 6 2 8 6 +--I (- 234375a b - 2578125a )%%EY0 + 46875a +--R * +--I %%EY1 +--R + +--R 6 2 8 2 6 4 +--I (- 234375a b - 234375a )%%EY0 + 46875a %%EY0 - 625a +--R * +--I %%EY2 +--R + +--R 6 2 8 4 2 6 2 +--I ((- 234375a b - 234375a )%%EY0 + 3125a b + 3125a )%%EY1 +--R + +--R 6 2 8 2 6 4 +--I ((- 234375a b - 234375a )%%EY0 + 46875a %%EY0 - 625a ) +--R * +--I %%EY1 +--R + +--R 4 2 6 2 4 +--I (3125a b + 3125a )%%EY0 - 625a %%EY0 +--R * +--R ROOT +--R 2 2 +--R (10b + 10a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY2 +--R + +--R 2 4 4 2 6 +--I (- 250a b - 500a b - 250a )%%EY1 +--R + +--R 2 4 4 2 6 +--I (- 250a b - 500a b - 250a )%%EY0 +--R + +--R 2 2 4 +--R 50a b + 50a +--R * +--I %%EY2 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY1 +--R + +--R 2 4 4 2 6 +--I (- 250a b - 500a b - 250a )%%EY0 +--R + +--R 2 2 4 +--R 50a b + 50a +--R * +--I %%EY1 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY0 +--R + +--R 2 2 4 2 2 +--I (50a b + 50a )%%EY0 - 8b - 3a +--R / +--R 2 4 4 2 6 +--R 125a b + 250a b + 125a +--R + +--R 2 2 2 2 +--I (- 10b - 10a )%%EY2 + (- 10b - 10a )%%EY1 +--R + +--R 2 2 +--I (- 10b - 10a )%%EY0 + 2 +--R / +--R 2 2 +--R 5b + 5a +--R + +--R 7 2 9 5 2 +--I (2343750a b + 2343750a )%%EY0 - 31250a b +--R + +--R 7 +--R - 31250a +--R * +--I %%EY1 +--R + +--R 5 2 7 +--I (- 31250a b - 31250a )%%EY0 +--R * +--I %%EY2 +--R + +--R 5 2 7 +--I (- 31250a b - 31250a )%%EY0 %%EY1 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY2 +--R + +--R 2 4 4 2 6 +--I (- 250a b - 500a b - 250a )%%EY1 +--R + +--R 2 4 4 2 6 2 2 4 +--I (- 250a b - 500a b - 250a )%%EY0 + 50a b + 50a +--R * +--I %%EY2 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY1 +--R + +--R 2 4 4 2 6 2 2 4 +--I ((- 250a b - 500a b - 250a )%%EY0 + 50a b + 50a ) +--R * +--I %%EY1 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b - 750a b - 375a )%%EY0 +--R + +--R 2 2 4 2 2 +--I (50a b + 50a )%%EY0 - 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2109375a )%%EY0 + (3125a b + 143750a )%%EY0 +--R + +--R 4 2 +--I - 4375a %%EY0 + 50a +--R * +--R +------+ +--I \|4%%EY0 +--R + +--R 7 2 9 4 5 2 7 3 +--I (- 2343750a b - 2343750a )%%EY0 + (- 31250a b + 437500a )%%EY0 +--R + +--R 5 2 3 +--I - 31250a %%EY0 + 1000a %%EY0 + 2b sinh(x) + 2b cosh(x) - 12a +--R + +--R - +--R +----------------------+ +---------------------+ +--R 5+-+4 | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 +--R 5\|a \|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +-------------+ +--------------------+ +--------------------+ +--R |5+-+2 5+-+2 |5+---+2 5+-+2 5+-+2 |5+---+4 5+-+2 5+-+2 +--R \|\|b + \|a \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%EY0 +--R * +--R log +--R 8 2 10 4 +--I (- 11718750a b - 11718750a )%%EY0 +--R + +--R 6 2 8 3 +--I (- 234375a b + 2109375a )%%EY0 +--R + +--R 4 2 6 2 4 2 +--I (- 3125a b - 143750a )%%EY0 + 4375a %%EY0 - 50a +--R * +--R +------+ +--I \|4%%EY0 +--R + +--R 7 2 9 4 +--I (- 2343750a b - 2343750a )%%EY0 +--R + +--R 5 2 7 3 5 2 3 +--I (- 31250a b + 437500a )%%EY0 - 31250a %%EY0 + 1000a %%EY0 +--R + +--R 2b sinh(x) + 2b cosh(x) - 12a +--R + +--R - +--R +---------------------+ +-------------+ +--------------------+ +--R | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 |5+---+2 5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+4 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b + tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +----------------------+ +--R | 5+---+3 5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +-------------+ +--------------------+ +--R | 5+---+3 5+-+2 5+-+2 |5+-+2 5+-+2 |5+---+2 5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+3 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b - tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +---------------------+ +--R | 5+---+5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +---------------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +--------------------+ +--------------------+ +--R |5+---+2 5+-+2 5+-+2 |5+---+4 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+-+ x 5+-+ +--R \|b + tanh(-)\|a +--R 2 +--R atanh(------------------) +--R +-------------+ +--R |5+-+2 5+-+2 +--R \|\|b + \|a +--R + +--R +----------------------+ +---------------------+ +-------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R 5+---+5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b - tanh(-)\|a +--R |5+---+4 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(------------------------) +--R +--------------------+ +--R |5+---+2 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +---------------------+ +-------------+ +--R | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R 5+---+2 5+-+ x 5+-+ +--R +--------------------+ \|- 1 \|b + tanh(-)\|a +--R |5+---+2 5+-+2 5+-+2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------) +--R +--------------------+ +--R |5+---+4 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------------+ +-------------+ +--R 5+-+4 | 5+---+3 5+-+2 5+-+2 | 5+---+5+-+2 5+-+2 |5+-+2 5+-+2 +--R 10\|a \|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|\|b + \|a +--R * +--R +--------------------+ +--------------------+ +--R |5+---+2 5+-+2 5+-+2 |5+---+4 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 510 +--d0081:= D(m0081,x) +--E 420 + +--S 421 of 510 +t0082:= 1/(a-b*sinh(x)^6) +--R +--R +--R 1 +--R (364) - -------------- +--R 6 +--R b sinh(x) - a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 510 +r0082:= 1/3*atan((-a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2)*_ + tanh(x)/a^(1/6))/a^(5/6)/(-a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2)+_ + 1/3*atanh((a^(1/3)+b^(1/3))^(1/2)*tanh(x)/a^(1/6))/a^(5/6)/_ + (a^(1/3)+b^(1/3))^(1/2)+1/3*atanh((a^(1/3)+(-1)^(2/3)*_ + b^(1/3))^(1/2)*tanh(x)/a^(1/6))/a^(5/6)/(a^(1/3)+_ + (-1)^(2/3)*b^(1/3))^(1/2) +--R +--R +--R (365) +--R +------------------+ +--R +-----------+ +-----------------+ |3+---+2 3+-+ 3+-+ +--R |3+-+ 3+-+ |3+---+3+-+ 3+-+ tanh(x)\|\|- 1 \|b + \|a +--R \|\|b + \|a \|\|- 1 \|b - \|a atanh(----------------------------) +--R 6+-+ +--R \|a +--R + +--R +-----------+ +--R +-----------------+ +------------------+ |3+-+ 3+-+ +--R |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|\|b + \|a +--R \|\|- 1 \|b - \|a \|\|- 1 \|b + \|a atanh(---------------------) +--R 6+-+ +--R \|a +--R + +--R +-----------------+ +--R +-----------+ +------------------+ |3+---+3+-+ 3+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|\|- 1 \|b - \|a +--R \|\|b + \|a \|\|- 1 \|b + \|a atan(---------------------------) +--R 6+-+ +--R \|a +--R / +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|\|b + \|a \|\|- 1 \|b - \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 510 +a0082:= integrate(t0082,x) +--R +--R +--R (366) +--R - +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b + 3888a )%%EZ0 - 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b + 3888a )%%EZ0 + (108a b - 216a )%%EZ0 - 6a b + 3a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((1296a b + 1296a )%%EZ0 - 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (1296a b + 1296a )%%EZ0 + (36a b - 72a )%%EZ0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + a +--R + +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b + 3888a )%%EZ0 - 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b - 3888a )%%EZ0 + (- 108a b + 216a )%%EZ0 + 6a b +--R + +--R 2 +--R - 3a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b - 1296a )%%EZ0 + 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (1296a b + 1296a )%%EZ0 + (36a b - 72a )%%EZ0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + a +--R + +--R - +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b - 3888a )%%EZ0 + 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b + 3888a )%%EZ0 + (108a b - 216a )%%EZ0 - 6a b + 3a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b - 1296a )%%EZ0 + 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (1296a b + 1296a )%%EZ0 + (36a b - 72a )%%EZ0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + a +--R + +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b - 3888a )%%EZ0 + 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b - 3888a )%%EZ0 + (- 108a b + 216a )%%EZ0 + 6a b +--R + +--R 2 +--R - 3a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((1296a b + 1296a )%%EZ0 - 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (1296a b + 1296a )%%EZ0 + (36a b - 72a )%%EZ0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + a +--R + +--R +------+ +--I \|4%%EZ0 +--R * +--R log +--R 5 6 2 3 4 2 +--I ((7776a b + 7776a )%%EZ0 + (216a b - 432a )%%EZ0 + 6a b + 6a ) +--R * +--R +------+ +--I \|4%%EZ0 +--R + +--R 4 5 2 2 3 2 +--I (- 2592a b - 2592a )%%EZ0 + (- 72a b + 144a )%%EZ0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b - 2a +--R + +--R - +--R +------+ +--I \|4%%EZ0 +--R * +--R log +--R 5 6 2 3 4 +--I (- 7776a b - 7776a )%%EZ0 + (- 216a b + 432a )%%EZ0 - 6a b +--R + +--R 2 +--R - 6a +--R * +--R +------+ +--I \|4%%EZ0 +--R + +--R 4 5 2 2 3 +--I (- 2592a b - 2592a )%%EZ0 + (- 72a b + 144a )%%EZ0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b - 2a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 510 +m0082:= a0082-r0082 +--R +--R +--R (367) +--R - +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|\|b + \|a \|\|- 1 \|b - \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b + 3888a )%%EZ0 - 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b + 3888a )%%EZ0 + (108a b - 216a )%%EZ0 - 6a b + 3a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((1296a b + 1296a )%%EZ0 - 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (1296a b + 1296a )%%EZ0 + (36a b - 72a )%%EZ0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + a +--R + +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|\|b + \|a \|\|- 1 \|b - \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b + 3888a )%%EZ0 - 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b - 3888a )%%EZ0 + (- 108a b + 216a )%%EZ0 + 6a b +--R + +--R 2 +--R - 3a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b - 1296a )%%EZ0 + 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (1296a b + 1296a )%%EZ0 + (36a b - 72a )%%EZ0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + a +--R + +--R - +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|\|b + \|a \|\|- 1 \|b - \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b - 3888a )%%EZ0 + 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b + 3888a )%%EZ0 + (108a b - 216a )%%EZ0 - 6a b + 3a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b - 1296a )%%EZ0 + 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (1296a b + 1296a )%%EZ0 + (36a b - 72a )%%EZ0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + a +--R + +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|\|b + \|a \|\|- 1 \|b - \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b - 3888a )%%EZ0 + 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b - 3888a )%%EZ0 + (- 108a b + 216a )%%EZ0 + 6a b +--R + +--R 2 +--R - 3a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EZ0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((1296a b + 1296a )%%EZ0 - 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EZ0 +--R + +--R 2 3 +--I (72a b + 72a )%%EZ0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (1296a b + 1296a )%%EZ0 + (36a b - 72a )%%EZ0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b + a +--R + +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +------+ +--I 3\|a \|\|b + \|a \|\|- 1 \|b - \|a \|\|- 1 \|b + \|a \|4%%EZ0 +--R * +--R log +--R 5 6 2 3 4 2 +--I ((7776a b + 7776a )%%EZ0 + (216a b - 432a )%%EZ0 + 6a b + 6a ) +--R * +--R +------+ +--I \|4%%EZ0 +--R + +--R 4 5 2 2 3 2 +--I (- 2592a b - 2592a )%%EZ0 + (- 72a b + 144a )%%EZ0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b - 2a +--R + +--R - +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|\|b + \|a \|\|- 1 \|b - \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%EZ0 +--R * +--R log +--R 5 6 2 3 4 +--I (- 7776a b - 7776a )%%EZ0 + (- 216a b + 432a )%%EZ0 - 6a b +--R + +--R 2 +--R - 6a +--R * +--R +------+ +--I \|4%%EZ0 +--R + +--R 4 5 2 2 3 +--I (- 2592a b - 2592a )%%EZ0 + (- 72a b + 144a )%%EZ0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b - 2a +--R + +--R +------------------+ +--R +-----------+ +-----------------+ |3+---+2 3+-+ 3+-+ +--R |3+-+ 3+-+ |3+---+3+-+ 3+-+ tanh(x)\|\|- 1 \|b + \|a +--R - 2\|\|b + \|a \|\|- 1 \|b - \|a atanh(----------------------------) +--R 6+-+ +--R \|a +--R + +--R +-----------+ +--R +-----------------+ +------------------+ |3+-+ 3+-+ +--R |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|\|b + \|a +--R - 2\|\|- 1 \|b - \|a \|\|- 1 \|b + \|a atanh(---------------------) +--R 6+-+ +--R \|a +--R + +--R +-----------------+ +--R +-----------+ +------------------+ |3+---+3+-+ 3+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|\|- 1 \|b - \|a +--R - 2\|\|b + \|a \|\|- 1 \|b + \|a atan(---------------------------) +--R 6+-+ +--R \|a +--R / +--R +-----------+ +-----------------+ +------------------+ +--R 6+-+5 |3+-+ 3+-+ |3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 6\|a \|\|b + \|a \|\|- 1 \|b - \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 510 +d0082:= D(m0082,x) +--R +--R +--R (368) +--R 3+---+2 3+---+ +--R (- 384b - 960a)\|- 1 + (384b + 960a)\|- 1 - 384b +--R + +--R - 960a +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 2304b - 5760a)\|- 1 + (2304b + 5760a)\|- 1 - 2304b +--R + +--R - 5760a +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 5760b - 14400a)\|- 1 + (5760b + 14400a)\|- 1 +--R + +--R - 5760b - 14400a +--R * +--R 2 4 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 7680b - 19200a)\|- 1 + (7680b + 19200a)\|- 1 +--R + +--R - 7680b - 19200a +--R * +--R 3 3 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 5760b - 14400a)\|- 1 + (5760b + 14400a)\|- 1 +--R + +--R - 5760b - 14400a +--R * +--R 4 2 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 2304b - 5760a)\|- 1 + (2304b + 5760a)\|- 1 - 2304b +--R + +--R - 5760a +--R * +--R 5 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 384b - 960a)\|- 1 + (384b + 960a)\|- 1 - 384b +--R + +--R - 960a +--R * +--R 6 +--R cosh(x) +--R * +--R 6 +--R tanh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (- 3b \|- 1 + 3b\|- 1 - 3b)sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (- 36b \|- 1 + 36b\|- 1 - 36b)cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 198b \|- 1 + 198b\|- 1 - 198b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 18b \|- 1 - 18b\|- 1 + 18b +--R * +--R 10 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 660b \|- 1 + 660b\|- 1 - 660b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (180b \|- 1 - 180b\|- 1 + 180b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 1485b \|- 1 + 1485b\|- 1 - 1485b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (810b \|- 1 - 810b\|- 1 + 810b)cosh(x) - 45b \|- 1 +--R + +--R 3+---+ +--R 45b\|- 1 - 45b +--R * +--R 8 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 2376b \|- 1 + 2376b\|- 1 - 2376b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (2160b \|- 1 - 2160b\|- 1 + 2160b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 360b \|- 1 + 360b\|- 1 - 360b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 2772b \|- 1 + 2772b\|- 1 - 2772b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (3780b \|- 1 - 3780b\|- 1 + 3780b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 1260b \|- 1 + 1260b\|- 1 - 1260b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (60b + 192a)\|- 1 + (- 60b - 192a)\|- 1 + 60b + 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 2376b \|- 1 + 2376b\|- 1 - 2376b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (4536b \|- 1 - 4536b\|- 1 + 4536b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 2520b \|- 1 + 2520b\|- 1 - 2520b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (360b + 1152a)\|- 1 + (- 360b - 1152a)\|- 1 + 360b +--R + +--R 1152a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 1485b \|- 1 + 1485b\|- 1 - 1485b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (3780b \|- 1 - 3780b\|- 1 + 3780b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 3150b \|- 1 + 3150b\|- 1 - 3150b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (900b + 2880a)\|- 1 + (- 900b - 2880a)\|- 1 + 900b +--R + +--R 2880a +--R * +--R 2 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 45b \|- 1 + 45b\|- 1 - 45b +--R * +--R 4 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (- 660b \|- 1 + 660b\|- 1 - 660b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (2160b \|- 1 - 2160b\|- 1 + 2160b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 2520b \|- 1 + 2520b\|- 1 - 2520b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (1200b + 3840a)\|- 1 + (- 1200b - 3840a)\|- 1 +--R + +--R 1200b + 3840a +--R * +--R 3 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 180b \|- 1 + 180b\|- 1 - 180b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (- 198b \|- 1 + 198b\|- 1 - 198b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (810b \|- 1 - 810b\|- 1 + 810b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 1260b \|- 1 + 1260b\|- 1 - 1260b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (900b + 2880a)\|- 1 + (- 900b - 2880a)\|- 1 + 900b +--R + +--R 2880a +--R * +--R 4 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 270b \|- 1 + 270b\|- 1 - 270b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 18b \|- 1 - 18b\|- 1 + 18b +--R * +--R 2 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (- 36b \|- 1 + 36b\|- 1 - 36b)cosh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (180b \|- 1 - 180b\|- 1 + 180b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 360b \|- 1 + 360b\|- 1 - 360b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (360b + 1152a)\|- 1 + (- 360b - 1152a)\|- 1 + 360b +--R + +--R 1152a +--R * +--R 5 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 180b \|- 1 + 180b\|- 1 - 180b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (36b \|- 1 - 36b\|- 1 + 36b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (- 3b \|- 1 + 3b\|- 1 - 3b)cosh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (18b \|- 1 - 18b\|- 1 + 18b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 45b \|- 1 + 45b\|- 1 - 45b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R ((60b + 192a)\|- 1 + (- 60b - 192a)\|- 1 + 60b + 192a) +--R * +--R 6 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 45b \|- 1 + 45b\|- 1 - 45b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (18b \|- 1 - 18b\|- 1 + 18b)cosh(x) - 3b \|- 1 +--R + +--R 3+---+ +--R 3b\|- 1 - 3b +--R * +--R 2 +--R tanh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (3b \|- 1 - 3b\|- 1 + 3b)sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (36b \|- 1 - 36b\|- 1 + 36b)cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (198b \|- 1 - 198b\|- 1 + 198b)cosh(x) - 18b \|- 1 +--R + +--R 3+---+ +--R 18b\|- 1 - 18b +--R * +--R 10 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (660b \|- 1 - 660b\|- 1 + 660b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 180b \|- 1 + 180b\|- 1 - 180b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (1485b \|- 1 - 1485b\|- 1 + 1485b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (- 810b \|- 1 + 810b\|- 1 - 810b)cosh(x) + 45b \|- 1 +--R + +--R 3+---+ +--R - 45b\|- 1 + 45b +--R * +--R 8 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (2376b \|- 1 - 2376b\|- 1 + 2376b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 2160b \|- 1 + 2160b\|- 1 - 2160b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (360b \|- 1 - 360b\|- 1 + 360b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (2772b \|- 1 - 2772b\|- 1 + 2772b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 3780b \|- 1 + 3780b\|- 1 - 3780b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (1260b \|- 1 - 1260b\|- 1 + 1260b)cosh(x) - 60b \|- 1 +--R + +--R 3+---+ +--R 60b\|- 1 - 60b +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (2376b \|- 1 - 2376b\|- 1 + 2376b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 4536b \|- 1 + 4536b\|- 1 - 4536b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (2520b \|- 1 - 2520b\|- 1 + 2520b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 360b \|- 1 + 360b\|- 1 - 360b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (1485b \|- 1 - 1485b\|- 1 + 1485b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3780b \|- 1 + 3780b\|- 1 - 3780b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (3150b \|- 1 - 3150b\|- 1 + 3150b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (- 900b \|- 1 + 900b\|- 1 - 900b)cosh(x) + 45b \|- 1 +--R + +--R 3+---+ +--R - 45b\|- 1 + 45b +--R * +--R 4 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (660b \|- 1 - 660b\|- 1 + 660b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 2160b \|- 1 + 2160b\|- 1 - 2160b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (2520b \|- 1 - 2520b\|- 1 + 2520b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 1200b \|- 1 + 1200b\|- 1 - 1200b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (180b \|- 1 - 180b\|- 1 + 180b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (198b \|- 1 - 198b\|- 1 + 198b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 810b \|- 1 + 810b\|- 1 - 810b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (1260b \|- 1 - 1260b\|- 1 + 1260b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 900b \|- 1 + 900b\|- 1 - 900b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (270b \|- 1 - 270b\|- 1 + 270b)cosh(x) - 18b \|- 1 +--R + +--R 3+---+ +--R 18b\|- 1 - 18b +--R * +--R 2 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (36b \|- 1 - 36b\|- 1 + 36b)cosh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (- 180b \|- 1 + 180b\|- 1 - 180b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (360b \|- 1 - 360b\|- 1 + 360b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 360b \|- 1 + 360b\|- 1 - 360b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (180b \|- 1 - 180b\|- 1 + 180b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 36b \|- 1 + 36b\|- 1 - 36b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (3b \|- 1 - 3b\|- 1 + 3b)cosh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (- 18b \|- 1 + 18b\|- 1 - 18b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (45b \|- 1 - 45b\|- 1 + 45b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 60b \|- 1 + 60b\|- 1 - 60b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (45b \|- 1 - 45b\|- 1 + 45b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 3+---+ +--R (- 18b \|- 1 + 18b\|- 1 - 18b)cosh(x) + 3b \|- 1 - 3b\|- 1 +--R + +--R 3b +--R * +--R 3+-+6+-+4 +--R \|a \|a +--R + +--R 3+---+2 3+---+ 12 +--R (12b \|- 1 - 12b\|- 1 + 12b)sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (144b \|- 1 - 144b\|- 1 + 144b)cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (792b \|- 1 - 792b\|- 1 + 792b)cosh(x) - 72b \|- 1 +--R + +--R 3+---+ +--R 72b\|- 1 - 72b +--R * +--R 10 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (2640b \|- 1 - 2640b\|- 1 + 2640b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 720b \|- 1 + 720b\|- 1 - 720b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (5940b \|- 1 - 5940b\|- 1 + 5940b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 3240b \|- 1 + 3240b\|- 1 - 3240b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 180b \|- 1 - 180b\|- 1 + 180b +--R * +--R 8 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (9504b \|- 1 - 9504b\|- 1 + 9504b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 8640b \|- 1 + 8640b\|- 1 - 8640b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (1440b \|- 1 - 1440b\|- 1 + 1440b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (11088b \|- 1 - 11088b\|- 1 + 11088b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 15120b \|- 1 + 15120b\|- 1 - 15120b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (5040b \|- 1 - 5040b\|- 1 + 5040b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 240b - 768a)\|- 1 + (240b + 768a)\|- 1 - 240b - 768a +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (9504b \|- 1 - 9504b\|- 1 + 9504b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 18144b \|- 1 + 18144b\|- 1 - 18144b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (10080b \|- 1 - 10080b\|- 1 + 10080b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 1440b - 4608a)\|- 1 + (1440b + 4608a)\|- 1 +--R + +--R - 1440b - 4608a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (5940b \|- 1 - 5940b\|- 1 + 5940b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 15120b \|- 1 + 15120b\|- 1 - 15120b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (12600b \|- 1 - 12600b\|- 1 + 12600b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 3600b - 11520a)\|- 1 + (3600b + 11520a)\|- 1 +--R + +--R - 3600b - 11520a +--R * +--R 2 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R 180b \|- 1 - 180b\|- 1 + 180b +--R * +--R 4 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (2640b \|- 1 - 2640b\|- 1 + 2640b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 8640b \|- 1 + 8640b\|- 1 - 8640b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (10080b \|- 1 - 10080b\|- 1 + 10080b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 4800b - 15360a)\|- 1 + (4800b + 15360a)\|- 1 +--R + +--R - 4800b - 15360a +--R * +--R 3 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R (720b \|- 1 - 720b\|- 1 + 720b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (792b \|- 1 - 792b\|- 1 + 792b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 3240b \|- 1 + 3240b\|- 1 - 3240b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (5040b \|- 1 - 5040b\|- 1 + 5040b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 3600b - 11520a)\|- 1 + (3600b + 11520a)\|- 1 +--R + +--R - 3600b - 11520a +--R * +--R 4 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (1080b \|- 1 - 1080b\|- 1 + 1080b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 72b \|- 1 + 72b\|- 1 - 72b +--R * +--R 2 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (144b \|- 1 - 144b\|- 1 + 144b)cosh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (- 720b \|- 1 + 720b\|- 1 - 720b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (1440b \|- 1 - 1440b\|- 1 + 1440b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 1440b - 4608a)\|- 1 + (1440b + 4608a)\|- 1 +--R + +--R - 1440b - 4608a +--R * +--R 5 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (720b \|- 1 - 720b\|- 1 + 720b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 144b \|- 1 + 144b\|- 1 - 144b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (12b \|- 1 - 12b\|- 1 + 12b)cosh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (- 72b \|- 1 + 72b\|- 1 - 72b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (180b \|- 1 - 180b\|- 1 + 180b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 240b - 768a)\|- 1 + (240b + 768a)\|- 1 - 240b +--R + +--R - 768a +--R * +--R 6 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (180b \|- 1 - 180b\|- 1 + 180b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (- 72b \|- 1 + 72b\|- 1 - 72b)cosh(x) + 12b \|- 1 +--R + +--R 3+---+ +--R - 12b\|- 1 + 12b +--R * +--R 4 +--R tanh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (- 12b \|- 1 + 12b\|- 1 - 12b)sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (- 144b \|- 1 + 144b\|- 1 - 144b)cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 792b \|- 1 + 792b\|- 1 - 792b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 72b \|- 1 - 72b\|- 1 + 72b +--R * +--R 10 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 2640b \|- 1 + 2640b\|- 1 - 2640b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (720b \|- 1 - 720b\|- 1 + 720b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 5940b \|- 1 + 5940b\|- 1 - 5940b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (3240b \|- 1 - 3240b\|- 1 + 3240b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 180b \|- 1 + 180b\|- 1 - 180b +--R * +--R 8 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 9504b \|- 1 + 9504b\|- 1 - 9504b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (8640b \|- 1 - 8640b\|- 1 + 8640b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 1440b \|- 1 + 1440b\|- 1 - 1440b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 11088b \|- 1 + 11088b\|- 1 - 11088b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (15120b \|- 1 - 15120b\|- 1 + 15120b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 5040b \|- 1 + 5040b\|- 1 - 5040b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (240b - 384a)\|- 1 + (- 240b + 384a)\|- 1 + 240b - 384a +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 9504b \|- 1 + 9504b\|- 1 - 9504b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (18144b \|- 1 - 18144b\|- 1 + 18144b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 10080b \|- 1 + 10080b\|- 1 - 10080b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (1440b - 2304a)\|- 1 + (- 1440b + 2304a)\|- 1 +--R + +--R 1440b - 2304a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 5940b \|- 1 + 5940b\|- 1 - 5940b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (15120b \|- 1 - 15120b\|- 1 + 15120b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 12600b \|- 1 + 12600b\|- 1 - 12600b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (3600b - 5760a)\|- 1 + (- 3600b + 5760a)\|- 1 +--R + +--R 3600b - 5760a +--R * +--R 2 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 180b \|- 1 + 180b\|- 1 - 180b +--R * +--R 4 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (- 2640b \|- 1 + 2640b\|- 1 - 2640b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (8640b \|- 1 - 8640b\|- 1 + 8640b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 10080b \|- 1 + 10080b\|- 1 - 10080b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (4800b - 7680a)\|- 1 + (- 4800b + 7680a)\|- 1 +--R + +--R 4800b - 7680a +--R * +--R 3 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 720b \|- 1 + 720b\|- 1 - 720b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (- 792b \|- 1 + 792b\|- 1 - 792b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (3240b \|- 1 - 3240b\|- 1 + 3240b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 5040b \|- 1 + 5040b\|- 1 - 5040b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (3600b - 5760a)\|- 1 + (- 3600b + 5760a)\|- 1 +--R + +--R 3600b - 5760a +--R * +--R 4 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 1080b \|- 1 + 1080b\|- 1 - 1080b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 72b \|- 1 - 72b\|- 1 + 72b +--R * +--R 2 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (- 144b \|- 1 + 144b\|- 1 - 144b)cosh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (720b \|- 1 - 720b\|- 1 + 720b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 1440b \|- 1 + 1440b\|- 1 - 1440b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (1440b - 2304a)\|- 1 + (- 1440b + 2304a)\|- 1 +--R + +--R 1440b - 2304a +--R * +--R 5 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 720b \|- 1 + 720b\|- 1 - 720b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (144b \|- 1 - 144b\|- 1 + 144b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (- 12b \|- 1 + 12b\|- 1 - 12b)cosh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (72b \|- 1 - 72b\|- 1 + 72b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 180b \|- 1 + 180b\|- 1 - 180b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (240b - 384a)\|- 1 + (- 240b + 384a)\|- 1 + 240b +--R + +--R - 384a +--R * +--R 6 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 180b \|- 1 + 180b\|- 1 - 180b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (72b \|- 1 - 72b\|- 1 + 72b)cosh(x) - 12b \|- 1 +--R + +--R 3+---+ +--R 12b\|- 1 - 12b +--R * +--R 2 +--R tanh(x) +--R * +--R 3+-+2 6+-+2 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- b - 10a b)\|- 1 + (b + 10a b)\|- 1 - b - 10a b) +--R * +--R 12 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 12b - 120a b)\|- 1 + (12b + 120a b)\|- 1 - 12b +--R + +--R - 120a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 66b - 660a b)\|- 1 + (66b + 660a b)\|- 1 - 66b +--R + +--R - 660a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (6b + 60a b)\|- 1 + (- 6b - 60a b)\|- 1 + 6b + 60a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 220b - 2200a b)\|- 1 + (220b + 2200a b)\|- 1 +--R + +--R 2 +--R - 220b - 2200a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (60b + 600a b)\|- 1 + (- 60b - 600a b)\|- 1 + 60b +--R + +--R 600a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 495b - 4950a b)\|- 1 + (495b + 4950a b)\|- 1 +--R + +--R 2 +--R - 495b - 4950a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (270b + 2700a b)\|- 1 + (- 270b - 2700a b)\|- 1 +--R + +--R 2 +--R 270b + 2700a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 15b - 150a b)\|- 1 + (15b + 150a b)\|- 1 - 15b +--R + +--R - 150a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 792b - 7920a b)\|- 1 + (792b + 7920a b)\|- 1 +--R + +--R 2 +--R - 792b - 7920a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (720b + 7200a b)\|- 1 + (- 720b - 7200a b)\|- 1 +--R + +--R 2 +--R 720b + 7200a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 120b - 1200a b)\|- 1 + (120b + 1200a b)\|- 1 +--R + +--R 2 +--R - 120b - 1200a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 924b - 9240a b)\|- 1 + (924b + 9240a b)\|- 1 +--R + +--R 2 +--R - 924b - 9240a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1260b + 12600a b)\|- 1 + (- 1260b - 12600a b)\|- 1 +--R + +--R 2 +--R 1260b + 12600a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 420b - 4200a b)\|- 1 + (420b + 4200a b)\|- 1 +--R + +--R 2 +--R - 420b - 4200a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (20b + 264a b + 640a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 20b - 264a b - 640a )\|- 1 + 20b + 264a b + 640a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 792b - 7920a b)\|- 1 + (792b + 7920a b)\|- 1 +--R + +--R 2 +--R - 792b - 7920a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1512b + 15120a b)\|- 1 + (- 1512b - 15120a b)\|- 1 +--R + +--R 2 +--R 1512b + 15120a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 840b - 8400a b)\|- 1 + (840b + 8400a b)\|- 1 +--R + +--R 2 +--R - 840b - 8400a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (120b + 1584a b + 3840a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (- 120b - 1584a b - 3840a )\|- 1 + 120b + 1584a b +--R + +--R 2 +--R 3840a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 495b - 4950a b)\|- 1 + (495b + 4950a b)\|- 1 +--R + +--R 2 +--R - 495b - 4950a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1260b + 12600a b)\|- 1 + (- 1260b - 12600a b)\|- 1 +--R + +--R 2 +--R 1260b + 12600a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 1050b - 10500a b)\|- 1 + (1050b + 10500a b)\|- 1 +--R + +--R 2 +--R - 1050b - 10500a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (300b + 3960a b + 9600a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (- 300b - 3960a b - 9600a )\|- 1 + 300b + 3960a b +--R + +--R 2 +--R 9600a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 15b - 150a b)\|- 1 + (15b + 150a b)\|- 1 - 15b +--R + +--R - 150a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 220b - 2200a b)\|- 1 + (220b + 2200a b)\|- 1 +--R + +--R 2 +--R - 220b - 2200a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (720b + 7200a b)\|- 1 + (- 720b - 7200a b)\|- 1 +--R + +--R 2 +--R 720b + 7200a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 840b - 8400a b)\|- 1 + (840b + 8400a b)\|- 1 +--R + +--R 2 +--R - 840b - 8400a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (400b + 5280a b + 12800a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (- 400b - 5280a b - 12800a )\|- 1 + 400b + 5280a b +--R + +--R 2 +--R 12800a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 60b - 600a b)\|- 1 + (60b + 600a b)\|- 1 - 60b +--R + +--R - 600a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 66b - 660a b)\|- 1 + (66b + 660a b)\|- 1 - 66b +--R + +--R - 660a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (270b + 2700a b)\|- 1 + (- 270b - 2700a b)\|- 1 +--R + +--R 2 +--R 270b + 2700a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 420b - 4200a b)\|- 1 + (420b + 4200a b)\|- 1 +--R + +--R 2 +--R - 420b - 4200a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (300b + 3960a b + 9600a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (- 300b - 3960a b - 9600a )\|- 1 + 300b + 3960a b +--R + +--R 2 +--R 9600a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 90b - 900a b)\|- 1 + (90b + 900a b)\|- 1 - 90b +--R + +--R - 900a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (6b + 60a b)\|- 1 + (- 6b - 60a b)\|- 1 + 6b + 60a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 12b - 120a b)\|- 1 + (12b + 120a b)\|- 1 - 12b +--R + +--R - 120a b +--R * +--R 11 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (60b + 600a b)\|- 1 + (- 60b - 600a b)\|- 1 + 60b +--R + +--R 600a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 120b - 1200a b)\|- 1 + (120b + 1200a b)\|- 1 +--R + +--R 2 +--R - 120b - 1200a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (120b + 1584a b + 3840a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (- 120b - 1584a b - 3840a )\|- 1 + 120b + 1584a b +--R + +--R 2 +--R 3840a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 60b - 600a b)\|- 1 + (60b + 600a b)\|- 1 - 60b +--R + +--R - 600a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (12b + 120a b)\|- 1 + (- 12b - 120a b)\|- 1 + 12b +--R + +--R 120a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- b - 10a b)\|- 1 + (b + 10a b)\|- 1 - b - 10a b) +--R * +--R 12 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((6b + 60a b)\|- 1 + (- 6b - 60a b)\|- 1 + 6b + 60a b) +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 15b - 150a b)\|- 1 + (15b + 150a b)\|- 1 - 15b +--R + +--R - 150a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (20b + 264a b + 640a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 20b - 264a b - 640a )\|- 1 + 20b + 264a b + 640a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 15b - 150a b)\|- 1 + (15b + 150a b)\|- 1 - 15b +--R + +--R - 150a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((6b + 60a b)\|- 1 + (- 6b - 60a b)\|- 1 + 6b + 60a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- b - 10a b)\|- 1 + (b + 10a b)\|- 1 - b - 10a b +--R * +--R 6 +--R tanh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((b + 10a b)\|- 1 + (- b - 10a b)\|- 1 + b + 10a b) +--R * +--R 12 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (12b + 120a b)\|- 1 + (- 12b - 120a b)\|- 1 + 12b +--R + +--R 120a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (66b + 660a b)\|- 1 + (- 66b - 660a b)\|- 1 + 66b +--R + +--R 660a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 6b - 60a b)\|- 1 + (6b + 60a b)\|- 1 - 6b - 60a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (220b + 2200a b)\|- 1 + (- 220b - 2200a b)\|- 1 +--R + +--R 2 +--R 220b + 2200a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 60b - 600a b)\|- 1 + (60b + 600a b)\|- 1 - 60b +--R + +--R - 600a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (495b + 4950a b)\|- 1 + (- 495b - 4950a b)\|- 1 +--R + +--R 2 +--R 495b + 4950a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 270b - 2700a b)\|- 1 + (270b + 2700a b)\|- 1 +--R + +--R 2 +--R - 270b - 2700a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (15b + 150a b)\|- 1 + (- 15b - 150a b)\|- 1 + 15b +--R + +--R 150a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (792b + 7920a b)\|- 1 + (- 792b - 7920a b)\|- 1 +--R + +--R 2 +--R 792b + 7920a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 720b - 7200a b)\|- 1 + (720b + 7200a b)\|- 1 +--R + +--R 2 +--R - 720b - 7200a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (120b + 1200a b)\|- 1 + (- 120b - 1200a b)\|- 1 +--R + +--R 2 +--R 120b + 1200a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (924b + 9240a b)\|- 1 + (- 924b - 9240a b)\|- 1 +--R + +--R 2 +--R 924b + 9240a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 1260b - 12600a b)\|- 1 + (1260b + 12600a b)\|- 1 +--R + +--R 2 +--R - 1260b - 12600a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (420b + 4200a b)\|- 1 + (- 420b - 4200a b)\|- 1 +--R + +--R 2 +--R 420b + 4200a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 20b - 72a b + 1280a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (20b + 72a b - 1280a )\|- 1 - 20b - 72a b + 1280a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (792b + 7920a b)\|- 1 + (- 792b - 7920a b)\|- 1 +--R + +--R 2 +--R 792b + 7920a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 1512b - 15120a b)\|- 1 + (1512b + 15120a b)\|- 1 +--R + +--R 2 +--R - 1512b - 15120a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (840b + 8400a b)\|- 1 + (- 840b - 8400a b)\|- 1 +--R + +--R 2 +--R 840b + 8400a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 120b - 432a b + 7680a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (120b + 432a b - 7680a )\|- 1 - 120b - 432a b + 7680a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (495b + 4950a b)\|- 1 + (- 495b - 4950a b)\|- 1 +--R + +--R 2 +--R 495b + 4950a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 1260b - 12600a b)\|- 1 + (1260b + 12600a b)\|- 1 +--R + +--R 2 +--R - 1260b - 12600a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1050b + 10500a b)\|- 1 + (- 1050b - 10500a b)\|- 1 +--R + +--R 2 +--R 1050b + 10500a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 300b - 1080a b + 19200a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (300b + 1080a b - 19200a )\|- 1 - 300b - 1080a b +--R + +--R 2 +--R 19200a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (15b + 150a b)\|- 1 + (- 15b - 150a b)\|- 1 + 15b +--R + +--R 150a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (220b + 2200a b)\|- 1 + (- 220b - 2200a b)\|- 1 +--R + +--R 2 +--R 220b + 2200a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 720b - 7200a b)\|- 1 + (720b + 7200a b)\|- 1 +--R + +--R 2 +--R - 720b - 7200a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (840b + 8400a b)\|- 1 + (- 840b - 8400a b)\|- 1 +--R + +--R 2 +--R 840b + 8400a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 400b - 1440a b + 25600a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (400b + 1440a b - 25600a )\|- 1 - 400b - 1440a b +--R + +--R 2 +--R 25600a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (60b + 600a b)\|- 1 + (- 60b - 600a b)\|- 1 + 60b +--R + +--R 600a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (66b + 660a b)\|- 1 + (- 66b - 660a b)\|- 1 + 66b +--R + +--R 660a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 270b - 2700a b)\|- 1 + (270b + 2700a b)\|- 1 +--R + +--R 2 +--R - 270b - 2700a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (420b + 4200a b)\|- 1 + (- 420b - 4200a b)\|- 1 +--R + +--R 2 +--R 420b + 4200a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 300b - 1080a b + 19200a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (300b + 1080a b - 19200a )\|- 1 - 300b - 1080a b +--R + +--R 2 +--R 19200a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (90b + 900a b)\|- 1 + (- 90b - 900a b)\|- 1 + 90b +--R + +--R 900a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 6b - 60a b)\|- 1 + (6b + 60a b)\|- 1 - 6b - 60a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (12b + 120a b)\|- 1 + (- 12b - 120a b)\|- 1 + 12b +--R + +--R 120a b +--R * +--R 11 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 60b - 600a b)\|- 1 + (60b + 600a b)\|- 1 - 60b +--R + +--R - 600a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (120b + 1200a b)\|- 1 + (- 120b - 1200a b)\|- 1 +--R + +--R 2 +--R 120b + 1200a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 120b - 432a b + 7680a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (120b + 432a b - 7680a )\|- 1 - 120b - 432a b + 7680a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (60b + 600a b)\|- 1 + (- 60b - 600a b)\|- 1 + 60b +--R + +--R 600a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 12b - 120a b)\|- 1 + (12b + 120a b)\|- 1 - 12b +--R + +--R - 120a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((b + 10a b)\|- 1 + (- b - 10a b)\|- 1 + b + 10a b) +--R * +--R 12 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 6b - 60a b)\|- 1 + (6b + 60a b)\|- 1 - 6b - 60a b) +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (15b + 150a b)\|- 1 + (- 15b - 150a b)\|- 1 + 15b +--R + +--R 150a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 20b - 72a b + 1280a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (20b + 72a b - 1280a )\|- 1 - 20b - 72a b + 1280a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (15b + 150a b)\|- 1 + (- 15b - 150a b)\|- 1 + 15b +--R + +--R 150a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 6b - 60a b)\|- 1 + (6b + 60a b)\|- 1 - 6b - 60a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (b + 10a b)\|- 1 + (- b - 10a b)\|- 1 + b + 10a b +--R * +--R 4 +--R tanh(x) +--R * +--R 3+-+2 +--R \|b +--R + +--R 3+---+2 3+---+ +--R (- 960b - 384a)\|- 1 + (960b + 384a)\|- 1 - 960b +--R + +--R - 384a +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 5760b - 2304a)\|- 1 + (5760b + 2304a)\|- 1 - 5760b +--R + +--R - 2304a +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 14400b - 5760a)\|- 1 + (14400b + 5760a)\|- 1 +--R + +--R - 14400b - 5760a +--R * +--R 2 4 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 19200b - 7680a)\|- 1 + (19200b + 7680a)\|- 1 +--R + +--R - 19200b - 7680a +--R * +--R 3 3 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 14400b - 5760a)\|- 1 + (14400b + 5760a)\|- 1 +--R + +--R - 14400b - 5760a +--R * +--R 4 2 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 5760b - 2304a)\|- 1 + (5760b + 2304a)\|- 1 - 5760b +--R + +--R - 2304a +--R * +--R 5 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ +--R (- 960b - 384a)\|- 1 + (960b + 384a)\|- 1 - 960b +--R + +--R - 384a +--R * +--R 6 +--R cosh(x) +--R * +--R 6 +--R tanh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (- 3b \|- 1 + 3b\|- 1 - 3b)sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (- 36b \|- 1 + 36b\|- 1 - 36b)cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 198b \|- 1 + 198b\|- 1 - 198b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 18b \|- 1 - 18b\|- 1 + 18b +--R * +--R 10 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 660b \|- 1 + 660b\|- 1 - 660b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (180b \|- 1 - 180b\|- 1 + 180b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 1485b \|- 1 + 1485b\|- 1 - 1485b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (810b \|- 1 - 810b\|- 1 + 810b)cosh(x) - 45b \|- 1 +--R + +--R 3+---+ +--R 45b\|- 1 - 45b +--R * +--R 8 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 2376b \|- 1 + 2376b\|- 1 - 2376b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (2160b \|- 1 - 2160b\|- 1 + 2160b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 360b \|- 1 + 360b\|- 1 - 360b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 2772b \|- 1 + 2772b\|- 1 - 2772b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (3780b \|- 1 - 3780b\|- 1 + 3780b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 1260b \|- 1 + 1260b\|- 1 - 1260b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (60b + 192a)\|- 1 + (- 60b - 192a)\|- 1 + 60b + 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 2376b \|- 1 + 2376b\|- 1 - 2376b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (4536b \|- 1 - 4536b\|- 1 + 4536b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 2520b \|- 1 + 2520b\|- 1 - 2520b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (360b + 1152a)\|- 1 + (- 360b - 1152a)\|- 1 + 360b +--R + +--R 1152a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 1485b \|- 1 + 1485b\|- 1 - 1485b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (3780b \|- 1 - 3780b\|- 1 + 3780b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 3150b \|- 1 + 3150b\|- 1 - 3150b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (900b + 2880a)\|- 1 + (- 900b - 2880a)\|- 1 + 900b +--R + +--R 2880a +--R * +--R 2 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 45b \|- 1 + 45b\|- 1 - 45b +--R * +--R 4 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (- 660b \|- 1 + 660b\|- 1 - 660b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (2160b \|- 1 - 2160b\|- 1 + 2160b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 2520b \|- 1 + 2520b\|- 1 - 2520b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (1200b + 3840a)\|- 1 + (- 1200b - 3840a)\|- 1 +--R + +--R 1200b + 3840a +--R * +--R 3 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 180b \|- 1 + 180b\|- 1 - 180b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (- 198b \|- 1 + 198b\|- 1 - 198b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (810b \|- 1 - 810b\|- 1 + 810b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 1260b \|- 1 + 1260b\|- 1 - 1260b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (900b + 2880a)\|- 1 + (- 900b - 2880a)\|- 1 + 900b +--R + +--R 2880a +--R * +--R 4 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 270b \|- 1 + 270b\|- 1 - 270b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 18b \|- 1 - 18b\|- 1 + 18b +--R * +--R 2 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (- 36b \|- 1 + 36b\|- 1 - 36b)cosh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (180b \|- 1 - 180b\|- 1 + 180b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 360b \|- 1 + 360b\|- 1 - 360b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (360b + 1152a)\|- 1 + (- 360b - 1152a)\|- 1 + 360b +--R + +--R 1152a +--R * +--R 5 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 180b \|- 1 + 180b\|- 1 - 180b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (36b \|- 1 - 36b\|- 1 + 36b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (- 3b \|- 1 + 3b\|- 1 - 3b)cosh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (18b \|- 1 - 18b\|- 1 + 18b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 45b \|- 1 + 45b\|- 1 - 45b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R ((60b + 192a)\|- 1 + (- 60b - 192a)\|- 1 + 60b + 192a) +--R * +--R 6 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 45b \|- 1 + 45b\|- 1 - 45b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (18b \|- 1 - 18b\|- 1 + 18b)cosh(x) - 3b \|- 1 +--R + +--R 3+---+ +--R 3b\|- 1 - 3b +--R * +--R 2 +--R tanh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (3b \|- 1 - 3b\|- 1 + 3b)sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (36b \|- 1 - 36b\|- 1 + 36b)cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (198b \|- 1 - 198b\|- 1 + 198b)cosh(x) - 18b \|- 1 +--R + +--R 3+---+ +--R 18b\|- 1 - 18b +--R * +--R 10 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (660b \|- 1 - 660b\|- 1 + 660b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 180b \|- 1 + 180b\|- 1 - 180b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (1485b \|- 1 - 1485b\|- 1 + 1485b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (- 810b \|- 1 + 810b\|- 1 - 810b)cosh(x) + 45b \|- 1 +--R + +--R 3+---+ +--R - 45b\|- 1 + 45b +--R * +--R 8 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (2376b \|- 1 - 2376b\|- 1 + 2376b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 2160b \|- 1 + 2160b\|- 1 - 2160b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (360b \|- 1 - 360b\|- 1 + 360b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (2772b \|- 1 - 2772b\|- 1 + 2772b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 3780b \|- 1 + 3780b\|- 1 - 3780b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (1260b \|- 1 - 1260b\|- 1 + 1260b)cosh(x) - 60b \|- 1 +--R + +--R 3+---+ +--R 60b\|- 1 - 60b +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (2376b \|- 1 - 2376b\|- 1 + 2376b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 4536b \|- 1 + 4536b\|- 1 - 4536b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (2520b \|- 1 - 2520b\|- 1 + 2520b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 360b \|- 1 + 360b\|- 1 - 360b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (1485b \|- 1 - 1485b\|- 1 + 1485b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3780b \|- 1 + 3780b\|- 1 - 3780b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (3150b \|- 1 - 3150b\|- 1 + 3150b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (- 900b \|- 1 + 900b\|- 1 - 900b)cosh(x) + 45b \|- 1 +--R + +--R 3+---+ +--R - 45b\|- 1 + 45b +--R * +--R 4 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (660b \|- 1 - 660b\|- 1 + 660b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 2160b \|- 1 + 2160b\|- 1 - 2160b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (2520b \|- 1 - 2520b\|- 1 + 2520b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 1200b \|- 1 + 1200b\|- 1 - 1200b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (180b \|- 1 - 180b\|- 1 + 180b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (198b \|- 1 - 198b\|- 1 + 198b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 810b \|- 1 + 810b\|- 1 - 810b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (1260b \|- 1 - 1260b\|- 1 + 1260b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 900b \|- 1 + 900b\|- 1 - 900b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (270b \|- 1 - 270b\|- 1 + 270b)cosh(x) - 18b \|- 1 +--R + +--R 3+---+ +--R 18b\|- 1 - 18b +--R * +--R 2 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (36b \|- 1 - 36b\|- 1 + 36b)cosh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (- 180b \|- 1 + 180b\|- 1 - 180b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (360b \|- 1 - 360b\|- 1 + 360b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 360b \|- 1 + 360b\|- 1 - 360b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (180b \|- 1 - 180b\|- 1 + 180b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 36b \|- 1 + 36b\|- 1 - 36b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (3b \|- 1 - 3b\|- 1 + 3b)cosh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (- 18b \|- 1 + 18b\|- 1 - 18b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (45b \|- 1 - 45b\|- 1 + 45b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 60b \|- 1 + 60b\|- 1 - 60b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (45b \|- 1 - 45b\|- 1 + 45b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 3+---+ +--R (- 18b \|- 1 + 18b\|- 1 - 18b)cosh(x) + 3b \|- 1 - 3b\|- 1 +--R + +--R 3b +--R * +--R 3+-+2 6+-+4 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((2b + 8a b)\|- 1 + (- 2b - 8a b)\|- 1 + 2b + 8a b) +--R * +--R 12 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (24b + 96a b)\|- 1 + (- 24b - 96a b)\|- 1 + 24b +--R + +--R 96a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (132b + 528a b)\|- 1 + (- 132b - 528a b)\|- 1 +--R + +--R 2 +--R 132b + 528a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 12b - 48a b)\|- 1 + (12b + 48a b)\|- 1 - 12b +--R + +--R - 48a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (440b + 1760a b)\|- 1 + (- 440b - 1760a b)\|- 1 +--R + +--R 2 +--R 440b + 1760a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 120b - 480a b)\|- 1 + (120b + 480a b)\|- 1 +--R + +--R 2 +--R - 120b - 480a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (990b + 3960a b)\|- 1 + (- 990b - 3960a b)\|- 1 +--R + +--R 2 +--R 990b + 3960a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 540b - 2160a b)\|- 1 + (540b + 2160a b)\|- 1 +--R + +--R 2 +--R - 540b - 2160a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (30b + 120a b)\|- 1 + (- 30b - 120a b)\|- 1 + 30b +--R + +--R 120a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (1584b + 6336a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 1584b - 6336a b)\|- 1 + 1584b + 6336a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 1440b - 5760a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (1440b + 5760a b)\|- 1 - 1440b - 5760a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (240b + 960a b)\|- 1 + (- 240b - 960a b)\|- 1 +--R + +--R 2 +--R 240b + 960a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (1848b + 7392a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 1848b - 7392a b)\|- 1 + 1848b + 7392a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 2520b - 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4320a b - 7680a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (600b + 4320a b + 7680a )\|- 1 - 600b - 4320a b +--R + +--R 2 +--R - 7680a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (180b + 720a b)\|- 1 + (- 180b - 720a b)\|- 1 +--R + +--R 2 +--R 180b + 720a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 12b - 48a b)\|- 1 + (12b + 48a b)\|- 1 - 12b +--R + +--R - 48a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (24b + 96a b)\|- 1 + (- 24b - 96a b)\|- 1 + 24b +--R + +--R 96a b +--R * +--R 11 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 120b - 480a b)\|- 1 + (120b + 480a b)\|- 1 +--R + +--R 2 +--R - 120b - 480a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (240b + 960a b)\|- 1 + (- 240b - 960a b)\|- 1 +--R + +--R 2 +--R 240b + 960a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 240b - 1728a b - 3072a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (240b + 1728a b + 3072a )\|- 1 - 240b - 1728a b +--R + +--R 2 +--R - 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2475a b)\|- 1 + 2475b + 2475a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 6300b - 6300a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (6300b + 6300a b)\|- 1 - 6300b - 6300a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (5250b + 5250a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 5250b - 5250a b)\|- 1 + 5250b + 5250a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1500b + 8100a b + 9600a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (1500b - 8100a b - 9600a )\|- 1 - 1500b + 8100a b +--R + +--R 2 +--R 9600a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (75b + 75a b)\|- 1 + (- 75b - 75a b)\|- 1 + 75b +--R + +--R 75a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (1100b + 1100a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 1100b - 1100a b)\|- 1 + 1100b + 1100a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 3600b - 3600a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (3600b + 3600a b)\|- 1 - 3600b - 3600a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (4200b + 4200a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 4200b - 4200a b)\|- 1 + 4200b + 4200a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 2000b + 10800a b + 12800a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (2000b - 10800a b - 12800a )\|- 1 - 2000b +--R + +--R 2 +--R 10800a b + 12800a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (300b + 300a b)\|- 1 + (- 300b - 300a b)\|- 1 +--R + +--R 2 +--R 300b + 300a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (330b + 330a b)\|- 1 + (- 330b - 330a b)\|- 1 +--R + +--R 2 +--R 330b + 330a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 1350b - 1350a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (1350b + 1350a b)\|- 1 - 1350b - 1350a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (2100b + 2100a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 2100b - 2100a b)\|- 1 + 2100b + 2100a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1500b + 8100a b + 9600a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (1500b - 8100a b - 9600a )\|- 1 - 1500b + 8100a b +--R + +--R 2 +--R 9600a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (450b + 450a b)\|- 1 + (- 450b - 450a b)\|- 1 +--R + +--R 2 +--R 450b + 450a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 30b - 30a b)\|- 1 + (30b + 30a b)\|- 1 - 30b +--R + +--R - 30a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (60b + 60a b)\|- 1 + (- 60b - 60a b)\|- 1 + 60b +--R + +--R 60a b +--R * +--R 11 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 300b - 300a b)\|- 1 + (300b + 300a b)\|- 1 +--R + +--R 2 +--R - 300b - 300a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (600b + 600a b)\|- 1 + (- 600b - 600a b)\|- 1 +--R + +--R 2 +--R 600b + 600a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 600b + 3240a b + 3840a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (600b - 3240a b - 3840a )\|- 1 - 600b + 3240a b +--R + +--R 2 +--R 3840a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (300b + 300a b)\|- 1 + (- 300b - 300a b)\|- 1 +--R + +--R 2 +--R 300b + 300a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 60b - 60a b)\|- 1 + (60b + 60a b)\|- 1 - 60b +--R + +--R - 60a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((5b + 5a b)\|- 1 + (- 5b - 5a b)\|- 1 + 5b + 5a b) +--R * +--R 12 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 30b - 30a b)\|- 1 + (30b + 30a b)\|- 1 - 30b +--R + +--R - 30a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (75b + 75a b)\|- 1 + (- 75b - 75a b)\|- 1 + 75b +--R + +--R 75a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 100b + 540a b + 640a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (100b - 540a b - 640a )\|- 1 - 100b + 540a b + 640a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (75b + 75a b)\|- 1 + (- 75b - 75a b)\|- 1 + 75b +--R + +--R 75a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 30b - 30a b)\|- 1 + (30b + 30a b)\|- 1 - 30b +--R + +--R - 30a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (5b + 5a b)\|- 1 + (- 5b - 5a b)\|- 1 + 5b + 5a b +--R * +--R 4 +--R tanh(x) +--R * +--R 3+-+ +--R \|a +--R * +--R 3+-+ +--R \|b +--R + +--R 3+---+2 3+---+ 2 2 +--R (- 1152a b \|- 1 + 1152a b\|- 1 - 192b - 1536a b - 192a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 2 2 +--R (- 6912a b \|- 1 + 6912a b\|- 1 - 1152b - 9216a b - 1152a ) +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ 2 +--R - 17280a b \|- 1 + 17280a b\|- 1 - 2880b - 23040a b +--R + +--R 2 +--R - 2880a +--R * +--R 2 4 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ 2 +--R - 23040a b \|- 1 + 23040a b\|- 1 - 3840b - 30720a b +--R + +--R 2 +--R - 3840a +--R * +--R 3 3 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ 2 +--R - 17280a b \|- 1 + 17280a b\|- 1 - 2880b - 23040a b +--R + +--R 2 +--R - 2880a +--R * +--R 4 2 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ 2 2 +--R (- 6912a b \|- 1 + 6912a b\|- 1 - 1152b - 9216a b - 1152a ) +--R * +--R 5 +--R cosh(x) sinh(x) +--R + +--R 3+---+2 3+---+ 2 2 +--R (- 1152a b \|- 1 + 1152a b\|- 1 - 192b - 1536a b - 192a ) +--R * +--R 6 +--R cosh(x) +--R * +--R 6 +--R tanh(x) +--R + +--R 2 12 2 11 +--R (- 3b - 3a b)sinh(x) + (- 36b - 36a b)cosh(x)sinh(x) +--R + +--R 2 2 2 10 +--R ((- 198b - 198a b)cosh(x) + 18b + 18a b)sinh(x) +--R + +--R 2 3 2 9 +--R ((- 660b - 660a b)cosh(x) + (180b + 180a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R (- 1485b - 1485a b)cosh(x) + (810b + 810a b)cosh(x) +--R + +--R 2 +--R - 45b - 45a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 2376b - 2376a b)cosh(x) + (2160b + 2160a b)cosh(x) +--R + +--R 2 +--R (- 360b - 360a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 2772b - 2772a b)cosh(x) + (3780b + 3780a b)cosh(x) +--R + +--R 2 2 2 2 +--R (- 1260b - 1260a b)cosh(x) + 60b + 252a b + 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (- 2376b - 2376a b)cosh(x) + (4536b + 4536a b)cosh(x) +--R + +--R 2 3 +--R (- 2520b - 2520a b)cosh(x) +--R + +--R 2 2 +--R (360b + 1512a b + 1152a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 8 2 6 +--R (- 1485b - 1485a b)cosh(x) + (3780b + 3780a b)cosh(x) +--R + +--R 2 4 +--R (- 3150b - 3150a b)cosh(x) +--R + +--R 2 2 2 2 +--R (900b + 3780a b + 2880a )cosh(x) - 45b - 45a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 9 2 7 +--R (- 660b - 660a b)cosh(x) + (2160b + 2160a b)cosh(x) +--R + +--R 2 5 +--R (- 2520b - 2520a b)cosh(x) +--R + +--R 2 2 3 2 +--R (1200b + 5040a b + 3840a )cosh(x) + (- 180b - 180a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 2 8 +--R (- 198b - 198a b)cosh(x) + (810b + 810a b)cosh(x) +--R + +--R 2 6 +--R (- 1260b - 1260a b)cosh(x) +--R + +--R 2 2 4 +--R (900b + 3780a b + 2880a )cosh(x) +--R + +--R 2 2 2 +--R (- 270b - 270a b)cosh(x) + 18b + 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 9 +--R (- 36b - 36a b)cosh(x) + (180b + 180a b)cosh(x) +--R + +--R 2 7 +--R (- 360b - 360a b)cosh(x) +--R + +--R 2 2 5 +--R (360b + 1512a b + 1152a )cosh(x) +--R + +--R 2 3 2 +--R (- 180b - 180a b)cosh(x) + (36b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 12 2 10 +--R (- 3b - 3a b)cosh(x) + (18b + 18a b)cosh(x) +--R + +--R 2 8 2 2 6 +--R (- 45b - 45a b)cosh(x) + (60b + 252a b + 192a )cosh(x) +--R + +--R 2 4 2 2 2 +--R (- 45b - 45a b)cosh(x) + (18b + 18a b)cosh(x) - 3b - 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 12 2 11 +--R (3b + 3a b)sinh(x) + (36b + 36a b)cosh(x)sinh(x) +--R + +--R 2 2 2 10 +--R ((198b + 198a b)cosh(x) - 18b - 18a b)sinh(x) +--R + +--R 2 3 2 9 +--R ((660b + 660a b)cosh(x) + (- 180b - 180a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (1485b + 1485a b)cosh(x) + (- 810b - 810a b)cosh(x) + 45b +--R + +--R 45a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (2376b + 2376a b)cosh(x) + (- 2160b - 2160a b)cosh(x) +--R + +--R 2 +--R (360b + 360a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (2772b + 2772a b)cosh(x) + (- 3780b - 3780a b)cosh(x) +--R + +--R 2 2 2 +--R (1260b + 1260a b)cosh(x) - 60b - 60a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (2376b + 2376a b)cosh(x) + (- 4536b - 4536a b)cosh(x) +--R + +--R 2 3 2 +--R (2520b + 2520a b)cosh(x) + (- 360b - 360a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 8 2 6 +--R (1485b + 1485a b)cosh(x) + (- 3780b - 3780a b)cosh(x) +--R + +--R 2 4 2 2 2 +--R (3150b + 3150a b)cosh(x) + (- 900b - 900a b)cosh(x) + 45b +--R + +--R 45a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 9 2 7 +--R (660b + 660a b)cosh(x) + (- 2160b - 2160a b)cosh(x) +--R + +--R 2 5 2 3 +--R (2520b + 2520a b)cosh(x) + (- 1200b - 1200a b)cosh(x) +--R + +--R 2 +--R (180b + 180a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 2 8 +--R (198b + 198a b)cosh(x) + (- 810b - 810a b)cosh(x) +--R + +--R 2 6 2 4 +--R (1260b + 1260a b)cosh(x) + (- 900b - 900a b)cosh(x) +--R + +--R 2 2 2 +--R (270b + 270a b)cosh(x) - 18b - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 9 +--R (36b + 36a b)cosh(x) + (- 180b - 180a b)cosh(x) +--R + +--R 2 7 2 5 +--R (360b + 360a b)cosh(x) + (- 360b - 360a b)cosh(x) +--R + +--R 2 3 2 +--R (180b + 180a b)cosh(x) + (- 36b - 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 12 2 10 +--R (3b + 3a b)cosh(x) + (- 18b - 18a b)cosh(x) +--R + +--R 2 8 2 6 +--R (45b + 45a b)cosh(x) + (- 60b - 60a b)cosh(x) +--R + +--R 2 4 2 2 2 +--R (45b + 45a b)cosh(x) + (- 18b - 18a b)cosh(x) + 3b + 3a b +--R * +--R 6+-+4 +--R \|a +--R + +--R 2 3+---+2 2 3+---+ 2 12 +--R (6b \|- 1 - 6b \|- 1 + 12b + 6a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 11 +--R (72b \|- 1 - 72b \|- 1 + 144b + 72a b)cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (396b \|- 1 - 396b \|- 1 + 792b + 396a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 36b \|- 1 + 36b \|- 1 - 72b - 36a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (1320b \|- 1 - 1320b \|- 1 + 2640b + 1320a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 360b \|- 1 + 360b \|- 1 - 720b - 360a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (2970b \|- 1 - 2970b \|- 1 + 5940b + 2970a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 1620b \|- 1 + 1620b \|- 1 - 3240b - 1620a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 90b \|- 1 - 90b \|- 1 + 180b + 90a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (4752b \|- 1 - 4752b \|- 1 + 9504b + 4752a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 4320b \|- 1 + 4320b \|- 1 - 8640b - 4320a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (720b \|- 1 - 720b \|- 1 + 1440b + 720a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (5544b \|- 1 - 5544b \|- 1 + 11088b + 5544a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 7560b \|- 1 + 7560b \|- 1 - 15120b - 7560a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (2520b \|- 1 - 2520b \|- 1 + 5040b + 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 120b - 384a b)\|- 1 + (120b + 384a b)\|- 1 - 240b +--R + +--R 2 +--R - 888a b - 384a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (4752b \|- 1 - 4752b \|- 1 + 9504b + 4752a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 9072b \|- 1 + 9072b \|- 1 - 18144b - 9072a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (5040b \|- 1 - 5040b \|- 1 + 10080b + 5040a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 720b - 2304a b)\|- 1 + (720b + 2304a b)\|- 1 +--R + +--R 2 2 +--R - 1440b - 5328a b - 2304a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (2970b \|- 1 - 2970b \|- 1 + 5940b + 2970a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 7560b \|- 1 + 7560b \|- 1 - 15120b - 7560a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (6300b \|- 1 - 6300b \|- 1 + 12600b + 6300a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 1800b - 5760a b)\|- 1 + (1800b + 5760a b)\|- 1 +--R + +--R 2 2 +--R - 3600b - 13320a b - 5760a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 90b \|- 1 - 90b \|- 1 + 180b + 90a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 9 +--R (1320b \|- 1 - 1320b \|- 1 + 2640b + 1320a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (- 4320b \|- 1 + 4320b \|- 1 - 8640b - 4320a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (5040b \|- 1 - 5040b \|- 1 + 10080b + 5040a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 2400b - 7680a b)\|- 1 + (2400b + 7680a b)\|- 1 +--R + +--R 2 2 +--R - 4800b - 17760a b - 7680a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (360b \|- 1 - 360b \|- 1 + 720b + 360a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 10 +--R (396b \|- 1 - 396b \|- 1 + 792b + 396a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (- 1620b \|- 1 + 1620b \|- 1 - 3240b - 1620a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (2520b \|- 1 - 2520b \|- 1 + 5040b + 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 1800b - 5760a b)\|- 1 + (1800b + 5760a b)\|- 1 +--R + +--R 2 2 +--R - 3600b - 13320a b - 5760a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (540b \|- 1 - 540b \|- 1 + 1080b + 540a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 36b \|- 1 + 36b \|- 1 - 72b - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 11 +--R (72b \|- 1 - 72b \|- 1 + 144b + 72a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 9 +--R (- 360b \|- 1 + 360b \|- 1 - 720b - 360a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (720b \|- 1 - 720b \|- 1 + 1440b + 720a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 720b - 2304a b)\|- 1 + (720b + 2304a b)\|- 1 +--R + +--R 2 2 +--R - 1440b - 5328a b - 2304a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (360b \|- 1 - 360b \|- 1 + 720b + 360a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 72b \|- 1 + 72b \|- 1 - 144b - 72a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 12 +--R (6b \|- 1 - 6b \|- 1 + 12b + 6a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 10 +--R (- 36b \|- 1 + 36b \|- 1 - 72b - 36a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (90b \|- 1 - 90b \|- 1 + 180b + 90a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 120b - 384a b)\|- 1 + (120b + 384a b)\|- 1 - 240b +--R + +--R 2 +--R - 888a b - 384a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (90b \|- 1 - 90b \|- 1 + 180b + 90a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (- 36b \|- 1 + 36b \|- 1 - 72b - 36a b)cosh(x) + 6b \|- 1 +--R + +--R 2 3+---+ 2 +--R - 6b \|- 1 + 12b + 6a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 12 +--R (- 6b \|- 1 + 6b \|- 1 - 12b - 6a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 11 +--R (- 72b \|- 1 + 72b \|- 1 - 144b - 72a b)cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 396b \|- 1 + 396b \|- 1 - 792b - 396a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 36b \|- 1 - 36b \|- 1 + 72b + 36a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 1320b \|- 1 + 1320b \|- 1 - 2640b - 1320a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (360b \|- 1 - 360b \|- 1 + 720b + 360a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 2970b \|- 1 + 2970b \|- 1 - 5940b - 2970a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (1620b \|- 1 - 1620b \|- 1 + 3240b + 1620a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 90b \|- 1 + 90b \|- 1 - 180b - 90a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 4752b \|- 1 + 4752b \|- 1 - 9504b - 4752a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (4320b \|- 1 - 4320b \|- 1 + 8640b + 4320a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 720b \|- 1 + 720b \|- 1 - 1440b - 720a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 5544b \|- 1 + 5544b \|- 1 - 11088b - 5544a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (7560b \|- 1 - 7560b \|- 1 + 15120b + 7560a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 2520b \|- 1 + 2520b \|- 1 - 5040b - 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (120b - 192a b)\|- 1 + (- 120b + 192a b)\|- 1 + 240b +--R + +--R 2 +--R - 264a b - 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (- 4752b \|- 1 + 4752b \|- 1 - 9504b - 4752a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (9072b \|- 1 - 9072b \|- 1 + 18144b + 9072a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 5040b \|- 1 + 5040b \|- 1 - 10080b - 5040a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (720b - 1152a b)\|- 1 + (- 720b + 1152a b)\|- 1 +--R + +--R 2 2 +--R 1440b - 1584a b - 1152a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (- 2970b \|- 1 + 2970b \|- 1 - 5940b - 2970a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (7560b \|- 1 - 7560b \|- 1 + 15120b + 7560a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 6300b \|- 1 + 6300b \|- 1 - 12600b - 6300a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1800b - 2880a b)\|- 1 + (- 1800b + 2880a b)\|- 1 +--R + +--R 2 2 +--R 3600b - 3960a b - 2880a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 90b \|- 1 + 90b \|- 1 - 180b - 90a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 9 +--R (- 1320b \|- 1 + 1320b \|- 1 - 2640b - 1320a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (4320b \|- 1 - 4320b \|- 1 + 8640b + 4320a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 5040b \|- 1 + 5040b \|- 1 - 10080b - 5040a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (2400b - 3840a b)\|- 1 + (- 2400b + 3840a b)\|- 1 +--R + +--R 2 2 +--R 4800b - 5280a b - 3840a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 360b \|- 1 + 360b \|- 1 - 720b - 360a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 10 +--R (- 396b \|- 1 + 396b \|- 1 - 792b - 396a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (1620b \|- 1 - 1620b \|- 1 + 3240b + 1620a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 2520b \|- 1 + 2520b \|- 1 - 5040b - 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1800b - 2880a b)\|- 1 + (- 1800b + 2880a b)\|- 1 +--R + +--R 2 2 +--R 3600b - 3960a b - 2880a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 540b \|- 1 + 540b \|- 1 - 1080b - 540a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 36b \|- 1 - 36b \|- 1 + 72b + 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 11 +--R (- 72b \|- 1 + 72b \|- 1 - 144b - 72a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 9 +--R (360b \|- 1 - 360b \|- 1 + 720b + 360a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (- 720b \|- 1 + 720b \|- 1 - 1440b - 720a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (720b - 1152a b)\|- 1 + (- 720b + 1152a b)\|- 1 +--R + +--R 2 2 +--R 1440b - 1584a b - 1152a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 360b \|- 1 + 360b \|- 1 - 720b - 360a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (72b \|- 1 - 72b \|- 1 + 144b + 72a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 12 +--R (- 6b \|- 1 + 6b \|- 1 - 12b - 6a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 10 +--R (36b \|- 1 - 36b \|- 1 + 72b + 36a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (- 90b \|- 1 + 90b \|- 1 - 180b - 90a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (120b - 192a b)\|- 1 + (- 120b + 192a b)\|- 1 + 240b +--R + +--R 2 +--R - 264a b - 192a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 90b \|- 1 + 90b \|- 1 - 180b - 90a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (36b \|- 1 - 36b \|- 1 + 72b + 36a b)cosh(x) - 6b \|- 1 +--R + +--R 2 3+---+ 2 +--R 6b \|- 1 - 12b - 6a b +--R * +--R 2 +--R tanh(x) +--R * +--R 3+-+6+-+2 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 12 +--R (- 9b \|- 1 + 9b \|- 1 - 12b - 3a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 11 +--R (- 108b \|- 1 + 108b \|- 1 - 144b - 36a b)cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 594b \|- 1 + 594b \|- 1 - 792b - 198a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 54b \|- 1 - 54b \|- 1 + 72b + 18a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 1980b \|- 1 + 1980b \|- 1 - 2640b - 660a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (540b \|- 1 - 540b \|- 1 + 720b + 180a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 4455b \|- 1 + 4455b \|- 1 - 5940b - 1485a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (2430b \|- 1 - 2430b \|- 1 + 3240b + 810a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 135b \|- 1 + 135b \|- 1 - 180b - 45a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 7128b \|- 1 + 7128b \|- 1 - 9504b - 2376a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (6480b \|- 1 - 6480b \|- 1 + 8640b + 2160a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 1080b \|- 1 + 1080b \|- 1 - 1440b - 360a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 8316b \|- 1 + 8316b \|- 1 - 11088b - 2772a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (11340b \|- 1 - 11340b \|- 1 + 15120b + 3780a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 3780b \|- 1 + 3780b \|- 1 - 5040b - 1260a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (180b + 576a b)\|- 1 + (- 180b - 576a b)\|- 1 + 240b +--R + +--R 2 +--R 828a b + 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (- 7128b \|- 1 + 7128b \|- 1 - 9504b - 2376a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (13608b \|- 1 - 13608b \|- 1 + 18144b + 4536a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 7560b \|- 1 + 7560b \|- 1 - 10080b - 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1080b + 3456a b)\|- 1 + (- 1080b - 3456a b)\|- 1 +--R + +--R 2 2 +--R 1440b + 4968a b + 1152a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (- 4455b \|- 1 + 4455b \|- 1 - 5940b - 1485a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (11340b \|- 1 - 11340b \|- 1 + 15120b + 3780a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 9450b \|- 1 + 9450b \|- 1 - 12600b - 3150a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (2700b + 8640a b)\|- 1 + (- 2700b - 8640a b)\|- 1 +--R + +--R 2 2 +--R 3600b + 12420a b + 2880a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 135b \|- 1 + 135b \|- 1 - 180b - 45a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 9 +--R (- 1980b \|- 1 + 1980b \|- 1 - 2640b - 660a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (6480b \|- 1 - 6480b \|- 1 + 8640b + 2160a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (- 7560b \|- 1 + 7560b \|- 1 - 10080b - 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (3600b + 11520a b)\|- 1 + (- 3600b - 11520a b)\|- 1 +--R + +--R 2 2 +--R 4800b + 16560a b + 3840a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 540b \|- 1 + 540b \|- 1 - 720b - 180a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 10 +--R (- 594b \|- 1 + 594b \|- 1 - 792b - 198a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (2430b \|- 1 - 2430b \|- 1 + 3240b + 810a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 3780b \|- 1 + 3780b \|- 1 - 5040b - 1260a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (2700b + 8640a b)\|- 1 + (- 2700b - 8640a b)\|- 1 +--R + +--R 2 2 +--R 3600b + 12420a b + 2880a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 810b \|- 1 + 810b \|- 1 - 1080b - 270a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 54b \|- 1 - 54b \|- 1 + 72b + 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 11 +--R (- 108b \|- 1 + 108b \|- 1 - 144b - 36a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 9 +--R (540b \|- 1 - 540b \|- 1 + 720b + 180a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (- 1080b \|- 1 + 1080b \|- 1 - 1440b - 360a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1080b + 3456a b)\|- 1 + (- 1080b - 3456a b)\|- 1 +--R + +--R 2 2 +--R 1440b + 4968a b + 1152a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 540b \|- 1 + 540b \|- 1 - 720b - 180a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (108b \|- 1 - 108b \|- 1 + 144b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 12 +--R (- 9b \|- 1 + 9b \|- 1 - 12b - 3a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 10 +--R (54b \|- 1 - 54b \|- 1 + 72b + 18a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (- 135b \|- 1 + 135b \|- 1 - 180b - 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (180b + 576a b)\|- 1 + (- 180b - 576a b)\|- 1 + 240b +--R + +--R 2 +--R 828a b + 192a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (- 135b \|- 1 + 135b \|- 1 - 180b - 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (54b \|- 1 - 54b \|- 1 + 72b + 18a b)cosh(x) - 9b \|- 1 +--R + +--R 2 3+---+ 2 +--R 9b \|- 1 - 12b - 3a b +--R * +--R 6 +--R tanh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 12 +--R (9b \|- 1 - 9b \|- 1 + 12b + 3a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 11 +--R (108b \|- 1 - 108b \|- 1 + 144b + 36a b)cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (594b \|- 1 - 594b \|- 1 + 792b + 198a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 54b \|- 1 + 54b \|- 1 - 72b - 18a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (1980b \|- 1 - 1980b \|- 1 + 2640b + 660a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 540b \|- 1 + 540b \|- 1 - 720b - 180a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (4455b \|- 1 - 4455b \|- 1 + 5940b + 1485a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 2430b \|- 1 + 2430b \|- 1 - 3240b - 810a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 135b \|- 1 - 135b \|- 1 + 180b + 45a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (7128b \|- 1 - 7128b \|- 1 + 9504b + 2376a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (- 6480b \|- 1 + 6480b \|- 1 - 8640b - 2160a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (1080b \|- 1 - 1080b \|- 1 + 1440b + 360a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (8316b \|- 1 - 8316b \|- 1 + 11088b + 2772a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 11340b \|- 1 + 11340b \|- 1 - 15120b - 3780a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (3780b \|- 1 - 3780b \|- 1 + 5040b + 1260a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 180b + 1152a b)\|- 1 + (180b - 1152a b)\|- 1 - 240b +--R + +--R 2 +--R 1476a b + 384a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (7128b \|- 1 - 7128b \|- 1 + 9504b + 2376a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 13608b \|- 1 + 13608b \|- 1 - 18144b - 4536a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (7560b \|- 1 - 7560b \|- 1 + 10080b + 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 1080b + 6912a b)\|- 1 + (1080b - 6912a b)\|- 1 +--R + +--R 2 2 +--R - 1440b + 8856a b + 2304a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (4455b \|- 1 - 4455b \|- 1 + 5940b + 1485a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 11340b \|- 1 + 11340b \|- 1 - 15120b - 3780a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (9450b \|- 1 - 9450b \|- 1 + 12600b + 3150a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 2700b + 17280a b)\|- 1 + (2700b - 17280a b)\|- 1 +--R + +--R 2 2 +--R - 3600b + 22140a b + 5760a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R 135b \|- 1 - 135b \|- 1 + 180b + 45a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 9 +--R (1980b \|- 1 - 1980b \|- 1 + 2640b + 660a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (- 6480b \|- 1 + 6480b \|- 1 - 8640b - 2160a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 5 +--R (7560b \|- 1 - 7560b \|- 1 + 10080b + 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 3600b + 23040a b)\|- 1 + (3600b - 23040a b)\|- 1 +--R + +--R 2 2 +--R - 4800b + 29520a b + 7680a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (540b \|- 1 - 540b \|- 1 + 720b + 180a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 10 +--R (594b \|- 1 - 594b \|- 1 + 792b + 198a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (- 2430b \|- 1 + 2430b \|- 1 - 3240b - 810a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (3780b \|- 1 - 3780b \|- 1 + 5040b + 1260a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 2700b + 17280a b)\|- 1 + (2700b - 17280a b)\|- 1 +--R + +--R 2 2 +--R - 3600b + 22140a b + 5760a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (810b \|- 1 - 810b \|- 1 + 1080b + 270a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R - 54b \|- 1 + 54b \|- 1 - 72b - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 11 +--R (108b \|- 1 - 108b \|- 1 + 144b + 36a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 9 +--R (- 540b \|- 1 + 540b \|- 1 - 720b - 180a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 7 +--R (1080b \|- 1 - 1080b \|- 1 + 1440b + 360a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 1080b + 6912a b)\|- 1 + (1080b - 6912a b)\|- 1 +--R + +--R 2 2 +--R - 1440b + 8856a b + 2304a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 +--R (540b \|- 1 - 540b \|- 1 + 720b + 180a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 108b \|- 1 + 108b \|- 1 - 144b - 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 12 +--R (9b \|- 1 - 9b \|- 1 + 12b + 3a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 10 +--R (- 54b \|- 1 + 54b \|- 1 - 72b - 18a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 8 +--R (135b \|- 1 - 135b \|- 1 + 180b + 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 180b + 1152a b)\|- 1 + (180b - 1152a b)\|- 1 - 240b +--R + +--R 2 +--R 1476a b + 384a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 +--R (135b \|- 1 - 135b \|- 1 + 180b + 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 3+---+2 +--R (- 54b \|- 1 + 54b \|- 1 - 72b - 18a b)cosh(x) + 9b \|- 1 +--R + +--R 2 3+---+ 2 +--R - 9b \|- 1 + 12b + 3a b +--R * +--R 4 +--R tanh(x) +--R * +--R 3+-+2 +--R \|a +--R / +--R 2 3+---+2 2 3+---+ 2 +--R (6b + 15a b)\|- 1 + (- 6b - 15a b)\|- 1 + 6b +--R + +--R 15a b +--R * +--R 12 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (72b + 180a b)\|- 1 + (- 72b - 180a b)\|- 1 + 72b +--R + +--R 180a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (396b + 990a b)\|- 1 + (- 396b - 990a b)\|- 1 +--R + +--R 2 +--R 396b + 990a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 36b - 90a b)\|- 1 + (36b + 90a b)\|- 1 - 36b +--R + +--R - 90a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (1320b + 3300a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 1320b - 3300a b)\|- 1 + 1320b + 3300a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 360b - 900a b)\|- 1 + (360b + 900a b)\|- 1 +--R + +--R 2 +--R - 360b - 900a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (2970b + 7425a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 2970b - 7425a b)\|- 1 + 2970b + 7425a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 1620b - 4050a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (1620b + 4050a b)\|- 1 - 1620b - 4050a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (90b + 225a b)\|- 1 + (- 90b - 225a b)\|- 1 + 90b +--R + +--R 225a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (4752b + 11880a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 4752b - 11880a b)\|- 1 + 4752b + 11880a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 4320b - 10800a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (4320b + 10800a b)\|- 1 - 4320b - 10800a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (720b + 1800a b)\|- 1 + (- 720b - 1800a b)\|- 1 +--R + +--R 2 +--R 720b + 1800a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (5544b + 13860a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 5544b - 13860a b)\|- 1 + 5544b + 13860a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 7560b - 18900a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (7560b + 18900a b)\|- 1 - 7560b - 18900a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (2520b + 6300a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 2520b - 6300a b)\|- 1 + 2520b + 6300a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 120b - 684a b - 960a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (120b + 684a b + 960a )\|- 1 - 120b - 684a b - 960a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (4752b + 11880a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 4752b - 11880a b)\|- 1 + 4752b + 11880a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 9072b - 22680a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (9072b + 22680a b)\|- 1 - 9072b - 22680a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (5040b + 12600a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 5040b - 12600a b)\|- 1 + 5040b + 12600a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 720b - 4104a b - 5760a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (720b + 4104a b + 5760a )\|- 1 - 720b - 4104a b +--R + +--R 2 +--R - 5760a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (2970b + 7425a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 2970b - 7425a b)\|- 1 + 2970b + 7425a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 7560b - 18900a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (7560b + 18900a b)\|- 1 - 7560b - 18900a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (6300b + 15750a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 6300b - 15750a b)\|- 1 + 6300b + 15750a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1800b - 10260a b - 14400a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (1800b + 10260a b + 14400a )\|- 1 - 1800b +--R + +--R 2 +--R - 10260a b - 14400a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (90b + 225a b)\|- 1 + (- 90b - 225a b)\|- 1 + 90b +--R + +--R 225a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (1320b + 3300a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 1320b - 3300a b)\|- 1 + 1320b + 3300a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 4320b - 10800a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (4320b + 10800a b)\|- 1 - 4320b - 10800a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (5040b + 12600a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 5040b - 12600a b)\|- 1 + 5040b + 12600a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 2400b - 13680a b - 19200a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (2400b + 13680a b + 19200a )\|- 1 - 2400b +--R + +--R 2 +--R - 13680a b - 19200a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (360b + 900a b)\|- 1 + (- 360b - 900a b)\|- 1 +--R + +--R 2 +--R 360b + 900a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (396b + 990a b)\|- 1 + (- 396b - 990a b)\|- 1 +--R + +--R 2 +--R 396b + 990a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 1620b - 4050a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (1620b + 4050a b)\|- 1 - 1620b - 4050a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (2520b + 6300a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 2520b - 6300a b)\|- 1 + 2520b + 6300a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1800b - 10260a b - 14400a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (1800b + 10260a b + 14400a )\|- 1 - 1800b +--R + +--R 2 +--R - 10260a b - 14400a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (540b + 1350a b)\|- 1 + (- 540b - 1350a b)\|- 1 +--R + +--R 2 +--R 540b + 1350a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 36b - 90a b)\|- 1 + (36b + 90a b)\|- 1 - 36b +--R + +--R - 90a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (72b + 180a b)\|- 1 + (- 72b - 180a b)\|- 1 +--R + +--R 2 +--R 72b + 180a b +--R * +--R 11 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 360b - 900a b)\|- 1 + (360b + 900a b)\|- 1 +--R + +--R 2 +--R - 360b - 900a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (720b + 1800a b)\|- 1 + (- 720b - 1800a b)\|- 1 +--R + +--R 2 +--R 720b + 1800a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 720b - 4104a b - 5760a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (720b + 4104a b + 5760a )\|- 1 - 720b - 4104a b +--R + +--R 2 +--R - 5760a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (360b + 900a b)\|- 1 + (- 360b - 900a b)\|- 1 +--R + +--R 2 +--R 360b + 900a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 72b - 180a b)\|- 1 + (72b + 180a b)\|- 1 +--R + +--R 2 +--R - 72b - 180a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (6b + 15a b)\|- 1 + (- 6b - 15a b)\|- 1 + 6b +--R + +--R 15a b +--R * +--R 12 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 36b - 90a b)\|- 1 + (36b + 90a b)\|- 1 - 36b +--R + +--R - 90a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (90b + 225a b)\|- 1 + (- 90b - 225a b)\|- 1 + 90b +--R + +--R 225a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 120b - 684a b - 960a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (120b + 684a b + 960a )\|- 1 - 120b - 684a b - 960a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (90b + 225a b)\|- 1 + (- 90b - 225a b)\|- 1 + 90b +--R + +--R 225a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 36b - 90a b)\|- 1 + (36b + 90a b)\|- 1 - 36b +--R + +--R - 90a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (6b + 15a b)\|- 1 + (- 6b - 15a b)\|- 1 + 6b + 15a b +--R * +--R 6 +--R tanh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 198a b \|- 1 + 198a b\|- 1 - 198a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 18a b \|- 1 - 18a b\|- 1 + 18a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 660a b \|- 1 + 660a b\|- 1 - 660a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (180a b \|- 1 - 180a b\|- 1 + 180a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 1485a b \|- 1 + 1485a b\|- 1 - 1485a b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (810a b \|- 1 - 810a b\|- 1 + 810a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 45a b \|- 1 + 45a b\|- 1 - 45a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 2376a b \|- 1 + 2376a b\|- 1 - 2376a b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (2160a b \|- 1 - 2160a b\|- 1 + 2160a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 360a b \|- 1 + 360a b\|- 1 - 360a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 2772a b \|- 1 + 2772a b\|- 1 - 2772a b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (3780a b \|- 1 - 3780a b\|- 1 + 3780a b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 1260a b \|- 1 + 1260a b\|- 1 - 1260a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (60a b + 192a )\|- 1 + (- 60a b - 192a )\|- 1 + 60a b +--R + +--R 2 +--R 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 2376a b \|- 1 + 2376a b\|- 1 - 2376a b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (4536a b \|- 1 - 4536a b\|- 1 + 4536a b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 2520a b \|- 1 + 2520a b\|- 1 - 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (360a b + 1152a )\|- 1 + (- 360a b - 1152a )\|- 1 +--R + +--R 2 +--R 360a b + 1152a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 1485a b \|- 1 + 1485a b\|- 1 - 1485a b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (3780a b \|- 1 - 3780a b\|- 1 + 3780a b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 3150a b \|- 1 + 3150a b\|- 1 - 3150a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (900a b + 2880a )\|- 1 + (- 900a b - 2880a )\|- 1 +--R + +--R 2 +--R 900a b + 2880a +--R * +--R 2 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 45a b \|- 1 + 45a b\|- 1 - 45a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (- 660a b \|- 1 + 660a b\|- 1 - 660a b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (2160a b \|- 1 - 2160a b\|- 1 + 2160a b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 2520a b \|- 1 + 2520a b\|- 1 - 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1200a b + 3840a )\|- 1 + (- 1200a b - 3840a )\|- 1 +--R + +--R 2 +--R 1200a b + 3840a +--R * +--R 3 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 180a b \|- 1 + 180a b\|- 1 - 180a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (- 198a b \|- 1 + 198a b\|- 1 - 198a b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (810a b \|- 1 - 810a b\|- 1 + 810a b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 1260a b \|- 1 + 1260a b\|- 1 - 1260a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (900a b + 2880a )\|- 1 + (- 900a b - 2880a )\|- 1 +--R + +--R 2 +--R 900a b + 2880a +--R * +--R 4 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 270a b \|- 1 + 270a b\|- 1 - 270a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 18a b \|- 1 - 18a b\|- 1 + 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (180a b \|- 1 - 180a b\|- 1 + 180a b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 360a b \|- 1 + 360a b\|- 1 - 360a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (360a b + 1152a )\|- 1 + (- 360a b - 1152a )\|- 1 +--R + +--R 2 +--R 360a b + 1152a +--R * +--R 5 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 180a b \|- 1 + 180a b\|- 1 - 180a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (36a b \|- 1 - 36a b\|- 1 + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cosh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (60a b + 192a )\|- 1 + (- 60a b - 192a )\|- 1 + 60a b +--R + +--R 2 +--R 192a +--R * +--R 6 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) - 3a b \|- 1 +--R + +--R 3+---+ +--R 3a b\|- 1 - 3a b +--R * +--R 3+-+6+-+4 +--R \|a \|a +--R + +--R 3+---+2 3+---+ 12 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (216a b \|- 1 - 216a b\|- 1 + 216a b)cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (1188a b \|- 1 - 1188a b\|- 1 + 1188a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 108a b \|- 1 + 108a b\|- 1 - 108a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (3960a b \|- 1 - 3960a b\|- 1 + 3960a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 1080a b \|- 1 + 1080a b\|- 1 - 1080a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (8910a b \|- 1 - 8910a b\|- 1 + 8910a b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 4860a b \|- 1 + 4860a b\|- 1 - 4860a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 270a b \|- 1 - 270a b\|- 1 + 270a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (14256a b \|- 1 - 14256a b\|- 1 + 14256a b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 12960a b \|- 1 + 12960a b\|- 1 - 12960a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (2160a b \|- 1 - 2160a b\|- 1 + 2160a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (16632a b \|- 1 - 16632a b\|- 1 + 16632a b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 22680a b \|- 1 + 22680a b\|- 1 - 22680a b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (7560a b \|- 1 - 7560a b\|- 1 + 7560a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 360a b - 1152a )\|- 1 + (360a b + 1152a )\|- 1 - 360a b +--R + +--R 2 +--R - 1152a +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (14256a b \|- 1 - 14256a b\|- 1 + 14256a b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 27216a b \|- 1 + 27216a b\|- 1 - 27216a b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (15120a b \|- 1 - 15120a b\|- 1 + 15120a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 2160a b - 6912a )\|- 1 + (2160a b + 6912a )\|- 1 +--R + +--R 2 +--R - 2160a b - 6912a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (8910a b \|- 1 - 8910a b\|- 1 + 8910a b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 22680a b \|- 1 + 22680a b\|- 1 - 22680a b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (18900a b \|- 1 - 18900a b\|- 1 + 18900a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 5400a b - 17280a )\|- 1 + (5400a b + 17280a )\|- 1 +--R + +--R 2 +--R - 5400a b - 17280a +--R * +--R 2 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R 270a b \|- 1 - 270a b\|- 1 + 270a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (3960a b \|- 1 - 3960a b\|- 1 + 3960a b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 12960a b \|- 1 + 12960a b\|- 1 - 12960a b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (15120a b \|- 1 - 15120a b\|- 1 + 15120a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 7200a b - 23040a )\|- 1 + (7200a b + 23040a )\|- 1 +--R + +--R 2 +--R - 7200a b - 23040a +--R * +--R 3 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R (1080a b \|- 1 - 1080a b\|- 1 + 1080a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (1188a b \|- 1 - 1188a b\|- 1 + 1188a b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 4860a b \|- 1 + 4860a b\|- 1 - 4860a b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (7560a b \|- 1 - 7560a b\|- 1 + 7560a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 5400a b - 17280a )\|- 1 + (5400a b + 17280a )\|- 1 +--R + +--R 2 +--R - 5400a b - 17280a +--R * +--R 4 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (1620a b \|- 1 - 1620a b\|- 1 + 1620a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 108a b \|- 1 + 108a b\|- 1 - 108a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (216a b \|- 1 - 216a b\|- 1 + 216a b)cosh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (- 1080a b \|- 1 + 1080a b\|- 1 - 1080a b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (2160a b \|- 1 - 2160a b\|- 1 + 2160a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 2160a b - 6912a )\|- 1 + (2160a b + 6912a )\|- 1 +--R + +--R 2 +--R - 2160a b - 6912a +--R * +--R 5 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (1080a b \|- 1 - 1080a b\|- 1 + 1080a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 216a b \|- 1 + 216a b\|- 1 - 216a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (270a b \|- 1 - 270a b\|- 1 + 270a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 360a b - 1152a )\|- 1 + (360a b + 1152a )\|- 1 - 360a b +--R + +--R 2 +--R - 1152a +--R * +--R 6 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (270a b \|- 1 - 270a b\|- 1 + 270a b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 108a b \|- 1 + 108a b\|- 1 - 108a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 18a b \|- 1 - 18a b\|- 1 + 18a b +--R * +--R 2 3+-+2 6+-+2 +--R tanh(x) \|a \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 3a b - 30a b)\|- 1 + (3a b + 30a b)\|- 1 - 3a b +--R + +--R 2 +--R - 30a b +--R * +--R 12 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 36a b - 360a b)\|- 1 + (36a b + 360a b)\|- 1 - 36a b +--R + +--R 2 +--R - 360a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 198a b - 1980a b)\|- 1 + (198a b + 1980a b)\|- 1 +--R + +--R 2 2 +--R - 198a b - 1980a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (18a b + 180a b)\|- 1 + (- 18a b - 180a b)\|- 1 + 18a b +--R + +--R 2 +--R 180a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 660a b - 6600a b)\|- 1 + (660a b + 6600a b)\|- 1 +--R + +--R 2 2 +--R - 660a b - 6600a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (180a b + 1800a b)\|- 1 + (- 180a b - 1800a b)\|- 1 +--R + +--R 2 2 +--R 180a b + 1800a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 1485a b - 14850a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (1485a b + 14850a b)\|- 1 - 1485a b - 14850a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (810a b + 8100a b)\|- 1 + (- 810a b - 8100a b)\|- 1 +--R + +--R 2 2 +--R 810a b + 8100a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 45a b - 450a b)\|- 1 + (45a b + 450a b)\|- 1 - 45a b +--R + +--R 2 +--R - 450a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 2376a b - 23760a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (2376a b + 23760a b)\|- 1 - 2376a b - 23760a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (2160a b + 21600a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 2160a b - 21600a b)\|- 1 + 2160a b + 21600a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 360a b - 3600a b)\|- 1 + (360a b + 3600a b)\|- 1 +--R + +--R 2 2 +--R - 360a b - 3600a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 2772a b - 27720a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (2772a b + 27720a b)\|- 1 - 2772a b - 27720a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (3780a b + 37800a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 3780a b - 37800a b)\|- 1 + 3780a b + 37800a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1260a b - 12600a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (1260a b + 12600a b)\|- 1 - 1260a b - 12600a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (60a b + 792a b + 1920a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 60a b - 792a b - 1920a )\|- 1 + 60a b + 792a b + 1920a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 2376a b - 23760a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (2376a b + 23760a b)\|- 1 - 2376a b - 23760a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (4536a b + 45360a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 4536a b - 45360a b)\|- 1 + 4536a b + 45360a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 2520a b - 25200a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (2520a b + 25200a b)\|- 1 - 2520a b - 25200a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (360a b + 4752a b + 11520a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 +--R (- 360a b - 4752a b - 11520a )\|- 1 + 360a b + 4752a b +--R + +--R 3 +--R 11520a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 1485a b - 14850a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (1485a b + 14850a b)\|- 1 - 1485a b - 14850a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (3780a b + 37800a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 3780a b - 37800a b)\|- 1 + 3780a b + 37800a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 3150a b - 31500a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (3150a b + 31500a b)\|- 1 - 3150a b - 31500a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (900a b + 11880a b + 28800a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 +--R (- 900a b - 11880a b - 28800a )\|- 1 + 900a b +--R + +--R 2 3 +--R 11880a b + 28800a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 45a b - 450a b)\|- 1 + (45a b + 450a b)\|- 1 - 45a b +--R + +--R 2 +--R - 450a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 660a b - 6600a b)\|- 1 + (660a b + 6600a b)\|- 1 +--R + +--R 2 2 +--R - 660a b - 6600a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (2160a b + 21600a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 2160a b - 21600a b)\|- 1 + 2160a b + 21600a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 2520a b - 25200a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (2520a b + 25200a b)\|- 1 - 2520a b - 25200a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (1200a b + 15840a b + 38400a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 +--R (- 1200a b - 15840a b - 38400a )\|- 1 + 1200a b +--R + +--R 2 3 +--R 15840a b + 38400a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 180a b - 1800a b)\|- 1 + (180a b + 1800a b)\|- 1 +--R + +--R 2 2 +--R - 180a b - 1800a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 198a b - 1980a b)\|- 1 + (198a b + 1980a b)\|- 1 +--R + +--R 2 2 +--R - 198a b - 1980a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (810a b + 8100a b)\|- 1 + (- 810a b - 8100a b)\|- 1 +--R + +--R 2 2 +--R 810a b + 8100a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1260a b - 12600a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (1260a b + 12600a b)\|- 1 - 1260a b - 12600a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (900a b + 11880a b + 28800a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 +--R (- 900a b - 11880a b - 28800a )\|- 1 + 900a b +--R + +--R 2 3 +--R 11880a b + 28800a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 270a b - 2700a b)\|- 1 + (270a b + 2700a b)\|- 1 +--R + +--R 2 2 +--R - 270a b - 2700a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (18a b + 180a b)\|- 1 + (- 18a b - 180a b)\|- 1 + 18a b +--R + +--R 2 +--R 180a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 36a b - 360a b)\|- 1 + (36a b + 360a b)\|- 1 +--R + +--R 2 2 +--R - 36a b - 360a b +--R * +--R 11 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (180a b + 1800a b)\|- 1 + (- 180a b - 1800a b)\|- 1 +--R + +--R 2 2 +--R 180a b + 1800a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 360a b - 3600a b)\|- 1 + (360a b + 3600a b)\|- 1 +--R + +--R 2 2 +--R - 360a b - 3600a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (360a b + 4752a b + 11520a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 +--R (- 360a b - 4752a b - 11520a )\|- 1 + 360a b + 4752a b +--R + +--R 3 +--R 11520a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 180a b - 1800a b)\|- 1 + (180a b + 1800a b)\|- 1 +--R + +--R 2 2 +--R - 180a b - 1800a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (36a b + 360a b)\|- 1 + (- 36a b - 360a b)\|- 1 +--R + +--R 2 2 +--R 36a b + 360a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 3a b - 30a b)\|- 1 + (3a b + 30a b)\|- 1 - 3a b +--R + +--R 2 +--R - 30a b +--R * +--R 12 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (18a b + 180a b)\|- 1 + (- 18a b - 180a b)\|- 1 + 18a b +--R + +--R 2 +--R 180a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 45a b - 450a b)\|- 1 + (45a b + 450a b)\|- 1 - 45a b +--R + +--R 2 +--R - 450a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (60a b + 792a b + 1920a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 60a b - 792a b - 1920a )\|- 1 + 60a b + 792a b + 1920a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 45a b - 450a b)\|- 1 + (45a b + 450a b)\|- 1 - 45a b +--R + +--R 2 +--R - 450a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (18a b + 180a b)\|- 1 + (- 18a b - 180a b)\|- 1 + 18a b +--R + +--R 2 +--R 180a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 3a b - 30a b)\|- 1 + (3a b + 30a b)\|- 1 - 3a b - 30a b +--R * +--R 4 +--R tanh(x) +--R * +--R 3+-+2 +--R \|b +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (15b + 6a b)\|- 1 + (- 15b - 6a b)\|- 1 + 15b +--R + +--R 6a b +--R * +--R 12 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (180b + 72a b)\|- 1 + (- 180b - 72a b)\|- 1 + 180b +--R + +--R 72a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (990b + 396a b)\|- 1 + (- 990b - 396a b)\|- 1 +--R + +--R 2 +--R 990b + 396a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 90b - 36a b)\|- 1 + (90b + 36a b)\|- 1 - 90b +--R + +--R - 36a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (3300b + 1320a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 3300b - 1320a b)\|- 1 + 3300b + 1320a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 900b - 360a b)\|- 1 + (900b + 360a b)\|- 1 +--R + +--R 2 +--R - 900b - 360a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (7425b + 2970a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 7425b - 2970a b)\|- 1 + 7425b + 2970a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 4050b - 1620a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (4050b + 1620a b)\|- 1 - 4050b - 1620a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (225b + 90a b)\|- 1 + (- 225b - 90a b)\|- 1 + 225b +--R + +--R 90a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (11880b + 4752a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 11880b - 4752a b)\|- 1 + 11880b + 4752a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 10800b - 4320a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (10800b + 4320a b)\|- 1 - 10800b - 4320a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1800b + 720a b)\|- 1 + (- 1800b - 720a b)\|- 1 +--R + +--R 2 +--R 1800b + 720a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (13860b + 5544a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 13860b - 5544a b)\|- 1 + 13860b + 5544a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 18900b - 7560a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (18900b + 7560a b)\|- 1 - 18900b - 7560a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (6300b + 2520a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 6300b - 2520a b)\|- 1 + 6300b + 2520a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 300b - 1080a b - 384a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (300b + 1080a b + 384a )\|- 1 - 300b - 1080a b - 384a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (11880b + 4752a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 11880b - 4752a b)\|- 1 + 11880b + 4752a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 22680b - 9072a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (22680b + 9072a b)\|- 1 - 22680b - 9072a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (12600b + 5040a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 12600b - 5040a b)\|- 1 + 12600b + 5040a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1800b - 6480a b - 2304a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (1800b + 6480a b + 2304a )\|- 1 - 1800b - 6480a b +--R + +--R 2 +--R - 2304a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (7425b + 2970a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 7425b - 2970a b)\|- 1 + 7425b + 2970a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 18900b - 7560a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (18900b + 7560a b)\|- 1 - 18900b - 7560a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (15750b + 6300a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 15750b - 6300a b)\|- 1 + 15750b + 6300a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 4500b - 16200a b - 5760a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (4500b + 16200a b + 5760a )\|- 1 - 4500b +--R + +--R 2 +--R - 16200a b - 5760a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (225b + 90a b)\|- 1 + (- 225b - 90a b)\|- 1 + 225b +--R + +--R 90a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 +--R (3300b + 1320a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 3300b - 1320a b)\|- 1 + 3300b + 1320a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 10800b - 4320a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (10800b + 4320a b)\|- 1 - 10800b - 4320a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (12600b + 5040a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 12600b - 5040a b)\|- 1 + 12600b + 5040a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 6000b - 21600a b - 7680a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (6000b + 21600a b + 7680a )\|- 1 - 6000b +--R + +--R 2 +--R - 21600a b - 7680a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (900b + 360a b)\|- 1 + (- 900b - 360a b)\|- 1 +--R + +--R 2 +--R 900b + 360a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (990b + 396a b)\|- 1 + (- 990b - 396a b)\|- 1 +--R + +--R 2 +--R 990b + 396a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (- 4050b - 1620a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (4050b + 1620a b)\|- 1 - 4050b - 1620a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 +--R (6300b + 2520a b)\|- 1 +--R + +--R 2 3+---+ 2 +--R (- 6300b - 2520a b)\|- 1 + 6300b + 2520a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 4500b - 16200a b - 5760a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (4500b + 16200a b + 5760a )\|- 1 - 4500b +--R + +--R 2 +--R - 16200a b - 5760a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1350b + 540a b)\|- 1 + (- 1350b - 540a b)\|- 1 +--R + +--R 2 +--R 1350b + 540a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 90b - 36a b)\|- 1 + (90b + 36a b)\|- 1 - 90b +--R + +--R - 36a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (180b + 72a b)\|- 1 + (- 180b - 72a b)\|- 1 +--R + +--R 2 +--R 180b + 72a b +--R * +--R 11 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 900b - 360a b)\|- 1 + (900b + 360a b)\|- 1 +--R + +--R 2 +--R - 900b - 360a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1800b + 720a b)\|- 1 + (- 1800b - 720a b)\|- 1 +--R + +--R 2 +--R 1800b + 720a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1800b - 6480a b - 2304a )\|- 1 +--R + +--R 2 2 3+---+ 2 +--R (1800b + 6480a b + 2304a )\|- 1 - 1800b - 6480a b +--R + +--R 2 +--R - 2304a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (900b + 360a b)\|- 1 + (- 900b - 360a b)\|- 1 +--R + +--R 2 +--R 900b + 360a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 180b - 72a b)\|- 1 + (180b + 72a b)\|- 1 +--R + +--R 2 +--R - 180b - 72a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (15b + 6a b)\|- 1 + (- 15b - 6a b)\|- 1 + 15b +--R + +--R 6a b +--R * +--R 12 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 90b - 36a b)\|- 1 + (90b + 36a b)\|- 1 - 90b +--R + +--R - 36a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (225b + 90a b)\|- 1 + (- 225b - 90a b)\|- 1 + 225b +--R + +--R 90a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 300b - 1080a b - 384a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (300b + 1080a b + 384a )\|- 1 - 300b - 1080a b - 384a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (225b + 90a b)\|- 1 + (- 225b - 90a b)\|- 1 + 225b +--R + +--R 90a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 90b - 36a b)\|- 1 + (90b + 36a b)\|- 1 - 90b +--R + +--R - 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (15b + 6a b)\|- 1 + (- 15b - 6a b)\|- 1 + 15b + 6a b +--R * +--R 6 +--R tanh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x)sinh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 198a b \|- 1 + 198a b\|- 1 - 198a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 18a b \|- 1 - 18a b\|- 1 + 18a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 660a b \|- 1 + 660a b\|- 1 - 660a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (180a b \|- 1 - 180a b\|- 1 + 180a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 1485a b \|- 1 + 1485a b\|- 1 - 1485a b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (810a b \|- 1 - 810a b\|- 1 + 810a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 45a b \|- 1 + 45a b\|- 1 - 45a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 2376a b \|- 1 + 2376a b\|- 1 - 2376a b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (2160a b \|- 1 - 2160a b\|- 1 + 2160a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 360a b \|- 1 + 360a b\|- 1 - 360a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 2772a b \|- 1 + 2772a b\|- 1 - 2772a b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (3780a b \|- 1 - 3780a b\|- 1 + 3780a b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 1260a b \|- 1 + 1260a b\|- 1 - 1260a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (60a b + 192a )\|- 1 + (- 60a b - 192a )\|- 1 + 60a b +--R + +--R 2 +--R 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 2376a b \|- 1 + 2376a b\|- 1 - 2376a b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (4536a b \|- 1 - 4536a b\|- 1 + 4536a b)cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 2520a b \|- 1 + 2520a b\|- 1 - 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (360a b + 1152a )\|- 1 + (- 360a b - 1152a )\|- 1 +--R + +--R 2 +--R 360a b + 1152a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 1485a b \|- 1 + 1485a b\|- 1 - 1485a b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (3780a b \|- 1 - 3780a b\|- 1 + 3780a b)cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 3150a b \|- 1 + 3150a b\|- 1 - 3150a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (900a b + 2880a )\|- 1 + (- 900a b - 2880a )\|- 1 +--R + +--R 2 +--R 900a b + 2880a +--R * +--R 2 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R - 45a b \|- 1 + 45a b\|- 1 - 45a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (- 660a b \|- 1 + 660a b\|- 1 - 660a b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (2160a b \|- 1 - 2160a b\|- 1 + 2160a b)cosh(x) +--R + +--R 3+---+2 3+---+ 5 +--R (- 2520a b \|- 1 + 2520a b\|- 1 - 2520a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (1200a b + 3840a )\|- 1 + (- 1200a b - 3840a )\|- 1 +--R + +--R 2 +--R 1200a b + 3840a +--R * +--R 3 +--R cosh(x) +--R + +--R 3+---+2 3+---+ +--R (- 180a b \|- 1 + 180a b\|- 1 - 180a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (- 198a b \|- 1 + 198a b\|- 1 - 198a b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (810a b \|- 1 - 810a b\|- 1 + 810a b)cosh(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 1260a b \|- 1 + 1260a b\|- 1 - 1260a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (900a b + 2880a )\|- 1 + (- 900a b - 2880a )\|- 1 +--R + +--R 2 +--R 900a b + 2880a +--R * +--R 4 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 2 +--R (- 270a b \|- 1 + 270a b\|- 1 - 270a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R 18a b \|- 1 - 18a b\|- 1 + 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3+---+2 3+---+ 11 +--R (- 36a b \|- 1 + 36a b\|- 1 - 36a b)cosh(x) +--R + +--R 3+---+2 3+---+ 9 +--R (180a b \|- 1 - 180a b\|- 1 + 180a b)cosh(x) +--R + +--R 3+---+2 3+---+ 7 +--R (- 360a b \|- 1 + 360a b\|- 1 - 360a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (360a b + 1152a )\|- 1 + (- 360a b - 1152a )\|- 1 +--R + +--R 2 +--R 360a b + 1152a +--R * +--R 5 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 3 +--R (- 180a b \|- 1 + 180a b\|- 1 - 180a b)cosh(x) +--R + +--R 3+---+2 3+---+ +--R (36a b \|- 1 - 36a b\|- 1 + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3+---+2 3+---+ 12 +--R (- 3a b \|- 1 + 3a b\|- 1 - 3a b)cosh(x) +--R + +--R 3+---+2 3+---+ 10 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) +--R + +--R 3+---+2 3+---+ 8 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (60a b + 192a )\|- 1 + (- 60a b - 192a )\|- 1 + 60a b +--R + +--R 2 +--R 192a +--R * +--R 6 +--R cosh(x) +--R + +--R 3+---+2 3+---+ 4 +--R (- 45a b \|- 1 + 45a b\|- 1 - 45a b)cosh(x) +--R + +--R 3+---+2 3+---+ 2 3+---+2 +--R (18a b \|- 1 - 18a b\|- 1 + 18a b)cosh(x) - 3a b \|- 1 +--R + +--R 3+---+ +--R 3a b\|- 1 - 3a b +--R * +--R 3+-+2 6+-+4 +--R \|a \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (3a b + 12a b)\|- 1 + (- 3a b - 12a b)\|- 1 + 3a b +--R + +--R 2 +--R 12a b +--R * +--R 12 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (36a b + 144a b)\|- 1 + (- 36a b - 144a b)\|- 1 + 36a b +--R + +--R 2 +--R 144a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (198a b + 792a b)\|- 1 + (- 198a b - 792a b)\|- 1 +--R + +--R 2 2 +--R 198a b + 792a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 18a b - 72a b)\|- 1 + (18a b + 72a b)\|- 1 - 18a b +--R + +--R 2 +--R - 72a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (660a b + 2640a b)\|- 1 + (- 660a b - 2640a b)\|- 1 +--R + +--R 2 2 +--R 660a b + 2640a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 180a b - 720a b)\|- 1 + (180a b + 720a b)\|- 1 +--R + +--R 2 2 +--R - 180a b - 720a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (1485a b + 5940a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 1485a b - 5940a b)\|- 1 + 1485a b + 5940a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 810a b - 3240a b)\|- 1 + (810a b + 3240a b)\|- 1 +--R + +--R 2 2 +--R - 810a b - 3240a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (45a b + 180a b)\|- 1 + (- 45a b - 180a b)\|- 1 + 45a b +--R + +--R 2 +--R 180a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (2376a b + 9504a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 2376a b - 9504a b)\|- 1 + 2376a b + 9504a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 2160a b - 8640a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (2160a b + 8640a b)\|- 1 - 2160a b - 8640a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (360a b + 1440a b)\|- 1 + (- 360a b - 1440a b)\|- 1 +--R + +--R 2 2 +--R 360a b + 1440a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (2772a b + 11088a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 2772a b - 11088a b)\|- 1 + 2772a b + 11088a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 3780a b - 15120a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (3780a b + 15120a b)\|- 1 - 3780a b - 15120a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (1260a b + 5040a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 1260a b - 5040a b)\|- 1 + 1260a b + 5040a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (- 60a b - 432a b - 768a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (60a b + 432a b + 768a )\|- 1 - 60a b - 432a b - 768a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (2376a b + 9504a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 2376a b - 9504a b)\|- 1 + 2376a b + 9504a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 4536a b - 18144a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (4536a b + 18144a b)\|- 1 - 4536a b - 18144a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (2520a b + 10080a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 2520a b - 10080a b)\|- 1 + 2520a b + 10080a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (- 360a b - 2592a b - 4608a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 +--R (360a b + 2592a b + 4608a )\|- 1 - 360a b - 2592a b +--R + +--R 3 +--R - 4608a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (1485a b + 5940a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 1485a b - 5940a b)\|- 1 + 1485a b + 5940a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 3780a b - 15120a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (3780a b + 15120a b)\|- 1 - 3780a b - 15120a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (3150a b + 12600a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 3150a b - 12600a b)\|- 1 + 3150a b + 12600a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (- 900a b - 6480a b - 11520a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 +--R (900a b + 6480a b + 11520a )\|- 1 - 900a b - 6480a b +--R + +--R 3 +--R - 11520a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (45a b + 180a b)\|- 1 + (- 45a b - 180a b)\|- 1 + 45a b +--R + +--R 2 +--R 180a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (660a b + 2640a b)\|- 1 + (- 660a b - 2640a b)\|- 1 +--R + +--R 2 2 +--R 660a b + 2640a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 2160a b - 8640a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (2160a b + 8640a b)\|- 1 - 2160a b - 8640a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (2520a b + 10080a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 2520a b - 10080a b)\|- 1 + 2520a b + 10080a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (- 1200a b - 8640a b - 15360a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 +--R (1200a b + 8640a b + 15360a )\|- 1 - 1200a b - 8640a b +--R + +--R 3 +--R - 15360a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (180a b + 720a b)\|- 1 + (- 180a b - 720a b)\|- 1 +--R + +--R 2 2 +--R 180a b + 720a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (198a b + 792a b)\|- 1 + (- 198a b - 792a b)\|- 1 +--R + +--R 2 2 +--R 198a b + 792a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 810a b - 3240a b)\|- 1 + (810a b + 3240a b)\|- 1 +--R + +--R 2 2 +--R - 810a b - 3240a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (1260a b + 5040a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 1260a b - 5040a b)\|- 1 + 1260a b + 5040a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (- 900a b - 6480a b - 11520a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 +--R (900a b + 6480a b + 11520a )\|- 1 - 900a b - 6480a b +--R + +--R 3 +--R - 11520a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (270a b + 1080a b)\|- 1 + (- 270a b - 1080a b)\|- 1 +--R + +--R 2 2 +--R 270a b + 1080a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 18a b - 72a b)\|- 1 + (18a b + 72a b)\|- 1 - 18a b +--R + +--R 2 +--R - 72a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (36a b + 144a b)\|- 1 + (- 36a b - 144a b)\|- 1 +--R + +--R 2 2 +--R 36a b + 144a b +--R * +--R 11 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 180a b - 720a b)\|- 1 + (180a b + 720a b)\|- 1 +--R + +--R 2 2 +--R - 180a b - 720a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (360a b + 1440a b)\|- 1 + (- 360a b - 1440a b)\|- 1 +--R + +--R 2 2 +--R 360a b + 1440a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (- 360a b - 2592a b - 4608a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 +--R (360a b + 2592a b + 4608a )\|- 1 - 360a b - 2592a b +--R + +--R 3 +--R - 4608a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (180a b + 720a b)\|- 1 + (- 180a b - 720a b)\|- 1 +--R + +--R 2 2 +--R 180a b + 720a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 36a b - 144a b)\|- 1 + (36a b + 144a b)\|- 1 +--R + +--R 2 2 +--R - 36a b - 144a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (3a b + 12a b)\|- 1 + (- 3a b - 12a b)\|- 1 + 3a b +--R + +--R 2 +--R 12a b +--R * +--R 12 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 18a b - 72a b)\|- 1 + (18a b + 72a b)\|- 1 - 18a b +--R + +--R 2 +--R - 72a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (45a b + 180a b)\|- 1 + (- 45a b - 180a b)\|- 1 + 45a b +--R + +--R 2 +--R 180a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (- 60a b - 432a b - 768a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (60a b + 432a b + 768a )\|- 1 - 60a b - 432a b - 768a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (45a b + 180a b)\|- 1 + (- 45a b - 180a b)\|- 1 + 45a b +--R + +--R 2 +--R 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 18a b - 72a b)\|- 1 + (18a b + 72a b)\|- 1 - 18a b +--R + +--R 2 +--R - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (3a b + 12a b)\|- 1 + (- 3a b - 12a b)\|- 1 + 3a b + 12a b +--R * +--R 2 6+-+2 +--R tanh(x) \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 15a b - 15a b)\|- 1 + (15a b + 15a b)\|- 1 - 15a b +--R + +--R 2 +--R - 15a b +--R * +--R 12 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 180a b - 180a b)\|- 1 + (180a b + 180a b)\|- 1 +--R + +--R 2 2 +--R - 180a b - 180a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 990a b - 990a b)\|- 1 + (990a b + 990a b)\|- 1 +--R + +--R 2 2 +--R - 990a b - 990a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (90a b + 90a b)\|- 1 + (- 90a b - 90a b)\|- 1 + 90a b +--R + +--R 2 +--R 90a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 3300a b - 3300a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (3300a b + 3300a b)\|- 1 - 3300a b - 3300a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (900a b + 900a b)\|- 1 + (- 900a b - 900a b)\|- 1 +--R + +--R 2 2 +--R 900a b + 900a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 7425a b - 7425a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (7425a b + 7425a b)\|- 1 - 7425a b - 7425a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (4050a b + 4050a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 4050a b - 4050a b)\|- 1 + 4050a b + 4050a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 225a b - 225a b)\|- 1 + (225a b + 225a b)\|- 1 +--R + +--R 2 2 +--R - 225a b - 225a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 11880a b - 11880a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (11880a b + 11880a b)\|- 1 - 11880a b - 11880a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (10800a b + 10800a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 10800a b - 10800a b)\|- 1 + 10800a b + 10800a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1800a b - 1800a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (1800a b + 1800a b)\|- 1 - 1800a b - 1800a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 13860a b - 13860a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (13860a b + 13860a b)\|- 1 - 13860a b - 13860a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (18900a b + 18900a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 18900a b - 18900a b)\|- 1 + 18900a b + 18900a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 6300a b - 6300a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (6300a b + 6300a b)\|- 1 - 6300a b - 6300a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (300a b + 1260a b + 960a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 300a b - 1260a b - 960a )\|- 1 + 300a b + 1260a b + 960a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 11880a b - 11880a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (11880a b + 11880a b)\|- 1 - 11880a b - 11880a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (22680a b + 22680a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 22680a b - 22680a b)\|- 1 + 22680a b + 22680a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 12600a b - 12600a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (12600a b + 12600a b)\|- 1 - 12600a b - 12600a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (1800a b + 7560a b + 5760a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 +--R (- 1800a b - 7560a b - 5760a )\|- 1 + 1800a b +--R + +--R 2 3 +--R 7560a b + 5760a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 7425a b - 7425a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (7425a b + 7425a b)\|- 1 - 7425a b - 7425a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (18900a b + 18900a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 18900a b - 18900a b)\|- 1 + 18900a b + 18900a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 15750a b - 15750a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (15750a b + 15750a b)\|- 1 - 15750a b - 15750a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (4500a b + 18900a b + 14400a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 +--R (- 4500a b - 18900a b - 14400a )\|- 1 + 4500a b +--R + +--R 2 3 +--R 18900a b + 14400a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 225a b - 225a b)\|- 1 + (225a b + 225a b)\|- 1 +--R + +--R 2 2 +--R - 225a b - 225a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3+---+2 +--R (- 3300a b - 3300a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (3300a b + 3300a b)\|- 1 - 3300a b - 3300a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (10800a b + 10800a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 10800a b - 10800a b)\|- 1 + 10800a b + 10800a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 12600a b - 12600a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (12600a b + 12600a b)\|- 1 - 12600a b - 12600a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (6000a b + 25200a b + 19200a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 +--R (- 6000a b - 25200a b - 19200a )\|- 1 + 6000a b +--R + +--R 2 3 +--R 25200a b + 19200a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 900a b - 900a b)\|- 1 + (900a b + 900a b)\|- 1 +--R + +--R 2 2 +--R - 900a b - 900a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 990a b - 990a b)\|- 1 + (990a b + 990a b)\|- 1 +--R + +--R 2 2 +--R - 990a b - 990a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (4050a b + 4050a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 4050a b - 4050a b)\|- 1 + 4050a b + 4050a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 6300a b - 6300a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (6300a b + 6300a b)\|- 1 - 6300a b - 6300a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (4500a b + 18900a b + 14400a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 +--R (- 4500a b - 18900a b - 14400a )\|- 1 + 4500a b +--R + +--R 2 3 +--R 18900a b + 14400a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1350a b - 1350a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (1350a b + 1350a b)\|- 1 - 1350a b - 1350a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (90a b + 90a b)\|- 1 + (- 90a b - 90a b)\|- 1 + 90a b +--R + +--R 2 +--R 90a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 180a b - 180a b)\|- 1 + (180a b + 180a b)\|- 1 +--R + +--R 2 2 +--R - 180a b - 180a b +--R * +--R 11 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (900a b + 900a b)\|- 1 + (- 900a b - 900a b)\|- 1 +--R + +--R 2 2 +--R 900a b + 900a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 1800a b - 1800a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (1800a b + 1800a b)\|- 1 - 1800a b - 1800a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (1800a b + 7560a b + 5760a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 +--R (- 1800a b - 7560a b - 5760a )\|- 1 + 1800a b +--R + +--R 2 3 +--R 7560a b + 5760a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 900a b - 900a b)\|- 1 + (900a b + 900a b)\|- 1 +--R + +--R 2 2 +--R - 900a b - 900a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (180a b + 180a b)\|- 1 + (- 180a b - 180a b)\|- 1 +--R + +--R 2 2 +--R 180a b + 180a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 15a b - 15a b)\|- 1 + (15a b + 15a b)\|- 1 - 15a b +--R + +--R 2 +--R - 15a b +--R * +--R 12 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (90a b + 90a b)\|- 1 + (- 90a b - 90a b)\|- 1 + 90a b +--R + +--R 2 +--R 90a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 225a b - 225a b)\|- 1 + (225a b + 225a b)\|- 1 +--R + +--R 2 2 +--R - 225a b - 225a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 2 3 3+---+2 +--R (300a b + 1260a b + 960a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 300a b - 1260a b - 960a )\|- 1 + 300a b + 1260a b + 960a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 225a b - 225a b)\|- 1 + (225a b + 225a b)\|- 1 +--R + +--R 2 2 +--R - 225a b - 225a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (90a b + 90a b)\|- 1 + (- 90a b - 90a b)\|- 1 + 90a b +--R + +--R 2 +--R 90a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (- 15a b - 15a b)\|- 1 + (15a b + 15a b)\|- 1 - 15a b - 15a b +--R * +--R 4 3+-+ +--R tanh(x) \|a +--R * +--R 3+-+ +--R \|b +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 12 +--R (18a b \|- 1 - 18a b \|- 1 + 3b + 24a b + 3a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 +--R (216a b \|- 1 - 216a b \|- 1 + 36b + 288a b + 36a b) +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 1188a b \|- 1 - 1188a b \|- 1 + 198b + 1584a b +--R + +--R 2 +--R 198a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 +--R - 108a b \|- 1 + 108a b \|- 1 - 18b - 144a b - 18a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 3960a b \|- 1 - 3960a b \|- 1 + 660b + 5280a b +--R + +--R 2 +--R 660a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R - 1080a b \|- 1 + 1080a b \|- 1 - 180b - 1440a b +--R + +--R 2 +--R - 180a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 8910a b \|- 1 - 8910a b \|- 1 + 1485b + 11880a b +--R + +--R 2 +--R 1485a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R - 4860a b \|- 1 + 4860a b \|- 1 - 810b - 6480a b +--R + +--R 2 +--R - 810a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 +--R 270a b \|- 1 - 270a b \|- 1 + 45b + 360a b + 45a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 14256a b \|- 1 - 14256a b \|- 1 + 2376b + 19008a b +--R + +--R 2 +--R 2376a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R - 12960a b \|- 1 + 12960a b \|- 1 - 2160b - 17280a b +--R + +--R 2 +--R - 2160a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 2160a b \|- 1 - 2160a b \|- 1 + 360b + 2880a b +--R + +--R 2 +--R 360a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 16632a b \|- 1 - 16632a b \|- 1 + 2772b + 22176a b +--R + +--R 2 +--R 2772a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R - 22680a b \|- 1 + 22680a b \|- 1 - 3780b - 30240a b +--R + +--R 2 +--R - 3780a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 7560a b \|- 1 - 7560a b \|- 1 + 1260b + 10080a b +--R + +--R 2 +--R 1260a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 360a b - 1152a b)\|- 1 + (360a b + 1152a b)\|- 1 +--R + +--R 3 2 2 3 +--R - 60b - 672a b - 1596a b - 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 14256a b \|- 1 - 14256a b \|- 1 + 2376b + 19008a b +--R + +--R 2 +--R 2376a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R - 27216a b \|- 1 + 27216a b \|- 1 - 4536b - 36288a b +--R + +--R 2 +--R - 4536a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 15120a b \|- 1 - 15120a b \|- 1 + 2520b + 20160a b +--R + +--R 2 +--R 2520a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 2160a b - 6912a b)\|- 1 +--R + +--R 2 2 3+---+ 3 2 2 +--R (2160a b + 6912a b)\|- 1 - 360b - 4032a b - 9576a b +--R + +--R 3 +--R - 1152a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 8910a b \|- 1 - 8910a b \|- 1 + 1485b + 11880a b +--R + +--R 2 +--R 1485a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R - 22680a b \|- 1 + 22680a b \|- 1 - 3780b - 30240a b +--R + +--R 2 +--R - 3780a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 18900a b \|- 1 - 18900a b \|- 1 + 3150b + 25200a b +--R + +--R 2 +--R 3150a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 5400a b - 17280a b)\|- 1 +--R + +--R 2 2 3+---+ 3 2 +--R (5400a b + 17280a b)\|- 1 - 900b - 10080a b +--R + +--R 2 3 +--R - 23940a b - 2880a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 +--R 270a b \|- 1 - 270a b \|- 1 + 45b + 360a b + 45a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 3960a b \|- 1 - 3960a b \|- 1 + 660b + 5280a b +--R + +--R 2 +--R 660a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R - 12960a b \|- 1 + 12960a b \|- 1 - 2160b - 17280a b +--R + +--R 2 +--R - 2160a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 15120a b \|- 1 - 15120a b \|- 1 + 2520b + 20160a b +--R + +--R 2 +--R 2520a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 7200a b - 23040a b)\|- 1 +--R + +--R 2 2 3+---+ 3 2 +--R (7200a b + 23040a b)\|- 1 - 1200b - 13440a b +--R + +--R 2 3 +--R - 31920a b - 3840a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 1080a b \|- 1 - 1080a b \|- 1 + 180b + 1440a b +--R + +--R 2 +--R 180a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 1188a b \|- 1 - 1188a b \|- 1 + 198b + 1584a b +--R + +--R 2 +--R 198a b +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R - 4860a b \|- 1 + 4860a b \|- 1 - 810b - 6480a b +--R + +--R 2 +--R - 810a b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 7560a b \|- 1 - 7560a b \|- 1 + 1260b + 10080a b +--R + +--R 2 +--R 1260a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 5400a b - 17280a b)\|- 1 +--R + +--R 2 2 3+---+ 3 2 +--R (5400a b + 17280a b)\|- 1 - 900b - 10080a b +--R + +--R 2 3 +--R - 23940a b - 2880a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 1620a b \|- 1 - 1620a b \|- 1 + 270b + 2160a b +--R + +--R 2 +--R 270a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 +--R - 108a b \|- 1 + 108a b \|- 1 - 18b - 144a b - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 +--R (216a b \|- 1 - 216a b \|- 1 + 36b + 288a b + 36a b) +--R * +--R 11 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R - 1080a b \|- 1 + 1080a b \|- 1 - 180b - 1440a b +--R + +--R 2 +--R - 180a b +--R * +--R 9 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 2160a b \|- 1 - 2160a b \|- 1 + 360b + 2880a b +--R + +--R 2 +--R 360a b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (- 2160a b - 6912a b)\|- 1 +--R + +--R 2 2 3+---+ 3 2 2 +--R (2160a b + 6912a b)\|- 1 - 360b - 4032a b - 9576a b +--R + +--R 3 +--R - 1152a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 +--R 1080a b \|- 1 - 1080a b \|- 1 + 180b + 1440a b +--R + +--R 2 +--R 180a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 +--R (- 216a b \|- 1 + 216a b \|- 1 - 36b - 288a b - 36a b) +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 12 +--R (18a b \|- 1 - 18a b \|- 1 + 3b + 24a b + 3a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 +--R (- 108a b \|- 1 + 108a b \|- 1 - 18b - 144a b - 18a b) +--R * +--R 10 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 8 +--R (270a b \|- 1 - 270a b \|- 1 + 45b + 360a b + 45a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 360a b - 1152a b)\|- 1 + (360a b + 1152a b)\|- 1 +--R + +--R 3 2 2 3 +--R - 60b - 672a b - 1596a b - 192a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 4 +--R (270a b \|- 1 - 270a b \|- 1 + 45b + 360a b + 45a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 +--R (- 108a b \|- 1 + 108a b \|- 1 - 18b - 144a b - 18a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 3 2 2 +--R 18a b \|- 1 - 18a b \|- 1 + 3b + 24a b + 3a b +--R * +--R 6 +--R tanh(x) +--R + +--R 2 2 12 2 2 11 +--R (- 3a b - 3a b)sinh(x) + (- 36a b - 36a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 10 +--R ((- 198a b - 198a b)cosh(x) + 18a b + 18a b)sinh(x) +--R + +--R 2 2 3 2 2 9 +--R ((- 660a b - 660a b)cosh(x) + (180a b + 180a b)cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 1485a b - 1485a b)cosh(x) + (810a b + 810a b)cosh(x) +--R + +--R 2 2 +--R - 45a b - 45a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 2376a b - 2376a b)cosh(x) + (2160a b + 2160a b)cosh(x) +--R + +--R 2 2 +--R (- 360a b - 360a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2772a b - 2772a b)cosh(x) + (3780a b + 3780a b)cosh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 1260a b - 1260a b)cosh(x) + 60a b + 252a b + 192a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 2376a b - 2376a b)cosh(x) + (4536a b + 4536a b)cosh(x) +--R + +--R 2 2 3 +--R (- 2520a b - 2520a b)cosh(x) +--R + +--R 2 2 3 +--R (360a b + 1512a b + 1152a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 1485a b - 1485a b)cosh(x) + (3780a b + 3780a b)cosh(x) +--R + +--R 2 2 4 +--R (- 3150a b - 3150a b)cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (900a b + 3780a b + 2880a )cosh(x) - 45a b - 45a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 9 2 2 7 +--R (- 660a b - 660a b)cosh(x) + (2160a b + 2160a b)cosh(x) +--R + +--R 2 2 5 +--R (- 2520a b - 2520a b)cosh(x) +--R + +--R 2 2 3 3 2 2 +--R (1200a b + 5040a b + 3840a )cosh(x) + (- 180a b - 180a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 10 2 2 8 +--R (- 198a b - 198a b)cosh(x) + (810a b + 810a b)cosh(x) +--R + +--R 2 2 6 +--R (- 1260a b - 1260a b)cosh(x) +--R + +--R 2 2 3 4 +--R (900a b + 3780a b + 2880a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 270a b - 270a b)cosh(x) + 18a b + 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 11 2 2 9 +--R (- 36a b - 36a b)cosh(x) + (180a b + 180a b)cosh(x) +--R + +--R 2 2 7 +--R (- 360a b - 360a b)cosh(x) +--R + +--R 2 2 3 5 +--R (360a b + 1512a b + 1152a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 180a b - 180a b)cosh(x) + (36a b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 12 2 2 10 +--R (- 3a b - 3a b)cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 2 2 8 2 2 3 6 +--R (- 45a b - 45a b)cosh(x) + (60a b + 252a b + 192a )cosh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 45a b - 45a b)cosh(x) + (18a b + 18a b)cosh(x) - 3a b - 3a b +--R * +--R 6+-+4 +--R \|a +--R + +--R 2 3+---+2 2 3+---+ 2 2 12 +--R (9a b \|- 1 - 9a b \|- 1 + 18a b + 9a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 11 +--R (108a b \|- 1 - 108a b \|- 1 + 216a b + 108a b)cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 +--R (594a b \|- 1 - 594a b \|- 1 + 1188a b + 594a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R - 54a b \|- 1 + 54a b \|- 1 - 108a b - 54a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 +--R (1980a b \|- 1 - 1980a b \|- 1 + 3960a b + 1980a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 540a b \|- 1 + 540a b \|- 1 - 1080a b - 540a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (4455a b \|- 1 - 4455a b \|- 1 + 8910a b + 4455a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 +--R (- 2430a b \|- 1 + 2430a b \|- 1 - 4860a b - 2430a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R 135a b \|- 1 - 135a b \|- 1 + 270a b + 135a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 5 +--R (7128a b \|- 1 - 7128a b \|- 1 + 14256a b + 7128a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 6480a b \|- 1 + 6480a b \|- 1 - 12960a b - 6480a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (1080a b \|- 1 - 1080a b \|- 1 + 2160a b + 1080a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 6 +--R (8316a b \|- 1 - 8316a b \|- 1 + 16632a b + 8316a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 11340a b \|- 1 + 11340a b \|- 1 - 22680a b - 11340a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 +--R (3780a b \|- 1 - 3780a b \|- 1 + 7560a b + 3780a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 180a b - 576a b)\|- 1 + (180a b + 576a b)\|- 1 - 360a b +--R + +--R 2 3 +--R - 1332a b - 576a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 7 +--R (7128a b \|- 1 - 7128a b \|- 1 + 14256a b + 7128a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 13608a b \|- 1 + 13608a b \|- 1 - 27216a b - 13608a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 +--R (7560a b \|- 1 - 7560a b \|- 1 + 15120a b + 7560a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 1080a b - 3456a b)\|- 1 + (1080a b + 3456a b)\|- 1 +--R + +--R 2 2 3 +--R - 2160a b - 7992a b - 3456a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 8 +--R (4455a b \|- 1 - 4455a b \|- 1 + 8910a b + 4455a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 11340a b \|- 1 + 11340a b \|- 1 - 22680a b - 11340a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (9450a b \|- 1 - 9450a b \|- 1 + 18900a b + 9450a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 2700a b - 8640a b)\|- 1 + (2700a b + 8640a b)\|- 1 +--R + +--R 2 2 3 +--R - 5400a b - 19980a b - 8640a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R 135a b \|- 1 - 135a b \|- 1 + 270a b + 135a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 9 +--R (1980a b \|- 1 - 1980a b \|- 1 + 3960a b + 1980a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 6480a b \|- 1 + 6480a b \|- 1 - 12960a b - 6480a b) +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 5 +--R (7560a b \|- 1 - 7560a b \|- 1 + 15120a b + 7560a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 3600a b - 11520a b)\|- 1 + (3600a b + 11520a b)\|- 1 +--R + +--R 2 2 3 +--R - 7200a b - 26640a b - 11520a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (540a b \|- 1 - 540a b \|- 1 + 1080a b + 540a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 10 +--R (594a b \|- 1 - 594a b \|- 1 + 1188a b + 594a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 8 +--R (- 2430a b \|- 1 + 2430a b \|- 1 - 4860a b - 2430a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 6 +--R (3780a b \|- 1 - 3780a b \|- 1 + 7560a b + 3780a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 2700a b - 8640a b)\|- 1 + (2700a b + 8640a b)\|- 1 +--R + +--R 2 2 3 +--R - 5400a b - 19980a b - 8640a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 +--R (810a b \|- 1 - 810a b \|- 1 + 1620a b + 810a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R - 54a b \|- 1 + 54a b \|- 1 - 108a b - 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 11 +--R (108a b \|- 1 - 108a b \|- 1 + 216a b + 108a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 9 +--R (- 540a b \|- 1 + 540a b \|- 1 - 1080a b - 540a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 7 +--R (1080a b \|- 1 - 1080a b \|- 1 + 2160a b + 1080a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 1080a b - 3456a b)\|- 1 + (1080a b + 3456a b)\|- 1 +--R + +--R 2 2 3 +--R - 2160a b - 7992a b - 3456a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 +--R (540a b \|- 1 - 540a b \|- 1 + 1080a b + 540a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 108a b \|- 1 + 108a b \|- 1 - 216a b - 108a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 12 +--R (9a b \|- 1 - 9a b \|- 1 + 18a b + 9a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 10 +--R (- 54a b \|- 1 + 54a b \|- 1 - 108a b - 54a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 8 +--R (135a b \|- 1 - 135a b \|- 1 + 270a b + 135a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- 180a b - 576a b)\|- 1 + (180a b + 576a b)\|- 1 - 360a b +--R + +--R 2 3 +--R - 1332a b - 576a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (135a b \|- 1 - 135a b \|- 1 + 270a b + 135a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 +--R (- 54a b \|- 1 + 54a b \|- 1 - 108a b - 54a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R 9a b \|- 1 - 9a b \|- 1 + 18a b + 9a b +--R * +--R 2 3+-+6+-+2 +--R tanh(x) \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 2 12 +--R (- 27a b \|- 1 + 27a b \|- 1 - 36a b - 9a b)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 11 +--R (- 324a b \|- 1 + 324a b \|- 1 - 432a b - 108a b)cosh(x)sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 +--R (- 1782a b \|- 1 + 1782a b \|- 1 - 2376a b - 594a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R 162a b \|- 1 - 162a b \|- 1 + 216a b + 54a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 +--R (- 5940a b \|- 1 + 5940a b \|- 1 - 7920a b - 1980a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (1620a b \|- 1 - 1620a b \|- 1 + 2160a b + 540a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 13365a b \|- 1 + 13365a b \|- 1 - 17820a b - 4455a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 +--R (7290a b \|- 1 - 7290a b \|- 1 + 9720a b + 2430a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R - 405a b \|- 1 + 405a b \|- 1 - 540a b - 135a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 21384a b \|- 1 + 21384a b \|- 1 - 28512a b - 7128a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (19440a b \|- 1 - 19440a b \|- 1 + 25920a b + 6480a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 3240a b \|- 1 + 3240a b \|- 1 - 4320a b - 1080a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 24948a b \|- 1 + 24948a b \|- 1 - 33264a b - 8316a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (34020a b \|- 1 - 34020a b \|- 1 + 45360a b + 11340a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 11340a b \|- 1 + 11340a b \|- 1 - 15120a b - 3780a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (540a b + 1728a b)\|- 1 + (- 540a b - 1728a b)\|- 1 +--R + +--R 2 2 3 +--R 720a b + 2484a b + 576a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 21384a b \|- 1 + 21384a b \|- 1 - 28512a b - 7128a b) +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (40824a b \|- 1 - 40824a b \|- 1 + 54432a b + 13608a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 22680a b \|- 1 + 22680a b \|- 1 - 30240a b - 7560a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (3240a b + 10368a b)\|- 1 + (- 3240a b - 10368a b)\|- 1 +--R + +--R 2 2 3 +--R 4320a b + 14904a b + 3456a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 13365a b \|- 1 + 13365a b \|- 1 - 17820a b - 4455a b) +--R * +--R 8 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (34020a b \|- 1 - 34020a b \|- 1 + 45360a b + 11340a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 28350a b \|- 1 + 28350a b \|- 1 - 37800a b - 9450a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (8100a b + 25920a b)\|- 1 + (- 8100a b - 25920a b)\|- 1 +--R + +--R 2 2 3 +--R 10800a b + 37260a b + 8640a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R - 405a b \|- 1 + 405a b \|- 1 - 540a b - 135a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 9 +--R (- 5940a b \|- 1 + 5940a b \|- 1 - 7920a b - 1980a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (19440a b \|- 1 - 19440a b \|- 1 + 25920a b + 6480a b) +--R * +--R 7 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 22680a b \|- 1 + 22680a b \|- 1 - 30240a b - 7560a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 3+---+2 +--R (10800a b + 34560a b)\|- 1 +--R + +--R 2 2 3+---+ 2 2 3 +--R (- 10800a b - 34560a b)\|- 1 + 14400a b + 49680a b + 11520a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 1620a b \|- 1 + 1620a b \|- 1 - 2160a b - 540a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 10 +--R (- 1782a b \|- 1 + 1782a b \|- 1 - 2376a b - 594a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 8 +--R (7290a b \|- 1 - 7290a b \|- 1 + 9720a b + 2430a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (- 11340a b \|- 1 + 11340a b \|- 1 - 15120a b - 3780a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (8100a b + 25920a b)\|- 1 + (- 8100a b - 25920a b)\|- 1 +--R + +--R 2 2 3 +--R 10800a b + 37260a b + 8640a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 +--R (- 2430a b \|- 1 + 2430a b \|- 1 - 3240a b - 810a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R 162a b \|- 1 - 162a b \|- 1 + 216a b + 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 11 +--R (- 324a b \|- 1 + 324a b \|- 1 - 432a b - 108a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 9 +--R (1620a b \|- 1 - 1620a b \|- 1 + 2160a b + 540a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 7 +--R (- 3240a b \|- 1 + 3240a b \|- 1 - 4320a b - 1080a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (3240a b + 10368a b)\|- 1 + (- 3240a b - 10368a b)\|- 1 +--R + +--R 2 2 3 +--R 4320a b + 14904a b + 3456a +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 +--R (- 1620a b \|- 1 + 1620a b \|- 1 - 2160a b - 540a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R (324a b \|- 1 - 324a b \|- 1 + 432a b + 108a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 12 +--R (- 27a b \|- 1 + 27a b \|- 1 - 36a b - 9a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 10 +--R (162a b \|- 1 - 162a b \|- 1 + 216a b + 54a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 8 +--R (- 405a b \|- 1 + 405a b \|- 1 - 540a b - 135a b)cosh(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (540a b + 1728a b)\|- 1 + (- 540a b - 1728a b)\|- 1 +--R + +--R 2 2 3 +--R 720a b + 2484a b + 576a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (- 405a b \|- 1 + 405a b \|- 1 - 540a b - 135a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 2 +--R (162a b \|- 1 - 162a b \|- 1 + 216a b + 54a b)cosh(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 +--R - 27a b \|- 1 + 27a b \|- 1 - 36a b - 9a b +--R * +--R 4 3+-+2 +--R tanh(x) \|a +--R Type: Expression(Integer) +--E 425 + +--S 426 of 510 +t0083:= 1/(a-b*sinh(x)^8) +--R +--R +--R 1 +--R (369) - -------------- +--R 8 +--R b sinh(x) - a +--R Type: Expression(Integer) +--E 426 + +--S 427 of 510 +r0083:= 1/4*atan((-a^(1/4)+b^(1/4))^(1/2)*tanh(x)/a^(1/8))/a^(7/8)/_ + (-a^(1/4)+b^(1/4))^(1/2)+1/4*atanh((a^(1/4)-%i*b^(1/4))^(1/2)*_ + tanh(x)/a^(1/8))/a^(7/8)/(a^(1/4)-%i*b^(1/4))^(1/2)+_ + 1/4*atanh((a^(1/4)+%i*b^(1/4))^(1/2)*tanh(x)/a^(1/8))/a^(7/8)/_ + (a^(1/4)+%i*b^(1/4))^(1/2)+1/4*atanh((a^(1/4)+b^(1/4))^(1/2)*_ + tanh(x)/a^(1/8))/a^(7/8)/(a^(1/4)+b^(1/4))^(1/2) +--R +--R +--R (370) +--R +---------------+ +-------------+ +-----------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R \|- %i\|b + \|a \|%i\|b + \|a \|\|b - \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R tanh(x)\|\|b + \|a +--R atanh(---------------------) +--R 8+-+ +--R \|a +--R + +--R +---------------+ +-----------+ +-----------+ +--R | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R \|- %i\|b + \|a \|\|b - \|a \|\|b + \|a +--R * +--R +-------------+ +--R | 4+-+ 4+-+ +--R tanh(x)\|%i\|b + \|a +--R atanh(-----------------------) +--R 8+-+ +--R \|a +--R + +--R +-------------+ +-----------+ +-----------+ +--R | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R \|%i\|b + \|a \|\|b - \|a \|\|b + \|a +--R * +--R +---------------+ +--R | 4+-+ 4+-+ +--R tanh(x)\|- %i\|b + \|a +--R atanh(-------------------------) +--R 8+-+ +--R \|a +--R + +--R +-----------+ +--R +---------------+ +-------------+ +-----------+ |4+-+ 4+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tanh(x)\|\|b - \|a +--R \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a atan(---------------------) +--R 8+-+ +--R \|a +--R / +--R +---------------+ +-------------+ +-----------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R 4\|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b - \|a \|\|b + \|a +--R Type: Expression(Complex(Integer)) +--E 427 + +--S 428 of 510 +a0083:= integrate(t0083,x) +--R +--R +--R (371) +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%FA0 - 64a b + 64a ) +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%FA1 + (- 16a b + 16a )%%FA0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b - 1048576a )%%FA0 - 16384a b + 16384a )%%FA1 +--R + +--R 5 6 3 4 +--I (- 16384a b + 16384a )%%FA0 + 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b - 1048576a )%%FA0 - 16384a b + 16384a )%%FA1 +--R + +--R 7 8 2 6 3 +--I (1048576a b - 1048576a )%%FA0 + 65536a %%FA0 - 256a b +--R + +--R 4 +--R - 768a +--R * +--I %%FA1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b + 16384a )%%FA0 + (- 256a b - 768a )%%FA0 + 8a b +--R + +--R 2 +--R 8a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%FA1 + (- 16a b + 16a )%%FA0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b + 262144a )%%FA0 + 4096a b - 4096a )%%FA1 +--R + +--R 4 5 2 3 +--I (4096a b - 4096a )%%FA0 - 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%FA0 - 64a b + 64a ) +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((- 262144a b + 262144a )%%FA0 + 4096a b - 4096a )%%FA1 +--R + +--R 6 7 2 5 2 3 +--I ((- 262144a b + 262144a )%%FA0 - 16384a %%FA0 + 64a b + 192a ) +--R * +--I %%FA1 +--R + +--R 4 5 2 2 3 2 +--I (4096a b - 4096a )%%FA0 + (64a b + 192a )%%FA0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b - 2a +--R + +--R - +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%FA1 + (- 16a b + 16a )%%FA0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b - 1048576a )%%FA0 - 16384a b + 16384a ) +--R * +--I %%FA1 +--R + +--R 5 6 3 4 +--I (- 16384a b + 16384a )%%FA0 + 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 +--I ((- 1048576a b + 1048576a )%%FA0 + 16384a b - 16384a ) +--R * +--R 2 +--I %%FA1 +--R + +--R 7 8 2 6 +--I (- 1048576a b + 1048576a )%%FA0 - 65536a %%FA0 +--R + +--R 3 4 +--R 256a b + 768a +--R * +--I %%FA1 +--R + +--R 5 6 2 3 4 +--I (16384a b - 16384a )%%FA0 + (256a b + 768a )%%FA0 - 8a b +--R + +--R 2 +--R - 8a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%FA0 +--R + +--R 2 3 +--R - 64a b + 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%FA1 + (- 16a b + 16a )%%FA0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((262144a b - 262144a )%%FA0 - 4096a b + 4096a )%%FA1 +--R + +--R 4 5 2 3 +--I (- 4096a b + 4096a )%%FA0 + 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((- 262144a b + 262144a )%%FA0 + 4096a b - 4096a )%%FA1 +--R + +--R 6 7 2 5 2 +--I (- 262144a b + 262144a )%%FA0 - 16384a %%FA0 + 64a b +--R + +--R 3 +--R 192a +--R * +--I %%FA1 +--R + +--R 4 5 2 2 3 2 +--I (4096a b - 4096a )%%FA0 + (64a b + 192a )%%FA0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b - 2a +--R + +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%FA0 - 64a b + 64a ) +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%FA1 + (- 16a b + 16a )%%FA0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 6 +--I ((- 1048576a b + 1048576a )%%FA0 + 16384a b - 16384a ) +--R * +--I %%FA1 +--R + +--R 5 6 3 4 +--I (16384a b - 16384a )%%FA0 - 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b - 1048576a )%%FA0 - 16384a b + 16384a )%%FA1 +--R + +--R 7 8 2 6 3 +--I (1048576a b - 1048576a )%%FA0 + 65536a %%FA0 - 256a b +--R + +--R 4 +--R - 768a +--R * +--I %%FA1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b + 16384a )%%FA0 + (- 256a b - 768a )%%FA0 + 8a b +--R + +--R 2 +--R 8a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%FA1 + (- 16a b + 16a )%%FA0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((262144a b - 262144a )%%FA0 - 4096a b + 4096a )%%FA1 +--R + +--R 4 5 2 3 +--I (- 4096a b + 4096a )%%FA0 + 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%FA0 - 64a b + 64a ) +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((- 262144a b + 262144a )%%FA0 + 4096a b - 4096a )%%FA1 +--R + +--R 6 7 2 5 2 3 +--I ((- 262144a b + 262144a )%%FA0 - 16384a %%FA0 + 64a b + 192a ) +--R * +--I %%FA1 +--R + +--R 4 5 2 2 3 2 +--I (4096a b - 4096a )%%FA0 + (64a b + 192a )%%FA0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b - 2a +--R + +--R - +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%FA1 + (- 16a b + 16a )%%FA0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 +--I (- 1048576a b + 1048576a )%%FA0 + 16384a b +--R + +--R 6 +--R - 16384a +--R * +--I %%FA1 +--R + +--R 5 6 3 4 +--I (16384a b - 16384a )%%FA0 - 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 +--I ((- 1048576a b + 1048576a )%%FA0 + 16384a b - 16384a ) +--R * +--R 2 +--I %%FA1 +--R + +--R 7 8 2 6 +--I (- 1048576a b + 1048576a )%%FA0 - 65536a %%FA0 +--R + +--R 3 4 +--R 256a b + 768a +--R * +--I %%FA1 +--R + +--R 5 6 2 3 4 +--I (16384a b - 16384a )%%FA0 + (256a b + 768a )%%FA0 - 8a b +--R + +--R 2 +--R - 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a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%FA1 + (- 16a b + 16a )%%FA0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((262144a b - 262144a )%%FA0 - 4096a b + 4096a )%%FA1 +--R + +--R 4 5 2 3 +--I (- 4096a b + 4096a )%%FA0 + 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%FA0 - 64a b + 64a ) +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((- 262144a b + 262144a )%%FA0 + 4096a b - 4096a )%%FA1 +--R + +--R 6 7 2 5 2 3 +--I ((- 262144a b + 262144a )%%FA0 - 16384a %%FA0 + 64a b + 192a ) +--R * +--I %%FA1 +--R + +--R 4 5 2 2 3 2 +--I (4096a b - 4096a )%%FA0 + (64a b + 192a )%%FA0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b - 2a +--R + +--R - +--R +---------------+ +-------------+ +-----------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b - \|a \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%FA1 + (- 16a b + 16a )%%FA0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 +--I (- 1048576a b + 1048576a )%%FA0 + 16384a b +--R + +--R 6 +--R - 16384a +--R * +--I %%FA1 +--R + +--R 5 6 3 4 +--I (16384a b - 16384a )%%FA0 - 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 +--I ((- 1048576a b + 1048576a )%%FA0 + 16384a b - 16384a ) +--R * +--R 2 +--I %%FA1 +--R + +--R 7 8 2 6 +--I (- 1048576a b + 1048576a )%%FA0 - 65536a %%FA0 +--R + +--R 3 4 +--R 256a b + 768a +--R * +--I %%FA1 +--R + +--R 5 6 2 3 4 +--I (16384a b - 16384a )%%FA0 + (256a b + 768a )%%FA0 - 8a b +--R + +--R 2 +--R - 8a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%FA0 +--R + +--R 2 3 +--R - 64a b + 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%FA1 + (- 16a b + 16a )%%FA0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b + 262144a )%%FA0 + 4096a b - 4096a )%%FA1 +--R + +--R 4 5 2 3 +--I (4096a b - 4096a )%%FA0 - 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%FA0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%FA1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%FA0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%FA0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((- 262144a b + 262144a )%%FA0 + 4096a b - 4096a )%%FA1 +--R + +--R 6 7 2 5 2 +--I (- 262144a b + 262144a )%%FA0 - 16384a %%FA0 + 64a b +--R + +--R 3 +--R 192a +--R * +--I %%FA1 +--R + +--R 4 5 2 2 3 2 +--I (4096a b - 4096a )%%FA0 + (64a b + 192a )%%FA0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) - b - 2a +--R + +--R - +--R +---------------+ +-------------+ +-----------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b - \|a \|\|b + \|a +--R * +--R +------+ +--I \|4%%FA1 +--R * +--R log +--R 7 8 5 6 2 +--I ((2097152a b - 2097152a )%%FA0 - 32768a b + 32768a )%%FA1 +--R + +--R 7 8 2 6 3 +--I (2097152a b - 2097152a )%%FA0 + 131072a %%FA0 - 512a b +--R + +--R 4 +--R - 1536a +--R * +--I %%FA1 +--R + +--R 7 8 3 6 2 +--I (2097152a b - 2097152a )%%FA0 + 131072a %%FA0 +--R + +--R 4 2 +--I - 3072a %%FA0 - 8a b + 24a +--R * +--R +------+ +--I \|4%%FA1 +--R + +--R 6 7 4 5 2 +--I ((524288a b - 524288a )%%FA0 - 8192a b + 8192a )%%FA1 +--R + +--R 6 7 2 5 2 +--I (524288a b - 524288a )%%FA0 + 32768a %%FA0 - 128a b +--R + +--R 3 +--R - 384a +--R * +--I %%FA1 +--R + +--R 6 7 3 5 2 3 +--I (524288a b - 524288a )%%FA0 + 32768a %%FA0 - 768a %%FA0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 6a +--R + +--R +---------------+ +-------------+ +-----------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b - \|a \|\|b + \|a +--R * +--R +------+ +--I \|4%%FA1 +--R * +--R log +--R 7 8 5 6 2 +--I ((- 2097152a b + 2097152a )%%FA0 + 32768a b - 32768a )%%FA1 +--R + +--R 7 8 2 6 3 +--I (- 2097152a b + 2097152a )%%FA0 - 131072a %%FA0 + 512a b +--R + +--R 4 +--R 1536a +--R * +--I %%FA1 +--R + +--R 7 8 3 6 2 +--I (- 2097152a b + 2097152a )%%FA0 - 131072a %%FA0 +--R + +--R 4 2 +--I 3072a %%FA0 + 8a b - 24a +--R * +--R +------+ +--I \|4%%FA1 +--R + +--R 6 7 4 5 2 +--I ((524288a b - 524288a )%%FA0 - 8192a b + 8192a )%%FA1 +--R + +--R 6 7 2 5 2 3 +--I ((524288a b - 524288a )%%FA0 + 32768a %%FA0 - 128a b - 384a ) +--R * +--I %%FA1 +--R + +--R 6 7 3 5 2 3 +--I (524288a b - 524288a )%%FA0 + 32768a %%FA0 - 768a %%FA0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 6a +--R + +--R +---------------+ +-------------+ +-----------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b - \|a \|\|b + \|a +--R * +--R +------+ +--I \|4%%FA0 +--R * +--R log +--R 7 8 3 5 6 2 +--I (2097152a b - 2097152a )%%FA0 + (32768a b + 98304a )%%FA0 +--R + +--R 3 4 2 +--I (512a b - 1536a )%%FA0 + 8a b + 8a +--R * +--R +------+ +--I \|4%%FA0 +--R + +--R 6 7 3 4 5 2 +--I (- 524288a b + 524288a )%%FA0 + (- 8192a b - 24576a )%%FA0 +--R + +--R 2 3 2 +--I (- 128a b + 384a )%%FA0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) - b - 2a +--R + +--R - +--R +---------------+ +-------------+ +-----------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b - \|a \|\|b + \|a +--R * +--R +------+ +--I \|4%%FA0 +--R * +--R log +--R 7 8 3 +--I (- 2097152a b + 2097152a )%%FA0 +--R + +--R 5 6 2 3 4 +--I (- 32768a b - 98304a )%%FA0 + (- 512a b + 1536a )%%FA0 +--R + +--R 2 +--R - 8a b - 8a +--R * +--R +------+ +--I \|4%%FA0 +--R + +--R 6 7 3 4 5 2 +--I (- 524288a b + 524288a )%%FA0 + (- 8192a b - 24576a )%%FA0 +--R + +--R 2 3 2 +--I (- 128a b + 384a )%%FA0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) - b - 2a +--R + +--R - +--R +---------------+ +-------------+ +-----------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R \|- %i\|b + \|a \|%i\|b + \|a \|\|b - \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R tanh(x)\|\|b + \|a +--R atanh(---------------------) +--R 8+-+ +--R \|a +--R + +--R - +--R +---------------+ +-----------+ +-----------+ +--R | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R \|- %i\|b + \|a \|\|b - \|a \|\|b + \|a +--R * +--R +-------------+ +--R | 4+-+ 4+-+ +--R tanh(x)\|%i\|b + \|a +--R atanh(-----------------------) +--R 8+-+ +--R \|a +--R + +--R - +--R +-------------+ +-----------+ +-----------+ +--R | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R \|%i\|b + \|a \|\|b - \|a \|\|b + \|a +--R * +--R +---------------+ +--R | 4+-+ 4+-+ +--R tanh(x)\|- %i\|b + \|a +--R atanh(-------------------------) +--R 8+-+ +--R \|a +--R + +--R - +--R +---------------+ +-------------+ +-----------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R tanh(x)\|\|b - \|a +--R atan(---------------------) +--R 8+-+ +--R \|a +--R / +--R +---------------+ +-------------+ +-----------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ |4+-+ 4+-+ +--R 4\|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b - \|a \|\|b + \|a +--R Type: Expression(Complex(Integer)) +--E 429 + +--S 430 of 510 +--d0083:= D(m0083,x) +--E 430 + +--S 431 of 510 +t0084:= 1/(1+sinh(x)^3) +--R +--R +--R 1 +--R (373) ------------ +--R 3 +--R sinh(x) + 1 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 510 +r0084:= -1/3*2^(1/2)*atanh(1/2*(1-tanh(1/2*x))*2^(1/2))-_ + 2/3*atanh(((-1)^(2/3)-tanh(1/2*x))/(1-(-1)^(1/3))^(1/2))/_ + (1-(-1)^(1/3))^(1/2)+2/3*atanh(((-1)^(1/3)+_ + tanh(1/2*x))/(1+(-1)^(2/3))^(1/2))/(1+(-1)^(2/3))^(1/2) +--R +--R +--R (374) +--R +-+ x +-+ +--R +------------+ +-----------+ \|2 tanh(-) - \|2 +--R +-+ | 3+---+ |3+---+2 2 +--R \|2 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(------------------) +--R 2 +--R + +--R x 3+---+2 +--R +-----------+ tanh(-) - \|- 1 +--R |3+---+2 2 +--R 2\|\|- 1 + 1 atanh(-----------------) +--R +------------+ +--R | 3+---+ +--R \|- \|- 1 + 1 +--R + +--R x 3+---+ +--R +------------+ tanh(-) + \|- 1 +--R | 3+---+ 2 +--R 2\|- \|- 1 + 1 atanh(----------------) +--R +-----------+ +--R |3+---+2 +--R \|\|- 1 + 1 +--R / +--R +------------+ +-----------+ +--R | 3+---+ |3+---+2 +--R 3\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 510 +a0084:= integrate(t0084,x) +--R +--R +--R (375) +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + \|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R (- 2sinh(x) - 2cosh(x) + 1)cos(----------) + sinh(x) +--R 2 +--R + +--R 2 +--R (2cosh(x) - 1)sinh(x) + cosh(x) - cosh(x) + 1 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - \|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R (2sinh(x) + 2cosh(x) - 1)cos(----------) + sinh(x) +--R 2 +--R + +--R 2 +--R (2cosh(x) - 1)sinh(x) + cosh(x) - cosh(x) + 1 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +-+ +--R +-+ 2sin(----------) + \|3 +--R \|3 2 +--R 4sin(----------)atan(------------------------------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) - 2sinh(x) - 2cosh(x) + 1 +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +-+ +--R +-+ 2sin(----------) - \|3 +--R \|3 2 +--R - 4sin(----------)atan(------------------------------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) + 2sinh(x) + 2cosh(x) - 1 +--R 2 +--R + +--R +-+ +-+ +-+ +--R +-+ (\|2 - 1)sinh(x) + (- \|2 + 2)cosh(x) - \|2 + 1 +--R \|2 log(--------------------------------------------------) +--R sinh(x) + 1 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 510 +m0084:= a0084-r0084 +--R +--R +--R (376) +--R - +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R | 3+---+ |3+---+2 \|3 +--R 2\|- \|- 1 + 1 \|\|- 1 + 1 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + \|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R (- 2sinh(x) - 2cosh(x) + 1)cos(----------) + sinh(x) +--R 2 +--R + +--R 2 +--R (2cosh(x) - 1)sinh(x) + cosh(x) - cosh(x) + 1 +--R + +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R | 3+---+ |3+---+2 \|3 +--R 2\|- \|- 1 + 1 \|\|- 1 + 1 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - \|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R (2sinh(x) + 2cosh(x) - 1)cos(----------) + sinh(x) +--R 2 +--R + +--R 2 +--R (2cosh(x) - 1)sinh(x) + cosh(x) - cosh(x) + 1 +--R + +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R | 3+---+ |3+---+2 \|3 +--R 4\|- \|- 1 + 1 \|\|- 1 + 1 sin(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +-+ +--R 2sin(----------) + \|3 +--R 2 +--R atan(------------------------------------------) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) - 2sinh(x) - 2cosh(x) + 1 +--R 2 +--R + +--R - +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R | 3+---+ |3+---+2 \|3 +--R 4\|- \|- 1 + 1 \|\|- 1 + 1 sin(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +-+ +--R 2sin(----------) - \|3 +--R 2 +--R atan(------------------------------------------) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) + 2sinh(x) + 2cosh(x) - 1 +--R 2 +--R + +--R +------------+ +-----------+ +--R +-+ | 3+---+ |3+---+2 +--R \|2 \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R +-+ +-+ +-+ +--R (\|2 - 1)sinh(x) + (- \|2 + 2)cosh(x) - \|2 + 1 +--R log(--------------------------------------------------) +--R sinh(x) + 1 +--R + +--R +-+ x +-+ +--R +------------+ +-----------+ \|2 tanh(-) - \|2 +--R +-+ | 3+---+ |3+---+2 2 +--R - 2\|2 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(------------------) +--R 2 +--R + +--R x 3+---+2 +--R +-----------+ tanh(-) - \|- 1 +--R |3+---+2 2 +--R - 4\|\|- 1 + 1 atanh(-----------------) +--R +------------+ +--R | 3+---+ +--R \|- \|- 1 + 1 +--R + +--R x 3+---+ +--R +------------+ tanh(-) + \|- 1 +--R | 3+---+ 2 +--R - 4\|- \|- 1 + 1 atanh(----------------) +--R +-----------+ +--R |3+---+2 +--R \|\|- 1 + 1 +--R / +--R +------------+ +-----------+ +--R | 3+---+ |3+---+2 +--R 6\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 510 +--d0084:= D(m0084,x) +--E 435 + +--S 436 of 510 +t0085:= 1/(1+sinh(x)^4) +--R +--R +--R 1 +--R (377) ------------ +--R 4 +--R sinh(x) + 1 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 510 +r0085:= 1/2*atanh((1-%i)^(1/2)*tanh(x))/(1-%i)^(1/2)+_ + 1/2*atanh((1+%i)^(1/2)*tanh(x))/(1+%i)^(1/2) +--R +--R +--R +------+ +------+ +------+ +------+ +--R \|1 - %i atanh(\|1 + %i tanh(x)) + \|1 + %i atanh(\|1 - %i tanh(x)) +--R (378) ------------------------------------------------------------------- +--R +------+ +------+ +--R 2\|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 437 + +--S 438 of 510 +a0085:= integrate(t0085,x) +--R +--R +--R (379) +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (2\|2 \|2 sin(---) + 6cosh(x) - 2\|2 \|2 cos(---) - 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (- 4\|2 \|2 cos(---) - 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (2\|2 \|2 cosh(x) + 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (- 2\|2 \|2 cos(---) - 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (- 2\|2 \|2 sin(---) + 6cosh(x) + 2\|2 \|2 cos(---) - 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R - 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (4\|2 \|2 cos(---) - 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (- 2\|2 \|2 cosh(x) - 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (2\|2 \|2 cos(---) - 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R - 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R - +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) + 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) - 2\|2 cos(---) - \|2 +--R 8 +--R + +--R - +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) - 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) - 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) + 2\|2 cos(---) - \|2 +--R 8 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 510 +m0085:= a0085-r0085 +--R +--R +--R (380) +--R - +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (2\|2 \|2 sin(---) + 6cosh(x) - 2\|2 \|2 cos(---) - 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (- 4\|2 \|2 cos(---) - 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (2\|2 \|2 cosh(x) + 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (- 2\|2 \|2 cos(---) - 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (- 2\|2 \|2 sin(---) + 6cosh(x) + 2\|2 \|2 cos(---) - 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R - 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (4\|2 \|2 cos(---) - 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (- 2\|2 \|2 cosh(x) - 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (2\|2 \|2 cos(---) - 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R - 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R +------+ +-+ +------+ +--R - 2\|1 - %i \|2 atanh(\|1 + %i tanh(x)) +--R + +--R +------+ +-+ +------+ +--R - 2\|1 + %i \|2 atanh(\|1 - %i tanh(x)) +--R + +--R - +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) + 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) - 2\|2 cos(---) - \|2 +--R 8 +--R + +--R - +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) - 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) - 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) + 2\|2 cos(---) - \|2 +--R 8 +--R / +--R +------+ +------+ +-+ +--R 4\|1 - %i \|1 + %i \|2 +--R Type: Expression(Complex(Integer)) +--E 439 + +--S 440 of 510 +d0085:= D(m0085,x) +--R +--R +--R (381) +--R 16 15 +--R - sinh(x) - 16cosh(x)sinh(x) +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 2 +--R 4\|2 sin(---) + 8\|2 cos(---)sin(---) - 120cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 4\|2 cos(---) + 8 +--R 8 +--R * +--R 14 +--R sinh(x) +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi +--R 56\|2 cosh(x)sin(---) + 112\|2 cos(---)cosh(x)sin(---) +--R 8 8 8 +--R + +--R 3 4+-+2 %pi 2 +--R - 560cosh(x) + (- 56\|2 cos(---) + 112)cosh(x) +--R 8 +--R * +--R 13 +--R sinh(x) +--R + +--R 4+-+2 2 4+-+2 %pi 2 +--R (364\|2 cosh(x) - 40\|2 )sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi +--R (728\|2 cos(---)cosh(x) - 48\|2 cos(---))sin(---) +--R 8 8 8 +--R + +--R 4 4+-+2 %pi 2 2 +--R - 1820cosh(x) + (- 364\|2 cos(---) + 728)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 +--R 40\|2 cos(---) - 44 +--R 8 +--R * +--R 12 +--R sinh(x) +--R + +--R 4+-+2 3 4+-+2 %pi 2 +--R (1456\|2 cosh(x) - 480\|2 cosh(x))sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi +--R (2912\|2 cos(---)cosh(x) - 576\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 5 4+-+2 %pi 2 3 +--R - 4368cosh(x) + (- 1456\|2 cos(---) + 2912)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 +--R (480\|2 cos(---) - 528)cosh(x) +--R 8 +--R * +--R 11 +--R sinh(x) +--R + +--R %pi 4 %pi %pi 3 +--R 32sin(---) + 128cos(---)sin(---) +--R 8 8 8 +--R + +--R 4+-+2 4 4+-+2 2 %pi 2 +--R 4004\|2 cosh(x) - 2640\|2 cosh(x) + 320cos(---) +--R 8 +--R + +--R 4+-+2 +--R 220\|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R 8008\|2 cos(---)cosh(x) - 3168\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi +--R - 128cos(---) + 184\|2 cos(---) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 6 4+-+2 %pi 2 4 +--R - 8008cosh(x) + (- 4004\|2 cos(---) + 8008)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 2 %pi 4 +--R (2640\|2 cos(---) - 2904)cosh(x) + 32cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 220\|2 cos(---) + 152 +--R 8 +--R * +--R 10 +--R sinh(x) +--R + +--R %pi 4 %pi %pi 3 +--R 320cosh(x)sin(---) + 1280cos(---)cosh(x)sin(---) +--R 8 8 8 +--R + +--R 4+-+2 5 4+-+2 3 +--R 8008\|2 cosh(x) - 8800\|2 cosh(x) +--R + +--R %pi 2 4+-+2 +--R (3200cos(---) + 2200\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi 3 +--R 16016\|2 cos(---)cosh(x) - 10560\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi +--R (- 1280cos(---) + 1840\|2 cos(---))cosh(x) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 7 4+-+2 %pi 2 5 +--R - 11440cosh(x) + (- 8008\|2 cos(---) + 16016)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 3 +--R (8800\|2 cos(---) - 9680)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (320cos(---) - 2200\|2 cos(---) + 1520)cosh(x) +--R 8 8 +--R * +--R 9 +--R sinh(x) +--R + +--R 2 %pi 4 +--R (1440cosh(x) - 448)sin(---) +--R 8 +--R + +--R %pi 2 %pi %pi 3 +--R (5760cos(---)cosh(x) - 1536cos(---))sin(---) +--R 8 8 8 +--R + +--R 4+-+2 6 4+-+2 4 +--R 12012\|2 cosh(x) - 19800\|2 cosh(x) +--R + +--R %pi 2 4+-+2 2 %pi 2 4+-+2 +--R (14400cos(---) + 9900\|2 )cosh(x) - 384cos(---) - 752\|2 +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 6 4+-+2 %pi 4 +--R 24024\|2 cos(---)cosh(x) - 23760\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 2 %pi 3 +--R (- 5760cos(---) + 8280\|2 cos(---))cosh(x) + 1536cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi +--R - 320\|2 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 8 4+-+2 %pi 2 6 +--R - 12870cosh(x) + (- 12012\|2 cos(---) + 24024)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 4 +--R (19800\|2 cos(---) - 21780)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (1440cos(---) - 9900\|2 cos(---) + 6840)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R - 448cos(---) + 752\|2 cos(---) - 406 +--R 8 8 +--R * +--R 8 +--R sinh(x) +--R + +--R 3 %pi 4 +--R (3840cosh(x) - 3584cosh(x))sin(---) +--R 8 +--R + +--R %pi 3 %pi %pi 3 +--R (15360cos(---)cosh(x) - 12288cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 4+-+2 7 4+-+2 5 +--R 13728\|2 cosh(x) - 31680\|2 cosh(x) +--R + +--R %pi 2 4+-+2 3 +--R (38400cos(---) + 26400\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R (- 3072cos(---) - 6016\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 7 4+-+2 %pi 5 +--R 27456\|2 cos(---)cosh(x) - 38016\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 3 +--R (- 15360cos(---) + 22080\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi +--R (12288cos(---) - 2560\|2 cos(---))cosh(x) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 9 4+-+2 %pi 2 7 +--R - 11440cosh(x) + (- 13728\|2 cos(---) + 27456)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 5 +--R (31680\|2 cos(---) - 34848)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (3840cos(---) - 26400\|2 cos(---) + 18240)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (- 3584cos(---) + 6016\|2 cos(---) - 3248)cosh(x) +--R 8 8 +--R * +--R 7 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 4+-+2 %pi %pi 5 +--R 128\|2 sin(---) + 768\|2 cos(---)sin(---) +--R 8 8 8 +--R + +--R 4 2 4+-+2 %pi 2 +--R (6720cosh(x) - 12544cosh(x) + 128\|2 cos(---) + 2496) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 4 %pi 2 +--R 26880cos(---)cosh(x) - 43008cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R 1536\|2 cos(---) + 2816cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 8 4+-+2 6 +--R 12012\|2 cosh(x) - 36960\|2 cosh(x) +--R + +--R %pi 2 4+-+2 4 +--R (67200cos(---) + 46200\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 2 4+-+2 %pi 4 +--R (- 10752cos(---) - 21056\|2 )cosh(x) - 128\|2 cos(---) +--R 8 8 +--R + +--R %pi 2 4+-+2 +--R - 3712cos(---) + 1788\|2 +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 8 4+-+2 %pi 6 +--R 24024\|2 cos(---)cosh(x) - 44352\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 4 +--R (- 26880cos(---) + 38640\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 2 +--R (43008cos(---) - 8960\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R 768\|2 cos(---) - 2816cos(---) + 248\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 10 4+-+2 %pi 2 8 +--R - 8008cosh(x) + (- 12012\|2 cos(---) + 24024)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 6 +--R (36960\|2 cos(---) - 40656)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (6720cos(---) - 46200\|2 cos(---) + 31920)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (- 12544cos(---) + 21056\|2 cos(---) - 11368)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 128\|2 cos(---) + 2496cos(---) - 1788\|2 cos(---) + 760 +--R 8 8 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 4+-+2 %pi %pi 5 +--R 768\|2 cosh(x)sin(---) + 4608\|2 cos(---)cosh(x)sin(---) +--R 8 8 8 +--R + +--R 5 3 +--R 8064cosh(x) - 25088cosh(x) +--R + +--R 4+-+2 %pi 2 +--R (768\|2 cos(---) + 14976)cosh(x) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 5 %pi 3 +--R 32256cos(---)cosh(x) - 86016cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (9216\|2 cos(---) + 16896cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 9 4+-+2 7 +--R 8008\|2 cosh(x) - 31680\|2 cosh(x) +--R + +--R %pi 2 4+-+2 5 +--R (80640cos(---) + 55440\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 3 +--R (- 21504cos(---) - 42112\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R (- 768\|2 cos(---) - 22272cos(---) + 10728\|2 )cosh(x) +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 9 4+-+2 %pi 7 +--R 16016\|2 cos(---)cosh(x) - 38016\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 5 +--R (- 32256cos(---) + 46368\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 3 +--R (86016cos(---) - 17920\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (4608\|2 cos(---) - 16896cos(---) + 1488\|2 cos(---)) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 11 4+-+2 %pi 2 9 +--R - 4368cosh(x) + (- 8008\|2 cos(---) + 16016)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 7 +--R (31680\|2 cos(---) - 34848)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (8064cos(---) - 55440\|2 cos(---) + 38304)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (- 25088cos(---) + 42112\|2 cos(---) - 22736)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 768\|2 cos(---) + 14976cos(---) - 10728\|2 cos(---) +--R 8 8 8 +--R + +--R 4560 +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4+-+2 2 4+-+2 %pi 6 +--R (1920\|2 cosh(x) - 1792\|2 )sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 5 +--R (11520\|2 cos(---)cosh(x) - 1536\|2 cos(---))sin(---) +--R 8 8 8 +--R + +--R 6 4 +--R 6720cosh(x) - 31360cosh(x) +--R + +--R 4+-+2 %pi 2 2 4+-+2 %pi 2 +--R (1920\|2 cos(---) + 37440)cosh(x) - 1792\|2 cos(---) +--R 8 8 +--R + +--R - 5376 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 6 %pi 4 +--R 26880cos(---)cosh(x) - 107520cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (23040\|2 cos(---) + 42240cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R - 3072\|2 cos(---) + 512cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 10 4+-+2 8 +--R 4004\|2 cosh(x) - 19800\|2 cosh(x) +--R + +--R %pi 2 4+-+2 6 +--R (67200cos(---) + 46200\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 4 +--R (- 26880cos(---) - 52640\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 2 +--R (- 1920\|2 cos(---) - 55680cos(---) + 26820\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R 1792\|2 cos(---) + 7680cos(---) - 2856\|2 +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 10 4+-+2 %pi 8 +--R 8008\|2 cos(---)cosh(x) - 23760\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 6 +--R (- 26880cos(---) + 38640\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 4 +--R (107520cos(---) - 22400\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (11520\|2 cos(---) - 42240cos(---) + 3720\|2 cos(---)) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 1536\|2 cos(---) - 512cos(---) + 784\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 12 4+-+2 %pi 2 10 +--R - 1820cosh(x) + (- 4004\|2 cos(---) + 8008)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 8 +--R (19800\|2 cos(---) - 21780)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (6720cos(---) - 46200\|2 cos(---) + 31920)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (- 31360cos(---) + 52640\|2 cos(---) - 28420)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 1920\|2 cos(---) + 37440cos(---) - 26820\|2 cos(---) +--R 8 8 8 +--R + +--R 11400 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 1792\|2 cos(---) - 5376cos(---) + 2856\|2 cos(---) - 1100 +--R 8 8 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 4+-+2 3 4+-+2 %pi 6 +--R (2560\|2 cosh(x) - 7168\|2 cosh(x))sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi 5 +--R (15360\|2 cos(---)cosh(x) - 6144\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 7 5 +--R 3840cosh(x) - 25088cosh(x) +--R + +--R 4+-+2 %pi 2 3 +--R (2560\|2 cos(---) + 49920)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 +--R (- 7168\|2 cos(---) - 21504)cosh(x) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 7 %pi 5 +--R 15360cos(---)cosh(x) - 86016cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 3 +--R (30720\|2 cos(---) + 56320cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (- 12288\|2 cos(---) + 2048cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 11 4+-+2 9 +--R 1456\|2 cosh(x) - 8800\|2 cosh(x) +--R + +--R %pi 2 4+-+2 7 +--R (38400cos(---) + 26400\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 5 +--R (- 21504cos(---) - 42112\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 3 +--R (- 2560\|2 cos(---) - 74240cos(---) + 35760\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R (7168\|2 cos(---) + 30720cos(---) - 11424\|2 )cosh(x) +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 11 4+-+2 %pi 9 +--R 2912\|2 cos(---)cosh(x) - 10560\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 7 +--R (- 15360cos(---) + 22080\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 5 +--R (86016cos(---) - 17920\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (15360\|2 cos(---) - 56320cos(---) + 4960\|2 cos(---)) +--R 8 8 8 +--R * +--R 3 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 6144\|2 cos(---) - 2048cos(---) + 3136\|2 cos(---)) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 13 4+-+2 %pi 2 11 +--R - 560cosh(x) + (- 1456\|2 cos(---) + 2912)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 9 +--R (8800\|2 cos(---) - 9680)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 7 +--R (3840cos(---) - 26400\|2 cos(---) + 18240)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (- 25088cos(---) + 42112\|2 cos(---) - 22736)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 2560\|2 cos(---) + 49920cos(---) - 35760\|2 cos(---) +--R 8 8 8 +--R + +--R 15200 +--R * +--R 3 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 7168\|2 cos(---) - 21504cos(---) + 11424\|2 cos(---) +--R 8 8 8 +--R + +--R - 4400 +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R %pi 8 +--R 1024sin(---) +--R 8 +--R + +--R 4+-+2 4 4+-+2 2 %pi 2 +--R 1920\|2 cosh(x) - 10752\|2 cosh(x) + 4096cos(---) +--R 8 +--R + +--R 4+-+2 +--R 3200\|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R 11520\|2 cos(---)cosh(x) - 9216\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 1280\|2 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 8 6 +--R 1440cosh(x) - 12544cosh(x) +--R + +--R 4+-+2 %pi 2 4 +--R (1920\|2 cos(---) + 37440)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 2 %pi 4 +--R (- 10752\|2 cos(---) - 32256)cosh(x) + 6144cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi 2 +--R 3200\|2 cos(---) + 6432 +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 8 %pi 6 +--R 5760cos(---)cosh(x) - 43008cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 4 +--R (23040\|2 cos(---) + 42240cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (- 18432\|2 cos(---) + 3072cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R - 2560\|2 cos(---) - 6016cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 12 4+-+2 10 +--R 364\|2 cosh(x) - 2640\|2 cosh(x) +--R + +--R %pi 2 4+-+2 8 +--R (14400cos(---) + 9900\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 6 +--R (- 10752cos(---) - 21056\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 4 +--R (- 1920\|2 cos(---) - 55680cos(---) + 26820\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 2 +--R (10752\|2 cos(---) + 46080cos(---) - 17136\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R 4096cos(---) - 3200\|2 cos(---) - 5312cos(---) + 2980\|2 +--R 8 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 12 4+-+2 %pi 10 +--R 728\|2 cos(---)cosh(x) - 3168\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 8 +--R (- 5760cos(---) + 8280\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 6 +--R (43008cos(---) - 8960\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (11520\|2 cos(---) - 42240cos(---) + 3720\|2 cos(---)) +--R 8 8 8 +--R * +--R 4 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 9216\|2 cos(---) - 3072cos(---) + 4704\|2 cos(---)) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 1280\|2 cos(---) + 6016cos(---) - 1720\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 14 4+-+2 %pi 2 12 +--R - 120cosh(x) + (- 364\|2 cos(---) + 728)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 10 +--R (2640\|2 cos(---) - 2904)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 8 +--R (1440cos(---) - 9900\|2 cos(---) + 6840)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (- 12544cos(---) + 21056\|2 cos(---) - 11368)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 1920\|2 cos(---) + 37440cos(---) - 26820\|2 cos(---) +--R 8 8 8 +--R + +--R 11400 +--R * +--R 4 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 10752\|2 cos(---) - 32256cos(---) + 17136\|2 cos(---) +--R 8 8 8 +--R + +--R - 6600 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 1024cos(---) - 3200\|2 cos(---) + 6432cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 2980\|2 cos(---) + 1000 +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R %pi 8 +--R 2048cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 5 4+-+2 3 +--R 768\|2 cosh(x) - 7168\|2 cosh(x) +--R + +--R %pi 2 4+-+2 +--R (8192cos(---) + 6400\|2 )cosh(x) +--R 8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi 3 +--R 4608\|2 cos(---)cosh(x) - 6144\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 2560\|2 cos(---)cosh(x) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 9 7 +--R 320cosh(x) - 3584cosh(x) +--R + +--R 4+-+2 %pi 2 5 +--R (768\|2 cos(---) + 14976)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 3 +--R (- 7168\|2 cos(---) - 21504)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (12288cos(---) + 6400\|2 cos(---) + 12864)cosh(x) +--R 8 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 9 %pi 7 +--R 1280cos(---)cosh(x) - 12288cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 5 +--R (9216\|2 cos(---) + 16896cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 3 +--R (- 12288\|2 cos(---) + 2048cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (- 5120\|2 cos(---) - 12032cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 13 4+-+2 11 +--R 56\|2 cosh(x) - 480\|2 cosh(x) +--R + +--R %pi 2 4+-+2 9 +--R (3200cos(---) + 2200\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 7 +--R (- 3072cos(---) - 6016\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 5 +--R (- 768\|2 cos(---) - 22272cos(---) + 10728\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 3 +--R (7168\|2 cos(---) + 30720cos(---) - 11424\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 +--R 8192cos(---) - 6400\|2 cos(---) - 10624cos(---) +--R 8 8 8 +--R + +--R 4+-+2 +--R 5960\|2 +--R * +--R cosh(x) +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 13 4+-+2 %pi 11 +--R 112\|2 cos(---)cosh(x) - 576\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 9 +--R (- 1280cos(---) + 1840\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 7 +--R (12288cos(---) - 2560\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (4608\|2 cos(---) - 16896cos(---) + 1488\|2 cos(---)) +--R 8 8 8 +--R * +--R 5 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 6144\|2 cos(---) - 2048cos(---) + 3136\|2 cos(---)) +--R 8 8 8 +--R * +--R 3 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 2560\|2 cos(---) + 12032cos(---) - 3440\|2 cos(---)) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 15 4+-+2 %pi 2 13 +--R - 16cosh(x) + (- 56\|2 cos(---) + 112)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 11 +--R (480\|2 cos(---) - 528)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 9 +--R (320cos(---) - 2200\|2 cos(---) + 1520)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 7 +--R (- 3584cos(---) + 6016\|2 cos(---) - 3248)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 768\|2 cos(---) + 14976cos(---) - 10728\|2 cos(---) +--R 8 8 8 +--R + +--R 4560 +--R * +--R 5 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 7168\|2 cos(---) - 21504cos(---) + 11424\|2 cos(---) +--R 8 8 8 +--R + +--R - 4400 +--R * +--R 3 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 2048cos(---) - 6400\|2 cos(---) + 12864cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 5960\|2 cos(---) + 2000 +--R 8 +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 %pi 8 +--R (1024cosh(x) - 1024)sin(---) +--R 8 +--R + +--R 4+-+2 6 4+-+2 4 +--R 128\|2 cosh(x) - 1792\|2 cosh(x) +--R + +--R %pi 2 4+-+2 2 %pi 2 4+-+2 +--R (4096cos(---) + 3200\|2 )cosh(x) - 4096cos(---) - 2048\|2 +--R 8 8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 6 4+-+2 %pi 4 +--R 768\|2 cos(---)cosh(x) - 1536\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi +--R - 1280\|2 cos(---)cosh(x) + 3072\|2 cos(---) +--R 8 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 10 8 4+-+2 %pi 2 6 +--R 32cosh(x) - 448cosh(x) + (128\|2 cos(---) + 2496)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 4 +--R (- 1792\|2 cos(---) - 5376)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (6144cos(---) + 3200\|2 cos(---) + 6432)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R - 6144cos(---) - 2048\|2 cos(---) - 3648 +--R 8 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 10 %pi 8 +--R 128cos(---)cosh(x) - 1536cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 6 +--R (1536\|2 cos(---) + 2816cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 4 +--R (- 3072\|2 cos(---) + 512cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (- 2560\|2 cos(---) - 6016cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R 6144\|2 cos(---) + 6144cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 14 4+-+2 12 +--R 4\|2 cosh(x) - 40\|2 cosh(x) +--R + +--R %pi 2 4+-+2 10 +--R (320cos(---) + 220\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 8 +--R (- 384cos(---) - 752\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 6 +--R (- 128\|2 cos(---) - 3712cos(---) + 1788\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 4 +--R (1792\|2 cos(---) + 7680cos(---) - 2856\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 +--R 4096cos(---) - 3200\|2 cos(---) - 5312cos(---) +--R 8 8 8 +--R + +--R 4+-+2 +--R 2980\|2 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R - 4096cos(---) + 2048\|2 cos(---) - 3712cos(---) - 1600\|2 +--R 8 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 14 4+-+2 %pi 12 +--R 8\|2 cos(---)cosh(x) - 48\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 10 +--R (- 128cos(---) + 184\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 8 +--R (1536cos(---) - 320\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 6 +--R (768\|2 cos(---) - 2816cos(---) + 248\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 4 +--R (- 1536\|2 cos(---) - 512cos(---) + 784\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 1280\|2 cos(---) + 6016cos(---) - 1720\|2 cos(---)) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R 3072\|2 cos(---) - 6144cos(---) + 2400\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 16 4+-+2 %pi 2 14 +--R - cosh(x) + (- 4\|2 cos(---) + 8)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 12 +--R (40\|2 cos(---) - 44)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 10 +--R (32cos(---) - 220\|2 cos(---) + 152)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 8 +--R (- 448cos(---) + 752\|2 cos(---) - 406)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 128\|2 cos(---) + 2496cos(---) - 1788\|2 cos(---) + 760) +--R 8 8 8 +--R * +--R 6 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (1792\|2 cos(---) - 5376cos(---) + 2856\|2 cos(---) - 1100) +--R 8 8 8 +--R * +--R 4 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 1024cos(---) - 3200\|2 cos(---) + 6432cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 2980\|2 cos(---) + 1000 +--R 8 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R - 1024cos(---) + 2048\|2 cos(---) - 3648cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 1600\|2 cos(---) - 625 +--R 8 +--R * +--R 4 +--R tanh(x) +--R + +--R 16 15 +--R 2sinh(x) + 32cosh(x)sinh(x) +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 2 +--R - 4\|2 sin(---) - 8\|2 cos(---)sin(---) + 240cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 4\|2 cos(---) - 16 +--R 8 +--R * +--R 14 +--R sinh(x) +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi +--R - 56\|2 cosh(x)sin(---) - 112\|2 cos(---)cosh(x)sin(---) +--R 8 8 8 +--R + +--R 3 4+-+2 %pi 2 +--R 1120cosh(x) + (56\|2 cos(---) - 224)cosh(x) +--R 8 +--R * +--R 13 +--R sinh(x) +--R + +--R 4+-+2 2 4+-+2 %pi 2 +--R (- 364\|2 cosh(x) + 40\|2 )sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi +--R (- 728\|2 cos(---)cosh(x) + 80\|2 cos(---))sin(---) +--R 8 8 8 +--R + +--R 4 4+-+2 %pi 2 2 +--R 3640cosh(x) + (364\|2 cos(---) - 1456)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 +--R - 40\|2 cos(---) + 88 +--R 8 +--R * +--R 12 +--R sinh(x) +--R + +--R 4+-+2 3 4+-+2 %pi 2 +--R (- 1456\|2 cosh(x) + 480\|2 cosh(x))sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi +--R (- 2912\|2 cos(---)cosh(x) + 960\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 5 4+-+2 %pi 2 3 +--R 8736cosh(x) + (1456\|2 cos(---) - 5824)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 +--R (- 480\|2 cos(---) + 1056)cosh(x) +--R 8 +--R * +--R 11 +--R sinh(x) +--R + +--R %pi 4 %pi %pi 3 +--R - 32sin(---) - 128cos(---)sin(---) +--R 8 8 8 +--R + +--R 4+-+2 4 4+-+2 2 %pi 2 +--R - 4004\|2 cosh(x) + 2640\|2 cosh(x) - 320cos(---) +--R 8 +--R + +--R 4+-+2 +--R - 284\|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R - 8008\|2 cos(---)cosh(x) + 5280\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi +--R 128cos(---) - 376\|2 cos(---) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 6 4+-+2 %pi 2 4 +--R 16016cosh(x) + (4004\|2 cos(---) - 16016)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 2 %pi 4 +--R (- 2640\|2 cos(---) + 5808)cosh(x) - 32cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi 2 +--R 284\|2 cos(---) - 304 +--R 8 +--R * +--R 10 +--R sinh(x) +--R + +--R %pi 4 %pi %pi 3 +--R - 320cosh(x)sin(---) - 1280cos(---)cosh(x)sin(---) +--R 8 8 8 +--R + +--R 4+-+2 5 4+-+2 3 +--R - 8008\|2 cosh(x) + 8800\|2 cosh(x) +--R + +--R %pi 2 4+-+2 +--R (- 3200cos(---) - 2840\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi 3 +--R - 16016\|2 cos(---)cosh(x) + 17600\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi +--R (1280cos(---) - 3760\|2 cos(---))cosh(x) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 7 4+-+2 %pi 2 5 +--R 22880cosh(x) + (8008\|2 cos(---) - 32032)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 3 +--R (- 8800\|2 cos(---) + 19360)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (- 320cos(---) + 2840\|2 cos(---) - 3040)cosh(x) +--R 8 8 +--R * +--R 9 +--R sinh(x) +--R + +--R 2 %pi 4 +--R (- 1440cosh(x) + 512)sin(---) +--R 8 +--R + +--R %pi 2 %pi %pi 3 +--R (- 5760cos(---)cosh(x) + 1536cos(---))sin(---) +--R 8 8 8 +--R + +--R 4+-+2 6 4+-+2 4 +--R - 12012\|2 cosh(x) + 19800\|2 cosh(x) +--R + +--R %pi 2 4+-+2 2 %pi 2 +--R (- 14400cos(---) - 12780\|2 )cosh(x) + 1024cos(---) +--R 8 8 +--R + +--R 4+-+2 +--R 1072\|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 6 4+-+2 %pi 4 +--R - 24024\|2 cos(---)cosh(x) + 39600\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 2 %pi 3 +--R (5760cos(---) - 16920\|2 cos(---))cosh(x) - 1536cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi +--R 928\|2 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 8 4+-+2 %pi 2 6 +--R 25740cosh(x) + (12012\|2 cos(---) - 48048)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 4 +--R (- 19800\|2 cos(---) + 43560)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (- 1440cos(---) + 12780\|2 cos(---) - 13680)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R 512cos(---) - 1072\|2 cos(---) + 812 +--R 8 8 +--R * +--R 8 +--R sinh(x) +--R + +--R 3 %pi 4 +--R (- 3840cosh(x) + 4096cosh(x))sin(---) +--R 8 +--R + +--R %pi 3 %pi %pi 3 +--R (- 15360cos(---)cosh(x) + 12288cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 4+-+2 7 4+-+2 5 +--R - 13728\|2 cosh(x) + 31680\|2 cosh(x) +--R + +--R %pi 2 4+-+2 3 +--R (- 38400cos(---) - 34080\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R (8192cos(---) + 8576\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 7 4+-+2 %pi 5 +--R - 27456\|2 cos(---)cosh(x) + 63360\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 3 +--R (15360cos(---) - 45120\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi +--R (- 12288cos(---) + 7424\|2 cos(---))cosh(x) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 9 4+-+2 %pi 2 7 +--R 22880cosh(x) + (13728\|2 cos(---) - 54912)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 5 +--R (- 31680\|2 cos(---) + 69696)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (- 3840cos(---) + 34080\|2 cos(---) - 36480)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (4096cos(---) - 8576\|2 cos(---) + 6496)cosh(x) +--R 8 8 +--R * +--R 7 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 4+-+2 %pi %pi 5 +--R - 128\|2 sin(---) - 768\|2 cos(---)sin(---) +--R 8 8 8 +--R + +--R 4 2 4+-+2 %pi 2 +--R (- 6720cosh(x) + 14336cosh(x) - 128\|2 cos(---) - 2752) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 4 %pi 2 +--R - 26880cos(---)cosh(x) + 43008cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R - 1536\|2 cos(---) - 4864cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 8 4+-+2 6 +--R - 12012\|2 cosh(x) + 36960\|2 cosh(x) +--R + +--R %pi 2 4+-+2 4 +--R (- 67200cos(---) - 59640\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 2 4+-+2 %pi 4 +--R (28672cos(---) + 30016\|2 )cosh(x) + 128\|2 cos(---) +--R 8 8 +--R + +--R %pi 2 4+-+2 +--R 1152cos(---) - 2940\|2 +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 8 4+-+2 %pi 6 +--R - 24024\|2 cos(---)cosh(x) + 73920\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 4 +--R (26880cos(---) - 78960\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 2 +--R (- 43008cos(---) + 25984\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 768\|2 cos(---) + 4864cos(---) - 1400\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 10 4+-+2 %pi 2 8 +--R 16016cosh(x) + (12012\|2 cos(---) - 48048)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 6 +--R (- 36960\|2 cos(---) + 81312)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (- 6720cos(---) + 59640\|2 cos(---) - 63840)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (14336cos(---) - 30016\|2 cos(---) + 22736)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 128\|2 cos(---) - 2752cos(---) + 2940\|2 cos(---) - 1520 +--R 8 8 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 4+-+2 %pi %pi 5 +--R - 768\|2 cosh(x)sin(---) - 4608\|2 cos(---)cosh(x)sin(---) +--R 8 8 8 +--R + +--R 5 3 +--R - 8064cosh(x) + 28672cosh(x) +--R + +--R 4+-+2 %pi 2 +--R (- 768\|2 cos(---) - 16512)cosh(x) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 5 %pi 3 +--R - 32256cos(---)cosh(x) + 86016cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (- 9216\|2 cos(---) - 29184cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 9 4+-+2 7 +--R - 8008\|2 cosh(x) + 31680\|2 cosh(x) +--R + +--R %pi 2 4+-+2 5 +--R (- 80640cos(---) - 71568\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 3 +--R (57344cos(---) + 60032\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R (768\|2 cos(---) + 6912cos(---) - 17640\|2 )cosh(x) +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 9 4+-+2 %pi 7 +--R - 16016\|2 cos(---)cosh(x) + 63360\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 5 +--R (32256cos(---) - 94752\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 3 +--R (- 86016cos(---) + 51968\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 4608\|2 cos(---) + 29184cos(---) - 8400\|2 cos(---)) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 11 4+-+2 %pi 2 9 +--R 8736cosh(x) + (8008\|2 cos(---) - 32032)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 7 +--R (- 31680\|2 cos(---) + 69696)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (- 8064cos(---) + 71568\|2 cos(---) - 76608)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (28672cos(---) - 60032\|2 cos(---) + 45472)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 768\|2 cos(---) - 16512cos(---) + 17640\|2 cos(---) +--R 8 8 8 +--R + +--R - 9120 +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4+-+2 2 4+-+2 %pi 6 +--R (- 1920\|2 cosh(x) + 1792\|2 )sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 5 +--R (- 11520\|2 cos(---)cosh(x) + 2560\|2 cos(---))sin(---) +--R 8 8 8 +--R + +--R 6 4 +--R - 6720cosh(x) + 35840cosh(x) +--R + +--R 4+-+2 %pi 2 2 4+-+2 %pi 2 +--R (- 1920\|2 cos(---) - 41280)cosh(x) + 1792\|2 cos(---) +--R 8 8 +--R + +--R 8320 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 6 %pi 4 +--R - 26880cos(---)cosh(x) + 107520cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (- 23040\|2 cos(---) - 72960cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R 5120\|2 cos(---) + 5632cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 10 4+-+2 8 +--R - 4004\|2 cosh(x) + 19800\|2 cosh(x) +--R + +--R %pi 2 4+-+2 6 +--R (- 67200cos(---) - 59640\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 4 +--R (71680cos(---) + 75040\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 2 +--R (1920\|2 cos(---) + 17280cos(---) - 44100\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R - 1792\|2 cos(---) - 11008cos(---) + 5032\|2 +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 10 4+-+2 %pi 8 +--R - 8008\|2 cos(---)cosh(x) + 39600\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 6 +--R (26880cos(---) - 78960\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 4 +--R (- 107520cos(---) + 64960\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 +--R - 11520\|2 cos(---) + 72960cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 21000\|2 cos(---) +--R 8 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R 2560\|2 cos(---) - 5632cos(---) - 48\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 12 4+-+2 %pi 2 10 +--R 3640cosh(x) + (4004\|2 cos(---) - 16016)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 8 +--R (- 19800\|2 cos(---) + 43560)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (- 6720cos(---) + 59640\|2 cos(---) - 63840)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (35840cos(---) - 75040\|2 cos(---) + 56840)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 1920\|2 cos(---) - 41280cos(---) + 44100\|2 cos(---) +--R 8 8 8 +--R + +--R - 22800 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 1792\|2 cos(---) + 8320cos(---) - 5032\|2 cos(---) + 2200 +--R 8 8 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 4+-+2 3 4+-+2 %pi 6 +--R (- 2560\|2 cosh(x) + 7168\|2 cosh(x))sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi +--R (- 15360\|2 cos(---)cosh(x) + 10240\|2 cos(---)cosh(x)) +--R 8 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 7 5 +--R - 3840cosh(x) + 28672cosh(x) +--R + +--R 4+-+2 %pi 2 3 +--R (- 2560\|2 cos(---) - 55040)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 +--R (7168\|2 cos(---) + 33280)cosh(x) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 7 %pi 5 +--R - 15360cos(---)cosh(x) + 86016cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 3 +--R (- 30720\|2 cos(---) - 97280cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (20480\|2 cos(---) + 22528cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 11 4+-+2 9 +--R - 1456\|2 cosh(x) + 8800\|2 cosh(x) +--R + +--R %pi 2 4+-+2 7 +--R (- 38400cos(---) - 34080\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 5 +--R (57344cos(---) + 60032\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 3 +--R (2560\|2 cos(---) + 23040cos(---) - 58800\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R (- 7168\|2 cos(---) - 44032cos(---) + 20128\|2 )cosh(x) +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 11 4+-+2 %pi 9 +--R - 2912\|2 cos(---)cosh(x) + 17600\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 7 +--R (15360cos(---) - 45120\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 5 +--R (- 86016cos(---) + 51968\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 +--R - 15360\|2 cos(---) + 97280cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 28000\|2 cos(---) +--R 8 +--R * +--R 3 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (10240\|2 cos(---) - 22528cos(---) - 192\|2 cos(---)) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 13 4+-+2 %pi 2 11 +--R 1120cosh(x) + (1456\|2 cos(---) - 5824)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 9 +--R (- 8800\|2 cos(---) + 19360)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 7 +--R (- 3840cos(---) + 34080\|2 cos(---) - 36480)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (28672cos(---) - 60032\|2 cos(---) + 45472)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 2560\|2 cos(---) - 55040cos(---) + 58800\|2 cos(---) +--R 8 8 8 +--R + +--R - 30400 +--R * +--R 3 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 7168\|2 cos(---) + 33280cos(---) - 20128\|2 cos(---) +--R 8 8 8 +--R + +--R 8800 +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R %pi 8 +--R - 1024sin(---) +--R 8 +--R + +--R 4+-+2 4 4+-+2 2 %pi 2 +--R - 1920\|2 cosh(x) + 10752\|2 cosh(x) - 4096cos(---) +--R 8 +--R + +--R 4+-+2 +--R - 5248\|2 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R - 11520\|2 cos(---)cosh(x) + 15360\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 768\|2 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 8 6 +--R - 1440cosh(x) + 14336cosh(x) +--R + +--R 4+-+2 %pi 2 4 +--R (- 1920\|2 cos(---) - 41280)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 2 %pi 4 +--R (10752\|2 cos(---) + 49920)cosh(x) - 6144cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 5248\|2 cos(---) - 11808 +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 8 %pi 6 +--R - 5760cos(---)cosh(x) + 43008cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 4 +--R (- 23040\|2 cos(---) - 72960cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (30720\|2 cos(---) + 33792cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R - 1536\|2 cos(---) + 8064cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 12 4+-+2 10 +--R - 364\|2 cosh(x) + 2640\|2 cosh(x) +--R + +--R %pi 2 4+-+2 8 +--R (- 14400cos(---) - 12780\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 6 +--R (28672cos(---) + 30016\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 4 +--R (1920\|2 cos(---) + 17280cos(---) - 44100\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 2 +--R (- 10752\|2 cos(---) - 66048cos(---) + 30192\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 +--R - 4096cos(---) + 5248\|2 cos(---) + 17088cos(---) +--R 8 8 8 +--R + +--R 4+-+2 +--R - 5860\|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 12 4+-+2 %pi 10 +--R - 728\|2 cos(---)cosh(x) + 5280\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 8 +--R (5760cos(---) - 16920\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 6 +--R (- 43008cos(---) + 25984\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 +--R - 11520\|2 cos(---) + 72960cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 21000\|2 cos(---) +--R 8 +--R * +--R 4 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (15360\|2 cos(---) - 33792cos(---) - 288\|2 cos(---)) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 768\|2 cos(---) - 8064cos(---) + 2040\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 14 4+-+2 %pi 2 12 +--R 240cosh(x) + (364\|2 cos(---) - 1456)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 10 +--R (- 2640\|2 cos(---) + 5808)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 8 +--R (- 1440cos(---) + 12780\|2 cos(---) - 13680)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (14336cos(---) - 30016\|2 cos(---) + 22736)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 1920\|2 cos(---) - 41280cos(---) + 44100\|2 cos(---) +--R 8 8 8 +--R + +--R - 22800 +--R * +--R 4 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 10752\|2 cos(---) + 49920cos(---) - 30192\|2 cos(---) +--R 8 8 8 +--R + +--R 13200 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R - 1024cos(---) + 5248\|2 cos(---) - 11808cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 5860\|2 cos(---) - 2000 +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R %pi 8 +--R - 2048cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 5 4+-+2 3 +--R - 768\|2 cosh(x) + 7168\|2 cosh(x) +--R + +--R %pi 2 4+-+2 +--R (- 8192cos(---) - 10496\|2 )cosh(x) +--R 8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi 3 +--R - 4608\|2 cos(---)cosh(x) + 10240\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 1536\|2 cos(---)cosh(x) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 9 7 +--R - 320cosh(x) + 4096cosh(x) +--R + +--R 4+-+2 %pi 2 5 +--R (- 768\|2 cos(---) - 16512)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 3 +--R (7168\|2 cos(---) + 33280)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (- 12288cos(---) - 10496\|2 cos(---) - 23616)cosh(x) +--R 8 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 9 %pi 7 +--R - 1280cos(---)cosh(x) + 12288cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 5 +--R (- 9216\|2 cos(---) - 29184cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 3 +--R (20480\|2 cos(---) + 22528cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (- 3072\|2 cos(---) + 16128cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 13 4+-+2 11 +--R - 56\|2 cosh(x) + 480\|2 cosh(x) +--R + +--R %pi 2 4+-+2 9 +--R (- 3200cos(---) - 2840\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 7 +--R (8192cos(---) + 8576\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 5 +--R (768\|2 cos(---) + 6912cos(---) - 17640\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 3 +--R (- 7168\|2 cos(---) - 44032cos(---) + 20128\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 +--R - 8192cos(---) + 10496\|2 cos(---) + 34176cos(---) +--R 8 8 8 +--R + +--R 4+-+2 +--R - 11720\|2 +--R * +--R cosh(x) +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 13 4+-+2 %pi 11 +--R - 112\|2 cos(---)cosh(x) + 960\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 9 +--R (1280cos(---) - 3760\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 7 +--R (- 12288cos(---) + 7424\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 4608\|2 cos(---) + 29184cos(---) - 8400\|2 cos(---)) +--R 8 8 8 +--R * +--R 5 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (10240\|2 cos(---) - 22528cos(---) - 192\|2 cos(---)) +--R 8 8 8 +--R * +--R 3 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 1536\|2 cos(---) - 16128cos(---) + 4080\|2 cos(---)) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 15 4+-+2 %pi 2 13 +--R 32cosh(x) + (56\|2 cos(---) - 224)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 11 +--R (- 480\|2 cos(---) + 1056)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 9 +--R (- 320cos(---) + 2840\|2 cos(---) - 3040)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 7 +--R (4096cos(---) - 8576\|2 cos(---) + 6496)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 768\|2 cos(---) - 16512cos(---) + 17640\|2 cos(---) +--R 8 8 8 +--R + +--R - 9120 +--R * +--R 5 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 7168\|2 cos(---) + 33280cos(---) - 20128\|2 cos(---) +--R 8 8 8 +--R + +--R 8800 +--R * +--R 3 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R - 2048cos(---) + 10496\|2 cos(---) - 23616cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 11720\|2 cos(---) - 4000 +--R 8 +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 %pi 8 +--R (- 1024cosh(x) + 2048)sin(---) +--R 8 +--R + +--R 4+-+2 6 4+-+2 4 +--R - 128\|2 cosh(x) + 1792\|2 cosh(x) +--R + +--R %pi 2 4+-+2 2 %pi 2 4+-+2 +--R (- 4096cos(---) - 5248\|2 )cosh(x) + 8192cos(---) + 4096\|2 +--R 8 8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 6 4+-+2 %pi 4 +--R - 768\|2 cos(---)cosh(x) + 2560\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi +--R - 768\|2 cos(---)cosh(x) - 6144\|2 cos(---) +--R 8 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 10 8 +--R - 32cosh(x) + 512cosh(x) +--R + +--R 4+-+2 %pi 2 6 +--R (- 128\|2 cos(---) - 2752)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 4 +--R (1792\|2 cos(---) + 8320)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (- 6144cos(---) - 5248\|2 cos(---) - 11808)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R 12288cos(---) + 4096\|2 cos(---) + 7296 +--R 8 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 10 %pi 8 +--R - 128cos(---)cosh(x) + 1536cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 6 +--R (- 1536\|2 cos(---) - 4864cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 4 +--R (5120\|2 cos(---) + 5632cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (- 1536\|2 cos(---) + 8064cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R - 12288\|2 cos(---) - 12288cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 14 4+-+2 12 +--R - 4\|2 cosh(x) + 40\|2 cosh(x) +--R + +--R %pi 2 4+-+2 10 +--R (- 320cos(---) - 284\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 8 +--R (1024cos(---) + 1072\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 6 +--R (128\|2 cos(---) + 1152cos(---) - 2940\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 4 +--R (- 1792\|2 cos(---) - 11008cos(---) + 5032\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 +--R - 4096cos(---) + 5248\|2 cos(---) + 17088cos(---) +--R 8 8 8 +--R + +--R 4+-+2 +--R - 5860\|2 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R 8192cos(---) - 4096\|2 cos(---) + 7424cos(---) + 3200\|2 +--R 8 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 14 4+-+2 %pi 12 +--R - 8\|2 cos(---)cosh(x) + 80\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 10 +--R (128cos(---) - 376\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 8 +--R (- 1536cos(---) + 928\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 6 +--R (- 768\|2 cos(---) + 4864cos(---) - 1400\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 4 +--R (2560\|2 cos(---) - 5632cos(---) - 48\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 2 +--R (- 768\|2 cos(---) - 8064cos(---) + 2040\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 6144\|2 cos(---) + 12288cos(---) - 4800\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 16 4+-+2 %pi 2 14 +--R 2cosh(x) + (4\|2 cos(---) - 16)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 12 +--R (- 40\|2 cos(---) + 88)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 10 +--R (- 32cos(---) + 284\|2 cos(---) - 304)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 8 +--R (512cos(---) - 1072\|2 cos(---) + 812)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (128\|2 cos(---) - 2752cos(---) + 2940\|2 cos(---) - 1520) +--R 8 8 8 +--R * +--R 6 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 1792\|2 cos(---) + 8320cos(---) - 5032\|2 cos(---) + 2200) +--R 8 8 8 +--R * +--R 4 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R - 1024cos(---) + 5248\|2 cos(---) - 11808cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 5860\|2 cos(---) - 2000 +--R 8 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 2048cos(---) - 4096\|2 cos(---) + 7296cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 3200\|2 cos(---) + 1250 +--R 8 +--R * +--R 2 +--R tanh(x) +--R + +--R 16 15 +--R - sinh(x) - 16cosh(x)sinh(x) +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 2 +--R 2\|2 sin(---) + 4\|2 cos(---)sin(---) - 120cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 2\|2 cos(---) + 8 +--R 8 +--R * +--R 14 +--R sinh(x) +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi +--R 28\|2 cosh(x)sin(---) + 56\|2 cos(---)cosh(x)sin(---) +--R 8 8 8 +--R + +--R 3 4+-+2 %pi 2 +--R - 560cosh(x) + (- 28\|2 cos(---) + 112)cosh(x) +--R 8 +--R * +--R 13 +--R sinh(x) +--R + +--R 4+-+2 2 4+-+2 %pi 2 +--R (182\|2 cosh(x) - 20\|2 )sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 4 +--R (364\|2 cos(---)cosh(x) - 40\|2 cos(---))sin(---) - 1820cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 2 4+-+2 %pi 2 +--R (- 182\|2 cos(---) + 728)cosh(x) + 20\|2 cos(---) - 44 +--R 8 8 +--R * +--R 12 +--R sinh(x) +--R + +--R 4+-+2 3 4+-+2 %pi 2 +--R (728\|2 cosh(x) - 240\|2 cosh(x))sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi +--R (1456\|2 cos(---)cosh(x) - 480\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 5 4+-+2 %pi 2 3 +--R - 4368cosh(x) + (- 728\|2 cos(---) + 2912)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 +--R (240\|2 cos(---) - 528)cosh(x) +--R 8 +--R * +--R 11 +--R sinh(x) +--R + +--R %pi 4 %pi %pi 3 +--R 16sin(---) + 64cos(---)sin(---) +--R 8 8 8 +--R + +--R 4+-+2 4 4+-+2 2 %pi 2 4+-+2 +--R (2002\|2 cosh(x) - 1320\|2 cosh(x) + 160cos(---) + 142\|2 ) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R 4004\|2 cos(---)cosh(x) - 2640\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi +--R - 64cos(---) + 188\|2 cos(---) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 6 4+-+2 %pi 2 4 +--R - 8008cosh(x) + (- 2002\|2 cos(---) + 8008)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 2 %pi 4 4+-+2 %pi 2 +--R (1320\|2 cos(---) - 2904)cosh(x) + 16cos(---) - 142\|2 cos(---) +--R 8 8 8 +--R + +--R 152 +--R * +--R 10 +--R sinh(x) +--R + +--R %pi 4 %pi %pi 3 +--R 160cosh(x)sin(---) + 640cos(---)cosh(x)sin(---) +--R 8 8 8 +--R + +--R 4+-+2 5 4+-+2 3 +--R 4004\|2 cosh(x) - 4400\|2 cosh(x) +--R + +--R %pi 2 4+-+2 +--R (1600cos(---) + 1420\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi 3 +--R 8008\|2 cos(---)cosh(x) - 8800\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi +--R (- 640cos(---) + 1880\|2 cos(---))cosh(x) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 7 4+-+2 %pi 2 5 +--R - 11440cosh(x) + (- 4004\|2 cos(---) + 16016)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 3 +--R (4400\|2 cos(---) - 9680)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (160cos(---) - 1420\|2 cos(---) + 1520)cosh(x) +--R 8 8 +--R * +--R 9 +--R sinh(x) +--R + +--R 2 %pi 4 +--R (720cosh(x) - 256)sin(---) +--R 8 +--R + +--R %pi 2 %pi %pi 3 +--R (2880cos(---)cosh(x) - 768cos(---))sin(---) +--R 8 8 8 +--R + +--R 4+-+2 6 4+-+2 4 +--R 6006\|2 cosh(x) - 9900\|2 cosh(x) +--R + +--R %pi 2 4+-+2 2 %pi 2 4+-+2 +--R (7200cos(---) + 6390\|2 )cosh(x) - 512cos(---) - 536\|2 +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 6 4+-+2 %pi 4 +--R 12012\|2 cos(---)cosh(x) - 19800\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 2 %pi 3 +--R (- 2880cos(---) + 8460\|2 cos(---))cosh(x) + 768cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi +--R - 464\|2 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 8 4+-+2 %pi 2 6 +--R - 12870cosh(x) + (- 6006\|2 cos(---) + 24024)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 4 +--R (9900\|2 cos(---) - 21780)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 %pi 4 +--R (720cos(---) - 6390\|2 cos(---) + 6840)cosh(x) - 256cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 536\|2 cos(---) - 406 +--R 8 +--R * +--R 8 +--R sinh(x) +--R + +--R 3 %pi 4 +--R (1920cosh(x) - 2048cosh(x))sin(---) +--R 8 +--R + +--R %pi 3 %pi %pi 3 +--R (7680cos(---)cosh(x) - 6144cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 4+-+2 7 4+-+2 5 +--R 6864\|2 cosh(x) - 15840\|2 cosh(x) +--R + +--R %pi 2 4+-+2 3 +--R (19200cos(---) + 17040\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R (- 4096cos(---) - 4288\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 7 4+-+2 %pi 5 +--R 13728\|2 cos(---)cosh(x) - 31680\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 3 +--R (- 7680cos(---) + 22560\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi +--R (6144cos(---) - 3712\|2 cos(---))cosh(x) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 9 4+-+2 %pi 2 7 +--R - 11440cosh(x) + (- 6864\|2 cos(---) + 27456)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 5 +--R (15840\|2 cos(---) - 34848)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (1920cos(---) - 17040\|2 cos(---) + 18240)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (- 2048cos(---) + 4288\|2 cos(---) - 3248)cosh(x) +--R 8 8 +--R * +--R 7 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 4+-+2 %pi %pi 5 +--R 64\|2 sin(---) + 384\|2 cos(---)sin(---) +--R 8 8 8 +--R + +--R 4 2 4+-+2 %pi 2 %pi 4 +--R (3360cosh(x) - 7168cosh(x) + 64\|2 cos(---) + 1376)sin(---) +--R 8 8 +--R + +--R %pi 4 %pi 2 4+-+2 %pi 3 +--R 13440cos(---)cosh(x) - 21504cos(---)cosh(x) + 768\|2 cos(---) +--R 8 8 8 +--R + +--R %pi +--R 2432cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 8 4+-+2 6 +--R 6006\|2 cosh(x) - 18480\|2 cosh(x) +--R + +--R %pi 2 4+-+2 4 +--R (33600cos(---) + 29820\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 2 4+-+2 %pi 4 +--R (- 14336cos(---) - 15008\|2 )cosh(x) - 64\|2 cos(---) +--R 8 8 +--R + +--R %pi 2 4+-+2 +--R - 576cos(---) + 1470\|2 +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 8 4+-+2 %pi 6 +--R 12012\|2 cos(---)cosh(x) - 36960\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 4 +--R (- 13440cos(---) + 39480\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 2 4+-+2 %pi 5 +--R (21504cos(---) - 12992\|2 cos(---))cosh(x) + 384\|2 cos(---) +--R 8 8 8 +--R + +--R %pi 3 4+-+2 %pi +--R - 2432cos(---) + 700\|2 cos(---) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 10 4+-+2 %pi 2 8 +--R - 8008cosh(x) + (- 6006\|2 cos(---) + 24024)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 6 +--R (18480\|2 cos(---) - 40656)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (3360cos(---) - 29820\|2 cos(---) + 31920)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (- 7168cos(---) + 15008\|2 cos(---) - 11368)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 64\|2 cos(---) + 1376cos(---) - 1470\|2 cos(---) + 760 +--R 8 8 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 4+-+2 %pi %pi 5 +--R 384\|2 cosh(x)sin(---) + 2304\|2 cos(---)cosh(x)sin(---) +--R 8 8 8 +--R + +--R 5 3 4+-+2 %pi 2 +--R (4032cosh(x) - 14336cosh(x) + (384\|2 cos(---) + 8256)cosh(x)) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 5 %pi 3 +--R 16128cos(---)cosh(x) - 43008cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (4608\|2 cos(---) + 14592cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 9 4+-+2 7 +--R 4004\|2 cosh(x) - 15840\|2 cosh(x) +--R + +--R %pi 2 4+-+2 5 +--R (40320cos(---) + 35784\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 3 +--R (- 28672cos(---) - 30016\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R (- 384\|2 cos(---) - 3456cos(---) + 8820\|2 )cosh(x) +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 9 4+-+2 %pi 7 +--R 8008\|2 cos(---)cosh(x) - 31680\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 5 +--R (- 16128cos(---) + 47376\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 3 +--R (43008cos(---) - 25984\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (2304\|2 cos(---) - 14592cos(---) + 4200\|2 cos(---))cosh(x) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 11 4+-+2 %pi 2 9 +--R - 4368cosh(x) + (- 4004\|2 cos(---) + 16016)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 7 +--R (15840\|2 cos(---) - 34848)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (4032cos(---) - 35784\|2 cos(---) + 38304)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (- 14336cos(---) + 30016\|2 cos(---) - 22736)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 384\|2 cos(---) + 8256cos(---) - 8820\|2 cos(---) + 4560) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4+-+2 2 4+-+2 %pi 6 +--R (960\|2 cosh(x) - 896\|2 )sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 5 +--R (5760\|2 cos(---)cosh(x) - 1280\|2 cos(---))sin(---) +--R 8 8 8 +--R + +--R 6 4 +--R 3360cosh(x) - 17920cosh(x) +--R + +--R 4+-+2 %pi 2 2 4+-+2 %pi 2 +--R (960\|2 cos(---) + 20640)cosh(x) - 896\|2 cos(---) - 4160 +--R 8 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 6 %pi 4 +--R 13440cos(---)cosh(x) - 53760cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (11520\|2 cos(---) + 36480cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R - 2560\|2 cos(---) - 2816cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 10 4+-+2 8 +--R 2002\|2 cosh(x) - 9900\|2 cosh(x) +--R + +--R %pi 2 4+-+2 6 +--R (33600cos(---) + 29820\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 4 +--R (- 35840cos(---) - 37520\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 2 +--R (- 960\|2 cos(---) - 8640cos(---) + 22050\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R 896\|2 cos(---) + 5504cos(---) - 2516\|2 +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 10 4+-+2 %pi 8 +--R 4004\|2 cos(---)cosh(x) - 19800\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 6 +--R (- 13440cos(---) + 39480\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 4 +--R (53760cos(---) - 32480\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (5760\|2 cos(---) - 36480cos(---) + 10500\|2 cos(---)) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 1280\|2 cos(---) + 2816cos(---) + 24\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 12 4+-+2 %pi 2 10 +--R - 1820cosh(x) + (- 2002\|2 cos(---) + 8008)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 8 +--R (9900\|2 cos(---) - 21780)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (3360cos(---) - 29820\|2 cos(---) + 31920)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (- 17920cos(---) + 37520\|2 cos(---) - 28420)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 960\|2 cos(---) + 20640cos(---) - 22050\|2 cos(---) +--R 8 8 8 +--R + +--R 11400 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 896\|2 cos(---) - 4160cos(---) + 2516\|2 cos(---) - 1100 +--R 8 8 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 4+-+2 3 4+-+2 %pi 6 +--R (1280\|2 cosh(x) - 3584\|2 cosh(x))sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi 5 +--R (7680\|2 cos(---)cosh(x) - 5120\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 7 5 +--R 1920cosh(x) - 14336cosh(x) +--R + +--R 4+-+2 %pi 2 3 +--R (1280\|2 cos(---) + 27520)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 +--R (- 3584\|2 cos(---) - 16640)cosh(x) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 7 %pi 5 +--R 7680cos(---)cosh(x) - 43008cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 3 +--R (15360\|2 cos(---) + 48640cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (- 10240\|2 cos(---) - 11264cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 11 4+-+2 9 +--R 728\|2 cosh(x) - 4400\|2 cosh(x) +--R + +--R %pi 2 4+-+2 7 +--R (19200cos(---) + 17040\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 5 +--R (- 28672cos(---) - 30016\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 3 +--R (- 1280\|2 cos(---) - 11520cos(---) + 29400\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R (3584\|2 cos(---) + 22016cos(---) - 10064\|2 )cosh(x) +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 11 4+-+2 %pi 9 +--R 1456\|2 cos(---)cosh(x) - 8800\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 7 +--R (- 7680cos(---) + 22560\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 5 +--R (43008cos(---) - 25984\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (7680\|2 cos(---) - 48640cos(---) + 14000\|2 cos(---)) +--R 8 8 8 +--R * +--R 3 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 5120\|2 cos(---) + 11264cos(---) + 96\|2 cos(---))cosh(x) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 13 4+-+2 %pi 2 11 +--R - 560cosh(x) + (- 728\|2 cos(---) + 2912)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 9 +--R (4400\|2 cos(---) - 9680)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 7 +--R (1920cos(---) - 17040\|2 cos(---) + 18240)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (- 14336cos(---) + 30016\|2 cos(---) - 22736)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 1280\|2 cos(---) + 27520cos(---) - 29400\|2 cos(---) +--R 8 8 8 +--R + +--R 15200 +--R * +--R 3 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (3584\|2 cos(---) - 16640cos(---) + 10064\|2 cos(---) - 4400) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R %pi 8 +--R 512sin(---) +--R 8 +--R + +--R 4+-+2 4 4+-+2 2 %pi 2 4+-+2 +--R (960\|2 cosh(x) - 5376\|2 cosh(x) + 2048cos(---) + 2624\|2 ) +--R 8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R 5760\|2 cos(---)cosh(x) - 7680\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R 384\|2 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 8 6 4+-+2 %pi 2 4 +--R 720cosh(x) - 7168cosh(x) + (960\|2 cos(---) + 20640)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 2 %pi 4 +--R (- 5376\|2 cos(---) - 24960)cosh(x) + 3072cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi 2 +--R 2624\|2 cos(---) + 5904 +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 8 %pi 6 +--R 2880cos(---)cosh(x) - 21504cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 4 +--R (11520\|2 cos(---) + 36480cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (- 15360\|2 cos(---) - 16896cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R 768\|2 cos(---) - 4032cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 12 4+-+2 10 +--R 182\|2 cosh(x) - 1320\|2 cosh(x) +--R + +--R %pi 2 4+-+2 8 +--R (7200cos(---) + 6390\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 6 +--R (- 14336cos(---) - 15008\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 4 +--R (- 960\|2 cos(---) - 8640cos(---) + 22050\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 2 +--R (5376\|2 cos(---) + 33024cos(---) - 15096\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R 2048cos(---) - 2624\|2 cos(---) - 8544cos(---) + 2930\|2 +--R 8 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 12 4+-+2 %pi 10 +--R 364\|2 cos(---)cosh(x) - 2640\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 8 +--R (- 2880cos(---) + 8460\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 6 +--R (21504cos(---) - 12992\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (5760\|2 cos(---) - 36480cos(---) + 10500\|2 cos(---)) +--R 8 8 8 +--R * +--R 4 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 7680\|2 cos(---) + 16896cos(---) + 144\|2 cos(---)) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R 384\|2 cos(---) + 4032cos(---) - 1020\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 14 4+-+2 %pi 2 12 +--R - 120cosh(x) + (- 182\|2 cos(---) + 728)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 10 +--R (1320\|2 cos(---) - 2904)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 8 +--R (720cos(---) - 6390\|2 cos(---) + 6840)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (- 7168cos(---) + 15008\|2 cos(---) - 11368)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 960\|2 cos(---) + 20640cos(---) - 22050\|2 cos(---) +--R 8 8 8 +--R + +--R 11400 +--R * +--R 4 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (5376\|2 cos(---) - 24960cos(---) + 15096\|2 cos(---) - 6600) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 512cos(---) - 2624\|2 cos(---) + 5904cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 2930\|2 cos(---) + 1000 +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R %pi 8 +--R 1024cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 5 4+-+2 3 +--R 384\|2 cosh(x) - 3584\|2 cosh(x) +--R + +--R %pi 2 4+-+2 +--R (4096cos(---) + 5248\|2 )cosh(x) +--R 8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi 3 +--R 2304\|2 cos(---)cosh(x) - 5120\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R 768\|2 cos(---)cosh(x) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 9 7 4+-+2 %pi 2 5 +--R 160cosh(x) - 2048cosh(x) + (384\|2 cos(---) + 8256)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 3 +--R (- 3584\|2 cos(---) - 16640)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (6144cos(---) + 5248\|2 cos(---) + 11808)cosh(x) +--R 8 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 9 %pi 7 +--R 640cos(---)cosh(x) - 6144cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 5 +--R (4608\|2 cos(---) + 14592cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 3 +--R (- 10240\|2 cos(---) - 11264cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (1536\|2 cos(---) - 8064cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 13 4+-+2 11 +--R 28\|2 cosh(x) - 240\|2 cosh(x) +--R + +--R %pi 2 4+-+2 9 +--R (1600cos(---) + 1420\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 7 +--R (- 4096cos(---) - 4288\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 5 +--R (- 384\|2 cos(---) - 3456cos(---) + 8820\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 3 +--R (3584\|2 cos(---) + 22016cos(---) - 10064\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 +--R 4096cos(---) - 5248\|2 cos(---) - 17088cos(---) +--R 8 8 8 +--R + +--R 4+-+2 +--R 5860\|2 +--R * +--R cosh(x) +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 13 4+-+2 %pi 11 +--R 56\|2 cos(---)cosh(x) - 480\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 9 +--R (- 640cos(---) + 1880\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 7 +--R (6144cos(---) - 3712\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 5 +--R (2304\|2 cos(---) - 14592cos(---) + 4200\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 3 +--R (- 5120\|2 cos(---) + 11264cos(---) + 96\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (768\|2 cos(---) + 8064cos(---) - 2040\|2 cos(---))cosh(x) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 15 4+-+2 %pi 2 13 +--R - 16cosh(x) + (- 28\|2 cos(---) + 112)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 11 +--R (240\|2 cos(---) - 528)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 9 +--R (160cos(---) - 1420\|2 cos(---) + 1520)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 7 +--R (- 2048cos(---) + 4288\|2 cos(---) - 3248)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 384\|2 cos(---) + 8256cos(---) - 8820\|2 cos(---) + 4560) +--R 8 8 8 +--R * +--R 5 +--R cosh(x) +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (3584\|2 cos(---) - 16640cos(---) + 10064\|2 cos(---) - 4400) +--R 8 8 8 +--R * +--R 3 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 1024cos(---) - 5248\|2 cos(---) + 11808cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 5860\|2 cos(---) + 2000 +--R 8 +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 %pi 8 +--R (512cosh(x) - 1024)sin(---) +--R 8 +--R + +--R 4+-+2 6 4+-+2 4 +--R 64\|2 cosh(x) - 896\|2 cosh(x) +--R + +--R %pi 2 4+-+2 2 %pi 2 4+-+2 +--R (2048cos(---) + 2624\|2 )cosh(x) - 4096cos(---) - 2048\|2 +--R 8 8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 6 4+-+2 %pi 4 +--R 384\|2 cos(---)cosh(x) - 1280\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi +--R 384\|2 cos(---)cosh(x) + 3072\|2 cos(---) +--R 8 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 10 8 4+-+2 %pi 2 6 +--R 16cosh(x) - 256cosh(x) + (64\|2 cos(---) + 1376)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 4 +--R (- 896\|2 cos(---) - 4160)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 %pi 4 +--R (3072cos(---) + 2624\|2 cos(---) + 5904)cosh(x) - 6144cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 2048\|2 cos(---) - 3648 +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 10 %pi 8 +--R 64cos(---)cosh(x) - 768cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 6 +--R (768\|2 cos(---) + 2432cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 4 +--R (- 2560\|2 cos(---) - 2816cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 4+-+2 %pi 3 +--R (768\|2 cos(---) - 4032cos(---))cosh(x) + 6144\|2 cos(---) +--R 8 8 8 +--R + +--R %pi +--R 6144cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 14 4+-+2 12 +--R 2\|2 cosh(x) - 20\|2 cosh(x) +--R + +--R %pi 2 4+-+2 10 +--R (160cos(---) + 142\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 8 +--R (- 512cos(---) - 536\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 6 +--R (- 64\|2 cos(---) - 576cos(---) + 1470\|2 )cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 4 +--R (896\|2 cos(---) + 5504cos(---) - 2516\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (2048cos(---) - 2624\|2 cos(---) - 8544cos(---) + 2930\|2 ) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R - 4096cos(---) + 2048\|2 cos(---) - 3712cos(---) - 1600\|2 +--R 8 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 14 4+-+2 %pi 12 +--R 4\|2 cos(---)cosh(x) - 40\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 10 +--R (- 64cos(---) + 188\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R %pi 3 4+-+2 %pi 8 +--R (768cos(---) - 464\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 6 +--R (384\|2 cos(---) - 2432cos(---) + 700\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 4 +--R (- 1280\|2 cos(---) + 2816cos(---) + 24\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 2 +--R (384\|2 cos(---) + 4032cos(---) - 1020\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R 3072\|2 cos(---) - 6144cos(---) + 2400\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 16 4+-+2 %pi 2 14 +--R - cosh(x) + (- 2\|2 cos(---) + 8)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 2 12 +--R (20\|2 cos(---) - 44)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 10 +--R (16cos(---) - 142\|2 cos(---) + 152)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 8 +--R (- 256cos(---) + 536\|2 cos(---) - 406)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 6 +--R (- 64\|2 cos(---) + 1376cos(---) - 1470\|2 cos(---) + 760)cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 4 +--R (896\|2 cos(---) - 4160cos(---) + 2516\|2 cos(---) - 1100)cosh(x) +--R 8 8 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 512cos(---) - 2624\|2 cos(---) + 5904cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 2930\|2 cos(---) + 1000 +--R 8 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 1024cos(---) + 2048\|2 cos(---) - 3648cos(---) + 1600\|2 cos(---) +--R 8 8 8 8 +--R + +--R - 625 +--R / +--R 16 15 2 14 +--R 2sinh(x) + 32cosh(x)sinh(x) + (240cosh(x) - 16)sinh(x) +--R + +--R 3 13 +--R (1120cosh(x) - 224cosh(x))sinh(x) +--R + +--R 4+-+2 %pi %pi 4 2 12 +--R (64\|2 cos(---)sin(---) + 3640cosh(x) - 1456cosh(x) + 88)sinh(x) +--R 8 8 +--R + +--R 4+-+2 %pi %pi 5 3 +--R 768\|2 cos(---)cosh(x)sin(---) + 8736cosh(x) - 5824cosh(x) +--R 8 8 +--R + +--R 1056cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +--R - 128\|2 sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi +--R (4224\|2 cos(---)cosh(x) - 384\|2 cos(---))sin(---) +--R 8 8 8 +--R + +--R 6 4 2 4+-+2 %pi 2 +--R 16016cosh(x) - 16016cosh(x) + 5808cosh(x) + 128\|2 cos(---) +--R 8 +--R + +--R - 304 +--R * +--R 10 +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +--R - 1280\|2 cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi +--R (14080\|2 cos(---)cosh(x) - 3840\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 7 5 3 +--R 22880cosh(x) - 32032cosh(x) + 19360cosh(x) +--R + +--R 4+-+2 %pi 2 +--R (1280\|2 cos(---) - 3040)cosh(x) +--R 8 +--R * +--R 9 +--R sinh(x) +--R + +--R %pi 4 +--R 128sin(---) +--R 8 +--R + +--R 4+-+2 2 %pi 2 4+-+2 %pi 2 +--R (- 5760\|2 cosh(x) + 1280cos(---) + 640\|2 )sin(---) +--R 8 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R 31680\|2 cos(---)cosh(x) - 17280\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R 1216\|2 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 8 6 4 +--R 25740cosh(x) - 48048cosh(x) + 43560cosh(x) +--R + +--R 4+-+2 %pi 2 2 %pi 4 +--R (5760\|2 cos(---) - 13680)cosh(x) + 128cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 640\|2 cos(---) + 812 +--R 8 +--R * +--R 8 +--R sinh(x) +--R + +--R %pi 4 +--R 1024cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 3 %pi 2 4+-+2 +--R (- 15360\|2 cosh(x) + (10240cos(---) + 5120\|2 )cosh(x)) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi 3 +--R 50688\|2 cos(---)cosh(x) - 46080\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R 9728\|2 cos(---)cosh(x) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 9 7 5 +--R 22880cosh(x) - 54912cosh(x) + 69696cosh(x) +--R + +--R 4+-+2 %pi 2 3 +--R (15360\|2 cos(---) - 36480)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (1024cos(---) - 5120\|2 cos(---) + 6496)cosh(x) +--R 8 8 +--R * +--R 7 +--R sinh(x) +--R + +--R 2 %pi 4 %pi %pi 3 +--R (3584cosh(x) - 512)sin(---) - 4096cos(---)sin(---) +--R 8 8 8 +--R + +--R 4+-+2 4 %pi 2 4+-+2 2 +--R - 26880\|2 cosh(x) + (35840cos(---) + 17920\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R - 5120cos(---) - 2304\|2 +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 6 4+-+2 %pi 4 +--R 59136\|2 cos(---)cosh(x) - 80640\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 2 %pi 3 4+-+2 %pi +--R 34048\|2 cos(---)cosh(x) + 4096cos(---) - 2304\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 10 8 6 +--R 16016cosh(x) - 48048cosh(x) + 81312cosh(x) +--R + +--R 4+-+2 %pi 2 4 +--R (26880\|2 cos(---) - 63840)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (3584cos(---) - 17920\|2 cos(---) + 22736)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R - 512cos(---) + 2304\|2 cos(---) - 1520 +--R 8 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 %pi 4 +--R (7168cosh(x) - 3072cosh(x))sin(---) +--R 8 +--R + +--R %pi %pi 3 +--R - 24576cos(---)cosh(x)sin(---) +--R 8 8 +--R + +--R 4+-+2 5 %pi 2 4+-+2 3 +--R - 32256\|2 cosh(x) + (71680cos(---) + 35840\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R (- 30720cos(---) - 13824\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 7 4+-+2 %pi 5 +--R 50688\|2 cos(---)cosh(x) - 96768\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 +--R 68096\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi +--R (24576cos(---) - 13824\|2 cos(---))cosh(x) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 11 9 7 +--R 8736cosh(x) - 32032cosh(x) + 69696cosh(x) +--R + +--R 4+-+2 %pi 2 5 +--R (32256\|2 cos(---) - 76608)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (7168cos(---) - 35840\|2 cos(---) + 45472)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (- 3072cos(---) + 13824\|2 cos(---) - 9120)cosh(x) +--R 8 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 4+-+2 %pi %pi 5 +--R 2048\|2 cos(---)sin(---) +--R 8 8 +--R + +--R 4 2 %pi 4 +--R (8960cosh(x) - 7680cosh(x) + 5888)sin(---) +--R 8 +--R + +--R %pi 2 4+-+2 %pi 3 %pi +--R (- 61440cos(---)cosh(x) + 4096\|2 cos(---) + 12288cos(---)) +--R 8 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 6 %pi 2 4+-+2 4 +--R - 26880\|2 cosh(x) + (89600cos(---) + 44800\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 2 %pi 2 +--R (- 76800cos(---) - 34560\|2 )cosh(x) - 6656cos(---) +--R 8 8 +--R + +--R 4+-+2 +--R 4352\|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 8 4+-+2 %pi 6 +--R 31680\|2 cos(---)cosh(x) - 80640\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 +--R 85120\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 2 +--R (61440cos(---) - 34560\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R 2048\|2 cos(---) - 12288cos(---) + 1472\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 12 10 8 +--R 3640cosh(x) - 16016cosh(x) + 43560cosh(x) +--R + +--R 4+-+2 %pi 2 6 +--R (26880\|2 cos(---) - 63840)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (8960cos(---) - 44800\|2 cos(---) + 56840)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (- 7680cos(---) + 34560\|2 cos(---) - 22800)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R 5888cos(---) - 4352\|2 cos(---) + 2200 +--R 8 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 4+-+2 %pi %pi 5 +--R 8192\|2 cos(---)cosh(x)sin(---) +--R 8 8 +--R + +--R 5 3 %pi 4 +--R (7168cosh(x) - 10240cosh(x) + 23552cosh(x))sin(---) +--R 8 +--R + +--R %pi 3 +--R - 81920cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (16384\|2 cos(---) + 49152cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 7 %pi 2 4+-+2 5 +--R - 15360\|2 cosh(x) + (71680cos(---) + 35840\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 3 +--R (- 102400cos(---) - 46080\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R (- 26624cos(---) + 17408\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 9 4+-+2 %pi 7 +--R 14080\|2 cos(---)cosh(x) - 46080\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 +--R 68096\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 3 +--R (81920cos(---) - 46080\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (8192\|2 cos(---) - 49152cos(---) + 5888\|2 cos(---)) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 13 11 9 +--R 1120cosh(x) - 5824cosh(x) + 19360cosh(x) +--R + +--R 4+-+2 %pi 2 7 +--R (15360\|2 cos(---) - 36480)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (7168cos(---) - 35840\|2 cos(---) + 45472)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (- 10240cos(---) + 46080\|2 cos(---) - 30400)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (23552cos(---) - 17408\|2 cos(---) + 8800)cosh(x) +--R 8 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 +--R - 4096\|2 sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 5 +--R (12288\|2 cos(---)cosh(x) - 4096\|2 cos(---))sin(---) +--R 8 8 8 +--R + +--R 6 4 2 +--R 3584cosh(x) - 7680cosh(x) + 35328cosh(x) +--R + +--R 4+-+2 %pi 2 +--R - 4096\|2 cos(---) - 10752 +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 4 +--R - 61440cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (24576\|2 cos(---) + 73728cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R - 8192\|2 cos(---) + 4096cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 8 %pi 2 4+-+2 6 +--R - 5760\|2 cosh(x) + (35840cos(---) + 17920\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 4 +--R (- 76800cos(---) - 34560\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 2 4+-+2 %pi 4 +--R (- 39936cos(---) + 26112\|2 )cosh(x) + 4096\|2 cos(---) +--R 8 8 +--R + +--R %pi 2 4+-+2 +--R 23552cos(---) - 5760\|2 +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 10 4+-+2 %pi 8 +--R 4224\|2 cos(---)cosh(x) - 17280\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 +--R 34048\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 4 +--R (61440cos(---) - 34560\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (12288\|2 cos(---) - 73728cos(---) + 8832\|2 cos(---)) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 4096\|2 cos(---) - 4096cos(---) + 640\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 14 12 10 +--R 240cosh(x) - 1456cosh(x) + 5808cosh(x) +--R + +--R 4+-+2 %pi 2 8 +--R (5760\|2 cos(---) - 13680)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (3584cos(---) - 17920\|2 cos(---) + 22736)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (- 7680cos(---) + 34560\|2 cos(---) - 22800)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (35328cos(---) - 26112\|2 cos(---) + 13200)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 4096\|2 cos(---) - 10752cos(---) + 5760\|2 cos(---) - 2000 +--R 8 8 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 +--R - 8192\|2 cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi 5 +--R (8192\|2 cos(---)cosh(x) - 8192\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 7 5 3 +--R 1024cosh(x) - 3072cosh(x) + 23552cosh(x) +--R + +--R 4+-+2 %pi 2 +--R (- 8192\|2 cos(---) - 21504)cosh(x) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 5 +--R - 24576cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi 3 +--R (16384\|2 cos(---) + 49152cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (- 16384\|2 cos(---) + 8192cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 9 %pi 2 4+-+2 7 +--R - 1280\|2 cosh(x) + (10240cos(---) + 5120\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 5 +--R (- 30720cos(---) - 13824\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 3 +--R (- 26624cos(---) + 17408\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R (8192\|2 cos(---) + 47104cos(---) - 11520\|2 )cosh(x) +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 11 4+-+2 %pi 9 +--R 768\|2 cos(---)cosh(x) - 3840\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 7 +--R 9728\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 5 +--R (24576cos(---) - 13824\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (8192\|2 cos(---) - 49152cos(---) + 5888\|2 cos(---)) +--R 8 8 8 +--R * +--R 3 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 8192\|2 cos(---) - 8192cos(---) + 1280\|2 cos(---)) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 15 13 11 +--R 32cosh(x) - 224cosh(x) + 1056cosh(x) +--R + +--R 4+-+2 %pi 2 9 +--R (1280\|2 cos(---) - 3040)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 7 +--R (1024cos(---) - 5120\|2 cos(---) + 6496)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (- 3072cos(---) + 13824\|2 cos(---) - 9120)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (23552cos(---) - 17408\|2 cos(---) + 8800)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 8192\|2 cos(---) - 21504cos(---) + 11520\|2 cos(---) +--R 8 8 8 +--R + +--R - 4000 +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R %pi 8 +--R 2048sin(---) +--R 8 +--R + +--R 4+-+2 2 %pi 2 4+-+2 %pi 6 +--R (- 4096\|2 cosh(x) + 8192cos(---) + 4096\|2 )sin(---) +--R 8 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R 2048\|2 cos(---)cosh(x) - 4096\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 6144\|2 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 8 6 4 +--R 128cosh(x) - 512cosh(x) + 5888cosh(x) +--R + +--R 4+-+2 %pi 2 2 %pi 4 +--R (- 4096\|2 cos(---) - 10752)cosh(x) + 12288cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi 2 +--R 4096\|2 cos(---) + 7296 +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 6 +--R - 4096cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi 4 +--R (4096\|2 cos(---) + 12288cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (- 8192\|2 cos(---) + 4096cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R - 12288\|2 cos(---) - 12288cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 10 %pi 2 4+-+2 8 +--R - 128\|2 cosh(x) + (1280cos(---) + 640\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 6 +--R (- 5120cos(---) - 2304\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 4 +--R (- 6656cos(---) + 4352\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 2 +--R (4096\|2 cos(---) + 23552cos(---) - 5760\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R 8192cos(---) - 4096\|2 cos(---) + 7424cos(---) + 3200\|2 +--R 8 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 12 4+-+2 %pi 10 +--R 64\|2 cos(---)cosh(x) - 384\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 8 +--R 1216\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 6 +--R (4096cos(---) - 2304\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 4 +--R (2048\|2 cos(---) - 12288cos(---) + 1472\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 2 +--R (- 4096\|2 cos(---) - 4096cos(---) + 640\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 6144\|2 cos(---) + 12288cos(---) - 4800\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 16 14 12 +--R 2cosh(x) - 16cosh(x) + 88cosh(x) +--R + +--R 4+-+2 %pi 2 10 +--R (128\|2 cos(---) - 304)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 8 +--R (128cos(---) - 640\|2 cos(---) + 812)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (- 512cos(---) + 2304\|2 cos(---) - 1520)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (5888cos(---) - 4352\|2 cos(---) + 2200)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (4096\|2 cos(---) - 10752cos(---) + 5760\|2 cos(---) - 2000) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R 2048cos(---) - 4096\|2 cos(---) + 7296cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 3200\|2 cos(---) + 1250 +--R 8 +--R * +--R 4 +--R tanh(x) +--R + +--R 16 15 2 14 +--R - 2sinh(x) - 32cosh(x)sinh(x) + (- 240cosh(x) + 16)sinh(x) +--R + +--R 3 13 +--R (- 1120cosh(x) + 224cosh(x))sinh(x) +--R + +--R 4+-+2 %pi %pi 4 2 +--R (- 64\|2 cos(---)sin(---) - 3640cosh(x) + 1456cosh(x) - 88) +--R 8 8 +--R * +--R 12 +--R sinh(x) +--R + +--R 4+-+2 %pi %pi 5 3 +--R - 768\|2 cos(---)cosh(x)sin(---) - 8736cosh(x) + 5824cosh(x) +--R 8 8 +--R + +--R - 1056cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +--R 128\|2 sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi +--R (- 4224\|2 cos(---)cosh(x) + 384\|2 cos(---))sin(---) +--R 8 8 8 +--R + +--R 6 4 2 +--R - 16016cosh(x) + 16016cosh(x) - 5808cosh(x) +--R + +--R 4+-+2 %pi 2 +--R - 128\|2 cos(---) + 304 +--R 8 +--R * +--R 10 +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +--R 1280\|2 cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi +--R (- 14080\|2 cos(---)cosh(x) + 3840\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 7 5 3 +--R - 22880cosh(x) + 32032cosh(x) - 19360cosh(x) +--R + +--R 4+-+2 %pi 2 +--R (- 1280\|2 cos(---) + 3040)cosh(x) +--R 8 +--R * +--R 9 +--R sinh(x) +--R + +--R %pi 4 +--R - 128sin(---) +--R 8 +--R + +--R 4+-+2 2 %pi 2 4+-+2 %pi 2 +--R (5760\|2 cosh(x) - 1280cos(---) - 640\|2 )sin(---) +--R 8 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R - 31680\|2 cos(---)cosh(x) + 17280\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 1216\|2 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 8 6 4 +--R - 25740cosh(x) + 48048cosh(x) - 43560cosh(x) +--R + +--R 4+-+2 %pi 2 2 %pi 4 +--R (- 5760\|2 cos(---) + 13680)cosh(x) - 128cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi 2 +--R 640\|2 cos(---) - 812 +--R 8 +--R * +--R 8 +--R sinh(x) +--R + +--R %pi 4 +--R - 1024cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 3 %pi 2 4+-+2 +--R (15360\|2 cosh(x) + (- 10240cos(---) - 5120\|2 )cosh(x)) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi 3 +--R - 50688\|2 cos(---)cosh(x) + 46080\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 9728\|2 cos(---)cosh(x) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 9 7 5 +--R - 22880cosh(x) + 54912cosh(x) - 69696cosh(x) +--R + +--R 4+-+2 %pi 2 3 +--R (- 15360\|2 cos(---) + 36480)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (- 1024cos(---) + 5120\|2 cos(---) - 6496)cosh(x) +--R 8 8 +--R * +--R 7 +--R sinh(x) +--R + +--R 2 %pi 4 %pi %pi 3 +--R (- 3584cosh(x) + 512)sin(---) + 4096cos(---)sin(---) +--R 8 8 8 +--R + +--R 4+-+2 4 %pi 2 4+-+2 2 +--R 26880\|2 cosh(x) + (- 35840cos(---) - 17920\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R 5120cos(---) + 2304\|2 +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 6 4+-+2 %pi 4 +--R - 59136\|2 cos(---)cosh(x) + 80640\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 2 %pi 3 +--R - 34048\|2 cos(---)cosh(x) - 4096cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi +--R 2304\|2 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 10 8 6 +--R - 16016cosh(x) + 48048cosh(x) - 81312cosh(x) +--R + +--R 4+-+2 %pi 2 4 +--R (- 26880\|2 cos(---) + 63840)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (- 3584cos(---) + 17920\|2 cos(---) - 22736)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R 512cos(---) - 2304\|2 cos(---) + 1520 +--R 8 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 %pi 4 +--R (- 7168cosh(x) + 3072cosh(x))sin(---) +--R 8 +--R + +--R %pi %pi 3 +--R 24576cos(---)cosh(x)sin(---) +--R 8 8 +--R + +--R 4+-+2 5 %pi 2 4+-+2 3 +--R 32256\|2 cosh(x) + (- 71680cos(---) - 35840\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R (30720cos(---) + 13824\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 7 4+-+2 %pi 5 +--R - 50688\|2 cos(---)cosh(x) + 96768\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 +--R - 68096\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi +--R (- 24576cos(---) + 13824\|2 cos(---))cosh(x) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 11 9 7 +--R - 8736cosh(x) + 32032cosh(x) - 69696cosh(x) +--R + +--R 4+-+2 %pi 2 5 +--R (- 32256\|2 cos(---) + 76608)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (- 7168cos(---) + 35840\|2 cos(---) - 45472)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (3072cos(---) - 13824\|2 cos(---) + 9120)cosh(x) +--R 8 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 4+-+2 %pi %pi 5 +--R - 2048\|2 cos(---)sin(---) +--R 8 8 +--R + +--R 4 2 %pi 4 +--R (- 8960cosh(x) + 7680cosh(x) - 5888)sin(---) +--R 8 +--R + +--R %pi 2 4+-+2 %pi 3 %pi +--R (61440cos(---)cosh(x) - 4096\|2 cos(---) - 12288cos(---)) +--R 8 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 6 %pi 2 4+-+2 4 +--R 26880\|2 cosh(x) + (- 89600cos(---) - 44800\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 2 %pi 2 +--R (76800cos(---) + 34560\|2 )cosh(x) + 6656cos(---) +--R 8 8 +--R + +--R 4+-+2 +--R - 4352\|2 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 8 4+-+2 %pi 6 +--R - 31680\|2 cos(---)cosh(x) + 80640\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 +--R - 85120\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 2 +--R (- 61440cos(---) + 34560\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 2048\|2 cos(---) + 12288cos(---) - 1472\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 12 10 8 +--R - 3640cosh(x) + 16016cosh(x) - 43560cosh(x) +--R + +--R 4+-+2 %pi 2 6 +--R (- 26880\|2 cos(---) + 63840)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (- 8960cos(---) + 44800\|2 cos(---) - 56840)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (7680cos(---) - 34560\|2 cos(---) + 22800)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R - 5888cos(---) + 4352\|2 cos(---) - 2200 +--R 8 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 4+-+2 %pi %pi 5 +--R - 8192\|2 cos(---)cosh(x)sin(---) +--R 8 8 +--R + +--R 5 3 %pi 4 +--R (- 7168cosh(x) + 10240cosh(x) - 23552cosh(x))sin(---) +--R 8 +--R + +--R %pi 3 +--R 81920cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (- 16384\|2 cos(---) - 49152cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 7 %pi 2 4+-+2 5 +--R 15360\|2 cosh(x) + (- 71680cos(---) - 35840\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 3 +--R (102400cos(---) + 46080\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R (26624cos(---) - 17408\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 9 4+-+2 %pi 7 +--R - 14080\|2 cos(---)cosh(x) + 46080\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 +--R - 68096\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 3 +--R (- 81920cos(---) + 46080\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 8192\|2 cos(---) + 49152cos(---) - 5888\|2 cos(---)) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 13 11 9 +--R - 1120cosh(x) + 5824cosh(x) - 19360cosh(x) +--R + +--R 4+-+2 %pi 2 7 +--R (- 15360\|2 cos(---) + 36480)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (- 7168cos(---) + 35840\|2 cos(---) - 45472)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (10240cos(---) - 46080\|2 cos(---) + 30400)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (- 23552cos(---) + 17408\|2 cos(---) - 8800)cosh(x) +--R 8 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 +--R 4096\|2 sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 5 +--R (- 12288\|2 cos(---)cosh(x) + 4096\|2 cos(---))sin(---) +--R 8 8 8 +--R + +--R 6 4 2 +--R - 3584cosh(x) + 7680cosh(x) - 35328cosh(x) +--R + +--R 4+-+2 %pi 2 +--R 4096\|2 cos(---) + 10752 +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 4 +--R 61440cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (- 24576\|2 cos(---) - 73728cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R 8192\|2 cos(---) - 4096cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 8 %pi 2 4+-+2 6 +--R 5760\|2 cosh(x) + (- 35840cos(---) - 17920\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 4 +--R (76800cos(---) + 34560\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 2 4+-+2 %pi 4 +--R (39936cos(---) - 26112\|2 )cosh(x) - 4096\|2 cos(---) +--R 8 8 +--R + +--R %pi 2 4+-+2 +--R - 23552cos(---) + 5760\|2 +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 10 4+-+2 %pi 8 +--R - 4224\|2 cos(---)cosh(x) + 17280\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 +--R - 34048\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 4 +--R (- 61440cos(---) + 34560\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 +--R - 12288\|2 cos(---) + 73728cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 8832\|2 cos(---) +--R 8 +--R * +--R 2 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R 4096\|2 cos(---) + 4096cos(---) - 640\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 14 12 10 +--R - 240cosh(x) + 1456cosh(x) - 5808cosh(x) +--R + +--R 4+-+2 %pi 2 8 +--R (- 5760\|2 cos(---) + 13680)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (- 3584cos(---) + 17920\|2 cos(---) - 22736)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (7680cos(---) - 34560\|2 cos(---) + 22800)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (- 35328cos(---) + 26112\|2 cos(---) - 13200)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 4096\|2 cos(---) + 10752cos(---) - 5760\|2 cos(---) + 2000 +--R 8 8 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 +--R 8192\|2 cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi 5 +--R (- 8192\|2 cos(---)cosh(x) + 8192\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 7 5 3 +--R - 1024cosh(x) + 3072cosh(x) - 23552cosh(x) +--R + +--R 4+-+2 %pi 2 +--R (8192\|2 cos(---) + 21504)cosh(x) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 5 +--R 24576cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi 3 +--R (- 16384\|2 cos(---) - 49152cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (16384\|2 cos(---) - 8192cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 9 %pi 2 4+-+2 7 +--R 1280\|2 cosh(x) + (- 10240cos(---) - 5120\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 5 +--R (30720cos(---) + 13824\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 3 +--R (26624cos(---) - 17408\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R (- 8192\|2 cos(---) - 47104cos(---) + 11520\|2 )cosh(x) +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 11 4+-+2 %pi 9 +--R - 768\|2 cos(---)cosh(x) + 3840\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 7 +--R - 9728\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 5 +--R (- 24576cos(---) + 13824\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 8192\|2 cos(---) + 49152cos(---) - 5888\|2 cos(---)) +--R 8 8 8 +--R * +--R 3 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (8192\|2 cos(---) + 8192cos(---) - 1280\|2 cos(---))cosh(x) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 15 13 11 +--R - 32cosh(x) + 224cosh(x) - 1056cosh(x) +--R + +--R 4+-+2 %pi 2 9 +--R (- 1280\|2 cos(---) + 3040)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 7 +--R (- 1024cos(---) + 5120\|2 cos(---) - 6496)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (3072cos(---) - 13824\|2 cos(---) + 9120)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (- 23552cos(---) + 17408\|2 cos(---) - 8800)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R - 8192\|2 cos(---) + 21504cos(---) - 11520\|2 cos(---) +--R 8 8 8 +--R + +--R 4000 +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R %pi 8 +--R - 2048sin(---) +--R 8 +--R + +--R 4+-+2 2 %pi 2 4+-+2 %pi 6 +--R (4096\|2 cosh(x) - 8192cos(---) - 4096\|2 )sin(---) +--R 8 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R - 2048\|2 cos(---)cosh(x) + 4096\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R 6144\|2 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 8 6 4 +--R - 128cosh(x) + 512cosh(x) - 5888cosh(x) +--R + +--R 4+-+2 %pi 2 2 %pi 4 +--R (4096\|2 cos(---) + 10752)cosh(x) - 12288cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi 2 +--R - 4096\|2 cos(---) - 7296 +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 6 +--R 4096cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi 4 +--R (- 4096\|2 cos(---) - 12288cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 4+-+2 %pi 3 +--R (8192\|2 cos(---) - 4096cos(---))cosh(x) + 12288\|2 cos(---) +--R 8 8 8 +--R + +--R %pi +--R 12288cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 10 %pi 2 4+-+2 8 +--R 128\|2 cosh(x) + (- 1280cos(---) - 640\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 6 +--R (5120cos(---) + 2304\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 4 +--R (6656cos(---) - 4352\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 2 +--R (- 4096\|2 cos(---) - 23552cos(---) + 5760\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R - 8192cos(---) + 4096\|2 cos(---) - 7424cos(---) - 3200\|2 +--R 8 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 12 4+-+2 %pi 10 +--R - 64\|2 cos(---)cosh(x) + 384\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 8 +--R - 1216\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 6 +--R (- 4096cos(---) + 2304\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 2048\|2 cos(---) + 12288cos(---) - 1472\|2 cos(---)) +--R 8 8 8 +--R * +--R 4 +--R cosh(x) +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 2 +--R (4096\|2 cos(---) + 4096cos(---) - 640\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R 6144\|2 cos(---) - 12288cos(---) + 4800\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 16 14 12 +--R - 2cosh(x) + 16cosh(x) - 88cosh(x) +--R + +--R 4+-+2 %pi 2 10 +--R (- 128\|2 cos(---) + 304)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 8 +--R (- 128cos(---) + 640\|2 cos(---) - 812)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (512cos(---) - 2304\|2 cos(---) + 1520)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (- 5888cos(---) + 4352\|2 cos(---) - 2200)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (- 4096\|2 cos(---) + 10752cos(---) - 5760\|2 cos(---) + 2000) +--R 8 8 8 +--R * +--R 2 +--R cosh(x) +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R - 2048cos(---) + 4096\|2 cos(---) - 7296cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 3200\|2 cos(---) - 1250 +--R 8 +--R * +--R 2 +--R tanh(x) +--R + +--R 16 15 2 14 +--R sinh(x) + 16cosh(x)sinh(x) + (120cosh(x) - 8)sinh(x) +--R + +--R 3 13 +--R (560cosh(x) - 112cosh(x))sinh(x) +--R + +--R 4+-+2 %pi %pi 4 2 12 +--R (32\|2 cos(---)sin(---) + 1820cosh(x) - 728cosh(x) + 44)sinh(x) +--R 8 8 +--R + +--R 4+-+2 %pi %pi 5 3 +--R 384\|2 cos(---)cosh(x)sin(---) + 4368cosh(x) - 2912cosh(x) +--R 8 8 +--R + +--R 528cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +--R - 64\|2 sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 6 +--R (2112\|2 cos(---)cosh(x) - 192\|2 cos(---))sin(---) + 8008cosh(x) +--R 8 8 8 +--R + +--R 4 2 4+-+2 %pi 2 +--R - 8008cosh(x) + 2904cosh(x) + 64\|2 cos(---) - 152 +--R 8 +--R * +--R 10 +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +--R - 640\|2 cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi +--R (7040\|2 cos(---)cosh(x) - 1920\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 7 5 3 +--R 11440cosh(x) - 16016cosh(x) + 9680cosh(x) +--R + +--R 4+-+2 %pi 2 +--R (640\|2 cos(---) - 1520)cosh(x) +--R 8 +--R * +--R 9 +--R sinh(x) +--R + +--R %pi 4 +--R 64sin(---) +--R 8 +--R + +--R 4+-+2 2 %pi 2 4+-+2 %pi 2 +--R (- 2880\|2 cosh(x) + 640cos(---) + 320\|2 )sin(---) +--R 8 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R 15840\|2 cos(---)cosh(x) - 8640\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R 608\|2 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 8 6 4 +--R 12870cosh(x) - 24024cosh(x) + 21780cosh(x) +--R + +--R 4+-+2 %pi 2 2 %pi 4 4+-+2 %pi 2 +--R (2880\|2 cos(---) - 6840)cosh(x) + 64cos(---) - 320\|2 cos(---) +--R 8 8 8 +--R + +--R 406 +--R * +--R 8 +--R sinh(x) +--R + +--R %pi 4 +--R 512cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 3 %pi 2 4+-+2 %pi 2 +--R (- 7680\|2 cosh(x) + (5120cos(---) + 2560\|2 )cosh(x))sin(---) +--R 8 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi 3 +--R 25344\|2 cos(---)cosh(x) - 23040\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R 4864\|2 cos(---)cosh(x) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 9 7 5 +--R 11440cosh(x) - 27456cosh(x) + 34848cosh(x) +--R + +--R 4+-+2 %pi 2 3 +--R (7680\|2 cos(---) - 18240)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (512cos(---) - 2560\|2 cos(---) + 3248)cosh(x) +--R 8 8 +--R * +--R 7 +--R sinh(x) +--R + +--R 2 %pi 4 %pi %pi 3 +--R (1792cosh(x) - 256)sin(---) - 2048cos(---)sin(---) +--R 8 8 8 +--R + +--R 4+-+2 4 %pi 2 4+-+2 2 +--R - 13440\|2 cosh(x) + (17920cos(---) + 8960\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R - 2560cos(---) - 1152\|2 +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 6 4+-+2 %pi 4 +--R 29568\|2 cos(---)cosh(x) - 40320\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 2 %pi 3 4+-+2 %pi +--R 17024\|2 cos(---)cosh(x) + 2048cos(---) - 1152\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 10 8 6 +--R 8008cosh(x) - 24024cosh(x) + 40656cosh(x) +--R + +--R 4+-+2 %pi 2 4 +--R (13440\|2 cos(---) - 31920)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 %pi 4 +--R (1792cos(---) - 8960\|2 cos(---) + 11368)cosh(x) - 256cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 1152\|2 cos(---) - 760 +--R 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 %pi 4 %pi %pi 3 +--R (3584cosh(x) - 1536cosh(x))sin(---) - 12288cos(---)cosh(x)sin(---) +--R 8 8 8 +--R + +--R 4+-+2 5 %pi 2 4+-+2 3 +--R - 16128\|2 cosh(x) + (35840cos(---) + 17920\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R (- 15360cos(---) - 6912\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 7 4+-+2 %pi 5 +--R 25344\|2 cos(---)cosh(x) - 48384\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 +--R 34048\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi +--R (12288cos(---) - 6912\|2 cos(---))cosh(x) +--R 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 11 9 7 +--R 4368cosh(x) - 16016cosh(x) + 34848cosh(x) +--R + +--R 4+-+2 %pi 2 5 +--R (16128\|2 cos(---) - 38304)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (3584cos(---) - 17920\|2 cos(---) + 22736)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (- 1536cos(---) + 6912\|2 cos(---) - 4560)cosh(x) +--R 8 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 4+-+2 %pi %pi 5 +--R 1024\|2 cos(---)sin(---) +--R 8 8 +--R + +--R 4 2 %pi 4 +--R (4480cosh(x) - 3840cosh(x) + 2944)sin(---) +--R 8 +--R + +--R %pi 2 4+-+2 %pi 3 %pi +--R (- 30720cos(---)cosh(x) + 2048\|2 cos(---) + 6144cos(---)) +--R 8 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 6 %pi 2 4+-+2 4 +--R - 13440\|2 cosh(x) + (44800cos(---) + 22400\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 2 %pi 2 4+-+2 +--R (- 38400cos(---) - 17280\|2 )cosh(x) - 3328cos(---) + 2176\|2 +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 8 4+-+2 %pi 6 +--R 15840\|2 cos(---)cosh(x) - 40320\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 4 +--R 42560\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 2 +--R (30720cos(---) - 17280\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R 1024\|2 cos(---) - 6144cos(---) + 736\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 12 10 8 +--R 1820cosh(x) - 8008cosh(x) + 21780cosh(x) +--R + +--R 4+-+2 %pi 2 6 +--R (13440\|2 cos(---) - 31920)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (4480cos(---) - 22400\|2 cos(---) + 28420)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (- 3840cos(---) + 17280\|2 cos(---) - 11400)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R 2944cos(---) - 2176\|2 cos(---) + 1100 +--R 8 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 4+-+2 %pi %pi 5 +--R 4096\|2 cos(---)cosh(x)sin(---) +--R 8 8 +--R + +--R 5 3 %pi 4 +--R (3584cosh(x) - 5120cosh(x) + 11776cosh(x))sin(---) +--R 8 +--R + +--R %pi 3 +--R - 40960cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (8192\|2 cos(---) + 24576cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 7 %pi 2 4+-+2 5 +--R - 7680\|2 cosh(x) + (35840cos(---) + 17920\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 3 +--R (- 51200cos(---) - 23040\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 +--R (- 13312cos(---) + 8704\|2 )cosh(x) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 9 4+-+2 %pi 7 +--R 7040\|2 cos(---)cosh(x) - 23040\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 +--R 34048\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 3 +--R (40960cos(---) - 23040\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (4096\|2 cos(---) - 24576cos(---) + 2944\|2 cos(---))cosh(x) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 13 11 9 +--R 560cosh(x) - 2912cosh(x) + 9680cosh(x) +--R + +--R 4+-+2 %pi 2 7 +--R (7680\|2 cos(---) - 18240)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (3584cos(---) - 17920\|2 cos(---) + 22736)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (- 5120cos(---) + 23040\|2 cos(---) - 15200)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 +--R (11776cos(---) - 8704\|2 cos(---) + 4400)cosh(x) +--R 8 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 +--R - 2048\|2 sin(---) +--R 8 +--R + +--R 4+-+2 %pi 2 4+-+2 %pi %pi 5 +--R (6144\|2 cos(---)cosh(x) - 2048\|2 cos(---))sin(---) +--R 8 8 8 +--R + +--R 6 4 2 4+-+2 %pi 2 +--R 1792cosh(x) - 3840cosh(x) + 17664cosh(x) - 2048\|2 cos(---) +--R 8 +--R + +--R - 5376 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 4 +--R - 30720cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi 2 +--R (12288\|2 cos(---) + 36864cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R - 4096\|2 cos(---) + 2048cos(---) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 8 %pi 2 4+-+2 6 +--R - 2880\|2 cosh(x) + (17920cos(---) + 8960\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 4 +--R (- 38400cos(---) - 17280\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 2 4+-+2 %pi 4 +--R (- 19968cos(---) + 13056\|2 )cosh(x) + 2048\|2 cos(---) +--R 8 8 +--R + +--R %pi 2 4+-+2 +--R 11776cos(---) - 2880\|2 +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 10 4+-+2 %pi 8 +--R 2112\|2 cos(---)cosh(x) - 8640\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 +--R 17024\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 4 +--R (30720cos(---) - 17280\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 2 +--R (6144\|2 cos(---) - 36864cos(---) + 4416\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 2048\|2 cos(---) - 2048cos(---) + 320\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 14 12 10 +--R 120cosh(x) - 728cosh(x) + 2904cosh(x) +--R + +--R 4+-+2 %pi 2 8 +--R (2880\|2 cos(---) - 6840)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (1792cos(---) - 8960\|2 cos(---) + 11368)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (- 3840cos(---) + 17280\|2 cos(---) - 11400)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 2 +--R (17664cos(---) - 13056\|2 cos(---) + 6600)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 2048\|2 cos(---) - 5376cos(---) + 2880\|2 cos(---) - 1000 +--R 8 8 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 4+-+2 %pi 6 +--R - 4096\|2 cosh(x)sin(---) +--R 8 +--R + +--R 4+-+2 %pi 3 4+-+2 %pi %pi 5 +--R (4096\|2 cos(---)cosh(x) - 4096\|2 cos(---)cosh(x))sin(---) +--R 8 8 8 +--R + +--R 7 5 3 +--R 512cosh(x) - 1536cosh(x) + 11776cosh(x) +--R + +--R 4+-+2 %pi 2 +--R (- 4096\|2 cos(---) - 10752)cosh(x) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 5 +--R - 12288cos(---)cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 3 %pi 3 +--R (8192\|2 cos(---) + 24576cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 3 %pi +--R (- 8192\|2 cos(---) + 4096cos(---))cosh(x) +--R 8 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 9 %pi 2 4+-+2 7 +--R - 640\|2 cosh(x) + (5120cos(---) + 2560\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 5 +--R (- 15360cos(---) - 6912\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 3 +--R (- 13312cos(---) + 8704\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 +--R (4096\|2 cos(---) + 23552cos(---) - 5760\|2 )cosh(x) +--R 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 11 4+-+2 %pi 9 +--R 384\|2 cos(---)cosh(x) - 1920\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 7 +--R 4864\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 5 +--R (12288cos(---) - 6912\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 3 +--R (4096\|2 cos(---) - 24576cos(---) + 2944\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R (- 4096\|2 cos(---) - 4096cos(---) + 640\|2 cos(---))cosh(x) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 15 13 11 +--R 16cosh(x) - 112cosh(x) + 528cosh(x) +--R + +--R 4+-+2 %pi 2 9 +--R (640\|2 cos(---) - 1520)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 7 +--R (512cos(---) - 2560\|2 cos(---) + 3248)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 5 +--R (- 1536cos(---) + 6912\|2 cos(---) - 4560)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 3 +--R (11776cos(---) - 8704\|2 cos(---) + 4400)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R (4096\|2 cos(---) - 10752cos(---) + 5760\|2 cos(---) - 2000) +--R 8 8 8 +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R %pi 8 +--R 1024sin(---) +--R 8 +--R + +--R 4+-+2 2 %pi 2 4+-+2 %pi 6 +--R (- 2048\|2 cosh(x) + 4096cos(---) + 2048\|2 )sin(---) +--R 8 8 +--R + +--R 4+-+2 %pi 4 4+-+2 %pi 2 +--R 1024\|2 cos(---)cosh(x) - 2048\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi +--R - 3072\|2 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 8 6 4 +--R 64cosh(x) - 256cosh(x) + 2944cosh(x) +--R + +--R 4+-+2 %pi 2 2 %pi 4 +--R (- 2048\|2 cos(---) - 5376)cosh(x) + 6144cos(---) +--R 8 8 +--R + +--R 4+-+2 %pi 2 +--R 2048\|2 cos(---) + 3648 +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R %pi 6 4+-+2 %pi 3 %pi 4 +--R - 2048cos(---)cosh(x) + (2048\|2 cos(---) + 6144cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 3 %pi 2 4+-+2 %pi 3 +--R (- 4096\|2 cos(---) + 2048cos(---))cosh(x) - 6144\|2 cos(---) +--R 8 8 8 +--R + +--R %pi +--R - 6144cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4+-+2 10 %pi 2 4+-+2 8 +--R - 64\|2 cosh(x) + (640cos(---) + 320\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 6 +--R (- 2560cos(---) - 1152\|2 )cosh(x) +--R 8 +--R + +--R %pi 2 4+-+2 4 +--R (- 3328cos(---) + 2176\|2 )cosh(x) +--R 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 2 +--R (2048\|2 cos(---) + 11776cos(---) - 2880\|2 )cosh(x) +--R 8 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R 4096cos(---) - 2048\|2 cos(---) + 3712cos(---) + 1600\|2 +--R 8 8 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 12 4+-+2 %pi 10 +--R 32\|2 cos(---)cosh(x) - 192\|2 cos(---)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 8 +--R 608\|2 cos(---)cosh(x) +--R 8 +--R + +--R %pi 3 4+-+2 %pi 6 +--R (2048cos(---) - 1152\|2 cos(---))cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 4 +--R (1024\|2 cos(---) - 6144cos(---) + 736\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi 2 +--R (- 2048\|2 cos(---) - 2048cos(---) + 320\|2 cos(---))cosh(x) +--R 8 8 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi +--R - 3072\|2 cos(---) + 6144cos(---) - 2400\|2 cos(---) +--R 8 8 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 16 14 12 4+-+2 %pi 2 10 +--R cosh(x) - 8cosh(x) + 44cosh(x) + (64\|2 cos(---) - 152)cosh(x) +--R 8 +--R + +--R %pi 4 4+-+2 %pi 2 8 +--R (64cos(---) - 320\|2 cos(---) + 406)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 6 +--R (- 256cos(---) + 1152\|2 cos(---) - 760)cosh(x) +--R 8 8 +--R + +--R %pi 4 4+-+2 %pi 2 4 +--R (2944cos(---) - 2176\|2 cos(---) + 1100)cosh(x) +--R 8 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 2 +--R (2048\|2 cos(---) - 5376cos(---) + 2880\|2 cos(---) - 1000)cosh(x) +--R 8 8 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 +--R 1024cos(---) - 2048\|2 cos(---) + 3648cos(---) - 1600\|2 cos(---) +--R 8 8 8 8 +--R + +--R 625 +--R Type: Expression(Complex(Integer)) +--E 440 + +--S 441 of 510 +t0086:= 1/(1+sinh(x)^5) +--R +--R +--R 1 +--R (382) ------------ +--R 5 +--R sinh(x) + 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 510 +r0086:= -1/5*2^(1/2)*atanh(1/2*(1-tanh(1/2*x))*2^(1/2))-_ + 2/5*atanh(((-1)^(2/5)-tanh(1/2*x))/(1+(-1)^(4/5))^(1/2))/_ + (1+(-1)^(4/5))^(1/2)-2/5*atanh(((-1)^(4/5)-tanh(1/2*x))/_ + (1-(-1)^(3/5))^(1/2))/(1-(-1)^(3/5))^(1/2)+_ + 2/5*atanh(((-1)^(1/5)+tanh(1/2*x))/(1+(-1)^(2/5))^(1/2))/_ + (1+(-1)^(2/5))^(1/2)+2/5*atanh(((-1)^(3/5)+tanh(1/2*x))/_ + (1-(-1)^(1/5))^(1/2))/(1-(-1)^(1/5))^(1/2) +--R +--R +--R (383) +--R +-------------+ +------------+ +-----------+ +-----------+ +--R +-+ | 5+---+3 | 5+---+ |5+---+2 |5+---+4 +--R \|2 \|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R * +--R +-+ x +-+ +--R \|2 tanh(-) - \|2 +--R 2 +--R atanh(------------------) +--R 2 +--R + +--R x 5+---+4 +--R +------------+ +-----------+ +-----------+ tanh(-) - \|- 1 +--R | 5+---+ |5+---+2 |5+---+4 2 +--R 2\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +-------------+ +--R | 5+---+3 +--R \|- \|- 1 + 1 +--R + +--R x 5+---+3 +--R +-------------+ +-----------+ +-----------+ tanh(-) + \|- 1 +--R | 5+---+3 |5+---+2 |5+---+4 2 +--R 2\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +------------+ +--R | 5+---+ +--R \|- \|- 1 + 1 +--R + +--R x 5+---+ +--R +-------------+ +------------+ +-----------+ tanh(-) + \|- 1 +--R | 5+---+3 | 5+---+ |5+---+4 2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(----------------) +--R +-----------+ +--R |5+---+2 +--R \|\|- 1 + 1 +--R + +--R x 5+---+2 +--R +-------------+ +------------+ +-----------+ tanh(-) - \|- 1 +--R | 5+---+3 | 5+---+ |5+---+2 2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +-----------+ +--R |5+---+4 +--R \|\|- 1 + 1 +--R / +--R +-------------+ +------------+ +-----------+ +-----------+ +--R | 5+---+3 | 5+---+ |5+---+2 |5+---+4 +--R 5\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 510 +a0086:= integrate(t0086,x) +--R +--R +--R (384) +--R - +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +-----------+ +--R | +-+ | +-+ +--R +-+ |\|5 + 2 |24\|5 + 40 +--R (150\|5 - 250) |-------- |----------- +--R | +-+ 4| +-+ +--R \| 125\|5 \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 125\|5 +--R sin(-------------------) +--R 2 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((- 4\|5 + 20)sinh(x) + (- 4\|5 + 20)cosh(x) + 6\|5 - 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |24\|5 + 40 \| 125\|5 +--R (- 150\|5 + 250) |-------- |----------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 125\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((4\|5 - 20)sinh(x) + (4\|5 - 20)cosh(x) - 6\|5 + 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 + 20)cosh(x) + 8\|5 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +-----------+ +--R | +-+ | +-+ +--R +-+ |\|5 - 2 |24\|5 - 40 +--R (150\|5 + 250) |-------- |----------- +--R | +-+ 4| +-+ +--R \| 125\|5 \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 125\|5 +--R sin(-------------------) +--R 2 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((- 4\|5 - 20)sinh(x) + (- 4\|5 - 20)cosh(x) + 6\|5 + 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |24\|5 - 40 \| 125\|5 +--R (- 150\|5 - 250) |-------- |----------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 125\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((4\|5 + 20)sinh(x) + (4\|5 + 20)cosh(x) - 6\|5 - 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 - 20)cosh(x) + 8\|5 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R 2 |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (- 25\|5 + 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- cos(------------------- - 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R - 4cosh(x) - \|5 + 1 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R 2 |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (25\|5 - 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- cos(------------------- + 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R 4cosh(x) + \|5 - 1 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R 2 |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (25\|5 + 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- cos(------------------- - 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R - 4cosh(x) + \|5 + 1 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R 2 |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (- 25\|5 - 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- cos(------------------- + 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R 4cosh(x) - \|5 - 1 +--R + +--R +-+ +-+ +-+ +--R +-+ (\|2 - 1)sinh(x) + (- \|2 + 2)cosh(x) - \|2 + 1 +--R \|2 log(--------------------------------------------------) +--R sinh(x) + 1 +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 510 +m0086:= a0086-r0086 +--R +--R +--R (385) +--R - +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 + 40 |5+---+2 +--R \|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +-----------+ +--R | +-+ | +-+ +--R +-+ |\|5 + 2 |24\|5 + 40 +--R (150\|5 - 250) |-------- |----------- +--R | +-+ 4| +-+ +--R \| 125\|5 \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 125\|5 +--R sin(-------------------) +--R 2 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((- 4\|5 + 20)sinh(x) + (- 4\|5 + 20)cosh(x) + 6\|5 - 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 + 40 |5+---+2 +--R \|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |24\|5 + 40 \| 125\|5 +--R (- 150\|5 + 250) |-------- |----------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 125\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((4\|5 - 20)sinh(x) + (4\|5 - 20)cosh(x) - 6\|5 + 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 + 20)cosh(x) + 8\|5 +--R + +--R - +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 - 40 |5+---+2 +--R \|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +-----------+ +--R | +-+ | +-+ +--R +-+ |\|5 - 2 |24\|5 - 40 +--R (150\|5 + 250) |-------- |----------- +--R | +-+ 4| +-+ +--R \| 125\|5 \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 125\|5 +--R sin(-------------------) +--R 2 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((- 4\|5 - 20)sinh(x) + (- 4\|5 - 20)cosh(x) + 6\|5 + 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 - 40 |5+---+2 +--R \|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |24\|5 - 40 \| 125\|5 +--R (- 150\|5 - 250) |-------- |----------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 125\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((4\|5 + 20)sinh(x) + (4\|5 + 20)cosh(x) - 6\|5 - 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 - 20)cosh(x) + 8\|5 +--R + +--R - +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 + 40 |5+---+2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (- 25\|5 + 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- cos(------------------- - 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R - 4cosh(x) - \|5 + 1 +--R + +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 + 40 |5+---+2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (25\|5 - 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- cos(------------------- + 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R 4cosh(x) + \|5 - 1 +--R + +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 - 40 |5+---+2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (25\|5 + 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- cos(------------------- - 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R - 4cosh(x) + \|5 + 1 +--R + +--R - +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 - 40 |5+---+2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (- 25\|5 - 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- cos(------------------- + 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R 4cosh(x) - \|5 - 1 +--R + +--R +-------------+ +------------+ +-----------+ +-----------+ +--R +-+ | 5+---+3 | 5+---+ |5+---+2 |5+---+4 +--R \|2 \|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R * +--R +-+ +-+ +-+ +--R (\|2 - 1)sinh(x) + (- \|2 + 2)cosh(x) - \|2 + 1 +--R log(--------------------------------------------------) +--R sinh(x) + 1 +--R + +--R - +--R +-------------+ +------------+ +-----------+ +-----------+ +--R +-+ | 5+---+3 | 5+---+ |5+---+2 |5+---+4 +--R 2\|2 \|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R * +--R +-+ x +-+ +--R \|2 tanh(-) - \|2 +--R 2 +--R atanh(------------------) +--R 2 +--R + +--R x 5+---+4 +--R +------------+ +-----------+ +-----------+ tanh(-) - \|- 1 +--R | 5+---+ |5+---+2 |5+---+4 2 +--R - 4\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +-------------+ +--R | 5+---+3 +--R \|- \|- 1 + 1 +--R + +--R x 5+---+3 +--R +-------------+ +-----------+ +-----------+ tanh(-) + \|- 1 +--R | 5+---+3 |5+---+2 |5+---+4 2 +--R - 4\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +------------+ +--R | 5+---+ +--R \|- \|- 1 + 1 +--R + +--R x 5+---+ +--R +-------------+ +------------+ +-----------+ tanh(-) + \|- 1 +--R | 5+---+3 | 5+---+ |5+---+4 2 +--R - 4\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(----------------) +--R +-----------+ +--R |5+---+2 +--R \|\|- 1 + 1 +--R + +--R x 5+---+2 +--R +-------------+ +------------+ +-----------+ tanh(-) - \|- 1 +--R | 5+---+3 | 5+---+ |5+---+2 2 +--R - 4\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +-----------+ +--R |5+---+4 +--R \|\|- 1 + 1 +--R / +--R +-------------+ +------------+ +-----------+ +-----------+ +--R | 5+---+3 | 5+---+ |5+---+2 |5+---+4 +--R 10\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 510 +--d0086:= D(m0086,x) +--E 445 + +--S 446 of 510 +t0087:= 1/(1+sinh(x)^6) +--R +--R +--R 1 +--R (386) ------------ +--R 6 +--R sinh(x) + 1 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 510 +r0087:= 1/3*atanh((1+(-1)^(1/3))^(1/2)*tanh(x))/(1+(-1)^(1/3))^(1/2)+_ + 1/3*atanh((1-(-1)^(2/3))^(1/2)*tanh(x))/(1-(-1)^(2/3))^(1/2)+1/3*tanh(x) +--R +--R +--R (387) +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 atanh(tanh(x)\|\|- 1 + 1 ) +--R + +--R +----------+ +-------------+ +--R |3+---+ | 3+---+2 +--R \|\|- 1 + 1 atanh(tanh(x)\|- \|- 1 + 1 ) +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R tanh(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R 3\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 510 +a0087:= integrate(t0087,x) +--R +--R +--R (388) +--R %pi 2 %pi %pi 2 +--R - cos(---)sinh(x) - 2cos(---)cosh(x)sinh(x) - cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi +--R - cos(---) +--R 12 +--R * +--R log +--R 4+-+2 4 4+-+2 3 +--R \|3 sinh(x) + 4\|3 cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 2 4+-+ %pi 4+-+2 +--R (2\|3 \|3 sin(---) + 6\|3 cosh(x) - 6\|3 cos(---) - 4\|3 ) +--R 12 12 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 3 +--R 4\|3 \|3 cosh(x)sin(---) + 4\|3 cosh(x) +--R 12 +--R + +--R 4+-+ %pi 4+-+2 +--R (- 12\|3 cos(---) - 8\|3 )cosh(x) +--R 12 +--R * +--R sinh(x) +--R + +--R %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 12sin(---) + (2\|3 \|3 cosh(x) + 2\|3 \|3 )sin(---) +--R 12 12 +--R + +--R 4+-+2 4 4+-+ %pi 4+-+2 2 %pi 2 +--R \|3 cosh(x) + (- 6\|3 cos(---) - 4\|3 )cosh(x) + 12cos(---) +--R 12 12 +--R + +--R 4+-+ %pi 4+-+2 +--R 18\|3 cos(---) + 7\|3 +--R 12 +--R + +--R %pi 2 %pi %pi 2 +--R cos(---)sinh(x) + 2cos(---)cosh(x)sinh(x) + cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi +--R cos(---) +--R 12 +--R * +--R log +--R 4+-+2 4 4+-+2 3 +--R \|3 sinh(x) + 4\|3 cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 2 4+-+ %pi 4+-+2 +--R (- 2\|3 \|3 sin(---) + 6\|3 cosh(x) + 6\|3 cos(---) - 4\|3 ) +--R 12 12 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 3 +--R - 4\|3 \|3 cosh(x)sin(---) + 4\|3 cosh(x) +--R 12 +--R + +--R 4+-+ %pi 4+-+2 +--R (12\|3 cos(---) - 8\|3 )cosh(x) +--R 12 +--R * +--R sinh(x) +--R + +--R %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 12sin(---) + (- 2\|3 \|3 cosh(x) - 2\|3 \|3 )sin(---) +--R 12 12 +--R + +--R 4+-+2 4 4+-+ %pi 4+-+2 2 %pi 2 +--R \|3 cosh(x) + (6\|3 cos(---) - 4\|3 )cosh(x) + 12cos(---) +--R 12 12 +--R + +--R 4+-+ %pi 4+-+2 +--R - 18\|3 cos(---) + 7\|3 +--R 12 +--R + +--R %pi 2 %pi +--R - 2sin(---)sinh(x) - 4cosh(x)sin(---)sinh(x) +--R 12 12 +--R + +--R 2 %pi +--R (- 2cosh(x) - 2)sin(---) +--R 12 +--R * +--R atan +--R +-+ %pi %pi 4+-+ +--R 3\|3 sin(---) + 3cos(---) + 3\|3 +--R 12 12 +--R / +--R +-+4+-+ 2 +-+4+-+ %pi +--R \|3 \|3 sinh(x) + 2\|3 \|3 cosh(x)sinh(x) + 3sin(---) +--R 12 +--R + +--R +-+4+-+ 2 +-+ %pi +-+4+-+ +--R \|3 \|3 cosh(x) - 3\|3 cos(---) - 2\|3 \|3 +--R 12 +--R + +--R %pi 2 %pi +--R - 2sin(---)sinh(x) - 4cosh(x)sin(---)sinh(x) +--R 12 12 +--R + +--R 2 %pi +--R (- 2cosh(x) - 2)sin(---) +--R 12 +--R * +--R atan +--R +-+ %pi %pi 4+-+ +--R 3\|3 sin(---) + 3cos(---) - 3\|3 +--R 12 12 +--R / +--R +-+4+-+ 2 +-+4+-+ %pi +--R \|3 \|3 sinh(x) + 2\|3 \|3 cosh(x)sinh(x) - 3sin(---) +--R 12 +--R + +--R +-+4+-+ 2 +-+ %pi +-+4+-+ +--R \|3 \|3 cosh(x) + 3\|3 cos(---) - 2\|3 \|3 +--R 12 +--R + +--R 4+-+ +--R - 4\|3 +--R / +--R 4+-+ 2 4+-+ 4+-+ 2 4+-+ +--R 6\|3 sinh(x) + 12\|3 cosh(x)sinh(x) + 6\|3 cosh(x) + 6\|3 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 510 +m0087:= a0087-r0087 +--R +--R +--R (389) +--R %pi 2 %pi %pi 2 +--R - cos(---)sinh(x) - 2cos(---)cosh(x)sinh(x) - cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi +--R - cos(---) +--R 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R 4+-+2 4 4+-+2 3 +--R \|3 sinh(x) + 4\|3 cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 2 4+-+ %pi 4+-+2 +--R (2\|3 \|3 sin(---) + 6\|3 cosh(x) - 6\|3 cos(---) - 4\|3 ) +--R 12 12 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 3 +--R 4\|3 \|3 cosh(x)sin(---) + 4\|3 cosh(x) +--R 12 +--R + +--R 4+-+ %pi 4+-+2 +--R (- 12\|3 cos(---) - 8\|3 )cosh(x) +--R 12 +--R * +--R sinh(x) +--R + +--R %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 12sin(---) + (2\|3 \|3 cosh(x) + 2\|3 \|3 )sin(---) +--R 12 12 +--R + +--R 4+-+2 4 4+-+ %pi 4+-+2 2 %pi 2 +--R \|3 cosh(x) + (- 6\|3 cos(---) - 4\|3 )cosh(x) + 12cos(---) +--R 12 12 +--R + +--R 4+-+ %pi 4+-+2 +--R 18\|3 cos(---) + 7\|3 +--R 12 +--R + +--R %pi 2 %pi %pi 2 +--R cos(---)sinh(x) + 2cos(---)cosh(x)sinh(x) + cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi +--R cos(---) +--R 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R 4+-+2 4 4+-+2 3 +--R \|3 sinh(x) + 4\|3 cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 2 4+-+ %pi 4+-+2 +--R (- 2\|3 \|3 sin(---) + 6\|3 cosh(x) + 6\|3 cos(---) - 4\|3 ) +--R 12 12 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 3 +--R - 4\|3 \|3 cosh(x)sin(---) + 4\|3 cosh(x) +--R 12 +--R + +--R 4+-+ %pi 4+-+2 +--R (12\|3 cos(---) - 8\|3 )cosh(x) +--R 12 +--R * +--R sinh(x) +--R + +--R %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 12sin(---) + (- 2\|3 \|3 cosh(x) - 2\|3 \|3 )sin(---) +--R 12 12 +--R + +--R 4+-+2 4 4+-+ %pi 4+-+2 2 %pi 2 +--R \|3 cosh(x) + (6\|3 cos(---) - 4\|3 )cosh(x) + 12cos(---) +--R 12 12 +--R + +--R 4+-+ %pi 4+-+2 +--R - 18\|3 cos(---) + 7\|3 +--R 12 +--R + +--R 4+-+ 2 4+-+ 4+-+ 2 4+-+ +--R (- 2\|3 sinh(x) - 4\|3 cosh(x)sinh(x) - 2\|3 cosh(x) - 2\|3 ) +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 atanh(tanh(x)\|\|- 1 + 1 ) +--R + +--R 4+-+ 2 4+-+ 4+-+ 2 4+-+ +--R (- 2\|3 sinh(x) - 4\|3 cosh(x)sinh(x) - 2\|3 cosh(x) - 2\|3 ) +--R * +--R +----------+ +-------------+ +--R |3+---+ | 3+---+2 +--R \|\|- 1 + 1 atanh(tanh(x)\|- \|- 1 + 1 ) +--R + +--R %pi 2 %pi +--R - 2sin(---)sinh(x) - 4cosh(x)sin(---)sinh(x) +--R 12 12 +--R + +--R 2 %pi +--R (- 2cosh(x) - 2)sin(---) +--R 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R atan +--R +-+ %pi %pi 4+-+ +--R 3\|3 sin(---) + 3cos(---) + 3\|3 +--R 12 12 +--R / +--R +-+4+-+ 2 +-+4+-+ %pi +--R \|3 \|3 sinh(x) + 2\|3 \|3 cosh(x)sinh(x) + 3sin(---) +--R 12 +--R + +--R +-+4+-+ 2 +-+ %pi +-+4+-+ +--R \|3 \|3 cosh(x) - 3\|3 cos(---) - 2\|3 \|3 +--R 12 +--R + +--R %pi 2 %pi +--R - 2sin(---)sinh(x) - 4cosh(x)sin(---)sinh(x) +--R 12 12 +--R + +--R 2 %pi +--R (- 2cosh(x) - 2)sin(---) +--R 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R atan +--R +-+ %pi %pi 4+-+ +--R 3\|3 sin(---) + 3cos(---) - 3\|3 +--R 12 12 +--R / +--R +-+4+-+ 2 +-+4+-+ %pi +--R \|3 \|3 sinh(x) + 2\|3 \|3 cosh(x)sinh(x) - 3sin(---) +--R 12 +--R + +--R +-+4+-+ 2 +-+ %pi +-+4+-+ +--R \|3 \|3 cosh(x) + 3\|3 cos(---) - 2\|3 \|3 +--R 12 +--R + +--R 4+-+ 2 4+-+ 4+-+ 2 4+-+ +--R (- 2\|3 sinh(x) - 4\|3 cosh(x)sinh(x) - 2\|3 cosh(x) - 2\|3 ) +--R * +--R tanh(x) +--R + +--R 4+-+ +--R - 4\|3 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R 4+-+ 2 4+-+ 4+-+ 2 4+-+ +--R (6\|3 sinh(x) + 12\|3 cosh(x)sinh(x) + 6\|3 cosh(x) + 6\|3 ) +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 510 +--d0087:= D(m0087,x) +--E 450 + +--S 451 of 510 +t0088:= 1/(1+sinh(x)^8) +--R +--R +--R 1 +--R (390) ------------ +--R 8 +--R sinh(x) + 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 510 +r0088:= 1/4*atanh((1-(-1)^(1/4))^(1/2)*tanh(x))/(1-(-1)^(1/4))^(1/2)+_ + 1/4*atanh((1+(-1)^(1/4))^(1/2)*tanh(x))/(1+(-1)^(1/4))^(1/2)+_ + 1/4*atanh((1-(-1)^(3/4))^(1/2)*tanh(x))/(1-(-1)^(3/4))^(1/2)+_ + 1/4*atanh((1+(-1)^(3/4))^(1/2)*tanh(x))/(1+(-1)^(3/4))^(1/2) +--R +--R +--R (391) +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R atanh(tanh(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 - 1 +--R atanh(tanh(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 + 1 +--R atanh(tanh(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 - 1 +--R atanh(tanh(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R / +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 4 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 510 +a0088:= integrate(t0088,x) +--R +--R +--R (392) +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (128\|2 - 256)sinh(x) + (256\|2 - 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (128\|2 - 256)cosh(x) + 128\|2 - 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)sinh(x) + (- 4\|2 + 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)cosh(x) + 6\|2 - 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - 2\|2 + 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (- 4\|2 + 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)cosh(x) + 5\|2 - 4 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 128\|2 + 256)sinh(x) + (- 256\|2 + 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 128\|2 + 256)cosh(x) - 128\|2 + 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)sinh(x) + (4\|2 - 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)cosh(x) - 6\|2 + 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - 2\|2 + 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (- 4\|2 + 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)cosh(x) + 5\|2 - 4 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (128\|2 + 256)sinh(x) + (256\|2 + 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (128\|2 + 256)cosh(x) + 128\|2 + 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)sinh(x) + (- 4\|2 - 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)cosh(x) + 6\|2 + 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - 2\|2 - 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (- 4\|2 - 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)cosh(x) + 5\|2 + 4 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 128\|2 - 256)sinh(x) + (- 256\|2 - 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 128\|2 - 256)cosh(x) - 128\|2 - 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)sinh(x) + (4\|2 + 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)cosh(x) - 6\|2 - 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - 2\|2 - 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (- 4\|2 - 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)cosh(x) + 5\|2 + 4 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (\|2 + 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 +--R (64\|2 + 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R (128\|2 + 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 +--R (64\|2 + 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R sin(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (- \|2 - 2) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) - \|2 - 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (\|2 + 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R (64\|2 + 128) |--------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R (- 128\|2 - 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R (64\|2 + 128) |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +-+ 2 +--R (- \|2 - 2) |--------- cos(-------------------- - \|2 sinh(x) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ +-+ 2 +-+ +--R - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) + \|2 + 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (\|2 - 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R (64\|2 - 128) |--------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R (128\|2 - 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R (64\|2 - 128) |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +-+ 2 +--R (- \|2 + 2) |--------- cos(-------------------- + \|2 sinh(x) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ +-+ 2 +-+ +--R 2\|2 cosh(x)sinh(x) + \|2 cosh(x) - \|2 + 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (\|2 - 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 +--R (64\|2 - 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R (- 128\|2 + 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 +--R (64\|2 - 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R sin(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (- \|2 + 2) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R - \|2 sinh(x) - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) + \|2 - 2 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 510 +m0088:= a0088-r0088 +--R +--R +--R (393) +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 + 4 \| 4096\|2 +--R |----------------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (128\|2 - 256)sinh(x) + (256\|2 - 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (128\|2 - 256)cosh(x) + 128\|2 - 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)sinh(x) + (- 4\|2 + 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)cosh(x) + 6\|2 - 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - 2\|2 + 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (- 4\|2 + 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)cosh(x) + 5\|2 - 4 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 + 4 \| 4096\|2 +--R |----------------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 128\|2 + 256)sinh(x) + (- 256\|2 + 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 128\|2 + 256)cosh(x) - 128\|2 + 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)sinh(x) + (4\|2 - 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)cosh(x) - 6\|2 + 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - 2\|2 + 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (- 4\|2 + 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)cosh(x) + 5\|2 - 4 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 - 4 \| 4096\|2 +--R |----------------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (128\|2 + 256)sinh(x) + (256\|2 + 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (128\|2 + 256)cosh(x) + 128\|2 + 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)sinh(x) + (- 4\|2 - 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)cosh(x) + 6\|2 + 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - 2\|2 - 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (- 4\|2 - 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)cosh(x) + 5\|2 + 4 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 - 4 \| 4096\|2 +--R |----------------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 128\|2 - 256)sinh(x) + (- 256\|2 - 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 128\|2 - 256)cosh(x) - 128\|2 - 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)sinh(x) + (4\|2 + 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)cosh(x) - 6\|2 - 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - 2\|2 - 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (- 4\|2 - 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)cosh(x) + 5\|2 + 4 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 - 4 \| 4096\|2 +--R |----------------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (\|2 + 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 +--R (64\|2 + 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R (128\|2 + 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 +--R (64\|2 + 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R sin(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (- \|2 - 2) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) - \|2 - 2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 - 4 \| 4096\|2 +--R |----------------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (\|2 + 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R (64\|2 + 128) |--------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R (- 128\|2 - 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R (64\|2 + 128) |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +-+ 2 +--R (- \|2 - 2) |--------- cos(-------------------- - \|2 sinh(x) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ +-+ 2 +-+ +--R - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) + \|2 + 2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 + 4 \| 4096\|2 +--R |----------------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (\|2 - 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R (64\|2 - 128) |--------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R (128\|2 - 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R (64\|2 - 128) |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +-+ 2 +--R (- \|2 + 2) |--------- cos(-------------------- + \|2 sinh(x) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ +-+ 2 +-+ +--R 2\|2 cosh(x)sinh(x) + \|2 cosh(x) - \|2 + 2 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 + 4 \| 4096\|2 +--R |----------------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (\|2 - 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 +--R (64\|2 - 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R (- 128\|2 + 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 +--R (64\|2 - 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R sin(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (- \|2 + 2) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R - \|2 sinh(x) - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) + \|2 - 2 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R +-+ |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 2\|2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R atanh(tanh(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R +-+ |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 + 1 +--R 2\|2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 - 1 +--R atanh(tanh(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R +-+ |\|2 - \|- 1 - 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R 2\|2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 + 1 +--R atanh(tanh(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R +-+ |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R 2\|2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 - 1 +--R atanh(tanh(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R / +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R +-+ |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 8\|2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 510 +--d0088:= D(m0088,x) +--E 455 + +--S 456 of 510 +t0089:= 1/(1-sinh(x)^3) +--R +--R +--R 1 +--R (394) - ------------ +--R 3 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 510 +r0089:= -2/3*atanh(((-1)^(1/3)-tanh(1/2*x))/(1+(-1)^(2/3))^(1/2))/_ + (1+(-1)^(2/3))^(1/2)+1/3*2^(1/2)*_ + atanh(1/2*(1+tanh(1/2*x))*2^(1/2))+2/3*_ + atanh(((-1)^(2/3)+tanh(1/2*x))/(1-(-1)^(1/3))^(1/2))/_ + (1-(-1)^(1/3))^(1/2) +--R +--R +--R (395) +--R +-+ x +-+ +--R +------------+ +-----------+ \|2 tanh(-) + \|2 +--R +-+ | 3+---+ |3+---+2 2 +--R \|2 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(------------------) +--R 2 +--R + +--R x 3+---+2 +--R +-----------+ tanh(-) + \|- 1 +--R |3+---+2 2 +--R 2\|\|- 1 + 1 atanh(-----------------) +--R +------------+ +--R | 3+---+ +--R \|- \|- 1 + 1 +--R + +--R x 3+---+ +--R +------------+ tanh(-) - \|- 1 +--R | 3+---+ 2 +--R 2\|- \|- 1 + 1 atanh(----------------) +--R +-----------+ +--R |3+---+2 +--R \|\|- 1 + 1 +--R / +--R +------------+ +-----------+ +--R | 3+---+ |3+---+2 +--R 3\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 510 +a0089:= integrate(t0089,x) +--R +--R +--R (396) +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + \|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R (2sinh(x) + 2cosh(x) + 1)cos(----------) + sinh(x) +--R 2 +--R + +--R 2 +--R (2cosh(x) + 1)sinh(x) + cosh(x) + cosh(x) + 1 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - \|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R (- 2sinh(x) - 2cosh(x) - 1)cos(----------) + sinh(x) +--R 2 +--R + +--R 2 +--R (2cosh(x) + 1)sinh(x) + cosh(x) + cosh(x) + 1 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +-+ +--R +-+ 2sin(----------) - \|3 +--R \|3 2 +--R - 4sin(----------)atan(------------------------------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) - 2sinh(x) - 2cosh(x) - 1 +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +-+ +--R +-+ 2sin(----------) + \|3 +--R \|3 2 +--R 4sin(----------)atan(------------------------------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) + 2sinh(x) + 2cosh(x) + 1 +--R 2 +--R + +--R +-+ +-+ +-+ +--R +-+ (\|2 - 1)sinh(x) + (- \|2 + 2)cosh(x) + \|2 - 1 +--R \|2 log(--------------------------------------------------) +--R sinh(x) - 1 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 510 +m0089:= a0089-r0089 +--R +--R +--R (397) +--R - +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R | 3+---+ |3+---+2 \|3 +--R 2\|- \|- 1 + 1 \|\|- 1 + 1 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + \|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R (2sinh(x) + 2cosh(x) + 1)cos(----------) + sinh(x) +--R 2 +--R + +--R 2 +--R (2cosh(x) + 1)sinh(x) + cosh(x) + cosh(x) + 1 +--R + +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R | 3+---+ |3+---+2 \|3 +--R 2\|- \|- 1 + 1 \|\|- 1 + 1 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - \|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R (- 2sinh(x) - 2cosh(x) - 1)cos(----------) + sinh(x) +--R 2 +--R + +--R 2 +--R (2cosh(x) + 1)sinh(x) + cosh(x) + cosh(x) + 1 +--R + +--R - +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R | 3+---+ |3+---+2 \|3 +--R 4\|- \|- 1 + 1 \|\|- 1 + 1 sin(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +-+ +--R 2sin(----------) - \|3 +--R 2 +--R atan(------------------------------------------) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) - 2sinh(x) - 2cosh(x) - 1 +--R 2 +--R + +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R | 3+---+ |3+---+2 \|3 +--R 4\|- \|- 1 + 1 \|\|- 1 + 1 sin(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +-+ +--R 2sin(----------) + \|3 +--R 2 +--R atan(------------------------------------------) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) + 2sinh(x) + 2cosh(x) + 1 +--R 2 +--R + +--R +------------+ +-----------+ +--R +-+ | 3+---+ |3+---+2 +--R \|2 \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R +-+ +-+ +-+ +--R (\|2 - 1)sinh(x) + (- \|2 + 2)cosh(x) + \|2 - 1 +--R log(--------------------------------------------------) +--R sinh(x) - 1 +--R + +--R +-+ x +-+ +--R +------------+ +-----------+ \|2 tanh(-) + \|2 +--R +-+ | 3+---+ |3+---+2 2 +--R - 2\|2 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(------------------) +--R 2 +--R + +--R x 3+---+2 +--R +-----------+ tanh(-) + \|- 1 +--R |3+---+2 2 +--R - 4\|\|- 1 + 1 atanh(-----------------) +--R +------------+ +--R | 3+---+ +--R \|- \|- 1 + 1 +--R + +--R x 3+---+ +--R +------------+ tanh(-) - \|- 1 +--R | 3+---+ 2 +--R - 4\|- \|- 1 + 1 atanh(----------------) +--R +-----------+ +--R |3+---+2 +--R \|\|- 1 + 1 +--R / +--R +------------+ +-----------+ +--R | 3+---+ |3+---+2 +--R 6\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 510 +--d0089:= D(m0089,x) +--E 460 + +--S 461 of 510 +t0090:= 1/(1-sinh(x)^4) +--R +--R +--R 1 +--R (398) - ------------ +--R 4 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 510 +r0090:= 1/4*atanh(2^(1/2)*tanh(x))*2^(1/2)+1/2*tanh(x) +--R +--R +--R +-+ +-+ +--R \|2 atanh(\|2 tanh(x)) + 2tanh(x) +--R (399) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 510 +a0090:= integrate(t0090,x) +--R +--R +--R (400) +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1) +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ +--R - 4\|2 +--R / +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|2 sinh(x) + 8\|2 cosh(x)sinh(x) + 4\|2 cosh(x) + 4\|2 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 510 +m0090:= a0090-r0090 +--R +--R +--R (401) +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1) +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R 2 2 +-+ +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2)atanh(\|2 tanh(x)) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- 2\|2 sinh(x) - 4\|2 cosh(x)sinh(x) - 2\|2 cosh(x) - 2\|2 )tanh(x) +--R + +--R +-+ +--R - 4\|2 +--R / +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|2 sinh(x) + 8\|2 cosh(x)sinh(x) + 4\|2 cosh(x) + 4\|2 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 510 +d0090:= D(m0090,x) +--R +--R +--R (402) +--R +-+ 8 +-+ 7 +--R (9\|2 - 12)sinh(x) + (20\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (8\|2 cosh(x) - 12\|2 + 16)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((- 4\|2 + 24)cosh(x) + (- 68\|2 + 88)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 2\|2 + 24)cosh(x) + (- 28\|2 + 16)cosh(x) - 42\|2 + 56) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 4\|2 + 24)cosh(x) + (56\|2 - 112)cosh(x) +--R + +--R +-+ +--R (- 4\|2 - 8)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 8\|2 cosh(x) + (- 28\|2 + 16)cosh(x) + (144\|2 - 224)cosh(x) +--R + +--R +-+ +--R - 12\|2 + 16 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (20\|2 - 24)cosh(x) + (- 68\|2 + 88)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 4\|2 - 8)cosh(x) + (84\|2 - 120)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (9\|2 - 12)cosh(x) + (- 12\|2 + 16)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 42\|2 + 56)cosh(x) + (- 12\|2 + 16)cosh(x) + 9\|2 - 12 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R (- 12\|2 + 16)sinh(x) + (- 16\|2 + 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R ((8\|2 - 32)cosh(x) + 54\|2 - 72)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((- 16\|2 - 16)cosh(x) + (128\|2 - 160)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 56\|2 + 32)cosh(x) + (26\|2 + 8)cosh(x) - 66\|2 + 88) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 16\|2 - 16)cosh(x) + (- 96\|2 + 192)cosh(x) +--R + +--R +-+ +--R (- 48\|2 + 48)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (8\|2 - 32)cosh(x) + (26\|2 + 8)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 100\|2 + 112)cosh(x) + 42\|2 - 56 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 16\|2 + 16)cosh(x) + (128\|2 - 160)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 48\|2 + 48)cosh(x) + (- 64\|2 + 96)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 12\|2 + 16)cosh(x) + (54\|2 - 72)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 66\|2 + 88)cosh(x) + (42\|2 - 56)cosh(x) - 18\|2 + 24 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R (6\|2 - 8)sinh(x) + (8\|2 - 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R ((- 4\|2 + 16)cosh(x) - 27\|2 + 36)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((8\|2 + 8)cosh(x) + (- 64\|2 + 80)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R ((28\|2 - 16)cosh(x) + (- 13\|2 - 4)cosh(x) + 33\|2 - 44)sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R ((8\|2 + 8)cosh(x) + (48\|2 - 96)cosh(x) + (24\|2 - 24)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 4\|2 + 16)cosh(x) + (- 13\|2 - 4)cosh(x) +--R + +--R +-+ 2 +-+ +--R (50\|2 - 56)cosh(x) - 21\|2 + 28 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R (8\|2 - 8)cosh(x) + (- 64\|2 + 80)cosh(x) + (24\|2 - 24)cosh(x) +--R + +--R +-+ +--R (32\|2 - 48)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R (6\|2 - 8)cosh(x) + (- 27\|2 + 36)cosh(x) + (33\|2 - 44)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 21\|2 + 28)cosh(x) + 9\|2 - 12 +--R / +--R +-+ 8 +-+ 7 +--R (18\|2 - 24)sinh(x) + (40\|2 - 48)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (16\|2 cosh(x) - 24\|2 + 32)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((- 8\|2 + 48)cosh(x) + (- 136\|2 + 176)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 4\|2 + 48)cosh(x) + (- 56\|2 + 32)cosh(x) - 84\|2 + 112) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 8\|2 + 48)cosh(x) + (112\|2 - 224)cosh(x) +--R + +--R +-+ +--R (- 8\|2 - 16)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R 16\|2 cosh(x) + (- 56\|2 + 32)cosh(x) +--R + +--R +-+ 2 +-+ +--R (288\|2 - 448)cosh(x) - 24\|2 + 32 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (40\|2 - 48)cosh(x) + (- 136\|2 + 176)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 8\|2 - 16)cosh(x) + (168\|2 - 240)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (18\|2 - 24)cosh(x) + (- 24\|2 + 32)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 84\|2 + 112)cosh(x) + (- 24\|2 + 32)cosh(x) + 18\|2 - 24 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R (- 9\|2 + 12)sinh(x) + (- 20\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 8\|2 cosh(x) + 12\|2 - 16)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((4\|2 - 24)cosh(x) + (68\|2 - 88)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R ((2\|2 - 24)cosh(x) + (28\|2 - 16)cosh(x) + 42\|2 - 56)sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R ((4\|2 - 24)cosh(x) + (- 56\|2 + 112)cosh(x) + (4\|2 + 8)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 8\|2 cosh(x) + (28\|2 - 16)cosh(x) + (- 144\|2 + 224)cosh(x) +--R + +--R +-+ +--R 12\|2 - 16 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R (- 20\|2 + 24)cosh(x) + (68\|2 - 88)cosh(x) + (4\|2 + 8)cosh(x) +--R + +--R +-+ +--R (- 84\|2 + 120)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R (- 9\|2 + 12)cosh(x) + (12\|2 - 16)cosh(x) + (42\|2 - 56)cosh(x) +--R + +--R +-+ 2 +-+ +--R (12\|2 - 16)cosh(x) - 9\|2 + 12 +--R Type: Expression(Integer) +--E 465 + +--S 466 of 510 +t0091:= 1/(1-sinh(x)^5) +--R +--R +--R 1 +--R (403) - ------------ +--R 5 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 510 +r0091:= -2/5*atanh(((-1)^(1/5)-tanh(1/2*x))/(1+(-1)^(2/5))^(1/2))/_ + (1+(-1)^(2/5))^(1/2)-2/5*atanh(((-1)^(3/5)-tanh(1/2*x))/_ + (1-(-1)^(1/5))^(1/2))/(1-(-1)^(1/5))^(1/2)+1/5*2^(1/2)*_ + atanh(1/2*(1+tanh(1/2*x))*2^(1/2))+2/5*_ + atanh(((-1)^(2/5)+tanh(1/2*x))/(1+(-1)^(4/5))^(1/2))/_ + (1+(-1)^(4/5))^(1/2)+2/5*atanh(((-1)^(4/5)+_ + tanh(1/2*x))/(1-(-1)^(3/5))^(1/2))/(1-(-1)^(3/5))^(1/2) +--R +--R +--R (404) +--R +-------------+ +------------+ +-----------+ +-----------+ +--R +-+ | 5+---+3 | 5+---+ |5+---+2 |5+---+4 +--R \|2 \|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R * +--R +-+ x +-+ +--R \|2 tanh(-) + \|2 +--R 2 +--R atanh(------------------) +--R 2 +--R + +--R x 5+---+4 +--R +------------+ +-----------+ +-----------+ tanh(-) + \|- 1 +--R | 5+---+ |5+---+2 |5+---+4 2 +--R 2\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +-------------+ +--R | 5+---+3 +--R \|- \|- 1 + 1 +--R + +--R x 5+---+3 +--R +-------------+ +-----------+ +-----------+ tanh(-) - \|- 1 +--R | 5+---+3 |5+---+2 |5+---+4 2 +--R 2\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +------------+ +--R | 5+---+ +--R \|- \|- 1 + 1 +--R + +--R x 5+---+ +--R +-------------+ +------------+ +-----------+ tanh(-) - \|- 1 +--R | 5+---+3 | 5+---+ |5+---+4 2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(----------------) +--R +-----------+ +--R |5+---+2 +--R \|\|- 1 + 1 +--R + +--R x 5+---+2 +--R +-------------+ +------------+ +-----------+ tanh(-) + \|- 1 +--R | 5+---+3 | 5+---+ |5+---+2 2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +-----------+ +--R |5+---+4 +--R \|\|- 1 + 1 +--R / +--R +-------------+ +------------+ +-----------+ +-----------+ +--R | 5+---+3 | 5+---+ |5+---+2 |5+---+4 +--R 5\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 510 +a0091:= integrate(t0091,x) +--R +--R +--R (405) +--R - +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +-----------+ +--R | +-+ | +-+ +--R +-+ |\|5 + 2 |24\|5 + 40 +--R (150\|5 - 250) |-------- |----------- +--R | +-+ 4| +-+ +--R \| 125\|5 \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 125\|5 +--R sin(-------------------) +--R 2 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((4\|5 - 20)sinh(x) + (4\|5 - 20)cosh(x) + 6\|5 - 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |24\|5 + 40 \| 125\|5 +--R (- 150\|5 + 250) |-------- |----------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 125\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((- 4\|5 + 20)sinh(x) + (- 4\|5 + 20)cosh(x) - 6\|5 + 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 - 20)cosh(x) + 8\|5 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +-----------+ +--R | +-+ | +-+ +--R +-+ |\|5 - 2 |24\|5 - 40 +--R (150\|5 + 250) |-------- |----------- +--R | +-+ 4| +-+ +--R \| 125\|5 \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 125\|5 +--R sin(-------------------) +--R 2 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((4\|5 + 20)sinh(x) + (4\|5 + 20)cosh(x) + 6\|5 + 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |24\|5 - 40 \| 125\|5 +--R (- 150\|5 - 250) |-------- |----------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 125\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((- 4\|5 - 20)sinh(x) + (- 4\|5 - 20)cosh(x) - 6\|5 - 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R 2 |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (25\|5 - 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- cos(------------------- - 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R - 4cosh(x) + \|5 - 1 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R 2 |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (- 25\|5 + 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- cos(------------------- + 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R 4cosh(x) - \|5 + 1 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R 2 |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (- 25\|5 - 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- cos(------------------- - 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R - 4cosh(x) - \|5 - 1 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R 2 |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (25\|5 + 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- cos(------------------- + 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R 4cosh(x) + \|5 + 1 +--R + +--R +-+ +-+ +-+ +--R +-+ (\|2 - 1)sinh(x) + (- \|2 + 2)cosh(x) + \|2 - 1 +--R \|2 log(--------------------------------------------------) +--R sinh(x) - 1 +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 510 +m0091:= a0091-r0091 +--R +--R +--R (406) +--R - +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 + 40 |5+---+2 +--R \|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +-----------+ +--R | +-+ | +-+ +--R +-+ |\|5 + 2 |24\|5 + 40 +--R (150\|5 - 250) |-------- |----------- +--R | +-+ 4| +-+ +--R \| 125\|5 \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 125\|5 +--R sin(-------------------) +--R 2 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((4\|5 - 20)sinh(x) + (4\|5 - 20)cosh(x) + 6\|5 - 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 + 40 |5+---+2 +--R \|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |24\|5 + 40 \| 125\|5 +--R (- 150\|5 + 250) |-------- |----------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 125\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (3\|5 - 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((- 4\|5 + 20)sinh(x) + (- 4\|5 + 20)cosh(x) - 6\|5 + 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 + 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 - 20)cosh(x) + 8\|5 +--R + +--R - +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 - 40 |5+---+2 +--R \|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +-----------+ +--R | +-+ | +-+ +--R +-+ |\|5 - 2 |24\|5 - 40 +--R (150\|5 + 250) |-------- |----------- +--R | +-+ 4| +-+ +--R \| 125\|5 \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 125\|5 +--R sin(-------------------) +--R 2 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((4\|5 + 20)sinh(x) + (4\|5 + 20)cosh(x) + 6\|5 + 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 - 40 |5+---+2 +--R \|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |24\|5 - 40 \| 125\|5 +--R (- 150\|5 - 250) |-------- |----------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 125\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +-----------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (3\|5 + 5) |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R ((- 4\|5 - 20)sinh(x) + (- 4\|5 - 20)cosh(x) - 6\|5 - 10) +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |24\|5 - 40 \| 125\|5 +--R |----------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 + 40 |5+---+2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (25\|5 - 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- cos(------------------- - 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R - 4cosh(x) + \|5 - 1 +--R + +--R - +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 + 40 |5+---+2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (- 25\|5 + 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 + 40 \| 125\|5 +--R (\|5 - 1) |----------- cos(------------------- + 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R 4cosh(x) - \|5 + 1 +--R + +--R - +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 - 40 |5+---+2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (- 25\|5 - 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- cos(------------------- - 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R - 4cosh(x) - \|5 - 1 +--R + +--R +-----------+ +--R +-------------+ +------------+ | +-+ +-----------+ +--R | 5+---+3 | 5+---+ |24\|5 - 40 |5+---+2 +--R 2\|- \|- 1 + 1 \|- \|- 1 + 1 |----------- \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R +-----------+ | +-+ +--R |5+---+4 \| 125\|5 +--R \|\|- 1 + 1 sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (25\|5 + 25) |-------- +--R | +-+ +--R \| 125\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +-----------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |24\|5 - 40 \| 125\|5 +--R (\|5 + 1) |----------- cos(------------------- + 4sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +--R 4cosh(x) + \|5 + 1 +--R + +--R +-------------+ +------------+ +-----------+ +-----------+ +--R +-+ | 5+---+3 | 5+---+ |5+---+2 |5+---+4 +--R \|2 \|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R * +--R +-+ +-+ +-+ +--R (\|2 - 1)sinh(x) + (- \|2 + 2)cosh(x) + \|2 - 1 +--R log(--------------------------------------------------) +--R sinh(x) - 1 +--R + +--R - +--R +-------------+ +------------+ +-----------+ +-----------+ +--R +-+ | 5+---+3 | 5+---+ |5+---+2 |5+---+4 +--R 2\|2 \|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R * +--R +-+ x +-+ +--R \|2 tanh(-) + \|2 +--R 2 +--R atanh(------------------) +--R 2 +--R + +--R x 5+---+4 +--R +------------+ +-----------+ +-----------+ tanh(-) + \|- 1 +--R | 5+---+ |5+---+2 |5+---+4 2 +--R - 4\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +-------------+ +--R | 5+---+3 +--R \|- \|- 1 + 1 +--R + +--R x 5+---+3 +--R +-------------+ +-----------+ +-----------+ tanh(-) - \|- 1 +--R | 5+---+3 |5+---+2 |5+---+4 2 +--R - 4\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +------------+ +--R | 5+---+ +--R \|- \|- 1 + 1 +--R + +--R x 5+---+ +--R +-------------+ +------------+ +-----------+ tanh(-) - \|- 1 +--R | 5+---+3 | 5+---+ |5+---+4 2 +--R - 4\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(----------------) +--R +-----------+ +--R |5+---+2 +--R \|\|- 1 + 1 +--R + +--R x 5+---+2 +--R +-------------+ +------------+ +-----------+ tanh(-) + \|- 1 +--R | 5+---+3 | 5+---+ |5+---+2 2 +--R - 4\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(-----------------) +--R +-----------+ +--R |5+---+4 +--R \|\|- 1 + 1 +--R / +--R +-------------+ +------------+ +-----------+ +-----------+ +--R | 5+---+3 | 5+---+ |5+---+2 |5+---+4 +--R 10\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 510 +--d0091:= D(m0091,x) +--E 470 + +--S 471 of 510 +t0092:= 1/(1-sinh(x)^6) +--R +--R +--R 1 +--R (407) - ------------ +--R 6 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 510 +r0092:= 1/6*atanh(2^(1/2)*tanh(x))*2^(1/2)+1/3*atanh((1-(-1)^(1/3))^(1/2)*_ + tanh(x))/(1-(-1)^(1/3))^(1/2)+1/3*atanh((1+(-1)^(2/3))^(1/2)*_ + tanh(x))/(1+(-1)^(2/3))^(1/2) +--R +--R +--R (408) +--R +------------+ +-----------+ +--R | 3+---+ |3+---+2 +--R 2\|- \|- 1 + 1 atanh(tanh(x)\|\|- 1 + 1 ) +--R + +--R +-----------+ +------------+ +--R |3+---+2 | 3+---+ +--R 2\|\|- 1 + 1 atanh(tanh(x)\|- \|- 1 + 1 ) +--R + +--R +------------+ +-----------+ +--R +-+ | 3+---+ |3+---+2 +-+ +--R \|2 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(\|2 tanh(x)) +--R / +--R +------------+ +-----------+ +--R | 3+---+ |3+---+2 +--R 6\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 510 +a0092:= integrate(t0092,x) +--R +--R +--R (409) +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R \|2 cos(----------) +--R 2 +--R * +--R log +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4sin(----------) +--R 2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (2\|3 sinh(x) + 4\|3 cosh(x)sinh(x) + 2\|3 cosh(x) + 2\|3 ) +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 2 2 \|3 +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 6)cos(----------) +--R 2 +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) + 3 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R \|2 cos(----------) +--R 2 +--R * +--R log +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4sin(----------) +--R 2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- 2\|3 sinh(x) - 4\|3 cosh(x)sinh(x) - 2\|3 cosh(x) - 2\|3 ) +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 2 2 \|3 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 6)cos(----------) +--R 2 +--R + +--R 4 3 2 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) + 4cosh(x) sinh(x) +--R + +--R 4 +--R cosh(x) + 3 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|2 sin(----------) +--R 2 +--R * +--R atan +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +-+ +--R sin(----------) + \|3 cos(----------) - \|3 +--R 2 2 +--R / +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 2 +--R \|3 sin(----------) - cos(----------) - sinh(x) +--R 2 2 +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|2 sin(----------) +--R 2 +--R * +--R atan +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +-+ +--R sin(----------) + \|3 cos(----------) + \|3 +--R 2 2 +--R / +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 2 +--R \|3 sin(----------) - cos(----------) + sinh(x) +--R 2 2 +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) +--R + +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R / +--R +-+ +--R 6\|2 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 510 +m0092:= a0092-r0092 +--R +--R +--R (410) +--R - +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R +-+ | 3+---+ |3+---+2 \|3 +--R \|2 \|- \|- 1 + 1 \|\|- 1 + 1 cos(----------) +--R 2 +--R * +--R log +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4sin(----------) +--R 2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (2\|3 sinh(x) + 4\|3 cosh(x)sinh(x) + 2\|3 cosh(x) + 2\|3 ) +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 2 2 \|3 +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 6)cos(----------) +--R 2 +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) + 3 +--R + +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R +-+ | 3+---+ |3+---+2 \|3 +--R \|2 \|- \|- 1 + 1 \|\|- 1 + 1 cos(----------) +--R 2 +--R * +--R log +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4sin(----------) +--R 2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- 2\|3 sinh(x) - 4\|3 cosh(x)sinh(x) - 2\|3 cosh(x) - 2\|3 ) +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 2 2 \|3 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 6)cos(----------) +--R 2 +--R + +--R 4 3 2 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) + 4cosh(x) sinh(x) +--R + +--R 4 +--R cosh(x) + 3 +--R + +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R +-+ | 3+---+ |3+---+2 \|3 +--R 2\|2 \|- \|- 1 + 1 \|\|- 1 + 1 sin(----------) +--R 2 +--R * +--R atan +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +-+ +--R sin(----------) + \|3 cos(----------) - \|3 +--R 2 2 +--R / +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 2 +--R \|3 sin(----------) - cos(----------) - sinh(x) +--R 2 2 +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) +--R + +--R - +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R +-+ | 3+---+ |3+---+2 \|3 +--R 2\|2 \|- \|- 1 + 1 \|\|- 1 + 1 sin(----------) +--R 2 +--R * +--R atan +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +-+ +--R sin(----------) + \|3 cos(----------) + \|3 +--R 2 2 +--R / +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 2 +--R \|3 sin(----------) - cos(----------) + sinh(x) +--R 2 2 +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) +--R + +--R +------------+ +-----------+ +--R | 3+---+ |3+---+2 +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +------------+ +-----------+ +--R +-+ | 3+---+ |3+---+2 +--R - 2\|2 \|- \|- 1 + 1 atanh(tanh(x)\|\|- 1 + 1 ) +--R + +--R +-----------+ +------------+ +--R +-+ |3+---+2 | 3+---+ +--R - 2\|2 \|\|- 1 + 1 atanh(tanh(x)\|- \|- 1 + 1 ) +--R + +--R +------------+ +-----------+ +--R | 3+---+ |3+---+2 +-+ +--R - 2\|- \|- 1 + 1 \|\|- 1 + 1 atanh(\|2 tanh(x)) +--R / +--R +------------+ +-----------+ +--R +-+ | 3+---+ |3+---+2 +--R 6\|2 \|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 510 +--d0092:= D(m0092,x) +--E 475 + +--S 476 of 510 +t0093:= 1/(1-sinh(x)^8) +--R +--R +--R 1 +--R (411) - ------------ +--R 8 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 510 +r0093:= 1/4*atanh((1-%i)^(1/2)*tanh(x))/(1-%i)^(1/2)+_ + 1/4*atanh((1+%i)^(1/2)*tanh(x))/(1+%i)^(1/2)+_ + 1/8*atanh(2^(1/2)*tanh(x))*2^(1/2)+1/4*tanh(x) +--R +--R +--R (412) +--R +------+ +------+ +-+ +-+ +--R \|1 - %i \|1 + %i \|2 atanh(\|2 tanh(x)) +--R + +--R +------+ +------+ +------+ +------+ +--R 2\|1 - %i atanh(\|1 + %i tanh(x)) + 2\|1 + %i atanh(\|1 - %i tanh(x)) +--R + +--R +------+ +------+ +--R 2\|1 - %i \|1 + %i tanh(x) +--R / +--R +------+ +------+ +--R 8\|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 477 + +--S 478 of 510 +a0093:= integrate(t0093,x) +--R +--R +--R (413) +--R 4+-+ %pi 2 4+-+ %pi +--R - \|2 cos(---)sinh(x) - 2\|2 cos(---)cosh(x)sinh(x) +--R 8 8 +--R + +--R 4+-+ %pi 2 4+-+ %pi +--R - \|2 cos(---)cosh(x) - \|2 cos(---) +--R 8 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (2\|2 \|2 sin(---) + 6cosh(x) - 2\|2 \|2 cos(---) - 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (- 4\|2 \|2 cos(---) - 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (2\|2 \|2 cosh(x) + 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (- 2\|2 \|2 cos(---) - 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R 4+-+ %pi 2 4+-+ %pi +--R \|2 cos(---)sinh(x) + 2\|2 cos(---)cosh(x)sinh(x) +--R 8 8 +--R + +--R 4+-+ %pi 2 4+-+ %pi +--R \|2 cos(---)cosh(x) + \|2 cos(---) +--R 8 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (- 2\|2 \|2 sin(---) + 6cosh(x) + 2\|2 \|2 cos(---) - 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R - 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (4\|2 \|2 cos(---) - 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (- 2\|2 \|2 cosh(x) - 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (2\|2 \|2 cos(---) - 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R - 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1) +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R 4+-+ %pi 2 4+-+ %pi +--R - 2\|2 sin(---)sinh(x) - 4\|2 cosh(x)sin(---)sinh(x) +--R 8 8 +--R + +--R 4+-+ 2 4+-+ %pi +--R (- 2\|2 cosh(x) - 2\|2 )sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) + 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) - 2\|2 cos(---) - \|2 +--R 8 +--R + +--R 4+-+ %pi 2 4+-+ %pi +--R - 2\|2 sin(---)sinh(x) - 4\|2 cosh(x)sin(---)sinh(x) +--R 8 8 +--R + +--R 4+-+ 2 4+-+ %pi +--R (- 2\|2 cosh(x) - 2\|2 )sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) - 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) - 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) + 2\|2 cos(---) - \|2 +--R 8 +--R + +--R +-+ +--R - 4\|2 +--R / +--R +-+ 2 +-+ +-+ 2 +-+ +--R 8\|2 sinh(x) + 16\|2 cosh(x)sinh(x) + 8\|2 cosh(x) + 8\|2 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 510 +m0093:= a0093-r0093 +--R +--R +--R (414) +--R +------+ +------+4+-+ %pi 2 +--R - \|1 - %i \|1 + %i \|2 cos(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R - 2\|1 - %i \|1 + %i \|2 cos(---)cosh(x)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi 2 +--R - \|1 - %i \|1 + %i \|2 cos(---)cosh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R - \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (2\|2 \|2 sin(---) + 6cosh(x) - 2\|2 \|2 cos(---) - 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (- 4\|2 \|2 cos(---) - 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (2\|2 \|2 cosh(x) + 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (- 2\|2 \|2 cos(---) - 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R +------+ +------+4+-+ %pi 2 +--R \|1 - %i \|1 + %i \|2 cos(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 cos(---)cosh(x)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi 2 +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---)cosh(x) + \|1 - %i \|1 + %i \|2 cos(---) +--R 8 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (- 2\|2 \|2 sin(---) + 6cosh(x) + 2\|2 \|2 cos(---) - 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R - 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (4\|2 \|2 cos(---) - 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (- 2\|2 \|2 cosh(x) - 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (2\|2 \|2 cos(---) - 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R - 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R +------+ +------+ 2 +------+ +------+ +--R \|1 - %i \|1 + %i sinh(x) + 2\|1 - %i \|1 + %i cosh(x)sinh(x) +--R + +--R +------+ +------+ 2 +------+ +------+ +--R \|1 - %i \|1 + %i cosh(x) + \|1 - %i \|1 + %i +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +------+ +------+ 2 +------+ +------+ +--R - 2\|1 - %i \|1 + %i sinh(x) - 4\|1 - %i \|1 + %i cosh(x)sinh(x) +--R + +--R +------+ +------+ 2 +------+ +------+ +--R - 2\|1 - %i \|1 + %i cosh(x) - 2\|1 - %i \|1 + %i +--R * +--R +-+ +--R atanh(\|2 tanh(x)) +--R + +--R +------+ +-+ 2 +------+ +-+ +--R - 2\|1 - %i \|2 sinh(x) - 4\|1 - %i \|2 cosh(x)sinh(x) +--R + +--R +------+ +-+ 2 +------+ +-+ +--R - 2\|1 - %i \|2 cosh(x) - 2\|1 - %i \|2 +--R * +--R +------+ +--R atanh(\|1 + %i tanh(x)) +--R + +--R +------+ +-+ 2 +------+ +-+ +--R - 2\|1 + %i \|2 sinh(x) - 4\|1 + %i \|2 cosh(x)sinh(x) +--R + +--R +------+ +-+ 2 +------+ +-+ +--R - 2\|1 + %i \|2 cosh(x) - 2\|1 + %i \|2 +--R * +--R +------+ +--R atanh(\|1 - %i tanh(x)) +--R + +--R +------+ +------+4+-+ %pi 2 +--R - 2\|1 - %i \|1 + %i \|2 sin(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R - 4\|1 - %i \|1 + %i \|2 cosh(x)sin(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ 2 +------+ +------+4+-+ %pi +--R (- 2\|1 - %i \|1 + %i \|2 cosh(x) - 2\|1 - %i \|1 + %i \|2 )sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) + 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) - 2\|2 cos(---) - \|2 +--R 8 +--R + +--R +------+ +------+4+-+ %pi 2 +--R - 2\|1 - %i \|1 + %i \|2 sin(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R - 4\|1 - %i \|1 + %i \|2 cosh(x)sin(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ 2 +------+ +------+4+-+ %pi +--R (- 2\|1 - %i \|1 + %i \|2 cosh(x) - 2\|1 - %i \|1 + %i \|2 )sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) - 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) - 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) + 2\|2 cos(---) - \|2 +--R 8 +--R + +--R +------+ +------+ +-+ 2 +--R - 2\|1 - %i \|1 + %i \|2 sinh(x) +--R + +--R +------+ +------+ +-+ +--R - 4\|1 - %i \|1 + %i \|2 cosh(x)sinh(x) +--R + +--R +------+ +------+ +-+ 2 +------+ +------+ +-+ +--R - 2\|1 - %i \|1 + %i \|2 cosh(x) - 2\|1 - %i \|1 + %i \|2 +--R * +--R tanh(x) +--R + +--R +------+ +------+ +-+ +--R - 4\|1 - %i \|1 + %i \|2 +--R / +--R +------+ +------+ +-+ 2 +------+ +------+ +-+ +--R 8\|1 - %i \|1 + %i \|2 sinh(x) + 16\|1 - %i \|1 + %i \|2 cosh(x)sinh(x) +--R + +--R +------+ +------+ +-+ 2 +------+ +------+ +-+ +--R 8\|1 - %i \|1 + %i \|2 cosh(x) + 8\|1 - %i \|1 + %i \|2 +--R Type: Expression(Complex(Integer)) +--E 479 + +--S 480 of 510 +--d0093:= D(m0093,x) +--E 480 + +--S 481 of 510 +t0094:= x^2*sinh(a+b*x+c*x^2) +--R +--R +--R 2 2 +--R (415) x sinh(c x + b x + a) +--R Type: Expression(Integer) +--E 481 + +--S 482 of 510 +r0094:= -1/4*b*cosh(a+b*x+c*x^2)/c^2+1/2*x*cosh(a+b*x+c*x^2)/c-_ + 1/16*(b^2+2*c)*exp(1)^(-a+1/4*b^2/c)*%pi^(1/2)*_ + erf(1/2*(b+2*c*x)/c^(1/2))/c^(5/2)+1/16*(b^2-2*c)*_ + exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)/c^(1/2))/c^(5/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 482 + +--S 483 of 510 +a0094:= integrate(t0094,x) +--R +--R +--R x +--R ++ 2 2 +--R (416) | %N sinh(%N c + %N b + a)d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 510 +m0094:= a0094-r0094 +--R +--R +--R x +--R ++ 2 2 +--R (417) | %N sinh(%N c + %N b + a)d%N - r0094 +--R ++ +--R Type: Expression(Integer) +--E 484 + +--S 485 of 510 +d0094:= D(m0094,x) +--R +--R +--R 2 2 +--R (418) x sinh(c x + b x + a) +--R Type: Expression(Integer) +--E 485 + +--S 486 of 510 +t0095:= x*sinh(a+b*x+c*x^2) +--R +--R +--R 2 +--R (419) x sinh(c x + b x + a) +--R Type: Expression(Integer) +--E 486 + +--S 487 of 510 +r0095:= 1/8/c^(3/2)*(4*cosh(a+b*x+c*x^2)*c^(1/2)+_ + b*exp(-1/4*(-b^2+4*a*c)/c)*%pi^(1/2)*erf(1/2*(b+2*c*x)/c^(1/2))+_ + %i*b*exp(1/4*(-b^2+4*a*c)/c)*%pi^(1/2)*erf(1/2*%i*(b+2*c*x)/c^(1/2))) +--R +--R There are 15 exposed and 12 unexposed library operations named / +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op / +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named / +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 487 + +--S 488 of 510 +a0095:= integrate(t0095,x) +--R +--R +--R x +--R ++ 2 +--R (420) | %N sinh(%N c + %N b + a)d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 510 +m0095:= a0095-r0095 +--R +--R +--R x +--R ++ 2 +--R (421) | %N sinh(%N c + %N b + a)d%N - r0095 +--R ++ +--R Type: Expression(Integer) +--E 489 + +--S 490 of 510 +d0095:= D(m0095,x) +--R +--R +--R 2 +--R (422) x sinh(c x + b x + a) +--R Type: Expression(Integer) +--E 490 + +--S 491 of 510 +t0096:= sinh(a+b*x+c*x^2)/x^2-b*cosh(a+b*x+c*x^2)/x +--R +--R +--R 2 2 +--R sinh(c x + b x + a) - b x cosh(c x + b x + a) +--R (423) ----------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 491 + +--S 492 of 510 +r0096:= 1/2*c^(1/2)*exp(1)^(-a+1/4*b^2/c)*%pi^(1/2)*_ + erf(1/2*(b+2*c*x)/c^(1/2))+1/2*c^(1/2)*exp(1)^(a-1/4*b^2/c)*_ + %pi^(1/2)*erfi(1/2*(b+2*c*x)/c^(1/2))-sinh(a+b*x+c*x^2)/x +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 492 + +--S 493 of 510 +a0096:= integrate(t0096,x) +--R +--R +--R x 2 2 +--R ++ sinh(%N c + %N b + a) - %N b cosh(%N c + %N b + a) +--R (424) | -------------------------------------------------- d%N +--R ++ 2 +--R %N +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 510 +m0096:= a0096-r0096 +--R +--R +--R x 2 2 +--R ++ sinh(%N c + %N b + a) - %N b cosh(%N c + %N b + a) +--R (425) | -------------------------------------------------- d%N - r0096 +--R ++ 2 +--R %N +--R Type: Expression(Integer) +--E 494 + +--S 495 of 510 +d0096:= D(m0096,x) +--R +--R +--R 2 2 +--R sinh(c x + b x + a) - b x cosh(c x + b x + a) +--R (426) ----------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 495 + +--S 496 of 510 +t0097:= x^2*sinh(a+b*x-c*x^2) +--R +--R +--R 2 2 +--R (427) - x sinh(c x - b x - a) +--R Type: Expression(Integer) +--E 496 + +--S 497 of 510 +r0097:= -1/4*b*cosh(a+b*x-c*x^2)/c^2-1/2*x*cosh(a+b*x-c*x^2)/c-_ + 1/16*(b^2+2*c)*exp(1)^(a+1/4*b^2/c)*%pi^(1/2)*_ + erf(1/2*(b-2*c*x)/c^(1/2))/c^(5/2)+1/16*(b^2-2*c)*_ + exp(1)^(-a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b-2*c*x)/c^(1/2))/c^(5/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 497 + +--S 498 of 510 +a0097:= integrate(t0097,x) +--R +--R +--R x +--R ++ 2 2 +--R (428) | - %N sinh(%N c - %N b - a)d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 510 +m0097:= a0097-r0097 +--R +--R +--R x +--R ++ 2 2 +--R (429) | - %N sinh(%N c - %N b - a)d%N - r0097 +--R ++ +--R Type: Expression(Integer) +--E 499 + +--S 500 of 510 +d0097:= D(m0097,x) +--R +--R +--R 2 2 +--R (430) - x sinh(c x - b x - a) +--R Type: Expression(Integer) +--E 500 + +--S 501 of 510 +t0098:= x*sinh(a+b*x-c*x^2) +--R +--R +--R 2 +--R (431) - x sinh(c x - b x - a) +--R Type: Expression(Integer) +--E 501 + +--S 502 of 510 +r0098:= -1/8/c^(3/2)*(4*cosh(a+b*x-c*x^2)*c^(1/2)+_ + b*exp(1/4*(b^2+4*a*c)/c)*%pi^(1/2)*_ + erf(1/2*(b-2*c*x)/c^(1/2))+%i*b*_ + exp(-1/4*(b^2+4*a*c)/c)*%pi^(1/2)*_ + erf(1/2*%i*(b-2*c*x)/c^(1/2))) +--R +--R There are 15 exposed and 12 unexposed library operations named / +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op / +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named / +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 502 + +--S 503 of 510 +a0098:= integrate(t0098,x) +--R +--R +--R x +--R ++ 2 +--R (432) | - %N sinh(%N c - %N b - a)d%N +--R ++ +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 510 +m0098:= a0098-r0098 +--R +--R +--R x +--R ++ 2 +--R (433) | - %N sinh(%N c - %N b - a)d%N - r0098 +--R ++ +--R Type: Expression(Integer) +--E 504 + +--S 505 of 510 +d0098:= D(m0098,x) +--R +--R +--R 2 +--R (434) - x sinh(c x - b x - a) +--R Type: Expression(Integer) +--E 505 + +--S 506 of 510 +t0099:= sinh(a+b*x-c*x^2)/x^2-b*cosh(a+b*x-c*x^2)/x +--R +--R +--R 2 2 +--R - sinh(c x - b x - a) - b x cosh(c x - b x - a) +--R (435) ------------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 506 + +--S 507 of 510 +r0099:= 1/2*c^(1/2)*exp(1)^(a+1/4*b^2/c)*%pi^(1/2)*_ + erf(1/2*(b-2*c*x)/c^(1/2))+1/2*c^(1/2)*_ + exp(1)^(-a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b-2*c*x)/c^(1/2))-sinh(a+b*x-c*x^2)/x +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 507 + +--S 508 of 510 +a0099:= integrate(t0099,x) +--R +--R +--R x 2 2 +--R ++ - sinh(%N c - %N b - a) - %N b cosh(%N c - %N b - a) +--R (436) | ---------------------------------------------------- d%N +--R ++ 2 +--R %N +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 510 +m0099:= a0099-r0099 +--R +--R +--R (437) +--R x 2 2 +--R ++ - sinh(%N c - %N b - a) - %N b cosh(%N c - %N b - a) +--R | ---------------------------------------------------- d%N - r0099 +--R ++ 2 +--R %N +--R Type: Expression(Integer) +--E 509 + +--S 510 of 510 +d0099:= D(m0099,x) +--R +--R +--R 2 2 +--R - sinh(c x - b x - a) - b x cosh(c x - b x - a) +--R (438) ------------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 510 + +)spool + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper000-099.input.pdf b/src/axiom-website/CATS/richhyper000-099.input.pdf new file mode 100644 index 0000000..874b4b4 Binary files /dev/null and b/src/axiom-website/CATS/richhyper000-099.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper100-199,input.pamphlet b/src/axiom-website/CATS/richhyper100-199,input.pamphlet new file mode 100644 index 0000000..060b166 --- /dev/null +++ b/src/axiom-website/CATS/richhyper100-199,input.pamphlet @@ -0,0 +1,7880 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richinvhyper100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richinvhyper100-199.output +)spool richinvhyper100-199.output +)set message auto off +)clear all + +--S 1 OF 506 +t0100:= atanh(x^(1/2)) +--R +--R +--R +-+ +--R (1) atanh(\|x ) +--R Type: Expression Integer +--E 1 + +--S 2 OF 506 +r0100:= x^(1/2)-atanh(x^(1/2))+x*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (2) (x - 1)atanh(\|x ) + \|x +--R Type: Expression Integer +--E 2 + +--S 3 OF 506 +a0100:= integrate(t0100,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R (x - 1)log(----------) + 2\|x +--R +-+ +--R \|x - 1 +--R (3) ------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 OF 506 +m0100:= a0100-r0100 +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (4) ---------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 4 + +--S 5 OF 506 +d0100:= D(m0100,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (5) ------------------------------ +--R 2 +--R Type: Expression Integer +--E 5 + +--S 6 OF 506 +t0101:= x*atanh(x^(1/2)) +--R +--R +--R +-+ +--R (6) x atanh(\|x ) +--R Type: Expression Integer +--E 6 + +--S 7 OF 506 +r0101:= 1/2*x^(1/2)+1/6*x^(3/2)-1/2*atanh(x^(1/2))+1/2*x^2*atanh(x^(1/2)) +--R +--R +--R 2 +-+ +-+ +--R (3x - 3)atanh(\|x ) + (x + 3)\|x +--R (7) ---------------------------------- +--R 6 +--R Type: Expression Integer +--E 7 + +--S 8 OF 506 +a0101:= integrate(t0101,x) +--R +--R +--R +-+ +--R 2 - \|x - 1 +-+ +--R (3x - 3)log(----------) + (2x + 6)\|x +--R +-+ +--R \|x - 1 +--R (8) --------------------------------------- +--R 12 +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 OF 506 +m0101:= a0101-r0101 +--R +--R +--R +-+ +--R 2 - \|x - 1 2 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (9) ------------------------------------------------ +--R 4 +--R Type: Expression Integer +--E 9 + +--S 10 OF 506 +d0101:= D(m0101,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R x log(----------) - 2x atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (10) ---------------------------------- +--R 2 +--R Type: Expression Integer +--E 10 + +--S 11 OF 506 +t0102:= atanh(x^(1/2))/x^2 +--R +--R +--R +-+ +--R atanh(\|x ) +--R (11) ----------- +--R 2 +--R x +--R Type: Expression Integer +--E 11 + +--S 12 OF 506 +r0102:= -1/x^(1/2)+atanh(x^(1/2))-atanh(x^(1/2))/x +--R +--R +--R +-+ +-+ +--R (x - 1)\|x atanh(\|x ) - x +--R (12) -------------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 12 + +--S 13 OF 506 +a0102:= integrate(t0102,x) +--R +--R +--R +-+ +--R +-+ - \|x - 1 +--R (x - 1)\|x log(----------) - 2x +--R +-+ +--R \|x - 1 +--R (13) ------------------------------- +--R +-+ +--R 2x\|x +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 OF 506 +m0102:= a0102-r0102 +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (14) ---------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 14 + +--S 15 OF 506 +d0102:= D(m0102,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (15) ------------------------------ +--R 2 +--R 2x +--R Type: Expression Integer +--E 15 + +--S 16 OF 506 +t0103:= atanh(x^(1/2))/x^3 +--R +--R +--R +-+ +--R atanh(\|x ) +--R (16) ----------- +--R 3 +--R x +--R Type: Expression Integer +--E 16 + +--S 17 OF 506 +r0103:= -1/6/x^(3/2)-1/2/x^(1/2)+1/2*atanh(x^(1/2))-1/2*atanh(x^(1/2))/x^2 +--R +--R +--R 2 +-+ +-+ 2 +--R (3x - 3)\|x atanh(\|x ) - 3x - x +--R (17) ---------------------------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression Integer +--E 17 + +--S 18 OF 506 +a0103:= integrate(t0103,x) +--R +--R +--R +-+ +--R 2 +-+ - \|x - 1 2 +--R (3x - 3)\|x log(----------) - 6x - 2x +--R +-+ +--R \|x - 1 +--R (18) --------------------------------------- +--R 2 +-+ +--R 12x \|x +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 OF 506 +m0103:= a0103-r0103 +--R +--R +--R +-+ +--R 2 - \|x - 1 2 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (19) ------------------------------------------------ +--R 2 +--R 4x +--R Type: Expression Integer +--E 19 + +--S 20 OF 506 +d0103:= D(m0103,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (20) ------------------------------ +--R 3 +--R 2x +--R Type: Expression Integer +--E 20 + +--S 21 OF 506 +t0104:= x^(1/2)*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (21) \|x atanh(\|x ) +--R Type: Expression Integer +--E 21 + +--S 22 OF 506 +r0104:= 1/3*x+2/3*x^(3/2)*atanh(x^(1/2))+1/3*log(1-x) +--R +--R +--R +-+ +-+ +--R 2x\|x atanh(\|x ) + log(- x + 1) + x +--R (22) ------------------------------------ +--R 3 +--R Type: Expression Integer +--E 22 + +--S 23 OF 506 +a0104:= integrate(t0104,x) +--R +--R +--R +-+ +--R +-+ - \|x - 1 +--R x\|x log(----------) + log(x - 1) + x +--R +-+ +--R \|x - 1 +--R (23) ------------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 OF 506 +m0104:= a0104-r0104 +--R +--R +--R +-+ +--R +-+ - \|x - 1 +-+ +-+ +--R x\|x log(----------) - 2x\|x atanh(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R (24) -------------------------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 24 + +--S 25 OF 506 +d0104:= D(m0104,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R x log(----------) - 2x atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (25) ---------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression Integer +--E 25 + +--S 26 OF 506 +t0105:= x^(3/2)*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (26) x\|x atanh(\|x ) +--R Type: Expression Integer +--E 26 + +--S 27 OF 506 +r0105:= 1/5*x+1/10*x^2+2/5*x^(5/2)*atanh(x^(1/2))+1/5*log(1-x) +--R +--R +--R 2 +-+ +-+ 2 +--R 4x \|x atanh(\|x ) + 2log(- x + 1) + x + 2x +--R (27) -------------------------------------------- +--R 10 +--R Type: Expression Integer +--E 27 + +--S 28 OF 506 +a0105:= integrate(t0105,x) +--R +--R +--R +-+ +--R 2 +-+ - \|x - 1 2 +--R 2x \|x log(----------) + 2log(x - 1) + x + 2x +--R +-+ +--R \|x - 1 +--R (28) ---------------------------------------------- +--R 10 +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 OF 506 +m0105:= a0105-r0105 +--R +--R +--R (29) +--R +-+ +--R 2 +-+ - \|x - 1 2 +-+ +-+ +--R x \|x log(----------) - 2x \|x atanh(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R ---------------------------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 29 + +--S 30 OF 506 +d0105:= D(m0105,x) +--R +--R +--R +-+ +--R 2 - \|x - 1 2 +-+ +--R x log(----------) - 2x atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (30) ---------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression Integer +--E 30 + +--S 31 OF 506 +t0106:= atanh(x^(1/2))/x^(3/2) +--R +--R +--R +-+ +--R atanh(\|x ) +--R (31) ----------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 31 + +--S 32 OF 506 +r0106:= 2*atanh(-1+2*x)-2*atanh(x^(1/2))/x^(1/2) +--R +--R +--R +-+ +-+ +--R - 2atanh(\|x ) + 2atanh(2x - 1)\|x +--R (32) ----------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 32 + +--S 33 OF 506 +a0106:= integrate(t0106,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R - log(----------) + (log(x) - log(x - 1))\|x +--R +-+ +--R \|x - 1 +--R (33) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 OF 506 +m0106:= a0106-r0106 +--R +--R +--R (34) +--R +-+ +--R - \|x - 1 +-+ +-+ +--R - log(----------) + 2atanh(\|x ) + (log(x) - log(x - 1) - 2atanh(2x - 1))\|x +--R +-+ +--R \|x - 1 +--R ----------------------------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 34 + +--S 35 OF 506 +d0106:= D(m0106,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (35) ------------------------------ +--R +-+ +--R 2x\|x +--R Type: Expression Integer +--E 35 + +--S 36 OF 506 +t0107:= x*acoth(a*x) +--R +--R +--R (36) x acoth(a x) +--R Type: Expression Integer +--E 36 + +--S 37 OF 506 +r0107:= 1/2*(a*x+x^2*acoth(a*x)*a^2-atanh(a*x))/a^2 +--R +--R +--R 2 2 +--R - atanh(a x) + a x acoth(a x) + a x +--R (37) ----------------------------------- +--R 2 +--R 2a +--R Type: Expression Integer +--E 37 + +--S 38 OF 506 +a0107:= integrate(t0107,x) +--R +--R +--R 2 2 a x + 1 +--R (a x - 1)log(-------) + 2a x +--R a x - 1 +--R (38) ----------------------------- +--R 2 +--R 4a +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 OF 506 +m0107:= a0107-r0107 +--R +--R +--R 2 2 a x + 1 2 2 +--R (a x - 1)log(-------) + 2atanh(a x) - 2a x acoth(a x) +--R a x - 1 +--R (39) ------------------------------------------------------ +--R 2 +--R 4a +--R Type: Expression Integer +--E 39 + +--S 40 OF 506 +d0107:= D(m0107,x) +--R +--R +--R a x + 1 +--R x log(-------) - 2x acoth(a x) +--R a x - 1 +--R (40) ------------------------------ +--R 2 +--R Type: Expression Integer +--E 40 + +--S 41 OF 506 +t0108:= acoth(a*x)/x +--R +--R +--R acoth(a x) +--R (41) ---------- +--R x +--R Type: Expression Integer +--E 41 + +--S 42 OF 506 +r0108:= 1/2*polylog(2,-1/a/x)-1/2*polylog(2,1/a/x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 OF 506 +a0108:= integrate(t0108,x) +--R +--R +--R x +--R ++ acoth(%Q a) +--R (42) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 OF 506 +--m0108:= a0108-r0108 +--E 44 + +--S 45 OF 506 +--d0108:= D(m0108,x) +--E 45 + +--S 46 OF 506 +t0109:= acoth(a*x)/x^3 +--R +--R +--R acoth(a x) +--R (43) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 46 + +--S 47 OF 506 +r0109:= -1/2*(a*x+acoth(a*x)-a^2*atanh(a*x)*x^2)/x^2 +--R +--R +--R 2 2 +--R a x atanh(a x) - acoth(a x) - a x +--R (44) --------------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 47 + +--S 48 OF 506 +a0109:= integrate(t0109,x) +--R +--R +--R 2 2 a x + 1 +--R (a x - 1)log(-------) - 2a x +--R a x - 1 +--R (45) ----------------------------- +--R 2 +--R 4x +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 OF 506 +m0109:= a0109-r0109 +--R +--R +--R 2 2 a x + 1 2 2 +--R (a x - 1)log(-------) - 2a x atanh(a x) + 2acoth(a x) +--R a x - 1 +--R (46) ------------------------------------------------------ +--R 2 +--R 4x +--R Type: Expression Integer +--E 49 + +--S 50 OF 506 +d0109:= D(m0109,x) +--R +--R +--R a x + 1 +--R log(-------) - 2acoth(a x) +--R a x - 1 +--R (47) -------------------------- +--R 3 +--R 2x +--R Type: Expression Integer +--E 50 + +--S 51 OF 506 +t0110:= (a+b*x)*acoth(a+b*x) +--R +--R +--R (48) (b x + a)acoth(b x + a) +--R Type: Expression Integer +--E 51 + +--S 52 OF 506 +r0110:= 1/2/b*(a+b*x)+1/2*(a+b*x)^2*acoth(a+b*x)/b-1/2*atanh(a+b*x)/b +--R +--R +--R 2 2 2 +--R - atanh(b x + a) + (b x + 2a b x + a )acoth(b x + a) + b x + a +--R (49) --------------------------------------------------------------- +--R 2b +--R Type: Expression Integer +--E 52 + +--S 53 OF 506 +a0110:= integrate(t0110,x) +--R +--R +--R 2 2 2 b x + a + 1 +--R (b x + 2a b x + a - 1)log(-----------) + 2b x +--R b x + a - 1 +--R (50) ----------------------------------------------- +--R 4b +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 OF 506 +m0110:= a0110-r0110 +--R +--R +--R (51) +--R 2 2 2 b x + a + 1 +--R (b x + 2a b x + a - 1)log(-----------) + 2atanh(b x + a) +--R b x + a - 1 +--R + +--R 2 2 2 +--R (- 2b x - 4a b x - 2a )acoth(b x + a) - 2a +--R / +--R 4b +--R Type: Expression Integer +--E 54 + +--S 55 OF 506 +d0110:= D(m0110,x) +--R +--R +--R b x + a + 1 +--R (b x + a)log(-----------) + (- 2b x - 2a)acoth(b x + a) +--R b x + a - 1 +--R (52) ------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 55 + +--S 56 OF 506 +t0111:= (a+b*x)^2*acoth(a+b*x) +--R +--R +--R 2 2 2 +--R (53) (b x + 2a b x + a )acoth(b x + a) +--R Type: Expression Integer +--E 56 + +--S 57 OF 506 +r0111:= 1/6*(a+b*x)^2/b+1/3*(a+b*x)^3*acoth(a+b*x)/b+1/6*log(1-(a+b*x)^2)/b +--R +--R +--R (54) +--R 2 2 2 +--R log(- b x - 2a b x - a + 1) +--R + +--R 3 3 2 2 2 3 2 2 2 +--R (2b x + 6a b x + 6a b x + 2a )acoth(b x + a) + b x + 2a b x + a +--R / +--R 6b +--R Type: Expression Integer +--E 57 + +--S 58 OF 506 +a0111:= integrate(t0111,x) +--R +--R +--R (55) +--R 3 3 +--R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) +--R + +--R 3 3 2 2 2 b x + a + 1 2 2 +--R (b x + 3a b x + 3a b x)log(-----------) + b x + 2a b x +--R b x + a - 1 +--R / +--R 6b +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 OF 506 +m0111:= a0111-r0111 +--R +--R +--R (56) +--R 3 3 +--R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) +--R + +--R 3 3 2 2 2 b x + a + 1 2 2 2 +--R (b x + 3a b x + 3a b x)log(-----------) - log(- b x - 2a b x - a + 1) +--R b x + a - 1 +--R + +--R 3 3 2 2 2 3 2 +--R (- 2b x - 6a b x - 6a b x - 2a )acoth(b x + a) - a +--R / +--R 6b +--R Type: Expression Integer +--E 59 + +--S 60 OF 506 +d0111:= D(m0111,x) +--R +--R +--R (57) +--R 2 2 2 b x + a + 1 2 2 2 +--R (b x + 2a b x + a )log(-----------) + (- 2b x - 4a b x - 2a )acoth(b x + a) +--R b x + a - 1 +--R ----------------------------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 60 + +--S 61 OF 506 +t0112:= acoth(1+x)/(2+2*x) +--R +--R +--R acoth(x + 1) +--R (58) ------------ +--R 2x + 2 +--R Type: Expression Integer +--E 61 + +--S 62 OF 506 +r0112:= 1/4*polylog(2,-1/(1+x))-1/4*polylog(2,1/(1+x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 OF 506 +a0112:= integrate(t0112,x) +--R +--R +--R x +--R ++ acoth(%Q + 1) +--R (59) | ------------- d%Q +--R ++ 2%Q + 2 +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 OF 506 +--m0112:= a0112-r0112 +--E 64 + +--S 65 OF 506 +--d0112:= D(m0112,x) +--E 65 + +--S 66 OF 506 +t0113:= acoth(a+b*x)/(a+b*x) +--R +--R +--R acoth(b x + a) +--R (60) -------------- +--R b x + a +--R Type: Expression Integer +--E 66 + +--S 67 OF 506 +r0113:= 1/2*(polylog(2,-1/(a+b*x))-polylog(2,1/(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 OF 506 +a0113:= integrate(t0113,x) +--R +--R +--R x +--R ++ acoth(%Q b + a) +--R (61) | --------------- d%Q +--R ++ %Q b + a +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 OF 506 +--m0113:= a0113-r0113 +--E 69 + +--S 70 OF 506 +--d0113:= D(m0113,x) +--E 70 + +--S 71 OF 506 +t0114:= 1/(1-x^2)/acoth(x) +--R +--R +--R 1 +--R (62) - ---------------- +--R 2 +--R (x - 1)acoth(x) +--R Type: Expression Integer +--E 71 + +--S 72 OF 506 +r0114:= log(acoth(x)) +--R +--R +--R (63) log(acoth(x)) +--R Type: Expression Integer +--E 72 + +--S 73 OF 506 +a0114:= integrate(t0114,x) +--R +--R +--R x + 1 +--R (64) log(log(-----)) +--R x - 1 +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 OF 506 +m0114:= a0114-r0114 +--R +--R +--R x + 1 +--R (65) log(log(-----)) - log(acoth(x)) +--R x - 1 +--R Type: Expression Integer +--E 74 + +--S 75 OF 506 +d0114:= D(m0114,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (66) -------------------------- +--R 2 x + 1 +--R (x - 1)acoth(x)log(-----) +--R x - 1 +--R Type: Expression Integer +--E 75 + +--S 76 OF 506 +t0115:= acoth(x)^n/(1-x^2) +--R +--R +--R n +--R acoth(x) +--R (67) - --------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 76 + +--S 77 OF 506 +r0115:= acoth(x)^(1+n)/(1+n) +--R +--R +--R n + 1 +--R acoth(x) +--R (68) ------------- +--R n + 1 +--R Type: Expression Integer +--E 77 + +--S 78 OF 506 +a0115:= integrate(t0115,x) +--R +--R +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x + 1 x - 1 x + 1 x - 1 +--R log(-----)sinh(n log(----------)) + log(-----)cosh(n log(----------)) +--R x - 1 2 x - 1 2 +--R (69) --------------------------------------------------------------------- +--R 2n + 2 +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 OF 506 +m0115:= a0115-r0115 +--R +--R +--R (70) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x + 1 x - 1 x + 1 x - 1 +--R log(-----)sinh(n log(----------)) + log(-----)cosh(n log(----------)) +--R x - 1 2 x - 1 2 +--R + +--R n + 1 +--R - 2acoth(x) +--R / +--R 2n + 2 +--R Type: Expression Integer +--E 79 + +--S 80 OF 506 +d0115:= D(m0115,x) +--R +--R +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 n +--R - sinh(n log(----------)) - cosh(n log(----------)) + acoth(x) +--R 2 2 +--R (71) --------------------------------------------------------------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 80 + +--S 81 OF 506 +t0116:= acoth(x)/(1-x^2)^2 +--R +--R +--R acoth(x) +--R (72) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 81 + +--S 82 OF 506 +r0116:= 1/(-4+4*x^2)-x*acoth(x)/(-2+2*x^2)+1/4*acoth(x)^2 +--R +--R +--R 2 2 +--R (x - 1)acoth(x) - 2x acoth(x) + 1 +--R (73) ----------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 82 + +--S 83 OF 506 +a0116:= integrate(t0116,x) +--R +--R +--R 2 x + 1 2 x + 1 +--R (x - 1)log(-----) - 4x log(-----) + 4 +--R x - 1 x - 1 +--R (74) --------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 OF 506 +m0116:= a0116-r0116 +--R +--R +--R (75) +--R 2 x + 1 2 x + 1 2 2 +--R (x - 1)log(-----) - 4x log(-----) + (- 4x + 4)acoth(x) + 8x acoth(x) +--R x - 1 x - 1 +--R ------------------------------------------------------------------------ +--R 2 +--R 16x - 16 +--R Type: Expression Integer +--E 84 + +--S 85 OF 506 +d0116:= D(m0116,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (76) ---------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression Integer +--E 85 + +--S 86 OF 506 +t0117:= acoth(x)^2/(1-x^2)^2 +--R +--R +--R 2 +--R acoth(x) +--R (77) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 86 + +--S 87 OF 506 +r0117:= 1/12*(-3*x+3*acoth(x)+3*x^2*acoth(x)-6*x*acoth(x)^2-2*acoth(x)^3+_ + 2*acoth(x)^3*x^2)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (2x - 2)acoth(x) - 6x acoth(x) + (3x + 3)acoth(x) - 3x +--R (78) ---------------------------------------------------------- +--R 2 +--R 12x - 12 +--R Type: Expression Integer +--E 87 + +--S 88 OF 506 +a0117:= integrate(t0117,x) +--R +--R +--R 2 x + 1 3 x + 1 2 2 x + 1 +--R (x - 1)log(-----) - 6x log(-----) + (6x + 6)log(-----) - 12x +--R x - 1 x - 1 x - 1 +--R (79) ---------------------------------------------------------------- +--R 2 +--R 48x - 48 +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 OF 506 +m0117:= a0117-r0117 +--R +--R +--R (80) +--R 2 x + 1 3 x + 1 2 2 x + 1 +--R (x - 1)log(-----) - 6x log(-----) + (6x + 6)log(-----) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (- 8x + 8)acoth(x) + 24x acoth(x) + (- 12x - 12)acoth(x) +--R / +--R 2 +--R 48x - 48 +--R Type: Expression Integer +--E 89 + +--S 90 OF 506 +d0117:= D(m0117,x) +--R +--R +--R x + 1 2 2 +--R log(-----) - 4acoth(x) +--R x - 1 +--R (81) ------------------------ +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression Integer +--E 90 + +--S 91 OF 506 +t0118:= 1/(a-a*x^2)/(b-2*b*acoth(x)) +--R +--R +--R 1 +--R (82) --------------------------------------- +--R 2 2 +--R (2a b x - 2a b)acoth(x) - a b x + a b +--R Type: Expression Integer +--E 91 + +--S 92 OF 506 +r0118:= -1/2*log(1-2*acoth(x))/a/b +--R +--R +--R log(- 2acoth(x) + 1) +--R (83) - -------------------- +--R 2a b +--R Type: Expression Integer +--E 92 + +--S 93 OF 506 +a0118:= integrate(t0118,x) +--R +--R +--R x + 1 +--R log(log(-----) - 1) +--R x - 1 +--R (84) - ------------------- +--R 2a b +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 OF 506 +m0118:= a0118-r0118 +--R +--R +--R x + 1 +--R - log(log(-----) - 1) + log(- 2acoth(x) + 1) +--R x - 1 +--R (85) -------------------------------------------- +--R 2a b +--R Type: Expression Integer +--E 94 + +--S 95 OF 506 +d0118:= D(m0118,x) +--R +--R +--R (86) +--R x + 1 +--R - log(-----) + 2acoth(x) +--R x - 1 +--R / +--R 2 2 x + 1 +--R ((2a b x - 2a b)acoth(x) - a b x + a b)log(-----) +--R x - 1 +--R + +--R 2 2 +--R (- 2a b x + 2a b)acoth(x) + a b x - a b +--R Type: Expression Integer +--E 95 + +--S 96 OF 506 +t0119:= x*acoth(x)/(1-x^2) +--R +--R +--R x acoth(x) +--R (87) - ---------- +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 96 + +--S 97 OF 506 +r0119:= -1/2*acoth(x)^2+acoth(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 OF 506 +a0119:= integrate(t0119,x) +--R +--R +--R x +--R ++ %Q acoth(%Q) +--R (88) | - ------------ d%Q +--R ++ 2 +--R %Q - 1 +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 OF 506 +--m0119:= a0119-r0119 +--E 99 + +--S 100 OF 506 +--d0119:= D(m0119,x) +--E 100 + +--S 101 OF 506 +t0120:= x*acoth(x)/(1-x^2)^2 +--R +--R +--R x acoth(x) +--R (89) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 101 + +--S 102 OF 506 +r0120:= -1/4*(-x+acoth(x)+x^2*acoth(x))/(-1+x^2) +--R +--R +--R 2 +--R (- x - 1)acoth(x) + x +--R (90) ---------------------- +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 102 + +--S 103 OF 506 +a0120:= integrate(t0120,x) +--R +--R +--R 2 x + 1 +--R (- x - 1)log(-----) + 2x +--R x - 1 +--R (91) ------------------------- +--R 2 +--R 8x - 8 +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 OF 506 +m0120:= a0120-r0120 +--R +--R +--R 2 x + 1 2 +--R (- x - 1)log(-----) + (2x + 2)acoth(x) +--R x - 1 +--R (92) ---------------------------------------- +--R 2 +--R 8x - 8 +--R Type: Expression Integer +--E 104 + +--S 105 OF 506 +d0120:= D(m0120,x) +--R +--R +--R x + 1 +--R x log(-----) - 2x acoth(x) +--R x - 1 +--R (93) -------------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression Integer +--E 105 + +--S 106 OF 506 +t0121:= x*acoth(x)/(1-x^2)^3 +--R +--R +--R x acoth(x) +--R (94) - ------------------ +--R 6 4 2 +--R x - 3x + 3x - 1 +--R Type: Expression Integer +--E 106 + +--S 107 OF 506 +r0121:= -1/32*(5*x-3*x^3-5*acoth(x)+3*acoth(x)*x^4-6*x^2*acoth(x))/(-1+x^2)^2 +--R +--R +--R 4 2 3 +--R (- 3x + 6x + 5)acoth(x) + 3x - 5x +--R (95) ------------------------------------ +--R 4 2 +--R 32x - 64x + 32 +--R Type: Expression Integer +--E 107 + +--S 108 OF 506 +a0121:= integrate(t0121,x) +--R +--R +--R 4 2 x + 1 3 +--R (- 3x + 6x + 5)log(-----) + 6x - 10x +--R x - 1 +--R (96) --------------------------------------- +--R 4 2 +--R 64x - 128x + 64 +--R Type: Union(Expression Integer,...) +--E 108 + +--S 109 OF 506 +m0121:= a0121-r0121 +--R +--R +--R 4 2 x + 1 4 2 +--R (- 3x + 6x + 5)log(-----) + (6x - 12x - 10)acoth(x) +--R x - 1 +--R (97) ------------------------------------------------------- +--R 4 2 +--R 64x - 128x + 64 +--R Type: Expression Integer +--E 109 + +--S 110 OF 506 +d0121:= D(m0121,x) +--R +--R +--R x + 1 +--R - x log(-----) + 2x acoth(x) +--R x - 1 +--R (98) ---------------------------- +--R 6 4 2 +--R 2x - 6x + 6x - 2 +--R Type: Expression Integer +--E 110 + +--S 111 OF 506 +t0122:= acoth(x)/(a+b*x^2)^(3/2) +--R +--R +--R acoth(x) +--R (99) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression Integer +--E 111 + +--S 112 OF 506 +r0122:= x*acoth(x)/a/(a+b*x^2)^(1/2)-_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a/(a+b)^(1/2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-----+ +--R - \|b x + a atanh(-----------) + x acoth(x)\|b + a +--R +-----+ +--R \|b + a +--R (100) ---------------------------------------------------- +--R +--------+ +--R +-----+ | 2 +--R a\|b + a \|b x + a +--R Type: Expression Integer +--E 112 + +--S 113 OF 506 +a0122:= integrate(t0122,x) +--R +--R +--R (101) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R +--------+ +--R x + 1 +-----+ | 2 x + 1 +-+ +-----+ +--R - x log(-----)\|b + a \|b x + a + x log(-----)\|a \|b + a +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-+ +-----+ | 2 2 2 +-----+ +--R 2a\|a \|b + a \|b x + a + (- 2a b x - 2a )\|b + a +--R , +--R +--R +--------+ +--R +-+ | 2 2 +--R (- 2\|a \|b x + a + 2b x + 2a) +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R +--------+ +--R x + 1 +-------+ | 2 x + 1 +-------+ +-+ +--R - x log(-----)\|- b - a \|b x + a + x log(-----)\|- b - a \|a +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-------+ +-+ | 2 2 2 +-------+ +--R 2a\|- b - a \|a \|b x + a + (- 2a b x - 2a )\|- b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 113 + +--S 114 OF 506 +m0122a:= a0122.1-r0122 +--R +--R +--R (102) +--R +--------+ +--R 2 | 2 2 +-+ +--R ((b x + a)\|b x + a + (- b x - a)\|a ) +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((2b x + 2a)\|b x + a + (- 2b x - 2a)\|a )atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +--------+ +--R x + 1 +-+ +-----+ | 2 +--R (- x log(-----) + 2x acoth(x))\|a \|b + a \|b x + a +--R x - 1 +--R + +--R 3 x + 1 3 +-----+ +--R ((b x + a x)log(-----) + (- 2b x - 2a x)acoth(x))\|b + a +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-----+ | 2 2 2 +-+ +-----+ +--R (2a b x + 2a )\|b + a \|b x + a + (- 2a b x - 2a )\|a \|b + a +--R Type: Expression Integer +--E 114 + +--S 115 OF 506 +d0122a:= D(m0122a,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (103) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 115 + +--S 116 OF 506 +m0122b:= a0122.2-r0122 +--R +--R +--R (104) +--R +--------+ +--R 2 +-------+ | 2 2 +-------+ +-+ +--R ((2b x + 2a)\|- b - a \|b x + a + (- 2b x - 2a)\|- b - a \|a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +--------+ +--R 2 +-----+ | 2 2 +-+ +-----+ +--R ((- 2b x - 2a)\|b + a \|b x + a + (2b x + 2a)\|a \|b + a ) +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R +--------+ +--R x + 1 +-------+ +-+ +-----+ | 2 +--R (- x log(-----) + 2x acoth(x))\|- b - a \|a \|b + a \|b x + a +--R x - 1 +--R + +--R 3 x + 1 3 +-------+ +-----+ +--R ((b x + a x)log(-----) + (- 2b x - 2a x)acoth(x))\|- b - a \|b + a +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ +-----+ | 2 +--R (2a b x + 2a )\|- b - a \|b + a \|b x + a +--R + +--R 2 2 +-------+ +-+ +-----+ +--R (- 2a b x - 2a )\|- b - a \|a \|b + a +--R Type: Expression Integer +--E 116 + +--S 117 OF 506 +d0122b:= D(m0122b,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (105) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression Integer +--E 117 + +--S 118 OF 506 +t0123:= acoth(x)/(a+b*x^2)^(5/2) +--R +--R +--R acoth(x) +--R (106) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression Integer +--E 118 + +--S 119 OF 506 +r0123:= 1/3/a/(a+b)/(a+b*x^2)^(1/2)+_ + 1/3*x*(3*a+2*b*x^2)*acoth(x)/a^2/(a+b*x^2)^(3/2)-_ + 1/3*(3*a+2*b)*atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^2/(a+b)^(3/2) +--R +--R +--R (107) +--R +--------+ +--R +--------+ | 2 +--R 2 2 2 | 2 \|b x + a +--R ((- 2b - 3a b)x - 2a b - 3a )\|b x + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 2 2 +-----+ +--R (((2b + 2a b)x + (3a b + 3a )x)acoth(x) + a b x + a )\|b + a +--R / +--R +--------+ +--R 2 2 3 2 3 4 +-----+ | 2 +--R ((3a b + 3a b)x + 3a b + 3a )\|b + a \|b x + a +--R Type: Expression Integer +--E 119 + +--S 120 OF 506 +a0123:= integrate(t0123,x) +--R +--R +--R (108) +--R [ +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b + 12a b )x + (32a b + 48a b )x + (40a b + 60a b)x +--R + +--R 3 4 +--R 16a b + 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b - 3a b )x + (- 20a b - 30a b )x + (- 50a b - 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b - 72a b)x - 16a b - 24a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b - 2a b )x + (- 19a b - 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b - 40a b)x + (- 24a b - 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b + 8a b )x + (36a b + 36a b )x + (52a b + 52a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b + 24a b )x + (96a b + 96a b )x + (120a b + 120a b)x +--R + +--R 5 6 +--R 48a b + 48a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b - 6a b )x + (- 60a b - 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b - 150a b )x + (- 144a b - 144a b)x - 48a b - 48a +--R * +--R +-----+ +--R \|b + a +--R , +--R +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (4b + 6a b )x + (40a b + 60a b )x + (100a b + 150a b )x +--R + +--R 3 2 4 2 4 5 +--R (96a b + 144a b)x + 32a b + 48a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b - 2a b )x + (- 19a b - 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b - 40a b)x + (- 24a b - 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b + 8a b )x + (36a b + 36a b )x + (52a b + 52a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b + 24a b )x + (96a b + 96a b )x + (120a b + 120a b)x +--R + +--R 5 6 +--R 48a b + 48a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b - a \|a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b - 6a b )x + (- 60a b - 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b - 150a b )x + (- 144a b - 144a b)x - 48a b - 48a +--R * +--R +-------+ +--R \|- b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 120 + +--S 121 OF 506 +m0123a:= a0123.1-r0123 +--R +--R +--R (109) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b + 3a b )x + (18a b + 27a b )x + (32a b + 48a b)x +--R + +--R 3 4 +--R 16a b + 24a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b - 12a b )x + (- 32a b - 48a b )x + (- 40a b - 60a b)x +--R + +--R 3 4 +--R - 16a b - 24a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b - 8a b )x + (- 28a b - 28a b)x + (- 24a b - 24a )x) +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b + 16a b )x + (56a b + 56a b)x + (48a b + 48a )x)acoth(x) +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b + 2a b )x + (19a b + 19a b )x + (40a b + 40a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b - 4a b )x + (- 38a b - 38a b )x + (- 80a b - 80a b)x +--R + +--R 3 4 +--R (- 48a b - 48a )x +--R * +--R acoth(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-----+ +--R \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b + 6a b )x + (54a b + 54a b )x + (96a b + 96a b)x + 48a b +--R + +--R 6 +--R 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b - 24a b )x + (- 96a b - 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b - 120a b)x - 48a b - 48a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression Integer +--E 121 + +--S 122 OF 506 +d0123a:= D(m0123a,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (110) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 122 + +--S 123 OF 506 +m0123b:= a0123.2-r0123 +--R +--R +--R (111) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 4b - 6a b )x + (- 36a b - 54a b )x + (- 64a b - 96a b)x +--R + +--R 3 4 +--R - 32a b - 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (16b + 24a b )x + (64a b + 96a b )x + (80a b + 120a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b - 8a b )x + (- 28a b - 28a b)x + (- 24a b - 24a )x) +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b + 16a b )x + (56a b + 56a b)x + (48a b + 48a )x)acoth(x) +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b - a \|a \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b + 2a b )x + (19a b + 19a b )x + (40a b + 40a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b - 4a b )x + (- 38a b - 38a b )x + (- 80a b - 80a b)x +--R + +--R 3 4 +--R (- 48a b - 48a )x +--R * +--R acoth(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-------+ +-----+ +--R \|- b - a \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b + 6a b )x + (54a b + 54a b )x + (96a b + 96a b)x + 48a b +--R + +--R 6 +--R 48a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b - a \|b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b - 24a b )x + (- 96a b - 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b - 120a b)x - 48a b - 48a +--R * +--R +-------+ +-+ +-----+ +--R \|- b - a \|a \|b + a +--R Type: Expression Integer +--E 123 + +--S 124 OF 506 +d0123b:= D(m0123b,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (112) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 124 + +--S 125 OF 506 +t0124:= acoth(x)/(a+b*x^2)^(7/2) +--R +--R +--R acoth(x) +--R (113) ------------------------------------------ +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression Integer +--E 125 + +--S 126 OF 506 +r0124:= 1/15/a/(a+b)/(a+b*x^2)^(3/2)+_ + 1/15*(7*a+4*b)/a^2/(a+b)^2/(a+b*x^2)^(1/2)+_ + 1/15*x*(8*(a+b*x^2)^2+a*(7*a+4*b*x^2))*acoth(x)/a^3/(a+b*x^2)^(5/2)-_ + 1/15*(15*a^2+20*a*b+8*b^2)*_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^3/(a+b)^(5/2) +--R +--R +--R (114) +--R 4 3 2 2 4 3 2 2 3 2 2 2 +--R (- 8b - 20a b - 15a b )x + (- 16a b - 40a b - 30a b)x - 8a b +--R + +--R 3 4 +--R - 20a b - 15a +--R * +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +--R \|b x + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 3 2 2 5 3 2 2 3 3 +--R (8b + 16a b + 8a b )x + (20a b + 40a b + 20a b)x +--R + +--R 2 2 3 4 +--R (15a b + 30a b + 15a )x +--R * +--R acoth(x) +--R + +--R 3 2 2 4 2 2 3 2 3 4 +--R (4a b + 7a b )x + (9a b + 15a b)x + 5a b + 8a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 5 2 +--R (15a b + 30a b + 15a b )x + (30a b + 60a b + 30a b)x + 15a b +--R + +--R 6 7 +--R 30a b + 15a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R Type: Expression Integer +--E 126 + +--S 127 OF 506 +a0124:= integrate(t0124,x) +--R +--R +--R (115) +--R [ +--R 8 7 2 6 12 +--R (64b + 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b + 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b + 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b + 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b + 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b + 11520a b + 8640a b)x + 1024a b + 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b - 20a b - 15a b )x + (- 280a b - 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b - 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b - 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b - 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b - 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b - 12800a b - 9600a b)x - 1024a b - 2560a b - 1920a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 8 7 2 6 13 +--R (- 8b - 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b - 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b - 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b - 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b - 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b - 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b + 114a b )x + (766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b + 4080a b )x + (4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b + 4608a b )x + (896a b + 1280a b)x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b + 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b + 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b + 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b + 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b + 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b + 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b - 16a b )x + (- 286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b - 2672a b )x + (- 4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b - 8480a b )x + (- 3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b - 1280a b)x +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b + 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b + 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b + 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b + 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b + 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b + 34560a b + 17280a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b - 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b - 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b - 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b - 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b - 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b - 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b - 38400a b - 19200a b)x - 3840a b - 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-----+ +--R \|b + a +--R , +--R +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b +--R + +--R 8 +--R - 3840a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (16b + 40a b + 30a b )x + (560a b + 1400a b + 1050a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (4144a b + 10360a b + 7770a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (13328a b + 33320a b + 24990a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (22528a b + 56320a b + 42240a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (20992a b + 52480a b + 39360a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (10240a b + 25600a b + 19200a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 8 7 2 6 13 +--R (- 8b - 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b - 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b - 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b - 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b - 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b - 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b + 114a b )x + (766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b + 4080a b )x + (4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b + 4608a b )x + (896a b + 1280a b)x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b + 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b + 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b + 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b + 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b + 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b + 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b - 16a b )x + (- 286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b - 2672a b )x + (- 4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b - 8480a b )x + (- 3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b - 1280a b)x +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b + 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b + 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b + 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b + 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b + 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b + 34560a b + 17280a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b - a \|a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b - 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b - 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b - 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b - 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b - 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b - 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b - 38400a b - 19200a b)x - 3840a b - 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-------+ +--R \|- b - a +--R ] +--R Type: Union(List Expression Integer,...) +--E 127 + +--S 128 OF 506 +m0124a:= a0124.1-r0124 +--R +--R +--R (116) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b + 20a b + 15a b )x + (272a b + 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b + 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b + 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b + 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b + 10240a b + 7680a b)x + 1024a b + 2560a b + 1920a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b - 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b - 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b - 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b - 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b - 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b - 11520a b - 8640a b)x - 1024a b - 2560a b - 1920a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b + 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b + 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b + 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b + 20480a b + 15360a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b - 3840a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 7 6 2 5 11 +--R (- 64b - 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b - 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b - 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b - 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b - 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b + 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b + 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b + 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b + 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b + 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b + 7680a b + 3840a )x +--R * +--R acoth(x) +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b + 16a b )x + (340a b + 544a b )x + (2250a b + 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b + 9728a b )x + (8000a b + 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b + 8192a b)x + 1280a b + 2048a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b + 16a b + 8a b )x + (276a b + 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b + 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b + 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b + 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b + 12800a b + 6400a b)x + (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b - 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b - 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b - 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b - 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b - 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b - 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b - 7680a b - 3840a )x +--R * +--R acoth(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b - 128a b )x + (- 1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b - 7296a b )x + (- 9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b - 16640a b )x + (- 5760a b - 9216a b)x - 1280a b +--R + +--R 8 +--R - 2048a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b + 60a b + 30a b )x + (1020a b + 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b + 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b + 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b + 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b + 30720a b + 15360a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b - 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b - 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b - 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b - 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b - 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b - 34560a b - 17280a b)x - 3840a b - 7680a b - 3840a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression Integer +--E 128 + +--S 129 OF 506 +d0124a:= D(m0124a,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (117) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 129 + +--S 130 OF 506 +m0124b:= a0124.2-r0124 +--R +--R +--R (118) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b + 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b + 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b + 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b + 20480a b + 15360a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b - 3840a +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 8 7 2 6 12 +--R (- 16b - 40a b - 30a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 544a b - 1360a b - 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3600a b - 9000a b - 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 9728a b - 24320a b - 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 12800a b - 32000a b - 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 8192a b - 20480a b - 15360a b)x - 2048a b - 5120a b - 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 8 7 2 6 12 +--R (128b + 320a b + 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (1664a b + 4160a b + 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (7296a b + 18240a b + 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (15232a b + 38080a b + 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (16640a b + 41600a b + 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (9216a b + 23040a b + 17280a b)x + 2048a b + 5120a b + 3840a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 7 6 2 5 11 +--R (- 64b - 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b - 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b - 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b - 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b - 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b + 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b + 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b + 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b + 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b + 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b + 7680a b + 3840a )x +--R * +--R acoth(x) +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b + 16a b )x + (340a b + 544a b )x + (2250a b + 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b + 9728a b )x + (8000a b + 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b + 8192a b)x + 1280a b + 2048a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b - a \|a \|b + a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b + 16a b + 8a b )x + (276a b + 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b + 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b + 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b + 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b + 12800a b + 6400a b)x + (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b - 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b - 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b - 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b - 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b - 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b - 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b - 7680a b - 3840a )x +--R * +--R acoth(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b - 128a b )x + (- 1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b - 7296a b )x + (- 9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b - 16640a b )x + (- 5760a b - 9216a b)x - 1280a b +--R + +--R 8 +--R - 2048a +--R * +--R +-------+ +-----+ +--R \|- b - a \|b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b + 60a b + 30a b )x + (1020a b + 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b + 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b + 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b + 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b + 30720a b + 15360a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b - a \|b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b - 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b - 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b - 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b - 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b - 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b - 34560a b - 17280a b)x - 3840a b - 7680a b - 3840a +--R * +--R +-------+ +-+ +-----+ +--R \|- b - a \|a \|b + a +--R Type: Expression Integer +--E 130 + +--S 131 OF 506 +d0124b:= D(m0124b,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (119) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression Integer +--E 131 + +--S 132 OF 506 +t0125:= acoth(x)*(a-a*x^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (120) acoth(x)\|- a x + a +--R Type: Expression Integer +--E 132 + +--S 133 OF 506 +r0125:= 1/2/(1-1/x^2)^(1/2)/x*(a*(1-x^2))^(1/2)*((1-1/x^2)^(1/2)*x+_ + (1-1/x^2)^(1/2)*x^2*acoth(x)-2*acoth(x)*atanh(exp(1)^acoth(x))-_ + polylog(2,-exp(1)^acoth(x))+polylog(2,exp(1)^acoth(x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 133 + +--S 134 OF 506 +a0125:= integrate(t0125,x) +--R +--R +--R x +------------+ +--R ++ | 2 +--R (121) | acoth(%Q)\|(- %Q + 1)a d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 134 + +--S 135 OF 506 +--m0125:= a0125-r0125 +--E 135 + +--S 136 OF 506 +--d0125:= D(m0125,x) +--E 136 + +--S 137 OF 506 +t0126:= acoth(x)/(a-a*x^2)^(1/2) +--R +--R +--R acoth(x) +--R (122) ------------- +--R +----------+ +--R | 2 +--R \|- a x + a +--R Type: Expression Integer +--E 137 + +--S 138 OF 506 +r0126:= (1-1/x^2)^(1/2)*x*(2*acoth(x)*atanh(exp(1)^acoth(x))+_ + polylog(2,-exp(1)^acoth(x))-_ + polylog(2,exp(1)^acoth(x)))/(a*(1-x^2))^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 138 + +--S 139 OF 506 +a0126:= integrate(t0126,x) +--R +--R +--R x +--R ++ acoth(%Q) +--R (123) | --------------- d%Q +--R ++ +------------+ +--R | 2 +--R \|(- %Q + 1)a +--R Type: Union(Expression Integer,...) +--E 139 + +--S 140 OF 506 +--m0126:= a0126-r0126 +--E 140 + +--S 141 OF 506 +--d0126:= D(m0126,x) +--E 141 + +--S 142 OF 506 +t0127:= acoth(x)/(a-a*x^2)^(3/2) +--R +--R +--R acoth(x) +--R (124) - ----------------------- +--R +----------+ +--R 2 | 2 +--R (a x - a)\|- a x + a +--R Type: Expression Integer +--E 142 + +--S 143 OF 506 +r0127:= (x*acoth(x)-1)/a/(-a*(-1+x^2))^(1/2) +--R +--R +--R x acoth(x) - 1 +--R (125) -------------- +--R +----------+ +--R | 2 +--R a\|- a x + a +--R Type: Expression Integer +--E 143 + +--S 144 OF 506 +a0127:= integrate(t0127,x) +--R +--R +--R +----------+ +--R x + 1 2 +-+ x + 1 | 2 +--R (x log(-----) - 2x )\|a - x log(-----)\|- a x + a +--R x - 1 x - 1 +--R (126) ---------------------------------------------------- +--R +----------+ +--R | 2 +-+ 2 2 2 +--R 2a\|- a x + a \|a + 2a x - 2a +--R Type: Union(Expression Integer,...) +--E 144 + +--S 145 OF 506 +m0127:= a0127-r0127 +--R +--R +--R (127) +--R +----------+ +--R x + 1 2 | 2 +-+ +--R (- x log(-----) + 2x acoth(x) + 2x - 2)\|- a x + a \|a +--R x - 1 +--R + +--R 3 x + 1 3 2 +--R (- a x + a x)log(-----) + (2a x - 2a x)acoth(x) - 2a x + 2a +--R x - 1 +--R / +--R +----------+ +--R 2 2 2 +-+ 2 2 2 | 2 +--R (2a x - 2a )\|a + (- 2a x + 2a )\|- a x + a +--R Type: Expression Integer +--E 145 + +--S 146 OF 506 +d0127:= D(m0127,x) +--R +--R +--R x + 1 +--R - log(-----) + 2acoth(x) +--R x - 1 +--R (128) ------------------------- +--R +----------+ +--R 2 | 2 +--R (2a x - 2a)\|- a x + a +--R Type: Expression Integer +--E 146 + +--S 147 OF 506 +t0128:= acoth(x)/(a-a*x^2)^(5/2) +--R +--R +--R acoth(x) +--R (129) -------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (a x - 2a x + a )\|- a x + a +--R Type: Expression Integer +--E 147 + +--S 148 OF 506 +r0128:= 1/9*(6*acoth(x)*x^3-6*x^2-_ + 9*x*acoth(x)+7)/a^2/(-1+x^2)/(-a*(-1+x^2))^(1/2) +--R +--R +--R 3 2 +--R (6x - 9x)acoth(x) - 6x + 7 +--R (130) ---------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (9a x - 9a )\|- a x + a +--R Type: Expression Integer +--E 148 + +--S 149 OF 506 +a0128:= integrate(t0128,x) +--R +--R +--R (131) +--R 5 3 x + 1 6 4 2 +-+ +--R ((18x - 51x + 36x)log(-----) - 14x + 48x - 36x )\|a +--R x - 1 +--R + +--R +----------+ +--R 5 3 x + 1 4 2 | 2 +--R ((- 6x + 33x - 36x)log(-----) - 30x + 36x )\|- a x + a +--R x - 1 +--R / +--R +----------+ +--R 2 4 2 2 2 | 2 +-+ 3 6 3 4 3 2 +--R (54a x - 126a x + 72a )\|- a x + a \|a + 18a x - 108a x + 162a x +--R + +--R 3 +--R - 72a +--R Type: Union(Expression Integer,...) +--E 149 + +--S 150 OF 506 +m0128:= a0128-r0128 +--R +--R +--R (132) +--R 5 3 x + 1 5 3 6 +--R (- 18x + 51x - 36x)log(-----) + (36x - 102x + 72x)acoth(x) + 14x +--R x - 1 +--R + +--R 4 2 +--R - 84x + 126x - 56 +--R * +--R +----------+ +--R | 2 +-+ +--R \|- a x + a \|a +--R + +--R 7 5 3 x + 1 +--R (- 6a x + 39a x - 69a x + 36a x)log(-----) +--R x - 1 +--R + +--R 7 5 3 6 4 2 +--R (12a x - 78a x + 138a x - 72a x)acoth(x) - 42a x + 140a x - 154a x +--R + +--R 56a +--R / +--R 3 6 3 4 3 2 3 +-+ +--R (54a x - 180a x + 198a x - 72a )\|a +--R + +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (- 18a x + 108a x - 162a x + 72a )\|- a x + a +--R Type: Expression Integer +--E 150 + +--S 151 OF 506 +d0128:= D(m0128,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (133) ---------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (2a x - 4a x + 2a )\|- a x + a +--R Type: Expression Integer +--E 151 + +--S 152 OF 506 +t0129:= acoth(x)/(a-a*x^2)^(7/2) +--R +--R +--R acoth(x) +--R (134) - ---------------------------------------- +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x - 3a x + 3a x - a )\|- a x + a +--R Type: Expression Integer +--E 152 + +--S 153 OF 506 +r0129:= 1/225*(120*acoth(x)*x^5-120*x^4-_ + 300*acoth(x)*x^3+260*x^2+225*x*_ + acoth(x)-149)/a^3/(-1+x^2)^2/(-a*(-1+x^2))^(1/2) +--R +--R +--R 5 3 4 2 +--R (120x - 300x + 225x)acoth(x) - 120x + 260x - 149 +--R (135) ---------------------------------------------------- +--R +----------+ +--R 3 4 3 2 3 | 2 +--R (225a x - 450a x + 225a )\|- a x + a +--R Type: Expression Integer +--E 153 + +--S 154 OF 506 +a0129:= integrate(t0129,x) +--R +--R +--R (136) +--R 9 7 5 3 x + 1 10 +--R (600x - 3900x + 9045x - 9300x + 3600x)log(-----) - 298x +--R x - 1 +--R + +--R 8 6 4 2 +--R 3270x - 8990x + 9600x - 3600x +--R * +--R +-+ +--R \|a +--R + +--R 9 7 5 3 x + 1 8 +--R (- 120x + 1740x - 5745x + 7500x - 3600x)log(-----) - 1250x +--R x - 1 +--R + +--R 6 4 2 +--R 5540x - 7800x + 3600x +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R / +--R +----------+ +--R 3 8 3 6 3 4 3 2 3 | 2 +-+ +--R (2250a x - 13500a x + 27450a x - 23400a x + 7200a )\|- a x + a \|a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R 450a x - 6750a x + 24750a x - 38250a x + 27000a x - 7200a +--R Type: Union(Expression Integer,...) +--E 154 + +--S 155 OF 506 +m0129:= a0129-r0129 +--R +--R +--R (137) +--R 9 7 5 3 x + 1 +--R (- 600x + 3900x - 9045x + 9300x - 3600x)log(-----) +--R x - 1 +--R + +--R 9 7 5 3 10 +--R (1200x - 7800x + 18090x - 18600x + 7200x)acoth(x) + 298x +--R + +--R 8 6 4 2 +--R - 4470x + 16390x - 25330x + 17880x - 4768 +--R * +--R +----------+ +--R | 2 +-+ +--R \|- a x + a \|a +--R + +--R 11 9 7 5 3 +--R (- 120a x + 1860a x - 7485a x + 13245a x - 11100a x + 3600a x) +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 11 9 7 5 3 +--R (240a x - 3720a x + 14970a x - 26490a x + 22200a x - 7200a x) +--R * +--R acoth(x) +--R + +--R 10 8 6 4 2 +--R - 1490a x + 10430a x - 27118a x + 33674a x - 20264a x + 4768a +--R / +--R 4 10 4 8 4 6 4 4 4 2 4 +-+ +--R (2250a x - 15750a x + 40950a x - 50850a x + 30600a x - 7200a )\|a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R (- 450a x + 6750a x - 24750a x + 38250a x - 27000a x + 7200a ) +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R Type: Expression Integer +--E 155 + +--S 156 OF 506 +d0129:= D(m0129,x) +--R +--R +--R x + 1 +--R - log(-----) + 2acoth(x) +--R x - 1 +--R (138) ------------------------------------------ +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (2a x - 6a x + 6a x - 2a )\|- a x + a +--R Type: Expression Integer +--E 156 + +--S 157 OF 506 +t0130:= acoth(x^(1/2)) +--R +--R +--R +-+ +--R (139) acoth(\|x ) +--R Type: Expression Integer +--E 157 + +--S 158 OF 506 +r0130:= x^(1/2)+x*acoth(x^(1/2))-atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R (140) - atanh(\|x ) + x acoth(\|x ) + \|x +--R Type: Expression Integer +--E 158 + +--S 159 OF 506 +a0130:= integrate(t0130,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R (x - 1)log(--------) + 2\|x +--R +-+ +--R \|x - 1 +--R (141) ---------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 159 + +--S 160 OF 506 +m0130:= a0130-r0130 +--R +--R +--R +-+ +--R \|x + 1 +-+ +-+ +--R (x - 1)log(--------) + 2atanh(\|x ) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (142) ---------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 160 + +--S 161 OF 506 +d0130:= D(m0130,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (143) ---------------------------- +--R 2 +--R Type: Expression Integer +--E 161 + +--S 162 OF 506 +t0131:= x*acoth(x^(1/2)) +--R +--R +--R +-+ +--R (144) x acoth(\|x ) +--R Type: Expression Integer +--E 162 + +--S 163 OF 506 +r0131:= 1/2*x^(1/2)+1/6*x^(3/2)+1/2*x^2*acoth(x^(1/2))-1/2*atanh(x^(1/2)) +--R +--R +--R +-+ 2 +-+ +-+ +--R - 3atanh(\|x ) + 3x acoth(\|x ) + (x + 3)\|x +--R (145) --------------------------------------------- +--R 6 +--R Type: Expression Integer +--E 163 + +--S 164 OF 506 +a0131:= integrate(t0131,x) +--R +--R +--R +-+ +--R 2 \|x + 1 +-+ +--R (3x - 3)log(--------) + (2x + 6)\|x +--R +-+ +--R \|x - 1 +--R (146) ------------------------------------- +--R 12 +--R Type: Union(Expression Integer,...) +--E 164 + +--S 165 OF 506 +m0131:= a0131-r0131 +--R +--R +--R +-+ +--R 2 \|x + 1 +-+ 2 +-+ +--R (x - 1)log(--------) + 2atanh(\|x ) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (147) ----------------------------------------------------- +--R 4 +--R Type: Expression Integer +--E 165 + +--S 166 OF 506 +d0131:= D(m0131,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R x log(--------) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (148) -------------------------------- +--R 2 +--R Type: Expression Integer +--E 166 + +--S 167 OF 506 +t0132:= acoth(x^(1/2))/x +--R +--R +--R +-+ +--R acoth(\|x ) +--R (149) ----------- +--R x +--R Type: Expression Integer +--E 167 + +--S 168 OF 506 +r0132:= polylog(2,-1/x^(1/2))-polylog(2,1/x^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 168 + +--S 169 OF 506 +a0132:= integrate(t0132,x) +--R +--R +--R x +--+ +--R ++ acoth(\|%Q ) +--R (150) | ------------ d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 169 + +--S 170 OF 506 +--m0132:= a0132-r0132 +--E 170 + +--S 171 OF 506 +--d0132:= D(m0132,x) +--E 171 + +--S 172 OF 506 +t0133:= acoth(x^(1/2))/x^2 +--R +--R +--R +-+ +--R acoth(\|x ) +--R (151) ----------- +--R 2 +--R x +--R Type: Expression Integer +--E 172 + +--S 173 OF 506 +r0133:= -1/x^(1/2)-acoth(x^(1/2))/x+atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +-+ +-+ +--R x\|x atanh(\|x ) - \|x acoth(\|x ) - x +--R (152) -------------------------------------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 173 + +--S 174 OF 506 +a0133:= integrate(t0133,x) +--R +--R +--R +-+ +--R +-+ \|x + 1 +--R (x - 1)\|x log(--------) - 2x +--R +-+ +--R \|x - 1 +--R (153) ----------------------------- +--R +-+ +--R 2x\|x +--R Type: Union(Expression Integer,...) +--E 174 + +--S 175 OF 506 +m0133:= a0133-r0133 +--R +--R +--R +-+ +--R \|x + 1 +-+ +-+ +--R (x - 1)log(--------) - 2x atanh(\|x ) + 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (154) ---------------------------------------------------- +--R 2x +--R Type: Expression Integer +--E 175 + +--S 176 OF 506 +d0133:= D(m0133,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (155) ---------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 176 + +--S 177 OF 506 +t0134:= acoth(x^(1/2))/x^3 +--R +--R +--R +-+ +--R acoth(\|x ) +--R (156) ----------- +--R 3 +--R x +--R Type: Expression Integer +--E 177 + +--S 178 OF 506 +r0134:= -1/6/x^(3/2)-1/2/x^(1/2)-1/2*acoth(x^(1/2))/x^2+1/2*atanh(x^(1/2)) +--R +--R +--R 2 +-+ +-+ +-+ +-+ 2 +--R 3x \|x atanh(\|x ) - 3\|x acoth(\|x ) - 3x - x +--R (157) ----------------------------------------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression Integer +--E 178 + +--S 179 OF 506 +a0134:= integrate(t0134,x) +--R +--R +--R +-+ +--R 2 +-+ \|x + 1 2 +--R (3x - 3)\|x log(--------) - 6x - 2x +--R +-+ +--R \|x - 1 +--R (158) ------------------------------------- +--R 2 +-+ +--R 12x \|x +--R Type: Union(Expression Integer,...) +--E 179 + +--S 180 OF 506 +m0134:= a0134-r0134 +--R +--R +--R +-+ +--R 2 \|x + 1 2 +-+ +-+ +--R (x - 1)log(--------) - 2x atanh(\|x ) + 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (159) ----------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 180 + +--S 181 OF 506 +d0134:= D(m0134,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (160) ---------------------------- +--R 3 +--R 2x +--R Type: Expression Integer +--E 181 + +--S 182 OF 506 +t0135:= x^(1/2)*acoth(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (161) \|x acoth(\|x ) +--R Type: Expression Integer +--E 182 + +--S 183 OF 506 +r0135:= 1/3*x+2/3*x^(3/2)*acoth(x^(1/2))+1/3*log(1-x) +--R +--R +--R +-+ +-+ +--R 2x\|x acoth(\|x ) + log(- x + 1) + x +--R (162) ------------------------------------ +--R 3 +--R Type: Expression Integer +--E 183 + +--S 184 OF 506 +a0135:= integrate(t0135,x) +--R +--R +--R +-+ +--R +-+ \|x + 1 +--R x\|x log(--------) + log(x - 1) + x +--R +-+ +--R \|x - 1 +--R (163) ----------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 184 + +--S 185 OF 506 +m0135:= a0135-r0135 +--R +--R +--R +-+ +--R +-+ \|x + 1 +-+ +-+ +--R x\|x log(--------) - 2x\|x acoth(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R (164) ------------------------------------------------------------------ +--R 3 +--R Type: Expression Integer +--E 185 + +--S 186 OF 506 +d0135:= D(m0135,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R x log(--------) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (165) -------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression Integer +--E 186 + +--S 187 OF 506 +t0136:= x^(3/2)*acoth(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (166) x\|x acoth(\|x ) +--R Type: Expression Integer +--E 187 + +--S 188 OF 506 +r0136:= 1/5*x+1/10*x^2+2/5*x^(5/2)*acoth(x^(1/2))+1/5*log(1-x) +--R +--R +--R 2 +-+ +-+ 2 +--R 4x \|x acoth(\|x ) + 2log(- x + 1) + x + 2x +--R (167) -------------------------------------------- +--R 10 +--R Type: Expression Integer +--E 188 + +--S 189 OF 506 +a0136:= integrate(t0136,x) +--R +--R +--R +-+ +--R 2 +-+ \|x + 1 2 +--R 2x \|x log(--------) + 2log(x - 1) + x + 2x +--R +-+ +--R \|x - 1 +--R (168) -------------------------------------------- +--R 10 +--R Type: Union(Expression Integer,...) +--E 189 + +--S 190 OF 506 +m0136:= a0136-r0136 +--R +--R +--R +-+ +--R 2 +-+ \|x + 1 2 +-+ +-+ +--R x \|x log(--------) - 2x \|x acoth(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R (169) -------------------------------------------------------------------- +--R 5 +--R Type: Expression Integer +--E 190 + +--S 191 OF 506 +d0136:= D(m0136,x) +--R +--R +--R +-+ +--R 2 \|x + 1 2 +-+ +--R x log(--------) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (170) -------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression Integer +--E 191 + +--S 192 OF 506 +t0137:= acoth(x^(1/2))/x^(3/2) +--R +--R +--R +-+ +--R acoth(\|x ) +--R (171) ----------- +--R +-+ +--R x\|x +--R Type: Expression Integer +--E 192 + +--S 193 OF 506 +r0137:= -2*acoth(x^(1/2))/x^(1/2)+2*atanh(-1+2*x) +--R +--R +--R +-+ +-+ +--R - 2acoth(\|x ) + 2atanh(2x - 1)\|x +--R (172) ----------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 193 + +--S 194 OF 506 +a0137:= integrate(t0137,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R - log(--------) + (log(x) - log(x - 1))\|x +--R +-+ +--R \|x - 1 +--R (173) ------------------------------------------- +--R +-+ +--R \|x +--R Type: Union(Expression Integer,...) +--E 194 + +--S 195 OF 506 +m0137:= a0137-r0137 +--R +--R +--R (174) +--R +-+ +--R \|x + 1 +-+ +-+ +--R - log(--------) + 2acoth(\|x ) + (log(x) - log(x - 1) - 2atanh(2x - 1))\|x +--R +-+ +--R \|x - 1 +--R --------------------------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression Integer +--E 195 + +--S 196 OF 506 +d0137:= D(m0137,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (175) ---------------------------- +--R +-+ +--R 2x\|x +--R Type: Expression Integer +--E 196 + +--S 197 OF 506 +t0138:= x^3*asech(a*x) +--R +--R +--R 3 +--R (176) x asech(a x) +--R Type: Expression Integer +--E 197 + +--S 198 OF 506 +r0138:= -1/16*((1-a*x)/(1+a*x))^(1/2)*(1+a*x)^3/a^4-_ + 1/24*((1-a*x)/(1+a*x))^(3/2)*(1+a*x)^3/a^4-_ + 1/16*((1-a*x)/(1+a*x))^(5/2)*(1+a*x)^3/a^4+1/4*x^4*asech(a*x) +--R +--R +--R +---------+ +--R 3 3 2 2 |- a x + 1 4 4 +--R (- a x - a x - 2a x - 2) |--------- + 3a x asech(a x) +--R \| a x + 1 +--R (177) -------------------------------------------------------- +--R 4 +--R 12a +--R Type: Expression Integer +--E 198 + +--S 199 OF 506 +a0138:= integrate(t0138,x) +--R +--R +--R (178) +--R +----------+ +--R +----------+ | 2 2 +--R 2 6 4 | 2 2 2 6 4 \|- a x + 1 + 1 +--R ((3a x - 12x )\|- a x + 1 - 9a x + 12x )log(-----------------) +--R a x +--R + +--R +----------+ +--R 4 | 2 2 2 6 4 +--R 3x \|- a x + 1 + a x - 3x +--R / +--R +----------+ +--R 2 2 | 2 2 2 2 +--R (12a x - 48)\|- a x + 1 - 36a x + 48 +--R Type: Union(Expression Integer,...) +--E 199 + +--S 200 OF 506 +m0138:= a0138-r0138 +--R +--R +--R (179) +--R +----------+ +--R +----------+ | 2 2 +--R 6 6 4 4 | 2 2 6 6 4 4 \|- a x + 1 + 1 +--R ((3a x - 12a x )\|- a x + 1 - 9a x + 12a x )log(-----------------) +--R a x +--R + +--R +----------+ +--R 5 5 4 4 3 3 2 2 | 2 2 5 5 4 4 +--R (a x + a x - 2a x - 2a x - 8a x - 8)\|- a x + 1 - 3a x - 3a x +--R + +--R 3 3 2 2 +--R - 2a x - 2a x + 8a x + 8 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 6 6 4 4 4 4 | 2 2 +--R ((- 3a x + 12a x )asech(a x) + 3a x )\|- a x + 1 +--R + +--R 6 6 4 4 6 6 4 4 +--R (9a x - 12a x )asech(a x) + a x - 3a x +--R / +--R +----------+ +--R 6 2 4 | 2 2 6 2 4 +--R (12a x - 48a )\|- a x + 1 - 36a x + 48a +--R Type: Expression Integer +--E 200 + +--S 201 OF 506 +d0138:= D(m0138,x) +--R +--R +--R (180) +--R 7 10 6 9 5 8 4 7 3 6 2 5 4 +--R 4a x + 4a x - 72a x - 72a x + 192a x + 192a x - 128a x +--R + +--R 3 +--R - 128x +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 4 +--R - 24a x - 24a x + 152a x + 152a x - 256a x - 256a x + 128a x +--R + +--R 3 +--R 128x +--R * +--R +----------+ +--R +---------+ | 2 2 +--R |- a x + 1 \|- a x + 1 + 1 +--R |--------- log(-----------------) +--R \| a x + 1 a x +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 +--R - 4a x - 4a x + 72a x + 72a x - 192a x - 192a x +--R + +--R 4 3 +--R 128a x + 128x +--R * +--R asech(a x) +--R + +--R 5 8 4 7 3 6 2 5 4 3 +--R 6a x + 6a x - 32a x - 32a x + 32a x + 32x +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 +--R 24a x + 24a x - 152a x - 152a x + 256a x + 256a x +--R + +--R 4 3 +--R - 128a x - 128x +--R * +--R asech(a x) +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 4 3 +--R a x + a x - 18a x - 18a x + 48a x + 48a x - 32a x - 32x +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 6 9 4 7 2 5 3 | 2 2 6 9 4 7 2 5 +--R (- a x + 18a x - 48a x + 32x )\|- a x + 1 + 6a x - 38a x + 64a x +--R + +--R 3 +--R - 32x +--R / +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R (4a x + 4a x - 72a x - 72a x + 192a x + 192a x - 128a x - 128) +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - 24a x - 24a x + 152a x + 152a x - 256a x - 256a x + 128a x + 128 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R Type: Expression Integer +--E 201 + +--S 202 OF 506 +t0139:= asech(a*x)/x +--R +--R +--R asech(a x) +--R (181) ---------- +--R x +--R Type: Expression Integer +--E 202 + +--S 203 OF 506 +r0139:= -1/2*asech(a*x)^2-asech(a*x)*log(1+exp(1)^(-2*asech(a*x)))+_ + 1/2*polylog(2,-exp(1)^(-2*asech(a*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 203 + +--S 204 OF 506 +a0139:= integrate(t0139,x) +--R +--R +--R x +--R ++ asech(%Q a) +--R (182) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 204 + +--S 205 OF 506 +--m0139:= a0139-r0139 +--E 205 + +--S 206 OF 506 +--d0139:= D(m0139,x) +--E 206 + +--S 207 OF 506 +t0140:= asech(a*x)/x^3 +--R +--R +--R asech(a x) +--R (183) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 207 + +--S 208 OF 506 +r0140:= 1/4*((-(-1+a*x)/(1+a*x))^(1/2)*a*x+(-(-1+a*x)/(1+a*x))^(1/2)-_ + 2*asech(a*x)+2*a^2*atanh((-(-1+a*x)/(1+a*x))^(1/2))*x^2)/x^2 +--R +--R +--R +---------+ +---------+ +--R 2 2 |- a x + 1 |- a x + 1 +--R 2a x atanh( |--------- ) + (a x + 1) |--------- - 2asech(a x) +--R \| a x + 1 \| a x + 1 +--R (184) -------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 208 + +--S 209 OF 506 +a0140:= integrate(t0140,x) +--R +--R +--R (185) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 4 4 2 2 \|- a x + 1 + 1 +--R ((2a x - 4)\|- a x + 1 + a x - 4a x + 4)log(-----------------) +--R a x +--R + +--R +----------+ +--R 2 2 | 2 2 2 2 +--R (a x - 2)\|- a x + 1 - 2a x + 2 +--R / +--R +----------+ +--R 2 | 2 2 2 4 2 +--R 8x \|- a x + 1 + 4a x - 8x +--R Type: Union(Expression Integer,...) +--E 209 + +--S 210 OF 506 +m0140:= a0140-r0140 +--R +--R +--R (186) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 4 4 2 2 \|- a x + 1 + 1 +--R ((2a x - 4)\|- a x + 1 + a x - 4a x + 4)log(-----------------) +--R a x +--R + +--R +----------+ +---------+ +--R 2 2 | 2 2 4 4 2 2 |- a x + 1 +--R (- 4a x \|- a x + 1 - 2a x + 4a x )atanh( |--------- ) +--R \| a x + 1 +--R + +--R +----------+ +---------+ +--R | 2 2 3 3 2 2 |- a x + 1 +--R ((- 2a x - 2)\|- a x + 1 - a x - a x + 2a x + 2) |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 2 2 | 2 2 2 2 2 2 +--R (4asech(a x) + a x - 2)\|- a x + 1 + (2a x - 4)asech(a x) - 2a x + 2 +--R / +--R +----------+ +--R 2 | 2 2 2 4 2 +--R 8x \|- a x + 1 + 4a x - 8x +--R Type: Expression Integer +--E 210 + +--S 211 OF 506 +d0140:= D(m0140,x) +--R +--R +--R (187) +--R +----------+ +--R 5 5 4 4 3 3 2 2 | 2 2 5 5 +--R (2a x + 2a x - 16a x - 16a x + 16a x + 16)\|- a x + 1 - 8a x +--R + +--R 4 4 3 3 2 2 +--R - 8a x + 24a x + 24a x - 16a x - 16 +--R * +--R +----------+ +--R +---------+ | 2 2 +--R |- a x + 1 \|- a x + 1 + 1 +--R |--------- log(-----------------) +--R \| a x + 1 a x +--R + +--R 5 5 4 4 3 3 2 2 +--R (- 2a x - 2a x + 16a x + 16a x - 16a x - 16)asech(a x) +--R + +--R 3 3 2 2 +--R - 4a x - 4a x + 8a x + 8 +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 5 5 4 4 3 3 2 2 5 5 +--R (8a x + 8a x - 24a x - 24a x + 16a x + 16)asech(a x) - a x +--R + +--R 4 4 3 3 2 2 +--R - a x + 8a x + 8a x - 8a x - 8 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 4 4 2 2 | 2 2 4 4 2 2 +--R (a x - 8a x + 8)\|- a x + 1 - 4a x + 12a x - 8 +--R / +--R +----------+ +--R 5 8 4 7 3 6 2 5 4 3 | 2 2 5 8 +--R (2a x + 2a x - 16a x - 16a x + 16a x + 16x )\|- a x + 1 - 8a x +--R + +--R 4 7 3 6 2 5 4 3 +--R - 8a x + 24a x + 24a x - 16a x - 16x +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R Type: Expression Integer +--E 211 + +--S 212 OF 506 +t0141:= asech(a*x)/x^4 +--R +--R +--R asech(a x) +--R (188) ---------- +--R 4 +--R x +--R Type: Expression Integer +--E 212 + +--S 213 OF 506 +r0141:= 1/12*((1-a*x)/(1+a*x))^(1/2)*(1+a*x)^3/x^3-_ + 1/18*((1-a*x)/(1+a*x))^(3/2)*(1+a*x)^3/x^3+_ + 1/12*((1-a*x)/(1+a*x))^(5/2)*(1+a*x)^3/x^3-1/3*asech(a*x)/x^3 +--R +--R +--R +---------+ +--R 3 3 2 2 |- a x + 1 +--R (2a x + 2a x + a x + 1) |--------- - 3asech(a x) +--R \| a x + 1 +--R (189) --------------------------------------------------- +--R 3 +--R 9x +--R Type: Expression Integer +--E 213 + +--S 214 OF 506 +a0141:= integrate(t0141,x) +--R +--R +--R (190) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 2 2 \|- a x + 1 + 1 +--R ((- 3a x + 12)\|- a x + 1 + 9a x - 12)log(-----------------) +--R a x +--R + +--R +----------+ +--R 4 4 2 2 | 2 2 6 6 4 4 2 2 +--R (- 6a x + 5a x + 4)\|- a x + 1 - 2a x + 9a x - 3a x - 4 +--R / +--R +----------+ +--R 2 5 3 | 2 2 2 5 3 +--R (9a x - 36x )\|- a x + 1 - 27a x + 36x +--R Type: Union(Expression Integer,...) +--E 214 + +--S 215 OF 506 +m0141:= a0141-r0141 +--R +--R +--R (191) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 2 2 \|- a x + 1 + 1 +--R ((- 3a x + 12)\|- a x + 1 + 9a x - 12)log(-----------------) +--R a x +--R + +--R +----------+ +--R 5 5 4 4 3 3 2 2 | 2 2 5 5 +--R (- 2a x - 2a x + 7a x + 7a x + 4a x + 4)\|- a x + 1 + 6a x +--R + +--R 4 4 3 3 2 2 +--R 6a x - 5a x - 5a x - 4a x - 4 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 2 2 4 4 2 2 | 2 2 +--R ((3a x - 12)asech(a x) - 6a x + 5a x + 4)\|- a x + 1 +--R + +--R 2 2 6 6 4 4 2 2 +--R (- 9a x + 12)asech(a x) - 2a x + 9a x - 3a x - 4 +--R / +--R +----------+ +--R 2 5 3 | 2 2 2 5 3 +--R (9a x - 36x )\|- a x + 1 - 27a x + 36x +--R Type: Expression Integer +--E 215 + +--S 216 OF 506 +d0141:= D(m0141,x) +--R +--R +--R (192) +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R (3a x + 3a x - 54a x - 54a x + 144a x + 144a x - 96a x - 96) +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - 18a x - 18a x + 114a x + 114a x - 192a x - 192a x + 96a x + 96 +--R * +--R +----------+ +--R +---------+ | 2 2 +--R |- a x + 1 \|- a x + 1 + 1 +--R |--------- log(-----------------) +--R \| a x + 1 a x +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - 3a x - 3a x + 54a x + 54a x - 144a x - 144a x + 96a x +--R + +--R 96 +--R * +--R asech(a x) +--R + +--R 5 5 4 4 3 3 2 2 +--R - 6a x - 6a x + 32a x + 32a x - 32a x - 32 +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R 18a x + 18a x - 114a x - 114a x + 192a x + 192a x - 96a x +--R + +--R - 96 +--R * +--R asech(a x) +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - a x - a x + 18a x + 18a x - 48a x - 48a x + 32a x + 32 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 6 6 4 4 2 2 | 2 2 6 6 4 4 2 2 +--R (a x - 18a x + 48a x - 32)\|- a x + 1 - 6a x + 38a x - 64a x + 32 +--R / +--R 7 11 6 10 5 9 4 8 3 7 2 6 5 +--R 3a x + 3a x - 54a x - 54a x + 144a x + 144a x - 96a x +--R + +--R 4 +--R - 96x +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 11 6 10 5 9 4 8 3 7 2 6 5 +--R - 18a x - 18a x + 114a x + 114a x - 192a x - 192a x + 96a x +--R + +--R 4 +--R 96x +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R Type: Expression Integer +--E 216 + +--S 217 OF 506 +t0142:= x*asech(x^(1/2)) +--R +--R +--R +-+ +--R (193) x asech(\|x ) +--R Type: Expression Integer +--E 217 + +--S 218 OF 506 +r0142:= -1/8*((1-x^(1/2))/(1+x^(1/2)))^(1/2)*(1+x^(1/2))^3-_ + 1/12*((1-x^(1/2))/(1+x^(1/2)))^(3/2)*(1+x^(1/2))^3-_ + 1/8*((1-x^(1/2))/(1+x^(1/2)))^(5/2)*(1+x^(1/2))^3+_ + 1/2*x^2*asech(x^(1/2)) +--R +--R +--R (194) +--R +----------+ +--R | +-+ +--R 2 +-+ 3 2 |- \|x + 1 +--R ((- 4x - 12x - 8)\|x - x - 8x - 13x - 2) |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R 3 2 +-+ 3 2 +-+ +--R ((3x + 9x )\|x + 9x + 3x )asech(\|x ) +--R / +--R +-+ +--R (6x + 18)\|x + 18x + 6 +--R Type: Expression Integer +--E 218 + +--S 219 OF 506 +a0142:= integrate(t0142,x) +--R +--R +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +-------+ +--R 2 \| x |- x + 1 +-+ +--R 3x log(------------------) + (- x - 2) |------- \|x +--R +-+ \| x +--R \|x +--R (195) ---------------------------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 219 + +--S 220 OF 506 +m0142:= a0142-r0142 +--R +--R +--R (196) +--R +----------+ +--R | +-+ +--R 2 +-+ 3 2 |- \|x + 1 +--R ((4x + 12x + 8)\|x + x + 8x + 13x + 2) |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R 3 2 +-+ 3 2 \| x +--R ((3x + 9x )\|x + 9x + 3x )log(------------------) +--R +-+ +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+ +--R ((- 3x - 9x )\|x - 9x - 3x )asech(\|x ) +--R + +--R +-------+ +-------+ +--R 2 |- x + 1 +-+ 3 2 |- x + 1 +--R (- 3x - 7x - 2) |------- \|x + (- x - 5x - 6x) |------- +--R \| x \| x +--R / +--R +-+ +--R (6x + 18)\|x + 18x + 6 +--R Type: Expression Integer +--E 220 + +--S 221 OF 506 +d0142:= D(m0142,x) +--R +--R +--R (197) +--R 7 6 5 4 3 2 +-------+ +--R (4x + 220x + 1320x + 1848x + 660x + 44x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (44x + 660x + 1848x + 1320x + 220x + 4x)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (44x + 660x + 1848x + 1320x + 220x + 4x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (4x + 220x + 1320x + 1848x + 660x + 44x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R \| x +--R log(------------------) +--R +-+ +--R \|x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (- 4x - 220x - 1320x - 1848x - 660x - 44x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (- 44x - 660x - 1848x - 1320x - 220x - 4x)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (- 44x - 660x - 1848x - 1320x - 220x - 4x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (- 4x - 220x - 1320x - 1848x - 660x - 44x )\|- x + 1 +--R * +--R +-+ +--R asech(\|x ) +--R + +--R +-------+ +--R 7 6 5 4 3 2 |- x + 1 6 +--R (x + 55x + 330x + 462x + 165x + 11x ) |------- + 11x +--R \| x +--R + +--R 5 4 3 2 +--R 165x + 462x + 330x + 55x + x +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 7 6 5 4 3 2 |- x + 1 7 6 +--R (11x + 165x + 462x + 330x + 55x + x ) |------- + x + 55x +--R \| x +--R + +--R 5 4 3 2 +--R 330x + 462x + 165x + 11x +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R 6 5 4 3 2 +-------+ |- x + 1 +--R (- 10x - 120x - 252x - 120x - 10x )\|- x + 1 |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (- x - 45x - 210x - 210x - 45x - x)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 7 6 5 4 3 2 +-------+ |- x + 1 +--R (- x - 45x - 210x - 210x - 45x - x )\|- x + 1 |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (- 10x - 120x - 252x - 120x - 10x )\|- x + 1 +--R / +--R +-------+ +--R 6 5 4 3 2 +-------+ |- x + 1 +--R (4x + 220x + 1320x + 1848x + 660x + 44x)\|- x + 1 |------- +--R \| x +--R + +--R 5 4 3 2 +-------+ +--R (44x + 660x + 1848x + 1320x + 220x + 4)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 6 5 4 3 2 +-------+ |- x + 1 +--R (44x + 660x + 1848x + 1320x + 220x + 4x)\|- x + 1 |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (4x + 220x + 1320x + 1848x + 660x + 44x)\|- x + 1 +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R Type: Expression Integer +--E 221 + +--S 222 OF 506 +t0143:= x^2*asech(x^(1/2)) +--R +--R +--R 2 +-+ +--R (198) x asech(\|x ) +--R Type: Expression Integer +--E 222 + +--S 223 OF 506 +r0143:= -8/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)+1/3*x^3*asech(x^(1/2))-_ + 8/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(1/2)-_ + 4/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x-_ + 4/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(3/2)-_ + 1/15*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^2-_ + 1/15*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(5/2) +--R +--R +--R +----------+ +--R | +-+ +--R 2 +-+ 2 |- \|x + 1 3 +-+ +--R ((- 3x - 4x - 8)\|x - 3x - 4x - 8) |---------- + 15x asech(\|x ) +--R | +-+ +--R \| \|x + 1 +--R (199) -------------------------------------------------------------------- +--R 45 +--R Type: Expression Integer +--E 223 + +--S 224 OF 506 +a0143:= integrate(t0143,x) +--R +--R +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +-------+ +--R 3 \| x 2 |- x + 1 +-+ +--R 15x log(------------------) + (- 3x - 4x - 8) |------- \|x +--R +-+ \| x +--R \|x +--R (200) ------------------------------------------------------------ +--R 45 +--R Type: Union(Expression Integer,...) +--E 224 + +--S 225 OF 506 +m0143:= a0143-r0143 +--R +--R +--R (201) +--R +----------+ +--R | +-+ +--R 2 +-+ 2 |- \|x + 1 +--R ((3x + 4x + 8)\|x + 3x + 4x + 8) |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R 3 \| x 3 +-+ +--R 15x log(------------------) - 15x asech(\|x ) +--R +-+ +--R \|x +--R + +--R +-------+ +--R 2 |- x + 1 +-+ +--R (- 3x - 4x - 8) |------- \|x +--R \| x +--R / +--R 45 +--R Type: Expression Integer +--E 225 + +--S 226 OF 506 +d0143:= D(m0143,x) +--R +--R +--R (202) +--R +-------+ +--R 3 2 +-------+ |- x + 1 3 2 +-------+ +-+ +--R ((18x + 6x )\|- x + 1 |------- + (6x + 18x )\|- x + 1 )\|x +--R \| x +--R + +--R +-------+ +--R 4 3 +-------+ |- x + 1 3 2 +-------+ +--R (6x + 18x )\|- x + 1 |------- + (18x + 6x )\|- x + 1 +--R \| x +--R * +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R \| x +--R log(------------------) +--R +-+ +--R \|x +--R + +--R +-------+ +--R 3 2 +-------+ |- x + 1 3 2 +-------+ +--R ((- 18x - 6x )\|- x + 1 |------- + (- 6x - 18x )\|- x + 1 ) +--R \| x +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 4 3 +-------+ |- x + 1 3 2 +-------+ +--R (- 6x - 18x )\|- x + 1 |------- + (- 18x - 6x )\|- x + 1 +--R \| x +--R * +--R +-+ +--R asech(\|x ) +--R + +--R +-------+ +-------+ +--R 3 2 |- x + 1 3 2 +-+ 4 3 |- x + 1 3 2 +--R ((3x + x ) |------- + x + 3x )\|x + (x + 3x ) |------- + 3x + x +--R \| x \| x +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R 3 2 +-------+ |- x + 1 2 +-------+ +-+ +--R ((- x - x )\|- x + 1 |------- - 2x \|- x + 1 )\|x +--R \| x +--R + +--R +-------+ +--R 3 +-------+ |- x + 1 3 2 +-------+ +--R - 2x \|- x + 1 |------- + (- x - x )\|- x + 1 +--R \| x +--R / +--R +-------+ +--R +-------+ |- x + 1 +-------+ +-+ +--R ((18x + 6)\|- x + 1 |------- + (6x + 18)\|- x + 1 )\|x +--R \| x +--R + +--R +-------+ +--R 2 +-------+ |- x + 1 +-------+ +--R (6x + 18x)\|- x + 1 |------- + (18x + 6)\|- x + 1 +--R \| x +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R Type: Expression Integer +--E 226 + +--S 227 OF 506 +t0144:= asech(x^(1/2))/x +--R +--R +--R +-+ +--R asech(\|x ) +--R (203) ----------- +--R x +--R Type: Expression Integer +--E 227 + +--S 228 OF 506 +r0144:= -asech(x^(1/2))^2-2*asech(x^(1/2))*_ + log(1+exp(1)^(-2*asech(x^(1/2))))+_ + polylog(2,-exp(1)^(-2*asech(x^(1/2)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 228 + +--S 229 OF 506 +a0144:= integrate(t0144,x) +--R +--R +--R x +--+ +--R ++ asech(\|%Q ) +--R (204) | ------------ d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 229 + +--S 230 OF 506 +--m0144:= a0144-r0144 +--E 230 + +--S 231 OF 506 +--d0144:= D(m0144,x) +--E 231 + +--S 232 OF 506 +t0145:= asech(x^(1/2))/x^3 +--R +--R +--R +-+ +--R asech(\|x ) +--R (205) ----------- +--R 3 +--R x +--R Type: Expression Integer +--E 232 + +--S 233 OF 506 +r0145:= 1/16*(2*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x+_ + 3*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^2+_ + 3*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(3/2)+_ + 2*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(1/2)+_ + 6*atanh((-(-1+x^(1/2))/(1+x^(1/2)))^(1/2))*x^(5/2)-_ + 8*asech(x^(1/2))*x^(1/2))/x^(5/2) +--R +--R +--R (206) +--R +----------+ +----------+ +--R | +-+ | +-+ +--R 2 +-+ |- \|x + 1 +-+ 2 |- \|x + 1 +--R 6x \|x atanh( |---------- ) + ((3x + 2)\|x + 3x + 2x) |---------- +--R | +-+ | +-+ +--R \| \|x + 1 \| \|x + 1 +--R + +--R +-+ +-+ +--R - 8\|x asech(\|x ) +--R / +--R 2 +-+ +--R 16x \|x +--R Type: Expression Integer +--E 233 + +--S 234 OF 506 +a0145:= integrate(t0145,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 234 + +--S 235 OF 506 +--m0145:= a0145-r0145 +--E 235 + +--S 236 OF 506 +--d0145:= D(m0145,x) +--E 236 + +--S 237 OF 506 +t0146:= x^2*acsch(a*x) +--R +--R +--R 2 +--R (207) x acsch(a x) +--R Type: Expression Integer +--E 237 + +--S 238 OF 506 +r0146:= 1/6*(1+1/a^2/x^2)^(1/2)*x^2/a+1/3*x^3*acsch(a*x)-_ + 1/6*atanh((1+1/a^2/x^2)^(1/2))/a^3 +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x + 1 2 2 |a x + 1 3 3 +--R - atanh( |-------- ) + a x |-------- + 2a x acsch(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R (208) -------------------------------------------------------- +--R 3 +--R 6a +--R Type: Expression Integer +--E 238 + +--S 239 OF 506 +a0146:= integrate(t0146,x) +--R +--R +--R (209) +--R +--------+ +--------+ +--R | 2 2 2 2 | 2 2 +--R (2a x\|a x + 1 - 2a x - 1)log(\|a x + 1 - a x) +--R + +--R +--------+ +--R +--------+ | 2 2 +--R 4 4 | 2 2 5 5 3 3 \|a x + 1 + 1 +--R (4a x \|a x + 1 - 4a x - 2a x )log(---------------) +--R a x +--R + +--R +--------+ +--R 3 3 | 2 2 4 4 2 2 +--R (- 2a x - a x)\|a x + 1 + 2a x + 2a x +--R / +--R +--------+ +--R 4 | 2 2 5 2 3 +--R 12a x\|a x + 1 - 12a x - 6a +--R Type: Union(Expression Integer,...) +--E 239 + +--S 240 OF 506 +m0146:= a0146-r0146 +--R +--R +--R (210) +--R +--------+ +--------+ +--R | 2 2 2 2 | 2 2 +--R (2a x\|a x + 1 - 2a x - 1)log(\|a x + 1 - a x) +--R + +--R +--------+ +--R +--------+ | 2 2 +--R 4 4 | 2 2 5 5 3 3 \|a x + 1 + 1 +--R (4a x \|a x + 1 - 4a x - 2a x )log(---------------) +--R a x +--R + +--R +--------+ +--R +--------+ | 2 2 +--R | 2 2 2 2 |a x + 1 +--R (2a x\|a x + 1 - 2a x - 1)atanh( |-------- ) +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--------+ +--R 3 3 |a x + 1 4 4 3 3 | 2 2 +--R (- 2a x |-------- - 4a x acsch(a x) - 2a x - a x)\|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 4 4 2 2 |a x + 1 5 5 3 3 4 4 2 2 +--R (2a x + a x ) |-------- + (4a x + 2a x )acsch(a x) + 2a x + 2a x +--R | 2 2 +--R \| a x +--R / +--R +--------+ +--R 4 | 2 2 5 2 3 +--R 12a x\|a x + 1 - 12a x - 6a +--R Type: Expression Integer +--E 240 + +--S 241 OF 506 +d0146:= D(m0146,x) +--R +--R +--R (211) +--R +--------+ +--R | 2 2 +--------+ +--R 5 6 3 4 2 |a x + 1 | 2 2 +--R (24a x + 24a x + 3a x ) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 7 4 5 2 3 |a x + 1 +--R (- 24a x - 36a x - 12a x ) |-------- +--R | 2 2 +--R \| a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 + 1 +--R log(---------------) +--R a x +--R + +--R +--------+ +--R | 2 2 +--R 5 6 3 4 2 4 5 2 3 |a x + 1 +--R ((- 24a x - 24a x - 3a x )acsch(a x) - 8a x - 4a x ) |-------- +--R | 2 2 +--R \| a x +--R + +--R 4 5 2 3 +--R - 8a x - 8a x - x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 +--R + +--R +--------+ +--R | 2 2 +--R 6 7 4 5 2 3 5 6 3 4 2 |a x + 1 +--R ((24a x + 36a x + 12a x )acsch(a x) + 8a x + 8a x + a x ) |-------- +--R | 2 2 +--R \| a x +--R + +--R 5 6 3 4 2 +--R 8a x + 12a x + 4a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R 5 4 3 2 |a x + 1 | 2 2 +--R (24a x + 24a x + 3a) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 5 4 3 2 |a x + 1 +--R (- 24a x - 36a x - 12a x) |-------- +--R | 2 2 +--R \| a x +--R Type: Expression Integer +--E 241 + +--S 242 OF 506 +t0147:= acsch(a*x)/x +--R +--R +--R acsch(a x) +--R (212) ---------- +--R x +--R Type: Expression Integer +--E 242 + +--S 243 OF 506 +r0147:= -1/2*acsch(a*x)^2-acsch(a*x)*log(1-exp(1)^(-2*acsch(a*x)))+_ + 1/2*polylog(2,exp(1)^(-2*acsch(a*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 243 + +--S 244 OF 506 +a0147:= integrate(t0147,x) +--R +--R +--R x +--R ++ acsch(%Q a) +--R (213) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 244 + +--S 245 OF 506 +--m0147:= a0147-r0147 +--E 245 + +--S 246 OF 506 +--d0147:= D(m0147,x) +--E 246 + +--S 247 OF 506 +t0148:= acsch(a*x)/x^3 +--R +--R +--R acsch(a x) +--R (214) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 247 + +--S 248 OF 506 +r0148:= 1/4*a*(1+1/a^2/x^2)^(1/2)/x-1/2*acsch(a*x)/x^2-1/4*a^2*asinh(1/a/x) +--R +--R +--R +--------+ +--R | 2 2 +--R |a x + 1 2 2 1 +--R a x |-------- - a x asinh(---) - 2acsch(a x) +--R | 2 2 a x +--R \| a x +--R (215) --------------------------------------------- +--R 2 +--R 4x +--R Type: Expression Integer +--E 248 + +--S 249 OF 506 +a0148:= integrate(t0148,x) +--R +--R +--R (216) +--R +--------+ +--R +--------+ | 2 2 +--R 3 3 | 2 2 4 4 2 2 \|a x + 1 + 1 +--R ((- 2a x - 4a x)\|a x + 1 + 2a x + 5a x + 2)log(---------------) +--R a x +--R + +--R +--------+ +--R 2 2 | 2 2 3 3 +--R (- 2a x - 1)\|a x + 1 + 2a x + 2a x +--R / +--R +--------+ +--R 3 | 2 2 2 4 2 +--R 8a x \|a x + 1 - 8a x - 4x +--R Type: Union(Expression Integer,...) +--E 249 + +--S 250 OF 506 +m0148:= a0148-r0148 +--R +--R +--R (217) +--R +--------+ +--R +--------+ | 2 2 +--R 3 3 | 2 2 4 4 2 2 \|a x + 1 + 1 +--R ((- 2a x - 4a x)\|a x + 1 + 2a x + 5a x + 2)log(---------------) +--R a x +--R + +--R +--------+ +--R | 2 2 +--R 2 2 |a x + 1 3 3 1 2 2 +--R (- 2a x |-------- + 2a x asinh(---) + 4a x acsch(a x) - 2a x - 1) +--R | 2 2 a x +--R \| a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 +--R + +--R +--------+ +--R | 2 2 +--R 3 3 |a x + 1 4 4 2 2 1 +--R (2a x + a x) |-------- + (- 2a x - a x )asinh(---) +--R | 2 2 a x +--R \| a x +--R + +--R 2 2 3 3 +--R (- 4a x - 2)acsch(a x) + 2a x + 2a x +--R / +--R +--------+ +--R 3 | 2 2 2 4 2 +--R 8a x \|a x + 1 - 8a x - 4x +--R Type: Expression Integer +--E 250 + +--S 251 OF 506 +d0148:= D(m0148,x) +--R +--R +--R (218) +--R +--------+ +--R | 2 2 +--------+ +--R 5 5 3 3 |a x + 1 | 2 2 +--R (16a x + 16a x + 2a x) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 6 4 4 2 2 |a x + 1 +--R (- 16a x - 24a x - 8a x ) |-------- +--R | 2 2 +--R \| a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 + 1 +--R log(---------------) +--R a x +--R + +--R +--------+ +--R | 2 2 +--R 5 5 3 3 4 4 2 2 |a x + 1 +--R ((- 16a x - 16a x - 2a x)acsch(a x) + 8a x + 4a x ) |-------- +--R | 2 2 +--R \| a x +--R + +--R 4 4 2 2 +--R 8a x + 8a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 +--R + +--R +--------+ +--R | 2 2 +--R 6 6 4 4 2 2 5 5 3 3 |a x + 1 +--R ((16a x + 24a x + 8a x )acsch(a x) - 8a x - 8a x - a x) |-------- +--R | 2 2 +--R \| a x +--R + +--R 5 5 3 3 +--R - 8a x - 12a x - 4a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R 5 8 3 6 4 |a x + 1 | 2 2 +--R (16a x + 16a x + 2a x ) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 9 4 7 2 5 |a x + 1 +--R (- 16a x - 24a x - 8a x ) |-------- +--R | 2 2 +--R \| a x +--R Type: Expression Integer +--E 251 + +--S 252 OF 506 +t0149:= acsch(x^(1/2))/x +--R +--R +--R +-+ +--R acsch(\|x ) +--R (219) ----------- +--R x +--R Type: Expression Integer +--E 252 + +--S 253 OF 506 +r0149:= -acsch(x^(1/2))^2-2*acsch(x^(1/2))*_ + log(1-exp(1)^(-2*acsch(x^(1/2))))+_ + polylog(2,exp(1)^(-2*acsch(x^(1/2)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 253 + +--S 254 OF 506 +a0149:= integrate(t0149,x) +--R +--R +--R x +--+ +--R ++ acsch(\|%Q ) +--R (220) | ------------ d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 254 + +--S 255 OF 506 +--m0149:= a0149-r0149 +--E 255 + +--S 256 OF 506 +--d0149:= D(m0149,x) +--E 256 + +--S 257 OF 506 +t0150:= acsch(x^(1/2))/x^2 +--R +--R +--R +-+ +--R acsch(\|x ) +--R (221) ----------- +--R 2 +--R x +--R Type: Expression Integer +--E 257 + +--S 258 OF 506 +r0150:= 1/2*(1/x+1)^(1/2)/x^(1/2)-1/2*acsch(x^(1/2))-acsch(x^(1/2))/x +--R +--R +--R +-----+ +--R +-+ +-+ |x + 1 +--R (- x - 2)\|x acsch(\|x ) + x |----- +--R \| x +--R (222) ------------------------------------ +--R +-+ +--R 2x\|x +--R Type: Expression Integer +--E 258 + +--S 259 OF 506 +a0150:= integrate(t0150,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 259 + +--S 260 OF 506 +--m0150:= a0150-r0150 +--E 260 + +--S 261 OF 506 +--d0150:= D(m0150,x) +--E 261 + +--S 262 OF 506 +t0151:= acosh(1/x) +--R +--R +--R 1 +--R (223) acosh(-) +--R x +--R Type: Expression Integer +--E 262 + +--S 263 OF 506 +r0151:= x*asech(x)-2*atan((-(-1+x)/(1+x))^(1/2)) +--R +--R +--R +-------+ +--R |- x + 1 +--R (224) - 2atan( |------- ) + x asech(x) +--R \| x + 1 +--R Type: Expression Integer +--E 263 + +--S 264 OF 506 +a0151:= integrate(t0151,x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 + 1 \|- x + 1 - 1 +--R (225) x log(---------------) - 2atan(---------------) +--R x x +--R Type: Union(Expression Integer,...) +--E 264 + +--S 265 OF 506 +m0151:= a0151-r0151 +--R +--R +--R (226) +--R +--------+ +--------+ +--R | 2 +-------+ | 2 +--R \|- x + 1 + 1 |- x + 1 \|- x + 1 - 1 +--R x log(---------------) + 2atan( |------- ) - 2atan(---------------) +--R x \| x + 1 x +--R + +--R - x asech(x) +--R Type: Expression Integer +--E 265 + +--S 266 OF 506 +d0151:= D(m0151,x) +--R +--R +--R (227) +--R +--------+ +--R +--------+ +-------+ | 2 +--R | 2 |- x + 1 \|- x + 1 + 1 +--R (x + 1)\|- x + 1 |------- log(---------------) +--R \| x + 1 x +--R + +--R +--------+ +-------+ +--------+ +--R | 2 |- x + 1 | 2 +--R ((- x - 1)asech(x)\|- x + 1 + x + 1) |------- - \|- x + 1 +--R \| x + 1 +--R / +--R +--------+ +-------+ +--R | 2 |- x + 1 +--R (x + 1)\|- x + 1 |------- +--R \| x + 1 +--R Type: Expression Integer +--E 266 + +--S 267 OF 506 +t0152:= atanh(1/x) +--R +--R +--R 1 +--R (228) atanh(-) +--R x +--R Type: Expression Integer +--E 267 + +--S 268 OF 506 +r0152:= x*acoth(x)+1/2*log(1-x^2) +--R +--R +--R 2 +--R log(- x + 1) + 2x acoth(x) +--R (229) --------------------------- +--R 2 +--R Type: Expression Integer +--E 268 + +--S 269 OF 506 +a0152:= integrate(t0152,x) +--R +--R +--R 2 x + 1 +--R log(x - 1) + x log(-----) +--R x - 1 +--R (230) -------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 269 + +--S 270 OF 506 +m0152:= a0152-r0152 +--R +--R +--R 2 x + 1 2 +--R log(x - 1) + x log(-----) - log(- x + 1) - 2x acoth(x) +--R x - 1 +--R (231) -------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 270 + +--S 271 OF 506 +d0152:= D(m0152,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (232) ---------------------- +--R 2 +--R Type: Expression Integer +--E 271 + +--S 272 OF 506 +t0153:= acoth(1/x) +--R +--R +--R 1 +--R (233) acoth(-) +--R x +--R Type: Expression Integer +--E 272 + +--S 273 OF 506 +r0153:= x*atanh(x)+1/2*log(1-x^2) +--R +--R +--R 2 +--R log(- x + 1) + 2x atanh(x) +--R (234) --------------------------- +--R 2 +--R Type: Expression Integer +--E 273 + +--S 274 OF 506 +a0153:= integrate(t0153,x) +--R +--R +--R 2 - x - 1 +--R log(x - 1) + x log(-------) +--R x - 1 +--R (235) ---------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 274 + +--S 275 OF 506 +m0153:= a0153-r0153 +--R +--R +--R 2 - x - 1 2 +--R log(x - 1) + x log(-------) - log(- x + 1) - 2x atanh(x) +--R x - 1 +--R (236) ---------------------------------------------------------- +--R 2 +--R Type: Expression Integer +--E 275 + +--S 276 OF 506 +d0153:= D(m0153,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (237) ------------------------ +--R 2 +--R Type: Expression Integer +--E 276 + +--S 277 OF 506 +t0154:= atanh(a+b*x)/x +--R +--R +--R atanh(b x + a) +--R (238) -------------- +--R x +--R Type: Expression Integer +--E 277 + +--S 278 OF 506 +r0154:= -1/2*log(b*x/(1-a))*log(1-a-b*x)+1/2*log(-b*x/(1+a))*log(a+1+b*x)-_ + 1/2*polylog(2,1-b*x/(1-a))+1/2*polylog(2,1+b*x/(1+a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 278 + +--S 279 OF 506 +a0154:= integrate(t0154,x) +--R +--R +--R x +--R ++ atanh(%Q b + a) +--R (239) | --------------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 279 + +--S 280 OF 506 +--m0154:= a0154-r0154 +--E 280 + +--S 281 OF 506 +--d0154:= D(m0154,x) +--E 281 + +--S 282 OF 506 +t0155:= acoth(a+b*x)/x +--R +--R +--R acoth(b x + a) +--R (240) -------------- +--R x +--R Type: Expression Integer +--E 282 + +--S 283 OF 506 +r0155:= 1/2*log(x)*log((a+b*x-1)/(-1+a))-_ + 1/2*log(x)*log((a+1+b*x)/(1+a))-_ + 1/2*log(x)*log((a+b*x-1)/(a+b*x))+_ + 1/2*log(x)*log((a+1+b*x)/(a+b*x))+_ + 1/2*polylog(2,-b*x/(-1+a))-_ + 1/2*polylog(2,-b*x/(1+a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 283 + +--S 284 OF 506 +a0155:= integrate(t0155,x) +--R +--R +--R x +--R ++ acoth(%Q b + a) +--R (241) | --------------- d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 284 + +--S 285 OF 506 +--m0155:= a0155-r0155 +--E 285 + +--S 286 OF 506 +--d0155:= D(m0155,x) +--E 286 + +--S 287 OF 506 +t0156:= asinh(a+b*x)/(a*d/b+d*x) +--R +--R +--R b asinh(b x + a) +--R (242) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 287 + +--S 288 OF 506 +r0156:= 1/2*asinh(a+b*x)^2/d+asinh(a+b*x)*_ + log(1-exp(1)^(-2*asinh(a+b*x)))/d-1/2*_ + polylog(2,exp(1)^(-2*asinh(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 288 + +--S 289 OF 506 +a0156:= integrate(t0156,x) +--R +--R +--R x +--R ++ b asinh(%Q b + a) +--R (243) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 289 + +--S 290 OF 506 +--m0156:= a0156-r0156 +--E 290 + +--S 291 OF 506 +--d0156:= D(m0156,x) +--E 291 + +--S 292 OF 506 +t0157:= acosh(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acosh(b x + a) +--R (244) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 292 + +--S 293 OF 506 +r0157:= 1/2*acosh(a+b*x)^2/d+acosh(a+b*x)*_ + log(1+exp(1)^(-2*acosh(a+b*x)))/d-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 293 + +--S 294 OF 506 +a0157:= integrate(t0157,x) +--R +--R +--R x +--R ++ b acosh(%Q b + a) +--R (245) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 294 + +--S 295 OF 506 +--m0157:= a0157-r0157 +--E 295 + +--S 296 OF 506 +--d0157:= D(m0157,x) +--E 296 + +--S 297 OF 506 +t0158:= atanh(a+b*x)/(a*d/b+d*x) +--R +--R +--R b atanh(b x + a) +--R (246) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 297 + +--S 298 OF 506 +r0158:= -1/2*(polylog(2,-a-b*x)-polylog(2,a+b*x))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 298 + +--S 299 OF 506 +a0158:= integrate(t0158,x) +--R +--R +--R x +--R ++ b atanh(%Q b + a) +--R (247) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 299 + +--S 300 OF 506 +--m0158:= a0158-r0158 +--E 300 + +--S 301 OF 506 +--d0158:= D(m0158,x) +--E 301 + +--S 302 OF 506 +t0159:= acoth(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acoth(b x + a) +--R (248) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 302 + +--S 303 OF 506 +r0159:= 1/2*(polylog(2,-1/(a+b*x))-polylog(2,1/(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction Polynomial Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 303 + +--S 304 OF 506 +a0159:= integrate(t0159,x) +--R +--R +--R x +--R ++ b acoth(%Q b + a) +--R (249) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 304 + +--S 305 OF 506 +--m0159:= a0159-r0159 +--E 305 + +--S 306 OF 506 +--d0159:= D(m0159,x) +--E 306 + +--S 307 OF 506 +t0160:= asech(a+b*x)/(a*d/b+d*x) +--R +--R +--R b asech(b x + a) +--R (250) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 307 + +--S 308 OF 506 +r0160:= -1/2*asech(a+b*x)^2/d-asech(a+b*x)*log(1+exp(1)^(-2*asech(a+b*x)))/d+_ + 1/2*polylog(2,-exp(1)^(-2*asech(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 308 + +--S 309 OF 506 +a0160:= integrate(t0160,x) +--R +--R +--R x +--R ++ b asech(%Q b + a) +--R (251) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 309 + +--S 310 OF 506 +--m0160:= a0160-r0160 +--E 310 + +--S 311 OF 506 +--d0160:= D(m0160,x) +--E 311 + +--S 312 OF 506 +t0161:= acsch(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acsch(b x + a) +--R (252) ---------------- +--R b d x + a d +--R Type: Expression Integer +--E 312 + +--S 313 OF 506 +r0161:= -1/2*acsch(a+b*x)^2/d-acsch(a+b*x)*log(1-exp(1)^(-2*acsch(a+b*x)))/d+_ + 1/2*polylog(2,exp(1)^(-2*acsch(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 313 + +--S 314 OF 506 +a0161:= integrate(t0161,x) +--R +--R +--R x +--R ++ b acsch(%Q b + a) +--R (253) | ----------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression Integer,...) +--E 314 + +--S 315 OF 506 +--m0161:= a0161-r0161 +--E 315 + +--S 316 OF 506 +--d0161:= D(m0161,x) +--E 316 + +--S 317 OF 506 +t0162:= x/(1+x^2)^(1/2)/asinh(x) +--R +--R +--R x +--R (254) ----------------- +--R +------+ +--R | 2 +--R asinh(x)\|x + 1 +--R Type: Expression Integer +--E 317 + +--S 318 OF 506 +r0162:= Shi(asinh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 318 + +--S 319 OF 506 +a0162:= integrate(t0162,x) +--R +--R +--R x +--R ++ %Q +--R (255) | ------------------- d%Q +--R ++ +-------+ +--R | 2 +--R asinh(%Q)\|%Q + 1 +--R Type: Union(Expression Integer,...) +--E 319 + +--S 320 OF 506 +--m0162:= a0162-r0162 +--E 320 + +--S 321 OF 506 +--d0162:= D(m0162,x) +--E 321 + +--S 322 OF 506 +t0163:= x/(-1+x)^(1/2)/(1+x)^(1/2)/acosh(x) +--R +--R +--R x +--R (256) ------------------------ +--R +-----+ +-----+ +--R acosh(x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 322 + +--S 323 OF 506 +r0163:= Chi(acosh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 323 + +--S 324 OF 506 +a0163:= integrate(t0163,x) +--R +--R +--R x +--R ++ %Q +--R (257) | --------------------------- d%Q +--R ++ +------+ +------+ +--R acosh(%Q)\|%Q - 1 \|%Q + 1 +--R Type: Union(Expression Integer,...) +--E 324 + +--S 325 OF 506 +--m0163:= a0163-r0163 +--E 325 + +--S 326 OF 506 +--d0163:= D(m0163,x) +--E 326 + +--S 327 OF 506 +t0164:= asinh(a*x^n)/x +--R +--R +--R n +--R asinh(a x ) +--R (258) ----------- +--R x +--R Type: Expression Integer +--E 327 + +--S 328 OF 506 +r0164:= 1/2*asinh(a*x^n)^2/n+asinh(a*x^n)*log(1-exp(1)^(-2*asinh(a*x^n)))/n-_ + 1/2*polylog(2,exp(1)^(-2*asinh(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 328 + +--S 329 OF 506 +a0164:= integrate(t0164,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 329 + +--S 330 OF 506 +--m0164:= a0164-r0164 +--E 330 + +--S 331 OF 506 +--d0164:= D(m0164,x) +--E 331 + +--S 332 OF 506 +t0165:= acosh(a*x^n)/x +--R +--R +--R n +--R acosh(a x ) +--R (259) ----------- +--R x +--R Type: Expression Integer +--E 332 + +--S 333 OF 506 +r0165:= 1/2*acosh(a*x^n)^2/n+acosh(a*x^n)*log(1+exp(1)^(-2*acosh(a*x^n)))/n-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 333 + +--S 334 OF 506 +a0165:= integrate(t0165,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 334 + +--S 335 OF 506 +--m0165:= a0165-r0165 +--E 335 + +--S 336 OF 506 +--d0165:= D(m0165,x) +--E 336 + +--S 337 OF 506 +t0166:= atanh(a*x^n)/x +--R +--R +--R n +--R atanh(a x ) +--R (260) ----------- +--R x +--R Type: Expression Integer +--E 337 + +--S 338 OF 506 +r0166:= -1/2/n*(polylog(2,-a*x^n)-polylog(2,a*x^n)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 338 + +--S 339 OF 506 +a0166:= integrate(t0166,x) +--R +--R +--R x n +--R ++ atanh(a %Q ) +--R (261) | ------------ d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 339 + +--S 340 OF 506 +--m0166:= a0166-r0166 +--E 340 + +--S 341 OF 506 +--d0166:= D(m0166,x) +--E 341 + +--S 342 OF 506 +t0167:= acoth(a*x^n)/x +--R +--R +--R n +--R acoth(a x ) +--R (262) ----------- +--R x +--R Type: Expression Integer +--E 342 + +--S 343 OF 506 +r0167:= 1/2/n*(polylog(2,-1/a*x^(-n))-polylog(2,1/a*x^(-n))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 343 + +--S 344 OF 506 +a0167:= integrate(t0167,x) +--R +--R +--R x n +--R ++ acoth(a %Q ) +--R (263) | ------------ d%Q +--R ++ %Q +--R Type: Union(Expression Integer,...) +--E 344 + +--S 345 OF 506 +--m0167:= a0167-r0167 +--E 345 + +--S 346 OF 506 +--d0167:= D(m0167,x) +--E 346 + +--S 347 OF 506 +t0168:= asech(a*x^n)/x +--R +--R +--R n +--R asech(a x ) +--R (264) ----------- +--R x +--R Type: Expression Integer +--E 347 + +--S 348 OF 506 +r0168:= -1/2*asech(a*x^n)^2/n-asech(a*x^n)*_ + log(1+exp(1)^(-2*asech(a*x^n)))/n+_ + 1/2*polylog(2,-exp(1)^(-2*asech(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 348 + +--S 349 OF 506 +a0168:= integrate(t0168,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 349 + +--S 350 OF 506 +--m0168:= a0168-r0168 +--E 350 + +--S 351 OF 506 +--d0168:= D(m0168,x) +--E 351 + +--S 352 OF 506 +t0169:= acsch(a*x^n)/x +--R +--R +--R n +--R acsch(a x ) +--R (265) ----------- +--R x +--R Type: Expression Integer +--E 352 + +--S 353 OF 506 +r0169:= -1/2*acsch(a*x^n)^2/n-acsch(a*x^n)*_ + log(1-exp(1)^(-2*acsch(a*x^n)))/n+_ + 1/2*polylog(2,exp(1)^(-2*acsch(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 353 + +--S 354 OF 506 +a0169:= integrate(t0169,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 354 + +--S 355 OF 506 +--m0169:= a0169-r0169 +--E 355 + +--S 356 OF 506 +--d0169:= D(m0169,x) +--E 356 + +--S 357 OF 506 +t0170:= x^3*acsch(a+b*x^4) +--R +--R +--R 3 4 +--R (266) x acsch(b x + a) +--R Type: Expression Integer +--E 357 + +--S 358 OF 506 +r0170:= 1/4*(a+b*x^4)*acsch(a+b*x^4)/b+1/4*atanh((1+1/(a+b*x^4)^2)^(1/2))/b +--R +--R +--R +-----------------------+ +--R | 2 8 4 2 +--R |b x + 2a b x + a + 1 4 4 +--R atanh( |----------------------- ) + (b x + a)acsch(b x + a) +--R | 2 8 4 2 +--R \| b x + 2a b x + a +--R (267) ------------------------------------------------------------- +--R 4b +--R Type: Expression Integer +--E 358 + +--S 359 OF 506 +a0170:= integrate(t0170,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 359 + +--S 360 OF 506 +--m0170:= a0170-r0170 +--E 360 + +--S 361 OF 506 +--d0170:= D(m0170,x) +--E 361 + +--S 362 OF 506 +t0171:= x^(-1+n)*asinh(a+b*x^n) +--R +--R +--R n - 1 n +--R (268) x asinh(b x + a) +--R Type: Expression Integer +--E 362 + +--S 363 OF 506 +r0171:= -(1+(a+b*x^n)^2)^(1/2)/b/n+(a+b*x^n)*asinh(a+b*x^n)/b/n +--R +--R +--R +--------------------------+ +--R | 2 n 2 n 2 n n +--R - \|b (x ) + 2a b x + a + 1 + (b x + a)asinh(b x + a) +--R (269) ----------------------------------------------------------- +--R b n +--R Type: Expression Integer +--E 363 + +--S 364 OF 506 +a0171:= integrate(t0171,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 364 + +--S 365 OF 506 +--m0171:= a0171-r0171 +--E 365 + +--S 366 OF 506 +--d0171:= D(m0171,x) +--E 366 + +--S 367 OF 506 +t0172:= x^(-1+n)*acosh(a+b*x^n) +--R +--R +--R n - 1 n +--R (270) x acosh(b x + a) +--R Type: Expression Integer +--E 367 + +--S 368 OF 506 +r0172:= -(-1+a+b*x^n)^(1/2)*(1+a+b*x^n)^(1/2)/b/n+(a+b*x^n)*acosh(a+b*x^n)/b/n +--R +--R +--R +------------+ +------------+ +--R | n | n n n +--R - \|b x + a - 1 \|b x + a + 1 + (b x + a)acosh(b x + a) +--R (271) ------------------------------------------------------------ +--R b n +--R Type: Expression Integer +--E 368 + +--S 369 OF 506 +a0172:= integrate(t0172,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 369 + +--S 370 OF 506 +--m0172:= a0172-r0172 +--E 370 + +--S 371 OF 506 +--d0172:= D(m0172,x) +--E 371 + +--S 372 OF 506 +t0173:= x^(-1+n)*atanh(a+b*x^n) +--R +--R +--R n - 1 n +--R (272) x atanh(b x + a) +--R Type: Expression Integer +--E 372 + +--S 373 OF 506 +r0173:= (a+b*x^n)*atanh(a+b*x^n)/b/n+1/2*log(1-(a+b*x^n)^2)/b/n +--R +--R +--R 2 n 2 n 2 n n +--R log(- b (x ) - 2a b x - a + 1) + (2b x + 2a)atanh(b x + a) +--R (273) --------------------------------------------------------------- +--R 2b n +--R Type: Expression Integer +--E 373 + +--S 374 OF 506 +a0173:= integrate(t0173,x) +--R +--R +--R (274) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R - b sinh(n log(x)) - b cosh(n log(x)) - a - 1 +--R log(---------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R / +--R 2b n +--R Type: Union(Expression Integer,...) +--E 374 + +--S 375 OF 506 +m0173:= a0173-r0173 +--R +--R +--R (275) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R - b sinh(n log(x)) - b cosh(n log(x)) - a - 1 +--R log(---------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R 2 n 2 n 2 n n +--R - log(- b (x ) - 2a b x - a + 1) + (- 2b x - 2a)atanh(b x + a) +--R / +--R 2b n +--R Type: Expression Integer +--E 375 + +--S 376 OF 506 +d0173:= D(m0173,x) +--R +--R +--R (276) +--R (sinh(n log(x)) + cosh(n log(x))) +--R * +--R - b sinh(n log(x)) - b cosh(n log(x)) - a - 1 +--R log(---------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R n - 1 n +--R - 2x x atanh(b x + a) +--R / +--R 2x +--R Type: Expression Integer +--E 376 + +--S 377 OF 506 +t0174:= x^(-1+n)*acoth(a+b*x^n) +--R +--R +--R n - 1 n +--R (277) x acoth(b x + a) +--R Type: Expression Integer +--E 377 + +--S 378 OF 506 +r0174:= (a+b*x^n)*acoth(a+b*x^n)/b/n+1/2*log(1-(a+b*x^n)^2)/b/n +--R +--R +--R 2 n 2 n 2 n n +--R log(- b (x ) - 2a b x - a + 1) + (2b x + 2a)acoth(b x + a) +--R (278) --------------------------------------------------------------- +--R 2b n +--R Type: Expression Integer +--E 378 + +--S 379 OF 506 +a0174:= integrate(t0174,x) +--R +--R +--R (279) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R b sinh(n log(x)) + b cosh(n log(x)) + a + 1 +--R log(-------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R / +--R 2b n +--R Type: Union(Expression Integer,...) +--E 379 + +--S 380 OF 506 +m0174:= a0174-r0174 +--R +--R +--R (280) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R b sinh(n log(x)) + b cosh(n log(x)) + a + 1 +--R log(-------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R 2 n 2 n 2 n n +--R - log(- b (x ) - 2a b x - a + 1) + (- 2b x - 2a)acoth(b x + a) +--R / +--R 2b n +--R Type: Expression Integer +--E 380 + +--S 381 OF 506 +d0174:= D(m0174,x) +--R +--R +--R (281) +--R (sinh(n log(x)) + cosh(n log(x))) +--R * +--R b sinh(n log(x)) + b cosh(n log(x)) + a + 1 +--R log(-------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R n - 1 n +--R - 2x x acoth(b x + a) +--R / +--R 2x +--R Type: Expression Integer +--E 381 + +--S 382 OF 506 +t0175:= x^(-1+n)*asech(a+b*x^n) +--R +--R +--R n - 1 n +--R (282) x asech(b x + a) +--R Type: Expression Integer +--E 382 + +--S 383 OF 506 +r0175:= (a+b*x^n)*asech(a+b*x^n)/b/n-_ + 2*atan(((1-a-b*x^n)/(1+a+b*x^n))^(1/2))/b/n +--R +--R +--R +--------------+ +--R | n +--R |- b x - a + 1 n n +--R - 2atan( |-------------- ) + (b x + a)asech(b x + a) +--R | n +--R \| b x + a + 1 +--R (283) ------------------------------------------------------ +--R b n +--R Type: Expression Integer +--E 383 + +--S 384 OF 506 +a0175:= integrate(t0175,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 384 + +--S 385 OF 506 +--m0175:= a0175-r0175 +--E 385 + +--S 386 OF 506 +--d0175:= D(m0175,x) +--E 386 + +--S 387 OF 506 +t0176:= x^(-1+n)*acsch(a+b*x^n) +--R +--R +--R n - 1 n +--R (284) x acsch(b x + a) +--R Type: Expression Integer +--E 387 + +--S 388 OF 506 +r0176:= (a+b*x^n)*acsch(a+b*x^n)/b/n+atanh((1+1/(a+b*x^n)^2)^(1/2))/b/n +--R +--R +--R +--------------------------+ +--R | 2 n 2 n 2 +--R |b (x ) + 2a b x + a + 1 n n +--R atanh( |-------------------------- ) + (b x + a)acsch(b x + a) +--R | 2 n 2 n 2 +--R \| b (x ) + 2a b x + a +--R (285) ---------------------------------------------------------------- +--R b n +--R Type: Expression Integer +--E 388 + +--S 389 OF 506 +a0176:= integrate(t0176,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 389 + +--S 390 OF 506 +--m0176:= a0176-r0176 +--E 390 + +--S 391 OF 506 +--d0176:= D(m0176,x) +--E 391 + +--S 392 OF 506 +t0177:= asinh(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (286) asinh(c %e ) +--R Type: Expression Integer +--E 392 + +--S 393 OF 506 +r0177:= 1/2*asinh(c*exp(1)^(a+b*x))^2/b+asinh(c*exp(1)^(a+b*x))*_ + log(1-exp(1)^(-2*asinh(c*exp(1)^(a+b*x))))/b-_ + 1/2*polylog(2,exp(1)^(-2*asinh(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 393 + +--S 394 OF 506 +a0177:= integrate(t0177,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 394 + +--S 395 OF 506 +--m0177:= a0177-r0177 +--E 395 + +--S 396 OF 506 +--d0177:= D(m0177,x) +--E 396 + +--S 397 OF 506 +t0178:= acosh(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (287) acosh(c %e ) +--R Type: Expression Integer +--E 397 + +--S 398 OF 506 +r0178:= 1/2*acosh(c*exp(1)^(a+b*x))^2/b+acosh(c*exp(1)^(a+b*x))*_ + log(1+exp(1)^(-2*acosh(c*exp(1)^(a+b*x))))/b-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 398 + +--S 399 OF 506 +a0178:= integrate(t0178,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 399 + +--S 400 OF 506 +--m0178:= a0178-r0178 +--E 400 + +--S 401 OF 506 +--d0178:= D(m0178,x) +--E 401 + +--S 402 OF 506 +t0179:= asech(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (288) asech(c %e ) +--R Type: Expression Integer +--E 402 + +--S 403 OF 506 +r0179:= -1/2*asech(c*exp(1)^(a+b*x))^2/b-asech(c*exp(1)^(a+b*x))*_ + log(1+exp(1)^(-2*asech(c*exp(1)^(a+b*x))))/b+_ + 1/2*polylog(2,-exp(1)^(-2*asech(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 403 + +--S 404 OF 506 +a0179:= integrate(t0179,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 404 + +--S 405 OF 506 +--m0179:= a0179-r0179 +--E 405 + +--S 406 OF 506 +--d0179:= D(m0179,x) +--E 406 + +--S 407 OF 506 +t0180:= acsch(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (289) acsch(c %e ) +--R Type: Expression Integer +--E 407 + +--S 408 OF 506 +r0180:= -1/2*acsch(c*exp(1)^(a+b*x))^2/b-acsch(c*exp(1)^(a+b*x))*_ + log(1-exp(1)^(-2*acsch(c*exp(1)^(a+b*x))))/b+_ + 1/2*polylog(2,exp(1)^(-2*acsch(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 408 + +--S 409 OF 506 +a0180:= integrate(t0180,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 409 + +--S 410 OF 506 +--m0180:= a0180-r0180 +--E 410 + +--S 411 OF 506 +--d0180:= D(m0180,x) +--E 411 + +--S 412 OF 506 +t0181:= atanh(exp(x)) +--R +--R +--R x +--R (290) atanh(%e ) +--R Type: Expression Integer +--E 412 + +--S 413 OF 506 +r0181:= -1/2*polylog(2,-exp(x))+1/2*polylog(2,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 413 + +--S 414 OF 506 +a0181:= integrate(t0181,x) +--R +--R +--R x +--R ++ %Q +--R (291) | atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 414 + +--S 415 OF 506 +--m0181:= a0181-r0181 +--E 415 + +--S 416 OF 506 +--d0181:= D(m0181,x) +--E 416 + +--S 417 OF 506 +t0182:= x*atanh(exp(x)) +--R +--R +--R x +--R (292) x atanh(%e ) +--R Type: Expression Integer +--E 417 + +--S 418 OF 506 +r0182:= -1/2*x*polylog(2,-exp(x))+1/2*x*polylog(2,exp(x))+_ + 1/2*polylog(3,-exp(x))-1/2*polylog(3,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 418 + +--S 419 OF 506 +a0182:= integrate(t0182,x) +--R +--R +--R x +--R ++ %Q +--R (293) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 419 + +--S 420 OF 506 +--m0182:= a0182-r0182 +--E 420 + +--S 421 OF 506 +--d0182:= D(m0182,x) +--E 421 + +--S 422 OF 506 +t0183:= x^2*atanh(exp(x)) +--R +--R +--R 2 x +--R (294) x atanh(%e ) +--R Type: Expression Integer +--E 422 + +--S 423 OF 506 +r0183:= -1/2*x^2*polylog(2,-exp(x))+1/2*x^2*polylog(2,exp(x))+_ + x*polylog(3,-exp(x))-x*polylog(3,exp(x))-_ + polylog(4,-exp(x))+polylog(4,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 423 + +--S 424 OF 506 +a0183:= integrate(t0183,x) +--R +--R +--R x +--R ++ 2 %Q +--R (295) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 424 + +--S 425 OF 506 +--m0183:= a0183-r0183 +--E 425 + +--S 426 OF 506 +--d0183:= D(m0183,x) +--E 426 + +--S 427 OF 506 +t0184:= atanh(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (296) atanh(%e ) +--R Type: Expression Integer +--E 427 + +--S 428 OF 506 +r0184:= -1/2*(polylog(2,-exp(a+b*x))-polylog(2,exp(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 428 + +--S 429 OF 506 +a0184:= integrate(t0184,x) +--R +--R +--R x +--R ++ %Q b + a +--R (297) | atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 429 + +--S 430 OF 506 +--m0184:= a0184-r0184 +--E 430 + +--S 431 OF 506 +--d0184:= D(m0184,x) +--E 431 + +--S 432 OF 506 +t0185:= x*atanh(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (298) x atanh(%e ) +--R Type: Expression Integer +--E 432 + +--S 433 OF 506 +r0185:= 1/2*(-x*polylog(2,-exp(a+b*x))*b+x*polylog(2,exp(a+b*x))*b+_ + polylog(3,-exp(a+b*x))-polylog(3,exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 433 + +--S 434 OF 506 +a0185:= integrate(t0185,x) +--R +--R +--R x +--R ++ %Q b + a +--R (299) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 434 + +--S 435 OF 506 +--m0185:= a0185-r0185 +--E 435 + +--S 436 OF 506 +--d0185:= D(m0185,x) +--E 436 + +--S 437 OF 506 +t0186:= x^2*atanh(exp(1)^(a+b*x)) +--R +--R +--R 2 b x + a +--R (300) x atanh(%e ) +--R Type: Expression Integer +--E 437 + +--S 438 OF 506 +r0186:= 1/2*(-x^2*polylog(2,-exp(a+b*x))*b^2+_ + x^2*polylog(2,exp(a+b*x))*b^2+_ + 2*x*polylog(3,-exp(a+b*x))*b-_ + 2*x*polylog(3,exp(a+b*x))*b-_ + 2*polylog(4,-exp(a+b*x))+_ + 2*polylog(4,exp(a+b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 438 + +--S 439 OF 506 +a0186:= integrate(t0186,x) +--R +--R +--R x +--R ++ 2 %Q b + a +--R (301) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 439 + +--S 440 OF 506 +--m0186:= a0186-r0186 +--E 440 + +--S 441 OF 506 +--d0186:= D(m0186,x) +--E 441 + +--S 442 OF 506 +t0187:= atanh(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (302) atanh(b f + a) +--R Type: Expression Integer +--E 442 + +--S 443 OF 506 +r0187:= 1/2/d/log(f)*(2*x*atanh(a+b*f^(c+d*x))*d*log(f)+_ + x*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d*log(f)-_ + x*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d*log(f)+_ + polylog(2,-b*f^(c+d*x)/(-1+a))-polylog(2,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 443 + +--S 444 OF 506 +a0187:= integrate(t0187,x) +--R +--R +--R x +--R ++ %Q d + c +--R (303) | atanh(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 444 + +--S 445 OF 506 +--m0187:= a0187-r0187 +--E 445 + +--S 446 OF 506 +--d0187:= D(m0187,x) +--E 446 + +--S 447 OF 506 +t0188:= x*atanh(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (304) x atanh(b f + a) +--R Type: Expression Integer +--E 447 + +--S 448 OF 506 +r0188:= 1/4/d^2/log(f)^2*(2*x^2*atanh(a+b*f^(c+d*x))*d^2*log(f)^2+_ + x^2*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^2*log(f)^2-_ + x^2*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^2*log(f)^2+_ + 2*x*polylog(2,-b*f^(c+d*x)/(-1+a))*d*log(f)-_ + 2*x*polylog(2,-b*f^(c+d*x)/(1+a))*d*log(f)-_ + 2*polylog(3,-b*f^(c+d*x)/(-1+a))+2*polylog(3,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 448 + +--S 449 OF 506 +a0188:= integrate(t0188,x) +--R +--R +--R x +--R ++ %Q d + c +--R (305) | %Q atanh(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 449 + +--S 450 OF 506 +--m0188:= a0188-r0188 +--E 450 + +--S 451 OF 506 +--d0188:= D(m0188,x) +--E 451 + +--S 452 OF 506 +t0189:= x^2*atanh(a+b*f^(c+d*x)) +--R +--R +--R 2 d x + c +--R (306) x atanh(b f + a) +--R Type: Expression Integer +--E 452 + +--S 453 OF 506 +r0189:= 1/6/d^3/log(f)^3*(2*x^3*atanh(a+b*f^(c+d*x))*d^3*log(f)^3+_ + x^3*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^3*log(f)^3-_ + x^3*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^3*log(f)^3+_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(-1+a))*d^2*log(f)^2-_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(1+a))*d^2*log(f)^2-_ + 6*x*polylog(3,-b*f^(c+d*x)/(-1+a))*d*log(f)+_ + 6*x*polylog(3,-b*f^(c+d*x)/(1+a))*d*log(f)+_ + 6*polylog(4,-b*f^(c+d*x)/(-1+a))-6*polylog(4,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 453 + +--S 454 OF 506 +a0189:= integrate(t0189,x) +--R +--R +--R x +--R ++ 2 %Q d + c +--R (307) | %Q atanh(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 454 + +--S 455 OF 506 +--m0189:= a0189-r0189 +--E 455 + +--S 456 OF 506 +--d0189:= D(m0189,x) +--E 456 + +--S 457 OF 506 +t0190:= acoth(exp(x)) +--R +--R +--R x +--R (308) acoth(%e ) +--R Type: Expression Integer +--E 457 + +--S 458 OF 506 +r0190:= 1/2*polylog(2,-exp(-x))-1/2*polylog(2,exp(-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 458 + +--S 459 OF 506 +a0190:= integrate(t0190,x) +--R +--R +--R x +--R ++ %Q +--R (309) | acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 459 + +--S 460 OF 506 +--m0190:= a0190-r0190 +--E 460 + +--S 461 OF 506 +--d0190:= D(m0190,x) +--E 461 + +--S 462 OF 506 +t0191:= x*acoth(exp(x)) +--R +--R +--R x +--R (310) x acoth(%e ) +--R Type: Expression Integer +--E 462 + +--S 463 OF 506 +r0191:= 1/2*x*polylog(2,-exp(-x))-1/2*x*polylog(2,exp(-x))+_ + 1/2*polylog(3,-exp(-x))-1/2*polylog(3,exp(-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 463 + +--S 464 OF 506 +a0191:= integrate(t0191,x) +--R +--R +--R x +--R ++ %Q +--R (311) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 464 + +--S 465 OF 506 +--m0191:= a0191-r0191 +--E 465 + +--S 466 OF 506 +--d0191:= D(m0191,x) +--E 466 + +--S 467 OF 506 +t0192:= x^2*acoth(exp(x)) +--R +--R +--R 2 x +--R (312) x acoth(%e ) +--R Type: Expression Integer +--E 467 + +--S 468 OF 506 +r0192:= 1/2*x^2*polylog(2,-exp(-x))-1/2*x^2*polylog(2,exp(-x))+_ + x*polylog(3,-exp(-x))-x*polylog(3,exp(-x))+_ + polylog(4,-exp(-x))-polylog(4,exp(-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 468 + +--S 469 OF 506 +a0192:= integrate(t0192,x) +--R +--R +--R x +--R ++ 2 %Q +--R (313) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 469 + +--S 470 OF 506 +--m0192:= a0192-r0192 +--E 470 + +--S 471 OF 506 +--d0192:= D(m0192,x) +--E 471 + +--S 472 OF 506 +t0193:= acoth(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (314) acoth(%e ) +--R Type: Expression Integer +--E 472 + +--S 473 OF 506 +r0193:= 1/2*(polylog(2,-exp(-a-b*x))-polylog(2,exp(-a-b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 473 + +--S 474 OF 506 +a0193:= integrate(t0193,x) +--R +--R +--R x +--R ++ %Q b + a +--R (315) | acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 474 + +--S 475 OF 506 +--m0193:= a0193-r0193 +--E 475 + +--S 476 OF 506 +--d0193:= D(m0193,x) +--E 476 + +--S 477 OF 506 +t0194:= x*acoth(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (316) x acoth(%e ) +--R Type: Expression Integer +--E 477 + +--S 478 OF 506 +r0194:= 1/2*(x*polylog(2,-exp(-a-b*x))*b-_ + x*polylog(2,exp(-a-b*x))*b+polylog(3,-exp(-a-b*x))-_ + polylog(3,exp(-a-b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 478 + +--S 479 OF 506 +a0194:= integrate(t0194,x) +--R +--R +--R x +--R ++ %Q b + a +--R (317) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 479 + +--S 480 OF 506 +--m0194:= a0194-r0194 +--E 480 + +--S 481 OF 506 +--d0194:= D(m0194,x) +--E 481 + +--S 482 OF 506 +t0195:= x^2*acoth(exp(1)^(a+b*x)) +--R +--R +--R 2 b x + a +--R (318) x acoth(%e ) +--R Type: Expression Integer +--E 482 + +--S 483 OF 506 +r0195:= 1/2*(x^2*polylog(2,-exp(-a-b*x))*b^2-_ + x^2*polylog(2,exp(-a-b*x))*b^2+_ + 2*x*polylog(3,-exp(-a-b*x))*b-_ + 2*x*polylog(3,exp(-a-b*x))*b+_ + 2*polylog(4,-exp(-a-b*x))-_ + 2*polylog(4,exp(-a-b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 483 + +--S 484 OF 506 +a0195:= integrate(t0195,x) +--R +--R +--R x +--R ++ 2 %Q b + a +--R (319) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 484 + +--S 485 OF 506 +--m0195:= a0195-r0195 +--E 485 + +--S 486 OF 506 +--d0195:= D(m0195,x) +--E 486 + +--S 487 OF 506 +t0196:= acoth(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (320) acoth(b f + a) +--R Type: Expression Integer +--E 487 + +--S 488 OF 506 +r0196:= 1/2/d/log(f)*(2*x*acoth(a+b*f^(c+d*x))*d*log(f)+_ + x*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d*log(f)-_ + x*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d*log(f)+_ + polylog(2,-b*f^(c+d*x)/(-1+a))-polylog(2,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 488 + +--S 489 OF 506 +a0196:= integrate(t0196,x) +--R +--R +--R x +--R ++ %Q d + c +--R (321) | acoth(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 489 + +--S 490 OF 506 +--m0196:= a0196-r0196 +--E 490 + +--S 491 OF 506 +--d0196:= D(m0196,x) +--E 491 + +--S 492 OF 506 +t0197:= x*acoth(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (322) x acoth(b f + a) +--R Type: Expression Integer +--E 492 + +--S 493 OF 506 +r0197:= 1/4/d^2/log(f)^2*(2*x^2*acoth(a+b*f^(c+d*x))*d^2*log(f)^2+_ + x^2*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^2*log(f)^2-_ + x^2*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^2*log(f)^2+_ + 2*x*polylog(2,-b*f^(c+d*x)/(-1+a))*d*log(f)-_ + 2*x*polylog(2,-b*f^(c+d*x)/(1+a))*d*log(f)-_ + 2*polylog(3,-b*f^(c+d*x)/(-1+a))+2*polylog(3,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 493 + +--S 494 OF 506 +a0197:= integrate(t0197,x) +--R +--R +--R x +--R ++ %Q d + c +--R (323) | %Q acoth(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 494 + +--S 495 OF 506 +--m0197:= a0197-r0197 +--E 495 + +--S 496 OF 506 +--d0197:= D(m0197,x) +--E 496 + +--S 497 OF 506 +t0198:= x^2*acoth(a+b*f^(c+d*x)) +--R +--R +--R 2 d x + c +--R (324) x acoth(b f + a) +--R Type: Expression Integer +--E 497 + +--S 498 OF 506 +r0198:= 1/6/d^3/log(f)^3*(2*x^3*acoth(a+b*f^(c+d*x))*d^3*log(f)^3+_ + x^3*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^3*log(f)^3-_ + x^3*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^3*log(f)^3+_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(-1+a))*d^2*log(f)^2-_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(1+a))*d^2*log(f)^2-_ + 6*x*polylog(3,-b*f^(c+d*x)/(-1+a))*d*log(f)+_ + 6*x*polylog(3,-b*f^(c+d*x)/(1+a))*d*log(f)+_ + 6*polylog(4,-b*f^(c+d*x)/(-1+a))-6*polylog(4,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 498 + +--S 499 OF 506 +a0198:= integrate(t0198,x) +--R +--R +--R x +--R ++ 2 %Q d + c +--R (325) | %Q acoth(b f + a)d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 499 + +--S 500 OF 506 +--m0198:= a0198-r0198 +--E 500 + +--S 501 OF 506 +--d0198:= D(m0198,x) +--E 501 + +--S 502 OF 506 +t0199:= atanh(cosh(x)) +--R +--R +--R (326) atanh(cosh(x)) +--R Type: Expression Integer +--E 502 + +--S 503 OF 506 +r0199:= -2*x*atanh(exp(x))+x*atanh(cosh(x))-_ + polylog(2,-exp(x))+polylog(2,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 503 + +--S 504 OF 506 +a0199:= integrate(t0199,x) +--R +--R +--R x +--R ++ +--R (327) | atanh(cosh(%Q))d%Q +--R ++ +--R Type: Union(Expression Integer,...) +--E 504 + +--S 505 OF 506 +--m0199:= a0199-r0199 +--E 505 + +--S 506 OF 506 +--d0199:= D(m0199,x) +--E 506 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper100-199,input.pdf b/src/axiom-website/CATS/richhyper100-199,input.pdf new file mode 100644 index 0000000..624d8c9 Binary files /dev/null and b/src/axiom-website/CATS/richhyper100-199,input.pdf differ diff --git a/src/axiom-website/CATS/richhyper100-199.input.pamphlet b/src/axiom-website/CATS/richhyper100-199.input.pamphlet new file mode 100644 index 0000000..7c6cfcd --- /dev/null +++ b/src/axiom-website/CATS/richhyper100-199.input.pamphlet @@ -0,0 +1,23816 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper100-199.output +)spool richhyper100-199.output +)set message auto off +)clear all + +--S 1 of 510 +t0100:= x^2*sinh(a+b*x+c*x^2)^2 +--R +--R +--R 2 2 2 +--R (1) x sinh(c x + b x + a) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 510 +r0100:= -1/6*x^3+1/64*(b^2+c)*exp(1)^(-2*a+1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erf(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)+_ + 1/64*(-c+b^2)*exp(1)^(2*a-1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)-_ + 1/16*b*sinh(2*a+2*b*x+2*c*x^2)/c^2+1/8*x*sinh(2*a+2*b*x+2*c*x^2)/c +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R AlgebraicNumber +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 510 +a0100:= integrate(t0100,x) +--R +--R +--R x +--R ++ 2 2 2 +--R (2) | %I sinh(%I c + %I b + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 510 +--m0100:= a0100-r0100 +--E 4 + +--S 5 of 510 +--d0100:= D(m0100,x) +--E 5 + +--S 6 of 510 +t0101:= x^2*sinh(a+b*x-c*x^2)^2 +--R +--R +--R 2 2 2 +--R (3) x sinh(c x - b x - a) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 510 +r0101:= -1/6*x^3-1/64*(b^2+c)*exp(1)^(2*a+1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erf(1/2*(b-2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)-_ + 1/64*(-c+b^2)*exp(1)^(-2*a-1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erfi(1/2*(b-2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)-_ + 1/16*b*sinh(2*a+2*b*x-2*c*x^2)/c^2-1/8*x*sinh(2*a+2*b*x-2*c*x^2)/c +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R AlgebraicNumber +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 510 +a0101:= integrate(t0101,x) +--R +--R +--R x +--R ++ 2 2 2 +--R (4) | %I sinh(%I c - %I b - a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 510 +--m0101:= a0101-r0101 +--E 9 + +--S 10 of 510 +--d0101:= D(m0101,x) +--E 10 + +--S 11 of 510 +t0102:= x^2*sinh(1/4+x+x^2)^2 +--R +--R +--R 2 2 +--R 2 4x + 4x + 1 +--R (5) x sinh(------------) +--R 4 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 510 +r0102:= -1/6*x^3+1/32*2^(1/2)*%pi^(1/2)*erf(1/2*(1+2*x)*2^(1/2))-_ + 1/16*sinh(1/2+2*x+2*x^2)+1/8*x*sinh(1/2+2*x+2*x^2) +--R +--R There are 1 exposed and 1 unexposed library operations named erf +--R having 1 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op erf +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named erf +--R with argument type(s) +--R UnivariatePolynomial(x,AlgebraicNumber) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 510 +a0102:= integrate(t0102,x) +--R +--R +--R x 2 2 +--R ++ 2 4%I + 4%I + 1 +--R (6) | %I sinh(--------------) d%I +--R ++ 4 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 510 +--m0102:= a0102-r0102 +--E 14 + +--S 15 of 510 +--d0102:= D(m0102,x) +--E 15 + +--S 16 of 510 +t0103:= (d+e*x)^2*sinh(a+b*x+c*x^2) +--R +--R +--R 2 2 2 2 +--R (7) (e x + 2d e x + d )sinh(c x + b x + a) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 510 +r0103:= 1/4*e*(4*c*d-b*e)*cosh(a+b*x+c*x^2)/c^2+1/2*e^2*x*_ + cosh(a+b*x+c*x^2)/c-1/16*(4*c^2*d^2-2*c*(2*b*d-e)*e+b^2*e^2)*_ + exp(1)^(-a+1/4*b^2/c)*%pi^(1/2)*erf(1/2*(b+2*c*x)/c^(1/2))/c^(5/2)+_ + 1/16*(4*c^2*d^2+b^2*e^2-2*c*e*(2*b*d+e))*_ + exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)/c^(1/2))/c^(5/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 510 +a0103:= integrate(t0103,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--R (8) | (%I e + 2%I d e + d )sinh(%I c + %I b + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 510 +--m0103:= a0103-r0103 +--E 19 + +--S 20 of 510 +--d0103:= D(m0103,x) +--E 20 + +--S 21 of 510 +t0104:= (d+e*x)*sinh(a+b*x+c*x^2) +--R +--R +--R 2 +--R (9) (e x + d)sinh(c x + b x + a) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 510 +r0104:= 1/2*e*cosh(a+b*x+c*x^2)/c-1/8*(2*c*d-b*e)*_ + exp(1)^(-a+1/4*b^2/c)*%pi^(1/2)*erf(1/2*(b+2*c*x)/c^(1/2))/c^(3/2)+_ + 1/8*(2*c*d-b*e)*exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)/c^(1/2))/c^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 510 +a0104:= integrate(t0104,x) +--R +--R +--R x +--R ++ 2 +--R (10) | (%I e + d)sinh(%I c + %I b + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 510 +--m0104:= a0104-r0104 +--E 24 + +--S 25 of 510 +--d0104:= D(m0104,x) +--E 25 + +--S 26 of 510 +t0105:= (d+e*x)^2*sinh(a+b*x+c*x^2)^2 +--R +--R +--R 2 2 2 2 2 +--R (11) (e x + 2d e x + d )sinh(c x + b x + a) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 510 +r0105:= -1/2*d^2*x-1/2*d*e*x^2-1/6*e^2*x^3+1/64*(4*c^2*d^2-c*(4*b*d-e)*e+_ + b^2*e^2)*exp(1)^(-2*a+1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erf(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)+_ + 1/64*(4*c^2*d^2+b^2*e^2-c*e*(4*b*d+e))*_ + exp(1)^(2*a-1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)+1/4*d*e*_ + sinh(2*a+2*b*x+2*c*x^2)/c-1/16*b*e^2*sinh(2*a+2*b*x+2*c*x^2)/c^2+_ + 1/8*e^2*x*sinh(2*a+2*b*x+2*c*x^2)/c +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R AlgebraicNumber +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 510 +a0105:= integrate(t0105,x) +--R +--R +--R x +--R ++ 2 2 2 2 2 +--R (12) | (%I e + 2%I d e + d )sinh(%I c + %I b + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 510 +--m0105:= a0105-r0105 +--E 29 + +--S 30 of 510 +--d0105:= D(m0105,x) +--E 30 + +--S 31 of 510 +t0106:= (d+e*x)*sinh(a+b*x+c*x^2)^2 +--R +--R +--R 2 2 +--R (13) (e x + d)sinh(c x + b x + a) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 510 +r0106:= -1/2*d*x-1/4*e*x^2+1/32*(2*c*d-b*e)*exp(1)^(-2*a+1/2*b^2/c)*_ + 2^(1/2)*%pi^(1/2)*erf(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(3/2)+_ + 1/32*(2*c*d-b*e)*exp(1)^(2*a-1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(3/2)+1/8*e*_ + sinh(2*a+2*b*x+2*c*x^2)/c +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R AlgebraicNumber +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 510 +a0106:= integrate(t0106,x) +--R +--R +--R x +--R ++ 2 2 +--R (14) | (%I e + d)sinh(%I c + %I b + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 510 +--m0106:= a0106-r0106 +--E 34 + +--S 35 of 510 +--d0106:= D(m0106,x) +--E 35 + +--S 36 of 510 +t0107:= sinh((a+b*x)/(c+d*x)) +--R +--R +--R b x + a +--R (15) sinh(-------) +--R d x + c +--R Type: Expression(Integer) +--E 36 + +--S 37 of 510 +r0107:= (b*c-a*d)*cosh(b/d)*Chi(-(b*c-a*d)/d/(c+d*x))/d^2+_ + (c+d*x)*sinh((a+b*x)/(c+d*x))/d+(b*c-a*d)*_ + sinh(b/d)*Shi(a/(c+d*x)-b*c/d/(c+d*x))/d^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 510 +a0107:= integrate(t0107,x) +--R +--R +--R x +--R ++ %I b + a +--R (16) | sinh(--------)d%I +--R ++ %I d + c +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 510 +--m0107:= a0107-r0107 +--E 39 + +--S 40 of 510 +--d0107:= D(m0107,x) +--E 40 + +--S 41 of 510 +t0108:= sinh((a+b*x)/(c+d*x))^2 +--R +--R +--R b x + a 2 +--R (17) sinh(-------) +--R d x + c +--R Type: Expression(Integer) +--E 41 + +--S 42 of 510 +r0108:= -1/2*x+1/2*(c+d*x)*cosh(2*(a+b*x)/(c+d*x))/d+(b*c-a*d)*_ + Chi(-2*(b*c-a*d)/d/(c+d*x))*sinh(2*b/d)/d^2+_ + (b*c-a*d)*cosh(2*b/d)*Shi(2*a/(c+d*x)-2*b*c/d/(c+d*x))/d^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 of 510 +a0108:= integrate(t0108,x) +--R +--R +--R x +--R ++ %I b + a 2 +--R (18) | sinh(--------) d%I +--R ++ %I d + c +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 510 +--m0108:= a0108-r0108 +--E 44 + +--S 45 of 510 +--d0108:= D(m0108,x) +--E 45 + +--S 46 of 510 +t0109:= x^2*sinh(a+b*x^2) +--R +--R +--R 2 2 +--R (19) x sinh(b x + a) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 510 +r0109:= 1/8*(4*x*cosh(a+b*x^2)*exp(a)*b^(1/2)-%pi^(1/2)*erf(b^(1/2)*x)+_ + %i*exp(2*a)*%pi^(1/2)*erf(%i*b^(1/2)*x))*exp(-a)/b^(3/2) +--R +--R +--R (20) +--R - a +---+ +-+ - a 2a +---+ +-+ +--R - %e \|%pi erf(x\|b ) + %i %e %e \|%pi erf(%i x\|b ) +--R + +--R 2 - a a +-+ +--R 4x cosh(b x + a)%e %e \|b +--R / +--R +-+ +--R 8b\|b +--R Type: Expression(Complex(Integer)) +--E 47 + +--S 48 of 510 +a0109:= integrate(t0109,x) +--R +--R +--R x +--R ++ 2 2 +--R (21) | %I sinh(%I b + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 510 +--m0109:= a0109-r0109 +--E 49 + +--S 50 of 510 +--d0109:= D(m0109,x) +--E 50 + +--S 51 of 510 +t0110:= sinh(a+b*x^2) +--R +--R +--R 2 +--R (22) sinh(b x + a) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 510 +r0110:= -1/4*%pi^(1/2)*(erf(b^(1/2)*x)+%i*exp(2*a)*_ + erf(%i*b^(1/2)*x))*exp(-a)/b^(1/2) +--R +--R +--R - a +---+ +-+ - a 2a +---+ +-+ +--R - %e \|%pi erf(x\|b ) - %i %e %e \|%pi erf(%i x\|b ) +--R (23) --------------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Complex(Integer)) +--E 52 + +--S 53 of 510 +a0110:= integrate(t0110,x) +--R +--R +--R x +--R ++ 2 +--R (24) | sinh(%I b + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 510 +--m0110:= a0110-r0110 +--E 54 + +--S 55 of 510 +--d0110:= D(m0110,x) +--E 55 + +--S 56 of 510 +t0111:= sinh(a+b*x^2)/x^2 +--R +--R +--R 2 +--R sinh(b x + a) +--R (25) -------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 510 +r0111:= 1/2*b^(1/2)*%pi^(1/2)*erf(b^(1/2)*x)/(exp(1)^a)+_ + 1/2*b^(1/2)*exp(1)^a*%pi^(1/2)*erfi(b^(1/2)*x)-sinh(a+b*x^2)/x +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 510 +a0111:= integrate(t0111,x) +--R +--R +--R x 2 +--R ++ sinh(%I b + a) +--R (26) | -------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 510 +--m0111:= a0111-r0111 +--E 59 + +--S 60 of 510 +--d0111:= D(m0111,x) +--E 60 + +--S 61 of 510 +t0112:= sinh(a+b*x^2)/x^3 +--R +--R +--R 2 +--R sinh(b x + a) +--R (27) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 510 +r0112:= 1/2*b*cosh(a)*Chi(b*x^2)-1/2*sinh(a+b*x^2)/x^2+_ + 1/2*b*sinh(a)*Shi(b*x^2) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 510 +a0112:= integrate(t0112,x) +--R +--R +--R x 2 +--R ++ sinh(%I b + a) +--R (28) | -------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 510 +--m0112:= a0112-r0112 +--E 64 + +--S 65 of 510 +--d0112:= D(m0112,x) +--E 65 + +--S 66 of 510 +t0113:= sinh(a+b*x^2)^2/x^3 +--R +--R +--R 2 2 +--R sinh(b x + a) +--R (29) --------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 510 +r0113:= -1/4*(-1+cosh(2*a+2*b*x^2)-2*b*Chi(2*b*x^2)*sinh(2*a)*x^2-_ + 2*b*cosh(2*a)*Shi(2*b*x^2)*x^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 of 510 +a0113:= integrate(t0113,x) +--R +--R +--R x 2 2 +--R ++ sinh(%I b + a) +--R (30) | --------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 510 +--m0113:= a0113-r0113 +--E 69 + +--S 70 of 510 +--d0113:= D(m0113,x) +--E 70 + +--S 71 of 510 +t0114:= x^2*sinh(a+b*x^2)^3 +--R +--R +--R 2 2 3 +--R (31) x sinh(b x + a) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 510 +r0114:= 1/288*exp(-3*a)*(-108*x*cosh(a+b*x^2)*exp(3*a)*b^(1/2)+_ + 12*x*cosh(3*a+3*b*x^2)*exp(3*a)*b^(1/2)+27*%pi^(1/2)*_ + erf(b^(1/2)*x)*exp(2*a)-3^(1/2)*%pi^(1/2)*erf(3^(1/2)*b^(1/2)*x)-_ + 27*%i*exp(4*a)*%pi^(1/2)*erf(%i*b^(1/2)*x)+_ + %i*exp(6*a)*3^(1/2)*%pi^(1/2)*erf(%i*3^(1/2)*b^(1/2)*x))/b^(3/2) +--R +--R +--R (32) +--R +-+ - 3a +---+ +-+ +-+ +--R - \|3 %e \|%pi erf(x\|3 \|b ) +--R + +--R +-+ - 3a 6a +---+ +-+ +-+ - 3a 2a +---+ +-+ +--R %i\|3 %e %e \|%pi erf(%i x\|3 \|b ) + 27%e %e \|%pi erf(x\|b ) +--R + +--R - 3a 4a +---+ +-+ +--R - 27%i %e %e \|%pi erf(%i x\|b ) +--R + +--R 2 2 - 3a 3a +-+ +--R (12x cosh(3b x + 3a) - 108x cosh(b x + a))%e %e \|b +--R / +--R +-+ +--R 288b\|b +--R Type: Expression(Complex(Integer)) +--E 72 + +--S 73 of 510 +a0114:= integrate(t0114,x) +--R +--R +--R x +--R ++ 2 2 3 +--R (33) | %I sinh(%I b + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 510 +--m0114:= a0114-r0114 +--E 74 + +--S 75 of 510 +--d0114:= D(m0114,x) +--E 75 + +--S 76 of 510 +t0115:= sinh(a+b*x^2)^3 +--R +--R +--R 2 3 +--R (34) sinh(b x + a) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 510 +r0115:= 1/48*%pi^(1/2)*exp(-3*a)*(9*erf(b^(1/2)*x)*exp(2*a)-_ + 3^(1/2)*erf(3^(1/2)*b^(1/2)*x)+9*%i*exp(4*a)*erf(%i*b^(1/2)*x)-_ + %i*exp(6*a)*3^(1/2)*erf(%i*3^(1/2)*b^(1/2)*x))/b^(1/2) +--R +--R +--R (35) +--R +-+ - 3a +---+ +-+ +-+ +--R - \|3 %e \|%pi erf(x\|3 \|b ) +--R + +--R +-+ - 3a 6a +---+ +-+ +-+ - 3a 2a +---+ +-+ +--R - %i\|3 %e %e \|%pi erf(%i x\|3 \|b ) + 9%e %e \|%pi erf(x\|b ) +--R + +--R - 3a 4a +---+ +-+ +--R 9%i %e %e \|%pi erf(%i x\|b ) +--R / +--R +-+ +--R 48\|b +--R Type: Expression(Complex(Integer)) +--E 77 + +--S 78 of 510 +a0115:= integrate(t0115,x) +--R +--R +--R x +--R ++ 2 3 +--R (36) | sinh(%I b + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 510 +--m0115:= a0115-r0115 +--E 79 + +--S 80 of 510 +--d0115:= D(m0115,x) +--E 80 + +--S 81 of 510 +t0116:= sinh(a+b*x^2)^3/x^3 +--R +--R +--R 2 3 +--R sinh(b x + a) +--R (37) --------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 81 + +--S 82 of 510 +r0116:= -3/8*b*cosh(a)*Chi(b*x^2)+3/8*b*cosh(3*a)*Chi(3*b*x^2)+_ + 3/8*sinh(a+b*x^2)/x^2-1/8*sinh(3*a+3*b*x^2)/x^2-_ + 3/8*b*sinh(a)*Shi(b*x^2)+3/8*b*sinh(3*a)*Shi(3*b*x^2) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 510 +a0116:= integrate(t0116,x) +--R +--R +--R x 2 3 +--R ++ sinh(%I b + a) +--R (38) | --------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 510 +--m0116:= a0116-r0116 +--E 84 + +--S 85 of 510 +--d0116:= D(m0116,x) +--E 85 + +--S 86 of 510 +t0117:= sinh(a+b*x^n) +--R +--R +--R n +--R (39) sinh(b x + a) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 510 +r0117:= 1/2*x*(-exp(a)*Gamma(1/n,-b*x^n)*(-b*x^n)^(-1/n)+_ + Gamma(1/n,b*x^n)*exp(-a)*(b*x^n)^(-1/n))/n +--R +--R +--R 1 1 +--R - - - - +--R - a n n _ 1 n a n n _ 1 n +--R x %e (b x ) | (-,b x ) - x %e (- b x ) | (-,- b x ) +--R n n +--R (40) --------------------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 87 + +--S 88 of 510 +a0117:= integrate(t0117,x) +--R +--R +--R x +--R ++ n +--R (41) | sinh(b %I + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 510 +--m0117:= a0117-r0117 +--E 89 + +--S 90 of 510 +--d0117:= D(m0117,x) +--E 90 + +--S 91 of 510 +t0118:= sinh(a+b*x^n)^2 +--R +--R +--R n 2 +--R (42) sinh(b x + a) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 510 +r0118:= -1/2*x*(2^(-(1+n)/n)*exp(2*a)*(-b*x^n)^(-1/n)*_ + Gamma(1/n,-2*b*x^n)+2^(-(1+n)/n)*exp(-2*a)*(b*x^n)^(-1/n)*_ + Gamma(1/n,2*b*x^n)+n)/n +--R +--R +--R (43) +--R - n - 1 1 +--R ------- - - +--R - 2a n n n _ 1 n +--R - x %e 2 (b x ) | (-,2b x ) +--R n +--R + +--R - n - 1 1 +--R ------- - - +--R 2a n n n _ 1 n +--R - x %e 2 (- b x ) | (-,- 2b x ) - n x +--R n +--R / +--R 2n +--R Type: Expression(Integer) +--E 92 + +--S 93 of 510 +a0118:= integrate(t0118,x) +--R +--R +--R x +--R ++ n 2 +--R (44) | sinh(b %I + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 510 +--m0118:= a0118-r0118 +--E 94 + +--S 95 of 510 +--d0118:= D(m0118,x) +--E 95 + +--S 96 of 510 +t0119:= sinh(a+b*x^n)^3 +--R +--R +--R n 3 +--R (45) sinh(b x + a) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 510 +r0119:= -1/8*x*(exp(3*a)*Gamma(1/n,-3*b*x^n)*3^(-1/n)*(-b*x^n)^(-1/n)-_ + 3*exp(a)*Gamma(1/n,-b*x^n)*(-b*x^n)^(-1/n)+_ + 3*Gamma(1/n,b*x^n)*exp(-a)*(b*x^n)^(-1/n)-_ + Gamma(1/n,3*b*x^n)*3^(-1/n)*exp(-3*a)*(b*x^n)^(-1/n))/n +--R +--R +--R (46) +--R 1 1 1 +--R - - - - - - +--R - 3a n n n _ 1 n - a n n _ 1 n +--R x %e 3 (b x ) | (-,3b x ) - 3x %e (b x ) | (-,b x ) +--R n n +--R + +--R 1 1 1 +--R - - - - - - +--R a n n _ 1 n 3a n n n _ 1 n +--R 3x %e (- b x ) | (-,- b x ) - x %e 3 (- b x ) | (-,- 3b x ) +--R n n +--R / +--R 8n +--R Type: Expression(Integer) +--E 97 + +--S 98 of 510 +a0119:= integrate(t0119,x) +--R +--R +--R x +--R ++ n 3 +--R (47) | sinh(b %I + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 510 +--m0119:= a0119-r0119 +--E 99 + +--S 100 of 510 +--d0119:= D(m0119,x) +--E 100 + +--S 101 of 510 +t0120:= x^m*sinh(a+b*x^n) +--R +--R +--R m n +--R (48) x sinh(b x + a) +--R Type: Expression(Integer) +--E 101 + +--S 102 of 510 +r0120:= -1/2*x*x^m*(exp(a)*Gamma((1+m)/n,-b*x^n)*(-b*x^n)^(-(1+m)/n)-_ + Gamma((1+m)/n,b*x^n)*exp(-a)*(b*x^n)^(-(1+m)/n))/n +--R +--R +--R (49) +--R - m - 1 - m - 1 +--R ------- ------- +--R - a m n n _ m + 1 n a m n n _ m + 1 n +--R x %e x (b x ) | (-----,b x ) - x %e x (- b x ) | (-----,- b x ) +--R n n +--R ----------------------------------------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 102 + +--S 103 of 510 +a0120:= integrate(t0120,x) +--R +--R +--R x +--R ++ m n +--R (50) | %I sinh(b %I + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 510 +--m0120:= a0120-r0120 +--E 104 + +--S 105 of 510 +--d0120:= D(m0120,x) +--E 105 + +--S 106 of 510 +t0121:= x^m*sinh(a+b*x^n)^2 +--R +--R +--R m n 2 +--R (51) x sinh(b x + a) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 510 +r0121:= -x^(1+m)/(2+2*m)-2^(-2-(1+m)/n)*exp(1)^(2*a)*x^(1+m)*_ + Gamma((1+m)/n,-2*b*x^n)/((-b*x^n)^((1+m)/n))/n-_ + 2^(-2-(1+m)/n)*x^(1+m)*_ + Gamma((1+m)/n,2*b*x^n)/(exp(1)^(2*a))/((b*x^n)^((1+m)/n))/n +--R +--R +--R (52) +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R n m + 1 n n _ m + 1 n +--R (- 2m - 2)2 x (- b x ) | (-----,2b x ) +--R n +--R + +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R 2a 2 n m + 1 n n _ m + 1 n +--R (- 2m - 2)(%e ) 2 x (b x ) | (-----,- 2b x ) +--R n +--R + +--R m + 1 m + 1 +--R ----- ----- +--R 2a m + 1 n n n n +--R - n %e x (- b x ) (b x ) +--R / +--R m + 1 m + 1 +--R ----- ----- +--R 2a n n n n +--R (2m + 2)n %e (- b x ) (b x ) +--R Type: Expression(Integer) +--E 107 + +--S 108 of 510 +a0121:= integrate(t0121,x) +--R +--R +--R x +--R ++ m n 2 +--R (53) | %I sinh(b %I + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 510 +--m0121:= a0121-r0121 +--E 109 + +--S 110 of 510 +--d0121:= D(m0121,x) +--E 110 + +--S 111 of 510 +t0122:= x^m*sinh(a+b*x^n)^3 +--R +--R +--R m n 3 +--R (54) x sinh(b x + a) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 510 +r0122:= 1/8*x*x^m*(-exp(3*a)*_ + Gamma((1+m)/n,-3*b*x^n)*3^(-(1+m)/n)*(-b*x^n)^(-(1+m)/n)+3*exp(a)*_ + Gamma((1+m)/n,-b*x^n)*(-b*x^n)^(-(1+m)/n)-3*_ + Gamma((1+m)/n,b*x^n)*exp(-a)*(b*x^n)^(-(1+m)/n)+_ + Gamma((1+m)/n,3*b*x^n)*3^(-(1+m)/n)*exp(-3*a)*(b*x^n)^(-(1+m)/n))/n +--R +--R +--R (55) +--R - m - 1 - m - 1 +--R ------- ------- +--R - 3a n m n n _ m + 1 n +--R x %e 3 x (b x ) | (-----,3b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R - a m n n _ m + 1 n +--R - 3x %e x (b x ) | (-----,b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R a m n n _ m + 1 n +--R 3x %e x (- b x ) | (-----,- b x ) +--R n +--R + +--R - m - 1 - m - 1 +--R ------- ------- +--R 3a n m n n _ m + 1 n +--R - x %e 3 x (- b x ) | (-----,- 3b x ) +--R n +--R / +--R 8n +--R Type: Expression(Integer) +--E 112 + +--S 113 of 510 +a0122:= integrate(t0122,x) +--R +--R +--R x +--R ++ m n 3 +--R (56) | %I sinh(b %I + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 510 +--m0122:= a0122-r0122 +--E 114 + +--S 115 of 510 +--d0122:= D(m0122,x) +--E 115 + +--S 116 of 510 +t0123:= sinh(a+b/x) +--R +--R +--R a x + b +--R (57) sinh(-------) +--R x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 510 +r0123:= -b*cosh(a)*Chi(b/x)+x*sinh(a+b/x)-b*sinh(a)*Shi(b/x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 510 +a0123:= integrate(t0123,x) +--R +--R +--R x +--R ++ b + %I a +--R (58) | sinh(--------)d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 510 +--m0123:= a0123-r0123 +--E 119 + +--S 120 of 510 +--d0123:= D(m0123,x) +--E 120 + +--S 121 of 510 +t0124:= sinh(a+b/x)/x +--R +--R +--R a x + b +--R sinh(-------) +--R x +--R (59) ------------- +--R x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 510 +r0124:= -Chi(b/x)*sinh(a)-cosh(a)*Shi(b/x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 510 +a0124:= integrate(t0124,x) +--R +--R +--R b + %I a +--R x sinh(--------) +--R ++ %I +--R (60) | -------------- d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 510 +--m0124:= a0124-r0124 +--E 124 + +--S 125 of 510 +--d0124:= D(m0124,x) +--E 125 + +--S 126 of 510 +t0125:= sinh(a+b/x^2)/x^4 +--R +--R +--R 2 +--R a x + b +--R sinh(--------) +--R 2 +--R x +--R (61) -------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 510 +r0125:= -1/2*cosh(a+b/x^2)/b/x+1/8*%pi^(1/2)*_ + erf(b^(1/2)/x)/(exp(1)^a)/b^(3/2)+1/8*_ + exp(1)^a*%pi^(1/2)*erfi(b^(1/2)/x)/b^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 510 +a0125:= integrate(t0125,x) +--R +--R +--R 2 +--R b + %I a +--R sinh(--------) +--R x 2 +--R ++ %I +--R (62) | -------------- d%I +--R ++ 4 +--R %I +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 510 +--m0125:= a0125-r0125 +--E 129 + +--S 130 of 510 +--d0125:= D(m0125,x) +--E 130 + +--S 131 of 510 +t0126:= x/sinh(x)^(3/2)-x*sinh(x)^(1/2) +--R +--R +--R 2 +--R - x sinh(x) + x +--R (63) ----------------- +--R +-------+ +--R sinh(x)\|sinh(x) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 510 +r0126:= -2*(x*cosh(x)-2*sinh(x))/sinh(x)^(1/2) +--R +--R +--R 4sinh(x) - 2x cosh(x) +--R (64) --------------------- +--R +-------+ +--R \|sinh(x) +--R Type: Expression(Integer) +--E 132 + +--S 133 of 510 +a0126:= integrate(t0126,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 133 + +--S 134 of 510 +--m0126:= a0126-r0126 +--E 134 + +--S 135 of 510 +--d0126:= D(m0126,x) +--E 135 + +--S 136 of 510 +t0127:= x/sinh(x)^(5/2)+1/3*x/sinh(x)^(1/2) +--R +--R +--R 2 +--R x sinh(x) + 3x +--R (65) ------------------- +--R 2 +-------+ +--R 3sinh(x) \|sinh(x) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 510 +r0127:= -2/3*(x*cosh(x)+2*sinh(x))/sinh(x)^(3/2) +--R +--R +--R - 4sinh(x) - 2x cosh(x) +--R (66) ----------------------- +--R +-------+ +--R 3sinh(x)\|sinh(x) +--R Type: Expression(Integer) +--E 137 + +--S 138 of 510 +a0127:= integrate(t0127,x) +--R +--R +--R (67) +--R 3 2 +--R (- 4x - 8)sinh(x) + (- 12x - 24)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((- 12x - 24)cosh(x) - 4x + 8)sinh(x) + (- 4x - 8)cosh(x) +--R + +--R (- 4x + 8)cosh(x) +--R * +--R +-------+ +--R \|sinh(x) +--R / +--R 4 3 2 2 +--R 3sinh(x) + 12cosh(x)sinh(x) + (18cosh(x) - 6)sinh(x) +--R + +--R 3 4 2 +--R (12cosh(x) - 12cosh(x))sinh(x) + 3cosh(x) - 6cosh(x) + 3 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 510 +m0127:= a0127-r0127 +--R +--R +--R (68) +--R 5 4 +--R (- 4x - 4)sinh(x) + (- 10x - 8)cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 4x cosh(x) - 4x)sinh(x) +--R + +--R 3 2 +--R ((8x + 8)cosh(x) + (- 8x - 8)cosh(x))sinh(x) +--R + +--R 4 2 5 +--R ((8x + 4)cosh(x) + (- 8x - 8)cosh(x) + 4)sinh(x) + 2x cosh(x) +--R + +--R 3 +--R - 4x cosh(x) + 2x cosh(x) +--R / +--R 5 4 2 3 +--R 3sinh(x) + 12cosh(x)sinh(x) + (18cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 2 +--R (12cosh(x) - 12cosh(x))sinh(x) + (3cosh(x) - 6cosh(x) + 3)sinh(x) +--R * +--R +-------+ +--R \|sinh(x) +--R Type: Expression(Integer) +--E 139 + +--S 140 of 510 +d0127:= D(m0127,x) +--R +--R +--R (69) +--R 8 7 +--R (6x + 4)sinh(x) + (30x + 16)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((57x + 20)cosh(x) + 18x)sinh(x) +--R + +--R 3 5 +--R (42x cosh(x) + (48x + 8)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R ((- 15x - 20)cosh(x) + (45x + 24)cosh(x) + 10x - 4)sinh(x) +--R + +--R 5 3 3 +--R ((- 54x - 16)cosh(x) + (36x + 24)cosh(x) + (18x - 8)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R ((- 45x - 4)cosh(x) + (48x + 8)cosh(x) + (- x - 4)cosh(x) - 2x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 8 +--R (- 18x cosh(x) + 36x cosh(x) - 18x cosh(x) )sinh(x) - 3x cosh(x) +--R + +--R 6 4 2 +--R 9x cosh(x) - 9x cosh(x) + 3x cosh(x) +--R / +--R 8 7 2 6 +--R 3sinh(x) + 18cosh(x)sinh(x) + (45cosh(x) - 9)sinh(x) +--R + +--R 3 5 +--R (60cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (45cosh(x) - 54cosh(x) + 9)sinh(x) +--R + +--R 5 3 3 +--R (18cosh(x) - 36cosh(x) + 18cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (3cosh(x) - 9cosh(x) + 9cosh(x) - 3)sinh(x) +--R * +--R +-------+ +--R \|sinh(x) +--R Type: Expression(Integer) +--E 140 + +--S 141 of 510 +t0128:= x/sinh(x)^(7/2)+3/5*x*sinh(x)^(1/2) +--R +--R +--R 4 +--R 3x sinh(x) + 5x +--R (70) ------------------- +--R 3 +-------+ +--R 5sinh(x) \|sinh(x) +--R Type: Expression(Integer) +--E 141 + +--S 142 of 510 +r0128:= 2/15*(16*sinh(x)-18*sinh(x)*cosh(x)^2-_ + 12*x*cosh(x)+9*x*cosh(x)^3)/sinh(x)^(5/2) +--R +--R +--R 2 3 +--R (- 36cosh(x) + 32)sinh(x) + 18x cosh(x) - 24x cosh(x) +--R (71) ------------------------------------------------------- +--R 2 +-------+ +--R 15sinh(x) \|sinh(x) +--R Type: Expression(Integer) +--E 142 + +--S 143 of 510 +a0128:= integrate(t0128,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 143 + +--S 144 of 510 +--m0128:= a0128-r0128 +--E 144 + +--S 145 of 510 +--d0128:= D(m0128,x) +--E 145 + +--S 146 of 510 +t0129:= x^2/sinh(x)^(3/2)-x^2*sinh(x)^(1/2) +--R +--R +--R 2 2 2 +--R - x sinh(x) + x +--R (72) ----------------- +--R +-------+ +--R sinh(x)\|sinh(x) +--R Type: Expression(Integer) +--E 146 + +--S 147 of 510 +r0129:= -2*x^2*cosh(x)/sinh(x)^(1/2)+8*x*sinh(x)^(1/2)+_ + 16*%i*EllipticE(-1/4*%pi+1/2*%i*x,2)*sinh(x)^(1/2)/(%i*sinh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 510 +a0129:= integrate(t0129,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 148 + +--S 149 of 510 +--m0129:= a0129-r0129 +--E 149 + +--S 150 of 510 +--d0129:= D(m0129,x) +--E 150 + +--S 151 of 510 +t0130:= sinh(a+b*log(c*x^n)) +--R +--R +--R n +--R (73) sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 510 +r0130:= x*(b*n*cosh(a+b*log(c*x^n))-sinh(a+b*log(c*x^n)))/(-1+b^2*n^2) +--R +--R +--R n n +--R - x sinh(b log(c x ) + a) + b n x cosh(b log(c x ) + a) +--R (74) ------------------------------------------------------- +--R 2 2 +--R b n - 1 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 510 +a0130:= integrate(t0130,x) +--R +--R +--R (75) +--R - x sinh(b n log(x) + b log(c) + a) + b n x cosh(b n log(x) + b log(c) + a) +--R --------------------------------------------------------------------------- +--R 2 2 +--R b n - 1 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 510 +m0130:= a0130-r0130 +--R +--R +--R (76) +--R n n +--R x sinh(b log(c x ) + a) - b n x cosh(b log(c x ) + a) +--R + +--R - x sinh(b n log(x) + b log(c) + a) + b n x cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n - 1 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 510 +d0130:= D(m0130,x) +--R +--R +--R (77) +--R n 2 2 n - 1 n +--R (x - b n x x )sinh(b log(c x ) + a) +--R + +--R n n - 1 n +--R (- b n x + b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n - 1)x sinh(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n - 1)x +--R Type: Expression(Integer) +--E 155 + +--S 156 of 510 +t0131:= x*sinh(a+b*log(c*x^n)) +--R +--R +--R n +--R (78) x sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 156 + +--S 157 of 510 +r0131:= x^2*(b*n*cosh(a+b*log(c*x^n))-2*sinh(a+b*log(c*x^n)))/(-4+b^2*n^2) +--R +--R +--R 2 n 2 n +--R - 2x sinh(b log(c x ) + a) + b n x cosh(b log(c x ) + a) +--R (79) -------------------------------------------------------- +--R 2 2 +--R b n - 4 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 510 +a0131:= integrate(t0131,x) +--R +--R +--R (80) +--R 2 2 +--R - 2x sinh(b n log(x) + b log(c) + a) + b n x cosh(b n log(x) + b log(c) + a) +--R ---------------------------------------------------------------------------- +--R 2 2 +--R b n - 4 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 510 +m0131:= a0131-r0131 +--R +--R +--R (81) +--R 2 n 2 n +--R 2x sinh(b log(c x ) + a) - b n x cosh(b log(c x ) + a) +--R + +--R 2 +--R - 2x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 +--R b n x cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n - 4 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 510 +d0131:= D(m0131,x) +--R +--R +--R (82) +--R n 2 2 2 n - 1 n +--R (4x x - b n x x )sinh(b log(c x ) + a) +--R + +--R n 2 n - 1 n +--R (- 2b n x x + 2b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n - 4)x x sinh(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n - 4)x +--R Type: Expression(Integer) +--E 160 + +--S 161 of 510 +t0132:= x^2*sinh(a+b*log(c*x^n)) +--R +--R +--R 2 n +--R (83) x sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 161 + +--S 162 of 510 +r0132:= x^3*(b*n*cosh(a+b*log(c*x^n))-3*sinh(a+b*log(c*x^n)))/(-9+b^2*n^2) +--R +--R +--R 3 n 3 n +--R - 3x sinh(b log(c x ) + a) + b n x cosh(b log(c x ) + a) +--R (84) -------------------------------------------------------- +--R 2 2 +--R b n - 9 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 510 +a0132:= integrate(t0132,x) +--R +--R +--R (85) +--R 3 3 +--R - 3x sinh(b n log(x) + b log(c) + a) + b n x cosh(b n log(x) + b log(c) + a) +--R ---------------------------------------------------------------------------- +--R 2 2 +--R b n - 9 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 510 +m0132:= a0132-r0132 +--R +--R +--R (86) +--R 3 n 3 n +--R 3x sinh(b log(c x ) + a) - b n x cosh(b log(c x ) + a) +--R + +--R 3 +--R - 3x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 +--R b n x cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n - 9 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 510 +d0132:= D(m0132,x) +--R +--R +--R (87) +--R 2 n 2 2 3 n - 1 n +--R (9x x - b n x x )sinh(b log(c x ) + a) +--R + +--R 2 n 3 n - 1 n +--R (- 3b n x x + 3b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 2 n +--R (b n - 9)x x sinh(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n - 9)x +--R Type: Expression(Integer) +--E 165 + +--S 166 of 510 +t0133:= sinh(a+b*log(c*x^n))/x^2 +--R +--R +--R n +--R sinh(b log(c x ) + a) +--R (88) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 166 + +--S 167 of 510 +r0133:= (sinh(a+b*log(c*x^n))+b*n*cosh(a+b*log(c*x^n)))/(-1+b^2*n^2)/x +--R +--R +--R n n +--R sinh(b log(c x ) + a) + b n cosh(b log(c x ) + a) +--R (89) ------------------------------------------------- +--R 2 2 +--R (b n - 1)x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 510 +a0133:= integrate(t0133,x) +--R +--R +--R sinh(b n log(x) + b log(c) + a) + b n cosh(b n log(x) + b log(c) + a) +--R (90) --------------------------------------------------------------------- +--R 2 2 +--R (b n - 1)x +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 510 +m0133:= a0133-r0133 +--R +--R +--R (91) +--R n n +--R - sinh(b log(c x ) + a) - b n cosh(b log(c x ) + a) +--R + +--R sinh(b n log(x) + b log(c) + a) + b n cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R (b n - 1)x +--R Type: Expression(Integer) +--E 169 + +--S 170 of 510 +d0133:= D(m0133,x) +--R +--R +--R (92) +--R n 2 2 n - 1 n +--R (x - b n x x )sinh(b log(c x ) + a) +--R + +--R n n - 1 n +--R (b n x - b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n - 1)x sinh(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (b n - 1)x x +--R Type: Expression(Integer) +--E 170 + +--S 171 of 510 +t0134:= x^m*sinh(a+b*log(c*x^n)) +--R +--R +--R m n +--R (93) x sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 510 +r0134:= -b*n*x^(1+m)*cosh(a+b*log(c*x^n))/((1+m)^2-b^2*n^2)+_ + (1+m)*x^(1+m)*sinh(a+b*log(c*x^n))/((1+m)^2-b^2*n^2) +--R +--R +--R (94) +--R m + 1 n m + 1 n +--R (- m - 1)x sinh(b log(c x ) + a) + b n x cosh(b log(c x ) + a) +--R ---------------------------------------------------------------------- +--R 2 2 2 +--R b n - m - 2m - 1 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 510 +a0134:= integrate(t0134,x) +--R +--R +--R (95) +--R ((- m - 1)x sinh(m log(x)) + (- m - 1)x cosh(m log(x))) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R b n x cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R b n x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 +--R b n - m - 2m - 1 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 510 +m0134:= a0134-r0134 +--R +--R +--R (96) +--R m + 1 n m + 1 n +--R (m + 1)x sinh(b log(c x ) + a) - b n x cosh(b log(c x ) + a) +--R + +--R ((- m - 1)x sinh(m log(x)) + (- m - 1)x cosh(m log(x))) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R b n x cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R b n x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 +--R b n - m - 2m - 1 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 510 +d0134:= D(m0134,x) +--R +--R +--R (97) +--R 2 m n 2 2 m + 1 n - 1 n +--R ((m + 2m + 1)x x - b n x x )sinh(b log(c x ) + a) +--R + +--R m n m + 1 n - 1 n +--R ((- b m - b)n x x + (b m + b)n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 2 n +--R (b n - m - 2m - 1)x sinh(m log(x)) +--R + +--R 2 2 2 n +--R (b n - m - 2m - 1)x cosh(m log(x)) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (b n - m - 2m - 1)x +--R Type: Expression(Integer) +--E 175 + +--S 176 of 510 +t0135:= sinh(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (98) sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 176 + +--S 177 of 510 +r0135:= -x*(2*b^2*n^2-2*b*n*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))+_ + cosh(a+b*log(c*x^n))^2-1)/(-1+4*b^2*n^2) +--R +--R +--R (99) +--R n n +--R 2b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 2 +--R - x cosh(b log(c x ) + a) + (- 2b n + 1)x +--R / +--R 2 2 +--R 4b n - 1 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 510 +a0135:= integrate(t0135,x) +--R +--R +--R (100) +--R 2 +--R - x sinh(b n log(x) + b log(c) + a) +--R + +--R 4b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R - x cosh(b n log(x) + b log(c) + a) + (- 4b n + 1)x +--R / +--R 2 2 +--R 8b n - 2 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 510 +m0135:= a0135-r0135 +--R +--R +--R (101) +--R n n +--R - 4b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 +--R 2x cosh(b log(c x ) + a) - x sinh(b n log(x) + b log(c) + a) +--R + +--R 4b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 +--R - x cosh(b n log(x) + b log(c) + a) - x +--R / +--R 2 2 +--R 8b n - 2 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 510 +d0135:= D(m0135,x) +--R +--R +--R (102) +--R 2 2 n - 1 n 2 +--R - 4b n x x sinh(b log(c x ) + a) +--R + +--R n n - 1 n n +--R (- 4b n x + 4b n x x )cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n 2 +--R (2x - 4b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R (4b n - 1)x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 n +--R (4b n - 1)x cosh(b n log(x) + b log(c) + a) - x +--R / +--R 2 2 n +--R (8b n - 2)x +--R Type: Expression(Integer) +--E 180 + +--S 181 of 510 +t0136:= x*sinh(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (103) x sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 510 +r0136:= -1/4*x^2*(b^2*n^2-2*b*n*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))+_ + 2*cosh(a+b*log(c*x^n))^2-2)/(-1+b^2*n^2) +--R +--R +--R (104) +--R 2 n n +--R 2b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 n 2 2 2 2 +--R - 2x cosh(b log(c x ) + a) + (- b n + 2)x +--R / +--R 2 2 +--R 4b n - 4 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 510 +a0136:= integrate(t0136,x) +--R +--R +--R (105) +--R 2 2 +--R - x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 +--R 2b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 +--R - x cosh(b n log(x) + b log(c) + a) + (- b n + 1)x +--R / +--R 2 2 +--R 4b n - 4 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 510 +m0136:= a0136-r0136 +--R +--R +--R (106) +--R 2 n n +--R - 2b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 n 2 2 2 +--R 2x cosh(b log(c x ) + a) - x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 +--R 2b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R - x cosh(b n log(x) + b log(c) + a) - x +--R / +--R 2 2 +--R 4b n - 4 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 510 +d0136:= D(m0136,x) +--R +--R +--R (107) +--R 2 2 2 n - 1 n 2 +--R - b n x x sinh(b log(c x ) + a) +--R + +--R n 2 n - 1 n n +--R (- 2b n x x + 2b n x x )cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 2 n - 1 n 2 +--R (2x x - b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R (b n - 1)x x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 n +--R (b n - 1)x x cosh(b n log(x) + b log(c) + a) - x x +--R / +--R 2 2 n +--R (2b n - 2)x +--R Type: Expression(Integer) +--E 185 + +--S 186 of 510 +t0137:= x^2*sinh(a+b*log(c*x^n))^2 +--R +--R +--R 2 n 2 +--R (108) x sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 510 +r0137:= -1/3*x^3*(2*b^2*n^2-6*b*n*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))+_ + 9*cosh(a+b*log(c*x^n))^2-9)/(-9+4*b^2*n^2) +--R +--R +--R (109) +--R 3 n n +--R 6b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 3 n 2 2 2 3 +--R - 9x cosh(b log(c x ) + a) + (- 2b n + 9)x +--R / +--R 2 2 +--R 12b n - 27 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 510 +a0137:= integrate(t0137,x) +--R +--R +--R (110) +--R 3 2 +--R - 9x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 +--R 12b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 3 2 2 2 3 +--R - 9x cosh(b n log(x) + b log(c) + a) + (- 4b n + 9)x +--R / +--R 2 2 +--R 24b n - 54 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 510 +m0137:= a0137-r0137 +--R +--R +--R (111) +--R 3 n n +--R - 4b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 3 n 2 3 2 +--R 6x cosh(b log(c x ) + a) - 3x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 +--R 4b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 3 2 3 +--R - 3x cosh(b n log(x) + b log(c) + a) - 3x +--R / +--R 2 2 +--R 8b n - 18 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 510 +d0137:= D(m0137,x) +--R +--R +--R (112) +--R 2 2 3 n - 1 n 2 +--R - 4b n x x sinh(b log(c x ) + a) +--R + +--R 2 n 3 n - 1 n n +--R (- 12b n x x + 12b n x x )cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 n 2 2 3 n - 1 n 2 +--R (18x x - 4b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 2 n 2 +--R (4b n - 9)x x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 2 n +--R (4b n - 9)x x cosh(b n log(x) + b log(c) + a) - 9x x +--R / +--R 2 2 n +--R (8b n - 18)x +--R Type: Expression(Integer) +--E 190 + +--S 191 of 510 +t0138:= sinh(a+b*log(c*x^n))^2/x^2 +--R +--R +--R n 2 +--R sinh(b log(c x ) + a) +--R (113) ---------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 191 + +--S 192 of 510 +r0138:= 1/(-1+4*b^2*n^2)/x*(2*b^2*n^2+2*b*n*cosh(a+b*log(c*x^n))*_ + sinh(a+b*log(c*x^n))+cosh(a+b*log(c*x^n))^2-1) +--R +--R +--R (114) +--R n n n 2 +--R 2b n cosh(b log(c x ) + a)sinh(b log(c x ) + a) + cosh(b log(c x ) + a) +--R + +--R 2 2 +--R 2b n - 1 +--R / +--R 2 2 +--R (4b n - 1)x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 510 +a0138:= integrate(t0138,x) +--R +--R +--R (115) +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 4b n cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R cosh(b n log(x) + b log(c) + a) + 4b n - 1 +--R / +--R 2 2 +--R (8b n - 2)x +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 510 +m0138:= a0138-r0138 +--R +--R +--R (116) +--R n n +--R - 4b n cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 +--R - 2cosh(b log(c x ) + a) + sinh(b n log(x) + b log(c) + a) +--R + +--R 4b n cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 +--R cosh(b n log(x) + b log(c) + a) + 1 +--R / +--R 2 2 +--R (8b n - 2)x +--R Type: Expression(Integer) +--E 194 + +--S 195 of 510 +d0138:= D(m0138,x) +--R +--R +--R (117) +--R 2 2 n - 1 n 2 +--R - 4b n x x sinh(b log(c x ) + a) +--R + +--R n n - 1 n n +--R (4b n x - 4b n x x )cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n 2 +--R (2x - 4b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R (4b n - 1)x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 n +--R (4b n - 1)x cosh(b n log(x) + b log(c) + a) - x +--R / +--R 2 2 2 n +--R (8b n - 2)x x +--R Type: Expression(Integer) +--E 195 + +--S 196 of 510 +t0139:= x^m*sinh(a+b*log(c*x^n))^2 +--R +--R +--R m n 2 +--R (118) x sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 196 + +--S 197 of 510 +r0139:= 2*b^2*n^2*x^(1+m)/(1+m)/((1+m)^2-4*b^2*n^2)-2*b*n*x^(1+m)*_ + cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))/((1+m)^2-4*b^2*n^2)+_ + (1+m)*x^(1+m)*sinh(a+b*log(c*x^n))^2/((1+m)^2-4*b^2*n^2) +--R +--R +--R (119) +--R 2 m + 1 n 2 +--R (- m - 2m - 1)x sinh(b log(c x ) + a) +--R + +--R m + 1 n n 2 2 m + 1 +--R (2b m + 2b)n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) - 2b n x +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n - m - 3m - 3m - 1 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 510 +a0139:= integrate(t0139,x) +--R +--R +--R (120) +--R 2 2 +--R ((- m - 2m - 1)x sinh(m log(x)) + (- m - 2m - 1)x cosh(m log(x))) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R (4b m + 4b)n x cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R (4b m + 4b)n x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- m - 2m - 1)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (- 4b n + m + 2m + 1)x +--R * +--R sinh(m log(x)) +--R + +--R 2 2 +--R (- m - 2m - 1)x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (- 4b n + m + 2m + 1)x cosh(m log(x)) +--R / +--R 2 2 2 3 2 +--R (8b m + 8b )n - 2m - 6m - 6m - 2 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 510 +m0139:= a0139-r0139 +--R +--R +--R (121) +--R 2 m + 1 n 2 +--R (2m + 4m + 2)x sinh(b log(c x ) + a) +--R + +--R m + 1 n n +--R (- 4b m - 4b)n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 2 +--R ((- m - 2m - 1)x sinh(m log(x)) + (- m - 2m - 1)x cosh(m log(x))) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R (4b m + 4b)n x cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R (4b m + 4b)n x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- m - 2m - 1)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (- 4b n + m + 2m + 1)x +--R * +--R sinh(m log(x)) +--R + +--R 2 2 +--R (- m - 2m - 1)x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 m + 1 +--R (- 4b n + m + 2m + 1)x cosh(m log(x)) + 4b n x +--R / +--R 2 2 2 3 2 +--R (8b m + 8b )n - 2m - 6m - 6m - 2 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 510 +d0139:= D(m0139,x) +--R +--R +--R (122) +--R 2 m n 2 2 m + 1 n - 1 n 2 +--R ((2m + 4m + 2)x x - 4b n x x )sinh(b log(c x ) + a) +--R + +--R m n m + 1 n - 1 n +--R ((- 4b m - 4b)n x x + (4b m + 4b)n x x )cosh(b log(c x ) + a) +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 m + 1 n - 1 n 2 +--R - 4b n x x cosh(b log(c x ) + a) +--R + +--R 2 2 2 n +--R (4b n - m - 2m - 1)x sinh(m log(x)) +--R + +--R 2 2 2 n +--R (4b n - m - 2m - 1)x cosh(m log(x)) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 +--R (4b n - m - 2m - 1)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n +--R (- 4b n + m + 2m + 1)x +--R * +--R sinh(m log(x)) +--R + +--R 2 2 2 n 2 +--R (4b n - m - 2m - 1)x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 2 m n +--R (- 4b n + m + 2m + 1)x cosh(m log(x)) + 4b n x x +--R / +--R 2 2 2 n +--R (8b n - 2m - 4m - 2)x +--R Type: Expression(Integer) +--E 200 + +--S 201 of 510 +t0140:= sinh(a+b*log(c*x^n))^3 +--R +--R +--R n 3 +--R (123) sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 201 + +--S 202 of 510 +r0140:= -6*b^3*n^3*x*cosh(a+b*log(c*x^n))/(1-9*b^2*n^2)/(1-b^2*n^2)+_ + 6*b^2*n^2*x*sinh(a+b*log(c*x^n))/(1-9*b^2*n^2)/(1-b^2*n^2)-_ + 3*b*n*x*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))^2/(1-9*b^2*n^2)+_ + x*sinh(a+b*log(c*x^n))^3/(1-9*b^2*n^2) +--R +--R +--R (124) +--R 2 2 n 3 +--R (- b n + 1)x sinh(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (3b n - 3b n)x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R 6b n x sinh(b log(c x ) + a) - 6b n x cosh(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 9b n - 10b n + 1 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 510 +a0140:= integrate(t0140,x) +--R +--R +--R (125) +--R 2 2 3 +--R (- b n + 1)x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (9b n - 9b n)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 +--R ((- 3b n + 3)x cosh(b n log(x) + b log(c) + a) + (27b n - 3)x) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n - 3b n)x cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 27b n + 3b n)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 36b n - 40b n + 4 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 510 +m0140:= a0140-r0140 +--R +--R +--R (126) +--R 2 2 n 3 +--R (4b n - 4)x sinh(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (- 12b n + 12b n)x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R - 24b n x sinh(b log(c x ) + a) + 24b n x cosh(b log(c x ) + a) +--R + +--R 2 2 3 +--R (- b n + 1)x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (9b n - 9b n)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 +--R ((- 3b n + 3)x cosh(b n log(x) + b log(c) + a) + (27b n - 3)x) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n - 3b n)x cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 27b n + 3b n)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 36b n - 40b n + 4 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 510 +d0140:= D(m0140,x) +--R +--R +--R (127) +--R 2 2 n 4 4 2 2 n - 1 n 3 +--R ((4b n - 4)x + (- 12b n + 12b n )x x )sinh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R ((- 12b n + 12b n)x + (12b n - 12b n)x x )cosh(b log(c x ) + a) +--R * +--R n 2 +--R sinh(b log(c x ) + a) +--R + +--R 4 4 2 2 n - 1 n 2 2 2 n +--R (- 24b n + 24b n )x x cosh(b log(c x ) + a) - 24b n x +--R + +--R 4 4 n - 1 +--R 24b n x x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R (24b n x - 24b n x x )cosh(b log(c x ) + a) +--R + +--R 4 4 2 2 n 3 +--R (9b n - 10b n + 1)x sinh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 2 +--R (27b n - 30b n + 3)x cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (- 27b n + 30b n - 3)x +--R * +--R sinh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (36b n - 40b n + 4)x +--R Type: Expression(Integer) +--E 205 + +--S 206 of 510 +t0141:= x*sinh(a+b*log(c*x^n))^3 +--R +--R +--R n 3 +--R (128) x sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 510 +r0141:= -6*b^3*n^3*x^2*cosh(a+b*log(c*x^n))/(4-9*b^2*n^2)/(4-b^2*n^2)+_ + 12*b^2*n^2*x^2*sinh(a+b*log(c*x^n))/(4-9*b^2*n^2)/(4-b^2*n^2)-_ + 3*b*n*x^2*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))^2/(4-9*b^2*n^2)+_ + 2*x^2*sinh(a+b*log(c*x^n))^3/(4-9*b^2*n^2) +--R +--R +--R (129) +--R 2 2 2 n 3 +--R (- 2b n + 8)x sinh(b log(c x ) + a) +--R + +--R 3 3 2 n n 2 +--R (3b n - 12b n)x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 2 2 n 3 3 2 n +--R 12b n x sinh(b log(c x ) + a) - 6b n x cosh(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 9b n - 40b n + 16 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 510 +a0141:= integrate(t0141,x) +--R +--R +--R (130) +--R 2 2 2 3 +--R (- 2b n + 8)x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (9b n - 36b n)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 2 2 +--R ((- 6b n + 24)x cosh(b n log(x) + b log(c) + a) + (54b n - 24)x ) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n - 12b n)x cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 27b n + 12b n)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 36b n - 160b n + 64 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 510 +m0141:= a0141-r0141 +--R +--R +--R (131) +--R 2 2 2 n 3 +--R (8b n - 32)x sinh(b log(c x ) + a) +--R + +--R 3 3 2 n n 2 +--R (- 12b n + 48b n)x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 2 2 n 3 3 2 n +--R - 48b n x sinh(b log(c x ) + a) + 24b n x cosh(b log(c x ) + a) +--R + +--R 2 2 2 3 +--R (- 2b n + 8)x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (9b n - 36b n)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 2 2 +--R ((- 6b n + 24)x cosh(b n log(x) + b log(c) + a) + (54b n - 24)x ) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n - 12b n)x cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 27b n + 12b n)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 36b n - 160b n + 64 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 510 +d0141:= D(m0141,x) +--R +--R +--R (132) +--R 2 2 n 4 4 2 2 2 n - 1 n 3 +--R ((16b n - 64)x x + (- 12b n + 48b n )x x )sinh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 2 n - 1 +--R ((- 24b n + 96b n)x x + (24b n - 96b n)x x ) +--R * +--R n n 2 +--R cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 4 4 2 2 2 n - 1 n 2 2 2 n +--R (- 24b n + 96b n )x x cosh(b log(c x ) + a) - 96b n x x +--R + +--R 4 4 2 n - 1 +--R 24b n x x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 2 n - 1 n +--R (48b n x x - 48b n x x )cosh(b log(c x ) + a) +--R + +--R 4 4 2 2 n 3 +--R (9b n - 40b n + 16)x x sinh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 2 +--R (27b n - 120b n + 48)x x cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (- 27b n + 120b n - 48)x x +--R * +--R sinh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (36b n - 160b n + 64)x +--R Type: Expression(Integer) +--E 210 + +--S 211 of 510 +t0142:= x^2*sinh(a+b*log(c*x^n))^3 +--R +--R +--R 2 n 3 +--R (133) x sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 510 +r0142:= -2/3*b^3*n^3*x^3*cosh(a+b*log(c*x^n))/(1-b^2*n^2)/(9-b^2*n^2)+_ + 2*b^2*n^2*x^3*sinh(a+b*log(c*x^n))/(1-b^2*n^2)/(9-b^2*n^2)-_ + b*n*x^3*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))^2/(3-3*b^2*n^2)+_ + x^3*sinh(a+b*log(c*x^n))^3/(3-3*b^2*n^2) +--R +--R +--R (134) +--R 2 2 3 n 3 +--R (- b n + 9)x sinh(b log(c x ) + a) +--R + +--R 3 3 3 n n 2 +--R (b n - 9b n)x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 2 3 n 3 3 3 n +--R 6b n x sinh(b log(c x ) + a) - 2b n x cosh(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 3b n - 30b n + 27 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 510 +a0142:= integrate(t0142,x) +--R +--R +--R (135) +--R 2 2 3 3 +--R (- b n + 9)x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n - 27b n)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 3b n + 27)x cosh(b n log(x) + b log(c) + a) + (27b n - 27)x ) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 3 +--R (b n - 9b n)x cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (- 9b n + 9b n)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 12b n - 120b n + 108 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 510 +m0142:= a0142-r0142 +--R +--R +--R (136) +--R 2 2 3 n 3 +--R (4b n - 36)x sinh(b log(c x ) + a) +--R + +--R 3 3 3 n n 2 +--R (- 4b n + 36b n)x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 2 3 n 3 3 3 n +--R - 24b n x sinh(b log(c x ) + a) + 8b n x cosh(b log(c x ) + a) +--R + +--R 2 2 3 3 +--R (- b n + 9)x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n - 27b n)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 3b n + 27)x cosh(b n log(x) + b log(c) + a) + (27b n - 27)x ) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 3 +--R (b n - 9b n)x cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (- 9b n + 9b n)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 12b n - 120b n + 108 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 510 +d0142:= D(m0142,x) +--R +--R +--R (137) +--R 2 2 2 n 4 4 2 2 3 n - 1 n 3 +--R ((12b n - 108)x x + (- 4b n + 36b n )x x )sinh(b log(c x ) + a) +--R + +--R 3 3 2 n 3 3 3 n - 1 +--R ((- 12b n + 108b n)x x + (12b n - 108b n)x x ) +--R * +--R n n 2 +--R cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 4 4 2 2 3 n - 1 n 2 2 2 2 n +--R (- 8b n + 72b n )x x cosh(b log(c x ) + a) - 72b n x x +--R + +--R 4 4 3 n - 1 +--R 8b n x x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 3 3 2 n 3 3 3 n - 1 n +--R (24b n x x - 24b n x x )cosh(b log(c x ) + a) +--R + +--R 4 4 2 2 2 n 3 +--R (3b n - 30b n + 27)x x sinh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 n 2 +--R (9b n - 90b n + 81)x x cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 n +--R (- 9b n + 90b n - 81)x x +--R * +--R sinh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (12b n - 120b n + 108)x +--R Type: Expression(Integer) +--E 215 + +--S 216 of 510 +t0143:= sinh(a+b*log(c*x^n))^3/x^2 +--R +--R +--R n 3 +--R sinh(b log(c x ) + a) +--R (138) ---------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 216 + +--S 217 of 510 +r0143:= -6*b^3*n^3*cosh(a+b*log(c*x^n))/(1-9*b^2*n^2)/(1-b^2*n^2)/x-_ + 6*b^2*n^2*sinh(a+b*log(c*x^n))/(1-9*b^2*n^2)/(1-b^2*n^2)/x-_ + 3*b*n*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))^2/(1-9*b^2*n^2)/x-_ + sinh(a+b*log(c*x^n))^3/(1-9*b^2*n^2)/x +--R +--R +--R (139) +--R 2 2 n 3 +--R (b n - 1)sinh(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (3b n - 3b n)cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R - 6b n sinh(b log(c x ) + a) - 6b n cosh(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R (9b n - 10b n + 1)x +--R Type: Expression(Integer) +--E 217 + +--S 218 of 510 +a0143:= integrate(t0143,x) +--R +--R +--R (140) +--R 2 2 3 +--R (b n - 1)sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (9b n - 9b n)cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 +--R ((3b n - 3)cosh(b n log(x) + b log(c) + a) - 27b n + 3) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n - 3b n)cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 27b n + 3b n)cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R (36b n - 40b n + 4)x +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 510 +m0143:= a0143-r0143 +--R +--R +--R (141) +--R 2 2 n 3 +--R (- 4b n + 4)sinh(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (- 12b n + 12b n)cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R 24b n sinh(b log(c x ) + a) + 24b n cosh(b log(c x ) + a) +--R + +--R 2 2 3 +--R (b n - 1)sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (9b n - 9b n)cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 +--R ((3b n - 3)cosh(b n log(x) + b log(c) + a) - 27b n + 3) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n - 3b n)cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 27b n + 3b n)cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R (36b n - 40b n + 4)x +--R Type: Expression(Integer) +--E 219 + +--S 220 of 510 +d0143:= D(m0143,x) +--R +--R +--R (142) +--R 2 2 n 4 4 2 2 n - 1 n 3 +--R ((4b n - 4)x + (- 12b n + 12b n )x x )sinh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R ((12b n - 12b n)x + (- 12b n + 12b n)x x )cosh(b log(c x ) + a) +--R * +--R n 2 +--R sinh(b log(c x ) + a) +--R + +--R 4 4 2 2 n - 1 n 2 2 2 n +--R (- 24b n + 24b n )x x cosh(b log(c x ) + a) - 24b n x +--R + +--R 4 4 n - 1 +--R 24b n x x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R (- 24b n x + 24b n x x )cosh(b log(c x ) + a) +--R + +--R 4 4 2 2 n 3 +--R (9b n - 10b n + 1)x sinh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 2 +--R (27b n - 30b n + 3)x cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (- 27b n + 30b n - 3)x +--R * +--R sinh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 n +--R (36b n - 40b n + 4)x x +--R Type: Expression(Integer) +--E 220 + +--S 221 of 510 +t0144:= x^m*sinh(a+b*log(c*x^n))^3 +--R +--R +--R m n 3 +--R (143) x sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 221 + +--S 222 of 510 +r0144:= -6*b^3*n^3*x^(1+m)*cosh(a+b*log(c*x^n))/((1+m)^2-9*b^2*n^2)/((1+m)^2-_ + b^2*n^2)+6*b^2*(1+m)*n^2*x^(1+m)*sinh(a+b*log(c*x^n))/((1+m)^2-_ + 9*b^2*n^2)/((1+m)^2-b^2*n^2)-3*b*n*x^(1+m)*cosh(a+b*log(c*x^n))*_ + sinh(a+b*log(c*x^n))^2/((1+m)^2-9*b^2*n^2)+(1+m)*x^(1+m)*_ + sinh(a+b*log(c*x^n))^3/((1+m)^2-9*b^2*n^2) +--R +--R +--R (144) +--R 2 2 2 3 2 m + 1 n 3 +--R ((- b m - b )n + m + 3m + 3m + 1)x sinh(b log(c x ) + a) +--R + +--R 3 3 2 m + 1 n +--R (3b n + (- 3b m - 6b m - 3b)n)x cosh(b log(c x ) + a) +--R * +--R n 2 +--R sinh(b log(c x ) + a) +--R + +--R 2 2 2 m + 1 n +--R (6b m + 6b )n x sinh(b log(c x ) + a) +--R + +--R 3 3 m + 1 n +--R - 6b n x cosh(b log(c x ) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (- 10b m - 20b m - 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 510 +a0144:= integrate(t0144,x) +--R +--R +--R (145) +--R 2 2 2 3 2 +--R ((- b m - b )n + m + 3m + 3m + 1)x sinh(m log(x)) +--R + +--R 2 2 2 3 2 +--R ((- b m - b )n + m + 3m + 3m + 1)x cosh(m log(x)) +--R * +--R 3 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (9b n + (- 9b m - 18b m - 9b)n)x cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(m log(x)) +--R + +--R 3 3 2 +--R (9b n + (- 9b m - 18b m - 9b)n)x cosh(m log(x)) +--R * +--R cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((- 3b m - 3b )n + 3m + 9m + 9m + 3)x +--R * +--R 2 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((27b m + 27b )n - 3m - 9m - 9m - 3)x +--R * +--R sinh(m log(x)) +--R + +--R 2 2 2 3 2 +--R ((- 3b m - 3b )n + 3m + 9m + 9m + 3)x cosh(m log(x)) +--R * +--R 2 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((27b m + 27b )n - 3m - 9m - 9m - 3)x cosh(m log(x)) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n + (- 3b m - 6b m - 3b)n)x cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 27b n + (3b m + 6b m + 3b)n)x cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(m log(x)) +--R + +--R 3 3 2 +--R (3b n + (- 3b m - 6b m - 3b)n)x cosh(m log(x)) +--R * +--R 3 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 27b n + (3b m + 6b m + 3b)n)x cosh(m log(x)) +--R * +--R cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 36b n + (- 40b m - 80b m - 40b )n + 4m + 16m + 24m + 16m + 4 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 510 +m0144:= a0144-r0144 +--R +--R +--R (146) +--R 2 2 2 3 2 m + 1 n 3 +--R ((4b m + 4b )n - 4m - 12m - 12m - 4)x sinh(b log(c x ) + a) +--R + +--R 3 3 2 m + 1 n +--R (- 12b n + (12b m + 24b m + 12b)n)x cosh(b log(c x ) + a) +--R * +--R n 2 +--R sinh(b log(c x ) + a) +--R + +--R 2 2 2 m + 1 n +--R (- 24b m - 24b )n x sinh(b log(c x ) + a) +--R + +--R 3 3 m + 1 n +--R 24b n x cosh(b log(c x ) + a) +--R + +--R 2 2 2 3 2 +--R ((- b m - b )n + m + 3m + 3m + 1)x sinh(m log(x)) +--R + +--R 2 2 2 3 2 +--R ((- b m - b )n + m + 3m + 3m + 1)x cosh(m log(x)) +--R * +--R 3 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (9b n + (- 9b m - 18b m - 9b)n)x cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(m log(x)) +--R + +--R 3 3 2 +--R (9b n + (- 9b m - 18b m - 9b)n)x cosh(m log(x)) +--R * +--R cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((- 3b m - 3b )n + 3m + 9m + 9m + 3)x +--R * +--R 2 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((27b m + 27b )n - 3m - 9m - 9m - 3)x +--R * +--R sinh(m log(x)) +--R + +--R 2 2 2 3 2 +--R ((- 3b m - 3b )n + 3m + 9m + 9m + 3)x cosh(m log(x)) +--R * +--R 2 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((27b m + 27b )n - 3m - 9m - 9m - 3)x cosh(m log(x)) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n + (- 3b m - 6b m - 3b)n)x cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 27b n + (3b m + 6b m + 3b)n)x cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(m log(x)) +--R + +--R 3 3 2 +--R (3b n + (- 3b m - 6b m - 3b)n)x cosh(m log(x)) +--R * +--R 3 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 27b n + (3b m + 6b m + 3b)n)x cosh(m log(x)) +--R * +--R cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 36b n + (- 40b m - 80b m - 40b )n + 4m + 16m + 24m + 16m + 4 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 510 +d0144:= D(m0144,x) +--R +--R +--R (147) +--R 2 2 2 2 2 4 3 2 m n +--R ((4b m + 8b m + 4b )n - 4m - 16m - 24m - 16m - 4)x x +--R + +--R 4 4 2 2 2 2 2 m + 1 n - 1 +--R (- 12b n + (12b m + 24b m + 12b )n )x x +--R * +--R n 3 +--R sinh(b log(c x ) + a) +--R + +--R 3 3 3 3 2 m n +--R ((- 12b m - 12b )n + (12b m + 36b m + 36b m + 12b)n)x x +--R + +--R 3 3 3 3 2 m + 1 n - 1 +--R ((12b m + 12b )n + (- 12b m - 36b m - 36b m - 12b)n)x x +--R * +--R n n 2 +--R cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 4 4 2 2 2 2 2 m + 1 n - 1 +--R (- 24b n + (24b m + 48b m + 24b )n )x x +--R * +--R n 2 +--R cosh(b log(c x ) + a) +--R + +--R 2 2 2 2 2 m n 4 4 m + 1 n - 1 +--R (- 24b m - 48b m - 24b )n x x + 24b n x x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 3 3 3 m n 3 3 3 m + 1 n - 1 +--R ((24b m + 24b )n x x + (- 24b m - 24b )n x x ) +--R * +--R n +--R cosh(b log(c x ) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 n +--R (9b n + (- 10b m - 20b m - 10b )n + m + 4m + 6m + 4m + 1)x +--R * +--R sinh(m log(x)) +--R + +--R 4 4 2 2 2 2 2 4 3 2 n +--R (9b n + (- 10b m - 20b m - 10b )n + m + 4m + 6m + 4m + 1)x +--R * +--R cosh(m log(x)) +--R * +--R 3 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 +--R 27b n + (- 30b m - 60b m - 30b )n + 3m + 12m + 18m +--R + +--R 12m + 3 +--R * +--R n 2 +--R x cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 +--R - 27b n + (30b m + 60b m + 30b )n - 3m - 12m - 18m +--R + +--R - 12m - 3 +--R * +--R n +--R x +--R * +--R sinh(m log(x)) +--R + +--R 4 4 2 2 2 2 2 4 3 2 +--R 27b n + (- 30b m - 60b m - 30b )n + 3m + 12m + 18m + 12m +--R + +--R 3 +--R * +--R n 2 +--R x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 +--R - 27b n + (30b m + 60b m + 30b )n - 3m - 12m - 18m - 12m +--R + +--R - 3 +--R * +--R n +--R x cosh(m log(x)) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 n +--R (36b n + (- 40b m - 80b m - 40b )n + 4m + 16m + 24m + 16m + 4)x +--R Type: Expression(Integer) +--E 225 + +--S 226 of 510 +t0145:= cosh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (148) \|cosh(b x + a) +--R Type: Expression(Integer) +--E 226 + +--S 227 of 510 +r0145:= -2*%i*EllipticE(1/2*%i*(a+b*x),2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 510 +a0145:= integrate(t0145,x) +--R +--R +--R x +--R ++ +--------------+ +--R (149) | \|cosh(%I b + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 510 +--m0145:= a0145-r0145 +--E 229 + +--S 230 of 510 +--d0145:= D(m0145,x) +--E 230 + +--S 231 of 510 +t0146:= cosh(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (150) cosh(b x + a)\|cosh(b x + a) +--R Type: Expression(Integer) +--E 231 + +--S 232 of 510 +r0146:= 2/3*(-%i*EllipticF(1/2*%i*(a+b*x),2)+cosh(a+b*x)^(1/2)*sinh(a+b*x))/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 232 + +--S 233 of 510 +a0146:= integrate(t0146,x) +--R +--R +--R x +--R ++ +--------------+ +--R (151) | cosh(%I b + a)\|cosh(%I b + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 510 +--m0146:= a0146-r0146 +--E 234 + +--S 235 of 510 +--d0146:= D(m0146,x) +--E 235 + +--S 236 of 510 +t0147:= cosh(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (152) cosh(b x + a) \|cosh(b x + a) +--R Type: Expression(Integer) +--E 236 + +--S 237 of 510 +r0147:= 2/5*(-3*%i*EllipticE(1/2*%i*(a+b*x),2)+cosh(a+b*x)^(3/2)*sinh(a+b*x))/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 510 +a0147:= integrate(t0147,x) +--R +--R +--R x +--R ++ 2 +--------------+ +--R (153) | cosh(%I b + a) \|cosh(%I b + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 510 +--m0147:= a0147-r0147 +--E 239 + +--S 240 of 510 +--d0147:= D(m0147,x) +--E 240 + +--S 241 of 510 +t0148:= 1/cosh(a+b*x)^(1/2) +--R +--R +--R 1 +--R (154) ---------------- +--R +-------------+ +--R \|cosh(b x + a) +--R Type: Expression(Integer) +--E 241 + +--S 242 of 510 +r0148:= -2*%i*EllipticF(1/2*%i*(a+b*x),2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 242 + +--S 243 of 510 +a0148:= integrate(t0148,x) +--R +--R +--R x +--R ++ 1 +--R (155) | ----------------- d%I +--R ++ +--------------+ +--R \|cosh(%I b + a) +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 510 +--m0148:= a0148-r0148 +--E 244 + +--S 245 of 510 +--d0148:= D(m0148,x) +--E 245 + +--S 246 of 510 +t0149:= 1/cosh(a+b*x)^(3/2) +--R +--R +--R 1 +--R (156) ----------------------------- +--R +-------------+ +--R cosh(b x + a)\|cosh(b x + a) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 510 +r0149:= 2*%i*EllipticE(1/2*%i*(a+b*x),2)/b+2*sinh(a+b*x)/b/cosh(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 247 + +--S 248 of 510 +a0149:= integrate(t0149,x) +--R +--R +--R x +--R ++ 1 +--R (157) | ------------------------------- d%I +--R ++ +--------------+ +--R cosh(%I b + a)\|cosh(%I b + a) +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 510 +--m0149:= a0149-r0149 +--E 249 + +--S 250 of 510 +--d0149:= D(m0149,x) +--E 250 + +--S 251 of 510 +t0150:= 1/cosh(a+b*x)^(5/2) +--R +--R +--R 1 +--R (158) ------------------------------ +--R 2 +-------------+ +--R cosh(b x + a) \|cosh(b x + a) +--R Type: Expression(Integer) +--E 251 + +--S 252 of 510 +r0150:= -2/3*%i*EllipticF(1/2*%i*(a+b*x),2)/b+_ + 2/3*sinh(a+b*x)/b/cosh(a+b*x)^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 252 + +--S 253 of 510 +a0150:= integrate(t0150,x) +--R +--R +--R x +--R ++ 1 +--R (159) | -------------------------------- d%I +--R ++ 2 +--------------+ +--R cosh(%I b + a) \|cosh(%I b + a) +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 510 +--m0150:= a0150-r0150 +--E 254 + +--S 255 of 510 +--d0150:= D(m0150,x) +--E 255 + +--S 256 of 510 +t0151:= cosh(a+b*x^n)/x +--R +--R +--R n +--R cosh(b x + a) +--R (160) -------------- +--R x +--R Type: Expression(Integer) +--E 256 + +--S 257 of 510 +r0151:= (cosh(a)*Chi(b*x^n)+sinh(a)*Shi(b*x^n))/n +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 257 + +--S 258 of 510 +a0151:= integrate(t0151,x) +--R +--R +--R x n +--R ++ cosh(b %I + a) +--R (161) | --------------- d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 510 +--m0151:= a0151-r0151 +--E 259 + +--S 260 of 510 +--d0151:= D(m0151,x) +--E 260 + +--S 261 of 510 +t0152:= cosh(a+b*x)/x^2 +--R +--R +--R cosh(b x + a) +--R (162) ------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 261 + +--S 262 of 510 +r0152:= -cosh(a+b*x)/x+b*Chi(b*x)*sinh(a)+b*cosh(a)*Shi(b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 262 + +--S 263 of 510 +a0152:= integrate(t0152,x) +--R +--R +--R x +--R ++ cosh(%I b + a) +--R (163) | -------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 510 +--m0152:= a0152-r0152 +--E 264 + +--S 265 of 510 +--d0152:= D(m0152,x) +--E 265 + +--S 266 of 510 +t0153:= cosh(a+b*x)^3/x^2 +--R +--R +--R 3 +--R cosh(b x + a) +--R (164) -------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 266 + +--S 267 of 510 +r0153:= -1/4*(3*cosh(a+b*x)+cosh(3*a+3*b*x)-3*b*Chi(b*x)*sinh(a)*x-_ + 3*b*Chi(3*b*x)*sinh(3*a)*x-3*b*cosh(a)*Shi(b*x)*x-_ + 3*b*cosh(3*a)*Shi(3*b*x)*x)/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 510 +a0153:= integrate(t0153,x) +--R +--R +--R x 3 +--R ++ cosh(%I b + a) +--R (165) | --------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 510 +--m0153:= a0153-r0153 +--E 269 + +--S 270 of 510 +--d0153:= D(m0153,x) +--E 270 + +--S 271 of 510 +t0154:= cosh(a+b*x)/x^3 +--R +--R +--R cosh(b x + a) +--R (166) ------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 510 +r0154:= -1/2*(cosh(a+b*x)-b^2*cosh(a)*Chi(b*x)*x^2+_ + x*sinh(a+b*x)*b-b^2*sinh(a)*Shi(b*x)*x^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 272 + +--S 273 of 510 +a0154:= integrate(t0154,x) +--R +--R +--R x +--R ++ cosh(%I b + a) +--R (167) | -------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 510 +--m0154:= a0154-r0154 +--E 274 + +--S 275 of 510 +--d0154:= D(m0154,x) +--E 275 + +--S 276 of 510 +t0155:= cosh(a+b*x)^2/x^3 +--R +--R +--R 2 +--R cosh(b x + a) +--R (168) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 276 + +--S 277 of 510 +r0155:= -1/2*cosh(a+b*x)^2/x^2+b^2*cosh(2*a)*Chi(2*b*x)-_ + b*cosh(a+b*x)*sinh(a+b*x)/x+b^2*sinh(2*a)*Shi(2*b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 277 + +--S 278 of 510 +a0155:= integrate(t0155,x) +--R +--R +--R x 2 +--R ++ cosh(%I b + a) +--R (169) | --------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 510 +--m0155:= a0155-r0155 +--E 279 + +--S 280 of 510 +--d0155:= D(m0155,x) +--E 280 + +--S 281 of 510 +t0156:= cosh(a+b*x)^3/x^3 +--R +--R +--R 3 +--R cosh(b x + a) +--R (170) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 281 + +--S 282 of 510 +r0156:= -1/2*cosh(a+b*x)^3/x^2+3/8*b^2*cosh(a)*Chi(b*x)+_ + 9/8*b^2*cosh(3*a)*Chi(3*b*x)-3/2*b*cosh(a+b*x)^2*sinh(a+b*x)/x+_ + 3/8*b^2*sinh(a)*Shi(b*x)+9/8*b^2*sinh(3*a)*Shi(3*b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 510 +a0156:= integrate(t0156,x) +--R +--R +--R x 3 +--R ++ cosh(%I b + a) +--R (171) | --------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 510 +--m0156:= a0156-r0156 +--E 284 + +--S 285 of 510 +--d0156:= D(m0156,x) +--E 285 + +--S 286 of 510 +t0157:= cosh(x)^(1/2) +--R +--R +--R +-------+ +--R (172) \|cosh(x) +--R Type: Expression(Integer) +--E 286 + +--S 287 of 510 +r0157:= -2*%i*EllipticE(1/2*%i*x,2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 287 + +--S 288 of 510 +a0157:= integrate(t0157,x) +--R +--R +--R x +--R ++ +--------+ +--R (173) | \|cosh(%I) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 510 +--m0157:= a0157-r0157 +--E 289 + +--S 290 of 510 +--d0157:= D(m0157,x) +--E 290 + +--S 291 of 510 +t0158:= (cosh(x)^3)^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R (174) \|cosh(x) +--R Type: Expression(Integer) +--E 291 + +--S 292 of 510 +r0158:= 2/3*(cosh(x)^3)^(1/2)*(-%i*EllipticF(1/2*%i*x,2)+_ + cosh(x)^(1/2)*sinh(x))/cosh(x)^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 292 + +--S 293 of 510 +a0158:= integrate(t0158,x) +--R +--R +--R x +---------+ +--R ++ | 3 +--R (175) | \|cosh(%I) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 510 +--m0158:= a0158-r0158 +--E 294 + +--S 295 of 510 +--d0158:= D(m0158,x) +--E 295 + +--S 296 of 510 +t0159:= (cosh(x)^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (176) \|cosh(x) +--R Type: Expression(Integer) +--E 296 + +--S 297 of 510 +r0159:= 1/2*csgn(cosh(x)^2)*(x+cosh(x)*sinh(x)) +--R +--R There are no library operations named csgn +--R Use HyperDoc Browse or issue +--R )what op csgn +--R to learn if there is any operation containing " csgn " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named csgn +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 297 + +--S 298 of 510 +a0159:= integrate(t0159,x) +--R +--R +--R cosh(x)sinh(x) + x +--R (177) ------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 510 +--m0159:= a0159-r0159 +--E 299 + +--S 300 of 510 +--d0159:= D(m0159,x) +--E 300 + +--S 301 of 510 +t0160:= 1/(a+b*cosh(c+d*x))^4 +--R +--R +--R (178) +--R 1 +--R / +--R 4 4 3 3 2 2 2 +--R b cosh(d x + c) + 4a b cosh(d x + c) + 6a b cosh(d x + c) +--R + +--R 3 4 +--R 4a b cosh(d x + c) + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 510 +r0160:= a*(2*a^2+3*b^2)*atanh((a-b)*tanh(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/_ + (a^2-b^2)^(7/2)/d-1/3*b*sinh(c+d*x)/(a^2-b^2)/d/(a+b*cosh(c+d*x))^3-_ + 5/6*a*b*sinh(c+d*x)/(a^2-b^2)^2/d/(a+b*cosh(c+d*x))^2-_ + 1/6*b*(11*a^2+4*b^2)*sinh(c+d*x)/(a^2-b^2)^3/d/(a+b*cosh(c+d*x)) +--R +--R +--R (179) +--R 5 3 3 3 2 4 4 2 2 +--R (18a b + 12a b )cosh(d x + c) + (54a b + 36a b )cosh(d x + c) +--R + +--R 3 3 5 4 2 6 +--R (54a b + 36a b)cosh(d x + c) + 18a b + 12a +--R * +--R d x + c +--R (b - a)tanh(-------) +--R 2 +--R atanh(--------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 2 4 3 2 5 +--R (4b + 11a b )cosh(d x + c) + (3a b + 27a b )cosh(d x + c) + 2b +--R + +--R 2 3 4 +--R - 5a b + 18a b +--R * +--R +---------+ +--R | 2 2 +--R sinh(d x + c)\|- b + a +--R / +--R 9 2 7 4 5 6 3 3 +--R (6b - 18a b + 18a b - 6a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 +--R (18a b - 54a b + 54a b - 18a b)d cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 +--R (6a b - 18a b + 18a b - 6a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 302 + +--S 303 of 510 +a0160:= integrate(t0160,x) +--R +--R +--R (180) +--R [ +--R 5 3 3 6 +--R (9a b + 6a b )sinh(d x + c) +--R + +--R 5 3 3 2 4 4 2 5 +--R ((54a b + 36a b )cosh(d x + c) + 54a b + 36a b )sinh(d x + c) +--R + +--R 5 3 3 2 +--R (135a b + 90a b )cosh(d x + c) +--R + +--R 2 4 4 2 5 3 3 5 +--R (270a b + 180a b )cosh(d x + c) + 27a b + 126a b + 72a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 5 3 3 3 +--R (180a b + 120a b )cosh(d x + c) +--R + +--R 2 4 4 2 2 +--R (540a b + 360a b )cosh(d x + c) +--R + +--R 5 3 3 5 2 4 4 2 +--R (108a b + 504a b + 288a b)cosh(d x + c) + 108a b + 144a b +--R + +--R 6 +--R 48a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 5 3 3 4 +--R (135a b + 90a b )cosh(d x + c) +--R + +--R 2 4 4 2 3 +--R (540a b + 360a b )cosh(d x + c) +--R + +--R 5 3 3 5 2 +--R (162a b + 756a b + 432a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 5 3 3 +--R (324a b + 432a b + 144a )cosh(d x + c) + 27a b + 126a b +--R + +--R 5 +--R 72a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 3 3 5 +--R (54a b + 36a b )cosh(d x + c) +--R + +--R 2 4 4 2 4 +--R (270a b + 180a b )cosh(d x + c) +--R + +--R 5 3 3 5 3 +--R (108a b + 504a b + 288a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 2 +--R (324a b + 432a b + 144a )cosh(d x + c) +--R + +--R 5 3 3 5 2 4 4 2 +--R (54a b + 252a b + 144a b)cosh(d x + c) + 54a b + 36a b +--R * +--R sinh(d x + c) +--R + +--R 5 3 3 6 2 4 4 2 5 +--R (9a b + 6a b )cosh(d x + c) + (54a b + 36a b )cosh(d x + c) +--R + +--R 5 3 3 5 4 +--R (27a b + 126a b + 72a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 3 +--R (108a b + 144a b + 48a )cosh(d x + c) +--R + +--R 5 3 3 5 2 +--R (27a b + 126a b + 72a b)cosh(d x + c) +--R + +--R 2 4 4 2 5 3 3 +--R (54a b + 36a b )cosh(d x + c) + 9a b + 6a b +--R * +--R log +--R 2 2 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a b)sinh(d x + c) +--R + +--R 2 2 2 2 +--R b cosh(d x + c) + 2a b cosh(d x + c) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 +--R (- 2b + 2a b)sinh(d x + c) + (- 2b + 2a b)cosh(d x + c) +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R 2 +--R b cosh(d x + c) + 2a cosh(d x + c) + b +--R + +--R 4 3 2 5 +--R (- 18a b - 12a b )sinh(d x + c) +--R + +--R 4 3 2 2 3 4 4 +--R ((- 90a b - 60a b )cosh(d x + c) - 90a b - 60a b)sinh(d x + c) +--R + +--R 4 3 2 2 +--R (- 180a b - 120a b )cosh(d x + c) +--R + +--R 2 3 4 4 3 2 5 +--R (- 360a b - 240a b)cosh(d x + c) - 48a b - 164a b - 88a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 3 +--R (- 180a b - 120a b )cosh(d x + c) +--R + +--R 2 3 4 2 +--R (- 540a b - 360a b)cosh(d x + c) +--R + +--R 4 3 2 5 5 2 3 +--R (- 144a b - 492a b - 264a )cosh(d x + c) - 24b - 72a b +--R + +--R 4 +--R - 204a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 3 2 4 +--R (- 90a b - 60a b )cosh(d x + c) +--R + +--R 2 3 4 3 +--R (- 360a b - 240a b)cosh(d x + c) +--R + +--R 4 3 2 5 2 +--R (- 144a b - 492a b - 264a )cosh(d x + c) +--R + +--R 5 2 3 4 4 3 2 +--R (- 48b - 144a b - 408a b)cosh(d x + c) - 30a b - 120a b +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 5 +--R (- 18a b - 12a b )cosh(d x + c) +--R + +--R 2 3 4 4 +--R (- 90a b - 60a b)cosh(d x + c) +--R + +--R 4 3 2 5 3 +--R (- 48a b - 164a b - 88a )cosh(d x + c) +--R + +--R 5 2 3 4 2 +--R (- 24b - 72a b - 204a b)cosh(d x + c) +--R + +--R 4 3 2 5 2 3 +--R (- 30a b - 120a b )cosh(d x + c) - 8b - 22a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 9 2 7 4 5 6 3 6 +--R (6b - 18a b + 18a b - 6a b )d sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 +--R (36b - 108a b + 108a b - 36a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (36a b - 108a b + 108a b - 36a b )d +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 2 +--R (90b - 270a b + 270a b - 90a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (180a b - 540a b + 540a b - 180a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (18b + 18a b - 162a b + 198a b - 72a b)d +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 3 +--R (120b - 360a b + 360a b - 120a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (360a b - 1080a b + 1080a b - 360a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (72b + 72a b - 648a b + 792a b - 288a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 +--R (72a b - 168a b + 72a b + 72a b - 48a )d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 4 +--R (90b - 270a b + 270a b - 90a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 3 +--R (360a b - 1080a b + 1080a b - 360a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (108b + 108a b - 972a b + 1188a b - 432a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 +--R (216a b - 504a b + 216a b + 216a b - 144a )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (18b + 18a b - 162a b + 198a b - 72a b)d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 5 +--R (36b - 108a b + 108a b - 36a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 4 +--R (180a b - 540a b + 540a b - 180a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (72b + 72a b - 648a b + 792a b - 288a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (216a b - 504a b + 216a b + 216a b - 144a )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (36b + 36a b - 324a b + 396a b - 144a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (36a b - 108a b + 108a b - 36a b )d +--R * +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 6 +--R (6b - 18a b + 18a b - 6a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 5 +--R (36a b - 108a b + 108a b - 36a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (18b + 18a b - 162a b + 198a b - 72a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (72a b - 168a b + 72a b + 72a b - 48a )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (18b + 18a b - 162a b + 198a b - 72a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (36a b - 108a b + 108a b - 36a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 +--R (6b - 18a b + 18a b - 6a b )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 5 3 3 6 +--R (- 9a b - 6a b )sinh(d x + c) +--R + +--R 5 3 3 2 4 4 2 5 +--R ((- 54a b - 36a b )cosh(d x + c) - 54a b - 36a b )sinh(d x + c) +--R + +--R 5 3 3 2 +--R (- 135a b - 90a b )cosh(d x + c) +--R + +--R 2 4 4 2 5 3 3 5 +--R (- 270a b - 180a b )cosh(d x + c) - 27a b - 126a b - 72a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 5 3 3 3 +--R (- 180a b - 120a b )cosh(d x + c) +--R + +--R 2 4 4 2 2 +--R (- 540a b - 360a b )cosh(d x + c) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 108a b - 504a b - 288a b)cosh(d x + c) - 108a b - 144a b +--R + +--R 6 +--R - 48a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 5 3 3 4 +--R (- 135a b - 90a b )cosh(d x + c) +--R + +--R 2 4 4 2 3 +--R (- 540a b - 360a b )cosh(d x + c) +--R + +--R 5 3 3 5 2 +--R (- 162a b - 756a b - 432a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 5 3 3 +--R (- 324a b - 432a b - 144a )cosh(d x + c) - 27a b - 126a b +--R + +--R 5 +--R - 72a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 3 3 5 +--R (- 54a b - 36a b )cosh(d x + c) +--R + +--R 2 4 4 2 4 +--R (- 270a b - 180a b )cosh(d x + c) +--R + +--R 5 3 3 5 3 +--R (- 108a b - 504a b - 288a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 2 +--R (- 324a b - 432a b - 144a )cosh(d x + c) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 54a b - 252a b - 144a b)cosh(d x + c) - 54a b - 36a b +--R * +--R sinh(d x + c) +--R + +--R 5 3 3 6 2 4 4 2 5 +--R (- 9a b - 6a b )cosh(d x + c) + (- 54a b - 36a b )cosh(d x + c) +--R + +--R 5 3 3 5 4 +--R (- 27a b - 126a b - 72a b)cosh(d x + c) +--R + +--R 2 4 4 2 6 3 +--R (- 108a b - 144a b - 48a )cosh(d x + c) +--R + +--R 5 3 3 5 2 +--R (- 27a b - 126a b - 72a b)cosh(d x + c) +--R + +--R 2 4 4 2 5 3 3 +--R (- 54a b - 36a b )cosh(d x + c) - 9a b - 6a b +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(d x + c) + b cosh(d x + c) + a)\|b - a +--R atan(-------------------------------------------------) +--R 2 2 +--R b - a +--R + +--R 4 3 2 5 +--R (- 9a b - 6a b )sinh(d x + c) +--R + +--R 4 3 2 2 3 4 4 +--R ((- 45a b - 30a b )cosh(d x + c) - 45a b - 30a b)sinh(d x + c) +--R + +--R 4 3 2 2 +--R (- 90a b - 60a b )cosh(d x + c) +--R + +--R 2 3 4 4 3 2 5 +--R (- 180a b - 120a b)cosh(d x + c) - 24a b - 82a b - 44a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 3 +--R (- 90a b - 60a b )cosh(d x + c) +--R + +--R 2 3 4 2 +--R (- 270a b - 180a b)cosh(d x + c) +--R + +--R 4 3 2 5 5 2 3 +--R (- 72a b - 246a b - 132a )cosh(d x + c) - 12b - 36a b +--R + +--R 4 +--R - 102a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 3 2 4 +--R (- 45a b - 30a b )cosh(d x + c) +--R + +--R 2 3 4 3 +--R (- 180a b - 120a b)cosh(d x + c) +--R + +--R 4 3 2 5 2 +--R (- 72a b - 246a b - 132a )cosh(d x + c) +--R + +--R 5 2 3 4 4 3 2 +--R (- 24b - 72a b - 204a b)cosh(d x + c) - 15a b - 60a b +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 5 2 3 4 4 +--R (- 9a b - 6a b )cosh(d x + c) + (- 45a b - 30a b)cosh(d x + c) +--R + +--R 4 3 2 5 3 +--R (- 24a b - 82a b - 44a )cosh(d x + c) +--R + +--R 5 2 3 4 2 +--R (- 12b - 36a b - 102a b)cosh(d x + c) +--R + +--R 4 3 2 5 2 3 +--R (- 15a b - 60a b )cosh(d x + c) - 4b - 11a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 9 2 7 4 5 6 3 6 +--R (3b - 9a b + 9a b - 3a b )d sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 +--R (18b - 54a b + 54a b - 18a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (18a b - 54a b + 54a b - 18a b )d +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 2 +--R (45b - 135a b + 135a b - 45a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (90a b - 270a b + 270a b - 90a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (9b + 9a b - 81a b + 99a b - 36a b)d +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 3 +--R (60b - 180a b + 180a b - 60a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (180a b - 540a b + 540a b - 180a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (36b + 36a b - 324a b + 396a b - 144a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 +--R (36a b - 84a b + 36a b + 36a b - 24a )d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 4 +--R (45b - 135a b + 135a b - 45a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 3 +--R (180a b - 540a b + 540a b - 180a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (54b + 54a b - 486a b + 594a b - 216a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 +--R (108a b - 252a b + 108a b + 108a b - 72a )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (9b + 9a b - 81a b + 99a b - 36a b)d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 5 +--R (18b - 54a b + 54a b - 18a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 4 +--R (90a b - 270a b + 270a b - 90a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (36b + 36a b - 324a b + 396a b - 144a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (108a b - 252a b + 108a b + 108a b - 72a )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 +--R (18b + 18a b - 162a b + 198a b - 72a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (18a b - 54a b + 54a b - 18a b )d +--R * +--R sinh(d x + c) +--R + +--R 9 2 7 4 5 6 3 6 +--R (3b - 9a b + 9a b - 3a b )d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 5 +--R (18a b - 54a b + 54a b - 18a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (9b + 9a b - 81a b + 99a b - 36a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (36a b - 84a b + 36a b + 36a b - 24a )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (9b + 9a b - 81a b + 99a b - 36a b)d cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 +--R (18a b - 54a b + 54a b - 18a b )d cosh(d x + c) +--R + +--R 9 2 7 4 5 6 3 +--R (3b - 9a b + 9a b - 3a b )d +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 303 + +--S 304 of 510 +m0160a:= a0160.1-r0160 +--R +--R +--R (181) +--R 8 3 6 3 2 7 4 5 2 +--R (9a b + 6a b )cosh(d x + c) + (27a b + 18a b )cosh(d x + c) +--R + +--R 3 6 5 4 4 5 6 3 +--R (27a b + 18a b )cosh(d x + c) + 9a b + 6a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 3 6 4 +--R (54a b + 36a b )cosh(d x + c) +--R + +--R 2 7 4 5 3 +--R (216a b + 144a b )cosh(d x + c) +--R + +--R 3 6 5 4 2 +--R (324a b + 216a b )cosh(d x + c) +--R + +--R 4 5 6 3 5 4 7 2 +--R (216a b + 144a b )cosh(d x + c) + 54a b + 36a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 3 6 5 +--R (135a b + 90a b )cosh(d x + c) +--R + +--R 2 7 4 5 4 +--R (675a b + 450a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 3 +--R (27a b + 1341a b + 882a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 2 +--R (81a b + 1323a b + 846a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 4 5 6 3 +--R (81a b + 648a b + 396a b )cosh(d x + c) + 27a b + 126a b +--R + +--R 8 +--R 72a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 3 6 6 +--R (180a b + 120a b )cosh(d x + c) +--R + +--R 2 7 4 5 5 +--R (1080a b + 720a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 4 +--R (108a b + 2664a b + 1728a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 3 +--R (432a b + 3456a b + 2112a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 2 +--R (648a b + 2484a b + 1368a b )cosh(d x + c) +--R + +--R 4 5 6 3 8 5 4 7 2 +--R (432a b + 936a b + 432a b)cosh(d x + c) + 108a b + 144a b +--R + +--R 9 +--R 48a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 8 3 6 7 +--R (135a b + 90a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 +--R (945a b + 630a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 5 +--R (162a b + 2781a b + 1782a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 4 +--R (810a b + 4455a b + 2610a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 3 +--R (27a b + 1584a b + 4176a b + 2088a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 2 +--R (81a b + 1512a b + 2268a b + 864a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 4 5 +--R (81a b + 702a b + 648a b + 144a )cosh(d x + c) + 27a b +--R + +--R 6 3 8 +--R 126a b + 72a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 8 3 6 8 +--R (54a b + 36a b )cosh(d x + c) +--R + +--R 2 7 4 5 7 +--R (432a b + 288a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 6 +--R (108a b + 1476a b + 936a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 5 +--R (648a b + 2808a b + 1584a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 4 +--R (54a b + 1548a b + 3222a b + 1476a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 3 +--R (216a b + 1872a b + 2232a b + 720a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 2 +--R (324a b + 1188a b + 864a b + 144a )cosh(d x + c) +--R + +--R 4 5 6 3 8 5 4 7 2 +--R (216a b + 360a b + 144a b)cosh(d x + c) + 54a b + 36a b +--R * +--R sinh(d x + c) +--R + +--R 8 3 6 9 2 7 4 5 8 +--R (9a b + 6a b )cosh(d x + c) + (81a b + 54a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 +--R (27a b + 315a b + 198a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 6 +--R (189a b + 693a b + 378a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 5 +--R (27a b + 531a b + 936a b + 396a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 4 +--R (135a b + 765a b + 774a b + 216a b)cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (9a b + 249a b + 594a b + 360a b + 48a )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 2 +--R (27a b + 207a b + 234a b + 72a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 4 5 6 3 +--R (27a b + 72a b + 36a b )cosh(d x + c) + 9a b + 6a b +--R * +--R log +--R 2 2 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a b)sinh(d x + c) +--R + +--R 2 2 2 2 +--R b cosh(d x + c) + 2a b cosh(d x + c) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 +--R (- 2b + 2a b)sinh(d x + c) + (- 2b + 2a b)cosh(d x + c) +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R b sinh(d x + c) + (2b cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R 2 +--R b cosh(d x + c) + 2a cosh(d x + c) + b +--R + +--R 8 3 6 3 +--R (- 18a b - 12a b )cosh(d x + c) +--R + +--R 2 7 4 5 2 +--R (- 54a b - 36a b )cosh(d x + c) +--R + +--R 3 6 5 4 4 5 6 3 +--R (- 54a b - 36a b )cosh(d x + c) - 18a b - 12a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 3 6 4 +--R (- 108a b - 72a b )cosh(d x + c) +--R + +--R 2 7 4 5 3 +--R (- 432a b - 288a b )cosh(d x + c) +--R + +--R 3 6 5 4 2 +--R (- 648a b - 432a b )cosh(d x + c) +--R + +--R 4 5 6 3 5 4 7 2 +--R (- 432a b - 288a b )cosh(d x + c) - 108a b - 72a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 3 6 5 +--R (- 270a b - 180a b )cosh(d x + c) +--R + +--R 2 7 4 5 4 +--R (- 1350a b - 900a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 3 +--R (- 54a b - 2682a b - 1764a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 2 +--R (- 162a b - 2646a b - 1692a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 4 5 6 3 +--R (- 162a b - 1296a b - 792a b )cosh(d x + c) - 54a b - 252a b +--R + +--R 8 +--R - 144a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 3 6 6 +--R (- 360a b - 240a b )cosh(d x + c) +--R + +--R 2 7 4 5 5 +--R (- 2160a b - 1440a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 4 +--R (- 216a b - 5328a b - 3456a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 3 +--R (- 864a b - 6912a b - 4224a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 2 +--R (- 1296a b - 4968a b - 2736a b )cosh(d x + c) +--R + +--R 4 5 6 3 8 5 4 7 2 +--R (- 864a b - 1872a b - 864a b)cosh(d x + c) - 216a b - 288a b +--R + +--R 9 +--R - 96a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 8 3 6 7 +--R (- 270a b - 180a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 +--R (- 1890a b - 1260a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 5 +--R (- 324a b - 5562a b - 3564a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 4 +--R (- 1620a b - 8910a b - 5220a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 54a b - 3168a b - 8352a b - 4176a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 162a b - 3024a b - 4536a b - 1728a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 4 5 +--R (- 162a b - 1404a b - 1296a b - 288a )cosh(d x + c) - 54a b +--R + +--R 6 3 8 +--R - 252a b - 144a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 8 3 6 8 +--R (- 108a b - 72a b )cosh(d x + c) +--R + +--R 2 7 4 5 7 +--R (- 864a b - 576a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 6 +--R (- 216a b - 2952a b - 1872a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 5 +--R (- 1296a b - 5616a b - 3168a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 108a b - 3096a b - 6444a b - 2952a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 432a b - 3744a b - 4464a b - 1440a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 2 +--R (- 648a b - 2376a b - 1728a b - 288a )cosh(d x + c) +--R + +--R 4 5 6 3 8 5 4 7 2 +--R (- 432a b - 720a b - 288a b)cosh(d x + c) - 108a b - 72a b +--R * +--R sinh(d x + c) +--R + +--R 8 3 6 9 +--R (- 18a b - 12a b )cosh(d x + c) +--R + +--R 2 7 4 5 8 +--R (- 162a b - 108a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 +--R (- 54a b - 630a b - 396a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 6 +--R (- 378a b - 1386a b - 756a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 54a b - 1062a b - 1872a b - 792a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 270a b - 1530a b - 1548a b - 432a b)cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 18a b - 498a b - 1188a b - 720a b - 96a )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 54a b - 414a b - 468a b - 144a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 4 5 6 3 +--R (- 54a b - 144a b - 72a b )cosh(d x + c) - 18a b - 12a b +--R * +--R d x + c +--R (b - a)tanh(-------) +--R 2 +--R atanh(--------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 8 2 6 2 7 3 5 +--R (- 4b - 11a b )cosh(d x + c) + (- 3a b - 27a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 +--R - 2b + 5a b - 18a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 8 2 6 3 +--R (- 24b - 66a b )cosh(d x + c) +--R + +--R 7 3 5 2 +--R (- 42a b - 228a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 7 3 5 +--R (- 12b + 12a b - 270a b )cosh(d x + c) - 12a b + 30a b +--R + +--R 5 3 +--R - 108a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 2 6 4 +--R (- 60b - 165a b )cosh(d x + c) +--R + +--R 7 3 5 3 +--R (- 183a b - 747a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 2 +--R (- 42b - 150a b - 1248a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (- 69a b - 21a b - 900a b )cosh(d x + c) - 6b - 9a b - 12a b +--R + +--R 6 2 +--R - 228a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 2 6 5 +--R (- 80b - 220a b )cosh(d x + c) +--R + +--R 7 3 5 4 +--R (- 390a b - 1260a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 3 +--R (- 88b - 764a b - 2748a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 2 +--R (- 204a b - 872a b - 2824a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 7 +--R (- 24b - 72a b - 684a b - 1320a b )cosh(d x + c) - 24a b +--R + +--R 3 5 5 3 7 +--R 44a b - 266a b - 204a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 2 6 6 +--R (- 60b - 165a b )cosh(d x + c) +--R + +--R 7 3 5 5 +--R (- 465a b - 1185a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 4 +--R (- 102b - 1491a b - 3282a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 3 +--R (- 366a b - 2678a b - 4456a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 48b - 387a b - 2892a b - 3048a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 8 +--R (- 81a b - 129a b - 1704a b - 936a b)cosh(d x + c) - 6b +--R + +--R 2 6 4 4 6 2 8 +--R - 9a b - 42a b - 380a b - 88a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 8 2 6 7 +--R (- 24b - 66a b )cosh(d x + c) +--R + +--R 7 3 5 6 +--R (- 318a b - 612a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 5 +--R (- 60b - 1464a b - 2166a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 4 +--R (- 384a b - 3462a b - 3804a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 72b - 810a b - 4764a b - 3504a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (- 186a b - 816a b - 3804a b - 1584a b)cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 +--R (- 12b - 108a b - 510a b - 1536a b - 264a )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 +--R - 12a b + 6a b - 180a b - 204a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 8 2 6 8 +--R (- 4b - 11a b )cosh(d x + c) +--R + +--R 7 3 5 7 +--R (- 117a b - 153a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 +--R (- 14b - 724a b - 732a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 5 +--R (- 213a b - 2093a b - 1684a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 66b - 702a b - 3528a b - 2004a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 3 +--R (- 231a b - 1123a b - 3560a b - 1176a b)cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- 10b - 272a b - 1092a b - 1932a b - 264a )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 8 +--R (- 15a b - 135a b - 612a b - 408a b)cosh(d x + c) - 2b +--R + +--R 2 6 4 4 6 2 +--R 5a b - 48a b - 120a b +--R * +--R sinh(d x + c) +--R + +--R 7 3 5 8 +--R (- 18a b - 12a b )cosh(d x + c) +--R + +--R 2 6 4 4 7 +--R (- 144a b - 96a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 6 +--R (- 48a b - 488a b - 304a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 24b - 216a b - 984a b - 456a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 4 +--R (- 102a b - 480a b - 1194a b - 324a b)cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (- 8b - 184a b - 624a b - 776a b - 88a )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (- 24a b - 180a b - 432a b - 204a b)cosh(d x + c) +--R + +--R 2 6 4 4 6 2 3 5 5 3 +--R (- 24a b - 96a b - 120a b )cosh(d x + c) - 8a b - 22a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 12 2 10 4 8 6 6 3 +--R (6b - 18a b + 18a b - 6a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 2 +--R (18a b - 54a b + 54a b - 18a b )d cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 +--R (18a b - 54a b + 54a b - 18a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 +--R (6a b - 18a b + 18a b - 6a b )d +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 4 +--R (36b - 108a b + 108a b - 36a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 3 +--R (144a b - 432a b + 432a b - 144a b )d cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 2 +--R (216a b - 648a b + 648a b - 216a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 +--R (144a b - 432a b + 432a b - 144a b )d cosh(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 +--R (36a b - 108a b + 108a b - 36a b )d +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 5 +--R (90b - 270a b + 270a b - 90a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 4 +--R (450a b - 1350a b + 1350a b - 450a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 3 +--R (18b + 828a b - 2592a b + 2628a b - 882a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 2 +--R (54a b + 684a b - 2376a b + 2484a b - 846a b )d cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (54a b + 234a b - 1026a b + 1134a b - 396a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 11 +--R (18a b + 18a b - 162a b + 198a b - 72a b)d +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 6 +--R (120b - 360a b + 360a b - 120a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 5 +--R (720a b - 2160a b + 2160a b - 720a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (72b + 1512a b - 4968a b + 5112a b - 1728a b )d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (288a b + 1248a b - 5472a b + 6048a b - 2112a b )d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (432a b + 72a b - 2808a b + 3672a b - 1368a b )d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 11 +--R (288a b - 432a b - 432a b + 1008a b - 432a b)d cosh(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 12 +--R (72a b - 168a b + 72a b + 72a b - 48a )d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 7 +--R (90b - 270a b + 270a b - 90a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 6 +--R (630a b - 1890a b + 1890a b - 630a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (108b + 1458a b - 5022a b + 5238a b - 1782a b )d +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (540a b + 990a b - 6210a b + 7290a b - 2610a b )d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (18b + 990a b - 990a b - 3150a b + 5220a b - 2088a b )d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (54a b + 810a b - 1890a b + 270a b + 1620a b - 864a b)d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 12 +--R (54a b + 270a b - 990a b + 810a b - 144a )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 11 +--R (18a b + 18a b - 162a b + 198a b - 72a b)d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 +--R (36b - 108a b + 108a b - 36a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 7 +--R (288a b - 864a b + 864a b - 288a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 6 +--R (72b + 720a b - 2592a b + 2736a b - 936a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (432a b + 288a b - 3456a b + 4320a b - 1584a b )d +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (36b + 900a b - 1440a b - 1440a b + 3420a b - 1476a b )d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (144a b + 720a b - 2304a b + 1152a b + 1008a b - 720a b)d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 10 6 6 8 4 10 2 12 +--R (216a b - 1152a b + 1296a b - 216a b - 144a )d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 3 9 5 7 9 3 11 +--R (144a b - 288a b + 288a b - 144a b)d cosh(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 +--R (36a b - 108a b + 108a b - 36a b )d +--R * +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 9 +--R (6b - 18a b + 18a b - 6a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 8 +--R (54a b - 162a b + 162a b - 54a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 7 +--R (18b + 144a b - 540a b + 576a b - 198a b )d cosh(d x + c) +--R + +--R 11 5 7 7 5 9 3 6 +--R (126a b - 756a b + 1008a b - 378a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (18b + 288a b - 576a b - 180a b + 846a b - 396a b )d +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (90a b + 180a b - 864a b + 612a b + 198a b - 216a b)d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 12 +--R (6b + 144a b - 180a b - 336a b + 558a b - 144a b - 48a )d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (18a b + 72a b - 252a b + 144a b + 90a b - 72a b)d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (18a b - 18a b - 54a b + 90a b - 36a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 +--R (6a b - 18a b + 18a b - 6a b )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 304 + +--S 305 of 510 +d0160a:= D(m01601,x) +--R +--R +--R (182) 0 +--R Type: Polynomial(Integer) +--E 305 + +--S 306 of 510 +m0160b:= a0160.2-r0160 +--R +--R +--R (183) +--R 8 3 6 3 +--R (- 18a b - 12a b )cosh(d x + c) +--R + +--R 2 7 4 5 2 +--R (- 54a b - 36a b )cosh(d x + c) +--R + +--R 3 6 5 4 4 5 6 3 +--R (- 54a b - 36a b )cosh(d x + c) - 18a b - 12a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 3 6 4 +--R (- 108a b - 72a b )cosh(d x + c) +--R + +--R 2 7 4 5 3 +--R (- 432a b - 288a b )cosh(d x + c) +--R + +--R 3 6 5 4 2 +--R (- 648a b - 432a b )cosh(d x + c) +--R + +--R 4 5 6 3 5 4 7 2 +--R (- 432a b - 288a b )cosh(d x + c) - 108a b - 72a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 3 6 5 +--R (- 270a b - 180a b )cosh(d x + c) +--R + +--R 2 7 4 5 4 +--R (- 1350a b - 900a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 3 +--R (- 54a b - 2682a b - 1764a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 2 +--R (- 162a b - 2646a b - 1692a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 4 5 6 3 +--R (- 162a b - 1296a b - 792a b )cosh(d x + c) - 54a b - 252a b +--R + +--R 8 +--R - 144a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 3 6 6 +--R (- 360a b - 240a b )cosh(d x + c) +--R + +--R 2 7 4 5 5 +--R (- 2160a b - 1440a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 4 +--R (- 216a b - 5328a b - 3456a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 3 +--R (- 864a b - 6912a b - 4224a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 2 +--R (- 1296a b - 4968a b - 2736a b )cosh(d x + c) +--R + +--R 4 5 6 3 8 5 4 7 2 +--R (- 864a b - 1872a b - 864a b)cosh(d x + c) - 216a b - 288a b +--R + +--R 9 +--R - 96a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 8 3 6 7 +--R (- 270a b - 180a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 +--R (- 1890a b - 1260a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 5 +--R (- 324a b - 5562a b - 3564a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 4 +--R (- 1620a b - 8910a b - 5220a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 54a b - 3168a b - 8352a b - 4176a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 162a b - 3024a b - 4536a b - 1728a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 4 5 +--R (- 162a b - 1404a b - 1296a b - 288a )cosh(d x + c) - 54a b +--R + +--R 6 3 8 +--R - 252a b - 144a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 8 3 6 8 +--R (- 108a b - 72a b )cosh(d x + c) +--R + +--R 2 7 4 5 7 +--R (- 864a b - 576a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 6 +--R (- 216a b - 2952a b - 1872a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 5 +--R (- 1296a b - 5616a b - 3168a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 108a b - 3096a b - 6444a b - 2952a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 432a b - 3744a b - 4464a b - 1440a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 2 +--R (- 648a b - 2376a b - 1728a b - 288a )cosh(d x + c) +--R + +--R 4 5 6 3 8 5 4 7 2 +--R (- 432a b - 720a b - 288a b)cosh(d x + c) - 108a b - 72a b +--R * +--R sinh(d x + c) +--R + +--R 8 3 6 9 +--R (- 18a b - 12a b )cosh(d x + c) +--R + +--R 2 7 4 5 8 +--R (- 162a b - 108a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 +--R (- 54a b - 630a b - 396a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 6 +--R (- 378a b - 1386a b - 756a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 54a b - 1062a b - 1872a b - 792a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 270a b - 1530a b - 1548a b - 432a b)cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 18a b - 498a b - 1188a b - 720a b - 96a )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 54a b - 414a b - 468a b - 144a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 4 5 6 3 +--R (- 54a b - 144a b - 72a b )cosh(d x + c) - 18a b - 12a b +--R * +--R d x + c +--R +-------+ (b - a)tanh(-------) +--R | 2 2 2 +--R \|b - a atanh(--------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 8 3 6 3 +--R (- 18a b - 12a b )cosh(d x + c) +--R + +--R 2 7 4 5 2 +--R (- 54a b - 36a b )cosh(d x + c) +--R + +--R 3 6 5 4 4 5 6 3 +--R (- 54a b - 36a b )cosh(d x + c) - 18a b - 12a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 3 6 4 +--R (- 108a b - 72a b )cosh(d x + c) +--R + +--R 2 7 4 5 3 +--R (- 432a b - 288a b )cosh(d x + c) +--R + +--R 3 6 5 4 2 +--R (- 648a b - 432a b )cosh(d x + c) +--R + +--R 4 5 6 3 5 4 7 2 +--R (- 432a b - 288a b )cosh(d x + c) - 108a b - 72a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 3 6 5 +--R (- 270a b - 180a b )cosh(d x + c) +--R + +--R 2 7 4 5 4 +--R (- 1350a b - 900a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 3 +--R (- 54a b - 2682a b - 1764a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 2 +--R (- 162a b - 2646a b - 1692a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 4 5 6 3 +--R (- 162a b - 1296a b - 792a b )cosh(d x + c) - 54a b - 252a b +--R + +--R 8 +--R - 144a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 3 6 6 +--R (- 360a b - 240a b )cosh(d x + c) +--R + +--R 2 7 4 5 5 +--R (- 2160a b - 1440a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 4 +--R (- 216a b - 5328a b - 3456a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 3 +--R (- 864a b - 6912a b - 4224a b )cosh(d x + c) +--R + +--R 3 6 5 4 7 2 2 +--R (- 1296a b - 4968a b - 2736a b )cosh(d x + c) +--R + +--R 4 5 6 3 8 5 4 7 2 +--R (- 864a b - 1872a b - 864a b)cosh(d x + c) - 216a b - 288a b +--R + +--R 9 +--R - 96a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 8 3 6 7 +--R (- 270a b - 180a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 +--R (- 1890a b - 1260a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 5 +--R (- 324a b - 5562a b - 3564a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 4 +--R (- 1620a b - 8910a b - 5220a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 54a b - 3168a b - 8352a b - 4176a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 162a b - 3024a b - 4536a b - 1728a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 4 5 +--R (- 162a b - 1404a b - 1296a b - 288a )cosh(d x + c) - 54a b +--R + +--R 6 3 8 +--R - 252a b - 144a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 8 3 6 8 +--R (- 108a b - 72a b )cosh(d x + c) +--R + +--R 2 7 4 5 7 +--R (- 864a b - 576a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 6 +--R (- 216a b - 2952a b - 1872a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 5 +--R (- 1296a b - 5616a b - 3168a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 108a b - 3096a b - 6444a b - 2952a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 432a b - 3744a b - 4464a b - 1440a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 9 2 +--R (- 648a b - 2376a b - 1728a b - 288a )cosh(d x + c) +--R + +--R 4 5 6 3 8 5 4 7 2 +--R (- 432a b - 720a b - 288a b)cosh(d x + c) - 108a b - 72a b +--R * +--R sinh(d x + c) +--R + +--R 8 3 6 9 +--R (- 18a b - 12a b )cosh(d x + c) +--R + +--R 2 7 4 5 8 +--R (- 162a b - 108a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 +--R (- 54a b - 630a b - 396a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 6 +--R (- 378a b - 1386a b - 756a b )cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 54a b - 1062a b - 1872a b - 792a b )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 270a b - 1530a b - 1548a b - 432a b)cosh(d x + c) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 18a b - 498a b - 1188a b - 720a b - 96a )cosh(d x + c) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 54a b - 414a b - 468a b - 144a b)cosh(d x + c) +--R + +--R 3 6 5 4 7 2 4 5 6 3 +--R (- 54a b - 144a b - 72a b )cosh(d x + c) - 18a b - 12a b +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sinh(d x + c) + b cosh(d x + c) + a)\|b - a +--R \|- b + a atan(-------------------------------------------------) +--R 2 2 +--R b - a +--R + +--R 8 2 6 2 7 3 5 +--R (- 4b - 11a b )cosh(d x + c) + (- 3a b - 27a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 +--R - 2b + 5a b - 18a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 8 2 6 3 +--R (- 24b - 66a b )cosh(d x + c) +--R + +--R 7 3 5 2 +--R (- 42a b - 228a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 7 3 5 +--R (- 12b + 12a b - 270a b )cosh(d x + c) - 12a b + 30a b +--R + +--R 5 3 +--R - 108a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 8 2 6 4 +--R (- 60b - 165a b )cosh(d x + c) +--R + +--R 7 3 5 3 +--R (- 183a b - 747a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 2 +--R (- 42b - 150a b - 1248a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (- 69a b - 21a b - 900a b )cosh(d x + c) - 6b - 9a b - 12a b +--R + +--R 6 2 +--R - 228a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 8 2 6 5 +--R (- 80b - 220a b )cosh(d x + c) +--R + +--R 7 3 5 4 +--R (- 390a b - 1260a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 3 +--R (- 88b - 764a b - 2748a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 2 +--R (- 204a b - 872a b - 2824a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 7 +--R (- 24b - 72a b - 684a b - 1320a b )cosh(d x + c) - 24a b +--R + +--R 3 5 5 3 7 +--R 44a b - 266a b - 204a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 8 2 6 6 +--R (- 60b - 165a b )cosh(d x + c) +--R + +--R 7 3 5 5 +--R (- 465a b - 1185a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 4 +--R (- 102b - 1491a b - 3282a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 3 +--R (- 366a b - 2678a b - 4456a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 48b - 387a b - 2892a b - 3048a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 8 +--R (- 81a b - 129a b - 1704a b - 936a b)cosh(d x + c) - 6b +--R + +--R 2 6 4 4 6 2 8 +--R - 9a b - 42a b - 380a b - 88a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 8 2 6 7 +--R (- 24b - 66a b )cosh(d x + c) +--R + +--R 7 3 5 6 +--R (- 318a b - 612a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 5 +--R (- 60b - 1464a b - 2166a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 4 +--R (- 384a b - 3462a b - 3804a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 72b - 810a b - 4764a b - 3504a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (- 186a b - 816a b - 3804a b - 1584a b)cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 +--R (- 12b - 108a b - 510a b - 1536a b - 264a )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 +--R - 12a b + 6a b - 180a b - 204a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 8 2 6 8 +--R (- 4b - 11a b )cosh(d x + c) +--R + +--R 7 3 5 7 +--R (- 117a b - 153a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 +--R (- 14b - 724a b - 732a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 5 +--R (- 213a b - 2093a b - 1684a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 66b - 702a b - 3528a b - 2004a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 3 +--R (- 231a b - 1123a b - 3560a b - 1176a b)cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- 10b - 272a b - 1092a b - 1932a b - 264a )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 8 +--R (- 15a b - 135a b - 612a b - 408a b)cosh(d x + c) - 2b +--R + +--R 2 6 4 4 6 2 +--R 5a b - 48a b - 120a b +--R * +--R sinh(d x + c) +--R + +--R 7 3 5 8 +--R (- 18a b - 12a b )cosh(d x + c) +--R + +--R 2 6 4 4 7 +--R (- 144a b - 96a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 6 +--R (- 48a b - 488a b - 304a b )cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 24b - 216a b - 984a b - 456a b )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 4 +--R (- 102a b - 480a b - 1194a b - 324a b)cosh(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (- 8b - 184a b - 624a b - 776a b - 88a )cosh(d x + c) +--R + +--R 7 3 5 5 3 7 2 +--R (- 24a b - 180a b - 432a b - 204a b)cosh(d x + c) +--R + +--R 2 6 4 4 6 2 3 5 5 3 +--R (- 24a b - 96a b - 120a b )cosh(d x + c) - 8a b - 22a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 12 2 10 4 8 6 6 3 +--R (6b - 18a b + 18a b - 6a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 2 +--R (18a b - 54a b + 54a b - 18a b )d cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 +--R (18a b - 54a b + 54a b - 18a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 +--R (6a b - 18a b + 18a b - 6a b )d +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 4 +--R (36b - 108a b + 108a b - 36a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 3 +--R (144a b - 432a b + 432a b - 144a b )d cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 2 +--R (216a b - 648a b + 648a b - 216a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 +--R (144a b - 432a b + 432a b - 144a b )d cosh(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 +--R (36a b - 108a b + 108a b - 36a b )d +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 5 +--R (90b - 270a b + 270a b - 90a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 4 +--R (450a b - 1350a b + 1350a b - 450a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 3 +--R (18b + 828a b - 2592a b + 2628a b - 882a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 2 +--R (54a b + 684a b - 2376a b + 2484a b - 846a b )d cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (54a b + 234a b - 1026a b + 1134a b - 396a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 11 +--R (18a b + 18a b - 162a b + 198a b - 72a b)d +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 6 +--R (120b - 360a b + 360a b - 120a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 5 +--R (720a b - 2160a b + 2160a b - 720a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (72b + 1512a b - 4968a b + 5112a b - 1728a b )d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (288a b + 1248a b - 5472a b + 6048a b - 2112a b )d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (432a b + 72a b - 2808a b + 3672a b - 1368a b )d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 11 +--R (288a b - 432a b - 432a b + 1008a b - 432a b)d cosh(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 12 +--R (72a b - 168a b + 72a b + 72a b - 48a )d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 7 +--R (90b - 270a b + 270a b - 90a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 6 +--R (630a b - 1890a b + 1890a b - 630a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (108b + 1458a b - 5022a b + 5238a b - 1782a b )d +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (540a b + 990a b - 6210a b + 7290a b - 2610a b )d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (18b + 990a b - 990a b - 3150a b + 5220a b - 2088a b )d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (54a b + 810a b - 1890a b + 270a b + 1620a b - 864a b)d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 12 +--R (54a b + 270a b - 990a b + 810a b - 144a )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 11 +--R (18a b + 18a b - 162a b + 198a b - 72a b)d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 +--R (36b - 108a b + 108a b - 36a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 7 +--R (288a b - 864a b + 864a b - 288a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 6 +--R (72b + 720a b - 2592a b + 2736a b - 936a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (432a b + 288a b - 3456a b + 4320a b - 1584a b )d +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (36b + 900a b - 1440a b - 1440a b + 3420a b - 1476a b )d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (144a b + 720a b - 2304a b + 1152a b + 1008a b - 720a b)d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 10 6 6 8 4 10 2 12 +--R (216a b - 1152a b + 1296a b - 216a b - 144a )d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 3 9 5 7 9 3 11 +--R (144a b - 288a b + 288a b - 144a b)d cosh(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 +--R (36a b - 108a b + 108a b - 36a b )d +--R * +--R sinh(d x + c) +--R + +--R 12 2 10 4 8 6 6 9 +--R (6b - 18a b + 18a b - 6a b )d cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 8 +--R (54a b - 162a b + 162a b - 54a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 7 +--R (18b + 144a b - 540a b + 576a b - 198a b )d cosh(d x + c) +--R + +--R 11 5 7 7 5 9 3 6 +--R (126a b - 756a b + 1008a b - 378a b )d cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (18b + 288a b - 576a b - 180a b + 846a b - 396a b )d +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (90a b + 180a b - 864a b + 612a b + 198a b - 216a b)d +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 12 +--R (6b + 144a b - 180a b - 336a b + 558a b - 144a b - 48a )d +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (18a b + 72a b - 252a b + 144a b + 90a b - 72a b)d +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (18a b - 18a b - 54a b + 90a b - 36a b )d cosh(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 +--R (6a b - 18a b + 18a b - 6a b )d +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 510 +d0160b:= D(m0160b,x) +--R +--R +--R (184) +--R 11 10 2 9 3 8 2 +--R (4b - 4a b + 11a b - 11a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 11 10 +--R (- 2a b + 2a b + 32a b - 32a b )cosh(d x + c) + 6b - 6a b +--R + +--R 2 9 3 8 4 7 5 6 +--R - 18a b + 18a b + 27a b - 27a b +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 3 +--R (32b - 32a b + 88a b - 88a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 2 +--R (16a b - 16a b + 344a b - 344a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (48b - 48a b - 160a b + 160a b + 472a b - 472a b ) +--R * +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 48a b - 48a b - 144a b + 144a b + 216a b - 216a b +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 4 +--R (108b - 117a b + 297a b - 303a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 3 +--R (161a b - 197a b + 1474a b - 1498a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (182b - 182a b - 474a b + 420a b + 2767a b - 2803a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R (326a b - 326a b - 923a b + 887a b + 2262a b - 2286a b ) +--R * +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R 24b - 24a b + 72a b - 72a b - 324a b + 315a b + 648a b +--R + +--R 7 4 +--R - 654a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 5 +--R (192b - 264a b + 528a b - 576a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 4 +--R (472a b - 832a b + 3248a b - 3488a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (416b - 416a b - 544a b - 176a b + 7808a b - 8288a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 1024a b - 1024a b - 2096a b + 1376a b + 8992a b +--R + +--R 6 5 +--R - 9472a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 144b - 144a b + 368a b - 368a b - 1200a b + 840a b +--R + +--R 6 5 7 4 +--R 4768a b - 5008a b +--R * +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 144a b - 144a b - 240a b + 240a b + 72a b - 144a b +--R + +--R 7 4 8 3 +--R 864a b - 912a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 6 +--R (168b - 420a b + 462a b - 630a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 +--R (560a b - 2072a b + 3640a b - 4648a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 +--R 588b - 624a b - 196a b - 3572a b + 11158a b +--R + +--R 5 6 +--R - 13654a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 1844a b - 1988a b - 1948a b - 3044a b + 16904a b +--R + +--R 6 5 +--R - 20168a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 376b - 376a b + 946a b - 1162a b - 600a b - 3108a b +--R + +--R 6 5 7 4 +--R 12928a b - 15304a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 700a b - 700a b - 1132a b + 988a b + 1912a b - 3376a b +--R + +--R 7 4 8 3 +--R 4400a b - 5312a b +--R * +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 36b - 36a b + 180a b - 180a b - 606a b + 570a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 1008a b - 1248a b + 432a b - 576a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 10 3 8 7 +--R (- 504a b - 336a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 6 +--R (- 56a b - 3472a b + 896a b - 3248a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (448b - 664a b - 672a b - 9840a b + 5264a b - 12176a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 1768a b - 2848a b - 1216a b - 16064a b + 12048a b +--R + +--R 6 5 +--R - 23088a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 +--R 528b - 528a b + 1248a b - 3408a b + 1840a b +--R + +--R 5 6 6 5 7 4 +--R - 18760a b + 13184a b - 23504a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 1392a b - 1392a b - 1808a b - 352a b + 6360a b +--R + +--R 6 5 7 4 8 3 +--R - 16224a b + 6656a b - 12272a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 144b - 144a b + 624a b - 624a b - 1664a b + 584a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 4784a b - 7952a b + 1152a b - 2784a b +--R * +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 144a b - 144a b - 240a b + 240a b + 72a b - 288a b +--R + +--R 7 4 8 3 10 +--R 864a b - 1296a b - 192a b +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 8 +--R (- 168b - 462a b - 462a b + 42a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 7 +--R (- 994a b - 4046a b - 2996a b - 364a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (28b - 568a b - 2660a b - 14800a b - 7658a b - 3742a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 248a b - 3488a b - 3754a b - 30446a b - 9724a b +--R + +--R 6 5 +--R - 11636a b +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 456b - 510a b - 398a b - 7630a b - 832a b - 40550a b +--R + +--R 6 5 7 4 +--R - 6576a b - 17460a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 1638a b - 1854a b - 2864a b - 7648a b + 5656a b +--R + +--R 6 5 7 4 8 3 +--R - 37264a b - 2960a b - 13504a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 220b - 220a b + 1328a b - 1652a b - 2914a b - 4754a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 7360a b - 22192a b - 1584a b - 4992a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 412a b - 412a b - 322a b + 106a b - 68a b - 2884a b +--R + +--R 7 4 8 3 9 2 10 +--R 2960a b - 6848a b - 672a b - 672a b +--R * +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R 24b - 24a b + 72a b - 72a b - 228a b + 174a b + 360a b +--R + +--R 7 4 8 3 9 2 10 +--R - 828a b + 288a b - 720a b - 96a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 9 +--R (- 192b - 312a b - 528a b + 192a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 8 +--R (- 1304a b - 3232a b - 4336a b + 1312a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 288b - 432a b - 4064a b - 13840a b - 14848a b +--R + +--R 5 6 +--R 3232a b +--R * +--R 7 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 1424a b - 3616a b - 8048a b - 32608a b - 27488a b +--R + +--R 6 5 +--R 2624a b +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 +--R 368b - 584a b - 4000a b - 10832a b - 9872a b +--R + +--R 5 6 6 5 7 4 +--R - 48520a b - 30176a b - 2224a b +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 1592a b - 2672a b - 7616a b - 16144a b - 5256a b +--R + +--R 6 5 7 4 8 3 +--R - 49488a b - 20640a b - 5616a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 +--R 128b - 128a b + 2176a b - 4336a b - 8096a b +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R - 14224a b + 1568a b - 34784a b - 9216a b - 3648a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 352a b - 352a b + 784a b - 2944a b - 3472a b - 8768a b +--R + +--R 7 4 8 3 9 2 10 +--R 2624a b - 15008a b - 2688a b - 768a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 48b - 48a b + 80a b - 80a b + 48a b - 1128a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 128a b - 3472a b + 576a b - 3072a b - 384a b +--R * +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 48a b - 48a b - 144a b + 144a b + 216a b - 432a b +--R + +--R 8 3 10 +--R - 432a b - 192a b +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 10 +--R (- 108b - 144a b - 297a b + 129a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 9 +--R (- 838a b - 1682a b - 2792a b + 1112a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 274b - 266a b - 3114a b - 8046a b - 11057a b +--R + +--R 5 6 +--R 3857a b +--R * +--R 8 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 1636a b - 2684a b - 7916a b - 20884a b - 23928a b +--R + +--R 6 5 +--R 6648a b +--R * +--R 7 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 +--R 360b - 684a b - 5610a b - 9078a b - 13352a b +--R + +--R 5 6 6 5 7 4 +--R - 34420a b - 31168a b + 5752a b +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 1392a b - 3336a b - 11804a b - 15844a b - 13272a b +--R + +--R 6 5 7 4 8 3 +--R - 39504a b - 25456a b + 1984a b +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 11 2 9 3 8 4 7 5 6 +--R - 36b + 2100a b - 6876a b - 14354a b - 17002a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 6736a b - 32000a b - 13104a b - 192a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 76a b - 68a b + 1468a b - 7612a b - 9432a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 12312a b - 1248a b - 16896a b - 4032a b - 192a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 20b - 20a b - 117a b - 99a b + 544a b - 4900a b +--R + +--R 6 5 7 4 9 2 10 +--R - 2976a b - 5880a b - 4896a b - 576a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 38a b - 38a b - 140a b - 4a b + 264a b - 1872a b +--R + +--R 7 4 8 3 10 +--R - 432a b - 1440a b - 576a b +--R * +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 7 4 +--R 6b - 6a b - 18a b + 18a b + 27a b - 63a b - 240a b +--R + +--R 9 2 +--R - 144a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 11 +--R (- 32b - 40a b - 88a b + 40a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 10 +--R (- 280a b - 512a b - 920a b + 392a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 112b - 104a b - 1216a b - 2672a b - 4072a b +--R + +--R 5 6 +--R 1576a b +--R * +--R 9 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 776a b - 1168a b - 3728a b - 7504a b - 9896a b +--R + +--R 6 5 +--R 3272a b +--R * +--R 8 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 +--R 240b - 456a b - 3376a b - 4112a b - 7408a b +--R + +--R 5 6 6 5 7 4 +--R - 13688a b - 14656a b + 3856a b +--R * +--R 7 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 792a b - 2304a b - 8288a b - 7840a b - 8984a b +--R + +--R 6 5 7 4 8 3 +--R - 17728a b - 13760a b + 2672a b +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 80b + 8a b + 944a b - 5312a b - 11392a b - 9848a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 6608a b - 16144a b - 8064a b + 1056a b +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 280a b - 80a b + 496a b - 7216a b - 9080a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 8416a b - 2848a b - 9680a b - 2688a b + 192a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 16b + 16a b - 280a b - 440a b - 16a b - 5864a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 4128a b - 4656a b - 576a b - 3456a b - 384a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R - 32a b + 32a b - 40a b - 680a b - 264a b - 2592a b +--R + +--R 7 4 8 3 10 +--R - 864a b - 1584a b - 576a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 +--R - 16a b + 16a b + 40a b - 400a b - 144a b - 528a b +--R + +--R 9 2 +--R - 288a b +--R * +--R cosh(d x + c) +--R + +--R 6 5 8 3 +--R - 72a b - 48a b +--R * +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 12 +--R (- 4b - 5a b - 11a b + 5a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 11 +--R (- 39a b - 69a b - 126a b + 54a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (- 18b - 18a b - 194a b - 388a b - 613a b + 241a b ) +--R * +--R 10 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R (- 142a b - 218a b - 691a b - 1169a b - 1642a b + 562a b ) +--R * +--R 9 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 64b - 118a b - 770a b - 778a b - 1532a b - 2365a b +--R + +--R 6 5 7 4 +--R - 2712a b + 786a b +--R * +--R 8 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 190a b - 622a b - 2152a b - 1592a b - 2104a b - 3440a b +--R + +--R 7 4 8 3 +--R - 2864a b + 704a b +--R * +--R 7 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 28b - 8a b + 136a b - 1564a b - 3278a b - 2302a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 1888a b - 3440a b - 1872a b + 384a b +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R - 120a b - 96a b - 106a b - 2414a b - 2980a b - 2276a b +--R + +--R 7 4 8 3 9 2 10 +--R - 1072a b - 2240a b - 672a b + 96a b +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 12b + 3a b - 155a b - 355a b - 284a b - 2266a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 1640a b - 1420a b - 288a b - 912a b - 96a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R - 31a b - 5a b - 50a b - 550a b - 312a b - 1152a b +--R + +--R 7 4 8 3 10 +--R - 432a b - 576a b - 192a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R - 2b + 2a b - 14a b - 40a b - 5a b - 355a b - 144a b +--R + +--R 7 4 9 2 +--R - 288a b - 144a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 8 3 +--R (- 2a b + 2a b + 5a b - 41a b - 18a b - 78a b - 48a b ) +--R * +--R cosh(d x + c) +--R + +--R 5 6 7 4 +--R - 9a b - 6a b +--R * +--R d x + c 2 +--R tanh(-------) +--R 2 +--R + +--R 11 10 2 9 3 8 2 +--R (4b + 4a b + 11a b + 11a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 11 10 +--R (- 2a b - 2a b + 32a b + 32a b )cosh(d x + c) + 6b + 6a b +--R + +--R 2 9 3 8 4 7 5 6 +--R - 18a b - 18a b + 27a b + 27a b +--R * +--R 10 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 3 +--R (32b + 32a b + 88a b + 88a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 2 +--R (16a b + 16a b + 344a b + 344a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (48b + 48a b - 160a b - 160a b + 472a b + 472a b ) +--R * +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 48a b + 48a b - 144a b - 144a b + 216a b + 216a b +--R * +--R 9 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 4 +--R (108b + 117a b + 297a b + 303a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 3 +--R (161a b + 197a b + 1474a b + 1498a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (182b + 182a b - 474a b - 420a b + 2767a b + 2803a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R (326a b + 326a b - 923a b - 887a b + 2262a b + 2286a b ) +--R * +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R 24b + 24a b + 72a b + 72a b - 324a b - 315a b + 648a b +--R + +--R 7 4 +--R 654a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 5 +--R (192b + 264a b + 528a b + 576a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 4 +--R (472a b + 832a b + 3248a b + 3488a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (416b + 416a b - 544a b + 176a b + 7808a b + 8288a b ) +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R (1024a b + 1024a b - 2096a b - 1376a b + 8992a b + 9472a b ) +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 144b + 144a b + 368a b + 368a b - 1200a b - 840a b +--R + +--R 6 5 7 4 +--R 4768a b + 5008a b +--R * +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 7 4 +--R 144a b + 144a b - 240a b - 240a b + 72a b + 144a b + 864a b +--R + +--R 8 3 +--R 912a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 6 +--R (168b + 420a b + 462a b + 630a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 +--R (560a b + 2072a b + 3640a b + 4648a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (588b + 624a b - 196a b + 3572a b + 11158a b + 13654a b ) +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 1844a b + 1988a b - 1948a b + 3044a b + 16904a b +--R + +--R 6 5 +--R 20168a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 376b + 376a b + 946a b + 1162a b - 600a b + 3108a b +--R + +--R 6 5 7 4 +--R 12928a b + 15304a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 700a b + 700a b - 1132a b - 988a b + 1912a b + 3376a b +--R + +--R 7 4 8 3 +--R 4400a b + 5312a b +--R * +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R 36b + 36a b + 180a b + 180a b - 606a b - 570a b + 1008a b +--R + +--R 7 4 8 3 9 2 +--R 1248a b + 432a b + 576a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 10 3 8 7 +--R (504a b + 336a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 6 +--R (- 56a b + 3472a b + 896a b + 3248a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (448b + 664a b - 672a b + 9840a b + 5264a b + 12176a b ) +--R * +--R 5 +--R cosh(d x + c) 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2996a b + 364a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (28b + 568a b - 2660a b + 14800a b - 7658a b + 3742a b ) +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R (248a b + 3488a b - 3754a b + 30446a b - 9724a b + 11636a b ) +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 456b + 510a b - 398a b + 7630a b - 832a b + 40550a b +--R + +--R 6 5 7 4 +--R - 6576a b + 17460a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 1638a b + 1854a b - 2864a b + 7648a b + 5656a b + 37264a b +--R + +--R 7 4 8 3 +--R - 2960a b + 13504a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 220b + 220a b + 1328a b + 1652a b - 2914a b + 4754a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 7360a b + 22192a b - 1584a b + 4992a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 412a b + 412a b - 322a b - 106a b - 68a b + 2884a b +--R + +--R 7 4 8 3 9 2 10 +--R 2960a b + 6848a b - 672a b + 672a 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274b + 266a b - 3114a b + 8046a b - 11057a b - 3857a b ) +--R * +--R 8 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 1636a b + 2684a b - 7916a b + 20884a b - 23928a b +--R + +--R 6 5 +--R - 6648a b +--R * +--R 7 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 360b + 684a b - 5610a b + 9078a b - 13352a b + 34420a b +--R + +--R 6 5 7 4 +--R - 31168a b - 5752a b +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 1392a b + 3336a b - 11804a b + 15844a b - 13272a b +--R + +--R 6 5 7 4 8 3 +--R 39504a b - 25456a b - 1984a b +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 11 2 9 3 8 4 7 5 6 6 5 +--R - 36b + 2100a b + 6876a b - 14354a b + 17002a b - 6736a b +--R + +--R 7 4 8 3 9 2 +--R 32000a b - 13104a b + 192a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R - 76a b + 68a b + 1468a b + 7612a b - 9432a b + 12312a b +--R + +--R 7 4 8 3 9 2 10 +--R - 1248a b + 16896a b - 4032a b + 192a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 20b + 20a b - 117a b + 99a b + 544a b + 4900a b +--R + +--R 6 5 7 4 9 2 10 +--R - 2976a b + 5880a b + 4896a b - 576a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 7 4 +--R 38a b + 38a b - 140a b + 4a b + 264a b + 1872a b - 432a b +--R + +--R 8 3 10 +--R 1440a b + 576a b +--R * +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 7 4 9 2 +--R 6b + 6a b - 18a b - 18a b + 27a b + 63a b + 240a b + 144a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 11 10 2 9 3 8 11 +--R (- 32b + 40a b - 88a b - 40a b )cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 10 +--R (- 280a b + 512a b - 920a b - 392a b )cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (- 112b + 104a b - 1216a b + 2672a b - 4072a b - 1576a b ) +--R * +--R 9 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R (- 776a b + 1168a b - 3728a b + 7504a b - 9896a b - 3272a b ) +--R * +--R 8 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 240b + 456a b - 3376a b + 4112a b - 7408a b 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7 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 28b + 8a b + 136a b + 1564a b - 3278a b + 2302a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 1888a b + 3440a b - 1872a b - 384a b +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R - 120a b + 96a b - 106a b + 2414a b - 2980a b + 2276a b +--R + +--R 7 4 8 3 9 2 10 +--R - 1072a b + 2240a b - 672a b - 96a b +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R - 12b - 3a b - 155a b + 355a b - 284a b + 2266a b - 1640a b +--R + +--R 7 4 8 3 9 2 10 +--R 1420a b - 288a b + 912a b - 96a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 7 4 +--R - 31a b + 5a b - 50a b + 550a b - 312a b + 1152a b - 432a b +--R + +--R 8 3 10 +--R 576a b + 192a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R - 2b - 2a b - 14a b + 40a b - 5a b + 355a b - 144a b +--R + +--R 7 4 9 2 +--R 288a b + 144a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 8 3 +--R (- 2a b - 2a b + 5a b + 41a b - 18a b + 78a b + 48a b ) +--R * +--R cosh(d x + c) +--R + +--R 5 6 7 4 +--R 9a b + 6a b +--R / +--R 15 14 2 13 3 12 4 11 5 10 6 9 +--R 6b - 6a b - 18a b + 18a b + 18a b - 18a b - 6a b +--R + +--R 7 8 +--R 6a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 14 2 13 3 12 4 11 5 10 6 9 +--R 24a b - 24a b - 72a b + 72a b + 72a b - 72a b +--R + +--R 7 8 8 7 +--R - 24a b + 24a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 13 3 12 4 11 5 10 6 9 7 8 +--R 36a b - 36a b - 108a b + 108a b + 108a b - 108a b +--R + +--R 8 7 9 6 +--R - 36a b + 36a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 3 12 4 11 5 10 6 9 7 8 8 7 +--R 24a b - 24a b - 72a b + 72a b + 72a b - 72a b +--R + +--R 9 6 10 5 +--R - 24a b + 24a b +--R * +--R cosh(d x + c) +--R + +--R 4 11 5 10 6 9 7 8 8 7 9 6 10 5 +--R 6a b - 6a b - 18a b + 18a b + 18a b - 18a b - 6a b +--R + +--R 11 4 +--R 6a b +--R * +--R 8 +--R sinh(d x + c) +--R + +--R 15 14 2 13 3 12 4 11 5 10 +--R 48b - 48a b - 144a b + 144a b + 144a b - 144a b +--R + +--R 6 9 7 8 +--R - 48a b + 48a b +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 14 2 13 3 12 4 11 5 10 +--R 240a b - 240a b - 720a b + 720a b + 720a b +--R + +--R 6 9 7 8 8 7 +--R - 720a b - 240a b + 240a b +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 2 13 3 12 4 11 5 10 6 9 +--R 480a b - 480a b - 1440a b + 1440a b + 1440a b +--R + +--R 7 8 8 7 9 6 +--R - 1440a b - 480a b + 480a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 3 12 4 11 5 10 6 9 7 8 +--R 480a b - 480a b - 1440a b + 1440a b + 1440a b +--R + +--R 8 7 9 6 10 5 +--R - 1440a b - 480a b + 480a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 4 11 5 10 6 9 7 8 8 7 9 6 +--R 240a b - 240a b - 720a b + 720a b + 720a b - 720a b +--R + +--R 10 5 11 4 +--R - 240a b + 240a b +--R * +--R cosh(d x + c) +--R + +--R 5 10 6 9 7 8 8 7 9 6 10 5 +--R 48a b - 48a b - 144a b + 144a b + 144a b - 144a b +--R + +--R 11 4 12 3 +--R - 48a b + 48a b +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 15 14 2 13 3 12 4 11 5 10 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2448a b + 2448a b +--R + +--R 9 6 10 5 11 4 12 3 +--R 2640a b - 2640a b - 912a b + 912a b +--R * +--R cosh(d x + c) +--R + +--R 4 11 5 10 6 9 7 8 8 7 9 6 +--R 24a b - 24a b + 72a b - 72a b - 360a b + 360a b +--R + +--R 10 5 11 4 12 3 13 2 +--R 408a b - 408a b - 144a b + 144a b +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 15 14 2 13 3 12 4 11 +--R 336b - 336a b - 1008a b + 1008a b + 1008a b +--R + +--R 5 10 6 9 7 8 +--R - 1008a b - 336a b + 336a b +--R * +--R 7 +--R cosh(d x + c) +--R + +--R 14 2 13 3 12 4 11 5 10 +--R 2352a b - 2352a b - 7056a b + 7056a b + 7056a b +--R + +--R 6 9 7 8 8 7 +--R - 7056a b - 2352a b + 2352a b +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 15 14 2 13 3 12 4 11 +--R 144b - 144a b + 6480a b - 6480a b - 20304a b +--R + +--R 5 10 6 9 7 8 8 7 9 6 +--R 20304a b + 20592a b - 20592a b - 6912a b + 6912a b +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 14 2 13 3 12 4 11 5 10 +--R 720a b - 720a b + 8880a b - 8880a b - 30960a b +--R + +--R 6 9 7 8 8 7 9 6 10 5 +--R 30960a 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+--R + +--R 7 8 8 7 9 6 10 5 +--R 3000a b + 3000a b - 1080a b - 1080a b +--R * +--R 9 +--R cosh(d x + c) +--R + +--R 15 14 2 13 3 12 4 11 5 10 +--R 36b + 36a b + 900a b + 900a b - 990a b - 990a b +--R + +--R 6 9 7 8 8 7 9 6 10 5 11 4 +--R - 2790a b - 2790a b + 4770a b + 4770a b - 1926a b - 1926a b +--R * +--R 8 +--R cosh(d x + c) +--R + +--R 14 2 13 3 12 4 11 5 10 6 9 +--R 288a b + 288a b + 1440a b + 1440a b - 3888a b - 3888a b +--R + +--R 7 8 8 7 9 6 10 5 11 4 12 3 +--R 144a b + 144a b + 4176a b + 4176a b - 2160a b - 2160a b +--R * +--R 7 +--R cosh(d x + c) +--R + +--R 15 14 2 13 3 12 4 11 5 10 +--R 24b + 24a b + 864a b + 864a b + 360a b + 360a b +--R + +--R 6 9 7 8 8 7 9 6 10 5 11 4 +--R - 5016a b - 5016a b + 3888a b + 3888a b + 1368a b + 1368a b +--R + +--R 12 3 13 2 +--R - 1488a b - 1488a b +--R * +--R 6 +--R cosh(d x + c) +--R + +--R 14 2 13 3 12 4 11 5 10 6 9 +--R 144a b + 144a b + 1152a b + 1152a b - 1872a b - 1872a b +--R + +--R 7 8 8 7 9 6 10 5 11 4 12 3 +--R - 2160a b - 2160a b + 4032a b + 4032a b - 720a b - 720a b +--R + +--R 13 2 14 +--R - 576a b - 576a b +--R * +--R 5 +--R cosh(d x + c) +--R + +--R 15 14 2 13 3 12 4 11 5 10 6 9 +--R 6b + 6a b + 318a b + 318a b + 486a b + 486a b - 2370a b +--R + +--R 7 8 8 7 9 6 10 5 11 4 12 3 +--R - 2370a b + 1020a b + 1020a b + 1404a b + 1404a b - 768a b +--R + +--R 13 2 14 15 +--R - 768a b - 96a b - 96a +--R * +--R 4 +--R cosh(d x + c) +--R + +--R 14 2 13 3 12 4 11 5 10 6 9 +--R 24a b + 24a b + 312a b + 312a b - 360a b - 360a b +--R + +--R 7 8 8 7 9 6 10 5 11 4 12 3 +--R - 840a b - 840a b + 1200a b + 1200a b - 144a b - 144a b +--R + +--R 13 2 14 +--R - 192a b - 192a b +--R * +--R 3 +--R cosh(d x + c) +--R + +--R 2 13 3 12 4 11 5 10 6 9 7 8 8 7 +--R 36a b + 36a b + 108a b + 108a b - 396a b - 396a b + 180a b +--R + +--R 9 6 10 5 11 4 12 3 13 2 +--R 180a b + 216a b + 216a b - 144a b - 144a b +--R * +--R 2 +--R cosh(d x + c) +--R + +--R 3 12 4 11 5 10 6 9 7 8 8 7 9 6 +--R 24a b + 24a b - 24a b - 24a b - 72a b - 72a b + 120a b +--R + +--R 10 5 11 4 12 3 +--R 120a b - 48a b - 48a b +--R * +--R cosh(d x + c) +--R + +--R 4 11 5 10 6 9 7 8 8 7 9 6 10 5 11 4 +--R 6a b + 6a b - 18a b - 18a b + 18a b + 18a b - 6a b - 6a b +--R Type: Expression(Integer) +--E 307 + +--S 308 of 510 +t0161:= (a+b*cosh(c+d*x))^(1/2) +--R +--R +--R +-------------------+ +--R (185) \|b cosh(d x + c) + a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 510 +r0161:= -2*%i*(a+b*cosh(c+d*x))^(1/2)*_ + EllipticE(1/2*%i*(c+d*x),2*b/(a+b))/d/((a+b*cosh(c+d*x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 309 + +--S 310 of 510 +a0161:= integrate(t0161,x) +--R +--R +--R x +--R ++ +--------------------+ +--R (186) | \|b cosh(%I d + c) + a d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 310 + +--S 311 of 510 +--m0161:= a0161-r0161 +--E 311 + +--S 312 of 510 +--d0161:= D(m0161,x) +--E 312 + +--S 313 of 510 +t0162:= 1/(a+b*cosh(x))^(1/2) +--R +--R +--R 1 +--R (187) ---------------- +--R +-------------+ +--R \|b cosh(x) + a +--R Type: Expression(Integer) +--E 313 + +--S 314 of 510 +r0162:= -2*%i*((a+b*cosh(x))/(a+b))^(1/2)*_ + EllipticF(1/2*%i*x,2*b/(a+b))/(a+b*cosh(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 314 + +--S 315 of 510 +a0162:= integrate(t0162,x) +--R +--R +--R x +--R ++ 1 +--R (188) | ----------------- d%I +--R ++ +--------------+ +--R \|b cosh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 315 + +--S 316 of 510 +--m0162:= a0162-r0162 +--E 316 + +--S 317 of 510 +--d0162:= D(m0162,x) +--E 317 + +--S 318 of 510 +t0163:= 1/(a+b*cosh(x))^(3/2) +--R +--R +--R 1 +--R (189) ------------------------------- +--R +-------------+ +--R (b cosh(x) + a)\|b cosh(x) + a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 510 +r0163:= -2*%i*(a+b*cosh(x))^(1/2)*_ + EllipticE(1/2*%i*x,2*b/(a+b))/(a^2-b^2)/((a+b*cosh(x))/(a+b))^(1/2)-_ + 2*b*sinh(x)/(a^2-b^2)/(a+b*cosh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 319 + +--S 320 of 510 +a0163:= integrate(t0163,x) +--R +--R +--R x +--R ++ 1 +--R (190) | --------------------------------- d%I +--R ++ +--------------+ +--R (b cosh(%I) + a)\|b cosh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 320 + +--S 321 of 510 +--m0163:= a0163-r0163 +--E 321 + +--S 322 of 510 +--d0163:= D(m0163,x) +--E 322 + +--S 323 of 510 +t0164:= 1/(a+b*cosh(x))^(5/2) +--R +--R +--R 1 +--R (191) ------------------------------------------------ +--R 2 2 2 +-------------+ +--R (b cosh(x) + 2a b cosh(x) + a )\|b cosh(x) + a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 510 +r0164:= -8/3*%i*a*(a+b*cosh(x))^(1/2)*_ + EllipticE(1/2*%i*x,2*b/(a+b))/(a^2-b^2)^2/_ + ((a+b*cosh(x))/(a+b))^(1/2)+2/3*%i*((a+b*cosh(x))/(a+b))^(1/2)*_ + EllipticF(1/2*%i*x,2*b/(a+b))/(a^2-b^2)/(a+b*cosh(x))^(1/2)-_ + 2/3*b*sinh(x)/(a^2-b^2)/(a+b*cosh(x))^(3/2)-_ + 8/3*a*b*sinh(x)/(a^2-b^2)^2/(a+b*cosh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 324 + +--S 325 of 510 +a0164:= integrate(t0164,x) +--R +--R +--R x +--R ++ 1 +--R (192) | --------------------------------------------------- d%I +--R ++ 2 2 2 +--------------+ +--R (b cosh(%I) + 2a b cosh(%I) + a )\|b cosh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 325 + +--S 326 of 510 +--m0164:= a0164-r0164 +--E 326 + +--S 327 of 510 +--d0164:= D(m0164,x) +--E 327 + +--S 328 of 510 +t0165:= (a+a*cosh(c+d*x))^(1/2) +--R +--R +--R +-------------------+ +--R (193) \|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 510 +r0165:= 2*a*sinh(c+d*x)/d/(a+a*cosh(c+d*x))^(1/2) +--R +--R +--R 2a sinh(d x + c) +--R (194) ----------------------- +--R +-------------------+ +--R d\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 329 + +--S 330 of 510 +a0165:= integrate(t0165,x) +--R +--R +--R (195) +--R a sinh(d x + c) + a cosh(d x + c) - a +--R --------------------------------------------------------------------- +--R +-------------------------------+ +--R | a +--R (d sinh(d x + c) + d cosh(d x + c)) |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Union(Expression(Integer),...) +--E 330 + +--S 331 of 510 +m0165:= a0165-r0165 +--R +--R +--R (196) +--R +-------------------+ +--R (a sinh(d x + c) + a cosh(d x + c) - a)\|a cosh(d x + c) + a +--R + +--R 2 +--R (- 2a sinh(d x + c) - 2a cosh(d x + c)sinh(d x + c)) +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R +-------------------------------+ +--R | a +--R (d sinh(d x + c) + d cosh(d x + c)) |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 510 +d0165:= D(m0165,x) +--R +--R +--R (197) +--R 2 +--R (a cosh(d x + c) + a)sinh(d x + c) + a cosh(d x + c) +--R + +--R 2a cosh(d x + c) + a +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R + +--R 3 2 +--R 2a sinh(d x + c) + 2a cosh(d x + c)sinh(d x + c) +--R + +--R 2 +--R (- 4a cosh(d x + c) - 4a cosh(d x + c))sinh(d x + c) +--R + +--R 3 2 +--R - 4a cosh(d x + c) - 4a cosh(d x + c) +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2 +--R ((2cosh(d x + c) + 2)sinh(d x + c) + 2cosh(d x + c) + 2cosh(d x + c)) +--R * +--R +-------------------------------+ +--R | a +-------------------+ +--R |------------------------------- \|a cosh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Integer) +--E 332 + +--S 333 of 510 +t0166:= (a+a*cosh(c+d*x))^(3/2) +--R +--R +--R +-------------------+ +--R (198) (a cosh(d x + c) + a)\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 510 +r0166:= 2/3*a^2*sinh(c+d*x)*(5+cosh(c+d*x))/(a*(1+cosh(c+d*x)))^(1/2)/d +--R +--R +--R 2 2 +--R (2a cosh(d x + c) + 10a )sinh(d x + c) +--R (199) -------------------------------------- +--R +-------------------+ +--R 3d\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 510 +a0166:= integrate(t0166,x) +--R +--R +--R (200) +--R 2 3 2 2 2 +--R a sinh(d x + c) + (3a cosh(d x + c) + 9a )sinh(d x + c) +--R + +--R 2 2 2 2 +--R (3a cosh(d x + c) + 18a cosh(d x + c) - 9a )sinh(d x + c) +--R + +--R 2 3 2 2 2 2 +--R a cosh(d x + c) + 9a cosh(d x + c) - 9a cosh(d x + c) - a +--R / +--R 2 2 +--R (6d sinh(d x + c) + 12d cosh(d x + c)sinh(d x + c) + 6d cosh(d x + c) ) +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Union(Expression(Integer),...) +--E 335 + +--S 336 of 510 +m0166:= a0166-r0166 +--R +--R +--R (201) +--R 2 3 2 2 2 +--R a sinh(d x + c) + (3a cosh(d x + c) + 9a )sinh(d x + c) +--R + +--R 2 2 2 2 +--R (3a cosh(d x + c) + 18a cosh(d x + c) - 9a )sinh(d x + c) +--R + +--R 2 3 2 2 2 2 +--R a cosh(d x + c) + 9a cosh(d x + c) - 9a cosh(d x + c) - a +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R + +--R 2 2 3 +--R (- 4a cosh(d x + c) - 20a )sinh(d x + c) +--R + +--R 2 2 2 2 +--R (- 8a cosh(d x + c) - 40a cosh(d x + c))sinh(d x + c) +--R + +--R 2 3 2 2 +--R (- 4a cosh(d x + c) - 20a cosh(d x + c) )sinh(d x + c) +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2 2 +--R (6d sinh(d x + c) + 12d cosh(d x + c)sinh(d x + c) + 6d cosh(d x + c) ) +--R * +--R +-------------------------------+ +--R | a +-------------------+ +--R |------------------------------- \|a cosh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Integer) +--E 336 + +--S 337 of 510 +d0166:= D(m0166,x) +--R +--R +--R (202) +--R 2 2 3 +--R (3a cosh(d x + c) + 3a )sinh(d x + c) +--R + +--R 2 2 2 2 2 +--R (9a cosh(d x + c) + 18a cosh(d x + c) + 9a )sinh(d x + c) +--R + +--R 2 3 2 2 2 2 +--R (9a cosh(d x + c) + 27a cosh(d x + c) + 27a cosh(d x + c) + 9a ) +--R * +--R sinh(d x + c) +--R + +--R 2 4 2 3 2 2 +--R 3a cosh(d x + c) + 12a cosh(d x + c) + 18a cosh(d x + c) +--R + +--R 2 2 +--R 12a cosh(d x + c) + 3a +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R + +--R 2 2 4 +--R (- 4a cosh(d x + c) + 12a )sinh(d x + c) +--R + +--R 2 2 2 3 +--R (- 8a cosh(d x + c) + 24a cosh(d x + c))sinh(d x + c) +--R + +--R 2 3 2 2 2 +--R (- 12a cosh(d x + c) - 36a cosh(d x + c) - 40a cosh(d x + c)) +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 4 2 3 2 2 +--R (- 16a cosh(d x + c) - 96a cosh(d x + c) - 80a cosh(d x + c) ) +--R * +--R sinh(d x + c) +--R + +--R 2 5 2 4 2 3 +--R - 8a cosh(d x + c) - 48a cosh(d x + c) - 40a cosh(d x + c) +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2 +--R (12cosh(d x + c) + 12)sinh(d x + c) +--R + +--R 2 3 +--R (24cosh(d x + c) + 24cosh(d x + c))sinh(d x + c) + 12cosh(d x + c) +--R + +--R 2 +--R 12cosh(d x + c) +--R * +--R +-------------------------------+ +--R | a +-------------------+ +--R |------------------------------- \|a cosh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Integer) +--E 337 + +--S 338 of 510 +t0167:= (a+a*cosh(c+d*x))^(5/2) +--R +--R +--R 2 2 2 2 +-------------------+ +--R (203) (a cosh(d x + c) + 2a cosh(d x + c) + a )\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 510 +r0167:= 2/15*a^3*sinh(c+d*x)*(43+14*cosh(c+d*x)+3*cosh(c+d*x)^2)/_ + (a*(1+cosh(c+d*x)))^(1/2)/d +--R +--R +--R 3 2 3 3 +--R (6a cosh(d x + c) + 28a cosh(d x + c) + 86a )sinh(d x + c) +--R (204) ----------------------------------------------------------- +--R +-------------------+ +--R 15d\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 510 +a0167:= integrate(t0167,x) +--R +--R +--R (205) +--R 3 5 3 3 4 +--R 3a sinh(d x + c) + (15a cosh(d x + c) + 25a )sinh(d x + c) +--R + +--R 3 2 3 3 3 +--R (30a cosh(d x + c) + 100a cosh(d x + c) + 150a )sinh(d x + c) +--R + +--R 3 3 3 2 3 3 +--R (30a cosh(d x + c) + 150a cosh(d x + c) + 450a cosh(d x + c) - 150a ) +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 4 3 3 3 2 +--R 15a cosh(d x + c) + 100a cosh(d x + c) + 450a cosh(d x + c) +--R + +--R 3 3 +--R - 300a cosh(d x + c) - 25a +--R * +--R sinh(d x + c) +--R + +--R 3 5 3 4 3 3 +--R 3a cosh(d x + c) + 25a cosh(d x + c) + 150a cosh(d x + c) +--R + +--R 3 2 3 3 +--R - 150a cosh(d x + c) - 25a cosh(d x + c) - 3a +--R / +--R 3 2 +--R 60d sinh(d x + c) + 180d cosh(d x + c)sinh(d x + c) +--R + +--R 2 3 +--R 180d cosh(d x + c) sinh(d x + c) + 60d cosh(d x + c) +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Union(Expression(Integer),...) +--E 340 + +--S 341 of 510 +m0167:= a0167-r0167 +--R +--R +--R (206) +--R 3 5 3 3 4 +--R 3a sinh(d x + c) + (15a cosh(d x + c) + 25a )sinh(d x + c) +--R + +--R 3 2 3 3 3 +--R (30a cosh(d x + c) + 100a cosh(d x + c) + 150a )sinh(d x + c) +--R + +--R 3 3 3 2 3 +--R 30a cosh(d x + c) + 150a cosh(d x + c) + 450a cosh(d x + c) +--R + +--R 3 +--R - 150a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 4 3 3 3 2 +--R 15a cosh(d x + c) + 100a cosh(d x + c) + 450a cosh(d x + c) +--R + +--R 3 3 +--R - 300a cosh(d x + c) - 25a +--R * +--R sinh(d x + c) +--R + +--R 3 5 3 4 3 3 +--R 3a cosh(d x + c) + 25a cosh(d x + c) + 150a cosh(d x + c) +--R + +--R 3 2 3 3 +--R - 150a cosh(d x + c) - 25a cosh(d x + c) - 3a +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R + +--R 3 2 3 3 4 +--R (- 24a cosh(d x + c) - 112a cosh(d x + c) - 344a )sinh(d x + c) +--R + +--R 3 3 3 2 3 +--R (- 72a cosh(d x + c) - 336a cosh(d x + c) - 1032a cosh(d x + c)) +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 4 3 3 3 2 +--R (- 72a cosh(d x + c) - 336a cosh(d x + c) - 1032a cosh(d x + c) ) +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 5 3 4 3 3 +--R (- 24a cosh(d x + c) - 112a cosh(d x + c) - 344a cosh(d x + c) ) +--R * +--R sinh(d x + c) +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 3 2 +--R 60d sinh(d x + c) + 180d cosh(d x + c)sinh(d x + c) +--R + +--R 2 3 +--R 180d cosh(d x + c) sinh(d x + c) + 60d cosh(d x + c) +--R * +--R +-------------------------------+ +--R | a +-------------------+ +--R |------------------------------- \|a cosh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 510 +d0167:= D(m0167,x) +--R +--R +--R (207) +--R 3 3 5 +--R (15a cosh(d x + c) + 15a )sinh(d x + c) +--R + +--R 3 2 3 3 4 +--R (75a cosh(d x + c) + 150a cosh(d x + c) + 75a )sinh(d x + c) +--R + +--R 3 3 3 2 3 +--R 150a cosh(d x + c) + 450a cosh(d x + c) + 450a cosh(d x + c) +--R + +--R 3 +--R 150a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 4 3 3 3 2 +--R 150a cosh(d x + c) + 600a cosh(d x + c) + 900a cosh(d x + c) +--R + +--R 3 3 +--R 600a cosh(d x + c) + 150a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 5 3 4 3 3 +--R 75a cosh(d x + c) + 375a cosh(d x + c) + 750a cosh(d x + c) +--R + +--R 3 2 3 3 +--R 750a cosh(d x + c) + 375a cosh(d x + c) + 75a +--R * +--R sinh(d x + c) +--R + +--R 3 6 3 5 3 4 +--R 15a cosh(d x + c) + 90a cosh(d x + c) + 225a cosh(d x + c) +--R + +--R 3 3 3 2 3 3 +--R 300a cosh(d x + c) + 225a cosh(d x + c) + 90a cosh(d x + c) + 15a +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R + +--R 3 2 3 3 5 +--R (- 72a cosh(d x + c) - 208a cosh(d x + c) + 120a )sinh(d x + c) +--R + +--R 3 3 3 2 3 +--R (- 216a cosh(d x + c) - 624a cosh(d x + c) + 360a cosh(d x + c)) +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 3 4 3 3 3 2 +--R - 264a cosh(d x + c) - 896a cosh(d x + c) - 552a cosh(d x + c) +--R + +--R 3 +--R - 688a cosh(d x + c) +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 5 3 4 +--R - 216a cosh(d x + c) - 1024a cosh(d x + c) +--R + +--R 3 3 3 2 +--R - 2616a cosh(d x + c) - 2064a cosh(d x + c) +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 6 3 5 +--R - 144a cosh(d x + c) - 816a cosh(d x + c) +--R + +--R 3 4 3 3 +--R - 2736a cosh(d x + c) - 2064a cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 3 7 3 6 3 5 +--R - 48a cosh(d x + c) - 272a cosh(d x + c) - 912a cosh(d x + c) +--R + +--R 3 4 +--R - 688a cosh(d x + c) +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 3 +--R (120cosh(d x + c) + 120)sinh(d x + c) +--R + +--R 2 2 +--R (360cosh(d x + c) + 360cosh(d x + c))sinh(d x + c) +--R + +--R 3 2 +--R (360cosh(d x + c) + 360cosh(d x + c) )sinh(d x + c) +--R + +--R 4 3 +--R 120cosh(d x + c) + 120cosh(d x + c) +--R * +--R +-------------------------------+ +--R | a +-------------------+ +--R |------------------------------- \|a cosh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Integer) +--E 342 + +--S 343 of 510 +t0168:= 1/(a+a*cosh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (208) ---------------------- +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 510 +r0168:= 2*atan(sinh(1/2*c+1/2*d*x))*cosh(1/2*c+1/2*d*x)/d/_ + (a+a*cosh(c+d*x))^(1/2) +--R +--R +--R d x + c d x + c +--R 2cosh(-------)atan(sinh(-------)) +--R 2 2 +--R (209) --------------------------------- +--R +-------------------+ +--R d\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 510 +a0168:= integrate(t0168,x) +--R +--R +--R (210) +--R [ +--R +---+ +--R | 2 +--R |- - +--R \| a +--R * +--R log +--R +---+ +--R | 2 +--R (- 2sinh(d x + c) - 2cosh(d x + c)) |- - +--R \| a +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R - sinh(d x + c) - cosh(d x + c) + 1 +--R / +--R sinh(d x + c) + cosh(d x + c) + 1 +--R / +--R d +--R , +--R +-------------------------------+ +--R | a +--R +-+ 2 |------------------------------- +--R |2 \|2sinh(d x + c) + 2cosh(d x + c) +--R 2 |- atan(-----------------------------------) +--R \|a +-+ +--R |2 +--R a |- +--R \|a +--R - ----------------------------------------------] +--R d +--R Type: Union(List(Expression(Integer)),...) +--E 345 + +--S 346 of 510 +m0168a:= a0168.1-r0168 +--R +--R +--R (211) +--R +---+ +--R | 2 +-------------------+ +--R |- - \|a cosh(d x + c) + a +--R \| a +--R * +--R log +--R +---+ +--R | 2 +--R (- 2sinh(d x + c) - 2cosh(d x + c)) |- - +--R \| a +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R - sinh(d x + c) - cosh(d x + c) + 1 +--R / +--R sinh(d x + c) + cosh(d x + c) + 1 +--R + +--R d x + c d x + c +--R - 2cosh(-------)atan(sinh(-------)) +--R 2 2 +--R / +--R +-------------------+ +--R d\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 510 +d0168a:= D(m0168a,x) +--R +--R +--R (212) +--R d x + c 2 +--R ((2cosh(d x + c) + 2)sinh(-------) + 2cosh(d x + c) + 2) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R 2 d x + c 2 +--R (2cosh(d x + c) + 2cosh(d x + c))sinh(-------) +--R 2 +--R + +--R 2 +--R 2cosh(d x + c) + 2cosh(d x + c) +--R * +--R +---+ +-------------------------------+ +--R | 2 | a +--R |- - |------------------------------- +--R \| a \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R d x + c 2 +--R ((cosh(d x + c) + 1)sinh(-------) + cosh(d x + c) + 1)sinh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 +--R (cosh(d x + c) - 1)sinh(-------) + cosh(d x + c) - 1 +--R 2 +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R + +--R d x + c d x + c 2 d x + c 3 +--R (cosh(-------)sinh(-------) + cosh(-------))sinh(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (- cosh(d x + c) - 1)sinh(-------) +--R 2 +--R + +--R d x + c d x + c 2 +--R 2cosh(-------)cosh(d x + c)sinh(-------) +--R 2 2 +--R + +--R d x + c +--R (- cosh(d x + c) - 1)sinh(-------) +--R 2 +--R + +--R d x + c +--R 2cosh(-------)cosh(d x + c) +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 d x + c 3 +--R (- 2cosh(d x + c) - 2cosh(d x + c))sinh(-------) +--R 2 +--R + +--R d x + c 2 d x + c d x + c 2 +--R (cosh(-------)cosh(d x + c) - cosh(-------))sinh(-------) +--R 2 2 2 +--R + +--R 2 d x + c +--R (- 2cosh(d x + c) - 2cosh(d x + c))sinh(-------) +--R 2 +--R + +--R d x + c 2 d x + c +--R cosh(-------)cosh(d x + c) - cosh(-------) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R 3 2 +--R (- cosh(d x + c) - cosh(d x + c) + cosh(d x + c) + 1) +--R * +--R d x + c 3 +--R sinh(-------) +--R 2 +--R + +--R 3 2 +--R (- cosh(d x + c) - cosh(d x + c) + cosh(d x + c) + 1) +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R * +--R d x + c +--R atan(sinh(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 2 +--R (- cosh(-------) cosh(d x + c) - cosh(-------) )sinh(d x + c) +--R 2 2 +--R + +--R d x + c 2 2 d x + c 2 +--R (- 2cosh(-------) cosh(d x + c) - 2cosh(-------) cosh(d x + c)) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 2 3 d x + c 2 2 +--R - cosh(-------) cosh(d x + c) - cosh(-------) cosh(d x + c) +--R 2 2 +--R + +--R d x + c 2 d x + c 2 +--R cosh(-------) cosh(d x + c) + cosh(-------) +--R 2 2 +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R d x + c d x + c 2 d x + c 2 +--R (a cosh(-------)sinh(-------) + a cosh(-------))sinh(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (- a cosh(d x + c) - a)sinh(-------) +--R 2 +--R + +--R d x + c d x + c d x + c 2 +--R (a cosh(-------)cosh(d x + c) + a cosh(-------))sinh(-------) +--R 2 2 2 +--R + +--R d x + c +--R (- a cosh(d x + c) - a)sinh(-------) +--R 2 +--R + +--R d x + c d x + c +--R a cosh(-------)cosh(d x + c) + a cosh(-------) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R 2 d x + c 3 +--R (- a cosh(d x + c) - 2a cosh(d x + c) - a)sinh(-------) +--R 2 +--R + +--R 2 d x + c +--R (- a cosh(d x + c) - 2a cosh(d x + c) - a)sinh(-------) +--R 2 +--R * +--R +---+ +--R | 2 d x + c +--R |- - atan(sinh(-------)) +--R \| a 2 +--R + +--R d x + c 2 d x + c 2 +--R (- a cosh(-------) cosh(d x + c) - a cosh(-------) )sinh(d x + c) +--R 2 2 +--R + +--R d x + c 2 2 d x + c 2 +--R - a cosh(-------) cosh(d x + c) - 2a cosh(-------) cosh(d x + c) +--R 2 2 +--R + +--R d x + c 2 +--R - a cosh(-------) +--R 2 +--R * +--R +---+ +--R | 2 +--R |- - +--R \| a +--R / +--R d x + c 2 +--R ((cosh(d x + c) + 1)sinh(-------) + cosh(d x + c) + 1) +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 +--R (2cosh(d x + c) + 2cosh(d x + c))sinh(-------) +--R 2 +--R + +--R 2 +--R 2cosh(d x + c) + 2cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 3 2 d x + c 2 +--R (cosh(d x + c) + cosh(d x + c) - cosh(d x + c) - 1)sinh(-------) +--R 2 +--R + +--R 3 2 +--R cosh(d x + c) + cosh(d x + c) - cosh(d x + c) - 1 +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R d x + c 2 +--R ((a cosh(d x + c) + a)sinh(-------) + a cosh(d x + c) + a) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R 2 d x + c 2 +--R (a cosh(d x + c) + 2a cosh(d x + c) + a)sinh(-------) +--R 2 +--R + +--R 2 +--R a cosh(d x + c) + 2a cosh(d x + c) + a +--R * +--R +---+ +--R | 2 +--R |- - +--R \| a +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 510 +m0168b:= a0168.2-r0168 +--R +--R +--R (213) +--R +-------------------------------+ +--R | a +--R +-+ 2 |------------------------------- +--R |2 +-------------------+ \|2sinh(d x + c) + 2cosh(d x + c) +--R - 2 |- \|a cosh(d x + c) + a atan(-----------------------------------) +--R \|a +-+ +--R |2 +--R a |- +--R \|a +--R + +--R d x + c d x + c +--R - 2cosh(-------)atan(sinh(-------)) +--R 2 2 +--R / +--R +-------------------+ +--R d\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 348 + +--S 349 of 510 +d0168b:= D(m0168b,x) +--R +--R +--R (214) +--R d x + c 2 +--R ((cosh(d x + c) + 1)sinh(-------) + cosh(d x + c) + 1) +--R 2 +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R + +--R d x + c d x + c 2 d x + c 2 +--R (cosh(-------)sinh(-------) + cosh(-------))sinh(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (- cosh(d x + c) - 1)sinh(-------) +--R 2 +--R + +--R d x + c d x + c d x + c 2 +--R (cosh(-------)cosh(d x + c) + cosh(-------))sinh(-------) +--R 2 2 2 +--R + +--R d x + c +--R (- cosh(d x + c) - 1)sinh(-------) +--R 2 +--R + +--R d x + c d x + c +--R cosh(-------)cosh(d x + c) + cosh(-------) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R 2 d x + c 3 +--R (- cosh(d x + c) - 2cosh(d x + c) - 1)sinh(-------) +--R 2 +--R + +--R 2 d x + c +--R (- cosh(d x + c) - 2cosh(d x + c) - 1)sinh(-------) +--R 2 +--R * +--R d x + c +--R atan(sinh(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- cosh(-------) cosh(d x + c) - cosh(-------) )sinh(d x + c) +--R 2 2 +--R + +--R d x + c 2 2 d x + c 2 +--R - cosh(-------) cosh(d x + c) - 2cosh(-------) cosh(d x + c) +--R 2 2 +--R + +--R d x + c 2 +--R - cosh(-------) +--R 2 +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R d x + c 2 +--R ((cosh(d x + c) + 1)sinh(-------) + cosh(d x + c) + 1)sinh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 +--R (cosh(d x + c) + 2cosh(d x + c) + 1)sinh(-------) + cosh(d x + c) +--R 2 +--R + +--R 2cosh(d x + c) + 1 +--R * +--R +-------------------------------+ +--R | a +-------------------+ +--R |------------------------------- \|a cosh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Integer) +--E 349 + +--S 350 of 510 +t0169:= 1/(a+a*cosh(c+d*x))^(3/2) +--R +--R +--R 1 +--R (215) ------------------------------------------- +--R +-------------------+ +--R (a cosh(d x + c) + a)\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 510 +r0169:= 1/2*atan(sinh(1/2*c+1/2*d*x))*cosh(1/2*c+1/2*d*x)/a/d/_ + (a+a*cosh(c+d*x))^(1/2)+1/2*sinh(c+d*x)/d/(a+a*cosh(c+d*x))^(3/2) +--R +--R +--R (216) +--R d x + c d x + c d x + c +--R (cosh(-------)cosh(d x + c) + cosh(-------))atan(sinh(-------)) +--R 2 2 2 +--R + +--R sinh(d x + c) +--R / +--R +-------------------+ +--R (2a d cosh(d x + c) + 2a d)\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 510 +a0169:= integrate(t0169,x) +--R +--R +--R (217) +--R 2 +--R - a sinh(d x + c) + (- 2a cosh(d x + c) - 2a)sinh(d x + c) +--R + +--R 2 +--R - a cosh(d x + c) - 2a cosh(d x + c) - a +--R * +--R +-------------------------------+ +--R +--+ | a +--R \|2a |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R atan(---------------------------------------) +--R a +--R + +--R 2 2 +--R sinh(d x + c) + (2cosh(d x + c) - 1)sinh(d x + c) + cosh(d x + c) +--R + +--R - cosh(d x + c) +--R * +--R +-------------------------------+ +--R +--+ | a +--R \|2a |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2 2 2 2 +--R a d sinh(d x + c) + (2a d cosh(d x + c) + 2a d)sinh(d x + c) +--R + +--R 2 2 2 2 +--R a d cosh(d x + c) + 2a d cosh(d x + c) + a d +--R * +--R +--+ +--R \|2a +--R Type: Union(Expression(Integer),...) +--E 352 + +--S 353 of 510 +m0169:= a0169-r0169 +--R +--R +--R (218) +--R 2 +--R (- 2a cosh(d x + c) - 2a)sinh(d x + c) +--R + +--R 2 +--R (- 4a cosh(d x + c) - 8a cosh(d x + c) - 4a)sinh(d x + c) +--R + +--R 3 2 +--R - 2a cosh(d x + c) - 6a cosh(d x + c) - 6a cosh(d x + c) - 2a +--R * +--R +-------------------------------+ +--R +--+ | a +--R \|2a |------------------------------- +--R +-------------------+ \|2sinh(d x + c) + 2cosh(d x + c) +--R \|a cosh(d x + c) + a atan(---------------------------------------) +--R a +--R + +--R 2 +--R (2cosh(d x + c) + 2)sinh(d x + c) +--R + +--R 2 3 +--R (4cosh(d x + c) + 2cosh(d x + c) - 2)sinh(d x + c) + 2cosh(d x + c) +--R + +--R - 2cosh(d x + c) +--R * +--R +-------------------------------+ +--R +--+ | a +-------------------+ +--R \|2a |------------------------------- \|a cosh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R d x + c d x + c 2 +--R (- a cosh(-------)cosh(d x + c) - a cosh(-------))sinh(d x + c) +--R 2 2 +--R + +--R d x + c 2 d x + c +--R - 2a cosh(-------)cosh(d x + c) - 4a cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c +--R - 2a cosh(-------) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 3 d x + c 2 +--R - a cosh(-------)cosh(d x + c) - 3a cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c d x + c +--R - 3a cosh(-------)cosh(d x + c) - a cosh(-------) +--R 2 2 +--R * +--R +--+ d x + c +--R \|2a atan(sinh(-------)) +--R 2 +--R + +--R 3 2 +--R - a sinh(d x + c) + (- 2a cosh(d x + c) - 2a)sinh(d x + c) +--R + +--R 2 +--R (- a cosh(d x + c) - 2a cosh(d x + c) - a)sinh(d x + c) +--R * +--R +--+ +--R \|2a +--R / +--R 2 2 2 +--R (2a d cosh(d x + c) + 2a d)sinh(d x + c) +--R + +--R 2 2 2 2 +--R (4a d cosh(d x + c) + 8a d cosh(d x + c) + 4a d)sinh(d x + c) +--R + +--R 2 3 2 2 2 2 +--R 2a d cosh(d x + c) + 6a d cosh(d x + c) + 6a d cosh(d x + c) + 2a d +--R * +--R +--+ +-------------------+ +--R \|2a \|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 353 + +--S 354 of 510 +d0169:= D(m0169,x) +--R +--R +--R (219) +--R 2 d x + c 2 +--R (8cosh(d x + c) + 16cosh(d x + c) + 8)sinh(-------) +--R 2 +--R + +--R 2 +--R 8cosh(d x + c) + 16cosh(d x + c) + 8 +--R * +--R sinh(d x + c) +--R + +--R 3 2 d x + c 2 +--R (8cosh(d x + c) + 16cosh(d x + c) + 8cosh(d x + c))sinh(-------) +--R 2 +--R + +--R 3 2 +--R 8cosh(d x + c) + 16cosh(d x + c) + 8cosh(d x + c) +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R + +--R d x + c d x + c d x + c 2 +--R (cosh(-------)cosh(d x + c) + cosh(-------))sinh(-------) +--R 2 2 2 +--R + +--R d x + c d x + c +--R cosh(-------)cosh(d x + c) + cosh(-------) +--R 2 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 2 d x + c 3 +--R (- cosh(d x + c) - 2cosh(d x + c) - 1)sinh(-------) +--R 2 +--R + +--R d x + c 2 +--R 3cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 6cosh(-------)cosh(d x + c) + 3cosh(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 2 d x + c +--R (- cosh(d x + c) - 2cosh(d x + c) - 1)sinh(-------) +--R 2 +--R + +--R d x + c 2 d x + c +--R 3cosh(-------)cosh(d x + c) + 6cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c +--R 3cosh(-------) +--R 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 2 +--R (- 3cosh(d x + c) - 9cosh(d x + c) - 9cosh(d x + c) - 3) +--R * +--R d x + c 3 +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 +--R 3cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 9cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 9cosh(-------)cosh(d x + c) + 3cosh(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 3 2 +--R (- 3cosh(d x + c) - 9cosh(d x + c) - 9cosh(d x + c) - 3) +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 2 +--R 3cosh(-------)cosh(d x + c) + 9cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c d x + c +--R 9cosh(-------)cosh(d x + c) + 3cosh(-------) +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - 3cosh(d x + c) - 12cosh(d x + c) - 18cosh(d x + c) +--R + +--R - 12cosh(d x + c) - 3 +--R * +--R d x + c 3 +--R sinh(-------) +--R 2 +--R + +--R d x + c 4 +--R cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R 4cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 6cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 4cosh(-------)cosh(d x + c) + cosh(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 4 3 2 +--R - 3cosh(d x + c) - 12cosh(d x + c) - 18cosh(d x + c) +--R + +--R - 12cosh(d x + c) - 3 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 4 d x + c 3 +--R cosh(-------)cosh(d x + c) + 4cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c 2 d x + c +--R 6cosh(-------)cosh(d x + c) + 4cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c +--R cosh(-------) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R 5 4 3 +--R - cosh(d x + c) - 5cosh(d x + c) - 10cosh(d x + c) +--R + +--R 2 +--R - 10cosh(d x + c) - 5cosh(d x + c) - 1 +--R * +--R d x + c 3 +--R sinh(-------) +--R 2 +--R + +--R 5 4 3 +--R - cosh(d x + c) - 5cosh(d x + c) - 10cosh(d x + c) +--R + +--R 2 +--R - 10cosh(d x + c) - 5cosh(d x + c) - 1 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R * +--R d x + c +--R atan(sinh(-------)) +--R 2 +--R + +--R d x + c 2 5 +--R (3sinh(-------) + 3)sinh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R ((9cosh(d x + c) + 9)sinh(-------) + 9cosh(d x + c) + 9) +--R 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 +--R (7cosh(d x + c) + 16cosh(d x + c) + 9)sinh(-------) +--R 2 +--R + +--R d x + c 2 2 +--R (- cosh(-------) + 7)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 2cosh(-------) + 16)cosh(d x + c) - cosh(-------) + 9 +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 2 +--R (- 3cosh(d x + c) - 3cosh(d x + c) + 3cosh(d x + c) + 3) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (- 3cosh(-------) - 3)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 9cosh(-------) - 3)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 9cosh(-------) + 3)cosh(d x + c) - 3cosh(-------) + 3 +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - 6cosh(d x + c) - 18cosh(d x + c) - 18cosh(d x + c) +--R + +--R - 6cosh(d x + c) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 4 +--R (- 3cosh(-------) - 6)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 12cosh(-------) - 18)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 18cosh(-------) - 18)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 12cosh(-------) - 6)cosh(d x + c) - 3cosh(-------) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R 5 4 3 +--R - 2cosh(d x + c) - 8cosh(d x + c) - 12cosh(d x + c) +--R + +--R 2 +--R - 8cosh(d x + c) - 2cosh(d x + c) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 5 +--R (- cosh(-------) - 2)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 5cosh(-------) - 8)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 10cosh(-------) - 12)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 10cosh(-------) - 8)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 5cosh(-------) - 2)cosh(d x + c) - cosh(-------) +--R 2 2 +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2 d x + c 2 +--R (4a cosh(d x + c) + 8a cosh(d x + c) + 4a)sinh(-------) +--R 2 +--R + +--R 2 +--R 4a cosh(d x + c) + 8a cosh(d x + c) + 4a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 2 +--R 12a cosh(d x + c) + 36a cosh(d x + c) + 36a cosh(d x + c) +--R + +--R 12a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 3 2 +--R 12a cosh(d x + c) + 36a cosh(d x + c) + 36a cosh(d x + c) + 12a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 12a cosh(d x + c) + 48a cosh(d x + c) + 72a cosh(d x + c) +--R + +--R 48a cosh(d x + c) + 12a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 4 3 2 +--R 12a cosh(d x + c) + 48a cosh(d x + c) + 72a cosh(d x + c) +--R + +--R 48a cosh(d x + c) + 12a +--R * +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 4a cosh(d x + c) + 20a cosh(d x + c) + 40a cosh(d x + c) +--R + +--R 2 +--R 40a cosh(d x + c) + 20a cosh(d x + c) + 4a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 5 4 3 +--R 4a cosh(d x + c) + 20a cosh(d x + c) + 40a cosh(d x + c) +--R + +--R 2 +--R 40a cosh(d x + c) + 20a cosh(d x + c) + 4a +--R * +--R +-------------------------------+ +--R | a +-------------------+ +--R |------------------------------- \|a cosh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Integer) +--E 354 + +--S 355 of 510 +t0170:= 1/(a+a*cosh(c+d*x))^(5/2) +--R +--R +--R 1 +--R (220) ---------------------------------------------------------------- +--R 2 2 2 2 +-------------------+ +--R (a cosh(d x + c) + 2a cosh(d x + c) + a )\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 355 + +--S 356 of 510 +r0170:= 3/16*atan(sinh(1/2*c+1/2*d*x))*cosh(1/2*c+1/2*d*x)/a^2/d/_ + (a+a*cosh(c+d*x))^(1/2)+1/4*sinh(c+d*x)/d/_ + (a+a*cosh(c+d*x))^(5/2)+3/16*sinh(c+d*x)/a/d/(a+a*cosh(c+d*x))^(3/2) +--R +--R +--R (221) +--R d x + c 2 d x + c +--R 3cosh(-------)cosh(d x + c) + 6cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c +--R 3cosh(-------) +--R 2 +--R * +--R d x + c +--R atan(sinh(-------)) +--R 2 +--R + +--R (3cosh(d x + c) + 7)sinh(d x + c) +--R / +--R 2 2 2 2 +-------------------+ +--R (16a d cosh(d x + c) + 32a d cosh(d x + c) + 16a d)\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 510 +a0170:= integrate(t0170,x) +--R +--R +--R (222) +--R 4 3 +--R - 3a sinh(d x + c) + (- 12a cosh(d x + c) - 12a)sinh(d x + c) +--R + +--R 2 2 +--R (- 18a cosh(d x + c) - 36a cosh(d x + c) - 18a)sinh(d x + c) +--R + +--R 3 2 +--R - 12a cosh(d x + c) - 36a cosh(d x + c) - 36a cosh(d x + c) +--R + +--R - 12a +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - 3a cosh(d x + c) - 12a cosh(d x + c) - 18a cosh(d x + c) +--R + +--R - 12a cosh(d x + c) - 3a +--R * +--R +-------------------------------+ +--R +--+ | a +--R \|2a |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R atan(---------------------------------------) +--R a +--R + +--R 4 3 +--R 3sinh(d x + c) + (12cosh(d x + c) + 11)sinh(d x + c) +--R + +--R 2 2 +--R (18cosh(d x + c) + 33cosh(d x + c) - 11)sinh(d x + c) +--R + +--R 3 2 +--R (12cosh(d x + c) + 33cosh(d x + c) - 22cosh(d x + c) - 3) +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 3cosh(d x + c) + 11cosh(d x + c) - 11cosh(d x + c) - 3cosh(d x + c) +--R * +--R +-------------------------------+ +--R +--+ | a +--R \|2a |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 3 4 3 3 3 +--R 8a d sinh(d x + c) + (32a d cosh(d x + c) + 32a d)sinh(d x + c) +--R + +--R 3 2 3 3 2 +--R (48a d cosh(d x + c) + 96a d cosh(d x + c) + 48a d)sinh(d x + c) +--R + +--R 3 3 3 2 3 +--R 32a d cosh(d x + c) + 96a d cosh(d x + c) + 96a d cosh(d x + c) +--R + +--R 3 +--R 32a d +--R * +--R sinh(d x + c) +--R + +--R 3 4 3 3 3 2 +--R 8a d cosh(d x + c) + 32a d cosh(d x + c) + 48a d cosh(d x + c) +--R + +--R 3 3 +--R 32a d cosh(d x + c) + 8a d +--R * +--R +--+ +--R \|2a +--R Type: Union(Expression(Integer),...) +--E 357 + +--S 358 of 510 +m0170:= a0170-r0170 +--R +--R +--R (223) +--R 2 4 +--R (- 6a cosh(d x + c) - 12a cosh(d x + c) - 6a)sinh(d x + c) +--R + +--R 3 2 +--R - 24a cosh(d x + c) - 72a cosh(d x + c) - 72a cosh(d x + c) +--R + +--R - 24a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - 36a cosh(d x + c) - 144a cosh(d x + c) - 216a cosh(d x + c) +--R + +--R - 144a cosh(d x + c) - 36a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R - 24a cosh(d x + c) - 120a cosh(d x + c) - 240a cosh(d x + c) +--R + +--R 2 +--R - 240a cosh(d x + c) - 120a cosh(d x + c) - 24a +--R * +--R sinh(d x + c) +--R + +--R 6 5 4 +--R - 6a cosh(d x + c) - 36a cosh(d x + c) - 90a cosh(d x + c) +--R + +--R 3 2 +--R - 120a cosh(d x + c) - 90a cosh(d x + c) - 36a cosh(d x + c) - 6a +--R * +--R +-------------------------------+ +--R +--+ | a +--R \|2a |------------------------------- +--R +-------------------+ \|2sinh(d x + c) + 2cosh(d x + c) +--R \|a cosh(d x + c) + a atan(---------------------------------------) +--R a +--R + +--R 2 4 +--R (6cosh(d x + c) + 12cosh(d x + c) + 6)sinh(d x + c) +--R + +--R 3 2 +--R (24cosh(d x + c) + 70cosh(d x + c) + 68cosh(d x + c) + 22) +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 36cosh(d x + c) + 138cosh(d x + c) + 146cosh(d x + c) +--R + +--R 22cosh(d x + c) - 22 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 24cosh(d x + c) + 114cosh(d x + c) + 112cosh(d x + c) +--R + +--R 2 +--R - 28cosh(d x + c) - 56cosh(d x + c) - 6 +--R * +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 6cosh(d x + c) + 34cosh(d x + c) + 28cosh(d x + c) +--R + +--R 3 2 +--R - 28cosh(d x + c) - 34cosh(d x + c) - 6cosh(d x + c) +--R * +--R +-------------------------------+ +--R +--+ | a +-------------------+ +--R \|2a |------------------------------- \|a cosh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R + +--R d x + c 2 d x + c +--R - 3a cosh(-------)cosh(d x + c) - 6a cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c +--R - 3a cosh(-------) +--R 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R d x + c 3 +--R - 12a cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R - 36a cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R - 36a cosh(-------)cosh(d x + c) - 12a cosh(-------) +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R d x + c 4 +--R - 18a cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R - 72a cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R - 108a cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R - 72a cosh(-------)cosh(d x + c) - 18a cosh(-------) +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R d x + c 5 +--R - 12a cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 4 +--R - 60a cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R - 120a cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R - 120a cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R - 60a cosh(-------)cosh(d x + c) - 12a cosh(-------) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 6 d x + c 5 +--R - 3a cosh(-------)cosh(d x + c) - 18a cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c 4 d x + c 3 +--R - 45a cosh(-------)cosh(d x + c) - 60a cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c 2 d x + c +--R - 45a cosh(-------)cosh(d x + c) - 18a cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c +--R - 3a cosh(-------) +--R 2 +--R * +--R +--+ d x + c +--R \|2a atan(sinh(-------)) +--R 2 +--R + +--R 5 +--R (- 3a cosh(d x + c) - 7a)sinh(d x + c) +--R + +--R 2 4 +--R (- 12a cosh(d x + c) - 40a cosh(d x + c) - 28a)sinh(d x + c) +--R + +--R 3 2 +--R - 18a cosh(d x + c) - 78a cosh(d x + c) - 102a cosh(d x + c) +--R + +--R - 42a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - 12a cosh(d x + c) - 64a cosh(d x + c) - 120a cosh(d x + c) +--R + +--R - 96a cosh(d x + c) - 28a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R - 3a cosh(d x + c) - 19a cosh(d x + c) - 46a cosh(d x + c) +--R + +--R 2 +--R - 54a cosh(d x + c) - 31a cosh(d x + c) - 7a +--R * +--R sinh(d x + c) +--R * +--R +--+ +--R \|2a +--R / +--R 3 2 3 3 4 +--R (16a d cosh(d x + c) + 32a d cosh(d x + c) + 16a d)sinh(d x + c) +--R + +--R 3 3 3 2 3 +--R 64a d cosh(d x + c) + 192a d cosh(d x + c) + 192a d cosh(d x + c) +--R + +--R 3 +--R 64a d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 4 3 3 +--R 96a d cosh(d x + c) + 384a d cosh(d x + c) +--R + +--R 3 2 3 3 +--R 576a d cosh(d x + c) + 384a d cosh(d x + c) + 96a d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 5 3 4 +--R 64a d cosh(d x + c) + 320a d cosh(d x + c) +--R + +--R 3 3 3 2 +--R 640a d cosh(d x + c) + 640a d cosh(d x + c) +--R + +--R 3 3 +--R 320a d cosh(d x + c) + 64a d +--R * +--R sinh(d x + c) +--R + +--R 3 6 3 5 3 4 +--R 16a d cosh(d x + c) + 96a d cosh(d x + c) + 240a d cosh(d x + c) +--R + +--R 3 3 3 2 3 +--R 320a d cosh(d x + c) + 240a d cosh(d x + c) + 96a d cosh(d x + c) +--R + +--R 3 +--R 16a d +--R * +--R +--+ +-------------------+ +--R \|2a \|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 358 + +--S 359 of 510 +d0170:= D(m0170,x) +--R +--R +--R (224) +--R 3 2 +--R 128cosh(d x + c) + 384cosh(d x + c) + 384cosh(d x + c) +--R + +--R 128 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 3 2 +--R 128cosh(d x + c) + 384cosh(d x + c) + 384cosh(d x + c) + 128 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 256cosh(d x + c) + 768cosh(d x + c) + 768cosh(d x + c) +--R + +--R 256cosh(d x + c) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 4 3 2 +--R 256cosh(d x + c) + 768cosh(d x + c) + 768cosh(d x + c) +--R + +--R 256cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 128cosh(d x + c) + 384cosh(d x + c) + 384cosh(d x + c) +--R + +--R 2 +--R 128cosh(d x + c) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 5 4 3 +--R 128cosh(d x + c) + 384cosh(d x + c) + 384cosh(d x + c) +--R + +--R 2 +--R 128cosh(d x + c) +--R * +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R + +--R d x + c 2 +--R 3cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 6cosh(-------)cosh(d x + c) + 3cosh(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 d x + c +--R 3cosh(-------)cosh(d x + c) + 6cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c +--R 3cosh(-------) +--R 2 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 3 2 +--R (- 3cosh(d x + c) - 9cosh(d x + c) - 9cosh(d x + c) - 3) +--R * +--R d x + c 3 +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 +--R 15cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 45cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 45cosh(-------)cosh(d x + c) + 15cosh(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 3 2 +--R (- 3cosh(d x + c) - 9cosh(d x + c) - 9cosh(d x + c) - 3) +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 2 +--R 15cosh(-------)cosh(d x + c) + 45cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c d x + c +--R 45cosh(-------)cosh(d x + c) + 15cosh(-------) +--R 2 2 +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - 15cosh(d x + c) - 60cosh(d x + c) - 90cosh(d x + c) +--R + +--R - 60cosh(d x + c) - 15 +--R * +--R d x + c 3 +--R sinh(-------) +--R 2 +--R + +--R d x + c 4 +--R 30cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R 120cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 180cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 120cosh(-------)cosh(d x + c) + 30cosh(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 4 3 2 +--R - 15cosh(d x + c) - 60cosh(d x + c) - 90cosh(d x + c) +--R + +--R - 60cosh(d x + c) - 15 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 4 +--R 30cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R 120cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 180cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 120cosh(-------)cosh(d x + c) + 30cosh(-------) +--R 2 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 5 4 +--R - 30cosh(d x + c) - 150cosh(d x + c) +--R + +--R 3 2 +--R - 300cosh(d x + c) - 300cosh(d x + c) +--R + +--R - 150cosh(d x + c) - 30 +--R * +--R d x + c 3 +--R sinh(-------) +--R 2 +--R + +--R d x + c 5 +--R 30cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 4 +--R 150cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R 300cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 300cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 150cosh(-------)cosh(d x + c) + 30cosh(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 5 4 +--R - 30cosh(d x + c) - 150cosh(d x + c) +--R + +--R 3 2 +--R - 300cosh(d x + c) - 300cosh(d x + c) +--R + +--R - 150cosh(d x + c) - 30 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 5 +--R 30cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 4 +--R 150cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R 300cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 300cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 150cosh(-------)cosh(d x + c) + 30cosh(-------) +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 5 +--R - 30cosh(d x + c) - 180cosh(d x + c) +--R + +--R 4 3 +--R - 450cosh(d x + c) - 600cosh(d x + c) +--R + +--R 2 +--R - 450cosh(d x + c) - 180cosh(d x + c) - 30 +--R * +--R d x + c 3 +--R sinh(-------) +--R 2 +--R + +--R d x + c 6 +--R 15cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 5 +--R 90cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 4 +--R 225cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R 300cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 225cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 90cosh(-------)cosh(d x + c) + 15cosh(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 6 5 +--R - 30cosh(d x + c) - 180cosh(d x + c) +--R + +--R 4 3 +--R - 450cosh(d x + c) - 600cosh(d x + c) +--R + +--R 2 +--R - 450cosh(d x + c) - 180cosh(d x + c) - 30 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 6 d x + c 5 +--R 15cosh(-------)cosh(d x + c) + 90cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c 4 +--R 225cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R 300cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c +--R 225cosh(-------)cosh(d x + c) + 90cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c +--R 15cosh(-------) +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 7 6 +--R - 15cosh(d x + c) - 105cosh(d x + c) +--R + +--R 5 4 +--R - 315cosh(d x + c) - 525cosh(d x + c) +--R + +--R 3 2 +--R - 525cosh(d x + c) - 315cosh(d x + c) +--R + +--R - 105cosh(d x + c) - 15 +--R * +--R d x + c 3 +--R sinh(-------) +--R 2 +--R + +--R d x + c 7 +--R 3cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 6 +--R 21cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 5 +--R 63cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 4 +--R 105cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R 105cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 63cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c d x + c +--R 21cosh(-------)cosh(d x + c) + 3cosh(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 7 6 +--R - 15cosh(d x + c) - 105cosh(d x + c) +--R + +--R 5 4 +--R - 315cosh(d x + c) - 525cosh(d x + c) +--R + +--R 3 2 +--R - 525cosh(d x + c) - 315cosh(d x + c) +--R + +--R - 105cosh(d x + c) - 15 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 7 d x + c 6 +--R 3cosh(-------)cosh(d x + c) + 21cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c 5 +--R 63cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 4 +--R 105cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 3 +--R 105cosh(-------)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c +--R 63cosh(-------)cosh(d x + c) + 21cosh(-------)cosh(d x + c) +--R 2 2 +--R + +--R d x + c +--R 3cosh(-------) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R 8 7 6 +--R - 3cosh(d x + c) - 24cosh(d x + c) - 84cosh(d x + c) +--R + +--R 5 4 3 +--R - 168cosh(d x + c) - 210cosh(d x + c) - 168cosh(d x + c) +--R + +--R 2 +--R - 84cosh(d x + c) - 24cosh(d x + c) - 3 +--R * +--R d x + c 3 +--R sinh(-------) +--R 2 +--R + +--R 8 7 6 +--R - 3cosh(d x + c) - 24cosh(d x + c) - 84cosh(d x + c) +--R + +--R 5 4 3 +--R - 168cosh(d x + c) - 210cosh(d x + c) - 168cosh(d x + c) +--R + +--R 2 +--R - 84cosh(d x + c) - 24cosh(d x + c) - 3 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R * +--R d x + c +--R atan(sinh(-------)) +--R 2 +--R + +--R d x + c 2 +--R ((9cosh(d x + c) + 29)sinh(-------) + 9cosh(d x + c) + 29) +--R 2 +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 +--R (45cosh(d x + c) + 190cosh(d x + c) + 145)sinh(-------) +--R 2 +--R + +--R 2 +--R 45cosh(d x + c) + 190cosh(d x + c) + 145 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 3 2 +--R (84cosh(d x + c) + 450cosh(d x + c) + 656cosh(d x + c) + 290) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (- 3cosh(-------) + 84)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 9cosh(-------) + 450)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 9cosh(-------) + 656)cosh(d x + c) - 3cosh(-------) + 290 +--R 2 2 +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 60cosh(d x + c) + 430cosh(d x + c) + 970cosh(d x + c) +--R + +--R 890cosh(d x + c) + 290 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 4 +--R (- 15cosh(-------) + 60)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 60cosh(-------) + 430)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 90cosh(-------) + 970)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 60cosh(-------) + 890)cosh(d x + c) - 15cosh(-------) + 290 +--R 2 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R - 15cosh(d x + c) + 5cosh(d x + c) + 250cosh(d x + c) +--R + +--R 2 +--R 570cosh(d x + c) + 485cosh(d x + c) + 145 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 5 +--R (- 30cosh(-------) - 15)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 150cosh(-------) + 5)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 300cosh(-------) + 250)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 300cosh(-------) + 570)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 150cosh(-------) + 485)cosh(d x + c) - 30cosh(-------) + 145 +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 6 5 4 +--R - 51cosh(d x + c) - 306cosh(d x + c) - 685cosh(d x + c) +--R + +--R 3 2 +--R - 700cosh(d x + c) - 285cosh(d x + c) + 14cosh(d x + c) + 29 +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 6 +--R (- 30cosh(-------) - 51)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 180cosh(-------) - 306)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 450cosh(-------) - 685)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 600cosh(-------) - 700)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 450cosh(-------) - 285)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 180cosh(-------) + 14)cosh(d x + c) - 30cosh(-------) + 29 +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 7 6 5 +--R - 30cosh(d x + c) - 220cosh(d x + c) - 650cosh(d x + c) +--R + +--R 4 3 2 +--R - 1000cosh(d x + c) - 850cosh(d x + c) - 380cosh(d x + c) +--R + +--R - 70cosh(d x + c) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 7 +--R (- 15cosh(-------) - 30)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (- 105cosh(-------) - 220)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 315cosh(-------) - 650)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 525cosh(-------) - 1000)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 525cosh(-------) - 850)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 315cosh(-------) - 380)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 105cosh(-------) - 70)cosh(d x + c) - 15cosh(-------) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R 8 7 6 +--R - 6cosh(d x + c) - 50cosh(d x + c) - 174cosh(d x + c) +--R + +--R 5 4 3 +--R - 330cosh(d x + c) - 370cosh(d x + c) - 246cosh(d x + c) +--R + +--R 2 +--R - 90cosh(d x + c) - 14cosh(d x + c) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 8 +--R (- 3cosh(-------) - 6)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 7 +--R (- 24cosh(-------) - 50)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (- 84cosh(-------) - 174)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 168cosh(-------) - 330)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 210cosh(-------) - 370)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 168cosh(-------) - 246)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 84cosh(-------) - 90)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 24cosh(-------) - 14)cosh(d x + c) - 3cosh(-------) +--R 2 2 +--R * +--R +-------------------------------+ +--R | a +--R |------------------------------- +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2 3 2 2 2 +--R 32a cosh(d x + c) + 96a cosh(d x + c) + 96a cosh(d x + c) +--R + +--R 2 +--R 32a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 2 3 2 2 2 2 +--R 32a cosh(d x + c) + 96a cosh(d x + c) + 96a cosh(d x + c) + 32a +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 2 4 2 3 2 2 +--R 160a cosh(d x + c) + 640a cosh(d x + c) + 960a cosh(d x + c) +--R + +--R 2 2 +--R 640a cosh(d x + c) + 160a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 2 4 2 3 2 2 +--R 160a cosh(d x + c) + 640a cosh(d x + c) + 960a cosh(d x + c) +--R + +--R 2 2 +--R 640a cosh(d x + c) + 160a +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 2 5 2 4 +--R 320a cosh(d x + c) + 1600a cosh(d x + c) +--R + +--R 2 3 2 2 +--R 3200a cosh(d x + c) + 3200a cosh(d x + c) +--R + +--R 2 2 +--R 1600a cosh(d x + c) + 320a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 2 5 2 4 2 3 +--R 320a cosh(d x + c) + 1600a cosh(d x + c) + 3200a cosh(d x + c) +--R + +--R 2 2 2 2 +--R 3200a cosh(d x + c) + 1600a cosh(d x + c) + 320a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 6 2 5 +--R 320a cosh(d x + c) + 1920a cosh(d x + c) +--R + +--R 2 4 2 3 +--R 4800a cosh(d x + c) + 6400a cosh(d x + c) +--R + +--R 2 2 2 2 +--R 4800a cosh(d x + c) + 1920a cosh(d x + c) + 320a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 2 6 2 5 2 4 +--R 320a cosh(d x + c) + 1920a cosh(d x + c) + 4800a cosh(d x + c) +--R + +--R 2 3 2 2 2 +--R 6400a cosh(d x + c) + 4800a cosh(d x + c) + 1920a cosh(d x + c) +--R + +--R 2 +--R 320a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 7 2 6 +--R 160a cosh(d x + c) + 1120a cosh(d x + c) +--R + +--R 2 5 2 4 +--R 3360a cosh(d x + c) + 5600a cosh(d x + c) +--R + +--R 2 3 2 2 +--R 5600a cosh(d x + c) + 3360a cosh(d x + c) +--R + +--R 2 2 +--R 1120a cosh(d x + c) + 160a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 2 7 2 6 2 5 +--R 160a cosh(d x + c) + 1120a cosh(d x + c) + 3360a cosh(d x + c) +--R + +--R 2 4 2 3 2 2 +--R 5600a cosh(d x + c) + 5600a cosh(d x + c) + 3360a cosh(d x + c) +--R + +--R 2 2 +--R 1120a cosh(d x + c) + 160a +--R * +--R sinh(d x + c) +--R + +--R 2 8 2 7 2 6 +--R 32a cosh(d x + c) + 256a cosh(d x + c) + 896a cosh(d x + c) +--R + +--R 2 5 2 4 2 3 +--R 1792a cosh(d x + c) + 2240a cosh(d x + c) + 1792a cosh(d x + c) +--R + +--R 2 2 2 2 +--R 896a cosh(d x + c) + 256a cosh(d x + c) + 32a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R 2 8 2 7 2 6 +--R 32a cosh(d x + c) + 256a cosh(d x + c) + 896a cosh(d x + c) +--R + +--R 2 5 2 4 2 3 +--R 1792a cosh(d x + c) + 2240a cosh(d x + c) + 1792a cosh(d x + c) +--R + +--R 2 2 2 2 +--R 896a cosh(d x + c) + 256a cosh(d x + c) + 32a +--R * +--R +-------------------------------+ +--R | a +-------------------+ +--R |------------------------------- \|a cosh(d x + c) + a +--R \|2sinh(d x + c) + 2cosh(d x + c) +--R Type: Expression(Integer) +--E 359 + +--S 360 of 510 +t0171:= 1/(a-a*cosh(c+d*x))^(3/2) +--R +--R +--R 1 +--R (225) - --------------------------------------------- +--R +---------------------+ +--R (a cosh(d x + c) - a)\|- a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 360 + +--S 361 of 510 +r0171:= -1/2*atanh(cosh(1/2*c+1/2*d*x))*sinh(1/2*c+1/2*d*x)/a/d/_ + (a-a*cosh(c+d*x))^(1/2)-1/2*sinh(c+d*x)/d/(a-a*cosh(c+d*x))^(3/2) +--R +--R +--R (226) +--R d x + c d x + c +--R (- cosh(d x + c) + 1)sinh(-------)atanh(cosh(-------)) + sinh(d x + c) +--R 2 2 +--R ---------------------------------------------------------------------- +--R +---------------------+ +--R (2a d cosh(d x + c) - 2a d)\|- a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 510 +a0171:= integrate(t0171,x) +--R +--R +--R (227) +--R 2 +--R a sinh(d x + c) + (2a cosh(d x + c) - 2a)sinh(d x + c) +--R + +--R 2 +--R a cosh(d x + c) - 2a cosh(d x + c) + a +--R * +--R log +--R (4sinh(d x + c) + 4cosh(d x + c)) +--R * +--R +---------------------------------+ +--R | a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R +----+ +--R (- sinh(d x + c) - cosh(d x + c) - 1)\|- 2a +--R / +--R sinh(d x + c) + cosh(d x + c) - 1 +--R + +--R 2 +--R - 2sinh(d x + c) + (- 4cosh(d x + c) - 2)sinh(d x + c) +--R + +--R 2 +--R - 2cosh(d x + c) - 2cosh(d x + c) +--R * +--R +---------------------------------+ +--R +----+ | a +--R \|- 2a |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 2 2 2 2 +--R 2a d sinh(d x + c) + (4a d cosh(d x + c) - 4a d)sinh(d x + c) +--R + +--R 2 2 2 2 +--R 2a d cosh(d x + c) - 4a d cosh(d x + c) + 2a d +--R * +--R +----+ +--R \|- 2a +--R Type: Union(Expression(Integer),...) +--E 362 + +--S 363 of 510 +m0171:= a0171-r0171 +--R +--R +--R (228) +--R 2 +--R (a cosh(d x + c) - a)sinh(d x + c) +--R + +--R 2 +--R (2a cosh(d x + c) - 4a cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R 3 2 +--R a cosh(d x + c) - 3a cosh(d x + c) + 3a cosh(d x + c) - a +--R * +--R +---------------------+ +--R \|- a cosh(d x + c) + a +--R * +--R log +--R (4sinh(d x + c) + 4cosh(d x + c)) +--R * +--R +---------------------------------+ +--R | a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R +----+ +--R (- sinh(d x + c) - cosh(d x + c) - 1)\|- 2a +--R / +--R sinh(d x + c) + cosh(d x + c) - 1 +--R + +--R 2 +--R (- 2cosh(d x + c) + 2)sinh(d x + c) +--R + +--R 2 +--R (- 4cosh(d x + c) + 2cosh(d x + c) + 2)sinh(d x + c) +--R + +--R 3 +--R - 2cosh(d x + c) + 2cosh(d x + c) +--R * +--R +---------------------------------+ +--R +----+ +---------------------+ | a +--R \|- 2a \|- a cosh(d x + c) + a |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R d x + c 2 +--R (a cosh(d x + c) - a)sinh(-------)sinh(d x + c) +--R 2 +--R + +--R 2 d x + c +--R (2a cosh(d x + c) - 4a cosh(d x + c) + 2a)sinh(-------)sinh(d x + c) +--R 2 +--R + +--R 3 2 +--R (a cosh(d x + c) - 3a cosh(d x + c) + 3a cosh(d x + c) - a) +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R * +--R +----+ d x + c +--R \|- 2a atanh(cosh(-------)) +--R 2 +--R + +--R 3 2 +--R - a sinh(d x + c) + (- 2a cosh(d x + c) + 2a)sinh(d x + c) +--R + +--R 2 +--R (- a cosh(d x + c) + 2a cosh(d x + c) - a)sinh(d x + c) +--R * +--R +----+ +--R \|- 2a +--R / +--R 2 2 2 +--R (2a d cosh(d x + c) - 2a d)sinh(d x + c) +--R + +--R 2 2 2 2 +--R (4a d cosh(d x + c) - 8a d cosh(d x + c) + 4a d)sinh(d x + c) +--R + +--R 2 3 2 2 2 2 +--R 2a d cosh(d x + c) - 6a d cosh(d x + c) + 6a d cosh(d x + c) - 2a d +--R * +--R +----+ +---------------------+ +--R \|- 2a \|- a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 363 + +--S 364 of 510 +d0171:= D(m0171,x) +--R +--R +--R (229) +--R d x + c 2 2 +--R (- 16cosh(-------) + 16)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (32cosh(-------) - 32)cosh(d x + c) - 16cosh(-------) + 16 +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R d x + c 2 3 +--R (- 48cosh(-------) + 48)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (80cosh(-------) - 80)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 16cosh(-------) + 16)cosh(d x + c) - 16cosh(-------) + 16 +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R d x + c 2 4 +--R (- 48cosh(-------) + 48)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (64cosh(-------) - 64)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (16cosh(-------) - 16)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 32cosh(-------) + 32)cosh(d x + c) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 2 5 +--R (- 16cosh(-------) + 16)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (16cosh(-------) - 16)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (16cosh(-------) - 16)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 16cosh(-------) + 16)cosh(d x + c) +--R 2 +--R * +--R +----+ +---------------------+ +--R \|- 2a \|- a cosh(d x + c) + a +--R + +--R d x + c 2 d x + c 2 +--R (- 4a cosh(-------) + 4a)cosh(d x + c) + 4a cosh(-------) +--R 2 2 +--R + +--R - 4a +--R * +--R d x + c 5 +--R sinh(-------)sinh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 16a cosh(-------) + 16a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (28a cosh(-------) - 28a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R - 12a cosh(-------) + 12a +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 2 +--R (4a cosh(-------) - 4a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 8a cosh(-------) + 8a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 4a cosh(-------) - 4a cosh(-------) +--R 2 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R d x + c 2 3 +--R (- 24a cosh(-------) + 24a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (60a cosh(-------) - 60a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 48a cosh(-------) + 48a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 12a cosh(-------) - 12a +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 3 +--R (16a cosh(-------) - 16a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 44a cosh(-------) + 44a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (40a cosh(-------) - 40a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R - 12a cosh(-------) + 12a cosh(-------) +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R d x + c 2 4 +--R (- 16a cosh(-------) + 16a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (52a cosh(-------) - 52a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 60a cosh(-------) + 60a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (28a cosh(-------) - 28a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R - 4a cosh(-------) + 4a +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 4 +--R (24a cosh(-------) - 24a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 84a cosh(-------) + 84a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (108a cosh(-------) - 108a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 60a cosh(-------) + 60a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 12a cosh(-------) - 12a cosh(-------) +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R d x + c 2 5 +--R (- 4a cosh(-------) + 4a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (16a cosh(-------) - 16a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 24a cosh(-------) + 24a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (16a cosh(-------) - 16a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 4a cosh(-------) + 4a)cosh(d x + c) +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 5 +--R (16a cosh(-------) - 16a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 68a cosh(-------) + 68a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (112a cosh(-------) - 112a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 88a cosh(-------) + 88a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (32a cosh(-------) - 32a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R - 4a cosh(-------) + 4a cosh(-------) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 3 d x + c 6 +--R (4a cosh(-------) - 4a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 5 +--R (- 20a cosh(-------) + 20a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (40a cosh(-------) - 40a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 40a cosh(-------) + 40a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (20a cosh(-------) - 20a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 4a cosh(-------) + 4a cosh(-------))cosh(d x + c) +--R 2 2 +--R * +--R d x + c +--R atanh(cosh(-------)) +--R 2 +--R + +--R d x + c 2 6 +--R (12a cosh(-------) - 12a)sinh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (48a cosh(-------) - 48a)cosh(d x + c) - 36a cosh(-------) +--R 2 2 +--R + +--R 36a +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 +--R (- 4a cosh(d x + c) + 8a cosh(d x + c) - 4a)sinh(-------) +--R 2 +--R + +--R d x + c 2 2 +--R (64a cosh(-------) - 64a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 100a cosh(-------) + 100a)cosh(d x + c) + 36a cosh(-------) +--R 2 2 +--R + +--R - 36a +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 3 2 +--R - 16a cosh(d x + c) + 44a cosh(d x + c) - 40a cosh(d x + c) +--R + +--R 12a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (16a cosh(-------) - 16a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 52a cosh(-------) + 52a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (48a cosh(-------) - 48a)cosh(d x + c) - 12a cosh(-------) + 12a +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 +--R - 24a cosh(d x + c) + 84a cosh(d x + c) +--R + +--R 2 +--R - 108a cosh(d x + c) + 60a cosh(d x + c) - 12a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 4 +--R (- 36a cosh(-------) + 36a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (84a cosh(-------) - 84a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 60a cosh(-------) + 60a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (12a cosh(-------) - 12a)cosh(d x + c) +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 4 +--R - 16a cosh(d x + c) + 68a cosh(d x + c) +--R + +--R 3 2 +--R - 112a cosh(d x + c) + 88a cosh(d x + c) +--R + +--R - 32a cosh(d x + c) + 4a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 5 +--R (- 32a cosh(-------) + 32a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (104a cosh(-------) - 104a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 120a cosh(-------) + 120a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (56a cosh(-------) - 56a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 8a cosh(-------) + 8a)cosh(d x + c) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R 6 5 4 +--R - 4a cosh(d x + c) + 20a cosh(d x + c) - 40a cosh(d x + c) +--R + +--R 3 2 +--R 40a cosh(d x + c) - 20a cosh(d x + c) + 4a cosh(d x + c) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 6 +--R (- 8a cosh(-------) + 8a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (32a cosh(-------) - 32a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 48a cosh(-------) + 48a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (32a cosh(-------) - 32a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 8a cosh(-------) + 8a)cosh(d x + c) +--R 2 +--R * +--R +---------------------------------+ +--R | a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R d x + c 2 2 +--R (- 32a cosh(-------) + 32a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (64a cosh(-------) - 64a)cosh(d x + c) - 32a cosh(-------) + 32a +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R d x + c 2 3 +--R (- 64a cosh(-------) + 64a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (128a cosh(-------) - 128a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 64a cosh(-------) + 64a)cosh(d x + c) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 2 4 +--R (- 32a cosh(-------) + 32a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (64a cosh(-------) - 64a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 32a cosh(-------) + 32a)cosh(d x + c) +--R 2 +--R * +--R +---------------------+ +--R \|- a cosh(d x + c) + a +--R + +--R d x + c 2 d x + c 2 +--R ((a cosh(-------) - a)cosh(d x + c) - a cosh(-------) + a) +--R 2 2 +--R * +--R d x + c 5 +--R sinh(-------)sinh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (4a cosh(-------) - 4a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 6a cosh(-------) + 6a)cosh(d x + c) + 2a cosh(-------) +--R 2 2 +--R + +--R - 2a +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 2 +--R (- a cosh(-------) + a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (2a cosh(-------) - 2a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R - a cosh(-------) + a cosh(-------) +--R 2 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R d x + c 2 3 +--R (6a cosh(-------) - 6a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 12a cosh(-------) + 12a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (6a cosh(-------) - 6a)cosh(d x + c) +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 4a cosh(-------) + 4a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (10a cosh(-------) - 10a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 8a cosh(-------) + 8a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 2a cosh(-------) - 2a cosh(-------) +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R d x + c 2 4 +--R (4a cosh(-------) - 4a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 10a cosh(-------) + 10a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (6a cosh(-------) - 6a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (2a cosh(-------) - 2a)cosh(d x + c) - 2a cosh(-------) + 2a +--R 2 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 6a cosh(-------) + 6a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (18a cosh(-------) - 18a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 18a cosh(-------) + 18a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (6a cosh(-------) - 6a cosh(-------))cosh(d x + c) +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R d x + c 2 5 +--R (a cosh(-------) - a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 3a cosh(-------) + 3a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (2a cosh(-------) - 2a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (2a cosh(-------) - 2a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 3a cosh(-------) + 3a)cosh(d x + c) + a cosh(-------) - a +--R 2 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 5 +--R (- 4a cosh(-------) + 4a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (14a cosh(-------) - 14a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 16a cosh(-------) + 16a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (4a cosh(-------) - 4a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (4a cosh(-------) - 4a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R - 2a cosh(-------) + 2a cosh(-------) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 3 d x + c 6 +--R (- a cosh(-------) + a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 5 +--R (4a cosh(-------) - 4a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 5a cosh(-------) + 5a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (5a cosh(-------) - 5a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 4a cosh(-------) + 4a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R a cosh(-------) - a cosh(-------) +--R 2 2 +--R * +--R +----+ d x + c +--R \|- 2a atanh(cosh(-------)) +--R 2 +--R + +--R d x + c 2 6 +--R (- 3a cosh(-------) + 3a)sinh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 12a cosh(-------) + 12a)cosh(d x + c) + 6a cosh(-------) +--R 2 2 +--R + +--R - 6a +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 +--R (a cosh(d x + c) - 2a cosh(d x + c) + a)sinh(-------) +--R 2 +--R + +--R d x + c 2 2 +--R (- 16a cosh(-------) + 16a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (16a cosh(-------) - 16a)cosh(d x + c) +--R 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 3 2 +--R 4a cosh(d x + c) - 10a cosh(d x + c) + 8a cosh(d x + c) +--R + +--R - 2a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (- 4a cosh(-------) + 4a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (6a cosh(-------) - 6a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (4a cosh(-------) - 4a)cosh(d x + c) - 6a cosh(-------) + 6a +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 6a cosh(d x + c) - 18a cosh(d x + c) + 18a cosh(d x + c) +--R + +--R - 6a cosh(d x + c) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 4 +--R (9a cosh(-------) - 9a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 18a cosh(-------) + 18a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (12a cosh(-------) - 12a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 6a cosh(-------) + 6a)cosh(d x + c) + 3a cosh(-------) - 3a +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 4a cosh(d x + c) - 14a cosh(d x + c) + 16a cosh(d x + c) +--R + +--R 2 +--R - 4a cosh(d x + c) - 4a cosh(d x + c) + 2a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 5 +--R (8a cosh(-------) - 8a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 20a cosh(-------) + 20a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (12a cosh(-------) - 12a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (4a cosh(-------) - 4a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 4a cosh(-------) + 4a)cosh(d x + c) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R 6 5 4 +--R a cosh(d x + c) - 4a cosh(d x + c) + 5a cosh(d x + c) +--R + +--R 2 +--R - 5a cosh(d x + c) + 4a cosh(d x + c) - a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 6 +--R (2a cosh(-------) - 2a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 6a cosh(-------) + 6a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (4a cosh(-------) - 4a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (4a cosh(-------) - 4a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 6a cosh(-------) + 6a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (2a cosh(-------) - 2a)cosh(d x + c) +--R 2 +--R * +--R +----+ +--R \|- 2a +--R / +--R 2 d x + c 2 2 2 +--R (16a cosh(-------) - 16a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 +--R (- 32a cosh(-------) + 32a )cosh(d x + c) + 16a cosh(-------) +--R 2 2 +--R + +--R 2 +--R - 16a +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 2 3 +--R (64a cosh(-------) - 64a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (- 176a cosh(-------) + 176a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 +--R (160a cosh(-------) - 160a )cosh(d x + c) - 48a cosh(-------) +--R 2 2 +--R + +--R 2 +--R 48a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 2 4 +--R (96a cosh(-------) - 96a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 3 +--R (- 336a cosh(-------) + 336a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (432a cosh(-------) - 432a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 +--R (- 240a cosh(-------) + 240a )cosh(d x + c) + 48a cosh(-------) +--R 2 2 +--R + +--R 2 +--R - 48a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 2 5 +--R (64a cosh(-------) - 64a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 4 +--R (- 272a cosh(-------) + 272a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 3 +--R (448a cosh(-------) - 448a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (- 352a cosh(-------) + 352a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 +--R (128a cosh(-------) - 128a )cosh(d x + c) - 16a cosh(-------) +--R 2 2 +--R + +--R 2 +--R 16a +--R * +--R sinh(d x + c) +--R + +--R 2 d x + c 2 2 6 +--R (16a cosh(-------) - 16a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 5 +--R (- 80a cosh(-------) + 80a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 4 +--R (160a cosh(-------) - 160a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 3 +--R (- 160a cosh(-------) + 160a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (80a cosh(-------) - 80a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 +--R (- 16a cosh(-------) + 16a )cosh(d x + c) +--R 2 +--R * +--R +---------------------------------+ +--R +---------------------+ | a +--R \|- a cosh(d x + c) + a |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R 2 d x + c 2 2 2 +--R (- 4a cosh(-------) + 4a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 2 +--R (8a cosh(-------) - 8a )cosh(d x + c) - 4a cosh(-------) + 4a +--R 2 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 2 3 +--R (- 16a cosh(-------) + 16a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (40a cosh(-------) - 40a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 +--R (- 32a cosh(-------) + 32a )cosh(d x + c) + 8a cosh(-------) +--R 2 2 +--R + +--R 2 +--R - 8a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 2 4 +--R (- 24a cosh(-------) + 24a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 3 +--R (72a cosh(-------) - 72a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (- 72a cosh(-------) + 72a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 +--R (24a cosh(-------) - 24a )cosh(d x + c) +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 d x + c 2 2 5 +--R (- 16a cosh(-------) + 16a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 4 +--R (56a cosh(-------) - 56a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 3 +--R (- 64a cosh(-------) + 64a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (16a cosh(-------) - 16a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 2 +--R (16a cosh(-------) - 16a )cosh(d x + c) - 8a cosh(-------) + 8a +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R 2 d x + c 2 2 6 +--R (- 4a cosh(-------) + 4a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 5 +--R (16a cosh(-------) - 16a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 4 +--R (- 20a cosh(-------) + 20a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (20a cosh(-------) - 20a )cosh(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 2 +--R (- 16a cosh(-------) + 16a )cosh(d x + c) + 4a cosh(-------) - 4a +--R 2 2 +--R * +--R +----+ +---------------------+ +--R \|- 2a \|- a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 364 + +--S 365 of 510 +t0172:= 1/(a-a*cosh(c+d*x))^(5/2) +--R +--R +--R 1 +--R (230) ------------------------------------------------------------------ +--R 2 2 2 2 +---------------------+ +--R (a cosh(d x + c) - 2a cosh(d x + c) + a )\|- a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 365 + +--S 366 of 510 +r0172:= -3/16*atanh(cosh(1/2*c+1/2*d*x))*sinh(1/2*c+1/2*d*x)/a^2/d/_ + (a-a*cosh(c+d*x))^(1/2)-1/4*sinh(c+d*x)/d/(a-a*cosh(c+d*x))^(5/2)-_ + 3/16*sinh(c+d*x)/a/d/(a-a*cosh(c+d*x))^(3/2) +--R +--R +--R (231) +--R 2 d x + c d x + c +--R (- 3cosh(d x + c) + 6cosh(d x + c) - 3)sinh(-------)atanh(cosh(-------)) +--R 2 2 +--R + +--R (3cosh(d x + c) - 7)sinh(d x + c) +--R / +--R 2 2 2 2 +--R (16a d cosh(d x + c) - 32a d cosh(d x + c) + 16a d) +--R * +--R +---------------------+ +--R \|- a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 366 + +--S 367 of 510 +a0172:= integrate(t0172,x) +--R +--R +--R (232) +--R 4 3 +--R 3a sinh(d x + c) + (12a cosh(d x + c) - 12a)sinh(d x + c) +--R + +--R 2 2 +--R (18a cosh(d x + c) - 36a cosh(d x + c) + 18a)sinh(d x + c) +--R + +--R 3 2 +--R (12a cosh(d x + c) - 36a cosh(d x + c) + 36a cosh(d x + c) - 12a) +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 3a cosh(d x + c) - 12a cosh(d x + c) + 18a cosh(d x + c) +--R + +--R - 12a cosh(d x + c) + 3a +--R * +--R log +--R (4sinh(d x + c) + 4cosh(d x + c)) +--R * +--R +---------------------------------+ +--R | a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R +----+ +--R (- sinh(d x + c) - cosh(d x + c) - 1)\|- 2a +--R / +--R sinh(d x + c) + cosh(d x + c) - 1 +--R + +--R 4 3 +--R - 6sinh(d x + c) + (- 24cosh(d x + c) + 22)sinh(d x + c) +--R + +--R 2 2 +--R (- 36cosh(d x + c) + 66cosh(d x + c) + 22)sinh(d x + c) +--R + +--R 3 2 +--R (- 24cosh(d x + c) + 66cosh(d x + c) + 44cosh(d x + c) - 6) +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - 6cosh(d x + c) + 22cosh(d x + c) + 22cosh(d x + c) +--R + +--R - 6cosh(d x + c) +--R * +--R +---------------------------------+ +--R +----+ | a +--R \|- 2a |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R / +--R 3 4 3 3 3 +--R 16a d sinh(d x + c) + (64a d cosh(d x + c) - 64a d)sinh(d x + c) +--R + +--R 3 2 3 3 2 +--R (96a d cosh(d x + c) - 192a d cosh(d x + c) + 96a d)sinh(d x + c) +--R + +--R 3 3 3 2 3 +--R 64a d cosh(d x + c) - 192a d cosh(d x + c) + 192a d cosh(d x + c) +--R + +--R 3 +--R - 64a d +--R * +--R sinh(d x + c) +--R + +--R 3 4 3 3 3 2 +--R 16a d cosh(d x + c) - 64a d cosh(d x + c) + 96a d cosh(d x + c) +--R + +--R 3 3 +--R - 64a d cosh(d x + c) + 16a d +--R * +--R +----+ +--R \|- 2a +--R Type: Union(Expression(Integer),...) +--E 367 + +--S 368 of 510 +m0172:= a0172-r0172 +--R +--R +--R (233) +--R 2 4 +--R (3a cosh(d x + c) - 6a cosh(d x + c) + 3a)sinh(d x + c) +--R + +--R 3 2 +--R (12a cosh(d x + c) - 36a cosh(d x + c) + 36a cosh(d x + c) - 12a) +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 18a cosh(d x + c) - 72a cosh(d x + c) + 108a cosh(d x + c) +--R + +--R - 72a cosh(d x + c) + 18a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R 12a cosh(d x + c) - 60a cosh(d x + c) + 120a cosh(d x + c) +--R + +--R 2 +--R - 120a cosh(d x + c) + 60a cosh(d x + c) - 12a +--R * +--R sinh(d x + c) +--R + +--R 6 5 4 +--R 3a cosh(d x + c) - 18a cosh(d x + c) + 45a cosh(d x + c) +--R + +--R 3 2 +--R - 60a cosh(d x + c) + 45a cosh(d x + c) - 18a cosh(d x + c) + 3a +--R * +--R +---------------------+ +--R \|- a cosh(d x + c) + a +--R * +--R log +--R (4sinh(d x + c) + 4cosh(d x + c)) +--R * +--R +---------------------------------+ +--R | a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R +----+ +--R (- sinh(d x + c) - cosh(d x + c) - 1)\|- 2a +--R / +--R sinh(d x + c) + cosh(d x + c) - 1 +--R + +--R 2 4 +--R (- 6cosh(d x + c) + 12cosh(d x + c) - 6)sinh(d x + c) +--R + +--R 3 2 +--R (- 24cosh(d x + c) + 70cosh(d x + c) - 68cosh(d x + c) + 22) +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - 36cosh(d x + c) + 138cosh(d x + c) - 146cosh(d x + c) +--R + +--R 22cosh(d x + c) + 22 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R - 24cosh(d x + c) + 114cosh(d x + c) - 112cosh(d x + c) +--R + +--R 2 +--R - 28cosh(d x + c) + 56cosh(d x + c) - 6 +--R * +--R sinh(d x + c) +--R + +--R 6 5 4 +--R - 6cosh(d x + c) + 34cosh(d x + c) - 28cosh(d x + c) +--R + +--R 3 2 +--R - 28cosh(d x + c) + 34cosh(d x + c) - 6cosh(d x + c) +--R * +--R +---------------------------------+ +--R +----+ +---------------------+ | a +--R \|- 2a \|- a cosh(d x + c) + a |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R 2 d x + c +--R (3a cosh(d x + c) - 6a cosh(d x + c) + 3a)sinh(-------) +--R 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 3 2 +--R (12a cosh(d x + c) - 36a cosh(d x + c) + 36a cosh(d x + c) - 12a) +--R * +--R d x + c 3 +--R sinh(-------)sinh(d x + c) +--R 2 +--R + +--R 4 3 2 +--R 18a cosh(d x + c) - 72a cosh(d x + c) + 108a cosh(d x + c) +--R + +--R - 72a cosh(d x + c) + 18a +--R * +--R d x + c 2 +--R sinh(-------)sinh(d x + c) +--R 2 +--R + +--R 5 4 3 +--R 12a cosh(d x + c) - 60a cosh(d x + c) + 120a cosh(d x + c) +--R + +--R 2 +--R - 120a cosh(d x + c) + 60a cosh(d x + c) - 12a +--R * +--R d x + c +--R sinh(-------)sinh(d x + c) +--R 2 +--R + +--R 6 5 4 +--R 3a cosh(d x + c) - 18a cosh(d x + c) + 45a cosh(d x + c) +--R + +--R 3 2 +--R - 60a cosh(d x + c) + 45a cosh(d x + c) - 18a cosh(d x + c) + 3a +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R * +--R +----+ d x + c +--R \|- 2a atanh(cosh(-------)) +--R 2 +--R + +--R 5 +--R (- 3a cosh(d x + c) + 7a)sinh(d x + c) +--R + +--R 2 4 +--R (- 12a cosh(d x + c) + 40a cosh(d x + c) - 28a)sinh(d x + c) +--R + +--R 3 2 +--R - 18a cosh(d x + c) + 78a cosh(d x + c) - 102a cosh(d x + c) +--R + +--R 42a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R - 12a cosh(d x + c) + 64a cosh(d x + c) - 120a cosh(d x + c) +--R + +--R 96a cosh(d x + c) - 28a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 5 4 3 +--R - 3a cosh(d x + c) + 19a cosh(d x + c) - 46a cosh(d x + c) +--R + +--R 2 +--R 54a cosh(d x + c) - 31a cosh(d x + c) + 7a +--R * +--R sinh(d x + c) +--R * +--R +----+ +--R \|- 2a +--R / +--R 3 2 3 3 4 +--R (16a d cosh(d x + c) - 32a d cosh(d x + c) + 16a d)sinh(d x + c) +--R + +--R 3 3 3 2 3 +--R 64a d cosh(d x + c) - 192a d cosh(d x + c) + 192a d cosh(d x + c) +--R + +--R 3 +--R - 64a d +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 4 3 3 +--R 96a d cosh(d x + c) - 384a d cosh(d x + c) +--R + +--R 3 2 3 3 +--R 576a d cosh(d x + c) - 384a d cosh(d x + c) + 96a d +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 5 3 4 +--R 64a d cosh(d x + c) - 320a d cosh(d x + c) +--R + +--R 3 3 3 2 +--R 640a d cosh(d x + c) - 640a d cosh(d x + c) +--R + +--R 3 3 +--R 320a d cosh(d x + c) - 64a d +--R * +--R sinh(d x + c) +--R + +--R 3 6 3 5 3 4 +--R 16a d cosh(d x + c) - 96a d cosh(d x + c) + 240a d cosh(d x + c) +--R + +--R 3 3 3 2 3 +--R - 320a d cosh(d x + c) + 240a d cosh(d x + c) - 96a d cosh(d x + c) +--R + +--R 3 +--R 16a d +--R * +--R +----+ +---------------------+ +--R \|- 2a \|- a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 368 + +--S 369 of 510 +d0172:= D(m0172,x) +--R +--R +--R (234) +--R d x + c 2 3 +--R (256cosh(-------) - 256)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 768cosh(-------) + 768)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (768cosh(-------) - 768)cosh(d x + c) - 256cosh(-------) +--R 2 2 +--R + +--R 256 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R d x + c 2 4 +--R (1024cosh(-------) - 1024)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 2816cosh(-------) + 2816)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (2304cosh(-------) - 2304)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 256cosh(-------) + 256)cosh(d x + c) - 256cosh(-------) +--R 2 2 +--R + +--R 256 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R d x + c 2 5 +--R (1536cosh(-------) - 1536)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 3840cosh(-------) + 3840)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (2304cosh(-------) - 2304)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (768cosh(-------) - 768)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 768cosh(-------) + 768)cosh(d x + c) +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R d x + c 2 6 +--R (1024cosh(-------) - 1024)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 2304cosh(-------) + 2304)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (768cosh(-------) - 768)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (1280cosh(-------) - 1280)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 768cosh(-------) + 768)cosh(d x + c) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 2 7 +--R (256cosh(-------) - 256)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (- 512cosh(-------) + 512)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (512cosh(-------) - 512)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 256cosh(-------) + 256)cosh(d x + c) +--R 2 +--R * +--R +----+ +---------------------+ +--R \|- 2a \|- a cosh(d x + c) + a +--R + +--R d x + c 2 2 +--R (- 12a cosh(-------) + 12a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (24a cosh(-------) - 24a)cosh(d x + c) - 12a cosh(-------) +--R 2 2 +--R + +--R 12a +--R * +--R d x + c 7 +--R sinh(-------)sinh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 72a cosh(-------) + 72a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (204a cosh(-------) - 204a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 192a cosh(-------) + 192a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 60a cosh(-------) - 60a +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 3 +--R (12a cosh(-------) - 12a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 36a cosh(-------) + 36a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (36a cosh(-------) - 36a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R - 12a cosh(-------) + 12a cosh(-------) +--R 2 2 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R d x + c 2 4 +--R (- 180a cosh(-------) + 180a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (660a cosh(-------) - 660a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 900a cosh(-------) + 900a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (540a cosh(-------) - 540a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R - 120a cosh(-------) + 120a +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 4 +--R (72a cosh(-------) - 72a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 276a cosh(-------) + 276a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (396a cosh(-------) - 396a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 252a cosh(-------) + 252a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 60a cosh(-------) - 60a cosh(-------) +--R 2 2 +--R * +--R 5 +--R sinh(d x + c) +--R + +--R d x + c 2 5 +--R (- 240a cosh(-------) + 240a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (1080a cosh(-------) - 1080a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 1920a cosh(-------) + 1920a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (1680a cosh(-------) - 1680a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 720a cosh(-------) + 720a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 120a cosh(-------) - 120a +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 5 +--R (180a cosh(-------) - 180a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 840a cosh(-------) + 840a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (1560a cosh(-------) - 1560a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 1440a cosh(-------) + 1440a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (660a cosh(-------) - 660a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R - 120a cosh(-------) + 120a cosh(-------) +--R 2 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R d x + c 2 6 +--R (- 180a cosh(-------) + 180a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (960a cosh(-------) - 960a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 2100a cosh(-------) + 2100a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (2400a cosh(-------) - 2400a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 1500a cosh(-------) + 1500a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (480a cosh(-------) - 480a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R - 60a cosh(-------) + 60a +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 6 +--R (240a cosh(-------) - 240a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 5 +--R (- 1320a cosh(-------) + 1320a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (3000a cosh(-------) - 3000a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 3600a cosh(-------) + 3600a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (2400a cosh(-------) - 2400a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 840a cosh(-------) + 840a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 120a cosh(-------) - 120a cosh(-------) +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R d x + c 2 7 +--R (- 72a cosh(-------) + 72a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (444a cosh(-------) - 444a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 1152a cosh(-------) + 1152a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (1620a cosh(-------) - 1620a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 1320a cosh(-------) + 1320a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (612a cosh(-------) - 612a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 144a cosh(-------) + 144a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 12a cosh(-------) - 12a +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 7 +--R (180a cosh(-------) - 180a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 6 +--R (- 1140a cosh(-------) + 1140a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 5 +--R (3060a cosh(-------) - 3060a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 4500a cosh(-------) + 4500a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (3900a cosh(-------) - 3900a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 1980a cosh(-------) + 1980a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (540a cosh(-------) - 540a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R - 60a cosh(-------) + 60a cosh(-------) +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R d x + c 2 8 +--R (- 12a cosh(-------) + 12a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 7 +--R (84a cosh(-------) - 84a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (- 252a cosh(-------) + 252a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (420a cosh(-------) - 420a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 420a cosh(-------) + 420a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (252a cosh(-------) - 252a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 84a cosh(-------) + 84a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (12a cosh(-------) - 12a)cosh(d x + c) +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 8 +--R (72a cosh(-------) - 72a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 7 +--R (- 516a cosh(-------) + 516a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 6 +--R (1596a cosh(-------) - 1596a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 5 +--R (- 2772a cosh(-------) + 2772a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (2940a cosh(-------) - 2940a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 1932a cosh(-------) + 1932a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (756a cosh(-------) - 756a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 156a cosh(-------) + 156a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 12a cosh(-------) - 12a cosh(-------) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 3 d x + c 9 +--R (12a cosh(-------) - 12a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 8 +--R (- 96a cosh(-------) + 96a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 7 +--R (336a cosh(-------) - 336a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 6 +--R (- 672a cosh(-------) + 672a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 5 +--R (840a cosh(-------) - 840a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 672a cosh(-------) + 672a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (336a cosh(-------) - 336a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 96a cosh(-------) + 96a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (12a cosh(-------) - 12a cosh(-------))cosh(d x + c) +--R 2 2 +--R * +--R d x + c +--R atanh(cosh(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (36a cosh(-------) - 36a)cosh(d x + c) - 116a cosh(-------) +--R 2 2 +--R + +--R 116a +--R * +--R 8 +--R sinh(d x + c) +--R + +--R d x + c 2 2 +--R (216a cosh(-------) - 216a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 876a cosh(-------) + 876a)cosh(d x + c) + 580a cosh(-------) +--R 2 2 +--R + +--R - 580a +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 3 2 +--R - 12a cosh(d x + c) + 36a cosh(d x + c) - 36a cosh(d x + c) +--R + +--R 12a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (516a cosh(-------) - 516a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 2560a cosh(-------) + 2560a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (3204a cosh(-------) - 3204a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R - 1160a cosh(-------) + 1160a +--R 2 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 4 3 +--R - 72a cosh(d x + c) + 276a cosh(d x + c) +--R + +--R 2 +--R - 396a cosh(d x + c) + 252a cosh(d x + c) - 60a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 4 +--R (576a cosh(-------) - 576a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 3520a cosh(-------) + 3520a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (6504a cosh(-------) - 6504a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 4720a cosh(-------) + 4720a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 1160a cosh(-------) - 1160a +--R 2 +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 5 4 +--R - 180a cosh(d x + c) + 840a cosh(d x + c) +--R + +--R 3 2 +--R - 1560a cosh(d x + c) + 1440a cosh(d x + c) +--R + +--R - 660a cosh(d x + c) + 120a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 5 +--R (180a cosh(-------) - 180a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 1740a cosh(-------) + 1740a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (4880a cosh(-------) - 4880a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 5840a cosh(-------) + 5840a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (3100a cosh(-------) - 3100a)cosh(d x + c) - 580a cosh(-------) +--R 2 2 +--R + +--R 580a +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 6 5 +--R - 240a cosh(d x + c) + 1320a cosh(d x + c) +--R + +--R 4 3 +--R - 3000a cosh(d x + c) + 3600a cosh(d x + c) +--R + +--R 2 +--R - 2400a cosh(d x + c) + 840a cosh(d x + c) - 120a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 6 +--R (- 264a cosh(-------) + 264a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (1204a cosh(-------) - 1204a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 1740a cosh(-------) + 1740a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (520a cosh(-------) - 520a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (800a cosh(-------) - 800a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 636a cosh(-------) + 636a)cosh(d x + c) + 116a cosh(-------) +--R 2 2 +--R + +--R - 116a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 7 6 +--R - 180a cosh(d x + c) + 1140a cosh(d x + c) +--R + +--R 5 4 +--R - 3060a cosh(d x + c) + 4500a cosh(d x + c) +--R + +--R 3 2 +--R - 3900a cosh(d x + c) + 1980a cosh(d x + c) +--R + +--R - 540a cosh(d x + c) + 60a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 7 +--R (- 324a cosh(-------) + 324a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (2104a cosh(-------) - 2104a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 5340a cosh(-------) + 5340a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (6800a cosh(-------) - 6800a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 4540a cosh(-------) + 4540a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (1464a cosh(-------) - 1464a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 164a cosh(-------) + 164a)cosh(d x + c) +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 8 7 +--R - 72a cosh(d x + c) + 516a cosh(d x + c) +--R + +--R 6 5 +--R - 1596a cosh(d x + c) + 2772a cosh(d x + c) +--R + +--R 4 3 +--R - 2940a cosh(d x + c) + 1932a cosh(d x + c) +--R + +--R 2 +--R - 756a cosh(d x + c) + 156a cosh(d x + c) - 12a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 8 +--R (- 144a cosh(-------) + 144a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 7 +--R (1080a cosh(-------) - 1080a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (- 3296a cosh(-------) + 3296a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (5320a cosh(-------) - 5320a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 4880a cosh(-------) + 4880a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (2504a cosh(-------) - 2504a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 640a cosh(-------) + 640a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (56a cosh(-------) - 56a)cosh(d x + c) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R 9 8 7 +--R - 12a cosh(d x + c) + 96a cosh(d x + c) - 336a cosh(d x + c) +--R + +--R 6 5 4 +--R 672a cosh(d x + c) - 840a cosh(d x + c) + 672a cosh(d x + c) +--R + +--R 3 2 +--R - 336a cosh(d x + c) + 96a cosh(d x + c) - 12a cosh(d x + c) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 9 +--R (- 24a cosh(-------) + 24a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 8 +--R (200a cosh(-------) - 200a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 7 +--R (- 696a cosh(-------) + 696a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (1320a cosh(-------) - 1320a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 1480a cosh(-------) + 1480a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (984a cosh(-------) - 984a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 360a cosh(-------) + 360a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (56a cosh(-------) - 56a)cosh(d x + c) +--R 2 +--R * +--R +---------------------------------+ +--R | a +--R |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R d x + c 2 3 +--R (512a cosh(-------) - 512a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 1536a cosh(-------) + 1536a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (1536a cosh(-------) - 1536a)cosh(d x + c) - 512a cosh(-------) +--R 2 2 +--R + +--R 512a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R d x + c 2 4 +--R (1536a cosh(-------) - 1536a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 4608a cosh(-------) + 4608a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (4608a cosh(-------) - 4608a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 1536a cosh(-------) + 1536a)cosh(d x + c) +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R d x + c 2 5 +--R (1536a cosh(-------) - 1536a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 4608a cosh(-------) + 4608a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (4608a cosh(-------) - 4608a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 1536a cosh(-------) + 1536a)cosh(d x + c) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 2 6 +--R (512a cosh(-------) - 512a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 1536a cosh(-------) + 1536a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (1536a cosh(-------) - 1536a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 512a cosh(-------) + 512a)cosh(d x + c) +--R 2 +--R * +--R +---------------------+ +--R \|- a cosh(d x + c) + a +--R + +--R d x + c 2 2 +--R (3a cosh(-------) - 3a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 6a cosh(-------) + 6a)cosh(d x + c) + 3a cosh(-------) - 3a +--R 2 2 +--R * +--R d x + c 7 +--R sinh(-------)sinh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (18a cosh(-------) - 18a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 48a cosh(-------) + 48a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (42a cosh(-------) - 42a)cosh(d x + c) - 12a cosh(-------) +--R 2 2 +--R + +--R 12a +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 3a cosh(-------) + 3a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (9a cosh(-------) - 9a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 9a cosh(-------) + 9a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 3a cosh(-------) - 3a cosh(-------) +--R 2 2 +--R * +--R 6 +--R sinh(d x + c) +--R + +--R d x + c 2 4 +--R (45a cosh(-------) - 45a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 150a cosh(-------) + 150a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (180a cosh(-------) - 180a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 90a cosh(-------) + 90a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 15a cosh(-------) - 15a +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 18a cosh(-------) + 18a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (66a cosh(-------) - 66a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 90a cosh(-------) + 90a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (54a cosh(-------) - 54a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R - 12a cosh(-------) + 12a cosh(-------) +--R 2 2 +--R * +--R 5 +--R sinh(d x + c) +--R + +--R d x + c 2 5 +--R (60a cosh(-------) - 60a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 240a cosh(-------) + 240a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (360a cosh(-------) - 360a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 240a cosh(-------) + 240a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (60a cosh(-------) - 60a)cosh(d x + c) +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 5 +--R (- 45a cosh(-------) + 45a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (195a cosh(-------) - 195a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 330a cosh(-------) + 330a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (270a cosh(-------) - 270a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 105a cosh(-------) + 105a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 15a cosh(-------) - 15a cosh(-------) +--R 2 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R d x + c 2 6 +--R (45a cosh(-------) - 45a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 210a cosh(-------) + 210a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (375a cosh(-------) - 375a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 300a cosh(-------) + 300a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (75a cosh(-------) - 75a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (30a cosh(-------) - 30a)cosh(d x + c) - 15a cosh(-------) +--R 2 2 +--R + +--R 15a +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 6 +--R (- 60a cosh(-------) + 60a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 5 +--R (300a cosh(-------) - 300a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 600a cosh(-------) + 600a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (600a cosh(-------) - 600a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 300a cosh(-------) + 300a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (60a cosh(-------) - 60a cosh(-------))cosh(d x + c) +--R 2 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R d x + c 2 7 +--R (18a cosh(-------) - 18a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (- 96a cosh(-------) + 96a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (198a cosh(-------) - 198a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 180a cosh(-------) + 180a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (30a cosh(-------) - 30a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (72a cosh(-------) - 72a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 54a cosh(-------) + 54a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R 12a cosh(-------) - 12a +--R 2 +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 7 +--R (- 45a cosh(-------) + 45a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 6 +--R (255a cosh(-------) - 255a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 5 +--R (- 585a cosh(-------) + 585a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (675a cosh(-------) - 675a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 375a cosh(-------) + 375a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (45a cosh(-------) - 45a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (45a cosh(-------) - 45a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R - 15a cosh(-------) + 15a cosh(-------) +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R d x + c 2 8 +--R (3a cosh(-------) - 3a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 7 +--R (- 18a cosh(-------) + 18a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (42a cosh(-------) - 42a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 42a cosh(-------) + 42a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (42a cosh(-------) - 42a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 42a cosh(-------) + 42a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (18a cosh(-------) - 18a)cosh(d x + c) - 3a cosh(-------) +--R 2 2 +--R + +--R 3a +--R * +--R d x + c +--R sinh(-------) +--R 2 +--R + +--R d x + c 3 d x + c 8 +--R (- 18a cosh(-------) + 18a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 7 +--R (114a cosh(-------) - 114a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 6 +--R (- 294a cosh(-------) + 294a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 5 +--R (378a cosh(-------) - 378a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 210a cosh(-------) + 210a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 42a cosh(-------) + 42a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (126a cosh(-------) - 126a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 66a cosh(-------) + 66a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 12a cosh(-------) - 12a cosh(-------) +--R 2 2 +--R * +--R sinh(d x + c) +--R + +--R d x + c 3 d x + c 9 +--R (- 3a cosh(-------) + 3a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 8 +--R (21a cosh(-------) - 21a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 7 +--R (- 60a cosh(-------) + 60a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 6 +--R (84a cosh(-------) - 84a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 5 +--R (- 42a cosh(-------) + 42a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 42a cosh(-------) + 42a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (84a cosh(-------) - 84a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 60a cosh(-------) + 60a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (21a cosh(-------) - 21a cosh(-------))cosh(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R - 3a cosh(-------) + 3a cosh(-------) +--R 2 2 +--R * +--R +----+ d x + c +--R \|- 2a atanh(cosh(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 9a cosh(-------) + 9a)cosh(d x + c) + 29a cosh(-------) +--R 2 2 +--R + +--R - 29a +--R * +--R 8 +--R sinh(d x + c) +--R + +--R d x + c 2 2 +--R (- 54a cosh(-------) + 54a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (210a cosh(-------) - 210a)cosh(d x + c) - 116a cosh(-------) +--R 2 2 +--R + +--R 116a +--R * +--R 7 +--R sinh(d x + c) +--R + +--R 3 2 +--R (3a cosh(d x + c) - 9a cosh(d x + c) + 9a cosh(d x + c) - 3a) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (- 129a cosh(-------) + 129a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (595a cosh(-------) - 595a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 611a cosh(-------) + 611a)cosh(d x + c) + 145a cosh(-------) +--R 2 2 +--R + +--R - 145a +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 4 3 2 +--R 18a cosh(d x + c) - 66a cosh(d x + c) + 90a cosh(d x + c) +--R + +--R - 54a cosh(d x + c) + 12a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 4 +--R (- 144a cosh(-------) + 144a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (796a cosh(-------) - 796a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 1176a cosh(-------) + 1176a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (524a cosh(-------) - 524a)cosh(d x + c) +--R 2 +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 5 4 +--R 45a cosh(d x + c) - 195a cosh(d x + c) +--R + +--R 3 2 +--R 330a cosh(d x + c) - 270a cosh(d x + c) +--R + +--R 105a cosh(d x + c) - 15a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 5 +--R (- 45a cosh(-------) + 45a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (375a cosh(-------) - 375a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 790a cosh(-------) + 790a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (490a cosh(-------) - 490a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (115a cosh(-------) - 115a)cosh(d x + c) - 145a cosh(-------) +--R 2 2 +--R + +--R 145a +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 6 5 +--R 60a cosh(d x + c) - 300a cosh(d x + c) +--R + +--R 4 3 +--R 600a cosh(d x + c) - 600a cosh(d x + c) +--R + +--R 2 +--R 300a cosh(d x + c) - 60a cosh(d x + c) +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 6 +--R (66a cosh(-------) - 66a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 286a cosh(-------) + 286a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (440a cosh(-------) - 440a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 380a cosh(-------) + 380a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (370a cosh(-------) - 370a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 326a cosh(-------) + 326a)cosh(d x + c) + 116a cosh(-------) +--R 2 2 +--R + +--R - 116a +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 7 6 +--R 45a cosh(d x + c) - 255a cosh(d x + c) +--R + +--R 5 4 +--R 585a cosh(d x + c) - 675a cosh(d x + c) +--R + +--R 3 2 +--R 375a cosh(d x + c) - 45a cosh(d x + c) - 45a cosh(d x + c) +--R + +--R 15a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 7 +--R (81a cosh(-------) - 81a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (- 475a cosh(-------) + 475a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (1029a cosh(-------) - 1029a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (- 1015a cosh(-------) + 1015a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (435a cosh(-------) - 435a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 81a cosh(-------) + 81a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (55a cosh(-------) - 55a)cosh(d x + c) - 29a cosh(-------) + 29a +--R 2 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 8 7 +--R 18a cosh(d x + c) - 114a cosh(d x + c) +--R + +--R 6 5 +--R 294a cosh(d x + c) - 378a cosh(d x + c) +--R + +--R 4 3 +--R 210a cosh(d x + c) + 42a cosh(d x + c) +--R + +--R 2 +--R - 126a cosh(d x + c) + 66a cosh(d x + c) - 12a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 8 +--R (36a cosh(-------) - 36a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 7 +--R (- 240a cosh(-------) + 240a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (604a cosh(-------) - 604a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (- 680a cosh(-------) + 680a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (220a cosh(-------) - 220a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (224a cosh(-------) - 224a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 220a cosh(-------) + 220a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (56a cosh(-------) - 56a)cosh(d x + c) +--R 2 +--R * +--R sinh(d x + c) +--R + +--R 9 8 7 +--R 3a cosh(d x + c) - 21a cosh(d x + c) + 60a cosh(d x + c) +--R + +--R 6 5 4 +--R - 84a cosh(d x + c) + 42a cosh(d x + c) + 42a cosh(d x + c) +--R + +--R 3 2 +--R - 84a cosh(d x + c) + 60a cosh(d x + c) - 21a cosh(d x + c) + 3a +--R * +--R d x + c 2 +--R sinh(-------) +--R 2 +--R + +--R d x + c 2 9 +--R (6a cosh(-------) - 6a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 8 +--R (- 44a cosh(-------) + 44a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 7 +--R (124a cosh(-------) - 124a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 6 +--R (- 156a cosh(-------) + 156a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 5 +--R (40a cosh(-------) - 40a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (124a cosh(-------) - 124a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 156a cosh(-------) + 156a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (76a cosh(-------) - 76a)cosh(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 14a cosh(-------) + 14a)cosh(d x + c) +--R 2 +--R * +--R +----+ +--R \|- 2a +--R / +--R 3 d x + c 2 3 3 +--R (128a cosh(-------) - 128a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (- 384a cosh(-------) + 384a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 d x + c 2 +--R (384a cosh(-------) - 384a )cosh(d x + c) - 128a cosh(-------) +--R 2 2 +--R + +--R 3 +--R 128a +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 4 +--R (768a cosh(-------) - 768a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (- 2944a cosh(-------) + 2944a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (4224a cosh(-------) - 4224a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R (- 2688a cosh(-------) + 2688a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R 640a cosh(-------) - 640a +--R 2 +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 5 +--R (1920a cosh(-------) - 1920a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (- 8960a cosh(-------) + 8960a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (16640a cosh(-------) - 16640a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (- 15360a cosh(-------) + 15360a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R (7040a cosh(-------) - 7040a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R - 1280a cosh(-------) + 1280a +--R 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 6 +--R (2560a cosh(-------) - 2560a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 5 +--R (- 14080a cosh(-------) + 14080a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (32000a cosh(-------) - 32000a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (- 38400a cosh(-------) + 38400a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (25600a cosh(-------) - 25600a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R (- 8960a cosh(-------) + 8960a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R 1280a cosh(-------) - 1280a +--R 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 7 +--R (1920a cosh(-------) - 1920a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 6 +--R (- 12160a cosh(-------) + 12160a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 5 +--R (32640a cosh(-------) - 32640a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (- 48000a cosh(-------) + 48000a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (41600a cosh(-------) - 41600a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (- 21120a cosh(-------) + 21120a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R (5760a cosh(-------) - 5760a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R - 640a cosh(-------) + 640a +--R 2 +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 8 +--R (768a cosh(-------) - 768a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 7 +--R (- 5504a cosh(-------) + 5504a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 6 +--R (17024a cosh(-------) - 17024a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 5 +--R (- 29568a cosh(-------) + 29568a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (31360a cosh(-------) - 31360a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (- 20608a cosh(-------) + 20608a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (8064a cosh(-------) - 8064a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R (- 1664a cosh(-------) + 1664a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R 128a cosh(-------) - 128a +--R 2 +--R * +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 9 +--R (128a cosh(-------) - 128a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 8 +--R (- 1024a cosh(-------) + 1024a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 7 +--R (3584a cosh(-------) - 3584a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 6 +--R (- 7168a cosh(-------) + 7168a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 5 +--R (8960a cosh(-------) - 8960a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (- 7168a cosh(-------) + 7168a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (3584a cosh(-------) - 3584a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (- 1024a cosh(-------) + 1024a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R (128a cosh(-------) - 128a )cosh(d x + c) +--R 2 +--R * +--R +---------------------------------+ +--R +---------------------+ | a +--R \|- a cosh(d x + c) + a |- ------------------------------- +--R \| 2sinh(d x + c) + 2cosh(d x + c) +--R + +--R 3 d x + c 2 3 3 +--R (- 32a cosh(-------) + 32a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (96a cosh(-------) - 96a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 d x + c 2 +--R (- 96a cosh(-------) + 96a )cosh(d x + c) + 32a cosh(-------) +--R 2 2 +--R + +--R 3 +--R - 32a +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 4 +--R (- 192a cosh(-------) + 192a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (704a cosh(-------) - 704a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (- 960a cosh(-------) + 960a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 d x + c 2 +--R (576a cosh(-------) - 576a )cosh(d x + c) - 128a cosh(-------) +--R 2 2 +--R + +--R 3 +--R 128a +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 5 +--R (- 480a cosh(-------) + 480a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (2080a cosh(-------) - 2080a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (- 3520a cosh(-------) + 3520a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (2880a cosh(-------) - 2880a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R (- 1120a cosh(-------) + 1120a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R 160a cosh(-------) - 160a +--R 2 +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 6 +--R (- 640a cosh(-------) + 640a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 5 +--R (3200a cosh(-------) - 3200a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (- 6400a cosh(-------) + 6400a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (6400a cosh(-------) - 6400a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (- 3200a cosh(-------) + 3200a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R (640a cosh(-------) - 640a )cosh(d x + c) +--R 2 +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 7 +--R (- 480a cosh(-------) + 480a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 6 +--R (2720a cosh(-------) - 2720a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 5 +--R (- 6240a cosh(-------) + 6240a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (7200a cosh(-------) - 7200a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (- 4000a cosh(-------) + 4000a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (480a cosh(-------) - 480a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 d x + c 2 +--R (480a cosh(-------) - 480a )cosh(d x + c) - 160a cosh(-------) +--R 2 2 +--R + +--R 3 +--R 160a +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 8 +--R (- 192a cosh(-------) + 192a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 7 +--R (1216a cosh(-------) - 1216a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 6 +--R (- 3136a cosh(-------) + 3136a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 5 +--R (4032a cosh(-------) - 4032a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (- 2240a cosh(-------) + 2240a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (- 448a cosh(-------) + 448a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (1344a cosh(-------) - 1344a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R (- 704a cosh(-------) + 704a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 +--R 128a cosh(-------) - 128a +--R 2 +--R * +--R sinh(d x + c) +--R + +--R 3 d x + c 2 3 9 +--R (- 32a cosh(-------) + 32a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 8 +--R (224a cosh(-------) - 224a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 7 +--R (- 640a cosh(-------) + 640a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 6 +--R (896a cosh(-------) - 896a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 5 +--R (- 448a cosh(-------) + 448a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (- 448a cosh(-------) + 448a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (896a cosh(-------) - 896a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (- 640a cosh(-------) + 640a )cosh(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 d x + c 2 3 +--R (224a cosh(-------) - 224a )cosh(d x + c) - 32a cosh(-------) + 32a +--R 2 2 +--R * +--R +----+ +---------------------+ +--R \|- 2a \|- a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 369 + +--S 370 of 510 +t0173:= (b*cosh(c+d*x))^(1/2) +--R +--R +--R +---------------+ +--R (235) \|b cosh(d x + c) +--R Type: Expression(Integer) +--E 370 + +--S 371 of 510 +r0173:= -2*%i*(b*cosh(c+d*x))^(1/2)*EllipticE(1/2*%i*(c+d*x),2)/d/_ + cosh(c+d*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 371 + +--S 372 of 510 +a0173:= integrate(t0173,x) +--R +--R +--R x +--R ++ +----------------+ +--R (236) | \|b cosh(%I d + c) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 372 + +--S 373 of 510 +--m0173:= a0173-r0173 +--E 373 + +--S 374 of 510 +--d0173:= D(m0173,x) +--E 374 + +--S 375 of 510 +t0174:= (b*cosh(c+d*x))^(3/2) +--R +--R +--R +---------------+ +--R (237) b cosh(d x + c)\|b cosh(d x + c) +--R Type: Expression(Integer) +--E 375 + +--S 376 of 510 +r0174:= 2/3*b^2*(-%i*cosh(c+d*x)^(1/2)*EllipticF(1/2*%i*(c+d*x),2)+_ + cosh(c+d*x)*sinh(c+d*x))/d/(b*cosh(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 376 + +--S 377 of 510 +a0174:= integrate(t0174,x) +--R +--R +--R x +--R ++ +----------------+ +--R (238) | b cosh(%I d + c)\|b cosh(%I d + c) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 377 + +--S 378 of 510 +--m0174:= a0174-r0174 +--E 378 + +--S 379 of 510 +--d0174:= D(m0174,x) +--E 379 + +--S 380 of 510 +t0175:= (b*cosh(c+d*x))^(5/2) +--R +--R +--R 2 2 +---------------+ +--R (239) b cosh(d x + c) \|b cosh(d x + c) +--R Type: Expression(Integer) +--E 380 + +--S 381 of 510 +r0175:= 2/5*b^2*(b*cosh(c+d*x))^(1/2)*(-3*%i*EllipticE(1/2*%i*(c+d*x),2)+_ + cosh(c+d*x)^(3/2)*sinh(c+d*x))/d/cosh(c+d*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 381 + +--S 382 of 510 +a0175:= integrate(t0175,x) +--R +--R +--R x +--R ++ 2 2 +----------------+ +--R (240) | b cosh(%I d + c) \|b cosh(%I d + c) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 382 + +--S 383 of 510 +--m0175:= a0175-r0175 +--E 383 + +--S 384 of 510 +--d0175:= D(m0175,x) +--E 384 + +--S 385 of 510 +t0176:= 1/(b*cosh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (241) ------------------ +--R +---------------+ +--R \|b cosh(d x + c) +--R Type: Expression(Integer) +--E 385 + +--S 386 of 510 +r0176:= -2*%i*cosh(c+d*x)^(1/2)*EllipticF(1/2*%i*(c+d*x),2)/d/_ + (b*cosh(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 386 + +--S 387 of 510 +a0176:= integrate(t0176,x) +--R +--R +--R x +--R ++ 1 +--R (242) | ------------------- d%I +--R ++ +----------------+ +--R \|b cosh(%I d + c) +--R Type: Union(Expression(Integer),...) +--E 387 + +--S 388 of 510 +--m0176:= a0176-r0176 +--E 388 + +--S 389 of 510 +--d0176:= D(m0176,x) +--E 389 + +--S 390 of 510 +t0177:= 1/(b*cosh(c+d*x))^(3/2) +--R +--R +--R 1 +--R (243) --------------------------------- +--R +---------------+ +--R b cosh(d x + c)\|b cosh(d x + c) +--R Type: Expression(Integer) +--E 390 + +--S 391 of 510 +r0177:= 2/b*(%i*cosh(c+d*x)*EllipticE(1/2*%i*(c+d*x),2)+sinh(c+d*x)*_ + cosh(c+d*x)^(1/2))/d/cosh(c+d*x)^(1/2)/(b*cosh(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 391 + +--S 392 of 510 +a0177:= integrate(t0177,x) +--R +--R +--R x +--R ++ 1 +--R (244) | ----------------------------------- d%I +--R ++ +----------------+ +--R b cosh(%I d + c)\|b cosh(%I d + c) +--R Type: Union(Expression(Integer),...) +--E 392 + +--S 393 of 510 +--m0177:= a0177-r0177 +--E 393 + +--S 394 of 510 +--d0177:= D(m0177,x) +--E 394 + +--S 395 of 510 +t0178:= 1/(b*cosh(c+d*x))^(5/2) +--R +--R +--R 1 +--R (245) ---------------------------------- +--R 2 2 +---------------+ +--R b cosh(d x + c) \|b cosh(d x + c) +--R Type: Expression(Integer) +--E 395 + +--S 396 of 510 +r0178:= -2/3/b^2*(%i*cosh(c+d*x)^(3/2)*EllipticF(1/2*%i*(c+d*x),2)-_ + sinh(c+d*x))/d/cosh(c+d*x)/(b*cosh(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 396 + +--S 397 of 510 +a0178:= integrate(t0178,x) +--R +--R +--R x +--R ++ 1 +--R (246) | ------------------------------------ d%I +--R ++ 2 2 +----------------+ +--R b cosh(%I d + c) \|b cosh(%I d + c) +--R Type: Union(Expression(Integer),...) +--E 397 + +--S 398 of 510 +--m0178:= a0178-r0178 +--E 398 + +--S 399 of 510 +--d0178:= D(m0178,x) +--E 399 + +--S 400 of 510 +t0179:= x^2/(a+b*cosh(x)) +--R +--R +--R 2 +--R x +--R (247) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 400 + +--S 401 of 510 +r0179:= (x^2*log(-(a-(a^2-b^2)^(1/2)+b*exp(x))/(-a+(a^2-b^2)^(1/2)))-_ + x^2*log((a+(a^2-b^2)^(1/2)+b*exp(x))/(a+(a^2-b^2)^(1/2)))+_ + 2*x*polylog(2,b*exp(x)/(-a+(a^2-b^2)^(1/2)))-_ + 2*x*polylog(2,-b*exp(x)/(a+(a^2-b^2)^(1/2)))-_ + 2*polylog(3,b*exp(x)/(-a+(a^2-b^2)^(1/2)))+_ + 2*polylog(3,-b*exp(x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 401 + +--S 402 of 510 +a0179:= integrate(t0179,x) +--R +--R +--R x 2 +--R ++ %I +--R (248) | -------------- d%I +--R ++ b cosh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 402 + +--S 403 of 510 +--m0179:= a0179-r0179 +--E 403 + +--S 404 of 510 +--d0179:= D(m0179,x) +--E 404 + +--S 405 of 510 +t0180:= x^3/(a+b*cosh(x)) +--R +--R +--R 3 +--R x +--R (249) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 405 + +--S 406 of 510 +r0180:= (x^3*log(-(a-(a^2-b^2)^(1/2)+b*exp(x))/(-a+(a^2-b^2)^(1/2)))-_ + x^3*log((a+(a^2-b^2)^(1/2)+b*exp(x))/(a+(a^2-b^2)^(1/2)))+_ + 3*x^2*polylog(2,b*exp(x)/(-a+(a^2-b^2)^(1/2)))-_ + 3*x^2*polylog(2,-b*exp(x)/(a+(a^2-b^2)^(1/2)))-_ + 6*x*polylog(3,b*exp(x)/(-a+(a^2-b^2)^(1/2)))+_ + 6*x*polylog(3,-b*exp(x)/(a+(a^2-b^2)^(1/2)))+_ + 6*polylog(4,b*exp(x)/(-a+(a^2-b^2)^(1/2)))-_ + 6*polylog(4,-b*exp(x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 406 + +--S 407 of 510 +a0180:= integrate(t0180,x) +--R +--R +--R x 3 +--R ++ %I +--R (250) | -------------- d%I +--R ++ b cosh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 407 + +--S 408 of 510 +--m0180:= a0180-r0180 +--E 408 + +--S 409 of 510 +--d0180:= D(m0180,x) +--E 409 + +--S 410 of 510 +t0181:= x/(a+b*cosh(x))^2 +--R +--R +--R x +--R (251) ------------------------------ +--R 2 2 2 +--R b cosh(x) + 2a b cosh(x) + a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 510 +r0181:= a*x*log(1+b*exp(x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-_ + a*x*log(1+b*exp(x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+_ + log(a+b*cosh(x))/(a^2-b^2)+a*polylog(2,-b*exp(x)/_ + (a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-a*polylog(2,-b*exp(x)/_ + (a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-b*x*sinh(x)/_ + (a^2-b^2)/(a+b*cosh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 411 + +--S 412 of 510 +a0181:= integrate(t0181,x) +--R +--R +--R x +--R ++ %I +--R (252) | -------------------------------- d%I +--R ++ 2 2 2 +--R b cosh(%I) + 2a b cosh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 412 + +--S 413 of 510 +--m0181:= a0181-r0181 +--E 413 + +--S 414 of 510 +--d0181:= D(m0181,x) +--E 414 + +--S 415 of 510 +t0182:= x*(a+a*cosh(c+d*x))^(1/2) +--R +--R +--R +-------------------+ +--R (253) x\|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 415 + +--S 416 of 510 +r0182:= -2*2^(1/2)*(a*cosh(1/2*c+1/2*d*x)^2)^(1/2)*_ + sech(1/2*c+1/2*d*x)*(2*cosh(1/2*c+1/2*d*x)-_ + d*x*sinh(1/2*c+1/2*d*x))/d^2 +--R +--R +--R (254) +--R +-+ d x + c d x + c +-+ d x + c d x + c +--R (2d x\|2 sech(-------)sinh(-------) - 4\|2 cosh(-------)sech(-------)) +--R 2 2 2 2 +--R * +--R +----------------+ +--R | d x + c 2 +--R |a cosh(-------) +--R \| 2 +--R / +--R 2 +--R d +--R Type: Expression(Integer) +--E 416 + +--S 417 of 510 +a0182:= integrate(t0182,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 417 + +--S 418 of 510 +--m0182:= a0182-r0182 +--E 418 + +--S 419 of 510 +--d0182:= D(m0182,x) +--E 419 + +--S 420 of 510 +t0183:= x^2*(a+a*cosh(c+d*x))^(1/2) +--R +--R +--R 2 +-------------------+ +--R (255) x \|a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 420 + +--S 421 of 510 +r0183:= -2*2^(1/2)*(a*cosh(1/2*c+1/2*d*x)^2)^(1/2)*_ + sech(1/2*c+1/2*d*x)*(4*d*x*cosh(1/2*c+1/2*d*x)-_ + (8+d^2*x^2)*sinh(1/2*c+1/2*d*x))/d^3 +--R +--R +--R (256) +--R 2 2 +-+ d x + c d x + c +--R (2d x + 16)\|2 sech(-------)sinh(-------) +--R 2 2 +--R + +--R +-+ d x + c d x + c +--R - 8d x\|2 cosh(-------)sech(-------) +--R 2 2 +--R * +--R +----------------+ +--R | d x + c 2 +--R |a cosh(-------) +--R \| 2 +--R / +--R 3 +--R d +--R Type: Expression(Integer) +--E 421 + +--S 422 of 510 +a0183:= integrate(t0183,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 422 + +--S 423 of 510 +--m0183:= a0183-r0183 +--E 423 + +--S 424 of 510 +--d0183:= D(m0183,x) +--E 424 + +--S 425 of 510 +t0184:= (a+a*cosh(c+d*x))^(1/2)/x +--R +--R +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R (257) ---------------------- +--R x +--R Type: Expression(Integer) +--E 425 + +--S 426 of 510 +r0184:= 2^(1/2)*(a*cosh(1/2*c+1/2*d*x)^2)^(1/2)*sech(1/2*c+1/2*d*x)*_ + (cosh(1/2*c)*Chi(1/2*d*x)+sinh(1/2*c)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 426 + +--S 427 of 510 +a0184:= integrate(t0184,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 427 + +--S 428 of 510 +--m0184:= a0184-r0184 +--E 428 + +--S 429 of 510 +--d0184:= D(m0184,x) +--E 429 + +--S 430 of 510 +t0185:= (a+a*cosh(c+d*x))^(1/2)/x^2 +--R +--R +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R (258) ---------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 430 + +--S 431 of 510 +r0185:= -1/2*2^(1/2)*(a*cosh(1/2*c+1/2*d*x)^2)^(1/2)*sech(1/2*c+1/2*d*x)*_ + (2*cosh(1/2*c+1/2*d*x)/x-d*Chi(1/2*d*x)*sinh(1/2*c)-d*cosh(1/2*c)*_ + Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 431 + +--S 432 of 510 +a0185:= integrate(t0185,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 432 + +--S 433 of 510 +--m0185:= a0185-r0185 +--E 433 + +--S 434 of 510 +--d0185:= D(m0185,x) +--E 434 + +--S 435 of 510 +t0186:= (a+a*cosh(c+d*x))^(1/2)/x^3 +--R +--R +--R +-------------------+ +--R \|a cosh(d x + c) + a +--R (259) ---------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 435 + +--S 436 of 510 +r0186:= -1/8*2^(1/2)*(a*cosh(1/2*c+1/2*d*x)^2)^(1/2)*sech(1/2*c+1/2*d*x)*_ + (4*cosh(1/2*c+1/2*d*x)/x^2-d^2*cosh(1/2*c)*Chi(1/2*d*x)+_ + 2*d*sinh(1/2*c+1/2*d*x)/x-d^2*sinh(1/2*c)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 436 + +--S 437 of 510 +a0186:= integrate(t0186,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 437 + +--S 438 of 510 +--m0186:= a0186-r0186 +--E 438 + +--S 439 of 510 +--d0186:= D(m0186,x) +--E 439 + +--S 440 of 510 +t0187:= x*(a-a*cosh(c+d*x))^(1/2) +--R +--R +--R +---------------------+ +--R (260) x\|- a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 440 + +--S 441 of 510 +r0187:= 2*2^(1/2)*csch(1/2*c+1/2*d*x)*(d*x*cosh(1/2*c+1/2*d*x)-_ + 2*sinh(1/2*c+1/2*d*x))*(-a*sinh(1/2*c+1/2*d*x)^2)^(1/2)/d^2 +--R +--R +--R (261) +--R +-+ d x + c d x + c +-+ d x + c d x + c +--R (- 4\|2 csch(-------)sinh(-------) + 2d x\|2 cosh(-------)csch(-------)) +--R 2 2 2 2 +--R * +--R +------------------+ +--R | d x + c 2 +--R |- a sinh(-------) +--R \| 2 +--R / +--R 2 +--R d +--R Type: Expression(Integer) +--E 441 + +--S 442 of 510 +a0187:= integrate(t0187,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 442 + +--S 443 of 510 +--m0187:= a0187-r0187 +--E 443 + +--S 444 of 510 +--d0187:= D(m0187,x) +--E 444 + +--S 445 of 510 +t0188:= x^2*(a-a*cosh(c+d*x))^(1/2) +--R +--R +--R 2 +---------------------+ +--R (262) x \|- a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 510 +r0188:= 2*2^(1/2)*csch(1/2*c+1/2*d*x)*(8*cosh(1/2*c+1/2*d*x)+_ + d*x*(d*x*cosh(1/2*c+1/2*d*x)-_ + 4*sinh(1/2*c+1/2*d*x)))*(-a*sinh(1/2*c+1/2*d*x)^2)^(1/2)/d^3 +--R +--R +--R (263) +--R +-+ d x + c d x + c +--R - 8d x\|2 csch(-------)sinh(-------) +--R 2 2 +--R + +--R 2 2 +-+ d x + c d x + c +--R (2d x + 16)\|2 cosh(-------)csch(-------) +--R 2 2 +--R * +--R +------------------+ +--R | d x + c 2 +--R |- a sinh(-------) +--R \| 2 +--R / +--R 3 +--R d +--R Type: Expression(Integer) +--E 446 + +--S 447 of 510 +a0188:= integrate(t0188,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 447 + +--S 448 of 510 +--m0188:= a0188-r0188 +--E 448 + +--S 449 of 510 +--d0188:= D(m0188,x) +--E 449 + +--S 450 of 510 +t0189:= (a-a*cosh(c+d*x))^(1/2)/x +--R +--R +--R +---------------------+ +--R \|- a cosh(d x + c) + a +--R (264) ------------------------ +--R x +--R Type: Expression(Integer) +--E 450 + +--S 451 of 510 +r0189:= 2^(1/2)*csch(1/2*c+1/2*d*x)*(-a*sinh(1/2*c+1/2*d*x)^2)^(1/2)*_ + (Chi(1/2*d*x)*sinh(1/2*c)+cosh(1/2*c)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 451 + +--S 452 of 510 +a0189:= integrate(t0189,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 452 + +--S 453 of 510 +--m0189:= a0189-r0189 +--E 453 + +--S 454 of 510 +--d0189:= D(m0189,x) +--E 454 + +--S 455 of 510 +t0190:= (a-a*cosh(c+d*x))^(1/2)/x^2 +--R +--R +--R +---------------------+ +--R \|- a cosh(d x + c) + a +--R (265) ------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 455 + +--S 456 of 510 +r0190:= 1/2*2^(1/2)*csch(1/2*c+1/2*d*x)*(-a*sinh(1/2*c+1/2*d*x)^2)^(1/2)*_ + (d*cosh(1/2*c)*Chi(1/2*d*x)-2*sinh(1/2*c+_ + 1/2*d*x)/x+d*sinh(1/2*c)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 456 + +--S 457 of 510 +a0190:= integrate(t0190,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 457 + +--S 458 of 510 +--m0190:= a0190-r0190 +--E 458 + +--S 459 of 510 +--d0190:= D(m0190,x) +--E 459 + +--S 460 of 510 +t0191:= (a-a*cosh(c+d*x))^(1/2)/x^3 +--R +--R +--R +---------------------+ +--R \|- a cosh(d x + c) + a +--R (266) ------------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 460 + +--S 461 of 510 +r0191:= -1/8*2^(1/2)*csch(1/2*c+1/2*d*x)*(-a*sinh(1/2*c+1/2*d*x)^2)^(1/2)*_ + (2*d*cosh(1/2*c+1/2*d*x)/x-d^2*Chi(1/2*d*x)*sinh(1/2*c)+_ + 4*sinh(1/2*c+1/2*d*x)/x^2-d^2*cosh(1/2*c)*Shi(1/2*d*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 461 + +--S 462 of 510 +a0191:= integrate(t0191,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 462 + +--S 463 of 510 +--m0191:= a0191-r0191 +--E 463 + +--S 464 of 510 +--d0191:= D(m0191,x) +--E 464 + +--S 465 of 510 +t0192:= 1/(a+b*cosh(x)^2) +--R +--R +--R 1 +--R (267) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 465 + +--S 466 of 510 +r0192:= atanh(a^(1/2)*tanh(x)/(a+b)^(1/2))/a^(1/2)/(a+b)^(1/2) +--R +--R +--R +-+ +--R tanh(x)\|a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R (268) ------------------ +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 510 +a0192:= integrate(t0192,x) +--R +--R +--R (269) +--R [ +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R * +--R +--------+ +--R | 2 +--R \|a b + a +--R + +--R 2 2 2 2 2 +--R (- 4a b - 4a b)sinh(x) + (- 8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 4a b - 4a b)cosh(x) - 4a b - 12a b - 8a +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R / +--R +--------+ +--R | 2 +--R 2\|a b + a +--R , +--R +----------+ +--R 2 2 | 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a)\|- a b - a +--R atan(-------------------------------------------------------------------) +--R 2 +--R 2a b + 2a +--R - -------------------------------------------------------------------------] +--R +----------+ +--R | 2 +--R \|- a b - a +--R Type: Union(List(Expression(Integer)),...) +--E 467 + +--S 468 of 510 +m0192a:= a0192.1-r0192 +--R +--R +--R (270) +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R * +--R +--------+ +--R | 2 +--R \|a b + a +--R + +--R 2 2 2 2 2 +--R (- 4a b - 4a b)sinh(x) + (- 8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 4a b - 4a b)cosh(x) - 4a b - 12a b - 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R +--------+ +-+ +--R | 2 tanh(x)\|a +--R - 2\|a b + a atanh(-----------) +--R +-----+ +--R \|b + a +--R / +--R +--------+ +--R +-+ +-----+ | 2 +--R 2\|a \|b + a \|a b + a +--R Type: Expression(Integer) +--E 468 + +--S 469 of 510 +d0192a:= D(m0192a,x) +--R +--R +--R (271) +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) - 2b)sinh(x) +--R + +--R 3 4 2 +--R (- 4b cosh(x) - 4b cosh(x))sinh(x) - b cosh(x) - 2b cosh(x) - b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) - 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) - 4b cosh(x))sinh(x) + b cosh(x) - 2b cosh(x) + b +--R / +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) + 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (2a b + 4a )cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (- b - a b)sinh(x) + (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 6a b)cosh(x) - 2b - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4b - 4a b)cosh(x) + (- 4b - 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- b - a b)cosh(x) + (- 2b - 6a b - 4a )cosh(x) - b - a b +--R Type: Expression(Integer) +--E 469 + +--S 470 of 510 +m0192b:= a0192.2-r0192 +--R +--R +--R (272) +--R +----------+ +-+ +--R | 2 tanh(x)\|a +--R - \|- a b - a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R - +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R atan +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a) +--R * +--R +----------+ +--R | 2 +--R \|- a b - a +--R / +--R 2 +--R 2a b + 2a +--R / +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- a b - a \|a \|b + a +--R Type: Expression(Integer) +--E 470 + +--S 471 of 510 +d0192b:= D(m0192b,x) +--R +--R +--R (273) +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) - 2b)sinh(x) +--R + +--R 3 4 2 +--R (- 4b cosh(x) - 4b cosh(x))sinh(x) - b cosh(x) - 2b cosh(x) - b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) - 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) - 4b cosh(x))sinh(x) + b cosh(x) - 2b cosh(x) + b +--R / +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) + 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (2a b + 4a )cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (- b - a b)sinh(x) + (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 6a b)cosh(x) - 2b - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4b - 4a b)cosh(x) + (- 4b - 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- b - a b)cosh(x) + (- 2b - 6a b - 4a )cosh(x) - b - a b +--R Type: Expression(Integer) +--E 471 + +--S 472 of 510 +t0193:= 1/(a+b*cosh(x)^2)^2 +--R +--R +--R 1 +--R (274) ------------------------------- +--R 2 4 2 2 +--R b cosh(x) + 2a b cosh(x) + a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 510 +r0193:= 1/2*(2*a+b)*atanh(a^(1/2)*tanh(x)/(a+b)^(1/2))/a^(3/2)/(a+b)^(3/2)-_ + tanh(x)/a/(b+a*sech(x)^2)+1/2*(2*a+b)*tanh(x)/a/(a+b)/(b+a*sech(x)^2) +--R +--R +--R (275) +--R +-+ +--R 2 2 2 tanh(x)\|a +-+ +-----+ +--R ((a b + 2a )sech(x) + b + 2a b)atanh(-----------) - b tanh(x)\|a \|b + a +--R +-----+ +--R \|b + a +--R --------------------------------------------------------------------------- +--R 2 3 2 2 2 +-+ +-----+ +--R ((2a b + 2a )sech(x) + 2a b + 2a b)\|a \|b + a +--R Type: Expression(Integer) +--E 473 + +--S 474 of 510 +a0193:= integrate(t0193,x) +--R +--R +--R (276) +--R [ +--R 2 4 2 3 +--R (b + 2a b)sinh(x) + (4b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b + 12a b)cosh(x) + 2b + 8a b + 8a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b + 8a b)cosh(x) + (4b + 16a b + 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b + 2a b)cosh(x) + (2b + 8a b + 8a )cosh(x) + b + 2a b +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R * +--R +--------+ +--R | 2 +--R \|a b + a +--R + +--R 2 2 2 2 2 +--R (- 4a b - 4a b)sinh(x) + (- 8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 4a b - 4a b)cosh(x) - 4a b - 12a b - 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 2 +--R (4b + 8a)sinh(x) + (8b + 16a)cosh(x)sinh(x) + (4b + 8a)cosh(x) +--R + +--R 4b +--R * +--R +--------+ +--R | 2 +--R \|a b + a +--R / +--R 2 2 4 2 2 3 +--R (4a b + 4a b)sinh(x) + (16a b + 16a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((24a b + 24a b)cosh(x) + 8a b + 24a b + 16a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((16a b + 16a b)cosh(x) + (16a b + 48a b + 32a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 2 +--R (4a b + 4a b)cosh(x) + (8a b + 24a b + 16a )cosh(x) + 4a b + 4a b +--R * +--R +--------+ +--R | 2 +--R \|a b + a +--R , +--R +--R 2 4 2 3 +--R (- b - 2a b)sinh(x) + (- 4b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 12a b)cosh(x) - 2b - 8a b - 8a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4b - 8a b)cosh(x) + (- 4b - 16a b - 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- b - 2a b)cosh(x) + (- 2b - 8a b - 8a )cosh(x) - b - 2a b +--R * +--R atan +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a) +--R * +--R +----------+ +--R | 2 +--R \|- a b - a +--R / +--R 2 +--R 2a b + 2a +--R + +--R 2 2 +--R (2b + 4a)sinh(x) + (4b + 8a)cosh(x)sinh(x) + (2b + 4a)cosh(x) +--R + +--R 2b +--R * +--R +----------+ +--R | 2 +--R \|- a b - a +--R / +--R 2 2 4 2 2 3 +--R (2a b + 2a b)sinh(x) + (8a b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((12a b + 12a b)cosh(x) + 4a b + 12a b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((8a b + 8a b)cosh(x) + (8a b + 24a b + 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 2 +--R (2a b + 2a b)cosh(x) + (4a b + 12a b + 8a )cosh(x) + 2a b + 2a b +--R * +--R +----------+ +--R | 2 +--R \|- a b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 474 + +--S 475 of 510 +m0193a:= a0193.1-r0193 +--R +--R +--R (277) +--R 2 2 2 3 2 4 +--R ((a b + 2a b)sech(x) + b + 2a b )sinh(x) +--R + +--R 2 2 2 3 2 3 +--R ((4a b + 8a b)cosh(x)sech(x) + (4b + 8a b )cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((6a b + 12a b)cosh(x) + 2a b + 8a b + 8a )sech(x) +--R + +--R 3 2 2 3 2 2 +--R (6b + 12a b )cosh(x) + 2b + 8a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 2 2 3 2 +--R ((4a b + 8a b)cosh(x) + (4a b + 16a b + 16a )cosh(x))sech(x) +--R + +--R 3 2 3 3 2 2 +--R (4b + 8a b )cosh(x) + (4b + 16a b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 +--R (a b + 2a b)cosh(x) + (2a b + 8a b + 8a )cosh(x) + a b +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 2 2 3 2 +--R (b + 2a b )cosh(x) + (2b + 8a b + 8a b)cosh(x) + b + 2a b +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R * +--R +--------+ +--R | 2 +--R \|a b + a +--R + +--R 2 2 2 2 2 +--R (- 4a b - 4a b)sinh(x) + (- 8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 4a b - 4a b)cosh(x) - 4a b - 12a b - 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 2 2 3 2 4 +--R ((- 2a b - 4a b)sech(x) - 2b - 4a b )sinh(x) +--R + +--R 2 2 2 3 2 3 +--R ((- 8a b - 16a b)cosh(x)sech(x) + (- 8b - 16a b )cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((- 12a b - 24a b)cosh(x) - 4a b - 16a b - 16a )sech(x) +--R + +--R 3 2 2 3 2 2 +--R (- 12b - 24a b )cosh(x) - 4b - 16a b - 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 8a b - 16a b)cosh(x) + (- 8a b - 32a b - 32a )cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 3 3 2 2 +--R (- 8b - 16a b )cosh(x) + (- 8b - 32a b - 32a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 3 2 +--R (- 2a b - 4a b)cosh(x) + (- 4a b - 16a b - 16a )cosh(x) +--R + +--R 2 2 +--R - 2a b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 2 2 3 +--R (- 2b - 4a b )cosh(x) + (- 4b - 16a b - 16a b)cosh(x) - 2b +--R + +--R 2 +--R - 4a b +--R * +--R +--------+ +-+ +--R | 2 tanh(x)\|a +--R \|a b + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 4 2 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (12b cosh(x) + 4b + 8a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (8b cosh(x) + (8b + 16a b)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 2 2 +--R (4b + 8a b)cosh(x) + 2b +--R * +--R tanh(x) +--R + +--R 2 2 2 2 +--R ((4a b + 8a )sech(x) + 4b + 8a b)sinh(x) +--R + +--R 2 2 2 +--R ((8a b + 16a )cosh(x)sech(x) + (8b + 16a b)cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((4a b + 8a )cosh(x) + 4a b)sech(x) + (4b + 8a b)cosh(x) + 4b +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|a b + a +--R / +--R 2 2 3 2 3 2 2 4 +--R ((4a b + 4a b)sech(x) + 4a b + 4a b )sinh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R ((16a b + 16a b)cosh(x)sech(x) + (16a b + 16a b )cosh(x))sinh(x) +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((24a b + 24a b)cosh(x) + 8a b + 24a b + 16a )sech(x) +--R + +--R 3 2 2 2 3 2 2 3 +--R (24a b + 24a b )cosh(x) + 8a b + 24a b + 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 3 4 2 +--R ((16a b + 16a b)cosh(x) + (16a b + 48a b + 32a )cosh(x))sech(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R (16a b + 16a b )cosh(x) + (16a b + 48a b + 32a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 2 2 3 4 2 2 2 +--R (4a b + 4a b)cosh(x) + (8a b + 24a b + 16a )cosh(x) + 4a b +--R + +--R 3 +--R 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 4 3 2 2 3 2 3 +--R (4a b + 4a b )cosh(x) + (8a b + 24a b + 16a b)cosh(x) + 4a b +--R + +--R 2 2 +--R 4a b +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|a b + a +--R Type: Expression(Integer) +--E 475 + +--S 476 of 510 +d0193a:= D(m0193a,x) +--R +--R +--R (278) +--R 3 2 4 8 +--R (a b sech(x) - b )sinh(x) +--R + +--R 3 2 4 7 +--R (8a b cosh(x)sech(x) - 8b cosh(x))sinh(x) +--R + +--R 3 2 3 2 2 2 4 2 4 +--R (28a b cosh(x) + 4a b + 8a b )sech(x) - 28b cosh(x) - 4b +--R + +--R 3 +--R - 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3 2 2 2 +--R (56a b cosh(x) + (24a b + 48a b )cosh(x))sech(x) +--R + +--R 4 3 4 3 +--R - 56b cosh(x) + (- 24b - 48a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 3 2 2 2 3 2 2 +--R 70a b cosh(x) + (60a b + 120a b )cosh(x) + 6a b + 16a b +--R + +--R 3 +--R 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 4 4 3 2 4 3 2 2 +--R - 70b cosh(x) + (- 60b - 120a b )cosh(x) - 6b - 16a b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 3 2 2 3 +--R 56a b cosh(x) + (80a b + 160a b )cosh(x) +--R + +--R 3 2 2 3 +--R (24a b + 64a b + 64a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 4 5 4 3 3 +--R - 56b cosh(x) + (- 80b - 160a b )cosh(x) +--R + +--R 4 3 2 2 +--R (- 24b - 64a b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 2 2 4 +--R 28a b cosh(x) + (60a b + 120a b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (36a b + 96a b + 96a b)cosh(x) + 4a b + 8a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 6 4 3 4 +--R - 28b cosh(x) + (- 60b - 120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 36b - 96a b - 96a b )cosh(x) - 4b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 2 2 5 +--R 8a b cosh(x) + (24a b + 48a b )cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 +--R (24a b + 64a b + 64a b)cosh(x) + (8a b + 16a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 4 7 4 3 5 +--R - 8b cosh(x) + (- 24b - 48a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 24b - 64a b - 64a b )cosh(x) + (- 8b - 16a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 3 2 2 6 +--R a b cosh(x) + (4a b + 8a b )cosh(x) +--R + +--R 3 2 2 3 4 3 2 2 2 3 +--R (6a b + 16a b + 16a b)cosh(x) + (4a b + 8a b )cosh(x) + a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 8 4 3 6 +--R - b cosh(x) + (- 4b - 8a b )cosh(x) +--R + +--R 4 3 2 2 4 4 3 2 4 +--R (- 6b - 16a b - 16a b )cosh(x) + (- 4b - 8a b )cosh(x) - b +--R * +--R 4 +--R tanh(x) +--R + +--R 3 2 2 4 4 3 2 8 +--R ((- a b - 2a b )sech(x) + (- 3b - 4a b )sech(x) )sinh(x) +--R + +--R 3 2 2 4 +--R (- 8a b - 16a b )cosh(x)sech(x) +--R + +--R 4 3 2 +--R (- 24b - 32a b )cosh(x)sech(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 4 +--R ((- 28a b - 56a b )cosh(x) - 4a b - 16a b - 16a b)sech(x) +--R + +--R 4 3 2 4 3 2 2 2 +--R ((- 84b - 112a b )cosh(x) - 12b - 40a b - 32a b )sech(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 56a b - 112a b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24a b - 96a b - 96a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 3 +--R (- 168b - 224a b )cosh(x) +--R + +--R 4 3 2 2 +--R (- 72b - 240a b - 192a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 70a b - 140a b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 60a b - 240a b - 240a b)cosh(x) - 6a b - 28a b - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 4 +--R (- 210b - 280a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (- 180b - 600a b - 480a b )cosh(x) - 18b - 72a b - 48a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 +--R 32a b + 32a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 56a b - 112a b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80a b - 320a b - 320a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 24a b - 112a b - 64a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 +--R (- 168b - 224a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 240b - 800a b - 640a b )cosh(x) +--R + +--R 4 3 2 2 +--R (- 72b - 288a b - 192a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 +--R (128a b + 128a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (- 28a b - 56a b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60a b - 240a b - 240a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 36a b - 168a b - 96a b)cosh(x) - 4a b - 16a b - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 6 +--R (- 84b - 112a b )cosh(x) +--R + +--R 4 3 2 2 4 +--R (- 180b - 600a b - 480a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (- 108b - 432a b - 288a b )cosh(x) - 12b - 40a b - 32a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 2 +--R (192a b + 192a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (- 8a b - 16a b )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24a b - 96a b - 96a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 24a b - 112a b - 64a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 8a b - 32a b - 32a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 7 +--R (- 24b - 32a b )cosh(x) +--R + +--R 4 3 2 2 5 +--R (- 72b - 240a b - 192a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 72b - 288a b - 192a b )cosh(x) +--R + +--R 4 3 2 2 +--R (- 24b - 80a b - 64a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 3 +--R (128a b + 128a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 3 6 +--R (- a b - 2a b )cosh(x) + (- 4a b - 16a b - 16a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 6a b - 28a b - 16a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 4a b - 16a b - 16a b)cosh(x) - a b - 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (- 3b - 4a b )cosh(x) + (- 12b - 40a b - 32a b )cosh(x) +--R + +--R 4 3 2 2 4 +--R (- 18b - 72a b - 48a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 12b - 40a b - 32a b )cosh(x) - 3b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 4 +--R (32a b + 32a b )cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 2 4 4 3 2 4 8 +--R ((a b + 2a b )sech(x) + (b + 3a b )sech(x) + b )sinh(x) +--R + +--R 3 2 2 4 4 3 2 +--R (8a b + 16a b )cosh(x)sech(x) + (8b + 24a b )cosh(x)sech(x) +--R + +--R 4 +--R 8b cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 4 +--R ((28a b + 56a b )cosh(x) + 4a b + 16a b + 16a b)sech(x) +--R + +--R 4 3 2 4 3 2 2 2 +--R ((28b + 84a b )cosh(x) + 4b + 20a b + 24a b )sech(x) +--R + +--R 4 2 4 3 +--R 28b cosh(x) + 4b + 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((56a b + 112a b )cosh(x) + (24a b + 96a b + 96a b)cosh(x)) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 3 4 3 2 2 +--R ((56b + 168a b )cosh(x) + (24b + 120a b + 144a b )cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 4 3 4 3 +--R 56b cosh(x) + (24b + 48a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 3 2 2 3 2 +--R (70a b + 140a b )cosh(x) + (60a b + 240a b + 240a b)cosh(x) +--R + +--R 3 2 2 3 +--R 6a b - 4a b - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 4 4 3 2 2 2 +--R (70b + 210a b )cosh(x) + (60b + 300a b + 360a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R 6b - 30a b - 64a b - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 4 4 3 2 4 3 2 2 +--R 70b cosh(x) + (60b + 120a b )cosh(x) - 26b - 48a b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 3 2 2 3 3 +--R (56a b + 112a b )cosh(x) + (80a b + 320a b + 320a b)cosh(x) +--R + +--R 3 2 2 3 +--R (24a b - 16a b - 64a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 4 3 2 2 3 +--R (56b + 168a b )cosh(x) + (80b + 400a b + 480a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (24b - 120a b - 256a b - 64a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 4 5 4 3 3 +--R 56b cosh(x) + (80b + 160a b )cosh(x) +--R + +--R 4 3 2 2 +--R (- 104b - 192a b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 3 4 +--R (28a b + 56a b )cosh(x) + (60a b + 240a b + 240a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (36a b - 24a b - 96a b)cosh(x) + 4a b + 16a b + 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 6 4 3 2 2 4 +--R (28b + 84a b )cosh(x) + (60b + 300a b + 360a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (36b - 180a b - 384a b - 96a b)cosh(x) + 4b + 20a b + 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 6 4 3 4 +--R 28b cosh(x) + (60b + 120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 156b - 288a b - 96a b )cosh(x) + 4b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 3 5 +--R (8a b + 16a b )cosh(x) + (24a b + 96a b + 96a b)cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 3 +--R (24a b - 16a b - 64a b)cosh(x) + (8a b + 32a b + 32a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 7 4 3 2 2 5 +--R (8b + 24a b )cosh(x) + (24b + 120a b + 144a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (24b - 120a b - 256a b - 64a b)cosh(x) +--R + +--R 4 3 2 2 +--R (8b + 40a b + 48a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 4 7 4 3 5 +--R 8b cosh(x) + (24b + 48a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 104b - 192a b - 64a b )cosh(x) + (8b + 16a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 3 6 +--R (a b + 2a b )cosh(x) + (4a b + 16a b + 16a b)cosh(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (6a b - 4a b - 16a b)cosh(x) + (4a b + 16a b + 16a b)cosh(x) +--R + +--R 3 2 2 +--R a b + 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (b + 3a b )cosh(x) + (4b + 20a b + 24a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (6b - 30a b - 64a b - 16a b)cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (4b + 20a b + 24a b )cosh(x) + b + 3a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 8 4 3 6 4 3 2 2 4 +--R b cosh(x) + (4b + 8a b )cosh(x) + (- 26b - 48a b - 16a b )cosh(x) +--R + +--R 4 3 2 4 +--R (4b + 8a b )cosh(x) + b +--R / +--R 3 3 4 2 4 2 4 3 3 2 5 2 4 +--R ((2a b + 2a b )sech(x) + (4a b + 4a b )sech(x) + 2a b + 2a b ) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 3 4 2 4 +--R (16a b + 16a b )cosh(x)sech(x) +--R + +--R 2 4 3 3 2 5 2 4 +--R (32a b + 32a b )cosh(x)sech(x) + (16a b + 16a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 3 4 2 2 3 3 4 2 5 4 +--R ((56a b + 56a b )cosh(x) + 8a b + 24a b + 16a b)sech(x) +--R + +--R 2 4 3 3 2 2 4 3 3 4 2 2 +--R ((112a b + 112a b )cosh(x) + 16a b + 48a b + 32a b )sech(x) +--R + +--R 5 2 4 2 5 2 4 3 3 +--R (56a b + 56a b )cosh(x) + 8a b + 24a b + 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 4 2 3 +--R (112a b + 112a b )cosh(x) +--R + +--R 3 3 4 2 5 +--R (48a b + 144a b + 96a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 3 +--R (224a b + 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 +--R (96a b + 288a b + 192a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 3 5 2 4 3 3 +--R (112a b + 112a b )cosh(x) + (48a b + 144a b + 96a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 3 4 2 4 +--R (140a b + 140a b )cosh(x) +--R + +--R 3 3 4 2 5 2 3 3 4 2 +--R (120a b + 360a b + 240a b)cosh(x) + 12a b + 44a b +--R + +--R 5 6 +--R 64a b + 32a +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 4 +--R (280a b + 280a b )cosh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (240a b + 720a b + 480a b )cosh(x) + 24a b + 88a b +--R + +--R 4 2 5 +--R 128a b + 64a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 4 +--R (140a b + 140a b )cosh(x) +--R + +--R 5 2 4 3 3 2 5 2 4 3 3 +--R (120a b + 360a b + 240a b )cosh(x) + 12a b + 44a b + 64a b +--R + +--R 4 2 +--R 32a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 4 2 5 +--R (112a b + 112a b )cosh(x) +--R + +--R 3 3 4 2 5 3 +--R (160a b + 480a b + 320a b)cosh(x) +--R + +--R 3 3 4 2 5 6 +--R (48a b + 176a b + 256a b + 128a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 5 +--R (224a b + 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (320a b + 960a b + 640a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (96a b + 352a b + 512a b + 256a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 5 +--R (112a b + 112a b )cosh(x) +--R + +--R 5 2 4 3 3 3 +--R (160a b + 480a b + 320a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (48a b + 176a b + 256a b + 128a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 6 +--R (56a b + 56a b )cosh(x) +--R + +--R 3 3 4 2 5 4 +--R (120a b + 360a b + 240a b)cosh(x) +--R + +--R 3 3 4 2 5 6 2 3 3 4 2 +--R (72a b + 264a b + 384a b + 192a )cosh(x) + 8a b + 24a b +--R + +--R 5 +--R 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 6 +--R (112a b + 112a b )cosh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (240a b + 720a b + 480a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (144a b + 528a b + 768a b + 384a b)cosh(x) + 16a b +--R + +--R 3 3 4 2 +--R 48a b + 32a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 6 5 2 4 3 3 4 +--R (56a b + 56a b )cosh(x) + (120a b + 360a b + 240a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 2 4 +--R (72a b + 264a b + 384a b + 192a b )cosh(x) + 8a b + 24a b +--R + +--R 3 3 +--R 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 7 +--R (16a b + 16a b )cosh(x) +--R + +--R 3 3 4 2 5 5 +--R (48a b + 144a b + 96a b)cosh(x) +--R + +--R 3 3 4 2 5 6 3 +--R (48a b + 176a b + 256a b + 128a )cosh(x) +--R + +--R 3 3 4 2 5 +--R (16a b + 48a b + 32a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 7 +--R (32a b + 32a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (96a b + 288a b + 192a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (96a b + 352a b + 512a b + 256a b)cosh(x) +--R + +--R 2 4 3 3 4 2 +--R (32a b + 96a b + 64a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 7 5 2 4 3 3 5 +--R (16a b + 16a b )cosh(x) + (48a b + 144a b + 96a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (48a b + 176a b + 256a b + 128a b )cosh(x) +--R + +--R 5 2 4 3 3 +--R (16a b + 48a b + 32a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 4 2 8 3 3 4 2 5 6 +--R (2a b + 2a b )cosh(x) + (8a b + 24a b + 16a b)cosh(x) +--R + +--R 3 3 4 2 5 6 4 +--R (12a b + 44a b + 64a b + 32a )cosh(x) +--R + +--R 3 3 4 2 5 2 3 3 4 2 +--R (8a b + 24a b + 16a b)cosh(x) + 2a b + 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 8 2 4 3 3 4 2 6 +--R (4a b + 4a b )cosh(x) + (16a b + 48a b + 32a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (24a b + 88a b + 128a b + 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (16a b + 48a b + 32a b )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 8 5 2 4 3 3 6 +--R (2a b + 2a b )cosh(x) + (8a b + 24a b + 16a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (12a b + 44a b + 64a b + 32a b )cosh(x) +--R + +--R 5 2 4 3 3 2 5 2 4 +--R (8a b + 24a b + 16a b )cosh(x) + 2a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 3 3 4 2 4 5 2 4 3 3 2 +--R (- 2a b - 4a b - 2a b )sech(x) + (- 4a b - 8a b - 4a b )sech(x) +--R + +--R 6 5 2 4 +--R - 2b - 4a b - 2a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 16a b - 32a b - 16a b )cosh(x)sech(x) +--R + +--R 5 2 4 3 3 2 +--R (- 32a b - 64a b - 32a b )cosh(x)sech(x) +--R + +--R 6 5 2 4 +--R (- 16b - 32a b - 16a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 4 2 +--R (- 56a b - 112a b - 56a b )cosh(x) - 8a b - 32a b - 40a b +--R + +--R 5 +--R - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 2 5 2 4 +--R (- 112a b - 224a b - 112a b )cosh(x) - 16a b - 64a b +--R + +--R 3 3 4 2 +--R - 80a b - 32a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 2 6 5 2 4 3 3 +--R (- 56b - 112a b - 56a b )cosh(x) - 8b - 32a b - 40a b - 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 48a b - 192a b - 240a b - 96a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 3 +--R (- 224a b - 448a b - 224a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 96a b - 384a b - 480a b - 192a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 3 +--R (- 112b - 224a b - 112a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (- 48b - 192a b - 240a b - 96a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 140a b - 280a b - 140a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (- 120a b - 480a b - 600a b - 240a b)cosh(x) - 12a b +--R + +--R 3 3 4 2 5 6 +--R - 56a b - 108a b - 96a b - 32a +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 4 +--R (- 280a b - 560a b - 280a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 240a b - 960a b - 1200a b - 480a b )cosh(x) - 24a b +--R + +--R 2 4 3 3 4 2 5 +--R - 112a b - 216a b - 192a b - 64a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 4 +--R (- 140b - 280a b - 140a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (- 120b - 480a b - 600a b - 240a b )cosh(x) - 12b - 56a b +--R + +--R 2 4 3 3 4 2 +--R - 108a b - 96a b - 32a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 160a b - 640a b - 800a b - 320a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 48a b - 224a b - 432a b - 384a b - 128a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 5 +--R (- 224a b - 448a b - 224a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 320a b - 1280a b - 1600a b - 640a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 96a b - 448a b - 864a b - 768a b - 256a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 5 +--R (- 112b - 224a b - 112a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 160b - 640a b - 800a b - 320a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 48b - 224a b - 432a b - 384a b - 128a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (- 56a b - 112a b - 56a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 120a b - 480a b - 600a b - 240a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 2 4 +--R (- 72a b - 336a b - 648a b - 576a b - 192a )cosh(x) - 8a b +--R + +--R 3 3 4 2 5 +--R - 32a b - 40a b - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 6 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 240a b - 960a b - 1200a b - 480a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 144a b - 672a b - 1296a b - 1152a b - 384a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R - 16a b - 64a b - 80a b - 32a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 6 +--R (- 56b - 112a b - 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- 120b - 480a b - 600a b - 240a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (- 72b - 336a b - 648a b - 576a b - 192a b )cosh(x) - 8b +--R + +--R 5 2 4 3 3 +--R - 32a b - 40a b - 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 16a b - 32a b - 16a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 48a b - 192a b - 240a b - 96a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 48a b - 224a b - 432a b - 384a b - 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 16a b - 64a b - 80a b - 32a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 7 +--R (- 32a b - 64a b - 32a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 96a b - 384a b - 480a b - 192a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (- 96a b - 448a b - 864a b - 768a b - 256a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 32a b - 128a b - 160a b - 64a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 7 +--R (- 16b - 32a b - 16a b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 48b - 192a b - 240a b - 96a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 48b - 224a b - 432a b - 384a b - 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (- 16b - 64a b - 80a b - 32a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 2a b - 4a b - 2a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 8a b - 32a b - 40a b - 16a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 12a b - 56a b - 108a b - 96a b - 32a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 4 2 +--R (- 8a b - 32a b - 40a b - 16a b)cosh(x) - 2a b - 4a b - 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 8 +--R (- 4a b - 8a b - 4a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 16a b - 64a b - 80a b - 32a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 24a b - 112a b - 216a b - 192a b - 64a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 2 4 3 3 +--R (- 16a b - 64a b - 80a b - 32a b )cosh(x) - 4a b - 8a b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 8 +--R (- 2b - 4a b - 2a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 +--R (- 8b - 32a b - 40a b - 16a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 12b - 56a b - 108a b - 96a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 2 4 +--R (- 8b - 32a b - 40a b - 16a b )cosh(x) - 2b - 4a b - 2a b +--R Type: Expression(Integer) +--E 476 + +--S 477 of 510 +m0193b:= a0193.2-r0193 +--R +--R +--R (279) +--R 2 2 2 3 2 4 +--R ((- a b - 2a b)sech(x) - b - 2a b )sinh(x) +--R + +--R 2 2 2 3 2 3 +--R ((- 4a b - 8a b)cosh(x)sech(x) + (- 4b - 8a b )cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6a b - 12a b)cosh(x) - 2a b - 8a b - 8a )sech(x) +--R + +--R 3 2 2 3 2 2 +--R (- 6b - 12a b )cosh(x) - 2b - 8a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 4a b - 8a b)cosh(x) + (- 4a b - 16a b - 16a )cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 3 3 2 2 +--R (- 4b - 8a b )cosh(x) + (- 4b - 16a b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 +--R (- a b - 2a b)cosh(x) + (- 2a b - 8a b - 8a )cosh(x) - a b +--R + +--R 2 +--R - 2a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 2 2 3 2 +--R (- b - 2a b )cosh(x) + (- 2b - 8a b - 8a b)cosh(x) - b - 2a b +--R * +--R +----------+ +-+ +--R | 2 tanh(x)\|a +--R \|- a b - a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 2 2 3 2 4 +--R ((- a b - 2a b)sech(x) - b - 2a b )sinh(x) +--R + +--R 2 2 2 3 2 3 +--R ((- 4a b - 8a b)cosh(x)sech(x) + (- 4b - 8a b )cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((- 6a b - 12a b)cosh(x) - 2a b - 8a b - 8a )sech(x) +--R + +--R 3 2 2 3 2 2 +--R (- 6b - 12a b )cosh(x) - 2b - 8a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 4a b - 8a b)cosh(x) + (- 4a b - 16a b - 16a )cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 3 3 2 2 +--R (- 4b - 8a b )cosh(x) + (- 4b - 16a b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 +--R (- a b - 2a b)cosh(x) + (- 2a b - 8a b - 8a )cosh(x) - a b +--R + +--R 2 +--R - 2a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 2 2 3 2 +--R (- b - 2a b )cosh(x) + (- 2b - 8a b - 8a b)cosh(x) - b - 2a b +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +----------+ +--R 2 2 | 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a)\|- a b - a +--R atan(-------------------------------------------------------------------) +--R 2 +--R 2a b + 2a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 +--R (2b + 4a b)cosh(x) + b +--R * +--R tanh(x) +--R + +--R 2 2 2 2 +--R ((2a b + 4a )sech(x) + 2b + 4a b)sinh(x) +--R + +--R 2 2 2 +--R ((4a b + 8a )cosh(x)sech(x) + (4b + 8a b)cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((2a b + 4a )cosh(x) + 2a b)sech(x) + (2b + 4a b)cosh(x) + 2b +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- a b - a \|a \|b + a +--R / +--R 2 2 3 2 3 2 2 4 +--R ((2a b + 2a b)sech(x) + 2a b + 2a b )sinh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R ((8a b + 8a b)cosh(x)sech(x) + (8a b + 8a b )cosh(x))sinh(x) +--R + +--R 2 2 3 2 2 2 3 4 2 +--R ((12a b + 12a b)cosh(x) + 4a b + 12a b + 8a )sech(x) +--R + +--R 3 2 2 2 3 2 2 3 +--R (12a b + 12a b )cosh(x) + 4a b + 12a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 3 4 2 +--R ((8a b + 8a b)cosh(x) + (8a b + 24a b + 16a )cosh(x))sech(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R (8a b + 8a b )cosh(x) + (8a b + 24a b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 2 2 3 4 2 2 2 +--R (2a b + 2a b)cosh(x) + (4a b + 12a b + 8a )cosh(x) + 2a b +--R + +--R 3 +--R 2a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 4 3 2 2 3 2 3 2 2 +--R (2a b + 2a b )cosh(x) + (4a b + 12a b + 8a b)cosh(x) + 2a b + 2a b +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- a b - a \|a \|b + a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 510 +d0193b:= D(m0193b,x) +--R +--R +--R (280) +--R 3 2 4 8 +--R (a b sech(x) - b )sinh(x) +--R + +--R 3 2 4 7 +--R (8a b cosh(x)sech(x) - 8b cosh(x))sinh(x) +--R + +--R 3 2 3 2 2 2 4 2 4 +--R (28a b cosh(x) + 4a b + 8a b )sech(x) - 28b cosh(x) - 4b +--R + +--R 3 +--R - 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3 2 2 2 +--R (56a b cosh(x) + (24a b + 48a b )cosh(x))sech(x) +--R + +--R 4 3 4 3 +--R - 56b cosh(x) + (- 24b - 48a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 3 2 2 2 3 2 2 +--R 70a b cosh(x) + (60a b + 120a b )cosh(x) + 6a b + 16a b +--R + +--R 3 +--R 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 4 4 3 2 4 3 2 2 +--R - 70b cosh(x) + (- 60b - 120a b )cosh(x) - 6b - 16a b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 3 2 2 3 +--R 56a b cosh(x) + (80a b + 160a b )cosh(x) +--R + +--R 3 2 2 3 +--R (24a b + 64a b + 64a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 4 5 4 3 3 +--R - 56b cosh(x) + (- 80b - 160a b )cosh(x) +--R + +--R 4 3 2 2 +--R (- 24b - 64a b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 2 2 4 +--R 28a b cosh(x) + (60a b + 120a b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (36a b + 96a b + 96a b)cosh(x) + 4a b + 8a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 6 4 3 4 +--R - 28b cosh(x) + (- 60b - 120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 36b - 96a b - 96a b )cosh(x) - 4b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 2 2 5 +--R 8a b cosh(x) + (24a b + 48a b )cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 +--R (24a b + 64a b + 64a b)cosh(x) + (8a b + 16a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 4 7 4 3 5 +--R - 8b cosh(x) + (- 24b - 48a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 24b - 64a b - 64a b )cosh(x) + (- 8b - 16a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 3 2 2 6 +--R a b cosh(x) + (4a b + 8a b )cosh(x) +--R + +--R 3 2 2 3 4 3 2 2 2 3 +--R (6a b + 16a b + 16a b)cosh(x) + (4a b + 8a b )cosh(x) + a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 8 4 3 6 +--R - b cosh(x) + (- 4b - 8a b )cosh(x) +--R + +--R 4 3 2 2 4 4 3 2 4 +--R (- 6b - 16a b - 16a b )cosh(x) + (- 4b - 8a b )cosh(x) - b +--R * +--R 4 +--R tanh(x) +--R + +--R 3 2 2 4 4 3 2 8 +--R ((- a b - 2a b )sech(x) + (- 3b - 4a b )sech(x) )sinh(x) +--R + +--R 3 2 2 4 +--R (- 8a b - 16a b )cosh(x)sech(x) +--R + +--R 4 3 2 +--R (- 24b - 32a b )cosh(x)sech(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 4 +--R ((- 28a b - 56a b )cosh(x) - 4a b - 16a b - 16a b)sech(x) +--R + +--R 4 3 2 4 3 2 2 2 +--R ((- 84b - 112a b )cosh(x) - 12b - 40a b - 32a b )sech(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 56a b - 112a b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24a b - 96a b - 96a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 3 +--R (- 168b - 224a b )cosh(x) +--R + +--R 4 3 2 2 +--R (- 72b - 240a b - 192a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 70a b - 140a b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 60a b - 240a b - 240a b)cosh(x) - 6a b - 28a b - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 4 +--R (- 210b - 280a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (- 180b - 600a b - 480a b )cosh(x) - 18b - 72a b - 48a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 +--R 32a b + 32a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 56a b - 112a b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80a b - 320a b - 320a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 24a b - 112a b - 64a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 +--R (- 168b - 224a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 240b - 800a b - 640a b )cosh(x) +--R + +--R 4 3 2 2 +--R (- 72b - 288a b - 192a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 +--R (128a b + 128a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (- 28a b - 56a b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60a b - 240a b - 240a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 36a b - 168a b - 96a b)cosh(x) - 4a b - 16a b - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 6 +--R (- 84b - 112a b )cosh(x) +--R + +--R 4 3 2 2 4 +--R (- 180b - 600a b - 480a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (- 108b - 432a b - 288a b )cosh(x) - 12b - 40a b - 32a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 2 +--R (192a b + 192a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (- 8a b - 16a b )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24a b - 96a b - 96a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 24a b - 112a b - 64a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 8a b - 32a b - 32a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 7 +--R (- 24b - 32a b )cosh(x) +--R + +--R 4 3 2 2 5 +--R (- 72b - 240a b - 192a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 72b - 288a b - 192a b )cosh(x) +--R + +--R 4 3 2 2 +--R (- 24b - 80a b - 64a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 3 +--R (128a b + 128a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 3 6 +--R (- a b - 2a b )cosh(x) + (- 4a b - 16a b - 16a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 6a b - 28a b - 16a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 4a b - 16a b - 16a b)cosh(x) - a b - 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (- 3b - 4a b )cosh(x) + (- 12b - 40a b - 32a b )cosh(x) +--R + +--R 4 3 2 2 4 +--R (- 18b - 72a b - 48a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 12b - 40a b - 32a b )cosh(x) - 3b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 2 4 +--R (32a b + 32a b )cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 2 4 4 3 2 4 8 +--R ((a b + 2a b )sech(x) + (b + 3a b )sech(x) + b )sinh(x) +--R + +--R 3 2 2 4 4 3 2 +--R (8a b + 16a b )cosh(x)sech(x) + (8b + 24a b )cosh(x)sech(x) +--R + +--R 4 +--R 8b cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 4 +--R ((28a b + 56a b )cosh(x) + 4a b + 16a b + 16a b)sech(x) +--R + +--R 4 3 2 4 3 2 2 2 +--R ((28b + 84a b )cosh(x) + 4b + 20a b + 24a b )sech(x) +--R + +--R 4 2 4 3 +--R 28b cosh(x) + 4b + 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((56a b + 112a b )cosh(x) + (24a b + 96a b + 96a b)cosh(x)) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 3 4 3 2 2 +--R ((56b + 168a b )cosh(x) + (24b + 120a b + 144a b )cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 4 3 4 3 +--R 56b cosh(x) + (24b + 48a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 3 2 2 3 2 +--R (70a b + 140a b )cosh(x) + (60a b + 240a b + 240a b)cosh(x) +--R + +--R 3 2 2 3 +--R 6a b - 4a b - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 4 4 3 2 2 2 +--R (70b + 210a b )cosh(x) + (60b + 300a b + 360a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R 6b - 30a b - 64a b - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 4 4 3 2 4 3 2 2 +--R 70b cosh(x) + (60b + 120a b )cosh(x) - 26b - 48a b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 3 2 2 3 3 +--R (56a b + 112a b )cosh(x) + (80a b + 320a b + 320a b)cosh(x) +--R + +--R 3 2 2 3 +--R (24a b - 16a b - 64a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 4 3 2 2 3 +--R (56b + 168a b )cosh(x) + (80b + 400a b + 480a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (24b - 120a b - 256a b - 64a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 4 5 4 3 3 +--R 56b cosh(x) + (80b + 160a b )cosh(x) +--R + +--R 4 3 2 2 +--R (- 104b - 192a b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 3 4 +--R (28a b + 56a b )cosh(x) + (60a b + 240a b + 240a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (36a b - 24a b - 96a b)cosh(x) + 4a b + 16a b + 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 6 4 3 2 2 4 +--R (28b + 84a b )cosh(x) + (60b + 300a b + 360a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (36b - 180a b - 384a b - 96a b)cosh(x) + 4b + 20a b + 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 6 4 3 4 +--R 28b cosh(x) + (60b + 120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 156b - 288a b - 96a b )cosh(x) + 4b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 3 5 +--R (8a b + 16a b )cosh(x) + (24a b + 96a b + 96a b)cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 3 +--R (24a b - 16a b - 64a b)cosh(x) + (8a b + 32a b + 32a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 7 4 3 2 2 5 +--R (8b + 24a b )cosh(x) + (24b + 120a b + 144a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (24b - 120a b - 256a b - 64a b)cosh(x) +--R + +--R 4 3 2 2 +--R (8b + 40a b + 48a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 4 7 4 3 5 +--R 8b cosh(x) + (24b + 48a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 104b - 192a b - 64a b )cosh(x) + (8b + 16a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 3 6 +--R (a b + 2a b )cosh(x) + (4a b + 16a b + 16a b)cosh(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (6a b - 4a b - 16a b)cosh(x) + (4a b + 16a b + 16a b)cosh(x) +--R + +--R 3 2 2 +--R a b + 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (b + 3a b )cosh(x) + (4b + 20a b + 24a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (6b - 30a b - 64a b - 16a b)cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (4b + 20a b + 24a b )cosh(x) + b + 3a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 8 4 3 6 4 3 2 2 4 +--R b cosh(x) + (4b + 8a b )cosh(x) + (- 26b - 48a b - 16a b )cosh(x) +--R + +--R 4 3 2 4 +--R (4b + 8a b )cosh(x) + b +--R / +--R 3 3 4 2 4 2 4 3 3 2 5 2 4 +--R ((2a b + 2a b )sech(x) + (4a b + 4a b )sech(x) + 2a b + 2a b ) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 3 4 2 4 +--R (16a b + 16a b )cosh(x)sech(x) +--R + +--R 2 4 3 3 2 5 2 4 +--R (32a b + 32a b )cosh(x)sech(x) + (16a b + 16a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 3 4 2 2 3 3 4 2 5 4 +--R ((56a b + 56a b )cosh(x) + 8a b + 24a b + 16a b)sech(x) +--R + +--R 2 4 3 3 2 2 4 3 3 4 2 2 +--R ((112a b + 112a b )cosh(x) + 16a b + 48a b + 32a b )sech(x) +--R + +--R 5 2 4 2 5 2 4 3 3 +--R (56a b + 56a b )cosh(x) + 8a b + 24a b + 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 4 2 3 +--R (112a b + 112a b )cosh(x) +--R + +--R 3 3 4 2 5 +--R (48a b + 144a b + 96a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 3 +--R (224a b + 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 +--R (96a b + 288a b + 192a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 3 5 2 4 3 3 +--R (112a b + 112a b )cosh(x) + (48a b + 144a b + 96a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 3 4 2 4 +--R (140a b + 140a b )cosh(x) +--R + +--R 3 3 4 2 5 2 3 3 4 2 +--R (120a b + 360a b + 240a b)cosh(x) + 12a b + 44a b +--R + +--R 5 6 +--R 64a b + 32a +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 4 +--R (280a b + 280a b )cosh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (240a b + 720a b + 480a b )cosh(x) + 24a b + 88a b +--R + +--R 4 2 5 +--R 128a b + 64a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 4 +--R (140a b + 140a b )cosh(x) +--R + +--R 5 2 4 3 3 2 5 2 4 3 3 +--R (120a b + 360a b + 240a b )cosh(x) + 12a b + 44a b + 64a b +--R + +--R 4 2 +--R 32a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 4 2 5 +--R (112a b + 112a b )cosh(x) +--R + +--R 3 3 4 2 5 3 +--R (160a b + 480a b + 320a b)cosh(x) +--R + +--R 3 3 4 2 5 6 +--R (48a b + 176a b + 256a b + 128a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 5 +--R (224a b + 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (320a b + 960a b + 640a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (96a b + 352a b + 512a b + 256a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 5 +--R (112a b + 112a b )cosh(x) +--R + +--R 5 2 4 3 3 3 +--R (160a b + 480a b + 320a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (48a b + 176a b + 256a b + 128a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 6 +--R (56a b + 56a b )cosh(x) +--R + +--R 3 3 4 2 5 4 +--R (120a b + 360a b + 240a b)cosh(x) +--R + +--R 3 3 4 2 5 6 2 3 3 4 2 +--R (72a b + 264a b + 384a b + 192a )cosh(x) + 8a b + 24a b +--R + +--R 5 +--R 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 6 +--R (112a b + 112a b )cosh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (240a b + 720a b + 480a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (144a b + 528a b + 768a b + 384a b)cosh(x) + 16a b +--R + +--R 3 3 4 2 +--R 48a b + 32a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 6 5 2 4 3 3 4 +--R (56a b + 56a b )cosh(x) + (120a b + 360a b + 240a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 2 4 +--R (72a b + 264a b + 384a b + 192a b )cosh(x) + 8a b + 24a b +--R + +--R 3 3 +--R 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 7 +--R (16a b + 16a b )cosh(x) +--R + +--R 3 3 4 2 5 5 +--R (48a b + 144a b + 96a b)cosh(x) +--R + +--R 3 3 4 2 5 6 3 +--R (48a b + 176a b + 256a b + 128a )cosh(x) +--R + +--R 3 3 4 2 5 +--R (16a b + 48a b + 32a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 7 +--R (32a b + 32a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (96a b + 288a b + 192a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (96a b + 352a b + 512a b + 256a b)cosh(x) +--R + +--R 2 4 3 3 4 2 +--R (32a b + 96a b + 64a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 7 5 2 4 3 3 5 +--R (16a b + 16a b )cosh(x) + (48a b + 144a b + 96a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (48a b + 176a b + 256a b + 128a b )cosh(x) +--R + +--R 5 2 4 3 3 +--R (16a b + 48a b + 32a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 4 2 8 3 3 4 2 5 6 +--R (2a b + 2a b )cosh(x) + (8a b + 24a b + 16a b)cosh(x) +--R + +--R 3 3 4 2 5 6 4 +--R (12a b + 44a b + 64a b + 32a )cosh(x) +--R + +--R 3 3 4 2 5 2 3 3 4 2 +--R (8a b + 24a b + 16a b)cosh(x) + 2a b + 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 4 3 3 8 2 4 3 3 4 2 6 +--R (4a b + 4a b )cosh(x) + (16a b + 48a b + 32a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (24a b + 88a b + 128a b + 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (16a b + 48a b + 32a b )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 4 8 5 2 4 3 3 6 +--R (2a b + 2a b )cosh(x) + (8a b + 24a b + 16a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (12a b + 44a b + 64a b + 32a b )cosh(x) +--R + +--R 5 2 4 3 3 2 5 2 4 +--R (8a b + 24a b + 16a b )cosh(x) + 2a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 3 3 4 2 4 5 2 4 3 3 2 +--R (- 2a b - 4a b - 2a b )sech(x) + (- 4a b - 8a b - 4a b )sech(x) +--R + +--R 6 5 2 4 +--R - 2b - 4a b - 2a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 16a b - 32a b - 16a b )cosh(x)sech(x) +--R + +--R 5 2 4 3 3 2 +--R (- 32a b - 64a b - 32a b )cosh(x)sech(x) +--R + +--R 6 5 2 4 +--R (- 16b - 32a b - 16a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 4 2 +--R (- 56a b - 112a b - 56a b )cosh(x) - 8a b - 32a b - 40a b +--R + +--R 5 +--R - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 2 5 2 4 +--R (- 112a b - 224a b - 112a b )cosh(x) - 16a b - 64a b +--R + +--R 3 3 4 2 +--R - 80a b - 32a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 2 6 5 2 4 3 3 +--R (- 56b - 112a b - 56a b )cosh(x) - 8b - 32a b - 40a b - 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 48a b - 192a b - 240a b - 96a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 3 +--R (- 224a b - 448a b - 224a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 96a b - 384a b - 480a b - 192a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 3 +--R (- 112b - 224a b - 112a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (- 48b - 192a b - 240a b - 96a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 140a b - 280a b - 140a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (- 120a b - 480a b - 600a b - 240a b)cosh(x) - 12a b +--R + +--R 3 3 4 2 5 6 +--R - 56a b - 108a b - 96a b - 32a +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 4 +--R (- 280a b - 560a b - 280a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 240a b - 960a b - 1200a b - 480a b )cosh(x) - 24a b +--R + +--R 2 4 3 3 4 2 5 +--R - 112a b - 216a b - 192a b - 64a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 4 +--R (- 140b - 280a b - 140a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (- 120b - 480a b - 600a b - 240a b )cosh(x) - 12b - 56a b +--R + +--R 2 4 3 3 4 2 +--R - 108a b - 96a b - 32a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 160a b - 640a b - 800a b - 320a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 48a b - 224a b - 432a b - 384a b - 128a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 5 +--R (- 224a b - 448a b - 224a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 320a b - 1280a b - 1600a b - 640a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 96a b - 448a b - 864a b - 768a b - 256a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 5 +--R (- 112b - 224a b - 112a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 160b - 640a b - 800a b - 320a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 48b - 224a b - 432a b - 384a b - 128a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (- 56a b - 112a b - 56a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 120a b - 480a b - 600a b - 240a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 2 4 +--R (- 72a b - 336a b - 648a b - 576a b - 192a )cosh(x) - 8a b +--R + +--R 3 3 4 2 5 +--R - 32a b - 40a b - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 6 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 240a b - 960a b - 1200a b - 480a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 144a b - 672a b - 1296a b - 1152a b - 384a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R - 16a b - 64a b - 80a b - 32a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 6 +--R (- 56b - 112a b - 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- 120b - 480a b - 600a b - 240a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (- 72b - 336a b - 648a b - 576a b - 192a b )cosh(x) - 8b +--R + +--R 5 2 4 3 3 +--R - 32a b - 40a b - 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 16a b - 32a b - 16a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 48a b - 192a b - 240a b - 96a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 48a b - 224a b - 432a b - 384a b - 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 16a b - 64a b - 80a b - 32a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 7 +--R (- 32a b - 64a b - 32a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 96a b - 384a b - 480a b - 192a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (- 96a b - 448a b - 864a b - 768a b - 256a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 32a b - 128a b - 160a b - 64a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 7 +--R (- 16b - 32a b - 16a b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 48b - 192a b - 240a b - 96a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 48b - 224a b - 432a b - 384a b - 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (- 16b - 64a b - 80a b - 32a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 2a b - 4a b - 2a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 8a b - 32a b - 40a b - 16a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 12a b - 56a b - 108a b - 96a b - 32a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 4 2 +--R (- 8a b - 32a b - 40a b - 16a b)cosh(x) - 2a b - 4a b - 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 8 +--R (- 4a b - 8a b - 4a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 16a b - 64a b - 80a b - 32a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 24a b - 112a b - 216a b - 192a b - 64a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 2 4 3 3 +--R (- 16a b - 64a b - 80a b - 32a b )cosh(x) - 4a b - 8a b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 8 +--R (- 2b - 4a b - 2a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 +--R (- 8b - 32a b - 40a b - 16a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 12b - 56a b - 108a b - 96a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 2 4 +--R (- 8b - 32a b - 40a b - 16a b )cosh(x) - 2b - 4a b - 2a b +--R Type: Expression(Integer) +--E 478 + +--S 479 of 510 +t0194:= 1/(a+b*cosh(x)^2)^3 +--R +--R +--R 1 +--R (281) ----------------------------------------------- +--R 3 6 2 4 2 2 3 +--R b cosh(x) + 3a b cosh(x) + 3a b cosh(x) + a +--R Type: Expression(Integer) +--E 479 + +--S 480 of 510 +r0194:= 1/8*(8*a^2+8*a*b+3*b^2)*atanh(a^(1/2)*tanh(x)/(a+b)^(1/2))/_ + a^(5/2)/(a+b)^(5/2)-1/3*(5*a+3*b)*tanh(x)/a^2/(b+a*sech(x)^2)^2+_ + 1/12*(8*a^2+8*a*b+3*b^2)*tanh(x)/a^2/(a+b)/(b+a*sech(x)^2)^2+_ + 1/8*(8*a^2+8*a*b+3*b^2)*tanh(x)/a^2/(a+b)^2/(b+a*sech(x)^2)+_ + tanh(x)^3/a/(b+a*sech(x)^2)^2 +--R +--R +--R (282) +--R 2 2 3 4 4 3 2 2 3 2 4 +--R (3a b + 8a b + 8a )sech(x) + (6a b + 16a b + 16a b)sech(x) + 3b +--R + +--R 3 2 2 +--R 8a b + 8a b +--R * +--R +-+ +--R tanh(x)\|a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 2 3 3 +--R (8a b + 16a b + 8a )tanh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R ((3a b + 8a b + 8a )sech(x) - 3b - 14a b - 16a b - 8a )tanh(x) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 4 2 5 6 4 3 3 4 2 5 2 +--R (8a b + 16a b + 8a )sech(x) + (16a b + 32a b + 16a b)sech(x) +--R + +--R 2 4 3 3 4 2 +--R 8a b + 16a b + 8a b +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression(Integer) +--E 480 + +--S 481 of 510 +a0194:= integrate(t0194,x) +--R +--R +--R (283) +--R [ +--R 4 3 2 2 8 +--R (3b + 8a b + 8a b )sinh(x) +--R + +--R 4 3 2 2 7 +--R (24b + 64a b + 64a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (84b + 224a b + 224a b )cosh(x) + 12b + 56a b + 96a b +--R + +--R 3 +--R 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 +--R (168b + 448a b + 448a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (72b + 336a b + 576a b + 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 4 +--R (210b + 560a b + 560a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (180b + 840a b + 1440a b + 960a b)cosh(x) + 18b + 96a b +--R + +--R 2 2 3 4 +--R 224a b + 256a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 5 +--R (168b + 448a b + 448a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (240b + 1120a b + 1920a b + 1280a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (72b + 384a b + 896a b + 1024a b + 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 6 +--R (84b + 224a b + 224a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (180b + 840a b + 1440a b + 960a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (108b + 576a b + 1344a b + 1536a b + 768a )cosh(x) + 12b +--R + +--R 3 2 2 3 +--R 56a b + 96a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 7 +--R (24b + 64a b + 64a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (72b + 336a b + 576a b + 384a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (72b + 384a b + 896a b + 1024a b + 512a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (24b + 112a b + 192a b + 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 8 +--R (3b + 8a b + 8a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (12b + 56a b + 96a b + 64a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (18b + 96a b + 224a b + 256a b + 128a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (12b + 56a b + 96a b + 64a b)cosh(x) + 3b + 8a b + 8a b +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R * +--R +--------+ +--R | 2 +--R \|a b + a +--R + +--R 2 2 2 2 2 +--R (- 4a b - 4a b)sinh(x) + (- 8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 4a b - 4a b)cosh(x) - 4a b - 12a b - 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 3 2 2 6 +--R (12b + 32a b + 32a b)sinh(x) +--R + +--R 3 2 2 5 +--R (72b + 192a b + 192a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (180b + 480a b + 480a b)cosh(x) + 36b + 168a b + 288a b +--R + +--R 3 +--R 192a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (240b + 640a b + 640a b)cosh(x) +--R + +--R 3 2 2 3 +--R (144b + 672a b + 1152a b + 768a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (180b + 480a b + 480a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (216b + 1008a b + 1728a b + 1152a )cosh(x) + 36b + 160a b +--R + +--R 2 +--R 160a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (72b + 192a b + 192a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (144b + 672a b + 1152a b + 768a )cosh(x) +--R + +--R 3 2 2 +--R (72b + 320a b + 320a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 +--R (12b + 32a b + 32a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (36b + 168a b + 288a b + 192a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (36b + 160a b + 160a b)cosh(x) + 12b + 24a b +--R * +--R +--------+ +--R | 2 +--R \|a b + a +--R / +--R 2 4 3 3 4 2 8 +--R (16a b + 32a b + 16a b )sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (128a b + 256a b + 128a b )cosh(x)sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (448a b + 896a b + 448a b )cosh(x) + 64a b + 256a b +--R + +--R 4 2 5 +--R 320a b + 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (896a b + 1792a b + 896a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (384a b + 1536a b + 1920a b + 768a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (1120a b + 2240a b + 1120a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (960a b + 3840a b + 4800a b + 1920a b)cosh(x) + 96a b +--R + +--R 3 3 4 2 5 6 +--R 448a b + 864a b + 768a b + 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (896a b + 1792a b + 896a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (1280a b + 5120a b + 6400a b + 2560a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (384a b + 1792a b + 3456a b + 3072a b + 1024a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (448a b + 896a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (960a b + 3840a b + 4800a b + 1920a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (576a b + 2688a b + 5184a b + 4608a b + 1536a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R 64a b + 256a b + 320a b + 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (128a b + 256a b + 128a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (384a b + 1536a b + 1920a b + 768a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (384a b + 1792a b + 3456a b + 3072a b + 1024a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (128a b + 512a b + 640a b + 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (16a b + 32a b + 16a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (64a b + 256a b + 320a b + 128a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (96a b + 448a b + 864a b + 768a b + 256a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 +--R (64a b + 256a b + 320a b + 128a b)cosh(x) + 16a b + 32a b +--R + +--R 4 2 +--R 16a b +--R * +--R +--------+ +--R | 2 +--R \|a b + a +--R , +--R +--R 4 3 2 2 8 +--R (- 3b - 8a b - 8a b )sinh(x) +--R + +--R 4 3 2 2 7 +--R (- 24b - 64a b - 64a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (- 84b - 224a b - 224a b )cosh(x) - 12b - 56a b - 96a b +--R + +--R 3 +--R - 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 +--R (- 168b - 448a b - 448a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 72b - 336a b - 576a b - 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 4 +--R (- 210b - 560a b - 560a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 180b - 840a b - 1440a b - 960a b)cosh(x) - 18b - 96a b +--R + +--R 2 2 3 4 +--R - 224a b - 256a b - 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 5 +--R (- 168b - 448a b - 448a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 240b - 1120a b - 1920a b - 1280a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 72b - 384a b - 896a b - 1024a b - 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 6 +--R (- 84b - 224a b - 224a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 180b - 840a b - 1440a b - 960a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (- 108b - 576a b - 1344a b - 1536a b - 768a )cosh(x) - 12b +--R + +--R 3 2 2 3 +--R - 56a b - 96a b - 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 7 +--R (- 24b - 64a b - 64a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 72b - 336a b - 576a b - 384a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 72b - 384a b - 896a b - 1024a b - 512a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 24b - 112a b - 192a b - 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 8 +--R (- 3b - 8a b - 8a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 12b - 56a b - 96a b - 64a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 18b - 96a b - 224a b - 256a b - 128a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (- 12b - 56a b - 96a b - 64a b)cosh(x) - 3b - 8a b - 8a b +--R * +--R atan +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a) +--R * +--R +----------+ +--R | 2 +--R \|- a b - a +--R / +--R 2 +--R 2a b + 2a +--R + +--R 3 2 2 6 +--R (6b + 16a b + 16a b)sinh(x) +--R + +--R 3 2 2 5 +--R (36b + 96a b + 96a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (90b + 240a b + 240a b)cosh(x) + 18b + 84a b + 144a b +--R + +--R 3 +--R 96a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (120b + 320a b + 320a b)cosh(x) +--R + +--R 3 2 2 3 +--R (72b + 336a b + 576a b + 384a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (90b + 240a b + 240a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (108b + 504a b + 864a b + 576a )cosh(x) + 18b + 80a b +--R + +--R 2 +--R 80a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (36b + 96a b + 96a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (72b + 336a b + 576a b + 384a )cosh(x) +--R + +--R 3 2 2 +--R (36b + 160a b + 160a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 +--R (6b + 16a b + 16a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (18b + 84a b + 144a b + 96a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (18b + 80a b + 80a b)cosh(x) + 6b + 12a b +--R * +--R +----------+ +--R | 2 +--R \|- a b - a +--R / +--R 2 4 3 3 4 2 8 +--R (8a b + 16a b + 8a b )sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (64a b + 128a b + 64a b )cosh(x)sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (224a b + 448a b + 224a b )cosh(x) + 32a b + 128a b +--R + +--R 4 2 5 +--R 160a b + 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (448a b + 896a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (192a b + 768a b + 960a b + 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (560a b + 1120a b + 560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (480a b + 1920a b + 2400a b + 960a b)cosh(x) + 48a b +--R + +--R 3 3 4 2 5 6 +--R 224a b + 432a b + 384a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (448a b + 896a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (640a b + 2560a b + 3200a b + 1280a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (192a b + 896a b + 1728a b + 1536a b + 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (224a b + 448a b + 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (480a b + 1920a b + 2400a b + 960a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (288a b + 1344a b + 2592a b + 2304a b + 768a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R 32a b + 128a b + 160a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (64a b + 128a b + 64a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (192a b + 768a b + 960a b + 384a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (192a b + 896a b + 1728a b + 1536a b + 512a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (64a b + 256a b + 320a b + 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (8a b + 16a b + 8a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (32a b + 128a b + 160a b + 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (48a b + 224a b + 432a b + 384a b + 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 4 2 +--R (32a b + 128a b + 160a b + 64a b)cosh(x) + 8a b + 16a b + 8a b +--R * +--R +----------+ +--R | 2 +--R \|- a b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 481 + +--S 482 of 510 +m0194a:= a0194.1-r0194 +--R +--R +--R (284) +--R 2 4 3 3 4 2 4 +--R (3a b + 8a b + 8a b )sech(x) +--R + +--R 5 2 4 3 3 2 6 5 2 4 +--R (6a b + 16a b + 16a b )sech(x) + 3b + 8a b + 8a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (24a b + 64a b + 64a b )cosh(x)sech(x) +--R + +--R 5 2 4 3 3 2 +--R (48a b + 128a b + 128a b )cosh(x)sech(x) +--R + +--R 6 5 2 4 +--R (24b + 64a b + 64a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (84a b + 224a b + 224a b )cosh(x) + 12a b + 56a b +--R + +--R 4 2 5 +--R 96a b + 64a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 2 5 2 4 +--R (168a b + 448a b + 448a b )cosh(x) + 24a b + 112a b +--R + +--R 3 3 4 2 +--R 192a b + 128a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 2 6 5 2 4 +--R (84b + 224a b + 224a b )cosh(x) + 12b + 56a b + 96a b +--R + +--R 3 3 +--R 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (168a b + 448a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (72a b + 336a b + 576a b + 384a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 3 +--R (336a b + 896a b + 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (144a b + 672a b + 1152a b + 768a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 3 +--R (168b + 448a b + 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (72b + 336a b + 576a b + 384a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (210a b + 560a b + 560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (180a b + 840a b + 1440a b + 960a b)cosh(x) + 18a b +--R + +--R 3 3 4 2 5 6 +--R 96a b + 224a b + 256a b + 128a +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 4 +--R (420a b + 1120a b + 1120a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (360a b + 1680a b + 2880a b + 1920a b )cosh(x) + 36a b +--R + +--R 2 4 3 3 4 2 5 +--R 192a b + 448a b + 512a b + 256a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 4 +--R (210b + 560a b + 560a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (180b + 840a b + 1440a b + 960a b )cosh(x) + 18b + 96a b +--R + +--R 2 4 3 3 4 2 +--R 224a b + 256a b + 128a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (168a b + 448a b + 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (240a b + 1120a b + 1920a b + 1280a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (72a b + 384a b + 896a b + 1024a b + 512a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 5 +--R (336a b + 896a b + 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (480a b + 2240a b + 3840a b + 2560a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (144a b + 768a b + 1792a b + 2048a b + 1024a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 5 +--R (168b + 448a b + 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (240b + 1120a b + 1920a b + 1280a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (72b + 384a b + 896a b + 1024a b + 512a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (84a b + 224a b + 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (180a b + 840a b + 1440a b + 960a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (108a b + 576a b + 1344a b + 1536a b + 768a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R 12a b + 56a b + 96a b + 64a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 6 +--R (168a b + 448a b + 448a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (360a b + 1680a b + 2880a b + 1920a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (216a b + 1152a b + 2688a b + 3072a b + 1536a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R 24a b + 112a b + 192a b + 128a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 6 +--R (84b + 224a b + 224a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (180b + 840a b + 1440a b + 960a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (108b + 576a b + 1344a b + 1536a b + 768a b )cosh(x) + 12b +--R + +--R 5 2 4 3 3 +--R 56a b + 96a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (24a b + 64a b + 64a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (72a b + 336a b + 576a b + 384a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (72a b + 384a b + 896a b + 1024a b + 512a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (24a b + 112a b + 192a b + 128a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 7 +--R (48a b + 128a b + 128a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (144a b + 672a b + 1152a b + 768a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (144a b + 768a b + 1792a b + 2048a b + 1024a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (48a b + 224a b + 384a b + 256a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 7 +--R (24b + 64a b + 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (72b + 336a b + 576a b + 384a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (72b + 384a b + 896a b + 1024a b + 512a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (24b + 112a b + 192a b + 128a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (3a b + 8a b + 8a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (12a b + 56a b + 96a b + 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (18a b + 96a b + 224a b + 256a b + 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 4 2 +--R (12a b + 56a b + 96a b + 64a b)cosh(x) + 3a b + 8a b + 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 8 +--R (6a b + 16a b + 16a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (24a b + 112a b + 192a b + 128a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (36a b + 192a b + 448a b + 512a b + 256a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 2 4 +--R (24a b + 112a b + 192a b + 128a b )cosh(x) + 6a b + 16a b +--R + +--R 3 3 +--R 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 8 +--R (3b + 8a b + 8a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 +--R (12b + 56a b + 96a b + 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (18b + 96a b + 224a b + 256a b + 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 2 4 +--R (12b + 56a b + 96a b + 64a b )cosh(x) + 3b + 8a b + 8a b +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R * +--R +--------+ +--R | 2 +--R \|a b + a +--R + +--R 2 2 2 2 2 +--R (- 4a b - 4a b)sinh(x) + (- 8a b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 4a b - 4a b)cosh(x) - 4a b - 12a b - 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 4 3 3 4 2 4 +--R (- 6a b - 16a b - 16a b )sech(x) +--R + +--R 5 2 4 3 3 2 6 5 2 4 +--R (- 12a b - 32a b - 32a b )sech(x) - 6b - 16a b - 16a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 48a b - 128a b - 128a b )cosh(x)sech(x) +--R + +--R 5 2 4 3 3 2 +--R (- 96a b - 256a b - 256a b )cosh(x)sech(x) +--R + +--R 6 5 2 4 +--R (- 48b - 128a b - 128a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (- 168a b - 448a b - 448a b )cosh(x) - 24a b - 112a b +--R + +--R 4 2 5 +--R - 192a b - 128a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 2 5 2 4 +--R (- 336a b - 896a b - 896a b )cosh(x) - 48a b - 224a b +--R + +--R 3 3 4 2 +--R - 384a b - 256a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 2 6 5 2 4 +--R (- 168b - 448a b - 448a b )cosh(x) - 24b - 112a b - 192a b +--R + +--R 3 3 +--R - 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (- 336a b - 896a b - 896a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 144a b - 672a b - 1152a b - 768a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 3 +--R (- 672a b - 1792a b - 1792a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 288a b - 1344a b - 2304a b - 1536a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 3 +--R (- 336b - 896a b - 896a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (- 144b - 672a b - 1152a b - 768a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 420a b - 1120a b - 1120a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (- 360a b - 1680a b - 2880a b - 1920a b)cosh(x) - 36a b +--R + +--R 3 3 4 2 5 6 +--R - 192a b - 448a b - 512a b - 256a +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 4 +--R (- 840a b - 2240a b - 2240a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 720a b - 3360a b - 5760a b - 3840a b )cosh(x) - 72a b +--R + +--R 2 4 3 3 4 2 5 +--R - 384a b - 896a b - 1024a b - 512a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 4 +--R (- 420b - 1120a b - 1120a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 +--R (- 360b - 1680a b - 2880a b - 1920a b )cosh(x) - 36b +--R + +--R 5 2 4 3 3 4 2 +--R - 192a b - 448a b - 512a b - 256a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 336a b - 896a b - 896a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 480a b - 2240a b - 3840a b - 2560a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 144a b - 768a b - 1792a b - 2048a b - 1024a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 5 +--R (- 672a b - 1792a b - 1792a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 960a b - 4480a b - 7680a b - 5120a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 288a b - 1536a b - 3584a b - 4096a b - 2048a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 5 +--R (- 336b - 896a b - 896a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 480b - 2240a b - 3840a b - 2560a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 144b - 768a b - 1792a b - 2048a b - 1024a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (- 168a b - 448a b - 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 360a b - 1680a b - 2880a b - 1920a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (- 216a b - 1152a b - 2688a b - 3072a b - 1536a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R - 24a b - 112a b - 192a b - 128a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 6 +--R (- 336a b - 896a b - 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 720a b - 3360a b - 5760a b - 3840a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 432a b - 2304a b - 5376a b - 6144a b - 3072a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R - 48a b - 224a b - 384a b - 256a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 6 +--R (- 168b - 448a b - 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- 360b - 1680a b - 2880a b - 1920a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- 216b - 1152a b - 2688a b - 3072a b - 1536a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R - 24b - 112a b - 192a b - 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 48a b - 128a b - 128a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 144a b - 672a b - 1152a b - 768a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 144a b - 768a b - 1792a b - 2048a b - 1024a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 48a b - 224a b - 384a b - 256a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 7 +--R (- 96a b - 256a b - 256a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 288a b - 1344a b - 2304a b - 1536a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 288a b - 1536a b - 3584a b - 4096a b - 2048a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 96a b - 448a b - 768a b - 512a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 7 +--R (- 48b - 128a b - 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 144b - 672a b - 1152a b - 768a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 144b - 768a b - 1792a b - 2048a b - 1024a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (- 48b - 224a b - 384a b - 256a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 6a b - 16a b - 16a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 24a b - 112a b - 192a b - 128a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 36a b - 192a b - 448a b - 512a b - 256a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 +--R (- 24a b - 112a b - 192a b - 128a b)cosh(x) - 6a b - 16a b +--R + +--R 4 2 +--R - 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 8 +--R (- 12a b - 32a b - 32a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 48a b - 224a b - 384a b - 256a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 72a b - 384a b - 896a b - 1024a b - 512a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 48a b - 224a b - 384a b - 256a b )cosh(x) - 12a b +--R + +--R 2 4 3 3 +--R - 32a b - 32a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 8 +--R (- 6b - 16a b - 16a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 +--R (- 24b - 112a b - 192a b - 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 36b - 192a b - 448a b - 512a b - 256a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 2 4 +--R (- 24b - 112a b - 192a b - 128a b )cosh(x) - 6b - 16a b - 16a b +--R * +--R +--------+ +-+ +--R | 2 tanh(x)\|a +--R \|a b + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 2 3 3 2 8 +--R (- 16a b - 32a b - 16a b )sinh(x) +--R + +--R 4 2 3 3 2 7 +--R (- 128a b - 256a b - 128a b )cosh(x)sinh(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (- 448a b - 896a b - 448a b )cosh(x) - 64a b - 256a b +--R + +--R 3 2 4 +--R - 320a b - 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 2 3 +--R (- 896a b - 1792a b - 896a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 384a b - 1536a b - 1920a b - 768a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 1120a b - 2240a b - 1120a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (- 960a b - 3840a b - 4800a b - 1920a b)cosh(x) - 96a b +--R + +--R 2 3 3 2 4 5 +--R - 448a b - 864a b - 768a b - 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 3 2 5 +--R (- 896a b - 1792a b - 896a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 1280a b - 5120a b - 6400a b - 2560a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 384a b - 1792a b - 3456a b - 3072a b - 1024a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 3 2 6 +--R (- 448a b - 896a b - 448a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 960a b - 3840a b - 4800a b - 1920a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 576a b - 2688a b - 5184a b - 4608a b - 1536a )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R - 64a b - 256a b - 320a b - 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 7 +--R (- 128a b - 256a b - 128a b )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 384a b - 1536a b - 1920a b - 768a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 384a b - 1792a b - 3456a b - 3072a b - 1024a )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 128a b - 512a b - 640a b - 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 8 +--R (- 16a b - 32a b - 16a b )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 64a b - 256a b - 320a b - 128a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 96a b - 448a b - 864a b - 768a b - 256a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 2 3 +--R (- 64a b - 256a b - 320a b - 128a b)cosh(x) - 16a b - 32a b +--R + +--R 3 2 +--R - 16a b +--R * +--R 3 +--R tanh(x) +--R + +--R 4 2 3 3 2 2 5 4 2 3 +--R (- 6a b - 16a b - 16a b )sech(x) + 6b + 28a b + 32a b +--R + +--R 3 2 +--R 16a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 3 2 2 +--R (- 48a b - 128a b - 128a b )cosh(x)sech(x) +--R + +--R 5 4 2 3 3 2 +--R (48b + 224a b + 256a b + 128a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 3 2 2 4 +--R (- 168a b - 448a b - 448a b )cosh(x) - 24a b +--R + +--R 2 3 3 2 4 +--R - 112a b - 192a b - 128a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 2 5 +--R (168b + 784a b + 896a b + 448a b )cosh(x) + 24b +--R + +--R 4 2 3 3 2 4 +--R 160a b + 352a b + 320a b + 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 2 3 +--R (- 336a b - 896a b - 896a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 144a b - 672a b - 1152a b - 768a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 3 +--R (336b + 1568a b + 1792a b + 896a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (144b + 960a b + 2112a b + 1920a b + 768a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 420a b - 1120a b - 1120a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (- 360a b - 1680a b - 2880a b - 1920a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R - 36a b - 192a b - 448a b - 512a b - 256a +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 +--R (420b + 1960a b + 2240a b + 1120a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (360b + 2400a b + 5280a b + 4800a b + 1920a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R 36b + 264a b + 736a b + 1056a b + 768a b + 256a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 3 2 5 +--R (- 336a b - 896a b - 896a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 480a b - 2240a b - 3840a b - 2560a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 144a b - 768a b - 1792a b - 2048a b - 1024a )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 5 +--R (336b + 1568a b + 1792a b + 896a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (480b + 3200a b + 7040a b + 6400a b + 2560a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (144b + 1056a b + 2944a b + 4224a b + 3072a b + 1024a ) +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 3 2 6 +--R (- 168a b - 448a b - 448a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 360a b - 1680a b - 2880a b - 1920a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 216a b - 1152a b - 2688a b - 3072a b - 1536a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 4 +--R - 24a b - 112a b - 192a b - 128a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 6 +--R (168b + 784a b + 896a b + 448a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (360b + 2400a b + 5280a b + 4800a b + 1920a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (216b + 1584a b + 4416a b + 6336a b + 4608a b + 1536a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 24b + 160a b + 352a b + 320a b + 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 7 +--R (- 48a b - 128a b - 128a b )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 144a b - 672a b - 1152a b - 768a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 144a b - 768a b - 1792a b - 2048a b - 1024a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 48a b - 224a b - 384a b - 256a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 7 +--R (48b + 224a b + 256a b + 128a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (144b + 960a b + 2112a b + 1920a b + 768a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (144b + 1056a b + 2944a b + 4224a b + 3072a b + 1024a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (48b + 320a b + 704a b + 640a b + 256a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 8 +--R (- 6a b - 16a b - 16a b )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 24a b - 112a b - 192a b - 128a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 36a b - 192a b - 448a b - 512a b - 256a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (- 24a b - 112a b - 192a b - 128a b)cosh(x) - 6a b +--R + +--R 2 3 3 2 +--R - 16a b - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 8 +--R (6b + 28a b + 32a b + 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (24b + 160a b + 352a b + 320a b + 128a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (36b + 264a b + 736a b + 1056a b + 768a b + 256a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (24b + 160a b + 352a b + 320a b + 128a b)cosh(x) + 6b +--R + +--R 4 2 3 3 2 +--R 28a b + 32a b + 16a b +--R * +--R tanh(x) +--R + +--R 2 3 3 2 4 4 +--R (12a b + 32a b + 32a b)sech(x) +--R + +--R 4 2 3 3 2 2 5 4 2 3 +--R (24a b + 64a b + 64a b )sech(x) + 12b + 32a b + 32a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 4 4 +--R (72a b + 192a b + 192a b)cosh(x)sech(x) +--R + +--R 4 2 3 3 2 2 +--R (144a b + 384a b + 384a b )cosh(x)sech(x) +--R + +--R 5 4 2 3 +--R (72b + 192a b + 192a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 +--R (180a b + 480a b + 480a b)cosh(x) + 36a b + 168a b +--R + +--R 4 5 +--R 288a b + 192a +--R * +--R 4 +--R sech(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (360a b + 960a b + 960a b )cosh(x) + 72a b + 336a b +--R + +--R 3 2 4 +--R 576a b + 384a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 2 5 4 2 3 +--R (180b + 480a b + 480a b )cosh(x) + 36b + 168a b + 288a b +--R + +--R 3 2 +--R 192a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 +--R (240a b + 640a b + 640a b)cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (144a b + 672a b + 1152a b + 768a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 2 3 3 2 3 +--R (480a b + 1280a b + 1280a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (288a b + 1344a b + 2304a b + 1536a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 +--R (240b + 640a b + 640a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (144b + 672a b + 1152a b + 768a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 4 4 +--R (180a b + 480a b + 480a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 2 3 +--R (216a b + 1008a b + 1728a b + 1152a )cosh(x) + 36a b +--R + +--R 3 2 4 +--R 160a b + 160a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 2 3 3 2 4 +--R (360a b + 960a b + 960a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (432a b + 2016a b + 3456a b + 2304a b)cosh(x) + 72a b +--R + +--R 2 3 3 2 +--R 320a b + 320a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 4 +--R (180b + 480a b + 480a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (216b + 1008a b + 1728a b + 1152a b )cosh(x) + 36b + 160a b +--R + +--R 2 3 +--R 160a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 4 5 +--R (72a b + 192a b + 192a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (144a b + 672a b + 1152a b + 768a )cosh(x) +--R + +--R 2 3 3 2 4 +--R (72a b + 320a b + 320a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 2 3 3 2 5 +--R (144a b + 384a b + 384a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (288a b + 1344a b + 2304a b + 1536a b)cosh(x) +--R + +--R 4 2 3 3 2 +--R (144a b + 640a b + 640a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 5 +--R (72b + 192a b + 192a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (144b + 672a b + 1152a b + 768a b )cosh(x) +--R + +--R 5 4 2 3 +--R (72b + 320a b + 320a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3 2 4 6 +--R (12a b + 32a b + 32a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (36a b + 168a b + 288a b + 192a )cosh(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 +--R (36a b + 160a b + 160a b)cosh(x) + 12a b + 24a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 2 3 3 2 6 +--R (24a b + 64a b + 64a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (72a b + 336a b + 576a b + 384a b)cosh(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (72a b + 320a b + 320a b )cosh(x) + 24a b + 48a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 6 +--R (12b + 32a b + 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (36b + 168a b + 288a b + 192a b )cosh(x) +--R + +--R 5 4 2 3 2 5 4 +--R (36b + 160a b + 160a b )cosh(x) + 12b + 24a b +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|a b + a +--R / +--R 4 4 5 3 6 2 4 +--R (16a b + 32a b + 16a b )sech(x) +--R + +--R 3 5 4 4 5 3 2 2 6 3 5 4 4 +--R (32a b + 64a b + 32a b )sech(x) + 16a b + 32a b + 16a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 4 +--R (128a b + 256a b + 128a b )cosh(x)sech(x) +--R + +--R 3 5 4 4 5 3 2 +--R (256a b + 512a b + 256a b )cosh(x)sech(x) +--R + +--R 2 6 3 5 4 4 +--R (128a b + 256a b + 128a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 2 4 4 5 3 +--R (448a b + 896a b + 448a b )cosh(x) + 64a b + 256a b +--R + +--R 6 2 7 +--R 320a b + 128a b +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 2 3 5 4 4 +--R (896a b + 1792a b + 896a b )cosh(x) + 128a b + 512a b +--R + +--R 5 3 6 2 +--R 640a b + 256a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 2 2 6 3 5 4 4 +--R (448a b + 896a b + 448a b )cosh(x) + 64a b + 256a b + 320a b +--R + +--R 5 3 +--R 128a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 3 +--R (896a b + 1792a b + 896a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (384a b + 1536a b + 1920a b + 768a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 3 +--R (1792a b + 3584a b + 1792a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R (768a b + 3072a b + 3840a b + 1536a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 3 +--R (896a b + 1792a b + 896a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R (384a b + 1536a b + 1920a b + 768a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 4 +--R (1120a b + 2240a b + 1120a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 4 4 +--R (960a b + 3840a b + 4800a b + 1920a b)cosh(x) + 96a b +--R + +--R 5 3 6 2 7 8 +--R 448a b + 864a b + 768a b + 256a +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 4 +--R (2240a b + 4480a b + 2240a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 3 5 +--R (1920a b + 7680a b + 9600a b + 3840a b )cosh(x) + 192a b +--R + +--R 4 4 5 3 6 2 7 +--R 896a b + 1728a b + 1536a b + 512a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 4 +--R (1120a b + 2240a b + 1120a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 2 2 6 +--R (960a b + 3840a b + 4800a b + 1920a b )cosh(x) + 96a b +--R + +--R 3 5 4 4 5 3 6 2 +--R 448a b + 864a b + 768a b + 256a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 5 +--R (896a b + 1792a b + 896a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (1280a b + 5120a b + 6400a b + 2560a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (384a b + 1792a b + 3456a b + 3072a b + 1024a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 5 +--R (1792a b + 3584a b + 1792a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 3 +--R (2560a b + 10240a b + 12800a b + 5120a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (768a b + 3584a b + 6912a b + 6144a b + 2048a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 5 +--R (896a b + 1792a b + 896a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 3 +--R (1280a b + 5120a b + 6400a b + 2560a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (384a b + 1792a b + 3456a b + 3072a b + 1024a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 6 +--R (448a b + 896a b + 448a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (960a b + 3840a b + 4800a b + 1920a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 2 +--R (576a b + 2688a b + 5184a b + 4608a b + 1536a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 +--R 64a b + 256a b + 320a b + 128a b +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 6 +--R (896a b + 1792a b + 896a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 4 +--R (1920a b + 7680a b + 9600a b + 3840a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 2 +--R (1152a b + 5376a b + 10368a b + 9216a b + 3072a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R 128a b + 512a b + 640a b + 256a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 6 +--R (448a b + 896a b + 448a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 4 +--R (960a b + 3840a b + 4800a b + 1920a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (576a b + 2688a b + 5184a b + 4608a b + 1536a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R 64a b + 256a b + 320a b + 128a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (128a b + 256a b + 128a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (384a b + 1536a b + 1920a b + 768a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 3 +--R (384a b + 1792a b + 3456a b + 3072a b + 1024a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (128a b + 512a b + 640a b + 256a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 7 +--R (256a b + 512a b + 256a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 5 +--R (768a b + 3072a b + 3840a b + 1536a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 +--R (768a b + 3584a b + 6912a b + 6144a b + 2048a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R (256a b + 1024a b + 1280a b + 512a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 7 +--R (128a b + 256a b + 128a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 5 +--R (384a b + 1536a b + 1920a b + 768a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 3 +--R (384a b + 1792a b + 3456a b + 3072a b + 1024a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R (128a b + 512a b + 640a b + 256a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 8 +--R (16a b + 32a b + 16a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 6 +--R (64a b + 256a b + 320a b + 128a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (96a b + 448a b + 864a b + 768a b + 256a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 4 4 5 3 +--R (64a b + 256a b + 320a b + 128a b)cosh(x) + 16a b + 32a b +--R + +--R 6 2 +--R 16a b +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 8 +--R (32a b + 64a b + 32a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 6 +--R (128a b + 512a b + 640a b + 256a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 4 +--R (192a b + 896a b + 1728a b + 1536a b + 512a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 3 5 4 4 +--R (128a b + 512a b + 640a b + 256a b )cosh(x) + 32a b + 64a b +--R + +--R 5 3 +--R 32a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 8 +--R (16a b + 32a b + 16a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 +--R (64a b + 256a b + 320a b + 128a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 4 +--R (96a b + 448a b + 864a b + 768a b + 256a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 2 2 6 3 5 4 4 +--R (64a b + 256a b + 320a b + 128a b )cosh(x) + 16a b + 32a b + 16a b +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|a b + a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 510 +--d0194a:= D(m0194a,x) +--E 483 + +--S 484 of 510 +m0194b:= a0194.2-r0194 +--R +--R +--R (285) +--R 2 4 3 3 4 2 4 +--R (- 3a b - 8a b - 8a b )sech(x) +--R + +--R 5 2 4 3 3 2 6 5 2 4 +--R (- 6a b - 16a b - 16a b )sech(x) - 3b - 8a b - 8a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 24a b - 64a b - 64a b )cosh(x)sech(x) +--R + +--R 5 2 4 3 3 2 +--R (- 48a b - 128a b - 128a b )cosh(x)sech(x) +--R + +--R 6 5 2 4 +--R (- 24b - 64a b - 64a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (- 84a b - 224a b - 224a b )cosh(x) - 12a b - 56a b +--R + +--R 4 2 5 +--R - 96a b - 64a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 2 5 2 4 +--R (- 168a b - 448a b - 448a b )cosh(x) - 24a b - 112a b +--R + +--R 3 3 4 2 +--R - 192a b - 128a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 2 6 5 2 4 +--R (- 84b - 224a b - 224a b )cosh(x) - 12b - 56a b - 96a b +--R + +--R 3 3 +--R - 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (- 168a b - 448a b - 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 72a b - 336a b - 576a b - 384a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 3 +--R (- 336a b - 896a b - 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 144a b - 672a b - 1152a b - 768a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 3 +--R (- 168b - 448a b - 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (- 72b - 336a b - 576a b - 384a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 210a b - 560a b - 560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (- 180a b - 840a b - 1440a b - 960a b)cosh(x) - 18a b +--R + +--R 3 3 4 2 5 6 +--R - 96a b - 224a b - 256a b - 128a +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 4 +--R (- 420a b - 1120a b - 1120a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 360a b - 1680a b - 2880a b - 1920a b )cosh(x) - 36a b +--R + +--R 2 4 3 3 4 2 5 +--R - 192a b - 448a b - 512a b - 256a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 4 +--R (- 210b - 560a b - 560a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (- 180b - 840a b - 1440a b - 960a b )cosh(x) - 18b - 96a b +--R + +--R 2 4 3 3 4 2 +--R - 224a b - 256a b - 128a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 168a b - 448a b - 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 240a b - 1120a b - 1920a b - 1280a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 72a b - 384a b - 896a b - 1024a b - 512a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 5 +--R (- 336a b - 896a b - 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 480a b - 2240a b - 3840a b - 2560a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 144a b - 768a b - 1792a b - 2048a b - 1024a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 5 +--R (- 168b - 448a b - 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 240b - 1120a b - 1920a b - 1280a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 72b - 384a b - 896a b - 1024a b - 512a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (- 84a b - 224a b - 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 180a b - 840a b - 1440a b - 960a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (- 108a b - 576a b - 1344a b - 1536a b - 768a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R - 12a b - 56a b - 96a b - 64a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 6 +--R (- 168a b - 448a b - 448a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 360a b - 1680a b - 2880a b - 1920a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 216a b - 1152a b - 2688a b - 3072a b - 1536a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R - 24a b - 112a b - 192a b - 128a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 6 +--R (- 84b - 224a b - 224a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- 180b - 840a b - 1440a b - 960a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- 108b - 576a b - 1344a b - 1536a b - 768a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R - 12b - 56a b - 96a b - 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 24a b - 64a b - 64a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 72a b - 336a b - 576a b - 384a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 72a b - 384a b - 896a b - 1024a b - 512a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 24a b - 112a b - 192a b - 128a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 7 +--R (- 48a b - 128a b - 128a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 144a b - 672a b - 1152a b - 768a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (- 144a b - 768a b - 1792a b - 2048a b - 1024a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 48a b - 224a b - 384a b - 256a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 7 +--R (- 24b - 64a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 72b - 336a b - 576a b - 384a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 72b - 384a b - 896a b - 1024a b - 512a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (- 24b - 112a b - 192a b - 128a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 3a b - 8a b - 8a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b - 56a b - 96a b - 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 18a b - 96a b - 224a b - 256a b - 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 +--R (- 12a b - 56a b - 96a b - 64a b)cosh(x) - 3a b - 8a b +--R + +--R 4 2 +--R - 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 8 +--R (- 6a b - 16a b - 16a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 24a b - 112a b - 192a b - 128a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 36a b - 192a b - 448a b - 512a b - 256a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 2 4 +--R (- 24a b - 112a b - 192a b - 128a b )cosh(x) - 6a b - 16a b +--R + +--R 3 3 +--R - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 8 +--R (- 3b - 8a b - 8a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 +--R (- 12b - 56a b - 96a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 18b - 96a b - 224a b - 256a b - 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 2 4 +--R (- 12b - 56a b - 96a b - 64a b )cosh(x) - 3b - 8a b - 8a b +--R * +--R +----------+ +-+ +--R | 2 tanh(x)\|a +--R \|- a b - a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 4 3 3 4 2 4 +--R (- 3a b - 8a b - 8a b )sech(x) +--R + +--R 5 2 4 3 3 2 6 5 2 4 +--R (- 6a b - 16a b - 16a b )sech(x) - 3b - 8a b - 8a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 24a b - 64a b - 64a b )cosh(x)sech(x) +--R + +--R 5 2 4 3 3 2 +--R (- 48a b - 128a b - 128a b )cosh(x)sech(x) +--R + +--R 6 5 2 4 +--R (- 24b - 64a b - 64a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 2 2 4 3 3 +--R (- 84a b - 224a b - 224a b )cosh(x) - 12a b - 56a b +--R + +--R 4 2 5 +--R - 96a b - 64a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 2 5 2 4 +--R (- 168a b - 448a b - 448a b )cosh(x) - 24a b - 112a b +--R + +--R 3 3 4 2 +--R - 192a b - 128a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 2 6 5 2 4 +--R (- 84b - 224a b - 224a b )cosh(x) - 12b - 56a b - 96a b +--R + +--R 3 3 +--R - 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 3 +--R (- 168a b - 448a b - 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 72a b - 336a b - 576a b - 384a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 3 +--R (- 336a b - 896a b - 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 144a b - 672a b - 1152a b - 768a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 3 +--R (- 168b - 448a b - 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (- 72b - 336a b - 576a b - 384a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 4 +--R (- 210a b - 560a b - 560a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 +--R (- 180a b - 840a b - 1440a b - 960a b)cosh(x) - 18a b +--R + +--R 3 3 4 2 5 6 +--R - 96a b - 224a b - 256a b - 128a +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 4 +--R (- 420a b - 1120a b - 1120a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 360a b - 1680a b - 2880a b - 1920a b )cosh(x) - 36a b +--R + +--R 2 4 3 3 4 2 5 +--R - 192a b - 448a b - 512a b - 256a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 4 +--R (- 210b - 560a b - 560a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (- 180b - 840a b - 1440a b - 960a b )cosh(x) - 18b - 96a b +--R + +--R 2 4 3 3 4 2 +--R - 224a b - 256a b - 128a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 168a b - 448a b - 448a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 240a b - 1120a b - 1920a b - 1280a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 72a b - 384a b - 896a b - 1024a b - 512a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 5 +--R (- 336a b - 896a b - 896a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 480a b - 2240a b - 3840a b - 2560a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 144a b - 768a b - 1792a b - 2048a b - 1024a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 5 +--R (- 168b - 448a b - 448a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 240b - 1120a b - 1920a b - 1280a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 72b - 384a b - 896a b - 1024a b - 512a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (- 84a b - 224a b - 224a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 180a b - 840a b - 1440a b - 960a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (- 108a b - 576a b - 1344a b - 1536a b - 768a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R - 12a b - 56a b - 96a b - 64a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 6 +--R (- 168a b - 448a b - 448a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 360a b - 1680a b - 2880a b - 1920a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 216a b - 1152a b - 2688a b - 3072a b - 1536a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R - 24a b - 112a b - 192a b - 128a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 6 +--R (- 84b - 224a b - 224a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- 180b - 840a b - 1440a b - 960a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- 108b - 576a b - 1344a b - 1536a b - 768a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R - 12b - 56a b - 96a b - 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 7 +--R (- 24a b - 64a b - 64a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 72a b - 336a b - 576a b - 384a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 72a b - 384a b - 896a b - 1024a b - 512a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 24a b - 112a b - 192a b - 128a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 7 +--R (- 48a b - 128a b - 128a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 144a b - 672a b - 1152a b - 768a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (- 144a b - 768a b - 1792a b - 2048a b - 1024a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 48a b - 224a b - 384a b - 256a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 7 +--R (- 24b - 64a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 72b - 336a b - 576a b - 384a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 72b - 384a b - 896a b - 1024a b - 512a b )cosh(x) +--R + +--R 6 5 2 4 3 3 +--R (- 24b - 112a b - 192a b - 128a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (- 3a b - 8a b - 8a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b - 56a b - 96a b - 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 18a b - 96a b - 224a b - 256a b - 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 +--R (- 12a b - 56a b - 96a b - 64a b)cosh(x) - 3a b - 8a b +--R + +--R 4 2 +--R - 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 5 2 4 3 3 8 +--R (- 6a b - 16a b - 16a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 24a b - 112a b - 192a b - 128a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 36a b - 192a b - 448a b - 512a b - 256a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 2 4 +--R (- 24a b - 112a b - 192a b - 128a b )cosh(x) - 6a b - 16a b +--R + +--R 3 3 +--R - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 2 4 8 +--R (- 3b - 8a b - 8a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 +--R (- 12b - 56a b - 96a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 18b - 96a b - 224a b - 256a b - 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 2 4 +--R (- 12b - 56a b - 96a b - 64a b )cosh(x) - 3b - 8a b - 8a b +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +----------+ +--R 2 2 | 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a)\|- a b - a +--R atan(-------------------------------------------------------------------) +--R 2 +--R 2a b + 2a +--R + +--R 4 2 3 3 2 8 +--R (- 8a b - 16a b - 8a b )sinh(x) +--R + +--R 4 2 3 3 2 7 +--R (- 64a b - 128a b - 64a b )cosh(x)sinh(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (- 224a b - 448a b - 224a b )cosh(x) - 32a b - 128a b +--R + +--R 3 2 4 +--R - 160a b - 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 2 3 +--R (- 448a b - 896a b - 448a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 192a b - 768a b - 960a b - 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 560a b - 1120a b - 560a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (- 480a b - 1920a b - 2400a b - 960a b)cosh(x) - 48a b +--R + +--R 2 3 3 2 4 5 +--R - 224a b - 432a b - 384a b - 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 3 2 5 +--R (- 448a b - 896a b - 448a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 640a b - 2560a b - 3200a b - 1280a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 192a b - 896a b - 1728a b - 1536a b - 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 3 2 6 +--R (- 224a b - 448a b - 224a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 480a b - 1920a b - 2400a b - 960a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 288a b - 1344a b - 2592a b - 2304a b - 768a )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R - 32a b - 128a b - 160a b - 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 7 +--R (- 64a b - 128a b - 64a b )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 192a b - 768a b - 960a b - 384a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 192a b - 896a b - 1728a b - 1536a b - 512a )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 64a b - 256a b - 320a b - 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 8 +--R (- 8a b - 16a b - 8a b )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 32a b - 128a b - 160a b - 64a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 48a b - 224a b - 432a b - 384a b - 128a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 2 3 +--R (- 32a b - 128a b - 160a b - 64a b)cosh(x) - 8a b - 16a b +--R + +--R 3 2 +--R - 8a b +--R * +--R 3 +--R tanh(x) +--R + +--R 4 2 3 3 2 2 5 4 2 3 +--R (- 3a b - 8a b - 8a b )sech(x) + 3b + 14a b + 16a b +--R + +--R 3 2 +--R 8a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 3 2 2 +--R (- 24a b - 64a b - 64a b )cosh(x)sech(x) +--R + +--R 5 4 2 3 3 2 +--R (24b + 112a b + 128a b + 64a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (- 84a b - 224a b - 224a b )cosh(x) - 12a b - 56a b +--R + +--R 3 2 4 +--R - 96a b - 64a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (84b + 392a b + 448a b + 224a b )cosh(x) + 12b + 80a b +--R + +--R 2 3 3 2 4 +--R 176a b + 160a b + 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 2 3 +--R (- 168a b - 448a b - 448a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 72a b - 336a b - 576a b - 384a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 3 +--R (168b + 784a b + 896a b + 448a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (72b + 480a b + 1056a b + 960a b + 384a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 210a b - 560a b - 560a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (- 180a b - 840a b - 1440a b - 960a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R - 18a b - 96a b - 224a b - 256a b - 128a +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 +--R (210b + 980a b + 1120a b + 560a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (180b + 1200a b + 2640a b + 2400a b + 960a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R 18b + 132a b + 368a b + 528a b + 384a b + 128a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 3 2 5 +--R (- 168a b - 448a b - 448a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 240a b - 1120a b - 1920a b - 1280a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 72a b - 384a b - 896a b - 1024a b - 512a )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 5 +--R (168b + 784a b + 896a b + 448a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (240b + 1600a b + 3520a b + 3200a b + 1280a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (72b + 528a b + 1472a b + 2112a b + 1536a b + 512a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 3 2 6 +--R (- 84a b - 224a b - 224a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 180a b - 840a b - 1440a b - 960a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 108a b - 576a b - 1344a b - 1536a b - 768a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 4 +--R - 12a b - 56a b - 96a b - 64a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 6 +--R (84b + 392a b + 448a b + 224a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (180b + 1200a b + 2640a b + 2400a b + 960a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (108b + 792a b + 2208a b + 3168a b + 2304a b + 768a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 12b + 80a b + 176a b + 160a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 7 +--R (- 24a b - 64a b - 64a b )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 72a b - 336a b - 576a b - 384a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 72a b - 384a b - 896a b - 1024a b - 512a )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 24a b - 112a b - 192a b - 128a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 7 +--R (24b + 112a b + 128a b + 64a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (72b + 480a b + 1056a b + 960a b + 384a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (72b + 528a b + 1472a b + 2112a b + 1536a b + 512a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (24b + 160a b + 352a b + 320a b + 128a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 8 +--R (- 3a b - 8a b - 8a b )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 12a b - 56a b - 96a b - 64a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 18a b - 96a b - 224a b - 256a b - 128a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 2 3 +--R (- 12a b - 56a b - 96a b - 64a b)cosh(x) - 3a b - 8a b +--R + +--R 3 2 +--R - 8a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 2 8 +--R (3b + 14a b + 16a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (12b + 80a b + 176a b + 160a b + 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (18b + 132a b + 368a b + 528a b + 384a b + 128a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (12b + 80a b + 176a b + 160a b + 64a b)cosh(x) + 3b +--R + +--R 4 2 3 3 2 +--R 14a b + 16a b + 8a b +--R * +--R tanh(x) +--R + +--R 2 3 3 2 4 4 +--R (6a b + 16a b + 16a b)sech(x) +--R + +--R 4 2 3 3 2 2 5 4 2 3 +--R (12a b + 32a b + 32a b )sech(x) + 6b + 16a b + 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 4 4 +--R (36a b + 96a b + 96a b)cosh(x)sech(x) +--R + +--R 4 2 3 3 2 2 +--R (72a b + 192a b + 192a b )cosh(x)sech(x) +--R + +--R 5 4 2 3 +--R (36b + 96a b + 96a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 +--R (90a b + 240a b + 240a b)cosh(x) + 18a b + 84a b +--R + +--R 4 5 +--R 144a b + 96a +--R * +--R 4 +--R sech(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (180a b + 480a b + 480a b )cosh(x) + 36a b + 168a b +--R + +--R 3 2 4 +--R 288a b + 192a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 2 5 4 2 3 +--R (90b + 240a b + 240a b )cosh(x) + 18b + 84a b + 144a b +--R + +--R 3 2 +--R 96a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 +--R (120a b + 320a b + 320a b)cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (72a b + 336a b + 576a b + 384a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 2 3 3 2 3 +--R (240a b + 640a b + 640a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (144a b + 672a b + 1152a b + 768a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 3 +--R (120b + 320a b + 320a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (72b + 336a b + 576a b + 384a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 4 4 +--R (90a b + 240a b + 240a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 2 3 +--R (108a b + 504a b + 864a b + 576a )cosh(x) + 18a b +--R + +--R 3 2 4 +--R 80a b + 80a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 2 3 3 2 4 +--R (180a b + 480a b + 480a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (216a b + 1008a b + 1728a b + 1152a b)cosh(x) + 36a b +--R + +--R 2 3 3 2 +--R 160a b + 160a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 4 +--R (90b + 240a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (108b + 504a b + 864a b + 576a b )cosh(x) + 18b + 80a b +--R + +--R 2 3 +--R 80a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 4 5 +--R (36a b + 96a b + 96a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (72a b + 336a b + 576a b + 384a )cosh(x) +--R + +--R 2 3 3 2 4 +--R (36a b + 160a b + 160a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 2 3 3 2 5 +--R (72a b + 192a b + 192a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (144a b + 672a b + 1152a b + 768a b)cosh(x) +--R + +--R 4 2 3 3 2 +--R (72a b + 320a b + 320a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 5 +--R (36b + 96a b + 96a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (72b + 336a b + 576a b + 384a b )cosh(x) +--R + +--R 5 4 2 3 +--R (36b + 160a b + 160a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3 2 4 6 +--R (6a b + 16a b + 16a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (18a b + 84a b + 144a b + 96a )cosh(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 +--R (18a b + 80a b + 80a b)cosh(x) + 6a b + 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 2 3 3 2 6 +--R (12a b + 32a b + 32a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (36a b + 168a b + 288a b + 192a b)cosh(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (36a b + 160a b + 160a b )cosh(x) + 12a b + 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 2 3 6 +--R (6b + 16a b + 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (18b + 84a b + 144a b + 96a b )cosh(x) +--R + +--R 5 4 2 3 2 5 4 +--R (18b + 80a b + 80a b )cosh(x) + 6b + 12a b +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- a b - a \|a \|b + a +--R / +--R 4 4 5 3 6 2 4 +--R (8a b + 16a b + 8a b )sech(x) +--R + +--R 3 5 4 4 5 3 2 2 6 3 5 4 4 +--R (16a b + 32a b + 16a b )sech(x) + 8a b + 16a b + 8a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 4 +--R (64a b + 128a b + 64a b )cosh(x)sech(x) +--R + +--R 3 5 4 4 5 3 2 +--R (128a b + 256a b + 128a b )cosh(x)sech(x) +--R + +--R 2 6 3 5 4 4 +--R (64a b + 128a b + 64a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 2 4 4 5 3 +--R (224a b + 448a b + 224a b )cosh(x) + 32a b + 128a b +--R + +--R 6 2 7 +--R 160a b + 64a b +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 2 3 5 4 4 +--R (448a b + 896a b + 448a b )cosh(x) + 64a b + 256a b +--R + +--R 5 3 6 2 +--R 320a b + 128a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 2 2 6 3 5 4 4 +--R (224a b + 448a b + 224a b )cosh(x) + 32a b + 128a b + 160a b +--R + +--R 5 3 +--R 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 3 +--R (448a b + 896a b + 448a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (192a b + 768a b + 960a b + 384a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 3 +--R (896a b + 1792a b + 896a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R (384a b + 1536a b + 1920a b + 768a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 3 +--R (448a b + 896a b + 448a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R (192a b + 768a b + 960a b + 384a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 4 +--R (560a b + 1120a b + 560a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 4 4 +--R (480a b + 1920a b + 2400a b + 960a b)cosh(x) + 48a b +--R + +--R 5 3 6 2 7 8 +--R 224a b + 432a b + 384a b + 128a +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 4 +--R (1120a b + 2240a b + 1120a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 3 5 +--R (960a b + 3840a b + 4800a b + 1920a b )cosh(x) + 96a b +--R + +--R 4 4 5 3 6 2 7 +--R 448a b + 864a b + 768a b + 256a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 4 +--R (560a b + 1120a b + 560a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 2 2 6 +--R (480a b + 1920a b + 2400a b + 960a b )cosh(x) + 48a b +--R + +--R 3 5 4 4 5 3 6 2 +--R 224a b + 432a b + 384a b + 128a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 5 +--R (448a b + 896a b + 448a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (640a b + 2560a b + 3200a b + 1280a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (192a b + 896a b + 1728a b + 1536a b + 512a )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 5 +--R (896a b + 1792a b + 896a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 3 +--R (1280a b + 5120a b + 6400a b + 2560a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (384a b + 1792a b + 3456a b + 3072a b + 1024a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 5 +--R (448a b + 896a b + 448a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 3 +--R (640a b + 2560a b + 3200a b + 1280a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (192a b + 896a b + 1728a b + 1536a b + 512a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 6 +--R (224a b + 448a b + 224a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (480a b + 1920a b + 2400a b + 960a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 2 +--R (288a b + 1344a b + 2592a b + 2304a b + 768a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 +--R 32a b + 128a b + 160a b + 64a b +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 6 +--R (448a b + 896a b + 448a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 4 +--R (960a b + 3840a b + 4800a b + 1920a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 2 +--R (576a b + 2688a b + 5184a b + 4608a b + 1536a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R 64a b + 256a b + 320a b + 128a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 6 +--R (224a b + 448a b + 224a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 4 +--R (480a b + 1920a b + 2400a b + 960a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (288a b + 1344a b + 2592a b + 2304a b + 768a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R 32a b + 128a b + 160a b + 64a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (64a b + 128a b + 64a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (192a b + 768a b + 960a b + 384a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 3 +--R (192a b + 896a b + 1728a b + 1536a b + 512a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 +--R (64a b + 256a b + 320a b + 128a b)cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 7 +--R (128a b + 256a b + 128a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 5 +--R (384a b + 1536a b + 1920a b + 768a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 +--R (384a b + 1792a b + 3456a b + 3072a b + 1024a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R (128a b + 512a b + 640a b + 256a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 7 +--R (64a b + 128a b + 64a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 5 +--R (192a b + 768a b + 960a b + 384a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 3 +--R (192a b + 896a b + 1728a b + 1536a b + 512a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R (64a b + 256a b + 320a b + 128a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 8 +--R (8a b + 16a b + 8a b )cosh(x) +--R + +--R 4 4 5 3 6 2 7 6 +--R (32a b + 128a b + 160a b + 64a b)cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (48a b + 224a b + 432a b + 384a b + 128a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 4 4 5 3 6 2 +--R (32a b + 128a b + 160a b + 64a b)cosh(x) + 8a b + 16a b + 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 3 5 4 4 5 3 8 +--R (16a b + 32a b + 16a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 6 +--R (64a b + 256a b + 320a b + 128a b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 4 +--R (96a b + 448a b + 864a b + 768a b + 256a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 3 5 4 4 +--R (64a b + 256a b + 320a b + 128a b )cosh(x) + 16a b + 32a b +--R + +--R 5 3 +--R 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 6 3 5 4 4 8 +--R (8a b + 16a b + 8a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 +--R (32a b + 128a b + 160a b + 64a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 4 +--R (48a b + 224a b + 432a b + 384a b + 128a b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 2 2 6 3 5 4 4 +--R (32a b + 128a b + 160a b + 64a b )cosh(x) + 8a b + 16a b + 8a b +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- a b - a \|a \|b + a +--R Type: Expression(Integer) +--E 484 + +--S 485 of 510 +--d0194b:= D(m0194b,x) +--E 485 + +--S 486 of 510 +t0195:= 1/(1+cosh(x)^2) +--R +--R +--R 1 +--R (286) ------------ +--R 2 +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 510 +r0195:= 1/2*atanh(1/2*2^(1/2)*tanh(x))*2^(1/2) +--R +--R +--R +-+ +--R +-+ \|2 tanh(x) +--R \|2 atanh(-----------) +--R 2 +--R (287) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 510 +a0195:= integrate(t0195,x) +--R +--R +--R (288) +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 510 +m0195:= a0195-r0195 +--R +--R +--R (289) +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ +--R \|2 tanh(x) +--R - 2atanh(-----------) +--R 2 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 510 +d0195:= D(m0195,x) +--R +--R +--R (290) +--R +-+ 4 +-+ 3 +--R (- 3\|2 + 4)sinh(x) + (16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 30\|2 + 40)cosh(x) - 12\|2 + 16)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((16\|2 - 24)cosh(x) + (16\|2 - 24)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 3\|2 + 4)cosh(x) + (- 12\|2 + 16)cosh(x) - 9\|2 + 12 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 3\|2 + 4)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((42\|2 - 56)cosh(x) - 6\|2 + 8)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 16\|2 + 24)cosh(x) + (16\|2 - 24)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 3\|2 + 4)cosh(x) + (- 6\|2 + 8)cosh(x) + 9\|2 - 12 +--R / +--R +-+ 4 +-+ 3 +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((18\|2 - 24)cosh(x) + 30\|2 - 40)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 16\|2 + 24)cosh(x) + (- 48\|2 + 72)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + (30\|2 - 40)cosh(x) + 9\|2 - 12 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 18\|2 + 24)sinh(x) + (32\|2 - 48)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 36\|2 + 48)cosh(x) - 60\|2 + 80)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((32\|2 - 48)cosh(x) + (96\|2 - 144)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 18\|2 + 24)cosh(x) + (- 60\|2 + 80)cosh(x) - 18\|2 + 24 +--R Type: Expression(Integer) +--E 490 + +--S 491 of 510 +t0196:= 1/(1+cosh(x)^2)^2 +--R +--R +--R 1 +--R (291) ------------------------ +--R 4 2 +--R cosh(x) + 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 510 +r0196:= 3/8*atanh(1/2*2^(1/2)*tanh(x))*2^(1/2)-tanh(x)/(8-4*tanh(x)^2) +--R +--R +--R +-+ +--R +-+ 2 +-+ \|2 tanh(x) +--R (3\|2 tanh(x) - 6\|2 )atanh(-----------) + 2tanh(x) +--R 2 +--R (292) ---------------------------------------------------- +--R 2 +--R 8tanh(x) - 16 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 510 +a0196:= integrate(t0196,x) +--R +--R +--R (293) +--R 4 3 2 2 +--R 3sinh(x) + 12cosh(x)sinh(x) + (18cosh(x) + 18)sinh(x) +--R + +--R 3 4 2 +--R (12cosh(x) + 36cosh(x))sinh(x) + 3cosh(x) + 18cosh(x) + 3 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R 12\|2 sinh(x) + 24\|2 cosh(x)sinh(x) + 12\|2 cosh(x) + 4\|2 +--R / +--R +-+ 4 +-+ 3 +-+ 2 +-+ 2 +--R 8\|2 sinh(x) + 32\|2 cosh(x)sinh(x) + (48\|2 cosh(x) + 48\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (32\|2 cosh(x) + 96\|2 cosh(x))sinh(x) + 8\|2 cosh(x) + 48\|2 cosh(x) +--R + +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 510 +m0196:= a0196-r0196 +--R +--R +--R (294) +--R 4 3 2 2 +--R 3sinh(x) + 12cosh(x)sinh(x) + (18cosh(x) + 18)sinh(x) +--R + +--R 3 4 2 +--R (12cosh(x) + 36cosh(x))sinh(x) + 3cosh(x) + 18cosh(x) + 3 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 6sinh(x) - 24cosh(x)sinh(x) + (- 36cosh(x) - 36)sinh(x) +--R + +--R 3 4 2 +--R (- 24cosh(x) - 72cosh(x))sinh(x) - 6cosh(x) - 36cosh(x) - 6 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R 4 3 2 2 +--R - 6sinh(x) - 24cosh(x)sinh(x) + (- 36cosh(x) - 36)sinh(x) +--R + +--R 3 4 2 +--R (- 24cosh(x) - 72cosh(x))sinh(x) - 6cosh(x) - 36cosh(x) - 6 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R 12sinh(x) + 48cosh(x)sinh(x) + (72cosh(x) + 72)sinh(x) +--R + +--R 3 4 2 +--R (48cosh(x) + 144cosh(x))sinh(x) + 12cosh(x) + 72cosh(x) + 12 +--R * +--R +-+ +--R \|2 tanh(x) +--R atanh(-----------) +--R 2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ 2 +--R (12\|2 sinh(x) + 24\|2 cosh(x)sinh(x) + 12\|2 cosh(x) + 4\|2 )tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 2\|2 sinh(x) - 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 12\|2 cosh(x) - 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 8\|2 cosh(x) - 24\|2 cosh(x))sinh(x) - 2\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 12\|2 cosh(x) - 2\|2 +--R * +--R tanh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R - 24\|2 sinh(x) - 48\|2 cosh(x)sinh(x) - 24\|2 cosh(x) - 8\|2 +--R / +--R +-+ 4 +-+ 3 +--R 8\|2 sinh(x) + 32\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (48\|2 cosh(x) + 48\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (32\|2 cosh(x) + 96\|2 cosh(x))sinh(x) + 8\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 48\|2 cosh(x) + 8\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 16\|2 sinh(x) - 64\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 96\|2 cosh(x) - 96\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 64\|2 cosh(x) - 192\|2 cosh(x))sinh(x) - 16\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 96\|2 cosh(x) - 16\|2 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 510 +d0196:= D(m0196,x) +--R +--R +--R (295) +--R +-+ 12 +-+ 11 +--R (- 9\|2 + 12)sinh(x) + (- 40\|2 + 48)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 50\|2 + 24)cosh(x) - 195\|2 + 260)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 8\|2 - 144)cosh(x) + (- 708\|2 + 856)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 103\|2 - 204)cosh(x) + (- 879\|2 + 628)cosh(x) - 972\|2 +--R + +--R 1296 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 464\|2 + 96)cosh(x) + (- 864\|2 - 352)cosh(x) +--R + +--R +-+ +--R (- 2968\|2 + 3600)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 700\|2 + 336)cosh(x) + (- 1998\|2 + 136)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 3808\|2 + 3360)cosh(x) - 1806\|2 + 2408 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 464\|2 + 96)cosh(x) + (- 3000\|2 + 1040)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 4072\|2 + 1776)cosh(x) + (- 4944\|2 + 6176)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 103\|2 - 204)cosh(x) + (- 1998\|2 + 136)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 4520\|2 + 1440)cosh(x) + (- 5562\|2 + 5912)cosh(x) +--R + +--R +-+ +--R - 1305\|2 + 1740 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 8\|2 - 144)cosh(x) + (- 864\|2 - 352)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 4072\|2 + 1776)cosh(x) + (- 4848\|2 + 4288)cosh(x) +--R + +--R +-+ +--R (- 3136\|2 + 4032)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 50\|2 + 24)cosh(x) + (- 879\|2 + 628)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 3808\|2 + 3360)cosh(x) + (- 5562\|2 + 5912)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 3798\|2 + 4776)cosh(x) - 303\|2 + 404 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 40\|2 + 48)cosh(x) + (- 708\|2 + 856)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 2968\|2 + 3600)cosh(x) + (- 4944\|2 + 6176)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 3136\|2 + 4032)cosh(x) + (- 492\|2 + 648)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 9\|2 + 12)cosh(x) + (- 195\|2 + 260)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 972\|2 + 1296)cosh(x) + (- 1806\|2 + 2408)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 1305\|2 + 1740)cosh(x) + (- 303\|2 + 404)cosh(x) - 18\|2 + 24 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 11 +--R (- 64\|2 + 96)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 368\|2 + 576)cosh(x) + 228\|2 - 304)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 704\|2 + 1248)cosh(x) + (240\|2 - 128)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 64\|2 + 768)cosh(x) + (- 1164\|2 + 2704)cosh(x) + 1044\|2 +--R + +--R - 1392 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (1792\|2 - 1344)cosh(x) + (- 384\|2 + 3584)cosh(x) +--R + +--R +-+ +--R (2208\|2 - 2304)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (2912\|2 - 2688)cosh(x) + (7080\|2 - 4448)cosh(x) +--R + +--R +-+ 2 +-+ +--R (3792\|2 - 2112)cosh(x) + 1800\|2 - 2400 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (1792\|2 - 1344)cosh(x) + (12576\|2 - 11008)cosh(x) +--R + +--R +-+ 3 +-+ +--R (12000\|2 - 9984)cosh(x) + (6144\|2 - 7872)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 64\|2 + 768)cosh(x) + (7080\|2 - 4448)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (18744\|2 - 17568)cosh(x) + (13272\|2 - 16800)cosh(x) +--R + +--R +-+ +--R 2376\|2 - 3168 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 704\|2 + 1248)cosh(x) + (- 384\|2 + 3584)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (12000\|2 - 9984)cosh(x) + (17856\|2 - 22656)cosh(x) +--R + +--R +-+ +--R (6560\|2 - 8544)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 368\|2 + 576)cosh(x) + (- 1164\|2 + 2704)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (3792\|2 - 2112)cosh(x) + (13272\|2 - 16800)cosh(x) +--R + +--R +-+ 2 +-+ +--R (8640\|2 - 11136)cosh(x) + 660\|2 - 880 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 64\|2 + 96)cosh(x) + (240\|2 - 128)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (2208\|2 - 2304)cosh(x) + (6144\|2 - 7872)cosh(x) +--R + +--R +-+ 3 +-+ +--R (6560\|2 - 8544)cosh(x) + (1296\|2 - 1728)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (228\|2 - 304)cosh(x) + (1044\|2 - 1392)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (1800\|2 - 2400)cosh(x) + (2376\|2 - 3168)cosh(x) +--R + +--R +-+ 2 +-+ +--R (660\|2 - 880)cosh(x) + 36\|2 - 48 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (18\|2 - 24)sinh(x) + (176\|2 - 240)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((652\|2 - 912)cosh(x) + 48\|2 - 64)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((1072\|2 - 1584)cosh(x) + (1056\|2 - 1520)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((302\|2 - 744)cosh(x) + (3504\|2 - 5312)cosh(x) + 378\|2 - 504) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 1760\|2 + 1824)cosh(x) + (2304\|2 - 4672)cosh(x) +--R + +--R +-+ +--R (2624\|2 - 3744)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 2968\|2 + 3360)cosh(x) + (- 6624\|2 + 6400)cosh(x) +--R + +--R +-+ 2 +-+ +--R (1928\|2 - 3552)cosh(x) + 912\|2 - 1216 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 1760\|2 + 1824)cosh(x) + (- 12864\|2 + 14432)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 9856\|2 + 11424)cosh(x) + (672\|2 - 544)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (302\|2 - 744)cosh(x) + (- 6624\|2 + 6400)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 19076\|2 + 23472)cosh(x) + (- 8784\|2 + 13376)cosh(x) +--R + +--R +-+ +--R - 954\|2 + 1272 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (1072\|2 - 1584)cosh(x) + (2304\|2 - 4672)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 9856\|2 + 11424)cosh(x) + (- 17088\|2 + 25408)cosh(x) +--R + +--R +-+ +--R (- 3568\|2 + 4752)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (652\|2 - 912)cosh(x) + (3504\|2 - 5312)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (1928\|2 - 3552)cosh(x) + (- 8784\|2 + 13376)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 5364\|2 + 7152)cosh(x) - 384\|2 + 512 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (176\|2 - 240)cosh(x) + (1056\|2 - 1520)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (2624\|2 - 3744)cosh(x) + (672\|2 - 544)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 3568\|2 + 4752)cosh(x) + (- 960\|2 + 1296)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R (18\|2 - 24)cosh(x) + (48\|2 - 64)cosh(x) + (378\|2 - 504)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (912\|2 - 1216)cosh(x) + (- 954\|2 + 1272)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 384\|2 + 512)cosh(x) - 18\|2 + 24 +--R / +--R +-+ 12 +-+ 11 +--R (18\|2 - 24)sinh(x) + (112\|2 - 144)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((284\|2 - 336)cosh(x) + 276\|2 - 368)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((368\|2 - 336)cosh(x) + (1296\|2 - 1648)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (238\|2 + 24)cosh(x) + (2340\|2 - 2608)cosh(x) + 1422\|2 +--R + +--R - 1896 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (32\|2 + 480)cosh(x) + (1920\|2 - 1088)cosh(x) +--R + +--R +-+ +--R (4832\|2 - 6048)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 56\|2 + 672)cosh(x) + (456\|2 + 1952)cosh(x) +--R + +--R +-+ 2 +-+ +--R (5720\|2 - 5664)cosh(x) + 2712\|2 - 3616 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (32\|2 + 480)cosh(x) + (- 288\|2 + 3424)cosh(x) +--R + +--R +-+ 3 +-+ +--R (2144\|2 + 1440)cosh(x) + (6816\|2 - 8416)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (238\|2 + 24)cosh(x) + (456\|2 + 1952)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 332\|2 + 5904)cosh(x) + (4488\|2 - 3424)cosh(x) + 1422\|2 +--R + +--R - 1896 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (368\|2 - 336)cosh(x) + (1920\|2 - 1088)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (2144\|2 + 1440)cosh(x) + (768\|2 + 2752)cosh(x) +--R + +--R +-+ +--R (2992\|2 - 3792)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (284\|2 - 336)cosh(x) + (2340\|2 - 2608)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (5720\|2 - 5664)cosh(x) + (4488\|2 - 3424)cosh(x) +--R + +--R +-+ 2 +-+ +--R (3276\|2 - 3984)cosh(x) + 276\|2 - 368 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (112\|2 - 144)cosh(x) + (1296\|2 - 1648)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (4832\|2 - 6048)cosh(x) + (6816\|2 - 8416)cosh(x) +--R + +--R +-+ 3 +-+ +--R (2992\|2 - 3792)cosh(x) + (336\|2 - 432)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (18\|2 - 24)cosh(x) + (276\|2 - 368)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (1422\|2 - 1896)cosh(x) + (2712\|2 - 3616)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (1422\|2 - 1896)cosh(x) + (276\|2 - 368)cosh(x) + 18\|2 - 24 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 72\|2 + 96)sinh(x) + (- 448\|2 + 576)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 1136\|2 + 1344)cosh(x) - 1104\|2 + 1472)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 1472\|2 + 1344)cosh(x) + (- 5184\|2 + 6592)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 952\|2 - 96)cosh(x) + (- 9360\|2 + 10432)cosh(x) +--R + +--R +-+ +--R - 5688\|2 + 7584 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 128\|2 - 1920)cosh(x) + (- 7680\|2 + 4352)cosh(x) +--R + +--R +-+ +--R (- 19328\|2 + 24192)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (224\|2 - 2688)cosh(x) + (- 1824\|2 - 7808)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 22880\|2 + 22656)cosh(x) - 10848\|2 + 14464 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 128\|2 - 1920)cosh(x) + (1152\|2 - 13696)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 8576\|2 - 5760)cosh(x) + (- 27264\|2 + 33664)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 952\|2 - 96)cosh(x) + (- 1824\|2 - 7808)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (1328\|2 - 23616)cosh(x) + (- 17952\|2 + 13696)cosh(x) +--R + +--R +-+ +--R - 5688\|2 + 7584 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 1472\|2 + 1344)cosh(x) + (- 7680\|2 + 4352)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 8576\|2 - 5760)cosh(x) + (- 3072\|2 - 11008)cosh(x) +--R + +--R +-+ +--R (- 11968\|2 + 15168)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 1136\|2 + 1344)cosh(x) + (- 9360\|2 + 10432)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 22880\|2 + 22656)cosh(x) + (- 17952\|2 + 13696)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 13104\|2 + 15936)cosh(x) - 1104\|2 + 1472 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 448\|2 + 576)cosh(x) + (- 5184\|2 + 6592)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 19328\|2 + 24192)cosh(x) + (- 27264\|2 + 33664)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 11968\|2 + 15168)cosh(x) + (- 1344\|2 + 1728)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 72\|2 + 96)cosh(x) + (- 1104\|2 + 1472)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 5688\|2 + 7584)cosh(x) + (- 10848\|2 + 14464)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 5688\|2 + 7584)cosh(x) + (- 1104\|2 + 1472)cosh(x) - 72\|2 + 96 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (72\|2 - 96)sinh(x) + (448\|2 - 576)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((1136\|2 - 1344)cosh(x) + 1104\|2 - 1472)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((1472\|2 - 1344)cosh(x) + (5184\|2 - 6592)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((952\|2 + 96)cosh(x) + (9360\|2 - 10432)cosh(x) + 5688\|2 - 7584) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (128\|2 + 1920)cosh(x) + (7680\|2 - 4352)cosh(x) +--R + +--R +-+ +--R (19328\|2 - 24192)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 224\|2 + 2688)cosh(x) + (1824\|2 + 7808)cosh(x) +--R + +--R +-+ 2 +-+ +--R (22880\|2 - 22656)cosh(x) + 10848\|2 - 14464 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (128\|2 + 1920)cosh(x) + (- 1152\|2 + 13696)cosh(x) +--R + +--R +-+ 3 +-+ +--R (8576\|2 + 5760)cosh(x) + (27264\|2 - 33664)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (952\|2 + 96)cosh(x) + (1824\|2 + 7808)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 1328\|2 + 23616)cosh(x) + (17952\|2 - 13696)cosh(x) + 5688\|2 +--R + +--R - 7584 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (1472\|2 - 1344)cosh(x) + (7680\|2 - 4352)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (8576\|2 + 5760)cosh(x) + (3072\|2 + 11008)cosh(x) +--R + +--R +-+ +--R (11968\|2 - 15168)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (1136\|2 - 1344)cosh(x) + (9360\|2 - 10432)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (22880\|2 - 22656)cosh(x) + (17952\|2 - 13696)cosh(x) +--R + +--R +-+ 2 +-+ +--R (13104\|2 - 15936)cosh(x) + 1104\|2 - 1472 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (448\|2 - 576)cosh(x) + (5184\|2 - 6592)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (19328\|2 - 24192)cosh(x) + (27264\|2 - 33664)cosh(x) +--R + +--R +-+ 3 +-+ +--R (11968\|2 - 15168)cosh(x) + (1344\|2 - 1728)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (72\|2 - 96)cosh(x) + (1104\|2 - 1472)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (5688\|2 - 7584)cosh(x) + (10848\|2 - 14464)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (5688\|2 - 7584)cosh(x) + (1104\|2 - 1472)cosh(x) + 72\|2 - 96 +--R Type: Expression(Integer) +--E 495 + +--S 496 of 510 +t0197:= 1/(1+cosh(x)^2)^3 +--R +--R +--R 1 +--R (296) ------------------------------------ +--R 6 4 2 +--R cosh(x) + 3cosh(x) + 3cosh(x) + 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 510 +r0197:= 19/64*atanh(1/2*2^(1/2)*tanh(x))*2^(1/2)-15/8*tanh(x)/(2-tanh(x)^2)^2+_ + tanh(x)^3/(2-tanh(x)^2)^2+19*tanh(x)/(64-32*tanh(x)^2) +--R +--R +--R (297) +--R +-+ +--R +-+ 4 +-+ 2 +-+ \|2 tanh(x) 3 +--R (19\|2 tanh(x) - 76\|2 tanh(x) + 76\|2 )atanh(-----------) + 26tanh(x) +--R 2 +--R + +--R - 44tanh(x) +--R / +--R 4 2 +--R 64tanh(x) - 256tanh(x) + 256 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 510 +a0197:= integrate(t0197,x) +--R +--R +--R (298) +--R 8 7 2 6 +--R 19sinh(x) + 152cosh(x)sinh(x) + (532cosh(x) + 228)sinh(x) +--R + +--R 3 5 +--R (1064cosh(x) + 1368cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1330cosh(x) + 3420cosh(x) + 722)sinh(x) +--R + +--R 5 3 3 +--R (1064cosh(x) + 4560cosh(x) + 2888cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (532cosh(x) + 3420cosh(x) + 4332cosh(x) + 228)sinh(x) +--R + +--R 7 5 3 +--R (152cosh(x) + 1368cosh(x) + 2888cosh(x) + 456cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 19cosh(x) + 228cosh(x) + 722cosh(x) + 228cosh(x) + 19 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ 6 +-+ 5 +--R 76\|2 sinh(x) + 456\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (1140\|2 cosh(x) + 684\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (1520\|2 cosh(x) + 2736\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (1140\|2 cosh(x) + 4104\|2 cosh(x) + 356\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (456\|2 cosh(x) + 2736\|2 cosh(x) + 712\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 76\|2 cosh(x) + 684\|2 cosh(x) + 356\|2 cosh(x) + 36\|2 +--R / +--R +-+ 8 +-+ 7 +--R 64\|2 sinh(x) + 512\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (1792\|2 cosh(x) + 768\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (3584\|2 cosh(x) + 4608\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (4480\|2 cosh(x) + 11520\|2 cosh(x) + 2432\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (3584\|2 cosh(x) + 15360\|2 cosh(x) + 9728\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (1792\|2 cosh(x) + 11520\|2 cosh(x) + 14592\|2 cosh(x) + 768\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 512\|2 cosh(x) + 4608\|2 cosh(x) + 9728\|2 cosh(x) +--R + +--R +-+ +--R 1536\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 64\|2 cosh(x) + 768\|2 cosh(x) + 2432\|2 cosh(x) + 768\|2 cosh(x) +--R + +--R +-+ +--R 64\|2 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 510 +m0197:= a0197-r0197 +--R +--R +--R (299) +--R 8 7 2 6 +--R 19sinh(x) + 152cosh(x)sinh(x) + (532cosh(x) + 228)sinh(x) +--R + +--R 3 5 +--R (1064cosh(x) + 1368cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1330cosh(x) + 3420cosh(x) + 722)sinh(x) +--R + +--R 5 3 3 +--R (1064cosh(x) + 4560cosh(x) + 2888cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (532cosh(x) + 3420cosh(x) + 4332cosh(x) + 228)sinh(x) +--R + +--R 7 5 3 +--R (152cosh(x) + 1368cosh(x) + 2888cosh(x) + 456cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 19cosh(x) + 228cosh(x) + 722cosh(x) + 228cosh(x) + 19 +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 +--R - 76sinh(x) - 608cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 2128cosh(x) - 912)sinh(x) +--R + +--R 3 5 +--R (- 4256cosh(x) - 5472cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 5320cosh(x) - 13680cosh(x) - 2888)sinh(x) +--R + +--R 5 3 3 +--R (- 4256cosh(x) - 18240cosh(x) - 11552cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 2128cosh(x) - 13680cosh(x) - 17328cosh(x) - 912)sinh(x) +--R + +--R 7 5 3 +--R (- 608cosh(x) - 5472cosh(x) - 11552cosh(x) - 1824cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - 76cosh(x) - 912cosh(x) - 2888cosh(x) - 912cosh(x) - 76 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 76sinh(x) + 608cosh(x)sinh(x) + (2128cosh(x) + 912)sinh(x) +--R + +--R 3 5 +--R (4256cosh(x) + 5472cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (5320cosh(x) + 13680cosh(x) + 2888)sinh(x) +--R + +--R 5 3 3 +--R (4256cosh(x) + 18240cosh(x) + 11552cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (2128cosh(x) + 13680cosh(x) + 17328cosh(x) + 912)sinh(x) +--R + +--R 7 5 3 +--R (608cosh(x) + 5472cosh(x) + 11552cosh(x) + 1824cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 76cosh(x) + 912cosh(x) + 2888cosh(x) + 912cosh(x) + 76 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R 8 7 +--R - 38sinh(x) - 304cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 1064cosh(x) - 456)sinh(x) +--R + +--R 3 5 +--R (- 2128cosh(x) - 2736cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 2660cosh(x) - 6840cosh(x) - 1444)sinh(x) +--R + +--R 5 3 3 +--R (- 2128cosh(x) - 9120cosh(x) - 5776cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 1064cosh(x) - 6840cosh(x) - 8664cosh(x) - 456)sinh(x) +--R + +--R 7 5 3 +--R (- 304cosh(x) - 2736cosh(x) - 5776cosh(x) - 912cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 38cosh(x) - 456cosh(x) - 1444cosh(x) - 456cosh(x) - 38 +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 152sinh(x) + 1216cosh(x)sinh(x) + (4256cosh(x) + 1824)sinh(x) +--R + +--R 3 5 +--R (8512cosh(x) + 10944cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (10640cosh(x) + 27360cosh(x) + 5776)sinh(x) +--R + +--R 5 3 3 +--R (8512cosh(x) + 36480cosh(x) + 23104cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (4256cosh(x) + 27360cosh(x) + 34656cosh(x) + 1824)sinh(x) +--R + +--R 7 5 3 +--R (1216cosh(x) + 10944cosh(x) + 23104cosh(x) + 3648cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R 152cosh(x) + 1824cosh(x) + 5776cosh(x) + 1824cosh(x) + 152 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 152sinh(x) - 1216cosh(x)sinh(x) + (- 4256cosh(x) - 1824)sinh(x) +--R + +--R 3 5 +--R (- 8512cosh(x) - 10944cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 10640cosh(x) - 27360cosh(x) - 5776)sinh(x) +--R + +--R 5 3 3 +--R (- 8512cosh(x) - 36480cosh(x) - 23104cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 4256cosh(x) - 27360cosh(x) - 34656cosh(x) - 1824)sinh(x) +--R + +--R 7 5 3 +--R (- 1216cosh(x) - 10944cosh(x) - 23104cosh(x) - 3648cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 152cosh(x) - 1824cosh(x) - 5776cosh(x) - 1824cosh(x) - 152 +--R * +--R +-+ +--R \|2 tanh(x) +--R atanh(-----------) +--R 2 +--R + +--R +-+ 6 +-+ 5 +--R 76\|2 sinh(x) + 456\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (1140\|2 cosh(x) + 684\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (1520\|2 cosh(x) + 2736\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (1140\|2 cosh(x) + 4104\|2 cosh(x) + 356\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (456\|2 cosh(x) + 2736\|2 cosh(x) + 712\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 76\|2 cosh(x) + 684\|2 cosh(x) + 356\|2 cosh(x) + 36\|2 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 26\|2 sinh(x) - 208\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 728\|2 cosh(x) - 312\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 1456\|2 cosh(x) - 1872\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 1820\|2 cosh(x) - 4680\|2 cosh(x) - 988\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 1456\|2 cosh(x) - 6240\|2 cosh(x) - 3952\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 728\|2 cosh(x) - 4680\|2 cosh(x) - 5928\|2 cosh(x) - 312\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 208\|2 cosh(x) - 1872\|2 cosh(x) - 3952\|2 cosh(x) +--R + +--R +-+ +--R - 624\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 26\|2 cosh(x) - 312\|2 cosh(x) - 988\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 312\|2 cosh(x) - 26\|2 +--R * +--R 3 +--R tanh(x) +--R + +--R +-+ 6 +-+ 5 +--R - 304\|2 sinh(x) - 1824\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (- 4560\|2 cosh(x) - 2736\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (- 6080\|2 cosh(x) - 10944\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 4560\|2 cosh(x) - 16416\|2 cosh(x) - 1424\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 1824\|2 cosh(x) - 10944\|2 cosh(x) - 2848\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 304\|2 cosh(x) - 2736\|2 cosh(x) - 1424\|2 cosh(x) - 144\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 44\|2 sinh(x) + 352\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (1232\|2 cosh(x) + 528\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (2464\|2 cosh(x) + 3168\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (3080\|2 cosh(x) + 7920\|2 cosh(x) + 1672\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (2464\|2 cosh(x) + 10560\|2 cosh(x) + 6688\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (1232\|2 cosh(x) + 7920\|2 cosh(x) + 10032\|2 cosh(x) + 528\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 352\|2 cosh(x) + 3168\|2 cosh(x) + 6688\|2 cosh(x) +--R + +--R +-+ +--R 1056\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 44\|2 cosh(x) + 528\|2 cosh(x) + 1672\|2 cosh(x) + 528\|2 cosh(x) +--R + +--R +-+ +--R 44\|2 +--R * +--R tanh(x) +--R + +--R +-+ 6 +-+ 5 +--R 304\|2 sinh(x) + 1824\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (4560\|2 cosh(x) + 2736\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (6080\|2 cosh(x) + 10944\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (4560\|2 cosh(x) + 16416\|2 cosh(x) + 1424\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (1824\|2 cosh(x) + 10944\|2 cosh(x) + 2848\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 304\|2 cosh(x) + 2736\|2 cosh(x) + 1424\|2 cosh(x) + 144\|2 +--R / +--R +-+ 8 +-+ 7 +--R 64\|2 sinh(x) + 512\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (1792\|2 cosh(x) + 768\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (3584\|2 cosh(x) + 4608\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (4480\|2 cosh(x) + 11520\|2 cosh(x) + 2432\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (3584\|2 cosh(x) + 15360\|2 cosh(x) + 9728\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 1792\|2 cosh(x) + 11520\|2 cosh(x) + 14592\|2 cosh(x) +--R + +--R +-+ +--R 768\|2 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 512\|2 cosh(x) + 4608\|2 cosh(x) + 9728\|2 cosh(x) +--R + +--R +-+ +--R 1536\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 64\|2 cosh(x) + 768\|2 cosh(x) + 2432\|2 cosh(x) + 768\|2 cosh(x) +--R + +--R +-+ +--R 64\|2 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 256\|2 sinh(x) - 2048\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 7168\|2 cosh(x) - 3072\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 14336\|2 cosh(x) - 18432\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 17920\|2 cosh(x) - 46080\|2 cosh(x) - 9728\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 14336\|2 cosh(x) - 61440\|2 cosh(x) - 38912\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 7168\|2 cosh(x) - 46080\|2 cosh(x) - 58368\|2 cosh(x) +--R + +--R +-+ +--R - 3072\|2 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 2048\|2 cosh(x) - 18432\|2 cosh(x) - 38912\|2 cosh(x) +--R + +--R +-+ +--R - 6144\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 256\|2 cosh(x) - 3072\|2 cosh(x) - 9728\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 3072\|2 cosh(x) - 256\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 256\|2 sinh(x) + 2048\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (7168\|2 cosh(x) + 3072\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (14336\|2 cosh(x) + 18432\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (17920\|2 cosh(x) + 46080\|2 cosh(x) + 9728\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (14336\|2 cosh(x) + 61440\|2 cosh(x) + 38912\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (7168\|2 cosh(x) + 46080\|2 cosh(x) + 58368\|2 cosh(x) + 3072\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 2048\|2 cosh(x) + 18432\|2 cosh(x) + 38912\|2 cosh(x) +--R + +--R +-+ +--R 6144\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 256\|2 cosh(x) + 3072\|2 cosh(x) + 9728\|2 cosh(x) + 3072\|2 cosh(x) +--R + +--R +-+ +--R 256\|2 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 510 +--d0197:= D(m0197,x) +--E 500 + +--S 501 of 510 +t0198:= (1+cosh(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (300) \|cosh(x) + 1 +--R Type: Expression(Integer) +--E 501 + +--S 502 of 510 +r0198:= -%i*2^(1/2)*EllipticE(%i*x,1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Integer)) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 502 + +--S 503 of 510 +--a0198:= integrate(t0198,x) +--E 503 + +--S 504 of 510 +--m0198:= a0198-r0198 +--E 504 + +--S 505 of 510 +d0198:= D(m0198,x) +--R +--R +--R (301) 0 +--R Type: Polynomial(Integer) +--E 505 + +--S 506 of 510 +t0199:= (-1-cosh(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (302) \|- cosh(x) - 1 +--R Type: Expression(Integer) +--E 506 + +--S 507 of 510 +r0199:= -%i*2^(1/2)*(-3-cosh(2*x))^(1/2)*_ + EllipticE(%i*x,1/2)/(3+cosh(2*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Integer)) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 507 + +--S 508 of 510 +a0199:= integrate(t0199,x) +--R +--R +--R (303) +--R +------------------------+ +--R x %I 2 | %I 4 %I 2 +--R x 2 x ++ (4(%e ) + 4)\|- (%e ) - 6(%e ) - 1 +--R (2(%e ) - 2%e ) | ----------------------------------------- d%I +--R ++ %I 6 %I 4 %I 2 +--R (%e ) + 6(%e ) + (%e ) +--R + +--R +----------------------+ +--R x | x 4 x 2 +--R (%e + 1)\|- (%e ) - 6(%e ) - 1 +--R / +--R x 2 x +--R 2(%e ) - 2%e +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 510 +--m0199:= a0199-r0199 +--E 509 + +--S 510 of 510 +--d0199:= D(m0199,x) +--E 510 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper100-199.input.pdf b/src/axiom-website/CATS/richhyper100-199.input.pdf new file mode 100644 index 0000000..2455a47 Binary files /dev/null and b/src/axiom-website/CATS/richhyper100-199.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper1000-1098.input.pamphlet b/src/axiom-website/CATS/richhyper1000-1098.input.pamphlet new file mode 100644 index 0000000..5e4c6ca --- /dev/null +++ b/src/axiom-website/CATS/richhyper1000-1098.input.pamphlet @@ -0,0 +1,48532 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper1000-1098.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper1000-1098.output +)spool richhyper1000-1098.output +)set message auto off +)clear all + + +--S 1 of 531 +t1000:= sech(6*x)*sinh(x) +--R +--R +--R (1) sech(6x)sinh(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 531 +r1000:= -1/12*2^(1/2)*(-2*atanh(2^(1/2)*cosh(x))+atanh(2*cosh(x)*_ + 2^(1/2)/(3^(1/2)-1))*3^(1/2)+atanh(2*cosh(x)*2^(1/2)/(3^(1/2)-1))+_ + atanh(2*cosh(x)*2^(1/2)/(1+3^(1/2)))*3^(1/2)-_ + atanh(2*cosh(x)*2^(1/2)/(1+3^(1/2)))) +--R +--R +--R (2) +--R +-+ +--R +-+ +-+ +-+ +-+ +-+ 2\|2 cosh(x) +--R 2\|2 atanh(\|2 cosh(x)) + (- \|2 \|3 - \|2 )atanh(------------) +--R +-+ +--R \|3 - 1 +--R + +--R +-+ +--R +-+ +-+ +-+ 2\|2 cosh(x) +--R (- \|2 \|3 + \|2 )atanh(------------) +--R +-+ +--R \|3 + 1 +--R / +--R 12 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 531 +a1000:= integrate(t1000,x) +--R +--R +--R (3) +--R +---------+ +--R | +-+ +--R +-+ |2\|3 + 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 + 3 2 +--R ((6\|3 - 12)sinh(x) + (6\|3 - 12)cosh(x)) |--------- + sinh(x) +--R | +-+ +--R \| 36\|3 +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R - +--R +---------+ +--R | +-+ +--R +-+ |2\|3 - 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 - 3 +--R ((6\|3 + 12)sinh(x) + (6\|3 + 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 2 +-+ 2 +-+ +--R \|2 sinh(x) + \|2 cosh(x) + 4cosh(x) + 2\|2 +--R log(----------------------------------------------) +--R 2 2 +--R sinh(x) + cosh(x) +--R + +--R +---------+ +--R | +-+ +--R +-+ |2\|3 - 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 - 3 +--R ((- 6\|3 - 12)sinh(x) + (- 6\|3 - 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R - +--R +---------+ +--R | +-+ +--R +-+ |2\|3 + 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 + 3 +--R ((- 6\|3 + 12)sinh(x) + (- 6\|3 + 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R / +--R +-+ +--R 6\|2 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 531 +m1000:= a1000-r1000 +--R +--R +--R (4) +--R +---------+ +--R | +-+ +--R +-+ |2\|3 + 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 + 3 2 +--R ((6\|3 - 12)sinh(x) + (6\|3 - 12)cosh(x)) |--------- + sinh(x) +--R | +-+ +--R \| 36\|3 +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R - +--R +---------+ +--R | +-+ +--R +-+ |2\|3 - 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 - 3 +--R ((6\|3 + 12)sinh(x) + (6\|3 + 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 2 +-+ 2 +-+ +--R \|2 sinh(x) + \|2 cosh(x) + 4cosh(x) + 2\|2 +--R log(----------------------------------------------) +--R 2 2 +--R sinh(x) + cosh(x) +--R + +--R +---------+ +--R | +-+ +--R +-+ |2\|3 - 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 - 3 +--R ((- 6\|3 - 12)sinh(x) + (- 6\|3 - 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R - +--R +---------+ +--R | +-+ +--R +-+ |2\|3 + 3 +--R 3\|2 |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R log +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 + 3 +--R ((- 6\|3 + 12)sinh(x) + (- 6\|3 + 12)cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +--R +-+ +-+ 2\|2 cosh(x) +--R - 2atanh(\|2 cosh(x)) + (\|3 + 1)atanh(------------) +--R +-+ +--R \|3 - 1 +--R + +--R +-+ +--R +-+ 2\|2 cosh(x) +--R (\|3 - 1)atanh(------------) +--R +-+ +--R \|3 + 1 +--R / +--R +-+ +--R 6\|2 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 531 +d1000:= D(m1000,x) +--R +--R +--R (5) +--R +-+ 13 +-+ 12 +--R - 3\|2 sinh(x) - 24\|2 cosh(x)sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (64\|2 cosh(x) - 96\|2 cosh(x) - 54\|2 cosh(x) - 12cosh(x) - 8\|2 ) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 2 +--R 480\|2 cosh(x) - 720\|2 cosh(x) + 54\|2 cosh(x) - 96cosh(x) +--R + +--R +-+ +--R - 63\|2 cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 3 +--R 1536\|2 cosh(x) - 2272\|2 cosh(x) + 435\|2 cosh(x) - 348cosh(x) +--R + +--R +-+ 2 +-+ +--R - 204\|2 cosh(x) + 2\|2 +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R 2592\|2 cosh(x) - 128cosh(x) - 3600\|2 cosh(x) + 192cosh(x) +--R + +--R +-+ 5 4 +-+ 3 2 +--R 498\|2 cosh(x) - 840cosh(x) - 303\|2 cosh(x) + 4cosh(x) +--R + +--R +-+ +--R 3\|2 cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 10 9 +-+ 8 7 +--R 2048\|2 cosh(x) - 768cosh(x) - 2048\|2 cosh(x) + 1024cosh(x) +--R + +--R +-+ 6 5 +-+ 4 3 +--R - 1036\|2 cosh(x) - 1416cosh(x) + 20\|2 cosh(x) - 48cosh(x) +--R + +--R +-+ 2 +-+ +--R - 44\|2 cosh(x) + 16cosh(x) + 8\|2 +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 11 10 +-+ 9 8 +--R - 448\|2 cosh(x) - 1792cosh(x) + 2720\|2 cosh(x) + 2048cosh(x) +--R + +--R +-+ 7 6 +-+ 5 4 +--R - 4204\|2 cosh(x) - 1392cosh(x) + 1022\|2 cosh(x) - 304cosh(x) +--R + +--R +-+ 3 2 +-+ +--R - 226\|2 cosh(x) + 68cosh(x) + 35\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 12 11 +-+ 10 +--R - 2688\|2 cosh(x) - 1792cosh(x) + 6784\|2 cosh(x) +--R + +--R 9 +-+ 8 7 +-+ 6 +--R 1280cosh(x) - 6661\|2 cosh(x) + 184cosh(x) + 2036\|2 cosh(x) +--R + +--R 5 +-+ 4 3 +-+ 2 +--R - 1120cosh(x) - 452\|2 cosh(x) + 272cosh(x) + 80\|2 cosh(x) +--R + +--R +-+ +--R - 8cosh(x) - 4\|2 +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 10 +--R - 2624\|2 cosh(x) + 6688\|2 cosh(x) - 1920cosh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R - 6300\|2 cosh(x) + 3008cosh(x) + 2126\|2 cosh(x) - 2424cosh(x) +--R + +--R +-+ 5 4 +-+ 3 2 +--R - 560\|2 cosh(x) + 660cosh(x) + 153\|2 cosh(x) - 28cosh(x) +--R + +--R +-+ +--R - 5\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 14 13 +-+ 12 +--R - 1088\|2 cosh(x) + 1792cosh(x) + 3680\|2 cosh(x) +--R + +--R 11 +-+ 10 9 +-+ 8 +--R - 4608cosh(x) - 3966\|2 cosh(x) + 4820cosh(x) + 1492\|2 cosh(x) +--R + +--R 7 +-+ 6 5 +-+ 4 +--R - 3184cosh(x) - 468\|2 cosh(x) + 1056cosh(x) + 204\|2 cosh(x) +--R + +--R 3 +-+ 2 +-+ +--R - 112cosh(x) - 30\|2 cosh(x) - 8cosh(x) - 5\|2 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 15 14 +-+ 13 12 +--R - 32\|2 cosh(x) + 1792cosh(x) + 1072\|2 cosh(x) - 4096cosh(x) +--R + +--R +-+ 11 10 +-+ 9 8 +--R - 1738\|2 cosh(x) + 4048cosh(x) + 961\|2 cosh(x) - 2512cosh(x) +--R + +--R +-+ 7 6 +-+ 5 4 +--R - 462\|2 cosh(x) + 860cosh(x) + 233\|2 cosh(x) - 104cosh(x) +--R + +--R +-+ 3 2 +-+ +--R - 42\|2 cosh(x) + 4cosh(x) + 2\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 16 15 +-+ 14 13 +--R 128\|2 cosh(x) + 768cosh(x) + 96\|2 cosh(x) - 1792cosh(x) +--R + +--R +-+ 12 11 +-+ 10 9 +--R - 491\|2 cosh(x) + 1892cosh(x) + 504\|2 cosh(x) - 1280cosh(x) +--R + +--R +-+ 8 7 +-+ 6 5 +--R - 478\|2 cosh(x) + 384cosh(x) + 340\|2 cosh(x) + 104cosh(x) +--R + +--R +-+ 4 3 +-+ 2 +--R - 98\|2 cosh(x) - 80cosh(x) - \|2 cosh(x) + 4cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 17 16 +-+ 15 14 +--R 32\|2 cosh(x) + 128cosh(x) - 16\|2 cosh(x) - 320cosh(x) +--R + +--R +-+ 13 12 +-+ 11 10 +--R - 62\|2 cosh(x) + 392cosh(x) + 97\|2 cosh(x) - 396cosh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R - 131\|2 cosh(x) + 268cosh(x) + 115\|2 cosh(x) - 76cosh(x) +--R + +--R +-+ 5 4 +-+ 3 +--R - 37\|2 cosh(x) + 4cosh(x) + 2\|2 cosh(x) +--R / +--R +-+ 6 +-+ 4 +-+ 2 +-+ 12 +--R (96\|2 cosh(x) - 144\|2 cosh(x) + 54\|2 cosh(x) - 3\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (768\|2 cosh(x) - 1152\|2 cosh(x) + 432\|2 cosh(x) - 24\|2 cosh(x)) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 8 7 +-+ 6 5 +--R 2880\|2 cosh(x) + 384cosh(x) - 4128\|2 cosh(x) - 576cosh(x) +--R + +--R +-+ 4 3 +-+ 2 +-+ +--R 1332\|2 cosh(x) + 216cosh(x) + 18\|2 cosh(x) - 12cosh(x) - 6\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R 6912\|2 cosh(x) + 3072cosh(x) - 8832\|2 cosh(x) - 4608cosh(x) +--R + +--R +-+ 5 4 +-+ 3 2 +--R 1584\|2 cosh(x) + 1728cosh(x) + 648\|2 cosh(x) - 96cosh(x) +--R + +--R +-+ +--R - 48\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 10 9 +-+ 8 +--R 12192\|2 cosh(x) + 11136cosh(x) - 12720\|2 cosh(x) +--R + +--R 7 +-+ 6 5 +-+ 4 +--R - 16704cosh(x) - 1590\|2 cosh(x) + 6264cosh(x) + 2895\|2 cosh(x) +--R + +--R 3 +-+ 2 +-+ +--R - 348cosh(x) - 228\|2 cosh(x) + 3\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 11 10 +-+ 9 +--R 16896\|2 cosh(x) + 24576cosh(x) - 13056\|2 cosh(x) +--R + +--R 8 +-+ 7 6 +-+ 5 +--R - 36864cosh(x) - 9312\|2 cosh(x) + 13824cosh(x) + 6960\|2 cosh(x) +--R + +--R 4 +-+ 3 +-+ +--R - 768cosh(x) - 600\|2 cosh(x) + 12\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 12 11 +-+ 10 +--R 18816\|2 cosh(x) + 37632cosh(x) - 9408\|2 cosh(x) +--R + +--R 9 +-+ 8 7 +--R - 56448cosh(x) - 18408\|2 cosh(x) + 20784cosh(x) +--R + +--R +-+ 6 5 +-+ 4 3 +--R 10956\|2 cosh(x) - 600cosh(x) - 732\|2 cosh(x) - 216cosh(x) +--R + +--R +-+ 2 +-+ +--R - 84\|2 cosh(x) + 12cosh(x) + 6\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 13 12 +-+ 11 +--R 16896\|2 cosh(x) + 43008cosh(x) - 3840\|2 cosh(x) +--R + +--R 10 +-+ 9 8 +--R - 64512cosh(x) - 23904\|2 cosh(x) + 22656cosh(x) +--R + +--R +-+ 7 6 +-+ 5 4 +--R 12528\|2 cosh(x) + 960cosh(x) - 168\|2 cosh(x) - 864cosh(x) +--R + +--R +-+ 3 2 +-+ +--R - 396\|2 cosh(x) + 48cosh(x) + 24\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 14 13 +-+ 12 +--R 12192\|2 cosh(x) + 37632cosh(x) + 528\|2 cosh(x) +--R + +--R 11 +-+ 10 9 +--R - 56448cosh(x) - 22710\|2 cosh(x) + 18480cosh(x) +--R + +--R +-+ 8 7 +-+ 6 5 +--R 10875\|2 cosh(x) + 2856cosh(x) + 768\|2 cosh(x) - 1512cosh(x) +--R + +--R +-+ 4 3 +-+ 2 +-+ +--R - 858\|2 cosh(x) + 84cosh(x) + 96\|2 cosh(x) - 3\|2 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 15 14 +-+ 13 +--R 6912\|2 cosh(x) + 24576cosh(x) + 1920\|2 cosh(x) +--R + +--R 12 +-+ 11 10 +--R - 36864cosh(x) - 15696\|2 cosh(x) + 10752cosh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R 6888\|2 cosh(x) + 3840cosh(x) + 1272\|2 cosh(x) - 1728cosh(x) +--R + +--R +-+ 5 4 +-+ 3 +--R - 828\|2 cosh(x) + 96cosh(x) + 48\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 16 15 +-+ 14 +--R 2880\|2 cosh(x) + 11136cosh(x) + 1248\|2 cosh(x) +--R + +--R 13 +-+ 12 11 +--R - 16704cosh(x) - 7500\|2 cosh(x) + 3576cosh(x) +--R + +--R +-+ 10 9 +-+ 8 7 +--R 2850\|2 cosh(x) + 3684cosh(x) + 1602\|2 cosh(x) - 1128cosh(x) +--R + +--R +-+ 6 5 +-+ 4 3 +--R - 828\|2 cosh(x) - 492cosh(x) - 138\|2 cosh(x) + 216cosh(x) +--R + +--R +-+ 2 +-+ +--R 102\|2 cosh(x) - 12cosh(x) - 6\|2 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 17 16 +-+ 15 14 +--R 768\|2 cosh(x) + 3072cosh(x) + 384\|2 cosh(x) - 4608cosh(x) +--R + +--R +-+ 13 12 +-+ 11 10 +--R - 2256\|2 cosh(x) + 192cosh(x) + 648\|2 cosh(x) + 2208cosh(x) +--R + +--R +-+ 9 8 +-+ 7 6 +--R 888\|2 cosh(x) - 864cosh(x) - 420\|2 cosh(x) + 48cosh(x) +--R + +--R +-+ 5 +--R 24\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 18 17 +-+ 16 15 +--R 96\|2 cosh(x) + 384cosh(x) + 48\|2 cosh(x) - 576cosh(x) +--R + +--R +-+ 14 13 +-+ 12 11 +--R - 330\|2 cosh(x) - 168cosh(x) + 57\|2 cosh(x) + 564cosh(x) +--R + +--R +-+ 10 9 +-+ 8 7 +--R 324\|2 cosh(x) + 168cosh(x) - 57\|2 cosh(x) - 564cosh(x) +--R + +--R +-+ 6 5 +-+ 4 3 +--R - 228\|2 cosh(x) + 216cosh(x) + 105\|2 cosh(x) - 12cosh(x) +--R + +--R +-+ 2 +--R - 6\|2 cosh(x) +--R Type: Expression(Integer) +--E 5 + +)clear all + + +--S 6 of 531 +t1001:= csch(2*x)*sinh(x) +--R +--R +--R (1) csch(2x)sinh(x) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 531 +r1001:= 1/2*atan(sinh(x)) +--R +--R +--R atan(sinh(x)) +--R (2) ------------- +--R 2 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 531 +a1001:= integrate(t1001,x) +--R +--R +--R (3) atan(sinh(x) + cosh(x)) +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 531 +m1001:= a1001-r1001 +--R +--R +--R 2atan(sinh(x) + cosh(x)) - atan(sinh(x)) +--R (4) ---------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 531 +d1001:= D(m1001,x) +--R +--R +--R (5) +--R 3 2 2 3 +--R 2sinh(x) + cosh(x)sinh(x) + (- 2cosh(x) + 2)sinh(x) - cosh(x) + cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 4cosh(x)sinh(x) + (2cosh(x) + 4)sinh(x) + 4cosh(x)sinh(x) +--R + +--R 2 +--R 2cosh(x) + 2 +--R Type: Expression(Integer) +--E 10 + +)clear all + + +--S 11 of 531 +t1002:= csch(3*x)*sinh(x) +--R +--R +--R (1) csch(3x)sinh(x) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 531 +r1002:= 1/3*atan(1/3*tanh(x)*3^(1/2))*3^(1/2) +--R +--R +--R +-+ +--R +-+ \|3 tanh(x) +--R \|3 atan(-----------) +--R 3 +--R (2) --------------------- +--R 3 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 531 +a1002:= integrate(t1002,x) +--R +--R +--R +-+ +-+ +--R \|3 sinh(x) + 3\|3 cosh(x) +--R atan(--------------------------) +--R 3sinh(x) - 3cosh(x) +--R (3) - -------------------------------- +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 531 +m1002:= a1002-r1002 +--R +--R +--R +-+ +-+ +-+ +--R \|3 tanh(x) \|3 sinh(x) + 3\|3 cosh(x) +--R - atan(-----------) - atan(--------------------------) +--R 3 3sinh(x) - 3cosh(x) +--R (4) ------------------------------------------------------ +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 531 +d1002:= D(m1002,x) +--R +--R +--R 2 2 2 +--R 4cosh(x) tanh(x) - 4sinh(x) +--R (5) ------------------------------------------------------ +--R 2 2 2 2 2 +--R (sinh(x) + 3cosh(x) )tanh(x) + 3sinh(x) + 9cosh(x) +--R Type: Expression(Integer) +--E 15 + +)clear all + + +--S 16 of 531 +t1003:= csch(4*x)*sinh(x) +--R +--R +--R (1) csch(4x)sinh(x) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 531 +r1003:= -1/4*atan(sinh(x))+1/4*atan(2^(1/2)*sinh(x))*2^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 atan(\|2 sinh(x)) - atan(sinh(x)) +--R (2) ------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 531 +a1003:= integrate(t1003,x) +--R +--R +--R (3) +--R +-+ +-+ +--R \|2 sinh(x) + \|2 cosh(x) +-+ +--R atan(-------------------------) - \|2 atan(sinh(x) + cosh(x)) +--R 2 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R - atan(-----------------------------------------) +--R +-+ +-+ +--R \|2 sinh(x) - \|2 cosh(x) +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 531 +m1003:= a1003-r1003 +--R +--R +--R (4) +--R +-+ +-+ +--R +-+ \|2 sinh(x) + \|2 cosh(x) +--R - 2atan(\|2 sinh(x)) + 2atan(-------------------------) +--R 2 +--R + +--R +-+ +-+ +--R - 2\|2 atan(sinh(x) + cosh(x)) + \|2 atan(sinh(x)) +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R - 2atan(-----------------------------------------) +--R +-+ +-+ +--R \|2 sinh(x) - \|2 cosh(x) +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 531 +d1003:= D(m1003,x) +--R +--R +--R (5) +--R 11 10 2 9 +--R - 12sinh(x) - 60cosh(x)sinh(x) + (- 108cosh(x) - 62)sinh(x) +--R + +--R 3 8 +--R (- 60cosh(x) - 231cosh(x))sinh(x) +--R + +--R 4 2 7 +--R (60cosh(x) - 290cosh(x) - 124)sinh(x) +--R + +--R 5 3 6 +--R (108cosh(x) - 78cosh(x) - 299cosh(x))sinh(x) +--R + +--R 6 4 2 5 +--R (60cosh(x) + 134cosh(x) - 248cosh(x) - 112)sinh(x) +--R + +--R 7 5 3 4 +--R (12cosh(x) + 128cosh(x) - 23cosh(x) - 159cosh(x))sinh(x) +--R + +--R 6 4 2 3 +--R (34cosh(x) + 88cosh(x) - 66cosh(x) - 44)sinh(x) +--R + +--R 7 5 3 2 +--R (- 10cosh(x) + 35cosh(x) + 8cosh(x) - 31cosh(x))sinh(x) +--R + +--R 8 6 4 2 9 +--R (- 8cosh(x) - 4cosh(x) + 14cosh(x) + 4cosh(x) - 6)sinh(x) - cosh(x) +--R + +--R 7 5 3 +--R - cosh(x) + 3cosh(x) - cosh(x) +--R / +--R 12 11 2 10 +--R 8sinh(x) + 64cosh(x)sinh(x) + (224cosh(x) + 68)sinh(x) +--R + +--R 3 9 +--R (448cosh(x) + 368cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (560cosh(x) + 920cosh(x) + 208)sinh(x) +--R + +--R 5 3 7 +--R (448cosh(x) + 1408cosh(x) + 728cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (224cosh(x) + 1424cosh(x) + 1324cosh(x) + 296)sinh(x) +--R + +--R 7 5 3 5 +--R (64cosh(x) + 944cosh(x) + 1616cosh(x) + 616cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (8cosh(x) + 392cosh(x) + 1276cosh(x) + 884cosh(x) + 208)sinh(x) +--R + +--R 7 5 3 3 +--R (96cosh(x) + 632cosh(x) + 800cosh(x) + 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (12cosh(x) + 196cosh(x) + 472cosh(x) + 300cosh(x) + 68)sinh(x) +--R + +--R 7 5 3 8 +--R (32cosh(x) + 136cosh(x) + 144cosh(x) + 24cosh(x))sinh(x) + 4cosh(x) +--R + +--R 6 4 2 +--R 28cosh(x) + 60cosh(x) + 44cosh(x) + 8 +--R Type: Expression(Integer) +--E 20 + +)clear all + + +--S 21 of 531 +t1004:= csch(5*x)*sinh(x) +--R +--R +--R (1) csch(5x)sinh(x) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 531 +r1004:= -1/10*(10+2*5^(1/2))^(1/2)*atan(1/5*(25-10*5^(1/2))^(1/2)*tanh(x))+_ + 1/10*(10-2*5^(1/2))^(1/2)*atan(1/5*(25+10*5^(1/2))^(1/2)*tanh(x)) +--R +--R +--R (2) +--R +-----------+ +--R +------------+ | +-+ +--R | +-+ tanh(x)\|10\|5 + 25 +--R \|- 2\|5 + 10 atan(---------------------) +--R 5 +--R + +--R +-------------+ +--R +----------+ | +-+ +--R | +-+ tanh(x)\|- 10\|5 + 25 +--R - \|2\|5 + 10 atan(-----------------------) +--R 5 +--R / +--R 10 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 531 +a1004:= integrate(t1004,x) +--R +--R +--R (3) +--R - +--R +--------+ +--R | +-+ +--R |\|5 + 1 +--R |-------- +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 1 +--R (5\|5 - 25) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(--------------------------------------------------------------) +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|5 sinh(x) + 8\|5 cosh(x)sinh(x) + 4\|5 cosh(x) + \|5 + 5 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 - 1 +--R |-------- +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 1 +--R (5\|5 + 25) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(--------------------------------------------------------------) +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|5 sinh(x) + 8\|5 cosh(x)sinh(x) + 4\|5 cosh(x) + \|5 - 5 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 531 +m1004:= a1004-r1004 +--R +--R +--R (4) +--R +-----------+ +--R +------------+ | +-+ +--R | +-+ tanh(x)\|10\|5 + 25 +--R - \|- 2\|5 + 10 atan(---------------------) +--R 5 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 + 1 +--R 10 |-------- +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 1 +--R (5\|5 - 25) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(--------------------------------------------------------------) +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|5 sinh(x) + 8\|5 cosh(x)sinh(x) + 4\|5 cosh(x) + \|5 + 5 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|5 - 1 +--R 10 |-------- +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 1 +--R (5\|5 + 25) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(--------------------------------------------------------------) +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|5 sinh(x) + 8\|5 cosh(x)sinh(x) + 4\|5 cosh(x) + \|5 - 5 +--R + +--R +-------------+ +--R +----------+ | +-+ +--R | +-+ tanh(x)\|- 10\|5 + 25 +--R \|2\|5 + 10 atan(-----------------------) +--R 5 +--R / +--R 10 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 531 +d1004:= D(m1004,x) +--R +--R +--R (5) +--R +-+ 8 +-+ 7 +--R (- 2\|5 + 5)sinh(x) + (- 16\|5 + 40)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R ((- 56\|5 + 140)cosh(x) - 2\|5 + 5)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((- 112\|5 + 280)cosh(x) + (- 12\|5 + 30)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 140\|5 + 350)cosh(x) + (- 30\|5 + 75)cosh(x) - 2\|5 +--R + +--R 5 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 112\|5 + 280)cosh(x) + (- 40\|5 + 100)cosh(x) +--R + +--R +-+ +--R (- 8\|5 + 20)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 56\|5 + 140)cosh(x) + (- 30\|5 + 75)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 12\|5 + 30)cosh(x) - 2\|5 + 5 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 16\|5 + 40)cosh(x) + (- 12\|5 + 30)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 8\|5 + 20)cosh(x) + (- 4\|5 + 10)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 2\|5 + 5)cosh(x) + (- 2\|5 + 5)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 2\|5 + 5)cosh(x) + (- 2\|5 + 5)cosh(x) - 2\|5 + 5 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 2\|5 sinh(x) + 16\|5 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (56\|5 cosh(x) + 2\|5 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (112\|5 cosh(x) + 12\|5 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (140\|5 cosh(x) + 30\|5 cosh(x) + 2\|5 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (112\|5 cosh(x) + 40\|5 cosh(x) + 8\|5 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (56\|5 cosh(x) + 30\|5 cosh(x) + 12\|5 cosh(x) + 2\|5 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 16\|5 cosh(x) + 12\|5 cosh(x) + 8\|5 cosh(x) +--R + +--R +-+ +--R 4\|5 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 2\|5 cosh(x) + 2\|5 cosh(x) + 2\|5 cosh(x) + 2\|5 cosh(x) +--R + +--R +-+ +--R 2\|5 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 5sinh(x) - 40cosh(x)sinh(x) + (- 140cosh(x) - 5)sinh(x) +--R + +--R 3 5 +--R (- 280cosh(x) - 30cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 350cosh(x) - 75cosh(x) - 5)sinh(x) +--R + +--R 5 3 3 +--R (- 280cosh(x) - 100cosh(x) - 20cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 140cosh(x) - 75cosh(x) - 30cosh(x) - 5)sinh(x) +--R + +--R 7 5 3 +--R (- 40cosh(x) - 30cosh(x) - 20cosh(x) - 10cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 5cosh(x) - 5cosh(x) - 5cosh(x) - 5cosh(x) - 5 +--R * +--R +------------+ +-----------+ +--R | +-+ | +-+ +--R \|- 2\|5 + 10 \|10\|5 + 25 +--R + +--R +-+ 8 +-+ 7 +--R (- 2\|5 - 5)sinh(x) + (- 16\|5 - 40)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R ((- 56\|5 - 140)cosh(x) - 2\|5 - 5)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((- 112\|5 - 280)cosh(x) + (- 12\|5 - 30)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 140\|5 - 350)cosh(x) + (- 30\|5 - 75)cosh(x) - 2\|5 +--R + +--R - 5 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 112\|5 - 280)cosh(x) + (- 40\|5 - 100)cosh(x) +--R + +--R +-+ +--R (- 8\|5 - 20)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 56\|5 - 140)cosh(x) + (- 30\|5 - 75)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 12\|5 - 30)cosh(x) - 2\|5 - 5 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 16\|5 - 40)cosh(x) + (- 12\|5 - 30)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 8\|5 - 20)cosh(x) + (- 4\|5 - 10)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 2\|5 - 5)cosh(x) + (- 2\|5 - 5)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 2\|5 - 5)cosh(x) + (- 2\|5 - 5)cosh(x) - 2\|5 - 5 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 2\|5 sinh(x) + 16\|5 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (56\|5 cosh(x) + 2\|5 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (112\|5 cosh(x) + 12\|5 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (140\|5 cosh(x) + 30\|5 cosh(x) + 2\|5 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (112\|5 cosh(x) + 40\|5 cosh(x) + 8\|5 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (56\|5 cosh(x) + 30\|5 cosh(x) + 12\|5 cosh(x) + 2\|5 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 16\|5 cosh(x) + 12\|5 cosh(x) + 8\|5 cosh(x) +--R + +--R +-+ +--R 4\|5 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 2\|5 cosh(x) + 2\|5 cosh(x) + 2\|5 cosh(x) + 2\|5 cosh(x) +--R + +--R +-+ +--R 2\|5 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 5sinh(x) + 40cosh(x)sinh(x) + (140cosh(x) + 5)sinh(x) +--R + +--R 3 5 +--R (280cosh(x) + 30cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (350cosh(x) + 75cosh(x) + 5)sinh(x) +--R + +--R 5 3 3 +--R (280cosh(x) + 100cosh(x) + 20cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (140cosh(x) + 75cosh(x) + 30cosh(x) + 5)sinh(x) +--R + +--R 7 5 3 8 +--R (40cosh(x) + 30cosh(x) + 20cosh(x) + 10cosh(x))sinh(x) + 5cosh(x) +--R + +--R 6 4 2 +--R 5cosh(x) + 5cosh(x) + 5cosh(x) + 5 +--R * +--R +-------------+ +----------+ +--R | +-+ | +-+ +--R \|- 10\|5 + 25 \|2\|5 + 10 +--R + +--R 4 3 2 2 +--R 50sinh(x) + 200cosh(x)sinh(x) + 300cosh(x) sinh(x) +--R + +--R 3 4 +--R 200cosh(x) sinh(x) + 50cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 4 3 2 2 +--R 500sinh(x) + 2000cosh(x)sinh(x) + 3000cosh(x) sinh(x) +--R + +--R 3 4 +--R 2000cosh(x) sinh(x) + 500cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R 250sinh(x) + 1000cosh(x)sinh(x) + 1500cosh(x) sinh(x) +--R + +--R 3 4 +--R 1000cosh(x) sinh(x) + 250cosh(x) +--R / +--R 8 7 2 6 +--R 50sinh(x) + 400cosh(x)sinh(x) + (1400cosh(x) + 50)sinh(x) +--R + +--R 3 5 +--R (2800cosh(x) + 300cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (3500cosh(x) + 750cosh(x) + 50)sinh(x) +--R + +--R 5 3 3 +--R (2800cosh(x) + 1000cosh(x) + 200cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (1400cosh(x) + 750cosh(x) + 300cosh(x) + 50)sinh(x) +--R + +--R 7 5 3 +--R (400cosh(x) + 300cosh(x) + 200cosh(x) + 100cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 50cosh(x) + 50cosh(x) + 50cosh(x) + 50cosh(x) + 50 +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 500sinh(x) + 4000cosh(x)sinh(x) + (14000cosh(x) + 500)sinh(x) +--R + +--R 3 5 +--R (28000cosh(x) + 3000cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (35000cosh(x) + 7500cosh(x) + 500)sinh(x) +--R + +--R 5 3 3 +--R (28000cosh(x) + 10000cosh(x) + 2000cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (14000cosh(x) + 7500cosh(x) + 3000cosh(x) + 500)sinh(x) +--R + +--R 7 5 3 +--R (4000cosh(x) + 3000cosh(x) + 2000cosh(x) + 1000cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 500cosh(x) + 500cosh(x) + 500cosh(x) + 500cosh(x) + 500 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 250sinh(x) + 2000cosh(x)sinh(x) + (7000cosh(x) + 250)sinh(x) +--R + +--R 3 5 +--R (14000cosh(x) + 1500cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (17500cosh(x) + 3750cosh(x) + 250)sinh(x) +--R + +--R 5 3 3 +--R (14000cosh(x) + 5000cosh(x) + 1000cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (7000cosh(x) + 3750cosh(x) + 1500cosh(x) + 250)sinh(x) +--R + +--R 7 5 3 +--R (2000cosh(x) + 1500cosh(x) + 1000cosh(x) + 500cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 250cosh(x) + 250cosh(x) + 250cosh(x) + 250cosh(x) + 250 +--R Type: Expression(Integer) +--E 25 + +)clear all + + +--S 26 of 531 +t1005:= csch(6*x)*sinh(x) +--R +--R +--R (1) csch(6x)sinh(x) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 531 +r1005:= 1/6*atan(sinh(x))+1/6*atan(2*sinh(x))-_ + 1/6*atan(2/3*sinh(x)*3^(1/2))*3^(1/2) +--R +--R +--R +-+ +--R +-+ 2\|3 sinh(x) +--R - \|3 atan(------------) + atan(2sinh(x)) + atan(sinh(x)) +--R 3 +--R (2) --------------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 531 +a1005:= integrate(t1005,x) +--R +--R +--R (3) +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R - 3atan(-------------------------) +--R 3 +--R + +--R 2 2 +--R +-+ sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R - \|3 atan(-------------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +-+ +--R 3\|3 atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 2 +--R 3atan(-----------------------------------------) +--R +-+ +-+ +--R \|3 sinh(x) - \|3 cosh(x) +--R / +--R +-+ +--R 6\|3 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 531 +m1005:= a1005-r1005 +--R +--R +--R (4) +--R +-+ +-+ +-+ +--R 2\|3 sinh(x) \|3 sinh(x) + \|3 cosh(x) +--R 3atan(------------) - 3atan(-------------------------) +--R 3 3 +--R + +--R 2 2 +--R +-+ +-+ sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R - \|3 atan(2sinh(x)) - \|3 atan(-------------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +-+ +-+ +--R 3\|3 atan(sinh(x) + cosh(x)) - \|3 atan(sinh(x)) +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 2 +--R 3atan(-----------------------------------------) +--R +-+ +-+ +--R \|3 sinh(x) - \|3 cosh(x) +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 531 +d1005:= D(m1005,x) +--R +--R +--R (5) +--R 17 16 2 15 +--R 32sinh(x) + 288cosh(x)sinh(x) + (1120cosh(x) + 192)sinh(x) +--R + +--R 3 14 +--R (2400cosh(x) + 1536cosh(x))sinh(x) +--R + +--R 4 2 13 +--R (2880cosh(x) + 5312cosh(x) + 486)sinh(x) +--R + +--R 5 3 12 +--R (1344cosh(x) + 10176cosh(x) + 3093cosh(x))sinh(x) +--R + +--R 6 4 2 11 +--R (- 1344cosh(x) + 11136cosh(x) + 9318cosh(x) + 670)sinh(x) +--R + +--R 7 5 3 10 +--R (- 2880cosh(x) + 5376cosh(x) + 16800cosh(x) + 2142cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 2400cosh(x) - 2688cosh(x) + 18368cosh(x) + 7722cosh(x) + 540) +--R * +--R 9 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 1120cosh(x) - 6528cosh(x) + 10253cosh(x) + 15126cosh(x) +--R + +--R - 894cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 288cosh(x) - 5184cosh(x) - 660cosh(x) + 16428cosh(x) +--R + +--R 2 +--R 3380cosh(x) + 252 +--R * +--R 7 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 32cosh(x) - 2304cosh(x) - 5560cosh(x) + 9948cosh(x) +--R + +--R 3 +--R 8748cosh(x) - 1968cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 576cosh(x) - 4410cosh(x) + 1300cosh(x) + 8372cosh(x) +--R + +--R 2 +--R 1148cosh(x) + 62 +--R * +--R 5 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 64cosh(x) - 1953cosh(x) - 2436cosh(x) + 4712cosh(x) +--R + +--R 3 +--R 3268cosh(x) - 903cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 562cosh(x) - 1898cosh(x) + 844cosh(x) + 2324cosh(x) +--R + +--R 2 +--R 454cosh(x) + 6 +--R * +--R 3 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 104cosh(x) - 698cosh(x) - 476cosh(x) + 1016cosh(x) +--R + +--R 3 +--R 604cosh(x) - 126cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 12cosh(x) - 158cosh(x) - 336cosh(x) + 116cosh(x) +--R + +--R 4 2 +--R 300cosh(x) + 90cosh(x) +--R * +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R - cosh(x) - 18cosh(x) - 58cosh(x) - 12cosh(x) + 59cosh(x) +--R + +--R 3 +--R 30cosh(x) +--R / +--R 18 17 2 16 +--R 32sinh(x) + 384cosh(x)sinh(x) + (2112cosh(x) + 448)sinh(x) +--R + +--R 3 15 +--R (7040cosh(x) + 4096cosh(x))sinh(x) +--R + +--R 4 2 14 +--R (15840cosh(x) + 17408cosh(x) + 2278)sinh(x) +--R + +--R 5 3 13 +--R (25344cosh(x) + 45824cosh(x) + 15560cosh(x))sinh(x) +--R + +--R 6 4 2 12 +--R (29568cosh(x) + 83648cosh(x) + 51660cosh(x) + 5710)sinh(x) +--R + +--R 7 5 3 11 +--R (25344cosh(x) + 111616cosh(x) + 110504cosh(x) + 27576cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 15840cosh(x) + 111104cosh(x) + 168442cosh(x) + 73652cosh(x) +--R + +--R 7996 +--R * +--R 10 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 7040cosh(x) + 82432cosh(x) + 190608cosh(x) + 131688cosh(x) +--R + +--R 24352cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 2112cosh(x) + 44864cosh(x) + 161832cosh(x) + 168106cosh(x) +--R + +--R 2 +--R 55832cosh(x) + 6532 +--R * +--R 8 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 384cosh(x) + 17408cosh(x) + 102032cosh(x) + 161072cosh(x) +--R + +--R 3 +--R 82960cosh(x) + 9488cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 32cosh(x) + 4608cosh(x) + 46650cosh(x) + 115128cosh(x) +--R + +--R 4 2 +--R 89640cosh(x) + 23424cosh(x) + 3062 +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 768cosh(x) + 15016cosh(x) + 59344cosh(x) + 70640cosh(x) +--R + +--R 3 +--R 26256cosh(x) + 168cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 64cosh(x) + 3276cosh(x) + 21570cosh(x) + 41408cosh(x) +--R + +--R 4 2 +--R 25992cosh(x) + 5684cosh(x) + 750 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 456cosh(x) + 5272cosh(x) + 15984cosh(x) + 15152cosh(x) +--R + +--R 3 +--R 3336cosh(x) - 840cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 38cosh(x) + 852cosh(x) + 4220cosh(x) + 7008cosh(x) +--R + +--R 4 2 +--R 4118cosh(x) + 876cosh(x) + 72 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R 72cosh(x) + 624cosh(x) + 1584cosh(x) + 1248cosh(x) + 72cosh(x) +--R + +--R - 144cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 6cosh(x) + 72cosh(x) + 276cosh(x) + 432cosh(x) + 294cosh(x) +--R + +--R 2 +--R 72cosh(x) +--R Type: Expression(Integer) +--E 30 + +)clear all + + +--S 31 of 531 +t1006:= x*cosh(2*x)*sech(x)^2 +--R +--R +--R 2 +--R (1) x cosh(2x)sech(x) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 531 +r1006:= x^2+log(cosh(x))-x*tanh(x) +--R +--R +--R 2 +--R (2) log(cosh(x)) - x tanh(x) + x +--R Type: Expression(Integer) +--E 32 + +--S 33 of 531 +a1006:= integrate(t1006,x) +--R +--R +--R (3) +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (x - 2x)sinh(x) + (2x - 4x)cosh(x)sinh(x) + (x - 2x)cosh(x) + x +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 531 +m1006:= a1006-r1006 +--R +--R +--R (4) +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)log(cosh(x)) +--R + +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 +--R (x sinh(x) + 2x cosh(x)sinh(x) + x cosh(x) + x)tanh(x) - 2x sinh(x) +--R + +--R 2 +--R - 4x cosh(x)sinh(x) - 2x cosh(x) +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 531 +d1006:= D(m1006,x) +--R +--R +--R (5) +--R 4 3 2 2 +--R - x sinh(x) - 4x cosh(x)sinh(x) + (- 6x cosh(x) - 2x)sinh(x) +--R + +--R 3 4 2 +--R (- 4x cosh(x) - 4x cosh(x))sinh(x) - x cosh(x) - 2x cosh(x) - x +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 4 3 +--R (x - 1)sinh(x) + (4x - 4)cosh(x)sinh(x) +--R + +--R 2 2 3 +--R ((6x - 6)cosh(x) - 2x)sinh(x) + ((4x - 4)cosh(x) - 4x cosh(x))sinh(x) +--R + +--R 4 2 +--R (x - 1)cosh(x) - 2x cosh(x) + x + 1 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 35 + +)clear all + + +--S 36 of 531 +t1007:= x*cosh(2*x)*sech(x)^3 +--R +--R +--R 3 +--R (1) x cosh(2x)sech(x) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 531 +r1007:= 3*x*atan(exp(x))-3/2*%i*polylog(2,-%i*exp(x))+_ + 3/2*%i*polylog(2,%i*exp(x))-1/2*sech(x)-1/2*x*sech(x)*tanh(x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 531 +a1007:= integrate(t1007,x) +--R +--R +--R x +--R ++ 3 +--I (2) | %U cosh(2%U)sech(%U) d%U +--R ++ +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 531 +--m1007:= a1007-r1007 +--E 39 + +--S 40 of 531 +--d1007:= D(m1007,x) +--E 40 + +)clear all + + +--S 41 of 531 +t1008:= sinh(a+b*x)^(1/2)/cosh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R \|sinh(b x + a) +--R (1) ---------------- +--R +-------------+ +--R \|cosh(b x + a) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 531 +r1008:= -(atan(sinh(a+b*x)^(1/2)/cosh(a+b*x)^(1/2))-_ + atanh(sinh(a+b*x)^(1/2)/cosh(a+b*x)^(1/2)))/b +--R +--R +--R +-------------+ +-------------+ +--R \|sinh(b x + a) \|sinh(b x + a) +--R atanh(----------------) - atan(----------------) +--R +-------------+ +-------------+ +--R \|cosh(b x + a) \|cosh(b x + a) +--R (2) ------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 42 + +--S 43 of 531 +a1008:= integrate(t1008,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 43 + +--S 44 of 531 +--m1008:= a1008-r1008 +--E 44 + +--S 45 of 531 +--d1008:= D(m1008,x) +--E 45 + +)clear all + + +--S 46 of 531 +t1009:= cosh(a+b*x)^(1/2)/sinh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R \|cosh(b x + a) +--R (1) ---------------- +--R +-------------+ +--R \|sinh(b x + a) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 531 +r1009:= -(atan(cosh(a+b*x)^(1/2)/sinh(a+b*x)^(1/2))-_ + atanh(cosh(a+b*x)^(1/2)/sinh(a+b*x)^(1/2)))/b +--R +--R +--R +-------------+ +-------------+ +--R \|cosh(b x + a) \|cosh(b x + a) +--R atanh(----------------) - atan(----------------) +--R +-------------+ +-------------+ +--R \|sinh(b x + a) \|sinh(b x + a) +--R (2) ------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 47 + +--S 48 of 531 +a1009:= integrate(t1009,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 48 + +--S 49 of 531 +--m1009:= a1009-r1009 +--E 49 + +--S 50 of 531 +--d1009:= D(m1009,x) +--E 50 + +)clear all + + +--S 51 of 531 +t1010:= sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3) +--R +--R +--R 3+-------------+ +--R \|sinh(b x + a) +--R (1) ---------------- +--R 3+-------------+ +--R \|cosh(b x + a) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 531 +r1010:= -1/2*3^(1/2)*atan(1/3*(1+2*sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))*_ + 3^(1/2))/b-1/2*log(1-sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/b+1/4*_ + log(1+sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3)+_ + sinh(a+b*x)^(4/3)/cosh(a+b*x)^(4/3))/b +--R +--R +--R (2) +--R log +--R 3+-------------+2 +--R cosh(b x + a)\|sinh(b x + a) +--R + +--R 3+-------------+3+-------------+ +--R sinh(b x + a)\|cosh(b x + a) \|sinh(b x + a) +--R + +--R 3+-------------+2 +--R cosh(b x + a)\|cosh(b x + a) +--R / +--R 3+-------------+2 +--R cosh(b x + a)\|cosh(b x + a) +--R + +--R 3+-------------+2 3+-------------+2 +--R - \|sinh(b x + a) + \|cosh(b x + a) +--R - 2log(---------------------------------------) +--R 3+-------------+2 +--R \|cosh(b x + a) +--R + +--R +-+3+-------------+2 +-+3+-------------+2 +--R +-+ 2\|3 \|sinh(b x + a) + \|3 \|cosh(b x + a) +--R - 2\|3 atan(----------------------------------------------) +--R 3+-------------+2 +--R 3\|cosh(b x + a) +--R / +--R 4b +--R Type: Expression(Integer) +--E 52 + +--S 53 of 531 +a1010:= integrate(t1010,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 53 + +--S 54 of 531 +--m1010:= a1010-r1010 +--E 54 + +--S 55 of 531 +--d1010:= D(m1010,x) +--E 55 + +)clear all + + +--S 56 of 531 +t1011:= cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3) +--R +--R +--R 3+-------------+ +--R \|cosh(b x + a) +--R (1) ---------------- +--R 3+-------------+ +--R \|sinh(b x + a) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 531 +r1011:= -1/2*3^(1/2)*atan(1/3*(1+2*cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))*_ + 3^(1/2))/b-1/2*log(1-cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b+1/4*_ + log(1+cosh(a+b*x)^(4/3)/sinh(a+b*x)^(4/3)+_ + cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b +--R +--R +--R (2) +--R log +--R 3+-------------+2 +--R sinh(b x + a)\|sinh(b x + a) +--R + +--R 3+-------------+3+-------------+ +--R cosh(b x + a)\|cosh(b x + a) \|sinh(b x + a) +--R + +--R 3+-------------+2 +--R sinh(b x + a)\|cosh(b x + a) +--R / +--R 3+-------------+2 +--R sinh(b x + a)\|sinh(b x + a) +--R + +--R 3+-------------+2 3+-------------+2 +--R \|sinh(b x + a) - \|cosh(b x + a) +--R - 2log(-------------------------------------) +--R 3+-------------+2 +--R \|sinh(b x + a) +--R + +--R +-+3+-------------+2 +-+3+-------------+2 +--R +-+ \|3 \|sinh(b x + a) + 2\|3 \|cosh(b x + a) +--R - 2\|3 atan(----------------------------------------------) +--R 3+-------------+2 +--R 3\|sinh(b x + a) +--R / +--R 4b +--R Type: Expression(Integer) +--E 57 + +--S 58 of 531 +a1011:= integrate(t1011,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (non-algebraic residues) +--R +--R Continuing to read the file... +--R +--E 58 + +--S 59 of 531 +--m1011:= a1011-r1011 +--E 59 + +--S 60 of 531 +--d1011:= D(m1011,x) +--E 60 + +)clear all + + +--S 61 of 531 +t1012:= cosh(x)^(2/3)/sinh(x)^(8/3) +--R +--R +--R 3+-------+2 +--R \|cosh(x) +--R (1) ------------------- +--R 2 3+-------+2 +--R sinh(x) \|sinh(x) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 531 +r1012:= -3/5*cosh(x)^(5/3)/sinh(x)^(5/3) +--R +--R +--R 3+-------+2 +--R 3cosh(x)\|cosh(x) +--R (2) - ------------------- +--R 3+-------+2 +--R 5sinh(x)\|sinh(x) +--R Type: Expression(Integer) +--E 62 + + +-- +-- (3) +-- 3 2 +-- - 31914sinh(x) - 95742cosh(x)sinh(x) +-- + +-- 2 3 +-- (- 95742cosh(x) - 31914)sinh(x) - 31914cosh(x) - 31914cosh(x) +-- * +-- 3+-------+2 3+-------+ +-- \|cosh(x) \|sinh(x) +-- + +-- 4 3 2 2 +-- 61805sinh(x) + 247220cosh(x)sinh(x) + (370830cosh(x) - 123610)sinh(x) +-- + +-- 3 4 2 +-- (247220cosh(x) - 247220cosh(x))sinh(x) + 61805cosh(x) - 123610cosh(x) +-- + +-- 61805 +-- / +-- 4 3 2 2 +-- 26595sinh(x) + 106380cosh(x)sinh(x) + (159570cosh(x) - 53190)sinh(x) +-- + +-- 3 4 2 +-- (106380cosh(x) - 106380cosh(x))sinh(x) + 26595cosh(x) - 53190cosh(x) +-- + +-- 26595 +-- Type: Union(Expression(Integer),...) + +--S 63 of 531 ok to fail. seems there are 2 answers (see above) +a1012:= integrate(t1012,x) +--R +--R +--R (3) +--R 3 2 +--R - 30294sinh(x) - 90882cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 90882cosh(x) - 30294)sinh(x) - 30294cosh(x) - 30294cosh(x) +--R * +--R 3+-------+2 3+-------+ +--R \|cosh(x) \|sinh(x) +--R + +--R 4 3 2 2 +--R 30605sinh(x) + 122420cosh(x)sinh(x) + (183630cosh(x) - 61210)sinh(x) +--R + +--R 3 4 2 +--R (122420cosh(x) - 122420cosh(x))sinh(x) + 30605cosh(x) - 61210cosh(x) +--R + +--R 30605 +--R / +--R 4 3 2 2 +--R 25245sinh(x) + 100980cosh(x)sinh(x) + (151470cosh(x) - 50490)sinh(x) +--R + +--R 3 4 2 +--R (100980cosh(x) - 100980cosh(x))sinh(x) + 25245cosh(x) - 50490cosh(x) +--R + +--R 25245 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 531 ok to fail. due to 2 answers (see above) +m1012:= a1012-r1012 +--R +--R +--R (4) +--R 5 4 +--R 30605sinh(x) + 122420cosh(x)sinh(x) +--R + +--R 2 3 +--R (183630cosh(x) - 61210)sinh(x) +--R + +--R 3 2 +--R (122420cosh(x) - 122420cosh(x))sinh(x) +--R + +--R 4 2 +--R (30605cosh(x) - 61210cosh(x) + 30605)sinh(x) +--R * +--R 3+-------+2 +--R \|sinh(x) +--R + +--R 5 4 +--R - 30294sinh(x) - 75735cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 30294cosh(x) - 30294)sinh(x) +--R + +--R 3 2 +--R (60588cosh(x) - 60588cosh(x))sinh(x) +--R + +--R 4 2 5 +--R (60588cosh(x) - 60588cosh(x) )sinh(x) + 15147cosh(x) +--R + +--R 3 +--R - 30294cosh(x) + 15147cosh(x) +--R * +--R 3+-------+2 +--R \|cosh(x) +--R / +--R 5 4 +--R 25245sinh(x) + 100980cosh(x)sinh(x) +--R + +--R 2 3 +--R (151470cosh(x) - 50490)sinh(x) +--R + +--R 3 2 +--R (100980cosh(x) - 100980cosh(x))sinh(x) +--R + +--R 4 2 +--R (25245cosh(x) - 50490cosh(x) + 25245)sinh(x) +--R * +--R 3+-------+2 +--R \|sinh(x) +--R Type: Expression(Integer) +--E 64 + +--S 65 of 531 +d1012:= D(m1012,x) +--R +--R +--R (5) +--R 9 8 2 7 +--R - 4sinh(x) - 9cosh(x)sinh(x) + 18cosh(x) sinh(x) +--R + +--R 3 6 4 2 5 +--R (80cosh(x) + 21cosh(x))sinh(x) + (90cosh(x) + 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 4 +--R (6cosh(x) + 33cosh(x) + 25cosh(x))sinh(x) +--R + +--R 6 4 2 3 +--R (- 74cosh(x) + 36cosh(x) + 38cosh(x) )sinh(x) +--R + +--R 7 5 3 2 +--R (- 72cosh(x) + 75cosh(x) + 2cosh(x) - 5cosh(x))sinh(x) +--R + +--R 8 6 4 9 7 +--R (- 30cosh(x) + 60cosh(x) - 30cosh(x) )sinh(x) - 5cosh(x) + 15cosh(x) +--R + +--R 5 3 +--R - 15cosh(x) + 5cosh(x) +--R / +--R 8 7 2 6 +--R 5sinh(x) + 30cosh(x)sinh(x) + (75cosh(x) - 15)sinh(x) +--R + +--R 3 5 +--R (100cosh(x) - 60cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (75cosh(x) - 90cosh(x) + 15)sinh(x) +--R + +--R 5 3 3 +--R (30cosh(x) - 60cosh(x) + 30cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (5cosh(x) - 15cosh(x) + 15cosh(x) - 5)sinh(x) +--R * +--R 3+-------+3+-------+2 +--R \|cosh(x) \|sinh(x) +--R Type: Expression(Integer) +--E 65 + +)clear all + + +--S 66 of 531 +t1013:= sinh(x)^(2/3)/cosh(x)^(8/3) +--R +--R +--R 3+-------+2 +--R \|sinh(x) +--R (1) ------------------- +--R 2 3+-------+2 +--R cosh(x) \|cosh(x) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 531 +r1013:= 3/5*sinh(x)^(5/3)/cosh(x)^(5/3) +--R +--R +--R 3+-------+2 +--R 3sinh(x)\|sinh(x) +--R (2) ------------------- +--R 3+-------+2 +--R 5cosh(x)\|cosh(x) +--R Type: Expression(Integer) +--E 67 + + +-- (3) +-- 3 2 2 +-- 14250sinh(x) + 42750cosh(x)sinh(x) + (42750cosh(x) - 14250)sinh(x) +-- + +-- 3 +-- 14250cosh(x) - 14250cosh(x) +-- * +-- 3+-------+3+-------+2 +-- \|cosh(x) \|sinh(x) +-- + +-- 4 3 2 2 +-- - 5869sinh(x) - 23476cosh(x)sinh(x) + (- 35214cosh(x) - 11738)sinh(x) +-- + +-- 3 4 2 +-- (- 23476cosh(x) - 23476cosh(x))sinh(x) - 5869cosh(x) - 11738cosh(x) +-- + +-- - 5869 +-- / +-- 4 3 2 2 +-- 11875sinh(x) + 47500cosh(x)sinh(x) + (71250cosh(x) + 23750)sinh(x) +-- + +-- 3 4 2 +-- (47500cosh(x) + 47500cosh(x))sinh(x) + 11875cosh(x) + 23750cosh(x) +-- + +-- 11875 +-- Type: Union(Expression(Integer),...) + +--S 68 of 531 ok to fail. seems there are 2 answers (see above) +a1013:= integrate(t1013,x) +--R +--R +--R (3) +--R 3 2 2 +--R 150sinh(x) + 450cosh(x)sinh(x) + (450cosh(x) - 150)sinh(x) +--R + +--R 3 +--R 150cosh(x) - 150cosh(x) +--R * +--R 3+-------+3+-------+2 +--R \|cosh(x) \|sinh(x) +--R + +--R 4 3 2 2 +--R 67sinh(x) + 268cosh(x)sinh(x) + (402cosh(x) + 134)sinh(x) +--R + +--R 3 4 2 +--R (268cosh(x) + 268cosh(x))sinh(x) + 67cosh(x) + 134cosh(x) + 67 +--R / +--R 4 3 2 2 +--R 125sinh(x) + 500cosh(x)sinh(x) + (750cosh(x) + 250)sinh(x) +--R + +--R 3 4 2 +--R (500cosh(x) + 500cosh(x))sinh(x) + 125cosh(x) + 250cosh(x) + 125 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 531 ok to fail. due to 2 answers (see above) +m1013:= a1013-r1013 +--R +--R +--R (4) +--R 5 4 2 3 +--R - 75sinh(x) - 300cosh(x)sinh(x) + (- 300cosh(x) - 150)sinh(x) +--R + +--R 3 2 +--R (150cosh(x) - 300cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (375cosh(x) - 300cosh(x) - 75)sinh(x) + 150cosh(x) - 150cosh(x) +--R * +--R 3+-------+2 +--R \|sinh(x) +--R + +--R 4 2 3 +--R 67cosh(x)sinh(x) + 268cosh(x) sinh(x) +--R + +--R 3 2 +--R (402cosh(x) + 134cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (268cosh(x) + 268cosh(x) )sinh(x) + 67cosh(x) + 134cosh(x) +--R + +--R 67cosh(x) +--R * +--R 3+-------+2 +--R \|cosh(x) +--R / +--R 4 2 3 +--R 125cosh(x)sinh(x) + 500cosh(x) sinh(x) +--R + +--R 3 2 4 2 +--R (750cosh(x) + 250cosh(x))sinh(x) + (500cosh(x) + 500cosh(x) )sinh(x) +--R + +--R 5 3 +--R 125cosh(x) + 250cosh(x) + 125cosh(x) +--R * +--R 3+-------+2 +--R \|cosh(x) +--R Type: Expression(Integer) +--E 69 + +--S 70 of 531 +d1013:= D(m1013,x) +--R +--R +--R (5) +--R 9 8 2 7 +--R 5sinh(x) + 30cosh(x)sinh(x) + (72cosh(x) + 15)sinh(x) +--R + +--R 3 6 +--R (74cosh(x) + 60cosh(x))sinh(x) +--R + +--R 4 2 5 +--R (- 6cosh(x) + 75cosh(x) + 15)sinh(x) +--R + +--R 5 3 4 +--R (- 90cosh(x) + 36cosh(x) + 30cosh(x))sinh(x) +--R + +--R 6 4 2 3 +--R (- 80cosh(x) + 33cosh(x) - 2cosh(x) + 5)sinh(x) +--R + +--R 7 5 3 2 +--R (- 18cosh(x) + 48cosh(x) - 38cosh(x) )sinh(x) +--R + +--R 8 6 4 2 9 +--R (9cosh(x) + 21cosh(x) - 25cosh(x) - 5cosh(x) )sinh(x) + 4cosh(x) +--R + +--R 5 +--R - 4cosh(x) +--R / +--R 2 6 3 5 +--R 5cosh(x) sinh(x) + 30cosh(x) sinh(x) +--R + +--R 4 2 4 5 3 3 +--R (75cosh(x) + 15cosh(x) )sinh(x) + (100cosh(x) + 60cosh(x) )sinh(x) +--R + +--R 6 4 2 2 +--R (75cosh(x) + 90cosh(x) + 15cosh(x) )sinh(x) +--R + +--R 7 5 3 8 6 +--R (30cosh(x) + 60cosh(x) + 30cosh(x) )sinh(x) + 5cosh(x) + 15cosh(x) +--R + +--R 4 2 +--R 15cosh(x) + 5cosh(x) +--R * +--R 3+-------+2 3+-------+ +--R \|cosh(x) \|sinh(x) +--R Type: Expression(Integer) +--E 70 + +)clear all + + +--S 71 of 531 +t1014:= cosh(x)*csch(x)^(7/3) +--R +--R +--R 2 3+-------+ +--R (1) cosh(x)csch(x) \|csch(x) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 531 +r1014:= -3/4*csch(x)^(4/3) +--R +--R +--R 3+-------+ +--R 3csch(x)\|csch(x) +--R (2) - ------------------ +--R 4 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 531 +a1014:= integrate(t1014,x) +--R +--R +--R (3) +--R +-----------------------------------------+ +--R | 2sinh(x) + 2cosh(x) +--R (- 3sinh(x) - 3cosh(x)) |----------------------------------------- +--R 3| 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) - 6)sinh(x) +--R + +--R 3 3 4 2 2 +--R (40cosh(x) - 24cosh(x))sinh(x) + (30cosh(x) - 36cosh(x) + 6)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) - 24cosh(x) + 12cosh(x))sinh(x) + 2cosh(x) - 6cosh(x) +--R + +--R 2 +--R 6cosh(x) - 2 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 531 +m1014:= a1014-r1014 +--R +--R +--R (4) +--R 6 5 +--R 3csch(x)sinh(x) + 18cosh(x)csch(x)sinh(x) +--R + +--R 2 4 +--R (45cosh(x) - 9)csch(x)sinh(x) +--R + +--R 3 3 +--R (60cosh(x) - 36cosh(x))csch(x)sinh(x) +--R + +--R 4 2 2 +--R (45cosh(x) - 54cosh(x) + 9)csch(x)sinh(x) +--R + +--R 5 3 +--R (18cosh(x) - 36cosh(x) + 18cosh(x))csch(x)sinh(x) +--R + +--R 6 4 2 +--R (3cosh(x) - 9cosh(x) + 9cosh(x) - 3)csch(x) +--R * +--R 3+-------+ +--R \|csch(x) +--R + +--R +-----------------------------------------+ +--R | 2sinh(x) + 2cosh(x) +--R (- 6sinh(x) - 6cosh(x)) |----------------------------------------- +--R 3| 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 12)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) - 48cosh(x))sinh(x) + (60cosh(x) - 72cosh(x) + 12)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 48cosh(x) + 24cosh(x))sinh(x) + 4cosh(x) - 12cosh(x) +--R + +--R 2 +--R 12cosh(x) - 4 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 531 +d1014:= D(m1014,x) +--R +--R +--R (5) +--R 4 3 2 2 +--R 16sinh(x) + 64cosh(x)sinh(x) + (96cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (64cosh(x) + 8cosh(x))sinh(x) + 16cosh(x) + 4cosh(x) +--R * +--R 3+-------+2 +--R \|csch(x) +--R + +--R 2 10 2 9 +--R - coth(x)csch(x) sinh(x) - 10cosh(x)coth(x)csch(x) sinh(x) +--R + +--R 2 2 8 +--R (- 45cosh(x) + 5)coth(x)csch(x) sinh(x) +--R + +--R 3 2 7 +--R (- 120cosh(x) + 40cosh(x))coth(x)csch(x) sinh(x) +--R + +--R 4 2 2 6 +--R (- 210cosh(x) + 140cosh(x) - 10)coth(x)csch(x) sinh(x) +--R + +--R 5 3 2 5 +--R (- 252cosh(x) + 280cosh(x) - 60cosh(x))coth(x)csch(x) sinh(x) +--R + +--R 6 4 2 2 +--R (- 210cosh(x) + 350cosh(x) - 150cosh(x) + 10)coth(x)csch(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 120cosh(x) + 280cosh(x) - 200cosh(x) + 40cosh(x))coth(x) +--R * +--R 2 3 +--R csch(x) sinh(x) +--R + +--R 8 6 4 2 +--R (- 45cosh(x) + 140cosh(x) - 150cosh(x) + 60cosh(x) - 5)coth(x) +--R * +--R 2 2 +--R csch(x) sinh(x) +--R + +--R 9 7 5 3 +--R (- 10cosh(x) + 40cosh(x) - 60cosh(x) + 40cosh(x) - 10cosh(x)) +--R * +--R 2 +--R coth(x)csch(x) sinh(x) +--R + +--R 10 8 6 4 2 +--R (- cosh(x) + 5cosh(x) - 10cosh(x) + 10cosh(x) - 5cosh(x) + 1) +--R * +--R 2 +--R coth(x)csch(x) +--R * +--R +-----------------------------------------+2 +--R | 2sinh(x) + 2cosh(x) +--R |----------------------------------------- +--R 3| 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 10 9 2 8 +--R sinh(x) + 10cosh(x)sinh(x) + (45cosh(x) - 5)sinh(x) +--R + +--R 3 7 +--R (120cosh(x) - 40cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (210cosh(x) - 140cosh(x) + 10)sinh(x) +--R + +--R 5 3 5 +--R (252cosh(x) - 280cosh(x) + 60cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (210cosh(x) - 350cosh(x) + 150cosh(x) - 10)sinh(x) +--R + +--R 7 5 3 3 +--R (120cosh(x) - 280cosh(x) + 200cosh(x) - 40cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (45cosh(x) - 140cosh(x) + 150cosh(x) - 60cosh(x) + 5)sinh(x) +--R + +--R 9 7 5 3 +--R (10cosh(x) - 40cosh(x) + 60cosh(x) - 40cosh(x) + 10cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) - 5cosh(x) + 10cosh(x) - 10cosh(x) + 5cosh(x) - 1 +--R * +--R +-----------------------------------------+2 +--R | 2sinh(x) + 2cosh(x) 3+-------+2 +--R |----------------------------------------- \|csch(x) +--R 3| 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression(Integer) +--E 75 + +)clear all + + +--S 76 of 531 +t1015:= (1+coth(x))^(1/2)*sech(x)^2 +--R +--R +--R 2 +-----------+ +--R (1) sech(x) \|coth(x) + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 531 +r1015:= atanh((1+coth(x))^(1/2))+(1+coth(x))^(1/2)*tanh(x) +--R +--R +--R +-----------+ +-----------+ +--R (2) atanh(\|coth(x) + 1 ) + tanh(x)\|coth(x) + 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 531 +a1015:= integrate(t1015,x) +--R +--R +--R (3) +--R 12 11 2 10 +--R sinh(x) + 12cosh(x)sinh(x) + (66cosh(x) + 8)sinh(x) +--R + +--R 3 9 +--R (220cosh(x) + 80cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (495cosh(x) + 360cosh(x) - 16)sinh(x) +--R + +--R 5 3 7 +--R (792cosh(x) + 960cosh(x) - 128cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (924cosh(x) + 1680cosh(x) - 448cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 5 +--R (792cosh(x) + 2016cosh(x) - 896cosh(x) + 144cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (495cosh(x) + 1680cosh(x) - 1120cosh(x) + 360cosh(x) - 32) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 220cosh(x) + 960cosh(x) - 896cosh(x) + 480cosh(x) +--R + +--R - 128cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 66cosh(x) + 360cosh(x) - 448cosh(x) + 360cosh(x) +--R + +--R 2 +--R - 192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 12cosh(x) + 80cosh(x) - 128cosh(x) + 144cosh(x) +--R + +--R 3 +--R - 128cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R cosh(x) + 8cosh(x) - 16cosh(x) + 24cosh(x) - 32cosh(x) + 16 +--R * +--R log +--R 5 4 2 3 +--R 4sinh(x) + 20cosh(x)sinh(x) + (40cosh(x) - 4)sinh(x) +--R + +--R 3 2 +--R (40cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (20cosh(x) - 12cosh(x) )sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) + 16cosh(x) )sinh(x) + cosh(x) + 4cosh(x) - 4 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 2)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 12cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 8cosh(x) + 2cosh(x))sinh(x) + cosh(x) - 2cosh(x) +--R + +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 +--R - sinh(x) - 12cosh(x)sinh(x) + (- 66cosh(x) - 8)sinh(x) +--R + +--R 3 9 +--R (- 220cosh(x) - 80cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 495cosh(x) - 360cosh(x) + 16)sinh(x) +--R + +--R 5 3 7 +--R (- 792cosh(x) - 960cosh(x) + 128cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 924cosh(x) - 1680cosh(x) + 448cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 5 +--R (- 792cosh(x) - 2016cosh(x) + 896cosh(x) - 144cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 495cosh(x) - 1680cosh(x) + 1120cosh(x) - 360cosh(x) + 32) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 220cosh(x) - 960cosh(x) + 896cosh(x) - 480cosh(x) +--R + +--R 128cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 66cosh(x) - 360cosh(x) + 448cosh(x) - 360cosh(x) +--R + +--R 2 +--R 192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 12cosh(x) - 80cosh(x) + 128cosh(x) - 144cosh(x) +--R + +--R 3 +--R 128cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - cosh(x) - 8cosh(x) + 16cosh(x) - 24cosh(x) + 32cosh(x) - 16 +--R * +--R log +--R 5 4 2 3 +--R - 4sinh(x) - 20cosh(x)sinh(x) + (- 40cosh(x) + 4)sinh(x) +--R + +--R 3 2 +--R (- 40cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (- 20cosh(x) + 12cosh(x) )sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) + 16cosh(x) )sinh(x) + cosh(x) + 4cosh(x) - 4 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 2)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 12cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 8cosh(x) + 2cosh(x))sinh(x) + cosh(x) - 2cosh(x) +--R + +--R 2 +--R cosh(x) +--R + +--R 11 10 2 9 +--R - 8sinh(x) - 88cosh(x)sinh(x) + (- 440cosh(x) + 104)sinh(x) +--R + +--R 3 8 +--R (- 1320cosh(x) + 936cosh(x))sinh(x) +--R + +--R 4 2 7 +--R (- 2640cosh(x) + 3744cosh(x) - 224)sinh(x) +--R + +--R 5 3 6 +--R (- 3696cosh(x) + 8736cosh(x) - 1568cosh(x))sinh(x) +--R + +--R 6 4 2 5 +--R (- 3696cosh(x) + 13104cosh(x) - 4704cosh(x) + 160)sinh(x) +--R + +--R 7 5 3 4 +--R (- 2640cosh(x) + 13104cosh(x) - 7840cosh(x) + 800cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1320cosh(x) + 8736cosh(x) - 7840cosh(x) + 1600cosh(x) - 32) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 440cosh(x) + 3744cosh(x) - 4704cosh(x) + 1600cosh(x) +--R + +--R - 96cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 88cosh(x) + 936cosh(x) - 1568cosh(x) + 800cosh(x) +--R + +--R 2 +--R - 96cosh(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R - 8cosh(x) + 104cosh(x) - 224cosh(x) + 160cosh(x) - 32cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 12 11 2 10 +--R 4sinh(x) + 48cosh(x)sinh(x) + (264cosh(x) + 32)sinh(x) +--R + +--R 3 9 +--R (880cosh(x) + 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (1980cosh(x) + 1440cosh(x) - 64)sinh(x) +--R + +--R 5 3 7 +--R (3168cosh(x) + 3840cosh(x) - 512cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (3696cosh(x) + 6720cosh(x) - 1792cosh(x) + 96)sinh(x) +--R + +--R 7 5 3 5 +--R (3168cosh(x) + 8064cosh(x) - 3584cosh(x) + 576cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (1980cosh(x) + 6720cosh(x) - 4480cosh(x) + 1440cosh(x) - 128)sinh(x) +--R + +--R 9 7 5 3 +--R (880cosh(x) + 3840cosh(x) - 3584cosh(x) + 1920cosh(x) - 512cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 264cosh(x) + 1440cosh(x) - 1792cosh(x) + 1440cosh(x) +--R + +--R 2 +--R - 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R (48cosh(x) + 320cosh(x) - 512cosh(x) + 576cosh(x) - 512cosh(x) ) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 4cosh(x) + 32cosh(x) - 64cosh(x) + 96cosh(x) - 128cosh(x) + 64 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 531 +m1015:= a1015-r1015 +--R +--R +--R (4) +--R 12 11 2 10 +--R sinh(x) + 12cosh(x)sinh(x) + (66cosh(x) + 8)sinh(x) +--R + +--R 3 9 +--R (220cosh(x) + 80cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (495cosh(x) + 360cosh(x) - 16)sinh(x) +--R + +--R 5 3 7 +--R (792cosh(x) + 960cosh(x) - 128cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (924cosh(x) + 1680cosh(x) - 448cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 5 +--R (792cosh(x) + 2016cosh(x) - 896cosh(x) + 144cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (495cosh(x) + 1680cosh(x) - 1120cosh(x) + 360cosh(x) - 32) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 220cosh(x) + 960cosh(x) - 896cosh(x) + 480cosh(x) +--R + +--R - 128cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 66cosh(x) + 360cosh(x) - 448cosh(x) + 360cosh(x) +--R + +--R 2 +--R - 192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 12cosh(x) + 80cosh(x) - 128cosh(x) + 144cosh(x) +--R + +--R 3 +--R - 128cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R cosh(x) + 8cosh(x) - 16cosh(x) + 24cosh(x) - 32cosh(x) + 16 +--R * +--R log +--R 5 4 2 3 +--R 4sinh(x) + 20cosh(x)sinh(x) + (40cosh(x) - 4)sinh(x) +--R + +--R 3 2 +--R (40cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (20cosh(x) - 12cosh(x) )sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) + 16cosh(x) )sinh(x) + cosh(x) + 4cosh(x) - 4 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 2)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 12cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 8cosh(x) + 2cosh(x))sinh(x) + cosh(x) - 2cosh(x) +--R + +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 +--R - sinh(x) - 12cosh(x)sinh(x) + (- 66cosh(x) - 8)sinh(x) +--R + +--R 3 9 +--R (- 220cosh(x) - 80cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 495cosh(x) - 360cosh(x) + 16)sinh(x) +--R + +--R 5 3 7 +--R (- 792cosh(x) - 960cosh(x) + 128cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 924cosh(x) - 1680cosh(x) + 448cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 5 +--R (- 792cosh(x) - 2016cosh(x) + 896cosh(x) - 144cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 495cosh(x) - 1680cosh(x) + 1120cosh(x) - 360cosh(x) + 32) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 220cosh(x) - 960cosh(x) + 896cosh(x) - 480cosh(x) +--R + +--R 128cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 66cosh(x) - 360cosh(x) + 448cosh(x) - 360cosh(x) +--R + +--R 2 +--R 192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 12cosh(x) - 80cosh(x) + 128cosh(x) - 144cosh(x) +--R + +--R 3 +--R 128cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - cosh(x) - 8cosh(x) + 16cosh(x) - 24cosh(x) + 32cosh(x) - 16 +--R * +--R log +--R 5 4 2 3 +--R - 4sinh(x) - 20cosh(x)sinh(x) + (- 40cosh(x) + 4)sinh(x) +--R + +--R 3 2 +--R (- 40cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (- 20cosh(x) + 12cosh(x) )sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) + 16cosh(x) )sinh(x) + cosh(x) + 4cosh(x) - 4 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 2)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 12cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 8cosh(x) + 2cosh(x))sinh(x) + cosh(x) - 2cosh(x) +--R + +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 +--R - 4sinh(x) - 48cosh(x)sinh(x) + (- 264cosh(x) - 32)sinh(x) +--R + +--R 3 9 +--R (- 880cosh(x) - 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 1980cosh(x) - 1440cosh(x) + 64)sinh(x) +--R + +--R 5 3 7 +--R (- 3168cosh(x) - 3840cosh(x) + 512cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 3696cosh(x) - 6720cosh(x) + 1792cosh(x) - 96)sinh(x) +--R + +--R 7 5 3 5 +--R (- 3168cosh(x) - 8064cosh(x) + 3584cosh(x) - 576cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1980cosh(x) - 6720cosh(x) + 4480cosh(x) - 1440cosh(x) + 128) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 880cosh(x) - 3840cosh(x) + 3584cosh(x) - 1920cosh(x) +--R + +--R 512cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 264cosh(x) - 1440cosh(x) + 1792cosh(x) - 1440cosh(x) +--R + +--R 2 +--R 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 48cosh(x) - 320cosh(x) + 512cosh(x) - 576cosh(x) +--R + +--R 3 +--R 512cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 4cosh(x) - 32cosh(x) + 64cosh(x) - 96cosh(x) + 128cosh(x) - 64 +--R * +--R +-----------+ +--R atanh(\|coth(x) + 1 ) +--R + +--R 12 11 2 10 +--R - 4sinh(x) - 48cosh(x)sinh(x) + (- 264cosh(x) - 32)sinh(x) +--R + +--R 3 9 +--R (- 880cosh(x) - 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 1980cosh(x) - 1440cosh(x) + 64)sinh(x) +--R + +--R 5 3 7 +--R (- 3168cosh(x) - 3840cosh(x) + 512cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 3696cosh(x) - 6720cosh(x) + 1792cosh(x) - 96)sinh(x) +--R + +--R 7 5 3 5 +--R (- 3168cosh(x) - 8064cosh(x) + 3584cosh(x) - 576cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1980cosh(x) - 6720cosh(x) + 4480cosh(x) - 1440cosh(x) + 128) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 880cosh(x) - 3840cosh(x) + 3584cosh(x) - 1920cosh(x) +--R + +--R 512cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 264cosh(x) - 1440cosh(x) + 1792cosh(x) - 1440cosh(x) +--R + +--R 2 +--R 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 48cosh(x) - 320cosh(x) + 512cosh(x) - 576cosh(x) +--R + +--R 3 +--R 512cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 4cosh(x) - 32cosh(x) + 64cosh(x) - 96cosh(x) + 128cosh(x) - 64 +--R * +--R +-----------+ +--R tanh(x)\|coth(x) + 1 +--R + +--R 11 10 2 9 +--R - 8sinh(x) - 88cosh(x)sinh(x) + (- 440cosh(x) + 104)sinh(x) +--R + +--R 3 8 +--R (- 1320cosh(x) + 936cosh(x))sinh(x) +--R + +--R 4 2 7 +--R (- 2640cosh(x) + 3744cosh(x) - 224)sinh(x) +--R + +--R 5 3 6 +--R (- 3696cosh(x) + 8736cosh(x) - 1568cosh(x))sinh(x) +--R + +--R 6 4 2 5 +--R (- 3696cosh(x) + 13104cosh(x) - 4704cosh(x) + 160)sinh(x) +--R + +--R 7 5 3 4 +--R (- 2640cosh(x) + 13104cosh(x) - 7840cosh(x) + 800cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1320cosh(x) + 8736cosh(x) - 7840cosh(x) + 1600cosh(x) - 32) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 440cosh(x) + 3744cosh(x) - 4704cosh(x) + 1600cosh(x) +--R + +--R - 96cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 88cosh(x) + 936cosh(x) - 1568cosh(x) + 800cosh(x) +--R + +--R 2 +--R - 96cosh(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R - 8cosh(x) + 104cosh(x) - 224cosh(x) + 160cosh(x) - 32cosh(x) +--R * +--R +-----------------------------------------+ +--R | 2 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 12 11 2 10 +--R 4sinh(x) + 48cosh(x)sinh(x) + (264cosh(x) + 32)sinh(x) +--R + +--R 3 9 +--R (880cosh(x) + 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (1980cosh(x) + 1440cosh(x) - 64)sinh(x) +--R + +--R 5 3 7 +--R (3168cosh(x) + 3840cosh(x) - 512cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (3696cosh(x) + 6720cosh(x) - 1792cosh(x) + 96)sinh(x) +--R + +--R 7 5 3 5 +--R (3168cosh(x) + 8064cosh(x) - 3584cosh(x) + 576cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (1980cosh(x) + 6720cosh(x) - 4480cosh(x) + 1440cosh(x) - 128)sinh(x) +--R + +--R 9 7 5 3 +--R (880cosh(x) + 3840cosh(x) - 3584cosh(x) + 1920cosh(x) - 512cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 264cosh(x) + 1440cosh(x) - 1792cosh(x) + 1440cosh(x) +--R + +--R 2 +--R - 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R (48cosh(x) + 320cosh(x) - 512cosh(x) + 576cosh(x) - 512cosh(x) ) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 4cosh(x) + 32cosh(x) - 64cosh(x) + 96cosh(x) - 128cosh(x) + 64 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 531 +--d1015:= D(m1015,x) +--E 80 + +)clear all + + +--S 81 of 531 +t1016:= sinh(x)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 531 +r1016:= (-b*x+a*log(a*cosh(x)+b*sinh(x)))/(a^2-b^2) +--R +--R +--R - a log(b sinh(x) + a cosh(x)) + b x +--R (2) ------------------------------------ +--R 2 2 +--R b - a +--R Type: Expression(Integer) +--E 82 + +--S 83 of 531 +a1016:= integrate(t1016,x) +--R +--R +--R - 2b sinh(x) - 2a cosh(x) +--R - a log(-------------------------) + (b + a)x +--R sinh(x) - cosh(x) +--R (3) --------------------------------------------- +--R 2 2 +--R b - a +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 531 +m1016:= a1016-r1016 +--R +--R +--R - 2b sinh(x) - 2a cosh(x) +--R a log(b sinh(x) + a cosh(x)) - a log(-------------------------) + a x +--R sinh(x) - cosh(x) +--R (4) --------------------------------------------------------------------- +--R 2 2 +--R b - a +--R Type: Expression(Integer) +--E 84 + +--S 85 of 531 +d1016:= D(m1016,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + + +--S 86 of 531 +t1017:= sinh(x)^2/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 2 +--R sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 531 +r1017:= -a^2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ + b*cosh(x)/(a^2-b^2)+a*sinh(x)/(a^2-b^2) +--R +--R +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R a atan(---------------------) + (- a sinh(x) + b cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) --------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 531 +a1017:= integrate(t1017,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (2a sinh(x) + 2a cosh(x)) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|- b + a +--R (- 4a sinh(x) - 4a cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 88 + +--S 89 of 531 +m1017a:= a1017.1-r1017 +--R +--R +--R (4) +--R +---------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R +-------+ +--R 2 2 | 2 2 a sinh(x) + b cosh(x) +--R (- 2a sinh(x) - 2a cosh(x))\|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 | 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a \|b - a +--R Type: Expression(Integer) +--E 89 + +--S 90 of 531 +d1017a:= D(m1017a,x) +--R +--R +--R (5) +--R 2 2 3 4 6 +--R (- a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (- b - 6a b - 9a b - 4a b)cosh(x) + b + 2a b - 2a b - 6a b +--R + +--R 4 +--R a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 4a b - 12a b - 12a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4a b + 9a b + 6a b + a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 6a b - 14a b - 2a b - 2a )cosh(x) + 2a b + a b - 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 3 3 4 3 +--R (- 4b - 12a b + 4a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 6a b - 6a b - 6a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 3 2 2 4 4 +--R (b + 2a b + a b )cosh(x) + (- 3b - 4a b + 4a b - a )cosh(x) +--R + +--R 4 3 2 2 4 2 4 2 2 4 +--R (3b + 2a b - 7a b + 2a )cosh(x) - b + 2a b - a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 90 + +--S 91 of 531 +m1017b:= a1017.2-r1017 +--R +--R +--R (6) +--R +---------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|- b + a +--R (- 4a sinh(x) - 4a cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 a sinh(x) + b cosh(x) +--R (- 2a sinh(x) - 2a cosh(x))atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 91 + +--S 92 of 531 +d1017b:= D(m1017b,x) +--R +--R +--R (7) +--R 2 2 3 4 6 +--R (- a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (- b - 6a b - 9a b - 4a b)cosh(x) + b + 2a b - 2a b - 6a b +--R + +--R 4 +--R a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 4a b - 12a b - 12a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4a b + 9a b + 6a b + a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 6a b - 14a b - 2a b - 2a )cosh(x) + 2a b + a b - 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 3 3 4 3 +--R (- 4b - 12a b + 4a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 6a b - 6a b - 6a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 3 2 2 4 4 +--R (b + 2a b + a b )cosh(x) + (- 3b - 4a b + 4a b - a )cosh(x) +--R + +--R 4 3 2 2 4 2 4 2 2 4 +--R (3b + 2a b - 7a b + 2a )cosh(x) - b + 2a b - a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 92 + +)clear all + + +--S 93 of 531 +t1018:= sinh(x)^3/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 3 +--R sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 93 + +--S 94 of 531 +r1018:= -1/2*(-3*a^2*b*x+b^3*x+2*a^3*log(a*cosh(x)+_ + b*sinh(x))+a^2*cosh(x)*b*sinh(x)-b^3*cosh(x)*sinh(x)+_ + a^3-cosh(x)^2*a^3-b^2*a+cosh(x)^2*b^2*a)/(a^2-b^2)^2 +--R +--R +--R (2) +--R 3 3 2 +--R - 2a log(b sinh(x) + a cosh(x)) + (b - a b)cosh(x)sinh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- a b + a )cosh(x) + (- b + 3a b)x + a b - a +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 531 +a1018:= integrate(t1018,x) +--R +--R +--R (3) +--R 3 2 3 3 2 +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 3 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (- 4b + 12a b + 8a )x)sinh(x) +--R + +--R 3 2 2 3 3 3 2 3 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (- 8b + 24a b + 16a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 3 2 3 +--R (b - a b - a b + a )cosh(x) + (- 4b + 12a b + 8a )x cosh(x) - b +--R + +--R 2 2 3 +--R - a b + a b + a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 95 + +--S 96 of 531 +m1018:= a1018-r1018 +--R +--R +--R (4) +--R 3 2 3 3 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 3 2 3 3 2 +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (b - a b - a b + a )sinh(x) + (- 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 3 2 +--R ((- 2b - 2a b + 2a b + 2a )cosh(x) + 8a x - 4a b + 4a )sinh(x) +--R + +--R 2 3 3 3 2 3 +--R ((4a b - 4a )cosh(x) + (16a x - 8a b + 8a )cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 3 2 3 2 3 +--R (b + 3a b - a b - 3a )cosh(x) + (8a x - 4a b + 4a )cosh(x) - b +--R + +--R 2 2 3 +--R - a b + a b + a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 531 +d1018:= D(m1018,x) +--R +--R +--R 4 2 2 4 +--R - sinh(x) + 2cosh(x) sinh(x) - cosh(x) + 1 +--R (5) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression(Integer) +--E 97 + +)clear all + + +--S 98 of 531 +t1019:= sinh(x)/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R sinh(x) +--R (1) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 98 + +--S 99 of 531 +r1019:= -b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ + a/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R (b sinh(x) + a b cosh(x))atan(---------------------) + a\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) -------------------------------------------------------------------- +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sinh(x) + (a b - a )cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 99 + +--S 100 of 531 +a1019:= integrate(t1019,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (b + a b)sinh(x) + (2b + 2a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (b + a b)cosh(x) - b + a b +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R +-------+ +--R | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|b - a +--R / +--R 3 2 2 3 2 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )cosh(x) - b + a b + a b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 2 2 2 +--R (- 2b - 2a b)sinh(x) + (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 2b - 2a b)cosh(x) + 2b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R +---------+ +--R | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|- b + a +--R / +--R 3 2 2 3 2 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )cosh(x) - b + a b + a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 100 + +--S 101 of 531 +m1019a:= a1019.1-r1019 +--R +--R +--R (4) +--R 3 2 3 3 2 2 2 +--R (b + a b )sinh(x) + (2b + 3a b + a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 +--R ((b + 3a b + 2a b)cosh(x) - b + a b )sinh(x) +--R + +--R 2 2 3 2 2 +--R (a b + a b)cosh(x) + (- a b + a b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R 3 2 3 3 2 2 2 +--R (- b - a b )sinh(x) + (- 2b - 3a b - a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 +--R ((- b - 3a b - 2a b)cosh(x) + b - a b )sinh(x) +--R + +--R 2 2 3 2 2 +--R (- a b - a b)cosh(x) + (a b - a b)cosh(x) +--R * +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R \|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((a b - a )sinh(x) + (- a b + a )cosh(x) + a b - a )\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 3 2 2 3 3 +--R (b + a b - a b - a b)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b - a b - 3a b - a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R ((b + 3a b + a b - 3a b - 2a )cosh(x) - b + a b + a b - a b) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 2 3 4 +--R (a b + a b - a b - a )cosh(x) + (- a b + a b + a b - a )cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 101 + +--S 102 of 531 +d1019a:= D(m1019a,x) +--R +--R +--R (5) +--R 4 3 3 4 7 +--R (- b - 2a b - 2a b - a )sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 7a b - 8a b - 7a b - 4a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 2 2 3 4 +--R ((- 4b - 12a b - 22a b - 12a b - 4a )cosh(x) - a b - 2a b - 3a ) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b - 9a b - 16a b - 9a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - 3a b - 2a b - 15a b - 8a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (5b + 6a b + 8a b + 6a b + 5a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (- 6b - 8a b - 18a b - 20a b - 8a )cosh(x) + b + 2a b - 2a b +--R + +--R 3 4 +--R 2a b - 3a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (2b + 15a b + 20a b + 15a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 4b - 18a b - 28a b - 10a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 3a b + 8a b - 9a b - 4a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (8a b + 14a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 16a b - 17a b - 2a b + 5a )cosh(x) +--R + +--R 3 2 2 3 4 2 2 2 3 4 +--R (8a b + 4a b - 8a b - 4a )cosh(x) - a b + 2a b - a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 7 3 2 2 3 4 5 +--R (a b + 4a b + a b)cosh(x) + (- 3a b - 6a b + a b + 2a )cosh(x) +--R + +--R 3 3 4 3 3 2 2 3 +--R (3a b - a b - 2a )cosh(x) + (- a b + 2a b - a b)cosh(x) +--R / +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) - b +--R + +--R 5 2 4 3 3 4 2 +--R - 2a b - 2a b + 2a b + 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 4b - 14a b - 8a b + 8a b + 12a b + 6a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (6b + 28a b + 64a b + 84a b + 64a b + 28a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 8b - 28a b - 25a b + 10a b + 30a b + 18a b + 3a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 +--R 2b - 3a b - 2a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (- 8b - 28a b - 40a b + 40a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 6a b - 12a b - 4a b + 6a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 3b - 18a b - 30a b - 10a b + 25a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (3b + 6a b + 3a b - 24a b + 3a b + 6a b + 3a )cosh(x) - b +--R + +--R 5 3 3 4 2 +--R 2a b - 2a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b - 12a b - 8a b + 8a b + 14a b + 4a )cosh(x) +--R + +--R 5 3 3 4 2 5 6 3 +--R (6a b - 4a b - 12a b + 6a b + 4a )cosh(x) +--R + +--R 5 2 4 4 2 5 +--R (- 2a b + 4a b - 4a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 3a b - 2a b + 2a b + 2a b + a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 4 +--R (3a b - 2a b - 3a b + 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 +--R (- a b + 2a b - 2a b + a )cosh(x) +--R Type: Expression(Integer) +--E 102 + +--S 103 of 531 +m1019b:= a1019.2-r1019 +--R +--R +--R (6) +--R 3 2 3 3 2 2 2 +--R (- 2b - 2a b )sinh(x) + (- 4b - 6a b - 2a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 +--R ((- 2b - 6a b - 4a b)cosh(x) + 2b - 2a b )sinh(x) +--R + +--R 2 2 3 2 2 +--R (- 2a b - 2a b)cosh(x) + (2a b - 2a b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 2 3 3 2 2 2 +--R (- b - a b )sinh(x) + (- 2b - 3a b - a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 +--R ((- b - 3a b - 2a b)cosh(x) + b - a b )sinh(x) +--R + +--R 2 2 3 2 2 +--R (- a b - a b)cosh(x) + (a b - a b)cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((a b - a )sinh(x) + (- a b + a )cosh(x) + a b - a )\|- b + a +--R / +--R 4 3 2 2 3 3 +--R (b + a b - a b - a b)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b - a b - 3a b - a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R ((b + 3a b + a b - 3a b - 2a )cosh(x) - b + a b + a b - a b) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 2 3 4 +--R (a b + a b - a b - a )cosh(x) + (- a b + a b + a b - a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 103 + +--S 104 of 531 +d1019b:= D(m1019b,x) +--R +--R +--R (7) +--R 4 3 3 4 7 +--R (- b - 2a b - 2a b - a )sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 7a b - 8a b - 7a b - 4a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 2 2 3 4 +--R ((- 4b - 12a b - 22a b - 12a b - 4a )cosh(x) - a b - 2a b - 3a ) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b - 9a b - 16a b - 9a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - 3a b - 2a b - 15a b - 8a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (5b + 6a b + 8a b + 6a b + 5a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (- 6b - 8a b - 18a b - 20a b - 8a )cosh(x) + b + 2a b - 2a b +--R + +--R 3 4 +--R 2a b - 3a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (2b + 15a b + 20a b + 15a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 4b - 18a b - 28a b - 10a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 3a b + 8a b - 9a b - 4a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (8a b + 14a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 16a b - 17a b - 2a b + 5a )cosh(x) +--R + +--R 3 2 2 3 4 2 2 2 3 4 +--R (8a b + 4a b - 8a b - 4a )cosh(x) - a b + 2a b - a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 7 3 2 2 3 4 5 +--R (a b + 4a b + a b)cosh(x) + (- 3a b - 6a b + a b + 2a )cosh(x) +--R + +--R 3 3 4 3 3 2 2 3 +--R (3a b - a b - 2a )cosh(x) + (- a b + 2a b - a b)cosh(x) +--R / +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) - b +--R + +--R 5 2 4 3 3 4 2 +--R - 2a b - 2a b + 2a b + 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 4b - 14a b - 8a b + 8a b + 12a b + 6a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (6b + 28a b + 64a b + 84a b + 64a b + 28a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 8b - 28a b - 25a b + 10a b + 30a b + 18a b + 3a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 +--R 2b - 3a b - 2a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (- 8b - 28a b - 40a b + 40a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 6a b - 12a b - 4a b + 6a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 3b - 18a b - 30a b - 10a b + 25a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (3b + 6a b + 3a b - 24a b + 3a b + 6a b + 3a )cosh(x) - b +--R + +--R 5 3 3 4 2 +--R 2a b - 2a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b - 12a b - 8a b + 8a b + 14a b + 4a )cosh(x) +--R + +--R 5 3 3 4 2 5 6 3 +--R (6a b - 4a b - 12a b + 6a b + 4a )cosh(x) +--R + +--R 5 2 4 4 2 5 +--R (- 2a b + 4a b - 4a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 3a b - 2a b + 2a b + 2a b + a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 4 +--R (3a b - 2a b - 3a b + 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 +--R (- a b + 2a b - 2a b + a )cosh(x) +--R Type: Expression(Integer) +--E 104 + +)clear all + + +--S 105 of 531 +t1020:= sinh(x)^2/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R 2 +--R sinh(x) +--R (1) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 105 + +--S 106 of 531 +r1020:= (a^2+b^2)*x/(a^2-b^2)^2-a/(a^2-b^2)/(b+a*coth(x))-_ + 2*a*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2 +--R +--R +--R (2) +--R 2 2 2 3 +--R (- 2a b coth(x) - 2a b )log(b sinh(x) + a cosh(x)) + (a b + a )x coth(x) +--R + +--R 3 2 2 3 +--R (b + a b)x + a b - a +--R / +--R 4 3 2 5 5 2 3 4 +--R (a b - 2a b + a )coth(x) + b - 2a b + a b +--R Type: Expression(Integer) +--E 106 + +--S 107 of 531 +a1020:= integrate(t1020,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (- 2a b - 2a b)sinh(x) + (- 4a b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 2a b - 2a b)cosh(x) + 2a b - 2a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 2 +--R (b + 3a b + 3a b + a )x sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 6a b + 6a b + 2a )x cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 2 3 +--R (b + 3a b + 3a b + a )x cosh(x) + (- b - a b + a b + a )x - 2a b + 2a +--R / +--R 5 4 2 3 3 2 4 5 2 +--R (b + a b - 2a b - 2a b + a b + a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b + 2a b - 4a b - 4a b + 2a b + 2a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 2 3 +--R (b + a b - 2a b - 2a b + a b + a )cosh(x) - b + a b + 2a b +--R + +--R 3 2 4 5 +--R - 2a b - a b + a +--R Type: Union(Expression(Integer),...) +--E 107 + +--S 108 of 531 +m1020:= a1020-r1020 +--R +--R +--R (4) +--R 2 2 3 3 2 2 2 +--R ((2a b + 2a b)coth(x) + 2a b + 2a b )sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((4a b + 4a b)cosh(x)coth(x) + (4a b + 4a b )cosh(x))sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((2a b + 2a b)cosh(x) - 2a b + 2a b)coth(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2a b + 2a b )cosh(x) - 2a b + 2a b +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 2 2 3 3 2 2 2 +--R ((- 2a b - 2a b)coth(x) - 2a b - 2a b )sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((- 4a b - 4a b)cosh(x)coth(x) + (- 4a b - 4a b )cosh(x))sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 2a b - 2a b)cosh(x) + 2a b - 2a b)coth(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2a b - 2a b )cosh(x) + 2a b - 2a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 3 3 2 2 3 2 2 3 4 +--R ((2a b + 2a b)x coth(x) + (2a b + 2a b )x - a b - a b + a b + a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 +--R (4a b + 4a b)x cosh(x)coth(x) +--R + +--R 3 2 2 3 2 2 3 4 +--R ((4a b + 4a b )x - 2a b - 2a b + 2a b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 2 2 2 3 3 4 +--R ((2a b + 2a b)x cosh(x) + (- 2a b + 2a b)x - 2a b + 2a )coth(x) +--R + +--R 3 2 2 3 2 2 3 4 2 3 2 2 +--R ((2a b + 2a b )x - a b - a b + a b + a )cosh(x) + (- 2a b + 2a b )x +--R + +--R 3 2 2 3 4 +--R a b - 3a b + a b + a +--R / +--R 5 2 4 3 3 4 2 5 6 6 5 2 4 +--R (a b + a b - 2a b - 2a b + a b + a )coth(x) + b + a b - 2a b +--R + +--R 3 3 4 2 5 +--R - 2a b + a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (2a b + 2a b - 4a b - 4a b + 2a b + 2a )cosh(x)coth(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b + 2a b - 4a b - 4a b + 2a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 5 2 4 +--R (a b + a b - 2a b - 2a b + a b + a )cosh(x) - a b + a b +--R + +--R 3 3 4 2 5 6 +--R 2a b - 2a b - a b + a +--R * +--R coth(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 6 5 2 4 +--R (b + a b - 2a b - 2a b + a b + a b)cosh(x) - b + a b + 2a b +--R + +--R 3 3 4 2 5 +--R - 2a b - a b + a b +--R Type: Expression(Integer) +--E 108 + +--S 109 of 531 +d1020:= D(m1020,x) +--R +--R +--R (5) +--R 2 2 3 4 2 2 2 3 4 4 +--R ((- a b - 2a b - a )coth(x) + a b + 2a b + a )sinh(x) +--R + +--R 2 2 3 4 2 2 2 3 4 +--R ((- 4a b - 8a b - 4a )cosh(x)coth(x) + (4a b + 8a b + 4a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 4 2 2 2 4 2 +--R ((- 6a b - 12a b - 6a )cosh(x) + 2a b + 2a )coth(x) +--R + +--R 3 2 2 3 4 2 2 2 4 +--R 8a b coth(x) + (6a b + 12a b + 6a )cosh(x) + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 4 3 2 2 4 2 +--R ((- 4a b - 8a b - 4a )cosh(x) + (4a b + 4a )cosh(x))coth(x) +--R + +--R 3 2 2 3 4 3 +--R 16a b cosh(x)coth(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 4 +--R (4a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 4 2 2 4 2 2 2 3 +--R (- a b - 2a b - a )cosh(x) + (2a b + 2a )cosh(x) - a b + 2a b +--R + +--R 4 +--R - a +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 2 3 4 4 2 2 4 2 +--R 8a b cosh(x) coth(x) + (a b + 2a b + a )cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 3 4 +--R a b - 2a b + a +--R / +--R 2 4 3 3 5 6 2 +--R (a b + 2a b - 2a b - a )coth(x) +--R + +--R 5 2 4 4 2 5 6 5 3 3 4 2 +--R (2a b + 4a b - 4a b - 2a b)coth(x) + b + 2a b - 2a b - a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 3 3 5 6 2 +--R (4a b + 8a b - 8a b - 4a )cosh(x)coth(x) +--R + +--R 5 2 4 4 2 5 +--R (8a b + 16a b - 16a b - 8a b)cosh(x)coth(x) +--R + +--R 6 5 3 3 4 2 +--R (4b + 8a b - 8a b - 4a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 5 6 2 2 4 4 2 6 +--R ((6a b + 12a b - 12a b - 6a )cosh(x) - 2a b + 4a b - 2a ) +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 4 4 2 5 2 5 3 3 5 +--R ((12a b + 24a b - 24a b - 12a b)cosh(x) - 4a b + 8a b - 4a b) +--R * +--R coth(x) +--R + +--R 6 5 3 3 4 2 2 6 2 4 4 2 +--R (6b + 12a b - 12a b - 6a b )cosh(x) - 2b + 4a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 5 6 3 +--R (4a b + 8a b - 8a b - 4a )cosh(x) +--R + +--R 2 4 4 2 6 +--R (- 4a b + 8a b - 4a )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 4 4 2 5 3 +--R (8a b + 16a b - 16a b - 8a b)cosh(x) +--R + +--R 5 3 3 5 +--R (- 8a b + 16a b - 8a b)cosh(x) +--R * +--R coth(x) +--R + +--R 6 5 3 3 4 2 3 6 2 4 4 2 +--R (4b + 8a b - 8a b - 4a b )cosh(x) + (- 4b + 8a b - 4a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 5 6 4 2 4 4 2 6 2 +--R (a b + 2a b - 2a b - a )cosh(x) + (- 2a b + 4a b - 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 +--R a b - 2a b + 2a b - a +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 4 4 2 5 4 +--R (2a b + 4a b - 4a b - 2a b)cosh(x) +--R + +--R 5 3 3 5 2 5 2 4 4 2 5 +--R (- 4a b + 8a b - 4a b)cosh(x) + 2a b - 4a b + 4a b - 2a b +--R * +--R coth(x) +--R + +--R 6 5 3 3 4 2 4 6 2 4 4 2 2 +--R (b + 2a b - 2a b - a b )cosh(x) + (- 2b + 4a b - 2a b )cosh(x) +--R + +--R 6 5 3 3 4 2 +--R b - 2a b + 2a b - a b +--R Type: Expression(Integer) +--E 109 + +)clear all + + +--S 110 of 531 +t1021:= sinh(x)/(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R sinh(x) +--R (1) --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 110 + +--S 111 of 531 +r1021:= -1/2*a/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^2-_ + b*sinh(x)/a/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R (2) +--R 2 2 2 +--R 2b sinh(x) + 2a b cosh(x)sinh(x) + a +--R / +--R 4 3 2 2 2 3 4 +--R (2a b - 2a b )sinh(x) + (4a b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 5 2 +--R (2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 531 +a1021:= integrate(t1021,x) +--R +--R +--R (3) +--R (- 4b - 2a)sinh(x) - 2a cosh(x) +--R / +--R 4 3 2 2 3 4 3 +--R (b + 4a b + 6a b + 4a b + a )sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (3b + 12a b + 18a b + 12a b + 3a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (3b + 12a b + 18a b + 12a b + 3a )cosh(x) - 3b - 4a b + 2a b +--R + +--R 3 4 +--R 4a b + a +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b + 4a b + 6a b + 4a b + a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- b - 4a b - 2a b + 4a b + 3a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 112 + +--S 113 of 531 +m1021:= a1021-r1021 +--R +--R +--R (4) +--R 5 4 2 3 3 2 5 +--R (- 2b - 6a b - 6a b - 2a b )sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 6b - 20a b - 24a b - 12a b - 2a b)cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 4 +--R (- 6b - 24a b - 36a b - 24a b - 6a b)cosh(x) + 6b - 6a b +--R + +--R 2 3 3 2 4 5 +--R - 3a b - a b - 3a b - a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 2b - 12a b - 24a b - 20a b - 6a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b + 12a b - 23a b - 9a b - 3a b - 3a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 2a b - 6a b - 6a b - 2a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 2 3 3 2 4 5 +--R (2a b + 3a b - 27a b - 3a b + a )cosh(x) + 3a b + a b - 3a b - a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 4 5 3 2 3 3 2 4 5 +--R (- a b - 3a b - 7a b + 3a )cosh(x) + (a b + 3a b - a b - 3a )cosh(x) +--R / +--R 7 2 6 3 5 4 4 5 3 6 2 5 +--R (2a b + 6a b + 4a b - 4a b - 6a b - 2a b )sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 4 +--R (6a b + 22a b + 24a b - 4a b - 26a b - 18a b - 4a b)cosh(x)sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 +--R (6a b + 30a b + 50a b + 18a b - 38a b - 46a b - 18a b - 2a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 6a b - 2a b + 12a b + 4a b - 6a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 +--R (2a b + 18a b + 46a b + 38a b - 18a b - 50a b - 30a b - 6a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 7 2 6 4 4 5 3 6 2 7 +--R (- 2a b - 18a b + 36a b + 6a b - 18a b - 4a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 4 +--R (4a b + 18a b + 26a b + 4a b - 24a b - 22a b - 6a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 7 8 2 +--R (- 4a b - 18a b + 6a b + 36a b - 18a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 5 +--R (2a b + 6a b + 4a b - 4a b - 6a b - 2a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (- 2a b - 6a b + 4a b + 12a b - 2a b - 6a )cosh(x) +--R Type: Expression(Integer) +--E 113 + +--S 114 of 531 +d1021:= D(m1021,x) +--R +--R +--R (5) +--R 6 5 2 4 3 3 4 2 9 +--R (b + 4a b + 6a b + 4a b + a b )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (6b + 25a b + 40a b + 30a b + 10a b + a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 6 +--R (14b + 62a b + 108a b + 92a b + 38a b + 6a b)cosh(x) + 6b +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 4a b - 7a b + 8a b + 8a b + 4a b + a +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (14b + 70a b + 140a b + 140a b + 70a b + 14a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (12b + 15a b - 10a b + 14a b + 48a b + 27a b + 6a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (14a b + 56a b + 84a b + 56a b + 14a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (6b + 66a b + 63a b + 36a b + 84a b + 66a b + 15a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 5b - 8a b - 4a b - 8a b + 5a b + 8a b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 14b - 56a b - 84a b - 56a b - 14a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (8b + 85a b + 192a b + 138a b + 64a b + 57a b + 16a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (6b - a b - 56a b - 10a b + 14a b + 35a b + 12a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 14b - 70a b - 140a b - 140a b - 70a b - 14a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b + 72a b + 215a b + 224a b + 48a b - 16a b - a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 4b - 2a b - 64a b - 68a b + 60a b + 54a b + 24a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R 9a b - 12a b - 2a b + 4a b + a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 6b - 38a b - 92a b - 108a b - 62a b - 14a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (12b + 57a b + 126a b + 162a b + 48a b - 51a b - 18a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (- 6b - 28a b - 28a b - 56a b + 34a b + 68a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (9a b - 6a b + 6a b - 24a b + 9a b + 6a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (- b - 10a b - 30a b - 40a b - 25a b - 6a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (2b + 26a b + 49a b + 52a b + 20a b - 22a b - 15a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- b - 22a b - 28a b + 12a b - a b + 34a b + 6a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (6a b + 9a b - 24a b + 6a b - 6a b + 9a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 9 +--R (- a b - 4a b - 6a b - 4a b - a b)cosh(x) +--R + +--R 5 2 4 3 3 5 6 7 +--R (3a b + 12a b + 6a b - a b - 4a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 3a b - 12a b + 2a b + 16a b - 7a b + 4a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (a b + 4a b - 2a b - 12a b + 9a b)cosh(x) +--R / +--R 9 8 2 7 4 5 5 4 6 3 9 +--R (b + 4a b + 5a b - 5a b - 4a b - a b )sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (6b + 27a b + 42a b + 15a b - 30a b - 39a b - 18a b - 3a b ) +--R * +--R 8 +--R cosh(x)sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 15b + 78a b + 150a b + 102a b - 60a b - 150a b - 102a b +--R + +--R 7 2 8 +--R - 30a b - 3a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 6b - 8a b + 10a b + 16a b - 2a b - 8a b - 2a b +--R * +--R 7 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 20b + 125a b + 298a b + 298a b - 6a b - 300a b - 290a b +--R + +--R 7 2 8 9 +--R - 122a b - 22a b - a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 20b - 50a b + 4a b + 94a b + 52a b - 38a b - 36a b +--R + +--R 7 2 +--R - 6a b +--R * +--R cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 15b + 120a b + 360a b + 486a b + 174a b - 330a b - 480a b +--R + +--R 7 2 8 9 +--R - 270a b - 69a b - 6a +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 24b - 108a b - 90a b + 156a b + 246a b + 12a b - 126a b +--R + +--R 7 2 8 +--R - 60a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 9b - 12a b - 11a b + 16a b + 3a b - 4a b - a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b + 69a b + 270a b + 480a b + 330a b - 174a b - 486a b +--R + +--R 7 2 8 9 +--R - 360a b - 120a b - 15a +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 12b - 104a b - 200a b + 34a b + 392a b + 242a b - 136a b +--R + +--R 7 2 8 9 +--R - 170a b - 44a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (6b + 35a b - 70a b - 33a b + 82a b + a b - 18a b - 3a b ) +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R b + 22a b + 122a b + 290a b + 300a b + 6a b - 298a b +--R + +--R 7 2 8 9 +--R - 298a b - 125a b - 20a +--R * +--R 6 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 2b - 44a b - 170a b - 136a b + 242a b + 392a b + 34a b +--R + +--R 7 2 8 9 +--R - 200a b - 104a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R b + 22a b + 48a b - 154a b - 22a b + 162a b - 24a b +--R + +--R 7 2 8 +--R - 30a b - 3a b +--R * +--R 2 +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 3a b + 30a b + 102a b + 150a b + 60a b - 102a b - 150a b +--R + +--R 8 9 +--R - 78a b - 15a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 6a b - 60a b - 126a b + 12a b + 246a b + 156a b - 90a b +--R + +--R 8 9 +--R - 108a b - 24a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 3a b + 30a b + 24a b - 162a b + 22a b + 154a b - 48a b +--R + +--R 8 9 +--R - 22a b - a +--R * +--R 3 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (3a b + 18a b + 39a b + 30a b - 15a b - 42a b - 27a b - 6a ) +--R * +--R 8 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R - 6a b - 36a b - 38a b + 52a b + 94a b + 4a b - 50a b +--R + +--R 9 +--R - 20a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (3a b + 18a b - a b - 82a b + 33a b + 70a b - 35a b - 6a ) +--R * +--R 4 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 6 4 5 5 4 7 2 8 9 9 +--R (a b + 4a b + 5a b - 5a b - 4a b - a )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 7 +--R (- 2a b - 8a b - 2a b + 16a b + 10a b - 8a b - 6a )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 5 +--R (a b + 4a b - 3a b - 16a b + 11a b + 12a b - 9a )cosh(x) +--R Type: Expression(Integer) +--E 114 + +)clear all + + +--S 115 of 531 +t1022:= sinh(x)^3/(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R 3 +--R sinh(x) +--R (1) --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 115 + +--S 116 of 531 +r1022:= -b*(3*a^2+b^2)*x/(a^2-b^2)^3-1/2*a/(a^2-b^2)/(b+a*coth(x))^2+_ + 2*a*b/(a^2-b^2)^2/(b+a*coth(x))+a*(a^2+3*b^2)*_ + log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3 +--R +--R +--R (2) +--R 3 2 5 2 2 3 4 4 3 2 +--R ((- 6a b - 2a )coth(x) + (- 12a b - 4a b)coth(x) - 6a b - 2a b ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 2 3 4 2 4 3 2 2 3 4 +--R (2a b + 6a b)x coth(x) + ((4a b + 12a b )x + 4a b - 4a b)coth(x) +--R + +--R 5 2 3 4 3 2 5 +--R (2b + 6a b )x + 5a b - 6a b + a +--R / +--R 2 6 4 4 6 2 8 2 +--R (2a b - 6a b + 6a b - 2a )coth(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 6 2 +--R (4a b - 12a b + 12a b - 4a b)coth(x) + 2b - 6a b + 6a b - 2a b +--R Type: Expression(Integer) +--E 116 + +--S 117 of 531 +a1022:= integrate(t1022,x) +--R +--R +--R (3) +--R 4 2 3 3 2 4 5 4 +--R (- 3a b - 6a b - 4a b - 2a b - a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 12a b - 24a b - 16a b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 4 2 3 3 2 4 5 2 4 +--R (- 18a b - 36a b - 24a b - 12a b - 6a )cosh(x) + 6a b +--R + +--R 3 2 5 +--R - 4a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 12a b - 24a b - 16a b - 8a b - 4a )cosh(x) +--R + +--R 4 3 2 5 +--R (12a b - 8a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 3a b - 6a b - 4a b - 2a b - a )cosh(x) +--R + +--R 4 3 2 5 2 4 2 3 3 2 4 5 +--R (6a b - 4a b - 2a )cosh(x) - 3a b + 6a b - 4a b + 2a b - a +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (b + 5a b + 10a b + 10a b + 5a b + a )x sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (4b + 20a b + 40a b + 40a b + 20a b + 4a )x cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (6b + 30a b + 60a b + 60a b + 30a b + 6a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 3 3 2 4 +--R (- 2b - 6a b - 4a b + 4a b + 6a b + 2a )x - 6a b + 2a b + 6a b +--R + +--R 5 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (4b + 20a b + 40a b + 40a b + 20a b + 4a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 3 3 2 +--R (- 4b - 12a b - 8a b + 8a b + 12a b + 4a )x - 12a b + 4a b +--R + +--R 4 5 +--R 12a b - 4a +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (b + 5a b + 10a b + 10a b + 5a b + a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 3 3 2 4 +--R (- 2b - 6a b - 4a b + 4a b + 6a b + 2a )x - 6a b + 2a b + 6a b +--R + +--R 5 +--R - 2a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 3 3 2 4 +--R (b + a b - 2a b - 2a b + a b + a )x + 6a b - 12a b + 6a b +--R / +--R 8 7 2 6 3 5 5 3 6 2 7 8 4 +--R (b + 2a b - 2a b - 6a b + 6a b + 2a b - 2a b - a )sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (4b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (6b + 12a b - 12a b - 36a b + 36a b + 12a b - 12a b - 6a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R - 2b + 8a b - 12a b + 8a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 3 +--R (4b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a )cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R (- 4b + 16a b - 24a b + 16a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 4 +--R (b + 2a b - 2a b - 6a b + 6a b + 2a b - 2a b - a )cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 8 7 2 6 +--R (- 2b + 8a b - 12a b + 8a b - 2a )cosh(x) + b - 2a b - 2a b +--R + +--R 3 5 5 3 6 2 7 8 +--R 6a b - 6a b + 2a b + 2a b - a +--R Type: Union(Expression(Integer),...) +--E 117 + +--S 118 of 531 +m1022:= a1022-r1022 +--R +--R +--R (4) +--R 3 4 4 3 5 2 6 7 2 +--R (6a b + 12a b + 8a b + 4a b + 2a )coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 2 5 +--R (12a b + 24a b + 16a b + 8a b + 4a b)coth(x) + 6a b + 12a b +--R + +--R 3 4 4 3 5 2 +--R 8a b + 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (24a b + 48a b + 32a b + 16a b + 8a )cosh(x)coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (48a b + 96a b + 64a b + 32a b + 16a b)cosh(x)coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (24a b + 48a b + 32a b + 16a b + 8a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 3 4 +--R (36a b + 72a b + 48a b + 24a b + 12a )cosh(x) - 12a b +--R + +--R 5 2 7 +--R 8a b + 4a +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 2 5 +--R (72a b + 144a b + 96a b + 48a b + 24a b)cosh(x) - 24a b +--R + +--R 4 3 6 +--R 16a b + 8a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 6 +--R (36a b + 72a b + 48a b + 24a b + 12a b )cosh(x) - 12a b +--R + +--R 3 4 5 2 +--R 8a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (24a b + 48a b + 32a b + 16a b + 8a )cosh(x) +--R + +--R 3 4 5 2 7 +--R (- 24a b + 16a b + 8a )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (48a b + 96a b + 64a b + 32a b + 16a b)cosh(x) +--R + +--R 2 5 4 3 6 +--R (- 48a b + 32a b + 16a b)cosh(x) +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (24a b + 48a b + 32a b + 16a b + 8a b )cosh(x) +--R + +--R 6 3 4 5 2 +--R (- 24a b + 16a b + 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (6a b + 12a b + 8a b + 4a b + 2a )cosh(x) +--R + +--R 3 4 5 2 7 2 3 4 4 3 5 2 6 +--R (- 12a b + 8a b + 4a )cosh(x) + 6a b - 12a b + 8a b - 4a b +--R + +--R 7 +--R 2a +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (12a b + 24a b + 16a b + 8a b + 4a b)cosh(x) +--R + +--R 2 5 4 3 6 2 2 5 3 4 4 3 +--R (- 24a b + 16a b + 8a b)cosh(x) + 12a b - 24a b + 16a b +--R + +--R 5 2 6 +--R - 8a b + 4a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (6a b + 12a b + 8a b + 4a b + 2a b )cosh(x) +--R + +--R 6 3 4 5 2 2 6 2 5 3 4 4 3 +--R (- 12a b + 8a b + 4a b )cosh(x) + 6a b - 12a b + 8a b - 4a b +--R + +--R 5 2 +--R 2a b +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (- 6a b - 12a b - 8a b - 4a b - 2a )coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (- 12a b - 24a b - 16a b - 8a b - 4a b)coth(x) - 6a b +--R + +--R 2 5 3 4 4 3 5 2 +--R - 12a b - 8a b - 4a b - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (- 24a b - 48a b - 32a b - 16a b - 8a )cosh(x)coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 48a b - 96a b - 64a b - 32a b - 16a b)cosh(x)coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (- 24a b - 48a b - 32a b - 16a b - 8a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 3 4 +--R (- 36a b - 72a b - 48a b - 24a b - 12a )cosh(x) + 12a b +--R + +--R 5 2 7 +--R - 8a b - 4a +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 +--R (- 72a b - 144a b - 96a b - 48a b - 24a b)cosh(x) +--R + +--R 2 5 4 3 6 +--R 24a b - 16a b - 8a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 6 +--R (- 36a b - 72a b - 48a b - 24a b - 12a b )cosh(x) + 12a b +--R + +--R 3 4 5 2 +--R - 8a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (- 24a b - 48a b - 32a b - 16a b - 8a )cosh(x) +--R + +--R 3 4 5 2 7 +--R (24a b - 16a b - 8a )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 48a b - 96a b - 64a b - 32a b - 16a b)cosh(x) +--R + +--R 2 5 4 3 6 +--R (48a b - 32a b - 16a b)cosh(x) +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (- 24a b - 48a b - 32a b - 16a b - 8a b )cosh(x) +--R + +--R 6 3 4 5 2 +--R (24a b - 16a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- 6a b - 12a b - 8a b - 4a b - 2a )cosh(x) +--R + +--R 3 4 5 2 7 2 3 4 4 3 5 2 6 +--R (12a b - 8a b - 4a )cosh(x) - 6a b + 12a b - 8a b + 4a b +--R + +--R 7 +--R - 2a +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 12a b - 24a b - 16a b - 8a b - 4a b)cosh(x) +--R + +--R 2 5 4 3 6 2 2 5 3 4 4 3 +--R (24a b - 16a b - 8a b)cosh(x) - 12a b + 24a b - 16a b +--R + +--R 5 2 6 +--R 8a b - 4a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (- 6a b - 12a b - 8a b - 4a b - 2a b )cosh(x) +--R + +--R 6 3 4 5 2 2 6 2 5 3 4 4 3 +--R (12a b - 8a b - 4a b )cosh(x) - 6a b + 12a b - 8a b + 4a b +--R + +--R 5 2 +--R - 2a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (6a b + 12a b + 8a b + 4a b + 2a )x coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (12a b + 24a b + 16a b + 8a b + 4a b)x - 4a b - 8a b +--R + +--R 5 2 6 +--R 8a b + 4a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (6a b + 12a b + 8a b + 4a b + 2a b )x - 5a b - 10a b + a b +--R + +--R 4 3 5 2 6 7 +--R 12a b + 5a b - 2a b - a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (24a b + 48a b + 32a b + 16a b + 8a )x cosh(x)coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (48a b + 96a b + 64a b + 32a b + 16a b)x - 16a b - 32a b +--R + +--R 5 2 6 +--R 32a b + 16a b +--R * +--R cosh(x)coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (24a b + 48a b + 32a b + 16a b + 8a b )x - 20a b - 40a b +--R + +--R 3 4 4 3 5 2 6 7 +--R 4a b + 48a b + 20a b - 8a b - 4a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (36a b + 72a b + 48a b + 24a b + 12a )x cosh(x) +--R + +--R 3 4 5 2 7 4 3 5 2 6 7 +--R (- 12a b + 8a b + 4a )x - 12a b + 4a b + 12a b - 4a +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 +--R (72a b + 144a b + 96a b + 48a b + 24a b)x - 24a b +--R + +--R 3 4 5 2 6 +--R - 48a b + 48a b + 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 5 4 3 6 2 5 3 4 4 3 5 2 +--R (- 24a b + 16a b + 8a b)x + 8a b - 24a b - 8a b + 24a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (36a b + 72a b + 48a b + 24a b + 12a b )x - 30a b - 60a b +--R + +--R 3 4 4 3 5 2 6 7 +--R 6a b + 72a b + 30a b - 12a b - 6a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 3 4 5 2 6 2 5 3 4 4 3 +--R (- 12a b + 8a b + 4a b )x + 10a b - 12a b - 18a b + 12a b +--R + +--R 5 2 7 +--R 10a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (24a b + 48a b + 32a b + 16a b + 8a )x cosh(x) +--R + +--R 3 4 5 2 7 4 3 5 2 6 7 +--R ((- 24a b + 16a b + 8a )x - 24a b + 8a b + 24a b - 8a )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 +--R (48a b + 96a b + 64a b + 32a b + 16a b)x - 16a b +--R + +--R 3 4 5 2 6 +--R - 32a b + 32a b + 16a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 5 4 3 6 2 5 3 4 4 3 +--R (- 48a b + 32a b + 16a b)x + 16a b - 48a b - 16a b +--R + +--R 5 2 +--R 48a b +--R * +--R cosh(x) +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (24a b + 48a b + 32a b + 16a b + 8a b )x - 20a b - 40a b +--R + +--R 3 4 4 3 5 2 6 7 +--R 4a b + 48a b + 20a b - 8a b - 4a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 3 4 5 2 6 2 5 3 4 4 3 +--R (- 24a b + 16a b + 8a b )x + 20a b - 24a b - 36a b + 24a b +--R + +--R 5 2 7 +--R 20a b - 4a +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (6a b + 12a b + 8a b + 4a b + 2a )x cosh(x) +--R + +--R 3 4 5 2 7 4 3 5 2 6 7 2 +--R ((- 12a b + 8a b + 4a )x - 12a b + 4a b + 12a b - 4a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 3 5 2 6 +--R (6a b - 12a b + 8a b - 4a b + 2a )x + 12a b - 24a b + 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (12a b + 24a b + 16a b + 8a b + 4a b)x - 4a b - 8a b +--R + +--R 5 2 6 +--R 8a b + 4a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 5 4 3 6 2 5 3 4 4 3 5 2 +--R ((- 24a b + 16a b + 8a b)x + 8a b - 24a b - 8a b + 24a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 3 4 4 3 +--R (12a b - 24a b + 16a b - 8a b + 4a b)x - 4a b + 32a b - 48a b +--R + +--R 5 2 6 +--R 16a b + 4a b +--R * +--R coth(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (6a b + 12a b + 8a b + 4a b + 2a b )x - 5a b - 10a b + a b +--R + +--R 4 3 5 2 6 7 +--R 12a b + 5a b - 2a b - a +--R * +--R 4 +--R cosh(x) +--R + +--R 6 3 4 5 2 6 2 5 3 4 4 3 +--R (- 12a b + 8a b + 4a b )x + 10a b - 12a b - 18a b + 12a b +--R + +--R 5 2 7 +--R 10a b - 2a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (6a b - 12a b + 8a b - 4a b + 2a b )x - 5a b + 22a b - 23a b +--R + +--R 5 2 6 7 +--R 5a b + 2a b - a +--R / +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 +--R (2a b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a ) +--R * +--R 2 +--R coth(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 9 +--R (4a b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a b) +--R * +--R coth(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 8 2 +--R 2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 +--R (8a b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b - 8a ) +--R * +--R 2 +--R cosh(x)coth(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 +--R 16a b + 32a b - 32a b - 96a b + 96a b + 32a b - 32a b +--R + +--R 9 +--R - 16a b +--R * +--R cosh(x)coth(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 8b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b +--R + +--R 8 2 +--R - 8a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 +--R 12a b + 24a b - 24a b - 72a b + 72a b + 24a b - 24a b +--R + +--R 10 +--R - 12a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 +--R - 4a b + 16a b - 24a b + 16a b - 4a +--R * +--R 2 +--R coth(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 +--R 24a b + 48a b - 48a b - 144a b + 144a b + 48a b +--R + +--R 8 2 9 +--R - 48a b - 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 +--R - 8a b + 32a b - 48a b + 32a b - 8a b +--R * +--R coth(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 12b + 24a b - 24a b - 72a b + 72a b + 24a b - 24a b +--R + +--R 8 2 +--R - 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 +--R - 4b + 16a b - 24a b + 16a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 +--R 8a b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b +--R + +--R 10 +--R - 8a +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 +--R (- 8a b + 32a b - 48a b + 32a b - 8a )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 +--R 16a b + 32a b - 32a b - 96a b + 96a b + 32a b - 32a b +--R + +--R 9 +--R - 16a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 +--R (- 16a b + 64a b - 96a b + 64a b - 16a b)cosh(x) +--R * +--R coth(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 8b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b +--R + +--R 8 2 +--R - 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 +--R (- 8b + 32a b - 48a b + 32a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 +--R (2a b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a ) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 2 8 3 7 +--R (- 4a b + 16a b - 24a b + 16a b - 4a )cosh(x) + 2a b - 4a b +--R + +--R 4 6 5 5 7 3 8 2 9 10 +--R - 4a b + 12a b - 12a b + 4a b + 4a b - 2a +--R * +--R 2 +--R coth(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 9 +--R (4a b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 2 9 2 8 +--R (- 8a b + 32a b - 48a b + 32a b - 8a b)cosh(x) + 4a b - 8a b +--R + +--R 3 7 4 6 6 4 7 3 8 2 9 +--R - 8a b + 24a b - 24a b + 8a b + 8a b - 4a b +--R * +--R coth(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 8 2 4 +--R (2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 10 9 +--R (- 4b + 16a b - 24a b + 16a b - 4a b )cosh(x) + 2b - 4a b +--R + +--R 2 8 3 7 5 5 6 4 7 3 8 2 +--R - 4a b + 12a b - 12a b + 4a b + 4a b - 2a b +--R Type: Expression(Integer) +--E 118 + +--S 119 of 531 +--d1022:= D(m1022,x) +--E 119 + +)clear all + + +--S 120 of 531 +t1023:= cosh(x)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R cosh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 120 + +--S 121 of 531 +r1023:= -(-a*x+b*log(a*cosh(x)+b*sinh(x)))/(a^2-b^2) +--R +--R +--R b log(b sinh(x) + a cosh(x)) - a x +--R (2) ---------------------------------- +--R 2 2 +--R b - a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 531 +a1023:= integrate(t1023,x) +--R +--R +--R - 2b sinh(x) - 2a cosh(x) +--R b log(-------------------------) + (- b - a)x +--R sinh(x) - cosh(x) +--R (3) --------------------------------------------- +--R 2 2 +--R b - a +--R Type: Union(Expression(Integer),...) +--E 122 + +--S 123 of 531 +m1023:= a1023-r1023 +--R +--R +--R (4) +--R - 2b sinh(x) - 2a cosh(x) +--R - b log(b sinh(x) + a cosh(x)) + b log(-------------------------) - b x +--R sinh(x) - cosh(x) +--R ----------------------------------------------------------------------- +--R 2 2 +--R b - a +--R Type: Expression(Integer) +--E 123 + +--S 124 of 531 +d1023:= D(m1023,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 124 + +)clear all + + +--S 125 of 531 +t1024:= cosh(x)^2/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 2 +--R cosh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 125 + +--S 126 of 531 +r1024:= -b^2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ + b*cosh(x)/(a^2-b^2)+a*sinh(x)/(a^2-b^2) +--R +--R +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R b atan(---------------------) + (- a sinh(x) + b cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) --------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 531 +a1024:= integrate(t1024,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|- b + a +--R (- 4b sinh(x) - 4b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 127 + +--S 128 of 531 +m1024a:= a1024.1-r1024 +--R +--R +--R (4) +--R +---------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R +-------+ +--R 2 2 | 2 2 a sinh(x) + b cosh(x) +--R (- 2b sinh(x) - 2b cosh(x))\|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 | 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a \|b - a +--R Type: Expression(Integer) +--E 128 + +--S 129 of 531 +d1024a:= D(m1024a,x) +--R +--R +--R (5) +--R 2 2 3 4 6 +--R (- a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 4 +--R ((- b - 6a b - 9a b - 4a b)cosh(x) - b + 4a b - 4a b - 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 3 4 +--R (- 4b + 4a b - 12a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4a b + 9a b + 6a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 +--R (- 2b - 2a b - 14a b - 6a b)cosh(x) - 2b + 7a b - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b - 12a b - 12a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 4b + 6a b + 6a b - 6a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 3 2 2 3 4 4 +--R (b + 2a b + a b )cosh(x) + (b - 6a b - 2a b + 2a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 +--R (- b + 4a b - a b - 2a b)cosh(x) - b + 2a b - a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 129 + +--S 130 of 531 +m1024b:= a1024.2-r1024 +--R +--R +--R (6) +--R +---------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|- b + a +--R (- 4b sinh(x) - 4b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 a sinh(x) + b cosh(x) +--R (- 2b sinh(x) - 2b cosh(x))atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 130 + +--S 131 of 531 +d1024b:= D(m1024b,x) +--R +--R +--R (7) +--R 2 2 3 4 6 +--R (- a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 4 +--R ((- b - 6a b - 9a b - 4a b)cosh(x) - b + 4a b - 4a b - 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 3 4 +--R (- 4b + 4a b - 12a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4a b + 9a b + 6a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 +--R (- 2b - 2a b - 14a b - 6a b)cosh(x) - 2b + 7a b - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b - 12a b - 12a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 4b + 6a b + 6a b - 6a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 3 2 2 3 4 4 +--R (b + 2a b + a b )cosh(x) + (b - 6a b - 2a b + 2a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 +--R (- b + 4a b - a b - 2a b)cosh(x) - b + 2a b - a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 131 + +)clear all + + +--S 132 of 531 +t1025:= cosh(x)^3/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 3 +--R cosh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 132 + +--S 133 of 531 +r1025:= 1/2/(a^2-b^2)^2*(-3*a*b^2*x+a^3*x+2*log(a*cosh(x)+_ + b*sinh(x))*b^3+a^3*cosh(x)*sinh(x)-cosh(x)*b^2*a*sinh(x)+a^2*b-_ + a^2*b*cosh(x)^2-b^3+cosh(x)^2*b^3) +--R +--R +--R (2) +--R 3 2 3 +--R 2b log(b sinh(x) + a cosh(x)) + (- a b + a )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (b - a b)cosh(x) + (- 3a b + a )x - b + a b +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression(Integer) +--E 133 + +--S 134 of 531 +a1025:= integrate(t1025,x) +--R +--R +--R (3) +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 3 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (- 8b - 12a b + 4a )x)sinh(x) +--R + +--R 3 2 2 3 3 3 2 3 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (- 16b - 24a b + 8a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 3 2 3 +--R (b - a b - a b + a )cosh(x) + (- 8b - 12a b + 4a )x cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 134 + +--S 135 of 531 +m1025:= a1025-r1025 +--R +--R +--R (4) +--R 3 2 3 3 2 +--R (- 8b sinh(x) - 16b cosh(x)sinh(x) - 8b cosh(x) ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (b - a b - a b + a )sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 3 2 2 +--R ((2b + 2a b - 2a b - 2a )cosh(x) - 8b x + 4b - 4a b)sinh(x) +--R + +--R 3 2 3 3 3 2 +--R ((- 4b + 4a b)cosh(x) + (- 16b x + 8b - 8a b)cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 2 3 +--R (- 3b - a b + 3a b + a )cosh(x) + (- 8b x + 4b - 4a b)cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 135 + +--S 136 of 531 +d1025:= D(m1025,x) +--R +--R +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 +--R (5) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression(Integer) +--E 136 + +)clear all + + +--S 137 of 531 +t1026:= cosh(x)/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R cosh(x) +--R (1) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 137 + +--S 138 of 531 +r1026:= a*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ + b/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R (- a b sinh(x) - a cosh(x))atan(---------------------) - b\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) ---------------------------------------------------------------------- +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sinh(x) + (a b - a )cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 138 + +--S 139 of 531 +a1026:= integrate(t1026,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R (a b + a )sinh(x) + (2a b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (a b + a )cosh(x) - a b + a +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R +-------+ +--R | 2 2 +--R (- 2b sinh(x) - 2b cosh(x))\|b - a +--R / +--R 3 2 2 3 2 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )cosh(x) - b + a b + a b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 2 2 2 +--R (2a b + 2a )sinh(x) + (4a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (2a b + 2a )cosh(x) - 2a b + 2a +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R +---------+ +--R | 2 2 +--R (- 2b sinh(x) - 2b cosh(x))\|- b + a +--R / +--R 3 2 2 3 2 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )cosh(x) - b + a b + a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 139 + +--S 140 of 531 +m1026a:= a1026.1-r1026 +--R +--R +--R (4) +--R 2 2 3 2 2 3 2 +--R (a b + a b)sinh(x) + (2a b + 3a b + a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 +--R ((a b + 3a b + 2a )cosh(x) - a b + a b)sinh(x) +--R + +--R 2 3 3 2 3 +--R (a b + a )cosh(x) + (- a b + a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R 2 2 3 2 2 3 2 +--R (a b + a b)sinh(x) + (2a b + 3a b + a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 +--R ((a b + 3a b + 2a )cosh(x) - a b + a b)sinh(x) +--R + +--R 2 3 3 2 3 +--R (a b + a )cosh(x) + (- a b + a )cosh(x) +--R * +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R \|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((- b + a b)sinh(x) + (b - a b)cosh(x) - b + a b)\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 3 2 2 3 3 +--R (b + a b - a b - a b)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b - a b - 3a b - a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R ((b + 3a b + a b - 3a b - 2a )cosh(x) - b + a b + a b - a b) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 2 3 4 +--R (a b + a b - a b - a )cosh(x) + (- a b + a b + a b - a )cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 140 + +--S 141 of 531 +d1026a:= D(m1026a,x) +--R +--R +--R (5) +--R 3 2 2 3 7 3 2 2 3 6 +--R (a b + 4a b + a b)sinh(x) + (8a b + 14a b + 8a b)cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (2b + 15a b + 20a b + 15a b + 2a )cosh(x) - 2b - a b + 6a b +--R + +--R 3 +--R 3a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (5b + 6a b + 8a b + 6a b + 5a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 5b + 2a b + 17a b + 16a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (2b - 9a b - 16a b - 9a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 2 4 3 3 +--R (10a b + 28a b + 18a b + 4a )cosh(x) - 2b - a b + 3a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 4b - 12a b - 22a b - 12a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (8b + 20a b + 18a b + 8a b + 6a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 4b - 8a b + 4a b + 8a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 7a b - 8a b - 7a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (8b + 15a b + 2a b + 3a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 3 2 2 3 +--R (- 4b - 9a b + 8a b + 3a b + 2a )cosh(x) + a b - 2a b + a b +--R * +--R sinh(x) +--R + +--R 4 3 3 4 7 4 3 2 2 5 +--R (- b - 2a b - 2a b - a )cosh(x) + (3b + 2a b + a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 4 3 2 2 +--R (- 3b + 2a b - 2a b + 2a b + a )cosh(x) + (b - 2a b + a b )cosh(x) +--R / +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) - b +--R + +--R 5 2 4 3 3 4 2 +--R - 2a b - 2a b + 2a b + 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 4b - 14a b - 8a b + 8a b + 12a b + 6a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (6b + 28a b + 64a b + 84a b + 64a b + 28a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 8b - 28a b - 25a b + 10a b + 30a b + 18a b + 3a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 +--R 2b - 3a b - 2a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (- 8b - 28a b - 40a b + 40a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 6a b - 12a b - 4a b + 6a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 3b - 18a b - 30a b - 10a b + 25a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (3b + 6a b + 3a b - 24a b + 3a b + 6a b + 3a )cosh(x) - b +--R + +--R 5 3 3 4 2 +--R 2a b - 2a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b - 12a b - 8a b + 8a b + 14a b + 4a )cosh(x) +--R + +--R 5 3 3 4 2 5 6 3 +--R (6a b - 4a b - 12a b + 6a b + 4a )cosh(x) +--R + +--R 5 2 4 4 2 5 +--R (- 2a b + 4a b - 4a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 3a b - 2a b + 2a b + 2a b + a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 4 +--R (3a b - 2a b - 3a b + 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 +--R (- a b + 2a b - 2a b + a )cosh(x) +--R Type: Expression(Integer) +--E 141 + +--S 142 of 531 +m1026b:= a1026.2-r1026 +--R +--R +--R (6) +--R 2 2 3 2 2 3 2 +--R (2a b + 2a b)sinh(x) + (4a b + 6a b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 +--R ((2a b + 6a b + 4a )cosh(x) - 2a b + 2a b)sinh(x) +--R + +--R 2 3 3 2 3 +--R (2a b + 2a )cosh(x) + (- 2a b + 2a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 2 2 3 2 2 3 2 +--R (a b + a b)sinh(x) + (2a b + 3a b + a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 +--R ((a b + 3a b + 2a )cosh(x) - a b + a b)sinh(x) +--R + +--R 2 3 3 2 3 +--R (a b + a )cosh(x) + (- a b + a )cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((- b + a b)sinh(x) + (b - a b)cosh(x) - b + a b)\|- b + a +--R / +--R 4 3 2 2 3 3 +--R (b + a b - a b - a b)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b - a b - 3a b - a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R ((b + 3a b + a b - 3a b - 2a )cosh(x) - b + a b + a b - a b) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 2 3 4 +--R (a b + a b - a b - a )cosh(x) + (- a b + a b + a b - a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 142 + +--S 143 of 531 +d1026b:= D(m1026b,x) +--R +--R +--R (7) +--R 3 2 2 3 7 3 2 2 3 6 +--R (a b + 4a b + a b)sinh(x) + (8a b + 14a b + 8a b)cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (2b + 15a b + 20a b + 15a b + 2a )cosh(x) - 2b - a b + 6a b +--R + +--R 3 +--R 3a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (5b + 6a b + 8a b + 6a b + 5a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 5b + 2a b + 17a b + 16a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (2b - 9a b - 16a b - 9a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 2 4 3 3 +--R (10a b + 28a b + 18a b + 4a )cosh(x) - 2b - a b + 3a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 4b - 12a b - 22a b - 12a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (8b + 20a b + 18a b + 8a b + 6a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 4b - 8a b + 4a b + 8a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 7a b - 8a b - 7a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (8b + 15a b + 2a b + 3a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 3 2 2 3 +--R (- 4b - 9a b + 8a b + 3a b + 2a )cosh(x) + a b - 2a b + a b +--R * +--R sinh(x) +--R + +--R 4 3 3 4 7 4 3 2 2 5 +--R (- b - 2a b - 2a b - a )cosh(x) + (3b + 2a b + a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 4 3 2 2 +--R (- 3b + 2a b - 2a b + 2a b + a )cosh(x) + (b - 2a b + a b )cosh(x) +--R / +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) - b +--R + +--R 5 2 4 3 3 4 2 +--R - 2a b - 2a b + 2a b + 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 4b - 14a b - 8a b + 8a b + 12a b + 6a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (6b + 28a b + 64a b + 84a b + 64a b + 28a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 8b - 28a b - 25a b + 10a b + 30a b + 18a b + 3a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 +--R 2b - 3a b - 2a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (4b + 22a b + 52a b + 68a b + 52a b + 22a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (- 8b - 28a b - 40a b + 40a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 6a b - 12a b - 4a b + 6a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (b + 10a b + 27a b + 36a b + 27a b + 10a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 3b - 18a b - 30a b - 10a b + 25a b + 28a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (3b + 6a b + 3a b - 24a b + 3a b + 6a b + 3a )cosh(x) - b +--R + +--R 5 3 3 4 2 +--R 2a b - 2a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (2a b + 8a b + 12a b + 8a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b - 12a b - 8a b + 8a b + 14a b + 4a )cosh(x) +--R + +--R 5 3 3 4 2 5 6 3 +--R (6a b - 4a b - 12a b + 6a b + 4a )cosh(x) +--R + +--R 5 2 4 4 2 5 +--R (- 2a b + 4a b - 4a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 8 +--R (a b + 2a b + a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 3a b - 2a b + 2a b + 2a b + a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 4 +--R (3a b - 2a b - 3a b + 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 +--R (- a b + 2a b - 2a b + a )cosh(x) +--R Type: Expression(Integer) +--E 143 + +)clear all + + +--S 144 of 531 +t1027:= cosh(x)^2/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R 2 +--R cosh(x) +--R (1) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 144 + +--S 145 of 531 +r1027:= (a^2+b^2)*x/(a^2-b^2)^2-2*a*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2+_ + b/(a^2-b^2)/(a+b*tanh(x)) +--R +--R +--R (2) +--R 2 2 3 2 +--R (- 2a b tanh(x) - 2a b)log(b sinh(x) + a cosh(x)) + (b + a b)x tanh(x) +--R + +--R 2 3 3 2 +--R (a b + a )x - b + a b +--R / +--R 5 2 3 4 4 3 2 5 +--R (b - 2a b + a b)tanh(x) + a b - 2a b + a +--R Type: Expression(Integer) +--E 145 + +--S 146 of 531 +a1027:= integrate(t1027,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (- 2a b - 2a b)sinh(x) + (- 4a b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 2a b - 2a b)cosh(x) + 2a b - 2a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 2 +--R (b + 3a b + 3a b + a )x sinh(x) +--R + +--R 3 2 2 3 +--R (2b + 6a b + 6a b + 2a )x cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 3 +--R (b + 3a b + 3a b + a )x cosh(x) + (- b - a b + a b + a )x - 2b +--R + +--R 2 +--R 2a b +--R / +--R 5 4 2 3 3 2 4 5 2 +--R (b + a b - 2a b - 2a b + a b + a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b + 2a b - 4a b - 4a b + 2a b + 2a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 2 3 +--R (b + a b - 2a b - 2a b + a b + a )cosh(x) - b + a b + 2a b +--R + +--R 3 2 4 5 +--R - 2a b - a b + a +--R Type: Union(Expression(Integer),...) +--E 146 + +--S 147 of 531 +m1027:= a1027-r1027 +--R +--R +--R (4) +--R 3 2 2 2 3 2 2 +--R (2a b + 2a b )sinh(x) + (4a b + 4a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2a b + 2a b )cosh(x) - 2a b + 2a b +--R * +--R tanh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 2a b)sinh(x) + (4a b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 2a b)cosh(x) - 2a b + 2a b +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2a b - 2a b )sinh(x) + (- 4a b - 4a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2a b - 2a b )cosh(x) + 2a b - 2a b +--R * +--R tanh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 2a b - 2a b)sinh(x) + (- 4a b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 2a b - 2a b)cosh(x) + 2a b - 2a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2a b + 2a b )x sinh(x) + (4a b + 4a b )x cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 3 +--R (2a b + 2a b )x cosh(x) + (- 2a b + 2a b )x - 2b + 2a b +--R * +--R tanh(x) +--R + +--R 2 2 3 4 3 2 2 3 2 +--R ((2a b + 2a b)x + b + a b - a b - a b)sinh(x) +--R + +--R 2 2 3 4 3 2 2 3 +--R ((4a b + 4a b)x + 2b + 2a b - 2a b - 2a b)cosh(x)sinh(x) +--R + +--R 2 2 3 4 3 2 2 3 2 2 2 3 +--R ((2a b + 2a b)x + b + a b - a b - a b)cosh(x) + (- 2a b + 2a b)x +--R + +--R 4 3 2 2 3 +--R - b - a b + 3a b - a b +--R / +--R 6 5 2 4 3 3 4 2 5 2 +--R (b + a b - 2a b - 2a b + a b + a b)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b + 2a b - 4a b - 4a b + 2a b + 2a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 6 5 2 4 +--R (b + a b - 2a b - 2a b + a b + a b)cosh(x) - b + a b + 2a b +--R + +--R 3 3 4 2 5 +--R - 2a b - a b + a b +--R * +--R tanh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (a b + a b - 2a b - 2a b + a b + a )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (2a b + 2a b - 4a b - 4a b + 2a b + 2a )cosh(x)sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 5 2 4 3 3 +--R (a b + a b - 2a b - 2a b + a b + a )cosh(x) - a b + a b + 2a b +--R + +--R 4 2 5 6 +--R - 2a b - a b + a +--R Type: Expression(Integer) +--E 147 + +--S 148 of 531 +d1027:= D(m1027,x) +--R +--R +--R (5) +--R 4 3 2 2 4 4 3 2 2 3 +--R (b + 2a b + a b )sinh(x) + (4b + 8a b + 4a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 2 2 2 +--R ((6b + 12a b + 6a b )cosh(x) + 2b + 2a b )sinh(x) +--R + +--R 4 3 2 2 3 4 2 2 +--R ((4b + 8a b + 4a b )cosh(x) + (4b + 4a b )cosh(x))sinh(x) +--R + +--R 4 3 2 2 4 4 2 2 2 4 3 2 2 +--R (b + 2a b + a b )cosh(x) + (2b + 2a b )cosh(x) + b - 2a b + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 3 3 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) )tanh(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (- b - 2a b - a b )sinh(x) + (- 4b - 8a b - 4a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 2 2 2 +--R ((- 6b - 12a b - 6a b )cosh(x) + 2b + 2a b )sinh(x) +--R + +--R 4 3 2 2 3 4 2 2 +--R ((- 4b - 8a b - 4a b )cosh(x) + (4b + 4a b )cosh(x))sinh(x) +--R + +--R 4 3 2 2 4 4 2 2 2 4 3 2 2 +--R (- b - 2a b - a b )cosh(x) + (2b + 2a b )cosh(x) - b + 2a b - a b +--R / +--R 6 5 3 3 4 2 4 +--R (b + 2a b - 2a b - a b )sinh(x) +--R + +--R 6 5 3 3 4 2 3 +--R (4b + 8a b - 8a b - 4a b )cosh(x)sinh(x) +--R + +--R 6 5 3 3 4 2 2 6 2 4 4 2 +--R ((6b + 12a b - 12a b - 6a b )cosh(x) - 2b + 4a b - 2a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 3 3 4 2 3 +--R (4b + 8a b - 8a b - 4a b )cosh(x) +--R + +--R 6 2 4 4 2 +--R (- 4b + 8a b - 4a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 5 3 3 4 2 4 6 2 4 4 2 2 +--R (b + 2a b - 2a b - a b )cosh(x) + (- 2b + 4a b - 2a b )cosh(x) +--R + +--R 6 5 3 3 4 2 +--R b - 2a b + 2a b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 5 2 4 4 2 5 4 +--R (2a b + 4a b - 4a b - 2a b)sinh(x) +--R + +--R 5 2 4 4 2 5 3 +--R (8a b + 16a b - 16a b - 8a b)cosh(x)sinh(x) +--R + +--R 5 2 4 4 2 5 2 5 3 3 5 +--R ((12a b + 24a b - 24a b - 12a b)cosh(x) - 4a b + 8a b - 4a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 4 2 5 3 +--R (8a b + 16a b - 16a b - 8a b)cosh(x) +--R + +--R 5 3 3 5 +--R (- 8a b + 16a b - 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 4 2 5 4 +--R (2a b + 4a b - 4a b - 2a b)cosh(x) +--R + +--R 5 3 3 5 2 5 2 4 4 2 5 +--R (- 4a b + 8a b - 4a b)cosh(x) + 2a b - 4a b + 4a b - 2a b +--R * +--R tanh(x) +--R + +--R 2 4 3 3 5 6 4 +--R (a b + 2a b - 2a b - a )sinh(x) +--R + +--R 2 4 3 3 5 6 3 +--R (4a b + 8a b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 4 3 3 5 6 2 2 4 4 2 6 2 +--R ((6a b + 12a b - 12a b - 6a )cosh(x) - 2a b + 4a b - 2a )sinh(x) +--R + +--R 2 4 3 3 5 6 3 2 4 4 2 6 +--R ((4a b + 8a b - 8a b - 4a )cosh(x) + (- 4a b + 8a b - 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 5 6 4 2 4 4 2 6 2 +--R (a b + 2a b - 2a b - a )cosh(x) + (- 2a b + 4a b - 2a )cosh(x) +--R + +--R 2 4 3 3 5 6 +--R a b - 2a b + 2a b - a +--R Type: Expression(Integer) +--E 148 + +)clear all + + +--S 149 of 531 +t1028:= cosh(x)/(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R cosh(x) +--R (1) --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 149 + +--S 150 of 531 +r1028:= 1/2*b/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^2+_ + sinh(x)/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R (2) +--R 2 +--R - 2b sinh(x) - 2a cosh(x)sinh(x) - b +--R ---------------------------------------------------------------------------- +--R 4 2 2 2 3 3 2 2 4 2 +--R (2b - 2a b )sinh(x) + (4a b - 4a b)cosh(x)sinh(x) + (2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 150 + +--S 151 of 531 +a1028:= integrate(t1028,x) +--R +--R +--R (3) +--R - 2b sinh(x) + (- 2b - 4a)cosh(x) +--R / +--R 4 3 2 2 3 4 3 +--R (b + 4a b + 6a b + 4a b + a )sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (3b + 12a b + 18a b + 12a b + 3a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (3b + 12a b + 18a b + 12a b + 3a )cosh(x) - 3b - 4a b + 2a b +--R + +--R 3 4 +--R 4a b + a +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b + 4a b + 6a b + 4a b + a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- b - 4a b - 2a b + 4a b + 3a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 151 + +--S 152 of 531 +m1028:= a1028-r1028 +--R +--R +--R (4) +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (6b + 20a b + 24a b + 12a b + 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 +--R (6b + 24a b + 36a b + 24a b + 6a )cosh(x) - 9b + 5a b + 9a b +--R + +--R 3 +--R 3a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b + 12a b + 24a b + 20a b + 6a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 3b - 15a b + 25a b + 15a b + 2a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (2a b + 6a b + 6a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R (3b - a b - 9a b + 25a b + 6a )cosh(x) - 3b - a b + 3a b + a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b + 3a b - a b - 3a b + 8a )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- b - 3a b + a b + 3a b)cosh(x) +--R / +--R 7 6 2 5 3 4 4 3 5 2 5 +--R (2b + 6a b + 4a b - 4a b - 6a b - 2a b )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 4 +--R (6b + 22a b + 24a b - 4a b - 26a b - 18a b - 4a b)cosh(x)sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (6b + 30a b + 50a b + 18a b - 38a b - 46a b - 18a b - 2a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 6b - 2a b + 12a b + 4a b - 6a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (2b + 18a b + 46a b + 38a b - 18a b - 50a b - 30a b - 6a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 +--R (- 2b - 18a b + 36a b + 6a b - 18a b - 4a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 4 +--R (4a b + 18a b + 26a b + 4a b - 24a b - 22a b - 6a )cosh(x) +--R + +--R 6 2 5 3 4 4 3 6 7 2 +--R (- 4a b - 18a b + 6a b + 36a b - 18a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 5 +--R (2a b + 6a b + 4a b - 4a b - 6a b - 2a )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 3 +--R (- 2a b - 6a b + 4a b + 12a b - 2a b - 6a )cosh(x) +--R Type: Expression(Integer) +--E 152 + +--S 153 of 531 +d1028:= D(m1028,x) +--R +--R +--R (5) +--R 5 2 4 3 3 4 2 5 9 +--R (- a b - 4a b - 6a b - 4a b - a b)sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 8 +--R (- 6a b - 25a b - 40a b - 30a b - 10a b - a )cosh(x)sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 6 +--R (- 14a b - 62a b - 108a b - 92a b - 38a b - 6a )cosh(x) + 4b +--R + +--R 5 3 3 4 2 5 +--R a b - 6a b - 12a b - 3a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 14a b - 70a b - 140a b - 140a b - 70a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (15b + 22a b - 20a b - 52a b - 49a b - 26a b - 2a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 14a b - 56a b - 84a b - 56a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (18b + 51a b - 48a b - 162a b - 126a b - 57a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 4b - 7a b + 16a b + 2a b - 12a b - 3a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (14a b + 56a b + 84a b + 56a b + 14a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (b + 16a b - 48a b - 224a b - 215a b - 72a b - 18a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (6b + 34a b - a b + 12a b - 28a b - 22a b - a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (14a b + 70a b + 140a b + 140a b + 70a b + 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 16b - 57a b - 64a b - 138a b - 192a b - 85a b - 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (16b + 68a b + 34a b - 56a b - 28a b - 28a b - 6a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 9a b + 12a b + 2a b - 4a b - a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (6a b + 38a b + 92a b + 108a b + 62a b + 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 15b - 66a b - 84a b - 36a b - 63a b - 66a b - 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (24b + 54a b + 60a b - 68a b - 64a b - 2a b - 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 9b + 6a b - 6a b + 24a b - 9a b - 6a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 8 +--R (a b + 10a b + 30a b + 40a b + 25a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 6b - 27a b - 48a b - 14a b + 10a b - 15a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (12b + 35a b + 14a b - 10a b - 56a b - a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 6b - 9a b + 24a b - 6a b + 6a b - 9a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (a b + 4a b + 6a b + 4a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 7 +--R (- b - 4a b - 8a b - 8a b + 7a b + 4a b - 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (2b + 8a b + 5a b - 8a b - 4a b - 8a b + 5a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- b - 4a b + 2a b + 12a b - 9a b )cosh(x) +--R / +--R 9 8 2 7 4 5 5 4 6 3 9 +--R (b + 4a b + 5a b - 5a b - 4a b - a b )sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (6b + 27a b + 42a b + 15a b - 30a b - 39a b - 18a b - 3a b ) +--R * +--R 8 +--R cosh(x)sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 15b + 78a b + 150a b + 102a b - 60a b - 150a b - 102a b +--R + +--R 7 2 8 +--R - 30a b - 3a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 6b - 8a b + 10a b + 16a b - 2a b - 8a b - 2a b +--R * +--R 7 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 20b + 125a b + 298a b + 298a b - 6a b - 300a b - 290a b +--R + +--R 7 2 8 9 +--R - 122a b - 22a b - a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 20b - 50a b + 4a b + 94a b + 52a b - 38a b - 36a b +--R + +--R 7 2 +--R - 6a b +--R * +--R cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 15b + 120a b + 360a b + 486a b + 174a b - 330a b - 480a b +--R + +--R 7 2 8 9 +--R - 270a b - 69a b - 6a +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 24b - 108a b - 90a b + 156a b + 246a b + 12a b - 126a b +--R + +--R 7 2 8 +--R - 60a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 9b - 12a b - 11a b + 16a b + 3a b - 4a b - a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b + 69a b + 270a b + 480a b + 330a b - 174a b - 486a b +--R + +--R 7 2 8 9 +--R - 360a b - 120a b - 15a +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 12b - 104a b - 200a b + 34a b + 392a b + 242a b - 136a b +--R + +--R 7 2 8 9 +--R - 170a b - 44a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (6b + 35a b - 70a b - 33a b + 82a b + a b - 18a b - 3a b ) +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R b + 22a b + 122a b + 290a b + 300a b + 6a b - 298a b +--R + +--R 7 2 8 9 +--R - 298a b - 125a b - 20a +--R * +--R 6 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 2b - 44a b - 170a b - 136a b + 242a b + 392a b + 34a b +--R + +--R 7 2 8 9 +--R - 200a b - 104a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R b + 22a b + 48a b - 154a b - 22a b + 162a b - 24a b +--R + +--R 7 2 8 +--R - 30a b - 3a b +--R * +--R 2 +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 3a b + 30a b + 102a b + 150a b + 60a b - 102a b - 150a b +--R + +--R 8 9 +--R - 78a b - 15a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 6a b - 60a b - 126a b + 12a b + 246a b + 156a b - 90a b +--R + +--R 8 9 +--R - 108a b - 24a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 3a b + 30a b + 24a b - 162a b + 22a b + 154a b - 48a b +--R + +--R 8 9 +--R - 22a b - a +--R * +--R 3 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (3a b + 18a b + 39a b + 30a b - 15a b - 42a b - 27a b - 6a ) +--R * +--R 8 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R - 6a b - 36a b - 38a b + 52a b + 94a b + 4a b - 50a b +--R + +--R 9 +--R - 20a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (3a b + 18a b - a b - 82a b + 33a b + 70a b - 35a b - 6a ) +--R * +--R 4 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 6 4 5 5 4 7 2 8 9 9 +--R (a b + 4a b + 5a b - 5a b - 4a b - a )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 7 +--R (- 2a b - 8a b - 2a b + 16a b + 10a b - 8a b - 6a )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 5 +--R (a b + 4a b - 3a b - 16a b + 11a b + 12a b - 9a )cosh(x) +--R Type: Expression(Integer) +--E 153 + +)clear all + + +--S 154 of 531 +t1029:= cosh(x)^3/(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R 3 +--R cosh(x) +--R (1) --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 154 + +--S 155 of 531 +r1029:= a*(a^2+3*b^2)*x/(a^2-b^2)^3-b*(3*a^2+b^2)*log(a*cosh(x)+_ + b*sinh(x))/(a^2-b^2)^3+1/2*b/(a^2-b^2)/(a+b*tanh(x))^2+_ + 2*a*b/(a^2-b^2)^2/(a+b*tanh(x)) +--R +--R +--R (2) +--R 5 2 3 2 4 3 2 2 3 4 +--R ((2b + 6a b )tanh(x) + (4a b + 12a b )tanh(x) + 2a b + 6a b) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 6a b - 2a b )x tanh(x) + ((- 12a b - 4a b)x + 4a b - 4a b )tanh(x) +--R + +--R 3 2 5 5 2 3 4 +--R (- 6a b - 2a )x - b + 6a b - 5a b +--R / +--R 8 2 6 4 4 6 2 2 +--R (2b - 6a b + 6a b - 2a b )tanh(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 8 +--R (4a b - 12a b + 12a b - 4a b)tanh(x) + 2a b - 6a b + 6a b - 2a +--R Type: Expression(Integer) +--E 155 + +--S 156 of 531 +a1029:= integrate(t1029,x) +--R +--R +--R (3) +--R 5 4 2 3 3 2 4 4 +--R (b + 2a b + 4a b + 6a b + 3a b)sinh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b + 8a b + 16a b + 24a b + 12a b)cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 2 3 +--R (6b + 12a b + 24a b + 36a b + 18a b)cosh(x) - 2b - 4a b +--R + +--R 4 +--R 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b + 8a b + 16a b + 24a b + 12a b)cosh(x) +--R + +--R 5 2 3 4 +--R (- 4b - 8a b + 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (b + 2a b + 4a b + 6a b + 3a b)cosh(x) +--R + +--R 5 2 3 4 2 5 4 2 3 3 2 4 +--R (- 2b - 4a b + 6a b)cosh(x) + b - 2a b + 4a b - 6a b + 3a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- b - 5a b - 10a b - 10a b - 5a b - a )x sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 4b - 20a b - 40a b - 40a b - 20a b - 4a )x cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 6b - 30a b - 60a b - 60a b - 30a b - 6a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 2 3 +--R (2b + 6a b + 4a b - 4a b - 6a b - 2a )x - 2b + 6a b + 2a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 4b - 20a b - 40a b - 40a b - 20a b - 4a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 +--R (4b + 12a b + 8a b - 8a b - 12a b - 4a )x - 4b + 12a b +--R + +--R 2 3 3 2 +--R 4a b - 12a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- b - 5a b - 10a b - 10a b - 5a b - a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 2 3 +--R (2b + 6a b + 4a b - 4a b - 6a b - 2a )x - 2b + 6a b + 2a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 3 2 +--R (- b - a b + 2a b + 2a b - a b - a )x - 6a b + 12a b - 6a b +--R / +--R 8 7 2 6 3 5 5 3 6 2 7 8 4 +--R (b + 2a b - 2a b - 6a b + 6a b + 2a b - 2a b - a )sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (4b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (6b + 12a b - 12a b - 36a b + 36a b + 12a b - 12a b - 6a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R - 2b + 8a b - 12a b + 8a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 3 +--R (4b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a )cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R (- 4b + 16a b - 24a b + 16a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 4 +--R (b + 2a b - 2a b - 6a b + 6a b + 2a b - 2a b - a )cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 8 7 2 6 +--R (- 2b + 8a b - 12a b + 8a b - 2a )cosh(x) + b - 2a b - 2a b +--R + +--R 3 5 5 3 6 2 7 8 +--R 6a b - 6a b + 2a b + 2a b - a +--R Type: Union(Expression(Integer),...) +--E 156 + +--S 157 of 531 +m1029:= a1029-r1029 +--R +--R +--R (4) +--R 7 6 2 5 3 4 4 3 4 +--R (- 2b - 4a b - 8a b - 12a b - 6a b )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 8b - 16a b - 32a b - 48a b - 24a b )cosh(x)sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 7 +--R (- 12b - 24a b - 48a b - 72a b - 36a b )cosh(x) + 4b +--R + +--R 2 5 4 3 +--R 8a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 8b - 16a b - 32a b - 48a b - 24a b )cosh(x) +--R + +--R 7 2 5 4 3 +--R (8b + 16a b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 2b - 4a b - 8a b - 12a b - 6a b )cosh(x) +--R + +--R 7 2 5 4 3 2 7 6 2 5 3 4 +--R (4b + 8a b - 12a b )cosh(x) - 2b + 4a b - 8a b + 12a b +--R + +--R 4 3 +--R - 6a b +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (- 4a b - 8a b - 16a b - 24a b - 12a b )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (- 16a b - 32a b - 64a b - 96a b - 48a b )cosh(x)sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 +--R (- 24a b - 48a b - 96a b - 144a b - 72a b )cosh(x) +--R + +--R 6 3 4 5 2 +--R 8a b + 16a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (- 16a b - 32a b - 64a b - 96a b - 48a b )cosh(x) +--R + +--R 6 3 4 5 2 +--R (16a b + 32a b - 48a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (- 4a b - 8a b - 16a b - 24a b - 12a b )cosh(x) +--R + +--R 6 3 4 5 2 2 6 2 5 3 4 +--R (8a b + 16a b - 24a b )cosh(x) - 4a b + 8a b - 16a b +--R + +--R 4 3 5 2 +--R 24a b - 12a b +--R * +--R tanh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 2a b - 4a b - 8a b - 12a b - 6a b)sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 8a b - 16a b - 32a b - 48a b - 24a b)cosh(x)sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 2 5 +--R (- 12a b - 24a b - 48a b - 72a b - 36a b)cosh(x) + 4a b +--R + +--R 4 3 6 +--R 8a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 8a b - 16a b - 32a b - 48a b - 24a b)cosh(x) +--R + +--R 2 5 4 3 6 +--R (8a b + 16a b - 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 2a b - 4a b - 8a b - 12a b - 6a b)cosh(x) +--R + +--R 2 5 4 3 6 2 2 5 3 4 4 3 5 2 6 +--R (4a b + 8a b - 12a b)cosh(x) - 2a b + 4a b - 8a b + 12a b - 6a b +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (2b + 4a b + 8a b + 12a b + 6a b )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (8b + 16a b + 32a b + 48a b + 24a b )cosh(x)sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 7 +--R (12b + 24a b + 48a b + 72a b + 36a b )cosh(x) - 4b +--R + +--R 2 5 4 3 +--R - 8a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (8b + 16a b + 32a b + 48a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 +--R (- 8b - 16a b + 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (2b + 4a b + 8a b + 12a b + 6a b )cosh(x) +--R + +--R 7 2 5 4 3 2 7 6 2 5 3 4 +--R (- 4b - 8a b + 12a b )cosh(x) + 2b - 4a b + 8a b - 12a b +--R + +--R 4 3 +--R 6a b +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (4a b + 8a b + 16a b + 24a b + 12a b )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (16a b + 32a b + 64a b + 96a b + 48a b )cosh(x)sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 6 +--R (24a b + 48a b + 96a b + 144a b + 72a b )cosh(x) - 8a b +--R + +--R 3 4 5 2 +--R - 16a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (16a b + 32a b + 64a b + 96a b + 48a b )cosh(x) +--R + +--R 6 3 4 5 2 +--R (- 16a b - 32a b + 48a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (4a b + 8a b + 16a b + 24a b + 12a b )cosh(x) +--R + +--R 6 3 4 5 2 2 6 2 5 3 4 +--R (- 8a b - 16a b + 24a b )cosh(x) + 4a b - 8a b + 16a b +--R + +--R 4 3 5 2 +--R - 24a b + 12a b +--R * +--R tanh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (2a b + 4a b + 8a b + 12a b + 6a b)sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (8a b + 16a b + 32a b + 48a b + 24a b)cosh(x)sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 2 5 +--R (12a b + 24a b + 48a b + 72a b + 36a b)cosh(x) - 4a b +--R + +--R 4 3 6 +--R - 8a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (8a b + 16a b + 32a b + 48a b + 24a b)cosh(x) +--R + +--R 2 5 4 3 6 +--R (- 8a b - 16a b + 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (2a b + 4a b + 8a b + 12a b + 6a b)cosh(x) +--R + +--R 2 5 4 3 6 2 2 5 3 4 4 3 5 2 +--R (- 4a b - 8a b + 12a b)cosh(x) + 2a b - 4a b + 8a b - 12a b +--R + +--R 6 +--R 6a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 2b - 4a b - 8a b - 12a b - 6a b )x sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 8b - 16a b - 32a b - 48a b - 24a b )x cosh(x)sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 +--R (- 12b - 24a b - 48a b - 72a b - 36a b )x cosh(x) +--R + +--R 7 2 5 4 3 7 6 2 5 3 4 +--R (4b + 8a b - 12a b )x - 4b + 12a b + 4a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 8b - 16a b - 32a b - 48a b - 24a b )x cosh(x) +--R + +--R 7 2 5 4 3 7 6 2 5 3 4 +--R ((8b + 16a b - 24a b )x - 8b + 24a b + 8a b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 2b - 4a b - 8a b - 12a b - 6a b )x cosh(x) +--R + +--R 7 2 5 4 3 7 6 2 5 3 4 2 +--R ((4b + 8a b - 12a b )x - 4b + 12a b + 4a b - 12a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 6 2 5 3 4 +--R (- 2b + 4a b - 8a b + 12a b - 6a b )x - 12a b + 24a b - 12a b +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (- 4a b - 8a b - 16a b - 24a b - 12a b )x - 4a b - 8a b +--R + +--R 4 3 5 2 +--R 8a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (- 16a b - 32a b - 64a b - 96a b - 48a b )x - 16a b - 32a b +--R + +--R 4 3 5 2 +--R 32a b + 16a b +--R * +--R 3 +--R cosh(x)sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 24a b - 48a b - 96a b - 144a b - 72a b )x - 24a b +--R + +--R 2 5 4 3 5 2 +--R - 48a b + 48a b + 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 3 4 5 2 2 5 3 4 4 3 5 2 +--R (8a b + 16a b - 24a b )x + 24a b - 8a b - 24a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 16a b - 32a b - 64a b - 96a b - 48a b )x - 16a b +--R + +--R 2 5 4 3 5 2 +--R - 32a b + 32a b + 16a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 3 4 5 2 2 5 3 4 4 3 +--R (16a b + 32a b - 48a b )x + 48a b - 16a b - 48a b +--R + +--R 5 2 +--R 16a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (- 4a b - 8a b - 16a b - 24a b - 12a b )x - 4a b - 8a b +--R + +--R 4 3 5 2 +--R 8a b + 4a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 3 4 5 2 2 5 3 4 4 3 5 2 +--R ((8a b + 16a b - 24a b )x + 24a b - 8a b - 24a b + 8a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 5 +--R (- 4a b + 8a b - 16a b + 24a b - 12a b )x - 4a b - 16a b +--R + +--R 3 4 4 3 5 2 +--R 48a b - 32a b + 4a b +--R * +--R tanh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 +--R (- 2a b - 4a b - 8a b - 12a b - 6a b)x + b + 2a b - 5a b +--R + +--R 3 4 4 3 5 2 6 +--R - 12a b - a b + 10a b + 5a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 +--R (- 8a b - 16a b - 32a b - 48a b - 24a b)x + 4b + 8a b - 20a b +--R + +--R 3 4 4 3 5 2 6 +--R - 48a b - 4a b + 40a b + 20a b +--R * +--R 3 +--R cosh(x)sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 +--R (- 12a b - 24a b - 48a b - 72a b - 36a b)x + 6b + 12a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 30a b - 72a b - 6a b + 60a b + 30a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 5 4 3 6 7 2 5 3 4 4 3 5 2 +--R (4a b + 8a b - 12a b)x - 2b + 10a b + 12a b - 18a b - 12a b +--R + +--R 6 +--R 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 +--R (- 8a b - 16a b - 32a b - 48a b - 24a b)x + 4b + 8a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 20a b - 48a b - 4a b + 40a b + 20a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 5 4 3 6 7 2 5 3 4 4 3 +--R (8a b + 16a b - 24a b)x - 4b + 20a b + 24a b - 36a b +--R + +--R 5 2 6 +--R - 24a b + 20a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 +--R (- 2a b - 4a b - 8a b - 12a b - 6a b)x + b + 2a b - 5a b +--R + +--R 3 4 4 3 5 2 6 +--R - 12a b - a b + 10a b + 5a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 5 4 3 6 7 2 5 3 4 4 3 5 2 +--R (4a b + 8a b - 12a b)x - 2b + 10a b + 12a b - 18a b - 12a b +--R + +--R 6 +--R 10a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 4 3 +--R (- 2a b + 4a b - 8a b + 12a b - 6a b)x + b - 2a b - 5a b + 23a b +--R + +--R 5 2 6 +--R - 22a b + 5a b +--R / +--R 10 9 2 8 3 7 5 5 6 4 7 3 8 2 +--R (2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 8b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b +--R + +--R 8 2 +--R - 8a b +--R * +--R 3 +--R cosh(x)sinh(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 12b + 24a b - 24a b - 72a b + 72a b + 24a b - 24a b +--R + +--R 8 2 +--R - 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 +--R - 4b + 16a b - 24a b + 16a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 +--R 8b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b +--R + +--R 8 2 +--R - 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 +--R (- 8b + 32a b - 48a b + 32a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 10 9 2 8 3 7 5 5 6 4 7 3 8 2 +--R (2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 10 9 +--R (- 4b + 16a b - 24a b + 16a b - 4a b )cosh(x) + 2b - 4a b +--R + +--R 2 8 3 7 5 5 6 4 7 3 8 2 +--R - 4a b + 12a b - 12a b + 4a b + 4a b - 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 9 +--R (4a b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 +--R 16a b + 32a b - 32a b - 96a b + 96a b + 32a b - 32a b +--R + +--R 9 +--R - 16a b +--R * +--R 3 +--R cosh(x)sinh(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 +--R 24a b + 48a b - 48a b - 144a b + 144a b + 48a b +--R + +--R 8 2 9 +--R - 48a b - 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 +--R - 8a b + 32a b - 48a b + 32a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 +--R 16a b + 32a b - 32a b - 96a b + 96a b + 32a b - 32a b +--R + +--R 9 +--R - 16a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 +--R (- 16a b + 64a b - 96a b + 64a b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 6 4 7 3 8 2 9 +--R (4a b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 2 9 2 8 +--R (- 8a b + 32a b - 48a b + 32a b - 8a b)cosh(x) + 4a b - 8a b +--R + +--R 3 7 4 6 6 4 7 3 8 2 9 +--R - 8a b + 24a b - 24a b + 8a b + 8a b - 4a b +--R * +--R tanh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 4 +--R (2a b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a )sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 +--R (8a b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b - 8a ) +--R * +--R 3 +--R cosh(x)sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 +--R 12a b + 24a b - 24a b - 72a b + 72a b + 24a b - 24a b +--R + +--R 10 +--R - 12a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 +--R - 4a b + 16a b - 24a b + 16a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 +--R (8a b + 16a b - 16a b - 48a b + 48a b + 16a b - 16a b - 8a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 +--R (- 8a b + 32a b - 48a b + 32a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 7 3 8 2 9 10 4 +--R (2a b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a )cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 2 8 3 7 +--R (- 4a b + 16a b - 24a b + 16a b - 4a )cosh(x) + 2a b - 4a b +--R + +--R 4 6 5 5 7 3 8 2 9 10 +--R - 4a b + 12a b - 12a b + 4a b + 4a b - 2a +--R Type: Expression(Integer) +--E 157 + +--S 158 of 531 +d1029:= D(m1029,x) +--R +--R +--R (5) +--R 6 2 5 3 4 4 3 6 +--R (- 2a b - 6a b - 6a b - 2a b )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 +--R (- 12a b - 36a b - 36a b - 12a b )cosh(x)sinh(x) +--R + +--R 6 2 5 3 4 4 3 2 7 6 +--R (- 30a b - 90a b - 90a b - 30a b )cosh(x) + 4b - 2a b +--R + +--R 2 5 3 4 4 3 +--R - 6a b - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (- 40a b - 120a b - 120a b - 40a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R (16b - 8a b - 24a b - 24a b - 24a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (- 30a b - 90a b - 90a b - 30a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 7 6 +--R (24b - 12a b - 36a b - 36a b - 36a b )cosh(x) + 4b + 2a b +--R + +--R 2 5 3 4 4 3 +--R - 6a b + 6a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 +--R (- 12a b - 36a b - 36a b - 12a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (16b - 8a b - 24a b - 24a b - 24a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R (8b + 4a b - 12a b + 12a b - 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (- 2a b - 6a b - 6a b - 2a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (4b - 2a b - 6a b - 6a b - 6a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 6 2 5 3 4 +--R (4b + 2a b - 6a b + 6a b - 6a b )cosh(x) + 2a b - 6a b + 6a b +--R + +--R 4 3 +--R - 2a b +--R * +--R 3 +--R tanh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 +--R (b + 3a b - 8a b - 9a b - 3a b )sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 5 +--R (6b + 18a b - 48a b - 54a b - 18a b )cosh(x)sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 2 7 +--R (15b + 45a b - 120a b - 135a b - 45a b )cosh(x) - 3b +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 9a b - 12a b - 24a b - 9a b - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 3 +--R (20b + 60a b - 160a b - 180a b - 60a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R (- 12b + 36a b - 48a b - 96a b - 36a b - 36a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 4 +--R (15b + 45a b - 120a b - 135a b - 45a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 2 +--R (- 18b + 54a b - 72a b - 144a b - 54a b - 54a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 3b + 9a b + 12a b - 24a b + 9a b - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 5 +--R (6b + 18a b - 48a b - 54a b - 18a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (- 12b + 36a b - 48a b - 96a b - 36a b - 36a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R (6b + 18a b + 24a b - 48a b + 18a b - 18a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 +--R (b + 3a b - 8a b - 9a b - 3a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (- 3b + 9a b - 12a b - 24a b - 9a b - 9a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 2 7 6 +--R (3b + 9a b + 12a b - 24a b + 9a b - 9a b )cosh(x) - b + 3a b +--R + +--R 3 4 4 3 5 2 +--R - 8a b + 9a b - 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (2a b + 6a b + 6a b + 2a b )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 +--R (12a b + 36a b + 36a b + 12a b )cosh(x)sinh(x) +--R + +--R 6 2 5 3 4 4 3 2 6 2 5 +--R (30a b + 90a b + 90a b + 30a b )cosh(x) - 6a b + 6a b +--R + +--R 3 4 4 3 +--R - 18a b - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (40a b + 120a b + 120a b + 40a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 +--R (- 24a b + 24a b - 72a b - 120a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (30a b + 90a b + 90a b + 30a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 2 6 2 5 +--R (- 36a b + 36a b - 108a b - 180a b )cosh(x) + 6a b + 6a b +--R + +--R 3 4 4 3 +--R 18a b - 30a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 +--R (12a b + 36a b + 36a b + 12a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (- 24a b + 24a b - 72a b - 120a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 +--R (12a b + 12a b + 36a b - 60a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (2a b + 6a b + 6a b + 2a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (- 6a b + 6a b - 18a b - 30a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 2 6 2 5 3 4 +--R (6a b + 6a b + 18a b - 30a b )cosh(x) - 2a b + 6a b - 6a b +--R + +--R 4 3 +--R 2a b +--R * +--R tanh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 +--R (- b - 3a b + 8a b + 9a b + 3a b )sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 5 +--R (- 6b - 18a b + 48a b + 54a b + 18a b )cosh(x)sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 2 7 6 +--R (- 15b - 45a b + 120a b + 135a b + 45a b )cosh(x) + 3b + 3a b +--R + +--R 2 5 3 4 4 3 5 2 +--R - 12a b - 8a b + a b - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 3 +--R (- 20b - 60a b + 160a b + 180a b + 60a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R (12b + 12a b - 48a b - 32a b + 4a b - 12a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 4 +--R (- 15b - 45a b + 120a b + 135a b + 45a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 2 7 +--R (18b + 18a b - 72a b - 48a b + 6a b - 18a b )cosh(x) - 3b +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 3a b + 12a b - 8a b - a b - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 5 +--R (- 6b - 18a b + 48a b + 54a b + 18a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (12b + 12a b - 48a b - 32a b + 4a b - 12a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R (- 6b + 6a b + 24a b - 16a b - 2a b - 6a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 +--R (- b - 3a b + 8a b + 9a b + 3a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (3b + 3a b - 12a b - 8a b + a b - 3a b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 2 7 6 +--R (- 3b + 3a b + 12a b - 8a b - a b - 3a b )cosh(x) + b - 3a b +--R + +--R 3 4 4 3 5 2 +--R 8a b - 9a b + 3a b +--R / +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 6 +--R (b + 3a b + a b - 5a b - 5a b + a b + 3a b + a b )sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R (6b + 18a b + 6a b - 30a b - 30a b + 6a b + 18a b + 6a b ) +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 15b + 45a b + 15a b - 75a b - 75a b + 15a b + 45a b +--R + +--R 7 3 +--R 15a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 3b - 3a b + 9a b + 9a b - 9a b - 9a b + 3a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 20b + 60a b + 20a b - 100a b - 100a b + 20a b + 60a b +--R + +--R 7 3 +--R 20a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 12b - 12a b + 36a b + 36a b - 36a b - 36a b + 12a b +--R + +--R 7 3 +--R 12a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 15b + 45a b + 15a b - 75a b - 75a b + 15a b + 45a b +--R + +--R 7 3 +--R 15a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 18b - 18a b + 54a b + 54a b - 54a b - 54a b + 18a b +--R + +--R 7 3 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 3b - 3a b - 9a b + 9a b + 9a b - 9a b - 3a b + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 6b + 18a b + 6a b - 30a b - 30a b + 6a b + 18a b +--R + +--R 7 3 +--R 6a b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 12b - 12a b + 36a b + 36a b - 36a b - 36a b + 12a b +--R + +--R 7 3 +--R 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 6b - 6a b - 18a b + 18a b + 18a b - 18a b - 6a b +--R + +--R 7 3 +--R 6a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 6 +--R (b + 3a b + a b - 5a b - 5a b + a b + 3a b + a b )cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R (- 3b - 3a b + 9a b + 9a b - 9a b - 9a b + 3a b + 3a b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R (3b - 3a b - 9a b + 9a b + 9a b - 9a b - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - b + 3a b - a b - 5a b + 5a b + a b - 3a b + a b +--R * +--R 3 +--R tanh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (3a b + 9a b + 3a b - 15a b - 15a b + 3a b + 9a b + 3a b ) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 18a b + 54a b + 18a b - 90a b - 90a b + 18a b + 54a b +--R + +--R 8 2 +--R 18a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 45a b + 135a b + 45a b - 225a b - 225a b + 45a b +--R + +--R 7 3 8 2 +--R 135a b + 45a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 9a b - 9a b + 27a b + 27a b - 27a b - 27a b + 9a b + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 60a b + 180a b + 60a b - 300a b - 300a b + 60a b +--R + +--R 7 3 8 2 +--R 180a b + 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 36a b - 36a b + 108a b + 108a b - 108a b - 108a b +--R + +--R 7 3 8 2 +--R 36a b + 36a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 45a b + 135a b + 45a b - 225a b - 225a b + 45a b +--R + +--R 7 3 8 2 +--R 135a b + 45a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 54a b - 54a b + 162a b + 162a b - 162a b - 162a b +--R + +--R 7 3 8 2 +--R 54a b + 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 9a b - 9a b - 27a b + 27a b + 27a b - 27a b - 9a b + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 18a b + 54a b + 18a b - 90a b - 90a b + 18a b + 54a b +--R + +--R 8 2 +--R 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 36a b - 36a b + 108a b + 108a b - 108a b - 108a b +--R + +--R 7 3 8 2 +--R 36a b + 36a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 18a b - 18a b - 54a b + 54a b + 54a b - 54a b - 18a b +--R + +--R 8 2 +--R 18a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (3a b + 9a b + 3a b - 15a b - 15a b + 3a b + 9a b + 3a b ) +--R * +--R 6 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 9a b - 9a b + 27a b + 27a b - 27a b - 27a b + 9a b +--R + +--R 8 2 +--R 9a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (9a b - 9a b - 27a b + 27a b + 27a b - 27a b - 9a b + 9a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 3a b + 9a b - 3a b - 15a b + 15a b + 3a b - 9a b + 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (3a b + 9a b + 3a b - 15a b - 15a b + 3a b + 9a b + 3a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 18a b + 54a b + 18a b - 90a b - 90a b + 18a b + 54a b +--R + +--R 9 +--R 18a b +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 45a b + 135a b + 45a b - 225a b - 225a b + 45a b +--R + +--R 8 2 9 +--R 135a b + 45a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 9a b - 9a b + 27a b + 27a b - 27a b - 27a b + 9a b + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 60a b + 180a b + 60a b - 300a b - 300a b + 60a b +--R + +--R 8 2 9 +--R 180a b + 60a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 36a b - 36a b + 108a b + 108a b - 108a b - 108a b +--R + +--R 8 2 9 +--R 36a b + 36a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 45a b + 135a b + 45a b - 225a b - 225a b + 45a b +--R + +--R 8 2 9 +--R 135a b + 45a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 54a b - 54a b + 162a b + 162a b - 162a b - 162a b +--R + +--R 8 2 9 +--R 54a b + 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 9a b - 9a b - 27a b + 27a b + 27a b - 27a b - 9a b + 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 18a b + 54a b + 18a b - 90a b - 90a b + 18a b + 54a b +--R + +--R 9 +--R 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 36a b - 36a b + 108a b + 108a b - 108a b - 108a b +--R + +--R 8 2 9 +--R 36a b + 36a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 18a b - 18a b - 54a b + 54a b + 54a b - 54a b - 18a b +--R + +--R 9 +--R 18a b +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (3a b + 9a b + 3a b - 15a b - 15a b + 3a b + 9a b + 3a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 9a b - 9a b + 27a b + 27a b - 27a b - 27a b + 9a b +--R + +--R 9 +--R 9a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (9a b - 9a b - 27a b + 27a b + 27a b - 27a b - 9a b + 9a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 3a b + 9a b - 3a b - 15a b + 15a b + 3a b - 9a b + 3a b +--R * +--R tanh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 6 +--R (a b + 3a b + a b - 5a b - 5a b + a b + 3a b + a )sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R (6a b + 18a b + 6a b - 30a b - 30a b + 6a b + 18a b + 6a ) +--R * +--R 5 +--R cosh(x)sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 15a b + 45a b + 15a b - 75a b - 75a b + 15a b + 45a b +--R + +--R 10 +--R 15a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R - 3a b - 3a b + 9a b + 9a b - 9a b - 9a b + 3a b + 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 20a b + 60a b + 20a b - 100a b - 100a b + 20a b + 60a b +--R + +--R 10 +--R 20a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 12a b - 12a b + 36a b + 36a b - 36a b - 36a b + 12a b +--R + +--R 10 +--R 12a +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 15a b + 45a b + 15a b - 75a b - 75a b + 15a b + 45a b +--R + +--R 10 +--R 15a +--R * +--R 4 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 18a b - 18a b + 54a b + 54a b - 54a b - 54a b + 18a b +--R + +--R 10 +--R 18a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R 3a b - 3a b - 9a b + 9a b + 9a b - 9a b - 3a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R (6a b + 18a b + 6a b - 30a b - 30a b + 6a b + 18a b + 6a ) +--R * +--R 5 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 12a b - 12a b + 36a b + 36a b - 36a b - 36a b + 12a b +--R + +--R 10 +--R 12a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R (6a b - 6a b - 18a b + 18a b + 18a b - 18a b - 6a b + 6a ) +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 6 +--R (a b + 3a b + a b - 5a b - 5a b + a b + 3a b + a )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 4 +--R (- 3a b - 3a b + 9a b + 9a b - 9a b - 9a b + 3a b + 3a )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 2 +--R (3a b - 3a b - 9a b + 9a b + 9a b - 9a b - 3a b + 3a )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R - a b + 3a b - a b - 5a b + 5a b + a b - 3a b + a +--R Type: Expression(Integer) +--E 158 + +)clear all + + +--S 159 of 531 +t1030:= cosh(x)*sinh(x)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R cosh(x)sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 159 + +--S 160 of 531 +r1030:= a*b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ + a*cosh(x)/(a^2-b^2)-b*sinh(x)/(a^2-b^2) +--R +--R +--R (2) +--R +---------+ +--R a sinh(x) + b cosh(x) | 2 2 +--R - a b atan(---------------------) + (b sinh(x) - a cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ----------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression(Integer) +--E 160 + +--S 161 of 531 +a1030:= integrate(t1030,x) +--R +--R +--R (3) +--R [ +--R (2a b sinh(x) + 2a b cosh(x)) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) - b - a) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R (4a b sinh(x) + 4a b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) - b - a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 161 + +--S 162 of 531 +m1030a:= a1030.1-r1030 +--R +--R +--R (4) +--R +---------+ +--R | 2 2 +--R (2a b sinh(x) + 2a b cosh(x))\|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R (2a b sinh(x) + 2a b cosh(x))\|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R ((- b - a)sinh(x) + (b + a)cosh(x) - b - a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 | 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a \|b - a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 531 +d1030a:= D(m1030a,x) +--R +--R +--R (5) +--R 2 2 3 4 6 3 2 2 3 4 5 +--R (a b + 2a b + a )sinh(x) + (2a b + 6a b + 6a b + 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 4 +--R ((b + 6a b + 9a b + 4a b)cosh(x) - b + 2a b + 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (2b + 4a b - 4a b - 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b + 2a b + 6a b + 6a b + 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 4a b - 9a b - 6a b - a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 4 +--R (8a b + 8a b + 8a b)cosh(x) - a b - 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 2b - 6a b - 6a b - 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 4 4 +--R (4b + 6a b + 6a b + 2a b - 2a )cosh(x) + (- 2b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 2 2 4 4 +--R (- b - 2a b - a b )cosh(x) + (3b + 2a b - a )cosh(x) +--R + +--R 4 3 2 2 2 4 2 2 4 +--R (- 3b + 2a b + a b )cosh(x) + b - 2a b + a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 163 + +--S 164 of 531 +m1030b:= a1030.2-r1030 +--R +--R +--R (6) +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R (4a b sinh(x) + 4a b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R a sinh(x) + b cosh(x) +--R (2a b sinh(x) + 2a b cosh(x))atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((- b - a)sinh(x) + (b + a)cosh(x) - b - a)\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 164 + +--S 165 of 531 +d1030b:= D(m1030b,x) +--R +--R +--R (7) +--R 2 2 3 4 6 3 2 2 3 4 5 +--R (a b + 2a b + a )sinh(x) + (2a b + 6a b + 6a b + 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 4 +--R ((b + 6a b + 9a b + 4a b)cosh(x) - b + 2a b + 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (2b + 4a b - 4a b - 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b + 2a b + 6a b + 6a b + 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 4a b - 9a b - 6a b - a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 4 +--R (8a b + 8a b + 8a b)cosh(x) - a b - 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 2b - 6a b - 6a b - 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 4 4 +--R (4b + 6a b + 6a b + 2a b - 2a )cosh(x) + (- 2b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 2 2 4 4 +--R (- b - 2a b - a b )cosh(x) + (3b + 2a b - a )cosh(x) +--R + +--R 4 3 2 2 2 4 2 2 4 +--R (- 3b + 2a b + a b )cosh(x) + b - 2a b + a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 165 + +)clear all + + +--S 166 of 531 +t1031:= cosh(x)*sinh(x)^2/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 2 +--R cosh(x)sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 166 + +--S 167 of 531 +r1031:= 1/2/(a^2-b^2)^2*(-a^3*x-a*b^2*x+2*a^2*b*log(a*cosh(x)+b*sinh(x))+_ + a^3*cosh(x)*sinh(x)-a*cosh(x)*sinh(x)*b^2+a^2*b-_ + a^2*b*cosh(x)^2-b^3+cosh(x)^2*b^3) +--R +--R +--R (2) +--R 2 2 3 +--R 2a b log(b sinh(x) + a cosh(x)) + (- a b + a )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (b - a b)cosh(x) + (- a b - a )x - b + a b +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 531 +a1031:= integrate(t1031,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 2 3 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (- 4a b - 8a b - 4a )x)sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (- 8a b - 16a b - 8a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 2 2 3 2 3 +--R (b - a b - a b + a )cosh(x) + (- 4a b - 8a b - 4a )x cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 531 +m1031:= a1031-r1031 +--R +--R +--R (4) +--R 2 2 2 2 2 +--R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 2 2 2 2 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (b - a b - a b + a )sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 2 2 +--R ((2b + 2a b - 2a b - 2a )cosh(x) - 8a b x + 4b - 4a b)sinh(x) +--R + +--R 3 2 3 2 3 2 +--R ((- 4b + 4a b)cosh(x) + (- 16a b x + 8b - 8a b)cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (- 3b - a b + 3a b + a )cosh(x) + (- 8a b x + 4b - 4a b)cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 169 + +--S 170 of 531 +d1031:= D(m1031,x) +--R +--R +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 +--R (5) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression(Integer) +--E 170 + +)clear all + + +--S 171 of 531 +t1032:= cosh(x)*sinh(x)^3/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 3 +--R cosh(x)sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 531 +r1032:= -a^3*b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)-_ + a^3*cosh(x)/(a^2-b^2)^2+a*cosh(x)^3/(3*a^2-3*b^2)+_ + a^4*sinh(x)/b/(a^2-b^2)^2-a^2*sinh(x)/b/(a^2-b^2)-_ + b*sinh(x)^3/(3*a^2-3*b^2) +--R +--R +--R (2) +--R 3 a sinh(x) + b cosh(x) +--R - 3a b atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 3 +--R (b - a b)sinh(x) + 3a b sinh(x) + (- a b + a )cosh(x) +--R + +--R 3 +--R - 3a cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 4 | 2 2 +--R (3b - 6a b + 3a )\|- b + a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 531 +a1032:= integrate(t1032,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b - 15a b - 15a b + 15a )cosh(x) - 3b - 3a b + 15a b +--R + +--R 3 +--R - 9a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b - 20a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b - 12a b + 60a b - 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b - 15a b - 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 90a b - 54a )cosh(x) + 3b - 3a b - 15a b +--R + +--R 3 +--R - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b - 12a b + 60a b - 36a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 3b - 3a b + 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (3b - 3a b - 15a b - 9a )cosh(x) - b - a b + a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 2 2 4 3 +--R (24b - 48a b + 24a )sinh(x) +--R + +--R 4 2 2 4 2 +--R (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 3 3 2 3 2 +--R 48a b sinh(x) + 144a b cosh(x)sinh(x) + 144a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 48a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b - 15a b - 15a b + 15a )cosh(x) - 3b - 3a b + 15a b +--R + +--R 3 +--R - 9a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b - 20a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b - 12a b + 60a b - 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b - 15a b - 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 90a b - 54a )cosh(x) + 3b - 3a b - 15a b +--R + +--R 3 +--R - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b - 12a b + 60a b - 36a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 3b - 3a b + 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (3b - 3a b - 15a b - 9a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 +--R (24b - 48a b + 24a )sinh(x) +--R + +--R 4 2 2 4 2 +--R (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 173 + +--S 174 of 531 +m1032a:= a1032.1-r1032 +--R +--R +--R (4) +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R \|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 6 +--R (- 7b - a b + 7a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 18b - 6a b + 18a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((- 9b - 15a b + 9a b + 15a )cosh(x) - 3b - 3a b - 9a b - 9a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (12b - 12a b - 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b - 12a b - 12a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 9a b - 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 18a b + 18a )cosh(x) + 3b - 3a b - 15a b +--R + +--R 3 +--R - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 18a b - 6a b - 18a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b - 12a b + 36a b + 36a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b + 7a b - a b - 7a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 3b - 3a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (3b - 3a b - 15a b - 9a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 2 4 3 4 2 2 4 2 +--R (24b - 48a b + 24a )sinh(x) + (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 174 + +--S 175 of 531 +d1032a:= D(m1032a,x) +--R +--R +--R (5) +--R 2 4 4 2 6 10 +--R (a b - 2a b + a )sinh(x) +--R + +--R 5 3 3 4 2 5 6 9 +--R (2a b - 12a b - 8a b + 10a b + 8a )cosh(x)sinh(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 6 2 4 +--R (b - 30a b - 48a b + 9a b + 48a b + 20a )cosh(x) - b + a b +--R + +--R 4 2 5 6 +--R a b + 8a b + 7a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 32a b - 96a b - 48a b + 80a b + 80a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (4a b + 4a b - 16a b + 8a b + 60a b + 36a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b - 80a b - 98a b + 48a b + 120a b + 32a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (10b + 24a b - 22a b - 72a b + 62a b + 160a b + 62a )cosh(x) +--R + +--R 6 2 4 4 2 6 +--R 2b - 6a b + 6a b + 14a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 24b - 60a b + 24a b + 120a b + 24a b - 60a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (20b + 20a b - 104a b - 80a b + 164a b + 172a b + 32a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4b + 8a b - 12a b - 8a b + 20a b + 32a b + 52a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 10b + 32a b + 120a b + 48a b - 98a b - 80a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 64a b - 144a b + 40a b + 164a b + 24a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (6b + 32a b - 10a b - 16a b + 50a b + 112a b + 66a )cosh(x) +--R + +--R 2 4 4 2 5 6 +--R 2a b - 4a b - 8a b + 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (16b + 80a b + 80a b - 48a b - 96a b - 32a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 32b - 132a b - 68a b + 112a b + 24a b - 92a b - 36a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (16b + 48a b - 8a b + 96a b + 144a b + 24a )cosh(x) +--R + +--R 5 2 4 4 2 5 6 +--R (4a b - 4a b - 8a b - 20a b + 28a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 8 +--R (20b + 48a b + 9a b - 48a b - 30a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 42b - 88a b + 6a b + 40a b - 62a b - 64a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (22b + 32a b + 6a b + 16a b + 98a b + 80a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (2b + 8a b - 26a b + 8a b - 2a b - 16a b + 26a )cosh(x) - 2b +--R + +--R 2 4 4 2 6 +--R 5a b - 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 9 +--R (8b + 10a b - 8a b - 12a b + 2a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 20b - 20a b + 8a b - 16a b - 36a b - 12a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (12b + 8a b + 20a b + 8a b + 44a b + 16a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 4a b - 32a b + 16a b + 4a b - 4a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 4b - 2a b + 12a b + 4a b - 12a b - 2a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 4 4 2 10 +--R (b - 2a b + a b )cosh(x) +--R + +--R 6 2 4 3 3 4 2 6 8 +--R (- 3b - a b - 8a b - 5a b + a )cosh(x) +--R + +--R 6 2 4 4 2 6 6 +--R (2b + 10a b + 6a b - 2a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 4 +--R (2b - 12a b + 8a b + 2a b )cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (- 3b + 8a b - 7a b + 2a )cosh(x) + b - 3a b + 3a b - a +--R / +--R 2 5 3 4 4 3 5 2 6 7 7 +--R (8a b + 8a b - 16a b - 16a b + 8a b + 8a )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (16a b + 56a b + 8a b - 112a b - 64a b + 56a b + 40a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 8b + 88a b + 144a b - 96a b - 312a b - 72a b + 160a b +--R + +--R 7 +--R 80a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R - 8b - 8a b + 16a b + 32a b - 8a b - 40a b + 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 40b + 200a b + 160a b - 320a b - 440a b + 40a b + 240a b +--R + +--R 7 +--R 80a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 40b - 56a b + 112a b + 176a b - 104a b - 184a b + 32a b +--R + +--R 7 +--R 64a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 240a b + 40a b - 440a b - 320a b + 160a b + 200a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 88b - 120a b + 280a b + 344a b - 296a b - 328a b + 104a b +--R + +--R 7 +--R 104a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R 8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 160a b - 72a b - 312a b - 96a b + 144a b + 88a b +--R + +--R 7 +--R 8a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 104b - 104a b + 328a b + 296a b - 344a b - 280a b +--R + +--R 6 7 +--R 120a b + 88a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (40b + 56a b - 64a b - 112a b + 8a b + 56a b + 16a b)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 64b - 32a b + 184a b + 104a b - 176a b - 112a b + 56a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R 2 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R (8b + 8a b - 16a b - 16a b + 8a b + 8a b )cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (- 16b + 40a b + 8a b - 32a b - 16a b + 8a b + 8a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 3 +--R (8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 175 + +--S 176 of 531 +m1032b:= a1032.2-r1032 +--R +--R +--R (6) +--R 3 3 3 2 3 2 +--R 48a b sinh(x) + 144a b cosh(x)sinh(x) + 144a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 48a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 6 +--R (- 7b - a b + 7a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 18b - 6a b + 18a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((- 9b - 15a b + 9a b + 15a )cosh(x) - 3b - 3a b - 9a b - 9a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (12b - 12a b - 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b - 12a b - 12a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 9a b - 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 18a b + 18a )cosh(x) + 3b - 3a b - 15a b +--R + +--R 3 +--R - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 18a b - 6a b - 18a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b - 12a b + 36a b + 36a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b + 7a b - a b - 7a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 3b - 3a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (3b - 3a b - 15a b - 9a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 4 2 2 4 2 +--R (24b - 48a b + 24a )sinh(x) + (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 176 + +--S 177 of 531 +d1032b:= D(m1032b,x) +--R +--R +--R (7) +--R 2 4 4 2 6 10 +--R (a b - 2a b + a )sinh(x) +--R + +--R 5 3 3 4 2 5 6 9 +--R (2a b - 12a b - 8a b + 10a b + 8a )cosh(x)sinh(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 6 2 4 +--R (b - 30a b - 48a b + 9a b + 48a b + 20a )cosh(x) - b + a b +--R + +--R 4 2 5 6 +--R a b + 8a b + 7a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 32a b - 96a b - 48a b + 80a b + 80a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (4a b + 4a b - 16a b + 8a b + 60a b + 36a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b - 80a b - 98a b + 48a b + 120a b + 32a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (10b + 24a b - 22a b - 72a b + 62a b + 160a b + 62a )cosh(x) +--R + +--R 6 2 4 4 2 6 +--R 2b - 6a b + 6a b + 14a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 24b - 60a b + 24a b + 120a b + 24a b - 60a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (20b + 20a b - 104a b - 80a b + 164a b + 172a b + 32a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4b + 8a b - 12a b - 8a b + 20a b + 32a b + 52a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 10b + 32a b + 120a b + 48a b - 98a b - 80a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 64a b - 144a b + 40a b + 164a b + 24a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (6b + 32a b - 10a b - 16a b + 50a b + 112a b + 66a )cosh(x) +--R + +--R 2 4 4 2 5 6 +--R 2a b - 4a b - 8a b + 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (16b + 80a b + 80a b - 48a b - 96a b - 32a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 32b - 132a b - 68a b + 112a b + 24a b - 92a b - 36a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (16b + 48a b - 8a b + 96a b + 144a b + 24a )cosh(x) +--R + +--R 5 2 4 4 2 5 6 +--R (4a b - 4a b - 8a b - 20a b + 28a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 8 +--R (20b + 48a b + 9a b - 48a b - 30a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 42b - 88a b + 6a b + 40a b - 62a b - 64a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (22b + 32a b + 6a b + 16a b + 98a b + 80a b - 14a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (2b + 8a b - 26a b + 8a b - 2a b - 16a b + 26a )cosh(x) - 2b +--R + +--R 2 4 4 2 6 +--R 5a b - 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 9 +--R (8b + 10a b - 8a b - 12a b + 2a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 20b - 20a b + 8a b - 16a b - 36a b - 12a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (12b + 8a b + 20a b + 8a b + 44a b + 16a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4b + 4a b - 32a b + 16a b + 4a b - 4a b + 8a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 4b - 2a b + 12a b + 4a b - 12a b - 2a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 4 4 2 10 +--R (b - 2a b + a b )cosh(x) +--R + +--R 6 2 4 3 3 4 2 6 8 +--R (- 3b - a b - 8a b - 5a b + a )cosh(x) +--R + +--R 6 2 4 4 2 6 6 +--R (2b + 10a b + 6a b - 2a )cosh(x) +--R + +--R 6 2 4 3 3 4 2 4 +--R (2b - 12a b + 8a b + 2a b )cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (- 3b + 8a b - 7a b + 2a )cosh(x) + b - 3a b + 3a b - a +--R / +--R 2 5 3 4 4 3 5 2 6 7 7 +--R (8a b + 8a b - 16a b - 16a b + 8a b + 8a )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (16a b + 56a b + 8a b - 112a b - 64a b + 56a b + 40a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 8b + 88a b + 144a b - 96a b - 312a b - 72a b + 160a b +--R + +--R 7 +--R 80a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R - 8b - 8a b + 16a b + 32a b - 8a b - 40a b + 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 40b + 200a b + 160a b - 320a b - 440a b + 40a b + 240a b +--R + +--R 7 +--R 80a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 40b - 56a b + 112a b + 176a b - 104a b - 184a b + 32a b +--R + +--R 7 +--R 64a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 240a b + 40a b - 440a b - 320a b + 160a b + 200a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 88b - 120a b + 280a b + 344a b - 296a b - 328a b + 104a b +--R + +--R 7 +--R 104a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R 8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 160a b - 72a b - 312a b - 96a b + 144a b + 88a b +--R + +--R 7 +--R 8a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 104b - 104a b + 328a b + 296a b - 344a b - 280a b +--R + +--R 6 7 +--R 120a b + 88a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (40b + 56a b - 64a b - 112a b + 8a b + 56a b + 16a b)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 64b - 32a b + 184a b + 104a b - 176a b - 112a b + 56a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R 2 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R (8b + 8a b - 16a b - 16a b + 8a b + 8a b )cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (- 16b + 40a b + 8a b - 32a b - 16a b + 8a b + 8a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 3 +--R (8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 177 + +)clear all + + +--S 178 of 531 +t1033:= sinh(x)*cosh(x)^2/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 2 +--R cosh(x) sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 178 + +--S 179 of 531 +r1033:= -1/2*(-b^3*x-a^2*b*x+2*a*b^2*log(a*cosh(x)+b*sinh(x))+_ + a^2*b*sinh(x)*cosh(x)-b^3*sinh(x)*cosh(x)+a^3-cosh(x)^2*a^3-_ + b^2*a+cosh(x)^2*b^2*a)/(a^2-b^2)^2 +--R +--R +--R (2) +--R 2 3 2 +--R - 2a b log(b sinh(x) + a cosh(x)) + (b - a b)cosh(x)sinh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- a b + a )cosh(x) + (b + a b)x + a b - a +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression(Integer) +--E 179 + +--S 180 of 531 +a1033:= integrate(t1033,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (4b + 8a b + 4a b)x)sinh(x) +--R + +--R 3 2 2 3 3 3 2 2 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (8b + 16a b + 8a b)x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 2 3 +--R (b - a b - a b + a )cosh(x) + (4b + 8a b + 4a b)x cosh(x) - b +--R + +--R 2 2 3 +--R - a b + a b + a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 180 + +--S 181 of 531 +m1033:= a1033-r1033 +--R +--R +--R (4) +--R 2 2 2 2 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 2 2 2 2 2 +--R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (b - a b - a b + a )sinh(x) + (- 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 2 3 2 +--R ((- 2b - 2a b + 2a b + 2a )cosh(x) + 8a b x - 4a b + 4a )sinh(x) +--R + +--R 2 3 3 2 2 3 +--R ((4a b - 4a )cosh(x) + (16a b x - 8a b + 8a )cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 2 2 3 2 3 +--R (b + 3a b - a b - 3a )cosh(x) + (8a b x - 4a b + 4a )cosh(x) - b +--R + +--R 2 2 3 +--R - a b + a b + a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 531 +d1033:= D(m1033,x) +--R +--R +--R 4 2 2 4 +--R - sinh(x) + 2cosh(x) sinh(x) - cosh(x) + 1 +--R (5) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression(Integer) +--E 182 + +)clear all + + +--S 183 of 531 +t1034:= sinh(x)*cosh(x)^3/(a*cosh(x)+b*sinh(x)) +--R +--R +--R 3 +--R cosh(x) sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 183 + +--S 184 of 531 +r1034:= -a*b^3*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)-_ + a*b^2*cosh(x)/(a^2-b^2)^2+a*cosh(x)^3/(3*a^2-3*b^2)+_ + a^2*b*sinh(x)/(a^2-b^2)^2-b*sinh(x)/(a^2-b^2)-b*sinh(x)^3/(3*a^2-3*b^2) +--R +--R +--R (2) +--R 3 a sinh(x) + b cosh(x) +--R - 3a b atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 3 2 3 3 +--R (b - a b)sinh(x) + 3b sinh(x) + (- a b + a )cosh(x) +--R + +--R 2 +--R - 3a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 4 | 2 2 +--R (3b - 6a b + 3a )\|- b + a +--R Type: Expression(Integer) +--E 184 + +--S 185 of 531 +a1034:= integrate(t1034,x) +--R +--R +--R (3) +--R [ +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b - 15a b - 15a b + 15a )cosh(x) + 9b - 15a b + 3a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b - 20a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (36b - 60a b + 12a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b - 15a b - 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (54b - 90a b + 18a b + 18a )cosh(x) - 9b - 15a b - 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (36b - 60a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 18b - 30a b - 6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (9b - 15a b + 3a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 9b - 15a b - 3a b + 3a )cosh(x) - b - a b + a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 2 2 4 3 +--R (24b - 48a b + 24a )sinh(x) +--R + +--R 4 2 2 4 2 +--R (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 3 3 2 3 2 +--R 48a b sinh(x) + 144a b cosh(x)sinh(x) + 144a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 48a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b - 15a b - 15a b + 15a )cosh(x) + 9b - 15a b + 3a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b - 20a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (36b - 60a b + 12a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b - 15a b - 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (54b - 90a b + 18a b + 18a )cosh(x) - 9b - 15a b - 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (36b - 60a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 18b - 30a b - 6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b - a b - a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (9b - 15a b + 3a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 9b - 15a b - 3a b + 3a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 +--R (24b - 48a b + 24a )sinh(x) +--R + +--R 4 2 2 4 2 +--R (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 185 + +--S 186 of 531 +m1034a:= a1034.1-r1034 +--R +--R +--R (4) +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R \|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 6 +--R (- 7b - a b + 7a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 18b - 6a b + 18a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 9b - 15a b + 9a b + 15a )cosh(x) - 15b - 15a b + 3a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (12b - 12a b - 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 36b - 36a b + 12a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 9a b - 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 18a b + 18a )cosh(x) - 9b - 15a b - 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 18a b - 6a b - 18a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (12b + 12a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 18b - 30a b - 6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 3 2 2 3 4 +--R (b + 7a b - a b - 7a )cosh(x) + (9b + 9a b + 3a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 9b - 15a b - 3a b + 3a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 2 4 3 4 2 2 4 2 +--R (24b - 48a b + 24a )sinh(x) + (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 186 + +--S 187 of 531 +d1034a:= D(m1034a,x) +--R +--R +--R (5) +--R 2 4 4 2 6 10 +--R (a b - 2a b + a )sinh(x) +--R + +--R 5 3 3 4 2 5 6 9 +--R (2a b - 12a b - 8a b + 10a b + 8a )cosh(x)sinh(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 6 2 4 +--R (b - 30a b - 48a b + 9a b + 48a b + 20a )cosh(x) - b + 5a b +--R + +--R 3 3 4 2 6 +--R 8a b + a b + 3a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 32a b - 96a b - 48a b + 80a b + 80a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (12a b + 36a b + 16a b - 8a b + 20a b + 20a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b - 80a b - 98a b + 48a b + 120a b + 32a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (14b + 64a b + 62a b - 40a b - 6a b + 88a b + 42a )cosh(x) +--R + +--R 6 2 4 4 2 6 +--R - 2b + 6a b + 10a b + 2a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 24b - 60a b + 24a b + 120a b + 24a b - 60a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (36b + 92a b - 24a b - 112a b + 68a b + 132a b + 32a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b + 16a b + 44a b + 8a b + 20a b + 8a b + 12a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 10b + 32a b + 120a b + 48a b - 98a b - 80a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (24b - 24a b - 164a b - 40a b + 144a b + 64a b - 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 14b + 80a b + 98a b + 16a b + 6a b + 32a b + 22a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 +--R - 2a b - 8a b + 12a b - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (16b + 80a b + 80a b - 48a b - 96a b - 32a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 32b - 172a b - 164a b + 80a b + 104a b - 20a b - 20a ) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (24b + 144a b + 96a b - 8a b + 48a b + 16a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 8b + 4a b - 4a b - 16a b + 32a b - 4a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 8 +--R (20b + 48a b + 9a b - 48a b - 30a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 62b - 160a b - 62a b + 72a b + 22a b - 24a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (66b + 112a b + 50a b - 16a b - 10a b + 32a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (- 26b + 16a b + 2a b - 8a b + 26a b - 8a b - 2a )cosh(x) + 2b +--R + +--R 2 4 4 2 6 +--R - 7a b + 8a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 9 +--R (8b + 10a b - 8a b - 12a b + 2a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 36b - 60a b - 8a b + 16a b - 4a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (52b + 32a b + 20a b - 8a b - 12a b + 8a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 3 +--R (- 28b + 20a b + 8a b + 4a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4b - 2a b - 12a b + 4a b + 12a b - 2a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 4 4 2 10 6 5 2 4 4 2 6 8 +--R (b - 2a b + a b )cosh(x) + (- 7b - 8a b - a b - a b + a )cosh(x) +--R + +--R 6 2 4 4 2 6 6 +--R (14b + 6a b - 6a b + 2a )cosh(x) +--R + +--R 6 5 2 4 4 2 4 +--R (- 10b + 8a b + 4a b - 2a b )cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (b - 4a b + 5a b - 2a )cosh(x) + b - 3a b + 3a b - a +--R / +--R 2 5 3 4 4 3 5 2 6 7 7 +--R (8a b + 8a b - 16a b - 16a b + 8a b + 8a )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (16a b + 56a b + 8a b - 112a b - 64a b + 56a b + 40a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 8b + 88a b + 144a b - 96a b - 312a b - 72a b + 160a b +--R + +--R 7 +--R 80a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R - 8b - 8a b + 16a b + 32a b - 8a b - 40a b + 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 40b + 200a b + 160a b - 320a b - 440a b + 40a b + 240a b +--R + +--R 7 +--R 80a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 40b - 56a b + 112a b + 176a b - 104a b - 184a b + 32a b +--R + +--R 7 +--R 64a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 240a b + 40a b - 440a b - 320a b + 160a b + 200a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 88b - 120a b + 280a b + 344a b - 296a b - 328a b + 104a b +--R + +--R 7 +--R 104a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R 8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 160a b - 72a b - 312a b - 96a b + 144a b + 88a b +--R + +--R 7 +--R 8a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 104b - 104a b + 328a b + 296a b - 344a b - 280a b +--R + +--R 6 7 +--R 120a b + 88a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (40b + 56a b - 64a b - 112a b + 8a b + 56a b + 16a b)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 64b - 32a b + 184a b + 104a b - 176a b - 112a b + 56a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R 2 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R (8b + 8a b - 16a b - 16a b + 8a b + 8a b )cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (- 16b + 40a b + 8a b - 32a b - 16a b + 8a b + 8a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 3 +--R (8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 187 + +--S 188 of 531 +m1034b:= a1034.2-r1034 +--R +--R +--R (6) +--R 3 3 3 2 3 2 +--R 48a b sinh(x) + 144a b cosh(x)sinh(x) + 144a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 48a b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 3 3 2 3 2 +--R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) +--R + +--R 3 3 +--R 24a b cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 6 +--R (- 7b - a b + 7a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 18b - 6a b + 18a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 9b - 15a b + 9a b + 15a )cosh(x) - 15b - 15a b + 3a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (12b - 12a b - 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 36b - 36a b + 12a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 9a b - 15a b - 9a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 18b - 18a b + 18a b + 18a )cosh(x) - 9b - 15a b - 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 18a b - 6a b - 18a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (12b + 12a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 18b - 30a b - 6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 3 2 2 3 4 +--R (b + 7a b - a b - 7a )cosh(x) + (9b + 9a b + 3a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 9b - 15a b - 3a b + 3a )cosh(x) - b - a b + a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 4 2 2 4 2 +--R (24b - 48a b + 24a )sinh(x) + (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 188 + +--S 189 of 531 +d1034b:= D(m1034b,x) +--R +--R +--R (7) +--R 2 4 4 2 6 10 +--R (a b - 2a b + a )sinh(x) +--R + +--R 5 3 3 4 2 5 6 9 +--R (2a b - 12a b - 8a b + 10a b + 8a )cosh(x)sinh(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 6 2 4 +--R (b - 30a b - 48a b + 9a b + 48a b + 20a )cosh(x) - b + 5a b +--R + +--R 3 3 4 2 6 +--R 8a b + a b + 3a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 32a b - 96a b - 48a b + 80a b + 80a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (12a b + 36a b + 16a b - 8a b + 20a b + 20a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b - 80a b - 98a b + 48a b + 120a b + 32a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (14b + 64a b + 62a b - 40a b - 6a b + 88a b + 42a )cosh(x) +--R + +--R 6 2 4 4 2 6 +--R - 2b + 6a b + 10a b + 2a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 24b - 60a b + 24a b + 120a b + 24a b - 60a b - 24a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (36b + 92a b - 24a b - 112a b + 68a b + 132a b + 32a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b + 16a b + 44a b + 8a b + 20a b + 8a b + 12a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 10b + 32a b + 120a b + 48a b - 98a b - 80a b - 12a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (24b - 24a b - 164a b - 40a b + 144a b + 64a b - 4a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 14b + 80a b + 98a b + 16a b + 6a b + 32a b + 22a )cosh(x) +--R + +--R 2 4 3 3 4 2 6 +--R - 2a b - 8a b + 12a b - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (16b + 80a b + 80a b - 48a b - 96a b - 32a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 32b - 172a b - 164a b + 80a b + 104a b - 20a b - 20a ) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 4 2 5 6 3 +--R (24b + 144a b + 96a b - 8a b + 48a b + 16a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 8b + 4a b - 4a b - 16a b + 32a b - 4a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 8 +--R (20b + 48a b + 9a b - 48a b - 30a b + a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 62b - 160a b - 62a b + 72a b + 22a b - 24a b - 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (66b + 112a b + 50a b - 16a b - 10a b + 32a b + 6a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 6 +--R (- 26b + 16a b + 2a b - 8a b + 26a b - 8a b - 2a )cosh(x) + 2b +--R + +--R 2 4 4 2 6 +--R - 7a b + 8a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 9 +--R (8b + 10a b - 8a b - 12a b + 2a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 36b - 60a b - 8a b + 16a b - 4a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (52b + 32a b + 20a b - 8a b - 12a b + 8a b + 4a )cosh(x) +--R + +--R 6 5 2 4 4 2 5 3 +--R (- 28b + 20a b + 8a b + 4a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4b - 2a b - 12a b + 4a b + 12a b - 2a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 2 4 4 2 10 6 5 2 4 4 2 6 8 +--R (b - 2a b + a b )cosh(x) + (- 7b - 8a b - a b - a b + a )cosh(x) +--R + +--R 6 2 4 4 2 6 6 +--R (14b + 6a b - 6a b + 2a )cosh(x) +--R + +--R 6 5 2 4 4 2 4 +--R (- 10b + 8a b + 4a b - 2a b )cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (b - 4a b + 5a b - 2a )cosh(x) + b - 3a b + 3a b - a +--R / +--R 2 5 3 4 4 3 5 2 6 7 7 +--R (8a b + 8a b - 16a b - 16a b + 8a b + 8a )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (16a b + 56a b + 8a b - 112a b - 64a b + 56a b + 40a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 8b + 88a b + 144a b - 96a b - 312a b - 72a b + 160a b +--R + +--R 7 +--R 80a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R - 8b - 8a b + 16a b + 32a b - 8a b - 40a b + 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 40b + 200a b + 160a b - 320a b - 440a b + 40a b + 240a b +--R + +--R 7 +--R 80a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 40b - 56a b + 112a b + 176a b - 104a b - 184a b + 32a b +--R + +--R 7 +--R 64a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 240a b + 40a b - 440a b - 320a b + 160a b + 200a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 88b - 120a b + 280a b + 344a b - 296a b - 328a b + 104a b +--R + +--R 7 +--R 104a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R 8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 80b + 160a b - 72a b - 312a b - 96a b + 144a b + 88a b +--R + +--R 7 +--R 8a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 104b - 104a b + 328a b + 296a b - 344a b - 280a b +--R + +--R 6 7 +--R 120a b + 88a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (40b + 56a b - 64a b - 112a b + 8a b + 56a b + 16a b)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 64b - 32a b + 184a b + 104a b - 176a b - 112a b + 56a b +--R + +--R 7 +--R 40a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (24b - 24a b - 72a b + 72a b + 72a b - 72a b - 24a b + 24a ) +--R * +--R 2 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R (8b + 8a b - 16a b - 16a b + 8a b + 8a b )cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (- 16b + 40a b + 8a b - 32a b - 16a b + 8a b + 8a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 3 +--R (8b - 8a b - 24a b + 24a b + 24a b - 24a b - 8a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 189 + +)clear all + + +--S 190 of 531 +t1035:= (A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R C sinh(x) + A +--R (1) ------------------------- +--R c sinh(x) + b cosh(x) + a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 531 +r1035:= -c*C*x/(b^2-c^2)-2*(A+a*c*C/(b^2-c^2))*_ + atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(1/2)+b*C*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2) +--R +--R +--R (2) +--R +------------+ +--R | 2 2 2 +--R - C b\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R x +--R (b - a)tanh(-) + c +------------+ +--R 2 2 2 | 2 2 2 +--R (- 2A c + 2C a c + 2A b )atanh(------------------) + C c x\|c - b + a +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression(Integer) +--E 191 + +--S 192 of 531 +a1035:= integrate(t1035,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (- A c + C a c + A b ) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R - C b\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +------------+ +--R | 2 2 2 +--R (C c + C b)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R , +--R +--R +--------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R - C b\|- c + b - a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 2A c + 2C a c + 2A b ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (C c + C b)x\|- c + b - a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 192 + +--S 193 of 531 +m1035a:= a1035.1-r1035 +--R +--R +--R (4) +--R 2 2 +--R (- A c + C a c + A b ) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 +--R C b\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R - C b\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R (b - a)tanh(-) + c +------------+ +--R 2 2 2 | 2 2 2 +--R (2A c - 2C a c - 2A b )atanh(------------------) + C b x\|c - b + a +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression(Integer) +--E 193 + +--S 194 of 531 +d1035a:= D(m1035a,x) +--R +--R +--R (5) +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b - C a b)c - A b )sinh(x) +--R + +--R 3 2 2 3 +--R (2A c + (2A b - 2C a)c + (- 2A b - 2C a b)c - 2A b )cosh(x) +--R + +--R 2 3 +--R 2A b c - 2C a b c - 2A b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b - C a b)c - A b )cosh(x) +--R + +--R 2 3 3 2 +--R (2A b c - 2C a b c - 2A b )cosh(x) - A c + (A b + C a)c +--R + +--R 2 3 +--R (A b - C a b)c - A b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R ((4A c - 4C a c - 4A b c)sinh(x) + (4A c - 4C a c - 4A b c)cosh(x)) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 +--R (- A c + (- A b + C a)c + (A b + C a b)c + A b )sinh(x) +--R + +--R 3 2 2 3 +--R (- 2A c + (- 2A b + 2C a)c + (2A b + 2C a b)c + 2A b )cosh(x) +--R + +--R 2 3 +--R 2A b c - 2C a b c - 2A b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (- A c + (- A b + C a)c + (A b + C a b)c + A b )cosh(x) +--R + +--R 2 3 3 2 +--R (2A b c - 2C a b c - 2A b )cosh(x) + A c + (- A b - C a)c +--R + +--R 2 3 +--R (- A b + C a b)c + A b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression(Integer) +--E 194 + +--S 195 of 531 +m1035b:= a1035.2-r1035 +--R +--R +--R (6) +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R C b\|- c + b - a \|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R - C b\|- c + b - a \|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R +--------------+ (b - a)tanh(-) + c +--R 2 2 | 2 2 2 2 +--R (2A c - 2C a c - 2A b )\|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R 2 2 | 2 2 2 +--R (- 2A c + 2C a c + 2A b )\|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R C b x\|- c + b - a \|c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c - b )\|- c + b - a \|c - b + a +--R Type: Expression(Integer) +--E 195 + +--S 196 of 531 +d1035b:= D(m1035b,x) +--R +--R +--R (7) +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b - C a b)c - A b )sinh(x) +--R + +--R 3 2 2 3 +--R (2A c + (2A b - 2C a)c + (- 2A b - 2C a b)c - 2A b )cosh(x) +--R + +--R 2 3 +--R 2A b c - 2C a b c - 2A b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b - C a b)c - A b )cosh(x) +--R + +--R 2 3 3 2 +--R (2A b c - 2C a b c - 2A b )cosh(x) - A c + (A b + C a)c +--R + +--R 2 3 +--R (A b - C a b)c - A b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R ((4A c - 4C a c - 4A b c)sinh(x) + (4A c - 4C a c - 4A b c)cosh(x)) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 +--R (- A c + (- A b + C a)c + (A b + C a b)c + A b )sinh(x) +--R + +--R 3 2 2 3 +--R (- 2A c + (- 2A b + 2C a)c + (2A b + 2C a b)c + 2A b )cosh(x) +--R + +--R 2 3 +--R 2A b c - 2C a b c - 2A b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (- A c + (- A b + C a)c + (A b + C a b)c + A b )cosh(x) +--R + +--R 2 3 3 2 +--R (2A b c - 2C a b c - 2A b )cosh(x) + A c + (- A b - C a)c +--R + +--R 2 3 +--R (- A b + C a b)c + A b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression(Integer) +--E 196 + +)clear all + + +--S 197 of 531 +t1036:= (A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^2 +--R +--R +--R (1) +--R C sinh(x) + A +--R -------------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sinh(x) + (2b c cosh(x) + 2a c)sinh(x) + b cosh(x) + 2a b cosh(x) + a +--R Type: Expression(Integer) +--E 197 + +--S 198 of 531 +r1036:= -2*(a*A+c*C)*atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(3/2)+(b*C-(A*c-a*C)*cosh(x)-A*b*sinh(x))/_ + (a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (2) +--R 2 +--R (- 2C c - 2A a c)sinh(x) + (- 2C b c - 2A a b)cosh(x) - 2C a c +--R + +--R 2 +--R - 2A a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R (- A b sinh(x) + (- A c + C a)cosh(x) + C b)\|c - b + a +--R / +--R 3 2 2 2 3 2 2 2 +--R (c + (- b + a )c)sinh(x) + (b c - b + a b)cosh(x) + a c - a b +--R + +--R 3 +--R a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 198 + +--S 199 of 531 +a1036:= integrate(t1036,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 2 2 +--R (C c + (2C b + A a)c + (C b + 2A a b)c + A a b )sinh(x) +--R + +--R 3 2 2 2 +--R (2C c + (4C b + 2A a)c + (2C b + 4A a b)c + 2A a b )cosh(x) +--R + +--R 2 2 2 +--R 2C a c + (2C a b + 2A a )c + 2A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 2 2 +--R (C c + (2C b + A a)c + (C b + 2A a b)c + A a b )cosh(x) +--R + +--R 2 2 2 3 2 +--R (2C a c + (2C a b + 2A a )c + 2A a b)cosh(x) - C c - A a c +--R + +--R 2 2 +--R C b c + A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 2 2 +--R ((2C b + 2A a)c + 2C b + 2A a b - 2C a )sinh(x) +--R + +--R 2 2 2 +--R ((2C b + 2A a)c + 2C b + 2A a b - 2C a )cosh(x) - 2A c + 2C a c +--R + +--R 2 +--R 2A b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R , +--R +--R 3 2 2 2 +--R (- 2C c + (- 4C b - 2A a)c + (- 2C b - 4A a b)c - 2A a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 2 +--R (- 4C c + (- 8C b - 4A a)c + (- 4C b - 8A a b)c - 4A a b ) +--R * +--R cosh(x) +--R + +--R 2 2 2 +--R - 4C a c + (- 4C a b - 4A a )c - 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 2 +--R (- 2C c + (- 4C b - 2A a)c + (- 2C b - 4A a b)c - 2A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 2 +--R (- 4C a c + (- 4C a b - 4A a )c - 4A a b)cosh(x) + 2C c + 2A a c +--R + +--R 2 2 +--R - 2C b c - 2A a b +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 +--R ((2C b + 2A a)c + 2C b + 2A a b - 2C a )sinh(x) +--R + +--R 2 2 2 +--R ((2C b + 2A a)c + 2C b + 2A a b - 2C a )cosh(x) - 2A c + 2C a c +--R + +--R 2 +--R 2A b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 199 + +--S 200 of 531 +m1036a:= a1036.1-r1036 +--R +--R +--R (4) +--R 4 3 2 2 2 3 +--R (C c + (2C b + A a)c + (C b + 2A a b)c + A a b c)sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + (5C b + 2A a)c + (4C b + 5A a b)c +--R + +--R 3 2 3 +--R (C b + 4A a b )c + A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R 3C a c + (4C a b + 3A a )c + (C a b + 4A a b)c + A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R C c + (4C b + A a)c + (5C b + 4A a b)c +--R + +--R 3 2 3 +--R (2C b + 5A a b )c + 2A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R (4C a c + (8C a b + 4A a )c + (4C a b + 8A a b)c + 4A a b ) +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 2 2 3 +--R - C c - A a c + (C b + 2C a )c + (A a b + 2C a b + 2A a )c +--R + +--R 3 +--R 2A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 3 3 +--R (C b c + (2C b + A a b)c + (C b + 2A a b )c + A a b )cosh(x) +--R + +--R 3 2 2 2 2 2 2 2 +--R (C a c + (4C a b + A a )c + (3C a b + 4A a b)c + 3A a b )cosh(x) +--R + +--R 3 2 2 3 2 3 +--R - C b c + (- A a b + 2C a )c + (C b + 2C a b + 2A a )c +--R + +--R 3 3 +--R A a b + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - C a c - A a c + C a b c + A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 4 3 2 2 2 3 +--R (2C c + (4C b + 2A a)c + (2C b + 4A a b)c + 2A a b c)sinh(x) +--R + +--R 4 3 2 2 +--R 4C c + (10C b + 4A a)c + (8C b + 10A a b)c +--R + +--R 3 2 3 +--R (2C b + 8A a b )c + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R 6C a c + (8C a b + 6A a )c + (2C a b + 8A a b)c + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + (8C b + 2A a)c + (10C b + 8A a b)c +--R + +--R 3 2 3 +--R (4C b + 10A a b )c + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 8C a c + (16C a b + 8A a )c + (8C a b + 16A a b)c +--R + +--R 2 2 +--R 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c - 2A a c + (2C b + 4C a )c +--R + +--R 2 2 3 3 +--R (2A a b + 4C a b + 4A a )c + 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 3 3 +--R (2C b c + (4C b + 2A a b)c + (2C b + 4A a b )c + 2A a b )cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R (2C a c + (8C a b + 2A a )c + (6C a b + 8A a b)c + 6A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 3 2 3 +--R - 2C b c + (- 2A a b + 4C a )c + (2C b + 4C a b + 4A a )c +--R + +--R 3 3 +--R 2A a b + 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - 2C a c - 2A a c + 2C a b c + 2A a b +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 3 3 +--R (A b c + 2A b c + A b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (4A b - C a)c + (5A b - 2C a b)c + 2A b - C a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 +--R (C b + 2A a)c + (4A a b - 2C a )c - C b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + (5A b - 2C a)c + (4A b - 4C a b)c + A b - 2C a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (4A a c + (8A a b - 4C a )c + 4A a b - 4C a b)cosh(x) - 2A c +--R + +--R 2 2 2 3 2 3 +--R (- A b + 2C a)c + (2A b + 2A a )c + A b + 2A a b - 2C a +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 +--R (A c + (2A b - C a)c + (A b - 2C a b)c - C a b )cosh(x) +--R + +--R 2 2 3 2 2 +--R ((- C b + 2A a)c + (4A a b - 2C a )c + C b + 2A a b - 4C a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - A c + (- 2A b + C a)c + (A b + 2C a b + 2A a )c + 2A b +--R + +--R 2 2 3 +--R - C a b + 2A a b - 2C a +--R * +--R cosh(x) +--R + +--R 2 2 3 2 +--R (C b - 2A a)c + 2C a c - C b + 2A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 200 + +--S 201 of 531 +--d1036a:= D(m1036a,x) +--E 201 + +--S 202 of 531 +m1036b:= a1036.2-r1036 +--R +--R +--R (5) +--R 4 3 2 2 2 3 +--R (2C c + (4C b + 2A a)c + (2C b + 4A a b)c + 2A a b c)sinh(x) +--R + +--R 4 3 2 2 +--R 4C c + (10C b + 4A a)c + (8C b + 10A a b)c +--R + +--R 3 2 3 +--R (2C b + 8A a b )c + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R 6C a c + (8C a b + 6A a )c + (2C a b + 8A a b)c + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + (8C b + 2A a)c + (10C b + 8A a b)c +--R + +--R 3 2 3 +--R (4C b + 10A a b )c + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 8C a c + (16C a b + 8A a )c + (8C a b + 16A a b)c +--R + +--R 2 2 +--R 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c - 2A a c + (2C b + 4C a )c +--R + +--R 2 2 3 3 +--R (2A a b + 4C a b + 4A a )c + 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 3 3 +--R (2C b c + (4C b + 2A a b)c + (2C b + 4A a b )c + 2A a b )cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R (2C a c + (8C a b + 2A a )c + (6C a b + 8A a b)c + 6A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 3 2 3 +--R - 2C b c + (- 2A a b + 4C a )c + (2C b + 4C a b + 4A a )c +--R + +--R 3 3 +--R 2A a b + 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - 2C a c - 2A a c + 2C a b c + 2A a b +--R * +--R x +--R +--------------+ (b - a)tanh(-) + c +--R | 2 2 2 2 +--R \|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 4 3 2 2 2 +--R (- 2C c + (- 4C b - 2A a)c + (- 2C b - 4A a b)c - 2A a b c) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 4C c + (- 10C b - 4A a)c + (- 8C b - 10A a b)c +--R + +--R 3 2 3 +--R (- 2C b - 8A a b )c - 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 2 +--R - 6C a c + (- 8C a b - 6A a )c + (- 2C a b - 8A a b)c - 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 2C c + (- 8C b - 2A a)c + (- 10C b - 8A a b)c +--R + +--R 3 2 3 +--R (- 4C b - 10A a b )c - 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R - 8C a c + (- 16C a b - 8A a )c + (- 8C a b - 16A a b)c +--R + +--R 2 2 +--R - 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R 2C c + 2A a c + (- 2C b - 4C a )c +--R + +--R 2 2 3 3 +--R (- 2A a b - 4C a b - 4A a )c - 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 2C b c + (- 4C b - 2A a b)c + (- 2C b - 4A a b )c - 2A a b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R - 2C a c + (- 8C a b - 2A a )c + (- 6C a b - 8A a b)c +--R + +--R 2 2 +--R - 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 3 2 3 +--R 2C b c + (2A a b - 4C a )c + (- 2C b - 4C a b - 4A a )c +--R + +--R 3 3 +--R - 2A a b - 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R 2C a c + 2A a c - 2C a b c - 2A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 3 3 +--R (A b c + 2A b c + A b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (4A b - C a)c + (5A b - 2C a b)c + 2A b - C a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 +--R (C b + 2A a)c + (4A a b - 2C a )c - C b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + (5A b - 2C a)c + (4A b - 4C a b)c + A b - 2C a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (4A a c + (8A a b - 4C a )c + 4A a b - 4C a b)cosh(x) - 2A c +--R + +--R 2 2 2 3 2 3 +--R (- A b + 2C a)c + (2A b + 2A a )c + A b + 2A a b - 2C a +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 +--R (A c + (2A b - C a)c + (A b - 2C a b)c - C a b )cosh(x) +--R + +--R 2 2 3 2 2 +--R ((- C b + 2A a)c + (4A a b - 2C a )c + C b + 2A a b - 4C a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - A c + (- 2A b + C a)c + (A b + 2C a b + 2A a )c + 2A b +--R + +--R 2 2 3 +--R - C a b + 2A a b - 2C a +--R * +--R cosh(x) +--R + +--R 2 2 3 2 +--R (C b - 2A a)c + 2C a c - C b + 2A a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R Type: Expression(Integer) +--E 202 + +--S 203 of 531 +--d1036b:= D(m1036b,x) +--E 203 + +)clear all + + +--S 204 of 531 +t1037:= (A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^3 +--R +--R +--R (1) +--R C sinh(x) + A +--R / +--R 3 3 2 2 2 +--R c sinh(x) + (3b c cosh(x) + 3a c )sinh(x) +--R + +--R 2 2 2 3 3 +--R (3b c cosh(x) + 6a b c cosh(x) + 3a c)sinh(x) + b cosh(x) +--R + +--R 2 2 2 3 +--R 3a b cosh(x) + 3a b cosh(x) + a +--R Type: Expression(Integer) +--E 204 + +--S 205 of 531 +r1037:= -(2*a^2*A+A*b^2-c*(A*c-3*a*C))*atanh((c-(a-b)*tanh(1/2*x))/_ + (a^2-b^2+c^2)^(1/2))/(a^2-b^2+c^2)^(5/2)+1/2*(b*C-(A*c-a*C)*_ + cosh(x)-A*b*sinh(x))/(a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x))^2+_ + 1/2*(a*b*C-(2*c^2*C+a*(3*A*c-a*C))*cosh(x)-b*(3*a*A+2*c*C)*_ + sinh(x))/(a^2-b^2+c^2)^2/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (2) +--R 4 3 2 2 2 2 +--R (2A c - 6C a c + (- 2A b - 4A a )c )sinh(x) +--R + +--R 3 2 3 2 3 +--R (4A b c - 12C a b c + (- 4A b - 8A a b)c)cosh(x) + 4A a c +--R + +--R 2 2 2 3 +--R - 12C a c + (- 4A a b - 8A a )c +--R * +--R sinh(x) +--R + +--R 2 2 2 4 2 2 2 +--R (2A b c - 6C a b c - 2A b - 4A a b )cosh(x) +--R + +--R 2 2 3 3 2 2 3 +--R (4A a b c - 12C a b c - 4A a b - 8A a b)cosh(x) + 2A a c - 6C a c +--R + +--R 2 2 4 +--R - 2A a b - 4A a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 +--R (- 2C b c - 3A a b c)sinh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 2C c - 3A a c + (- 2C b + C a )c - 3A a b )cosh(x) - A b c +--R + +--R 3 2 +--R - C a b c + A b - 4A a b +--R * +--R sinh(x) +--R + +--R 2 2 2 +--R (- 2C b c - 3A a b c + C a b)cosh(x) +--R + +--R 3 2 2 2 3 2 3 +--R (- A c - C a c + (A b - 4A a )c + 2C a )cosh(x) + C b c - C b +--R + +--R 2 +--R 2C a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (- 4b + 4a )c + (2b - 4a b + 2a )c )sinh(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (- 8b + 8a b)c + (4b - 8a b + 4a b)c)cosh(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (- 8a b + 8a )c + (4a b - 8a b + 4a )c +--R * +--R sinh(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (- 4b + 4a b )c + 2b - 4a b + 2a b )cosh(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (- 8a b + 8a b)c + 4a b - 8a b + 4a b)cosh(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (- 4a b + 4a )c + 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 205 + +--S 206 of 531 +a1037:= integrate(t1037,x) +--R +--R +--R (3) +--R [ +--R 5 4 2 2 3 +--R A c + (3A b - 3C a)c + (2A b - 9C a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b - 9C a b - 6A a b)c + (- 3A b - 3C a b - 6A a b )c +--R + +--R 5 2 3 +--R - A b - 2A a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + (12A b - 12C a)c + (8A b - 36C a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b - 36C a b - 24A a b)c +--R + +--R 4 3 2 2 5 2 3 +--R (- 12A b - 12C a b - 24A a b )c - 4A b - 8A a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 4A a c + (8A a b - 12C a )c + (- 24C a b - 8A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 8A a b - 12C a b - 16A a b)c - 4A a b - 8A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 6A c + (18A b - 18C a)c + (12A b - 54C a b - 12A a )c +--R + +--R 3 2 2 2 +--R (- 12A b - 54C a b - 36A a b)c +--R + +--R 4 3 2 2 5 2 3 +--R (- 18A b - 18C a b - 36A a b )c - 6A b - 12A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 12A a c + (24A a b - 36C a )c + (- 72C a b - 24A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 24A a b - 36C a b - 48A a b)c - 12A a b - 24A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c + (- 2A b + 6C a)c + (4A b + 6C a b + 8A a )c +--R + +--R 3 2 2 3 2 +--R (4A b - 6C a b + 8A a b - 12C a )c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b - 6C a b - 8A a b - 12C a b - 8A a )c - 2A b +--R + +--R 2 3 4 +--R - 8A a b - 8A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + (12A b - 12C a)c + (8A b - 36C a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b - 36C a b - 24A a b)c +--R + +--R 4 3 2 2 5 2 3 +--R (- 12A b - 12C a b - 24A a b )c - 4A b - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 12A a c + (24A a b - 36C a )c + (- 72C a b - 24A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 24A a b - 36C a b - 48A a b)c - 12A a b - 24A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 4A c + (- 4A b + 12C a)c + (8A b + 12C a b + 16A a )c +--R + +--R 3 2 2 3 2 +--R (8A b - 12C a b + 16A a b - 24C a )c +--R + +--R 4 3 2 2 3 4 5 +--R (- 4A b - 12C a b - 16A a b - 24C a b - 16A a )c - 4A b +--R + +--R 2 3 4 +--R - 16A a b - 16A a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 3 2 2 2 +--R - 4A a c + 12C a c + (8A a b + 8A a )c - 12C a b c +--R + +--R 4 3 2 +--R - 4A a b - 8A a b +--R * +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R A c + (3A b - 3C a)c + (2A b - 9C a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b - 9C a b - 6A a b)c + (- 3A b - 3C a b - 6A a b )c +--R + +--R 5 2 3 +--R - A b - 2A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 4A a c + (8A a b - 12C a )c + (- 24C a b - 8A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 8A a b - 12C a b - 16A a b)c - 4A a b - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c + (- 2A b + 6C a)c + (4A b + 6C a b + 8A a )c +--R + +--R 3 2 2 3 2 +--R (4A b - 6C a b + 8A a b - 12C a )c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b - 6C a b - 8A a b - 12C a b - 8A a )c - 2A b +--R + +--R 2 3 4 +--R - 8A a b - 8A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 2 2 +--R - 4A a c + 12C a c + (8A a b + 8A a )c - 12C a b c +--R + +--R 4 3 2 +--R - 4A a b - 8A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R A c + (- A b - 3C a)c + (- 2A b + 3C a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 5 +--R (2A b + 3C a b + 2A a b)c + (A b - 3C a b + 2A a b )c - A b +--R + +--R 2 3 +--R - 2A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 4 3 2 2 +--R - 2A c + (- 4A b + 6C a)c + (12C a b + 4A a )c +--R + +--R 3 2 2 4 2 2 +--R (4A b + 6C a b + 8A a b)c + 2A b + 4A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 6A c + (- 12A b + 18C a)c + (36C a b + 12A a )c +--R + +--R 3 2 2 4 2 2 +--R (12A b + 18C a b + 24A a b)c + 6A b + 12A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 4C c - 6A a c + (8C b - 6A a b + 10C a )c +--R + +--R 2 2 3 4 3 2 2 +--R (6A a b + 18C a b + 12A a )c - 4C b + 6A a b + 8C a b +--R + +--R 3 4 +--R 12A a b - 4C a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 6A c + (- 12A b + 18C a)c + (36C a b + 12A a )c +--R + +--R 3 2 2 4 2 2 +--R (12A b + 18C a b + 24A a b)c + 6A b + 12A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 8C c - 12A a c + (16C b - 12A a b + 20C a )c +--R + +--R 2 2 3 4 3 +--R (12A a b + 36C a b + 24A a )c - 8C b + 12A a b +--R + +--R 2 2 3 4 +--R 16C a b + 24A a b - 8C a +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 2 3 +--R - 2A c - 10C a c + (4A b - 20A a )c + (10C a b + 8C a )c +--R + +--R 4 2 2 +--R - 2A b + 20A a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 2A c + (- 4A b + 6C a)c + (12C a b + 4A a )c +--R + +--R 3 2 2 4 2 2 +--R (4A b + 6C a b + 8A a b)c + 2A b + 4A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 4C c - 6A a c + (8C b - 6A a b + 10C a )c +--R + +--R 2 2 3 4 3 2 2 +--R (6A a b + 18C a b + 12A a )c - 4C b + 6A a b + 8C a b +--R + +--R 3 4 +--R 12A a b - 4C a +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 2 2 2 3 +--R - 2A c - 10C a c + (4A b - 20A a )c + (10C a b + 8C a )c +--R + +--R 4 2 2 +--R - 2A b + 20A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R 4C c + (- 4C b + 6A a)c + (- 4C b - 6A a b - 2C a )c +--R + +--R 3 2 2 3 +--R (4C b - 6A a b + 2C a b)c + 6A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 7 6 2 2 5 3 2 4 +--R 2c + 6b c + (2b + 4a )c + (- 10b + 12a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 10b + 8a b + 2a )c + (2b - 8a b + 6a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (6b - 12a b + 6a b )c + 2b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 8c + 24b c + (8b + 16a )c + (- 40b + 48a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 40b + 32a b + 8a )c + (8b - 32a b + 24a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (24b - 48a b + 24a b )c + 8b - 16a b + 8a b +--R * +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 8a c + 16a b c + (- 8a b + 16a )c + (- 32a b + 32a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 8a b + 8a )c + (16a b - 32a b + 16a b)c + 8a b - 16a b +--R + +--R 5 2 +--R 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 12c + 36b c + (12b + 24a )c + (- 60b + 72a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 60b + 48a b + 12a )c + (12b - 48a b + 36a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (36b - 72a b + 36a b )c + 12b - 24a b + 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 24a c + 48a b c + (- 24a b + 48a )c +--R + +--R 3 3 3 4 5 2 +--R (- 96a b + 96a b)c + (- 24a b + 24a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (48a b - 96a b + 48a b)c + 24a b - 48a b + 24a b +--R * +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 4c - 4b c + 12b c + 12b c + (- 12b + 12a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 12b + 12a b)c + (4b - 12a b + 8a )c + 4b - 12a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 8c + 24b c + (8b + 16a )c + (- 40b + 48a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 40b + 32a b + 8a )c + (8b - 32a b + 24a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (24b - 48a b + 24a b )c + 8b - 16a b + 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 24a c + 48a b c + (- 24a b + 48a )c +--R + +--R 3 3 3 4 5 2 +--R (- 96a b + 96a b)c + (- 24a b + 24a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (48a b - 96a b + 48a b)c + 24a b - 48a b + 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 8c - 8b c + 24b c + 24b c + (- 24b + 24a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 +--R (- 24b + 24a b)c + (8b - 24a b + 16a )c + 8b - 24a b +--R + +--R 6 +--R 16a b +--R * +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 8a c + (24a b - 16a )c + (- 24a b + 32a b - 8a )c + 8a b +--R + +--R 3 4 5 2 +--R - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 2c + 6b c + (2b + 4a )c + (- 10b + 12a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 10b + 8a b + 2a )c + (2b - 8a b + 6a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (6b - 12a b + 6a b )c + 2b - 4a b + 2a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 8a c + 16a b c + (- 8a b + 16a )c + (- 32a b + 32a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 8a b + 8a )c + (16a b - 32a b + 16a b)c + 8a b - 16a b +--R + +--R 5 2 +--R 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 4c - 4b c + 12b c + 12b c + (- 12b + 12a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 12b + 12a b)c + (4b - 12a b + 8a )c + 4b - 12a b + 8a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 8a c + (24a b - 16a )c + (- 24a b + 32a b - 8a )c + 8a b +--R + +--R 3 4 5 2 +--R - 16a b + 8a b +--R * +--R cosh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 2c - 2b c + (- 6b + 4a )c + (6b - 4a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (6b - 8a b + 2a )c + (- 6b + 8a b - 2a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (- 2b + 4a b - 2a b )c + 2b - 4a b + 2a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R , +--R +--R 5 4 2 2 3 +--R A c + (3A b - 3C a)c + (2A b - 9C a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b - 9C a b - 6A a b)c + (- 3A b - 3C a b - 6A a b )c +--R + +--R 5 2 3 +--R - A b - 2A a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + (12A b - 12C a)c + (8A b - 36C a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b - 36C a b - 24A a b)c +--R + +--R 4 3 2 2 5 2 3 +--R (- 12A b - 12C a b - 24A a b )c - 4A b - 8A a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 4A a c + (8A a b - 12C a )c + (- 24C a b - 8A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 8A a b - 12C a b - 16A a b)c - 4A a b - 8A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 6A c + (18A b - 18C a)c + (12A b - 54C a b - 12A a )c +--R + +--R 3 2 2 2 +--R (- 12A b - 54C a b - 36A a b)c +--R + +--R 4 3 2 2 5 2 3 +--R (- 18A b - 18C a b - 36A a b )c - 6A b - 12A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 12A a c + (24A a b - 36C a )c + (- 72C a b - 24A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 24A a b - 36C a b - 48A a b)c - 12A a b - 24A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c + (- 2A b + 6C a)c + (4A b + 6C a b + 8A a )c +--R + +--R 3 2 2 3 2 +--R (4A b - 6C a b + 8A a b - 12C a )c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b - 6C a b - 8A a b - 12C a b - 8A a )c - 2A b +--R + +--R 2 3 4 +--R - 8A a b - 8A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + (12A b - 12C a)c + (8A b - 36C a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b - 36C a b - 24A a b)c +--R + +--R 4 3 2 2 5 2 3 +--R (- 12A b - 12C a b - 24A a b )c - 4A b - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 12A a c + (24A a b - 36C a )c + (- 72C a b - 24A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 24A a b - 36C a b - 48A a b)c - 12A a b - 24A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 4A c + (- 4A b + 12C a)c + (8A b + 12C a b + 16A a )c +--R + +--R 3 2 2 3 2 +--R (8A b - 12C a b + 16A a b - 24C a )c +--R + +--R 4 3 2 2 3 4 5 +--R (- 4A b - 12C a b - 16A a b - 24C a b - 16A a )c - 4A b +--R + +--R 2 3 4 +--R - 16A a b - 16A a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 3 2 2 2 +--R - 4A a c + 12C a c + (8A a b + 8A a )c - 12C a b c +--R + +--R 4 3 2 +--R - 4A a b - 8A a b +--R * +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R A c + (3A b - 3C a)c + (2A b - 9C a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b - 9C a b - 6A a b)c + (- 3A b - 3C a b - 6A a b )c +--R + +--R 5 2 3 +--R - A b - 2A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 4A a c + (8A a b - 12C a )c + (- 24C a b - 8A a )c +--R + +--R 3 2 2 3 4 3 2 +--R (- 8A a b - 12C a b - 16A a b)c - 4A a b - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c + (- 2A b + 6C a)c + (4A b + 6C a b + 8A a )c +--R + +--R 3 2 2 3 2 +--R (4A b - 6C a b + 8A a b - 12C a )c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b - 6C a b - 8A a b - 12C a b - 8A a )c - 2A b +--R + +--R 2 3 4 +--R - 8A a b - 8A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 2 2 +--R - 4A a c + 12C a c + (8A a b + 8A a )c - 12C a b c +--R + +--R 4 3 2 +--R - 4A a b - 8A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R A c + (- A b - 3C a)c + (- 2A b + 3C a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 5 +--R (2A b + 3C a b + 2A a b)c + (A b - 3C a b + 2A a b )c - A b +--R + +--R 2 3 +--R - 2A a b +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 4 3 2 2 +--R - A c + (- 2A b + 3C a)c + (6C a b + 2A a )c +--R + +--R 3 2 2 4 2 2 +--R (2A b + 3C a b + 4A a b)c + A b + 2A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 3A c + (- 6A b + 9C a)c + (18C a b + 6A a )c +--R + +--R 3 2 2 4 2 2 +--R (6A b + 9C a b + 12A a b)c + 3A b + 6A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c - 3A a c + (4C b - 3A a b + 5C a )c +--R + +--R 2 2 3 4 3 2 2 +--R (3A a b + 9C a b + 6A a )c - 2C b + 3A a b + 4C a b +--R + +--R 3 4 +--R 6A a b - 2C a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 3A c + (- 6A b + 9C a)c + (18C a b + 6A a )c +--R + +--R 3 2 2 4 2 2 +--R (6A b + 9C a b + 12A a b)c + 3A b + 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 4C c - 6A a c + (8C b - 6A a b + 10C a )c +--R + +--R 2 2 3 4 3 2 2 +--R (6A a b + 18C a b + 12A a )c - 4C b + 6A a b + 8C a b +--R + +--R 3 4 +--R 12A a b - 4C a +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 2 3 +--R - A c - 5C a c + (2A b - 10A a )c + (5C a b + 4C a )c +--R + +--R 4 2 2 +--R - A b + 10A a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 +--R - A c + (- 2A b + 3C a)c + (6C a b + 2A a )c +--R + +--R 3 2 2 4 2 2 +--R (2A b + 3C a b + 4A a b)c + A b + 2A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c - 3A a c + (4C b - 3A a b + 5C a )c +--R + +--R 2 2 3 4 3 2 2 +--R (3A a b + 9C a b + 6A a )c - 2C b + 3A a b + 4C a b +--R + +--R 3 4 +--R 6A a b - 2C a +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 2 2 2 3 +--R - A c - 5C a c + (2A b - 10A a )c + (5C a b + 4C a )c +--R + +--R 4 2 2 +--R - A b + 10A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R 2C c + (- 2C b + 3A a)c + (- 2C b - 3A a b - C a )c +--R + +--R 3 2 2 3 +--R (2C b - 3A a b + C a b)c + 3A a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R 7 6 2 2 5 3 2 4 +--R c + 3b c + (b + 2a )c + (- 5b + 6a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 5b + 4a b + a )c + (b - 4a b + 3a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (3b - 6a b + 3a b )c + b - 2a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 4c + 12b c + (4b + 8a )c + (- 20b + 24a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 20b + 16a b + 4a )c + (4b - 16a b + 12a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (12b - 24a b + 12a b )c + 4b - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 4a c + 8a b c + (- 4a b + 8a )c + (- 16a b + 16a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 4a b + 4a )c + (8a b - 16a b + 8a b)c + 4a b - 8a b +--R + +--R 5 2 +--R 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 6c + 18b c + (6b + 12a )c + (- 30b + 36a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 30b + 24a b + 6a )c + (6b - 24a b + 18a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (18b - 36a b + 18a b )c + 6b - 12a b + 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 12a c + 24a b c + (- 12a b + 24a )c +--R + +--R 3 3 3 4 5 2 +--R (- 48a b + 48a b)c + (- 12a b + 12a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (24a b - 48a b + 24a b)c + 12a b - 24a b + 12a b +--R * +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 2c - 2b c + 6b c + 6b c + (- 6b + 6a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 6b + 6a b)c + (2b - 6a b + 4a )c + 2b - 6a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 4c + 12b c + (4b + 8a )c + (- 20b + 24a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 20b + 16a b + 4a )c + (4b - 16a b + 12a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (12b - 24a b + 12a b )c + 4b - 8a b + 4a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 12a c + 24a b c + (- 12a b + 24a )c +--R + +--R 3 3 3 4 5 2 +--R (- 48a b + 48a b)c + (- 12a b + 12a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (24a b - 48a b + 24a b)c + 12a b - 24a b + 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 4c - 4b c + 12b c + 12b c + (- 12b + 12a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 +--R (- 12b + 12a b)c + (4b - 12a b + 8a )c + 4b - 12a b +--R + +--R 6 +--R 8a b +--R * +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 4a c + (12a b - 8a )c + (- 12a b + 16a b - 4a )c + 4a b +--R + +--R 3 4 5 2 +--R - 8a b + 4a b +--R * +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R c + 3b c + (b + 2a )c + (- 5b + 6a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 5b + 4a b + a )c + (b - 4a b + 3a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (3b - 6a b + 3a b )c + b - 2a b + a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 4a c + 8a b c + (- 4a b + 8a )c + (- 16a b + 16a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 4a b + 4a )c + (8a b - 16a b + 8a b)c + 4a b - 8a b +--R + +--R 5 2 +--R 4a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 2c - 2b c + 6b c + 6b c + (- 6b + 6a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 6b + 6a b)c + (2b - 6a b + 4a )c + 2b - 6a b + 4a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 4a c + (12a b - 8a )c + (- 12a b + 16a b - 4a )c + 4a b +--R + +--R 3 4 5 2 +--R - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 7 6 2 2 5 3 2 4 4 2 2 4 3 +--R c - b c + (- 3b + 2a )c + (3b - 2a b)c + (3b - 4a b + a )c +--R + +--R 5 2 3 4 2 6 2 4 4 2 7 2 5 4 3 +--R (- 3b + 4a b - a b)c + (- b + 2a b - a b )c + b - 2a b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 206 + +--S 207 of 531 +--m1037a:= a1037.1-r1037 +--E 207 + +--S 208 of 531 +--d1037a:= D(m1037a,x) +--E 208 + +--S 209 of 531 +--m1037b:= a1037.2-r1037 +--E 209 + +--S 210 of 531 +--d1037b:= D(m1037b,x) +--E 210 + +)clear all + + +--S 211 of 531 +t1038:= (A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R B cosh(x) + A +--R (1) ------------------------- +--R c sinh(x) + b cosh(x) + a +--R Type: Expression(Integer) +--E 211 + +--S 212 of 531 +r1038:= b*B*x/(b^2-c^2)-2*(A-a*b*B/(b^2-c^2))*_ + atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(1/2)-B*c*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2) +--R +--R +--R (2) +--R +------------+ +--R | 2 2 2 +--R B c\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R x +--R (b - a)tanh(-) + c +------------+ +--R 2 2 2 | 2 2 2 +--R (- 2A c + 2A b - 2B a b)atanh(------------------) - B b x\|c - b + a +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression(Integer) +--E 212 + +--S 213 of 531 +a1038:= integrate(t1038,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (A c - A b + B a b) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R B c\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +------------+ +--R | 2 2 2 +--R (- B c - B b)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R , +--R +--R +--------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R B c\|- c + b - a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 2A c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (- B c - B b)x\|- c + b - a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 213 + +--S 214 of 531 +m1038a:= a1038.1-r1038 +--R +--R +--R (4) +--R 2 2 +--R (A c - A b + B a b) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 +--R - B c\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R B c\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R (b - a)tanh(-) + c +------------+ +--R 2 2 2 | 2 2 2 +--R (2A c - 2A b + 2B a b)atanh(------------------) - B c x\|c - b + a +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 531 +d1038a:= D(m1038a,x) +--R +--R +--R (5) +--R 3 2 2 3 2 2 +--R (A c + A b c + (- A b + B a b)c - A b + B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + 2A b c + (- 2A b + 2B a b)c - 2A b + 2B a b )cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (A c + A b c + (- A b + B a b)c - A b + B a b )cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (2A b c - 2A b + 2B a b )cosh(x) - A c + A b c + (A b - B a b)c +--R + +--R 3 2 +--R - A b + B a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 +--R (4A c + (- 4A b + 4B a b)c)sinh(x) +--R + +--R 3 2 +--R (4A c + (- 4A b + 4B a b)c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R (- A c - A b c + (A b - B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (- 2A c - 2A b c + (2A b - 2B a b)c + 2A b - 2B a b )cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c - A b c + (A b - B a b)c + A b - B a b )cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (2A b c - 2A b + 2B a b )cosh(x) + A c - A b c + (- A b + B a b)c +--R + +--R 3 2 +--R A b - B a b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression(Integer) +--E 215 + +--S 216 of 531 +m1038b:= a1038.2-r1038 +--R +--R +--R (6) +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - B c\|- c + b - a \|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R B c\|- c + b - a \|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R +--------------+ (b - a)tanh(-) + c +--R 2 2 | 2 2 2 2 +--R (2A c - 2A b + 2B a b)\|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R 2 2 | 2 2 2 +--R (- 2A c + 2A b - 2B a b)\|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - B c x\|- c + b - a \|c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c - b )\|- c + b - a \|c - b + a +--R Type: Expression(Integer) +--E 216 + +--S 217 of 531 +d1038b:= D(m1038b,x) +--R +--R +--R (7) +--R 3 2 2 3 2 2 +--R (A c + A b c + (- A b + B a b)c - A b + B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + 2A b c + (- 2A b + 2B a b)c - 2A b + 2B a b )cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (A c + A b c + (- A b + B a b)c - A b + B a b )cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (2A b c - 2A b + 2B a b )cosh(x) - A c + A b c + (A b - B a b)c +--R + +--R 3 2 +--R - A b + B a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 +--R (4A c + (- 4A b + 4B a b)c)sinh(x) +--R + +--R 3 2 +--R (4A c + (- 4A b + 4B a b)c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R (- A c - A b c + (A b - B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (- 2A c - 2A b c + (2A b - 2B a b)c + 2A b - 2B a b )cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c - A b c + (A b - B a b)c + A b - B a b )cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (2A b c - 2A b + 2B a b )cosh(x) + A c - A b c + (- A b + B a b)c +--R + +--R 3 2 +--R A b - B a b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression(Integer) +--E 217 + +)clear all + + +--S 218 of 531 +t1039:= (A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x))^2 +--R +--R +--R (1) +--R B cosh(x) + A +--R -------------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sinh(x) + (2b c cosh(x) + 2a c)sinh(x) + b cosh(x) + 2a b cosh(x) + a +--R Type: Expression(Integer) +--E 218 + +--S 219 of 531 +r1039:= -2*(a*A-b*B)*atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(3/2)-(B*c+A*c*cosh(x)+(A*b-a*B)*sinh(x))/_ + (a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (2) +--R 2 2 +--R ((2B b - 2A a)c sinh(x) + (2B b - 2A a b)cosh(x) + 2B a b - 2A a ) +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R ((- A b + B a)sinh(x) - A c cosh(x) - B c)\|c - b + a +--R / +--R 3 2 2 2 3 2 2 2 +--R (c + (- b + a )c)sinh(x) + (b c - b + a b)cosh(x) + a c - a b +--R + +--R 3 +--R a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 531 +a1039:= integrate(t1039,x) +--R +--R +--R (3) +--R [ +--R 2 2 3 2 2 +--R ((B b - A a)c + (2B b - 2A a b)c + B b - A a b )sinh(x) +--R + +--R 2 2 3 2 +--R ((2B b - 2A a)c + (4B b - 4A a b)c + 2B b - 2A a b )cosh(x) +--R + +--R 2 2 2 +--R (2B a b - 2A a )c + 2B a b - 2A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 2 +--R ((B b - A a)c + (2B b - 2A a b)c + B b - A a b )cosh(x) +--R + +--R 2 2 2 2 +--R ((2B a b - 2A a )c + 2B a b - 2A a b)cosh(x) + (- B b + A a)c +--R + +--R 3 2 +--R B b - A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 2 2 +--R (- 2B c + (- 2B b + 2A a)c + 2A a b - 2B a )sinh(x) +--R + +--R 2 2 2 +--R (- 2B c + (- 2B b + 2A a)c + 2A a b - 2B a )cosh(x) - 2A c +--R + +--R 2 +--R 2A b - 2B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R , +--R +--R 2 2 3 2 2 +--R ((2B b - 2A a)c + (4B b - 4A a b)c + 2B b - 2A a b )sinh(x) +--R + +--R 2 2 3 2 +--R ((4B b - 4A a)c + (8B b - 8A a b)c + 4B b - 4A a b )cosh(x) +--R + +--R 2 2 2 +--R (4B a b - 4A a )c + 4B a b - 4A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 2 +--R ((2B b - 2A a)c + (4B b - 4A a b)c + 2B b - 2A a b )cosh(x) +--R + +--R 2 2 2 2 +--R ((4B a b - 4A a )c + 4B a b - 4A a b)cosh(x) + (- 2B b + 2A a)c +--R + +--R 3 2 +--R 2B b - 2A a b +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 +--R (- 2B c + (- 2B b + 2A a)c + 2A a b - 2B a )sinh(x) +--R + +--R 2 2 2 +--R (- 2B c + (- 2B b + 2A a)c + 2A a b - 2B a )cosh(x) - 2A c +--R + +--R 2 +--R 2A b - 2B a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 220 + +--S 221 of 531 +m1039a:= a1039.1-r1039 +--R +--R +--R (4) +--R 3 2 2 3 2 3 +--R ((B b - A a)c + (2B b - 2A a b)c + (B b - A a b )c)sinh(x) +--R + +--R 3 2 2 3 2 +--R (2B b - 2A a)c + (5B b - 5A a b)c + (4B b - 4A a b )c +--R + +--R 4 3 +--R B b - A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (3B a b - 3A a )c + (4B a b - 4A a b)c + B a b - A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (B b - A a)c + (4B b - 4A a b)c + (5B b - 5A a b )c +--R + +--R 4 3 +--R 2B b - 2A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((4B a b - 4A a )c + (8B a b - 8A a b)c + 4B a b - 4A a b ) +--R * +--R cosh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (- B b + A a)c + (B b - A a b + 2B a b - 2A a )c + 2B a b +--R + +--R 3 +--R - 2A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 4 3 3 +--R ((B b - A a b)c + (2B b - 2A a b )c + B b - A a b )cosh(x) +--R + +--R 2 2 2 2 3 2 2 2 +--R ((B a b - A a )c + (4B a b - 4A a b)c + 3B a b - 3A a b )cosh(x) +--R + +--R 2 2 2 3 4 3 2 2 +--R (- B b + A a b)c + (2B a b - 2A a )c + B b - A a b + 2B a b +--R + +--R 3 +--R - 2A a b +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (- B a b + A a )c + B a b - A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 3 2 2 3 2 +--R ((- 2B b + 2A a)c + (- 4B b + 4A a b)c + (- 2B b + 2A a b )c) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 4B b + 4A a)c + (- 10B b + 10A a b)c +--R + +--R 3 2 4 3 +--R (- 8B b + 8A a b )c - 2B b + 2A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 6B a b + 6A a )c + (- 8B a b + 8A a b)c - 2B a b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 2B b + 2A a)c + (- 8B b + 8A a b)c +--R + +--R 3 2 4 3 +--R (- 10B b + 10A a b )c - 4B b + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (- 8B a b + 8A a )c + (- 16B a b + 16A a b)c - 8B a b +--R + +--R 2 2 +--R 8A a b +--R * +--R cosh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (2B b - 2A a)c + (- 2B b + 2A a b - 4B a b + 4A a )c - 4B a b +--R + +--R 3 +--R 4A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 4 3 +--R ((- 2B b + 2A a b)c + (- 4B b + 4A a b )c - 2B b + 2A a b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((- 2B a b + 2A a )c + (- 8B a b + 8A a b)c - 6B a b + 6A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 4 3 +--R (2B b - 2A a b)c + (- 4B a b + 4A a )c - 2B b + 2A a b +--R + +--R 2 2 3 +--R - 4B a b + 4A a b +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2B a b - 2A a )c - 2B a b + 2A a b +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 3 2 3 +--R ((A b - B a)c + (2A b - 2B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (4A b - 2B a)c + (5A b - 4B a b)c + 2A b - 2B a b ) +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - B c + 2A a c + (B b + 4A a b - 4B a )c + 2A a b - 2B a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + (5A b - B a)c + (4A b - 2B a b)c + A b - B a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (4A a c + (8A a b - 4B a )c + 4A a b - 4B a b)cosh(x) - 2A c +--R + +--R 2 2 2 3 2 +--R (- A b + B a)c + (2A b - 2B a b + 2A a )c + A b - B a b +--R + +--R 2 3 +--R 2A a b - 2B a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 +--R (A c + 2A b c + A b c)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (B c + 2A a c + (- B b + 4A a b)c + 2A a b - 2B a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - A c - 2A b c + (A b + 2A a )c + 2A b - 2B a b + 2A a b +--R + +--R 3 +--R - 2B a +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R - B c - 2A a c + B b c + 2A a b - 2B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 531 +--d1039a:= D(m1039a,x) +--E 222 + +--S 223 of 531 +m1039b:= a1039.2-r1039 +--R +--R +--R (5) +--R 3 2 2 3 2 +--R ((- 2B b + 2A a)c + (- 4B b + 4A a b)c + (- 2B b + 2A a b )c) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 4B b + 4A a)c + (- 10B b + 10A a b)c +--R + +--R 3 2 4 3 +--R (- 8B b + 8A a b )c - 2B b + 2A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 6B a b + 6A a )c + (- 8B a b + 8A a b)c - 2B a b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 2B b + 2A a)c + (- 8B b + 8A a b)c +--R + +--R 3 2 4 3 +--R (- 10B b + 10A a b )c - 4B b + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (- 8B a b + 8A a )c + (- 16B a b + 16A a b)c - 8B a b +--R + +--R 2 2 +--R 8A a b +--R * +--R cosh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (2B b - 2A a)c + (- 2B b + 2A a b - 4B a b + 4A a )c - 4B a b +--R + +--R 3 +--R 4A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 4 3 +--R ((- 2B b + 2A a b)c + (- 4B b + 4A a b )c - 2B b + 2A a b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((- 2B a b + 2A a )c + (- 8B a b + 8A a b)c - 6B a b + 6A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 4 3 +--R (2B b - 2A a b)c + (- 4B a b + 4A a )c - 2B b + 2A a b +--R + +--R 2 2 3 +--R - 4B a b + 4A a b +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2B a b - 2A a )c - 2B a b + 2A a b +--R * +--R x +--R +--------------+ (b - a)tanh(-) + c +--R | 2 2 2 2 +--R \|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 3 2 3 +--R ((2B b - 2A a)c + (4B b - 4A a b)c + (2B b - 2A a b )c)sinh(x) +--R + +--R 3 2 2 3 2 +--R (4B b - 4A a)c + (10B b - 10A a b)c + (8B b - 8A a b )c +--R + +--R 4 3 +--R 2B b - 2A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (6B a b - 6A a )c + (8B a b - 8A a b)c + 2B a b - 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (2B b - 2A a)c + (8B b - 8A a b)c + (10B b - 10A a b )c +--R + +--R 4 3 +--R 4B b - 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (8B a b - 8A a )c + (16B a b - 16A a b)c + 8B a b +--R + +--R 2 2 +--R - 8A a b +--R * +--R cosh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (- 2B b + 2A a)c + (2B b - 2A a b + 4B a b - 4A a )c + 4B a b +--R + +--R 3 +--R - 4A a b +--R * +--R sinh(x) +--R + +--R 2 2 3 2 4 3 3 +--R ((2B b - 2A a b)c + (4B b - 4A a b )c + 2B b - 2A a b )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((2B a b - 2A a )c + (8B a b - 8A a b)c + 6B a b - 6A a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 4 3 +--R (- 2B b + 2A a b)c + (4B a b - 4A a )c + 2B b - 2A a b +--R + +--R 2 2 3 +--R 4B a b - 4A a b +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 2B a b + 2A a )c + 2B a b - 2A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 3 2 3 +--R ((A b - B a)c + (2A b - 2B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (4A b - 2B a)c + (5A b - 4B a b)c + 2A b - 2B a b ) +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - B c + 2A a c + (B b + 4A a b - 4B a )c + 2A a b - 2B a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (2A c + (5A b - B a)c + (4A b - 2B a b)c + A b - B a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R (4A a c + (8A a b - 4B a )c + 4A a b - 4B a b)cosh(x) - 2A c +--R + +--R 2 2 2 3 2 +--R (- A b + B a)c + (2A b - 2B a b + 2A a )c + A b - B a b +--R + +--R 2 3 +--R 2A a b - 2B a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 +--R (A c + 2A b c + A b c)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (B c + 2A a c + (- B b + 4A a b)c + 2A a b - 2B a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - A c - 2A b c + (A b + 2A a )c + 2A b - 2B a b + 2A a b +--R + +--R 3 +--R - 2B a +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R - B c - 2A a c + B b c + 2A a b - 2B a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R Type: Expression(Integer) +--E 223 + +--S 224 of 531 +--d1039b:= D(m1039b,x) +--E 224 + +)clear all + + +--S 225 of 531 +t1040:= (A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x))^3 +--R +--R +--R (1) +--R B cosh(x) + A +--R / +--R 3 3 2 2 2 +--R c sinh(x) + (3b c cosh(x) + 3a c )sinh(x) +--R + +--R 2 2 2 3 3 +--R (3b c cosh(x) + 6a b c cosh(x) + 3a c)sinh(x) + b cosh(x) +--R + +--R 2 2 2 3 +--R 3a b cosh(x) + 3a b cosh(x) + a +--R Type: Expression(Integer) +--E 225 + +--S 226 of 531 +r1040:= -(2*a^2*A+b*(A*b-3*a*B)-A*c^2)*atanh((c-(a-b)*tanh(1/2*x))/_ + (a^2-b^2+c^2)^(1/2))/(a^2-b^2+c^2)^(5/2)-1/2*(B*c+A*c*cosh(x)+_ + (A*b-a*B)*sinh(x))/(a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x))^2-_ + 1/2*(a*B*c+(3*a*A-2*b*B)*c*cosh(x)-(2*b^2*B-a*(3*A*b-a*B))*_ + sinh(x))/(a^2-b^2+c^2)^2/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (2) +--R 4 2 2 2 2 +--R (2A c + (- 2A b + 6B a b - 4A a )c )sinh(x) +--R + +--R 3 3 2 2 3 +--R (4A b c + (- 4A b + 12B a b - 8A a b)c)cosh(x) + 4A a c +--R + +--R 2 2 3 +--R (- 4A a b + 12B a b - 8A a )c +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R (2A b c - 2A b + 6B a b - 4A a b )cosh(x) +--R + +--R 2 3 2 2 3 2 2 2 2 +--R (4A a b c - 4A a b + 12B a b - 8A a b)cosh(x) + 2A a c - 2A a b +--R + +--R 3 4 +--R 6B a b - 4A a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 2 +--R (2B b - 3A a b + B a )c sinh(x) +--R + +--R 2 3 2 2 2 +--R ((2B b - 3A a)c + 2B b - 3A a b + B a b)cosh(x) - A b c +--R + +--R 3 2 2 3 +--R A b + B a b - 4A a b + 2B a +--R * +--R sinh(x) +--R + +--R 2 2 +--R (2B b - 3A a b)c cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c + (A b + B a b - 4A a )c)cosh(x) - B c + (B b - 2B a )c +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (- 4b + 4a )c + (2b - 4a b + 2a )c )sinh(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (- 8b + 8a b)c + (4b - 8a b + 4a b)c)cosh(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (- 8a b + 8a )c + (4a b - 8a b + 4a )c +--R * +--R sinh(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (- 4b + 4a b )c + 2b - 4a b + 2a b )cosh(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (- 8a b + 8a b)c + 4a b - 8a b + 4a b)cosh(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (- 4a b + 4a )c + 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 531 +a1040:= integrate(t1040,x) +--R +--R +--R (3) +--R [ +--R 5 4 2 2 3 +--R A c + 3A b c + (2A b + 3B a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b + 9B a b - 6A a b)c + (- 3A b + 9B a b - 6A a b )c +--R + +--R 5 4 2 3 +--R - A b + 3B a b - 2A a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + 12A b c + (8A b + 12B a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b + 36B a b - 24A a b)c +--R + +--R 4 3 2 2 5 4 +--R (- 12A b + 36B a b - 24A a b )c - 4A b + 12B a b +--R + +--R 2 3 +--R - 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 4A a c + 8A a b c + (12B a b - 8A a )c +--R + +--R 3 2 2 3 4 2 3 3 2 +--R (- 8A a b + 24B a b - 16A a b)c - 4A a b + 12B a b - 8A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 6A c + 18A b c + (12A b + 18B a b - 12A a )c +--R + +--R 3 2 2 2 +--R (- 12A b + 54B a b - 36A a b)c +--R + +--R 4 3 2 2 5 4 +--R (- 18A b + 54B a b - 36A a b )c - 6A b + 18B a b +--R + +--R 2 3 +--R - 12A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 12A a c + 24A a b c + (36B a b - 24A a )c +--R + +--R 3 2 2 3 4 2 3 +--R (- 24A a b + 72B a b - 48A a b)c - 12A a b + 36B a b +--R + +--R 3 2 +--R - 24A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c - 2A b c + (4A b - 6B a b + 8A a )c +--R + +--R 3 2 2 2 +--R (4A b - 6B a b + 8A a b)c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b + 6B a b - 8A a b + 12B a b - 8A a )c - 2A b +--R + +--R 4 2 3 3 2 4 +--R 6B a b - 8A a b + 12B a b - 8A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + 12A b c + (8A b + 12B a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b + 36B a b - 24A a b)c +--R + +--R 4 3 2 2 5 4 +--R (- 12A b + 36B a b - 24A a b )c - 4A b + 12B a b +--R + +--R 2 3 +--R - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 12A a c + 24A a b c + (36B a b - 24A a )c +--R + +--R 3 2 2 3 4 2 3 +--R (- 24A a b + 72B a b - 48A a b)c - 12A a b + 36B a b +--R + +--R 3 2 +--R - 24A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 4A c - 4A b c + (8A b - 12B a b + 16A a )c +--R + +--R 3 2 2 2 +--R (8A b - 12B a b + 16A a b)c +--R + +--R 4 3 2 2 3 4 5 +--R (- 4A b + 12B a b - 16A a b + 24B a b - 16A a )c - 4A b +--R + +--R 4 2 3 3 2 4 +--R 12B a b - 16A a b + 24B a b - 16A a b +--R * +--R cosh(x) +--R + +--R 4 2 2 3 2 4 2 3 +--R - 4A a c + (8A a b - 12B a b + 8A a )c - 4A a b + 12B a b +--R + +--R 3 2 +--R - 8A a b +--R * +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R A c + 3A b c + (2A b + 3B a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b + 9B a b - 6A a b)c + (- 3A b + 9B a b - 6A a b )c +--R + +--R 5 4 2 3 +--R - A b + 3B a b - 2A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 4A a c + 8A a b c + (12B a b - 8A a )c +--R + +--R 3 2 2 3 4 2 3 3 2 +--R (- 8A a b + 24B a b - 16A a b)c - 4A a b + 12B a b - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c - 2A b c + (4A b - 6B a b + 8A a )c +--R + +--R 3 2 2 2 +--R (4A b - 6B a b + 8A a b)c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b + 6B a b - 8A a b + 12B a b - 8A a )c - 2A b +--R + +--R 4 2 3 3 2 4 +--R 6B a b - 8A a b + 12B a b - 8A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 2 3 2 4 2 3 +--R - 4A a c + (8A a b - 12B a b + 8A a )c - 4A a b + 12B a b +--R + +--R 3 2 +--R - 8A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R A c - A b c + (- 2A b + 3B a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 5 +--R (2A b - 3B a b + 2A a b)c + (A b - 3B a b + 2A a b )c - A b +--R + +--R 4 2 3 +--R 3B a b - 2A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 4 3 2 2 +--R - 2A c - 4A b c + (- 6B a b + 4A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (4A b - 12B a b + 8A a b)c + 2A b - 6B a b + 4A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 6A c - 12A b c + (- 18B a b + 12A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (12A b - 36B a b + 24A a b)c + 6A b - 18B a b + 12A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 4B c - 6A a c + (8B b - 6A a b - 8B a )c +--R + +--R 2 2 3 4 3 2 2 +--R (6A a b - 18B a b + 12A a )c - 4B b + 6A a b - 10B a b +--R + +--R 3 4 +--R 12A a b - 4B a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 6A c - 12A b c + (- 18B a b + 12A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (12A b - 36B a b + 24A a b)c + 6A b - 18B a b + 12A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 8B c - 12A a c + (16B b - 12A a b - 16B a )c +--R + +--R 2 2 3 4 3 +--R (12A a b - 36B a b + 24A a )c - 8B b + 12A a b +--R + +--R 2 2 3 4 +--R - 20B a b + 24A a b - 8B a +--R * +--R cosh(x) +--R + +--R 4 2 2 2 4 3 +--R - 2A c + (4A b + 10B a b - 20A a )c - 2A b - 10B a b +--R + +--R 2 2 3 +--R 20A a b - 8B a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 2A c - 4A b c + (- 6B a b + 4A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (4A b - 12B a b + 8A a b)c + 2A b - 6B a b + 4A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 4B c - 6A a c + (8B b - 6A a b - 8B a )c +--R + +--R 2 2 3 4 3 2 2 +--R (6A a b - 18B a b + 12A a )c - 4B b + 6A a b - 10B a b +--R + +--R 3 4 +--R 12A a b - 4B a +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 2 2 4 3 +--R - 2A c + (4A b + 10B a b - 20A a )c - 2A b - 10B a b +--R + +--R 2 2 3 +--R 20A a b - 8B a b +--R * +--R cosh(x) +--R + +--R 3 2 2 +--R (- 4B b + 6A a)c + (4B b - 6A a b)c +--R + +--R 3 2 2 4 3 2 2 +--R (4B b - 6A a b + 2B a b)c - 4B b + 6A a b - 2B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 7 6 2 2 5 3 2 4 +--R 2c + 6b c + (2b + 4a )c + (- 10b + 12a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 10b + 8a b + 2a )c + (2b - 8a b + 6a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (6b - 12a b + 6a b )c + 2b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 8c + 24b c + (8b + 16a )c + (- 40b + 48a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 40b + 32a b + 8a )c + (8b - 32a b + 24a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (24b - 48a b + 24a b )c + 8b - 16a b + 8a b +--R * +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 8a c + 16a b c + (- 8a b + 16a )c + (- 32a b + 32a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 8a b + 8a )c + (16a b - 32a b + 16a b)c + 8a b - 16a b +--R + +--R 5 2 +--R 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 12c + 36b c + (12b + 24a )c + (- 60b + 72a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 60b + 48a b + 12a )c + (12b - 48a b + 36a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (36b - 72a b + 36a b )c + 12b - 24a b + 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 24a c + 48a b c + (- 24a b + 48a )c +--R + +--R 3 3 3 4 5 2 +--R (- 96a b + 96a b)c + (- 24a b + 24a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (48a b - 96a b + 48a b)c + 24a b - 48a b + 24a b +--R * +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 4c - 4b c + 12b c + 12b c + (- 12b + 12a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 12b + 12a b)c + (4b - 12a b + 8a )c + 4b - 12a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 8c + 24b c + (8b + 16a )c + (- 40b + 48a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 40b + 32a b + 8a )c + (8b - 32a b + 24a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (24b - 48a b + 24a b )c + 8b - 16a b + 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 24a c + 48a b c + (- 24a b + 48a )c +--R + +--R 3 3 3 4 5 2 +--R (- 96a b + 96a b)c + (- 24a b + 24a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (48a b - 96a b + 48a b)c + 24a b - 48a b + 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 8c - 8b c + 24b c + 24b c + (- 24b + 24a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 +--R (- 24b + 24a b)c + (8b - 24a b + 16a )c + 8b - 24a b +--R + +--R 6 +--R 16a b +--R * +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 8a c + (24a b - 16a )c + (- 24a b + 32a b - 8a )c + 8a b +--R + +--R 3 4 5 2 +--R - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 2c + 6b c + (2b + 4a )c + (- 10b + 12a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 10b + 8a b + 2a )c + (2b - 8a b + 6a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (6b - 12a b + 6a b )c + 2b - 4a b + 2a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 8a c + 16a b c + (- 8a b + 16a )c + (- 32a b + 32a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 8a b + 8a )c + (16a b - 32a b + 16a b)c + 8a b - 16a b +--R + +--R 5 2 +--R 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 4c - 4b c + 12b c + 12b c + (- 12b + 12a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 12b + 12a b)c + (4b - 12a b + 8a )c + 4b - 12a b + 8a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 8a c + (24a b - 16a )c + (- 24a b + 32a b - 8a )c + 8a b +--R + +--R 3 4 5 2 +--R - 16a b + 8a b +--R * +--R cosh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 2c - 2b c + (- 6b + 4a )c + (6b - 4a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (6b - 8a b + 2a )c + (- 6b + 8a b - 2a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (- 2b + 4a b - 2a b )c + 2b - 4a b + 2a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R , +--R +--R 5 4 2 2 3 +--R A c + 3A b c + (2A b + 3B a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b + 9B a b - 6A a b)c + (- 3A b + 9B a b - 6A a b )c +--R + +--R 5 4 2 3 +--R - A b + 3B a b - 2A a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + 12A b c + (8A b + 12B a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b + 36B a b - 24A a b)c +--R + +--R 4 3 2 2 5 4 +--R (- 12A b + 36B a b - 24A a b )c - 4A b + 12B a b +--R + +--R 2 3 +--R - 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 4A a c + 8A a b c + (12B a b - 8A a )c +--R + +--R 3 2 2 3 4 2 3 3 2 +--R (- 8A a b + 24B a b - 16A a b)c - 4A a b + 12B a b - 8A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 6A c + 18A b c + (12A b + 18B a b - 12A a )c +--R + +--R 3 2 2 2 +--R (- 12A b + 54B a b - 36A a b)c +--R + +--R 4 3 2 2 5 4 +--R (- 18A b + 54B a b - 36A a b )c - 6A b + 18B a b +--R + +--R 2 3 +--R - 12A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 12A a c + 24A a b c + (36B a b - 24A a )c +--R + +--R 3 2 2 3 4 2 3 +--R (- 24A a b + 72B a b - 48A a b)c - 12A a b + 36B a b +--R + +--R 3 2 +--R - 24A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c - 2A b c + (4A b - 6B a b + 8A a )c +--R + +--R 3 2 2 2 +--R (4A b - 6B a b + 8A a b)c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b + 6B a b - 8A a b + 12B a b - 8A a )c - 2A b +--R + +--R 4 2 3 3 2 4 +--R 6B a b - 8A a b + 12B a b - 8A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R 4A c + 12A b c + (8A b + 12B a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b + 36B a b - 24A a b)c +--R + +--R 4 3 2 2 5 4 +--R (- 12A b + 36B a b - 24A a b )c - 4A b + 12B a b +--R + +--R 2 3 +--R - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 12A a c + 24A a b c + (36B a b - 24A a )c +--R + +--R 3 2 2 3 4 2 3 +--R (- 24A a b + 72B a b - 48A a b)c - 12A a b + 36B a b +--R + +--R 3 2 +--R - 24A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 4A c - 4A b c + (8A b - 12B a b + 16A a )c +--R + +--R 3 2 2 2 +--R (8A b - 12B a b + 16A a b)c +--R + +--R 4 3 2 2 3 4 5 +--R (- 4A b + 12B a b - 16A a b + 24B a b - 16A a )c - 4A b +--R + +--R 4 2 3 3 2 4 +--R 12B a b - 16A a b + 24B a b - 16A a b +--R * +--R cosh(x) +--R + +--R 4 2 2 3 2 4 2 3 +--R - 4A a c + (8A a b - 12B a b + 8A a )c - 4A a b + 12B a b +--R + +--R 3 2 +--R - 8A a b +--R * +--R sinh(x) +--R + +--R 5 4 2 2 3 +--R A c + 3A b c + (2A b + 3B a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 +--R (- 2A b + 9B a b - 6A a b)c + (- 3A b + 9B a b - 6A a b )c +--R + +--R 5 4 2 3 +--R - A b + 3B a b - 2A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 3 2 3 2 +--R 4A a c + 8A a b c + (12B a b - 8A a )c +--R + +--R 3 2 2 3 4 2 3 3 2 +--R (- 8A a b + 24B a b - 16A a b)c - 4A a b + 12B a b - 8A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R - 2A c - 2A b c + (4A b - 6B a b + 8A a )c +--R + +--R 3 2 2 2 +--R (4A b - 6B a b + 8A a b)c +--R + +--R 4 3 2 2 3 4 5 +--R (- 2A b + 6B a b - 8A a b + 12B a b - 8A a )c - 2A b +--R + +--R 4 2 3 3 2 4 +--R 6B a b - 8A a b + 12B a b - 8A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 2 3 2 4 2 3 +--R - 4A a c + (8A a b - 12B a b + 8A a )c - 4A a b + 12B a b +--R + +--R 3 2 +--R - 8A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R A c - A b c + (- 2A b + 3B a b - 2A a )c +--R + +--R 3 2 2 2 4 3 2 2 5 +--R (2A b - 3B a b + 2A a b)c + (A b - 3B a b + 2A a b )c - A b +--R + +--R 4 2 3 +--R 3B a b - 2A a b +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 4 3 2 2 +--R - A c - 2A b c + (- 3B a b + 2A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (2A b - 6B a b + 4A a b)c + A b - 3B a b + 2A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 3A c - 6A b c + (- 9B a b + 6A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (6A b - 18B a b + 12A a b)c + 3A b - 9B a b + 6A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2B c - 3A a c + (4B b - 3A a b - 4B a )c +--R + +--R 2 2 3 4 3 2 2 +--R (3A a b - 9B a b + 6A a )c - 2B b + 3A a b - 5B a b +--R + +--R 3 4 +--R 6A a b - 2B a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R - 3A c - 6A b c + (- 9B a b + 6A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (6A b - 18B a b + 12A a b)c + 3A b - 9B a b + 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 4B c - 6A a c + (8B b - 6A a b - 8B a )c +--R + +--R 2 2 3 4 3 2 2 +--R (6A a b - 18B a b + 12A a )c - 4B b + 6A a b - 10B a b +--R + +--R 3 4 +--R 12A a b - 4B a +--R * +--R cosh(x) +--R + +--R 4 2 2 2 4 3 +--R - A c + (2A b + 5B a b - 10A a )c - A b - 5B a b +--R + +--R 2 2 3 +--R 10A a b - 4B a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 +--R - A c - 2A b c + (- 3B a b + 2A a )c +--R + +--R 3 2 2 4 3 2 2 +--R (2A b - 6B a b + 4A a b)c + A b - 3B a b + 2A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2B c - 3A a c + (4B b - 3A a b - 4B a )c +--R + +--R 2 2 3 4 3 2 2 +--R (3A a b - 9B a b + 6A a )c - 2B b + 3A a b - 5B a b +--R + +--R 3 4 +--R 6A a b - 2B a +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 2 2 4 3 +--R - A c + (2A b + 5B a b - 10A a )c - A b - 5B a b +--R + +--R 2 2 3 +--R 10A a b - 4B a b +--R * +--R cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 2B b + 3A a)c + (2B b - 3A a b)c + (2B b - 3A a b + B a b)c +--R + +--R 4 3 2 2 +--R - 2B b + 3A a b - B a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R 7 6 2 2 5 3 2 4 +--R c + 3b c + (b + 2a )c + (- 5b + 6a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 5b + 4a b + a )c + (b - 4a b + 3a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (3b - 6a b + 3a b )c + b - 2a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 4c + 12b c + (4b + 8a )c + (- 20b + 24a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 20b + 16a b + 4a )c + (4b - 16a b + 12a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (12b - 24a b + 12a b )c + 4b - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 4a c + 8a b c + (- 4a b + 8a )c + (- 16a b + 16a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 4a b + 4a )c + (8a b - 16a b + 8a b)c + 4a b - 8a b +--R + +--R 5 2 +--R 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 6c + 18b c + (6b + 12a )c + (- 30b + 36a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 30b + 24a b + 6a )c + (6b - 24a b + 18a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (18b - 36a b + 18a b )c + 6b - 12a b + 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 12a c + 24a b c + (- 12a b + 24a )c +--R + +--R 3 3 3 4 5 2 +--R (- 48a b + 48a b)c + (- 12a b + 12a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (24a b - 48a b + 24a b)c + 12a b - 24a b + 12a b +--R * +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 2c - 2b c + 6b c + 6b c + (- 6b + 6a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 6b + 6a b)c + (2b - 6a b + 4a )c + 2b - 6a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 4c + 12b c + (4b + 8a )c + (- 20b + 24a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 20b + 16a b + 4a )c + (4b - 16a b + 12a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (12b - 24a b + 12a b )c + 4b - 8a b + 4a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 3 4 +--R 12a c + 24a b c + (- 12a b + 24a )c +--R + +--R 3 3 3 4 5 2 +--R (- 48a b + 48a b)c + (- 12a b + 12a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (24a b - 48a b + 24a b)c + 12a b - 24a b + 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 4c - 4b c + 12b c + 12b c + (- 12b + 12a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 +--R (- 12b + 12a b)c + (4b - 12a b + 8a )c + 4b - 12a b +--R + +--R 6 +--R 8a b +--R * +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 4a c + (12a b - 8a )c + (- 12a b + 16a b - 4a )c + 4a b +--R + +--R 3 4 5 2 +--R - 8a b + 4a b +--R * +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R c + 3b c + (b + 2a )c + (- 5b + 6a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 5b + 4a b + a )c + (b - 4a b + 3a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (3b - 6a b + 3a b )c + b - 2a b + a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 4a c + 8a b c + (- 4a b + 8a )c + (- 16a b + 16a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 4a b + 4a )c + (8a b - 16a b + 8a b)c + 4a b - 8a b +--R + +--R 5 2 +--R 4a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 4 3 +--R - 2c - 2b c + 6b c + 6b c + (- 6b + 6a )c +--R + +--R 5 4 2 6 4 2 6 7 4 3 6 +--R (- 6b + 6a b)c + (2b - 6a b + 4a )c + 2b - 6a b + 4a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 3 4 4 3 2 5 2 6 +--R - 4a c + (12a b - 8a )c + (- 12a b + 16a b - 4a )c + 4a b +--R + +--R 3 4 5 2 +--R - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 7 6 2 2 5 3 2 4 4 2 2 4 3 +--R c - b c + (- 3b + 2a )c + (3b - 2a b)c + (3b - 4a b + a )c +--R + +--R 5 2 3 4 2 6 2 4 4 2 7 2 5 4 3 +--R (- 3b + 4a b - a b)c + (- b + 2a b - a b )c + b - 2a b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 227 + +--S 228 of 531 +--m1040a:= a1040.1-r1040 +--E 228 + +--S 229 of 531 +--d1040a:= D(m1040a,x) +--E 229 + +--S 230 of 531 +--m1040b:= a1040.2-r1040 +--E 230 + +--S 231 of 531 +--d1040b:= D(m1040b,x) +--E 231 + +)clear all + + +--S 232 of 531 +t1041:= (A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R C sinh(x) + B cosh(x) + A +--R (1) ------------------------- +--R c sinh(x) + b cosh(x) + a +--R Type: Expression(Integer) +--E 232 + +--S 233 of 531 +r1041:= (b*B-c*C)*x/(b^2-c^2)-2*(A-a*(b*B-c*C)/(b^2-c^2))*_ + atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(1/2)-(B*c-b*C)*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2) +--R +--R +--R (2) +--R +------------+ +--R | 2 2 2 +--R (B c - C b)\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R x +--R (b - a)tanh(-) + c +--R 2 2 2 +--R (- 2A c + 2C a c + 2A b - 2B a b)atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R (C c - B b)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 531 +a1041:= integrate(t1041,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (- A c + C a c + A b - B a b) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R (B c - C b)\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +------------+ +--R | 2 2 2 +--R ((C - B)c + (C - B)b)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R , +--R +--R +--------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R (B c - C b)\|- c + b - a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 2A c + 2C a c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R ((C - B)c + (C - B)b)x\|- c + b - a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 234 + +--S 235 of 531 +m1041a:= a1041.1-r1041 +--R +--R +--R (4) +--R 2 2 +--R (- A c + C a c + A b - B a b) +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 +--R (- B c + C b)\|c - b + a log(c sinh(x) + b cosh(x) + a) +--R + +--R +------------+ +--R | 2 2 2 - 2c sinh(x) - 2b cosh(x) - 2a +--R (B c - C b)\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R (b - a)tanh(-) + c +--R 2 2 2 +--R (2A c - 2C a c - 2A b + 2B a b)atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R (- B c + C b)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 531 +d1041a:= D(m1041a,x) +--R +--R +--R (5) +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b + (- C + B)a b)c - A b + B a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 +--R 2A c + (2A b - 2C a)c + (- 2A b + (- 2C + 2B)a b)c - 2A b +--R + +--R 2 +--R 2B a b +--R * +--R cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2C a b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b + (- C + B)a b)c - A b + B a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 3 2 +--R (2A b c - 2C a b c - 2A b + 2B a b )cosh(x) - A c + (A b + C a)c +--R + +--R 2 3 2 +--R (A b + (- C - B)a b)c - A b + B a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 +--R (4A c - 4C a c + (- 4A b + 4B a b)c)sinh(x) +--R + +--R 3 2 2 +--R (4A c - 4C a c + (- 4A b + 4B a b)c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R (- A c + (- A b + C a)c + (A b + (C - B)a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 +--R - 2A c + (- 2A b + 2C a)c + (2A b + (2C - 2B)a b)c + 2A b +--R + +--R 2 +--R - 2B a b +--R * +--R cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2C a b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c + (- A b + C a)c + (A b + (C - B)a b)c + A b - B a b )cosh(x) +--R + +--R 2 3 2 3 2 +--R (2A b c - 2C a b c - 2A b + 2B a b )cosh(x) + A c + (- A b - C a)c +--R + +--R 2 3 2 +--R (- A b + (C + B)a b)c + A b - B a b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression(Integer) +--E 236 + +--S 237 of 531 +m1041b:= a1041.2-r1041 +--R +--R +--R (6) +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (- B c + C b)\|- c + b - a \|c - b + a +--R * +--R log(c sinh(x) + b cosh(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (B c - C b)\|- c + b - a \|c - b + a +--R * +--R - 2c sinh(x) - 2b cosh(x) - 2a +--R log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +--------------+ +--R 2 2 | 2 2 2 +--R (2A c - 2C a c - 2A b + 2B a b)\|- c + b - a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R 2 2 | 2 2 2 +--R (- 2A c + 2C a c + 2A b - 2B a b)\|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (- B c + C b)x\|- c + b - a \|c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c - b )\|- c + b - a \|c - b + a +--R Type: Expression(Integer) +--E 237 + +--S 238 of 531 +d1041b:= D(m1041b,x) +--R +--R +--R (7) +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b + (- C + B)a b)c - A b + B a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 +--R 2A c + (2A b - 2C a)c + (- 2A b + (- 2C + 2B)a b)c - 2A b +--R + +--R 2 +--R 2B a b +--R * +--R cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2C a b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R (A c + (A b - C a)c + (- A b + (- C + B)a b)c - A b + B a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 3 2 +--R (2A b c - 2C a b c - 2A b + 2B a b )cosh(x) - A c + (A b + C a)c +--R + +--R 2 3 2 +--R (A b + (- C - B)a b)c - A b + B a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 +--R (4A c - 4C a c + (- 4A b + 4B a b)c)sinh(x) +--R + +--R 3 2 2 +--R (4A c - 4C a c + (- 4A b + 4B a b)c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R (- A c + (- A b + C a)c + (A b + (C - B)a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 3 +--R - 2A c + (- 2A b + 2C a)c + (2A b + (2C - 2B)a b)c + 2A b +--R + +--R 2 +--R - 2B a b +--R * +--R cosh(x) +--R + +--R 2 3 2 +--R 2A b c - 2C a b c - 2A b + 2B a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c + (- A b + C a)c + (A b + (C - B)a b)c + A b - B a b )cosh(x) +--R + +--R 2 3 2 3 2 +--R (2A b c - 2C a b c - 2A b + 2B a b )cosh(x) + A c + (- A b - C a)c +--R + +--R 2 3 2 +--R (- A b + (C + B)a b)c + A b - B a b +--R / +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b - 2a)c + (2b - 2a b)c + (- 2b + 2a b )c - 2b + 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b - 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b - a)c + (b - a b)c + (- b + a b )c - b + a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b - 2a )c - 2a b + 2a b )cosh(x) + (- b + a)c + (b - a b)c +--R + +--R 3 2 4 3 +--R (b - a b )c - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (2c + 2b c - 2b c - 2b c)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((4c + 4b c - 4b c - 4b c)cosh(x) + 4a c - 4a b c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 4 +--R (2c + 2b c - 2b c - 2b c)cosh(x) + (4a c - 4a b c)cosh(x) - 2c +--R + +--R 3 2 2 3 +--R 2b c + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )sinh(x) +--R + +--R 3 2 2 3 2 4 3 +--R ((2b + 2a)c + (2b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b ) +--R * +--R cosh(x) +--R + +--R 2 2 3 2 2 +--R (2a b + 2a )c - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 3 2 +--R ((b + a)c + (b + a b)c + (- b - a b )c - b - a b )cosh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R ((2a b + 2a )c - 2a b - 2a b )cosh(x) + (- b - a)c + (b + a b)c +--R + +--R 3 2 4 3 +--R (b + a b )c - b - a b +--R Type: Expression(Integer) +--E 238 + +)clear all + + +--S 239 of 531 +t1042:= (A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^2 +--R +--R +--R (1) +--R C sinh(x) + B cosh(x) + A +--R -------------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sinh(x) + (2b c cosh(x) + 2a c)sinh(x) + b cosh(x) + 2a b cosh(x) + a +--R Type: Expression(Integer) +--E 239 + +--S 240 of 531 +r1042:= -2*(a*A-b*B+c*C)*atanh((c-(a-b)*tanh(1/2*x))/_ + (a^2-b^2+c^2)^(1/2))/(a^2-b^2+c^2)^(3/2)-(B*c-b*C+(A*c-a*C)*_ + cosh(x)+(A*b-a*B)*sinh(x))/(a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (2) +--R 2 +--R (- 2C c + (2B b - 2A a)c)sinh(x) +--R + +--R 2 2 +--R (- 2C b c + 2B b - 2A a b)cosh(x) - 2C a c + 2B a b - 2A a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R ((- A b + B a)sinh(x) + (- A c + C a)cosh(x) - B c + C b)\|c - b + a +--R / +--R 3 2 2 2 3 2 2 2 +--R (c + (- b + a )c)sinh(x) + (b c - b + a b)cosh(x) + a c - a b +--R + +--R 3 +--R a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 240 + +--S 241 of 531 +a1042:= integrate(t1042,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 +--R C c + ((2C - B)b + A a)c + ((C - 2B)b + 2A a b)c - B b +--R + +--R 2 +--R A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 +--R 2C c + ((4C - 2B)b + 2A a)c + ((2C - 4B)b + 4A a b)c +--R + +--R 3 2 +--R - 2B b + 2A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 +--R 2C a c + ((2C - 2B)a b + 2A a )c - 2B a b + 2A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 +--R C c + ((2C - B)b + A a)c + ((C - 2B)b + 2A a b)c - B b +--R + +--R 2 +--R A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 +--R (2C a c + ((2C - 2B)a b + 2A a )c - 2B a b + 2A a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R - C c + (B b - A a)c + C b c - B b + A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 2 2 2 +--R (- 2B c + ((2C - 2B)b + 2A a)c + 2C b + 2A a b + (- 2C - 2B)a ) +--R * +--R sinh(x) +--R + +--R 2 2 2 +--R (- 2B c + ((2C - 2B)b + 2A a)c + 2C b + 2A a b + (- 2C - 2B)a ) +--R * +--R cosh(x) +--R + +--R 2 2 +--R - 2A c + 2C a c + 2A b - 2B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R , +--R +--R 3 2 2 +--R - 2C c + ((- 4C + 2B)b - 2A a)c + ((- 2C + 4B)b - 4A a b)c +--R + +--R 3 2 +--R 2B b - 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 +--R - 4C c + ((- 8C + 4B)b - 4A a)c +--R + +--R 2 3 2 +--R ((- 4C + 8B)b - 8A a b)c + 4B b - 4A a b +--R * +--R cosh(x) +--R + +--R 2 2 2 2 +--R - 4C a c + ((- 4C + 4B)a b - 4A a )c + 4B a b - 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 +--R - 2C c + ((- 4C + 2B)b - 2A a)c + ((- 2C + 4B)b - 4A a b)c +--R + +--R 3 2 +--R 2B b - 2A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 +--R (- 4C a c + ((- 4C + 4B)a b - 4A a )c + 4B a b - 4A a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R 2C c + (- 2B b + 2A a)c - 2C b c + 2B b - 2A a b +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 2 +--R (- 2B c + ((2C - 2B)b + 2A a)c + 2C b + 2A a b + (- 2C - 2B)a ) +--R * +--R sinh(x) +--R + +--R 2 2 2 +--R (- 2B c + ((2C - 2B)b + 2A a)c + 2C b + 2A a b + (- 2C - 2B)a ) +--R * +--R cosh(x) +--R + +--R 2 2 +--R - 2A c + 2C a c + 2A b - 2B a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 2a c + (- 4b + 4a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + 2b c + a c + (- 2b + 2a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (2a c + 2a b c + (- 2a b + 2a )c - 2a b + 2a b)cosh(x) - c +--R + +--R 2 2 2 4 2 2 +--R (2b - a )c - b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 241 + +--S 242 of 531 +m1042a:= a1042.1-r1042 +--R +--R +--R (4) +--R 4 3 2 2 +--R C c + ((2C - B)b + A a)c + ((C - 2B)b + 2A a b)c +--R + +--R 3 2 +--R (- B b + A a b )c +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + ((5C - 2B)b + 2A a)c + ((4C - 5B)b + 5A a b)c +--R + +--R 3 2 4 3 +--R ((C - 4B)b + 4A a b )c - B b + A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 3C a c + ((4C - 3B)a b + 3A a )c + ((C - 4B)a b + 4A a b)c +--R + +--R 3 2 2 +--R - B a b + A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R C c + ((4C - B)b + A a)c + ((5C - 4B)b + 4A a b)c +--R + +--R 3 2 4 3 +--R ((2C - 5B)b + 5A a b )c - 2B b + 2A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 +--R 4C a c + ((8C - 4B)a b + 4A a )c +--R + +--R 2 2 3 2 2 +--R ((4C - 8B)a b + 8A a b)c - 4B a b + 4A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - C c + (B b - A a)c + (C b + 2C a )c +--R + +--R 3 2 2 3 2 2 3 +--R (- B b + A a b + (2C - 2B)a b + 2A a )c - 2B a b + 2A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 +--R C b c + ((2C - B)b + A a b)c + ((C - 2B)b + 2A a b )c - B b +--R + +--R 3 +--R A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R C a c + ((4C - B)a b + A a )c + ((3C - 4B)a b + 4A a b)c +--R + +--R 3 2 2 +--R - 3B a b + 3A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 +--R - C b c + (B b - A a b + 2C a )c +--R + +--R 3 2 3 4 3 2 2 3 +--R (C b + (2C - 2B)a b + 2A a )c - B b + A a b - 2B a b + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - C a c + (B a b - A a )c + C a b c - B a b + A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 4 3 2 2 +--R 2C c + ((4C - 2B)b + 2A a)c + ((2C - 4B)b + 4A a b)c +--R + +--R 3 2 +--R (- 2B b + 2A a b )c +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 4C c + ((10C - 4B)b + 4A a)c + ((8C - 10B)b + 10A a b)c +--R + +--R 3 2 4 3 +--R ((2C - 8B)b + 8A a b )c - 2B b + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 6C a c + ((8C - 6B)a b + 6A a )c + ((2C - 8B)a b + 8A a b)c +--R + +--R 3 2 2 +--R - 2B a b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + ((8C - 2B)b + 2A a)c + ((10C - 8B)b + 8A a b)c +--R + +--R 3 2 4 3 +--R ((4C - 10B)b + 10A a b )c - 4B b + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 +--R 8C a c + ((16C - 8B)a b + 8A a )c +--R + +--R 2 2 3 2 2 +--R ((8C - 16B)a b + 16A a b)c - 8B a b + 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c + (2B b - 2A a)c + (2C b + 4C a )c +--R + +--R 3 2 2 3 2 2 3 +--R (- 2B b + 2A a b + (4C - 4B)a b + 4A a )c - 4B a b + 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R 2C b c + ((4C - 2B)b + 2A a b)c + ((2C - 4B)b + 4A a b )c +--R + +--R 4 3 +--R - 2B b + 2A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 2C a c + ((8C - 2B)a b + 2A a )c + ((6C - 8B)a b + 8A a b)c +--R + +--R 3 2 2 +--R - 6B a b + 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 +--R - 2C b c + (2B b - 2A a b + 4C a )c +--R + +--R 3 2 3 4 3 2 2 +--R (2C b + (4C - 4B)a b + 4A a )c - 2B b + 2A a b - 4B a b +--R + +--R 3 +--R 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - 2C a c + (2B a b - 2A a )c + 2C a b c - 2B a b + 2A a b +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 3 2 3 +--R ((A b - B a)c + (2A b - 2B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 +--R A c + (4A b + (- C - 2B)a)c + (5A b + (- 2C - 4B)a b)c +--R + +--R 3 2 +--R 2A b + (- C - 2B)a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - B c + (C b + 2A a)c + (B b + 4A a b + (- 2C - 4B)a )c - C b +--R + +--R 2 2 +--R 2A a b - 2B a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 +--R 2A c + (5A b + (- 2C - B)a)c + (4A b + (- 4C - 2B)a b)c +--R + +--R 3 2 +--R A b + (- 2C - B)a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 +--R 4A a c + (8A a b + (- 4C - 4B)a )c + 4A a b +--R + +--R 2 +--R (- 4C - 4B)a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 +--R - 2A c + (- A b + (2C + B)a)c + (2A b - 2B a b + 2A a )c +--R + +--R 3 2 2 3 +--R A b - B a b + 2A a b + (- 2C - 2B)a +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 +--R (A c + (2A b - C a)c + (A b - 2C a b)c - C a b )cosh(x) +--R + +--R 3 2 2 2 3 +--R B c + (- C b + 2A a)c + (- B b + 4A a b - 2C a )c + C b +--R + +--R 2 2 +--R 2A a b + (- 4C - 2B)a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - A c + (- 2A b + C a)c + (A b + 2C a b + 2A a )c + 2A b +--R + +--R 2 2 3 +--R (- C - 2B)a b + 2A a b + (- 2C - 2B)a +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - B c + (C b - 2A a)c + (B b + 2C a )c - C b + 2A a b - 2B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 242 + +--S 243 of 531 +--d1042a:= D(m1042a,x) +--E 243 + +--S 244 of 531 +m1042b:= a1042.2-r1042 +--R +--R +--R (5) +--R 4 3 2 2 +--R 2C c + ((4C - 2B)b + 2A a)c + ((2C - 4B)b + 4A a b)c +--R + +--R 3 2 +--R (- 2B b + 2A a b )c +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 4C c + ((10C - 4B)b + 4A a)c + ((8C - 10B)b + 10A a b)c +--R + +--R 3 2 4 3 +--R ((2C - 8B)b + 8A a b )c - 2B b + 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 6C a c + ((8C - 6B)a b + 6A a )c + ((2C - 8B)a b + 8A a b)c +--R + +--R 3 2 2 +--R - 2B a b + 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 +--R 2C c + ((8C - 2B)b + 2A a)c + ((10C - 8B)b + 8A a b)c +--R + +--R 3 2 4 3 +--R ((4C - 10B)b + 10A a b )c - 4B b + 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 +--R 8C a c + ((16C - 8B)a b + 8A a )c +--R + +--R 2 2 3 2 2 +--R ((8C - 16B)a b + 16A a b)c - 8B a b + 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R - 2C c + (2B b - 2A a)c + (2C b + 4C a )c +--R + +--R 3 2 2 3 2 2 3 +--R (- 2B b + 2A a b + (4C - 4B)a b + 4A a )c - 4B a b + 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 +--R 2C b c + ((4C - 2B)b + 2A a b)c + ((2C - 4B)b + 4A a b )c +--R + +--R 4 3 +--R - 2B b + 2A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 2 2 +--R 2C a c + ((8C - 2B)a b + 2A a )c + ((6C - 8B)a b + 8A a b)c +--R + +--R 3 2 2 +--R - 6B a b + 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 +--R - 2C b c + (2B b - 2A a b + 4C a )c +--R + +--R 3 2 3 4 3 2 2 +--R (2C b + (4C - 4B)a b + 4A a )c - 2B b + 2A a b - 4B a b +--R + +--R 3 +--R 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - 2C a c + (2B a b - 2A a )c + 2C a b c - 2B a b + 2A a b +--R * +--R x +--R +--------------+ (b - a)tanh(-) + c +--R | 2 2 2 2 +--R \|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 4 3 2 2 +--R - 2C c + ((- 4C + 2B)b - 2A a)c + ((- 2C + 4B)b - 4A a b)c +--R + +--R 3 2 +--R (2B b - 2A a b )c +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 +--R - 4C c + ((- 10C + 4B)b - 4A a)c +--R + +--R 2 2 3 2 +--R ((- 8C + 10B)b - 10A a b)c + ((- 2C + 8B)b - 8A a b )c +--R + +--R 4 3 +--R 2B b - 2A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 +--R - 6C a c + ((- 8C + 6B)a b - 6A a )c +--R + +--R 2 2 3 2 2 +--R ((- 2C + 8B)a b - 8A a b)c + 2B a b - 2A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 +--R - 2C c + ((- 8C + 2B)b - 2A a)c +--R + +--R 2 2 3 2 +--R ((- 10C + 8B)b - 8A a b)c + ((- 4C + 10B)b - 10A a b )c +--R + +--R 4 3 +--R 4B b - 4A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 +--R - 8C a c + ((- 16C + 8B)a b - 8A a )c +--R + +--R 2 2 3 2 2 +--R ((- 8C + 16B)a b - 16A a b)c + 8B a b - 8A a b +--R * +--R cosh(x) +--R + +--R 4 3 2 2 2 +--R 2C c + (- 2B b + 2A a)c + (- 2C b - 4C a )c +--R + +--R 3 2 2 3 2 2 3 +--R (2B b - 2A a b + (- 4C + 4B)a b - 4A a )c + 4B a b - 4A a b +--R * +--R sinh(x) +--R + +--R 3 2 2 +--R - 2C b c + ((- 4C + 2B)b - 2A a b)c +--R + +--R 3 2 4 3 +--R ((- 2C + 4B)b - 4A a b )c + 2B b - 2A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 +--R - 2C a c + ((- 8C + 2B)a b - 2A a )c +--R + +--R 2 2 3 2 2 +--R ((- 6C + 8B)a b - 8A a b)c + 6B a b - 6A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 +--R 2C b c + (- 2B b + 2A a b - 4C a )c +--R + +--R 3 2 3 4 3 2 2 +--R (- 2C b + (- 4C + 4B)a b - 4A a )c + 2B b - 2A a b + 4B a b +--R + +--R 3 +--R - 4A a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R 2C a c + (- 2B a b + 2A a )c - 2C a b c + 2B a b - 2A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 2 3 2 3 +--R ((A b - B a)c + (2A b - 2B a b)c + A b - B a b )sinh(x) +--R + +--R 3 2 2 +--R A c + (4A b + (- C - 2B)a)c + (5A b + (- 2C - 4B)a b)c +--R + +--R 3 2 +--R 2A b + (- C - 2B)a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - B c + (C b + 2A a)c + (B b + 4A a b + (- 2C - 4B)a )c - C b +--R + +--R 2 2 +--R 2A a b - 2B a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 +--R 2A c + (5A b + (- 2C - B)a)c + (4A b + (- 4C - 2B)a b)c +--R + +--R 3 2 +--R A b + (- 2C - B)a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 +--R 4A a c + (8A a b + (- 4C - 4B)a )c + 4A a b +--R + +--R 2 +--R (- 4C - 4B)a b +--R * +--R cosh(x) +--R + +--R 3 2 2 2 +--R - 2A c + (- A b + (2C + B)a)c + (2A b - 2B a b + 2A a )c +--R + +--R 3 2 2 3 +--R A b - B a b + 2A a b + (- 2C - 2B)a +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 +--R (A c + (2A b - C a)c + (A b - 2C a b)c - C a b )cosh(x) +--R + +--R 3 2 2 2 3 +--R B c + (- C b + 2A a)c + (- B b + 4A a b - 2C a )c + C b +--R + +--R 2 2 +--R 2A a b + (- 4C - 2B)a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 2 3 +--R - A c + (- 2A b + C a)c + (A b + 2C a b + 2A a )c + 2A b +--R + +--R 2 2 3 +--R (- C - 2B)a b + 2A a b + (- 2C - 2B)a +--R * +--R cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R - B c + (C b - 2A a)c + (B b + 2C a )c - C b + 2A a b - 2B a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R / +--R 5 4 2 3 3 2 2 4 2 2 3 +--R (c + 2b c + a c + (- 2b + 2a b)c + (- b + a b )c)sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 5b c + (2b + 2a )c + (- 4b + 5a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 4b + 4a b )c - b + a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R 3a c + 4a b c + (- 2a b + 3a )c + (- 4a b + 4a b)c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 4b c + (4b + a )c + (- 2b + 4a b)c + (- 5b + 5a b )c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (4a c + 8a b c + 4a c + (- 8a b + 8a b)c - 4a b + 4a b ) +--R * +--R cosh(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 2 3 4 +--R - c + (2b + a )c + 2a b c + (- b - a b + 2a )c - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 3 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 3 2 +--R (a c + 4a b c + (2a b + a )c + (- 4a b + 4a b)c - 3a b + 3a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 2 3 +--R - b c + 2a c + (2b + a b)c + (- 2a b + 2a )c - b - a b +--R + +--R 4 +--R 2a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 4 3 2 +--R - a c + (2a b - a )c - a b + a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 531 +--d1042b:= D(m1042b,x) +--E 245 + +)clear all + + +--S 246 of 531 +t1043:= (A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^3 +--R +--R +--R (1) +--R C sinh(x) + B cosh(x) + A +--R / +--R 3 3 2 2 2 +--R c sinh(x) + (3b c cosh(x) + 3a c )sinh(x) +--R + +--R 2 2 2 3 3 +--R (3b c cosh(x) + 6a b c cosh(x) + 3a c)sinh(x) + b cosh(x) +--R + +--R 2 2 2 3 +--R 3a b cosh(x) + 3a b cosh(x) + a +--R Type: Expression(Integer) +--E 246 + +--S 247 of 531 +r1043:= -(2*a^2*A+b*(A*b-3*a*B)-c*(A*c-3*a*C))*_ + atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(5/2)-1/2*(B*c-b*C+(A*c-a*C)*cosh(x)+_ + (A*b-a*B)*sinh(x))/(a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x))^2-_ + 1/2*(a*B*c-a*b*C+(a*(3*A*c-a*C)-2*c*(b*B-c*C))*cosh(x)+_ + (a*(3*A*b-a*B)-2*b*(b*B-c*C))*sinh(x))/(a^2-b^2+c^2)^2/_ + (a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (2) +--R 4 3 2 2 2 2 +--R (2A c - 6C a c + (- 2A b + 6B a b - 4A a )c )sinh(x) +--R + +--R 3 2 3 2 2 +--R (4A b c - 12C a b c + (- 4A b + 12B a b - 8A a b)c)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R 4A a c - 12C a c + (- 4A a b + 12B a b - 8A a )c +--R * +--R sinh(x) +--R + +--R 2 2 2 4 3 2 2 2 +--R (2A b c - 6C a b c - 2A b + 6B a b - 4A a b )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4A a b c - 12C a b c - 4A a b + 12B a b - 8A a b)cosh(x) +--R + +--R 2 2 3 2 2 3 4 +--R 2A a c - 6C a c - 2A a b + 6B a b - 4A a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 2 2 2 +--R (- 2C b c + (2B b - 3A a b + B a )c)sinh(x) +--R + +--R 3 2 2 2 3 +--R - 2C c + (2B b - 3A a)c + (- 2C b + C a )c + 2B b +--R + +--R 2 2 +--R - 3A a b + B a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 3 +--R - A b c - C a b c + A b + B a b - 4A a b + 2B a +--R * +--R sinh(x) +--R + +--R 2 2 2 2 +--R (- 2C b c + (2B b - 3A a b)c + C a b)cosh(x) +--R + +--R 3 2 2 2 3 3 +--R (- A c - C a c + (A b + B a b - 4A a )c + 2C a )cosh(x) - B c +--R + +--R 2 2 2 3 2 +--R C b c + (B b - 2B a )c - C b + 2C a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (- 4b + 4a )c + (2b - 4a b + 2a )c )sinh(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (- 8b + 8a b)c + (4b - 8a b + 4a b)c)cosh(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (- 8a b + 8a )c + (4a b - 8a b + 4a )c +--R * +--R sinh(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (- 4b + 4a b )c + 2b - 4a b + 2a b )cosh(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (- 8a b + 8a b)c + 4a b - 8a b + 4a b)cosh(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (- 4a b + 4a )c + 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 531 +a1043:= integrate(t1043,x) +--R +--R +--R (3) +--R [ +--R 5 4 2 2 3 +--R A c + (3A b - 3C a)c + (2A b + (- 9C + 3B)a b - 2A a )c +--R + +--R 3 2 2 2 +--R (- 2A b + (- 9C + 9B)a b - 6A a b)c +--R + +--R 4 3 2 2 5 4 2 3 +--R (- 3A b + (- 3C + 9B)a b - 6A a b )c - A b + 3B a b - 2A a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 +--R 4A c + (12A b - 12C a)c +--R + +--R 2 2 3 +--R (8A b + (- 36C + 12B)a b - 8A a )c +--R + +--R 3 2 2 2 +--R (- 8A b + (- 36C + 36B)a b - 24A a b)c +--R + +--R 4 3 2 2 5 +--R (- 12A b + (- 12C + 36B)a b - 24A a b )c - 4A b +--R + +--R 4 2 3 +--R 12B a b - 8A a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R 4A a c + (8A a b - 12C a )c + ((- 24C + 12B)a b - 8A a )c +--R + +--R 3 2 2 3 4 2 3 +--R (- 8A a b + (- 12C + 24B)a b - 16A a b)c - 4A a b + 12B a b +--R + 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+ +--R 4 2 3 2 2 3 2 +--R - 4A a c + 12C a c + (8A a b - 12B a b + 8A a )c +--R + +--R 2 2 4 2 3 3 2 +--R - 12C a b c - 4A a b + 12B a b - 8A a b +--R * +--R cosh(x) +--R + +--R 5 4 2 2 3 +--R A c + (- A b - 3C a)c + (- 2A b + (3C + 3B)a b - 2A a )c +--R + +--R 3 2 2 2 +--R (2A b + (3C - 3B)a b + 2A a b)c +--R + +--R 4 3 2 2 5 4 2 3 +--R (A b + (- 3C - 3B)a b + 2A a b )c - A b + 3B a b - 2A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b 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a b +--R * +--R cosh(x) +--R + +--R 4 3 +--R 4C c + ((- 4C - 4B)b + 6A a)c +--R + +--R 2 2 2 +--R ((- 4C + 4B)b - 6A a b - 2C a )c +--R + +--R 3 2 2 4 3 2 2 +--R ((4C + 4B)b - 6A a b + (2C + 2B)a b)c - 4B b + 6A a b - 2B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 7 6 2 2 5 3 2 4 +--R 2c + 6b c + (2b + 4a )c + (- 10b + 12a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 10b + 8a b + 2a )c + (2b - 8a b + 6a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (6b - 12a b + 6a b )c + 2b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 2 5 3 2 4 +--R 8c + 24b c + (8b + 16a )c + (- 40b + 48a b)c +--R + +--R 4 2 2 4 3 5 2 3 4 2 +--R (- 40b + 32a b + 8a )c + (8b - 32a b + 24a b)c +--R + +--R 6 2 4 4 2 7 2 5 4 3 +--R (24b - 48a b + 24a b )c + 8b - 16a b + 8a b +--R * +--R cosh(x) +--R + +--R 6 5 2 3 4 3 3 3 +--R 8a c + 16a b c + (- 8a b + 16a )c + (- 32a b + 32a b)c +--R + +--R 4 5 2 5 3 3 5 6 3 4 +--R (- 8a b + 8a )c + (16a b - 32a b + 16a b)c + 8a b - 16a b +--R + 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b )c +--R + +--R 5 2 4 3 3 6 +--R (- 68A a b + (- 36C + 204B)a b - 136A a b )c - 12A a b +--R + +--R 2 5 3 4 +--R 36B a b - 24A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 +--R - 4A c + (- 8A b + 12C a)c +--R + +--R 2 2 5 +--R (4A b + (24C - 12B)a b + 44A a )c +--R + +--R 3 2 2 3 4 +--R (16A b - 24B a b + 100A a b - 108C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (4A b - 24C a b + 24A a b + (- 252C + 108B)a b - 72A a )c +--R + +--R 5 4 2 3 +--R - 8A b + (- 12C + 24B)a b - 88A a b +--R + +--R 3 2 4 +--R (- 180C + 252B)a b - 168A a b +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 3 3 +--R - 4A b + 12B a b - 68A a b + (- 36C + 180B)a b +--R + +--R 4 2 +--R - 120A a b +--R * +--R c +--R + +--R 2 5 3 4 4 3 +--R - 12A a b + 36B a b - 24A a b +--R * +--R cosh(x) +--R + +--R 6 2 5 +--R - 8A a c + (- 4A a b + 24C a )c +--R + +--R 2 2 3 4 +--R (16A a b + (12C - 24B)a b + 28A a )c +--R + +--R 3 2 2 3 4 3 +--R (8A a b + (- 24C - 12B)a b + 24A a b - 36C a )c +--R + +--R 4 2 3 3 2 4 +--R - 8A a b + (- 12C + 24B)a b - 24A a b + (- 48C + 36B)a b +--R + +--R 5 +--R - 24A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 4A a b + 12B a b - 24A a b + (- 12C + 48B)a b - 32A a b)c +--R + +--R 3 4 4 3 5 2 +--R - 4A a b + 12B a b - 8A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 +--R A c + (11A b - 3C a)c +--R + +--R 2 2 5 +--R (32A b + (- 33C + 3B)a b - 2A a )c +--R + +--R 3 2 2 4 +--R (32A b + (- 99C + 33B)a b - 22A a b)c +--R + +--R 4 3 2 2 3 +--R (- 7A b + (- 129C + 99B)a b - 66A a b )c +--R + +--R 5 4 2 3 2 +--R (- 37A b + (- 78C + 129B)a b - 86A a b )c +--R + +--R 6 5 2 4 7 6 +--R (- 26A b + (- 18C + 78B)a b - 52A a b )c - 6A b + 18B a b +--R + +--R 2 5 +--R - 12A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 2 5 +--R 12A a c + (68A a b - 36C a )c +--R + +--R 2 2 3 4 +--R (112A a b + (- 204C + 36B)a b - 24A a )c +--R + +--R 3 2 2 3 3 +--R (24A a b + (- 372C + 204B)a b - 136A a b)c +--R + +--R 4 2 3 3 2 2 +--R (- 100A a b + (- 276C + 372B)a b - 248A a b )c +--R + +--R 5 2 4 3 3 6 +--R (- 92A a b + (- 72C + 276B)a b - 184A a b )c - 24A a b +--R + +--R 2 5 3 4 +--R 72B a b - 48A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 +--R - 2A c + (- 10A b + 6C a)c +--R + +--R 2 2 5 +--R (- 6A b + (30C - 6B)a b + 38A a )c +--R + +--R 3 2 2 3 4 +--R (18A b + (24C - 30B)a b + 130A a b - 102C a )c +--R + +--R 4 3 2 2 +--R 18A b + (- 24C - 24B)a b + 92A a b +--R + +--R 3 4 +--R (- 330C + 102B)a b - 68A a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 +--R - 6A b + (- 30C + 24B)a b - 92A a b +--R + +--R 3 2 4 +--R (- 330C + 330B)a b - 220A a b +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 +--R - 10A b + (- 6C + 30B)a b - 130A a b +--R + +--R 3 3 4 2 +--R (- 102C + 330B)a b - 220A a b +--R * +--R c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2A b + 6B a b - 38A a b + 102B a b - 68A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 +--R - 12A a c + (- 20A a b + 36C a )c +--R + +--R 2 2 3 4 +--R (20A a b + (60C - 36B)a b + 52A a )c +--R + +--R 3 2 2 3 4 3 +--R (40A a b + (- 24C - 60B)a b + 88A a b - 84C a )c +--R + +--R 4 2 3 3 2 +--R - 4A a b + (- 60C + 24B)a b - 24A a b +--R + +--R 4 5 +--R (- 144C + 84B)a b - 56A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 +--R - 20A a b + (- 12C + 60B)a b - 88A a b +--R + +--R 4 2 5 +--R (- 60C + 144B)a b - 96A a b +--R * +--R c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 4A a b + 12B a b - 28A a b + 60B a b - 40A a b +--R * +--R cosh(x) +--R + +--R 7 6 2 2 5 +--R A c + (- A b - 3C a)c + (- 2A b + (3C + 3B)a b - 12A a )c +--R + +--R 3 2 3 4 +--R (2A b + (3C - 3B)a b + 30C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (A b + (- 3C - 3B)a b + 22A a b + (6C - 30B)a b + 24A a )c +--R + +--R 5 4 2 3 3 2 4 +--R - A b + 3B a b + 2A a b + (- 30C - 6B)a b + 8A a b +--R + +--R 5 +--R - 12C a +--R * +--R 2 +--R c +--R + +--R 2 4 3 3 4 2 5 +--R - 10A a b + (- 6C + 30B)a b - 24A a b + (- 12C + 12B)a b +--R + +--R 6 +--R - 8A a +--R * +--R c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 2A a b + 6B a b - 8A a b + 12B a b - 8A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 +--R 2A b c + (10A b - 6C a b)c +--R + +--R 3 2 2 4 +--R (16A b + (- 30C + 6B)a b - 4A a b)c +--R + +--R 4 3 2 2 3 +--R (4A b + (- 54C + 30B)a b - 20A a b )c +--R + +--R 5 4 2 3 2 +--R (- 14A b + (- 42C + 54B)a b - 36A a b )c +--R + +--R 6 5 2 4 7 6 +--R (- 14A b + (- 12C + 42B)a b - 28A a b )c - 4A b + 12B a b +--R + +--R 2 5 +--R - 8A a b +--R * +--R 5 +--R cosh(x) +--R + +--R 6 2 5 +--R 2A a c + (22A a b - 6C a )c +--R + +--R 2 2 3 4 +--R (56A a b + (- 66C + 6B)a b - 4A a )c +--R + +--R 3 2 2 3 3 +--R (36A a b + (- 174C + 66B)a b - 44A a b)c +--R + +--R 4 2 3 3 2 2 +--R (- 38A a b + (- 174C + 174B)a b - 116A a b )c +--R + +--R 5 2 4 3 3 6 +--R (- 58A a b + (- 60C + 174B)a b - 116A a b )c - 20A a b +--R + +--R 2 5 3 4 +--R 60B a b - 40A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 2 2 5 +--R - 4A b c + (- 8A b + 12C a b + 12A a )c +--R + +--R 3 2 2 3 4 +--R (4A b + (24C - 12B)a b + 68A a b - 36C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (16A b - 24B a b + 88A a b + (- 180C + 36B)a b - 24A a )c +--R + +--R 5 4 2 3 3 2 +--R 4A b - 24C a b - 24A a b + (- 252C + 180B)a b +--R + +--R 4 +--R - 120A a b +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 +--R - 8A b + (- 12C + 24B)a b - 100A a b +--R + +--R 3 3 4 2 +--R (- 108C + 252B)a b - 168A a b +--R * +--R c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 4A b + 12B a b - 44A a b + 108B a b - 72A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 2 5 +--R - 4A a c + (- 20A a b + 12C a )c +--R + +--R 2 2 3 4 +--R (- 4A a b + (60C - 12B)a b + 28A a )c +--R + +--R 3 2 2 3 4 3 +--R (40A a b + (24C - 60B)a b + 88A a b - 60C a )c +--R + +--R 4 2 3 3 2 +--R 20A a b + (- 60C - 24B)a b + 24A a b +--R + +--R 4 5 +--R (- 144C + 60B)a b - 40A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 +--R - 20A a b + (- 36C + 60B)a b - 88A a b +--R + +--R 4 2 5 +--R (- 84C + 144B)a b - 96A a b +--R * +--R c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 12A a b + 36B a b - 52A a b + 84B a b - 56A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 2 5 +--R 2A b c + (- 2A b - 6C a b - 12A a )c +--R + +--R 3 2 2 3 4 +--R (- 4A b + (6C + 6B)a b - 16A a b + 36C a )c +--R + +--R 4 3 2 2 3 +--R 4A b + (6C - 6B)a b + 28A a b + (36C - 36B)a b +--R + +--R 4 +--R 32A a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 +--R 2A b + (- 6C - 6B)a b + 28A a b + (- 36C - 36B)a b +--R + +--R 4 5 +--R 32A a b - 24C a +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 3 3 +--R - 2A b + 6B a b - 16A a b + (- 36C + 36B)a b +--R + +--R 4 2 5 6 +--R - 32A a b + (- 24C + 24B)a b - 16A a +--R * +--R c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 12A a b + 36B a b - 32A a b + 24B a b - 16A a b +--R * +--R cosh(x) +--R + +--R 6 2 5 +--R 2A a c + (- 2A a b - 6C a )c +--R + +--R 2 2 3 4 +--R (- 4A a b + (6C + 6B)a b - 8A a )c +--R + +--R 3 2 2 3 4 3 +--R (4A a b + (6C - 6B)a b + 4A a b + 12C a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2A a b + (- 6C - 6B)a b + 12A a b - 12B a b + 8A a )c +--R + +--R 5 2 4 3 3 4 2 3 4 4 3 +--R (- 2A a b + 6B a b - 4A a b - 12C a b )c - 4A a b + 12B a b +--R + +--R 5 2 +--R - 8A a b +--R * +--R sinh(x) +--R + +--R 2 5 3 2 4 +--R A b c + (3A b - 3C a b )c +--R + +--R 4 3 2 2 3 +--R (2A b + (- 9C + 3B)a b - 2A a b )c +--R + +--R 5 4 2 3 2 +--R (- 2A b + (- 9C + 9B)a b - 6A a b )c +--R + +--R 6 5 2 4 7 6 2 5 +--R (- 3A b + (- 3C + 9B)a b - 6A a b )c - A b + 3B a b - 2A a b +--R * +--R 6 +--R cosh(x) +--R + +--R 5 2 2 4 +--R 2A a b c + (10A a b - 6C a b)c +--R + +--R 3 2 2 3 3 +--R (12A a b + (- 30C + 6B)a b - 4A a b)c +--R + +--R 4 2 3 3 2 2 +--R (- 4A a b + (- 42C + 30B)a b - 20A a b )c +--R + +--R 5 2 4 3 3 6 2 5 +--R (- 14A a b + (- 18C + 42B)a b - 28A a b )c - 6A a b + 18B a b +--R + +--R 3 4 +--R - 12A a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- 2A b + A a )c + (- 2A b + 6C a b + 11A a b - 3C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (4A b + (6C - 6B)a b + 26A a b + (- 33C + 3B)a b - 2A a )c +--R + +--R 5 4 2 3 3 2 +--R 4A b + (- 6C - 6B)a b + 6A a b + (- 69C + 33B)a b +--R + +--R 4 +--R - 22A a b +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 3 3 +--R - 2A b + (- 6C + 6B)a b - 27A a b + (- 39C + 69B)a b +--R + +--R 4 2 +--R - 46A a b +--R * +--R c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2A b + 6B a b - 17A a b + 39B a b - 26A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 2 3 4 +--R - 4A a b c + (- 8A a b + 12C a b + 4A a )c +--R + +--R 3 2 2 3 4 3 +--R (8A a b + (24C - 12B)a b + 24A a b - 12C a )c +--R + +--R 4 2 3 3 2 4 +--R 16A a b + (- 12C - 24B)a b + 24A a b + (- 48C + 12B)a b +--R + +--R 5 +--R - 8A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 4 2 +--R - 4A a b + (- 24C + 12B)a b - 24A a b + (- 36C + 48B)a b +--R + +--R 5 +--R - 32A a b +--R * +--R c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 8A a b + 24B a b - 28A a b + 36B a b - 24A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (A b - 2A a )c + (- A b - 3C a b - 10A a b + 6C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- 2A b + (3C + 3B)a b + 2A a b + (30C - 6B)a b + 8A a )c +--R + +--R 5 4 2 3 3 2 4 +--R 2A b + (3C - 3B)a b + 22A a b + (- 6C - 30B)a b + 24A a b +--R + +--R 5 +--R - 12C a +--R * +--R 2 +--R c +--R + +--R 6 5 3 3 4 2 +--R A b + (- 3C - 3B)a b + (- 30C + 6B)a b - 8A a b +--R + +--R 5 6 +--R (- 12C + 12B)a b - 8A a +--R * +--R c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - A b + 3B a b - 12A a b + 30B a b - 24A a b + 12B a b +--R + +--R 6 +--R - 8A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 2 3 4 +--R 2A a b c + (- 2A a b - 6C a b - 4A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 4A a b + (6C + 6B)a b - 4A a b + 12C a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (4A a b + (6C - 6B)a b + 12A a b - 12B a b + 8A a )c +--R + +--R 5 2 4 3 3 4 2 6 +--R (2A a b + (- 6C - 6B)a b + 4A a b - 12C a b )c - 2A a b +--R + +--R 2 5 3 4 4 3 5 2 +--R 6B a b - 8A a b + 12B a b - 8A a b +--R * +--R cosh(x) +--R + +--R 2 5 2 3 4 2 2 3 4 3 +--R A a c + (- A a b - 3C a )c + (- 2A a b + (3C + 3B)a b - 2A a )c +--R + +--R 2 3 3 2 4 2 +--R (2A a b + (3C - 3B)a b + 2A a b)c +--R + +--R 2 4 3 3 4 2 2 5 3 4 4 3 +--R (A a b + (- 3C - 3B)a b + 2A a b )c - A a b + 3B a b - 2A a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 7 6 2 2 5 +--R - 2A c + (- 6A b + 6C a)c + (- 4A b + (18C - 6B)a b + 4A a )c +--R + +--R 3 2 2 4 +--R (4A b + (18C - 18B)a b + 12A a b)c +--R + +--R 4 3 2 2 3 +--R (6A b + (6C - 18B)a b + 12A a b )c +--R + +--R 5 4 2 3 2 +--R (2A b - 6B a b + 4A a b )c +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 +--R - 8A c + (- 28A b + 24C a)c +--R + +--R 2 2 5 +--R (- 28A b + (84C - 24B)a b + 16A a )c +--R + +--R 3 2 2 4 +--R (8A b + (108C - 84B)a b + 56A a b)c +--R + +--R 4 3 2 2 3 +--R (32A b + (60C - 108B)a b + 72A a b )c +--R + +--R 5 4 2 3 2 +--R (20A b + (12C - 60B)a b + 40A a b )c +--R + +--R 6 5 2 4 +--R (4A b - 12B a b + 8A a b )c +--R * +--R cosh(x) +--R + +--R 6 2 5 +--R - 12A a c + (- 28A a b + 36C a )c +--R + +--R 2 2 3 4 +--R (- 8A a b + (84C - 36B)a b + 24A a )c +--R + +--R 3 2 2 3 3 +--R (24A a b + (60C - 84B)a b + 56A a b)c +--R + +--R 4 2 3 3 2 2 +--R (20A a b + (12C - 60B)a b + 40A a b )c +--R + +--R 5 2 4 3 3 +--R (4A a b - 12B a b + 8A a b )c +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 +--R - 12A c + (- 52A b + 36C a)c +--R + +--R 2 2 5 +--R (- 74A b + (156C - 36B)a b + 24A a )c +--R + +--R 3 2 2 4 +--R (- 14A b + (258C - 156B)a b + 104A a b)c +--R + +--R 4 3 2 2 3 +--R (64A b + (198C - 258B)a b + 172A a b )c +--R + +--R 5 4 2 3 2 +--R (64A b + (66C - 198B)a b + 132A a b )c +--R + +--R 6 5 2 4 7 6 +--R (22A b + (6C - 66B)a b + 44A a b )c + 2A b - 6B a b +--R + +--R 2 5 +--R 4A a 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3 2 2 3 +--R - 8A b + 48C a b - 48A a b + (504C - 216B)a b +--R + +--R 4 +--R 144A a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 +--R 16A b + (24C - 48B)a b + 176A a b + (360C - 504B)a b +--R + +--R 4 +--R 336A a b +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 3 3 +--R 8A b - 24B a b + 136A a b + (72C - 360B)a b +--R + +--R 4 2 +--R 240A a b +--R * +--R c +--R + +--R 2 5 3 4 4 3 +--R 24A a b - 72B a b + 48A a b +--R * +--R cosh(x) +--R + +--R 6 2 5 +--R 16A a c + (8A a b - 48C a )c +--R + +--R 2 2 3 4 +--R (- 32A a b + (- 24C + 48B)a b - 56A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 16A a b + (48C + 24B)a b - 48A a b + 72C a )c +--R + +--R 4 2 3 3 2 4 +--R 16A a b + (24C - 48B)a b + 48A a b + (96C - 72B)a b +--R + +--R 5 +--R 48A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 4 2 5 +--R (8A a b - 24B a b + 48A a b + (24C - 96B)a b + 64A a b)c +--R + +--R 3 4 4 3 5 2 +--R 8A a b - 24B a b + 16A a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 +--R - 2A c + (- 22A b + 6C a)c +--R + +--R 2 2 5 +--R (- 64A b + (66C - 6B)a b + 4A a )c +--R + +--R 3 2 2 4 +--R (- 64A b + (198C - 66B)a b + 44A a b)c +--R + +--R 4 3 2 2 3 +--R (14A b + (258C - 198B)a b + 132A a b )c +--R + +--R 5 4 2 3 2 +--R (74A b + (156C - 258B)a b + 172A a b )c +--R + +--R 6 5 2 4 7 6 +--R (52A b + (36C - 156B)a b + 104A a b )c + 12A b - 36B a b +--R + +--R 2 5 +--R 24A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 2 5 +--R - 24A a c + (- 136A a b + 72C a )c +--R + +--R 2 2 3 4 +--R (- 224A a b + (408C - 72B)a b + 48A a )c +--R + +--R 3 2 2 3 3 +--R (- 48A a b + (744C - 408B)a b + 272A a b)c +--R + +--R 4 2 3 3 2 2 +--R (200A a b + (552C - 744B)a b + 496A a b )c +--R + +--R 5 2 4 3 3 6 +--R (184A a b + (144C - 552B)a b + 368A a b )c + 48A a b +--R + +--R 2 5 3 4 +--R - 144B a b + 96A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 +--R 4A c + (20A b - 12C a)c +--R + +--R 2 2 5 +--R (12A b + (- 60C + 12B)a b - 76A a )c +--R + +--R 3 2 2 3 4 +--R (- 36A b + (- 48C + 60B)a b - 260A a b + 204C a )c +--R + +--R 4 3 2 2 3 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a b + 80A a b +--R * +--R cosh(x) +--R + +--R 7 6 2 2 5 +--R - 2A c + (2A b + 6C a)c + (4A b + (- 6C - 6B)a b + 24A a )c +--R + +--R 3 2 3 4 +--R (- 4A b + (- 6C + 6B)a b - 60C a )c +--R + +--R 4 3 2 2 3 +--R - 2A b + (6C + 6B)a b - 44A a b + (- 12C + 60B)a b +--R + +--R 4 +--R - 48A a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 4 +--R 2A b - 6B a b - 4A a b + (60C + 12B)a b - 16A a b +--R + +--R 5 +--R 24C a +--R * +--R 2 +--R c +--R + +--R 2 4 3 3 4 2 5 +--R 20A a b + (12C - 60B)a b + 48A a b + (24C - 24B)a b +--R + +--R 6 +--R 16A a +--R * +--R c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R 4A a b - 12B a b + 16A a b - 24B a b + 16A a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 +--R - 4A b c + (- 20A b + 12C a b)c +--R + +--R 3 2 2 4 +--R (- 32A b + (60C - 12B)a b + 8A a b)c +--R + +--R 4 3 2 2 3 +--R (- 8A b + (108C - 60B)a b + 40A a b )c +--R + +--R 5 4 2 3 2 +--R (28A b + (84C - 108B)a b + 72A a b )c +--R + +--R 6 5 2 4 7 6 +--R (28A b + (24C - 84B)a b + 56A a b )c + 8A b - 24B a b 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3 4 4 3 +--R 8A b - 24B a b + 88A a b - 216B a b + 144A a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 2 5 +--R 8A a c + (40A a b - 24C a )c +--R + +--R 2 2 3 4 +--R (8A a b + (- 120C + 24B)a b - 56A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 80A a b + (- 48C + 120B)a b - 176A a b + 120C a )c +--R + +--R 4 2 3 3 2 +--R - 40A a b + (120C + 48B)a b - 48A a b +--R + +--R 4 5 +--R (288C - 120B)a b + 80A a +--R * +--R 2 +--R c +--R + +--R 5 2 4 3 3 +--R 40A a b + (72C - 120B)a b + 176A a b +--R + +--R 4 2 5 +--R (168C - 288B)a b + 192A a b +--R * +--R c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 24A a b - 72B a b + 104A a b - 168B a b + 112A a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 2 5 +--R - 4A b c + (4A b + 12C a b + 24A a )c +--R + +--R 3 2 2 3 4 +--R (8A b + (- 12C - 12B)a b + 32A a b - 72C a )c +--R + +--R 4 3 2 2 3 +--R - 8A b + (- 12C + 12B)a b - 56A a b + (- 72C + 72B)a b +--R + +--R 4 +--R - 64A a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 +--R - 4A b + (12C + 12B)a b - 56A a b + (72C + 72B)a b +--R + +--R 4 5 +--R - 64A a b + 48C a +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 3 3 4 2 +--R 4A b - 12B a b + 32A a b + (72C - 72B)a b + 64A a b +--R + +--R 5 6 +--R (48C - 48B)a b + 32A a +--R * +--R c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R 24A a b - 72B a b + 64A a b - 48B a b + 32A a b +--R * +--R cosh(x) +--R + +--R 6 2 5 +--R - 4A a c + (4A a b + 12C a )c +--R + +--R 2 2 3 4 +--R (8A a b + (- 12C - 12B)a b + 16A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 8A a b + (- 12C + 12B)a b - 8A a b - 24C a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 4A a b + (12C + 12B)a b - 24A a b + 24B a b - 16A a )c +--R + +--R 5 2 4 3 3 4 2 3 4 4 3 +--R (4A a b - 12B a b + 8A a b + 24C a b )c + 8A a b - 24B a b +--R + +--R 5 2 +--R 16A a b +--R * +--R sinh(x) +--R + +--R 2 5 3 2 4 +--R - 2A b c + (- 6A b + 6C a b )c +--R + +--R 4 3 2 2 3 +--R (- 4A b + (18C - 6B)a b + 4A a b )c +--R + +--R 5 4 2 3 2 +--R (4A b + (18C - 18B)a b + 12A a b )c +--R + +--R 6 5 2 4 7 6 2 5 +--R (6A b + (6C - 18B)a b + 12A a b )c + 2A b - 6B a b + 4A a b +--R * +--R 6 +--R cosh(x) +--R + +--R 5 2 2 4 +--R - 4A a b c + (- 20A a b + 12C a b)c +--R + +--R 3 2 2 3 3 +--R (- 24A a b + (60C - 12B)a b + 8A a b)c +--R + +--R 4 2 3 3 2 2 +--R (8A a b + (84C - 60B)a b + 40A a b )c +--R + +--R 5 2 4 3 3 6 2 5 +--R (28A a b + (36C - 84B)a b + 56A a b )c + 12A a b - 36B a b +--R + +--R 3 4 +--R 24A a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (4A b - 2A a )c + (4A b - 12C a b - 22A a b + 6C a )c +--R + +--R 4 3 2 2 3 +--R - 8A b + (- 12C + 12B)a b - 52A a b + (66C - 6B)a b +--R + +--R 4 +--R 4A a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 +--R - 8A b + (12C + 12B)a b - 12A a b + (138C - 66B)a b +--R + +--R 4 +--R 44A a b +--R * +--R 2 +--R c +--R + +--R 6 5 2 4 3 3 +--R 4A b + (12C - 12B)a b + 54A a b + (78C - 138B)a b +--R + +--R 4 2 +--R 92A a b +--R * +--R c +--R + +--R 7 6 2 5 3 4 4 3 +--R 4A b - 12B a b + 34A a b - 78B a b + 52A a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 2 3 4 +--R 8A a b c + 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+--R 4 3 2 5 4 5 3 3 5 3 +--R (12a b + 16a b - 16a )c + (12a b - 16a b + 4a b)c +--R + +--R 6 3 4 5 2 7 2 7 3 5 5 3 +--R (- 12a b - 8a b + 28a b - 8a )c + (- 4a b + 8a b - 4a b )c +--R + +--R 8 5 4 7 2 +--R 4a b - 12a b + 8a b +--R * +--R cosh(x) +--R + +--R 2 7 2 6 2 2 4 5 2 3 4 4 +--R 2a c - 2a b c + (- 6a b + 4a )c + (6a b - 4a b)c +--R + +--R 2 4 4 2 6 3 2 5 4 3 6 2 +--R (6a b - 8a b + 2a )c + (- 6a b + 8a b - 2a b)c +--R + +--R 2 6 4 4 6 2 2 7 4 5 6 3 +--R (- 2a b + 4a b - 2a b )c + 2a b - 4a b + 2a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 249 + +--S 250 of 531 +--d1043a:= D(m1043a,x) +--E 250 + +--S 251 of 531 +m1043b:= a1043.2-r1043 +--R +--R +--R (5) +--R 7 6 2 2 5 +--R - 2A c + (- 6A b + 6C a)c + (- 4A b + (18C - 6B)a b + 4A a )c +--R + +--R 3 2 2 4 +--R (4A b + (18C - 18B)a b + 12A a b)c +--R + +--R 4 3 2 2 3 +--R (6A b + (6C - 18B)a b + 12A a b )c +--R + +--R 5 4 2 3 2 +--R (2A b - 6B a b + 4A a b )c +--R * +--R 6 +--R 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+--R cosh(x) +--R + +--R 7 2 3 6 3 3 5 +--R - 8a b c + (- 16a b + 8a )c + (24a b + 16a b)c +--R + +--R 4 3 2 5 4 5 3 3 5 3 +--R (48a b - 24a b + 16a )c + (- 24a b - 32a b + 56a b)c +--R + +--R 6 3 4 5 2 7 2 +--R (- 48a b + 24a b + 16a b + 8a )c +--R + +--R 7 3 5 5 3 7 8 3 6 5 4 7 2 +--R (8a b + 16a b - 56a b + 32a b)c + 16a b - 8a b - 32a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 7 3 2 6 4 2 2 5 +--R (2b - 4a )c + (- 2b - 20a b)c + (- 6b + 16a b )c +--R + +--R 5 2 3 4 4 6 2 4 4 2 6 3 +--R (6b + 56a b - 32a b)c + (6b - 20a b + 2a b + 12a )c +--R + +--R 7 2 5 4 3 6 2 +--R (- 6b - 52a b + 62a b - 4a b)c +--R + +--R 8 2 6 4 4 6 2 8 9 2 7 4 5 +--R (- 2b + 8a b - 2a b - 12a b + 8a )c + 2b + 16a b - 30a b +--R + +--R 6 3 8 +--R 4a b + 8a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 2 3 6 3 3 5 +--R 4a b c + (- 4a b - 8a )c + (- 12a b + 8a b)c +--R + +--R 4 3 2 5 4 5 3 3 5 3 +--R (12a b + 16a b - 16a )c + (12a b - 16a b + 4a b)c +--R + +--R 6 3 4 5 2 7 2 7 3 5 5 3 +--R (- 12a b - 8a b + 28a b - 8a )c + (- 4a b + 8a b - 4a b )c +--R + +--R 8 5 4 7 2 +--R 4a b - 12a b + 8a b +--R * +--R cosh(x) +--R + +--R 2 7 2 6 2 2 4 5 2 3 4 4 +--R 2a c - 2a b c + (- 6a b + 4a )c + (6a b - 4a b)c +--R + +--R 2 4 4 2 6 3 2 5 4 3 6 2 +--R (6a b - 8a b + 2a )c + (- 6a b + 8a b - 2a b)c +--R + +--R 2 6 4 4 6 2 2 7 4 5 6 3 +--R (- 2a b + 4a b - 2a b )c + 2a b - 4a b + 2a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R Type: Expression(Integer) +--E 251 + +--S 252 of 531 +--d1043b:= D(m1043b,x) +--E 252 + +)clear all + + +--S 253 of 531 +t1044:= 1/(a+b*sinh(x)+c*sinh(x)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 531 +r1044:= -4*c*atanh((2*c-(b-(b^2-4*a*c)^(1/2))*tanh(1/2*x))/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2))/(b^2-4*a*c)^(1/2)/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2)+_ + 4*c*atanh((2*c-(b+(b^2-4*a*c)^(1/2))*tanh(1/2*x))/_ + (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/(b^2-4*a*c)^(1/2)/_ + (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R - +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 4c\|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R - +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 4c\|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression(Integer) +--E 254 + +--S 255 of 531 +a1044:= integrate(t1044,x) +--R +--R +--R (3) +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 24a )c + (18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b - 22a b - 8a )c + (8a b + 6a b )c - b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c + (- 2b - 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 24a )c + (18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b - 22a b - 8a )c + (8a b + 6a b )c - b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 24a )c + (- 18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b + 22a b + 8a )c + (- 8a b - 6a b )c + b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + (2b + 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 24a )c + (- 18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b + 22a b + 8a )c + (- 8a b - 6a b )c + b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 255 + +--S 256 of 531 +m1044:= a1044-r1044 +--R +--R +--R (4) +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 24a )c + (18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b - 22a b - 8a )c + (8a b + 6a b )c - b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c + (- 2b - 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 24a )c + (18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b - 22a b - 8a )c + (8a b + 6a b )c - b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 24a )c + (- 18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b + 22a b + 8a )c + (- 8a b - 6a b )c + b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + (2b + 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 24a )c + (- 18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b + 22a b + 8a )c + (- 8a b - 6a b )c + b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R - 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 8c\|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 8c\|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression(Integer) +--E 256 + +--S 257 of 531 +d1044:= D(m1044,x) +--R +--R +--R (5) +--R 4 3 +--R - c sinh(x) + (- 4c cosh(x) - 2b)sinh(x) +--R + +--R 2 2 +--R (- 6c cosh(x) - 6b cosh(x) + 2c)sinh(x) +--R + +--R 3 2 4 +--R (- 4c cosh(x) - 6b cosh(x) + 4c cosh(x) + 2b)sinh(x) - c cosh(x) +--R + +--R 3 2 +--R - 2b cosh(x) + 2c cosh(x) + 2b cosh(x) - c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 x 3 +--R (- 8b sinh(x) - 16b cosh(x)sinh(x) - 8b cosh(x) )tanh(-) +--R 2 +--R + +--R 4 3 +--R 2c sinh(x) + (8c cosh(x) + 4b)sinh(x) +--R + +--R 2 2 +--R (12c cosh(x) + 12b cosh(x) + 12c)sinh(x) +--R + +--R 3 2 4 +--R (8c cosh(x) + 12b cosh(x) + 24c cosh(x) - 4b)sinh(x) + 2c cosh(x) +--R + +--R 3 2 +--R 4b cosh(x) + 12c cosh(x) - 4b cosh(x) + 2c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 x 4 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )tanh(-) - c sinh(x) +--R 2 +--R + +--R 3 2 2 +--R (- 4c cosh(x) - 2b)sinh(x) + (- 6c cosh(x) - 6b cosh(x) + 2c)sinh(x) +--R + +--R 3 2 4 +--R (- 4c cosh(x) - 6b cosh(x) + 4c cosh(x) + 2b)sinh(x) - c cosh(x) +--R + +--R 3 2 +--R - 2b cosh(x) + 2c cosh(x) + 2b cosh(x) - c +--R / +--R 4 3 +--R a c sinh(x) + (4a c cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 +--R (6a c cosh(x) + 6a b cosh(x) - 2a c + 4a )sinh(x) +--R + +--R 3 2 2 +--R (4a c cosh(x) + 6a b cosh(x) + (- 4a c + 8a )cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 2 2 +--R a c cosh(x) + 2a b cosh(x) + (- 2a c + 4a )cosh(x) - 2a b cosh(x) +--R + +--R a c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R - 2b c sinh(x) + (- 8b c cosh(x) - 4b )sinh(x) +--R + +--R 2 2 2 +--R (- 12b c cosh(x) - 12b cosh(x) + 4b c - 8a b)sinh(x) +--R + +--R 3 2 2 2 +--R (- 8b c cosh(x) - 12b cosh(x) + (8b c - 16a b)cosh(x) + 4b )sinh(x) +--R + +--R 4 2 3 2 2 +--R - 2b c cosh(x) - 4b cosh(x) + (4b c - 8a b)cosh(x) + 4b cosh(x) +--R + +--R - 2b c +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (4c - 2a c)sinh(x) + ((16c - 8a c)cosh(x) + 8b c - 4a b)sinh(x) +--R + +--R 2 2 2 +--R (24c - 12a c)cosh(x) + (24b c - 12a b)cosh(x) - 8c + 20a c +--R + +--R 2 +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (16c - 8a c)cosh(x) + (24b c - 12a b)cosh(x) +--R + +--R 2 2 +--R (- 16c + 40a c - 16a )cosh(x) - 8b c + 4a b +--R * +--R sinh(x) +--R + +--R 2 4 3 +--R (4c - 2a c)cosh(x) + (8b c - 4a b)cosh(x) +--R + +--R 2 2 2 2 +--R (- 8c + 20a c - 8a )cosh(x) + (- 8b c + 4a b)cosh(x) + 4c - 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2b c sinh(x) + (8b c cosh(x) + 4b )sinh(x) +--R + +--R 2 2 2 +--R (12b c cosh(x) + 12b cosh(x) - 4b c + 8a b)sinh(x) +--R + +--R 3 2 2 2 +--R (8b c cosh(x) + 12b cosh(x) + (- 8b c + 16a b)cosh(x) - 4b )sinh(x) +--R + +--R 4 2 3 2 2 +--R 2b c cosh(x) + 4b cosh(x) + (- 4b c + 8a b)cosh(x) - 4b cosh(x) +--R + +--R 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R a c sinh(x) + (4a c cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 +--R (6a c cosh(x) + 6a b cosh(x) - 2a c + 4a )sinh(x) +--R + +--R 3 2 2 +--R (4a c cosh(x) + 6a b cosh(x) + (- 4a c + 8a )cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 2 2 +--R a c cosh(x) + 2a b cosh(x) + (- 2a c + 4a )cosh(x) - 2a b cosh(x) + a c +--R Type: Expression(Integer) +--E 257 + +)clear all + + +--S 258 of 531 +t1045:= sinh(x)/(a+b*sinh(x)+c*sinh(x)^2) +--R +--R +--R sinh(x) +--R (1) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a +--R Type: Expression(Integer) +--E 258 + +--S 259 of 531 +r1045:= -2*(1-b/(b^2-4*a*c)^(1/2))*atanh((2*c-(b-(b^2-4*a*c)^(1/2))*_ + tanh(1/2*x))/(4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2))/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2)-2*(1+b/(b^2-4*a*c)^(1/2))*_ + atanh((2*c-(b+(b^2-4*a*c)^(1/2))*tanh(1/2*x))/(4*c^2+_ + (b+(b^2-4*a*c)^(1/2))^2)^(1/2))/(4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +-----------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (- 2\|- 4a c + b + 2b)\|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (2\|- 4a c + b + 2b)\|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression(Integer) +--E 259 + +--S 260 of 531 +a1045:= integrate(t1045,x) +--R +--R +--R (3) +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b - 4a b)c + (5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b + 5a b + 4a b)c - a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R - 4a b c + (b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 3 2 +--R (- 8a c + (2a b + 16a )c + (- 12a b - 8a )c + 2a b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b - 4a b)c + (5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b + 5a b + 4a b)c - a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R 4a b c + (- b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b + 4a b)c + (- 5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b - 5a b - 4a b)c + a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R - 4a b c + (b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 3 2 +--R (8a c + (- 2a b - 16a )c + (12a b + 8a )c - 2a b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b + 4a b)c + (- 5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b - 5a b - 4a b)c + a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R 4a b c + (- b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c + 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 260 + +--S 261 of 531 +m1045:= a1045-r1045 +--R +--R +--R (4) +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b - 4a b)c + (5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b + 5a b + 4a b)c - a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R - 4a b c + (b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 3 2 +--R (- 8a c + (2a b + 16a )c + (- 12a b - 8a )c + 2a b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R - +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b - 4a b)c + (5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b + 5a b + 4a b)c - a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R 4a b c + (- b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b + 4a b)c + (- 5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b - 5a b - 4a b)c + a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R - 4a b c + (b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 3 2 +--R (8a c + (- 2a b - 16a )c + (12a b + 8a )c - 2a b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b + 4a b)c + (- 5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b - 5a b - 4a b)c + a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 +--R 4a b c + (- b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b - 16a )c +--R + +--R 2 3 3 +--R (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c + 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R +-----------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (4\|- 4a c + b - 4b)\|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (- 4\|- 4a c + b - 4b)\|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression(Integer) +--E 261 + +--S 262 of 531 +d1045:= D(m1045,x) +--R +--R +--R (5) +--R 3 2 2 +--R 2a sinh(x) + 6a cosh(x)sinh(x) + (6a cosh(x) - 2a)sinh(x) +--R + +--R 3 +--R 2a cosh(x) - 2a cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R 2c sinh(x) + 8c cosh(x)sinh(x) + (12c cosh(x) - 4c + 8a)sinh(x) +--R + +--R 3 4 +--R (8c cosh(x) + (- 8c + 16a)cosh(x))sinh(x) + 2c cosh(x) +--R + +--R 2 +--R (- 4c + 8a)cosh(x) + 2c +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 3 2 +--R (8c - 4a)sinh(x) + (24c - 12a)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((24c - 12a)cosh(x) - 8c + 4a)sinh(x) + (8c - 4a)cosh(x) +--R + +--R (- 8c + 4a)cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - 2c sinh(x) - 8c cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12c cosh(x) + 4c - 8a)sinh(x) +--R + +--R 3 4 +--R (- 8c cosh(x) + (8c - 16a)cosh(x))sinh(x) - 2c cosh(x) +--R + +--R 2 +--R (4c - 8a)cosh(x) - 2c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 +--R 2a sinh(x) + 6a cosh(x)sinh(x) + (6a cosh(x) - 2a)sinh(x) +--R + +--R 3 +--R 2a cosh(x) - 2a cosh(x) +--R / +--R 4 3 +--R a c sinh(x) + (4a c cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 +--R (6a c cosh(x) + 6a b cosh(x) - 2a c + 4a )sinh(x) +--R + +--R 3 2 2 +--R (4a c cosh(x) + 6a b cosh(x) + (- 4a c + 8a )cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 2 2 +--R a c cosh(x) + 2a b cosh(x) + (- 2a c + 4a )cosh(x) - 2a b cosh(x) +--R + +--R a c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R - 2b c sinh(x) + (- 8b c cosh(x) - 4b )sinh(x) +--R + +--R 2 2 2 +--R (- 12b c cosh(x) - 12b cosh(x) + 4b c - 8a b)sinh(x) +--R + +--R 3 2 2 2 +--R (- 8b c cosh(x) - 12b cosh(x) + (8b c - 16a b)cosh(x) + 4b )sinh(x) +--R + +--R 4 2 3 2 2 +--R - 2b c cosh(x) - 4b cosh(x) + (4b c - 8a b)cosh(x) + 4b cosh(x) +--R + +--R - 2b c +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (4c - 2a c)sinh(x) + ((16c - 8a c)cosh(x) + 8b c - 4a b)sinh(x) +--R + +--R 2 2 2 +--R (24c - 12a c)cosh(x) + (24b c - 12a b)cosh(x) - 8c + 20a c +--R + +--R 2 +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (16c - 8a c)cosh(x) + (24b c - 12a b)cosh(x) +--R + +--R 2 2 +--R (- 16c + 40a c - 16a )cosh(x) - 8b c + 4a b +--R * +--R sinh(x) +--R + +--R 2 4 3 +--R (4c - 2a c)cosh(x) + (8b c - 4a b)cosh(x) +--R + +--R 2 2 2 2 +--R (- 8c + 20a c - 8a )cosh(x) + (- 8b c + 4a b)cosh(x) + 4c - 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2b c sinh(x) + (8b c cosh(x) + 4b )sinh(x) +--R + +--R 2 2 2 +--R (12b c cosh(x) + 12b cosh(x) - 4b c + 8a b)sinh(x) +--R + +--R 3 2 2 2 +--R (8b c cosh(x) + 12b cosh(x) + (- 8b c + 16a b)cosh(x) - 4b )sinh(x) +--R + +--R 4 2 3 2 2 +--R 2b c cosh(x) + 4b cosh(x) + (- 4b c + 8a b)cosh(x) - 4b cosh(x) +--R + +--R 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R a c sinh(x) + (4a c cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 +--R (6a c cosh(x) + 6a b cosh(x) - 2a c + 4a )sinh(x) +--R + +--R 3 2 2 +--R (4a c cosh(x) + 6a b cosh(x) + (- 4a c + 8a )cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 2 2 +--R a c cosh(x) + 2a b cosh(x) + (- 2a c + 4a )cosh(x) - 2a b cosh(x) + a c +--R Type: Expression(Integer) +--E 262 + +)clear all + + +--S 263 of 531 +t1046:= sinh(x)^2/(a+b*sinh(x)+c*sinh(x)^2) +--R +--R +--R 2 +--R sinh(x) +--R (1) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a +--R Type: Expression(Integer) +--E 263 + +--S 264 of 531 +r1046:= x/c+2*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ + atanh((2*c-(b-(b^2-4*a*c)^(1/2))*tanh(1/2*x))/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2))/c/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2)+2*(b+(b^2-2*a*c)/_ + (b^2-4*a*c)^(1/2))*atanh((2*c-(b+(b^2-4*a*c)^(1/2))*_ + tanh(1/2*x))/(4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/c/_ + (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +-----------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 2 | | 2 2 2 +--R (2b\|- 4a c + b + 4a c - 2b )\|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-----------+ +--R | 2 2 +--R (- 2b\|- 4a c + b + 4a c - 2b ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R x\|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression(Integer) +--E 264 + +--S 265 of 531 +a1046:= integrate(t1046,x) +--R +--R +--R (3) +--R - +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R 8a c + (- 6a b - 24a )c + (b + 22a b + 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (- 8a b - 18a b - 8a )c + (b + 3a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R - 8a b c + (6a b + 4a b )c + (- b - a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b + 4a b )c - b - 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 8a )c + (6a b + 4a )c +--R + +--R 4 2 2 2 +--R (- b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b - 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b - 4a b)c)cosh(x) + 4a b c - 2a b - 2a b +--R + +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R 8a c + (- 6a b - 24a )c + (b + 22a b + 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (- 8a b - 18a b - 8a )c + (b + 3a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R 8a b c + (- 6a b - 4a b )c + (b + a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b - 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b - 4a b)c)cosh(x) + 4a b c - 2a b - 2a b +--R + +--R - +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R - 8a c + (6a b + 24a )c + (- b - 22a b - 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (8a b + 18a b + 8a )c + (- b - 3a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R - 8a b c + (6a b + 4a b )c + (- b - a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b + 4a b )c - b - 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 8a )c + (6a b + 4a )c +--R + +--R 4 2 2 2 +--R (- b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b - 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b - 4a b)c)cosh(x) + 4a b c - 2a b - 2a b +--R + +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R - 8a c + (6a b + 24a )c + (- b - 22a b - 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (8a b + 18a b + 8a )c + (- b - 3a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R 8a b c + (- 6a b - 4a b )c + (b + a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b - 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b - 4a b)c)cosh(x) + 4a b c - 2a b - 2a b +--R + +--R 2x +--R / +--R 2c +--R Type: Union(Expression(Integer),...) +--E 265 + +--S 266 of 531 +m1046:= a1046-r1046 +--R +--R +--R (4) +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R 8a c + (- 6a b - 24a )c + (b + 22a b + 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (- 8a b - 18a b - 8a )c + (b + 3a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R - 8a b c + (6a b + 4a b )c + (- b - a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b + 4a b )c - b - 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 8a )c + (6a b + 4a )c +--R + +--R 4 2 2 2 +--R (- b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b - 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b - 4a b)c)cosh(x) + 4a b c - 2a b - 2a b +--R + +--R +-----------+ +--R | 2 +--R c\|- 4a c + b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R 8a c + (- 6a b - 24a )c + (b + 22a b + 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (- 8a b - 18a b - 8a )c + (b + 3a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a 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24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b - 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b - 4a b)c)cosh(x) + 4a b c - 2a b - 2a b +--R + +--R - +--R +-----------+ +--R | 2 +--R c\|- 4a c + b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R - 8a c + (6a b + 24a )c + (- b - 22a b - 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (8a b + 18a b + 8a )c + (- b - 3a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R - 8a b c + (6a b + 4a b )c + (- b - a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 2 +--R (2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b + 4a b )c - b - 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 8a )c + (6a b + 4a )c +--R + +--R 4 2 2 2 +--R (- b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b - 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b - 4a b)c)cosh(x) + 4a b c - 2a b - 2a b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R - 8a c + (6a b + 24a )c + (- b - 22a b - 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (8a b + 18a b + 8a )c + (- b - 3a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R 8a b c + (- 6a b - 4a b )c + (b + a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 2 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b + 4a )c - 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b + 4a b )c - b - 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b - 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b - 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b - 4a b)c)cosh(x) + 4a b c - 2a b - 2a b +--R + +--R +-----------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 2 | | 2 2 2 +--R (- 4b\|- 4a c + b - 8a c + 4b )\|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 2 | | 2 2 2 +--R (4b\|- 4a c + b - 8a c + 4b )\|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2c\|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression(Integer) +--E 266 + +--S 267 of 531 +d1046:= D(m1046,x) +--R +--R +--R (5) +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) - 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) - 4a cosh(x))sinh(x) + a cosh(x) - 2a cosh(x) + a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) + 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) + 8b cosh(x))sinh(x) - 2b cosh(x) + 4b cosh(x) - 2b +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - 2a sinh(x) + (- 8a cosh(x) - 8b)sinh(x) +--R + +--R 2 2 +--R (- 12a cosh(x) - 24b cosh(x) - 12a)sinh(x) +--R + +--R 3 2 +--R (- 8a cosh(x) - 24b cosh(x) - 24a cosh(x) + 8b)sinh(x) +--R + +--R 4 3 2 +--R - 2a cosh(x) - 8b cosh(x) - 12a cosh(x) + 8b cosh(x) - 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (8b cosh(x) - 8b cosh(x))sinh(x) + 2b cosh(x) - 4b cosh(x) + 2b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) - 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) - 4a cosh(x))sinh(x) + a cosh(x) - 2a cosh(x) + a +--R / +--R 4 3 +--R a c sinh(x) + (4a c cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 +--R (6a c cosh(x) + 6a b cosh(x) - 2a c + 4a )sinh(x) +--R + +--R 3 2 2 +--R (4a c cosh(x) + 6a b cosh(x) + (- 4a c + 8a )cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 2 2 +--R a c cosh(x) + 2a b cosh(x) + (- 2a c + 4a )cosh(x) - 2a b cosh(x) +--R + +--R a c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R - 2b c sinh(x) + (- 8b c cosh(x) - 4b )sinh(x) +--R + +--R 2 2 2 +--R (- 12b c cosh(x) - 12b cosh(x) + 4b c - 8a b)sinh(x) +--R + +--R 3 2 2 2 +--R (- 8b c cosh(x) - 12b cosh(x) + (8b c - 16a b)cosh(x) + 4b )sinh(x) +--R + +--R 4 2 3 2 2 +--R - 2b c cosh(x) - 4b cosh(x) + (4b c - 8a b)cosh(x) + 4b cosh(x) +--R + +--R - 2b c +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (4c - 2a c)sinh(x) + ((16c - 8a c)cosh(x) + 8b c - 4a b)sinh(x) +--R + +--R 2 2 2 +--R (24c - 12a c)cosh(x) + (24b c - 12a b)cosh(x) - 8c + 20a c +--R + +--R 2 +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (16c - 8a c)cosh(x) + (24b c - 12a b)cosh(x) +--R + +--R 2 2 +--R (- 16c + 40a c - 16a )cosh(x) - 8b c + 4a b +--R * +--R sinh(x) +--R + +--R 2 4 3 +--R (4c - 2a c)cosh(x) + (8b c - 4a b)cosh(x) +--R + +--R 2 2 2 2 +--R (- 8c + 20a c - 8a )cosh(x) + (- 8b c + 4a b)cosh(x) + 4c - 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2b c sinh(x) + (8b c cosh(x) + 4b )sinh(x) +--R + +--R 2 2 2 +--R (12b c cosh(x) + 12b cosh(x) - 4b c + 8a b)sinh(x) +--R + +--R 3 2 2 2 +--R (8b c cosh(x) + 12b cosh(x) + (- 8b c + 16a b)cosh(x) - 4b )sinh(x) +--R + +--R 4 2 3 2 2 +--R 2b c cosh(x) + 4b cosh(x) + (- 4b c + 8a b)cosh(x) - 4b cosh(x) +--R + +--R 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R a c sinh(x) + (4a c cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 +--R (6a c cosh(x) + 6a b cosh(x) - 2a c + 4a )sinh(x) +--R + +--R 3 2 2 +--R (4a c cosh(x) + 6a b cosh(x) + (- 4a c + 8a )cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 2 2 +--R a c cosh(x) + 2a b cosh(x) + (- 2a c + 4a )cosh(x) - 2a b cosh(x) + a c +--R Type: Expression(Integer) +--E 267 + +)clear all + + +--S 268 of 531 +t1047:= sinh(x)^3/(a+b*sinh(x)+c*sinh(x)^2) +--R +--R +--R 3 +--R sinh(x) +--R (1) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a +--R Type: Expression(Integer) +--E 268 + +--S 269 of 531 +r1047:= -b*x/c^2-2*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ + atanh((2*c-(b-(b^2-4*a*c)^(1/2))*tanh(1/2*x))/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2))/c^2/(4*c^2+_ + (b-(b^2-4*a*c)^(1/2))^2)^(1/2)-2*(b^2-a*c+b*(b^2-3*a*c)/_ + (b^2-4*a*c)^(1/2))*atanh((2*c-(b+(b^2-4*a*c)^(1/2))*_ + tanh(1/2*x))/(4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/c^2/_ + (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2)+cosh(x)/c +--R +--R +--R (2) +--R +-----------+ +--R 2 | 2 3 +--R ((2a c - 2b )\|- 4a c + b - 6a b c + 2b ) +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-----------+ +--R 2 | 2 3 +--R ((- 2a c + 2b )\|- 4a c + b - 6a b c + 2b ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (c cosh(x) - b x)\|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 2 2 +--R c \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression(Integer) +--E 269 + +--S 270 of 531 +a1047:= integrate(t1047,x) +--R +--R +--R (3) +--R 2 2 +--R (- c sinh(x) - c cosh(x)) +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 4 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R 12a b c + (- 7a b - 28a b)c + (b + 27a b + 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (- 9a b - 13a b - 4a b)c + (b + 2a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R - 12a b c + (31a b + 20a b)c + (- 27a b - 33a b - 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (9a b + 15a b + 6a b )c + (- b - 2a b - a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 4 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b - 22a b - 4a b )c + (8a b + 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b - 4a b )c + 2a b + 2a b +--R + +--R 2 2 +--R (c sinh(x) + c cosh(x)) +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 4 +--R (2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R 12a b c + (- 7a b - 28a b)c + (b + 27a b + 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (- 9a b - 13a b - 4a b)c + (b + 2a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R 12a b c + (- 31a b - 20a b)c + (27a b + 33a b + 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (- 9a b - 15a b - 6a b )c + (b + 2a b + a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 4 +--R (2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (- 2a b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b - 22a b - 4a b )c + (8a b + 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b - 4a b )c + 2a b + 2a b +--R + +--R 2 2 +--R (- c sinh(x) - c cosh(x)) +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 4 +--R (2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R - 12a b c + (7a b + 28a b)c + (- b - 27a b - 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (9a b + 13a b + 4a b)c + (- b - 2a b - a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R - 12a b c + (31a b + 20a b)c + (- 27a b - 33a b - 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (9a b + 15a b + 6a b )c + (- b - 2a b - a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 4 +--R (2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (- 2a b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b - 22a b - 4a b )c + (8a b + 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b - 4a b )c + 2a b + 2a b +--R + +--R 2 2 +--R (c sinh(x) + c cosh(x)) +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 4 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R - 12a b c + (7a b + 28a b)c + (- b - 27a b - 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (9a b + 13a b + 4a b)c + (- b - 2a b - a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R 12a b c + (- 31a b - 20a b)c + (27a b + 33a b + 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (- 9a b - 15a b - 6a b )c + (b + 2a b + a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 4 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b - 22a b - 4a b )c + (8a b + 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b - 4a b )c + 2a b + 2a b +--R + +--R 2 2 +--R c sinh(x) + (2c cosh(x) - 2b x)sinh(x) + c cosh(x) - 2b x cosh(x) + c +--R / +--R 2 2 +--R 2c sinh(x) + 2c cosh(x) +--R Type: Union(Expression(Integer),...) +--E 270 + +--S 271 of 531 +m1047:= a1047-r1047 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 | 2 +--R (- c sinh(x) - c cosh(x))\|- 4a c + b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 4 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R 12a b c + (- 7a b - 28a b)c + (b + 27a b + 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (- 9a b - 13a b - 4a b)c + (b + 2a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R - 12a b c + (31a b + 20a b)c + (- 27a b - 33a b - 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (9a b + 15a b + 6a b )c + (- b - 2a b - a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 4 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b - 22a b - 4a b )c + (8a b + 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b - 4a b )c + 2a b + 2a b +--R + +--R +-----------+ +--R 2 2 | 2 +--R (c sinh(x) + c cosh(x))\|- 4a c + b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 4 +--R (2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R 12a b c + (- 7a b - 28a b)c + (b + 27a b + 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (- 9a b - 13a b - 4a b)c + (b + 2a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R 12a b c + (- 31a b - 20a b)c + (27a b + 33a b + 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (- 9a b - 15a b - 6a b )c + (b + 2a b + a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 4 +--R (2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (- 2a b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b - 22a b - 4a b )c + (8a b + 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b - 4a b )c + 2a b + 2a b +--R + +--R +-----------+ +--R 2 2 | 2 +--R (- c sinh(x) - c cosh(x))\|- 4a c + b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 4 +--R (2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R - 12a b c + (7a b + 28a b)c + (- b - 27a b - 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (9a b + 13a b + 4a b)c + (- b - 2a b - a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R - 12a b c + (31a b + 20a b)c + (- 27a b - 33a b - 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (9a b + 15a b + 6a b )c + (- b - 2a b - a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 4 +--R (2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b - 16a )c + (12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (- 2a b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b - 22a b - 4a b )c + (8a b + 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b - 4a b )c + 2a b + 2a b +--R + +--R +-----------+ +--R 2 2 | 2 +--R (c sinh(x) + c cosh(x))\|- 4a c + b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 4 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R - 12a b c + (7a b + 28a b)c + (- b - 27a b - 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (9a b + 13a b + 4a b)c + (- b - 2a b - a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R 12a b c + (- 31a b - 20a b)c + (27a b + 33a b + 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (- 9a b - 15a b - 6a b )c + (b + 2a b + a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c +--R + +--R 4 2 2 4 +--R (- 2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b - 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b + 12a b + 4a b )c - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b + 12a b + 4a )c + (- b - 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b - 4a )c + (12a b + 8a b )c - 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b - 8a )c + (6a b + 4a )c + (- b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b + 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b - 22a b - 4a b )c + (8a b + 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b - 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b - 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b - 8a b)c + (4a b + 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b - 4a b )c + 2a b + 2a b +--R + +--R +-----------+ +--R 2 2 | 2 +--R ((- 4a c + 4b )sinh(x) + (- 4a c + 4b )cosh(x))\|- 4a c + b +--R + +--R 3 3 +--R (12a b c - 4b )sinh(x) + (12a b c - 4b )cosh(x) +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-----------+ +--R 2 2 | 2 +--R ((4a c - 4b )sinh(x) + (4a c - 4b )cosh(x))\|- 4a c + b +--R + +--R 3 3 +--R (12a b c - 4b )sinh(x) + (12a b c - 4b )cosh(x) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-----------+ +--R 2 2 | 2 +--R (c sinh(x) - c cosh(x) + c)\|- 4a c + b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (2c sinh(x) + 2c cosh(x))\|- 4a c + b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression(Integer) +--E 271 + +--S 272 of 531 +d1047:= D(m1047,x) +--R +--R +--R (5) +--R 6 5 +--R - a c sinh(x) + (- 4a c cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 4 +--R (- 5a c cosh(x) - 16a b cosh(x) + a c - 8a )sinh(x) +--R + +--R 2 2 3 +--R (- 24a b cosh(x) - 24a cosh(x) + 4a b)sinh(x) +--R + +--R 4 3 2 2 +--R 5a c cosh(x) - 16a b cosh(x) + (- 6a c - 24a )cosh(x) +--R + +--R 8a b cosh(x) + a c +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 +--R 4a c cosh(x) - 4a b cosh(x) + (- 8a c - 8a )cosh(x) +--R + +--R 2 +--R 4a b cosh(x) + 4a c cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R a c cosh(x) - 3a c cosh(x) + 3a c cosh(x) - a c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 6 2 5 +--R 2b c sinh(x) + (8b c cosh(x) - 4a c + 8b )sinh(x) +--R + +--R 2 2 4 +--R (10b c cosh(x) + (- 20a c + 32b )cosh(x) - 2b c + 8a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((- 40a c + 48b )cosh(x) + 16a b cosh(x) + 8a c - 8b - 16a ) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 2 +--R - 10b c cosh(x) + (- 40a c + 32b )cosh(x) + 12b c cosh(x) +--R + +--R 2 2 +--R (24a c - 16b - 48a )cosh(x) - 2b c + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 +--R - 8b c cosh(x) + (- 20a c + 8b )cosh(x) +--R + +--R 3 2 2 2 +--R (16b c - 16a b)cosh(x) + (24a c - 8b - 48a )cosh(x) +--R + +--R (- 8b c + 16a b)cosh(x) - 4a c +--R * +--R sinh(x) +--R + +--R 6 5 4 +--R - 2b c cosh(x) - 4a c cosh(x) + (6b c - 8a b)cosh(x) +--R + +--R 2 3 2 +--R (8a c - 16a )cosh(x) + (- 6b c + 8a b)cosh(x) - 4a c cosh(x) + 2b c +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 6 +--R (- 4c + 2a c)sinh(x) +--R + +--R 2 5 +--R ((- 16c + 8a c)cosh(x) - 8b c + 8a b)sinh(x) +--R + +--R 2 2 2 +--R (- 20c + 10a c)cosh(x) + (- 24b c + 32a b)cosh(x) + 4c - 34a c +--R + +--R 2 2 +--R 16b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 2 +--R (- 16b c + 48a b)cosh(x) + (- 96a c + 64b + 48a )cosh(x) +--R + +--R 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 +--R (20c - 10a c)cosh(x) + (16b c + 32a b)cosh(x) +--R + +--R 2 2 2 2 +--R (- 24c - 84a c + 96b + 48a )cosh(x) + (- 16b c + 80a b)cosh(x) +--R + +--R 2 2 +--R 4c - 2a c - 16b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 +--R (16c - 8a c)cosh(x) + (24b c + 8a b)cosh(x) +--R + +--R 2 2 2 3 +--R (- 32c - 16a c + 64b + 16a )cosh(x) +--R + +--R 2 2 2 +--R (- 32b c + 88a b)cosh(x) + (16c - 8a c - 32b )cosh(x) + 8b c +--R * +--R sinh(x) +--R + +--R 2 6 5 2 2 4 +--R (4c - 2a c)cosh(x) + 8b c cosh(x) + (- 12c + 6a c + 16b )cosh(x) +--R + +--R 3 2 2 2 +--R (- 16b c + 32a b)cosh(x) + (12c - 6a c - 16b )cosh(x) +--R + +--R 2 +--R 8b c cosh(x) - 4c + 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 2 5 +--R - 2b c sinh(x) + (- 8b c cosh(x) + 4a c - 8b )sinh(x) +--R + +--R 2 2 4 +--R (- 10b c cosh(x) + (20a c - 32b )cosh(x) + 2b c - 8a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R ((40a c - 48b )cosh(x) - 16a b cosh(x) - 8a c + 8b + 16a )sinh(x) +--R + +--R 4 2 3 2 +--R 10b c cosh(x) + (40a c - 32b )cosh(x) - 12b c cosh(x) +--R + +--R 2 2 +--R (- 24a c + 16b + 48a )cosh(x) + 2b c - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 +--R 8b c cosh(x) + (20a c - 8b )cosh(x) + (- 16b c + 16a b)cosh(x) +--R + +--R 2 2 2 +--R (- 24a c + 8b + 48a )cosh(x) + (8b c - 16a b)cosh(x) + 4a c +--R * +--R sinh(x) +--R + +--R 6 5 4 +--R 2b c cosh(x) + 4a c cosh(x) + (- 6b c + 8a b)cosh(x) +--R + +--R 2 3 2 +--R (- 8a c + 16a )cosh(x) + (6b c - 8a b)cosh(x) + 4a c cosh(x) - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 6 5 +--R - a c sinh(x) + (- 4a c cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 4 +--R (- 5a c cosh(x) - 16a b cosh(x) + a c - 8a )sinh(x) +--R + +--R 2 2 3 +--R (- 24a b cosh(x) - 24a cosh(x) + 4a b)sinh(x) +--R + +--R 4 3 2 2 +--R 5a c cosh(x) - 16a b cosh(x) + (- 6a c - 24a )cosh(x) +--R + +--R 8a b cosh(x) + a c +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 +--R 4a c cosh(x) - 4a b cosh(x) + (- 8a c - 8a )cosh(x) +--R + +--R 2 +--R 4a b cosh(x) + 4a c cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R a c cosh(x) - 3a c cosh(x) + 3a c cosh(x) - a c +--R / +--R 2 5 2 4 +--R 2a c sinh(x) + (10a c cosh(x) + 4a b c)sinh(x) +--R + +--R 2 2 2 2 3 +--R (20a c cosh(x) + 16a b c cosh(x) - 4a c + 8a c)sinh(x) +--R + +--R 2 3 2 2 2 +--R 20a c cosh(x) + 24a b c cosh(x) + (- 12a c + 24a c)cosh(x) +--R + +--R - 4a b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 2 2 2 +--R 10a c cosh(x) + 16a b c cosh(x) + (- 12a c + 24a c)cosh(x) +--R + +--R 2 +--R - 8a b c cosh(x) + 2a c +--R * +--R sinh(x) +--R + +--R 2 5 4 2 2 3 +--R 2a c cosh(x) + 4a b c cosh(x) + (- 4a c + 8a c)cosh(x) +--R + +--R 2 2 +--R - 4a b c cosh(x) + 2a c cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 5 2 2 4 +--R - 4b c sinh(x) + (- 20b c cosh(x) - 8b c)sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 40b c cosh(x) - 32b c cosh(x) + 8b c - 16a b c)sinh(x) +--R + +--R 2 3 2 2 2 +--R - 40b c cosh(x) - 48b c cosh(x) + (24b c - 48a b c)cosh(x) +--R + +--R 2 +--R 8b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R - 20b c cosh(x) - 32b c cosh(x) + (24b c - 48a b c)cosh(x) +--R + +--R 2 2 +--R 16b c cosh(x) - 4b c +--R * +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R - 4b c cosh(x) - 8b c cosh(x) + (8b c - 16a b c)cosh(x) +--R + +--R 2 2 2 +--R 8b c cosh(x) - 4b c cosh(x) +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 3 2 5 +--R (8c - 4a c )sinh(x) +--R + +--R 3 2 2 4 +--R ((40c - 20a c )cosh(x) + 16b c - 8a b c)sinh(x) +--R + +--R 3 2 2 2 3 +--R (80c - 40a c )cosh(x) + (64b c - 32a b c)cosh(x) - 16c +--R + +--R 2 2 +--R 40a c - 16a c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3 2 2 +--R (80c - 40a c )cosh(x) + (96b c - 48a b c)cosh(x) +--R + +--R 3 2 2 2 +--R (- 48c + 120a c - 48a c)cosh(x) - 16b c + 8a b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 2 3 +--R (40c - 20a c )cosh(x) + (64b c - 32a b c)cosh(x) +--R + +--R 3 2 2 2 2 +--R (- 48c + 120a c - 48a c)cosh(x) + (- 32b c + 16a b c)cosh(x) +--R + +--R 3 2 +--R 8c - 4a c +--R * +--R sinh(x) +--R + +--R 3 2 5 2 4 +--R (8c - 4a c )cosh(x) + (16b c - 8a b c)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 16c + 40a c - 16a c)cosh(x) + (- 16b c + 8a b c)cosh(x) +--R + +--R 3 2 +--R (8c - 4a c )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 5 2 2 4 +--R 4b c sinh(x) + (20b c cosh(x) + 8b c)sinh(x) +--R + +--R 2 2 2 2 3 +--R (40b c cosh(x) + 32b c cosh(x) - 8b c + 16a b c)sinh(x) +--R + +--R 2 3 2 2 2 +--R 40b c cosh(x) + 48b c cosh(x) + (- 24b c + 48a b c)cosh(x) +--R + +--R 2 +--R - 8b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 20b c cosh(x) + 32b c cosh(x) + (- 24b c + 48a b c)cosh(x) +--R + +--R 2 2 +--R - 16b c cosh(x) + 4b c +--R * +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 4b c cosh(x) + 8b c cosh(x) + (- 8b c + 16a b c)cosh(x) +--R + +--R 2 2 2 +--R - 8b c cosh(x) + 4b c cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 5 2 4 +--R 2a c sinh(x) + (10a c cosh(x) + 4a b c)sinh(x) +--R + +--R 2 2 2 2 3 +--R (20a c cosh(x) + 16a b c cosh(x) - 4a c + 8a c)sinh(x) +--R + +--R 2 3 2 2 2 +--R 20a c cosh(x) + 24a b c cosh(x) + (- 12a c + 24a c)cosh(x) +--R + +--R - 4a b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 2 2 2 +--R 10a c cosh(x) + 16a b c cosh(x) + (- 12a c + 24a c)cosh(x) +--R + +--R 2 +--R - 8a b c cosh(x) + 2a c +--R * +--R sinh(x) +--R + +--R 2 5 4 2 2 3 +--R 2a c cosh(x) + 4a b c cosh(x) + (- 4a c + 8a c)cosh(x) +--R + +--R 2 2 +--R - 4a b c cosh(x) + 2a c cosh(x) +--R Type: Expression(Integer) +--E 272 + +)clear all + + +--S 273 of 531 +t1048:= (a+b*sinh(x))/(b^2-2*a*b*sinh(x)+a^2*sinh(x)^2) +--R +--R +--R b sinh(x) + a +--R (1) ------------------------------ +--R 2 2 2 +--R a sinh(x) - 2a b sinh(x) + b +--R Type: Expression(Integer) +--E 273 + +--S 274 of 531 +r1048:= cosh(x)/(b-a*sinh(x)) +--R +--R +--R cosh(x) +--R (2) - ------------- +--R a sinh(x) - b +--R Type: Expression(Integer) +--E 274 + +--S 275 of 531 +a1048:= integrate(t1048,x) +--R +--R +--R (3) +--R - 2b sinh(x) - 2b cosh(x) - 2a +--R ------------------------------------------------------------------------ +--R 2 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) - 2a b)sinh(x) + a cosh(x) - 2a b cosh(x) - a +--R Type: Union(Expression(Integer),...) +--E 275 + +--S 276 of 531 +m1048:= a1048-r1048 +--R +--R +--R (4) +--R 2 2 +--R (a cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (2a cosh(x) - 4a b cosh(x) + 2b - 2a )sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R - 2a b cosh(x) + (2b - a )cosh(x) + 2a b +--R / +--R 3 3 3 2 2 +--R a sinh(x) + (2a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (a cosh(x) - 4a b cosh(x) + 2a b - a )sinh(x) - a b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + a b +--R Type: Expression(Integer) +--E 276 + +--S 277 of 531 +d1048:= D(m1048,x) +--R +--R +--R (5) +--R 3 6 3 2 5 +--R a sinh(x) + (4a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (5a cosh(x) - 10a b cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 2 2 3 3 2 3 +--R (- 8a b cosh(x) + (8a b + 4a )cosh(x) - 2b - 4a b)sinh(x) +--R + +--R 3 4 2 3 3 2 3 2 +--R - 5a cosh(x) + 6a b cosh(x) + 4a cosh(x) + (- 2b - 10a b)cosh(x) +--R + +--R 2 3 +--R 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R - 4a cosh(x) + 11a b cosh(x) + (- 8a b + 4a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (2b - 10a b)cosh(x) + 8a b cosh(x) - 2b - a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R - a cosh(x) + 4a b cosh(x) + (- 4a b + 2a )cosh(x) +--R + +--R 3 2 3 2 3 2 3 +--R (2b - 4a b)cosh(x) + (4a b - a )cosh(x) - 2b cosh(x) +--R / +--R 4 6 4 3 5 +--R a sinh(x) + (4a cosh(x) - 6a b)sinh(x) +--R + +--R 4 2 3 2 2 4 4 +--R (6a cosh(x) - 20a b cosh(x) + 13a b - 2a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 3 +--R (4a cosh(x) - 24a b cosh(x) + (36a b - 4a )cosh(x) - 12a b + 8a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R a cosh(x) - 12a b cosh(x) + (34a b - 2a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 28a b + 12a b)cosh(x) + 4b - 10a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R - 2a b cosh(x) + 12a b cosh(x) + (- 20a b + 4a b)cosh(x) +--R + +--R 4 2 2 3 3 +--R (8b - 12a b )cosh(x) + 4a b - 2a b +--R * +--R sinh(x) +--R + +--R 2 2 4 3 3 4 2 2 2 3 2 2 +--R a b cosh(x) - 4a b cosh(x) + (4b - 2a b )cosh(x) + 4a b cosh(x) + a b +--R Type: Expression(Integer) +--E 277 + +)clear all + + +--S 278 of 531 +t1049:= (d+e*sinh(x))/(a+b*sinh(x)+c*sinh(x)^2) +--R +--R +--R e sinh(x) + d +--R (1) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a +--R Type: Expression(Integer) +--E 278 + +--S 279 of 531 +r1049:= -2*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atanh((2*c-(b-(b^2-4*a*c)^(1/2))*tanh(1/2*x))/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2))/_ + (4*c^2+(b-(b^2-4*a*c)^(1/2))^2)^(1/2)-2*(e-(2*c*d-b*e)/_ + (b^2-4*a*c)^(1/2))*atanh((2*c-(b+(b^2-4*a*c)^(1/2))*_ + tanh(1/2*x))/(4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/_ + (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +-----------+ +--R | 2 +--R (- 2e\|- 4a c + b + 2b e - 4c d) +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-----------+ +--R | 2 +--R (2e\|- 4a c + b + 2b e - 4c d) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression(Integer) +--E 279 + +--S 280 of 531 +a1049:= integrate(t1049,x) +--R +--R +--R (3) +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c - 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c + 8a c + 2b - 4a )d e + (- 4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 2 2 2 +--R (4a c - 2b - 4a )e + (4b c + 4a b)d e + (- 4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b - 4a b)c + (5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b + 5a b + 4a b)c - a b - a b +--R * +--R e +--R + +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b + 24a )c + (- 18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b + 22a b + 8a )c + (- 8a b - 6a b )c + b + a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c - 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c + 8a c + 2b - 4a )d e + (- 4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 3 2 3 3 +--R (- 4a b c + (b + 4a b)c - a b )e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (8a c + (- 2b - 16a )c + 8a c + b - 2a b )d e +--R + +--R 2 3 2 3 2 2 4 3 +--R (12a b c + (- 3b - 12a b)c + 3a b )d e + (4a b c - b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c - 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c + 8a c + 2b - 4a )d e +--R + +--R 3 2 4 +--R (- 4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b - 4a )e + (4b c + 4a b)d e +--R + +--R 2 2 2 +--R (- 4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c + 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 2 +--R e +--R + +--R 3 3 2 2 3 3 5 +--R 8a b c + (- 2b - 16a b)c + (12a b + 8a b)c - 2b +--R + +--R 2 3 +--R - 2a b +--R * +--R d e +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 +--R (2b + 2a b )c +--R * +--R 2 +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c - 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c + 8a c + 2b - 4a )d e + (- 4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R - 2a b - a b +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b + 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c - 12a b c)d e + (- 8c + 8a c + 4b c)d e - 4b c d +--R * +--R sinh(x) +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b + 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c - 12a b c)d e + (- 8c + 8a c + 4b c)d e - 4b c d +--R * +--R cosh(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b + 4a b)d e + (6b c - 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c + 4a b c + 2b )d e - 2b c d +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c + 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c - 4a b)d e +--R + +--R 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2 2 3 2 4 +--R (12b c - 12a b c)d e + (- 8c + 8a c + 4b c)d e - 4b c d +--R * +--R cosh(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b + 4a b)d e + (6b c - 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c + 4a b c + 2b )d e - 2b c d +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 280 + +--S 281 of 531 +m1049:= a1049-r1049 +--R +--R +--R (4) +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c - 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c + 8a c + 2b - 4a )d e + (- 4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 2 2 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e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b - 4a )e + (4b c + 4a b)d e +--R + +--R 2 2 2 +--R (- 4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b + 4a b)c + (- 5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b - 5a b - 4a b)c + a b + a b +--R * +--R e +--R + +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b - 24a )c + (18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 +--R (- 3b - 22a b - 8a )c + (8a b + 6a b )c - b +--R + +--R 2 4 +--R - a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c - 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c + 8a c + 2b - 4a )d e +--R + +--R 3 2 4 +--R (- 4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 3 2 3 3 +--R (4a b c + (- b - 4a b)c + a b )e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (- 8a c + (2b + 16a )c - 8a c - b + 2a b )d e +--R + +--R 2 3 2 3 2 2 4 3 +--R (- 12a b c + (3b + 12a b)c - 3a b )d e + (- 4a b c + b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c - 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c + 8a c + 2b - 4a )d e +--R + +--R 3 2 4 +--R (- 4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (- 2b - 22a b - 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b + 12a b + 4a )c - b - 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b - 4a )e + (4b c + 4a b)d e +--R + +--R 2 2 2 +--R (- 4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b - 8a )c + (6a b + 4a )c - b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R - 8a c + (2a b + 16a )c + (- 12a b - 8a )c + 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 2 +--R e +--R + +--R 3 3 2 2 3 3 5 +--R 8a b c + (- 2b - 16a b)c + (12a b + 8a b)c - 2b +--R + +--R 2 3 +--R - 2a b +--R * +--R d e +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b + 16a )c + (- 12a b - 8a )c +--R + +--R 4 2 2 +--R (2b + 2a b )c +--R * +--R 2 +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c - 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c + 8a c + 2b - 4a )d e + (- 4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b - 16a )c + (12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- 2b - 22a b - 16a )c + (8a b + 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b - 2a b - a b +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b + 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c - 12a b c)d e + (- 8c + 8a c + 4b c)d e - 4b c d +--R * +--R sinh(x) +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b + 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c - 12a b c)d e + (- 8c + 8a c + 4b c)d e - 4b c d +--R * +--R cosh(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b + 4a b)d e + (6b c - 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c + 4a b c + 2b )d e - 2b c d +--R + +--R +-----------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (4e\|- 4a c + b - 4b e + 8c d)\|2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b - b tanh(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R + +--R +-----------+ +--R | 2 +--R (- 4e\|- 4a c + b - 4b e + 8c d) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + b tanh(-) - 2c +--R 2 2 +--R atanh(--------------------------------------) +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c - 4a c + 2b +--R * +--R +-----------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|2b\|- 4a c + b + 4c - 4a c + 2b +--R Type: Expression(Integer) +--E 281 + +--S 282 of 531 +d1049:= D(m1049,x) +--R +--R +--R (5) +--R 4 3 +--R - c d sinh(x) + (- 4c d cosh(x) + 2a e - 2b d)sinh(x) +--R + +--R 2 2 +--R (- 6c d cosh(x) + (6a e - 6b d)cosh(x) + 2c d)sinh(x) +--R + +--R 3 2 +--R - 4c d cosh(x) + (6a e - 6b d)cosh(x) + 4c d cosh(x) - 2a e +--R + +--R 2b d +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R - c d cosh(x) + (2a e - 2b d)cosh(x) + 2c d cosh(x) +--R + +--R (- 2a e + 2b d)cosh(x) - c d +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R 2c e sinh(x) + 8c e cosh(x)sinh(x) +--R + +--R 2 2 +--R (12c e cosh(x) + (- 4c + 8a)e - 8b d)sinh(x) +--R + +--R 3 +--R (8c e cosh(x) + ((- 8c + 16a)e - 16b d)cosh(x))sinh(x) +--R + +--R 4 2 +--R 2c e cosh(x) + ((- 4c + 8a)e - 8b d)cosh(x) + 2c e +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R 2c d sinh(x) + (8c d cosh(x) + (8c - 4a)e + 4b d)sinh(x) +--R + +--R 2 2 +--R (12c d cosh(x) + ((24c - 12a)e + 12b d)cosh(x) + 12c d)sinh(x) +--R + +--R 3 2 +--R 8c d cosh(x) + ((24c - 12a)e + 12b d)cosh(x) + 24c d cosh(x) +--R + +--R (- 8c + 4a)e - 4b d +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R 2c d cosh(x) + ((8c - 4a)e + 4b d)cosh(x) + 12c d cosh(x) +--R + +--R ((- 8c + 4a)e - 4b d)cosh(x) + 2c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - 2c e sinh(x) - 8c e cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12c e cosh(x) + (4c - 8a)e + 8b d)sinh(x) +--R + +--R 3 +--R (- 8c e cosh(x) + ((8c - 16a)e + 16b d)cosh(x))sinh(x) +--R + +--R 4 2 +--R - 2c e cosh(x) + ((4c - 8a)e + 8b d)cosh(x) - 2c e +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - c d sinh(x) + (- 4c d cosh(x) + 2a e - 2b d)sinh(x) +--R + +--R 2 2 +--R (- 6c d cosh(x) + (6a e - 6b d)cosh(x) + 2c d)sinh(x) +--R + +--R 3 2 +--R (- 4c d cosh(x) + (6a e - 6b d)cosh(x) + 4c d cosh(x) - 2a e + 2b d) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R - c d cosh(x) + (2a e - 2b d)cosh(x) + 2c d cosh(x) +--R + +--R (- 2a e + 2b d)cosh(x) - c d +--R / +--R 4 3 +--R a c sinh(x) + (4a c cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 +--R (6a c cosh(x) + 6a b cosh(x) - 2a c + 4a )sinh(x) +--R + +--R 3 2 2 +--R (4a c cosh(x) + 6a b cosh(x) + (- 4a c + 8a )cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 2 2 +--R a c cosh(x) + 2a b cosh(x) + (- 2a c + 4a )cosh(x) - 2a b cosh(x) +--R + +--R a c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R - 2b c sinh(x) + (- 8b c cosh(x) - 4b )sinh(x) +--R + +--R 2 2 2 +--R (- 12b c cosh(x) - 12b cosh(x) + 4b c - 8a b)sinh(x) +--R + +--R 3 2 2 2 +--R (- 8b c cosh(x) - 12b cosh(x) + (8b c - 16a b)cosh(x) + 4b )sinh(x) +--R + +--R 4 2 3 2 2 +--R - 2b c cosh(x) - 4b cosh(x) + (4b c - 8a b)cosh(x) + 4b cosh(x) +--R + +--R - 2b c +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (4c - 2a c)sinh(x) + ((16c - 8a c)cosh(x) + 8b c - 4a b)sinh(x) +--R + +--R 2 2 2 +--R (24c - 12a c)cosh(x) + (24b c - 12a b)cosh(x) - 8c + 20a c +--R + +--R 2 +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (16c - 8a c)cosh(x) + (24b c - 12a b)cosh(x) +--R + +--R 2 2 +--R (- 16c + 40a c - 16a )cosh(x) - 8b c + 4a b +--R * +--R sinh(x) +--R + +--R 2 4 3 +--R (4c - 2a c)cosh(x) + (8b c - 4a b)cosh(x) +--R + +--R 2 2 2 2 +--R (- 8c + 20a c - 8a )cosh(x) + (- 8b c + 4a b)cosh(x) + 4c - 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2b c sinh(x) + (8b c cosh(x) + 4b )sinh(x) +--R + +--R 2 2 2 +--R (12b c cosh(x) + 12b cosh(x) - 4b c + 8a b)sinh(x) +--R + +--R 3 2 2 2 +--R (8b c cosh(x) + 12b cosh(x) + (- 8b c + 16a b)cosh(x) - 4b )sinh(x) +--R + +--R 4 2 3 2 2 +--R 2b c cosh(x) + 4b cosh(x) + (- 4b c + 8a b)cosh(x) - 4b cosh(x) +--R + +--R 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R a c sinh(x) + (4a c cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 +--R (6a c cosh(x) + 6a b cosh(x) - 2a c + 4a )sinh(x) +--R + +--R 3 2 2 +--R (4a c cosh(x) + 6a b cosh(x) + (- 4a c + 8a )cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 2 2 +--R a c cosh(x) + 2a b cosh(x) + (- 2a c + 4a )cosh(x) - 2a b cosh(x) + a c +--R Type: Expression(Integer) +--E 282 + +)clear all + + +--S 283 of 531 +t1050:= 1/(a+b*cosh(x)+c*cosh(x)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 +--R c cosh(x) + b cosh(x) + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 531 +r1050:= -2*2^(1/2)*c*atan(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*_ + tanh(1/2*x)*2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ + (b^2-4*a*c)^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)+_ + 4*c*atan((b+(b^2-4*a*c)^(1/2)-2*c)*tanh(1/2*x)/(4*c^2-_ + (b+(b^2-4*a*c)^(1/2))^2)^(1/2))/(b^2-4*a*c)^(1/2)/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 4c\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + (- 2c + b)tanh(-) +--R 2 2 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-------------------------------------+ +--R | +-----------+ +--R +-+ | | 2 2 2 +--R 2c\|2 \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tanh(-)\|- 4a c + b + (2c - b)\|2 tanh(-) +--R 2 2 +--R atan(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 531 +a1050:= integrate(t1050,x) +--R +--R +--R (3) +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 24a )c + (- 18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b - 22a b + 8a )c + (8a b - 6a b )c - b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 24a )c + (- 18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b - 22a b + 8a )c + (8a b - 6a b )c - b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c + (- 2b + 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 24a )c + (18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b + 22a b - 8a )c + (- 8a b + 6a b )c + b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 24a )c + (18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b + 22a b - 8a )c + (- 8a b + 6a b )c + b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + (2b - 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 285 + +--S 286 of 531 +m1050:= a1050-r1050 +--R +--R +--R (4) +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 24a )c + (- 18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b - 22a b + 8a )c + (8a b - 6a b )c - b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 24a )c + (- 18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b - 22a b + 8a )c + (8a b - 6a b )c - b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c + (- 2b + 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 24a )c + (18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b + 22a b - 8a )c + (- 8a b + 6a b )c + b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 4 +--R 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 24a )c + (18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (- 3b + 22a b - 8a )c + (- 8a b + 6a b )c + b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 4 +--R - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4c + 4a c - 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + (2b - 2a b )c) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 2 2 +--R 4b c sinh(x) + 4b c cosh(x) + 2b c +--R + +--R - +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 8c\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + (- 2c + b)tanh(-) +--R 2 2 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R - +--R +-------------------------------------+ +--R | +-----------+ +--R +-+ | | 2 2 2 +--R 4c\|2 \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tanh(-)\|- 4a c + b + (2c - b)\|2 tanh(-) +--R 2 2 +--R atan(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 286 + +--S 287 of 531 +d1050:= D(m1050,x) +--R +--R +--R (5) +--R 4 3 +--R - c sinh(x) + (- 4c cosh(x) - 2b)sinh(x) +--R + +--R 2 2 +--R (- 6c cosh(x) - 6b cosh(x) + 2c - 4b)sinh(x) +--R + +--R 3 2 +--R (- 4c cosh(x) - 6b cosh(x) + (4c - 8b)cosh(x) - 2b)sinh(x) +--R + +--R 4 3 2 +--R - c cosh(x) - 2b cosh(x) + (2c - 4b)cosh(x) - 2b cosh(x) - c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R 2c sinh(x) + (8c cosh(x) + 4b)sinh(x) +--R + +--R 2 2 +--R (12c cosh(x) + 12b cosh(x) + 12c)sinh(x) +--R + +--R 3 2 4 +--R (8c cosh(x) + 12b cosh(x) + 24c cosh(x) + 4b)sinh(x) + 2c cosh(x) +--R + +--R 3 2 +--R 4b cosh(x) + 12c cosh(x) + 4b cosh(x) + 2c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - c sinh(x) + (- 4c cosh(x) - 2b)sinh(x) +--R + +--R 2 2 +--R (- 6c cosh(x) - 6b cosh(x) + 2c + 4b)sinh(x) +--R + +--R 3 2 4 +--R (- 4c cosh(x) - 6b cosh(x) + (4c + 8b)cosh(x) - 2b)sinh(x) - c cosh(x) +--R + +--R 3 2 +--R - 2b cosh(x) + (2c + 4b)cosh(x) - 2b cosh(x) - c +--R / +--R 2 4 +--R (c + (- b + a)c)sinh(x) +--R + +--R 2 2 3 +--R ((4c + (- 4b + 4a)c)cosh(x) + 2b c - 2b + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (6c + (- 6b + 6a)c)cosh(x) + (6b c - 6b + 6a b)cosh(x) + 2c +--R + +--R 2 +--R (- 2b + 6a)c - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4c + (- 4b + 4a)c)cosh(x) + (6b c - 6b + 6a b)cosh(x) +--R + +--R 2 2 2 +--R (4c + (- 4b + 12a)c - 8a b + 8a )cosh(x) + 2b c - 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 +--R (c + (- b + a)c)cosh(x) + (2b c - 2b + 2a b)cosh(x) +--R + +--R 2 2 2 +--R (2c + (- 2b + 6a)c - 4a b + 4a )cosh(x) +--R + +--R 2 2 +--R (2b c - 2b + 2a b)cosh(x) + c + (- b + a)c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (2c - 2a c)sinh(x) + ((8c - 8a c)cosh(x) + 4b c - 4a b)sinh(x) +--R + +--R 2 2 2 +--R (12c - 12a c)cosh(x) + (12b c - 12a b)cosh(x) + 4c + 4a c +--R + +--R 2 +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (8c - 8a c)cosh(x) + (12b c - 12a b)cosh(x) +--R + +--R 2 2 +--R (8c + 8a c - 16a )cosh(x) + 4b c - 4a b +--R * +--R sinh(x) +--R + +--R 2 4 3 +--R (2c - 2a c)cosh(x) + (4b c - 4a b)cosh(x) +--R + +--R 2 2 2 2 +--R (4c + 4a c - 8a )cosh(x) + (4b c - 4a b)cosh(x) + 2c - 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 +--R (c + (b + a)c)sinh(x) +--R + +--R 2 2 3 +--R ((4c + (4b + 4a)c)cosh(x) + 2b c + 2b + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (6c + (6b + 6a)c)cosh(x) + (6b c + 6b + 6a b)cosh(x) + 2c +--R + +--R 2 +--R (2b + 6a)c + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4c + (4b + 4a)c)cosh(x) + (6b c + 6b + 6a b)cosh(x) +--R + +--R 2 2 2 +--R (4c + (4b + 12a)c + 8a b + 8a )cosh(x) + 2b c + 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 +--R (c + (b + a)c)cosh(x) + (2b c + 2b + 2a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (2c + (2b + 6a)c + 4a b + 4a )cosh(x) + (2b c + 2b + 2a b)cosh(x) + c +--R + +--R (b + a)c +--R Type: Expression(Integer) +--E 287 + +)clear all + + +--S 288 of 531 +t1051:= cosh(x)/(a+b*cosh(x)+c*cosh(x)^2) +--R +--R +--R cosh(x) +--R (1) -------------------------- +--R 2 +--R c cosh(x) + b cosh(x) + a +--R Type: Expression(Integer) +--E 288 + +--S 289 of 531 +r1051:= -2^(1/2)*(1-b/(b^2-4*a*c)^(1/2))*_ + atan(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*_ + tanh(1/2*x)*2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)-_ + 2*(1+b/(b^2-4*a*c)^(1/2))*atan((b+(b^2-4*a*c)^(1/2)-2*c)*_ + tanh(1/2*x)/(4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (- 2\|- 4a c + b - 2b)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + (- 2c + b)tanh(-) +--R 2 2 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 2 2 +--R (\|2 \|- 4a c + b - b\|2 )\|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tanh(-)\|- 4a c + b + (2c - b)\|2 tanh(-) +--R 2 2 +--R atan(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 289 + +--S 290 of 531 +a1051:= integrate(t1051,x) +--R +--R +--R (3) +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 3 2 3 +--R 4a b c + (- b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 3 2 +--R (8a c + (- 2a b + 16a )c + (- 12a b + 8a )c + 2a b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 +--R - 4a b c + (b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 3 2 3 +--R 4a b c + (- b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 3 2 +--R (- 8a c + (2a b - 16a )c + (12a b - 8a )c - 2a b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 +--R - 4a b c + (b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c + 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 290 + +--S 291 of 531 +m1051:= a1051-r1051 +--R +--R +--R (4) +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 3 2 3 +--R 4a b c + (- b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 3 2 +--R (8a c + (- 2a b + 16a )c + (- 12a b + 8a )c + 2a b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R - +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 +--R - 4a b c + (b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 3 2 3 +--R 4a b c + (- b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 3 2 +--R (- 8a c + (2a b - 16a )c + (12a b - 8a )c - 2a b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 +--R - 4a b c + (b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4a c + 2b - 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c + 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 +--R 4a b c sinh(x) + 4a b c cosh(x) + 2a b +--R + +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (4\|- 4a c + b + 4b)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + (- 2c + b)tanh(-) +--R 2 2 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (- 2\|2 \|- 4a c + b + 2b\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tanh(-)\|- 4a c + b + (2c - b)\|2 tanh(-) +--R 2 2 +--R atan(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 291 + +--S 292 of 531 +d1051:= D(m1051,x) +--R +--R +--R (5) +--R 4 3 +--R c sinh(x) + (4c cosh(x) + 2c + 2a)sinh(x) +--R + +--R 2 2 +--R (6c cosh(x) + (6c + 6a)cosh(x) + 2c + 4a)sinh(x) +--R + +--R 3 2 +--R (4c cosh(x) + (6c + 6a)cosh(x) + (4c + 8a)cosh(x) + 2c + 2a)sinh(x) +--R + +--R 4 3 2 +--R c cosh(x) + (2c + 2a)cosh(x) + (2c + 4a)cosh(x) + (2c + 2a)cosh(x) +--R + +--R c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 3 2 +--R (4c - 4a)sinh(x) + (12c - 12a)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((12c - 12a)cosh(x) + 4c - 4a)sinh(x) + (4c - 4a)cosh(x) +--R + +--R (4c - 4a)cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - c sinh(x) + (- 4c cosh(x) + 2c + 2a)sinh(x) +--R + +--R 2 2 +--R (- 6c cosh(x) + (6c + 6a)cosh(x) - 2c - 4a)sinh(x) +--R + +--R 3 2 +--R (- 4c cosh(x) + (6c + 6a)cosh(x) + (- 4c - 8a)cosh(x) + 2c + 2a)sinh(x) +--R + +--R 4 3 2 +--R - c cosh(x) + (2c + 2a)cosh(x) + (- 2c - 4a)cosh(x) + (2c + 2a)cosh(x) +--R + +--R - c +--R / +--R 2 4 +--R (c + (- b + a)c)sinh(x) +--R + +--R 2 2 3 +--R ((4c + (- 4b + 4a)c)cosh(x) + 2b c - 2b + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (6c + (- 6b + 6a)c)cosh(x) + (6b c - 6b + 6a b)cosh(x) + 2c +--R + +--R 2 +--R (- 2b + 6a)c - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4c + (- 4b + 4a)c)cosh(x) + (6b c - 6b + 6a b)cosh(x) +--R + +--R 2 2 2 +--R (4c + (- 4b + 12a)c - 8a b + 8a )cosh(x) + 2b c - 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 +--R (c + (- b + a)c)cosh(x) + (2b c - 2b + 2a b)cosh(x) +--R + +--R 2 2 2 +--R (2c + (- 2b + 6a)c - 4a b + 4a )cosh(x) +--R + +--R 2 2 +--R (2b c - 2b + 2a b)cosh(x) + c + (- b + a)c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (2c - 2a c)sinh(x) + ((8c - 8a c)cosh(x) + 4b c - 4a b)sinh(x) +--R + +--R 2 2 2 +--R (12c - 12a c)cosh(x) + (12b c - 12a b)cosh(x) + 4c + 4a c +--R + +--R 2 +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (8c - 8a c)cosh(x) + (12b c - 12a b)cosh(x) +--R + +--R 2 2 +--R (8c + 8a c - 16a )cosh(x) + 4b c - 4a b +--R * +--R sinh(x) +--R + +--R 2 4 3 +--R (2c - 2a c)cosh(x) + (4b c - 4a b)cosh(x) +--R + +--R 2 2 2 2 +--R (4c + 4a c - 8a )cosh(x) + (4b c - 4a b)cosh(x) + 2c - 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 +--R (c + (b + a)c)sinh(x) +--R + +--R 2 2 3 +--R ((4c + (4b + 4a)c)cosh(x) + 2b c + 2b + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (6c + (6b + 6a)c)cosh(x) + (6b c + 6b + 6a b)cosh(x) + 2c +--R + +--R 2 +--R (2b + 6a)c + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4c + (4b + 4a)c)cosh(x) + (6b c + 6b + 6a b)cosh(x) +--R + +--R 2 2 2 +--R (4c + (4b + 12a)c + 8a b + 8a )cosh(x) + 2b c + 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 +--R (c + (b + a)c)cosh(x) + (2b c + 2b + 2a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (2c + (2b + 6a)c + 4a b + 4a )cosh(x) + (2b c + 2b + 2a b)cosh(x) + c +--R + +--R (b + a)c +--R Type: Expression(Integer) +--E 292 + +)clear all + + +--S 293 of 531 +t1052:= cosh(x)^2/(a+b*cosh(x)+c*cosh(x)^2) +--R +--R +--R 2 +--R cosh(x) +--R (1) -------------------------- +--R 2 +--R c cosh(x) + b cosh(x) + a +--R Type: Expression(Integer) +--E 293 + +--S 294 of 531 +r1052:= x/c+2^(1/2)*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ + atan(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*tanh(1/2*x)*2^(1/2)/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/c/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)+2*(b+(b^2-2*a*c)/_ + (b^2-4*a*c)^(1/2))*atan((b+(b^2-4*a*c)^(1/2)-2*c)*tanh(1/2*x)/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/c/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 2 | | 2 2 2 +--R (2b\|- 4a c + b - 4a c + 2b )\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + (- 2c + b)tanh(-) +--R 2 2 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +--R (- b\|2 \|- 4a c + b + (- 2a c + b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tanh(-)\|- 4a c + b + (2c - b)\|2 tanh(-) +--R 2 2 +--R atan(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R x\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 294 + +--S 295 of 531 +a1052:= integrate(t1052,x) +--R +--R +--R (3) +--R - +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R 8a c + (- 6a b + 24a )c + (b - 22a b + 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (8a b - 18a b + 8a )c + (- b + 3a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R 8a b c + (- 6a b + 4a b )c + (b - a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b + 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b + 4a b)c)cosh(x) + 4a b c - 2a b + 2a b +--R + +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R 8a c + (- 6a b + 24a )c + (b - 22a b + 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (8a b - 18a b + 8a )c + (- b + 3a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R - 8a b c + (6a b - 4a b )c + (- b + a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b + 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b + 4a b)c)cosh(x) + 4a b c - 2a b + 2a b +--R + +--R - +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R - 8a c + (6a b - 24a )c + (- b + 22a b - 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (- 8a b + 18a b - 8a )c + (b - 3a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R 8a b c + (- 6a b + 4a b )c + (b - a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b + 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b + 4a b)c)cosh(x) + 4a b c - 2a b + 2a b +--R + +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R - 8a c + (6a b - 24a )c + (- b + 22a b - 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (- 8a b + 18a b - 8a )c + (b - 3a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R - 8a b c + (6a b - 4a b )c + (- b + a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b + 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b + 4a b)c)cosh(x) + 4a b c - 2a b + 2a b +--R + +--R 2x +--R / +--R 2c +--R Type: Union(Expression(Integer),...) +--E 295 + +--S 296 of 531 +m1052:= a1052-r1052 +--R +--R +--R (4) +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R 8a c + (- 6a b + 24a )c + (b - 22a b + 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (8a b - 18a b + 8a )c + (- b + 3a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R 8a b c + (- 6a b + 4a b )c + (b - a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b + 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b + 4a b)c)cosh(x) + 4a b c - 2a b + 2a b +--R + +--R +-----------+ +--R | 2 +--R c\|- 4a c + b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R 8a c + (- 6a b + 24a )c + (b - 22a b + 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (8a b - 18a b + 8a )c + (- b + 3a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R - 8a b c + (6a b - 4a b )c + (- b + a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b + 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b + 4a b)c)cosh(x) + 4a b c - 2a b + 2a b +--R + +--R - +--R +-----------+ +--R | 2 +--R c\|- 4a c + b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R - 8a c + (6a b - 24a )c + (- b + 22a b - 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (- 8a b + 18a b - 8a )c + (b - 3a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R 8a b c + (- 6a b + 4a b )c + (b - a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b + 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b + 4a b)c)cosh(x) + 4a b c - 2a b + 2a b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 7 2 3 6 4 2 2 4 5 +--R - 8a c + (6a b - 24a )c + (- b + 22a b - 24a )c +--R + +--R 4 3 2 5 4 6 2 4 4 2 3 +--R (- 8a b + 18a b - 8a )c + (b - 3a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 4 3 2 2 6 2 4 +--R - 8a b c + (6a b - 4a b )c + (- b + a b )c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R 4a c + (- 8a b + 4a )c + 2b - 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 2 2 3 4 +--R (8a b c + (- 4a b + 4a b)c)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 4 4 2 +--R (8a b c + (- 4a b + 4a b)c)cosh(x) + 4a b c - 2a b + 2a b +--R + +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 2 | | 2 2 2 +--R (- 4b\|- 4a c + b + 8a c - 4b )\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + (- 2c + b)tanh(-) +--R 2 2 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +--R (2b\|2 \|- 4a c + b + (4a c - 2b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tanh(-)\|- 4a c + b + (2c - b)\|2 tanh(-) +--R 2 2 +--R atan(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 296 + +--S 297 of 531 +d1052:= D(m1052,x) +--R +--R +--R (5) +--R 4 3 +--R (- b + a)sinh(x) + ((- 4b + 4a)cosh(x) - 2b)sinh(x) +--R + +--R 2 2 +--R ((- 6b + 6a)cosh(x) - 6b cosh(x) - 2b - 2a)sinh(x) +--R + +--R 3 2 +--R ((- 4b + 4a)cosh(x) - 6b cosh(x) + (- 4b - 4a)cosh(x) - 2b)sinh(x) +--R + +--R 4 3 2 +--R (- b + a)cosh(x) - 2b cosh(x) + (- 2b - 2a)cosh(x) - 2b cosh(x) +--R + +--R - b + a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - 2a sinh(x) + (- 8a cosh(x) - 4b)sinh(x) +--R + +--R 2 2 +--R (- 12a cosh(x) - 12b cosh(x) - 12a)sinh(x) +--R + +--R 3 2 +--R (- 8a cosh(x) - 12b cosh(x) - 24a cosh(x) - 4b)sinh(x) +--R + +--R 4 3 2 +--R - 2a cosh(x) - 4b cosh(x) - 12a cosh(x) - 4b cosh(x) - 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R (b + a)sinh(x) + ((4b + 4a)cosh(x) - 2b)sinh(x) +--R + +--R 2 2 +--R ((6b + 6a)cosh(x) - 6b cosh(x) + 2b - 2a)sinh(x) +--R + +--R 3 2 +--R ((4b + 4a)cosh(x) - 6b cosh(x) + (4b - 4a)cosh(x) - 2b)sinh(x) +--R + +--R 4 3 2 +--R (b + a)cosh(x) - 2b cosh(x) + (2b - 2a)cosh(x) - 2b cosh(x) + b + a +--R / +--R 2 4 +--R (c + (- b + a)c)sinh(x) +--R + +--R 2 2 3 +--R ((4c + (- 4b + 4a)c)cosh(x) + 2b c - 2b + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (6c + (- 6b + 6a)c)cosh(x) + (6b c - 6b + 6a b)cosh(x) + 2c +--R + +--R 2 +--R (- 2b + 6a)c - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4c + (- 4b + 4a)c)cosh(x) + (6b c - 6b + 6a b)cosh(x) +--R + +--R 2 2 2 +--R (4c + (- 4b + 12a)c - 8a b + 8a )cosh(x) + 2b c - 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 +--R (c + (- b + a)c)cosh(x) + (2b c - 2b + 2a b)cosh(x) +--R + +--R 2 2 2 +--R (2c + (- 2b + 6a)c - 4a b + 4a )cosh(x) +--R + +--R 2 2 +--R (2b c - 2b + 2a b)cosh(x) + c + (- b + a)c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (2c - 2a c)sinh(x) + ((8c - 8a c)cosh(x) + 4b c - 4a b)sinh(x) +--R + +--R 2 2 2 +--R (12c - 12a c)cosh(x) + (12b c - 12a b)cosh(x) + 4c + 4a c +--R + +--R 2 +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (8c - 8a c)cosh(x) + (12b c - 12a b)cosh(x) +--R + +--R 2 2 +--R (8c + 8a c - 16a )cosh(x) + 4b c - 4a b +--R * +--R sinh(x) +--R + +--R 2 4 3 +--R (2c - 2a c)cosh(x) + (4b c - 4a b)cosh(x) +--R + +--R 2 2 2 2 +--R (4c + 4a c - 8a )cosh(x) + (4b c - 4a b)cosh(x) + 2c - 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 +--R (c + (b + a)c)sinh(x) +--R + +--R 2 2 3 +--R ((4c + (4b + 4a)c)cosh(x) + 2b c + 2b + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (6c + (6b + 6a)c)cosh(x) + (6b c + 6b + 6a b)cosh(x) + 2c +--R + +--R 2 +--R (2b + 6a)c + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4c + (4b + 4a)c)cosh(x) + (6b c + 6b + 6a b)cosh(x) +--R + +--R 2 2 2 +--R (4c + (4b + 12a)c + 8a b + 8a )cosh(x) + 2b c + 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 +--R (c + (b + a)c)cosh(x) + (2b c + 2b + 2a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (2c + (2b + 6a)c + 4a b + 4a )cosh(x) + (2b c + 2b + 2a b)cosh(x) + c +--R + +--R (b + a)c +--R Type: Expression(Integer) +--E 297 + +)clear all + + +--S 298 of 531 +t1053:= cosh(x)^3/(a+b*cosh(x)+c*cosh(x)^2) +--R +--R +--R 3 +--R cosh(x) +--R (1) -------------------------- +--R 2 +--R c cosh(x) + b cosh(x) + a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 531 +r1053:= -b*x/c^2-2^(1/2)*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ + atan(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*tanh(1/2*x)*2^(1/2)/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/c^2/(-b^2+2*c*(a+c)+_ + (b^2-4*a*c)^(1/2)*b)^(1/2)-2*(b^2-a*c+b*(b^2-3*a*c)/_ + (b^2-4*a*c)^(1/2))*atan((b+(b^2-4*a*c)^(1/2)-2*c)*_ + tanh(1/2*x)/(4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/c^2/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2)+sinh(x)/c +--R +--R +--R (2) +--R +-----------+ +--R 2 | 2 3 +--R ((2a c - 2b )\|- 4a c + b + 6a b c - 2b ) +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + (- 2c + b)tanh(-) +--R 2 2 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R 2 +-+ | 2 3 +-+ +--R ((- a c + b )\|2 \|- 4a c + b + (3a b c - b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tanh(-)\|- 4a c + b + (2c - b)\|2 tanh(-) +--R 2 2 +--R atan(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (c sinh(x) - b x)\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 2 2 +--R c \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 299 + +--S 300 of 531 +a1053:= integrate(t1053,x) +--R +--R +--R (3) +--R 2 2 +--R (- c sinh(x) - c cosh(x)) +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R 12a b c + (- 7a b + 28a b)c + (b - 27a b + 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (9a b - 13a b + 4a b)c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R 12a b c + (- 31a b + 20a b)c + (27a b - 33a b + 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (- 9a b + 15a b - 6a b )c + (b - 2a b + a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b + 22a b - 4a b )c + (8a b - 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b + 4a b )c + 2a b - 2a b +--R + +--R 2 2 +--R (c sinh(x) + c cosh(x)) +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R 12a b c + (- 7a b + 28a b)c + (b - 27a b + 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (9a b - 13a b + 4a b)c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R - 12a b c + (31a b - 20a b)c + (- 27a b + 33a b - 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (9a b - 15a b + 6a b )c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 3 4 5 2 4 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b + 22a b - 4a b )c + (8a b - 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b + 4a b )c + 2a b - 2a b +--R + +--R 2 2 +--R (- c sinh(x) - c cosh(x)) +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R - 12a b c + (7a b - 28a b)c + (- b + 27a b - 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (- 9a b + 13a b - 4a b)c + (b - 2a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R 12a b c + (- 31a b + 20a b)c + (27a b - 33a b + 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (- 9a b + 15a b - 6a b )c + (b - 2a b + a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 3 4 5 2 4 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b + 22a b - 4a b )c + (8a b - 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b + 4a b )c + 2a b - 2a b +--R + +--R 2 2 +--R (c sinh(x) + c cosh(x)) +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R - 12a b c + (7a b - 28a b)c + (- b + 27a b - 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (- 9a b + 13a b - 4a b)c + (b - 2a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R - 12a b c + (31a b - 20a b)c + (- 27a b + 33a b - 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (9a b - 15a b + 6a b )c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b + 22a b - 4a b )c + (8a b - 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b + 4a b )c + 2a b - 2a b +--R + +--R 2 2 +--R c sinh(x) + (2c cosh(x) - 2b x)sinh(x) + c cosh(x) - 2b x cosh(x) - c +--R / +--R 2 2 +--R 2c sinh(x) + 2c cosh(x) +--R Type: Union(Expression(Integer),...) +--E 300 + +--S 301 of 531 +m1053:= a1053-r1053 +--R +--R +--R (4) +--R +-----------+ +--R 2 2 | 2 +--R (- c sinh(x) - c cosh(x))\|- 4a c + b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R 12a b c + (- 7a b + 28a b)c + (b - 27a b + 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (9a b - 13a b + 4a b)c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R 12a b c + (- 31a b + 20a b)c + (27a b - 33a b + 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (- 9a b + 15a b - 6a b )c + (b - 2a b + a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a 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4a b )c + 2a b - 2a b +--R + +--R +-----------+ +--R 2 2 | 2 +--R (c sinh(x) + c cosh(x))\|- 4a c + b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R 12a b c + (- 7a b + 28a b)c + (b - 27a b + 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (9a b - 13a b + 4a b)c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R - 12a b c + (31a b - 20a b)c + (- 27a b + 33a b - 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (9a b - 15a b + 6a b )c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 3 4 5 2 4 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b + 22a b - 4a b )c + (8a b - 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b + 4a b )c + 2a b - 2a b +--R + +--R +-----------+ +--R 2 2 | 2 +--R (- c sinh(x) - c cosh(x))\|- 4a c + b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 9 3 3 8 5 2 3 4 7 +--R - 12a b c + (7a b - 28a b)c + (- b + 27a b - 20a b)c +--R + +--R 5 3 3 5 6 7 2 5 4 3 5 +--R (- 9a b + 13a b - 4a b)c + (b - 2a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R 12a b c + (- 31a b + 20a b)c + (27a b - 33a b + 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (- 9a b + 15a b - 6a b )c + (b - 2a b + a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + 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+--R 5 3 3 5 6 7 2 5 4 3 5 +--R (- 9a b + 13a b - 4a b)c + (b - 2a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 4 5 3 3 5 4 2 5 4 3 6 3 +--R - 12a b c + (31a b - 20a b)c + (- 27a b + 33a b - 8a b)c +--R + +--R 7 3 5 5 3 2 9 2 7 4 5 +--R (9a b - 15a b + 6a b )c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R - 4a c + (18a b - 4a )c + (- 12a b + 8a b )c + 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (- 22a b + 22a b - 4a b )c + (8a b - 12a b + 4a b )c +--R + +--R 10 2 8 4 6 +--R - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)sinh(x) +--R + +--R 5 3 4 3 6 2 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + (4a b - 4a b )c)cosh(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b + 4a b )c + 2a b - 2a b +--R + +--R +-----------+ +--R 2 2 | 2 +--R ((- 4a c + 4b )sinh(x) + (- 4a c + 4b )cosh(x))\|- 4a c + b +--R + +--R 3 3 +--R (- 12a b c + 4b )sinh(x) + (- 12a b c + 4b )cosh(x) +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + (- 2c + b)tanh(-) +--R 2 2 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R 2 +-+ 2 +-+ | 2 +--R ((2a c - 2b )\|2 sinh(x) + (2a c - 2b )\|2 cosh(x))\|- 4a c + b +--R + +--R 3 +-+ 3 +-+ +--R (- 6a b c + 2b )\|2 sinh(x) + (- 6a b c + 2b )\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tanh(-)\|- 4a c + b + (2c - b)\|2 tanh(-) +--R 2 2 +--R atan(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R + +--R +-----------+ +--R 2 2 | 2 +--R (- c sinh(x) + c cosh(x) - c)\|- 4a c + b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-----------+ +--R 2 2 | 2 +--R (2c sinh(x) + 2c cosh(x))\|- 4a c + b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 301 + +--S 302 of 531 +d1053:= D(m1053,x) +--R +--R +--R (5) +--R 2 6 +--R (c + (- b + a)c)sinh(x) +--R + +--R 2 5 +--R ((4c + (- 4b + 4a)c)cosh(x) + (2b - 2a)c)sinh(x) +--R + +--R 2 2 2 +--R (5c + (- 5b + 5a)c)cosh(x) + ((6b - 10a)c + 4b - 4a b)cosh(x) +--R + +--R 2 2 +--R 3c + (- 3b + 3a)c + 4b - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 +--R ((4b - 20a)c + 16b - 16a b)cosh(x) +--R + +--R 2 2 2 2 +--R (8c - 8b c + 16b - 8a b - 8a )cosh(x) + (4b - 4a)c + 8a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 +--R (- 5c + (5b - 5a)c)cosh(x) +--R + +--R 2 3 +--R ((- 4b - 20a)c + 24b - 24a b)cosh(x) +--R + +--R 2 2 2 2 +--R (6c + (- 6b - 18a)c + 24b - 24a )cosh(x) +--R + +--R 2 2 2 +--R ((8b - 12a)c + 4b + 20a b - 24a )cosh(x) + 3c + (- 3b + 3a)c +--R + +--R 2 +--R 4b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 +--R (- 4c + (4b - 4a)c)cosh(x) +--R + +--R 2 4 +--R ((- 6b - 10a)c + 16b - 16a b)cosh(x) +--R + +--R 2 2 3 +--R (- 24a c + 16b + 8a b - 24a )cosh(x) +--R + +--R 2 2 2 +--R ((4b - 12a)c + 8b + 16a b - 24a )cosh(x) +--R + +--R 2 2 +--R (4c + (- 4b + 4a)c + 8b - 8a b)cosh(x) + (2b - 2a)c +--R * +--R sinh(x) +--R + +--R 2 6 2 5 +--R (- c + (b - a)c)cosh(x) + ((- 2b - 2a)c + 4b - 4a b)cosh(x) +--R + +--R 2 2 2 4 +--R (- c + (b - 9a)c + 4b + 4a b - 8a )cosh(x) +--R + +--R 2 2 3 +--R (- 4a c + 4b + 4a b - 8a )cosh(x) +--R + +--R 2 2 2 2 +--R (c + (- b + a)c + 4b - 4a b)cosh(x) + (2b - 2a)c cosh(x) + c +--R + +--R (- b + a)c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 5 +--R (2c - 2a c)sinh(x) + ((8c - 8a c)cosh(x) + 4b c)sinh(x) +--R + +--R 2 2 2 2 +--R ((10c - 10a c)cosh(x) + (12b c + 8a b)cosh(x) + 6c - 6a c + 8b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 2 2 +--R (8b c + 32a b)cosh(x) + (16c - 32a c + 32b + 16a )cosh(x) +--R + +--R 8b c + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 +--R (- 10c + 10a c)cosh(x) + (- 8b c + 48a b)cosh(x) +--R + +--R 2 2 2 2 +--R (12c - 60a c + 48b + 48a )cosh(x) + (16b c + 56a b)cosh(x) +--R + +--R 2 2 +--R 6c - 6a c + 8b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 +--R (- 8c + 8a c)cosh(x) + (- 12b c + 32a b)cosh(x) +--R + +--R 2 2 3 2 +--R (- 48a c + 32b + 48a )cosh(x) + (8b c + 64a b)cosh(x) +--R + +--R 2 2 +--R (8c - 8a c + 16b )cosh(x) + 4b c +--R * +--R sinh(x) +--R + +--R 2 6 5 +--R (- 2c + 2a c)cosh(x) + (- 4b c + 8a b)cosh(x) +--R + +--R 2 2 2 4 3 +--R (- 2c - 14a c + 8b + 16a )cosh(x) + 24a b cosh(x) +--R + +--R 2 2 2 2 +--R (2c - 2a c + 8b )cosh(x) + 4b c cosh(x) + 2c - 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 +--R (c + (b + a)c)sinh(x) +--R + +--R 2 5 +--R ((4c + (4b + 4a)c)cosh(x) + (2b + 2a)c)sinh(x) +--R + +--R 2 2 2 2 +--R (5c + (5b + 5a)c)cosh(x) + ((6b + 10a)c - 4b - 4a b)cosh(x) + 3c +--R + +--R 2 +--R (3b + 3a)c + 4b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 +--R ((4b + 20a)c - 16b - 16a b)cosh(x) +--R + +--R 2 2 2 2 +--R (8c + 8b c + 16b + 8a b - 8a )cosh(x) + (4b + 4a)c + 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 +--R (- 5c + (- 5b - 5a)c)cosh(x) +--R + +--R 2 3 +--R ((- 4b + 20a)c - 24b - 24a b)cosh(x) +--R + +--R 2 2 2 2 +--R (6c + (6b - 18a)c + 24b - 24a )cosh(x) +--R + +--R 2 2 2 2 +--R ((8b + 12a)c - 4b + 20a b + 24a )cosh(x) + 3c + (3b + 3a)c + 4b +--R + +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 +--R (- 4c + (- 4b - 4a)c)cosh(x) +--R + +--R 2 4 +--R ((- 6b + 10a)c - 16b - 16a b)cosh(x) +--R + +--R 2 2 3 +--R (- 24a c + 16b - 8a b - 24a )cosh(x) +--R + +--R 2 2 2 +--R ((4b + 12a)c - 8b + 16a b + 24a )cosh(x) +--R + +--R 2 2 +--R (4c + (4b + 4a)c + 8b + 8a b)cosh(x) + (2b + 2a)c +--R * +--R sinh(x) +--R + +--R 2 6 2 5 +--R (- c + (- b - a)c)cosh(x) + ((- 2b + 2a)c - 4b - 4a b)cosh(x) +--R + +--R 2 2 2 4 +--R (- c + (- b - 9a)c + 4b - 4a b - 8a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (4a c - 4b + 4a b + 8a )cosh(x) + (c + (b + a)c + 4b + 4a b)cosh(x) +--R + +--R 2 +--R (2b + 2a)c cosh(x) + c + (b + a)c +--R / +--R 3 2 5 +--R (2c + (- 2b + 2a)c )sinh(x) +--R + +--R 3 2 2 2 4 +--R ((10c + (- 10b + 10a)c )cosh(x) + 4b c + (- 4b + 4a b)c)sinh(x) +--R + +--R 3 2 2 +--R (20c + (- 20b + 20a)c )cosh(x) +--R + +--R 2 2 3 2 +--R (16b c + (- 16b + 16a b)c)cosh(x) + 4c + (- 4b + 12a)c +--R + +--R 2 +--R (- 8a b + 8a )c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3 +--R (20c + (- 20b + 20a)c )cosh(x) +--R + +--R 2 2 2 +--R (24b c + (- 24b + 24a b)c)cosh(x) +--R + +--R 3 2 2 2 +--R (12c + (- 12b + 36a)c + (- 24a b + 24a )c)cosh(x) + 4b c +--R + +--R 2 +--R (- 4b + 4a b)c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 +--R (10c + (- 10b + 10a)c )cosh(x) +--R + +--R 2 2 3 +--R (16b c + (- 16b + 16a b)c)cosh(x) +--R + +--R 3 2 2 2 +--R (12c + (- 12b + 36a)c + (- 24a b + 24a )c)cosh(x) +--R + +--R 2 2 3 2 +--R (8b c + (- 8b + 8a b)c)cosh(x) + 2c + (- 2b + 2a)c +--R * +--R sinh(x) +--R + +--R 3 2 5 2 2 4 +--R (2c + (- 2b + 2a)c )cosh(x) + (4b c + (- 4b + 4a b)c)cosh(x) +--R + +--R 3 2 2 3 +--R (4c + (- 4b + 12a)c + (- 8a b + 8a )c)cosh(x) +--R + +--R 2 2 2 3 2 +--R (4b c + (- 4b + 4a b)c)cosh(x) + (2c + (- 2b + 2a)c )cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 3 2 5 +--R (4c - 4a c )sinh(x) +--R + +--R 3 2 2 4 +--R ((20c - 20a c )cosh(x) + 8b c - 8a b c)sinh(x) +--R + +--R 3 2 2 2 3 2 +--R (40c - 40a c )cosh(x) + (32b c - 32a b c)cosh(x) + 8c + 8a c +--R + +--R 2 +--R - 16a c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3 2 2 +--R (40c - 40a c )cosh(x) + (48b c - 48a b c)cosh(x) +--R + +--R 3 2 2 2 +--R (24c + 24a c - 48a c)cosh(x) + 8b c - 8a b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 2 3 +--R (20c - 20a c )cosh(x) + (32b c - 32a b c)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (24c + 24a c - 48a c)cosh(x) + (16b c - 16a b c)cosh(x) + 4c +--R + +--R 2 +--R - 4a c +--R * +--R sinh(x) +--R + +--R 3 2 5 2 4 +--R (4c - 4a c )cosh(x) + (8b c - 8a b c)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8c + 8a c - 16a c)cosh(x) + (8b c - 8a b c)cosh(x) +--R + +--R 3 2 +--R (4c - 4a c )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 5 +--R (2c + (2b + 2a)c )sinh(x) +--R + +--R 3 2 2 2 4 +--R ((10c + (10b + 10a)c )cosh(x) + 4b c + (4b + 4a b)c)sinh(x) +--R + +--R 3 2 2 2 2 +--R (20c + (20b + 20a)c )cosh(x) + (16b c + (16b + 16a b)c)cosh(x) +--R + +--R 3 2 2 +--R 4c + (4b + 12a)c + (8a b + 8a )c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3 2 2 2 +--R (20c + (20b + 20a)c )cosh(x) + (24b c + (24b + 24a b)c)cosh(x) +--R + +--R 3 2 2 2 2 +--R (12c + (12b + 36a)c + (24a b + 24a )c)cosh(x) + 4b c + (4b + 4a b)c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 2 2 3 +--R (10c + (10b + 10a)c )cosh(x) + (16b c + (16b + 16a b)c)cosh(x) +--R + +--R 3 2 2 2 +--R (12c + (12b + 36a)c + (24a b + 24a )c)cosh(x) +--R + +--R 2 2 3 2 +--R (8b c + (8b + 8a b)c)cosh(x) + 2c + (2b + 2a)c +--R * +--R sinh(x) +--R + +--R 3 2 5 2 2 4 +--R (2c + (2b + 2a)c )cosh(x) + (4b c + (4b + 4a b)c)cosh(x) +--R + +--R 3 2 2 3 +--R (4c + (4b + 12a)c + (8a b + 8a )c)cosh(x) +--R + +--R 2 2 2 3 2 +--R (4b c + (4b + 4a b)c)cosh(x) + (2c + (2b + 2a)c )cosh(x) +--R Type: Expression(Integer) +--E 302 + +)clear all + + +--S 303 of 531 +t1054:= (d+e*cosh(x))/(a+b*cosh(x)+c*cosh(x)^2) +--R +--R +--R e cosh(x) + d +--R (1) -------------------------- +--R 2 +--R c cosh(x) + b cosh(x) + a +--R Type: Expression(Integer) +--E 303 + +--S 304 of 531 +r1054:= -2^(1/2)*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atan(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*tanh(1/2*x)*2^(1/2)/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)-2*(e-(2*c*d-b*e)/_ + (b^2-4*a*c)^(1/2))*atan((b+(b^2-4*a*c)^(1/2)-2*c)*tanh(1/2*x)/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (- 2e\|- 4a c + b - 2b e + 4c d)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + (- 2c + b)tanh(-) +--R 2 2 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (e\|2 \|- 4a c + b + (- b e + 2c d)\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tanh(-)\|- 4a c + b + (2c - b)\|2 tanh(-) +--R 2 2 +--R atan(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 304 + +--S 305 of 531 +a1054:= integrate(t1054,x) +--R +--R +--R (3) +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 2 2 2 2 2 +--R (- 4a c + 2b - 4a )e + (- 4b c + 4a b)d e + (4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R e +--R + +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 24a )c + (18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 +--R (- 3b + 22a b - 8a )c + (- 8a b + 6a b )c + b +--R + +--R 2 4 +--R - a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 3 2 3 3 +--R (4a b c + (- b + 4a b)c - a b )e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (- 8a c + (2b - 16a )c - 8a c + b + 2a b )d e +--R + +--R 2 3 2 3 2 2 4 3 +--R (12a b c + (- 3b + 12a b)c - 3a b )d e + (- 4a b c + b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (- 4a c + 2b - 4a )e + (- 4b c + 4a b)d e +--R + +--R 2 2 2 +--R (4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c + 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R e +--R + +--R 3 3 2 2 3 3 5 +--R - 8a b c + (2b - 16a b)c + (12a b - 8a b)c - 2b +--R + +--R 2 3 +--R 2a b +--R * +--R d e +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R 2 +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R sinh(x) +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R cosh(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c - 4a b c - 2b )d e + 2b c d +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 2 +--R (- 4a c + 2b - 4a )e + (- 4b c + 4a b)d e +--R + +--R 2 2 2 +--R (4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R e +--R + +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 24a )c + (18a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 +--R (- 3b + 22a b - 8a )c + (- 8a b + 6a b )c + b +--R + +--R 2 4 +--R - a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 3 2 3 3 +--R (- 4a b c + (b - 4a b)c + a b )e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (8a c + (- 2b + 16a )c + 8a c - b - 2a b )d e +--R + +--R 2 3 2 3 2 2 4 3 +--R (- 12a b c + (3b - 12a b)c + 3a b )d e + (4a b c - b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (- 4a c + 2b - 4a )e + (- 4b c + 4a b)d e +--R + +--R 2 2 2 +--R (4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 2 +--R e +--R + +--R 3 3 2 2 3 3 5 +--R 8a b c + (- 2b + 16a b)c + (- 12a b + 8a b)c + 2b +--R + +--R 2 3 +--R - 2a b +--R * +--R d e +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R 2 +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R sinh(x) +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R cosh(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c - 4a b c - 2b )d e + 2b c d +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 2 2 2 2 2 +--R (- 4a c + 2b - 4a )e + (- 4b c + 4a b)d e + (4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R e +--R + +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 24a )c + (- 18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b - 22a b + 8a )c + (8a b - 6a b )c - b + a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 3 2 3 3 +--R (4a b c + (- b + 4a b)c - a b )e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (- 8a c + (2b - 16a )c - 8a c + b + 2a b )d e +--R + +--R 2 3 2 3 2 2 4 3 +--R (12a b c + (- 3b + 12a b)c - 3a b )d e + (- 4a b c + b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (- 4a c + 2b - 4a )e + (- 4b c + 4a b)d e +--R + +--R 2 2 2 +--R (4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 2 +--R e +--R + +--R 3 3 2 2 3 3 5 +--R 8a b c + (- 2b + 16a b)c + (- 12a b + 8a b)c + 2b +--R + +--R 2 3 +--R - 2a b +--R * +--R d e +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R 2 +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R sinh(x) +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R cosh(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c - 4a b c - 2b )d e + 2b c d +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 2 +--R (- 4a c + 2b - 4a )e + (- 4b c + 4a b)d e +--R + +--R 2 2 2 +--R (4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R e +--R + +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 24a )c + (- 18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b - 22a b + 8a )c + (8a b - 6a b )c - b + a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 3 2 3 3 +--R (- 4a b c + (b - 4a b)c + a b )e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (8a c + (- 2b + 16a )c + 8a c - b - 2a b )d e +--R + +--R 2 3 2 3 2 2 4 3 +--R (- 12a b c + (3b - 12a b)c + 3a b )d e + (4a b c - b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (- 4a c + 2b - 4a )e + (- 4b c + 4a b)d e +--R + +--R 2 2 2 +--R (4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c + 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R e +--R + +--R 3 3 2 2 3 3 5 +--R - 8a b c + (2b - 16a b)c + (12a b - 8a b)c - 2b +--R + +--R 2 3 +--R 2a b +--R * +--R d e +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R 2 +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R sinh(x) +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R cosh(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c - 4a b c - 2b )d e + 2b c d +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 305 + +--S 306 of 531 +m1054:= a1054-r1054 +--R +--R +--R (4) +--R 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- 8a )c - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 2 +--R e +--R + +--R 3 3 2 2 3 3 5 +--R 8a b c + (- 2b + 16a b)c + (- 12a b + 8a b)c + 2b +--R + +--R 2 3 +--R - 2a b +--R * +--R d e +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R 2 +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R sinh(x) +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R cosh(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c - 4a b c - 2b )d e + 2b c d +--R + +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 2 +--R (- 4a c + 2b - 4a )e + (- 4b c + 4a b)d e +--R + +--R 2 2 2 +--R (4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R e +--R + +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 24a )c + (- 18a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 6 2 4 +--R (3b - 22a b + 8a )c + (8a b - 6a b )c - b + a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 3 2 3 3 +--R (- 4a b c + (b - 4a b)c + a b )e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (8a c + (- 2b + 16a )c + 8a c - b - 2a b )d e +--R + +--R 2 3 2 3 2 2 4 3 +--R (- 12a b c + (3b - 12a b)c + 3a b )d e + (4a b c - b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (- 4a c + 2b - 4a )e + (- 4b c + 4a b)d e +--R + +--R 2 2 2 +--R (4c + 4a c - 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 4 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c + 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R e +--R + +--R 3 3 2 2 3 3 5 +--R - 8a b c + (2b - 16a b)c + (12a b - 8a b)c - 2b +--R + +--R 2 3 +--R 2a b +--R * +--R d e +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R 2 +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R sinh(x) +--R + +--R 4 2 2 2 3 +--R 4a b c e + (- 8a c + (- 4b - 8a )c)d e +--R + +--R 2 2 2 3 2 2 3 2 4 +--R (12b c + 12a b c)d e + (- 8c - 8a c - 4b c)d e + 4b c d +--R * +--R cosh(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c - 4a b c - 2b )d e + 2b c d +--R + +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (4e\|- 4a c + b + 4b e - 8c d)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tanh(-)\|- 4a c + b + (- 2c + b)tanh(-) +--R 2 2 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (- 2e\|2 \|- 4a c + b + (2b e - 4c d)\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tanh(-)\|- 4a c + b + (2c - b)\|2 tanh(-) +--R 2 2 +--R atan(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 306 + +--S 307 of 531 +d1054:= D(m1054,x) +--R +--R +--R (5) +--R 4 +--R (c e - c d)sinh(x) +--R + +--R 3 +--R ((4c e - 4c d)cosh(x) + (2c + 2a)e - 2b d)sinh(x) +--R + +--R 2 +--R (6c e - 6c d)cosh(x) + ((6c + 6a)e - 6b d)cosh(x) + (2c + 4a)e +--R + +--R (2c - 4b)d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 +--R (4c e - 4c d)cosh(x) + ((6c + 6a)e - 6b d)cosh(x) +--R + +--R ((4c + 8a)e + (4c - 8b)d)cosh(x) + (2c + 2a)e - 2b d +--R * +--R sinh(x) +--R + +--R 4 3 +--R (c e - c d)cosh(x) + ((2c + 2a)e - 2b d)cosh(x) +--R + +--R 2 +--R ((2c + 4a)e + (2c - 4b)d)cosh(x) + ((2c + 2a)e - 2b d)cosh(x) + c e +--R + +--R - c d +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R 2c d sinh(x) + (8c d cosh(x) + (4c - 4a)e + 4b d)sinh(x) +--R + +--R 2 2 +--R (12c d cosh(x) + ((12c - 12a)e + 12b d)cosh(x) + 12c d)sinh(x) +--R + +--R 3 2 +--R 8c d cosh(x) + ((12c - 12a)e + 12b d)cosh(x) + 24c d cosh(x) +--R + +--R (4c - 4a)e + 4b d +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R 2c d cosh(x) + ((4c - 4a)e + 4b d)cosh(x) + 12c d cosh(x) +--R + +--R ((4c - 4a)e + 4b d)cosh(x) + 2c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 +--R (- c e - c d)sinh(x) +--R + +--R 3 +--R ((- 4c e - 4c d)cosh(x) + (2c + 2a)e - 2b d)sinh(x) +--R + +--R 2 +--R (- 6c e - 6c d)cosh(x) + ((6c + 6a)e - 6b d)cosh(x) + (- 2c - 4a)e +--R + +--R (2c + 4b)d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 +--R (- 4c e - 4c d)cosh(x) + ((6c + 6a)e - 6b d)cosh(x) +--R + +--R ((- 4c - 8a)e + (4c + 8b)d)cosh(x) + (2c + 2a)e - 2b d +--R * +--R sinh(x) +--R + +--R 4 3 +--R (- c e - c d)cosh(x) + ((2c + 2a)e - 2b d)cosh(x) +--R + +--R 2 +--R ((- 2c - 4a)e + (2c + 4b)d)cosh(x) + ((2c + 2a)e - 2b d)cosh(x) - c e +--R + +--R - c d +--R / +--R 2 4 +--R (c + (- b + a)c)sinh(x) +--R + +--R 2 2 3 +--R ((4c + (- 4b + 4a)c)cosh(x) + 2b c - 2b + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (6c + (- 6b + 6a)c)cosh(x) + (6b c - 6b + 6a b)cosh(x) + 2c +--R + +--R 2 +--R (- 2b + 6a)c - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4c + (- 4b + 4a)c)cosh(x) + (6b c - 6b + 6a b)cosh(x) +--R + +--R 2 2 2 +--R (4c + (- 4b + 12a)c - 8a b + 8a )cosh(x) + 2b c - 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 +--R (c + (- b + a)c)cosh(x) + (2b c - 2b + 2a b)cosh(x) +--R + +--R 2 2 2 +--R (2c + (- 2b + 6a)c - 4a b + 4a )cosh(x) +--R + +--R 2 2 +--R (2b c - 2b + 2a b)cosh(x) + c + (- b + a)c +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (2c - 2a c)sinh(x) + ((8c - 8a c)cosh(x) + 4b c - 4a b)sinh(x) +--R + +--R 2 2 2 +--R (12c - 12a c)cosh(x) + (12b c - 12a b)cosh(x) + 4c + 4a c +--R + +--R 2 +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (8c - 8a c)cosh(x) + (12b c - 12a b)cosh(x) +--R + +--R 2 2 +--R (8c + 8a c - 16a )cosh(x) + 4b c - 4a b +--R * +--R sinh(x) +--R + +--R 2 4 3 +--R (2c - 2a c)cosh(x) + (4b c - 4a b)cosh(x) +--R + +--R 2 2 2 2 +--R (4c + 4a c - 8a )cosh(x) + (4b c - 4a b)cosh(x) + 2c - 2a c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 +--R (c + (b + a)c)sinh(x) +--R + +--R 2 2 3 +--R ((4c + (4b + 4a)c)cosh(x) + 2b c + 2b + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (6c + (6b + 6a)c)cosh(x) + (6b c + 6b + 6a b)cosh(x) + 2c +--R + +--R 2 +--R (2b + 6a)c + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4c + (4b + 4a)c)cosh(x) + (6b c + 6b + 6a b)cosh(x) +--R + +--R 2 2 2 +--R (4c + (4b + 12a)c + 8a b + 8a )cosh(x) + 2b c + 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 +--R (c + (b + a)c)cosh(x) + (2b c + 2b + 2a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (2c + (2b + 6a)c + 4a b + 4a )cosh(x) + (2b c + 2b + 2a b)cosh(x) + c +--R + +--R (b + a)c +--R Type: Expression(Integer) +--E 307 + +)clear all + + +--S 308 of 531 +t1055:= sinh(x)^2/(a*cosh(x)^2+b*sinh(x)^2) +--R +--R +--R 2 +--R sinh(x) +--R (1) ----------------------- +--R 2 2 +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 308 + +--S 309 of 531 +r1055:= x/(a+b)+a^(1/2)*atan(a^(1/2)*coth(x)/b^(1/2))/b^(1/2)/(a+b) +--R +--R +--R +-+ +--R +-+ coth(x)\|a +-+ +--R \|a atan(-----------) + x\|b +--R +-+ +--R \|b +--R (2) ----------------------------- +--R +-+ +--R (b + a)\|b +--R Type: Expression(Integer) +--E 309 + +--S 310 of 531 +a1055:= integrate(t1055,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +--R |- - +--R \| b +--R * +--R log +--R 2 2 2 +--R (- 4b - 4a b)sinh(x) + (- 8b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 4b - 4a b)cosh(x) + 4b - 4a b +--R * +--R +---+ +--R | a +--R |- - +--R \| b +--R + +--R 2 2 4 2 2 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a b + 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a b + 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (- 2b + 2a )cosh(x) + b - 6a b +--R + +--R 2 +--R a +--R / +--R 4 3 +--R (b + a)sinh(x) + (4b + 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((6b + 6a)cosh(x) - 2b + 2a)sinh(x) +--R + +--R 3 +--R ((4b + 4a)cosh(x) + (- 4b + 4a)cosh(x))sinh(x) +--R + +--R 4 2 +--R (b + a)cosh(x) + (- 2b + 2a)cosh(x) + b + a +--R + +--R 2x +--R / +--R 2b + 2a +--R , +--R +--R +-+ +--R |a +--R |- +--R \|b +--R * +--R atan +--R +-+ +--R |a +--R 2b |- +--R \|b +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R x +--R / +--R b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 310 + +--S 311 of 531 +m1055a:= a1055.1-r1055 +--R +--R +--R (4) +--R +---+ +--R | a +-+ +--R |- - \|b +--R \| b +--R * +--R log +--R 2 2 2 +--R (- 4b - 4a b)sinh(x) + (- 8b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 4b - 4a b)cosh(x) + 4b - 4a b +--R * +--R +---+ +--R | a +--R |- - +--R \| b +--R + +--R 2 2 4 2 2 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a b + 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a b + 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (- 2b + 2a )cosh(x) + b - 6a b + a +--R / +--R 4 3 +--R (b + a)sinh(x) + (4b + 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((6b + 6a)cosh(x) - 2b + 2a)sinh(x) +--R + +--R 3 +--R ((4b + 4a)cosh(x) + (- 4b + 4a)cosh(x))sinh(x) +--R + +--R 4 2 +--R (b + a)cosh(x) + (- 2b + 2a)cosh(x) + b + a +--R + +--R +-+ +--R +-+ coth(x)\|a +--R - 2\|a atan(-----------) +--R +-+ +--R \|b +--R / +--R +-+ +--R (2b + 2a)\|b +--R Type: Expression(Integer) +--E 311 + +--S 312 of 531 +d1055a:= D(m1055a,x) +--R +--R +--R (5) +--R 2 4 2 3 +--R (a coth(x) - a)sinh(x) + (4a cosh(x)coth(x) - 4a cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R ((6a cosh(x) - 2a)coth(x) - 6a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 3 +--R ((4a cosh(x) - 4a cosh(x))coth(x) - 4a cosh(x) - 4a cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (a cosh(x) - 2a cosh(x) + a)coth(x) - a cosh(x) - 2a cosh(x) - a +--R / +--R 2 2 2 4 +--R ((a b + a )coth(x) + b + a b)sinh(x) +--R + +--R 2 2 2 3 +--R ((4a b + 4a )cosh(x)coth(x) + (4b + 4a b)cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6a b + 6a )cosh(x) - 2a b + 2a )coth(x) + (6b + 6a b)cosh(x) +--R + +--R 2 +--R - 2b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R ((4a b + 4a )cosh(x) + (- 4a b + 4a )cosh(x))coth(x) +--R + +--R 2 3 2 +--R (4b + 4a b)cosh(x) + (- 4b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R ((a b + a )cosh(x) + (- 2a b + 2a )cosh(x) + a b + a )coth(x) +--R + +--R 2 4 2 2 2 +--R (b + a b)cosh(x) + (- 2b + 2a b)cosh(x) + b + a b +--R Type: Expression(Integer) +--E 312 + +--S 313 of 531 +m1055b:= a1055.2-r1055 +--R +--R +--R (6) +--R +-+ +--R |a +-+ +--R |- \|b +--R \|b +--R * +--R +-+ +--R |a +--R 2b |- +--R \|b +--R atan(-------------------------------------------------------------------) +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b + a +--R + +--R +-+ +--R +-+ coth(x)\|a +--R - \|a atan(-----------) +--R +-+ +--R \|b +--R / +--R +-+ +--R (b + a)\|b +--R Type: Expression(Integer) +--E 313 + +--S 314 of 531 +d1055b:= D(m1055b,x) +--R +--R +--R (7) +--R 2 4 2 3 +--R (a coth(x) - a)sinh(x) + (4a cosh(x)coth(x) - 4a cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R ((6a cosh(x) - 2a)coth(x) - 6a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 3 +--R ((4a cosh(x) - 4a cosh(x))coth(x) - 4a cosh(x) - 4a cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (a cosh(x) - 2a cosh(x) + a)coth(x) - a cosh(x) - 2a cosh(x) - a +--R / +--R 2 2 2 4 +--R ((a b + a )coth(x) + b + a b)sinh(x) +--R + +--R 2 2 2 3 +--R ((4a b + 4a )cosh(x)coth(x) + (4b + 4a b)cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6a b + 6a )cosh(x) - 2a b + 2a )coth(x) + (6b + 6a b)cosh(x) +--R + +--R 2 +--R - 2b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R ((4a b + 4a )cosh(x) + (- 4a b + 4a )cosh(x))coth(x) +--R + +--R 2 3 2 +--R (4b + 4a b)cosh(x) + (- 4b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R ((a b + a )cosh(x) + (- 2a b + 2a )cosh(x) + a b + a )coth(x) +--R + +--R 2 4 2 2 2 +--R (b + a b)cosh(x) + (- 2b + 2a b)cosh(x) + b + a b +--R Type: Expression(Integer) +--E 314 + +)clear all + + +--S 315 of 531 +t1056:= cosh(x)^2/(a*cosh(x)^2+b*sinh(x)^2) +--R +--R +--R 2 +--R cosh(x) +--R (1) ----------------------- +--R 2 2 +--R b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 315 + +--S 316 of 531 +r1056:= x/(a+b)+b^(1/2)*atan(b^(1/2)*tanh(x)/a^(1/2))/a^(1/2)/(a+b) +--R +--R +--R +-+ +--R +-+ tanh(x)\|b +-+ +--R \|b atan(-----------) + x\|a +--R +-+ +--R \|a +--R (2) ----------------------------- +--R +-+ +--R (b + a)\|a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 531 +a1056:= integrate(t1056,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +--R |- - +--R \| a +--R * +--R log +--R 2 2 2 +--R (4a b + 4a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (4a b + 4a )cosh(x) - 4a b + 4a +--R * +--R +---+ +--R | b +--R |- - +--R \| a +--R + +--R 2 2 4 2 2 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a b + 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a b + 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (- 2b + 2a )cosh(x) + b - 6a b +--R + +--R 2 +--R a +--R / +--R 4 3 +--R (b + a)sinh(x) + (4b + 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((6b + 6a)cosh(x) - 2b + 2a)sinh(x) +--R + +--R 3 +--R ((4b + 4a)cosh(x) + (- 4b + 4a)cosh(x))sinh(x) +--R + +--R 4 2 +--R (b + a)cosh(x) + (- 2b + 2a)cosh(x) + b + a +--R + +--R 2x +--R / +--R 2b + 2a +--R , +--R +--R - +--R +-+ +--R |b +--R |- +--R \|a +--R * +--R atan +--R +-+ +--R |b +--R 2a |- +--R \|a +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R x +--R / +--R b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 317 + +--S 318 of 531 +m1056a:= a1056.1-r1056 +--R +--R +--R (4) +--R +---+ +--R | b +-+ +--R |- - \|a +--R \| a +--R * +--R log +--R 2 2 2 +--R (4a b + 4a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (4a b + 4a )cosh(x) - 4a b + 4a +--R * +--R +---+ +--R | b +--R |- - +--R \| a +--R + +--R 2 2 4 2 2 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a b + 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a b + 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (- 2b + 2a )cosh(x) + b - 6a b + a +--R / +--R 4 3 +--R (b + a)sinh(x) + (4b + 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((6b + 6a)cosh(x) - 2b + 2a)sinh(x) +--R + +--R 3 +--R ((4b + 4a)cosh(x) + (- 4b + 4a)cosh(x))sinh(x) +--R + +--R 4 2 +--R (b + a)cosh(x) + (- 2b + 2a)cosh(x) + b + a +--R + +--R +-+ +--R +-+ tanh(x)\|b +--R - 2\|b atan(-----------) +--R +-+ +--R \|a +--R / +--R +-+ +--R (2b + 2a)\|a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 531 +d1056a:= D(m1056a,x) +--R +--R +--R (5) +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (- 4b cosh(x) + 4b cosh(x))sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 2 4 2 3 +--R (b + a b)sinh(x) + (4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((6b + 6a b)cosh(x) - 2b + 2a b)sinh(x) +--R + +--R 2 3 2 +--R ((4b + 4a b)cosh(x) + (- 4b + 4a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (b + a b)cosh(x) + (- 2b + 2a b)cosh(x) + b + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (a b + a )sinh(x) + (4a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((6a b + 6a )cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((4a b + 4a )cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (a b + a )cosh(x) + (- 2a b + 2a )cosh(x) + a b + a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 531 +m1056b:= a1056.2-r1056 +--R +--R +--R (6) +--R +-+ +--R +-+ tanh(x)\|b +--R - \|b atan(-----------) +--R +-+ +--R \|a +--R + +--R - +--R +-+ +--R +-+ |b +--R \|a |- +--R \|a +--R * +--R atan +--R +-+ +--R |b +--R 2a |- +--R \|a +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R / +--R +-+ +--R (b + a)\|a +--R Type: Expression(Integer) +--E 320 + +--S 321 of 531 +d1056b:= D(m1056b,x) +--R +--R +--R (7) +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (- 4b cosh(x) + 4b cosh(x))sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 2 4 2 3 +--R (b + a b)sinh(x) + (4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((6b + 6a b)cosh(x) - 2b + 2a b)sinh(x) +--R + +--R 2 3 2 +--R ((4b + 4a b)cosh(x) + (- 4b + 4a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (b + a b)cosh(x) + (- 2b + 2a b)cosh(x) + b + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (a b + a )sinh(x) + (4a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((6a b + 6a )cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((4a b + 4a )cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (a b + a )cosh(x) + (- 2a b + 2a )cosh(x) + a b + a +--R Type: Expression(Integer) +--E 321 + +)clear all + + +--S 322 of 531 +t1057:= sinh(x)^3/(cosh(x)^3+sinh(x)^3) +--R +--R +--R 3 +--R sinh(x) +--R (1) ------------------- +--R 3 3 +--R sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 322 + +--S 323 of 531 +r1057:= 1/2*x-2/9*atan(1/3*(1-2*coth(x))*3^(1/2))*3^(1/2)-1/(6+6*coth(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ 2\|3 coth(x) - \|3 +--R (4\|3 coth(x) + 4\|3 )atan(-------------------) + 9x coth(x) + 9x - 3 +--R 3 +--R (2) --------------------------------------------------------------------- +--R 18coth(x) + 18 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 531 +a1057:= integrate(t1057,x) +--R +--R +--R (3) +--R +-+ +-+ +--R 2 2 \|3 sinh(x) + \|3 cosh(x) +--R (8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) )atan(-------------------------) +--R 3sinh(x) - 3cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R 6x\|3 sinh(x) + 12x\|3 cosh(x)sinh(x) + 6x\|3 cosh(x) + \|3 +--R / +--R +-+ 2 +-+ +-+ 2 +--R 12\|3 sinh(x) + 24\|3 cosh(x)sinh(x) + 12\|3 cosh(x) +--R Type: Union(Expression(Integer),...) +--E 324 + +--S 325 of 531 +m1057:= a1057-r1057 +--R +--R +--R (4) +--R 2 +--R (- 8coth(x) - 8)sinh(x) + (- 16cosh(x)coth(x) - 16cosh(x))sinh(x) +--R + +--R 2 2 +--R - 8cosh(x) coth(x) - 8cosh(x) +--R * +--R +-+ +-+ +--R 2\|3 coth(x) - \|3 +--R atan(-------------------) +--R 3 +--R + +--R 2 +--R (8coth(x) + 8)sinh(x) + (16cosh(x)coth(x) + 16cosh(x))sinh(x) +--R + +--R 2 2 +--R 8cosh(x) coth(x) + 8cosh(x) +--R * +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R atan(-------------------------) +--R 3sinh(x) - 3cosh(x) +--R + +--R +-+ 2 +-+ +-+ +-+ 2 +-+ +--R 2\|3 sinh(x) + 4\|3 cosh(x)sinh(x) + \|3 coth(x) + 2\|3 cosh(x) + \|3 +--R / +--R +-+ +-+ 2 +--R (12\|3 coth(x) + 12\|3 )sinh(x) +--R + +--R +-+ +-+ +-+ 2 +--R (24\|3 cosh(x)coth(x) + 24\|3 cosh(x))sinh(x) + 12\|3 cosh(x) coth(x) +--R + +--R +-+ 2 +--R 12\|3 cosh(x) +--R Type: Expression(Integer) +--E 325 + +--S 326 of 531 +d1057:= D(m1057,x) +--R +--R +--R (5) +--R 3 4 3 3 +--R (5coth(x) - 1)sinh(x) + (7cosh(x)coth(x) + cosh(x))sinh(x) +--R + +--R 3 2 +--R (- coth(x) - 1)sinh(x) +--R + +--R 3 3 3 +--R ((- cosh(x) + cosh(x))coth(x) - 7cosh(x) + cosh(x))sinh(x) +--R + +--R 4 2 3 4 2 +--R (cosh(x) - cosh(x) )coth(x) - 5cosh(x) - cosh(x) +--R / +--R 3 4 3 3 +--R (6coth(x) + 6)sinh(x) + (6cosh(x)coth(x) + 6cosh(x))sinh(x) +--R + +--R 3 3 3 4 3 4 +--R (6cosh(x) coth(x) + 6cosh(x) )sinh(x) + 6cosh(x) coth(x) + 6cosh(x) +--R Type: Expression(Integer) +--E 326 + +)clear all + + +--S 327 of 531 +t1058:= cosh(x)^3/(cosh(x)^3+sinh(x)^3) +--R +--R +--R 3 +--R cosh(x) +--R (1) ------------------- +--R 3 3 +--R sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 327 + +--S 328 of 531 +r1058:= 1/2*x-2/9*atan(1/3*(1-2*tanh(x))*3^(1/2))*3^(1/2)-1/(6+6*tanh(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ 2\|3 tanh(x) - \|3 +--R (4\|3 tanh(x) + 4\|3 )atan(-------------------) + 9x tanh(x) + 9x - 3 +--R 3 +--R (2) --------------------------------------------------------------------- +--R 18tanh(x) + 18 +--R Type: Expression(Integer) +--E 328 + +--S 329 of 531 +a1058:= integrate(t1058,x) +--R +--R +--R (3) +--R 2 2 +--R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) ) +--R * +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R atan(-------------------------) +--R 3sinh(x) - 3cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R 6x\|3 sinh(x) + 12x\|3 cosh(x)sinh(x) + 6x\|3 cosh(x) - \|3 +--R / +--R +-+ 2 +-+ +-+ 2 +--R 12\|3 sinh(x) + 24\|3 cosh(x)sinh(x) + 12\|3 cosh(x) +--R Type: Union(Expression(Integer),...) +--E 329 + +--S 330 of 531 +m1058:= a1058-r1058 +--R +--R +--R (4) +--R 2 2 2 +--R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )tanh(x) - 8sinh(x) +--R + +--R 2 +--R - 16cosh(x)sinh(x) - 8cosh(x) +--R * +--R +-+ +-+ +--R 2\|3 tanh(x) - \|3 +--R atan(-------------------) +--R 3 +--R + +--R 2 2 2 +--R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )tanh(x) - 8sinh(x) +--R + +--R 2 +--R - 16cosh(x)sinh(x) - 8cosh(x) +--R * +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R atan(-------------------------) +--R 3sinh(x) - 3cosh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ 2 +-+ +--R - \|3 tanh(x) + 2\|3 sinh(x) + 4\|3 cosh(x)sinh(x) + 2\|3 cosh(x) - \|3 +--R / +--R +-+ 2 +-+ +-+ 2 +--R (12\|3 sinh(x) + 24\|3 cosh(x)sinh(x) + 12\|3 cosh(x) )tanh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R 12\|3 sinh(x) + 24\|3 cosh(x)sinh(x) + 12\|3 cosh(x) +--R Type: Expression(Integer) +--E 330 + +--S 331 of 531 +d1058:= D(m1058,x) +--R +--R +--R (5) +--R 4 3 2 3 +--R sinh(x) - cosh(x)sinh(x) + sinh(x) + (7cosh(x) - cosh(x))sinh(x) +--R + +--R 4 2 +--R 5cosh(x) + cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 4 3 2 3 +--R - 5sinh(x) - 7cosh(x)sinh(x) + sinh(x) + (cosh(x) - cosh(x))sinh(x) +--R + +--R 4 2 +--R - cosh(x) + cosh(x) +--R / +--R 4 3 3 4 3 +--R (6sinh(x) + 6cosh(x)sinh(x) + 6cosh(x) sinh(x) + 6cosh(x) )tanh(x) +--R + +--R 4 3 3 4 +--R 6sinh(x) + 6cosh(x)sinh(x) + 6cosh(x) sinh(x) + 6cosh(x) +--R Type: Expression(Integer) +--E 331 + +)clear all + + +--S 332 of 531 +t1059:= exp(1)^(a+b*x)*sinh(a+b*x) +--R +--R +--R b x + a +--R (1) %e sinh(b x + a) +--R Type: Expression(Integer) +--E 332 + +--S 333 of 531 +r1059:= 1/4*(exp(2*a+2*b*x)-2*b*x)/b +--R +--R +--R 2b x + 2a +--R %e - 2b x +--R (2) ------------------ +--R 4b +--R Type: Expression(Integer) +--E 333 + +--S 334 of 531 +a1059:= integrate(t1059,x) +--R +--R +--R (- 2b x - 1)sinh(b x + a) + (2b x - 1)cosh(b x + a) +--R (3) --------------------------------------------------- +--R 4b sinh(b x + a) - 4b cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 334 + +--S 335 of 531 +m1059:= a1059-r1059 +--R +--R +--R (4) +--R 2b x + 2a 2b x + 2a +--R (- %e - 1)sinh(b x + a) + cosh(b x + a)%e - cosh(b x + a) +--R --------------------------------------------------------------------------- +--R 4b sinh(b x + a) - 4b cosh(b x + a) +--R Type: Expression(Integer) +--E 335 + +--S 336 of 531 +d1059:= D(m1059,x) +--R +--R +--R (5) +--R 2b x + 2a 2b x + 2a +--R (- %e - 1)sinh(b x + a) + cosh(b x + a)%e - cosh(b x + a) +--R --------------------------------------------------------------------------- +--R 2sinh(b x + a) - 2cosh(b x + a) +--R Type: Expression(Integer) +--E 336 + +)clear all + + +--S 337 of 531 +t1060:= exp(1)^(a+b*x)*sinh(a+b*x)^3 +--R +--R +--R b x + a 3 +--R (1) %e sinh(b x + a) +--R Type: Expression(Integer) +--E 337 + +--S 338 of 531 +r1060:= 1/32*(2*exp(-2*a-2*b*x)-6*exp(2*a+2*b*x)+exp(4*a+4*b*x)+12*b*x)/b +--R +--R +--R 4b x + 4a 2b x + 2a - 2b x - 2a +--R %e - 6%e + 2%e + 12b x +--R (2) --------------------------------------------------- +--R 32b +--R Type: Expression(Integer) +--E 338 + +--S 339 of 531 +a1060:= integrate(t1060,x) +--R +--R +--R (3) +--R 3 2 +--R sinh(b x + a) - 9cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R (3cosh(b x + a) + 12b x + 6)sinh(b x + a) - 3cosh(b x + a) +--R + +--R (- 12b x + 6)cosh(b x + a) +--R / +--R 32b sinh(b x + a) - 32b cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 339 + +--S 340 of 531 +m1060:= a1060-r1060 +--R +--R +--R (4) +--R 3 2 +--R sinh(b x + a) - 9cosh(b x + a)sinh(b x + a) +--R + +--R 4b x + 4a 2b x + 2a - 2b x - 2a 2 +--R (- %e + 6%e - 2%e + 3cosh(b x + a) + 6) +--R * +--R sinh(b x + a) +--R + +--R 4b x + 4a 2b x + 2a +--R cosh(b x + a)%e - 6cosh(b x + a)%e +--R + +--R - 2b x - 2a 3 +--R 2cosh(b x + a)%e - 3cosh(b x + a) + 6cosh(b x + a) +--R / +--R 32b sinh(b x + a) - 32b cosh(b x + a) +--R Type: Expression(Integer) +--E 340 + +--S 341 of 531 +d1060:= D(m1060,x) +--R +--R +--R (5) +--R 3 +--R - 2sinh(b x + a) +--R + +--R 4b x + 4a 2b x + 2a - 2b x - 2a 2 +--R (- %e + 3%e + %e - 6cosh(b x + a) + 3) +--R * +--R sinh(b x + a) +--R + +--R 4b x + 4a 2b x + 2a +--R cosh(b x + a)%e - 3cosh(b x + a)%e +--R + +--R - 2b x - 2a +--R - cosh(b x + a)%e + 3cosh(b x + a) +--R / +--R 8sinh(b x + a) - 8cosh(b x + a) +--R Type: Expression(Integer) +--E 341 + +)clear all + + +--S 342 of 531 +t1061:= exp(1)^(a+b*x)*sinh(c+d*x)^(3/2)-3*d^2/(4*b^2-9*d^2)*_ + exp(1)^(a+b*x)/sinh(c+d*x)^(1/2) +--R +--R +--R 2 2 b x + a 2 2 b x + a +--R (9d - 4b )%e sinh(d x + c) + 3d %e +--R (1) ------------------------------------------------- +--R 2 2 +-------------+ +--R (9d - 4b )\|sinh(d x + c) +--R Type: Expression(Integer) +--E 342 + +--S 343 of 531 +r1061:= -2*exp(a+b*x)*sinh(c+d*x)^(1/2)*(3*d*cosh(c+d*x)-_ + 2*b*sinh(c+d*x))/(4*b^2-9*d^2) +--R +--R +--R (2) +--R b x + a b x + a +-------------+ +--R (- 4b %e sinh(d x + c) + 6d cosh(d x + c)%e )\|sinh(d x + c) +--R ------------------------------------------------------------------------- +--R 2 2 +--R 9d - 4b +--R Type: Expression(Integer) +--E 343 + +--S 344 of 531 +a1061:= integrate(t1061,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 344 + +--S 345 of 531 +--m1061:= a1061-r1061 +--E 345 + +--S 346 of 531 +--d1061:= D(m1061,x) +--E 346 + +)clear all + + +--S 347 of 531 +t1062:= exp(1)^(a+b*x)*cosh(a+b*x) +--R +--R +--R b x + a +--R (1) cosh(b x + a)%e +--R Type: Expression(Integer) +--E 347 + +--S 348 of 531 +r1062:= 1/4*(exp(2*a+2*b*x)+2*b*x)/b +--R +--R +--R 2b x + 2a +--R %e + 2b x +--R (2) ------------------ +--R 4b +--R Type: Expression(Integer) +--E 348 + +--S 349 of 531 +a1062:= integrate(t1062,x) +--R +--R +--R (2b x - 1)sinh(b x + a) + (- 2b x - 1)cosh(b x + a) +--R (3) --------------------------------------------------- +--R 4b sinh(b x + a) - 4b cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 349 + +--S 350 of 531 +m1062:= a1062-r1062 +--R +--R +--R (4) +--R 2b x + 2a 2b x + 2a +--R (- %e - 1)sinh(b x + a) + cosh(b x + a)%e - cosh(b x + a) +--R --------------------------------------------------------------------------- +--R 4b sinh(b x + a) - 4b cosh(b x + a) +--R Type: Expression(Integer) +--E 350 + +--S 351 of 531 +d1062:= D(m1062,x) +--R +--R +--R (5) +--R 2b x + 2a 2b x + 2a +--R (- %e - 1)sinh(b x + a) + cosh(b x + a)%e - cosh(b x + a) +--R --------------------------------------------------------------------------- +--R 2sinh(b x + a) - 2cosh(b x + a) +--R Type: Expression(Integer) +--E 351 + +)clear all + + +--S 352 of 531 +t1063:= exp(1)^(a+b*x)*cosh(a+b*x)^3 +--R +--R +--R 3 b x + a +--R (1) cosh(b x + a) %e +--R Type: Expression(Integer) +--E 352 + +--S 353 of 531 +r1063:= 1/32*(-2*exp(-2*a-2*b*x)+6*exp(2*a+2*b*x)+exp(4*a+4*b*x)+12*b*x)/b +--R +--R +--R 4b x + 4a 2b x + 2a - 2b x - 2a +--R %e + 6%e - 2%e + 12b x +--R (2) --------------------------------------------------- +--R 32b +--R Type: Expression(Integer) +--E 353 + +--S 354 of 531 +a1063:= integrate(t1063,x) +--R +--R +--R (3) +--R 3 2 +--R - 3sinh(b x + a) + 3cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R (- 9cosh(b x + a) + 12b x - 6)sinh(b x + a) + cosh(b x + a) +--R + +--R (- 12b x - 6)cosh(b x + a) +--R / +--R 32b sinh(b x + a) - 32b cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 354 + +--S 355 of 531 +m1063:= a1063-r1063 +--R +--R +--R (4) +--R 3 2 +--R - 3sinh(b x + a) + 3cosh(b x + a)sinh(b x + a) +--R + +--R 4b x + 4a 2b x + 2a - 2b x - 2a 2 +--R (- %e - 6%e + 2%e - 9cosh(b x + a) - 6) +--R * +--R sinh(b x + a) +--R + +--R 4b x + 4a 2b x + 2a +--R cosh(b x + a)%e + 6cosh(b x + a)%e +--R + +--R - 2b x - 2a 3 +--R - 2cosh(b x + a)%e + cosh(b x + a) - 6cosh(b x + a) +--R / +--R 32b sinh(b x + a) - 32b cosh(b x + a) +--R Type: Expression(Integer) +--E 355 + +--S 356 of 531 +d1063:= D(m1063,x) +--R +--R +--R (5) +--R 2 +--R - 6cosh(b x + a)sinh(b x + a) +--R + +--R 4b x + 4a 2b x + 2a - 2b x - 2a +--R (- %e - 3%e - %e - 3)sinh(b x + a) +--R + +--R 4b x + 4a 2b x + 2a +--R cosh(b x + a)%e + 3cosh(b x + a)%e +--R + +--R - 2b x - 2a 3 +--R cosh(b x + a)%e - 2cosh(b x + a) - 3cosh(b x + a) +--R / +--R 8sinh(b x + a) - 8cosh(b x + a) +--R Type: Expression(Integer) +--E 356 + +)clear all + + +--S 357 of 531 +t1064:= sech(x)^2/(a+b*tanh(x)) +--R +--R +--R 2 +--R sech(x) +--R (1) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 357 + +--S 358 of 531 +r1064:= log(a+b*tanh(x))/b +--R +--R +--R log(b tanh(x) + a) +--R (2) ------------------ +--R b +--R Type: Expression(Integer) +--E 358 + +--S 359 of 531 +a1064:= integrate(t1064,x) +--R +--R +--R 2cosh(x) - 2b sinh(x) - 2a cosh(x) +--R - log(- -----------------) + log(-------------------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R (3) ----------------------------------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 359 + +--S 360 of 531 +m1064:= a1064-r1064 +--R +--R +--R (4) +--R 2cosh(x) +--R - log(b tanh(x) + a) - log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R / +--R b +--R Type: Expression(Integer) +--E 360 + +--S 361 of 531 +d1064:= D(m1064,x) +--R +--R +--R (5) +--R 2 2 +--R (b cosh(x)sinh(x) + a cosh(x) )tanh(x) +--R + +--R 2 2 2 +--R (- b sinh(x) + b cosh(x) )tanh(x) - a sinh(x) - b cosh(x)sinh(x) +--R / +--R 2 2 2 2 +--R (b cosh(x)sinh(x) + a b cosh(x) )tanh(x) + a b cosh(x)sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 361 + +)clear all + + +--S 362 of 531 +t1065:= sech(x)^2*(a+b*tanh(x))^n +--R +--R +--R 2 n +--R (1) sech(x) (b tanh(x) + a) +--R Type: Expression(Integer) +--E 362 + +--S 363 of 531 +r1065:= (a+b*tanh(x))^(1+n)/b/(1+n) +--R +--R +--R n + 1 +--R (b tanh(x) + a) +--R (2) -------------------- +--R b n + b +--R Type: Expression(Integer) +--E 363 + +--S 364 of 531 +a1065:= integrate(t1065,x) +--R +--R +--R (3) +--R b sinh(x) + a cosh(x) +--R (b sinh(x) + a cosh(x))sinh(n log(---------------------)) +--R cosh(x) +--R + +--R b sinh(x) + a cosh(x) +--R (b sinh(x) + a cosh(x))cosh(n log(---------------------)) +--R cosh(x) +--R / +--R (b n + b)cosh(x) +--R Type: Union(Expression(Integer),...) +--E 364 + +--S 365 of 531 +m1065:= a1065-r1065 +--R +--R +--R (4) +--R b sinh(x) + a cosh(x) +--R (b sinh(x) + a cosh(x))sinh(n log(---------------------)) +--R cosh(x) +--R + +--R b sinh(x) + a cosh(x) +--R (b sinh(x) + a cosh(x))cosh(n log(---------------------)) +--R cosh(x) +--R + +--R n + 1 +--R - cosh(x)(b tanh(x) + a) +--R / +--R (b n + b)cosh(x) +--R Type: Expression(Integer) +--E 365 + +--S 366 of 531 +d1065:= D(m1065,x) +--R +--R +--R (5) +--R 2 2 b sinh(x) + a cosh(x) +--R (- sinh(x) + cosh(x) )sinh(n log(---------------------)) +--R cosh(x) +--R + +--R 2 2 b sinh(x) + a cosh(x) +--R (- sinh(x) + cosh(x) )cosh(n log(---------------------)) +--R cosh(x) +--R + +--R 2 2 2 n +--R (cosh(x) tanh(x) - cosh(x) )(b tanh(x) + a) +--R / +--R 2 +--R cosh(x) +--R Type: Expression(Integer) +--E 366 + +)clear all + + +--S 367 of 531 +t1066:= sech(x)^2*(1+1/(1-tanh(x)^2)) +--R +--R +--R 2 2 2 +--R sech(x) tanh(x) - 2sech(x) +--R (1) ---------------------------- +--R 2 +--R tanh(x) - 1 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 531 +r1066:= x+tanh(x) +--R +--R +--R (2) tanh(x) + x +--R Type: Expression(Integer) +--E 368 + +--S 369 of 531 +a1066:= integrate(t1066,x) +--R +--R +--R sinh(x) + (x - 1)cosh(x) +--R (3) ------------------------ +--R cosh(x) +--R Type: Union(Expression(Integer),...) +--E 369 + +--S 370 of 531 +m1066:= a1066-r1066 +--R +--R +--R - cosh(x)tanh(x) + sinh(x) - cosh(x) +--R (4) ------------------------------------ +--R cosh(x) +--R Type: Expression(Integer) +--E 370 + +--S 371 of 531 +d1066:= D(m1066,x) +--R +--R +--R 2 2 2 +--R cosh(x) tanh(x) - sinh(x) +--R (5) --------------------------- +--R 2 +--R cosh(x) +--R Type: Expression(Integer) +--E 371 + +)clear all + + +--S 372 of 531 +t1067:= sech(x)^2*(2-tanh(x)^2)/(1-tanh(x)^2) +--R +--R +--R 2 2 2 +--R sech(x) tanh(x) - 2sech(x) +--R (1) ---------------------------- +--R 2 +--R tanh(x) - 1 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 531 +r1067:= x+tanh(x) +--R +--R +--R (2) tanh(x) + x +--R Type: Expression(Integer) +--E 373 + +--S 374 of 531 +a1067:= integrate(t1067,x) +--R +--R +--R sinh(x) + (x - 1)cosh(x) +--R (3) ------------------------ +--R cosh(x) +--R Type: Union(Expression(Integer),...) +--E 374 + +--S 375 of 531 +m1067:= a1067-r1067 +--R +--R +--R - cosh(x)tanh(x) + sinh(x) - cosh(x) +--R (4) ------------------------------------ +--R cosh(x) +--R Type: Expression(Integer) +--E 375 + +--S 376 of 531 +d1067:= D(m1067,x) +--R +--R +--R 2 2 2 +--R cosh(x) tanh(x) - sinh(x) +--R (5) --------------------------- +--R 2 +--R cosh(x) +--R Type: Expression(Integer) +--E 376 + +)clear all + + +--S 377 of 531 +t1068:= sech(x)^2/(1+tanh(x)^2) +--R +--R +--R 2 +--R sech(x) +--R (1) ------------ +--R 2 +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 531 +r1068:= atan(tanh(x)) +--R +--R +--R (2) atan(tanh(x)) +--R Type: Expression(Integer) +--E 378 + +--S 379 of 531 +a1068:= integrate(t1068,x) +--R +--R +--R sinh(x) + cosh(x) +--R (3) - atan(-----------------) +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 379 + +--S 380 of 531 +m1068:= a1068-r1068 +--R +--R +--R sinh(x) + cosh(x) +--R (4) - atan(tanh(x)) - atan(-----------------) +--R sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 380 + +--S 381 of 531 +d1068:= D(m1068,x) +--R +--R +--R 2 2 2 +--R 2cosh(x) tanh(x) - 2sinh(x) +--R (5) --------------------------------------------------- +--R 2 2 2 2 2 +--R (sinh(x) + cosh(x) )tanh(x) + sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 381 + +)clear all + + +--S 382 of 531 +t1069:= sech(x)^2/(9+tanh(x)^2) +--R +--R +--R 2 +--R sech(x) +--R (1) ------------ +--R 2 +--R tanh(x) + 9 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 531 +r1069:= 1/3*atan(1/3*tanh(x)) +--R +--R +--R tanh(x) +--R atan(-------) +--R 3 +--R (2) ------------- +--R 3 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 531 +a1069:= integrate(t1069,x) +--R +--R +--R sinh(x) + 9cosh(x) +--R atan(-------------------) +--R 3sinh(x) - 3cosh(x) +--R (3) - ------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 384 + +--S 385 of 531 +m1069:= a1069-r1069 +--R +--R +--R tanh(x) sinh(x) + 9cosh(x) +--R - atan(-------) - atan(-------------------) +--R 3 3sinh(x) - 3cosh(x) +--R (4) ------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 385 + +--S 386 of 531 +d1069:= D(m1069,x) +--R +--R +--R 2 2 2 +--R 10cosh(x) tanh(x) - 10sinh(x) +--R (5) ------------------------------------------------------- +--R 2 2 2 2 2 +--R (sinh(x) + 9cosh(x) )tanh(x) + 9sinh(x) + 81cosh(x) +--R Type: Expression(Integer) +--E 386 + +)clear all + + +--S 387 of 531 +t1070:= sech(x)^2/(4-sech(x)^2)^(1/2) +--R +--R +--R 2 +--R sech(x) +--R (1) ----------------- +--R +--------------+ +--R | 2 +--R \|- sech(x) + 4 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 531 +r1070:= asinh(1/3*tanh(x)*3^(1/2)) +--R +--R +--R +-+ +--R \|3 tanh(x) +--R (2) asinh(-----------) +--R 3 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 531 +a1070:= integrate(t1070,x) +--R +--R +--R (3) +--R - +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 1 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) +--R + +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 1 2 +--R |------------------------------------- - sinh(x) - 2cosh(x)sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - cosh(x) - 2 +--R Type: Union(Expression(Integer),...) +--E 389 + +--S 390 of 531 +m1070:= a1070-r1070 +--R +--R +--R (4) +--R - +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 1 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) +--R + +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 1 2 +--R |------------------------------------- - sinh(x) - 2cosh(x)sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - cosh(x) - 2 +--R + +--R +-+ +--R \|3 tanh(x) +--R - asinh(-----------) +--R 3 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 531 +d1070:= D(m1070,x) +--R +--R +--R (5) +--R 4 2 2 +--R - 4sinh(x) + (8cosh(x) - 2)sinh(x) + 4cosh(x)sinh(x) +--R + +--R 4 2 +--R - 4cosh(x) - 2cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 1 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 6 2 4 +--R 8sinh(x) + (- 8cosh(x) + 4)sinh(x) +--R + +--R 4 2 2 6 4 +--R (- 8cosh(x) - 8cosh(x) )sinh(x) + 8cosh(x) + 4cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 3 +--R + +--R 6 2 4 3 +--R 4sinh(x) + (- 4cosh(x) + 6)sinh(x) - 8cosh(x)sinh(x) +--R + +--R 4 2 2 +--R (- 4cosh(x) + 4cosh(x) + 2)sinh(x) +--R + +--R 3 6 4 2 +--R (- 8cosh(x) - 4cosh(x))sinh(x) + 4cosh(x) + 6cosh(x) + 2cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 4 3 +--R - 4sinh(x) + (4cosh(x) - 6)sinh(x) + 8cosh(x)sinh(x) +--R + +--R 4 2 2 3 +--R (4cosh(x) - 4cosh(x) - 2)sinh(x) + (8cosh(x) + 4cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 4cosh(x) - 6cosh(x) - 2cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 1 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 6 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 5sinh(x) +--R + +--R 3 5 4 2 4 +--R (4cosh(x) - 2cosh(x))sinh(x) + (4cosh(x) + 5cosh(x) - 6)sinh(x) +--R + +--R 5 3 3 4 2 2 +--R (4cosh(x) + 4cosh(x) )sinh(x) + (5cosh(x) - 4cosh(x) - 4)sinh(x) +--R + +--R 7 5 8 6 4 +--R (- 4cosh(x) - 2cosh(x) )sinh(x) - 2cosh(x) - 5cosh(x) - 6cosh(x) +--R + +--R 2 +--R - 4cosh(x) - 1 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 6 +--R 2sinh(x) + 4cosh(x)sinh(x) + 5sinh(x) +--R + +--R 3 5 4 2 4 +--R (- 4cosh(x) + 2cosh(x))sinh(x) + (- 4cosh(x) - 5cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 4 2 2 +--R (- 4cosh(x) - 4cosh(x) )sinh(x) + (- 5cosh(x) + 4cosh(x) + 4)sinh(x) +--R + +--R 7 5 8 6 4 +--R (4cosh(x) + 2cosh(x) )sinh(x) + 2cosh(x) + 5cosh(x) + 6cosh(x) +--R + +--R 2 +--R 4cosh(x) + 1 +--R / +--R 6 2 4 3 +--R 4sinh(x) + (- 4cosh(x) + 6)sinh(x) - 8cosh(x)sinh(x) +--R + +--R 4 2 2 +--R (- 4cosh(x) + 4cosh(x) + 2)sinh(x) +--R + +--R 3 6 4 2 +--R (- 8cosh(x) - 4cosh(x))sinh(x) + 4cosh(x) + 6cosh(x) + 2cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 1 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 6 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 5sinh(x) +--R + +--R 3 5 4 2 4 +--R (4cosh(x) - 2cosh(x))sinh(x) + (4cosh(x) + 5cosh(x) - 6)sinh(x) +--R + +--R 5 3 3 4 2 2 +--R (4cosh(x) + 4cosh(x) )sinh(x) + (5cosh(x) - 4cosh(x) - 4)sinh(x) +--R + +--R 7 5 8 6 4 +--R (- 4cosh(x) - 2cosh(x) )sinh(x) - 2cosh(x) - 5cosh(x) - 6cosh(x) +--R + +--R 2 +--R - 4cosh(x) - 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 3 +--R Type: Expression(Integer) +--E 391 + +)clear all + + +--S 392 of 531 +t1071:= sech(x)^2/(1-4*tanh(x)^2)^(1/2) +--R +--R +--R 2 +--R sech(x) +--R (1) ------------------ +--R +---------------+ +--R | 2 +--R \|- 4tanh(x) + 1 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 531 +r1071:= 1/2*asin(2*tanh(x)) +--R +--R +--R asin(2tanh(x)) +--R (2) -------------- +--R 2 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 531 +a1071:= integrate(t1071,x) +--R +--R +--R +-------------------------------------+ +--R | 2 2 +--R | - 6sinh(x) - 6cosh(x) + 10 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R atan(-------------------------------------------) +--R 2 2 +--R 2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 2 +--R (3) - ------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 394 + +--S 395 of 531 +m1071:= a1071-r1071 +--R +--R +--R +-------------------------------------+ +--R | 2 2 +--R | - 6sinh(x) - 6cosh(x) + 10 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R - atan(-------------------------------------------) - asin(2tanh(x)) +--R 2 2 +--R 2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 2 +--R (4) -------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 531 +d1071:= D(m1071,x) +--R +--R +--R (5) +--R 6 5 2 4 +--R 2sinh(x) + 4cosh(x)sinh(x) + (- 2cosh(x) - 4)sinh(x) +--R + +--R 3 3 4 2 2 +--R - 8cosh(x) sinh(x) + (- 2cosh(x) + 8cosh(x) - 1)sinh(x) +--R + +--R 5 6 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) - cosh(x) +--R + +--R 5 +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 2sinh(x) - 4cosh(x)sinh(x) + (2cosh(x) + 4)sinh(x) +--R + +--R 3 3 4 2 2 +--R 8cosh(x) sinh(x) + (2cosh(x) - 8cosh(x) + 1)sinh(x) +--R + +--R 5 6 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - 2cosh(x) + 4cosh(x) + cosh(x) - 5 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 6sinh(x) - 6cosh(x) + 10 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 2 2 4 +--R - 3sinh(x) + (6cosh(x) + 2)sinh(x) + 4cosh(x)sinh(x) - 3cosh(x) +--R + +--R 2 +--R 2cosh(x) + 5 +--R * +--R +---------------+ +--R | 2 +--R \|- 4tanh(x) + 1 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 4cosh(x)sinh(x) + (- 2cosh(x) - 4)sinh(x) +--R + +--R 3 3 4 2 2 +--R - 8cosh(x) sinh(x) + (- 2cosh(x) + 8cosh(x) - 1)sinh(x) +--R + +--R 5 6 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) - cosh(x) + 5 +--R * +--R +-------------------------------------+ +--R +---------------+ | 2 2 +--R | 2 | - 6sinh(x) - 6cosh(x) + 10 +--R \|- 4tanh(x) + 1 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 396 + +)clear all + + +--S 397 of 531 +t1072:= sech(x)^2/(-4+tanh(x)^2)^(1/2) +--R +--R +--R 2 +--R sech(x) +--R (1) --------------- +--R +------------+ +--R | 2 +--R \|tanh(x) - 4 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 531 +r1072:= atanh(coth(x)*(-4+tanh(x)^2)^(1/2)) +--R +--R +--R +------------+ +--R | 2 +--R (2) atanh(coth(x)\|tanh(x) - 4 ) +--R Type: Expression(Integer) +--E 398 + +--S 399 of 531 +a1072:= integrate(t1072,x) +--R +--R +--R (3) 0 +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 531 +m1072:= a1072-r1072 +--R +--R +--R +------------+ +--R | 2 +--R (4) - atanh(coth(x)\|tanh(x) - 4 ) +--R Type: Expression(Integer) +--E 400 + +--S 401 of 531 +d1072:= D(m1072,x) +--R +--R +--R (5) +--R 3 2 2 2 +--R - coth(x)tanh(x) + (- coth(x) + 1)tanh(x) + coth(x)tanh(x) + 4coth(x) - 4 +--R ----------------------------------------------------------------------------- +--R +------------+ +--R 2 2 2 | 2 +--R (coth(x) tanh(x) - 4coth(x) - 1)\|tanh(x) - 4 +--R Type: Expression(Integer) +--E 401 + +)clear all + + +--S 402 of 531 +t1073:= sech(x)^2*(1+coth(x)^2)^(1/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (1) sech(x) \|coth(x) + 1 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 531 +r1073:= -acsch(tanh(x))+(1+coth(x)^2)^(1/2)*tanh(x) +--R +--R +--R +------------+ +--R | 2 +--R (2) tanh(x)\|coth(x) + 1 - acsch(tanh(x)) +--R Type: Expression(Integer) +--E 403 + +--S 404 of 531 +a1073:= integrate(t1073,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- \|2 sinh(x) - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 ) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R 2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- + (\|2 + 2)sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R (2\|2 + 4)cosh(x)sinh(x) + (\|2 + 2)cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (\|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 ) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- + (\|2 - 2)sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R (2\|2 - 4)cosh(x)sinh(x) + (\|2 - 2)cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) ) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ 2 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) + (12\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (8\|2 cosh(x) - 4\|2 cosh(x))sinh(x) + 2\|2 cosh(x) - 2\|2 cosh(x) +--R / +--R +-+ 2 +-+ +-+ 2 +-+ +--R (\|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 ) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R Type: Union(Expression(Integer),...) +--E 404 + +--S 405 of 531 +m1073:= a1073-r1073 +--R +--R +--R (4) +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- \|2 sinh(x) - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 ) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R 2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- + (\|2 + 2)sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R (2\|2 + 4)cosh(x)sinh(x) + (\|2 + 2)cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (\|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 ) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- + (\|2 - 2)sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R (2\|2 - 4)cosh(x)sinh(x) + (\|2 - 2)cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- \|2 sinh(x) - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 )tanh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)tanh(x) +--R * +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (\|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 ) +--R * +--R acsch(tanh(x)) +--R + +--R 2 2 +--R 2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2)acsch(tanh(x)) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ 2 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) + (12\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (8\|2 cosh(x) - 4\|2 cosh(x))sinh(x) + 2\|2 cosh(x) - 2\|2 cosh(x) +--R / +--R +-+ 2 +-+ +-+ 2 +-+ +--R (\|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 ) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 531 +--d1073:= D(m1073,x) +--E 406 + +)clear all + + +--S 407 of 531 +t1074:= sech(x)^2*(1+tanh(x)^2)^(1/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (1) sech(x) \|tanh(x) + 1 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 531 +r1074:= 1/2*asinh(tanh(x))+1/2*tanh(x)*(1+tanh(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R tanh(x)\|tanh(x) + 1 + asinh(tanh(x)) +--R (2) --------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 531 +a1074:= integrate(t1074,x) +--R +--R +--R (3) +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + 4\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 2\|2 cosh(x) + \|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - sinh(x) - 8cosh(x)sinh(x) + (- 28cosh(x) - 2)sinh(x) +--R + +--R 3 5 +--R (- 56cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70cosh(x) - 30cosh(x) - 3)sinh(x) +--R + +--R 5 3 3 +--R (- 56cosh(x) - 40cosh(x) - 12cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28cosh(x) - 30cosh(x) - 18cosh(x) - 4)sinh(x) +--R + +--R 7 5 3 8 +--R (- 8cosh(x) - 12cosh(x) - 12cosh(x) - 8cosh(x))sinh(x) - cosh(x) +--R + +--R 6 4 2 +--R - 2cosh(x) - 3cosh(x) - 4cosh(x) - 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- + (- \|2 + 2)sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R (- 2\|2 + 4)cosh(x)sinh(x) + (- \|2 + 2)cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R - \|2 sinh(x) - 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 6\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 4\|2 cosh(x) - 4\|2 cosh(x))sinh(x) - \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 2\|2 cosh(x) - \|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R sinh(x) + 8cosh(x)sinh(x) + (28cosh(x) + 2)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) + 30cosh(x) + 3)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) + 40cosh(x) + 12cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) + 30cosh(x) + 18cosh(x) + 4)sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) + 12cosh(x) + 12cosh(x) + 8cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R 2cosh(x) + 3cosh(x) + 4cosh(x) + 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- + (- \|2 - 2)sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R (- 2\|2 - 4)cosh(x)sinh(x) + (- \|2 - 2)cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 6 5 2 4 +--R - sinh(x) - 6cosh(x)sinh(x) + (- 15cosh(x) - 1)sinh(x) +--R + +--R 3 3 +--R (- 20cosh(x) - 4cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 15cosh(x) - 6cosh(x) - 6)sinh(x) +--R + +--R 5 3 6 4 +--R (- 6cosh(x) - 4cosh(x) - 12cosh(x))sinh(x) - cosh(x) - cosh(x) +--R + +--R 2 +--R - 6cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +-+ 2 +-+ 6 +--R \|2 sinh(x) + 8\|2 cosh(x)sinh(x) + (28\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (56\|2 cosh(x) + 24\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (70\|2 cosh(x) + 60\|2 cosh(x) + \|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (56\|2 cosh(x) + 80\|2 cosh(x) + 4\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (28\|2 cosh(x) + 60\|2 cosh(x) + 6\|2 cosh(x) + 6\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (8\|2 cosh(x) + 24\|2 cosh(x) + 4\|2 cosh(x) + 12\|2 cosh(x))sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R \|2 cosh(x) + 4\|2 cosh(x) + \|2 cosh(x) + 6\|2 cosh(x) +--R / +--R +-+ 4 +-+ 3 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (8\|2 cosh(x) + 8\|2 cosh(x))sinh(x) + 2\|2 cosh(x) + 4\|2 cosh(x) +--R + +--R +-+ +--R 2\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 4)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) - 24cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 60cosh(x) - 6)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) - 80cosh(x) - 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) - 60cosh(x) - 36cosh(x) - 8)sinh(x) +--R + +--R 7 5 3 8 +--R (- 16cosh(x) - 24cosh(x) - 24cosh(x) - 16cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R - 4cosh(x) - 6cosh(x) - 8cosh(x) - 4 +--R Type: Union(Expression(Integer),...) +--E 409 + +--S 410 of 531 +m1074:= a1074-r1074 +--R +--R +--R (4) +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + 4\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 2\|2 cosh(x) + \|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - sinh(x) - 8cosh(x)sinh(x) + (- 28cosh(x) - 2)sinh(x) +--R + +--R 3 5 +--R (- 56cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70cosh(x) - 30cosh(x) - 3)sinh(x) +--R + +--R 5 3 3 +--R (- 56cosh(x) - 40cosh(x) - 12cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28cosh(x) - 30cosh(x) - 18cosh(x) - 4)sinh(x) +--R + +--R 7 5 3 8 +--R (- 8cosh(x) - 12cosh(x) - 12cosh(x) - 8cosh(x))sinh(x) - cosh(x) +--R + +--R 6 4 2 +--R - 2cosh(x) - 3cosh(x) - 4cosh(x) - 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- + (- \|2 + 2)sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R (- 2\|2 + 4)cosh(x)sinh(x) + (- \|2 + 2)cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R - \|2 sinh(x) - 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 6\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 4\|2 cosh(x) - 4\|2 cosh(x))sinh(x) - \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 2\|2 cosh(x) - \|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R sinh(x) + 8cosh(x)sinh(x) + (28cosh(x) + 2)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) + 30cosh(x) + 3)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) + 40cosh(x) + 12cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) + 30cosh(x) + 18cosh(x) + 4)sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) + 12cosh(x) + 12cosh(x) + 8cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R 2cosh(x) + 3cosh(x) + 4cosh(x) + 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- + (- \|2 - 2)sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R (- 2\|2 - 4)cosh(x)sinh(x) + (- \|2 - 2)cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R - \|2 sinh(x) - 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 6\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 4\|2 cosh(x) - 4\|2 cosh(x))sinh(x) - \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 2\|2 cosh(x) - \|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R tanh(x) |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R sinh(x) + 8cosh(x)sinh(x) + (28cosh(x) + 2)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) + 30cosh(x) + 3)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) + 40cosh(x) + 12cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) + 30cosh(x) + 18cosh(x) + 4)sinh(x) +--R + +--R 7 5 3 +--R (8cosh(x) + 12cosh(x) + 12cosh(x) + 8cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R cosh(x) + 2cosh(x) + 3cosh(x) + 4cosh(x) + 2 +--R * +--R tanh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R + +--R +-+ 4 +-+ 3 +--R - \|2 sinh(x) - 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 6\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 4\|2 cosh(x) - 4\|2 cosh(x))sinh(x) - \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 2\|2 cosh(x) - \|2 +--R * +--R asinh(tanh(x)) +--R + +--R 6 5 2 4 +--R - sinh(x) - 6cosh(x)sinh(x) + (- 15cosh(x) - 1)sinh(x) +--R + +--R 3 3 +--R (- 20cosh(x) - 4cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 15cosh(x) - 6cosh(x) - 6)sinh(x) +--R + +--R 5 3 6 4 +--R (- 6cosh(x) - 4cosh(x) - 12cosh(x))sinh(x) - cosh(x) - cosh(x) +--R + +--R 2 +--R - 6cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R sinh(x) + 8cosh(x)sinh(x) + (28cosh(x) + 2)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) + 30cosh(x) + 3)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) + 40cosh(x) + 12cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) + 30cosh(x) + 18cosh(x) + 4)sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) + 12cosh(x) + 12cosh(x) + 8cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R 2cosh(x) + 3cosh(x) + 4cosh(x) + 2 +--R * +--R asinh(tanh(x)) +--R + +--R +-+ 8 +-+ 7 +-+ 2 +-+ 6 +--R \|2 sinh(x) + 8\|2 cosh(x)sinh(x) + (28\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (56\|2 cosh(x) + 24\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (70\|2 cosh(x) + 60\|2 cosh(x) + \|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (56\|2 cosh(x) + 80\|2 cosh(x) + 4\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (28\|2 cosh(x) + 60\|2 cosh(x) + 6\|2 cosh(x) + 6\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (8\|2 cosh(x) + 24\|2 cosh(x) + 4\|2 cosh(x) + 12\|2 cosh(x))sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R \|2 cosh(x) + 4\|2 cosh(x) + \|2 cosh(x) + 6\|2 cosh(x) +--R / +--R +-+ 4 +-+ 3 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (8\|2 cosh(x) + 8\|2 cosh(x))sinh(x) + 2\|2 cosh(x) + 4\|2 cosh(x) +--R + +--R +-+ +--R 2\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 4)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) - 24cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 60cosh(x) - 6)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) - 80cosh(x) - 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) - 60cosh(x) - 36cosh(x) - 8)sinh(x) +--R + +--R 7 5 3 8 +--R (- 16cosh(x) - 24cosh(x) - 24cosh(x) - 16cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R - 4cosh(x) - 6cosh(x) - 8cosh(x) - 4 +--R Type: Expression(Integer) +--E 410 + +--S 411 of 531 +--d1074:= D(m1074,x) +--E 411 + +)clear all + + +--S 412 of 531 +t1075:= sech(x)^2/(tanh(x)^2+tanh(x)^3) +--R +--R +--R 2 +--R sech(x) +--R (1) ------------------- +--R 3 2 +--R tanh(x) + tanh(x) +--R Type: Expression(Integer) +--E 412 + +--S 413 of 531 +r1075:= -coth(x)+log(1+coth(x)) +--R +--R +--R (2) log(coth(x) + 1) - coth(x) +--R Type: Expression(Integer) +--E 413 + +--S 414 of 531 +a1075:= integrate(t1075,x) +--R +--R +--R (3) +--R 2 2 2sinh(x) +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R 2x sinh(x) + 4x cosh(x)sinh(x) + 2x cosh(x) - 2x - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 414 + +--S 415 of 531 +m1075:= a1075-r1075 +--R +--R +--R (4) +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(coth(x) + 1) +--R + +--R 2 2 2sinh(x) +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (coth(x) + 2x)sinh(x) + (2cosh(x)coth(x) + 4x cosh(x))sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 1)coth(x) + 2x cosh(x) - 2x - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 531 +d1075:= D(m1075,x) +--R +--R +--R (5) +--R 2 5 +--R (- coth(x) + coth(x) + 1)sinh(x) +--R + +--R 2 4 +--R (- 4cosh(x)coth(x) + 4cosh(x)coth(x) + 3cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R ((- 6cosh(x) + 2)coth(x) + (6cosh(x) - 2)coth(x) + 2cosh(x) + 2) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3 +--R (- 4cosh(x) + 4cosh(x))coth(x) + (4cosh(x) - 4cosh(x))coth(x) +--R + +--R 3 +--R - 2cosh(x) + 6cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 +--R (- cosh(x) + 2cosh(x) - 1)coth(x) +--R + +--R 4 2 4 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x) - 3cosh(x) + 6cosh(x) + 1 +--R * +--R sinh(x) +--R + +--R 5 3 +--R - cosh(x) + 2cosh(x) - cosh(x) +--R / +--R 5 4 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 2 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + (cosh(x) - 2cosh(x) + 1)sinh(x) +--R Type: Expression(Integer) +--E 416 + +)clear all + + +--S 417 of 531 +t1076:= sech(x)^2/(-tanh(x)^2+tanh(x)^3) +--R +--R +--R 2 +--R sech(x) +--R (1) ------------------- +--R 3 2 +--R tanh(x) - tanh(x) +--R Type: Expression(Integer) +--E 417 + +--S 418 of 531 +r1076:= coth(x)+log(1-coth(x)) +--R +--R +--R (2) log(- coth(x) + 1) + coth(x) +--R Type: Expression(Integer) +--E 418 + +--S 419 of 531 +a1076:= integrate(t1076,x) +--R +--R +--R (3) +--R 2 2 2sinh(x) +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(- -----------------) + 2 +--R sinh(x) - cosh(x) +--R ------------------------------------------------------------------------- +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 419 + +--S 420 of 531 +m1076:= a1076-r1076 +--R +--R +--R (4) +--R 2 2 2sinh(x) +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(- coth(x) + 1) +--R + +--R 2 2 +--R - coth(x)sinh(x) - 2cosh(x)coth(x)sinh(x) + (- cosh(x) + 1)coth(x) + 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 531 +d1076:= D(m1076,x) +--R +--R +--R (5) +--R 2 5 +--R (coth(x) + coth(x) - 1)sinh(x) +--R + +--R 2 4 +--R (4cosh(x)coth(x) + 4cosh(x)coth(x) - 5cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R ((6cosh(x) - 2)coth(x) + (6cosh(x) - 2)coth(x) - 10cosh(x) - 2) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) - 4cosh(x))coth(x) + (4cosh(x) - 4cosh(x))coth(x) +--R + +--R 3 +--R - 10cosh(x) - 2cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x) +--R + +--R 4 2 4 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x) - 5cosh(x) + 2cosh(x) - 1 +--R * +--R sinh(x) +--R + +--R 5 3 +--R - cosh(x) + 2cosh(x) - cosh(x) +--R / +--R 5 4 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 2 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + (cosh(x) - 2cosh(x) + 1)sinh(x) +--R Type: Expression(Integer) +--E 421 + +)clear all + + +--S 422 of 531 +t1077:= sech(x)^2/(2+2*tanh(x)+tanh(x)^2) +--R +--R +--R 2 +--R sech(x) +--R (1) ----------------------- +--R 2 +--R tanh(x) + 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 531 +r1077:= atan(1+tanh(x)) +--R +--R +--R (2) atan(tanh(x) + 1) +--R Type: Expression(Integer) +--E 423 + +--S 424 of 531 +a1077:= integrate(t1077,x) +--R +--R +--R 2sinh(x) + 3cosh(x) +--R (3) - atan(-------------------) +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 424 + +--S 425 of 531 +m1077:= a1077-r1077 +--R +--R +--R 2sinh(x) + 3cosh(x) +--R (4) - atan(tanh(x) + 1) - atan(-------------------) +--R sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 425 + +--S 426 of 531 +d1077:= D(m1077,x) +--R +--R +--R (5) +--R 2 2 2 2 +--R (2cosh(x)sinh(x) + 3cosh(x) )tanh(x) + (- 2sinh(x) + 2cosh(x) )tanh(x) +--R + +--R 2 +--R - 3sinh(x) - 2cosh(x)sinh(x) +--R / +--R 2 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + 2cosh(x) )tanh(x) +--R + +--R 2 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 2sinh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 426 + +)clear all + + +--S 427 of 531 +t1078:= sech(x)^2/(3-4*tanh(x)^3) +--R +--R +--R 2 +--R sech(x) +--R (1) - ------------- +--R 3 +--R 4tanh(x) - 3 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 531 +r1078:= 1/18*atan(1/6*(6^(1/3)+4*tanh(x))*2^(2/3)*3^(1/6))*2^(1/3)*3^(5/6)-_ + 1/18*log(6^(1/3)-2*tanh(x))*6^(1/3)+1/36*log(6^(2/3)+_ + 2*6^(1/3)*tanh(x)+4*tanh(x)^2)*6^(1/3) +--R +--R +--R (2) +--R 3+-+ 2 3+-+ 3+-+2 3+-+ 3+-+ +--R \|6 log(4tanh(x) + 2\|6 tanh(x) + \|6 ) - 2\|6 log(- 2tanh(x) + \|6 ) +--R + +--R 3+-+2 6+-+ 3+-+2 6+-+3+-+ +--R 3+-+6+-+5 4\|2 \|3 tanh(x + \|2 \|3 \|6 +--R 2\|2 \|3 atan(---------------------------------) +--R 6 +--R / +--R 36 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 531 +a1078:= integrate(t1078,x) +--R +--R +--R (3) +--R - +--R 3+---+ +-+ +--R \|- 1 \|3 +--R * +--R log +--R 3+---+2 3+--+2 3+--+ 3+---+ 2 +--R (2\|- 1 \|36 + 2\|36 + 24\|- 1 )sinh(x) +--R + +--R 3+---+2 3+--+2 3+---+ +--R (- 4\|- 1 \|36 - 48\|- 1 )cosh(x)sinh(x) +--R + +--R 3+---+2 3+--+2 3+--+ 3+---+ 2 3+---+2 3+--+2 +--R (2\|- 1 \|36 + 2\|36 + 24\|- 1 )cosh(x) + 2\|- 1 \|36 +--R + +--R 3+--+ 3+---+ +--R - 14\|36 - 24\|- 1 +--R / +--R 2 2 +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3+---+ +-+ +--R 2\|- 1 \|3 +--R * +--R log +--R 3+--+2 3+---+3+--+ 3+---+2 +--R (- 8\|36 + 24\|- 1 \|36 - 72\|- 1 )sinh(x) +--R + +--R 3+--+2 3+---+3+--+ 3+---+2 +--R (6\|36 - 24\|- 1 \|36 + 72\|- 1 )cosh(x) +--R / +--R sinh(x) - cosh(x) +--R + +--R - +--R 3+---+ +--R 6\|- 1 +--R * +--R atan +--R +-+3+--+2 3+---+ +-+3+--+ 3+---+2 +-+ +--R (4\|3 \|36 + 6\|- 1 \|3 \|36 - 18\|- 1 \|3 )sinh(x) +--R + +--R +-+3+--+2 3+---+ +-+3+--+ 3+---+2 +-+ +--R (- 3\|3 \|36 - 6\|- 1 \|3 \|36 + 18\|- 1 \|3 )cosh(x) +--R / +--R 3+---+3+--+ 3+---+2 +--R (18\|- 1 \|36 + 54\|- 1 )sinh(x) +--R + +--R 3+---+3+--+ 3+---+2 +--R (- 18\|- 1 \|36 - 54\|- 1 )cosh(x) +--R / +--R +-+3+--+ +--R 6\|3 \|36 +--R Type: Union(Expression(Integer),...) +--E 429 + +--S 430 of 531 +m1078:= a1078-r1078 +--R +--R +--R (4) +--R +-+3+-+3+--+ 2 3+-+ 3+-+2 +--R - \|3 \|6 \|36 log(4tanh(x) + 2\|6 tanh(x) + \|6 ) +--R + +--R - +--R 3+---+ +-+ +--R 6\|- 1 \|3 +--R * +--R log +--R 3+---+2 3+--+2 3+--+ 3+---+ 2 +--R (2\|- 1 \|36 + 2\|36 + 24\|- 1 )sinh(x) +--R + +--R 3+---+2 3+--+2 3+---+ +--R (- 4\|- 1 \|36 - 48\|- 1 )cosh(x)sinh(x) +--R + +--R 3+---+2 3+--+2 3+--+ 3+---+ 2 3+---+2 3+--+2 +--R (2\|- 1 \|36 + 2\|36 + 24\|- 1 )cosh(x) + 2\|- 1 \|36 +--R + +--R 3+--+ 3+---+ +--R - 14\|36 - 24\|- 1 +--R / +--R 2 2 +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3+---+ +-+ +--R 12\|- 1 \|3 +--R * +--R log +--R 3+--+2 3+---+3+--+ 3+---+2 +--R (- 8\|36 + 24\|- 1 \|36 - 72\|- 1 )sinh(x) +--R + +--R 3+--+2 3+---+3+--+ 3+---+2 +--R (6\|36 - 24\|- 1 \|36 + 72\|- 1 )cosh(x) +--R / +--R sinh(x) - cosh(x) +--R + +--R +-+3+-+3+--+ 3+-+ +--R 2\|3 \|6 \|36 log(- 2tanh(x) + \|6 ) +--R + +--R 3+-+2 6+-+ 3+-+2 6+-+3+-+ +--R 3+-+ +-+6+-+5 3+--+ 4\|2 \|3 tanh(x + \|2 \|3 \|6 +--R - 2\|2 \|3 \|3 \|36 atan(---------------------------------) +--R 6 +--R + +--R - +--R 3+---+ +--R 36\|- 1 +--R * +--R atan +--R +-+3+--+2 3+---+ +-+3+--+ 3+---+2 +-+ +--R (4\|3 \|36 + 6\|- 1 \|3 \|36 - 18\|- 1 \|3 )sinh(x) +--R + +--R +-+3+--+2 3+---+ +-+3+--+ 3+---+2 +-+ +--R (- 3\|3 \|36 - 6\|- 1 \|3 \|36 + 18\|- 1 \|3 )cosh(x) +--R / +--R 3+---+3+--+ 3+---+2 +--R (18\|- 1 \|36 + 54\|- 1 )sinh(x) +--R + +--R 3+---+3+--+ 3+---+2 +--R (- 18\|- 1 \|36 - 54\|- 1 )cosh(x) +--R / +--R +-+3+--+ +--R 36\|3 \|36 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 531 +--d1078:= D(m1078,x) +--E 431 + +)clear all + + +--S 432 of 531 +t1079:= sech(x)^2/(11-5*tanh(x)+5*tanh(x)^2) +--R +--R +--R 2 +--R sech(x) +--R (1) ------------------------- +--R 2 +--R 5tanh(x) - 5tanh(x) + 11 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 531 +r1079:= -2/195*atan(1/39*195^(1/2)*(1-2*tanh(x)))*195^(1/2) +--R +--R +--R +---+ +---+ +--R +---+ 2\|195 tanh(x) - \|195 +--R 2\|195 atan(-----------------------) +--R 39 +--R (2) ------------------------------------ +--R 195 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 531 +a1079:= integrate(t1079,x) +--R +--R +--R +---+ +---+ +--R 5\|195 sinh(x) + 17\|195 cosh(x) +--R 2atan(--------------------------------) +--R 195sinh(x) - 195cosh(x) +--R (3) - --------------------------------------- +--R +---+ +--R \|195 +--R Type: Union(Expression(Integer),...) +--E 434 + +--S 435 of 531 +m1079:= a1079-r1079 +--R +--R +--R (4) +--R +---+ +---+ +---+ +---+ +--R 2\|195 tanh(x) - \|195 5\|195 sinh(x) + 17\|195 cosh(x) +--R - 2atan(-----------------------) - 2atan(--------------------------------) +--R 39 195sinh(x) - 195cosh(x) +--R -------------------------------------------------------------------------- +--R +---+ +--R \|195 +--R Type: Expression(Integer) +--E 435 + +--S 436 of 531 +d1079:= D(m1079,x) +--R +--R +--R (5) +--R 2 2 2 2 +--R (- 5cosh(x)sinh(x) + 16cosh(x) )tanh(x) + (5sinh(x) - 5cosh(x) )tanh(x) +--R + +--R 2 +--R - 16sinh(x) + 5cosh(x)sinh(x) +--R / +--R 2 2 2 +--R (25sinh(x) - 25cosh(x)sinh(x) + 55cosh(x) )tanh(x) +--R + +--R 2 2 2 +--R (- 25sinh(x) + 25cosh(x)sinh(x) - 55cosh(x) )tanh(x) + 55sinh(x) +--R + +--R 2 +--R - 55cosh(x)sinh(x) + 121cosh(x) +--R Type: Expression(Integer) +--E 436 + +)clear all + + +--S 437 of 531 +t1080:= sech(x)^2/(1+sech(x)^2-3*tanh(x)) +--R +--R +--R 2 +--R sech(x) +--R (1) - ----------------------- +--R 2 +--R 3tanh(x) - sech(x) - 1 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 531 +r1080:= 2/17*atanh(1/17*(3+2*tanh(x))*17^(1/2))*17^(1/2) +--R +--R +--R +--+ +--+ +--R +--+ 2\|17 tanh(x) + 3\|17 +--R 2\|17 atanh(----------------------) +--R 17 +--R (2) ----------------------------------- +--R 17 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 531 +a1080:= integrate(t1080,x) +--R +--R +--R (3) +--R log +--R +--+ 2 +--+ +--R (- 15\|17 + 51)sinh(x) + (22\|17 - 102)cosh(x)sinh(x) +--R + +--R +--+ 2 +--+ +--R (- 15\|17 + 51)cosh(x) + 6\|17 - 34 +--R / +--R 2 2 +--R sinh(x) - 6cosh(x)sinh(x) + cosh(x) + 3 +--R / +--R +--+ +--R \|17 +--R Type: Union(Expression(Integer),...) +--E 439 + +--S 440 of 531 +m1080:= a1080-r1080 +--R +--R +--R (4) +--R log +--R +--+ 2 +--+ +--R (- 15\|17 + 51)sinh(x) + (22\|17 - 102)cosh(x)sinh(x) +--R + +--R +--+ 2 +--+ +--R (- 15\|17 + 51)cosh(x) + 6\|17 - 34 +--R / +--R 2 2 +--R sinh(x) - 6cosh(x)sinh(x) + cosh(x) + 3 +--R + +--R +--+ +--+ +--R 2\|17 tanh(x) + 3\|17 +--R - 2atanh(----------------------) +--R 17 +--R / +--R +--+ +--R \|17 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 531 +d1080:= D(m1080,x) +--R +--R +--R (5) +--R +--+ 4 +--+ 3 +--R (- 27\|17 + 119)sinh(x) + (112\|17 - 408)cosh(x)sinh(x) +--R + +--R +--+ 2 +--+ 2 +--R ((- 138\|17 + 578)cosh(x) - 9\|17 + 17)sinh(x) +--R + +--R +--+ 3 +--+ +--R ((112\|17 - 408)cosh(x) + (- 14\|17 + 102)cosh(x))sinh(x) +--R + +--R +--+ 4 +--+ 2 +--+ +--R (- 27\|17 + 119)cosh(x) + (- 9\|17 + 17)cosh(x) + 18\|17 - 102 +--R * +--R 2 +--R tanh(x) +--R + +--R +--+ 4 +--R (- 36\|17 + 204)sinh(x) +--R + +--R +--+ 2 +--+ 2 +--R ((72\|17 - 408)cosh(x) + 90\|17 - 306)sinh(x) +--R + +--R +--+ +--+ 4 +--R (- 132\|17 + 612)cosh(x)sinh(x) + (- 36\|17 + 204)cosh(x) +--R + +--R +--+ 2 +--R (90\|17 - 306)cosh(x) +--R * +--R tanh(x) +--R + +--R +--+ 4 +--+ 3 +--R (39\|17 - 187)sinh(x) + (- 112\|17 + 408)cosh(x)sinh(x) +--R + +--R +--+ 2 +--+ 2 +--R ((114\|17 - 442)cosh(x) - 21\|17 + 85)sinh(x) +--R + +--R +--+ 3 +--+ +--R ((- 112\|17 + 408)cosh(x) + (58\|17 - 306)cosh(x))sinh(x) +--R + +--R +--+ 4 +--+ 2 +--+ +--R (39\|17 - 187)cosh(x) + (- 21\|17 + 85)cosh(x) - 18\|17 + 102 +--R / +--R +--+ 4 +--+ 3 +--R (15\|17 - 51)sinh(x) + (- 112\|17 + 408)cosh(x)sinh(x) +--R + +--R +--+ 2 +--+ 2 +--R ((162\|17 - 714)cosh(x) + 39\|17 - 119)sinh(x) +--R + +--R +--+ 3 +--+ +--R ((- 112\|17 + 408)cosh(x) + (- 30\|17 + 102)cosh(x))sinh(x) +--R + +--R +--+ 4 +--+ 2 +--+ +--R (15\|17 - 51)cosh(x) + (39\|17 - 119)cosh(x) - 18\|17 + 102 +--R * +--R 2 +--R tanh(x) +--R + +--R +--+ 4 +--+ 3 +--R (45\|17 - 153)sinh(x) + (- 336\|17 + 1224)cosh(x)sinh(x) +--R + +--R +--+ 2 +--+ 2 +--R ((486\|17 - 2142)cosh(x) + 117\|17 - 357)sinh(x) +--R + +--R +--+ 3 +--+ +--R ((- 336\|17 + 1224)cosh(x) + (- 90\|17 + 306)cosh(x))sinh(x) +--R + +--R +--+ 4 +--+ 2 +--+ +--R (45\|17 - 153)cosh(x) + (117\|17 - 357)cosh(x) - 54\|17 + 306 +--R * +--R tanh(x) +--R + +--R +--+ 4 +--+ 3 +--R (- 30\|17 + 102)sinh(x) + (224\|17 - 816)cosh(x)sinh(x) +--R + +--R +--+ 2 +--+ 2 +--R ((- 324\|17 + 1428)cosh(x) - 78\|17 + 238)sinh(x) +--R + +--R +--+ 3 +--+ +--R ((224\|17 - 816)cosh(x) + (60\|17 - 204)cosh(x))sinh(x) +--R + +--R +--+ 4 +--+ 2 +--+ +--R (- 30\|17 + 102)cosh(x) + (- 78\|17 + 238)cosh(x) + 36\|17 - 204 +--R Type: Expression(Integer) +--E 441 + +)clear all + + +--S 442 of 531 +t1081:= sech(x)^2*(a+b*tanh(x))/(c+d*tanh(x)) +--R +--R +--R 2 2 +--R b sech(x) tanh(x) + a sech(x) +--R (1) ------------------------------ +--R d tanh(x) + c +--R Type: Expression(Integer) +--E 442 + +--S 443 of 531 +r1081:= -(b*c-a*d)*log(c+d*tanh(x))/d^2+b*tanh(x)/d +--R +--R +--R (a d - b c)log(d tanh(x) + c) + b d tanh(x) +--R (2) ------------------------------------------- +--R 2 +--R d +--R Type: Expression(Integer) +--E 443 + +--S 444 of 531 +a1081:= integrate(t1081,x) +--R +--R +--R (3) +--R 2 +--R (- a d + b c)sinh(x) + (- 2a d + 2b c)cosh(x)sinh(x) +--R + +--R 2 +--R (- a d + b c)cosh(x) - a d + b c +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (a d - b c)sinh(x) + (2a d - 2b c)cosh(x)sinh(x) +--R + +--R 2 +--R (a d - b c)cosh(x) + a d - b c +--R * +--R - 2d sinh(x) - 2c cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R - 2b d +--R / +--R 2 2 2 2 2 2 +--R d sinh(x) + 2d cosh(x)sinh(x) + d cosh(x) + d +--R Type: Union(Expression(Integer),...) +--E 444 + +--S 445 of 531 +m1081:= a1081-r1081 +--R +--R +--R (4) +--R 2 +--R (- a d + b c)sinh(x) + (- 2a d + 2b c)cosh(x)sinh(x) +--R + +--R 2 +--R (- a d + b c)cosh(x) - a d + b c +--R * +--R log(d tanh(x) + c) +--R + +--R 2 +--R (- a d + b c)sinh(x) + (- 2a d + 2b c)cosh(x)sinh(x) +--R + +--R 2 +--R (- a d + b c)cosh(x) - a d + b c +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (a d - b c)sinh(x) + (2a d - 2b c)cosh(x)sinh(x) +--R + +--R 2 +--R (a d - b c)cosh(x) + a d - b c +--R * +--R - 2d sinh(x) - 2c cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- b d sinh(x) - 2b d cosh(x)sinh(x) - b d cosh(x) - b d)tanh(x) - 2b d +--R / +--R 2 2 2 2 2 2 +--R d sinh(x) + 2d cosh(x)sinh(x) + d cosh(x) + d +--R Type: Expression(Integer) +--E 445 + +--S 446 of 531 +d1081:= D(m1081,x) +--R +--R +--R (5) +--R 2 5 2 2 4 +--R b d cosh(x)sinh(x) + (4b d + b c d)cosh(x) sinh(x) +--R + +--R 2 3 2 3 +--R ((6b d + 4b c d)cosh(x) + 2b d cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R ((4b d + 6b c d)cosh(x) + (4b d + 2b c d)cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((b d + 4b c d)cosh(x) + (2b d + 4b c d)cosh(x) + b d cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R b c d cosh(x) + 2b c d cosh(x) + b c d cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 2 5 2 2 4 +--R a d cosh(x)sinh(x) + (4a d + a c d)cosh(x) sinh(x) +--R + +--R 2 3 2 3 +--R ((6a d + 4a c d)cosh(x) + 2a d cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R ((4a d + 6a c d)cosh(x) + (4a d + 2a c d)cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((a d + 4a c d)cosh(x) + (2a d + 4a c d)cosh(x) + a d cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R a c d cosh(x) + 2a c d cosh(x) + a c d cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 5 +--R (- a d + b c d)sinh(x) + ((- b - 4a)d + 4b c d)cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R (((- 4b - 5a)d + 4b c d)cosh(x) - 2a d + 2b c d)sinh(x) +--R + +--R 2 3 2 3 +--R ((- 6b d - 4b c d)cosh(x) + ((2b - 4a)d + 4b c d)cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R ((- 4b + 5a)d - 11b c d)cosh(x) + (4b d + 2b c d)cosh(x) +--R + +--R 2 +--R - a d + b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R ((- b + 4a)d - 8b c d)cosh(x) + (2b + 4a)d cosh(x) +--R + +--R 2 +--R - b d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (a d - 2b c d)cosh(x) + 2a d cosh(x) + (a d - 2b c d)cosh(x) +--R * +--R tanh(x) +--R + +--R 2 6 2 2 5 +--R (- a c d + b c )sinh(x) + (- a d - 4a c d + 4b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R ((- 4a d - 6a c d + 5b c )cosh(x) - 2a c d + 2b c )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 6a d - 4a c d)cosh(x) + (- 2a d + (4b - 4a)c d + 4b c )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 4a d - a c d - 5b c )cosh(x) +--R + +--R 2 2 2 2 +--R (- 4a d + (8b - 2a)c d + 4b c )cosh(x) - a c d + b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- a d - 4b c )cosh(x) + (- 2a d + 4b c d + 4b c )cosh(x) +--R + +--R 2 +--R - a d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R - b c cosh(x) + 2b c cosh(x) - b c cosh(x) +--R / +--R 3 5 3 2 2 4 +--R d cosh(x)sinh(x) + (4d + c d )cosh(x) sinh(x) +--R + +--R 3 2 3 3 3 +--R ((6d + 4c d )cosh(x) + 2d cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R ((4d + 6c d )cosh(x) + (4d + 2c d )cosh(x) )sinh(x) +--R + +--R 3 2 5 3 2 3 3 +--R ((d + 4c d )cosh(x) + (2d + 4c d )cosh(x) + d cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 +--R c d cosh(x) + 2c d cosh(x) + c d cosh(x) +--R * +--R tanh(x) +--R + +--R 2 5 2 2 2 4 +--R c d cosh(x)sinh(x) + (4c d + c d)cosh(x) sinh(x) +--R + +--R 2 2 3 2 3 +--R ((6c d + 4c d)cosh(x) + 2c d cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R ((4c d + 6c d)cosh(x) + (4c d + 2c d)cosh(x) )sinh(x) +--R + +--R 2 2 5 2 2 3 2 +--R ((c d + 4c d)cosh(x) + (2c d + 4c d)cosh(x) + c d cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 +--R c d cosh(x) + 2c d cosh(x) + c d cosh(x) +--R Type: Expression(Integer) +--E 446 + +)clear all + + +--S 447 of 531 +t1082:= sech(x)^2*(a+b*tanh(x))^2/(c+d*tanh(x)) +--R +--R +--R 2 2 2 2 2 2 +--R b sech(x) tanh(x) + 2a b sech(x) tanh(x) + a sech(x) +--R (1) ------------------------------------------------------ +--R d tanh(x) + c +--R Type: Expression(Integer) +--E 447 + +--S 448 of 531 +r1082:= (b*c-a*d)^2*log(c+d*tanh(x))/d^3-b*(b*c-a*d)*tanh(x)/d^2+_ + 1/2*(a+b*tanh(x))^2/d +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(d tanh(x) + c) + b d tanh(x) +--R + +--R 2 2 2 2 +--R (4a b d - 2b c d)tanh(x) + a d +--R / +--R 3 +--R 2d +--R Type: Expression(Integer) +--E 448 + +--S 449 of 531 +a1082:= integrate(t1082,x) +--R +--R +--R (3) +--R 2 2 2 2 4 +--R (- a d + 2a b c d - b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 4a d + 8a b c d - 4b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- 6a d + 12a b c d - 6b c )cosh(x) - 2a d + 4a b c d - 2b c ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 4a d + 8a b c d - 4b c )cosh(x) +--R + +--R 2 2 2 2 +--R (- 4a d + 8a b c d - 4b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 4 +--R (- a d + 2a b c d - b c )cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 2a d + 4a b c d - 2b c )cosh(x) - a d + 2a b c d - b c +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 4 +--R (a d - 2a b c d + b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (4a d - 8a b c d + 4b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((6a d - 12a b c d + 6b c )cosh(x) + 2a d - 4a b c d + 2b c ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 2 3 +--R (4a d - 8a b c d + 4b c )cosh(x) +--R + +--R 2 2 2 2 +--R (4a d - 8a b c d + 4b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 4 2 2 2 2 2 +--R (a d - 2a b c d + b c )cosh(x) + (2a d - 4a b c d + 2b c )cosh(x) +--R + +--R 2 2 2 2 +--R a d - 2a b c d + b c +--R * +--R - 2d sinh(x) - 2c cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 +--R ((- 2b - 4a b)d + 2b c d)sinh(x) +--R + +--R 2 2 2 +--R ((- 4b - 8a b)d + 4b c d)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 2b - 4a b)d + 2b c d)cosh(x) - 4a b d + 2b c d +--R / +--R 3 4 3 3 3 2 3 2 +--R d sinh(x) + 4d cosh(x)sinh(x) + (6d cosh(x) + 2d )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4d cosh(x) + 4d cosh(x))sinh(x) + d cosh(x) + 2d cosh(x) + d +--R Type: Union(Expression(Integer),...) +--E 449 + +--S 450 of 531 +m1082:= a1082-r1082 +--R +--R +--R (4) +--R 2 2 2 2 4 +--R (- 2a d + 4a b c d - 2b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 8a d + 16a b c d - 8b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 12a d + 24a b c d - 12b c )cosh(x) - 4a d + 8a b c d +--R + +--R 2 2 +--R - 4b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 8a d + 16a b c d - 8b c )cosh(x) +--R + +--R 2 2 2 2 +--R (- 8a d + 16a b c d - 8b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 2a d + 4a b c d - 2b c )cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 4a d + 8a b c d - 4b c )cosh(x) - 2a d + 4a b c d - 2b c +--R * +--R log(d tanh(x) + c) +--R + +--R 2 2 2 2 4 +--R (- 2a d + 4a b c d - 2b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 8a d + 16a b c d - 8b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 12a d + 24a b c d - 12b c )cosh(x) - 4a d + 8a b c d +--R + +--R 2 2 +--R - 4b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 8a d + 16a b c d - 8b c )cosh(x) +--R + +--R 2 2 2 2 +--R (- 8a d + 16a b c d - 8b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 2a d + 4a b c d - 2b c )cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 4a d + 8a b c d - 4b c )cosh(x) - 2a d + 4a b c d - 2b c +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 4 +--R (2a d - 4a b c d + 2b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (8a d - 16a b c d + 8b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((12a d - 24a b c d + 12b c )cosh(x) + 4a d - 8a b c d + 4b c ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 2 3 +--R (8a d - 16a b c d + 8b c )cosh(x) +--R + +--R 2 2 2 2 +--R (8a d - 16a b c d + 8b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 4 +--R (2a d - 4a b c d + 2b c )cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4a d - 8a b c d + 4b c )cosh(x) + 2a d - 4a b c d + 2b c +--R * +--R - 2d sinh(x) - 2c cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R - b d sinh(x) - 4b d cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (- 6b d cosh(x) - 2b d )sinh(x) +--R + +--R 2 2 3 2 2 2 2 4 +--R (- 4b d cosh(x) - 4b d cosh(x))sinh(x) - b d cosh(x) +--R + +--R 2 2 2 2 2 +--R - 2b d cosh(x) - b d +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 4a b d + 2b c d)sinh(x) + (- 16a b d + 8b c d)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 24a b d + 12b c d)cosh(x) - 8a b d + 4b c d)sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 16a b d + 8b c d)cosh(x) + (- 16a b d + 8b c d)cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (- 4a b d + 2b c d)cosh(x) + (- 8a b d + 4b c d)cosh(x) - 4a b d +--R + +--R 2 +--R 2b c d +--R * +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R - a d sinh(x) - 4a d cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 6a d cosh(x) + (- 4b - 8a b - 2a )d + 4b c d)sinh(x) +--R + +--R 2 2 3 2 2 2 2 +--R (- 4a d cosh(x) + ((- 8b - 16a b - 4a )d + 8b c d)cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R - a d cosh(x) + ((- 4b - 8a b - 2a )d + 4b c d)cosh(x) +--R + +--R 2 2 2 +--R (- 8a b - a )d + 4b c d +--R / +--R 3 4 3 3 3 2 3 2 +--R 2d sinh(x) + 8d cosh(x)sinh(x) + (12d cosh(x) + 4d )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8d cosh(x) + 8d cosh(x))sinh(x) + 2d cosh(x) + 4d cosh(x) + 2d +--R Type: Expression(Integer) +--E 450 + +--S 451 of 531 +d1082:= D(m1082,x) +--R +--R +--R (5) +--R 2 3 7 2 3 2 2 2 6 +--R b d cosh(x)sinh(x) + (6b d + b c d )cosh(x) sinh(x) +--R + +--R 2 3 2 2 3 2 3 5 +--R ((15b d + 6b c d )cosh(x) + 3b d cosh(x))sinh(x) +--R + +--R 2 3 2 2 4 2 3 2 2 2 4 +--R ((20b d + 15b c d )cosh(x) + (12b d + 3b c d )cosh(x) )sinh(x) +--R + +--R 2 3 2 2 5 2 3 2 2 3 +--R (15b d + 20b c d )cosh(x) + (18b d + 12b c d )cosh(x) +--R + +--R 2 3 +--R 3b d cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 2 2 6 2 3 2 2 4 +--R (6b d + 15b c d )cosh(x) + (12b d + 18b c d )cosh(x) +--R + +--R 2 3 2 2 2 +--R (6b d + 3b c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 7 2 3 2 2 5 +--R (b d + 6b c d )cosh(x) + (3b d + 12b c d )cosh(x) +--R + +--R 2 3 2 2 3 2 3 +--R (3b d + 6b c d )cosh(x) + b d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 2 2 4 2 2 2 +--R b c d cosh(x) + 3b c d cosh(x) + 3b c d cosh(x) + b c d cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 3 7 3 2 2 6 +--R 2a b d cosh(x)sinh(x) + (12a b d + 2a b c d )cosh(x) sinh(x) +--R + +--R 3 2 3 3 5 +--R ((30a b d + 12a b c d )cosh(x) + 6a b d cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 +--R ((40a b d + 30a b c d )cosh(x) + (24a b d + 6a b c d )cosh(x) ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (30a b d + 40a b c d )cosh(x) + (36a b d + 24a b c d )cosh(x) +--R + +--R 3 +--R 6a b d cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (12a b d + 30a b c d )cosh(x) + (24a b d + 36a b c d )cosh(x) +--R + +--R 3 2 2 +--R (12a b d + 6a b c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 7 3 2 5 +--R (2a b d + 12a b c d )cosh(x) + (6a b d + 24a b c d )cosh(x) +--R + +--R 3 2 3 3 +--R (6a b d + 12a b c d )cosh(x) + 2a b d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R 2a b c d cosh(x) + 6a b c d cosh(x) + 6a b c d cosh(x) +--R + +--R 2 2 +--R 2a b c d cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 2 2 3 7 +--R (- b + a )d cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 2 6 +--R ((- 6b + 6a )d + (- b + a )c d )cosh(x) sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 15b + 15a )d + (- 6b + 6a )c d )cosh(x) +--R + +--R 2 2 3 +--R (- 3b + 3a )d cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 2 2 2 4 +--R ((- 20b + 20a )d + (- 15b + 15a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 2 +--R ((- 12b + 12a )d + (- 3b + 3a )c d )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 2 2 2 5 +--R ((- 15b + 15a )d + (- 20b + 20a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 18b + 18a )d + (- 12b + 12a )c d )cosh(x) +--R + +--R 2 2 3 +--R (- 3b + 3a )d cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 2 2 2 6 +--R ((- 6b + 6a )d + (- 15b + 15a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 4 +--R ((- 12b + 12a )d + (- 18b + 18a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 2 +--R ((- 6b + 6a )d + (- 3b + 3a )c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 2 2 2 7 +--R ((- b + a )d + (- 6b + 6a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 5 +--R ((- 3b + 3a )d + (- 12b + 12a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 3b + 3a )d + (- 6b + 6a )c d )cosh(x) +--R + +--R 2 2 3 +--R (- b + a )d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 8 2 2 2 6 +--R (- b + a )c d cosh(x) + (- 3b + 3a )c d cosh(x) +--R + +--R 2 2 2 4 2 2 2 2 +--R (- 3b + 3a )c d cosh(x) + (- b + a )c d cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 2 2 2 8 +--R (- a d + 2a b c d - b c d)sinh(x) +--R + +--R 2 3 2 2 2 7 +--R ((- 2a b - 6a )d + 12a b c d - 6b c d)cosh(x)sinh(x) +--R + +--R 2 3 2 2 2 2 2 3 +--R ((- 12a b - 14a )d + 26a b c d - 14b c d)cosh(x) - 3a d +--R + +--R 2 2 2 +--R 6a b c d - 3b c d +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 2 2 2 3 +--R ((- 30a b - 14a )d + 16a b c d - 14b c d)cosh(x) +--R + +--R 2 2 3 2 2 2 2 +--R ((4b + 2a b - 12a )d + (- 4b + 24a b)c d - 12b c d)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 +--R (- 40a b d - 30a b c d )cosh(x) +--R + +--R 2 2 3 2 2 2 2 2 +--R ((16b + 8a b - 15a )d + (- 12b + 32a b)c d - 19b c d)cosh(x) +--R + +--R 2 3 2 2 2 +--R - 3a d + 6a b c d - 3b c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 2 5 +--R ((- 30a b + 14a )d - 68a b c d + 14b c d)cosh(x) +--R + +--R 2 3 2 2 2 2 3 +--R ((24b + 12a b)d + (- 8b + 8a b)c d - 16b c d)cosh(x) +--R + +--R 2 2 3 2 2 2 2 +--R ((- 4b + 2a b - 6a )d + (- 4b + 12a b)c d - 6b c d)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 2 2 2 6 +--R ((- 12a b + 14a )d - 58a b c d + 14b c d)cosh(x) +--R + +--R 2 2 3 2 2 2 2 4 +--R ((16b + 8a b + 15a )d + (8b - 18a b)c d - 9b c d)cosh(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R ((- 8b + 4a b)d + (- 12b + 2a b)c d - 4b c d)cosh(x) - a d +--R + +--R 2 2 2 +--R 2a b c d - b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 2 7 +--R ((- 2a b + 6a )d - 24a b c d + 6b c d)cosh(x) +--R + +--R 2 2 3 2 2 2 2 5 +--R ((4b + 2a b + 12a )d + (12b - 16a b)c d - 4b c d)cosh(x) +--R + +--R 2 2 3 2 2 2 2 3 +--R ((- 4b + 2a b + 6a )d + (- 12b - 8a b)c d - 2b c d)cosh(x) +--R + +--R 3 +--R - 2a b d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 2 2 2 8 +--R (a d - 4a b c d + b c d)cosh(x) +--R + +--R 2 3 2 2 2 2 6 +--R (3a d + (4b - 4a b)c d - b c d)cosh(x) +--R + +--R 2 3 2 2 2 2 4 +--R (3a d + (- 4b - 4a b)c d - b c d)cosh(x) +--R + +--R 2 3 2 2 2 2 +--R (a d - 4a b c d + b c d)cosh(x) +--R * +--R tanh(x) +--R + +--R 2 2 2 2 3 8 +--R (- a c d + 2a b c d - b c )sinh(x) +--R + +--R 2 3 2 2 2 2 3 7 +--R (- a d - 6a c d + 12a b c d - 6b c )cosh(x)sinh(x) +--R + +--R 2 3 2 2 2 2 3 2 2 2 +--R (- 6a d - 15a c d + 28a b c d - 14b c )cosh(x) - 3a c d +--R + +--R 2 2 3 +--R 6a b c d - 3b c +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 2 2 2 2 3 3 +--R (- 15a d - 20a c d + 28a b c d - 14b c )cosh(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 3a d + (4b + 8a b - 12a )c d + (- 4b + 24a b)c d - 12b c ) +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 2 2 4 +--R (- 20a d - 15a c d )cosh(x) +--R + +--R 2 3 2 2 2 2 2 +--R - 12a d + (16b + 32a b - 18a )c d + (- 12b + 38a b)c d +--R + +--R 2 3 +--R - 19b c +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R - 3a c d + 6a b c d - 3b c +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 2 2 3 5 +--R (- 15a d - 6a c d - 28a b c d + 14b c )cosh(x) +--R + +--R 2 3 2 2 2 2 2 +--R - 18a d + (24b + 48a b - 12a )c d + (- 8b + 32a b)c d +--R + +--R 2 3 +--R - 16b c +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 3a d + (- 4b + 8a b - 6a )c d + (- 4b + 12a b)c d - 6b c ) +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 2 2 2 2 3 6 +--R (- 6a d - a c d - 28a b c d + 14b c )cosh(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 12a d + (16b + 32a b - 3a )c d + (8b + 18a b)c d - 9b c ) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 6a d + (- 8b + 16a b - 3a )c d + (- 12b + 8a b)c d - 4b c ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R - a c d + 2a b c d - b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 3 7 +--R (- a d - 12a b c d + 6b c )cosh(x) +--R + +--R 2 3 2 2 2 2 2 3 5 +--R (- 3a d + (4b + 8a b)c d + (12b + 8a b)c d - 4b c )cosh(x) +--R + +--R 2 3 2 2 2 2 2 3 3 +--R (- 3a d + (- 4b + 8a b)c d + (- 12b + 4a b)c d - 2b c )cosh(x) +--R + +--R 2 3 +--R - a d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 2 3 6 +--R (- 2a b c d + b c )cosh(x) + ((4b + 2a b)c d - b c )cosh(x) +--R + +--R 2 2 2 3 4 2 2 3 2 +--R ((- 4b + 2a b)c d - b c )cosh(x) + (- 2a b c d + b c )cosh(x) +--R / +--R 4 7 4 3 2 6 +--R d cosh(x)sinh(x) + (6d + c d )cosh(x) sinh(x) +--R + +--R 4 3 3 4 5 +--R ((15d + 6c d )cosh(x) + 3d cosh(x))sinh(x) +--R + +--R 4 3 4 4 3 2 4 +--R ((20d + 15c d )cosh(x) + (12d + 3c d )cosh(x) )sinh(x) +--R + +--R 4 3 5 4 3 3 4 +--R ((15d + 20c d )cosh(x) + (18d + 12c d )cosh(x) + 3d cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 4 3 4 +--R (6d + 15c d )cosh(x) + (12d + 18c d )cosh(x) +--R + +--R 4 3 2 +--R (6d + 3c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 4 3 5 +--R (d + 6c d )cosh(x) + (3d + 12c d )cosh(x) +--R + +--R 4 3 3 4 +--R (3d + 6c d )cosh(x) + d cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 3 6 3 4 3 2 +--R c d cosh(x) + 3c d cosh(x) + 3c d cosh(x) + c d cosh(x) +--R * +--R tanh(x) +--R + +--R 3 7 3 2 2 2 6 +--R c d cosh(x)sinh(x) + (6c d + c d )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 5 +--R ((15c d + 6c d )cosh(x) + 3c d cosh(x))sinh(x) +--R + +--R 3 2 2 4 3 2 2 2 4 +--R ((20c d + 15c d )cosh(x) + (12c d + 3c d )cosh(x) )sinh(x) +--R + +--R 3 2 2 5 3 2 2 3 3 +--R ((15c d + 20c d )cosh(x) + (18c d + 12c d )cosh(x) + 3c d cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (6c d + 15c d )cosh(x) + (12c d + 18c d )cosh(x) +--R + +--R 3 2 2 2 +--R (6c d + 3c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 5 +--R (c d + 6c d )cosh(x) + (3c d + 12c d )cosh(x) +--R + +--R 3 2 2 3 3 +--R (3c d + 6c d )cosh(x) + c d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 2 2 4 2 2 2 +--R c d cosh(x) + 3c d cosh(x) + 3c d cosh(x) + c d cosh(x) +--R Type: Expression(Integer) +--E 451 + +)clear all + + +--S 452 of 531 +t1083:= sech(x)^2*(a+b*tanh(x))^3/(c+d*tanh(x)) +--R +--R +--R (1) +--R 3 2 3 2 2 2 2 2 +--R b sech(x) tanh(x) + 3a b sech(x) tanh(x) + 3a b sech(x) tanh(x) +--R + +--R 3 2 +--R a sech(x) +--R / +--R d tanh(x) + c +--R Type: Expression(Integer) +--E 452 + +--S 453 of 531 +r1083:= -(b*c-a*d)^3*log(c+d*tanh(x))/d^4+b*(b*c-a*d)^2*tanh(x)/d^3-_ + 1/2*(b*c-a*d)*(a+b*tanh(x))^2/d^2+1/3*(a+b*tanh(x))^3/d +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )log(d tanh(x) + c) +--R + +--R 3 3 3 2 3 3 2 2 +--R 2b d tanh(x) + (9a b d - 3b c d )tanh(x) +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (18a b d - 18a b c d + 6b c d)tanh(x) + 5a d - 3a b c d +--R / +--R 4 +--R 6d +--R Type: Expression(Integer) +--E 453 + +--S 454 of 531 +a1083:= integrate(t1083,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 6 +--R (- 3a d + 9a b c d - 9a b c d + 3b c )sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 45a d + 135a b c d - 135a b c d + 45b c )cosh(x) - 9a d +--R + +--R 2 2 2 2 3 3 +--R 27a b c d - 27a b c d + 9b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 60a d + 180a b c d - 180a b c d + 60b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 45a d + 135a b c d - 135a b c d + 45b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 54a d + 162a b c d - 162a b c d + 54b c )cosh(x) - 9a d +--R + +--R 2 2 2 2 3 3 +--R 27a b c d - 27a b c d + 9b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (- 3a d + 9a b c d - 9a b c d + 3b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 9a d + 27a b c d - 27a b c d + 9b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 9a d + 27a b c d - 27a b c d + 9b c )cosh(x) - 3a d +--R + +--R 2 2 2 2 3 3 +--R 9a b c d - 9a b c d + 3b c +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (3a d - 9a b c d + 9a b c d - 3b c )sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (45a d - 135a b c d + 135a b c d - 45b c )cosh(x) + 9a d +--R + +--R 2 2 2 2 3 3 +--R - 27a b c d + 27a b c d - 9b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (60a d - 180a b c d + 180a b c d - 60b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (45a d - 135a b c d + 135a b c d - 45b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (54a d - 162a b c d + 162a b c d - 54b c )cosh(x) + 9a d +--R + +--R 2 2 2 2 3 3 +--R - 27a b c d + 27a b c d - 9b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (3a d - 9a b c d + 9a b c d - 3b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (9a d - 27a b c d + 27a b c d - 9b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 2 2 +--R (9a d - 27a b c d + 27a b c d - 9b c )cosh(x) + 3a d - 9a b c d +--R + +--R 2 2 3 3 +--R 9a b c d - 3b c +--R * +--R - 2d sinh(x) - 2c cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 4 +--R ((- 6b - 18a b - 18a b)d + (6b + 18a b )c d - 6b c d)sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 +--R ((- 24b - 72a b - 72a b)d + (24b + 72a b )c d - 24b c d)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 +--R ((- 36b - 108a b - 108a b)d + (36b + 108a b )c d - 36b c d) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3 3 2 2 3 2 +--R (- 18a b - 36a b)d + (6b + 36a b )c d - 12b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 3 +--R ((- 24b - 72a b - 72a b)d + (24b + 72a b )c d - 24b c d)cosh(x) +--R + +--R 2 2 3 3 2 2 3 2 +--R ((- 36a b - 72a b)d + (12b + 72a b )c d - 24b c d)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 4 +--R ((- 6b - 18a b - 18a b)d + (6b + 18a b )c d - 6b c d)cosh(x) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((- 18a b - 36a b)d + (6b + 36a b )c d - 12b c d)cosh(x) +--R + +--R 3 2 3 2 2 3 2 +--R (- 2b - 18a b)d + 18a b c d - 6b c d +--R / +--R 4 6 4 5 4 2 4 4 +--R 3d sinh(x) + 18d cosh(x)sinh(x) + (45d cosh(x) + 9d )sinh(x) +--R + +--R 4 3 4 3 +--R (60d cosh(x) + 36d cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45d cosh(x) + 54d cosh(x) + 9d )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18d cosh(x) + 36d cosh(x) + 18d cosh(x))sinh(x) + 3d cosh(x) +--R + +--R 4 4 4 2 4 +--R 9d cosh(x) + 9d cosh(x) + 3d +--R Type: Union(Expression(Integer),...) +--E 454 + +--S 455 of 531 +m1083:= a1083-r1083 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 6 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 90a d + 270a b c d - 270a b c d + 90b c )cosh(x) - 18a d +--R + +--R 2 2 2 2 3 3 +--R 54a b c d - 54a b c d + 18b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 120a d + 360a b c d - 360a b c d + 120b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 72a d + 216a b c d - 216a b c d + 72b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 90a d + 270a b c d - 270a b c d + 90b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 108a d + 324a b c d - 324a b c d + 108b c )cosh(x) - 18a d +--R + +--R 2 2 2 2 3 3 +--R 54a b c d - 54a b c d + 18b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 72a d + 216a b c d - 216a b c d + 72b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) - 6a d +--R + +--R 2 2 2 2 3 3 +--R 18a b c d - 18a b c d + 6b c +--R * +--R log(d tanh(x) + c) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 90a d + 270a b c d - 270a b c d + 90b c )cosh(x) - 18a d +--R + +--R 2 2 2 2 3 3 +--R 54a b c d - 54a b c d + 18b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 120a d + 360a b c d - 360a b c d + 120b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 72a d + 216a b c d - 216a b c d + 72b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 90a d + 270a b c d - 270a b c d + 90b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 108a d + 324a b c d - 324a b c d + 108b c )cosh(x) - 18a d +--R + +--R 2 2 2 2 3 3 +--R 54a b c d - 54a b c d + 18b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 72a d + 216a b c d - 216a b c d + 72b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) - 6a d +--R + +--R 2 2 2 2 3 3 +--R 18a b c d - 18a b c d + 6b c +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (6a d - 18a b c d + 18a b c d - 6b c )sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (90a d - 270a b c d + 270a b c d - 90b c )cosh(x) + 18a d +--R + +--R 2 2 2 2 3 3 +--R - 54a b c d + 54a b c d - 18b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (120a d - 360a b c d + 360a b c d - 120b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (72a d - 216a b c d + 216a b c d - 72b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (90a d - 270a b c d + 270a b c d - 90b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (108a d - 324a b c d + 324a b c d - 108b c )cosh(x) + 18a d +--R + +--R 2 2 2 2 3 3 +--R - 54a b c d + 54a b c d - 18b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (72a d - 216a b c d + 216a b c d - 72b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (6a d - 18a b c d + 18a b c d - 6b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x) + 6a d +--R + +--R 2 2 2 2 3 3 +--R - 18a b c d + 18a b c d - 6b c +--R * +--R - 2d sinh(x) - 2c cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 6 3 3 5 +--R - 2b d sinh(x) - 12b d cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 4 +--R (- 30b d cosh(x) - 6b d )sinh(x) +--R + +--R 3 3 3 3 3 3 +--R (- 40b d cosh(x) - 24b d cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 30b d cosh(x) - 36b d cosh(x) - 6b d )sinh(x) +--R + +--R 3 3 5 3 3 3 3 3 +--R (- 12b d cosh(x) - 24b d cosh(x) - 12b d cosh(x))sinh(x) +--R + +--R 3 3 6 3 3 4 3 3 2 3 3 +--R - 2b d cosh(x) - 6b d cosh(x) - 6b d cosh(x) - 2b d +--R * +--R 3 +--R tanh(x) +--R + +--R 2 3 3 2 6 +--R (- 9a b d + 3b c d )sinh(x) +--R + +--R 2 3 3 2 5 +--R (- 54a b d + 18b c d )cosh(x)sinh(x) +--R + +--R 2 3 3 2 2 2 3 3 2 4 +--R ((- 135a b d + 45b c d )cosh(x) - 27a b d + 9b c d )sinh(x) +--R + +--R 2 3 3 2 3 +--R (- 180a b d + 60b c d )cosh(x) +--R + +--R 2 3 3 2 +--R (- 108a b d + 36b c d )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 4 +--R (- 135a b d + 45b c d )cosh(x) +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (- 162a b d + 54b c d )cosh(x) - 27a b d + 9b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 5 +--R (- 54a b d + 18b c d )cosh(x) +--R + +--R 2 3 3 2 3 2 3 3 2 +--R (- 108a b d + 36b c d )cosh(x) + (- 54a b d + 18b c d )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3 2 6 2 3 3 2 4 +--R (- 9a b d + 3b c d )cosh(x) + (- 27a b d + 9b c d )cosh(x) +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (- 27a b d + 9b c d )cosh(x) - 9a b d + 3b c d +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 2 2 3 2 6 +--R (- 18a b d + 18a b c d - 6b c d)sinh(x) +--R + +--R 2 3 2 2 3 2 5 +--R (- 108a b d + 108a b c d - 36b c d)cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 2 2 3 +--R (- 270a b d + 270a b c d - 90b c d)cosh(x) - 54a b d +--R + +--R 2 2 3 2 +--R 54a b c d - 18b c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 360a b d + 360a b c d - 120b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 +--R (- 216a b d + 216a b c d - 72b c d)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 2 2 3 2 4 +--R (- 270a b d + 270a b c d - 90b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 2 2 3 +--R (- 324a b d + 324a b c d - 108b c d)cosh(x) - 54a b d +--R + +--R 2 2 3 2 +--R 54a b c d - 18b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 3 2 5 +--R (- 108a b d + 108a b c d - 36b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 216a b d + 216a b c d - 72b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 +--R (- 108a b d + 108a b c d - 36b c d)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 2 2 3 2 6 +--R (- 18a b d + 18a b c d - 6b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 4 +--R (- 54a b d + 54a b c d - 18b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 2 2 3 2 2 +--R (- 54a b d + 54a b c d - 18b c d)cosh(x) - 18a b d + 18a b c d +--R + +--R 3 2 +--R - 6b c d +--R * +--R tanh(x) +--R + +--R 3 3 2 2 6 3 3 2 2 5 +--R (- 5a d + 3a b c d )sinh(x) + (- 30a d + 18a b c d )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 3 2 2 3 3 +--R (- 75a d + 45a b c d )cosh(x) + (- 12b - 36a b - 36a b - 15a )d +--R + +--R 3 2 2 2 3 2 +--R (12b + 36a b + 9a b)c d - 12b c d +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 3 +--R (- 100a d + 60a b c d )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 48b - 144a b - 144a b - 60a )d +--R + +--R 3 2 2 2 3 2 +--R (48b + 144a b + 36a b)c d - 48b c d +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 4 +--R (- 75a d + 45a b c d )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 72b - 216a b - 216a b - 90a )d +--R + +--R 3 2 2 2 3 2 +--R (72b + 216a b + 54a b)c d - 72b c d +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R (- 36a b - 72a b - 15a )d + (12b + 72a b + 9a b)c d - 24b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 5 +--R (- 30a d + 18a b c d )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 48b - 144a b - 144a b - 60a )d +--R + +--R 3 2 2 2 3 2 +--R (48b + 144a b + 36a b)c d - 48b c d +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 72a b - 144a b - 30a )d + (24b + 144a b + 18a b)c d +--R + +--R 3 2 +--R - 48b c d +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 6 +--R (- 5a d + 3a b c d )cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 2 +--R (- 12b - 36a b - 36a b - 15a )d + (12b + 36a b + 9a b)c d +--R + +--R 3 2 +--R - 12b c d +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((- 36a b - 72a b - 15a )d + (12b + 72a b + 9a b)c d - 24b c d) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3 3 2 2 2 3 2 +--R (- 4b - 36a b - 5a )d + (36a b + 3a b)c d - 12b c d +--R / +--R 4 6 4 5 4 2 4 4 +--R 6d sinh(x) + 36d cosh(x)sinh(x) + (90d cosh(x) + 18d )sinh(x) +--R + +--R 4 3 4 3 +--R (120d cosh(x) + 72d cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90d cosh(x) + 108d cosh(x) + 18d )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36d cosh(x) + 72d cosh(x) + 36d cosh(x))sinh(x) + 6d cosh(x) +--R + +--R 4 4 4 2 4 +--R 18d cosh(x) + 18d cosh(x) + 6d +--R Type: Expression(Integer) +--E 455 + +--S 456 of 531 +d1083:= D(m1083,x) +--R +--R +--R (5) +--R 3 4 9 3 4 3 3 2 8 +--R b d cosh(x)sinh(x) + (8b d + b c d )cosh(x) sinh(x) +--R + +--R 3 4 3 3 3 3 4 7 +--R ((28b d + 8b c d )cosh(x) + 4b d cosh(x))sinh(x) +--R + +--R 3 4 3 3 4 3 4 3 3 2 6 +--R ((56b d + 28b c d )cosh(x) + (24b d + 4b c d )cosh(x) )sinh(x) +--R + +--R 3 4 3 3 5 3 4 3 3 3 +--R (70b d + 56b c d )cosh(x) + (60b d + 24b c d )cosh(x) +--R + +--R 3 4 +--R 6b d cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 3 3 6 3 4 3 3 4 +--R (56b d + 70b c d )cosh(x) + (80b d + 60b c d )cosh(x) +--R + +--R 3 4 3 3 2 +--R (24b d + 6b c d )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 3 3 7 3 4 3 3 5 +--R (28b d + 56b c d )cosh(x) + (60b d + 80b c d )cosh(x) +--R + +--R 3 4 3 3 3 3 4 +--R (36b d + 24b c d )cosh(x) + 4b d cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 3 3 8 3 4 3 3 6 +--R (8b d + 28b c d )cosh(x) + (24b d + 60b c d )cosh(x) +--R + +--R 3 4 3 3 4 3 4 3 3 2 +--R (24b d + 36b c d )cosh(x) + (8b d + 4b c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 3 9 3 4 3 3 7 +--R (b d + 8b c d )cosh(x) + (4b d + 24b c d )cosh(x) +--R + +--R 3 4 3 3 5 3 4 3 3 3 +--R (6b d + 24b c d )cosh(x) + (4b d + 8b c d )cosh(x) +--R + +--R 3 4 +--R b d cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 10 3 3 8 3 3 6 3 3 4 +--R b c d cosh(x) + 4b c d cosh(x) + 6b c d cosh(x) + 4b c d cosh(x) +--R + +--R 3 3 2 +--R b c d cosh(x) +--R * +--R 5 +--R tanh(x) +--R + +--R 2 4 9 2 4 2 3 2 8 +--R 3a b d cosh(x)sinh(x) + (24a b d + 3a b c d )cosh(x) sinh(x) +--R + +--R 2 4 2 3 3 2 4 7 +--R ((84a b d + 24a b c d )cosh(x) + 12a b d cosh(x))sinh(x) +--R + +--R 2 4 2 3 4 +--R (168a b d + 84a b c d )cosh(x) +--R + +--R 2 4 2 3 2 +--R (72a b d + 12a b c d )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 2 3 5 +--R (210a b d + 168a b c d )cosh(x) +--R + +--R 2 4 2 3 3 2 4 +--R (180a b d + 72a b c d )cosh(x) + 18a b d cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 2 3 6 +--R (168a b d + 210a b c d )cosh(x) +--R + +--R 2 4 2 3 4 2 4 2 3 2 +--R (240a b d + 180a b c d )cosh(x) + (72a b d + 18a b c d )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 2 3 7 +--R (84a b d + 168a b c d )cosh(x) +--R + +--R 2 4 2 3 5 +--R (180a b d + 240a b c d )cosh(x) +--R + +--R 2 4 2 3 3 2 4 +--R (108a b d + 72a b c d )cosh(x) + 12a b d cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 8 +--R (24a b d + 84a b c d )cosh(x) +--R + +--R 2 4 2 3 6 +--R (72a b d + 180a b c d )cosh(x) +--R + +--R 2 4 2 3 4 2 4 2 3 2 +--R (72a b d + 108a b c d )cosh(x) + (24a b d + 12a b c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 3 9 2 4 2 3 7 +--R (3a b d + 24a b c d )cosh(x) + (12a b d + 72a b c d )cosh(x) +--R + +--R 2 4 2 3 5 2 4 2 3 3 +--R (18a b d + 72a b c d )cosh(x) + (12a b d + 24a b c d )cosh(x) +--R + +--R 2 4 +--R 3a b d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 10 2 3 8 2 3 6 +--R 3a b c d cosh(x) + 12a b c d cosh(x) + 18a b c d cosh(x) +--R + +--R 2 3 4 2 3 2 +--R 12a b c d cosh(x) + 3a b c d cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 3 2 4 9 +--R (- b + 3a b)d cosh(x)sinh(x) +--R + +--R 3 2 4 3 2 3 2 8 +--R ((- 8b + 24a b)d + (- b + 3a b)c d )cosh(x) sinh(x) +--R + +--R 3 2 4 3 2 3 3 +--R ((- 28b + 84a b)d + (- 8b + 24a b)c d )cosh(x) +--R + +--R 3 2 4 +--R (- 4b + 12a b)d cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 4 +--R ((- 56b + 168a b)d + (- 28b + 84a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 2 +--R ((- 24b + 72a b)d + (- 4b + 12a b)c d )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 5 +--R ((- 70b + 210a b)d + (- 56b + 168a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 3 +--R ((- 60b + 180a b)d + (- 24b + 72a b)c d )cosh(x) +--R + +--R 3 2 4 +--R (- 6b + 18a b)d cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 6 +--R ((- 56b + 168a b)d + (- 70b + 210a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 4 +--R ((- 80b + 240a b)d + (- 60b + 180a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 2 +--R ((- 24b + 72a b)d + (- 6b + 18a b)c d )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 7 +--R ((- 28b + 84a b)d + (- 56b + 168a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 5 +--R ((- 60b + 180a b)d + (- 80b + 240a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 3 +--R ((- 36b + 108a b)d + (- 24b + 72a b)c d )cosh(x) +--R + +--R 3 2 4 +--R (- 4b + 12a b)d cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 8 +--R ((- 8b + 24a b)d + (- 28b + 84a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 6 +--R ((- 24b + 72a b)d + (- 60b + 180a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 4 +--R ((- 24b + 72a b)d + (- 36b + 108a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 2 +--R ((- 8b + 24a b)d + (- 4b + 12a b)c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 9 +--R ((- b + 3a b)d + (- 8b + 24a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 7 +--R ((- 4b + 12a b)d + (- 24b + 72a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 5 +--R ((- 6b + 18a b)d + (- 24b + 72a b)c d )cosh(x) +--R + +--R 3 2 4 3 2 3 3 +--R ((- 4b + 12a b)d + (- 8b + 24a b)c d )cosh(x) +--R + +--R 3 2 4 +--R (- b + 3a b)d cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 3 10 3 2 3 8 +--R (- b + 3a b)c d cosh(x) + (- 4b + 12a b)c d cosh(x) +--R + +--R 3 2 3 6 3 2 3 4 +--R (- 6b + 18a b)c d cosh(x) + (- 4b + 12a b)c d cosh(x) +--R + +--R 3 2 3 2 +--R (- b + 3a b)c d cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 2 3 4 9 +--R (- 3a b + a )d cosh(x)sinh(x) +--R + +--R 2 3 4 2 3 3 2 8 +--R ((- 24a b + 8a )d + (- 3a b + a )c d )cosh(x) sinh(x) +--R + +--R 2 3 4 2 3 3 3 +--R ((- 84a b + 28a )d + (- 24a b + 8a )c d )cosh(x) +--R + +--R 2 3 4 +--R (- 12a b + 4a )d cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 4 2 3 3 4 +--R ((- 168a b + 56a )d + (- 84a b + 28a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 2 +--R ((- 72a b + 24a )d + (- 12a b + 4a )c d )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 2 3 3 5 +--R ((- 210a b + 70a )d + (- 168a b + 56a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 3 +--R ((- 180a b + 60a )d + (- 72a b + 24a )c d )cosh(x) +--R + +--R 2 3 4 +--R (- 18a b + 6a )d cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 4 2 3 3 6 +--R ((- 168a b + 56a )d + (- 210a b + 70a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 4 +--R ((- 240a b + 80a )d + (- 180a b + 60a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 2 +--R ((- 72a b + 24a )d + (- 18a b + 6a )c d )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 2 3 3 7 +--R ((- 84a b + 28a )d + (- 168a b + 56a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 5 +--R ((- 180a b + 60a )d + (- 240a b + 80a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 3 +--R ((- 108a b + 36a )d + (- 72a b + 24a )c d )cosh(x) +--R + +--R 2 3 4 +--R (- 12a b + 4a )d cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 3 3 8 +--R ((- 24a b + 8a )d + (- 84a b + 28a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 6 +--R ((- 72a b + 24a )d + (- 180a b + 60a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 4 +--R ((- 72a b + 24a )d + (- 108a b + 36a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 2 +--R ((- 24a b + 8a )d + (- 12a b + 4a )c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 2 3 3 9 +--R ((- 3a b + a )d + (- 24a b + 8a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 7 +--R ((- 12a b + 4a )d + (- 72a b + 24a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 5 +--R ((- 18a b + 6a )d + (- 72a b + 24a )c d )cosh(x) +--R + +--R 2 3 4 2 3 3 3 +--R ((- 12a b + 4a )d + (- 24a b + 8a )c d )cosh(x) +--R + +--R 2 3 4 +--R (- 3a b + a )d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3 10 2 3 3 8 +--R (- 3a b + a )c d cosh(x) + (- 12a b + 4a )c d cosh(x) +--R + +--R 2 3 3 6 2 3 3 4 +--R (- 18a b + 6a )c d cosh(x) + (- 12a b + 4a )c d cosh(x) +--R + +--R 2 3 3 2 +--R (- 3a b + a )c d cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 4 2 3 2 2 2 3 3 10 +--R (- a d + 3a b c d - 3a b c d + b c d)sinh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 3 9 +--R ((- 3a b - 8a )d + 24a b c d - 24a b c d + 8b c d)cosh(x)sinh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 3 2 +--R ((- 24a b - 27a )d + 78a b c d - 81a b c d + 27b c d)cosh(x) +--R + +--R 3 4 2 3 2 2 2 3 3 +--R - 4a d + 12a b c d - 12a b c d + 4b c d +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 3 +--R ((- 84a b - 48a )d + 120a b c d - 144a b c d + 48b c d) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (4b + 12a b - 24a )d + (- 4b - 12a b + 72a b)c d +--R + +--R 3 2 2 2 3 3 +--R (4b - 72a b )c d + 24b c d +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 3 +--R ((- 168a b - 42a )d + 42a b c d - 126a b c d + 42b c d) +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (24b + 72a b - 56a )d + (- 20b - 60a b + 168a b)c d +--R + +--R 3 2 2 2 3 3 +--R (20b - 180a b )c d + 60b c d +--R * +--R 2 +--R cosh(x) +--R + +--R 3 4 2 3 2 2 2 3 3 +--R - 6a d + 18a b c d - 18a b c d + 6b c d +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 2 3 5 +--R (- 210a b d - 168a b c d )cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (60b + 180a b - 56a )d + (- 36b - 108a b + 168a b)c d +--R + +--R 3 2 2 2 3 3 +--R (36b - 240a b )c d + 80b c d +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3 4 2 2 3 +--R (- 8b + 6a b - 24a )d + (- 24a b + 72a b)c d +--R + +--R 3 2 2 2 3 3 +--R (8b - 72a b )c d + 24b c d +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 3 +--R ((- 168a b + 42a )d - 336a b c d + 126a b c d - 42b c d) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 2 4 3 2 3 +--R (80b + 240a b )d + (- 20b - 60a b )c d +--R + +--R 3 2 2 2 3 3 +--R (20b - 180a b )c d + 60b c d +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (- 32b + 24a b - 30a )d + (- 8b - 96a b + 96a b)c d +--R + +--R 3 2 2 2 3 3 +--R (32b - 114a b )c d + 38b c d +--R * +--R 2 +--R cosh(x) +--R + +--R 3 4 2 3 2 2 2 3 3 +--R - 4a d + 12a b c d - 12a b c d + 4b c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 3 +--R ((- 84a b + 48a )d - 312a b c d + 144a b c d - 48b c d) +--R * +--R 7 +--R cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (60b + 180a b + 56a )d + (20b + 60a b - 168a b)c d +--R + +--R 3 2 2 2 3 3 +--R (- 20b - 72a b )c d + 24b c d +--R * +--R 5 +--R cosh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 48b + 36a b)d + (- 32b - 144a b + 24a b)c d +--R + +--R 3 2 2 2 3 3 +--R (48b - 96a b )c d + 32b c d +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (4b - 12a b - 8a )d + (4b - 12a b + 24a b)c d +--R + +--R 3 2 2 2 3 3 +--R (4b - 24a b )c d + 8b c d +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 3 8 +--R ((- 24a b + 27a )d - 165a b c d + 81a b c d - 27b c d)cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (24b + 72a b + 56a )d + (36b + 108a b - 168a b)c d +--R + +--R 3 2 2 2 3 3 +--R (- 36b - 12a b )c d + 4b c d +--R * +--R 6 +--R cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (- 32b + 24a b + 30a )d + (- 48b - 96a b - 54a b)c d +--R + +--R 3 2 2 2 3 3 +--R (32b - 54a b )c d + 18b c d +--R * +--R 4 +--R cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 2 2 +--R (8b - 24a b )d + (12b - 36a b )c d + (12b - 12a b )c d +--R + +--R 3 3 +--R 4b c d +--R * +--R 2 +--R cosh(x) +--R + +--R 3 4 2 3 2 2 2 3 3 +--R - a d + 3a b c d - 3a b c d + b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 3 9 +--R ((- 3a b + 8a )d - 48a b c d + 24a b c d - 8b c d)cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (4b + 12a b + 24a )d + (20b + 60a b - 72a b)c d +--R + +--R 3 2 2 +--R - 20b c d +--R * +--R 7 +--R cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (- 8b + 6a b + 24a )d + (- 32b - 24a b - 48a b)c d +--R + +--R 3 2 2 2 3 3 +--R (8b - 24a b )c d + 8b c d +--R * +--R 5 +--R cosh(x) +--R + +--R 3 2 3 4 3 2 2 3 +--R (4b - 12a b + 8a )d + (12b - 36a b - 24a b)c d +--R + +--R 3 2 2 +--R 12b c d +--R * +--R 3 +--R cosh(x) +--R + +--R 2 4 +--R - 3a b d cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 2 3 2 2 2 3 3 10 +--R (a d - 6a b c d + 3a b c d - b c d)cosh(x) +--R + +--R 3 4 3 2 2 3 3 2 2 8 +--R (4a d + (4b + 12a b - 12a b)c d - 4b c d )cosh(x) +--R + +--R 3 4 3 2 3 2 2 2 3 3 6 +--R (6a d + (- 8b - 12a b)c d - 6a b c d + 2b c d)cosh(x) +--R + +--R 3 4 3 2 2 3 3 2 2 4 +--R (4a d + (4b - 12a b - 12a b)c d + 4b c d )cosh(x) +--R + +--R 3 4 2 3 2 2 2 3 3 2 +--R (a d - 6a b c d + 3a b c d - b c d)cosh(x) +--R * +--R tanh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 10 +--R (- a c d + 3a b c d - 3a b c d + b c )sinh(x) +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 9 +--R (- a d - 8a c d + 24a b c d - 24a b c d + 8b c )cosh(x)sinh(x) +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 2 +--R (- 8a d - 28a c d + 81a b c d - 81a b c d + 27b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R - 4a c d + 12a b c d - 12a b c d + 4b c +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 3 +--R (- 28a d - 56a c d + 144a b c d - 144a b c d + 48b c )cosh(x) +--R + +--R 3 4 3 2 2 3 3 +--R - 4a d + (4b + 12a b + 12a b - 24a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (- 4b - 12a b + 72a b)c d + (4b - 72a b )c d + 24b c +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 4 +--R (- 56a d - 70a c d + 126a b c d - 126a b c d + 42b c )cosh(x) +--R + +--R 3 4 3 2 2 3 3 +--R - 24a d + (24b + 72a b + 72a b - 60a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (- 20b - 60a b + 180a b)c d + (20b - 180a b )c d + 60b c +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R - 6a c d + 18a b c d - 18a b c d + 6b c +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 3 3 5 +--R (- 70a d - 56a c d )cosh(x) +--R + +--R 3 4 3 2 2 3 3 +--R - 60a d + (60b + 180a b + 180a b - 80a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (- 36b - 108a b + 240a b)c d + (36b - 240a b )c d + 80b c +--R * +--R 3 +--R cosh(x) +--R + +--R 3 4 3 2 3 3 2 2 2 2 +--R - 6a d + (- 8b + 24a b - 24a )c d + (- 24a b + 72a b)c d +--R + +--R 3 2 3 3 4 +--R (8b - 72a b )c d + 24b c +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 6 +--R (- 56a d - 28a c d - 126a b c d + 126a b c d - 42b c )cosh(x) +--R + +--R 3 4 3 2 2 3 3 +--R - 80a d + (80b + 240a b + 240a b - 60a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (- 20b - 60a b + 180a b)c d + (20b - 180a b )c d + 60b c +--R * +--R 4 +--R cosh(x) +--R + +--R 3 4 3 2 3 3 +--R - 24a d + (- 32b + 96a b - 36a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (- 8b - 96a b + 114a b)c d + (32b - 114a b )c d + 38b c +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R - 4a c d + 12a b c d - 12a b c d + 4b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 7 +--R (- 28a d - 8a c d - 144a b c d + 144a b c d - 48b c )cosh(x) +--R + +--R 3 4 3 2 2 3 3 +--R - 60a d + (60b + 180a b + 180a b - 24a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (20b + 60a b + 72a b)c d + (- 20b - 72a b )c d + 24b c +--R * +--R 5 +--R cosh(x) +--R + +--R 3 4 3 2 3 3 +--R - 36a d + (- 48b + 144a b - 24a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (- 32b - 144a b + 96a b)c d + (48b - 96a b )c d + 32b c +--R * +--R 3 +--R cosh(x) +--R + +--R 3 4 3 2 2 3 3 +--R - 4a d + (4b - 12a b + 12a b - 8a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (4b - 12a b + 24a b)c d + (4b - 24a b )c d + 8b c +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 3 3 2 2 2 2 3 3 4 8 +--R (- 8a d - a c d - 81a b c d + 81a b c d - 27b c )cosh(x) +--R + +--R 3 4 3 2 2 3 3 +--R - 24a d + (24b + 72a b + 72a b - 4a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (36b + 108a b + 12a b)c d + (- 36b - 12a b )c d + 4b c +--R * +--R 6 +--R cosh(x) +--R + +--R 3 4 3 2 3 3 +--R - 24a d + (- 32b + 96a b - 6a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (- 48b - 96a b + 54a b)c d + (32b - 54a b )c d + 18b c +--R * +--R 4 +--R cosh(x) +--R + +--R 3 4 3 2 2 3 3 +--R - 8a d + (8b - 24a b + 24a b - 4a )c d +--R + +--R 3 2 2 2 2 3 2 3 3 4 +--R (12b - 36a b + 12a b)c d + (12b - 12a b )c d + 4b c +--R * +--R 2 +--R cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R - a c d + 3a b c d - 3a b c d + b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 2 2 2 3 3 4 9 +--R (- a d - 24a b c d + 24a b c d - 8b c )cosh(x) +--R + +--R 3 4 3 2 2 3 3 2 2 2 +--R - 4a d + (4b + 12a b + 12a b)c d + (20b + 60a b )c d +--R + +--R 3 3 +--R - 20b c d +--R * +--R 7 +--R cosh(x) +--R + +--R 3 4 3 2 3 3 2 2 2 2 +--R - 6a d + (- 8b + 24a b)c d + (- 32b - 24a b + 24a b)c d +--R + +--R 3 2 3 3 4 +--R (8b - 24a b )c d + 8b c +--R * +--R 5 +--R cosh(x) +--R + +--R 3 4 3 2 2 3 3 2 2 2 +--R - 4a d + (4b - 12a b + 12a b)c d + (12b - 36a b )c d +--R + +--R 3 3 +--R 12b c d +--R * +--R 3 +--R cosh(x) +--R + +--R 3 4 +--R - a d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 3 3 4 10 +--R (- 3a b c d + 3a b c d - b c )cosh(x) +--R + +--R 3 2 2 2 3 3 8 +--R ((4b + 12a b )c d - 4b c d)cosh(x) +--R + +--R 3 2 2 2 2 3 3 4 6 +--R ((- 8b + 6a b)c d - 6a b c d + 2b c )cosh(x) +--R + +--R 3 2 2 2 3 3 4 +--R ((4b - 12a b )c d + 4b c d)cosh(x) +--R + +--R 2 2 2 2 3 3 4 2 +--R (- 3a b c d + 3a b c d - b c )cosh(x) +--R / +--R 5 9 5 4 2 8 +--R d cosh(x)sinh(x) + (8d + c d )cosh(x) sinh(x) +--R + +--R 5 4 3 5 7 +--R ((28d + 8c d )cosh(x) + 4d cosh(x))sinh(x) +--R + +--R 5 4 4 5 4 2 6 +--R ((56d + 28c d )cosh(x) + (24d + 4c d )cosh(x) )sinh(x) +--R + +--R 5 4 5 5 4 3 5 +--R ((70d + 56c d )cosh(x) + (60d + 24c d )cosh(x) + 6d cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 6 5 4 4 +--R (56d + 70c d )cosh(x) + (80d + 60c d )cosh(x) +--R + +--R 5 4 2 +--R (24d + 6c d )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 7 5 4 5 +--R (28d + 56c d )cosh(x) + (60d + 80c d )cosh(x) +--R + +--R 5 4 3 5 +--R (36d + 24c d )cosh(x) + 4d cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 8 5 4 6 +--R (8d + 28c d )cosh(x) + (24d + 60c d )cosh(x) +--R + +--R 5 4 4 5 4 2 +--R (24d + 36c d )cosh(x) + (8d + 4c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 9 5 4 7 +--R (d + 8c d )cosh(x) + (4d + 24c d )cosh(x) +--R + +--R 5 4 5 5 4 3 5 +--R (6d + 24c d )cosh(x) + (4d + 8c d )cosh(x) + d cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 4 8 4 6 4 4 +--R c d cosh(x) + 4c d cosh(x) + 6c d cosh(x) + 4c d cosh(x) +--R + +--R 4 2 +--R c d cosh(x) +--R * +--R tanh(x) +--R + +--R 4 9 4 2 3 2 8 +--R c d cosh(x)sinh(x) + (8c d + c d )cosh(x) sinh(x) +--R + +--R 4 2 3 3 4 7 +--R ((28c d + 8c d )cosh(x) + 4c d cosh(x))sinh(x) +--R + +--R 4 2 3 4 4 2 3 2 6 +--R ((56c d + 28c d )cosh(x) + (24c d + 4c d )cosh(x) )sinh(x) +--R + +--R 4 2 3 5 4 2 3 3 4 +--R ((70c d + 56c d )cosh(x) + (60c d + 24c d )cosh(x) + 6c d cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 6 4 2 3 4 +--R (56c d + 70c d )cosh(x) + (80c d + 60c d )cosh(x) +--R + +--R 4 2 3 2 +--R (24c d + 6c d )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 7 4 2 3 5 +--R (28c d + 56c d )cosh(x) + (60c d + 80c d )cosh(x) +--R + +--R 4 2 3 3 4 +--R (36c d + 24c d )cosh(x) + 4c d cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 8 4 2 3 6 +--R (8c d + 28c d )cosh(x) + (24c d + 60c d )cosh(x) +--R + +--R 4 2 3 4 4 2 3 2 +--R (24c d + 36c d )cosh(x) + (8c d + 4c d )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 9 4 2 3 7 +--R (c d + 8c d )cosh(x) + (4c d + 24c d )cosh(x) +--R + +--R 4 2 3 5 4 2 3 3 4 +--R (6c d + 24c d )cosh(x) + (4c d + 8c d )cosh(x) + c d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 10 2 3 8 2 3 6 2 3 4 +--R c d cosh(x) + 4c d cosh(x) + 6c d cosh(x) + 4c d cosh(x) +--R + +--R 2 3 2 +--R c d cosh(x) +--R Type: Expression(Integer) +--E 456 + +)clear all + + +--S 457 of 531 +t1084:= sech(x)^2*tanh(x)^2/(2+tanh(x)^3)^2 +--R +--R +--R 2 2 +--R sech(x) tanh(x) +--R (1) ------------------------ +--R 6 3 +--R tanh(x) + 4tanh(x) + 4 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 531 +r1084:= -1/(6+3*tanh(x)^3) +--R +--R +--R 1 +--R (2) - ------------- +--R 3 +--R 3tanh(x) + 6 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 531 +a1084:= integrate(t1084,x) +--R +--R +--R (3) +--R 2 2 +--R - 8sinh(x) - 8cosh(x)sinh(x) - 8cosh(x) +--R / +--R 4 3 2 2 +--R 27sinh(x) + 108cosh(x)sinh(x) + (162cosh(x) + 36)sinh(x) +--R + +--R 3 4 2 +--R (108cosh(x) + 36cosh(x))sinh(x) + 27cosh(x) + 36cosh(x) + 81 +--R Type: Union(Expression(Integer),...) +--E 459 + +--S 460 of 531 +m1084:= a1084-r1084 +--R +--R +--R (4) +--R 2 2 3 4 +--R (- 8sinh(x) - 8cosh(x)sinh(x) - 8cosh(x) )tanh(x) + 9sinh(x) +--R + +--R 3 2 2 +--R 36cosh(x)sinh(x) + (54cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (36cosh(x) - 4cosh(x))sinh(x) + 9cosh(x) - 4cosh(x) + 27 +--R / +--R 4 3 2 2 +--R 27sinh(x) + 108cosh(x)sinh(x) + (162cosh(x) + 36)sinh(x) +--R + +--R 3 4 2 +--R (108cosh(x) + 36cosh(x))sinh(x) + 27cosh(x) + 36cosh(x) + 81 +--R * +--R 3 +--R tanh(x) +--R + +--R 4 3 2 2 +--R 54sinh(x) + 216cosh(x)sinh(x) + (324cosh(x) + 72)sinh(x) +--R + +--R 3 4 2 +--R (216cosh(x) + 72cosh(x))sinh(x) + 54cosh(x) + 72cosh(x) + 162 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 531 +d1084:= D(m1084,x) +--R +--R +--R (5) +--R 6 5 2 4 +--R 8sinh(x) + 32cosh(x)sinh(x) + 56cosh(x) sinh(x) +--R + +--R 3 3 4 2 +--R 64cosh(x) sinh(x) + (56cosh(x) - 8)sinh(x) +--R + +--R 5 6 2 +--R (32cosh(x) - 32cosh(x))sinh(x) + 8cosh(x) - 8cosh(x) +--R * +--R 6 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 9sinh(x) + 72cosh(x)sinh(x) + (252cosh(x) + 24)sinh(x) +--R + +--R 3 5 +--R (504cosh(x) + 120cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (630cosh(x) + 264cosh(x) + 70)sinh(x) +--R + +--R 5 3 3 +--R (504cosh(x) + 336cosh(x) + 248cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (252cosh(x) + 264cosh(x) + 372cosh(x) + 72)sinh(x) +--R + +--R 7 5 3 +--R (72cosh(x) + 120cosh(x) + 248cosh(x) + 72cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 9cosh(x) + 24cosh(x) + 70cosh(x) + 72cosh(x) + 81 +--R * +--R 4 +--R tanh(x) +--R + +--R 6 5 2 4 +--R 32sinh(x) + 128cosh(x)sinh(x) + 224cosh(x) sinh(x) +--R + +--R 3 3 4 2 +--R 256cosh(x) sinh(x) + (224cosh(x) - 32)sinh(x) +--R + +--R 5 6 2 +--R (128cosh(x) - 128cosh(x))sinh(x) + 32cosh(x) - 32cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 9sinh(x) - 72cosh(x)sinh(x) + (- 252cosh(x) - 24)sinh(x) +--R + +--R 3 5 +--R (- 504cosh(x) - 120cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 630cosh(x) - 264cosh(x) - 70)sinh(x) +--R + +--R 5 3 3 +--R (- 504cosh(x) - 336cosh(x) - 248cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 252cosh(x) - 264cosh(x) - 372cosh(x) - 72)sinh(x) +--R + +--R 7 5 3 +--R (- 72cosh(x) - 120cosh(x) - 248cosh(x) - 72cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 9cosh(x) - 24cosh(x) - 70cosh(x) - 72cosh(x) - 81 +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 2 4 +--R 32sinh(x) + 128cosh(x)sinh(x) + 224cosh(x) sinh(x) +--R + +--R 3 3 4 2 +--R 256cosh(x) sinh(x) + (224cosh(x) - 32)sinh(x) +--R + +--R 5 6 2 +--R (128cosh(x) - 128cosh(x))sinh(x) + 32cosh(x) - 32cosh(x) +--R / +--R 8 7 2 6 +--R 9sinh(x) + 72cosh(x)sinh(x) + (252cosh(x) + 24)sinh(x) +--R + +--R 3 5 +--R (504cosh(x) + 120cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (630cosh(x) + 264cosh(x) + 70)sinh(x) +--R + +--R 5 3 3 +--R (504cosh(x) + 336cosh(x) + 248cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (252cosh(x) + 264cosh(x) + 372cosh(x) + 72)sinh(x) +--R + +--R 7 5 3 +--R (72cosh(x) + 120cosh(x) + 248cosh(x) + 72cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 9cosh(x) + 24cosh(x) + 70cosh(x) + 72cosh(x) + 81 +--R * +--R 6 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 36sinh(x) + 288cosh(x)sinh(x) + (1008cosh(x) + 96)sinh(x) +--R + +--R 3 5 +--R (2016cosh(x) + 480cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (2520cosh(x) + 1056cosh(x) + 280)sinh(x) +--R + +--R 5 3 3 +--R (2016cosh(x) + 1344cosh(x) + 992cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (1008cosh(x) + 1056cosh(x) + 1488cosh(x) + 288)sinh(x) +--R + +--R 7 5 3 +--R (288cosh(x) + 480cosh(x) + 992cosh(x) + 288cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 36cosh(x) + 96cosh(x) + 280cosh(x) + 288cosh(x) + 324 +--R * +--R 3 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 36sinh(x) + 288cosh(x)sinh(x) + (1008cosh(x) + 96)sinh(x) +--R + +--R 3 5 +--R (2016cosh(x) + 480cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (2520cosh(x) + 1056cosh(x) + 280)sinh(x) +--R + +--R 5 3 3 +--R (2016cosh(x) + 1344cosh(x) + 992cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (1008cosh(x) + 1056cosh(x) + 1488cosh(x) + 288)sinh(x) +--R + +--R 7 5 3 +--R (288cosh(x) + 480cosh(x) + 992cosh(x) + 288cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 36cosh(x) + 96cosh(x) + 280cosh(x) + 288cosh(x) + 324 +--R Type: Expression(Integer) +--E 461 + +)clear all + + +--S 462 of 531 +t1085:= sech(x)^2*(2+tanh(x)^2)/(1+tanh(x)^3) +--R +--R +--R 2 2 2 +--R sech(x) tanh(x) + 2sech(x) +--R (1) ---------------------------- +--R 3 +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 531 +r1085:= -2/3*atan(1/3*(1-2*tanh(x))*3^(1/2))*3^(1/2)+log(1+tanh(x)) +--R +--R +--R +-+ +-+ +--R +-+ 2\|3 tanh(x) - \|3 +--R 3log(tanh(x) + 1) + 2\|3 atan(-------------------) +--R 3 +--R (2) -------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 531 +a1085:= integrate(t1085,x) +--R +--R +--R (3) +--R +-+ +-+ +--R +-+ 2cosh(x) \|3 sinh(x) + \|3 cosh(x) +-+ +--R - \|3 log(- -----------------) - 2atan(-------------------------) + 2x\|3 +--R sinh(x) - cosh(x) 3sinh(x) - 3cosh(x) +--R -------------------------------------------------------------------------- +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 464 + +--S 465 of 531 +m1085:= a1085-r1085 +--R +--R +--R (4) +--R +-+ +-+ 2cosh(x) +--R - \|3 log(tanh(x) + 1) - \|3 log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R +-+ +-+ +-+ +-+ +--R 2\|3 tanh(x) - \|3 \|3 sinh(x) + \|3 cosh(x) +-+ +--R - 2atan(-------------------) - 2atan(-------------------------) + 2x\|3 +--R 3 3sinh(x) - 3cosh(x) +--R / +--R +-+ +--R \|3 +--R Type: Expression(Integer) +--E 465 + +--S 466 of 531 +d1085:= D(m1085,x) +--R +--R +--R (5) +--R 2 2 3 3 +--R (cosh(x)sinh(x) - cosh(x) sinh(x) + cosh(x) )tanh(x) +--R + +--R 3 2 3 2 +--R (- sinh(x) - cosh(x) sinh(x) + cosh(x) )tanh(x) +--R + +--R 3 2 3 2 +--R (sinh(x) + cosh(x)sinh(x) )tanh(x) - sinh(x) - cosh(x)sinh(x) +--R / +--R 2 2 3 2 +--R (cosh(x)sinh(x) - cosh(x) sinh(x) + cosh(x) )tanh(x) +--R + +--R 2 2 3 2 +--R (- cosh(x)sinh(x) + cosh(x) sinh(x) - cosh(x) )tanh(x) + cosh(x)sinh(x) +--R + +--R 2 3 +--R - cosh(x) sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 466 + +)clear all + + +--S 467 of 531 +t1086:= sech(x)^4*(-1+sech(x)^2)^2*tanh(x) +--R +--R +--R 8 6 4 +--R (1) (sech(x) - 2sech(x) + sech(x) )tanh(x) +--R Type: Expression(Integer) +--E 467 + +--S 468 of 531 +r1086:= -1/24*tanh(x)^6*(-4+3*tanh(x)^2) +--R +--R +--R 8 6 +--R - 3tanh(x) + 4tanh(x) +--R (2) ----------------------- +--R 24 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 531 +a1086:= integrate(t1086,x) +--R +--R +--R (3) +--R 6 5 2 4 +--R - 12sinh(x) - 72cosh(x)sinh(x) + (- 180cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (- 240cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 180cosh(x) + 96cosh(x) - 52)sinh(x) +--R + +--R 5 3 6 4 +--R (- 72cosh(x) + 64cosh(x) - 56cosh(x))sinh(x) - 12cosh(x) + 16cosh(x) +--R + +--R 2 +--R - 52cosh(x) + 16 +--R / +--R 10 9 2 8 +--R 3sinh(x) + 30cosh(x)sinh(x) + (135cosh(x) + 24)sinh(x) +--R + +--R 3 7 +--R (360cosh(x) + 192cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (630cosh(x) + 672cosh(x) + 87)sinh(x) +--R + +--R 5 3 5 +--R (756cosh(x) + 1344cosh(x) + 486cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (630cosh(x) + 1680cosh(x) + 1305cosh(x) + 192)sinh(x) +--R + +--R 7 5 3 3 +--R (360cosh(x) + 1344cosh(x) + 1620cosh(x) + 576cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (135cosh(x) + 672cosh(x) + 1305cosh(x) + 1152cosh(x) + 294)sinh(x) +--R + +--R 9 7 5 3 +--R (30cosh(x) + 192cosh(x) + 486cosh(x) + 576cosh(x) + 252cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R 3cosh(x) + 24cosh(x) + 87cosh(x) + 192cosh(x) + 294cosh(x) + 168 +--R Type: Union(Expression(Integer),...) +--E 469 + +--S 470 of 531 +m1086:= a1086-r1086 +--R +--R +--R (4) +--R 10 9 2 8 +--R 3sinh(x) + 30cosh(x)sinh(x) + (135cosh(x) + 24)sinh(x) +--R + +--R 3 7 +--R (360cosh(x) + 192cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (630cosh(x) + 672cosh(x) + 87)sinh(x) +--R + +--R 5 3 5 +--R (756cosh(x) + 1344cosh(x) + 486cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (630cosh(x) + 1680cosh(x) + 1305cosh(x) + 192)sinh(x) +--R + +--R 7 5 3 3 +--R (360cosh(x) + 1344cosh(x) + 1620cosh(x) + 576cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (135cosh(x) + 672cosh(x) + 1305cosh(x) + 1152cosh(x) + 294) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (30cosh(x) + 192cosh(x) + 486cosh(x) + 576cosh(x) + 252cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R 3cosh(x) + 24cosh(x) + 87cosh(x) + 192cosh(x) + 294cosh(x) + 168 +--R * +--R 8 +--R tanh(x) +--R + +--R 10 9 2 8 +--R - 4sinh(x) - 40cosh(x)sinh(x) + (- 180cosh(x) - 32)sinh(x) +--R + +--R 3 7 +--R (- 480cosh(x) - 256cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 840cosh(x) - 896cosh(x) - 116)sinh(x) +--R + +--R 5 3 5 +--R (- 1008cosh(x) - 1792cosh(x) - 648cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 840cosh(x) - 2240cosh(x) - 1740cosh(x) - 256)sinh(x) +--R + +--R 7 5 3 3 +--R (- 480cosh(x) - 1792cosh(x) - 2160cosh(x) - 768cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 180cosh(x) - 896cosh(x) - 1740cosh(x) - 1536cosh(x) - 392) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 40cosh(x) - 256cosh(x) - 648cosh(x) - 768cosh(x) +--R + +--R - 336cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 4cosh(x) - 32cosh(x) - 116cosh(x) - 256cosh(x) - 392cosh(x) +--R + +--R - 224 +--R * +--R 6 +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 96sinh(x) - 576cosh(x)sinh(x) + (- 1440cosh(x) + 128)sinh(x) +--R + +--R 3 3 +--R (- 1920cosh(x) + 512cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 1440cosh(x) + 768cosh(x) - 416)sinh(x) +--R + +--R 5 3 6 +--R (- 576cosh(x) + 512cosh(x) - 448cosh(x))sinh(x) - 96cosh(x) +--R + +--R 4 2 +--R 128cosh(x) - 416cosh(x) + 128 +--R / +--R 10 9 2 8 +--R 24sinh(x) + 240cosh(x)sinh(x) + (1080cosh(x) + 192)sinh(x) +--R + +--R 3 7 +--R (2880cosh(x) + 1536cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (5040cosh(x) + 5376cosh(x) + 696)sinh(x) +--R + +--R 5 3 5 +--R (6048cosh(x) + 10752cosh(x) + 3888cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (5040cosh(x) + 13440cosh(x) + 10440cosh(x) + 1536)sinh(x) +--R + +--R 7 5 3 3 +--R (2880cosh(x) + 10752cosh(x) + 12960cosh(x) + 4608cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (1080cosh(x) + 5376cosh(x) + 10440cosh(x) + 9216cosh(x) + 2352) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 240cosh(x) + 1536cosh(x) + 3888cosh(x) + 4608cosh(x) +--R + +--R 2016cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R 24cosh(x) + 192cosh(x) + 696cosh(x) + 1536cosh(x) + 2352cosh(x) +--R + +--R 1344 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 531 +d1086:= D(m1086,x) +--R +--R +--R (5) +--R 20 19 2 18 +--R - 3sinh(x) - 60cosh(x)sinh(x) + (- 570cosh(x) - 48)sinh(x) +--R + +--R 3 17 +--R (- 3420cosh(x) - 864cosh(x))sinh(x) +--R + +--R 4 2 16 +--R (- 14535cosh(x) - 7344cosh(x) - 366)sinh(x) +--R + +--R 5 3 15 +--R (- 46512cosh(x) - 39168cosh(x) - 5784cosh(x))sinh(x) +--R + +--R 6 4 2 14 +--R (- 116280cosh(x) - 146880cosh(x) - 43200cosh(x) - 1776)sinh(x) +--R + +--R 7 5 3 +--R (- 232560cosh(x) - 411264cosh(x) - 201480cosh(x) - 23904cosh(x)) +--R * +--R 13 +--R sinh(x) +--R + +--R 8 6 4 +--R - 377910cosh(x) - 891072cosh(x) - 655080cosh(x) +--R + +--R 2 +--R - 153168cosh(x) - 6183 +--R * +--R 12 +--R sinh(x) +--R + +--R 9 7 5 +--R - 503880cosh(x) - 1527552cosh(x) - 1572696cosh(x) +--R + +--R 3 +--R - 610752cosh(x) - 68364cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 10 8 6 +--R - 554268cosh(x) - 2100384cosh(x) - 2883264cosh(x) +--R + +--R 4 2 +--R - 1680240cosh(x) - 364686cosh(x) - 16176 +--R * +--R 10 +--R sinh(x) +--R + +--R 11 9 7 +--R - 503880cosh(x) - 2333760cosh(x) - 4118280cosh(x) +--R + +--R 5 3 +--R - 3362976cosh(x) - 1202652cosh(x) - 140640cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 12 10 8 +--R - 377910cosh(x) - 2100384cosh(x) - 4632660cosh(x) +--R + +--R 6 4 2 +--R - 5046096cosh(x) - 2702697cosh(x) - 604272cosh(x) - 32028 +--R * +--R 8 +--R sinh(x) +--R + +--R 13 11 9 +--R - 232560cosh(x) - 1527552cosh(x) - 4118280cosh(x) +--R + +--R 7 5 3 +--R - 5767296cosh(x) - 4316952cosh(x) - 1569408cosh(x) +--R + +--R - 205104cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 14 12 10 +--R - 116280cosh(x) - 891072cosh(x) - 2883264cosh(x) +--R + +--R 8 6 4 +--R - 5046096cosh(x) - 5041092cosh(x) - 2746464cosh(x) +--R + +--R 2 +--R - 687792cosh(x) - 47376 +--R * +--R 6 +--R sinh(x) +--R + +--R 15 13 11 +--R - 46512cosh(x) - 411264cosh(x) - 1572696cosh(x) +--R + +--R 9 7 5 +--R - 3362976cosh(x) - 4316952cosh(x) - 3264576cosh(x) +--R + +--R 3 +--R - 1298640cosh(x) - 199584cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 16 14 12 +--R - 14535cosh(x) - 146880cosh(x) - 655080cosh(x) +--R + +--R 10 8 6 +--R - 1680240cosh(x) - 2702697cosh(x) - 2746464cosh(x) +--R + +--R 4 2 +--R - 1660008cosh(x) - 506352cosh(x) - 50316 +--R * +--R 4 +--R sinh(x) +--R + +--R 17 15 13 +--R - 3420cosh(x) - 39168cosh(x) - 201480cosh(x) +--R + +--R 11 9 7 +--R - 610752cosh(x) - 1202652cosh(x) - 1569408cosh(x) +--R + +--R 5 3 +--R - 1298640cosh(x) - 600768cosh(x) - 113904cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 18 16 14 12 +--R - 570cosh(x) - 7344cosh(x) - 43200cosh(x) - 153168cosh(x) +--R + +--R 10 8 6 +--R - 364686cosh(x) - 604272cosh(x) - 687792cosh(x) +--R + +--R 4 2 +--R - 506352cosh(x) - 207816cosh(x) - 32928 +--R * +--R 2 +--R sinh(x) +--R + +--R 19 17 15 13 +--R - 60cosh(x) - 864cosh(x) - 5784cosh(x) - 23904cosh(x) +--R + +--R 11 9 7 +--R - 68364cosh(x) - 140640cosh(x) - 205104cosh(x) +--R + +--R 5 3 +--R - 199584cosh(x) - 113904cosh(x) - 28224cosh(x) +--R * +--R sinh(x) +--R + +--R 20 18 16 14 +--R - 3cosh(x) - 48cosh(x) - 366cosh(x) - 1776cosh(x) +--R + +--R 12 10 8 6 +--R - 6183cosh(x) - 16176cosh(x) - 32028cosh(x) - 47376cosh(x) +--R + +--R 4 2 +--R - 50316cosh(x) - 32928cosh(x) - 9408 +--R * +--R 9 +--R tanh(x) +--R + +--R 20 19 2 18 +--R 6sinh(x) + 120cosh(x)sinh(x) + (1140cosh(x) + 96)sinh(x) +--R + +--R 3 17 +--R (6840cosh(x) + 1728cosh(x))sinh(x) +--R + +--R 4 2 16 +--R (29070cosh(x) + 14688cosh(x) + 732)sinh(x) +--R + +--R 5 3 15 +--R (93024cosh(x) + 78336cosh(x) + 11568cosh(x))sinh(x) +--R + +--R 6 4 2 14 +--R (232560cosh(x) + 293760cosh(x) + 86400cosh(x) + 3552)sinh(x) +--R + +--R 7 5 3 +--R (465120cosh(x) + 822528cosh(x) + 402960cosh(x) + 47808cosh(x)) +--R * +--R 13 +--R sinh(x) +--R + +--R 8 6 4 +--R 755820cosh(x) + 1782144cosh(x) + 1310160cosh(x) +--R + +--R 2 +--R 306336cosh(x) + 12366 +--R * +--R 12 +--R sinh(x) +--R + +--R 9 7 5 +--R 1007760cosh(x) + 3055104cosh(x) + 3145392cosh(x) +--R + +--R 3 +--R 1221504cosh(x) + 136728cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 10 8 6 +--R 1108536cosh(x) + 4200768cosh(x) + 5766528cosh(x) +--R + +--R 4 2 +--R 3360480cosh(x) + 729372cosh(x) + 32352 +--R * +--R 10 +--R sinh(x) +--R + +--R 11 9 7 +--R 1007760cosh(x) + 4667520cosh(x) + 8236560cosh(x) +--R + +--R 5 3 +--R 6725952cosh(x) + 2405304cosh(x) + 281280cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 12 10 8 +--R 755820cosh(x) + 4200768cosh(x) + 9265320cosh(x) +--R + +--R 6 4 2 +--R 10092192cosh(x) + 5405394cosh(x) + 1208544cosh(x) + 64056 +--R * +--R 8 +--R sinh(x) +--R + +--R 13 11 9 +--R 465120cosh(x) + 3055104cosh(x) + 8236560cosh(x) +--R + +--R 7 5 3 +--R 11534592cosh(x) + 8633904cosh(x) + 3138816cosh(x) +--R + +--R 410208cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 14 12 10 +--R 232560cosh(x) + 1782144cosh(x) + 5766528cosh(x) +--R + +--R 8 6 4 +--R 10092192cosh(x) + 10082184cosh(x) + 5492928cosh(x) +--R + +--R 2 +--R 1375584cosh(x) + 94752 +--R * +--R 6 +--R sinh(x) +--R + +--R 15 13 11 +--R 93024cosh(x) + 822528cosh(x) + 3145392cosh(x) +--R + +--R 9 7 5 +--R 6725952cosh(x) + 8633904cosh(x) + 6529152cosh(x) +--R + +--R 3 +--R 2597280cosh(x) + 399168cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 16 14 12 +--R 29070cosh(x) + 293760cosh(x) + 1310160cosh(x) +--R + +--R 10 8 6 +--R 3360480cosh(x) + 5405394cosh(x) + 5492928cosh(x) +--R + +--R 4 2 +--R 3320016cosh(x) + 1012704cosh(x) + 100632 +--R * +--R 4 +--R sinh(x) +--R + +--R 17 15 13 +--R 6840cosh(x) + 78336cosh(x) + 402960cosh(x) +--R + +--R 11 9 7 +--R 1221504cosh(x) + 2405304cosh(x) + 3138816cosh(x) +--R + +--R 5 3 +--R 2597280cosh(x) + 1201536cosh(x) + 227808cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 18 16 14 12 +--R 1140cosh(x) + 14688cosh(x) + 86400cosh(x) + 306336cosh(x) +--R + +--R 10 8 6 +--R 729372cosh(x) + 1208544cosh(x) + 1375584cosh(x) +--R + +--R 4 2 +--R 1012704cosh(x) + 415632cosh(x) + 65856 +--R * +--R 2 +--R sinh(x) +--R + +--R 19 17 15 13 +--R 120cosh(x) + 1728cosh(x) + 11568cosh(x) + 47808cosh(x) +--R + +--R 11 9 7 +--R 136728cosh(x) + 281280cosh(x) + 410208cosh(x) +--R + +--R 5 3 +--R 399168cosh(x) + 227808cosh(x) + 56448cosh(x) +--R * +--R sinh(x) +--R + +--R 20 18 16 14 +--R 6cosh(x) + 96cosh(x) + 732cosh(x) + 3552cosh(x) +--R + +--R 12 10 8 6 +--R 12366cosh(x) + 32352cosh(x) + 64056cosh(x) + 94752cosh(x) +--R + +--R 4 2 +--R 100632cosh(x) + 65856cosh(x) + 18816 +--R * +--R 7 +--R tanh(x) +--R + +--R 20 19 2 18 +--R - 3sinh(x) - 60cosh(x)sinh(x) + (- 570cosh(x) - 48)sinh(x) +--R + +--R 3 17 +--R (- 3420cosh(x) - 864cosh(x))sinh(x) +--R + +--R 4 2 16 +--R (- 14535cosh(x) - 7344cosh(x) - 366)sinh(x) +--R + +--R 5 3 15 +--R (- 46512cosh(x) - 39168cosh(x) - 5784cosh(x))sinh(x) +--R + +--R 6 4 2 14 +--R (- 116280cosh(x) - 146880cosh(x) - 43200cosh(x) - 1776)sinh(x) +--R + +--R 7 5 3 +--R (- 232560cosh(x) - 411264cosh(x) - 201480cosh(x) - 23904cosh(x)) +--R * +--R 13 +--R sinh(x) +--R + +--R 8 6 4 +--R - 377910cosh(x) - 891072cosh(x) - 655080cosh(x) +--R + +--R 2 +--R - 153168cosh(x) - 6183 +--R * +--R 12 +--R sinh(x) +--R + +--R 9 7 5 +--R - 503880cosh(x) - 1527552cosh(x) - 1572696cosh(x) +--R + +--R 3 +--R - 610752cosh(x) - 68364cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 10 8 6 +--R - 554268cosh(x) - 2100384cosh(x) - 2883264cosh(x) +--R + +--R 4 2 +--R - 1680240cosh(x) - 364686cosh(x) - 16176 +--R * +--R 10 +--R sinh(x) +--R + +--R 11 9 7 +--R - 503880cosh(x) - 2333760cosh(x) - 4118280cosh(x) +--R + +--R 5 3 +--R - 3362976cosh(x) - 1202652cosh(x) - 140640cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 12 10 8 +--R - 377910cosh(x) - 2100384cosh(x) - 4632660cosh(x) +--R + +--R 6 4 2 +--R - 5046096cosh(x) - 2702697cosh(x) - 604272cosh(x) - 32028 +--R * +--R 8 +--R sinh(x) +--R + +--R 13 11 9 +--R - 232560cosh(x) - 1527552cosh(x) - 4118280cosh(x) +--R + +--R 7 5 3 +--R - 5767296cosh(x) - 4316952cosh(x) - 1569408cosh(x) +--R + +--R - 205104cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 14 12 10 +--R - 116280cosh(x) - 891072cosh(x) - 2883264cosh(x) +--R + +--R 8 6 4 +--R - 5046096cosh(x) - 5041092cosh(x) - 2746464cosh(x) +--R + +--R 2 +--R - 687792cosh(x) - 47376 +--R * +--R 6 +--R sinh(x) +--R + +--R 15 13 11 +--R - 46512cosh(x) - 411264cosh(x) - 1572696cosh(x) +--R + +--R 9 7 5 +--R - 3362976cosh(x) - 4316952cosh(x) - 3264576cosh(x) +--R + +--R 3 +--R - 1298640cosh(x) - 199584cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 16 14 12 +--R - 14535cosh(x) - 146880cosh(x) - 655080cosh(x) +--R + +--R 10 8 6 +--R - 1680240cosh(x) - 2702697cosh(x) - 2746464cosh(x) +--R + +--R 4 2 +--R - 1660008cosh(x) - 506352cosh(x) - 50316 +--R * +--R 4 +--R sinh(x) +--R + +--R 17 15 13 +--R - 3420cosh(x) - 39168cosh(x) - 201480cosh(x) +--R + +--R 11 9 7 +--R - 610752cosh(x) - 1202652cosh(x) - 1569408cosh(x) +--R + +--R 5 3 +--R - 1298640cosh(x) - 600768cosh(x) - 113904cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 18 16 14 12 +--R - 570cosh(x) - 7344cosh(x) - 43200cosh(x) - 153168cosh(x) +--R + +--R 10 8 6 +--R - 364686cosh(x) - 604272cosh(x) - 687792cosh(x) +--R + +--R 4 2 +--R - 506352cosh(x) - 207816cosh(x) - 32928 +--R * +--R 2 +--R sinh(x) +--R + +--R 19 17 15 13 +--R - 60cosh(x) - 864cosh(x) - 5784cosh(x) - 23904cosh(x) +--R + +--R 11 9 7 +--R - 68364cosh(x) - 140640cosh(x) - 205104cosh(x) +--R + +--R 5 3 +--R - 199584cosh(x) - 113904cosh(x) - 28224cosh(x) +--R * +--R sinh(x) +--R + +--R 20 18 16 14 +--R - 3cosh(x) - 48cosh(x) - 366cosh(x) - 1776cosh(x) +--R + +--R 12 10 8 6 +--R - 6183cosh(x) - 16176cosh(x) - 32028cosh(x) - 47376cosh(x) +--R + +--R 4 2 +--R - 50316cosh(x) - 32928cosh(x) - 9408 +--R * +--R 5 +--R tanh(x) +--R + +--R 16 15 2 14 +--R 48sinh(x) + 768cosh(x)sinh(x) + (5760cosh(x) + 96)sinh(x) +--R + +--R 3 13 +--R (26880cosh(x) + 1344cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (87360cosh(x) + 8736cosh(x) - 192)sinh(x) +--R + +--R 5 3 11 +--R (209664cosh(x) + 34944cosh(x) - 1152cosh(x))sinh(x) +--R + +--R 6 4 2 10 +--R (384384cosh(x) + 96096cosh(x) - 8064cosh(x) - 320)sinh(x) +--R + +--R 7 5 3 9 +--R (549120cosh(x) + 192192cosh(x) - 36480cosh(x) - 1280cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (617760cosh(x) + 288288cosh(x) - 95040cosh(x) - 6720cosh(x) + 752) +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 549120cosh(x) + 329472cosh(x) - 158976cosh(x) - 40960cosh(x) +--R + +--R 2432cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 384384cosh(x) + 288288cosh(x) - 186624cosh(x) - 115840cosh(x) +--R + +--R 2 +--R - 4032cosh(x) + 4704 +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 209664cosh(x) + 192192cosh(x) - 158976cosh(x) - 161280cosh(x) +--R + +--R 3 +--R 6784cosh(x) + 17856cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 87360cosh(x) + 96096cosh(x) - 95040cosh(x) - 115840cosh(x) +--R + +--R 4 2 +--R 12704cosh(x) - 6240cosh(x) - 608 +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 26880cosh(x) + 34944cosh(x) - 36480cosh(x) - 40960cosh(x) +--R + +--R 5 3 +--R 6784cosh(x) - 32640cosh(x) - 2048cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 8 +--R 5760cosh(x) + 8736cosh(x) - 8064cosh(x) - 6720cosh(x) +--R + +--R 6 4 2 +--R - 4032cosh(x) - 6240cosh(x) + 5312cosh(x) - 4480 +--R * +--R 2 +--R sinh(x) +--R + +--R 15 13 11 9 +--R 768cosh(x) + 1344cosh(x) - 1152cosh(x) - 1280cosh(x) +--R + +--R 7 5 3 +--R 2432cosh(x) + 17856cosh(x) - 2048cosh(x) - 17920cosh(x) +--R * +--R sinh(x) +--R + +--R 16 14 12 10 8 +--R 48cosh(x) + 96cosh(x) - 192cosh(x) - 320cosh(x) + 752cosh(x) +--R + +--R 6 4 2 +--R 4704cosh(x) - 608cosh(x) - 4480cosh(x) +--R / +--R 20 19 2 18 +--R 3sinh(x) + 60cosh(x)sinh(x) + (570cosh(x) + 48)sinh(x) +--R + +--R 3 17 +--R (3420cosh(x) + 864cosh(x))sinh(x) +--R + +--R 4 2 16 +--R (14535cosh(x) + 7344cosh(x) + 366)sinh(x) +--R + +--R 5 3 15 +--R (46512cosh(x) + 39168cosh(x) + 5784cosh(x))sinh(x) +--R + +--R 6 4 2 14 +--R (116280cosh(x) + 146880cosh(x) + 43200cosh(x) + 1776)sinh(x) +--R + +--R 7 5 3 +--R (232560cosh(x) + 411264cosh(x) + 201480cosh(x) + 23904cosh(x)) +--R * +--R 13 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 377910cosh(x) + 891072cosh(x) + 655080cosh(x) + 153168cosh(x) +--R + +--R 6183 +--R * +--R 12 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 503880cosh(x) + 1527552cosh(x) + 1572696cosh(x) + 610752cosh(x) +--R + +--R 68364cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 554268cosh(x) + 2100384cosh(x) + 2883264cosh(x) + 1680240cosh(x) +--R + +--R 2 +--R 364686cosh(x) + 16176 +--R * +--R 10 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 503880cosh(x) + 2333760cosh(x) + 4118280cosh(x) + 3362976cosh(x) +--R + +--R 3 +--R 1202652cosh(x) + 140640cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 12 10 8 +--R 377910cosh(x) + 2100384cosh(x) + 4632660cosh(x) +--R + +--R 6 4 2 +--R 5046096cosh(x) + 2702697cosh(x) + 604272cosh(x) + 32028 +--R * +--R 8 +--R sinh(x) +--R + +--R 13 11 9 +--R 232560cosh(x) + 1527552cosh(x) + 4118280cosh(x) +--R + +--R 7 5 3 +--R 5767296cosh(x) + 4316952cosh(x) + 1569408cosh(x) + 205104cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 14 12 10 +--R 116280cosh(x) + 891072cosh(x) + 2883264cosh(x) +--R + +--R 8 6 4 2 +--R 5046096cosh(x) + 5041092cosh(x) + 2746464cosh(x) + 687792cosh(x) +--R + +--R 47376 +--R * +--R 6 +--R sinh(x) +--R + +--R 15 13 11 9 +--R 46512cosh(x) + 411264cosh(x) + 1572696cosh(x) + 3362976cosh(x) +--R + +--R 7 5 3 +--R 4316952cosh(x) + 3264576cosh(x) + 1298640cosh(x) + 199584cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 16 14 12 10 +--R 14535cosh(x) + 146880cosh(x) + 655080cosh(x) + 1680240cosh(x) +--R + +--R 8 6 4 2 +--R 2702697cosh(x) + 2746464cosh(x) + 1660008cosh(x) + 506352cosh(x) +--R + +--R 50316 +--R * +--R 4 +--R sinh(x) +--R + +--R 17 15 13 11 +--R 3420cosh(x) + 39168cosh(x) + 201480cosh(x) + 610752cosh(x) +--R + +--R 9 7 5 3 +--R 1202652cosh(x) + 1569408cosh(x) + 1298640cosh(x) + 600768cosh(x) +--R + +--R 113904cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 18 16 14 12 +--R 570cosh(x) + 7344cosh(x) + 43200cosh(x) + 153168cosh(x) +--R + +--R 10 8 6 4 +--R 364686cosh(x) + 604272cosh(x) + 687792cosh(x) + 506352cosh(x) +--R + +--R 2 +--R 207816cosh(x) + 32928 +--R * +--R 2 +--R sinh(x) +--R + +--R 19 17 15 13 +--R 60cosh(x) + 864cosh(x) + 5784cosh(x) + 23904cosh(x) +--R + +--R 11 9 7 5 +--R 68364cosh(x) + 140640cosh(x) + 205104cosh(x) + 199584cosh(x) +--R + +--R 3 +--R 113904cosh(x) + 28224cosh(x) +--R * +--R sinh(x) +--R + +--R 20 18 16 14 12 +--R 3cosh(x) + 48cosh(x) + 366cosh(x) + 1776cosh(x) + 6183cosh(x) +--R + +--R 10 8 6 4 +--R 16176cosh(x) + 32028cosh(x) + 47376cosh(x) + 50316cosh(x) +--R + +--R 2 +--R 32928cosh(x) + 9408 +--R Type: Expression(Integer) +--E 471 + +)clear all + + +--S 472 of 531 +t1087:= csch(x)^2/(a+b*coth(x)) +--R +--R +--R 2 +--R csch(x) +--R (1) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 531 +r1087:= -log(a+b*coth(x))/b +--R +--R +--R log(b coth(x) + a) +--R (2) - ------------------ +--R b +--R Type: Expression(Integer) +--E 473 + +--S 474 of 531 +a1087:= integrate(t1087,x) +--R +--R +--R 2sinh(x) - 2a sinh(x) - 2b cosh(x) +--R log(- -----------------) - log(-------------------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R (3) --------------------------------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 474 + +--S 475 of 531 +m1087:= a1087-r1087 +--R +--R +--R (4) +--R 2sinh(x) +--R log(b coth(x) + a) + log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2a sinh(x) - 2b cosh(x) +--R - log(-------------------------) +--R sinh(x) - cosh(x) +--R / +--R b +--R Type: Expression(Integer) +--E 475 + +--S 476 of 531 +d1087:= D(m1087,x) +--R +--R +--R (5) +--R 2 2 +--R (- a coth(x) - b coth(x))sinh(x) +--R + +--R 2 2 2 +--R (- b cosh(x)coth(x) + b cosh(x))sinh(x) + b cosh(x) coth(x) + a cosh(x) +--R / +--R 2 2 2 +--R (a b coth(x) + a )sinh(x) + (b cosh(x)coth(x) + a b cosh(x))sinh(x) +--R Type: Expression(Integer) +--E 476 + +)clear all + + +--S 477 of 531 +t1088:= csch(x)^2*(a+b*coth(x))^n +--R +--R +--R 2 n +--R (1) csch(x) (b coth(x) + a) +--R Type: Expression(Integer) +--E 477 + +--S 478 of 531 +r1088:= -(a+b*coth(x))^(1+n)/b/(1+n) +--R +--R +--R n + 1 +--R (b coth(x) + a) +--R (2) - -------------------- +--R b n + b +--R Type: Expression(Integer) +--E 478 + +--S 479 of 531 +a1088:= integrate(t1088,x) +--R +--R +--R (3) +--R a sinh(x) + b cosh(x) +--R (- a sinh(x) - b cosh(x))sinh(n log(---------------------)) +--R sinh(x) +--R + +--R a sinh(x) + b cosh(x) +--R (- a sinh(x) - b cosh(x))cosh(n log(---------------------)) +--R sinh(x) +--R / +--R (b n + b)sinh(x) +--R Type: Union(Expression(Integer),...) +--E 479 + +--S 480 of 531 +m1088:= a1088-r1088 +--R +--R +--R (4) +--R a sinh(x) + b cosh(x) +--R (- a sinh(x) - b cosh(x))sinh(n log(---------------------)) +--R sinh(x) +--R + +--R a sinh(x) + b cosh(x) +--R (- a sinh(x) - b cosh(x))cosh(n log(---------------------)) +--R sinh(x) +--R + +--R n + 1 +--R sinh(x)(b coth(x) + a) +--R / +--R (b n + b)sinh(x) +--R Type: Expression(Integer) +--E 480 + +--S 481 of 531 +d1088:= D(m1088,x) +--R +--R +--R (5) +--R 2 2 a sinh(x) + b cosh(x) +--R (- sinh(x) + cosh(x) )sinh(n log(---------------------)) +--R sinh(x) +--R + +--R 2 2 a sinh(x) + b cosh(x) +--R (- sinh(x) + cosh(x) )cosh(n log(---------------------)) +--R sinh(x) +--R + +--R 2 2 n +--R (- coth(x) + 1)sinh(x) (b coth(x) + a) +--R / +--R 2 +--R sinh(x) +--R Type: Expression(Integer) +--E 481 + +)clear all + + +--S 482 of 531 +t1089:= csch(x)^2*(-1-1/(1-coth(x)^2)) +--R +--R +--R 2 2 +--R (- coth(x) + 2)csch(x) +--R (1) ------------------------ +--R 2 +--R coth(x) - 1 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 531 +r1089:= x+coth(x) +--R +--R +--R (2) coth(x) + x +--R Type: Expression(Integer) +--E 483 + +--S 484 of 531 +a1089:= integrate(t1089,x) +--R +--R +--R (x - 1)sinh(x) + cosh(x) +--R (3) ------------------------ +--R sinh(x) +--R Type: Union(Expression(Integer),...) +--E 484 + +--S 485 of 531 +m1089:= a1089-r1089 +--R +--R +--R (- coth(x) - 1)sinh(x) + cosh(x) +--R (4) -------------------------------- +--R sinh(x) +--R Type: Expression(Integer) +--E 485 + +--S 486 of 531 +d1089:= D(m1089,x) +--R +--R +--R 2 2 2 +--R coth(x) sinh(x) - cosh(x) +--R (5) --------------------------- +--R 2 +--R sinh(x) +--R Type: Expression(Integer) +--E 486 + +)clear all + + +--S 487 of 531 +t1090:= csch(x)^2*(a+b*coth(x))/(c+d*coth(x)) +--R +--R +--R 2 +--R (b coth(x) + a)csch(x) +--R (1) ----------------------- +--R d coth(x) + c +--R Type: Expression(Integer) +--E 487 + +--S 488 of 531 +r1090:= -b*coth(x)/d+(b*c-a*d)*log(c+d*coth(x))/d^2 +--R +--R +--R (- a d + b c)log(d coth(x) + c) - b d coth(x) +--R (2) --------------------------------------------- +--R 2 +--R d +--R Type: Expression(Integer) +--E 488 + +--S 489 of 531 +a1090:= integrate(t1090,x) +--R +--R +--R (3) +--R 2 +--R (a d - b c)sinh(x) + (2a d - 2b c)cosh(x)sinh(x) +--R + +--R 2 +--R (a d - b c)cosh(x) - a d + b c +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (- a d + b c)sinh(x) + (- 2a d + 2b c)cosh(x)sinh(x) +--R + +--R 2 +--R (- a d + b c)cosh(x) + a d - b c +--R * +--R - 2c sinh(x) - 2d cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R - 2b d +--R / +--R 2 2 2 2 2 2 +--R d sinh(x) + 2d cosh(x)sinh(x) + d cosh(x) - d +--R Type: Union(Expression(Integer),...) +--E 489 + +--S 490 of 531 +m1090:= a1090-r1090 +--R +--R +--R (4) +--R 2 +--R (a d - b c)sinh(x) + (2a d - 2b c)cosh(x)sinh(x) +--R + +--R 2 +--R (a d - b c)cosh(x) - a d + b c +--R * +--R log(d coth(x) + c) +--R + +--R 2 +--R (a d - b c)sinh(x) + (2a d - 2b c)cosh(x)sinh(x) +--R + +--R 2 +--R (a d - b c)cosh(x) - a d + b c +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (- a d + b c)sinh(x) + (- 2a d + 2b c)cosh(x)sinh(x) +--R + +--R 2 +--R (- a d + b c)cosh(x) + a d - b c +--R * +--R - 2c sinh(x) - 2d cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R b d coth(x)sinh(x) + 2b d cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (b d cosh(x) - b d)coth(x) - 2b d +--R / +--R 2 2 2 2 2 2 +--R d sinh(x) + 2d cosh(x)sinh(x) + d cosh(x) - d +--R Type: Expression(Integer) +--E 490 + +--S 491 of 531 +d1090:= D(m1090,x) +--R +--R +--R (5) +--R 3 2 2 2 +--R (- b c d coth(x) - a c d coth(x) + (- a d + 2b c d)coth(x) + b c ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- b d - 4b c d)cosh(x)coth(x) + (- a d - 4a c d)cosh(x)coth(x) +--R + +--R 2 2 2 +--R ((b - 4a)d + 8b c d)cosh(x)coth(x) + (a d + 4b c )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 +--R ((- 4b d - 6b c d)cosh(x) + 2b c d)coth(x) +--R + +--R 2 2 2 +--R ((- 4a d - 6a c d)cosh(x) + 2a c d)coth(x) +--R + +--R 2 2 2 +--R (((4b - 5a)d + 11b c d)cosh(x) + 2a d )coth(x) +--R + +--R 2 2 2 2 +--R (4a d + a c d + 5b c )cosh(x) + 2b c +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 3 +--R ((- 6b d - 4b c d)cosh(x) + (2b d + 4b c d)cosh(x))coth(x) +--R + +--R 2 3 2 2 +--R ((- 6a d - 4a c d)cosh(x) + (2a d + 4a c d)cosh(x))coth(x) +--R + +--R 2 3 2 +--R ((6b d + 4b c d)cosh(x) + (2b + 4a)d cosh(x))coth(x) +--R + +--R 2 3 2 2 +--R (6a d + 4a c d)cosh(x) + (- 2a d + 4b c d + 4b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 +--R ((- 4b d - b c d)cosh(x) + (4b d + 2b c d)cosh(x) - b c d) +--R * +--R 3 +--R coth(x) +--R + +--R 2 4 2 2 +--R ((- 4a d - a c d)cosh(x) + (4a d + 2a c d)cosh(x) - a c d) +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 2 2 2 +--R ((4b + 5a)d - 4b c d)cosh(x) + (4b d + 2b c d)cosh(x) - a d +--R + +--R 2b c d +--R * +--R coth(x) +--R + +--R 2 2 4 +--R (4a d + 6a c d - 5b c )cosh(x) +--R + +--R 2 2 2 2 +--R (- 4a d + (8b - 2a)c d + 4b c )cosh(x) + b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (- b d cosh(x) + 2b d cosh(x) - b d cosh(x))coth(x) +--R + +--R 2 5 2 3 2 2 +--R (- a d cosh(x) + 2a d cosh(x) - a d cosh(x))coth(x) +--R + +--R 2 5 2 3 +--R ((b + 4a)d - 4b c d)cosh(x) + ((2b - 4a)d + 4b c d)cosh(x) +--R + +--R 2 +--R b d cosh(x) +--R * +--R coth(x) +--R + +--R 2 2 5 +--R (a d + 4a c d - 4b c )cosh(x) +--R + +--R 2 2 3 2 +--R (- 2a d + (4b - 4a)c d + 4b c )cosh(x) + a d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 +--R (a d - b c d)cosh(x) + (- 2a d + 2b c d)cosh(x) +--R + +--R 2 2 +--R (a d - b c d)cosh(x) +--R * +--R coth(x) +--R + +--R 2 6 2 4 +--R (a c d - b c )cosh(x) + (- 2a c d + 2b c )cosh(x) +--R + +--R 2 2 +--R (a c d - b c )cosh(x) +--R / +--R 2 2 6 +--R (c d coth(x) + c d)sinh(x) +--R + +--R 3 2 2 2 5 +--R ((d + 4c d )cosh(x)coth(x) + (c d + 4c d)cosh(x))sinh(x) +--R + +--R 3 2 2 2 2 2 2 +--R ((4d + 6c d )cosh(x) - 2c d )coth(x) + (4c d + 6c d)cosh(x) +--R + +--R 2 +--R - 2c d +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 3 2 +--R ((6d + 4c d )cosh(x) + (- 2d - 4c d )cosh(x))coth(x) +--R + +--R 2 2 3 2 2 +--R (6c d + 4c d)cosh(x) + (- 2c d - 4c d)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R ((4d + c d )cosh(x) + (- 4d - 2c d )cosh(x) + c d )coth(x) +--R + +--R 2 2 4 2 2 2 2 +--R (4c d + c d)cosh(x) + (- 4c d - 2c d)cosh(x) + c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 3 3 3 2 5 +--R (d cosh(x) - 2d cosh(x) + d cosh(x))coth(x) + c d cosh(x) +--R + +--R 2 3 2 +--R - 2c d cosh(x) + c d cosh(x) +--R * +--R sinh(x) +--R Type: Expression(Integer) +--E 491 + +)clear all + + +--S 492 of 531 +t1091:= csch(x)^2*(a+b*coth(x))^2/(c+d*coth(x)) +--R +--R +--R 2 2 2 2 +--R (b coth(x) + 2a b coth(x) + a )csch(x) +--R (1) ---------------------------------------- +--R d coth(x) + c +--R Type: Expression(Integer) +--E 492 + +--S 493 of 531 +r1091:= b*(b*c-a*d)*coth(x)/d^2-1/2*(a+b*coth(x))^2/d-_ + (b*c-a*d)^2*log(c+d*coth(x))/d^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (- 2a d + 4a b c d - 2b c )log(d coth(x) + c) - b d coth(x) +--R + +--R 2 2 2 2 +--R (- 4a b d + 2b c d)coth(x) - a d +--R / +--R 3 +--R 2d +--R Type: Expression(Integer) +--E 493 + +--S 494 of 531 +a1091:= integrate(t1091,x) +--R +--R +--R (3) +--R 2 2 2 2 4 +--R (a d - 2a b c d + b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (4a d - 8a b c d + 4b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((6a d - 12a b c d + 6b c )cosh(x) - 2a d + 4a b c d - 2b c ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 2 3 +--R (4a d - 8a b c d + 4b c )cosh(x) +--R + +--R 2 2 2 2 +--R (- 4a d + 8a b c d - 4b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 4 +--R (a d - 2a b c d + b c )cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 2a d + 4a b c d - 2b c )cosh(x) + a d - 2a b c d + b c +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 4 +--R (- a d + 2a b c d - b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 4a d + 8a b c d - 4b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- 6a d + 12a b c d - 6b c )cosh(x) + 2a d - 4a b c d + 2b c ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 4a d + 8a b c d - 4b c )cosh(x) +--R + +--R 2 2 2 2 +--R (4a d - 8a b c d + 4b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 4 +--R (- a d + 2a b c d - b c )cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )cosh(x) - a d + 2a b c d - b c +--R * +--R - 2c sinh(x) - 2d cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 +--R ((- 2b - 4a b)d + 2b c d)sinh(x) +--R + +--R 2 2 2 +--R ((- 4b - 8a b)d + 4b c d)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 2b - 4a b)d + 2b c d)cosh(x) + 4a b d - 2b c d +--R / +--R 3 4 3 3 3 2 3 2 +--R d sinh(x) + 4d cosh(x)sinh(x) + (6d cosh(x) - 2d )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4d cosh(x) - 4d cosh(x))sinh(x) + d cosh(x) - 2d cosh(x) + d +--R Type: Union(Expression(Integer),...) +--E 494 + +--S 495 of 531 +m1091:= a1091-r1091 +--R +--R +--R (4) +--R 2 2 2 2 4 +--R (2a d - 4a b c d + 2b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (8a d - 16a b c d + 8b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((12a d - 24a b c d + 12b c )cosh(x) - 4a d + 8a b c d - 4b c ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 2 3 +--R (8a d - 16a b c d + 8b c )cosh(x) +--R + +--R 2 2 2 2 +--R (- 8a d + 16a b c d - 8b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 4 +--R (2a d - 4a b c d + 2b c )cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 4a d + 8a b c d - 4b c )cosh(x) + 2a d - 4a b c d + 2b c +--R * +--R log(d coth(x) + c) +--R + +--R 2 2 2 2 4 +--R (2a d - 4a b c d + 2b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (8a d - 16a b c d + 8b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((12a d - 24a b c d + 12b c )cosh(x) - 4a d + 8a b c d - 4b c ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 2 3 +--R (8a d - 16a b c d + 8b c )cosh(x) +--R + +--R 2 2 2 2 +--R (- 8a d + 16a b c d - 8b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 4 +--R (2a d - 4a b c d + 2b c )cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 4a d + 8a b c d - 4b c )cosh(x) + 2a d - 4a b c d + 2b c +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 4 +--R (- 2a d + 4a b c d - 2b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 8a d + 16a b c d - 8b c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 12a d + 24a b c d - 12b c )cosh(x) + 4a d - 8a b c d +--R + +--R 2 2 +--R 4b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 8a d + 16a b c d - 8b c )cosh(x) +--R + +--R 2 2 2 2 +--R (8a d - 16a b c d + 8b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 2a d + 4a b c d - 2b c )cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (4a d - 8a b c d + 4b c )cosh(x) - 2a d + 4a b c d - 2b c +--R * +--R - 2c sinh(x) - 2d cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 2 4 +--R (b d coth(x) + (4a b d - 2b c d)coth(x) + a d )sinh(x) +--R + +--R 2 2 2 2 2 +--R 4b d cosh(x)coth(x) + (16a b d - 8b c d)cosh(x)coth(x) +--R + +--R 2 2 +--R 4a d cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (6b d cosh(x) - 2b d )coth(x) +--R + +--R 2 2 2 2 2 +--R ((24a b d - 12b c d)cosh(x) - 8a b d + 4b c d)coth(x) +--R + +--R 2 2 2 2 2 2 2 +--R 6a d cosh(x) + (- 4b - 8a b - 2a )d + 4b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 2 2 2 +--R (4b d cosh(x) - 4b d cosh(x))coth(x) +--R + +--R 2 2 3 2 2 +--R ((16a b d - 8b c d)cosh(x) + (- 16a b d + 8b c d)cosh(x))coth(x) +--R + +--R 2 2 3 2 2 2 2 +--R 4a d cosh(x) + ((- 8b - 16a b - 4a )d + 8b c d)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 2 +--R (b d cosh(x) - 2b d cosh(x) + b d )coth(x) +--R + +--R 2 2 4 2 2 2 2 +--R (4a b d - 2b c d)cosh(x) + (- 8a b d + 4b c d)cosh(x) + 4a b d +--R + +--R 2 +--R - 2b c d +--R * +--R coth(x) +--R + +--R 2 2 4 2 2 2 2 2 2 2 +--R a d cosh(x) + ((- 4b - 8a b - 2a )d + 4b c d)cosh(x) + (8a b + a )d +--R + +--R 2 +--R - 4b c d +--R / +--R 3 4 3 3 3 2 3 2 +--R 2d sinh(x) + 8d cosh(x)sinh(x) + (12d cosh(x) - 4d )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8d cosh(x) - 8d cosh(x))sinh(x) + 2d cosh(x) - 4d cosh(x) + 2d +--R Type: Expression(Integer) +--E 495 + +--S 496 of 531 +d1091:= D(m1091,x) +--R +--R +--R (5) +--R 2 2 4 2 3 2 2 2 2 +--R - b c d coth(x) - 2a b c d coth(x) + (b - a )c d coth(x) +--R + +--R 2 3 2 2 2 2 2 3 +--R (- a d + 4a b c d - b c d)coth(x) + 2a b c d - b c +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 2 2 4 +--R (- b d - 6b c d )cosh(x)coth(x) +--R + +--R 3 2 3 +--R (- 2a b d - 12a b c d )cosh(x)coth(x) +--R + +--R 2 2 3 2 2 2 2 +--R ((b - a )d + (6b - 6a )c d )cosh(x)coth(x) +--R + +--R 2 3 2 2 2 +--R ((2a b - 6a )d + 24a b c d - 6b c d)cosh(x)coth(x) +--R + +--R 2 3 2 2 3 +--R (a d + 12a b c d - 6b c )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 2 2 2 2 2 4 +--R ((- 6b d - 15b c d )cosh(x) + 3b c d )coth(x) +--R + +--R 3 2 2 2 3 +--R ((- 12a b d - 30a b c d )cosh(x) + 6a b c d )coth(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 +--R (((6b - 6a )d + (15b - 15a )c d )cosh(x) + (- 3b + 3a )c d ) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 2 2 2 2 2 3 +--R ((12a b - 14a )d + 58a b c d - 14b c d)cosh(x) + 3a d +--R + +--R 2 2 2 2 +--R (4b - 4a b)c d - b c d +--R * +--R coth(x) +--R + +--R 2 3 2 2 2 2 3 2 2 2 2 3 +--R (6a d + a c d + 28a b c d - 14b c )cosh(x) + (4b + 2a b)c d - b c +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 2 2 3 2 3 2 2 4 +--R ((- 15b d - 20b c d )cosh(x) + (3b d + 12b c d )cosh(x))coth(x) +--R + +--R 3 2 3 3 2 +--R ((- 30a b d - 40a b c d )cosh(x) + (6a b d + 24a b c d )cosh(x)) +--R * +--R 3 +--R coth(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((15b - 15a )d + (20b - 20a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R ((- 3b + 3a )d + (- 12b + 12a )c d )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 2 2 2 3 +--R ((30a b - 14a )d + 68a b c d - 14b c d)cosh(x) +--R + +--R 2 2 3 2 2 2 2 +--R ((4b + 2a b + 12a )d + (12b - 16a b)c d - 4b c d)cosh(x) +--R * +--R coth(x) +--R + +--R 2 3 2 2 2 2 3 3 +--R (15a d + 6a c d + 28a b c d - 14b c )cosh(x) +--R + +--R 2 3 2 2 2 2 2 3 +--R (- 3a d + (4b + 8a b)c d + (12b + 8a b)c d - 4b c )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 2 2 4 2 3 2 2 2 +--R (- 20b d - 15b c d )cosh(x) + (12b d + 18b c d )cosh(x) +--R + +--R 2 2 +--R - 3b c d +--R * +--R 4 +--R coth(x) +--R + +--R 3 2 4 +--R (- 40a b d - 30a b c d )cosh(x) +--R + +--R 3 2 2 2 +--R (24a b d + 36a b c d )cosh(x) - 6a b c d +--R * +--R 3 +--R coth(x) +--R + +--R 2 2 3 2 2 2 4 +--R ((20b - 20a )d + (15b - 15a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 +--R ((- 12b + 12a )d + (- 18b + 18a )c d )cosh(x) + (3b - 3a )c d +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 4 +--R (40a b d + 30a b c d )cosh(x) +--R + +--R 2 2 3 2 2 2 2 2 +--R ((16b + 8a b + 15a )d + (8b - 18a b)c d - 9b c d)cosh(x) +--R + +--R 2 3 2 2 2 2 +--R - 3a d + (4b + 4a b)c d + b c d +--R * +--R coth(x) +--R + +--R 2 3 2 2 4 +--R (20a d + 15a c d )cosh(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 12a d + (16b + 32a b - 3a )c d + (8b + 18a b)c d - 9b c ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 +--R (4b - 2a b)c d + b c +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 5 2 3 2 2 3 +--R (- 15b d - 6b c d )cosh(x) + (18b d + 12b c d )cosh(x) +--R + +--R 2 3 2 2 +--R (- 3b d - 6b c d )cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 3 2 5 +--R (- 30a b d - 12a b c d )cosh(x) +--R + +--R 3 2 3 3 2 +--R (36a b d + 24a b c d )cosh(x) + (- 6a b d - 12a b c d )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 2 2 3 2 2 2 5 +--R ((15b - 15a )d + (6b - 6a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 18b + 18a )d + (- 12b + 12a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R ((3b - 3a )d + (6b - 6a )c d )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 2 2 2 5 +--R ((30a b + 14a )d - 16a b c d + 14b c d)cosh(x) +--R + +--R 2 3 2 2 2 2 3 +--R ((24b + 12a b)d + (- 8b + 8a b)c d - 16b c d)cosh(x) +--R + +--R 2 2 3 2 2 2 2 +--R ((4b - 2a b - 6a )d + (12b + 8a b)c d + 2b c d)cosh(x) +--R * +--R coth(x) +--R + +--R 2 3 2 2 2 2 3 5 +--R (15a d + 20a c d - 28a b c d + 14b c )cosh(x) +--R + +--R 2 3 2 2 2 2 2 +--R - 18a d + (24b + 48a b - 12a )c d + (- 8b + 32a b)c d +--R + +--R 2 3 +--R - 16b c +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 2 2 2 2 2 3 +--R (3a d + (4b - 8a b)c d + (12b - 4a b)c d + 2b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 2 2 6 2 3 2 2 4 +--R (- 6b d - b c d )cosh(x) + (12b d + 3b c d )cosh(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 6b d - 3b c d )cosh(x) + b c d +--R * +--R 4 +--R coth(x) +--R + +--R 3 2 6 3 2 4 +--R (- 12a b d - 2a b c d )cosh(x) + (24a b d + 6a b c d )cosh(x) +--R + +--R 3 2 2 2 +--R (- 12a b d - 6a b c d )cosh(x) + 2a b c d +--R * +--R 3 +--R coth(x) +--R + +--R 2 2 3 2 2 2 6 +--R ((6b - 6a )d + (b - a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 4 +--R ((- 12b + 12a )d + (- 3b + 3a )c d )cosh(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 +--R ((6b - 6a )d + (3b - 3a )c d )cosh(x) + (- b + a )c d +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 2 2 2 6 +--R ((12a b + 14a )d - 26a b c d + 14b c d)cosh(x) +--R + +--R 2 2 3 2 2 2 2 4 +--R ((16b + 8a b - 15a )d + (- 12b + 32a b)c d - 19b c d)cosh(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R ((8b - 4a b)d + (12b - 2a b)c d + 4b c d)cosh(x) + a d +--R + +--R 2 2 2 +--R - 4a b c d + b c d +--R * +--R coth(x) +--R + +--R 2 3 2 2 2 2 3 6 +--R (6a d + 15a c d - 28a b c d + 14b c )cosh(x) +--R + +--R 2 3 2 2 2 2 2 +--R - 12a d + (16b + 32a b - 18a )c d + (- 12b + 38a b)c d +--R + +--R 2 3 +--R - 19b c +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 2 2 2 2 2 2 3 2 +--R (6a d + (8b - 16a b + 3a )c d + (12b - 8a b)c d + 4b c )cosh(x) +--R + +--R 2 2 3 +--R - 2a b c d + b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 7 2 3 5 2 3 3 2 3 +--R (- b d cosh(x) + 3b d cosh(x) - 3b d cosh(x) + b d cosh(x)) +--R * +--R 4 +--R coth(x) +--R + +--R 3 7 3 5 3 3 +--R - 2a b d cosh(x) + 6a b d cosh(x) - 6a b d cosh(x) +--R + +--R 3 +--R 2a b d cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 2 2 3 7 2 2 3 5 +--R (b - a )d cosh(x) + (- 3b + 3a )d cosh(x) +--R + +--R 2 2 3 3 2 2 3 +--R (3b - 3a )d cosh(x) + (- b + a )d cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 2 2 2 7 +--R ((2a b + 6a )d - 12a b c d + 6b c d)cosh(x) +--R + +--R 2 2 3 2 2 2 2 5 +--R ((4b + 2a b - 12a )d + (- 4b + 24a b)c d - 12b c d)cosh(x) +--R + +--R 2 2 3 2 2 2 2 3 +--R ((4b - 2a b + 6a )d + (4b - 12a b)c d + 6b c d)cosh(x) +--R + +--R 3 +--R - 2a b d cosh(x) +--R * +--R coth(x) +--R + +--R 2 3 2 2 2 2 3 7 +--R (a d + 6a c d - 12a b c d + 6b c )cosh(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 3a d + (4b + 8a b - 12a )c d + (- 4b + 24a b)c d - 12b c ) +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3 2 2 2 2 2 2 3 3 +--R (3a d + (4b - 8a b + 6a )c d + (4b - 12a b)c d + 6b c )cosh(x) +--R + +--R 2 3 +--R - a d cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 2 2 2 8 +--R (a d - 2a b c d + b c d)cosh(x) +--R + +--R 2 3 2 2 2 6 +--R (- 3a d + 6a b c d - 3b c d)cosh(x) +--R + +--R 2 3 2 2 2 4 +--R (3a d - 6a b c d + 3b c d)cosh(x) +--R + +--R 2 3 2 2 2 2 +--R (- a d + 2a b c d - b c d)cosh(x) +--R * +--R coth(x) +--R + +--R 2 2 2 2 3 8 +--R (a c d - 2a b c d + b c )cosh(x) +--R + +--R 2 2 2 2 3 6 +--R (- 3a c d + 6a b c d - 3b c )cosh(x) +--R + +--R 2 2 2 2 3 4 2 2 2 2 3 2 +--R (3a c d - 6a b c d + 3b c )cosh(x) + (- a c d + 2a b c d - b c )cosh(x) +--R / +--R 3 2 2 8 +--R (c d coth(x) + c d )sinh(x) +--R + +--R 4 3 3 2 2 7 +--R ((d + 6c d )cosh(x)coth(x) + (c d + 6c d )cosh(x))sinh(x) +--R + +--R 4 3 2 3 3 2 2 2 +--R ((6d + 15c d )cosh(x) - 3c d )coth(x) + (6c d + 15c d )cosh(x) +--R + +--R 2 2 +--R - 3c d +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 3 4 3 +--R ((15d + 20c d )cosh(x) + (- 3d - 12c d )cosh(x))coth(x) +--R + +--R 3 2 2 3 3 2 2 +--R (15c d + 20c d )cosh(x) + (- 3c d - 12c d )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 4 3 2 3 +--R ((20d + 15c d )cosh(x) + (- 12d - 18c d )cosh(x) + 3c d )coth(x) +--R + +--R 3 2 2 4 3 2 2 2 2 2 +--R (20c d + 15c d )cosh(x) + (- 12c d - 18c d )cosh(x) + 3c d +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 4 3 3 +--R (15d + 6c d )cosh(x) + (- 18d - 12c d )cosh(x) +--R + +--R 4 3 +--R (3d + 6c d )cosh(x) +--R * +--R coth(x) +--R + +--R 3 2 2 5 3 2 2 3 +--R (15c d + 6c d )cosh(x) + (- 18c d - 12c d )cosh(x) +--R + +--R 3 2 2 +--R (3c d + 6c d )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 4 3 4 +--R (6d + c d )cosh(x) + (- 12d - 3c d )cosh(x) +--R + +--R 4 3 2 3 +--R (6d + 3c d )cosh(x) - c d +--R * +--R coth(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (6c d + c d )cosh(x) + (- 12c d - 3c d )cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (6c d + 3c d )cosh(x) - c d +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 4 5 4 3 4 +--R (d cosh(x) - 3d cosh(x) + 3d cosh(x) - d cosh(x))coth(x) +--R + +--R 3 7 3 5 3 3 3 +--R c d cosh(x) - 3c d cosh(x) + 3c d cosh(x) - c d cosh(x) +--R * +--R sinh(x) +--R Type: Expression(Integer) +--E 496 + +)clear all + + +--S 497 of 531 +t1092:= csch(x)^2*(a+b*coth(x))^3/(c+d*coth(x)) +--R +--R +--R 3 3 2 2 2 3 2 +--R (b coth(x) + 3a b coth(x) + 3a b coth(x) + a )csch(x) +--R (1) -------------------------------------------------------- +--R d coth(x) + c +--R Type: Expression(Integer) +--E 497 + +--S 498 of 531 +r1092:= -b*(b*c-a*d)^2*coth(x)/d^3+1/2*(b*c-a*d)*(a+b*coth(x))^2/d^2-_ + 1/3*(a+b*coth(x))^3/d+(b*c-a*d)^3*log(c+d*coth(x))/d^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )log(d coth(x) + c) +--R + +--R 3 3 3 2 3 3 2 2 +--R - 2b d coth(x) + (- 9a b d + 3b c d )coth(x) +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 18a b d + 18a b c d - 6b c d)coth(x) - 5a d + 3a b c d +--R / +--R 4 +--R 6d +--R Type: Expression(Integer) +--E 498 + +--S 499 of 531 +a1092:= integrate(t1092,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 6 +--R (3a d - 9a b c d + 9a b c d - 3b c )sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (45a d - 135a b c d + 135a b c d - 45b c )cosh(x) - 9a d +--R + +--R 2 2 2 2 3 3 +--R 27a b c d - 27a b c d + 9b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (60a d - 180a b c d + 180a b c d - 60b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (45a d - 135a b c d + 135a b c d - 45b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 54a d + 162a b c d - 162a b c d + 54b c )cosh(x) + 9a d +--R + +--R 2 2 2 2 3 3 +--R - 27a b c d + 27a b c d - 9b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (3a d - 9a b c d + 9a b c d - 3b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 9a d + 27a b c d - 27a b c d + 9b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 2 2 +--R (9a d - 27a b c d + 27a b c d - 9b c )cosh(x) - 3a d + 9a b c d +--R + +--R 2 2 3 3 +--R - 9a b c d + 3b c +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (- 3a d + 9a b c d - 9a b c d + 3b c )sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 45a d + 135a b c d - 135a b c d + 45b c )cosh(x) + 9a d +--R + +--R 2 2 2 2 3 3 +--R - 27a b c d + 27a b c d - 9b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 60a d + 180a b c d - 180a b c d + 60b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 45a d + 135a b c d - 135a b c d + 45b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (54a d - 162a b c d + 162a b c d - 54b c )cosh(x) - 9a d +--R + +--R 2 2 2 2 3 3 +--R 27a b c d - 27a b c d + 9b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (- 3a d + 9a b c d - 9a b c d + 3b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (9a d - 27a b c d + 27a b c d - 9b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 9a d + 27a b c d - 27a b c d + 9b c )cosh(x) + 3a d +--R + +--R 2 2 2 2 3 3 +--R - 9a b c d + 9a b c d - 3b c +--R * +--R - 2c sinh(x) - 2d cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 4 +--R ((- 6b - 18a b - 18a b)d + (6b + 18a b )c d - 6b c d)sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 +--R ((- 24b - 72a b - 72a b)d + (24b + 72a b )c d - 24b c d)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 +--R ((- 36b - 108a b - 108a b)d + (36b + 108a b )c d - 36b c d) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3 3 2 2 3 2 +--R (18a b + 36a b)d + (- 6b - 36a b )c d + 12b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 3 +--R ((- 24b - 72a b - 72a b)d + (24b + 72a b )c d - 24b c d)cosh(x) +--R + +--R 2 2 3 3 2 2 3 2 +--R ((36a b + 72a b)d + (- 12b - 72a b )c d + 24b c d)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 4 +--R ((- 6b - 18a b - 18a b)d + (6b + 18a b )c d - 6b c d)cosh(x) +--R + +--R 2 2 3 3 2 2 3 2 2 +--R ((18a b + 36a b)d + (- 6b - 36a b )c d + 12b c d)cosh(x) +--R + +--R 3 2 3 2 2 3 2 +--R (- 2b - 18a b)d + 18a b c d - 6b c d +--R / +--R 4 6 4 5 4 2 4 4 +--R 3d sinh(x) + 18d cosh(x)sinh(x) + (45d cosh(x) - 9d )sinh(x) +--R + +--R 4 3 4 3 +--R (60d cosh(x) - 36d cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45d cosh(x) - 54d cosh(x) + 9d )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18d cosh(x) - 36d cosh(x) + 18d cosh(x))sinh(x) + 3d cosh(x) +--R + +--R 4 4 4 2 4 +--R - 9d cosh(x) + 9d cosh(x) - 3d +--R Type: Union(Expression(Integer),...) +--E 499 + +--S 500 of 531 +m1092:= a1092-r1092 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 6 +--R (6a d - 18a b c d + 18a b c d - 6b c )sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (90a d - 270a b c d + 270a b c d - 90b c )cosh(x) - 18a d +--R + +--R 2 2 2 2 3 3 +--R 54a b c d - 54a b c d + 18b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (120a d - 360a b c d + 360a b c d - 120b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 72a d + 216a b c d - 216a b c d + 72b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (90a d - 270a b c d + 270a b c d - 90b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 108a d + 324a b c d - 324a b c d + 108b c )cosh(x) + 18a d +--R + +--R 2 2 2 2 3 3 +--R - 54a b c d + 54a b c d - 18b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 72a d + 216a b c d - 216a b c d + 72b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (6a d - 18a b c d + 18a b c d - 6b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x) - 6a d +--R + +--R 2 2 2 2 3 3 +--R 18a b c d - 18a b c d + 6b c +--R * +--R log(d coth(x) + c) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (6a d - 18a b c d + 18a b c d - 6b c )sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (90a d - 270a b c d + 270a b c d - 90b c )cosh(x) - 18a d +--R + +--R 2 2 2 2 3 3 +--R 54a b c d - 54a b c d + 18b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (120a d - 360a b c d + 360a b c d - 120b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 72a d + 216a b c d - 216a b c d + 72b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (90a d - 270a b c d + 270a b c d - 90b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 108a d + 324a b c d - 324a b c d + 108b c )cosh(x) + 18a d +--R + +--R 2 2 2 2 3 3 +--R - 54a b c d + 54a b c d - 18b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 72a d + 216a b c d - 216a b c d + 72b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (36a d - 108a b c d + 108a b c d - 36b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (6a d - 18a b c d + 18a b c d - 6b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x) - 6a d +--R + +--R 2 2 2 2 3 3 +--R 18a b c d - 18a b c d + 6b c +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x)sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 90a d + 270a b c d - 270a b c d + 90b c )cosh(x) + 18a d +--R + +--R 2 2 2 2 3 3 +--R - 54a b c d + 54a b c d - 18b c +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 120a d + 360a b c d - 360a b c d + 120b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (72a d - 216a b c d + 216a b c d - 72b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (- 90a d + 270a b c d - 270a b c d + 90b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (108a d - 324a b c d + 324a b c d - 108b c )cosh(x) - 18a d +--R + +--R 2 2 2 2 3 3 +--R 54a b c d - 54a b c d + 18b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 5 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (72a d - 216a b c d + 216a b c d - 72b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 36a d + 108a b c d - 108a b c d + 36b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 2 3 3 6 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (18a d - 54a b c d + 54a b c d - 18b c )cosh(x) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 18a d + 54a b c d - 54a b c d + 18b c )cosh(x) + 6a d +--R + +--R 2 2 2 2 3 3 +--R - 18a b c d + 18a b c d - 6b c +--R * +--R - 2c sinh(x) - 2d cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 3 2 3 3 2 2 +--R 2b d coth(x) + (9a b d - 3b c d )coth(x) +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (18a b d - 18a b c d + 6b c d)coth(x) + 5a d - 3a b c d +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 3 2 3 3 2 2 +--R 12b d cosh(x)coth(x) + (54a b d - 18b c d )cosh(x)coth(x) +--R + +--R 2 3 2 2 3 2 +--R (108a b d - 108a b c d + 36b c d)cosh(x)coth(x) +--R + +--R 3 3 2 2 +--R (30a d - 18a b c d )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 3 2 3 3 3 +--R (30b d cosh(x) - 6b d )coth(x) +--R + +--R 2 3 3 2 2 2 3 3 2 2 +--R ((135a b d - 45b c d )cosh(x) - 27a b d + 9b c d )coth(x) +--R + +--R 2 3 2 2 3 2 2 2 3 +--R (270a b d - 270a b c d + 90b c d)cosh(x) - 54a b d +--R + +--R 2 2 3 2 +--R 54a b c d - 18b c d +--R * +--R coth(x) +--R + +--R 3 3 2 2 2 3 2 2 3 3 +--R (75a d - 45a b c d )cosh(x) + (- 12b - 36a b - 36a b - 15a )d +--R + +--R 3 2 2 2 3 2 +--R (12b + 36a b + 9a b)c d - 12b c d +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 3 3 3 +--R (40b d cosh(x) - 24b d cosh(x))coth(x) +--R + +--R 2 3 3 2 3 2 3 3 2 +--R ((180a b d - 60b c d )cosh(x) + (- 108a b d + 36b c d )cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 2 2 3 2 3 +--R (360a b d - 360a b c d + 120b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 +--R (- 216a b d + 216a b c d - 72b c d)cosh(x) +--R * +--R coth(x) +--R + +--R 3 3 2 2 3 +--R (100a d - 60a b c d )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 48b - 144a b - 144a b - 60a )d +--R + +--R 3 2 2 2 3 2 +--R (48b + 144a b + 36a b)c d - 48b c d +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 3 3 2 3 3 3 +--R (30b d cosh(x) - 36b d cosh(x) + 6b d )coth(x) +--R + +--R 2 3 3 2 4 2 3 3 2 2 +--R (135a b d - 45b c d )cosh(x) + (- 162a b d + 54b c d )cosh(x) +--R + +--R 2 3 3 2 +--R 27a b d - 9b c d +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 2 2 3 2 4 +--R (270a b d - 270a b c d + 90b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 2 2 3 +--R (- 324a b d + 324a b c d - 108b c d)cosh(x) + 54a b d +--R + +--R 2 2 3 2 +--R - 54a b c d + 18b c d +--R * +--R coth(x) +--R + +--R 3 3 2 2 4 +--R (75a d - 45a b c d )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 72b - 216a b - 216a b - 90a )d +--R + +--R 3 2 2 2 3 2 +--R (72b + 216a b + 54a b)c d - 72b c d +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R (36a b + 72a b + 15a )d + (- 12b - 72a b - 9a b)c d + 24b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 3 3 3 3 3 3 +--R (12b d cosh(x) - 24b d cosh(x) + 12b d cosh(x))coth(x) +--R + +--R 2 3 3 2 5 2 3 3 2 3 +--R (54a b d - 18b c d )cosh(x) + (- 108a b d + 36b c d )cosh(x) +--R + +--R 2 3 3 2 +--R (54a b d - 18b c d )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 2 2 3 2 5 +--R (108a b d - 108a b c d + 36b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 216a b d + 216a b c d - 72b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 +--R (108a b d - 108a b c d + 36b c d)cosh(x) +--R * +--R coth(x) +--R + +--R 3 3 2 2 5 +--R (30a d - 18a b c d )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 48b - 144a b - 144a b - 60a )d +--R + +--R 3 2 2 2 3 2 +--R (48b + 144a b + 36a b)c d - 48b c d +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 3 3 3 2 2 2 +--R (72a b + 144a b + 30a )d + (- 24b - 144a b - 18a b)c d +--R + +--R 3 2 +--R 48b c d +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 6 3 3 4 3 3 2 3 3 3 +--R (2b d cosh(x) - 6b d cosh(x) + 6b d cosh(x) - 2b d )coth(x) +--R + +--R 2 3 3 2 6 2 3 3 2 4 +--R (9a b d - 3b c d )cosh(x) + (- 27a b d + 9b c d )cosh(x) +--R + +--R 2 3 3 2 2 2 3 3 2 +--R (27a b d - 9b c d )cosh(x) - 9a b d + 3b c d +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 2 2 3 2 6 +--R (18a b d - 18a b c d + 6b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 4 +--R (- 54a b d + 54a b c d - 18b c d)cosh(x) +--R + +--R 2 3 2 2 3 2 2 2 3 2 2 +--R (54a b d - 54a b c d + 18b c d)cosh(x) - 18a b d + 18a b c d +--R + +--R 3 2 +--R - 6b c d +--R * +--R coth(x) +--R + +--R 3 3 2 2 6 +--R (5a d - 3a b c d )cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 2 +--R (- 12b - 36a b - 36a b - 15a )d + (12b + 36a b + 9a b)c d +--R + +--R 3 2 +--R - 12b c d +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 3 3 3 2 2 2 3 2 +--R ((36a b + 72a b + 15a )d + (- 12b - 72a b - 9a b)c d + 24b c d) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 3 3 2 2 2 3 2 +--R (- 4b - 36a b - 5a )d + (36a b + 3a b)c d - 12b c d +--R / +--R 4 6 4 5 4 2 4 4 +--R 6d sinh(x) + 36d cosh(x)sinh(x) + (90d cosh(x) - 18d )sinh(x) +--R + +--R 4 3 4 3 +--R (120d cosh(x) - 72d cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90d cosh(x) - 108d cosh(x) + 18d )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36d cosh(x) - 72d cosh(x) + 36d cosh(x))sinh(x) + 6d cosh(x) +--R + +--R 4 4 4 2 4 +--R - 18d cosh(x) + 18d cosh(x) - 6d +--R Type: Expression(Integer) +--E 500 + +--S 501 of 531 +--d1092:= D(m1092,x) +--E 501 + +)clear all + + +--S 502 of 531 +t1093:= (1+sinh(x)^2)/(1+cosh(x)+sinh(x)) +--R +--R +--R 2 +--R sinh(x) + 1 +--R (1) --------------------- +--R sinh(x) + cosh(x) + 1 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 531 +r1093:= 3/4*x+1/2*cosh(x)-1/4*cosh(x)^2-log(1+cosh(x)+sinh(x))+_ + 1/4*cosh(x)*sinh(x)+1/8 +--R +--R +--R (2) +--R 2 +--R - 8log(sinh(x) + cosh(x) + 1) + 2cosh(x)sinh(x) - 2cosh(x) + 4cosh(x) +--R + +--R 6x + 1 +--R / +--R 8 +--R Type: Expression(Integer) +--E 503 + +--S 504 of 531 +a1093:= integrate(t1093,x) +--R +--R +--R (3) +--R 2 2 +--R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 +--R 2sinh(x) + (6cosh(x) + 6x)sinh(x) +--R + +--R 2 3 2 +--R (6cosh(x) + 12x cosh(x) + 2)sinh(x) + 2cosh(x) + 6x cosh(x) + 2cosh(x) +--R + +--R - 1 +--R / +--R 2 2 +--R 8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) +--R Type: Union(Expression(Integer),...) +--E 504 + +--S 505 of 531 +m1093:= a1093-r1093 +--R +--R +--R (4) +--R 3 2 2 +--R (- 2cosh(x) + 2)sinh(x) + (- 2cosh(x) + 2cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 3 +--R (2cosh(x) - 2cosh(x) - 2cosh(x) + 2)sinh(x) + 2cosh(x) - 2cosh(x) +--R + +--R 2 +--R - cosh(x) + 2cosh(x) - 1 +--R / +--R 2 2 +--R 8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) +--R Type: Expression(Integer) +--E 505 + +--S 506 of 531 +d1093:= D(m1093,x) +--R +--R +--R (5) +--R 4 3 2 2 +--R - sinh(x) - sinh(x) + (2cosh(x) - cosh(x))sinh(x) +--R + +--R 2 4 3 +--R (cosh(x) - 1)sinh(x) - cosh(x) + cosh(x) - cosh(x) + 1 +--R / +--R 2 2 +--R 4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 506 + +)clear all + + +--S 507 of 531 +t1094:= cosh(x)^2/(1+exp(x)) +--R +--R +--R 2 +--R cosh(x) +--R (1) -------- +--R x +--R %e + 1 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 531 +r1094:= -1/8*exp(-2*x)+1/4*exp(-x)+1/4*exp(x)+3/4*x-log(1+exp(x)) +--R +--R +--R x x - x - 2x +--R - 8log(%e + 1) + 2%e + 2%e - %e + 6x +--R (2) --------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 508 + +--S 509 of 531 +a1094:= integrate(t1094,x) +--R +--R +--R (3) +--R 2 2 +--R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 +--R 2sinh(x) + (6cosh(x) + 6x)sinh(x) +--R + +--R 2 3 2 +--R (6cosh(x) + 12x cosh(x) + 2)sinh(x) + 2cosh(x) + 6x cosh(x) + 2cosh(x) +--R + +--R - 1 +--R / +--R 2 2 +--R 8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) +--R Type: Union(Expression(Integer),...) +--E 509 + +--S 510 of 531 +m1094:= a1094-r1094 +--R +--R +--R (4) +--R 2 2 +--R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 x 3 +--R (8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) )log(%e + 1) + 2sinh(x) +--R + +--R x - x - 2x 2 +--R (- 2%e - 2%e + %e + 6cosh(x))sinh(x) +--R + +--R x - x - 2x 2 +--R (- 4cosh(x)%e - 4cosh(x)%e + 2cosh(x)%e + 6cosh(x) + 2)sinh(x) +--R + +--R 2 x 2 - x 2 - 2x 3 +--R - 2cosh(x) %e - 2cosh(x) %e + cosh(x) %e + 2cosh(x) + 2cosh(x) - 1 +--R / +--R 2 2 +--R 8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) +--R Type: Expression(Integer) +--E 510 + +--S 511 of 531 +d1094:= D(m1094,x) +--R +--R +--R (5) +--R x 4 +--R (%e + 1)sinh(x) +--R + +--R x 2 - x - 2x x - x - 2x +--R - (%e ) + (%e - %e + 4cosh(x))%e + %e - %e + 4cosh(x) +--R + +--R - 3 +--R * +--R 3 +--R sinh(x) +--R + +--R x 2 +--R (- 3cosh(x) - 1)(%e ) +--R + +--R - x - 2x 2 x +--R ((3cosh(x) + 1)%e + (- 3cosh(x) - 1)%e + 6cosh(x) + 2)%e +--R + +--R - x - 2x 2 +--R (3cosh(x) + 1)%e + (- 3cosh(x) - 1)%e + 6cosh(x) - 9cosh(x) - 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 2 x 2 +--R (- 3cosh(x) - 2cosh(x))(%e ) +--R + +--R 2 - x 2 - 2x +--R (3cosh(x) + 2cosh(x))%e + (- 3cosh(x) - 2cosh(x))%e +--R + +--R 3 +--R 4cosh(x) + 4cosh(x) +--R * +--R x +--R %e +--R + +--R 2 - x 2 - 2x +--R (3cosh(x) + 2cosh(x))%e + (- 3cosh(x) - 2cosh(x))%e +--R + +--R 3 2 +--R 4cosh(x) - 9cosh(x) - 2cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 x 2 +--R (- cosh(x) - cosh(x) )(%e ) +--R + +--R 3 2 - x 3 2 - 2x 4 +--R (cosh(x) + cosh(x) )%e + (- cosh(x) - cosh(x) )%e + cosh(x) +--R + +--R 2 +--R 2cosh(x) + 1 +--R * +--R x +--R %e +--R + +--R 3 2 - x 3 2 - 2x 4 +--R (cosh(x) + cosh(x) )%e + (- cosh(x) - cosh(x) )%e + cosh(x) +--R + +--R 3 2 +--R - 3cosh(x) - cosh(x) + 1 +--R / +--R x 3 x 2 +--R (4%e + 4)sinh(x) + ((12cosh(x) + 4)%e + 12cosh(x) + 4)sinh(x) +--R + +--R 2 x 2 +--R ((12cosh(x) + 8cosh(x))%e + 12cosh(x) + 8cosh(x))sinh(x) +--R + +--R 3 2 x 3 2 +--R (4cosh(x) + 4cosh(x) )%e + 4cosh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 511 + +)clear all + + +--S 512 of 531 +t1095:= (1+sech(x))^(1/2)*sech(x)*tanh(x)^3 +--R +--R +--R 3 +-----------+ +--R (1) sech(x)tanh(x) \|sech(x) + 1 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 531 +r1095:= -4/5*(1+sech(x))^(5/2)+2/7*(1+sech(x))^(7/2) +--R +--R +--R 3 2 +-----------+ +--R (10sech(x) + 2sech(x) - 26sech(x) - 18)\|sech(x) + 1 +--R (2) ------------------------------------------------------- +--R 35 +--R Type: Expression(Integer) +--E 513 + +--S 514 of 531 +a1095:= integrate(t1095,x) +--R +--R +--R (3) +--R 12 11 +--R 4480sinh(x) + (53760cosh(x) + 2240)sinh(x) +--R + +--R 2 10 +--R (295680cosh(x) + 24640cosh(x) + 10080)sinh(x) +--R + +--R 3 2 9 +--R (985600cosh(x) + 123200cosh(x) + 100800cosh(x) + 2240)sinh(x) +--R + +--R 4 3 2 +--R 2217600cosh(x) + 369600cosh(x) + 453600cosh(x) + 20160cosh(x) +--R + +--R 13552 +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 3 +--R 3548160cosh(x) + 739200cosh(x) + 1209600cosh(x) +--R + +--R 2 +--R 80640cosh(x) + 108416cosh(x) + 2100 +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 +--R 4139520cosh(x) + 1034880cosh(x) + 2116800cosh(x) +--R + +--R 3 2 +--R 188160cosh(x) + 379456cosh(x) + 14700cosh(x) + 10742 +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 +--R 3548160cosh(x) + 1034880cosh(x) + 2540160cosh(x) +--R + +--R 4 3 2 +--R 282240cosh(x) + 758912cosh(x) + 44100cosh(x) + 64452cosh(x) +--R + +--R 1960 +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 +--R 2217600cosh(x) + 739200cosh(x) + 2116800cosh(x) +--R + +--R 5 4 3 2 +--R 282240cosh(x) + 948640cosh(x) + 73500cosh(x) + 161130cosh(x) +--R + +--R 9800cosh(x) + 3862 +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 +--R 985600cosh(x) + 369600cosh(x) + 1209600cosh(x) +--R + +--R 6 5 4 3 +--R 188160cosh(x) + 758912cosh(x) + 73500cosh(x) + 214840cosh(x) +--R + +--R 2 +--R 19600cosh(x) + 15448cosh(x) + 364 +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 295680cosh(x) + 123200cosh(x) + 453600cosh(x) + 80640cosh(x) +--R + +--R 6 5 4 3 +--R 379456cosh(x) + 44100cosh(x) + 161130cosh(x) + 19600cosh(x) +--R + +--R 2 +--R 23172cosh(x) + 1092cosh(x) + 530 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 53760cosh(x) + 24640cosh(x) + 100800cosh(x) + 20160cosh(x) +--R + +--R 7 6 5 4 +--R 108416cosh(x) + 14700cosh(x) + 64452cosh(x) + 9800cosh(x) +--R + +--R 3 2 +--R 15448cosh(x) + 1092cosh(x) + 1060cosh(x) - 56 +--R * +--R sinh(x) +--R + +--R 12 11 10 9 +--R 4480cosh(x) + 2240cosh(x) + 10080cosh(x) + 2240cosh(x) +--R + +--R 8 7 6 5 +--R 13552cosh(x) + 2100cosh(x) + 10742cosh(x) + 1960cosh(x) +--R + +--R 4 3 2 +--R 3862cosh(x) + 364cosh(x) + 530cosh(x) - 56cosh(x) + 18 +--R * +--R +-------------------+ +--R | 2cosh(x) +--R |- ----------------- +--R \| sinh(x) - cosh(x) +--R + +--R 13 12 +--R - 4480sinh(x) + (- 58240cosh(x) - 2240)sinh(x) +--R + +--R 2 11 +--R (- 349440cosh(x) - 26880cosh(x) - 12320)sinh(x) +--R + +--R 3 2 10 +--R (- 1281280cosh(x) - 147840cosh(x) - 135520cosh(x) - 3360)sinh(x) +--R + +--R 4 3 2 +--R - 3203200cosh(x) - 492800cosh(x) - 677600cosh(x) - 33600cosh(x) +--R + +--R - 18032 +--R * +--R 9 +--R sinh(x) +--R + +--R 5 4 3 +--R - 5765760cosh(x) - 1108800cosh(x) - 2032800cosh(x) +--R + +--R 2 +--R - 151200cosh(x) - 162288cosh(x) - 2940 +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 4 +--R - 7687680cosh(x) - 1774080cosh(x) - 4065600cosh(x) +--R + +--R 3 2 +--R - 403200cosh(x) - 649152cosh(x) - 23520cosh(x) - 16538 +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 5 +--R - 7687680cosh(x) - 2069760cosh(x) - 5691840cosh(x) +--R + +--R 4 3 2 +--R - 705600cosh(x) - 1514688cosh(x) - 82320cosh(x) - 115766cosh(x) +--R + +--R - 2870 +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 +--R - 5765760cosh(x) - 1774080cosh(x) - 5691840cosh(x) +--R + +--R 5 4 3 2 +--R - 846720cosh(x) - 2272032cosh(x) - 164640cosh(x) - 347298cosh(x) +--R + +--R - 17220cosh(x) - 7994 +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 7 +--R - 3203200cosh(x) - 1108800cosh(x) - 4065600cosh(x) +--R + +--R 6 5 4 3 +--R - 705600cosh(x) - 2272032cosh(x) - 205800cosh(x) - 578830cosh(x) +--R + +--R 2 +--R - 43050cosh(x) - 39970cosh(x) - 1134 +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 8 +--R - 1281280cosh(x) - 492800cosh(x) - 2032800cosh(x) +--R + +--R 7 6 5 4 +--R - 403200cosh(x) - 1514688cosh(x) - 164640cosh(x) - 578830cosh(x) +--R + +--R 3 2 +--R - 57400cosh(x) - 79940cosh(x) - 4536cosh(x) - 1694 +--R * +--R 3 +--R sinh(x) +--R + +--R 11 10 9 8 +--R - 349440cosh(x) - 147840cosh(x) - 677600cosh(x) - 151200cosh(x) +--R + +--R 7 6 5 4 +--R - 649152cosh(x) - 82320cosh(x) - 347298cosh(x) - 43050cosh(x) +--R + +--R 3 2 +--R - 79940cosh(x) - 6804cosh(x) - 5082cosh(x) + 14 +--R * +--R 2 +--R sinh(x) +--R + +--R 12 11 10 9 +--R - 58240cosh(x) - 26880cosh(x) - 135520cosh(x) - 33600cosh(x) +--R + +--R 8 7 6 5 +--R - 162288cosh(x) - 23520cosh(x) - 115766cosh(x) - 17220cosh(x) +--R + +--R 4 3 2 +--R - 39970cosh(x) - 4536cosh(x) - 5082cosh(x) + 28cosh(x) - 126 +--R * +--R sinh(x) +--R + +--R 13 12 11 10 +--R - 4480cosh(x) - 2240cosh(x) - 12320cosh(x) - 3360cosh(x) +--R + +--R 9 8 7 6 +--R - 18032cosh(x) - 2940cosh(x) - 16538cosh(x) - 2870cosh(x) +--R + +--R 5 4 3 2 +--R - 7994cosh(x) - 1134cosh(x) - 1694cosh(x) + 14cosh(x) - 126cosh(x) + 18 +--R / +--R 13 12 +--R 2240sinh(x) + 29120cosh(x)sinh(x) +--R + +--R 2 11 +--R (174720cosh(x) + 10640)sinh(x) +--R + +--R 3 10 +--R (640640cosh(x) + 117040cosh(x))sinh(x) +--R + +--R 4 2 9 +--R (1601600cosh(x) + 585200cosh(x) + 20440)sinh(x) +--R + +--R 5 3 8 +--R (2882880cosh(x) + 1755600cosh(x) + 183960cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (3843840cosh(x) + 3511200cosh(x) + 735840cosh(x) + 20125)sinh(x) +--R + +--R 7 5 3 +--R 3843840cosh(x) + 4915680cosh(x) + 1716960cosh(x) +--R + +--R 140875cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 8 6 4 +--R 2882880cosh(x) + 4915680cosh(x) + 2575440cosh(x) +--R + +--R 2 +--R 422625cosh(x) + 10535 +--R * +--R 5 +--R sinh(x) +--R + +--R 9 7 5 +--R 1601600cosh(x) + 3511200cosh(x) + 2575440cosh(x) +--R + +--R 3 +--R 704375cosh(x) + 52675cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 10 8 6 +--R 640640cosh(x) + 1755600cosh(x) + 1716960cosh(x) +--R + +--R 4 2 +--R 704375cosh(x) + 105350cosh(x) + 2695 +--R * +--R 3 +--R sinh(x) +--R + +--R 11 9 7 +--R 174720cosh(x) + 585200cosh(x) + 735840cosh(x) +--R + +--R 5 3 +--R 422625cosh(x) + 105350cosh(x) + 8085cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 12 10 8 +--R 29120cosh(x) + 117040cosh(x) + 183960cosh(x) +--R + +--R 6 4 2 +--R 140875cosh(x) + 52675cosh(x) + 8085cosh(x) + 245 +--R * +--R sinh(x) +--R + +--R 13 11 9 7 +--R 2240cosh(x) + 10640cosh(x) + 20440cosh(x) + 20125cosh(x) +--R + +--R 5 3 +--R 10535cosh(x) + 2695cosh(x) + 245cosh(x) +--R * +--R +-------------------+ +--R | 2cosh(x) +--R |- ----------------- +--R \| sinh(x) - cosh(x) +--R + +--R 14 13 +--R - 2240sinh(x) - 31360cosh(x)sinh(x) +--R + +--R 2 12 +--R (- 203840cosh(x) - 11760)sinh(x) +--R + +--R 3 11 +--R (- 815360cosh(x) - 141120cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 2242240cosh(x) - 776160cosh(x) - 25480)sinh(x) +--R + +--R 5 3 9 +--R (- 4484480cosh(x) - 2587200cosh(x) - 254800cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 6726720cosh(x) - 5821200cosh(x) - 1146600cosh(x) - 29155)sinh(x) +--R + +--R 7 5 3 +--R (- 7687680cosh(x) - 9313920cosh(x) - 3057600cosh(x) - 233240cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R - 6726720cosh(x) - 10866240cosh(x) - 5350800cosh(x) +--R + +--R 2 +--R - 816340cosh(x) - 18620 +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 4484480cosh(x) - 9313920cosh(x) - 6420960cosh(x) +--R + +--R 3 +--R - 1632680cosh(x) - 111720cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 2242240cosh(x) - 5821200cosh(x) - 5350800cosh(x) +--R + +--R 4 2 +--R - 2040850cosh(x) - 279300cosh(x) - 6370 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 815360cosh(x) - 2587200cosh(x) - 3057600cosh(x) +--R + +--R 5 3 +--R - 1632680cosh(x) - 372400cosh(x) - 25480cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R - 203840cosh(x) - 776160cosh(x) - 1146600cosh(x) +--R + +--R 6 4 2 +--R - 816340cosh(x) - 279300cosh(x) - 38220cosh(x) - 980 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 31360cosh(x) - 141120cosh(x) - 254800cosh(x) - 233240cosh(x) +--R + +--R 5 3 +--R - 111720cosh(x) - 25480cosh(x) - 1960cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 2240cosh(x) - 11760cosh(x) - 25480cosh(x) - 29155cosh(x) +--R + +--R 6 4 2 +--R - 18620cosh(x) - 6370cosh(x) - 980cosh(x) - 35 +--R Type: Union(Expression(Integer),...) +--E 514 + +--S 515 of 531 +--m1095:= a1095-r1095 +--E 515 + +--S 516 of 531 +--d1095:= D(m1095,x) +--E 516 + +)clear all + + +--S 517 of 531 +t1096:= (1+csch(x))^(1/2)*csch(x)*coth(x)^3 +--R +--R +--R 3 +-----------+ +--R (1) coth(x) csch(x)\|csch(x) + 1 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 531 +r1096:= -4/3*(1+csch(x))^(3/2)+4/5*(1+csch(x))^(5/2)-2/7*(1+csch(x))^(7/2) +--R +--R +--R 3 2 +-----------+ +--R (- 30csch(x) - 6csch(x) - 62csch(x) - 86)\|csch(x) + 1 +--R (2) --------------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 518 + +--S 519 of 531 +a1096:= integrate(t1096,x) +--R +--R +--R (3) +--R 6 5 +--R - 86sinh(x) + (- 516cosh(x) - 124)sinh(x) +--R + +--R 2 4 +--R (- 1290cosh(x) - 620cosh(x) + 234)sinh(x) +--R + +--R 3 2 3 +--R (- 1720cosh(x) - 1240cosh(x) + 936cosh(x) + 8)sinh(x) +--R + +--R 4 3 2 +--R (- 1290cosh(x) - 1240cosh(x) + 1404cosh(x) + 24cosh(x) - 234) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 516cosh(x) - 620cosh(x) + 936cosh(x) + 24cosh(x) - 468cosh(x) +--R + +--R - 124 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 86cosh(x) - 124cosh(x) + 234cosh(x) + 8cosh(x) - 234cosh(x) +--R + +--R - 124cosh(x) + 86 +--R * +--R +-----------+ +--R |sinh(x) + 1 +--R |----------- +--R \| sinh(x) +--R / +--R 10 9 2 8 +--R 105sinh(x) + 1050cosh(x)sinh(x) + (4725cosh(x) - 525)sinh(x) +--R + +--R 3 7 +--R (12600cosh(x) - 4200cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (22050cosh(x) - 14700cosh(x) + 1050)sinh(x) +--R + +--R 5 3 5 +--R (26460cosh(x) - 29400cosh(x) + 6300cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (22050cosh(x) - 36750cosh(x) + 15750cosh(x) - 1050)sinh(x) +--R + +--R 7 5 3 3 +--R (12600cosh(x) - 29400cosh(x) + 21000cosh(x) - 4200cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (4725cosh(x) - 14700cosh(x) + 15750cosh(x) - 6300cosh(x) + 525) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 1050cosh(x) - 4200cosh(x) + 6300cosh(x) - 4200cosh(x) +--R + +--R 1050cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R 105cosh(x) - 525cosh(x) + 1050cosh(x) - 1050cosh(x) + 525cosh(x) +--R + +--R - 105 +--R Type: Union(Expression(Integer),...) +--E 519 + +--S 520 of 531 +m1096:= a1096-r1096 +--R +--R +--R (4) +--R 3 2 10 +--R (30csch(x) + 6csch(x) + 62csch(x) + 86)sinh(x) +--R + +--R 3 2 +--R 300cosh(x)csch(x) + 60cosh(x)csch(x) + 620cosh(x)csch(x) +--R + +--R 860cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (1350cosh(x) - 150)csch(x) + (270cosh(x) - 30)csch(x) +--R + +--R 2 2 +--R (2790cosh(x) - 310)csch(x) + 3870cosh(x) - 430 +--R * +--R 8 +--R sinh(x) +--R + +--R 3 3 +--R (3600cosh(x) - 1200cosh(x))csch(x) +--R + +--R 3 2 +--R (720cosh(x) - 240cosh(x))csch(x) +--R + +--R 3 3 +--R (7440cosh(x) - 2480cosh(x))csch(x) + 10320cosh(x) - 3440cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 +--R (6300cosh(x) - 4200cosh(x) + 300)csch(x) +--R + +--R 4 2 2 +--R (1260cosh(x) - 840cosh(x) + 60)csch(x) +--R + +--R 4 2 4 +--R (13020cosh(x) - 8680cosh(x) + 620)csch(x) + 18060cosh(x) +--R + +--R 2 +--R - 12040cosh(x) + 860 +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 3 +--R (7560cosh(x) - 8400cosh(x) + 1800cosh(x))csch(x) +--R + +--R 5 3 2 +--R (1512cosh(x) - 1680cosh(x) + 360cosh(x))csch(x) +--R + +--R 5 3 +--R (15624cosh(x) - 17360cosh(x) + 3720cosh(x))csch(x) +--R + +--R 5 3 +--R 21672cosh(x) - 24080cosh(x) + 5160cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (6300cosh(x) - 10500cosh(x) + 4500cosh(x) - 300)csch(x) +--R + +--R 6 4 2 2 +--R (1260cosh(x) - 2100cosh(x) + 900cosh(x) - 60)csch(x) +--R + +--R 6 4 2 +--R (13020cosh(x) - 21700cosh(x) + 9300cosh(x) - 620)csch(x) +--R + +--R 6 4 2 +--R 18060cosh(x) - 30100cosh(x) + 12900cosh(x) - 860 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 3 +--R (3600cosh(x) - 8400cosh(x) + 6000cosh(x) - 1200cosh(x)) +--R * +--R 3 +--R csch(x) +--R + +--R 7 5 3 2 +--R (720cosh(x) - 1680cosh(x) + 1200cosh(x) - 240cosh(x))csch(x) +--R + +--R 7 5 3 +--R (7440cosh(x) - 17360cosh(x) + 12400cosh(x) - 2480cosh(x)) +--R * +--R csch(x) +--R + +--R 7 5 3 +--R 10320cosh(x) - 24080cosh(x) + 17200cosh(x) - 3440cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 1350cosh(x) - 4200cosh(x) + 4500cosh(x) - 1800cosh(x) +--R + +--R 150 +--R * +--R 3 +--R csch(x) +--R + +--R 8 6 4 2 +--R (270cosh(x) - 840cosh(x) + 900cosh(x) - 360cosh(x) + 30) +--R * +--R 2 +--R csch(x) +--R + +--R 8 6 4 2 +--R 2790cosh(x) - 8680cosh(x) + 9300cosh(x) - 3720cosh(x) +--R + +--R 310 +--R * +--R csch(x) +--R + +--R 8 6 4 2 +--R 3870cosh(x) - 12040cosh(x) + 12900cosh(x) - 5160cosh(x) + 430 +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 300cosh(x) - 1200cosh(x) + 1800cosh(x) - 1200cosh(x) +--R + +--R 300cosh(x) +--R * +--R 3 +--R csch(x) +--R + +--R 9 7 5 3 +--R 60cosh(x) - 240cosh(x) + 360cosh(x) - 240cosh(x) +--R + +--R 60cosh(x) +--R * +--R 2 +--R csch(x) +--R + +--R 9 7 5 3 +--R 620cosh(x) - 2480cosh(x) + 3720cosh(x) - 2480cosh(x) +--R + +--R 620cosh(x) +--R * +--R csch(x) +--R + +--R 9 7 5 3 +--R 860cosh(x) - 3440cosh(x) + 5160cosh(x) - 3440cosh(x) +--R + +--R 860cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 +--R 30cosh(x) - 150cosh(x) + 300cosh(x) - 300cosh(x) +--R + +--R 2 +--R 150cosh(x) - 30 +--R * +--R 3 +--R csch(x) +--R + +--R 10 8 6 4 2 +--R 6cosh(x) - 30cosh(x) + 60cosh(x) - 60cosh(x) + 30cosh(x) +--R + +--R - 6 +--R * +--R 2 +--R csch(x) +--R + +--R 10 8 6 4 +--R 62cosh(x) - 310cosh(x) + 620cosh(x) - 620cosh(x) +--R + +--R 2 +--R 310cosh(x) - 62 +--R * +--R csch(x) +--R + +--R 10 8 6 4 2 +--R 86cosh(x) - 430cosh(x) + 860cosh(x) - 860cosh(x) + 430cosh(x) +--R + +--R - 86 +--R * +--R +-----------+ +--R \|csch(x) + 1 +--R + +--R 6 5 +--R - 86sinh(x) + (- 516cosh(x) - 124)sinh(x) +--R + +--R 2 4 +--R (- 1290cosh(x) - 620cosh(x) + 234)sinh(x) +--R + +--R 3 2 3 +--R (- 1720cosh(x) - 1240cosh(x) + 936cosh(x) + 8)sinh(x) +--R + +--R 4 3 2 +--R (- 1290cosh(x) - 1240cosh(x) + 1404cosh(x) + 24cosh(x) - 234) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 516cosh(x) - 620cosh(x) + 936cosh(x) + 24cosh(x) +--R + +--R - 468cosh(x) - 124 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 86cosh(x) - 124cosh(x) + 234cosh(x) + 8cosh(x) - 234cosh(x) +--R + +--R - 124cosh(x) + 86 +--R * +--R +-----------+ +--R |sinh(x) + 1 +--R |----------- +--R \| sinh(x) +--R / +--R 10 9 2 8 +--R 105sinh(x) + 1050cosh(x)sinh(x) + (4725cosh(x) - 525)sinh(x) +--R + +--R 3 7 +--R (12600cosh(x) - 4200cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (22050cosh(x) - 14700cosh(x) + 1050)sinh(x) +--R + +--R 5 3 5 +--R (26460cosh(x) - 29400cosh(x) + 6300cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (22050cosh(x) - 36750cosh(x) + 15750cosh(x) - 1050)sinh(x) +--R + +--R 7 5 3 3 +--R (12600cosh(x) - 29400cosh(x) + 21000cosh(x) - 4200cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (4725cosh(x) - 14700cosh(x) + 15750cosh(x) - 6300cosh(x) + 525) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 1050cosh(x) - 4200cosh(x) + 6300cosh(x) - 4200cosh(x) +--R + +--R 1050cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R 105cosh(x) - 525cosh(x) + 1050cosh(x) - 1050cosh(x) + 525cosh(x) +--R + +--R - 105 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 531 +d1096:= D(m1096,x) +--R +--R +--R (5) +--R 10 9 +--R 344sinh(x) + (2752cosh(x) + 964)sinh(x) +--R + +--R 2 8 +--R (9632cosh(x) + 7135cosh(x) - 268)sinh(x) +--R + +--R 3 2 7 +--R (19264cosh(x) + 22996cosh(x) - 926cosh(x) - 324)sinh(x) +--R + +--R 4 3 2 +--R (24080cosh(x) + 42168cosh(x) + 134cosh(x) - 2668cosh(x) + 1500) +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 19264cosh(x) + 48188cosh(x) + 5242cosh(x) - 8640cosh(x) +--R + +--R 6498cosh(x) + 2028 +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 9632cosh(x) + 35294cosh(x) + 10550cosh(x) - 14520cosh(x) +--R + +--R 2 +--R 10926cosh(x) + 7254cosh(x) + 700 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 2752cosh(x) + 16380cosh(x) + 9862cosh(x) - 13700cosh(x) +--R + +--R 3 2 +--R 8724cosh(x) + 9828cosh(x) + 2558cosh(x) - 268 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 344cosh(x) + 4576cosh(x) + 4754cosh(x) - 7164cosh(x) +--R + +--R 4 3 2 +--R 3096cosh(x) + 6240cosh(x) + 3082cosh(x) - 820cosh(x) + 124 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 688cosh(x) + 1054cosh(x) - 1848cosh(x) + 234cosh(x) +--R + +--R 4 3 2 +--R 1872cosh(x) + 1290cosh(x) - 712cosh(x) + 62cosh(x) +--R * +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R 43cosh(x) + 62cosh(x) - 160cosh(x) - 66cosh(x) + 234cosh(x) +--R + +--R 4 3 2 +--R 66cosh(x) - 160cosh(x) - 62cosh(x) + 43cosh(x) +--R * +--R +-----------+ +--R \|csch(x) + 1 +--R + +--R 4 3 2 +--R - 105coth(x)csch(x) - 105coth(x)csch(x) - 105coth(x)csch(x) +--R + +--R - 105coth(x)csch(x) +--R * +--R 14 +--R sinh(x) +--R + +--R 4 3 +--R - 1260cosh(x)coth(x)csch(x) - 1260cosh(x)coth(x)csch(x) +--R + +--R 2 +--R - 1260cosh(x)coth(x)csch(x) - 1260cosh(x)coth(x)csch(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 2 4 +--R (- 6930cosh(x) + 630)coth(x)csch(x) +--R + +--R 2 3 +--R (- 6930cosh(x) + 630)coth(x)csch(x) +--R + +--R 2 2 +--R (- 6930cosh(x) + 630)coth(x)csch(x) +--R + +--R 2 +--R (- 6930cosh(x) + 630)coth(x)csch(x) +--R * +--R 12 +--R sinh(x) +--R + +--R 3 4 +--R (- 23100cosh(x) + 6300cosh(x))coth(x)csch(x) +--R + +--R 3 3 +--R (- 23100cosh(x) + 6300cosh(x))coth(x)csch(x) +--R + +--R 3 2 +--R (- 23100cosh(x) + 6300cosh(x))coth(x)csch(x) +--R + +--R 3 +--R (- 23100cosh(x) + 6300cosh(x))coth(x)csch(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 4 2 4 +--R (- 51975cosh(x) + 28350cosh(x) - 1575)coth(x)csch(x) +--R + +--R 4 2 3 +--R (- 51975cosh(x) + 28350cosh(x) - 1575)coth(x)csch(x) +--R + +--R 4 2 2 +--R (- 51975cosh(x) + 28350cosh(x) - 1575)coth(x)csch(x) +--R + +--R 4 2 +--R (- 51975cosh(x) + 28350cosh(x) - 1575)coth(x)csch(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 5 3 4 +--R (- 83160cosh(x) + 75600cosh(x) - 12600cosh(x))coth(x)csch(x) +--R + +--R 5 3 3 +--R (- 83160cosh(x) + 75600cosh(x) - 12600cosh(x))coth(x)csch(x) +--R + +--R 5 3 2 +--R (- 83160cosh(x) + 75600cosh(x) - 12600cosh(x))coth(x)csch(x) +--R + +--R 5 3 +--R (- 83160cosh(x) + 75600cosh(x) - 12600cosh(x))coth(x)csch(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 4 2 +--R (- 97020cosh(x) + 132300cosh(x) - 44100cosh(x) + 2100) +--R * +--R 4 +--R coth(x)csch(x) +--R + +--R 6 4 2 +--R (- 97020cosh(x) + 132300cosh(x) - 44100cosh(x) + 2100) +--R * +--R 3 +--R coth(x)csch(x) +--R + +--R 6 4 2 +--R (- 97020cosh(x) + 132300cosh(x) - 44100cosh(x) + 2100) +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 6 4 2 +--R (- 97020cosh(x) + 132300cosh(x) - 44100cosh(x) + 2100) +--R * +--R coth(x)csch(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R - 83160cosh(x) + 158760cosh(x) - 88200cosh(x) +--R + +--R 12600cosh(x) +--R * +--R 4 +--R coth(x)csch(x) +--R + +--R 7 5 3 +--R - 83160cosh(x) + 158760cosh(x) - 88200cosh(x) +--R + +--R 12600cosh(x) +--R * +--R 3 +--R coth(x)csch(x) +--R + +--R 7 5 3 +--R - 83160cosh(x) + 158760cosh(x) - 88200cosh(x) +--R + +--R 12600cosh(x) +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 7 5 3 +--R - 83160cosh(x) + 158760cosh(x) - 88200cosh(x) +--R + +--R 12600cosh(x) +--R * +--R coth(x)csch(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R - 51975cosh(x) + 132300cosh(x) - 110250cosh(x) +--R + +--R 2 +--R 31500cosh(x) - 1575 +--R * +--R 4 +--R coth(x)csch(x) +--R + +--R 8 6 4 +--R - 51975cosh(x) + 132300cosh(x) - 110250cosh(x) +--R + +--R 2 +--R 31500cosh(x) - 1575 +--R * +--R 3 +--R coth(x)csch(x) +--R + +--R 8 6 4 +--R - 51975cosh(x) + 132300cosh(x) - 110250cosh(x) +--R + +--R 2 +--R 31500cosh(x) - 1575 +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 8 6 4 +--R - 51975cosh(x) + 132300cosh(x) - 110250cosh(x) +--R + +--R 2 +--R 31500cosh(x) - 1575 +--R * +--R coth(x)csch(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 23100cosh(x) + 75600cosh(x) - 88200cosh(x) +--R + +--R 3 +--R 42000cosh(x) - 6300cosh(x) +--R * +--R 4 +--R coth(x)csch(x) +--R + +--R 9 7 5 +--R - 23100cosh(x) + 75600cosh(x) - 88200cosh(x) +--R + +--R 3 +--R 42000cosh(x) - 6300cosh(x) +--R * +--R 3 +--R coth(x)csch(x) +--R + +--R 9 7 5 +--R - 23100cosh(x) + 75600cosh(x) - 88200cosh(x) +--R + +--R 3 +--R 42000cosh(x) - 6300cosh(x) +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 9 7 5 +--R - 23100cosh(x) + 75600cosh(x) - 88200cosh(x) +--R + +--R 3 +--R 42000cosh(x) - 6300cosh(x) +--R * +--R coth(x)csch(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 6930cosh(x) + 28350cosh(x) - 44100cosh(x) +--R + +--R 4 2 +--R 31500cosh(x) - 9450cosh(x) + 630 +--R * +--R 4 +--R coth(x)csch(x) +--R + +--R 10 8 6 +--R - 6930cosh(x) + 28350cosh(x) - 44100cosh(x) +--R + +--R 4 2 +--R 31500cosh(x) - 9450cosh(x) + 630 +--R * +--R 3 +--R coth(x)csch(x) +--R + +--R 10 8 6 +--R - 6930cosh(x) + 28350cosh(x) - 44100cosh(x) +--R + +--R 4 2 +--R 31500cosh(x) - 9450cosh(x) + 630 +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 10 8 6 +--R - 6930cosh(x) + 28350cosh(x) - 44100cosh(x) +--R + +--R 4 2 +--R 31500cosh(x) - 9450cosh(x) + 630 +--R * +--R coth(x)csch(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 1260cosh(x) + 6300cosh(x) - 12600cosh(x) +--R + +--R 5 3 +--R 12600cosh(x) - 6300cosh(x) + 1260cosh(x) +--R * +--R 4 +--R coth(x)csch(x) +--R + +--R 11 9 7 +--R - 1260cosh(x) + 6300cosh(x) - 12600cosh(x) +--R + +--R 5 3 +--R 12600cosh(x) - 6300cosh(x) + 1260cosh(x) +--R * +--R 3 +--R coth(x)csch(x) +--R + +--R 11 9 7 +--R - 1260cosh(x) + 6300cosh(x) - 12600cosh(x) +--R + +--R 5 3 +--R 12600cosh(x) - 6300cosh(x) + 1260cosh(x) +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 11 9 7 +--R - 1260cosh(x) + 6300cosh(x) - 12600cosh(x) +--R + +--R 5 3 +--R 12600cosh(x) - 6300cosh(x) + 1260cosh(x) +--R * +--R coth(x)csch(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 105cosh(x) + 630cosh(x) - 1575cosh(x) + 2100cosh(x) +--R + +--R 4 2 +--R - 1575cosh(x) + 630cosh(x) - 105 +--R * +--R 4 +--R coth(x)csch(x) +--R + +--R 12 10 8 6 +--R - 105cosh(x) + 630cosh(x) - 1575cosh(x) + 2100cosh(x) +--R + +--R 4 2 +--R - 1575cosh(x) + 630cosh(x) - 105 +--R * +--R 3 +--R coth(x)csch(x) +--R + +--R 12 10 8 6 +--R - 105cosh(x) + 630cosh(x) - 1575cosh(x) + 2100cosh(x) +--R + +--R 4 2 +--R - 1575cosh(x) + 630cosh(x) - 105 +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 12 10 8 6 +--R - 105cosh(x) + 630cosh(x) - 1575cosh(x) + 2100cosh(x) +--R + +--R 4 2 +--R - 1575cosh(x) + 630cosh(x) - 105 +--R * +--R coth(x)csch(x) +--R * +--R 2 +--R sinh(x) +--R * +--R +-----------+ +--R |sinh(x) + 1 +--R |----------- +--R \| sinh(x) +--R / +--R 14 13 2 12 +--R 105sinh(x) + 1260cosh(x)sinh(x) + (6930cosh(x) - 630)sinh(x) +--R + +--R 3 11 +--R (23100cosh(x) - 6300cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (51975cosh(x) - 28350cosh(x) + 1575)sinh(x) +--R + +--R 5 3 9 +--R (83160cosh(x) - 75600cosh(x) + 12600cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (97020cosh(x) - 132300cosh(x) + 44100cosh(x) - 2100)sinh(x) +--R + +--R 7 5 3 7 +--R (83160cosh(x) - 158760cosh(x) + 88200cosh(x) - 12600cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 51975cosh(x) - 132300cosh(x) + 110250cosh(x) - 31500cosh(x) +--R + +--R 1575 +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 23100cosh(x) - 75600cosh(x) + 88200cosh(x) - 42000cosh(x) +--R + +--R 6300cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 6930cosh(x) - 28350cosh(x) + 44100cosh(x) - 31500cosh(x) +--R + +--R 2 +--R 9450cosh(x) - 630 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 1260cosh(x) - 6300cosh(x) + 12600cosh(x) - 12600cosh(x) +--R + +--R 3 +--R 6300cosh(x) - 1260cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 105cosh(x) - 630cosh(x) + 1575cosh(x) - 2100cosh(x) +--R + +--R 4 2 +--R 1575cosh(x) - 630cosh(x) + 105 +--R * +--R 2 +--R sinh(x) +--R * +--R +-----------+ +--R |sinh(x) + 1 +-----------+ +--R |----------- \|csch(x) + 1 +--R \| sinh(x) +--R Type: Expression(Integer) +--E 521 + +)clear all + + +--S 522 of 531 +t1097:= cosh(x)^x*(log(cosh(x))+x*tanh(x)) +--R +--R +--R x +--R (1) (log(cosh(x)) + x tanh(x))cosh(x) +--R Type: Expression(Integer) +--E 522 + +--S 523 of 531 +r1097:= cosh(x)^x +--R +--R +--R x +--R (2) cosh(x) +--R Type: Expression(Integer) +--E 523 + +--S 524 of 531 +a1097:= integrate(t1097,x) +--R +--R +--R (3) sinh(x log(cosh(x))) + cosh(x log(cosh(x))) +--R Type: Union(Expression(Integer),...) +--E 524 + +--S 525 of 531 +m1097:= a1097-r1097 +--R +--R +--R x +--R (4) sinh(x log(cosh(x))) + cosh(x log(cosh(x))) - cosh(x) +--R Type: Expression(Integer) +--E 525 + +--S 526 of 531 +d1097:= D(m1097,x) +--R +--R +--R (5) +--R (cosh(x)log(cosh(x)) + x sinh(x))sinh(x log(cosh(x))) +--R + +--R (cosh(x)log(cosh(x)) + x sinh(x))cosh(x log(cosh(x))) +--R + +--R x x - 1 +--R - cosh(x)log(cosh(x))cosh(x) - x cosh(x)sinh(x)cosh(x) +--R / +--R cosh(x) +--R Type: Expression(Integer) +--E 526 + +)clear all + + +--S 527 of 531 +t1098:= csch(x)*(1+log(coth(x))^2)^(1/2)*sech(x) +--R +--R +--R +-----------------+ +--R | 2 +--R (1) csch(x)sech(x)\|log(coth(x)) + 1 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 531 +r1098:= -1/2*asinh(log(coth(x)))-1/2*log(coth(x))*(1+log(coth(x))^2)^(1/2) +--R +--R +--R +-----------------+ +--R | 2 +--R - log(coth(x))\|log(coth(x)) + 1 - asinh(log(coth(x))) +--R (2) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 528 + +--S 529 of 531 +a1098:= integrate(t1098,x) +--R +--R +--R (3) +--R +-----------------+ +--R cosh(x) | cosh(x) 2 cosh(x) 2 +--R (2log(-------) |log(-------) + 1 - 2log(-------) - 1) +--R sinh(x) \| sinh(x) sinh(x) +--R * +--R +-----------------+ +--R | cosh(x) 2 cosh(x) +--R log( |log(-------) + 1 - log(-------)) +--R \| sinh(x) sinh(x) +--R + +--R +-----------------+ +--R cosh(x) 3 cosh(x) | cosh(x) 2 cosh(x) 4 +--R (2log(-------) + log(-------)) |log(-------) + 1 - 2log(-------) +--R sinh(x) sinh(x) \| sinh(x) sinh(x) +--R + +--R cosh(x) 2 +--R - 2log(-------) +--R sinh(x) +--R / +--R +-----------------+ +--R cosh(x) | cosh(x) 2 cosh(x) 2 +--R 4log(-------) |log(-------) + 1 - 4log(-------) - 2 +--R sinh(x) \| sinh(x) sinh(x) +--R Type: Union(Expression(Integer),...) +--E 529 + +--S 530 of 531 +m1098:= a1098-r1098 +--R +--R +--R (4) +--R +-----------------+ +--R cosh(x) | cosh(x) 2 cosh(x) 2 +--R (2log(-------) |log(-------) + 1 - 2log(-------) - 1) +--R sinh(x) \| sinh(x) sinh(x) +--R * +--R +-----------------+ +--R | cosh(x) 2 cosh(x) +--R log( |log(-------) + 1 - log(-------)) +--R \| sinh(x) sinh(x) +--R + +--R +-----------------+ +--R cosh(x) | cosh(x) 2 +--R 2log(-------)log(coth(x)) |log(-------) + 1 +--R sinh(x) \| sinh(x) +--R + +--R cosh(x) 2 +--R (- 2log(-------) - 1)log(coth(x)) +--R sinh(x) +--R * +--R +-----------------+ +--R | 2 +--R \|log(coth(x)) + 1 +--R + +--R cosh(x) cosh(x) 3 cosh(x) +--R (2log(-------)asinh(log(coth(x))) + 2log(-------) + log(-------)) +--R sinh(x) sinh(x) sinh(x) +--R * +--R +-----------------+ +--R | cosh(x) 2 +--R |log(-------) + 1 +--R \| sinh(x) +--R + +--R cosh(x) 2 cosh(x) 4 cosh(x) 2 +--R (- 2log(-------) - 1)asinh(log(coth(x))) - 2log(-------) - 2log(-------) +--R sinh(x) sinh(x) sinh(x) +--R / +--R +-----------------+ +--R cosh(x) | cosh(x) 2 cosh(x) 2 +--R 4log(-------) |log(-------) + 1 - 4log(-------) - 2 +--R sinh(x) \| sinh(x) sinh(x) +--R Type: Expression(Integer) +--E 530 + +--S 531 of 531 +d1098:= D(m1098,x) +--R +--R +--R (5) +--R 2 2 cosh(x) 5 +--R (8coth(x)sinh(x) - 8cosh(x) coth(x))log(-------) +--R sinh(x) +--R + +--R 2 2 cosh(x) 3 +--R (12coth(x)sinh(x) - 12cosh(x) coth(x))log(-------) +--R sinh(x) +--R + +--R 2 2 cosh(x) +--R (4coth(x)sinh(x) - 4cosh(x) coth(x))log(-------) +--R sinh(x) +--R * +--R +-----------------+ +--R | cosh(x) 2 +--R |log(-------) + 1 +--R \| sinh(x) +--R + +--R 2 2 cosh(x) 6 +--R (- 8coth(x)sinh(x) + 8cosh(x) coth(x))log(-------) +--R sinh(x) +--R + +--R 2 2 cosh(x) 4 +--R (- 16coth(x)sinh(x) + 16cosh(x) coth(x))log(-------) +--R sinh(x) +--R + +--R 2 2 cosh(x) 2 +--R (- 9coth(x)sinh(x) + 9cosh(x) coth(x))log(-------) +--R sinh(x) +--R + +--R 2 2 +--R - coth(x)sinh(x) + cosh(x) coth(x) +--R * +--R +-----------------+ +--R | 2 +--R \|log(coth(x)) + 1 +--R + +--R 2 cosh(x) 4 +--R (- 8cosh(x)coth(x) + 8cosh(x))sinh(x)log(-------) +--R sinh(x) +--R + +--R 2 cosh(x) 2 +--R (- 8cosh(x)coth(x) + 8cosh(x))sinh(x)log(-------) +--R sinh(x) +--R + +--R 2 +--R (- cosh(x)coth(x) + cosh(x))sinh(x) +--R * +--R 2 +--R log(coth(x)) +--R + +--R 2 cosh(x) 4 +--R (- 8cosh(x)coth(x) + 8cosh(x))sinh(x)log(-------) +--R sinh(x) +--R + +--R 2 cosh(x) 2 +--R (- 8cosh(x)coth(x) + 8cosh(x))sinh(x)log(-------) +--R sinh(x) +--R + +--R 2 +--R (- cosh(x)coth(x) + cosh(x))sinh(x) +--R * +--R +-----------------+ +--R | cosh(x) 2 +--R |log(-------) + 1 +--R \| sinh(x) +--R + +--R 2 cosh(x) 5 +--R (8cosh(x)coth(x) - 8cosh(x))sinh(x)log(-------) +--R sinh(x) +--R + +--R 2 cosh(x) 3 +--R (12cosh(x)coth(x) - 12cosh(x))sinh(x)log(-------) +--R sinh(x) +--R + +--R 2 cosh(x) +--R (4cosh(x)coth(x) - 4cosh(x))sinh(x)log(-------) +--R sinh(x) +--R * +--R 2 +--R log(coth(x)) +--R + +--R 2 cosh(x) 5 +--R (8cosh(x)coth(x) - 8cosh(x))sinh(x)log(-------) +--R sinh(x) +--R + +--R 2 cosh(x) 3 +--R (12cosh(x)coth(x) - 12cosh(x))sinh(x)log(-------) +--R sinh(x) +--R + +--R 2 cosh(x) +--R (4cosh(x)coth(x) - 4cosh(x))sinh(x)log(-------) +--R sinh(x) +--R / +--R cosh(x) 4 +--R 8cosh(x)coth(x)sinh(x)log(-------) +--R sinh(x) +--R + +--R cosh(x) 2 +--R 8cosh(x)coth(x)sinh(x)log(-------) + cosh(x)coth(x)sinh(x) +--R sinh(x) +--R * +--R +-----------------+ +--R | cosh(x) 2 +--R |log(-------) + 1 +--R \| sinh(x) +--R + +--R cosh(x) 5 +--R - 8cosh(x)coth(x)sinh(x)log(-------) +--R sinh(x) +--R + +--R cosh(x) 3 +--R - 12cosh(x)coth(x)sinh(x)log(-------) +--R sinh(x) +--R + +--R cosh(x) +--R - 4cosh(x)coth(x)sinh(x)log(-------) +--R sinh(x) +--R * +--R +-----------------+ +--R | 2 +--R \|log(coth(x)) + 1 +--R Type: Expression(Integer) +--E 531 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper1000-1098.input.pdf b/src/axiom-website/CATS/richhyper1000-1098.input.pdf new file mode 100644 index 0000000..e69944b Binary files /dev/null and b/src/axiom-website/CATS/richhyper1000-1098.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper200-299.input.pamphlet b/src/axiom-website/CATS/richhyper200-299.input.pamphlet new file mode 100644 index 0000000..bb5c029 --- /dev/null +++ b/src/axiom-website/CATS/richhyper200-299.input.pamphlet @@ -0,0 +1,31946 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper200-299.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper200-299.output +)spool richhyper200-299.output +)set message auto off +)clear all + +--S 1 of 500 +t0200:= (a+b*cosh(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (1) \|b cosh(x) + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0200:= -%i*(2*a+b+b*cosh(2*x))^(1/2)*EllipticE(%i*x,b/(a+b))/_ + ((2*a+b+b*cosh(2*x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Integer)) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 500 +a0200:= integrate(t0200,x) +--R +--R +--R x +---------------+ +--R ++ | 2 +--R (2) | \|b cosh(%R) + a d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +--m0200:= a0200-r0200 +--E 4 + +--S 5 of 500 +--d0200:= D(m0200,x) +--E 5 + +--S 6 of 500 +t0201:= 1/(1+cosh(x)^2)^(1/2) +--R +--R +--R 1 +--R (3) --------------- +--R +------------+ +--R | 2 +--R \|cosh(x) + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0201:= -1/2*%i*EllipticF(%i*x,1/2)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Integer)) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 500 +a0201:= integrate(t0201,x) +--R +--R +--R x +--R ++ 1 +--R (4) | ---------------- d%R +--R ++ +-------------+ +--R | 2 +--R \|cosh(%R) + 1 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +--m0201:= a0201-r0201 +--E 9 + +--S 10 of 500 +--d0201:= D(m0201,x) +--E 10 + +--S 11 of 500 +t0202:= 1/(-1-cosh(x)^2)^(1/2) +--R +--R +--R 1 +--R (5) ----------------- +--R +--------------+ +--R | 2 +--R \|- cosh(x) - 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0202:= -1/2*%i*(3+cosh(2*x))^(1/2)*_ + EllipticF(%i*x,1/2)*2^(1/2)/(-3-cosh(2*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Integer)) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 500 +a0202:= integrate(t0202,x) +--R +--R +--R +------------------------+ +--R x | %R 4 %R 2 +--R ++ 2\|- (%e ) - 6(%e ) - 1 +--R (6) | ---------------------------- d%R +--R ++ %R 6 %R 4 %R 2 +--R (%e ) + 6(%e ) + (%e ) +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +--m0202:= a0202-r0202 +--E 14 + +--S 15 of 500 +--d0202:= D(m0202,x) +--E 15 + +--S 16 of 500 +t0203:= 1/(a+b*cosh(x)^2)^(1/2) +--R +--R +--R 1 +--R (7) ----------------- +--R +--------------+ +--R | 2 +--R \|b cosh(x) + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0203:= -%i*((2*a+b+b*cosh(2*x))/(a+b))^(1/2)*_ + EllipticF(%i*x,b/(a+b))/(2*a+b+b*cosh(2*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Integer)) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 500 +a0203:= integrate(t0203,x) +--R +--R +--R x +--R ++ 1 +--R (8) | ------------------ d%R +--R ++ +---------------+ +--R | 2 +--R \|b cosh(%R) + a +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +--m0203:= a0203-r0203 +--E 19 + +--S 20 of 500 +--d0203:= D(m0203,x) +--E 20 + +--S 21 of 500 +t0204:= x/(a+b*cosh(x)^2) +--R +--R +--R x +--R (9) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0204:= 1/4*(2*x*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*x))/_ + (-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 2*x*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*x))/(2*a+b+2*a^(1/2)*_ + (a+b)^(1/2)))+polylog(2,b*exp(2*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + polylog(2,-1/(2*a+b+2*a^(1/2)*(a+b)^(1/2))*b*exp(2*x)))/_ + a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 500 +a0204:= integrate(t0204,x) +--R +--R +--R x +--R ++ %R +--R (10) | --------------- d%R +--R ++ 2 +--R b cosh(%R) + a +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +--m0204:= a0204-r0204 +--E 24 + +--S 25 of 500 +--d0204:= D(m0204,x) +--E 25 + +--S 26 of 500 +t0205:= x^2/(a+b*cosh(x)^2) +--R +--R +--R 2 +--R x +--R (11) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0205:= 1/4*(2*x^2*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*x))/_ + (-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 2*x^2*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*x))/_ + (2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + 2*x*polylog(2,b*exp(2*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 2*x*polylog(2,-1/(2*a+b+2*a^(1/2)*(a+b)^(1/2))*b*exp(2*x))-_ + polylog(3,b*exp(2*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + polylog(3,-1/(2*a+b+2*a^(1/2)*(a+b)^(1/2))*b*exp(2*x)))/_ + a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 500 +a0205:= integrate(t0205,x) +--R +--R +--R x 2 +--R ++ %R +--R (12) | --------------- d%R +--R ++ 2 +--R b cosh(%R) + a +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +--m0205:= a0205-r0205 +--E 29 + +--S 30 of 500 +--d0205:= D(m0205,x) +--E 30 + +--S 31 of 500 +t0206:= x^3/(a+b*cosh(x)^2) +--R +--R +--R 3 +--R x +--R (13) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0206:= -1/8*(-4*x^3*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*x))/_ + (-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 4*x^3*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*x))/_ + (2*a+b+2*a^(1/2)*(a+b)^(1/2)))-_ + 6*x^2*polylog(2,b*exp(2*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 6*x^2*polylog(2,-1/(2*a+b+2*a^(1/2)*(a+b)^(1/2))*b*exp(2*x))+_ + 6*x*polylog(3,b*exp(2*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 6*x*polylog(3,-1/(2*a+b+2*a^(1/2)*(a+b)^(1/2))*b*exp(2*x))-_ + 3*polylog(4,b*exp(2*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 3*polylog(4,-1/(2*a+b+2*a^(1/2)*(a+b)^(1/2))*b*exp(2*x)))/_ + a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 500 +a0206:= integrate(t0206,x) +--R +--R +--R x 3 +--R ++ %R +--R (14) | --------------- d%R +--R ++ 2 +--R b cosh(%R) + a +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +--m0206:= a0206-r0206 +--E 34 + +--S 35 of 500 +--d0206:= D(m0206,x) +--E 35 + +--S 36 of 500 +t0207:= 1/(a+b*cosh(x)^3) +--R +--R +--R 1 +--R (15) -------------- +--R 3 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0207:= 2/3*atanh((a^(1/3)-b^(1/3))*tanh(1/2*x)/(a^(2/3)-b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+_ + 2/3*atanh((a^(1/3)-(-1)^(2/3)*b^(1/3))*tanh(1/2*x)/_ + (a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/a^(2/3)/_ + (a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+_ + 2/3*atanh((a^(1/3)+(-1)^(1/3)*b^(1/3))*_ + tanh(1/2*x)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) +--R +--R +--R (16) +--R +---------------+ +-------------------+ +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+ x 3+-+ x 3+-+ +--R \|- 1 tanh(-)\|b + tanh(-)\|a +--R 2 2 +--R atanh(-------------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +-------------------+ +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 3+-+ x 3+-+ +--R tanh(-)\|b - tanh(-)\|a +--R 2 2 +--R atanh(-------------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R - +--R +----------------------+ +---------------+ +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 3+---+2 x 3+-+ x 3+-+ +--R \|- 1 tanh(-)\|b - tanh(-)\|a +--R 2 2 +--R atanh(--------------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0207:= integrate(t0207,x) +--R +--R +--R (17) +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--R ((486a b - 486a )%%BK0 - 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--R (486a b - 486a )%%BK0 + (27a b + 135a )%%BK0 - 9a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--R (- 162a b + 162a )%%BK0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--R (- 162a b + 162a )%%BK0 - 54a %%BK0 + 4b sinh(x) + 4b cosh(x) + 4a +--R + +--R - +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--R ((486a b - 486a )%%BK0 - 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--R (- 486a b + 486a )%%BK0 + (- 27a b - 135a )%%BK0 + 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--R (162a b - 162a )%%BK0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--R (- 162a b + 162a )%%BK0 - 54a %%BK0 + 4b sinh(x) + 4b cosh(x) +--R + +--R 4a +--R + +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--R ((- 486a b + 486a )%%BK0 + 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--R (486a b - 486a )%%BK0 + (27a b + 135a )%%BK0 - 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--R (162a b - 162a )%%BK0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--R (- 162a b + 162a )%%BK0 - 54a %%BK0 + 4b sinh(x) + 4b cosh(x) + 4a +--R + +--R - +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--R ((- 486a b + 486a )%%BK0 + 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--R (- 486a b + 486a )%%BK0 + (- 27a b - 135a )%%BK0 + 9a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--R (- 162a b + 162a )%%BK0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--R (- 162a b + 162a )%%BK0 - 54a %%BK0 + 4b sinh(x) + 4b cosh(x) +--R + +--R 4a +--R + +--R - +--R +------+ +--R \|4%%BK0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--R ((486a b - 486a )%%BK0 + (27a b + 135a )%%BK0 - 9a ) +--R * +--R +------+ +--R \|4%%BK0 +--R + +--R 3 2 5 2 3 +--R (162a b - 162a )%%BK0 + 54a %%BK0 + 2b sinh(x) + 2b cosh(x) +--R + +--R - 4a +--R + +--R +------+ +--R \|4%%BK0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--R ((- 486a b + 486a )%%BK0 + (- 27a b - 135a )%%BK0 + 9a ) +--R * +--R +------+ +--R \|4%%BK0 +--R + +--R 3 2 5 2 3 +--R (162a b - 162a )%%BK0 + 54a %%BK0 + 2b sinh(x) + 2b cosh(x) - 4a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0207:= a0207-r0207 +--R +--R +--R (18) +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--R ((486a b - 486a )%%BK0 - 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--R (486a b - 486a )%%BK0 + (27a b + 135a )%%BK0 - 9a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--R (- 162a b + 162a )%%BK0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--R (- 162a b + 162a )%%BK0 - 54a %%BK0 + 4b sinh(x) + 4b cosh(x) + 4a +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--R ((486a b - 486a )%%BK0 - 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--R (- 486a b + 486a )%%BK0 + (- 27a b - 135a )%%BK0 + 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--R (162a b - 162a )%%BK0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--R (- 162a b + 162a )%%BK0 - 54a %%BK0 + 4b sinh(x) + 4b cosh(x) +--R + +--R 4a +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--R ((- 486a b + 486a )%%BK0 + 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--R (486a b - 486a )%%BK0 + (27a b + 135a )%%BK0 - 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--R (162a b - 162a )%%BK0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--R (- 162a b + 162a )%%BK0 - 54a %%BK0 + 4b sinh(x) + 4b cosh(x) + 4a +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--R ((- 486a b + 486a )%%BK0 + 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--R (- 486a b + 486a )%%BK0 + (- 27a b - 135a )%%BK0 + 9a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--R (- 6b + 6a )%%BK0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--R (- 162a b + 162a )%%BK0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--R (- 81a b + 162a b - 81a )%%BK0 +--R + +--R 2 2 4 2 2 +--R (- 18a b + 18a )%%BK0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--R (- 162a b + 162a )%%BK0 - 54a %%BK0 + 4b sinh(x) + 4b cosh(x) +--R + +--R 4a +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +------+ +--R \|\|- 1 \|b + \|a \|4%%BK0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--R ((486a b - 486a )%%BK0 + (27a b + 135a )%%BK0 - 9a ) +--R * +--R +------+ +--R \|4%%BK0 +--R + +--R 3 2 5 2 3 +--R (162a b - 162a )%%BK0 + 54a %%BK0 + 2b sinh(x) + 2b cosh(x) +--R + +--R - 4a +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--R \|4%%BK0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--R ((- 486a b + 486a )%%BK0 + (- 27a b - 135a )%%BK0 + 9a ) +--R * +--R +------+ +--R \|4%%BK0 +--R + +--R 3 2 5 2 3 +--R (162a b - 162a )%%BK0 + 54a %%BK0 + 2b sinh(x) + 2b cosh(x) - 4a +--R + +--R - +--R +---------------+ +-------------------+ +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 4\|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+ x 3+-+ x 3+-+ +--R \|- 1 tanh(-)\|b + tanh(-)\|a +--R 2 2 +--R atanh(-------------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +-------------------+ +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 4\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 3+-+ x 3+-+ +--R tanh(-)\|b - tanh(-)\|a +--R 2 2 +--R atanh(-------------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R +----------------------+ +---------------+ +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 3+---+2 x 3+-+ x 3+-+ +--R \|- 1 tanh(-)\|b - tanh(-)\|a +--R 2 2 +--R atanh(--------------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 6\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +--d0207:= D(m0207,x) +--E 40 + +--S 41 of 500 +t0208:= 1/(a+b*cosh(x)^4) +--R +--R +--R 1 +--R (19) -------------- +--R 4 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0208:= 1/2*atanh(a^(1/4)*tanh(x)/(a^(1/2)-(-b)^(1/2))^(1/2))/a^(3/4)/_ + (a^(1/2)-(-b)^(1/2))^(1/2)+1/2*atanh(a^(1/4)*tanh(x)/_ + (a^(1/2)+(-b)^(1/2))^(1/2))/a^(3/4)/(a^(1/2)+(-b)^(1/2))^(1/2) +--R +--R +--R (20) +--R +-------------+ 4+-+ +--R | +-+ +---+ tanh(x)\|a +--R \|\|a + \|- b atanh(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a - \|- b +--R + +--R +-------------+ 4+-+ +--R | +-+ +---+ tanh(x)\|a +--R \|\|a - \|- b atanh(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R / +--R +-------------+ +-------------+ +--R 4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|a \|\|a - \|- b \|\|a + \|- b +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0208:= integrate(t0208,x) +--R +--R +--R (21) +--R - +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((32a b + 32a ) |- ---------------------- + 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (16a b + 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((32a b + 32a ) |- ---------------------- - 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (- 16a b - 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((- 32a b - 32a ) |- ---------------------- + 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (- 16a b - 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((- 32a b - 32a ) |- ---------------------- - 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (16a b + 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0208:= a0208-r0208 +--R +--R +--R (22) +--R - +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((32a b + 32a ) |- ---------------------- + 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (16a b + 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |--------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((32a b + 32a ) |- ---------------------- - 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (- 16a b - 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R 4+-+3 | \| 64a b + 128a b + 64a +--R \|a |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +-------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|\|a - \|- b \|\|a + \|- b +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((- 32a b - 32a ) |- ---------------------- + 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (- 16a b - 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R log +--R +------------------------+ +--R 3 4 | b +--R ((- 32a b - 32a ) |- ---------------------- - 4a b) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- + 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R +------------------------+ +--R 2 3 | b 2 +--R (16a b + 16a ) |- ---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R +-------------+ 4+-+ +--R | +-+ +---+ tanh(x)\|a +--R - \|\|a + \|- b atanh(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a - \|- b +--R + +--R +-------------+ 4+-+ +--R | +-+ +---+ tanh(x)\|a +--R - \|\|a - \|- b atanh(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R / +--R +-------------+ +-------------+ +--R 4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|a \|\|a - \|- b \|\|a + \|- b +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0208:= D(m0208,x) +--R +--R +--R (23) +--R 8 7 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) - 4b)sinh(x) +--R + +--R 3 5 +--R (- 56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70b cosh(x) - 60b cosh(x) - 6b)sinh(x) +--R + +--R 5 3 3 +--R (- 56b cosh(x) - 80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28b cosh(x) - 60b cosh(x) - 36b cosh(x) - 4b)sinh(x) +--R + +--R 7 5 3 +--R (- 8b cosh(x) - 24b cosh(x) - 24b cosh(x) - 8b cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - b cosh(x) - 4b cosh(x) - 6b cosh(x) - 4b cosh(x) - b +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) + 4b)sinh(x) +--R + +--R 3 5 +--R (56b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70b cosh(x) + 60b cosh(x) + 6b + 16a)sinh(x) +--R + +--R 5 3 3 +--R (56b cosh(x) + 80b cosh(x) + (24b + 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28b cosh(x) + 60b cosh(x) + (36b + 96a)cosh(x) + 4b)sinh(x) +--R + +--R 7 5 3 +--R (8b cosh(x) + 24b cosh(x) + (24b + 64a)cosh(x) + 8b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) + 4b cosh(x) + (6b + 16a)cosh(x) + 4b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R (16b + 16a)sinh(x) + (64b + 64a)cosh(x)sinh(x) +--R + +--R 2 2 3 +--R (96b + 96a)cosh(x) sinh(x) + (64b + 64a)cosh(x) sinh(x) +--R + +--R 4 +--R (16b + 16a)cosh(x) +--R * +--R 4+-+2 +--R \|a +--R + +--R 8 7 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) + 4b)sinh(x) +--R + +--R 3 5 +--R (56b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70b cosh(x) + 60b cosh(x) + 6b - 16a)sinh(x) +--R + +--R 5 3 3 +--R (56b cosh(x) + 80b cosh(x) + (24b - 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28b cosh(x) + 60b cosh(x) + (36b - 96a)cosh(x) + 4b)sinh(x) +--R + +--R 7 5 3 +--R (8b cosh(x) + 24b cosh(x) + (24b - 64a)cosh(x) + 8b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) + 4b cosh(x) + (6b - 16a)cosh(x) + 4b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) - 4b)sinh(x) +--R + +--R 3 5 +--R (- 56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70b cosh(x) - 60b cosh(x) - 6b - 16a)sinh(x) +--R + +--R 5 3 3 +--R (- 56b cosh(x) - 80b cosh(x) + (- 24b - 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28b cosh(x) - 60b cosh(x) + (- 36b - 96a)cosh(x) - 4b)sinh(x) +--R + +--R 7 5 3 +--R (- 8b cosh(x) - 24b cosh(x) + (- 24b - 64a)cosh(x) - 8b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - b cosh(x) - 4b cosh(x) + (- 6b - 16a)cosh(x) - 4b cosh(x) - b +--R * +--R +-+ +--R \|a +--R / +--R 8 7 +--R a b sinh(x) + 8a b cosh(x)sinh(x) +--R + +--R 2 6 +--R (28a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 5 +--R (56a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 4 2 2 4 +--R (70a b cosh(x) + 60a b cosh(x) + 6a b + 16a )sinh(x) +--R + +--R 5 3 2 3 +--R (56a b cosh(x) + 80a b cosh(x) + (24a b + 64a )cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R 28a b cosh(x) + 60a b cosh(x) + (36a b + 96a )cosh(x) +--R + +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 2 3 +--R 8a b cosh(x) + 24a b cosh(x) + (24a b + 64a )cosh(x) +--R + +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 2 4 +--R a b cosh(x) + 4a b cosh(x) + (6a b + 16a )cosh(x) +--R + +--R 2 +--R 4a b cosh(x) + a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 8 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4b + 4a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b + 56a b)cosh(x) + (24b + 24a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (70b + 70a b)cosh(x) + (60b + 60a b)cosh(x) + 6b + 22a b +--R + +--R 2 +--R 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (56b + 56a b)cosh(x) + (80b + 80a b)cosh(x) +--R + +--R 2 2 +--R (24b + 88a b + 64a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (28b + 28a b)cosh(x) + (60b + 60a b)cosh(x) +--R + +--R 2 2 2 2 +--R (36b + 132a b + 96a )cosh(x) + 4b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (8b + 8a b)cosh(x) + (24b + 24a b)cosh(x) +--R + +--R 2 2 3 2 +--R (24b + 88a b + 64a )cosh(x) + (8b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 +--R (b + a b)cosh(x) + (4b + 4a b)cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (6b + 22a b + 16a )cosh(x) + (4b + 4a b)cosh(x) + b + a b +--R * +--R 4+-+2 +--R \|a +--R + +--R 8 7 +--R - 2a b sinh(x) - 16a b cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 56a b cosh(x) - 8a b)sinh(x) +--R + +--R 3 5 +--R (- 112a b cosh(x) - 48a b cosh(x))sinh(x) +--R + +--R 4 2 2 4 +--R (- 140a b cosh(x) - 120a b cosh(x) - 12a b - 32a )sinh(x) +--R + +--R 5 3 2 +--R (- 112a b cosh(x) - 160a b cosh(x) + (- 48a b - 128a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 2 +--R - 56a b cosh(x) - 120a b cosh(x) + (- 72a b - 192a )cosh(x) +--R + +--R - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 2 3 +--R - 16a b cosh(x) - 48a b cosh(x) + (- 48a b - 128a )cosh(x) +--R + +--R - 16a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 2 4 +--R - 2a b cosh(x) - 8a b cosh(x) + (- 12a b - 32a )cosh(x) +--R + +--R 2 +--R - 8a b cosh(x) - 2a b +--R * +--R 2 +-+ +--R tanh(x) \|a +--R Type: Expression(Integer) +--E 45 + +--S 46 of 500 +t0209:= 1/(a+b*cosh(x)^5) +--R +--R +--R 1 +--R (24) -------------- +--R 5 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0209:= 2/5*atanh((a^(1/5)-b^(1/5))*tanh(1/2*x)/(a^(2/5)-b^(2/5))^(1/2))/_ + a^(4/5)/(a^(2/5)-b^(2/5))^(1/2)+_ + 2/5*atanh((a^(1/5)+(-1)^(3/5)*b^(1/5))*_ + tanh(1/2*x)/(a^(2/5)+(-1)^(1/5)*b^(2/5))^(1/2))/a^(4/5)/(a^(2/5)+_ + (-1)^(1/5)*b^(2/5))^(1/2)+2/5*atanh((a^(1/5)+(-1)^(1/5)*b^(1/5))*_ + tanh(1/2*x)/(a^(2/5)-(-1)^(2/5)*b^(2/5))^(1/2))/_ + a^(4/5)/(a^(2/5)-(-1)^(2/5)*b^(2/5))^(1/2)+_ + 2/5*atanh((a^(1/5)-(-1)^(4/5)*b^(1/5))*tanh(1/2*x)/_ + (a^(2/5)+(-1)^(3/5)*b^(2/5))^(1/2))/a^(4/5)/(a^(2/5)+_ + (-1)^(3/5)*b^(2/5))^(1/2)+2/5*atanh((a^(1/5)-(-1)^(2/5)*b^(1/5))*_ + tanh(1/2*x)/(a^(2/5)-(-1)^(4/5)*b^(2/5))^(1/2))/_ + a^(4/5)/(a^(2/5)-(-1)^(4/5)*b^(2/5))^(1/2) +--R +--R +--R (25) +--R - +--R +----------------------+ +---------------+ +-------------------+ +--R | 5+---+2 5+-+2 5+-+2 | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+2 x 5+-+ x 5+-+ +--R +--------------------+ \|- 1 tanh(-)\|b - tanh(-)\|a +--R |5+---+3 5+-+2 5+-+2 2 2 +--R \|\|- 1 \|b + \|a atanh(--------------------------------) +--R +----------------------+ +--R | 5+---+4 5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+ x 5+-+ x 5+-+ +--R +--------------------+ \|- 1 tanh(-)\|b + tanh(-)\|a +--R |5+---+3 5+-+2 5+-+2 2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------------) +--R +----------------------+ +--R | 5+---+2 5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +----------------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +-------------------+ +--------------------+ +--R |5+---+5+-+2 5+-+2 |5+---+3 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 5+-+ x 5+-+ +--R tanh(-)\|b - tanh(-)\|a +--R 2 2 +--R atanh(-------------------------) +--R +---------------+ +--R | 5+-+2 5+-+2 +--R \|- \|b + \|a +--R + +--R +----------------------+ +----------------------+ +---------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 | 5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 5+---+3 x 5+-+ x 5+-+ +--R +--------------------+ \|- 1 tanh(-)\|b + tanh(-)\|a +--R |5+---+3 5+-+2 5+-+2 2 2 +--R \|\|- 1 \|b + \|a atanh(--------------------------------) +--R +-------------------+ +--R |5+---+5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +----------------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +---------------+ +-------------------+ +--R | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 +--R \|- \|b + \|a \|\|- 1 \|b + \|a 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+--R + +--R 4 2 6 2 4 2 +--I (- 3125a b + 143750a )%%BR0 - 4375a %%BR0 + 50a +--R * +--R +------+ +--I \|4%%BR0 +--R + +--R 7 2 9 4 +--I (- 2343750a b + 2343750a )%%BR0 +--R + +--R 5 2 7 3 5 2 3 +--I (- 31250a b - 437500a )%%BR0 + 31250a %%BR0 - 1000a %%BR0 +--R + +--R 2b sinh(x) + 2b cosh(x) + 12a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +--m0209:= a0209-r0209 +--E 49 + +--S 50 of 500 +--d0209:= D(m0209,x) +--E 50 + +--S 51 of 500 +t0210:= 1/(a+b*cosh(x)^6) +--R +--R +--R 1 +--R (27) -------------- +--R 6 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0210:= 1/3*atanh(a^(1/6)*tanh(x)/(a^(1/3)+b^(1/3))^(1/2))/a^(5/6)/_ + (a^(1/3)+b^(1/3))^(1/2)+1/3*atanh(a^(1/6)*tanh(x)/(a^(1/3)-_ + (-1)^(1/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-_ + (-1)^(1/3)*b^(1/3))^(1/2)+1/3*atanh(a^(1/6)*tanh(x)/(a^(1/3)+_ + (-1)^(2/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2) +--R +--R +--R (28) +--R +-----------+ +------------------+ 6+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|a +--R \|\|b + \|a \|\|- 1 \|b + \|a atanh(----------------------) +--R +-------------------+ +--R | 3+---+3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +-------------------+ +------------------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|a +--R \|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atanh(--------------) +--R +-----------+ +--R |3+-+ 3+-+ +--R \|\|b + \|a +--R + +--R +-------------------+ +-----------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+-+ 3+-+ tanh(x)\|a +--R \|- \|- 1 \|b + \|a \|\|b + \|a atanh(---------------------) +--R +------------------+ +--R |3+---+2 3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0210:= integrate(t0210,x) +--R +--R +--R (29) +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b + 3888a )%%BS0 - 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b + 3888a )%%BS0 + (108a b - 216a )%%BS0 - 6a b + 3a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b - 1296a )%%BS0 + 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b - 1296a )%%BS0 + (- 36a b + 72a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - a +--R + +--R - +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b + 3888a )%%BS0 - 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b - 3888a )%%BS0 + (- 108a b + 216a )%%BS0 + 6a b +--R + +--R 2 +--R - 3a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((1296a b + 1296a )%%BS0 - 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b - 1296a )%%BS0 + (- 36a b + 72a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - a +--R + +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b - 3888a )%%BS0 + 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b + 3888a )%%BS0 + (108a b - 216a )%%BS0 - 6a b + 3a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((1296a b + 1296a )%%BS0 - 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b - 1296a )%%BS0 + (- 36a b + 72a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - a +--R + +--R - +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b - 3888a )%%BS0 + 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b - 3888a )%%BS0 + (- 108a b + 216a )%%BS0 + 6a b +--R + +--R 2 +--R - 3a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b - 1296a )%%BS0 + 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b - 1296a )%%BS0 + (- 36a b + 72a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - a +--R + +--R - +--R +------+ +--I \|4%%BS0 +--R * +--R log +--R 5 6 2 3 4 +--I (7776a b + 7776a )%%BS0 + (216a b - 432a )%%BS0 + 6a b +--R + +--R 2 +--R 6a +--R * +--R +------+ +--I \|4%%BS0 +--R + +--R 4 5 2 2 3 2 +--I (2592a b + 2592a )%%BS0 + (72a b - 144a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R +------+ +--I \|4%%BS0 +--R * +--R log +--R 5 6 2 3 4 +--I (- 7776a b - 7776a )%%BS0 + (- 216a b + 432a )%%BS0 - 6a b +--R + +--R 2 +--R - 6a +--R * +--R +------+ +--I \|4%%BS0 +--R + +--R 4 5 2 2 3 2 +--I (2592a b + 2592a )%%BS0 + (72a b - 144a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0210:= a0210-r0210 +--R +--R +--R (30) +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b + 3888a )%%BS0 - 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b + 3888a )%%BS0 + (108a b - 216a )%%BS0 - 6a b + 3a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b - 1296a )%%BS0 + 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b - 1296a )%%BS0 + (- 36a b + 72a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - a +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b + 3888a )%%BS0 - 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b - 3888a )%%BS0 + (- 108a b + 216a )%%BS0 + 6a b +--R + +--R 2 +--R - 3a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((1296a b + 1296a )%%BS0 - 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b - 1296a )%%BS0 + (- 36a b + 72a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - a +--R + +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b - 3888a )%%BS0 + 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b + 3888a )%%BS0 + (108a b - 216a )%%BS0 - 6a b + 3a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((1296a b + 1296a )%%BS0 - 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b - 1296a )%%BS0 + (- 36a b + 72a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - a +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b - 3888a )%%BS0 + 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b - 3888a )%%BS0 + (- 108a b + 216a )%%BS0 + 6a b +--R + +--R 2 +--R - 3a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%BS0 + 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b - 1296a )%%BS0 + 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%BS0 +--R + +--R 2 3 +--I (72a b + 72a )%%BS0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b - 1296a )%%BS0 + (- 36a b + 72a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - a +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%BS0 +--R * +--R log +--R 5 6 2 3 4 +--I (7776a b + 7776a )%%BS0 + (216a b - 432a )%%BS0 + 6a b +--R + +--R 2 +--R 6a +--R * +--R +------+ +--I \|4%%BS0 +--R + +--R 4 5 2 2 3 2 +--I (2592a b + 2592a )%%BS0 + (72a b - 144a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%BS0 +--R * +--R log +--R 5 6 2 3 4 +--I (- 7776a b - 7776a )%%BS0 + (- 216a b + 432a )%%BS0 - 6a b +--R + +--R 2 +--R - 6a +--R * +--R +------+ +--I \|4%%BS0 +--R + +--R 4 5 2 2 3 2 +--I (2592a b + 2592a )%%BS0 + (72a b - 144a )%%BS0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R +-----------+ +------------------+ 6+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|a +--R - 2\|\|b + \|a \|\|- 1 \|b + \|a atanh(----------------------) +--R +-------------------+ +--R | 3+---+3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +-------------------+ +------------------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tanh(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atanh(--------------) +--R +-----------+ +--R |3+-+ 3+-+ +--R \|\|b + \|a +--R + +--R +-------------------+ +-----------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+-+ 3+-+ tanh(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|\|b + \|a atanh(---------------------) +--R +------------------+ +--R |3+---+2 3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 6\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +--d0210:= D(m0210,x) +--E 55 + +--S 56 of 500 +t0211:= 1/(a+b*cosh(x)^8) +--R +--R +--R 1 +--R (31) -------------- +--R 8 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0211:= 1/4*atanh(a^(1/8)*tanh(x)/(a^(1/4)+(-b)^(1/4))^(1/2))/_ + a^(7/8)/(a^(1/4)+(-b)^(1/4))^(1/2)+1/4*atanh(a^(1/4)*_ + tanh(x)/(a^(1/2)-a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/_ + (a^(1/2)-a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atanh(a^(1/4)*_ + tanh(x)/(a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/_ + (a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atanh(a^(1/4)*_ + tanh(x)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/_ + (a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2) +--R +--R +--R (32) +--R +---------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- %i\|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R 4+-+ +--R tanh(x)\|a +--R atanh(----------------------) +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|- \|- b \|a + \|a +--R + +--R +-------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R 4+-+ +--R tanh(x)\|a +--R atanh(------------------------) +--R +---------------------+ +--R | 4+---+4+-+ +-+ +--R \|- %i\|- b \|a + \|a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------------+ 8+-+ +--R | 4+---+4+-+ +-+ tanh(x)\|a +--R \|%i\|- b \|a + \|a atanh(----------------) +--R +-------------+ +--R |4+-+ 4+---+ +--R \|\|a + \|- b +--R + +--R +-------------------+ +---------------------+ +-------------+ +--R 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R 4+-+ +--R tanh(x)\|a +--R atanh(----------------------) +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R / +--R +-------------------+ +---------------------+ +-------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R 4\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R Type: Expression(Complex(Integer)) +--E 57 + +--S 58 of 500 +a0211:= integrate(t0211,x) +--R +--R +--R (33) +--R - +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b + 1048576a )%%BT0 - 16384a b - 16384a ) +--R * +--I %%BT1 +--R + +--R 5 6 3 4 +--I (- 16384a b - 16384a )%%BT0 + 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b + 1048576a )%%BT0 - 16384a b - 16384a )%%BT1 +--R + +--R 7 8 2 6 3 +--I (1048576a b + 1048576a )%%BT0 - 65536a %%BT0 - 256a b +--R + +--R 4 +--R 768a +--R * +--I %%BT1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b - 16384a )%%BT0 + (- 256a b + 768a )%%BT0 +--R + +--R 2 +--R 8a b - 8a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%BT0 +--R + +--R 2 3 +--R 64a b + 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 4 5 2 3 +--I (- 4096a b - 4096a )%%BT0 + 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b + 262144a )%%BT0 - 16384a %%BT0 - 64a b + 192a ) +--R * +--I %%BT1 +--R + +--R 4 5 2 2 3 +--I (- 4096a b - 4096a )%%BT0 + (- 64a b + 192a )%%BT0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%BT0 + 64a b + 64a ) +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b + 1048576a )%%BT0 - 16384a b - 16384a )%%BT1 +--R + +--R 5 6 3 4 +--I (- 16384a b - 16384a )%%BT0 + 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((- 1048576a b - 1048576a )%%BT0 + 16384a b + 16384a )%%BT1 +--R + +--R 7 8 2 6 3 +--I (- 1048576a b - 1048576a )%%BT0 + 65536a %%BT0 + 256a b +--R + +--R 4 +--R - 768a +--R * +--I %%BT1 +--R + +--R 5 6 2 3 4 2 +--I (16384a b + 16384a )%%BT0 + (256a b - 768a )%%BT0 - 8a b + 8a +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b - 262144a )%%BT0 + 4096a b + 4096a )%%BT1 +--R + +--R 4 5 2 3 +--I (4096a b + 4096a )%%BT0 - 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%BT0 + 64a b + 64a ) +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b + 262144a )%%BT0 - 16384a %%BT0 - 64a b + 192a )%%BT1 +--R + +--R 4 5 2 2 3 2 +--I (- 4096a b - 4096a )%%BT0 + (- 64a b + 192a )%%BT0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R - +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 +--I (- 1048576a b - 1048576a )%%BT0 + 16384a b +--R + +--R 6 +--R 16384a +--R * +--I %%BT1 +--R + +--R 5 6 3 4 +--I (16384a b + 16384a )%%BT0 - 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b + 1048576a )%%BT0 - 16384a b - 16384a )%%BT1 +--R + +--R 7 8 2 6 3 +--I (1048576a b + 1048576a )%%BT0 - 65536a %%BT0 - 256a b +--R + +--R 4 +--R 768a +--R * +--I %%BT1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b - 16384a )%%BT0 + (- 256a b + 768a )%%BT0 +--R + +--R 2 +--R 8a b - 8a +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%BT0 +--R + +--R 2 3 +--R 64a b + 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b - 262144a )%%BT0 + 4096a b + 4096a )%%BT1 +--R + +--R 4 5 2 3 +--I (4096a b + 4096a )%%BT0 - 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b + 262144a )%%BT0 - 16384a %%BT0 - 64a b + 192a ) +--R * +--I %%BT1 +--R + +--R 4 5 2 2 3 +--I (- 4096a b - 4096a )%%BT0 + (- 64a b + 192a )%%BT0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%BT0 + 64a b + 64a ) +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 6 +--I ((- 1048576a b - 1048576a )%%BT0 + 16384a b + 16384a ) +--R * +--I %%BT1 +--R + +--R 5 6 3 4 +--I (16384a b + 16384a )%%BT0 - 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((- 1048576a b - 1048576a )%%BT0 + 16384a b + 16384a )%%BT1 +--R + +--R 7 8 2 6 3 +--I (- 1048576a b - 1048576a )%%BT0 + 65536a %%BT0 + 256a b +--R + +--R 4 +--R - 768a +--R * +--I %%BT1 +--R + +--R 5 6 2 3 4 2 +--I (16384a b + 16384a )%%BT0 + (256a b - 768a )%%BT0 - 8a b + 8a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 4 5 2 3 +--I (- 4096a b - 4096a )%%BT0 + 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%BT0 + 64a b + 64a ) +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b + 262144a )%%BT0 - 16384a %%BT0 - 64a b + 192a )%%BT1 +--R + +--R 4 5 2 2 3 2 +--I (- 4096a b - 4096a )%%BT0 + (- 64a b + 192a )%%BT0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R +------+ +--I \|4%%BT1 +--R * +--R log +--R 7 8 5 6 2 +--I ((2097152a b + 2097152a )%%BT0 - 32768a b - 32768a )%%BT1 +--R + +--R 7 8 2 6 3 +--I (2097152a b + 2097152a )%%BT0 - 131072a %%BT0 - 512a b +--R + +--R 4 +--R 1536a +--R * +--I %%BT1 +--R + +--R 7 8 3 6 2 4 +--I (2097152a b + 2097152a )%%BT0 - 131072a %%BT0 + 3072a %%BT0 +--R + +--R 2 +--R - 8a b - 24a +--R * +--R +------+ +--I \|4%%BT1 +--R + +--R 6 7 4 5 2 +--I ((- 524288a b - 524288a )%%BT0 + 8192a b + 8192a )%%BT1 +--R + +--R 6 7 2 5 2 3 +--I ((- 524288a b - 524288a )%%BT0 + 32768a %%BT0 + 128a b - 384a ) +--R * +--I %%BT1 +--R + +--R 6 7 3 5 2 3 +--I (- 524288a b - 524288a )%%BT0 + 32768a %%BT0 - 768a %%BT0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 6a +--R + +--R - +--R +------+ +--I \|4%%BT1 +--R * +--R log +--R 7 8 5 6 +--I ((- 2097152a b - 2097152a )%%BT0 + 32768a b + 32768a ) +--R * +--R 2 +--I %%BT1 +--R + +--R 7 8 2 6 +--I (- 2097152a b - 2097152a )%%BT0 + 131072a %%BT0 +--R + +--R 3 4 +--R 512a b - 1536a +--R * +--I %%BT1 +--R + +--R 7 8 3 6 2 +--I (- 2097152a b - 2097152a )%%BT0 + 131072a %%BT0 +--R + +--R 4 2 +--I - 3072a %%BT0 + 8a b + 24a +--R * +--R +------+ +--I \|4%%BT1 +--R + +--R 6 7 4 5 2 +--I ((- 524288a b - 524288a )%%BT0 + 8192a b + 8192a )%%BT1 +--R + +--R 6 7 2 5 2 +--I (- 524288a b - 524288a )%%BT0 + 32768a %%BT0 + 128a b +--R + +--R 3 +--R - 384a +--R * +--I %%BT1 +--R + +--R 6 7 3 5 2 3 +--I (- 524288a b - 524288a )%%BT0 + 32768a %%BT0 - 768a %%BT0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 6a +--R + +--R - +--R +------+ +--I \|4%%BT0 +--R * +--R log +--R 7 8 3 5 6 2 +--I (2097152a b + 2097152a )%%BT0 + (32768a b - 98304a )%%BT0 +--R + +--R 3 4 2 +--I (512a b + 1536a )%%BT0 + 8a b - 8a +--R * +--R +------+ +--I \|4%%BT0 +--R + +--R 6 7 3 4 5 2 +--I (524288a b + 524288a )%%BT0 + (8192a b - 24576a )%%BT0 +--R + +--R 2 3 2 +--I (128a b + 384a )%%BT0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) + b - 2a +--R + +--R +------+ +--I \|4%%BT0 +--R * +--R log +--R 7 8 3 +--I (- 2097152a b - 2097152a )%%BT0 +--R + +--R 5 6 2 3 4 +--I (- 32768a b + 98304a )%%BT0 + (- 512a b - 1536a )%%BT0 - 8a b +--R + +--R 2 +--R 8a +--R * +--R +------+ +--I \|4%%BT0 +--R + +--R 6 7 3 4 5 2 +--I (524288a b + 524288a )%%BT0 + (8192a b - 24576a )%%BT0 +--R + +--R 2 3 2 +--I (128a b + 384a )%%BT0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) + b - 2a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0211:= a0211-r0211 +--R +--R +--R (34) +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b + 1048576a )%%BT0 - 16384a b - 16384a ) +--R * +--I %%BT1 +--R + +--R 5 6 3 4 +--I (- 16384a b - 16384a )%%BT0 + 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b + 1048576a )%%BT0 - 16384a b - 16384a )%%BT1 +--R + +--R 7 8 2 6 3 +--I (1048576a b + 1048576a )%%BT0 - 65536a %%BT0 - 256a b +--R + +--R 4 +--R 768a +--R * +--I %%BT1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b - 16384a )%%BT0 + (- 256a b + 768a )%%BT0 +--R + +--R 2 +--R 8a b - 8a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%BT0 +--R + +--R 2 3 +--R 64a b + 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 4 5 2 3 +--I (- 4096a b - 4096a )%%BT0 + 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b + 262144a )%%BT0 - 16384a %%BT0 - 64a b + 192a ) +--R * +--I %%BT1 +--R + +--R 4 5 2 2 3 +--I (- 4096a b - 4096a )%%BT0 + (- 64a b + 192a )%%BT0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%BT0 + 64a b + 64a ) +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b + 1048576a )%%BT0 - 16384a b - 16384a )%%BT1 +--R + +--R 5 6 3 4 +--I (- 16384a b - 16384a )%%BT0 + 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((- 1048576a b - 1048576a )%%BT0 + 16384a b + 16384a )%%BT1 +--R + +--R 7 8 2 6 3 +--I (- 1048576a b - 1048576a )%%BT0 + 65536a %%BT0 + 256a b +--R + +--R 4 +--R - 768a +--R * +--I %%BT1 +--R + +--R 5 6 2 3 4 2 +--I (16384a b + 16384a )%%BT0 + (256a b - 768a )%%BT0 - 8a b + 8a +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b - 262144a )%%BT0 + 4096a b + 4096a )%%BT1 +--R + +--R 4 5 2 3 +--I (4096a b + 4096a )%%BT0 - 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%BT0 + 64a b + 64a ) +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b + 262144a )%%BT0 - 16384a %%BT0 - 64a b + 192a )%%BT1 +--R + +--R 4 5 2 2 3 2 +--I (- 4096a b - 4096a )%%BT0 + (- 64a b + 192a )%%BT0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 +--I (- 1048576a b - 1048576a )%%BT0 + 16384a b +--R + +--R 6 +--R 16384a +--R * +--I %%BT1 +--R + +--R 5 6 3 4 +--I (16384a b + 16384a )%%BT0 - 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b + 1048576a )%%BT0 - 16384a b - 16384a )%%BT1 +--R + +--R 7 8 2 6 3 +--I (1048576a b + 1048576a )%%BT0 - 65536a %%BT0 - 256a b +--R + +--R 4 +--R 768a +--R * +--I %%BT1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b - 16384a )%%BT0 + (- 256a b + 768a )%%BT0 +--R + +--R 2 +--R 8a b - 8a +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%BT0 +--R + +--R 2 3 +--R 64a b + 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b - 262144a )%%BT0 + 4096a b + 4096a )%%BT1 +--R + +--R 4 5 2 3 +--I (4096a b + 4096a )%%BT0 - 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b + 262144a )%%BT0 - 16384a %%BT0 - 64a b + 192a ) +--R * +--I %%BT1 +--R + +--R 4 5 2 2 3 +--I (- 4096a b - 4096a )%%BT0 + (- 64a b + 192a )%%BT0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%BT0 + 64a b + 64a ) +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 7 8 5 6 +--I ((- 1048576a b - 1048576a )%%BT0 + 16384a b + 16384a ) +--R * +--I %%BT1 +--R + +--R 5 6 3 4 +--I (16384a b + 16384a )%%BT0 - 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((- 1048576a b - 1048576a )%%BT0 + 16384a b + 16384a )%%BT1 +--R + +--R 7 8 2 6 3 +--I (- 1048576a b - 1048576a )%%BT0 + 65536a %%BT0 + 256a b +--R + +--R 4 +--R - 768a +--R * +--I %%BT1 +--R + +--R 5 6 2 3 4 2 +--I (16384a b + 16384a )%%BT0 + (256a b - 768a )%%BT0 - 8a b + 8a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%BT0 + 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%BT1 + (- 16a b - 16a )%%BT0 + 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R 6 7 4 5 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 4 5 2 3 +--I (- 4096a b - 4096a )%%BT0 + 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%BT0 + 64a b + 64a ) +--R * +--I %%BT1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%BT0 +--R + +--R 2 3 +--I (64a b + 64a )%%BT0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b + 262144a )%%BT0 - 4096a b - 4096a )%%BT1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b + 262144a )%%BT0 - 16384a %%BT0 - 64a b + 192a )%%BT1 +--R + +--R 4 5 2 2 3 2 +--I (- 4096a b - 4096a )%%BT0 + (- 64a b + 192a )%%BT0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%BT1 +--R * +--R log +--R 7 8 5 6 2 +--I ((2097152a b + 2097152a )%%BT0 - 32768a b - 32768a )%%BT1 +--R + +--R 7 8 2 6 3 +--I (2097152a b + 2097152a )%%BT0 - 131072a %%BT0 - 512a b +--R + +--R 4 +--R 1536a +--R * +--I %%BT1 +--R + +--R 7 8 3 6 2 4 +--I (2097152a b + 2097152a )%%BT0 - 131072a %%BT0 + 3072a %%BT0 +--R + +--R 2 +--R - 8a b - 24a +--R * +--R +------+ +--I \|4%%BT1 +--R + +--R 6 7 4 5 2 +--I ((- 524288a b - 524288a )%%BT0 + 8192a b + 8192a )%%BT1 +--R + +--R 6 7 2 5 2 3 +--I ((- 524288a b - 524288a )%%BT0 + 32768a %%BT0 + 128a b - 384a ) +--R * +--I %%BT1 +--R + +--R 6 7 3 5 2 3 +--I (- 524288a b - 524288a )%%BT0 + 32768a %%BT0 - 768a %%BT0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 6a +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%BT1 +--R * +--R log +--R 7 8 5 6 +--I ((- 2097152a b - 2097152a )%%BT0 + 32768a b + 32768a ) +--R * +--R 2 +--I %%BT1 +--R + +--R 7 8 2 6 +--I (- 2097152a b - 2097152a )%%BT0 + 131072a %%BT0 +--R + +--R 3 4 +--R 512a b - 1536a +--R * +--I %%BT1 +--R + +--R 7 8 3 6 2 +--I (- 2097152a b - 2097152a )%%BT0 + 131072a %%BT0 +--R + +--R 4 2 +--I - 3072a %%BT0 + 8a b + 24a +--R * +--R +------+ +--I \|4%%BT1 +--R + +--R 6 7 4 5 2 +--I ((- 524288a b - 524288a )%%BT0 + 8192a b + 8192a )%%BT1 +--R + +--R 6 7 2 5 2 +--I (- 524288a b - 524288a )%%BT0 + 32768a %%BT0 + 128a b +--R + +--R 3 +--R - 384a +--R * +--I %%BT1 +--R + +--R 6 7 3 5 2 3 +--I (- 524288a b - 524288a )%%BT0 + 32768a %%BT0 - 768a %%BT0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 6a +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%BT0 +--R * +--R log +--R 7 8 3 5 6 2 +--I (2097152a b + 2097152a )%%BT0 + (32768a b - 98304a )%%BT0 +--R + +--R 3 4 2 +--I (512a b + 1536a )%%BT0 + 8a b - 8a +--R * +--R +------+ +--I \|4%%BT0 +--R + +--R 6 7 3 4 5 2 +--I (524288a b + 524288a )%%BT0 + (8192a b - 24576a )%%BT0 +--R + +--R 2 3 2 +--I (128a b + 384a )%%BT0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) + b - 2a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%BT0 +--R * +--R log +--R 7 8 3 +--I (- 2097152a b - 2097152a )%%BT0 +--R + +--R 5 6 2 3 4 +--I (- 32768a b + 98304a )%%BT0 + (- 512a b - 1536a )%%BT0 - 8a b +--R + +--R 2 +--R 8a +--R * +--R +------+ +--I \|4%%BT0 +--R + +--R 6 7 3 4 5 2 +--I (524288a b + 524288a )%%BT0 + (8192a b - 24576a )%%BT0 +--R + +--R 2 3 2 +--I (128a b + 384a )%%BT0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) + b - 2a +--R + +--R - +--R +---------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- %i\|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R 4+-+ +--R tanh(x)\|a +--R atanh(----------------------) +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|- \|- b \|a + \|a +--R + +--R - +--R +-------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R 4+-+ +--R tanh(x)\|a +--R atanh(------------------------) +--R +---------------------+ +--R | 4+---+4+-+ +-+ +--R \|- %i\|- b \|a + \|a +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------------+ 8+-+ +--R | 4+---+4+-+ +-+ tanh(x)\|a +--R \|%i\|- b \|a + \|a atanh(----------------) +--R +-------------+ +--R |4+-+ 4+---+ +--R \|\|a + \|- b +--R + +--R - +--R +-------------------+ +---------------------+ +-------------+ +--R 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R 4+-+ +--R tanh(x)\|a +--R atanh(----------------------) +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R / +--R +-------------------+ +---------------------+ +-------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R 4\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R Type: Expression(Complex(Integer)) +--E 59 + +--S 60 of 500 +--d0211:= D(m0211,x) +--E 60 + +--S 61 of 500 +t0212:= 1/(a-b*cosh(x)^3) +--R +--R +--R 1 +--R (35) - -------------- +--R 3 +--R b cosh(x) - a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0212:= 2/3*atanh((a^(1/3)+b^(1/3))*tanh(1/2*x)/(a^(2/3)-b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atanh((a^(1/3)+_ + (-1)^(2/3)*b^(1/3))*tanh(1/2*x)/(a^(2/3)+_ + (-1)^(1/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)+_ + (-1)^(1/3)*b^(2/3))^(1/2)+2/3*atanh((a^(1/3)-_ + (-1)^(1/3)*b^(1/3))*tanh(1/2*x)/(a^(2/3)-_ + (-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-_ + (-1)^(2/3)*b^(2/3))^(1/2) +--R +--R +--R (36) +--R - +--R +---------------+ +-------------------+ +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+ x 3+-+ x 3+-+ +--R \|- 1 tanh(-)\|b - tanh(-)\|a +--R 2 2 +--R atanh(-------------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +-------------------+ +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 3+-+ x 3+-+ +--R tanh(-)\|b + tanh(-)\|a +--R 2 2 +--R atanh(-------------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R +----------------------+ +---------------+ +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 3+---+2 x 3+-+ x 3+-+ +--R \|- 1 tanh(-)\|b + tanh(-)\|a +--R 2 2 +--R atanh(--------------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0212:= integrate(t0212,x) +--R +--R +--R (37) +--R - +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b - 486a )%%BU0 - 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b - 486a )%%BU0 + (27a b + 135a )%%BU0 - 9a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--I (162a b - 162a )%%BU0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b - 162a )%%BU0 + 54a %%BU0 + 4b sinh(x) + 4b cosh(x) +--R + +--R - 4a +--R + +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b - 486a )%%BU0 - 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b + 486a )%%BU0 + (- 27a b - 135a )%%BU0 + 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--I (- 162a b + 162a )%%BU0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b - 162a )%%BU0 + 54a %%BU0 + 4b sinh(x) + 4b cosh(x) - 4a +--R + +--R - +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b + 486a )%%BU0 + 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b - 486a )%%BU0 + (27a b + 135a )%%BU0 - 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--I (- 162a b + 162a )%%BU0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b - 162a )%%BU0 + 54a %%BU0 + 4b sinh(x) + 4b cosh(x) +--R + +--R - 4a +--R + +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b + 486a )%%BU0 + 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b + 486a )%%BU0 + (- 27a b - 135a )%%BU0 + 9a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--I (162a b - 162a )%%BU0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b - 162a )%%BU0 + 54a %%BU0 + 4b sinh(x) + 4b cosh(x) - 4a +--R + +--R +------+ +--I \|4%%BU0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +------+ +--I ((486a b - 486a )%%BU0 + (27a b + 135a )%%BU0 - 9a )\|4%%BU0 +--R + +--R 3 2 5 2 3 +--I (- 162a b + 162a )%%BU0 - 54a %%BU0 + 2b sinh(x) + 2b cosh(x) + 4a +--R + +--R - +--R +------+ +--I \|4%%BU0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--I ((- 486a b + 486a )%%BU0 + (- 27a b - 135a )%%BU0 + 9a ) +--R * +--R +------+ +--I \|4%%BU0 +--R + +--R 3 2 5 2 3 +--I (- 162a b + 162a )%%BU0 - 54a %%BU0 + 2b sinh(x) + 2b cosh(x) +--R + +--R 4a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0212:= a0212-r0212 +--R +--R +--R (38) +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b - 486a )%%BU0 - 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b - 486a )%%BU0 + (27a b + 135a )%%BU0 - 9a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--I (162a b - 162a )%%BU0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b - 162a )%%BU0 + 54a %%BU0 + 4b sinh(x) + 4b cosh(x) +--R + +--R - 4a +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((486a b - 486a )%%BU0 - 27a b + 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b + 486a )%%BU0 + (- 27a b - 135a )%%BU0 + 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--I (- 162a b + 162a )%%BU0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b - 162a )%%BU0 + 54a %%BU0 + 4b sinh(x) + 4b cosh(x) - 4a +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b + 486a )%%BU0 + 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (486a b - 486a )%%BU0 + (27a b + 135a )%%BU0 - 9a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--I (- 162a b + 162a )%%BU0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b - 162a )%%BU0 + 54a %%BU0 + 4b sinh(x) + 4b cosh(x) +--R + +--R - 4a +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 2 2 4 +--I ((- 486a b + 486a )%%BU0 + 27a b - 27a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 2 2 2 4 2 +--I (- 486a b + 486a )%%BU0 + (- 27a b - 135a )%%BU0 + 9a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%BU0 - 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 +--I (162a b - 162a )%%BU0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%BU0 +--R + +--R 2 2 4 2 2 +--I (- 18a b + 18a )%%BU0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 2 3 +--I (162a b - 162a )%%BU0 + 54a %%BU0 + 4b sinh(x) + 4b cosh(x) - 4a +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%BU0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +------+ +--I ((486a b - 486a )%%BU0 + (27a b + 135a )%%BU0 - 9a )\|4%%BU0 +--R + +--R 3 2 5 2 3 +--I (- 162a b + 162a )%%BU0 - 54a %%BU0 + 2b sinh(x) + 2b cosh(x) + 4a +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +------+ +--I \|\|- 1 \|b + \|a \|4%%BU0 +--R * +--R log +--R 4 2 6 2 2 2 4 2 +--I ((- 486a b + 486a )%%BU0 + (- 27a b - 135a )%%BU0 + 9a ) +--R * +--R +------+ +--I \|4%%BU0 +--R + +--R 3 2 5 2 3 +--I (- 162a b + 162a )%%BU0 - 54a %%BU0 + 2b sinh(x) + 2b cosh(x) +--R + +--R 4a +--R + +--R +---------------+ +-------------------+ +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 4\|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+ x 3+-+ x 3+-+ +--R \|- 1 tanh(-)\|b - tanh(-)\|a +--R 2 2 +--R atanh(-------------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +-------------------+ +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 4\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 3+-+ x 3+-+ +--R tanh(-)\|b + tanh(-)\|a +--R 2 2 +--R atanh(-------------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R - +--R +----------------------+ +---------------+ +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 3+---+2 x 3+-+ x 3+-+ +--R \|- 1 tanh(-)\|b + tanh(-)\|a +--R 2 2 +--R atanh(--------------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 6\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +--d0212:= D(m0212,x) +--E 65 + +--S 66 of 500 +t0213:= 1/(a-b*cosh(x)^4) +--R +--R +--R 1 +--R (39) - -------------- +--R 4 +--R b cosh(x) - a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0213:= 1/2*atanh(a^(1/4)*tanh(x)/(a^(1/2)-b^(1/2))^(1/2))/a^(3/4)/_ + (a^(1/2)-b^(1/2))^(1/2)+1/2*atanh(a^(1/4)*tanh(x)/_ + (a^(1/2)+b^(1/2))^(1/2))/a^(3/4)/(a^(1/2)+b^(1/2))^(1/2) +--R +--R +--R (40) +--R +-----------+ 4+-+ +-------------+ 4+-+ +--R | +-+ +-+ tanh(x)\|a | +-+ +-+ tanh(x)\|a +--R \|\|b + \|a atanh(----------------) + \|- \|b + \|a atanh(--------------) +--R +-------------+ +-----------+ +--R | +-+ +-+ | +-+ +-+ +--R \|- \|b + \|a \|\|b + \|a +--R ----------------------------------------------------------------------------- +--R +-------------+ +-----------+ +--R 4+-+3 | +-+ +-+ | +-+ +-+ +--R 2\|a \|- \|b + \|a \|\|b + \|a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0213:= integrate(t0213,x) +--R +--R +--R (41) +--R - +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((32a b - 32a ) |---------------------- + 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (16a b - 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((32a b - 32a ) |---------------------- - 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (- 16a b + 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R - +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((- 32a b + 32a ) |---------------------- + 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (- 16a b + 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((- 32a b + 32a ) |---------------------- - 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (16a b - 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0213:= a0213-r0213 +--R +--R +--R (42) +--R - +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R +-------------+ | | 3 2 4 5 +--R 4+-+3 | +-+ +-+ | \|64a b - 128a b + 64a +--R \|a \|- \|b + \|a |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((32a b - 32a ) |---------------------- + 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (16a b - 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R +-------------+ | | 3 2 4 5 +--R 4+-+3 | +-+ +-+ | \|64a b - 128a b + 64a +--R \|a \|- \|b + \|a |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((32a b - 32a ) |---------------------- - 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (- 16a b + 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R - +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R +-------------+ | | 3 2 4 5 +--R 4+-+3 | +-+ +-+ | \|64a b - 128a b + 64a +--R \|a \|- \|b + \|a |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((- 32a b + 32a ) |---------------------- + 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (- 16a b + 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R +-------------+ | | 3 2 4 5 +--R 4+-+3 | +-+ +-+ | \|64a b - 128a b + 64a +--R \|a \|- \|b + \|a |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 3 4 | b +--R ((- 32a b + 32a ) |---------------------- - 4a b) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- - 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R +----------------------+ +--R 2 3 | b 2 +--R (16a b - 16a ) |---------------------- + b sinh(x) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b +--R + +--R +-----------+ 4+-+ +--R | +-+ +-+ tanh(x)\|a +--R - \|\|b + \|a atanh(----------------) +--R +-------------+ +--R | +-+ +-+ +--R \|- \|b + \|a +--R + +--R +-------------+ 4+-+ +--R | +-+ +-+ tanh(x)\|a +--R - \|- \|b + \|a atanh(--------------) +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R / +--R +-------------+ +-----------+ +--R 4+-+3 | +-+ +-+ | +-+ +-+ +--R 2\|a \|- \|b + \|a \|\|b + \|a +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0213:= D(m0213,x) +--R +--R +--R (43) +--R 8 7 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) - 4b)sinh(x) +--R + +--R 3 5 +--R (- 56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70b cosh(x) - 60b cosh(x) - 6b)sinh(x) +--R + +--R 5 3 3 +--R (- 56b cosh(x) - 80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28b cosh(x) - 60b cosh(x) - 36b cosh(x) - 4b)sinh(x) +--R + +--R 7 5 3 +--R (- 8b cosh(x) - 24b cosh(x) - 24b cosh(x) - 8b cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - b cosh(x) - 4b cosh(x) - 6b cosh(x) - 4b cosh(x) - b +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) + 4b)sinh(x) +--R + +--R 3 5 +--R (56b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70b cosh(x) + 60b cosh(x) + 6b - 16a)sinh(x) +--R + +--R 5 3 3 +--R (56b cosh(x) + 80b cosh(x) + (24b - 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28b cosh(x) + 60b cosh(x) + (36b - 96a)cosh(x) + 4b)sinh(x) +--R + +--R 7 5 3 +--R (8b cosh(x) + 24b cosh(x) + (24b - 64a)cosh(x) + 8b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) + 4b cosh(x) + (6b - 16a)cosh(x) + 4b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R (16b - 16a)sinh(x) + (64b - 64a)cosh(x)sinh(x) +--R + +--R 2 2 3 +--R (96b - 96a)cosh(x) sinh(x) + (64b - 64a)cosh(x) sinh(x) +--R + +--R 4 +--R (16b - 16a)cosh(x) +--R * +--R 4+-+2 +--R \|a +--R + +--R 8 7 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) + 4b)sinh(x) +--R + +--R 3 5 +--R (56b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70b cosh(x) + 60b cosh(x) + 6b + 16a)sinh(x) +--R + +--R 5 3 3 +--R (56b cosh(x) + 80b cosh(x) + (24b + 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28b cosh(x) + 60b cosh(x) + (36b + 96a)cosh(x) + 4b)sinh(x) +--R + +--R 7 5 3 +--R (8b cosh(x) + 24b cosh(x) + (24b + 64a)cosh(x) + 8b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) + 4b cosh(x) + (6b + 16a)cosh(x) + 4b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) - 4b)sinh(x) +--R + +--R 3 5 +--R (- 56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70b cosh(x) - 60b cosh(x) - 6b + 16a)sinh(x) +--R + +--R 5 3 3 +--R (- 56b cosh(x) - 80b cosh(x) + (- 24b + 64a)cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28b cosh(x) - 60b cosh(x) + (- 36b + 96a)cosh(x) - 4b)sinh(x) +--R + +--R 7 5 3 +--R (- 8b cosh(x) - 24b cosh(x) + (- 24b + 64a)cosh(x) - 8b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - b cosh(x) - 4b cosh(x) + (- 6b + 16a)cosh(x) - 4b cosh(x) - b +--R * +--R +-+ +--R \|a +--R / +--R 8 7 +--R a b sinh(x) + 8a b cosh(x)sinh(x) +--R + +--R 2 6 +--R (28a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 5 +--R (56a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 4 2 2 4 +--R (70a b cosh(x) + 60a b cosh(x) + 6a b - 16a )sinh(x) +--R + +--R 5 3 2 3 +--R (56a b cosh(x) + 80a b cosh(x) + (24a b - 64a )cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R 28a b cosh(x) + 60a b cosh(x) + (36a b - 96a )cosh(x) +--R + +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 2 3 +--R 8a b cosh(x) + 24a b cosh(x) + (24a b - 64a )cosh(x) +--R + +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 2 4 +--R a b cosh(x) + 4a b cosh(x) + (6a b - 16a )cosh(x) +--R + +--R 2 +--R 4a b cosh(x) + a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 8 2 7 +--R (- b + a b)sinh(x) + (- 8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((- 28b + 28a b)cosh(x) - 4b + 4a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((- 56b + 56a b)cosh(x) + (- 24b + 24a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 70b + 70a b)cosh(x) + (- 60b + 60a b)cosh(x) - 6b + 22a b +--R + +--R 2 +--R - 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 56b + 56a b)cosh(x) + (- 80b + 80a b)cosh(x) +--R + +--R 2 2 +--R (- 24b + 88a b - 64a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 28b + 28a b)cosh(x) + (- 60b + 60a b)cosh(x) +--R + +--R 2 2 2 2 +--R (- 36b + 132a b - 96a )cosh(x) - 4b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (- 8b + 8a b)cosh(x) + (- 24b + 24a b)cosh(x) +--R + +--R 2 2 3 2 +--R (- 24b + 88a b - 64a )cosh(x) + (- 8b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 +--R (- b + a b)cosh(x) + (- 4b + 4a b)cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 6b + 22a b - 16a )cosh(x) + (- 4b + 4a b)cosh(x) - b + a b +--R * +--R 4+-+2 +--R \|a +--R + +--R 8 7 +--R - 2a b sinh(x) - 16a b cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 56a b cosh(x) - 8a b)sinh(x) +--R + +--R 3 5 +--R (- 112a b cosh(x) - 48a b cosh(x))sinh(x) +--R + +--R 4 2 2 4 +--R (- 140a b cosh(x) - 120a b cosh(x) - 12a b + 32a )sinh(x) +--R + +--R 5 3 2 +--R (- 112a b cosh(x) - 160a b cosh(x) + (- 48a b + 128a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 2 +--R - 56a b cosh(x) - 120a b cosh(x) + (- 72a b + 192a )cosh(x) +--R + +--R - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 2 3 +--R - 16a b cosh(x) - 48a b cosh(x) + (- 48a b + 128a )cosh(x) +--R + +--R - 16a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 2 4 +--R - 2a b cosh(x) - 8a b cosh(x) + (- 12a b + 32a )cosh(x) +--R + +--R 2 +--R - 8a b cosh(x) - 2a b +--R * +--R 2 +-+ +--R tanh(x) \|a +--R Type: Expression(Integer) +--E 70 + +--S 71 of 500 +t0214:= 1/(a-b*cosh(x)^5) +--R +--R +--R 1 +--R (44) - -------------- +--R 5 +--R b cosh(x) - a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0214:= 2/5*atanh((a^(1/5)+b^(1/5))*tanh(1/2*x)/(a^(2/5)-b^(2/5))^(1/2))/_ + a^(4/5)/(a^(2/5)-b^(2/5))^(1/2)+2/5*atanh((a^(1/5)-_ + (-1)^(3/5)*b^(1/5))*tanh(1/2*x)/(a^(2/5)+_ + (-1)^(1/5)*b^(2/5))^(1/2))/a^(4/5)/(a^(2/5)+_ + (-1)^(1/5)*b^(2/5))^(1/2)+2/5*atanh((a^(1/5)-_ + (-1)^(1/5)*b^(1/5))*tanh(1/2*x)/(a^(2/5)-_ + (-1)^(2/5)*b^(2/5))^(1/2))/a^(4/5)/(a^(2/5)-_ + (-1)^(2/5)*b^(2/5))^(1/2)+2/5*atanh((a^(1/5)+_ + (-1)^(4/5)*b^(1/5))*tanh(1/2*x)/(a^(2/5)+_ + (-1)^(3/5)*b^(2/5))^(1/2))/a^(4/5)/(a^(2/5)+_ + (-1)^(3/5)*b^(2/5))^(1/2)+2/5*atanh((a^(1/5)+_ + (-1)^(2/5)*b^(1/5))*tanh(1/2*x)/(a^(2/5)-_ + (-1)^(4/5)*b^(2/5))^(1/2))/a^(4/5)/(a^(2/5)-(-1)^(4/5)*b^(2/5))^(1/2) +--R +--R +--R (45) +--R +----------------------+ +---------------+ +-------------------+ +--R | 5+---+2 5+-+2 5+-+2 | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+2 x 5+-+ x 5+-+ +--R +--------------------+ \|- 1 tanh(-)\|b + tanh(-)\|a +--R |5+---+3 5+-+2 5+-+2 2 2 +--R \|\|- 1 \|b + \|a atanh(--------------------------------) +--R +----------------------+ +--R | 5+---+4 5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +---------------+ +-------------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+ x 5+-+ x 5+-+ +--R +--------------------+ \|- 1 tanh(-)\|b - tanh(-)\|a +--R |5+---+3 5+-+2 5+-+2 2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------------) +--R +----------------------+ +--R | 5+---+2 5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +----------------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +-------------------+ +--------------------+ +--R |5+---+5+-+2 5+-+2 |5+---+3 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 5+-+ x 5+-+ +--R tanh(-)\|b + tanh(-)\|a +--R 2 2 +--R atanh(-------------------------) +--R +---------------+ +--R | 5+-+2 5+-+2 +--R \|- \|b + \|a +--R + +--R - +--R +----------------------+ +----------------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +---------------+ +--------------------+ +--R | 5+-+2 5+-+2 |5+---+3 5+-+2 5+-+2 +--R \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+3 x 5+-+ x 5+-+ +--R \|- 1 tanh(-)\|b - tanh(-)\|a +--R 2 2 +--R atanh(--------------------------------) +--R +-------------------+ +--R |5+---+5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R + +--R +----------------------+ +----------------------+ +---------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 | 5+-+2 5+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 5+---+4 x 5+-+ x 5+-+ +--R +-------------------+ \|- 1 tanh(-)\|b + tanh(-)\|a +--R |5+---+5+-+2 5+-+2 2 2 +--R \|\|- 1 \|b + \|a atanh(--------------------------------) +--R +--------------------+ +--R |5+---+3 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +----------------------+ +--R 5+-+4 | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 +--R 5\|a \|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +---------------+ +-------------------+ +--------------------+ +--R | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 |5+---+3 5+-+2 5+-+2 +--R \|- \|b + \|a \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0214:= integrate(t0214,x) +--R +--R +--R (46) +--R ROOT +--R 2 2 +--R (10b - 10a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 375a b + 750a b - 375a )%%BW2 +--R + +--R 2 4 4 2 6 +--I (- 250a b + 500a b - 250a )%%BW1 +--R + +--R 2 4 4 2 6 2 2 4 +--I (- 250a b + 500a b - 250a )%%BW0 - 50a b + 50a +--R * +--I %%BW2 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b + 750a b - 375a )%%BW1 +--R + +--R 2 4 4 2 6 2 2 4 +--I ((- 250a b + 500a b - 250a )%%BW0 - 50a b + 50a ) +--R * +--I %%BW1 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b + 750a b - 375a )%%BW0 +--R + +--R 2 2 4 2 2 +--I (- 50a b + 50a )%%BW0 + 8b - 3a +--R / +--R 2 4 4 2 6 +--R 125a b - 250a b + 125a +--R + +--R 2 2 2 2 +--I (- 10b + 10a )%%BW2 + (- 10b + 10a )%%BW1 +--R + +--R 2 2 +--I (- 10b + 10a )%%BW0 - 2 +--R / +--R 2 2 +--R 5b - 5a +--R * +--R log +--R 8 2 10 6 2 +--I (11718750a b - 11718750a )%%BW0 - 234375a b +--R + +--R 8 +--R 234375a +--R * +--I %%BW1 +--R + +--R 6 2 8 4 2 6 +--I (- 234375a b + 234375a )%%BW0 + 3125a b - 3125a +--R * +--I %%BW2 +--R + +--R 6 2 8 4 2 6 +--I ((- 234375a b + 234375a )%%BW0 + 3125a b - 3125a )%%BW1 +--R + +--R 4 2 6 +--I (3125a b - 3125a )%%BW0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 375a b + 750a b - 375a )%%BW2 +--R + +--R 2 4 4 2 6 +--I (- 250a b + 500a b - 250a )%%BW1 +--R + +--R 2 4 4 2 6 2 2 4 +--I (- 250a b + 500a b - 250a )%%BW0 - 50a b + 50a +--R * +--I %%BW2 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b + 750a b - 375a )%%BW1 +--R + +--R 2 4 4 2 6 2 2 +--I (- 250a b + 500a b - 250a )%%BW0 - 50a b +--R + +--R 4 +--R 50a +--R * +--I %%BW1 +--R + +--R 2 4 4 2 6 2 +--I (- 375a b + 750a b - 375a )%%BW0 +--R + +--R 2 2 4 2 2 +--I (- 50a b + 50a )%%BW0 + 8b - 3a +--R / +--R 2 4 4 2 6 +--R 125a b - 250a b + 125a +--R 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4 +--I (11718750a b - 11718750a )%%BW0 +--R + +--R 6 2 8 3 +--I (234375a b + 2109375a )%%BW0 +--R + +--R 4 2 6 2 4 2 +--I (3125a b - 143750a )%%BW0 + 4375a %%BW0 - 50a +--R * +--R +------+ +--I \|4%%BW0 +--R + +--R 7 2 9 4 5 2 7 3 +--I (2343750a b - 2343750a )%%BW0 + (31250a b + 437500a )%%BW0 +--R + +--R 5 2 3 +--I - 31250a %%BW0 + 1000a %%BW0 + 2b sinh(x) + 2b cosh(x) - 12a +--R + +--R +----------------------+ +----------------------+ +--R 5+-+4 | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 +--R 5\|a \|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +---------------+ +-------------------+ +--------------------+ +--R | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 |5+---+3 5+-+2 5+-+2 +--R \|- \|b + \|a \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%BW0 +--R * +--R log +--R 8 2 10 4 +--I (- 11718750a b + 11718750a )%%BW0 +--R + +--R 6 2 8 3 +--I (- 234375a b - 2109375a )%%BW0 +--R + +--R 4 2 6 2 4 2 +--I (- 3125a b + 143750a )%%BW0 - 4375a %%BW0 + 50a +--R * +--R +------+ +--I \|4%%BW0 +--R + +--R 7 2 9 4 5 2 7 3 +--I (2343750a b - 2343750a )%%BW0 + (31250a b + 437500a )%%BW0 +--R + +--R 5 2 3 +--I - 31250a %%BW0 + 1000a %%BW0 + 2b sinh(x) + 2b cosh(x) - 12a +--R + +--R - +--R +----------------------+ +---------------+ +-------------------+ +--R | 5+---+2 5+-+2 5+-+2 | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+2 x 5+-+ x 5+-+ +--R +--------------------+ \|- 1 tanh(-)\|b + tanh(-)\|a +--R |5+---+3 5+-+2 5+-+2 2 2 +--R \|\|- 1 \|b + \|a atanh(--------------------------------) +--R +----------------------+ +--R | 5+---+4 5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+ x 5+-+ x 5+-+ +--R +--------------------+ \|- 1 tanh(-)\|b - tanh(-)\|a +--R |5+---+3 5+-+2 5+-+2 2 2 +--R \|\|- 1 \|b + \|a atanh(-------------------------------) +--R +----------------------+ +--R | 5+---+2 5+-+2 5+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +----------------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +-------------------+ +--------------------+ +--R |5+---+5+-+2 5+-+2 |5+---+3 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 5+-+ x 5+-+ +--R tanh(-)\|b + tanh(-)\|a +--R 2 2 +--R atanh(-------------------------) +--R +---------------+ +--R | 5+-+2 5+-+2 +--R \|- \|b + \|a +--R + +--R +----------------------+ +----------------------+ +---------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 | 5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 5+---+3 x 5+-+ x 5+-+ +--R +--------------------+ \|- 1 tanh(-)\|b - tanh(-)\|a +--R |5+---+3 5+-+2 5+-+2 2 2 +--R \|\|- 1 \|b + \|a atanh(--------------------------------) +--R +-------------------+ +--R |5+---+5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +----------------------+ +--R | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +---------------+ +-------------------+ +--R | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 +--R \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 5+---+4 x 5+-+ x 5+-+ +--R \|- 1 tanh(-)\|b + tanh(-)\|a +--R 2 2 +--R atanh(--------------------------------) +--R +--------------------+ +--R |5+---+3 5+-+2 5+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +----------------------+ +--R 5+-+4 | 5+---+4 5+-+2 5+-+2 | 5+---+2 5+-+2 5+-+2 +--R 10\|a \|- \|- 1 \|b + \|a \|- \|- 1 \|b + \|a +--R * +--R +---------------+ +-------------------+ +--------------------+ +--R | 5+-+2 5+-+2 |5+---+5+-+2 5+-+2 |5+---+3 5+-+2 5+-+2 +--R \|- \|b + \|a \|\|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +--d0214:= D(m0214,x) +--E 75 + +--S 76 of 500 +t0215:= 1/(a-b*cosh(x)^6) +--R +--R +--R 1 +--R (48) - -------------- +--R 6 +--R b cosh(x) - a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0215:= 1/3*atanh(a^(1/6)*tanh(x)/(a^(1/3)-b^(1/3))^(1/2))/a^(5/6)/_ + (a^(1/3)-b^(1/3))^(1/2)+1/3*atanh(a^(1/6)*tanh(x)/(a^(1/3)+_ + (-1)^(1/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+_ + (-1)^(1/3)*b^(1/3))^(1/2)+1/3*atanh(a^(1/6)*tanh(x)/(a^(1/3)-_ + (-1)^(2/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2) +--R +--R +--R (49) +--R +-------------+ +-----------------+ 6+-+ +--R | 3+-+ 3+-+ |3+---+3+-+ 3+-+ tanh(x)\|a +--R \|- \|b + \|a \|\|- 1 \|b + \|a atanh(-----------------------) +--R +--------------------+ +--R | 3+---+2 3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +--------------------+ +-----------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ |3+---+3+-+ 3+-+ tanh(x)\|a +--R \|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atanh(----------------) +--R +-------------+ +--R | 3+-+ 3+-+ +--R \|- \|b + \|a +--R + +--R +--------------------+ +-------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ tanh(x)\|a +--R \|- \|- 1 \|b + \|a \|- \|b + \|a atanh(--------------------) +--R +-----------------+ +--R |3+---+3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0215:= integrate(t0215,x) +--R +--R +--R (50) +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b - 3888a )%%BX0 - 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b - 3888a )%%BX0 + (108a b + 216a )%%BX0 - 6a b - 3a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b + 1296a )%%BX0 + 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b + 1296a )%%BX0 + (- 36a b - 72a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + a +--R + +--R - +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b - 3888a )%%BX0 - 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b + 3888a )%%BX0 + (- 108a b - 216a )%%BX0 + 6a b +--R + +--R 2 +--R 3a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R 4 5 2 3 +--I ((1296a b - 1296a )%%BX0 - 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b + 1296a )%%BX0 + (- 36a b - 72a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + a +--R + +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b + 3888a )%%BX0 + 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b - 3888a )%%BX0 + (108a b + 216a )%%BX0 - 6a b - 3a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R 4 5 2 3 +--I ((1296a b - 1296a )%%BX0 - 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b + 1296a )%%BX0 + (- 36a b - 72a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + a +--R + +--R - +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b + 3888a )%%BX0 + 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b + 3888a )%%BX0 + (- 108a b - 216a )%%BX0 + 6a b +--R + +--R 2 +--R 3a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b + 1296a )%%BX0 + 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b + 1296a )%%BX0 + (- 36a b - 72a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + a +--R + +--R - +--R +------+ +--I \|4%%BX0 +--R * +--R log +--R 5 6 2 3 4 +--I (7776a b - 7776a )%%BX0 + (216a b + 432a )%%BX0 + 6a b +--R + +--R 2 +--R - 6a +--R * +--R +------+ +--I \|4%%BX0 +--R + +--R 4 5 2 2 3 2 +--I (2592a b - 2592a )%%BX0 + (72a b + 144a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R +------+ +--I \|4%%BX0 +--R * +--R log +--R 5 6 2 3 4 +--I (- 7776a b + 7776a )%%BX0 + (- 216a b - 432a )%%BX0 - 6a b +--R + +--R 2 +--R 6a +--R * +--R +------+ +--I \|4%%BX0 +--R + +--R 4 5 2 2 3 2 +--I (2592a b - 2592a )%%BX0 + (72a b + 144a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0215:= a0215-r0215 +--R +--R +--R (51) +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b - 3888a )%%BX0 - 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b - 3888a )%%BX0 + (108a b + 216a )%%BX0 - 6a b - 3a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b + 1296a )%%BX0 + 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b + 1296a )%%BX0 + (- 36a b - 72a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + a +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 5 6 3 4 +--I ((3888a b - 3888a )%%BX0 - 108a b + 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b + 3888a )%%BX0 + (- 108a b - 216a )%%BX0 + 6a b +--R + +--R 2 +--R 3a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R 4 5 2 3 +--I ((1296a b - 1296a )%%BX0 - 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b + 1296a )%%BX0 + (- 36a b - 72a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + a +--R + +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b + 3888a )%%BX0 + 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 5 6 2 3 4 2 +--I (3888a b - 3888a )%%BX0 + (108a b + 216a )%%BX0 - 6a b - 3a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R 4 5 2 3 +--I ((1296a b - 1296a )%%BX0 - 36a b + 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b + 1296a )%%BX0 + (- 36a b - 72a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + a +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 5 6 3 4 +--I ((- 3888a b + 3888a )%%BX0 + 108a b - 108a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 5 6 2 3 4 +--I (- 3888a b + 3888a )%%BX0 + (- 108a b - 216a )%%BX0 + 6a b +--R + +--R 2 +--R 3a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%BX0 - 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R 4 5 2 3 +--I ((- 1296a b + 1296a )%%BX0 + 36a b - 36a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%BX0 +--R + +--R 2 3 +--I (- 72a b + 72a )%%BX0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 2 3 2 +--I (- 1296a b + 1296a )%%BX0 + (- 36a b - 72a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + a +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%BX0 +--R * +--R log +--R 5 6 2 3 4 +--I (7776a b - 7776a )%%BX0 + (216a b + 432a )%%BX0 + 6a b +--R + +--R 2 +--R - 6a +--R * +--R +------+ +--I \|4%%BX0 +--R + +--R 4 5 2 2 3 2 +--I (2592a b - 2592a )%%BX0 + (72a b + 144a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%BX0 +--R * +--R log +--R 5 6 2 3 4 +--I (- 7776a b + 7776a )%%BX0 + (- 216a b - 432a )%%BX0 - 6a b +--R + +--R 2 +--R 6a +--R * +--R +------+ +--I \|4%%BX0 +--R + +--R 4 5 2 2 3 2 +--I (2592a b - 2592a )%%BX0 + (72a b + 144a )%%BX0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b - 2a +--R + +--R +-------------+ +-----------------+ 6+-+ +--R | 3+-+ 3+-+ |3+---+3+-+ 3+-+ tanh(x)\|a +--R - 2\|- \|b + \|a \|\|- 1 \|b + \|a atanh(-----------------------) +--R +--------------------+ +--R | 3+---+2 3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +--------------------+ +-----------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ |3+---+3+-+ 3+-+ tanh(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atanh(----------------) +--R +-------------+ +--R | 3+-+ 3+-+ +--R \|- \|b + \|a +--R + +--R +--------------------+ +-------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ tanh(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|- \|b + \|a atanh(--------------------) +--R +-----------------+ +--R |3+---+3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 6\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +--d0215:= D(m0215,x) +--E 80 + +--S 81 of 500 +t0216:= 1/(a-b*cosh(x)^8) +--R +--R +--R 1 +--R (52) - -------------- +--R 8 +--R b cosh(x) - a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0216:= 1/4*atanh(a^(1/8)*tanh(x)/(a^(1/4)-b^(1/4))^(1/2))/a^(7/8)/_ + (a^(1/4)-b^(1/4))^(1/2)+1/4*atanh(a^(1/8)*tanh(x)/_ + (a^(1/4)-%i*b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)-%i*b^(1/4))^(1/2)+_ + 1/4*atanh(a^(1/8)*tanh(x)/(a^(1/4)+%i*b^(1/4))^(1/2))/_ + a^(7/8)/(a^(1/4)+%i*b^(1/4))^(1/2)+1/4*atanh(a^(1/8)*_ + tanh(x)/(a^(1/4)+b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)+b^(1/4))^(1/2) +--R +--R +--R (53) +--R +---------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tanh(x)\|a +--R \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a atanh(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|- \|b + \|a +--R + +--R +-------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tanh(x)\|a +--R \|- \|b + \|a \|%i\|b + \|a \|\|b + \|a atanh(------------------) +--R +---------------+ +--R | 4+-+ 4+-+ +--R \|- %i\|b + \|a +--R + +--R +-------------+ +---------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tanh(x)\|a +--R \|- \|b + \|a \|- %i\|b + \|a \|\|b + \|a atanh(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|%i\|b + \|a +--R + +--R +-------------+ +---------------+ +-------------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ tanh(x)\|a +--R \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a atanh(--------------) +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R / +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 4\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R Type: Expression(Complex(Integer)) +--E 82 + +--S 83 of 500 +a0216:= integrate(t0216,x) +--R +--R +--R (54) +--R - +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b - 1048576a )%%BY0 - 16384a b + 16384a ) +--R * +--I %%BY1 +--R + +--R 5 6 3 4 +--I (- 16384a b + 16384a )%%BY0 + 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b - 1048576a )%%BY0 - 16384a b + 16384a )%%BY1 +--R + +--R 7 8 2 6 3 +--I (1048576a b - 1048576a )%%BY0 + 65536a %%BY0 - 256a b +--R + +--R 4 +--R - 768a +--R * +--I %%BY1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b + 16384a )%%BY0 + (- 256a b - 768a )%%BY0 +--R + +--R 2 +--R 8a b + 8a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%BY0 +--R + +--R 2 3 +--R - 64a b + 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 4 5 2 3 +--I (- 4096a b + 4096a )%%BY0 + 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b - 262144a )%%BY0 + 16384a %%BY0 - 64a b - 192a ) +--R * +--I %%BY1 +--R + +--R 4 5 2 2 3 +--I (- 4096a b + 4096a )%%BY0 + (- 64a b - 192a )%%BY0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%BY0 - 64a b + 64a ) +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b - 1048576a )%%BY0 - 16384a b + 16384a )%%BY1 +--R + +--R 5 6 3 4 +--I (- 16384a b + 16384a )%%BY0 + 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((- 1048576a b + 1048576a )%%BY0 + 16384a b - 16384a )%%BY1 +--R + +--R 7 8 2 6 3 +--I (- 1048576a b + 1048576a )%%BY0 - 65536a %%BY0 + 256a b +--R + +--R 4 +--R 768a +--R * +--I %%BY1 +--R + +--R 5 6 2 3 4 2 +--I (16384a b - 16384a )%%BY0 + (256a b + 768a )%%BY0 - 8a b - 8a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b + 262144a )%%BY0 + 4096a b - 4096a )%%BY1 +--R + +--R 4 5 2 3 +--I (4096a b - 4096a )%%BY0 - 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%BY0 - 64a b + 64a ) +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b - 262144a )%%BY0 + 16384a %%BY0 - 64a b - 192a )%%BY1 +--R + +--R 4 5 2 2 3 2 +--I (- 4096a b + 4096a )%%BY0 + (- 64a b - 192a )%%BY0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R - +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 +--I (- 1048576a b + 1048576a )%%BY0 + 16384a b +--R + +--R 6 +--R - 16384a +--R * +--I %%BY1 +--R + +--R 5 6 3 4 +--I (16384a b - 16384a )%%BY0 - 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b - 1048576a )%%BY0 - 16384a b + 16384a )%%BY1 +--R + +--R 7 8 2 6 3 +--I (1048576a b - 1048576a )%%BY0 + 65536a %%BY0 - 256a b +--R + +--R 4 +--R - 768a +--R * +--I %%BY1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b + 16384a )%%BY0 + (- 256a b - 768a )%%BY0 +--R + +--R 2 +--R 8a b + 8a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%BY0 +--R + +--R 2 3 +--R - 64a b + 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b + 262144a )%%BY0 + 4096a b - 4096a )%%BY1 +--R + +--R 4 5 2 3 +--I (4096a b - 4096a )%%BY0 - 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b - 262144a )%%BY0 + 16384a %%BY0 - 64a b - 192a ) +--R * +--I %%BY1 +--R + +--R 4 5 2 2 3 +--I (- 4096a b + 4096a )%%BY0 + (- 64a b - 192a )%%BY0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%BY0 - 64a b + 64a ) +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 6 +--I ((- 1048576a b + 1048576a )%%BY0 + 16384a b - 16384a ) +--R * +--I %%BY1 +--R + +--R 5 6 3 4 +--I (16384a b - 16384a )%%BY0 - 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((- 1048576a b + 1048576a )%%BY0 + 16384a b - 16384a )%%BY1 +--R + +--R 7 8 2 6 3 +--I (- 1048576a b + 1048576a )%%BY0 - 65536a %%BY0 + 256a b +--R + +--R 4 +--R 768a +--R * +--I %%BY1 +--R + +--R 5 6 2 3 4 2 +--I (16384a b - 16384a )%%BY0 + (256a b + 768a )%%BY0 - 8a b - 8a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 4 5 2 3 +--I (- 4096a b + 4096a )%%BY0 + 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%BY0 - 64a b + 64a ) +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b - 262144a )%%BY0 + 16384a %%BY0 - 64a b - 192a )%%BY1 +--R + +--R 4 5 2 2 3 2 +--I (- 4096a b + 4096a )%%BY0 + (- 64a b - 192a )%%BY0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R +------+ +--I \|4%%BY1 +--R * +--R log +--R 7 8 5 6 2 +--I ((2097152a b - 2097152a )%%BY0 - 32768a b + 32768a )%%BY1 +--R + +--R 7 8 2 6 3 +--I (2097152a b - 2097152a )%%BY0 + 131072a %%BY0 - 512a b +--R + +--R 4 +--R - 1536a +--R * +--I %%BY1 +--R + +--R 7 8 3 6 2 4 +--I (2097152a b - 2097152a )%%BY0 + 131072a %%BY0 - 3072a %%BY0 +--R + +--R 2 +--R - 8a b + 24a +--R * +--R +------+ +--I \|4%%BY1 +--R + +--R 6 7 4 5 2 +--I ((- 524288a b + 524288a )%%BY0 + 8192a b - 8192a )%%BY1 +--R + +--R 6 7 2 5 2 3 +--I ((- 524288a b + 524288a )%%BY0 - 32768a %%BY0 + 128a b + 384a ) +--R * +--I %%BY1 +--R + +--R 6 7 3 5 2 3 +--I (- 524288a b + 524288a )%%BY0 - 32768a %%BY0 + 768a %%BY0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b - 6a +--R + +--R - +--R +------+ +--I \|4%%BY1 +--R * +--R log +--R 7 8 5 6 +--I ((- 2097152a b + 2097152a )%%BY0 + 32768a b - 32768a ) +--R * +--R 2 +--I %%BY1 +--R + +--R 7 8 2 6 +--I (- 2097152a b + 2097152a )%%BY0 - 131072a %%BY0 +--R + +--R 3 4 +--R 512a b + 1536a +--R * +--I %%BY1 +--R + +--R 7 8 3 6 2 +--I (- 2097152a b + 2097152a )%%BY0 - 131072a %%BY0 +--R + +--R 4 2 +--I 3072a %%BY0 + 8a b - 24a +--R * +--R +------+ +--I \|4%%BY1 +--R + +--R 6 7 4 5 2 +--I ((- 524288a b + 524288a )%%BY0 + 8192a b - 8192a )%%BY1 +--R + +--R 6 7 2 5 2 +--I (- 524288a b + 524288a )%%BY0 - 32768a %%BY0 + 128a b +--R + +--R 3 +--R 384a +--R * +--I %%BY1 +--R + +--R 6 7 3 5 2 3 +--I (- 524288a b + 524288a )%%BY0 - 32768a %%BY0 + 768a %%BY0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b - 6a +--R + +--R - +--R +------+ +--I \|4%%BY0 +--R * +--R log +--R 7 8 3 5 6 2 +--I (2097152a b - 2097152a )%%BY0 + (32768a b + 98304a )%%BY0 +--R + +--R 3 4 2 +--I (512a b - 1536a )%%BY0 + 8a b + 8a +--R * +--R +------+ +--I \|4%%BY0 +--R + +--R 6 7 3 4 5 2 +--I (524288a b - 524288a )%%BY0 + (8192a b + 24576a )%%BY0 +--R + +--R 2 3 2 +--I (128a b - 384a )%%BY0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) + b + 2a +--R + +--R +------+ +--I \|4%%BY0 +--R * +--R log +--R 7 8 3 +--I (- 2097152a b + 2097152a )%%BY0 +--R + +--R 5 6 2 3 4 +--I (- 32768a b - 98304a )%%BY0 + (- 512a b + 1536a )%%BY0 - 8a b +--R + +--R 2 +--R - 8a +--R * +--R +------+ +--I \|4%%BY0 +--R + +--R 6 7 3 4 5 2 +--I (524288a b - 524288a )%%BY0 + (8192a b + 24576a )%%BY0 +--R + +--R 2 3 2 +--I (128a b - 384a )%%BY0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) + b + 2a +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0216:= a0216-r0216 +--R +--R +--R (55) +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b - 1048576a )%%BY0 - 16384a b + 16384a ) +--R * +--I %%BY1 +--R + +--R 5 6 3 4 +--I (- 16384a b + 16384a )%%BY0 + 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b - 1048576a )%%BY0 - 16384a b + 16384a )%%BY1 +--R + +--R 7 8 2 6 3 +--I (1048576a b - 1048576a )%%BY0 + 65536a %%BY0 - 256a b +--R + +--R 4 +--R - 768a +--R * +--I %%BY1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b + 16384a )%%BY0 + (- 256a b - 768a )%%BY0 +--R + +--R 2 +--R 8a b + 8a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%BY0 +--R + +--R 2 3 +--R - 64a b + 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 4 5 2 3 +--I (- 4096a b + 4096a )%%BY0 + 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b - 262144a )%%BY0 + 16384a %%BY0 - 64a b - 192a ) +--R * +--I %%BY1 +--R + +--R 4 5 2 2 3 +--I (- 4096a b + 4096a )%%BY0 + (- 64a b - 192a )%%BY0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%BY0 - 64a b + 64a ) +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 6 +--I ((1048576a b - 1048576a )%%BY0 - 16384a b + 16384a )%%BY1 +--R + +--R 5 6 3 4 +--I (- 16384a b + 16384a )%%BY0 + 256a b - 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((- 1048576a b + 1048576a )%%BY0 + 16384a b - 16384a )%%BY1 +--R + +--R 7 8 2 6 3 +--I (- 1048576a b + 1048576a )%%BY0 - 65536a %%BY0 + 256a b +--R + +--R 4 +--R 768a +--R * +--I %%BY1 +--R + +--R 5 6 2 3 4 2 +--I (16384a b - 16384a )%%BY0 + (256a b + 768a )%%BY0 - 8a b - 8a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b + 262144a )%%BY0 + 4096a b - 4096a )%%BY1 +--R + +--R 4 5 2 3 +--I (4096a b - 4096a )%%BY0 - 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%BY0 - 64a b + 64a ) +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b - 262144a )%%BY0 + 16384a %%BY0 - 64a b - 192a )%%BY1 +--R + +--R 4 5 2 2 3 2 +--I (- 4096a b + 4096a )%%BY0 + (- 64a b - 192a )%%BY0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 +--I (- 1048576a b + 1048576a )%%BY0 + 16384a b +--R + +--R 6 +--R - 16384a +--R * +--I %%BY1 +--R + +--R 5 6 3 4 +--I (16384a b - 16384a )%%BY0 - 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((1048576a b - 1048576a )%%BY0 - 16384a b + 16384a )%%BY1 +--R + +--R 7 8 2 6 3 +--I (1048576a b - 1048576a )%%BY0 + 65536a %%BY0 - 256a b +--R + +--R 4 +--R - 768a +--R * +--I %%BY1 +--R + +--R 5 6 2 3 4 +--I (- 16384a b + 16384a )%%BY0 + (- 256a b - 768a )%%BY0 +--R + +--R 2 +--R 8a b + 8a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%BY0 +--R + +--R 2 3 +--R - 64a b + 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((- 262144a b + 262144a )%%BY0 + 4096a b - 4096a )%%BY1 +--R + +--R 4 5 2 3 +--I (4096a b - 4096a )%%BY0 - 64a b + 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b - 262144a )%%BY0 + 16384a %%BY0 - 64a b - 192a ) +--R * +--I %%BY1 +--R + +--R 4 5 2 2 3 +--I (- 4096a b + 4096a )%%BY0 + (- 64a b - 192a )%%BY0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%BY0 - 64a b + 64a ) +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 7 8 5 6 +--I ((- 1048576a b + 1048576a )%%BY0 + 16384a b - 16384a ) +--R * +--I %%BY1 +--R + +--R 5 6 3 4 +--I (16384a b - 16384a )%%BY0 - 256a b + 256a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 7 8 5 6 2 +--I ((- 1048576a b + 1048576a )%%BY0 + 16384a b - 16384a )%%BY1 +--R + +--R 7 8 2 6 3 +--I (- 1048576a b + 1048576a )%%BY0 - 65536a %%BY0 + 256a b +--R + +--R 4 +--R 768a +--R * +--I %%BY1 +--R + +--R 5 6 2 3 4 2 +--I (16384a b - 16384a )%%BY0 + (256a b + 768a )%%BY0 - 8a b - 8a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%BY0 - 64a b +--R + +--R 3 +--R 64a +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%BY1 + (- 16a b + 16a )%%BY0 - 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R 6 7 4 5 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 4 5 2 3 +--I (- 4096a b + 4096a )%%BY0 + 64a b - 64a +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%BY0 - 64a b + 64a ) +--R * +--I %%BY1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%BY0 +--R + +--R 2 3 +--I (- 64a b + 64a )%%BY0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 4 5 2 +--I ((262144a b - 262144a )%%BY0 - 4096a b + 4096a )%%BY1 +--R + +--R 6 7 2 5 2 3 +--I ((262144a b - 262144a )%%BY0 + 16384a %%BY0 - 64a b - 192a )%%BY1 +--R + +--R 4 5 2 2 3 2 +--I (- 4096a b + 4096a )%%BY0 + (- 64a b - 192a )%%BY0 + b sinh(x) +--R + +--R 2 +--R 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +------+ +--I \|4%%BY1 +--R * +--R log +--R 7 8 5 6 2 +--I ((2097152a b - 2097152a )%%BY0 - 32768a b + 32768a )%%BY1 +--R + +--R 7 8 2 6 3 +--I (2097152a b - 2097152a )%%BY0 + 131072a %%BY0 - 512a b +--R + +--R 4 +--R - 1536a +--R * +--I %%BY1 +--R + +--R 7 8 3 6 2 4 +--I (2097152a b - 2097152a )%%BY0 + 131072a %%BY0 - 3072a %%BY0 +--R + +--R 2 +--R - 8a b + 24a +--R * +--R +------+ +--I \|4%%BY1 +--R + +--R 6 7 4 5 2 +--I ((- 524288a b + 524288a )%%BY0 + 8192a b - 8192a )%%BY1 +--R + +--R 6 7 2 5 2 3 +--I ((- 524288a b + 524288a )%%BY0 - 32768a %%BY0 + 128a b + 384a ) +--R * +--I %%BY1 +--R + +--R 6 7 3 5 2 3 +--I (- 524288a b + 524288a )%%BY0 - 32768a %%BY0 + 768a %%BY0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b - 6a +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +------+ +--I \|\|b + \|a \|4%%BY1 +--R * +--R log +--R 7 8 5 6 +--I ((- 2097152a b + 2097152a )%%BY0 + 32768a b - 32768a ) +--R * +--R 2 +--I %%BY1 +--R + +--R 7 8 2 6 +--I (- 2097152a b + 2097152a )%%BY0 - 131072a %%BY0 +--R + +--R 3 4 +--R 512a b + 1536a +--R * +--I %%BY1 +--R + +--R 7 8 3 6 2 +--I (- 2097152a b + 2097152a )%%BY0 - 131072a %%BY0 +--R + +--R 4 2 +--I 3072a %%BY0 + 8a b - 24a +--R * +--R +------+ +--I \|4%%BY1 +--R + +--R 6 7 4 5 2 +--I ((- 524288a b + 524288a )%%BY0 + 8192a b - 8192a )%%BY1 +--R + +--R 6 7 2 5 2 +--I (- 524288a b + 524288a )%%BY0 - 32768a %%BY0 + 128a b +--R + +--R 3 +--R 384a +--R * +--I %%BY1 +--R + +--R 6 7 3 5 2 3 +--I (- 524288a b + 524288a )%%BY0 - 32768a %%BY0 + 768a %%BY0 +--R + +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b - 6a +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +------+ +--I \|\|b + \|a \|4%%BY0 +--R * +--R log +--R 7 8 3 5 6 2 +--I (2097152a b - 2097152a )%%BY0 + (32768a b + 98304a )%%BY0 +--R + +--R 3 4 2 +--I (512a b - 1536a )%%BY0 + 8a b + 8a +--R * +--R +------+ +--I \|4%%BY0 +--R + +--R 6 7 3 4 5 2 +--I (524288a b - 524288a )%%BY0 + (8192a b + 24576a )%%BY0 +--R + +--R 2 3 2 +--I (128a b - 384a )%%BY0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) + b + 2a +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +------+ +--I \|4%%BY0 +--R * +--R log +--R 7 8 3 +--I (- 2097152a b + 2097152a )%%BY0 +--R + +--R 5 6 2 3 4 +--I (- 32768a b - 98304a )%%BY0 + (- 512a b + 1536a )%%BY0 - 8a b +--R + +--R 2 +--R - 8a +--R * +--R +------+ +--I \|4%%BY0 +--R + +--R 6 7 3 4 5 2 +--I (524288a b - 524288a )%%BY0 + (8192a b + 24576a )%%BY0 +--R + +--R 2 3 2 +--I (128a b - 384a )%%BY0 + b sinh(x) + 2b cosh(x)sinh(x) +--R + +--R 2 +--R b cosh(x) + b + 2a +--R + +--R +---------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tanh(x)\|a +--R - \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a atanh(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|- \|b + \|a +--R + +--R +-------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tanh(x)\|a +--R - \|- \|b + \|a \|%i\|b + \|a \|\|b + \|a atanh(------------------) +--R +---------------+ +--R | 4+-+ 4+-+ +--R \|- %i\|b + \|a +--R + +--R +-------------+ +---------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tanh(x)\|a +--R - \|- \|b + \|a \|- %i\|b + \|a \|\|b + \|a atanh(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|%i\|b + \|a +--R + +--R +-------------+ +---------------+ +-------------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ tanh(x)\|a +--R - \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a atanh(--------------) +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R / +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 4\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R Type: Expression(Complex(Integer)) +--E 84 + +--S 85 of 500 +--d0216:= D(m0216,x) +--E 85 + +--S 86 of 500 +t0217:= 1/(1+cosh(x)^3) +--R +--R +--R 1 +--R (56) ------------ +--R 3 +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0217:= -2/3*atanh((-1)^(2/3)*(1+(-1)^(1/3))^(1/2)*tanh(1/2*x))/_ + (1+(-1)^(1/3))^(1/2)+2/3*atanh((-1)^(1/3)*(1-(-1)^(2/3))^(1/2)*_ + tanh(1/2*x))/(1-(-1)^(2/3))^(1/2)+sinh(x)/(3+3*cosh(x)) +--R +--R +--R (57) +--R +-------------+ +----------+ +--R | 3+---+2 3+---+2 x |3+---+ +--R (- 2cosh(x) - 2)\|- \|- 1 + 1 atanh(\|- 1 tanh(-)\|\|- 1 + 1 ) +--R 2 +--R + +--R +----------+ +-------------+ +--R |3+---+ 3+---+ x | 3+---+2 +--R (2cosh(x) + 2)\|\|- 1 + 1 atanh(\|- 1 tanh(-)\|- \|- 1 + 1 ) +--R 2 +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R sinh(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R (3cosh(x) + 3)\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0217:= integrate(t0217,x) +--R +--R +--R (58) +--R %pi %pi %pi +--R (cos(---)sinh(x) + cos(---)cosh(x) + cos(---)) +--R 12 12 12 +--R * +--R log +--R 4+-+2 2 +-+4+-+ %pi 4+-+2 4+-+2 +--R \|3 sinh(x) + (2\|3 \|3 sin(---) + 2\|3 cosh(x) - \|3 )sinh(x) +--R 12 +--R + +--R %pi 2 +-+4+-+ +-+4+-+ %pi 4+-+2 2 +--R 3sin(---) + (2\|3 \|3 cosh(x) - \|3 \|3 )sin(---) + \|3 cosh(x) +--R 12 12 +--R + +--R 4+-+2 %pi 2 4+-+ %pi 4+-+2 +--R - \|3 cosh(x) + 3cos(---) - 3\|3 cos(---) + \|3 +--R 12 12 +--R + +--R %pi %pi %pi +--R (- cos(---)sinh(x) - cos(---)cosh(x) - cos(---)) +--R 12 12 12 +--R * +--R log +--R 4+-+2 2 +--R \|3 sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 4+-+2 %pi 2 +--R (- 2\|3 \|3 sin(---) + 2\|3 cosh(x) - \|3 )sinh(x) + 3sin(---) +--R 12 12 +--R + +--R +-+4+-+ +-+4+-+ %pi 4+-+2 2 +--R (- 2\|3 \|3 cosh(x) + \|3 \|3 )sin(---) + \|3 cosh(x) +--R 12 +--R + +--R 4+-+2 %pi 2 4+-+ %pi 4+-+2 +--R - \|3 cosh(x) + 3cos(---) + 3\|3 cos(---) + \|3 +--R 12 12 +--R + +--R %pi %pi +--R (2sin(---)sinh(x) + (2cosh(x) + 2)sin(---)) +--R 12 12 +--R * +--R %pi 4+-+ +--R 6cos(---) + 3\|3 +--R 12 +--R atan(----------------------------------------------------------) +--R +-+4+-+ %pi +-+4+-+ +-+4+-+ +--R 2\|3 \|3 sinh(x) - 6sin(---) + 2\|3 \|3 cosh(x) - \|3 \|3 +--R 12 +--R + +--R %pi %pi +--R (2sin(---)sinh(x) + (2cosh(x) + 2)sin(---)) +--R 12 12 +--R * +--R %pi 4+-+ +--R 6cos(---) - 3\|3 +--R 12 +--R atan(----------------------------------------------------------) +--R +-+4+-+ %pi +-+4+-+ +-+4+-+ +--R 2\|3 \|3 sinh(x) + 6sin(---) + 2\|3 \|3 cosh(x) - \|3 \|3 +--R 12 +--R + +--R 4+-+ +--R - 2\|3 +--R / +--R 4+-+ 4+-+ 4+-+ +--R 3\|3 sinh(x) + 3\|3 cosh(x) + 3\|3 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0217:= a0217-r0217 +--R +--R +--R (59) +--R %pi %pi %pi 2 +--R (cos(---)cosh(x) + cos(---))sinh(x) + cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi %pi +--R 2cos(---)cosh(x) + cos(---) +--R 12 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R 4+-+2 2 +-+4+-+ %pi 4+-+2 4+-+2 +--R \|3 sinh(x) + (2\|3 \|3 sin(---) + 2\|3 cosh(x) - \|3 )sinh(x) +--R 12 +--R + +--R %pi 2 +-+4+-+ +-+4+-+ %pi 4+-+2 2 +--R 3sin(---) + (2\|3 \|3 cosh(x) - \|3 \|3 )sin(---) + \|3 cosh(x) +--R 12 12 +--R + +--R 4+-+2 %pi 2 4+-+ %pi 4+-+2 +--R - \|3 cosh(x) + 3cos(---) - 3\|3 cos(---) + \|3 +--R 12 12 +--R + +--R %pi %pi %pi 2 +--R (- cos(---)cosh(x) - cos(---))sinh(x) - cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi %pi +--R - 2cos(---)cosh(x) - cos(---) +--R 12 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R 4+-+2 2 +--R \|3 sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 4+-+2 %pi 2 +--R (- 2\|3 \|3 sin(---) + 2\|3 cosh(x) - \|3 )sinh(x) + 3sin(---) +--R 12 12 +--R + +--R +-+4+-+ +-+4+-+ %pi 4+-+2 2 +--R (- 2\|3 \|3 cosh(x) + \|3 \|3 )sin(---) + \|3 cosh(x) +--R 12 +--R + +--R 4+-+2 %pi 2 4+-+ %pi 4+-+2 +--R - \|3 cosh(x) + 3cos(---) + 3\|3 cos(---) + \|3 +--R 12 12 +--R + +--R 4+-+ 4+-+ 4+-+ 2 4+-+ 4+-+ +--R ((2\|3 cosh(x) + 2\|3 )sinh(x) + 2\|3 cosh(x) + 4\|3 cosh(x) + 2\|3 ) +--R * +--R +-------------+ +----------+ +--R | 3+---+2 3+---+2 x |3+---+ +--R \|- \|- 1 + 1 atanh(\|- 1 tanh(-)\|\|- 1 + 1 ) +--R 2 +--R + +--R 4+-+ 4+-+ 4+-+ 2 4+-+ +--R (- 2\|3 cosh(x) - 2\|3 )sinh(x) - 2\|3 cosh(x) - 4\|3 cosh(x) +--R + +--R 4+-+ +--R - 2\|3 +--R * +--R +----------+ +-------------+ +--R |3+---+ 3+---+ x | 3+---+2 +--R \|\|- 1 + 1 atanh(\|- 1 tanh(-)\|- \|- 1 + 1 ) +--R 2 +--R + +--R %pi 2 %pi +--R ((2cosh(x) + 2)sin(---)sinh(x) + (2cosh(x) + 4cosh(x) + 2)sin(---)) +--R 12 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R %pi 4+-+ +--R 6cos(---) + 3\|3 +--R 12 +--R atan(----------------------------------------------------------) +--R +-+4+-+ %pi +-+4+-+ +-+4+-+ +--R 2\|3 \|3 sinh(x) - 6sin(---) + 2\|3 \|3 cosh(x) - \|3 \|3 +--R 12 +--R + +--R %pi 2 %pi +--R ((2cosh(x) + 2)sin(---)sinh(x) + (2cosh(x) + 4cosh(x) + 2)sin(---)) +--R 12 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R %pi 4+-+ +--R 6cos(---) - 3\|3 +--R 12 +--R atan(----------------------------------------------------------) +--R +-+4+-+ %pi +-+4+-+ +-+4+-+ +--R 2\|3 \|3 sinh(x) + 6sin(---) + 2\|3 \|3 cosh(x) - \|3 \|3 +--R 12 +--R + +--R 4+-+ 2 4+-+ 4+-+ 4+-+ 4+-+ +--R (- \|3 sinh(x) + (- \|3 cosh(x) - \|3 )sinh(x) - 2\|3 cosh(x) - 2\|3 ) +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R 4+-+ 4+-+ 4+-+ 2 4+-+ 4+-+ +--R ((3\|3 cosh(x) + 3\|3 )sinh(x) + 3\|3 cosh(x) + 6\|3 cosh(x) + 3\|3 ) +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +--d0217:= D(m0217,x) +--E 90 + +--S 91 of 500 +t0218:= 1/(1+cosh(x)^4) +--R +--R +--R 1 +--R (60) ------------ +--R 4 +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0218:= 1/2*atanh(tanh(x)/(1-%i)^(1/2))/(1-%i)^(1/2)+_ + 1/2*atanh(tanh(x)/(1+%i)^(1/2))/(1+%i)^(1/2) +--R +--R +--R +------+ tanh(x) +------+ tanh(x) +--R \|1 + %i atanh(---------) + \|1 - %i atanh(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R (61) ----------------------------------------------------- +--R +------+ +------+ +--R 2\|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 92 + +--S 93 of 500 +a0218:= integrate(t0218,x) +--R +--R +--R (62) +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (2\|2 \|2 sin(---) + 6cosh(x) - 2\|2 \|2 cos(---) + 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (- 4\|2 \|2 cos(---) + 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (2\|2 \|2 cosh(x) - 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (- 2\|2 \|2 cos(---) + 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R - 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi +--R (- 2\|2 \|2 sin(---) + 6cosh(x) + 2\|2 \|2 cos(---) + 2) +--R 8 8 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+4+-+ %pi 3 +--R - 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (4\|2 \|2 cos(---) + 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (- 2\|2 \|2 cosh(x) + 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (2\|2 \|2 cos(---) + 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) + 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) - 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) + 2\|2 cos(---) + \|2 +--R 8 +--R + +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) - 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) - 2\|2 cos(---) + \|2 +--R 8 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0218:= a0218-r0218 +--R +--R +--R (63) +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (2\|2 \|2 sin(---) + 6cosh(x) - 2\|2 \|2 cos(---) + 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (- 4\|2 \|2 cos(---) + 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (2\|2 \|2 cosh(x) - 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (- 2\|2 \|2 cos(---) + 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R - 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R - +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi +--R (- 2\|2 \|2 sin(---) + 6cosh(x) + 2\|2 \|2 cos(---) + 2) +--R 8 8 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+4+-+ %pi 3 +--R - 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (4\|2 \|2 cos(---) + 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (- 2\|2 \|2 cosh(x) + 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (2\|2 \|2 cos(---) + 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R +------+ +-+ tanh(x) +------+ +-+ tanh(x) +--R - 2\|1 + %i \|2 atanh(---------) - 2\|1 - %i \|2 atanh(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R + +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) + 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) - 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) + 2\|2 cos(---) + \|2 +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) - 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) - 2\|2 cos(---) + \|2 +--R 8 +--R / +--R +------+ +------+ +-+ +--R 4\|1 - %i \|1 + %i \|2 +--R Type: Expression(Complex(Integer)) +--E 94 + +--S 95 of 500 +--d0218:= D(m0218,x) +--E 95 + +--S 96 of 500 +t0219:= 1/(1+cosh(x)^5) +--R +--R +--R 1 +--R (64) ------------ +--R 5 +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0219:= 2/5*atanh((1+(-1)^(1/5))*_ + tanh(1/2*x)/(1-(-1)^(2/5))^(1/2))/(1-(-1)^(2/5))^(1/2)+2/5*_ + atanh((1+(-1)^(3/5))*_ + tanh(1/2*x)/(1+(-1)^(1/5))^(1/2))/(1+(-1)^(1/5))^(1/2)+2/5*_ + atanh((1-(-1)^(2/5))*_ + tanh(1/2*x)/(1-(-1)^(4/5))^(1/2))/(1-(-1)^(4/5))^(1/2)+2/5*_ + atanh((1-(-1)^(4/5))*tanh(1/2*x)/(1+(-1)^(3/5))^(1/2))/_ + (1+(-1)^(3/5))^(1/2)+sinh(x)/(5+5*cosh(x)) +--R +--R +--R (65) +--R +-------------+ +----------+ +-----------+ +--R | 5+---+2 |5+---+ |5+---+3 +--R (- 2cosh(x) - 2)\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R * +--R 5+---+2 x +--R (\|- 1 - 1)tanh(-) +--R 2 +--R atanh(--------------------) +--R +-------------+ +--R | 5+---+4 +--R \|- \|- 1 + 1 +--R + +--R +-------------+ +----------+ +-----------+ +--R | 5+---+4 |5+---+ |5+---+3 +--R (2cosh(x) + 2)\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R * +--R 5+---+ x +--R (\|- 1 + 1)tanh(-) +--R 2 +--R atanh(-------------------) +--R +-------------+ +--R | 5+---+2 +--R \|- \|- 1 + 1 +--R + +--R +-------------+ +-------------+ +-----------+ +--R | 5+---+4 | 5+---+2 |5+---+3 +--R (2cosh(x) + 2)\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R 5+---+3 x +--R (\|- 1 + 1)tanh(-) +--R 2 +--R atanh(--------------------) +--R +----------+ +--R |5+---+ +--R \|\|- 1 + 1 +--R + +--R +-------------+ +-------------+ +----------+ +--R | 5+---+4 | 5+---+2 |5+---+ +--R (- 2cosh(x) - 2)\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R 5+---+4 x +--R (\|- 1 - 1)tanh(-) +--R 2 +--R atanh(--------------------) +--R +-----------+ +--R |5+---+3 +--R \|\|- 1 + 1 +--R + +--R +-------------+ +-------------+ +----------+ +-----------+ +--R | 5+---+4 | 5+---+2 |5+---+ |5+---+3 +--R sinh(x)\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +-------------+ +----------+ +-----------+ +--R | 5+---+4 | 5+---+2 |5+---+ |5+---+3 +--R (5cosh(x) + 5)\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0219:= integrate(t0219,x) +--R +--R +--R (66) +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 + 8 \| 625\|5 +--R (- sinh(x) - cosh(x) - 1) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R (500\|5 - 1500)sinh(x) + (500\|5 - 1500)cosh(x) + 250\|5 +--R + +--R - 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +-+ 2 +--R (10\|5 - 10) |--------- cos(------------------- + 8\|5 sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ 2 +--R (16\|5 cosh(x) - 4\|5 - 20)sinh(x) + 8\|5 cosh(x) +--R + +--R +-+ +-+ +--R (- 4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 + 8 \| 625\|5 +--R (sinh(x) + cosh(x) + 1) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +--R (- 500\|5 + 1500)sinh(x) + (- 500\|5 + 1500)cosh(x) +--R + +--R +-+ +--R - 250\|5 + 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (- 10\|5 + 10) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 - 8 \| 625\|5 +--R (- sinh(x) - cosh(x) - 1) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R (500\|5 + 1500)sinh(x) + (500\|5 + 1500)cosh(x) + 250\|5 +--R + +--R 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +-+ 2 +--R (10\|5 + 10) |--------- cos(------------------- + 8\|5 sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ 2 +--R (16\|5 cosh(x) - 4\|5 + 20)sinh(x) + 8\|5 cosh(x) +--R + +--R +-+ +-+ +--R (- 4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 - 8 \| 625\|5 +--R (sinh(x) + cosh(x) + 1) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +--R (- 500\|5 - 1500)sinh(x) + (- 500\|5 - 1500)cosh(x) +--R + +--R +-+ +--R - 250\|5 - 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (- 10\|5 - 10) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 - 8 \| 625\|5 +--R (- 2sinh(x) - 2cosh(x) - 2) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (125\|5 + 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R 4\|5 sinh(x) + 4\|5 cosh(x) - \|5 + 5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 - 8 \| 625\|5 +--R (2sinh(x) + 2cosh(x) + 2) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (- 125\|5 - 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R - 4\|5 sinh(x) - 4\|5 cosh(x) + \|5 - 5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 + 8 \| 625\|5 +--R (- 2sinh(x) - 2cosh(x) - 2) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (125\|5 - 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R 4\|5 sinh(x) + 4\|5 cosh(x) - \|5 - 5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 + 8 \| 625\|5 +--R (2sinh(x) + 2cosh(x) + 2) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (- 125\|5 + 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R - 4\|5 sinh(x) - 4\|5 cosh(x) + \|5 + 5 +--R + +--R - 4 +--R / +--R 10sinh(x) + 10cosh(x) + 10 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0219:= a0219-r0219 +--R +--R +--R (67) +--R +-------------+ +--R 2 | 5+---+4 +--R ((- cosh(x) - 1)sinh(x) - cosh(x) - 2cosh(x) - 1)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 + 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R (500\|5 - 1500)sinh(x) + (500\|5 - 1500)cosh(x) + 250\|5 +--R + +--R - 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +-+ 2 +--R (10\|5 - 10) |--------- cos(------------------- + 8\|5 sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ 2 +--R (16\|5 cosh(x) - 4\|5 - 20)sinh(x) + 8\|5 cosh(x) +--R + +--R +-+ +-+ +--R (- 4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((cosh(x) + 1)sinh(x) + cosh(x) + 2cosh(x) + 1)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 + 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +--R (- 500\|5 + 1500)sinh(x) + (- 500\|5 + 1500)cosh(x) +--R + +--R +-+ +--R - 250\|5 + 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (- 10\|5 + 10) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((- cosh(x) - 1)sinh(x) - cosh(x) - 2cosh(x) - 1)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 - 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R (500\|5 + 1500)sinh(x) + (500\|5 + 1500)cosh(x) + 250\|5 +--R + +--R 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +-+ 2 +--R (10\|5 + 10) |--------- cos(------------------- + 8\|5 sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ 2 +--R (16\|5 cosh(x) - 4\|5 + 20)sinh(x) + 8\|5 cosh(x) +--R + +--R +-+ +-+ +--R (- 4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((cosh(x) + 1)sinh(x) + cosh(x) + 2cosh(x) + 1)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 - 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +--R (- 500\|5 - 1500)sinh(x) + (- 500\|5 - 1500)cosh(x) +--R + +--R +-+ +--R - 250\|5 - 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (- 10\|5 - 10) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) - 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (- 4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((- 2cosh(x) - 2)sinh(x) - 2cosh(x) - 4cosh(x) - 2)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 - 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (125\|5 + 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R 4\|5 sinh(x) + 4\|5 cosh(x) - \|5 + 5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((2cosh(x) + 2)sinh(x) + 2cosh(x) + 4cosh(x) + 2)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 - 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (- 125\|5 - 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R - 4\|5 sinh(x) - 4\|5 cosh(x) + \|5 - 5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((- 2cosh(x) - 2)sinh(x) - 2cosh(x) - 4cosh(x) - 2)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 + 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (125\|5 - 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R 4\|5 sinh(x) + 4\|5 cosh(x) - \|5 - 5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((2cosh(x) + 2)sinh(x) + 2cosh(x) + 4cosh(x) + 2)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 + 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (- 125\|5 + 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R - 4\|5 sinh(x) - 4\|5 cosh(x) + \|5 + 5 +--R + +--R +-------------+ +--R 2 | 5+---+2 +--R ((4cosh(x) + 4)sinh(x) + 4cosh(x) + 8cosh(x) + 4)\|- \|- 1 + 1 +--R * +--R 5+---+2 x +--R +----------+ +-----------+ (\|- 1 - 1)tanh(-) +--R |5+---+ |5+---+3 2 +--R \|\|- 1 + 1 \|\|- 1 + 1 atanh(--------------------) +--R +-------------+ +--R | 5+---+4 +--R \|- \|- 1 + 1 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((- 4cosh(x) - 4)sinh(x) - 4cosh(x) - 8cosh(x) - 4)\|- \|- 1 + 1 +--R * +--R 5+---+ x +--R +----------+ +-----------+ (\|- 1 + 1)tanh(-) +--R |5+---+ |5+---+3 2 +--R \|\|- 1 + 1 \|\|- 1 + 1 atanh(-------------------) +--R +-------------+ +--R | 5+---+2 +--R \|- \|- 1 + 1 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((- 4cosh(x) - 4)sinh(x) - 4cosh(x) - 8cosh(x) - 4)\|- \|- 1 + 1 +--R * +--R 5+---+3 x +--R +-------------+ +-----------+ (\|- 1 + 1)tanh(-) +--R | 5+---+2 |5+---+3 2 +--R \|- \|- 1 + 1 \|\|- 1 + 1 atanh(--------------------) +--R +----------+ +--R |5+---+ +--R \|\|- 1 + 1 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((4cosh(x) + 4)sinh(x) + 4cosh(x) + 8cosh(x) + 4)\|- \|- 1 + 1 +--R * +--R 5+---+4 x +--R +-------------+ +----------+ (\|- 1 - 1)tanh(-) +--R | 5+---+2 |5+---+ 2 +--R \|- \|- 1 + 1 \|\|- 1 + 1 atanh(--------------------) +--R +-----------+ +--R |5+---+3 +--R \|\|- 1 + 1 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R (- 2sinh(x) + (- 2cosh(x) - 2)sinh(x) - 4cosh(x) - 4)\|- \|- 1 + 1 +--R * +--R +-------------+ +----------+ +-----------+ +--R | 5+---+2 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +--R 2 | 5+---+4 +--R ((10cosh(x) + 10)sinh(x) + 10cosh(x) + 20cosh(x) + 10)\|- \|- 1 + 1 +--R * +--R +-------------+ +----------+ +-----------+ +--R | 5+---+2 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +--d0219:= D(m0219,x) +--E 100 + +--S 101 of 500 +t0220:= 1/(1+cosh(x)^6) +--R +--R +--R 1 +--R (68) ------------ +--R 6 +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0220:= 1/6*atanh(1/2*2^(1/2)*tanh(x))*2^(1/2)+1/3*atanh(tanh(x)/_ + (1-(-1)^(1/3))^(1/2))/(1-(-1)^(1/3))^(1/2)+_ + 1/3*atanh(tanh(x)/(1+(-1)^(2/3))^(1/2))/(1+(-1)^(2/3))^(1/2) +--R +--R +--R (69) +--R +------------+ +-----------+ +-+ +--R +-+ | 3+---+ |3+---+2 \|2 tanh(x) +--R \|2 \|- \|- 1 + 1 \|\|- 1 + 1 atanh(-----------) +--R 2 +--R + +--R +-----------+ +--R |3+---+2 tanh(x) +--R 2\|\|- 1 + 1 atanh(---------------) +--R +------------+ +--R | 3+---+ +--R \|- \|- 1 + 1 +--R + +--R +------------+ +--R | 3+---+ tanh(x) +--R 2\|- \|- 1 + 1 atanh(--------------) +--R +-----------+ +--R |3+---+2 +--R \|\|- 1 + 1 +--R / +--R +------------+ +-----------+ +--R | 3+---+ |3+---+2 +--R 6\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0220:= integrate(t0220,x) +--R +--R +--R (70) +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R \|2 cos(----------) +--R 2 +--R * +--R log +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4sin(----------) +--R 2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (2\|3 sinh(x) + 4\|3 cosh(x)sinh(x) + 2\|3 cosh(x) - 2\|3 ) +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 2 2 \|3 +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 6)cos(----------) +--R 2 +--R + +--R 4 3 2 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) + 4cosh(x) sinh(x) +--R + +--R 4 +--R cosh(x) + 3 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R \|2 cos(----------) +--R 2 +--R * +--R log +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4sin(----------) +--R 2 +--R + +--R +-+ 2 +-+ +-+ 2 +--R - 2\|3 sinh(x) - 4\|3 cosh(x)sinh(x) - 2\|3 cosh(x) +--R + +--R +-+ +--R 2\|3 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 2 2 \|3 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 6)cos(----------) +--R 2 +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) + 3 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|2 sin(----------) +--R 2 +--R * +--R atan +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +-+ +--R sin(----------) + \|3 cos(----------) + \|3 +--R 2 2 +--R / +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 2 +--R \|3 sin(----------) - cos(----------) - sinh(x) +--R 2 2 +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|2 sin(----------) +--R 2 +--R * +--R atan +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +-+ +--R sin(----------) + \|3 cos(----------) - \|3 +--R 2 2 +--R / +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 2 +--R \|3 sin(----------) - cos(----------) + sinh(x) +--R 2 2 +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) +--R + +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R / +--R +-+ +--R 6\|2 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0220:= a0220-r0220 +--R +--R +--R (71) +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R +-+ | 3+---+ |3+---+2 \|3 +--R \|2 \|- \|- 1 + 1 \|\|- 1 + 1 cos(----------) +--R 2 +--R * +--R log +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4sin(----------) +--R 2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (2\|3 sinh(x) + 4\|3 cosh(x)sinh(x) + 2\|3 cosh(x) - 2\|3 ) +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 2 2 \|3 +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 6)cos(----------) +--R 2 +--R + +--R 4 3 2 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) + 4cosh(x) sinh(x) +--R + +--R 4 +--R cosh(x) + 3 +--R + +--R - +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R +-+ | 3+---+ |3+---+2 \|3 +--R \|2 \|- \|- 1 + 1 \|\|- 1 + 1 cos(----------) +--R 2 +--R * +--R log +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4sin(----------) +--R 2 +--R + +--R +-+ 2 +-+ +-+ 2 +--R - 2\|3 sinh(x) - 4\|3 cosh(x)sinh(x) - 2\|3 cosh(x) +--R + +--R +-+ +--R 2\|3 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R 4cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 2 2 \|3 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 6)cos(----------) +--R 2 +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) + 3 +--R + +--R - +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R +-+ | 3+---+ |3+---+2 \|3 +--R 2\|2 \|- \|- 1 + 1 \|\|- 1 + 1 sin(----------) +--R 2 +--R * +--R atan +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +-+ +--R sin(----------) + \|3 cos(----------) + \|3 +--R 2 2 +--R / +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 2 +--R \|3 sin(----------) - cos(----------) - sinh(x) +--R 2 2 +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) +--R + +--R 3 +--R atan(----) +--R +------------+ +-----------+ +-+ +--R +-+ | 3+---+ |3+---+2 \|3 +--R 2\|2 \|- \|- 1 + 1 \|\|- 1 + 1 sin(----------) +--R 2 +--R * +--R atan +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +-+ +--R sin(----------) + \|3 cos(----------) - \|3 +--R 2 2 +--R / +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 2 +--R \|3 sin(----------) - cos(----------) + sinh(x) +--R 2 2 +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) +--R + +--R +------------+ +-----------+ +--R | 3+---+ |3+---+2 +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +------------+ +-----------+ +-+ +--R | 3+---+ |3+---+2 \|2 tanh(x) +--R - 2\|- \|- 1 + 1 \|\|- 1 + 1 atanh(-----------) +--R 2 +--R + +--R +-----------+ +--R +-+ |3+---+2 tanh(x) +--R - 2\|2 \|\|- 1 + 1 atanh(---------------) +--R +------------+ +--R | 3+---+ +--R \|- \|- 1 + 1 +--R + +--R +------------+ +--R +-+ | 3+---+ tanh(x) +--R - 2\|2 \|- \|- 1 + 1 atanh(--------------) +--R +-----------+ +--R |3+---+2 +--R \|\|- 1 + 1 +--R / +--R +------------+ +-----------+ +--R +-+ | 3+---+ |3+---+2 +--R 6\|2 \|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +--d0220:= D(m0220,x) +--E 105 + +--S 106 of 500 +t0221:= 1/(1+cosh(x)^8) +--R +--R +--R 1 +--R (72) ------------ +--R 8 +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0221:= 1/4*atanh(tanh(x)/(1-(-1)^(1/4))^(1/2))/(1-(-1)^(1/4))^(1/2)+_ + 1/4*atanh(tanh(x)/(1+(-1)^(1/4))^(1/2))/(1+(-1)^(1/4))^(1/2)+_ + 1/4*atanh(tanh(x)/(1-(-1)^(3/4))^(1/2))/(1-(-1)^(3/4))^(1/2)+_ + 1/4*atanh(tanh(x)/(1+(-1)^(3/4))^(1/2))/(1+(-1)^(3/4))^(1/2) +--R +--R +--R (73) +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tanh(x) +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 - 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tanh(x) +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tanh(x) +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 - 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tanh(x) +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R / +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 4 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0221:= integrate(t0221,x) +--R +--R +--R (74) +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (128\|2 - 256)sinh(x) + (256\|2 - 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (128\|2 - 256)cosh(x) - 128\|2 + 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)sinh(x) + (- 4\|2 + 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)cosh(x) - 6\|2 + 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + 2\|2 - 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (4\|2 - 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)cosh(x) + 5\|2 - 4 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 128\|2 + 256)sinh(x) + (- 256\|2 + 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 128\|2 + 256)cosh(x) + 128\|2 - 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)sinh(x) + (4\|2 - 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)cosh(x) + 6\|2 - 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + 2\|2 - 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (4\|2 - 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)cosh(x) + 5\|2 - 4 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (128\|2 + 256)sinh(x) + (256\|2 + 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (128\|2 + 256)cosh(x) - 128\|2 - 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)sinh(x) + (- 4\|2 - 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)cosh(x) - 6\|2 - 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + 2\|2 + 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (4\|2 + 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)cosh(x) + 5\|2 + 4 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 128\|2 - 256)sinh(x) + (- 256\|2 - 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 128\|2 - 256)cosh(x) + 128\|2 + 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)sinh(x) + (4\|2 + 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)cosh(x) + 6\|2 + 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + 2\|2 + 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (4\|2 + 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)cosh(x) + 5\|2 + 4 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (\|2 + 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 +--R (64\|2 + 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R (128\|2 + 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 +--R (64\|2 + 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R sin(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (- \|2 - 2) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R - \|2 sinh(x) - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 - 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (\|2 + 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R (64\|2 + 128) |--------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R (- 128\|2 - 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R (64\|2 + 128) |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +-+ 2 +--R (- \|2 - 2) |--------- cos(-------------------- + \|2 sinh(x) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ +-+ 2 +-+ +--R 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 + 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (\|2 - 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R (64\|2 - 128) |--------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R (128\|2 - 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R (64\|2 - 128) |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +-+ 2 +--R (- \|2 + 2) |--------- cos(-------------------- - \|2 sinh(x) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ +-+ 2 +-+ +--R - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 + 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (\|2 - 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 +--R (64\|2 - 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R (- 128\|2 + 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 +--R (64\|2 - 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R sin(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (- \|2 + 2) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 - 2 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0221:= a0221-r0221 +--R +--R +--R (75) +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 + 4 \| 4096\|2 +--R |----------------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (128\|2 - 256)sinh(x) + (256\|2 - 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (128\|2 - 256)cosh(x) - 128\|2 + 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)sinh(x) + (- 4\|2 + 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 4)cosh(x) - 6\|2 + 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + 2\|2 - 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (4\|2 - 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)cosh(x) + 5\|2 - 4 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 + 4 \| 4096\|2 +--R |----------------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 128\|2 + 256)sinh(x) + (- 256\|2 + 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 128\|2 + 256)cosh(x) + 128\|2 - 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (4\|2 - 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)sinh(x) + (4\|2 - 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)cosh(x) + 6\|2 - 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + 2\|2 - 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (4\|2 - 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 4)cosh(x) + 5\|2 - 4 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 - 4 \| 4096\|2 +--R |----------------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (128\|2 + 256)sinh(x) + (256\|2 + 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (128\|2 + 256)cosh(x) - 128\|2 - 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)sinh(x) + (- 4\|2 - 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 4)cosh(x) - 6\|2 - 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + 2\|2 + 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (4\|2 + 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)cosh(x) + 5\|2 + 4 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 - 4 \| 4096\|2 +--R |----------------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R log +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (- 128\|2 - 256)sinh(x) + (- 256\|2 - 512)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 128\|2 - 256)cosh(x) + 128\|2 + 256 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (4\|2 + 4) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)sinh(x) + (4\|2 + 8)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)cosh(x) + 6\|2 + 12 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + 2\|2 + 4)sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + (4\|2 + 8)cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 4)cosh(x) + 5\|2 + 4 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 - 4 \| 4096\|2 +--R |----------------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (\|2 + 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 +--R (64\|2 + 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R (128\|2 + 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 +--R (64\|2 + 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R sin(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (- \|2 - 2) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R - \|2 sinh(x) - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 - 2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 - 4 \| 4096\|2 +--R |----------------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +--R (\|2 + 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R (64\|2 + 128) |--------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R (- 128\|2 - 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 - 4 |4\|2 - 4 \| 4096\|2 +--R (64\|2 + 128) |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 - 4 \| 4096\|2 +-+ 2 +--R (- \|2 - 2) |--------- cos(-------------------- + \|2 sinh(x) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ +-+ 2 +-+ +--R 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 + 2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 + 4 \| 4096\|2 +--R |----------------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (\|2 - 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R (64\|2 - 128) |--------- |--------- cos(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R (128\|2 - 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ +---------+ atan(64 |--------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 \| 4096\|2 +--R (64\|2 - 128) |--------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| 4096\|2 \| \|2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +-+ 2 +--R (- \|2 + 2) |--------- cos(-------------------- - \|2 sinh(x) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ +-+ 2 +-+ +--R - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 + 2 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +-----------------+ +---------+ atan(64 |--------- ) +--R | +-+ +---+ | +-+ | +-+ +--R |\|2 + \|- 1 + 1 |4\|2 + 4 \| 4096\|2 +--R |----------------- |--------- sin(--------------------) +--R | +-+ 4| +-+ 2 +--R \| \|2 \| \|2 +--R * +--R atan +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (\|2 - 2) |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 +--R (64\|2 - 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R (- 128\|2 + 128) |--------- +--R | +-+ +--R \| 4096\|2 +--R / +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ |3\|2 + 4 |4\|2 + 4 +--R (64\|2 - 128) |--------- |--------- +--R | +-+ 4| +-+ +--R \| 4096\|2 \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R sin(--------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R +-+ |4\|2 + 4 \| 4096\|2 +--R (- \|2 + 2) |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 - 2 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R +-+ |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R 2\|2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tanh(x) +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 - 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R +-+ |\|2 - \|- 1 - 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R 2\|2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tanh(x) +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R +-+ |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 + 1 +--R 2\|2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tanh(x) +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 - 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R - +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R +-+ |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 2\|2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tanh(x) +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R / +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R +-+ |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 8\|2 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +--d0221:= D(m0221,x) +--E 110 + +--S 111 of 500 +t0222:= 1/(1-cosh(x)^3) +--R +--R +--R 1 +--R (76) - ------------ +--R 3 +--R cosh(x) - 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0222:= 2/3*atanh((1-(-1)^(1/3))*tanh(1/2*x)/(1-(-1)^(2/3))^(1/2))/_ + (1-(-1)^(2/3))^(1/2)+2/3*atanh((1+(-1)^(2/3))*tanh(1/2*x)/_ + (1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)-sinh(x)/(3-3*cosh(x)) +--R +--R +--R (77) +--R 3+---+ x +--R +----------+ (\|- 1 - 1)tanh(-) +--R |3+---+ 2 +--R (- 2cosh(x) + 2)\|\|- 1 + 1 atanh(-------------------) +--R +-------------+ +--R | 3+---+2 +--R \|- \|- 1 + 1 +--R + +--R 3+---+2 x +--R +-------------+ (\|- 1 + 1)tanh(-) +--R | 3+---+2 2 +--R (2cosh(x) - 2)\|- \|- 1 + 1 atanh(--------------------) +--R +----------+ +--R |3+---+ +--R \|\|- 1 + 1 +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R sinh(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R (3cosh(x) - 3)\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0222:= integrate(t0222,x) +--R +--R +--R (78) +--R %pi %pi %pi +--R (- cos(---)sinh(x) - cos(---)cosh(x) + cos(---)) +--R 12 12 12 +--R * +--R log +--R 4+-+2 2 +-+4+-+ %pi 4+-+2 4+-+2 +--R \|3 sinh(x) + (2\|3 \|3 sin(---) + 2\|3 cosh(x) + \|3 )sinh(x) +--R 12 +--R + +--R %pi 2 +-+4+-+ +-+4+-+ %pi 4+-+2 2 +--R 3sin(---) + (2\|3 \|3 cosh(x) + \|3 \|3 )sin(---) + \|3 cosh(x) +--R 12 12 +--R + +--R 4+-+2 %pi 2 4+-+ %pi 4+-+2 +--R \|3 cosh(x) + 3cos(---) + 3\|3 cos(---) + \|3 +--R 12 12 +--R + +--R %pi %pi %pi +--R (cos(---)sinh(x) + cos(---)cosh(x) - cos(---)) +--R 12 12 12 +--R * +--R log +--R 4+-+2 2 +--R \|3 sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 4+-+2 %pi 2 +--R (- 2\|3 \|3 sin(---) + 2\|3 cosh(x) + \|3 )sinh(x) + 3sin(---) +--R 12 12 +--R + +--R +-+4+-+ +-+4+-+ %pi 4+-+2 2 +--R (- 2\|3 \|3 cosh(x) - \|3 \|3 )sin(---) + \|3 cosh(x) +--R 12 +--R + +--R 4+-+2 %pi 2 4+-+ %pi 4+-+2 +--R \|3 cosh(x) + 3cos(---) - 3\|3 cos(---) + \|3 +--R 12 12 +--R + +--R %pi %pi +--R (- 2sin(---)sinh(x) + (- 2cosh(x) + 2)sin(---)) +--R 12 12 +--R * +--R %pi 4+-+ +--R 6cos(---) + 3\|3 +--R 12 +--R atan(----------------------------------------------------------) +--R +-+4+-+ %pi +-+4+-+ +-+4+-+ +--R 2\|3 \|3 sinh(x) + 6sin(---) + 2\|3 \|3 cosh(x) + \|3 \|3 +--R 12 +--R + +--R %pi %pi +--R (- 2sin(---)sinh(x) + (- 2cosh(x) + 2)sin(---)) +--R 12 12 +--R * +--R %pi 4+-+ +--R 6cos(---) - 3\|3 +--R 12 +--R atan(----------------------------------------------------------) +--R +-+4+-+ %pi +-+4+-+ +-+4+-+ +--R 2\|3 \|3 sinh(x) - 6sin(---) + 2\|3 \|3 cosh(x) + \|3 \|3 +--R 12 +--R + +--R 4+-+ +--R 2\|3 +--R / +--R 4+-+ 4+-+ 4+-+ +--R 3\|3 sinh(x) + 3\|3 cosh(x) - 3\|3 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0222:= a0222-r0222 +--R +--R +--R (79) +--R %pi %pi %pi 2 +--R (- cos(---)cosh(x) + cos(---))sinh(x) - cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi %pi +--R 2cos(---)cosh(x) - cos(---) +--R 12 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R 4+-+2 2 +-+4+-+ %pi 4+-+2 4+-+2 +--R \|3 sinh(x) + (2\|3 \|3 sin(---) + 2\|3 cosh(x) + \|3 )sinh(x) +--R 12 +--R + +--R %pi 2 +-+4+-+ +-+4+-+ %pi 4+-+2 2 +--R 3sin(---) + (2\|3 \|3 cosh(x) + \|3 \|3 )sin(---) + \|3 cosh(x) +--R 12 12 +--R + +--R 4+-+2 %pi 2 4+-+ %pi 4+-+2 +--R \|3 cosh(x) + 3cos(---) + 3\|3 cos(---) + \|3 +--R 12 12 +--R + +--R %pi %pi %pi 2 +--R (cos(---)cosh(x) - cos(---))sinh(x) + cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi %pi +--R - 2cos(---)cosh(x) + cos(---) +--R 12 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R 4+-+2 2 +--R \|3 sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 4+-+2 %pi 2 +--R (- 2\|3 \|3 sin(---) + 2\|3 cosh(x) + \|3 )sinh(x) + 3sin(---) +--R 12 12 +--R + +--R +-+4+-+ +-+4+-+ %pi 4+-+2 2 +--R (- 2\|3 \|3 cosh(x) - \|3 \|3 )sin(---) + \|3 cosh(x) +--R 12 +--R + +--R 4+-+2 %pi 2 4+-+ %pi 4+-+2 +--R \|3 cosh(x) + 3cos(---) - 3\|3 cos(---) + \|3 +--R 12 12 +--R + +--R 4+-+ 4+-+ 4+-+ 2 4+-+ 4+-+ +--R ((2\|3 cosh(x) - 2\|3 )sinh(x) + 2\|3 cosh(x) - 4\|3 cosh(x) + 2\|3 ) +--R * +--R 3+---+ x +--R +----------+ (\|- 1 - 1)tanh(-) +--R |3+---+ 2 +--R \|\|- 1 + 1 atanh(-------------------) +--R +-------------+ +--R | 3+---+2 +--R \|- \|- 1 + 1 +--R + +--R 4+-+ 4+-+ 4+-+ 2 4+-+ +--R (- 2\|3 cosh(x) + 2\|3 )sinh(x) - 2\|3 cosh(x) + 4\|3 cosh(x) +--R + +--R 4+-+ +--R - 2\|3 +--R * +--R 3+---+2 x +--R +-------------+ (\|- 1 + 1)tanh(-) +--R | 3+---+2 2 +--R \|- \|- 1 + 1 atanh(--------------------) +--R +----------+ +--R |3+---+ +--R \|\|- 1 + 1 +--R + +--R %pi +--R (- 2cosh(x) + 2)sin(---)sinh(x) +--R 12 +--R + +--R 2 %pi +--R (- 2cosh(x) + 4cosh(x) - 2)sin(---) +--R 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R %pi 4+-+ +--R 6cos(---) + 3\|3 +--R 12 +--R atan(----------------------------------------------------------) +--R +-+4+-+ %pi +-+4+-+ +-+4+-+ +--R 2\|3 \|3 sinh(x) + 6sin(---) + 2\|3 \|3 cosh(x) + \|3 \|3 +--R 12 +--R + +--R %pi +--R (- 2cosh(x) + 2)sin(---)sinh(x) +--R 12 +--R + +--R 2 %pi +--R (- 2cosh(x) + 4cosh(x) - 2)sin(---) +--R 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R %pi 4+-+ +--R 6cos(---) - 3\|3 +--R 12 +--R atan(----------------------------------------------------------) +--R +-+4+-+ %pi +-+4+-+ +-+4+-+ +--R 2\|3 \|3 sinh(x) - 6sin(---) + 2\|3 \|3 cosh(x) + \|3 \|3 +--R 12 +--R + +--R 4+-+ 2 4+-+ 4+-+ 4+-+ 4+-+ +--R (- \|3 sinh(x) + (- \|3 cosh(x) + \|3 )sinh(x) + 2\|3 cosh(x) - 2\|3 ) +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R 4+-+ 4+-+ 4+-+ 2 4+-+ 4+-+ +--R ((3\|3 cosh(x) - 3\|3 )sinh(x) + 3\|3 cosh(x) - 6\|3 cosh(x) + 3\|3 ) +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +--d0222:= D(m0222,x) +--E 115 + +--S 116 of 500 +t0223:= 1/(1-cosh(x)^4) +--R +--R +--R 1 +--R (80) - ------------ +--R 4 +--R cosh(x) - 1 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0223:= 1/4*atanh(1/2*2^(1/2)*tanh(x))*2^(1/2)+1/2*coth(x) +--R +--R +--R +-+ +--R +-+ \|2 tanh(x) +--R \|2 atanh(-----------) + 2coth(x) +--R 2 +--R (81) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0223:= integrate(t0223,x) +--R +--R +--R (82) +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1) +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ +--R 4\|2 +--R / +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|2 sinh(x) + 8\|2 cosh(x)sinh(x) + 4\|2 cosh(x) - 4\|2 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0223:= a0223-r0223 +--R +--R +--R (83) +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1) +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ +--R 2 2 \|2 tanh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2)atanh(-----------) +--R 2 +--R + +--R +-+ 2 +-+ +--R - 2\|2 coth(x)sinh(x) - 4\|2 cosh(x)coth(x)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 2\|2 cosh(x) + 2\|2 )coth(x) + 4\|2 +--R / +--R +-+ 2 +-+ +-+ 2 +-+ +--R 4\|2 sinh(x) + 8\|2 cosh(x)sinh(x) + 4\|2 cosh(x) - 4\|2 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0223:= D(m0223,x) +--R +--R +--R (84) +--R +-+ 2 +-+ 8 +--R ((9\|2 - 12)coth(x) - 12\|2 + 16)sinh(x) +--R + +--R +-+ 2 +-+ 7 +--R ((20\|2 - 24)cosh(x)coth(x) + (- 16\|2 + 16)cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +--R (8\|2 cosh(x) + 12\|2 - 16)coth(x) + (8\|2 - 32)cosh(x) +--R + +--R +-+ +--R - 54\|2 + 72 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R ((- 4\|2 + 24)cosh(x) + (68\|2 - 88)cosh(x))coth(x) +--R + +--R +-+ 3 +-+ +--R (- 16\|2 - 16)cosh(x) + (- 128\|2 + 160)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 2\|2 + 24)cosh(x) + (28\|2 - 16)cosh(x) - 42\|2 + 56) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 56\|2 + 32)cosh(x) + (- 26\|2 - 8)cosh(x) - 66\|2 + 88 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 4\|2 + 24)cosh(x) + (- 56\|2 + 112)cosh(x) +--R + +--R +-+ +--R (- 4\|2 - 8)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 16\|2 - 16)cosh(x) + (96\|2 - 192)cosh(x) +--R + +--R +-+ +--R (- 48\|2 + 48)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R 8\|2 cosh(x) + (28\|2 - 16)cosh(x) +--R + +--R +-+ 2 +-+ +--R (144\|2 - 224)cosh(x) + 12\|2 - 16 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +--R (8\|2 - 32)cosh(x) + (- 26\|2 - 8)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 100\|2 + 112)cosh(x) - 42\|2 + 56 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (20\|2 - 24)cosh(x) + (68\|2 - 88)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 4\|2 - 8)cosh(x) + (- 84\|2 + 120)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 16\|2 + 16)cosh(x) + (- 128\|2 + 160)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 48\|2 + 48)cosh(x) + (64\|2 - 96)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (9\|2 - 12)cosh(x) + (12\|2 - 16)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 42\|2 + 56)cosh(x) + (12\|2 - 16)cosh(x) + 9\|2 - 12 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 12\|2 + 16)cosh(x) + (- 54\|2 + 72)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 66\|2 + 88)cosh(x) + (- 42\|2 + 56)cosh(x) - 18\|2 + 24 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 2 +-+ 8 +--R ((- 18\|2 + 24)coth(x) + 15\|2 - 20)sinh(x) +--R + +--R +-+ 2 +-+ 7 +--R ((- 40\|2 + 48)cosh(x)coth(x) + (12\|2 - 8)cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +--R (- 16\|2 cosh(x) - 24\|2 + 32)coth(x) + (- 24\|2 + 64)cosh(x) +--R + +--R +-+ +--R 96\|2 - 128 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R ((8\|2 - 48)cosh(x) + (- 136\|2 + 176)cosh(x))coth(x) +--R + +--R +-+ 3 +-+ +--R (36\|2 + 8)cosh(x) + (188\|2 - 232)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((4\|2 - 48)cosh(x) + (- 56\|2 + 32)cosh(x) + 84\|2 - 112) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (114\|2 - 88)cosh(x) + (24\|2 + 32)cosh(x) + 174\|2 - 232 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (8\|2 - 48)cosh(x) + (112\|2 - 224)cosh(x) +--R + +--R +-+ +--R (8\|2 + 16)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 5 +-+ 3 +--R (36\|2 + 8)cosh(x) + (- 136\|2 + 272)cosh(x) +--R + +--R +-+ +--R (100\|2 - 88)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 16\|2 cosh(x) + (- 56\|2 + 32)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 288\|2 + 448)cosh(x) - 24\|2 + 32 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R (- 24\|2 + 64)cosh(x) + (24\|2 + 32)cosh(x) + 56\|2 cosh(x) +--R + +--R +-+ +--R 72\|2 - 96 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 40\|2 + 48)cosh(x) + (- 136\|2 + 176)cosh(x) +--R + +--R +-+ 3 +-+ +--R (8\|2 + 16)cosh(x) + (168\|2 - 240)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 7 +-+ 5 +--R (12\|2 - 8)cosh(x) + (188\|2 - 232)cosh(x) +--R + +--R +-+ 3 +-+ +--R (100\|2 - 88)cosh(x) + (- 44\|2 + 72)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 18\|2 + 24)cosh(x) + (- 24\|2 + 32)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (84\|2 - 112)cosh(x) + (- 24\|2 + 32)cosh(x) - 18\|2 + 24 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R (15\|2 - 20)cosh(x) + (96\|2 - 128)cosh(x) + (174\|2 - 232)cosh(x) +--R + +--R +-+ 2 +-+ +--R (72\|2 - 96)cosh(x) + 27\|2 - 36 +--R / +--R +-+ 8 +-+ 7 +--R (18\|2 - 24)sinh(x) + (40\|2 - 48)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (16\|2 cosh(x) + 24\|2 - 32)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((- 8\|2 + 48)cosh(x) + (136\|2 - 176)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 4\|2 + 48)cosh(x) + (56\|2 - 32)cosh(x) - 84\|2 + 112) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 8\|2 + 48)cosh(x) + (- 112\|2 + 224)cosh(x) +--R + +--R +-+ +--R (- 8\|2 - 16)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 16\|2 cosh(x) + (56\|2 - 32)cosh(x) + (288\|2 - 448)cosh(x) +--R + +--R +-+ +--R 24\|2 - 32 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (40\|2 - 48)cosh(x) + (136\|2 - 176)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 8\|2 - 16)cosh(x) + (- 168\|2 + 240)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (18\|2 - 24)cosh(x) + (24\|2 - 32)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 84\|2 + 112)cosh(x) + (24\|2 - 32)cosh(x) + 18\|2 - 24 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R (- 36\|2 + 48)sinh(x) + (- 80\|2 + 96)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 32\|2 cosh(x) - 48\|2 + 64)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((16\|2 - 96)cosh(x) + (- 272\|2 + 352)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R ((8\|2 - 96)cosh(x) + (- 112\|2 + 64)cosh(x) + 168\|2 - 224)sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (16\|2 - 96)cosh(x) + (224\|2 - 448)cosh(x) +--R + +--R +-+ +--R (16\|2 + 32)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 32\|2 cosh(x) + (- 112\|2 + 64)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 576\|2 + 896)cosh(x) - 48\|2 + 64 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 80\|2 + 96)cosh(x) + (- 272\|2 + 352)cosh(x) +--R + +--R +-+ 3 +-+ +--R (16\|2 + 32)cosh(x) + (336\|2 - 480)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 36\|2 + 48)cosh(x) + (- 48\|2 + 64)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (168\|2 - 224)cosh(x) + (- 48\|2 + 64)cosh(x) - 36\|2 + 48 +--R Type: Expression(Integer) +--E 120 + +--S 121 of 500 +t0224:= 1/(1-cosh(x)^5) +--R +--R +--R 1 +--R (85) - ------------ +--R 5 +--R cosh(x) - 1 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0224:= 2/5*atanh((1-(-1)^(1/5))*_ + tanh(1/2*x)/(1-(-1)^(2/5))^(1/2))/(1-(-1)^(2/5))^(1/2)+2/5*_ + atanh((1-(-1)^(3/5))*_ + tanh(1/2*x)/(1+(-1)^(1/5))^(1/2))/(1+(-1)^(1/5))^(1/2)+2/5*_ + atanh((1+(-1)^(2/5))*_ + tanh(1/2*x)/(1-(-1)^(4/5))^(1/2))/(1-(-1)^(4/5))^(1/2)+2/5*_ + atanh((1+(-1)^(4/5))*_ + tanh(1/2*x)/(1+(-1)^(3/5))^(1/2))/(1+(-1)^(3/5))^(1/2)-_ + sinh(x)/(5-5*cosh(x)) +--R +--R +--R (86) +--R +-------------+ +----------+ +-----------+ +--R | 5+---+2 |5+---+ |5+---+3 +--R (2cosh(x) - 2)\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R * +--R 5+---+2 x +--R (\|- 1 + 1)tanh(-) +--R 2 +--R atanh(--------------------) +--R +-------------+ +--R | 5+---+4 +--R \|- \|- 1 + 1 +--R + +--R +-------------+ +----------+ +-----------+ +--R | 5+---+4 |5+---+ |5+---+3 +--R (- 2cosh(x) + 2)\|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R * +--R 5+---+ x +--R (\|- 1 - 1)tanh(-) +--R 2 +--R atanh(-------------------) +--R +-------------+ +--R | 5+---+2 +--R \|- \|- 1 + 1 +--R + +--R +-------------+ +-------------+ +-----------+ +--R | 5+---+4 | 5+---+2 |5+---+3 +--R (- 2cosh(x) + 2)\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R 5+---+3 x +--R (\|- 1 - 1)tanh(-) +--R 2 +--R atanh(--------------------) +--R +----------+ +--R |5+---+ +--R \|\|- 1 + 1 +--R + +--R +-------------+ +-------------+ +----------+ +--R | 5+---+4 | 5+---+2 |5+---+ +--R (2cosh(x) - 2)\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R 5+---+4 x +--R (\|- 1 + 1)tanh(-) +--R 2 +--R atanh(--------------------) +--R +-----------+ +--R |5+---+3 +--R \|\|- 1 + 1 +--R + +--R +-------------+ +-------------+ +----------+ +-----------+ +--R | 5+---+4 | 5+---+2 |5+---+ |5+---+3 +--R sinh(x)\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +-------------+ +----------+ +-----------+ +--R | 5+---+4 | 5+---+2 |5+---+ |5+---+3 +--R (5cosh(x) - 5)\|- \|- 1 + 1 \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0224:= integrate(t0224,x) +--R +--R +--R (87) +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 + 8 \| 625\|5 +--R (sinh(x) + cosh(x) - 1) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R (500\|5 - 1500)sinh(x) + (500\|5 - 1500)cosh(x) - 250\|5 +--R + +--R 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (- 10\|5 + 10) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 + 8 \| 625\|5 +--R (- sinh(x) - cosh(x) + 1) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +--R (- 500\|5 + 1500)sinh(x) + (- 500\|5 + 1500)cosh(x) +--R + +--R +-+ +--R 250\|5 - 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +-+ 2 +--R (10\|5 - 10) |--------- cos(------------------- + 8\|5 sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ 2 +--R (16\|5 cosh(x) + 4\|5 + 20)sinh(x) + 8\|5 cosh(x) +--R + +--R +-+ +-+ +--R (4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 - 8 \| 625\|5 +--R (sinh(x) + cosh(x) - 1) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R (500\|5 + 1500)sinh(x) + (500\|5 + 1500)cosh(x) - 250\|5 +--R + +--R - 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (- 10\|5 - 10) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 - 8 \| 625\|5 +--R (- sinh(x) - cosh(x) + 1) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +--R (- 500\|5 - 1500)sinh(x) + (- 500\|5 - 1500)cosh(x) +--R + +--R +-+ +--R 250\|5 + 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +-+ 2 +--R (10\|5 + 10) |--------- cos(------------------- + 8\|5 sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ 2 +--R (16\|5 cosh(x) + 4\|5 - 20)sinh(x) + 8\|5 cosh(x) +--R + +--R +-+ +-+ +--R (4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 - 8 \| 625\|5 +--R (- 2sinh(x) - 2cosh(x) + 2) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (125\|5 + 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R - 4\|5 sinh(x) - 4\|5 cosh(x) - \|5 + 5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 - 8 \| 625\|5 +--R (2sinh(x) + 2cosh(x) - 2) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (- 125\|5 - 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R 4\|5 sinh(x) + 4\|5 cosh(x) + \|5 - 5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 + 8 \| 625\|5 +--R (- 2sinh(x) - 2cosh(x) + 2) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (125\|5 - 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R - 4\|5 sinh(x) - 4\|5 cosh(x) - \|5 - 5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R |8\|5 + 8 \| 625\|5 +--R (2sinh(x) + 2cosh(x) - 2) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (- 125\|5 + 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R 4\|5 sinh(x) + 4\|5 cosh(x) + \|5 + 5 +--R + +--R 4 +--R / +--R 10sinh(x) + 10cosh(x) - 10 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0224:= a0224-r0224 +--R +--R +--R (88) +--R +-------------+ +--R 2 | 5+---+4 +--R ((cosh(x) - 1)sinh(x) + cosh(x) - 2cosh(x) + 1)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 + 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R (500\|5 - 1500)sinh(x) + (500\|5 - 1500)cosh(x) - 250\|5 +--R + +--R 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (- 10\|5 + 10) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 + 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((- cosh(x) + 1)sinh(x) - cosh(x) + 2cosh(x) - 1)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 + 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +--R (- 500\|5 + 1500)sinh(x) + (- 500\|5 + 1500)cosh(x) +--R + +--R +-+ +--R 250\|5 - 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 + 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +--R (5\|5 - 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 + 8 \| 625\|5 +-+ 2 +--R (10\|5 - 10) |--------- cos(------------------- + 8\|5 sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ 2 +--R (16\|5 cosh(x) + 4\|5 + 20)sinh(x) + 8\|5 cosh(x) +--R + +--R +-+ +-+ +--R (4\|5 + 20)cosh(x) + 8\|5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((cosh(x) - 1)sinh(x) + cosh(x) - 2cosh(x) + 1)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 - 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ +--R (500\|5 + 1500)sinh(x) + (500\|5 + 1500)cosh(x) - 250\|5 +--R + +--R - 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (- 10\|5 - 10) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 sinh(x) + (16\|5 cosh(x) + 4\|5 - 20)sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 8\|5 cosh(x) + (4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((- cosh(x) + 1)sinh(x) - cosh(x) + 2cosh(x) - 1)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 - 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R cos(-------------------) +--R 2 +--R * +--R log +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- sin(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +--R (- 500\|5 - 1500)sinh(x) + (- 500\|5 - 1500)cosh(x) +--R + +--R +-+ +--R 250\|5 + 250 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ 2 +--R | +-+ +--R |\|5 - 2 +--R +---------+2 atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +--R (5\|5 + 5) |--------- cos(-------------------) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +---------+ atan(25 |-------- ) +--R | +-+ | +-+ +--R +-+ |8\|5 - 8 \| 625\|5 +-+ 2 +--R (10\|5 + 10) |--------- cos(------------------- + 8\|5 sinh(x) +--R 4| +-+ 2 +--R \| \|5 +--R + +--R +-+ +-+ +-+ 2 +--R (16\|5 cosh(x) + 4\|5 - 20)sinh(x) + 8\|5 cosh(x) +--R + +--R +-+ +-+ +--R (4\|5 - 20)cosh(x) + 8\|5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((- 2cosh(x) + 2)sinh(x) - 2cosh(x) + 4cosh(x) - 2)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 - 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (125\|5 + 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R - 4\|5 sinh(x) - 4\|5 cosh(x) - \|5 + 5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((2cosh(x) - 2)sinh(x) + 2cosh(x) - 4cosh(x) + 2)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 - 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 - 2 +--R (- 125\|5 - 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 - 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 - 2 |8\|5 - 8 \| 625\|5 +--R (125\|5 + 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R 4\|5 sinh(x) + 4\|5 cosh(x) + \|5 - 5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((- 2cosh(x) + 2)sinh(x) - 2cosh(x) + 4cosh(x) - 2)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 + 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (125\|5 - 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R - 4\|5 sinh(x) - 4\|5 cosh(x) - \|5 - 5 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((2cosh(x) - 2)sinh(x) + 2cosh(x) - 4cosh(x) + 2)\|- \|- 1 + 1 +--R * +--R +---------+ +--R +-------------+ | +-+ +----------+ +-----------+ +--R | 5+---+2 |8\|5 + 8 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 |--------- \|\|- 1 + 1 \|\|- 1 + 1 +--R 4| +-+ +--R \| \|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R atan(25 |-------- ) +--R | +-+ +--R \| 625\|5 +--R sin(-------------------) +--R 2 +--R * +--R atan +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- cos(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|5 + 2 +--R (- 125\|5 + 375) |-------- +--R | +-+ +--R \| 625\|5 +--R / +--R +--------+ +--R | +-+ +--R |\|5 + 2 +--R +--------+ +---------+ atan(25 |-------- ) +--R | +-+ | +-+ | +-+ +--R +-+ |\|5 + 2 |8\|5 + 8 \| 625\|5 +--R (125\|5 - 375) |-------- |--------- sin(-------------------) +--R | +-+ 4| +-+ 2 +--R \| 625\|5 \| \|5 +--R + +--R +-+ +-+ +-+ +--R 4\|5 sinh(x) + 4\|5 cosh(x) + \|5 + 5 +--R + +--R +-------------+ +--R 2 | 5+---+2 +--R ((- 4cosh(x) + 4)sinh(x) - 4cosh(x) + 8cosh(x) - 4)\|- \|- 1 + 1 +--R * +--R 5+---+2 x +--R +----------+ +-----------+ (\|- 1 + 1)tanh(-) +--R |5+---+ |5+---+3 2 +--R \|\|- 1 + 1 \|\|- 1 + 1 atanh(--------------------) +--R +-------------+ +--R | 5+---+4 +--R \|- \|- 1 + 1 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((4cosh(x) - 4)sinh(x) + 4cosh(x) - 8cosh(x) + 4)\|- \|- 1 + 1 +--R * +--R 5+---+ x +--R +----------+ +-----------+ (\|- 1 - 1)tanh(-) +--R |5+---+ |5+---+3 2 +--R \|\|- 1 + 1 \|\|- 1 + 1 atanh(-------------------) +--R +-------------+ +--R | 5+---+2 +--R \|- \|- 1 + 1 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((4cosh(x) - 4)sinh(x) + 4cosh(x) - 8cosh(x) + 4)\|- \|- 1 + 1 +--R * +--R 5+---+3 x +--R +-------------+ +-----------+ (\|- 1 - 1)tanh(-) +--R | 5+---+2 |5+---+3 2 +--R \|- \|- 1 + 1 \|\|- 1 + 1 atanh(--------------------) +--R +----------+ +--R |5+---+ +--R \|\|- 1 + 1 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R ((- 4cosh(x) + 4)sinh(x) - 4cosh(x) + 8cosh(x) - 4)\|- \|- 1 + 1 +--R * +--R 5+---+4 x +--R +-------------+ +----------+ (\|- 1 + 1)tanh(-) +--R | 5+---+2 |5+---+ 2 +--R \|- \|- 1 + 1 \|\|- 1 + 1 atanh(--------------------) +--R +-----------+ +--R |5+---+3 +--R \|\|- 1 + 1 +--R + +--R +-------------+ +--R 2 | 5+---+4 +--R (- 2sinh(x) + (- 2cosh(x) + 2)sinh(x) + 4cosh(x) - 4)\|- \|- 1 + 1 +--R * +--R +-------------+ +----------+ +-----------+ +--R | 5+---+2 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +--R 2 | 5+---+4 +--R ((10cosh(x) - 10)sinh(x) + 10cosh(x) - 20cosh(x) + 10)\|- \|- 1 + 1 +--R * +--R +-------------+ +----------+ +-----------+ +--R | 5+---+2 |5+---+ |5+---+3 +--R \|- \|- 1 + 1 \|\|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +--d0224:= D(m0224,x) +--E 125 + +--S 126 of 500 +t0225:= 1/(1-cosh(x)^6) +--R +--R +--R 1 +--R (89) - ------------ +--R 6 +--R cosh(x) - 1 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0225:= 1/3*atanh(tanh(x)/(1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)+_ + 1/3*atanh(tanh(x)/(1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)+_ + 1/3*coth(x) +--R +--R +--R (90) +--R +----------+ +--R |3+---+ tanh(x) +--R \|\|- 1 + 1 atanh(----------------) +--R +-------------+ +--R | 3+---+2 +--R \|- \|- 1 + 1 +--R + +--R +-------------+ +-------------+ +----------+ +--R | 3+---+2 tanh(x) | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 atanh(-------------) + coth(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R +----------+ +--R |3+---+ +--R \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R 3\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0225:= integrate(t0225,x) +--R +--R +--R (91) +--R %pi 2 %pi %pi 2 +--R cos(---)sinh(x) + 2cos(---)cosh(x)sinh(x) + cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi +--R - cos(---) +--R 12 +--R * +--R log +--R 4+-+2 4 4+-+2 3 +--R \|3 sinh(x) + 4\|3 cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 2 4+-+ %pi 4+-+2 +--R (2\|3 \|3 sin(---) + 6\|3 cosh(x) - 6\|3 cos(---) + 4\|3 ) +--R 12 12 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 3 +--R 4\|3 \|3 cosh(x)sin(---) + 4\|3 cosh(x) +--R 12 +--R + +--R 4+-+ %pi 4+-+2 +--R (- 12\|3 cos(---) + 8\|3 )cosh(x) +--R 12 +--R * +--R sinh(x) +--R + +--R %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 12sin(---) + (2\|3 \|3 cosh(x) - 2\|3 \|3 )sin(---) +--R 12 12 +--R + +--R 4+-+2 4 4+-+ %pi 4+-+2 2 %pi 2 +--R \|3 cosh(x) + (- 6\|3 cos(---) + 4\|3 )cosh(x) + 12cos(---) +--R 12 12 +--R + +--R 4+-+ %pi 4+-+2 +--R - 18\|3 cos(---) + 7\|3 +--R 12 +--R + +--R %pi 2 %pi %pi 2 +--R - cos(---)sinh(x) - 2cos(---)cosh(x)sinh(x) - cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi +--R cos(---) +--R 12 +--R * +--R log +--R 4+-+2 4 4+-+2 3 +--R \|3 sinh(x) + 4\|3 cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 2 4+-+ %pi 4+-+2 +--R (- 2\|3 \|3 sin(---) + 6\|3 cosh(x) + 6\|3 cos(---) + 4\|3 ) +--R 12 12 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 3 +--R - 4\|3 \|3 cosh(x)sin(---) + 4\|3 cosh(x) +--R 12 +--R + +--R 4+-+ %pi 4+-+2 +--R (12\|3 cos(---) + 8\|3 )cosh(x) +--R 12 +--R * +--R sinh(x) +--R + +--R %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 12sin(---) + (- 2\|3 \|3 cosh(x) + 2\|3 \|3 )sin(---) +--R 12 12 +--R + +--R 4+-+2 4 4+-+ %pi 4+-+2 2 %pi 2 +--R \|3 cosh(x) + (6\|3 cos(---) + 4\|3 )cosh(x) + 12cos(---) +--R 12 12 +--R + +--R 4+-+ %pi 4+-+2 +--R 18\|3 cos(---) + 7\|3 +--R 12 +--R + +--R %pi 2 %pi 2 %pi +--R (2sin(---)sinh(x) + 4cosh(x)sin(---)sinh(x) + (2cosh(x) - 2)sin(---)) +--R 12 12 12 +--R * +--R atan +--R +-+ %pi %pi 4+-+ +--R 3\|3 sin(---) + 3cos(---) + 3\|3 +--R 12 12 +--R / +--R +-+4+-+ 2 +-+4+-+ %pi +--R \|3 \|3 sinh(x) + 2\|3 \|3 cosh(x)sinh(x) - 3sin(---) +--R 12 +--R + +--R +-+4+-+ 2 +-+ %pi +-+4+-+ +--R \|3 \|3 cosh(x) + 3\|3 cos(---) + 2\|3 \|3 +--R 12 +--R + +--R %pi 2 %pi 2 %pi +--R (2sin(---)sinh(x) + 4cosh(x)sin(---)sinh(x) + (2cosh(x) - 2)sin(---)) +--R 12 12 12 +--R * +--R atan +--R +-+ %pi %pi 4+-+ +--R 3\|3 sin(---) + 3cos(---) - 3\|3 +--R 12 12 +--R / +--R +-+4+-+ 2 +-+4+-+ %pi +--R \|3 \|3 sinh(x) + 2\|3 \|3 cosh(x)sinh(x) + 3sin(---) +--R 12 +--R + +--R +-+4+-+ 2 +-+ %pi +-+4+-+ +--R \|3 \|3 cosh(x) - 3\|3 cos(---) + 2\|3 \|3 +--R 12 +--R + +--R 4+-+ +--R 4\|3 +--R / +--R 4+-+ 2 4+-+ 4+-+ 2 4+-+ +--R 6\|3 sinh(x) + 12\|3 cosh(x)sinh(x) + 6\|3 cosh(x) - 6\|3 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0225:= a0225-r0225 +--R +--R +--R (92) +--R %pi 2 %pi %pi 2 +--R cos(---)sinh(x) + 2cos(---)cosh(x)sinh(x) + cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi +--R - cos(---) +--R 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R 4+-+2 4 4+-+2 3 +--R \|3 sinh(x) + 4\|3 cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 2 4+-+ %pi 4+-+2 +--R (2\|3 \|3 sin(---) + 6\|3 cosh(x) - 6\|3 cos(---) + 4\|3 ) +--R 12 12 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 3 +--R 4\|3 \|3 cosh(x)sin(---) + 4\|3 cosh(x) +--R 12 +--R + +--R 4+-+ %pi 4+-+2 +--R (- 12\|3 cos(---) + 8\|3 )cosh(x) +--R 12 +--R * +--R sinh(x) +--R + +--R %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 12sin(---) + (2\|3 \|3 cosh(x) - 2\|3 \|3 )sin(---) +--R 12 12 +--R + +--R 4+-+2 4 4+-+ %pi 4+-+2 2 %pi 2 +--R \|3 cosh(x) + (- 6\|3 cos(---) + 4\|3 )cosh(x) + 12cos(---) +--R 12 12 +--R + +--R 4+-+ %pi 4+-+2 +--R - 18\|3 cos(---) + 7\|3 +--R 12 +--R + +--R %pi 2 %pi %pi 2 +--R - cos(---)sinh(x) - 2cos(---)cosh(x)sinh(x) - cos(---)cosh(x) +--R 12 12 12 +--R + +--R %pi +--R cos(---) +--R 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R 4+-+2 4 4+-+2 3 +--R \|3 sinh(x) + 4\|3 cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 2 4+-+ %pi 4+-+2 +--R (- 2\|3 \|3 sin(---) + 6\|3 cosh(x) + 6\|3 cos(---) + 4\|3 ) +--R 12 12 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+4+-+ %pi 4+-+2 3 +--R - 4\|3 \|3 cosh(x)sin(---) + 4\|3 cosh(x) +--R 12 +--R + +--R 4+-+ %pi 4+-+2 +--R (12\|3 cos(---) + 8\|3 )cosh(x) +--R 12 +--R * +--R sinh(x) +--R + +--R %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 12sin(---) + (- 2\|3 \|3 cosh(x) + 2\|3 \|3 )sin(---) +--R 12 12 +--R + +--R 4+-+2 4 4+-+ %pi 4+-+2 2 %pi 2 +--R \|3 cosh(x) + (6\|3 cos(---) + 4\|3 )cosh(x) + 12cos(---) +--R 12 12 +--R + +--R 4+-+ %pi 4+-+2 +--R 18\|3 cos(---) + 7\|3 +--R 12 +--R + +--R 4+-+ 2 4+-+ 4+-+ 2 4+-+ +--R (- 2\|3 sinh(x) - 4\|3 cosh(x)sinh(x) - 2\|3 cosh(x) + 2\|3 ) +--R * +--R +----------+ +--R |3+---+ tanh(x) +--R \|\|- 1 + 1 atanh(----------------) +--R +-------------+ +--R | 3+---+2 +--R \|- \|- 1 + 1 +--R + +--R 4+-+ 2 4+-+ 4+-+ 2 4+-+ +--R (- 2\|3 sinh(x) - 4\|3 cosh(x)sinh(x) - 2\|3 cosh(x) + 2\|3 ) +--R * +--R +-------------+ +--R | 3+---+2 tanh(x) +--R \|- \|- 1 + 1 atanh(-------------) +--R +----------+ +--R |3+---+ +--R \|\|- 1 + 1 +--R + +--R %pi 2 %pi 2 %pi +--R (2sin(---)sinh(x) + 4cosh(x)sin(---)sinh(x) + (2cosh(x) - 2)sin(---)) +--R 12 12 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R atan +--R +-+ %pi %pi 4+-+ +--R 3\|3 sin(---) + 3cos(---) + 3\|3 +--R 12 12 +--R / +--R +-+4+-+ 2 +-+4+-+ %pi +--R \|3 \|3 sinh(x) + 2\|3 \|3 cosh(x)sinh(x) - 3sin(---) +--R 12 +--R + +--R +-+4+-+ 2 +-+ %pi +-+4+-+ +--R \|3 \|3 cosh(x) + 3\|3 cos(---) + 2\|3 \|3 +--R 12 +--R + +--R %pi 2 %pi 2 %pi +--R (2sin(---)sinh(x) + 4cosh(x)sin(---)sinh(x) + (2cosh(x) - 2)sin(---)) +--R 12 12 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R atan +--R +-+ %pi %pi 4+-+ +--R 3\|3 sin(---) + 3cos(---) - 3\|3 +--R 12 12 +--R / +--R +-+4+-+ 2 +-+4+-+ %pi +--R \|3 \|3 sinh(x) + 2\|3 \|3 cosh(x)sinh(x) + 3sin(---) +--R 12 +--R + +--R +-+4+-+ 2 +-+ %pi +-+4+-+ +--R \|3 \|3 cosh(x) - 3\|3 cos(---) + 2\|3 \|3 +--R 12 +--R + +--R 4+-+ 2 4+-+ +--R - 2\|3 coth(x)sinh(x) - 4\|3 cosh(x)coth(x)sinh(x) +--R + +--R 4+-+ 2 4+-+ 4+-+ +--R (- 2\|3 cosh(x) + 2\|3 )coth(x) + 4\|3 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R 4+-+ 2 4+-+ 4+-+ 2 4+-+ +--R (6\|3 sinh(x) + 12\|3 cosh(x)sinh(x) + 6\|3 cosh(x) - 6\|3 ) +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +--d0225:= D(m0225,x) +--E 130 + +--S 131 of 500 +t0226:= 1/(1-cosh(x)^8) +--R +--R +--R 1 +--R (93) - ------------ +--R 8 +--R cosh(x) - 1 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0226:= 1/4*atanh(tanh(x)/(1-%i)^(1/2))/(1-%i)^(1/2)+_ + 1/4*atanh(tanh(x)/(1+%i)^(1/2))/(1+%i)^(1/2)+_ + 1/8*atanh(1/2*2^(1/2)*tanh(x))*2^(1/2)+1/4*coth(x) +--R +--R +--R (94) +--R +-+ +--R +------+ +------+ +-+ \|2 tanh(x) +------+ tanh(x) +--R \|1 - %i \|1 + %i \|2 atanh(-----------) + 2\|1 + %i atanh(---------) +--R 2 +------+ +--R \|1 - %i +--R + +--R +------+ tanh(x) +------+ +------+ +--R 2\|1 - %i atanh(---------) + 2\|1 - %i \|1 + %i coth(x) +--R +------+ +--R \|1 + %i +--R / +--R +------+ +------+ +--R 8\|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 132 + +--S 133 of 500 +a0226:= integrate(t0226,x) +--R +--R +--R (95) +--R 4+-+ %pi 2 4+-+ %pi +--R \|2 cos(---)sinh(x) + 2\|2 cos(---)cosh(x)sinh(x) +--R 8 8 +--R + +--R 4+-+ %pi 2 4+-+ %pi +--R \|2 cos(---)cosh(x) - \|2 cos(---) +--R 8 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (2\|2 \|2 sin(---) + 6cosh(x) - 2\|2 \|2 cos(---) + 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (- 4\|2 \|2 cos(---) + 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (2\|2 \|2 cosh(x) - 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (- 2\|2 \|2 cos(---) + 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R - 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R 4+-+ %pi 2 4+-+ %pi +--R - \|2 cos(---)sinh(x) - 2\|2 cos(---)cosh(x)sinh(x) +--R 8 8 +--R + +--R 4+-+ %pi 2 4+-+ %pi +--R - \|2 cos(---)cosh(x) + \|2 cos(---) +--R 8 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (- 2\|2 \|2 sin(---) + 6cosh(x) + 2\|2 \|2 cos(---) + 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R - 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (4\|2 \|2 cos(---) + 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (- 2\|2 \|2 cosh(x) + 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (2\|2 \|2 cos(---) + 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1) +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R 4+-+ %pi 2 4+-+ %pi +--R 2\|2 sin(---)sinh(x) + 4\|2 cosh(x)sin(---)sinh(x) +--R 8 8 +--R + +--R 4+-+ 2 4+-+ %pi +--R (2\|2 cosh(x) - 2\|2 )sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) + 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) - 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) + 2\|2 cos(---) + \|2 +--R 8 +--R + +--R 4+-+ %pi 2 4+-+ %pi +--R 2\|2 sin(---)sinh(x) + 4\|2 cosh(x)sin(---)sinh(x) +--R 8 8 +--R + +--R 4+-+ 2 4+-+ %pi +--R (2\|2 cosh(x) - 2\|2 )sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) - 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) - 2\|2 cos(---) + \|2 +--R 8 +--R + +--R +-+ +--R 4\|2 +--R / +--R +-+ 2 +-+ +-+ 2 +-+ +--R 8\|2 sinh(x) + 16\|2 cosh(x)sinh(x) + 8\|2 cosh(x) - 8\|2 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0226:= a0226-r0226 +--R +--R +--R (96) +--R +------+ +------+4+-+ %pi 2 +--R \|1 - %i \|1 + %i \|2 cos(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 cos(---)cosh(x)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi 2 +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---)cosh(x) - \|1 - %i \|1 + %i \|2 cos(---) +--R 8 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (2\|2 \|2 sin(---) + 6cosh(x) - 2\|2 \|2 cos(---) + 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (- 4\|2 \|2 cos(---) + 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (2\|2 \|2 cosh(x) - 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (- 2\|2 \|2 cos(---) + 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R - 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R +------+ +------+4+-+ %pi 2 +--R - \|1 - %i \|1 + %i \|2 cos(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R - 2\|1 - %i \|1 + %i \|2 cos(---)cosh(x)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi 2 +--R - \|1 - %i \|1 + %i \|2 cos(---)cosh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R 4 3 +--R sinh(x) + 4cosh(x)sinh(x) +--R + +--R +-+4+-+ %pi 2 +-+4+-+ %pi 2 +--R (- 2\|2 \|2 sin(---) + 6cosh(x) + 2\|2 \|2 cos(---) + 2)sinh(x) +--R 8 8 +--R + +--R +-+4+-+ %pi 3 +--R - 4\|2 \|2 cosh(x)sin(---) + 4cosh(x) +--R 8 +--R + +--R +-+4+-+ %pi +--R (4\|2 \|2 cos(---) + 4)cosh(x) +--R 8 +--R * +--R sinh(x) +--R + +--R 4+-+2 %pi 2 +-+4+-+ 2 +-+4+-+ %pi +--R 4\|2 sin(---) + (- 2\|2 \|2 cosh(x) + 2\|2 \|2 )sin(---) +--R 8 8 +--R + +--R 4 +-+4+-+ %pi 2 4+-+2 %pi 2 +--R cosh(x) + (2\|2 \|2 cos(---) + 2)cosh(x) + 4\|2 cos(---) +--R 8 8 +--R + +--R +-+4+-+ %pi +--R 6\|2 \|2 cos(---) + 5 +--R 8 +--R + +--R +------+ +------+ 2 +------+ +------+ +--R \|1 - %i \|1 + %i sinh(x) + 2\|1 - %i \|1 + %i cosh(x)sinh(x) +--R + +--R +------+ +------+ 2 +------+ +------+ +--R \|1 - %i \|1 + %i cosh(x) - \|1 - %i \|1 + %i +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) + 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +------+ +------+ 2 +------+ +------+ +--R - 2\|1 - %i \|1 + %i sinh(x) - 4\|1 - %i \|1 + %i cosh(x)sinh(x) +--R + +--R +------+ +------+ 2 +------+ +------+ +--R - 2\|1 - %i \|1 + %i cosh(x) + 2\|1 - %i \|1 + %i +--R * +--R +-+ +--R \|2 tanh(x) +--R atanh(-----------) +--R 2 +--R + +--R +------+ +-+ 2 +------+ +-+ +--R - 2\|1 + %i \|2 sinh(x) - 4\|1 + %i \|2 cosh(x)sinh(x) +--R + +--R +------+ +-+ 2 +------+ +-+ +--R - 2\|1 + %i \|2 cosh(x) + 2\|1 + %i \|2 +--R * +--R tanh(x) +--R atanh(---------) +--R +------+ +--R \|1 - %i +--R + +--R +------+ +-+ 2 +------+ +-+ +--R - 2\|1 - %i \|2 sinh(x) - 4\|1 - %i \|2 cosh(x)sinh(x) +--R + +--R +------+ +-+ 2 +------+ +-+ +--R - 2\|1 - %i \|2 cosh(x) + 2\|1 - %i \|2 +--R * +--R tanh(x) +--R atanh(---------) +--R +------+ +--R \|1 + %i +--R + +--R +------+ +------+4+-+ %pi 2 +--R 2\|1 - %i \|1 + %i \|2 sin(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R 4\|1 - %i \|1 + %i \|2 cosh(x)sin(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ 2 +------+ +------+4+-+ %pi +--R (2\|1 - %i \|1 + %i \|2 cosh(x) - 2\|1 - %i \|1 + %i \|2 )sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) + 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) - 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) + 2\|2 cos(---) + \|2 +--R 8 +--R + +--R +------+ +------+4+-+ %pi 2 +--R 2\|1 - %i \|1 + %i \|2 sin(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ %pi +--R 4\|1 - %i \|1 + %i \|2 cosh(x)sin(---)sinh(x) +--R 8 +--R + +--R +------+ +------+4+-+ 2 +------+ +------+4+-+ %pi +--R (2\|1 - %i \|1 + %i \|2 cosh(x) - 2\|1 - %i \|1 + %i \|2 )sin(---) +--R 8 +--R * +--R atan +--R 4+-+ %pi 4+-+ %pi +-+ +--R 2\|2 sin(---) + 2\|2 cos(---) - 2\|2 +--R 8 8 +--R / +--R +-+ 2 +-+ 4+-+ %pi +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + 2\|2 sin(---) +--R 8 +--R + +--R +-+ 2 4+-+ %pi +-+ +--R \|2 cosh(x) - 2\|2 cos(---) + \|2 +--R 8 +--R + +--R +------+ +------+ +-+ 2 +--R - 2\|1 - %i \|1 + %i \|2 coth(x)sinh(x) +--R + +--R +------+ +------+ +-+ +--R - 4\|1 - %i \|1 + %i \|2 cosh(x)coth(x)sinh(x) +--R + +--R +------+ +------+ +-+ 2 +------+ +------+ +-+ +--R (- 2\|1 - %i \|1 + %i \|2 cosh(x) + 2\|1 - %i \|1 + %i \|2 )coth(x) +--R + +--R +------+ +------+ +-+ +--R 4\|1 - %i \|1 + %i \|2 +--R / +--R +------+ +------+ +-+ 2 +------+ +------+ +-+ +--R 8\|1 - %i \|1 + %i \|2 sinh(x) + 16\|1 - %i \|1 + %i \|2 cosh(x)sinh(x) +--R + +--R +------+ +------+ +-+ 2 +------+ +------+ +-+ +--R 8\|1 - %i \|1 + %i \|2 cosh(x) - 8\|1 - %i \|1 + %i \|2 +--R Type: Expression(Complex(Integer)) +--E 134 + +--S 135 of 500 +--d0226:= D(m0226,x) +--E 135 + +--S 136 of 500 +t0227:= x^2*cosh(a+b*x+c*x^2) +--R +--R +--R 2 2 +--R (97) x cosh(c x + b x + a) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0227:= 1/16*(b^2+2*c)*exp(1)^(-a+1/4*b^2/c)*%pi^(1/2)*_ + erf(1/2*(b+2*c*x)/c^(1/2))/c^(5/2)+1/16*(b^2-2*c)*_ + exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)/c^(1/2))/_ + c^(5/2)-1/4*b*sinh(a+b*x+c*x^2)/c^2+1/2*x*sinh(a+b*x+c*x^2)/c +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 137 + +--S 138 of 500 +a0227:= integrate(t0227,x) +--R +--R +--R x +--R ++ 2 2 +--R (98) | %R cosh(%R c + %R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +--m0227:= a0227-r0227 +--E 139 + +--S 140 of 500 +--d0227:= D(m0227,x) +--E 140 + +--S 141 of 500 +t0228:= x*cosh(a+b*x+c*x^2) +--R +--R +--R 2 +--R (99) x cosh(c x + b x + a) +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0228:= 1/8*(-b*exp(-1/4*(-b^2+4*a*c)/c)*%pi^(1/2)*_ + erf(1/2*(b+2*c*x)/c^(1/2))+%i*b*_ + exp(1/4*(-b^2+4*a*c)/c)*%pi^(1/2)*_ + erf(1/2*%i*(b+2*c*x)/c^(1/2))+4*_ + sinh(a+b*x+c*x^2)*c^(1/2))/c^(3/2) +--R +--R There are 15 exposed and 12 unexposed library operations named / +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op / +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named / +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 142 + +--S 143 of 500 +a0228:= integrate(t0228,x) +--R +--R +--R x +--R ++ 2 +--R (100) | %R cosh(%R c + %R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +--m0228:= a0228-r0228 +--E 144 + +--S 145 of 500 +--d0228:= D(m0228,x) +--E 145 + +--S 146 of 500 +t0229:= cosh(a+b*x+c*x^2)/x^2-b*sinh(a+b*x+c*x^2)/x +--R +--R +--R 2 2 +--R - b x sinh(c x + b x + a) + cosh(c x + b x + a) +--R (101) ------------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0229:= -cosh(a+b*x+c*x^2)/x-1/2*c^(1/2)*exp(1)^(-a+1/4*b^2/c)*%pi^(1/2)*_ + erf(1/2*(b+2*c*x)/c^(1/2))+1/2*c^(1/2)*_ + exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)/c^(1/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 500 +a0229:= integrate(t0229,x) +--R +--R +--R x 2 2 +--R ++ - %R b sinh(%R c + %R b + a) + cosh(%R c + %R b + a) +--R (102) | ---------------------------------------------------- d%R +--R ++ 2 +--R %R +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +--m0229:= a0229-r0229 +--E 149 + +--S 150 of 500 +--d0229:= D(m0229,x) +--E 150 + +--S 151 of 500 +t0230:= x^2*cosh(a+b*x-c*x^2) +--R +--R +--R 2 2 +--R (103) x cosh(c x - b x - a) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0230:= -1/16*(b^2+2*c)*exp(1)^(a+1/4*b^2/c)*%pi^(1/2)*_ + erf(1/2*(b-2*c*x)/c^(1/2))/c^(5/2)-1/16*(b^2-2*c)*_ + exp(1)^(-a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b-2*c*x)/c^(1/2))/c^(5/2)-1/4*b*_ + sinh(a+b*x-c*x^2)/c^2-1/2*x*sinh(a+b*x-c*x^2)/c +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 152 + +--S 153 of 500 +a0230:= integrate(t0230,x) +--R +--R +--R x +--R ++ 2 2 +--R (104) | %R cosh(%R c - %R b - a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +--m0230:= a0230-r0230 +--E 154 + +--S 155 of 500 +--d0230:= D(m0230,x) +--E 155 + +--S 156 of 500 +t0231:= x*cosh(a+b*x-c*x^2) +--R +--R +--R 2 +--R (105) x cosh(c x - b x - a) +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0231:= -1/8/c^(3/2)*(b*exp(1/4*(b^2+4*a*c)/c)*%pi^(1/2)*_ + erf(1/2*(b-2*c*x)/c^(1/2))-%i*b*_ + exp(-1/4*(b^2+4*a*c)/c)*%pi^(1/2)*_ + erf(1/2*%i*(b-2*c*x)/c^(1/2))+4*_ + sinh(a+b*x-c*x^2)*c^(1/2)) +--R +--R There are 15 exposed and 12 unexposed library operations named / +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op / +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named / +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 157 + +--S 158 of 500 +a0231:= integrate(t0231,x) +--R +--R +--R x +--R ++ 2 +--R (106) | %R cosh(%R c - %R b - a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +--m0231:= a0231-r0231 +--E 159 + +--S 160 of 500 +--d0231:= D(m0231,x) +--E 160 + +--S 161 of 500 +t0232:= cosh(a+b*x-c*x^2)/x^2-b*sinh(a+b*x-c*x^2)/x +--R +--R +--R 2 2 +--R b x sinh(c x - b x - a) + cosh(c x - b x - a) +--R (107) ----------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0232:= 1/2/x*(-2*cosh(a+b*x-c*x^2)+c^(1/2)*exp(1/4*(b^2+4*a*c)/c)*%pi^(1/2)*_ + erf(1/2*(b-2*c*x)/c^(1/2))*x+%i*c^(1/2)*_ + exp(-1/4*(b^2+4*a*c)/c)*%pi^(1/2)*_ + erf(1/2*%i*(b-2*c*x)/c^(1/2))*x) +--R +--R There are 15 exposed and 12 unexposed library operations named / +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op / +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named / +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 500 +a0232:= integrate(t0232,x) +--R +--R +--R x 2 2 +--R ++ %R b sinh(%R c - %R b - a) + cosh(%R c - %R b - a) +--R (108) | -------------------------------------------------- d%R +--R ++ 2 +--R %R +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +--m0232:= a0232-r0232 +--E 164 + +--S 165 of 500 +--d0232:= D(m0232,x) +--E 165 + +--S 166 of 500 +t0233:= x^2*cosh(a+b*x+c*x^2)^2 +--R +--R +--R 2 2 2 +--R (109) x cosh(c x + b x + a) +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0233:= 1/6*x^3+1/64*(b^2+c)*exp(1)^(-2*a+1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erf(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)+1/64*(-c+b^2)*_ + exp(1)^(2*a-1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)-1/16*b*_ + sinh(2*a+2*b*x+2*c*x^2)/c^2+1/8*x*sinh(2*a+2*b*x+2*c*x^2)/c +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R AlgebraicNumber +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 167 + +--S 168 of 500 +a0233:= integrate(t0233,x) +--R +--R +--R x +--R ++ 2 2 2 +--R (110) | %R cosh(%R c + %R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +--m0233:= a0233-r0233 +--E 169 + +--S 170 of 500 +--d0233:= D(m0233,x) +--E 170 + +--S 171 of 500 +t0234:= x^2*cosh(a+b*x-c*x^2)^2 +--R +--R +--R 2 2 2 +--R (111) x cosh(c x - b x - a) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0234:= 1/6*x^3-1/64*(b^2+c)*exp(1)^(2*a+1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erf(1/2*(b-2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)-1/64*(-c+b^2)*_ + exp(1)^(-2*a-1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erfi(1/2*(b-2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)-1/16*b*_ + sinh(2*a+2*b*x-2*c*x^2)/c^2-1/8*x*sinh(2*a+2*b*x-2*c*x^2)/c +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R AlgebraicNumber +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 172 + +--S 173 of 500 +a0234:= integrate(t0234,x) +--R +--R +--R x +--R ++ 2 2 2 +--R (112) | %R cosh(%R c - %R b - a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +--m0234:= a0234-r0234 +--E 174 + +--S 175 of 500 +--d0234:= D(m0234,x) +--E 175 + +--S 176 of 500 +t0235:= x^2*cosh(1/4+x+x^2)^2 +--R +--R +--R 2 2 +--R 2 4x + 4x + 1 +--R (113) x cosh(------------) +--R 4 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0235:= 1/6*x^3+1/32*2^(1/2)*%pi^(1/2)*erf(1/2*(1+2*x)*2^(1/2))-_ + 1/16*sinh(1/2+2*x+2*x^2)+1/8*x*sinh(1/2+2*x+2*x^2) +--R +--R There are 1 exposed and 1 unexposed library operations named erf +--R having 1 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op erf +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named erf +--R with argument type(s) +--R UnivariatePolynomial(x,AlgebraicNumber) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 177 + +--S 178 of 500 +a0235:= integrate(t0235,x) +--R +--R +--R x 2 2 +--R ++ 2 4%R + 4%R + 1 +--R (114) | %R cosh(--------------) d%R +--R ++ 4 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +--m0235:= a0235-r0235 +--E 179 + +--S 180 of 500 +--d0235:= D(m0235,x) +--E 180 + +--S 181 of 500 +t0236:= (d+e*x)^2*cosh(a+b*x+c*x^2) +--R +--R +--R 2 2 2 2 +--R (115) (e x + 2d e x + d )cosh(c x + b x + a) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0236:= 1/16*(4*c^2*d^2-2*c*(2*b*d-e)*e+b^2*e^2)*_ + exp(1)^(-a+1/4*b^2/c)*%pi^(1/2)*erf(1/2*(b+2*c*x)/c^(1/2))/_ + c^(5/2)+1/16*(4*c^2*d^2+b^2*e^2-2*c*e*(2*b*d+e))*_ + exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*erfi(1/2*(b+2*c*x)/_ + c^(1/2))/c^(5/2)+1/4*e*(4*c*d-b*e)*sinh(a+b*x+c*x^2)/_ + c^2+1/2*e^2*x*sinh(a+b*x+c*x^2)/c +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 182 + +--S 183 of 500 +a0236:= integrate(t0236,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--R (116) | (%R e + 2%R d e + d )cosh(%R c + %R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +--m0236:= a0236-r0236 +--E 184 + +--S 185 of 500 +--d0236:= D(m0236,x) +--E 185 + +--S 186 of 500 +t0237:= (d+e*x)*cosh(a+b*x+c*x^2) +--R +--R +--R 2 +--R (117) (e x + d)cosh(c x + b x + a) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0237:= 1/8*(2*c*d-b*e)*exp(1)^(-a+1/4*b^2/c)*%pi^(1/2)*_ + erf(1/2*(b+2*c*x)/c^(1/2))/c^(3/2)+1/8*(2*c*d-b*e)*_ + exp(1)^(a-1/4*b^2/c)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)/c^(1/2))/c^(3/2)+1/2*e*_ + sinh(a+b*x+c*x^2)/c +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 187 + +--S 188 of 500 +a0237:= integrate(t0237,x) +--R +--R +--R x +--R ++ 2 +--R (118) | (%R e + d)cosh(%R c + %R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +--m0237:= a0237-r0237 +--E 189 + +--S 190 of 500 +--d0237:= D(m0237,x) +--E 190 + +--S 191 of 500 +t0238:= (d+e*x)^2*cosh(a+b*x+c*x^2)^2 +--R +--R +--R 2 2 2 2 2 +--R (119) (e x + 2d e x + d )cosh(c x + b x + a) +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0238:= 1/2*d^2*x+1/2*d*e*x^2+1/6*e^2*x^3+_ + 1/64*(4*c^2*d^2-c*(4*b*d-e)*e+b^2*e^2)*_ + exp(1)^(-2*a+1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erf(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)+_ + 1/64*(4*c^2*d^2+b^2*e^2-c*e*(4*b*d+e))*exp(1)^(2*a-1/2*b^2/c)*_ + 2^(1/2)*%pi^(1/2)*erfi(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(5/2)+_ + 1/4*d*e*sinh(2*a+2*b*x+2*c*x^2)/c-_ + 1/16*b*e^2*sinh(2*a+2*b*x+2*c*x^2)/c^2+_ + 1/8*e^2*x*sinh(2*a+2*b*x+2*c*x^2)/c +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R AlgebraicNumber +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 192 + +--S 193 of 500 +a0238:= integrate(t0238,x) +--R +--R +--R x +--R ++ 2 2 2 2 2 +--R (120) | (%R e + 2%R d e + d )cosh(%R c + %R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +--m0238:= a0238-r0238 +--E 194 + +--S 195 of 500 +--d0238:= D(m0238,x) +--E 195 + +--S 196 of 500 +t0239:= (d+e*x)*cosh(a+b*x+c*x^2)^2 +--R +--R +--R 2 2 +--R (121) (e x + d)cosh(c x + b x + a) +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0239:= 1/2*d*x+1/4*e*x^2+1/32*(2*c*d-b*e)*exp(1)^(-2*a+1/2*b^2/c)*_ + 2^(1/2)*%pi^(1/2)*erf(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/_ + c^(3/2)+1/32*(2*c*d-b*e)*exp(1)^(2*a-1/2*b^2/c)*2^(1/2)*%pi^(1/2)*_ + erfi(1/2*(b+2*c*x)*2^(1/2)/c^(1/2))/c^(3/2)+1/8*e*_ + sinh(2*a+2*b*x+2*c*x^2)/c +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial(Fraction(Integer)) +--R AlgebraicNumber +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 197 + +--S 198 of 500 +a0239:= integrate(t0239,x) +--R +--R +--R x +--R ++ 2 2 +--R (122) | (%R e + d)cosh(%R c + %R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +--m0239:= a0239-r0239 +--E 199 + +--S 200 of 500 +--d0239:= D(m0239,x) +--E 200 + +--S 201 of 500 +t0240:= cosh((a+b*x)/(c+d*x)) +--R +--R +--R b x + a +--R (123) cosh(-------) +--R d x + c +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0240:= (c+d*x)*cosh((a+b*x)/(c+d*x))/d+(b*c-a*d)*_ + Chi(-(b*c-a*d)/d/(c+d*x))*sinh(b/d)/d^2+(b*c-a*d)*_ + cosh(b/d)*Shi(a/(c+d*x)-b*c/d/(c+d*x))/d^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 202 + +--S 203 of 500 +a0240:= integrate(t0240,x) +--R +--R +--R x +--R ++ %R b + a +--R (124) | cosh(--------)d%R +--R ++ %R d + c +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +--m0240:= a0240-r0240 +--E 204 + +--S 205 of 500 +--d0240:= D(m0240,x) +--E 205 + +--S 206 of 500 +t0241:= cosh((a+b*x)/(c+d*x))^2 +--R +--R +--R b x + a 2 +--R (125) cosh(-------) +--R d x + c +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0241:= 1/2*x+1/2*(c+d*x)*cosh(2*(a+b*x)/(c+d*x))/d+(b*c-a*d)*_ + Chi(-2*(b*c-a*d)/d/(c+d*x))*sinh(2*b/d)/d^2+(b*c-a*d)*_ + cosh(2*b/d)*Shi(2*a/(c+d*x)-2*b*c/d/(c+d*x))/d^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 207 + +--S 208 of 500 +a0241:= integrate(t0241,x) +--R +--R +--R x +--R ++ %R b + a 2 +--R (126) | cosh(--------) d%R +--R ++ %R d + c +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +--m0241:= a0241-r0241 +--E 209 + +--S 210 of 500 +--d0241:= D(m0241,x) +--E 210 + +--S 211 of 500 +t0242:= x^2*cosh(a+b*x^2) +--R +--R +--R 2 2 +--R (127) x cosh(b x + a) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0242:= 1/8/b^(3/2)*(%pi^(1/2)*erf(b^(1/2)*x)+%i*exp(2*a)*%pi^(1/2)*_ + erf(%i*b^(1/2)*x)+4*x*sinh(a+b*x^2)*exp(a)*b^(1/2))*exp(-a) +--R +--R +--R (128) +--R - a +---+ +-+ - a 2a +---+ +-+ +--R %e \|%pi erf(x\|b ) + %i %e %e \|%pi erf(%i x\|b ) +--R + +--R - a a 2 +-+ +--R 4x %e %e sinh(b x + a)\|b +--R / +--R +-+ +--R 8b\|b +--R Type: Expression(Complex(Integer)) +--E 212 + +--S 213 of 500 +a0242:= integrate(t0242,x) +--R +--R +--R x +--R ++ 2 2 +--R (129) | %R cosh(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +--m0242:= a0242-r0242 +--E 214 + +--S 215 of 500 +--d0242:= D(m0242,x) +--E 215 + +--S 216 of 500 +t0243:= cosh(a+b*x^2)/x^2 +--R +--R +--R 2 +--R cosh(b x + a) +--R (130) -------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0243:= -cosh(a+b*x^2)/x-1/2*b^(1/2)*%pi^(1/2)*erf(b^(1/2)*x)/_ + (exp(1)^a)+1/2*b^(1/2)*exp(1)^a*%pi^(1/2)*erfi(b^(1/2)*x) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 217 + +--S 218 of 500 +a0243:= integrate(t0243,x) +--R +--R +--R x 2 +--R ++ cosh(%R b + a) +--R (131) | -------------- d%R +--R ++ 2 +--R %R +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +--m0243:= a0243-r0243 +--E 219 + +--S 220 of 500 +--d0243:= D(m0243,x) +--E 220 + +--S 221 of 500 +t0244:= cosh(a+b*x^2)/x^3 +--R +--R +--R 2 +--R cosh(b x + a) +--R (132) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0244:= -1/2*cosh(a+b*x^2)/x^2+1/2*b*Chi(b*x^2)*sinh(a)+_ + 1/2*b*cosh(a)*Shi(b*x^2) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 222 + +--S 223 of 500 +a0244:= integrate(t0244,x) +--R +--R +--R x 2 +--R ++ cosh(%R b + a) +--R (133) | -------------- d%R +--R ++ 3 +--R %R +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +--m0244:= a0244-r0244 +--E 224 + +--S 225 of 500 +--d0244:= D(m0244,x) +--E 225 + +--S 226 of 500 +t0245:= cosh(a+b*x^2)^2/x^3 +--R +--R +--R 2 2 +--R cosh(b x + a) +--R (134) --------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0245:= -1/4*(1+cosh(2*a+2*b*x^2)-2*b*Chi(2*b*x^2)*sinh(2*a)*x^2-_ + 2*b*cosh(2*a)*Shi(2*b*x^2)*x^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 500 +a0245:= integrate(t0245,x) +--R +--R +--R x 2 2 +--R ++ cosh(%R b + a) +--R (135) | --------------- d%R +--R ++ 3 +--R %R +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +--m0245:= a0245-r0245 +--E 229 + +--S 230 of 500 +--d0245:= D(m0245,x) +--E 230 + +--S 231 of 500 +t0246:= x^2*cosh(a+b*x^2)^3 +--R +--R +--R 2 2 3 +--R (136) x cosh(b x + a) +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0246:= 1/288*exp(-3*a)*(27*%pi^(1/2)*erf(b^(1/2)*x)*exp(2*a)+_ + %pi^(1/2)*3^(1/2)*erf(3^(1/2)*b^(1/2)*x)+_ + 27*%i*exp(4*a)*%pi^(1/2)*erf(%i*b^(1/2)*x)+_ + %i*exp(6*a)*3^(1/2)*%pi^(1/2)*erf(%i*3^(1/2)*b^(1/2)*x)+_ + 108*x*sinh(a+b*x^2)*exp(3*a)*b^(1/2)+_ + 12*x*sinh(3*a+3*b*x^2)*exp(3*a)*b^(1/2))/b^(3/2) +--R +--R +--R (137) +--R +-+ - 3a +---+ +-+ +-+ +-+ - 3a 6a +---+ +-+ +-+ +--R \|3 %e \|%pi erf(x\|3 \|b ) + %i\|3 %e %e \|%pi erf(%i x\|3 \|b ) +--R + +--R - 3a 2a +---+ +-+ - 3a 4a +---+ +-+ +--R 27%e %e \|%pi erf(x\|b ) + 27%i %e %e \|%pi erf(%i x\|b ) +--R + +--R - 3a 3a 2 - 3a 3a 2 +-+ +--R (12x %e %e sinh(3b x + 3a) + 108x %e %e sinh(b x + a))\|b +--R / +--R +-+ +--R 288b\|b +--R Type: Expression(Complex(Integer)) +--E 232 + +--S 233 of 500 +a0246:= integrate(t0246,x) +--R +--R +--R x +--R ++ 2 2 3 +--R (138) | %R cosh(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +--m0246:= a0246-r0246 +--E 234 + +--S 235 of 500 +--d0246:= D(m0246,x) +--E 235 + +--S 236 of 500 +t0247:= cosh(a+b*x^2)^3 +--R +--R +--R 2 3 +--R (139) cosh(b x + a) +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0247:= -1/48*%pi^(1/2)*exp(-3*a)*(-9*erf(b^(1/2)*x)*exp(2*a)-_ + 3^(1/2)*erf(3^(1/2)*b^(1/2)*x)+9*%i*exp(4*a)*erf(%i*b^(1/2)*x)+_ + %i*exp(6*a)*3^(1/2)*erf(%i*3^(1/2)*b^(1/2)*x))/b^(1/2) +--R +--R +--R (140) +--R +-+ - 3a +---+ +-+ +-+ +-+ - 3a 6a +---+ +-+ +-+ +--R \|3 %e \|%pi erf(x\|3 \|b ) - %i\|3 %e %e \|%pi erf(%i x\|3 \|b ) +--R + +--R - 3a 2a +---+ +-+ - 3a 4a +---+ +-+ +--R 9%e %e \|%pi erf(x\|b ) - 9%i %e %e \|%pi erf(%i x\|b ) +--R / +--R +-+ +--R 48\|b +--R Type: Expression(Complex(Integer)) +--E 237 + +--S 238 of 500 +a0247:= integrate(t0247,x) +--R +--R +--R x +--R ++ 2 3 +--R (141) | cosh(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +--m0247:= a0247-r0247 +--E 239 + +--S 240 of 500 +--d0247:= D(m0247,x) +--E 240 + +--S 241 of 500 +t0248:= cosh(a+b*x^2)^3/x^3 +--R +--R +--R 2 3 +--R cosh(b x + a) +--R (142) --------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0248:= -1/8*(3*cosh(a+b*x^2)+cosh(3*a+3*b*x^2)-_ + 3*b*Chi(b*x^2)*sinh(a)*x^2-3*b*Chi(3*b*x^2)*sinh(3*a)*x^2-_ + 3*b*cosh(a)*Shi(b*x^2)*x^2-3*b*cosh(3*a)*Shi(3*b*x^2)*x^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 242 + +--S 243 of 500 +a0248:= integrate(t0248,x) +--R +--R +--R x 2 3 +--R ++ cosh(%R b + a) +--R (143) | --------------- d%R +--R ++ 3 +--R %R +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +--m0248:= a0248-r0248 +--E 244 + +--S 245 of 500 +--d0248:= D(m0248,x) +--E 245 + +--S 246 of 500 +t0249:= cosh(a+b*x^n) +--R +--R +--R n +--R (144) cosh(b x + a) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0249:= -1/2*x*(exp(a)*Gamma(1/n,-b*x^n)*(-b*x^n)^(-1/n)+_ + Gamma(1/n,b*x^n)*exp(-a)*(b*x^n)^(-1/n))/n +--R +--R +--R 1 1 +--R - - - - +--R - a n n _ 1 n a n n _ 1 n +--R - x %e (b x ) | (-,b x ) - x %e (- b x ) | (-,- b x ) +--R n n +--R (145) ----------------------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0249:= integrate(t0249,x) +--R +--R +--R x +--R ++ n +--R (146) | cosh(b %R + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +--m0249:= a0249-r0249 +--E 249 + +--S 250 of 500 +--d0249:= D(m0249,x) +--E 250 + +--S 251 of 500 +t0250:= cosh(a+b*x^n)^2 +--R +--R +--R n 2 +--R (147) cosh(b x + a) +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0250:= -1/2*x*(2^(-(1+n)/n)*exp(2*a)*(-b*x^n)^(-1/n)*_ + Gamma(1/n,-2*b*x^n)+2^(-(1+n)/n)*exp(-2*a)*(b*x^n)^(-1/n)*_ + Gamma(1/n,2*b*x^n)-n)/n +--R +--R +--R (148) +--R - n - 1 1 +--R ------- - - +--R - 2a n n n _ 1 n +--R - x %e 2 (b x ) | (-,2b x ) +--R n +--R + +--R - n - 1 1 +--R ------- - - +--R 2a n n n _ 1 n +--R - x %e 2 (- b x ) | (-,- 2b x ) + n x +--R n +--R / +--R 2n +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0250:= integrate(t0250,x) +--R +--R +--R x +--R ++ n 2 +--R (149) | cosh(b %R + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +--m0250:= a0250-r0250 +--E 254 + +--S 255 of 500 +--d0250:= D(m0250,x) +--E 255 + +--S 256 of 500 +t0251:= cosh(a+b*x^n)^3 +--R +--R +--R n 3 +--R (150) cosh(b x + a) +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0251:= -1/8*x*(exp(3*a)*Gamma(1/n,-3*b*x^n)*3^(-1/n)*(-b*x^n)^(-1/n)+_ + 3*exp(a)*Gamma(1/n,-b*x^n)*(-b*x^n)^(-1/n)+_ + 3*Gamma(1/n,b*x^n)*exp(-a)*(b*x^n)^(-1/n)+_ + Gamma(1/n,3*b*x^n)*3^(-1/n)*exp(-3*a)*(b*x^n)^(-1/n))/n +--R +--R +--R (151) +--R 1 1 1 +--R - - - - - - +--R - 3a n n n _ 1 n - a n n _ 1 n +--R - x %e 3 (b x ) | (-,3b x ) - 3x %e (b x ) | (-,b x ) +--R n n +--R + +--R 1 1 1 +--R - - - - - - +--R a n n _ 1 n 3a n n n _ 1 n +--R - 3x %e (- b x ) | (-,- b x ) - x %e 3 (- b x ) | (-,- 3b x ) +--R n n +--R / +--R 8n +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0251:= integrate(t0251,x) +--R +--R +--R x +--R ++ n 3 +--R (152) | cosh(b %R + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +--m0251:= a0251-r0251 +--E 259 + +--S 260 of 500 +--d0251:= D(m0251,x) +--E 260 + +--S 261 of 500 +t0252:= x^m*cosh(a+b*x^n) +--R +--R +--R m n +--R (153) x cosh(b x + a) +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0252:= -1/2*x*x^m*(exp(a)*Gamma((1+m)/n,-b*x^n)*(-b*x^n)^(-(1+m)/n)+_ + Gamma((1+m)/n,b*x^n)*exp(-a)*(b*x^n)^(-(1+m)/n))/n +--R +--R +--R (154) +--R - m - 1 +--R ------- +--R - a m n n _ m + 1 n +--R - x %e x (b x ) | (-----,b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R a m n n _ m + 1 n +--R - x %e x (- b x ) | (-----,- b x ) +--R n +--R / +--R 2n +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0252:= integrate(t0252,x) +--R +--R +--R x +--R ++ m n +--R (155) | %R cosh(b %R + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +--m0252:= a0252-r0252 +--E 264 + +--S 265 of 500 +--d0252:= D(m0252,x) +--E 265 + +--S 266 of 500 +t0253:= x^m*cosh(a+b*x^n)^2 +--R +--R +--R m n 2 +--R (156) x cosh(b x + a) +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0253:= x^(1+m)/(2+2*m)-2^(-2-(1+m)/n)*exp(1)^(2*a)*x^(1+m)*_ + Gamma((1+m)/n,-2*b*x^n)/((-b*x^n)^((1+m)/n))/n-_ + 2^(-2-(1+m)/n)*x^(1+m)*Gamma((1+m)/n,2*b*x^n)/_ + (exp(1)^(2*a))/((b*x^n)^((1+m)/n))/n +--R +--R +--R (157) +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R n m + 1 n n _ m + 1 n +--R (- 2m - 2)2 x (- b x ) | (-----,2b x ) +--R n +--R + +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R 2a 2 n m + 1 n n _ m + 1 n +--R (- 2m - 2)(%e ) 2 x (b x ) | (-----,- 2b x ) +--R n +--R + +--R m + 1 m + 1 +--R ----- ----- +--R 2a m + 1 n n n n +--R n %e x (- b x ) (b x ) +--R / +--R m + 1 m + 1 +--R ----- ----- +--R 2a n n n n +--R (2m + 2)n %e (- b x ) (b x ) +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0253:= integrate(t0253,x) +--R +--R +--R x +--R ++ m n 2 +--R (158) | %R cosh(b %R + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +--m0253:= a0253-r0253 +--E 269 + +--S 270 of 500 +--d0253:= D(m0253,x) +--E 270 + +--S 271 of 500 +t0254:= x^m*cosh(a+b*x^n)^3 +--R +--R +--R m n 3 +--R (159) x cosh(b x + a) +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0254:= -1/8*x*x^m*(exp(3*a)*Gamma((1+m)/n,-3*b*x^n)*3^(-(1+m)/n)*_ + (-b*x^n)^(-(1+m)/n)+3*exp(a)*Gamma((1+m)/n,-b*x^n)*_ + (-b*x^n)^(-(1+m)/n)+3*Gamma((1+m)/n,b*x^n)*_ + exp(-a)*(b*x^n)^(-(1+m)/n)+Gamma((1+m)/n,3*b*x^n)*_ + 3^(-(1+m)/n)*exp(-3*a)*(b*x^n)^(-(1+m)/n))/n +--R +--R +--R (160) +--R - m - 1 - m - 1 +--R ------- ------- +--R - 3a n m n n _ m + 1 n +--R - x %e 3 x (b x ) | (-----,3b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R - a m n n _ m + 1 n +--R - 3x %e x (b x ) | (-----,b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R a m n n _ m + 1 n +--R - 3x %e x (- b x ) | (-----,- b x ) +--R n +--R + +--R - m - 1 - m - 1 +--R ------- ------- +--R 3a n m n n _ m + 1 n +--R - x %e 3 x (- b x ) | (-----,- 3b x ) +--R n +--R / +--R 8n +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0254:= integrate(t0254,x) +--R +--R +--R x +--R ++ m n 3 +--R (161) | %R cosh(b %R + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +--m0254:= a0254-r0254 +--E 274 + +--S 275 of 500 +--d0254:= D(m0254,x) +--E 275 + +--S 276 of 500 +t0255:= cosh(a+b/x) +--R +--R +--R a x + b +--R (162) cosh(-------) +--R x +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0255:= x*cosh(a+b/x)-b*Chi(b/x)*sinh(a)-b*cosh(a)*Shi(b/x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 277 + +--S 278 of 500 +a0255:= integrate(t0255,x) +--R +--R +--R x +--R ++ b + %R a +--R (163) | cosh(--------)d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +--m0255:= a0255-r0255 +--E 279 + +--S 280 of 500 +--d0255:= D(m0255,x) +--E 280 + +--S 281 of 500 +t0256:= cosh(a+b/x)/x +--R +--R +--R a x + b +--R cosh(-------) +--R x +--R (164) ------------- +--R x +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0256:= -cosh(a)*Chi(b/x)-sinh(a)*Shi(b/x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 500 +a0256:= integrate(t0256,x) +--R +--R +--R b + %R a +--R x cosh(--------) +--R ++ %R +--R (165) | -------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +--m0256:= a0256-r0256 +--E 284 + +--S 285 of 500 +--d0256:= D(m0256,x) +--E 285 + +--S 286 of 500 +t0257:= cosh(a+b/x^2)/x^4 +--R +--R +--R 2 +--R a x + b +--R cosh(--------) +--R 2 +--R x +--R (166) -------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0257:= -1/8*%pi^(1/2)*erf(b^(1/2)/x)/(exp(1)^a)/b^(3/2)+_ + 1/8*exp(1)^a*%pi^(1/2)*erfi(b^(1/2)/x)/b^(3/2)-1/2*sinh(a+b/x^2)/b/x +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 287 + +--S 288 of 500 +a0257:= integrate(t0257,x) +--R +--R +--R 2 +--R b + %R a +--R cosh(--------) +--R x 2 +--R ++ %R +--R (167) | -------------- d%R +--R ++ 4 +--R %R +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +--m0257:= a0257-r0257 +--E 289 + +--S 290 of 500 +--d0257:= D(m0257,x) +--E 290 + +--S 291 of 500 +t0258:= x/cosh(x)^(3/2)+x*cosh(x)^(1/2) +--R +--R +--R 2 +--R x cosh(x) + x +--R (168) ----------------- +--R +-------+ +--R cosh(x)\|cosh(x) +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0258:= -2*(2*cosh(x)-x*sinh(x))/cosh(x)^(1/2) +--R +--R +--R 2x sinh(x) - 4cosh(x) +--R (169) --------------------- +--R +-------+ +--R \|cosh(x) +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0258:= integrate(t0258,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 293 + +--S 294 of 500 +--m0258:= a0258-r0258 +--E 294 + +--S 295 of 500 +--d0258:= D(m0258,x) +--E 295 + +--S 296 of 500 +t0259:= x/cosh(x)^(5/2)-1/3*x/cosh(x)^(1/2) +--R +--R +--R 2 +--R - x cosh(x) + 3x +--R (170) ------------------- +--R 2 +-------+ +--R 3cosh(x) \|cosh(x) +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0259:= 2/3*(2*cosh(x)+x*sinh(x))/cosh(x)^(3/2) +--R +--R +--R 2x sinh(x) + 4cosh(x) +--R (171) --------------------- +--R +-------+ +--R 3cosh(x)\|cosh(x) +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0259:= integrate(t0259,x) +--R +--R +--R (172) +--R 3 2 +--R (4x + 8)sinh(x) + (12x + 24)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((12x + 24)cosh(x) - 4x + 8)sinh(x) + (4x + 8)cosh(x) +--R + +--R (- 4x + 8)cosh(x) +--R * +--R +-------+ +--R \|cosh(x) +--R / +--R 4 3 2 2 +--R 3sinh(x) + 12cosh(x)sinh(x) + (18cosh(x) + 6)sinh(x) +--R + +--R 3 4 2 +--R (12cosh(x) + 12cosh(x))sinh(x) + 3cosh(x) + 6cosh(x) + 3 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0259:= a0259-r0259 +--R +--R +--R (173) +--R 5 4 +--R - 2x sinh(x) + (- 8x - 4)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((- 8x - 8)cosh(x) - 4x)sinh(x) +--R + +--R 3 2 +--R (4x cosh(x) + (- 8x - 8)cosh(x))sinh(x) +--R + +--R 4 2 5 +--R ((10x + 8)cosh(x) + (- 8x - 8)cosh(x) - 2x)sinh(x) + (4x + 4)cosh(x) +--R + +--R 3 +--R - 4x cosh(x) - 4cosh(x) +--R / +--R 4 2 3 3 2 +--R 3cosh(x)sinh(x) + 12cosh(x) sinh(x) + (18cosh(x) + 6cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (12cosh(x) + 12cosh(x) )sinh(x) + 3cosh(x) + 6cosh(x) + 3cosh(x) +--R * +--R +-------+ +--R \|cosh(x) +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0259:= D(m0259,x) +--R +--R +--R (174) +--R 8 7 2 6 +--R 3x sinh(x) + 18x cosh(x)sinh(x) + ((45x + 4)cosh(x) + 9x)sinh(x) +--R + +--R 3 5 +--R ((54x + 16)cosh(x) + 36x cosh(x))sinh(x) +--R + +--R 4 2 4 +--R ((15x + 20)cosh(x) + (48x + 8)cosh(x) + 9x)sinh(x) +--R + +--R 5 3 3 +--R (- 42x cosh(x) + (36x + 24)cosh(x) + 18x cosh(x))sinh(x) +--R + +--R 6 4 2 +--R ((- 57x - 20)cosh(x) + (45x + 24)cosh(x) + (x + 4)cosh(x) + 3x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R ((- 30x - 16)cosh(x) + (48x + 8)cosh(x) + (- 18x + 8)cosh(x) )sinh(x) +--R + +--R 8 6 4 2 +--R (- 6x - 4)cosh(x) + 18x cosh(x) + (- 10x + 4)cosh(x) - 2x cosh(x) +--R / +--R 2 6 3 5 +--R 3cosh(x) sinh(x) + 18cosh(x) sinh(x) +--R + +--R 4 2 4 5 3 3 +--R (45cosh(x) + 9cosh(x) )sinh(x) + (60cosh(x) + 36cosh(x) )sinh(x) +--R + +--R 6 4 2 2 +--R (45cosh(x) + 54cosh(x) + 9cosh(x) )sinh(x) +--R + +--R 7 5 3 8 6 +--R (18cosh(x) + 36cosh(x) + 18cosh(x) )sinh(x) + 3cosh(x) + 9cosh(x) +--R + +--R 4 2 +--R 9cosh(x) + 3cosh(x) +--R * +--R +-------+ +--R \|cosh(x) +--R Type: Expression(Integer) +--E 300 + +--S 301 of 500 +t0260:= x/cosh(x)^(7/2)+3/5*x*cosh(x)^(1/2) +--R +--R +--R 4 +--R 3x cosh(x) + 5x +--R (175) ------------------- +--R 3 +-------+ +--R 5cosh(x) \|cosh(x) +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0260:= -2/15*(-2*cosh(x)+18*cosh(x)^3-3*x*sinh(x)-_ + 9*x*sinh(x)*cosh(x)^2)/cosh(x)^(5/2) +--R +--R +--R 2 3 +--R (18x cosh(x) + 6x)sinh(x) - 36cosh(x) + 4cosh(x) +--R (176) -------------------------------------------------- +--R 2 +-------+ +--R 15cosh(x) \|cosh(x) +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0260:= integrate(t0260,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 303 + +--S 304 of 500 +--m0260:= a0260-r0260 +--E 304 + +--S 305 of 500 +--d0260:= D(m0260,x) +--E 305 + +--S 306 of 500 +t0261:= x^2/cosh(x)^(3/2)+x^2*cosh(x)^(1/2) +--R +--R +--R 2 2 2 +--R x cosh(x) + x +--R (177) ----------------- +--R +-------+ +--R cosh(x)\|cosh(x) +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0261:= -8*x*cosh(x)^(1/2)-16*%i*_ + EllipticE(1/2*%i*x,2)+2*x^2*sinh(x)/cosh(x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 307 + +--S 308 of 500 +a0261:= integrate(t0261,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 308 + +--S 309 of 500 +--m0261:= a0261-r0261 +--E 309 + +--S 310 of 500 +--d0261:= D(m0261,x) +--E 310 + +--S 311 of 500 +t0262:= cosh(a+b*log(c*x^n)) +--R +--R +--R n +--R (178) cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0262:= -x*(cosh(a+b*log(c*x^n))-_ + b*n*sinh(a+b*log(c*x^n)))/(-1+b^2*n^2) +--R +--R +--R n n +--R b n x sinh(b log(c x ) + a) - x cosh(b log(c x ) + a) +--R (179) ----------------------------------------------------- +--R 2 2 +--R b n - 1 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0262:= integrate(t0262,x) +--R +--R +--R (180) +--R b n x sinh(b n log(x) + b log(c) + a) - x cosh(b n log(x) + b log(c) + a) +--R ------------------------------------------------------------------------- +--R 2 2 +--R b n - 1 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0262:= a0262-r0262 +--R +--R +--R (181) +--R n n +--R - b n x sinh(b log(c x ) + a) + x cosh(b log(c x ) + a) +--R + +--R b n x sinh(b n log(x) + b log(c) + a) - x cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n - 1 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0262:= D(m0262,x) +--R +--R +--R (182) +--R n n - 1 n +--R (- b n x + b n x x )sinh(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n +--R (x - b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n - 1)x cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n - 1)x +--R Type: Expression(Integer) +--E 315 + +--S 316 of 500 +t0263:= x*cosh(a+b*log(c*x^n)) +--R +--R +--R n +--R (183) x cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0263:= -x^2*(2*cosh(a+b*log(c*x^n))-b*n*sinh(a+b*log(c*x^n)))/(-4+b^2*n^2) +--R +--R +--R 2 n 2 n +--R b n x sinh(b log(c x ) + a) - 2x cosh(b log(c x ) + a) +--R (184) ------------------------------------------------------ +--R 2 2 +--R b n - 4 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0263:= integrate(t0263,x) +--R +--R +--R (185) +--R 2 2 +--R b n x sinh(b n log(x) + b log(c) + a) - 2x cosh(b n log(x) + b log(c) + a) +--R -------------------------------------------------------------------------- +--R 2 2 +--R b n - 4 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0263:= a0263-r0263 +--R +--R +--R (186) +--R 2 n 2 n +--R - b n x sinh(b log(c x ) + a) + 2x cosh(b log(c x ) + a) +--R + +--R 2 2 +--R b n x sinh(b n log(x) + b log(c) + a) - 2x cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n - 4 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0263:= D(m0263,x) +--R +--R +--R (187) +--R n 2 n - 1 n +--R (- 2b n x x + 2b n x x )sinh(b log(c x ) + a) +--R + +--R n 2 2 2 n - 1 n +--R (4x x - b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n - 4)x x cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n - 4)x +--R Type: Expression(Integer) +--E 320 + +--S 321 of 500 +t0264:= x^2*cosh(a+b*log(c*x^n)) +--R +--R +--R 2 n +--R (188) x cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0264:= -x^3*(3*cosh(a+b*log(c*x^n))-b*n*sinh(a+b*log(c*x^n)))/(-9+b^2*n^2) +--R +--R +--R 3 n 3 n +--R b n x sinh(b log(c x ) + a) - 3x cosh(b log(c x ) + a) +--R (189) ------------------------------------------------------ +--R 2 2 +--R b n - 9 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0264:= integrate(t0264,x) +--R +--R +--R (190) +--R 3 3 +--R b n x sinh(b n log(x) + b log(c) + a) - 3x cosh(b n log(x) + b log(c) + a) +--R -------------------------------------------------------------------------- +--R 2 2 +--R b n - 9 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0264:= a0264-r0264 +--R +--R +--R (191) +--R 3 n 3 n +--R - b n x sinh(b log(c x ) + a) + 3x cosh(b log(c x ) + a) +--R + +--R 3 3 +--R b n x sinh(b n log(x) + b log(c) + a) - 3x cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n - 9 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0264:= D(m0264,x) +--R +--R +--R (192) +--R 2 n 3 n - 1 n +--R (- 3b n x x + 3b n x x )sinh(b log(c x ) + a) +--R + +--R 2 n 2 2 3 n - 1 n +--R (9x x - b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 2 n +--R (b n - 9)x x cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n - 9)x +--R Type: Expression(Integer) +--E 325 + +--S 326 of 500 +t0265:= cosh(a+b*log(c*x^n))/x^2 +--R +--R +--R n +--R cosh(b log(c x ) + a) +--R (193) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0265:= (cosh(a+b*log(c*x^n))+b*n*sinh(a+b*log(c*x^n)))/(-1+b^2*n^2)/x +--R +--R +--R n n +--R b n sinh(b log(c x ) + a) + cosh(b log(c x ) + a) +--R (194) ------------------------------------------------- +--R 2 2 +--R (b n - 1)x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0265:= integrate(t0265,x) +--R +--R +--R (195) +--R b n sinh(b n log(x) + b log(c) + a) + cosh(b n log(x) + b log(c) + a) +--R --------------------------------------------------------------------- +--R 2 2 +--R (b n - 1)x +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0265:= a0265-r0265 +--R +--R +--R (196) +--R n n +--R - b n sinh(b log(c x ) + a) - cosh(b log(c x ) + a) +--R + +--R b n sinh(b n log(x) + b log(c) + a) + cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R (b n - 1)x +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0265:= D(m0265,x) +--R +--R +--R (197) +--R n n - 1 n +--R (b n x - b n x x )sinh(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n +--R (x - b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n - 1)x cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (b n - 1)x x +--R Type: Expression(Integer) +--E 330 + +--S 331 of 500 +t0266:= x^m*cosh(a+b*log(c*x^n)) +--R +--R +--R m n +--R (198) x cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0266:= (1+m)*x^(1+m)*cosh(a+b*log(c*x^n))/((1+m)^2-b^2*n^2)-_ + b*n*x^(1+m)*sinh(a+b*log(c*x^n))/((1+m)^2-b^2*n^2) +--R +--R +--R (199) +--R m + 1 n m + 1 n +--R b n x sinh(b log(c x ) + a) + (- m - 1)x cosh(b log(c x ) + a) +--R ---------------------------------------------------------------------- +--R 2 2 2 +--R b n - m - 2m - 1 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0266:= integrate(t0266,x) +--R +--R +--R (200) +--R (b n x sinh(m log(x)) + b n x cosh(m log(x))) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R (- m - 1)x cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R (- m - 1)x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 +--R b n - m - 2m - 1 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0266:= a0266-r0266 +--R +--R +--R (201) +--R m + 1 n m + 1 n +--R - b n x sinh(b log(c x ) + a) + (m + 1)x cosh(b log(c x ) + a) +--R + +--R (b n x sinh(m log(x)) + b n x cosh(m log(x))) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R (- m - 1)x cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R (- m - 1)x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 +--R b n - m - 2m - 1 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0266:= D(m0266,x) +--R +--R +--R (202) +--R m n m + 1 n - 1 n +--R ((- b m - b)n x x + (b m + b)n x x )sinh(b log(c x ) + a) +--R + +--R 2 m n 2 2 m + 1 n - 1 n +--R ((m + 2m + 1)x x - b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 2 n +--R (b n - m - 2m - 1)x cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R 2 2 2 n +--R (b n - m - 2m - 1)x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (b n - m - 2m - 1)x +--R Type: Expression(Integer) +--E 335 + +--S 336 of 500 +t0267:= cosh(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (203) cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0267:= -x*(-2*b^2*n^2+cosh(a+b*log(c*x^n))^2-_ + 2*b*n*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n)))/(-1+4*b^2*n^2) +--R +--R +--R (204) +--R n n +--R 2b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 2 +--R - x cosh(b log(c x ) + a) + 2b n x +--R / +--R 2 2 +--R 4b n - 1 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0267:= integrate(t0267,x) +--R +--R +--R (205) +--R 2 +--R - x sinh(b n log(x) + b log(c) + a) +--R + +--R 4b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R - x cosh(b n log(x) + b log(c) + a) + (4b n - 1)x +--R / +--R 2 2 +--R 8b n - 2 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0267:= a0267-r0267 +--R +--R +--R (206) +--R n n +--R - 4b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 +--R 2x cosh(b log(c x ) + a) - x sinh(b n log(x) + b log(c) + a) +--R + +--R 4b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 +--R - x cosh(b n log(x) + b log(c) + a) - x +--R / +--R 2 2 +--R 8b n - 2 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0267:= D(m0267,x) +--R +--R +--R (207) +--R 2 2 n - 1 n 2 +--R - 4b n x x sinh(b log(c x ) + a) +--R + +--R n n - 1 n n +--R (- 4b n x + 4b n x x )cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n 2 +--R (2x - 4b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R (4b n - 1)x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 n +--R (4b n - 1)x cosh(b n log(x) + b log(c) + a) - x +--R / +--R 2 2 n +--R (8b n - 2)x +--R Type: Expression(Integer) +--E 340 + +--S 341 of 500 +t0268:= x*cosh(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (208) x cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0268:= -1/4/(-1+b^2*n^2)*x^2*(-b^2*n^2+2*cosh(a+b*log(c*x^n))^2-_ + 2*b*n*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))) +--R +--R +--R (209) +--R 2 n n +--R 2b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 n 2 2 2 2 +--R - 2x cosh(b log(c x ) + a) + b n x +--R / +--R 2 2 +--R 4b n - 4 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0268:= integrate(t0268,x) +--R +--R +--R (210) +--R 2 2 +--R - x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 +--R 2b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 +--R - x cosh(b n log(x) + b log(c) + a) + (b n - 1)x +--R / +--R 2 2 +--R 4b n - 4 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0268:= a0268-r0268 +--R +--R +--R (211) +--R 2 n n +--R - 2b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 n 2 2 2 +--R 2x cosh(b log(c x ) + a) - x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 +--R 2b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R - x cosh(b n log(x) + b log(c) + a) - x +--R / +--R 2 2 +--R 4b n - 4 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0268:= D(m0268,x) +--R +--R +--R (212) +--R 2 2 2 n - 1 n 2 +--R - b n x x sinh(b log(c x ) + a) +--R + +--R n 2 n - 1 n n +--R (- 2b n x x + 2b n x x )cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 2 n - 1 n 2 +--R (2x x - b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R (b n - 1)x x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 n +--R (b n - 1)x x cosh(b n log(x) + b log(c) + a) - x x +--R / +--R 2 2 n +--R (2b n - 2)x +--R Type: Expression(Integer) +--E 345 + +--S 346 of 500 +t0269:= x^2*cosh(a+b*log(c*x^n))^2 +--R +--R +--R 2 n 2 +--R (213) x cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0269:= -1/3/(-9+4*b^2*n^2)*x^3*(-2*b^2*n^2+9*cosh(a+b*log(c*x^n))^2-_ + 6*b*n*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))) +--R +--R +--R (214) +--R 3 n n +--R 6b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 3 n 2 2 2 3 +--R - 9x cosh(b log(c x ) + a) + 2b n x +--R / +--R 2 2 +--R 12b n - 27 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0269:= integrate(t0269,x) +--R +--R +--R (215) +--R 3 2 +--R - 9x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 +--R 12b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 3 2 2 2 3 +--R - 9x cosh(b n log(x) + b log(c) + a) + (4b n - 9)x +--R / +--R 2 2 +--R 24b n - 54 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0269:= a0269-r0269 +--R +--R +--R (216) +--R 3 n n +--R - 4b n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 3 n 2 3 2 +--R 6x cosh(b log(c x ) + a) - 3x sinh(b n log(x) + b log(c) + a) +--R + +--R 3 +--R 4b n x cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 3 2 3 +--R - 3x cosh(b n log(x) + b log(c) + a) - 3x +--R / +--R 2 2 +--R 8b n - 18 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0269:= D(m0269,x) +--R +--R +--R (217) +--R 2 2 3 n - 1 n 2 +--R - 4b n x x sinh(b log(c x ) + a) +--R + +--R 2 n 3 n - 1 n n +--R (- 12b n x x + 12b n x x )cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 n 2 2 3 n - 1 n 2 +--R (18x x - 4b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 2 n 2 +--R (4b n - 9)x x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 2 n +--R (4b n - 9)x x cosh(b n log(x) + b log(c) + a) - 9x x +--R / +--R 2 2 n +--R (8b n - 18)x +--R Type: Expression(Integer) +--E 350 + +--S 351 of 500 +t0270:= cosh(a+b*log(c*x^n))^2/x^2 +--R +--R +--R n 2 +--R cosh(b log(c x ) + a) +--R (218) ---------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0270:= (-2*b^2*n^2+cosh(a+b*log(c*x^n))^2+_ + 2*b*n*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n)))/(-1+4*b^2*n^2)/x +--R +--R +--R (219) +--R n n n 2 +--R 2b n cosh(b log(c x ) + a)sinh(b log(c x ) + a) + cosh(b log(c x ) + a) +--R + +--R 2 2 +--R - 2b n +--R / +--R 2 2 +--R (4b n - 1)x +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0270:= integrate(t0270,x) +--R +--R +--R (220) +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 4b n cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R cosh(b n log(x) + b log(c) + a) - 4b n + 1 +--R / +--R 2 2 +--R (8b n - 2)x +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0270:= a0270-r0270 +--R +--R +--R (221) +--R n n +--R - 4b n cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 +--R - 2cosh(b log(c x ) + a) + sinh(b n log(x) + b log(c) + a) +--R + +--R 4b n cosh(b n log(x) + b log(c) + a)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 +--R cosh(b n log(x) + b log(c) + a) + 1 +--R / +--R 2 2 +--R (8b n - 2)x +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0270:= D(m0270,x) +--R +--R +--R (222) +--R 2 2 n - 1 n 2 +--R - 4b n x x sinh(b log(c x ) + a) +--R + +--R n n - 1 n n +--R (4b n x - 4b n x x )cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n 2 +--R (2x - 4b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R (4b n - 1)x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 n +--R (4b n - 1)x cosh(b n log(x) + b log(c) + a) - x +--R / +--R 2 2 2 n +--R (8b n - 2)x x +--R Type: Expression(Integer) +--E 355 + +--S 356 of 500 +t0271:= x^m*cosh(a+b*log(c*x^n))^2 +--R +--R +--R m n 2 +--R (223) x cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0271:= -2*b^2*n^2*x^(1+m)/(1+m)/((1+m)^2-4*b^2*n^2)+_ + (1+m)*x^(1+m)*cosh(a+b*log(c*x^n))^2/((1+m)^2-4*b^2*n^2)-_ + 2*b*n*x^(1+m)*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))/((1+m)^2-_ + 4*b^2*n^2) +--R +--R +--R (224) +--R m + 1 n n +--R (2b m + 2b)n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 m + 1 n 2 2 2 m + 1 +--R (- m - 2m - 1)x cosh(b log(c x ) + a) + 2b n x +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n - m - 3m - 3m - 1 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0271:= integrate(t0271,x) +--R +--R +--R (225) +--R 2 2 +--R ((- m - 2m - 1)x sinh(m log(x)) + (- m - 2m - 1)x cosh(m log(x))) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R (4b m + 4b)n x cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R (4b m + 4b)n x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- m - 2m - 1)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (4b n - m - 2m - 1)x +--R * +--R sinh(m log(x)) +--R + +--R 2 2 +--R (- m - 2m - 1)x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (4b n - m - 2m - 1)x cosh(m log(x)) +--R / +--R 2 2 2 3 2 +--R (8b m + 8b )n - 2m - 6m - 6m - 2 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0271:= a0271-r0271 +--R +--R +--R (226) +--R m + 1 n n +--R (- 4b m - 4b)n x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 2 m + 1 n 2 +--R (2m + 4m + 2)x cosh(b log(c x ) + a) +--R + +--R 2 2 +--R ((- m - 2m - 1)x sinh(m log(x)) + (- m - 2m - 1)x cosh(m log(x))) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R (4b m + 4b)n x cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R (4b m + 4b)n x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- m - 2m - 1)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (4b n - m - 2m - 1)x +--R * +--R sinh(m log(x)) +--R + +--R 2 2 +--R (- m - 2m - 1)x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 m + 1 +--R (4b n - m - 2m - 1)x cosh(m log(x)) - 4b n x +--R / +--R 2 2 2 3 2 +--R (8b m + 8b )n - 2m - 6m - 6m - 2 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0271:= D(m0271,x) +--R +--R +--R (227) +--R 2 2 m + 1 n - 1 n 2 +--R - 4b n x x sinh(b log(c x ) + a) +--R + +--R m n m + 1 n - 1 n +--R ((- 4b m - 4b)n x x + (4b m + 4b)n x x )cosh(b log(c x ) + a) +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 m n 2 2 m + 1 n - 1 n 2 +--R ((2m + 4m + 2)x x - 4b n x x )cosh(b log(c x ) + a) +--R + +--R 2 2 2 n +--R (4b n - m - 2m - 1)x sinh(m log(x)) +--R + +--R 2 2 2 n +--R (4b n - m - 2m - 1)x cosh(m log(x)) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 +--R (4b n - m - 2m - 1)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n +--R (4b n - m - 2m - 1)x +--R * +--R sinh(m log(x)) +--R + +--R 2 2 2 n 2 +--R (4b n - m - 2m - 1)x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 2 m n +--R (4b n - m - 2m - 1)x cosh(m log(x)) - 4b n x x +--R / +--R 2 2 2 n +--R (8b n - 2m - 4m - 2)x +--R Type: Expression(Integer) +--E 360 + +--S 361 of 500 +t0272:= cosh(a+b*log(c*x^n))^3 +--R +--R +--R n 3 +--R (228) cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0272:= -6*b^2*n^2*x*cosh(a+b*log(c*x^n))/(1-9*b^2*n^2)/(1-b^2*n^2)+_ + x*cosh(a+b*log(c*x^n))^3/(1-9*b^2*n^2)+_ + 6*b^3*n^3*x*sinh(a+b*log(c*x^n))/(1-9*b^2*n^2)/(1-b^2*n^2)-_ + 3*b*n*x*cosh(a+b*log(c*x^n))^2*sinh(a+b*log(c*x^n))/(1-9*b^2*n^2) +--R +--R +--R (229) +--R 3 3 n 2 3 3 n +--R ((3b n - 3b n)x cosh(b log(c x ) + a) + 6b n x)sinh(b log(c x ) + a) +--R + +--R 2 2 n 3 2 2 n +--R (- b n + 1)x cosh(b log(c x ) + a) - 6b n x cosh(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 9b n - 10b n + 1 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0272:= integrate(t0272,x) +--R +--R +--R (230) +--R 3 3 3 +--R (3b n - 3b n)x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- 3b n + 3)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 3 +--R ((9b n - 9b n)x cosh(b n log(x) + b log(c) + a) + (27b n - 3b n)x) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (- b n + 1)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- 27b n + 3)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 36b n - 40b n + 4 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0272:= a0272-r0272 +--R +--R +--R (231) +--R 3 3 n 2 3 3 +--R ((- 12b n + 12b n)x cosh(b log(c x ) + a) - 24b n x) +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 n 3 2 2 n +--R (4b n - 4)x cosh(b log(c x ) + a) + 24b n x cosh(b log(c x ) + a) +--R + +--R 3 3 3 +--R (3b n - 3b n)x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- 3b n + 3)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 3 +--R ((9b n - 9b n)x cosh(b n log(x) + b log(c) + a) + (27b n - 3b n)x) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (- b n + 1)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- 27b n + 3)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 36b n - 40b n + 4 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0272:= D(m0272,x) +--R +--R +--R (232) +--R 4 4 2 2 n - 1 n n 2 +--R (- 24b n + 24b n )x x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 +--R ((- 12b n + 12b n)x + (12b n - 12b n)x x ) +--R * +--R n 2 +--R cosh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 +--R - 24b n x + 24b n x x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 n 4 4 2 2 n - 1 n 3 +--R ((4b n - 4)x + (- 12b n + 12b n )x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n 4 4 n - 1 n +--R (24b n x - 24b n x x )cosh(b log(c x ) + a) +--R + +--R 4 4 2 2 n +--R (27b n - 30b n + 3)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 3 +--R (9b n - 10b n + 1)x cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (27b n - 30b n + 3)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (36b n - 40b n + 4)x +--R Type: Expression(Integer) +--E 365 + +--S 366 of 500 +t0273:= x*cosh(a+b*log(c*x^n))^3 +--R +--R +--R n 3 +--R (233) x cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0273:= -x^2*(12*b^2*n^2*cosh(a+b*log(c*x^n))-8*cosh(a+b*log(c*x^n))^3+_ + 2*cosh(a+b*log(c*x^n))^3*b^2*n^2-6*b^3*n^3*sinh(a+b*log(c*x^n))+_ + 12*b*n*cosh(a+b*log(c*x^n))^2*sinh(a+b*log(c*x^n))-_ + 3*b^3*n^3*cosh(a+b*log(c*x^n))^2*_ + sinh(a+b*log(c*x^n)))/(-4+9*b^2*n^2)/(-4+b^2*n^2) +--R +--R +--R (234) +--R 3 3 2 n 2 3 3 2 n +--R ((3b n - 12b n)x cosh(b log(c x ) + a) + 6b n x )sinh(b log(c x ) + a) +--R + +--R 2 2 2 n 3 2 2 2 n +--R (- 2b n + 8)x cosh(b log(c x ) + a) - 12b n x cosh(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 9b n - 40b n + 16 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0273:= integrate(t0273,x) +--R +--R +--R (235) +--R 3 3 2 3 +--R (3b n - 12b n)x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (- 6b n + 24)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 2 +--R (9b n - 36b n)x cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (27b n - 12b n)x +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 +--R (- 2b n + 8)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (- 54b n + 24)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 36b n - 160b n + 64 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0273:= a0273-r0273 +--R +--R +--R (236) +--R 3 3 2 n 2 3 3 2 +--R ((- 12b n + 48b n)x cosh(b log(c x ) + a) - 24b n x ) +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 2 n 3 2 2 2 n +--R (8b n - 32)x cosh(b log(c x ) + a) + 48b n x cosh(b log(c x ) + a) +--R + +--R 3 3 2 3 +--R (3b n - 12b n)x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (- 6b n + 24)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 2 +--R (9b n - 36b n)x cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (27b n - 12b n)x +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 +--R (- 2b n + 8)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (- 54b n + 24)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 36b n - 160b n + 64 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0273:= D(m0273,x) +--R +--R +--R (237) +--R 4 4 2 2 2 n - 1 n n 2 +--R (- 24b n + 96b n )x x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 2 n - 1 +--R ((- 24b n + 96b n)x x + (24b n - 96b n)x x ) +--R * +--R n 2 +--R cosh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 2 n - 1 +--R - 48b n x x + 48b n x x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 n 4 4 2 2 2 n - 1 n 3 +--R ((16b n - 64)x x + (- 12b n + 48b n )x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n 4 4 2 n - 1 n +--R (96b n x x - 24b n x x )cosh(b log(c x ) + a) +--R + +--R 4 4 2 2 n +--R (27b n - 120b n + 48)x x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 3 +--R (9b n - 40b n + 16)x x cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (27b n - 120b n + 48)x x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (36b n - 160b n + 64)x +--R Type: Expression(Integer) +--E 370 + +--S 371 of 500 +t0274:= x^2*cosh(a+b*log(c*x^n))^3 +--R +--R +--R 2 n 3 +--R (238) x cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0274:= -1/3*x^3*(6*b^2*n^2*cosh(a+b*log(c*x^n))-_ + 9*cosh(a+b*log(c*x^n))^3+cosh(a+b*log(c*x^n))^3*b^2*n^2-_ + 2*b^3*n^3*sinh(a+b*log(c*x^n))+9*b*n*cosh(a+b*log(c*x^n))^2*_ + sinh(a+b*log(c*x^n))-b^3*n^3*cosh(a+b*log(c*x^n))^2*_ + sinh(a+b*log(c*x^n)))/(-1+b^2*n^2)/(-9+b^2*n^2) +--R +--R +--R (239) +--R 3 3 3 n 2 3 3 3 n +--R ((b n - 9b n)x cosh(b log(c x ) + a) + 2b n x )sinh(b log(c x ) + a) +--R + +--R 2 2 3 n 3 2 2 3 n +--R (- b n + 9)x cosh(b log(c x ) + a) - 6b n x cosh(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 3b n - 30b n + 27 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0274:= integrate(t0274,x) +--R +--R +--R (240) +--R 3 3 3 3 +--R (b n - 9b n)x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (- 3b n + 27)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 2 3 3 3 +--R ((3b n - 27b n)x cosh(b n log(x) + b log(c) + a) + (9b n - 9b n)x ) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 3 +--R (- b n + 9)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (- 27b n + 27)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 12b n - 120b n + 108 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0274:= a0274-r0274 +--R +--R +--R (241) +--R 3 3 3 n 2 3 3 3 +--R ((- 4b n + 36b n)x cosh(b log(c x ) + a) - 8b n x ) +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 3 n 3 2 2 3 n +--R (4b n - 36)x cosh(b log(c x ) + a) + 24b n x cosh(b log(c x ) + a) +--R + +--R 3 3 3 3 +--R (b n - 9b n)x sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (- 3b n + 27)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 2 3 3 3 +--R ((3b n - 27b n)x cosh(b n log(x) + b log(c) + a) + (9b n - 9b n)x ) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 3 +--R (- b n + 9)x cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (- 27b n + 27)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 12b n - 120b n + 108 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0274:= D(m0274,x) +--R +--R +--R (242) +--R 4 4 2 2 3 n - 1 n n 2 +--R (- 8b n + 72b n )x x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 3 3 2 n 3 3 3 n - 1 +--R ((- 12b n + 108b n)x x + (12b n - 108b n)x x ) +--R * +--R n 2 +--R cosh(b log(c x ) + a) +--R + +--R 3 3 2 n 3 3 3 n - 1 +--R - 24b n x x + 24b n x x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 2 n 4 4 2 2 3 n - 1 n 3 +--R ((12b n - 108)x x + (- 4b n + 36b n )x x )cosh(b log(c x ) + a) +--R + +--R 2 2 2 n 4 4 3 n - 1 n +--R (72b n x x - 8b n x x )cosh(b log(c x ) + a) +--R + +--R 4 4 2 2 2 n +--R (9b n - 90b n + 81)x x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 n 3 +--R (3b n - 30b n + 27)x x cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 n +--R (9b n - 90b n + 81)x x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (12b n - 120b n + 108)x +--R Type: Expression(Integer) +--E 375 + +--S 376 of 500 +t0275:= cosh(a+b*log(c*x^n))^3/x^2 +--R +--R +--R n 3 +--R cosh(b log(c x ) + a) +--R (243) ---------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0275:= (6*b^2*n^2*cosh(a+b*log(c*x^n))-cosh(a+b*log(c*x^n))^3+_ + cosh(a+b*log(c*x^n))^3*b^2*n^2+6*b^3*n^3*sinh(a+b*log(c*x^n))-_ + 3*b*n*cosh(a+b*log(c*x^n))^2*sinh(a+b*log(c*x^n))+_ + 3*b^3*n^3*cosh(a+b*log(c*x^n))^2*_ + sinh(a+b*log(c*x^n)))/(-1+9*b^2*n^2)/(-1+b^2*n^2)/x +--R +--R +--R (244) +--R 3 3 n 2 3 3 n +--R ((3b n - 3b n)cosh(b log(c x ) + a) + 6b n )sinh(b log(c x ) + a) +--R + +--R 2 2 n 3 2 2 n +--R (b n - 1)cosh(b log(c x ) + a) + 6b n cosh(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R (9b n - 10b n + 1)x +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0275:= integrate(t0275,x) +--R +--R +--R (245) +--R 3 3 3 +--R (3b n - 3b n)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (3b n - 3)cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 3 +--R ((9b n - 9b n)cosh(b n log(x) + b log(c) + a) + 27b n - 3b n) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (b n - 1)cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (27b n - 3)cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R (36b n - 40b n + 4)x +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0275:= a0275-r0275 +--R +--R +--R (246) +--R 3 3 n 2 3 3 n +--R ((- 12b n + 12b n)cosh(b log(c x ) + a) - 24b n )sinh(b log(c x ) + a) +--R + +--R 2 2 n 3 2 2 n +--R (- 4b n + 4)cosh(b log(c x ) + a) - 24b n cosh(b log(c x ) + a) +--R + +--R 3 3 3 +--R (3b n - 3b n)sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (3b n - 3)cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 3 +--R ((9b n - 9b n)cosh(b n log(x) + b log(c) + a) + 27b n - 3b n) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (b n - 1)cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (27b n - 3)cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R (36b n - 40b n + 4)x +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0275:= D(m0275,x) +--R +--R +--R (247) +--R 4 4 2 2 n - 1 n n 2 +--R (- 24b n + 24b n )x x cosh(b log(c x ) + a)sinh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 +--R ((12b n - 12b n)x + (- 12b n + 12b n)x x ) +--R * +--R n 2 +--R cosh(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 +--R 24b n x - 24b n x x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 n 4 4 2 2 n - 1 n 3 +--R ((4b n - 4)x + (- 12b n + 12b n )x x )cosh(b log(c x ) + a) +--R + +--R 2 2 n 4 4 n - 1 n +--R (24b n x - 24b n x x )cosh(b log(c x ) + a) +--R + +--R 4 4 2 2 n +--R (27b n - 30b n + 3)x cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 3 +--R (9b n - 10b n + 1)x cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (27b n - 30b n + 3)x cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 n +--R (36b n - 40b n + 4)x x +--R Type: Expression(Integer) +--E 380 + +--S 381 of 500 +t0276:= x^m*cosh(a+b*log(c*x^n))^3 +--R +--R +--R m n 3 +--R (248) x cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0276:= -6*b^2*(1+m)*n^2*x^(1+m)*cosh(a+b*log(c*x^n))/_ + ((1+m)^2-9*b^2*n^2)/((1+m)^2-b^2*n^2)+(1+m)*x^(1+m)*_ + cosh(a+b*log(c*x^n))^3/((1+m)^2-9*b^2*n^2)+6*b^3*n^3*x^(1+m)*_ + sinh(a+b*log(c*x^n))/((1+m)^2-9*b^2*n^2)/((1+m)^2-b^2*n^2)-_ + 3*b*n*x^(1+m)*cosh(a+b*log(c*x^n))^2*_ + sinh(a+b*log(c*x^n))/((1+m)^2-9*b^2*n^2) +--R +--R +--R (249) +--R 3 3 2 m + 1 n 2 +--R (3b n + (- 3b m - 6b m - 3b)n)x cosh(b log(c x ) + a) +--R + +--R 3 3 m + 1 +--R 6b n x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 2 3 2 m + 1 n 3 +--R ((- b m - b )n + m + 3m + 3m + 1)x cosh(b log(c x ) + a) +--R + +--R 2 2 2 m + 1 n +--R (- 6b m - 6b )n x cosh(b log(c x ) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (- 10b m - 20b m - 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0276:= integrate(t0276,x) +--R +--R +--R (250) +--R 3 3 2 +--R (3b n + (- 3b m - 6b m - 3b)n)x sinh(m log(x)) +--R + +--R 3 3 2 +--R (3b n + (- 3b m - 6b m - 3b)n)x cosh(m log(x)) +--R * +--R 3 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((- 3b m - 3b )n + 3m + 9m + 9m + 3)x +--R * +--R cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R 2 2 2 3 2 +--R ((- 3b m - 3b )n + 3m + 9m + 9m + 3)x cosh(m log(x)) +--R * +--R cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (9b n + (- 9b m - 18b m - 9b)n)x +--R * +--R 2 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (27b n + (- 3b m - 6b m - 3b)n)x +--R * +--R sinh(m log(x)) +--R + +--R 3 3 2 +--R (9b n + (- 9b m - 18b m - 9b)n)x cosh(m log(x)) +--R * +--R 2 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (27b n + (- 3b m - 6b m - 3b)n)x cosh(m log(x)) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((- b m - b )n + m + 3m + 3m + 1)x +--R * +--R 3 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((- 27b m - 27b )n + 3m + 9m + 9m + 3)x +--R * +--R cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(m log(x)) +--R + +--R 2 2 2 3 2 +--R ((- b m - b )n + m + 3m + 3m + 1)x cosh(m log(x)) +--R * +--R 3 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((- 27b m - 27b )n + 3m + 9m + 9m + 3)x cosh(m log(x)) +--R * +--R cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 36b n + (- 40b m - 80b m - 40b )n + 4m + 16m + 24m + 16m + 4 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0276:= a0276-r0276 +--R +--R +--R (251) +--R 3 3 2 m + 1 n 2 +--R (- 12b n + (12b m + 24b m + 12b)n)x cosh(b log(c x ) + a) +--R + +--R 3 3 m + 1 +--R - 24b n x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 2 3 2 m + 1 n 3 +--R ((4b m + 4b )n - 4m - 12m - 12m - 4)x cosh(b log(c x ) + a) +--R + +--R 2 2 2 m + 1 n +--R (24b m + 24b )n x cosh(b log(c x ) + a) +--R + +--R 3 3 2 +--R (3b n + (- 3b m - 6b m - 3b)n)x sinh(m log(x)) +--R + +--R 3 3 2 +--R (3b n + (- 3b m - 6b m - 3b)n)x cosh(m log(x)) +--R * +--R 3 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((- 3b m - 3b )n + 3m + 9m + 9m + 3)x +--R * +--R cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R 2 2 2 3 2 +--R ((- 3b m - 3b )n + 3m + 9m + 9m + 3)x cosh(m log(x)) +--R * +--R cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (9b n + (- 9b m - 18b m - 9b)n)x +--R * +--R 2 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (27b n + (- 3b m - 6b m - 3b)n)x +--R * +--R sinh(m log(x)) +--R + +--R 3 3 2 +--R (9b n + (- 9b m - 18b m - 9b)n)x cosh(m log(x)) +--R * +--R 2 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (27b n + (- 3b m - 6b m - 3b)n)x cosh(m log(x)) +--R * +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((- b m - b )n + m + 3m + 3m + 1)x +--R * +--R 3 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((- 27b m - 27b )n + 3m + 9m + 9m + 3)x +--R * +--R cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(m log(x)) +--R + +--R 2 2 2 3 2 +--R ((- b m - b )n + m + 3m + 3m + 1)x cosh(m log(x)) +--R * +--R 3 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((- 27b m - 27b )n + 3m + 9m + 9m + 3)x cosh(m log(x)) +--R * +--R cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 36b n + (- 40b m - 80b m - 40b )n + 4m + 16m + 24m + 16m + 4 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0276:= D(m0276,x) +--R +--R +--R (252) +--R 4 4 2 2 2 2 2 m + 1 n - 1 n +--R (- 24b n + (24b m + 48b m + 24b )n )x x cosh(b log(c x ) + a) +--R * +--R n 2 +--R sinh(b log(c x ) + a) +--R + +--R 3 3 3 3 2 m n +--R ((- 12b m - 12b )n + (12b m + 36b m + 36b m + 12b)n)x x +--R + +--R 3 3 3 3 2 m + 1 n - 1 +--R ((12b m + 12b )n + (- 12b m - 36b m - 36b m - 12b)n)x x +--R * +--R n 2 +--R cosh(b log(c x ) + a) +--R + +--R 3 3 3 m n 3 3 3 m + 1 n - 1 +--R (- 24b m - 24b )n x x + (24b m + 24b )n x x +--R * +--R n +--R sinh(b log(c x ) + a) +--R + +--R 2 2 2 2 2 4 3 2 m n +--R ((4b m + 8b m + 4b )n - 4m - 16m - 24m - 16m - 4)x x +--R + +--R 4 4 2 2 2 2 2 m + 1 n - 1 +--R (- 12b n + (12b m + 24b m + 12b )n )x x +--R * +--R n 3 +--R cosh(b log(c x ) + a) +--R + +--R 2 2 2 2 2 m n 4 4 m + 1 n - 1 n +--R ((24b m + 48b m + 24b )n x x - 24b n x x )cosh(b log(c x ) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 +--R 27b n + (- 30b m - 60b m - 30b )n + 3m + 12m + 18m + 12m +--R + +--R 3 +--R * +--R n +--R x cosh(b n log(x) + b log(c) + a)sinh(m log(x)) +--R + +--R 4 4 2 2 2 2 2 4 3 2 +--R 27b n + (- 30b m - 60b m - 30b )n + 3m + 12m + 18m + 12m +--R + +--R 3 +--R * +--R n +--R x cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sinh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 n +--R (9b n + (- 10b m - 20b m - 10b )n + m + 4m + 6m + 4m + 1)x +--R * +--R 3 +--R cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 +--R 27b n + (- 30b m - 60b m - 30b )n + 3m + 12m + 18m + 12m +--R + +--R 3 +--R * +--R n +--R x cosh(b n log(x) + b log(c) + a) +--R * +--R sinh(m log(x)) +--R + +--R 4 4 2 2 2 2 2 4 3 2 n +--R (9b n + (- 10b m - 20b m - 10b )n + m + 4m + 6m + 4m + 1)x +--R * +--R 3 +--R cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 n +--R (27b n + (- 30b m - 60b m - 30b )n + 3m + 12m + 18m + 12m + 3)x +--R * +--R cosh(m log(x))cosh(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 n +--R (36b n + (- 40b m - 80b m - 40b )n + 4m + 16m + 24m + 16m + 4)x +--R Type: Expression(Integer) +--E 385 + +--S 386 of 500 +t0277:= tanh(a+b*x) +--R +--R +--R (253) tanh(b x + a) +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0277:= log(cosh(a+b*x))/b +--R +--R +--R log(cosh(b x + a)) +--R (254) ------------------ +--R b +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0277:= integrate(t0277,x) +--R +--R +--R 2cosh(b x + a) +--R log(- -----------------------------) - b x +--R sinh(b x + a) - cosh(b x + a) +--R (255) ------------------------------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0277:= a0277-r0277 +--R +--R +--R 2cosh(b x + a) +--R - log(cosh(b x + a)) + log(- -----------------------------) - b x +--R sinh(b x + a) - cosh(b x + a) +--R (256) ----------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0277:= D(m0277,x) +--R +--R +--R (257) 0 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 500 +t0278:= tanh(a+b*x)^2 +--R +--R +--R 2 +--R (258) tanh(b x + a) +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0278:= x-tanh(a+b*x)/b +--R +--R +--R - tanh(b x + a) + b x +--R (259) --------------------- +--R b +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0278:= integrate(t0278,x) +--R +--R +--R - sinh(b x + a) + (b x + 1)cosh(b x + a) +--R (260) ---------------------------------------- +--R b cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0278:= a0278-r0278 +--R +--R +--R cosh(b x + a)tanh(b x + a) - sinh(b x + a) + cosh(b x + a) +--R (261) ---------------------------------------------------------- +--R b cosh(b x + a) +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0278:= D(m0278,x) +--R +--R +--R 2 2 2 +--R - cosh(b x + a) tanh(b x + a) + sinh(b x + a) +--R (262) ----------------------------------------------- +--R 2 +--R cosh(b x + a) +--R Type: Expression(Integer) +--E 395 + +--S 396 of 500 +t0279:= tanh(a+b*x)^4 +--R +--R +--R 4 +--R (263) tanh(b x + a) +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0279:= x-tanh(a+b*x)/b-1/3*tanh(a+b*x)^3/b +--R +--R +--R 3 +--R - tanh(b x + a) - 3tanh(b x + a) + 3b x +--R (264) ---------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0279:= integrate(t0279,x) +--R +--R +--R (265) +--R 3 2 +--R - 4sinh(b x + a) + (9b x + 12)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R - 12cosh(b x + a) sinh(b x + a) + (3b x + 4)cosh(b x + a) +--R + +--R (9b x + 12)cosh(b x + a) +--R / +--R 2 3 +--R 9b cosh(b x + a)sinh(b x + a) + 3b cosh(b x + a) + 9b cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0279:= a0279-r0279 +--R +--R +--R (266) +--R 2 3 +--R (3cosh(b x + a)sinh(b x + a) + cosh(b x + a) + 3cosh(b x + a)) +--R * +--R 3 +--R tanh(b x + a) +--R + +--R 2 3 +--R (9cosh(b x + a)sinh(b x + a) + 3cosh(b x + a) + 9cosh(b x + a)) +--R * +--R tanh(b x + a) +--R + +--R 3 2 +--R - 4sinh(b x + a) + 12cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R - 12cosh(b x + a) sinh(b x + a) + 4cosh(b x + a) + 12cosh(b x + a) +--R / +--R 2 3 +--R 9b cosh(b x + a)sinh(b x + a) + 3b cosh(b x + a) + 9b cosh(b x + a) +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0279:= D(m0279,x) +--R +--R +--R (267) +--R 2 4 +--R - 9cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 2 6 +--R (- 6cosh(b x + a) - 18cosh(b x + a) )sinh(b x + a) - cosh(b x + a) +--R + +--R 4 2 +--R - 6cosh(b x + a) - 9cosh(b x + a) +--R * +--R 4 +--R tanh(b x + a) +--R + +--R 6 2 4 +--R 4sinh(b x + a) + (- 3cosh(b x + a) + 4)sinh(b x + a) +--R + +--R 4 2 2 6 +--R (18cosh(b x + a) - 6cosh(b x + a) )sinh(b x + a) - 3cosh(b x + a) +--R + +--R 4 2 +--R - 6cosh(b x + a) + 9cosh(b x + a) +--R / +--R 2 4 +--R 9cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 2 6 +--R (6cosh(b x + a) + 18cosh(b x + a) )sinh(b x + a) + cosh(b x + a) +--R + +--R 4 2 +--R 6cosh(b x + a) + 9cosh(b x + a) +--R Type: Expression(Integer) +--E 400 + +--S 401 of 500 +t0280:= tanh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (268) \|tanh(b x + a) +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0280:= -(atan(tanh(a+b*x)^(1/2))-atanh(tanh(a+b*x)^(1/2)))/b +--R +--R +--R +-------------+ +-------------+ +--R atanh(\|tanh(b x + a) ) - atan(\|tanh(b x + a) ) +--R (269) ------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0280:= integrate(t0280,x) +--R +--R +--R (270) +--R - +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R - +--R 2 +--R * +--R atan +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) + 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0280:= a0280-r0280 +--R +--R +--R (271) +--R - +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R +-------------+ +-------------+ +--R - 2atanh(\|tanh(b x + a) ) + 2atan(\|tanh(b x + a) ) +--R + +--R - +--R 2 +--R * +--R atan +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) + 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R / +--R 2b +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0280:= D(m0280,x) +--R +--R +--R (272) +--R 8 7 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 6 +--R (- 18cosh(b x + a) + 3)sinh(b x + a) +--R + +--R 3 5 +--R - 86cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 4 +--R (- 160cosh(b x + a) - 13cosh(b x + a) + 3)sinh(b x + a) +--R + +--R 5 3 +--R (- 154cosh(b x + a) - 8cosh(b x + a) - 2cosh(b x + a)) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 78cosh(b x + a) + 9cosh(b x + a) - 4cosh(b x + a) + 1) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R (- 18cosh(b x + a) + 8cosh(b x + a) + 2cosh(b x + a) ) +--R * +--R sinh(b x + a) +--R + +--R 8 6 4 2 +--R - cosh(b x + a) + cosh(b x + a) + cosh(b x + a) - cosh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 8 7 +--R - 2sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 6 +--R (46cosh(b x + a) - 2)sinh(b x + a) +--R + +--R 3 5 +--R (130cosh(b x + a) + 2cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 4 +--R (170cosh(b x + a) + 12cosh(b x + a) + 2)sinh(b x + a) +--R + +--R 5 3 3 +--R (118cosh(b x + a) + 4cosh(b x + a) - 2cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 +--R (42cosh(b x + a) - 10cosh(b x + a) - 2cosh(b x + a) + 2) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 6cosh(b x + a) - 6cosh(b x + a) + 2cosh(b x + a) +--R + +--R - 2cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R + +--R 7 2 6 +--R - 4cosh(b x + a)sinh(b x + a) - 32cosh(b x + a) sinh(b x + a) +--R + +--R 3 5 +--R (- 100cosh(b x + a) - 12cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 4 +--R (- 160cosh(b x + a) - 48cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 140cosh(b x + a) - 72cosh(b x + a) - 12cosh(b x + a)) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 64cosh(b x + a) - 48cosh(b x + a) - 16cosh(b x + a) ) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 12cosh(b x + a) - 12cosh(b x + a) - 4cosh(b x + a) +--R + +--R - 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 7 2 6 +--R 12cosh(b x + a)sinh(b x + a) + 64cosh(b x + a) sinh(b x + a) +--R + +--R 3 5 +--R (140cosh(b x + a) + 24cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 4 +--R (160cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (100cosh(b x + a) + 72cosh(b x + a) + 12cosh(b x + a)) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (32cosh(b x + a) + 24cosh(b x + a) + 16cosh(b x + a) ) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 7 3 +--R (4cosh(b x + a) + 4cosh(b x + a) )sinh(b x + a) +--R * +--R tanh(b x + a) +--R / +--R 7 2 6 +--R 4cosh(b x + a)sinh(b x + a) + 32cosh(b x + a) sinh(b x + a) +--R + +--R 3 5 +--R (100cosh(b x + a) + 12cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 4 +--R (160cosh(b x + a) + 48cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (140cosh(b x + a) + 72cosh(b x + a) + 12cosh(b x + a)) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (64cosh(b x + a) + 48cosh(b x + a) + 16cosh(b x + a) ) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 12cosh(b x + a) + 12cosh(b x + a) + 4cosh(b x + a) +--R + +--R 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 7 2 6 +--R - 12cosh(b x + a)sinh(b x + a) - 64cosh(b x + a) sinh(b x + a) +--R + +--R 3 5 +--R (- 140cosh(b x + a) - 24cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 4 +--R (- 160cosh(b x + a) - 72cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 100cosh(b x + a) - 72cosh(b x + a) - 12cosh(b x + a)) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 32cosh(b x + a) - 24cosh(b x + a) - 16cosh(b x + a) ) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 7 3 +--R (- 4cosh(b x + a) - 4cosh(b x + a) )sinh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R Type: Expression(Integer) +--E 405 + +--S 406 of 500 +t0281:= tanh(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (273) tanh(b x + a)\|tanh(b x + a) +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0281:= (atan(tanh(a+b*x)^(1/2))+atanh(tanh(a+b*x)^(1/2))-_ + 2*tanh(a+b*x)^(1/2))/b +--R +--R +--R +-------------+ +-------------+ +-------------+ +--R atanh(\|tanh(b x + a) ) + atan(\|tanh(b x + a) ) - 2\|tanh(b x + a) +--R (274) -------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0281:= integrate(t0281,x) +--R +--R +--R (275) +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) + 1 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) +--R + +--R 2 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) - 2 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 8 +--R / +--R 2 2 +--R 2b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 2b +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - 2b sinh(b x + a) - 4b cosh(b x + a)sinh(b x + a) - 2b cosh(b x + a) +--R + +--R - 2b +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0281:= a0281-r0281 +--R +--R +--R (276) +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) + 1 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) +--R + +--R - 2 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) + 2 +--R * +--R +-------------+ +--R atanh(\|tanh(b x + a) ) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) +--R + +--R - 2 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) + 2 +--R * +--R +-------------+ +--R atan(\|tanh(b x + a) ) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) +--R + +--R 2 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) - 2 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R 4sinh(b x + a) + 8cosh(b x + a)sinh(b x + a) + 4cosh(b x + a) +--R + +--R 4 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - 4sinh(b x + a) - 8cosh(b x + a)sinh(b x + a) - 4cosh(b x + a) - 4 +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R + +--R 8 +--R / +--R 2 2 +--R 2b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 2b +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - 2b sinh(b x + a) - 4b cosh(b x + a)sinh(b x + a) - 2b cosh(b x + a) +--R + +--R - 2b +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0281:= D(m0281,x) +--R +--R +--R (277) +--R 13 12 +--R sinh(b x + a) + 11cosh(b x + a)sinh(b x + a) +--R + +--R 2 11 +--R (14cosh(b x + a) + 5)sinh(b x + a) +--R + +--R 3 10 +--R (- 230cosh(b x + a) + 25cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (- 1381cosh(b x + a) - 5cosh(b x + a) + 10)sinh(b x + a) +--R + +--R 5 3 +--R (- 3927cosh(b x + a) - 273cosh(b x + a) + 14cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 6924cosh(b x + a) - 718cosh(b x + a) - 40cosh(b x + a) +--R + +--R 10 +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 8196cosh(b x + a) - 742cosh(b x + a) - 72cosh(b x + a) +--R + +--R 2cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R - 6681cosh(b x + a) - 42cosh(b x + a) + 28cosh(b x + a) +--R + +--R 2 +--R - 30cosh(b x + a) + 5 +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R - 3731cosh(b x + a) + 670cosh(b x + a) + 100cosh(b x + a) +--R + +--R 3 +--R - 6cosh(b x + a) + 7cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R - 1378cosh(b x + a) + 697cosh(b x + a) + 24cosh(b x + a) +--R + +--R 4 2 +--R 30cosh(b x + a) - 14cosh(b x + a) + 1 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R - 310cosh(b x + a) + 317cosh(b x + a) - 40cosh(b x + a) +--R + +--R 5 3 +--R 6cosh(b x + a) - 10cosh(b x + a) + 5cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R - 35cosh(b x + a) + 63cosh(b x + a) - 22cosh(b x + a) +--R + +--R 6 4 2 +--R - 10cosh(b x + a) + 9cosh(b x + a) - 5cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 13 11 9 +--R - cosh(b x + a) + 3cosh(b x + a) - 2cosh(b x + a) +--R + +--R 7 5 3 +--R - 2cosh(b x + a) + 3cosh(b x + a) - cosh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 13 12 +--R - 4sinh(b x + a) - 20cosh(b x + a)sinh(b x + a) +--R + +--R 2 11 +--R (44cosh(b x + a) - 12)sinh(b x + a) +--R + +--R 3 10 +--R (644cosh(b x + a) - 32cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (2496cosh(b x + a) + 92cosh(b x + a) - 8)sinh(b x + a) +--R + +--R 5 3 +--R (5496cosh(b x + a) + 512cosh(b x + a) - 8cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (7896cosh(b x + a) + 840cosh(b x + a) + 40cosh(b x + a) + 8) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R (7752cosh(b x + a) + 448cosh(b x + a) + 56cosh(b x + a) ) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 5244cosh(b x + a) - 392cosh(b x + a) - 40cosh(b x + a) +--R + +--R 2 +--R - 24cosh(b x + a) + 12 +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 2396cosh(b x + a) - 768cosh(b x + a) - 88cosh(b x + a) +--R + +--R - 4cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 700cosh(b x + a) - 508cosh(b x + a) - 8cosh(b x + a) +--R + +--R 4 2 +--R 24cosh(b x + a) - 20cosh(b x + a) + 4 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R 116cosh(b x + a) - 160cosh(b x + a) + 40cosh(b x + a) +--R + +--R 3 +--R 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R 8cosh(b x + a) - 20cosh(b x + a) + 16cosh(b x + a) +--R + +--R 6 4 2 +--R - 8cosh(b x + a) + 8cosh(b x + a) - 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R + +--R 12 2 11 +--R - 4cosh(b x + a)sinh(b x + a) - 76cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (- 524cosh(b x + a) - 20cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (- 1956cosh(b x + a) - 292cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 4584cosh(b x + a) - 1536cosh(b x + a) - 40cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 7224cosh(b x + a) - 4256cosh(b x + a) - 424cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 7896cosh(b x + a) - 7112cosh(b x + a) - 1576cosh(b x + a) +--R + +--R - 40cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R - 6024cosh(b x + a) - 7560cosh(b x + a) - 2920cosh(b x + a) +--R + +--R 2 +--R - 280cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R - 3156cosh(b x + a) - 5152cosh(b x + a) - 3000cosh(b x + a) +--R + +--R 3 +--R - 640cosh(b x + a) - 20cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R - 1084cosh(b x + a) - 2176cosh(b x + a) - 1720cosh(b x + a) +--R + +--R 4 2 +--R - 640cosh(b x + a) - 76cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R - 220cosh(b x + a) - 516cosh(b x + a) - 504cosh(b x + a) +--R + +--R 5 3 +--R - 280cosh(b x + a) - 76cosh(b x + a) - 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R - 20cosh(b x + a) - 52cosh(b x + a) - 56cosh(b x + a) +--R + +--R 6 4 2 +--R - 40cosh(b x + a) - 20cosh(b x + a) - 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R 2 |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 12 2 11 +--R 20cosh(b x + a)sinh(b x + a) + 220cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (1084cosh(b x + a) + 88cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (3156cosh(b x + a) + 744cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (6024cosh(b x + a) + 2752cosh(b x + a) + 152cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (7896cosh(b x + a) + 5824cosh(b x + a) + 920cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 7224cosh(b x + a) + 7728cosh(b x + a) + 2328cosh(b x + a) +--R + +--R 128cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 4584cosh(b x + a) + 6608cosh(b x + a) + 3160cosh(b x + a) +--R + +--R 2 +--R 488cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 1956cosh(b x + a) + 3584cosh(b x + a) + 2440cosh(b x + a) +--R + +--R 3 +--R 704cosh(b x + a) + 52cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 524cosh(b x + a) + 1152cosh(b x + a) + 1032cosh(b x + a) +--R + +--R 4 2 +--R 464cosh(b x + a) + 92cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R 76cosh(b x + a) + 184cosh(b x + a) + 200cosh(b x + a) +--R + +--R 5 3 +--R 128cosh(b x + a) + 44cosh(b x + a) + 8cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R 4cosh(b x + a) + 8cosh(b x + a) + 8cosh(b x + a) +--R + +--R 6 4 +--R 8cosh(b x + a) + 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R 2 +--R tanh(b x + a) +--R / +--R 12 2 11 +--R 4cosh(b x + a)sinh(b x + a) + 76cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (524cosh(b x + a) + 20cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (1956cosh(b x + a) + 292cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (4584cosh(b x + a) + 1536cosh(b x + a) + 40cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (7224cosh(b x + a) + 4256cosh(b x + a) + 424cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 7896cosh(b x + a) + 7112cosh(b x + a) + 1576cosh(b x + a) +--R + +--R 40cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 6024cosh(b x + a) + 7560cosh(b x + a) + 2920cosh(b x + a) +--R + +--R 2 +--R 280cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 3156cosh(b x + a) + 5152cosh(b x + a) + 3000cosh(b x + a) +--R + +--R 3 +--R 640cosh(b x + a) + 20cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 1084cosh(b x + a) + 2176cosh(b x + a) + 1720cosh(b x + a) +--R + +--R 4 2 +--R 640cosh(b x + a) + 76cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R 220cosh(b x + a) + 516cosh(b x + a) + 504cosh(b x + a) +--R + +--R 5 3 +--R 280cosh(b x + a) + 76cosh(b x + a) + 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R 20cosh(b x + a) + 52cosh(b x + a) + 56cosh(b x + a) +--R + +--R 6 4 2 +--R 40cosh(b x + a) + 20cosh(b x + a) + 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 12 2 11 +--R - 20cosh(b x + a)sinh(b x + a) - 220cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (- 1084cosh(b x + a) - 88cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (- 3156cosh(b x + a) - 744cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 6024cosh(b x + a) - 2752cosh(b x + a) - 152cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 7896cosh(b x + a) - 5824cosh(b x + a) - 920cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 7224cosh(b x + a) - 7728cosh(b x + a) - 2328cosh(b x + a) +--R + +--R - 128cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R - 4584cosh(b x + a) - 6608cosh(b x + a) - 3160cosh(b x + a) +--R + +--R 2 +--R - 488cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R - 1956cosh(b x + a) - 3584cosh(b x + a) - 2440cosh(b x + a) +--R + +--R 3 +--R - 704cosh(b x + a) - 52cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R - 524cosh(b x + a) - 1152cosh(b x + a) - 1032cosh(b x + a) +--R + +--R 4 2 +--R - 464cosh(b x + a) - 92cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R - 76cosh(b x + a) - 184cosh(b x + a) - 200cosh(b x + a) +--R + +--R 5 3 +--R - 128cosh(b x + a) - 44cosh(b x + a) - 8cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R - 4cosh(b x + a) - 8cosh(b x + a) - 8cosh(b x + a) +--R + +--R 6 4 +--R - 8cosh(b x + a) - 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R Type: Expression(Integer) +--E 410 + +--S 411 of 500 +t0282:= tanh(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (278) tanh(b x + a) \|tanh(b x + a) +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0282:= -1/3*(3*atan(tanh(a+b*x)^(1/2))-3*atanh(tanh(a+b*x)^(1/2))+_ + 2*tanh(a+b*x)^(3/2))/b +--R +--R +--R (279) +--R +-------------+ +-------------+ +--R 3atanh(\|tanh(b x + a) ) - 3atan(\|tanh(b x + a) ) +--R + +--R +-------------+ +--R - 2tanh(b x + a)\|tanh(b x + a) +--R / +--R 3b +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0282:= integrate(t0282,x) +--R +--R +--R (280) +--R 6 5 +--R - 6sinh(b x + a) - 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 90cosh(b x + a) - 15)sinh(b x + a) +--R + +--R 3 3 +--R (- 120cosh(b x + a) - 60cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 90cosh(b x + a) - 90cosh(b x + a) - 12)sinh(b x + a) +--R + +--R 5 3 +--R (- 36cosh(b x + a) - 60cosh(b x + a) - 24cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 6cosh(b x + a) - 15cosh(b x + a) - 12cosh(b x + a) - 3 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R 6sinh(b x + a) + 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (90cosh(b x + a) + 9)sinh(b x + a) +--R + +--R 3 3 +--R (120cosh(b x + a) + 36cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (90cosh(b x + a) + 54cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (36cosh(b x + a) + 36cosh(b x + a) )sinh(b x + a) + 6cosh(b x + a) +--R + +--R 4 +--R 9cosh(b x + a) - 3 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) - 30)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) - 120cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) - 180cosh(b x + a) - 24)sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) - 120cosh(b x + a) - 48cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 12cosh(b x + a) - 30cosh(b x + a) - 24cosh(b x + a) - 6 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) + 18)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) + 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (72cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) + 12cosh(b x + a) +--R + +--R 4 +--R 18cosh(b x + a) - 6 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R - 24sinh(b x + a) - 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 144cosh(b x + a) - 24)sinh(b x + a) +--R + +--R 3 +--R (- 96cosh(b x + a) - 48cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R - 24cosh(b x + a) - 24cosh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 4 3 +--R 24sinh(b x + a) + 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 3 +--R 144cosh(b x + a) sinh(b x + a) + 96cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R 24cosh(b x + a) - 8 +--R / +--R 6 5 +--R 12b sinh(b x + a) + 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180b cosh(b x + a) + 30b)sinh(b x + a) +--R + +--R 3 3 +--R (240b cosh(b x + a) + 120b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180b cosh(b x + a) + 180b cosh(b x + a) + 24b)sinh(b x + a) +--R + +--R 5 3 +--R (72b cosh(b x + a) + 120b cosh(b x + a) + 48b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12b cosh(b x + a) + 30b cosh(b x + a) + 24b cosh(b x + a) + 6b +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R - 12b sinh(b x + a) - 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180b cosh(b x + a) - 18b)sinh(b x + a) +--R + +--R 3 3 +--R (- 240b cosh(b x + a) - 72b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180b cosh(b x + a) - 108b cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72b cosh(b x + a) - 72b cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12b cosh(b x + a) - 18b cosh(b x + a) + 6b +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0282:= a0282-r0282 +--R +--R +--R (281) +--R 6 5 +--R - 6sinh(b x + a) - 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 90cosh(b x + a) - 15)sinh(b x + a) +--R + +--R 3 3 +--R (- 120cosh(b x + a) - 60cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 90cosh(b x + a) - 90cosh(b x + a) - 12)sinh(b x + a) +--R + +--R 5 3 +--R (- 36cosh(b x + a) - 60cosh(b x + a) - 24cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 6cosh(b x + a) - 15cosh(b x + a) - 12cosh(b x + a) - 3 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R 6sinh(b x + a) + 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (90cosh(b x + a) + 9)sinh(b x + a) +--R + +--R 3 3 +--R (120cosh(b x + a) + 36cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (90cosh(b x + a) + 54cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (36cosh(b x + a) + 36cosh(b x + a) )sinh(b x + a) + 6cosh(b x + a) +--R + +--R 4 +--R 9cosh(b x + a) - 3 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) - 30)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) - 120cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) - 180cosh(b x + a) - 24)sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) - 120cosh(b x + a) - 48cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 12cosh(b x + a) - 30cosh(b x + a) - 24cosh(b x + a) - 6 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) + 18)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) + 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (72cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) + 12cosh(b x + a) +--R + +--R 4 +--R 18cosh(b x + a) - 6 +--R * +--R +-------------+ +--R atanh(\|tanh(b x + a) ) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) + 30)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) + 120cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) + 180cosh(b x + a) + 24)sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) + 120cosh(b x + a) + 48cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12cosh(b x + a) + 30cosh(b x + a) + 24cosh(b x + a) + 6 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) - 18)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) - 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) - 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) - 72cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12cosh(b x + a) - 18cosh(b x + a) + 6 +--R * +--R +-------------+ +--R atan(\|tanh(b x + a) ) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) - 30)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) - 120cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) - 180cosh(b x + a) - 24)sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) - 120cosh(b x + a) - 48cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 12cosh(b x + a) - 30cosh(b x + a) - 24cosh(b x + a) - 6 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) + 18)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) + 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (72cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) + 12cosh(b x + a) +--R + +--R 4 +--R 18cosh(b x + a) - 6 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 6 5 +--R 8sinh(b x + a) + 48cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (120cosh(b x + a) + 20)sinh(b x + a) +--R + +--R 3 3 +--R (160cosh(b x + a) + 80cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (120cosh(b x + a) + 120cosh(b x + a) + 16)sinh(b x + a) +--R + +--R 5 3 +--R (48cosh(b x + a) + 80cosh(b x + a) + 32cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 8cosh(b x + a) + 20cosh(b x + a) + 16cosh(b x + a) + 4 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R - 8sinh(b x + a) - 48cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 120cosh(b x + a) - 12)sinh(b x + a) +--R + +--R 3 3 +--R (- 160cosh(b x + a) - 48cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 120cosh(b x + a) - 72cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 48cosh(b x + a) - 48cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 8cosh(b x + a) - 12cosh(b x + a) + 4 +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R + +--R 4 3 +--R - 24sinh(b x + a) - 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 144cosh(b x + a) - 24)sinh(b x + a) +--R + +--R 3 +--R (- 96cosh(b x + a) - 48cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R - 24cosh(b x + a) - 24cosh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 4 3 +--R 24sinh(b x + a) + 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 3 +--R 144cosh(b x + a) sinh(b x + a) + 96cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R 24cosh(b x + a) - 8 +--R / +--R 6 5 +--R 12b sinh(b x + a) + 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180b cosh(b x + a) + 30b)sinh(b x + a) +--R + +--R 3 3 +--R (240b cosh(b x + a) + 120b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180b cosh(b x + a) + 180b cosh(b x + a) + 24b)sinh(b x + a) +--R + +--R 5 3 +--R (72b cosh(b x + a) + 120b cosh(b x + a) + 48b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12b cosh(b x + a) + 30b cosh(b x + a) + 24b cosh(b x + a) + 6b +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R - 12b sinh(b x + a) - 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180b cosh(b x + a) - 18b)sinh(b x + a) +--R + +--R 3 3 +--R (- 240b cosh(b x + a) - 72b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180b cosh(b x + a) - 108b cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72b cosh(b x + a) - 72b cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12b cosh(b x + a) - 18b cosh(b x + a) + 6b +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0282:= D(m0282,x) +--R +--R +--R (282) +--R 19 18 +--R 12sinh(b x + a) + 204cosh(b x + a)sinh(b x + a) +--R + +--R 2 17 +--R (1140cosh(b x + a) + 84)sinh(b x + a) +--R + +--R 3 16 +--R (468cosh(b x + a) + 1284cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 15 +--R (- 27792cosh(b x + a) + 9168cosh(b x + a) + 255)sinh(b x + a) +--R + +--R 5 3 +--R - 182544cosh(b x + a) + 40944cosh(b x + a) +--R + +--R 3195cosh(b x + a) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 666288cosh(b x + a) + 129312cosh(b x + a) +--R + +--R 2 +--R 19875cosh(b x + a) + 438 +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 1675440cosh(b x + a) + 309504cosh(b x + a) +--R + +--R 3 +--R 80751cosh(b x + a) + 3930cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 3124056cosh(b x + a) + 585936cosh(b x + a) +--R + +--R 4 2 +--R 235059cosh(b x + a) + 15688cosh(b x + a) + 465 +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 4471896cosh(b x + a) + 899184cosh(b x + a) +--R + +--R 5 3 +--R 507903cosh(b x + a) + 36888cosh(b x + a) + 2373cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 5000424cosh(b x + a) + 1129128cosh(b x + a) +--R + +--R 6 4 +--R 825495cosh(b x + a) + 57710cosh(b x + a) +--R + +--R 2 +--R 1815cosh(b x + a) + 312 +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 4398888cosh(b x + a) + 1156584cosh(b x + a) +--R + +--R 7 5 +--R 1012275cosh(b x + a) + 66306cosh(b x + a) +--R + +--R 3 +--R - 14501cosh(b x + a) + 528cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 3042000cosh(b x + a) + 954096cosh(b x + a) +--R + +--R 8 6 +--R 932877cosh(b x + a) + 63360cosh(b x + a) +--R + +--R 4 2 +--R - 50678cosh(b x + a) - 3096cosh(b x + a) + 129 +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 1640016cosh(b x + a) + 620880cosh(b x + a) +--R + +--R 9 7 +--R 638913cosh(b x + a) + 56256cosh(b x + a) +--R + +--R 5 3 +--R - 79758cosh(b x + a) - 12984cosh(b x + a) - 27cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 14 12 +--R - 677616cosh(b x + a) + 309504cosh(b x + a) +--R + +--R 10 8 +--R 318681cosh(b x + a) + 45426cosh(b x + a) +--R + +--R 6 4 +--R - 71890cosh(b x + a) - 21864cosh(b x + a) +--R + +--R 2 +--R - 1215cosh(b x + a) + 30 +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 15 13 +--R - 208368cosh(b x + a) + 113184cosh(b x + a) +--R + +--R 11 9 +--R 112125cosh(b x + a) + 29310cosh(b x + a) +--R + +--R 7 5 +--R - 37930cosh(b x + a) - 20568cosh(b x + a) +--R + +--R 3 +--R - 2267cosh(b x + a) + 18cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 16 14 +--R - 45396cosh(b x + a) + 28272cosh(b x + a) +--R + +--R 12 10 +--R 26625cosh(b x + a) + 13368cosh(b x + a) +--R + +--R 8 6 +--R - 10731cosh(b x + a) - 11592cosh(b x + a) +--R + +--R 4 2 +--R - 1701cosh(b x + a) - 160cosh(b x + a) + 3 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 17 15 +--R - 6420cosh(b x + a) + 4176cosh(b x + a) +--R + +--R 13 11 +--R 4101cosh(b x + a) + 3880cosh(b x + a) +--R + +--R 9 7 5 +--R - 1223cosh(b x + a) - 3816cosh(b x + a) - 537cosh(b x + a) +--R + +--R 3 +--R - 208cosh(b x + a) + 15cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 18 16 +--R - 492cosh(b x + a) + 228cosh(b x + a) +--R + +--R 14 12 10 +--R 429cosh(b x + a) + 618cosh(b x + a) - 53cosh(b x + a) +--R + +--R 8 6 4 +--R - 624cosh(b x + a) - 29cosh(b x + a) - 62cosh(b x + a) +--R + +--R 2 +--R - 15cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 19 17 15 +--R - 12cosh(b x + a) - 12cosh(b x + a) + 33cosh(b x + a) +--R + +--R 13 11 9 +--R 38cosh(b x + a) - 33cosh(b x + a) - 24cosh(b x + a) +--R + +--R 7 5 3 +--R 15cosh(b x + a) - 2cosh(b x + a) - 3cosh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 19 18 +--R - 48sinh(b x + a) - 528cosh(b x + a)sinh(b x + a) +--R + +--R 2 17 +--R (- 1632cosh(b x + a) - 264)sinh(b x + a) +--R + +--R 3 16 +--R (6336cosh(b x + a) - 3360cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 15 +--R (78720cosh(b x + a) - 20160cosh(b x + a) - 576)sinh(b x + a) +--R + +--R 5 3 +--R (368256cosh(b x + a) - 76512cosh(b x + a) - 7044cosh(b x + a)) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 6 4 +--R 1100736cosh(b x + a) - 208416cosh(b x + a) +--R + +--R 2 +--R - 40548cosh(b x + a) - 580 +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 7 5 +--R 2368704cosh(b x + a) - 438048cosh(b x + a) +--R + +--R 3 +--R - 145800cosh(b x + a) - 5364cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 8 6 +--R 3857568cosh(b x + a) - 741312cosh(b x + a) +--R + +--R 4 2 +--R - 365640cosh(b x + a) - 21812cosh(b x + a) - 156 +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 9 7 +--R 4873440cosh(b x + a) - 1029600cosh(b x + a) +--R + +--R 5 3 +--R - 674652cosh(b x + a) - 51036cosh(b x + a) + 488cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 10 8 +--R 4832256cosh(b x + a) - 1173744cosh(b x + a) +--R + +--R 6 4 2 +--R - 939708cosh(b x + a) - 75744cosh(b x + a) + 8228cosh(b x + a) +--R + +--R 208 +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 11 9 +--R 3771456cosh(b x + a) - 1084512cosh(b x + a) +--R + +--R 7 5 +--R - 996336cosh(b x + a) - 75336cosh(b x + a) +--R + +--R 3 +--R 31008cosh(b x + a) + 2584cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 12 10 +--R 2306304cosh(b x + a) - 796224cosh(b x + a) +--R + +--R 8 6 +--R - 799920cosh(b x + a) - 55272cosh(b x + a) +--R + +--R 4 2 +--R 60424cosh(b x + a) + 10264cosh(b x + a) + 200 +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 13 11 +--R 1091328cosh(b x + a) - 453024cosh(b x + a) +--R + +--R 9 7 +--R - 477180cosh(b x + a) - 38520cosh(b x + a) +--R + +--R 5 3 +--R 71344cosh(b x + a) + 19928cosh(b x + a) + 1004cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 14 12 +--R 390720cosh(b x + a) - 193440cosh(b x + a) +--R + +--R 10 8 +--R - 203676cosh(b x + a) - 31236cosh(b x + a) +--R + +--R 6 4 2 +--R 53928cosh(b x + a) + 21560cosh(b x + a) + 2244cosh(b x + a) + 60 +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 15 13 +--R 101952cosh(b x + a) - 59232cosh(b x + a) +--R + +--R 11 9 +--R - 57864cosh(b x + a) - 23044cosh(b x + a) +--R + +--R 7 5 3 +--R 26528cosh(b x + a) + 13448cosh(b x + a) + 2760cosh(b x + a) +--R + +--R 60cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 16 14 12 +--R 18192cosh(b x + a) - 12096cosh(b x + a) - 9288cosh(b x + a) +--R + +--R 10 8 6 +--R - 11556cosh(b x + a) + 8468cosh(b x + a) + 4744cosh(b x + a) +--R + +--R 4 2 +--R 1856cosh(b x + a) - 4cosh(b x + a) + 4 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 17 15 13 +--R 1968cosh(b x + a) - 1440cosh(b x + a) - 420cosh(b x + a) +--R + +--R 11 9 7 +--R - 3308cosh(b x + a) + 1704cosh(b x + a) + 904cosh(b x + a) +--R + +--R 5 3 +--R 588cosh(b x + a) + 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 18 16 14 +--R 96cosh(b x + a) - 72cosh(b x + a) + 60cosh(b x + a) +--R + +--R 12 10 8 +--R - 408cosh(b x + a) + 180cosh(b x + a) + 88cosh(b x + a) +--R + +--R 6 4 2 +--R 52cosh(b x + a) + 8cosh(b x + a) - 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R + +--R 18 2 17 +--R - 48cosh(b x + a)sinh(b x + a) - 1200cosh(b x + a) sinh(b x + a) +--R + +--R 3 16 +--R (- 12480cosh(b x + a) - 336cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 15 +--R (- 75840cosh(b x + a) - 6768cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 309120cosh(b x + a) - 58128cosh(b x + a) - 1020cosh(b x + a)) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 908544cosh(b x + a) - 292656cosh(b x + a) +--R + +--R 2 +--R - 15996cosh(b x + a) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 2009280cosh(b x + a) - 982800cosh(b x + a) +--R + +--R 3 +--R - 109368cosh(b x + a) - 1752cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 3432000cosh(b x + a) - 2354352cosh(b x + a) +--R + +--R 4 2 +--R - 439032cosh(b x + a) - 20424cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 4598880cosh(b x + a) - 4180176cosh(b x + a) +--R + +--R 5 3 +--R - 1164900cosh(b x + a) - 105288cosh(b x + a) - 1860cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 4873440cosh(b x + a) - 5621616cosh(b x + a) +--R + +--R 6 4 +--R - 2168100cosh(b x + a) - 317592cosh(b x + a) +--R + +--R 2 +--R - 15108cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 4090944cosh(b x + a) - 5786352cosh(b x + a) +--R + +--R 7 5 +--R - 2919312cosh(b x + a) - 623088cosh(b x + a) +--R + +--R 3 +--R - 53760cosh(b x + a) - 1248cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 2708160cosh(b x + a) - 4564560cosh(b x + a) +--R + +--R 8 6 +--R - 2881296cosh(b x + a) - 833616cosh(b x + a) +--R + +--R 4 2 +--R - 109536cosh(b x + a) - 6432cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 1397760cosh(b x + a) - 2738736cosh(b x + a) +--R + +--R 9 7 +--R - 2082564cosh(b x + a) - 773136cosh(b x + a) +--R + +--R 5 3 +--R - 139944cosh(b x + a) - 13392cosh(b x + a) - 516cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 14 12 +--R - 551040cosh(b x + a) - 1227408cosh(b x + a) +--R + +--R 10 8 +--R - 1085700cosh(b x + a) - 493488cosh(b x + a) +--R + +--R 6 4 2 +--R - 115080cosh(b x + a) - 14160cosh(b x + a) - 1476cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 15 13 +--R - 160320cosh(b x + a) - 397488cosh(b x + a) +--R + +--R 11 9 +--R - 394680cosh(b x + a) - 209592cosh(b x + a) +--R + +--R 7 5 3 +--R - 59808cosh(b x + a) - 7680cosh(b x + a) - 1224cosh(b x + a) +--R + +--R - 120cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 16 14 +--R - 32448cosh(b x + a) - 87696cosh(b x + a) +--R + +--R 12 10 +--R - 93816cosh(b x + a) - 54888cosh(b x + a) +--R + +--R 8 6 4 +--R - 18240cosh(b x + a) - 1728cosh(b x + a) + 24cosh(b x + a) +--R + +--R 2 +--R - 168cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 17 15 +--R - 4080cosh(b x + a) - 11760cosh(b x + a) +--R + +--R 13 11 9 +--R - 12828cosh(b x + a) - 7464cosh(b x + a) - 2676cosh(b x + a) +--R + +--R 7 5 3 +--R 48cosh(b x + a) + 396cosh(b x + a) - 24cosh(b x + a) +--R + +--R - 12cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 18 16 14 +--R - 240cosh(b x + a) - 720cosh(b x + a) - 732cosh(b x + a) +--R + +--R 12 10 8 +--R - 312cosh(b x + a) - 84cosh(b x + a) + 48cosh(b x + a) +--R + +--R 6 4 2 +--R 108cosh(b x + a) + 24cosh(b x + a) - 12cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R 3 |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 18 2 17 +--R 240cosh(b x + a)sinh(b x + a) + 4080cosh(b x + a) sinh(b x + a) +--R + +--R 3 16 +--R (32448cosh(b x + a) + 1440cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 15 +--R (160320cosh(b x + a) + 20640cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (551040cosh(b x + a) + 137376cosh(b x + a) + 3612cosh(b x + a)) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 6 4 +--R 1397760cosh(b x + a) + 562848cosh(b x + a) +--R + +--R 2 +--R 42588cosh(b x + a) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 7 5 +--R 2708160cosh(b x + a) + 1586208cosh(b x + a) +--R + +--R 3 +--R 230136cosh(b x + a) + 4836cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 8 6 +--R 4090944cosh(b x + a) + 3253536cosh(b x + a) +--R + +--R 4 2 +--R 753720cosh(b x + a) + 45372cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 9 7 +--R 4873440cosh(b x + a) + 5010720cosh(b x + a) +--R + +--R 5 3 +--R 1666500cosh(b x + a) + 190764cosh(b x + a) + 3600cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 10 8 +--R 4598880cosh(b x + a) + 5889312cosh(b x + a) +--R + +--R 6 4 2 +--R 2621124cosh(b x + a) + 473076cosh(b x + a) + 25632cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 11 9 +--R 3432000cosh(b x + a) + 5312736cosh(b x + a) +--R + +--R 7 5 +--R 3008016cosh(b x + a) + 765864cosh(b x + a) +--R + +--R 3 +--R 78624cosh(b x + a) + 1320cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 12 10 +--R 2009280cosh(b x + a) + 3665376cosh(b x + a) +--R + +--R 8 6 +--R 2539152cosh(b x + a) + 845208cosh(b x + a) +--R + +--R 4 2 +--R 135072cosh(b x + a) + 6624cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 13 11 +--R 908544cosh(b x + a) + 1908192cosh(b x + a) +--R + +--R 9 7 +--R 1566180cosh(b x + a) + 643608cosh(b x + a) +--R + +--R 5 3 +--R 141120cosh(b x + a) + 13272cosh(b x + a) + 60cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 14 12 +--R 309120cosh(b x + a) + 730080cosh(b x + a) +--R + +--R 10 8 +--R 689700cosh(b x + a) + 333864cosh(b x + a) +--R + +--R 6 4 2 +--R 90720cosh(b x + a) + 13200cosh(b x + a) + 180cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 15 13 +--R 75840cosh(b x + a) + 195936cosh(b x + a) +--R + +--R 11 9 +--R 206712cosh(b x + a) + 113076cosh(b x + a) +--R + +--R 7 5 3 +--R 34272cosh(b x + a) + 6360cosh(b x + a) + 168cosh(b x + a) +--R + +--R - 108cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 16 14 +--R 12480cosh(b x + a) + 33888cosh(b x + a) +--R + +--R 12 10 8 +--R 38328cosh(b x + a) + 22764cosh(b x + a) + 6624cosh(b x + a) +--R + +--R 6 4 2 +--R 960cosh(b x + a) + 24cosh(b x + a) - 156cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 17 15 13 +--R 1200cosh(b x + a) + 3168cosh(b x + a) + 3516cosh(b x + a) +--R + +--R 11 9 7 +--R 2172cosh(b x + a) + 432cosh(b x + a) - 216cosh(b x + a) +--R + +--R 5 3 +--R - 36cosh(b x + a) - 36cosh(b x + a) - 24cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 18 16 14 +--R 48cosh(b x + a) + 96cosh(b x + a) + 60cosh(b x + a) +--R + +--R 12 8 6 +--R 36cosh(b x + a) - 48cosh(b x + a) - 12cosh(b x + a) +--R + +--R 4 +--R 12cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R 3 +--R tanh(b x + a) +--R / +--R 18 2 17 +--R 48cosh(b x + a)sinh(b x + a) + 1200cosh(b x + a) sinh(b x + a) +--R + +--R 3 16 +--R (12480cosh(b x + a) + 336cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 15 +--R (75840cosh(b x + a) + 6768cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (309120cosh(b x + a) + 58128cosh(b x + a) + 1020cosh(b x + a)) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 6 4 +--R 908544cosh(b x + a) + 292656cosh(b x + a) +--R + +--R 2 +--R 15996cosh(b x + a) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 7 5 +--R 2009280cosh(b x + a) + 982800cosh(b x + a) +--R + +--R 3 +--R 109368cosh(b x + a) + 1752cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 8 6 +--R 3432000cosh(b x + a) + 2354352cosh(b x + a) +--R + +--R 4 2 +--R 439032cosh(b x + a) + 20424cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 9 7 +--R 4598880cosh(b x + a) + 4180176cosh(b x + a) +--R + +--R 5 3 +--R 1164900cosh(b x + a) + 105288cosh(b x + a) + 1860cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 10 8 +--R 4873440cosh(b x + a) + 5621616cosh(b x + a) +--R + +--R 6 4 +--R 2168100cosh(b x + a) + 317592cosh(b x + a) +--R + +--R 2 +--R 15108cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 11 9 +--R 4090944cosh(b x + a) + 5786352cosh(b x + a) +--R + +--R 7 5 +--R 2919312cosh(b x + a) + 623088cosh(b x + a) +--R + +--R 3 +--R 53760cosh(b x + a) + 1248cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 12 10 +--R 2708160cosh(b x + a) + 4564560cosh(b x + a) +--R + +--R 8 6 +--R 2881296cosh(b x + a) + 833616cosh(b x + a) +--R + +--R 4 2 +--R 109536cosh(b x + a) + 6432cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 13 11 +--R 1397760cosh(b x + a) + 2738736cosh(b x + a) +--R + +--R 9 7 +--R 2082564cosh(b x + a) + 773136cosh(b x + a) +--R + +--R 5 3 +--R 139944cosh(b x + a) + 13392cosh(b x + a) + 516cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 14 12 +--R 551040cosh(b x + a) + 1227408cosh(b x + a) +--R + +--R 10 8 +--R 1085700cosh(b x + a) + 493488cosh(b x + a) +--R + +--R 6 4 2 +--R 115080cosh(b x + a) + 14160cosh(b x + a) + 1476cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 15 13 +--R 160320cosh(b x + a) + 397488cosh(b x + a) +--R + +--R 11 9 +--R 394680cosh(b x + a) + 209592cosh(b x + a) +--R + +--R 7 5 3 +--R 59808cosh(b x + a) + 7680cosh(b x + a) + 1224cosh(b x + a) +--R + +--R 120cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 16 14 +--R 32448cosh(b x + a) + 87696cosh(b x + a) +--R + +--R 12 10 +--R 93816cosh(b x + a) + 54888cosh(b x + a) +--R + +--R 8 6 4 +--R 18240cosh(b x + a) + 1728cosh(b x + a) - 24cosh(b x + a) +--R + +--R 2 +--R 168cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 17 15 +--R 4080cosh(b x + a) + 11760cosh(b x + a) +--R + +--R 13 11 9 +--R 12828cosh(b x + a) + 7464cosh(b x + a) + 2676cosh(b x + a) +--R + +--R 7 5 3 +--R - 48cosh(b x + a) - 396cosh(b x + a) + 24cosh(b x + a) +--R + +--R 12cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 18 16 14 +--R 240cosh(b x + a) + 720cosh(b x + a) + 732cosh(b x + a) +--R + +--R 12 10 8 +--R 312cosh(b x + a) + 84cosh(b x + a) - 48cosh(b x + a) +--R + +--R 6 4 2 +--R - 108cosh(b x + a) - 24cosh(b x + a) + 12cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 18 2 17 +--R - 240cosh(b x + a)sinh(b x + a) - 4080cosh(b x + a) sinh(b x + a) +--R + +--R 3 16 +--R (- 32448cosh(b x + a) - 1440cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 15 +--R (- 160320cosh(b x + a) - 20640cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 551040cosh(b x + a) - 137376cosh(b x + a) - 3612cosh(b x + a)) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 1397760cosh(b x + a) - 562848cosh(b x + a) +--R + +--R 2 +--R - 42588cosh(b x + a) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 2708160cosh(b x + a) - 1586208cosh(b x + a) +--R + +--R 3 +--R - 230136cosh(b x + a) - 4836cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 4090944cosh(b x + a) - 3253536cosh(b x + a) +--R + +--R 4 2 +--R - 753720cosh(b x + a) - 45372cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 4873440cosh(b x + a) - 5010720cosh(b x + a) +--R + +--R 5 3 +--R - 1666500cosh(b x + a) - 190764cosh(b x + a) - 3600cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 4598880cosh(b x + a) - 5889312cosh(b x + a) +--R + +--R 6 4 2 +--R - 2621124cosh(b x + a) - 473076cosh(b x + a) - 25632cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 3432000cosh(b x + a) - 5312736cosh(b x + a) +--R + +--R 7 5 +--R - 3008016cosh(b x + a) - 765864cosh(b x + a) +--R + +--R 3 +--R - 78624cosh(b x + a) - 1320cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 2009280cosh(b x + a) - 3665376cosh(b x + a) +--R + +--R 8 6 +--R - 2539152cosh(b x + a) - 845208cosh(b x + a) +--R + +--R 4 2 +--R - 135072cosh(b x + a) - 6624cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 908544cosh(b x + a) - 1908192cosh(b x + a) +--R + +--R 9 7 +--R - 1566180cosh(b x + a) - 643608cosh(b x + a) +--R + +--R 5 3 +--R - 141120cosh(b x + a) - 13272cosh(b x + a) - 60cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 14 12 +--R - 309120cosh(b x + a) - 730080cosh(b x + a) +--R + +--R 10 8 +--R - 689700cosh(b x + a) - 333864cosh(b x + a) +--R + +--R 6 4 2 +--R - 90720cosh(b x + a) - 13200cosh(b x + a) - 180cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 15 13 +--R - 75840cosh(b x + a) - 195936cosh(b x + a) +--R + +--R 11 9 +--R - 206712cosh(b x + a) - 113076cosh(b x + a) +--R + +--R 7 5 3 +--R - 34272cosh(b x + a) - 6360cosh(b x + a) - 168cosh(b x + a) +--R + +--R 108cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 16 14 +--R - 12480cosh(b x + a) - 33888cosh(b x + a) +--R + +--R 12 10 8 +--R - 38328cosh(b x + a) - 22764cosh(b x + a) - 6624cosh(b x + a) +--R + +--R 6 4 2 +--R - 960cosh(b x + a) - 24cosh(b x + a) + 156cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 17 15 13 +--R - 1200cosh(b x + a) - 3168cosh(b x + a) - 3516cosh(b x + a) +--R + +--R 11 9 7 +--R - 2172cosh(b x + a) - 432cosh(b x + a) + 216cosh(b x + a) +--R + +--R 5 3 +--R 36cosh(b x + a) + 36cosh(b x + a) + 24cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 18 16 14 +--R - 48cosh(b x + a) - 96cosh(b x + a) - 60cosh(b x + a) +--R + +--R 12 8 6 +--R - 36cosh(b x + a) + 48cosh(b x + a) + 12cosh(b x + a) +--R + +--R 4 +--R - 12cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R Type: Expression(Integer) +--E 415 + +--S 416 of 500 +t0283:= 1/tanh(a+b*x)^(3/2) +--R +--R +--R 1 +--R (283) ----------------------------- +--R +-------------+ +--R tanh(b x + a)\|tanh(b x + a) +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0283:= -atan(tanh(a+b*x)^(1/2))/b+atanh(tanh(a+b*x)^(1/2))/b-_ + 2/b/tanh(a+b*x)^(1/2) +--R +--R +--R (284) +--R +-------------+ +-------------+ +--R \|tanh(b x + a) atanh(\|tanh(b x + a) ) +--R + +--R +-------------+ +-------------+ +--R - \|tanh(b x + a) atan(\|tanh(b x + a) ) - 2 +--R / +--R +-------------+ +--R b\|tanh(b x + a) +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0283:= integrate(t0283,x) +--R +--R +--R (285) +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) +--R + +--R - 2 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) - 2 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R - 8 +--R / +--R 2 2 +--R 2b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 2b +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - 2b sinh(b x + a) - 4b cosh(b x + a)sinh(b x + a) - 2b cosh(b x + a) +--R + +--R 2b +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0283:= a0283-r0283 +--R +--R +--R (286) +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1 +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) +--R + +--R - 2 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) - 2 +--R * +--R +-------------+ +-------------+ +--R \|tanh(b x + a) atanh(\|tanh(b x + a) ) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) +--R + +--R 2 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) + 2 +--R * +--R +-------------+ +-------------+ +--R \|tanh(b x + a) atan(\|tanh(b x + a) ) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) +--R + +--R - 2 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) - 2 +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R +-------------+ +--R - 8\|tanh(b x + a) +--R + +--R 2 2 +--R (4sinh(b x + a) + 8cosh(b x + a)sinh(b x + a) + 4cosh(b x + a) + 4) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - 4sinh(b x + a) - 8cosh(b x + a)sinh(b x + a) - 4cosh(b x + a) + 4 +--R / +--R 2 +--R 2b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R 2b cosh(b x + a) + 2b +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - 2b sinh(b x + a) - 4b cosh(b x + a)sinh(b x + a) - 2b cosh(b x + a) +--R + +--R 2b +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0283:= D(m0283,x) +--R +--R +--R (287) +--R 13 12 +--R sinh(b x + a) + 11cosh(b x + a)sinh(b x + a) +--R + +--R 2 11 +--R (14cosh(b x + a) + 5)sinh(b x + a) +--R + +--R 3 10 +--R (- 230cosh(b x + a) + 49cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (- 1381cosh(b x + a) + 43cosh(b x + a) + 10)sinh(b x + a) +--R + +--R 5 3 +--R (- 3927cosh(b x + a) - 761cosh(b x + a) + 86cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 6924cosh(b x + a) - 3470cosh(b x + a) + 40cosh(b x + a) +--R + +--R 10 +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 8196cosh(b x + a) - 7350cosh(b x + a) - 920cosh(b x + a) +--R + +--R 74cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 6681cosh(b x + a) - 9226cosh(b x + a) +--R + +--R 4 2 +--R - 2900cosh(b x + a) + 2cosh(b x + a) + 5 +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 3731cosh(b x + a) - 7282cosh(b x + a) +--R + +--R 5 3 +--R - 4060cosh(b x + a) - 478cosh(b x + a) + 31cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 1378cosh(b x + a) - 3591cosh(b x + a) +--R + +--R 6 4 2 +--R - 3064cosh(b x + a) - 866cosh(b x + a) - 14cosh(b x + a) + 1 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 310cosh(b x + a) - 1035cosh(b x + a) +--R + +--R 7 5 3 +--R - 1240cosh(b x + a) - 610cosh(b x + a) - 90cosh(b x + a) +--R + +--R 5cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R - 35cosh(b x + a) - 145cosh(b x + a) - 230cosh(b x + a) +--R + +--R 6 4 2 +--R - 170cosh(b x + a) - 55cosh(b x + a) - 5cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 13 11 9 +--R - cosh(b x + a) - 5cosh(b x + a) - 10cosh(b x + a) +--R + +--R 7 5 3 +--R - 10cosh(b x + a) - 5cosh(b x + a) - cosh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 13 12 +--R - 4sinh(b x + a) - 20cosh(b x + a)sinh(b x + a) +--R + +--R 2 11 +--R (44cosh(b x + a) - 20)sinh(b x + a) +--R + +--R 3 10 +--R (644cosh(b x + a) - 80cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (2496cosh(b x + a) + 180cosh(b x + a) - 40)sinh(b x + a) +--R + +--R 5 3 +--R (5496cosh(b x + a) + 1856cosh(b x + a) - 120cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 7896cosh(b x + a) + 5432cosh(b x + a) + 280cosh(b x + a) +--R + +--R - 40 +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 7752cosh(b x + a) + 8736cosh(b x + a) + 1864cosh(b x + a) +--R + +--R - 80cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 5244cosh(b x + a) + 8680cosh(b x + a) + 3720cosh(b x + a) +--R + +--R 2 +--R 200cosh(b x + a) - 20 +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 2396cosh(b x + a) + 5440cosh(b x + a) + 3800cosh(b x + a) +--R + +--R 3 +--R 736cosh(b x + a) - 20cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 700cosh(b x + a) + 2076cosh(b x + a) + 2120cosh(b x + a) +--R + +--R 4 2 +--R 808cosh(b x + a) + 60cosh(b x + a) - 4 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R 116cosh(b x + a) + 432cosh(b x + a) + 600cosh(b x + a) +--R + +--R 5 3 +--R 368cosh(b x + a) + 84cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R 8cosh(b x + a) + 36cosh(b x + a) + 64cosh(b x + a) +--R + +--R 6 4 2 +--R 56cosh(b x + a) + 24cosh(b x + a) + 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R + +--R 12 2 11 +--R - 4cosh(b x + a)sinh(b x + a) - 76cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (- 524cosh(b x + a) - 20cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (- 1956cosh(b x + a) - 228cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 4584cosh(b x + a) - 1024cosh(b x + a) - 40cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 7224cosh(b x + a) - 2464cosh(b x + a) - 232cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 7896cosh(b x + a) - 3528cosh(b x + a) - 552cosh(b x + a) +--R + +--R - 40cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R - 6024cosh(b x + a) - 3080cosh(b x + a) - 680cosh(b x + a) +--R + +--R 2 +--R - 88cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R - 3156cosh(b x + a) - 1568cosh(b x + a) - 440cosh(b x + a) +--R + +--R 3 +--R - 32cosh(b x + a) - 20cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R - 1084cosh(b x + a) - 384cosh(b x + a) - 120cosh(b x + a) +--R + +--R 4 2 +--R 32cosh(b x + a) - 12cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R - 220cosh(b x + a) - 4cosh(b x + a) + 8cosh(b x + a) +--R + +--R 5 3 +--R 8cosh(b x + a) + 20cosh(b x + a) - 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R - 20cosh(b x + a) + 12cosh(b x + a) + 8cosh(b x + a) +--R + +--R 6 4 2 +--R - 8cosh(b x + a) + 12cosh(b x + a) - 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 12 2 11 +--R 20cosh(b x + a)sinh(b x + a) + 220cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (1084cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (3156cosh(b x + a) + 536cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 8 +--R (6024cosh(b x + a) + 1728cosh(b x + a) + 88cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 +--R (7896cosh(b x + a) + 3136cosh(b x + a) + 408cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 7224cosh(b x + a) + 3472cosh(b x + a) + 728cosh(b x + a) +--R + +--R 32cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 4584cosh(b x + a) + 2352cosh(b x + a) + 600cosh(b x + a) +--R + +--R 2 +--R 88cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 1956cosh(b x + a) + 896cosh(b x + a) + 200cosh(b x + a) +--R + +--R 3 +--R 64cosh(b x + a) - 12cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 524cosh(b x + a) + 128cosh(b x + a) + 8cosh(b x + a) +--R + +--R 4 2 +--R - 16cosh(b x + a) - 4cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R 76cosh(b x + a) - 24cosh(b x + a) + 8cosh(b x + a) +--R + +--R 5 3 +--R - 32cosh(b x + a) + 12cosh(b x + a) - 8cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R 4cosh(b x + a) - 8cosh(b x + a) + 8cosh(b x + a) +--R + +--R 6 4 +--R - 8cosh(b x + a) + 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R / +--R 12 2 11 +--R 4cosh(b x + a)sinh(b x + a) + 76cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (524cosh(b x + a) + 20cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (1956cosh(b x + a) + 228cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (4584cosh(b x + a) + 1024cosh(b x + a) + 40cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (7224cosh(b x + a) + 2464cosh(b x + a) + 232cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 7896cosh(b x + a) + 3528cosh(b x + a) + 552cosh(b x + a) +--R + +--R 40cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 6024cosh(b x + a) + 3080cosh(b x + a) + 680cosh(b x + a) +--R + +--R 2 +--R 88cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 3156cosh(b x + a) + 1568cosh(b x + a) + 440cosh(b x + a) +--R + +--R 3 +--R 32cosh(b x + a) + 20cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 1084cosh(b x + a) + 384cosh(b x + a) + 120cosh(b x + a) +--R + +--R 4 2 +--R - 32cosh(b x + a) + 12cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R 220cosh(b x + a) + 4cosh(b x + a) - 8cosh(b x + a) +--R + +--R 5 3 +--R - 8cosh(b x + a) - 20cosh(b x + a) + 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R 20cosh(b x + a) - 12cosh(b x + a) - 8cosh(b x + a) +--R + +--R 6 4 2 +--R 8cosh(b x + a) - 12cosh(b x + a) + 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 12 2 11 +--R - 20cosh(b x + a)sinh(b x + a) - 220cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (- 1084cosh(b x + a) - 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (- 3156cosh(b x + a) - 536cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 6024cosh(b x + a) - 1728cosh(b x + a) - 88cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 7896cosh(b x + a) - 3136cosh(b x + a) - 408cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 7224cosh(b x + a) - 3472cosh(b x + a) - 728cosh(b x + a) +--R + +--R - 32cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R - 4584cosh(b x + a) - 2352cosh(b x + a) - 600cosh(b x + a) +--R + +--R 2 +--R - 88cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R - 1956cosh(b x + a) - 896cosh(b x + a) - 200cosh(b x + a) +--R + +--R 3 +--R - 64cosh(b x + a) + 12cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R - 524cosh(b x + a) - 128cosh(b x + a) - 8cosh(b x + a) +--R + +--R 4 2 +--R 16cosh(b x + a) + 4cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R - 76cosh(b x + a) + 24cosh(b x + a) - 8cosh(b x + a) +--R + +--R 5 3 +--R 32cosh(b x + a) - 12cosh(b x + a) + 8cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R - 4cosh(b x + a) + 8cosh(b x + a) - 8cosh(b x + a) +--R + +--R 6 4 +--R 8cosh(b x + a) - 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R Type: Expression(Integer) +--E 420 + +--S 421 of 500 +t0284:= 1/tanh(a+b*x)^(5/2) +--R +--R +--R 1 +--R (288) ------------------------------ +--R 2 +-------------+ +--R tanh(b x + a) \|tanh(b x + a) +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0284:= atan(tanh(a+b*x)^(1/2))/b+atanh(tanh(a+b*x)^(1/2))/b-_ + 2/3/b/tanh(a+b*x)^(3/2) +--R +--R +--R (289) +--R +-------------+ +-------------+ +--R 3tanh(b x + a)\|tanh(b x + a) atanh(\|tanh(b x + a) ) +--R + +--R +-------------+ +-------------+ +--R 3tanh(b x + a)\|tanh(b x + a) atan(\|tanh(b x + a) ) - 2 +--R / +--R +-------------+ +--R 3b tanh(b x + a)\|tanh(b x + a) +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0284:= integrate(t0284,x) +--R +--R +--R (290) +--R 6 5 +--R - 6sinh(b x + a) - 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 90cosh(b x + a) + 3)sinh(b x + a) +--R + +--R 3 3 +--R (- 120cosh(b x + a) + 12cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 90cosh(b x + a) + 18cosh(b x + a) + 6)sinh(b x + a) +--R + +--R 5 3 +--R (- 36cosh(b x + a) + 12cosh(b x + a) + 12cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 6cosh(b x + a) + 3cosh(b x + a) + 6cosh(b x + a) - 3 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R 6sinh(b x + a) + 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (90cosh(b x + a) - 9)sinh(b x + a) +--R + +--R 3 3 +--R (120cosh(b x + a) - 36cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (90cosh(b x + a) - 54cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (36cosh(b x + a) - 36cosh(b x + a) )sinh(b x + a) + 6cosh(b x + a) +--R + +--R 4 +--R - 9cosh(b x + a) + 3 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) - 6)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) - 24cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) - 36cosh(b x + a) - 12)sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) - 24cosh(b x + a) - 24cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12cosh(b x + a) - 6cosh(b x + a) - 12cosh(b x + a) + 6 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) + 18)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) + 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12cosh(b x + a) + 18cosh(b x + a) - 6 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R 24sinh(b x + a) + 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (144cosh(b x + a) + 24)sinh(b x + a) +--R + +--R 3 4 +--R (96cosh(b x + a) + 48cosh(b x + a))sinh(b x + a) + 24cosh(b x + a) +--R + +--R 2 +--R 24cosh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 4 3 +--R - 24sinh(b x + a) - 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 3 +--R - 144cosh(b x + a) sinh(b x + a) - 96cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R - 24cosh(b x + a) + 8 +--R / +--R 6 5 +--R 12b sinh(b x + a) + 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180b cosh(b x + a) - 6b)sinh(b x + a) +--R + +--R 3 3 +--R (240b cosh(b x + a) - 24b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180b cosh(b x + a) - 36b cosh(b x + a) - 12b)sinh(b x + a) +--R + +--R 5 3 +--R (72b cosh(b x + a) - 24b cosh(b x + a) - 24b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12b cosh(b x + a) - 6b cosh(b x + a) - 12b cosh(b x + a) + 6b +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R - 12b sinh(b x + a) - 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180b cosh(b x + a) + 18b)sinh(b x + a) +--R + +--R 3 3 +--R (- 240b cosh(b x + a) + 72b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180b cosh(b x + a) + 108b cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72b cosh(b x + a) + 72b cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12b cosh(b x + a) + 18b cosh(b x + a) - 6b +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0284:= a0284-r0284 +--R +--R +--R (291) +--R 6 5 +--R - 6sinh(b x + a) - 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 90cosh(b x + a) + 3)sinh(b x + a) +--R + +--R 3 3 +--R (- 120cosh(b x + a) + 12cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 90cosh(b x + a) + 18cosh(b x + a) + 6)sinh(b x + a) +--R + +--R 5 3 +--R (- 36cosh(b x + a) + 12cosh(b x + a) + 12cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 6cosh(b x + a) + 3cosh(b x + a) + 6cosh(b x + a) - 3 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R 6sinh(b x + a) + 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (90cosh(b x + a) - 9)sinh(b x + a) +--R + +--R 3 3 +--R (120cosh(b x + a) - 36cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (90cosh(b x + a) - 54cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (36cosh(b x + a) - 36cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R 6cosh(b x + a) - 9cosh(b x + a) + 3 +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) + 6)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) + 24cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) + 36cosh(b x + a) + 12)sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) + 24cosh(b x + a) + 24cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 12cosh(b x + a) + 6cosh(b x + a) + 12cosh(b x + a) - 6 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) - 18)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) - 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) - 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) - 72cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R 12cosh(b x + a) - 18cosh(b x + a) + 6 +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +-------------+ +--R \|tanh(b x + a) atanh(\|tanh(b x + a) ) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) + 6)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) + 24cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) + 36cosh(b x + a) + 12)sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) + 24cosh(b x + a) + 24cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 12cosh(b x + a) + 6cosh(b x + a) + 12cosh(b x + a) - 6 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) - 18)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) - 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) - 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) - 72cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R 12cosh(b x + a) - 18cosh(b x + a) + 6 +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +-------------+ +--R \|tanh(b x + a) atan(\|tanh(b x + a) ) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) - 6)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) - 24cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) - 36cosh(b x + a) - 12)sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) - 24cosh(b x + a) - 24cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12cosh(b x + a) - 6cosh(b x + a) - 12cosh(b x + a) + 6 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) + 18)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) + 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12cosh(b x + a) + 18cosh(b x + a) - 6 +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R 24sinh(b x + a) + 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (144cosh(b x + a) + 24)sinh(b x + a) +--R + +--R 3 +--R (96cosh(b x + a) + 48cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R 24cosh(b x + a) + 24cosh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 4 3 +--R - 24sinh(b x + a) - 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 3 +--R - 144cosh(b x + a) sinh(b x + a) - 96cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R - 24cosh(b x + a) + 8 +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R + +--R 6 5 +--R 8sinh(b x + a) + 48cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (120cosh(b x + a) - 4)sinh(b x + a) +--R + +--R 3 3 +--R (160cosh(b x + a) - 16cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (120cosh(b x + a) - 24cosh(b x + a) - 8)sinh(b x + a) +--R + +--R 5 3 +--R (48cosh(b x + a) - 16cosh(b x + a) - 16cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 +--R 8cosh(b x + a) - 4cosh(b x + a) - 8cosh(b x + a) + 4 +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R - 8sinh(b x + a) - 48cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 120cosh(b x + a) + 12)sinh(b x + a) +--R + +--R 3 3 +--R (- 160cosh(b x + a) + 48cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 120cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (- 48cosh(b x + a) + 48cosh(b x + a) )sinh(b x + a) - 8cosh(b x + a) +--R + +--R 4 +--R 12cosh(b x + a) - 4 +--R / +--R 6 5 +--R 12b sinh(b x + a) + 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180b cosh(b x + a) - 6b)sinh(b x + a) +--R + +--R 3 3 +--R (240b cosh(b x + a) - 24b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180b cosh(b x + a) - 36b cosh(b x + a) - 12b)sinh(b x + a) +--R + +--R 5 3 +--R (72b cosh(b x + a) - 24b cosh(b x + a) - 24b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12b cosh(b x + a) - 6b cosh(b x + a) - 12b cosh(b x + a) + 6b +--R * +--R +-------------+ +--R |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 6 5 +--R - 12b sinh(b x + a) - 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180b cosh(b x + a) + 18b)sinh(b x + a) +--R + +--R 3 3 +--R (- 240b cosh(b x + a) + 72b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180b cosh(b x + a) + 108b cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72b cosh(b x + a) + 72b cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12b cosh(b x + a) + 18b cosh(b x + a) - 6b +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0284:= D(m0284,x) +--R +--R +--R (292) +--R 21 20 +--R 12sinh(b x + a) + 228cosh(b x + a)sinh(b x + a) +--R + +--R 2 19 +--R (1560cosh(b x + a) + 24)sinh(b x + a) +--R + +--R 3 18 +--R (2952cosh(b x + a) + 192cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 17 +--R (- 25716cosh(b x + a) - 2040cosh(b x + a) - 21)sinh(b x + a) +--R + +--R 5 3 +--R - 237660cosh(b x + a) - 38208cosh(b x + a) +--R + +--R - 1323cosh(b x + a) +--R * +--R 16 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 1059168cosh(b x + a) - 271200cosh(b x + a) +--R + +--R 2 +--R - 19608cosh(b x + a) - 63 +--R * +--R 15 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 3190560cosh(b x + a) - 1178688cosh(b x + a) +--R + +--R 3 +--R - 144096cosh(b x + a) - 2595cosh(b x + a) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 7141224cosh(b x + a) - 3573024cosh(b x + a) +--R + +--R 4 2 +--R - 652620cosh(b x + a) - 28687cosh(b x + a) + 3 +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 12395448cosh(b x + a) - 8024640cosh(b x + a) +--R + +--R 5 3 +--R - 2015052cosh(b x + a) - 162179cosh(b x + a) +--R + +--R - 1227cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 17068272cosh(b x + a) - 13803504cosh(b x + a) +--R + +--R 6 4 +--R - 4481256cosh(b x + a) - 569739cosh(b x + a) +--R + +--R 2 +--R - 11086cosh(b x + a) + 57 +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 18871632cosh(b x + a) - 18532800cosh(b x + a) +--R + +--R 7 5 +--R - 7406256cosh(b x + a) - 1359391cosh(b x + a) +--R + +--R 3 +--R - 44818cosh(b x + a) + 597cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 16840200cosh(b x + a) - 19610448cosh(b x + a) +--R + +--R 8 6 +--R - 9248382cosh(b x + a) - 2306315cosh(b x + a) +--R + +--R 4 2 +--R - 108503cosh(b x + a) + 6183cosh(b x + a) + 9 +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 12122904cosh(b x + a) - 16396224cosh(b x + a) +--R + +--R 9 7 +--R - 8773050cosh(b x + a) - 2845359cosh(b x + a) +--R + +--R 5 3 +--R - 177681cosh(b x + a) + 31859cosh(b x + a) + 711cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 14 12 +--R - 6999648cosh(b x + a) - 10788960cosh(b x + a) +--R + +--R 10 8 +--R - 6290856cosh(b x + a) - 2568093cosh(b x + a) +--R + +--R 6 4 +--R - 212052cosh(b x + a) + 88058cosh(b x + a) +--R + +--R 2 +--R 5844cosh(b x + a) - 21 +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 15 13 +--R - 3203616cosh(b x + a) - 5525184cosh(b x + a) +--R + +--R 11 9 +--R - 3352128cosh(b x + a) - 1680393cosh(b x + a) +--R + +--R 7 5 +--R - 194604cosh(b x + a) + 144690cosh(b x + a) +--R + +--R 3 +--R 19892cosh(b x + a) + 255cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 16 14 +--R - 1139748cosh(b x + a) - 2157600cosh(b x + a) +--R + +--R 12 10 +--R - 1281228cosh(b x + a) - 775533cosh(b x + a) +--R + +--R 8 6 +--R - 141339cosh(b x + a) + 148078cosh(b x + a) +--R + +--R 4 2 +--R 36094cosh(b x + a) + 1327cosh(b x + a) - 3 +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 17 15 +--R - 305580cosh(b x + a) - 620736cosh(b x + a) +--R + +--R 13 11 +--R - 327036cosh(b x + a) - 238345cosh(b x + a) +--R + +--R 9 7 +--R - 80253cosh(b x + a) + 94438cosh(b x + a) +--R + +--R 5 3 +--R 37994cosh(b x + a) + 2387cosh(b x + a) + 75cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 18 16 +--R - 58728cosh(b x + a) - 124008cosh(b x + a) +--R + +--R 14 12 +--R - 46680cosh(b x + a) - 43097cosh(b x + a) +--R + +--R 10 8 +--R - 33534cosh(b x + a) + 35709cosh(b x + a) +--R + +--R 6 4 2 +--R 23396cosh(b x + a) + 2081cosh(b x + a) + 58cosh(b x + a) + 3 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 19 17 +--R - 7416cosh(b x + a) - 15360cosh(b x + a) +--R + +--R 15 13 +--R - 1200cosh(b x + a) - 3189cosh(b x + a) +--R + +--R 11 9 +--R - 9250cosh(b x + a) + 6953cosh(b x + a) +--R + +--R 7 5 3 +--R 7924cosh(b x + a) + 925cosh(b x + a) - 74cosh(b x + a) +--R + +--R 15cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 20 18 +--R - 516cosh(b x + a) - 888cosh(b x + a) +--R + +--R 16 14 12 +--R 555cosh(b x + a) + 71cosh(b x + a) - 1393cosh(b x + a) +--R + +--R 10 8 6 +--R 443cosh(b x + a) + 1217cosh(b x + a) + 197cosh(b x + a) +--R + +--R 4 2 +--R - 55cosh(b x + a) - 15cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 21 17 15 +--R - 12cosh(b x + a) + 45cosh(b x + a) - 5cosh(b x + a) +--R + +--R 13 11 9 +--R - 71cosh(b x + a) - 9cosh(b x + a) + 39cosh(b x + a) +--R + +--R 7 5 3 +--R 17cosh(b x + a) - cosh(b x + a) - 3cosh(b x + a) +--R * +--R +-------------+ +--R 2 |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 21 20 +--R - 48sinh(b x + a) - 624cosh(b x + a)sinh(b x + a) +--R + +--R 2 19 +--R (- 2736cosh(b x + a) - 72)sinh(b x + a) +--R + +--R 3 18 +--R 2544cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 17 +--R (89760cosh(b x + a) + 10536cosh(b x + a) + 120)sinh(b x + a) +--R + +--R 5 3 +--R 532032cosh(b x + a) + 109248cosh(b x + a) +--R + +--R 4860cosh(b x + a) +--R * +--R 16 +--R sinh(b x + a) +--R + +--R 6 4 +--R 1915968cosh(b x + a) + 594720cosh(b x + a) +--R + +--R 2 +--R 54516cosh(b x + a) + 196 +--R * +--R 15 +--R sinh(b x + a) +--R + +--R 7 5 +--R 4938432cosh(b x + a) + 2138304cosh(b x + a) +--R + +--R 3 +--R 320748cosh(b x + a) + 7040cosh(b x + a) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 8 6 +--R 9695712cosh(b x + a) + 5547360cosh(b x + a) +--R + +--R 4 2 +--R 1201668cosh(b x + a) + 65508cosh(b x + a) - 128 +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 9 7 +--R 14957280cosh(b x + a) + 10865088cosh(b x + a) +--R + +--R 5 3 +--R 3135756cosh(b x + a) + 312064cosh(b x + a) + 844cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 10 8 +--R 18436704cosh(b x + a) + 16480464cosh(b x + a) +--R + +--R 6 4 +--R 5980260cosh(b x + a) + 926420cosh(b x + a) +--R + +--R 2 +--R 13076cosh(b x + a) - 244 +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 11 9 +--R 18309408cosh(b x + a) + 19631040cosh(b x + a) +--R + +--R 7 5 +--R 8557692cosh(b x + a) + 1871232cosh(b x + a) +--R + +--R 3 +--R 58980cosh(b x + a) - 4160cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 12 10 +--R 14681472cosh(b x + a) + 18471024cosh(b x + a) +--R + +--R 8 6 +--R 9302436cosh(b x + a) + 2688180cosh(b x + a) +--R + +--R 4 2 +--R 145020cosh(b x + a) - 23772cosh(b x + a) + 24 +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 13 11 +--R 9475392cosh(b x + a) + 13715520cosh(b x + a) +--R + +--R 9 7 +--R 7689396cosh(b x + a) + 2804736cosh(b x + a) +--R + +--R 5 3 +--R 226104cosh(b x + a) - 70592cosh(b x + a) - 2572cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 14 12 +--R 4879680cosh(b x + a) + 7975968cosh(b x + a) +--R + +--R 10 8 +--R 4782492cosh(b x + a) + 2135628cosh(b x + a) +--R + +--R 6 4 +--R 238728cosh(b x + a) - 126728cosh(b x + a) +--R + +--R 2 +--R - 14884cosh(b x + a) + 124 +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 15 13 +--R 1974720cosh(b x + a) + 3576384cosh(b x + a) +--R + +--R 11 9 +--R 2180100cosh(b x + a) + 1175680cosh(b x + a) +--R + +--R 7 5 +--R 177672cosh(b x + a) - 146496cosh(b x + a) +--R + +--R 3 +--R - 35212cosh(b x + a) - 320cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 16 14 +--R 612816cosh(b x + a) + 1204320cosh(b x + a) +--R + +--R 12 10 +--R 689676cosh(b x + a) + 456236cosh(b x + a) +--R + +--R 8 6 +--R 97080cosh(b x + a) - 111160cosh(b x + a) +--R + +--R 4 2 +--R - 44500cosh(b x + a) - 2228cosh(b x + a) + 32 +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 17 15 +--R 140304cosh(b x + a) + 291648cosh(b x + a) +--R + +--R 13 11 +--R 133188cosh(b x + a) + 119040cosh(b x + a) +--R + +--R 9 7 +--R 41020cosh(b x + a) - 54592cosh(b x + a) +--R + +--R 5 3 +--R - 32196cosh(b x + a) - 3584cosh(b x + a) + 52cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 18 16 +--R 22224cosh(b x + a) + 47160cosh(b x + a) +--R + +--R 14 12 +--R 9228cosh(b x + a) + 19228cosh(b x + a) +--R + +--R 10 8 +--R 13732cosh(b x + a) - 16452cosh(b x + a) +--R + +--R 6 4 2 +--R - 13132cosh(b x + a) - 2444cosh(b x + a) + 76cosh(b x + a) +--R + +--R - 4 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 19 17 +--R 2160cosh(b x + a) + 4416cosh(b x + a) +--R + +--R 15 13 +--R - 1644cosh(b x + a) + 1664cosh(b x + a) +--R + +--R 11 9 7 +--R 3284cosh(b x + a) - 2688cosh(b x + a) - 2724cosh(b x + a) +--R + +--R 5 3 +--R - 704cosh(b x + a) + 76cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 20 18 16 +--R 96cosh(b x + a) + 168cosh(b x + a) - 300cosh(b x + a) +--R + +--R 14 12 10 +--R 60cosh(b x + a) + 396cosh(b x + a) - 172cosh(b x + a) +--R + +--R 8 6 4 +--R - 212cosh(b x + a) - 60cosh(b x + a) + 20cosh(b x + a) +--R + +--R 2 +--R 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R 2 +--R tanh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R + +--R 20 2 19 +--R - 48cosh(b x + a)sinh(b x + a) - 1296cosh(b x + a) sinh(b x + a) +--R + +--R 3 18 +--R (- 14928cosh(b x + a) - 96cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 17 +--R (- 102000cosh(b x + a) - 1440cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 473280cosh(b x + a) - 9600cosh(b x + a) + 84cosh(b x + a)) +--R * +--R 16 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 1602624cosh(b x + a) - 36480cosh(b x + a) +--R + +--R 2 +--R 2556cosh(b x + a) +--R * +--R 15 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 4135488cosh(b x + a) - 80640cosh(b x + a) +--R + +--R 3 +--R 25572cosh(b x + a) + 252cosh(b x + a) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 8359104cosh(b x + a) - 69888cosh(b x + a) +--R + +--R 4 2 +--R 138060cosh(b x + a) + 2748cosh(b x + a) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 13472160cosh(b x + a) + 174720cosh(b x + a) +--R + +--R 5 3 +--R 477828cosh(b x + a) + 13176cosh(b x + a) - 12cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 17503200cosh(b x + a) + 823680cosh(b x + a) +--R + +--R 6 4 2 +--R 1151436cosh(b x + a) + 35640cosh(b x + a) - 1668cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 18436704cosh(b x + a) + 1784640cosh(b x + a) +--R + +--R 7 5 3 +--R 2019732cosh(b x + a) + 56100cosh(b x + a) - 14244cosh(b x + a) +--R + +--R - 228cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 15763488cosh(b x + a) + 2608320cosh(b x + a) +--R + +--R 8 6 4 +--R 2640924cosh(b x + a) + 39204cosh(b x + a) - 55116cosh(b x + a) +--R + +--R 2 +--R - 1572cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 10905024cosh(b x + a) + 2800512cosh(b x + a) +--R + +--R 9 7 +--R 2599740cosh(b x + a) - 33264cosh(b x + a) +--R + +--R 5 3 +--R - 124344cosh(b x + a) - 4752cosh(b x + a) - 36cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 14 12 +--R - 6054720cosh(b x + a) + 2271360cosh(b x + a) +--R + +--R 10 8 +--R 1923636cosh(b x + a) - 121968cosh(b x + a) +--R + +--R 6 4 2 +--R - 178920cosh(b x + a) - 8400cosh(b x + a) + 468cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 15 13 +--R - 2660160cosh(b x + a) + 1397760cosh(b x + a) +--R + +--R 11 9 +--R 1055340cosh(b x + a) - 160380cosh(b x + a) +--R + +--R 7 5 3 +--R - 168840cosh(b x + a) - 9912cosh(b x + a) + 2940cosh(b x + a) +--R + +--R 84cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 16 14 +--R - 904128cosh(b x + a) + 645120cosh(b x + a) +--R + +--R 12 10 +--R 416676cosh(b x + a) - 128700cosh(b x + a) +--R + +--R 8 6 4 +--R - 102744cosh(b x + a) - 8568cosh(b x + a) + 6420cosh(b x + a) +--R + +--R 2 +--R 276cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 17 15 +--R - 229296cosh(b x + a) + 216960cosh(b x + a) +--R + +--R 13 11 +--R 111852cosh(b x + a) - 67848cosh(b x + a) +--R + +--R 9 7 5 +--R - 37116cosh(b x + a) - 5712cosh(b x + a) + 6900cosh(b x + a) +--R + +--R 3 +--R 408cosh(b x + a) + 12cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 18 16 +--R - 40848cosh(b x + a) + 50304cosh(b x + a) +--R + +--R 14 12 10 +--R 18180cosh(b x + a) - 23112cosh(b x + a) - 5844cosh(b x + a) +--R + +--R 8 6 4 +--R - 2832cosh(b x + a) + 3804cosh(b x + a) + 408cosh(b x + a) +--R + +--R 2 +--R - 60cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 19 17 15 +--R - 4560cosh(b x + a) + 7200cosh(b x + a) + 1308cosh(b x + a) +--R + +--R 13 11 9 +--R - 4644cosh(b x + a) + 492cosh(b x + a) - 900cosh(b x + a) +--R + +--R 7 5 3 +--R 948cosh(b x + a) + 276cosh(b x + a) - 108cosh(b x + a) +--R + +--R - 12cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 20 18 16 +--R - 240cosh(b x + a) + 480cosh(b x + a) - 12cosh(b x + a) +--R + +--R 14 12 10 +--R - 420cosh(b x + a) + 228cosh(b x + a) - 132cosh(b x + a) +--R + +--R 8 6 4 +--R 60cosh(b x + a) + 84cosh(b x + a) - 36cosh(b x + a) +--R + +--R 2 +--R - 12cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 20 2 19 +--R 240cosh(b x + a)sinh(b x + a) + 4560cosh(b x + a) sinh(b x + a) +--R + +--R 3 18 +--R (40848cosh(b x + a) + 240cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 17 +--R (229296cosh(b x + a) + 3120cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (904128cosh(b x + a) + 17856cosh(b x + a) - 708cosh(b x + a)) +--R * +--R 16 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (2660160cosh(b x + a) + 56640cosh(b x + a) - 10188cosh(b x + a) ) +--R * +--R 15 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 6054720cosh(b x + a) + 94080cosh(b x + a) - 67860cosh(b x + a) +--R + +--R - 672cosh(b x + a) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 8 4 2 +--R (10905024cosh(b x + a) - 277212cosh(b x + a) - 6432cosh(b x + a) ) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 15763488cosh(b x + a) - 436800cosh(b x + a) - 775476cosh(b x + a) +--R + +--R 3 +--R - 26496cosh(b x + a) + 756cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 10 8 +--R 18436704cosh(b x + a) - 1290432cosh(b x + a) +--R + +--R 6 4 2 +--R - 1570140cosh(b x + a) - 59136cosh(b x + a) + 7356cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 11 9 +--R 17503200cosh(b x + a) - 2265120cosh(b x + a) +--R + +--R 7 5 3 +--R - 2369796cosh(b x + a) - 68640cosh(b x + a) + 32220cosh(b x + a) +--R + +--R 648cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 12 10 +--R 13472160cosh(b x + a) - 2814240cosh(b x + a) +--R + +--R 8 6 4 +--R - 2702700cosh(b x + a) - 9504cosh(b x + a) + 83700cosh(b x + a) +--R + +--R 2 +--R 4080cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 13 11 +--R 8359104cosh(b x + a) - 2608320cosh(b x + a) +--R + +--R 9 7 5 +--R - 2332044cosh(b x + a) + 101376cosh(b x + a) + 142920cosh(b x + a) +--R + +--R 3 +--R 10464cosh(b x + a) - 348cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 14 12 +--R 4135488cosh(b x + a) - 1834560cosh(b x + a) +--R + +--R 10 8 +--R - 1504932cosh(b x + a) + 177408cosh(b x + a) +--R + +--R 6 4 2 +--R 167832cosh(b x + a) + 13440cosh(b x + a) - 1812cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 15 13 +--R 1602624cosh(b x + a) - 978432cosh(b x + a) +--R + +--R 11 9 7 +--R - 705276cosh(b x + a) + 161568cosh(b x + a) + 137592cosh(b x + a) +--R + +--R 5 3 +--R 7728cosh(b x + a) - 3900cosh(b x + a) - 240cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 16 14 12 +--R 473280cosh(b x + a) - 389760cosh(b x + a) - 225108cosh(b x + a) +--R + +--R 10 8 6 +--R 89760cosh(b x + a) + 78120cosh(b x + a) - 672cosh(b x + a) +--R + +--R 4 2 +--R - 4500cosh(b x + a) - 768cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 17 15 13 +--R 102000cosh(b x + a) - 112320cosh(b x + a) - 41340cosh(b x + a) +--R + +--R 11 9 7 +--R 29568cosh(b x + a) + 29700cosh(b x + a) - 3360cosh(b x + a) +--R + +--R 5 3 +--R - 3060cosh(b x + a) - 864cosh(b x + a) + 60cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 18 16 14 +--R 14928cosh(b x + a) - 22080cosh(b x + a) - 1332cosh(b x + a) +--R + +--R 12 10 8 +--R 4608cosh(b x + a) + 7020cosh(b x + a) - 1536cosh(b x + a) +--R + +--R 6 4 2 +--R - 1308cosh(b x + a) - 384cosh(b x + a) + 84cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 19 17 15 +--R 1296cosh(b x + a) - 2640cosh(b x + a) + 1044cosh(b x + a) +--R + +--R 13 11 9 +--R - 96cosh(b x + a) + 876cosh(b x + a) - 120cosh(b x + a) +--R + +--R 7 5 3 +--R - 372cosh(b x + a) - 48cosh(b x + a) + 36cosh(b x + a) +--R + +--R 24cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 20 18 16 +--R 48cosh(b x + a) - 144cosh(b x + a) + 156cosh(b x + a) +--R + +--R 14 12 10 +--R - 96cosh(b x + a) + 36cosh(b x + a) + 48cosh(b x + a) +--R + +--R 8 4 +--R - 60cosh(b x + a) + 12cosh(b x + a) +--R * +--R sinh(b x + a) +--R / +--R 20 2 19 +--R 48cosh(b x + a)sinh(b x + a) + 1296cosh(b x + a) sinh(b x + a) +--R + +--R 3 18 +--R (14928cosh(b x + a) + 96cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 17 +--R (102000cosh(b x + a) + 1440cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (473280cosh(b x + a) + 9600cosh(b x + a) - 84cosh(b x + a)) +--R * +--R 16 +--R sinh(b x + a) +--R + +--R 6 4 +--R 1602624cosh(b x + a) + 36480cosh(b x + a) +--R + +--R 2 +--R - 2556cosh(b x + a) +--R * +--R 15 +--R sinh(b x + a) +--R + +--R 7 5 +--R 4135488cosh(b x + a) + 80640cosh(b x + a) +--R + +--R 3 +--R - 25572cosh(b x + a) - 252cosh(b x + a) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 8 6 +--R 8359104cosh(b x + a) + 69888cosh(b x + a) +--R + +--R 4 2 +--R - 138060cosh(b x + a) - 2748cosh(b x + a) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 9 7 +--R 13472160cosh(b x + a) - 174720cosh(b x + a) +--R + +--R 5 3 +--R - 477828cosh(b x + a) - 13176cosh(b x + a) + 12cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 10 8 +--R 17503200cosh(b x + a) - 823680cosh(b x + a) +--R + +--R 6 4 +--R - 1151436cosh(b x + a) - 35640cosh(b x + a) +--R + +--R 2 +--R 1668cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 11 9 +--R 18436704cosh(b x + a) - 1784640cosh(b x + a) +--R + +--R 7 5 +--R - 2019732cosh(b x + a) - 56100cosh(b x + a) +--R + +--R 3 +--R 14244cosh(b x + a) + 228cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 12 10 +--R 15763488cosh(b x + a) - 2608320cosh(b x + a) +--R + +--R 8 6 +--R - 2640924cosh(b x + a) - 39204cosh(b x + a) +--R + +--R 4 2 +--R 55116cosh(b x + a) + 1572cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 13 11 +--R 10905024cosh(b x + a) - 2800512cosh(b x + a) +--R + +--R 9 7 +--R - 2599740cosh(b x + a) + 33264cosh(b x + a) +--R + +--R 5 3 +--R 124344cosh(b x + a) + 4752cosh(b x + a) + 36cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 14 12 +--R 6054720cosh(b x + a) - 2271360cosh(b x + a) +--R + +--R 10 8 +--R - 1923636cosh(b x + a) + 121968cosh(b x + a) +--R + +--R 6 4 2 +--R 178920cosh(b x + a) + 8400cosh(b x + a) - 468cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 15 13 +--R 2660160cosh(b x + a) - 1397760cosh(b x + a) +--R + +--R 11 9 +--R - 1055340cosh(b x + a) + 160380cosh(b x + a) +--R + +--R 7 5 3 +--R 168840cosh(b x + a) + 9912cosh(b x + a) - 2940cosh(b x + a) +--R + +--R - 84cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 16 14 +--R 904128cosh(b x + a) - 645120cosh(b x + a) +--R + +--R 12 10 +--R - 416676cosh(b x + a) + 128700cosh(b x + a) +--R + +--R 8 6 4 +--R 102744cosh(b x + a) + 8568cosh(b x + a) - 6420cosh(b x + a) +--R + +--R 2 +--R - 276cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 17 15 +--R 229296cosh(b x + a) - 216960cosh(b x + a) +--R + +--R 13 11 +--R - 111852cosh(b x + a) + 67848cosh(b x + a) +--R + +--R 9 7 5 +--R 37116cosh(b x + a) + 5712cosh(b x + a) - 6900cosh(b x + a) +--R + +--R 3 +--R - 408cosh(b x + a) - 12cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 18 16 +--R 40848cosh(b x + a) - 50304cosh(b x + a) +--R + +--R 14 12 +--R - 18180cosh(b x + a) + 23112cosh(b x + a) +--R + +--R 10 8 6 +--R 5844cosh(b x + a) + 2832cosh(b x + a) - 3804cosh(b x + a) +--R + +--R 4 2 +--R - 408cosh(b x + a) + 60cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 19 17 15 +--R 4560cosh(b x + a) - 7200cosh(b x + a) - 1308cosh(b x + a) +--R + +--R 13 11 9 +--R 4644cosh(b x + a) - 492cosh(b x + a) + 900cosh(b x + a) +--R + +--R 7 5 3 +--R - 948cosh(b x + a) - 276cosh(b x + a) + 108cosh(b x + a) +--R + +--R 12cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 20 18 16 +--R 240cosh(b x + a) - 480cosh(b x + a) + 12cosh(b x + a) +--R + +--R 14 12 10 +--R 420cosh(b x + a) - 228cosh(b x + a) + 132cosh(b x + a) +--R + +--R 8 6 4 +--R - 60cosh(b x + a) - 84cosh(b x + a) + 36cosh(b x + a) +--R + +--R 2 +--R 12cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R 2 |sinh(b x + a) +--R tanh(b x + a) |------------- +--R \|cosh(b x + a) +--R + +--R 20 +--R - 240cosh(b x + a)sinh(b x + a) +--R + +--R 2 19 +--R - 4560cosh(b x + a) sinh(b x + a) +--R + +--R 3 18 +--R (- 40848cosh(b x + a) - 240cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 17 +--R (- 229296cosh(b x + a) - 3120cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 904128cosh(b x + a) - 17856cosh(b x + a) + 708cosh(b x + a)) +--R * +--R 16 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 2660160cosh(b x + a) - 56640cosh(b x + a) +--R + +--R 2 +--R 10188cosh(b x + a) +--R * +--R 15 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 6054720cosh(b x + a) - 94080cosh(b x + a) +--R + +--R 3 +--R 67860cosh(b x + a) + 672cosh(b x + a) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 8 4 +--R - 10905024cosh(b x + a) + 277212cosh(b x + a) +--R + +--R 2 +--R 6432cosh(b x + a) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 15763488cosh(b x + a) + 436800cosh(b x + a) +--R + +--R 5 3 +--R 775476cosh(b x + a) + 26496cosh(b x + a) - 756cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 18436704cosh(b x + a) + 1290432cosh(b x + a) +--R + +--R 6 4 2 +--R 1570140cosh(b x + a) + 59136cosh(b x + a) - 7356cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 17503200cosh(b x + a) + 2265120cosh(b x + a) +--R + +--R 7 5 +--R 2369796cosh(b x + a) + 68640cosh(b x + a) +--R + +--R 3 +--R - 32220cosh(b x + a) - 648cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 13472160cosh(b x + a) + 2814240cosh(b x + a) +--R + +--R 8 6 +--R 2702700cosh(b x + a) + 9504cosh(b x + a) +--R + +--R 4 2 +--R - 83700cosh(b x + a) - 4080cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 8359104cosh(b x + a) + 2608320cosh(b x + a) +--R + +--R 9 7 +--R 2332044cosh(b x + a) - 101376cosh(b x + a) +--R + +--R 5 3 +--R - 142920cosh(b x + a) - 10464cosh(b x + a) + 348cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 14 12 +--R - 4135488cosh(b x + a) + 1834560cosh(b x + a) +--R + +--R 10 8 +--R 1504932cosh(b x + a) - 177408cosh(b x + a) +--R + +--R 6 4 2 +--R - 167832cosh(b x + a) - 13440cosh(b x + a) + 1812cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 15 13 +--R - 1602624cosh(b x + a) + 978432cosh(b x + a) +--R + +--R 11 9 +--R 705276cosh(b x + a) - 161568cosh(b x + a) +--R + +--R 7 5 +--R - 137592cosh(b x + a) - 7728cosh(b x + a) +--R + +--R 3 +--R 3900cosh(b x + a) + 240cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 16 14 +--R - 473280cosh(b x + a) + 389760cosh(b x + a) +--R + +--R 12 10 +--R 225108cosh(b x + a) - 89760cosh(b x + a) +--R + +--R 8 6 4 +--R - 78120cosh(b x + a) + 672cosh(b x + a) + 4500cosh(b x + a) +--R + +--R 2 +--R 768cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 17 15 +--R - 102000cosh(b x + a) + 112320cosh(b x + a) +--R + +--R 13 11 +--R 41340cosh(b x + a) - 29568cosh(b x + a) +--R + +--R 9 7 5 +--R - 29700cosh(b x + a) + 3360cosh(b x + a) + 3060cosh(b x + a) +--R + +--R 3 +--R 864cosh(b x + a) - 60cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 18 16 +--R - 14928cosh(b x + a) + 22080cosh(b x + a) +--R + +--R 14 12 10 +--R 1332cosh(b x + a) - 4608cosh(b x + a) - 7020cosh(b x + a) +--R + +--R 8 6 4 +--R 1536cosh(b x + a) + 1308cosh(b x + a) + 384cosh(b x + a) +--R + +--R 2 +--R - 84cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 19 17 +--R - 1296cosh(b x + a) + 2640cosh(b x + a) +--R + +--R 15 13 11 +--R - 1044cosh(b x + a) + 96cosh(b x + a) - 876cosh(b x + a) +--R + +--R 9 7 5 +--R 120cosh(b x + a) + 372cosh(b x + a) + 48cosh(b x + a) +--R + +--R 3 +--R - 36cosh(b x + a) - 24cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 20 18 16 +--R - 48cosh(b x + a) + 144cosh(b x + a) - 156cosh(b x + a) +--R + +--R 14 12 10 +--R 96cosh(b x + a) - 36cosh(b x + a) - 48cosh(b x + a) +--R + +--R 8 4 +--R 60cosh(b x + a) - 12cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R 2 +--R tanh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R Type: Expression(Integer) +--E 425 + +--S 426 of 500 +t0285:= tanh(8*x)^(1/3) +--R +--R +--R 3+--------+ +--R (293) \|tanh(8x) +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0285:= -1/16*3^(1/2)*atan(1/3*(1+2*tanh(8*x)^(2/3))*3^(1/2))-_ + 1/16*log(1-tanh(8*x)^(2/3))+_ + 1/32*log(1+tanh(8*x)^(2/3)+tanh(8*x)^(4/3)) +--R +--R +--R (294) +--R 3+--------+2 3+--------+ 3+--------+2 +--R log(\|tanh(8x) + tanh(8x)\|tanh(8x) + 1) - 2log(- \|tanh(8x) + 1) +--R + +--R +-+3+--------+2 +-+ +--R +-+ 2\|3 \|tanh(8x) + \|3 +--R - 2\|3 atan(------------------------) +--R 3 +--R / +--R 32 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +--a0285:= integrate(t0285,x) +--E 428 + +--S 429 of 500 +--m0285:= a0285-r0285 +--E 429 + +--S 430 of 500 +--d0285:= D(m0285,x) +--E 430 + +--S 431 of 500 +t0286:= x*tanh(a+b*x) +--R +--R +--R (295) x tanh(b x + a) +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0286:= 1/2*(-b^2*x^2+2*x*log(exp(2*a+2*b*x)+1)*b+_ + polylog(2,-exp(2*a+2*b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 432 + +--S 433 of 500 +a0286:= integrate(t0286,x) +--R +--R +--R x +--R ++ +--R (296) | %R tanh(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +--m0286:= a0286-r0286 +--E 434 + +--S 435 of 500 +--d0286:= D(m0286,x) +--E 435 + +--S 436 of 500 +t0287:= x*tanh(a+b*x)^2 +--R +--R +--R 2 +--R (297) x tanh(b x + a) +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0287:= 1/2*x^2+log(cosh(a+b*x))/b^2-x*tanh(a+b*x)/b +--R +--R +--R 2 2 +--R 2log(cosh(b x + a)) - 2b x tanh(b x + a) + b x +--R (298) ----------------------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0287:= integrate(t0287,x) +--R +--R +--R (299) +--R 2 2 +--R (2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) + 2) +--R * +--R 2cosh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 2 2 2 +--R (b x - 4b x)sinh(b x + a) + (2b x - 8b x)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 2 +--R (b x - 4b x)cosh(b x + a) + b x +--R / +--R 2 2 2 2 2 2 +--R 2b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) + 2b cosh(b x + a) + 2b +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0287:= a0287-r0287 +--R +--R +--R (300) +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) - 1) +--R * +--R log(cosh(b x + a)) +--R + +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) + 1) +--R * +--R 2cosh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R b x sinh(b x + a) + 2b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R b x cosh(b x + a) + b x +--R * +--R tanh(b x + a) +--R + +--R 2 +--R - 2b x sinh(b x + a) - 4b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) + b +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0287:= D(m0287,x) +--R +--R +--R (301) +--R 4 3 +--R - b x sinh(b x + a) - 4b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 6b x cosh(b x + a) - 2b x)sinh(b x + a) +--R + +--R 3 +--R (- 4b x cosh(b x + a) - 4b x cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R - b x cosh(b x + a) - 2b x cosh(b x + a) - b x +--R * +--R 2 +--R tanh(b x + a) +--R + +--R 4 3 +--R sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (6cosh(b x + a) + 2)sinh(b x + a) +--R + +--R 3 4 +--R (4cosh(b x + a) + 4cosh(b x + a))sinh(b x + a) + cosh(b x + a) +--R + +--R 2 +--R 2cosh(b x + a) + 1 +--R * +--R tanh(b x + a) +--R + +--R 4 3 +--R (b x - 1)sinh(b x + a) + (4b x - 4)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R ((6b x - 6)cosh(b x + a) - 2b x)sinh(b x + a) +--R + +--R 3 +--R ((4b x - 4)cosh(b x + a) - 4b x cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R (b x - 1)cosh(b x + a) - 2b x cosh(b x + a) + b x + 1 +--R / +--R 4 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (6b cosh(b x + a) + 2b)sinh(b x + a) +--R + +--R 3 4 +--R (4b cosh(b x + a) + 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 2 +--R 2b cosh(b x + a) + b +--R Type: Expression(Integer) +--E 440 + +--S 441 of 500 +t0288:= x*tanh(a+b*x)^3 +--R +--R +--R 3 +--R (302) x tanh(b x + a) +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0288:= -1/2*x^2+x*log(1+exp(1)^(2*a+2*b*x))/b+_ + 1/2*polylog(2,-exp(1)^(2*a+2*b*x))/b^2+_ + 1/2*x*sech(a+b*x)^2/b-1/2*tanh(a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 442 + +--S 443 of 500 +a0288:= integrate(t0288,x) +--R +--R +--R x +--R ++ 3 +--R (303) | %R tanh(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +--m0288:= a0288-r0288 +--E 444 + +--S 445 of 500 +--d0288:= D(m0288,x) +--E 445 + +--S 446 of 500 +t0289:= x^2*tanh(a+b*x) +--R +--R +--R 2 +--R (304) x tanh(b x + a) +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0289:= 1/6*(-2*b^3*x^3+6*x^2*log(exp(2*a+2*b*x)+1)*b^2+_ + 6*x*polylog(2,-exp(2*a+2*b*x))*b-3*polylog(3,-exp(2*a+2*b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 447 + +--S 448 of 500 +a0289:= integrate(t0289,x) +--R +--R +--R x +--R ++ 2 +--R (305) | %R tanh(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +--m0289:= a0289-r0289 +--E 449 + +--S 450 of 500 +--d0289:= D(m0289,x) +--E 450 + +--S 451 of 500 +t0290:= x^2*tanh(a+b*x)^2 +--R +--R +--R 2 2 +--R (306) x tanh(b x + a) +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0290:= 1/3*(-3*b^2*x^2+b^3*x^3+6*x*log(exp(2*a+2*b*x)+1)*b+_ + 3*polylog(2,-exp(2*a+2*b*x))-3*x^2*tanh(a+b*x)*b^2)/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 452 + +--S 453 of 500 +a0290:= integrate(t0290,x) +--R +--R +--R x +--R ++ 2 2 +--R (307) | %R tanh(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +--m0290:= a0290-r0290 +--E 454 + +--S 455 of 500 +--d0290:= D(m0290,x) +--E 455 + +--S 456 of 500 +t0291:= x^2*tanh(a+b*x)^3 +--R +--R +--R 2 3 +--R (308) x tanh(b x + a) +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0291:= -1/3*x^3+x^2*log(1+exp(1)^(2*a+2*b*x))/b+log(cosh(a+b*x))/b^3+_ + x*polylog(2,-exp(1)^(2*a+2*b*x))/b^2-_ + 1/2*polylog(3,-exp(1)^(2*a+2*b*x))/b^3+_ + 1/2*x^2*sech(a+b*x)^2/b-x*tanh(a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 457 + +--S 458 of 500 +a0291:= integrate(t0291,x) +--R +--R +--R x +--R ++ 2 3 +--R (309) | %R tanh(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +--m0291:= a0291-r0291 +--E 459 + +--S 460 of 500 +--d0291:= D(m0291,x) +--E 460 + +--S 461 of 500 +t0292:= x^3*tanh(a+b*x)^2 +--R +--R +--R 3 2 +--R (310) x tanh(b x + a) +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0292:= -1/4*(4*b^3*x^3-x^4*b^4-12*x^2*log(exp(2*a+2*b*x)+1)*b^2-_ + 12*x*polylog(2,-exp(2*a+2*b*x))*b+6*polylog(3,-exp(2*a+2*b*x))+_ + 4*x^3*tanh(a+b*x)*b^3)/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 462 + +--S 463 of 500 +a0292:= integrate(t0292,x) +--R +--R +--R x +--R ++ 3 2 +--R (311) | %R tanh(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +--m0292:= a0292-r0292 +--E 464 + +--S 465 of 500 +--d0292:= D(m0292,x) +--E 465 + +--S 466 of 500 +t0293:= x^3*tanh(a+b*x)^3 +--R +--R +--R 3 3 +--R (312) x tanh(b x + a) +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0293:= -3/2*x^2/b^2-1/4*x^4+3*x*log(1+exp(1)^(2*a+2*b*x))/b^3+_ + x^3*log(1+exp(1)^(2*a+2*b*x))/b+3/2*(1+b^2*x^2)*_ + polylog(2,-exp(1)^(2*a+2*b*x))/b^4-3/2*x*_ + polylog(3,-exp(1)^(2*a+2*b*x))/b^3+3/4*_ + polylog(4,-exp(1)^(2*a+2*b*x))/b^4+1/2*x^3*_ + sech(a+b*x)^2/b-3/2*x^2*tanh(a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 467 + +--S 468 of 500 +a0293:= integrate(t0293,x) +--R +--R +--R x +--R ++ 3 3 +--R (313) | %R tanh(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +--m0293:= a0293-r0293 +--E 469 + +--S 470 of 500 +--d0293:= D(m0293,x) +--E 470 + +--S 471 of 500 +t0294:= (a*tanh(x)^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (314) \|a tanh(x) +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0294:= coth(x)*log(cosh(x))*(a*tanh(x)^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (315) coth(x)log(cosh(x))\|a tanh(x) +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0294:= integrate(t0294,x) +--R +--R +--R +-+ 2cosh(x) +-+ +--R (316) \|a log(- -----------------) - x\|a +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0294:= a0294-r0294 +--R +--R +--R (317) +--R +----------+ +--R | 2 +-+ 2cosh(x) +-+ +--R - coth(x)log(cosh(x))\|a tanh(x) + \|a log(- -----------------) - x\|a +--R sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0294:= D(m0294,x) +--R +--R +--R (318) +--R +----------+ +--R +-+ | 2 +--R sinh(x)\|a \|a tanh(x) +--R + +--R 3 2 2 +--R a cosh(x)coth(x)tanh(x) + (a cosh(x)coth(x) - a cosh(x))tanh(x) +--R + +--R - a cosh(x)coth(x)tanh(x) +--R * +--R log(cosh(x)) +--R + +--R 2 +--R - a coth(x)sinh(x)tanh(x) +--R / +--R +----------+ +--R | 2 +--R cosh(x)\|a tanh(x) +--R Type: Expression(Integer) +--E 475 + +--S 476 of 500 +t0295:= (a*tanh(x)^3)^(1/2) +--R +--R +--R +----------+ +--R | 3 +--R (319) \|a tanh(x) +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0295:= (atan(tanh(x)^(1/2))+atanh(tanh(x)^(1/2))-2*tanh(x)^(1/2))*_ + (a*tanh(x)^3)^(1/2)/tanh(x)^(3/2) +--R +--R +--R (320) +--R +----------+ +----------+ +--R | 3 +-------+ | 3 +-------+ +--R \|a tanh(x) atanh(\|tanh(x) ) + \|a tanh(x) atan(\|tanh(x) ) +--R + +--R +----------+ +--R +-------+ | 3 +--R - 2\|tanh(x) \|a tanh(x) +--R / +--R +-------+ +--R tanh(x)\|tanh(x) +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0295:= integrate(t0295,x) +--R +--R +--R (321) +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)\|- a |--------- +--R \| cosh(x) +--R + +--R 2 2 +--R - a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2)\|- a |--------- +--R \| cosh(x) +--R + +--R 2 2 +--R - 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R - 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) +--R / +--R +---------+ +--R 2 2 |a sinh(x) +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2) |--------- +--R \| cosh(x) +--R + +--R 2 2 +---+ +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2)\|- a +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0295:= a0295-r0295 +--R +--R +--R (322) +--R 2 2 +---+ +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)tanh(x)\|- a +--R * +--R +---------+ +--R |a sinh(x) +--R |--------- +--R \| cosh(x) +--R + +--R 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a)tanh(x) +--R * +--R +-------+ +--R \|tanh(x) +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R +---------+ +--R 2 2 |a sinh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2) |--------- +--R \| cosh(x) +--R + +--R 2 2 +---+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)\|- a +--R * +--R +----------+ +--R | 3 +-------+ +--R \|a tanh(x) atanh(\|tanh(x) ) +--R + +--R +---------+ +--R 2 2 |a sinh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2) |--------- +--R \| cosh(x) +--R + +--R 2 2 +---+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)\|- a +--R * +--R +----------+ +--R | 3 +-------+ +--R \|a tanh(x) atan(\|tanh(x) ) +--R + +--R 2 2 +---+ +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2)tanh(x)\|- a +--R * +--R +---------+ +--R |a sinh(x) +--R |--------- +--R \| cosh(x) +--R + +--R 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)tanh(x) +--R * +--R +-------+ +--R \|tanh(x) +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R +---------+ +--R 2 2 |a sinh(x) +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) + 4) |--------- +--R \| cosh(x) +--R + +--R 2 2 +---+ +--R (- 4sinh(x) - 8cosh(x)sinh(x) - 4cosh(x) - 4)\|- a +--R * +--R +----------+ +--R +-------+ | 3 +--R \|tanh(x) \|a tanh(x) +--R + +--R 2 2 +-------+ +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) )tanh(x)\|tanh(x) +--R / +--R +---------+ +--R 2 2 |a sinh(x) +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)tanh(x) |--------- +--R \| cosh(x) +--R + +--R 2 2 +---+ +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2)tanh(x)\|- a +--R * +--R +-------+ +--R \|tanh(x) +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0295:= D(m0295,x) +--R +--R +--R (323) +--R 14 13 +--R - a sinh(x) - 4a cosh(x)sinh(x) +--R + +--R 2 12 +--R (15a cosh(x) - 5a)sinh(x) +--R + +--R 3 11 +--R (144a cosh(x) - 38a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (451a cosh(x) - 108a cosh(x) - 10a)sinh(x) +--R + +--R 5 3 9 +--R (748a cosh(x) - 90a cosh(x) - 88a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (627a cosh(x) + 255a cosh(x) - 342a cosh(x) - 10a)sinh(x) +--R + +--R 5 3 7 +--R (900a cosh(x) - 768a cosh(x) - 76a cosh(x))sinh(x) +--R + +--R 8 6 4 +--R - 627a cosh(x) + 1344a cosh(x) - 1092a cosh(x) +--R + +--R 2 +--R - 244a cosh(x) - 5a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 748a cosh(x) + 1164a cosh(x) - 1008a cosh(x) +--R + +--R 3 +--R - 428a cosh(x) - 20a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 451a cosh(x) + 585a cosh(x) - 588a cosh(x) +--R + +--R 4 2 +--R - 440a cosh(x) + 15a cosh(x) - a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 144a cosh(x) + 130a cosh(x) - 192a cosh(x) +--R + +--R 5 3 +--R - 260a cosh(x) + 112a cosh(x) + 2a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 15a cosh(x) - 20a cosh(x) - 18a cosh(x) - 76a cosh(x) +--R + +--R 4 2 +--R 121a cosh(x) + 40a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 4a cosh(x) - 18a cosh(x) + 8a cosh(x) - 4a cosh(x) +--R + +--R 5 3 +--R 36a cosh(x) - 26a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R a cosh(x) - 3a cosh(x) + 2a cosh(x) + 2a cosh(x) +--R + +--R 6 4 +--R - 3a cosh(x) + a cosh(x) +--R * +--R +---------+ +--R |a sinh(x) +--R |--------- +--R \| cosh(x) +--R + +--R 14 13 +--R - 4a sinh(x) - 36a cosh(x)sinh(x) +--R + +--R 2 12 +--R (- 136a cosh(x) - 12a)sinh(x) +--R + +--R 3 11 +--R (- 264a cosh(x) - 112a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 220a cosh(x) - 460a cosh(x) - 8a)sinh(x) +--R + +--R 5 3 9 +--R (132a cosh(x) - 1080a cosh(x) - 72a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (528a cosh(x) - 1560a cosh(x) - 288a cosh(x) + 8a)sinh(x) +--R + +--R 7 5 3 +--R (528a cosh(x) - 1344a cosh(x) - 672a cosh(x) + 64a cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R 132a cosh(x) - 504a cosh(x) - 1008a cosh(x) +--R + +--R 2 +--R 216a cosh(x) + 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 220a cosh(x) + 240a cosh(x) - 1008a cosh(x) +--R + +--R 3 +--R 400a cosh(x) + 76a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 264a cosh(x) + 420a cosh(x) - 672a cosh(x) +--R + +--R 4 2 +--R 440a cosh(x) + 136a cosh(x) + 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 136a cosh(x) + 240a cosh(x) - 288a cosh(x) +--R + +--R 5 3 +--R 288a cosh(x) + 72a cosh(x) + 16a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R - 36a cosh(x) + 68a cosh(x) - 72a cosh(x) +--R + +--R 6 4 2 +--R 104a cosh(x) - 20a cosh(x) - 44a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 4a cosh(x) + 8a cosh(x) - 8a cosh(x) + 16a cosh(x) +--R + +--R 5 3 +--R - 20a cosh(x) + 8a cosh(x) +--R * +--R sinh(x) +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R | 3 +--R \|a tanh(x) +--R + +--R 13 2 12 +--R - 4a cosh(x)sinh(x) - 32a cosh(x) sinh(x) +--R + +--R 3 11 +--R (- 104a cosh(x) - 20a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 160a cosh(x) - 104a cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (- 60a cosh(x) - 132a cosh(x) - 40a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (192a cosh(x) + 288a cosh(x) - 80a cosh(x) )sinh(x) +--R + +--R 7 5 3 +--R (336a cosh(x) + 1176a cosh(x) + 320a cosh(x) - 40a cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (192a cosh(x) + 1680a cosh(x) + 1360a cosh(x) + 64a cosh(x) ) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 60a cosh(x) + 1176a cosh(x) + 2000a cosh(x) + 600a cosh(x) +--R + +--R - 20a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 160a cosh(x) + 288a cosh(x) + 1360a cosh(x) + 960a cosh(x) +--R + +--R 2 +--R 112a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 104a cosh(x) - 132a cosh(x) + 320a cosh(x) + 520a cosh(x) +--R + +--R 3 +--R 232a cosh(x) - 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 4 +--R - 32a cosh(x) - 104a cosh(x) - 80a cosh(x) + 48a cosh(x) +--R + +--R 2 +--R 40a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 4a cosh(x) - 20a cosh(x) - 40a cosh(x) - 56a cosh(x) +--R + +--R 5 3 +--R - 52a cosh(x) - 20a cosh(x) +--R * +--R sinh(x) +--R * +--R +---------+ +--R 3 +---+ |a sinh(x) +--R tanh(x) \|- a |--------- +--R \| cosh(x) +--R + +--R 2 13 2 2 12 +--R - 8a cosh(x)sinh(x) - 72a cosh(x) sinh(x) +--R + +--R 2 3 2 11 +--R (- 280a cosh(x) - 52a cosh(x))sinh(x) +--R + +--R 2 4 2 2 10 +--R (- 600a cosh(x) - 376a cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 9 +--R (- 720a cosh(x) - 1140a cosh(x) - 128a cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 8 +--R (- 336a cosh(x) - 1824a cosh(x) - 664a cosh(x) )sinh(x) +--R + +--R 2 7 2 5 2 3 2 +--R (336a cosh(x) - 1512a cosh(x) - 1304a cosh(x) - 152a cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 +--R (720a cosh(x) - 336a cosh(x) - 1048a cosh(x) - 448a cosh(x) ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 7 2 5 2 3 +--R 600a cosh(x) + 504a cosh(x) + 40a cosh(x) - 280a cosh(x) +--R + +--R 2 +--R - 88a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 10 2 8 2 6 2 4 +--R 280a cosh(x) + 480a cosh(x) + 632a cosh(x) + 320a cosh(x) +--R + +--R 2 2 +--R - 48a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 11 2 9 2 7 2 5 +--R 72a cosh(x) + 156a cosh(x) + 376a cosh(x) + 440a cosh(x) +--R + +--R 2 3 2 +--R 160a cosh(x) - 20a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 12 2 10 2 8 2 6 +--R 8a cosh(x) + 8a cosh(x) + 56a cosh(x) + 128a cosh(x) +--R + +--R 2 4 2 2 +--R 112a cosh(x) + 40a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 9 2 7 2 5 +--R - 4a cosh(x) - 8a cosh(x) - 8a cosh(x) - 8a cosh(x) +--R + +--R 2 3 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R * +--R 3 +--R tanh(x) +--R / +--R 13 2 12 +--R 4cosh(x)sinh(x) + 32cosh(x) sinh(x) +--R + +--R 3 11 +--R (104cosh(x) + 20cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (160cosh(x) + 104cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (60cosh(x) + 132cosh(x) + 40cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 192cosh(x) - 288cosh(x) + 80cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (- 336cosh(x) - 1176cosh(x) - 320cosh(x) + 40cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (- 192cosh(x) - 1680cosh(x) - 1360cosh(x) - 64cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R 60cosh(x) - 1176cosh(x) - 2000cosh(x) - 600cosh(x) +--R + +--R 20cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 160cosh(x) - 288cosh(x) - 1360cosh(x) - 960cosh(x) +--R + +--R 2 +--R - 112cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 104cosh(x) + 132cosh(x) - 320cosh(x) - 520cosh(x) +--R + +--R 3 +--R - 232cosh(x) + 4cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 4 +--R 32cosh(x) + 104cosh(x) + 80cosh(x) - 48cosh(x) +--R + +--R 2 +--R - 40cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R 4cosh(x) + 20cosh(x) + 40cosh(x) + 56cosh(x) + 52cosh(x) +--R + +--R 3 +--R 20cosh(x) +--R * +--R sinh(x) +--R * +--R +---------+ +--R +---+ |a sinh(x) +--R \|- a |--------- +--R \| cosh(x) +--R + +--R 13 2 12 +--R 8a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 3 11 +--R (280a cosh(x) + 52a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (600a cosh(x) + 376a cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (720a cosh(x) + 1140a cosh(x) + 128a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (336a cosh(x) + 1824a cosh(x) + 664a cosh(x) )sinh(x) +--R + +--R 7 5 3 +--R (- 336a cosh(x) + 1512a cosh(x) + 1304a cosh(x) + 152a cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 720a cosh(x) + 336a cosh(x) + 1048a cosh(x) + 448a cosh(x) ) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 600a cosh(x) - 504a cosh(x) - 40a cosh(x) + 280a cosh(x) +--R + +--R 88a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 280a cosh(x) - 480a cosh(x) - 632a cosh(x) - 320a cosh(x) +--R + +--R 2 +--R 48a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 72a cosh(x) - 156a cosh(x) - 376a cosh(x) - 440a cosh(x) +--R + +--R 3 +--R - 160a cosh(x) + 20a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 8a cosh(x) - 8a cosh(x) - 56a cosh(x) - 128a cosh(x) +--R + +--R 4 2 +--R - 112a cosh(x) - 40a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 4a cosh(x) + 8a cosh(x) + 8a cosh(x) + 8a cosh(x) +--R + +--R 3 +--R 4a cosh(x) +--R * +--R sinh(x) +--R * +--R +----------+ +--R | 3 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 480 + +--S 481 of 500 +t0296:= (a*tanh(x)^4)^(1/2) +--R +--R +--R +----------+ +--R | 4 +--R (324) \|a tanh(x) +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0296:= coth(x)^2*(x-tanh(x))*(a*tanh(x)^4)^(1/2) +--R +--R +--R +----------+ +--R 2 2 | 4 +--R (325) (- coth(x) tanh(x) + x coth(x) )\|a tanh(x) +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0296:= integrate(t0296,x) +--R +--R +--R 2 2 +-+ +--R (x sinh(x) + 2x cosh(x)sinh(x) + x cosh(x) + x + 2)\|a +--R (326) --------------------------------------------------------- +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0296:= a0296-r0296 +--R +--R +--R (327) +--R 2 2 2 +--R coth(x) sinh(x) + 2cosh(x)coth(x) sinh(x) +--R + +--R 2 2 +--R (cosh(x) + 1)coth(x) +--R * +--R tanh(x) +--R + +--R 2 2 2 +--R - x coth(x) sinh(x) - 2x cosh(x)coth(x) sinh(x) +--R + +--R 2 2 +--R (- x cosh(x) - x)coth(x) +--R * +--R +----------+ +--R | 4 +--R \|a tanh(x) +--R + +--R 2 2 +-+ +--R (x sinh(x) + 2x cosh(x)sinh(x) + x cosh(x) + x + 2)\|a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0296:= D(m0296,x) +--R +--R +--R (328) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R +----------+ +--R +-+ | 4 +--R \|a \|a tanh(x) +--R + +--R 2 4 2 3 +--R - 3a coth(x) sinh(x) - 12a cosh(x)coth(x) sinh(x) +--R + +--R 2 2 2 +--R (- 18a cosh(x) - 6a)coth(x) sinh(x) +--R + +--R 3 2 +--R (- 12a cosh(x) - 12a cosh(x))coth(x) sinh(x) +--R + +--R 4 2 2 +--R (- 3a cosh(x) - 6a cosh(x) - 3a)coth(x) +--R * +--R 6 +--R tanh(x) +--R + +--R 3 2 4 +--R (- 2a coth(x) + 2a x coth(x) + 2a coth(x))sinh(x) +--R + +--R 3 2 +--R (- 8a cosh(x)coth(x) + 8a x cosh(x)coth(x) + 8a cosh(x)coth(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 12a cosh(x) - 4a)coth(x) + (12a x cosh(x) + 4a x)coth(x) +--R + +--R 2 +--R (12a cosh(x) + 4a)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 +--R (- 8a cosh(x) - 8a cosh(x))coth(x) +--R + +--R 3 2 +--R (8a x cosh(x) + 8a x cosh(x))coth(x) +--R + +--R 3 +--R (8a cosh(x) + 8a cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 +--R (- 2a cosh(x) - 4a cosh(x) - 2a)coth(x) +--R + +--R 4 2 2 +--R (2a x cosh(x) + 4a x cosh(x) + 2a x)coth(x) +--R + +--R 4 2 +--R (2a cosh(x) + 4a cosh(x) + 2a)coth(x) +--R * +--R 5 +--R tanh(x) +--R + +--R 3 2 4 +--R (2a x coth(x) + 2a coth(x) - 2a x coth(x))sinh(x) +--R + +--R 3 2 +--R (8a x cosh(x)coth(x) + 8a cosh(x)coth(x) - 8a x cosh(x)coth(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (12a x cosh(x) + 4a x)coth(x) + (12a cosh(x) + 4a)coth(x) +--R + +--R 2 +--R (- 12a x cosh(x) - 4a x)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 +--R (8a x cosh(x) + 8a x cosh(x))coth(x) +--R + +--R 3 2 +--R (8a cosh(x) + 8a cosh(x))coth(x) +--R + +--R 3 +--R (- 8a x cosh(x) - 8a x cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 +--R (2a x cosh(x) + 4a x cosh(x) + 2a x)coth(x) +--R + +--R 4 2 2 +--R (2a cosh(x) + 4a cosh(x) + 2a)coth(x) +--R + +--R 4 2 +--R (- 2a x cosh(x) - 4a x cosh(x) - 2a x)coth(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 2 4 2 3 +--R - 2a x coth(x) sinh(x) - 8a x cosh(x)coth(x) sinh(x) +--R + +--R 2 2 2 +--R (- 12a x cosh(x) - 4a x)coth(x) sinh(x) +--R + +--R 3 2 +--R (- 8a x cosh(x) - 8a x cosh(x))coth(x) sinh(x) +--R + +--R 4 2 2 +--R (- 2a x cosh(x) - 4a x cosh(x) - 2a x)coth(x) +--R * +--R 3 +--R tanh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R * +--R +----------+ +--R | 4 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 485 + +--S 486 of 500 +t0297:= (a*tanh(x)^3)^(3/2) +--R +--R +--R +----------+ +--R 3 | 3 +--R (329) a tanh(x) \|a tanh(x) +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0297:= -1/21*a*(a*tanh(x)^3)^(1/2)*(21*atan(tanh(x)^(1/2))-_ + 21*atanh(tanh(x)^(1/2))+14*tanh(x)^(3/2)+_ + 6*tanh(x)^(7/2))/tanh(x)^(3/2) +--R +--R +--R (330) +--R +----------+ +----------+ +--R | 3 +-------+ | 3 +-------+ +--R 21a\|a tanh(x) atanh(\|tanh(x) ) - 21a\|a tanh(x) atan(\|tanh(x) ) +--R + +--R +----------+ +--R 3 +-------+ | 3 +--R (- 6a tanh(x) - 14a tanh(x))\|tanh(x) \|a tanh(x) +--R / +--R +-------+ +--R 21tanh(x)\|tanh(x) +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0297:= integrate(t0297,x) +--R +--R +--R (331) +--R 14 13 +--R 21a sinh(x) + 294a cosh(x)sinh(x) +--R + +--R 2 12 +--R (1911a cosh(x) + 168a)sinh(x) +--R + +--R 3 11 +--R (7644a cosh(x) + 2016a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (21021a cosh(x) + 11088a cosh(x) + 378a)sinh(x) +--R + +--R 5 3 9 +--R (42042a cosh(x) + 36960a cosh(x) + 3780a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (63063a cosh(x) + 83160a cosh(x) + 17010a cosh(x) + 84a) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R 72072a cosh(x) + 133056a cosh(x) + 45360a cosh(x) +--R + +--R 672a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R 63063a cosh(x) + 155232a cosh(x) + 79380a cosh(x) +--R + +--R 2 +--R 2352a cosh(x) - 819a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R 42042a cosh(x) + 133056a cosh(x) + 95256a cosh(x) +--R + +--R 3 +--R 4704a cosh(x) - 4914a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R 21021a cosh(x) + 83160a cosh(x) + 79380a cosh(x) +--R + +--R 4 2 +--R 5880a cosh(x) - 12285a cosh(x) - 1260a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R 7644a cosh(x) + 36960a cosh(x) + 45360a cosh(x) +--R + +--R 5 3 +--R 4704a cosh(x) - 16380a cosh(x) - 5040a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R 1911a cosh(x) + 11088a cosh(x) + 17010a cosh(x) +--R + +--R 6 4 2 +--R 2352a cosh(x) - 12285a cosh(x) - 7560a cosh(x) - 756a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R 294a cosh(x) + 2016a cosh(x) + 3780a cosh(x) +--R + +--R 7 5 3 +--R 672a cosh(x) - 4914a cosh(x) - 5040a cosh(x) - 1512a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R 21a cosh(x) + 168a cosh(x) + 378a cosh(x) + 84a cosh(x) +--R + +--R 6 4 2 +--R - 819a cosh(x) - 1260a cosh(x) - 756a cosh(x) - 168a +--R * +--R +---------+ +--R +---+ |a sinh(x) +--R \|- a |--------- +--R \| cosh(x) +--R + +--R 2 14 2 13 2 2 12 +--R - 21a sinh(x) - 294a cosh(x)sinh(x) - 1911a cosh(x) sinh(x) +--R + +--R 2 3 11 2 4 2 10 +--R - 7644a cosh(x) sinh(x) + (- 21021a cosh(x) + 294a )sinh(x) +--R + +--R 2 5 2 9 +--R (- 42042a cosh(x) + 2940a cosh(x))sinh(x) +--R + +--R 2 6 2 2 2 8 +--R (- 63063a cosh(x) + 13230a cosh(x) + 588a )sinh(x) +--R + +--R 2 7 2 3 2 7 +--R (- 72072a cosh(x) + 35280a cosh(x) + 4704a cosh(x))sinh(x) +--R + +--R 2 8 2 4 2 2 2 +--R (- 63063a cosh(x) + 61740a cosh(x) + 16464a cosh(x) + 147a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 5 2 3 +--R - 42042a cosh(x) + 74088a cosh(x) + 32928a cosh(x) +--R + +--R 2 +--R 882a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 10 2 6 2 4 +--R - 21021a cosh(x) + 61740a cosh(x) + 41160a cosh(x) +--R + +--R 2 2 2 +--R 2205a cosh(x) - 588a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 11 2 7 2 5 +--R - 7644a cosh(x) + 35280a cosh(x) + 32928a cosh(x) +--R + +--R 2 3 2 +--R 2940a cosh(x) - 2352a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 12 2 8 2 6 +--R - 1911a cosh(x) + 13230a cosh(x) + 16464a cosh(x) +--R + +--R 2 4 2 2 2 +--R 2205a cosh(x) - 3528a cosh(x) - 588a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 13 2 9 2 7 +--R - 294a cosh(x) + 2940a cosh(x) + 4704a cosh(x) +--R + +--R 2 5 2 3 2 +--R 882a cosh(x) - 2352a cosh(x) - 1176a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 14 2 10 2 8 2 6 +--R - 21a cosh(x) + 294a cosh(x) + 588a cosh(x) + 147a cosh(x) +--R + +--R 2 4 2 2 2 +--R - 588a cosh(x) - 588a cosh(x) - 168a +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R 14 13 +--R - 42a sinh(x) - 588a cosh(x)sinh(x) +--R + +--R 2 12 +--R (- 3822a cosh(x) - 336a)sinh(x) +--R + +--R 3 11 +--R (- 15288a cosh(x) - 4032a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 42042a cosh(x) - 22176a cosh(x) - 756a)sinh(x) +--R + +--R 5 3 9 +--R (- 84084a cosh(x) - 73920a cosh(x) - 7560a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 126126a cosh(x) - 166320a cosh(x) - 34020a cosh(x) +--R + +--R - 168a +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R - 144144a cosh(x) - 266112a cosh(x) - 90720a cosh(x) +--R + +--R - 1344a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R - 126126a cosh(x) - 310464a cosh(x) - 158760a cosh(x) +--R + +--R 2 +--R - 4704a cosh(x) + 1638a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 84084a cosh(x) - 266112a cosh(x) - 190512a cosh(x) +--R + +--R 3 +--R - 9408a cosh(x) + 9828a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 42042a cosh(x) - 166320a cosh(x) - 158760a cosh(x) +--R + +--R 4 2 +--R - 11760a cosh(x) + 24570a cosh(x) + 2520a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 15288a cosh(x) - 73920a cosh(x) - 90720a cosh(x) +--R + +--R 5 3 +--R - 9408a cosh(x) + 32760a cosh(x) + 10080a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R - 3822a cosh(x) - 22176a cosh(x) - 34020a cosh(x) +--R + +--R 6 4 2 +--R - 4704a cosh(x) + 24570a cosh(x) + 15120a cosh(x) + 1512a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R - 588a cosh(x) - 4032a cosh(x) - 7560a cosh(x) +--R + +--R 7 5 3 +--R - 1344a cosh(x) + 9828a cosh(x) + 10080a cosh(x) +--R + +--R 3024a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 42a cosh(x) - 336a cosh(x) - 756a cosh(x) - 168a cosh(x) +--R + +--R 6 4 2 +--R 1638a cosh(x) + 2520a cosh(x) + 1512a cosh(x) + 336a +--R * +--R +---------+ +--R +---+ |a sinh(x) +--R \|- a |--------- +--R \| cosh(x) +--R + +--R 2 14 2 13 2 2 12 +--R 42a sinh(x) + 588a cosh(x)sinh(x) + 3822a cosh(x) sinh(x) +--R + +--R 2 3 11 2 4 2 10 +--R 15288a cosh(x) sinh(x) + (42042a cosh(x) - 588a )sinh(x) +--R + +--R 2 5 2 9 +--R (84084a cosh(x) - 5880a cosh(x))sinh(x) +--R + +--R 2 6 2 2 2 8 +--R (126126a cosh(x) - 26460a cosh(x) - 1176a )sinh(x) +--R + +--R 2 7 2 3 2 7 +--R (144144a cosh(x) - 70560a cosh(x) - 9408a cosh(x))sinh(x) +--R + +--R 2 8 2 4 2 2 2 +--R (126126a cosh(x) - 123480a cosh(x) - 32928a cosh(x) - 294a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 5 2 3 +--R 84084a cosh(x) - 148176a cosh(x) - 65856a cosh(x) +--R + +--R 2 +--R - 1764a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 10 2 6 2 4 +--R 42042a cosh(x) - 123480a cosh(x) - 82320a cosh(x) +--R + +--R 2 2 2 +--R - 4410a cosh(x) + 1176a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 11 2 7 2 5 +--R 15288a cosh(x) - 70560a cosh(x) - 65856a cosh(x) +--R + +--R 2 3 2 +--R - 5880a cosh(x) + 4704a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 12 2 8 2 6 +--R 3822a cosh(x) - 26460a cosh(x) - 32928a cosh(x) +--R + +--R 2 4 2 2 2 +--R - 4410a cosh(x) + 7056a cosh(x) + 1176a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 13 2 9 2 7 2 5 +--R 588a cosh(x) - 5880a cosh(x) - 9408a cosh(x) - 1764a cosh(x) +--R + +--R 2 3 2 +--R 4704a cosh(x) + 2352a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 14 2 10 2 8 2 6 +--R 42a cosh(x) - 588a cosh(x) - 1176a cosh(x) - 294a cosh(x) +--R + +--R 2 4 2 2 2 +--R 1176a cosh(x) + 1176a cosh(x) + 336a +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R 12 11 +--R 448a sinh(x) + 5376a cosh(x)sinh(x) +--R + +--R 2 10 +--R (29568a cosh(x) + 1008a)sinh(x) +--R + +--R 3 9 +--R (98560a cosh(x) + 10080a cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (221760a cosh(x) + 45360a cosh(x) )sinh(x) +--R + +--R 5 3 7 +--R (354816a cosh(x) + 120960a cosh(x) )sinh(x) +--R + +--R 6 4 6 +--R (413952a cosh(x) + 211680a cosh(x) - 1904a)sinh(x) +--R + +--R 7 5 5 +--R (354816a cosh(x) + 254016a cosh(x) - 11424a cosh(x))sinh(x) +--R + +--R 8 6 2 +--R (221760a cosh(x) + 211680a cosh(x) - 28560a cosh(x) - 2688a) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 3 +--R 98560a cosh(x) + 120960a cosh(x) - 38080a cosh(x) +--R + +--R - 10752a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 4 +--R 29568a cosh(x) + 45360a cosh(x) - 28560a cosh(x) +--R + +--R 2 +--R - 16128a cosh(x) - 1344a +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 5 +--R 5376a cosh(x) + 10080a cosh(x) - 11424a cosh(x) +--R + +--R 3 +--R - 10752a cosh(x) - 2688a cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 6 4 +--R 448a cosh(x) + 1008a cosh(x) - 1904a cosh(x) - 2688a cosh(x) +--R + +--R 2 +--R - 1344a cosh(x) +--R * +--R +---------+ +--R +---+ |a sinh(x) +--R \|- a |--------- +--R \| cosh(x) +--R + +--R 2 14 2 13 +--R - 80a sinh(x) - 1120a cosh(x)sinh(x) +--R + +--R 2 2 2 12 +--R (- 7280a cosh(x) - 112a )sinh(x) +--R + +--R 2 3 2 11 +--R (- 29120a cosh(x) - 1344a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 10 +--R (- 80080a cosh(x) - 7392a cosh(x) + 896a )sinh(x) +--R + +--R 2 5 2 3 2 9 +--R (- 160160a cosh(x) - 24640a cosh(x) + 8960a cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 8 +--R (- 240240a cosh(x) - 55440a cosh(x) + 40320a cosh(x) + 1232a )sinh(x) +--R + +--R 2 7 2 5 2 3 +--R - 274560a cosh(x) - 88704a cosh(x) + 107520a cosh(x) +--R + +--R 2 +--R 9856a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R - 240240a cosh(x) - 103488a cosh(x) + 188160a cosh(x) +--R + +--R 2 2 2 +--R 34496a cosh(x) + 112a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 7 2 5 +--R - 160160a cosh(x) - 88704a cosh(x) + 225792a cosh(x) +--R + +--R 2 3 2 +--R 68992a cosh(x) + 672a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 10 2 8 2 6 +--R - 80080a cosh(x) - 55440a cosh(x) + 188160a cosh(x) +--R + +--R 2 4 2 2 2 +--R 86240a cosh(x) + 1680a cosh(x) - 1344a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 11 2 9 2 7 +--R - 29120a cosh(x) - 24640a cosh(x) + 107520a cosh(x) +--R + +--R 2 5 2 3 2 +--R 68992a cosh(x) + 2240a cosh(x) - 5376a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 12 2 10 2 8 +--R - 7280a cosh(x) - 7392a cosh(x) + 40320a cosh(x) +--R + +--R 2 6 2 4 2 2 2 +--R 34496a cosh(x) + 1680a cosh(x) - 8064a cosh(x) - 1344a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 13 2 11 2 9 2 7 +--R - 1120a cosh(x) - 1344a cosh(x) + 8960a cosh(x) + 9856a cosh(x) +--R + +--R 2 5 2 3 2 +--R 672a cosh(x) - 5376a cosh(x) - 2688a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 14 2 12 2 10 2 8 +--R - 80a cosh(x) - 112a cosh(x) + 896a cosh(x) + 1232a cosh(x) +--R + +--R 2 6 2 4 2 2 +--R 112a cosh(x) - 1344a cosh(x) - 1344a cosh(x) +--R / +--R 14 13 2 12 +--R 42sinh(x) + 588cosh(x)sinh(x) + (3822cosh(x) + 336)sinh(x) +--R + +--R 3 11 +--R (15288cosh(x) + 4032cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (42042cosh(x) + 22176cosh(x) + 756)sinh(x) +--R + +--R 5 3 9 +--R (84084cosh(x) + 73920cosh(x) + 7560cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (126126cosh(x) + 166320cosh(x) + 34020cosh(x) + 168)sinh(x) +--R + +--R 7 5 3 +--R (144144cosh(x) + 266112cosh(x) + 90720cosh(x) + 1344cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 126126cosh(x) + 310464cosh(x) + 158760cosh(x) + 4704cosh(x) +--R + +--R - 1638 +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 84084cosh(x) + 266112cosh(x) + 190512cosh(x) + 9408cosh(x) +--R + +--R - 9828cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 42042cosh(x) + 166320cosh(x) + 158760cosh(x) + 11760cosh(x) +--R + +--R 2 +--R - 24570cosh(x) - 2520 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 15288cosh(x) + 73920cosh(x) + 90720cosh(x) + 9408cosh(x) +--R + +--R 3 +--R - 32760cosh(x) - 10080cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 3822cosh(x) + 22176cosh(x) + 34020cosh(x) + 4704cosh(x) +--R + +--R 4 2 +--R - 24570cosh(x) - 15120cosh(x) - 1512 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 588cosh(x) + 4032cosh(x) + 7560cosh(x) + 1344cosh(x) +--R + +--R 5 3 +--R - 9828cosh(x) - 10080cosh(x) - 3024cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R 42cosh(x) + 336cosh(x) + 756cosh(x) + 168cosh(x) +--R + +--R 6 4 2 +--R - 1638cosh(x) - 2520cosh(x) - 1512cosh(x) - 336 +--R * +--R +---------+ +--R |a sinh(x) +--R |--------- +--R \| cosh(x) +--R + +--R 14 13 2 12 +--R 42sinh(x) + 588cosh(x)sinh(x) + 3822cosh(x) sinh(x) +--R + +--R 3 11 4 10 +--R 15288cosh(x) sinh(x) + (42042cosh(x) - 588)sinh(x) +--R + +--R 5 9 +--R (84084cosh(x) - 5880cosh(x))sinh(x) +--R + +--R 6 2 8 +--R (126126cosh(x) - 26460cosh(x) - 1176)sinh(x) +--R + +--R 7 3 7 +--R (144144cosh(x) - 70560cosh(x) - 9408cosh(x))sinh(x) +--R + +--R 8 4 2 6 +--R (126126cosh(x) - 123480cosh(x) - 32928cosh(x) - 294)sinh(x) +--R + +--R 9 5 3 +--R (84084cosh(x) - 148176cosh(x) - 65856cosh(x) - 1764cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 4 2 +--R 42042cosh(x) - 123480cosh(x) - 82320cosh(x) - 4410cosh(x) +--R + +--R 1176 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 5 3 +--R 15288cosh(x) - 70560cosh(x) - 65856cosh(x) - 5880cosh(x) +--R + +--R 4704cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 6 4 +--R 3822cosh(x) - 26460cosh(x) - 32928cosh(x) - 4410cosh(x) +--R + +--R 2 +--R 7056cosh(x) + 1176 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 7 5 +--R 588cosh(x) - 5880cosh(x) - 9408cosh(x) - 1764cosh(x) +--R + +--R 3 +--R 4704cosh(x) + 2352cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 8 6 +--R 42cosh(x) - 588cosh(x) - 1176cosh(x) - 294cosh(x) +--R + +--R 4 2 +--R 1176cosh(x) + 1176cosh(x) + 336 +--R * +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0297:= a0297-r0297 +--R +--R +--R (332) +--R 14 13 +--R 21a sinh(x) + 294a cosh(x)sinh(x) +--R + +--R 2 12 +--R (1911a cosh(x) + 168a)sinh(x) +--R + +--R 3 11 +--R (7644a cosh(x) + 2016a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (21021a cosh(x) + 11088a cosh(x) + 378a)sinh(x) +--R + +--R 5 3 9 +--R (42042a cosh(x) + 36960a cosh(x) + 3780a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (63063a cosh(x) + 83160a cosh(x) + 17010a cosh(x) + 84a) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R 72072a cosh(x) + 133056a cosh(x) + 45360a cosh(x) +--R + +--R 672a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R 63063a cosh(x) + 155232a cosh(x) + 79380a cosh(x) +--R + +--R 2 +--R 2352a cosh(x) - 819a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R 42042a cosh(x) + 133056a cosh(x) + 95256a cosh(x) +--R + +--R 3 +--R 4704a cosh(x) - 4914a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R 21021a cosh(x) + 83160a cosh(x) + 79380a cosh(x) +--R + +--R 4 2 +--R 5880a cosh(x) - 12285a cosh(x) - 1260a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R 7644a cosh(x) + 36960a cosh(x) + 45360a cosh(x) +--R + +--R 5 3 +--R 4704a cosh(x) - 16380a cosh(x) - 5040a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R 1911a cosh(x) + 11088a cosh(x) + 17010a cosh(x) +--R + +--R 6 4 2 +--R 2352a cosh(x) - 12285a cosh(x) - 7560a cosh(x) - 756a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R 294a cosh(x) + 2016a cosh(x) + 3780a cosh(x) +--R + +--R 7 5 3 +--R 672a cosh(x) - 4914a cosh(x) - 5040a cosh(x) - 1512a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R 21a cosh(x) + 168a cosh(x) + 378a cosh(x) + 84a cosh(x) +--R + +--R 6 4 2 +--R - 819a cosh(x) - 1260a cosh(x) - 756a cosh(x) - 168a +--R * +--R +---------+ +--R +---+ |a sinh(x) +--R tanh(x)\|- a |--------- +--R \| cosh(x) +--R + +--R 2 14 2 13 2 2 12 +--R - 21a sinh(x) - 294a cosh(x)sinh(x) - 1911a cosh(x) sinh(x) +--R + +--R 2 3 11 2 4 2 10 +--R - 7644a cosh(x) sinh(x) + (- 21021a cosh(x) + 294a )sinh(x) +--R + +--R 2 5 2 9 +--R (- 42042a cosh(x) + 2940a cosh(x))sinh(x) +--R + +--R 2 6 2 2 2 8 +--R (- 63063a cosh(x) + 13230a cosh(x) + 588a )sinh(x) +--R + +--R 2 7 2 3 2 7 +--R (- 72072a cosh(x) + 35280a cosh(x) + 4704a cosh(x))sinh(x) +--R + +--R 2 8 2 4 2 2 2 +--R (- 63063a cosh(x) + 61740a cosh(x) + 16464a cosh(x) + 147a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 5 2 3 +--R - 42042a cosh(x) + 74088a cosh(x) + 32928a cosh(x) +--R + +--R 2 +--R 882a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 10 2 6 2 4 +--R - 21021a cosh(x) + 61740a cosh(x) + 41160a cosh(x) +--R + +--R 2 2 2 +--R 2205a cosh(x) - 588a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 11 2 7 2 5 +--R - 7644a cosh(x) + 35280a cosh(x) + 32928a cosh(x) +--R + +--R 2 3 2 +--R 2940a cosh(x) - 2352a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 12 2 8 2 6 +--R - 1911a cosh(x) + 13230a cosh(x) + 16464a cosh(x) +--R + +--R 2 4 2 2 2 +--R 2205a cosh(x) - 3528a cosh(x) - 588a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 13 2 9 2 7 +--R - 294a cosh(x) + 2940a cosh(x) + 4704a cosh(x) +--R + +--R 2 5 2 3 2 +--R 882a cosh(x) - 2352a cosh(x) - 1176a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 14 2 10 2 8 2 6 +--R - 21a cosh(x) + 294a cosh(x) + 588a cosh(x) + 147a cosh(x) +--R + +--R 2 4 2 2 2 +--R - 588a cosh(x) - 588a cosh(x) - 168a +--R * +--R tanh(x) +--R * +--R +-------+ +--R \|tanh(x) +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R 14 13 +--R - 42a sinh(x) - 588a cosh(x)sinh(x) +--R + +--R 2 12 +--R (- 3822a cosh(x) - 336a)sinh(x) +--R + +--R 3 11 +--R (- 15288a cosh(x) - 4032a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 42042a cosh(x) - 22176a cosh(x) - 756a)sinh(x) +--R + +--R 5 3 9 +--R (- 84084a cosh(x) - 73920a cosh(x) - 7560a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 126126a cosh(x) - 166320a cosh(x) - 34020a cosh(x) +--R + +--R - 168a +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R - 144144a cosh(x) - 266112a cosh(x) - 90720a cosh(x) +--R + +--R - 1344a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R - 126126a cosh(x) - 310464a cosh(x) - 158760a cosh(x) +--R + +--R 2 +--R - 4704a cosh(x) + 1638a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 84084a cosh(x) - 266112a cosh(x) - 190512a cosh(x) +--R + +--R 3 +--R - 9408a cosh(x) + 9828a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 42042a cosh(x) - 166320a cosh(x) - 158760a cosh(x) +--R + +--R 4 2 +--R - 11760a cosh(x) + 24570a cosh(x) + 2520a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 15288a cosh(x) - 73920a cosh(x) - 90720a cosh(x) +--R + +--R 5 3 +--R - 9408a cosh(x) + 32760a cosh(x) + 10080a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R - 3822a cosh(x) - 22176a cosh(x) - 34020a cosh(x) +--R + +--R 6 4 2 +--R - 4704a cosh(x) + 24570a cosh(x) + 15120a cosh(x) + 1512a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R - 588a cosh(x) - 4032a cosh(x) - 7560a cosh(x) +--R + +--R 7 5 3 +--R - 1344a cosh(x) + 9828a cosh(x) + 10080a cosh(x) +--R + +--R 3024a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 42a cosh(x) - 336a cosh(x) - 756a cosh(x) - 168a cosh(x) +--R + +--R 6 4 2 +--R 1638a cosh(x) + 2520a cosh(x) + 1512a cosh(x) + 336a +--R * +--R +---------+ +--R |a sinh(x) +--R |--------- +--R \| cosh(x) +--R + +--R 14 13 2 12 +--R - 42a sinh(x) - 588a cosh(x)sinh(x) - 3822a cosh(x) sinh(x) +--R + +--R 3 11 4 10 +--R - 15288a cosh(x) sinh(x) + (- 42042a cosh(x) + 588a)sinh(x) +--R + +--R 5 9 +--R (- 84084a cosh(x) + 5880a cosh(x))sinh(x) +--R + +--R 6 2 8 +--R (- 126126a cosh(x) + 26460a cosh(x) + 1176a)sinh(x) +--R + +--R 7 3 7 +--R (- 144144a cosh(x) + 70560a cosh(x) + 9408a cosh(x))sinh(x) +--R + +--R 8 4 2 +--R - 126126a cosh(x) + 123480a cosh(x) + 32928a cosh(x) +--R + +--R 294a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 5 3 +--R - 84084a cosh(x) + 148176a cosh(x) + 65856a cosh(x) +--R + +--R 1764a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 4 +--R - 42042a cosh(x) + 123480a cosh(x) + 82320a cosh(x) +--R + +--R 2 +--R 4410a cosh(x) - 1176a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 5 +--R - 15288a cosh(x) + 70560a cosh(x) + 65856a cosh(x) +--R + +--R 3 +--R 5880a cosh(x) - 4704a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 6 +--R - 3822a cosh(x) + 26460a cosh(x) + 32928a cosh(x) +--R + +--R 4 2 +--R 4410a cosh(x) - 7056a cosh(x) - 1176a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 7 +--R - 588a cosh(x) + 5880a cosh(x) + 9408a cosh(x) +--R + +--R 5 3 +--R 1764a cosh(x) - 4704a cosh(x) - 2352a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 8 6 +--R - 42a cosh(x) + 588a cosh(x) + 1176a cosh(x) + 294a cosh(x) +--R + +--R 4 2 +--R - 1176a cosh(x) - 1176a cosh(x) - 336a +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R | 3 +-------+ +--R \|a tanh(x) atanh(\|tanh(x) ) +--R + +--R 14 13 +--R 42a sinh(x) + 588a cosh(x)sinh(x) +--R + +--R 2 12 +--R (3822a cosh(x) + 336a)sinh(x) +--R + +--R 3 11 +--R (15288a cosh(x) + 4032a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (42042a cosh(x) + 22176a cosh(x) + 756a)sinh(x) +--R + +--R 5 3 9 +--R (84084a cosh(x) + 73920a cosh(x) + 7560a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (126126a cosh(x) + 166320a cosh(x) + 34020a cosh(x) + 168a) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R 144144a cosh(x) + 266112a cosh(x) + 90720a cosh(x) +--R + +--R 1344a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R 126126a cosh(x) + 310464a cosh(x) + 158760a cosh(x) +--R + +--R 2 +--R 4704a cosh(x) - 1638a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R 84084a cosh(x) + 266112a cosh(x) + 190512a cosh(x) +--R + +--R 3 +--R 9408a cosh(x) - 9828a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R 42042a cosh(x) + 166320a cosh(x) + 158760a cosh(x) +--R + +--R 4 2 +--R 11760a cosh(x) - 24570a cosh(x) - 2520a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R 15288a cosh(x) + 73920a cosh(x) + 90720a cosh(x) +--R + +--R 5 3 +--R 9408a cosh(x) - 32760a cosh(x) - 10080a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R 3822a cosh(x) + 22176a cosh(x) + 34020a cosh(x) +--R + +--R 6 4 2 +--R 4704a cosh(x) - 24570a cosh(x) - 15120a cosh(x) - 1512a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R 588a cosh(x) + 4032a cosh(x) + 7560a cosh(x) +--R + +--R 7 5 3 +--R 1344a cosh(x) - 9828a cosh(x) - 10080a cosh(x) +--R + +--R - 3024a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R 42a cosh(x) + 336a cosh(x) + 756a cosh(x) + 168a cosh(x) +--R + +--R 6 4 2 +--R - 1638a cosh(x) - 2520a cosh(x) - 1512a cosh(x) - 336a +--R * +--R +---------+ +--R |a sinh(x) +--R |--------- +--R \| cosh(x) +--R + +--R 14 13 2 12 +--R 42a sinh(x) + 588a cosh(x)sinh(x) + 3822a cosh(x) sinh(x) +--R + +--R 3 11 4 10 +--R 15288a cosh(x) sinh(x) + (42042a cosh(x) - 588a)sinh(x) +--R + +--R 5 9 +--R (84084a cosh(x) - 5880a cosh(x))sinh(x) +--R + +--R 6 2 8 +--R (126126a cosh(x) - 26460a cosh(x) - 1176a)sinh(x) +--R + +--R 7 3 7 +--R (144144a cosh(x) - 70560a cosh(x) - 9408a cosh(x))sinh(x) +--R + +--R 8 4 2 +--R (126126a cosh(x) - 123480a cosh(x) - 32928a cosh(x) - 294a) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 5 3 +--R 84084a cosh(x) - 148176a cosh(x) - 65856a cosh(x) +--R + +--R - 1764a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 4 +--R 42042a cosh(x) - 123480a cosh(x) - 82320a cosh(x) +--R + +--R 2 +--R - 4410a cosh(x) + 1176a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 5 +--R 15288a cosh(x) - 70560a cosh(x) - 65856a cosh(x) +--R + +--R 3 +--R - 5880a cosh(x) + 4704a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 6 +--R 3822a cosh(x) - 26460a cosh(x) - 32928a cosh(x) +--R + +--R 4 2 +--R - 4410a cosh(x) + 7056a cosh(x) + 1176a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 7 +--R 588a cosh(x) - 5880a cosh(x) - 9408a cosh(x) +--R + +--R 5 3 +--R - 1764a cosh(x) + 4704a cosh(x) + 2352a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 8 6 +--R 42a cosh(x) - 588a cosh(x) - 1176a cosh(x) - 294a cosh(x) +--R + +--R 4 2 +--R 1176a cosh(x) + 1176a cosh(x) + 336a +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R | 3 +-------+ +--R \|a tanh(x) atan(\|tanh(x) ) +--R + +--R 14 13 +--R - 42a sinh(x) - 588a cosh(x)sinh(x) +--R + +--R 2 12 +--R (- 3822a cosh(x) - 336a)sinh(x) +--R + +--R 3 11 +--R (- 15288a cosh(x) - 4032a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 42042a cosh(x) - 22176a cosh(x) - 756a)sinh(x) +--R + +--R 5 3 9 +--R (- 84084a cosh(x) - 73920a cosh(x) - 7560a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 126126a cosh(x) - 166320a cosh(x) - 34020a cosh(x) +--R + +--R - 168a +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R - 144144a cosh(x) - 266112a cosh(x) - 90720a cosh(x) +--R + +--R - 1344a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R - 126126a cosh(x) - 310464a cosh(x) - 158760a cosh(x) +--R + +--R 2 +--R - 4704a cosh(x) + 1638a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 84084a cosh(x) - 266112a cosh(x) - 190512a cosh(x) +--R + +--R 3 +--R - 9408a cosh(x) + 9828a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 42042a cosh(x) - 166320a cosh(x) - 158760a cosh(x) +--R + +--R 4 2 +--R - 11760a cosh(x) + 24570a cosh(x) + 2520a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 15288a cosh(x) - 73920a cosh(x) - 90720a cosh(x) +--R + +--R 5 3 +--R - 9408a cosh(x) + 32760a cosh(x) + 10080a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R - 3822a cosh(x) - 22176a cosh(x) - 34020a cosh(x) +--R + +--R 6 4 2 +--R - 4704a cosh(x) + 24570a cosh(x) + 15120a cosh(x) + 1512a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R - 588a cosh(x) - 4032a cosh(x) - 7560a cosh(x) +--R + +--R 7 5 3 +--R - 1344a cosh(x) + 9828a cosh(x) + 10080a cosh(x) +--R + +--R 3024a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 42a cosh(x) - 336a cosh(x) - 756a cosh(x) - 168a cosh(x) +--R + +--R 6 4 2 +--R 1638a cosh(x) + 2520a cosh(x) + 1512a cosh(x) + 336a +--R * +--R +---------+ +--R +---+ |a sinh(x) +--R tanh(x)\|- a |--------- +--R \| cosh(x) +--R + +--R 2 14 2 13 2 2 12 +--R 42a sinh(x) + 588a cosh(x)sinh(x) + 3822a cosh(x) sinh(x) +--R + +--R 2 3 11 2 4 2 10 +--R 15288a cosh(x) sinh(x) + (42042a cosh(x) - 588a )sinh(x) +--R + +--R 2 5 2 9 +--R (84084a cosh(x) - 5880a cosh(x))sinh(x) +--R + +--R 2 6 2 2 2 8 +--R (126126a cosh(x) - 26460a cosh(x) - 1176a )sinh(x) +--R + +--R 2 7 2 3 2 7 +--R (144144a cosh(x) - 70560a cosh(x) - 9408a cosh(x))sinh(x) +--R + +--R 2 8 2 4 2 2 2 +--R (126126a cosh(x) - 123480a cosh(x) - 32928a cosh(x) - 294a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 5 2 3 +--R 84084a cosh(x) - 148176a cosh(x) - 65856a cosh(x) +--R + +--R 2 +--R - 1764a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 10 2 6 2 4 +--R 42042a cosh(x) - 123480a cosh(x) - 82320a cosh(x) +--R + +--R 2 2 2 +--R - 4410a cosh(x) + 1176a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 11 2 7 2 5 +--R 15288a cosh(x) - 70560a cosh(x) - 65856a cosh(x) +--R + +--R 2 3 2 +--R - 5880a cosh(x) + 4704a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 12 2 8 2 6 +--R 3822a cosh(x) - 26460a cosh(x) - 32928a cosh(x) +--R + +--R 2 4 2 2 2 +--R - 4410a cosh(x) + 7056a cosh(x) + 1176a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 13 2 9 2 7 +--R 588a cosh(x) - 5880a cosh(x) - 9408a cosh(x) +--R + +--R 2 5 2 3 2 +--R - 1764a cosh(x) + 4704a cosh(x) + 2352a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 14 2 10 2 8 2 6 +--R 42a cosh(x) - 588a cosh(x) - 1176a cosh(x) - 294a cosh(x) +--R + +--R 2 4 2 2 2 +--R 1176a cosh(x) + 1176a cosh(x) + 336a +--R * +--R tanh(x) +--R * +--R +-------+ +--R \|tanh(x) +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R 14 13 +--R 12a sinh(x) + 168a cosh(x)sinh(x) +--R + +--R 2 12 +--R (1092a cosh(x) + 96a)sinh(x) +--R + +--R 3 11 +--R (4368a cosh(x) + 1152a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (12012a cosh(x) + 6336a cosh(x) + 216a)sinh(x) +--R + +--R 5 3 9 +--R (24024a cosh(x) + 21120a cosh(x) + 2160a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (36036a cosh(x) + 47520a cosh(x) + 9720a cosh(x) + 48a) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R 41184a cosh(x) + 76032a cosh(x) + 25920a cosh(x) +--R + +--R 384a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R 36036a cosh(x) + 88704a cosh(x) + 45360a cosh(x) +--R + +--R 2 +--R 1344a cosh(x) - 468a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R 24024a cosh(x) + 76032a cosh(x) + 54432a cosh(x) +--R + +--R 3 +--R 2688a cosh(x) - 2808a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R 12012a cosh(x) + 47520a cosh(x) + 45360a cosh(x) +--R + +--R 4 2 +--R 3360a cosh(x) - 7020a cosh(x) - 720a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R 4368a cosh(x) + 21120a cosh(x) + 25920a cosh(x) +--R + +--R 5 3 +--R 2688a cosh(x) - 9360a cosh(x) - 2880a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R 1092a cosh(x) + 6336a cosh(x) + 9720a cosh(x) +--R + +--R 6 4 2 +--R 1344a cosh(x) - 7020a cosh(x) - 4320a cosh(x) - 432a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R 168a cosh(x) + 1152a cosh(x) + 2160a cosh(x) +--R + +--R 7 5 3 +--R 384a cosh(x) - 2808a cosh(x) - 2880a cosh(x) +--R + +--R - 864a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R 12a cosh(x) + 96a cosh(x) + 216a cosh(x) + 48a cosh(x) +--R + +--R 6 4 2 +--R - 468a cosh(x) - 720a cosh(x) - 432a cosh(x) - 96a +--R * +--R 3 +--R tanh(x) +--R + +--R 14 13 +--R 28a sinh(x) + 392a cosh(x)sinh(x) +--R + +--R 2 12 +--R (2548a cosh(x) + 224a)sinh(x) +--R + +--R 3 11 +--R (10192a cosh(x) + 2688a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (28028a cosh(x) + 14784a cosh(x) + 504a)sinh(x) +--R + +--R 5 3 9 +--R (56056a cosh(x) + 49280a cosh(x) + 5040a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 84084a cosh(x) + 110880a cosh(x) + 22680a cosh(x) +--R + +--R 112a +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R 96096a cosh(x) + 177408a cosh(x) + 60480a cosh(x) +--R + +--R 896a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R 84084a cosh(x) + 206976a cosh(x) + 105840a cosh(x) +--R + +--R 2 +--R 3136a cosh(x) - 1092a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R 56056a cosh(x) + 177408a cosh(x) + 127008a cosh(x) +--R + +--R 3 +--R 6272a cosh(x) - 6552a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R 28028a cosh(x) + 110880a cosh(x) + 105840a cosh(x) +--R + +--R 4 2 +--R 7840a cosh(x) - 16380a cosh(x) - 1680a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R 10192a cosh(x) + 49280a cosh(x) + 60480a cosh(x) +--R + +--R 5 3 +--R 6272a cosh(x) - 21840a cosh(x) - 6720a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R 2548a cosh(x) + 14784a cosh(x) + 22680a cosh(x) +--R + +--R 6 4 2 +--R 3136a cosh(x) - 16380a cosh(x) - 10080a cosh(x) - 1008a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R 392a cosh(x) + 2688a cosh(x) + 5040a cosh(x) +--R + +--R 7 5 3 +--R 896a cosh(x) - 6552a cosh(x) - 6720a cosh(x) +--R + +--R - 2016a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 +--R 28a cosh(x) + 224a cosh(x) + 504a cosh(x) +--R + +--R 8 6 4 +--R 112a cosh(x) - 1092a cosh(x) - 1680a cosh(x) +--R + +--R 2 +--R - 1008a cosh(x) - 224a +--R * +--R tanh(x) +--R * +--R +---------+ +--R |a sinh(x) +--R |--------- +--R \| cosh(x) +--R + +--R 14 13 +--R 12a sinh(x) + 168a cosh(x)sinh(x) +--R + +--R 2 12 3 11 +--R 1092a cosh(x) sinh(x) + 4368a cosh(x) sinh(x) +--R + +--R 4 10 +--R (12012a cosh(x) - 168a)sinh(x) +--R + +--R 5 9 +--R (24024a cosh(x) - 1680a cosh(x))sinh(x) +--R + +--R 6 2 8 +--R (36036a cosh(x) - 7560a cosh(x) - 336a)sinh(x) +--R + +--R 7 3 7 +--R (41184a cosh(x) - 20160a cosh(x) - 2688a cosh(x))sinh(x) +--R + +--R 8 4 2 +--R (36036a cosh(x) - 35280a cosh(x) - 9408a cosh(x) - 84a) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 5 3 +--R 24024a cosh(x) - 42336a cosh(x) - 18816a cosh(x) +--R + +--R - 504a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 4 +--R 12012a cosh(x) - 35280a cosh(x) - 23520a cosh(x) +--R + +--R 2 +--R - 1260a cosh(x) + 336a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 5 +--R 4368a cosh(x) - 20160a cosh(x) - 18816a cosh(x) +--R + +--R 3 +--R - 1680a cosh(x) + 1344a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 6 +--R 1092a cosh(x) - 7560a cosh(x) - 9408a cosh(x) +--R + +--R 4 2 +--R - 1260a cosh(x) + 2016a cosh(x) + 336a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 7 +--R 168a cosh(x) - 1680a cosh(x) - 2688a cosh(x) +--R + +--R 5 3 +--R - 504a cosh(x) + 1344a cosh(x) + 672a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 8 6 +--R 12a cosh(x) - 168a cosh(x) - 336a cosh(x) - 84a cosh(x) +--R + +--R 4 2 +--R 336a cosh(x) + 336a cosh(x) + 96a +--R * +--R 3 +--R tanh(x) +--R + +--R 14 13 +--R 28a sinh(x) + 392a cosh(x)sinh(x) +--R + +--R 2 12 3 11 +--R 2548a cosh(x) sinh(x) + 10192a cosh(x) sinh(x) +--R + +--R 4 10 +--R (28028a cosh(x) - 392a)sinh(x) +--R + +--R 5 9 +--R (56056a cosh(x) - 3920a cosh(x))sinh(x) +--R + +--R 6 2 8 +--R (84084a cosh(x) - 17640a cosh(x) - 784a)sinh(x) +--R + +--R 7 3 7 +--R (96096a cosh(x) - 47040a cosh(x) - 6272a cosh(x))sinh(x) +--R + +--R 8 4 2 +--R 84084a cosh(x) - 82320a cosh(x) - 21952a cosh(x) +--R + +--R - 196a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 5 3 +--R 56056a cosh(x) - 98784a cosh(x) - 43904a cosh(x) +--R + +--R - 1176a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 4 +--R 28028a cosh(x) - 82320a cosh(x) - 54880a cosh(x) +--R + +--R 2 +--R - 2940a cosh(x) + 784a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 5 +--R 10192a cosh(x) - 47040a cosh(x) - 43904a cosh(x) +--R + +--R 3 +--R - 3920a cosh(x) + 3136a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 6 +--R 2548a cosh(x) - 17640a cosh(x) - 21952a cosh(x) +--R + +--R 4 2 +--R - 2940a cosh(x) + 4704a cosh(x) + 784a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 7 +--R 392a cosh(x) - 3920a cosh(x) - 6272a cosh(x) +--R + +--R 5 3 +--R - 1176a cosh(x) + 3136a cosh(x) + 1568a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 8 +--R 28a cosh(x) - 392a cosh(x) - 784a cosh(x) +--R + +--R 6 4 2 +--R - 196a cosh(x) + 784a cosh(x) + 784a cosh(x) + 224a +--R * +--R tanh(x) +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R +-------+ | 3 +--R \|tanh(x) \|a tanh(x) +--R + +--R 12 11 +--R 448a sinh(x) + 5376a cosh(x)sinh(x) +--R + +--R 2 10 +--R (29568a cosh(x) + 1008a)sinh(x) +--R + +--R 3 9 +--R (98560a cosh(x) + 10080a cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (221760a cosh(x) + 45360a cosh(x) )sinh(x) +--R + +--R 5 3 7 +--R (354816a cosh(x) + 120960a cosh(x) )sinh(x) +--R + +--R 6 4 6 +--R (413952a cosh(x) + 211680a cosh(x) - 1904a)sinh(x) +--R + +--R 7 5 5 +--R (354816a cosh(x) + 254016a cosh(x) - 11424a cosh(x))sinh(x) +--R + +--R 8 6 2 +--R (221760a cosh(x) + 211680a cosh(x) - 28560a cosh(x) - 2688a) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 3 +--R 98560a cosh(x) + 120960a cosh(x) - 38080a cosh(x) +--R + +--R - 10752a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 4 +--R 29568a cosh(x) + 45360a cosh(x) - 28560a cosh(x) +--R + +--R 2 +--R - 16128a cosh(x) - 1344a +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 5 +--R 5376a cosh(x) + 10080a cosh(x) - 11424a cosh(x) +--R + +--R 3 +--R - 10752a cosh(x) - 2688a cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 6 +--R 448a cosh(x) + 1008a cosh(x) - 1904a cosh(x) +--R + +--R 4 2 +--R - 2688a cosh(x) - 1344a cosh(x) +--R * +--R +---------+ +--R +---+ |a sinh(x) +--R tanh(x)\|- a |--------- +--R \| cosh(x) +--R + +--R 2 14 2 13 +--R - 80a sinh(x) - 1120a cosh(x)sinh(x) +--R + +--R 2 2 2 12 +--R (- 7280a cosh(x) - 112a )sinh(x) +--R + +--R 2 3 2 11 +--R (- 29120a cosh(x) - 1344a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 10 +--R (- 80080a cosh(x) - 7392a cosh(x) + 896a )sinh(x) +--R + +--R 2 5 2 3 2 9 +--R (- 160160a cosh(x) - 24640a cosh(x) + 8960a cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 +--R - 240240a cosh(x) - 55440a cosh(x) + 40320a cosh(x) +--R + +--R 2 +--R 1232a +--R * +--R 8 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R - 274560a cosh(x) - 88704a cosh(x) + 107520a cosh(x) +--R + +--R 2 +--R 9856a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R - 240240a cosh(x) - 103488a cosh(x) + 188160a cosh(x) +--R + +--R 2 2 2 +--R 34496a cosh(x) + 112a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 7 2 5 +--R - 160160a cosh(x) - 88704a cosh(x) + 225792a cosh(x) +--R + +--R 2 3 2 +--R 68992a cosh(x) + 672a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 10 2 8 2 6 +--R - 80080a cosh(x) - 55440a cosh(x) + 188160a cosh(x) +--R + +--R 2 4 2 2 2 +--R 86240a cosh(x) + 1680a cosh(x) - 1344a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 11 2 9 2 7 +--R - 29120a cosh(x) - 24640a cosh(x) + 107520a cosh(x) +--R + +--R 2 5 2 3 2 +--R 68992a cosh(x) + 2240a cosh(x) - 5376a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 12 2 10 2 8 +--R - 7280a cosh(x) - 7392a cosh(x) + 40320a cosh(x) +--R + +--R 2 6 2 4 2 2 2 +--R 34496a cosh(x) + 1680a cosh(x) - 8064a cosh(x) - 1344a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 13 2 11 2 9 +--R - 1120a cosh(x) - 1344a cosh(x) + 8960a cosh(x) +--R + +--R 2 7 2 5 2 3 2 +--R 9856a cosh(x) + 672a cosh(x) - 5376a cosh(x) - 2688a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 14 2 12 2 10 +--R - 80a cosh(x) - 112a cosh(x) + 896a cosh(x) +--R + +--R 2 8 2 6 2 4 2 2 +--R 1232a cosh(x) + 112a cosh(x) - 1344a cosh(x) - 1344a cosh(x) +--R * +--R tanh(x) +--R * +--R +-------+ +--R \|tanh(x) +--R / +--R 14 13 2 12 +--R 42sinh(x) + 588cosh(x)sinh(x) + (3822cosh(x) + 336)sinh(x) +--R + +--R 3 11 +--R (15288cosh(x) + 4032cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (42042cosh(x) + 22176cosh(x) + 756)sinh(x) +--R + +--R 5 3 9 +--R (84084cosh(x) + 73920cosh(x) + 7560cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (126126cosh(x) + 166320cosh(x) + 34020cosh(x) + 168)sinh(x) +--R + +--R 7 5 3 +--R (144144cosh(x) + 266112cosh(x) + 90720cosh(x) + 1344cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 126126cosh(x) + 310464cosh(x) + 158760cosh(x) + 4704cosh(x) +--R + +--R - 1638 +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 84084cosh(x) + 266112cosh(x) + 190512cosh(x) + 9408cosh(x) +--R + +--R - 9828cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R 42042cosh(x) + 166320cosh(x) + 158760cosh(x) +--R + +--R 4 2 +--R 11760cosh(x) - 24570cosh(x) - 2520 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 15288cosh(x) + 73920cosh(x) + 90720cosh(x) + 9408cosh(x) +--R + +--R 3 +--R - 32760cosh(x) - 10080cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 3822cosh(x) + 22176cosh(x) + 34020cosh(x) + 4704cosh(x) +--R + +--R 4 2 +--R - 24570cosh(x) - 15120cosh(x) - 1512 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 588cosh(x) + 4032cosh(x) + 7560cosh(x) + 1344cosh(x) +--R + +--R 5 3 +--R - 9828cosh(x) - 10080cosh(x) - 3024cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R 42cosh(x) + 336cosh(x) + 756cosh(x) + 168cosh(x) +--R + +--R 6 4 2 +--R - 1638cosh(x) - 2520cosh(x) - 1512cosh(x) - 336 +--R * +--R +---------+ +--R |a sinh(x) +--R tanh(x) |--------- +--R \| cosh(x) +--R + +--R 14 13 2 12 +--R 42sinh(x) + 588cosh(x)sinh(x) + 3822cosh(x) sinh(x) +--R + +--R 3 11 4 10 +--R 15288cosh(x) sinh(x) + (42042cosh(x) - 588)sinh(x) +--R + +--R 5 9 +--R (84084cosh(x) - 5880cosh(x))sinh(x) +--R + +--R 6 2 8 +--R (126126cosh(x) - 26460cosh(x) - 1176)sinh(x) +--R + +--R 7 3 7 +--R (144144cosh(x) - 70560cosh(x) - 9408cosh(x))sinh(x) +--R + +--R 8 4 2 6 +--R (126126cosh(x) - 123480cosh(x) - 32928cosh(x) - 294)sinh(x) +--R + +--R 9 5 3 +--R (84084cosh(x) - 148176cosh(x) - 65856cosh(x) - 1764cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 4 2 +--R 42042cosh(x) - 123480cosh(x) - 82320cosh(x) - 4410cosh(x) +--R + +--R 1176 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 5 3 +--R 15288cosh(x) - 70560cosh(x) - 65856cosh(x) - 5880cosh(x) +--R + +--R 4704cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 6 4 +--R 3822cosh(x) - 26460cosh(x) - 32928cosh(x) - 4410cosh(x) +--R + +--R 2 +--R 7056cosh(x) + 1176 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 7 5 +--R 588cosh(x) - 5880cosh(x) - 9408cosh(x) - 1764cosh(x) +--R + +--R 3 +--R 4704cosh(x) + 2352cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 8 6 +--R 42cosh(x) - 588cosh(x) - 1176cosh(x) - 294cosh(x) +--R + +--R 4 2 +--R 1176cosh(x) + 1176cosh(x) + 336 +--R * +--R +---+ +--R tanh(x)\|- a +--R * +--R +-------+ +--R \|tanh(x) +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +--d0297:= D(m0297,x) +--E 490 + +--S 491 of 500 +t0298:= 1/(a*tanh(x)^2)^(1/2) +--R +--R +--R 1 +--R (333) ------------- +--R +----------+ +--R | 2 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0298:= log(sinh(x))*tanh(x)/(a*tanh(x)^2)^(1/2) +--R +--R +--R tanh(x)log(sinh(x)) +--R (334) ------------------- +--R +----------+ +--R | 2 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0298:= integrate(t0298,x) +--R +--R +--R 2sinh(x) +--R log(- -----------------) - x +--R sinh(x) - cosh(x) +--R (335) ---------------------------- +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0298:= a0298-r0298 +--R +--R +--R (336) +--R +----------+ +--R 2sinh(x) | 2 +-+ +--R (log(- -----------------) - x)\|a tanh(x) - tanh(x)\|a log(sinh(x)) +--R sinh(x) - cosh(x) +--R --------------------------------------------------------------------- +--R +----------+ +--R +-+ | 2 +--R \|a \|a tanh(x) +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0298:= D(m0298,x) +--R +--R +--R +----------+ +--R +-+ | 2 +--R cosh(x)\|a \|a tanh(x) - a cosh(x)tanh(x) +--R (337) ------------------------------------------- +--R +----------+ +--R | 2 +--R a sinh(x)\|a tanh(x) +--R Type: Expression(Integer) +--E 495 + +--S 496 of 500 +t0299:= 1/(a*tanh(x)^3)^(1/2) +--R +--R +--R 1 +--R (338) ------------- +--R +----------+ +--R | 3 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0299:= -(2+(atan(tanh(x)^(1/2))-atanh(tanh(x)^(1/2)))*tanh(x)^(1/2))*_ + tanh(x)/(a*tanh(x)^3)^(1/2) +--R +--R +--R (339) +--R +-------+ +-------+ +-------+ +-------+ +--R tanh(x)\|tanh(x) atanh(\|tanh(x) ) - tanh(x)\|tanh(x) atan(\|tanh(x) ) +--R + +--R - 2tanh(x) +--R / +--R +----------+ +--R | 3 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0299:= integrate(t0299,x) +--R +--R +--R (340) +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- +--R \| cosh(x) +--R + +--R 2 2 +--R - a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2)\|- a |--------- +--R \| cosh(x) +--R + +--R 2 2 +--R 2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) - 2a +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R - 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) +--R / +--R +---------+ +--R 2 2 |a sinh(x) +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) + 2a) |--------- +--R \| cosh(x) +--R + +--R 2 2 +---+ +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) - 2a)\|- a +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0299:= a0299-r0299 +--R +--R +--R (341) +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- +--R \| cosh(x) +--R + +--R 2 2 +--R - a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a +--R * +--R +----------+ +--R | 3 +--R \|a tanh(x) +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)tanh(x) +--R * +--R +---------+ +--R |a sinh(x) +--R |--------- +--R \| cosh(x) +--R + +--R 2 2 +---+ +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) + 2a)tanh(x)\|- a +--R * +--R +-------+ +-------+ +--R \|tanh(x) atanh(\|tanh(x) ) +--R + +--R 2 2 +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) + 2a)tanh(x) +--R * +--R +---------+ +--R |a sinh(x) +--R |--------- +--R \| cosh(x) +--R + +--R 2 2 +---+ +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) - 2a)tanh(x)\|- a +--R * +--R +-------+ +-------+ +--R \|tanh(x) atan(\|tanh(x) ) +--R + +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2)\|- a |--------- +--R \| cosh(x) +--R + +--R 2 2 +--R 2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) - 2a +--R * +--R +----------+ +--R | 3 +--R \|a tanh(x) +--R * +--R +---------+ +--R 2 2 +---+ |a sinh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a |--------- + a +--R \| cosh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R +----------+ +--R 2 2 | 3 +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) )\|a tanh(x) +--R + +--R +---------+ +--R 2 2 |a sinh(x) +--R (4a sinh(x) + 8a cosh(x)sinh(x) + 4a cosh(x) + 4a)tanh(x) |--------- +--R \| cosh(x) +--R + +--R 2 2 +---+ +--R (4a sinh(x) + 8a cosh(x)sinh(x) + 4a cosh(x) - 4a)tanh(x)\|- a +--R / +--R +---------+ +--R 2 2 |a sinh(x) +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) + 2a) |--------- +--R \| cosh(x) +--R + +--R 2 2 +---+ +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) - 2a)\|- a +--R * +--R +----------+ +--R | 3 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0299:= D(m0299,x) +--R +--R +--R (342) +--R 14 13 2 12 +--R sinh(x) + 4cosh(x)sinh(x) + (- 15cosh(x) + 5)sinh(x) +--R + +--R 3 11 +--R (- 144cosh(x) + 14cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 451cosh(x) - 108cosh(x) + 10)sinh(x) +--R + +--R 5 3 9 +--R (- 748cosh(x) - 718cosh(x) + 16cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 627cosh(x) - 1831cosh(x) - 274cosh(x) + 10)sinh(x) +--R + +--R 5 3 7 +--R (- 2420cosh(x) - 1280cosh(x) + 4cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (627cosh(x) - 1456cosh(x) - 2300cosh(x) - 324cosh(x) + 5) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 748cosh(x) + 292cosh(x) - 1760cosh(x) - 956cosh(x) +--R + +--R - 4cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 451cosh(x) + 1127cosh(x) - 4cosh(x) - 864cosh(x) +--R + +--R 2 +--R - 183cosh(x) + 1 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 144cosh(x) + 774cosh(x) + 896cosh(x) + 44cosh(x) +--R + +--R 3 +--R - 224cosh(x) - 2cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 15cosh(x) + 220cosh(x) + 530cosh(x) + 420cosh(x) +--R + +--R 4 2 +--R 55cosh(x) - 40cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 4cosh(x) + 10cosh(x) + 80cosh(x) + 140cosh(x) +--R + +--R 5 3 +--R 100cosh(x) + 26cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R - cosh(x) - 5cosh(x) - 10cosh(x) - 10cosh(x) - 5cosh(x) +--R + +--R 4 +--R - cosh(x) +--R * +--R +---------+ +--R |a sinh(x) +--R |--------- +--R \| cosh(x) +--R + +--R 14 13 2 12 +--R - 4sinh(x) - 36cosh(x)sinh(x) + (- 136cosh(x) - 20)sinh(x) +--R + +--R 3 11 +--R (- 264cosh(x) - 160cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 220cosh(x) - 500cosh(x) - 40)sinh(x) +--R + +--R 5 3 9 +--R (132cosh(x) - 664cosh(x) - 280cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (528cosh(x) + 88cosh(x) - 640cosh(x) - 40)sinh(x) +--R + +--R 7 5 3 7 +--R (528cosh(x) + 1568cosh(x) - 256cosh(x) - 240cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (132cosh(x) + 2296cosh(x) + 1264cosh(x) - 280cosh(x) - 20) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 220cosh(x) + 1520cosh(x) + 2320cosh(x) + 416cosh(x) +--R + +--R - 100cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 264cosh(x) + 316cosh(x) + 1600cosh(x) + 1064cosh(x) +--R + +--R 2 +--R 40cosh(x) - 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 136cosh(x) - 192cosh(x) + 320cosh(x) + 656cosh(x) +--R + +--R 3 +--R 264cosh(x) - 16cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 36cosh(x) - 132cosh(x) - 136cosh(x) + 24cosh(x) +--R + +--R 4 2 +--R 108cosh(x) + 44cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 4cosh(x) - 24cosh(x) - 56cosh(x) - 64cosh(x) +--R + +--R 5 3 +--R - 36cosh(x) - 8cosh(x) +--R * +--R sinh(x) +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R | 3 +--R \|a tanh(x) +--R + +--R 13 2 12 +--R - 4cosh(x)sinh(x) - 32cosh(x) sinh(x) +--R + +--R 3 11 +--R (- 104cosh(x) - 20cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 160cosh(x) - 168cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (- 60cosh(x) - 612cosh(x) - 40cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (192cosh(x) - 1248cosh(x) - 272cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (336cosh(x) - 1512cosh(x) - 800cosh(x) - 40cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (192cosh(x) - 1008cosh(x) - 1328cosh(x) - 128cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R - 60cosh(x) - 168cosh(x) - 1360cosh(x) - 104cosh(x) +--R + +--R - 20cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 160cosh(x) + 288cosh(x) - 880cosh(x) + 64cosh(x) +--R + +--R 2 +--R 48cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 104cosh(x) + 252cosh(x) - 352cosh(x) + 136cosh(x) +--R + +--R 3 +--R 168cosh(x) - 4cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 32cosh(x) + 88cosh(x) - 80cosh(x) + 64cosh(x) +--R + +--R 4 2 +--R 112cosh(x) + 40cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R - 4cosh(x) + 12cosh(x) - 8cosh(x) + 8cosh(x) + 12cosh(x) +--R + +--R 3 +--R - 20cosh(x) +--R * +--R sinh(x) +--R * +--R +---------+ +--R +---+ |a sinh(x) +--R \|- a |--------- +--R \| cosh(x) +--R + +--R 13 2 12 +--R 8a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 3 11 +--R (280a cosh(x) + 12a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (600a cosh(x) + 104a cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (720a cosh(x) + 396a cosh(x) - 32a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (336a cosh(x) + 864a cosh(x) - 200a cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (- 336a cosh(x) + 1176a cosh(x) - 520a cosh(x) - 88a cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 720a cosh(x) + 1008a cosh(x) - 712a cosh(x) - 384a cosh(x) ) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 600a cosh(x) + 504a cosh(x) - 520a cosh(x) - 664a cosh(x) +--R + +--R - 72a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 280a cosh(x) + 96a cosh(x) - 152a cosh(x) - 576a cosh(x) +--R + +--R 2 +--R - 112a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 72a cosh(x) - 36a cosh(x) + 40a cosh(x) - 264a cosh(x) +--R + +--R - 20a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 8a cosh(x) - 24a cosh(x) + 40a cosh(x) - 64a cosh(x) +--R + +--R 4 2 +--R 48a cosh(x) + 40a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 4a cosh(x) + 8a cosh(x) - 8a cosh(x) + 8a cosh(x) +--R + +--R 3 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R / +--R 13 2 12 +--R 4cosh(x)sinh(x) + 32cosh(x) sinh(x) +--R + +--R 3 11 +--R (104cosh(x) + 20cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (160cosh(x) + 168cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (60cosh(x) + 612cosh(x) + 40cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 192cosh(x) + 1248cosh(x) + 272cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (- 336cosh(x) + 1512cosh(x) + 800cosh(x) + 40cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (- 192cosh(x) + 1008cosh(x) + 1328cosh(x) + 128cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R 60cosh(x) + 168cosh(x) + 1360cosh(x) + 104cosh(x) +--R + +--R 20cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 160cosh(x) - 288cosh(x) + 880cosh(x) - 64cosh(x) +--R + +--R 2 +--R - 48cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 104cosh(x) - 252cosh(x) + 352cosh(x) - 136cosh(x) +--R + +--R 3 +--R - 168cosh(x) + 4cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 32cosh(x) - 88cosh(x) + 80cosh(x) - 64cosh(x) +--R + +--R 4 2 +--R - 112cosh(x) - 40cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R 4cosh(x) - 12cosh(x) + 8cosh(x) - 8cosh(x) - 12cosh(x) +--R + +--R 3 +--R 20cosh(x) +--R * +--R sinh(x) +--R * +--R +---------+ +--R +---+ |a sinh(x) +--R \|- a |--------- +--R \| cosh(x) +--R + +--R 13 2 12 +--R - 8a cosh(x)sinh(x) - 72a cosh(x) sinh(x) +--R + +--R 3 11 +--R (- 280a cosh(x) - 12a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 600a cosh(x) - 104a cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (- 720a cosh(x) - 396a cosh(x) + 32a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 336a cosh(x) - 864a cosh(x) + 200a cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (336a cosh(x) - 1176a cosh(x) + 520a cosh(x) + 88a cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (720a cosh(x) - 1008a cosh(x) + 712a cosh(x) + 384a cosh(x) ) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 600a cosh(x) - 504a cosh(x) + 520a cosh(x) + 664a cosh(x) +--R + +--R 72a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 280a cosh(x) - 96a cosh(x) + 152a cosh(x) + 576a cosh(x) +--R + +--R 2 +--R 112a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 72a cosh(x) + 36a cosh(x) - 40a cosh(x) + 264a cosh(x) +--R + +--R 20a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 8a cosh(x) + 24a cosh(x) - 40a cosh(x) + 64a cosh(x) +--R + +--R 4 2 +--R - 48a cosh(x) - 40a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 4a cosh(x) - 8a cosh(x) + 8a cosh(x) - 8a cosh(x) +--R + +--R 3 +--R 4a cosh(x) +--R * +--R sinh(x) +--R * +--R +----------+ +--R | 3 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 500 + +)spool + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper200-299.input.pdf b/src/axiom-website/CATS/richhyper200-299.input.pdf new file mode 100644 index 0000000..ba15ca3 Binary files /dev/null and b/src/axiom-website/CATS/richhyper200-299.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper300-399.input.pamphlet b/src/axiom-website/CATS/richhyper300-399.input.pamphlet new file mode 100644 index 0000000..592ce3e --- /dev/null +++ b/src/axiom-website/CATS/richhyper300-399.input.pamphlet @@ -0,0 +1,47436 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper300-399.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper300-399.output +)spool richhyper300-399.output +)set message auto off +)clear all + +--S 1 of 508 +t0300:= 1/(a*tanh(x)^4)^(1/2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 4 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 508 +r0300:= (x-coth(x))*tanh(x)^2/(a*tanh(x)^4)^(1/2) +--R +--R +--R 2 +--R (- coth(x) + x)tanh(x) +--R (2) ----------------------- +--R +----------+ +--R | 4 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 2 + +--S 3 of 508 +a0300:= integrate(t0300,x) +--R +--R +--R 2 2 +--R x sinh(x) + 2x cosh(x)sinh(x) + x cosh(x) - x - 2 +--R (3) --------------------------------------------------- +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|a +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 508 +m0300:= a0300-r0300 +--R +--R +--R (4) +--R +----------+ +--R 2 2 | 4 +--R (x sinh(x) + 2x cosh(x)sinh(x) + x cosh(x) - x - 2)\|a tanh(x) +--R + +--R 2 +--R (coth(x) - x)sinh(x) + (2cosh(x)coth(x) - 2x cosh(x))sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 1)coth(x) - x cosh(x) + x +--R * +--R 2 +-+ +--R tanh(x) \|a +--R / +--R +----------+ +--R 2 2 +-+ | 4 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|a \|a tanh(x) +--R Type: Expression(Integer) +--E 4 + +--S 5 of 508 +d0300:= D(m0300,x) +--R +--R +--R (5) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R * +--R +----------+ +--R +-+ | 4 +--R \|a \|a tanh(x) +--R + +--R 2 4 2 3 +--R - a coth(x) sinh(x) - 4a cosh(x)coth(x) sinh(x) +--R + +--R 2 2 2 +--R (- 6a cosh(x) + 2a)coth(x) sinh(x) +--R + +--R 3 2 +--R (- 4a cosh(x) + 4a cosh(x))coth(x) sinh(x) +--R + +--R 4 2 2 +--R (- a cosh(x) + 2a cosh(x) - a)coth(x) +--R * +--R 2 +--R tanh(x) +--R / +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) - 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) - 4a cosh(x))sinh(x) + a cosh(x) - 2a cosh(x) + a +--R * +--R +----------+ +--R | 4 +--R \|a tanh(x) +--R Type: Expression(Integer) +--E 5 + +--S 6 of 508 +t0301:= 1/(1+tanh(x)) +--R +--R +--R 1 +--R (6) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 508 +r0301:= 1/2*x-1/(2+2*tanh(x)) +--R +--R +--R x tanh(x) + x - 1 +--R (7) ----------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 508 +a0301:= integrate(t0301,x) +--R +--R +--R (2x + 1)sinh(x) + (2x - 1)cosh(x) +--R (8) --------------------------------- +--R 4sinh(x) + 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 508 +m0301:= a0301-r0301 +--R +--R +--R (sinh(x) - cosh(x))tanh(x) + 3sinh(x) + cosh(x) +--R (9) -------------------------------------------------- +--R (4sinh(x) + 4cosh(x))tanh(x) + 4sinh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 9 + +--S 10 of 508 +d0301:= D(m0301,x) +--R +--R +--R cosh(x)tanh(x) - sinh(x) +--R (10) ---------------------------------------------- +--R (sinh(x) + cosh(x))tanh(x) + sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 10 + +--S 11 of 508 +t0302:= 1/(1+tanh(x))^2 +--R +--R +--R 1 +--R (11) ----------------------- +--R 2 +--R tanh(x) + 2tanh(x) + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 508 +r0302:= 1/4*x-1/4/(1+tanh(x))^2-1/(4+4*tanh(x)) +--R +--R +--R 2 +--R x tanh(x) + (2x - 1)tanh(x) + x - 2 +--R (12) ------------------------------------ +--R 2 +--R 4tanh(x) + 8tanh(x) + 4 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 508 +a0302:= integrate(t0302,x) +--R +--R +--R 2 2 +--R (4x - 1)sinh(x) + (8x + 2)cosh(x)sinh(x) + (4x - 1)cosh(x) - 4 +--R (13) ---------------------------------------------------------------- +--R 2 2 +--R 16sinh(x) + 32cosh(x)sinh(x) + 16cosh(x) +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 508 +m0302:= a0302-r0302 +--R +--R +--R (14) +--R 2 2 2 +--R (- sinh(x) + 2cosh(x)sinh(x) - cosh(x) - 4)tanh(x) +--R + +--R 2 2 2 +--R (2sinh(x) + 12cosh(x)sinh(x) + 2cosh(x) - 8)tanh(x) + 7sinh(x) +--R + +--R 2 +--R 18cosh(x)sinh(x) + 7cosh(x) - 4 +--R / +--R 2 2 2 +--R (16sinh(x) + 32cosh(x)sinh(x) + 16cosh(x) )tanh(x) +--R + +--R 2 2 2 +--R (32sinh(x) + 64cosh(x)sinh(x) + 32cosh(x) )tanh(x) + 16sinh(x) +--R + +--R 2 +--R 32cosh(x)sinh(x) + 16cosh(x) +--R Type: Expression(Integer) +--E 14 + +--S 15 of 508 +d0302:= D(m0302,x) +--R +--R +--R (15) +--R 2 2 2 2 2 +--R (sinh(x) + cosh(x) + 1)tanh(x) + (2sinh(x) + 2cosh(x) + 2)tanh(x) +--R + +--R 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) - cosh(x) + 1 +--R / +--R 2 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )tanh(x) +--R + +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 2sinh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 15 + +--S 16 of 508 +t0303:= 1/(1+tanh(x))^3 +--R +--R +--R 1 +--R (16) ----------------------------------- +--R 3 2 +--R tanh(x) + 3tanh(x) + 3tanh(x) + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 508 +r0303:= 1/8*x-1/6/(1+tanh(x))^3-1/8/(1+tanh(x))^2-1/(8+8*tanh(x)) +--R +--R +--R 3 2 +--R 3x tanh(x) + (9x - 3)tanh(x) + (9x - 9)tanh(x) + 3x - 10 +--R (17) ---------------------------------------------------------- +--R 3 2 +--R 24tanh(x) + 72tanh(x) + 72tanh(x) + 24 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 508 +a0303:= integrate(t0303,x) +--R +--R +--R (18) +--R 3 2 +--R (12x + 2)sinh(x) + (36x - 6)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((36x + 6)cosh(x) - 9)sinh(x) + (12x - 2)cosh(x) - 27cosh(x) +--R / +--R 3 2 2 3 +--R 96sinh(x) + 288cosh(x)sinh(x) + 288cosh(x) sinh(x) + 96cosh(x) +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 508 +m0303:= a0303-r0303 +--R +--R +--R (19) +--R 3 2 2 3 +--R 2sinh(x) - 6cosh(x)sinh(x) + (6cosh(x) - 9)sinh(x) - 2cosh(x) +--R + +--R - 27cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 3 2 2 3 +--R 18sinh(x) + 18cosh(x)sinh(x) + (54cosh(x) - 27)sinh(x) + 6cosh(x) +--R + +--R - 81cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 2 +--R 42sinh(x) + 90cosh(x)sinh(x) + (126cosh(x) - 27)sinh(x) +--R + +--R 3 +--R 30cosh(x) - 81cosh(x) +--R * +--R tanh(x) +--R + +--R 3 2 2 3 +--R 42sinh(x) + 114cosh(x)sinh(x) + (126cosh(x) - 9)sinh(x) + 38cosh(x) +--R + +--R - 27cosh(x) +--R / +--R 3 2 2 3 +--R (96sinh(x) + 288cosh(x)sinh(x) + 288cosh(x) sinh(x) + 96cosh(x) ) +--R * +--R 3 +--R tanh(x) +--R + +--R 3 2 2 3 +--R (288sinh(x) + 864cosh(x)sinh(x) + 864cosh(x) sinh(x) + 288cosh(x) ) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 2 3 +--R (288sinh(x) + 864cosh(x)sinh(x) + 864cosh(x) sinh(x) + 288cosh(x) ) +--R * +--R tanh(x) +--R + +--R 3 2 2 3 +--R 96sinh(x) + 288cosh(x)sinh(x) + 288cosh(x) sinh(x) + 96cosh(x) +--R Type: Expression(Integer) +--E 19 + +--S 20 of 508 +d0303:= D(m0303,x) +--R +--R +--R (20) +--R 2 3 3 +--R (3cosh(x)sinh(x) + cosh(x) + 3cosh(x))tanh(x) +--R + +--R 2 3 2 +--R (9cosh(x)sinh(x) + 3cosh(x) + 9cosh(x))tanh(x) +--R + +--R 2 3 3 +--R (9cosh(x)sinh(x) + 3cosh(x) + 9cosh(x))tanh(x) - 4sinh(x) +--R + +--R 2 2 3 +--R - 9cosh(x)sinh(x) - 12cosh(x) sinh(x) - 3cosh(x) + 3cosh(x) +--R / +--R 3 2 2 3 3 +--R (4sinh(x) + 12cosh(x)sinh(x) + 12cosh(x) sinh(x) + 4cosh(x) )tanh(x) +--R + +--R 3 2 2 3 2 +--R (12sinh(x) + 36cosh(x)sinh(x) + 36cosh(x) sinh(x) + 12cosh(x) )tanh(x) +--R + +--R 3 2 2 3 +--R (12sinh(x) + 36cosh(x)sinh(x) + 36cosh(x) sinh(x) + 12cosh(x) )tanh(x) +--R + +--R 3 2 2 3 +--R 4sinh(x) + 12cosh(x)sinh(x) + 12cosh(x) sinh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 20 + +--S 21 of 508 +t0304:= (a+b*tanh(c+d*x))^3 +--R +--R +--R 3 3 2 2 2 3 +--R (21) b tanh(d x + c) + 3a b tanh(d x + c) + 3a b tanh(d x + c) + a +--R Type: Expression(Integer) +--E 21 + +--S 22 of 508 +r0304:= a^3*x+3*a*b^2*x+3*a^2*b*log(cosh(c+d*x))/d+_ + b^3*log(cosh(c+d*x))/d-3*a*b^2*tanh(c+d*x)/d-1/2*b^3*tanh(c+d*x)^2/d +--R +--R +--R (22) +--R 3 2 3 2 2 +--R (2b + 6a b)log(cosh(d x + c)) - b tanh(d x + c) - 6a b tanh(d x + c) +--R + +--R 2 3 +--R (6a b + 2a )d x +--R / +--R 2d +--R Type: Expression(Integer) +--E 22 + +--S 23 of 508 +a0304:= integrate(t0304,x) +--R +--R +--R (23) +--R 3 2 4 3 2 3 +--R (b + 3a b)sinh(d x + c) + (4b + 12a b)cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 2 3 2 2 +--R ((6b + 18a b)cosh(d x + c) + 2b + 6a b)sinh(d x + c) +--R + +--R 3 2 3 3 2 +--R ((4b + 12a b)cosh(d x + c) + (4b + 12a b)cosh(d x + c)) +--R * +--R sinh(d x + c) +--R + +--R 3 2 4 3 2 2 3 2 +--R (b + 3a b)cosh(d x + c) + (2b + 6a b)cosh(d x + c) + b + 3a b +--R * +--R 2cosh(d x + c) +--R log(- -----------------------------) +--R sinh(d x + c) - cosh(d x + c) +--R + +--R 3 2 2 3 4 +--R (- b + 3a b - 3a b + a )d x sinh(d x + c) +--R + +--R 3 2 2 3 3 +--R (- 4b + 12a b - 12a b + 4a )d x cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 2 3 2 +--R (- 6b + 18a b - 18a b + 6a )d x cosh(d x + c) +--R + +--R 3 2 2 3 3 2 +--R (- 2b + 6a b - 6a b + 2a )d x + 2b + 6a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 2 2 3 3 +--R (- 4b + 12a b - 12a b + 4a )d x cosh(d x + c) +--R + +--R 3 2 2 3 3 2 +--R ((- 4b + 12a b - 12a b + 4a )d x + 4b + 12a b )cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 3 2 2 3 4 +--R (- b + 3a b - 3a b + a )d x cosh(d x + c) +--R + +--R 3 2 2 3 3 2 2 +--R ((- 2b + 6a b - 6a b + 2a )d x + 2b + 6a b )cosh(d x + c) +--R + +--R 3 2 2 3 2 +--R (- b + 3a b - 3a b + a )d x + 6a b +--R / +--R 4 3 +--R d sinh(d x + c) + 4d cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 +--R (6d cosh(d x + c) + 2d)sinh(d x + c) +--R + +--R 3 4 +--R (4d cosh(d x + c) + 4d cosh(d x + c))sinh(d x + c) + d cosh(d x + c) +--R + +--R 2 +--R 2d cosh(d x + c) + d +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 508 +m0304:= a0304-r0304 +--R +--R +--R (24) +--R 3 2 4 +--R (- 2b - 6a b)sinh(d x + c) +--R + +--R 3 2 3 +--R (- 8b - 24a b)cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 2 3 2 2 +--R ((- 12b - 36a b)cosh(d x + c) - 4b - 12a b)sinh(d x + c) +--R + +--R 3 2 3 3 2 +--R ((- 8b - 24a b)cosh(d x + c) + (- 8b - 24a b)cosh(d x + c)) +--R * +--R sinh(d x + c) +--R + +--R 3 2 4 3 2 2 3 +--R (- 2b - 6a b)cosh(d x + c) + (- 4b - 12a b)cosh(d x + c) - 2b +--R + +--R 2 +--R - 6a b +--R * +--R log(cosh(d x + c)) +--R + +--R 3 2 4 3 2 3 +--R (2b + 6a b)sinh(d x + c) + (8b + 24a b)cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 2 3 2 2 +--R ((12b + 36a b)cosh(d x + c) + 4b + 12a b)sinh(d x + c) +--R + +--R 3 2 3 3 2 +--R ((8b + 24a b)cosh(d x + c) + (8b + 24a b)cosh(d x + c)) +--R * +--R sinh(d x + c) +--R + +--R 3 2 4 3 2 2 3 2 +--R (2b + 6a b)cosh(d x + c) + (4b + 12a b)cosh(d x + c) + 2b + 6a b +--R * +--R 2cosh(d x + c) +--R log(- -----------------------------) +--R sinh(d x + c) - cosh(d x + c) +--R + +--R 3 4 3 3 +--R b sinh(d x + c) + 4b cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 3 2 +--R (6b cosh(d x + c) + 2b )sinh(d x + c) +--R + +--R 3 3 3 +--R (4b cosh(d x + c) + 4b cosh(d x + c))sinh(d x + c) +--R + +--R 3 4 3 2 3 +--R b cosh(d x + c) + 2b cosh(d x + c) + b +--R * +--R 2 +--R tanh(d x + c) +--R + +--R 2 4 2 3 +--R 6a b sinh(d x + c) + 24a b cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 2 2 +--R (36a b cosh(d x + c) + 12a b )sinh(d x + c) +--R + +--R 2 3 2 +--R (24a b cosh(d x + c) + 24a b cosh(d x + c))sinh(d x + c) +--R + +--R 2 4 2 2 2 +--R 6a b cosh(d x + c) + 12a b cosh(d x + c) + 6a b +--R * +--R tanh(d x + c) +--R + +--R 3 2 4 +--R (- 2b - 6a b)d x sinh(d x + c) +--R + +--R 3 2 3 +--R (- 8b - 24a b)d x cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 2 3 2 3 +--R (- 12b - 36a b)d x cosh(d x + c) + (- 4b - 12a b)d x + 4b +--R + +--R 2 +--R 12a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 2 3 +--R (- 8b - 24a b)d x cosh(d x + c) +--R + +--R 3 2 3 2 +--R ((- 8b - 24a b)d x + 8b + 24a b )cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 3 2 4 +--R (- 2b - 6a b)d x cosh(d x + c) +--R + +--R 3 2 3 2 2 3 2 +--R ((- 4b - 12a b)d x + 4b + 12a b )cosh(d x + c) + (- 2b - 6a b)d x +--R + +--R 2 +--R 12a b +--R / +--R 4 3 +--R 2d sinh(d x + c) + 8d cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 +--R (12d cosh(d x + c) + 4d)sinh(d x + c) +--R + +--R 3 4 +--R (8d cosh(d x + c) + 8d cosh(d x + c))sinh(d x + c) + 2d cosh(d x + c) +--R + +--R 2 +--R 4d cosh(d x + c) + 2d +--R Type: Expression(Integer) +--E 24 + +--S 25 of 508 +d0304:= D(m0304,x) +--R +--R +--R (25) +--R 3 6 3 5 +--R - b sinh(d x + c) - 6b cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 3 4 +--R (- 15b cosh(d x + c) - 3b )sinh(d x + c) +--R + +--R 3 3 3 3 +--R (- 20b cosh(d x + c) - 12b cosh(d x + c))sinh(d x + c) +--R + +--R 3 4 3 2 3 2 +--R (- 15b cosh(d x + c) - 18b cosh(d x + c) - 3b )sinh(d x + c) +--R + +--R 3 5 3 3 3 +--R (- 6b cosh(d x + c) - 12b cosh(d x + c) - 6b cosh(d x + c)) +--R * +--R sinh(d x + c) +--R + +--R 3 6 3 4 3 2 3 +--R - b cosh(d x + c) - 3b cosh(d x + c) - 3b cosh(d x + c) - b +--R * +--R 3 +--R tanh(d x + c) +--R + +--R 2 6 2 5 +--R - 3a b sinh(d x + c) - 18a b cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 2 4 +--R (- 45a b cosh(d x + c) - 9a b )sinh(d x + c) +--R + +--R 2 3 2 3 +--R (- 60a b cosh(d x + c) - 36a b cosh(d x + c))sinh(d x + c) +--R + +--R 2 4 2 2 2 2 +--R (- 45a b cosh(d x + c) - 54a b cosh(d x + c) - 9a b )sinh(d x + c) +--R + +--R 2 5 2 3 +--R - 18a b cosh(d x + c) - 36a b cosh(d x + c) +--R + +--R 2 +--R - 18a b cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 2 6 2 4 2 2 +--R - 3a b cosh(d x + c) - 9a b cosh(d x + c) - 9a b cosh(d x + c) +--R + +--R 2 +--R - 3a b +--R * +--R 2 +--R tanh(d x + c) +--R + +--R 3 6 3 5 +--R b sinh(d x + c) + 6b cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 3 4 +--R (15b cosh(d x + c) + 3b )sinh(d x + c) +--R + +--R 3 3 3 3 +--R (20b cosh(d x + c) + 12b cosh(d x + c))sinh(d x + c) +--R + +--R 3 4 3 2 3 2 +--R (15b cosh(d x + c) + 18b cosh(d x + c) + 3b )sinh(d x + c) +--R + +--R 3 5 3 3 3 +--R (6b cosh(d x + c) + 12b cosh(d x + c) + 6b cosh(d x + c)) +--R * +--R sinh(d x + c) +--R + +--R 3 6 3 4 3 2 3 +--R b cosh(d x + c) + 3b cosh(d x + c) + 3b cosh(d x + c) + b +--R * +--R tanh(d x + c) +--R + +--R 2 6 2 5 +--R 3a b sinh(d x + c) + 18a b cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 3 2 4 +--R (45a b cosh(d x + c) - 4b - 3a b )sinh(d x + c) +--R + +--R 2 3 3 2 3 +--R (60a b cosh(d x + c) + (- 16b - 12a b )cosh(d x + c))sinh(d x + c) +--R + +--R 2 4 3 2 2 3 2 +--R (45a b cosh(d x + c) + (- 24b - 18a b )cosh(d x + c) + 4b - 3a b ) +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 5 3 2 3 +--R 18a b cosh(d x + c) + (- 16b - 12a b )cosh(d x + c) +--R + +--R 3 2 +--R (8b - 6a b )cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 2 6 3 2 4 +--R 3a b cosh(d x + c) + (- 4b - 3a b )cosh(d x + c) +--R + +--R 3 2 2 2 +--R (4b - 3a b )cosh(d x + c) + 3a b +--R / +--R 6 5 +--R sinh(d x + c) + 6cosh(d x + c)sinh(d x + c) +--R + +--R 2 4 +--R (15cosh(d x + c) + 3)sinh(d x + c) +--R + +--R 3 3 +--R (20cosh(d x + c) + 12cosh(d x + c))sinh(d x + c) +--R + +--R 4 2 2 +--R (15cosh(d x + c) + 18cosh(d x + c) + 3)sinh(d x + c) +--R + +--R 5 3 +--R (6cosh(d x + c) + 12cosh(d x + c) + 6cosh(d x + c))sinh(d x + c) +--R + +--R 6 4 2 +--R cosh(d x + c) + 3cosh(d x + c) + 3cosh(d x + c) + 1 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 508 +t0305:= (a+b*tanh(c+d*x))^2 +--R +--R +--R 2 2 2 +--R (26) b tanh(d x + c) + 2a b tanh(d x + c) + a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 508 +r0305:= a^2*x+b^2*x+2*a*b*log(cosh(c+d*x))/d-b^2*tanh(c+d*x)/d +--R +--R +--R 2 2 2 +--R 2a b log(cosh(d x + c)) - b tanh(d x + c) + (b + a )d x +--R (27) -------------------------------------------------------- +--R d +--R Type: Expression(Integer) +--E 27 + +--S 28 of 508 +a0305:= integrate(t0305,x) +--R +--R +--R (28) +--R 2 +--R 2a b sinh(d x + c) + 4a b cosh(d x + c)sinh(d x + c) +--R + +--R 2 +--R 2a b cosh(d x + c) + 2a b +--R * +--R 2cosh(d x + c) +--R log(- -----------------------------) +--R sinh(d x + c) - cosh(d x + c) +--R + +--R 2 2 2 +--R (b - 2a b + a )d x sinh(d x + c) +--R + +--R 2 2 +--R (2b - 4a b + 2a )d x cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 2 2 2 2 +--R (b - 2a b + a )d x cosh(d x + c) + (b - 2a b + a )d x + 2b +--R / +--R 2 2 +--R d sinh(d x + c) + 2d cosh(d x + c)sinh(d x + c) + d cosh(d x + c) + d +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 508 +m0305:= a0305-r0305 +--R +--R +--R (29) +--R 2 +--R - 2a b sinh(d x + c) - 4a b cosh(d x + c)sinh(d x + c) +--R + +--R 2 +--R - 2a b cosh(d x + c) - 2a b +--R * +--R log(cosh(d x + c)) +--R + +--R 2 +--R 2a b sinh(d x + c) + 4a b cosh(d x + c)sinh(d x + c) +--R + +--R 2 +--R 2a b cosh(d x + c) + 2a b +--R * +--R 2cosh(d x + c) +--R log(- -----------------------------) +--R sinh(d x + c) - cosh(d x + c) +--R + +--R 2 2 2 2 2 +--R b sinh(d x + c) + 2b cosh(d x + c)sinh(d x + c) + b cosh(d x + c) +--R + +--R 2 +--R b +--R * +--R tanh(d x + c) +--R + +--R 2 +--R - 2a b d x sinh(d x + c) - 4a b d x cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 +--R - 2a b d x cosh(d x + c) - 2a b d x + 2b +--R / +--R 2 2 +--R d sinh(d x + c) + 2d cosh(d x + c)sinh(d x + c) + d cosh(d x + c) + d +--R Type: Expression(Integer) +--E 29 + +--S 30 of 508 +d0305:= D(m0305,x) +--R +--R +--R (30) +--R 2 4 2 3 +--R - b sinh(d x + c) - 4b cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 2 2 +--R (- 6b cosh(d x + c) - 2b )sinh(d x + c) +--R + +--R 2 3 2 +--R (- 4b cosh(d x + c) - 4b cosh(d x + c))sinh(d x + c) +--R + +--R 2 4 2 2 2 +--R - b cosh(d x + c) - 2b cosh(d x + c) - b +--R * +--R 2 +--R tanh(d x + c) +--R + +--R 2 4 2 3 +--R b sinh(d x + c) + 4b cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 2 2 +--R (6b cosh(d x + c) - 2b )sinh(d x + c) +--R + +--R 2 3 2 2 4 +--R (4b cosh(d x + c) - 4b cosh(d x + c))sinh(d x + c) + b cosh(d x + c) +--R + +--R 2 2 2 +--R - 2b cosh(d x + c) + b +--R / +--R 4 3 +--R sinh(d x + c) + 4cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 +--R (6cosh(d x + c) + 2)sinh(d x + c) +--R + +--R 3 4 +--R (4cosh(d x + c) + 4cosh(d x + c))sinh(d x + c) + cosh(d x + c) +--R + +--R 2 +--R 2cosh(d x + c) + 1 +--R Type: Expression(Integer) +--E 30 + +--S 31 of 508 +t0306:= 1/(4-6*tanh(x)) +--R +--R +--R 1 +--R (31) - ------------ +--R 6tanh(x) - 4 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 508 +r0306:= -1/5*x-3/10*log(2*cosh(x)-3*sinh(x)) +--R +--R +--R - 3log(- 3sinh(x) + 2cosh(x)) - 2x +--R (32) ---------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 508 +a0306:= integrate(t0306,x) +--R +--R +--R - 6sinh(x) + 4cosh(x) +--R - 3log(---------------------) + x +--R sinh(x) - cosh(x) +--R (33) --------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 508 +m0306:= a0306-r0306 +--R +--R +--R - 6sinh(x) + 4cosh(x) +--R - 3log(---------------------) + 3log(- 3sinh(x) + 2cosh(x)) + 3x +--R sinh(x) - cosh(x) +--R (34) ---------------------------------------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 508 +d0306:= D(m0306,x) +--R +--R +--R (35) 0 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 508 +t0307:= 1/(a+b*tanh(c+d*x)) +--R +--R +--R 1 +--R (36) ------------------- +--R b tanh(d x + c) + a +--R Type: Expression(Integer) +--E 36 + +--S 37 of 508 +r0307:= -(-a*d*x+b*log(a*cosh(c+d*x)+b*sinh(c+d*x)))/(a^2-b^2)/d +--R +--R +--R b log(b sinh(d x + c) + a cosh(d x + c)) - a d x +--R (37) ------------------------------------------------ +--R 2 2 +--R (b - a )d +--R Type: Expression(Integer) +--E 37 + +--S 38 of 508 +a0307:= integrate(t0307,x) +--R +--R +--R - 2b sinh(d x + c) - 2a cosh(d x + c) +--R b log(-------------------------------------) + (- b - a)d x +--R sinh(d x + c) - cosh(d x + c) +--R (38) ----------------------------------------------------------- +--R 2 2 +--R (b - a )d +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 508 +m0307:= a0307-r0307 +--R +--R +--R (39) +--R - b log(b sinh(d x + c) + a cosh(d x + c)) +--R + +--R - 2b sinh(d x + c) - 2a cosh(d x + c) +--R b log(-------------------------------------) - b d x +--R sinh(d x + c) - cosh(d x + c) +--R / +--R 2 2 +--R (b - a )d +--R Type: Expression(Integer) +--E 39 + +--S 40 of 508 +d0307:= D(m0307,x) +--R +--R +--R (40) 0 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 508 +t0308:= 1/(1-2*tanh(x)^2) +--R +--R +--R 1 +--R (41) - ------------- +--R 2 +--R 2tanh(x) - 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 508 +r0308:= -x+atanh(2^(1/2)*tanh(x))*2^(1/2) +--R +--R +--R +-+ +-+ +--R (42) \|2 atanh(\|2 tanh(x)) - x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 508 +a0308:= integrate(t0308,x) +--R +--R +--R (43) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R - 2x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 508 +m0308:= a0308-r0308 +--R +--R +--R (44) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ +-+ +--R - 2\|2 atanh(\|2 tanh(x)) +--R / +--R 2 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 508 +d0308:= D(m0308,x) +--R +--R +--R (45) +--R +-+ 4 +-+ 3 +--R (4\|2 - 6)sinh(x) + (24\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 56\|2 + 84)cosh(x) - 8\|2 + 12)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 - 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (- 8\|2 + 12)cosh(x) - 12\|2 + 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (4\|2 - 6)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((40\|2 - 60)cosh(x) - 16\|2 + 24)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (- 16\|2 + 24)cosh(x) + 12\|2 - 18 +--R / +--R +-+ 4 +-+ 3 +--R (12\|2 - 18)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((24\|2 - 36)cosh(x) - 40\|2 + 60)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (72\|2 - 96)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (12\|2 - 18)cosh(x) + (- 40\|2 + 60)cosh(x) + 12\|2 - 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 12\|2 + 18)cosh(x) + 20\|2 - 30)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((12\|2 - 16)cosh(x) + (- 36\|2 + 48)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + (20\|2 - 30)cosh(x) - 6\|2 + 9 +--R Type: Expression(Integer) +--E 45 + +--S 46 of 508 +t0309:= 1/(1+tanh(x)^3) +--R +--R +--R 1 +--R (46) ------------ +--R 3 +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 508 +r0309:= 1/2*x-2/9*atan(1/3*(1-2*tanh(x))*3^(1/2))*3^(1/2)-1/(6+6*tanh(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ 2\|3 tanh(x) - \|3 +--R (4\|3 tanh(x) + 4\|3 )atan(-------------------) + 9x tanh(x) + 9x - 3 +--R 3 +--R (47) --------------------------------------------------------------------- +--R 18tanh(x) + 18 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 508 +a0309:= integrate(t0309,x) +--R +--R +--R (48) +--R 2 2 +--R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) ) +--R * +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R atan(-------------------------) +--R 3sinh(x) - 3cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R 6x\|3 sinh(x) + 12x\|3 cosh(x)sinh(x) + 6x\|3 cosh(x) - \|3 +--R / +--R +-+ 2 +-+ +-+ 2 +--R 12\|3 sinh(x) + 24\|3 cosh(x)sinh(x) + 12\|3 cosh(x) +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 508 +m0309:= a0309-r0309 +--R +--R +--R (49) +--R 2 2 2 +--R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )tanh(x) - 8sinh(x) +--R + +--R 2 +--R - 16cosh(x)sinh(x) - 8cosh(x) +--R * +--R +-+ +-+ +--R 2\|3 tanh(x) - \|3 +--R atan(-------------------) +--R 3 +--R + +--R 2 2 2 +--R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )tanh(x) - 8sinh(x) +--R + +--R 2 +--R - 16cosh(x)sinh(x) - 8cosh(x) +--R * +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R atan(-------------------------) +--R 3sinh(x) - 3cosh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ 2 +-+ +--R - \|3 tanh(x) + 2\|3 sinh(x) + 4\|3 cosh(x)sinh(x) + 2\|3 cosh(x) - \|3 +--R / +--R +-+ 2 +-+ +-+ 2 +--R (12\|3 sinh(x) + 24\|3 cosh(x)sinh(x) + 12\|3 cosh(x) )tanh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R 12\|3 sinh(x) + 24\|3 cosh(x)sinh(x) + 12\|3 cosh(x) +--R Type: Expression(Integer) +--E 49 + +--S 50 of 508 +d0309:= D(m0309,x) +--R +--R +--R (50) +--R 4 3 2 3 +--R sinh(x) - cosh(x)sinh(x) + sinh(x) + (7cosh(x) - cosh(x))sinh(x) +--R + +--R 4 2 +--R 5cosh(x) + cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 4 3 2 3 +--R - 5sinh(x) - 7cosh(x)sinh(x) + sinh(x) + (cosh(x) - cosh(x))sinh(x) +--R + +--R 4 2 +--R - cosh(x) + cosh(x) +--R / +--R 4 3 3 4 3 +--R (6sinh(x) + 6cosh(x)sinh(x) + 6cosh(x) sinh(x) + 6cosh(x) )tanh(x) +--R + +--R 4 3 3 4 +--R 6sinh(x) + 6cosh(x)sinh(x) + 6cosh(x) sinh(x) + 6cosh(x) +--R Type: Expression(Integer) +--E 50 + +--S 51 of 508 +t0310:= (1+tanh(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (51) \|tanh(x) + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 508 +r0310:= -asinh(tanh(x))+2^(1/2)*atanh(2^(1/2)*tanh(x)/(1+tanh(x)^2)^(1/2)) +--R +--R +--R +-+ +--R +-+ \|2 tanh(x) +--R (52) \|2 atanh(---------------) - asinh(tanh(x)) +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 508 +a0310:= integrate(t0310,x) +--R +--R +--R (53) +--R - +--R 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 2)sinh(x) + (4\|2 - 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (2\|2 - 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) 2 +--R \|2 |------------------------------------- - 2sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 2)sinh(x) + (- 4\|2 - 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (- 2\|2 - 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +--R \|2 +--R * +--R log +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 2) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - \|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) - 2\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - \|2 cosh(x) + 2\|2 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 508 +m0310:= a0310-r0310 +--R +--R +--R (54) +--R - +--R 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 2)sinh(x) + (4\|2 - 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (2\|2 - 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) 2 +--R \|2 |------------------------------------- - 2sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 2)sinh(x) + (- 4\|2 - 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (- 2\|2 - 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +--R \|2 +--R * +--R log +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 2) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - \|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) - 2\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - \|2 cosh(x) + 2\|2 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +-+ +--R +-+ \|2 tanh(x) +--R - 2\|2 atanh(---------------) + 2asinh(tanh(x)) +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 508 +d0310:= D(m0310,x) +--R +--R +--R (55) +--R +-+ 14 +-+ 13 +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 12 +--R (- 5\|2 cosh(x) + 9\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 11 +--R (- 12\|2 cosh(x) + 12\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 10 +--R (9\|2 cosh(x) - 30\|2 cosh(x) - 5\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 9 +--R (30\|2 cosh(x) - 36\|2 cosh(x) - 2\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 5\|2 cosh(x) + 39\|2 cosh(x) + 15\|2 cosh(x) - 9\|2 ) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 40\|2 cosh(x) + 24\|2 cosh(x) + 8\|2 cosh(x) +--R + +--R +-+ +--R - 12\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 5\|2 cosh(x) - 36\|2 cosh(x) - 10\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 12\|2 cosh(x) - 24\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 30\|2 cosh(x) + 24\|2 cosh(x) - 12\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 12\|2 cosh(x) + 64\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 9\|2 cosh(x) + 39\|2 cosh(x) - 10\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R - 6\|2 cosh(x) - 104\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 12\|2 cosh(x) - 36\|2 cosh(x) + 8\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R 12\|2 cosh(x) + 128\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 5\|2 cosh(x) - 30\|2 cosh(x) + 15\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R 12\|2 cosh(x) - 104\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 2\|2 cosh(x) + 12\|2 cosh(x) - 2\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R - 12\|2 cosh(x) + 64\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +-+ 8 +--R \|2 cosh(x) + 9\|2 cosh(x) - 5\|2 cosh(x) - 9\|2 cosh(x) +--R + +--R +-+ 6 +--R - 24\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 14 13 2 12 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 12cosh(x) - 24)sinh(x) +--R + +--R 3 11 +--R (32cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (60cosh(x) + 48cosh(x) + 16)sinh(x) +--R + +--R 5 3 9 +--R (16cosh(x) + 144cosh(x) + 32cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 44cosh(x) + 24cosh(x) + 16cosh(x) + 24)sinh(x) +--R + +--R 7 5 7 +--R (- 64cosh(x) - 96cosh(x) + 48cosh(x))sinh(x) +--R + +--R 8 6 4 6 +--R (- 44cosh(x) - 96cosh(x) - 32cosh(x) + 68)sinh(x) +--R + +--R 9 7 5 3 +--R (16cosh(x) - 96cosh(x) - 64cosh(x) - 48cosh(x) - 112cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R (60cosh(x) + 24cosh(x) - 32cosh(x) - 48cosh(x) + 220cosh(x) ) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 5 3 3 +--R (32cosh(x) + 144cosh(x) - 48cosh(x) - 224cosh(x) )sinh(x) +--R + +--R 12 10 8 4 2 +--R (- 12cosh(x) + 48cosh(x) + 16cosh(x) + 220cosh(x) )sinh(x) +--R + +--R 13 11 9 7 +--R - 16cosh(x) - 48cosh(x) + 32cosh(x) + 48cosh(x) +--R + +--R 5 +--R - 112cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R - 4cosh(x) - 24cosh(x) + 16cosh(x) + 24cosh(x) + 68cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R + +--R 14 13 2 12 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 3 11 +--R (16cosh(x) - 4cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (30cosh(x) + 4cosh(x) + 6)sinh(x) +--R + +--R 5 3 9 +--R (8cosh(x) + 12cosh(x) + 8cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 22cosh(x) + 2cosh(x) - 2cosh(x) - 18)sinh(x) +--R + +--R 7 5 7 +--R (- 32cosh(x) - 8cosh(x) + 28cosh(x))sinh(x) +--R + +--R 8 6 4 6 +--R (- 22cosh(x) - 8cosh(x) - 4cosh(x) - 24)sinh(x) +--R + +--R 9 7 5 3 +--R (8cosh(x) - 8cosh(x) - 16cosh(x) - 28cosh(x) + 64cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 30cosh(x) + 2cosh(x) - 4cosh(x) + 36cosh(x) +--R + +--R 2 +--R - 104cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 5 3 3 +--R (16cosh(x) + 12cosh(x) - 28cosh(x) + 128cosh(x) )sinh(x) +--R + +--R 12 10 8 4 2 +--R (- 6cosh(x) + 4cosh(x) - 2cosh(x) - 104cosh(x) )sinh(x) +--R + +--R 13 11 9 7 +--R - 8cosh(x) - 4cosh(x) + 8cosh(x) + 28cosh(x) +--R + +--R 5 +--R 64cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R - 2cosh(x) - 2cosh(x) + 6cosh(x) - 18cosh(x) - 24cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 14 13 2 12 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 3 11 +--R (16cosh(x) - 4cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (30cosh(x) + 4cosh(x) + 6)sinh(x) +--R + +--R 5 3 9 +--R (8cosh(x) + 12cosh(x) + 8cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 22cosh(x) + 2cosh(x) - 2cosh(x) - 18)sinh(x) +--R + +--R 7 5 7 +--R (- 32cosh(x) - 8cosh(x) + 28cosh(x))sinh(x) +--R + +--R 8 6 4 6 +--R (- 22cosh(x) - 8cosh(x) - 4cosh(x) - 24)sinh(x) +--R + +--R 9 7 5 3 5 +--R (8cosh(x) - 8cosh(x) - 16cosh(x) - 28cosh(x) + 64cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R (30cosh(x) + 2cosh(x) - 4cosh(x) + 36cosh(x) - 104cosh(x) ) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 5 3 3 +--R (16cosh(x) + 12cosh(x) - 28cosh(x) + 128cosh(x) )sinh(x) +--R + +--R 12 10 8 4 2 +--R (- 6cosh(x) + 4cosh(x) - 2cosh(x) - 104cosh(x) )sinh(x) +--R + +--R 13 11 9 7 5 +--R (- 8cosh(x) - 4cosh(x) + 8cosh(x) + 28cosh(x) + 64cosh(x) ) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R - 2cosh(x) - 2cosh(x) + 6cosh(x) - 18cosh(x) - 24cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 16 +-+ 15 +--R - \|2 sinh(x) - 6\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R (- 12\|2 cosh(x) + 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R (- 2\|2 cosh(x) + 8\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 12 +--R (28\|2 cosh(x) + 6\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 11 +--R (42\|2 cosh(x) - 16\|2 cosh(x) + 16\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 10 +--R (12\|2 cosh(x) - 30\|2 cosh(x) + 24\|2 cosh(x) - 8\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 34\|2 cosh(x) - 8\|2 cosh(x) + 16\|2 cosh(x) - 16\|2 cosh(x)) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 54\|2 cosh(x) + 22\|2 cosh(x) - 4\|2 cosh(x) - 8\|2 cosh(x) +--R + +--R +-+ +--R 25\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 34\|2 cosh(x) + 32\|2 cosh(x) - 32\|2 cosh(x) +--R + +--R +-+ +--R - 18\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 12\|2 cosh(x) + 22\|2 cosh(x) - 48\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 16\|2 cosh(x) - 16\|2 cosh(x) + 34\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +-+ 5 +--R 42\|2 cosh(x) - 8\|2 cosh(x) - 32\|2 cosh(x) + 32\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 14\|2 cosh(x) - 56\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 28\|2 cosh(x) - 30\|2 cosh(x) - 4\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 16\|2 cosh(x) - 82\|2 cosh(x) + 110\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 2\|2 cosh(x) - 16\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R - 14\|2 cosh(x) - 112\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 12\|2 cosh(x) + 6\|2 cosh(x) + 24\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 8\|2 cosh(x) - 16\|2 cosh(x) + 110\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 6\|2 cosh(x) + 8\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 16\|2 cosh(x) - 18\|2 cosh(x) - 56\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +-+ 10 +--R - \|2 cosh(x) + 2\|2 cosh(x) + 4\|2 cosh(x) - 8\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R 25\|2 cosh(x) + 34\|2 cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 16 +-+ 15 +--R - \|2 sinh(x) - 6\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R (- 12\|2 cosh(x) + 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R (- 2\|2 cosh(x) + 8\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 12 +--R (28\|2 cosh(x) + 6\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 11 +--R (42\|2 cosh(x) - 16\|2 cosh(x) + 16\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 10 +--R (12\|2 cosh(x) - 30\|2 cosh(x) + 24\|2 cosh(x) - 8\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 34\|2 cosh(x) - 8\|2 cosh(x) + 16\|2 cosh(x) - 16\|2 cosh(x)) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 54\|2 cosh(x) + 22\|2 cosh(x) - 4\|2 cosh(x) - 8\|2 cosh(x) +--R + +--R +-+ +--R 25\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ +--R (- 34\|2 cosh(x) + 32\|2 cosh(x) - 32\|2 cosh(x) - 18\|2 cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +-+ 4 +--R 12\|2 cosh(x) + 22\|2 cosh(x) - 48\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 16\|2 cosh(x) + 34\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +-+ 5 +--R 42\|2 cosh(x) - 8\|2 cosh(x) - 32\|2 cosh(x) + 32\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 14\|2 cosh(x) - 56\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +-+ 6 +--R 28\|2 cosh(x) - 30\|2 cosh(x) - 4\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R - 82\|2 cosh(x) + 110\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +-+ 5 +--R - 2\|2 cosh(x) - 16\|2 cosh(x) + 16\|2 cosh(x) - 14\|2 cosh(x) +--R + +--R +-+ 3 +--R - 112\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +-+ 8 +--R - 12\|2 cosh(x) + 6\|2 cosh(x) + 24\|2 cosh(x) - 8\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 16\|2 cosh(x) + 110\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +-+ 9 +--R - 6\|2 cosh(x) + 8\|2 cosh(x) + 16\|2 cosh(x) - 16\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R - 18\|2 cosh(x) - 56\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +-+ 10 +--R - \|2 cosh(x) + 2\|2 cosh(x) + 4\|2 cosh(x) - 8\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R 25\|2 cosh(x) + 34\|2 cosh(x) +--R / +--R 14 13 2 12 +--R 2sinh(x) + 8cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 11 +--R (- 16cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 30cosh(x) - 4cosh(x) - 6)sinh(x) +--R + +--R 5 3 9 +--R (- 8cosh(x) - 12cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (22cosh(x) - 2cosh(x) + 2cosh(x) + 18)sinh(x) +--R + +--R 7 5 7 +--R (32cosh(x) + 8cosh(x) - 28cosh(x))sinh(x) +--R + +--R 8 6 4 6 +--R (22cosh(x) + 8cosh(x) + 4cosh(x) + 24)sinh(x) +--R + +--R 9 7 5 3 +--R (- 8cosh(x) + 8cosh(x) + 16cosh(x) + 28cosh(x) - 64cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 30cosh(x) - 2cosh(x) + 4cosh(x) - 36cosh(x) +--R + +--R 2 +--R 104cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 5 3 3 +--R (- 16cosh(x) - 12cosh(x) + 28cosh(x) - 128cosh(x) )sinh(x) +--R + +--R 12 10 8 4 2 +--R (6cosh(x) - 4cosh(x) + 2cosh(x) + 104cosh(x) )sinh(x) +--R + +--R 13 11 9 7 5 +--R (8cosh(x) + 4cosh(x) - 8cosh(x) - 28cosh(x) - 64cosh(x) ) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R 2cosh(x) + 2cosh(x) - 6cosh(x) + 18cosh(x) + 24cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 16 +-+ 15 +--R \|2 sinh(x) + 6\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R (12\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R (2\|2 cosh(x) - 8\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 12 +--R (- 28\|2 cosh(x) - 6\|2 cosh(x) - 4\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 11 +--R (- 42\|2 cosh(x) + 16\|2 cosh(x) - 16\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 10 +--R (- 12\|2 cosh(x) + 30\|2 cosh(x) - 24\|2 cosh(x) + 8\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (34\|2 cosh(x) + 8\|2 cosh(x) - 16\|2 cosh(x) + 16\|2 cosh(x)) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 54\|2 cosh(x) - 22\|2 cosh(x) + 4\|2 cosh(x) + 8\|2 cosh(x) +--R + +--R +-+ +--R - 25\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ +--R (34\|2 cosh(x) - 32\|2 cosh(x) + 32\|2 cosh(x) + 18\|2 cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 12\|2 cosh(x) - 22\|2 cosh(x) + 48\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 16\|2 cosh(x) + 16\|2 cosh(x) - 34\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +-+ 5 +--R - 42\|2 cosh(x) + 8\|2 cosh(x) + 32\|2 cosh(x) - 32\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 14\|2 cosh(x) + 56\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 28\|2 cosh(x) + 30\|2 cosh(x) + 4\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 16\|2 cosh(x) + 82\|2 cosh(x) - 110\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +-+ 5 +--R 2\|2 cosh(x) + 16\|2 cosh(x) - 16\|2 cosh(x) + 14\|2 cosh(x) +--R + +--R +-+ 3 +--R 112\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +-+ 8 +--R 12\|2 cosh(x) - 6\|2 cosh(x) - 24\|2 cosh(x) + 8\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R 16\|2 cosh(x) - 110\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +-+ 9 +--R 6\|2 cosh(x) - 8\|2 cosh(x) - 16\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R 18\|2 cosh(x) + 56\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +-+ 10 +--R \|2 cosh(x) - 2\|2 cosh(x) - 4\|2 cosh(x) + 8\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 25\|2 cosh(x) - 34\|2 cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 508 +t0311:= (-1-tanh(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (56) \|- tanh(x) - 1 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 508 +r0311:= -2^(1/2)*atan(2^(1/2)*tanh(x)/(-1-tanh(x)^2)^(1/2))-_ + atan(coth(x)*(-1-tanh(x)^2)^(1/2)) +--R +--R +--R +--------------+ +-+ +--R | 2 +-+ \|2 tanh(x) +--R (57) - atan(coth(x)\|- tanh(x) - 1 ) - \|2 atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 508 +a0311:= integrate(t0311,x) +--R +--R +--R (58) +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 + (2\|- 2 \|- 1 + 2)(%e ) + 2 +--R - 2\|- 1 log(------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ | x 4 x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 + 2(%e ) + 2 +--R - \|- 2 log(------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 + (- 2\|- 2 \|- 1 + 2)(%e ) + 2 +--R 2\|- 1 log(--------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +---+ +--R \|- 2 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +---+ x 2 +--R (- 2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) + 2\|- 2 (%e ) +--R + +--R +---+ +--R - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 508 +m0311:= a0311-r0311 +--R +--R +--R (59) +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 + (2\|- 2 \|- 1 + 2)(%e ) + 2 +--R - 2\|- 1 log(------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ | x 4 x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 + 2(%e ) + 2 +--R - \|- 2 log(------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 + (- 2\|- 2 \|- 1 + 2)(%e ) + 2 +--R 2\|- 1 log(--------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +---+ +--R \|- 2 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +---+ x 2 +--R (- 2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) + 2\|- 2 (%e ) +--R + +--R +---+ +--R - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R + +--R +--------------+ +-+ +--R | 2 +-+ \|2 tanh(x) +--R 2atan(coth(x)\|- tanh(x) - 1 ) + 2\|2 atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 508 +d0311:= D(m0311,x) +--R +--R +--R (60) +--R +---+ 2 x 4 +---+ 2 2 +--R (- 3\|- 2 coth(x) (%e ) - 4\|- 2 coth(x) )tanh(x) +--R + +--R +---+ 2 +---+ x 4 +---+ 2 +---+ +--R (- 3\|- 2 coth(x) + 3\|- 2 )(%e ) - 4\|- 2 coth(x) + 4\|- 2 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R + +--R x 6 x 4 x 2 3 +--R (- coth(x)(%e ) - coth(x)(%e ) - 4coth(x)(%e ) - 4coth(x))tanh(x) +--R + +--R 2 x 6 2 x 4 +--R (coth(x) + 1)(%e ) + (coth(x) + 1)(%e ) +--R + +--R 2 x 2 2 +--R (4coth(x) + 4)(%e ) + 4coth(x) + 4 +--R * +--R 2 +--R tanh(x) +--R + +--R x 6 x 4 x 2 +--R (coth(x)(%e ) + coth(x)(%e ) + 4coth(x)(%e ) + 4coth(x))tanh(x) +--R + +--R 2 x 6 2 x 4 2 x 2 +--R (coth(x) - 1)(%e ) + (coth(x) - 1)(%e ) + (4coth(x) - 4)(%e ) +--R + +--R 2 +--R 4coth(x) - 4 +--R * +--R +-------------+ +--R | x 4 +--R \|- 2(%e ) - 2 +--R + +--R 2 x 8 2 x 4 2 2 +--R (- 2coth(x) (%e ) - 10coth(x) (%e ) - 8coth(x) )tanh(x) +--R + +--R 2 x 8 2 x 4 2 +--R (- 2coth(x) + 2)(%e ) + (- 10coth(x) + 10)(%e ) - 8coth(x) + 8 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +--R 3\|- 2 coth(x)(%e ) + 3\|- 2 coth(x)(%e ) + 4\|- 2 coth(x)(%e ) +--R + +--R +---+ +--R 4\|- 2 coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 6 +--R (- 3\|- 2 coth(x) - 3\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 3\|- 2 coth(x) - 3\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 4\|- 2 coth(x) - 4\|- 2 )(%e ) - 4\|- 2 coth(x) - 4\|- 2 +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +--R - 3\|- 2 coth(x)(%e ) - 3\|- 2 coth(x)(%e ) - 4\|- 2 coth(x)(%e ) +--R + +--R +---+ +--R - 4\|- 2 coth(x) +--R * +--R tanh(x) +--R + +--R +---+ 2 +---+ x 6 +---+ 2 +---+ x 4 +--R (- 3\|- 2 coth(x) + 3\|- 2 )(%e ) + (- 3\|- 2 coth(x) + 3\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 4\|- 2 coth(x) + 4\|- 2 )(%e ) - 4\|- 2 coth(x) + 4\|- 2 +--R / +--R 2 x 6 2 x 4 2 x 2 2 +--R (coth(x) (%e ) + coth(x) (%e ) + 4coth(x) (%e ) + 4coth(x) ) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 6 2 x 4 2 x 2 +--R (coth(x) - 1)(%e ) + (coth(x) - 1)(%e ) + (4coth(x) - 4)(%e ) +--R + +--R 2 +--R 4coth(x) - 4 +--R * +--R +--------------+ +-------------+ +--R | 2 | x 4 +--R \|- tanh(x) - 1 \|- 2(%e ) - 2 +--R + +--R +---+ 2 x 6 +---+ 2 x 4 +--R - 3\|- 2 coth(x) (%e ) - 3\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 x 2 +---+ 2 +--R - 4\|- 2 coth(x) (%e ) - 4\|- 2 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 6 +--R (- 3\|- 2 coth(x) + 3\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 3\|- 2 coth(x) + 3\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 4\|- 2 coth(x) + 4\|- 2 )(%e ) - 4\|- 2 coth(x) + 4\|- 2 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R Type: Expression(Integer) +--E 60 + +--S 61 of 508 +t0312:= (a+b*tanh(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (61) \|b tanh(x) + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 508 +r0312:= (a+b)^(1/2)*atanh((a+b)^(1/2)*tanh(x)/(a+b*tanh(x)^2)^(1/2))-_ + b^(1/2)*atanh(coth(x)*(a+b*tanh(x)^2)^(1/2)/b^(1/2)) +--R +--R +--R (62) +--R +--------------+ +--R | 2 +-----+ +--R +-+ coth(x)\|b tanh(x) + a +-----+ tanh(x)\|b + a +--R - \|b atanh(------------------------) + \|b + a atanh(-----------------) +--R +-+ +--------------+ +--R \|b | 2 +--R \|b tanh(x) + a +--R Type: Expression(Integer) +--E 62 + +--S 63 of 508 +a0312:= integrate(t0312,x) +--R +--R +--R (63) +--R [ +--R (- b - a) +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R (b + a) +--R * +--R log +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +-+ +-----+ +--R 2\|b \|b + a +--R * +--R log +--R 4 3 +--R - 2a sinh(x) - 8a cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12a cosh(x) - 2b - 2a)sinh(x) +--R + +--R 3 +--R (- 8a cosh(x) + (- 4b - 4a)cosh(x))sinh(x) +--R + +--R 4 2 +--R - 2a cosh(x) + (- 2b - 2a)cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R + +--R 2 2 4 +--R (- b - 2a b - a )sinh(x) +--R + +--R 2 2 3 +--R (- 4b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 12a b - 6a )cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((- 4b - 8a b - 4a )cosh(x) + (- 4a b - 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- b - 2a b - a )cosh(x) + (- 2a b - 2a )cosh(x) - b +--R + +--R 2 +--R - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- b + 2a b + a )sinh(x) +--R + +--R 2 2 5 +--R (- 6b + 12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 15b + 30a b + 15a )cosh(x) + b + 2a b + 3a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 +--R (- 20b + 40a b + 20a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 15b + 30a b + 15a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (6b + 12a b + 18a )cosh(x) - b + 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 6b + 12a b + 6a )cosh(x) +--R + +--R 2 2 3 +--R (4b + 8a b + 12a )cosh(x) +--R + +--R 2 2 +--R (- 2b + 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- b + 2a b + a )cosh(x) + (b + 2a b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- b + 2a b + 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 6 2 5 +--R (2a b + 2a )sinh(x) + (12a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R ((30a b + 30a )cosh(x) - 2b + 2a b + 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((40a b + 40a )cosh(x) + (- 8b + 8a b + 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 +--R (30a b + 30a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 12b + 12a b + 24a )cosh(x) + 2b + 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (12a b + 12a )cosh(x) + (- 8b + 8a b + 16a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (2a b + 2a )cosh(x) + (- 2b + 2a b + 4a )cosh(x) +--R + +--R 2 2 2 +--R (2b + 4a b + 2a )cosh(x) +--R * +--R +-+ +--R \|b +--R / +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a )cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((4b - 4a )cosh(x) + (- 4a b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (b - a )cosh(x) + (- 2a b - 2a )cosh(x) - b - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (b + a )sinh(x) + (6b + 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((15b + 15a )cosh(x) - b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((20b + 20a )cosh(x) + (- 4b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (15b + 15a )cosh(x) + (- 6b + 18a )cosh(x) - b +--R + +--R 2 +--R 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (6b + 6a )cosh(x) + (- 4b + 12a )cosh(x) +--R + +--R 2 2 +--R (- 2b + 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (b + a )cosh(x) + (- b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- b + 2a b + 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R +-----+ +--R 2\|b + a +--R , +--R +--R (- b - a) +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R (b + a) +--R * +--R log +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R - +--R +---+ +-----+ +--R 4\|- b \|b + a +--R * +--R atan +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +---+ +-----+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|b + a +--R / +--R +-----+ +--R 2\|b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 63 + +--S 64 of 508 +m0312a:= a0312.1-r0312 +--R +--R +--R (64) +--R (- b - a) +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R (b + a) +--R * +--R log +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +-+ +-----+ +--R 2\|b \|b + a +--R * +--R log +--R 4 3 +--R - 2a sinh(x) - 8a cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12a cosh(x) - 2b - 2a)sinh(x) +--R + +--R 3 +--R (- 8a cosh(x) + (- 4b - 4a)cosh(x))sinh(x) +--R + +--R 4 2 +--R - 2a cosh(x) + (- 2b - 2a)cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R + +--R 2 2 4 +--R (- b - 2a b - a )sinh(x) +--R + +--R 2 2 3 +--R (- 4b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 12a b - 6a )cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((- 4b - 8a b - 4a )cosh(x) + (- 4a b - 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- b - 2a b - a )cosh(x) + (- 2a b - 2a )cosh(x) - b +--R + +--R 2 +--R - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- b + 2a b + a )sinh(x) +--R + +--R 2 2 5 +--R (- 6b + 12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 15b + 30a b + 15a )cosh(x) + b + 2a b + 3a )sinh(x) +--R + +--R 2 2 3 +--R (- 20b + 40a b + 20a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 15b + 30a b + 15a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (6b + 12a b + 18a )cosh(x) - b + 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 6b + 12a b + 6a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (4b + 8a b + 12a )cosh(x) + (- 2b + 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- b + 2a b + a )cosh(x) + (b + 2a b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- b + 2a b + 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 6 2 5 +--R (2a b + 2a )sinh(x) + (12a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R ((30a b + 30a )cosh(x) - 2b + 2a b + 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((40a b + 40a )cosh(x) + (- 8b + 8a b + 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (30a b + 30a )cosh(x) + (- 12b + 12a b + 24a )cosh(x) +--R + +--R 2 2 +--R 2b + 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (12a b + 12a )cosh(x) + (- 8b + 8a b + 16a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (2a b + 2a )cosh(x) + (- 2b + 2a b + 4a )cosh(x) +--R + +--R 2 2 2 +--R (2b + 4a b + 2a )cosh(x) +--R * +--R +-+ +--R \|b +--R / +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a )cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((4b - 4a )cosh(x) + (- 4a b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (b - a )cosh(x) + (- 2a b - 2a )cosh(x) - b - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (b + a )sinh(x) + (6b + 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((15b + 15a )cosh(x) - b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((20b + 20a )cosh(x) + (- 4b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (15b + 15a )cosh(x) + (- 6b + 18a )cosh(x) - b +--R + +--R 2 +--R 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (6b + 6a )cosh(x) + (- 4b + 12a )cosh(x) +--R + +--R 2 2 +--R (- 2b + 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (b + a )cosh(x) + (- b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- b + 2a b + 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R +--------------+ +--R | 2 +--R +-+ +-----+ coth(x)\|b tanh(x) + a +--R 2\|b \|b + a atanh(------------------------) +--R +-+ +--R \|b +--R + +--R +-----+ +--R tanh(x)\|b + a +--R (- 2b - 2a)atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R / +--R +-----+ +--R 2\|b + a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 508 +--d0312a:= D(m0312a,x) +--E 65 + +--S 66 of 508 +m0312b:= a0312.2-r0312 +--R +--R +--R (65) +--R (- b - a) +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R (b + a) +--R * +--R log +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +--------------+ +--R | 2 +--R +-+ +-----+ coth(x)\|b tanh(x) + a +--R 2\|b \|b + a atanh(------------------------) +--R +-+ +--R \|b +--R + +--R +-----+ +--R tanh(x)\|b + a +--R (- 2b - 2a)atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R + +--R - +--R +---+ +-----+ +--R 4\|- b \|b + a +--R * +--R atan +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +---+ +-----+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|b + a +--R / +--R +-----+ +--R 2\|b + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 508 +--d0312b:= D(m0312b,x) +--E 67 + +--S 68 of 508 +t0313:= 1/(1+tanh(x)^2)^(1/2) +--R +--R +--R 1 +--R (66) --------------- +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R Type: Expression(Integer) +--E 68 + +--S 69 of 508 +r0313:= 1/2*2^(1/2)*atanh(2^(1/2)*tanh(x)/(1+tanh(x)^2)^(1/2)) +--R +--R +--R +-+ +--R +-+ \|2 tanh(x) +--R \|2 atanh(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R (67) -------------------------- +--R 2 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 508 +a0313:= integrate(t0313,x) +--R +--R +--R (68) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- - \|2 sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +--R \|2 +--R * +--R log +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 2) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - \|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) - 2\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - \|2 cosh(x) + 2\|2 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 70 + +--S 71 of 508 +m0313:= a0313-r0313 +--R +--R +--R (69) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- - \|2 sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +--R \|2 +--R * +--R log +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 2) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) - \|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) - 2\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - \|2 cosh(x) + 2\|2 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +-+ +--R +-+ \|2 tanh(x) +--R - 2\|2 atanh(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R / +--R 4 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 508 +d0313:= D(m0313,x) +--R +--R +--R (70) +--R 8 2 6 5 +--R sinh(x) + (- 4cosh(x) - 3)sinh(x) + 2cosh(x)sinh(x) +--R + +--R 4 2 4 +--R (6cosh(x) + 3cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (- 4cosh(x) + 8cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 4cosh(x) + 3cosh(x) - 8cosh(x) )sinh(x) +--R + +--R 5 3 8 6 4 +--R (2cosh(x) + 8cosh(x) )sinh(x) + cosh(x) - 3cosh(x) - 4cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +-+ 6 +--R - 2\|2 sinh(x) - 4\|2 cosh(x)sinh(x) + 4\|2 sinh(x) +--R + +--R +-+ 3 5 +--R 4\|2 cosh(x) sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (4\|2 cosh(x) - 4\|2 cosh(x) + 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (4\|2 cosh(x) - 4\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 2 +--R (- 4\|2 cosh(x) + 12\|2 cosh(x) )sinh(x) +--R + +--R +-+ 7 +-+ 3 +-+ 8 +--R (- 4\|2 cosh(x) - 4\|2 cosh(x) )sinh(x) - 2\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R 4\|2 cosh(x) + 6\|2 cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R + +--R +-+ 4 +-+ 3 +-+ 2 2 +--R - 4\|2 sinh(x) + 8\|2 cosh(x)sinh(x) - 8\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 +-+ 4 +--R 8\|2 cosh(x) sinh(x) - 4\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 10 9 2 8 +--R 2sinh(x) + 8cosh(x)sinh(x) + 10cosh(x) sinh(x) +--R + +--R 4 6 5 5 +--R (- 12cosh(x) - 2)sinh(x) + (- 16cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 2 4 +--R (- 12cosh(x) - 14cosh(x) + 12)sinh(x) +--R + +--R 3 3 +--R (- 16cosh(x) - 8cosh(x))sinh(x) +--R + +--R 8 4 2 2 +--R (10cosh(x) - 14cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 9 5 3 10 6 +--R (8cosh(x) - 8cosh(x) - 8cosh(x) )sinh(x) + 2cosh(x) - 2cosh(x) +--R + +--R 4 +--R 12cosh(x) +--R / +--R +-+ 4 +-+ 3 +-+ 2 2 +--R 4\|2 sinh(x) - 8\|2 cosh(x)sinh(x) + 8\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 +-+ 4 +--R - 8\|2 cosh(x) sinh(x) + 4\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 10 9 2 8 +--R - 2sinh(x) - 8cosh(x)sinh(x) - 10cosh(x) sinh(x) +--R + +--R 4 6 5 5 +--R (12cosh(x) + 2)sinh(x) + (16cosh(x) + 8cosh(x))sinh(x) +--R + +--R 6 2 4 +--R (12cosh(x) + 14cosh(x) - 12)sinh(x) +--R + +--R 3 3 +--R (16cosh(x) + 8cosh(x))sinh(x) +--R + +--R 8 4 2 2 +--R (- 10cosh(x) + 14cosh(x) - 24cosh(x) )sinh(x) +--R + +--R 9 5 3 10 6 +--R (- 8cosh(x) + 8cosh(x) + 8cosh(x) )sinh(x) - 2cosh(x) + 2cosh(x) +--R + +--R 4 +--R - 12cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 508 +t0314:= 1/(-1-tanh(x)^2)^(1/2) +--R +--R +--R 1 +--R (71) ----------------- +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R Type: Expression(Integer) +--E 73 + +--S 74 of 508 +r0314:= 1/2*2^(1/2)*atan(2^(1/2)*tanh(x)/(-1-tanh(x)^2)^(1/2)) +--R +--R +--R +-+ +--R +-+ \|2 tanh(x) +--R \|2 atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R (72) --------------------------- +--R 2 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 508 +a0314:= integrate(t0314,x) +--R +--R +--R (73) +--R +-------------+ +--R | x 4 +---+ x 2 +---+ +--R +---+ \|- 2(%e ) - 2 - \|- 2 (%e ) - \|- 2 +--R \|- 2 log(----------------------------------------) +--R x 2 +--R (%e ) +--R + +--R - +--R +---+ +--R \|- 2 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +--R (- 2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) +--R + +--R +---+ x 2 +---+ +--R 2\|- 2 (%e ) - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 75 + +--S 76 of 508 +m0314:= a0314-r0314 +--R +--R +--R (74) +--R +-------------+ +--R | x 4 +---+ x 2 +---+ +--R +---+ \|- 2(%e ) - 2 - \|- 2 (%e ) - \|- 2 +--R \|- 2 log(----------------------------------------) +--R x 2 +--R (%e ) +--R + +--R - +--R +---+ +--R \|- 2 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +--R (- 2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) +--R + +--R +---+ x 2 +---+ +--R 2\|- 2 (%e ) - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R + +--R +-+ +--R +-+ \|2 tanh(x) +--R - 2\|2 atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R / +--R 4 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 508 +d0314:= D(m0314,x) +--R +--R +--R (75) +--R +--------------+ +--R x 6 x 4 x 2 | 2 +---+ x 4 +--R (- (%e ) - (%e ) - 2(%e ) - 2)\|- tanh(x) - 1 - 2\|- 2 (%e ) +--R + +--R +---+ +--R - 2\|- 2 +--R * +--R +-------------+ +--R | x 4 +--R \|- 2(%e ) - 2 +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (2\|- 2 (%e ) + 2\|- 2 (%e ) + 2\|- 2 (%e ) + 2\|- 2 ) +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R + +--R x 8 x 4 +--R - 2(%e ) - 6(%e ) - 4 +--R / +--R +--------------+ +-------------+ +--R +---+ x 4 +---+ | 2 | x 4 +--R (2\|- 2 (%e ) + 2\|- 2 )\|- tanh(x) - 1 \|- 2(%e ) - 2 +--R + +--R +--------------+ +--R x 8 x 4 | 2 +--R (2(%e ) + 6(%e ) + 4)\|- tanh(x) - 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 508 +t0315:= 1/(a+b*tanh(x)^2)^(1/2) +--R +--R +--R 1 +--R (76) ----------------- +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R Type: Expression(Integer) +--E 78 + +--S 79 of 508 +r0315:= atanh((a+b)^(1/2)*tanh(x)/(a+b*tanh(x)^2)^(1/2))/(a+b)^(1/2) +--R +--R +--R +-----+ +--R tanh(x)\|b + a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R (77) ------------------------ +--R +-----+ +--R \|b + a +--R Type: Expression(Integer) +--E 79 + +--S 80 of 508 +a0315:= integrate(t0315,x) +--R +--R +--R (78) +--R - +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R log +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) + 4cosh(x) sinh(x) +--R + +--R 4 +--R cosh(x) +--R / +--R +-----+ +--R 2\|b + a +--R Type: Union(Expression(Integer),...) +--E 80 + +--S 81 of 508 +m0315:= a0315-r0315 +--R +--R +--R (79) +--R - +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R log +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) + 4cosh(x) sinh(x) +--R + +--R 4 +--R cosh(x) +--R + +--R +-----+ +--R tanh(x)\|b + a +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R / +--R +-----+ +--R 2\|b + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 508 +d0315:= D(m0315,x) +--R +--R +--R (80) +--R 2 8 +--R (- b - a b)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((4b + 4a b)cosh(x) + 2b + 2a b + 2a )sinh(x) +--R + +--R 5 +--R - 4a b cosh(x)sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 6b - 6a b)cosh(x) + (- 2b - 2a b - 2a )cosh(x) + b +--R + +--R 2 +--R 3a b + 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (8a b cosh(x) + (- 4b - 8a b - 4a )cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 +--R (4b + 4a b)cosh(x) + (- 2b - 2a b - 2a )cosh(x) +--R + +--R 2 2 2 2 +--R (6b + 10a b)cosh(x) - 2b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 2 3 +--R - 4a b cosh(x) + (- 4b - 8a b - 4a )cosh(x) +--R + +--R 2 2 +--R (4b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R (- b - a b)cosh(x) + (2b + 2a b + 2a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (b + 3a b + 4a )cosh(x) + (- 2b + 2a )cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (3b + 5a b + a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (6b + 10a b + 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 5b - 5a b - 3a b - 3a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 6b - 10a b - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 6b + 2a b + 6a b - 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 6b - 10a b - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (5b + 5a b + 3a b + 3a )cosh(x) - b - 7a b - 11a b - 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 10a b - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (12b - 4a b - 12a b + 4a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 6a b + 6a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (5b + 5a b + 3a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 10b - 22a b - 14a b - 2a )cosh(x) + 5b + 5a b - 5a b - 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (6b + 10a b + 2a b - 2a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b + 2a b + 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (2b + 6a b + 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (3b + 5a b + a b - a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 5b - 5a b - 3a b - 3a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- b - 7a b - 11a b - 5a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (5b + 5a b - 5a b - 5a )cosh(x) - 2b + 2a b + 2a b - 2a +--R * +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((2b + 2a b - 2a b - 2a )cosh(x) + 4b + 4a b + 4a b + 4a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b - 12a b - 12a b - 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 2 2 +--R (2b + 2a b - 2a b - 2a )cosh(x) + (16a b + 16a b)cosh(x) +--R + +--R 3 2 2 3 +--R - 2b - 2a b + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b - 12a b - 12a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b + 4a b - 4a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4b + 4a b + 4a b + 4a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 10 3 2 2 9 +--R (- b - 2a b - a b)sinh(x) + (- 4b - 8a b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 8 +--R ((- 5b - 10a b - 5a b)cosh(x) + 2b + a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (6b + 2a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (6b + 12a b + 6a b)cosh(x) + (4b - 4a b)cosh(x) + 2b +--R + +--R 2 3 +--R 5a b - 3a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (8b + 16a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 6b - 2a b + 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 10a b + 6a b - 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (6b + 12a b + 6a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12b - 2a b + 12a b + 2a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (6b + 11a b + 8a b + 3a )cosh(x) - 8b - 7a b - 4a b - 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 2a b + 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (12b + 12a b + 4a b + 4a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 6b + 6a b + 14a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 8 3 2 6 +--R (- 5b - 10a b - 5a b)cosh(x) + (4b - 4a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (6b + 11a b + 8a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 12b - 22a b - 12a b - 2a )cosh(x) + 7b + a b - 3a b - 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 9 +--R (- 4b - 8a b - 4a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (6b + 2a b - 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (2b + 10a b + 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 6b + 6a b + 14a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b - 10a b + 6a b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 10 3 2 2 3 8 +--R (- b - 2a b - a b)cosh(x) + (2b + a b - 2a b - a )cosh(x) +--R + +--R 3 2 3 6 3 2 2 3 4 +--R (2b + 5a b - 3a )cosh(x) + (- 8b - 7a b - 4a b - 5a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (7b + a b - 3a b - 5a )cosh(x) - 2b + 2a b + 2a b - 2a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 2 2 3 6 +--R (2b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((- 2b - 2a b + 2a b + 2a )cosh(x) - 4b - 4a b - 4a b - 4a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b + 12a b + 12a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 2 2 2 3 2 2 3 +--R (- 16a b - 16a b)cosh(x) + 2b + 2a b - 2a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b + 12a b + 12a b + 4a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b - 4a b + 4a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (2b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 4b - 4a b - 4a b - 4a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (2b + 2a b - 2a b - 2a )cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 10 3 2 2 9 +--R (b + 2a b + a b)sinh(x) + (4b + 8a b + 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 8 +--R ((5b + 10a b + 5a b)cosh(x) - 2b - a b + 2a b + a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 6b - 2a b + 6a b + 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (- 6b - 12a b - 6a b)cosh(x) + (- 4b + 4a b)cosh(x) - 2b +--R + +--R 2 3 +--R - 5a b + 3a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 8b - 16a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (6b + 2a b - 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 10a b - 6a b + 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (- 6b - 12a b - 6a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (12b + 2a b - 12a b - 2a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 6b - 11a b - 8a b - 3a )cosh(x) + 8b + 7a b + 4a b + 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 2a b - 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b - 12a b - 4a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 6a b - 14a b - 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 8 3 2 6 +--R (5b + 10a b + 5a b)cosh(x) + (- 4b + 4a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 6b - 11a b - 8a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (12b + 22a b + 12a b + 2a )cosh(x) - 7b - a b + 3a b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 9 +--R (4b + 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (- 6b - 2a b + 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 2b - 10a b - 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (6b - 6a b - 14a b - 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b + 10a b - 6a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 10 3 2 2 3 8 +--R (b + 2a b + a b)cosh(x) + (- 2b - a b + 2a b + a )cosh(x) +--R + +--R 3 2 3 6 3 2 2 3 4 +--R (- 2b - 5a b + 3a )cosh(x) + (8b + 7a b + 4a b + 5a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 7b - a b + 3a b + 5a )cosh(x) + 2b - 2a b - 2a b + 2a +--R * +--R +-----+ +--R \|b + a +--R * +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R Type: Expression(Integer) +--E 82 + +--S 83 of 508 +t0316:= (1+tanh(x)^2)^(3/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (81) (tanh(x) + 1)\|tanh(x) + 1 +--R Type: Expression(Integer) +--E 83 + +--S 84 of 508 +r0316:= -5/2*asinh(tanh(x))+2*2^(1/2)*atanh(2^(1/2)*tanh(x)/_ + (1+tanh(x)^2)^(1/2))-1/2*tanh(x)*(1+tanh(x)^2)^(1/2) +--R +--R +--R (82) +--R +-+ +------------+ +--R +-+ \|2 tanh(x) | 2 +--R 4\|2 atanh(---------------) - tanh(x)\|tanh(x) + 1 - 5asinh(tanh(x)) +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R ---------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 508 +a0316:= integrate(t0316,x) +--R +--R +--R (83) +--R 4 3 2 2 +--R - 10sinh(x) - 40cosh(x)sinh(x) + (- 60cosh(x) - 20)sinh(x) +--R + +--R 3 4 2 +--R (- 40cosh(x) - 40cosh(x))sinh(x) - 10cosh(x) - 20cosh(x) - 10 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R 5\|2 sinh(x) + 40\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (140\|2 cosh(x) + 10\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (280\|2 cosh(x) + 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (350\|2 cosh(x) + 150\|2 cosh(x) + 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (280\|2 cosh(x) + 200\|2 cosh(x) + 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (140\|2 cosh(x) + 150\|2 cosh(x) + 90\|2 cosh(x) + 20\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (40\|2 cosh(x) + 60\|2 cosh(x) + 60\|2 cosh(x) + 40\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 5\|2 cosh(x) + 10\|2 cosh(x) + 15\|2 cosh(x) + 20\|2 cosh(x) +--R + +--R +-+ +--R 10\|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 2)sinh(x) + (4\|2 - 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (2\|2 - 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R 10sinh(x) + 40cosh(x)sinh(x) + (60cosh(x) + 20)sinh(x) +--R + +--R 3 4 2 +--R (40cosh(x) + 40cosh(x))sinh(x) + 10cosh(x) + 20cosh(x) + 10 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 5\|2 sinh(x) - 40\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 140\|2 cosh(x) - 10\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 280\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 350\|2 cosh(x) - 150\|2 cosh(x) - 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 280\|2 cosh(x) - 200\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 140\|2 cosh(x) - 150\|2 cosh(x) - 90\|2 cosh(x) - 20\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 40\|2 cosh(x) - 60\|2 cosh(x) - 60\|2 cosh(x) +--R + +--R +-+ +--R - 40\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 5\|2 cosh(x) - 10\|2 cosh(x) - 15\|2 cosh(x) - 20\|2 cosh(x) +--R + +--R +-+ +--R - 10\|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 2)sinh(x) + (- 4\|2 - 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (- 2\|2 - 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 4\|2 sinh(x) - 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 24\|2 cosh(x) - 8\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 16\|2 cosh(x) - 16\|2 cosh(x))sinh(x) - 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 8\|2 cosh(x) - 4\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R 4sinh(x) + 32cosh(x)sinh(x) + (112cosh(x) + 8)sinh(x) +--R + +--R 3 5 +--R (224cosh(x) + 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (280cosh(x) + 120cosh(x) + 12)sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) + 160cosh(x) + 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (112cosh(x) + 120cosh(x) + 72cosh(x) + 16)sinh(x) +--R + +--R 7 5 3 8 +--R (32cosh(x) + 48cosh(x) + 48cosh(x) + 32cosh(x))sinh(x) + 4cosh(x) +--R + +--R 6 4 2 +--R 8cosh(x) + 12cosh(x) + 16cosh(x) + 8 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) 2 +--R \|2 |------------------------------------- - 2sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R / +--R +-+ 2 +-+ +-+ 2 +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R 4\|2 sinh(x) + 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (24\|2 cosh(x) + 8\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (16\|2 cosh(x) + 16\|2 cosh(x))sinh(x) + 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 8\|2 cosh(x) + 4\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 4sinh(x) - 32cosh(x)sinh(x) + (- 112cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (- 224cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 280cosh(x) - 120cosh(x) - 12)sinh(x) +--R + +--R 5 3 3 +--R (- 224cosh(x) - 160cosh(x) - 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 112cosh(x) - 120cosh(x) - 72cosh(x) - 16)sinh(x) +--R + +--R 7 5 3 +--R (- 32cosh(x) - 48cosh(x) - 48cosh(x) - 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 4cosh(x) - 8cosh(x) - 12cosh(x) - 16cosh(x) - 8 +--R * +--R log +--R 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 4) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8\|2 cosh(x) - 4\|2 cosh(x))sinh(x) + 2\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 2\|2 cosh(x) + 4\|2 +--R / +--R +-+ 4 +-+ 3 +-+ 2 2 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) + 6\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 +-+ 4 +--R 4\|2 cosh(x) sinh(x) + \|2 cosh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 2 +-+ 4 +--R \|2 sinh(x) + 6\|2 cosh(x)sinh(x) + (15\|2 cosh(x) + \|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (20\|2 cosh(x) + 4\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|2 cosh(x) + 6\|2 cosh(x) + 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +-+ 6 +--R (6\|2 cosh(x) + 4\|2 cosh(x) + 12\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R \|2 cosh(x) + 6\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 120cosh(x) - 2)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) - 160cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) - 120cosh(x) - 12cosh(x) - 12)sinh(x) +--R + +--R 7 5 3 8 +--R (- 16cosh(x) - 48cosh(x) - 8cosh(x) - 24cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) - 2cosh(x) - 12cosh(x) +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 8)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 16cosh(x))sinh(x) + 4cosh(x) + 8cosh(x) + 4 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 2\|2 sinh(x) - 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 56\|2 cosh(x) - 4\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 112\|2 cosh(x) - 24\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 140\|2 cosh(x) - 60\|2 cosh(x) - 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 112\|2 cosh(x) - 80\|2 cosh(x) - 24\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (- 56\|2 cosh(x) - 60\|2 cosh(x) - 36\|2 cosh(x) - 8\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 16\|2 cosh(x) - 24\|2 cosh(x) - 24\|2 cosh(x) - 16\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 2\|2 cosh(x) - 4\|2 cosh(x) - 6\|2 cosh(x) - 8\|2 cosh(x) - 4\|2 +--R Type: Union(Expression(Integer),...) +--E 85 + +--S 86 of 508 +m0316:= a0316-r0316 +--R +--R +--R (84) +--R 4 3 2 2 +--R - 10sinh(x) - 40cosh(x)sinh(x) + (- 60cosh(x) - 20)sinh(x) +--R + +--R 3 4 2 +--R (- 40cosh(x) - 40cosh(x))sinh(x) - 10cosh(x) - 20cosh(x) - 10 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R 5\|2 sinh(x) + 40\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (140\|2 cosh(x) + 10\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (280\|2 cosh(x) + 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (350\|2 cosh(x) + 150\|2 cosh(x) + 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (280\|2 cosh(x) + 200\|2 cosh(x) + 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (140\|2 cosh(x) + 150\|2 cosh(x) + 90\|2 cosh(x) + 20\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (40\|2 cosh(x) + 60\|2 cosh(x) + 60\|2 cosh(x) + 40\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 5\|2 cosh(x) + 10\|2 cosh(x) + 15\|2 cosh(x) + 20\|2 cosh(x) +--R + +--R +-+ +--R 10\|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 - 2)sinh(x) + (4\|2 - 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (2\|2 - 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R 10sinh(x) + 40cosh(x)sinh(x) + (60cosh(x) + 20)sinh(x) +--R + +--R 3 4 2 +--R (40cosh(x) + 40cosh(x))sinh(x) + 10cosh(x) + 20cosh(x) + 10 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 5\|2 sinh(x) - 40\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 140\|2 cosh(x) - 10\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 280\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 350\|2 cosh(x) - 150\|2 cosh(x) - 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 280\|2 cosh(x) - 200\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 140\|2 cosh(x) - 150\|2 cosh(x) - 90\|2 cosh(x) - 20\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 40\|2 cosh(x) - 60\|2 cosh(x) - 60\|2 cosh(x) +--R + +--R +-+ +--R - 40\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 5\|2 cosh(x) - 10\|2 cosh(x) - 15\|2 cosh(x) - 20\|2 cosh(x) +--R + +--R +-+ +--R - 10\|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 - 2)sinh(x) + (- 4\|2 - 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (- 2\|2 - 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 4\|2 sinh(x) - 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 24\|2 cosh(x) - 8\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 16\|2 cosh(x) - 16\|2 cosh(x))sinh(x) - 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 8\|2 cosh(x) - 4\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R 4sinh(x) + 32cosh(x)sinh(x) + (112cosh(x) + 8)sinh(x) +--R + +--R 3 5 +--R (224cosh(x) + 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (280cosh(x) + 120cosh(x) + 12)sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) + 160cosh(x) + 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (112cosh(x) + 120cosh(x) + 72cosh(x) + 16)sinh(x) +--R + +--R 7 5 3 8 +--R (32cosh(x) + 48cosh(x) + 48cosh(x) + 32cosh(x))sinh(x) + 4cosh(x) +--R + +--R 6 4 2 +--R 8cosh(x) + 12cosh(x) + 16cosh(x) + 8 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) 2 +--R \|2 |------------------------------------- - 2sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R / +--R +-+ 2 +-+ +-+ 2 +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R 4\|2 sinh(x) + 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (24\|2 cosh(x) + 8\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (16\|2 cosh(x) + 16\|2 cosh(x))sinh(x) + 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 8\|2 cosh(x) + 4\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 4sinh(x) - 32cosh(x)sinh(x) + (- 112cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (- 224cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 280cosh(x) - 120cosh(x) - 12)sinh(x) +--R + +--R 5 3 3 +--R (- 224cosh(x) - 160cosh(x) - 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 112cosh(x) - 120cosh(x) - 72cosh(x) - 16)sinh(x) +--R + +--R 7 5 3 +--R (- 32cosh(x) - 48cosh(x) - 48cosh(x) - 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 4cosh(x) - 8cosh(x) - 12cosh(x) - 16cosh(x) - 8 +--R * +--R log +--R 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 4) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8\|2 cosh(x) - 4\|2 cosh(x))sinh(x) + 2\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 2\|2 cosh(x) + 4\|2 +--R / +--R +-+ 4 +-+ 3 +-+ 2 2 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) + 6\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 +-+ 4 +--R 4\|2 cosh(x) sinh(x) + \|2 cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 8\|2 sinh(x) - 32\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 48\|2 cosh(x) - 16\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 32\|2 cosh(x) - 32\|2 cosh(x))sinh(x) - 8\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 16\|2 cosh(x) - 8\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R 8sinh(x) + 64cosh(x)sinh(x) + (224cosh(x) + 16)sinh(x) +--R + +--R 3 5 +--R (448cosh(x) + 96cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (560cosh(x) + 240cosh(x) + 24)sinh(x) +--R + +--R 5 3 3 +--R (448cosh(x) + 320cosh(x) + 96cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (224cosh(x) + 240cosh(x) + 144cosh(x) + 32)sinh(x) +--R + +--R 7 5 3 8 +--R (64cosh(x) + 96cosh(x) + 96cosh(x) + 64cosh(x))sinh(x) + 8cosh(x) +--R + +--R 6 4 2 +--R 16cosh(x) + 24cosh(x) + 32cosh(x) + 16 +--R * +--R +-+ +--R \|2 tanh(x) +--R atanh(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R + +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) + 8cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) + 2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R tanh(x) |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - \|2 sinh(x) - 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 28\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 56\|2 cosh(x) - 12\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 70\|2 cosh(x) - 30\|2 cosh(x) - 3\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 56\|2 cosh(x) - 40\|2 cosh(x) - 12\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 28\|2 cosh(x) - 30\|2 cosh(x) - 18\|2 cosh(x) - 4\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 8\|2 cosh(x) - 12\|2 cosh(x) - 12\|2 cosh(x) +--R + +--R +-+ +--R - 8\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - \|2 cosh(x) - 2\|2 cosh(x) - 3\|2 cosh(x) - 4\|2 cosh(x) +--R + +--R +-+ +--R - 2\|2 +--R * +--R tanh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R + +--R 4 3 2 2 +--R 10sinh(x) + 40cosh(x)sinh(x) + (60cosh(x) + 20)sinh(x) +--R + +--R 3 4 2 +--R (40cosh(x) + 40cosh(x))sinh(x) + 10cosh(x) + 20cosh(x) + 10 +--R * +--R asinh(tanh(x)) +--R + +--R +-+ 6 +-+ 5 +-+ 2 +-+ 4 +--R \|2 sinh(x) + 6\|2 cosh(x)sinh(x) + (15\|2 cosh(x) + \|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (20\|2 cosh(x) + 4\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|2 cosh(x) + 6\|2 cosh(x) + 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +-+ 6 +--R (6\|2 cosh(x) + 4\|2 cosh(x) + 12\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R \|2 cosh(x) + 6\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 5\|2 sinh(x) - 40\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 140\|2 cosh(x) - 10\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 280\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 350\|2 cosh(x) - 150\|2 cosh(x) - 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 280\|2 cosh(x) - 200\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 140\|2 cosh(x) - 150\|2 cosh(x) - 90\|2 cosh(x) - 20\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 40\|2 cosh(x) - 60\|2 cosh(x) - 60\|2 cosh(x) +--R + +--R +-+ +--R - 40\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 5\|2 cosh(x) - 10\|2 cosh(x) - 15\|2 cosh(x) - 20\|2 cosh(x) +--R + +--R +-+ +--R - 10\|2 +--R * +--R asinh(tanh(x)) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 120cosh(x) - 2)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) - 160cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) - 120cosh(x) - 12cosh(x) - 12)sinh(x) +--R + +--R 7 5 3 8 +--R (- 16cosh(x) - 48cosh(x) - 8cosh(x) - 24cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) - 2cosh(x) - 12cosh(x) +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 8)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 16cosh(x))sinh(x) + 4cosh(x) + 8cosh(x) + 4 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 2\|2 sinh(x) - 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 56\|2 cosh(x) - 4\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 112\|2 cosh(x) - 24\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 140\|2 cosh(x) - 60\|2 cosh(x) - 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 112\|2 cosh(x) - 80\|2 cosh(x) - 24\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (- 56\|2 cosh(x) - 60\|2 cosh(x) - 36\|2 cosh(x) - 8\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 16\|2 cosh(x) - 24\|2 cosh(x) - 24\|2 cosh(x) - 16\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 2\|2 cosh(x) - 4\|2 cosh(x) - 6\|2 cosh(x) - 8\|2 cosh(x) - 4\|2 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 508 +d0316:= D(m0316,x) +--R +--R +--R (85) +--R +-+ 30 +-+ 29 +--R 7\|2 sinh(x) + 98\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 28 +--R (581\|2 cosh(x) + 38\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 27 +--R (1764\|2 cosh(x) + 476\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 26 +--R (2107\|2 cosh(x) + 2484\|2 cosh(x) + 201\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 3626\|2 cosh(x) + 6412\|2 cosh(x) + 2246\|2 cosh(x)) +--R * +--R 25 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 17591\|2 cosh(x) + 5410\|2 cosh(x) + 10269\|2 cosh(x) +--R + +--R +-+ +--R 630\|2 +--R * +--R 24 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 22232\|2 cosh(x) - 14616\|2 cosh(x) + 22200\|2 cosh(x) +--R + +--R +-+ +--R 5920\|2 cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 13867\|2 cosh(x) - 46712\|2 cosh(x) + 10406\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 21432\|2 cosh(x) + 1045\|2 +--R * +--R 22 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 78386\|2 cosh(x) - 35288\|2 cosh(x) - 59124\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 29664\|2 cosh(x) + 6846\|2 cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 79233\|2 cosh(x) + 58806\|2 cosh(x) - 135594\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 24596\|2 cosh(x) + 10243\|2 cosh(x) + 1630\|2 +--R * +--R 20 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 48804\|2 cosh(x) + 137940\|2 cosh(x) - 72232\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 139936\|2 cosh(x) - 33388\|2 cosh(x) + 6956\|2 cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 188993\|2 cosh(x) + 42636\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 148395\|2 cosh(x) - 148776\|2 cosh(x) - 144737\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 4612\|2 cosh(x) + 435\|2 +--R * +--R 18 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 132202\|2 cosh(x) - 162108\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 270042\|2 cosh(x) + 80288\|2 cosh(x) - 167578\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 73908\|2 cosh(x) - 6262\|2 cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R 110789\|2 cosh(x) - 178942\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 106063\|2 cosh(x) + 312362\|2 cosh(x) + 103385\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 137658\|2 cosh(x) - 45829\|2 cosh(x) + 718\|2 +--R * +--R 16 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R 253232\|2 cosh(x) + 67184\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R - 119952\|2 cosh(x) + 213312\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 470768\|2 cosh(x) - 10256\|2 cosh(x) - 93584\|2 cosh(x) +--R + +--R +-+ +--R - 8328\|2 cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R 110789\|2 cosh(x) + 232560\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 139740\|2 cosh(x) - 75408\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 440162\|2 cosh(x) + 257104\|2 cosh(x) - 14180\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 42336\|2 cosh(x) - 5816\|2 +--R * +--R 14 +--R sinh(x) +--R + +--R +-+ 17 +-+ 15 +--R - 132202\|2 cosh(x) + 67184\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 86360\|2 cosh(x) - 189248\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 11812\|2 cosh(x) + 289968\|2 cosh(x) + 195736\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 43096\|2 cosh(x) - 21680\|2 cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 18 +-+ 16 +--R - 188993\|2 cosh(x) - 178942\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 139740\|2 cosh(x) - 171288\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 410098\|2 cosh(x) + 14172\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 243532\|2 cosh(x) + 50216\|2 cosh(x) - 19688\|2 cosh(x) +--R + +--R +-+ +--R - 8424\|2 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 48804\|2 cosh(x) - 162108\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 119952\|2 cosh(x) - 189248\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R - 529672\|2 cosh(x) - 212760\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 20240\|2 cosh(x) + 99384\|2 cosh(x) + 18720\|2 cosh(x) +--R + +--R +-+ +--R - 13600\|2 cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R 79233\|2 cosh(x) + 42636\|2 cosh(x) + 106063\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 75408\|2 cosh(x) - 410098\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 261272\|2 cosh(x) - 183958\|2 cosh(x) + 8928\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 38664\|2 cosh(x) + 304\|2 cosh(x) - 3520\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 21 +-+ 19 +--R 78386\|2 cosh(x) + 137940\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R 270042\|2 cosh(x) + 213312\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 11812\|2 cosh(x) - 212760\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 232260\|2 cosh(x) - 47960\|2 cosh(x) + 9648\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 5984\|2 cosh(x) + 2688\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 13867\|2 cosh(x) + 58806\|2 cosh(x) + 148395\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R 312362\|2 cosh(x) + 440162\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 14172\|2 cosh(x) - 183958\|2 cosh(x) - 35052\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 13160\|2 cosh(x) + 4968\|2 cosh(x) - 704\|2 cosh(x) +--R + +--R +-+ +--R - 2240\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 23 +-+ 21 +--R - 22232\|2 cosh(x) - 35288\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 72232\|2 cosh(x) + 80288\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R 470768\|2 cosh(x) + 289968\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 20240\|2 cosh(x) - 47960\|2 cosh(x) - 13376\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 7616\|2 cosh(x) - 512\|2 cosh(x) + 7808\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 24 +-+ 22 +--R - 17591\|2 cosh(x) - 46712\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R - 135594\|2 cosh(x) - 148776\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R 103385\|2 cosh(x) + 257104\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 243532\|2 cosh(x) + 8928\|2 cosh(x) - 13160\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 6304\|2 cosh(x) + 4224\|2 cosh(x) - 16384\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R - 3626\|2 cosh(x) - 14616\|2 cosh(x) - 59124\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 139936\|2 cosh(x) - 167578\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 10256\|2 cosh(x) + 195736\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 99384\|2 cosh(x) + 9648\|2 cosh(x) + 7616\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R - 4352\|2 cosh(x) + 24960\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R 2107\|2 cosh(x) + 5410\|2 cosh(x) + 10406\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R - 24596\|2 cosh(x) - 144737\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 137658\|2 cosh(x) - 14180\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 50216\|2 cosh(x) + 38664\|2 cosh(x) + 4968\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R 4224\|2 cosh(x) - 28288\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 27 +-+ 25 +-+ 23 +--R 1764\|2 cosh(x) + 6412\|2 cosh(x) + 22200\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R 29664\|2 cosh(x) - 33388\|2 cosh(x) - 73908\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 93584\|2 cosh(x) - 43096\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 18720\|2 cosh(x) + 5984\|2 cosh(x) - 512\|2 cosh(x) +--R + +--R +-+ 5 +--R 24960\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 28 +-+ 26 +-+ 24 +--R 581\|2 cosh(x) + 2484\|2 cosh(x) + 10269\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 21432\|2 cosh(x) + 10243\|2 cosh(x) - 4612\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 45829\|2 cosh(x) - 42336\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 19688\|2 cosh(x) + 304\|2 cosh(x) - 704\|2 cosh(x) +--R + +--R +-+ 6 +--R - 16384\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R 98\|2 cosh(x) + 476\|2 cosh(x) + 2246\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 5920\|2 cosh(x) + 6846\|2 cosh(x) + 6956\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R - 6262\|2 cosh(x) - 8328\|2 cosh(x) - 21680\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 13600\|2 cosh(x) + 2688\|2 cosh(x) + 7808\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R 7\|2 cosh(x) + 38\|2 cosh(x) + 201\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 630\|2 cosh(x) + 1045\|2 cosh(x) + 1630\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 435\|2 cosh(x) + 718\|2 cosh(x) - 5816\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 8424\|2 cosh(x) - 3520\|2 cosh(x) - 2240\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 30 29 2 28 +--R - 32sinh(x) - 512cosh(x)sinh(x) + (- 3680cosh(x) - 120)sinh(x) +--R + +--R 3 27 +--R (- 15360cosh(x) - 1680cosh(x))sinh(x) +--R + +--R 4 2 26 +--R (- 39328cosh(x) - 10320cosh(x) - 528)sinh(x) +--R + +--R 5 3 25 +--R (- 54784cosh(x) - 35280cosh(x) - 6176cosh(x))sinh(x) +--R + +--R 6 4 2 24 +--R (544cosh(x) - 66600cosh(x) - 29968cosh(x) - 1736)sinh(x) +--R + +--R 7 5 3 +--R (174080cosh(x) - 36960cosh(x) - 70400cosh(x) - 17712cosh(x)) +--R * +--R 23 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 364640cosh(x) + 142560cosh(x) - 40352cosh(x) - 73664cosh(x) +--R + +--R - 2992 +--R * +--R 22 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 298496cosh(x) + 404640cosh(x) + 222400cosh(x) - 143696cosh(x) +--R + +--R - 23104cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R 10 8 6 +--R - 193248cosh(x) + 415560cosh(x) + 658016cosh(x) +--R + +--R 4 2 +--R - 54352cosh(x) - 60240cosh(x) - 4664 +--R * +--R 20 +--R sinh(x) +--R + +--R 11 9 7 +--R - 820224cosh(x) - 116400cosh(x) + 688384cosh(x) +--R + +--R 5 3 +--R 342640cosh(x) - 9856cosh(x) - 25232cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 12 10 8 +--R - 945440cosh(x) - 907440cosh(x) - 288240cosh(x) +--R + +--R 6 4 2 +--R 708928cosh(x) + 274032cosh(x) - 20912cosh(x) - 1232 +--R * +--R 18 +--R sinh(x) +--R + +--R 13 11 9 +--R - 243200cosh(x) - 1144560cosh(x) - 1788384cosh(x) +--R + +--R 7 5 3 +--R 341264cosh(x) + 572096cosh(x) + 152560cosh(x) + 16672cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 14 12 10 +--R 816544cosh(x) - 348840cosh(x) - 2219248cosh(x) +--R + +--R 8 6 4 +--R - 742840cosh(x) + 260752cosh(x) + 489256cosh(x) +--R + +--R 2 +--R 148592cosh(x) - 2008 +--R * +--R 16 +--R sinh(x) +--R + +--R 15 13 11 +--R 1323008cosh(x) + 930240cosh(x) - 617984cosh(x) +--R + +--R 9 7 5 +--R - 1376992cosh(x) - 704000cosh(x) + 561856cosh(x) +--R + +--R 3 +--R 441216cosh(x) + 21936cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 16 14 12 +--R 816544cosh(x) + 1550400cosh(x) + 1920320cosh(x) +--R + +--R 10 8 6 +--R - 635264cosh(x) - 1254880cosh(x) + 83392cosh(x) +--R + +--R 4 2 +--R 619008cosh(x) + 143456cosh(x) + 16464 +--R * +--R 14 +--R sinh(x) +--R + +--R 17 15 13 +--R - 243200cosh(x) + 930240cosh(x) + 3144320cosh(x) +--R + +--R 11 9 7 +--R 854496cosh(x) - 548992cosh(x) - 448064cosh(x) +--R + +--R 5 3 +--R 369792cosh(x) + 288144cosh(x) + 77888cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 18 16 14 +--R - 945440cosh(x) - 348840cosh(x) + 1920320cosh(x) +--R + +--R 12 10 8 +--R 1597856cosh(x) + 783328cosh(x) - 484592cosh(x) +--R + +--R 6 4 2 +--R - 65664cosh(x) + 231072cosh(x) + 141808cosh(x) + 23824 +--R * +--R 12 +--R sinh(x) +--R + +--R 19 17 15 +--R - 820224cosh(x) - 1144560cosh(x) - 617984cosh(x) +--R + +--R 13 11 9 +--R 854496cosh(x) + 1427712cosh(x) - 241120cosh(x) +--R + +--R 7 5 3 +--R - 310144cosh(x) + 32048cosh(x) + 116608cosh(x) + 62240cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 20 18 16 +--R - 193248cosh(x) - 907440cosh(x) - 2219248cosh(x) +--R + +--R 14 12 10 +--R - 635264cosh(x) + 783328cosh(x) - 124960cosh(x) +--R + +--R 8 6 4 2 +--R - 438560cosh(x) - 110688cosh(x) + 16464cosh(x) + 72928cosh(x) +--R + +--R 9952 +--R * +--R 10 +--R sinh(x) +--R + +--R 21 19 17 +--R 298496cosh(x) - 116400cosh(x) - 1788384cosh(x) +--R + +--R 15 13 11 +--R - 1376992cosh(x) - 548992cosh(x) - 241120cosh(x) +--R + +--R 9 7 5 3 +--R - 510784cosh(x) - 276592cosh(x) - 94272cosh(x) + 73888cosh(x) +--R + +--R 2304cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 22 20 18 +--R 364640cosh(x) + 415560cosh(x) - 288240cosh(x) +--R + +--R 16 14 12 +--R - 742840cosh(x) - 1254880cosh(x) - 484592cosh(x) +--R + +--R 10 8 6 +--R - 438560cosh(x) - 392592cosh(x) - 207504cosh(x) +--R + +--R 4 2 +--R 54000cosh(x) + 9056cosh(x) + 6336 +--R * +--R 8 +--R sinh(x) +--R + +--R 23 21 19 +--R 174080cosh(x) + 404640cosh(x) + 688384cosh(x) +--R + +--R 17 15 13 +--R 341264cosh(x) - 704000cosh(x) - 448064cosh(x) +--R + +--R 11 9 7 +--R - 310144cosh(x) - 276592cosh(x) - 265984cosh(x) +--R + +--R 5 3 +--R 19520cosh(x) + 6144cosh(x) - 15744cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 24 22 20 +--R 544cosh(x) + 142560cosh(x) + 658016cosh(x) +--R + +--R 18 16 14 +--R 708928cosh(x) + 260752cosh(x) + 83392cosh(x) +--R + +--R 12 10 8 +--R - 65664cosh(x) - 110688cosh(x) - 207504cosh(x) +--R + +--R 6 4 2 +--R 9792cosh(x) - 6720cosh(x) + 33792cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 25 23 21 +--R - 54784cosh(x) - 36960cosh(x) + 222400cosh(x) +--R + +--R 19 17 15 +--R 342640cosh(x) + 572096cosh(x) + 561856cosh(x) +--R + +--R 13 11 9 7 +--R 369792cosh(x) + 32048cosh(x) - 94272cosh(x) + 19520cosh(x) +--R + +--R 5 3 +--R 7680cosh(x) - 47744cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 26 24 22 +--R - 39328cosh(x) - 66600cosh(x) - 40352cosh(x) +--R + +--R 20 18 16 +--R - 54352cosh(x) + 274032cosh(x) + 489256cosh(x) +--R + +--R 14 12 10 +--R 619008cosh(x) + 231072cosh(x) + 16464cosh(x) +--R + +--R 8 6 4 +--R 54000cosh(x) - 6720cosh(x) + 54912cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 27 25 23 +--R - 15360cosh(x) - 35280cosh(x) - 70400cosh(x) +--R + +--R 21 19 17 +--R - 143696cosh(x) - 9856cosh(x) + 152560cosh(x) +--R + +--R 15 13 11 +--R 441216cosh(x) + 288144cosh(x) + 116608cosh(x) +--R + +--R 9 7 5 +--R 73888cosh(x) + 6144cosh(x) - 47744cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 28 26 24 +--R - 3680cosh(x) - 10320cosh(x) - 29968cosh(x) +--R + +--R 22 20 18 +--R - 73664cosh(x) - 60240cosh(x) - 20912cosh(x) +--R + +--R 16 14 12 +--R 148592cosh(x) + 143456cosh(x) + 141808cosh(x) +--R + +--R 10 8 6 +--R 72928cosh(x) + 9056cosh(x) + 33792cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 29 27 25 23 +--R - 512cosh(x) - 1680cosh(x) - 6176cosh(x) - 17712cosh(x) +--R + +--R 21 19 17 +--R - 23104cosh(x) - 25232cosh(x) + 16672cosh(x) +--R + +--R 15 13 11 9 +--R 21936cosh(x) + 77888cosh(x) + 62240cosh(x) + 2304cosh(x) +--R + +--R 7 +--R - 15744cosh(x) +--R * +--R sinh(x) +--R + +--R 30 28 26 24 +--R - 32cosh(x) - 120cosh(x) - 528cosh(x) - 1736cosh(x) +--R + +--R 22 20 18 16 +--R - 2992cosh(x) - 4664cosh(x) - 1232cosh(x) - 2008cosh(x) +--R + +--R 14 12 10 8 +--R 16464cosh(x) + 23824cosh(x) + 9952cosh(x) + 6336cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R + +--R 30 29 2 28 +--R - 4sinh(x) - 64cosh(x)sinh(x) + (- 460cosh(x) - 8)sinh(x) +--R + +--R 3 27 +--R (- 1920cosh(x) - 112cosh(x))sinh(x) +--R + +--R 4 2 26 +--R (- 4916cosh(x) - 688cosh(x) - 20)sinh(x) +--R + +--R 5 3 25 +--R (- 6848cosh(x) - 2352cosh(x) - 224cosh(x))sinh(x) +--R + +--R 6 4 2 24 +--R (68cosh(x) - 4440cosh(x) - 996cosh(x) - 120)sinh(x) +--R + +--R 7 5 3 +--R (21760cosh(x) - 2464cosh(x) - 1792cosh(x) - 1232cosh(x)) +--R * +--R 23 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 45580cosh(x) + 9504cosh(x) + 1672cosh(x) - 5184cosh(x) +--R + +--R - 276 +--R * +--R 22 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 37312cosh(x) + 26976cosh(x) + 15680cosh(x) - 10416cosh(x) +--R + +--R - 2336cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R 10 8 6 +--R - 24156cosh(x) + 27704cosh(x) + 34248cosh(x) +--R + +--R 4 2 +--R - 5168cosh(x) - 7628cosh(x) - 728 +--R * +--R 20 +--R sinh(x) +--R + +--R 11 9 7 +--R - 102528cosh(x) - 7760cosh(x) + 27904cosh(x) +--R + +--R 5 3 +--R 21392cosh(x) - 9792cosh(x) - 4912cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 12 10 8 +--R - 118180cosh(x) - 60496cosh(x) - 28988cosh(x) +--R + +--R 6 4 2 +--R 47808cosh(x) + 5316cosh(x) - 11504cosh(x) - 1676 +--R * +--R 18 +--R sinh(x) +--R + +--R 13 11 9 +--R - 30400cosh(x) - 76304cosh(x) - 105760cosh(x) +--R + +--R 7 5 3 +--R 26864cosh(x) + 32096cosh(x) - 5040cosh(x) - 8384cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 14 12 10 +--R 102068cosh(x) - 23256cosh(x) - 119884cosh(x) +--R + +--R 8 6 4 +--R - 42760cosh(x) + 31964cosh(x) + 25352cosh(x) +--R + +--R 2 +--R - 11372cosh(x) - 2792 +--R * +--R 16 +--R sinh(x) +--R + +--R 15 13 11 +--R 165376cosh(x) + 62016cosh(x) - 26112cosh(x) +--R + +--R 9 7 5 +--R - 86304cosh(x) - 11008cosh(x) + 49728cosh(x) +--R + +--R 3 +--R 9728cosh(x) - 9104cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 16 14 12 +--R 102068cosh(x) + 103360cosh(x) + 113968cosh(x) +--R + +--R 10 8 6 +--R - 42624cosh(x) - 47368cosh(x) + 32448cosh(x) +--R + +--R 4 2 +--R 40528cosh(x) - 2528cosh(x) - 4648 +--R * +--R 14 +--R sinh(x) +--R + +--R 17 15 13 +--R - 30400cosh(x) + 62016cosh(x) + 180608cosh(x) +--R + +--R 11 9 7 5 +--R 49696cosh(x) - 29760cosh(x) - 4288cosh(x) + 38656cosh(x) +--R + +--R 3 +--R 19664cosh(x) - 7936cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 18 16 14 +--R - 118180cosh(x) - 23256cosh(x) + 113968cosh(x) +--R + +--R 12 10 8 +--R 96096cosh(x) + 17992cosh(x) - 24624cosh(x) +--R + +--R 6 4 2 +--R 12560cosh(x) + 22368cosh(x) + 5960cosh(x) - 6048 +--R * +--R 12 +--R sinh(x) +--R + +--R 19 17 15 +--R - 102528cosh(x) - 76304cosh(x) - 26112cosh(x) +--R + +--R 13 11 9 +--R 49696cosh(x) + 41600cosh(x) - 35488cosh(x) +--R + +--R 7 5 3 +--R - 9728cosh(x) + 7920cosh(x) + 10240cosh(x) - 448cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 20 18 16 +--R - 24156cosh(x) - 60496cosh(x) - 119884cosh(x) +--R + +--R 14 12 10 +--R - 42624cosh(x) + 17992cosh(x) - 41888cosh(x) +--R + +--R 8 6 4 2 +--R - 40040cosh(x) + 2528cosh(x) - 1256cosh(x) + 7488cosh(x) +--R + +--R - 4192 +--R * +--R 10 +--R sinh(x) +--R + +--R 21 19 17 +--R 37312cosh(x) - 7760cosh(x) - 105760cosh(x) +--R + +--R 15 13 11 +--R - 86304cosh(x) - 29760cosh(x) - 35488cosh(x) +--R + +--R 9 7 5 3 +--R - 60544cosh(x) - 18480cosh(x) + 7936cosh(x) - 7872cosh(x) +--R + +--R 7040cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 22 20 18 +--R 45580cosh(x) + 27704cosh(x) - 28988cosh(x) +--R + +--R 16 14 12 +--R - 42760cosh(x) - 47368cosh(x) - 24624cosh(x) +--R + +--R 10 8 6 4 +--R - 40040cosh(x) - 39152cosh(x) - 56cosh(x) + 6048cosh(x) +--R + +--R 2 +--R - 6112cosh(x) - 1120 +--R * +--R 8 +--R sinh(x) +--R + +--R 23 21 19 +--R 21760cosh(x) + 26976cosh(x) + 27904cosh(x) +--R + +--R 17 15 13 +--R 26864cosh(x) - 11008cosh(x) - 4288cosh(x) +--R + +--R 11 9 7 +--R - 9728cosh(x) - 18480cosh(x) - 20480cosh(x) +--R + +--R 5 +--R 8320cosh(x) + 3904cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 24 22 20 18 +--R 68cosh(x) + 9504cosh(x) + 34248cosh(x) + 47808cosh(x) +--R + +--R 16 14 12 +--R 31964cosh(x) + 32448cosh(x) + 12560cosh(x) +--R + +--R 10 8 6 4 +--R 2528cosh(x) - 56cosh(x) - 14976cosh(x) + 10304cosh(x) +--R + +--R 2 +--R - 8192cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 25 23 21 +--R - 6848cosh(x) - 2464cosh(x) + 15680cosh(x) +--R + +--R 19 17 15 +--R 21392cosh(x) + 32096cosh(x) + 49728cosh(x) +--R + +--R 13 11 9 7 +--R 38656cosh(x) + 7920cosh(x) + 7936cosh(x) + 8320cosh(x) +--R + +--R 5 3 +--R - 14080cosh(x) + 12480cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 26 24 22 +--R - 4916cosh(x) - 4440cosh(x) + 1672cosh(x) +--R + +--R 20 18 16 +--R - 5168cosh(x) + 5316cosh(x) + 25352cosh(x) +--R + +--R 14 12 10 +--R 40528cosh(x) + 22368cosh(x) - 1256cosh(x) +--R + +--R 8 6 4 +--R 6048cosh(x) + 10304cosh(x) - 14144cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 27 25 23 +--R - 1920cosh(x) - 2352cosh(x) - 1792cosh(x) +--R + +--R 21 19 17 +--R - 10416cosh(x) - 9792cosh(x) - 5040cosh(x) +--R + +--R 15 13 11 +--R 9728cosh(x) + 19664cosh(x) + 10240cosh(x) +--R + +--R 9 5 +--R - 7872cosh(x) + 12480cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 28 26 24 22 +--R - 460cosh(x) - 688cosh(x) - 996cosh(x) - 5184cosh(x) +--R + +--R 20 18 16 +--R - 7628cosh(x) - 11504cosh(x) - 11372cosh(x) +--R + +--R 14 12 10 +--R - 2528cosh(x) + 5960cosh(x) + 7488cosh(x) +--R + +--R 8 6 +--R - 6112cosh(x) - 8192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 29 27 25 23 +--R - 64cosh(x) - 112cosh(x) - 224cosh(x) - 1232cosh(x) +--R + +--R 21 19 17 +--R - 2336cosh(x) - 4912cosh(x) - 8384cosh(x) +--R + +--R 15 13 11 9 +--R - 9104cosh(x) - 7936cosh(x) - 448cosh(x) + 7040cosh(x) +--R + +--R 7 +--R 3904cosh(x) +--R * +--R sinh(x) +--R + +--R 30 28 26 24 +--R - 4cosh(x) - 8cosh(x) - 20cosh(x) - 120cosh(x) +--R + +--R 22 20 18 16 +--R - 276cosh(x) - 728cosh(x) - 1676cosh(x) - 2792cosh(x) +--R + +--R 14 12 10 8 +--R - 4648cosh(x) - 6048cosh(x) - 4192cosh(x) - 1120cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 30 29 +--R - 8sinh(x) - 128cosh(x)sinh(x) +--R + +--R 2 28 +--R (- 920cosh(x) - 16)sinh(x) +--R + +--R 3 27 +--R (- 3840cosh(x) - 224cosh(x))sinh(x) +--R + +--R 4 2 26 +--R (- 9832cosh(x) - 1376cosh(x) - 40)sinh(x) +--R + +--R 5 3 25 +--R (- 13696cosh(x) - 4704cosh(x) - 448cosh(x))sinh(x) +--R + +--R 6 4 2 24 +--R (136cosh(x) - 8880cosh(x) - 1992cosh(x) - 240)sinh(x) +--R + +--R 7 5 3 +--R (43520cosh(x) - 4928cosh(x) - 3584cosh(x) - 2464cosh(x)) +--R * +--R 23 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 91160cosh(x) + 19008cosh(x) + 3344cosh(x) - 10368cosh(x) +--R + +--R - 552 +--R * +--R 22 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 74624cosh(x) + 53952cosh(x) + 31360cosh(x) - 20832cosh(x) +--R + +--R - 4672cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R 10 8 6 +--R - 48312cosh(x) + 55408cosh(x) + 68496cosh(x) +--R + +--R 4 2 +--R - 10336cosh(x) - 15256cosh(x) - 1456 +--R * +--R 20 +--R sinh(x) +--R + +--R 11 9 7 +--R - 205056cosh(x) - 15520cosh(x) + 55808cosh(x) +--R + +--R 5 3 +--R 42784cosh(x) - 19584cosh(x) - 9824cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 12 10 8 +--R - 236360cosh(x) - 120992cosh(x) - 57976cosh(x) +--R + +--R 6 4 2 +--R 95616cosh(x) + 10632cosh(x) - 23008cosh(x) - 3352 +--R * +--R 18 +--R sinh(x) +--R + +--R 13 11 9 +--R - 60800cosh(x) - 152608cosh(x) - 211520cosh(x) +--R + +--R 7 5 3 +--R 53728cosh(x) + 64192cosh(x) - 10080cosh(x) - 16768cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 14 12 10 +--R 204136cosh(x) - 46512cosh(x) - 239768cosh(x) +--R + +--R 8 6 4 +--R - 85520cosh(x) + 63928cosh(x) + 50704cosh(x) +--R + +--R 2 +--R - 22744cosh(x) - 5584 +--R * +--R 16 +--R sinh(x) +--R + +--R 15 13 11 +--R 330752cosh(x) + 124032cosh(x) - 52224cosh(x) +--R + +--R 9 7 5 +--R - 172608cosh(x) - 22016cosh(x) + 99456cosh(x) +--R + +--R 3 +--R 19456cosh(x) - 18208cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 16 14 12 +--R 204136cosh(x) + 206720cosh(x) + 227936cosh(x) +--R + +--R 10 8 6 +--R - 85248cosh(x) - 94736cosh(x) + 64896cosh(x) +--R + +--R 4 2 +--R 81056cosh(x) - 5056cosh(x) - 9296 +--R * +--R 14 +--R sinh(x) +--R + +--R 17 15 13 +--R - 60800cosh(x) + 124032cosh(x) + 361216cosh(x) +--R + +--R 11 9 7 5 +--R 99392cosh(x) - 59520cosh(x) - 8576cosh(x) + 77312cosh(x) +--R + +--R 3 +--R 39328cosh(x) - 15872cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 18 16 14 +--R - 236360cosh(x) - 46512cosh(x) + 227936cosh(x) +--R + +--R 12 10 8 +--R 192192cosh(x) + 35984cosh(x) - 49248cosh(x) +--R + +--R 6 4 2 +--R 25120cosh(x) + 44736cosh(x) + 11920cosh(x) - 12096 +--R * +--R 12 +--R sinh(x) +--R + +--R 19 17 15 +--R - 205056cosh(x) - 152608cosh(x) - 52224cosh(x) +--R + +--R 13 11 9 +--R 99392cosh(x) + 83200cosh(x) - 70976cosh(x) +--R + +--R 7 5 3 +--R - 19456cosh(x) + 15840cosh(x) + 20480cosh(x) - 896cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 20 18 16 +--R - 48312cosh(x) - 120992cosh(x) - 239768cosh(x) +--R + +--R 14 12 10 +--R - 85248cosh(x) + 35984cosh(x) - 83776cosh(x) +--R + +--R 8 6 4 2 +--R - 80080cosh(x) + 5056cosh(x) - 2512cosh(x) + 14976cosh(x) +--R + +--R - 8384 +--R * +--R 10 +--R sinh(x) +--R + +--R 21 19 17 +--R 74624cosh(x) - 15520cosh(x) - 211520cosh(x) +--R + +--R 15 13 11 +--R - 172608cosh(x) - 59520cosh(x) - 70976cosh(x) +--R + +--R 9 7 5 +--R - 121088cosh(x) - 36960cosh(x) + 15872cosh(x) +--R + +--R 3 +--R - 15744cosh(x) + 14080cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 22 20 18 +--R 91160cosh(x) + 55408cosh(x) - 57976cosh(x) +--R + +--R 16 14 12 +--R - 85520cosh(x) - 94736cosh(x) - 49248cosh(x) +--R + +--R 10 8 6 +--R - 80080cosh(x) - 78304cosh(x) - 112cosh(x) +--R + +--R 4 2 +--R 12096cosh(x) - 12224cosh(x) - 2240 +--R * +--R 8 +--R sinh(x) +--R + +--R 23 21 19 +--R 43520cosh(x) + 53952cosh(x) + 55808cosh(x) +--R + +--R 17 15 13 +--R 53728cosh(x) - 22016cosh(x) - 8576cosh(x) +--R + +--R 11 9 7 +--R - 19456cosh(x) - 36960cosh(x) - 40960cosh(x) +--R + +--R 5 +--R 16640cosh(x) + 7808cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 24 22 20 +--R 136cosh(x) + 19008cosh(x) + 68496cosh(x) +--R + +--R 18 16 14 +--R 95616cosh(x) + 63928cosh(x) + 64896cosh(x) +--R + +--R 12 10 8 6 +--R 25120cosh(x) + 5056cosh(x) - 112cosh(x) - 29952cosh(x) +--R + +--R 4 2 +--R 20608cosh(x) - 16384cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 25 23 21 +--R - 13696cosh(x) - 4928cosh(x) + 31360cosh(x) +--R + +--R 19 17 15 +--R 42784cosh(x) + 64192cosh(x) + 99456cosh(x) +--R + +--R 13 11 9 +--R 77312cosh(x) + 15840cosh(x) + 15872cosh(x) +--R + +--R 7 5 3 +--R 16640cosh(x) - 28160cosh(x) + 24960cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 26 24 22 +--R - 9832cosh(x) - 8880cosh(x) + 3344cosh(x) +--R + +--R 20 18 16 +--R - 10336cosh(x) + 10632cosh(x) + 50704cosh(x) +--R + +--R 14 12 10 +--R 81056cosh(x) + 44736cosh(x) - 2512cosh(x) +--R + +--R 8 6 4 +--R 12096cosh(x) + 20608cosh(x) - 28288cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 27 25 23 +--R - 3840cosh(x) - 4704cosh(x) - 3584cosh(x) +--R + +--R 21 19 17 +--R - 20832cosh(x) - 19584cosh(x) - 10080cosh(x) +--R + +--R 15 13 11 +--R 19456cosh(x) + 39328cosh(x) + 20480cosh(x) +--R + +--R 9 5 +--R - 15744cosh(x) + 24960cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 28 26 24 +--R - 920cosh(x) - 1376cosh(x) - 1992cosh(x) +--R + +--R 22 20 18 +--R - 10368cosh(x) - 15256cosh(x) - 23008cosh(x) +--R + +--R 16 14 12 +--R - 22744cosh(x) - 5056cosh(x) + 11920cosh(x) +--R + +--R 10 8 6 +--R 14976cosh(x) - 12224cosh(x) - 16384cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 29 27 25 23 +--R - 128cosh(x) - 224cosh(x) - 448cosh(x) - 2464cosh(x) +--R + +--R 21 19 17 +--R - 4672cosh(x) - 9824cosh(x) - 16768cosh(x) +--R + +--R 15 13 11 +--R - 18208cosh(x) - 15872cosh(x) - 896cosh(x) +--R + +--R 9 7 +--R 14080cosh(x) + 7808cosh(x) +--R * +--R sinh(x) +--R + +--R 30 28 26 24 +--R - 8cosh(x) - 16cosh(x) - 40cosh(x) - 240cosh(x) +--R + +--R 22 20 18 16 +--R - 552cosh(x) - 1456cosh(x) - 3352cosh(x) - 5584cosh(x) +--R + +--R 14 12 10 8 +--R - 9296cosh(x) - 12096cosh(x) - 8384cosh(x) - 2240cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 30 29 2 28 +--R - 4sinh(x) - 64cosh(x)sinh(x) + (- 460cosh(x) - 8)sinh(x) +--R + +--R 3 27 +--R (- 1920cosh(x) - 112cosh(x))sinh(x) +--R + +--R 4 2 26 +--R (- 4916cosh(x) - 688cosh(x) - 20)sinh(x) +--R + +--R 5 3 25 +--R (- 6848cosh(x) - 2352cosh(x) - 224cosh(x))sinh(x) +--R + +--R 6 4 2 24 +--R (68cosh(x) - 4440cosh(x) - 996cosh(x) - 120)sinh(x) +--R + +--R 7 5 3 23 +--R (21760cosh(x) - 2464cosh(x) - 1792cosh(x) - 1232cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (45580cosh(x) + 9504cosh(x) + 1672cosh(x) - 5184cosh(x) - 276) +--R * +--R 22 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 37312cosh(x) + 26976cosh(x) + 15680cosh(x) - 10416cosh(x) +--R + +--R - 2336cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 24156cosh(x) + 27704cosh(x) + 34248cosh(x) - 5168cosh(x) +--R + +--R 2 +--R - 7628cosh(x) - 728 +--R * +--R 20 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 102528cosh(x) - 7760cosh(x) + 27904cosh(x) + 21392cosh(x) +--R + +--R 3 +--R - 9792cosh(x) - 4912cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 12 10 8 +--R - 118180cosh(x) - 60496cosh(x) - 28988cosh(x) +--R + +--R 6 4 2 +--R 47808cosh(x) + 5316cosh(x) - 11504cosh(x) - 1676 +--R * +--R 18 +--R sinh(x) +--R + +--R 13 11 9 +--R - 30400cosh(x) - 76304cosh(x) - 105760cosh(x) +--R + +--R 7 5 3 +--R 26864cosh(x) + 32096cosh(x) - 5040cosh(x) - 8384cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 14 12 10 +--R 102068cosh(x) - 23256cosh(x) - 119884cosh(x) +--R + +--R 8 6 4 2 +--R - 42760cosh(x) + 31964cosh(x) + 25352cosh(x) - 11372cosh(x) +--R + +--R - 2792 +--R * +--R 16 +--R sinh(x) +--R + +--R 15 13 11 9 +--R 165376cosh(x) + 62016cosh(x) - 26112cosh(x) - 86304cosh(x) +--R + +--R 7 5 3 +--R - 11008cosh(x) + 49728cosh(x) + 9728cosh(x) - 9104cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 16 14 12 +--R 102068cosh(x) + 103360cosh(x) + 113968cosh(x) +--R + +--R 10 8 6 4 +--R - 42624cosh(x) - 47368cosh(x) + 32448cosh(x) + 40528cosh(x) +--R + +--R 2 +--R - 2528cosh(x) - 4648 +--R * +--R 14 +--R sinh(x) +--R + +--R 17 15 13 +--R - 30400cosh(x) + 62016cosh(x) + 180608cosh(x) +--R + +--R 11 9 7 5 +--R 49696cosh(x) - 29760cosh(x) - 4288cosh(x) + 38656cosh(x) +--R + +--R 3 +--R 19664cosh(x) - 7936cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 18 16 14 +--R - 118180cosh(x) - 23256cosh(x) + 113968cosh(x) +--R + +--R 12 10 8 6 +--R 96096cosh(x) + 17992cosh(x) - 24624cosh(x) + 12560cosh(x) +--R + +--R 4 2 +--R 22368cosh(x) + 5960cosh(x) - 6048 +--R * +--R 12 +--R sinh(x) +--R + +--R 19 17 15 +--R - 102528cosh(x) - 76304cosh(x) - 26112cosh(x) +--R + +--R 13 11 9 7 +--R 49696cosh(x) + 41600cosh(x) - 35488cosh(x) - 9728cosh(x) +--R + +--R 5 3 +--R 7920cosh(x) + 10240cosh(x) - 448cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 20 18 16 +--R - 24156cosh(x) - 60496cosh(x) - 119884cosh(x) +--R + +--R 14 12 10 +--R - 42624cosh(x) + 17992cosh(x) - 41888cosh(x) +--R + +--R 8 6 4 2 +--R - 40040cosh(x) + 2528cosh(x) - 1256cosh(x) + 7488cosh(x) - 4192 +--R * +--R 10 +--R sinh(x) +--R + +--R 21 19 17 15 +--R 37312cosh(x) - 7760cosh(x) - 105760cosh(x) - 86304cosh(x) +--R + +--R 13 11 9 7 +--R - 29760cosh(x) - 35488cosh(x) - 60544cosh(x) - 18480cosh(x) +--R + +--R 5 3 +--R 7936cosh(x) - 7872cosh(x) + 7040cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 22 20 18 16 +--R 45580cosh(x) + 27704cosh(x) - 28988cosh(x) - 42760cosh(x) +--R + +--R 14 12 10 +--R - 47368cosh(x) - 24624cosh(x) - 40040cosh(x) +--R + +--R 8 6 4 2 +--R - 39152cosh(x) - 56cosh(x) + 6048cosh(x) - 6112cosh(x) - 1120 +--R * +--R 8 +--R sinh(x) +--R + +--R 23 21 19 17 +--R 21760cosh(x) + 26976cosh(x) + 27904cosh(x) + 26864cosh(x) +--R + +--R 15 13 11 9 +--R - 11008cosh(x) - 4288cosh(x) - 9728cosh(x) - 18480cosh(x) +--R + +--R 7 5 +--R - 20480cosh(x) + 8320cosh(x) + 3904cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 24 22 20 18 +--R 68cosh(x) + 9504cosh(x) + 34248cosh(x) + 47808cosh(x) +--R + +--R 16 14 12 10 +--R 31964cosh(x) + 32448cosh(x) + 12560cosh(x) + 2528cosh(x) +--R + +--R 8 6 4 2 +--R - 56cosh(x) - 14976cosh(x) + 10304cosh(x) - 8192cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 25 23 21 19 +--R - 6848cosh(x) - 2464cosh(x) + 15680cosh(x) + 21392cosh(x) +--R + +--R 17 15 13 11 +--R 32096cosh(x) + 49728cosh(x) + 38656cosh(x) + 7920cosh(x) +--R + +--R 9 7 5 3 +--R 7936cosh(x) + 8320cosh(x) - 14080cosh(x) + 12480cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 26 24 22 20 +--R - 4916cosh(x) - 4440cosh(x) + 1672cosh(x) - 5168cosh(x) +--R + +--R 18 16 14 12 +--R 5316cosh(x) + 25352cosh(x) + 40528cosh(x) + 22368cosh(x) +--R + +--R 10 8 6 4 +--R - 1256cosh(x) + 6048cosh(x) + 10304cosh(x) - 14144cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 27 25 23 21 +--R - 1920cosh(x) - 2352cosh(x) - 1792cosh(x) - 10416cosh(x) +--R + +--R 19 17 15 13 +--R - 9792cosh(x) - 5040cosh(x) + 9728cosh(x) + 19664cosh(x) +--R + +--R 11 9 5 +--R 10240cosh(x) - 7872cosh(x) + 12480cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 28 26 24 22 +--R - 460cosh(x) - 688cosh(x) - 996cosh(x) - 5184cosh(x) +--R + +--R 20 18 16 14 +--R - 7628cosh(x) - 11504cosh(x) - 11372cosh(x) - 2528cosh(x) +--R + +--R 12 10 8 6 +--R 5960cosh(x) + 7488cosh(x) - 6112cosh(x) - 8192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 29 27 25 23 +--R - 64cosh(x) - 112cosh(x) - 224cosh(x) - 1232cosh(x) +--R + +--R 21 19 17 15 +--R - 2336cosh(x) - 4912cosh(x) - 8384cosh(x) - 9104cosh(x) +--R + +--R 13 11 9 7 +--R - 7936cosh(x) - 448cosh(x) + 7040cosh(x) + 3904cosh(x) +--R * +--R sinh(x) +--R + +--R 30 28 26 24 22 +--R - 4cosh(x) - 8cosh(x) - 20cosh(x) - 120cosh(x) - 276cosh(x) +--R + +--R 20 18 16 14 +--R - 728cosh(x) - 1676cosh(x) - 2792cosh(x) - 4648cosh(x) +--R + +--R 12 10 8 +--R - 6048cosh(x) - 4192cosh(x) - 1120cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 32 +-+ 31 +--R - 2\|2 sinh(x) - 36\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 30 +--R (- 296\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 29 +--R (- 1452\|2 cosh(x) - 32\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 28 +--R (- 4608\|2 cosh(x) - 230\|2 cosh(x) + 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 27 +--R (- 9300\|2 cosh(x) - 960\|2 cosh(x) + 100\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 9272\|2 cosh(x) - 2458\|2 cosh(x) + 772\|2 cosh(x) + 42\|2 ) +--R * +--R 26 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 7524\|2 cosh(x) - 3424\|2 cosh(x) + 3636\|2 cosh(x) +--R + +--R +-+ +--R 584\|2 cosh(x) +--R * +--R 25 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 44584\|2 cosh(x) + 34\|2 cosh(x) + 11522\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 3682\|2 cosh(x) + 190\|2 +--R * +--R 24 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 75116\|2 cosh(x) + 10880\|2 cosh(x) + 25240\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 13760\|2 cosh(x) + 2204\|2 cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 48024\|2 cosh(x) + 22790\|2 cosh(x) + 36392\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 33068\|2 cosh(x) + 11216\|2 cosh(x) + 386\|2 +--R * +--R 22 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 56764\|2 cosh(x) + 18656\|2 cosh(x) + 24408\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 50000\|2 cosh(x) + 32004\|2 cosh(x) + 3584\|2 cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 173696\|2 cosh(x) - 12078\|2 cosh(x) - 28970\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 34636\|2 cosh(x) + 51916\|2 cosh(x) + 13550\|2 cosh(x) +--R + +--R +-+ +--R 1010\|2 +--R * +--R 20 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 184644\|2 cosh(x) - 51264\|2 cosh(x) - 110612\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 37696\|2 cosh(x) + 30676\|2 cosh(x) + 23552\|2 cosh(x) +--R + +--R +-+ +--R 7692\|2 cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 38456\|2 cosh(x) - 59090\|2 cosh(x) - 163780\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 145650\|2 cosh(x) - 65264\|2 cosh(x) + 2374\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 22868\|2 cosh(x) + 2366\|2 +--R * +--R 18 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 169556\|2 cosh(x) - 15200\|2 cosh(x) - 123652\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 212424\|2 cosh(x) - 202676\|2 cosh(x) - 80384\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 27820\|2 cosh(x) + 14200\|2 cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R 267444\|2 cosh(x) + 51034\|2 cosh(x) + 17442\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 157658\|2 cosh(x) - 277214\|2 cosh(x) - 195862\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 11958\|2 cosh(x) + 31582\|2 cosh(x) + 3956\|2 +--R * +--R 16 +--R sinh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R 169556\|2 cosh(x) + 82688\|2 cosh(x) + 180880\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 23936\|2 cosh(x) - 191272\|2 cosh(x) - 249856\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 91664\|2 cosh(x) + 25376\|2 cosh(x) + 16936\|2 cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 38456\|2 cosh(x) + 51034\|2 cosh(x) + 253232\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 231880\|2 cosh(x) + 54048\|2 cosh(x) - 157772\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 147344\|2 cosh(x) - 16248\|2 cosh(x) + 23152\|2 cosh(x) +--R + +--R +-+ +--R 6576\|2 +--R * +--R 14 +--R sinh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R - 184644\|2 cosh(x) - 15200\|2 cosh(x) + 180880\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 323680\|2 cosh(x) + 329064\|2 cosh(x) + 76800\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 116304\|2 cosh(x) - 56352\|2 cosh(x) + 4280\|2 cosh(x) +--R + +--R +-+ +--R 17824\|2 cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R - 173696\|2 cosh(x) - 59090\|2 cosh(x) + 17442\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 231880\|2 cosh(x) + 450216\|2 cosh(x) + 337324\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 10948\|2 cosh(x) - 62008\|2 cosh(x) - 20144\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 12752\|2 cosh(x) + 8552\|2 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R - 56764\|2 cosh(x) - 51264\|2 cosh(x) - 123652\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 23936\|2 cosh(x) + 329064\|2 cosh(x) + 452608\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 172456\|2 cosh(x) - 25376\|2 cosh(x) - 38680\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 3776\|2 cosh(x) + 9168\|2 cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 48024\|2 cosh(x) - 12078\|2 cosh(x) - 163780\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - 157658\|2 cosh(x) + 54048\|2 cosh(x) + 337324\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 248952\|2 cosh(x) + 44308\|2 cosh(x) - 55920\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 912\|2 cosh(x) + 2736\|2 cosh(x) + 5928\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 75116\|2 cosh(x) + 18656\|2 cosh(x) - 110612\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R - 212424\|2 cosh(x) - 191272\|2 cosh(x) + 76800\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 172456\|2 cosh(x) + 84304\|2 cosh(x) - 48072\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 26016\|2 cosh(x) + 13712\|2 cosh(x) - 4032\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 44584\|2 cosh(x) + 22790\|2 cosh(x) - 28970\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 145650\|2 cosh(x) - 277214\|2 cosh(x) - 157772\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 10948\|2 cosh(x) + 44308\|2 cosh(x) - 33160\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 34800\|2 cosh(x) - 2408\|2 cosh(x) + 7560\|2 cosh(x) +--R + +--R +-+ +--R 1584\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 7524\|2 cosh(x) + 10880\|2 cosh(x) + 24408\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R - 37696\|2 cosh(x) - 202676\|2 cosh(x) - 249856\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 116304\|2 cosh(x) - 25376\|2 cosh(x) - 48072\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 23936\|2 cosh(x) - 10592\|2 cosh(x) + 2560\|2 cosh(x) +--R + +--R +-+ +--R - 3936\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R - 9272\|2 cosh(x) + 34\|2 cosh(x) + 36392\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R 34636\|2 cosh(x) - 65264\|2 cosh(x) - 195862\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 147344\|2 cosh(x) - 62008\|2 cosh(x) - 55920\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 34800\|2 cosh(x) + 6816\|2 cosh(x) - 8368\|2 cosh(x) +--R + +--R +-+ 2 +--R 8448\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 27 +-+ 25 +-+ 23 +--R - 9300\|2 cosh(x) - 3424\|2 cosh(x) + 25240\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R 50000\|2 cosh(x) + 30676\|2 cosh(x) - 80384\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 91664\|2 cosh(x) - 56352\|2 cosh(x) - 38680\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 26016\|2 cosh(x) - 10592\|2 cosh(x) + 13184\|2 cosh(x) +--R + +--R +-+ 3 +--R - 11936\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 28 +-+ 26 +-+ 24 +--R - 4608\|2 cosh(x) - 2458\|2 cosh(x) + 11522\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 33068\|2 cosh(x) + 51916\|2 cosh(x) + 2374\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - 11958\|2 cosh(x) - 16248\|2 cosh(x) - 20144\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 912\|2 cosh(x) - 2408\|2 cosh(x) - 8368\|2 cosh(x) +--R + +--R +-+ 4 +--R 13728\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R - 1452\|2 cosh(x) - 960\|2 cosh(x) + 3636\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 13760\|2 cosh(x) + 32004\|2 cosh(x) + 23552\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R 27820\|2 cosh(x) + 25376\|2 cosh(x) + 4280\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 3776\|2 cosh(x) + 13712\|2 cosh(x) + 2560\|2 cosh(x) +--R + +--R +-+ 5 +--R - 11936\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R - 296\|2 cosh(x) - 230\|2 cosh(x) + 772\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 3682\|2 cosh(x) + 11216\|2 cosh(x) + 13550\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 22868\|2 cosh(x) + 31582\|2 cosh(x) + 23152\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 12752\|2 cosh(x) + 2736\|2 cosh(x) + 7560\|2 cosh(x) +--R + +--R +-+ 6 +--R 8448\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R - 36\|2 cosh(x) - 32\|2 cosh(x) + 100\|2 cosh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 584\|2 cosh(x) + 2204\|2 cosh(x) + 3584\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R 7692\|2 cosh(x) + 14200\|2 cosh(x) + 16936\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 17824\|2 cosh(x) + 9168\|2 cosh(x) - 4032\|2 cosh(x) +--R + +--R +-+ 7 +--R - 3936\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 32 +-+ 30 +-+ 28 +-+ 26 +--R - 2\|2 cosh(x) - 2\|2 cosh(x) + 6\|2 cosh(x) + 42\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 190\|2 cosh(x) + 386\|2 cosh(x) + 1010\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 2366\|2 cosh(x) + 3956\|2 cosh(x) + 6576\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 8552\|2 cosh(x) + 5928\|2 cosh(x) + 1584\|2 cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 32 +-+ 31 +--R - 4\|2 sinh(x) - 72\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 30 +--R (- 592\|2 cosh(x) - 4\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 29 +--R (- 2904\|2 cosh(x) - 64\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 28 +--R (- 9216\|2 cosh(x) - 460\|2 cosh(x) + 12\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 27 +--R (- 18600\|2 cosh(x) - 1920\|2 cosh(x) + 200\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 18544\|2 cosh(x) - 4916\|2 cosh(x) + 1544\|2 cosh(x) +--R + +--R +-+ +--R 84\|2 +--R * +--R 26 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 15048\|2 cosh(x) - 6848\|2 cosh(x) + 7272\|2 cosh(x) +--R + +--R +-+ +--R 1168\|2 cosh(x) +--R * +--R 25 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 89168\|2 cosh(x) + 68\|2 cosh(x) + 23044\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 7364\|2 cosh(x) + 380\|2 +--R * +--R 24 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 150232\|2 cosh(x) + 21760\|2 cosh(x) + 50480\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 27520\|2 cosh(x) + 4408\|2 cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 96048\|2 cosh(x) + 45580\|2 cosh(x) + 72784\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 66136\|2 cosh(x) + 22432\|2 cosh(x) + 772\|2 +--R * +--R 22 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 113528\|2 cosh(x) + 37312\|2 cosh(x) + 48816\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 100000\|2 cosh(x) + 64008\|2 cosh(x) + 7168\|2 cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 347392\|2 cosh(x) - 24156\|2 cosh(x) - 57940\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 69272\|2 cosh(x) + 103832\|2 cosh(x) + 27100\|2 cosh(x) +--R + +--R +-+ +--R 2020\|2 +--R * +--R 20 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 369288\|2 cosh(x) - 102528\|2 cosh(x) - 221224\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 75392\|2 cosh(x) + 61352\|2 cosh(x) + 47104\|2 cosh(x) +--R + +--R +-+ +--R 15384\|2 cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 76912\|2 cosh(x) - 118180\|2 cosh(x) - 327560\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 291300\|2 cosh(x) - 130528\|2 cosh(x) + 4748\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 45736\|2 cosh(x) + 4732\|2 +--R * +--R 18 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 339112\|2 cosh(x) - 30400\|2 cosh(x) - 247304\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 424848\|2 cosh(x) - 405352\|2 cosh(x) - 160768\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 55640\|2 cosh(x) + 28400\|2 cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R 534888\|2 cosh(x) + 102068\|2 cosh(x) + 34884\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 315316\|2 cosh(x) - 554428\|2 cosh(x) - 391724\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 23916\|2 cosh(x) + 63164\|2 cosh(x) + 7912\|2 +--R * +--R 16 +--R sinh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R 339112\|2 cosh(x) + 165376\|2 cosh(x) + 361760\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 47872\|2 cosh(x) - 382544\|2 cosh(x) - 499712\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 183328\|2 cosh(x) + 50752\|2 cosh(x) + 33872\|2 cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 76912\|2 cosh(x) + 102068\|2 cosh(x) + 506464\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 463760\|2 cosh(x) + 108096\|2 cosh(x) - 315544\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 294688\|2 cosh(x) - 32496\|2 cosh(x) + 46304\|2 cosh(x) +--R + +--R +-+ +--R 13152\|2 +--R * +--R 14 +--R sinh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R - 369288\|2 cosh(x) - 30400\|2 cosh(x) + 361760\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 647360\|2 cosh(x) + 658128\|2 cosh(x) + 153600\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 232608\|2 cosh(x) - 112704\|2 cosh(x) + 8560\|2 cosh(x) +--R + +--R +-+ +--R 35648\|2 cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R - 347392\|2 cosh(x) - 118180\|2 cosh(x) + 34884\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 463760\|2 cosh(x) + 900432\|2 cosh(x) + 674648\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 21896\|2 cosh(x) - 124016\|2 cosh(x) - 40288\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 25504\|2 cosh(x) + 17104\|2 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R - 113528\|2 cosh(x) - 102528\|2 cosh(x) - 247304\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 47872\|2 cosh(x) + 658128\|2 cosh(x) + 905216\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 344912\|2 cosh(x) - 50752\|2 cosh(x) - 77360\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 7552\|2 cosh(x) + 18336\|2 cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 96048\|2 cosh(x) - 24156\|2 cosh(x) - 327560\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - 315316\|2 cosh(x) + 108096\|2 cosh(x) + 674648\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 497904\|2 cosh(x) + 88616\|2 cosh(x) - 111840\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 1824\|2 cosh(x) + 5472\|2 cosh(x) + 11856\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 150232\|2 cosh(x) + 37312\|2 cosh(x) - 221224\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R - 424848\|2 cosh(x) - 382544\|2 cosh(x) + 153600\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 344912\|2 cosh(x) + 168608\|2 cosh(x) - 96144\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 52032\|2 cosh(x) + 27424\|2 cosh(x) - 8064\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 89168\|2 cosh(x) + 45580\|2 cosh(x) - 57940\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 291300\|2 cosh(x) - 554428\|2 cosh(x) - 315544\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 21896\|2 cosh(x) + 88616\|2 cosh(x) - 66320\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 69600\|2 cosh(x) - 4816\|2 cosh(x) + 15120\|2 cosh(x) +--R + +--R +-+ +--R 3168\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 15048\|2 cosh(x) + 21760\|2 cosh(x) + 48816\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R - 75392\|2 cosh(x) - 405352\|2 cosh(x) - 499712\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 232608\|2 cosh(x) - 50752\|2 cosh(x) - 96144\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 47872\|2 cosh(x) - 21184\|2 cosh(x) + 5120\|2 cosh(x) +--R + +--R +-+ +--R - 7872\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R - 18544\|2 cosh(x) + 68\|2 cosh(x) + 72784\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R 69272\|2 cosh(x) - 130528\|2 cosh(x) - 391724\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 294688\|2 cosh(x) - 124016\|2 cosh(x) - 111840\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 69600\|2 cosh(x) + 13632\|2 cosh(x) - 16736\|2 cosh(x) +--R + +--R +-+ 2 +--R 16896\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 27 +-+ 25 +-+ 23 +--R - 18600\|2 cosh(x) - 6848\|2 cosh(x) + 50480\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R 100000\|2 cosh(x) + 61352\|2 cosh(x) - 160768\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 183328\|2 cosh(x) - 112704\|2 cosh(x) - 77360\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 52032\|2 cosh(x) - 21184\|2 cosh(x) + 26368\|2 cosh(x) +--R + +--R +-+ 3 +--R - 23872\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 28 +-+ 26 +-+ 24 +--R - 9216\|2 cosh(x) - 4916\|2 cosh(x) + 23044\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 66136\|2 cosh(x) + 103832\|2 cosh(x) + 4748\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - 23916\|2 cosh(x) - 32496\|2 cosh(x) - 40288\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 1824\|2 cosh(x) - 4816\|2 cosh(x) - 16736\|2 cosh(x) +--R + +--R +-+ 4 +--R 27456\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R - 2904\|2 cosh(x) - 1920\|2 cosh(x) + 7272\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 27520\|2 cosh(x) + 64008\|2 cosh(x) + 47104\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R 55640\|2 cosh(x) + 50752\|2 cosh(x) + 8560\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 7552\|2 cosh(x) + 27424\|2 cosh(x) + 5120\|2 cosh(x) +--R + +--R +-+ 5 +--R - 23872\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R - 592\|2 cosh(x) - 460\|2 cosh(x) + 1544\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 7364\|2 cosh(x) + 22432\|2 cosh(x) + 27100\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 45736\|2 cosh(x) + 63164\|2 cosh(x) + 46304\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 25504\|2 cosh(x) + 5472\|2 cosh(x) + 15120\|2 cosh(x) +--R + +--R +-+ 6 +--R 16896\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R - 72\|2 cosh(x) - 64\|2 cosh(x) + 200\|2 cosh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 1168\|2 cosh(x) + 4408\|2 cosh(x) + 7168\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R 15384\|2 cosh(x) + 28400\|2 cosh(x) + 33872\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 35648\|2 cosh(x) + 18336\|2 cosh(x) - 8064\|2 cosh(x) +--R + +--R +-+ 7 +--R - 7872\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 32 +-+ 30 +-+ 28 +-+ 26 +--R - 4\|2 cosh(x) - 4\|2 cosh(x) + 12\|2 cosh(x) + 84\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 380\|2 cosh(x) + 772\|2 cosh(x) + 2020\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 4732\|2 cosh(x) + 7912\|2 cosh(x) + 13152\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 17104\|2 cosh(x) + 11856\|2 cosh(x) + 3168\|2 cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 32 +-+ 31 +--R - 2\|2 sinh(x) - 36\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 30 +--R (- 296\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 29 +--R (- 1452\|2 cosh(x) - 32\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 28 +--R (- 4608\|2 cosh(x) - 230\|2 cosh(x) + 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 27 +--R (- 9300\|2 cosh(x) - 960\|2 cosh(x) + 100\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 9272\|2 cosh(x) - 2458\|2 cosh(x) + 772\|2 cosh(x) + 42\|2 ) +--R * +--R 26 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 7524\|2 cosh(x) - 3424\|2 cosh(x) + 3636\|2 cosh(x) +--R + +--R +-+ +--R 584\|2 cosh(x) +--R * +--R 25 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 44584\|2 cosh(x) + 34\|2 cosh(x) + 11522\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 3682\|2 cosh(x) + 190\|2 +--R * +--R 24 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 75116\|2 cosh(x) + 10880\|2 cosh(x) + 25240\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 13760\|2 cosh(x) + 2204\|2 cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 48024\|2 cosh(x) + 22790\|2 cosh(x) + 36392\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 33068\|2 cosh(x) + 11216\|2 cosh(x) + 386\|2 +--R * +--R 22 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 56764\|2 cosh(x) + 18656\|2 cosh(x) + 24408\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 50000\|2 cosh(x) + 32004\|2 cosh(x) + 3584\|2 cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 173696\|2 cosh(x) - 12078\|2 cosh(x) - 28970\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 34636\|2 cosh(x) + 51916\|2 cosh(x) + 13550\|2 cosh(x) + 1010\|2 +--R * +--R 20 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 184644\|2 cosh(x) - 51264\|2 cosh(x) - 110612\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 37696\|2 cosh(x) + 30676\|2 cosh(x) + 23552\|2 cosh(x) +--R + +--R +-+ +--R 7692\|2 cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 38456\|2 cosh(x) - 59090\|2 cosh(x) - 163780\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 145650\|2 cosh(x) - 65264\|2 cosh(x) + 2374\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 22868\|2 cosh(x) + 2366\|2 +--R * +--R 18 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 169556\|2 cosh(x) - 15200\|2 cosh(x) - 123652\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 212424\|2 cosh(x) - 202676\|2 cosh(x) - 80384\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 27820\|2 cosh(x) + 14200\|2 cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R 267444\|2 cosh(x) + 51034\|2 cosh(x) + 17442\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 157658\|2 cosh(x) - 277214\|2 cosh(x) - 195862\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 11958\|2 cosh(x) + 31582\|2 cosh(x) + 3956\|2 +--R * +--R 16 +--R sinh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R 169556\|2 cosh(x) + 82688\|2 cosh(x) + 180880\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 23936\|2 cosh(x) - 191272\|2 cosh(x) - 249856\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 91664\|2 cosh(x) + 25376\|2 cosh(x) + 16936\|2 cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 38456\|2 cosh(x) + 51034\|2 cosh(x) + 253232\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 231880\|2 cosh(x) + 54048\|2 cosh(x) - 157772\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 147344\|2 cosh(x) - 16248\|2 cosh(x) + 23152\|2 cosh(x) + 6576\|2 +--R * +--R 14 +--R sinh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R - 184644\|2 cosh(x) - 15200\|2 cosh(x) + 180880\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 323680\|2 cosh(x) + 329064\|2 cosh(x) + 76800\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 116304\|2 cosh(x) - 56352\|2 cosh(x) + 4280\|2 cosh(x) +--R + +--R +-+ +--R 17824\|2 cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R - 173696\|2 cosh(x) - 59090\|2 cosh(x) + 17442\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 231880\|2 cosh(x) + 450216\|2 cosh(x) + 337324\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 10948\|2 cosh(x) - 62008\|2 cosh(x) - 20144\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 12752\|2 cosh(x) + 8552\|2 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R - 56764\|2 cosh(x) - 51264\|2 cosh(x) - 123652\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 23936\|2 cosh(x) + 329064\|2 cosh(x) + 452608\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 172456\|2 cosh(x) - 25376\|2 cosh(x) - 38680\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 3776\|2 cosh(x) + 9168\|2 cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 48024\|2 cosh(x) - 12078\|2 cosh(x) - 163780\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - 157658\|2 cosh(x) + 54048\|2 cosh(x) + 337324\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 248952\|2 cosh(x) + 44308\|2 cosh(x) - 55920\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 912\|2 cosh(x) + 2736\|2 cosh(x) + 5928\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 75116\|2 cosh(x) + 18656\|2 cosh(x) - 110612\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R - 212424\|2 cosh(x) - 191272\|2 cosh(x) + 76800\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 172456\|2 cosh(x) + 84304\|2 cosh(x) - 48072\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 26016\|2 cosh(x) + 13712\|2 cosh(x) - 4032\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 44584\|2 cosh(x) + 22790\|2 cosh(x) - 28970\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 145650\|2 cosh(x) - 277214\|2 cosh(x) - 157772\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 10948\|2 cosh(x) + 44308\|2 cosh(x) - 33160\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 34800\|2 cosh(x) - 2408\|2 cosh(x) + 7560\|2 cosh(x) + 1584\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 7524\|2 cosh(x) + 10880\|2 cosh(x) + 24408\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R - 37696\|2 cosh(x) - 202676\|2 cosh(x) - 249856\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 116304\|2 cosh(x) - 25376\|2 cosh(x) - 48072\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 23936\|2 cosh(x) - 10592\|2 cosh(x) + 2560\|2 cosh(x) +--R + +--R +-+ +--R - 3936\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R - 9272\|2 cosh(x) + 34\|2 cosh(x) + 36392\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R 34636\|2 cosh(x) - 65264\|2 cosh(x) - 195862\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 147344\|2 cosh(x) - 62008\|2 cosh(x) - 55920\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 34800\|2 cosh(x) + 6816\|2 cosh(x) - 8368\|2 cosh(x) +--R + +--R +-+ 2 +--R 8448\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 27 +-+ 25 +-+ 23 +--R - 9300\|2 cosh(x) - 3424\|2 cosh(x) + 25240\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R 50000\|2 cosh(x) + 30676\|2 cosh(x) - 80384\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 91664\|2 cosh(x) - 56352\|2 cosh(x) - 38680\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 26016\|2 cosh(x) - 10592\|2 cosh(x) + 13184\|2 cosh(x) +--R + +--R +-+ 3 +--R - 11936\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 28 +-+ 26 +-+ 24 +--R - 4608\|2 cosh(x) - 2458\|2 cosh(x) + 11522\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 33068\|2 cosh(x) + 51916\|2 cosh(x) + 2374\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - 11958\|2 cosh(x) - 16248\|2 cosh(x) - 20144\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 912\|2 cosh(x) - 2408\|2 cosh(x) - 8368\|2 cosh(x) +--R + +--R +-+ 4 +--R 13728\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R - 1452\|2 cosh(x) - 960\|2 cosh(x) + 3636\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 13760\|2 cosh(x) + 32004\|2 cosh(x) + 23552\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R 27820\|2 cosh(x) + 25376\|2 cosh(x) + 4280\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 3776\|2 cosh(x) + 13712\|2 cosh(x) + 2560\|2 cosh(x) +--R + +--R +-+ 5 +--R - 11936\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R - 296\|2 cosh(x) - 230\|2 cosh(x) + 772\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 3682\|2 cosh(x) + 11216\|2 cosh(x) + 13550\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 22868\|2 cosh(x) + 31582\|2 cosh(x) + 23152\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 12752\|2 cosh(x) + 2736\|2 cosh(x) + 7560\|2 cosh(x) +--R + +--R +-+ 6 +--R 8448\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R - 36\|2 cosh(x) - 32\|2 cosh(x) + 100\|2 cosh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 584\|2 cosh(x) + 2204\|2 cosh(x) + 3584\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R 7692\|2 cosh(x) + 14200\|2 cosh(x) + 16936\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 17824\|2 cosh(x) + 9168\|2 cosh(x) - 4032\|2 cosh(x) +--R + +--R +-+ 7 +--R - 3936\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 32 +-+ 30 +-+ 28 +-+ 26 +--R - 2\|2 cosh(x) - 2\|2 cosh(x) + 6\|2 cosh(x) + 42\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 190\|2 cosh(x) + 386\|2 cosh(x) + 1010\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 2366\|2 cosh(x) + 3956\|2 cosh(x) + 6576\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 8552\|2 cosh(x) + 5928\|2 cosh(x) + 1584\|2 cosh(x) +--R / +--R 30 29 2 28 +--R 4sinh(x) + 64cosh(x)sinh(x) + (460cosh(x) + 8)sinh(x) +--R + +--R 3 27 +--R (1920cosh(x) + 112cosh(x))sinh(x) +--R + +--R 4 2 26 +--R (4916cosh(x) + 688cosh(x) + 20)sinh(x) +--R + +--R 5 3 25 +--R (6848cosh(x) + 2352cosh(x) + 224cosh(x))sinh(x) +--R + +--R 6 4 2 24 +--R (- 68cosh(x) + 4440cosh(x) + 996cosh(x) + 120)sinh(x) +--R + +--R 7 5 3 +--R (- 21760cosh(x) + 2464cosh(x) + 1792cosh(x) + 1232cosh(x)) +--R * +--R 23 +--R sinh(x) +--R + +--R 8 6 4 2 +--R - 45580cosh(x) - 9504cosh(x) - 1672cosh(x) + 5184cosh(x) +--R + +--R 276 +--R * +--R 22 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 37312cosh(x) - 26976cosh(x) - 15680cosh(x) + 10416cosh(x) +--R + +--R 2336cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 24156cosh(x) - 27704cosh(x) - 34248cosh(x) + 5168cosh(x) +--R + +--R 2 +--R 7628cosh(x) + 728 +--R * +--R 20 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 102528cosh(x) + 7760cosh(x) - 27904cosh(x) - 21392cosh(x) +--R + +--R 3 +--R 9792cosh(x) + 4912cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 12 10 8 +--R 118180cosh(x) + 60496cosh(x) + 28988cosh(x) +--R + +--R 6 4 2 +--R - 47808cosh(x) - 5316cosh(x) + 11504cosh(x) + 1676 +--R * +--R 18 +--R sinh(x) +--R + +--R 13 11 9 +--R 30400cosh(x) + 76304cosh(x) + 105760cosh(x) +--R + +--R 7 5 3 +--R - 26864cosh(x) - 32096cosh(x) + 5040cosh(x) + 8384cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 14 12 10 +--R - 102068cosh(x) + 23256cosh(x) + 119884cosh(x) +--R + +--R 8 6 4 2 +--R 42760cosh(x) - 31964cosh(x) - 25352cosh(x) + 11372cosh(x) +--R + +--R 2792 +--R * +--R 16 +--R sinh(x) +--R + +--R 15 13 11 +--R - 165376cosh(x) - 62016cosh(x) + 26112cosh(x) +--R + +--R 9 7 5 3 +--R 86304cosh(x) + 11008cosh(x) - 49728cosh(x) - 9728cosh(x) +--R + +--R 9104cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 16 14 12 +--R - 102068cosh(x) - 103360cosh(x) - 113968cosh(x) +--R + +--R 10 8 6 4 +--R 42624cosh(x) + 47368cosh(x) - 32448cosh(x) - 40528cosh(x) +--R + +--R 2 +--R 2528cosh(x) + 4648 +--R * +--R 14 +--R sinh(x) +--R + +--R 17 15 13 +--R 30400cosh(x) - 62016cosh(x) - 180608cosh(x) +--R + +--R 11 9 7 5 +--R - 49696cosh(x) + 29760cosh(x) + 4288cosh(x) - 38656cosh(x) +--R + +--R 3 +--R - 19664cosh(x) + 7936cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 18 16 14 +--R 118180cosh(x) + 23256cosh(x) - 113968cosh(x) +--R + +--R 12 10 8 +--R - 96096cosh(x) - 17992cosh(x) + 24624cosh(x) +--R + +--R 6 4 2 +--R - 12560cosh(x) - 22368cosh(x) - 5960cosh(x) + 6048 +--R * +--R 12 +--R sinh(x) +--R + +--R 19 17 15 +--R 102528cosh(x) + 76304cosh(x) + 26112cosh(x) +--R + +--R 13 11 9 +--R - 49696cosh(x) - 41600cosh(x) + 35488cosh(x) +--R + +--R 7 5 3 +--R 9728cosh(x) - 7920cosh(x) - 10240cosh(x) + 448cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 20 18 16 +--R 24156cosh(x) + 60496cosh(x) + 119884cosh(x) +--R + +--R 14 12 10 +--R 42624cosh(x) - 17992cosh(x) + 41888cosh(x) +--R + +--R 8 6 4 2 +--R 40040cosh(x) - 2528cosh(x) + 1256cosh(x) - 7488cosh(x) + 4192 +--R * +--R 10 +--R sinh(x) +--R + +--R 21 19 17 +--R - 37312cosh(x) + 7760cosh(x) + 105760cosh(x) +--R + +--R 15 13 11 +--R 86304cosh(x) + 29760cosh(x) + 35488cosh(x) +--R + +--R 9 7 5 3 +--R 60544cosh(x) + 18480cosh(x) - 7936cosh(x) + 7872cosh(x) +--R + +--R - 7040cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 22 20 18 +--R - 45580cosh(x) - 27704cosh(x) + 28988cosh(x) +--R + +--R 16 14 12 +--R 42760cosh(x) + 47368cosh(x) + 24624cosh(x) +--R + +--R 10 8 6 4 +--R 40040cosh(x) + 39152cosh(x) + 56cosh(x) - 6048cosh(x) +--R + +--R 2 +--R 6112cosh(x) + 1120 +--R * +--R 8 +--R sinh(x) +--R + +--R 23 21 19 +--R - 21760cosh(x) - 26976cosh(x) - 27904cosh(x) +--R + +--R 17 15 13 +--R - 26864cosh(x) + 11008cosh(x) + 4288cosh(x) +--R + +--R 11 9 7 5 +--R 9728cosh(x) + 18480cosh(x) + 20480cosh(x) - 8320cosh(x) +--R + +--R - 3904cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 24 22 20 18 +--R - 68cosh(x) - 9504cosh(x) - 34248cosh(x) - 47808cosh(x) +--R + +--R 16 14 12 +--R - 31964cosh(x) - 32448cosh(x) - 12560cosh(x) +--R + +--R 10 8 6 4 +--R - 2528cosh(x) + 56cosh(x) + 14976cosh(x) - 10304cosh(x) +--R + +--R 2 +--R 8192cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 25 23 21 19 +--R 6848cosh(x) + 2464cosh(x) - 15680cosh(x) - 21392cosh(x) +--R + +--R 17 15 13 +--R - 32096cosh(x) - 49728cosh(x) - 38656cosh(x) +--R + +--R 11 9 7 5 +--R - 7920cosh(x) - 7936cosh(x) - 8320cosh(x) + 14080cosh(x) +--R + +--R 3 +--R - 12480cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 26 24 22 20 +--R 4916cosh(x) + 4440cosh(x) - 1672cosh(x) + 5168cosh(x) +--R + +--R 18 16 14 +--R - 5316cosh(x) - 25352cosh(x) - 40528cosh(x) +--R + +--R 12 10 8 6 +--R - 22368cosh(x) + 1256cosh(x) - 6048cosh(x) - 10304cosh(x) +--R + +--R 4 +--R 14144cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 27 25 23 21 +--R 1920cosh(x) + 2352cosh(x) + 1792cosh(x) + 10416cosh(x) +--R + +--R 19 17 15 13 +--R 9792cosh(x) + 5040cosh(x) - 9728cosh(x) - 19664cosh(x) +--R + +--R 11 9 5 +--R - 10240cosh(x) + 7872cosh(x) - 12480cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 28 26 24 22 +--R 460cosh(x) + 688cosh(x) + 996cosh(x) + 5184cosh(x) +--R + +--R 20 18 16 14 +--R 7628cosh(x) + 11504cosh(x) + 11372cosh(x) + 2528cosh(x) +--R + +--R 12 10 8 6 +--R - 5960cosh(x) - 7488cosh(x) + 6112cosh(x) + 8192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 29 27 25 23 +--R 64cosh(x) + 112cosh(x) + 224cosh(x) + 1232cosh(x) +--R + +--R 21 19 17 15 +--R 2336cosh(x) + 4912cosh(x) + 8384cosh(x) + 9104cosh(x) +--R + +--R 13 11 9 7 +--R 7936cosh(x) + 448cosh(x) - 7040cosh(x) - 3904cosh(x) +--R * +--R sinh(x) +--R + +--R 30 28 26 24 22 +--R 4cosh(x) + 8cosh(x) + 20cosh(x) + 120cosh(x) + 276cosh(x) +--R + +--R 20 18 16 14 +--R 728cosh(x) + 1676cosh(x) + 2792cosh(x) + 4648cosh(x) +--R + +--R 12 10 8 +--R 6048cosh(x) + 4192cosh(x) + 1120cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 32 +-+ 31 +--R 2\|2 sinh(x) + 36\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 30 +--R (296\|2 cosh(x) + 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 29 +--R (1452\|2 cosh(x) + 32\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 28 +--R (4608\|2 cosh(x) + 230\|2 cosh(x) - 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 27 +--R (9300\|2 cosh(x) + 960\|2 cosh(x) - 100\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (9272\|2 cosh(x) + 2458\|2 cosh(x) - 772\|2 cosh(x) - 42\|2 ) +--R * +--R 26 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 7524\|2 cosh(x) + 3424\|2 cosh(x) - 3636\|2 cosh(x) +--R + +--R +-+ +--R - 584\|2 cosh(x) +--R * +--R 25 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 44584\|2 cosh(x) - 34\|2 cosh(x) - 11522\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 3682\|2 cosh(x) - 190\|2 +--R * +--R 24 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 75116\|2 cosh(x) - 10880\|2 cosh(x) - 25240\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 13760\|2 cosh(x) - 2204\|2 cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 48024\|2 cosh(x) - 22790\|2 cosh(x) - 36392\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 33068\|2 cosh(x) - 11216\|2 cosh(x) - 386\|2 +--R * +--R 22 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 56764\|2 cosh(x) - 18656\|2 cosh(x) - 24408\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 50000\|2 cosh(x) - 32004\|2 cosh(x) - 3584\|2 cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 173696\|2 cosh(x) + 12078\|2 cosh(x) + 28970\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 34636\|2 cosh(x) - 51916\|2 cosh(x) - 13550\|2 cosh(x) +--R + +--R +-+ +--R - 1010\|2 +--R * +--R 20 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 184644\|2 cosh(x) + 51264\|2 cosh(x) + 110612\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 37696\|2 cosh(x) - 30676\|2 cosh(x) - 23552\|2 cosh(x) +--R + +--R +-+ +--R - 7692\|2 cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 38456\|2 cosh(x) + 59090\|2 cosh(x) + 163780\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 145650\|2 cosh(x) + 65264\|2 cosh(x) - 2374\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 22868\|2 cosh(x) - 2366\|2 +--R * +--R 18 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 169556\|2 cosh(x) + 15200\|2 cosh(x) + 123652\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 212424\|2 cosh(x) + 202676\|2 cosh(x) + 80384\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 27820\|2 cosh(x) - 14200\|2 cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - 267444\|2 cosh(x) - 51034\|2 cosh(x) - 17442\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 157658\|2 cosh(x) + 277214\|2 cosh(x) + 195862\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 11958\|2 cosh(x) - 31582\|2 cosh(x) - 3956\|2 +--R * +--R 16 +--R sinh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R - 169556\|2 cosh(x) - 82688\|2 cosh(x) - 180880\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 23936\|2 cosh(x) + 191272\|2 cosh(x) + 249856\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 91664\|2 cosh(x) - 25376\|2 cosh(x) - 16936\|2 cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 38456\|2 cosh(x) - 51034\|2 cosh(x) - 253232\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 231880\|2 cosh(x) - 54048\|2 cosh(x) + 157772\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 147344\|2 cosh(x) + 16248\|2 cosh(x) - 23152\|2 cosh(x) - 6576\|2 +--R * +--R 14 +--R sinh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R 184644\|2 cosh(x) + 15200\|2 cosh(x) - 180880\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 323680\|2 cosh(x) - 329064\|2 cosh(x) - 76800\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 116304\|2 cosh(x) + 56352\|2 cosh(x) - 4280\|2 cosh(x) +--R + +--R +-+ +--R - 17824\|2 cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R 173696\|2 cosh(x) + 59090\|2 cosh(x) - 17442\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 231880\|2 cosh(x) - 450216\|2 cosh(x) - 337324\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 10948\|2 cosh(x) + 62008\|2 cosh(x) + 20144\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 12752\|2 cosh(x) - 8552\|2 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R 56764\|2 cosh(x) + 51264\|2 cosh(x) + 123652\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 23936\|2 cosh(x) - 329064\|2 cosh(x) - 452608\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 172456\|2 cosh(x) + 25376\|2 cosh(x) + 38680\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 3776\|2 cosh(x) - 9168\|2 cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R - 48024\|2 cosh(x) + 12078\|2 cosh(x) + 163780\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R 157658\|2 cosh(x) - 54048\|2 cosh(x) - 337324\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 248952\|2 cosh(x) - 44308\|2 cosh(x) + 55920\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 912\|2 cosh(x) - 2736\|2 cosh(x) - 5928\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R - 75116\|2 cosh(x) - 18656\|2 cosh(x) + 110612\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R 212424\|2 cosh(x) + 191272\|2 cosh(x) - 76800\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 172456\|2 cosh(x) - 84304\|2 cosh(x) + 48072\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 26016\|2 cosh(x) - 13712\|2 cosh(x) + 4032\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R - 44584\|2 cosh(x) - 22790\|2 cosh(x) + 28970\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 145650\|2 cosh(x) + 277214\|2 cosh(x) + 157772\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 10948\|2 cosh(x) - 44308\|2 cosh(x) + 33160\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 34800\|2 cosh(x) + 2408\|2 cosh(x) - 7560\|2 cosh(x) - 1584\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R - 7524\|2 cosh(x) - 10880\|2 cosh(x) - 24408\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R 37696\|2 cosh(x) + 202676\|2 cosh(x) + 249856\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 116304\|2 cosh(x) + 25376\|2 cosh(x) + 48072\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 23936\|2 cosh(x) + 10592\|2 cosh(x) - 2560\|2 cosh(x) +--R + +--R +-+ +--R 3936\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R 9272\|2 cosh(x) - 34\|2 cosh(x) - 36392\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R - 34636\|2 cosh(x) + 65264\|2 cosh(x) + 195862\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 147344\|2 cosh(x) + 62008\|2 cosh(x) + 55920\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 34800\|2 cosh(x) - 6816\|2 cosh(x) + 8368\|2 cosh(x) +--R + +--R +-+ 2 +--R - 8448\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 27 +-+ 25 +-+ 23 +--R 9300\|2 cosh(x) + 3424\|2 cosh(x) - 25240\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R - 50000\|2 cosh(x) - 30676\|2 cosh(x) + 80384\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 91664\|2 cosh(x) + 56352\|2 cosh(x) + 38680\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 26016\|2 cosh(x) + 10592\|2 cosh(x) - 13184\|2 cosh(x) +--R + +--R +-+ 3 +--R 11936\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 28 +-+ 26 +-+ 24 +--R 4608\|2 cosh(x) + 2458\|2 cosh(x) - 11522\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R - 33068\|2 cosh(x) - 51916\|2 cosh(x) - 2374\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R 11958\|2 cosh(x) + 16248\|2 cosh(x) + 20144\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 912\|2 cosh(x) + 2408\|2 cosh(x) + 8368\|2 cosh(x) +--R + +--R +-+ 4 +--R - 13728\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R 1452\|2 cosh(x) + 960\|2 cosh(x) - 3636\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R - 13760\|2 cosh(x) - 32004\|2 cosh(x) - 23552\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R - 27820\|2 cosh(x) - 25376\|2 cosh(x) - 4280\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 3776\|2 cosh(x) - 13712\|2 cosh(x) - 2560\|2 cosh(x) +--R + +--R +-+ 5 +--R 11936\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R 296\|2 cosh(x) + 230\|2 cosh(x) - 772\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R - 3682\|2 cosh(x) - 11216\|2 cosh(x) - 13550\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 22868\|2 cosh(x) - 31582\|2 cosh(x) - 23152\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 12752\|2 cosh(x) - 2736\|2 cosh(x) - 7560\|2 cosh(x) +--R + +--R +-+ 6 +--R - 8448\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R 36\|2 cosh(x) + 32\|2 cosh(x) - 100\|2 cosh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R - 584\|2 cosh(x) - 2204\|2 cosh(x) - 3584\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R - 7692\|2 cosh(x) - 14200\|2 cosh(x) - 16936\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 17824\|2 cosh(x) - 9168\|2 cosh(x) + 4032\|2 cosh(x) +--R + +--R +-+ 7 +--R 3936\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 32 +-+ 30 +-+ 28 +-+ 26 +--R 2\|2 cosh(x) + 2\|2 cosh(x) - 6\|2 cosh(x) - 42\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R - 190\|2 cosh(x) - 386\|2 cosh(x) - 1010\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 2366\|2 cosh(x) - 3956\|2 cosh(x) - 6576\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 8552\|2 cosh(x) - 5928\|2 cosh(x) - 1584\|2 cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 508 +t0317:= (-1+tanh(x)^2)^(3/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (86) (tanh(x) - 1)\|tanh(x) - 1 +--R Type: Expression(Integer) +--E 88 + +--S 89 of 508 +r0317:= -1/2*cosh(x)*(-sech(x)^2)^(1/2)*(atan(sinh(x))+sech(x)*tanh(x)) +--R +--R +--R +----------+ +--R | 2 +--R (- cosh(x)atan(sinh(x)) - cosh(x)sech(x)tanh(x))\|- sech(x) +--R (87) ------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 508 +a0317:= integrate(t0317,x) +--R +--R +--R (88) 0 +--R Type: Union(Expression(Integer),...) +--E 90 + +--S 91 of 508 +m0317:= a0317-r0317 +--R +--R +--R +----------+ +--R | 2 +--R (cosh(x)atan(sinh(x)) + cosh(x)sech(x)tanh(x))\|- sech(x) +--R (89) ----------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 508 +d0317:= D(m0317,x) +--R +--R +--R (90) +--R 2 2 2 2 3 +--R (cosh(x)sech(x) sinh(x) + cosh(x)sech(x) )tanh(x) - sech(x) sinh(x) +--R + +--R 2 +--R - sech(x) sinh(x) +--R * +--R atan(sinh(x)) +--R + +--R 3 2 3 2 +--R (3cosh(x)sech(x) sinh(x) + 3cosh(x)sech(x) )tanh(x) +--R + +--R 3 3 3 3 2 +--R (- sech(x) sinh(x) - sech(x) sinh(x))tanh(x) - cosh(x)sech(x) sinh(x) +--R + +--R 3 2 2 +--R - cosh(x)sech(x) - cosh(x) sech(x) +--R / +--R +----------+ +--R 2 | 2 +--R (2sinh(x) + 2)\|- sech(x) +--R Type: Expression(Integer) +--E 92 + +--S 93 of 508 +t0318:= (-1-tanh(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (91) (- tanh(x) - 1)\|- tanh(x) - 1 +--R Type: Expression(Integer) +--E 93 + +--S 94 of 508 +r0318:= 2*2^(1/2)*atan(2^(1/2)*tanh(x)/(-1-tanh(x)^2)^(1/2))+_ + 5/2*atan(coth(x)*(-1-tanh(x)^2)^(1/2))+1/2*tanh(x)*(-1-tanh(x)^2)^(1/2) +--R +--R +--R (92) +--R +--------------+ +-+ +--R | 2 +-+ \|2 tanh(x) +--R 5atan(coth(x)\|- tanh(x) - 1 ) + 4\|2 atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R + +--R +--------------+ +--R | 2 +--R tanh(x)\|- tanh(x) - 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 508 +a0318:= integrate(t0318,x) +--R +--R +--R (93) +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 +--R (10\|- 1 (%e ) + 20\|- 1 (%e ) + 10\|- 1 )\|- 2(%e ) - 2 +--R + +--R +---+ +---+ x 8 +---+ +---+ x 6 +---+ +---+ x 4 +--R - 5\|- 2 \|- 1 (%e ) - 10\|- 2 \|- 1 (%e ) - 15\|- 2 \|- 1 (%e ) +--R + +--R +---+ +---+ x 2 +---+ +---+ +--R - 20\|- 2 \|- 1 (%e ) - 10\|- 2 \|- 1 +--R * +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R \|- 2 \|- 2(%e ) - 2 + (2\|- 2 \|- 1 + 2)(%e ) + 2 +--R log(------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 x 8 +--R (4\|- 2 (%e ) + 8\|- 2 (%e ) + 4\|- 2 )\|- 2(%e ) - 2 + 4(%e ) +--R + +--R x 6 x 4 x 2 +--R 8(%e ) + 12(%e ) + 16(%e ) + 8 +--R * +--R +-------------+ +--R +---+ | x 4 x 2 +--R \|- 2 \|- 2(%e ) - 2 + 2(%e ) + 2 +--R log(------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 +--R (- 10\|- 1 (%e ) - 20\|- 1 (%e ) - 10\|- 1 )\|- 2(%e ) - 2 +--R + +--R +---+ +---+ x 8 +---+ +---+ x 6 +---+ +---+ x 4 +--R 5\|- 2 \|- 1 (%e ) + 10\|- 2 \|- 1 (%e ) + 15\|- 2 \|- 1 (%e ) +--R + +--R +---+ +---+ x 2 +---+ +---+ +--R 20\|- 2 \|- 1 (%e ) + 10\|- 2 \|- 1 +--R * +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R \|- 2 \|- 2(%e ) - 2 + (- 2\|- 2 \|- 1 + 2)(%e ) + 2 +--R log(--------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 x 8 +--R (- 4\|- 2 (%e ) - 8\|- 2 (%e ) - 4\|- 2 )\|- 2(%e ) - 2 - 4(%e ) +--R + +--R x 6 x 4 x 2 +--R - 8(%e ) - 12(%e ) - 16(%e ) - 8 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +---+ x 2 +--R (- 2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) + 2\|- 2 (%e ) +--R + +--R +---+ +--R - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 6 +---+ x 4 +---+ x 2 | x 4 x 8 +--R (- \|- 2 (%e ) - \|- 2 (%e ) - 6\|- 2 (%e ) )\|- 2(%e ) - 2 - 2(%e ) +--R + +--R x 6 x 4 x 2 +--R - 8(%e ) - 2(%e ) - 12(%e ) +--R / +--R +-------------+ +--R x 4 x 2 | x 4 +---+ x 8 +---+ x 6 +--R (4(%e ) + 8(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) - 4\|- 2 (%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R - 6\|- 2 (%e ) - 8\|- 2 (%e ) - 4\|- 2 +--R Type: Union(Expression(Integer),...) +--E 95 + +--S 96 of 508 +m0318:= a0318-r0318 +--R +--R +--R (94) +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 +--R (10\|- 1 (%e ) + 20\|- 1 (%e ) + 10\|- 1 )\|- 2(%e ) - 2 +--R + +--R +---+ +---+ x 8 +---+ +---+ x 6 +---+ +---+ x 4 +--R - 5\|- 2 \|- 1 (%e ) - 10\|- 2 \|- 1 (%e ) - 15\|- 2 \|- 1 (%e ) +--R + +--R +---+ +---+ x 2 +---+ +---+ +--R - 20\|- 2 \|- 1 (%e ) - 10\|- 2 \|- 1 +--R * +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R \|- 2 \|- 2(%e ) - 2 + (2\|- 2 \|- 1 + 2)(%e ) + 2 +--R log(------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 x 8 +--R (4\|- 2 (%e ) + 8\|- 2 (%e ) + 4\|- 2 )\|- 2(%e ) - 2 + 4(%e ) +--R + +--R x 6 x 4 x 2 +--R 8(%e ) + 12(%e ) + 16(%e ) + 8 +--R * +--R +-------------+ +--R +---+ | x 4 x 2 +--R \|- 2 \|- 2(%e ) - 2 + 2(%e ) + 2 +--R log(------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 +--R (- 10\|- 1 (%e ) - 20\|- 1 (%e ) - 10\|- 1 )\|- 2(%e ) - 2 +--R + +--R +---+ +---+ x 8 +---+ +---+ x 6 +---+ +---+ x 4 +--R 5\|- 2 \|- 1 (%e ) + 10\|- 2 \|- 1 (%e ) + 15\|- 2 \|- 1 (%e ) +--R + +--R +---+ +---+ x 2 +---+ +---+ +--R 20\|- 2 \|- 1 (%e ) + 10\|- 2 \|- 1 +--R * +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R \|- 2 \|- 2(%e ) - 2 + (- 2\|- 2 \|- 1 + 2)(%e ) + 2 +--R log(--------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 x 8 +--R (- 4\|- 2 (%e ) - 8\|- 2 (%e ) - 4\|- 2 )\|- 2(%e ) - 2 - 4(%e ) +--R + +--R x 6 x 4 x 2 +--R - 8(%e ) - 12(%e ) - 16(%e ) - 8 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +---+ x 2 +--R (- 2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) + 2\|- 2 (%e ) +--R + +--R +---+ +--R - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R x 4 x 2 | x 4 +---+ x 8 +--R (- 10(%e ) - 20(%e ) - 10)\|- 2(%e ) - 2 + 5\|- 2 (%e ) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R 10\|- 2 (%e ) + 15\|- 2 (%e ) + 20\|- 2 (%e ) + 10\|- 2 +--R * +--R +--------------+ +--R | 2 +--R atan(coth(x)\|- tanh(x) - 1 ) +--R + +--R +-------------+ +--R +-+ x 4 +-+ x 2 +-+ | x 4 +--R (- 8\|2 (%e ) - 16\|2 (%e ) - 8\|2 )\|- 2(%e ) - 2 +--R + +--R +---+ +-+ x 8 +---+ +-+ x 6 +---+ +-+ x 4 +--R 4\|- 2 \|2 (%e ) + 8\|- 2 \|2 (%e ) + 12\|- 2 \|2 (%e ) +--R + +--R +---+ +-+ x 2 +---+ +-+ +--R 16\|- 2 \|2 (%e ) + 8\|- 2 \|2 +--R * +--R +-+ +--R \|2 tanh(x) +--R atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R + +--R +--------------+ +--R x 4 x 2 | 2 +---+ x 6 +--R (- 2(%e ) - 4(%e ) - 2)tanh(x)\|- tanh(x) - 1 - \|- 2 (%e ) +--R + +--R +---+ x 4 +---+ x 2 +--R - \|- 2 (%e ) - 6\|- 2 (%e ) +--R * +--R +-------------+ +--R | x 4 +--R \|- 2(%e ) - 2 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R \|- 2 (%e ) + 2\|- 2 (%e ) + 3\|- 2 (%e ) + 4\|- 2 (%e ) +--R + +--R +---+ +--R 2\|- 2 +--R * +--R +--------------+ +--R | 2 +--R tanh(x)\|- tanh(x) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R - 2(%e ) - 8(%e ) - 2(%e ) - 12(%e ) +--R / +--R +-------------+ +--R x 4 x 2 | x 4 +---+ x 8 +---+ x 6 +--R (4(%e ) + 8(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) - 4\|- 2 (%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R - 6\|- 2 (%e ) - 8\|- 2 (%e ) - 4\|- 2 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 508 +d0318:= D(m0318,x) +--R +--R +--R (95) +--R +---+ 2 x 16 +---+ 2 x 12 +--R 28\|- 2 coth(x) (%e ) + 252\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 x 8 +---+ 2 x 4 +--R 672\|- 2 coth(x) (%e ) + 704\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 +--R 256\|- 2 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 16 +--R (28\|- 2 coth(x) - 28\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (252\|- 2 coth(x) - 252\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (672\|- 2 coth(x) - 672\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +---+ 2 +--R (704\|- 2 coth(x) - 704\|- 2 )(%e ) + 256\|- 2 coth(x) +--R + +--R +---+ +--R - 256\|- 2 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R + +--R 2 x 18 2 x 16 2 x 14 +--R - 2coth(x) (%e ) - 6coth(x) (%e ) - 54coth(x) (%e ) +--R + +--R 2 x 12 2 x 10 2 x 8 +--R - 146coth(x) (%e ) - 304coth(x) (%e ) - 528coth(x) (%e ) +--R + +--R 2 x 6 2 x 4 2 x 2 +--R - 608coth(x) (%e ) - 544coth(x) (%e ) - 384coth(x) (%e ) +--R + +--R 2 +--R - 128coth(x) +--R * +--R 6 +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R (- coth(x) + 2)(%e ) + (- 3coth(x) + 6)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (- 27coth(x) + 54)(%e ) + (- 73coth(x) + 146)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (- 152coth(x) + 304)(%e ) + (- 264coth(x) + 528)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (- 304coth(x) + 608)(%e ) + (- 272coth(x) + 544)(%e ) +--R + +--R 2 x 2 2 +--R (- 192coth(x) + 384)(%e ) - 64coth(x) + 128 +--R * +--R 4 +--R tanh(x) +--R + +--R x 18 x 16 x 14 +--R 5coth(x)(%e ) + 15coth(x)(%e ) + 135coth(x)(%e ) +--R + +--R x 12 x 10 x 8 +--R 365coth(x)(%e ) + 760coth(x)(%e ) + 1320coth(x)(%e ) +--R + +--R x 6 x 4 x 2 +--R 1520coth(x)(%e ) + 1360coth(x)(%e ) + 960coth(x)(%e ) +--R + +--R 320coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R (- coth(x) - 6)(%e ) + (- 3coth(x) - 18)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (- 27coth(x) - 162)(%e ) + (- 73coth(x) - 438)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (- 152coth(x) - 912)(%e ) + (- 264coth(x) - 1584)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (- 304coth(x) - 1824)(%e ) + (- 272coth(x) - 1632)(%e ) +--R + +--R 2 x 2 2 +--R (- 192coth(x) - 1152)(%e ) - 64coth(x) - 384 +--R * +--R 2 +--R tanh(x) +--R + +--R x 18 x 16 x 14 +--R - 5coth(x)(%e ) - 15coth(x)(%e ) - 135coth(x)(%e ) +--R + +--R x 12 x 10 x 8 +--R - 365coth(x)(%e ) - 760coth(x)(%e ) - 1320coth(x)(%e ) +--R + +--R x 6 x 4 x 2 +--R - 1520coth(x)(%e ) - 1360coth(x)(%e ) - 960coth(x)(%e ) +--R + +--R - 320coth(x) +--R * +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R (- 2coth(x) + 2)(%e ) + (- 6coth(x) + 6)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (- 54coth(x) + 54)(%e ) + (- 146coth(x) + 146)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (- 304coth(x) + 304)(%e ) + (- 528coth(x) + 528)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (- 608coth(x) + 608)(%e ) + (- 544coth(x) + 544)(%e ) +--R + +--R 2 x 2 2 +--R (- 384coth(x) + 384)(%e ) - 128coth(x) + 128 +--R * +--R +-------------+ +--R | x 4 +--R \|- 2(%e ) - 2 +--R + +--R 2 x 20 2 x 16 2 x 12 +--R 8coth(x) (%e ) + 208coth(x) (%e ) + 1032coth(x) (%e ) +--R + +--R 2 x 8 2 x 4 2 +--R 1984coth(x) (%e ) + 1664coth(x) (%e ) + 512coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 20 2 x 16 +--R (8coth(x) - 8)(%e ) + (208coth(x) - 208)(%e ) +--R + +--R 2 x 12 2 x 8 +--R (1032coth(x) - 1032)(%e ) + (1984coth(x) - 1984)(%e ) +--R + +--R 2 x 4 2 +--R (1664coth(x) - 1664)(%e ) + 512coth(x) - 512 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R + +--R +---+ 2 x 18 +---+ 2 x 16 +--R 14\|- 2 coth(x) (%e ) + 42\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 x 14 +---+ 2 x 12 +--R 154\|- 2 coth(x) (%e ) + 350\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 x 10 +---+ 2 x 8 +--R 560\|- 2 coth(x) (%e ) + 784\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 x 6 +---+ 2 x 4 +--R 800\|- 2 coth(x) (%e ) + 608\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 x 2 +---+ 2 +--R 384\|- 2 coth(x) (%e ) + 128\|- 2 coth(x) +--R * +--R 6 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 18 +--R (7\|- 2 coth(x) - 14\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (21\|- 2 coth(x) - 42\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (77\|- 2 coth(x) - 154\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (175\|- 2 coth(x) - 350\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (280\|- 2 coth(x) - 560\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (392\|- 2 coth(x) - 784\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (400\|- 2 coth(x) - 800\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (304\|- 2 coth(x) - 608\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (192\|- 2 coth(x) - 384\|- 2 )(%e ) + 64\|- 2 coth(x) - 128\|- 2 +--R * +--R 4 +--R tanh(x) +--R + +--R +---+ x 18 +---+ x 16 +--R - 35\|- 2 coth(x)(%e ) - 105\|- 2 coth(x)(%e ) +--R + +--R +---+ x 14 +---+ x 12 +--R - 385\|- 2 coth(x)(%e ) - 875\|- 2 coth(x)(%e ) +--R + +--R +---+ x 10 +---+ x 8 +--R - 1400\|- 2 coth(x)(%e ) - 1960\|- 2 coth(x)(%e ) +--R + +--R +---+ x 6 +---+ x 4 +--R - 2000\|- 2 coth(x)(%e ) - 1520\|- 2 coth(x)(%e ) +--R + +--R +---+ x 2 +---+ +--R - 960\|- 2 coth(x)(%e ) - 320\|- 2 coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 18 +--R (7\|- 2 coth(x) + 42\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (21\|- 2 coth(x) + 126\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (77\|- 2 coth(x) + 462\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (175\|- 2 coth(x) + 1050\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (280\|- 2 coth(x) + 1680\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (392\|- 2 coth(x) + 2352\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (400\|- 2 coth(x) + 2400\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (304\|- 2 coth(x) + 1824\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (192\|- 2 coth(x) + 1152\|- 2 )(%e ) + 64\|- 2 coth(x) + 384\|- 2 +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ x 18 +---+ x 16 +--R 35\|- 2 coth(x)(%e ) + 105\|- 2 coth(x)(%e ) +--R + +--R +---+ x 14 +---+ x 12 +--R 385\|- 2 coth(x)(%e ) + 875\|- 2 coth(x)(%e ) +--R + +--R +---+ x 10 +---+ x 8 +--R 1400\|- 2 coth(x)(%e ) + 1960\|- 2 coth(x)(%e ) +--R + +--R +---+ x 6 +---+ x 4 +--R 2000\|- 2 coth(x)(%e ) + 1520\|- 2 coth(x)(%e ) +--R + +--R +---+ x 2 +---+ +--R 960\|- 2 coth(x)(%e ) + 320\|- 2 coth(x) +--R * +--R tanh(x) +--R + +--R +---+ 2 +---+ x 18 +--R (14\|- 2 coth(x) - 14\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (42\|- 2 coth(x) - 42\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (154\|- 2 coth(x) - 154\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (350\|- 2 coth(x) - 350\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (560\|- 2 coth(x) - 560\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (784\|- 2 coth(x) - 784\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (800\|- 2 coth(x) - 800\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (608\|- 2 coth(x) - 608\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (384\|- 2 coth(x) - 384\|- 2 )(%e ) + 128\|- 2 coth(x) - 128\|- 2 +--R / +--R 2 x 18 2 x 16 2 x 14 +--R 2coth(x) (%e ) + 6coth(x) (%e ) + 54coth(x) (%e ) +--R + +--R 2 x 12 2 x 10 2 x 8 +--R 146coth(x) (%e ) + 304coth(x) (%e ) + 528coth(x) (%e ) +--R + +--R 2 x 6 2 x 4 2 x 2 +--R 608coth(x) (%e ) + 544coth(x) (%e ) + 384coth(x) (%e ) +--R + +--R 2 +--R 128coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R (2coth(x) - 2)(%e ) + (6coth(x) - 6)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (54coth(x) - 54)(%e ) + (146coth(x) - 146)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (304coth(x) - 304)(%e ) + (528coth(x) - 528)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (608coth(x) - 608)(%e ) + (544coth(x) - 544)(%e ) +--R + +--R 2 x 2 2 +--R (384coth(x) - 384)(%e ) + 128coth(x) - 128 +--R * +--R +--------------+ +-------------+ +--R | 2 | x 4 +--R \|- tanh(x) - 1 \|- 2(%e ) - 2 +--R + +--R +---+ 2 x 18 +---+ 2 x 16 +--R - 14\|- 2 coth(x) (%e ) - 42\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 x 14 +---+ 2 x 12 +--R - 154\|- 2 coth(x) (%e ) - 350\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 x 10 +---+ 2 x 8 +--R - 560\|- 2 coth(x) (%e ) - 784\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 x 6 +---+ 2 x 4 +--R - 800\|- 2 coth(x) (%e ) - 608\|- 2 coth(x) (%e ) +--R + +--R +---+ 2 x 2 +---+ 2 +--R - 384\|- 2 coth(x) (%e ) - 128\|- 2 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 18 +--R (- 14\|- 2 coth(x) + 14\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (- 42\|- 2 coth(x) + 42\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (- 154\|- 2 coth(x) + 154\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (- 350\|- 2 coth(x) + 350\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (- 560\|- 2 coth(x) + 560\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (- 784\|- 2 coth(x) + 784\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (- 800\|- 2 coth(x) + 800\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 608\|- 2 coth(x) + 608\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 384\|- 2 coth(x) + 384\|- 2 )(%e ) - 128\|- 2 coth(x) + 128\|- 2 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) - 1 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 508 +t0319:= (a+b*tanh(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (96) (b tanh(x) + a)\|b tanh(x) + a +--R Type: Expression(Integer) +--E 98 + +--S 99 of 508 +r0319:= (a+b)^(3/2)*atanh((a+b)^(1/2)*tanh(x)/(a+b*tanh(x)^2)^(1/2))-_ + 3/2*a*b^(1/2)*atanh(coth(x)*(a+b*tanh(x)^2)^(1/2)/b^(1/2))-_ + b^(3/2)*atanh(coth(x)*(a+b*tanh(x)^2)^(1/2)/b^(1/2))-_ + 1/2*b*tanh(x)*(a+b*tanh(x)^2)^(1/2) +--R +--R +--R (97) +--R +--------------+ +--R | 2 +--R +-+ coth(x)\|b tanh(x) + a +--R (- 2b - 3a)\|b atanh(------------------------) +--R +-+ +--R \|b +--R + +--R +-----+ +--------------+ +--R +-----+ tanh(x)\|b + a | 2 +--R (2b + 2a)\|b + a atanh(-----------------) - b tanh(x)\|b tanh(x) + a +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 508 +a0319:= integrate(t0319,x) +--R +--R +--R (98) +--R [ +--R 3 2 2 3 6 +--R (- b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) - b + a b + 5a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 20b - 20a b + 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 6b + 6a b + 30a b + 18a )cosh(x) + b + 5a b + 7a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- b + a b + 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + 5a b + 7a b + 3a )cosh(x) + b + 3a b + 3a b + a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- b - a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 28b - 28a b - 28a b - 28a )cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 +--R (- 24a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 70b - 70a b - 70a b - 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 60a b - 60a )cosh(x) + 2b - 8a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 80a b - 80a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 28b - 28a b - 28a b - 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 60a b - 60a )cosh(x) + (12b - 48a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R - 4a b - 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (- 24a b - 24a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- b - a b - a b - a )cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (2b - 8a b - 6a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R - b - 3a b - 3a b - a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +-----+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|b + a +--R + +--R 3 2 2 3 6 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b + 15a b - 15a b - 15a )cosh(x) + b - a b - 5a b +--R + +--R 3 +--R - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b + 20a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 15a b - 15a b - 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (6b - 6a b - 30a b - 18a )cosh(x) - b - 5a b - 7a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 10a b - 14a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b + a b - a b - a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - 5a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- b - 5a b - 7a b - 3a )cosh(x) - b - 3a b - 3a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (b + a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (8b + 8a b + 8a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((28b + 28a b + 28a b + 28a )cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 +--R (24a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (70b + 70a b + 70a b + 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (60a b + 60a )cosh(x) - 2b + 8a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (80a b + 80a )cosh(x) + (- 8b + 32a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (28b + 28a b + 28a b + 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (60a b + 60a )cosh(x) + (- 12b + 48a b + 36a )cosh(x) +--R + +--R 2 2 3 +--R 4a b + 8a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 2 3 5 +--R (8b + 8a b + 8a b + 8a )cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 2 3 3 2 2 3 +--R (- 8b + 32a b + 24a )cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (b + a b + a b + a )cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (- 2b + 8a b + 6a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 3 2 2 3 +--R b + 3a b + 3a b + a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) - 2b - 2a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) - 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (- 8b + 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (- 4b + 2a)cosh(x) + 2b + 2a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 2 6 2 2 5 +--R (2b + a b - 3a )sinh(x) + (12b + 6a b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 15a b - 45a )cosh(x) + 2b - 3a b - 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 20a b - 60a )cosh(x) + (8b - 12a b - 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 15a b - 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (12b - 18a b - 54a )cosh(x) - 2b - 9a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 6a b - 18a )cosh(x) + (8b - 12a b - 36a )cosh(x) +--R + +--R 2 2 +--R (- 4b - 18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + a b - 3a )cosh(x) + (2b - 3a b - 9a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b - 9a b - 9a )cosh(x) - 2b - 5a b - 3a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (2b + 3a b + 2a b + 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 24a b + 16a b + 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((56b + 84a b + 56a b + 84a )cosh(x) + 8a b + 12a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (112b + 168a b + 112a b + 168a )cosh(x) +--R + +--R 2 3 +--R (48a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (140b + 210a b + 140a b + 210a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (120a b + 180a )cosh(x) - 4b - 2a b + 18a b + 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (112b + 168a b + 112a b + 168a )cosh(x) +--R + +--R 2 3 3 +--R (160a b + 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 16b - 8a b + 72a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (56b + 84a b + 56a b + 84a )cosh(x) +--R + +--R 2 3 4 +--R (120a b + 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 24b - 12a b + 108a b + 108a )cosh(x) + 8a b + 20a b +--R + +--R 3 +--R 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 24a b + 16a b + 24a )cosh(x) +--R + +--R 2 3 5 +--R (48a b + 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 16b - 8a b + 72a b + 72a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 40a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (2b + 3a b + 2a b + 3a )cosh(x) + (8a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 4b - 2a b + 18a b + 18a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (8a b + 20a b + 12a )cosh(x) + 2b + 7a b + 8a b + 3a +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 3 +--R - 2a sinh(x) - 8a cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12a cosh(x) - 2b - 2a)sinh(x) +--R + +--R 3 +--R (- 8a cosh(x) + (- 4b - 4a)cosh(x))sinh(x) +--R + +--R 4 2 +--R - 2a cosh(x) + (- 2b - 2a)cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R + +--R 2 2 4 +--R (- b - 2a b - a )sinh(x) +--R + +--R 2 2 3 +--R (- 4b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 12a b - 6a )cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((- 4b - 8a b - 4a )cosh(x) + (- 4a b - 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- b - 2a b - a )cosh(x) + (- 2a b - 2a )cosh(x) - b +--R + +--R 2 +--R - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- b + 2a b + a )sinh(x) +--R + +--R 2 2 5 +--R (- 6b + 12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 15b + 30a b + 15a )cosh(x) + b + 2a b + 3a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 +--R (- 20b + 40a b + 20a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 15b + 30a b + 15a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (6b + 12a b + 18a )cosh(x) - b + 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 6b + 12a b + 6a )cosh(x) +--R + +--R 2 2 3 +--R (4b + 8a b + 12a )cosh(x) +--R + +--R 2 2 +--R (- 2b + 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- b + 2a b + a )cosh(x) + (b + 2a b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- b + 2a b + 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 6 2 5 +--R (2a b + 2a )sinh(x) + (12a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R ((30a b + 30a )cosh(x) - 2b + 2a b + 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((40a b + 40a )cosh(x) + (- 8b + 8a b + 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 +--R (30a b + 30a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 12b + 12a b + 24a )cosh(x) + 2b + 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (12a b + 12a )cosh(x) + (- 8b + 8a b + 16a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (2a b + 2a )cosh(x) + (- 2b + 2a b + 4a )cosh(x) +--R + +--R 2 2 2 +--R (2b + 4a b + 2a )cosh(x) +--R * +--R +-+ +--R \|b +--R / +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a )cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((4b - 4a )cosh(x) + (- 4a b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (b - a )cosh(x) + (- 2a b - 2a )cosh(x) - b - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (b + a )sinh(x) + (6b + 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((15b + 15a )cosh(x) - b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((20b + 20a )cosh(x) + (- 4b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (15b + 15a )cosh(x) + (- 6b + 18a )cosh(x) - b +--R + +--R 2 +--R 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (6b + 6a )cosh(x) + (- 4b + 12a )cosh(x) +--R + +--R 2 2 +--R (- 2b + 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (b + a )cosh(x) + (- b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- b + 2a b + 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 6 2 5 +--R - 2a b sinh(x) - 12a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (- 30a b cosh(x) + 4b - 2a b - 4a b)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (- 40a b cosh(x) + (16b - 8a b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 +--R - 30a b cosh(x) + (24b - 12a b - 24a b)cosh(x) - 4b +--R + +--R 2 2 +--R - 6a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R - 12a b cosh(x) + (16b - 8a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (- 8b - 12a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R - 2a b cosh(x) + (4b - 2a b - 4a b)cosh(x) +--R + +--R 3 2 2 2 +--R (- 4b - 6a b - 2a b)cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 8 2 7 +--R 2a b sinh(x) + 16a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 6 +--R (56a b cosh(x) + 4b - 2a b + 6a b)sinh(x) +--R + +--R 2 3 3 2 2 5 +--R (112a b cosh(x) + (24b - 12a b + 36a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R 140a b cosh(x) + (60b - 30a b + 90a b)cosh(x) - 8b + 4a b +--R + +--R 2 +--R 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 112a b cosh(x) + (80b - 40a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 56a b cosh(x) + (60b - 30a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 48b + 24a b + 36a b)cosh(x) + 4b + 6a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 2 2 5 +--R 16a b cosh(x) + (24b - 12a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) + (8b + 12a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 2 2 6 +--R 2a b cosh(x) + (4b - 2a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 8b + 4a b + 6a b)cosh(x) + (4b + 6a b + 2a b)cosh(x) +--R * +--R +-----+ +--R \|b + a +--R / +--R 6 5 +--R (2b - 2a)sinh(x) + (12b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((30b - 30a)cosh(x) + 2b - 6a)sinh(x) +--R + +--R 3 3 +--R ((40b - 40a)cosh(x) + (8b - 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((30b - 30a)cosh(x) + (12b - 36a)cosh(x) - 2b - 6a)sinh(x) +--R + +--R 5 3 +--R ((12b - 12a)cosh(x) + (8b - 24a)cosh(x) + (- 4b - 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (2b - 2a)cosh(x) + (2b - 6a)cosh(x) + (- 2b - 6a)cosh(x) - 2b - 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (2b + 2a )sinh(x) + (16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((56b + 56a )cosh(x) + 8a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((112b + 112a )cosh(x) + 48a cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 4 +--R ((140b + 140a )cosh(x) + 120a cosh(x) - 4b + 4a b + 12a )sinh(x) +--R + +--R 2 2 5 2 3 +--R (112b + 112a )cosh(x) + 160a cosh(x) +--R + +--R 2 2 +--R (- 16b + 16a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 4 +--R (56b + 56a )cosh(x) + 120a cosh(x) +--R + +--R 2 2 2 2 +--R (- 24b + 24a b + 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 +--R (16b + 16a )cosh(x) + 48a cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b + 16a b + 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (2b + 2a )cosh(x) + 8a cosh(x) + (- 4b + 4a b + 12a )cosh(x) +--R + +--R 2 2 2 2 +--R (8a b + 8a )cosh(x) + 2b + 4a b + 2a +--R , +--R +--R 3 2 2 3 6 +--R (- b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) - b + a b + 5a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 20b - 20a b + 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 6b + 6a b + 30a b + 18a )cosh(x) + b + 5a b + 7a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- b + a b + 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + 5a b + 7a b + 3a )cosh(x) + b + 3a b + 3a b + a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- b - a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 28b - 28a b - 28a b - 28a )cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 +--R (- 24a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 70b - 70a b - 70a b - 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 60a b - 60a )cosh(x) + 2b - 8a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 80a b - 80a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 28b - 28a b - 28a b - 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 60a b - 60a )cosh(x) + (12b - 48a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R - 4a b - 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (- 24a b - 24a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- b - a b - a b - a )cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (2b - 8a b - 6a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R - b - 3a b - 3a b - a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +-----+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|b + a +--R + +--R 3 2 2 3 6 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b + 15a b - 15a b - 15a )cosh(x) + b - a b - 5a b +--R + +--R 3 +--R - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b + 20a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 15a b - 15a b - 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (6b - 6a b - 30a b - 18a )cosh(x) - b - 5a b - 7a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 10a b - 14a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b + a b - a b - a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - 5a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- b - 5a b - 7a b - 3a )cosh(x) - b - 3a b - 3a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (b + a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (8b + 8a b + 8a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((28b + 28a b + 28a b + 28a )cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 +--R (24a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (70b + 70a b + 70a b + 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (60a b + 60a )cosh(x) - 2b + 8a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (80a b + 80a )cosh(x) + (- 8b + 32a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (28b + 28a b + 28a b + 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (60a b + 60a )cosh(x) + (- 12b + 48a b + 36a )cosh(x) +--R + +--R 2 2 3 +--R 4a b + 8a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 2 3 5 +--R (8b + 8a b + 8a b + 8a )cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 2 3 3 2 2 3 +--R (- 8b + 32a b + 24a )cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (b + a b + a b + a )cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (- 2b + 8a b + 6a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 3 2 2 3 +--R b + 3a b + 3a b + a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) - 2b - 2a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) - 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (- 8b + 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (- 4b + 2a)cosh(x) + 2b + 2a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 2 6 +--R (- 4b - 2a b + 6a )sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 12a b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 60b - 30a b + 90a )cosh(x) - 4b + 6a b + 18a )sinh(x) +--R + +--R 2 2 3 +--R (- 80b - 40a b + 120a )cosh(x) +--R + +--R 2 2 +--R (- 16b + 24a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 60b - 30a b + 90a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 24b + 36a b + 108a )cosh(x) + 4b + 18a b + 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 12a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 16b + 24a b + 72a )cosh(x) + (8b + 36a b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 4b - 2a b + 6a )cosh(x) + (- 4b + 6a b + 18a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (4b + 18a b + 18a )cosh(x) + 4b + 10a b + 6a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +---+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|- b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 4b - 6a b - 4a b - 6a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 32b - 48a b - 32a b - 48a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 +--R ((- 112b - 168a b - 112a b - 168a )cosh(x) - 16a b - 24a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 224b - 336a b - 224a b - 336a )cosh(x) +--R + +--R 2 3 +--R (- 96a b - 144a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 280b - 420a b - 280a b - 420a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 240a b - 360a )cosh(x) + 8b + 4a b - 36a b - 36a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 224b - 336a b - 224a b - 336a )cosh(x) +--R + +--R 2 3 3 +--R (- 320a b - 480a )cosh(x) +--R + +--R 3 2 2 3 +--R (32b + 16a b - 144a b - 144a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 112b - 168a b - 112a b - 168a )cosh(x) +--R + +--R 2 3 4 +--R (- 240a b - 360a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (48b + 24a b - 216a b - 216a )cosh(x) - 16a b - 40a b +--R + +--R 3 +--R - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 32b - 48a b - 32a b - 48a )cosh(x) +--R + +--R 2 3 5 +--R (- 96a b - 144a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (32b + 16a b - 144a b - 144a )cosh(x) +--R + +--R 2 2 3 +--R (- 32a b - 80a b - 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- 4b - 6a b - 4a b - 6a )cosh(x) + (- 16a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (8b + 4a b - 36a b - 36a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (- 16a b - 40a b - 24a )cosh(x) - 4b - 14a b - 16a b - 6a +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +---+ +-----+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|b + a +--R + +--R 2 6 2 5 +--R - 2a b sinh(x) - 12a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (- 30a b cosh(x) + 4b - 2a b - 4a b)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (- 40a b cosh(x) + (16b - 8a b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 +--R - 30a b cosh(x) + (24b - 12a b - 24a b)cosh(x) - 4b +--R + +--R 2 2 +--R - 6a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R - 12a b cosh(x) + (16b - 8a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (- 8b - 12a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R - 2a b cosh(x) + (4b - 2a b - 4a b)cosh(x) +--R + +--R 3 2 2 2 +--R (- 4b - 6a b - 2a b)cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 8 2 7 +--R 2a b sinh(x) + 16a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 6 +--R (56a b cosh(x) + 4b - 2a b + 6a b)sinh(x) +--R + +--R 2 3 3 2 2 5 +--R (112a b cosh(x) + (24b - 12a b + 36a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R 140a b cosh(x) + (60b - 30a b + 90a b)cosh(x) - 8b + 4a b +--R + +--R 2 +--R 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 112a b cosh(x) + (80b - 40a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 56a b cosh(x) + (60b - 30a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 48b + 24a b + 36a b)cosh(x) + 4b + 6a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 2 2 5 +--R 16a b cosh(x) + (24b - 12a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) + (8b + 12a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 2 2 6 +--R 2a b cosh(x) + (4b - 2a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 8b + 4a b + 6a b)cosh(x) + (4b + 6a b + 2a b)cosh(x) +--R * +--R +-----+ +--R \|b + a +--R / +--R 6 5 +--R (2b - 2a)sinh(x) + (12b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((30b - 30a)cosh(x) + 2b - 6a)sinh(x) +--R + +--R 3 3 +--R ((40b - 40a)cosh(x) + (8b - 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((30b - 30a)cosh(x) + (12b - 36a)cosh(x) - 2b - 6a)sinh(x) +--R + +--R 5 3 +--R ((12b - 12a)cosh(x) + (8b - 24a)cosh(x) + (- 4b - 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (2b - 2a)cosh(x) + (2b - 6a)cosh(x) + (- 2b - 6a)cosh(x) - 2b - 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (2b + 2a )sinh(x) + (16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((56b + 56a )cosh(x) + 8a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((112b + 112a )cosh(x) + 48a cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 4 +--R ((140b + 140a )cosh(x) + 120a cosh(x) - 4b + 4a b + 12a )sinh(x) +--R + +--R 2 2 5 2 3 +--R (112b + 112a )cosh(x) + 160a cosh(x) +--R + +--R 2 2 +--R (- 16b + 16a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 4 +--R (56b + 56a )cosh(x) + 120a cosh(x) +--R + +--R 2 2 2 2 +--R (- 24b + 24a b + 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 +--R (16b + 16a )cosh(x) + 48a cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b + 16a b + 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (2b + 2a )cosh(x) + 8a cosh(x) + (- 4b + 4a b + 12a )cosh(x) +--R + +--R 2 2 2 2 +--R (8a b + 8a )cosh(x) + 2b + 4a b + 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 100 + +--S 101 of 508 +m0319a:= a0319.1-r0319 +--R +--R +--R (99) +--R 3 2 2 3 6 +--R (- b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) - b + a b + 5a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 20b - 20a b + 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 6b + 6a b + 30a b + 18a )cosh(x) + b + 5a b + 7a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- b + a b + 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + 5a b + 7a b + 3a )cosh(x) + b + 3a b + 3a b + a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- b - a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 28b - 28a b - 28a b - 28a )cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 +--R (- 24a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 70b - 70a b - 70a b - 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 60a b - 60a )cosh(x) + 2b - 8a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 80a b - 80a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 28b - 28a b - 28a b - 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 60a b - 60a )cosh(x) + (12b - 48a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R - 4a b - 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (- 24a b - 24a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- b - a b - a b - a )cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 3 +--R (2b - 8a b - 6a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) - b +--R + +--R 2 2 3 +--R - 3a b - 3a b - a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +-----+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|b + a +--R + +--R 3 2 2 3 6 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b + 15a b - 15a b - 15a )cosh(x) + b - a b - 5a b +--R + +--R 3 +--R - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b + 20a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 15a b - 15a b - 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) - b - 5a b - 7a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 10a b - 14a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 3 2 2 3 4 +--R (b + a b - a b - a )cosh(x) + (b - a b - 5a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- b - 5a b - 7a b - 3a )cosh(x) - b - 3a b - 3a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (b + a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (8b + 8a b + 8a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((28b + 28a b + 28a b + 28a )cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 +--R (24a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (70b + 70a b + 70a b + 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (60a b + 60a )cosh(x) - 2b + 8a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (80a b + 80a )cosh(x) + (- 8b + 32a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (28b + 28a b + 28a b + 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (60a b + 60a )cosh(x) + (- 12b + 48a b + 36a )cosh(x) +--R + +--R 2 2 3 +--R 4a b + 8a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 2 3 5 +--R (8b + 8a b + 8a b + 8a )cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 2 3 3 2 2 3 +--R (- 8b + 32a b + 24a )cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (b + a b + a b + a )cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 3 +--R (- 2b + 8a b + 6a )cosh(x) + (4a b + 8a b + 4a )cosh(x) + b +--R + +--R 2 2 3 +--R 3a b + 3a b + a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) - 2b - 2a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) - 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (- 8b + 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (- 4b + 2a)cosh(x) + 2b + 2a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 2 6 2 2 5 +--R (2b + a b - 3a )sinh(x) + (12b + 6a b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 15a b - 45a )cosh(x) + 2b - 3a b - 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 20a b - 60a )cosh(x) + (8b - 12a b - 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b + 15a b - 45a )cosh(x) + (12b - 18a b - 54a )cosh(x) +--R + +--R 2 2 +--R - 2b - 9a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 6a b - 18a )cosh(x) + (8b - 12a b - 36a )cosh(x) +--R + +--R 2 2 +--R (- 4b - 18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + a b - 3a )cosh(x) + (2b - 3a b - 9a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b - 9a b - 9a )cosh(x) - 2b - 5a b - 3a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (2b + 3a b + 2a b + 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 24a b + 16a b + 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((56b + 84a b + 56a b + 84a )cosh(x) + 8a b + 12a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (112b + 168a b + 112a b + 168a )cosh(x) +--R + +--R 2 3 +--R (48a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (140b + 210a b + 140a b + 210a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (120a b + 180a )cosh(x) - 4b - 2a b + 18a b + 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (112b + 168a b + 112a b + 168a )cosh(x) +--R + +--R 2 3 3 +--R (160a b + 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 16b - 8a b + 72a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (56b + 84a b + 56a b + 84a )cosh(x) +--R + +--R 2 3 4 +--R (120a b + 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 24b - 12a b + 108a b + 108a )cosh(x) + 8a b + 20a b +--R + +--R 3 +--R 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 24a b + 16a b + 24a )cosh(x) +--R + +--R 2 3 5 +--R (48a b + 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 16b - 8a b + 72a b + 72a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 40a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (2b + 3a b + 2a b + 3a )cosh(x) + (8a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 4b - 2a b + 18a b + 18a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (8a b + 20a b + 12a )cosh(x) + 2b + 7a b + 8a b + 3a +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 3 +--R - 2a sinh(x) - 8a cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12a cosh(x) - 2b - 2a)sinh(x) +--R + +--R 3 +--R (- 8a cosh(x) + (- 4b - 4a)cosh(x))sinh(x) +--R + +--R 4 2 +--R - 2a cosh(x) + (- 2b - 2a)cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R + +--R 2 2 4 +--R (- b - 2a b - a )sinh(x) +--R + +--R 2 2 3 +--R (- 4b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 12a b - 6a )cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((- 4b - 8a b - 4a )cosh(x) + (- 4a b - 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- b - 2a b - a )cosh(x) + (- 2a b - 2a )cosh(x) - b +--R + +--R 2 +--R - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- b + 2a b + a )sinh(x) +--R + +--R 2 2 5 +--R (- 6b + 12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 15b + 30a b + 15a )cosh(x) + b + 2a b + 3a )sinh(x) +--R + +--R 2 2 3 +--R (- 20b + 40a b + 20a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 15b + 30a b + 15a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (6b + 12a b + 18a )cosh(x) - b + 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 6b + 12a b + 6a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (4b + 8a b + 12a )cosh(x) + (- 2b + 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- b + 2a b + a )cosh(x) + (b + 2a b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- b + 2a b + 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 6 2 5 +--R (2a b + 2a )sinh(x) + (12a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R ((30a b + 30a )cosh(x) - 2b + 2a b + 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((40a b + 40a )cosh(x) + (- 8b + 8a b + 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (30a b + 30a )cosh(x) + (- 12b + 12a b + 24a )cosh(x) +--R + +--R 2 2 +--R 2b + 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (12a b + 12a )cosh(x) + (- 8b + 8a b + 16a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (2a b + 2a )cosh(x) + (- 2b + 2a b + 4a )cosh(x) +--R + +--R 2 2 2 +--R (2b + 4a b + 2a )cosh(x) +--R * +--R +-+ +--R \|b +--R / +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a )cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((4b - 4a )cosh(x) + (- 4a b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (b - a )cosh(x) + (- 2a b - 2a )cosh(x) - b - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (b + a )sinh(x) + (6b + 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((15b + 15a )cosh(x) - b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((20b + 20a )cosh(x) + (- 4b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (15b + 15a )cosh(x) + (- 6b + 18a )cosh(x) - b +--R + +--R 2 +--R 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (6b + 6a )cosh(x) + (- 4b + 12a )cosh(x) +--R + +--R 2 2 +--R (- 2b + 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (b + a )cosh(x) + (- b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- b + 2a b + 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 2 6 2 2 5 +--R (2b + a b - 3a )sinh(x) + (12b + 6a b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 15a b - 45a )cosh(x) + 2b - 3a b - 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 20a b - 60a )cosh(x) + (8b - 12a b - 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b + 15a b - 45a )cosh(x) + (12b - 18a b - 54a )cosh(x) +--R + +--R 2 2 +--R - 2b - 9a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 6a b - 18a )cosh(x) + (8b - 12a b - 36a )cosh(x) +--R + +--R 2 2 +--R (- 4b - 18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + a b - 3a )cosh(x) + (2b - 3a b - 9a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b - 9a b - 9a )cosh(x) - 2b - 5a b - 3a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (2b + 3a b + 2a b + 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 24a b + 16a b + 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((56b + 84a b + 56a b + 84a )cosh(x) + 8a b + 12a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (112b + 168a b + 112a b + 168a )cosh(x) +--R + +--R 2 3 +--R (48a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (140b + 210a b + 140a b + 210a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (120a b + 180a )cosh(x) - 4b - 2a b + 18a b + 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (112b + 168a b + 112a b + 168a )cosh(x) +--R + +--R 2 3 3 +--R (160a b + 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 16b - 8a b + 72a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (56b + 84a b + 56a b + 84a )cosh(x) +--R + +--R 2 3 4 +--R (120a b + 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 24b - 12a b + 108a b + 108a )cosh(x) + 8a b + 20a b +--R + +--R 3 +--R 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 24a b + 16a b + 24a )cosh(x) +--R + +--R 2 3 5 +--R (48a b + 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 16b - 8a b + 72a b + 72a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 40a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (2b + 3a b + 2a b + 3a )cosh(x) + (8a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 4b - 2a b + 18a b + 18a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (8a b + 20a b + 12a )cosh(x) + 2b + 7a b + 8a b + 3a +--R * +--R +-+ +--R \|b +--R * +--R +--------------+ +--R | 2 +--R coth(x)\|b tanh(x) + a +--R atanh(------------------------) +--R +-+ +--R \|b +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 12b - 12a b + 12a b + 12a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 30b - 30a b + 30a b + 30a )cosh(x) - 2b + 2a b +--R + +--R 2 3 +--R 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 40b - 40a b + 40a b + 40a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b + 8a b + 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 30b - 30a b + 30a b + 30a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 12b + 12a b + 60a b + 36a )cosh(x) + 2b + 10a b +--R + +--R 2 3 +--R 14a b + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 12b - 12a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b + 8a b + 40a b + 24a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b + 20a b + 28a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b + 2a b + 10a b + 6a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) + 2b + 6a b + 6a b + 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 2a b - 2a b - 2a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 16a b - 16a b - 16a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 56b - 56a b - 56a b - 56a )cosh(x) - 8a b - 8a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 112a b - 112a b - 112a )cosh(x) +--R + +--R 2 3 +--R (- 48a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 140a b - 140a b - 140a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 120a b - 120a )cosh(x) + 4b - 16a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 112a b - 112a b - 112a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 160a b - 160a )cosh(x) + (16b - 64a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 120a b - 120a )cosh(x) + (24b - 96a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R - 8a b - 16a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 16a b - 16a b - 16a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (- 48a b - 48a )cosh(x) + (16b - 64a b - 48a )cosh(x) +--R + +--R 2 2 3 +--R (- 16a b - 32a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- 2b - 2a b - 2a b - 2a )cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (4b - 16a b - 12a )cosh(x) + (- 8a b - 16a b - 8a )cosh(x) +--R + +--R 3 2 2 3 +--R - 2b - 6a b - 6a b - 2a +--R * +--R +-----+ +--R \|b + a +--R * +--R +-----+ +--R tanh(x)\|b + a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R + +--R 2 6 2 5 +--R (b - a b)sinh(x) + (6b - 6a b)cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((15b - 15a b)cosh(x) + b - 3a b)sinh(x) +--R + +--R 2 3 2 3 +--R ((20b - 20a b)cosh(x) + (4b - 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R ((15b - 15a b)cosh(x) + (6b - 18a b)cosh(x) - b - 3a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (6b - 6a b)cosh(x) + (4b - 12a b)cosh(x) +--R + +--R 2 +--R (- 2b - 6a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (b - a b)cosh(x) + (b - 3a b)cosh(x) + (- b - 3a b)cosh(x) +--R + +--R 2 +--R - b - a b +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R tanh(x)\|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 8 3 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 3 2 5 +--R ((56b + 56a b)cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 3 2 4 2 2 3 2 2 +--R ((70b + 70a b)cosh(x) + 60a b cosh(x) - 2b + 2a b + 6a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 5 2 3 +--R (56b + 56a b)cosh(x) + 80a b cosh(x) +--R + +--R 3 2 2 +--R (- 8b + 8a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 2 4 +--R (28b + 28a b)cosh(x) + 60a b cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 12b + 12a b + 36a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 7 2 5 +--R (8b + 8a b)cosh(x) + 24a b cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 8b + 8a b + 24a b)cosh(x) + (8a b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 8 2 6 +--R (b + a b)cosh(x) + 4a b cosh(x) +--R + +--R 3 2 2 4 2 2 2 3 +--R (- 2b + 2a b + 6a b)cosh(x) + (4a b + 4a b)cosh(x) + b +--R + +--R 2 2 +--R 2a b + a b +--R * +--R tanh(x) +--R * +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R + +--R 2 6 2 5 +--R - 2a b sinh(x) - 12a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (- 30a b cosh(x) + 4b - 2a b - 4a b)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (- 40a b cosh(x) + (16b - 8a b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R - 30a b cosh(x) + (24b - 12a b - 24a b)cosh(x) - 4b - 6a b +--R + +--R 2 +--R - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R - 12a b cosh(x) + (16b - 8a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (- 8b - 12a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R - 2a b cosh(x) + (4b - 2a b - 4a b)cosh(x) +--R + +--R 3 2 2 2 +--R (- 4b - 6a b - 2a b)cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 8 2 7 +--R 2a b sinh(x) + 16a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 6 +--R (56a b cosh(x) + 4b - 2a b + 6a b)sinh(x) +--R + +--R 2 3 3 2 2 5 +--R (112a b cosh(x) + (24b - 12a b + 36a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R 140a b cosh(x) + (60b - 30a b + 90a b)cosh(x) - 8b + 4a b +--R + +--R 2 +--R 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 112a b cosh(x) + (80b - 40a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 56a b cosh(x) + (60b - 30a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 48b + 24a b + 36a b)cosh(x) + 4b + 6a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 2 2 5 +--R 16a b cosh(x) + (24b - 12a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) + (8b + 12a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 2 2 6 +--R 2a b cosh(x) + (4b - 2a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 8b + 4a b + 6a b)cosh(x) + (4b + 6a b + 2a b)cosh(x) +--R * +--R +-----+ +--R \|b + a +--R / +--R 6 5 +--R (2b - 2a)sinh(x) + (12b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((30b - 30a)cosh(x) + 2b - 6a)sinh(x) +--R + +--R 3 3 +--R ((40b - 40a)cosh(x) + (8b - 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((30b - 30a)cosh(x) + (12b - 36a)cosh(x) - 2b - 6a)sinh(x) +--R + +--R 5 3 +--R ((12b - 12a)cosh(x) + (8b - 24a)cosh(x) + (- 4b - 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (2b - 2a)cosh(x) + (2b - 6a)cosh(x) + (- 2b - 6a)cosh(x) - 2b - 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (2b + 2a )sinh(x) + (16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((56b + 56a )cosh(x) + 8a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((112b + 112a )cosh(x) + 48a cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 4 +--R ((140b + 140a )cosh(x) + 120a cosh(x) - 4b + 4a b + 12a )sinh(x) +--R + +--R 2 2 5 2 3 +--R (112b + 112a )cosh(x) + 160a cosh(x) +--R + +--R 2 2 +--R (- 16b + 16a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 4 +--R (56b + 56a )cosh(x) + 120a cosh(x) +--R + +--R 2 2 2 2 +--R (- 24b + 24a b + 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 +--R (16b + 16a )cosh(x) + 48a cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b + 16a b + 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (2b + 2a )cosh(x) + 8a cosh(x) + (- 4b + 4a b + 12a )cosh(x) +--R + +--R 2 2 2 2 +--R (8a b + 8a )cosh(x) + 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 101 + +--S 102 of 508 +--d0319a:= D(m0319a,x) +--E 102 + +--S 103 of 508 +m0319b:= a0319.2-r0319 +--R +--R +--R (100) +--R 3 2 2 3 6 +--R (- b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) - b + a b + 5a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 20b - 20a b + 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 6b + 6a b + 30a b + 18a )cosh(x) + b + 5a b + 7a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- b + a b + 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + 5a b + 7a b + 3a )cosh(x) + b + 3a b + 3a b + a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- b - a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 28b - 28a b - 28a b - 28a )cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 +--R (- 24a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 70b - 70a b - 70a b - 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 60a b - 60a )cosh(x) + 2b - 8a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 80a b - 80a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 28b - 28a b - 28a b - 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 60a b - 60a )cosh(x) + (12b - 48a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R - 4a b - 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (- 24a b - 24a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- b - a b - a b - a )cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 3 +--R (2b - 8a b - 6a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) - b +--R + +--R 2 2 3 +--R - 3a b - 3a b - a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +-----+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|b + a +--R + +--R 3 2 2 3 6 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b + 15a b - 15a b - 15a )cosh(x) + b - a b - 5a b +--R + +--R 3 +--R - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b + 20a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 15a b - 15a b - 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) - b - 5a b - 7a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 10a b - 14a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 3 2 2 3 4 +--R (b + a b - a b - a )cosh(x) + (b - a b - 5a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- b - 5a b - 7a b - 3a )cosh(x) - b - 3a b - 3a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (b + a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (8b + 8a b + 8a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((28b + 28a b + 28a b + 28a )cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 +--R (24a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (70b + 70a b + 70a b + 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (60a b + 60a )cosh(x) - 2b + 8a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (80a b + 80a )cosh(x) + (- 8b + 32a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (28b + 28a b + 28a b + 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (60a b + 60a )cosh(x) + (- 12b + 48a b + 36a )cosh(x) +--R + +--R 2 2 3 +--R 4a b + 8a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 2 3 5 +--R (8b + 8a b + 8a b + 8a )cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 2 3 3 2 2 3 +--R (- 8b + 32a b + 24a )cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (b + a b + a b + a )cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 3 +--R (- 2b + 8a b + 6a )cosh(x) + (4a b + 8a b + 4a )cosh(x) + b +--R + +--R 2 2 3 +--R 3a b + 3a b + a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) - 2b - 2a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) - 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (- 8b + 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (- 4b + 2a)cosh(x) + 2b + 2a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 2 6 2 2 5 +--R (2b + a b - 3a )sinh(x) + (12b + 6a b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 15a b - 45a )cosh(x) + 2b - 3a b - 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 20a b - 60a )cosh(x) + (8b - 12a b - 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b + 15a b - 45a )cosh(x) + (12b - 18a b - 54a )cosh(x) +--R + +--R 2 2 +--R - 2b - 9a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 6a b - 18a )cosh(x) + (8b - 12a b - 36a )cosh(x) +--R + +--R 2 2 +--R (- 4b - 18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + a b - 3a )cosh(x) + (2b - 3a b - 9a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b - 9a b - 9a )cosh(x) - 2b - 5a b - 3a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (2b + 3a b + 2a b + 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 24a b + 16a b + 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((56b + 84a b + 56a b + 84a )cosh(x) + 8a b + 12a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (112b + 168a b + 112a b + 168a )cosh(x) +--R + +--R 2 3 +--R (48a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (140b + 210a b + 140a b + 210a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (120a b + 180a )cosh(x) - 4b - 2a b + 18a b + 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (112b + 168a b + 112a b + 168a )cosh(x) +--R + +--R 2 3 3 +--R (160a b + 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 16b - 8a b + 72a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (56b + 84a b + 56a b + 84a )cosh(x) +--R + +--R 2 3 4 +--R (120a b + 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 24b - 12a b + 108a b + 108a )cosh(x) + 8a b + 20a b +--R + +--R 3 +--R 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 24a b + 16a b + 24a )cosh(x) +--R + +--R 2 3 5 +--R (48a b + 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 16b - 8a b + 72a b + 72a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 40a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (2b + 3a b + 2a b + 3a )cosh(x) + (8a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 4b - 2a b + 18a b + 18a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (8a b + 20a b + 12a )cosh(x) + 2b + 7a b + 8a b + 3a +--R * +--R +-+ +--R \|b +--R * +--R +--------------+ +--R | 2 +--R coth(x)\|b tanh(x) + a +--R atanh(------------------------) +--R +-+ +--R \|b +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 12b - 12a b + 12a b + 12a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 30b - 30a b + 30a b + 30a )cosh(x) - 2b + 2a b +--R + +--R 2 3 +--R 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 40b - 40a b + 40a b + 40a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b + 8a b + 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 30b - 30a b + 30a b + 30a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 12b + 12a b + 60a b + 36a )cosh(x) + 2b + 10a b +--R + +--R 2 3 +--R 14a b + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 12b - 12a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b + 8a b + 40a b + 24a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b + 20a b + 28a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b + 2a b + 10a b + 6a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) + 2b + 6a b + 6a b + 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 2a b - 2a b - 2a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 16a b - 16a b - 16a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 56b - 56a b - 56a b - 56a )cosh(x) - 8a b - 8a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 112a b - 112a b - 112a )cosh(x) +--R + +--R 2 3 +--R (- 48a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 140a b - 140a b - 140a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 120a b - 120a )cosh(x) + 4b - 16a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 112a b - 112a b - 112a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 160a b - 160a )cosh(x) + (16b - 64a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 120a b - 120a )cosh(x) + (24b - 96a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R - 8a b - 16a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 16a b - 16a b - 16a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (- 48a b - 48a )cosh(x) + (16b - 64a b - 48a )cosh(x) +--R + +--R 2 2 3 +--R (- 16a b - 32a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- 2b - 2a b - 2a b - 2a )cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (4b - 16a b - 12a )cosh(x) + (- 8a b - 16a b - 8a )cosh(x) +--R + +--R 3 2 2 3 +--R - 2b - 6a b - 6a b - 2a +--R * +--R +-----+ +--R \|b + a +--R * +--R +-----+ +--R tanh(x)\|b + a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R + +--R 2 2 6 +--R (- 4b - 2a b + 6a )sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 12a b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 60b - 30a b + 90a )cosh(x) - 4b + 6a b + 18a )sinh(x) +--R + +--R 2 2 3 +--R (- 80b - 40a b + 120a )cosh(x) +--R + +--R 2 2 +--R (- 16b + 24a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 60b - 30a b + 90a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 24b + 36a b + 108a )cosh(x) + 4b + 18a b + 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 12a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 16b + 24a b + 72a )cosh(x) + (8b + 36a b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 4b - 2a b + 6a )cosh(x) + (- 4b + 6a b + 18a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (4b + 18a b + 18a )cosh(x) + 4b + 10a b + 6a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +---+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|- b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 4b - 6a b - 4a b - 6a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 32b - 48a b - 32a b - 48a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 +--R ((- 112b - 168a b - 112a b - 168a )cosh(x) - 16a b - 24a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 224b - 336a b - 224a b - 336a )cosh(x) +--R + +--R 2 3 +--R (- 96a b - 144a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 280b - 420a b - 280a b - 420a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 240a b - 360a )cosh(x) + 8b + 4a b - 36a b - 36a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 224b - 336a b - 224a b - 336a )cosh(x) +--R + +--R 2 3 3 +--R (- 320a b - 480a )cosh(x) +--R + +--R 3 2 2 3 +--R (32b + 16a b - 144a b - 144a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 112b - 168a b - 112a b - 168a )cosh(x) +--R + +--R 2 3 4 +--R (- 240a b - 360a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (48b + 24a b - 216a b - 216a )cosh(x) - 16a b - 40a b +--R + +--R 3 +--R - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 32b - 48a b - 32a b - 48a )cosh(x) +--R + +--R 2 3 5 +--R (- 96a b - 144a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (32b + 16a b - 144a b - 144a )cosh(x) +--R + +--R 2 2 3 +--R (- 32a b - 80a b - 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- 4b - 6a b - 4a b - 6a )cosh(x) + (- 16a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (8b + 4a b - 36a b - 36a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (- 16a b - 40a b - 24a )cosh(x) - 4b - 14a b - 16a b - 6a +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (- b - a)cosh(x) - b - a +--R / +--R 2 2 +---+ +-----+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|b + a +--R + +--R 2 6 2 5 +--R (b - a b)sinh(x) + (6b - 6a b)cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((15b - 15a b)cosh(x) + b - 3a b)sinh(x) +--R + +--R 2 3 2 3 +--R ((20b - 20a b)cosh(x) + (4b - 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R ((15b - 15a b)cosh(x) + (6b - 18a b)cosh(x) - b - 3a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (6b - 6a b)cosh(x) + (4b - 12a b)cosh(x) +--R + +--R 2 +--R (- 2b - 6a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (b - a b)cosh(x) + (b - 3a b)cosh(x) + (- b - 3a b)cosh(x) +--R + +--R 2 +--R - b - a b +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R tanh(x)\|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 8 3 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 3 2 5 +--R ((56b + 56a b)cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 3 2 4 2 2 3 2 2 +--R ((70b + 70a b)cosh(x) + 60a b cosh(x) - 2b + 2a b + 6a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 5 2 3 +--R (56b + 56a b)cosh(x) + 80a b cosh(x) +--R + +--R 3 2 2 +--R (- 8b + 8a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 2 4 +--R (28b + 28a b)cosh(x) + 60a b cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 12b + 12a b + 36a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 7 2 5 +--R (8b + 8a b)cosh(x) + 24a b cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 8b + 8a b + 24a b)cosh(x) + (8a b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 8 2 6 +--R (b + a b)cosh(x) + 4a b cosh(x) +--R + +--R 3 2 2 4 2 2 2 3 +--R (- 2b + 2a b + 6a b)cosh(x) + (4a b + 4a b)cosh(x) + b +--R + +--R 2 2 +--R 2a b + a b +--R * +--R tanh(x) +--R * +--R +--------------+ +--R | 2 +--R \|b tanh(x) + a +--R + +--R 2 6 2 5 +--R - 2a b sinh(x) - 12a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (- 30a b cosh(x) + 4b - 2a b - 4a b)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (- 40a b cosh(x) + (16b - 8a b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R - 30a b cosh(x) + (24b - 12a b - 24a b)cosh(x) - 4b - 6a b +--R + +--R 2 +--R - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R - 12a b cosh(x) + (16b - 8a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (- 8b - 12a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R - 2a b cosh(x) + (4b - 2a b - 4a b)cosh(x) +--R + +--R 3 2 2 2 +--R (- 4b - 6a b - 2a b)cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 8 2 7 +--R 2a b sinh(x) + 16a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 6 +--R (56a b cosh(x) + 4b - 2a b + 6a b)sinh(x) +--R + +--R 2 3 3 2 2 5 +--R (112a b cosh(x) + (24b - 12a b + 36a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R 140a b cosh(x) + (60b - 30a b + 90a b)cosh(x) - 8b + 4a b +--R + +--R 2 +--R 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 112a b cosh(x) + (80b - 40a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 56a b cosh(x) + (60b - 30a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 48b + 24a b + 36a b)cosh(x) + 4b + 6a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 2 2 5 +--R 16a b cosh(x) + (24b - 12a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) + (8b + 12a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 2 2 6 +--R 2a b cosh(x) + (4b - 2a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 8b + 4a b + 6a b)cosh(x) + (4b + 6a b + 2a b)cosh(x) +--R * +--R +-----+ +--R \|b + a +--R / +--R 6 5 +--R (2b - 2a)sinh(x) + (12b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((30b - 30a)cosh(x) + 2b - 6a)sinh(x) +--R + +--R 3 3 +--R ((40b - 40a)cosh(x) + (8b - 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((30b - 30a)cosh(x) + (12b - 36a)cosh(x) - 2b - 6a)sinh(x) +--R + +--R 5 3 +--R ((12b - 12a)cosh(x) + (8b - 24a)cosh(x) + (- 4b - 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (2b - 2a)cosh(x) + (2b - 6a)cosh(x) + (- 2b - 6a)cosh(x) - 2b - 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) - 2b + 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (2b + 2a )sinh(x) + (16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((56b + 56a )cosh(x) + 8a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((112b + 112a )cosh(x) + 48a cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 4 +--R ((140b + 140a )cosh(x) + 120a cosh(x) - 4b + 4a b + 12a )sinh(x) +--R + +--R 2 2 5 2 3 +--R (112b + 112a )cosh(x) + 160a cosh(x) +--R + +--R 2 2 +--R (- 16b + 16a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 4 +--R (56b + 56a )cosh(x) + 120a cosh(x) +--R + +--R 2 2 2 2 +--R (- 24b + 24a b + 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 +--R (16b + 16a )cosh(x) + 48a cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b + 16a b + 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (2b + 2a )cosh(x) + 8a cosh(x) + (- 4b + 4a b + 12a )cosh(x) +--R + +--R 2 2 2 2 +--R (8a b + 8a )cosh(x) + 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 103 + +--S 104 of 508 +--d0319b:= D(m0319b,x) +--E 104 + +--S 105 of 508 +t0320:= coth(a+b*x) +--R +--R +--R (101) coth(b x + a) +--R Type: Expression(Integer) +--E 105 + +--S 106 of 508 +r0320:= log(sinh(a+b*x))/b +--R +--R +--R log(sinh(b x + a)) +--R (102) ------------------ +--R b +--R Type: Expression(Integer) +--E 106 + +--S 107 of 508 +a0320:= integrate(t0320,x) +--R +--R +--R 2sinh(b x + a) +--R log(- -----------------------------) - b x +--R sinh(b x + a) - cosh(b x + a) +--R (103) ------------------------------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 107 + +--S 108 of 508 +m0320:= a0320-r0320 +--R +--R +--R 2sinh(b x + a) +--R - log(sinh(b x + a)) + log(- -----------------------------) - b x +--R sinh(b x + a) - cosh(b x + a) +--R (104) ----------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 108 + +--S 109 of 508 +d0320:= D(m0320,x) +--R +--R +--R (105) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 508 +t0321:= coth(a+b*x)^2 +--R +--R +--R 2 +--R (106) coth(b x + a) +--R Type: Expression(Integer) +--E 110 + +--S 111 of 508 +r0321:= x-coth(a+b*x)/b +--R +--R +--R - coth(b x + a) + b x +--R (107) --------------------- +--R b +--R Type: Expression(Integer) +--E 111 + +--S 112 of 508 +a0321:= integrate(t0321,x) +--R +--R +--R (b x + 1)sinh(b x + a) - cosh(b x + a) +--R (108) -------------------------------------- +--R b sinh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 112 + +--S 113 of 508 +m0321:= a0321-r0321 +--R +--R +--R (coth(b x + a) + 1)sinh(b x + a) - cosh(b x + a) +--R (109) ------------------------------------------------ +--R b sinh(b x + a) +--R Type: Expression(Integer) +--E 113 + +--S 114 of 508 +d0321:= D(m0321,x) +--R +--R +--R 2 2 2 +--R - coth(b x + a) sinh(b x + a) + cosh(b x + a) +--R (110) ----------------------------------------------- +--R 2 +--R sinh(b x + a) +--R Type: Expression(Integer) +--E 114 + +--S 115 of 508 +t0322:= coth(a+b*x)^4 +--R +--R +--R 4 +--R (111) coth(b x + a) +--R Type: Expression(Integer) +--E 115 + +--S 116 of 508 +r0322:= x-coth(a+b*x)/b-1/3*coth(a+b*x)^3/b +--R +--R +--R 3 +--R - coth(b x + a) - 3coth(b x + a) + 3b x +--R (112) ---------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 116 + +--S 117 of 508 +a0322:= integrate(t0322,x) +--R +--R +--R (113) +--R 3 2 +--R (3b x + 4)sinh(b x + a) - 12cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R ((9b x + 12)cosh(b x + a) - 9b x - 12)sinh(b x + a) - 4cosh(b x + a) +--R / +--R 3 2 +--R 3b sinh(b x + a) + (9b cosh(b x + a) - 9b)sinh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 117 + +--S 118 of 508 +m0322:= a0322-r0322 +--R +--R +--R (114) +--R 3 3 +--R (coth(b x + a) + 3coth(b x + a) + 4)sinh(b x + a) +--R + +--R 2 +--R - 12cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R (3cosh(b x + a) - 3)coth(b x + a) +--R + +--R 2 2 +--R (9cosh(b x + a) - 9)coth(b x + a) + 12cosh(b x + a) - 12 +--R * +--R sinh(b x + a) +--R + +--R 3 +--R - 4cosh(b x + a) +--R / +--R 3 2 +--R 3b sinh(b x + a) + (9b cosh(b x + a) - 9b)sinh(b x + a) +--R Type: Expression(Integer) +--E 118 + +--S 119 of 508 +d0322:= D(m0322,x) +--R +--R +--R (115) +--R 4 6 +--R (- coth(b x + a) - 3)sinh(b x + a) +--R + +--R 2 4 2 +--R ((- 6cosh(b x + a) + 6)coth(b x + a) + 18cosh(b x + a) + 6) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 4 2 4 +--R (- 9cosh(b x + a) + 18cosh(b x + a) - 9)coth(b x + a) +--R + +--R 4 2 +--R - 3cosh(b x + a) + 6cosh(b x + a) + 9 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 6 4 +--R 4cosh(b x + a) - 4cosh(b x + a) +--R / +--R 6 2 4 +--R sinh(b x + a) + (6cosh(b x + a) - 6)sinh(b x + a) +--R + +--R 4 2 2 +--R (9cosh(b x + a) - 18cosh(b x + a) + 9)sinh(b x + a) +--R Type: Expression(Integer) +--E 119 + +--S 120 of 508 +t0323:= coth(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (116) \|coth(b x + a) +--R Type: Expression(Integer) +--E 120 + +--S 121 of 508 +r0323:= -(atan(coth(a+b*x)^(1/2))-atanh(coth(a+b*x)^(1/2)))/b +--R +--R +--R +-------------+ +-------------+ +--R atanh(\|coth(b x + a) ) - atan(\|coth(b x + a) ) +--R (117) ------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 121 + +--S 122 of 508 +a0323:= integrate(t0323,x) +--R +--R +--R (118) +--R - +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 122 + +--S 123 of 508 +m0323:= a0323-r0323 +--R +--R +--R (119) +--R - +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R +-------------+ +-------------+ +--R - 2atanh(\|coth(b x + a) ) + 2atan(\|coth(b x + a) ) +--R + +--R 2 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R / +--R 2b +--R Type: Expression(Integer) +--E 123 + +--S 124 of 508 +d0323:= D(m0323,x) +--R +--R +--R (120) +--R 8 7 +--R - sinh(b x + a) - 18cosh(b x + a)sinh(b x + a) +--R + +--R 2 6 +--R (- 78cosh(b x + a) - 1)sinh(b x + a) +--R + +--R 3 5 +--R (- 154cosh(b x + a) - 8cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 4 +--R (- 160cosh(b x + a) - 9cosh(b x + a) + 1)sinh(b x + a) +--R + +--R 5 3 +--R (- 86cosh(b x + a) + 8cosh(b x + a) + 2cosh(b x + a)) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 18cosh(b x + a) + 13cosh(b x + a) - 4cosh(b x + a) + 1) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 7 3 8 +--R (2cosh(b x + a) - 2cosh(b x + a) )sinh(b x + a) + cosh(b x + a) +--R + +--R 6 4 2 +--R - 3cosh(b x + a) + 3cosh(b x + a) - cosh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 7 2 6 +--R 6cosh(b x + a)sinh(b x + a) + 42cosh(b x + a) sinh(b x + a) +--R + +--R 3 5 +--R (118cosh(b x + a) + 6cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 4 +--R (170cosh(b x + a) + 10cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 3 +--R (130cosh(b x + a) - 4cosh(b x + a) + 2cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 2 +--R (46cosh(b x + a) - 12cosh(b x + a) - 2cosh(b x + a) )sinh(b x + a) +--R + +--R 7 5 3 +--R 2cosh(b x + a) - 2cosh(b x + a) - 2cosh(b x + a) +--R + +--R 2cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 8 6 4 2 +--R - 2cosh(b x + a) + 2cosh(b x + a) + 2cosh(b x + a) - 2cosh(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R + +--R 7 +--R - 12cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 6 +--R - 64cosh(b x + a) coth(b x + a)sinh(b x + a) +--R + +--R 3 5 +--R (- 140cosh(b x + a) + 12cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 4 +--R (- 160cosh(b x + a) + 48cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (- 100cosh(b x + a) + 72cosh(b x + a) - 4cosh(b x + a)) +--R * +--R 3 +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 2 +--R (- 32cosh(b x + a) + 48cosh(b x + a) - 16cosh(b x + a) ) +--R * +--R 2 +--R coth(b x + a)sinh(b x + a) +--R + +--R 7 5 3 +--R - 4cosh(b x + a) + 12cosh(b x + a) - 12cosh(b x + a) +--R + +--R 4cosh(b x + a) +--R * +--R coth(b x + a)sinh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 7 +--R 4cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 6 +--R 32cosh(b x + a) coth(b x + a)sinh(b x + a) +--R + +--R 3 5 +--R 100cosh(b x + a) coth(b x + a)sinh(b x + a) +--R + +--R 4 2 4 +--R (160cosh(b x + a) - 24cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (140cosh(b x + a) - 72cosh(b x + a) + 4cosh(b x + a))coth(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (64cosh(b x + a) - 72cosh(b x + a) + 16cosh(b x + a) )coth(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R (12cosh(b x + a) - 24cosh(b x + a) + 12cosh(b x + a) )coth(b x + a) +--R * +--R sinh(b x + a) +--R / +--R 7 2 6 +--R 12cosh(b x + a)sinh(b x + a) + 64cosh(b x + a) sinh(b x + a) +--R + +--R 3 5 +--R (140cosh(b x + a) - 12cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 4 +--R (160cosh(b x + a) - 48cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (100cosh(b x + a) - 72cosh(b x + a) + 4cosh(b x + a)) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (32cosh(b x + a) - 48cosh(b x + a) + 16cosh(b x + a) ) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 4cosh(b x + a) - 12cosh(b x + a) + 12cosh(b x + a) +--R + +--R - 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 7 2 6 +--R - 4cosh(b x + a)sinh(b x + a) - 32cosh(b x + a) sinh(b x + a) +--R + +--R 3 5 +--R - 100cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 4 +--R (- 160cosh(b x + a) + 24cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 3 +--R (- 140cosh(b x + a) + 72cosh(b x + a) - 4cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 +--R (- 64cosh(b x + a) + 72cosh(b x + a) - 16cosh(b x + a) ) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R (- 12cosh(b x + a) + 24cosh(b x + a) - 12cosh(b x + a) )sinh(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R Type: Expression(Integer) +--E 124 + +--S 125 of 508 +t0324:= coth(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (121) coth(b x + a)\|coth(b x + a) +--R Type: Expression(Integer) +--E 125 + +--S 126 of 508 +r0324:= (atan(coth(a+b*x)^(1/2))+atanh(coth(a+b*x)^(1/2))-_ + 2*coth(a+b*x)^(1/2))/b +--R +--R +--R +-------------+ +-------------+ +-------------+ +--R atanh(\|coth(b x + a) ) + atan(\|coth(b x + a) ) - 2\|coth(b x + a) +--R (122) -------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 126 + +--S 127 of 508 +a0324:= integrate(t0324,x) +--R +--R +--R (123) +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) +--R + +--R 2 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) - 2 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R - 8 +--R / +--R 2 2 +--R 2b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) + 2b cosh(b x + a) +--R + +--R - 2b +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - 2b sinh(b x + a) - 4b cosh(b x + a)sinh(b x + a) - 2b cosh(b x + a) +--R + +--R 2b +--R Type: Union(Expression(Integer),...) +--E 127 + +--S 128 of 508 +m0324:= a0324-r0324 +--R +--R +--R (124) +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) +--R + +--R 2 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) - 2 +--R * +--R +-------------+ +--R atanh(\|coth(b x + a) ) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) +--R + +--R 2 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) - 2 +--R * +--R +-------------+ +--R atan(\|coth(b x + a) ) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) +--R + +--R 2 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) - 2 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R 4sinh(b x + a) + 8cosh(b x + a)sinh(b x + a) + 4cosh(b x + a) +--R + +--R - 4 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - 4sinh(b x + a) - 8cosh(b x + a)sinh(b x + a) - 4cosh(b x + a) + 4 +--R * +--R +-------------+ +--R \|coth(b x + a) +--R + +--R - 8 +--R / +--R 2 2 +--R 2b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) + 2b cosh(b x + a) +--R + +--R - 2b +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - 2b sinh(b x + a) - 4b cosh(b x + a)sinh(b x + a) - 2b cosh(b x + a) +--R + +--R 2b +--R Type: Expression(Integer) +--E 128 + +--S 129 of 508 +d0324:= D(m0324,x) +--R +--R +--R (125) +--R 13 12 +--R - sinh(b x + a) - 35cosh(b x + a)sinh(b x + a) +--R + +--R 2 11 +--R (- 310cosh(b x + a) - 3)sinh(b x + a) +--R + +--R 3 10 +--R (- 1378cosh(b x + a) - 63cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (- 3731cosh(b x + a) - 317cosh(b x + a) - 2)sinh(b x + a) +--R + +--R 5 3 +--R (- 6681cosh(b x + a) - 697cosh(b x + a) - 22cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 8196cosh(b x + a) - 670cosh(b x + a) - 40cosh(b x + a) +--R + +--R 2 +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 6924cosh(b x + a) + 42cosh(b x + a) + 24cosh(b x + a) +--R + +--R 10cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R - 3927cosh(b x + a) + 742cosh(b x + a) + 100cosh(b x + a) +--R + +--R 2 +--R - 6cosh(b x + a) + 3 +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R - 1381cosh(b x + a) + 718cosh(b x + a) + 28cosh(b x + a) +--R + +--R 3 +--R - 30cosh(b x + a) + 9cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R - 230cosh(b x + a) + 273cosh(b x + a) - 72cosh(b x + a) +--R + +--R 4 2 +--R 6cosh(b x + a) - 10cosh(b x + a) + 1 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R 14cosh(b x + a) + 5cosh(b x + a) - 40cosh(b x + a) +--R + +--R 5 3 +--R 30cosh(b x + a) - 14cosh(b x + a) + 5cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R 11cosh(b x + a) - 25cosh(b x + a) + 14cosh(b x + a) +--R + +--R 6 4 2 +--R - 2cosh(b x + a) + 7cosh(b x + a) - 5cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 13 11 9 +--R cosh(b x + a) - 5cosh(b x + a) + 10cosh(b x + a) +--R + +--R 7 5 3 +--R - 10cosh(b x + a) + 5cosh(b x + a) - cosh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 12 2 11 +--R 8cosh(b x + a)sinh(b x + a) + 116cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (700cosh(b x + a) + 20cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (2396cosh(b x + a) + 160cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (5244cosh(b x + a) + 508cosh(b x + a) + 16cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (7752cosh(b x + a) + 768cosh(b x + a) + 40cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 7896cosh(b x + a) + 392cosh(b x + a) - 8cosh(b x + a) +--R + +--R 8cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R (5496cosh(b x + a) - 448cosh(b x + a) - 88cosh(b x + a) ) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 2496cosh(b x + a) - 840cosh(b x + a) - 40cosh(b x + a) +--R + +--R 3 +--R - 24cosh(b x + a) + 8cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 644cosh(b x + a) - 512cosh(b x + a) + 56cosh(b x + a) +--R + +--R 2 +--R 4cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R 44cosh(b x + a) - 92cosh(b x + a) + 40cosh(b x + a) +--R + +--R 5 3 +--R 24cosh(b x + a) - 20cosh(b x + a) + 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R - 20cosh(b x + a) + 32cosh(b x + a) - 8cosh(b x + a) +--R + +--R 4 +--R - 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 13 11 9 +--R - 4cosh(b x + a) + 12cosh(b x + a) - 8cosh(b x + a) +--R + +--R 7 5 3 +--R - 8cosh(b x + a) + 12cosh(b x + a) - 4cosh(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R + +--R 2 12 +--R - 20cosh(b x + a)coth(b x + a) sinh(b x + a) +--R + +--R 2 2 11 +--R - 220cosh(b x + a) coth(b x + a) sinh(b x + a) +--R + +--R 3 2 10 +--R (- 1084cosh(b x + a) + 52cosh(b x + a))coth(b x + a) sinh(b x + a) +--R + +--R 4 2 2 +--R (- 3156cosh(b x + a) + 516cosh(b x + a) )coth(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 5 3 +--R (- 6024cosh(b x + a) + 2176cosh(b x + a) - 56cosh(b x + a)) +--R * +--R 2 8 +--R coth(b x + a) sinh(b x + a) +--R + +--R 6 4 2 +--R (- 7896cosh(b x + a) + 5152cosh(b x + a) - 504cosh(b x + a) ) +--R * +--R 2 7 +--R coth(b x + a) sinh(b x + a) +--R + +--R 7 5 3 +--R - 7224cosh(b x + a) + 7560cosh(b x + a) - 1720cosh(b x + a) +--R + +--R 40cosh(b x + a) +--R * +--R 2 6 +--R coth(b x + a) sinh(b x + a) +--R + +--R 8 6 4 +--R - 4584cosh(b x + a) + 7112cosh(b x + a) - 3000cosh(b x + a) +--R + +--R 2 +--R 280cosh(b x + a) +--R * +--R 2 5 +--R coth(b x + a) sinh(b x + a) +--R + +--R 9 7 5 +--R - 1956cosh(b x + a) + 4256cosh(b x + a) - 2920cosh(b x + a) +--R + +--R 3 +--R 640cosh(b x + a) - 20cosh(b x + a) +--R * +--R 2 4 +--R coth(b x + a) sinh(b x + a) +--R + +--R 10 8 6 +--R - 524cosh(b x + a) + 1536cosh(b x + a) - 1576cosh(b x + a) +--R + +--R 4 2 +--R 640cosh(b x + a) - 76cosh(b x + a) +--R * +--R 2 3 +--R coth(b x + a) sinh(b x + a) +--R + +--R 11 9 7 +--R - 76cosh(b x + a) + 292cosh(b x + a) - 424cosh(b x + a) +--R + +--R 5 3 +--R 280cosh(b x + a) - 76cosh(b x + a) + 4cosh(b x + a) +--R * +--R 2 2 +--R coth(b x + a) sinh(b x + a) +--R + +--R 12 10 8 +--R - 4cosh(b x + a) + 20cosh(b x + a) - 40cosh(b x + a) +--R + +--R 6 4 2 +--R 40cosh(b x + a) - 20cosh(b x + a) + 4cosh(b x + a) +--R * +--R 2 +--R coth(b x + a) sinh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 12 +--R 4cosh(b x + a)coth(b x + a) sinh(b x + a) +--R + +--R 2 2 11 +--R 76cosh(b x + a) coth(b x + a) sinh(b x + a) +--R + +--R 3 2 10 +--R (524cosh(b x + a) - 8cosh(b x + a))coth(b x + a) sinh(b x + a) +--R + +--R 4 2 2 9 +--R (1956cosh(b x + a) - 184cosh(b x + a) )coth(b x + a) sinh(b x + a) +--R + +--R 5 3 +--R (4584cosh(b x + a) - 1152cosh(b x + a) + 8cosh(b x + a)) +--R * +--R 2 8 +--R coth(b x + a) sinh(b x + a) +--R + +--R 6 4 2 +--R (7224cosh(b x + a) - 3584cosh(b x + a) + 200cosh(b x + a) ) +--R * +--R 2 7 +--R coth(b x + a) sinh(b x + a) +--R + +--R 7 5 3 +--R 7896cosh(b x + a) - 6608cosh(b x + a) + 1032cosh(b x + a) +--R + +--R - 8cosh(b x + a) +--R * +--R 2 6 +--R coth(b x + a) sinh(b x + a) +--R + +--R 8 6 4 +--R 6024cosh(b x + a) - 7728cosh(b x + a) + 2440cosh(b x + a) +--R + +--R 2 +--R - 128cosh(b x + a) +--R * +--R 2 5 +--R coth(b x + a) sinh(b x + a) +--R + +--R 9 7 5 +--R 3156cosh(b x + a) - 5824cosh(b x + a) + 3160cosh(b x + a) +--R + +--R 3 +--R - 464cosh(b x + a) + 4cosh(b x + a) +--R * +--R 2 4 +--R coth(b x + a) sinh(b x + a) +--R + +--R 10 8 6 +--R 1084cosh(b x + a) - 2752cosh(b x + a) + 2328cosh(b x + a) +--R + +--R 4 2 +--R - 704cosh(b x + a) + 44cosh(b x + a) +--R * +--R 2 3 +--R coth(b x + a) sinh(b x + a) +--R + +--R 11 9 7 +--R 220cosh(b x + a) - 744cosh(b x + a) + 920cosh(b x + a) +--R + +--R 5 3 +--R - 488cosh(b x + a) + 92cosh(b x + a) +--R * +--R 2 2 +--R coth(b x + a) sinh(b x + a) +--R + +--R 12 10 8 +--R 20cosh(b x + a) - 88cosh(b x + a) + 152cosh(b x + a) +--R + +--R 6 4 2 +--R - 128cosh(b x + a) + 52cosh(b x + a) - 8cosh(b x + a) +--R * +--R 2 +--R coth(b x + a) sinh(b x + a) +--R / +--R 12 2 11 +--R 20cosh(b x + a)sinh(b x + a) + 220cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (1084cosh(b x + a) - 52cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (3156cosh(b x + a) - 516cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (6024cosh(b x + a) - 2176cosh(b x + a) + 56cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (7896cosh(b x + a) - 5152cosh(b x + a) + 504cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 7224cosh(b x + a) - 7560cosh(b x + a) + 1720cosh(b x + a) +--R + +--R - 40cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 4584cosh(b x + a) - 7112cosh(b x + a) + 3000cosh(b x + a) +--R + +--R 2 +--R - 280cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 1956cosh(b x + a) - 4256cosh(b x + a) + 2920cosh(b x + a) +--R + +--R 3 +--R - 640cosh(b x + a) + 20cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 524cosh(b x + a) - 1536cosh(b x + a) + 1576cosh(b x + a) +--R + +--R 4 2 +--R - 640cosh(b x + a) + 76cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R 76cosh(b x + a) - 292cosh(b x + a) + 424cosh(b x + a) +--R + +--R 5 3 +--R - 280cosh(b x + a) + 76cosh(b x + a) - 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R 4cosh(b x + a) - 20cosh(b x + a) + 40cosh(b x + a) +--R + +--R 6 4 2 +--R - 40cosh(b x + a) + 20cosh(b x + a) - 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 12 2 11 +--R - 4cosh(b x + a)sinh(b x + a) - 76cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (- 524cosh(b x + a) + 8cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (- 1956cosh(b x + a) + 184cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 4584cosh(b x + a) + 1152cosh(b x + a) - 8cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 7224cosh(b x + a) + 3584cosh(b x + a) - 200cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 7896cosh(b x + a) + 6608cosh(b x + a) - 1032cosh(b x + a) +--R + +--R 8cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R - 6024cosh(b x + a) + 7728cosh(b x + a) - 2440cosh(b x + a) +--R + +--R 2 +--R 128cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R - 3156cosh(b x + a) + 5824cosh(b x + a) - 3160cosh(b x + a) +--R + +--R 3 +--R 464cosh(b x + a) - 4cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R - 1084cosh(b x + a) + 2752cosh(b x + a) - 2328cosh(b x + a) +--R + +--R 4 2 +--R 704cosh(b x + a) - 44cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R - 220cosh(b x + a) + 744cosh(b x + a) - 920cosh(b x + a) +--R + +--R 5 3 +--R 488cosh(b x + a) - 92cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R - 20cosh(b x + a) + 88cosh(b x + a) - 152cosh(b x + a) +--R + +--R 6 4 2 +--R 128cosh(b x + a) - 52cosh(b x + a) + 8cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R Type: Expression(Integer) +--E 129 + +--S 130 of 508 +t0325:= coth(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (126) coth(b x + a) \|coth(b x + a) +--R Type: Expression(Integer) +--E 130 + +--S 131 of 508 +r0325:= -1/3*(3*atan(coth(a+b*x)^(1/2))-3*atanh(coth(a+b*x)^(1/2))+_ + 2*coth(a+b*x)^(3/2))/b +--R +--R +--R (127) +--R +-------------+ +-------------+ +--R 3atanh(\|coth(b x + a) ) - 3atan(\|coth(b x + a) ) +--R + +--R +-------------+ +--R - 2coth(b x + a)\|coth(b x + a) +--R / +--R 3b +--R Type: Expression(Integer) +--E 131 + +--S 132 of 508 +a0325:= integrate(t0325,x) +--R +--R +--R (128) +--R 6 5 +--R - 6sinh(b x + a) - 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 90cosh(b x + a) + 15)sinh(b x + a) +--R + +--R 3 3 +--R (- 120cosh(b x + a) + 60cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 90cosh(b x + a) + 90cosh(b x + a) - 12)sinh(b x + a) +--R + +--R 5 3 +--R (- 36cosh(b x + a) + 60cosh(b x + a) - 24cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 6cosh(b x + a) + 15cosh(b x + a) - 12cosh(b x + a) + 3 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R 6sinh(b x + a) + 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (90cosh(b x + a) - 9)sinh(b x + a) +--R + +--R 3 3 +--R (120cosh(b x + a) - 36cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (90cosh(b x + a) - 54cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (36cosh(b x + a) - 36cosh(b x + a) )sinh(b x + a) + 6cosh(b x + a) +--R + +--R 4 +--R - 9cosh(b x + a) + 3 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) - 30)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) - 120cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) - 180cosh(b x + a) + 24)sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) - 120cosh(b x + a) + 48cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12cosh(b x + a) - 30cosh(b x + a) + 24cosh(b x + a) - 6 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) + 18)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) + 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12cosh(b x + a) + 18cosh(b x + a) - 6 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R 24sinh(b x + a) + 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (144cosh(b x + a) - 24)sinh(b x + a) +--R + +--R 3 4 +--R (96cosh(b x + a) - 48cosh(b x + a))sinh(b x + a) + 24cosh(b x + a) +--R + +--R 2 +--R - 24cosh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 4 3 +--R - 24sinh(b x + a) - 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 3 +--R - 144cosh(b x + a) sinh(b x + a) - 96cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R - 24cosh(b x + a) + 8 +--R / +--R 6 5 +--R 12b sinh(b x + a) + 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180b cosh(b x + a) - 30b)sinh(b x + a) +--R + +--R 3 3 +--R (240b cosh(b x + a) - 120b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180b cosh(b x + a) - 180b cosh(b x + a) + 24b)sinh(b x + a) +--R + +--R 5 3 +--R (72b cosh(b x + a) - 120b cosh(b x + a) + 48b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12b cosh(b x + a) - 30b cosh(b x + a) + 24b cosh(b x + a) - 6b +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R - 12b sinh(b x + a) - 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180b cosh(b x + a) + 18b)sinh(b x + a) +--R + +--R 3 3 +--R (- 240b cosh(b x + a) + 72b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180b cosh(b x + a) + 108b cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72b cosh(b x + a) + 72b cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12b cosh(b x + a) + 18b cosh(b x + a) - 6b +--R Type: Union(Expression(Integer),...) +--E 132 + +--S 133 of 508 +m0325:= a0325-r0325 +--R +--R +--R (129) +--R 6 5 +--R - 6sinh(b x + a) - 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 90cosh(b x + a) + 15)sinh(b x + a) +--R + +--R 3 3 +--R (- 120cosh(b x + a) + 60cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 90cosh(b x + a) + 90cosh(b x + a) - 12)sinh(b x + a) +--R + +--R 5 3 +--R (- 36cosh(b x + a) + 60cosh(b x + a) - 24cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 6cosh(b x + a) + 15cosh(b x + a) - 12cosh(b x + a) + 3 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R 6sinh(b x + a) + 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (90cosh(b x + a) - 9)sinh(b x + a) +--R + +--R 3 3 +--R (120cosh(b x + a) - 36cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (90cosh(b x + a) - 54cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (36cosh(b x + a) - 36cosh(b x + a) )sinh(b x + a) + 6cosh(b x + a) +--R + +--R 4 +--R - 9cosh(b x + a) + 3 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) + 30)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) + 120cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) + 180cosh(b x + a) - 24)sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) + 120cosh(b x + a) - 48cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 12cosh(b x + a) + 30cosh(b x + a) - 24cosh(b x + a) + 6 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) - 18)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) - 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) - 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (72cosh(b x + a) - 72cosh(b x + a) )sinh(b x + a) + 12cosh(b x + a) +--R + +--R 4 +--R - 18cosh(b x + a) + 6 +--R * +--R +-------------+ +--R atanh(\|coth(b x + a) ) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) - 30)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) - 120cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) - 180cosh(b x + a) + 24)sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) - 120cosh(b x + a) + 48cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12cosh(b x + a) - 30cosh(b x + a) + 24cosh(b x + a) - 6 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) + 18)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) + 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12cosh(b x + a) + 18cosh(b x + a) - 6 +--R * +--R +-------------+ +--R atan(\|coth(b x + a) ) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) - 30)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) - 120cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) - 180cosh(b x + a) + 24)sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) - 120cosh(b x + a) + 48cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12cosh(b x + a) - 30cosh(b x + a) + 24cosh(b x + a) - 6 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) + 18)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) + 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12cosh(b x + a) + 18cosh(b x + a) - 6 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 6 +--R 8coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R 48cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (120cosh(b x + a) - 20)coth(b x + a)sinh(b x + a) +--R + +--R 3 3 +--R (160cosh(b x + a) - 80cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 +--R (120cosh(b x + a) - 120cosh(b x + a) + 16)coth(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R (48cosh(b x + a) - 80cosh(b x + a) + 32cosh(b x + a)) +--R * +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 2 +--R (8cosh(b x + a) - 20cosh(b x + a) + 16cosh(b x + a) - 4) +--R * +--R coth(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 +--R - 8coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R - 48cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 120cosh(b x + a) + 12)coth(b x + a)sinh(b x + a) +--R + +--R 3 3 +--R (- 160cosh(b x + a) + 48cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 2 +--R (- 120cosh(b x + a) + 72cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (- 48cosh(b x + a) + 48cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R (- 8cosh(b x + a) + 12cosh(b x + a) - 4)coth(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R + +--R 4 3 +--R 24sinh(b x + a) + 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (144cosh(b x + a) - 24)sinh(b x + a) +--R + +--R 3 4 +--R (96cosh(b x + a) - 48cosh(b x + a))sinh(b x + a) + 24cosh(b x + a) +--R + +--R 2 +--R - 24cosh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 4 3 +--R - 24sinh(b x + a) - 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 3 +--R - 144cosh(b x + a) sinh(b x + a) - 96cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R - 24cosh(b x + a) + 8 +--R / +--R 6 5 +--R 12b sinh(b x + a) + 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180b cosh(b x + a) - 30b)sinh(b x + a) +--R + +--R 3 3 +--R (240b cosh(b x + a) - 120b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180b cosh(b x + a) - 180b cosh(b x + a) + 24b)sinh(b x + a) +--R + +--R 5 3 +--R (72b cosh(b x + a) - 120b cosh(b x + a) + 48b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12b cosh(b x + a) - 30b cosh(b x + a) + 24b cosh(b x + a) - 6b +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R - 12b sinh(b x + a) - 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180b cosh(b x + a) + 18b)sinh(b x + a) +--R + +--R 3 3 +--R (- 240b cosh(b x + a) + 72b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180b cosh(b x + a) + 108b cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72b cosh(b x + a) + 72b cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12b cosh(b x + a) + 18b cosh(b x + a) - 6b +--R Type: Expression(Integer) +--E 133 + +--S 134 of 508 +d0325:= D(m0325,x) +--R +--R +--R (130) +--R 19 18 +--R - 12sinh(b x + a) - 492cosh(b x + a)sinh(b x + a) +--R + +--R 2 17 +--R (- 6420cosh(b x + a) + 12)sinh(b x + a) +--R + +--R 3 16 +--R (- 45396cosh(b x + a) - 228cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 15 +--R (- 208368cosh(b x + a) - 4176cosh(b x + a) + 33)sinh(b x + a) +--R + +--R 5 3 +--R - 677616cosh(b x + a) - 28272cosh(b x + a) +--R + +--R 429cosh(b x + a) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 1640016cosh(b x + a) - 113184cosh(b x + a) +--R + +--R 2 +--R 4101cosh(b x + a) - 38 +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 3042000cosh(b x + a) - 309504cosh(b x + a) +--R + +--R 3 +--R 26625cosh(b x + a) - 618cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 4398888cosh(b x + a) - 620880cosh(b x + a) +--R + +--R 4 2 +--R 112125cosh(b x + a) - 3880cosh(b x + a) - 33 +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 5000424cosh(b x + a) - 954096cosh(b x + a) +--R + +--R 5 3 +--R 318681cosh(b x + a) - 13368cosh(b x + a) - 53cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 4471896cosh(b x + a) - 1156584cosh(b x + a) +--R + +--R 6 4 +--R 638913cosh(b x + a) - 29310cosh(b x + a) +--R + +--R 2 +--R - 1223cosh(b x + a) + 24 +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 3124056cosh(b x + a) - 1129128cosh(b x + a) +--R + +--R 7 5 +--R 932877cosh(b x + a) - 45426cosh(b x + a) +--R + +--R 3 +--R - 10731cosh(b x + a) + 624cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 1675440cosh(b x + a) - 899184cosh(b x + a) +--R + +--R 8 6 +--R 1012275cosh(b x + a) - 56256cosh(b x + a) +--R + +--R 4 2 +--R - 37930cosh(b x + a) + 3816cosh(b x + a) + 15 +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 666288cosh(b x + a) - 585936cosh(b x + a) +--R + +--R 9 7 +--R 825495cosh(b x + a) - 63360cosh(b x + a) +--R + +--R 5 3 +--R - 71890cosh(b x + a) + 11592cosh(b x + a) - 29cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 14 12 +--R - 182544cosh(b x + a) - 309504cosh(b x + a) +--R + +--R 10 8 +--R 507903cosh(b x + a) - 66306cosh(b x + a) +--R + +--R 6 4 +--R - 79758cosh(b x + a) + 20568cosh(b x + a) +--R + +--R 2 +--R - 537cosh(b x + a) + 2 +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 15 13 +--R - 27792cosh(b x + a) - 129312cosh(b x + a) +--R + +--R 11 9 +--R 235059cosh(b x + a) - 57710cosh(b x + a) +--R + +--R 7 5 +--R - 50678cosh(b x + a) + 21864cosh(b x + a) +--R + +--R 3 +--R - 1701cosh(b x + a) + 62cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 16 14 +--R 468cosh(b x + a) - 40944cosh(b x + a) +--R + +--R 12 10 +--R 80751cosh(b x + a) - 36888cosh(b x + a) +--R + +--R 8 6 +--R - 14501cosh(b x + a) + 12984cosh(b x + a) +--R + +--R 4 2 +--R - 2267cosh(b x + a) + 208cosh(b x + a) - 3 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 17 15 +--R 1140cosh(b x + a) - 9168cosh(b x + a) +--R + +--R 13 11 +--R 19875cosh(b x + a) - 15688cosh(b x + a) +--R + +--R 9 7 5 +--R 1815cosh(b x + a) + 3096cosh(b x + a) - 1215cosh(b x + a) +--R + +--R 3 +--R 160cosh(b x + a) - 15cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 18 16 +--R 204cosh(b x + a) - 1284cosh(b x + a) +--R + +--R 14 12 +--R 3195cosh(b x + a) - 3930cosh(b x + a) +--R + +--R 10 8 6 +--R 2373cosh(b x + a) - 528cosh(b x + a) - 27cosh(b x + a) +--R + +--R 4 2 +--R - 18cosh(b x + a) + 15cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 19 17 15 +--R 12cosh(b x + a) - 84cosh(b x + a) + 255cosh(b x + a) +--R + +--R 13 11 9 +--R - 438cosh(b x + a) + 465cosh(b x + a) - 312cosh(b x + a) +--R + +--R 7 5 3 +--R 129cosh(b x + a) - 30cosh(b x + a) + 3cosh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 18 2 17 +--R 96cosh(b x + a)sinh(b x + a) + 1968cosh(b x + a) sinh(b x + a) +--R + +--R 3 16 +--R (18192cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 15 +--R (101952cosh(b x + a) + 1440cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (390720cosh(b x + a) + 12096cosh(b x + a) + 60cosh(b x + a)) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (1091328cosh(b x + a) + 59232cosh(b x + a) - 420cosh(b x + a) ) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 2306304cosh(b x + a) + 193440cosh(b x + a) - 9288cosh(b x + a) +--R + +--R 408cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 8 6 +--R 3771456cosh(b x + a) + 453024cosh(b x + a) +--R + +--R 4 2 +--R - 57864cosh(b x + a) + 3308cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 9 7 +--R 4832256cosh(b x + a) + 796224cosh(b x + a) +--R + +--R 5 3 +--R - 203676cosh(b x + a) + 11556cosh(b x + a) + 180cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 10 8 +--R 4873440cosh(b x + a) + 1084512cosh(b x + a) +--R + +--R 6 4 2 +--R - 477180cosh(b x + a) + 23044cosh(b x + a) + 1704cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 11 9 +--R 3857568cosh(b x + a) + 1173744cosh(b x + a) +--R + +--R 7 5 3 +--R - 799920cosh(b x + a) + 31236cosh(b x + a) + 8468cosh(b x + a) +--R + +--R - 88cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 12 10 +--R 2368704cosh(b x + a) + 1029600cosh(b x + a) +--R + +--R 8 6 +--R - 996336cosh(b x + a) + 38520cosh(b x + a) +--R + +--R 4 2 +--R 26528cosh(b x + a) - 904cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 13 11 +--R 1100736cosh(b x + a) + 741312cosh(b x + a) +--R + +--R 9 7 +--R - 939708cosh(b x + a) + 55272cosh(b x + a) +--R + +--R 5 3 +--R 53928cosh(b x + a) - 4744cosh(b x + a) + 52cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 14 12 +--R 368256cosh(b x + a) + 438048cosh(b x + a) +--R + +--R 10 8 +--R - 674652cosh(b x + a) + 75336cosh(b x + a) +--R + +--R 6 4 2 +--R 71344cosh(b x + a) - 13448cosh(b x + a) + 588cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 15 13 +--R 78720cosh(b x + a) + 208416cosh(b x + a) +--R + +--R 11 9 +--R - 365640cosh(b x + a) + 75744cosh(b x + a) +--R + +--R 7 5 3 +--R 60424cosh(b x + a) - 21560cosh(b x + a) + 1856cosh(b x + a) +--R + +--R - 8cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 16 14 +--R 6336cosh(b x + a) + 76512cosh(b x + a) +--R + +--R 12 10 +--R - 145800cosh(b x + a) + 51036cosh(b x + a) +--R + +--R 8 6 4 +--R 31008cosh(b x + a) - 19928cosh(b x + a) + 2760cosh(b x + a) +--R + +--R 2 +--R - 4cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 17 15 +--R - 1632cosh(b x + a) + 20160cosh(b x + a) +--R + +--R 13 11 +--R - 40548cosh(b x + a) + 21812cosh(b x + a) +--R + +--R 9 7 5 +--R 8228cosh(b x + a) - 10264cosh(b x + a) + 2244cosh(b x + a) +--R + +--R 3 +--R 4cosh(b x + a) - 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 18 16 14 +--R - 528cosh(b x + a) + 3360cosh(b x + a) - 7044cosh(b x + a) +--R + +--R 12 10 8 +--R 5364cosh(b x + a) + 488cosh(b x + a) - 2584cosh(b x + a) +--R + +--R 6 4 +--R 1004cosh(b x + a) - 60cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 19 17 15 +--R - 48cosh(b x + a) + 264cosh(b x + a) - 576cosh(b x + a) +--R + +--R 13 11 9 +--R 580cosh(b x + a) - 156cosh(b x + a) - 208cosh(b x + a) +--R + +--R 7 5 3 +--R 200cosh(b x + a) - 60cosh(b x + a) + 4cosh(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R + +--R 3 18 +--R - 240cosh(b x + a)coth(b x + a) sinh(b x + a) +--R + +--R 2 3 17 +--R - 4080cosh(b x + a) coth(b x + a) sinh(b x + a) +--R + +--R 3 3 +--R (- 32448cosh(b x + a) + 720cosh(b x + a))coth(b x + a) +--R * +--R 16 +--R sinh(b x + a) +--R + +--R 4 2 3 +--R (- 160320cosh(b x + a) + 11760cosh(b x + a) )coth(b x + a) +--R * +--R 15 +--R sinh(b x + a) +--R + +--R 5 3 +--R (- 551040cosh(b x + a) + 87696cosh(b x + a) - 732cosh(b x + a)) +--R * +--R 3 14 +--R coth(b x + a) sinh(b x + a) +--R + +--R 6 4 +--R - 1397760cosh(b x + a) + 397488cosh(b x + a) +--R + +--R 2 +--R - 12828cosh(b x + a) +--R * +--R 3 13 +--R coth(b x + a) sinh(b x + a) +--R + +--R 7 5 +--R - 2708160cosh(b x + a) + 1227408cosh(b x + a) +--R + +--R 3 +--R - 93816cosh(b x + a) + 312cosh(b x + a) +--R * +--R 3 12 +--R coth(b x + a) sinh(b x + a) +--R + +--R 8 6 +--R - 4090944cosh(b x + a) + 2738736cosh(b x + a) +--R + +--R 4 2 +--R - 394680cosh(b x + a) + 7464cosh(b x + a) +--R * +--R 3 11 +--R coth(b x + a) sinh(b x + a) +--R + +--R 9 7 +--R - 4873440cosh(b x + a) + 4564560cosh(b x + a) +--R + +--R 5 3 +--R - 1085700cosh(b x + a) + 54888cosh(b x + a) - 84cosh(b x + a) +--R * +--R 3 10 +--R coth(b x + a) sinh(b x + a) +--R + +--R 10 8 +--R - 4598880cosh(b x + a) + 5786352cosh(b x + a) +--R + +--R 6 4 2 +--R - 2082564cosh(b x + a) + 209592cosh(b x + a) - 2676cosh(b x + a) +--R * +--R 3 9 +--R coth(b x + a) sinh(b x + a) +--R + +--R 11 9 +--R - 3432000cosh(b x + a) + 5621616cosh(b x + a) +--R + +--R 7 5 +--R - 2881296cosh(b x + a) + 493488cosh(b x + a) +--R + +--R 3 +--R - 18240cosh(b x + a) - 48cosh(b x + a) +--R * +--R 3 8 +--R coth(b x + a) sinh(b x + a) +--R + +--R 12 10 +--R - 2009280cosh(b x + a) + 4180176cosh(b x + a) +--R + +--R 8 6 +--R - 2919312cosh(b x + a) + 773136cosh(b x + a) +--R + +--R 4 2 +--R - 59808cosh(b x + a) - 48cosh(b x + a) +--R * +--R 3 7 +--R coth(b x + a) sinh(b x + a) +--R + +--R 13 11 +--R - 908544cosh(b x + a) + 2354352cosh(b x + a) +--R + +--R 9 7 +--R - 2168100cosh(b x + a) + 833616cosh(b x + a) +--R + +--R 5 3 +--R - 115080cosh(b x + a) + 1728cosh(b x + a) + 108cosh(b x + a) +--R * +--R 3 6 +--R coth(b x + a) sinh(b x + a) +--R + +--R 14 12 +--R - 309120cosh(b x + a) + 982800cosh(b x + a) +--R + +--R 10 8 +--R - 1164900cosh(b x + a) + 623088cosh(b x + a) +--R + +--R 6 4 2 +--R - 139944cosh(b x + a) + 7680cosh(b x + a) + 396cosh(b x + a) +--R * +--R 3 5 +--R coth(b x + a) sinh(b x + a) +--R + +--R 15 13 +--R - 75840cosh(b x + a) + 292656cosh(b x + a) +--R + +--R 11 9 +--R - 439032cosh(b x + a) + 317592cosh(b x + a) +--R + +--R 7 5 3 +--R - 109536cosh(b x + a) + 14160cosh(b x + a) + 24cosh(b x + a) +--R + +--R - 24cosh(b x + a) +--R * +--R 3 4 +--R coth(b x + a) sinh(b x + a) +--R + +--R 16 14 +--R - 12480cosh(b x + a) + 58128cosh(b x + a) +--R + +--R 12 10 +--R - 109368cosh(b x + a) + 105288cosh(b x + a) +--R + +--R 8 6 4 +--R - 53760cosh(b x + a) + 13392cosh(b x + a) - 1224cosh(b x + a) +--R + +--R 2 +--R 24cosh(b x + a) +--R * +--R 3 3 +--R coth(b x + a) sinh(b x + a) +--R + +--R 17 15 +--R - 1200cosh(b x + a) + 6768cosh(b x + a) +--R + +--R 13 11 +--R - 15996cosh(b x + a) + 20424cosh(b x + a) +--R + +--R 9 7 5 +--R - 15108cosh(b x + a) + 6432cosh(b x + a) - 1476cosh(b x + a) +--R + +--R 3 +--R 168cosh(b x + a) - 12cosh(b x + a) +--R * +--R 3 2 +--R coth(b x + a) sinh(b x + a) +--R + +--R 18 16 14 +--R - 48cosh(b x + a) + 336cosh(b x + a) - 1020cosh(b x + a) +--R + +--R 12 10 8 +--R 1752cosh(b x + a) - 1860cosh(b x + a) + 1248cosh(b x + a) +--R + +--R 6 4 2 +--R - 516cosh(b x + a) + 120cosh(b x + a) - 12cosh(b x + a) +--R * +--R 3 +--R coth(b x + a) sinh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 3 18 +--R 48cosh(b x + a)coth(b x + a) sinh(b x + a) +--R + +--R 2 3 17 +--R 1200cosh(b x + a) coth(b x + a) sinh(b x + a) +--R + +--R 3 3 16 +--R (12480cosh(b x + a) - 96cosh(b x + a))coth(b x + a) sinh(b x + a) +--R + +--R 4 2 3 15 +--R (75840cosh(b x + a) - 3168cosh(b x + a) )coth(b x + a) sinh(b x + a) +--R + +--R 5 3 +--R (309120cosh(b x + a) - 33888cosh(b x + a) + 60cosh(b x + a)) +--R * +--R 3 14 +--R coth(b x + a) sinh(b x + a) +--R + +--R 6 4 2 +--R (908544cosh(b x + a) - 195936cosh(b x + a) + 3516cosh(b x + a) ) +--R * +--R 3 13 +--R coth(b x + a) sinh(b x + a) +--R + +--R 7 5 3 +--R 2009280cosh(b x + a) - 730080cosh(b x + a) + 38328cosh(b x + a) +--R + +--R - 36cosh(b x + a) +--R * +--R 3 12 +--R coth(b x + a) sinh(b x + a) +--R + +--R 8 6 4 +--R 3432000cosh(b x + a) - 1908192cosh(b x + a) + 206712cosh(b x + a) +--R + +--R 2 +--R - 2172cosh(b x + a) +--R * +--R 3 11 +--R coth(b x + a) sinh(b x + a) +--R + +--R 9 7 5 +--R 4598880cosh(b x + a) - 3665376cosh(b x + a) + 689700cosh(b x + a) +--R + +--R 3 +--R - 22764cosh(b x + a) +--R * +--R 3 10 +--R coth(b x + a) sinh(b x + a) +--R + +--R 10 8 +--R 4873440cosh(b x + a) - 5312736cosh(b x + a) +--R + +--R 6 4 2 +--R 1566180cosh(b x + a) - 113076cosh(b x + a) + 432cosh(b x + a) +--R * +--R 3 9 +--R coth(b x + a) sinh(b x + a) +--R + +--R 11 9 +--R 4090944cosh(b x + a) - 5889312cosh(b x + a) +--R + +--R 7 5 3 +--R 2539152cosh(b x + a) - 333864cosh(b x + a) + 6624cosh(b x + a) +--R + +--R 48cosh(b x + a) +--R * +--R 3 8 +--R coth(b x + a) sinh(b x + a) +--R + +--R 12 10 +--R 2708160cosh(b x + a) - 5010720cosh(b x + a) +--R + +--R 8 6 4 +--R 3008016cosh(b x + a) - 643608cosh(b x + a) + 34272cosh(b x + a) +--R + +--R 2 +--R 216cosh(b x + a) +--R * +--R 3 7 +--R coth(b x + a) sinh(b x + a) +--R + +--R 13 11 +--R 1397760cosh(b x + a) - 3253536cosh(b x + a) +--R + +--R 9 7 5 +--R 2621124cosh(b x + a) - 845208cosh(b x + a) + 90720cosh(b x + a) +--R + +--R 3 +--R - 960cosh(b x + a) - 12cosh(b x + a) +--R * +--R 3 6 +--R coth(b x + a) sinh(b x + a) +--R + +--R 14 12 +--R 551040cosh(b x + a) - 1586208cosh(b x + a) +--R + +--R 10 8 6 +--R 1666500cosh(b x + a) - 765864cosh(b x + a) + 141120cosh(b x + a) +--R + +--R 4 2 +--R - 6360cosh(b x + a) - 36cosh(b x + a) +--R * +--R 3 5 +--R coth(b x + a) sinh(b x + a) +--R + +--R 15 13 11 +--R 160320cosh(b x + a) - 562848cosh(b x + a) + 753720cosh(b x + a) +--R + +--R 9 7 5 +--R - 473076cosh(b x + a) + 135072cosh(b x + a) - 13200cosh(b x + a) +--R + +--R 3 +--R 24cosh(b x + a) - 12cosh(b x + a) +--R * +--R 3 4 +--R coth(b x + a) sinh(b x + a) +--R + +--R 16 14 12 +--R 32448cosh(b x + a) - 137376cosh(b x + a) + 230136cosh(b x + a) +--R + +--R 10 8 6 +--R - 190764cosh(b x + a) + 78624cosh(b x + a) - 13272cosh(b x + a) +--R + +--R 4 2 +--R 168cosh(b x + a) + 36cosh(b x + a) +--R * +--R 3 3 +--R coth(b x + a) sinh(b x + a) +--R + +--R 17 15 13 +--R 4080cosh(b x + a) - 20640cosh(b x + a) + 42588cosh(b x + a) +--R + +--R 11 9 7 +--R - 45372cosh(b x + a) + 25632cosh(b x + a) - 6624cosh(b x + a) +--R + +--R 5 3 +--R 180cosh(b x + a) + 156cosh(b x + a) +--R * +--R 3 2 +--R coth(b x + a) sinh(b x + a) +--R + +--R 18 16 14 +--R 240cosh(b x + a) - 1440cosh(b x + a) + 3612cosh(b x + a) +--R + +--R 12 10 8 +--R - 4836cosh(b x + a) + 3600cosh(b x + a) - 1320cosh(b x + a) +--R + +--R 6 4 2 +--R 60cosh(b x + a) + 108cosh(b x + a) - 24cosh(b x + a) +--R * +--R 3 +--R coth(b x + a) sinh(b x + a) +--R / +--R 18 2 17 +--R 240cosh(b x + a)sinh(b x + a) + 4080cosh(b x + a) sinh(b x + a) +--R + +--R 3 16 +--R (32448cosh(b x + a) - 720cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 15 +--R (160320cosh(b x + a) - 11760cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (551040cosh(b x + a) - 87696cosh(b x + a) + 732cosh(b x + a)) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 6 4 +--R 1397760cosh(b x + a) - 397488cosh(b x + a) +--R + +--R 2 +--R 12828cosh(b x + a) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 7 5 +--R 2708160cosh(b x + a) - 1227408cosh(b x + a) +--R + +--R 3 +--R 93816cosh(b x + a) - 312cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 8 6 +--R 4090944cosh(b x + a) - 2738736cosh(b x + a) +--R + +--R 4 2 +--R 394680cosh(b x + a) - 7464cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 9 7 +--R 4873440cosh(b x + a) - 4564560cosh(b x + a) +--R + +--R 5 3 +--R 1085700cosh(b x + a) - 54888cosh(b x + a) + 84cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 10 8 +--R 4598880cosh(b x + a) - 5786352cosh(b x + a) +--R + +--R 6 4 2 +--R 2082564cosh(b x + a) - 209592cosh(b x + a) + 2676cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 11 9 +--R 3432000cosh(b x + a) - 5621616cosh(b x + a) +--R + +--R 7 5 +--R 2881296cosh(b x + a) - 493488cosh(b x + a) +--R + +--R 3 +--R 18240cosh(b x + a) + 48cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 12 10 +--R 2009280cosh(b x + a) - 4180176cosh(b x + a) +--R + +--R 8 6 +--R 2919312cosh(b x + a) - 773136cosh(b x + a) +--R + +--R 4 2 +--R 59808cosh(b x + a) + 48cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 13 11 +--R 908544cosh(b x + a) - 2354352cosh(b x + a) +--R + +--R 9 7 +--R 2168100cosh(b x + a) - 833616cosh(b x + a) +--R + +--R 5 3 +--R 115080cosh(b x + a) - 1728cosh(b x + a) - 108cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 14 12 +--R 309120cosh(b x + a) - 982800cosh(b x + a) +--R + +--R 10 8 +--R 1164900cosh(b x + a) - 623088cosh(b x + a) +--R + +--R 6 4 2 +--R 139944cosh(b x + a) - 7680cosh(b x + a) - 396cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 15 13 +--R 75840cosh(b x + a) - 292656cosh(b x + a) +--R + +--R 11 9 +--R 439032cosh(b x + a) - 317592cosh(b x + a) +--R + +--R 7 5 3 +--R 109536cosh(b x + a) - 14160cosh(b x + a) - 24cosh(b x + a) +--R + +--R 24cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 16 14 +--R 12480cosh(b x + a) - 58128cosh(b x + a) +--R + +--R 12 10 +--R 109368cosh(b x + a) - 105288cosh(b x + a) +--R + +--R 8 6 4 +--R 53760cosh(b x + a) - 13392cosh(b x + a) + 1224cosh(b x + a) +--R + +--R 2 +--R - 24cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 17 15 +--R 1200cosh(b x + a) - 6768cosh(b x + a) +--R + +--R 13 11 +--R 15996cosh(b x + a) - 20424cosh(b x + a) +--R + +--R 9 7 5 +--R 15108cosh(b x + a) - 6432cosh(b x + a) + 1476cosh(b x + a) +--R + +--R 3 +--R - 168cosh(b x + a) + 12cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 18 16 14 +--R 48cosh(b x + a) - 336cosh(b x + a) + 1020cosh(b x + a) +--R + +--R 12 10 +--R - 1752cosh(b x + a) + 1860cosh(b x + a) +--R + +--R 8 6 4 +--R - 1248cosh(b x + a) + 516cosh(b x + a) - 120cosh(b x + a) +--R + +--R 2 +--R 12cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 18 2 17 +--R - 48cosh(b x + a)sinh(b x + a) - 1200cosh(b x + a) sinh(b x + a) +--R + +--R 3 16 +--R (- 12480cosh(b x + a) + 96cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 15 +--R (- 75840cosh(b x + a) + 3168cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 309120cosh(b x + a) + 33888cosh(b x + a) - 60cosh(b x + a)) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 908544cosh(b x + a) + 195936cosh(b x + a) - 3516cosh(b x + a) ) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 2009280cosh(b x + a) + 730080cosh(b x + a) +--R + +--R 3 +--R - 38328cosh(b x + a) + 36cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 3432000cosh(b x + a) + 1908192cosh(b x + a) +--R + +--R 4 2 +--R - 206712cosh(b x + a) + 2172cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 4598880cosh(b x + a) + 3665376cosh(b x + a) +--R + +--R 5 3 +--R - 689700cosh(b x + a) + 22764cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 4873440cosh(b x + a) + 5312736cosh(b x + a) +--R + +--R 6 4 2 +--R - 1566180cosh(b x + a) + 113076cosh(b x + a) - 432cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 4090944cosh(b x + a) + 5889312cosh(b x + a) +--R + +--R 7 5 3 +--R - 2539152cosh(b x + a) + 333864cosh(b x + a) - 6624cosh(b x + a) +--R + +--R - 48cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 2708160cosh(b x + a) + 5010720cosh(b x + a) +--R + +--R 8 6 +--R - 3008016cosh(b x + a) + 643608cosh(b x + a) +--R + +--R 4 2 +--R - 34272cosh(b x + a) - 216cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 1397760cosh(b x + a) + 3253536cosh(b x + a) +--R + +--R 9 7 +--R - 2621124cosh(b x + a) + 845208cosh(b x + a) +--R + +--R 5 3 +--R - 90720cosh(b x + a) + 960cosh(b x + a) + 12cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 14 12 +--R - 551040cosh(b x + a) + 1586208cosh(b x + a) +--R + +--R 10 8 +--R - 1666500cosh(b x + a) + 765864cosh(b x + a) +--R + +--R 6 4 2 +--R - 141120cosh(b x + a) + 6360cosh(b x + a) + 36cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 15 13 +--R - 160320cosh(b x + a) + 562848cosh(b x + a) +--R + +--R 11 9 +--R - 753720cosh(b x + a) + 473076cosh(b x + a) +--R + +--R 7 5 3 +--R - 135072cosh(b x + a) + 13200cosh(b x + a) - 24cosh(b x + a) +--R + +--R 12cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 16 14 +--R - 32448cosh(b x + a) + 137376cosh(b x + a) +--R + +--R 12 10 +--R - 230136cosh(b x + a) + 190764cosh(b x + a) +--R + +--R 8 6 4 +--R - 78624cosh(b x + a) + 13272cosh(b x + a) - 168cosh(b x + a) +--R + +--R 2 +--R - 36cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 17 15 13 +--R - 4080cosh(b x + a) + 20640cosh(b x + a) - 42588cosh(b x + a) +--R + +--R 11 9 7 +--R 45372cosh(b x + a) - 25632cosh(b x + a) + 6624cosh(b x + a) +--R + +--R 5 3 +--R - 180cosh(b x + a) - 156cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 18 16 14 +--R - 240cosh(b x + a) + 1440cosh(b x + a) - 3612cosh(b x + a) +--R + +--R 12 10 8 +--R 4836cosh(b x + a) - 3600cosh(b x + a) + 1320cosh(b x + a) +--R + +--R 6 4 2 +--R - 60cosh(b x + a) - 108cosh(b x + a) + 24cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R Type: Expression(Integer) +--E 134 + +--S 135 of 508 +t0326:= 1/coth(a+b*x)^(3/2) +--R +--R +--R 1 +--R (131) ----------------------------- +--R +-------------+ +--R coth(b x + a)\|coth(b x + a) +--R Type: Expression(Integer) +--E 135 + +--S 136 of 508 +r0326:= -atan(coth(a+b*x)^(1/2))/b+atanh(coth(a+b*x)^(1/2))/b-_ + 2/b/coth(a+b*x)^(1/2) +--R +--R +--R (132) +--R +-------------+ +-------------+ +--R \|coth(b x + a) atanh(\|coth(b x + a) ) +--R + +--R +-------------+ +-------------+ +--R - \|coth(b x + a) atan(\|coth(b x + a) ) - 2 +--R / +--R +-------------+ +--R b\|coth(b x + a) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 508 +a0326:= integrate(t0326,x) +--R +--R +--R (133) +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) + 1 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) +--R + +--R - 2 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) - 2 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 8 +--R / +--R 2 2 +--R 2b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) + 2b cosh(b x + a) +--R + +--R - 2b +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - 2b sinh(b x + a) - 4b cosh(b x + a)sinh(b x + a) - 2b cosh(b x + a) +--R + +--R - 2b +--R Type: Union(Expression(Integer),...) +--E 137 + +--S 138 of 508 +m0326:= a0326-r0326 +--R +--R +--R (134) +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) + 1 +--R * +--R +-------------+ +--R \|coth(b x + a) +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) +--R + +--R 2 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) + 2 +--R * +--R +-------------+ +-------------+ +--R \|coth(b x + a) atanh(\|coth(b x + a) ) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) +--R + +--R - 2 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) - 2 +--R * +--R +-------------+ +-------------+ +--R \|coth(b x + a) atan(\|coth(b x + a) ) +--R + +--R 2 2 +--R 2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) +--R + +--R - 2 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - 2sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) - 2cosh(b x + a) - 2 +--R * +--R +-------------+ +--R \|coth(b x + a) +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R +-------------+ +--R 8\|coth(b x + a) +--R + +--R 2 2 +--R (4sinh(b x + a) + 8cosh(b x + a)sinh(b x + a) + 4cosh(b x + a) - 4) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - 4sinh(b x + a) - 8cosh(b x + a)sinh(b x + a) - 4cosh(b x + a) - 4 +--R / +--R 2 +--R 2b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R 2b cosh(b x + a) - 2b +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - 2b sinh(b x + a) - 4b cosh(b x + a)sinh(b x + a) - 2b cosh(b x + a) +--R + +--R - 2b +--R * +--R +-------------+ +--R \|coth(b x + a) +--R Type: Expression(Integer) +--E 138 + +--S 139 of 508 +d0326:= D(m0326,x) +--R +--R +--R (135) +--R 13 +--R - coth(b x + a)sinh(b x + a) +--R + +--R 12 +--R - 35cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 11 +--R (- 310cosh(b x + a) + 5)coth(b x + a)sinh(b x + a) +--R + +--R 3 +--R (- 1378cosh(b x + a) + 145cosh(b x + a))coth(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 3731cosh(b x + a) + 1035cosh(b x + a) - 10)coth(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 5 3 +--R (- 6681cosh(b x + a) + 3591cosh(b x + a) - 230cosh(b x + a)) +--R * +--R 8 +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R - 8196cosh(b x + a) + 7282cosh(b x + a) +--R + +--R 2 +--R - 1240cosh(b x + a) + 10 +--R * +--R 7 +--R coth(b x + a)sinh(b x + a) +--R + +--R 7 5 +--R - 6924cosh(b x + a) + 9226cosh(b x + a) +--R + +--R 3 +--R - 3064cosh(b x + a) + 170cosh(b x + a) +--R * +--R 6 +--R coth(b x + a)sinh(b x + a) +--R + +--R 8 6 +--R - 3927cosh(b x + a) + 7350cosh(b x + a) +--R + +--R 4 2 +--R - 4060cosh(b x + a) + 610cosh(b x + a) - 5 +--R * +--R 5 +--R coth(b x + a)sinh(b x + a) +--R + +--R 9 7 +--R - 1381cosh(b x + a) + 3470cosh(b x + a) +--R + +--R 5 3 +--R - 2900cosh(b x + a) + 866cosh(b x + a) - 55cosh(b x + a) +--R * +--R 4 +--R coth(b x + a)sinh(b x + a) +--R + +--R 10 8 6 +--R - 230cosh(b x + a) + 761cosh(b x + a) - 920cosh(b x + a) +--R + +--R 4 2 +--R 478cosh(b x + a) - 90cosh(b x + a) + 1 +--R * +--R 3 +--R coth(b x + a)sinh(b x + a) +--R + +--R 11 9 7 +--R 14cosh(b x + a) - 43cosh(b x + a) + 40cosh(b x + a) +--R + +--R 5 3 +--R - 2cosh(b x + a) - 14cosh(b x + a) + 5cosh(b x + a) +--R * +--R 2 +--R coth(b x + a)sinh(b x + a) +--R + +--R 12 10 8 +--R 11cosh(b x + a) - 49cosh(b x + a) + 86cosh(b x + a) +--R + +--R 6 4 2 +--R - 74cosh(b x + a) + 31cosh(b x + a) - 5cosh(b x + a) +--R * +--R coth(b x + a)sinh(b x + a) +--R + +--R 13 11 9 +--R cosh(b x + a) - 5cosh(b x + a) + 10cosh(b x + a) +--R + +--R 7 5 3 +--R - 10cosh(b x + a) + 5cosh(b x + a) - cosh(b x + a) +--R * +--R coth(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 12 +--R 8cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 11 +--R 116cosh(b x + a) coth(b x + a)sinh(b x + a) +--R + +--R 3 10 +--R (700cosh(b x + a) - 36cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 9 +--R (2396cosh(b x + a) - 432cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (5244cosh(b x + a) - 2076cosh(b x + a) + 64cosh(b x + a)) +--R * +--R 8 +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 2 +--R (7752cosh(b x + a) - 5440cosh(b x + a) + 600cosh(b x + a) ) +--R * +--R 7 +--R coth(b x + a)sinh(b x + a) +--R + +--R 7 5 3 +--R 7896cosh(b x + a) - 8680cosh(b x + a) + 2120cosh(b x + a) +--R + +--R - 56cosh(b x + a) +--R * +--R 6 +--R coth(b x + a)sinh(b x + a) +--R + +--R 8 6 4 +--R 5496cosh(b x + a) - 8736cosh(b x + a) + 3800cosh(b x + a) +--R + +--R 2 +--R - 368cosh(b x + a) +--R * +--R 5 +--R coth(b x + a)sinh(b x + a) +--R + +--R 9 7 5 +--R 2496cosh(b x + a) - 5432cosh(b x + a) + 3720cosh(b x + a) +--R + +--R 3 +--R - 808cosh(b x + a) + 24cosh(b x + a) +--R * +--R 4 +--R coth(b x + a)sinh(b x + a) +--R + +--R 10 8 6 +--R 644cosh(b x + a) - 1856cosh(b x + a) + 1864cosh(b x + a) +--R + +--R 4 2 +--R - 736cosh(b x + a) + 84cosh(b x + a) +--R * +--R 3 +--R coth(b x + a)sinh(b x + a) +--R + +--R 11 9 7 +--R 44cosh(b x + a) - 180cosh(b x + a) + 280cosh(b x + a) +--R + +--R 5 3 +--R - 200cosh(b x + a) + 60cosh(b x + a) - 4cosh(b x + a) +--R * +--R 2 +--R coth(b x + a)sinh(b x + a) +--R + +--R 12 10 8 +--R - 20cosh(b x + a) + 80cosh(b x + a) - 120cosh(b x + a) +--R + +--R 6 4 +--R 80cosh(b x + a) - 20cosh(b x + a) +--R * +--R coth(b x + a)sinh(b x + a) +--R + +--R 13 11 9 +--R - 4cosh(b x + a) + 20cosh(b x + a) - 40cosh(b x + a) +--R + +--R 7 5 3 +--R 40cosh(b x + a) - 20cosh(b x + a) + 4cosh(b x + a) +--R * +--R coth(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R + +--R 12 2 11 +--R - 20cosh(b x + a)sinh(b x + a) - 220cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (- 1084cosh(b x + a) - 12cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (- 3156cosh(b x + a) + 4cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 6024cosh(b x + a) + 384cosh(b x + a) + 8cosh(b x + a)) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 7896cosh(b x + a) + 1568cosh(b x + a) + 8cosh(b x + a) ) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 7224cosh(b x + a) + 3080cosh(b x + a) - 120cosh(b x + a) +--R + +--R 8cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R - 4584cosh(b x + a) + 3528cosh(b x + a) - 440cosh(b x + a) +--R + +--R 2 +--R - 8cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R - 1956cosh(b x + a) + 2464cosh(b x + a) - 680cosh(b x + a) +--R + +--R 3 +--R - 32cosh(b x + a) + 12cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R - 524cosh(b x + a) + 1024cosh(b x + a) - 552cosh(b x + a) +--R + +--R 4 2 +--R 32cosh(b x + a) + 20cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R - 76cosh(b x + a) + 228cosh(b x + a) - 232cosh(b x + a) +--R + +--R 5 3 +--R 88cosh(b x + a) - 12cosh(b x + a) + 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R - 4cosh(b x + a) + 20cosh(b x + a) - 40cosh(b x + a) +--R + +--R 6 4 2 +--R 40cosh(b x + a) - 20cosh(b x + a) + 4cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 12 2 11 +--R 4cosh(b x + a)sinh(b x + a) + 76cosh(b x + a) sinh(b x + a) +--R + +--R 3 10 +--R (524cosh(b x + a) + 8cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 9 +--R (1956cosh(b x + a) + 24cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 8 +--R (4584cosh(b x + a) - 128cosh(b x + a) + 8cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 7 +--R (7224cosh(b x + a) - 896cosh(b x + a) + 8cosh(b x + a) )sinh(b x + a) +--R + +--R 7 5 3 +--R 7896cosh(b x + a) - 2352cosh(b x + a) + 8cosh(b x + a) +--R + +--R 8cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 6024cosh(b x + a) - 3472cosh(b x + a) + 200cosh(b x + a) +--R + +--R 2 +--R 32cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 3156cosh(b x + a) - 3136cosh(b x + a) + 600cosh(b x + a) +--R + +--R 3 +--R 16cosh(b x + a) + 4cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 1084cosh(b x + a) - 1728cosh(b x + a) + 728cosh(b x + a) +--R + +--R 4 2 +--R - 64cosh(b x + a) + 12cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 11 9 7 +--R 220cosh(b x + a) - 536cosh(b x + a) + 408cosh(b x + a) +--R + +--R 5 3 +--R - 88cosh(b x + a) - 4cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 12 10 8 +--R 20cosh(b x + a) - 72cosh(b x + a) + 88cosh(b x + a) +--R + +--R 6 4 2 +--R - 32cosh(b x + a) - 12cosh(b x + a) + 8cosh(b x + a) +--R * +--R sinh(b x + a) +--R / +--R 12 +--R 20cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 11 +--R 220cosh(b x + a) coth(b x + a)sinh(b x + a) +--R + +--R 3 10 +--R (1084cosh(b x + a) + 12cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 9 +--R (3156cosh(b x + a) - 4cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (6024cosh(b x + a) - 384cosh(b x + a) - 8cosh(b x + a)) +--R * +--R 8 +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 2 +--R (7896cosh(b x + a) - 1568cosh(b x + a) - 8cosh(b x + a) ) +--R * +--R 7 +--R coth(b x + a)sinh(b x + a) +--R + +--R 7 5 3 +--R 7224cosh(b x + a) - 3080cosh(b x + a) + 120cosh(b x + a) +--R + +--R - 8cosh(b x + a) +--R * +--R 6 +--R coth(b x + a)sinh(b x + a) +--R + +--R 8 6 4 +--R 4584cosh(b x + a) - 3528cosh(b x + a) + 440cosh(b x + a) +--R + +--R 2 +--R 8cosh(b x + a) +--R * +--R 5 +--R coth(b x + a)sinh(b x + a) +--R + +--R 9 7 5 +--R 1956cosh(b x + a) - 2464cosh(b x + a) + 680cosh(b x + a) +--R + +--R 3 +--R 32cosh(b x + a) - 12cosh(b x + a) +--R * +--R 4 +--R coth(b x + a)sinh(b x + a) +--R + +--R 10 8 6 +--R 524cosh(b x + a) - 1024cosh(b x + a) + 552cosh(b x + a) +--R + +--R 4 2 +--R - 32cosh(b x + a) - 20cosh(b x + a) +--R * +--R 3 +--R coth(b x + a)sinh(b x + a) +--R + +--R 11 9 7 +--R 76cosh(b x + a) - 228cosh(b x + a) + 232cosh(b x + a) +--R + +--R 5 3 +--R - 88cosh(b x + a) + 12cosh(b x + a) - 4cosh(b x + a) +--R * +--R 2 +--R coth(b x + a)sinh(b x + a) +--R + +--R 12 10 8 +--R 4cosh(b x + a) - 20cosh(b x + a) + 40cosh(b x + a) +--R + +--R 6 4 2 +--R - 40cosh(b x + a) + 20cosh(b x + a) - 4cosh(b x + a) +--R * +--R coth(b x + a)sinh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 12 +--R - 4cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 11 +--R - 76cosh(b x + a) coth(b x + a)sinh(b x + a) +--R + +--R 3 10 +--R (- 524cosh(b x + a) - 8cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 9 +--R (- 1956cosh(b x + a) - 24cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (- 4584cosh(b x + a) + 128cosh(b x + a) - 8cosh(b x + a)) +--R * +--R 8 +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 2 +--R (- 7224cosh(b x + a) + 896cosh(b x + a) - 8cosh(b x + a) ) +--R * +--R 7 +--R coth(b x + a)sinh(b x + a) +--R + +--R 7 5 3 +--R - 7896cosh(b x + a) + 2352cosh(b x + a) - 8cosh(b x + a) +--R + +--R - 8cosh(b x + a) +--R * +--R 6 +--R coth(b x + a)sinh(b x + a) +--R + +--R 8 6 4 +--R - 6024cosh(b x + a) + 3472cosh(b x + a) - 200cosh(b x + a) +--R + +--R 2 +--R - 32cosh(b x + a) +--R * +--R 5 +--R coth(b x + a)sinh(b x + a) +--R + +--R 9 7 5 +--R - 3156cosh(b x + a) + 3136cosh(b x + a) - 600cosh(b x + a) +--R + +--R 3 +--R - 16cosh(b x + a) - 4cosh(b x + a) +--R * +--R 4 +--R coth(b x + a)sinh(b x + a) +--R + +--R 10 8 6 +--R - 1084cosh(b x + a) + 1728cosh(b x + a) - 728cosh(b x + a) +--R + +--R 4 2 +--R 64cosh(b x + a) - 12cosh(b x + a) +--R * +--R 3 +--R coth(b x + a)sinh(b x + a) +--R + +--R 11 9 7 +--R - 220cosh(b x + a) + 536cosh(b x + a) - 408cosh(b x + a) +--R + +--R 5 3 +--R 88cosh(b x + a) + 4cosh(b x + a) +--R * +--R 2 +--R coth(b x + a)sinh(b x + a) +--R + +--R 12 10 8 +--R - 20cosh(b x + a) + 72cosh(b x + a) - 88cosh(b x + a) +--R + +--R 6 4 2 +--R 32cosh(b x + a) + 12cosh(b x + a) - 8cosh(b x + a) +--R * +--R coth(b x + a)sinh(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R Type: Expression(Integer) +--E 139 + +--S 140 of 508 +t0327:= 1/coth(a+b*x)^(5/2) +--R +--R +--R 1 +--R (136) ------------------------------ +--R 2 +-------------+ +--R coth(b x + a) \|coth(b x + a) +--R Type: Expression(Integer) +--E 140 + +--S 141 of 508 +r0327:= atan(coth(a+b*x)^(1/2))/b+atanh(coth(a+b*x)^(1/2))/b-_ + 2/3/b/coth(a+b*x)^(3/2) +--R +--R +--R (137) +--R +-------------+ +-------------+ +--R 3coth(b x + a)\|coth(b x + a) atanh(\|coth(b x + a) ) +--R + +--R +-------------+ +-------------+ +--R 3coth(b x + a)\|coth(b x + a) atan(\|coth(b x + a) ) - 2 +--R / +--R +-------------+ +--R 3b coth(b x + a)\|coth(b x + a) +--R Type: Expression(Integer) +--E 141 + +--S 142 of 508 +a0327:= integrate(t0327,x) +--R +--R +--R (138) +--R 6 5 +--R - 6sinh(b x + a) - 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 90cosh(b x + a) - 3)sinh(b x + a) +--R + +--R 3 3 +--R (- 120cosh(b x + a) - 12cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 90cosh(b x + a) - 18cosh(b x + a) + 6)sinh(b x + a) +--R + +--R 5 3 +--R (- 36cosh(b x + a) - 12cosh(b x + a) + 12cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 6cosh(b x + a) - 3cosh(b x + a) + 6cosh(b x + a) + 3 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R 6sinh(b x + a) + 36cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (90cosh(b x + a) + 9)sinh(b x + a) +--R + +--R 3 3 +--R (120cosh(b x + a) + 36cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (90cosh(b x + a) + 54cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (36cosh(b x + a) + 36cosh(b x + a) )sinh(b x + a) + 6cosh(b x + a) +--R + +--R 4 +--R 9cosh(b x + a) - 3 +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 6 5 +--R - 12sinh(b x + a) - 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) - 6)sinh(b x + a) +--R + +--R 3 3 +--R (- 240cosh(b x + a) - 24cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180cosh(b x + a) - 36cosh(b x + a) + 12)sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) - 24cosh(b x + a) + 24cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 12cosh(b x + a) - 6cosh(b x + a) + 12cosh(b x + a) + 6 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R 12sinh(b x + a) + 72cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) + 18)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) + 72cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) + 108cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (72cosh(b x + a) + 72cosh(b x + a) )sinh(b x + a) + 12cosh(b x + a) +--R + +--R 4 +--R 18cosh(b x + a) - 6 +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R - 24sinh(b x + a) - 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 144cosh(b x + a) + 24)sinh(b x + a) +--R + +--R 3 +--R (- 96cosh(b x + a) + 48cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R - 24cosh(b x + a) + 24cosh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 4 3 +--R 24sinh(b x + a) + 96cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 3 +--R 144cosh(b x + a) sinh(b x + a) + 96cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R 24cosh(b x + a) - 8 +--R / +--R 6 5 +--R 12b sinh(b x + a) + 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180b cosh(b x + a) + 6b)sinh(b x + a) +--R + +--R 3 3 +--R (240b cosh(b x + a) + 24b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (180b cosh(b x + a) + 36b cosh(b x + a) - 12b)sinh(b x + a) +--R + +--R 5 3 +--R (72b cosh(b x + a) + 24b cosh(b x + a) - 24b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 12b cosh(b x + a) + 6b cosh(b x + a) - 12b cosh(b x + a) - 6b +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R - 12b sinh(b x + a) - 72b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180b cosh(b x + a) - 18b)sinh(b x + a) +--R + +--R 3 3 +--R (- 240b cosh(b x + a) - 72b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 180b cosh(b x + a) - 108b cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 72b cosh(b x + a) - 72b cosh(b x + a) )sinh(b x + a) +--R + +--R 6 4 +--R - 12b cosh(b x + a) - 18b cosh(b x + a) + 6b +--R Type: Union(Expression(Integer),...) +--E 142 + +--S 143 of 508 +m0327:= a0327-r0327 +--R +--R +--R (139) +--R 6 +--R - 6coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R - 36cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 90cosh(b x + a) - 3)coth(b x + a)sinh(b x + a) +--R + +--R 3 +--R (- 120cosh(b x + a) - 12cosh(b x + a))coth(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 90cosh(b x + a) - 18cosh(b x + a) + 6)coth(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R (- 36cosh(b x + a) - 12cosh(b x + a) + 12cosh(b x + a)) +--R * +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 2 +--R (- 6cosh(b x + a) - 3cosh(b x + a) + 6cosh(b x + a) + 3) +--R * +--R coth(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 +--R 6coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R 36cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (90cosh(b x + a) + 9)coth(b x + a)sinh(b x + a) +--R + +--R 3 3 +--R (120cosh(b x + a) + 36cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 2 +--R (90cosh(b x + a) + 54cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (36cosh(b x + a) + 36cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R (6cosh(b x + a) + 9cosh(b x + a) - 3)coth(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R * +--R log +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 6 +--R - 12coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R - 72cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) - 6)coth(b x + a)sinh(b x + a) +--R + +--R 3 +--R (- 240cosh(b x + a) - 24cosh(b x + a))coth(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 180cosh(b x + a) - 36cosh(b x + a) + 12)coth(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) - 24cosh(b x + a) + 24cosh(b x + a)) +--R * +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 2 +--R (- 12cosh(b x + a) - 6cosh(b x + a) + 12cosh(b x + a) + 6) +--R * +--R coth(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 +--R 12coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R 72cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) + 18)coth(b x + a)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) + 72cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) + 108cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) + 72cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R (12cosh(b x + a) + 18cosh(b x + a) - 6)coth(b x + a) +--R * +--R +-------------+ +-------------+ +--R \|coth(b x + a) atanh(\|coth(b x + a) ) +--R + +--R 6 +--R - 12coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R - 72cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) - 6)coth(b x + a)sinh(b x + a) +--R + +--R 3 +--R (- 240cosh(b x + a) - 24cosh(b x + a))coth(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 180cosh(b x + a) - 36cosh(b x + a) + 12)coth(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) - 24cosh(b x + a) + 24cosh(b x + a)) +--R * +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 2 +--R (- 12cosh(b x + a) - 6cosh(b x + a) + 12cosh(b x + a) + 6) +--R * +--R coth(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 +--R 12coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R 72cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) + 18)coth(b x + a)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) + 72cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) + 108cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) + 72cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R (12cosh(b x + a) + 18cosh(b x + a) - 6)coth(b x + a) +--R * +--R +-------------+ +-------------+ +--R \|coth(b x + a) atan(\|coth(b x + a) ) +--R + +--R 6 +--R - 12coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R - 72cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180cosh(b x + a) - 6)coth(b x + a)sinh(b x + a) +--R + +--R 3 +--R (- 240cosh(b x + a) - 24cosh(b x + a))coth(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 180cosh(b x + a) - 36cosh(b x + a) + 12)coth(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R (- 72cosh(b x + a) - 24cosh(b x + a) + 24cosh(b x + a)) +--R * +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 2 +--R (- 12cosh(b x + a) - 6cosh(b x + a) + 12cosh(b x + a) + 6) +--R * +--R coth(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 +--R 12coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R 72cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180cosh(b x + a) + 18)coth(b x + a)sinh(b x + a) +--R + +--R 3 3 +--R (240cosh(b x + a) + 72cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 2 +--R (180cosh(b x + a) + 108cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (72cosh(b x + a) + 72cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R (12cosh(b x + a) + 18cosh(b x + a) - 6)coth(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R * +--R atan +--R 2 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) +--R + +--R - 1 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) +--R + +--R 4 +--R - 24coth(b x + a)sinh(b x + a) +--R + +--R 3 +--R - 96cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 144cosh(b x + a) + 24)coth(b x + a)sinh(b x + a) +--R + +--R 3 +--R (- 96cosh(b x + a) + 48cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 +--R (- 24cosh(b x + a) + 24cosh(b x + a) )coth(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 4 +--R 24coth(b x + a)sinh(b x + a) +--R + +--R 3 +--R 96cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R 144cosh(b x + a) coth(b x + a)sinh(b x + a) +--R + +--R 3 +--R 96cosh(b x + a) coth(b x + a)sinh(b x + a) +--R + +--R 4 +--R (24cosh(b x + a) - 8)coth(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R + +--R 6 5 +--R 8sinh(b x + a) + 48cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (120cosh(b x + a) + 4)sinh(b x + a) +--R + +--R 3 3 +--R (160cosh(b x + a) + 16cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (120cosh(b x + a) + 24cosh(b x + a) - 8)sinh(b x + a) +--R + +--R 5 3 +--R (48cosh(b x + a) + 16cosh(b x + a) - 16cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 +--R 8cosh(b x + a) + 4cosh(b x + a) - 8cosh(b x + a) - 4 +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 5 +--R - 8sinh(b x + a) - 48cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 120cosh(b x + a) - 12)sinh(b x + a) +--R + +--R 3 3 +--R (- 160cosh(b x + a) - 48cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (- 120cosh(b x + a) - 72cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 6 +--R (- 48cosh(b x + a) - 48cosh(b x + a) )sinh(b x + a) - 8cosh(b x + a) +--R + +--R 4 +--R - 12cosh(b x + a) + 4 +--R / +--R 6 +--R 12b coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R 72b cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (180b cosh(b x + a) + 6b)coth(b x + a)sinh(b x + a) +--R + +--R 3 +--R (240b cosh(b x + a) + 24b cosh(b x + a))coth(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (180b cosh(b x + a) + 36b cosh(b x + a) - 12b)coth(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R (72b cosh(b x + a) + 24b cosh(b x + a) - 24b cosh(b x + a)) +--R * +--R coth(b x + a)sinh(b x + a) +--R + +--R 6 4 2 +--R 12b cosh(b x + a) + 6b cosh(b x + a) - 12b cosh(b x + a) +--R + +--R - 6b +--R * +--R coth(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 6 +--R - 12b coth(b x + a)sinh(b x + a) +--R + +--R 5 +--R - 72b cosh(b x + a)coth(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 180b cosh(b x + a) - 18b)coth(b x + a)sinh(b x + a) +--R + +--R 3 3 +--R (- 240b cosh(b x + a) - 72b cosh(b x + a))coth(b x + a)sinh(b x + a) +--R + +--R 4 2 +--R (- 180b cosh(b x + a) - 108b cosh(b x + a) )coth(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R (- 72b cosh(b x + a) - 72b cosh(b x + a) )coth(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R (- 12b cosh(b x + a) - 18b cosh(b x + a) + 6b)coth(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R Type: Expression(Integer) +--E 143 + +--S 144 of 508 +d0327:= D(m0327,x) +--R +--R +--R (140) +--R 2 21 +--R - 12coth(b x + a) sinh(b x + a) +--R + +--R 2 20 +--R - 516cosh(b x + a)coth(b x + a) sinh(b x + a) +--R + +--R 2 2 19 +--R - 7416cosh(b x + a) coth(b x + a) sinh(b x + a) +--R + +--R 3 2 +--R (- 58728cosh(b x + a) + 888cosh(b x + a))coth(b x + a) +--R * +--R 18 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 305580cosh(b x + a) + 15360cosh(b x + a) + 45) +--R * +--R 2 17 +--R coth(b x + a) sinh(b x + a) +--R + +--R 5 3 +--R - 1139748cosh(b x + a) + 124008cosh(b x + a) +--R + +--R 555cosh(b x + a) +--R * +--R 2 16 +--R coth(b x + a) sinh(b x + a) +--R + +--R 6 4 +--R - 3203616cosh(b x + a) + 620736cosh(b x + a) +--R + +--R 2 +--R - 1200cosh(b x + a) + 5 +--R * +--R 2 15 +--R coth(b x + a) sinh(b x + a) +--R + +--R 7 5 +--R - 6999648cosh(b x + a) + 2157600cosh(b x + a) +--R + +--R 3 +--R - 46680cosh(b x + a) - 71cosh(b x + a) +--R * +--R 2 14 +--R coth(b x + a) sinh(b x + a) +--R + +--R 8 6 +--R - 12122904cosh(b x + a) + 5525184cosh(b x + a) +--R + +--R 4 2 +--R - 327036cosh(b x + a) + 3189cosh(b x + a) - 71 +--R * +--R 2 13 +--R coth(b x + a) sinh(b x + a) +--R + +--R 9 7 +--R - 16840200cosh(b x + a) + 10788960cosh(b x + a) +--R + +--R 5 3 +--R - 1281228cosh(b x + a) + 43097cosh(b x + a) +--R + +--R - 1393cosh(b x + a) +--R * +--R 2 12 +--R coth(b x + a) sinh(b x + a) +--R + +--R 10 8 +--R - 18871632cosh(b x + a) + 16396224cosh(b x + a) +--R + +--R 6 4 +--R - 3352128cosh(b x + a) + 238345cosh(b x + a) +--R + +--R 2 +--R - 9250cosh(b x + a) + 9 +--R * +--R 2 11 +--R coth(b x + a) sinh(b x + a) +--R + +--R 11 9 +--R - 17068272cosh(b x + a) + 19610448cosh(b x + a) +--R + +--R 7 5 +--R - 6290856cosh(b x + a) + 775533cosh(b x + a) +--R + +--R 3 +--R - 33534cosh(b x + a) - 443cosh(b x + a) +--R * +--R 2 10 +--R coth(b x + a) sinh(b x + a) +--R + +--R 12 10 +--R - 12395448cosh(b x + a) + 18532800cosh(b x + a) +--R + +--R 8 6 +--R - 8773050cosh(b x + a) + 1680393cosh(b x + a) +--R + +--R 4 2 +--R - 80253cosh(b x + a) - 6953cosh(b x + a) + 39 +--R * +--R 2 9 +--R coth(b x + a) sinh(b x + a) +--R + +--R 13 11 +--R - 7141224cosh(b x + a) + 13803504cosh(b x + a) +--R + +--R 9 7 +--R - 9248382cosh(b x + a) + 2568093cosh(b x + a) +--R + +--R 5 3 +--R - 141339cosh(b x + a) - 35709cosh(b x + a) +--R + +--R 1217cosh(b x + a) +--R * +--R 2 8 +--R coth(b x + a) sinh(b x + a) +--R + +--R 14 12 +--R - 3190560cosh(b x + a) + 8024640cosh(b x + a) +--R + +--R 10 8 +--R - 7406256cosh(b x + a) + 2845359cosh(b x + a) +--R + +--R 6 4 +--R - 194604cosh(b x + a) - 94438cosh(b x + a) +--R + +--R 2 +--R 7924cosh(b x + a) - 17 +--R * +--R 2 7 +--R coth(b x + a) sinh(b x + a) +--R + +--R 15 13 +--R - 1059168cosh(b x + a) + 3573024cosh(b x + a) +--R + +--R 11 9 +--R - 4481256cosh(b x + a) + 2306315cosh(b x + a) +--R + +--R 7 5 +--R - 212052cosh(b x + a) - 148078cosh(b x + a) +--R + +--R 3 +--R 23396cosh(b x + a) - 197cosh(b x + a) +--R * +--R 2 6 +--R coth(b x + a) sinh(b x + a) +--R + +--R 16 14 +--R - 237660cosh(b x + a) + 1178688cosh(b x + a) +--R + +--R 12 10 +--R - 2015052cosh(b x + a) + 1359391cosh(b x + a) +--R + +--R 8 6 +--R - 177681cosh(b x + a) - 144690cosh(b x + a) +--R + +--R 4 2 +--R 37994cosh(b x + a) - 925cosh(b x + a) - 1 +--R * +--R 2 5 +--R coth(b x + a) sinh(b x + a) +--R + +--R 17 15 +--R - 25716cosh(b x + a) + 271200cosh(b x + a) +--R + +--R 13 11 +--R - 652620cosh(b x + a) + 569739cosh(b x + a) +--R + +--R 9 7 +--R - 108503cosh(b x + a) - 88058cosh(b x + a) +--R + +--R 5 3 +--R 36094cosh(b x + a) - 2081cosh(b x + a) - 55cosh(b x + a) +--R * +--R 2 4 +--R coth(b x + a) sinh(b x + a) +--R + +--R 18 16 +--R 2952cosh(b x + a) + 38208cosh(b x + a) +--R + +--R 14 12 +--R - 144096cosh(b x + a) + 162179cosh(b x + a) +--R + +--R 10 8 +--R - 44818cosh(b x + a) - 31859cosh(b x + a) +--R + +--R 6 4 2 +--R 19892cosh(b x + a) - 2387cosh(b x + a) - 74cosh(b x + a) + 3 +--R * +--R 2 3 +--R coth(b x + a) sinh(b x + a) +--R + +--R 19 17 +--R 1560cosh(b x + a) + 2040cosh(b x + a) +--R + +--R 15 13 +--R - 19608cosh(b x + a) + 28687cosh(b x + a) +--R + +--R 11 9 +--R - 11086cosh(b x + a) - 6183cosh(b x + a) +--R + +--R 7 5 3 +--R 5844cosh(b x + a) - 1327cosh(b x + a) + 58cosh(b x + a) +--R + +--R 15cosh(b x + a) +--R * +--R 2 2 +--R coth(b x + a) sinh(b x + a) +--R + +--R 20 18 16 +--R 228cosh(b x + a) - 192cosh(b x + a) - 1323cosh(b x + a) +--R + +--R 14 12 +--R 2595cosh(b x + a) - 1227cosh(b x + a) +--R + +--R 10 8 6 +--R - 597cosh(b x + a) + 711cosh(b x + a) - 255cosh(b x + a) +--R + +--R 4 2 +--R 75cosh(b x + a) - 15cosh(b x + a) +--R * +--R 2 +--R coth(b x + a) sinh(b x + a) +--R + +--R 21 19 17 +--R 12cosh(b x + a) - 24cosh(b x + a) - 21cosh(b x + a) +--R + +--R 15 13 11 +--R 63cosh(b x + a) + 3cosh(b x + a) - 57cosh(b x + a) +--R + +--R 9 7 5 +--R 9cosh(b x + a) + 21cosh(b x + a) - 3cosh(b x + a) +--R + +--R 3 +--R - 3cosh(b x + a) +--R * +--R 2 +--R coth(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 20 +--R 96cosh(b x + a)coth(b x + a) sinh(b x + a) +--R + +--R 2 2 19 +--R 2160cosh(b x + a) coth(b x + a) sinh(b x + a) +--R + +--R 3 2 18 +--R (22224cosh(b x + a) - 168cosh(b x + a))coth(b x + a) sinh(b x + a) +--R + +--R 4 2 2 +--R (140304cosh(b x + a) - 4416cosh(b x + a) )coth(b x + a) +--R * +--R 17 +--R sinh(b x + a) +--R + +--R 5 3 +--R (612816cosh(b x + a) - 47160cosh(b x + a) - 300cosh(b x + a)) +--R * +--R 2 16 +--R coth(b x + a) sinh(b x + a) +--R + +--R 6 4 2 +--R (1974720cosh(b x + a) - 291648cosh(b x + a) - 1644cosh(b x + a) ) +--R * +--R 2 15 +--R coth(b x + a) sinh(b x + a) +--R + +--R 7 5 +--R 4879680cosh(b x + a) - 1204320cosh(b x + a) +--R + +--R 3 +--R 9228cosh(b x + a) - 60cosh(b x + a) +--R * +--R 2 14 +--R coth(b x + a) sinh(b x + a) +--R + +--R 8 6 +--R 9475392cosh(b x + a) - 3576384cosh(b x + a) +--R + +--R 4 2 +--R 133188cosh(b x + a) - 1664cosh(b x + a) +--R * +--R 2 13 +--R coth(b x + a) sinh(b x + a) +--R + +--R 9 7 +--R 14681472cosh(b x + a) - 7975968cosh(b x + a) +--R + +--R 5 3 +--R 689676cosh(b x + a) - 19228cosh(b x + a) + 396cosh(b x + a) +--R * +--R 2 12 +--R coth(b x + a) sinh(b x + a) +--R + +--R 10 8 +--R 18309408cosh(b x + a) - 13715520cosh(b x + a) +--R + +--R 6 4 2 +--R 2180100cosh(b x + a) - 119040cosh(b x + a) + 3284cosh(b x + a) +--R * +--R 2 11 +--R coth(b x + a) sinh(b x + a) +--R + +--R 11 9 +--R 18436704cosh(b x + a) - 18471024cosh(b x + a) +--R + +--R 7 5 +--R 4782492cosh(b x + a) - 456236cosh(b x + a) +--R + +--R 3 +--R 13732cosh(b x + a) + 172cosh(b x + a) +--R * +--R 2 10 +--R coth(b x + a) sinh(b x + a) +--R + +--R 12 10 +--R 14957280cosh(b x + a) - 19631040cosh(b x + a) +--R + +--R 8 6 +--R 7689396cosh(b x + a) - 1175680cosh(b x + a) +--R + +--R 4 2 +--R 41020cosh(b x + a) + 2688cosh(b x + a) +--R * +--R 2 9 +--R coth(b x + a) sinh(b x + a) +--R + +--R 13 11 +--R 9695712cosh(b x + a) - 16480464cosh(b x + a) +--R + +--R 9 7 +--R 9302436cosh(b x + a) - 2135628cosh(b x + a) +--R + +--R 5 3 +--R 97080cosh(b x + a) + 16452cosh(b x + a) - 212cosh(b x + a) +--R * +--R 2 8 +--R coth(b x + a) sinh(b x + a) +--R + +--R 14 12 +--R 4938432cosh(b x + a) - 10865088cosh(b x + a) +--R + +--R 10 8 +--R 8557692cosh(b x + a) - 2804736cosh(b x + a) +--R + +--R 6 4 2 +--R 177672cosh(b x + a) + 54592cosh(b x + a) - 2724cosh(b x + a) +--R * +--R 2 7 +--R coth(b x + a) sinh(b x + a) +--R + +--R 15 13 +--R 1915968cosh(b x + a) - 5547360cosh(b x + a) +--R + +--R 11 9 +--R 5980260cosh(b x + a) - 2688180cosh(b x + a) +--R + +--R 7 5 3 +--R 238728cosh(b x + a) + 111160cosh(b x + a) - 13132cosh(b x + a) +--R + +--R 60cosh(b x + a) +--R * +--R 2 6 +--R coth(b x + a) sinh(b x + a) +--R + +--R 16 14 +--R 532032cosh(b x + a) - 2138304cosh(b x + a) +--R + +--R 12 10 +--R 3135756cosh(b x + a) - 1871232cosh(b x + a) +--R + +--R 8 6 4 +--R 226104cosh(b x + a) + 146496cosh(b x + a) - 32196cosh(b x + a) +--R + +--R 2 +--R 704cosh(b x + a) +--R * +--R 2 5 +--R coth(b x + a) sinh(b x + a) +--R + +--R 17 15 +--R 89760cosh(b x + a) - 594720cosh(b x + a) +--R + +--R 13 11 +--R 1201668cosh(b x + a) - 926420cosh(b x + a) +--R + +--R 9 7 5 +--R 145020cosh(b x + a) + 126728cosh(b x + a) - 44500cosh(b x + a) +--R + +--R 3 +--R 2444cosh(b x + a) + 20cosh(b x + a) +--R * +--R 2 4 +--R coth(b x + a) sinh(b x + a) +--R + +--R 18 16 +--R 2544cosh(b x + a) - 109248cosh(b x + a) +--R + +--R 14 12 +--R 320748cosh(b x + a) - 312064cosh(b x + a) +--R + +--R 10 8 6 +--R 58980cosh(b x + a) + 70592cosh(b x + a) - 35212cosh(b x + a) +--R + +--R 4 2 +--R 3584cosh(b x + a) + 76cosh(b x + a) +--R * +--R 2 3 +--R coth(b x + a) sinh(b x + a) +--R + +--R 19 17 +--R - 2736cosh(b x + a) - 10536cosh(b x + a) +--R + +--R 15 13 +--R 54516cosh(b x + a) - 65508cosh(b x + a) +--R + +--R 11 9 7 +--R 13076cosh(b x + a) + 23772cosh(b x + a) - 14884cosh(b x + a) +--R + +--R 5 3 +--R 2228cosh(b x + a) + 76cosh(b x + a) - 4cosh(b x + a) +--R * +--R 2 2 +--R coth(b x + a) sinh(b x + a) +--R + +--R 20 16 14 +--R - 624cosh(b x + a) + 4860cosh(b x + a) - 7040cosh(b x + a) +--R + +--R 12 10 8 +--R 844cosh(b x + a) + 4160cosh(b x + a) - 2572cosh(b x + a) +--R + +--R 6 4 +--R 320cosh(b x + a) + 52cosh(b x + a) +--R * +--R 2 +--R coth(b x + a) sinh(b x + a) +--R + +--R 21 19 17 +--R - 48cosh(b x + a) + 72cosh(b x + a) + 120cosh(b x + a) +--R + +--R 15 13 11 +--R - 196cosh(b x + a) - 128cosh(b x + a) + 244cosh(b x + a) +--R + +--R 9 7 5 +--R 24cosh(b x + a) - 124cosh(b x + a) + 32cosh(b x + a) +--R + +--R 3 +--R 4cosh(b x + a) +--R * +--R 2 +--R coth(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R + +--R 20 2 19 +--R - 240cosh(b x + a)sinh(b x + a) - 4560cosh(b x + a) sinh(b x + a) +--R + +--R 3 18 +--R (- 40848cosh(b x + a) - 480cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 17 +--R (- 229296cosh(b x + a) - 7200cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (- 904128cosh(b x + a) - 50304cosh(b x + a) - 12cosh(b x + a)) +--R * +--R 16 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 2660160cosh(b x + a) - 216960cosh(b x + a) +--R + +--R 2 +--R 1308cosh(b x + a) +--R * +--R 15 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 6054720cosh(b x + a) - 645120cosh(b x + a) +--R + +--R 3 +--R 18180cosh(b x + a) + 420cosh(b x + a) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 10905024cosh(b x + a) - 1397760cosh(b x + a) +--R + +--R 4 2 +--R 111852cosh(b x + a) + 4644cosh(b x + a) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 15763488cosh(b x + a) - 2271360cosh(b x + a) +--R + +--R 5 3 +--R 416676cosh(b x + a) + 23112cosh(b x + a) + 228cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 18436704cosh(b x + a) - 2800512cosh(b x + a) +--R + +--R 6 4 2 +--R 1055340cosh(b x + a) + 67848cosh(b x + a) + 492cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 17503200cosh(b x + a) - 2608320cosh(b x + a) +--R + +--R 7 5 3 +--R 1923636cosh(b x + a) + 128700cosh(b x + a) - 5844cosh(b x + a) +--R + +--R 132cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 13472160cosh(b x + a) - 1784640cosh(b x + a) +--R + +--R 8 6 +--R 2599740cosh(b x + a) + 160380cosh(b x + a) +--R + +--R 4 2 +--R - 37116cosh(b x + a) + 900cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 8359104cosh(b x + a) - 823680cosh(b x + a) +--R + +--R 9 7 +--R 2640924cosh(b x + a) + 121968cosh(b x + a) +--R + +--R 5 3 +--R - 102744cosh(b x + a) + 2832cosh(b x + a) + 60cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 14 12 +--R - 4135488cosh(b x + a) - 174720cosh(b x + a) +--R + +--R 10 8 +--R 2019732cosh(b x + a) + 33264cosh(b x + a) +--R + +--R 6 4 2 +--R - 168840cosh(b x + a) + 5712cosh(b x + a) + 948cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 15 13 +--R - 1602624cosh(b x + a) + 69888cosh(b x + a) +--R + +--R 11 9 +--R 1151436cosh(b x + a) - 39204cosh(b x + a) +--R + +--R 7 5 3 +--R - 178920cosh(b x + a) + 8568cosh(b x + a) + 3804cosh(b x + a) +--R + +--R - 84cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 16 14 +--R - 473280cosh(b x + a) + 80640cosh(b x + a) +--R + +--R 12 10 +--R 477828cosh(b x + a) - 56100cosh(b x + a) +--R + +--R 8 6 4 +--R - 124344cosh(b x + a) + 9912cosh(b x + a) + 6900cosh(b x + a) +--R + +--R 2 +--R - 276cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 17 15 +--R - 102000cosh(b x + a) + 36480cosh(b x + a) +--R + +--R 13 11 +--R 138060cosh(b x + a) - 35640cosh(b x + a) +--R + +--R 9 7 5 +--R - 55116cosh(b x + a) + 8400cosh(b x + a) + 6420cosh(b x + a) +--R + +--R 3 +--R - 408cosh(b x + a) - 36cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 18 16 +--R - 14928cosh(b x + a) + 9600cosh(b x + a) +--R + +--R 14 12 +--R 25572cosh(b x + a) - 13176cosh(b x + a) +--R + +--R 10 8 6 +--R - 14244cosh(b x + a) + 4752cosh(b x + a) + 2940cosh(b x + a) +--R + +--R 4 2 +--R - 408cosh(b x + a) - 108cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 19 17 15 +--R - 1296cosh(b x + a) + 1440cosh(b x + a) + 2556cosh(b x + a) +--R + +--R 13 11 9 +--R - 2748cosh(b x + a) - 1668cosh(b x + a) + 1572cosh(b x + a) +--R + +--R 7 5 3 +--R 468cosh(b x + a) - 276cosh(b x + a) - 60cosh(b x + a) +--R + +--R 12cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 20 18 16 +--R - 48cosh(b x + a) + 96cosh(b x + a) + 84cosh(b x + a) +--R + +--R 14 12 10 +--R - 252cosh(b x + a) - 12cosh(b x + a) + 228cosh(b x + a) +--R + +--R 8 6 4 +--R - 36cosh(b x + a) - 84cosh(b x + a) + 12cosh(b x + a) +--R + +--R 2 +--R 12cosh(b x + a) +--R * +--R sinh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 20 2 19 +--R 48cosh(b x + a)sinh(b x + a) + 1296cosh(b x + a) sinh(b x + a) +--R + +--R 3 18 +--R (14928cosh(b x + a) + 144cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 17 +--R (102000cosh(b x + a) + 2640cosh(b x + a) )sinh(b x + a) +--R + +--R 5 3 +--R (473280cosh(b x + a) + 22080cosh(b x + a) + 156cosh(b x + a)) +--R * +--R 16 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (1602624cosh(b x + a) + 112320cosh(b x + a) + 1044cosh(b x + a) ) +--R * +--R 15 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 4135488cosh(b x + a) + 389760cosh(b x + a) - 1332cosh(b x + a) +--R + +--R 96cosh(b x + a) +--R * +--R 14 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 8359104cosh(b x + a) + 978432cosh(b x + a) - 41340cosh(b x + a) +--R + +--R 2 +--R 96cosh(b x + a) +--R * +--R 13 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 13472160cosh(b x + a) + 1834560cosh(b x + a) - 225108cosh(b x + a) +--R + +--R 3 +--R - 4608cosh(b x + a) + 36cosh(b x + a) +--R * +--R 12 +--R sinh(b x + a) +--R + +--R 10 8 +--R 17503200cosh(b x + a) + 2608320cosh(b x + a) +--R + +--R 6 4 2 +--R - 705276cosh(b x + a) - 29568cosh(b x + a) + 876cosh(b x + a) +--R * +--R 11 +--R sinh(b x + a) +--R + +--R 11 9 +--R 18436704cosh(b x + a) + 2814240cosh(b x + a) +--R + +--R 7 5 3 +--R - 1504932cosh(b x + a) - 89760cosh(b x + a) + 7020cosh(b x + a) +--R + +--R - 48cosh(b x + a) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 12 10 +--R 15763488cosh(b x + a) + 2265120cosh(b x + a) +--R + +--R 8 6 4 +--R - 2332044cosh(b x + a) - 161568cosh(b x + a) + 29700cosh(b x + a) +--R + +--R 2 +--R 120cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 13 11 +--R 10905024cosh(b x + a) + 1290432cosh(b x + a) +--R + +--R 9 7 5 +--R - 2702700cosh(b x + a) - 177408cosh(b x + a) + 78120cosh(b x + a) +--R + +--R 3 +--R 1536cosh(b x + a) - 60cosh(b x + a) +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 14 12 +--R 6054720cosh(b x + a) + 436800cosh(b x + a) +--R + +--R 10 8 +--R - 2369796cosh(b x + a) - 101376cosh(b x + a) +--R + +--R 6 4 2 +--R 137592cosh(b x + a) + 3360cosh(b x + a) - 372cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 15 11 9 +--R 2660160cosh(b x + a) - 1570140cosh(b x + a) + 9504cosh(b x + a) +--R + +--R 7 5 3 +--R 167832cosh(b x + a) + 672cosh(b x + a) - 1308cosh(b x + a) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 16 14 12 +--R 904128cosh(b x + a) - 94080cosh(b x + a) - 775476cosh(b x + a) +--R + +--R 10 8 6 +--R 68640cosh(b x + a) + 142920cosh(b x + a) - 7728cosh(b x + a) +--R + +--R 4 2 +--R - 3060cosh(b x + a) + 48cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 17 15 13 +--R 229296cosh(b x + a) - 56640cosh(b x + a) - 277212cosh(b x + a) +--R + +--R 11 9 7 +--R 59136cosh(b x + a) + 83700cosh(b x + a) - 13440cosh(b x + a) +--R + +--R 5 3 +--R - 4500cosh(b x + a) + 384cosh(b x + a) + 12cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 18 16 14 +--R 40848cosh(b x + a) - 17856cosh(b x + a) - 67860cosh(b x + a) +--R + +--R 12 10 8 +--R 26496cosh(b x + a) + 32220cosh(b x + a) - 10464cosh(b x + a) +--R + +--R 6 4 2 +--R - 3900cosh(b x + a) + 864cosh(b x + a) + 36cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 19 17 15 +--R 4560cosh(b x + a) - 3120cosh(b x + a) - 10188cosh(b x + a) +--R + +--R 13 11 9 +--R 6432cosh(b x + a) + 7356cosh(b x + a) - 4080cosh(b x + a) +--R + +--R 7 5 3 +--R - 1812cosh(b x + a) + 768cosh(b x + a) + 84cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 20 18 16 +--R 240cosh(b x + a) - 240cosh(b x + a) - 708cosh(b x + a) +--R + +--R 14 12 10 +--R 672cosh(b x + a) + 756cosh(b x + a) - 648cosh(b x + a) +--R + +--R 8 6 4 +--R - 348cosh(b x + a) + 240cosh(b x + a) + 60cosh(b x + a) +--R + +--R 2 +--R - 24cosh(b x + a) +--R * +--R sinh(b x + a) +--R / +--R 2 20 +--R 240cosh(b x + a)coth(b x + a) sinh(b x + a) +--R + +--R 2 2 19 +--R 4560cosh(b x + a) coth(b x + a) sinh(b x + a) +--R + +--R 3 2 +--R (40848cosh(b x + a) + 480cosh(b x + a))coth(b x + a) +--R * +--R 18 +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (229296cosh(b x + a) + 7200cosh(b x + a) )coth(b x + a) +--R * +--R 17 +--R sinh(b x + a) +--R + +--R 5 3 +--R (904128cosh(b x + a) + 50304cosh(b x + a) + 12cosh(b x + a)) +--R * +--R 2 16 +--R coth(b x + a) sinh(b x + a) +--R + +--R 6 4 +--R 2660160cosh(b x + a) + 216960cosh(b x + a) +--R + +--R 2 +--R - 1308cosh(b x + a) +--R * +--R 2 15 +--R coth(b x + a) sinh(b x + a) +--R + +--R 7 5 +--R 6054720cosh(b x + a) + 645120cosh(b x + a) +--R + +--R 3 +--R - 18180cosh(b x + a) - 420cosh(b x + a) +--R * +--R 2 14 +--R coth(b x + a) sinh(b x + a) +--R + +--R 8 6 +--R 10905024cosh(b x + a) + 1397760cosh(b x + a) +--R + +--R 4 2 +--R - 111852cosh(b x + a) - 4644cosh(b x + a) +--R * +--R 2 13 +--R coth(b x + a) sinh(b x + a) +--R + +--R 9 7 +--R 15763488cosh(b x + a) + 2271360cosh(b x + a) +--R + +--R 5 3 +--R - 416676cosh(b x + a) - 23112cosh(b x + a) - 228cosh(b x + a) +--R * +--R 2 12 +--R coth(b x + a) sinh(b x + a) +--R + +--R 10 8 +--R 18436704cosh(b x + a) + 2800512cosh(b x + a) +--R + +--R 6 4 2 +--R - 1055340cosh(b x + a) - 67848cosh(b x + a) - 492cosh(b x + a) +--R * +--R 2 11 +--R coth(b x + a) sinh(b x + a) +--R + +--R 11 9 +--R 17503200cosh(b x + a) + 2608320cosh(b x + a) +--R + +--R 7 5 +--R - 1923636cosh(b x + a) - 128700cosh(b x + a) +--R + +--R 3 +--R 5844cosh(b x + a) - 132cosh(b x + a) +--R * +--R 2 10 +--R coth(b x + a) sinh(b x + a) +--R + +--R 12 10 +--R 13472160cosh(b x + a) + 1784640cosh(b x + a) +--R + +--R 8 6 +--R - 2599740cosh(b x + a) - 160380cosh(b x + a) +--R + +--R 4 2 +--R 37116cosh(b x + a) - 900cosh(b x + a) +--R * +--R 2 9 +--R coth(b x + a) sinh(b x + a) +--R + +--R 13 11 +--R 8359104cosh(b x + a) + 823680cosh(b x + a) +--R + +--R 9 7 +--R - 2640924cosh(b x + a) - 121968cosh(b x + a) +--R + +--R 5 3 +--R 102744cosh(b x + a) - 2832cosh(b x + a) - 60cosh(b x + a) +--R * +--R 2 8 +--R coth(b x + a) sinh(b x + a) +--R + +--R 14 12 +--R 4135488cosh(b x + a) + 174720cosh(b x + a) +--R + +--R 10 8 +--R - 2019732cosh(b x + a) - 33264cosh(b x + a) +--R + +--R 6 4 2 +--R 168840cosh(b x + a) - 5712cosh(b x + a) - 948cosh(b x + a) +--R * +--R 2 7 +--R coth(b x + a) sinh(b x + a) +--R + +--R 15 13 +--R 1602624cosh(b x + a) - 69888cosh(b x + a) +--R + +--R 11 9 +--R - 1151436cosh(b x + a) + 39204cosh(b x + a) +--R + +--R 7 5 3 +--R 178920cosh(b x + a) - 8568cosh(b x + a) - 3804cosh(b x + a) +--R + +--R 84cosh(b x + a) +--R * +--R 2 6 +--R coth(b x + a) sinh(b x + a) +--R + +--R 16 14 +--R 473280cosh(b x + a) - 80640cosh(b x + a) +--R + +--R 12 10 +--R - 477828cosh(b x + a) + 56100cosh(b x + a) +--R + +--R 8 6 4 +--R 124344cosh(b x + a) - 9912cosh(b x + a) - 6900cosh(b x + a) +--R + +--R 2 +--R 276cosh(b x + a) +--R * +--R 2 5 +--R coth(b x + a) sinh(b x + a) +--R + +--R 17 15 +--R 102000cosh(b x + a) - 36480cosh(b x + a) +--R + +--R 13 11 +--R - 138060cosh(b x + a) + 35640cosh(b x + a) +--R + +--R 9 7 5 +--R 55116cosh(b x + a) - 8400cosh(b x + a) - 6420cosh(b x + a) +--R + +--R 3 +--R 408cosh(b x + a) + 36cosh(b x + a) +--R * +--R 2 4 +--R coth(b x + a) sinh(b x + a) +--R + +--R 18 16 +--R 14928cosh(b x + a) - 9600cosh(b x + a) +--R + +--R 14 12 +--R - 25572cosh(b x + a) + 13176cosh(b x + a) +--R + +--R 10 8 6 +--R 14244cosh(b x + a) - 4752cosh(b x + a) - 2940cosh(b x + a) +--R + +--R 4 2 +--R 408cosh(b x + a) + 108cosh(b x + a) +--R * +--R 2 3 +--R coth(b x + a) sinh(b x + a) +--R + +--R 19 17 15 +--R 1296cosh(b x + a) - 1440cosh(b x + a) - 2556cosh(b x + a) +--R + +--R 13 11 9 +--R 2748cosh(b x + a) + 1668cosh(b x + a) - 1572cosh(b x + a) +--R + +--R 7 5 3 +--R - 468cosh(b x + a) + 276cosh(b x + a) + 60cosh(b x + a) +--R + +--R - 12cosh(b x + a) +--R * +--R 2 2 +--R coth(b x + a) sinh(b x + a) +--R + +--R 20 18 16 +--R 48cosh(b x + a) - 96cosh(b x + a) - 84cosh(b x + a) +--R + +--R 14 12 10 +--R 252cosh(b x + a) + 12cosh(b x + a) - 228cosh(b x + a) +--R + +--R 8 6 4 +--R 36cosh(b x + a) + 84cosh(b x + a) - 12cosh(b x + a) +--R + +--R 2 +--R - 12cosh(b x + a) +--R * +--R 2 +--R coth(b x + a) sinh(b x + a) +--R * +--R +-------------+ +--R |cosh(b x + a) +--R |------------- +--R \|sinh(b x + a) +--R + +--R 2 20 +--R - 48cosh(b x + a)coth(b x + a) sinh(b x + a) +--R + +--R 2 2 19 +--R - 1296cosh(b x + a) coth(b x + a) sinh(b x + a) +--R + +--R 3 2 18 +--R (- 14928cosh(b x + a) - 144cosh(b x + a))coth(b x + a) sinh(b x + a) +--R + +--R 4 2 2 +--R (- 102000cosh(b x + a) - 2640cosh(b x + a) )coth(b x + a) +--R * +--R 17 +--R sinh(b x + a) +--R + +--R 5 3 +--R (- 473280cosh(b x + a) - 22080cosh(b x + a) - 156cosh(b x + a)) +--R * +--R 2 16 +--R coth(b x + a) sinh(b x + a) +--R + +--R 6 4 2 +--R (- 1602624cosh(b x + a) - 112320cosh(b x + a) - 1044cosh(b x + a) ) +--R * +--R 2 15 +--R coth(b x + a) sinh(b x + a) +--R + +--R 7 5 3 +--R - 4135488cosh(b x + a) - 389760cosh(b x + a) + 1332cosh(b x + a) +--R + +--R - 96cosh(b x + a) +--R * +--R 2 14 +--R coth(b x + a) sinh(b x + a) +--R + +--R 8 6 +--R - 8359104cosh(b x + a) - 978432cosh(b x + a) +--R + +--R 4 2 +--R 41340cosh(b x + a) - 96cosh(b x + a) +--R * +--R 2 13 +--R coth(b x + a) sinh(b x + a) +--R + +--R 9 7 +--R - 13472160cosh(b x + a) - 1834560cosh(b x + a) +--R + +--R 5 3 +--R 225108cosh(b x + a) + 4608cosh(b x + a) - 36cosh(b x + a) +--R * +--R 2 12 +--R coth(b x + a) sinh(b x + a) +--R + +--R 10 8 +--R - 17503200cosh(b x + a) - 2608320cosh(b x + a) +--R + +--R 6 4 2 +--R 705276cosh(b x + a) + 29568cosh(b x + a) - 876cosh(b x + a) +--R * +--R 2 11 +--R coth(b x + a) sinh(b x + a) +--R + +--R 11 9 +--R - 18436704cosh(b x + a) - 2814240cosh(b x + a) +--R + +--R 7 5 3 +--R 1504932cosh(b x + a) + 89760cosh(b x + a) - 7020cosh(b x + a) +--R + +--R 48cosh(b x + a) +--R * +--R 2 10 +--R coth(b x + a) sinh(b x + a) +--R + +--R 12 10 +--R - 15763488cosh(b x + a) - 2265120cosh(b x + a) +--R + +--R 8 6 4 +--R 2332044cosh(b x + a) + 161568cosh(b x + a) - 29700cosh(b x + a) +--R + +--R 2 +--R - 120cosh(b x + a) +--R * +--R 2 9 +--R coth(b x + a) sinh(b x + a) +--R + +--R 13 11 +--R - 10905024cosh(b x + a) - 1290432cosh(b x + a) +--R + +--R 9 7 5 +--R 2702700cosh(b x + a) + 177408cosh(b x + a) - 78120cosh(b x + a) +--R + +--R 3 +--R - 1536cosh(b x + a) + 60cosh(b x + a) +--R * +--R 2 8 +--R coth(b x + a) sinh(b x + a) +--R + +--R 14 12 +--R - 6054720cosh(b x + a) - 436800cosh(b x + a) +--R + +--R 10 8 +--R 2369796cosh(b x + a) + 101376cosh(b x + a) +--R + +--R 6 4 2 +--R - 137592cosh(b x + a) - 3360cosh(b x + a) + 372cosh(b x + a) +--R * +--R 2 7 +--R coth(b x + a) sinh(b x + a) +--R + +--R 15 11 +--R - 2660160cosh(b x + a) + 1570140cosh(b x + a) +--R + +--R 9 7 5 +--R - 9504cosh(b x + a) - 167832cosh(b x + a) - 672cosh(b x + a) +--R + +--R 3 +--R 1308cosh(b x + a) +--R * +--R 2 6 +--R coth(b x + a) sinh(b x + a) +--R + +--R 16 14 +--R - 904128cosh(b x + a) + 94080cosh(b x + a) +--R + +--R 12 10 8 +--R 775476cosh(b x + a) - 68640cosh(b x + a) - 142920cosh(b x + a) +--R + +--R 6 4 2 +--R 7728cosh(b x + a) + 3060cosh(b x + a) - 48cosh(b x + a) +--R * +--R 2 5 +--R coth(b x + a) sinh(b x + a) +--R + +--R 17 15 +--R - 229296cosh(b x + a) + 56640cosh(b x + a) +--R + +--R 13 11 9 +--R 277212cosh(b x + a) - 59136cosh(b x + a) - 83700cosh(b x + a) +--R + +--R 7 5 3 +--R 13440cosh(b x + a) + 4500cosh(b x + a) - 384cosh(b x + a) +--R + +--R - 12cosh(b x + a) +--R * +--R 2 4 +--R coth(b x + a) sinh(b x + a) +--R + +--R 18 16 +--R - 40848cosh(b x + a) + 17856cosh(b x + a) +--R + +--R 14 12 10 +--R 67860cosh(b x + a) - 26496cosh(b x + a) - 32220cosh(b x + a) +--R + +--R 8 6 4 +--R 10464cosh(b x + a) + 3900cosh(b x + a) - 864cosh(b x + a) +--R + +--R 2 +--R - 36cosh(b x + a) +--R * +--R 2 3 +--R coth(b x + a) sinh(b x + a) +--R + +--R 19 17 15 +--R - 4560cosh(b x + a) + 3120cosh(b x + a) + 10188cosh(b x + a) +--R + +--R 13 11 9 +--R - 6432cosh(b x + a) - 7356cosh(b x + a) + 4080cosh(b x + a) +--R + +--R 7 5 3 +--R 1812cosh(b x + a) - 768cosh(b x + a) - 84cosh(b x + a) +--R * +--R 2 2 +--R coth(b x + a) sinh(b x + a) +--R + +--R 20 18 16 +--R - 240cosh(b x + a) + 240cosh(b x + a) + 708cosh(b x + a) +--R + +--R 14 12 10 +--R - 672cosh(b x + a) - 756cosh(b x + a) + 648cosh(b x + a) +--R + +--R 8 6 4 +--R 348cosh(b x + a) - 240cosh(b x + a) - 60cosh(b x + a) +--R + +--R 2 +--R 24cosh(b x + a) +--R * +--R 2 +--R coth(b x + a) sinh(b x + a) +--R * +--R +-------------+ +--R \|coth(b x + a) +--R Type: Expression(Integer) +--E 144 + +--S 145 of 508 +t0328:= coth(8*x)^(1/3) +--R +--R +--R 3+--------+ +--R (141) \|coth(8x) +--R Type: Expression(Integer) +--E 145 + +--S 146 of 508 +r0328:= -1/16*3^(1/2)*atan(1/3*(1+2*coth(8*x)^(2/3))*3^(1/2))-_ + 1/16*log(1-coth(8*x)^(2/3))+1/32*log(1+coth(8*x)^(2/3)+coth(8*x)^(4/3)) +--R +--R +--R (142) +--R 3+--------+2 3+--------+ 3+--------+2 +--R log(\|coth(8x) + coth(8x)\|coth(8x) + 1) - 2log(- \|coth(8x) + 1) +--R + +--R +-+3+--------+2 +-+ +--R +-+ 2\|3 \|coth(8x) + \|3 +--R - 2\|3 atan(------------------------) +--R 3 +--R / +--R 32 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 508 +--a0328:= integrate(t0328,x) +--E 147 + +--S 148 of 508 +--m0328:= a0328-r0328 +--E 148 + +--S 149 of 508 +--d0328:= D(m0328,x) +--E 149 + +--S 150 of 508 +t0329:= x*coth(a+b*x) +--R +--R +--R (143) x coth(b x + a) +--R Type: Expression(Integer) +--E 150 + +--S 151 of 508 +r0329:= 1/2*(-b^2*x^2+2*x*log(1-exp(2*a+2*b*x))*b+_ + polylog(2,exp(2*a+2*b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 151 + +--S 152 of 508 +a0329:= integrate(t0329,x) +--R +--R +--R x +--R ++ +--I (144) | %BC coth(%BC b + a)d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 152 + +--S 153 of 508 +--m0329:= a0329-r0329 +--E 153 + +--S 154 of 508 +--d0329:= D(m0329,x) +--E 154 + +--S 155 of 508 +t0330:= x*coth(a+b*x)^2 +--R +--R +--R 2 +--R (145) x coth(b x + a) +--R Type: Expression(Integer) +--E 155 + +--S 156 of 508 +r0330:= 1/2*x^2-x*coth(a+b*x)/b+log(sinh(a+b*x))/b^2 +--R +--R +--R 2 2 +--R 2log(sinh(b x + a)) - 2b x coth(b x + a) + b x +--R (146) ----------------------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 156 + +--S 157 of 508 +a0330:= integrate(t0330,x) +--R +--R +--R (147) +--R 2 2 +--R (2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) - 2) +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 2 2 2 +--R (b x - 4b x)sinh(b x + a) + (2b x - 8b x)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 2 +--R (b x - 4b x)cosh(b x + a) - b x +--R / +--R 2 2 2 2 2 2 +--R 2b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) + 2b cosh(b x + a) - 2b +--R Type: Union(Expression(Integer),...) +--E 157 + +--S 158 of 508 +m0330:= a0330-r0330 +--R +--R +--R (148) +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) + 1) +--R * +--R log(sinh(b x + a)) +--R + +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R (b x coth(b x + a) - 2b x)sinh(b x + a) +--R + +--R (2b x cosh(b x + a)coth(b x + a) - 4b x cosh(b x + a))sinh(b x + a) +--R + +--R 2 2 +--R (b x cosh(b x + a) - b x)coth(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Expression(Integer) +--E 158 + +--S 159 of 508 +d0330:= D(m0330,x) +--R +--R +--R (149) +--R 2 4 +--R (- b x coth(b x + a) + coth(b x + a) + b x - 1)sinh(b x + a) +--R + +--R 2 +--R - 4b x cosh(b x + a)coth(b x + a) + 4cosh(b x + a)coth(b x + a) +--R + +--R (4b x - 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 +--R (- 6b x cosh(b x + a) + 2b x)coth(b x + a) +--R + +--R 2 2 +--R (6cosh(b x + a) - 2)coth(b x + a) + (6b x - 6)cosh(b x + a) + 2b x +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 3 2 +--R (- 4b x cosh(b x + a) + 4b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R (4cosh(b x + a) - 4cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R (4b x - 4)cosh(b x + a) + 4b x cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (- b x cosh(b x + a) + 2b x cosh(b x + a) - b x)coth(b x + a) +--R + +--R 4 2 +--R (cosh(b x + a) - 2cosh(b x + a) + 1)coth(b x + a) +--R + +--R 4 2 +--R (b x - 1)cosh(b x + a) + 2b x cosh(b x + a) + b x + 1 +--R / +--R 4 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (6b cosh(b x + a) - 2b)sinh(b x + a) +--R + +--R 3 4 +--R (4b cosh(b x + a) - 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 2 +--R - 2b cosh(b x + a) + b +--R Type: Expression(Integer) +--E 159 + +--S 160 of 508 +t0331:= x*coth(a+b*x)^3 +--R +--R +--R 3 +--R (150) x coth(b x + a) +--R Type: Expression(Integer) +--E 160 + +--S 161 of 508 +r0331:= -1/2*x^2-1/2*coth(a+b*x)/b^2-1/2*x*csch(a+b*x)^2/b+_ + x*log(1-exp(1)^(2*a+2*b*x))/b+1/2*polylog(2,exp(1)^(2*a+2*b*x))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 161 + +--S 162 of 508 +a0331:= integrate(t0331,x) +--R +--R +--R x +--R ++ 3 +--I (151) | %BC coth(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 162 + +--S 163 of 508 +--m0331:= a0331-r0331 +--E 163 + +--S 164 of 508 +--d0331:= D(m0331,x) +--E 164 + +--S 165 of 508 +t0332:= x^2*coth(a+b*x) +--R +--R +--R 2 +--R (152) x coth(b x + a) +--R Type: Expression(Integer) +--E 165 + +--S 166 of 508 +r0332:= 1/6*(-2*b^3*x^3+6*x^2*log(1-exp(2*a+2*b*x))*b^2+_ + 6*x*polylog(2,exp(2*a+2*b*x))*b-3*polylog(3,exp(2*a+2*b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 166 + +--S 167 of 508 +a0332:= integrate(t0332,x) +--R +--R +--R x +--R ++ 2 +--I (153) | %BC coth(%BC b + a)d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 167 + +--S 168 of 508 +--m0332:= a0332-r0332 +--E 168 + +--S 169 of 508 +--d0332:= D(m0332,x) +--E 169 + +--S 170 of 508 +t0333:= x^2*coth(a+b*x)^2 +--R +--R +--R 2 2 +--R (154) x coth(b x + a) +--R Type: Expression(Integer) +--E 170 + +--S 171 of 508 +r0333:= 1/3*(-3*b^2*x^2+b^3*x^3-3*x^2*coth(a+b*x)*b^2+_ + 6*x*log(1-exp(2*a+2*b*x))*b+3*polylog(2,exp(2*a+2*b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 171 + +--S 172 of 508 +a0333:= integrate(t0333,x) +--R +--R +--R x +--R ++ 2 2 +--I (155) | %BC coth(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 172 + +--S 173 of 508 +--m0333:= a0333-r0333 +--E 173 + +--S 174 of 508 +--d0333:= D(m0333,x) +--E 174 + +--S 175 of 508 +t0334:= x^2*coth(a+b*x)^3 +--R +--R +--R 2 3 +--R (156) x coth(b x + a) +--R Type: Expression(Integer) +--E 175 + +--S 176 of 508 +r0334:= -1/3*x^3-x*coth(a+b*x)/b^2-1/2*x^2*csch(a+b*x)^2/b+_ + x^2*log(1-exp(1)^(2*a+2*b*x))/b+log(sinh(a+b*x))/b^3+_ + x*polylog(2,exp(1)^(2*a+2*b*x))/b^2-_ + 1/2*polylog(3,exp(1)^(2*a+2*b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 176 + +--S 177 of 508 +a0334:= integrate(t0334,x) +--R +--R +--R x +--R ++ 2 3 +--I (157) | %BC coth(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 177 + +--S 178 of 508 +--m0334:= a0334-r0334 +--E 178 + +--S 179 of 508 +--d0334:= D(m0334,x) +--E 179 + +--S 180 of 508 +t0335:= x^3*coth(a+b*x) +--R +--R +--R 3 +--R (158) x coth(b x + a) +--R Type: Expression(Integer) +--E 180 + +--S 181 of 508 +r0335:= 1/4*(-x^4*b^4+4*x^3*log(1-exp(2*a+2*b*x))*b^3+_ + 6*x^2*polylog(2,exp(2*a+2*b*x))*b^2-_ + 6*x*polylog(3,exp(2*a+2*b*x))*b+3*polylog(4,exp(2*a+2*b*x)))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 181 + +--S 182 of 508 +a0335:= integrate(t0335,x) +--R +--R +--R x +--R ++ 3 +--I (159) | %BC coth(%BC b + a)d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 182 + +--S 183 of 508 +--m0335:= a0335-r0335 +--E 183 + +--S 184 of 508 +--d0335:= D(m0335,x) +--E 184 + +--S 185 of 508 +t0336:= x^3*coth(a+b*x)^2 +--R +--R +--R 3 2 +--R (160) x coth(b x + a) +--R Type: Expression(Integer) +--E 185 + +--S 186 of 508 +r0336:= 1/4*(-4*b^3*x^3+x^4*b^4-4*x^3*coth(a+b*x)*b^3+_ + 12*x^2*log(1-exp(2*a+2*b*x))*b^2+_ + 12*x*polylog(2,exp(2*a+2*b*x))*b-6*polylog(3,exp(2*a+2*b*x)))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 186 + +--S 187 of 508 +a0336:= integrate(t0336,x) +--R +--R +--R x +--R ++ 3 2 +--I (161) | %BC coth(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 187 + +--S 188 of 508 +--m0336:= a0336-r0336 +--E 188 + +--S 189 of 508 +--d0336:= D(m0336,x) +--E 189 + +--S 190 of 508 +t0337:= x^3*coth(a+b*x)^3 +--R +--R +--R 3 3 +--R (162) x coth(b x + a) +--R Type: Expression(Integer) +--E 190 + +--S 191 of 508 +r0337:= -3/2*x^2/b^2-1/4*x^4-3/2*x^2*coth(a+b*x)/b^2-_ + 1/2*x^3*csch(a+b*x)^2/b+3*x*log(1-exp(1)^(2*a+2*b*x))/b^3+_ + x^3*log(1-exp(1)^(2*a+2*b*x))/b+3/2*(1+b^2*x^2)*_ + polylog(2,exp(1)^(2*a+2*b*x))/b^4-3/2*x*_ + polylog(3,exp(1)^(2*a+2*b*x))/b^3+3/4*_ + polylog(4,exp(1)^(2*a+2*b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 191 + +--S 192 of 508 +a0337:= integrate(t0337,x) +--R +--R +--R x +--R ++ 3 3 +--I (163) | %BC coth(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 192 + +--S 193 of 508 +--m0337:= a0337-r0337 +--E 193 + +--S 194 of 508 +--d0337:= D(m0337,x) +--E 194 + +--S 195 of 508 +t0338:= (a*coth(x)^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (164) \|a coth(x) +--R Type: Expression(Integer) +--E 195 + +--S 196 of 508 +r0338:= (a*coth(x)^2)^(1/2)*log(sinh(x))*tanh(x) +--R +--R +--R +----------+ +--R | 2 +--R (165) tanh(x)log(sinh(x))\|a coth(x) +--R Type: Expression(Integer) +--E 196 + +--S 197 of 508 +a0338:= integrate(t0338,x) +--R +--R +--R +-+ 2sinh(x) +-+ +--R (166) \|a log(- -----------------) - x\|a +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 197 + +--S 198 of 508 +m0338:= a0338-r0338 +--R +--R +--R (167) +--R +----------+ +--R | 2 +-+ 2sinh(x) +-+ +--R - tanh(x)log(sinh(x))\|a coth(x) + \|a log(- -----------------) - x\|a +--R sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 198 + +--S 199 of 508 +d0338:= D(m0338,x) +--R +--R +--R (168) +--R +----------+ +--R +-+ | 2 +--R cosh(x)\|a \|a coth(x) +--R + +--R 2 2 3 +--R a coth(x) sinh(x)tanh(x) + (a coth(x) - a coth(x))sinh(x)tanh(x) +--R + +--R 2 +--R - a coth(x) sinh(x) +--R * +--R log(sinh(x)) +--R + +--R 2 +--R - a cosh(x)coth(x) tanh(x) +--R / +--R +----------+ +--R | 2 +--R sinh(x)\|a coth(x) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 508 +t0339:= (a*coth(x)^3)^(1/2) +--R +--R +--R +----------+ +--R | 3 +--R (169) \|a coth(x) +--R Type: Expression(Integer) +--E 200 + +--S 201 of 508 +r0339:= (atan(coth(x)^(1/2))+atanh(coth(x)^(1/2))-_ + 2*coth(x)^(1/2))*(a*coth(x)^3)^(1/2)/coth(x)^(3/2) +--R +--R +--R (170) +--R +----------+ +----------+ +--R | 3 +-------+ | 3 +-------+ +--R \|a coth(x) atanh(\|coth(x) ) + \|a coth(x) atan(\|coth(x) ) +--R + +--R +----------+ +--R +-------+ | 3 +--R - 2\|coth(x) \|a coth(x) +--R / +--R +-------+ +--R coth(x)\|coth(x) +--R Type: Expression(Integer) +--E 201 + +--S 202 of 508 +a0339:= integrate(t0339,x) +--R +--R +--R (171) +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- +--R \| sinh(x) +--R + +--R 2 2 +--R - a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2)\|- a |--------- +--R \| sinh(x) +--R + +--R 2 2 +--R 2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) - 2a +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R - 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) +--R / +--R +---------+ +--R 2 2 |a cosh(x) +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 2) |--------- +--R \| sinh(x) +--R + +--R 2 2 +---+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 2)\|- a +--R Type: Union(Expression(Integer),...) +--E 202 + +--S 203 of 508 +m0339:= a0339-r0339 +--R +--R +--R (172) +--R 2 2 +--R (coth(x)sinh(x) + 2cosh(x)coth(x)sinh(x) + (cosh(x) - 1)coth(x)) +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 +--R - a coth(x)sinh(x) - 2a cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (- a cosh(x) + a)coth(x) +--R * +--R +-------+ +--R \|coth(x) +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R +---------+ +--R 2 2 |a cosh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2) |--------- +--R \| sinh(x) +--R + +--R 2 2 +---+ +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2)\|- a +--R * +--R +----------+ +--R | 3 +-------+ +--R \|a coth(x) atanh(\|coth(x) ) +--R + +--R +---------+ +--R 2 2 |a cosh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2) |--------- +--R \| sinh(x) +--R + +--R 2 2 +---+ +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2)\|- a +--R * +--R +----------+ +--R | 3 +-------+ +--R \|a coth(x) atan(\|coth(x) ) +--R + +--R 2 +--R - 2coth(x)sinh(x) - 4cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (- 2cosh(x) + 2)coth(x) +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 +--R 2a coth(x)sinh(x) + 4a cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (2a cosh(x) - 2a)coth(x) +--R * +--R +-------+ +--R \|coth(x) +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R +---------+ +--R 2 2 |a cosh(x) +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) - 4) |--------- +--R \| sinh(x) +--R + +--R 2 2 +---+ +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) - 4)\|- a +--R * +--R +----------+ +--R +-------+ | 3 +--R \|coth(x) \|a coth(x) +--R + +--R 2 2 +--R (- 8a coth(x)sinh(x) - 16a cosh(x)coth(x)sinh(x) - 8a cosh(x) coth(x)) +--R * +--R +-------+ +--R \|coth(x) +--R / +--R 2 2 +--R (2coth(x)sinh(x) + 4cosh(x)coth(x)sinh(x) + (2cosh(x) - 2)coth(x)) +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 2 2 +--R (2coth(x)sinh(x) + 4cosh(x)coth(x)sinh(x) + (2cosh(x) - 2)coth(x)) +--R * +--R +---+ +--R \|- a +--R * +--R +-------+ +--R \|coth(x) +--R Type: Expression(Integer) +--E 203 + +--S 204 of 508 +d0339:= D(m0339,x) +--R +--R +--R (173) +--R 14 13 +--R - a sinh(x) - 4a cosh(x)sinh(x) +--R + +--R 2 12 +--R (15a cosh(x) - 3a)sinh(x) +--R + +--R 3 11 +--R (144a cosh(x) - 18a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (451a cosh(x) - 20a cosh(x) - 2a)sinh(x) +--R + +--R 5 3 9 +--R (748a cosh(x) + 130a cosh(x) - 8a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (627a cosh(x) + 585a cosh(x) + 18a cosh(x) + 2a)sinh(x) +--R + +--R 5 3 7 +--R (1164a cosh(x) + 192a cosh(x) - 4a cosh(x))sinh(x) +--R + +--R 8 6 4 +--R - 627a cosh(x) + 1344a cosh(x) + 588a cosh(x) +--R + +--R 2 +--R - 76a cosh(x) + 3a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 748a cosh(x) + 900a cosh(x) + 1008a cosh(x) +--R + +--R 3 +--R - 260a cosh(x) - 36a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 451a cosh(x) + 255a cosh(x) + 1092a cosh(x) +--R + +--R 4 2 +--R - 440a cosh(x) - 121a cosh(x) + a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 144a cosh(x) - 90a cosh(x) + 768a cosh(x) +--R + +--R 5 3 +--R - 428a cosh(x) - 112a cosh(x) - 26a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R - 15a cosh(x) - 108a cosh(x) + 342a cosh(x) +--R + +--R 6 4 2 +--R - 244a cosh(x) - 15a cosh(x) + 40a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 4a cosh(x) - 38a cosh(x) + 88a cosh(x) - 76a cosh(x) +--R + +--R 5 3 +--R 20a cosh(x) + 2a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R a cosh(x) - 5a cosh(x) + 10a cosh(x) - 10a cosh(x) +--R + +--R 6 4 +--R 5a cosh(x) - a cosh(x) +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 13 2 12 +--R - 4a cosh(x)sinh(x) - 36a cosh(x) sinh(x) +--R + +--R 3 11 +--R (- 136a cosh(x) - 8a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 264a cosh(x) - 68a cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (- 220a cosh(x) - 240a cosh(x) - 8a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (132a cosh(x) - 420a cosh(x) - 72a cosh(x) )sinh(x) +--R + +--R 7 5 3 +--R (528a cosh(x) - 240a cosh(x) - 288a cosh(x) - 16a cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (528a cosh(x) + 504a cosh(x) - 672a cosh(x) - 104a cosh(x) ) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R 132a cosh(x) + 1344a cosh(x) - 1008a cosh(x) +--R + +--R 3 +--R - 288a cosh(x) - 20a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 220a cosh(x) + 1560a cosh(x) - 1008a cosh(x) +--R + +--R 4 2 +--R - 440a cosh(x) - 20a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 264a cosh(x) + 1080a cosh(x) - 672a cosh(x) +--R + +--R 5 3 +--R - 400a cosh(x) + 72a cosh(x) - 8a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R - 136a cosh(x) + 460a cosh(x) - 288a cosh(x) +--R + +--R 6 4 2 +--R - 216a cosh(x) + 136a cosh(x) + 44a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R - 36a cosh(x) + 112a cosh(x) - 72a cosh(x) +--R + +--R 7 5 3 +--R - 64a cosh(x) + 76a cosh(x) - 16a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 4a cosh(x) + 12a cosh(x) - 8a cosh(x) - 8a cosh(x) +--R + +--R 6 4 +--R 12a cosh(x) - 4a cosh(x) +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R | 3 +--R \|a coth(x) +--R + +--R 3 13 2 3 12 +--R - 4a cosh(x)coth(x) sinh(x) - 32a cosh(x) coth(x) sinh(x) +--R + +--R 3 3 11 +--R (- 104a cosh(x) + 20a cosh(x))coth(x) sinh(x) +--R + +--R 4 2 3 10 +--R (- 160a cosh(x) + 104a cosh(x) )coth(x) sinh(x) +--R + +--R 5 3 3 9 +--R (- 60a cosh(x) + 132a cosh(x) - 40a cosh(x))coth(x) sinh(x) +--R + +--R 6 4 2 3 8 +--R (192a cosh(x) - 288a cosh(x) - 80a cosh(x) )coth(x) sinh(x) +--R + +--R 7 5 3 +--R (336a cosh(x) - 1176a cosh(x) + 320a cosh(x) + 56a cosh(x)) +--R * +--R 3 7 +--R coth(x) sinh(x) +--R + +--R 8 6 4 3 6 +--R (192a cosh(x) - 1680a cosh(x) + 1360a cosh(x) )coth(x) sinh(x) +--R + +--R 9 7 5 3 +--R - 60a cosh(x) - 1176a cosh(x) + 2000a cosh(x) - 520a cosh(x) +--R + +--R - 52a cosh(x) +--R * +--R 3 5 +--R coth(x) sinh(x) +--R + +--R 10 8 6 4 +--R - 160a cosh(x) - 288a cosh(x) + 1360a cosh(x) - 960a cosh(x) +--R + +--R 2 +--R 48a cosh(x) +--R * +--R 3 4 +--R coth(x) sinh(x) +--R + +--R 11 9 7 5 +--R - 104a cosh(x) + 132a cosh(x) + 320a cosh(x) - 600a cosh(x) +--R + +--R 3 +--R 232a cosh(x) + 20a cosh(x) +--R * +--R 3 3 +--R coth(x) sinh(x) +--R + +--R 12 10 8 6 +--R - 32a cosh(x) + 104a cosh(x) - 80a cosh(x) - 64a cosh(x) +--R + +--R 4 2 +--R 112a cosh(x) - 40a cosh(x) +--R * +--R 3 2 +--R coth(x) sinh(x) +--R + +--R 13 11 9 7 +--R - 4a cosh(x) + 20a cosh(x) - 40a cosh(x) + 40a cosh(x) +--R + +--R 5 3 +--R - 20a cosh(x) + 4a cosh(x) +--R * +--R 3 +--R coth(x) sinh(x) +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 2 3 12 +--R - 8a cosh(x) coth(x) sinh(x) +--R + +--R 2 3 2 3 11 +--R (- 72a cosh(x) - 4a cosh(x))coth(x) sinh(x) +--R + +--R 2 4 2 2 3 10 +--R (- 280a cosh(x) + 8a cosh(x) )coth(x) sinh(x) +--R + +--R 2 5 2 3 2 3 9 +--R (- 600a cosh(x) + 156a cosh(x) + 8a cosh(x))coth(x) sinh(x) +--R + +--R 2 6 2 4 2 2 3 8 +--R (- 720a cosh(x) + 480a cosh(x) - 56a cosh(x) )coth(x) sinh(x) +--R + +--R 2 7 2 5 2 3 2 3 +--R (- 336a cosh(x) + 504a cosh(x) - 376a cosh(x) - 8a cosh(x))coth(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 3 +--R (336a cosh(x) - 336a cosh(x) - 632a cosh(x) + 128a cosh(x) )coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 7 2 5 2 3 +--R 720a cosh(x) - 1512a cosh(x) - 40a cosh(x) + 440a cosh(x) +--R + +--R 2 +--R 8a cosh(x) +--R * +--R 3 5 +--R coth(x) sinh(x) +--R + +--R 2 10 2 8 2 6 2 4 +--R 600a cosh(x) - 1824a cosh(x) + 1048a cosh(x) + 320a cosh(x) +--R + +--R 2 2 +--R - 112a cosh(x) +--R * +--R 3 4 +--R coth(x) sinh(x) +--R + +--R 2 11 2 9 2 7 2 5 +--R 280a cosh(x) - 1140a cosh(x) + 1304a cosh(x) - 280a cosh(x) +--R + +--R 2 3 2 +--R - 160a cosh(x) - 4a cosh(x) +--R * +--R 3 3 +--R coth(x) sinh(x) +--R + +--R 2 12 2 10 2 8 2 6 +--R 72a cosh(x) - 376a cosh(x) + 664a cosh(x) - 448a cosh(x) +--R + +--R 2 4 2 2 +--R 48a cosh(x) + 40a cosh(x) +--R * +--R 3 2 +--R coth(x) sinh(x) +--R + +--R 2 13 2 11 2 9 2 7 +--R 8a cosh(x) - 52a cosh(x) + 128a cosh(x) - 152a cosh(x) +--R + +--R 2 5 2 3 +--R 88a cosh(x) - 20a cosh(x) +--R * +--R 3 +--R coth(x) sinh(x) +--R / +--R 13 2 12 +--R 4cosh(x)sinh(x) + 32cosh(x) sinh(x) +--R + +--R 3 11 +--R (104cosh(x) - 20cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (160cosh(x) - 104cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (60cosh(x) - 132cosh(x) + 40cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 192cosh(x) + 288cosh(x) + 80cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (- 336cosh(x) + 1176cosh(x) - 320cosh(x) - 56cosh(x))sinh(x) +--R + +--R 8 6 4 6 +--R (- 192cosh(x) + 1680cosh(x) - 1360cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R 60cosh(x) + 1176cosh(x) - 2000cosh(x) + 520cosh(x) +--R + +--R 52cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 160cosh(x) + 288cosh(x) - 1360cosh(x) + 960cosh(x) +--R + +--R 2 +--R - 48cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 104cosh(x) - 132cosh(x) - 320cosh(x) + 600cosh(x) +--R + +--R 3 +--R - 232cosh(x) - 20cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 32cosh(x) - 104cosh(x) + 80cosh(x) + 64cosh(x) +--R + +--R 4 2 +--R - 112cosh(x) + 40cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R 4cosh(x) - 20cosh(x) + 40cosh(x) - 40cosh(x) + 20cosh(x) +--R + +--R 3 +--R - 4cosh(x) +--R * +--R sinh(x) +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 12 3 11 +--R 8a cosh(x) sinh(x) + (72a cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (280a cosh(x) - 8a cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (600a cosh(x) - 156a cosh(x) - 8a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (720a cosh(x) - 480a cosh(x) + 56a cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (336a cosh(x) - 504a cosh(x) + 376a cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 336a cosh(x) + 336a cosh(x) + 632a cosh(x) - 128a cosh(x) ) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 720a cosh(x) + 1512a cosh(x) + 40a cosh(x) - 440a cosh(x) +--R + +--R - 8a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 600a cosh(x) + 1824a cosh(x) - 1048a cosh(x) - 320a cosh(x) +--R + +--R 2 +--R 112a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 280a cosh(x) + 1140a cosh(x) - 1304a cosh(x) + 280a cosh(x) +--R + +--R 3 +--R 160a cosh(x) + 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 72a cosh(x) + 376a cosh(x) - 664a cosh(x) + 448a cosh(x) +--R + +--R 4 2 +--R - 48a cosh(x) - 40a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 8a cosh(x) + 52a cosh(x) - 128a cosh(x) + 152a cosh(x) +--R + +--R 5 3 +--R - 88a cosh(x) + 20a cosh(x) +--R * +--R sinh(x) +--R * +--R +----------+ +--R | 3 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 508 +t0340:= (a*coth(x)^4)^(1/2) +--R +--R +--R +----------+ +--R | 4 +--R (174) \|a coth(x) +--R Type: Expression(Integer) +--E 205 + +--S 206 of 508 +r0340:= (x-coth(x))*(a*coth(x)^4)^(1/2)*tanh(x)^2 +--R +--R +--R +----------+ +--R 2 | 4 +--R (175) (- coth(x) + x)tanh(x) \|a coth(x) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 508 +a0340:= integrate(t0340,x) +--R +--R +--R 2 2 +-+ +--R (x sinh(x) + 2x cosh(x)sinh(x) + x cosh(x) - x - 2)\|a +--R (176) --------------------------------------------------------- +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 207 + +--S 208 of 508 +m0340:= a0340-r0340 +--R +--R +--R (177) +--R 2 +--R (coth(x) - x)sinh(x) + (2cosh(x)coth(x) - 2x cosh(x))sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 1)coth(x) - x cosh(x) + x +--R * +--R +----------+ +--R 2 | 4 +--R tanh(x) \|a coth(x) +--R + +--R 2 2 +-+ +--R (x sinh(x) + 2x cosh(x)sinh(x) + x cosh(x) - x - 2)\|a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression(Integer) +--E 208 + +--S 209 of 508 +d0340:= D(m0340,x) +--R +--R +--R (178) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R * +--R +----------+ +--R +-+ | 4 +--R \|a \|a coth(x) +--R + +--R 5 4 4 +--R (- 2a coth(x) + 2a x coth(x) )sinh(x) +--R + +--R 5 4 3 +--R (- 8a cosh(x)coth(x) + 8a x cosh(x)coth(x) )sinh(x) +--R + +--R 2 5 2 4 +--R ((- 12a cosh(x) + 4a)coth(x) + (12a x cosh(x) - 4a x)coth(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 +--R (- 8a cosh(x) + 8a cosh(x))coth(x) +--R + +--R 3 4 +--R (8a x cosh(x) - 8a x cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 4 2 5 +--R (- 2a cosh(x) + 4a cosh(x) - 2a)coth(x) +--R + +--R 4 2 4 +--R (2a x cosh(x) - 4a x cosh(x) + 2a x)coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 6 5 4 3 4 +--R (- 3a coth(x) + 2a x coth(x) + 2a coth(x) - 2a x coth(x) )sinh(x) +--R + +--R 6 5 4 +--R - 12a cosh(x)coth(x) + 8a x cosh(x)coth(x) + 8a cosh(x)coth(x) +--R + +--R 3 +--R - 8a x cosh(x)coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 5 +--R (- 18a cosh(x) + 6a)coth(x) + (12a x cosh(x) - 4a x)coth(x) +--R + +--R 2 4 2 3 +--R (12a cosh(x) - 4a)coth(x) + (- 12a x cosh(x) + 4a x)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 +--R (- 12a cosh(x) + 12a cosh(x))coth(x) +--R + +--R 3 5 +--R (8a x cosh(x) - 8a x cosh(x))coth(x) +--R + +--R 3 4 +--R (8a cosh(x) - 8a cosh(x))coth(x) +--R + +--R 3 3 +--R (- 8a x cosh(x) + 8a x cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 4 2 6 +--R (- 3a cosh(x) + 6a cosh(x) - 3a)coth(x) +--R + +--R 4 2 5 +--R (2a x cosh(x) - 4a x cosh(x) + 2a x)coth(x) +--R + +--R 4 2 4 +--R (2a cosh(x) - 4a cosh(x) + 2a)coth(x) +--R + +--R 4 2 3 +--R (- 2a x cosh(x) + 4a x cosh(x) - 2a x)coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 5 4 4 +--R (2a coth(x) - 2a x coth(x) )sinh(x) +--R + +--R 5 4 3 +--R (8a cosh(x)coth(x) - 8a x cosh(x)coth(x) )sinh(x) +--R + +--R 2 5 2 4 +--R ((12a cosh(x) - 4a)coth(x) + (- 12a x cosh(x) + 4a x)coth(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 +--R (8a cosh(x) - 8a cosh(x))coth(x) +--R + +--R 3 4 +--R (- 8a x cosh(x) + 8a x cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 4 2 5 +--R (2a cosh(x) - 4a cosh(x) + 2a)coth(x) +--R + +--R 4 2 4 +--R (- 2a x cosh(x) + 4a x cosh(x) - 2a x)coth(x) +--R * +--R tanh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R +----------+ +--R | 4 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 209 + +--S 210 of 508 +t0341:= (a*coth(x)^3)^(3/2) +--R +--R +--R +----------+ +--R 3 | 3 +--R (179) a coth(x) \|a coth(x) +--R Type: Expression(Integer) +--E 210 + +--S 211 of 508 +r0341:= -1/21*a*(a*coth(x)^3)^(1/2)*(21*atan(coth(x)^(1/2))-_ + 21*atanh(coth(x)^(1/2))+14*coth(x)^(3/2)+6*coth(x)^(7/2))/coth(x)^(3/2) +--R +--R +--R (180) +--R +----------+ +----------+ +--R | 3 +-------+ | 3 +-------+ +--R 21a\|a coth(x) atanh(\|coth(x) ) - 21a\|a coth(x) atan(\|coth(x) ) +--R + +--R +----------+ +--R 3 +-------+ | 3 +--R (- 6a coth(x) - 14a coth(x))\|coth(x) \|a coth(x) +--R / +--R +-------+ +--R 21coth(x)\|coth(x) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 508 +a0341:= integrate(t0341,x) +--R +--R +--R (181) +--R 14 13 +--R - 21a sinh(x) - 294a cosh(x)sinh(x) +--R + +--R 2 12 +--R (- 1911a cosh(x) + 168a)sinh(x) +--R + +--R 3 11 +--R (- 7644a cosh(x) + 2016a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 21021a cosh(x) + 11088a cosh(x) - 378a)sinh(x) +--R + +--R 5 3 9 +--R (- 42042a cosh(x) + 36960a cosh(x) - 3780a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 63063a cosh(x) + 83160a cosh(x) - 17010a cosh(x) + 84a) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R - 72072a cosh(x) + 133056a cosh(x) - 45360a cosh(x) +--R + +--R 672a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R - 63063a cosh(x) + 155232a cosh(x) - 79380a cosh(x) +--R + +--R 2 +--R 2352a cosh(x) + 819a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 42042a cosh(x) + 133056a cosh(x) - 95256a cosh(x) +--R + +--R 3 +--R 4704a cosh(x) + 4914a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 21021a cosh(x) + 83160a cosh(x) - 79380a cosh(x) +--R + +--R 4 2 +--R 5880a cosh(x) + 12285a cosh(x) - 1260a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 7644a cosh(x) + 36960a cosh(x) - 45360a cosh(x) +--R + +--R 5 3 +--R 4704a cosh(x) + 16380a cosh(x) - 5040a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R - 1911a cosh(x) + 11088a cosh(x) - 17010a cosh(x) +--R + +--R 6 4 2 +--R 2352a cosh(x) + 12285a cosh(x) - 7560a cosh(x) + 756a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R - 294a cosh(x) + 2016a cosh(x) - 3780a cosh(x) +--R + +--R 7 5 3 +--R 672a cosh(x) + 4914a cosh(x) - 5040a cosh(x) + 1512a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 21a cosh(x) + 168a cosh(x) - 378a cosh(x) + 84a cosh(x) +--R + +--R 6 4 2 +--R 819a cosh(x) - 1260a cosh(x) + 756a cosh(x) - 168a +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 14 2 13 2 2 12 +--R - 21a sinh(x) - 294a cosh(x)sinh(x) - 1911a cosh(x) sinh(x) +--R + +--R 2 3 11 2 4 2 10 +--R - 7644a cosh(x) sinh(x) + (- 21021a cosh(x) + 294a )sinh(x) +--R + +--R 2 5 2 9 +--R (- 42042a cosh(x) + 2940a cosh(x))sinh(x) +--R + +--R 2 6 2 2 2 8 +--R (- 63063a cosh(x) + 13230a cosh(x) - 588a )sinh(x) +--R + +--R 2 7 2 3 2 7 +--R (- 72072a cosh(x) + 35280a cosh(x) - 4704a cosh(x))sinh(x) +--R + +--R 2 8 2 4 2 2 2 +--R (- 63063a cosh(x) + 61740a cosh(x) - 16464a cosh(x) + 147a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 5 2 3 +--R - 42042a cosh(x) + 74088a cosh(x) - 32928a cosh(x) +--R + +--R 2 +--R 882a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 10 2 6 2 4 +--R - 21021a cosh(x) + 61740a cosh(x) - 41160a cosh(x) +--R + +--R 2 2 2 +--R 2205a cosh(x) + 588a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 11 2 7 2 5 +--R - 7644a cosh(x) + 35280a cosh(x) - 32928a cosh(x) +--R + +--R 2 3 2 +--R 2940a cosh(x) + 2352a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 12 2 8 2 6 +--R - 1911a cosh(x) + 13230a cosh(x) - 16464a cosh(x) +--R + +--R 2 4 2 2 2 +--R 2205a cosh(x) + 3528a cosh(x) - 588a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 13 2 9 2 7 +--R - 294a cosh(x) + 2940a cosh(x) - 4704a cosh(x) +--R + +--R 2 5 2 3 2 +--R 882a cosh(x) + 2352a cosh(x) - 1176a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 14 2 10 2 8 2 6 +--R - 21a cosh(x) + 294a cosh(x) - 588a cosh(x) + 147a cosh(x) +--R + +--R 2 4 2 2 2 +--R 588a cosh(x) - 588a cosh(x) + 168a +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R 14 13 +--R - 42a sinh(x) - 588a cosh(x)sinh(x) +--R + +--R 2 12 +--R (- 3822a cosh(x) + 336a)sinh(x) +--R + +--R 3 11 +--R (- 15288a cosh(x) + 4032a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 42042a cosh(x) + 22176a cosh(x) - 756a)sinh(x) +--R + +--R 5 3 9 +--R (- 84084a cosh(x) + 73920a cosh(x) - 7560a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 126126a cosh(x) + 166320a cosh(x) - 34020a cosh(x) +--R + +--R 168a +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R - 144144a cosh(x) + 266112a cosh(x) - 90720a cosh(x) +--R + +--R 1344a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R - 126126a cosh(x) + 310464a cosh(x) - 158760a cosh(x) +--R + +--R 2 +--R 4704a cosh(x) + 1638a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 84084a cosh(x) + 266112a cosh(x) - 190512a cosh(x) +--R + +--R 3 +--R 9408a cosh(x) + 9828a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 42042a cosh(x) + 166320a cosh(x) - 158760a cosh(x) +--R + +--R 4 2 +--R 11760a cosh(x) + 24570a cosh(x) - 2520a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 15288a cosh(x) + 73920a cosh(x) - 90720a cosh(x) +--R + +--R 5 3 +--R 9408a cosh(x) + 32760a cosh(x) - 10080a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R - 3822a cosh(x) + 22176a cosh(x) - 34020a cosh(x) +--R + +--R 6 4 2 +--R 4704a cosh(x) + 24570a cosh(x) - 15120a cosh(x) + 1512a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R - 588a cosh(x) + 4032a cosh(x) - 7560a cosh(x) +--R + +--R 7 5 3 +--R 1344a cosh(x) + 9828a cosh(x) - 10080a cosh(x) +--R + +--R 3024a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 42a cosh(x) + 336a cosh(x) - 756a cosh(x) + 168a cosh(x) +--R + +--R 6 4 2 +--R 1638a cosh(x) - 2520a cosh(x) + 1512a cosh(x) - 336a +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 14 2 13 2 2 12 +--R - 42a sinh(x) - 588a cosh(x)sinh(x) - 3822a cosh(x) sinh(x) +--R + +--R 2 3 11 2 4 2 10 +--R - 15288a cosh(x) sinh(x) + (- 42042a cosh(x) + 588a )sinh(x) +--R + +--R 2 5 2 9 +--R (- 84084a cosh(x) + 5880a cosh(x))sinh(x) +--R + +--R 2 6 2 2 2 8 +--R (- 126126a cosh(x) + 26460a cosh(x) - 1176a )sinh(x) +--R + +--R 2 7 2 3 2 7 +--R (- 144144a cosh(x) + 70560a cosh(x) - 9408a cosh(x))sinh(x) +--R + +--R 2 8 2 4 2 2 2 +--R (- 126126a cosh(x) + 123480a cosh(x) - 32928a cosh(x) + 294a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 5 2 3 +--R - 84084a cosh(x) + 148176a cosh(x) - 65856a cosh(x) +--R + +--R 2 +--R 1764a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 10 2 6 2 4 +--R - 42042a cosh(x) + 123480a cosh(x) - 82320a cosh(x) +--R + +--R 2 2 2 +--R 4410a cosh(x) + 1176a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 11 2 7 2 5 +--R - 15288a cosh(x) + 70560a cosh(x) - 65856a cosh(x) +--R + +--R 2 3 2 +--R 5880a cosh(x) + 4704a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 12 2 8 2 6 +--R - 3822a cosh(x) + 26460a cosh(x) - 32928a cosh(x) +--R + +--R 2 4 2 2 2 +--R 4410a cosh(x) + 7056a cosh(x) - 1176a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 13 2 9 2 7 +--R - 588a cosh(x) + 5880a cosh(x) - 9408a cosh(x) +--R + +--R 2 5 2 3 2 +--R 1764a cosh(x) + 4704a cosh(x) - 2352a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 14 2 10 2 8 2 6 +--R - 42a cosh(x) + 588a cosh(x) - 1176a cosh(x) + 294a cosh(x) +--R + +--R 2 4 2 2 2 +--R 1176a cosh(x) - 1176a cosh(x) + 336a +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R 12 11 +--R 448a sinh(x) + 5376a cosh(x)sinh(x) +--R + +--R 2 10 +--R (29568a cosh(x) - 1008a)sinh(x) +--R + +--R 3 9 +--R (98560a cosh(x) - 10080a cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (221760a cosh(x) - 45360a cosh(x) )sinh(x) +--R + +--R 5 3 7 +--R (354816a cosh(x) - 120960a cosh(x) )sinh(x) +--R + +--R 6 4 6 +--R (413952a cosh(x) - 211680a cosh(x) + 1904a)sinh(x) +--R + +--R 7 5 5 +--R (354816a cosh(x) - 254016a cosh(x) + 11424a cosh(x))sinh(x) +--R + +--R 8 6 2 +--R (221760a cosh(x) - 211680a cosh(x) + 28560a cosh(x) - 2688a) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 3 +--R 98560a cosh(x) - 120960a cosh(x) + 38080a cosh(x) +--R + +--R - 10752a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 4 +--R 29568a cosh(x) - 45360a cosh(x) + 28560a cosh(x) +--R + +--R 2 +--R - 16128a cosh(x) + 1344a +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 5 +--R 5376a cosh(x) - 10080a cosh(x) + 11424a cosh(x) +--R + +--R 3 +--R - 10752a cosh(x) + 2688a cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 6 4 +--R 448a cosh(x) - 1008a cosh(x) + 1904a cosh(x) - 2688a cosh(x) +--R + +--R 2 +--R 1344a cosh(x) +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 14 2 13 +--R - 80a sinh(x) - 1120a cosh(x)sinh(x) +--R + +--R 2 2 2 12 +--R (- 7280a cosh(x) + 112a )sinh(x) +--R + +--R 2 3 2 11 +--R (- 29120a cosh(x) + 1344a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 10 +--R (- 80080a cosh(x) + 7392a cosh(x) + 896a )sinh(x) +--R + +--R 2 5 2 3 2 9 +--R (- 160160a cosh(x) + 24640a cosh(x) + 8960a cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 8 +--R (- 240240a cosh(x) + 55440a cosh(x) + 40320a cosh(x) - 1232a )sinh(x) +--R + +--R 2 7 2 5 2 3 +--R - 274560a cosh(x) + 88704a cosh(x) + 107520a cosh(x) +--R + +--R 2 +--R - 9856a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R - 240240a cosh(x) + 103488a cosh(x) + 188160a cosh(x) +--R + +--R 2 2 2 +--R - 34496a cosh(x) + 112a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 9 2 7 2 5 +--R - 160160a cosh(x) + 88704a cosh(x) + 225792a cosh(x) +--R + +--R 2 3 2 +--R - 68992a cosh(x) + 672a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 10 2 8 2 6 +--R - 80080a cosh(x) + 55440a cosh(x) + 188160a cosh(x) +--R + +--R 2 4 2 2 2 +--R - 86240a cosh(x) + 1680a cosh(x) + 1344a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 11 2 9 2 7 +--R - 29120a cosh(x) + 24640a cosh(x) + 107520a cosh(x) +--R + +--R 2 5 2 3 2 +--R - 68992a cosh(x) + 2240a cosh(x) + 5376a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 12 2 10 2 8 +--R - 7280a cosh(x) + 7392a cosh(x) + 40320a cosh(x) +--R + +--R 2 6 2 4 2 2 2 +--R - 34496a cosh(x) + 1680a cosh(x) + 8064a cosh(x) - 1344a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 13 2 11 2 9 2 7 +--R - 1120a cosh(x) + 1344a cosh(x) + 8960a cosh(x) - 9856a cosh(x) +--R + +--R 2 5 2 3 2 +--R 672a cosh(x) + 5376a cosh(x) - 2688a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 14 2 12 2 10 2 8 +--R - 80a cosh(x) + 112a cosh(x) + 896a cosh(x) - 1232a cosh(x) +--R + +--R 2 6 2 4 2 2 +--R 112a cosh(x) + 1344a cosh(x) - 1344a cosh(x) +--R / +--R 14 13 2 12 +--R 42sinh(x) + 588cosh(x)sinh(x) + (3822cosh(x) - 336)sinh(x) +--R + +--R 3 11 +--R (15288cosh(x) - 4032cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (42042cosh(x) - 22176cosh(x) + 756)sinh(x) +--R + +--R 5 3 9 +--R (84084cosh(x) - 73920cosh(x) + 7560cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (126126cosh(x) - 166320cosh(x) + 34020cosh(x) - 168)sinh(x) +--R + +--R 7 5 3 +--R (144144cosh(x) - 266112cosh(x) + 90720cosh(x) - 1344cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 126126cosh(x) - 310464cosh(x) + 158760cosh(x) - 4704cosh(x) +--R + +--R - 1638 +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 84084cosh(x) - 266112cosh(x) + 190512cosh(x) - 9408cosh(x) +--R + +--R - 9828cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 42042cosh(x) - 166320cosh(x) + 158760cosh(x) - 11760cosh(x) +--R + +--R 2 +--R - 24570cosh(x) + 2520 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 15288cosh(x) - 73920cosh(x) + 90720cosh(x) - 9408cosh(x) +--R + +--R 3 +--R - 32760cosh(x) + 10080cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 3822cosh(x) - 22176cosh(x) + 34020cosh(x) - 4704cosh(x) +--R + +--R 4 2 +--R - 24570cosh(x) + 15120cosh(x) - 1512 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 588cosh(x) - 4032cosh(x) + 7560cosh(x) - 1344cosh(x) +--R + +--R 5 3 +--R - 9828cosh(x) + 10080cosh(x) - 3024cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R 42cosh(x) - 336cosh(x) + 756cosh(x) - 168cosh(x) +--R + +--R 6 4 2 +--R - 1638cosh(x) + 2520cosh(x) - 1512cosh(x) + 336 +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 14 13 2 12 +--R - 42sinh(x) - 588cosh(x)sinh(x) - 3822cosh(x) sinh(x) +--R + +--R 3 11 4 10 +--R - 15288cosh(x) sinh(x) + (- 42042cosh(x) + 588)sinh(x) +--R + +--R 5 9 +--R (- 84084cosh(x) + 5880cosh(x))sinh(x) +--R + +--R 6 2 8 +--R (- 126126cosh(x) + 26460cosh(x) - 1176)sinh(x) +--R + +--R 7 3 7 +--R (- 144144cosh(x) + 70560cosh(x) - 9408cosh(x))sinh(x) +--R + +--R 8 4 2 6 +--R (- 126126cosh(x) + 123480cosh(x) - 32928cosh(x) + 294)sinh(x) +--R + +--R 9 5 3 +--R (- 84084cosh(x) + 148176cosh(x) - 65856cosh(x) + 1764cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 4 2 +--R - 42042cosh(x) + 123480cosh(x) - 82320cosh(x) + 4410cosh(x) +--R + +--R 1176 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 5 3 +--R - 15288cosh(x) + 70560cosh(x) - 65856cosh(x) + 5880cosh(x) +--R + +--R 4704cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 6 4 +--R - 3822cosh(x) + 26460cosh(x) - 32928cosh(x) + 4410cosh(x) +--R + +--R 2 +--R 7056cosh(x) - 1176 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 7 5 +--R - 588cosh(x) + 5880cosh(x) - 9408cosh(x) + 1764cosh(x) +--R + +--R 3 +--R 4704cosh(x) - 2352cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 8 6 +--R - 42cosh(x) + 588cosh(x) - 1176cosh(x) + 294cosh(x) +--R + +--R 4 2 +--R 1176cosh(x) - 1176cosh(x) + 336 +--R * +--R +---+ +--R \|- a +--R Type: Union(Expression(Integer),...) +--E 212 + +--S 213 of 508 +m0341:= a0341-r0341 +--R +--R +--R (182) +--R 14 13 +--R - 21a coth(x)sinh(x) - 294a cosh(x)coth(x)sinh(x) +--R + +--R 2 12 +--R (- 1911a cosh(x) + 168a)coth(x)sinh(x) +--R + +--R 3 11 +--R (- 7644a cosh(x) + 2016a cosh(x))coth(x)sinh(x) +--R + +--R 4 2 10 +--R (- 21021a cosh(x) + 11088a cosh(x) - 378a)coth(x)sinh(x) +--R + +--R 5 3 +--R (- 42042a cosh(x) + 36960a cosh(x) - 3780a cosh(x))coth(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 4 2 +--R (- 63063a cosh(x) + 83160a cosh(x) - 17010a cosh(x) + 84a) +--R * +--R 8 +--R coth(x)sinh(x) +--R + +--R 7 5 3 +--R - 72072a cosh(x) + 133056a cosh(x) - 45360a cosh(x) +--R + +--R 672a cosh(x) +--R * +--R 7 +--R coth(x)sinh(x) +--R + +--R 8 6 4 +--R - 63063a cosh(x) + 155232a cosh(x) - 79380a cosh(x) +--R + +--R 2 +--R 2352a cosh(x) + 819a +--R * +--R 6 +--R coth(x)sinh(x) +--R + +--R 9 7 5 +--R - 42042a cosh(x) + 133056a cosh(x) - 95256a cosh(x) +--R + +--R 3 +--R 4704a cosh(x) + 4914a cosh(x) +--R * +--R 5 +--R coth(x)sinh(x) +--R + +--R 10 8 6 +--R - 21021a cosh(x) + 83160a cosh(x) - 79380a cosh(x) +--R + +--R 4 2 +--R 5880a cosh(x) + 12285a cosh(x) - 1260a +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 11 9 7 +--R - 7644a cosh(x) + 36960a cosh(x) - 45360a cosh(x) +--R + +--R 5 3 +--R 4704a cosh(x) + 16380a cosh(x) - 5040a cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 12 10 8 +--R - 1911a cosh(x) + 11088a cosh(x) - 17010a cosh(x) +--R + +--R 6 4 2 +--R 2352a cosh(x) + 12285a cosh(x) - 7560a cosh(x) + 756a +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 13 11 9 +--R - 294a cosh(x) + 2016a cosh(x) - 3780a cosh(x) +--R + +--R 7 5 3 +--R 672a cosh(x) + 4914a cosh(x) - 5040a cosh(x) + 1512a cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 14 12 10 +--R - 21a cosh(x) + 168a cosh(x) - 378a cosh(x) +--R + +--R 8 6 4 2 +--R 84a cosh(x) + 819a cosh(x) - 1260a cosh(x) + 756a cosh(x) +--R + +--R - 168a +--R * +--R coth(x) +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 14 2 13 +--R - 21a coth(x)sinh(x) - 294a cosh(x)coth(x)sinh(x) +--R + +--R 2 2 12 2 3 11 +--R - 1911a cosh(x) coth(x)sinh(x) - 7644a cosh(x) coth(x)sinh(x) +--R + +--R 2 4 2 10 +--R (- 21021a cosh(x) + 294a )coth(x)sinh(x) +--R + +--R 2 5 2 9 +--R (- 42042a cosh(x) + 2940a cosh(x))coth(x)sinh(x) +--R + +--R 2 6 2 2 2 8 +--R (- 63063a cosh(x) + 13230a cosh(x) - 588a )coth(x)sinh(x) +--R + +--R 2 7 2 3 2 7 +--R (- 72072a cosh(x) + 35280a cosh(x) - 4704a cosh(x))coth(x)sinh(x) +--R + +--R 2 8 2 4 2 2 2 +--R (- 63063a cosh(x) + 61740a cosh(x) - 16464a cosh(x) + 147a ) +--R * +--R 6 +--R coth(x)sinh(x) +--R + +--R 2 9 2 5 2 3 +--R - 42042a cosh(x) + 74088a cosh(x) - 32928a cosh(x) +--R + +--R 2 +--R 882a cosh(x) +--R * +--R 5 +--R coth(x)sinh(x) +--R + +--R 2 10 2 6 2 4 +--R - 21021a cosh(x) + 61740a cosh(x) - 41160a cosh(x) +--R + +--R 2 2 2 +--R 2205a cosh(x) + 588a +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 2 11 2 7 2 5 +--R - 7644a cosh(x) + 35280a cosh(x) - 32928a cosh(x) +--R + +--R 2 3 2 +--R 2940a cosh(x) + 2352a cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 2 12 2 8 2 6 +--R - 1911a cosh(x) + 13230a cosh(x) - 16464a cosh(x) +--R + +--R 2 4 2 2 2 +--R 2205a cosh(x) + 3528a cosh(x) - 588a +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 2 13 2 9 2 7 +--R - 294a cosh(x) + 2940a cosh(x) - 4704a cosh(x) +--R + +--R 2 5 2 3 2 +--R 882a cosh(x) + 2352a cosh(x) - 1176a cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 2 14 2 10 2 8 2 6 +--R - 21a cosh(x) + 294a cosh(x) - 588a cosh(x) + 147a cosh(x) +--R + +--R 2 4 2 2 2 +--R 588a cosh(x) - 588a cosh(x) + 168a +--R * +--R coth(x) +--R * +--R +-------+ +--R \|coth(x) +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R 14 13 +--R - 42a sinh(x) - 588a cosh(x)sinh(x) +--R + +--R 2 12 +--R (- 3822a cosh(x) + 336a)sinh(x) +--R + +--R 3 11 +--R (- 15288a cosh(x) + 4032a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 42042a cosh(x) + 22176a cosh(x) - 756a)sinh(x) +--R + +--R 5 3 9 +--R (- 84084a cosh(x) + 73920a cosh(x) - 7560a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 126126a cosh(x) + 166320a cosh(x) - 34020a cosh(x) +--R + +--R 168a +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R - 144144a cosh(x) + 266112a cosh(x) - 90720a cosh(x) +--R + +--R 1344a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R - 126126a cosh(x) + 310464a cosh(x) - 158760a cosh(x) +--R + +--R 2 +--R 4704a cosh(x) + 1638a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R - 84084a cosh(x) + 266112a cosh(x) - 190512a cosh(x) +--R + +--R 3 +--R 9408a cosh(x) + 9828a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R - 42042a cosh(x) + 166320a cosh(x) - 158760a cosh(x) +--R + +--R 4 2 +--R 11760a cosh(x) + 24570a cosh(x) - 2520a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R - 15288a cosh(x) + 73920a cosh(x) - 90720a cosh(x) +--R + +--R 5 3 +--R 9408a cosh(x) + 32760a cosh(x) - 10080a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R - 3822a cosh(x) + 22176a cosh(x) - 34020a cosh(x) +--R + +--R 6 4 2 +--R 4704a cosh(x) + 24570a cosh(x) - 15120a cosh(x) + 1512a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R - 588a cosh(x) + 4032a cosh(x) - 7560a cosh(x) +--R + +--R 7 5 3 +--R 1344a cosh(x) + 9828a cosh(x) - 10080a cosh(x) +--R + +--R 3024a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 42a cosh(x) + 336a cosh(x) - 756a cosh(x) + 168a cosh(x) +--R + +--R 6 4 2 +--R 1638a cosh(x) - 2520a cosh(x) + 1512a cosh(x) - 336a +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 14 13 2 12 +--R 42a sinh(x) + 588a cosh(x)sinh(x) + 3822a cosh(x) sinh(x) +--R + +--R 3 11 4 10 +--R 15288a cosh(x) sinh(x) + (42042a cosh(x) - 588a)sinh(x) +--R + +--R 5 9 +--R (84084a cosh(x) - 5880a cosh(x))sinh(x) +--R + +--R 6 2 8 +--R (126126a cosh(x) - 26460a cosh(x) + 1176a)sinh(x) +--R + +--R 7 3 7 +--R (144144a cosh(x) - 70560a cosh(x) + 9408a cosh(x))sinh(x) +--R + +--R 8 4 2 +--R (126126a cosh(x) - 123480a cosh(x) + 32928a cosh(x) - 294a) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 5 3 +--R 84084a cosh(x) - 148176a cosh(x) + 65856a cosh(x) +--R + +--R - 1764a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 4 +--R 42042a cosh(x) - 123480a cosh(x) + 82320a cosh(x) +--R + +--R 2 +--R - 4410a cosh(x) - 1176a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 5 +--R 15288a cosh(x) - 70560a cosh(x) + 65856a cosh(x) +--R + +--R 3 +--R - 5880a cosh(x) - 4704a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 6 +--R 3822a cosh(x) - 26460a cosh(x) + 32928a cosh(x) +--R + +--R 4 2 +--R - 4410a cosh(x) - 7056a cosh(x) + 1176a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 7 +--R 588a cosh(x) - 5880a cosh(x) + 9408a cosh(x) +--R + +--R 5 3 +--R - 1764a cosh(x) - 4704a cosh(x) + 2352a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 8 6 +--R 42a cosh(x) - 588a cosh(x) + 1176a cosh(x) - 294a cosh(x) +--R + +--R 4 2 +--R - 1176a cosh(x) + 1176a cosh(x) - 336a +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R | 3 +-------+ +--R \|a coth(x) atanh(\|coth(x) ) +--R + +--R 14 13 +--R 42a sinh(x) + 588a cosh(x)sinh(x) +--R + +--R 2 12 +--R (3822a cosh(x) - 336a)sinh(x) +--R + +--R 3 11 +--R (15288a cosh(x) - 4032a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (42042a cosh(x) - 22176a cosh(x) + 756a)sinh(x) +--R + +--R 5 3 9 +--R (84084a cosh(x) - 73920a cosh(x) + 7560a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (126126a cosh(x) - 166320a cosh(x) + 34020a cosh(x) - 168a) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R 144144a cosh(x) - 266112a cosh(x) + 90720a cosh(x) +--R + +--R - 1344a cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R 126126a cosh(x) - 310464a cosh(x) + 158760a cosh(x) +--R + +--R 2 +--R - 4704a cosh(x) - 1638a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R 84084a cosh(x) - 266112a cosh(x) + 190512a cosh(x) +--R + +--R 3 +--R - 9408a cosh(x) - 9828a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R 42042a cosh(x) - 166320a cosh(x) + 158760a cosh(x) +--R + +--R 4 2 +--R - 11760a cosh(x) - 24570a cosh(x) + 2520a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R 15288a cosh(x) - 73920a cosh(x) + 90720a cosh(x) +--R + +--R 5 3 +--R - 9408a cosh(x) - 32760a cosh(x) + 10080a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R 3822a cosh(x) - 22176a cosh(x) + 34020a cosh(x) +--R + +--R 6 4 2 +--R - 4704a cosh(x) - 24570a cosh(x) + 15120a cosh(x) - 1512a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R 588a cosh(x) - 4032a cosh(x) + 7560a cosh(x) +--R + +--R 7 5 3 +--R - 1344a cosh(x) - 9828a cosh(x) + 10080a cosh(x) +--R + +--R - 3024a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R 42a cosh(x) - 336a cosh(x) + 756a cosh(x) - 168a cosh(x) +--R + +--R 6 4 2 +--R - 1638a cosh(x) + 2520a cosh(x) - 1512a cosh(x) + 336a +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 14 13 2 12 +--R - 42a sinh(x) - 588a cosh(x)sinh(x) - 3822a cosh(x) sinh(x) +--R + +--R 3 11 4 10 +--R - 15288a cosh(x) sinh(x) + (- 42042a cosh(x) + 588a)sinh(x) +--R + +--R 5 9 +--R (- 84084a cosh(x) + 5880a cosh(x))sinh(x) +--R + +--R 6 2 8 +--R (- 126126a cosh(x) + 26460a cosh(x) - 1176a)sinh(x) +--R + +--R 7 3 7 +--R (- 144144a cosh(x) + 70560a cosh(x) - 9408a cosh(x))sinh(x) +--R + +--R 8 4 2 +--R - 126126a cosh(x) + 123480a cosh(x) - 32928a cosh(x) +--R + +--R 294a +--R * +--R 6 +--R sinh(x) +--R + +--R 9 5 3 +--R - 84084a cosh(x) + 148176a cosh(x) - 65856a cosh(x) +--R + +--R 1764a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 4 +--R - 42042a cosh(x) + 123480a cosh(x) - 82320a cosh(x) +--R + +--R 2 +--R 4410a cosh(x) + 1176a +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 5 +--R - 15288a cosh(x) + 70560a cosh(x) - 65856a cosh(x) +--R + +--R 3 +--R 5880a cosh(x) + 4704a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 6 +--R - 3822a cosh(x) + 26460a cosh(x) - 32928a cosh(x) +--R + +--R 4 2 +--R 4410a cosh(x) + 7056a cosh(x) - 1176a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 7 +--R - 588a cosh(x) + 5880a cosh(x) - 9408a cosh(x) +--R + +--R 5 3 +--R 1764a cosh(x) + 4704a cosh(x) - 2352a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 8 6 +--R - 42a cosh(x) + 588a cosh(x) - 1176a cosh(x) + 294a cosh(x) +--R + +--R 4 2 +--R 1176a cosh(x) - 1176a cosh(x) + 336a +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R | 3 +-------+ +--R \|a coth(x) atan(\|coth(x) ) +--R + +--R 14 13 +--R - 42a coth(x)sinh(x) - 588a cosh(x)coth(x)sinh(x) +--R + +--R 2 12 +--R (- 3822a cosh(x) + 336a)coth(x)sinh(x) +--R + +--R 3 11 +--R (- 15288a cosh(x) + 4032a cosh(x))coth(x)sinh(x) +--R + +--R 4 2 10 +--R (- 42042a cosh(x) + 22176a cosh(x) - 756a)coth(x)sinh(x) +--R + +--R 5 3 +--R (- 84084a cosh(x) + 73920a cosh(x) - 7560a cosh(x))coth(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 4 2 +--R - 126126a cosh(x) + 166320a cosh(x) - 34020a cosh(x) +--R + +--R 168a +--R * +--R 8 +--R coth(x)sinh(x) +--R + +--R 7 5 3 +--R - 144144a cosh(x) + 266112a cosh(x) - 90720a cosh(x) +--R + +--R 1344a cosh(x) +--R * +--R 7 +--R coth(x)sinh(x) +--R + +--R 8 6 4 +--R - 126126a cosh(x) + 310464a cosh(x) - 158760a cosh(x) +--R + +--R 2 +--R 4704a cosh(x) + 1638a +--R * +--R 6 +--R coth(x)sinh(x) +--R + +--R 9 7 5 +--R - 84084a cosh(x) + 266112a cosh(x) - 190512a cosh(x) +--R + +--R 3 +--R 9408a cosh(x) + 9828a cosh(x) +--R * +--R 5 +--R coth(x)sinh(x) +--R + +--R 10 8 6 +--R - 42042a cosh(x) + 166320a cosh(x) - 158760a cosh(x) +--R + +--R 4 2 +--R 11760a cosh(x) + 24570a cosh(x) - 2520a +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 11 9 7 +--R - 15288a cosh(x) + 73920a cosh(x) - 90720a cosh(x) +--R + +--R 5 3 +--R 9408a cosh(x) + 32760a cosh(x) - 10080a cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 12 10 8 +--R - 3822a cosh(x) + 22176a cosh(x) - 34020a cosh(x) +--R + +--R 6 4 2 +--R 4704a cosh(x) + 24570a cosh(x) - 15120a cosh(x) + 1512a +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 13 11 9 +--R - 588a cosh(x) + 4032a cosh(x) - 7560a cosh(x) +--R + +--R 7 5 3 +--R 1344a cosh(x) + 9828a cosh(x) - 10080a cosh(x) +--R + +--R 3024a cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 14 12 10 +--R - 42a cosh(x) + 336a cosh(x) - 756a cosh(x) +--R + +--R 8 6 4 +--R 168a cosh(x) + 1638a cosh(x) - 2520a cosh(x) +--R + +--R 2 +--R 1512a cosh(x) - 336a +--R * +--R coth(x) +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 14 2 13 +--R - 42a coth(x)sinh(x) - 588a cosh(x)coth(x)sinh(x) +--R + +--R 2 2 12 2 3 11 +--R - 3822a cosh(x) coth(x)sinh(x) - 15288a cosh(x) coth(x)sinh(x) +--R + +--R 2 4 2 10 +--R (- 42042a cosh(x) + 588a )coth(x)sinh(x) +--R + +--R 2 5 2 9 +--R (- 84084a cosh(x) + 5880a cosh(x))coth(x)sinh(x) +--R + +--R 2 6 2 2 2 8 +--R (- 126126a cosh(x) + 26460a cosh(x) - 1176a )coth(x)sinh(x) +--R + +--R 2 7 2 3 2 7 +--R (- 144144a cosh(x) + 70560a cosh(x) - 9408a cosh(x))coth(x)sinh(x) +--R + +--R 2 8 2 4 2 2 2 +--R (- 126126a cosh(x) + 123480a cosh(x) - 32928a cosh(x) + 294a ) +--R * +--R 6 +--R coth(x)sinh(x) +--R + +--R 2 9 2 5 2 3 +--R - 84084a cosh(x) + 148176a cosh(x) - 65856a cosh(x) +--R + +--R 2 +--R 1764a cosh(x) +--R * +--R 5 +--R coth(x)sinh(x) +--R + +--R 2 10 2 6 2 4 +--R - 42042a cosh(x) + 123480a cosh(x) - 82320a cosh(x) +--R + +--R 2 2 2 +--R 4410a cosh(x) + 1176a +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 2 11 2 7 2 5 +--R - 15288a cosh(x) + 70560a cosh(x) - 65856a cosh(x) +--R + +--R 2 3 2 +--R 5880a cosh(x) + 4704a cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 2 12 2 8 2 6 +--R - 3822a cosh(x) + 26460a cosh(x) - 32928a cosh(x) +--R + +--R 2 4 2 2 2 +--R 4410a cosh(x) + 7056a cosh(x) - 1176a +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 2 13 2 9 2 7 +--R - 588a cosh(x) + 5880a cosh(x) - 9408a cosh(x) +--R + +--R 2 5 2 3 2 +--R 1764a cosh(x) + 4704a cosh(x) - 2352a cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 2 14 2 10 2 8 2 6 +--R - 42a cosh(x) + 588a cosh(x) - 1176a cosh(x) + 294a cosh(x) +--R + +--R 2 4 2 2 2 +--R 1176a cosh(x) - 1176a cosh(x) + 336a +--R * +--R coth(x) +--R * +--R +-------+ +--R \|coth(x) +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R 3 14 +--R (12a coth(x) + 28a coth(x))sinh(x) +--R + +--R 3 13 +--R (168a cosh(x)coth(x) + 392a cosh(x)coth(x))sinh(x) +--R + +--R 2 3 +--R (1092a cosh(x) - 96a)coth(x) +--R + +--R 2 +--R (2548a cosh(x) - 224a)coth(x) +--R * +--R 12 +--R sinh(x) +--R + +--R 3 3 +--R (4368a cosh(x) - 1152a cosh(x))coth(x) +--R + +--R 3 +--R (10192a cosh(x) - 2688a cosh(x))coth(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 4 2 3 +--R (12012a cosh(x) - 6336a cosh(x) + 216a)coth(x) +--R + +--R 4 2 +--R (28028a cosh(x) - 14784a cosh(x) + 504a)coth(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 5 3 3 +--R (24024a cosh(x) - 21120a cosh(x) + 2160a cosh(x))coth(x) +--R + +--R 5 3 +--R (56056a cosh(x) - 49280a cosh(x) + 5040a cosh(x))coth(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 4 2 +--R (36036a cosh(x) - 47520a cosh(x) + 9720a cosh(x) - 48a) +--R * +--R 3 +--R coth(x) +--R + +--R 6 4 2 +--R 84084a cosh(x) - 110880a cosh(x) + 22680a cosh(x) +--R + +--R - 112a +--R * +--R coth(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R 41184a cosh(x) - 76032a cosh(x) + 25920a cosh(x) +--R + +--R - 384a cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 7 5 3 +--R 96096a cosh(x) - 177408a cosh(x) + 60480a cosh(x) +--R + +--R - 896a cosh(x) +--R * +--R coth(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 +--R 36036a cosh(x) - 88704a cosh(x) + 45360a cosh(x) +--R + +--R 2 +--R - 1344a cosh(x) - 468a +--R * +--R 3 +--R coth(x) +--R + +--R 8 6 4 +--R 84084a cosh(x) - 206976a cosh(x) + 105840a cosh(x) +--R + +--R 2 +--R - 3136a cosh(x) - 1092a +--R * +--R coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 +--R 24024a cosh(x) - 76032a cosh(x) + 54432a cosh(x) +--R + +--R 3 +--R - 2688a cosh(x) - 2808a cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 9 7 5 +--R 56056a cosh(x) - 177408a cosh(x) + 127008a cosh(x) +--R + +--R 3 +--R - 6272a cosh(x) - 6552a cosh(x) +--R * +--R coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 +--R 12012a cosh(x) - 47520a cosh(x) + 45360a cosh(x) +--R + +--R 4 2 +--R - 3360a cosh(x) - 7020a cosh(x) + 720a +--R * +--R 3 +--R coth(x) +--R + +--R 10 8 6 +--R 28028a cosh(x) - 110880a cosh(x) + 105840a cosh(x) +--R + +--R 4 2 +--R - 7840a cosh(x) - 16380a cosh(x) + 1680a +--R * +--R coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 +--R 4368a cosh(x) - 21120a cosh(x) + 25920a cosh(x) +--R + +--R 5 3 +--R - 2688a cosh(x) - 9360a cosh(x) + 2880a cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 11 9 7 +--R 10192a cosh(x) - 49280a cosh(x) + 60480a cosh(x) +--R + +--R 5 3 +--R - 6272a cosh(x) - 21840a cosh(x) + 6720a cosh(x) +--R * +--R coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 +--R 1092a cosh(x) - 6336a cosh(x) + 9720a cosh(x) +--R + +--R 6 4 2 +--R - 1344a cosh(x) - 7020a cosh(x) + 4320a cosh(x) - 432a +--R * +--R 3 +--R coth(x) +--R + +--R 12 10 8 +--R 2548a cosh(x) - 14784a cosh(x) + 22680a cosh(x) +--R + +--R 6 4 2 +--R - 3136a cosh(x) - 16380a cosh(x) + 10080a cosh(x) +--R + +--R - 1008a +--R * +--R coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R 168a cosh(x) - 1152a cosh(x) + 2160a cosh(x) +--R + +--R 7 5 3 +--R - 384a cosh(x) - 2808a cosh(x) + 2880a cosh(x) +--R + +--R - 864a cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 13 11 9 +--R 392a cosh(x) - 2688a cosh(x) + 5040a cosh(x) +--R + +--R 7 5 3 +--R - 896a cosh(x) - 6552a cosh(x) + 6720a cosh(x) +--R + +--R - 2016a cosh(x) +--R * +--R coth(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R 12a cosh(x) - 96a cosh(x) + 216a cosh(x) - 48a cosh(x) +--R + +--R 6 4 2 +--R - 468a cosh(x) + 720a cosh(x) - 432a cosh(x) + 96a +--R * +--R 3 +--R coth(x) +--R + +--R 14 12 10 +--R 28a cosh(x) - 224a cosh(x) + 504a cosh(x) +--R + +--R 8 6 4 +--R - 112a cosh(x) - 1092a cosh(x) + 1680a cosh(x) +--R + +--R 2 +--R - 1008a cosh(x) + 224a +--R * +--R coth(x) +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 3 14 +--R (- 12a coth(x) - 28a coth(x))sinh(x) +--R + +--R 3 13 +--R (- 168a cosh(x)coth(x) - 392a cosh(x)coth(x))sinh(x) +--R + +--R 2 3 2 12 +--R (- 1092a cosh(x) coth(x) - 2548a cosh(x) coth(x))sinh(x) +--R + +--R 3 3 3 11 +--R (- 4368a cosh(x) coth(x) - 10192a cosh(x) coth(x))sinh(x) +--R + +--R 4 3 +--R (- 12012a cosh(x) + 168a)coth(x) +--R + +--R 4 +--R (- 28028a cosh(x) + 392a)coth(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 5 3 +--R (- 24024a cosh(x) + 1680a cosh(x))coth(x) +--R + +--R 5 +--R (- 56056a cosh(x) + 3920a cosh(x))coth(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 2 3 +--R (- 36036a cosh(x) + 7560a cosh(x) - 336a)coth(x) +--R + +--R 6 2 +--R (- 84084a cosh(x) + 17640a cosh(x) - 784a)coth(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 3 3 +--R (- 41184a cosh(x) + 20160a cosh(x) - 2688a cosh(x))coth(x) +--R + +--R 7 3 +--R (- 96096a cosh(x) + 47040a cosh(x) - 6272a cosh(x))coth(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 4 2 +--R - 36036a cosh(x) + 35280a cosh(x) - 9408a cosh(x) +--R + +--R 84a +--R * +--R 3 +--R coth(x) +--R + +--R 8 4 2 +--R - 84084a cosh(x) + 82320a cosh(x) - 21952a cosh(x) +--R + +--R 196a +--R * +--R coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 5 3 +--R - 24024a cosh(x) + 42336a cosh(x) - 18816a cosh(x) +--R + +--R 504a cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 9 5 3 +--R - 56056a cosh(x) + 98784a cosh(x) - 43904a cosh(x) +--R + +--R 1176a cosh(x) +--R * +--R coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 4 +--R - 12012a cosh(x) + 35280a cosh(x) - 23520a cosh(x) +--R + +--R 2 +--R 1260a cosh(x) + 336a +--R * +--R 3 +--R coth(x) +--R + +--R 10 6 4 +--R - 28028a cosh(x) + 82320a cosh(x) - 54880a cosh(x) +--R + +--R 2 +--R 2940a cosh(x) + 784a +--R * +--R coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 5 +--R - 4368a cosh(x) + 20160a cosh(x) - 18816a cosh(x) +--R + +--R 3 +--R 1680a cosh(x) + 1344a cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 11 7 5 +--R - 10192a cosh(x) + 47040a cosh(x) - 43904a cosh(x) +--R + +--R 3 +--R 3920a cosh(x) + 3136a cosh(x) +--R * +--R coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 6 +--R - 1092a cosh(x) + 7560a cosh(x) - 9408a cosh(x) +--R + +--R 4 2 +--R 1260a cosh(x) + 2016a cosh(x) - 336a +--R * +--R 3 +--R coth(x) +--R + +--R 12 8 6 +--R - 2548a cosh(x) + 17640a cosh(x) - 21952a cosh(x) +--R + +--R 4 2 +--R 2940a cosh(x) + 4704a cosh(x) - 784a +--R * +--R coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 7 +--R - 168a cosh(x) + 1680a cosh(x) - 2688a cosh(x) +--R + +--R 5 3 +--R 504a cosh(x) + 1344a cosh(x) - 672a cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 13 9 7 +--R - 392a cosh(x) + 3920a cosh(x) - 6272a cosh(x) +--R + +--R 5 3 +--R 1176a cosh(x) + 3136a cosh(x) - 1568a cosh(x) +--R * +--R coth(x) +--R * +--R sinh(x) +--R + +--R 14 10 8 +--R - 12a cosh(x) + 168a cosh(x) - 336a cosh(x) +--R + +--R 6 4 2 +--R 84a cosh(x) + 336a cosh(x) - 336a cosh(x) + 96a +--R * +--R 3 +--R coth(x) +--R + +--R 14 10 8 +--R - 28a cosh(x) + 392a cosh(x) - 784a cosh(x) +--R + +--R 6 4 2 +--R 196a cosh(x) + 784a cosh(x) - 784a cosh(x) + 224a +--R * +--R coth(x) +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R +-------+ | 3 +--R \|coth(x) \|a coth(x) +--R + +--R 12 11 +--R 448a coth(x)sinh(x) + 5376a cosh(x)coth(x)sinh(x) +--R + +--R 2 10 +--R (29568a cosh(x) - 1008a)coth(x)sinh(x) +--R + +--R 3 9 +--R (98560a cosh(x) - 10080a cosh(x))coth(x)sinh(x) +--R + +--R 4 2 8 +--R (221760a cosh(x) - 45360a cosh(x) )coth(x)sinh(x) +--R + +--R 5 3 7 +--R (354816a cosh(x) - 120960a cosh(x) )coth(x)sinh(x) +--R + +--R 6 4 6 +--R (413952a cosh(x) - 211680a cosh(x) + 1904a)coth(x)sinh(x) +--R + +--R 7 5 +--R (354816a cosh(x) - 254016a cosh(x) + 11424a cosh(x))coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 2 +--R (221760a cosh(x) - 211680a cosh(x) + 28560a cosh(x) - 2688a) +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 9 7 3 +--R 98560a cosh(x) - 120960a cosh(x) + 38080a cosh(x) +--R + +--R - 10752a cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 10 8 4 +--R 29568a cosh(x) - 45360a cosh(x) + 28560a cosh(x) +--R + +--R 2 +--R - 16128a cosh(x) + 1344a +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 11 9 5 +--R 5376a cosh(x) - 10080a cosh(x) + 11424a cosh(x) +--R + +--R 3 +--R - 10752a cosh(x) + 2688a cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 12 10 6 +--R 448a cosh(x) - 1008a cosh(x) + 1904a cosh(x) +--R + +--R 4 2 +--R - 2688a cosh(x) + 1344a cosh(x) +--R * +--R coth(x) +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 14 2 13 +--R - 80a coth(x)sinh(x) - 1120a cosh(x)coth(x)sinh(x) +--R + +--R 2 2 2 12 +--R (- 7280a cosh(x) + 112a )coth(x)sinh(x) +--R + +--R 2 3 2 11 +--R (- 29120a cosh(x) + 1344a cosh(x))coth(x)sinh(x) +--R + +--R 2 4 2 2 2 10 +--R (- 80080a cosh(x) + 7392a cosh(x) + 896a )coth(x)sinh(x) +--R + +--R 2 5 2 3 2 9 +--R (- 160160a cosh(x) + 24640a cosh(x) + 8960a cosh(x))coth(x)sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (- 240240a cosh(x) + 55440a cosh(x) + 40320a cosh(x) - 1232a ) +--R * +--R 8 +--R coth(x)sinh(x) +--R + +--R 2 7 2 5 2 3 +--R - 274560a cosh(x) + 88704a cosh(x) + 107520a cosh(x) +--R + +--R 2 +--R - 9856a cosh(x) +--R * +--R 7 +--R coth(x)sinh(x) +--R + +--R 2 8 2 6 2 4 +--R - 240240a cosh(x) + 103488a cosh(x) + 188160a cosh(x) +--R + +--R 2 2 2 +--R - 34496a cosh(x) + 112a +--R * +--R 6 +--R coth(x)sinh(x) +--R + +--R 2 9 2 7 2 5 +--R - 160160a cosh(x) + 88704a cosh(x) + 225792a cosh(x) +--R + +--R 2 3 2 +--R - 68992a cosh(x) + 672a cosh(x) +--R * +--R 5 +--R coth(x)sinh(x) +--R + +--R 2 10 2 8 2 6 +--R - 80080a cosh(x) + 55440a cosh(x) + 188160a cosh(x) +--R + +--R 2 4 2 2 2 +--R - 86240a cosh(x) + 1680a cosh(x) + 1344a +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 2 11 2 9 2 7 +--R - 29120a cosh(x) + 24640a cosh(x) + 107520a cosh(x) +--R + +--R 2 5 2 3 2 +--R - 68992a cosh(x) + 2240a cosh(x) + 5376a cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 2 12 2 10 2 8 +--R - 7280a cosh(x) + 7392a cosh(x) + 40320a cosh(x) +--R + +--R 2 6 2 4 2 2 2 +--R - 34496a cosh(x) + 1680a cosh(x) + 8064a cosh(x) - 1344a +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 2 13 2 11 2 9 +--R - 1120a cosh(x) + 1344a cosh(x) + 8960a cosh(x) +--R + +--R 2 7 2 5 2 3 2 +--R - 9856a cosh(x) + 672a cosh(x) + 5376a cosh(x) - 2688a cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 2 14 2 12 2 10 +--R - 80a cosh(x) + 112a cosh(x) + 896a cosh(x) +--R + +--R 2 8 2 6 2 4 2 2 +--R - 1232a cosh(x) + 112a cosh(x) + 1344a cosh(x) - 1344a cosh(x) +--R * +--R coth(x) +--R * +--R +-------+ +--R \|coth(x) +--R / +--R 14 13 +--R 42coth(x)sinh(x) + 588cosh(x)coth(x)sinh(x) +--R + +--R 2 12 +--R (3822cosh(x) - 336)coth(x)sinh(x) +--R + +--R 3 11 +--R (15288cosh(x) - 4032cosh(x))coth(x)sinh(x) +--R + +--R 4 2 10 +--R (42042cosh(x) - 22176cosh(x) + 756)coth(x)sinh(x) +--R + +--R 5 3 9 +--R (84084cosh(x) - 73920cosh(x) + 7560cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (126126cosh(x) - 166320cosh(x) + 34020cosh(x) - 168)coth(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 +--R (144144cosh(x) - 266112cosh(x) + 90720cosh(x) - 1344cosh(x)) +--R * +--R 7 +--R coth(x)sinh(x) +--R + +--R 8 6 4 2 +--R 126126cosh(x) - 310464cosh(x) + 158760cosh(x) - 4704cosh(x) +--R + +--R - 1638 +--R * +--R 6 +--R coth(x)sinh(x) +--R + +--R 9 7 5 3 +--R 84084cosh(x) - 266112cosh(x) + 190512cosh(x) - 9408cosh(x) +--R + +--R - 9828cosh(x) +--R * +--R 5 +--R coth(x)sinh(x) +--R + +--R 10 8 6 +--R 42042cosh(x) - 166320cosh(x) + 158760cosh(x) +--R + +--R 4 2 +--R - 11760cosh(x) - 24570cosh(x) + 2520 +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 11 9 7 5 +--R 15288cosh(x) - 73920cosh(x) + 90720cosh(x) - 9408cosh(x) +--R + +--R 3 +--R - 32760cosh(x) + 10080cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 12 10 8 6 +--R 3822cosh(x) - 22176cosh(x) + 34020cosh(x) - 4704cosh(x) +--R + +--R 4 2 +--R - 24570cosh(x) + 15120cosh(x) - 1512 +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 13 11 9 7 +--R 588cosh(x) - 4032cosh(x) + 7560cosh(x) - 1344cosh(x) +--R + +--R 5 3 +--R - 9828cosh(x) + 10080cosh(x) - 3024cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 14 12 10 8 +--R 42cosh(x) - 336cosh(x) + 756cosh(x) - 168cosh(x) +--R + +--R 6 4 2 +--R - 1638cosh(x) + 2520cosh(x) - 1512cosh(x) + 336 +--R * +--R coth(x) +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 14 13 +--R - 42coth(x)sinh(x) - 588cosh(x)coth(x)sinh(x) +--R + +--R 2 12 3 11 +--R - 3822cosh(x) coth(x)sinh(x) - 15288cosh(x) coth(x)sinh(x) +--R + +--R 4 10 +--R (- 42042cosh(x) + 588)coth(x)sinh(x) +--R + +--R 5 9 +--R (- 84084cosh(x) + 5880cosh(x))coth(x)sinh(x) +--R + +--R 6 2 8 +--R (- 126126cosh(x) + 26460cosh(x) - 1176)coth(x)sinh(x) +--R + +--R 7 3 7 +--R (- 144144cosh(x) + 70560cosh(x) - 9408cosh(x))coth(x)sinh(x) +--R + +--R 8 4 2 +--R (- 126126cosh(x) + 123480cosh(x) - 32928cosh(x) + 294)coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 5 3 +--R (- 84084cosh(x) + 148176cosh(x) - 65856cosh(x) + 1764cosh(x)) +--R * +--R 5 +--R coth(x)sinh(x) +--R + +--R 10 6 4 +--R - 42042cosh(x) + 123480cosh(x) - 82320cosh(x) +--R + +--R 2 +--R 4410cosh(x) + 1176 +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 11 7 5 3 +--R - 15288cosh(x) + 70560cosh(x) - 65856cosh(x) + 5880cosh(x) +--R + +--R 4704cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 12 8 6 4 +--R - 3822cosh(x) + 26460cosh(x) - 32928cosh(x) + 4410cosh(x) +--R + +--R 2 +--R 7056cosh(x) - 1176 +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 13 9 7 5 +--R - 588cosh(x) + 5880cosh(x) - 9408cosh(x) + 1764cosh(x) +--R + +--R 3 +--R 4704cosh(x) - 2352cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 14 10 8 6 +--R - 42cosh(x) + 588cosh(x) - 1176cosh(x) + 294cosh(x) +--R + +--R 4 2 +--R 1176cosh(x) - 1176cosh(x) + 336 +--R * +--R coth(x) +--R * +--R +---+ +--R \|- a +--R * +--R +-------+ +--R \|coth(x) +--R Type: Expression(Integer) +--E 213 + +--S 214 of 508 +--d0341:= D(m0341,x) +--E 214 + +--S 215 of 508 +t0342:= 1/(a*coth(x)^2)^(1/2) +--R +--R +--R 1 +--R (183) ------------- +--R +----------+ +--R | 2 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 215 + +--S 216 of 508 +r0342:= coth(x)*log(cosh(x))/(a*coth(x)^2)^(1/2) +--R +--R +--R coth(x)log(cosh(x)) +--R (184) ------------------- +--R +----------+ +--R | 2 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 216 + +--S 217 of 508 +a0342:= integrate(t0342,x) +--R +--R +--R 2cosh(x) +--R log(- -----------------) - x +--R sinh(x) - cosh(x) +--R (185) ---------------------------- +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 217 + +--S 218 of 508 +m0342:= a0342-r0342 +--R +--R +--R (186) +--R +----------+ +--R 2cosh(x) | 2 +-+ +--R (log(- -----------------) - x)\|a coth(x) - coth(x)\|a log(cosh(x)) +--R sinh(x) - cosh(x) +--R --------------------------------------------------------------------- +--R +----------+ +--R +-+ | 2 +--R \|a \|a coth(x) +--R Type: Expression(Integer) +--E 218 + +--S 219 of 508 +d0342:= D(m0342,x) +--R +--R +--R +----------+ +--R +-+ | 2 +--R sinh(x)\|a \|a coth(x) - a coth(x)sinh(x) +--R (187) ------------------------------------------- +--R +----------+ +--R | 2 +--R a cosh(x)\|a coth(x) +--R Type: Expression(Integer) +--E 219 + +--S 220 of 508 +t0343:= 1/(a*coth(x)^3)^(1/2) +--R +--R +--R 1 +--R (188) ------------- +--R +----------+ +--R | 3 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 220 + +--S 221 of 508 +r0343:= -(2+(atan(coth(x)^(1/2))-atanh(coth(x)^(1/2)))*_ + coth(x)^(1/2))*coth(x)/(a*coth(x)^3)^(1/2) +--R +--R +--R (189) +--R +-------+ +-------+ +-------+ +-------+ +--R coth(x)\|coth(x) atanh(\|coth(x) ) - coth(x)\|coth(x) atan(\|coth(x) ) +--R + +--R - 2coth(x) +--R / +--R +----------+ +--R | 3 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 221 + +--S 222 of 508 +a0343:= integrate(t0343,x) +--R +--R +--R (190) +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)\|- a |--------- +--R \| sinh(x) +--R + +--R 2 2 +--R - a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2)\|- a |--------- +--R \| sinh(x) +--R + +--R 2 2 +--R - 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R - 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) +--R / +--R +---------+ +--R 2 2 |a cosh(x) +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) - 2a) |--------- +--R \| sinh(x) +--R + +--R 2 2 +---+ +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)\|- a +--R Type: Union(Expression(Integer),...) +--E 222 + +--S 223 of 508 +m0343:= a0343-r0343 +--R +--R +--R (191) +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)\|- a |--------- +--R \| sinh(x) +--R + +--R 2 2 +--R - a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a +--R * +--R +----------+ +--R | 3 +--R \|a coth(x) +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R log(-----------------------------------------------------------------) +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|- a +--R + +--R 2 +--R - 2a coth(x)sinh(x) - 4a cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (- 2a cosh(x) + 2a)coth(x) +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 2 +--R 2a coth(x)sinh(x) + 4a cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (2a cosh(x) + 2a)coth(x) +--R * +--R +---+ +--R \|- a +--R * +--R +-------+ +-------+ +--R \|coth(x) atanh(\|coth(x) ) +--R + +--R 2 +--R 2a coth(x)sinh(x) + 4a cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (2a cosh(x) - 2a)coth(x) +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 2 +--R - 2a coth(x)sinh(x) - 4a cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (- 2a cosh(x) - 2a)coth(x) +--R * +--R +---+ +--R \|- a +--R * +--R +-------+ +-------+ +--R \|coth(x) atan(\|coth(x) ) +--R + +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2)\|- a |--------- +--R \| sinh(x) +--R + +--R 2 2 +--R - 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a +--R * +--R +----------+ +--R | 3 +--R \|a coth(x) +--R * +--R +---------+ +--R 2 2 +---+ |a cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a |--------- + a +--R \| sinh(x) +--R atan(-----------------------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) +--R + +--R +----------+ +--R 2 2 | 3 +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) )\|a coth(x) +--R + +--R 2 +--R 4a coth(x)sinh(x) + 8a cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (4a cosh(x) - 4a)coth(x) +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 2 +--R - 4a coth(x)sinh(x) - 8a cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (- 4a cosh(x) - 4a)coth(x) +--R * +--R +---+ +--R \|- a +--R / +--R +---------+ +--R 2 2 |a cosh(x) +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) - 2a) |--------- +--R \| sinh(x) +--R + +--R 2 2 +---+ +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)\|- a +--R * +--R +----------+ +--R | 3 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 223 + +--S 224 of 508 +d0343:= D(m0343,x) +--R +--R +--R (192) +--R 14 13 2 12 +--R sinh(x) + 4cosh(x)sinh(x) + (- 15cosh(x) - 5)sinh(x) +--R + +--R 3 11 +--R (- 144cosh(x) + 10cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 451cosh(x) + 220cosh(x) + 10)sinh(x) +--R + +--R 5 3 9 +--R (- 748cosh(x) + 774cosh(x) - 80cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 627cosh(x) + 1127cosh(x) - 530cosh(x) - 10)sinh(x) +--R + +--R 5 3 7 +--R (292cosh(x) - 896cosh(x) + 140cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (627cosh(x) - 1456cosh(x) + 4cosh(x) + 420cosh(x) + 5) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 748cosh(x) - 2420cosh(x) + 1760cosh(x) + 44cosh(x) +--R + +--R - 100cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 451cosh(x) - 1831cosh(x) + 2300cosh(x) - 864cosh(x) +--R + +--R 2 +--R - 55cosh(x) - 1 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 144cosh(x) - 718cosh(x) + 1280cosh(x) - 956cosh(x) +--R + +--R 3 +--R 224cosh(x) + 26cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 15cosh(x) - 108cosh(x) + 274cosh(x) - 324cosh(x) +--R + +--R 4 2 +--R 183cosh(x) - 40cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 4cosh(x) + 14cosh(x) - 16cosh(x) + 4cosh(x) +--R + +--R 5 3 +--R 4cosh(x) - 2cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R - cosh(x) + 5cosh(x) - 10cosh(x) + 10cosh(x) - 5cosh(x) +--R + +--R 4 +--R cosh(x) +--R * +--R +---------+ +--R |a cosh(x) +--R |--------- +--R \| sinh(x) +--R + +--R 13 2 12 +--R - 4cosh(x)sinh(x) - 36cosh(x) sinh(x) +--R + +--R 3 11 +--R (- 136cosh(x) + 24cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 264cosh(x) + 132cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (- 220cosh(x) + 192cosh(x) - 56cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (132cosh(x) - 316cosh(x) - 136cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (528cosh(x) - 1520cosh(x) + 320cosh(x) + 64cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (528cosh(x) - 2296cosh(x) + 1600cosh(x) - 24cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R 132cosh(x) - 1568cosh(x) + 2320cosh(x) - 656cosh(x) +--R + +--R - 36cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 220cosh(x) - 88cosh(x) + 1264cosh(x) - 1064cosh(x) +--R + +--R 2 +--R 108cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 264cosh(x) + 664cosh(x) - 256cosh(x) - 416cosh(x) +--R + +--R 3 +--R 264cosh(x) + 8cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 136cosh(x) + 500cosh(x) - 640cosh(x) + 280cosh(x) +--R + +--R 4 2 +--R 40cosh(x) - 44cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 36cosh(x) + 160cosh(x) - 280cosh(x) + 240cosh(x) +--R + +--R 5 3 +--R - 100cosh(x) + 16cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 4cosh(x) + 20cosh(x) - 40cosh(x) + 40cosh(x) +--R + +--R 6 4 +--R - 20cosh(x) + 4cosh(x) +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R | 3 +--R \|a coth(x) +--R + +--R 13 2 12 +--R - 4cosh(x)sinh(x) - 32cosh(x) sinh(x) +--R + +--R 3 11 +--R (- 104cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 160cosh(x) - 88cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (- 60cosh(x) - 252cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (192cosh(x) - 288cosh(x) - 80cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (336cosh(x) + 168cosh(x) - 352cosh(x) - 8cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (192cosh(x) + 1008cosh(x) - 880cosh(x) - 64cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R - 60cosh(x) + 1512cosh(x) - 1360cosh(x) - 136cosh(x) +--R + +--R 12cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 160cosh(x) + 1248cosh(x) - 1328cosh(x) - 64cosh(x) +--R + +--R 2 +--R 112cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 104cosh(x) + 612cosh(x) - 800cosh(x) + 104cosh(x) +--R + +--R 3 +--R 168cosh(x) + 20cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 32cosh(x) + 168cosh(x) - 272cosh(x) + 128cosh(x) +--R + +--R 4 2 +--R 48cosh(x) - 40cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R - 4cosh(x) + 20cosh(x) - 40cosh(x) + 40cosh(x) - 20cosh(x) +--R + +--R 3 +--R 4cosh(x) +--R * +--R sinh(x) +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 12 3 11 +--R 8a cosh(x) sinh(x) + (72a cosh(x) - 4a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (280a cosh(x) - 24a cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (600a cosh(x) - 36a cosh(x) - 8a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (720a cosh(x) + 96a cosh(x) - 40a cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (336a cosh(x) + 504a cosh(x) - 40a cosh(x) - 8a cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (- 336a cosh(x) + 1008a cosh(x) + 152a cosh(x) - 64a cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R - 720a cosh(x) + 1176a cosh(x) + 520a cosh(x) - 264a cosh(x) +--R + +--R - 8a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 600a cosh(x) + 864a cosh(x) + 712a cosh(x) - 576a cosh(x) +--R + +--R 2 +--R - 48a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 280a cosh(x) + 396a cosh(x) + 520a cosh(x) - 664a cosh(x) +--R + +--R - 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 72a cosh(x) + 104a cosh(x) + 200a cosh(x) - 384a cosh(x) +--R + +--R 4 2 +--R 112a cosh(x) + 40a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 8a cosh(x) + 12a cosh(x) + 32a cosh(x) - 88a cosh(x) +--R + +--R 5 3 +--R 72a cosh(x) - 20a cosh(x) +--R * +--R sinh(x) +--R / +--R 13 2 12 +--R 4cosh(x)sinh(x) + 32cosh(x) sinh(x) +--R + +--R 3 11 +--R (104cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (160cosh(x) + 88cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (60cosh(x) + 252cosh(x) + 8cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 192cosh(x) + 288cosh(x) + 80cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (- 336cosh(x) - 168cosh(x) + 352cosh(x) + 8cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (- 192cosh(x) - 1008cosh(x) + 880cosh(x) + 64cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R 60cosh(x) - 1512cosh(x) + 1360cosh(x) + 136cosh(x) +--R + +--R - 12cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 160cosh(x) - 1248cosh(x) + 1328cosh(x) + 64cosh(x) +--R + +--R 2 +--R - 112cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 104cosh(x) - 612cosh(x) + 800cosh(x) - 104cosh(x) +--R + +--R 3 +--R - 168cosh(x) - 20cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 32cosh(x) - 168cosh(x) + 272cosh(x) - 128cosh(x) +--R + +--R 4 2 +--R - 48cosh(x) + 40cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R 4cosh(x) - 20cosh(x) + 40cosh(x) - 40cosh(x) + 20cosh(x) +--R + +--R 3 +--R - 4cosh(x) +--R * +--R sinh(x) +--R * +--R +---------+ +--R +---+ |a cosh(x) +--R \|- a |--------- +--R \| sinh(x) +--R + +--R 2 12 3 11 +--R - 8a cosh(x) sinh(x) + (- 72a cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 280a cosh(x) + 24a cosh(x) )sinh(x) +--R + +--R 5 3 9 +--R (- 600a cosh(x) + 36a cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 720a cosh(x) - 96a cosh(x) + 40a cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (- 336a cosh(x) - 504a cosh(x) + 40a cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (336a cosh(x) - 1008a cosh(x) - 152a cosh(x) + 64a cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R 720a cosh(x) - 1176a cosh(x) - 520a cosh(x) + 264a cosh(x) +--R + +--R 8a cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 600a cosh(x) - 864a cosh(x) - 712a cosh(x) + 576a cosh(x) +--R + +--R 2 +--R 48a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 280a cosh(x) - 396a cosh(x) - 520a cosh(x) + 664a cosh(x) +--R + +--R 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 72a cosh(x) - 104a cosh(x) - 200a cosh(x) + 384a cosh(x) +--R + +--R 4 2 +--R - 112a cosh(x) - 40a cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 8a cosh(x) - 12a cosh(x) - 32a cosh(x) + 88a cosh(x) +--R + +--R 5 3 +--R - 72a cosh(x) + 20a cosh(x) +--R * +--R sinh(x) +--R * +--R +----------+ +--R | 3 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 224 + +--S 225 of 508 +t0344:= 1/(a*coth(x)^4)^(1/2) +--R +--R +--R 1 +--R (193) ------------- +--R +----------+ +--R | 4 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 225 + +--S 226 of 508 +r0344:= coth(x)^2*(x-tanh(x))/(a*coth(x)^4)^(1/2) +--R +--R +--R 2 2 +--R - coth(x) tanh(x) + x coth(x) +--R (194) ------------------------------ +--R +----------+ +--R | 4 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 226 + +--S 227 of 508 +a0344:= integrate(t0344,x) +--R +--R +--R 2 2 +--R x sinh(x) + 2x cosh(x)sinh(x) + x cosh(x) + x + 2 +--R (195) --------------------------------------------------- +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|a +--R Type: Union(Expression(Integer),...) +--E 227 + +--S 228 of 508 +m0344:= a0344-r0344 +--R +--R +--R (196) +--R +----------+ +--R 2 2 | 4 +--R (x sinh(x) + 2x cosh(x)sinh(x) + x cosh(x) + x + 2)\|a coth(x) +--R + +--R 2 2 2 +--R coth(x) sinh(x) + 2cosh(x)coth(x) sinh(x) +--R + +--R 2 2 +--R (cosh(x) + 1)coth(x) +--R * +--R tanh(x) +--R + +--R 2 2 2 +--R - x coth(x) sinh(x) - 2x cosh(x)coth(x) sinh(x) +--R + +--R 2 2 +--R (- x cosh(x) - x)coth(x) +--R * +--R +-+ +--R \|a +--R / +--R +----------+ +--R 2 2 +-+ | 4 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|a \|a coth(x) +--R Type: Expression(Integer) +--E 228 + +--S 229 of 508 +d0344:= D(m0344,x) +--R +--R +--R (197) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R +----------+ +--R +-+ | 4 +--R \|a \|a coth(x) +--R + +--R 2 4 2 3 +--R - a coth(x) sinh(x) - 4a cosh(x)coth(x) sinh(x) +--R + +--R 2 2 2 +--R (- 6a cosh(x) - 2a)coth(x) sinh(x) +--R + +--R 3 2 +--R (- 4a cosh(x) - 4a cosh(x))coth(x) sinh(x) +--R + +--R 4 2 2 +--R (- a cosh(x) - 2a cosh(x) - a)coth(x) +--R * +--R 2 +--R tanh(x) +--R / +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R +----------+ +--R | 4 +--R \|a coth(x) +--R Type: Expression(Integer) +--E 229 + +--S 230 of 508 +t0345:= 1/(1+coth(x)) +--R +--R +--R 1 +--R (198) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 230 + +--S 231 of 508 +r0345:= 1/2*x-1/(2+2*coth(x)) +--R +--R +--R x coth(x) + x - 1 +--R (199) ----------------- +--R 2coth(x) + 2 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 508 +a0345:= integrate(t0345,x) +--R +--R +--R (2x - 1)sinh(x) + (2x + 1)cosh(x) +--R (200) --------------------------------- +--R 4sinh(x) + 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 232 + +--S 233 of 508 +m0345:= a0345-r0345 +--R +--R +--R (- coth(x) + 1)sinh(x) + cosh(x)coth(x) + 3cosh(x) +--R (201) -------------------------------------------------- +--R (4coth(x) + 4)sinh(x) + 4cosh(x)coth(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 233 + +--S 234 of 508 +d0345:= D(m0345,x) +--R +--R +--R coth(x)sinh(x) - cosh(x) +--R (202) ----------------------------------------------- +--R (coth(x) + 1)sinh(x) + cosh(x)coth(x) + cosh(x) +--R Type: Expression(Integer) +--E 234 + +--S 235 of 508 +t0346:= 1/(1+coth(x))^2 +--R +--R +--R 1 +--R (203) ----------------------- +--R 2 +--R coth(x) + 2coth(x) + 1 +--R Type: Expression(Integer) +--E 235 + +--S 236 of 508 +r0346:= 1/4*x-1/4/(1+coth(x))^2-1/(4+4*coth(x)) +--R +--R +--R 2 +--R x coth(x) + (2x - 1)coth(x) + x - 2 +--R (204) ------------------------------------ +--R 2 +--R 4coth(x) + 8coth(x) + 4 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 508 +a0346:= integrate(t0346,x) +--R +--R +--R 2 2 +--R (4x - 1)sinh(x) + (8x + 2)cosh(x)sinh(x) + (4x - 1)cosh(x) + 4 +--R (205) ---------------------------------------------------------------- +--R 2 2 +--R 16sinh(x) + 32cosh(x)sinh(x) + 16cosh(x) +--R Type: Union(Expression(Integer),...) +--E 237 + +--S 238 of 508 +m0346:= a0346-r0346 +--R +--R +--R (206) +--R 2 2 +--R (- coth(x) + 2coth(x) + 7)sinh(x) +--R + +--R 2 +--R (2cosh(x)coth(x) + 12cosh(x)coth(x) + 18cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R (- cosh(x) + 4)coth(x) + (2cosh(x) + 8)coth(x) + 7cosh(x) + 4 +--R / +--R 2 2 +--R (16coth(x) + 32coth(x) + 16)sinh(x) +--R + +--R 2 +--R (32cosh(x)coth(x) + 64cosh(x)coth(x) + 32cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R 16cosh(x) coth(x) + 32cosh(x) coth(x) + 16cosh(x) +--R Type: Expression(Integer) +--E 238 + +--S 239 of 508 +d0346:= D(m0346,x) +--R +--R +--R (207) +--R 2 2 +--R (coth(x) + 2coth(x) - 1)sinh(x) - 4cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (cosh(x) - 1)coth(x) + (2cosh(x) - 2)coth(x) - cosh(x) - 1 +--R / +--R 2 2 +--R (2coth(x) + 4coth(x) + 2)sinh(x) +--R + +--R 2 +--R (4cosh(x)coth(x) + 8cosh(x)coth(x) + 4cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R 2cosh(x) coth(x) + 4cosh(x) coth(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 239 + +--S 240 of 508 +t0347:= 1/(1+coth(x))^3 +--R +--R +--R 1 +--R (208) ----------------------------------- +--R 3 2 +--R coth(x) + 3coth(x) + 3coth(x) + 1 +--R Type: Expression(Integer) +--E 240 + +--S 241 of 508 +r0347:= 1/8*x-1/6/(1+coth(x))^3-1/8/(1+coth(x))^2-1/(8+8*coth(x)) +--R +--R +--R 3 2 +--R 3x coth(x) + (9x - 3)coth(x) + (9x - 9)coth(x) + 3x - 10 +--R (209) ---------------------------------------------------------- +--R 3 2 +--R 24coth(x) + 72coth(x) + 72coth(x) + 24 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 508 +a0347:= integrate(t0347,x) +--R +--R +--R (210) +--R 3 2 +--R (12x - 2)sinh(x) + (36x + 6)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((36x - 6)cosh(x) + 27)sinh(x) + (12x + 2)cosh(x) + 9cosh(x) +--R / +--R 3 2 2 3 +--R 96sinh(x) + 288cosh(x)sinh(x) + 288cosh(x) sinh(x) + 96cosh(x) +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 508 +m0347:= a0347-r0347 +--R +--R +--R (211) +--R 3 2 3 +--R (- 2coth(x) + 6coth(x) + 30coth(x) + 38)sinh(x) +--R + +--R 3 2 +--R (6cosh(x)coth(x) + 54cosh(x)coth(x) + 126cosh(x)coth(x) + 126cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 6cosh(x) + 27)coth(x) + (18cosh(x) + 81)coth(x) +--R + +--R 2 2 +--R (90cosh(x) + 81)coth(x) + 114cosh(x) + 27 +--R * +--R sinh(x) +--R + +--R 3 3 3 2 +--R (2cosh(x) + 9cosh(x))coth(x) + (18cosh(x) + 27cosh(x))coth(x) +--R + +--R 3 3 +--R (42cosh(x) + 27cosh(x))coth(x) + 42cosh(x) + 9cosh(x) +--R / +--R 3 2 3 +--R (96coth(x) + 288coth(x) + 288coth(x) + 96)sinh(x) +--R + +--R 3 2 +--R 288cosh(x)coth(x) + 864cosh(x)coth(x) + 864cosh(x)coth(x) +--R + +--R 288cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 2 +--R 288cosh(x) coth(x) + 864cosh(x) coth(x) + 864cosh(x) coth(x) +--R + +--R 2 +--R 288cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3 2 3 3 +--R 96cosh(x) coth(x) + 288cosh(x) coth(x) + 288cosh(x) coth(x) + 96cosh(x) +--R Type: Expression(Integer) +--E 243 + +--S 244 of 508 +d0347:= D(m0347,x) +--R +--R +--R (212) +--R 3 2 3 2 +--R (coth(x) + 3coth(x) + 3coth(x) - 3)sinh(x) - 12cosh(x)sinh(x) +--R + +--R 2 3 2 2 +--R (3cosh(x) - 3)coth(x) + (9cosh(x) - 9)coth(x) +--R + +--R 2 2 +--R (9cosh(x) - 9)coth(x) - 9cosh(x) - 3 +--R * +--R sinh(x) +--R + +--R 3 +--R - 4cosh(x) +--R / +--R 3 2 3 +--R (4coth(x) + 12coth(x) + 12coth(x) + 4)sinh(x) +--R + +--R 3 2 +--R (12cosh(x)coth(x) + 36cosh(x)coth(x) + 36cosh(x)coth(x) + 12cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 2 +--R 12cosh(x) coth(x) + 36cosh(x) coth(x) + 36cosh(x) coth(x) +--R + +--R 2 +--R 12cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 3 2 3 3 +--R 4cosh(x) coth(x) + 12cosh(x) coth(x) + 12cosh(x) coth(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 244 + +--S 245 of 508 +t0348:= (a+b*coth(c+d*x))^3 +--R +--R +--R 3 3 2 2 2 3 +--R (213) b coth(d x + c) + 3a b coth(d x + c) + 3a b coth(d x + c) + a +--R Type: Expression(Integer) +--E 245 + +--S 246 of 508 +r0348:= a^3*x+3*a*b^2*x-3*a*b^2*coth(c+d*x)/d-1/2*b^3*coth(c+d*x)^2/d+_ + 3*a^2*b*log(sinh(c+d*x))/d+b^3*log(sinh(c+d*x))/d +--R +--R +--R (214) +--R 3 2 3 2 2 +--R (2b + 6a b)log(sinh(d x + c)) - b coth(d x + c) - 6a b coth(d x + c) +--R + +--R 2 3 +--R (6a b + 2a )d x +--R / +--R 2d +--R Type: Expression(Integer) +--E 246 + +--S 247 of 508 +a0348:= integrate(t0348,x) +--R +--R +--R (215) +--R 3 2 4 3 2 3 +--R (b + 3a b)sinh(d x + c) + (4b + 12a b)cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 2 3 2 2 +--R ((6b + 18a b)cosh(d x + c) - 2b - 6a b)sinh(d x + c) +--R + +--R 3 2 3 3 2 +--R ((4b + 12a b)cosh(d x + c) + (- 4b - 12a b)cosh(d x + c)) +--R * +--R sinh(d x + c) +--R + +--R 3 2 4 3 2 2 3 2 +--R (b + 3a b)cosh(d x + c) + (- 2b - 6a b)cosh(d x + c) + b + 3a b +--R * +--R 2sinh(d x + c) +--R log(- -----------------------------) +--R sinh(d x + c) - cosh(d x + c) +--R + +--R 3 2 2 3 4 +--R (- b + 3a b - 3a b + a )d x sinh(d x + c) +--R + +--R 3 2 2 3 3 +--R (- 4b + 12a b - 12a b + 4a )d x cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 2 3 2 +--R (- 6b + 18a b - 18a b + 6a )d x cosh(d x + c) +--R + +--R 3 2 2 3 3 2 +--R (2b - 6a b + 6a b - 2a )d x - 2b - 6a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 2 2 3 3 +--R (- 4b + 12a b - 12a b + 4a )d x cosh(d x + c) +--R + +--R 3 2 2 3 3 2 +--R ((4b - 12a b + 12a b - 4a )d x - 4b - 12a b )cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 3 2 2 3 4 +--R (- b + 3a b - 3a b + a )d x cosh(d x + c) +--R + +--R 3 2 2 3 3 2 2 +--R ((2b - 6a b + 6a b - 2a )d x - 2b - 6a b )cosh(d x + c) +--R + +--R 3 2 2 3 2 +--R (- b + 3a b - 3a b + a )d x + 6a b +--R / +--R 4 3 +--R d sinh(d x + c) + 4d cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 +--R (6d cosh(d x + c) - 2d)sinh(d x + c) +--R + +--R 3 4 +--R (4d cosh(d x + c) - 4d cosh(d x + c))sinh(d x + c) + d cosh(d x + c) +--R + +--R 2 +--R - 2d cosh(d x + c) + d +--R Type: Union(Expression(Integer),...) +--E 247 + +--S 248 of 508 +m0348:= a0348-r0348 +--R +--R +--R (216) +--R 3 2 4 +--R (- 2b - 6a b)sinh(d x + c) +--R + +--R 3 2 3 +--R (- 8b - 24a b)cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 2 3 2 2 +--R ((- 12b - 36a b)cosh(d x + c) + 4b + 12a b)sinh(d x + c) +--R + +--R 3 2 3 3 2 +--R ((- 8b - 24a b)cosh(d x + c) + (8b + 24a b)cosh(d x + c)) +--R * +--R sinh(d x + c) +--R + +--R 3 2 4 3 2 2 3 2 +--R (- 2b - 6a b)cosh(d x + c) + (4b + 12a b)cosh(d x + c) - 2b - 6a b +--R * +--R log(sinh(d x + c)) +--R + +--R 3 2 4 3 2 3 +--R (2b + 6a b)sinh(d x + c) + (8b + 24a b)cosh(d x + c)sinh(d x + c) +--R + +--R 3 2 2 3 2 2 +--R ((12b + 36a b)cosh(d x + c) - 4b - 12a b)sinh(d x + c) +--R + +--R 3 2 3 3 2 +--R ((8b + 24a b)cosh(d x + c) + (- 8b - 24a b)cosh(d x + c)) +--R * +--R sinh(d x + c) +--R + +--R 3 2 4 3 2 2 3 2 +--R (2b + 6a b)cosh(d x + c) + (- 4b - 12a b)cosh(d x + c) + 2b + 6a b +--R * +--R 2sinh(d x + c) +--R log(- -----------------------------) +--R sinh(d x + c) - cosh(d x + c) +--R + +--R 3 2 2 3 2 4 +--R (b coth(d x + c) + 6a b coth(d x + c) + (- 2b - 6a b)d x)sinh(d x + c) +--R + +--R 3 2 2 +--R 4b cosh(d x + c)coth(d x + c) + 24a b cosh(d x + c)coth(d x + c) +--R + +--R 3 2 +--R (- 8b - 24a b)d x cosh(d x + c) +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 2 3 2 +--R (6b cosh(d x + c) - 2b )coth(d x + c) +--R + +--R 2 2 2 +--R (36a b cosh(d x + c) - 12a b )coth(d x + c) +--R + +--R 3 2 2 3 2 3 2 +--R (- 12b - 36a b)d x cosh(d x + c) + (4b + 12a b)d x - 4b - 12a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 3 3 2 +--R (4b cosh(d x + c) - 4b cosh(d x + c))coth(d x + c) +--R + +--R 2 3 2 +--R (24a b cosh(d x + c) - 24a b cosh(d x + c))coth(d x + c) +--R + +--R 3 2 3 +--R (- 8b - 24a b)d x cosh(d x + c) +--R + +--R 3 2 3 2 +--R ((8b + 24a b)d x - 8b - 24a b )cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 3 4 3 2 3 2 +--R (b cosh(d x + c) - 2b cosh(d x + c) + b )coth(d x + c) +--R + +--R 2 4 2 2 2 +--R (6a b cosh(d x + c) - 12a b cosh(d x + c) + 6a b )coth(d x + c) +--R + +--R 3 2 4 +--R (- 2b - 6a b)d x cosh(d x + c) +--R + +--R 3 2 3 2 2 3 2 +--R ((4b + 12a b)d x - 4b - 12a b )cosh(d x + c) + (- 2b - 6a b)d x +--R + +--R 2 +--R 12a b +--R / +--R 4 3 +--R 2d sinh(d x + c) + 8d cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 +--R (12d cosh(d x + c) - 4d)sinh(d x + c) +--R + +--R 3 4 +--R (8d cosh(d x + c) - 8d cosh(d x + c))sinh(d x + c) + 2d cosh(d x + c) +--R + +--R 2 +--R - 4d cosh(d x + c) + 2d +--R Type: Expression(Integer) +--E 248 + +--S 249 of 508 +d0348:= D(m0348,x) +--R +--R +--R (217) +--R 3 3 2 2 3 2 +--R (- b coth(d x + c) - 3a b coth(d x + c) + b coth(d x + c) + 3a b ) +--R * +--R 6 +--R sinh(d x + c) +--R + +--R 3 3 2 2 +--R - 6b cosh(d x + c)coth(d x + c) - 18a b cosh(d x + c)coth(d x + c) +--R + +--R 3 2 +--R 6b cosh(d x + c)coth(d x + c) + 18a b cosh(d x + c) +--R * +--R 5 +--R sinh(d x + c) +--R + +--R 3 2 3 3 +--R (- 15b cosh(d x + c) + 3b )coth(d x + c) +--R + +--R 2 2 2 2 +--R (- 45a b cosh(d x + c) + 9a b )coth(d x + c) +--R + +--R 3 2 3 2 2 3 +--R (15b cosh(d x + c) - 3b )coth(d x + c) + 45a b cosh(d x + c) + 4b +--R + +--R 2 +--R 3a b +--R * +--R 4 +--R sinh(d x + c) +--R + +--R 3 3 3 3 +--R (- 20b cosh(d x + c) + 12b cosh(d x + c))coth(d x + c) +--R + +--R 2 3 2 2 +--R (- 60a b cosh(d x + c) + 36a b cosh(d x + c))coth(d x + c) +--R + +--R 3 3 3 +--R (20b cosh(d x + c) - 12b cosh(d x + c))coth(d x + c) +--R + +--R 2 3 3 2 +--R 60a b cosh(d x + c) + (16b + 12a b )cosh(d x + c) +--R * +--R 3 +--R sinh(d x + c) +--R + +--R 3 4 3 2 3 3 +--R (- 15b cosh(d x + c) + 18b cosh(d x + c) - 3b )coth(d x + c) +--R + +--R 2 4 2 2 2 2 +--R (- 45a b cosh(d x + c) + 54a b cosh(d x + c) - 9a b )coth(d x + c) +--R + +--R 3 4 3 2 3 +--R (15b cosh(d x + c) - 18b cosh(d x + c) + 3b )coth(d x + c) +--R + +--R 2 4 3 2 2 3 2 +--R 45a b cosh(d x + c) + (24b + 18a b )cosh(d x + c) + 4b - 3a b +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 3 5 3 3 3 +--R (- 6b cosh(d x + c) + 12b cosh(d x + c) - 6b cosh(d x + c)) +--R * +--R 3 +--R coth(d x + c) +--R + +--R 2 5 2 3 +--R - 18a b cosh(d x + c) + 36a b cosh(d x + c) +--R + +--R 2 +--R - 18a b cosh(d x + c) +--R * +--R 2 +--R coth(d x + c) +--R + +--R 3 5 3 3 3 +--R (6b cosh(d x + c) - 12b cosh(d x + c) + 6b cosh(d x + c)) +--R * +--R coth(d x + c) +--R + +--R 2 5 3 2 3 +--R 18a b cosh(d x + c) + (16b + 12a b )cosh(d x + c) +--R + +--R 3 2 +--R (8b - 6a b )cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 3 6 3 4 3 2 3 +--R (- b cosh(d x + c) + 3b cosh(d x + c) - 3b cosh(d x + c) + b ) +--R * +--R 3 +--R coth(d x + c) +--R + +--R 2 6 2 4 2 2 +--R - 3a b cosh(d x + c) + 9a b cosh(d x + c) - 9a b cosh(d x + c) +--R + +--R 2 +--R 3a b +--R * +--R 2 +--R coth(d x + c) +--R + +--R 3 6 3 4 3 2 3 +--R (b cosh(d x + c) - 3b cosh(d x + c) + 3b cosh(d x + c) - b ) +--R * +--R coth(d x + c) +--R + +--R 2 6 3 2 4 +--R 3a b cosh(d x + c) + (4b + 3a b )cosh(d x + c) +--R + +--R 3 2 2 2 +--R (4b - 3a b )cosh(d x + c) - 3a b +--R / +--R 6 5 +--R sinh(d x + c) + 6cosh(d x + c)sinh(d x + c) +--R + +--R 2 4 +--R (15cosh(d x + c) - 3)sinh(d x + c) +--R + +--R 3 3 +--R (20cosh(d x + c) - 12cosh(d x + c))sinh(d x + c) +--R + +--R 4 2 2 +--R (15cosh(d x + c) - 18cosh(d x + c) + 3)sinh(d x + c) +--R + +--R 5 3 +--R (6cosh(d x + c) - 12cosh(d x + c) + 6cosh(d x + c))sinh(d x + c) +--R + +--R 6 4 2 +--R cosh(d x + c) - 3cosh(d x + c) + 3cosh(d x + c) - 1 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 508 +t0349:= (a+b*coth(c+d*x))^2 +--R +--R +--R 2 2 2 +--R (218) b coth(d x + c) + 2a b coth(d x + c) + a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 508 +r0349:= a^2*x+b^2*x-b^2*coth(c+d*x)/d+2*a*b*log(sinh(c+d*x))/d +--R +--R +--R 2 2 2 +--R 2a b log(sinh(d x + c)) - b coth(d x + c) + (b + a )d x +--R (219) -------------------------------------------------------- +--R d +--R Type: Expression(Integer) +--E 251 + +--S 252 of 508 +a0349:= integrate(t0349,x) +--R +--R +--R (220) +--R 2 +--R 2a b sinh(d x + c) + 4a b cosh(d x + c)sinh(d x + c) +--R + +--R 2 +--R 2a b cosh(d x + c) - 2a b +--R * +--R 2sinh(d x + c) +--R log(- -----------------------------) +--R sinh(d x + c) - cosh(d x + c) +--R + +--R 2 2 2 +--R (b - 2a b + a )d x sinh(d x + c) +--R + +--R 2 2 +--R (2b - 4a b + 2a )d x cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 2 2 2 2 +--R (b - 2a b + a )d x cosh(d x + c) + (- b + 2a b - a )d x - 2b +--R / +--R 2 2 +--R d sinh(d x + c) + 2d cosh(d x + c)sinh(d x + c) + d cosh(d x + c) - d +--R Type: Union(Expression(Integer),...) +--E 252 + +--S 253 of 508 +m0349:= a0349-r0349 +--R +--R +--R (221) +--R 2 +--R - 2a b sinh(d x + c) - 4a b cosh(d x + c)sinh(d x + c) +--R + +--R 2 +--R - 2a b cosh(d x + c) + 2a b +--R * +--R log(sinh(d x + c)) +--R + +--R 2 +--R 2a b sinh(d x + c) + 4a b cosh(d x + c)sinh(d x + c) +--R + +--R 2 +--R 2a b cosh(d x + c) - 2a b +--R * +--R 2sinh(d x + c) +--R log(- -----------------------------) +--R sinh(d x + c) - cosh(d x + c) +--R + +--R 2 2 +--R (b coth(d x + c) - 2a b d x)sinh(d x + c) +--R + +--R 2 +--R (2b cosh(d x + c)coth(d x + c) - 4a b d x cosh(d x + c))sinh(d x + c) +--R + +--R 2 2 2 2 +--R (b cosh(d x + c) - b )coth(d x + c) - 2a b d x cosh(d x + c) + 2a b d x +--R + +--R 2 +--R - 2b +--R / +--R 2 2 +--R d sinh(d x + c) + 2d cosh(d x + c)sinh(d x + c) + d cosh(d x + c) - d +--R Type: Expression(Integer) +--E 253 + +--S 254 of 508 +d0349:= D(m0349,x) +--R +--R +--R (222) +--R 2 2 2 4 +--R (- b coth(d x + c) + b )sinh(d x + c) +--R + +--R 2 2 2 3 +--R (- 4b cosh(d x + c)coth(d x + c) + 4b cosh(d x + c))sinh(d x + c) +--R + +--R 2 2 2 2 2 2 2 +--R ((- 6b cosh(d x + c) + 2b )coth(d x + c) + 6b cosh(d x + c) + 2b ) +--R * +--R 2 +--R sinh(d x + c) +--R + +--R 2 3 2 2 +--R (- 4b cosh(d x + c) + 4b cosh(d x + c))coth(d x + c) +--R + +--R 2 3 2 +--R 4b cosh(d x + c) + 4b cosh(d x + c) +--R * +--R sinh(d x + c) +--R + +--R 2 4 2 2 2 2 +--R (- b cosh(d x + c) + 2b cosh(d x + c) - b )coth(d x + c) +--R + +--R 2 4 2 2 2 +--R b cosh(d x + c) + 2b cosh(d x + c) + b +--R / +--R 4 3 +--R sinh(d x + c) + 4cosh(d x + c)sinh(d x + c) +--R + +--R 2 2 +--R (6cosh(d x + c) - 2)sinh(d x + c) +--R + +--R 3 4 +--R (4cosh(d x + c) - 4cosh(d x + c))sinh(d x + c) + cosh(d x + c) +--R + +--R 2 +--R - 2cosh(d x + c) + 1 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 508 +t0350:= 1/(4-6*coth(x)) +--R +--R +--R 1 +--R (223) - ------------ +--R 6coth(x) - 4 +--R Type: Expression(Integer) +--E 255 + +--S 256 of 508 +r0350:= -1/5*x-3/10*log(-3*cosh(x)+2*sinh(x)) +--R +--R +--R - 3log(2sinh(x) - 3cosh(x)) - 2x +--R (224) -------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 508 +a0350:= integrate(t0350,x) +--R +--R +--R 4sinh(x) - 6cosh(x) +--R - 3log(-------------------) + x +--R sinh(x) - cosh(x) +--R (225) ------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 257 + +--S 258 of 508 +m0350:= a0350-r0350 +--R +--R +--R 4sinh(x) - 6cosh(x) +--R 3log(2sinh(x) - 3cosh(x)) - 3log(-------------------) + 3x +--R sinh(x) - cosh(x) +--R (226) ---------------------------------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 258 + +--S 259 of 508 +d0350:= D(m0350,x) +--R +--R +--R (227) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 508 +t0351:= 1/(a+b*coth(c+d*x)) +--R +--R +--R 1 +--R (228) ------------------- +--R b coth(d x + c) + a +--R Type: Expression(Integer) +--E 260 + +--S 261 of 508 +r0351:= -(-a*d*x+b*log(b*cosh(c+d*x)+a*sinh(c+d*x)))/(a^2-b^2)/d +--R +--R +--R b log(a sinh(d x + c) + b cosh(d x + c)) - a d x +--R (229) ------------------------------------------------ +--R 2 2 +--R (b - a )d +--R Type: Expression(Integer) +--E 261 + +--S 262 of 508 +a0351:= integrate(t0351,x) +--R +--R +--R - 2a sinh(d x + c) - 2b cosh(d x + c) +--R b log(-------------------------------------) + (- b - a)d x +--R sinh(d x + c) - cosh(d x + c) +--R (230) ----------------------------------------------------------- +--R 2 2 +--R (b - a )d +--R Type: Union(Expression(Integer),...) +--E 262 + +--S 263 of 508 +m0351:= a0351-r0351 +--R +--R +--R (231) +--R - b log(a sinh(d x + c) + b cosh(d x + c)) +--R + +--R - 2a sinh(d x + c) - 2b cosh(d x + c) +--R b log(-------------------------------------) - b d x +--R sinh(d x + c) - cosh(d x + c) +--R / +--R 2 2 +--R (b - a )d +--R Type: Expression(Integer) +--E 263 + +--S 264 of 508 +d0351:= D(m0351,x) +--R +--R +--R (232) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 508 +t0352:= 1/(1-2*coth(x)^2) +--R +--R +--R 1 +--R (233) - ------------- +--R 2 +--R 2coth(x) - 1 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 508 +r0352:= -x+2^(1/2)*atanh(2^(1/2)*coth(x)) +--R +--R +--R +-+ +-+ +--R (234) \|2 atanh(\|2 coth(x)) - x +--R Type: Expression(Integer) +--E 266 + +--S 267 of 508 +a0352:= integrate(t0352,x) +--R +--R +--R (235) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) - 2\|2 + 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R - 2x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 267 + +--S 268 of 508 +m0352:= a0352-r0352 +--R +--R +--R (236) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) - 2\|2 + 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ +-+ +--R - 2\|2 atanh(\|2 coth(x)) +--R / +--R 2 +--R Type: Expression(Integer) +--E 268 + +--S 269 of 508 +d0352:= D(m0352,x) +--R +--R +--R (237) +--R +-+ 2 +-+ 4 +--R ((4\|2 - 6)coth(x) + 4\|2 - 6)sinh(x) +--R + +--R +-+ 2 +-+ 3 +--R ((24\|2 - 32)cosh(x)coth(x) + (- 24\|2 + 32)cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 56\|2 + 84)cosh(x) + 8\|2 - 12)coth(x) +--R + +--R +-+ 2 +-+ +--R (40\|2 - 60)cosh(x) + 16\|2 - 24 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R ((24\|2 - 32)cosh(x) + (- 24\|2 + 32)cosh(x))coth(x) +--R + +--R +-+ 3 +-+ +--R (- 24\|2 + 32)cosh(x) + (- 24\|2 + 32)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R ((4\|2 - 6)cosh(x) + (8\|2 - 12)cosh(x) - 12\|2 + 18)coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (16\|2 - 24)cosh(x) + 12\|2 - 18 +--R / +--R +-+ 2 +-+ 4 +--R ((12\|2 - 18)coth(x) - 6\|2 + 9)sinh(x) +--R + +--R +-+ 2 +-+ 3 +--R ((- 24\|2 + 32)cosh(x)coth(x) + (12\|2 - 16)cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((24\|2 - 36)cosh(x) + 40\|2 - 60)coth(x) +--R + +--R +-+ 2 +-+ +--R (- 12\|2 + 18)cosh(x) - 20\|2 + 30 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R ((- 24\|2 + 32)cosh(x) + (- 72\|2 + 96)cosh(x))coth(x) +--R + +--R +-+ 3 +-+ +--R (12\|2 - 16)cosh(x) + (36\|2 - 48)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R ((12\|2 - 18)cosh(x) + (40\|2 - 60)cosh(x) + 12\|2 - 18)coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + (- 20\|2 + 30)cosh(x) - 6\|2 + 9 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 508 +t0353:= 1/(1+coth(x)^3) +--R +--R +--R 1 +--R (238) ------------ +--R 3 +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 270 + +--S 271 of 508 +r0353:= 1/2*x-2/9*atan(1/3*(1-2*coth(x))*3^(1/2))*3^(1/2)-1/(6+6*coth(x)) +--R +--R +--R (239) +--R +-+ +-+ +--R +-+ +-+ 2\|3 coth(x) - \|3 +--R (4\|3 coth(x) + 4\|3 )atan(-------------------) + 9x coth(x) + 9x - 3 +--R 3 +--R --------------------------------------------------------------------- +--R 18coth(x) + 18 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 508 +a0353:= integrate(t0353,x) +--R +--R +--R (240) +--R +-+ +-+ +--R 2 2 \|3 sinh(x) + \|3 cosh(x) +--R (8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) )atan(-------------------------) +--R 3sinh(x) - 3cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R 6x\|3 sinh(x) + 12x\|3 cosh(x)sinh(x) + 6x\|3 cosh(x) + \|3 +--R / +--R +-+ 2 +-+ +-+ 2 +--R 12\|3 sinh(x) + 24\|3 cosh(x)sinh(x) + 12\|3 cosh(x) +--R Type: Union(Expression(Integer),...) +--E 272 + +--S 273 of 508 +m0353:= a0353-r0353 +--R +--R +--R (241) +--R 2 +--R (- 8coth(x) - 8)sinh(x) + (- 16cosh(x)coth(x) - 16cosh(x))sinh(x) +--R + +--R 2 2 +--R - 8cosh(x) coth(x) - 8cosh(x) +--R * +--R +-+ +-+ +--R 2\|3 coth(x) - \|3 +--R atan(-------------------) +--R 3 +--R + +--R 2 +--R (8coth(x) + 8)sinh(x) + (16cosh(x)coth(x) + 16cosh(x))sinh(x) +--R + +--R 2 2 +--R 8cosh(x) coth(x) + 8cosh(x) +--R * +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R atan(-------------------------) +--R 3sinh(x) - 3cosh(x) +--R + +--R +-+ 2 +-+ +-+ +-+ 2 +-+ +--R 2\|3 sinh(x) + 4\|3 cosh(x)sinh(x) + \|3 coth(x) + 2\|3 cosh(x) + \|3 +--R / +--R +-+ +-+ 2 +--R (12\|3 coth(x) + 12\|3 )sinh(x) +--R + +--R +-+ +-+ +-+ 2 +--R (24\|3 cosh(x)coth(x) + 24\|3 cosh(x))sinh(x) + 12\|3 cosh(x) coth(x) +--R + +--R +-+ 2 +--R 12\|3 cosh(x) +--R Type: Expression(Integer) +--E 273 + +--S 274 of 508 +d0353:= D(m0353,x) +--R +--R +--R (242) +--R 3 4 3 3 +--R (5coth(x) - 1)sinh(x) + (7cosh(x)coth(x) + cosh(x))sinh(x) +--R + +--R 3 2 +--R (- coth(x) - 1)sinh(x) +--R + +--R 3 3 3 +--R ((- cosh(x) + cosh(x))coth(x) - 7cosh(x) + cosh(x))sinh(x) +--R + +--R 4 2 3 4 2 +--R (cosh(x) - cosh(x) )coth(x) - 5cosh(x) - cosh(x) +--R / +--R 3 4 3 3 +--R (6coth(x) + 6)sinh(x) + (6cosh(x)coth(x) + 6cosh(x))sinh(x) +--R + +--R 3 3 3 4 3 4 +--R (6cosh(x) coth(x) + 6cosh(x) )sinh(x) + 6cosh(x) coth(x) + 6cosh(x) +--R Type: Expression(Integer) +--E 274 + +--S 275 of 508 +t0354:= (1+coth(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (243) \|coth(x) + 1 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 508 +r0354:= -acsch(tanh(x))+2^(1/2)*atanh(2^(1/2)*coth(x)/(1+coth(x)^2)^(1/2)) +--R +--R +--R +-+ +--R +-+ \|2 coth(x) +--R (244) \|2 atanh(---------------) - acsch(tanh(x)) +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 508 +a0354:= integrate(t0354,x) +--R +--R +--R (245) +--R - +--R 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 2)sinh(x) + (4\|2 + 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (2\|2 + 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +--R \|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) 2 +--R \|2 |------------------------------------- + 2sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 2)sinh(x) + (- 4\|2 + 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (- 2\|2 + 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|2 +--R * +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 2) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + \|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + 2\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R \|2 cosh(x) + 2\|2 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 277 + +--S 278 of 508 +m0354:= a0354-r0354 +--R +--R +--R (246) +--R - +--R 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 2)sinh(x) + (4\|2 + 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (2\|2 + 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +--R \|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) 2 +--R \|2 |------------------------------------- + 2sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 2)sinh(x) + (- 4\|2 + 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (- 2\|2 + 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|2 +--R * +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 2) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + \|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + 2\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R \|2 cosh(x) + 2\|2 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +-+ +--R +-+ \|2 coth(x) +--R - 2\|2 atanh(---------------) + 2acsch(tanh(x)) +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 278 + +--S 279 of 508 +d0354:= D(m0354,x) +--R +--R +--R (247) +--R +-+ 14 +-+ 13 +--R - \|2 sinh(x) - 2\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 12 +--R (5\|2 cosh(x) + 9\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 11 +--R (12\|2 cosh(x) + 12\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 10 +--R (- 9\|2 cosh(x) - 30\|2 cosh(x) + 5\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 9 +--R (- 30\|2 cosh(x) - 36\|2 cosh(x) + 2\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (5\|2 cosh(x) + 39\|2 cosh(x) - 15\|2 cosh(x) - 9\|2 ) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 40\|2 cosh(x) + 24\|2 cosh(x) - 8\|2 cosh(x) +--R + +--R +-+ +--R - 12\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 5\|2 cosh(x) - 36\|2 cosh(x) + 10\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 12\|2 cosh(x) + 24\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 30\|2 cosh(x) + 24\|2 cosh(x) + 12\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 12\|2 cosh(x) - 64\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 9\|2 cosh(x) + 39\|2 cosh(x) + 10\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R - 6\|2 cosh(x) + 104\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 12\|2 cosh(x) - 36\|2 cosh(x) - 8\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R 12\|2 cosh(x) - 128\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 5\|2 cosh(x) - 30\|2 cosh(x) - 15\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R 12\|2 cosh(x) + 104\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 2\|2 cosh(x) + 12\|2 cosh(x) + 2\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R - 12\|2 cosh(x) - 64\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - \|2 cosh(x) + 9\|2 cosh(x) + 5\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 9\|2 cosh(x) + 24\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R tanh(x) |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 14 13 2 12 +--R 4sinh(x) + 16cosh(x)sinh(x) + (12cosh(x) - 24)sinh(x) +--R + +--R 3 11 +--R (- 32cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 60cosh(x) + 48cosh(x) - 16)sinh(x) +--R + +--R 5 3 9 +--R (- 16cosh(x) + 144cosh(x) - 32cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (44cosh(x) + 24cosh(x) - 16cosh(x) + 24)sinh(x) +--R + +--R 7 5 7 +--R (64cosh(x) - 96cosh(x) + 48cosh(x))sinh(x) +--R + +--R 8 6 4 6 +--R (44cosh(x) - 96cosh(x) + 32cosh(x) - 68)sinh(x) +--R + +--R 9 7 5 3 +--R - 16cosh(x) - 96cosh(x) + 64cosh(x) - 48cosh(x) +--R + +--R 112cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 60cosh(x) + 24cosh(x) + 32cosh(x) - 48cosh(x) +--R + +--R 2 +--R - 220cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 5 3 +--R (- 32cosh(x) + 144cosh(x) - 48cosh(x) + 224cosh(x) ) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 4 +--R (12cosh(x) + 48cosh(x) - 16cosh(x) - 220cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 16cosh(x) - 48cosh(x) - 32cosh(x) + 48cosh(x) +--R + +--R 5 +--R 112cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R 4cosh(x) - 24cosh(x) - 16cosh(x) + 24cosh(x) +--R + +--R 6 +--R - 68cosh(x) +--R * +--R tanh(x) +--R * +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R + +--R 14 13 2 12 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 12cosh(x) + 4)sinh(x) +--R + +--R 3 11 +--R (32cosh(x) + 8cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (60cosh(x) - 8cosh(x) + 12)sinh(x) +--R + +--R 5 3 9 +--R (16cosh(x) - 24cosh(x) + 16cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 44cosh(x) - 4cosh(x) - 4cosh(x) + 36)sinh(x) +--R + +--R 7 5 7 +--R (- 64cosh(x) + 16cosh(x) - 56cosh(x))sinh(x) +--R + +--R 8 6 4 6 +--R (- 44cosh(x) + 16cosh(x) - 8cosh(x) - 48)sinh(x) +--R + +--R 9 7 5 3 +--R 16cosh(x) + 16cosh(x) - 32cosh(x) + 56cosh(x) +--R + +--R 128cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 60cosh(x) - 4cosh(x) - 8cosh(x) - 72cosh(x) +--R + +--R 2 +--R - 208cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 5 3 3 +--R (32cosh(x) - 24cosh(x) + 56cosh(x) + 256cosh(x) )sinh(x) +--R + +--R 12 10 8 4 2 +--R (- 12cosh(x) - 8cosh(x) - 4cosh(x) - 208cosh(x) )sinh(x) +--R + +--R 13 11 9 7 +--R - 16cosh(x) + 8cosh(x) + 16cosh(x) - 56cosh(x) +--R + +--R 5 +--R 128cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R - 4cosh(x) + 4cosh(x) + 12cosh(x) + 36cosh(x) - 48cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R tanh(x) |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 16 +-+ 15 +--R 2\|2 sinh(x) + 12\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R (24\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R (4\|2 cosh(x) + 16\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 12 +--R (- 56\|2 cosh(x) + 12\|2 cosh(x) - 8\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 11 +--R (- 84\|2 cosh(x) - 32\|2 cosh(x) - 32\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 24\|2 cosh(x) - 60\|2 cosh(x) - 48\|2 cosh(x) - 16\|2 ) +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 68\|2 cosh(x) - 16\|2 cosh(x) - 32\|2 cosh(x) +--R + +--R +-+ +--R - 32\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 108\|2 cosh(x) + 44\|2 cosh(x) + 8\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 16\|2 cosh(x) - 50\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 68\|2 cosh(x) + 64\|2 cosh(x) + 64\|2 cosh(x) +--R + +--R +-+ +--R 36\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 24\|2 cosh(x) + 44\|2 cosh(x) + 96\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 32\|2 cosh(x) + 32\|2 cosh(x) + 68\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 84\|2 cosh(x) - 16\|2 cosh(x) + 64\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 64\|2 cosh(x) + 28\|2 cosh(x) - 112\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 56\|2 cosh(x) - 60\|2 cosh(x) + 8\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 32\|2 cosh(x) + 164\|2 cosh(x) + 220\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 4\|2 cosh(x) - 32\|2 cosh(x) - 32\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R 28\|2 cosh(x) - 224\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 24\|2 cosh(x) + 12\|2 cosh(x) - 48\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 16\|2 cosh(x) + 32\|2 cosh(x) + 220\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 12\|2 cosh(x) + 16\|2 cosh(x) - 32\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 32\|2 cosh(x) + 36\|2 cosh(x) - 112\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R 2\|2 cosh(x) + 4\|2 cosh(x) - 8\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 16\|2 cosh(x) - 50\|2 cosh(x) + 68\|2 cosh(x) +--R * +--R tanh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R + +--R 14 13 2 12 +--R 2sinh(x) + 8cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 11 +--R (- 16cosh(x) - 4cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 30cosh(x) + 4cosh(x) - 6)sinh(x) +--R + +--R 5 3 9 +--R (- 8cosh(x) + 12cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (22cosh(x) + 2cosh(x) + 2cosh(x) - 18)sinh(x) +--R + +--R 7 5 7 +--R (32cosh(x) - 8cosh(x) + 28cosh(x))sinh(x) +--R + +--R 8 6 4 6 +--R (22cosh(x) - 8cosh(x) + 4cosh(x) + 24)sinh(x) +--R + +--R 9 7 5 3 +--R - 8cosh(x) - 8cosh(x) + 16cosh(x) - 28cosh(x) +--R + +--R - 64cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 30cosh(x) + 2cosh(x) + 4cosh(x) + 36cosh(x) +--R + +--R 2 +--R 104cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 5 3 +--R (- 16cosh(x) + 12cosh(x) - 28cosh(x) - 128cosh(x) ) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 4 2 +--R (6cosh(x) + 4cosh(x) + 2cosh(x) + 104cosh(x) )sinh(x) +--R + +--R 13 11 9 7 +--R 8cosh(x) - 4cosh(x) - 8cosh(x) + 28cosh(x) +--R + +--R 5 +--R - 64cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R 2cosh(x) - 2cosh(x) - 6cosh(x) - 18cosh(x) + 24cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 14 13 2 12 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 11 +--R (16cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (30cosh(x) - 4cosh(x) + 6)sinh(x) +--R + +--R 5 3 9 +--R (8cosh(x) - 12cosh(x) + 8cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 22cosh(x) - 2cosh(x) - 2cosh(x) + 18)sinh(x) +--R + +--R 7 5 7 +--R (- 32cosh(x) + 8cosh(x) - 28cosh(x))sinh(x) +--R + +--R 8 6 4 6 +--R (- 22cosh(x) + 8cosh(x) - 4cosh(x) - 24)sinh(x) +--R + +--R 9 7 5 3 +--R (8cosh(x) + 8cosh(x) - 16cosh(x) + 28cosh(x) + 64cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 30cosh(x) - 2cosh(x) - 4cosh(x) - 36cosh(x) +--R + +--R 2 +--R - 104cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 5 3 3 +--R (16cosh(x) - 12cosh(x) + 28cosh(x) + 128cosh(x) )sinh(x) +--R + +--R 12 10 8 4 2 +--R (- 6cosh(x) - 4cosh(x) - 2cosh(x) - 104cosh(x) )sinh(x) +--R + +--R 13 11 9 7 +--R - 8cosh(x) + 4cosh(x) + 8cosh(x) - 28cosh(x) +--R + +--R 5 +--R 64cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R - 2cosh(x) + 2cosh(x) + 6cosh(x) + 18cosh(x) - 24cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 16 +-+ 15 +--R - \|2 sinh(x) - 6\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R (- 12\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R (- 2\|2 cosh(x) - 8\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 12 +--R (28\|2 cosh(x) - 6\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 11 +--R (42\|2 cosh(x) + 16\|2 cosh(x) + 16\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (12\|2 cosh(x) + 30\|2 cosh(x) + 24\|2 cosh(x) + 8\|2 ) +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 34\|2 cosh(x) + 8\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ +--R 16\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 54\|2 cosh(x) - 22\|2 cosh(x) - 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 8\|2 cosh(x) + 25\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 34\|2 cosh(x) - 32\|2 cosh(x) - 32\|2 cosh(x) +--R + +--R +-+ +--R - 18\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 12\|2 cosh(x) - 22\|2 cosh(x) - 48\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 16\|2 cosh(x) - 16\|2 cosh(x) - 34\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 42\|2 cosh(x) + 8\|2 cosh(x) - 32\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 32\|2 cosh(x) - 14\|2 cosh(x) + 56\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 28\|2 cosh(x) + 30\|2 cosh(x) - 4\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 16\|2 cosh(x) - 82\|2 cosh(x) - 110\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 2\|2 cosh(x) + 16\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R - 14\|2 cosh(x) + 112\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 12\|2 cosh(x) - 6\|2 cosh(x) + 24\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 8\|2 cosh(x) - 16\|2 cosh(x) - 110\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 6\|2 cosh(x) - 8\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 16\|2 cosh(x) - 18\|2 cosh(x) + 56\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - \|2 cosh(x) - 2\|2 cosh(x) + 4\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 8\|2 cosh(x) + 25\|2 cosh(x) - 34\|2 cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 16 +-+ 15 +--R \|2 sinh(x) + 6\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R (12\|2 cosh(x) + 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R (2\|2 cosh(x) + 8\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 12 +--R (- 28\|2 cosh(x) + 6\|2 cosh(x) - 4\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 11 +--R (- 42\|2 cosh(x) - 16\|2 cosh(x) - 16\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 10 +--R (- 12\|2 cosh(x) - 30\|2 cosh(x) - 24\|2 cosh(x) - 8\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (34\|2 cosh(x) - 8\|2 cosh(x) - 16\|2 cosh(x) - 16\|2 cosh(x)) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 54\|2 cosh(x) + 22\|2 cosh(x) + 4\|2 cosh(x) - 8\|2 cosh(x) +--R + +--R +-+ +--R - 25\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +-+ +--R (34\|2 cosh(x) + 32\|2 cosh(x) + 32\|2 cosh(x) + 18\|2 cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 12\|2 cosh(x) + 22\|2 cosh(x) + 48\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 16\|2 cosh(x) + 16\|2 cosh(x) + 34\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 42\|2 cosh(x) - 8\|2 cosh(x) + 32\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 32\|2 cosh(x) + 14\|2 cosh(x) - 56\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 28\|2 cosh(x) - 30\|2 cosh(x) + 4\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 16\|2 cosh(x) + 82\|2 cosh(x) + 110\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 2\|2 cosh(x) - 16\|2 cosh(x) - 16\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R 14\|2 cosh(x) - 112\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 12\|2 cosh(x) + 6\|2 cosh(x) - 24\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 8\|2 cosh(x) + 16\|2 cosh(x) + 110\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 6\|2 cosh(x) + 8\|2 cosh(x) - 16\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 16\|2 cosh(x) + 18\|2 cosh(x) - 56\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +-+ 10 +--R \|2 cosh(x) + 2\|2 cosh(x) - 4\|2 cosh(x) - 8\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 25\|2 cosh(x) + 34\|2 cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R / +--R 14 13 2 12 +--R 2sinh(x) + 8cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 11 +--R (- 16cosh(x) - 4cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 30cosh(x) + 4cosh(x) - 6)sinh(x) +--R + +--R 5 3 9 +--R (- 8cosh(x) + 12cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (22cosh(x) + 2cosh(x) + 2cosh(x) - 18)sinh(x) +--R + +--R 7 5 7 +--R (32cosh(x) - 8cosh(x) + 28cosh(x))sinh(x) +--R + +--R 8 6 4 6 +--R (22cosh(x) - 8cosh(x) + 4cosh(x) + 24)sinh(x) +--R + +--R 9 7 5 3 +--R (- 8cosh(x) - 8cosh(x) + 16cosh(x) - 28cosh(x) - 64cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 30cosh(x) + 2cosh(x) + 4cosh(x) + 36cosh(x) +--R + +--R 2 +--R 104cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 5 3 3 +--R (- 16cosh(x) + 12cosh(x) - 28cosh(x) - 128cosh(x) )sinh(x) +--R + +--R 12 10 8 4 2 +--R (6cosh(x) + 4cosh(x) + 2cosh(x) + 104cosh(x) )sinh(x) +--R + +--R 13 11 9 7 5 +--R (8cosh(x) - 4cosh(x) - 8cosh(x) + 28cosh(x) - 64cosh(x) ) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R 2cosh(x) - 2cosh(x) - 6cosh(x) - 18cosh(x) + 24cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R tanh(x) |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 16 +-+ 15 +--R - \|2 sinh(x) - 6\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 14 +--R (- 12\|2 cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 13 +--R (- 2\|2 cosh(x) - 8\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 12 +--R (28\|2 cosh(x) - 6\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 11 +--R (42\|2 cosh(x) + 16\|2 cosh(x) + 16\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 10 +--R (12\|2 cosh(x) + 30\|2 cosh(x) + 24\|2 cosh(x) + 8\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 34\|2 cosh(x) + 8\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ +--R 16\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 54\|2 cosh(x) - 22\|2 cosh(x) - 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 8\|2 cosh(x) + 25\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 34\|2 cosh(x) - 32\|2 cosh(x) - 32\|2 cosh(x) +--R + +--R +-+ +--R - 18\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 12\|2 cosh(x) - 22\|2 cosh(x) - 48\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 16\|2 cosh(x) - 16\|2 cosh(x) - 34\|2 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 42\|2 cosh(x) + 8\|2 cosh(x) - 32\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 32\|2 cosh(x) - 14\|2 cosh(x) + 56\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 28\|2 cosh(x) + 30\|2 cosh(x) - 4\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 16\|2 cosh(x) - 82\|2 cosh(x) - 110\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 2\|2 cosh(x) + 16\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R - 14\|2 cosh(x) + 112\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 12\|2 cosh(x) - 6\|2 cosh(x) + 24\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 8\|2 cosh(x) - 16\|2 cosh(x) - 110\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 6\|2 cosh(x) - 8\|2 cosh(x) + 16\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 16\|2 cosh(x) - 18\|2 cosh(x) + 56\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +-+ 10 +--R - \|2 cosh(x) - 2\|2 cosh(x) + 4\|2 cosh(x) + 8\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R 25\|2 cosh(x) - 34\|2 cosh(x) +--R * +--R tanh(x) +--R * +--R +------------+ +------------+ +--R | 2 | 2 +--R \|coth(x) + 1 \|tanh(x) + 1 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 508 +t0355:= (-1+coth(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (248) \|coth(x) - 1 +--R Type: Expression(Integer) +--E 280 + +--S 281 of 508 +r0355:= -acoth(cosh(x))*csgn(1/sinh(x)) +--R +--R There are no library operations named csgn +--R Use HyperDoc Browse or issue +--R )what op csgn +--R to learn if there is any operation containing " csgn " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named csgn +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 281 + +--S 282 of 508 +a0355:= integrate(t0355,x) +--R +--R +--R (249) - log(sinh(x) + cosh(x) + 1) + log(sinh(x) + cosh(x) - 1) +--R Type: Union(Expression(Integer),...) +--E 282 + +--S 283 of 508 +--m0355:= a0355-r0355 +--E 283 + +--S 284 of 508 +--d0355:= D(m0355,x) +--E 284 + +--S 285 of 508 +t0356:= (-1-coth(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (250) \|- coth(x) - 1 +--R Type: Expression(Integer) +--E 285 + +--S 286 of 508 +r0356:= -2^(1/2)*atan(2^(1/2)*coth(x)/(-1-coth(x)^2)^(1/2))-_ + atan((-1-coth(x)^2)^(1/2)*tanh(x)) +--R +--R +--R +--------------+ +-+ +--R | 2 +-+ \|2 coth(x) +--R (251) - atan(tanh(x)\|- coth(x) - 1 ) - \|2 atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 508 +a0356:= integrate(t0356,x) +--R +--R +--R (252) +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 + (2\|- 2 \|- 1 - 2)(%e ) + 2 +--R - 2\|- 1 log(------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ | x 4 x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 - 2(%e ) + 2 +--R \|- 2 log(------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 + (- 2\|- 2 \|- 1 - 2)(%e ) + 2 +--R 2\|- 1 log(--------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R - +--R +---+ +--R \|- 2 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +---+ x 2 +--R (2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) - 2\|- 2 (%e ) +--R + +--R +---+ +--R - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 287 + +--S 288 of 508 +m0356:= a0356-r0356 +--R +--R +--R (253) +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 + (2\|- 2 \|- 1 - 2)(%e ) + 2 +--R - 2\|- 1 log(------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ | x 4 x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 - 2(%e ) + 2 +--R \|- 2 log(------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R +---+ \|- 2 \|- 2(%e ) - 2 + (- 2\|- 2 \|- 1 - 2)(%e ) + 2 +--R 2\|- 1 log(--------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R - +--R +---+ +--R \|- 2 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +---+ x 2 +--R (2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) - 2\|- 2 (%e ) +--R + +--R +---+ +--R - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R + +--R +--------------+ +-+ +--R | 2 +-+ \|2 coth(x) +--R 2atan(tanh(x)\|- coth(x) - 1 ) + 2\|2 atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 288 + +--S 289 of 508 +d0356:= D(m0356,x) +--R +--R +--R (254) +--R +---+ 2 +---+ x 4 +---+ 2 +--R (- 3\|- 2 coth(x) - 3\|- 2 )(%e ) - 4\|- 2 coth(x) +--R + +--R +---+ +--R - 4\|- 2 +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ x 4 +---+ +--R 3\|- 2 (%e ) + 4\|- 2 +--R * +--R +-------------+ +--R | x 4 +--R \|- 2(%e ) - 2 +--R + +--R 2 x 8 2 x 4 2 +--R (- 2coth(x) - 2)(%e ) + (- 10coth(x) - 10)(%e ) - 8coth(x) +--R + +--R - 8 +--R * +--R 2 +--R tanh(x) +--R + +--R x 8 x 4 +--R 2(%e ) + 10(%e ) + 8 +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R + +--R 2 x 6 2 x 4 +--R (coth(x) + 1)(%e ) + (- coth(x) - 1)(%e ) +--R + +--R 2 x 2 2 +--R (4coth(x) + 4)(%e ) - 4coth(x) - 4 +--R * +--R 2 +--R tanh(x) +--R + +--R 3 x 6 3 x 4 +--R (- coth(x) + coth(x))(%e ) + (coth(x) - coth(x))(%e ) +--R + +--R 3 x 2 3 +--R (- 4coth(x) + 4coth(x))(%e ) + 4coth(x) - 4coth(x) +--R * +--R tanh(x) +--R + +--R 2 x 6 2 x 4 2 x 2 +--R (coth(x) - 1)(%e ) + (- coth(x) + 1)(%e ) + (4coth(x) - 4)(%e ) +--R + +--R 2 +--R - 4coth(x) + 4 +--R * +--R +-------------+ +--R | x 4 +--R \|- 2(%e ) - 2 +--R + +--R +---+ 2 +---+ x 6 +--R (- 3\|- 2 coth(x) - 3\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (3\|- 2 coth(x) + 3\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 4\|- 2 coth(x) - 4\|- 2 )(%e ) + 4\|- 2 coth(x) + 4\|- 2 +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 3 +---+ x 6 +--R (3\|- 2 coth(x) - 3\|- 2 coth(x))(%e ) +--R + +--R +---+ 3 +---+ x 4 +--R (- 3\|- 2 coth(x) + 3\|- 2 coth(x))(%e ) +--R + +--R +---+ 3 +---+ x 2 +---+ 3 +--R (4\|- 2 coth(x) - 4\|- 2 coth(x))(%e ) - 4\|- 2 coth(x) +--R + +--R +---+ +--R 4\|- 2 coth(x) +--R * +--R tanh(x) +--R + +--R +---+ 2 +---+ x 6 +---+ 2 +---+ x 4 +--R (- 3\|- 2 coth(x) + 3\|- 2 )(%e ) + (3\|- 2 coth(x) - 3\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 4\|- 2 coth(x) + 4\|- 2 )(%e ) + 4\|- 2 coth(x) - 4\|- 2 +--R / +--R 2 x 6 2 x 4 +--R (coth(x) + 1)(%e ) + (- coth(x) - 1)(%e ) +--R + +--R 2 x 2 2 +--R (4coth(x) + 4)(%e ) - 4coth(x) - 4 +--R * +--R 2 +--R tanh(x) +--R + +--R x 6 x 4 x 2 +--R - (%e ) + (%e ) - 4(%e ) + 4 +--R * +--R +-------------+ +--R | x 4 +--R \|- 2(%e ) - 2 +--R + +--R +---+ 2 +---+ x 6 +--R (- 3\|- 2 coth(x) - 3\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (3\|- 2 coth(x) + 3\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 4\|- 2 coth(x) - 4\|- 2 )(%e ) + 4\|- 2 coth(x) + 4\|- 2 +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R 3\|- 2 (%e ) - 3\|- 2 (%e ) + 4\|- 2 (%e ) - 4\|- 2 +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 508 +t0357:= (a+b*coth(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (255) \|b coth(x) + a +--R Type: Expression(Integer) +--E 290 + +--S 291 of 508 +r0357:= (a+b)^(1/2)*atanh((a+b)^(1/2)*coth(x)/(a+b*coth(x)^2)^(1/2))-_ + b^(1/2)*atanh((a+b*coth(x)^2)^(1/2)*tanh(x)/b^(1/2)) +--R +--R +--R (256) +--R +--------------+ +--R | 2 +-----+ +--R +-+ tanh(x)\|b coth(x) + a +-----+ coth(x)\|b + a +--R - \|b atanh(------------------------) + \|b + a atanh(-----------------) +--R +-+ +--------------+ +--R \|b | 2 +--R \|b coth(x) + a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 508 +a0357:= integrate(t0357,x) +--R +--R +--R (257) +--R [ +--R (b + a) +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-----+ +--R 2\|b \|b + a +--R * +--R log +--R 4 3 +--R 2a sinh(x) + 8a cosh(x)sinh(x) +--R + +--R 2 2 +--R (12a cosh(x) - 2b - 2a)sinh(x) +--R + +--R 3 +--R (8a cosh(x) + (- 4b - 4a)cosh(x))sinh(x) +--R + +--R 4 2 +--R 2a cosh(x) + (- 2b - 2a)cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R + +--R 2 2 4 +--R (- b - 2a b - a )sinh(x) +--R + +--R 2 2 3 +--R (- 4b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 12a b - 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((- 4b - 8a b - 4a )cosh(x) + (4a b + 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- b - 2a b - a )cosh(x) + (2a b + 2a )cosh(x) - b +--R + +--R 2 +--R - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (6b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((15b - 30a b - 15a )cosh(x) + b + 2a b + 3a )sinh(x) +--R + +--R 2 2 3 +--R (20b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (15b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (6b + 12a b + 18a )cosh(x) + b - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (6b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (4b + 8a b + 12a )cosh(x) + (2b - 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (b - 2a b - a )cosh(x) + (b + 2a b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (b - 2a b - 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 6 2 5 +--R (2a b + 2a )sinh(x) + (12a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R ((30a b + 30a )cosh(x) + 2b - 2a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((40a b + 40a )cosh(x) + (8b - 8a b - 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (30a b + 30a )cosh(x) + (12b - 12a b - 24a )cosh(x) +--R + +--R 2 2 +--R 2b + 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (12a b + 12a )cosh(x) + (8b - 8a b - 16a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (2a b + 2a )cosh(x) + (2b - 2a b - 4a )cosh(x) +--R + +--R 2 2 2 +--R (2b + 4a b + 2a )cosh(x) +--R * +--R +-+ +--R \|b +--R / +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((4b - 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (b - a )cosh(x) + (2a b + 2a )cosh(x) - b - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (- b - a )sinh(x) + (- 6b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 15b - 15a )cosh(x) - b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 20b - 20a )cosh(x) + (- 4b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (- 15b - 15a )cosh(x) + (- 6b + 18a )cosh(x) + b +--R + +--R 2 +--R - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 6b - 6a )cosh(x) + (- 4b + 12a )cosh(x) +--R + +--R 2 2 +--R (2b - 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- b - a )cosh(x) + (- b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (b - 2a b - 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R (- b - a) +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R / +--R +-----+ +--R 2\|b + a +--R , +--R +--R (b + a) +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R (- b - a) +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R - +--R +---+ +-----+ +--R 4\|- b \|b + a +--R * +--R atan +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b - a +--R / +--R 2 2 +---+ +-----+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|b + a +--R / +--R +-----+ +--R 2\|b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 292 + +--S 293 of 508 +m0357a:= a0357.1-r0357 +--R +--R +--R (258) +--R (b + a) +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-----+ +--R 2\|b \|b + a +--R * +--R log +--R 4 3 +--R 2a sinh(x) + 8a cosh(x)sinh(x) +--R + +--R 2 2 +--R (12a cosh(x) - 2b - 2a)sinh(x) +--R + +--R 3 4 +--R (8a cosh(x) + (- 4b - 4a)cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 2 +--R (- 2b - 2a)cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R + +--R 2 2 4 +--R (- b - 2a b - a )sinh(x) +--R + +--R 2 2 3 +--R (- 4b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 12a b - 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((- 4b - 8a b - 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- b - 2a b - a )cosh(x) + (2a b + 2a )cosh(x) - b +--R + +--R 2 +--R - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (6b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((15b - 30a b - 15a )cosh(x) + b + 2a b + 3a )sinh(x) +--R + +--R 2 2 3 +--R (20b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (15b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (6b + 12a b + 18a )cosh(x) + b - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (6b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (4b + 8a b + 12a )cosh(x) + (2b - 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (b - 2a b - a )cosh(x) + (b + 2a b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (b - 2a b - 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 6 2 5 +--R (2a b + 2a )sinh(x) + (12a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R ((30a b + 30a )cosh(x) + 2b - 2a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((40a b + 40a )cosh(x) + (8b - 8a b - 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (30a b + 30a )cosh(x) + (12b - 12a b - 24a )cosh(x) +--R + +--R 2 2 +--R 2b + 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (12a b + 12a )cosh(x) + (8b - 8a b - 16a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (2a b + 2a )cosh(x) + (2b - 2a b - 4a )cosh(x) +--R + +--R 2 2 2 +--R (2b + 4a b + 2a )cosh(x) +--R * +--R +-+ +--R \|b +--R / +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((4b - 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (b - a )cosh(x) + (2a b + 2a )cosh(x) - b - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (- b - a )sinh(x) + (- 6b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 15b - 15a )cosh(x) - b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 20b - 20a )cosh(x) + (- 4b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (- 15b - 15a )cosh(x) + (- 6b + 18a )cosh(x) + b +--R + +--R 2 +--R - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 6b - 6a )cosh(x) + (- 4b + 12a )cosh(x) +--R + +--R 2 2 +--R (2b - 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- b - a )cosh(x) + (- b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (b - 2a b - 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R (- b - a) +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +--------------+ +--R | 2 +--R +-+ +-----+ tanh(x)\|b coth(x) + a +--R 2\|b \|b + a atanh(------------------------) +--R +-+ +--R \|b +--R + +--R +-----+ +--R coth(x)\|b + a +--R (- 2b - 2a)atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R / +--R +-----+ +--R 2\|b + a +--R Type: Expression(Integer) +--E 293 + +--S 294 of 508 +--d0357a:= D(m0357a,x) +--E 294 + +--S 295 of 508 +m0357b:= a0357.2-r0357 +--R +--R +--R (259) +--R (b + a) +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R (- b - a) +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +--------------+ +--R | 2 +--R +-+ +-----+ tanh(x)\|b coth(x) + a +--R 2\|b \|b + a atanh(------------------------) +--R +-+ +--R \|b +--R + +--R +-----+ +--R coth(x)\|b + a +--R (- 2b - 2a)atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R + +--R - +--R +---+ +-----+ +--R 4\|- b \|b + a +--R * +--R atan +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b - a +--R / +--R 2 2 +---+ +-----+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|b + a +--R / +--R +-----+ +--R 2\|b + a +--R Type: Expression(Integer) +--E 295 + +--S 296 of 508 +d0357b:= D(m0357b,x) +--R +--R +--R (260) +--R 5 4 2 3 3 2 4 2 4 +--R (b - 4a b - 10a b - 4a b + a b)coth(x) + a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b - 10a b - 4a b + a +--R * +--R 12 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (4b - 16a b - 40a b - 16a b + 4a b)cosh(x)coth(x) +--R + +--R 4 2 3 3 2 4 5 +--R (4a b - 16a b - 40a b - 16a b + 4a )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (2b - 8a b - 20a b - 8a b + 2a b)cosh(x) + 8b +--R + +--R 4 2 3 3 2 4 +--R 36a b + 44a b + 12a b - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 2 4 +--R (2a b - 8a b - 20a b - 8a b + 2a )cosh(x) + 8a b +--R + +--R 2 3 3 2 4 5 +--R 36a b + 44a b + 12a b - 4a +--R * +--R 10 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 12b + 48a b + 120a b + 48a b - 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (16b + 72a b + 88a b + 24a b - 8a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 12a b + 48a b + 120a b + 48a b - 12a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (16a b + 72a b + 88a b + 24a b - 8a )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 17b + 68a b + 170a b + 68a b - 17a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 24b - 108a b - 132a b - 36a b + 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 30b + 28a b - 16a b + 4a b + 18a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 17a b + 68a b + 170a b + 68a b - 17a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 24a b - 108a b - 132a b - 36a b + 12a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R 30a b + 28a b - 16a b + 4a b + 18a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 32a b - 80a b - 32a b + 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 64b - 288a b - 352a b - 96a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (24b + 32a b + 16a b + 32a b + 24a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (8a b - 32a b - 80a b - 32a b + 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 64a b - 288a b - 352a b - 96a b + 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (24a b + 32a b + 16a b + 32a b + 24a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (28b - 112a b - 280a b - 112a b + 28a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (16b + 72a b + 88a b + 24a b - 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 72b - 48a b + 96a b + 48a b - 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 36b + 4a b - 44a b - 52a b - 40a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (28a b - 112a b - 280a b - 112a b + 28a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (16a b + 72a b + 88a b + 24a b - 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 72a b - 48a b + 96a b + 48a b - 24a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R 36a b + 4a b - 44a b - 52a b - 40a 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44a b + 52a b + 40a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 29b + 56a b + 66a b + 80a b + 41a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (- 17a b + 68a b + 170a b + 68a b - 17a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (16a b + 72a b + 88a b + 24a b - 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (84a b + 40a b - 160a b - 104a b + 12a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 36a b - 4a b + 44a b + 52a b + 40a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R 29a b + 56a b + 66a b + 80a b + 41a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (- 12b + 48a b + 120a b + 48a b - 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 64b - 288a b - 352a b - 96a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 24b - 32a b - 16a b - 32a b - 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 16b + 240a b + 176a b - 48a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 28b - 112a b - 168a b - 112a b - 28a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 9 +--R (- 12a b + 48a b + 120a b + 48a b - 12a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (- 64a b - 288a b - 352a b - 96a b + 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 24a b - 32a b - 16a b - 32a b - 24a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 16a b + 240a b + 176a b - 48a b + 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 28a b - 112a b - 168a b - 112a b - 28a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (2b - 8a b - 20a b - 8a b + 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 24b - 108a b - 132a b - 36a b + 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 72b - 48a b + 96a b + 48a b - 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 36b - 4a b + 44a b + 52a b + 40a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (14b + 176a b + 300a b + 128a b - 10a b)cosh(x) +--R + +--R 5 4 3 2 4 +--R 20b + 40a b - 40a b - 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 10 +--R (2a b - 8a b - 20a b - 8a b + 2a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (- 24a b - 108a b - 132a b - 36a b + 12a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (- 72a b - 48a b + 96a b + 48a b - 24a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 36a b - 4a b + 44a b + 52a b + 40a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (14a b + 176a b + 300a b + 128a b - 10a )cosh(x) +--R + +--R 4 2 3 4 5 +--R 20a b + 40a b - 40a b - 20a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 11 +--R (4b - 16a b - 40a b - 16a b + 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (16b + 72a b + 88a b + 24a b - 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (24b + 32a b + 16a b + 32a b + 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 120a b - 88a b + 24a b - 16a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 28b - 112a b - 168a b - 112a b - 28a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 3 2 4 +--R (- 24b - 48a b + 48a b + 24a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 11 +--R (4a b - 16a b - 40a b - 16a b + 4a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 9 +--R (16a b + 72a b + 88a b + 24a b - 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (24a b + 32a b + 16a b + 32a b + 24a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (8a b - 120a b - 88a b + 24a b - 16a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 28a b - 112a b - 168a b - 112a b - 28a )cosh(x) +--R + +--R 4 2 3 4 5 +--R (- 24a b - 48a b + 48a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 12 +--R (b - 4a b - 10a b - 4a b + a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (8b + 36a b + 44a b + 12a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (30b + 28a b - 16a b + 4a b + 18a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (36b + 4a b - 44a b - 52a b - 40a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (29b + 56a b + 66a b + 80a b + 41a b)cosh(x) +--R + +--R 5 4 3 2 4 2 5 2 3 +--R (20b + 40a b - 40a b - 20a b)cosh(x) + 4b - 8a b +--R + +--R 4 +--R 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 12 +--R (a b - 4a b - 10a b - 4a b + a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 10 +--R (8a b + 36a b + 44a b + 12a b - 4a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (30a b + 28a b - 16a b + 4a b + 18a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (36a b + 4a b - 44a b - 52a b - 40a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (29a b + 56a b + 66a b + 80a b + 41a )cosh(x) +--R + +--R 4 2 3 4 5 2 4 3 2 5 +--R (20a b + 40a b - 40a b - 20a )cosh(x) + 4a b - 8a b + 4a +--R * +--R 2 +--R tanh(x) +--R + +--R 5 4 2 3 3 2 4 12 +--R (- b + 4a b + 10a b + 4a b - a b)sinh(x) +--R + +--R 5 4 2 3 3 2 4 11 +--R (- 4b + 16a b + 40a b + 16a b - 4a b)cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (- 2b + 8a b + 20a b + 8a b - 2a b)cosh(x) - 8b +--R + +--R 4 2 3 3 2 4 +--R - 36a b - 44a b - 12a b + 4a b +--R * +--R 10 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (12b - 48a b - 120a b - 48a b + 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 16b - 72a b - 88a b - 24a b + 8a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (17b - 68a b - 170a b - 68a b + 17a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (24b + 108a b + 132a b + 36a b - 12a b)cosh(x) - 30b +--R + +--R 4 2 3 3 2 4 +--R - 28a b + 16a b - 4a b - 18a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 8b + 32a b + 80a b + 32a b - 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (64b + 288a b + 352a b + 96a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 24b - 32a b - 16a b - 32a b - 24a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 28b + 112a b + 280a b + 112a b - 28a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 16b - 72a b - 88a b - 24a b + 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (72b + 48a b - 96a b - 48a b + 24a b)cosh(x) - 36b +--R + +--R 4 2 3 3 2 4 +--R - 4a b + 44a b + 52a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 8b + 32a b + 80a b + 32a b - 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 96b - 432a b - 528a b - 144a b + 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (24b + 32a b + 16a b + 32a b + 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 8b + 120a b + 88a b - 24a b + 16a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (17b - 68a b - 170a b - 68a b + 17a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 16b - 72a b - 88a b - 24a b + 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 84b - 40a b + 160a b + 104a b - 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (36b + 4a b - 44a b - 52a b - 40a b)cosh(x) - 29b +--R + +--R 4 2 3 3 2 4 +--R - 56a b - 66a b - 80a b - 41a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (12b - 48a b - 120a b - 48a b + 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (64b + 288a b + 352a b + 96a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (24b + 32a b + 16a b + 32a b + 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (16b - 240a b - 176a b + 48a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (28b + 112a b + 168a b + 112a b + 28a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (- 2b + 8a b + 20a b + 8a b - 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (24b + 108a b + 132a b + 36a b - 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (72b + 48a b - 96a b - 48a b + 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (36b + 4a b - 44a b - 52a b - 40a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (- 14b - 176a b - 300a b - 128a b + 10a b)cosh(x) - 20b +--R + +--R 4 3 2 4 +--R - 40a b + 40a b + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 11 +--R (- 4b + 16a b + 40a b + 16a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (- 16b - 72a b - 88a b - 24a b + 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 24b - 32a b - 16a b - 32a b - 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 8b + 120a b + 88a b - 24a b + 16a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (28b + 112a b + 168a b + 112a b + 28a b)cosh(x) +--R + +--R 5 4 3 2 4 +--R (24b + 48a b - 48a b - 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 12 +--R (- b + 4a b + 10a b + 4a b - a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (- 8b - 36a b - 44a b - 12a b + 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 30b - 28a b + 16a b - 4a b - 18a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 36b - 4a b + 44a b + 52a b + 40a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 29b - 56a b - 66a b - 80a b - 41a b)cosh(x) +--R + +--R 5 4 3 2 4 2 5 2 3 4 +--R (- 20b - 40a b + 40a b + 20a b)cosh(x) - 4b + 8a b - 4a b +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 5 4 2 3 3 2 2 4 2 3 +--R (2b + 6a b + 6a b + 2a b )coth(x) + 2a b + 6a b +--R + +--R 3 2 4 +--R 6a b + 2a b +--R * +--R 12 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 2 +--R (8b + 24a b + 24a b + 8a b )cosh(x)coth(x) +--R + +--R 4 2 3 3 2 4 +--R (8a b + 24a b + 24a b + 8a b)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 2 5 +--R (4b + 12a b + 12a b + 4a b )cosh(x) - 12b +--R + +--R 4 2 3 3 2 4 +--R - 56a b - 68a b - 16a b + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (4a b + 12a b + 12a b + 4a b)cosh(x) - 12a b +--R + +--R 2 3 3 2 4 5 +--R - 56a b - 68a b - 16a b + 8a +--R * +--R 10 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 24b - 72a b - 72a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 40b - 192a b - 232a b - 48a b + 32a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 24a b - 72a b - 72a b - 24a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 40a b - 192a b - 232a b - 48a b + 32a )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 34b - 102a b - 102a b - 34a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 28b - 152a b - 180a b - 16a b + 40a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 52b - 64a b + 44a b + 24a b - 32a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 34a b - 102a b - 102a b - 34a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 28a b - 152a b - 180a b - 16a b + 40a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R - 52a b - 64a b + 44a b + 24a b - 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (16b + 48a b + 48a b + 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (32b + 128a b + 160a b + 64a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 112b - 176a b + 96a b + 80a b - 80a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 +--R (16a b + 48a b + 48a b + 16a b)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (32a b + 128a b + 160a b + 64a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 112a b - 176a b + 96a b + 80a b - 80a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (56b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (40b + 208a b + 248a b + 32a b - 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 16b - 96a b + 16a b + 64a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 72b + 20a b + 80a b + 52a b + 64a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 6 +--R (56a b + 168a b + 168a b + 56a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (40a b + 208a b + 248a b + 32a b - 48a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 16a b - 96a b + 16a b + 64a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R - 72a b + 20a b + 80a b + 52a b + 64a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (16b + 48a b + 48a b + 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (16b + 128a b + 144a b - 32a b - 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (112b + 176a b - 96a b - 80a b + 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 96b + 216a b + 256a b + 24a b + 80a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 7 +--R (16a b + 48a b + 48a b + 16a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b + 128a b + 144a b - 32a b - 64a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (112a b + 176a b - 96a b - 80a b + 80a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 96a b + 216a b + 256a b + 24a b + 80a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 34b - 102a b - 102a b - 34a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (40b + 208a b + 248a b + 32a b - 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (136b + 320a b - 120a b - 176a b + 128a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 +--R (8b + 172a b + 304a b + 140a b )cosh(x) - 62b +--R + +--R 4 2 3 3 2 4 +--R - 38a b - 82a b - 122a b - 80a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 8 +--R (- 34a b - 102a b - 102a b - 34a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (40a b + 208a b + 248a b + 32a b - 48a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (136a b + 320a b - 120a b - 176a b + 128a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (8a b + 172a b + 304a b + 140a b)cosh(x) - 62a b +--R + +--R 2 3 3 2 4 5 +--R - 38a b - 82a b - 122a b - 80a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (- 24b - 72a b - 72a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (32b + 128a b + 160a b + 64a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (112b + 176a b - 96a b - 80a b + 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (64b - 48a b + 256a b + 336a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 24b + 248a b + 72a b + 8a b - 48a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 9 +--R (- 24a b - 72a b - 72a b - 24a b)cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (32a b + 128a b + 160a b + 64a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (112a b + 176a b - 96a b - 80a b + 80a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (64a b - 48a b + 256a b + 336a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 24a b + 248a b + 72a b + 8a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (4b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 28b - 152a b - 180a b - 16a b + 40a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 16b - 96a b + 16a b + 64a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (8b + 172a b + 304a b + 140a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 52b + 60a b - 460a b - 252a b - 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 44b - 60a b - 12a b + 60a b + 56a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 10 +--R (4a b + 12a b + 12a b + 4a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (- 28a b - 152a b - 180a b - 16a b + 40a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (- 16a b - 96a b + 16a b + 64a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (8a b + 172a b + 304a b + 140a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 52a b + 60a b - 460a b - 252a b - 64a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R - 44a b - 60a b - 12a b + 60a b + 56a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 11 +--R (8b + 24a b + 24a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (- 40b - 192a b - 232a b - 48a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 112b - 176a b + 96a b + 80a b - 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 96b + 216a b + 256a b + 24a b + 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 24b + 248a b + 72a b + 8a b - 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (8b + 72a b - 24a b - 72a b + 16a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 11 +--R (8a b + 24a b + 24a b + 8a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 9 +--R (- 40a b - 192a b - 232a b - 48a b + 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (- 112a b - 176a b + 96a b + 80a b - 80a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 96a b + 216a b + 256a b + 24a b + 80a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 24a b + 248a b + 72a b + 8a b - 48a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (8a b + 72a b - 24a b - 72a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 12 +--R (2b + 6a b + 6a b + 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (- 12b - 56a b - 68a b - 16a b + 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 52b - 64a b + 44a b + 24a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 72b + 20a b + 80a b + 52a b + 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 62b - 38a b - 82a b - 122a b - 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 44b - 60a b - 12a b + 60a b + 56a b)cosh(x) +--R + +--R 5 2 3 4 +--R - 16b + 32a b - 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 12 +--R (2a b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 10 +--R (- 12a b - 56a b - 68a b - 16a b + 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (- 52a b - 64a b + 44a b + 24a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (- 72a b + 20a b + 80a b + 52a b + 64a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 62a b - 38a b - 82a b - 122a b - 80a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 4 +--R (- 44a b - 60a b - 12a b + 60a b + 56a )cosh(x) - 16a b +--R + +--R 3 2 5 +--R 32a b - 16a +--R * +--R 2 +--R tanh(x) +--R + +--R 5 4 2 3 3 2 12 +--R (- 2b - 6a b - 6a b - 2a b )sinh(x) +--R + +--R 5 4 2 3 3 2 11 +--R (- 8b - 24a b - 24a b - 8a b )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) + 12b + 56a b +--R + +--R 2 3 3 2 4 +--R 68a b + 16a b - 8a b +--R * +--R 10 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (24b + 72a b + 72a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (40b + 192a b + 232a b + 48a b - 32a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (34b + 102a b + 102a b + 34a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (28b + 152a b + 180a b + 16a b - 40a b)cosh(x) + 52b +--R + +--R 4 2 3 3 2 4 +--R 64a b - 44a b - 24a b + 32a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 16b - 48a b - 48a b - 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 32b - 128a b - 160a b - 64a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (112b + 176a b - 96a b - 80a b + 80a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 40b - 208a b - 248a b - 32a b + 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (16b + 96a b - 16a b - 64a b + 32a b)cosh(x) + 72b +--R + +--R 4 2 3 3 2 4 +--R - 20a b - 80a b - 52a b - 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 16b - 48a b - 48a b - 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 16b - 128a b - 144a b + 32a b + 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 112b - 176a b + 96a b + 80a b - 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (96b - 216a b - 256a b - 24a b - 80a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (34b + 102a b + 102a b + 34a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 40b - 208a b - 248a b - 32a b + 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 136b - 320a b + 120a b + 176a b - 128a b)cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 8b - 172a b - 304a b - 140a b )cosh(x) + 62b + 38a b +--R + +--R 2 3 3 2 4 +--R 82a b + 122a b + 80a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (24b + 72a b + 72a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 32b - 128a b - 160a b - 64a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 112b - 176a b + 96a b + 80a b - 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 64b + 48a b - 256a b - 336a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (24b - 248a b - 72a b - 8a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (28b + 152a b + 180a b + 16a b - 40a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (16b + 96a b - 16a b - 64a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 8b - 172a b - 304a b - 140a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (52b - 60a b + 460a b + 252a b + 64a b)cosh(x) + 44b +--R + +--R 4 2 3 3 2 4 +--R 60a b + 12a b - 60a b - 56a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 11 +--R (- 8b - 24a b - 24a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (40b + 192a b + 232a b + 48a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (112b + 176a b - 96a b - 80a b + 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (96b - 216a b - 256a b - 24a b - 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (24b - 248a b - 72a b - 8a b + 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 8b - 72a b + 24a b + 72a b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 12 +--R (- 2b - 6a b - 6a b - 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (12b + 56a b + 68a b + 16a b - 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (52b + 64a b - 44a b - 24a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (72b - 20a b - 80a b - 52a b - 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (62b + 38a b + 82a b + 122a b + 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 2 3 +--R (44b + 60a b + 12a b - 60a b - 56a b)cosh(x) + 16b - 32a b +--R + +--R 4 +--R 16a b +--R * +--R +-----+ +--R \|b + a +--R * +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R + +--R 4 2 3 3 2 2 2 3 3 2 4 14 +--R ((- 3a b - 2a b + a b )coth(x) - 3a b - 2a b + a b)sinh(x) +--R + +--R 4 2 3 3 2 2 +--R (- 18a b - 12a b + 6a b )cosh(x)coth(x) +--R + +--R 2 3 3 2 4 +--R (- 18a b - 12a b + 6a b)cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 4 2 3 3 2 2 4 2 3 +--R (- 33a b - 22a b + 11a b )cosh(x) - 5a b - 3a b +--R + +--R 3 2 4 +--R a b - a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 5 +--R (- 33a b - 22a b + 11a b)cosh(x) - 5a b - 3a b + a b - a +--R * +--R 12 +--R sinh(x) +--R + +--R 4 2 3 3 2 3 +--R (12a b + 8a b - 4a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 20a b - 12a b + 4a b - 4a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 3 +--R (12a b + 8a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (- 20a b - 12a b + 4a b - 4a )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 +--R (117a b + 78a b - 39a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (- 10a b - 6a b + 2a b - 2a b)cosh(x) + 10a b +--R + +--R 2 3 3 2 4 +--R 4a b - 2a b + 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 4 +--R (117a b + 78a b - 39a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 +--R (- 10a b - 6a b + 2a b - 2a )cosh(x) + 10a b + 4a b +--R + +--R 4 5 +--R - 2a b + 4a +--R * +--R 10 +--R sinh(x) +--R + +--R 4 2 3 3 2 5 +--R (114a b + 76a b - 38a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (60a b + 36a b - 12a b + 12a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (36a b + 24a b - 4a b + 8a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 5 +--R (114a b + 76a b - 38a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (60a b + 36a b - 12a b + 12a )cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (36a b + 24a b - 4a b + 8a )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 4 2 3 3 2 6 +--R (- 81a b - 54a b + 27a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (85a b + 51a b - 17a b + 17a b)cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (34a b + 52a b + 6a b - 12a b)cosh(x) + 34a b +--R + +--R 2 3 3 2 4 +--R 26a b - 10a b - 18a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 6 +--R (- 81a b - 54a b + 27a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (85a b + 51a b - 17a b + 17a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 +--R (34a b + 52a b + 6a b - 12a )cosh(x) + 34a b + 26a b +--R + +--R 4 5 +--R - 10a b - 18a +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 3 2 7 +--R (- 216a b - 144a b + 72a b )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 40a b - 24a b + 8a b - 8a b)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 16a b + 32a b + 16a b - 32a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (72a b + 24a b - 8a b - 24a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 7 +--R (- 216a b - 144a b + 72a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 40a b - 24a b + 8a b - 8a )cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 16a b + 32a b + 16a b - 32a )cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (72a b + 24a b - 8a b - 24a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 3 2 8 +--R (- 81a b - 54a b + 27a b )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 140a b - 84a b + 28a b - 28a b)cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 44a b - 56a b - 4a b + 8a b)cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (8a b - 56a b + 24a b + 24a b)cosh(x) + 17a b +--R + +--R 2 3 3 2 4 +--R 10a b + 33a b + 40a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 8 +--R (- 81a b - 54a b + 27a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 140a b - 84a b + 28a b - 28a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 44a b - 56a b - 4a b + 8a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 +--R (8a b - 56a b + 24a b + 24a )cosh(x) + 17a b + 10a b +--R + +--R 4 5 +--R 33a b + 40a +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 2 9 +--R (114a b + 76a b - 38a b )cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (- 40a b - 24a b + 8a b - 8a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 40a b - 112a b - 24a b + 48a b)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 72a b - 24a b + 8a b + 24a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (30a b - 52a b - 66a b + 16a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 9 +--R (114a b + 76a b - 38a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (- 40a b - 24a b + 8a b - 8a )cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 40a b - 112a b - 24a b + 48a )cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 72a b - 24a b + 8a b + 24a )cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (30a b - 52a b - 66a b + 16a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 3 2 10 +--R (117a b + 78a b - 39a b )cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (85a b + 51a b - 17a b + 17a b)cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 44a b - 56a b - 4a b + 8a b)cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 84a b + 60a b - 28a b - 12a b)cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (- 33a b - 42a b - 49a b - 40a b)cosh(x) - 25a b +--R + +--R 2 3 3 2 4 +--R - 27a b - 43a b - 41a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 10 +--R (117a b + 78a b - 39a b)cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (85a b + 51a b - 17a b + 17a )cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 44a b - 56a b - 4a b + 8a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 84a b + 60a b - 28a b - 12a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 +--R (- 33a b - 42a b - 49a b - 40a )cosh(x) - 25a b - 27a b +--R + +--R 4 5 +--R - 43a b - 41a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 3 2 11 +--R (12a b + 8a b - 4a b )cosh(x) +--R + +--R 4 2 3 3 2 4 9 +--R (60a b + 36a b - 12a b + 12a b)cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (- 16a b + 32a b + 16a b - 32a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 72a b - 24a b + 8a b + 24a b)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 92a b + 40a b + 100a b - 32a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (12a b + 84a b + 100a b + 28a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 11 +--R (12a b + 8a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (60a b + 36a b - 12a b + 12a )cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (- 16a b + 32a b + 16a b - 32a )cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 72a b - 24a b + 8a b + 24a )cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 92a b + 40a b + 100a b - 32a )cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (12a b + 84a b + 100a b + 28a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 3 2 12 +--R (- 33a b - 22a b + 11a b )cosh(x) +--R + +--R 4 2 3 3 2 4 10 +--R (- 10a b - 6a b + 2a b - 2a b)cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (34a b + 52a b + 6a b - 12a b)cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (8a b - 56a b + 24a b + 24a b)cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 33a b - 42a b - 49a b - 40a b)cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 +--R (- 54a b - 162a b - 98a b + 10a b)cosh(x) - 24a b +--R + +--R 2 3 3 2 4 +--R - 12a b + 16a b + 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 12 +--R (- 33a b - 22a b + 11a b)cosh(x) +--R + +--R 2 3 3 2 4 5 10 +--R (- 10a b - 6a b + 2a b - 2a )cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (34a b + 52a b + 6a b - 12a )cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (8a b - 56a b + 24a b + 24a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 33a b - 42a b - 49a b - 40a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 +--R (- 54a b - 162a b - 98a b + 10a )cosh(x) - 24a b - 12a b +--R + +--R 4 5 +--R 16a b + 20a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 13 +--R (- 18a b - 12a b + 6a b )cosh(x) +--R + +--R 4 2 3 3 2 4 11 +--R (- 20a b - 12a b + 4a b - 4a b)cosh(x) +--R + +--R 4 2 3 3 2 4 9 +--R (36a b + 24a b - 4a b + 8a b)cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (72a b + 24a b - 8a b - 24a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (30a b - 52a b - 66a b + 16a b)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (12a b + 84a b + 100a b + 28a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (16a b + 40a b - 32a b - 24a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 13 +--R (- 18a b - 12a b + 6a b)cosh(x) +--R + +--R 2 3 3 2 4 5 11 +--R (- 20a b - 12a b + 4a b - 4a )cosh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (36a b + 24a b - 4a b + 8a )cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (72a b + 24a b - 8a b - 24a )cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (30a b - 52a b - 66a b + 16a )cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (12a b + 84a b + 100a b + 28a )cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (16a b + 40a b - 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 14 +--R (- 3a b - 2a b + a b )cosh(x) +--R + +--R 4 2 3 3 2 4 12 +--R (- 5a b - 3a b + a b - a b)cosh(x) +--R + +--R 4 2 3 3 2 4 10 +--R (10a b + 4a b - 2a b + 4a b)cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (34a b + 26a b - 10a b - 18a b)cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (17a b + 10a b + 33a b + 40a b)cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 25a b - 27a b - 43a b - 41a b)cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 2 3 +--R (- 24a b - 12a b + 16a b + 20a b)cosh(x) - 4a b + 4a b +--R + +--R 3 2 4 +--R 4a b - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 4 14 +--R (- 3a b - 2a b + a b)cosh(x) +--R + +--R 2 3 3 2 4 5 12 +--R (- 5a b - 3a b + a b - a )cosh(x) +--R + +--R 2 3 3 2 4 5 10 +--R (10a b + 4a b - 2a b + 4a )cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (34a b + 26a b - 10a b - 18a )cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (17a b + 10a b + 33a b + 40a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 25a b - 27a b - 43a b - 41a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 4 +--R (- 24a b - 12a b + 16a b + 20a )cosh(x) - 4a b + 4a b + 4a b +--R + +--R 5 +--R - 4a +--R * +--R 2 +--R tanh(x) +--R + +--R 5 4 2 3 3 5 4 2 3 +--R ((3b + 2a b - a b )coth(x) + (- 3b - 2a b + a b )coth(x)) +--R * +--R 14 +--R sinh(x) +--R + +--R 5 4 2 3 3 +--R (18b + 12a b - 6a b )cosh(x)coth(x) +--R + +--R 5 4 2 3 +--R (- 18b - 12a b + 6a b )cosh(x)coth(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 5 4 2 3 2 5 4 2 3 +--R (33b + 22a b - 11a b )cosh(x) + 5b + 3a b - a b +--R + +--R 3 2 +--R a b +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 2 5 4 2 3 +--R (- 33b - 22a b + 11a b )cosh(x) - 5b - 3a b + a b +--R + +--R 3 2 +--R - a b +--R * +--R coth(x) +--R * +--R 12 +--R sinh(x) +--R + +--R 5 4 2 3 3 +--R (- 12b - 8a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (20b + 12a b - 4a b + 4a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 3 +--R (12b + 8a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 20b - 12a b + 4a b - 4a b )cosh(x) +--R * +--R coth(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 5 4 2 3 4 +--R (- 117b - 78a b + 39a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (10b + 6a b - 2a b + 2a b )cosh(x) - 10b - 4a b +--R + +--R 2 3 3 2 +--R 2a b - 4a b +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 4 +--R (117b + 78a b - 39a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 10b - 6a b + 2a b - 2a b )cosh(x) + 10b + 4a b +--R + +--R 2 3 3 2 +--R - 2a b + 4a b +--R * +--R coth(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 5 4 2 3 5 +--R (- 114b - 76a b + 38a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 60b - 36a b + 12a b - 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 36b - 24a b + 4a b - 8a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 5 +--R (114b + 76a b - 38a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (60b + 36a b - 12a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (36b + 24a b - 4a b + 8a b )cosh(x) +--R * +--R coth(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 4 2 3 6 +--R (81b + 54a b - 27a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 85b - 51a b + 17a b - 17a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 +--R (- 34b - 52a b - 6a b + 12a b )cosh(x) - 34b +--R + +--R 4 2 3 3 2 +--R - 26a b + 10a b + 18a b +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 6 +--R (- 81b - 54a b + 27a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (85b + 51a b - 17a b + 17a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (34b + 52a b + 6a b - 12a b )cosh(x) + 34b + 26a b +--R + +--R 2 3 3 2 +--R - 10a b - 18a b +--R * +--R coth(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 2 3 7 +--R (216b + 144a b - 72a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (40b + 24a b - 8a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (16b - 32a b - 16a b + 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 72b - 24a b + 8a b + 24a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 7 +--R (- 216b - 144a b + 72a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 40b - 24a b + 8a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 16b + 32a b + 16a b - 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (72b + 24a b - 8a b - 24a b )cosh(x) +--R * +--R coth(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 3 8 +--R (81b + 54a b - 27a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (140b + 84a b - 28a b + 28a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (44b + 56a b + 4a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 +--R (- 8b + 56a b - 24a b - 24a b )cosh(x) - 17b +--R + +--R 4 2 3 3 2 +--R - 10a b - 33a b - 40a b +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 8 +--R (- 81b - 54a b + 27a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 140b - 84a b + 28a b - 28a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 44b - 56a b - 4a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (8b - 56a b + 24a b + 24a b )cosh(x) + 17b + 10a b +--R + +--R 2 3 3 2 +--R 33a b + 40a b +--R * +--R coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 9 +--R (- 114b - 76a b + 38a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (40b + 24a b - 8a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (40b + 112a b + 24a b - 48a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (72b + 24a b - 8a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 30b + 52a b + 66a b - 16a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 9 +--R (114b + 76a b - 38a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 40b - 24a b + 8a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 40b - 112a b - 24a b + 48a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 72b - 24a b + 8a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (30b - 52a b - 66a b + 16a b )cosh(x) +--R * +--R coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 10 +--R (- 117b - 78a b + 39a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 85b - 51a b + 17a b - 17a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (44b + 56a b + 4a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (84b - 60a b + 28a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (33b + 42a b + 49a b + 40a b )cosh(x) + 25b + 27a b +--R + +--R 2 3 3 2 +--R 43a b + 41a b +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 10 +--R (117b + 78a b - 39a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (85b + 51a b - 17a b + 17a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 44b - 56a b - 4a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 84b + 60a b - 28a b - 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 +--R (- 33b - 42a b - 49a b - 40a b )cosh(x) - 25b +--R + +--R 4 2 3 3 2 +--R - 27a b - 43a b - 41a b +--R * +--R coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 11 +--R (- 12b - 8a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (- 60b - 36a b + 12a b - 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (16b - 32a b - 16a b + 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (72b + 24a b - 8a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (92b - 40a b - 100a b + 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 12b - 84a b - 100a b - 28a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 11 +--R (12b + 8a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (60b + 36a b - 12a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 16b + 32a b + 16a b - 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 72b - 24a b + 8a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 92b + 40a b + 100a b - 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (12b + 84a b + 100a b + 28a b )cosh(x) +--R * +--R coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 12 +--R (33b + 22a b - 11a b )cosh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (10b + 6a b - 2a b + 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 34b - 52a b - 6a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 8b + 56a b - 24a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (33b + 42a b + 49a b + 40a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 +--R (54b + 162a b + 98a b - 10a b )cosh(x) + 24b +--R + +--R 4 2 3 3 2 +--R 12a b - 16a b - 20a b +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 12 +--R (- 33b - 22a b + 11a b )cosh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (- 10b - 6a b + 2a b - 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (34b + 52a b + 6a b - 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (8b - 56a b + 24a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 33b - 42a b - 49a b - 40a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 +--R (- 54b - 162a b - 98a b + 10a b )cosh(x) - 24b +--R + +--R 4 2 3 3 2 +--R - 12a b + 16a b + 20a b +--R * +--R coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 13 +--R (18b + 12a b - 6a b )cosh(x) +--R + +--R 5 4 2 3 3 2 11 +--R (20b + 12a b - 4a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (- 36b - 24a b + 4a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 72b - 24a b + 8a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 30b + 52a b + 66a b - 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 12b - 84a b - 100a b - 28a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 16b - 40a b + 32a b + 24a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 13 +--R (- 18b - 12a b + 6a b )cosh(x) +--R + +--R 5 4 2 3 3 2 11 +--R (- 20b - 12a b + 4a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (36b + 24a b - 4a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (72b + 24a b - 8a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (30b - 52a b - 66a b + 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (12b + 84a b + 100a b + 28a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (16b + 40a b - 32a b - 24a b )cosh(x) +--R * +--R coth(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 14 +--R (3b + 2a b - a b )cosh(x) +--R + +--R 5 4 2 3 3 2 12 +--R (5b + 3a b - a b + a b )cosh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (- 10b - 4a b + 2a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 34b - 26a b + 10a b + 18a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 17b - 10a b - 33a b - 40a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (25b + 27a b + 43a b + 41a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (24b + 12a b - 16a b - 20a b )cosh(x) + 4b - 4a b +--R + +--R 2 3 3 2 +--R - 4a b + 4a b +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 2 3 14 +--R (- 3b - 2a b + a b )cosh(x) +--R + +--R 5 4 2 3 3 2 12 +--R (- 5b - 3a b + a b - a b )cosh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (10b + 4a b - 2a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (34b + 26a b - 10a b - 18a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (17b + 10a b + 33a b + 40a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 25b - 27a b - 43a b - 41a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 24b - 12a b + 16a b + 20a b )cosh(x) - 4b + 4a b +--R + +--R 2 3 3 2 +--R 4a b - 4a b +--R * +--R coth(x) +--R * +--R tanh(x) +--R + +--R 5 4 2 3 2 5 4 2 3 14 +--R ((- 3b - 2a b + a b )coth(x) + 3b + 2a b - a b )sinh(x) +--R + +--R 5 4 2 3 2 +--R (- 18b - 12a b + 6a b )cosh(x)coth(x) +--R + +--R 5 4 2 3 +--R (18b + 12a b - 6a b )cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 5 4 2 3 2 5 4 2 3 +--R (- 33b - 22a b + 11a b )cosh(x) - 5b - 3a b + a b +--R + +--R 3 2 +--R - a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 2 5 4 2 3 3 2 +--R (33b + 22a b - 11a b )cosh(x) + 5b + 3a b - a b + a b +--R * +--R 12 +--R sinh(x) +--R + +--R 5 4 2 3 3 +--R (12b + 8a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 20b - 12a b + 4a b - 4a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 3 +--R (- 12b - 8a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (20b + 12a b - 4a b + 4a b )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 5 4 2 3 4 +--R (117b + 78a b - 39a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 10b - 6a b + 2a b - 2a b )cosh(x) + 10b + 4a b +--R + +--R 2 3 3 2 +--R - 2a b + 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 4 +--R (- 117b - 78a b + 39a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 2 3 +--R (10b + 6a b - 2a b + 2a b )cosh(x) - 10b - 4a b + 2a b +--R + +--R 3 2 +--R - 4a b +--R * +--R 10 +--R sinh(x) +--R + +--R 5 4 2 3 5 +--R (114b + 76a b - 38a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (60b + 36a b - 12a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (36b + 24a b - 4a b + 8a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 5 +--R (- 114b - 76a b + 38a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 60b - 36a b + 12a b - 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 36b - 24a b + 4a b - 8a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 4 2 3 6 +--R (- 81b - 54a b + 27a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (85b + 51a b - 17a b + 17a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (34b + 52a b + 6a b - 12a b )cosh(x) + 34b + 26a b +--R + +--R 2 3 3 2 +--R - 10a b - 18a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 6 +--R (81b + 54a b - 27a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 85b - 51a b + 17a b - 17a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 34b - 52a b - 6a b + 12a b )cosh(x) - 34b - 26a b +--R + +--R 2 3 3 2 +--R 10a b + 18a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 2 3 7 +--R (- 216b - 144a b + 72a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 40b - 24a b + 8a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 16b + 32a b + 16a b - 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (72b + 24a b - 8a b - 24a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 7 +--R (216b + 144a b - 72a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (40b + 24a b - 8a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (16b - 32a b - 16a b + 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 72b - 24a b + 8a b + 24a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 3 8 +--R (- 81b - 54a b + 27a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 140b - 84a b + 28a b - 28a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 44b - 56a b - 4a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (8b - 56a b + 24a b + 24a b )cosh(x) + 17b + 10a b +--R + +--R 2 3 3 2 +--R 33a b + 40a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 8 +--R (81b + 54a b - 27a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (140b + 84a b - 28a b + 28a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (44b + 56a b + 4a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 8b + 56a b - 24a b - 24a b )cosh(x) - 17b - 10a b +--R + +--R 2 3 3 2 +--R - 33a b - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 9 +--R (114b + 76a b - 38a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 40b - 24a b + 8a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 40b - 112a b - 24a b + 48a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 72b - 24a b + 8a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (30b - 52a b - 66a b + 16a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 9 +--R (- 114b - 76a b + 38a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (40b + 24a b - 8a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (40b + 112a b + 24a b - 48a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (72b + 24a b - 8a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 30b + 52a b + 66a b - 16a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 10 +--R (117b + 78a b - 39a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (85b + 51a b - 17a b + 17a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 44b - 56a b - 4a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 84b + 60a b - 28a b - 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 33b - 42a b - 49a b - 40a b )cosh(x) - 25b - 27a b +--R + +--R 2 3 3 2 +--R - 43a b - 41a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 10 +--R (- 117b - 78a b + 39a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 85b - 51a b + 17a b - 17a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (44b + 56a b + 4a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (84b - 60a b + 28a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (33b + 42a b + 49a b + 40a b )cosh(x) + 25b + 27a b +--R + +--R 2 3 3 2 +--R 43a b + 41a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 11 +--R (12b + 8a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (60b + 36a b - 12a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 16b + 32a b + 16a b - 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 72b - 24a b + 8a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 92b + 40a b + 100a b - 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (12b + 84a b + 100a b + 28a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 11 +--R (- 12b - 8a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (- 60b - 36a b + 12a b - 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (16b - 32a b - 16a b + 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (72b + 24a b - 8a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (92b - 40a b - 100a b + 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 12b - 84a b - 100a b - 28a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 12 +--R (- 33b - 22a b + 11a b )cosh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (- 10b - 6a b + 2a b - 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (34b + 52a b + 6a b - 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (8b - 56a b + 24a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 33b - 42a b - 49a b - 40a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 54b - 162a b - 98a b + 10a b )cosh(x) - 24b - 12a b +--R + +--R 2 3 3 2 +--R 16a b + 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 12 +--R (33b + 22a b - 11a b )cosh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (10b + 6a b - 2a b + 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 34b - 52a b - 6a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 8b + 56a b - 24a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (33b + 42a b + 49a b + 40a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (54b + 162a b + 98a b - 10a b )cosh(x) + 24b + 12a b +--R + +--R 2 3 3 2 +--R - 16a b - 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 13 +--R (- 18b - 12a b + 6a b )cosh(x) +--R + +--R 5 4 2 3 3 2 11 +--R (- 20b - 12a b + 4a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (36b + 24a b - 4a b + 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (72b + 24a b - 8a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (30b - 52a b - 66a b + 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (12b + 84a b + 100a b + 28a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (16b + 40a b - 32a b - 24a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 13 +--R (18b + 12a b - 6a b )cosh(x) +--R + +--R 5 4 2 3 3 2 11 +--R (20b + 12a b - 4a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (- 36b - 24a b + 4a b - 8a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 72b - 24a b + 8a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 30b + 52a b + 66a b - 16a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 12b - 84a b - 100a b - 28a b )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R (- 16b - 40a b + 32a b + 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 14 +--R (- 3b - 2a b + a b )cosh(x) +--R + +--R 5 4 2 3 3 2 12 +--R (- 5b - 3a b + a b - a b )cosh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (10b + 4a b - 2a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (34b + 26a b - 10a b - 18a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (17b + 10a b + 33a b + 40a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 25b - 27a b - 43a b - 41a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 2 3 +--R (- 24b - 12a b + 16a b + 20a b )cosh(x) - 4b + 4a b + 4a b +--R + +--R 3 2 +--R - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 2 3 14 5 4 2 3 3 2 12 +--R (3b + 2a b - a b )cosh(x) + (5b + 3a b - a b + a b )cosh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (- 10b - 4a b + 2a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 34b - 26a b + 10a b + 18a b )cosh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 17b - 10a b - 33a b - 40a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (25b + 27a b + 43a b + 41a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 2 3 3 2 +--R (24b + 12a b - 16a b - 20a b )cosh(x) + 4b - 4a b - 4a b + 4a b +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 2 4 3 3 +--R (4a b + 12a b + 12a b + 4a b )coth(x) + 4a b + 12a b +--R + +--R 4 2 5 +--R 12a b + 4a b +--R * +--R 12 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 2 +--R (24a b + 72a b + 72a b + 24a b )cosh(x)coth(x) +--R + +--R 2 4 3 3 4 2 5 +--R (24a b + 72a b + 72a b + 24a b)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 2 4 +--R (56a b + 168a b + 168a b + 56a b )cosh(x) - 8a b - 8a b +--R + +--R 4 2 5 +--R - 8a b - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 +--R (56a b + 168a b + 168a b + 56a b)cosh(x) - 8a b - 8a b +--R + +--R 5 6 +--R - 8a b - 8a +--R * +--R 10 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (56a b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 24a b - 24a b - 8a b - 40a b - 32a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (56a b + 168a b + 168a b + 56a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 24a b - 24a b - 8a b - 40a b - 32a )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 4a b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 5 +--R (- 8a b - 8a b - 32a b - 72a b - 40a b)cosh(x) - 48a b +--R + +--R 2 4 3 3 4 2 5 +--R - 72a b - 32a b + 24a b + 32a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 4a b - 12a b - 12a b - 4a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 2 4 +--R (- 8a b - 8a b - 32a b - 72a b - 40a )cosh(x) - 48a b +--R + +--R 3 3 4 2 5 6 +--R - 72a b - 32a b + 24a b + 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 80a b - 240a b - 240a b - 80a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (32a b + 32a b - 32a b - 32a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 136a b - 168a b - 104a b + 8a b + 80a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 80a b - 240a b - 240a b - 80a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (32a b + 32a b - 32a b - 32a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 136a b - 168a b - 104a b + 8a b + 80a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 112a b - 336a b - 336a b - 112a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (16a b + 16a b + 32a b + 80a b + 48a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 112a b - 144a b - 176a b - 112a b + 32a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 40a b - 48a b - 40a b - 96a b - 64a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 112a b - 336a b - 336a b - 112a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (16a b + 16a b + 32a b + 80a b + 48a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 2 4 +--R (- 112a b - 144a b - 176a b - 112a b + 32a )cosh(x) - 40a b +--R + +--R 3 3 4 2 5 6 +--R - 48a b - 40a b - 96a b - 64a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 80a b - 240a b - 240a b - 80a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 16a b - 16a b + 80a b + 144a b + 64a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (8a b - 216a b - 280a b - 136a b - 80a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 104a b - 56a b + 120a b - 8a b - 80a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 80a b - 240a b - 240a b - 80a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 16a b - 16a b + 80a b + 144a b + 64a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (8a b - 216a b - 280a b - 136a b - 80a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 104a b - 56a b + 120a b - 8a b - 80a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 8 +--R (- 4a b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (16a b + 16a b + 32a b + 80a b + 48a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (64a b - 336a b - 352a b - 80a b - 128a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 5 +--R (- 56a b - 48a b + 72a b + 64a b )cosh(x) + 28a b +--R + +--R 2 4 3 3 4 2 5 +--R 60a b + 84a b + 132a b + 80a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (- 4a b - 12a b - 12a b - 4a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (16a b + 16a b + 32a b + 80a b + 48a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (64a b - 336a b - 352a b - 80a b - 128a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 2 4 3 3 +--R (- 56a b - 48a b + 72a b + 64a b)cosh(x) + 28a b + 60a b +--R + +--R 4 2 5 6 +--R 84a b + 132a b + 80a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 9 +--R (56a b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (32a b + 32a b - 32a b - 32a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (8a b - 216a b - 280a b - 136a b - 80a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (16a b - 80a b - 176a b - 48a b + 32a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 16a b - 64a b - 160a b - 64a b + 48a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 9 +--R (56a b + 168a b + 168a b + 56a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (32a b + 32a b - 32a b - 32a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (8a b - 216a b - 280a b - 136a b - 80a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (16a b - 80a b - 176a b - 48a b + 32a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 16a b - 64a b - 160a b - 64a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 10 +--R (56a b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 8 +--R (- 8a b - 8a b - 32a b - 72a b - 40a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 112a b - 144a b - 176a b - 112a b + 32a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 56a b - 48a b + 72a b + 64a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (40a b + 264a b + 280a b + 120a b + 64a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 48a b + 56a b + 8a b - 56a b - 56a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 10 +--R (56a b + 168a b + 168a b + 56a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 8 +--R (- 8a b - 8a b - 32a b - 72a b - 40a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 112a b - 144a b - 176a b - 112a b + 32a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 56a b - 48a b + 72a b + 64a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 2 4 +--R (40a b + 264a b + 280a b + 120a b + 64a )cosh(x) + 48a b +--R + +--R 3 3 4 2 5 6 +--R 56a b + 8a b - 56a b - 56a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 11 +--R (24a b + 72a b + 72a b + 24a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 9 +--R (- 24a b - 24a b - 8a b - 40a b - 32a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (- 136a b - 168a b - 104a b + 8a b + 80a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 104a b - 56a b + 120a b - 8a b - 80a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (- 16a b - 64a b - 160a b - 64a b + 48a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 80a b + 16a b + 80a b - 16a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 11 +--R (24a b + 72a b + 72a b + 24a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (- 24a b - 24a b - 8a b - 40a b - 32a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (- 136a b - 168a b - 104a b + 8a b + 80a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 104a b - 56a b + 120a b - 8a b - 80a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 16a b - 64a b - 160a b - 64a b + 48a )cosh(x) +--R + +--R 3 3 4 2 5 6 +--R (- 80a b + 16a b + 80a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 12 +--R (4a b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 5 2 4 4 2 5 10 +--R (- 8a b - 8a b - 8a b - 8a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 8 +--R (- 48a b - 72a b - 32a b + 24a b + 32a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 40a b - 48a b - 40a b - 96a b - 64a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (28a b + 60a b + 84a b + 132a b + 80a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 5 +--R (48a b + 56a b + 8a b - 56a b - 56a b)cosh(x) + 16a b +--R + +--R 3 3 5 +--R - 32a b + 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 3 4 2 5 12 +--R (4a b + 12a b + 12a b + 4a b)cosh(x) +--R + +--R 2 4 3 3 5 6 10 +--R (- 8a b - 8a b - 8a b - 8a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 8 +--R (- 48a b - 72a b - 32a b + 24a b + 32a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 40a b - 48a b - 40a b - 96a b - 64a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (28a b + 60a b + 84a b + 132a b + 80a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 2 4 4 2 +--R (48a b + 56a b + 8a b - 56a b - 56a )cosh(x) + 16a b - 32a b +--R + +--R 6 +--R 16a +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 4b - 12a b - 12a b - 4a b )coth(x) +--R + +--R 6 5 2 4 3 3 +--R (4b + 12a b + 12a b + 4a b )coth(x) +--R * +--R 12 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 24b - 72a b - 72a b - 24a b )cosh(x)coth(x) +--R + +--R 6 5 2 4 3 3 +--R (24b + 72a b + 72a b + 24a b )cosh(x)coth(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) + 8b + 8a b +--R + +--R 3 3 4 2 +--R 8a b + 8a b +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (56b + 168a b + 168a b + 56a b )cosh(x) - 8b - 8a b +--R + +--R 3 3 4 2 +--R - 8a b - 8a b +--R * +--R coth(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (24b + 24a b + 8a b + 40a b + 32a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 3 +--R (56b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 24b - 24a b - 8a b - 40a b - 32a b )cosh(x) +--R * +--R coth(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (4b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (8b + 8a b + 32a b + 72a b + 40a b )cosh(x) + 48b +--R + +--R 5 2 4 3 3 4 2 +--R 72a b + 32a b - 24a b - 32a b +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (- 8b - 8a b - 32a b - 72a b - 40a b )cosh(x) - 48b +--R + +--R 5 2 4 3 3 4 2 +--R - 72a b - 32a b + 24a b + 32a b +--R * +--R coth(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (80b + 240a b + 240a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 32b - 32a b + 32a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (136b + 168a b + 104a b - 8a b - 80a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 80b - 240a b - 240a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (32b + 32a b - 32a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 136b - 168a b - 104a b + 8a b + 80a b )cosh(x) +--R * +--R coth(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 6 +--R (112b + 336a b + 336a b + 112a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 16b - 16a b - 32a b - 80a b - 48a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (112b + 144a b + 176a b + 112a b - 32a b )cosh(x) + 40b +--R + +--R 5 2 4 3 3 4 2 +--R 48a b + 40a b + 96a b + 64a b +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 6 +--R (- 112b - 336a b - 336a b - 112a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (16b + 16a b + 32a b + 80a b + 48a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- 112b - 144a b - 176a b - 112a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 40b - 48a b - 40a b - 96a b - 64a b +--R * +--R coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 7 +--R (80b + 240a b + 240a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (16b + 16a b - 80a b - 144a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 8b + 216a b + 280a b + 136a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (104b + 56a b - 120a b + 8a b + 80a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 7 +--R (- 80b - 240a b - 240a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 16b - 16a b + 80a b + 144a b + 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (8b - 216a b - 280a b - 136a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 104b - 56a b + 120a b - 8a b - 80a b )cosh(x) +--R * +--R coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 8 +--R (4b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 16b - 16a b - 32a b - 80a b - 48a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 64b + 336a b + 352a b + 80a b + 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (56b + 48a b - 72a b - 64a b )cosh(x) - 28b - 60a b +--R + +--R 2 4 3 3 4 2 +--R - 84a b - 132a b - 80a b +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 8 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (16b + 16a b + 32a b + 80a b + 48a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (64b - 336a b - 352a b - 80a b - 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (- 56b - 48a b + 72a b + 64a b )cosh(x) + 28b + 60a b +--R + +--R 2 4 3 3 4 2 +--R 84a b + 132a b + 80a b +--R * +--R coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 9 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 7 +--R (- 32b - 32a b + 32a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 8b + 216a b + 280a b + 136a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 16b + 80a b + 176a b + 48a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (16b + 64a b + 160a b + 64a b - 48a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 9 +--R (56b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 7 +--R (32b + 32a b - 32a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (8b - 216a b - 280a b - 136a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (16b - 80a b - 176a b - 48a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 16b - 64a b - 160a b - 64a b + 48a b )cosh(x) +--R * +--R coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 10 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (8b + 8a b + 32a b + 72a b + 40a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (112b + 144a b + 176a b + 112a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (56b + 48a b - 72a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- 40b - 264a b - 280a b - 120a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 48b - 56a b - 8a b + 56a b + 56a b +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 10 +--R (56b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (- 8b - 8a b - 32a b - 72a b - 40a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 112b - 144a b - 176a b - 112a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- 56b - 48a b + 72a b + 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (40b + 264a b + 280a b + 120a b + 64a b )cosh(x) + 48b +--R + +--R 5 2 4 3 3 4 2 +--R 56a b + 8a b - 56a b - 56a b +--R * +--R coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 11 +--R (- 24b - 72a b - 72a b - 24a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 9 +--R (24b + 24a b + 8a b + 40a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (136b + 168a b + 104a b - 8a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (104b + 56a b - 120a b + 8a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (16b + 64a b + 160a b + 64a b - 48a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (80a b - 16a b - 80a b + 16a b )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 11 +--R (24b + 72a b + 72a b + 24a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 9 +--R (- 24b - 24a b - 8a b - 40a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (- 136b - 168a b - 104a b + 8a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 104b - 56a b + 120a b - 8a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 16b - 64a b - 160a b - 64a b + 48a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 80a b + 16a b + 80a b - 16a b )cosh(x) +--R * +--R coth(x) +--R * +--R sinh(x) +--R + +--R 6 5 2 4 3 3 12 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 6 5 3 3 4 2 10 +--R (8b + 8a b + 8a b + 8a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (48b + 72a b + 32a b - 24a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (40b + 48a b + 40a b + 96a b + 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 28b - 60a b - 84a b - 132a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (- 48b - 56a b - 8a b + 56a b + 56a b )cosh(x) - 16b +--R + +--R 2 4 4 2 +--R 32a b - 16a b +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 2 4 3 3 12 +--R (4b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 6 5 3 3 4 2 10 +--R (- 8b - 8a b - 8a b - 8a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (- 48b - 72a b - 32a b + 24a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 40b - 48a b - 40a b - 96a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (28b + 60a b + 84a b + 132a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 2 4 +--R (48b + 56a b + 8a b - 56a b - 56a b )cosh(x) + 16b - 32a b +--R + +--R 4 2 +--R 16a b +--R * +--R coth(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 2 4 +--R (4b + 12a b + 12a b + 4a b )coth(x) - 4b - 12a b - 12a b +--R + +--R 3 3 +--R - 4a b +--R * +--R 12 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 2 +--R (24b + 72a b + 72a b + 24a b )cosh(x)coth(x) +--R + +--R 6 5 2 4 3 3 +--R (- 24b - 72a b - 72a b - 24a b )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 3 3 +--R (56b + 168a b + 168a b + 56a b )cosh(x) - 8b - 8a b - 8a b +--R + +--R 4 2 +--R - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 2 6 5 3 3 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) + 8b + 8a b + 8a b +--R + +--R 4 2 +--R 8a b +--R * +--R 10 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (56b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 24b - 24a b - 8a b - 40a b - 32a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (24b + 24a b + 8a b + 40a b + 32a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (- 8b - 8a b - 32a b - 72a b - 40a b )cosh(x) - 48b +--R + +--R 5 2 4 3 3 4 2 +--R - 72a b - 32a b + 24a b + 32a b +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 4 +--R (4b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 5 +--R (8b + 8a b + 32a b + 72a b + 40a b )cosh(x) + 48b + 72a b +--R + +--R 2 4 3 3 4 2 +--R 32a b - 24a b - 32a b +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 80b - 240a b - 240a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (32b + 32a b - 32a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 136b - 168a b - 104a b + 8a b + 80a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 5 +--R (80b + 240a b + 240a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 32b - 32a b + 32a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (136b + 168a b + 104a b - 8a b - 80a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 6 +--R (- 112b - 336a b - 336a b - 112a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (16b + 16a b + 32a b + 80a b + 48a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (- 112b - 144a b - 176a b - 112a b + 32a b )cosh(x) - 40b +--R + +--R 5 2 4 3 3 4 2 +--R - 48a b - 40a b - 96a b - 64a b +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 6 +--R (112b + 336a b + 336a b + 112a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 16b - 16a b - 32a b - 80a b - 48a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (112b + 144a b + 176a b + 112a b - 32a b )cosh(x) + 40b +--R + +--R 5 2 4 3 3 4 2 +--R 48a b + 40a b + 96a b + 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 7 +--R (- 80b - 240a b - 240a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 16b - 16a b + 80a b + 144a b + 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (8b - 216a b - 280a b - 136a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 104b - 56a b + 120a b - 8a b - 80a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 7 +--R (80b + 240a b + 240a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (16b + 16a b - 80a b - 144a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 8b + 216a b + 280a b + 136a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (104b + 56a b - 120a b + 8a b + 80a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 8 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (16b + 16a b + 32a b + 80a b + 48a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (64b - 336a b - 352a b - 80a b - 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 +--R (- 56b - 48a b + 72a b + 64a b )cosh(x) + 28b + 60a b +--R + +--R 2 4 3 3 4 2 +--R 84a b + 132a b + 80a b +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 8 +--R (4b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 16b - 16a b - 32a b - 80a b - 48a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 64b + 336a b + 352a b + 80a b + 128a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 6 5 2 4 +--R (56b + 48a b - 72a b - 64a b )cosh(x) - 28b - 60a b - 84a b +--R + +--R 3 3 4 2 +--R - 132a b - 80a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 9 +--R (56b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 7 +--R (32b + 32a b - 32a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (8b - 216a b - 280a b - 136a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (16b - 80a b - 176a b - 48a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (- 16b - 64a b - 160a b - 64a b + 48a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 9 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 7 +--R (- 32b - 32a b + 32a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 8b + 216a b + 280a b + 136a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 16b + 80a b + 176a b + 48a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (16b + 64a b + 160a b + 64a b - 48a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 10 +--R (56b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (- 8b - 8a b - 32a b - 72a b - 40a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 112b - 144a b - 176a b - 112a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- 56b - 48a b + 72a b + 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (40b + 264a b + 280a b + 120a b + 64a b )cosh(x) + 48b +--R + +--R 5 2 4 3 3 4 2 +--R 56a b + 8a b - 56a b - 56a b +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 10 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (8b + 8a b + 32a b + 72a b + 40a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (112b + 144a b + 176a b + 112a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (56b + 48a b - 72a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 +--R (- 40b - 264a b - 280a b - 120a b - 64a b )cosh(x) - 48b +--R + +--R 5 2 4 3 3 4 2 +--R - 56a b - 8a b + 56a b + 56a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 11 +--R (24b + 72a b + 72a b + 24a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 9 +--R (- 24b - 24a b - 8a b - 40a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (- 136b - 168a b - 104a b + 8a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 104b - 56a b + 120a b - 8a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 16b - 64a b - 160a b - 64a b + 48a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- 80a b + 16a b + 80a b - 16a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 11 +--R (- 24b - 72a b - 72a b - 24a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 9 +--R (24b + 24a b + 8a b + 40a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 7 +--R (136b + 168a b + 104a b - 8a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (104b + 56a b - 120a b + 8a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (16b + 64a b + 160a b + 64a b - 48a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R (80a b - 16a b - 80a b + 16a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 6 5 2 4 3 3 12 +--R (4b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 6 5 3 3 4 2 10 +--R (- 8b - 8a b - 8a b - 8a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (- 48b - 72a b - 32a b + 24a b + 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 40b - 48a b - 40a b - 96a b - 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (28b + 60a b + 84a b + 132a b + 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 2 4 +--R (48b + 56a b + 8a b - 56a b - 56a b )cosh(x) + 16b - 32a b +--R + +--R 4 2 +--R 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 2 4 3 3 12 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 6 5 3 3 4 2 10 +--R (8b + 8a b + 8a b + 8a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 8 +--R (48b + 72a b + 32a b - 24a b - 32a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (40b + 48a b + 40a b + 96a b + 64a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 28b - 60a b - 84a b - 132a b - 80a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 2 6 2 4 +--R (- 48b - 56a b - 8a b + 56a b + 56a b )cosh(x) - 16b + 32a b +--R + +--R 4 2 +--R - 16a b +--R / +--R 4 3 2 2 2 3 2 2 3 14 +--R ((3b + 2a b - a b )coth(x) + 3a b + 2a b - a b)sinh(x) +--R + +--R 4 3 2 2 2 +--R (18b + 12a b - 6a b )cosh(x)coth(x) +--R + +--R 3 2 2 3 +--R (18a b + 12a b - 6a b)cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (33b + 22a b - 11a b )cosh(x) + 5b + 3a b - a b +--R + +--R 3 +--R a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 2 3 2 2 3 4 +--R (33a b + 22a b - 11a b)cosh(x) + 5a b + 3a b - a b + a +--R * +--R 12 +--R sinh(x) +--R + +--R 4 3 2 2 3 +--R (- 12b - 8a b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (20b + 12a b - 4a b + 4a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 3 +--R (- 12a b - 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (20a b + 12a b - 4a b + 4a )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 4 3 2 2 4 +--R (- 117b - 78a b + 39a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (10b + 6a b - 2a b + 2a b)cosh(x) - 10b - 4a b +--R + +--R 2 2 3 +--R 2a b - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 4 +--R (- 117a b - 78a b + 39a b)cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 +--R (10a b + 6a b - 2a b + 2a )cosh(x) - 10a b - 4a b +--R + +--R 3 4 +--R 2a b - 4a +--R * +--R 10 +--R sinh(x) +--R + +--R 4 3 2 2 5 +--R (- 114b - 76a b + 38a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 60b - 36a b + 12a b - 12a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 36b - 24a b + 4a b - 8a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 5 +--R (- 114a b - 76a b + 38a b)cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 60a b - 36a b + 12a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 36a b - 24a b + 4a b - 8a )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 4 3 2 2 6 +--R (81b + 54a b - 27a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 85b - 51a b + 17a b - 17a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 +--R (- 34b - 52a b - 6a b + 12a b)cosh(x) - 34b +--R + +--R 3 2 2 3 +--R - 26a b + 10a b + 18a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 6 +--R (81a b + 54a b - 27a b)cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 85a b - 51a b + 17a b - 17a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 +--R (- 34a b - 52a b - 6a b + 12a )cosh(x) - 34a b - 26a b +--R + +--R 3 4 +--R 10a b + 18a +--R * +--R 8 +--R sinh(x) +--R + +--R 4 3 2 2 7 +--R (216b + 144a b - 72a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (40b + 24a b - 8a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (16b - 32a b - 16a b + 32a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 72b - 24a b + 8a b + 24a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 7 +--R (216a b + 144a b - 72a b)cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (40a b + 24a b - 8a b + 8a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (16a b - 32a b - 16a b + 32a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 72a b - 24a b + 8a b + 24a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 3 2 2 8 +--R (81b + 54a b - 27a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (140b + 84a b - 28a b + 28a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (44b + 56a b + 4a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 +--R (- 8b + 56a b - 24a b - 24a b)cosh(x) - 17b +--R + +--R 3 2 2 3 +--R - 10a b - 33a b - 40a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 8 +--R (81a b + 54a b - 27a b)cosh(x) +--R + +--R 3 2 2 3 4 6 +--R (140a b + 84a b - 28a b + 28a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (44a b + 56a b + 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 +--R (- 8a b + 56a b - 24a b - 24a )cosh(x) - 17a b - 10a b +--R + +--R 3 4 +--R - 33a b - 40a +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 9 +--R (- 114b - 76a b + 38a b )cosh(x) +--R + +--R 4 3 2 2 3 7 +--R (40b + 24a b - 8a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (40b + 112a b + 24a b - 48a b)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (72b + 24a b - 8a b - 24a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 30b + 52a b + 66a b - 16a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 9 +--R (- 114a b - 76a b + 38a b)cosh(x) +--R + +--R 3 2 2 3 4 7 +--R (40a b + 24a b - 8a b + 8a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (40a b + 112a b + 24a b - 48a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (72a b + 24a b - 8a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 30a b + 52a b + 66a b - 16a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 10 +--R (- 117b - 78a b + 39a b )cosh(x) +--R + +--R 4 3 2 2 3 8 +--R (- 85b - 51a b + 17a b - 17a b)cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (44b + 56a b + 4a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (84b - 60a b + 28a b + 12a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 +--R (33b + 42a b + 49a b + 40a b)cosh(x) + 25b +--R + +--R 3 2 2 3 +--R 27a b + 43a b + 41a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 10 +--R (- 117a b - 78a b + 39a b)cosh(x) +--R + +--R 3 2 2 3 4 8 +--R (- 85a b - 51a b + 17a b - 17a )cosh(x) +--R + +--R 3 2 2 3 4 6 +--R (44a b + 56a b + 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (84a b - 60a b + 28a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 +--R (33a b + 42a b + 49a b + 40a )cosh(x) + 25a b + 27a b +--R + +--R 3 4 +--R 43a b + 41a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 11 +--R (- 12b - 8a b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 9 +--R (- 60b - 36a b + 12a b - 12a b)cosh(x) +--R + +--R 4 3 2 2 3 7 +--R (16b - 32a b - 16a b + 32a b)cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (72b + 24a b - 8a b - 24a b)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (92b - 40a b - 100a b + 32a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 12b - 84a b - 100a b - 28a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 11 +--R (- 12a b - 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 3 4 9 +--R (- 60a b - 36a b + 12a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 7 +--R (16a b - 32a b - 16a b + 32a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (72a b + 24a b - 8a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (92a b - 40a b - 100a b + 32a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12a b - 84a b - 100a b - 28a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 12 +--R (33b + 22a b - 11a b )cosh(x) +--R + +--R 4 3 2 2 3 10 +--R (10b + 6a b - 2a b + 2a b)cosh(x) +--R + +--R 4 3 2 2 3 8 +--R (- 34b - 52a b - 6a b + 12a b)cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 8b + 56a b - 24a b - 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (33b + 42a b + 49a b + 40a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 +--R (54b + 162a b + 98a b - 10a b)cosh(x) + 24b +--R + +--R 3 2 2 3 +--R 12a b - 16a b - 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 12 +--R (33a b + 22a b - 11a b)cosh(x) +--R + +--R 3 2 2 3 4 10 +--R (10a b + 6a b - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 8 +--R (- 34a b - 52a b - 6a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 6 +--R (- 8a b + 56a b - 24a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (33a b + 42a b + 49a b + 40a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 +--R (54a b + 162a b + 98a b - 10a )cosh(x) + 24a b + 12a b +--R + +--R 3 4 +--R - 16a b - 20a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 13 +--R (18b + 12a b - 6a b )cosh(x) +--R + +--R 4 3 2 2 3 11 +--R (20b + 12a b - 4a b + 4a b)cosh(x) +--R + +--R 4 3 2 2 3 9 +--R (- 36b - 24a b + 4a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 7 +--R (- 72b - 24a b + 8a b + 24a b)cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 30b + 52a b + 66a b - 16a b)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 12b - 84a b - 100a b - 28a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 16b - 40a b + 32a b + 24a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 13 +--R (18a b + 12a b - 6a b)cosh(x) +--R + +--R 3 2 2 3 4 11 +--R (20a b + 12a b - 4a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 9 +--R (- 36a b - 24a b + 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 7 +--R (- 72a b - 24a b + 8a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 30a b + 52a b + 66a b - 16a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 12a b - 84a b - 100a b - 28a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 16a b - 40a b + 32a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 14 +--R (3b + 2a b - a b )cosh(x) +--R + +--R 4 3 2 2 3 12 +--R (5b + 3a b - a b + a b)cosh(x) +--R + +--R 4 3 2 2 3 10 +--R (- 10b - 4a b + 2a b - 4a b)cosh(x) +--R + +--R 4 3 2 2 3 8 +--R (- 34b - 26a b + 10a b + 18a b)cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 17b - 10a b - 33a b - 40a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (25b + 27a b + 43a b + 41a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (24b + 12a b - 16a b - 20a b)cosh(x) + 4b - 4a b +--R + +--R 2 2 3 +--R - 4a b + 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 14 +--R (3a b + 2a b - a b)cosh(x) +--R + +--R 3 2 2 3 4 12 +--R (5a b + 3a b - a b + a )cosh(x) +--R + +--R 3 2 2 3 4 10 +--R (- 10a b - 4a b + 2a b - 4a )cosh(x) +--R + +--R 3 2 2 3 4 8 +--R (- 34a b - 26a b + 10a b + 18a )cosh(x) +--R + +--R 3 2 2 3 4 6 +--R (- 17a b - 10a b - 33a b - 40a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (25a b + 27a b + 43a b + 41a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (24a b + 12a b - 16a b - 20a )cosh(x) + 4a b - 4a b - 4a b +--R + +--R 4 +--R 4a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 14 +--R (- 3b - 2a b + a b )sinh(x) +--R + +--R 4 3 2 2 13 +--R (- 18b - 12a b + 6a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 3 +--R ((- 33b - 22a b + 11a b )cosh(x) - 5b - 3a b + a b - a b) +--R * +--R 12 +--R sinh(x) +--R + +--R 4 3 2 2 3 +--R (12b + 8a b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 20b - 12a b + 4a b - 4a b)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 4 3 2 2 4 +--R (117b + 78a b - 39a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (- 10b - 6a b + 2a b - 2a b)cosh(x) + 10b + 4a b - 2a b +--R + +--R 3 +--R 4a b +--R * +--R 10 +--R sinh(x) +--R + +--R 4 3 2 2 5 +--R (114b + 76a b - 38a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (60b + 36a b - 12a b + 12a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (36b + 24a b - 4a b + 8a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 4 3 2 2 6 +--R (- 81b - 54a b + 27a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (85b + 51a b - 17a b + 17a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (34b + 52a b + 6a b - 12a b)cosh(x) + 34b + 26a b +--R + +--R 2 2 3 +--R - 10a b - 18a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 3 2 2 7 +--R (- 216b - 144a b + 72a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 40b - 24a b + 8a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 16b + 32a b + 16a b - 32a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (72b + 24a b - 8a b - 24a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 3 2 2 8 +--R (- 81b - 54a b + 27a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 140b - 84a b + 28a b - 28a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 44b - 56a b - 4a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (8b - 56a b + 24a b + 24a b)cosh(x) + 17b + 10a b +--R + +--R 2 2 3 +--R 33a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 9 +--R (114b + 76a b - 38a b )cosh(x) +--R + +--R 4 3 2 2 3 7 +--R (- 40b - 24a b + 8a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 40b - 112a b - 24a b + 48a b)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 72b - 24a b + 8a b + 24a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (30b - 52a b - 66a b + 16a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 10 +--R (117b + 78a b - 39a b )cosh(x) +--R + +--R 4 3 2 2 3 8 +--R (85b + 51a b - 17a b + 17a b)cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 44b - 56a b - 4a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 84b + 60a b - 28a b - 12a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 33b - 42a b - 49a b - 40a b)cosh(x) - 25b - 27a b +--R + +--R 2 2 3 +--R - 43a b - 41a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 11 +--R (12b + 8a b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 9 +--R (60b + 36a b - 12a b + 12a b)cosh(x) +--R + +--R 4 3 2 2 3 7 +--R (- 16b + 32a b + 16a b - 32a b)cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 72b - 24a b + 8a b + 24a b)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 92b + 40a b + 100a b - 32a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (12b + 84a b + 100a b + 28a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 12 +--R (- 33b - 22a b + 11a b )cosh(x) +--R + +--R 4 3 2 2 3 10 +--R (- 10b - 6a b + 2a b - 2a b)cosh(x) +--R + +--R 4 3 2 2 3 8 +--R (34b + 52a b + 6a b - 12a b)cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (8b - 56a b + 24a b + 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 33b - 42a b - 49a b - 40a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 54b - 162a b - 98a b + 10a b)cosh(x) - 24b - 12a b +--R + +--R 2 2 3 +--R 16a b + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 13 +--R (- 18b - 12a b + 6a b )cosh(x) +--R + +--R 4 3 2 2 3 11 +--R (- 20b - 12a b + 4a b - 4a b)cosh(x) +--R + +--R 4 3 2 2 3 9 +--R (36b + 24a b - 4a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 7 +--R (72b + 24a b - 8a b - 24a b)cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (30b - 52a b - 66a b + 16a b)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (12b + 84a b + 100a b + 28a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (16b + 40a b - 32a b - 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 14 +--R (- 3b - 2a b + a b )cosh(x) +--R + +--R 4 3 2 2 3 12 +--R (- 5b - 3a b + a b - a b)cosh(x) +--R + +--R 4 3 2 2 3 10 +--R (10b + 4a b - 2a b + 4a b)cosh(x) +--R + +--R 4 3 2 2 3 8 +--R (34b + 26a b - 10a b - 18a b)cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (17b + 10a b + 33a b + 40a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 25b - 27a b - 43a b - 41a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (- 24b - 12a b + 16a b + 20a b)cosh(x) - 4b + 4a b + 4a b +--R + +--R 3 +--R - 4a b +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 5 4 2 3 3 2 2 4 2 3 +--R (- 4b - 12a b - 12a b - 4a b )coth(x) - 4a b - 12a b +--R + +--R 3 2 4 +--R - 12a b - 4a b +--R * +--R 12 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 2 +--R (- 24b - 72a b - 72a b - 24a b )cosh(x)coth(x) +--R + +--R 4 2 3 3 2 4 +--R (- 24a b - 72a b - 72a b - 24a b)cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) + 8b + 8a b +--R + +--R 3 2 4 +--R 8a b + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 2 4 2 3 +--R (- 56a b - 168a b - 168a b - 56a b)cosh(x) + 8a b + 8a b +--R + +--R 4 5 +--R 8a b + 8a +--R * +--R 10 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (24b + 24a b + 8a b + 40a b + 32a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 56a b - 168a b - 168a b - 56a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (24a b + 24a b + 8a b + 40a b + 32a )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (4b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (8b + 8a b + 32a b + 72a b + 40a b)cosh(x) + 48b +--R + +--R 4 2 3 3 2 4 +--R 72a b + 32a b - 24a b - 32a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 4 +--R (4a b + 12a b + 12a b + 4a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 4 +--R (8a b + 8a b + 32a b + 72a b + 40a )cosh(x) + 48a b +--R + +--R 2 3 3 2 4 5 +--R 72a b + 32a b - 24a b - 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (80b + 240a b + 240a b + 80a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 32b - 32a b + 32a b + 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (136b + 168a b + 104a b - 8a b - 80a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 5 +--R (80a b + 240a b + 240a b + 80a b)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 32a b - 32a b + 32a b + 32a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (136a b + 168a b + 104a b - 8a b - 80a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (112b + 336a b + 336a b + 112a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 16b - 16a b - 32a b - 80a b - 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (112b + 144a b + 176a b + 112a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 40b + 48a b + 40a b + 96a b + 64a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 6 +--R (112a b + 336a b + 336a b + 112a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 16a b - 16a b - 32a b - 80a b - 48a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 4 +--R (112a b + 144a b + 176a b + 112a b - 32a )cosh(x) + 40a b +--R + +--R 2 3 3 2 4 5 +--R 48a b + 40a b + 96a b + 64a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (80b + 240a b + 240a b + 80a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (16b + 16a b - 80a b - 144a b - 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 8b + 216a b + 280a b + 136a b + 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (104b + 56a b - 120a b + 8a b + 80a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 7 +--R (80a b + 240a b + 240a b + 80a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b + 16a b - 80a b - 144a b - 64a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 8a b + 216a b + 280a b + 136a b + 80a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (104a b + 56a b - 120a b + 8a b + 80a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (4b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 16b - 16a b - 32a b - 80a b - 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 64b + 336a b + 352a b + 80a b + 128a b)cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (56b + 48a b - 72a b - 64a b )cosh(x) - 28b - 60a b +--R + +--R 2 3 3 2 4 +--R - 84a b - 132a b - 80a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 8 +--R (4a b + 12a b + 12a b + 4a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (- 16a b - 16a b - 32a b - 80a b - 48a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 64a b + 336a b + 352a b + 80a b + 128a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 4 2 3 +--R (56a b + 48a b - 72a b - 64a b)cosh(x) - 28a b - 60a b +--R + +--R 3 2 4 5 +--R - 84a b - 132a b - 80a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 32b - 32a b + 32a b + 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 8b + 216a b + 280a b + 136a b + 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 16b + 80a b + 176a b + 48a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (16b + 64a b + 160a b + 64a b - 48a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 9 +--R (- 56a b - 168a b - 168a b - 56a b)cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (- 32a b - 32a b + 32a b + 32a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 8a b + 216a b + 280a b + 136a b + 80a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 16a b + 80a b + 176a b + 48a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (16a b + 64a b + 160a b + 64a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (- 56b - 168a b - 168a b - 56a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (8b + 8a b + 32a b + 72a b + 40a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (112b + 144a b + 176a b + 112a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (56b + 48a b - 72a b - 64a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 40b - 264a b - 280a b - 120a b - 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 48b - 56a b - 8a b + 56a b + 56a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 10 +--R (- 56a b - 168a b - 168a b - 56a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (8a b + 8a b + 32a b + 72a b + 40a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (112a b + 144a b + 176a b + 112a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (56a b + 48a b - 72a b - 64a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 4 +--R (- 40a b - 264a b - 280a b - 120a b - 64a )cosh(x) - 48a b +--R + +--R 2 3 3 2 4 5 +--R - 56a b - 8a b + 56a b + 56a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 11 +--R (- 24b - 72a b - 72a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (24b + 24a b + 8a b + 40a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (136b + 168a b + 104a b - 8a b - 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (104b + 56a b - 120a b + 8a b + 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (16b + 64a b + 160a b + 64a b - 48a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (80a b - 16a b - 80a b + 16a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 11 +--R (- 24a b - 72a b - 72a b - 24a b)cosh(x) +--R + +--R 4 2 3 3 2 4 5 9 +--R (24a b + 24a b + 8a b + 40a b + 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (136a b + 168a b + 104a b - 8a b - 80a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (104a b + 56a b - 120a b + 8a b + 80a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (16a b + 64a b + 160a b + 64a b - 48a )cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (80a b - 16a b - 80a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 12 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 5 4 3 2 4 10 +--R (8b + 8a b + 8a b + 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (48b + 72a b + 32a b - 24a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (40b + 48a b + 40a b + 96a b + 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 28b - 60a b - 84a b - 132a b - 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (- 48b - 56a b - 8a b + 56a b + 56a b)cosh(x) - 16b +--R + +--R 2 3 4 +--R 32a b - 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 3 3 2 4 12 +--R (- 4a b - 12a b - 12a b - 4a b)cosh(x) +--R + +--R 4 2 3 4 5 10 +--R (8a b + 8a b + 8a b + 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (48a b + 72a b + 32a b - 24a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (40a b + 48a b + 40a b + 96a b + 64a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 28a b - 60a b - 84a b - 132a b - 80a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 4 +--R (- 48a b - 56a b - 8a b + 56a b + 56a )cosh(x) - 16a b +--R + +--R 3 2 5 +--R 32a b - 16a +--R * +--R 2 +--R tanh(x) +--R + +--R 5 4 2 3 3 2 12 +--R (4b + 12a b + 12a b + 4a b )sinh(x) +--R + +--R 5 4 2 3 3 2 11 +--R (24b + 72a b + 72a b + 24a b )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 3 2 +--R (56b + 168a b + 168a b + 56a b )cosh(x) - 8b - 8a b - 8a b +--R + +--R 4 +--R - 8a b +--R * +--R 10 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (56b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 24b - 24a b - 8a b - 40a b - 32a b)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 4 +--R (- 8b - 8a b - 32a b - 72a b - 40a b)cosh(x) - 48b - 72a b +--R + +--R 2 3 3 2 4 +--R - 32a b + 24a b + 32a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 80b - 240a b - 240a b - 80a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (32b + 32a b - 32a b - 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 136b - 168a b - 104a b + 8a b + 80a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 112b - 336a b - 336a b - 112a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (16b + 16a b + 32a b + 80a b + 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (- 112b - 144a b - 176a b - 112a b + 32a b)cosh(x) - 40b +--R + +--R 4 2 3 3 2 4 +--R - 48a b - 40a b - 96a b - 64a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 80b - 240a b - 240a b - 80a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 16b - 16a b + 80a b + 144a b + 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (8b - 216a b - 280a b - 136a b - 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 104b - 56a b + 120a b - 8a b - 80a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 4b - 12a b - 12a b - 4a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (16b + 16a b + 32a b + 80a b + 48a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (64b - 336a b - 352a b - 80a b - 128a b)cosh(x) +--R + +--R 5 4 2 3 3 2 2 5 4 +--R (- 56b - 48a b + 72a b + 64a b )cosh(x) + 28b + 60a b +--R + +--R 2 3 3 2 4 +--R 84a b + 132a b + 80a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 9 +--R (56b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 5 4 2 3 3 2 7 +--R (32b + 32a b - 32a b - 32a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 216a b - 280a b - 136a b - 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (16b - 80a b - 176a b - 48a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 16b - 64a b - 160a b - 64a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 10 +--R (56b + 168a b + 168a b + 56a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 8b - 8a b - 32a b - 72a b - 40a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 112b - 144a b - 176a b - 112a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 56b - 48a b + 72a b + 64a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 +--R (40b + 264a b + 280a b + 120a b + 64a b)cosh(x) + 48b +--R + +--R 4 2 3 3 2 4 +--R 56a b + 8a b - 56a b - 56a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 11 +--R (24b + 72a b + 72a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (- 24b - 24a b - 8a b - 40a b - 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 136b - 168a b - 104a b + 8a b + 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 104b - 56a b + 120a b - 8a b - 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 16b - 64a b - 160a b - 64a b + 48a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 80a b + 16a b + 80a b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 12 +--R (4b + 12a b + 12a b + 4a b )cosh(x) +--R + +--R 5 4 3 2 4 10 +--R (- 8b - 8a b - 8a b - 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 48b - 72a b - 32a b + 24a b + 32a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 40b - 48a b - 40a b - 96a b - 64a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (28b + 60a b + 84a b + 132a b + 80a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 5 2 3 4 +--R (48b + 56a b + 8a b - 56a b - 56a b)cosh(x) + 16b - 32a b + 16a b +--R * +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 508 +t0358:= 1/(1+coth(x)^2)^(1/2) +--R +--R +--R 1 +--R (261) --------------- +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 508 +r0358:= 1/2*2^(1/2)*atanh(2^(1/2)*coth(x)/(1+coth(x)^2)^(1/2)) +--R +--R +--R +-+ +--R +-+ \|2 coth(x) +--R \|2 atanh(---------------) +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R (262) -------------------------- +--R 2 +--R Type: Expression(Integer) +--E 298 + +--S 299 of 508 +a0358:= integrate(t0358,x) +--R +--R +--R (263) +--R +-+ +--R \|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- + \|2 sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R 2\|2 cosh(x)sinh(x) + \|2 cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|2 +--R * +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 2) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + \|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + 2\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R \|2 cosh(x) + 2\|2 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 299 + +--S 300 of 508 +m0358:= a0358-r0358 +--R +--R +--R (264) +--R +-+ +--R \|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +-+ 2 +--R |------------------------------------- + \|2 sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ 2 +-+ +--R 2\|2 cosh(x)sinh(x) + \|2 cosh(x) - \|2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|2 +--R * +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 2) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (6\|2 cosh(x) + \|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (4\|2 cosh(x) + 2\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R \|2 cosh(x) + 2\|2 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +-+ +--R +-+ \|2 coth(x) +--R - 2\|2 atanh(---------------) +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R / +--R 4 +--R Type: Expression(Integer) +--E 300 + +--S 301 of 508 +d0358:= D(m0358,x) +--R +--R +--R (265) +--R 8 2 6 5 +--R - sinh(x) + (4cosh(x) - 3)sinh(x) + 2cosh(x)sinh(x) +--R + +--R 4 2 4 +--R (- 6cosh(x) + 3cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (- 4cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (4cosh(x) + 3cosh(x) + 8cosh(x) )sinh(x) +--R + +--R 5 3 8 6 4 +--R (2cosh(x) - 8cosh(x) )sinh(x) - cosh(x) - 3cosh(x) + 4cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +-+ 6 +--R 2\|2 sinh(x) + 4\|2 cosh(x)sinh(x) + 4\|2 sinh(x) +--R + +--R +-+ 3 5 +--R - 4\|2 cosh(x) sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 4\|2 cosh(x) - 4\|2 cosh(x) - 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 4\|2 cosh(x) + 4\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 2 +--R (- 4\|2 cosh(x) - 12\|2 cosh(x) )sinh(x) +--R + +--R +-+ 7 +-+ 3 +-+ 8 +--R (4\|2 cosh(x) + 4\|2 cosh(x) )sinh(x) + 2\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R 4\|2 cosh(x) - 6\|2 cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R + +--R +-+ 4 +-+ 3 +-+ 2 2 +--R - 4\|2 sinh(x) + 8\|2 cosh(x)sinh(x) - 8\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 +-+ 4 +--R 8\|2 cosh(x) sinh(x) - 4\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 10 9 2 8 +--R - 2sinh(x) - 8cosh(x)sinh(x) - 10cosh(x) sinh(x) +--R + +--R 4 6 5 5 +--R (12cosh(x) + 2)sinh(x) + (16cosh(x) + 8cosh(x))sinh(x) +--R + +--R 6 2 4 3 3 +--R (12cosh(x) + 14cosh(x) + 12)sinh(x) + (16cosh(x) - 8cosh(x))sinh(x) +--R + +--R 8 4 2 2 +--R (- 10cosh(x) + 14cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 9 5 3 10 6 +--R (- 8cosh(x) + 8cosh(x) - 8cosh(x) )sinh(x) - 2cosh(x) + 2cosh(x) +--R + +--R 4 +--R 12cosh(x) +--R / +--R +-+ 4 +-+ 3 +-+ 2 2 +--R 4\|2 sinh(x) - 8\|2 cosh(x)sinh(x) + 8\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 +-+ 4 +--R - 8\|2 cosh(x) sinh(x) + 4\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 10 9 2 8 +--R 2sinh(x) + 8cosh(x)sinh(x) + 10cosh(x) sinh(x) +--R + +--R 4 6 5 5 +--R (- 12cosh(x) - 2)sinh(x) + (- 16cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 2 4 +--R (- 12cosh(x) - 14cosh(x) - 12)sinh(x) +--R + +--R 3 3 +--R (- 16cosh(x) + 8cosh(x))sinh(x) +--R + +--R 8 4 2 2 +--R (10cosh(x) - 14cosh(x) - 24cosh(x) )sinh(x) +--R + +--R 9 5 3 10 6 +--R (8cosh(x) - 8cosh(x) + 8cosh(x) )sinh(x) + 2cosh(x) - 2cosh(x) +--R + +--R 4 +--R - 12cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 508 +t0359:= 1/(-1-coth(x)^2)^(1/2) +--R +--R +--R 1 +--R (266) ----------------- +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 508 +r0359:= 1/2*2^(1/2)*atan(2^(1/2)*coth(x)/(-1-coth(x)^2)^(1/2)) +--R +--R +--R +-+ +--R +-+ \|2 coth(x) +--R \|2 atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R (267) --------------------------- +--R 2 +--R Type: Expression(Integer) +--E 303 + +--S 304 of 508 +a0359:= integrate(t0359,x) +--R +--R +--R (268) +--R +-------------+ +--R | x 4 +---+ x 2 +---+ +--R +---+ \|- 2(%e ) - 2 + \|- 2 (%e ) - \|- 2 +--R - \|- 2 log(----------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ +--R \|- 2 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +---+ x 2 +--R (2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) - 2\|- 2 (%e ) +--R + +--R +---+ +--R - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 304 + +--S 305 of 508 +m0359:= a0359-r0359 +--R +--R +--R (269) +--R +-------------+ +--R | x 4 +---+ x 2 +---+ +--R +---+ \|- 2(%e ) - 2 + \|- 2 (%e ) - \|- 2 +--R - \|- 2 log(----------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ +--R \|- 2 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +---+ x 2 +--R (2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) - 2\|- 2 (%e ) +--R + +--R +---+ +--R - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R + +--R +-+ +--R +-+ \|2 coth(x) +--R - 2\|2 atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R / +--R 4 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 508 +d0359:= D(m0359,x) +--R +--R +--R (270) +--R +-------------+ +--R x 6 x 4 x 2 | x 4 +---+ x 6 +--R (- (%e ) + (%e ) - 2(%e ) + 2)\|- 2(%e ) - 2 + 2\|- 2 (%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R - 2\|- 2 (%e ) + 2\|- 2 (%e ) - 2\|- 2 +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R + +--R +-------------+ +--R +---+ x 4 +---+ | x 4 x 8 x 4 +--R (- 2\|- 2 (%e ) - 2\|- 2 )\|- 2(%e ) - 2 - 2(%e ) - 6(%e ) - 4 +--R / +--R +-------------+ +--R +---+ x 4 +---+ | x 4 x 8 x 4 +--R ((2\|- 2 (%e ) + 2\|- 2 )\|- 2(%e ) - 2 + 2(%e ) + 6(%e ) + 4) +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 508 +t0360:= 1/(a+b*coth(x)^2)^(1/2) +--R +--R +--R 1 +--R (271) ----------------- +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 508 +r0360:= atanh((a+b)^(1/2)*coth(x)/(a+b*coth(x)^2)^(1/2))/(a+b)^(1/2) +--R +--R +--R +-----+ +--R coth(x)\|b + a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R (272) ------------------------ +--R +-----+ +--R \|b + a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 508 +a0360:= integrate(t0360,x) +--R +--R +--R (273) +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R / +--R +-----+ +--R 2\|b + a +--R Type: Union(Expression(Integer),...) +--E 309 + +--S 310 of 508 +m0360:= a0360-r0360 +--R +--R +--R (274) +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b - a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - a)cosh(x) + b + a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +-----+ +--R coth(x)\|b + a +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R / +--R +-----+ +--R 2\|b + a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 508 +d0360:= D(m0360,x) +--R +--R +--R (275) +--R 2 8 +--R (- b - a b)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((4b + 4a b)cosh(x) - 2b - 2a b - 2a )sinh(x) +--R + +--R 5 +--R 4a b cosh(x)sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 6b - 6a b)cosh(x) + (2b + 2a b + 2a )cosh(x) + b +--R + +--R 2 +--R 3a b + 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 8a b cosh(x) + (- 4b - 8a b - 4a )cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 +--R (4b + 4a b)cosh(x) + (2b + 2a b + 2a )cosh(x) +--R + +--R 2 2 2 2 +--R (6b + 10a b)cosh(x) + 2b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 2 3 +--R 4a b cosh(x) + (- 4b - 8a b - 4a )cosh(x) +--R + +--R 2 2 +--R (- 4b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R (- b - a b)cosh(x) + (- 2b - 2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (b + 3a b + 4a )cosh(x) + (2b - 2a )cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (3b + 5a b + a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (6b + 10a b + 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 6 +--R (5b + 5a b + 3a b + 3a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 6b - 10a b - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 2a b - 6a b + 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 6b - 10a b - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 5b - 5a b - 3a b - 3a )cosh(x) - b - 7a b - 11a b - 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 10a b - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b + 4a b + 12a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 6a b + 6a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 5b - 5a b - 3a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 10b - 22a b - 14a b - 2a )cosh(x) - 5b - 5a b + 5a b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (6b + 10a b + 2a b - 2a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (6b - 2a b - 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (2b + 6a b + 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 3 2 2 3 6 +--R (3b + 5a b + a b - a )cosh(x) + (5b + 5a b + 3a b + 3a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- b - 7a b - 11a b - 5a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 5b - 5a b + 5a b + 5a )cosh(x) - 2b + 2a b + 2a b - 2a +--R * +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((2b + 2a b - 2a b - 2a )cosh(x) - 4b - 4a b - 4a b - 4a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b + 12a b + 12a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 2 2 +--R (2b + 2a b - 2a b - 2a )cosh(x) + (- 16a b - 16a b)cosh(x) +--R + +--R 3 2 2 3 +--R - 2b - 2a b + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b + 12a b + 12a b + 4a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b + 4a b - 4a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 4b - 4a b - 4a b - 4a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 10 3 2 2 9 +--R (- b - 2a b - a b)sinh(x) + (- 4b - 8a b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 8 +--R ((- 5b - 10a b - 5a b)cosh(x) - 2b - a b + 2a b + a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 6b - 2a b + 6a b + 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (6b + 12a b + 6a b)cosh(x) + (- 4b + 4a b)cosh(x) + 2b +--R + +--R 2 3 +--R 5a b - 3a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (8b + 16a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (6b + 2a b - 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 10a b + 6a b - 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (6b + 12a b + 6a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (12b + 2a b - 12a b - 2a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (6b + 11a b + 8a b + 3a )cosh(x) + 8b + 7a b + 4a b + 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 2a b - 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (12b + 12a b + 4a b + 4a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 6a b - 14a b - 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 8 3 2 6 +--R (- 5b - 10a b - 5a b)cosh(x) + (- 4b + 4a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (6b + 11a b + 8a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (12b + 22a b + 12a b + 2a )cosh(x) + 7b + a b - 3a b - 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 9 +--R (- 4b - 8a b - 4a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (- 6b - 2a b + 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (2b + 10a b + 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (6b - 6a b - 14a b - 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b - 10a b + 6a b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 10 3 2 2 3 8 +--R (- b - 2a b - a b)cosh(x) + (- 2b - a b + 2a b + a )cosh(x) +--R + +--R 3 2 3 6 3 2 2 3 4 +--R (2b + 5a b - 3a )cosh(x) + (8b + 7a b + 4a b + 5a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (7b + a b - 3a b - 5a )cosh(x) + 2b - 2a b - 2a b + 2a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 2 2 3 6 +--R (2b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((- 2b - 2a b + 2a b + 2a )cosh(x) + 4b + 4a b + 4a b + 4a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b - 12a b - 12a b - 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 2 2 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) + (16a b + 16a b)cosh(x) +--R + +--R 3 2 2 3 +--R 2b + 2a b - 2a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b - 12a b - 12a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b - 4a b + 4a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (2b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4b + 4a b + 4a b + 4a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (2b + 2a b - 2a b - 2a )cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 10 3 2 2 9 +--R (b + 2a b + a b)sinh(x) + (4b + 8a b + 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 3 8 +--R ((5b + 10a b + 5a b)cosh(x) + 2b + a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (6b + 2a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (- 6b - 12a b - 6a b)cosh(x) + (4b - 4a b)cosh(x) - 2b +--R + +--R 2 3 +--R - 5a b + 3a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 8b - 16a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 6b - 2a b + 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 10a b - 6a b + 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (- 6b - 12a b - 6a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12b - 2a b + 12a b + 2a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 6b - 11a b - 8a b - 3a )cosh(x) - 8b - 7a b - 4a b - 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 2a b + 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 12b - 12a b - 4a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 6b + 6a b + 14a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 8 3 2 6 +--R (5b + 10a b + 5a b)cosh(x) + (4b - 4a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 6b - 11a b - 8a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 12b - 22a b - 12a b - 2a )cosh(x) - 7b - a b + 3a b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 9 +--R (4b + 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (6b + 2a b - 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 2b - 10a b - 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 6b + 6a b + 14a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b + 10a b - 6a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 10 3 2 2 3 8 +--R (b + 2a b + a b)cosh(x) + (2b + a b - 2a b - a )cosh(x) +--R + +--R 3 2 3 6 +--R (- 2b - 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 8b - 7a b - 4a b - 5a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 7b - a b + 3a b + 5a )cosh(x) - 2b + 2a b + 2a b - 2a +--R * +--R +-----+ +--R \|b + a +--R * +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 508 +t0361:= (1+coth(x)^2)^(3/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (276) (coth(x) + 1)\|coth(x) + 1 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 508 +r0361:= -5/2*acsch(tanh(x))+2*2^(1/2)*atanh(2^(1/2)*_ + coth(x)/(1+coth(x)^2)^(1/2))-1/2*coth(x)*(1+coth(x)^2)^(1/2) +--R +--R +--R (277) +--R +-+ +------------+ +--R +-+ \|2 coth(x) | 2 +--R 4\|2 atanh(---------------) - coth(x)\|coth(x) + 1 - 5acsch(tanh(x)) +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R ---------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 313 + +--S 314 of 508 +a0361:= integrate(t0361,x) +--R +--R +--R (278) +--R 4 3 2 2 +--R - 10sinh(x) - 40cosh(x)sinh(x) + (- 60cosh(x) + 20)sinh(x) +--R + +--R 3 4 2 +--R (- 40cosh(x) + 40cosh(x))sinh(x) - 10cosh(x) + 20cosh(x) - 10 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R 5\|2 sinh(x) + 40\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (140\|2 cosh(x) - 10\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (280\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (350\|2 cosh(x) - 150\|2 cosh(x) + 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (280\|2 cosh(x) - 200\|2 cosh(x) + 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (140\|2 cosh(x) - 150\|2 cosh(x) + 90\|2 cosh(x) - 20\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (40\|2 cosh(x) - 60\|2 cosh(x) + 60\|2 cosh(x) - 40\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 5\|2 cosh(x) - 10\|2 cosh(x) + 15\|2 cosh(x) - 20\|2 cosh(x) +--R + +--R +-+ +--R 10\|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 2)sinh(x) + (4\|2 + 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (2\|2 + 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R 10sinh(x) + 40cosh(x)sinh(x) + (60cosh(x) - 20)sinh(x) +--R + +--R 3 4 2 +--R (40cosh(x) - 40cosh(x))sinh(x) + 10cosh(x) - 20cosh(x) + 10 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 5\|2 sinh(x) - 40\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 140\|2 cosh(x) + 10\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 280\|2 cosh(x) + 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 350\|2 cosh(x) + 150\|2 cosh(x) - 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 280\|2 cosh(x) + 200\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 140\|2 cosh(x) + 150\|2 cosh(x) - 90\|2 cosh(x) + 20\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 40\|2 cosh(x) + 60\|2 cosh(x) - 60\|2 cosh(x) +--R + +--R +-+ +--R 40\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 5\|2 cosh(x) + 10\|2 cosh(x) - 15\|2 cosh(x) + 20\|2 cosh(x) +--R + +--R +-+ +--R - 10\|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 2)sinh(x) + (- 4\|2 + 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (- 2\|2 + 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R 4\|2 sinh(x) + 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (24\|2 cosh(x) - 8\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (16\|2 cosh(x) - 16\|2 cosh(x))sinh(x) + 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 8\|2 cosh(x) + 4\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 4sinh(x) - 32cosh(x)sinh(x) + (- 112cosh(x) + 8)sinh(x) +--R + +--R 3 5 +--R (- 224cosh(x) + 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 280cosh(x) + 120cosh(x) - 12)sinh(x) +--R + +--R 5 3 3 +--R (- 224cosh(x) + 160cosh(x) - 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 112cosh(x) + 120cosh(x) - 72cosh(x) + 16)sinh(x) +--R + +--R 7 5 3 +--R (- 32cosh(x) + 48cosh(x) - 48cosh(x) + 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 4cosh(x) + 8cosh(x) - 12cosh(x) + 16cosh(x) - 8 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) 2 +--R \|2 |------------------------------------- + 2sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) - 2 +--R / +--R +-+ 2 +-+ +-+ 2 +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 4\|2 sinh(x) - 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 24\|2 cosh(x) + 8\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 16\|2 cosh(x) + 16\|2 cosh(x))sinh(x) - 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 8\|2 cosh(x) - 4\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R 4sinh(x) + 32cosh(x)sinh(x) + (112cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (224cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (280cosh(x) - 120cosh(x) + 12)sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) - 160cosh(x) + 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (112cosh(x) - 120cosh(x) + 72cosh(x) - 16)sinh(x) +--R + +--R 7 5 3 8 +--R (32cosh(x) - 48cosh(x) + 48cosh(x) - 32cosh(x))sinh(x) + 4cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) + 12cosh(x) - 16cosh(x) + 8 +--R * +--R log +--R 2 2 +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 4) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|2 cosh(x) + 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8\|2 cosh(x) + 4\|2 cosh(x))sinh(x) + 2\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 2\|2 cosh(x) + 4\|2 +--R / +--R +-+ 4 +-+ 3 +-+ 2 2 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) + 6\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 +-+ 4 +--R 4\|2 cosh(x) sinh(x) + \|2 cosh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 2 +-+ 4 +--R \|2 sinh(x) + 6\|2 cosh(x)sinh(x) + (15\|2 cosh(x) - \|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (20\|2 cosh(x) - 4\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|2 cosh(x) - 6\|2 cosh(x) + 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +-+ 6 +--R (6\|2 cosh(x) - 4\|2 cosh(x) + 12\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R - \|2 cosh(x) + 6\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) - 120cosh(x) + 2)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) - 160cosh(x) + 8cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 120cosh(x) + 12cosh(x) - 12)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) - 48cosh(x) + 8cosh(x) - 24cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) + 2cosh(x) - 12cosh(x) +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 8)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 16cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) + 4 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 2\|2 sinh(x) - 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 56\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 112\|2 cosh(x) + 24\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 140\|2 cosh(x) + 60\|2 cosh(x) - 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 112\|2 cosh(x) + 80\|2 cosh(x) - 24\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (- 56\|2 cosh(x) + 60\|2 cosh(x) - 36\|2 cosh(x) + 8\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 16\|2 cosh(x) + 24\|2 cosh(x) - 24\|2 cosh(x) + 16\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 2\|2 cosh(x) + 4\|2 cosh(x) - 6\|2 cosh(x) + 8\|2 cosh(x) - 4\|2 +--R Type: Union(Expression(Integer),...) +--E 314 + +--S 315 of 508 +m0361:= a0361-r0361 +--R +--R +--R (279) +--R 4 3 2 2 +--R - 10sinh(x) - 40cosh(x)sinh(x) + (- 60cosh(x) + 20)sinh(x) +--R + +--R 3 4 2 +--R (- 40cosh(x) + 40cosh(x))sinh(x) - 10cosh(x) + 20cosh(x) - 10 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R 5\|2 sinh(x) + 40\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (140\|2 cosh(x) - 10\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (280\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (350\|2 cosh(x) - 150\|2 cosh(x) + 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (280\|2 cosh(x) - 200\|2 cosh(x) + 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (140\|2 cosh(x) - 150\|2 cosh(x) + 90\|2 cosh(x) - 20\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (40\|2 cosh(x) - 60\|2 cosh(x) + 60\|2 cosh(x) - 40\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 5\|2 cosh(x) - 10\|2 cosh(x) + 15\|2 cosh(x) - 20\|2 cosh(x) +--R + +--R +-+ +--R 10\|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (2\|2 + 2)sinh(x) + (4\|2 + 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (2\|2 + 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R 10sinh(x) + 40cosh(x)sinh(x) + (60cosh(x) - 20)sinh(x) +--R + +--R 3 4 2 +--R (40cosh(x) - 40cosh(x))sinh(x) + 10cosh(x) - 20cosh(x) + 10 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 5\|2 sinh(x) - 40\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 140\|2 cosh(x) + 10\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 280\|2 cosh(x) + 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 350\|2 cosh(x) + 150\|2 cosh(x) - 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 280\|2 cosh(x) + 200\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 140\|2 cosh(x) + 150\|2 cosh(x) - 90\|2 cosh(x) + 20\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 40\|2 cosh(x) + 60\|2 cosh(x) - 60\|2 cosh(x) +--R + +--R +-+ +--R 40\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 5\|2 cosh(x) + 10\|2 cosh(x) - 15\|2 cosh(x) + 20\|2 cosh(x) +--R + +--R +-+ +--R - 10\|2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) +--R \|2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 2\|2 + 2)sinh(x) + (- 4\|2 + 4)cosh(x)sinh(x) +--R + +--R +-+ 2 +--R (- 2\|2 + 2)cosh(x) - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R 4\|2 sinh(x) + 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (24\|2 cosh(x) - 8\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (16\|2 cosh(x) - 16\|2 cosh(x))sinh(x) + 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 8\|2 cosh(x) + 4\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 4sinh(x) - 32cosh(x)sinh(x) + (- 112cosh(x) + 8)sinh(x) +--R + +--R 3 5 +--R (- 224cosh(x) + 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 280cosh(x) + 120cosh(x) - 12)sinh(x) +--R + +--R 5 3 3 +--R (- 224cosh(x) + 160cosh(x) - 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 112cosh(x) + 120cosh(x) - 72cosh(x) + 16)sinh(x) +--R + +--R 7 5 3 +--R (- 32cosh(x) + 48cosh(x) - 48cosh(x) + 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 4cosh(x) + 8cosh(x) - 12cosh(x) + 16cosh(x) - 8 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 4sinh(x) + 4cosh(x) 2 +--R \|2 |------------------------------------- + 2sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) - 2 +--R / +--R +-+ 2 +-+ +-+ 2 +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 4\|2 sinh(x) - 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 24\|2 cosh(x) + 8\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 16\|2 cosh(x) + 16\|2 cosh(x))sinh(x) - 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 8\|2 cosh(x) - 4\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R 4sinh(x) + 32cosh(x)sinh(x) + (112cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (224cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (280cosh(x) - 120cosh(x) + 12)sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) - 160cosh(x) + 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (112cosh(x) - 120cosh(x) + 72cosh(x) - 16)sinh(x) +--R + +--R 7 5 3 8 +--R (32cosh(x) - 48cosh(x) + 48cosh(x) - 32cosh(x))sinh(x) + 4cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) + 12cosh(x) - 16cosh(x) + 8 +--R * +--R log +--R 2 2 +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 4) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|2 cosh(x) + 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8\|2 cosh(x) + 4\|2 cosh(x))sinh(x) + 2\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 2\|2 cosh(x) + 4\|2 +--R / +--R +-+ 4 +-+ 3 +-+ 2 2 +--R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) + 6\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 +-+ 4 +--R 4\|2 cosh(x) sinh(x) + \|2 cosh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 8\|2 sinh(x) - 32\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 48\|2 cosh(x) + 16\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 32\|2 cosh(x) + 32\|2 cosh(x))sinh(x) - 8\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 16\|2 cosh(x) - 8\|2 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R 8sinh(x) + 64cosh(x)sinh(x) + (224cosh(x) - 16)sinh(x) +--R + +--R 3 5 +--R (448cosh(x) - 96cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (560cosh(x) - 240cosh(x) + 24)sinh(x) +--R + +--R 5 3 3 +--R (448cosh(x) - 320cosh(x) + 96cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (224cosh(x) - 240cosh(x) + 144cosh(x) - 32)sinh(x) +--R + +--R 7 5 3 8 +--R (64cosh(x) - 96cosh(x) + 96cosh(x) - 64cosh(x))sinh(x) + 8cosh(x) +--R + +--R 6 4 2 +--R - 16cosh(x) + 24cosh(x) - 32cosh(x) + 16 +--R * +--R +-+ +--R \|2 coth(x) +--R atanh(---------------) +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R + +--R 4 3 +--R 2coth(x)sinh(x) + 8cosh(x)coth(x)sinh(x) +--R + +--R 2 2 +--R (12cosh(x) - 4)coth(x)sinh(x) +--R + +--R 3 +--R (8cosh(x) - 8cosh(x))coth(x)sinh(x) +--R + +--R 4 2 +--R (2cosh(x) - 4cosh(x) + 2)coth(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - \|2 coth(x)sinh(x) - 8\|2 cosh(x)coth(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 28\|2 cosh(x) + 2\|2 )coth(x)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 56\|2 cosh(x) + 12\|2 cosh(x))coth(x)sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 70\|2 cosh(x) + 30\|2 cosh(x) - 3\|2 )coth(x)sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 56\|2 cosh(x) + 40\|2 cosh(x) - 12\|2 cosh(x))coth(x)sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 28\|2 cosh(x) + 30\|2 cosh(x) - 18\|2 cosh(x) + 4\|2 )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 8\|2 cosh(x) + 12\|2 cosh(x) - 12\|2 cosh(x) + 8\|2 cosh(x)) +--R * +--R coth(x)sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - \|2 cosh(x) + 2\|2 cosh(x) - 3\|2 cosh(x) + 4\|2 cosh(x) +--R + +--R +-+ +--R - 2\|2 +--R * +--R coth(x) +--R * +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R + +--R 4 3 2 2 +--R 10sinh(x) + 40cosh(x)sinh(x) + (60cosh(x) - 20)sinh(x) +--R + +--R 3 4 2 +--R (40cosh(x) - 40cosh(x))sinh(x) + 10cosh(x) - 20cosh(x) + 10 +--R * +--R acsch(tanh(x)) +--R + +--R +-+ 6 +-+ 5 +-+ 2 +-+ 4 +--R \|2 sinh(x) + 6\|2 cosh(x)sinh(x) + (15\|2 cosh(x) - \|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (20\|2 cosh(x) - 4\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|2 cosh(x) - 6\|2 cosh(x) + 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +-+ 6 +--R (6\|2 cosh(x) - 4\|2 cosh(x) + 12\|2 cosh(x))sinh(x) + \|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R - \|2 cosh(x) + 6\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 5\|2 sinh(x) - 40\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 140\|2 cosh(x) + 10\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 280\|2 cosh(x) + 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 350\|2 cosh(x) + 150\|2 cosh(x) - 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 280\|2 cosh(x) + 200\|2 cosh(x) - 60\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 140\|2 cosh(x) + 150\|2 cosh(x) - 90\|2 cosh(x) + 20\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 40\|2 cosh(x) + 60\|2 cosh(x) - 60\|2 cosh(x) +--R + +--R +-+ +--R 40\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 5\|2 cosh(x) + 10\|2 cosh(x) - 15\|2 cosh(x) + 20\|2 cosh(x) +--R + +--R +-+ +--R - 10\|2 +--R * +--R acsch(tanh(x)) +--R + +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) - 120cosh(x) + 2)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) - 160cosh(x) + 8cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 120cosh(x) + 12cosh(x) - 12)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) - 48cosh(x) + 8cosh(x) - 24cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) + 2cosh(x) - 12cosh(x) +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 8)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 16cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) + 4 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 2\|2 sinh(x) - 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 56\|2 cosh(x) + 4\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 112\|2 cosh(x) + 24\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 140\|2 cosh(x) + 60\|2 cosh(x) - 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 112\|2 cosh(x) + 80\|2 cosh(x) - 24\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (- 56\|2 cosh(x) + 60\|2 cosh(x) - 36\|2 cosh(x) + 8\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 16\|2 cosh(x) + 24\|2 cosh(x) - 24\|2 cosh(x) + 16\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 2\|2 cosh(x) + 4\|2 cosh(x) - 6\|2 cosh(x) + 8\|2 cosh(x) - 4\|2 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 508 +d0361:= D(m0361,x) +--R +--R +--R (280) +--R +-+ 30 +-+ 29 +--R - 7\|2 sinh(x) - 98\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 28 +--R (- 581\|2 cosh(x) + 38\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 27 +--R (- 1764\|2 cosh(x) + 476\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 26 +--R (- 2107\|2 cosh(x) + 2484\|2 cosh(x) - 201\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (3626\|2 cosh(x) + 6412\|2 cosh(x) - 2246\|2 cosh(x)) +--R * +--R 25 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 17591\|2 cosh(x) + 5410\|2 cosh(x) - 10269\|2 cosh(x) +--R + +--R +-+ +--R 630\|2 +--R * +--R 24 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 22232\|2 cosh(x) - 14616\|2 cosh(x) - 22200\|2 cosh(x) +--R + +--R +-+ +--R 5920\|2 cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 13867\|2 cosh(x) - 46712\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 10406\|2 cosh(x) + 21432\|2 cosh(x) - 1045\|2 +--R * +--R 22 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R - 78386\|2 cosh(x) - 35288\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 59124\|2 cosh(x) + 29664\|2 cosh(x) - 6846\|2 cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 79233\|2 cosh(x) + 58806\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R 135594\|2 cosh(x) - 24596\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 10243\|2 cosh(x) + 1630\|2 +--R * +--R 20 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R 48804\|2 cosh(x) + 137940\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R 72232\|2 cosh(x) - 139936\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 33388\|2 cosh(x) + 6956\|2 cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R 188993\|2 cosh(x) + 42636\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 148395\|2 cosh(x) - 148776\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 144737\|2 cosh(x) - 4612\|2 cosh(x) - 435\|2 +--R * +--R 18 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +--R 132202\|2 cosh(x) - 162108\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R - 270042\|2 cosh(x) + 80288\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 167578\|2 cosh(x) - 73908\|2 cosh(x) + 6262\|2 cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 110789\|2 cosh(x) - 178942\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 106063\|2 cosh(x) + 312362\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 103385\|2 cosh(x) - 137658\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 45829\|2 cosh(x) + 718\|2 +--R * +--R 16 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 253232\|2 cosh(x) + 67184\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R 119952\|2 cosh(x) + 213312\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R - 470768\|2 cosh(x) - 10256\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 93584\|2 cosh(x) - 8328\|2 cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 110789\|2 cosh(x) + 232560\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R 139740\|2 cosh(x) - 75408\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 440162\|2 cosh(x) + 257104\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 14180\|2 cosh(x) - 42336\|2 cosh(x) + 5816\|2 +--R * +--R 14 +--R sinh(x) +--R + +--R +-+ 17 +-+ 15 +--R 132202\|2 cosh(x) + 67184\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R 86360\|2 cosh(x) - 189248\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R 11812\|2 cosh(x) + 289968\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 195736\|2 cosh(x) - 43096\|2 cosh(x) + 21680\|2 cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 18 +-+ 16 +--R 188993\|2 cosh(x) - 178942\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R 139740\|2 cosh(x) - 171288\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R 410098\|2 cosh(x) + 14172\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 243532\|2 cosh(x) + 50216\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 19688\|2 cosh(x) - 8424\|2 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 19 +-+ 17 +--R 48804\|2 cosh(x) - 162108\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R 119952\|2 cosh(x) - 189248\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R 529672\|2 cosh(x) - 212760\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R - 20240\|2 cosh(x) + 99384\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 18720\|2 cosh(x) - 13600\|2 cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 20 +-+ 18 +--R - 79233\|2 cosh(x) + 42636\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 106063\|2 cosh(x) - 75408\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R 410098\|2 cosh(x) - 261272\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 183958\|2 cosh(x) + 8928\|2 cosh(x) - 38664\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 304\|2 cosh(x) + 3520\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 21 +-+ 19 +--R - 78386\|2 cosh(x) + 137940\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R - 270042\|2 cosh(x) + 213312\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R 11812\|2 cosh(x) - 212760\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 232260\|2 cosh(x) - 47960\|2 cosh(x) - 9648\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 5984\|2 cosh(x) - 2688\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 22 +-+ 20 +--R - 13867\|2 cosh(x) + 58806\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +--R - 148395\|2 cosh(x) + 312362\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 440162\|2 cosh(x) + 14172\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R 183958\|2 cosh(x) - 35052\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 13160\|2 cosh(x) + 4968\|2 cosh(x) + 704\|2 cosh(x) +--R + +--R +-+ +--R - 2240\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 23 +-+ 21 +--R 22232\|2 cosh(x) - 35288\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R 72232\|2 cosh(x) + 80288\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 470768\|2 cosh(x) + 289968\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R - 20240\|2 cosh(x) - 47960\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 13376\|2 cosh(x) + 7616\|2 cosh(x) + 512\|2 cosh(x) +--R + +--R +-+ +--R 7808\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 24 +-+ 22 +--R 17591\|2 cosh(x) - 46712\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R 135594\|2 cosh(x) - 148776\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 103385\|2 cosh(x) + 257104\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 243532\|2 cosh(x) + 8928\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 13160\|2 cosh(x) + 6304\|2 cosh(x) - 4224\|2 cosh(x) +--R + +--R +-+ 2 +--R - 16384\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 25 +-+ 23 +--R 3626\|2 cosh(x) - 14616\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +--R 59124\|2 cosh(x) - 139936\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R 167578\|2 cosh(x) - 10256\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 195736\|2 cosh(x) + 99384\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 9648\|2 cosh(x) + 7616\|2 cosh(x) + 4352\|2 cosh(x) +--R + +--R +-+ 3 +--R 24960\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 26 +-+ 24 +--R - 2107\|2 cosh(x) + 5410\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +--R - 10406\|2 cosh(x) - 24596\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +--R 144737\|2 cosh(x) - 137658\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R 14180\|2 cosh(x) + 50216\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 38664\|2 cosh(x) + 4968\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 4224\|2 cosh(x) - 28288\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 27 +-+ 25 +--R - 1764\|2 cosh(x) + 6412\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +--R - 22200\|2 cosh(x) + 29664\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R 33388\|2 cosh(x) - 73908\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R 93584\|2 cosh(x) - 43096\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 18720\|2 cosh(x) + 5984\|2 cosh(x) + 512\|2 cosh(x) +--R + +--R +-+ 5 +--R 24960\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 28 +-+ 26 +--R - 581\|2 cosh(x) + 2484\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +--R - 10269\|2 cosh(x) + 21432\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R - 10243\|2 cosh(x) - 4612\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R 45829\|2 cosh(x) - 42336\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 19688\|2 cosh(x) + 304\|2 cosh(x) + 704\|2 cosh(x) +--R + +--R +-+ 6 +--R - 16384\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R - 98\|2 cosh(x) + 476\|2 cosh(x) - 2246\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 5920\|2 cosh(x) - 6846\|2 cosh(x) + 6956\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R 6262\|2 cosh(x) - 8328\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R 21680\|2 cosh(x) - 13600\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R - 2688\|2 cosh(x) + 7808\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R - 7\|2 cosh(x) + 38\|2 cosh(x) - 201\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 630\|2 cosh(x) - 1045\|2 cosh(x) + 1630\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 435\|2 cosh(x) + 718\|2 cosh(x) + 5816\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 8424\|2 cosh(x) + 3520\|2 cosh(x) - 2240\|2 cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R tanh(x) |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 30 29 +--R 32sinh(x) + 512cosh(x)sinh(x) +--R + +--R 2 28 +--R (3680cosh(x) - 120)sinh(x) +--R + +--R 3 27 +--R (15360cosh(x) - 1680cosh(x))sinh(x) +--R + +--R 4 2 26 +--R (39328cosh(x) - 10320cosh(x) + 528)sinh(x) +--R + +--R 5 3 25 +--R (54784cosh(x) - 35280cosh(x) + 6176cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 544cosh(x) - 66600cosh(x) + 29968cosh(x) - 1736) +--R * +--R 24 +--R sinh(x) +--R + +--R 7 5 3 +--R - 174080cosh(x) - 36960cosh(x) + 70400cosh(x) +--R + +--R - 17712cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R 8 6 4 +--R - 364640cosh(x) + 142560cosh(x) + 40352cosh(x) +--R + +--R 2 +--R - 73664cosh(x) + 2992 +--R * +--R 22 +--R sinh(x) +--R + +--R 9 7 5 +--R - 298496cosh(x) + 404640cosh(x) - 222400cosh(x) +--R + +--R 3 +--R - 143696cosh(x) + 23104cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R 10 8 6 +--R 193248cosh(x) + 415560cosh(x) - 658016cosh(x) +--R + +--R 4 2 +--R - 54352cosh(x) + 60240cosh(x) - 4664 +--R * +--R 20 +--R sinh(x) +--R + +--R 11 9 7 +--R 820224cosh(x) - 116400cosh(x) - 688384cosh(x) +--R + +--R 5 3 +--R 342640cosh(x) + 9856cosh(x) - 25232cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 12 10 8 +--R 945440cosh(x) - 907440cosh(x) + 288240cosh(x) +--R + +--R 6 4 2 +--R 708928cosh(x) - 274032cosh(x) - 20912cosh(x) + 1232 +--R * +--R 18 +--R sinh(x) +--R + +--R 13 11 9 +--R 243200cosh(x) - 1144560cosh(x) + 1788384cosh(x) +--R + +--R 7 5 3 +--R 341264cosh(x) - 572096cosh(x) + 152560cosh(x) +--R + +--R - 16672cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 14 12 10 +--R - 816544cosh(x) - 348840cosh(x) + 2219248cosh(x) +--R + +--R 8 6 4 +--R - 742840cosh(x) - 260752cosh(x) + 489256cosh(x) +--R + +--R 2 +--R - 148592cosh(x) - 2008 +--R * +--R 16 +--R sinh(x) +--R + +--R 15 13 11 +--R - 1323008cosh(x) + 930240cosh(x) + 617984cosh(x) +--R + +--R 9 7 5 +--R - 1376992cosh(x) + 704000cosh(x) + 561856cosh(x) +--R + +--R 3 +--R - 441216cosh(x) + 21936cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 16 14 12 +--R - 816544cosh(x) + 1550400cosh(x) - 1920320cosh(x) +--R + +--R 10 8 6 +--R - 635264cosh(x) + 1254880cosh(x) + 83392cosh(x) +--R + +--R 4 2 +--R - 619008cosh(x) + 143456cosh(x) - 16464 +--R * +--R 14 +--R sinh(x) +--R + +--R 17 15 13 +--R 243200cosh(x) + 930240cosh(x) - 3144320cosh(x) +--R + +--R 11 9 7 +--R 854496cosh(x) + 548992cosh(x) - 448064cosh(x) +--R + +--R 5 3 +--R - 369792cosh(x) + 288144cosh(x) - 77888cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 18 16 14 +--R 945440cosh(x) - 348840cosh(x) - 1920320cosh(x) +--R + +--R 12 10 8 +--R 1597856cosh(x) - 783328cosh(x) - 484592cosh(x) +--R + +--R 6 4 2 +--R 65664cosh(x) + 231072cosh(x) - 141808cosh(x) + 23824 +--R * +--R 12 +--R sinh(x) +--R + +--R 19 17 15 +--R 820224cosh(x) - 1144560cosh(x) + 617984cosh(x) +--R + +--R 13 11 9 +--R 854496cosh(x) - 1427712cosh(x) - 241120cosh(x) +--R + +--R 7 5 3 +--R 310144cosh(x) + 32048cosh(x) - 116608cosh(x) +--R + +--R 62240cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 20 18 16 +--R 193248cosh(x) - 907440cosh(x) + 2219248cosh(x) +--R + +--R 14 12 10 +--R - 635264cosh(x) - 783328cosh(x) - 124960cosh(x) +--R + +--R 8 6 4 +--R 438560cosh(x) - 110688cosh(x) - 16464cosh(x) +--R + +--R 2 +--R 72928cosh(x) - 9952 +--R * +--R 10 +--R sinh(x) +--R + +--R 21 19 17 +--R - 298496cosh(x) - 116400cosh(x) + 1788384cosh(x) +--R + +--R 15 13 11 +--R - 1376992cosh(x) + 548992cosh(x) - 241120cosh(x) +--R + +--R 9 7 5 +--R 510784cosh(x) - 276592cosh(x) + 94272cosh(x) +--R + +--R 3 +--R 73888cosh(x) - 2304cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 22 20 18 +--R - 364640cosh(x) + 415560cosh(x) + 288240cosh(x) +--R + +--R 16 14 12 +--R - 742840cosh(x) + 1254880cosh(x) - 484592cosh(x) +--R + +--R 10 8 6 +--R 438560cosh(x) - 392592cosh(x) + 207504cosh(x) +--R + +--R 4 2 +--R 54000cosh(x) - 9056cosh(x) + 6336 +--R * +--R 8 +--R sinh(x) +--R + +--R 23 21 19 +--R - 174080cosh(x) + 404640cosh(x) - 688384cosh(x) +--R + +--R 17 15 13 +--R 341264cosh(x) + 704000cosh(x) - 448064cosh(x) +--R + +--R 11 9 7 +--R 310144cosh(x) - 276592cosh(x) + 265984cosh(x) +--R + +--R 5 3 +--R 19520cosh(x) - 6144cosh(x) - 15744cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 24 22 20 +--R - 544cosh(x) + 142560cosh(x) - 658016cosh(x) +--R + +--R 18 16 14 +--R 708928cosh(x) - 260752cosh(x) + 83392cosh(x) +--R + +--R 12 10 8 +--R 65664cosh(x) - 110688cosh(x) + 207504cosh(x) +--R + +--R 6 4 2 +--R 9792cosh(x) + 6720cosh(x) + 33792cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 25 23 21 +--R 54784cosh(x) - 36960cosh(x) - 222400cosh(x) +--R + +--R 19 17 15 +--R 342640cosh(x) - 572096cosh(x) + 561856cosh(x) +--R + +--R 13 11 9 +--R - 369792cosh(x) + 32048cosh(x) + 94272cosh(x) +--R + +--R 7 5 3 +--R 19520cosh(x) - 7680cosh(x) - 47744cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 26 24 22 +--R 39328cosh(x) - 66600cosh(x) + 40352cosh(x) +--R + +--R 20 18 16 +--R - 54352cosh(x) - 274032cosh(x) + 489256cosh(x) +--R + +--R 14 12 10 +--R - 619008cosh(x) + 231072cosh(x) - 16464cosh(x) +--R + +--R 8 6 4 +--R 54000cosh(x) + 6720cosh(x) + 54912cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 27 25 23 +--R 15360cosh(x) - 35280cosh(x) + 70400cosh(x) +--R + +--R 21 19 17 +--R - 143696cosh(x) + 9856cosh(x) + 152560cosh(x) +--R + +--R 15 13 11 +--R - 441216cosh(x) + 288144cosh(x) - 116608cosh(x) +--R + +--R 9 7 5 +--R 73888cosh(x) - 6144cosh(x) - 47744cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 28 26 24 +--R 3680cosh(x) - 10320cosh(x) + 29968cosh(x) +--R + +--R 22 20 18 +--R - 73664cosh(x) + 60240cosh(x) - 20912cosh(x) +--R + +--R 16 14 12 +--R - 148592cosh(x) + 143456cosh(x) - 141808cosh(x) +--R + +--R 10 8 6 +--R 72928cosh(x) - 9056cosh(x) + 33792cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 29 27 25 +--R 512cosh(x) - 1680cosh(x) + 6176cosh(x) +--R + +--R 23 21 19 +--R - 17712cosh(x) + 23104cosh(x) - 25232cosh(x) +--R + +--R 17 15 13 +--R - 16672cosh(x) + 21936cosh(x) - 77888cosh(x) +--R + +--R 11 9 7 +--R 62240cosh(x) - 2304cosh(x) - 15744cosh(x) +--R * +--R sinh(x) +--R + +--R 30 28 26 24 +--R 32cosh(x) - 120cosh(x) + 528cosh(x) - 1736cosh(x) +--R + +--R 22 20 18 16 +--R 2992cosh(x) - 4664cosh(x) + 1232cosh(x) - 2008cosh(x) +--R + +--R 14 12 10 +--R - 16464cosh(x) + 23824cosh(x) - 9952cosh(x) +--R + +--R 8 +--R 6336cosh(x) +--R * +--R tanh(x) +--R * +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R + +--R 4 2 30 +--R (- 4coth(x) + 2coth(x) - 14)sinh(x) +--R + +--R 4 2 29 +--R (- 64cosh(x)coth(x) + 32cosh(x)coth(x) - 224cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R (- 460cosh(x) + 8)coth(x) + (230cosh(x) - 4)coth(x) +--R + +--R 2 +--R - 1610cosh(x) + 28 +--R * +--R 28 +--R sinh(x) +--R + +--R 3 4 +--R (- 1920cosh(x) + 112cosh(x))coth(x) +--R + +--R 3 2 3 +--R (960cosh(x) - 56cosh(x))coth(x) - 6720cosh(x) + 392cosh(x) +--R * +--R 27 +--R sinh(x) +--R + +--R 4 2 4 +--R (- 4916cosh(x) + 688cosh(x) - 20)coth(x) +--R + +--R 4 2 2 4 +--R (2458cosh(x) - 344cosh(x) + 10)coth(x) - 17206cosh(x) +--R + +--R 2 +--R 2408cosh(x) - 70 +--R * +--R 26 +--R sinh(x) +--R + +--R 5 3 4 +--R (- 6848cosh(x) + 2352cosh(x) - 224cosh(x))coth(x) +--R + +--R 5 3 2 +--R (3424cosh(x) - 1176cosh(x) + 112cosh(x))coth(x) +--R + +--R 5 3 +--R - 23968cosh(x) + 8232cosh(x) - 784cosh(x) +--R * +--R 25 +--R sinh(x) +--R + +--R 6 4 2 4 +--R (68cosh(x) + 4440cosh(x) - 996cosh(x) + 120)coth(x) +--R + +--R 6 4 2 2 +--R (- 34cosh(x) - 2220cosh(x) + 498cosh(x) - 60)coth(x) +--R + +--R 6 4 2 +--R 238cosh(x) + 15540cosh(x) - 3486cosh(x) + 420 +--R * +--R 24 +--R sinh(x) +--R + +--R 7 5 3 +--R (21760cosh(x) + 2464cosh(x) - 1792cosh(x) + 1232cosh(x)) +--R * +--R 4 +--R coth(x) +--R + +--R 7 5 3 +--R (- 10880cosh(x) - 1232cosh(x) + 896cosh(x) - 616cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 7 5 3 +--R 76160cosh(x) + 8624cosh(x) - 6272cosh(x) + 4312cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R 8 6 4 +--R 45580cosh(x) - 9504cosh(x) + 1672cosh(x) +--R + +--R 2 +--R 5184cosh(x) - 276 +--R * +--R 4 +--R coth(x) +--R + +--R 8 6 4 +--R - 22790cosh(x) + 4752cosh(x) - 836cosh(x) +--R + +--R 2 +--R - 2592cosh(x) + 138 +--R * +--R 2 +--R coth(x) +--R + +--R 8 6 4 2 +--R 159530cosh(x) - 33264cosh(x) + 5852cosh(x) + 18144cosh(x) +--R + +--R - 966 +--R * +--R 22 +--R sinh(x) +--R + +--R 9 7 5 +--R 37312cosh(x) - 26976cosh(x) + 15680cosh(x) +--R + +--R 3 +--R 10416cosh(x) - 2336cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 9 7 5 +--R - 18656cosh(x) + 13488cosh(x) - 7840cosh(x) +--R + +--R 3 +--R - 5208cosh(x) + 1168cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 +--R 130592cosh(x) - 94416cosh(x) + 54880cosh(x) +--R + +--R 3 +--R 36456cosh(x) - 8176cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R 10 8 6 +--R - 24156cosh(x) - 27704cosh(x) + 34248cosh(x) +--R + +--R 4 2 +--R 5168cosh(x) - 7628cosh(x) + 728 +--R * +--R 4 +--R coth(x) +--R + +--R 10 8 6 +--R 12078cosh(x) + 13852cosh(x) - 17124cosh(x) +--R + +--R 4 2 +--R - 2584cosh(x) + 3814cosh(x) - 364 +--R * +--R 2 +--R coth(x) +--R + +--R 10 8 6 +--R - 84546cosh(x) - 96964cosh(x) + 119868cosh(x) +--R + +--R 4 2 +--R 18088cosh(x) - 26698cosh(x) + 2548 +--R * +--R 20 +--R sinh(x) +--R + +--R 11 9 7 +--R - 102528cosh(x) + 7760cosh(x) + 27904cosh(x) +--R + +--R 5 3 +--R - 21392cosh(x) - 9792cosh(x) + 4912cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 11 9 7 +--R 51264cosh(x) - 3880cosh(x) - 13952cosh(x) +--R + +--R 5 3 +--R 10696cosh(x) + 4896cosh(x) - 2456cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 11 9 7 +--R - 358848cosh(x) + 27160cosh(x) + 97664cosh(x) +--R + +--R 5 3 +--R - 74872cosh(x) - 34272cosh(x) + 17192cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 12 10 8 +--R - 118180cosh(x) + 60496cosh(x) - 28988cosh(x) +--R + +--R 6 4 2 +--R - 47808cosh(x) + 5316cosh(x) + 11504cosh(x) - 1676 +--R * +--R 4 +--R coth(x) +--R + +--R 12 10 8 +--R 59090cosh(x) - 30248cosh(x) + 14494cosh(x) +--R + +--R 6 4 2 +--R 23904cosh(x) - 2658cosh(x) - 5752cosh(x) + 838 +--R * +--R 2 +--R coth(x) +--R + +--R 12 10 8 +--R - 413630cosh(x) + 211736cosh(x) - 101458cosh(x) +--R + +--R 6 4 2 +--R - 167328cosh(x) + 18606cosh(x) + 40264cosh(x) - 5866 +--R * +--R 18 +--R sinh(x) +--R + +--R 13 11 9 +--R - 30400cosh(x) + 76304cosh(x) - 105760cosh(x) +--R + +--R 7 5 3 +--R - 26864cosh(x) + 32096cosh(x) + 5040cosh(x) +--R + +--R - 8384cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 13 11 9 +--R 15200cosh(x) - 38152cosh(x) + 52880cosh(x) +--R + +--R 7 5 3 +--R 13432cosh(x) - 16048cosh(x) - 2520cosh(x) + 4192cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 13 11 9 +--R - 106400cosh(x) + 267064cosh(x) - 370160cosh(x) +--R + +--R 7 5 3 +--R - 94024cosh(x) + 112336cosh(x) + 17640cosh(x) - 29344cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 14 12 10 +--R 102068cosh(x) + 23256cosh(x) - 119884cosh(x) +--R + +--R 8 6 4 +--R 42760cosh(x) + 31964cosh(x) - 25352cosh(x) +--R + +--R 2 +--R - 11372cosh(x) + 2792 +--R * +--R 4 +--R coth(x) +--R + +--R 14 12 10 +--R - 51034cosh(x) - 11628cosh(x) + 59942cosh(x) +--R + +--R 8 6 4 +--R - 21380cosh(x) - 15982cosh(x) + 12676cosh(x) +--R + +--R 2 +--R 5686cosh(x) - 1396 +--R * +--R 2 +--R coth(x) +--R + +--R 14 12 10 +--R 357238cosh(x) + 81396cosh(x) - 419594cosh(x) +--R + +--R 8 6 4 +--R 149660cosh(x) + 111874cosh(x) - 88732cosh(x) +--R + +--R 2 +--R - 39802cosh(x) + 9772 +--R * +--R 16 +--R sinh(x) +--R + +--R 15 13 11 +--R 165376cosh(x) - 62016cosh(x) - 26112cosh(x) +--R + +--R 9 7 5 +--R 86304cosh(x) - 11008cosh(x) - 49728cosh(x) +--R + +--R 3 +--R 9728cosh(x) + 9104cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 15 13 11 +--R - 82688cosh(x) + 31008cosh(x) + 13056cosh(x) +--R + +--R 9 7 5 +--R - 43152cosh(x) + 5504cosh(x) + 24864cosh(x) +--R + +--R 3 +--R - 4864cosh(x) - 4552cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 15 13 11 +--R 578816cosh(x) - 217056cosh(x) - 91392cosh(x) +--R + +--R 9 7 5 +--R 302064cosh(x) - 38528cosh(x) - 174048cosh(x) +--R + +--R 3 +--R 34048cosh(x) + 31864cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 16 14 12 +--R 102068cosh(x) - 103360cosh(x) + 113968cosh(x) +--R + +--R 10 8 6 +--R 42624cosh(x) - 47368cosh(x) - 32448cosh(x) +--R + +--R 4 2 +--R 40528cosh(x) + 2528cosh(x) - 4648 +--R * +--R 4 +--R coth(x) +--R + +--R 16 14 12 +--R - 51034cosh(x) + 51680cosh(x) - 56984cosh(x) +--R + +--R 10 8 6 +--R - 21312cosh(x) + 23684cosh(x) + 16224cosh(x) +--R + +--R 4 2 +--R - 20264cosh(x) - 1264cosh(x) + 2324 +--R * +--R 2 +--R coth(x) +--R + +--R 16 14 12 +--R 357238cosh(x) - 361760cosh(x) + 398888cosh(x) +--R + +--R 10 8 6 +--R 149184cosh(x) - 165788cosh(x) - 113568cosh(x) +--R + +--R 4 2 +--R 141848cosh(x) + 8848cosh(x) - 16268 +--R * +--R 14 +--R sinh(x) +--R + +--R 17 15 13 +--R - 30400cosh(x) - 62016cosh(x) + 180608cosh(x) +--R + +--R 11 9 7 +--R - 49696cosh(x) - 29760cosh(x) + 4288cosh(x) +--R + +--R 5 3 +--R 38656cosh(x) - 19664cosh(x) - 7936cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 17 15 13 +--R 15200cosh(x) + 31008cosh(x) - 90304cosh(x) +--R + +--R 11 9 7 +--R 24848cosh(x) + 14880cosh(x) - 2144cosh(x) +--R + +--R 5 3 +--R - 19328cosh(x) + 9832cosh(x) + 3968cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 17 15 13 +--R - 106400cosh(x) - 217056cosh(x) + 632128cosh(x) +--R + +--R 11 9 7 +--R - 173936cosh(x) - 104160cosh(x) + 15008cosh(x) +--R + +--R 5 3 +--R 135296cosh(x) - 68824cosh(x) - 27776cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 18 16 14 +--R - 118180cosh(x) + 23256cosh(x) + 113968cosh(x) +--R + +--R 12 10 8 +--R - 96096cosh(x) + 17992cosh(x) + 24624cosh(x) +--R + +--R 6 4 2 +--R 12560cosh(x) - 22368cosh(x) + 5960cosh(x) + 6048 +--R * +--R 4 +--R coth(x) +--R + +--R 18 16 14 +--R 59090cosh(x) - 11628cosh(x) - 56984cosh(x) +--R + +--R 12 10 8 +--R 48048cosh(x) - 8996cosh(x) - 12312cosh(x) +--R + +--R 6 4 2 +--R - 6280cosh(x) + 11184cosh(x) - 2980cosh(x) - 3024 +--R * +--R 2 +--R coth(x) +--R + +--R 18 16 14 +--R - 413630cosh(x) + 81396cosh(x) + 398888cosh(x) +--R + +--R 12 10 8 +--R - 336336cosh(x) + 62972cosh(x) + 86184cosh(x) +--R + +--R 6 4 2 +--R 43960cosh(x) - 78288cosh(x) + 20860cosh(x) + 21168 +--R * +--R 12 +--R sinh(x) +--R + +--R 19 17 15 +--R - 102528cosh(x) + 76304cosh(x) - 26112cosh(x) +--R + +--R 13 11 9 +--R - 49696cosh(x) + 41600cosh(x) + 35488cosh(x) +--R + +--R 7 5 3 +--R - 9728cosh(x) - 7920cosh(x) + 10240cosh(x) + 448cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 19 17 15 +--R 51264cosh(x) - 38152cosh(x) + 13056cosh(x) +--R + +--R 13 11 9 +--R 24848cosh(x) - 20800cosh(x) - 17744cosh(x) +--R + +--R 7 5 3 +--R 4864cosh(x) + 3960cosh(x) - 5120cosh(x) - 224cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 19 17 15 +--R - 358848cosh(x) + 267064cosh(x) - 91392cosh(x) +--R + +--R 13 11 9 +--R - 173936cosh(x) + 145600cosh(x) + 124208cosh(x) +--R + +--R 7 5 3 +--R - 34048cosh(x) - 27720cosh(x) + 35840cosh(x) + 1568cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 20 18 16 +--R - 24156cosh(x) + 60496cosh(x) - 119884cosh(x) +--R + +--R 14 12 10 +--R 42624cosh(x) + 17992cosh(x) + 41888cosh(x) +--R + +--R 8 6 4 +--R - 40040cosh(x) - 2528cosh(x) - 1256cosh(x) +--R + +--R 2 +--R - 7488cosh(x) - 4192 +--R * +--R 4 +--R coth(x) +--R + +--R 20 18 16 +--R 12078cosh(x) - 30248cosh(x) + 59942cosh(x) +--R + +--R 14 12 10 +--R - 21312cosh(x) - 8996cosh(x) - 20944cosh(x) +--R + +--R 8 6 4 2 +--R 20020cosh(x) + 1264cosh(x) + 628cosh(x) + 3744cosh(x) +--R + +--R 2096 +--R * +--R 2 +--R coth(x) +--R + +--R 20 18 16 +--R - 84546cosh(x) + 211736cosh(x) - 419594cosh(x) +--R + +--R 14 12 10 +--R 149184cosh(x) + 62972cosh(x) + 146608cosh(x) +--R + +--R 8 6 4 +--R - 140140cosh(x) - 8848cosh(x) - 4396cosh(x) +--R + +--R 2 +--R - 26208cosh(x) - 14672 +--R * +--R 10 +--R sinh(x) +--R + +--R 21 19 17 +--R 37312cosh(x) + 7760cosh(x) - 105760cosh(x) +--R + +--R 15 13 11 +--R 86304cosh(x) - 29760cosh(x) + 35488cosh(x) +--R + +--R 9 7 5 +--R - 60544cosh(x) + 18480cosh(x) + 7936cosh(x) +--R + +--R 3 +--R 7872cosh(x) + 7040cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 21 19 17 +--R - 18656cosh(x) - 3880cosh(x) + 52880cosh(x) +--R + +--R 15 13 11 +--R - 43152cosh(x) + 14880cosh(x) - 17744cosh(x) +--R + +--R 9 7 5 +--R 30272cosh(x) - 9240cosh(x) - 3968cosh(x) +--R + +--R 3 +--R - 3936cosh(x) - 3520cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 21 19 17 +--R 130592cosh(x) + 27160cosh(x) - 370160cosh(x) +--R + +--R 15 13 11 +--R 302064cosh(x) - 104160cosh(x) + 124208cosh(x) +--R + +--R 9 7 5 +--R - 211904cosh(x) + 64680cosh(x) + 27776cosh(x) +--R + +--R 3 +--R 27552cosh(x) + 24640cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 22 20 18 +--R 45580cosh(x) - 27704cosh(x) - 28988cosh(x) +--R + +--R 16 14 12 +--R 42760cosh(x) - 47368cosh(x) + 24624cosh(x) +--R + +--R 10 8 6 +--R - 40040cosh(x) + 39152cosh(x) - 56cosh(x) +--R + +--R 4 2 +--R - 6048cosh(x) - 6112cosh(x) + 1120 +--R * +--R 4 +--R coth(x) +--R + +--R 22 20 18 +--R - 22790cosh(x) + 13852cosh(x) + 14494cosh(x) +--R + +--R 16 14 12 +--R - 21380cosh(x) + 23684cosh(x) - 12312cosh(x) +--R + +--R 10 8 6 +--R 20020cosh(x) - 19576cosh(x) + 28cosh(x) +--R + +--R 4 2 +--R 3024cosh(x) + 3056cosh(x) - 560 +--R * +--R 2 +--R coth(x) +--R + +--R 22 20 18 +--R 159530cosh(x) - 96964cosh(x) - 101458cosh(x) +--R + +--R 16 14 12 +--R 149660cosh(x) - 165788cosh(x) + 86184cosh(x) +--R + +--R 10 8 6 +--R - 140140cosh(x) + 137032cosh(x) - 196cosh(x) +--R + +--R 4 2 +--R - 21168cosh(x) - 21392cosh(x) + 3920 +--R * +--R 8 +--R sinh(x) +--R + +--R 23 21 19 +--R 21760cosh(x) - 26976cosh(x) + 27904cosh(x) +--R + +--R 17 15 13 +--R - 26864cosh(x) - 11008cosh(x) + 4288cosh(x) +--R + +--R 11 9 7 +--R - 9728cosh(x) + 18480cosh(x) - 20480cosh(x) +--R + +--R 5 +--R - 8320cosh(x) - 3904cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 23 21 19 +--R - 10880cosh(x) + 13488cosh(x) - 13952cosh(x) +--R + +--R 17 15 13 +--R 13432cosh(x) + 5504cosh(x) - 2144cosh(x) +--R + +--R 11 9 7 +--R 4864cosh(x) - 9240cosh(x) + 10240cosh(x) +--R + +--R 5 +--R 4160cosh(x) + 1952cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 23 21 19 +--R 76160cosh(x) - 94416cosh(x) + 97664cosh(x) +--R + +--R 17 15 13 +--R - 94024cosh(x) - 38528cosh(x) + 15008cosh(x) +--R + +--R 11 9 7 +--R - 34048cosh(x) + 64680cosh(x) - 71680cosh(x) +--R + +--R 5 +--R - 29120cosh(x) - 13664cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 24 22 20 +--R 68cosh(x) - 9504cosh(x) + 34248cosh(x) +--R + +--R 18 16 14 +--R - 47808cosh(x) + 31964cosh(x) - 32448cosh(x) +--R + +--R 12 10 8 +--R 12560cosh(x) - 2528cosh(x) - 56cosh(x) +--R + +--R 6 4 2 +--R 14976cosh(x) + 10304cosh(x) + 8192cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 24 22 20 +--R - 34cosh(x) + 4752cosh(x) - 17124cosh(x) +--R + +--R 18 16 14 +--R 23904cosh(x) - 15982cosh(x) + 16224cosh(x) +--R + +--R 12 10 8 +--R - 6280cosh(x) + 1264cosh(x) + 28cosh(x) +--R + +--R 6 4 2 +--R - 7488cosh(x) - 5152cosh(x) - 4096cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 24 22 20 +--R 238cosh(x) - 33264cosh(x) + 119868cosh(x) +--R + +--R 18 16 14 +--R - 167328cosh(x) + 111874cosh(x) - 113568cosh(x) +--R + +--R 12 10 8 6 +--R 43960cosh(x) - 8848cosh(x) - 196cosh(x) + 52416cosh(x) +--R + +--R 4 2 +--R 36064cosh(x) + 28672cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 25 23 21 +--R - 6848cosh(x) + 2464cosh(x) + 15680cosh(x) +--R + +--R 19 17 15 +--R - 21392cosh(x) + 32096cosh(x) - 49728cosh(x) +--R + +--R 13 11 9 +--R 38656cosh(x) - 7920cosh(x) + 7936cosh(x) +--R + +--R 7 5 3 +--R - 8320cosh(x) - 14080cosh(x) - 12480cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 25 23 21 +--R 3424cosh(x) - 1232cosh(x) - 7840cosh(x) +--R + +--R 19 17 15 +--R 10696cosh(x) - 16048cosh(x) + 24864cosh(x) +--R + +--R 13 11 9 +--R - 19328cosh(x) + 3960cosh(x) - 3968cosh(x) +--R + +--R 7 5 3 +--R 4160cosh(x) + 7040cosh(x) + 6240cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 25 23 21 +--R - 23968cosh(x) + 8624cosh(x) + 54880cosh(x) +--R + +--R 19 17 15 +--R - 74872cosh(x) + 112336cosh(x) - 174048cosh(x) +--R + +--R 13 11 9 +--R 135296cosh(x) - 27720cosh(x) + 27776cosh(x) +--R + +--R 7 5 3 +--R - 29120cosh(x) - 49280cosh(x) - 43680cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 26 24 22 +--R - 4916cosh(x) + 4440cosh(x) + 1672cosh(x) +--R + +--R 20 18 16 +--R 5168cosh(x) + 5316cosh(x) - 25352cosh(x) +--R + +--R 14 12 10 +--R 40528cosh(x) - 22368cosh(x) - 1256cosh(x) +--R + +--R 8 6 4 +--R - 6048cosh(x) + 10304cosh(x) + 14144cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 26 24 22 +--R 2458cosh(x) - 2220cosh(x) - 836cosh(x) +--R + +--R 20 18 16 +--R - 2584cosh(x) - 2658cosh(x) + 12676cosh(x) +--R + +--R 14 12 10 +--R - 20264cosh(x) + 11184cosh(x) + 628cosh(x) +--R + +--R 8 6 4 +--R 3024cosh(x) - 5152cosh(x) - 7072cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 26 24 22 +--R - 17206cosh(x) + 15540cosh(x) + 5852cosh(x) +--R + +--R 20 18 16 +--R 18088cosh(x) + 18606cosh(x) - 88732cosh(x) +--R + +--R 14 12 10 +--R 141848cosh(x) - 78288cosh(x) - 4396cosh(x) +--R + +--R 8 6 4 +--R - 21168cosh(x) + 36064cosh(x) + 49504cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 27 25 23 +--R - 1920cosh(x) + 2352cosh(x) - 1792cosh(x) +--R + +--R 21 19 17 +--R 10416cosh(x) - 9792cosh(x) + 5040cosh(x) +--R + +--R 15 13 11 +--R 9728cosh(x) - 19664cosh(x) + 10240cosh(x) +--R + +--R 9 5 +--R 7872cosh(x) - 12480cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 27 25 23 +--R 960cosh(x) - 1176cosh(x) + 896cosh(x) +--R + +--R 21 19 17 +--R - 5208cosh(x) + 4896cosh(x) - 2520cosh(x) +--R + +--R 15 13 11 +--R - 4864cosh(x) + 9832cosh(x) - 5120cosh(x) +--R + +--R 9 5 +--R - 3936cosh(x) + 6240cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 27 25 23 +--R - 6720cosh(x) + 8232cosh(x) - 6272cosh(x) +--R + +--R 21 19 17 +--R 36456cosh(x) - 34272cosh(x) + 17640cosh(x) +--R + +--R 15 13 11 +--R 34048cosh(x) - 68824cosh(x) + 35840cosh(x) +--R + +--R 9 5 +--R 27552cosh(x) - 43680cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 28 26 24 +--R - 460cosh(x) + 688cosh(x) - 996cosh(x) +--R + +--R 22 20 18 +--R 5184cosh(x) - 7628cosh(x) + 11504cosh(x) +--R + +--R 16 14 12 +--R - 11372cosh(x) + 2528cosh(x) + 5960cosh(x) +--R + +--R 10 8 6 +--R - 7488cosh(x) - 6112cosh(x) + 8192cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 28 26 24 +--R 230cosh(x) - 344cosh(x) + 498cosh(x) +--R + +--R 22 20 18 +--R - 2592cosh(x) + 3814cosh(x) - 5752cosh(x) +--R + +--R 16 14 12 +--R 5686cosh(x) - 1264cosh(x) - 2980cosh(x) +--R + +--R 10 8 6 +--R 3744cosh(x) + 3056cosh(x) - 4096cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 28 26 24 +--R - 1610cosh(x) + 2408cosh(x) - 3486cosh(x) +--R + +--R 22 20 18 +--R 18144cosh(x) - 26698cosh(x) + 40264cosh(x) +--R + +--R 16 14 12 +--R - 39802cosh(x) + 8848cosh(x) + 20860cosh(x) +--R + +--R 10 8 6 +--R - 26208cosh(x) - 21392cosh(x) + 28672cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 29 27 25 +--R - 64cosh(x) + 112cosh(x) - 224cosh(x) +--R + +--R 23 21 19 +--R 1232cosh(x) - 2336cosh(x) + 4912cosh(x) +--R + +--R 17 15 13 +--R - 8384cosh(x) + 9104cosh(x) - 7936cosh(x) +--R + +--R 11 9 7 +--R 448cosh(x) + 7040cosh(x) - 3904cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 29 27 25 23 +--R 32cosh(x) - 56cosh(x) + 112cosh(x) - 616cosh(x) +--R + +--R 21 19 17 +--R 1168cosh(x) - 2456cosh(x) + 4192cosh(x) +--R + +--R 15 13 11 +--R - 4552cosh(x) + 3968cosh(x) - 224cosh(x) +--R + +--R 9 7 +--R - 3520cosh(x) + 1952cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 29 27 25 23 +--R - 224cosh(x) + 392cosh(x) - 784cosh(x) + 4312cosh(x) +--R + +--R 21 19 17 +--R - 8176cosh(x) + 17192cosh(x) - 29344cosh(x) +--R + +--R 15 13 11 +--R 31864cosh(x) - 27776cosh(x) + 1568cosh(x) +--R + +--R 9 7 +--R 24640cosh(x) - 13664cosh(x) +--R * +--R sinh(x) +--R + +--R 30 28 26 24 +--R - 4cosh(x) + 8cosh(x) - 20cosh(x) + 120cosh(x) +--R + +--R 22 20 18 16 +--R - 276cosh(x) + 728cosh(x) - 1676cosh(x) + 2792cosh(x) +--R + +--R 14 12 10 8 +--R - 4648cosh(x) + 6048cosh(x) - 4192cosh(x) + 1120cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 30 28 26 24 +--R 2cosh(x) - 4cosh(x) + 10cosh(x) - 60cosh(x) +--R + +--R 22 20 18 16 +--R 138cosh(x) - 364cosh(x) + 838cosh(x) - 1396cosh(x) +--R + +--R 14 12 10 8 +--R 2324cosh(x) - 3024cosh(x) + 2096cosh(x) - 560cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 30 28 26 24 +--R - 14cosh(x) + 28cosh(x) - 70cosh(x) + 420cosh(x) +--R + +--R 22 20 18 16 +--R - 966cosh(x) + 2548cosh(x) - 5866cosh(x) + 9772cosh(x) +--R + +--R 14 12 10 8 +--R - 16268cosh(x) + 21168cosh(x) - 14672cosh(x) + 3920cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R tanh(x) |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 32 +--R (2\|2 coth(x) - \|2 coth(x) + 7\|2 )sinh(x) +--R + +--R +-+ 4 +-+ 2 +--R 36\|2 cosh(x)coth(x) - 18\|2 cosh(x)coth(x) +--R + +--R +-+ +--R 126\|2 cosh(x) +--R * +--R 31 +--R sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (296\|2 cosh(x) - 2\|2 )coth(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (- 148\|2 cosh(x) + \|2 )coth(x) + 1036\|2 cosh(x) - 7\|2 +--R * +--R 30 +--R sinh(x) +--R + +--R +-+ 3 +-+ 4 +--R (1452\|2 cosh(x) - 32\|2 cosh(x))coth(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 726\|2 cosh(x) + 16\|2 cosh(x))coth(x) +--R + +--R +-+ 3 +-+ +--R 5082\|2 cosh(x) - 112\|2 cosh(x) +--R * +--R 29 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (4608\|2 cosh(x) - 230\|2 cosh(x) - 6\|2 )coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 2304\|2 cosh(x) + 115\|2 cosh(x) + 3\|2 )coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 16128\|2 cosh(x) - 805\|2 cosh(x) - 21\|2 +--R * +--R 28 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 4 +--R (9300\|2 cosh(x) - 960\|2 cosh(x) - 100\|2 cosh(x))coth(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 4650\|2 cosh(x) + 480\|2 cosh(x) + 50\|2 cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 32550\|2 cosh(x) - 3360\|2 cosh(x) - 350\|2 cosh(x) +--R * +--R 27 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 9272\|2 cosh(x) - 2458\|2 cosh(x) - 772\|2 cosh(x) +--R + +--R +-+ +--R 42\|2 +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 4636\|2 cosh(x) + 1229\|2 cosh(x) + 386\|2 cosh(x) +--R + +--R +-+ +--R - 21\|2 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 32452\|2 cosh(x) - 8603\|2 cosh(x) - 2702\|2 cosh(x) +--R + +--R +-+ +--R 147\|2 +--R * +--R 26 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 7524\|2 cosh(x) - 3424\|2 cosh(x) - 3636\|2 cosh(x) +--R + +--R +-+ +--R 584\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 3762\|2 cosh(x) + 1712\|2 cosh(x) + 1818\|2 cosh(x) +--R + +--R +-+ +--R - 292\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 26334\|2 cosh(x) - 11984\|2 cosh(x) - 12726\|2 cosh(x) +--R + +--R +-+ +--R 2044\|2 cosh(x) +--R * +--R 25 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 44584\|2 cosh(x) + 34\|2 cosh(x) - 11522\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 3682\|2 cosh(x) - 190\|2 +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 22292\|2 cosh(x) - 17\|2 cosh(x) + 5761\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 1841\|2 cosh(x) + 95\|2 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 156044\|2 cosh(x) + 119\|2 cosh(x) - 40327\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 12887\|2 cosh(x) - 665\|2 +--R * +--R 24 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R - 75116\|2 cosh(x) + 10880\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 25240\|2 cosh(x) + 13760\|2 cosh(x) - 2204\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 37558\|2 cosh(x) - 5440\|2 cosh(x) + 12620\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 6880\|2 cosh(x) + 1102\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 262906\|2 cosh(x) + 38080\|2 cosh(x) - 88340\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 48160\|2 cosh(x) - 7714\|2 cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 48024\|2 cosh(x) + 22790\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 36392\|2 cosh(x) + 33068\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 11216\|2 cosh(x) + 386\|2 +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 10 +-+ 8 +--R 24012\|2 cosh(x) - 11395\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 18196\|2 cosh(x) - 16534\|2 cosh(x) + 5608\|2 cosh(x) +--R + +--R +-+ +--R - 193\|2 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 10 +-+ 8 +--R - 168084\|2 cosh(x) + 79765\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 127372\|2 cosh(x) + 115738\|2 cosh(x) - 39256\|2 cosh(x) +--R + +--R +-+ +--R 1351\|2 +--R * +--R 22 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R 56764\|2 cosh(x) + 18656\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R - 24408\|2 cosh(x) + 50000\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 32004\|2 cosh(x) + 3584\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 11 +-+ 9 +--R - 28382\|2 cosh(x) - 9328\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 12204\|2 cosh(x) - 25000\|2 cosh(x) + 16002\|2 cosh(x) +--R + +--R +-+ +--R - 1792\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 198674\|2 cosh(x) + 65296\|2 cosh(x) - 85428\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 175000\|2 cosh(x) - 112014\|2 cosh(x) + 12544\|2 cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R 173696\|2 cosh(x) - 12078\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 28970\|2 cosh(x) + 34636\|2 cosh(x) - 51916\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 13550\|2 cosh(x) - 1010\|2 +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 12 +-+ 10 +--R - 86848\|2 cosh(x) + 6039\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 14485\|2 cosh(x) - 17318\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 25958\|2 cosh(x) - 6775\|2 cosh(x) + 505\|2 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 607936\|2 cosh(x) - 42273\|2 cosh(x) + 101395\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 121226\|2 cosh(x) - 181706\|2 cosh(x) + 47425\|2 cosh(x) +--R + +--R +-+ +--R - 3535\|2 +--R * +--R 20 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +--R 184644\|2 cosh(x) - 51264\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R 110612\|2 cosh(x) - 37696\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 30676\|2 cosh(x) + 23552\|2 cosh(x) - 7692\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 13 +-+ 11 +--R - 92322\|2 cosh(x) + 25632\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R - 55306\|2 cosh(x) + 18848\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 15338\|2 cosh(x) - 11776\|2 cosh(x) + 3846\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 13 +-+ 11 +--R 646254\|2 cosh(x) - 179424\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 387142\|2 cosh(x) - 131936\|2 cosh(x) - 107366\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 82432\|2 cosh(x) - 26922\|2 cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R 38456\|2 cosh(x) - 59090\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R 163780\|2 cosh(x) - 145650\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 65264\|2 cosh(x) + 2374\|2 cosh(x) - 22868\|2 cosh(x) +--R + +--R +-+ +--R 2366\|2 +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 14 +-+ 12 +--R - 19228\|2 cosh(x) + 29545\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 81890\|2 cosh(x) + 72825\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 32632\|2 cosh(x) - 1187\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 11434\|2 cosh(x) - 1183\|2 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 14 +-+ 12 +--R 134596\|2 cosh(x) - 206815\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 573230\|2 cosh(x) - 509775\|2 cosh(x) + 228424\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 8309\|2 cosh(x) - 80038\|2 cosh(x) + 8281\|2 +--R * +--R 18 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 169556\|2 cosh(x) - 15200\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R 123652\|2 cosh(x) - 212424\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R 202676\|2 cosh(x) - 80384\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 27820\|2 cosh(x) + 14200\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 15 +-+ 13 +--R 84778\|2 cosh(x) + 7600\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R - 61826\|2 cosh(x) + 106212\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R - 101338\|2 cosh(x) + 40192\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 13910\|2 cosh(x) - 7100\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 15 +-+ 13 +--R - 593446\|2 cosh(x) - 53200\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 432782\|2 cosh(x) - 743484\|2 cosh(x) + 709366\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 281344\|2 cosh(x) - 97370\|2 cosh(x) + 49700\|2 cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 267444\|2 cosh(x) + 51034\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 17442\|2 cosh(x) - 157658\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R 277214\|2 cosh(x) - 195862\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 11958\|2 cosh(x) + 31582\|2 cosh(x) - 3956\|2 +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 16 +-+ 14 +--R 133722\|2 cosh(x) - 25517\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R 8721\|2 cosh(x) + 78829\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 138607\|2 cosh(x) + 97931\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 5979\|2 cosh(x) - 15791\|2 cosh(x) + 1978\|2 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 16 +-+ 14 +--R - 936054\|2 cosh(x) + 178619\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 61047\|2 cosh(x) - 551803\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 970249\|2 cosh(x) - 685517\|2 cosh(x) + 41853\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 110537\|2 cosh(x) - 13846\|2 +--R * +--R 16 +--R sinh(x) +--R + +--R +-+ 17 +-+ 15 +--R - 169556\|2 cosh(x) + 82688\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 180880\|2 cosh(x) + 23936\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R 191272\|2 cosh(x) - 249856\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 91664\|2 cosh(x) + 25376\|2 cosh(x) - 16936\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 17 +-+ 15 +--R 84778\|2 cosh(x) - 41344\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R 90440\|2 cosh(x) - 11968\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R - 95636\|2 cosh(x) + 124928\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 45832\|2 cosh(x) - 12688\|2 cosh(x) + 8468\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 17 +-+ 15 +--R - 593446\|2 cosh(x) + 289408\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 633080\|2 cosh(x) + 83776\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 669452\|2 cosh(x) - 874496\|2 cosh(x) + 320824\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 88816\|2 cosh(x) - 59276\|2 cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R +-+ 18 +-+ 16 +--R 38456\|2 cosh(x) + 51034\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 253232\|2 cosh(x) + 231880\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 54048\|2 cosh(x) - 157772\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R 147344\|2 cosh(x) - 16248\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 23152\|2 cosh(x) + 6576\|2 +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 18 +-+ 16 +--R - 19228\|2 cosh(x) - 25517\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R 126616\|2 cosh(x) - 115940\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R 27024\|2 cosh(x) + 78886\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 73672\|2 cosh(x) + 8124\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 11576\|2 cosh(x) - 3288\|2 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 18 +-+ 16 +--R 134596\|2 cosh(x) + 178619\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 886312\|2 cosh(x) + 811580\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 189168\|2 cosh(x) - 552202\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 515704\|2 cosh(x) - 56868\|2 cosh(x) - 81032\|2 cosh(x) +--R + +--R +-+ +--R 23016\|2 +--R * +--R 14 +--R sinh(x) +--R + +--R +-+ 19 +-+ 17 +--R 184644\|2 cosh(x) - 15200\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 180880\|2 cosh(x) + 323680\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R - 329064\|2 cosh(x) + 76800\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 116304\|2 cosh(x) - 56352\|2 cosh(x) - 4280\|2 cosh(x) +--R + +--R +-+ +--R 17824\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 19 +-+ 17 +--R - 92322\|2 cosh(x) + 7600\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R 90440\|2 cosh(x) - 161840\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R 164532\|2 cosh(x) - 38400\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R - 58152\|2 cosh(x) + 28176\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 2140\|2 cosh(x) - 8912\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 19 +-+ 17 +--R 646254\|2 cosh(x) - 53200\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 633080\|2 cosh(x) + 1132880\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R - 1151724\|2 cosh(x) + 268800\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 407064\|2 cosh(x) - 197232\|2 cosh(x) - 14980\|2 cosh(x) +--R + +--R +-+ +--R 62384\|2 cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 20 +-+ 18 +--R 173696\|2 cosh(x) - 59090\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 17442\|2 cosh(x) + 231880\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 450216\|2 cosh(x) + 337324\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 10948\|2 cosh(x) - 62008\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 20144\|2 cosh(x) + 12752\|2 cosh(x) - 8552\|2 +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 20 +-+ 18 +--R - 86848\|2 cosh(x) + 29545\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R 8721\|2 cosh(x) - 115940\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R 225108\|2 cosh(x) - 168662\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 5474\|2 cosh(x) + 31004\|2 cosh(x) - 10072\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 6376\|2 cosh(x) + 4276\|2 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 20 +-+ 18 +--R 607936\|2 cosh(x) - 206815\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 61047\|2 cosh(x) + 811580\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 1575756\|2 cosh(x) + 1180634\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 38318\|2 cosh(x) - 217028\|2 cosh(x) + 70504\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 44632\|2 cosh(x) - 29932\|2 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 21 +-+ 19 +--R 56764\|2 cosh(x) - 51264\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R 123652\|2 cosh(x) + 23936\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 329064\|2 cosh(x) + 452608\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R - 172456\|2 cosh(x) - 25376\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 38680\|2 cosh(x) + 3776\|2 cosh(x) - 9168\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 21 +-+ 19 +--R - 28382\|2 cosh(x) + 25632\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R - 61826\|2 cosh(x) - 11968\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R 164532\|2 cosh(x) - 226304\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 86228\|2 cosh(x) + 12688\|2 cosh(x) - 19340\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 1888\|2 cosh(x) + 4584\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 21 +-+ 19 +--R 198674\|2 cosh(x) - 179424\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R 432782\|2 cosh(x) + 83776\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 1151724\|2 cosh(x) + 1584128\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 603596\|2 cosh(x) - 88816\|2 cosh(x) + 135380\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 13216\|2 cosh(x) - 32088\|2 cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 22 +-+ 20 +--R - 48024\|2 cosh(x) - 12078\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +--R 163780\|2 cosh(x) - 157658\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 54048\|2 cosh(x) + 337324\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 248952\|2 cosh(x) + 44308\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 55920\|2 cosh(x) - 912\|2 cosh(x) - 2736\|2 cosh(x) +--R + +--R +-+ +--R 5928\|2 +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 22 +-+ 20 +--R 24012\|2 cosh(x) + 6039\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +--R - 81890\|2 cosh(x) + 78829\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R 27024\|2 cosh(x) - 168662\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R 124476\|2 cosh(x) - 22154\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 27960\|2 cosh(x) + 456\|2 cosh(x) + 1368\|2 cosh(x) +--R + +--R +-+ +--R - 2964\|2 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 22 +-+ 20 +--R - 168084\|2 cosh(x) - 42273\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +--R 573230\|2 cosh(x) - 551803\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 189168\|2 cosh(x) + 1180634\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 871332\|2 cosh(x) + 155078\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 195720\|2 cosh(x) - 3192\|2 cosh(x) - 9576\|2 cosh(x) +--R + +--R +-+ +--R 20748\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 23 +-+ 21 +--R - 75116\|2 cosh(x) + 18656\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R 110612\|2 cosh(x) - 212424\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R 191272\|2 cosh(x) + 76800\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R - 172456\|2 cosh(x) + 84304\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 48072\|2 cosh(x) - 26016\|2 cosh(x) - 13712\|2 cosh(x) +--R + +--R +-+ +--R - 4032\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 23 +-+ 21 +--R 37558\|2 cosh(x) - 9328\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 55306\|2 cosh(x) + 106212\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 95636\|2 cosh(x) - 38400\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R 86228\|2 cosh(x) - 42152\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R - 24036\|2 cosh(x) + 13008\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 6856\|2 cosh(x) + 2016\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 23 +-+ 21 +--R - 262906\|2 cosh(x) + 65296\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R 387142\|2 cosh(x) - 743484\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R 669452\|2 cosh(x) + 268800\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R - 603596\|2 cosh(x) + 295064\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 168252\|2 cosh(x) - 91056\|2 cosh(x) - 47992\|2 cosh(x) +--R + +--R +-+ +--R - 14112\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 24 +-+ 22 +--R - 44584\|2 cosh(x) + 22790\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R 28970\|2 cosh(x) - 145650\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R 277214\|2 cosh(x) - 157772\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 10948\|2 cosh(x) + 44308\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 33160\|2 cosh(x) - 34800\|2 cosh(x) + 2408\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 7560\|2 cosh(x) - 1584\|2 +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 24 +-+ 22 +--R 22292\|2 cosh(x) - 11395\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R - 14485\|2 cosh(x) + 72825\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 138607\|2 cosh(x) + 78886\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R 5474\|2 cosh(x) - 22154\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 16580\|2 cosh(x) + 17400\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 1204\|2 cosh(x) - 3780\|2 cosh(x) + 792\|2 +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 24 +-+ 22 +--R - 156044\|2 cosh(x) + 79765\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R 101395\|2 cosh(x) - 509775\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R 970249\|2 cosh(x) - 552202\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 38318\|2 cosh(x) + 155078\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 116060\|2 cosh(x) - 121800\|2 cosh(x) + 8428\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 26460\|2 cosh(x) - 5544\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 25 +-+ 23 +--R - 7524\|2 cosh(x) + 10880\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +--R - 24408\|2 cosh(x) - 37696\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R 202676\|2 cosh(x) - 249856\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R 116304\|2 cosh(x) - 25376\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 48072\|2 cosh(x) - 23936\|2 cosh(x) + 10592\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 2560\|2 cosh(x) + 3936\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 25 +-+ 23 +--R 3762\|2 cosh(x) - 5440\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +--R 12204\|2 cosh(x) + 18848\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R - 101338\|2 cosh(x) + 124928\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 58152\|2 cosh(x) + 12688\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R - 24036\|2 cosh(x) + 11968\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 5296\|2 cosh(x) - 1280\|2 cosh(x) - 1968\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 25 +-+ 23 +--R - 26334\|2 cosh(x) + 38080\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +--R - 85428\|2 cosh(x) - 131936\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R 709366\|2 cosh(x) - 874496\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 407064\|2 cosh(x) - 88816\|2 cosh(x) + 168252\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 83776\|2 cosh(x) + 37072\|2 cosh(x) + 8960\|2 cosh(x) +--R + +--R +-+ +--R 13776\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R 9272\|2 cosh(x) + 34\|2 cosh(x) - 36392\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R 34636\|2 cosh(x) + 65264\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 195862\|2 cosh(x) + 147344\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 62008\|2 cosh(x) + 55920\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 34800\|2 cosh(x) - 6816\|2 cosh(x) - 8368\|2 cosh(x) +--R + +--R +-+ 2 +--R - 8448\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 26 +-+ 24 +--R - 4636\|2 cosh(x) - 17\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +--R 18196\|2 cosh(x) - 17318\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +--R - 32632\|2 cosh(x) + 97931\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 73672\|2 cosh(x) + 31004\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 27960\|2 cosh(x) + 17400\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 3408\|2 cosh(x) + 4184\|2 cosh(x) + 4224\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R 32452\|2 cosh(x) + 119\|2 cosh(x) - 127372\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R 121226\|2 cosh(x) + 228424\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 685517\|2 cosh(x) + 515704\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 217028\|2 cosh(x) + 195720\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 121800\|2 cosh(x) - 23856\|2 cosh(x) - 29288\|2 cosh(x) +--R + +--R +-+ 2 +--R - 29568\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 27 +-+ 25 +--R 9300\|2 cosh(x) - 3424\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +--R - 25240\|2 cosh(x) + 50000\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 30676\|2 cosh(x) - 80384\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R 91664\|2 cosh(x) - 56352\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R 38680\|2 cosh(x) - 26016\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 10592\|2 cosh(x) + 13184\|2 cosh(x) + 11936\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 27 +-+ 25 +--R - 4650\|2 cosh(x) + 1712\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +--R 12620\|2 cosh(x) - 25000\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R 15338\|2 cosh(x) + 40192\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 45832\|2 cosh(x) + 28176\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R - 19340\|2 cosh(x) + 13008\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 5296\|2 cosh(x) - 6592\|2 cosh(x) - 5968\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 27 +-+ 25 +-+ 23 +--R 32550\|2 cosh(x) - 11984\|2 cosh(x) - 88340\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +--R 175000\|2 cosh(x) - 107366\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R - 281344\|2 cosh(x) + 320824\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 197232\|2 cosh(x) + 135380\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 91056\|2 cosh(x) + 37072\|2 cosh(x) + 46144\|2 cosh(x) +--R + +--R +-+ 3 +--R 41776\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 28 +-+ 26 +--R 4608\|2 cosh(x) - 2458\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +--R - 11522\|2 cosh(x) + 33068\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R - 51916\|2 cosh(x) + 2374\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R 11958\|2 cosh(x) - 16248\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 20144\|2 cosh(x) - 912\|2 cosh(x) + 2408\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 8368\|2 cosh(x) - 13728\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 28 +-+ 26 +--R - 2304\|2 cosh(x) + 1229\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +--R 5761\|2 cosh(x) - 16534\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R 25958\|2 cosh(x) - 1187\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 5979\|2 cosh(x) + 8124\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 10072\|2 cosh(x) + 456\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 1204\|2 cosh(x) + 4184\|2 cosh(x) + 6864\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 28 +-+ 26 +-+ 24 +--R 16128\|2 cosh(x) - 8603\|2 cosh(x) - 40327\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 115738\|2 cosh(x) - 181706\|2 cosh(x) + 8309\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R 41853\|2 cosh(x) - 56868\|2 cosh(x) + 70504\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 3192\|2 cosh(x) + 8428\|2 cosh(x) - 29288\|2 cosh(x) +--R + +--R +-+ 4 +--R - 48048\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R 1452\|2 cosh(x) - 960\|2 cosh(x) - 3636\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +--R 13760\|2 cosh(x) - 32004\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R 23552\|2 cosh(x) - 27820\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R 25376\|2 cosh(x) - 4280\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 3776\|2 cosh(x) - 13712\|2 cosh(x) + 2560\|2 cosh(x) +--R + +--R +-+ 5 +--R 11936\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R - 726\|2 cosh(x) + 480\|2 cosh(x) + 1818\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +--R - 6880\|2 cosh(x) + 16002\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 11776\|2 cosh(x) + 13910\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 12688\|2 cosh(x) + 2140\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 1888\|2 cosh(x) + 6856\|2 cosh(x) - 1280\|2 cosh(x) +--R + +--R +-+ 5 +--R - 5968\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R 5082\|2 cosh(x) - 3360\|2 cosh(x) - 12726\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 48160\|2 cosh(x) - 112014\|2 cosh(x) + 82432\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R - 97370\|2 cosh(x) + 88816\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 14980\|2 cosh(x) + 13216\|2 cosh(x) - 47992\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R 8960\|2 cosh(x) + 41776\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R 296\|2 cosh(x) - 230\|2 cosh(x) - 772\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +--R 3682\|2 cosh(x) - 11216\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R 13550\|2 cosh(x) - 22868\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R 31582\|2 cosh(x) - 23152\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 12752\|2 cosh(x) - 2736\|2 cosh(x) + 7560\|2 cosh(x) +--R + +--R +-+ 6 +--R - 8448\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R - 148\|2 cosh(x) + 115\|2 cosh(x) + 386\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +--R - 1841\|2 cosh(x) + 5608\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R - 6775\|2 cosh(x) + 11434\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R - 15791\|2 cosh(x) + 11576\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 6376\|2 cosh(x) + 1368\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R - 3780\|2 cosh(x) + 4224\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R 1036\|2 cosh(x) - 805\|2 cosh(x) - 2702\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 12887\|2 cosh(x) - 39256\|2 cosh(x) + 47425\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +--R - 80038\|2 cosh(x) + 110537\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 81032\|2 cosh(x) + 44632\|2 cosh(x) - 9576\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R 26460\|2 cosh(x) - 29568\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R 36\|2 cosh(x) - 32\|2 cosh(x) - 100\|2 cosh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 584\|2 cosh(x) - 2204\|2 cosh(x) + 3584\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 7692\|2 cosh(x) + 14200\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 16936\|2 cosh(x) + 17824\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 9168\|2 cosh(x) - 4032\|2 cosh(x) + 3936\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R - 18\|2 cosh(x) + 16\|2 cosh(x) + 50\|2 cosh(x) +--R + +--R +-+ 25 +-+ 23 +--R - 292\|2 cosh(x) + 1102\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +--R - 1792\|2 cosh(x) + 3846\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R - 7100\|2 cosh(x) + 8468\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 8912\|2 cosh(x) + 4584\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +--R 2016\|2 cosh(x) - 1968\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R 126\|2 cosh(x) - 112\|2 cosh(x) - 350\|2 cosh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 2044\|2 cosh(x) - 7714\|2 cosh(x) + 12544\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 26922\|2 cosh(x) + 49700\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 59276\|2 cosh(x) + 62384\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 32088\|2 cosh(x) - 14112\|2 cosh(x) + 13776\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 32 +-+ 30 +-+ 28 +--R 2\|2 cosh(x) - 2\|2 cosh(x) - 6\|2 cosh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R 42\|2 cosh(x) - 190\|2 cosh(x) + 386\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R - 1010\|2 cosh(x) + 2366\|2 cosh(x) - 3956\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 6576\|2 cosh(x) - 8552\|2 cosh(x) + 5928\|2 cosh(x) +--R + +--R +-+ 8 +--R - 1584\|2 cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R +-+ 32 +-+ 30 +-+ 28 +--R - \|2 cosh(x) + \|2 cosh(x) + 3\|2 cosh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R - 21\|2 cosh(x) + 95\|2 cosh(x) - 193\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R 505\|2 cosh(x) - 1183\|2 cosh(x) + 1978\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 3288\|2 cosh(x) + 4276\|2 cosh(x) - 2964\|2 cosh(x) +--R + +--R +-+ 8 +--R 792\|2 cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 32 +-+ 30 +-+ 28 +--R 7\|2 cosh(x) - 7\|2 cosh(x) - 21\|2 cosh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R 147\|2 cosh(x) - 665\|2 cosh(x) + 1351\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R - 3535\|2 cosh(x) + 8281\|2 cosh(x) - 13846\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 23016\|2 cosh(x) - 29932\|2 cosh(x) + 20748\|2 cosh(x) +--R + +--R +-+ 8 +--R - 5544\|2 cosh(x) +--R * +--R tanh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) + 1 +--R + +--R 30 29 +--R 10sinh(x) + 160cosh(x)sinh(x) +--R + +--R 2 28 +--R (1150cosh(x) - 20)sinh(x) +--R + +--R 3 27 +--R (4800cosh(x) - 280cosh(x))sinh(x) +--R + +--R 4 2 26 +--R (12290cosh(x) - 1720cosh(x) + 50)sinh(x) +--R + +--R 5 3 25 +--R (17120cosh(x) - 5880cosh(x) + 560cosh(x))sinh(x) +--R + +--R 6 4 2 24 +--R (- 170cosh(x) - 11100cosh(x) + 2490cosh(x) - 300)sinh(x) +--R + +--R 7 5 3 +--R - 54400cosh(x) - 6160cosh(x) + 4480cosh(x) +--R + +--R - 3080cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R 8 6 4 +--R - 113950cosh(x) + 23760cosh(x) - 4180cosh(x) +--R + +--R 2 +--R - 12960cosh(x) + 690 +--R * +--R 22 +--R sinh(x) +--R + +--R 9 7 5 +--R - 93280cosh(x) + 67440cosh(x) - 39200cosh(x) +--R + +--R 3 +--R - 26040cosh(x) + 5840cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R 10 8 6 +--R 60390cosh(x) + 69260cosh(x) - 85620cosh(x) +--R + +--R 4 2 +--R - 12920cosh(x) + 19070cosh(x) - 1820 +--R * +--R 20 +--R sinh(x) +--R + +--R 11 9 7 +--R 256320cosh(x) - 19400cosh(x) - 69760cosh(x) +--R + +--R 5 3 +--R 53480cosh(x) + 24480cosh(x) - 12280cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 12 10 8 +--R 295450cosh(x) - 151240cosh(x) + 72470cosh(x) +--R + +--R 6 4 2 +--R 119520cosh(x) - 13290cosh(x) - 28760cosh(x) + 4190 +--R * +--R 18 +--R sinh(x) +--R + +--R 13 11 9 +--R 76000cosh(x) - 190760cosh(x) + 264400cosh(x) +--R + +--R 7 5 3 +--R 67160cosh(x) - 80240cosh(x) - 12600cosh(x) +--R + +--R 20960cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 14 12 10 +--R - 255170cosh(x) - 58140cosh(x) + 299710cosh(x) +--R + +--R 8 6 4 +--R - 106900cosh(x) - 79910cosh(x) + 63380cosh(x) +--R + +--R 2 +--R 28430cosh(x) - 6980 +--R * +--R 16 +--R sinh(x) +--R + +--R 15 13 11 +--R - 413440cosh(x) + 155040cosh(x) + 65280cosh(x) +--R + +--R 9 7 5 +--R - 215760cosh(x) + 27520cosh(x) + 124320cosh(x) +--R + +--R 3 +--R - 24320cosh(x) - 22760cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 16 14 12 +--R - 255170cosh(x) + 258400cosh(x) - 284920cosh(x) +--R + +--R 10 8 6 +--R - 106560cosh(x) + 118420cosh(x) + 81120cosh(x) +--R + +--R 4 2 +--R - 101320cosh(x) - 6320cosh(x) + 11620 +--R * +--R 14 +--R sinh(x) +--R + +--R 17 15 13 +--R 76000cosh(x) + 155040cosh(x) - 451520cosh(x) +--R + +--R 11 9 7 +--R 124240cosh(x) + 74400cosh(x) - 10720cosh(x) +--R + +--R 5 3 +--R - 96640cosh(x) + 49160cosh(x) + 19840cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 18 16 14 +--R 295450cosh(x) - 58140cosh(x) - 284920cosh(x) +--R + +--R 12 10 8 +--R 240240cosh(x) - 44980cosh(x) - 61560cosh(x) +--R + +--R 6 4 2 +--R - 31400cosh(x) + 55920cosh(x) - 14900cosh(x) - 15120 +--R * +--R 12 +--R sinh(x) +--R + +--R 19 17 15 +--R 256320cosh(x) - 190760cosh(x) + 65280cosh(x) +--R + +--R 13 11 9 +--R 124240cosh(x) - 104000cosh(x) - 88720cosh(x) +--R + +--R 7 5 3 +--R 24320cosh(x) + 19800cosh(x) - 25600cosh(x) - 1120cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 20 18 16 +--R 60390cosh(x) - 151240cosh(x) + 299710cosh(x) +--R + +--R 14 12 10 +--R - 106560cosh(x) - 44980cosh(x) - 104720cosh(x) +--R + +--R 8 6 4 +--R 100100cosh(x) + 6320cosh(x) + 3140cosh(x) +--R + +--R 2 +--R 18720cosh(x) + 10480 +--R * +--R 10 +--R sinh(x) +--R + +--R 21 19 17 +--R - 93280cosh(x) - 19400cosh(x) + 264400cosh(x) +--R + +--R 15 13 11 +--R - 215760cosh(x) + 74400cosh(x) - 88720cosh(x) +--R + +--R 9 7 5 +--R 151360cosh(x) - 46200cosh(x) - 19840cosh(x) +--R + +--R 3 +--R - 19680cosh(x) - 17600cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 22 20 18 +--R - 113950cosh(x) + 69260cosh(x) + 72470cosh(x) +--R + +--R 16 14 12 +--R - 106900cosh(x) + 118420cosh(x) - 61560cosh(x) +--R + +--R 10 8 6 +--R 100100cosh(x) - 97880cosh(x) + 140cosh(x) +--R + +--R 4 2 +--R 15120cosh(x) + 15280cosh(x) - 2800 +--R * +--R 8 +--R sinh(x) +--R + +--R 23 21 19 +--R - 54400cosh(x) + 67440cosh(x) - 69760cosh(x) +--R + +--R 17 15 13 +--R 67160cosh(x) + 27520cosh(x) - 10720cosh(x) +--R + +--R 11 9 7 +--R 24320cosh(x) - 46200cosh(x) + 51200cosh(x) +--R + +--R 5 +--R 20800cosh(x) + 9760cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 24 22 20 +--R - 170cosh(x) + 23760cosh(x) - 85620cosh(x) +--R + +--R 18 16 14 +--R 119520cosh(x) - 79910cosh(x) + 81120cosh(x) +--R + +--R 12 10 8 +--R - 31400cosh(x) + 6320cosh(x) + 140cosh(x) +--R + +--R 6 4 2 +--R - 37440cosh(x) - 25760cosh(x) - 20480cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 25 23 21 +--R 17120cosh(x) - 6160cosh(x) - 39200cosh(x) +--R + +--R 19 17 15 +--R 53480cosh(x) - 80240cosh(x) + 124320cosh(x) +--R + +--R 13 11 9 +--R - 96640cosh(x) + 19800cosh(x) - 19840cosh(x) +--R + +--R 7 5 3 +--R 20800cosh(x) + 35200cosh(x) + 31200cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 26 24 22 +--R 12290cosh(x) - 11100cosh(x) - 4180cosh(x) +--R + +--R 20 18 16 +--R - 12920cosh(x) - 13290cosh(x) + 63380cosh(x) +--R + +--R 14 12 10 +--R - 101320cosh(x) + 55920cosh(x) + 3140cosh(x) +--R + +--R 8 6 4 +--R 15120cosh(x) - 25760cosh(x) - 35360cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 27 25 23 +--R 4800cosh(x) - 5880cosh(x) + 4480cosh(x) +--R + +--R 21 19 17 +--R - 26040cosh(x) + 24480cosh(x) - 12600cosh(x) +--R + +--R 15 13 11 +--R - 24320cosh(x) + 49160cosh(x) - 25600cosh(x) +--R + +--R 9 5 +--R - 19680cosh(x) + 31200cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 28 26 24 +--R 1150cosh(x) - 1720cosh(x) + 2490cosh(x) +--R + +--R 22 20 18 +--R - 12960cosh(x) + 19070cosh(x) - 28760cosh(x) +--R + +--R 16 14 12 +--R 28430cosh(x) - 6320cosh(x) - 14900cosh(x) +--R + +--R 10 8 6 +--R 18720cosh(x) + 15280cosh(x) - 20480cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 29 27 25 +--R 160cosh(x) - 280cosh(x) + 560cosh(x) +--R + +--R 23 21 19 +--R - 3080cosh(x) + 5840cosh(x) - 12280cosh(x) +--R + +--R 17 15 13 +--R 20960cosh(x) - 22760cosh(x) + 19840cosh(x) +--R + +--R 11 9 7 +--R - 1120cosh(x) - 17600cosh(x) + 9760cosh(x) +--R * +--R sinh(x) +--R + +--R 30 28 26 24 +--R 10cosh(x) - 20cosh(x) + 50cosh(x) - 300cosh(x) +--R + +--R 22 20 18 16 +--R 690cosh(x) - 1820cosh(x) + 4190cosh(x) - 6980cosh(x) +--R + +--R 14 12 10 8 +--R 11620cosh(x) - 15120cosh(x) + 10480cosh(x) - 2800cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 30 29 +--R - 10sinh(x) - 160cosh(x)sinh(x) +--R + +--R 2 28 +--R (- 1150cosh(x) + 20)sinh(x) +--R + +--R 3 27 +--R (- 4800cosh(x) + 280cosh(x))sinh(x) +--R + +--R 4 2 26 +--R (- 12290cosh(x) + 1720cosh(x) - 50)sinh(x) +--R + +--R 5 3 25 +--R (- 17120cosh(x) + 5880cosh(x) - 560cosh(x))sinh(x) +--R + +--R 6 4 2 24 +--R (170cosh(x) + 11100cosh(x) - 2490cosh(x) + 300)sinh(x) +--R + +--R 7 5 3 +--R (54400cosh(x) + 6160cosh(x) - 4480cosh(x) + 3080cosh(x)) +--R * +--R 23 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 113950cosh(x) - 23760cosh(x) + 4180cosh(x) + 12960cosh(x) +--R + +--R - 690 +--R * +--R 22 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 93280cosh(x) - 67440cosh(x) + 39200cosh(x) + 26040cosh(x) +--R + +--R - 5840cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R 10 8 6 +--R - 60390cosh(x) - 69260cosh(x) + 85620cosh(x) +--R + +--R 4 2 +--R 12920cosh(x) - 19070cosh(x) + 1820 +--R * +--R 20 +--R sinh(x) +--R + +--R 11 9 7 +--R - 256320cosh(x) + 19400cosh(x) + 69760cosh(x) +--R + +--R 5 3 +--R - 53480cosh(x) - 24480cosh(x) + 12280cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 12 10 8 +--R - 295450cosh(x) + 151240cosh(x) - 72470cosh(x) +--R + +--R 6 4 2 +--R - 119520cosh(x) + 13290cosh(x) + 28760cosh(x) - 4190 +--R * +--R 18 +--R sinh(x) +--R + +--R 13 11 9 +--R - 76000cosh(x) + 190760cosh(x) - 264400cosh(x) +--R + +--R 7 5 3 +--R - 67160cosh(x) + 80240cosh(x) + 12600cosh(x) - 20960cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 14 12 10 +--R 255170cosh(x) + 58140cosh(x) - 299710cosh(x) +--R + +--R 8 6 4 +--R 106900cosh(x) + 79910cosh(x) - 63380cosh(x) +--R + +--R 2 +--R - 28430cosh(x) + 6980 +--R * +--R 16 +--R sinh(x) +--R + +--R 15 13 11 +--R 413440cosh(x) - 155040cosh(x) - 65280cosh(x) +--R + +--R 9 7 5 +--R 215760cosh(x) - 27520cosh(x) - 124320cosh(x) +--R + +--R 3 +--R 24320cosh(x) + 22760cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 16 14 12 +--R 255170cosh(x) - 258400cosh(x) + 284920cosh(x) +--R + +--R 10 8 6 +--R 106560cosh(x) - 118420cosh(x) - 81120cosh(x) +--R + +--R 4 2 +--R 101320cosh(x) + 6320cosh(x) - 11620 +--R * +--R 14 +--R sinh(x) +--R + +--R 17 15 13 +--R - 76000cosh(x) - 155040cosh(x) + 451520cosh(x) +--R + +--R 11 9 7 +--R - 124240cosh(x) - 74400cosh(x) + 10720cosh(x) +--R + +--R 5 3 +--R 96640cosh(x) - 49160cosh(x) - 19840cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 18 16 14 +--R - 295450cosh(x) + 58140cosh(x) + 284920cosh(x) +--R + +--R 12 10 8 +--R - 240240cosh(x) + 44980cosh(x) + 61560cosh(x) +--R + +--R 6 4 2 +--R 31400cosh(x) - 55920cosh(x) + 14900cosh(x) + 15120 +--R * +--R 12 +--R sinh(x) +--R + +--R 19 17 15 +--R - 256320cosh(x) + 190760cosh(x) - 65280cosh(x) +--R + +--R 13 11 9 +--R - 124240cosh(x) + 104000cosh(x) + 88720cosh(x) +--R + +--R 7 5 3 +--R - 24320cosh(x) - 19800cosh(x) + 25600cosh(x) + 1120cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 20 18 16 +--R - 60390cosh(x) + 151240cosh(x) - 299710cosh(x) +--R + +--R 14 12 10 +--R 106560cosh(x) + 44980cosh(x) + 104720cosh(x) +--R + +--R 8 6 4 +--R - 100100cosh(x) - 6320cosh(x) - 3140cosh(x) +--R + +--R 2 +--R - 18720cosh(x) - 10480 +--R * +--R 10 +--R sinh(x) +--R + +--R 21 19 17 +--R 93280cosh(x) + 19400cosh(x) - 264400cosh(x) +--R + +--R 15 13 11 +--R 215760cosh(x) - 74400cosh(x) + 88720cosh(x) +--R + +--R 9 7 5 +--R - 151360cosh(x) + 46200cosh(x) + 19840cosh(x) +--R + +--R 3 +--R 19680cosh(x) + 17600cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 22 20 18 +--R 113950cosh(x) - 69260cosh(x) - 72470cosh(x) +--R + +--R 16 14 12 +--R 106900cosh(x) - 118420cosh(x) + 61560cosh(x) +--R + +--R 10 8 6 +--R - 100100cosh(x) + 97880cosh(x) - 140cosh(x) +--R + +--R 4 2 +--R - 15120cosh(x) - 15280cosh(x) + 2800 +--R * +--R 8 +--R sinh(x) +--R + +--R 23 21 19 +--R 54400cosh(x) - 67440cosh(x) + 69760cosh(x) +--R + +--R 17 15 13 +--R - 67160cosh(x) - 27520cosh(x) + 10720cosh(x) +--R + +--R 11 9 7 +--R - 24320cosh(x) + 46200cosh(x) - 51200cosh(x) +--R + +--R 5 +--R - 20800cosh(x) - 9760cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 24 22 20 +--R 170cosh(x) - 23760cosh(x) + 85620cosh(x) +--R + +--R 18 16 14 +--R - 119520cosh(x) + 79910cosh(x) - 81120cosh(x) +--R + +--R 12 10 8 6 +--R 31400cosh(x) - 6320cosh(x) - 140cosh(x) + 37440cosh(x) +--R + +--R 4 2 +--R 25760cosh(x) + 20480cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 25 23 21 +--R - 17120cosh(x) + 6160cosh(x) + 39200cosh(x) +--R + +--R 19 17 15 +--R - 53480cosh(x) + 80240cosh(x) - 124320cosh(x) +--R + +--R 13 11 9 +--R 96640cosh(x) - 19800cosh(x) + 19840cosh(x) +--R + +--R 7 5 3 +--R - 20800cosh(x) - 35200cosh(x) - 31200cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 26 24 22 +--R - 12290cosh(x) + 11100cosh(x) + 4180cosh(x) +--R + +--R 20 18 16 +--R 12920cosh(x) + 13290cosh(x) - 63380cosh(x) +--R + +--R 14 12 10 +--R 101320cosh(x) - 55920cosh(x) - 3140cosh(x) +--R + +--R 8 6 4 +--R - 15120cosh(x) + 25760cosh(x) + 35360cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 27 25 23 +--R - 4800cosh(x) + 5880cosh(x) - 4480cosh(x) +--R + +--R 21 19 17 +--R 26040cosh(x) - 24480cosh(x) + 12600cosh(x) +--R + +--R 15 13 11 +--R 24320cosh(x) - 49160cosh(x) + 25600cosh(x) +--R + +--R 9 5 +--R 19680cosh(x) - 31200cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 28 26 24 +--R - 1150cosh(x) + 1720cosh(x) - 2490cosh(x) +--R + +--R 22 20 18 +--R 12960cosh(x) - 19070cosh(x) + 28760cosh(x) +--R + +--R 16 14 12 +--R - 28430cosh(x) + 6320cosh(x) + 14900cosh(x) +--R + +--R 10 8 6 +--R - 18720cosh(x) - 15280cosh(x) + 20480cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 29 27 25 23 +--R - 160cosh(x) + 280cosh(x) - 560cosh(x) + 3080cosh(x) +--R + +--R 21 19 17 +--R - 5840cosh(x) + 12280cosh(x) - 20960cosh(x) +--R + +--R 15 13 11 +--R 22760cosh(x) - 19840cosh(x) + 1120cosh(x) +--R + +--R 9 7 +--R 17600cosh(x) - 9760cosh(x) +--R * +--R sinh(x) +--R + +--R 30 28 26 24 +--R - 10cosh(x) + 20cosh(x) - 50cosh(x) + 300cosh(x) +--R + +--R 22 20 18 16 +--R - 690cosh(x) + 1820cosh(x) - 4190cosh(x) + 6980cosh(x) +--R + +--R 14 12 10 8 +--R - 11620cosh(x) + 15120cosh(x) - 10480cosh(x) + 2800cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 32 +-+ 31 +--R - 5\|2 sinh(x) - 90\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 30 +--R (- 740\|2 cosh(x) + 5\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 29 +--R (- 3630\|2 cosh(x) + 80\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 28 +--R (- 11520\|2 cosh(x) + 575\|2 cosh(x) + 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 23250\|2 cosh(x) + 2400\|2 cosh(x) + 250\|2 cosh(x)) +--R * +--R 27 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 23180\|2 cosh(x) + 6145\|2 cosh(x) + 1930\|2 cosh(x) +--R + +--R +-+ +--R - 105\|2 +--R * +--R 26 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 18810\|2 cosh(x) + 8560\|2 cosh(x) + 9090\|2 cosh(x) +--R + +--R +-+ +--R - 1460\|2 cosh(x) +--R * +--R 25 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 111460\|2 cosh(x) - 85\|2 cosh(x) + 28805\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 9205\|2 cosh(x) + 475\|2 +--R * +--R 24 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 187790\|2 cosh(x) - 27200\|2 cosh(x) + 63100\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 34400\|2 cosh(x) + 5510\|2 cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 120060\|2 cosh(x) - 56975\|2 cosh(x) + 90980\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 82670\|2 cosh(x) + 28040\|2 cosh(x) - 965\|2 +--R * +--R 22 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 141910\|2 cosh(x) - 46640\|2 cosh(x) + 61020\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 125000\|2 cosh(x) + 80010\|2 cosh(x) - 8960\|2 cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R - 434240\|2 cosh(x) + 30195\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 72425\|2 cosh(x) - 86590\|2 cosh(x) + 129790\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 33875\|2 cosh(x) + 2525\|2 +--R * +--R 20 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +--R - 461610\|2 cosh(x) + 128160\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 276530\|2 cosh(x) + 94240\|2 cosh(x) + 76690\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 58880\|2 cosh(x) + 19230\|2 cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 96140\|2 cosh(x) + 147725\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +--R - 409450\|2 cosh(x) + 364125\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 163160\|2 cosh(x) - 5935\|2 cosh(x) + 57170\|2 cosh(x) +--R + +--R +-+ +--R - 5915\|2 +--R * +--R 18 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +--R 423890\|2 cosh(x) + 38000\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +--R - 309130\|2 cosh(x) + 531060\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 506690\|2 cosh(x) + 200960\|2 cosh(x) + 69550\|2 cosh(x) +--R + +--R +-+ +--R - 35500\|2 cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +--R 668610\|2 cosh(x) - 127585\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 43605\|2 cosh(x) + 394145\|2 cosh(x) - 693035\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 489655\|2 cosh(x) - 29895\|2 cosh(x) - 78955\|2 cosh(x) +--R + +--R +-+ +--R 9890\|2 +--R * +--R 16 +--R sinh(x) +--R + +--R +-+ 17 +-+ 15 +--R 423890\|2 cosh(x) - 206720\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 452200\|2 cosh(x) - 59840\|2 cosh(x) - 478180\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 624640\|2 cosh(x) - 229160\|2 cosh(x) - 63440\|2 cosh(x) +--R + +--R +-+ +--R 42340\|2 cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R +-+ 18 +-+ 16 +--R - 96140\|2 cosh(x) - 127585\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R 633080\|2 cosh(x) - 579700\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 135120\|2 cosh(x) + 394430\|2 cosh(x) - 368360\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 40620\|2 cosh(x) + 57880\|2 cosh(x) - 16440\|2 +--R * +--R 14 +--R sinh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 461610\|2 cosh(x) + 38000\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R 452200\|2 cosh(x) - 809200\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 822660\|2 cosh(x) - 192000\|2 cosh(x) - 290760\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 140880\|2 cosh(x) + 10700\|2 cosh(x) - 44560\|2 cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 20 +-+ 18 +--R - 434240\|2 cosh(x) + 147725\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R 43605\|2 cosh(x) - 579700\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +--R 1125540\|2 cosh(x) - 843310\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 27370\|2 cosh(x) + 155020\|2 cosh(x) - 50360\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 31880\|2 cosh(x) + 21380\|2 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 21 +-+ 19 +--R - 141910\|2 cosh(x) + 128160\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R - 309130\|2 cosh(x) - 59840\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +--R 822660\|2 cosh(x) - 1131520\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 431140\|2 cosh(x) + 63440\|2 cosh(x) - 96700\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 9440\|2 cosh(x) + 22920\|2 cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 22 +-+ 20 +--R 120060\|2 cosh(x) + 30195\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +--R - 409450\|2 cosh(x) + 394145\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R 135120\|2 cosh(x) - 843310\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 622380\|2 cosh(x) - 110770\|2 cosh(x) - 139800\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 2280\|2 cosh(x) + 6840\|2 cosh(x) - 14820\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 23 +-+ 21 +--R 187790\|2 cosh(x) - 46640\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 276530\|2 cosh(x) + 531060\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 478180\|2 cosh(x) - 192000\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 431140\|2 cosh(x) - 210760\|2 cosh(x) - 120180\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 65040\|2 cosh(x) + 34280\|2 cosh(x) + 10080\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 111460\|2 cosh(x) - 56975\|2 cosh(x) - 72425\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +--R 364125\|2 cosh(x) - 693035\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R 394430\|2 cosh(x) + 27370\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 110770\|2 cosh(x) - 82900\|2 cosh(x) + 87000\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 6020\|2 cosh(x) - 18900\|2 cosh(x) + 3960\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 18810\|2 cosh(x) - 27200\|2 cosh(x) + 61020\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R 94240\|2 cosh(x) - 506690\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R 624640\|2 cosh(x) - 290760\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 63440\|2 cosh(x) - 120180\|2 cosh(x) + 59840\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 26480\|2 cosh(x) - 6400\|2 cosh(x) - 9840\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R - 23180\|2 cosh(x) - 85\|2 cosh(x) + 90980\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +--R - 86590\|2 cosh(x) - 163160\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +--R 489655\|2 cosh(x) - 368360\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 155020\|2 cosh(x) - 139800\|2 cosh(x) + 87000\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 17040\|2 cosh(x) + 20920\|2 cosh(x) + 21120\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 27 +-+ 25 +-+ 23 +--R - 23250\|2 cosh(x) + 8560\|2 cosh(x) + 63100\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +--R - 125000\|2 cosh(x) + 76690\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +--R 200960\|2 cosh(x) - 229160\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 140880\|2 cosh(x) - 96700\|2 cosh(x) + 65040\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 26480\|2 cosh(x) - 32960\|2 cosh(x) - 29840\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 28 +-+ 26 +-+ 24 +--R - 11520\|2 cosh(x) + 6145\|2 cosh(x) + 28805\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +--R - 82670\|2 cosh(x) + 129790\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 5935\|2 cosh(x) - 29895\|2 cosh(x) + 40620\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 50360\|2 cosh(x) + 2280\|2 cosh(x) - 6020\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R 20920\|2 cosh(x) + 34320\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R - 3630\|2 cosh(x) + 2400\|2 cosh(x) + 9090\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +--R - 34400\|2 cosh(x) + 80010\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 58880\|2 cosh(x) + 69550\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 63440\|2 cosh(x) + 10700\|2 cosh(x) - 9440\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 34280\|2 cosh(x) - 6400\|2 cosh(x) - 29840\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R - 740\|2 cosh(x) + 575\|2 cosh(x) + 1930\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R - 9205\|2 cosh(x) + 28040\|2 cosh(x) - 33875\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 57170\|2 cosh(x) - 78955\|2 cosh(x) + 57880\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 31880\|2 cosh(x) + 6840\|2 cosh(x) - 18900\|2 cosh(x) +--R + +--R +-+ 6 +--R 21120\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R - 90\|2 cosh(x) + 80\|2 cosh(x) + 250\|2 cosh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R - 1460\|2 cosh(x) + 5510\|2 cosh(x) - 8960\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R 19230\|2 cosh(x) - 35500\|2 cosh(x) + 42340\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 44560\|2 cosh(x) + 22920\|2 cosh(x) + 10080\|2 cosh(x) +--R + +--R +-+ 7 +--R - 9840\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 32 +-+ 30 +-+ 28 +--R - 5\|2 cosh(x) + 5\|2 cosh(x) + 15\|2 cosh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R - 105\|2 cosh(x) + 475\|2 cosh(x) - 965\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R 2525\|2 cosh(x) - 5915\|2 cosh(x) + 9890\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 16440\|2 cosh(x) + 21380\|2 cosh(x) - 14820\|2 cosh(x) +--R + +--R +-+ 8 +--R 3960\|2 cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 32 +-+ 31 +--R 5\|2 sinh(x) + 90\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 30 +--R (740\|2 cosh(x) - 5\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 29 +--R (3630\|2 cosh(x) - 80\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 28 +--R (11520\|2 cosh(x) - 575\|2 cosh(x) - 15\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 27 +--R (23250\|2 cosh(x) - 2400\|2 cosh(x) - 250\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (23180\|2 cosh(x) - 6145\|2 cosh(x) - 1930\|2 cosh(x) + 105\|2 ) +--R * +--R 26 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 18810\|2 cosh(x) - 8560\|2 cosh(x) - 9090\|2 cosh(x) +--R + +--R +-+ +--R 1460\|2 cosh(x) +--R * +--R 25 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 111460\|2 cosh(x) + 85\|2 cosh(x) - 28805\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 9205\|2 cosh(x) - 475\|2 +--R * +--R 24 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 187790\|2 cosh(x) + 27200\|2 cosh(x) - 63100\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 34400\|2 cosh(x) - 5510\|2 cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 120060\|2 cosh(x) + 56975\|2 cosh(x) - 90980\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 82670\|2 cosh(x) - 28040\|2 cosh(x) + 965\|2 +--R * +--R 22 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 141910\|2 cosh(x) + 46640\|2 cosh(x) - 61020\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 125000\|2 cosh(x) - 80010\|2 cosh(x) + 8960\|2 cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 434240\|2 cosh(x) - 30195\|2 cosh(x) + 72425\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 86590\|2 cosh(x) - 129790\|2 cosh(x) + 33875\|2 cosh(x) +--R + +--R +-+ +--R - 2525\|2 +--R * +--R 20 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 461610\|2 cosh(x) - 128160\|2 cosh(x) + 276530\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 94240\|2 cosh(x) - 76690\|2 cosh(x) + 58880\|2 cosh(x) +--R + +--R +-+ +--R - 19230\|2 cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 96140\|2 cosh(x) - 147725\|2 cosh(x) + 409450\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 364125\|2 cosh(x) + 163160\|2 cosh(x) + 5935\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 57170\|2 cosh(x) + 5915\|2 +--R * +--R 18 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 423890\|2 cosh(x) - 38000\|2 cosh(x) + 309130\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 531060\|2 cosh(x) + 506690\|2 cosh(x) - 200960\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 69550\|2 cosh(x) + 35500\|2 cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - 668610\|2 cosh(x) + 127585\|2 cosh(x) - 43605\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 394145\|2 cosh(x) + 693035\|2 cosh(x) - 489655\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 29895\|2 cosh(x) + 78955\|2 cosh(x) - 9890\|2 +--R * +--R 16 +--R sinh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R - 423890\|2 cosh(x) + 206720\|2 cosh(x) - 452200\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 59840\|2 cosh(x) + 478180\|2 cosh(x) - 624640\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 229160\|2 cosh(x) + 63440\|2 cosh(x) - 42340\|2 cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 96140\|2 cosh(x) + 127585\|2 cosh(x) - 633080\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 579700\|2 cosh(x) - 135120\|2 cosh(x) - 394430\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 368360\|2 cosh(x) - 40620\|2 cosh(x) - 57880\|2 cosh(x) +--R + +--R +-+ +--R 16440\|2 +--R * +--R 14 +--R sinh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R 461610\|2 cosh(x) - 38000\|2 cosh(x) - 452200\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 809200\|2 cosh(x) - 822660\|2 cosh(x) + 192000\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 290760\|2 cosh(x) - 140880\|2 cosh(x) - 10700\|2 cosh(x) +--R + +--R +-+ +--R 44560\|2 cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R 434240\|2 cosh(x) - 147725\|2 cosh(x) - 43605\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 579700\|2 cosh(x) - 1125540\|2 cosh(x) + 843310\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 27370\|2 cosh(x) - 155020\|2 cosh(x) + 50360\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 31880\|2 cosh(x) - 21380\|2 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R 141910\|2 cosh(x) - 128160\|2 cosh(x) + 309130\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 59840\|2 cosh(x) - 822660\|2 cosh(x) + 1131520\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 431140\|2 cosh(x) - 63440\|2 cosh(x) + 96700\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 9440\|2 cosh(x) - 22920\|2 cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R - 120060\|2 cosh(x) - 30195\|2 cosh(x) + 409450\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - 394145\|2 cosh(x) - 135120\|2 cosh(x) + 843310\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 622380\|2 cosh(x) + 110770\|2 cosh(x) + 139800\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 2280\|2 cosh(x) - 6840\|2 cosh(x) + 14820\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R - 187790\|2 cosh(x) + 46640\|2 cosh(x) + 276530\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R - 531060\|2 cosh(x) + 478180\|2 cosh(x) + 192000\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 431140\|2 cosh(x) + 210760\|2 cosh(x) + 120180\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 65040\|2 cosh(x) - 34280\|2 cosh(x) - 10080\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R - 111460\|2 cosh(x) + 56975\|2 cosh(x) + 72425\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 364125\|2 cosh(x) + 693035\|2 cosh(x) - 394430\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 27370\|2 cosh(x) + 110770\|2 cosh(x) + 82900\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 87000\|2 cosh(x) + 6020\|2 cosh(x) + 18900\|2 cosh(x) +--R + +--R +-+ +--R - 3960\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R - 18810\|2 cosh(x) + 27200\|2 cosh(x) - 61020\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R - 94240\|2 cosh(x) + 506690\|2 cosh(x) - 624640\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 290760\|2 cosh(x) - 63440\|2 cosh(x) + 120180\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 59840\|2 cosh(x) + 26480\|2 cosh(x) + 6400\|2 cosh(x) +--R + +--R +-+ +--R 9840\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R 23180\|2 cosh(x) + 85\|2 cosh(x) - 90980\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R 86590\|2 cosh(x) + 163160\|2 cosh(x) - 489655\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R 368360\|2 cosh(x) - 155020\|2 cosh(x) + 139800\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 87000\|2 cosh(x) - 17040\|2 cosh(x) - 20920\|2 cosh(x) +--R + +--R +-+ 2 +--R - 21120\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 27 +-+ 25 +-+ 23 +--R 23250\|2 cosh(x) - 8560\|2 cosh(x) - 63100\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R 125000\|2 cosh(x) - 76690\|2 cosh(x) - 200960\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 229160\|2 cosh(x) - 140880\|2 cosh(x) + 96700\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 65040\|2 cosh(x) + 26480\|2 cosh(x) + 32960\|2 cosh(x) +--R + +--R +-+ 3 +--R 29840\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 28 +-+ 26 +-+ 24 +--R 11520\|2 cosh(x) - 6145\|2 cosh(x) - 28805\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 82670\|2 cosh(x) - 129790\|2 cosh(x) + 5935\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R 29895\|2 cosh(x) - 40620\|2 cosh(x) + 50360\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 2280\|2 cosh(x) + 6020\|2 cosh(x) - 20920\|2 cosh(x) +--R + +--R +-+ 4 +--R - 34320\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R 3630\|2 cosh(x) - 2400\|2 cosh(x) - 9090\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 34400\|2 cosh(x) - 80010\|2 cosh(x) + 58880\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R - 69550\|2 cosh(x) + 63440\|2 cosh(x) - 10700\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 9440\|2 cosh(x) - 34280\|2 cosh(x) + 6400\|2 cosh(x) +--R + +--R +-+ 5 +--R 29840\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R 740\|2 cosh(x) - 575\|2 cosh(x) - 1930\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 9205\|2 cosh(x) - 28040\|2 cosh(x) + 33875\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 57170\|2 cosh(x) + 78955\|2 cosh(x) - 57880\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 31880\|2 cosh(x) - 6840\|2 cosh(x) + 18900\|2 cosh(x) +--R + +--R +-+ 6 +--R - 21120\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R 90\|2 cosh(x) - 80\|2 cosh(x) - 250\|2 cosh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 1460\|2 cosh(x) - 5510\|2 cosh(x) + 8960\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R - 19230\|2 cosh(x) + 35500\|2 cosh(x) - 42340\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R 44560\|2 cosh(x) - 22920\|2 cosh(x) - 10080\|2 cosh(x) +--R + +--R +-+ 7 +--R 9840\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 32 +-+ 30 +-+ 28 +-+ 26 +--R 5\|2 cosh(x) - 5\|2 cosh(x) - 15\|2 cosh(x) + 105\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R - 475\|2 cosh(x) + 965\|2 cosh(x) - 2525\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 5915\|2 cosh(x) - 9890\|2 cosh(x) + 16440\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 21380\|2 cosh(x) + 14820\|2 cosh(x) - 3960\|2 cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|coth(x) + 1 +--R / +--R 30 29 2 28 +--R 4sinh(x) + 64cosh(x)sinh(x) + (460cosh(x) - 8)sinh(x) +--R + +--R 3 27 +--R (1920cosh(x) - 112cosh(x))sinh(x) +--R + +--R 4 2 26 +--R (4916cosh(x) - 688cosh(x) + 20)sinh(x) +--R + +--R 5 3 25 +--R (6848cosh(x) - 2352cosh(x) + 224cosh(x))sinh(x) +--R + +--R 6 4 2 24 +--R (- 68cosh(x) - 4440cosh(x) + 996cosh(x) - 120)sinh(x) +--R + +--R 7 5 3 +--R (- 21760cosh(x) - 2464cosh(x) + 1792cosh(x) - 1232cosh(x)) +--R * +--R 23 +--R sinh(x) +--R + +--R 8 6 4 2 +--R - 45580cosh(x) + 9504cosh(x) - 1672cosh(x) - 5184cosh(x) +--R + +--R 276 +--R * +--R 22 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 37312cosh(x) + 26976cosh(x) - 15680cosh(x) - 10416cosh(x) +--R + +--R 2336cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 24156cosh(x) + 27704cosh(x) - 34248cosh(x) - 5168cosh(x) +--R + +--R 2 +--R 7628cosh(x) - 728 +--R * +--R 20 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 102528cosh(x) - 7760cosh(x) - 27904cosh(x) + 21392cosh(x) +--R + +--R 3 +--R 9792cosh(x) - 4912cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 12 10 8 +--R 118180cosh(x) - 60496cosh(x) + 28988cosh(x) +--R + +--R 6 4 2 +--R 47808cosh(x) - 5316cosh(x) - 11504cosh(x) + 1676 +--R * +--R 18 +--R sinh(x) +--R + +--R 13 11 9 +--R 30400cosh(x) - 76304cosh(x) + 105760cosh(x) +--R + +--R 7 5 3 +--R 26864cosh(x) - 32096cosh(x) - 5040cosh(x) + 8384cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 14 12 10 +--R - 102068cosh(x) - 23256cosh(x) + 119884cosh(x) +--R + +--R 8 6 4 2 +--R - 42760cosh(x) - 31964cosh(x) + 25352cosh(x) + 11372cosh(x) +--R + +--R - 2792 +--R * +--R 16 +--R sinh(x) +--R + +--R 15 13 11 +--R - 165376cosh(x) + 62016cosh(x) + 26112cosh(x) +--R + +--R 9 7 5 3 +--R - 86304cosh(x) + 11008cosh(x) + 49728cosh(x) - 9728cosh(x) +--R + +--R - 9104cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 16 14 12 +--R - 102068cosh(x) + 103360cosh(x) - 113968cosh(x) +--R + +--R 10 8 6 +--R - 42624cosh(x) + 47368cosh(x) + 32448cosh(x) +--R + +--R 4 2 +--R - 40528cosh(x) - 2528cosh(x) + 4648 +--R * +--R 14 +--R sinh(x) +--R + +--R 17 15 13 +--R 30400cosh(x) + 62016cosh(x) - 180608cosh(x) +--R + +--R 11 9 7 5 +--R 49696cosh(x) + 29760cosh(x) - 4288cosh(x) - 38656cosh(x) +--R + +--R 3 +--R 19664cosh(x) + 7936cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 18 16 14 +--R 118180cosh(x) - 23256cosh(x) - 113968cosh(x) +--R + +--R 12 10 8 6 +--R 96096cosh(x) - 17992cosh(x) - 24624cosh(x) - 12560cosh(x) +--R + +--R 4 2 +--R 22368cosh(x) - 5960cosh(x) - 6048 +--R * +--R 12 +--R sinh(x) +--R + +--R 19 17 15 +--R 102528cosh(x) - 76304cosh(x) + 26112cosh(x) +--R + +--R 13 11 9 7 +--R 49696cosh(x) - 41600cosh(x) - 35488cosh(x) + 9728cosh(x) +--R + +--R 5 3 +--R 7920cosh(x) - 10240cosh(x) - 448cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 20 18 16 +--R 24156cosh(x) - 60496cosh(x) + 119884cosh(x) +--R + +--R 14 12 10 +--R - 42624cosh(x) - 17992cosh(x) - 41888cosh(x) +--R + +--R 8 6 4 2 +--R 40040cosh(x) + 2528cosh(x) + 1256cosh(x) + 7488cosh(x) + 4192 +--R * +--R 10 +--R sinh(x) +--R + +--R 21 19 17 +--R - 37312cosh(x) - 7760cosh(x) + 105760cosh(x) +--R + +--R 15 13 11 +--R - 86304cosh(x) + 29760cosh(x) - 35488cosh(x) +--R + +--R 9 7 5 3 +--R 60544cosh(x) - 18480cosh(x) - 7936cosh(x) - 7872cosh(x) +--R + +--R - 7040cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 22 20 18 +--R - 45580cosh(x) + 27704cosh(x) + 28988cosh(x) +--R + +--R 16 14 12 +--R - 42760cosh(x) + 47368cosh(x) - 24624cosh(x) +--R + +--R 10 8 6 4 +--R 40040cosh(x) - 39152cosh(x) + 56cosh(x) + 6048cosh(x) +--R + +--R 2 +--R 6112cosh(x) - 1120 +--R * +--R 8 +--R sinh(x) +--R + +--R 23 21 19 +--R - 21760cosh(x) + 26976cosh(x) - 27904cosh(x) +--R + +--R 17 15 13 11 +--R 26864cosh(x) + 11008cosh(x) - 4288cosh(x) + 9728cosh(x) +--R + +--R 9 7 5 +--R - 18480cosh(x) + 20480cosh(x) + 8320cosh(x) + 3904cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 24 22 20 18 +--R - 68cosh(x) + 9504cosh(x) - 34248cosh(x) + 47808cosh(x) +--R + +--R 16 14 12 +--R - 31964cosh(x) + 32448cosh(x) - 12560cosh(x) +--R + +--R 10 8 6 4 +--R 2528cosh(x) + 56cosh(x) - 14976cosh(x) - 10304cosh(x) +--R + +--R 2 +--R - 8192cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 25 23 21 19 +--R 6848cosh(x) - 2464cosh(x) - 15680cosh(x) + 21392cosh(x) +--R + +--R 17 15 13 +--R - 32096cosh(x) + 49728cosh(x) - 38656cosh(x) +--R + +--R 11 9 7 5 +--R 7920cosh(x) - 7936cosh(x) + 8320cosh(x) + 14080cosh(x) +--R + +--R 3 +--R 12480cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 26 24 22 20 +--R 4916cosh(x) - 4440cosh(x) - 1672cosh(x) - 5168cosh(x) +--R + +--R 18 16 14 +--R - 5316cosh(x) + 25352cosh(x) - 40528cosh(x) +--R + +--R 12 10 8 6 +--R 22368cosh(x) + 1256cosh(x) + 6048cosh(x) - 10304cosh(x) +--R + +--R 4 +--R - 14144cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 27 25 23 21 +--R 1920cosh(x) - 2352cosh(x) + 1792cosh(x) - 10416cosh(x) +--R + +--R 19 17 15 13 +--R 9792cosh(x) - 5040cosh(x) - 9728cosh(x) + 19664cosh(x) +--R + +--R 11 9 5 +--R - 10240cosh(x) - 7872cosh(x) + 12480cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 28 26 24 22 +--R 460cosh(x) - 688cosh(x) + 996cosh(x) - 5184cosh(x) +--R + +--R 20 18 16 14 +--R 7628cosh(x) - 11504cosh(x) + 11372cosh(x) - 2528cosh(x) +--R + +--R 12 10 8 6 +--R - 5960cosh(x) + 7488cosh(x) + 6112cosh(x) - 8192cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 29 27 25 23 +--R 64cosh(x) - 112cosh(x) + 224cosh(x) - 1232cosh(x) +--R + +--R 21 19 17 15 +--R 2336cosh(x) - 4912cosh(x) + 8384cosh(x) - 9104cosh(x) +--R + +--R 13 11 9 7 +--R 7936cosh(x) - 448cosh(x) - 7040cosh(x) + 3904cosh(x) +--R * +--R sinh(x) +--R + +--R 30 28 26 24 22 +--R 4cosh(x) - 8cosh(x) + 20cosh(x) - 120cosh(x) + 276cosh(x) +--R + +--R 20 18 16 14 +--R - 728cosh(x) + 1676cosh(x) - 2792cosh(x) + 4648cosh(x) +--R + +--R 12 10 8 +--R - 6048cosh(x) + 4192cosh(x) - 1120cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 4sinh(x) + 4cosh(x) +--R tanh(x) |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ 32 +-+ 31 +--R - 2\|2 sinh(x) - 36\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 30 +--R (- 296\|2 cosh(x) + 2\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 29 +--R (- 1452\|2 cosh(x) + 32\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 28 +--R (- 4608\|2 cosh(x) + 230\|2 cosh(x) + 6\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 27 +--R (- 9300\|2 cosh(x) + 960\|2 cosh(x) + 100\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 9272\|2 cosh(x) + 2458\|2 cosh(x) + 772\|2 cosh(x) +--R + +--R +-+ +--R - 42\|2 +--R * +--R 26 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 7524\|2 cosh(x) + 3424\|2 cosh(x) + 3636\|2 cosh(x) +--R + +--R +-+ +--R - 584\|2 cosh(x) +--R * +--R 25 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 44584\|2 cosh(x) - 34\|2 cosh(x) + 11522\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 3682\|2 cosh(x) + 190\|2 +--R * +--R 24 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 75116\|2 cosh(x) - 10880\|2 cosh(x) + 25240\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R - 13760\|2 cosh(x) + 2204\|2 cosh(x) +--R * +--R 23 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 48024\|2 cosh(x) - 22790\|2 cosh(x) + 36392\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 33068\|2 cosh(x) + 11216\|2 cosh(x) - 386\|2 +--R * +--R 22 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 56764\|2 cosh(x) - 18656\|2 cosh(x) + 24408\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 50000\|2 cosh(x) + 32004\|2 cosh(x) - 3584\|2 cosh(x) +--R * +--R 21 +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 173696\|2 cosh(x) + 12078\|2 cosh(x) - 28970\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 34636\|2 cosh(x) + 51916\|2 cosh(x) - 13550\|2 cosh(x) +--R + +--R +-+ +--R 1010\|2 +--R * +--R 20 +--R sinh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 184644\|2 cosh(x) + 51264\|2 cosh(x) - 110612\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 37696\|2 cosh(x) + 30676\|2 cosh(x) - 23552\|2 cosh(x) +--R + +--R +-+ +--R 7692\|2 cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 38456\|2 cosh(x) + 59090\|2 cosh(x) - 163780\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 145650\|2 cosh(x) - 65264\|2 cosh(x) - 2374\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 22868\|2 cosh(x) - 2366\|2 +--R * +--R 18 +--R sinh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 169556\|2 cosh(x) + 15200\|2 cosh(x) - 123652\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 212424\|2 cosh(x) - 202676\|2 cosh(x) + 80384\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 27820\|2 cosh(x) - 14200\|2 cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R 267444\|2 cosh(x) - 51034\|2 cosh(x) + 17442\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 157658\|2 cosh(x) - 277214\|2 cosh(x) + 195862\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 11958\|2 cosh(x) - 31582\|2 cosh(x) + 3956\|2 +--R * +--R 16 +--R sinh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R 169556\|2 cosh(x) - 82688\|2 cosh(x) + 180880\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 23936\|2 cosh(x) - 191272\|2 cosh(x) + 249856\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 91664\|2 cosh(x) - 25376\|2 cosh(x) + 16936\|2 cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R - 38456\|2 cosh(x) - 51034\|2 cosh(x) + 253232\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 231880\|2 cosh(x) + 54048\|2 cosh(x) + 157772\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 147344\|2 cosh(x) + 16248\|2 cosh(x) + 23152\|2 cosh(x) +--R + +--R +-+ +--R - 6576\|2 +--R * +--R 14 +--R sinh(x) +--R + +--R +-+ 19 +-+ 17 +--R - 184644\|2 cosh(x) + 15200\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 180880\|2 cosh(x) - 323680\|2 cosh(x) + 329064\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 76800\|2 cosh(x) - 116304\|2 cosh(x) + 56352\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R 4280\|2 cosh(x) - 17824\|2 cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R - 173696\|2 cosh(x) + 59090\|2 cosh(x) + 17442\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +--R - 231880\|2 cosh(x) + 450216\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R - 337324\|2 cosh(x) + 10948\|2 cosh(x) + 62008\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 20144\|2 cosh(x) - 12752\|2 cosh(x) + 8552\|2 +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R - 56764\|2 cosh(x) + 51264\|2 cosh(x) - 123652\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +--R - 23936\|2 cosh(x) + 329064\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 452608\|2 cosh(x) + 172456\|2 cosh(x) + 25376\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 38680\|2 cosh(x) - 3776\|2 cosh(x) + 9168\|2 cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R 48024\|2 cosh(x) + 12078\|2 cosh(x) - 163780\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R 157658\|2 cosh(x) + 54048\|2 cosh(x) - 337324\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 248952\|2 cosh(x) - 44308\|2 cosh(x) - 55920\|2 cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 912\|2 cosh(x) + 2736\|2 cosh(x) - 5928\|2 +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R 75116\|2 cosh(x) - 18656\|2 cosh(x) - 110612\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R 212424\|2 cosh(x) - 191272\|2 cosh(x) - 76800\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 172456\|2 cosh(x) - 84304\|2 cosh(x) - 48072\|2 cosh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 26016\|2 cosh(x) + 13712\|2 cosh(x) + 4032\|2 cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R 44584\|2 cosh(x) - 22790\|2 cosh(x) - 28970\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 145650\|2 cosh(x) - 277214\|2 cosh(x) + 157772\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 10948\|2 cosh(x) - 44308\|2 cosh(x) - 33160\|2 cosh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 34800\|2 cosh(x) - 2408\|2 cosh(x) - 7560\|2 cosh(x) +--R + +--R +-+ +--R 1584\|2 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 7524\|2 cosh(x) - 10880\|2 cosh(x) + 24408\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R 37696\|2 cosh(x) - 202676\|2 cosh(x) + 249856\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 116304\|2 cosh(x) + 25376\|2 cosh(x) - 48072\|2 cosh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 23936\|2 cosh(x) - 10592\|2 cosh(x) - 2560\|2 cosh(x) +--R + +--R +-+ +--R - 3936\|2 cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R - 9272\|2 cosh(x) - 34\|2 cosh(x) + 36392\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R - 34636\|2 cosh(x) - 65264\|2 cosh(x) + 195862\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 147344\|2 cosh(x) + 62008\|2 cosh(x) - 55920\|2 cosh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 34800\|2 cosh(x) + 6816\|2 cosh(x) + 8368\|2 cosh(x) +--R + +--R +-+ 2 +--R 8448\|2 cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 27 +-+ 25 +-+ 23 +--R - 9300\|2 cosh(x) + 3424\|2 cosh(x) + 25240\|2 cosh(x) +--R + +--R +-+ 21 +-+ 19 +-+ 17 +--R - 50000\|2 cosh(x) + 30676\|2 cosh(x) + 80384\|2 cosh(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R - 91664\|2 cosh(x) + 56352\|2 cosh(x) - 38680\|2 cosh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 26016\|2 cosh(x) - 10592\|2 cosh(x) - 13184\|2 cosh(x) +--R + +--R +-+ 3 +--R - 11936\|2 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 28 +-+ 26 +-+ 24 +--R - 4608\|2 cosh(x) + 2458\|2 cosh(x) + 11522\|2 cosh(x) +--R + +--R +-+ 22 +-+ 20 +-+ 18 +--R - 33068\|2 cosh(x) + 51916\|2 cosh(x) - 2374\|2 cosh(x) +--R + +--R +-+ 16 +-+ 14 +-+ 12 +--R - 11958\|2 cosh(x) + 16248\|2 cosh(x) - 20144\|2 cosh(x) +--R + +--R +-+ 10 +-+ 8 +-+ 6 +--R 912\|2 cosh(x) - 2408\|2 cosh(x) + 8368\|2 cosh(x) +--R + +--R +-+ 4 +--R 13728\|2 cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 29 +-+ 27 +-+ 25 +--R - 1452\|2 cosh(x) + 960\|2 cosh(x) + 3636\|2 cosh(x) +--R + +--R +-+ 23 +-+ 21 +-+ 19 +--R - 13760\|2 cosh(x) + 32004\|2 cosh(x) - 23552\|2 cosh(x) +--R + +--R +-+ 17 +-+ 15 +-+ 13 +--R 27820\|2 cosh(x) - 25376\|2 cosh(x) + 4280\|2 cosh(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R - 3776\|2 cosh(x) + 13712\|2 cosh(x) - 2560\|2 cosh(x) +--R + +--R +-+ 5 +--R - 11936\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 30 +-+ 28 +-+ 26 +--R - 296\|2 cosh(x) + 230\|2 cosh(x) + 772\|2 cosh(x) +--R + +--R +-+ 24 +-+ 22 +-+ 20 +--R - 3682\|2 cosh(x) + 11216\|2 cosh(x) - 13550\|2 cosh(x) +--R + +--R +-+ 18 +-+ 16 +-+ 14 +--R 22868\|2 cosh(x) - 31582\|2 cosh(x) + 23152\|2 cosh(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 12752\|2 cosh(x) + 2736\|2 cosh(x) - 7560\|2 cosh(x) +--R + +--R +-+ 6 +--R 8448\|2 cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R - 36\|2 cosh(x) + 32\|2 cosh(x) + 100\|2 cosh(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R - 584\|2 cosh(x) + 2204\|2 cosh(x) - 3584\|2 cosh(x) +--R + +--R +-+ 19 +-+ 17 +-+ 15 +--R 7692\|2 cosh(x) - 14200\|2 cosh(x) + 16936\|2 cosh(x) +--R + +--R +-+ 13 +-+ 11 +-+ 9 +--R - 17824\|2 cosh(x) + 9168\|2 cosh(x) + 4032\|2 cosh(x) +--R + +--R +-+ 7 +--R - 3936\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 32 +-+ 30 +-+ 28 +--R - 2\|2 cosh(x) + 2\|2 cosh(x) + 6\|2 cosh(x) +--R + +--R +-+ 26 +-+ 24 +-+ 22 +--R - 42\|2 cosh(x) + 190\|2 cosh(x) - 386\|2 cosh(x) +--R + +--R +-+ 20 +-+ 18 +-+ 16 +--R 1010\|2 cosh(x) - 2366\|2 cosh(x) + 3956\|2 cosh(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 6576\|2 cosh(x) + 8552\|2 cosh(x) - 5928\|2 cosh(x) +--R + +--R +-+ 8 +--R 1584\|2 cosh(x) +--R * +--R tanh(x) +--R * +--R +------------+ +------------+ +--R | 2 | 2 +--R \|coth(x) + 1 \|tanh(x) + 1 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 508 +t0362:= (-1+coth(x)^2)^(3/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (281) (coth(x) - 1)\|coth(x) - 1 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 508 +r0362:= 1/2*(csch(x)^2)^(1/2)*(acoth(cosh(x))-coth(x)*csch(x))*sinh(x) +--R +--R +--R +--------+ +--R | 2 +--R (sinh(x)acoth(cosh(x)) - coth(x)csch(x)sinh(x))\|csch(x) +--R (282) ---------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 318 + +--S 319 of 508 +a0362:= integrate(t0362,x) +--R +--R +--R (283) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - cosh(x) + 2cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 2 2 3 +--R - 2sinh(x) - 6cosh(x)sinh(x) + (- 6cosh(x) - 2)sinh(x) - 2cosh(x) +--R + +--R - 2cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 508 +m0362:= a0362-r0362 +--R +--R +--R (284) +--R 5 4 2 3 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 2 +--R (- cosh(x) + 2cosh(x) - 1)sinh(x) +--R * +--R acoth(cosh(x)) +--R + +--R 5 4 +--R coth(x)csch(x)sinh(x) + 4cosh(x)coth(x)csch(x)sinh(x) +--R + +--R 2 3 +--R (6cosh(x) - 2)coth(x)csch(x)sinh(x) +--R + +--R 3 2 +--R (4cosh(x) - 4cosh(x))coth(x)csch(x)sinh(x) +--R + +--R 4 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x)csch(x)sinh(x) +--R * +--R +--------+ +--R | 2 +--R \|csch(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - cosh(x) + 2cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 2 2 3 +--R - 2sinh(x) - 6cosh(x)sinh(x) + (- 6cosh(x) - 2)sinh(x) - 2cosh(x) +--R + +--R - 2cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 508 +d0362:= D(m0362,x) +--R +--R +--R (285) +--R 2 3 3 2 +--R (16cosh(x) - 16)sinh(x) + (48cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (48cosh(x) - 48cosh(x) )sinh(x) + 16cosh(x) - 16cosh(x) +--R * +--R +--------+ +--R | 2 +--R \|csch(x) +--R + +--R 2 2 7 +--R (cosh(x) - 1)coth(x)csch(x) sinh(x) +--R + +--R 3 3 2 6 +--R ((6cosh(x) - 6cosh(x))coth(x) - cosh(x) + cosh(x))csch(x) sinh(x) +--R + +--R 4 2 4 2 +--R ((15cosh(x) - 18cosh(x) + 3)coth(x) - 6cosh(x) + 6cosh(x) ) +--R * +--R 2 5 +--R csch(x) sinh(x) +--R + +--R 5 3 5 +--R (20cosh(x) - 32cosh(x) + 12cosh(x))coth(x) - 15cosh(x) +--R + +--R 3 +--R 18cosh(x) - 3cosh(x) +--R * +--R 2 4 +--R csch(x) sinh(x) +--R + +--R 6 4 2 6 +--R (15cosh(x) - 33cosh(x) + 21cosh(x) - 3)coth(x) - 20cosh(x) +--R + +--R 4 2 +--R 32cosh(x) - 12cosh(x) +--R * +--R 2 3 +--R csch(x) sinh(x) +--R + +--R 7 5 3 +--R (6cosh(x) - 18cosh(x) + 18cosh(x) - 6cosh(x))coth(x) +--R + +--R 7 5 3 +--R - 15cosh(x) + 33cosh(x) - 21cosh(x) + 3cosh(x) +--R * +--R 2 2 +--R csch(x) sinh(x) +--R + +--R 8 6 4 2 +--R (cosh(x) - 4cosh(x) + 6cosh(x) - 4cosh(x) + 1)coth(x) +--R + +--R 8 6 4 2 +--R - 6cosh(x) + 18cosh(x) - 18cosh(x) + 6cosh(x) +--R * +--R 2 +--R csch(x) sinh(x) +--R + +--R 9 7 5 3 2 +--R (- cosh(x) + 4cosh(x) - 6cosh(x) + 4cosh(x) - cosh(x))csch(x) +--R * +--R acoth(cosh(x)) +--R + +--R 2 8 +--R csch(x) sinh(x) +--R + +--R 2 2 2 3 2 +--R (((- 3cosh(x) + 3)coth(x) + cosh(x) - 1)csch(x) + 6cosh(x)csch(x) ) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 3 +--R (- 18cosh(x) + 18cosh(x))coth(x) + (cosh(x) - cosh(x))coth(x) +--R + +--R 3 +--R 6cosh(x) - 6cosh(x) +--R * +--R 3 +--R csch(x) +--R + +--R 2 2 +--R (15cosh(x) - 3)csch(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) + 54cosh(x) - 9)coth(x) +--R + +--R 4 2 4 2 +--R (6cosh(x) - 6cosh(x) )coth(x) + 15cosh(x) - 18cosh(x) + 3 +--R * +--R 3 +--R csch(x) +--R + +--R 3 2 +--R (20cosh(x) - 12cosh(x))csch(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 60cosh(x) + 96cosh(x) - 36cosh(x))coth(x) +--R + +--R 5 3 5 +--R (15cosh(x) - 18cosh(x) + 3cosh(x))coth(x) + 20cosh(x) +--R + +--R 3 +--R - 32cosh(x) + 12cosh(x) +--R * +--R 3 +--R csch(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 18cosh(x) + 3)csch(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 45cosh(x) + 99cosh(x) - 63cosh(x) + 9)coth(x) +--R + +--R 6 4 2 6 +--R (20cosh(x) - 32cosh(x) + 12cosh(x) )coth(x) + 15cosh(x) +--R + +--R 4 2 +--R - 33cosh(x) + 21cosh(x) - 3 +--R * +--R 3 +--R csch(x) +--R + +--R 5 3 2 +--R (6cosh(x) - 12cosh(x) + 6cosh(x))csch(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (- 18cosh(x) + 54cosh(x) - 54cosh(x) + 18cosh(x))coth(x) +--R + +--R 7 5 3 +--R (15cosh(x) - 33cosh(x) + 21cosh(x) - 3cosh(x))coth(x) +--R + +--R 7 5 3 +--R 6cosh(x) - 18cosh(x) + 18cosh(x) - 6cosh(x) +--R * +--R 3 +--R csch(x) +--R + +--R 6 4 2 2 +--R (cosh(x) - 3cosh(x) + 3cosh(x) - 1)csch(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 3cosh(x) + 12cosh(x) - 18cosh(x) + 12cosh(x) - 3)coth(x) +--R + +--R 8 6 4 2 8 +--R (6cosh(x) - 18cosh(x) + 18cosh(x) - 6cosh(x) )coth(x) + cosh(x) +--R + +--R 6 4 2 +--R - 4cosh(x) + 6cosh(x) - 4cosh(x) + 1 +--R * +--R 3 +--R csch(x) sinh(x) +--R + +--R 9 7 5 3 3 +--R (cosh(x) - 4cosh(x) + 6cosh(x) - 4cosh(x) + cosh(x))coth(x)csch(x) +--R / +--R 2 6 3 5 +--R (2cosh(x) - 2)sinh(x) + (12cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (30cosh(x) - 36cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (40cosh(x) - 64cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (30cosh(x) - 66cosh(x) + 42cosh(x) - 6)sinh(x) +--R + +--R 7 5 3 8 +--R (12cosh(x) - 36cosh(x) + 36cosh(x) - 12cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) + 12cosh(x) - 8cosh(x) + 2 +--R * +--R +--------+ +--R | 2 +--R \|csch(x) +--R Type: Expression(Integer) +--E 321 + +--S 322 of 508 +t0363:= (-1-coth(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (286) (- coth(x) - 1)\|- coth(x) - 1 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 508 +r0363:= 2*2^(1/2)*atan(2^(1/2)*coth(x)/(-1-coth(x)^2)^(1/2))+_ + 5/2*atan((-1-coth(x)^2)^(1/2)*tanh(x))+1/2*coth(x)*(-1-coth(x)^2)^(1/2) +--R +--R +--R (287) +--R +--------------+ +-+ +--R | 2 +-+ \|2 coth(x) +--R 5atan(tanh(x)\|- coth(x) - 1 ) + 4\|2 atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R + +--R +--------------+ +--R | 2 +--R coth(x)\|- coth(x) - 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 508 +a0363:= integrate(t0363,x) +--R +--R +--R (288) +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 +--R (10\|- 1 (%e ) - 20\|- 1 (%e ) + 10\|- 1 )\|- 2(%e ) - 2 +--R + +--R +---+ +---+ x 8 +---+ +---+ x 6 +---+ +---+ x 4 +--R - 5\|- 2 \|- 1 (%e ) + 10\|- 2 \|- 1 (%e ) - 15\|- 2 \|- 1 (%e ) +--R + +--R +---+ +---+ x 2 +---+ +---+ +--R 20\|- 2 \|- 1 (%e ) - 10\|- 2 \|- 1 +--R * +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R \|- 2 \|- 2(%e ) - 2 + (2\|- 2 \|- 1 - 2)(%e ) + 2 +--R log(------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 x 8 +--R (- 4\|- 2 (%e ) + 8\|- 2 (%e ) - 4\|- 2 )\|- 2(%e ) - 2 - 4(%e ) +--R + +--R x 6 x 4 x 2 +--R 8(%e ) - 12(%e ) + 16(%e ) - 8 +--R * +--R +-------------+ +--R +---+ | x 4 x 2 +--R \|- 2 \|- 2(%e ) - 2 - 2(%e ) + 2 +--R log(------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 +--R (- 10\|- 1 (%e ) + 20\|- 1 (%e ) - 10\|- 1 )\|- 2(%e ) - 2 +--R + +--R +---+ +---+ x 8 +---+ +---+ x 6 +---+ +---+ x 4 +--R 5\|- 2 \|- 1 (%e ) - 10\|- 2 \|- 1 (%e ) + 15\|- 2 \|- 1 (%e ) +--R + +--R +---+ +---+ x 2 +---+ +---+ +--R - 20\|- 2 \|- 1 (%e ) + 10\|- 2 \|- 1 +--R * +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R \|- 2 \|- 2(%e ) - 2 + (- 2\|- 2 \|- 1 - 2)(%e ) + 2 +--R log(--------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 x 8 +--R (4\|- 2 (%e ) - 8\|- 2 (%e ) + 4\|- 2 )\|- 2(%e ) - 2 + 4(%e ) +--R + +--R x 6 x 4 x 2 +--R - 8(%e ) + 12(%e ) - 16(%e ) + 8 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +---+ x 2 +--R (2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) - 2\|- 2 (%e ) +--R + +--R +---+ +--R - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 6 +---+ x 4 +---+ x 2 | x 4 x 8 +--R (- \|- 2 (%e ) + \|- 2 (%e ) - 6\|- 2 (%e ) )\|- 2(%e ) - 2 + 2(%e ) +--R + +--R x 6 x 4 x 2 +--R - 8(%e ) + 2(%e ) - 12(%e ) +--R / +--R +-------------+ +--R x 4 x 2 | x 4 +---+ x 8 +---+ x 6 +--R (4(%e ) - 8(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) + 4\|- 2 (%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R - 6\|- 2 (%e ) + 8\|- 2 (%e ) - 4\|- 2 +--R Type: Union(Expression(Integer),...) +--E 324 + +--S 325 of 508 +m0363:= a0363-r0363 +--R +--R +--R (289) +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 +--R (10\|- 1 (%e ) - 20\|- 1 (%e ) + 10\|- 1 )\|- 2(%e ) - 2 +--R + +--R +---+ +---+ x 8 +---+ +---+ x 6 +---+ +---+ x 4 +--R - 5\|- 2 \|- 1 (%e ) + 10\|- 2 \|- 1 (%e ) - 15\|- 2 \|- 1 (%e ) +--R + +--R +---+ +---+ x 2 +---+ +---+ +--R 20\|- 2 \|- 1 (%e ) - 10\|- 2 \|- 1 +--R * +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R \|- 2 \|- 2(%e ) - 2 + (2\|- 2 \|- 1 - 2)(%e ) + 2 +--R log(------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 x 8 +--R (- 4\|- 2 (%e ) + 8\|- 2 (%e ) - 4\|- 2 )\|- 2(%e ) - 2 - 4(%e ) +--R + +--R x 6 x 4 x 2 +--R 8(%e ) - 12(%e ) + 16(%e ) - 8 +--R * +--R +-------------+ +--R +---+ | x 4 x 2 +--R \|- 2 \|- 2(%e ) - 2 - 2(%e ) + 2 +--R log(------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 +--R (- 10\|- 1 (%e ) + 20\|- 1 (%e ) - 10\|- 1 )\|- 2(%e ) - 2 +--R + +--R +---+ +---+ x 8 +---+ +---+ x 6 +---+ +---+ x 4 +--R 5\|- 2 \|- 1 (%e ) - 10\|- 2 \|- 1 (%e ) + 15\|- 2 \|- 1 (%e ) +--R + +--R +---+ +---+ x 2 +---+ +---+ +--R - 20\|- 2 \|- 1 (%e ) + 10\|- 2 \|- 1 +--R * +--R +-------------+ +--R +---+ | x 4 +---+ +---+ x 2 +--R \|- 2 \|- 2(%e ) - 2 + (- 2\|- 2 \|- 1 - 2)(%e ) + 2 +--R log(--------------------------------------------------------) +--R +---+ x 2 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R +---+ x 4 +---+ x 2 +---+ | x 4 x 8 +--R (4\|- 2 (%e ) - 8\|- 2 (%e ) + 4\|- 2 )\|- 2(%e ) - 2 + 4(%e ) +--R + +--R x 6 x 4 x 2 +--R - 8(%e ) + 12(%e ) - 16(%e ) + 8 +--R * +--R log +--R +-------------+ +--R x 2 | x 4 +---+ x 4 +---+ x 2 +--R (2(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) - 2\|- 2 (%e ) +--R + +--R +---+ +--R - 4\|- 2 +--R / +--R +---+ x 4 +--R \|- 2 (%e ) +--R + +--R +-------------+ +--R x 4 x 2 | x 4 +---+ x 8 +--R (- 10(%e ) + 20(%e ) - 10)\|- 2(%e ) - 2 + 5\|- 2 (%e ) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R - 10\|- 2 (%e ) + 15\|- 2 (%e ) - 20\|- 2 (%e ) + 10\|- 2 +--R * +--R +--------------+ +--R | 2 +--R atan(tanh(x)\|- coth(x) - 1 ) +--R + +--R +-------------+ +--R +-+ x 4 +-+ x 2 +-+ | x 4 +--R (- 8\|2 (%e ) + 16\|2 (%e ) - 8\|2 )\|- 2(%e ) - 2 +--R + +--R +---+ +-+ x 8 +---+ +-+ x 6 +---+ +-+ x 4 +--R 4\|- 2 \|2 (%e ) - 8\|- 2 \|2 (%e ) + 12\|- 2 \|2 (%e ) +--R + +--R +---+ +-+ x 2 +---+ +-+ +--R - 16\|- 2 \|2 (%e ) + 8\|- 2 \|2 +--R * +--R +-+ +--R \|2 coth(x) +--R atan(-----------------) +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R + +--R +-------------+ +--R x 4 x 2 | x 4 +--R (- 2coth(x)(%e ) + 4coth(x)(%e ) - 2coth(x))\|- 2(%e ) - 2 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +--R \|- 2 coth(x)(%e ) - 2\|- 2 coth(x)(%e ) + 3\|- 2 coth(x)(%e ) +--R + +--R +---+ x 2 +---+ +--R - 4\|- 2 coth(x)(%e ) + 2\|- 2 coth(x) +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R + +--R +-------------+ +--R +---+ x 6 +---+ x 4 +---+ x 2 | x 4 x 8 +--R (- \|- 2 (%e ) + \|- 2 (%e ) - 6\|- 2 (%e ) )\|- 2(%e ) - 2 + 2(%e ) +--R + +--R x 6 x 4 x 2 +--R - 8(%e ) + 2(%e ) - 12(%e ) +--R / +--R +-------------+ +--R x 4 x 2 | x 4 +---+ x 8 +---+ x 6 +--R (4(%e ) - 8(%e ) + 4)\|- 2(%e ) - 2 - 2\|- 2 (%e ) + 4\|- 2 (%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R - 6\|- 2 (%e ) + 8\|- 2 (%e ) - 4\|- 2 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 508 +d0363:= D(m0363,x) +--R +--R +--R (290) +--R +---+ 2 +---+ x 16 +--R (28\|- 2 coth(x) + 28\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (252\|- 2 coth(x) + 252\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (672\|- 2 coth(x) + 672\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +---+ 2 +--R (704\|- 2 coth(x) + 704\|- 2 )(%e ) + 256\|- 2 coth(x) +--R + +--R +---+ +--R 256\|- 2 +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ x 16 +---+ x 12 +---+ x 8 +--R - 28\|- 2 (%e ) - 252\|- 2 (%e ) - 672\|- 2 (%e ) +--R + +--R +---+ x 4 +---+ +--R - 704\|- 2 (%e ) - 256\|- 2 +--R * +--R +-------------+ +--R | x 4 +--R \|- 2(%e ) - 2 +--R + +--R 2 x 20 2 x 16 +--R (8coth(x) + 8)(%e ) + (208coth(x) + 208)(%e ) +--R + +--R 2 x 12 2 x 8 +--R (1032coth(x) + 1032)(%e ) + (1984coth(x) + 1984)(%e ) +--R + +--R 2 x 4 2 +--R (1664coth(x) + 1664)(%e ) + 512coth(x) + 512 +--R * +--R 2 +--R tanh(x) +--R + +--R x 20 x 16 x 12 x 8 x 4 +--R - 8(%e ) - 208(%e ) - 1032(%e ) - 1984(%e ) - 1664(%e ) - 512 +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R + +--R 6 4 2 x 18 +--R (- 2coth(x) - coth(x) - coth(x) - 2)(%e ) +--R + +--R 6 4 2 x 16 +--R (6coth(x) + 3coth(x) + 3coth(x) + 6)(%e ) +--R + +--R 6 4 2 x 14 +--R (- 54coth(x) - 27coth(x) - 27coth(x) - 54)(%e ) +--R + +--R 6 4 2 x 12 +--R (146coth(x) + 73coth(x) + 73coth(x) + 146)(%e ) +--R + +--R 6 4 2 x 10 +--R (- 304coth(x) - 152coth(x) - 152coth(x) - 304)(%e ) +--R + +--R 6 4 2 x 8 +--R (528coth(x) + 264coth(x) + 264coth(x) + 528)(%e ) +--R + +--R 6 4 2 x 6 +--R (- 608coth(x) - 304coth(x) - 304coth(x) - 608)(%e ) +--R + +--R 6 4 2 x 4 +--R (544coth(x) + 272coth(x) + 272coth(x) + 544)(%e ) +--R + +--R 6 4 2 x 2 +--R (- 384coth(x) - 192coth(x) - 192coth(x) - 384)(%e ) +--R + +--R 6 4 2 +--R 128coth(x) + 64coth(x) + 64coth(x) + 128 +--R * +--R 2 +--R tanh(x) +--R + +--R 3 x 18 3 x 16 +--R (5coth(x) - 5coth(x))(%e ) + (- 15coth(x) + 15coth(x))(%e ) +--R + +--R 3 x 14 +--R (135coth(x) - 135coth(x))(%e ) +--R + +--R 3 x 12 +--R (- 365coth(x) + 365coth(x))(%e ) +--R + +--R 3 x 10 +--R (760coth(x) - 760coth(x))(%e ) +--R + +--R 3 x 8 +--R (- 1320coth(x) + 1320coth(x))(%e ) +--R + +--R 3 x 6 +--R (1520coth(x) - 1520coth(x))(%e ) +--R + +--R 3 x 4 +--R (- 1360coth(x) + 1360coth(x))(%e ) +--R + +--R 3 x 2 3 +--R (960coth(x) - 960coth(x))(%e ) - 320coth(x) + 320coth(x) +--R * +--R tanh(x) +--R + +--R 4 2 x 18 +--R (2coth(x) - 6coth(x) + 2)(%e ) +--R + +--R 4 2 x 16 +--R (- 6coth(x) + 18coth(x) - 6)(%e ) +--R + +--R 4 2 x 14 +--R (54coth(x) - 162coth(x) + 54)(%e ) +--R + +--R 4 2 x 12 +--R (- 146coth(x) + 438coth(x) - 146)(%e ) +--R + +--R 4 2 x 10 +--R (304coth(x) - 912coth(x) + 304)(%e ) +--R + +--R 4 2 x 8 +--R (- 528coth(x) + 1584coth(x) - 528)(%e ) +--R + +--R 4 2 x 6 +--R (608coth(x) - 1824coth(x) + 608)(%e ) +--R + +--R 4 2 x 4 +--R (- 544coth(x) + 1632coth(x) - 544)(%e ) +--R + +--R 4 2 x 2 4 2 +--R (384coth(x) - 1152coth(x) + 384)(%e ) - 128coth(x) + 384coth(x) +--R + +--R - 128 +--R * +--R +-------------+ +--R | x 4 +--R \|- 2(%e ) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +---+ +--R (14\|- 2 coth(x) + 7\|- 2 coth(x) + 7\|- 2 coth(x) + 14\|- 2 ) +--R * +--R x 18 +--R (%e ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R - 42\|- 2 coth(x) - 21\|- 2 coth(x) - 21\|- 2 coth(x) +--R + +--R +---+ +--R - 42\|- 2 +--R * +--R x 16 +--R (%e ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R 154\|- 2 coth(x) + 77\|- 2 coth(x) + 77\|- 2 coth(x) +--R + +--R +---+ +--R 154\|- 2 +--R * +--R x 14 +--R (%e ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R - 350\|- 2 coth(x) - 175\|- 2 coth(x) - 175\|- 2 coth(x) +--R + +--R +---+ +--R - 350\|- 2 +--R * +--R x 12 +--R (%e ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R 560\|- 2 coth(x) + 280\|- 2 coth(x) + 280\|- 2 coth(x) +--R + +--R +---+ +--R 560\|- 2 +--R * +--R x 10 +--R (%e ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R - 784\|- 2 coth(x) - 392\|- 2 coth(x) - 392\|- 2 coth(x) +--R + +--R +---+ +--R - 784\|- 2 +--R * +--R x 8 +--R (%e ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R 800\|- 2 coth(x) + 400\|- 2 coth(x) + 400\|- 2 coth(x) +--R + +--R +---+ +--R 800\|- 2 +--R * +--R x 6 +--R (%e ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R - 608\|- 2 coth(x) - 304\|- 2 coth(x) - 304\|- 2 coth(x) +--R + +--R +---+ +--R - 608\|- 2 +--R * +--R x 4 +--R (%e ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R 384\|- 2 coth(x) + 192\|- 2 coth(x) + 192\|- 2 coth(x) +--R + +--R +---+ +--R 384\|- 2 +--R * +--R x 2 +--R (%e ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +---+ +--R - 128\|- 2 coth(x) - 64\|- 2 coth(x) - 64\|- 2 coth(x) - 128\|- 2 +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 3 +---+ x 18 +--R (- 35\|- 2 coth(x) + 35\|- 2 coth(x))(%e ) +--R + +--R +---+ 3 +---+ x 16 +--R (105\|- 2 coth(x) - 105\|- 2 coth(x))(%e ) +--R + +--R +---+ 3 +---+ x 14 +--R (- 385\|- 2 coth(x) + 385\|- 2 coth(x))(%e ) +--R + +--R +---+ 3 +---+ x 12 +--R (875\|- 2 coth(x) - 875\|- 2 coth(x))(%e ) +--R + +--R +---+ 3 +---+ x 10 +--R (- 1400\|- 2 coth(x) + 1400\|- 2 coth(x))(%e ) +--R + +--R +---+ 3 +---+ x 8 +--R (1960\|- 2 coth(x) - 1960\|- 2 coth(x))(%e ) +--R + +--R +---+ 3 +---+ x 6 +--R (- 2000\|- 2 coth(x) + 2000\|- 2 coth(x))(%e ) +--R + +--R +---+ 3 +---+ x 4 +--R (1520\|- 2 coth(x) - 1520\|- 2 coth(x))(%e ) +--R + +--R +---+ 3 +---+ x 2 +---+ 3 +--R (- 960\|- 2 coth(x) + 960\|- 2 coth(x))(%e ) + 320\|- 2 coth(x) +--R + +--R +---+ +--R - 320\|- 2 coth(x) +--R * +--R tanh(x) +--R + +--R +---+ 4 +---+ 2 +---+ x 18 +--R (- 14\|- 2 coth(x) + 42\|- 2 coth(x) - 14\|- 2 )(%e ) +--R + +--R +---+ 4 +---+ 2 +---+ x 16 +--R (42\|- 2 coth(x) - 126\|- 2 coth(x) + 42\|- 2 )(%e ) +--R + +--R +---+ 4 +---+ 2 +---+ x 14 +--R (- 154\|- 2 coth(x) + 462\|- 2 coth(x) - 154\|- 2 )(%e ) +--R + +--R +---+ 4 +---+ 2 +---+ x 12 +--R (350\|- 2 coth(x) - 1050\|- 2 coth(x) + 350\|- 2 )(%e ) +--R + +--R +---+ 4 +---+ 2 +---+ x 10 +--R (- 560\|- 2 coth(x) + 1680\|- 2 coth(x) - 560\|- 2 )(%e ) +--R + +--R +---+ 4 +---+ 2 +---+ x 8 +--R (784\|- 2 coth(x) - 2352\|- 2 coth(x) + 784\|- 2 )(%e ) +--R + +--R +---+ 4 +---+ 2 +---+ x 6 +--R (- 800\|- 2 coth(x) + 2400\|- 2 coth(x) - 800\|- 2 )(%e ) +--R + +--R +---+ 4 +---+ 2 +---+ x 4 +--R (608\|- 2 coth(x) - 1824\|- 2 coth(x) + 608\|- 2 )(%e ) +--R + +--R +---+ 4 +---+ 2 +---+ x 2 +--R (- 384\|- 2 coth(x) + 1152\|- 2 coth(x) - 384\|- 2 )(%e ) +--R + +--R +---+ 4 +---+ 2 +---+ +--R 128\|- 2 coth(x) - 384\|- 2 coth(x) + 128\|- 2 +--R / +--R 2 x 18 2 x 16 +--R (2coth(x) + 2)(%e ) + (- 6coth(x) - 6)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (54coth(x) + 54)(%e ) + (- 146coth(x) - 146)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (304coth(x) + 304)(%e ) + (- 528coth(x) - 528)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (608coth(x) + 608)(%e ) + (- 544coth(x) - 544)(%e ) +--R + +--R 2 x 2 2 +--R (384coth(x) + 384)(%e ) - 128coth(x) - 128 +--R * +--R 2 +--R tanh(x) +--R + +--R x 18 x 16 x 14 x 12 x 10 +--R - 2(%e ) + 6(%e ) - 54(%e ) + 146(%e ) - 304(%e ) +--R + +--R x 8 x 6 x 4 x 2 +--R 528(%e ) - 608(%e ) + 544(%e ) - 384(%e ) + 128 +--R * +--R +-------------+ +--R | x 4 +--R \|- 2(%e ) - 2 +--R + +--R +---+ 2 +---+ x 18 +--R (- 14\|- 2 coth(x) - 14\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (42\|- 2 coth(x) + 42\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (- 154\|- 2 coth(x) - 154\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (350\|- 2 coth(x) + 350\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (- 560\|- 2 coth(x) - 560\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (784\|- 2 coth(x) + 784\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (- 800\|- 2 coth(x) - 800\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (608\|- 2 coth(x) + 608\|- 2 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +--R (- 384\|- 2 coth(x) - 384\|- 2 )(%e ) + 128\|- 2 coth(x) +--R + +--R +---+ +--R 128\|- 2 +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ x 18 +---+ x 16 +---+ x 14 +---+ x 12 +--R 14\|- 2 (%e ) - 42\|- 2 (%e ) + 154\|- 2 (%e ) - 350\|- 2 (%e ) +--R + +--R +---+ x 10 +---+ x 8 +---+ x 6 +---+ x 4 +--R 560\|- 2 (%e ) - 784\|- 2 (%e ) + 800\|- 2 (%e ) - 608\|- 2 (%e ) +--R + +--R +---+ x 2 +---+ +--R 384\|- 2 (%e ) - 128\|- 2 +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) - 1 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 508 +t0364:= (a+b*coth(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (291) (b coth(x) + a)\|b coth(x) + a +--R Type: Expression(Integer) +--E 327 + +--S 328 of 508 +r0364:= (a+b)^(3/2)*atanh((a+b)^(1/2)*coth(x)/(a+b*coth(x)^2)^(1/2))-_ + 3/2*a*b^(1/2)*atanh((a+b*coth(x)^2)^(1/2)*tanh(x)/b^(1/2))-_ + b^(3/2)*atanh((a+b*coth(x)^2)^(1/2)*tanh(x)/b^(1/2))-_ + 1/2*b*coth(x)*(a+b*coth(x)^2)^(1/2) +--R +--R +--R (292) +--R +--------------+ +--R | 2 +--R +-+ tanh(x)\|b coth(x) + a +--R (- 2b - 3a)\|b atanh(------------------------) +--R +-+ +--R \|b +--R + +--R +-----+ +--------------+ +--R +-----+ coth(x)\|b + a | 2 +--R (2b + 2a)\|b + a atanh(-----------------) - b coth(x)\|b coth(x) + a +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 328 + +--S 329 of 508 +a0364:= integrate(t0364,x) +--R +--R +--R (293) +--R [ +--R 3 2 2 3 6 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b + 15a b - 15a b - 15a )cosh(x) - b + a b + 5a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b + 20a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 15a b - 15a b - 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 6b + 6a b + 30a b + 18a )cosh(x) - b - 5a b - 7a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 10a b - 14a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b + a b - a b - a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- b + a b + 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- b - 5a b - 7a b - 3a )cosh(x) + b + 3a b + 3a b + a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- b - a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 28b - 28a b - 28a b - 28a )cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 +--R (24a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 70b - 70a b - 70a b - 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (60a b + 60a )cosh(x) + 2b - 8a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (80a b + 80a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 28b - 28a b - 28a b - 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (60a b + 60a )cosh(x) + (12b - 48a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R 4a b + 8a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (24a b + 24a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 16a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- b - a b - a b - a )cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 3 +--R (2b - 8a b - 6a )cosh(x) + (4a b + 8a b + 4a )cosh(x) - b +--R + +--R 2 2 3 +--R - 3a b - 3a b - a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b - a +--R / +--R 2 2 +-----+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|b + a +--R + +--R 2 2 6 2 2 5 +--R (2b + a b - 3a )sinh(x) + (12b + 6a b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 15a b - 45a )cosh(x) - 2b + 3a b + 9a )sinh(x) +--R + +--R 2 2 3 +--R (40b + 20a b - 60a )cosh(x) +--R + +--R 2 2 +--R (- 8b + 12a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 15a b - 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 12b + 18a b + 54a )cosh(x) - 2b - 9a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (12b + 6a b - 18a )cosh(x) +--R + +--R 2 2 3 +--R (- 8b + 12a b + 36a )cosh(x) +--R + +--R 2 2 +--R (- 4b - 18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + a b - 3a )cosh(x) + (- 2b + 3a b + 9a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b - 9a b - 9a )cosh(x) + 2b + 5a b + 3a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 3a b - 2a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 24a b - 16a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 +--R ((- 56b - 84a b - 56a b - 84a )cosh(x) + 8a b + 12a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 168a b - 112a b - 168a )cosh(x) +--R + +--R 2 3 +--R (48a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 210a b - 140a b - 210a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (120a b + 180a )cosh(x) + 4b + 2a b - 18a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 168a b - 112a b - 168a )cosh(x) +--R + +--R 2 3 3 +--R (160a b + 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (16b + 8a b - 72a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 84a b - 56a b - 84a )cosh(x) +--R + +--R 2 3 4 +--R (120a b + 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (24b + 12a b - 108a b - 108a )cosh(x) + 8a b + 20a b +--R + +--R 3 +--R 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 24a b - 16a b - 24a )cosh(x) +--R + +--R 2 3 5 +--R (48a b + 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (16b + 8a b - 72a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 40a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- 2b - 3a b - 2a b - 3a )cosh(x) + (8a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4b + 2a b - 18a b - 18a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (8a b + 20a b + 12a )cosh(x) - 2b - 7a b - 8a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 3 +--R 2a sinh(x) + 8a cosh(x)sinh(x) +--R + +--R 2 2 +--R (12a cosh(x) - 2b - 2a)sinh(x) +--R + +--R 3 +--R (8a cosh(x) + (- 4b - 4a)cosh(x))sinh(x) +--R + +--R 4 2 +--R 2a cosh(x) + (- 2b - 2a)cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R + +--R 2 2 4 +--R (- b - 2a b - a )sinh(x) +--R + +--R 2 2 3 +--R (- 4b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 12a b - 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((- 4b - 8a b - 4a )cosh(x) + (4a b + 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- b - 2a b - a )cosh(x) + (2a b + 2a )cosh(x) - b +--R + +--R 2 +--R - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (6b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((15b - 30a b - 15a )cosh(x) + b + 2a b + 3a )sinh(x) +--R + +--R 2 2 3 +--R (20b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (15b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (6b + 12a b + 18a )cosh(x) + b - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (6b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (4b + 8a b + 12a )cosh(x) + (2b - 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (b - 2a b - a )cosh(x) + (b + 2a b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (b - 2a b - 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 6 2 5 +--R (2a b + 2a )sinh(x) + (12a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R ((30a b + 30a )cosh(x) + 2b - 2a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((40a b + 40a )cosh(x) + (8b - 8a b - 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (30a b + 30a )cosh(x) + (12b - 12a b - 24a )cosh(x) +--R + +--R 2 2 +--R 2b + 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (12a b + 12a )cosh(x) + (8b - 8a b - 16a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (2a b + 2a )cosh(x) + (2b - 2a b - 4a )cosh(x) +--R + +--R 2 2 2 +--R (2b + 4a b + 2a )cosh(x) +--R * +--R +-+ +--R \|b +--R / +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((4b - 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (b - a )cosh(x) + (2a b + 2a )cosh(x) - b - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (- b - a )sinh(x) + (- 6b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 15b - 15a )cosh(x) - b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 20b - 20a )cosh(x) + (- 4b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (- 15b - 15a )cosh(x) + (- 6b + 18a )cosh(x) + b +--R + +--R 2 +--R - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 6b - 6a )cosh(x) + (- 4b + 12a )cosh(x) +--R + +--R 2 2 +--R (2b - 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- b - a )cosh(x) + (- b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (b - 2a b - 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) + b - a b - 5a b +--R + +--R 3 +--R - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 20b - 20a b + 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (6b - 6a b - 30a b - 18a )cosh(x) + b + 5a b + 7a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - 5a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + 5a b + 7a b + 3a )cosh(x) - b - 3a b - 3a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (b + a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (8b + 8a b + 8a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((28b + 28a b + 28a b + 28a )cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 +--R (- 24a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (70b + 70a b + 70a b + 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 60a b - 60a )cosh(x) - 2b + 8a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 80a b - 80a )cosh(x) + (- 8b + 32a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (28b + 28a b + 28a b + 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 60a b - 60a )cosh(x) + (- 12b + 48a b + 36a )cosh(x) +--R + +--R 2 2 3 +--R - 4a b - 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (8b + 8a b + 8a b + 8a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (- 24a b - 24a )cosh(x) + (- 8b + 32a b + 24a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (b + a b + a b + a )cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (- 2b + 8a b + 6a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R b + 3a b + 3a b + a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2b - 2a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) + 4b - 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (8b - 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (4b - 2a)cosh(x) + 2b + 2a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 6 2 5 +--R 2a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (30a b cosh(x) + 4b - 2a b - 4a b)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (40a b cosh(x) + (16b - 8a b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R 30a b cosh(x) + (24b - 12a b - 24a b)cosh(x) + 4b + 6a b +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 12a b cosh(x) + (16b - 8a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (8b + 12a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 2a b cosh(x) + (4b - 2a b - 4a b)cosh(x) +--R + +--R 3 2 2 2 +--R (4b + 6a b + 2a b)cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 8 2 7 +--R 2a b sinh(x) + 16a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 6 +--R (56a b cosh(x) - 4b + 2a b - 6a b)sinh(x) +--R + +--R 2 3 3 2 2 5 +--R (112a b cosh(x) + (- 24b + 12a b - 36a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 +--R 140a b cosh(x) + (- 60b + 30a b - 90a b)cosh(x) - 8b +--R + +--R 2 2 +--R 4a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 112a b cosh(x) + (- 80b + 40a b - 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 56a b cosh(x) + (- 60b + 30a b - 90a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 48b + 24a b + 36a b)cosh(x) - 4b - 6a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 2 2 5 +--R 16a b cosh(x) + (- 24b + 12a b - 36a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 32b + 16a b + 24a b)cosh(x) +--R + +--R 3 2 2 +--R (- 8b - 12a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 2 2 6 +--R 2a b cosh(x) + (- 4b + 2a b - 6a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 8b + 4a b + 6a b)cosh(x) + (- 4b - 6a b - 2a b)cosh(x) +--R * +--R +-----+ +--R \|b + a +--R / +--R 6 5 +--R (2b - 2a)sinh(x) + (12b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((30b - 30a)cosh(x) - 2b + 6a)sinh(x) +--R + +--R 3 3 +--R ((40b - 40a)cosh(x) + (- 8b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((30b - 30a)cosh(x) + (- 12b + 36a)cosh(x) - 2b - 6a)sinh(x) +--R + +--R 5 3 +--R (12b - 12a)cosh(x) + (- 8b + 24a)cosh(x) +--R + +--R (- 4b - 12a)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (2b - 2a)cosh(x) + (- 2b + 6a)cosh(x) + (- 2b - 6a)cosh(x) + 2b +--R + +--R 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 2b - 2a )sinh(x) + (- 16b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((- 56b - 56a )cosh(x) + 8a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((- 112b - 112a )cosh(x) + 48a cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 4 +--R ((- 140b - 140a )cosh(x) + 120a cosh(x) + 4b - 4a b - 12a )sinh(x) +--R + +--R 2 2 5 2 3 +--R (- 112b - 112a )cosh(x) + 160a cosh(x) +--R + +--R 2 2 +--R (16b - 16a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 4 +--R (- 56b - 56a )cosh(x) + 120a cosh(x) +--R + +--R 2 2 2 2 +--R (24b - 24a b - 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 +--R (- 16b - 16a )cosh(x) + 48a cosh(x) +--R + +--R 2 2 3 2 +--R (16b - 16a b - 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (- 2b - 2a )cosh(x) + 8a cosh(x) + (4b - 4a b - 12a )cosh(x) +--R + +--R 2 2 2 2 +--R (8a b + 8a )cosh(x) - 2b - 4a b - 2a +--R , +--R +--R 3 2 2 3 6 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b + 15a b - 15a b - 15a )cosh(x) - b + a b + 5a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b + 20a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 15a b - 15a b - 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 6b + 6a b + 30a b + 18a )cosh(x) - b - 5a b - 7a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 10a b - 14a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b + a b - a b - a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- b + a b + 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- b - 5a b - 7a b - 3a )cosh(x) + b + 3a b + 3a b + a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- b - a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 28b - 28a b - 28a b - 28a )cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 +--R (24a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 70b - 70a b - 70a b - 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (60a b + 60a )cosh(x) + 2b - 8a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (80a b + 80a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 28b - 28a b - 28a b - 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (60a b + 60a )cosh(x) + (12b - 48a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R 4a b + 8a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (24a b + 24a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 16a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- b - a b - a b - a )cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 3 +--R (2b - 8a b - 6a )cosh(x) + (4a b + 8a b + 4a )cosh(x) - b +--R + +--R 2 2 3 +--R - 3a b - 3a b - a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b - a +--R / +--R 2 2 +-----+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|b + a +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) + b - a b - 5a b +--R + +--R 3 +--R - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 20b - 20a b + 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (6b - 6a b - 30a b - 18a )cosh(x) + b + 5a b + 7a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - 5a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + 5a b + 7a b + 3a )cosh(x) - b - 3a b - 3a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (b + a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (8b + 8a b + 8a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((28b + 28a b + 28a b + 28a )cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 +--R (- 24a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (70b + 70a b + 70a b + 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 60a b - 60a )cosh(x) - 2b + 8a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 80a b - 80a )cosh(x) + (- 8b + 32a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (28b + 28a b + 28a b + 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 60a b - 60a )cosh(x) + (- 12b + 48a b + 36a )cosh(x) +--R + +--R 2 2 3 +--R - 4a b - 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (8b + 8a b + 8a b + 8a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (- 24a b - 24a )cosh(x) + (- 8b + 32a b + 24a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (b + a b + a b + a )cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (- 2b + 8a b + 6a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R b + 3a b + 3a b + a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2b - 2a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) + 4b - 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (8b - 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (4b - 2a)cosh(x) + 2b + 2a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 2 6 +--R (- 4b - 2a b + 6a )sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 12a b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 60b - 30a b + 90a )cosh(x) + 4b - 6a b - 18a )sinh(x) +--R + +--R 2 2 3 +--R (- 80b - 40a b + 120a )cosh(x) +--R + +--R 2 2 +--R (16b - 24a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 60b - 30a b + 90a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b - 36a b - 108a )cosh(x) + 4b + 18a b + 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 12a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (16b - 24a b - 72a )cosh(x) + (8b + 36a b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 4b - 2a b + 6a )cosh(x) + (4b - 6a b - 18a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (4b + 18a b + 18a )cosh(x) - 4b - 10a b - 6a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +---+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|- b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (4b + 6a b + 4a b + 6a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 48a b + 32a b + 48a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 +--R ((112b + 168a b + 112a b + 168a )cosh(x) - 16a b - 24a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (224b + 336a b + 224a b + 336a )cosh(x) +--R + +--R 2 3 +--R (- 96a b - 144a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (280b + 420a b + 280a b + 420a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 240a b - 360a )cosh(x) - 8b - 4a b + 36a b + 36a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (224b + 336a b + 224a b + 336a )cosh(x) +--R + +--R 2 3 3 +--R (- 320a b - 480a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 32b - 16a b + 144a b + 144a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (112b + 168a b + 112a b + 168a )cosh(x) +--R + +--R 2 3 4 +--R (- 240a b - 360a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 48b - 24a b + 216a b + 216a )cosh(x) - 16a b - 40a b +--R + +--R 3 +--R - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 48a b + 32a b + 48a )cosh(x) +--R + +--R 2 3 5 +--R (- 96a b - 144a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 32b - 16a b + 144a b + 144a )cosh(x) +--R + +--R 2 2 3 +--R (- 32a b - 80a b - 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (4b + 6a b + 4a b + 6a )cosh(x) + (- 16a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 8b - 4a b + 36a b + 36a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (- 16a b - 40a b - 24a )cosh(x) + 4b + 14a b + 16a b + 6a +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b - a +--R / +--R 2 2 +---+ +-----+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|b + a +--R + +--R 2 6 2 5 +--R 2a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (30a b cosh(x) + 4b - 2a b - 4a b)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (40a b cosh(x) + (16b - 8a b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R 30a b cosh(x) + (24b - 12a b - 24a b)cosh(x) + 4b + 6a b +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 12a b cosh(x) + (16b - 8a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (8b + 12a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 2a b cosh(x) + (4b - 2a b - 4a b)cosh(x) +--R + +--R 3 2 2 2 +--R (4b + 6a b + 2a b)cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 8 2 7 +--R 2a b sinh(x) + 16a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 6 +--R (56a b cosh(x) - 4b + 2a b - 6a b)sinh(x) +--R + +--R 2 3 3 2 2 5 +--R (112a b cosh(x) + (- 24b + 12a b - 36a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 +--R 140a b cosh(x) + (- 60b + 30a b - 90a b)cosh(x) - 8b +--R + +--R 2 2 +--R 4a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 112a b cosh(x) + (- 80b + 40a b - 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 56a b cosh(x) + (- 60b + 30a b - 90a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 48b + 24a b + 36a b)cosh(x) - 4b - 6a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 2 2 5 +--R 16a b cosh(x) + (- 24b + 12a b - 36a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 32b + 16a b + 24a b)cosh(x) +--R + +--R 3 2 2 +--R (- 8b - 12a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 2 2 6 +--R 2a b cosh(x) + (- 4b + 2a b - 6a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 8b + 4a b + 6a b)cosh(x) + (- 4b - 6a b - 2a b)cosh(x) +--R * +--R +-----+ +--R \|b + a +--R / +--R 6 5 +--R (2b - 2a)sinh(x) + (12b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((30b - 30a)cosh(x) - 2b + 6a)sinh(x) +--R + +--R 3 3 +--R ((40b - 40a)cosh(x) + (- 8b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((30b - 30a)cosh(x) + (- 12b + 36a)cosh(x) - 2b - 6a)sinh(x) +--R + +--R 5 3 +--R (12b - 12a)cosh(x) + (- 8b + 24a)cosh(x) +--R + +--R (- 4b - 12a)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (2b - 2a)cosh(x) + (- 2b + 6a)cosh(x) + (- 2b - 6a)cosh(x) + 2b +--R + +--R 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 2b - 2a )sinh(x) + (- 16b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((- 56b - 56a )cosh(x) + 8a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((- 112b - 112a )cosh(x) + 48a cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 4 +--R ((- 140b - 140a )cosh(x) + 120a cosh(x) + 4b - 4a b - 12a )sinh(x) +--R + +--R 2 2 5 2 3 +--R (- 112b - 112a )cosh(x) + 160a cosh(x) +--R + +--R 2 2 +--R (16b - 16a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 4 +--R (- 56b - 56a )cosh(x) + 120a cosh(x) +--R + +--R 2 2 2 2 +--R (24b - 24a b - 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 +--R (- 16b - 16a )cosh(x) + 48a cosh(x) +--R + +--R 2 2 3 2 +--R (16b - 16a b - 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (- 2b - 2a )cosh(x) + 8a cosh(x) + (4b - 4a b - 12a )cosh(x) +--R + +--R 2 2 2 2 +--R (8a b + 8a )cosh(x) - 2b - 4a b - 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 329 + +--S 330 of 508 +m0364a:= a0364.1-r0364 +--R +--R +--R (294) +--R 3 2 2 3 6 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b + 15a b - 15a b - 15a )cosh(x) - b + a b + 5a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b + 20a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 15a b - 15a b - 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 6b + 6a b + 30a b + 18a )cosh(x) - b - 5a b - 7a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 10a b - 14a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b + a b - a b - a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- b + a b + 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- b - 5a b - 7a b - 3a )cosh(x) + b + 3a b + 3a b + a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- b - a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 28b - 28a b - 28a b - 28a )cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 +--R (24a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 70b - 70a b - 70a b - 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (60a b + 60a )cosh(x) + 2b - 8a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (80a b + 80a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 28b - 28a b - 28a b - 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (60a b + 60a )cosh(x) + (12b - 48a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R 4a b + 8a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 2 3 5 +--R (- 8b - 8a b - 8a b - 8a )cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 2 3 3 2 2 3 +--R (8b - 32a b - 24a )cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- b - a b - a b - a )cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 3 +--R (2b - 8a b - 6a )cosh(x) + (4a b + 8a b + 4a )cosh(x) - b +--R + +--R 2 2 3 +--R - 3a b - 3a b - a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R - a +--R / +--R 2 2 +-----+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|b + a +--R + +--R 2 2 6 2 2 5 +--R (2b + a b - 3a )sinh(x) + (12b + 6a b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 15a b - 45a )cosh(x) - 2b + 3a b + 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 20a b - 60a )cosh(x) + (- 8b + 12a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 15a b - 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 12b + 18a b + 54a )cosh(x) - 2b - 9a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 6a b - 18a )cosh(x) + (- 8b + 12a b + 36a )cosh(x) +--R + +--R 2 2 +--R (- 4b - 18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + a b - 3a )cosh(x) + (- 2b + 3a b + 9a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b - 9a b - 9a )cosh(x) + 2b + 5a b + 3a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 3a b - 2a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 24a b - 16a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 56b - 84a b - 56a b - 84a )cosh(x) + 8a b + 12a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 168a b - 112a b - 168a )cosh(x) +--R + +--R 2 3 +--R (48a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 210a b - 140a b - 210a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (120a b + 180a )cosh(x) + 4b + 2a b - 18a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 168a b - 112a b - 168a )cosh(x) +--R + +--R 2 3 3 3 2 2 3 +--R (160a b + 240a )cosh(x) + (16b + 8a b - 72a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 84a b - 56a b - 84a )cosh(x) +--R + +--R 2 3 4 +--R (120a b + 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (24b + 12a b - 108a b - 108a )cosh(x) + 8a b + 20a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 24a b - 16a b - 24a )cosh(x) +--R + +--R 2 3 5 +--R (48a b + 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (16b + 8a b - 72a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 40a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- 2b - 3a b - 2a b - 3a )cosh(x) + (8a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4b + 2a b - 18a b - 18a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (8a b + 20a b + 12a )cosh(x) - 2b - 7a b - 8a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 3 +--R 2a sinh(x) + 8a cosh(x)sinh(x) +--R + +--R 2 2 +--R (12a cosh(x) - 2b - 2a)sinh(x) +--R + +--R 3 4 +--R (8a cosh(x) + (- 4b - 4a)cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 2 +--R (- 2b - 2a)cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R + +--R 2 2 4 +--R (- b - 2a b - a )sinh(x) +--R + +--R 2 2 3 +--R (- 4b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 12a b - 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((- 4b - 8a b - 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- b - 2a b - a )cosh(x) + (2a b + 2a )cosh(x) - b +--R + +--R 2 +--R - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (6b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((15b - 30a b - 15a )cosh(x) + b + 2a b + 3a )sinh(x) +--R + +--R 2 2 3 +--R (20b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (15b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (6b + 12a b + 18a )cosh(x) + b - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (6b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (4b + 8a b + 12a )cosh(x) + (2b - 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (b - 2a b - a )cosh(x) + (b + 2a b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (b - 2a b - 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 6 2 5 +--R (2a b + 2a )sinh(x) + (12a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R ((30a b + 30a )cosh(x) + 2b - 2a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((40a b + 40a )cosh(x) + (8b - 8a b - 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (30a b + 30a )cosh(x) + (12b - 12a b - 24a )cosh(x) +--R + +--R 2 2 +--R 2b + 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (12a b + 12a )cosh(x) + (8b - 8a b - 16a )cosh(x) +--R + +--R 2 2 +--R (4b + 8a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (2a b + 2a )cosh(x) + (2b - 2a b - 4a )cosh(x) +--R + +--R 2 2 2 +--R (2b + 4a b + 2a )cosh(x) +--R * +--R +-+ +--R \|b +--R / +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 +--R ((4b - 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (b - a )cosh(x) + (2a b + 2a )cosh(x) - b - 2a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (- b - a )sinh(x) + (- 6b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 15b - 15a )cosh(x) - b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 20b - 20a )cosh(x) + (- 4b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (- 15b - 15a )cosh(x) + (- 6b + 18a )cosh(x) + b +--R + +--R 2 +--R - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 6b - 6a )cosh(x) + (- 4b + 12a )cosh(x) +--R + +--R 2 2 +--R (2b - 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- b - a )cosh(x) + (- b + 3a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (b - 2a b - 3a )cosh(x) + b + 2a b + a +--R * +--R +-----+ +--R \|b + a +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) + b - a b - 5a b +--R + +--R 3 +--R - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 20b - 20a b + 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) + b + 5a b + 7a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - 5a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + 5a b + 7a b + 3a )cosh(x) - b - 3a b - 3a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (b + a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (8b + 8a b + 8a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((28b + 28a b + 28a b + 28a )cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 +--R (- 24a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (70b + 70a b + 70a b + 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 60a b - 60a )cosh(x) - 2b + 8a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 80a b - 80a )cosh(x) + (- 8b + 32a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (28b + 28a b + 28a b + 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 60a b - 60a )cosh(x) + (- 12b + 48a b + 36a )cosh(x) +--R + +--R 2 2 3 +--R - 4a b - 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 2 3 5 +--R (8b + 8a b + 8a b + 8a )cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 3 2 3 3 2 2 3 +--R (- 8b + 32a b + 24a )cosh(x) + (- 8a b - 16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (b + a b + a b + a )cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (- 2b + 8a b + 6a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R b + 3a b + 3a b + a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2b - 2a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) + 4b - 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (8b - 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (4b - 2a)cosh(x) + 2b + 2a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 2 6 2 2 5 +--R (2b + a b - 3a )sinh(x) + (12b + 6a b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 15a b - 45a )cosh(x) - 2b + 3a b + 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 20a b - 60a )cosh(x) + (- 8b + 12a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 15a b - 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 12b + 18a b + 54a )cosh(x) - 2b - 9a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 6a b - 18a )cosh(x) + (- 8b + 12a b + 36a )cosh(x) +--R + +--R 2 2 +--R (- 4b - 18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + a b - 3a )cosh(x) + (- 2b + 3a b + 9a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b - 9a b - 9a )cosh(x) + 2b + 5a b + 3a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 3a b - 2a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 24a b - 16a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 56b - 84a b - 56a b - 84a )cosh(x) + 8a b + 12a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 168a b - 112a b - 168a )cosh(x) +--R + +--R 2 3 +--R (48a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 210a b - 140a b - 210a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (120a b + 180a )cosh(x) + 4b + 2a b - 18a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 168a b - 112a b - 168a )cosh(x) +--R + +--R 2 3 3 3 2 2 3 +--R (160a b + 240a )cosh(x) + (16b + 8a b - 72a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 84a b - 56a b - 84a )cosh(x) +--R + +--R 2 3 4 +--R (120a b + 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (24b + 12a b - 108a b - 108a )cosh(x) + 8a b + 20a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 24a b - 16a b - 24a )cosh(x) +--R + +--R 2 3 5 +--R (48a b + 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (16b + 8a b - 72a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 40a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- 2b - 3a b - 2a b - 3a )cosh(x) + (8a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4b + 2a b - 18a b - 18a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (8a b + 20a b + 12a )cosh(x) - 2b - 7a b - 8a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R +--------------+ +--R | 2 +--R tanh(x)\|b coth(x) + a +--R atanh(------------------------) +--R +-+ +--R \|b +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 12b - 12a b + 12a b + 12a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 30b - 30a b + 30a b + 30a )cosh(x) + 2b - 2a b +--R + +--R 2 3 +--R - 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 40b - 40a b + 40a b + 40a )cosh(x) +--R + +--R 3 2 2 3 +--R (8b - 8a b - 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 30b - 30a b + 30a b + 30a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (12b - 12a b - 60a b - 36a )cosh(x) + 2b + 10a b + 14a b +--R + +--R 3 +--R 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 12b - 12a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (8b - 8a b - 40a b - 24a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b + 20a b + 28a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (2b - 2a b - 10a b - 6a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) - 2b - 6a b - 6a b - 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (2b + 2a b + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 16a b + 16a b + 16a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((56b + 56a b + 56a b + 56a )cosh(x) - 8a b - 8a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (112b + 112a b + 112a b + 112a )cosh(x) +--R + +--R 2 3 +--R (- 48a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (140b + 140a b + 140a b + 140a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 120a b - 120a )cosh(x) - 4b + 16a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (112b + 112a b + 112a b + 112a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 160a b - 160a )cosh(x) + (- 16b + 64a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 120a b - 120a )cosh(x) + (- 24b + 96a b + 72a )cosh(x) +--R + +--R 2 2 3 +--R - 8a b - 16a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 16a b + 16a b + 16a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (- 48a b - 48a )cosh(x) + (- 16b + 64a b + 48a )cosh(x) +--R + +--R 2 2 3 +--R (- 16a b - 32a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (2b + 2a b + 2a b + 2a )cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (- 4b + 16a b + 12a )cosh(x) + (- 8a b - 16a b - 8a )cosh(x) +--R + +--R 3 2 2 3 +--R 2b + 6a b + 6a b + 2a +--R * +--R +-----+ +--R \|b + a +--R * +--R +-----+ +--R coth(x)\|b + a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R + +--R 2 6 2 5 +--R (b - a b)coth(x)sinh(x) + (6b - 6a b)cosh(x)coth(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((15b - 15a b)cosh(x) - b + 3a b)coth(x)sinh(x) +--R + +--R 2 3 2 3 +--R ((20b - 20a b)cosh(x) + (- 4b + 12a b)cosh(x))coth(x)sinh(x) +--R + +--R 2 4 2 2 2 +--R ((15b - 15a b)cosh(x) + (- 6b + 18a b)cosh(x) - b - 3a b) +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 2 5 2 3 +--R (6b - 6a b)cosh(x) + (- 4b + 12a b)cosh(x) +--R + +--R 2 +--R (- 2b - 6a b)cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 2 6 2 4 +--R (b - a b)cosh(x) + (- b + 3a b)cosh(x) +--R + +--R 2 2 2 +--R (- b - 3a b)cosh(x) + b + a b +--R * +--R coth(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 8 3 2 7 +--R (- b - a b)coth(x)sinh(x) + (- 8b - 8a b)cosh(x)coth(x)sinh(x) +--R + +--R 3 2 2 2 6 +--R ((- 28b - 28a b)cosh(x) + 4a b)coth(x)sinh(x) +--R + +--R 3 2 3 2 5 +--R ((- 56b - 56a b)cosh(x) + 24a b cosh(x))coth(x)sinh(x) +--R + +--R 3 2 4 2 2 3 2 2 +--R ((- 70b - 70a b)cosh(x) + 60a b cosh(x) + 2b - 2a b - 6a b) +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 3 2 5 2 3 +--R (- 56b - 56a b)cosh(x) + 80a b cosh(x) +--R + +--R 3 2 2 +--R (8b - 8a b - 24a b)cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 3 2 6 2 4 +--R (- 28b - 28a b)cosh(x) + 60a b cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b - 12a b - 36a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 3 2 7 2 5 +--R (- 8b - 8a b)cosh(x) + 24a b cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b - 8a b - 24a b)cosh(x) + (8a b + 8a b)cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 3 2 8 2 6 +--R (- b - a b)cosh(x) + 4a b cosh(x) +--R + +--R 3 2 2 4 2 2 2 3 +--R (2b - 2a b - 6a b)cosh(x) + (4a b + 4a b)cosh(x) - b +--R + +--R 2 2 +--R - 2a b - a b +--R * +--R coth(x) +--R * +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R + +--R 2 6 2 5 +--R 2a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (30a b cosh(x) + 4b - 2a b - 4a b)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (40a b cosh(x) + (16b - 8a b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R 30a b cosh(x) + (24b - 12a b - 24a b)cosh(x) + 4b + 6a b +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 12a b cosh(x) + (16b - 8a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (8b + 12a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 2a b cosh(x) + (4b - 2a b - 4a b)cosh(x) +--R + +--R 3 2 2 2 +--R (4b + 6a b + 2a b)cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 8 2 7 +--R 2a b sinh(x) + 16a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 6 +--R (56a b cosh(x) - 4b + 2a b - 6a b)sinh(x) +--R + +--R 2 3 3 2 2 5 +--R (112a b cosh(x) + (- 24b + 12a b - 36a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R 140a b cosh(x) + (- 60b + 30a b - 90a b)cosh(x) - 8b + 4a b +--R + +--R 2 +--R 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 112a b cosh(x) + (- 80b + 40a b - 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 56a b cosh(x) + (- 60b + 30a b - 90a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 48b + 24a b + 36a b)cosh(x) - 4b - 6a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 2 2 5 +--R 16a b cosh(x) + (- 24b + 12a b - 36a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) + (- 8b - 12a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 2 2 6 +--R 2a b cosh(x) + (- 4b + 2a b - 6a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 8b + 4a b + 6a b)cosh(x) + (- 4b - 6a b - 2a b)cosh(x) +--R * +--R +-----+ +--R \|b + a +--R / +--R 6 5 +--R (2b - 2a)sinh(x) + (12b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((30b - 30a)cosh(x) - 2b + 6a)sinh(x) +--R + +--R 3 3 +--R ((40b - 40a)cosh(x) + (- 8b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((30b - 30a)cosh(x) + (- 12b + 36a)cosh(x) - 2b - 6a)sinh(x) +--R + +--R 5 3 +--R ((12b - 12a)cosh(x) + (- 8b + 24a)cosh(x) + (- 4b - 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (2b - 2a)cosh(x) + (- 2b + 6a)cosh(x) + (- 2b - 6a)cosh(x) + 2b + 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 2b - 2a )sinh(x) + (- 16b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((- 56b - 56a )cosh(x) + 8a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((- 112b - 112a )cosh(x) + 48a cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 4 +--R ((- 140b - 140a )cosh(x) + 120a cosh(x) + 4b - 4a b - 12a )sinh(x) +--R + +--R 2 2 5 2 3 +--R (- 112b - 112a )cosh(x) + 160a cosh(x) +--R + +--R 2 2 +--R (16b - 16a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 4 +--R (- 56b - 56a )cosh(x) + 120a cosh(x) +--R + +--R 2 2 2 2 +--R (24b - 24a b - 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 +--R (- 16b - 16a )cosh(x) + 48a cosh(x) +--R + +--R 2 2 3 2 +--R (16b - 16a b - 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (- 2b - 2a )cosh(x) + 8a cosh(x) + (4b - 4a b - 12a )cosh(x) +--R + +--R 2 2 2 2 +--R (8a b + 8a )cosh(x) - 2b - 4a b - 2a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 508 +--d0364a:= D(m0364a,x) +--E 331 + +--S 332 of 508 +m0364b:= a0364.2-r0364 +--R +--R +--R (295) +--R 3 2 2 3 6 +--R (b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (15b + 15a b - 15a b - 15a )cosh(x) - b + a b + 5a b +--R + +--R 3 +--R 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20b + 20a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15b + 15a b - 15a b - 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 6b + 6a b + 30a b + 18a )cosh(x) - b - 5a b - 7a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 4b + 4a b + 20a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 10a b - 14a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (b + a b - a b - a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- b + a b + 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- b - 5a b - 7a b - 3a )cosh(x) + b + 3a b + 3a b + a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- b - a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 8b - 8a b - 8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 28b - 28a b - 28a b - 28a )cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 +--R (24a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 70b - 70a b - 70a b - 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (60a b + 60a )cosh(x) + 2b - 8a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 56b - 56a b - 56a b - 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (80a b + 80a )cosh(x) + (8b - 32a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 28b - 28a b - 28a b - 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (60a b + 60a )cosh(x) + (12b - 48a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R 4a b + 8a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 2 3 5 +--R (- 8b - 8a b - 8a b - 8a )cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 2 3 3 2 2 3 +--R (8b - 32a b - 24a )cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- b - a b - a b - a )cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 3 +--R (2b - 8a b - 6a )cosh(x) + (4a b + 8a b + 4a )cosh(x) - b +--R + +--R 2 2 3 +--R - 3a b - 3a b - a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R - a +--R / +--R 2 2 +-----+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|b + a +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) + b - a b - 5a b +--R + +--R 3 +--R - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 20b - 20a b + 20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 15b - 15a b + 15a b + 15a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (6b - 6a b - 30a b - 18a )cosh(x) + b + 5a b + 7a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 20a b - 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- b - a b + a b + a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - 5a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + 5a b + 7a b + 3a )cosh(x) - b - 3a b - 3a b - a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (b + a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (8b + 8a b + 8a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((28b + 28a b + 28a b + 28a )cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 +--R (- 24a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (70b + 70a b + 70a b + 70a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 60a b - 60a )cosh(x) - 2b + 8a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 80a b - 80a )cosh(x) + (- 8b + 32a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (28b + 28a b + 28a b + 28a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 60a b - 60a )cosh(x) + (- 12b + 48a b + 36a )cosh(x) +--R + +--R 2 2 3 +--R - 4a b - 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 2 3 5 +--R (8b + 8a b + 8a b + 8a )cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 3 2 3 3 2 2 3 +--R (- 8b + 32a b + 24a )cosh(x) + (- 8a b - 16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (b + a b + a b + a )cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (- 2b + 8a b + 6a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 3 2 2 3 +--R b + 3a b + 3a b + a +--R * +--R +-----+ +--R \|b + a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2b - 2a) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) + 4b - 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (8b - 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (4b - 2a)cosh(x) + 2b + 2a +--R * +--R +-----+ +--R \|b + a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-----+ +--R \|b + a +--R + +--R 2 2 6 2 2 5 +--R (2b + a b - 3a )sinh(x) + (12b + 6a b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 15a b - 45a )cosh(x) - 2b + 3a b + 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 20a b - 60a )cosh(x) + (- 8b + 12a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 15a b - 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 12b + 18a b + 54a )cosh(x) - 2b - 9a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 6a b - 18a )cosh(x) + (- 8b + 12a b + 36a )cosh(x) +--R + +--R 2 2 +--R (- 4b - 18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + a b - 3a )cosh(x) + (- 2b + 3a b + 9a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b - 9a b - 9a )cosh(x) + 2b + 5a b + 3a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 3a b - 2a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 24a b - 16a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((- 56b - 84a b - 56a b - 84a )cosh(x) + 8a b + 12a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 168a b - 112a b - 168a )cosh(x) +--R + +--R 2 3 +--R (48a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 210a b - 140a b - 210a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (120a b + 180a )cosh(x) + 4b + 2a b - 18a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 168a b - 112a b - 168a )cosh(x) +--R + +--R 2 3 3 3 2 2 3 +--R (160a b + 240a )cosh(x) + (16b + 8a b - 72a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 84a b - 56a b - 84a )cosh(x) +--R + +--R 2 3 4 +--R (120a b + 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (24b + 12a b - 108a b - 108a )cosh(x) + 8a b + 20a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 24a b - 16a b - 24a )cosh(x) +--R + +--R 2 3 5 +--R (48a b + 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (16b + 8a b - 72a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 40a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (- 2b - 3a b - 2a b - 3a )cosh(x) + (8a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4b + 2a b - 18a b - 18a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (8a b + 20a b + 12a )cosh(x) - 2b - 7a b - 8a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R +--------------+ +--R | 2 +--R tanh(x)\|b coth(x) + a +--R atanh(------------------------) +--R +-+ +--R \|b +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 12b - 12a b + 12a b + 12a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 30b - 30a b + 30a b + 30a )cosh(x) + 2b - 2a b +--R + +--R 2 3 +--R - 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 40b - 40a b + 40a b + 40a )cosh(x) +--R + +--R 3 2 2 3 +--R (8b - 8a b - 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 30b - 30a b + 30a b + 30a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (12b - 12a b - 60a b - 36a )cosh(x) + 2b + 10a b + 14a b +--R + +--R 3 +--R 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 12b - 12a b + 12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (8b - 8a b - 40a b - 24a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b + 20a b + 28a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 2b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (2b - 2a b - 10a b - 6a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (2b + 10a b + 14a b + 6a )cosh(x) - 2b - 6a b - 6a b - 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (2b + 2a b + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 16a b + 16a b + 16a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 6 +--R ((56b + 56a b + 56a b + 56a )cosh(x) - 8a b - 8a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (112b + 112a b + 112a b + 112a )cosh(x) +--R + +--R 2 3 +--R (- 48a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (140b + 140a b + 140a b + 140a )cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 120a b - 120a )cosh(x) - 4b + 16a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (112b + 112a b + 112a b + 112a )cosh(x) +--R + +--R 2 3 3 3 2 3 +--R (- 160a b - 160a )cosh(x) + (- 16b + 64a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (56b + 56a b + 56a b + 56a )cosh(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 120a b - 120a )cosh(x) + (- 24b + 96a b + 72a )cosh(x) +--R + +--R 2 2 3 +--R - 8a b - 16a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b + 16a b + 16a b + 16a )cosh(x) +--R + +--R 2 3 5 3 2 3 3 +--R (- 48a b - 48a )cosh(x) + (- 16b + 64a b + 48a )cosh(x) +--R + +--R 2 2 3 +--R (- 16a b - 32a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (2b + 2a b + 2a b + 2a )cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 3 2 3 4 2 2 3 2 +--R (- 4b + 16a b + 12a )cosh(x) + (- 8a b - 16a b - 8a )cosh(x) +--R + +--R 3 2 2 3 +--R 2b + 6a b + 6a b + 2a +--R * +--R +-----+ +--R \|b + a +--R * +--R +-----+ +--R coth(x)\|b + a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R + +--R 2 2 6 +--R (- 4b - 2a b + 6a )sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 12a b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 60b - 30a b + 90a )cosh(x) + 4b - 6a b - 18a )sinh(x) +--R + +--R 2 2 3 +--R (- 80b - 40a b + 120a )cosh(x) +--R + +--R 2 2 +--R (16b - 24a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 60b - 30a b + 90a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b - 36a b - 108a )cosh(x) + 4b + 18a b + 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 12a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (16b - 24a b - 72a )cosh(x) + (8b + 36a b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 4b - 2a b + 6a )cosh(x) + (4b - 6a b - 18a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (4b + 18a b + 18a )cosh(x) - 4b - 10a b - 6a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +---+ +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|- b \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (4b + 6a b + 4a b + 6a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 48a b + 32a b + 48a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 +--R ((112b + 168a b + 112a b + 168a )cosh(x) - 16a b - 24a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (224b + 336a b + 224a b + 336a )cosh(x) +--R + +--R 2 3 +--R (- 96a b - 144a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (280b + 420a b + 280a b + 420a )cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 240a b - 360a )cosh(x) - 8b - 4a b + 36a b + 36a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (224b + 336a b + 224a b + 336a )cosh(x) +--R + +--R 2 3 3 +--R (- 320a b - 480a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 32b - 16a b + 144a b + 144a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (112b + 168a b + 112a b + 168a )cosh(x) +--R + +--R 2 3 4 +--R (- 240a b - 360a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 48b - 24a b + 216a b + 216a )cosh(x) - 16a b - 40a b +--R + +--R 3 +--R - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 48a b + 32a b + 48a )cosh(x) +--R + +--R 2 3 5 +--R (- 96a b - 144a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 32b - 16a b + 144a b + 144a )cosh(x) +--R + +--R 2 2 3 +--R (- 32a b - 80a b - 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 2 3 6 +--R (4b + 6a b + 4a b + 6a )cosh(x) + (- 16a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 8b - 4a b + 36a b + 36a )cosh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (- 16a b - 40a b - 24a )cosh(x) + 4b + 14a b + 16a b + 6a +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R - a +--R / +--R 2 2 +---+ +-----+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|b + a +--R + +--R 2 6 2 5 +--R (b - a b)coth(x)sinh(x) + (6b - 6a b)cosh(x)coth(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((15b - 15a b)cosh(x) - b + 3a b)coth(x)sinh(x) +--R + +--R 2 3 2 3 +--R ((20b - 20a b)cosh(x) + (- 4b + 12a b)cosh(x))coth(x)sinh(x) +--R + +--R 2 4 2 2 2 +--R ((15b - 15a b)cosh(x) + (- 6b + 18a b)cosh(x) - b - 3a b) +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 2 5 2 3 +--R (6b - 6a b)cosh(x) + (- 4b + 12a b)cosh(x) +--R + +--R 2 +--R (- 2b - 6a b)cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 2 6 2 4 +--R (b - a b)cosh(x) + (- b + 3a b)cosh(x) +--R + +--R 2 2 2 +--R (- b - 3a b)cosh(x) + b + a b +--R * +--R coth(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 8 3 2 7 +--R (- b - a b)coth(x)sinh(x) + (- 8b - 8a b)cosh(x)coth(x)sinh(x) +--R + +--R 3 2 2 2 6 +--R ((- 28b - 28a b)cosh(x) + 4a b)coth(x)sinh(x) +--R + +--R 3 2 3 2 5 +--R ((- 56b - 56a b)cosh(x) + 24a b cosh(x))coth(x)sinh(x) +--R + +--R 3 2 4 2 2 3 2 2 +--R ((- 70b - 70a b)cosh(x) + 60a b cosh(x) + 2b - 2a b - 6a b) +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 3 2 5 2 3 +--R (- 56b - 56a b)cosh(x) + 80a b cosh(x) +--R + +--R 3 2 2 +--R (8b - 8a b - 24a b)cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 3 2 6 2 4 +--R (- 28b - 28a b)cosh(x) + 60a b cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b - 12a b - 36a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 3 2 7 2 5 +--R (- 8b - 8a b)cosh(x) + 24a b cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b - 8a b - 24a b)cosh(x) + (8a b + 8a b)cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 3 2 8 2 6 +--R (- b - a b)cosh(x) + 4a b cosh(x) +--R + +--R 3 2 2 4 2 2 2 3 +--R (2b - 2a b - 6a b)cosh(x) + (4a b + 4a b)cosh(x) - b +--R + +--R 2 2 +--R - 2a b - a b +--R * +--R coth(x) +--R * +--R +--------------+ +--R | 2 +--R \|b coth(x) + a +--R + +--R 2 6 2 5 +--R 2a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (30a b cosh(x) + 4b - 2a b - 4a b)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (40a b cosh(x) + (16b - 8a b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R 30a b cosh(x) + (24b - 12a b - 24a b)cosh(x) + 4b + 6a b +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 12a b cosh(x) + (16b - 8a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (8b + 12a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 2a b cosh(x) + (4b - 2a b - 4a b)cosh(x) +--R + +--R 3 2 2 2 +--R (4b + 6a b + 2a b)cosh(x) +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 8 2 7 +--R 2a b sinh(x) + 16a b cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 6 +--R (56a b cosh(x) - 4b + 2a b - 6a b)sinh(x) +--R + +--R 2 3 3 2 2 5 +--R (112a b cosh(x) + (- 24b + 12a b - 36a b)cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 3 2 +--R 140a b cosh(x) + (- 60b + 30a b - 90a b)cosh(x) - 8b + 4a b +--R + +--R 2 +--R 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 2 2 3 +--R 112a b cosh(x) + (- 80b + 40a b - 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 2 2 4 +--R 56a b cosh(x) + (- 60b + 30a b - 90a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 48b + 24a b + 36a b)cosh(x) - 4b - 6a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 2 2 5 +--R 16a b cosh(x) + (- 24b + 12a b - 36a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 32b + 16a b + 24a b)cosh(x) + (- 8b - 12a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 3 2 2 6 +--R 2a b cosh(x) + (- 4b + 2a b - 6a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 8b + 4a b + 6a b)cosh(x) + (- 4b - 6a b - 2a b)cosh(x) +--R * +--R +-----+ +--R \|b + a +--R / +--R 6 5 +--R (2b - 2a)sinh(x) + (12b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((30b - 30a)cosh(x) - 2b + 6a)sinh(x) +--R + +--R 3 3 +--R ((40b - 40a)cosh(x) + (- 8b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((30b - 30a)cosh(x) + (- 12b + 36a)cosh(x) - 2b - 6a)sinh(x) +--R + +--R 5 3 +--R ((12b - 12a)cosh(x) + (- 8b + 24a)cosh(x) + (- 4b - 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (2b - 2a)cosh(x) + (- 2b + 6a)cosh(x) + (- 2b - 6a)cosh(x) + 2b + 2a +--R * +--R +-----------------------------------------------+ +--R | 2 2 +--R +-----+ |(2b + 2a)sinh(x) + (2b + 2a)cosh(x) + 2b - 2a +--R \|b + a |----------------------------------------------- +--R | 2 2 +--R \| sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 2b - 2a )sinh(x) + (- 16b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((- 56b - 56a )cosh(x) + 8a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((- 112b - 112a )cosh(x) + 48a cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 4 +--R ((- 140b - 140a )cosh(x) + 120a cosh(x) + 4b - 4a b - 12a )sinh(x) +--R + +--R 2 2 5 2 3 +--R (- 112b - 112a )cosh(x) + 160a cosh(x) +--R + +--R 2 2 +--R (16b - 16a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 4 +--R (- 56b - 56a )cosh(x) + 120a cosh(x) +--R + +--R 2 2 2 2 +--R (24b - 24a b - 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 +--R (- 16b - 16a )cosh(x) + 48a cosh(x) +--R + +--R 2 2 3 2 +--R (16b - 16a b - 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (- 2b - 2a )cosh(x) + 8a cosh(x) + (4b - 4a b - 12a )cosh(x) +--R + +--R 2 2 2 2 +--R (8a b + 8a )cosh(x) - 2b - 4a b - 2a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 508 +--d0364b:= D(m0364b,x) +--E 333 + +--S 334 of 508 +t0365:= sech(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (296) \|sech(b x + a) +--R Type: Expression(Integer) +--E 334 + +--S 335 of 508 +r0365:= -2*%i*cosh(a+b*x)^(1/2)*EllipticF(1/2*%i*(a+b*x),2)*sech(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 335 + +--S 336 of 508 +a0365:= integrate(t0365,x) +--R +--R +--R x +--R ++ +---------------+ +--I (297) | \|sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 336 + +--S 337 of 508 +--m0365:= a0365-r0365 +--E 337 + +--S 338 of 508 +--d0365:= D(m0365,x) +--E 338 + +--S 339 of 508 +t0366:= sech(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (298) sech(b x + a)\|sech(b x + a) +--R Type: Expression(Integer) +--E 339 + +--S 340 of 508 +r0366:= 2*(1/cosh(a+b*x))^(1/2)*(%i*cosh(a+b*x)^(1/2)*_ + EllipticE(1/2*%i*(a+b*x),2)+sinh(a+b*x))/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 340 + +--S 341 of 508 +a0366:= integrate(t0366,x) +--R +--R +--R x +--R ++ +---------------+ +--I (299) | sech(%BC b + a)\|sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 341 + +--S 342 of 508 +--m0366:= a0366-r0366 +--E 342 + +--S 343 of 508 +--d0366:= D(m0366,x) +--E 343 + +--S 344 of 508 +t0367:= sech(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (300) sech(b x + a) \|sech(b x + a) +--R Type: Expression(Integer) +--E 344 + +--S 345 of 508 +r0367:= -2/3*(1/cosh(a+b*x))^(1/2)*(%i*cosh(a+b*x)^(3/2)*_ + EllipticF(1/2*%i*(a+b*x),2)-sinh(a+b*x))/b/cosh(a+b*x) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 345 + +--S 346 of 508 +a0367:= integrate(t0367,x) +--R +--R +--R x +--R ++ 2 +---------------+ +--I (301) | sech(%BC b + a) \|sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 346 + +--S 347 of 508 +--m0367:= a0367-r0367 +--E 347 + +--S 348 of 508 +--d0367:= D(m0367,x) +--E 348 + +--S 349 of 508 +t0368:= 1/sech(a+b*x)^(1/2) +--R +--R +--R 1 +--R (302) ---------------- +--R +-------------+ +--R \|sech(b x + a) +--R Type: Expression(Integer) +--E 349 + +--S 350 of 508 +r0368:= -2*%i*cosh(a+b*x)^(1/2)*EllipticE(1/2*%i*(a+b*x),2)*sech(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 350 + +--S 351 of 508 +a0368:= integrate(t0368,x) +--R +--R +--R x +--R ++ 1 +--I (303) | ------------------ d%BC +--R ++ +---------------+ +--I \|sech(%BC b + a) +--R Type: Union(Expression(Integer),...) +--E 351 + +--S 352 of 508 +--m0368:= a0368-r0368 +--E 352 + +--S 353 of 508 +--d0368:= D(m0368,x) +--E 353 + +--S 354 of 508 +t0369:= 1/sech(a+b*x)^(3/2) +--R +--R +--R 1 +--R (304) ----------------------------- +--R +-------------+ +--R sech(b x + a)\|sech(b x + a) +--R Type: Expression(Integer) +--E 354 + +--S 355 of 508 +r0369:= -2/3*%i*cosh(a+b*x)^(1/2)*EllipticF(1/2*%i*(a+b*x),2)*_ + sech(a+b*x)^(1/2)/b+2/3*sinh(a+b*x)/b/sech(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 355 + +--S 356 of 508 +a0369:= integrate(t0369,x) +--R +--R +--R x +--R ++ 1 +--I (305) | --------------------------------- d%BC +--R ++ +---------------+ +--I sech(%BC b + a)\|sech(%BC b + a) +--R Type: Union(Expression(Integer),...) +--E 356 + +--S 357 of 508 +--m0369:= a0369-r0369 +--E 357 + +--S 358 of 508 +--d0369:= D(m0369,x) +--E 358 + +--S 359 of 508 +t0370:= 1/sech(a+b*x)^(5/2) +--R +--R +--R 1 +--R (306) ------------------------------ +--R 2 +-------------+ +--R sech(b x + a) \|sech(b x + a) +--R Type: Expression(Integer) +--E 359 + +--S 360 of 508 +r0370:= -6/5*%i*cosh(a+b*x)^(1/2)*EllipticE(1/2*%i*(a+b*x),2)*_ + sech(a+b*x)^(1/2)/b+2/5*sinh(a+b*x)/b/sech(a+b*x)^(3/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 360 + +--S 361 of 508 +a0370:= integrate(t0370,x) +--R +--R +--R x +--R ++ 1 +--I (307) | ---------------------------------- d%BC +--R ++ 2 +---------------+ +--I sech(%BC b + a) \|sech(%BC b + a) +--R Type: Union(Expression(Integer),...) +--E 361 + +--S 362 of 508 +--m0370:= a0370-r0370 +--E 362 + +--S 363 of 508 +--d0370:= D(m0370,x) +--E 363 + +--S 364 of 508 +t0371:= x*sech(a+b*x) +--R +--R +--R (308) x sech(b x + a) +--R Type: Expression(Integer) +--E 364 + +--S 365 of 508 +r0371:= (2*x*atan(exp(a+b*x))*b-%i*polylog(2,-%i*exp(a+b*x))+_ + %i*polylog(2,%i*exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 365 + +--S 366 of 508 +a0371:= integrate(t0371,x) +--R +--R +--R x +--R ++ +--I (309) | %BC sech(%BC b + a)d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 366 + +--S 367 of 508 +--m0371:= a0371-r0371 +--E 367 + +--S 368 of 508 +--d0371:= D(m0371,x) +--E 368 + +--S 369 of 508 +t0372:= x^2*sech(a+b*x) +--R +--R +--R 2 +--R (310) x sech(b x + a) +--R Type: Expression(Integer) +--E 369 + +--S 370 of 508 +r0372:= 2*(x^2*atan(exp(a+b*x))*b^2-%i*x*polylog(2,-%i*exp(a+b*x))*b+_ + %i*x*polylog(2,%i*exp(a+b*x))*b+%i*polylog(3,-%i*exp(a+b*x))-_ + %i*polylog(3,%i*exp(a+b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 370 + +--S 371 of 508 +a0372:= integrate(t0372,x) +--R +--R +--R x +--R ++ 2 +--I (311) | %BC sech(%BC b + a)d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 371 + +--S 372 of 508 +--m0372:= a0372-r0372 +--E 372 + +--S 373 of 508 +--d0372:= D(m0372,x) +--E 373 + +--S 374 of 508 +t0373:= x^3*sech(a+b*x) +--R +--R +--R 3 +--R (312) x sech(b x + a) +--R Type: Expression(Integer) +--E 374 + +--S 375 of 508 +r0373:= (2*x^3*atan(exp(a+b*x))*b^3-3*%i*x^2*polylog(2,-%i*exp(a+b*x))*b^2+_ + 3*%i*x^2*polylog(2,%i*exp(a+b*x))*b^2+_ + 6*%i*x*polylog(3,-%i*exp(a+b*x))*b-_ + 6*%i*x*polylog(3,%i*exp(a+b*x))*b-_ + 6*%i*polylog(4,-%i*exp(a+b*x))+_ + 6*%i*polylog(4,%i*exp(a+b*x)))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 375 + +--S 376 of 508 +a0373:= integrate(t0373,x) +--R +--R +--R x +--R ++ 3 +--I (313) | %BC sech(%BC b + a)d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 376 + +--S 377 of 508 +--m0373:= a0373-r0373 +--E 377 + +--S 378 of 508 +--d0373:= D(m0373,x) +--E 378 + +--S 379 of 508 +t0374:= x*sech(a+b*x)^2 +--R +--R +--R 2 +--R (314) x sech(b x + a) +--R Type: Expression(Integer) +--E 379 + +--S 380 of 508 +r0374:= -log(cosh(a+b*x))/b^2+x*tanh(a+b*x)/b +--R +--R +--R - log(cosh(b x + a)) + b x tanh(b x + a) +--R (315) ---------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 380 + +--S 381 of 508 +a0374:= integrate(t0374,x) +--R +--R +--R (316) +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) - 1) +--R * +--R 2cosh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 +--R 2b x sinh(b x + a) + 4b x cosh(b x + a)sinh(b x + a) + 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) + b +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 508 +--m0374:= a0374-r0374 +--E 382 + +--S 383 of 508 +--d0374:= D(m0374,x) +--E 383 + +--S 384 of 508 +t0375:= x^2*sech(a+b*x)^2 +--R +--R +--R 2 2 +--R (317) x sech(b x + a) +--R Type: Expression(Integer) +--E 384 + +--S 385 of 508 +r0375:= (b^2*x^2-2*x*log(exp(2*a+2*b*x)+1)*b-polylog(2,-exp(2*a+2*b*x))+_ + x^2*tanh(a+b*x)*b^2)/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 385 + +--S 386 of 508 +a0375:= integrate(t0375,x) +--R +--R +--R x +--R ++ 2 2 +--I (318) | %BC sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 508 +--m0375:= a0375-r0375 +--E 387 + +--S 388 of 508 +--d0375:= D(m0375,x) +--E 388 + +--S 389 of 508 +t0376:= x^3*sech(a+b*x)^2 +--R +--R +--R 3 2 +--R (319) x sech(b x + a) +--R Type: Expression(Integer) +--E 389 + +--S 390 of 508 +r0376:= 1/2*(2*b^3*x^3-6*x^2*log(exp(2*a+2*b*x)+1)*b^2-_ + 6*x*polylog(2,-exp(2*a+2*b*x))*b+_ + 3*polylog(3,-exp(2*a+2*b*x))+2*x^3*tanh(a+b*x)*b^3)/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 390 + +--S 391 of 508 +a0376:= integrate(t0376,x) +--R +--R +--R x +--R ++ 3 2 +--I (320) | %BC sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 508 +--m0376:= a0376-r0376 +--E 392 + +--S 393 of 508 +--d0376:= D(m0376,x) +--E 393 + +--S 394 of 508 +t0377:= x*sech(a+b*x)^3 +--R +--R +--R 3 +--R (321) x sech(b x + a) +--R Type: Expression(Integer) +--E 394 + +--S 395 of 508 +r0377:= x*atan(exp(1)^(a+b*x))/b-1/2*%i*polylog(2,-%i*exp(1)^(a+b*x))/b^2+_ + 1/2*%i*polylog(2,%i*exp(1)^(a+b*x))/b^2+_ + 1/2*sech(a+b*x)/b^2+1/2*x*sech(a+b*x)*tanh(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 395 + +--S 396 of 508 +a0377:= integrate(t0377,x) +--R +--R +--R x +--R ++ 3 +--I (322) | %BC sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 508 +--m0377:= a0377-r0377 +--E 397 + +--S 398 of 508 +--d0377:= D(m0377,x) +--E 398 + +--S 399 of 508 +t0378:= x^2*sech(a+b*x)^3 +--R +--R +--R 2 3 +--R (323) x sech(b x + a) +--R Type: Expression(Integer) +--E 399 + +--S 400 of 508 +r0378:= x^2*atan(exp(1)^(a+b*x))/b-atan(sinh(a+b*x))/b^3-_ + %i*x*polylog(2,-%i*exp(1)^(a+b*x))/b^2+_ + %i*x*polylog(2,%i*exp(1)^(a+b*x))/b^2+_ + %i*polylog(3,-%i*exp(1)^(a+b*x))/b^3-_ + %i*polylog(3,%i*exp(1)^(a+b*x))/b^3+_ + x*sech(a+b*x)/b^2+1/2*x^2*sech(a+b*x)*tanh(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 400 + +--S 401 of 508 +a0378:= integrate(t0378,x) +--R +--R +--R x +--R ++ 2 3 +--I (324) | %BC sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 508 +--m0378:= a0378-r0378 +--E 402 + +--S 403 of 508 +--d0378:= D(m0378,x) +--E 403 + +--S 404 of 508 +t0379:= (c+d*x)*sech(a+b*x) +--R +--R +--R (325) (d x + c)sech(b x + a) +--R Type: Expression(Integer) +--E 404 + +--S 405 of 508 +r0379:= (2*atan(exp(a+b*x))*c*b+2*atan(exp(a+b*x))*d*x*b-_ + %i*d*polylog(2,-%i*exp(a+b*x))+%i*d*polylog(2,%i*exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 405 + +--S 406 of 508 +a0379:= integrate(t0379,x) +--R +--R +--R x +--R ++ +--I (326) | (%BC d + c)sech(%BC b + a)d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 508 +--m0379:= a0379-r0379 +--E 407 + +--S 408 of 508 +--d0379:= D(m0379,x) +--E 408 + +--S 409 of 508 +t0380:= (c+d*x)^2*sech(a+b*x) +--R +--R +--R 2 2 2 +--R (327) (d x + 2c d x + c )sech(b x + a) +--R Type: Expression(Integer) +--E 409 + +--S 410 of 508 +r0380:= 2*(c+d*x)^2*atan(exp(1)^(a+b*x))/b-2*%i*d*(c+d*x)*_ + polylog(2,-%i*exp(1)^(a+b*x))/b^2+2*%i*d*(c+d*x)*_ + polylog(2,%i*exp(1)^(a+b*x))/b^2+2*%i*d^2*_ + polylog(3,-%i*exp(1)^(a+b*x))/b^3-2*%i*d^2*_ + polylog(3,%i*exp(1)^(a+b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 410 + +--S 411 of 508 +a0380:= integrate(t0380,x) +--R +--R +--R x +--R ++ 2 2 2 +--I (328) | (%BC d + 2%BC c d + c )sech(%BC b + a)d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 508 +--m0380:= a0380-r0380 +--E 412 + +--S 413 of 508 +--d0380:= D(m0380,x) +--E 413 + +--S 414 of 508 +t0381:= (c+d*x)^3*sech(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R (329) (d x + 3c d x + 3c d x + c )sech(b x + a) +--R Type: Expression(Integer) +--E 414 + +--S 415 of 508 +r0381:= 2*(c+d*x)^3*atan(exp(1)^(a+b*x))/b-3*%i*d*(c+d*x)^2*_ + polylog(2,-%i*exp(1)^(a+b*x))/b^2+3*%i*d*(c+d*x)^2*_ + polylog(2,%i*exp(1)^(a+b*x))/b^2+6*%i*d^2*(c+d*x)*_ + polylog(3,-%i*exp(1)^(a+b*x))/b^3-6*%i*d^2*(c+d*x)*_ + polylog(3,%i*exp(1)^(a+b*x))/b^3-6*%i*d^3*_ + polylog(4,-%i*exp(1)^(a+b*x))/b^4+6*%i*d^3*_ + polylog(4,%i*exp(1)^(a+b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 415 + +--S 416 of 508 +a0381:= integrate(t0381,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 +--I (330) | (%BC d + 3%BC c d + 3%BC c d + c )sech(%BC b + a)d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 416 + +--S 417 of 508 +--m0381:= a0381-r0381 +--E 417 + +--S 418 of 508 +--d0381:= D(m0381,x) +--E 418 + +--S 419 of 508 +t0382:= (c+d*x)*sech(a+b*x)^2 +--R +--R +--R 2 +--R (331) (d x + c)sech(b x + a) +--R Type: Expression(Integer) +--E 419 + +--S 420 of 508 +r0382:= -d*log(cosh(a+b*x))/b^2+(c+d*x)*tanh(a+b*x)/b +--R +--R +--R - d log(cosh(b x + a)) + (b d x + b c)tanh(b x + a) +--R (332) --------------------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 420 + +--S 421 of 508 +a0382:= integrate(t0382,x) +--R +--R +--R (333) +--R 2 2 +--R - d sinh(b x + a) - 2d cosh(b x + a)sinh(b x + a) - d cosh(b x + a) +--R + +--R - d +--R * +--R 2cosh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R 2b d x sinh(b x + a) + 4b d x cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R 2b d x cosh(b x + a) - 2b c +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) + b +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 508 +m0382:= a0382-r0382 +--R +--R +--R (334) +--R 2 2 +--R d sinh(b x + a) + 2d cosh(b x + a)sinh(b x + a) + d cosh(b x + a) +--R + +--R d +--R * +--R log(cosh(b x + a)) +--R + +--R 2 2 +--R - d sinh(b x + a) - 2d cosh(b x + a)sinh(b x + a) - d cosh(b x + a) +--R + +--R - d +--R * +--R 2cosh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R (- b d x - b c)sinh(b x + a) +--R + +--R (- 2b d x - 2b c)cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R (- b d x - b c)cosh(b x + a) - b d x - b c +--R * +--R tanh(b x + a) +--R + +--R 2 +--R 2b d x sinh(b x + a) + 4b d x cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R 2b d x cosh(b x + a) - 2b c +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) + b +--R Type: Expression(Integer) +--E 422 + +--S 423 of 508 +d0382:= D(m0382,x) +--R +--R +--R (335) +--R 4 +--R (b d x + b c)sinh(b x + a) +--R + +--R 3 +--R (4b d x + 4b c)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R ((6b d x + 6b c)cosh(b x + a) + 2b d x + 2b c)sinh(b x + a) +--R + +--R 3 +--R ((4b d x + 4b c)cosh(b x + a) + (4b d x + 4b c)cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 4 2 +--R (b d x + b c)cosh(b x + a) + (2b d x + 2b c)cosh(b x + a) + b d x +--R + +--R b c +--R * +--R 2 +--R tanh(b x + a) +--R + +--R 4 3 +--R - d sinh(b x + a) - 4d cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 6d cosh(b x + a) - 2d)sinh(b x + a) +--R + +--R 3 +--R (- 4d cosh(b x + a) - 4d cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R - d cosh(b x + a) - 2d cosh(b x + a) - d +--R * +--R tanh(b x + a) +--R + +--R 4 +--R (- b d x + d - b c)sinh(b x + a) +--R + +--R 3 +--R (- 4b d x + 4d - 4b c)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R ((- 6b d x + 6d - 6b c)cosh(b x + a) + 2b d x + 2b c)sinh(b x + a) +--R + +--R 3 +--R ((- 4b d x + 4d - 4b c)cosh(b x + a) + (4b d x + 4b c)cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 4 2 +--R (- b d x + d - b c)cosh(b x + a) + (2b d x + 2b c)cosh(b x + a) - b d x +--R + +--R - d - b c +--R / +--R 4 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (6b cosh(b x + a) + 2b)sinh(b x + a) +--R + +--R 3 4 +--R (4b cosh(b x + a) + 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 2 +--R 2b cosh(b x + a) + b +--R Type: Expression(Integer) +--E 423 + +--S 424 of 508 +t0383:= (c+d*x)^2*sech(a+b*x)^2 +--R +--R +--R 2 2 2 2 +--R (336) (d x + 2c d x + c )sech(b x + a) +--R Type: Expression(Integer) +--E 424 + +--S 425 of 508 +r0383:= (c+d*x)^2/b-2*d*(c+d*x)*log(1+exp(1)^(2*a+2*b*x))/b^2-_ + d^2*polylog(2,-exp(1)^(2*a+2*b*x))/b^3+(c+d*x)^2*tanh(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 425 + +--S 426 of 508 +a0383:= integrate(t0383,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--I (337) | (%BC d + 2%BC c d + c )sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 426 + +--S 427 of 508 +--m0383:= a0383-r0383 +--E 427 + +--S 428 of 508 +--d0383:= D(m0383,x) +--E 428 + +--S 429 of 508 +t0384:= (c+d*x)^3*sech(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 2 +--R (338) (d x + 3c d x + 3c d x + c )sech(b x + a) +--R Type: Expression(Integer) +--E 429 + +--S 430 of 508 +r0384:= (c+d*x)^3/b-3*d*(c+d*x)^2*log(1+exp(1)^(2*a+2*b*x))/b^2-_ + 3*d^2*(c+d*x)*polylog(2,-exp(1)^(2*a+2*b*x))/b^3+_ + 3/2*d^3*polylog(3,-exp(1)^(2*a+2*b*x))/b^4+(c+d*x)^3*tanh(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 430 + +--S 431 of 508 +a0384:= integrate(t0384,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 2 +--I (339) | (%BC d + 3%BC c d + 3%BC c d + c )sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 431 + +--S 432 of 508 +--m0384:= a0384-r0384 +--E 432 + +--S 433 of 508 +--d0384:= D(m0384,x) +--E 433 + +--S 434 of 508 +t0385:= (c+d*x)*sech(a+b*x)^3 +--R +--R +--R 3 +--R (340) (d x + c)sech(b x + a) +--R Type: Expression(Integer) +--E 434 + +--S 435 of 508 +r0385:= (c+d*x)*atan(exp(1)^(a+b*x))/b-1/2*%i*d*_ + polylog(2,-%i*exp(1)^(a+b*x))/b^2+1/2*%i*d*_ + polylog(2,%i*exp(1)^(a+b*x))/b^2+1/2*d*_ + sech(a+b*x)/b^2+1/2*(c+d*x)*sech(a+b*x)*tanh(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 435 + +--S 436 of 508 +a0385:= integrate(t0385,x) +--R +--R +--R x +--R ++ 3 +--I (341) | (%BC d + c)sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 508 +--m0385:= a0385-r0385 +--E 437 + +--S 438 of 508 +--d0385:= D(m0385,x) +--E 438 + +--S 439 of 508 +t0386:= (c+d*x)^2*sech(a+b*x)^3 +--R +--R +--R 2 2 2 3 +--R (342) (d x + 2c d x + c )sech(b x + a) +--R Type: Expression(Integer) +--E 439 + +--S 440 of 508 +r0386:= (c+d*x)^2*atan(exp(1)^(a+b*x))/b-d^2*atan(sinh(a+b*x))/b^3-_ + %i*d*(c+d*x)*polylog(2,-%i*exp(1)^(a+b*x))/b^2+_ + %i*d*(c+d*x)*polylog(2,%i*exp(1)^(a+b*x))/b^2+_ + %i*d^2*polylog(3,-%i*exp(1)^(a+b*x))/b^3-_ + %i*d^2*polylog(3,%i*exp(1)^(a+b*x))/b^3+d*(c+d*x)*sech(a+b*x)/b^2+_ + 1/2*(c+d*x)^2*sech(a+b*x)*tanh(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 440 + +--S 441 of 508 +a0386:= integrate(t0386,x) +--R +--R +--R x +--R ++ 2 2 2 3 +--I (343) | (%BC d + 2%BC c d + c )sech(%BC b + a) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 508 +--m0386:= a0386-r0386 +--E 442 + +--S 443 of 508 +--d0386:= D(m0386,x) +--E 443 + +--S 444 of 508 +t0387:= sech(x)^(1/2) +--R +--R +--R +-------+ +--R (344) \|sech(x) +--R Type: Expression(Integer) +--E 444 + +--S 445 of 508 +r0387:= -2*%i*cosh(x)^(1/2)*EllipticF(1/2*%i*x,2)*sech(x)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 445 + +--S 446 of 508 +a0387:= integrate(t0387,x) +--R +--R +--R x +--R ++ +---------+ +--I (345) | \|sech(%BC) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 508 +--m0387:= a0387-r0387 +--E 447 + +--S 448 of 508 +--d0387:= D(m0387,x) +--E 448 + +--S 449 of 508 +t0388:= (sech(x)^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R (346) \|sech(x) +--R Type: Expression(Integer) +--E 449 + +--S 450 of 508 +r0388:= asin(tanh(x)) +--R +--R +--R (347) asin(tanh(x)) +--R Type: Expression(Integer) +--E 450 + +--S 451 of 508 +a0388:= integrate(t0388,x) +--R +--R +--R (348) 2atan(sinh(x) + cosh(x)) +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 508 +m0388:= a0388-r0388 +--R +--R +--R (349) 2atan(sinh(x) + cosh(x)) - asin(tanh(x)) +--R Type: Expression(Integer) +--E 452 + +--S 453 of 508 +d0388:= D(m0388,x) +--R +--R +--R (350) +--R +--------------+ +--R | 2 +--R (2sinh(x) + 2cosh(x))\|- tanh(x) + 1 +--R + +--R 2 2 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)tanh(x) - sinh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R / +--R +--------------+ +--R 2 2 | 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- tanh(x) + 1 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 508 +t0389:= (sech(x)^3)^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R (351) \|sech(x) +--R Type: Expression(Integer) +--E 454 + +--S 455 of 508 +r0389:= 2*cosh(x)*(sech(x)^3)^(1/2)*(%i*cosh(x)^(1/2)*_ + EllipticE(1/2*%i*x,2)+sinh(x)) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 455 + +--S 456 of 508 +a0389:= integrate(t0389,x) +--R +--R +--R x +----------+ +--R ++ | 3 +--I (352) | \|sech(%BC) d%BC +--R ++ +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 508 +--m0389:= a0389-r0389 +--E 457 + +--S 458 of 508 +--d0389:= D(m0389,x) +--E 458 + +--S 459 of 508 +t0390:= (sech(x)^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (353) \|sech(x) +--R Type: Expression(Integer) +--E 459 + +--S 460 of 508 +r0390:= 1/cosh(x)*csgn(1/cosh(x)^2)*sinh(x) +--R +--R There are no library operations named csgn +--R Use HyperDoc Browse or issue +--R )what op csgn +--R to learn if there is any operation containing " csgn " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named csgn +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 460 + +--S 461 of 508 +a0390:= integrate(t0390,x) +--R +--R +--R 2 +--R (354) - ----------------------------------------- +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 508 +--m0390:= a0390-r0390 +--E 462 + +--S 463 of 508 +--d0390:= D(m0390,x) +--E 463 + +--S 464 of 508 +t0391:= 1/(a+a*sech(c+d*x)) +--R +--R +--R 1 +--R (355) ------------------- +--R a sech(d x + c) + a +--R Type: Expression(Integer) +--E 464 + +--S 465 of 508 +r0391:= x/a-sinh(c+d*x)/a/d/(1+cosh(c+d*x)) +--R +--R +--R - sinh(d x + c) + d x cosh(d x + c) + d x +--R (356) ----------------------------------------- +--R a d cosh(d x + c) + a d +--R Type: Expression(Integer) +--E 465 + +--S 466 of 508 +a0391:= integrate(t0391,x) +--R +--R +--R d x sinh(d x + c) + d x cosh(d x + c) + d x + 2 +--R (357) ----------------------------------------------- +--R a d sinh(d x + c) + a d cosh(d x + c) + a d +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 508 +m0391:= a0391-r0391 +--R +--R +--R (358) +--R 2 +--R sinh(d x + c) + (cosh(d x + c) + 1)sinh(d x + c) + 2cosh(d x + c) + 2 +--R / +--R 2 +--R (a d cosh(d x + c) + a d)sinh(d x + c) + a d cosh(d x + c) +--R + +--R 2a d cosh(d x + c) + a d +--R Type: Expression(Integer) +--E 467 + +--S 468 of 508 +d0391:= D(m0391,x) +--R +--R +--R (359) +--R 4 3 +--R - sinh(d x + c) + (- 2cosh(d x + c) - 2)sinh(d x + c) +--R + +--R 2 +--R (- cosh(d x + c) - 1)sinh(d x + c) +--R + +--R 3 2 +--R (2cosh(d x + c) + 2cosh(d x + c) - 2cosh(d x + c) - 2)sinh(d x + c) +--R + +--R 4 3 2 +--R cosh(d x + c) + cosh(d x + c) - cosh(d x + c) - cosh(d x + c) +--R / +--R 2 2 +--R (a cosh(d x + c) + 2a cosh(d x + c) + a)sinh(d x + c) +--R + +--R 3 2 +--R (2a cosh(d x + c) + 6a cosh(d x + c) + 6a cosh(d x + c) + 2a) +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 +--R a cosh(d x + c) + 4a cosh(d x + c) + 6a cosh(d x + c) +--R + +--R 4a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 468 + +--S 469 of 508 +t0392:= 1/(a-a*sech(c+d*x)) +--R +--R +--R 1 +--R (360) - ------------------- +--R a sech(d x + c) - a +--R Type: Expression(Integer) +--E 469 + +--S 470 of 508 +r0392:= x/a+sinh(c+d*x)/a/d/(1-cosh(c+d*x)) +--R +--R +--R - sinh(d x + c) + d x cosh(d x + c) - d x +--R (361) ----------------------------------------- +--R a d cosh(d x + c) - a d +--R Type: Expression(Integer) +--E 470 + +--S 471 of 508 +a0392:= integrate(t0392,x) +--R +--R +--R d x sinh(d x + c) + d x cosh(d x + c) - d x - 2 +--R (362) ----------------------------------------------- +--R a d sinh(d x + c) + a d cosh(d x + c) - a d +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 508 +m0392:= a0392-r0392 +--R +--R +--R (363) +--R 2 +--R sinh(d x + c) + (cosh(d x + c) - 1)sinh(d x + c) - 2cosh(d x + c) + 2 +--R / +--R 2 +--R (a d cosh(d x + c) - a d)sinh(d x + c) + a d cosh(d x + c) +--R + +--R - 2a d cosh(d x + c) + a d +--R Type: Expression(Integer) +--E 472 + +--S 473 of 508 +d0392:= D(m0392,x) +--R +--R +--R (364) +--R 4 3 +--R - sinh(d x + c) + (- 2cosh(d x + c) + 2)sinh(d x + c) +--R + +--R 2 +--R (cosh(d x + c) - 1)sinh(d x + c) +--R + +--R 3 2 +--R (2cosh(d x + c) - 2cosh(d x + c) - 2cosh(d x + c) + 2)sinh(d x + c) +--R + +--R 4 3 2 +--R cosh(d x + c) - cosh(d x + c) - cosh(d x + c) + cosh(d x + c) +--R / +--R 2 2 +--R (a cosh(d x + c) - 2a cosh(d x + c) + a)sinh(d x + c) +--R + +--R 3 2 +--R (2a cosh(d x + c) - 6a cosh(d x + c) + 6a cosh(d x + c) - 2a) +--R * +--R sinh(d x + c) +--R + +--R 4 3 2 +--R a cosh(d x + c) - 4a cosh(d x + c) + 6a cosh(d x + c) +--R + +--R - 4a cosh(d x + c) + a +--R Type: Expression(Integer) +--E 473 + +--S 474 of 508 +t0393:= (3+3*sech(x))^(1/2) +--R +--R +--R +------------+ +--R (365) \|3sech(x) + 3 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 508 +r0393:= 2*3^(1/2)*atan((-1+sech(x))^(1/2))*tanh(x)/_ + (-1+sech(x))^(1/2)/(1+sech(x))^(1/2) +--R +--R +--R +-+ +-----------+ +--R 2\|3 tanh(x)atan(\|sech(x) - 1 ) +--R (366) -------------------------------- +--R +-----------+ +-----------+ +--R \|sech(x) - 1 \|sech(x) + 1 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 508 +a0393:= integrate(t0393,x) +--R +--R +--R (367) +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- - \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +-+ +--R - \|3 cosh(x) - \|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R \|3 +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4cosh(x) + 1)sinh(x) + cosh(x) - 2cosh(x) +--R + +--R cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R - \|3 sinh(x) + (- 3\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +-+ 3 +--R (- 3\|3 cosh(x) + 2\|3 cosh(x) - \|3 )sinh(x) - \|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R \|3 cosh(x) - \|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 508 +m0393:= a0393-r0393 +--R +--R +--R (368) +--R - +--R +-+ +-----------+ +-----------+ +--R \|3 \|sech(x) - 1 \|sech(x) + 1 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- - \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +-+ +--R - \|3 cosh(x) - \|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +-----------+ +-----------+ +--R \|3 \|sech(x) - 1 \|sech(x) + 1 +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4cosh(x) + 1)sinh(x) + cosh(x) - 2cosh(x) +--R + +--R cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R - \|3 sinh(x) + (- 3\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +-+ 3 +--R (- 3\|3 cosh(x) + 2\|3 cosh(x) - \|3 )sinh(x) - \|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R \|3 cosh(x) - \|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R + +--R +-+ +-----------+ +--R - 2\|3 tanh(x)atan(\|sech(x) - 1 ) +--R / +--R +-----------+ +-----------+ +--R \|sech(x) - 1 \|sech(x) + 1 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 508 +d0393:= D(m0393,x) +--R +--R +--R (369) +--R 6 5 2 4 +--R - 6sinh(x) - 36cosh(x)sinh(x) + (- 90cosh(x) + 6)sinh(x) +--R + +--R 3 3 +--R (- 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 90cosh(x) + 36cosh(x) + 36)sinh(x) +--R + +--R 5 3 6 +--R (- 36cosh(x) + 24cosh(x) + 72cosh(x))sinh(x) - 6cosh(x) +--R + +--R 4 2 +--R 6cosh(x) + 36cosh(x) + 24 +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 +--R (- 6sech(x) + 6)sinh(x) +--R + +--R 2 5 +--R (- 36cosh(x)sech(x) + 36cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 90cosh(x) + 6)sech(x) + 90cosh(x) - 6)sinh(x) +--R + +--R 3 2 3 +--R ((- 120cosh(x) + 24cosh(x))sech(x) + 120cosh(x) - 24cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 90cosh(x) + 36cosh(x) + 36)sech(x) + 90cosh(x) +--R + +--R 2 +--R - 36cosh(x) - 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 36cosh(x) + 24cosh(x) + 72cosh(x))sech(x) + 36cosh(x) +--R + +--R 3 +--R - 24cosh(x) - 72cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- 6cosh(x) + 6cosh(x) + 36cosh(x) + 24)sech(x) + 6cosh(x) +--R + +--R 4 2 +--R - 6cosh(x) - 36cosh(x) - 24 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 6 +-+ 5 +--R 6\|3 sinh(x) + 36\|3 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (90\|3 cosh(x) + 6\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (120\|3 cosh(x) + 24\|3 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90\|3 cosh(x) + 36\|3 cosh(x) - 24\|3 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (36\|3 cosh(x) + 24\|3 cosh(x) - 48\|3 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 6\|3 cosh(x) + 6\|3 cosh(x) - 24\|3 cosh(x) - 24\|3 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 2 +-+ 6 +--R (6\|3 sech(x) - 6\|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (36\|3 cosh(x)sech(x) - 36\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((90\|3 cosh(x) + 6\|3 )sech(x) - 90\|3 cosh(x) - 6\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (120\|3 cosh(x) + 24\|3 cosh(x))sech(x) - 120\|3 cosh(x) +--R + +--R +-+ +--R - 24\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90\|3 cosh(x) + 36\|3 cosh(x) - 24\|3 )sech(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 90\|3 cosh(x) - 36\|3 cosh(x) + 24\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (36\|3 cosh(x) + 24\|3 cosh(x) - 48\|3 cosh(x))sech(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 36\|3 cosh(x) - 24\|3 cosh(x) + 48\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (6\|3 cosh(x) + 6\|3 cosh(x) - 24\|3 cosh(x) - 24\|3 )sech(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 6\|3 cosh(x) - 6\|3 cosh(x) + 24\|3 cosh(x) + 24\|3 +--R * +--R +-----------+ +--R atan(\|sech(x) - 1 ) +--R + +--R 2 6 +--R (- 6sech(x) + 6)sinh(x) +--R + +--R 2 5 +--R ((- 36cosh(x) + 18)sech(x) + 36cosh(x) - 18)sinh(x) +--R + +--R 2 2 2 +--R (- 90cosh(x) + 90cosh(x) + 3)sech(x) + 90cosh(x) +--R + +--R - 90cosh(x) - 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 120cosh(x) + 180cosh(x) + 12cosh(x) + 30)sech(x) +--R + +--R 3 2 +--R 120cosh(x) - 180cosh(x) - 12cosh(x) - 30 +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 90cosh(x) + 180cosh(x) + 18cosh(x) + 90cosh(x) + 24) +--R * +--R 2 +--R sech(x) +--R + +--R 4 3 2 +--R 90cosh(x) - 180cosh(x) - 18cosh(x) - 90cosh(x) - 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 36cosh(x) + 90cosh(x) + 12cosh(x) + 90cosh(x) +--R + +--R 48cosh(x) + 12 +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 3 2 +--R 36cosh(x) - 90cosh(x) - 12cosh(x) - 90cosh(x) - 48cosh(x) +--R + +--R - 12 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 6cosh(x) + 18cosh(x) + 3cosh(x) + 30cosh(x) +--R + +--R 2 +--R 24cosh(x) + 12cosh(x) + 12 +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 4 3 2 +--R 6cosh(x) - 18cosh(x) - 3cosh(x) - 30cosh(x) - 24cosh(x) +--R + +--R - 12cosh(x) - 12 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 2 +-+ 6 +--R (3\|3 sech(x) - 3\|3 )sinh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ 5 +--R ((18\|3 cosh(x) - 6\|3 )sech(x) - 18\|3 cosh(x) + 6\|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ 2 +--R (45\|3 cosh(x) - 30\|3 cosh(x) + 3\|3 )sech(x) - 45\|3 cosh(x) +--R + +--R +-+ +-+ +--R 30\|3 cosh(x) - 3\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (60\|3 cosh(x) - 60\|3 cosh(x) + 12\|3 cosh(x) - 24\|3 ) +--R * +--R 2 +--R sech(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 60\|3 cosh(x) + 60\|3 cosh(x) - 12\|3 cosh(x) + 24\|3 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 45\|3 cosh(x) - 60\|3 cosh(x) + 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72\|3 cosh(x) - 18\|3 +--R * +--R 2 +--R sech(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 45\|3 cosh(x) + 60\|3 cosh(x) - 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R 72\|3 cosh(x) + 18\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 18\|3 cosh(x) - 30\|3 cosh(x) + 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72\|3 cosh(x) - 36\|3 cosh(x) - 12\|3 +--R * +--R 2 +--R sech(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 18\|3 cosh(x) + 30\|3 cosh(x) - 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 72\|3 cosh(x) + 36\|3 cosh(x) + 12\|3 +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 3\|3 cosh(x) - 6\|3 cosh(x) + 3\|3 cosh(x) - 24\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 18\|3 cosh(x) - 12\|3 cosh(x) - 12\|3 +--R * +--R 2 +--R sech(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R - 3\|3 cosh(x) + 6\|3 cosh(x) - 3\|3 cosh(x) + 24\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 18\|3 cosh(x) + 12\|3 cosh(x) + 12\|3 +--R * +--R +-----------+ +-----------+ +--R \|sech(x) - 1 \|sech(x) + 1 +--R + +--R 6 5 +--R (3sech(x) + 3)sinh(x) + (18cosh(x)sech(x) + 18cosh(x))sinh(x) +--R + +--R 2 2 4 +--R ((45cosh(x) - 3)sech(x) + 45cosh(x) - 3)sinh(x) +--R + +--R 3 3 +--R ((60cosh(x) - 12cosh(x))sech(x) + 60cosh(x) - 12cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 4 +--R (45cosh(x) - 18cosh(x) - 18)sech(x) + 45cosh(x) +--R + +--R 2 +--R - 18cosh(x) - 18 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 5 +--R (18cosh(x) - 12cosh(x) - 36cosh(x))sech(x) + 18cosh(x) +--R + +--R 3 +--R - 12cosh(x) - 36cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 6 +--R (3cosh(x) - 3cosh(x) - 18cosh(x) - 12)sech(x) + 3cosh(x) +--R + +--R 4 2 +--R - 3cosh(x) - 18cosh(x) - 12 +--R * +--R +-----------------------------------------+ +--R 2 | 3 +--R tanh(x) |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +-+ 6 +--R (- 3\|3 sech(x) - 3\|3 )sinh(x) +--R + +--R +-+ +-+ 5 +--R (- 18\|3 cosh(x)sech(x) - 18\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R ((- 45\|3 cosh(x) - 3\|3 )sech(x) - 45\|3 cosh(x) - 3\|3 ) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ +-+ 3 +--R (- 60\|3 cosh(x) - 12\|3 cosh(x))sech(x) - 60\|3 cosh(x) +--R + +--R +-+ +--R - 12\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 45\|3 cosh(x) - 18\|3 cosh(x) + 12\|3 )sech(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 45\|3 cosh(x) - 18\|3 cosh(x) + 12\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 18\|3 cosh(x) - 12\|3 cosh(x) + 24\|3 cosh(x))sech(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 18\|3 cosh(x) - 12\|3 cosh(x) + 24\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 3\|3 cosh(x) - 3\|3 cosh(x) + 12\|3 cosh(x) + 12\|3 ) +--R * +--R sech(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 3\|3 cosh(x) - 3\|3 cosh(x) + 12\|3 cosh(x) + 12\|3 +--R * +--R 2 +--R tanh(x) +--R * +--R +-----------+ +--R \|sech(x) - 1 +--R / +--R +-+ 2 +-+ 6 +--R (\|3 sech(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (6\|3 cosh(x)sech(x) - 6\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((15\|3 cosh(x) - \|3 )sech(x) - 15\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (20\|3 cosh(x) - 4\|3 cosh(x))sech(x) - 20\|3 cosh(x) +--R + +--R +-+ +--R 4\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|3 cosh(x) - 6\|3 cosh(x) - 6\|3 )sech(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 15\|3 cosh(x) + 6\|3 cosh(x) + 6\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (6\|3 cosh(x) - 4\|3 cosh(x) - 12\|3 cosh(x))sech(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 6\|3 cosh(x) + 4\|3 cosh(x) + 12\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (\|3 cosh(x) - \|3 cosh(x) - 6\|3 cosh(x) - 4\|3 )sech(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - \|3 cosh(x) + \|3 cosh(x) + 6\|3 cosh(x) + 4\|3 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 2 6 2 5 +--R (- 3sech(x) + 3)sinh(x) + (- 18cosh(x)sech(x) + 18cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 45cosh(x) - 3)sech(x) + 45cosh(x) + 3)sinh(x) +--R + +--R 3 2 3 3 +--R ((- 60cosh(x) - 12cosh(x))sech(x) + 60cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (- 45cosh(x) - 18cosh(x) + 12)sech(x) + 45cosh(x) + 18cosh(x) +--R + +--R - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 18cosh(x) - 12cosh(x) + 24cosh(x))sech(x) + 18cosh(x) +--R + +--R 3 +--R 12cosh(x) - 24cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- 3cosh(x) - 3cosh(x) + 12cosh(x) + 12)sech(x) + 3cosh(x) +--R + +--R 4 2 +--R 3cosh(x) - 12cosh(x) - 12 +--R * +--R +-----------+ +-----------+ +--R \|sech(x) - 1 \|sech(x) + 1 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 508 +t0394:= (3-3*sech(x))^(1/2) +--R +--R +--R +--------------+ +--R (370) \|- 3sech(x) + 3 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 508 +r0394:= 2*3^(1/2)*atan((-1-sech(x))^(1/2))*tanh(x)/_ + (-1-sech(x))^(1/2)/(1-sech(x))^(1/2) +--R +--R +--R +-+ +-------------+ +--R 2\|3 tanh(x)atan(\|- sech(x) - 1 ) +--R (371) ---------------------------------- +--R +-------------+ +-------------+ +--R \|- sech(x) - 1 \|- sech(x) + 1 +--R Type: Expression(Integer) +--E 480 + +--S 481 of 508 +a0394:= integrate(t0394,x) +--R +--R +--R (372) +--R +-+ +--R \|3 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- + \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +-+ +--R \|3 cosh(x) - \|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|3 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (- 3cosh(x) - 4cosh(x) - 1)sinh(x) - cosh(x) - 2cosh(x) +--R + +--R - cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R \|3 sinh(x) + (3\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +-+ 3 +--R (3\|3 cosh(x) + 2\|3 cosh(x) + \|3 )sinh(x) + \|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R \|3 cosh(x) + \|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 508 +m0394:= a0394-r0394 +--R +--R +--R (373) +--R +-+ +-------------+ +-------------+ +--R \|3 \|- sech(x) - 1 \|- sech(x) + 1 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- + \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +-+ +--R \|3 cosh(x) - \|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +-------------+ +-------------+ +--R \|3 \|- sech(x) - 1 \|- sech(x) + 1 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4cosh(x) - 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2cosh(x) - cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R \|3 sinh(x) + (3\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +-+ 3 +--R (3\|3 cosh(x) + 2\|3 cosh(x) + \|3 )sinh(x) + \|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R \|3 cosh(x) + \|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R + +--R +-+ +-------------+ +--R - 2\|3 tanh(x)atan(\|- sech(x) - 1 ) +--R / +--R +-------------+ +-------------+ +--R \|- sech(x) - 1 \|- sech(x) + 1 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 508 +d0394:= D(m0394,x) +--R +--R +--R (374) +--R 6 5 2 4 +--R - 6sinh(x) - 36cosh(x)sinh(x) + (- 90cosh(x) + 6)sinh(x) +--R + +--R 3 3 +--R (- 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 90cosh(x) + 36cosh(x) + 36)sinh(x) +--R + +--R 5 3 6 +--R (- 36cosh(x) + 24cosh(x) + 72cosh(x))sinh(x) - 6cosh(x) +--R + +--R 4 2 +--R 6cosh(x) + 36cosh(x) + 24 +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 +--R (- 6sech(x) + 6)sinh(x) +--R + +--R 2 5 +--R (- 36cosh(x)sech(x) + 36cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 90cosh(x) + 6)sech(x) + 90cosh(x) - 6)sinh(x) +--R + +--R 3 2 3 +--R ((- 120cosh(x) + 24cosh(x))sech(x) + 120cosh(x) - 24cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 90cosh(x) + 36cosh(x) + 36)sech(x) + 90cosh(x) +--R + +--R 2 +--R - 36cosh(x) - 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 36cosh(x) + 24cosh(x) + 72cosh(x))sech(x) + 36cosh(x) +--R + +--R 3 +--R - 24cosh(x) - 72cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- 6cosh(x) + 6cosh(x) + 36cosh(x) + 24)sech(x) + 6cosh(x) +--R + +--R 4 2 +--R - 6cosh(x) - 36cosh(x) - 24 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 6 +-+ 5 +--R 6\|3 sinh(x) + 36\|3 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (90\|3 cosh(x) + 6\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (120\|3 cosh(x) + 24\|3 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90\|3 cosh(x) + 36\|3 cosh(x) - 24\|3 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (36\|3 cosh(x) + 24\|3 cosh(x) - 48\|3 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 6\|3 cosh(x) + 6\|3 cosh(x) - 24\|3 cosh(x) - 24\|3 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 2 +-+ 6 +--R (6\|3 sech(x) - 6\|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (36\|3 cosh(x)sech(x) - 36\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((90\|3 cosh(x) + 6\|3 )sech(x) - 90\|3 cosh(x) - 6\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (120\|3 cosh(x) + 24\|3 cosh(x))sech(x) - 120\|3 cosh(x) +--R + +--R +-+ +--R - 24\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90\|3 cosh(x) + 36\|3 cosh(x) - 24\|3 )sech(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 90\|3 cosh(x) - 36\|3 cosh(x) + 24\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (36\|3 cosh(x) + 24\|3 cosh(x) - 48\|3 cosh(x))sech(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 36\|3 cosh(x) - 24\|3 cosh(x) + 48\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (6\|3 cosh(x) + 6\|3 cosh(x) - 24\|3 cosh(x) - 24\|3 )sech(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 6\|3 cosh(x) - 6\|3 cosh(x) + 24\|3 cosh(x) + 24\|3 +--R * +--R +-------------+ +--R atan(\|- sech(x) - 1 ) +--R + +--R 2 6 +--R (6sech(x) - 6)sinh(x) +--R + +--R 2 5 +--R ((36cosh(x) + 18)sech(x) - 36cosh(x) - 18)sinh(x) +--R + +--R 2 2 2 +--R (90cosh(x) + 90cosh(x) - 3)sech(x) - 90cosh(x) - 90cosh(x) +--R + +--R 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (120cosh(x) + 180cosh(x) - 12cosh(x) + 30)sech(x) +--R + +--R 3 2 +--R - 120cosh(x) - 180cosh(x) + 12cosh(x) - 30 +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R (90cosh(x) + 180cosh(x) - 18cosh(x) + 90cosh(x) - 24) +--R * +--R 2 +--R sech(x) +--R + +--R 4 3 2 +--R - 90cosh(x) - 180cosh(x) + 18cosh(x) - 90cosh(x) + 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 36cosh(x) + 90cosh(x) - 12cosh(x) + 90cosh(x) +--R + +--R - 48cosh(x) + 12 +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 3 2 +--R - 36cosh(x) - 90cosh(x) + 12cosh(x) - 90cosh(x) +--R + +--R 48cosh(x) - 12 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 6cosh(x) + 18cosh(x) - 3cosh(x) + 30cosh(x) - 24cosh(x) +--R + +--R 12cosh(x) - 12 +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 4 3 2 +--R - 6cosh(x) - 18cosh(x) + 3cosh(x) - 30cosh(x) + 24cosh(x) +--R + +--R - 12cosh(x) + 12 +--R * +--R +-------------+ +-------------+ +--R \|- sech(x) - 1 \|- sech(x) + 1 +--R + +--R 6 +--R (- 3sech(x) + 3)sinh(x) +--R + +--R 5 +--R (- 18cosh(x)sech(x) + 18cosh(x))sinh(x) +--R + +--R 2 2 4 +--R ((- 45cosh(x) + 3)sech(x) + 45cosh(x) - 3)sinh(x) +--R + +--R 3 3 +--R ((- 60cosh(x) + 12cosh(x))sech(x) + 60cosh(x) - 12cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 4 +--R (- 45cosh(x) + 18cosh(x) + 18)sech(x) + 45cosh(x) +--R + +--R 2 +--R - 18cosh(x) - 18 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 5 +--R (- 18cosh(x) + 12cosh(x) + 36cosh(x))sech(x) + 18cosh(x) +--R + +--R 3 +--R - 12cosh(x) - 36cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 6 +--R (- 3cosh(x) + 3cosh(x) + 18cosh(x) + 12)sech(x) + 3cosh(x) +--R + +--R 4 2 +--R - 3cosh(x) - 18cosh(x) - 12 +--R * +--R 2 +-------------+ +--R tanh(x) \|- sech(x) - 1 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ 2 +-+ 6 +--R (- 3\|3 sech(x) + 3\|3 )sinh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ 5 +--R ((- 18\|3 cosh(x) - 6\|3 )sech(x) + 18\|3 cosh(x) + 6\|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (- 45\|3 cosh(x) - 30\|3 cosh(x) - 3\|3 )sech(x) +--R + +--R +-+ 2 +-+ +-+ +--R 45\|3 cosh(x) + 30\|3 cosh(x) + 3\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 60\|3 cosh(x) - 60\|3 cosh(x) - 12\|3 cosh(x) - 24\|3 ) +--R * +--R 2 +--R sech(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 60\|3 cosh(x) + 60\|3 cosh(x) + 12\|3 cosh(x) + 24\|3 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 45\|3 cosh(x) - 60\|3 cosh(x) - 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72\|3 cosh(x) + 18\|3 +--R * +--R 2 +--R sech(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 45\|3 cosh(x) + 60\|3 cosh(x) + 18\|3 cosh(x) + 72\|3 cosh(x) +--R + +--R +-+ +--R - 18\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 18\|3 cosh(x) - 30\|3 cosh(x) - 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72\|3 cosh(x) + 36\|3 cosh(x) - 12\|3 +--R * +--R 2 +--R sech(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R 18\|3 cosh(x) + 30\|3 cosh(x) + 12\|3 cosh(x) + 72\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 36\|3 cosh(x) + 12\|3 +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R - 3\|3 cosh(x) - 6\|3 cosh(x) - 3\|3 cosh(x) - 24\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 18\|3 cosh(x) - 12\|3 cosh(x) + 12\|3 +--R * +--R 2 +--R sech(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 3\|3 cosh(x) + 6\|3 cosh(x) + 3\|3 cosh(x) + 24\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 18\|3 cosh(x) + 12\|3 cosh(x) - 12\|3 +--R * +--R +-------------+ +-------------+ +--R \|- sech(x) - 1 \|- sech(x) + 1 +--R + +--R +-+ +-+ 6 +--R (3\|3 sech(x) - 3\|3 )sinh(x) +--R + +--R +-+ +-+ 5 +--R (18\|3 cosh(x)sech(x) - 18\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ 4 +--R ((45\|3 cosh(x) + 3\|3 )sech(x) - 45\|3 cosh(x) - 3\|3 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 3 +--R (60\|3 cosh(x) + 12\|3 cosh(x))sech(x) - 60\|3 cosh(x) +--R + +--R +-+ +--R - 12\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (45\|3 cosh(x) + 18\|3 cosh(x) - 12\|3 )sech(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 45\|3 cosh(x) - 18\|3 cosh(x) + 12\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (18\|3 cosh(x) + 12\|3 cosh(x) - 24\|3 cosh(x))sech(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 18\|3 cosh(x) - 12\|3 cosh(x) + 24\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (3\|3 cosh(x) + 3\|3 cosh(x) - 12\|3 cosh(x) - 12\|3 )sech(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 3\|3 cosh(x) - 3\|3 cosh(x) + 12\|3 cosh(x) + 12\|3 +--R * +--R 2 +-------------+ +--R tanh(x) \|- sech(x) - 1 +--R / +--R +-+ 2 +-+ 6 +--R (\|3 sech(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (6\|3 cosh(x)sech(x) - 6\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((15\|3 cosh(x) - \|3 )sech(x) - 15\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (20\|3 cosh(x) - 4\|3 cosh(x))sech(x) - 20\|3 cosh(x) +--R + +--R +-+ +--R 4\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +-+ 4 +--R (15\|3 cosh(x) - 6\|3 cosh(x) - 6\|3 )sech(x) - 15\|3 cosh(x) +--R + +--R +-+ 2 +-+ +--R 6\|3 cosh(x) + 6\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (6\|3 cosh(x) - 4\|3 cosh(x) - 12\|3 cosh(x))sech(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 6\|3 cosh(x) + 4\|3 cosh(x) + 12\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (\|3 cosh(x) - \|3 cosh(x) - 6\|3 cosh(x) - 4\|3 )sech(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - \|3 cosh(x) + \|3 cosh(x) + 6\|3 cosh(x) + 4\|3 +--R * +--R +-------------+ +-------------+ +--R \|- sech(x) - 1 \|- sech(x) + 1 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 2 6 2 5 +--R (- 3sech(x) + 3)sinh(x) + (- 18cosh(x)sech(x) + 18cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 45cosh(x) - 3)sech(x) + 45cosh(x) + 3)sinh(x) +--R + +--R 3 2 3 3 +--R ((- 60cosh(x) - 12cosh(x))sech(x) + 60cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 2 4 +--R (- 45cosh(x) - 18cosh(x) + 12)sech(x) + 45cosh(x) +--R + +--R 2 +--R 18cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 18cosh(x) - 12cosh(x) + 24cosh(x))sech(x) + 18cosh(x) +--R + +--R 3 +--R 12cosh(x) - 24cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- 3cosh(x) - 3cosh(x) + 12cosh(x) + 12)sech(x) + 3cosh(x) +--R + +--R 4 2 +--R 3cosh(x) - 12cosh(x) - 12 +--R * +--R +-------------+ +-------------+ +--R \|- sech(x) - 1 \|- sech(x) + 1 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 508 +t0395:= (a+a*sech(x))^(1/2) +--R +--R +--R +-------------+ +--R (375) \|a sech(x) + a +--R Type: Expression(Integer) +--E 484 + +--S 485 of 508 +r0395:= 2*a*atan((-1+sech(x))^(1/2))*tanh(x)/_ + (-1+sech(x))^(1/2)/(a+a*sech(x))^(1/2) +--R +--R +--R +-----------+ +--R 2a tanh(x)atan(\|sech(x) - 1 ) +--R (376) ------------------------------ +--R +-----------+ +-------------+ +--R \|sech(x) - 1 \|a sech(x) + a +--R Type: Expression(Integer) +--E 485 + +--S 486 of 508 +a0395:= integrate(t0395,x) +--R +--R +--R (377) +--R - +--R +-+ +--R \|a +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +--R (- sinh(x) - cosh(x) - 1)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R \|a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4cosh(x) + 1)sinh(x) + cosh(x) - 2cosh(x) +--R + +--R cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 3 2 +--R - sinh(x) + (- 3cosh(x) + 1)sinh(x) +--R + +--R 2 3 2 +--R (- 3cosh(x) + 2cosh(x) - 1)sinh(x) - cosh(x) + cosh(x) +--R + +--R - cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 508 +m0395:= a0395-r0395 +--R +--R +--R (378) +--R - +--R +-+ +-----------+ +-------------+ +--R \|a \|sech(x) - 1 \|a sech(x) + a +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +--R (- sinh(x) - cosh(x) - 1)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +-----------+ +-------------+ +--R \|a \|sech(x) - 1 \|a sech(x) + a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4cosh(x) + 1)sinh(x) + cosh(x) - 2cosh(x) +--R + +--R cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 3 2 +--R - sinh(x) + (- 3cosh(x) + 1)sinh(x) +--R + +--R 2 3 2 +--R (- 3cosh(x) + 2cosh(x) - 1)sinh(x) - cosh(x) + cosh(x) +--R + +--R - cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R + +--R +-----------+ +--R - 2a tanh(x)atan(\|sech(x) - 1 ) +--R / +--R +-----------+ +-------------+ +--R \|sech(x) - 1 \|a sech(x) + a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 508 +d0395:= D(m0395,x) +--R +--R +--R (379) +--R 6 5 +--R - 2a sinh(x) - 12a cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 30a cosh(x) + 2a)sinh(x) +--R + +--R 3 3 +--R (- 40a cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30a cosh(x) + 12a cosh(x) + 12a)sinh(x) +--R + +--R 5 3 +--R (- 12a cosh(x) + 8a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 2a cosh(x) + 2a cosh(x) + 12a cosh(x) + 8a +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 +--R (- 2a sech(x) + 2a)sinh(x) +--R + +--R 2 5 +--R (- 12a cosh(x)sech(x) + 12a cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a cosh(x) + 2a)sech(x) + 30a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 3 +--R (- 40a cosh(x) + 8a cosh(x))sech(x) + 40a cosh(x) +--R + +--R - 8a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 30a cosh(x) + 12a cosh(x) + 12a)sech(x) + 30a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 12a cosh(x) + 8a cosh(x) + 24a cosh(x))sech(x) +--R + +--R 5 3 +--R 12a cosh(x) - 8a cosh(x) - 24a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 2a cosh(x) + 2a cosh(x) + 12a cosh(x) + 8a)sech(x) +--R + +--R 6 4 2 +--R 2a cosh(x) - 2a cosh(x) - 12a cosh(x) - 8a +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 2 6 2 5 2 2 2 4 +--R 2a sinh(x) + 12a cosh(x)sinh(x) + (30a cosh(x) + 2a )sinh(x) +--R + +--R 2 3 2 3 +--R (40a cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (30a cosh(x) + 12a cosh(x) - 8a )sinh(x) +--R + +--R 2 5 2 3 2 2 6 +--R (12a cosh(x) + 8a cosh(x) - 16a cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 2 4 2 2 2 +--R 2a cosh(x) - 8a cosh(x) - 8a +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 2 6 +--R (2a sech(x) - 2a )sinh(x) +--R + +--R 2 2 2 5 +--R (12a cosh(x)sech(x) - 12a cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 2 4 +--R ((30a cosh(x) + 2a )sech(x) - 30a cosh(x) - 2a )sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R ((40a cosh(x) + 8a cosh(x))sech(x) - 40a cosh(x) - 8a cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 2 4 +--R (30a cosh(x) + 12a cosh(x) - 8a )sech(x) - 30a cosh(x) +--R + +--R 2 2 2 +--R - 12a cosh(x) + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 2 5 +--R (12a cosh(x) + 8a cosh(x) - 16a cosh(x))sech(x) - 12a cosh(x) +--R + +--R 2 3 2 +--R - 8a cosh(x) + 16a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 2 6 +--R (2a cosh(x) + 2a cosh(x) - 8a cosh(x) - 8a )sech(x) - 2a cosh(x) +--R + +--R 2 4 2 2 2 +--R - 2a cosh(x) + 8a cosh(x) + 8a +--R * +--R +-----------+ +--R atan(\|sech(x) - 1 ) +--R + +--R 2 6 +--R (- 2a sech(x) + 2a)sinh(x) +--R + +--R 2 5 +--R ((- 12a cosh(x) + 6a)sech(x) + 12a cosh(x) - 6a)sinh(x) +--R + +--R 2 2 2 +--R (- 30a cosh(x) + 30a cosh(x) + a)sech(x) + 30a cosh(x) +--R + +--R - 30a cosh(x) - a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 40a cosh(x) + 60a cosh(x) + 4a cosh(x) + 10a)sech(x) +--R + +--R 3 2 +--R 40a cosh(x) - 60a cosh(x) - 4a cosh(x) - 10a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R - 30a cosh(x) + 60a cosh(x) + 6a cosh(x) + 30a cosh(x) +--R + +--R 8a +--R * +--R 2 +--R sech(x) +--R + +--R 4 3 2 +--R 30a cosh(x) - 60a cosh(x) - 6a cosh(x) - 30a cosh(x) - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R - 12a cosh(x) + 30a cosh(x) + 4a cosh(x) +--R + +--R 2 +--R 30a cosh(x) + 16a cosh(x) + 4a +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 3 2 +--R 12a cosh(x) - 30a cosh(x) - 4a cosh(x) - 30a cosh(x) +--R + +--R - 16a cosh(x) - 4a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 2a cosh(x) + 6a cosh(x) + a cosh(x) + 10a cosh(x) +--R + +--R 2 +--R 8a cosh(x) + 4a cosh(x) + 4a +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 4 3 +--R 2a cosh(x) - 6a cosh(x) - a cosh(x) - 10a cosh(x) +--R + +--R 2 +--R - 8a cosh(x) - 4a cosh(x) - 4a +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 2 6 +--R (a sech(x) - a)sinh(x) +--R + +--R 2 5 +--R ((6a cosh(x) - 2a)sech(x) - 6a cosh(x) + 2a)sinh(x) +--R + +--R 2 2 2 +--R (15a cosh(x) - 10a cosh(x) + a)sech(x) - 15a cosh(x) +--R + +--R 10a cosh(x) - a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (20a cosh(x) - 20a cosh(x) + 4a cosh(x) - 8a)sech(x) +--R + +--R 3 2 +--R - 20a cosh(x) + 20a cosh(x) - 4a cosh(x) + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 15a cosh(x) - 20a cosh(x) + 6a cosh(x) - 24a cosh(x) +--R + +--R - 6a +--R * +--R 2 +--R sech(x) +--R + +--R 4 3 2 +--R - 15a cosh(x) + 20a cosh(x) - 6a cosh(x) + 24a cosh(x) + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 6a cosh(x) - 10a cosh(x) + 4a cosh(x) - 24a cosh(x) +--R + +--R - 12a cosh(x) - 4a +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 3 2 +--R - 6a cosh(x) + 10a cosh(x) - 4a cosh(x) + 24a cosh(x) +--R + +--R 12a cosh(x) + 4a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R a cosh(x) - 2a cosh(x) + a cosh(x) - 8a cosh(x) +--R + +--R 2 +--R - 6a cosh(x) - 4a cosh(x) - 4a +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 4 3 +--R - a cosh(x) + 2a cosh(x) - a cosh(x) + 8a cosh(x) +--R + +--R 2 +--R 6a cosh(x) + 4a cosh(x) + 4a +--R * +--R +-+ +--R \|a +--R * +--R +-----------+ +-------------+ +--R \|sech(x) - 1 \|a sech(x) + a +--R + +--R 6 +--R (a sech(x) + a)sinh(x) +--R + +--R 5 +--R (6a cosh(x)sech(x) + 6a cosh(x))sinh(x) +--R + +--R 2 2 4 +--R ((15a cosh(x) - a)sech(x) + 15a cosh(x) - a)sinh(x) +--R + +--R 3 3 +--R (20a cosh(x) - 4a cosh(x))sech(x) + 20a cosh(x) +--R + +--R - 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 4 +--R (15a cosh(x) - 6a cosh(x) - 6a)sech(x) + 15a cosh(x) +--R + +--R 2 +--R - 6a cosh(x) - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 +--R (6a cosh(x) - 4a cosh(x) - 12a cosh(x))sech(x) +--R + +--R 5 3 +--R 6a cosh(x) - 4a cosh(x) - 12a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 6 +--R (a cosh(x) - a cosh(x) - 6a cosh(x) - 4a)sech(x) + a cosh(x) +--R + +--R 4 2 +--R - a cosh(x) - 6a cosh(x) - 4a +--R * +--R +-----------------------------------------+ +--R 2 +-+ | a +--R tanh(x) \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 2 2 6 +--R (- a sech(x) - a )sinh(x) +--R + +--R 2 2 5 +--R (- 6a cosh(x)sech(x) - 6a cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 4 +--R ((- 15a cosh(x) - a )sech(x) - 15a cosh(x) - a )sinh(x) +--R + +--R 2 3 2 2 3 +--R (- 20a cosh(x) - 4a cosh(x))sech(x) - 20a cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 4 +--R (- 15a cosh(x) - 6a cosh(x) + 4a )sech(x) - 15a cosh(x) +--R + +--R 2 2 2 +--R - 6a cosh(x) + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 +--R (- 6a cosh(x) - 4a cosh(x) + 8a cosh(x))sech(x) +--R + +--R 2 5 2 3 2 +--R - 6a cosh(x) - 4a cosh(x) + 8a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (- a cosh(x) - a cosh(x) + 4a cosh(x) + 4a )sech(x) +--R + +--R 2 6 2 4 2 2 2 +--R - a cosh(x) - a cosh(x) + 4a cosh(x) + 4a +--R * +--R 2 +--R tanh(x) +--R * +--R +-----------+ +--R \|sech(x) - 1 +--R / +--R 2 6 2 5 +--R (sech(x) - 1)sinh(x) + (6cosh(x)sech(x) - 6cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((15cosh(x) - 1)sech(x) - 15cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 3 +--R ((20cosh(x) - 4cosh(x))sech(x) - 20cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (15cosh(x) - 6cosh(x) - 6)sech(x) - 15cosh(x) + 6cosh(x) +--R + +--R 6 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (6cosh(x) - 4cosh(x) - 12cosh(x))sech(x) - 6cosh(x) +--R + +--R 3 +--R 4cosh(x) + 12cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (cosh(x) - cosh(x) - 6cosh(x) - 4)sech(x) - cosh(x) + cosh(x) +--R + +--R 2 +--R 6cosh(x) + 4 +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 2 6 +--R (- a sech(x) + a)sinh(x) +--R + +--R 2 5 +--R (- 6a cosh(x)sech(x) + 6a cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 15a cosh(x) - a)sech(x) + 15a cosh(x) + a)sinh(x) +--R + +--R 3 2 3 +--R ((- 20a cosh(x) - 4a cosh(x))sech(x) + 20a cosh(x) + 4a cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 15a cosh(x) - 6a cosh(x) + 4a)sech(x) + 15a cosh(x) +--R + +--R 2 +--R 6a cosh(x) - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 6a cosh(x) - 4a cosh(x) + 8a cosh(x))sech(x) + 6a cosh(x) +--R + +--R 3 +--R 4a cosh(x) - 8a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- a cosh(x) - a cosh(x) + 4a cosh(x) + 4a)sech(x) + a cosh(x) +--R + +--R 4 2 +--R a cosh(x) - 4a cosh(x) - 4a +--R * +--R +-----------+ +-------------+ +--R \|sech(x) - 1 \|a sech(x) + a +--R Type: Expression(Integer) +--E 488 + +--S 489 of 508 +t0396:= (a-a*sech(x))^(1/2) +--R +--R +--R +---------------+ +--R (380) \|- a sech(x) + a +--R Type: Expression(Integer) +--E 489 + +--S 490 of 508 +r0396:= 2*a*atan((-1-sech(x))^(1/2))*tanh(x)/_ + (-1-sech(x))^(1/2)/(a-a*sech(x))^(1/2) +--R +--R +--R +-------------+ +--R 2a tanh(x)atan(\|- sech(x) - 1 ) +--R (381) ---------------------------------- +--R +---------------+ +-------------+ +--R \|- a sech(x) + a \|- sech(x) - 1 +--R Type: Expression(Integer) +--E 490 + +--S 491 of 508 +a0396:= integrate(t0396,x) +--R +--R +--R (382) +--R +-+ +--R \|a +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +--R (sinh(x) + cosh(x) - 1)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|a +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (- 3cosh(x) - 4cosh(x) - 1)sinh(x) - cosh(x) - 2cosh(x) +--R + +--R - cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 3 2 +--R sinh(x) + (3cosh(x) + 1)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) + 2cosh(x) + 1)sinh(x) + cosh(x) + cosh(x) +--R + +--R cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 508 +m0396:= a0396-r0396 +--R +--R +--R (383) +--R +-+ +---------------+ +-------------+ +--R \|a \|- a sech(x) + a \|- sech(x) - 1 +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R +-+ +--R (sinh(x) + cosh(x) - 1)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +---------------+ +-------------+ +--R \|a \|- a sech(x) + a \|- sech(x) - 1 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4cosh(x) - 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2cosh(x) - cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 3 2 +--R sinh(x) + (3cosh(x) + 1)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) + 2cosh(x) + 1)sinh(x) + cosh(x) + cosh(x) +--R + +--R cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R + +--R +-------------+ +--R - 2a tanh(x)atan(\|- sech(x) - 1 ) +--R / +--R +---------------+ +-------------+ +--R \|- a sech(x) + a \|- sech(x) - 1 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 508 +d0396:= D(m0396,x) +--R +--R +--R (384) +--R 6 5 +--R - 2a sinh(x) - 12a cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 30a cosh(x) + 2a)sinh(x) +--R + +--R 3 3 +--R (- 40a cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30a cosh(x) + 12a cosh(x) + 12a)sinh(x) +--R + +--R 5 3 +--R (- 12a cosh(x) + 8a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 2a cosh(x) + 2a cosh(x) + 12a cosh(x) + 8a +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 +--R (- 2a sech(x) + 2a)sinh(x) +--R + +--R 2 5 +--R (- 12a cosh(x)sech(x) + 12a cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a cosh(x) + 2a)sech(x) + 30a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 3 +--R (- 40a cosh(x) + 8a cosh(x))sech(x) + 40a cosh(x) +--R + +--R - 8a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 30a cosh(x) + 12a cosh(x) + 12a)sech(x) + 30a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 12a cosh(x) + 8a cosh(x) + 24a cosh(x))sech(x) +--R + +--R 5 3 +--R 12a cosh(x) - 8a cosh(x) - 24a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 2a cosh(x) + 2a cosh(x) + 12a cosh(x) + 8a)sech(x) +--R + +--R 6 4 2 +--R 2a cosh(x) - 2a cosh(x) - 12a cosh(x) - 8a +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 2 6 2 5 2 2 2 4 +--R 2a sinh(x) + 12a cosh(x)sinh(x) + (30a cosh(x) + 2a )sinh(x) +--R + +--R 2 3 2 3 +--R (40a cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (30a cosh(x) + 12a cosh(x) - 8a )sinh(x) +--R + +--R 2 5 2 3 2 2 6 +--R (12a cosh(x) + 8a cosh(x) - 16a cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 2 4 2 2 2 +--R 2a cosh(x) - 8a cosh(x) - 8a +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 2 6 +--R (2a sech(x) - 2a )sinh(x) +--R + +--R 2 2 2 5 +--R (12a cosh(x)sech(x) - 12a cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 2 4 +--R ((30a cosh(x) + 2a )sech(x) - 30a cosh(x) - 2a )sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R ((40a cosh(x) + 8a cosh(x))sech(x) - 40a cosh(x) - 8a cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 2 4 +--R (30a cosh(x) + 12a cosh(x) - 8a )sech(x) - 30a cosh(x) +--R + +--R 2 2 2 +--R - 12a cosh(x) + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 2 5 +--R (12a cosh(x) + 8a cosh(x) - 16a cosh(x))sech(x) - 12a cosh(x) +--R + +--R 2 3 2 +--R - 8a cosh(x) + 16a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 2 6 +--R (2a cosh(x) + 2a cosh(x) - 8a cosh(x) - 8a )sech(x) - 2a cosh(x) +--R + +--R 2 4 2 2 2 +--R - 2a cosh(x) + 8a cosh(x) + 8a +--R * +--R +-------------+ +--R atan(\|- sech(x) - 1 ) +--R + +--R 2 6 +--R (2a sech(x) - 2a)sinh(x) +--R + +--R 2 5 +--R ((12a cosh(x) + 6a)sech(x) - 12a cosh(x) - 6a)sinh(x) +--R + +--R 2 2 2 +--R (30a cosh(x) + 30a cosh(x) - a)sech(x) - 30a cosh(x) +--R + +--R - 30a cosh(x) + a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (40a cosh(x) + 60a cosh(x) - 4a cosh(x) + 10a)sech(x) +--R + +--R 3 2 +--R - 40a cosh(x) - 60a cosh(x) + 4a cosh(x) - 10a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 30a cosh(x) + 60a cosh(x) - 6a cosh(x) + 30a cosh(x) +--R + +--R - 8a +--R * +--R 2 +--R sech(x) +--R + +--R 4 3 2 +--R - 30a cosh(x) - 60a cosh(x) + 6a cosh(x) - 30a cosh(x) + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 12a cosh(x) + 30a cosh(x) - 4a cosh(x) + 30a cosh(x) +--R + +--R - 16a cosh(x) + 4a +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 3 2 +--R - 12a cosh(x) - 30a cosh(x) + 4a cosh(x) - 30a cosh(x) +--R + +--R 16a cosh(x) - 4a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R 2a cosh(x) + 6a cosh(x) - a cosh(x) + 10a cosh(x) +--R + +--R 2 +--R - 8a cosh(x) + 4a cosh(x) - 4a +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 4 3 +--R - 2a cosh(x) - 6a cosh(x) + a cosh(x) - 10a cosh(x) +--R + +--R 2 +--R 8a cosh(x) - 4a cosh(x) + 4a +--R * +--R +---------------+ +--R \|- a sech(x) + a +--R + +--R 6 +--R (- a sech(x) + a)sinh(x) +--R + +--R 5 +--R (- 6a cosh(x)sech(x) + 6a cosh(x))sinh(x) +--R + +--R 2 2 4 +--R ((- 15a cosh(x) + a)sech(x) + 15a cosh(x) - a)sinh(x) +--R + +--R 3 3 +--R (- 20a cosh(x) + 4a cosh(x))sech(x) + 20a cosh(x) +--R + +--R - 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 4 +--R (- 15a cosh(x) + 6a cosh(x) + 6a)sech(x) + 15a cosh(x) +--R + +--R 2 +--R - 6a cosh(x) - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 +--R (- 6a cosh(x) + 4a cosh(x) + 12a cosh(x))sech(x) +--R + +--R 5 3 +--R 6a cosh(x) - 4a cosh(x) - 12a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (- a cosh(x) + a cosh(x) + 6a cosh(x) + 4a)sech(x) +--R + +--R 6 4 2 +--R a cosh(x) - a cosh(x) - 6a cosh(x) - 4a +--R * +--R 2 +-+ +--R tanh(x) \|a +--R * +--R +-----------------------------------------+ +--R +-------------+ | a +--R \|- sech(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 2 6 +--R (- a sech(x) + a)sinh(x) +--R + +--R 2 5 +--R ((- 6a cosh(x) - 2a)sech(x) + 6a cosh(x) + 2a)sinh(x) +--R + +--R 2 2 2 +--R (- 15a cosh(x) - 10a cosh(x) - a)sech(x) + 15a cosh(x) +--R + +--R 10a cosh(x) + a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 20a cosh(x) - 20a cosh(x) - 4a cosh(x) - 8a)sech(x) +--R + +--R 3 2 +--R 20a cosh(x) + 20a cosh(x) + 4a cosh(x) + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R - 15a cosh(x) - 20a cosh(x) - 6a cosh(x) - 24a cosh(x) +--R + +--R 6a +--R * +--R 2 +--R sech(x) +--R + +--R 4 3 2 +--R 15a cosh(x) + 20a cosh(x) + 6a cosh(x) + 24a cosh(x) - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 6a cosh(x) - 10a cosh(x) - 4a cosh(x) - 24a cosh(x) +--R + +--R 12a cosh(x) - 4a +--R * +--R 2 +--R sech(x) +--R + +--R 5 4 3 2 +--R 6a cosh(x) + 10a cosh(x) + 4a cosh(x) + 24a cosh(x) +--R + +--R - 12a cosh(x) + 4a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - a cosh(x) - 2a cosh(x) - a cosh(x) - 8a cosh(x) +--R + +--R 2 +--R 6a cosh(x) - 4a cosh(x) + 4a +--R * +--R 2 +--R sech(x) +--R + +--R 6 5 4 3 2 +--R a cosh(x) + 2a cosh(x) + a cosh(x) + 8a cosh(x) - 6a cosh(x) +--R + +--R 4a cosh(x) - 4a +--R * +--R +-+ +---------------+ +--R \|a \|- a sech(x) + a +--R + +--R 2 2 6 +--R (a sech(x) - a )sinh(x) +--R + +--R 2 2 5 +--R (6a cosh(x)sech(x) - 6a cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 4 +--R ((15a cosh(x) + a )sech(x) - 15a cosh(x) - a )sinh(x) +--R + +--R 2 3 2 2 3 +--R (20a cosh(x) + 4a cosh(x))sech(x) - 20a cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 4 +--R (15a cosh(x) + 6a cosh(x) - 4a )sech(x) - 15a cosh(x) +--R + +--R 2 2 2 +--R - 6a cosh(x) + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 5 +--R (6a cosh(x) + 4a cosh(x) - 8a cosh(x))sech(x) - 6a cosh(x) +--R + +--R 2 3 2 +--R - 4a cosh(x) + 8a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 6 +--R (a cosh(x) + a cosh(x) - 4a cosh(x) - 4a )sech(x) - a cosh(x) +--R + +--R 2 4 2 2 2 +--R - a cosh(x) + 4a cosh(x) + 4a +--R * +--R 2 +--R tanh(x) +--R * +--R +-------------+ +--R \|- sech(x) - 1 +--R / +--R 2 6 2 5 +--R (sech(x) - 1)sinh(x) + (6cosh(x)sech(x) - 6cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((15cosh(x) - 1)sech(x) - 15cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 3 +--R ((20cosh(x) - 4cosh(x))sech(x) - 20cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R ((15cosh(x) - 6cosh(x) - 6)sech(x) - 15cosh(x) + 6cosh(x) + 6) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (6cosh(x) - 4cosh(x) - 12cosh(x))sech(x) - 6cosh(x) +--R + +--R 3 +--R 4cosh(x) + 12cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (cosh(x) - cosh(x) - 6cosh(x) - 4)sech(x) - cosh(x) + cosh(x) +--R + +--R 2 +--R 6cosh(x) + 4 +--R * +--R +-+ +---------------+ +-------------+ +--R \|a \|- a sech(x) + a \|- sech(x) - 1 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 2 6 +--R (- a sech(x) + a)sinh(x) +--R + +--R 2 5 +--R (- 6a cosh(x)sech(x) + 6a cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 15a cosh(x) - a)sech(x) + 15a cosh(x) + a)sinh(x) +--R + +--R 3 2 3 +--R ((- 20a cosh(x) - 4a cosh(x))sech(x) + 20a cosh(x) + 4a cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 15a cosh(x) - 6a cosh(x) + 4a)sech(x) + 15a cosh(x) +--R + +--R 2 +--R 6a cosh(x) - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 6a cosh(x) - 4a cosh(x) + 8a cosh(x))sech(x) + 6a cosh(x) +--R + +--R 3 +--R 4a cosh(x) - 8a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- a cosh(x) - a cosh(x) + 4a cosh(x) + 4a)sech(x) + a cosh(x) +--R + +--R 4 2 +--R a cosh(x) - 4a cosh(x) - 4a +--R * +--R +---------------+ +-------------+ +--R \|- a sech(x) + a \|- sech(x) - 1 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 508 +t0397:= 1/(a+a*sech(x))^(1/2) +--R +--R +--R 1 +--R (385) ---------------- +--R +-------------+ +--R \|a sech(x) + a +--R Type: Expression(Integer) +--E 494 + +--S 495 of 508 +r0397:= -(2^(1/2)*atan(2^(1/2)*a^(1/2)/(-a+a*sech(x))^(1/2))+_ + 2*atan((-a+a*sech(x))^(1/2)/a^(1/2)))*coth(x)*_ + (-a+a*sech(x))^(1/2)*(a+a*sech(x))^(1/2)/a^(3/2) +--R +--R +--R (386) +--R +-------------+ +--R +-------------+ +-------------+ \|a sech(x) - a +--R - 2coth(x)\|a sech(x) - a \|a sech(x) + a atan(----------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +-------------+ +-------------+ \|2 \|a +--R - \|2 coth(x)\|a sech(x) - a \|a sech(x) + a atan(----------------) +--R +-------------+ +--R \|a sech(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 495 + +--S 496 of 508 +a0397:= integrate(t0397,x) +--R +--R +--R (387) +--R - +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R - a cosh(x) - a +--R / +--R sinh(x) + cosh(x) +--R + +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4cosh(x) + 1)sinh(x) + cosh(x) - 2cosh(x) +--R + +--R cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 3 2 +--R - sinh(x) + (- 3cosh(x) + 1)sinh(x) +--R + +--R 2 3 2 +--R (- 3cosh(x) + 2cosh(x) - 1)sinh(x) - cosh(x) + cosh(x) +--R + +--R - cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R - 2sinh(x) + (- 14cosh(x) - 12)sinh(x) +--R + +--R 2 5 +--R (- 42cosh(x) - 72cosh(x) - 10)sinh(x) +--R + +--R 3 2 4 +--R (- 70cosh(x) - 180cosh(x) - 50cosh(x) - 24)sinh(x) +--R + +--R 4 3 2 +--R - 70cosh(x) - 240cosh(x) - 100cosh(x) - 96cosh(x) +--R + +--R - 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 42cosh(x) - 180cosh(x) - 100cosh(x) +--R + +--R 2 +--R - 144cosh(x) - 48cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 14cosh(x) - 72cosh(x) - 50cosh(x) - 96cosh(x) +--R + +--R 2 +--R - 48cosh(x) - 24cosh(x) - 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 2cosh(x) - 12cosh(x) - 10cosh(x) - 24cosh(x) +--R + +--R 3 2 +--R - 16cosh(x) - 12cosh(x) - 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) - 12)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) - 72cosh(x) - 20)sinh(x) +--R + +--R 3 2 4 +--R (- 140cosh(x) - 180cosh(x) - 100cosh(x) - 28)sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) - 240cosh(x) - 200cosh(x) - 112cosh(x) +--R + +--R - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 84cosh(x) - 180cosh(x) - 200cosh(x) - 168cosh(x) +--R + +--R - 96cosh(x) - 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 28cosh(x) - 72cosh(x) - 100cosh(x) - 112cosh(x) +--R + +--R 2 +--R - 96cosh(x) - 48cosh(x) - 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) - 12cosh(x) - 20cosh(x) - 28cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) - 24cosh(x) - 16cosh(x) - 8 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 8 7 +--R - 3sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 2 6 +--R (- 84cosh(x) + 28cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (- 168cosh(x) + 84cosh(x) + 12)sinh(x) +--R + +--R 4 3 4 +--R (- 210cosh(x) + 140cosh(x) + 60cosh(x) + 16)sinh(x) +--R + +--R 5 4 2 +--R - 168cosh(x) + 140cosh(x) + 120cosh(x) + 64cosh(x) +--R + +--R 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 2 +--R - 84cosh(x) + 84cosh(x) + 120cosh(x) + 96cosh(x) +--R + +--R 72cosh(x) + 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 3 +--R - 24cosh(x) + 28cosh(x) + 60cosh(x) + 64cosh(x) +--R + +--R 2 +--R 72cosh(x) + 40cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 8 7 5 4 +--R - 3cosh(x) + 4cosh(x) + 12cosh(x) + 16cosh(x) +--R + +--R 3 2 +--R 24cosh(x) + 20cosh(x) + 16cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) + 2a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) + 14a cosh(x) + 2a)sinh(x) +--R + +--R 3 2 5 +--R (- 112a cosh(x) + 42a cosh(x) + 12a cosh(x) + 6a)sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) + 70a cosh(x) + 30a cosh(x) +--R + +--R 30a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) + 70a cosh(x) + 40a cosh(x) +--R + +--R 2 +--R 60a cosh(x) + 64a cosh(x) + 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) + 42a cosh(x) + 30a cosh(x) +--R + +--R 3 2 +--R 60a cosh(x) + 96a cosh(x) + 36a cosh(x) + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) + 14a cosh(x) + 12a cosh(x) +--R + +--R 4 3 2 +--R 30a cosh(x) + 64a cosh(x) + 36a cosh(x) + 24a cosh(x) +--R + +--R 8a +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 2a cosh(x) + 2a cosh(x) + 2a cosh(x) + 6a cosh(x) +--R + +--R 4 3 2 +--R 16a cosh(x) + 12a cosh(x) + 12a cosh(x) + 8a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) - 4)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) - 24cosh(x) - 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) - 60cosh(x) - 20cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R (140cosh(x) - 80cosh(x) - 40cosh(x) - 48cosh(x) - 24) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 84cosh(x) - 60cosh(x) - 40cosh(x) - 72cosh(x) +--R + +--R - 72cosh(x) - 16 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) - 24cosh(x) - 20cosh(x) - 48cosh(x) +--R + +--R 2 +--R - 72cosh(x) - 32cosh(x) - 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 4cosh(x) - 4cosh(x) - 4cosh(x) - 12cosh(x) - 24cosh(x) +--R + +--R 2 +--R - 16cosh(x) - 16cosh(x) - 8 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 8 7 +--R sinh(x) + (8cosh(x) - 4)sinh(x) +--R + +--R 2 6 +--R (28cosh(x) - 28cosh(x) + 4)sinh(x) +--R + +--R 3 2 5 +--R (56cosh(x) - 84cosh(x) + 24cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 +--R (70cosh(x) - 140cosh(x) + 60cosh(x) - 20cosh(x) + 8) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) - 140cosh(x) + 80cosh(x) - 40cosh(x) +--R + +--R 32cosh(x) + 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) - 84cosh(x) + 60cosh(x) - 40cosh(x) +--R + +--R 2 +--R 48cosh(x) + 48cosh(x) + 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 8cosh(x) - 28cosh(x) + 24cosh(x) - 20cosh(x) +--R + +--R 3 2 +--R 32cosh(x) + 48cosh(x) + 24cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) - 4cosh(x) + 4cosh(x) - 4cosh(x) + 8cosh(x) +--R + +--R 3 2 +--R 16cosh(x) + 12cosh(x) + 16cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R / +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 508 +m0397:= a0397-r0397 +--R +--R +--R (388) +--R - +--R a +--R * +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R - a cosh(x) - a +--R / +--R sinh(x) + cosh(x) +--R + +--R a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4cosh(x) + 1)sinh(x) + cosh(x) - 2cosh(x) +--R + +--R cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 3 2 +--R - sinh(x) + (- 3cosh(x) + 1)sinh(x) +--R + +--R 2 3 2 +--R (- 3cosh(x) + 2cosh(x) - 1)sinh(x) - cosh(x) + cosh(x) +--R + +--R - cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R a |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R - 2sinh(x) + (- 14cosh(x) - 12)sinh(x) +--R + +--R 2 5 +--R (- 42cosh(x) - 72cosh(x) - 10)sinh(x) +--R + +--R 3 2 4 +--R (- 70cosh(x) - 180cosh(x) - 50cosh(x) - 24)sinh(x) +--R + +--R 4 3 2 +--R - 70cosh(x) - 240cosh(x) - 100cosh(x) - 96cosh(x) +--R + +--R - 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 42cosh(x) - 180cosh(x) - 100cosh(x) +--R + +--R 2 +--R - 144cosh(x) - 48cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 14cosh(x) - 72cosh(x) - 50cosh(x) - 96cosh(x) +--R + +--R 2 +--R - 48cosh(x) - 24cosh(x) - 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 2cosh(x) - 12cosh(x) - 10cosh(x) - 24cosh(x) +--R + +--R 3 2 +--R - 16cosh(x) - 12cosh(x) - 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) - 12)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) - 72cosh(x) - 20)sinh(x) +--R + +--R 3 2 4 +--R (- 140cosh(x) - 180cosh(x) - 100cosh(x) - 28)sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) - 240cosh(x) - 200cosh(x) - 112cosh(x) +--R + +--R - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 84cosh(x) - 180cosh(x) - 200cosh(x) - 168cosh(x) +--R + +--R - 96cosh(x) - 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 28cosh(x) - 72cosh(x) - 100cosh(x) - 112cosh(x) +--R + +--R 2 +--R - 96cosh(x) - 48cosh(x) - 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) - 12cosh(x) - 20cosh(x) - 28cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) - 24cosh(x) - 16cosh(x) - 8 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 8 7 +--R - 3sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 2 6 +--R (- 84cosh(x) + 28cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (- 168cosh(x) + 84cosh(x) + 12)sinh(x) +--R + +--R 4 3 4 +--R (- 210cosh(x) + 140cosh(x) + 60cosh(x) + 16)sinh(x) +--R + +--R 5 4 2 +--R - 168cosh(x) + 140cosh(x) + 120cosh(x) + 64cosh(x) +--R + +--R 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 2 +--R - 84cosh(x) + 84cosh(x) + 120cosh(x) + 96cosh(x) +--R + +--R 72cosh(x) + 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 3 +--R - 24cosh(x) + 28cosh(x) + 60cosh(x) + 64cosh(x) +--R + +--R 2 +--R 72cosh(x) + 40cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 8 7 5 4 +--R - 3cosh(x) + 4cosh(x) + 12cosh(x) + 16cosh(x) +--R + +--R 3 2 +--R 24cosh(x) + 20cosh(x) + 16cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) + 2a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) + 14a cosh(x) + 2a)sinh(x) +--R + +--R 3 2 5 +--R (- 112a cosh(x) + 42a cosh(x) + 12a cosh(x) + 6a)sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) + 70a cosh(x) + 30a cosh(x) +--R + +--R 30a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) + 70a cosh(x) + 40a cosh(x) +--R + +--R 2 +--R 60a cosh(x) + 64a cosh(x) + 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) + 42a cosh(x) + 30a cosh(x) +--R + +--R 3 2 +--R 60a cosh(x) + 96a cosh(x) + 36a cosh(x) + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) + 14a cosh(x) + 12a cosh(x) +--R + +--R 4 3 2 +--R 30a cosh(x) + 64a cosh(x) + 36a cosh(x) + 24a cosh(x) +--R + +--R 8a +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 2a cosh(x) + 2a cosh(x) + 2a cosh(x) + 6a cosh(x) +--R + +--R 4 3 2 +--R 16a cosh(x) + 12a cosh(x) + 12a cosh(x) + 8a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) - 4)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) - 24cosh(x) - 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) - 60cosh(x) - 20cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R (140cosh(x) - 80cosh(x) - 40cosh(x) - 48cosh(x) - 24) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 84cosh(x) - 60cosh(x) - 40cosh(x) - 72cosh(x) +--R + +--R - 72cosh(x) - 16 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) - 24cosh(x) - 20cosh(x) - 48cosh(x) +--R + +--R 2 +--R - 72cosh(x) - 32cosh(x) - 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 4cosh(x) - 4cosh(x) - 4cosh(x) - 12cosh(x) - 24cosh(x) +--R + +--R 2 +--R - 16cosh(x) - 16cosh(x) - 8 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 8 7 +--R sinh(x) + (8cosh(x) - 4)sinh(x) +--R + +--R 2 6 +--R (28cosh(x) - 28cosh(x) + 4)sinh(x) +--R + +--R 3 2 5 +--R (56cosh(x) - 84cosh(x) + 24cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 +--R (70cosh(x) - 140cosh(x) + 60cosh(x) - 20cosh(x) + 8) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) - 140cosh(x) + 80cosh(x) - 40cosh(x) +--R + +--R 32cosh(x) + 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) - 84cosh(x) + 60cosh(x) - 40cosh(x) +--R + +--R 2 +--R 48cosh(x) + 48cosh(x) + 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 8cosh(x) - 28cosh(x) + 24cosh(x) - 20cosh(x) +--R + +--R 3 2 +--R 32cosh(x) + 48cosh(x) + 24cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) - 4cosh(x) + 4cosh(x) - 4cosh(x) + 8cosh(x) +--R + +--R 3 2 +--R 16cosh(x) + 12cosh(x) + 16cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R + +--R +-------------+ +--R +-------------+ +-------------+ \|a sech(x) - a +--R 2coth(x)\|a sech(x) - a \|a sech(x) + a atan(----------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +-------------+ +-------------+ \|2 \|a +--R \|2 coth(x)\|a sech(x) - a \|a sech(x) + a atan(----------------) +--R +-------------+ +--R \|a sech(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 497 + +--S 498 of 508 +--d0397:= D(m0397,x) +--E 498 + +--S 499 of 508 +t0398:= 1/(a-a*sech(x))^(1/2) +--R +--R +--R 1 +--R (389) ------------------ +--R +---------------+ +--R \|- a sech(x) + a +--R Type: Expression(Integer) +--E 499 + +--S 500 of 508 +r0398:= -(2^(1/2)*atan(2^(1/2)*a^(1/2)/(-a-a*sech(x))^(1/2))+_ + 2*atan((-a-a*sech(x))^(1/2)/a^(1/2)))*coth(x)*(-a-a*sech(x))^(1/2)*_ + (a-a*sech(x))^(1/2)/a^(3/2) +--R +--R +--R (390) +--R +---------------+ +--R +---------------+ +---------------+ \|- a sech(x) - a +--R - 2coth(x)\|- a sech(x) - a \|- a sech(x) + a atan(------------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +---------------+ +---------------+ \|2 \|a +--R - \|2 coth(x)\|- a sech(x) - a \|- a sech(x) + a atan(------------------) +--R +---------------+ +--R \|- a sech(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 500 + +--S 501 of 508 +a0398:= integrate(t0398,x) +--R +--R +--R (391) +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R a cosh(x) - a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R 2sinh(x) + (14cosh(x) - 12)sinh(x) +--R + +--R 2 5 +--R (42cosh(x) - 72cosh(x) + 10)sinh(x) +--R + +--R 3 2 4 +--R (70cosh(x) - 180cosh(x) + 50cosh(x) - 24)sinh(x) +--R + +--R 4 3 2 +--R 70cosh(x) - 240cosh(x) + 100cosh(x) - 96cosh(x) +--R + +--R 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 42cosh(x) - 180cosh(x) + 100cosh(x) - 144cosh(x) +--R + +--R 48cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 14cosh(x) - 72cosh(x) + 50cosh(x) - 96cosh(x) +--R + +--R 2 +--R 48cosh(x) - 24cosh(x) + 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 2cosh(x) - 12cosh(x) + 10cosh(x) - 24cosh(x) +--R + +--R 3 2 +--R 16cosh(x) - 12cosh(x) + 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) + 12)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) + 72cosh(x) - 20)sinh(x) +--R + +--R 3 2 4 +--R (- 140cosh(x) + 180cosh(x) - 100cosh(x) + 28)sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) + 240cosh(x) - 200cosh(x) + 112cosh(x) +--R + +--R - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 84cosh(x) + 180cosh(x) - 200cosh(x) + 168cosh(x) +--R + +--R - 96cosh(x) + 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 28cosh(x) + 72cosh(x) - 100cosh(x) + 112cosh(x) +--R + +--R 2 +--R - 96cosh(x) + 48cosh(x) - 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) + 12cosh(x) - 20cosh(x) + 28cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) + 24cosh(x) - 16cosh(x) + 8 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 8 7 +--R 3sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 2 6 +--R (84cosh(x) + 28cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (168cosh(x) + 84cosh(x) + 12)sinh(x) +--R + +--R 4 3 4 +--R (210cosh(x) + 140cosh(x) + 60cosh(x) - 16)sinh(x) +--R + +--R 5 4 2 +--R (168cosh(x) + 140cosh(x) + 120cosh(x) - 64cosh(x) + 24) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 2 +--R 84cosh(x) + 84cosh(x) + 120cosh(x) - 96cosh(x) +--R + +--R 72cosh(x) - 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 3 +--R 24cosh(x) + 28cosh(x) + 60cosh(x) - 64cosh(x) +--R + +--R 2 +--R 72cosh(x) - 40cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R 3cosh(x) + 4cosh(x) + 12cosh(x) - 16cosh(x) + 24cosh(x) +--R + +--R 2 +--R - 20cosh(x) + 16cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) - 2a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) - 14a cosh(x) + 2a)sinh(x) +--R + +--R 3 2 5 +--R (- 112a cosh(x) - 42a cosh(x) + 12a cosh(x) - 6a)sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) - 70a cosh(x) + 30a cosh(x) +--R + +--R - 30a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) - 70a cosh(x) + 40a cosh(x) +--R + +--R 2 +--R - 60a cosh(x) + 64a cosh(x) - 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) - 42a cosh(x) + 30a cosh(x) +--R + +--R 3 2 +--R - 60a cosh(x) + 96a cosh(x) - 36a cosh(x) + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) - 14a cosh(x) + 12a cosh(x) +--R + +--R 4 3 2 +--R - 30a cosh(x) + 64a cosh(x) - 36a cosh(x) +--R + +--R 24a cosh(x) - 8a +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 2a cosh(x) - 2a cosh(x) + 2a cosh(x) - 6a cosh(x) +--R + +--R 4 3 2 +--R 16a cosh(x) - 12a cosh(x) + 12a cosh(x) - 8a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) + 4)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) + 24cosh(x) - 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) + 60cosh(x) - 20cosh(x) + 12)sinh(x) +--R + +--R 4 3 2 +--R (140cosh(x) + 80cosh(x) - 40cosh(x) + 48cosh(x) - 24) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 84cosh(x) + 60cosh(x) - 40cosh(x) + 72cosh(x) +--R + +--R - 72cosh(x) + 16 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) + 24cosh(x) - 20cosh(x) + 48cosh(x) +--R + +--R 2 +--R - 72cosh(x) + 32cosh(x) - 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 4cosh(x) + 4cosh(x) - 4cosh(x) + 12cosh(x) - 24cosh(x) +--R + +--R 2 +--R 16cosh(x) - 16cosh(x) + 8 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 8 7 +--R - sinh(x) + (- 8cosh(x) - 4)sinh(x) +--R + +--R 2 6 +--R (- 28cosh(x) - 28cosh(x) - 4)sinh(x) +--R + +--R 3 2 5 +--R (- 56cosh(x) - 84cosh(x) - 24cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 +--R (- 70cosh(x) - 140cosh(x) - 60cosh(x) - 20cosh(x) - 8) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 56cosh(x) - 140cosh(x) - 80cosh(x) - 40cosh(x) +--R + +--R - 32cosh(x) + 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 28cosh(x) - 84cosh(x) - 60cosh(x) - 40cosh(x) +--R + +--R 2 +--R - 48cosh(x) + 48cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 8cosh(x) - 28cosh(x) - 24cosh(x) - 20cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) + 48cosh(x) - 24cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) - 4cosh(x) - 4cosh(x) - 4cosh(x) - 8cosh(x) +--R + +--R 3 2 +--R 16cosh(x) - 12cosh(x) + 16cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R - +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (- 3cosh(x) - 4cosh(x) - 1)sinh(x) - cosh(x) - 2cosh(x) +--R + +--R - cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 3 2 +--R sinh(x) + (3cosh(x) + 1)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) + 2cosh(x) + 1)sinh(x) + cosh(x) + cosh(x) +--R + +--R cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R / +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 508 +m0398:= a0398-r0398 +--R +--R +--R (392) +--R a +--R * +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R a cosh(x) - a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R a |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R 2sinh(x) + (14cosh(x) - 12)sinh(x) +--R + +--R 2 5 +--R (42cosh(x) - 72cosh(x) + 10)sinh(x) +--R + +--R 3 2 4 +--R (70cosh(x) - 180cosh(x) + 50cosh(x) - 24)sinh(x) +--R + +--R 4 3 2 +--R 70cosh(x) - 240cosh(x) + 100cosh(x) - 96cosh(x) +--R + +--R 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 42cosh(x) - 180cosh(x) + 100cosh(x) - 144cosh(x) +--R + +--R 48cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 14cosh(x) - 72cosh(x) + 50cosh(x) - 96cosh(x) +--R + +--R 2 +--R 48cosh(x) - 24cosh(x) + 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 2cosh(x) - 12cosh(x) + 10cosh(x) - 24cosh(x) +--R + +--R 3 2 +--R 16cosh(x) - 12cosh(x) + 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) + 12)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) + 72cosh(x) - 20)sinh(x) +--R + +--R 3 2 4 +--R (- 140cosh(x) + 180cosh(x) - 100cosh(x) + 28)sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) + 240cosh(x) - 200cosh(x) + 112cosh(x) +--R + +--R - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 84cosh(x) + 180cosh(x) - 200cosh(x) + 168cosh(x) +--R + +--R - 96cosh(x) + 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 28cosh(x) + 72cosh(x) - 100cosh(x) + 112cosh(x) +--R + +--R 2 +--R - 96cosh(x) + 48cosh(x) - 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) + 12cosh(x) - 20cosh(x) + 28cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) + 24cosh(x) - 16cosh(x) + 8 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 8 7 +--R 3sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 2 6 +--R (84cosh(x) + 28cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (168cosh(x) + 84cosh(x) + 12)sinh(x) +--R + +--R 4 3 4 +--R (210cosh(x) + 140cosh(x) + 60cosh(x) - 16)sinh(x) +--R + +--R 5 4 2 +--R (168cosh(x) + 140cosh(x) + 120cosh(x) - 64cosh(x) + 24) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 2 +--R 84cosh(x) + 84cosh(x) + 120cosh(x) - 96cosh(x) +--R + +--R 72cosh(x) - 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 3 +--R 24cosh(x) + 28cosh(x) + 60cosh(x) - 64cosh(x) +--R + +--R 2 +--R 72cosh(x) - 40cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R 3cosh(x) + 4cosh(x) + 12cosh(x) - 16cosh(x) + 24cosh(x) +--R + +--R 2 +--R - 20cosh(x) + 16cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) - 2a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) - 14a cosh(x) + 2a)sinh(x) +--R + +--R 3 2 5 +--R (- 112a cosh(x) - 42a cosh(x) + 12a cosh(x) - 6a)sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) - 70a cosh(x) + 30a cosh(x) +--R + +--R - 30a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) - 70a cosh(x) + 40a cosh(x) +--R + +--R 2 +--R - 60a cosh(x) + 64a cosh(x) - 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) - 42a cosh(x) + 30a cosh(x) +--R + +--R 3 2 +--R - 60a cosh(x) + 96a cosh(x) - 36a cosh(x) + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) - 14a cosh(x) + 12a cosh(x) +--R + +--R 4 3 2 +--R - 30a cosh(x) + 64a cosh(x) - 36a cosh(x) +--R + +--R 24a cosh(x) - 8a +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 2a cosh(x) - 2a cosh(x) + 2a cosh(x) - 6a cosh(x) +--R + +--R 4 3 2 +--R 16a cosh(x) - 12a cosh(x) + 12a cosh(x) - 8a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) + 4)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) + 24cosh(x) - 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) + 60cosh(x) - 20cosh(x) + 12)sinh(x) +--R + +--R 4 3 2 +--R (140cosh(x) + 80cosh(x) - 40cosh(x) + 48cosh(x) - 24) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 84cosh(x) + 60cosh(x) - 40cosh(x) + 72cosh(x) +--R + +--R - 72cosh(x) + 16 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) + 24cosh(x) - 20cosh(x) + 48cosh(x) +--R + +--R 2 +--R - 72cosh(x) + 32cosh(x) - 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 4cosh(x) + 4cosh(x) - 4cosh(x) + 12cosh(x) - 24cosh(x) +--R + +--R 2 +--R 16cosh(x) - 16cosh(x) + 8 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 8 7 +--R - sinh(x) + (- 8cosh(x) - 4)sinh(x) +--R + +--R 2 6 +--R (- 28cosh(x) - 28cosh(x) - 4)sinh(x) +--R + +--R 3 2 5 +--R (- 56cosh(x) - 84cosh(x) - 24cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 +--R (- 70cosh(x) - 140cosh(x) - 60cosh(x) - 20cosh(x) - 8) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 56cosh(x) - 140cosh(x) - 80cosh(x) - 40cosh(x) +--R + +--R - 32cosh(x) + 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 28cosh(x) - 84cosh(x) - 60cosh(x) - 40cosh(x) +--R + +--R 2 +--R - 48cosh(x) + 48cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 8cosh(x) - 28cosh(x) - 24cosh(x) - 20cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) + 48cosh(x) - 24cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) - 4cosh(x) - 4cosh(x) - 4cosh(x) - 8cosh(x) +--R + +--R 3 2 +--R 16cosh(x) - 12cosh(x) + 16cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R - +--R a +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4cosh(x) - 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2cosh(x) - cosh(x) - 2 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R + +--R 3 2 +--R sinh(x) + (3cosh(x) + 1)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) + 2cosh(x) + 1)sinh(x) + cosh(x) + cosh(x) +--R + +--R cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 2cosh(x))sinh(x) + cosh(x) + cosh(x) +--R + +--R +---------------+ +--R +---------------+ +---------------+ \|- a sech(x) - a +--R 2coth(x)\|- a sech(x) - a \|- a sech(x) + a atan(------------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +---------------+ +---------------+ \|2 \|a +--R \|2 coth(x)\|- a sech(x) - a \|- a sech(x) + a atan(------------------) +--R +---------------+ +--R \|- a sech(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 502 + +--S 503 of 508 +--d0398:= D(m0398,x) +--E 503 + +--S 504 of 508 +t0399:= 1/(3+5*sech(x)) +--R +--R +--R 1 +--R (393) ------------ +--R 5sech(x) + 3 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 508 +r0399:= 1/3*x-5/6*atanh(1/2*tanh(1/2*x)) +--R +--R +--R x +--R tanh(-) +--R 2 +--R - 5atanh(-------) + 2x +--R 2 +--R (394) ---------------------- +--R 6 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 508 +a0399:= integrate(t0399,x) +--R +--R +--R - 5log(3sinh(x) + 3cosh(x) + 1) + 5log(sinh(x) + cosh(x) + 3) + 4x +--R (395) ------------------------------------------------------------------ +--R 12 +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 508 +m0399:= a0399-r0399 +--R +--R +--R (396) +--R - 5log(3sinh(x) + 3cosh(x) + 1) + 5log(sinh(x) + cosh(x) + 3) +--R + +--R x +--R tanh(-) +--R 2 +--R 10atanh(-------) +--R 2 +--R / +--R 12 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 508 +d0399:= D(m0399,x) +--R +--R +--R (397) +--R 2 2 x 2 +--R (5sinh(x) + (10cosh(x) + 10)sinh(x) + 5cosh(x) + 10cosh(x) + 5)tanh(-) +--R 2 +--R + +--R 2 2 +--R - 5sinh(x) + (- 10cosh(x) + 10)sinh(x) - 5cosh(x) + 10cosh(x) - 5 +--R / +--R 2 2 x 2 +--R (6sinh(x) + (12cosh(x) + 20)sinh(x) + 6cosh(x) + 20cosh(x) + 6)tanh(-) +--R 2 +--R + +--R 2 2 +--R - 24sinh(x) + (- 48cosh(x) - 80)sinh(x) - 24cosh(x) - 80cosh(x) - 24 +--R Type: Expression(Integer) +--E 508 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper300-399.input.pdf b/src/axiom-website/CATS/richhyper300-399.input.pdf new file mode 100644 index 0000000..31a9707 Binary files /dev/null and b/src/axiom-website/CATS/richhyper300-399.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper400-499.input.pamphlet b/src/axiom-website/CATS/richhyper400-499.input.pamphlet new file mode 100644 index 0000000..aad86d4 --- /dev/null +++ b/src/axiom-website/CATS/richhyper400-499.input.pamphlet @@ -0,0 +1,39042 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper400-499.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper400-499.output +)spool richhyper400-499.output +)set message auto off +)clear all + +--S 1 of 526 +t0400:= 1/(a+b*sech(x)) +--R +--R +--R 1 +--R (1) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 526 +r0400:= x/a-2*b*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(1/2) +--R +--R +--R x +--R (b - a)tanh(-) +---------+ +--R 2 | 2 2 +--R 2b atan(--------------) + x\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) --------------------------------------- +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 526 +a0400:= integrate(t0400,x) +--R +--R +--R (3) +--R [ +--R b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R +-------+ +--R | 2 2 +--R x\|b - a +--R / +--R +-------+ +--R | 2 2 +--R a\|b - a +--R , +--R +---------+ +--R | 2 2 +---------+ +--R (a sinh(x) + a cosh(x) + b)\|- b + a | 2 2 +--R 2b atan(---------------------------------------) + x\|- b + a +--R 2 2 +--R b - a +--R ----------------------------------------------------------------] +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R Type: Union(List(Expression(Integer)),...) +--E 3 + +--S 4 of 526 +m0400a:= a0400.1-r0400 +--R +--R +--R (4) +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R - 2b\|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R a\|- b + a \|b - a +--R Type: Expression(Integer) +--E 4 + +--S 5 of 526 +d0400a:= D(m0400a,x) +--R +--R +--R (5) +--R 2 2 +--R (b sinh(x) + (2b cosh(x) + 2b)sinh(x) + b cosh(x) + 2b cosh(x) + b) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 +--R - b sinh(x) + (- 2b cosh(x) + 2b)sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 2 2 2 2 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) + 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (a b - a )cosh(x) + (2b - 2a b)cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 +--R (- a b - a )sinh(x) + ((- 2a b - 2a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (- a b - a )cosh(x) + (- 2b - 2a b)cosh(x) - a b - a +--R Type: Expression(Integer) +--E 5 + +--S 6 of 526 +m0400b:= a0400.2-r0400 +--R +--R +--R (6) +--R +---------+ x +--R | 2 2 (b - a)tanh(-) +--R (a sinh(x) + a cosh(x) + b)\|- b + a 2 +--R 2b atan(---------------------------------------) - 2b atan(--------------) +--R 2 2 +---------+ +--R b - a | 2 2 +--R \|- b + a +--R -------------------------------------------------------------------------- +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 526 +d0400b:= D(m0400b,x) +--R +--R +--R (7) +--R 2 2 +--R (b sinh(x) + (2b cosh(x) + 2b)sinh(x) + b cosh(x) + 2b cosh(x) + b) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 +--R - b sinh(x) + (- 2b cosh(x) + 2b)sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 2 2 2 2 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) + 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (a b - a )cosh(x) + (2b - 2a b)cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 +--R (- a b - a )sinh(x) + ((- 2a b - 2a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (- a b - a )cosh(x) + (- 2b - 2a b)cosh(x) - a b - a +--R Type: Expression(Integer) +--E 7 + +--S 8 of 526 +t0401:= 1/(a+b*sech(x))^2 +--R +--R +--R 1 +--R (8) ------------------------------ +--R 2 2 2 +--R b sech(x) + 2a b sech(x) + a +--R Type: Expression(Integer) +--E 8 + +--S 9 of 526 +r0401:= x/a^2-2*b^3*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a^2/_ + (a^2-b^2)^(3/2)-4*b*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/_ + a^2/(a^2-b^2)^(1/2)+b^2*sinh(x)/a/(a^2-b^2)/(b+a*cosh(x)) +--R +--R +--R (9) +--R x +--R (b - a)tanh(-) +--R 3 3 4 2 2 2 +--R ((2a b - 4a b)cosh(x) + 2b - 4a b )atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 3 3 2 | 2 2 +--R (- a b sinh(x) + (a b - a )x cosh(x) + (b - a b)x)\|- b + a +--R / +--R +---------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )cosh(x) + a b - a b)\|- b + a +--R Type: Expression(Integer) +--E 9 + +--S 10 of 526 +a0401:= integrate(t0401,x) +--R +--R +--R (10) +--R [ +--R 3 3 2 +--R (a b - 2a b)sinh(x) +--R + +--R 3 3 4 2 2 +--R ((2a b - 4a b)cosh(x) + 2b - 4a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (a b - 2a b)cosh(x) + (2b - 4a b )cosh(x) + a b - 2a b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 3 2 +--R (a b - a )x sinh(x) +--R + +--R 2 3 3 2 3 +--R ((2a b - 2a )x cosh(x) + (2b - 2a b)x + 2b )sinh(x) +--R + +--R 2 3 2 3 2 3 2 3 +--R (a b - a )x cosh(x) + ((2b - 2a b)x + 2b )cosh(x) + (a b - a )x +--R + +--R 2 +--R 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 3 2 5 2 3 2 5 2 3 4 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) + 2a b - 2a b)sinh(x) +--R + +--R 3 2 5 2 2 3 4 3 2 5 +--R (a b - a )cosh(x) + (2a b - 2a b)cosh(x) + a b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 3 2 +--R (2a b - 4a b)sinh(x) +--R + +--R 3 3 4 2 2 +--R ((4a b - 8a b)cosh(x) + 4b - 8a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (2a b - 4a b)cosh(x) + (4b - 8a b )cosh(x) + 2a b - 4a b +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 3 2 +--R (a b - a )x sinh(x) +--R + +--R 2 3 3 2 3 +--R ((2a b - 2a )x cosh(x) + (2b - 2a b)x + 2b )sinh(x) +--R + +--R 2 3 2 3 2 3 2 3 +--R (a b - a )x cosh(x) + ((2b - 2a b)x + 2b )cosh(x) + (a b - a )x +--R + +--R 2 +--R 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 2 5 2 3 2 5 2 3 4 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) + 2a b - 2a b)sinh(x) +--R + +--R 3 2 5 2 2 3 4 3 2 5 +--R (a b - a )cosh(x) + (2a b - 2a b)cosh(x) + a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 10 + +--S 11 of 526 +m0401a:= a0401.1-r0401 +--R +--R +--R (11) +--R 2 3 4 4 3 2 2 +--R ((a b - 2a b)cosh(x) + a b - 2a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 2 3 +--R ((2a b - 4a b)cosh(x) + (4a b - 8a b )cosh(x) + 2b - 4a b ) +--R * +--R sinh(x) +--R + +--R 2 3 4 3 4 3 2 2 +--R (a b - 2a b)cosh(x) + (3a b - 6a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (2b - 3a b - 2a b)cosh(x) + a b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 2 3 4 4 3 2 2 +--R ((- 2a b + 4a b)cosh(x) - 2a b + 4a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 +--R (- 4a b + 8a b)cosh(x) + (- 8a b + 16a b )cosh(x) - 4b +--R + +--R 2 3 +--R 8a b +--R * +--R sinh(x) +--R + +--R 2 3 4 3 4 3 2 2 +--R (- 2a b + 4a b)cosh(x) + (- 6a b + 12a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (- 4b + 6a b + 4a b)cosh(x) - 2a b + 4a b +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 2 2 3 2 +--R a b sinh(x) + (2a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 2 3 4 2 2 3 2 +--R (a b cosh(x) + 4a b cosh(x) + 2b + a b )sinh(x) + 2a b cosh(x) +--R + +--R 4 2 2 3 +--R (2b + 2a b )cosh(x) + 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 6 3 3 5 2 +--R ((a b - a )cosh(x) + a b - a b)sinh(x) +--R + +--R 4 2 6 2 3 3 5 2 4 4 2 +--R ((2a b - 2a )cosh(x) + (4a b - 4a b)cosh(x) + 2a b - 2a b )sinh(x) +--R + +--R 4 2 6 3 3 3 5 2 +--R (a b - a )cosh(x) + (3a b - 3a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (2a b - a b - a )cosh(x) + a b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 526 +d0401a:= D(m0401a,x) +--R +--R +--R (12) +--R 3 3 4 2 6 +--R (- a b + a b )sinh(x) +--R + +--R 3 3 4 2 2 4 3 3 5 +--R ((- 4a b + 4a b )cosh(x) - 4a b + 4a b )sinh(x) +--R + +--R 3 3 4 2 5 2 +--R (- 4a b + 5a b - 2a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 3 3 4 2 +--R (- 9a b + 11a b - 4a b )cosh(x) - 3a b + 4a b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 3 3 4 2 5 2 +--R (4a b - 8a b)cosh(x) + (4a b + 8a b - 20a b - 4a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 +--R (12a b - 20a b - 4a b )cosh(x) + 4a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 5 4 +--R (11a b - 5a b - 12a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (26a b - 2a b - 36a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (18a b + 16a b - 38a b - 28a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 5 +--R (4b + 16a b - 18a b - 18a b - 8a b )cosh(x) + 4b - 2a b +--R + +--R 2 4 3 3 4 2 +--R - 4a b - 5a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 5 5 +--R (8a b - 4a b - 8a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (24a b - 4a b - 28a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (24a b + 12a b - 32a b - 36a b - 8a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (8b + 20a b - 12a b - 32a b - 20a b - 4a b)cosh(x) +--R + +--R 6 2 4 3 3 4 2 5 2 4 3 3 +--R (8b - 4a b - 16a b - 8a b )cosh(x) + 4a b - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 5 +--R (2a b - a b - 2a b)cosh(x) + (7a b - a b - 8a b - 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (9a b + 4a b - 10a b - 14a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (4b + 8a b - 2a b - 14a b - 12a b - 4a b)cosh(x) +--R + +--R 6 5 3 3 4 2 5 2 +--R (4b + 2a b - 10a b - 9a b - 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 3 +--R (4a b - a b - 5a b - 4a b )cosh(x) + a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 4 2 6 3 3 4 2 2 4 3 3 5 +--R (a b + a b )sinh(x) + ((4a b + 4a b )cosh(x) + 4a b + 4a b )sinh(x) +--R + +--R 3 3 4 2 5 2 2 4 3 3 4 2 +--R (4a b + 5a b + 2a b)cosh(x) + (9a b + 11a b + 4a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R 3a b + 4a b + 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 3 3 4 2 5 2 +--R (- 4a b + 8a b)cosh(x) + (- 4a b + 8a b + 20a b - 4a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 +--R (12a b + 20a b - 4a b )cosh(x) + 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 5 4 +--R (- 11a b - 5a b + 12a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 26a b - 2a b + 36a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 18a b + 16a b + 38a b - 28a b + 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 5 +--R (- 4b + 16a b + 18a b - 18a b + 8a b )cosh(x) + 4b + 2a b +--R + +--R 2 4 3 3 4 2 +--R - 4a b + 5a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 5 5 +--R (- 8a b - 4a b + 8a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 24a b - 4a b + 28a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (- 24a b + 12a b + 32a b - 36a b + 8a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 8b + 20a b + 12a b - 32a b + 20a b - 4a b)cosh(x) +--R + +--R 6 2 4 3 3 4 2 5 2 4 3 3 +--R (8b - 4a b + 16a b - 8a b )cosh(x) + 4a b + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 5 +--R (- 2a b - a b + 2a b)cosh(x) + (- 7a b - a b + 8a b - 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 9a b + 4a b + 10a b - 14a b + 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (- 4b + 8a b + 2a b - 14a b + 12a b - 4a b)cosh(x) +--R + +--R 6 5 3 3 4 2 5 2 +--R (4b - 2a b + 10a b - 9a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 3 +--R (4a b + a b - 5a b + 4a b )cosh(x) - a b + 2a b +--R / +--R 5 3 6 2 7 8 2 +--R (a b - a b - a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 5 4 4 5 3 6 2 +--R (2a b - 2a b - 2a b + 2a b)cosh(x) + a b - a b - a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 3 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 +--R (12a b - 12a b - 12a b + 12a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 6 3 5 +--R (12a b - 12a b - 12a b + 12a b )cosh(x) + 4a b - 4a b +--R + +--R 4 4 5 3 +--R - 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 4 +--R (6a b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (24a b - 24a b - 24a b + 24a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 2 +--R (34a b - 34a b - 32a b + 32a b - 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 7 +--R (20a b - 20a b - 16a b + 16a b - 4a b + 4a b)cosh(x) + 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 4a b - 2a b + 2a b - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 5 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (20a b - 20a b - 20a b + 20a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (36a b - 36a b - 32a b + 32a b - 4a b + 4a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (28a b - 28a b - 16a b + 16a b - 12a b + 12a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 6 +--R (8a b - 8a b + 4a b - 4a b - 12a b + 12a b )cosh(x) + 4a b +--R + +--R 3 5 4 4 5 3 +--R - 4a b - 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 3 6 2 7 8 6 +--R (a b - a b - a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (6a b - 6a b - 6a b + 6a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (13a b - 13a b - 11a b + 11a b - 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 +--R (12a b - 12a b - 4a b + 4a b - 8a b + 8a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (4a b - 4a b + 6a b - 6a b - 9a b + 9a b - a b + a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 5 4 4 +--R (4a b - 4a b - 2a b + 2a b - 2a b + 2a b)cosh(x) + a b - a b +--R + +--R 5 3 6 2 +--R - a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 3 6 2 7 8 2 +--R (- a b - a b + a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 5 4 4 5 3 6 2 +--R (- 2a b - 2a b + 2a b + 2a b)cosh(x) - a b - a b + a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 3 +--R (- 4a b - 4a b + 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 +--R (- 12a b - 12a b + 12a b + 12a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 6 3 5 4 4 +--R (- 12a b - 12a b + 12a b + 12a b )cosh(x) - 4a b - 4a b + 4a b +--R + +--R 5 3 +--R 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 4 +--R (- 6a b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (- 24a b - 24a b + 24a b + 24a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 2 +--R (- 34a b - 34a b + 32a b + 32a b + 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 7 +--R (- 20a b - 20a b + 16a b + 16a b + 4a b + 4a b)cosh(x) - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 4a b + 2a b + 2a b + 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 5 +--R (- 4a b - 4a b + 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (- 20a b - 20a b + 20a b + 20a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (- 36a b - 36a b + 32a b + 32a b + 4a b + 4a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (- 28a b - 28a b + 16a b + 16a b + 12a b + 12a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 6 +--R (- 8a b - 8a b - 4a b - 4a b + 12a b + 12a b )cosh(x) - 4a b +--R + +--R 3 5 4 4 5 3 +--R - 4a b + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 3 6 2 7 8 6 +--R (- a b - a b + a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (- 6a b - 6a b + 6a b + 6a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (- 13a b - 13a b + 11a b + 11a b + 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 +--R (- 12a b - 12a b + 4a b + 4a b + 8a b + 8a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (- 4a b - 4a b - 6a b - 6a b + 9a b + 9a b + a b + a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 5 4 4 +--R (- 4a b - 4a b + 2a b + 2a b + 2a b + 2a b)cosh(x) - a b - a b +--R + +--R 5 3 6 2 +--R a b + a b +--R Type: Expression(Integer) +--E 12 + +--S 13 of 526 +m0401b:= a0401.2-r0401 +--R +--R +--R (13) +--R 2 3 4 4 3 2 2 +--R ((2a b - 4a b)cosh(x) + 2a b - 4a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 2 3 +--R ((4a b - 8a b)cosh(x) + (8a b - 16a b )cosh(x) + 4b - 8a b ) +--R * +--R sinh(x) +--R + +--R 2 3 4 3 4 3 2 2 +--R (2a b - 4a b)cosh(x) + (6a b - 12a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (4b - 6a b - 4a b)cosh(x) + 2a b - 4a b +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 3 4 4 3 2 2 +--R ((- 2a b + 4a b)cosh(x) - 2a b + 4a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 +--R (- 4a b + 8a b)cosh(x) + (- 8a b + 16a b )cosh(x) - 4b +--R + +--R 2 3 +--R 8a b +--R * +--R sinh(x) +--R + +--R 2 3 4 3 4 3 2 2 +--R (- 2a b + 4a b)cosh(x) + (- 6a b + 12a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (- 4b + 6a b + 4a b)cosh(x) - 2a b + 4a b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 2 2 3 2 +--R a b sinh(x) + (2a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 2 3 4 2 2 3 2 +--R (a b cosh(x) + 4a b cosh(x) + 2b + a b )sinh(x) + 2a b cosh(x) +--R + +--R 4 2 2 3 +--R (2b + 2a b )cosh(x) + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 6 3 3 5 2 +--R ((a b - a )cosh(x) + a b - a b)sinh(x) +--R + +--R 4 2 6 2 3 3 5 2 4 4 2 +--R ((2a b - 2a )cosh(x) + (4a b - 4a b)cosh(x) + 2a b - 2a b )sinh(x) +--R + +--R 4 2 6 3 3 3 5 2 +--R (a b - a )cosh(x) + (3a b - 3a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (2a b - a b - a )cosh(x) + a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 13 + +--S 14 of 526 +d0401b:= D(m0401b,x) +--R +--R +--R (14) +--R 3 3 4 2 6 +--R (- a b + a b )sinh(x) +--R + +--R 3 3 4 2 2 4 3 3 5 +--R ((- 4a b + 4a b )cosh(x) - 4a b + 4a b )sinh(x) +--R + +--R 3 3 4 2 5 2 +--R (- 4a b + 5a b - 2a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 3 3 4 2 +--R (- 9a b + 11a b - 4a b )cosh(x) - 3a b + 4a b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 3 3 4 2 5 2 +--R (4a b - 8a b)cosh(x) + (4a b + 8a b - 20a b - 4a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 +--R (12a b - 20a b - 4a b )cosh(x) + 4a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 5 4 +--R (11a b - 5a b - 12a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (26a b - 2a b - 36a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (18a b + 16a b - 38a b - 28a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 5 +--R (4b + 16a b - 18a b - 18a b - 8a b )cosh(x) + 4b - 2a b +--R + +--R 2 4 3 3 4 2 +--R - 4a b - 5a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 5 5 +--R (8a b - 4a b - 8a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (24a b - 4a b - 28a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (24a b + 12a b - 32a b - 36a b - 8a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (8b + 20a b - 12a b - 32a b - 20a b - 4a b)cosh(x) +--R + +--R 6 2 4 3 3 4 2 5 2 4 3 3 +--R (8b - 4a b - 16a b - 8a b )cosh(x) + 4a b - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 5 +--R (2a b - a b - 2a b)cosh(x) + (7a b - a b - 8a b - 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (9a b + 4a b - 10a b - 14a b - 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (4b + 8a b - 2a b - 14a b - 12a b - 4a b)cosh(x) +--R + +--R 6 5 3 3 4 2 5 2 +--R (4b + 2a b - 10a b - 9a b - 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 3 +--R (4a b - a b - 5a b - 4a b )cosh(x) + a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 4 2 6 3 3 4 2 2 4 3 3 5 +--R (a b + a b )sinh(x) + ((4a b + 4a b )cosh(x) + 4a b + 4a b )sinh(x) +--R + +--R 3 3 4 2 5 2 2 4 3 3 4 2 +--R (4a b + 5a b + 2a b)cosh(x) + (9a b + 11a b + 4a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 +--R 3a b + 4a b + 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 3 3 4 2 5 2 +--R (- 4a b + 8a b)cosh(x) + (- 4a b + 8a b + 20a b - 4a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 2 4 +--R (12a b + 20a b - 4a b )cosh(x) + 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 5 4 +--R (- 11a b - 5a b + 12a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 26a b - 2a b + 36a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 18a b + 16a b + 38a b - 28a b + 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 6 5 +--R (- 4b + 16a b + 18a b - 18a b + 8a b )cosh(x) + 4b + 2a b +--R + +--R 2 4 3 3 4 2 +--R - 4a b + 5a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 5 5 +--R (- 8a b - 4a b + 8a b)cosh(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 24a b - 4a b + 28a b - 12a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (- 24a b + 12a b + 32a b - 36a b + 8a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 8b + 20a b + 12a b - 32a b + 20a b - 4a b)cosh(x) +--R + +--R 6 2 4 3 3 4 2 5 2 4 3 3 +--R (8b - 4a b + 16a b - 8a b )cosh(x) + 4a b + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 5 +--R (- 2a b - a b + 2a b)cosh(x) + (- 7a b - a b + 8a b - 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 9a b + 4a b + 10a b - 14a b + 4a b)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (- 4b + 8a b + 2a b - 14a b + 12a b - 4a b)cosh(x) +--R + +--R 6 5 3 3 4 2 5 2 +--R (4b - 2a b + 10a b - 9a b + 2a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 3 +--R (4a b + a b - 5a b + 4a b )cosh(x) - a b + 2a b +--R / +--R 5 3 6 2 7 8 2 +--R (a b - a b - a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 5 4 4 5 3 6 2 +--R (2a b - 2a b - 2a b + 2a b)cosh(x) + a b - a b - a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 3 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 +--R (12a b - 12a b - 12a b + 12a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 6 3 5 +--R (12a b - 12a b - 12a b + 12a b )cosh(x) + 4a b - 4a b +--R + +--R 4 4 5 3 +--R - 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 4 +--R (6a b - 6a b - 6a b + 6a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (24a b - 24a b - 24a b + 24a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 2 +--R (34a b - 34a b - 32a b + 32a b - 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 7 +--R (20a b - 20a b - 16a b + 16a b - 4a b + 4a b)cosh(x) + 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 4a b - 2a b + 2a b - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 5 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (20a b - 20a b - 20a b + 20a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (36a b - 36a b - 32a b + 32a b - 4a b + 4a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (28a b - 28a b - 16a b + 16a b - 12a b + 12a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 6 +--R (8a b - 8a b + 4a b - 4a b - 12a b + 12a b )cosh(x) + 4a b +--R + +--R 3 5 4 4 5 3 +--R - 4a b - 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 3 6 2 7 8 6 +--R (a b - a b - a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (6a b - 6a b - 6a b + 6a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (13a b - 13a b - 11a b + 11a b - 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 +--R (12a b - 12a b - 4a b + 4a b - 8a b + 8a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (4a b - 4a b + 6a b - 6a b - 9a b + 9a b - a b + a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 5 4 4 +--R (4a b - 4a b - 2a b + 2a b - 2a b + 2a b)cosh(x) + a b - a b +--R + +--R 5 3 6 2 +--R - a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 3 6 2 7 8 2 +--R (- a b - a b + a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 5 4 4 5 3 6 2 +--R (- 2a b - 2a b + 2a b + 2a b)cosh(x) - a b - a b + a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 3 +--R (- 4a b - 4a b + 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 2 +--R (- 12a b - 12a b + 12a b + 12a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 2 6 3 5 4 4 +--R (- 12a b - 12a b + 12a b + 12a b )cosh(x) - 4a b - 4a b + 4a b +--R + +--R 5 3 +--R 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 4 +--R (- 6a b - 6a b + 6a b + 6a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 3 +--R (- 24a b - 24a b + 24a b + 24a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 2 +--R (- 34a b - 34a b + 32a b + 32a b + 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 7 +--R (- 20a b - 20a b + 16a b + 16a b + 4a b + 4a b)cosh(x) - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 4a b + 2a b + 2a b + 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 2 7 8 5 +--R (- 4a b - 4a b + 4a b + 4a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (- 20a b - 20a b + 20a b + 20a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (- 36a b - 36a b + 32a b + 32a b + 4a b + 4a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (- 28a b - 28a b + 16a b + 16a b + 12a b + 12a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 6 +--R (- 8a b - 8a b - 4a b - 4a b + 12a b + 12a b )cosh(x) - 4a b +--R + +--R 3 5 4 4 5 3 +--R - 4a b + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 3 6 2 7 8 6 +--R (- a b - a b + a b + a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 5 +--R (- 6a b - 6a b + 6a b + 6a b)cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (- 13a b - 13a b + 11a b + 11a b + 2a b + 2a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 +--R (- 12a b - 12a b + 4a b + 4a b + 8a b + 8a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (- 4a b - 4a b - 6a b - 6a b + 9a b + 9a b + a b + a )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 5 4 4 +--R (- 4a b - 4a b + 2a b + 2a b + 2a b + 2a b)cosh(x) - a b - a b +--R + +--R 5 3 6 2 +--R a b + a b +--R Type: Expression(Integer) +--E 14 + +--S 15 of 526 +t0402:= 1/(a+b*sech(x))^3 +--R +--R +--R 1 +--R (15) ---------------------------------------------- +--R 3 3 2 2 2 3 +--R b sech(x) + 3a b sech(x) + 3a b sech(x) + a +--R Type: Expression(Integer) +--E 15 + +--S 16 of 526 +r0402:= x/a^3-6*b^3*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/_ + (a^2-b^2)^(3/2)/a^3-6*b*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/_ + a^3/(a^2-b^2)^(1/2)-b^3*(a^2+2*b^2)*atan((a-b)*tanh(1/2*x)/_ + (a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)/a^3-1/2*b^3*_ + sinh(x)/a^2/(a^2-b^2)/(b+a*cosh(x))^2+3/2*b^4*_ + sinh(x)/a^2/(a^2-b^2)^2/(b+a*cosh(x))+3*_ + b^2*sinh(x)/a^2/(a^2-b^2)/(b+a*cosh(x)) +--R +--R +--R (16) +--R 2 5 4 3 6 2 6 3 4 5 2 +--R (4a b - 10a b + 12a b)cosh(x) + (8a b - 20a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 +--R 4b - 10a b + 12a b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 5 3 3 +--R ((- 3a b + 6a b )cosh(x) - 2a b + 5a b )sinh(x) +--R + +--R 2 4 4 2 6 2 5 3 3 5 +--R (2a b - 4a b + 2a )x cosh(x) + (4a b - 8a b + 4a b)x cosh(x) +--R + +--R 6 2 4 4 2 +--R (2b - 4a b + 2a b )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 7 2 9 2 4 5 6 3 8 3 6 +--R (2a b - 4a b + 2a )cosh(x) + (4a b - 8a b + 4a b)cosh(x) + 2a b +--R + +--R 5 4 7 2 +--R - 4a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 526 +a0402:= integrate(t0402,x) +--R +--R +--R (17) +--R [ +--R 2 5 4 3 6 4 +--R (2a b - 5a b + 6a b)sinh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 3 +--R ((8a b - 20a b + 24a b)cosh(x) + 8a b - 20a b + 24a b )sinh(x) +--R + +--R 2 5 4 3 6 2 +--R (12a b - 30a b + 36a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 6 +--R (24a b - 60a b + 72a b )cosh(x) + 8b - 16a b + 14a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 3 6 3 +--R (8a b - 20a b + 24a b)cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (24a b - 60a b + 72a b )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 +--R (16b - 32a b + 28a b + 24a b)cosh(x) + 8a b - 20a b + 24a b +--R * +--R sinh(x) +--R + +--R 2 5 4 3 6 4 6 3 4 5 2 3 +--R (2a b - 5a b + 6a b)cosh(x) + (8a b - 20a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (8b - 16a b + 14a b + 12a b)cosh(x) +--R + +--R 6 3 4 5 2 2 5 4 3 6 +--R (8a b - 20a b + 24a b )cosh(x) + 2a b - 5a b + 6a b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 4 4 2 6 4 +--R (2a b - 4a b + 2a )x sinh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (8a b - 16a b + 8a )x cosh(x) + (8a b - 16a b + 8a b)x +--R + +--R 5 3 3 +--R 8a b - 14a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 6 2 +--R (12a b - 24a b + 12a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((24a b - 48a b + 24a b)x + 24a b - 42a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R (8b - 12a b + 4a )x + 12b - 18a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 +--R (8a b - 16a b + 8a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 2 +--R ((24a b - 48a b + 24a b)x + 24a b - 42a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R ((16b - 24a b + 8a )x + 24b - 36a b - 24a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R (8a b - 16a b + 8a b)x + 16a b - 34a b +--R * +--R sinh(x) +--R + +--R 2 4 4 2 6 4 +--R (2a b - 4a b + 2a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 3 +--R ((8a b - 16a b + 8a b)x + 8a b - 14a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 2 +--R ((8b - 12a b + 4a )x + 12b - 18a b - 12a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((8a b - 16a b + 8a b)x + 16a b - 34a b )cosh(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (2a b - 4a b + 2a )x + 6a b - 12a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 5 4 7 2 9 4 +--R (2a b - 4a b + 2a )sinh(x) +--R + +--R 5 4 7 2 9 4 5 6 3 8 3 +--R ((8a b - 16a b + 8a )cosh(x) + 8a b - 16a b + 8a b)sinh(x) +--R + +--R 5 4 7 2 9 2 +--R (12a b - 24a b + 12a )cosh(x) +--R + +--R 4 5 6 3 8 3 6 5 4 9 +--R (24a b - 48a b + 24a b)cosh(x) + 8a b - 12a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 7 2 9 3 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 4 5 6 3 8 2 +--R (24a b - 48a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 9 4 5 6 3 8 +--R (16a b - 24a b + 8a )cosh(x) + 8a b - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 5 4 7 2 9 4 4 5 6 3 8 3 +--R (2a b - 4a b + 2a )cosh(x) + (8a b - 16a b + 8a b)cosh(x) +--R + +--R 3 6 5 4 9 2 4 5 6 3 8 +--R (8a b - 12a b + 4a )cosh(x) + (8a b - 16a b + 8a b)cosh(x) +--R + +--R 5 4 7 2 9 +--R 2a b - 4a b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 2 5 4 3 6 4 +--R (2a b - 5a b + 6a b)sinh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 3 +--R ((8a b - 20a b + 24a b)cosh(x) + 8a b - 20a b + 24a b )sinh(x) +--R + +--R 2 5 4 3 6 2 +--R (12a b - 30a b + 36a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 6 +--R (24a b - 60a b + 72a b )cosh(x) + 8b - 16a b + 14a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 3 6 3 +--R (8a b - 20a b + 24a b)cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (24a b - 60a b + 72a b )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 +--R (16b - 32a b + 28a b + 24a b)cosh(x) + 8a b - 20a b + 24a b +--R * +--R sinh(x) +--R + +--R 2 5 4 3 6 4 6 3 4 5 2 3 +--R (2a b - 5a b + 6a b)cosh(x) + (8a b - 20a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (8b - 16a b + 14a b + 12a b)cosh(x) +--R + +--R 6 3 4 5 2 2 5 4 3 6 +--R (8a b - 20a b + 24a b )cosh(x) + 2a b - 5a b + 6a b +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 4 4 2 6 4 +--R (a b - 2a b + a )x sinh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (4a b - 8a b + 4a )x cosh(x) + (4a b - 8a b + 4a b)x +--R + +--R 5 3 3 +--R 4a b - 7a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 6 2 +--R (6a b - 12a b + 6a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((12a b - 24a b + 12a b)x + 12a b - 21a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R (4b - 6a b + 2a )x + 6b - 9a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 +--R (4a b - 8a b + 4a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 2 +--R ((12a b - 24a b + 12a b)x + 12a b - 21a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R ((8b - 12a b + 4a )x + 12b - 18a b - 12a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R (4a b - 8a b + 4a b)x + 8a b - 17a b +--R * +--R sinh(x) +--R + +--R 2 4 4 2 6 4 +--R (a b - 2a b + a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 3 +--R ((4a b - 8a b + 4a b)x + 4a b - 7a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 2 +--R ((4b - 6a b + 2a )x + 6b - 9a b - 6a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((4a b - 8a b + 4a b)x + 8a b - 17a b )cosh(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (a b - 2a b + a )x + 3a b - 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 7 2 9 4 +--R (a b - 2a b + a )sinh(x) +--R + +--R 5 4 7 2 9 4 5 6 3 8 3 +--R ((4a b - 8a b + 4a )cosh(x) + 4a b - 8a b + 4a b)sinh(x) +--R + +--R 5 4 7 2 9 2 4 5 6 3 8 +--R (6a b - 12a b + 6a )cosh(x) + (12a b - 24a b + 12a b)cosh(x) +--R + +--R 3 6 5 4 9 +--R 4a b - 6a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 7 2 9 3 4 5 6 3 8 2 +--R (4a b - 8a b + 4a )cosh(x) + (12a b - 24a b + 12a b)cosh(x) +--R + +--R 3 6 5 4 9 4 5 6 3 8 +--R (8a b - 12a b + 4a )cosh(x) + 4a b - 8a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 4 7 2 9 4 4 5 6 3 8 3 +--R (a b - 2a b + a )cosh(x) + (4a b - 8a b + 4a b)cosh(x) +--R + +--R 3 6 5 4 9 2 4 5 6 3 8 5 4 +--R (4a b - 6a b + 2a )cosh(x) + (4a b - 8a b + 4a b)cosh(x) + a b +--R + +--R 7 2 9 +--R - 2a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 17 + +--S 18 of 526 +m0402a:= a0402.1-r0402 +--R +--R +--R (18) +--R 4 5 6 3 8 2 3 6 5 4 7 2 +--R (2a b - 5a b + 6a b)cosh(x) + (4a b - 10a b + 12a b )cosh(x) +--R + +--R 2 7 4 5 6 3 +--R 2a b - 5a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (8a b - 20a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (24a b - 60a b + 72a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (24a b - 60a b + 72a b )cosh(x) + 8a b - 20a b + 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (12a b - 30a b + 36a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (48a b - 120a b + 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (68a b - 166a b + 194a b + 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 2 7 +--R (40a b - 92a b + 100a b + 24a b )cosh(x) + 8b - 16a b +--R + +--R 4 5 6 3 +--R 14a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 6 3 8 5 +--R (8a b - 20a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (40a b - 100a b + 120a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (72a b - 172a b + 196a b + 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (56a b - 116a b + 108a b + 72a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 5 4 +--R (16b - 16a b - 12a b + 72a b )cosh(x) + 8a b - 20a b + 24a b +--R * +--R sinh(x) +--R + +--R 4 5 6 3 8 6 3 6 5 4 7 2 5 +--R (2a b - 5a b + 6a b)cosh(x) + (12a b - 30a b + 36a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (26a b - 61a b + 68a b + 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (24a b - 44a b + 32a b + 48a b )cosh(x) +--R + +--R 9 4 5 6 3 8 2 +--R (8b - 24a b + 55a b + 6a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 +--R (8a b - 16a b + 14a b + 12a b )cosh(x) + 2a b - 5a b + 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 4 5 6 3 8 2 +--R (- 4a b + 10a b - 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 +--R (- 8a b + 20a b - 24a b )cosh(x) - 4a b + 10a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (- 16a b + 40a b - 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 48a b + 120a b - 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (- 48a b + 120a b - 144a b )cosh(x) - 16a b + 40a b - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (- 24a b + 60a b - 72a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 96a b + 240a b - 288a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 136a b + 332a b - 388a b - 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 2 7 +--R (- 80a b + 184a b - 200a b - 48a b )cosh(x) - 16b + 32a b +--R + +--R 4 5 6 3 +--R - 28a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 6 3 8 5 +--R (- 16a b + 40a b - 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 80a b + 200a b - 240a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 144a b + 344a b - 392a b - 48a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 112a b + 232a b - 216a b - 144a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 +--R (- 32b + 32a b + 24a b - 144a b )cosh(x) - 16a b + 40a b +--R + +--R 5 4 +--R - 48a b +--R * +--R sinh(x) +--R + +--R 4 5 6 3 8 6 +--R (- 4a b + 10a b - 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- 24a b + 60a b - 72a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 52a b + 122a b - 136a b - 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 48a b + 88a b - 64a b - 96a b )cosh(x) +--R + +--R 9 4 5 6 3 8 2 +--R (- 16b + 48a b - 110a b - 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 +--R (- 16a b + 32a b - 28a b - 24a b )cosh(x) - 4a b + 10a b - 12a b +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 6 2 3 5 5 3 5 +--R ((3a b - 6a b )cosh(x) + 2a b - 5a b )sinh(x) +--R + +--R 4 4 6 2 2 3 5 5 3 2 6 +--R (12a b - 24a b )cosh(x) + (20a b - 44a b )cosh(x) + 8a b +--R + +--R 4 4 +--R - 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 6 2 3 3 5 5 3 2 +--R (18a b - 36a b )cosh(x) + (56a b - 116a b )cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 +--R (52a b - 106a b - 12a b )cosh(x) + 16a b - 30a b - 10a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (12a b - 24a b )cosh(x) + (68a b - 134a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (108a b - 198a b - 36a b )cosh(x) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (64a b - 98a b - 68a b )cosh(x) + 12b - 10a b - 32a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 5 3 5 5 3 4 +--R (3a b - 6a b )cosh(x) + (38a b - 71a b )cosh(x) +--R + +--R 2 6 4 4 6 2 3 +--R (92a b - 158a b - 36a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (80a b - 102a b - 116a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 7 3 5 5 3 +--R (24b + 4a b - 109a b - 6a b )cosh(x) + 16a b - 32a b - 5a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 5 2 6 4 4 6 2 4 +--R (8a b - 14a b )cosh(x) + (28a b - 46a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 3 +--R (32a b - 34a b - 58a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (12b + 14a b - 74a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 +--R (16a b - 22a b - 24a b )cosh(x) + 6a b - 12a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 7 4 9 2 11 2 6 5 8 3 10 +--R (2a b - 4a b + 2a )cosh(x) + (4a b - 8a b + 4a b)cosh(x) +--R + +--R 5 6 7 4 9 2 +--R 2a b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 4 9 2 11 3 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 6 5 8 3 10 2 +--R (24a b - 48a b + 24a b)cosh(x) +--R + +--R 5 6 7 4 9 2 4 7 6 5 8 3 +--R (24a b - 48a b + 24a b )cosh(x) + 8a b - 16a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 4 9 2 11 4 +--R (12a b - 24a b + 12a )cosh(x) +--R + +--R 6 5 8 3 10 3 +--R (48a b - 96a b + 48a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 2 +--R (68a b - 132a b + 60a b + 4a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 3 8 5 6 9 2 +--R (40a b - 72a b + 24a b + 8a b)cosh(x) + 8a b - 12a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 4 9 2 11 5 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 6 5 8 3 10 4 +--R (40a b - 80a b + 40a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 3 +--R (72a b - 136a b + 56a b + 8a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (56a b - 88a b + 8a b + 24a b)cosh(x) +--R + +--R 3 8 5 6 7 4 9 2 4 7 6 5 8 3 +--R (16a b - 8a b - 32a b + 24a b )cosh(x) + 8a b - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 7 4 9 2 11 6 6 5 8 3 10 5 +--R (2a b - 4a b + 2a )cosh(x) + (12a b - 24a b + 12a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 4 +--R (26a b - 48a b + 18a b + 4a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (24a b - 32a b - 8a b + 16a b)cosh(x) +--R + +--R 3 8 5 6 7 4 9 2 11 2 +--R (8a b + 4a b - 30a b + 16a b + 2a )cosh(x) +--R + +--R 4 7 6 5 10 5 6 7 4 9 2 +--R (8a b - 12a b + 4a b)cosh(x) + 2a b - 4a b + 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 18 + +--S 19 of 526 +d0402a:= D(m0402a,x) +--R +--R +--R (19) +--R 5 5 6 4 7 3 8 2 4 6 5 5 6 4 +--R (- 3a b + 3a b + 6a b - 6a b )cosh(x) - a b + a b + 4a b +--R + +--R 7 3 +--R - 4a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 2 +--R (- 18a b + 18a b + 36a b - 36a b )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 3 7 4 6 +--R (- 24a b + 24a b + 60a b - 60a b )cosh(x) - 6a b + 6a b +--R + +--R 5 5 6 4 +--R 24a b - 24a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 3 +--R (- 40a b + 42a b + 79a b - 84a b + 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 2 +--R (- 94a b + 100a b + 214a b - 229a b + 18a b )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 58a b + 64a b + 163a b - 178a b + 36a b - 18a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 10a b + 12a b + 40a b - 45a b + 18a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 4 +--R (- 30a b + 42a b + 54a b - 84a b + 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R (- 116a b + 164a b + 242a b - 362a b + 132a b + 12a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 126a b + 198a b + 288a b - 468a b + 252a b - 36a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (- 48a b + 96a b + 114a b - 234a b + 228a b - 84a b )cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 8a b + 20a b + 14a b - 44a b + 72a b - 36a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (30a b - 75a b + 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 4 +--R (60a b + 90a b - 180a b - 195a b + 390a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 30a b + 264a b - 171a b - 558a b + 753a b + 114a b +--R + +--R 9 +--R 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 6a b + 276a b - 144a b - 543a b + 804a b - 3a b +--R + +--R 8 2 +--R 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 132a b - 78a b - 234a b + 411a b - 60a b + 72a b +--R + +--R 8 2 +--R - 18a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b - 18a b - 36a b + 78a b - 21a b + 30a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 6 +--R (82a b - 42a b - 184a b + 84a b + 120a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 5 +--R (304a b - 64a b - 736a b + 136a b + 600a b + 120a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 430a b + 146a b - 1144a b - 272a b + 1212a b + 456a b +--R + +--R 9 +--R 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 304a b + 400a b - 924a b - 740a b + 1316a b + 556a b +--R + +--R 8 2 9 +--R 264a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 112a b + 344a b - 412a b - 584a b + 774a b + 234a b +--R + +--R 7 3 8 2 +--R 396a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b + 128a b - 88a b - 176a b + 204a b - 12a b +--R + +--R 6 4 7 3 +--R 276a b + 12a b +--R * +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b - 8a b - 8a b + 14a b - 26a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 7 +--R (72a b - 42a b - 159a b + 84a b + 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R (326a b - 116a b - 770a b + 245a b + 510a b + 120a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 7 5 5 6 4 7 3 8 2 9 +--R (594a b - 1467a b + 18a b + 1098a b + 594a b + 108a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 546a b + 324a b - 1368a b - 627a b + 1134a b + 1026a b +--R + +--R 8 2 9 +--R 468a b + 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 256a b + 440a b - 628a b - 764a b + 570a b + 654a b +--R + +--R 7 3 8 2 9 +--R 789a b + 240a b + 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 240a b - 108a b - 288a b + 90a b - 18a b +--R + +--R 6 4 7 3 8 2 +--R 654a b + 273a b + 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 3 7 4 6 5 5 6 4 +--R 48b + 24a b - 18a b - 180a b + 249a b + 138a b +--R + +--R 7 3 8 2 +--R 60a b - 6a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b - 6a b - 48a b + 32a b + 25a b + 22a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 8 +--R (30a b - 18a b - 66a b + 36a b + 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 7 +--R (156a b - 60a b - 366a b + 126a b + 228a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 342a b - 30a b - 816a b + 60a b + 528a b + 348a b +--R + +--R 9 +--R 72a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 384a b + 144a b - 870a b - 306a b + 504a b + 720a b +--R + +--R 8 2 9 +--R 360a b + 72a b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 216a b + 276a b - 402a b - 492a b + 102a b + 546a b +--R + +--R 7 3 8 2 9 +--R 678a b + 300a b + 36a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 192a b - 24a b - 192a b - 120a b - 72a b +--R + +--R 6 4 7 3 8 2 9 +--R 594a b + 438a b + 132a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 24a b + 72a b - 54a b - 270a b + 228a b +--R + +--R 6 4 7 3 8 2 +--R 240a b + 180a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 4 6 5 5 6 4 7 3 +--R (48a b - 72a b + 18a b + 6a b + 108a b + 36a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 12a b - 6a b - 24a b + 24a b + 12a b +--R * +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 9 +--R (5a b - 3a b - 11a b + 6a b + 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 8 +--R (29a b - 11a b - 68a b + 23a b + 42a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (74a b - 8a b - 173a b + 14a b + 105a b + 78a b + 18a b) +--R * +--R 7 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 98a b + 28a b - 208a b - 65a b + 92a b + 181a b + 102a b +--R + +--R 9 +--R 24a b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 64a b + 68a b - 94a b - 122a b - 33a b + 150a b + 213a b +--R + +--R 8 2 9 +--R 114a b + 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b + 56a b + 14a b - 44a b - 84a b - 45a b + 186a b +--R + +--R 7 3 8 2 9 +--R 189a b + 78a b + 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b + 16a b + 40a b - 22a b - 116a b + 53a b + 102a b +--R + +--R 7 3 8 2 9 +--R 115a b + 42a b + 6a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 6a b - 24a b - 4a b - 23a b + 64a b + 47a b +--R + +--R 8 2 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 2 8 +--R (12a b + 2a b - 26a b + 4a b + 17a b + 18a b )cosh(x) + 2a b +--R + +--R 4 6 6 4 +--R - 5a b + 6a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 5 6 4 7 3 8 2 4 6 5 5 6 4 7 3 +--R ((3a b + 3a b - 6a b - 6a b )cosh(x) + a b + a b - 4a b - 4a b ) +--R * +--R 8 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 2 +--R (18a b + 18a b - 36a b - 36a b )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 3 7 4 6 5 5 +--R (24a b + 24a b - 60a b - 60a b )cosh(x) + 6a b + 6a b - 24a b +--R + +--R 6 4 +--R - 24a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 3 +--R (40a b + 42a b - 79a b - 84a b - 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 2 +--R (94a b + 100a b - 214a b - 229a b - 18a b )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (58a b + 64a b - 163a b - 178a b - 36a b - 18a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 10a b + 12a b - 40a b - 45a b - 18a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 4 +--R (30a b + 42a b - 54a b - 84a b - 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 3 +--R (116a b + 164a b - 242a b - 362a b - 132a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 2 +--R (126a b + 198a b - 288a b - 468a b - 252a b - 36a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (48a b + 96a b - 114a b - 234a b - 228a b - 84a b )cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 8a b + 20a b - 14a b - 44a b - 72a b - 36a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (- 30a b + 75a b - 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 4 +--R (- 60a b + 90a b + 180a b - 195a b - 390a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 30a b + 264a b + 171a b - 558a b - 753a b + 114a b +--R + +--R 9 +--R - 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 6a b + 276a b + 144a b - 543a b - 804a b - 3a b - 54a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (132a b + 78a b - 234a b - 411a b - 60a b - 72a b - 18a b ) +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 18a b - 36a b - 78a b - 21a b - 30a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 6 +--R (- 82a b - 42a b + 184a b + 84a b - 120a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 5 +--R (- 304a b - 64a b + 736a b + 136a b - 600a b + 120a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 430a b + 146a b + 1144a b - 272a b - 1212a b + 456a b +--R + +--R 9 +--R - 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 304a b + 400a b + 924a b - 740a b - 1316a b + 556a b +--R + +--R 8 2 9 +--R - 264a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 112a b + 344a b + 412a b - 584a b - 774a b + 234a b +--R + +--R 7 3 8 2 +--R - 396a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 16b + 128a b + 88a b - 176a b - 204a b - 12a b - 276a b +--R + +--R 7 3 +--R 12a b +--R * +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b + 8a b - 8a b - 14a b - 26a b - 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 7 +--R (- 72a b - 42a b + 159a b + 84a b - 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 6 +--R (- 326a b - 116a b + 770a b + 245a b - 510a b + 120a b)cosh(x) +--R + +--R 3 7 5 5 6 4 7 3 8 2 9 5 +--R (- 594a b + 1467a b + 18a b - 1098a b + 594a b - 108a b)cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 546a b + 324a b + 1368a b - 627a b - 1134a b + 1026a b +--R + +--R 8 2 9 +--R - 468a b + 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 256a b + 440a b + 628a b - 764a b - 570a b + 654a b +--R + +--R 7 3 8 2 9 +--R - 789a b + 240a b - 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 48b + 240a b + 108a b - 288a b - 90a b - 18a b - 654a b +--R + +--R 7 3 8 2 +--R 273a b - 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 3 7 4 6 5 5 6 4 7 3 +--R 48b + 24a b + 18a b - 180a b - 249a b + 138a b - 60a b +--R + +--R 8 2 +--R - 6a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 6a b - 48a b - 32a b + 25a b - 22a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 8 +--R (- 30a b - 18a b + 66a b + 36a b - 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 7 +--R (- 156a b - 60a b + 366a b + 126a b - 228a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (- 342a b - 30a b + 816a b + 60a b - 528a b + 348a b - 72a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 384a b + 144a b + 870a b - 306a b - 504a b + 720a b +--R + +--R 8 2 9 +--R - 360a b + 72a b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 216a b + 276a b + 402a b - 492a b - 102a b + 546a b +--R + +--R 7 3 8 2 9 +--R - 678a b + 300a b - 36a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 48b + 192a b + 24a b - 192a b + 120a b - 72a b - 594a b +--R + +--R 7 3 8 2 9 +--R 438a b - 132a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 48b - 24a b + 72a b + 54a b - 270a b - 228a b + 240a b +--R + +--R 7 3 8 2 +--R - 180a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 4 6 5 5 6 4 7 3 2 8 +--R (48a b - 72a b - 18a b + 6a b - 108a b + 36a b )cosh(x) + 12a b +--R + +--R 3 7 4 6 5 5 6 4 +--R 6a b - 24a b - 24a b + 12a b +--R * +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 9 +--R (- 5a b - 3a b + 11a b + 6a b - 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 8 +--R (- 29a b - 11a b + 68a b + 23a b - 42a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 7 +--R (- 74a b - 8a b + 173a b + 14a b - 105a b + 78a b - 18a b)cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 98a b + 28a b + 208a b - 65a b - 92a b + 181a b - 102a b +--R + +--R 9 +--R 24a b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 64a b + 68a b + 94a b - 122a b + 33a b + 150a b - 213a b +--R + +--R 8 2 9 +--R 114a b - 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 16b + 56a b - 14a b - 44a b + 84a b - 45a b - 186a b +--R + +--R 7 3 8 2 9 +--R 189a b - 78a b + 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b - 16a b + 40a b + 22a b - 116a b - 53a b + 102a b +--R + +--R 7 3 8 2 9 +--R - 115a b + 42a b - 6a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (24a b - 6a b - 24a b + 4a b - 23a b - 64a b + 47a b - 18a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 2 8 +--R (12a b - 2a b - 26a b - 4a b + 17a b - 18a b )cosh(x) - 2a b +--R + +--R 4 6 6 4 +--R 5a b - 6a b +--R / +--R 8 5 9 4 10 3 11 2 12 13 3 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 2 +--R (6a b - 6a b - 12a b + 12a b + 6a b - 6a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R (6a b - 6a b - 12a b + 12a b + 6a b - 6a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 2a b - 2a b - 4a b + 4a b + 2a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 4 +--R (12a b - 12a b - 24a b + 24a b + 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 3 +--R (48a b - 48a b - 96a b + 96a b + 48a b - 48a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 2 +--R (72a b - 72a b - 144a b + 144a b + 72a b - 72a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R (48a b - 48a b - 96a b + 96a b + 48a b - 48a b )cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 12a b - 12a b - 24a b + 24a b + 12a b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 5 +--R (30a b - 30a b - 60a b + 60a b + 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (150a b - 150a b - 300a b + 300a b + 150a b - 150a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 294a b - 294a b - 582a b + 582a b + 282a b - 282a b +--R + +--R 12 13 +--R 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 282a b - 282a b - 546a b + 546a b + 246a b - 246a b +--R + +--R 11 2 12 +--R 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 132a b - 132a b - 246a b + 246a b + 96a b - 96a b +--R + +--R 10 3 11 2 +--R 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 42a b + 42a b + 12a b - 12a b + 6a b +--R + +--R 10 3 +--R - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 6 +--R (40a b - 40a b - 80a b + 80a b + 40a b - 40a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (240a b - 240a b - 480a b + 480a b + 240a b - 240a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 576a b - 576a b - 1128a b + 1128a b + 528a b - 528a b +--R + +--R 12 13 +--R 24a b - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 704a b - 704a b - 1312a b + 1312a b + 512a b - 512a b +--R + +--R 11 2 12 +--R 96a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 456a b - 456a b - 768a b + 768a b + 168a b - 168a b +--R + +--R 10 3 11 2 +--R 144a b - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 144a b - 144a b - 192a b + 192a b - 48a b + 48a b +--R + +--R 9 4 10 3 +--R 96a b - 96a b +--R * +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R 16a b - 16a b - 8a b + 8a b - 32a b + 32a b + 24a b +--R + +--R 9 4 +--R - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 7 +--R (30a b - 30a b - 60a b + 60a b + 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (210a b - 210a b - 420a b + 420a b + 210a b - 210a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 594a b - 594a b - 1152a b + 1152a b + 522a b - 522a b +--R + +--R 12 13 +--R 36a b - 36a +--R * +--R 5 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 870a b - 870a b - 1560a b + 1560a b + 510a b - 510a b +--R + +--R 11 2 12 +--R 180a b - 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 696a b - 696a b - 1044a b + 1044a b + 6a b - 6a b +--R + +--R 10 3 11 2 12 13 +--R 336a b - 336a b + 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 288a b - 288a b - 252a b + 252a b - 342a b + 342a b +--R + +--R 9 4 10 3 11 2 12 +--R 288a b - 288a b + 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R 48a b - 48a b + 48a b - 48a b - 222a b + 222a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 108a b - 108a b + 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 42a b + 42a b + 12a b - 12a b + 6a b +--R + +--R 10 3 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 8 +--R (12a b - 12a b - 24a b + 24a b + 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 7 +--R (96a b - 96a b - 192a b + 192a b + 96a b - 96a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 312a b - 312a b - 600a b + 600a b + 264a b - 264a b +--R + +--R 12 13 +--R 24a b - 24a +--R * +--R 6 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 528a b - 528a b - 912a b + 912a b + 240a b - 240a b +--R + +--R 11 2 12 +--R 144a b - 144a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 492a b - 492a b - 648a b + 648a b - 168a b + 168a b +--R + +--R 10 3 11 2 12 13 +--R 312a b - 312a b + 12a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 240a b - 240a b - 96a b + 96a b - 480a b + 480a b +--R + +--R 9 4 10 3 11 2 12 +--R 288a b - 288a b + 48a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R 48a b - 48a b + 120a b - 120a b - 312a b + 312a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 72a b - 72a b + 72a b - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 48a b - 48a b - 48a b + 48a b - 48a b + 48a b + 48a b +--R + +--R 10 3 +--R - 48a b +--R * +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 12a b - 12a b - 24a b + 24a b + 12a b - 12a b +--R * +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 9 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 8 +--R (18a b - 18a b - 36a b + 36a b + 18a b - 18a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 12 +--R 66a b - 66a b - 126a b + 126a b + 54a b - 54a b + 6a b +--R + +--R 13 +--R - 6a +--R * +--R 7 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 126a b - 126a b - 210a b + 210a b + 42a b - 42a b +--R + +--R 11 2 12 +--R 42a b - 42a b +--R * +--R 6 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 132a b - 132a b - 150a b + 150a b - 90a b + 90a b +--R + +--R 10 3 11 2 12 13 +--R 102a b - 102a b + 6a b - 6a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 72a b - 72a b + 6a b - 6a b - 198a b + 198a b + 90a b +--R + +--R 10 3 11 2 12 +--R - 90a b + 30a b - 30a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R 16a b - 16a b + 64a b - 64a b - 122a b + 122a b - 10a b +--R + +--R 9 4 10 3 11 2 12 13 +--R 10a b + 50a b - 50a b + 2a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 6a b + 6a b - 54a b + 54a b + 30a b +--R + +--R 10 3 11 2 12 +--R - 30a b + 6a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 10 3 11 2 5 8 +--R (12a b - 12a b - 18a b + 18a b + 6a b - 6a b )cosh(x) + 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b - 4a b + 4a b + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 5 9 4 10 3 11 2 12 13 3 +--R (- 2a b - 2a b + 4a b + 4a b - 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 2 +--R (- 6a b - 6a b + 12a b + 12a b - 6a b - 6a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 5 8 +--R (- 6a b - 6a b + 12a b + 12a b - 6a b - 6a b )cosh(x) - 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b + 4a b + 4a b - 2a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 4 +--R (- 12a b - 12a b + 24a b + 24a b - 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 3 +--R (- 48a b - 48a b + 96a b + 96a b - 48a b - 48a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 2 +--R (- 72a b - 72a b + 144a b + 144a b - 72a b - 72a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R (- 48a b - 48a b + 96a b + 96a b - 48a b - 48a b )cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 12a b - 12a b + 24a b + 24a b - 12a b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 5 +--R (- 30a b - 30a b + 60a b + 60a b - 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 150a b - 150a b + 300a b + 300a b - 150a b - 150a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 294a b - 294a b + 582a b + 582a b - 282a b - 282a b +--R + +--R 12 13 +--R - 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 282a b - 282a b + 546a b + 546a b - 246a b - 246a b +--R + +--R 11 2 12 +--R - 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 132a b - 132a b + 246a b + 246a b - 96a b - 96a b +--R + +--R 10 3 11 2 +--R - 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 24a b - 24a b + 42a b + 42a b - 12a b - 12a b - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 6 +--R (- 40a b - 40a b + 80a b + 80a b - 40a b - 40a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 240a b - 240a b + 480a b + 480a b - 240a b - 240a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 576a b - 576a b + 1128a b + 1128a b - 528a b - 528a b +--R + +--R 12 13 +--R - 24a b - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 704a b - 704a b + 1312a b + 1312a b - 512a b - 512a b +--R + +--R 11 2 12 +--R - 96a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 456a b - 456a b + 768a b + 768a b - 168a b - 168a b +--R + +--R 10 3 11 2 +--R - 144a b - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 144a b - 144a b + 192a b + 192a b + 48a b + 48a b +--R + +--R 9 4 10 3 +--R - 96a b - 96a b +--R * +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 16a b - 16a b + 8a b + 8a b + 32a b + 32a b - 24a b - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 7 +--R (- 30a b - 30a b + 60a b + 60a b - 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 210a b - 210a b + 420a b + 420a b - 210a b - 210a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 594a b - 594a b + 1152a b + 1152a b - 522a b - 522a b +--R + +--R 12 13 +--R - 36a b - 36a +--R * +--R 5 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 870a b - 870a b + 1560a b + 1560a b - 510a b - 510a b +--R + +--R 11 2 12 +--R - 180a b - 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 696a b - 696a b + 1044a b + 1044a b - 6a b - 6a b +--R + +--R 10 3 11 2 12 13 +--R - 336a b - 336a b - 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 288a b - 288a b + 252a b + 252a b + 342a b + 342a b +--R + +--R 9 4 10 3 11 2 12 +--R - 288a b - 288a b - 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 48a b - 48a b - 48a b + 222a b + 222a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 108a b - 108a b - 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 24a b - 24a b + 42a b + 42a b - 12a b - 12a b - 6a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 8 +--R (- 12a b - 12a b + 24a b + 24a b - 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 7 +--R (- 96a b - 96a b + 192a b + 192a b - 96a b - 96a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 312a b - 312a b + 600a b + 600a b - 264a b - 264a b +--R + +--R 12 13 +--R - 24a b - 24a +--R * +--R 6 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 528a b - 528a b + 912a b + 912a b - 240a b - 240a b +--R + +--R 11 2 12 +--R - 144a b - 144a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 492a b - 492a b + 648a b + 648a b + 168a b + 168a b +--R + +--R 10 3 11 2 12 13 +--R - 312a b - 312a b - 12a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 240a b - 240a b + 96a b + 96a b + 480a b + 480a b +--R + +--R 9 4 10 3 11 2 12 +--R - 288a b - 288a b - 48a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 48a b - 120a b - 120a b + 312a b + 312a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 72a b - 72a b - 72a b - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 48a b - 48a b + 48a b + 48a b + 48a b + 48a b - 48a b +--R + +--R 10 3 +--R - 48a b +--R * +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 12a b - 12a b + 24a b + 24a b - 12a b - 12a b +--R * +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 9 +--R (- 2a b - 2a b + 4a b + 4a b - 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 8 +--R (- 18a b - 18a b + 36a b + 36a b - 18a b - 18a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 12 +--R - 66a b - 66a b + 126a b + 126a b - 54a b - 54a b - 6a b +--R + +--R 13 +--R - 6a +--R * +--R 7 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 126a b - 126a b + 210a b + 210a b - 42a b - 42a b - 42a b +--R + +--R 12 +--R - 42a b +--R * +--R 6 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 132a b - 132a b + 150a b + 150a b + 90a b + 90a b - 102a b +--R + +--R 11 2 12 13 +--R - 102a b - 6a b - 6a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 72a b - 72a b - 6a b - 6a b + 198a b + 198a b - 90a b +--R + +--R 10 3 11 2 12 +--R - 90a b - 30a b - 30a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 16a b - 16a b - 64a b - 64a b + 122a b + 122a b + 10a b +--R + +--R 9 4 10 3 11 2 12 13 +--R 10a b - 50a b - 50a b - 2a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 24a b - 24a b + 6a b + 6a b + 54a b + 54a b - 30a b +--R + +--R 10 3 11 2 12 +--R - 30a b - 6a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 10 3 11 2 5 8 +--R (- 12a b - 12a b + 18a b + 18a b - 6a b - 6a b )cosh(x) - 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b + 4a b + 4a b - 2a b - 2a b +--R Type: Expression(Integer) +--E 19 + +--S 20 of 526 +m0402b:= a0402.2-r0402 +--R +--R +--R (20) +--R 4 5 6 3 8 2 +--R (4a b - 10a b + 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 +--R (8a b - 20a b + 24a b )cosh(x) + 4a b - 10a b + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (16a b - 40a b + 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (48a b - 120a b + 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (48a b - 120a b + 144a b )cosh(x) + 16a b - 40a b + 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (24a b - 60a b + 72a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (96a b - 240a b + 288a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (136a b - 332a b + 388a b + 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 2 7 +--R (80a b - 184a b + 200a b + 48a b )cosh(x) + 16b - 32a b +--R + +--R 4 5 6 3 +--R 28a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 6 3 8 5 +--R (16a b - 40a b + 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (80a b - 200a b + 240a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (144a b - 344a b + 392a b + 48a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (112a b - 232a b + 216a b + 144a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 +--R (32b - 32a b - 24a b + 144a b )cosh(x) + 16a b - 40a b +--R + +--R 5 4 +--R 48a b +--R * +--R sinh(x) +--R + +--R 4 5 6 3 8 6 3 6 5 4 7 2 5 +--R (4a b - 10a b + 12a b)cosh(x) + (24a b - 60a b + 72a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (52a b - 122a b + 136a b + 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (48a b - 88a b + 64a b + 96a b )cosh(x) +--R + +--R 9 4 5 6 3 8 2 +--R (16b - 48a b + 110a b + 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 +--R (16a b - 32a b + 28a b + 24a b )cosh(x) + 4a b - 10a b + 12a b +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 4 5 6 3 8 2 +--R (- 4a b + 10a b - 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 +--R (- 8a b + 20a b - 24a b )cosh(x) - 4a b + 10a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (- 16a b + 40a b - 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 48a b + 120a b - 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (- 48a b + 120a b - 144a b )cosh(x) - 16a b + 40a b - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (- 24a b + 60a b - 72a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 96a b + 240a b - 288a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 136a b + 332a b - 388a b - 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 2 7 +--R (- 80a b + 184a b - 200a b - 48a b )cosh(x) - 16b + 32a b +--R + +--R 4 5 6 3 +--R - 28a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 6 3 8 5 +--R (- 16a b + 40a b - 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 80a b + 200a b - 240a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 144a b + 344a b - 392a b - 48a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 112a b + 232a b - 216a b - 144a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 +--R (- 32b + 32a b + 24a b - 144a b )cosh(x) - 16a b + 40a b +--R + +--R 5 4 +--R - 48a b +--R * +--R sinh(x) +--R + +--R 4 5 6 3 8 6 +--R (- 4a b + 10a b - 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- 24a b + 60a b - 72a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 52a b + 122a b - 136a b - 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 48a b + 88a b - 64a b - 96a b )cosh(x) +--R + +--R 9 4 5 6 3 8 2 +--R (- 16b + 48a b - 110a b - 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 +--R (- 16a b + 32a b - 28a b - 24a b )cosh(x) - 4a b + 10a b - 12a b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 6 2 3 5 5 3 5 +--R ((3a b - 6a b )cosh(x) + 2a b - 5a b )sinh(x) +--R + +--R 4 4 6 2 2 3 5 5 3 2 6 +--R (12a b - 24a b )cosh(x) + (20a b - 44a b )cosh(x) + 8a b +--R + +--R 4 4 +--R - 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 6 2 3 3 5 5 3 2 +--R (18a b - 36a b )cosh(x) + (56a b - 116a b )cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 +--R (52a b - 106a b - 12a b )cosh(x) + 16a b - 30a b - 10a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (12a b - 24a b )cosh(x) + (68a b - 134a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (108a b - 198a b - 36a b )cosh(x) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (64a b - 98a b - 68a b )cosh(x) + 12b - 10a b - 32a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 5 3 5 5 3 4 +--R (3a b - 6a b )cosh(x) + (38a b - 71a b )cosh(x) +--R + +--R 2 6 4 4 6 2 3 +--R (92a b - 158a b - 36a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (80a b - 102a b - 116a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 7 3 5 5 3 +--R (24b + 4a b - 109a b - 6a b )cosh(x) + 16a b - 32a b - 5a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 5 2 6 4 4 6 2 4 +--R (8a b - 14a b )cosh(x) + (28a b - 46a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 3 +--R (32a b - 34a b - 58a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (12b + 14a b - 74a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 +--R (16a b - 22a b - 24a b )cosh(x) + 6a b - 12a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 7 4 9 2 11 2 6 5 8 3 10 +--R (2a b - 4a b + 2a )cosh(x) + (4a b - 8a b + 4a b)cosh(x) +--R + +--R 5 6 7 4 9 2 +--R 2a b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 4 9 2 11 3 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 6 5 8 3 10 2 +--R (24a b - 48a b + 24a b)cosh(x) +--R + +--R 5 6 7 4 9 2 4 7 6 5 8 3 +--R (24a b - 48a b + 24a b )cosh(x) + 8a b - 16a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 4 9 2 11 4 +--R (12a b - 24a b + 12a )cosh(x) +--R + +--R 6 5 8 3 10 3 +--R (48a b - 96a b + 48a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 2 +--R (68a b - 132a b + 60a b + 4a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 3 8 5 6 9 2 +--R (40a b - 72a b + 24a b + 8a b)cosh(x) + 8a b - 12a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 4 9 2 11 5 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 6 5 8 3 10 4 +--R (40a b - 80a b + 40a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 3 +--R (72a b - 136a b + 56a b + 8a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (56a b - 88a b + 8a b + 24a b)cosh(x) +--R + +--R 3 8 5 6 7 4 9 2 4 7 6 5 8 3 +--R (16a b - 8a b - 32a b + 24a b )cosh(x) + 8a b - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 7 4 9 2 11 6 6 5 8 3 10 5 +--R (2a b - 4a b + 2a )cosh(x) + (12a b - 24a b + 12a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 4 +--R (26a b - 48a b + 18a b + 4a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (24a b - 32a b - 8a b + 16a b)cosh(x) +--R + +--R 3 8 5 6 7 4 9 2 11 2 +--R (8a b + 4a b - 30a b + 16a b + 2a )cosh(x) +--R + +--R 4 7 6 5 10 5 6 7 4 9 2 +--R (8a b - 12a b + 4a b)cosh(x) + 2a b - 4a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 20 + +--S 21 of 526 +d0402b:= D(m0402b,x) +--R +--R +--R (21) +--R 5 5 6 4 7 3 8 2 4 6 5 5 6 4 +--R (- 3a b + 3a b + 6a b - 6a b )cosh(x) - a b + a b + 4a b +--R + +--R 7 3 +--R - 4a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 2 +--R (- 18a b + 18a b + 36a b - 36a b )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 3 7 4 6 +--R (- 24a b + 24a b + 60a b - 60a b )cosh(x) - 6a b + 6a b +--R + +--R 5 5 6 4 +--R 24a b - 24a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 3 +--R (- 40a b + 42a b + 79a b - 84a b + 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 2 +--R (- 94a b + 100a b + 214a b - 229a b + 18a b )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 58a b + 64a b + 163a b - 178a b + 36a b - 18a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 10a b + 12a b + 40a b - 45a b + 18a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 4 +--R (- 30a b + 42a b + 54a b - 84a b + 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R (- 116a b + 164a b + 242a b - 362a b + 132a b + 12a b) +--R * +--R 3 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 126a b + 198a b + 288a b - 468a b + 252a b - 36a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (- 48a b + 96a b + 114a b - 234a b + 228a b - 84a b )cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 8a b + 20a b + 14a b - 44a b + 72a b - 36a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (30a b - 75a b + 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 4 +--R (60a b + 90a b - 180a b - 195a b + 390a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 30a b + 264a b - 171a b - 558a b + 753a b + 114a b +--R + +--R 9 +--R 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 6a b + 276a b - 144a b - 543a b + 804a b - 3a b +--R + +--R 8 2 +--R 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 132a b - 78a b - 234a b + 411a b - 60a b + 72a b +--R + +--R 8 2 +--R - 18a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b - 18a b - 36a b + 78a b - 21a b + 30a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 6 +--R (82a b - 42a b - 184a b + 84a b + 120a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 5 +--R (304a b - 64a b - 736a b + 136a b + 600a b + 120a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 430a b + 146a b - 1144a b - 272a b + 1212a b + 456a b +--R + +--R 9 +--R 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 304a b + 400a b - 924a b - 740a b + 1316a b + 556a b +--R + +--R 8 2 9 +--R 264a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 112a b + 344a b - 412a b - 584a b + 774a b + 234a b +--R + +--R 7 3 8 2 +--R 396a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b + 128a b - 88a b - 176a b + 204a b - 12a b +--R + +--R 6 4 7 3 +--R 276a b + 12a b +--R * +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b - 8a b - 8a b + 14a b - 26a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 7 +--R (72a b - 42a b - 159a b + 84a b + 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R (326a b - 116a b - 770a b + 245a b + 510a b + 120a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 3 7 5 5 6 4 7 3 8 2 9 +--R (594a b - 1467a b + 18a b + 1098a b + 594a b + 108a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 546a b + 324a b - 1368a b - 627a b + 1134a b + 1026a b +--R + +--R 8 2 9 +--R 468a b + 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 256a b + 440a b - 628a b - 764a b + 570a b + 654a b +--R + +--R 7 3 8 2 9 +--R 789a b + 240a b + 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 240a b - 108a b - 288a b + 90a b - 18a b +--R + +--R 6 4 7 3 8 2 +--R 654a b + 273a b + 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 3 7 4 6 5 5 6 4 +--R 48b + 24a b - 18a b - 180a b + 249a b + 138a b +--R + +--R 7 3 8 2 +--R 60a b - 6a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b - 6a b - 48a b + 32a b + 25a b + 22a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 8 +--R (30a b - 18a b - 66a b + 36a b + 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 7 +--R (156a b - 60a b - 366a b + 126a b + 228a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 342a b - 30a b - 816a b + 60a b + 528a b + 348a b +--R + +--R 9 +--R 72a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 384a b + 144a b - 870a b - 306a b + 504a b + 720a b +--R + +--R 8 2 9 +--R 360a b + 72a b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 216a b + 276a b - 402a b - 492a b + 102a b + 546a b +--R + +--R 7 3 8 2 9 +--R 678a b + 300a b + 36a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 192a b - 24a b - 192a b - 120a b - 72a b +--R + +--R 6 4 7 3 8 2 9 +--R 594a b + 438a b + 132a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 48b + 24a b + 72a b - 54a b - 270a b + 228a b +--R + +--R 6 4 7 3 8 2 +--R 240a b + 180a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 4 6 5 5 6 4 7 3 +--R (48a b - 72a b + 18a b + 6a b + 108a b + 36a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 12a b - 6a b - 24a b + 24a b + 12a b +--R * +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 9 +--R (5a b - 3a b - 11a b + 6a b + 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 8 +--R (29a b - 11a b - 68a b + 23a b + 42a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (74a b - 8a b - 173a b + 14a b + 105a b + 78a b + 18a b) +--R * +--R 7 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 98a b + 28a b - 208a b - 65a b + 92a b + 181a b + 102a b +--R + +--R 9 +--R 24a b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 64a b + 68a b - 94a b - 122a b - 33a b + 150a b + 213a b +--R + +--R 8 2 9 +--R 114a b + 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b + 56a b + 14a b - 44a b - 84a b - 45a b + 186a b +--R + +--R 7 3 8 2 9 +--R 189a b + 78a b + 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b + 16a b + 40a b - 22a b - 116a b + 53a b + 102a b +--R + +--R 7 3 8 2 9 +--R 115a b + 42a b + 6a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 6a b - 24a b - 4a b - 23a b + 64a b + 47a b +--R + +--R 8 2 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 2 8 +--R (12a b + 2a b - 26a b + 4a b + 17a b + 18a b )cosh(x) + 2a b +--R + +--R 4 6 6 4 +--R - 5a b + 6a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 5 6 4 7 3 8 2 4 6 5 5 6 4 7 3 +--R ((3a b + 3a b - 6a b - 6a b )cosh(x) + a b + a b - 4a b - 4a b ) +--R * +--R 8 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 2 +--R (18a b + 18a b - 36a b - 36a b )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 3 7 4 6 5 5 +--R (24a b + 24a b - 60a b - 60a b )cosh(x) + 6a b + 6a b - 24a b +--R + +--R 6 4 +--R - 24a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 3 +--R (40a b + 42a b - 79a b - 84a b - 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 2 +--R (94a b + 100a b - 214a b - 229a b - 18a b )cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R (58a b + 64a b - 163a b - 178a b - 36a b - 18a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 10a b + 12a b - 40a b - 45a b - 18a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 4 +--R (30a b + 42a b - 54a b - 84a b - 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 3 +--R (116a b + 164a b - 242a b - 362a b - 132a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 2 +--R (126a b + 198a b - 288a b - 468a b - 252a b - 36a b )cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (48a b + 96a b - 114a b - 234a b - 228a b - 84a b )cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 8a b + 20a b - 14a b - 44a b - 72a b - 36a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (- 30a b + 75a b - 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 4 +--R (- 60a b + 90a b + 180a b - 195a b - 390a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 30a b + 264a b + 171a b - 558a b - 753a b + 114a b +--R + +--R 9 +--R - 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (- 6a b + 276a b + 144a b - 543a b - 804a b - 3a b - 54a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (132a b + 78a b - 234a b - 411a b - 60a b - 72a b - 18a b ) +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 18a b - 36a b - 78a b - 21a b - 30a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 6 +--R (- 82a b - 42a b + 184a b + 84a b - 120a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 5 +--R (- 304a b - 64a b + 736a b + 136a b - 600a b + 120a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 430a b + 146a b + 1144a b - 272a b - 1212a b + 456a b +--R + +--R 9 +--R - 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 304a b + 400a b + 924a b - 740a b - 1316a b + 556a b +--R + +--R 8 2 9 +--R - 264a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 112a b + 344a b + 412a b - 584a b - 774a b + 234a b +--R + +--R 7 3 8 2 +--R - 396a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 16b + 128a b + 88a b - 176a b - 204a b - 12a b - 276a b +--R + +--R 7 3 +--R 12a b +--R * +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 16b + 8a b - 8a b - 14a b - 26a b - 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 7 +--R (- 72a b - 42a b + 159a b + 84a b - 90a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 6 +--R (- 326a b - 116a b + 770a b + 245a b - 510a b + 120a b)cosh(x) +--R + +--R 3 7 5 5 6 4 7 3 8 2 9 5 +--R (- 594a b + 1467a b + 18a b - 1098a b + 594a b - 108a b)cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 546a b + 324a b + 1368a b - 627a b - 1134a b + 1026a b +--R + +--R 8 2 9 +--R - 468a b + 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 256a b + 440a b + 628a b - 764a b - 570a b + 654a b +--R + +--R 7 3 8 2 9 +--R - 789a b + 240a b - 18a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 48b + 240a b + 108a b - 288a b - 90a b - 18a b - 654a b +--R + +--R 7 3 8 2 +--R 273a b - 54a b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 8 3 7 4 6 5 5 6 4 7 3 +--R 48b + 24a b + 18a b - 180a b - 249a b + 138a b - 60a b +--R + +--R 8 2 +--R - 6a b +--R * +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 24a b + 6a b - 48a b - 32a b + 25a b - 22a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 8 +--R (- 30a b - 18a b + 66a b + 36a b - 36a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 7 +--R (- 156a b - 60a b + 366a b + 126a b - 228a b + 60a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R (- 342a b - 30a b + 816a b + 60a b - 528a b + 348a b - 72a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 384a b + 144a b + 870a b - 306a b - 504a b + 720a b +--R + +--R 8 2 9 +--R - 360a b + 72a b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 216a b + 276a b + 402a b - 492a b - 102a b + 546a b +--R + +--R 7 3 8 2 9 +--R - 678a b + 300a b - 36a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 48b + 192a b + 24a b - 192a b + 120a b - 72a b - 594a b +--R + +--R 7 3 8 2 9 +--R 438a b - 132a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 48b - 24a b + 72a b + 54a b - 270a b - 228a b + 240a b +--R + +--R 7 3 8 2 +--R - 180a b + 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 3 7 4 6 5 5 6 4 7 3 2 8 +--R (48a b - 72a b - 18a b + 6a b - 108a b + 36a b )cosh(x) + 12a b +--R + +--R 3 7 4 6 5 5 6 4 +--R 6a b - 24a b - 24a b + 12a b +--R * +--R sinh(x) +--R + +--R 5 5 6 4 7 3 8 2 9 9 +--R (- 5a b - 3a b + 11a b + 6a b - 6a b)cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 8 +--R (- 29a b - 11a b + 68a b + 23a b - 42a b + 12a b)cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 7 +--R (- 74a b - 8a b + 173a b + 14a b - 105a b + 78a b - 18a b)cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 98a b + 28a b + 208a b - 65a b - 92a b + 181a b - 102a b +--R + +--R 9 +--R 24a b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 64a b + 68a b + 94a b - 122a b + 33a b + 150a b - 213a b +--R + +--R 8 2 9 +--R 114a b - 18a b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 16b + 56a b - 14a b - 44a b + 84a b - 45a b - 186a b +--R + +--R 7 3 8 2 9 +--R 189a b - 78a b + 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 16b - 16a b + 40a b + 22a b - 116a b - 53a b + 102a b +--R + +--R 7 3 8 2 9 +--R - 115a b + 42a b - 6a b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R (24a b - 6a b - 24a b + 4a b - 23a b - 64a b + 47a b - 18a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 2 8 +--R (12a b - 2a b - 26a b - 4a b + 17a b - 18a b )cosh(x) - 2a b +--R + +--R 4 6 6 4 +--R 5a b - 6a b +--R / +--R 8 5 9 4 10 3 11 2 12 13 3 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 2 +--R (6a b - 6a b - 12a b + 12a b + 6a b - 6a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R (6a b - 6a b - 12a b + 12a b + 6a b - 6a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 2a b - 2a b - 4a b + 4a b + 2a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 4 +--R (12a b - 12a b - 24a b + 24a b + 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 3 +--R (48a b - 48a b - 96a b + 96a b + 48a b - 48a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 2 +--R (72a b - 72a b - 144a b + 144a b + 72a b - 72a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R (48a b - 48a b - 96a b + 96a b + 48a b - 48a b )cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 12a b - 12a b - 24a b + 24a b + 12a b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 5 +--R (30a b - 30a b - 60a b + 60a b + 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (150a b - 150a b - 300a b + 300a b + 150a b - 150a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 294a b - 294a b - 582a b + 582a b + 282a b - 282a b +--R + +--R 12 13 +--R 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 282a b - 282a b - 546a b + 546a b + 246a b - 246a b +--R + +--R 11 2 12 +--R 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 132a b - 132a b - 246a b + 246a b + 96a b - 96a b +--R + +--R 10 3 11 2 +--R 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 42a b + 42a b + 12a b - 12a b + 6a b +--R + +--R 10 3 +--R - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 6 +--R (40a b - 40a b - 80a b + 80a b + 40a b - 40a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (240a b - 240a b - 480a b + 480a b + 240a b - 240a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 576a b - 576a b - 1128a b + 1128a b + 528a b - 528a b +--R + +--R 12 13 +--R 24a b - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 704a b - 704a b - 1312a b + 1312a b + 512a b - 512a b +--R + +--R 11 2 12 +--R 96a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 456a b - 456a b - 768a b + 768a b + 168a b - 168a b +--R + +--R 10 3 11 2 +--R 144a b - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 144a b - 144a b - 192a b + 192a b - 48a b + 48a b +--R + +--R 9 4 10 3 +--R 96a b - 96a b +--R * +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R 16a b - 16a b - 8a b + 8a b - 32a b + 32a b + 24a b +--R + +--R 9 4 +--R - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 7 +--R (30a b - 30a b - 60a b + 60a b + 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (210a b - 210a b - 420a b + 420a b + 210a b - 210a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 594a b - 594a b - 1152a b + 1152a b + 522a b - 522a b +--R + +--R 12 13 +--R 36a b - 36a +--R * +--R 5 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 870a b - 870a b - 1560a b + 1560a b + 510a b - 510a b +--R + +--R 11 2 12 +--R 180a b - 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 696a b - 696a b - 1044a b + 1044a b + 6a b - 6a b +--R + +--R 10 3 11 2 12 13 +--R 336a b - 336a b + 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 288a b - 288a b - 252a b + 252a b - 342a b + 342a b +--R + +--R 9 4 10 3 11 2 12 +--R 288a b - 288a b + 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R 48a b - 48a b + 48a b - 48a b - 222a b + 222a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 108a b - 108a b + 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 42a b + 42a b + 12a b - 12a b + 6a b +--R + +--R 10 3 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 8 +--R (12a b - 12a b - 24a b + 24a b + 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 7 +--R (96a b - 96a b - 192a b + 192a b + 96a b - 96a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R 312a b - 312a b - 600a b + 600a b + 264a b - 264a b +--R + +--R 12 13 +--R 24a b - 24a +--R * +--R 6 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 528a b - 528a b - 912a b + 912a b + 240a b - 240a b +--R + +--R 11 2 12 +--R 144a b - 144a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 492a b - 492a b - 648a b + 648a b - 168a b + 168a b +--R + +--R 10 3 11 2 12 13 +--R 312a b - 312a b + 12a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 240a b - 240a b - 96a b + 96a b - 480a b + 480a b +--R + +--R 9 4 10 3 11 2 12 +--R 288a b - 288a b + 48a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R 48a b - 48a b + 120a b - 120a b - 312a b + 312a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 72a b - 72a b + 72a b - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 48a b - 48a b - 48a b + 48a b - 48a b + 48a b + 48a b +--R + +--R 10 3 +--R - 48a b +--R * +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 12a b - 12a b - 24a b + 24a b + 12a b - 12a b +--R * +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 9 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 8 +--R (18a b - 18a b - 36a b + 36a b + 18a b - 18a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 12 +--R 66a b - 66a b - 126a b + 126a b + 54a b - 54a b + 6a b +--R + +--R 13 +--R - 6a +--R * +--R 7 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R 126a b - 126a b - 210a b + 210a b + 42a b - 42a b +--R + +--R 11 2 12 +--R 42a b - 42a b +--R * +--R 6 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 132a b - 132a b - 150a b + 150a b - 90a b + 90a b +--R + +--R 10 3 11 2 12 13 +--R 102a b - 102a b + 6a b - 6a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 72a b - 72a b + 6a b - 6a b - 198a b + 198a b + 90a b +--R + +--R 10 3 11 2 12 +--R - 90a b + 30a b - 30a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R 16a b - 16a b + 64a b - 64a b - 122a b + 122a b - 10a b +--R + +--R 9 4 10 3 11 2 12 13 +--R 10a b + 50a b - 50a b + 2a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 24a b - 24a b - 6a b + 6a b - 54a b + 54a b + 30a b +--R + +--R 10 3 11 2 12 +--R - 30a b + 6a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 10 3 11 2 5 8 +--R (12a b - 12a b - 18a b + 18a b + 6a b - 6a b )cosh(x) + 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b - 4a b + 4a b + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 5 9 4 10 3 11 2 12 13 3 +--R (- 2a b - 2a b + 4a b + 4a b - 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 2 +--R (- 6a b - 6a b + 12a b + 12a b - 6a b - 6a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 5 8 +--R (- 6a b - 6a b + 12a b + 12a b - 6a b - 6a b )cosh(x) - 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b + 4a b + 4a b - 2a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 4 +--R (- 12a b - 12a b + 24a b + 24a b - 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 3 +--R (- 48a b - 48a b + 96a b + 96a b - 48a b - 48a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 2 +--R (- 72a b - 72a b + 144a b + 144a b - 72a b - 72a b )cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R (- 48a b - 48a b + 96a b + 96a b - 48a b - 48a b )cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 12a b - 12a b + 24a b + 24a b - 12a b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 5 +--R (- 30a b - 30a b + 60a b + 60a b - 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 150a b - 150a b + 300a b + 300a b - 150a b - 150a b) +--R * +--R 4 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 294a b - 294a b + 582a b + 582a b - 282a b - 282a b +--R + +--R 12 13 +--R - 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 282a b - 282a b + 546a b + 546a b - 246a b - 246a b +--R + +--R 11 2 12 +--R - 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 132a b - 132a b + 246a b + 246a b - 96a b - 96a b +--R + +--R 10 3 11 2 +--R - 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 24a b - 24a b + 42a b + 42a b - 12a b - 12a b - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 6 +--R (- 40a b - 40a b + 80a b + 80a b - 40a b - 40a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 240a b - 240a b + 480a b + 480a b - 240a b - 240a b) +--R * +--R 5 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 576a b - 576a b + 1128a b + 1128a b - 528a b - 528a b +--R + +--R 12 13 +--R - 24a b - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 704a b - 704a b + 1312a b + 1312a b - 512a b - 512a b +--R + +--R 11 2 12 +--R - 96a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 456a b - 456a b + 768a b + 768a b - 168a b - 168a b +--R + +--R 10 3 11 2 +--R - 144a b - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 144a b - 144a b + 192a b + 192a b + 48a b + 48a b +--R + +--R 9 4 10 3 +--R - 96a b - 96a b +--R * +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 16a b - 16a b + 8a b + 8a b + 32a b + 32a b - 24a b - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 7 +--R (- 30a b - 30a b + 60a b + 60a b - 30a b - 30a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 +--R (- 210a b - 210a b + 420a b + 420a b - 210a b - 210a b) +--R * +--R 6 +--R cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 594a b - 594a b + 1152a b + 1152a b - 522a b - 522a b +--R + +--R 12 13 +--R - 36a b - 36a +--R * +--R 5 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 870a b - 870a b + 1560a b + 1560a b - 510a b - 510a b +--R + +--R 11 2 12 +--R - 180a b - 180a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 696a b - 696a b + 1044a b + 1044a b - 6a b - 6a b +--R + +--R 10 3 11 2 12 13 +--R - 336a b - 336a b - 6a b - 6a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 288a b - 288a b + 252a b + 252a b + 342a b + 342a b +--R + +--R 9 4 10 3 11 2 12 +--R - 288a b - 288a b - 18a b - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 48a b - 48a b - 48a b + 222a b + 222a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 108a b - 108a b - 18a b - 18a b +--R * +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 24a b - 24a b + 42a b + 42a b - 12a b - 12a b - 6a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 8 +--R (- 12a b - 12a b + 24a b + 24a b - 12a b - 12a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 7 +--R (- 96a b - 96a b + 192a b + 192a b - 96a b - 96a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 312a b - 312a b + 600a b + 600a b - 264a b - 264a b +--R + +--R 12 13 +--R - 24a b - 24a +--R * +--R 6 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 528a b - 528a b + 912a b + 912a b - 240a b - 240a b +--R + +--R 11 2 12 +--R - 144a b - 144a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 492a b - 492a b + 648a b + 648a b + 168a b + 168a b +--R + +--R 10 3 11 2 12 13 +--R - 312a b - 312a b - 12a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 240a b - 240a b + 96a b + 96a b + 480a b + 480a b +--R + +--R 9 4 10 3 11 2 12 +--R - 288a b - 288a b - 48a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 48a b - 120a b - 120a b + 312a b + 312a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 72a b - 72a b - 72a b - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 48a b - 48a b + 48a b + 48a b + 48a b + 48a b - 48a b +--R + +--R 10 3 +--R - 48a b +--R * +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 12a b - 12a b + 24a b + 24a b - 12a b - 12a b +--R * +--R sinh(x) +--R + +--R 8 5 9 4 10 3 11 2 12 13 9 +--R (- 2a b - 2a b + 4a b + 4a b - 2a b - 2a )cosh(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 12 8 +--R (- 18a b - 18a b + 36a b + 36a b - 18a b - 18a b)cosh(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 12 +--R - 66a b - 66a b + 126a b + 126a b - 54a b - 54a b - 6a b +--R + +--R 13 +--R - 6a +--R * +--R 7 +--R cosh(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 126a b - 126a b + 210a b + 210a b - 42a b - 42a b - 42a b +--R + +--R 12 +--R - 42a b +--R * +--R 6 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 132a b - 132a b + 150a b + 150a b + 90a b + 90a b - 102a b +--R + +--R 11 2 12 13 +--R - 102a b - 6a b - 6a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 72a b - 72a b - 6a b - 6a b + 198a b + 198a b - 90a b +--R + +--R 10 3 11 2 12 +--R - 90a b - 30a b - 30a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 16a b - 16a b - 64a b - 64a b + 122a b + 122a b + 10a b +--R + +--R 9 4 10 3 11 2 12 13 +--R 10a b - 50a b - 50a b - 2a b - 2a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 24a b - 24a b + 6a b + 6a b + 54a b + 54a b - 30a b +--R + +--R 10 3 11 2 12 +--R - 30a b - 6a b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 9 5 8 6 7 7 6 10 3 11 2 5 8 +--R (- 12a b - 12a b + 18a b + 18a b - 6a b - 6a b )cosh(x) - 2a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 2a b + 4a b + 4a b - 2a b - 2a b +--R Type: Expression(Integer) +--E 21 + +--S 22 of 526 +t0403:= 1/(a+b*sech(x)^2) +--R +--R +--R 1 +--R (22) -------------- +--R 2 +--R b sech(x) + a +--R Type: Expression(Integer) +--E 22 + +--S 23 of 526 +r0403:= x/a-b^(1/2)*atanh(b^(1/2)*tanh(x)/(a+b)^(1/2))/a/(a+b)^(1/2) +--R +--R +--R +-+ +--R +-+ tanh(x)\|b +-----+ +--R - \|b atanh(-----------) + x\|b + a +--R +-----+ +--R \|b + a +--R (23) ------------------------------------ +--R +-----+ +--R a\|b + a +--R Type: Expression(Integer) +--E 23 + +--S 24 of 526 +a0403:= integrate(t0403,x) +--R +--R +--R (24) +--R [ +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4a b + 4a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b + 4a )cosh(x) + 8b + 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 2a )cosh(x) + 8b + 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b + 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b + 2a)cosh(x) + a +--R + +--R 2x +--R / +--R 2a +--R , +--R +-------+ +--R | b +--R +-------+ (2b + 2a) |- ----- +--R | b \| b + a +--R - |- ----- atan(----------------------------------------------------) + x +--R \| b + a 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b + a +--R --------------------------------------------------------------------------] +--R a +--R Type: Union(List(Expression(Integer)),...) +--E 24 + +--S 25 of 526 +m0403a:= a0403.1-r0403 +--R +--R +--R (25) +--R +-----+ +--R | b +-----+ +--R |----- \|b + a +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4a b + 4a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b + 4a )cosh(x) + 8b + 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 2a )cosh(x) + 8b + 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b + 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b + 2a)cosh(x) + a +--R + +--R +-+ +--R +-+ tanh(x)\|b +--R 2\|b atanh(-----------) +--R +-----+ +--R \|b + a +--R / +--R +-----+ +--R 2a\|b + a +--R Type: Expression(Integer) +--E 25 + +--S 26 of 526 +d0403a:= D(m0403a,x) +--R +--R +--R (26) +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (- 4b cosh(x) + 4b cosh(x))sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (8b + 4a b)cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (4b + 2a b)cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (- a b - a )sinh(x) + (- 4a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6a b - 6a )cosh(x) - 4b - 6a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4a b - 4a )cosh(x) + (- 8b - 12a b - 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- a b - a )cosh(x) + (- 4b - 6a b - 2a )cosh(x) - a b - a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 526 +m0403b:= a0403.2-r0403 +--R +--R +--R (27) +--R +-+ +--R +-+ tanh(x)\|b +--R \|b atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R - +--R +-------+ +--R | b +-----+ +--R |- ----- \|b + a +--R \| b + a +--R * +--R +-------+ +--R | b +--R (2b + 2a) |- ----- +--R \| b + a +--R atan(----------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b + a +--R / +--R +-----+ +--R a\|b + a +--R Type: Expression(Integer) +--E 27 + +--S 28 of 526 +d0403b:= D(m0403b,x) +--R +--R +--R (28) +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (- 4b cosh(x) + 4b cosh(x))sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (8b + 4a b)cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (4b + 2a b)cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (- a b - a )sinh(x) + (- 4a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6a b - 6a )cosh(x) - 4b - 6a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4a b - 4a )cosh(x) + (- 8b - 12a b - 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- a b - a )cosh(x) + (- 4b - 6a b - 2a )cosh(x) - a b - a +--R Type: Expression(Integer) +--E 28 + +--S 29 of 526 +t0404:= 1/(a+b*sech(x)^2)^2 +--R +--R +--R 1 +--R (29) ------------------------------- +--R 2 4 2 2 +--R b sech(x) + 2a b sech(x) + a +--R Type: Expression(Integer) +--E 29 + +--S 30 of 526 +r0404:= x/a^2-2*b^(1/2)*atanh(b^(1/2)*tanh(x)/(a+b)^(1/2))/a^2/(a+b)^(1/2)+_ + 1/2*b^(1/2)*(a+2*b)*atanh(b^(1/2)*tanh(x)/(a+b)^(1/2))/a^2/_ + (a+b)^(3/2)-b*tanh(x)/a^2/(a+b*sech(x)^2)+1/2*b*(a+2*b)*_ + tanh(x)/a^2/(a+b)/(a+b*sech(x)^2) +--R +--R +--R (30) +--R +-+ +--R 2 2 2 +-+ tanh(x)\|b +--R ((- 2b - 3a b)sech(x) - 2a b - 3a )\|b atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 2 2 +-----+ +--R (- a b tanh(x) + (2b + 2a b)x sech(x) + (2a b + 2a )x)\|b + a +--R / +--R 2 2 3 2 3 4 +-----+ +--R ((2a b + 2a b)sech(x) + 2a b + 2a )\|b + a +--R Type: Expression(Integer) +--E 30 + +--S 31 of 526 +a0404:= integrate(t0404,x) +--R +--R +--R (31) +--R [ +--R 2 4 2 3 +--R (2a b + 3a )sinh(x) + (8a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((12a b + 18a )cosh(x) + 8b + 16a b + 6a )sinh(x) +--R + +--R 2 3 2 2 +--R ((8a b + 12a )cosh(x) + (16b + 32a b + 12a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (2a b + 3a )cosh(x) + (8b + 16a b + 6a )cosh(x) + 2a b + 3a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4a b + 4a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b + 4a )cosh(x) + 8b + 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 2a )cosh(x) + 8b + 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b + 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b + 2a)cosh(x) + a +--R + +--R 2 4 2 3 +--R (4a b + 4a )x sinh(x) + (16a b + 16a )x cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24a b + 24a )x cosh(x) + (16b + 24a b + 8a )x + 8b + 4a b)sinh(x) +--R + +--R 2 3 +--R (16a b + 16a )x cosh(x) +--R + +--R 2 2 2 +--R ((32b + 48a b + 16a )x + 16b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (4a b + 4a )x cosh(x) + ((16b + 24a b + 8a )x + 8b + 4a b)cosh(x) +--R + +--R 2 +--R (4a b + 4a )x + 4a b +--R / +--R 3 4 4 3 4 3 +--R (4a b + 4a )sinh(x) + (16a b + 16a )cosh(x)sinh(x) +--R + +--R 3 4 2 2 2 3 4 2 +--R ((24a b + 24a )cosh(x) + 16a b + 24a b + 8a )sinh(x) +--R + +--R 3 4 3 2 2 3 4 +--R ((16a b + 16a )cosh(x) + (32a b + 48a b + 16a )cosh(x))sinh(x) +--R + +--R 3 4 4 2 2 3 4 2 3 4 +--R (4a b + 4a )cosh(x) + (16a b + 24a b + 8a )cosh(x) + 4a b + 4a +--R , +--R +--R 2 4 2 3 +--R (- 2a b - 3a )sinh(x) + (- 8a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 12a b - 18a )cosh(x) - 8b - 16a b - 6a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 8a b - 12a )cosh(x) + (- 16b - 32a b - 12a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 2a b - 3a )cosh(x) + (- 8b - 16a b - 6a )cosh(x) - 2a b - 3a +--R * +--R +-------+ +--R | b +--R +-------+ (2b + 2a) |- ----- +--R | b \| b + a +--R |- ----- atan(----------------------------------------------------) +--R \| b + a 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b + a +--R + +--R 2 4 2 3 +--R (2a b + 2a )x sinh(x) + (8a b + 8a )x cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12a b + 12a )x cosh(x) + (8b + 12a b + 4a )x + 4b + 2a b)sinh(x) +--R + +--R 2 3 +--R (8a b + 8a )x cosh(x) +--R + +--R 2 2 2 +--R ((16b + 24a b + 8a )x + 8b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (2a b + 2a )x cosh(x) + ((8b + 12a b + 4a )x + 4b + 2a b)cosh(x) +--R + +--R 2 +--R (2a b + 2a )x + 2a b +--R / +--R 3 4 4 3 4 3 +--R (2a b + 2a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 3 4 2 2 2 3 4 2 +--R ((12a b + 12a )cosh(x) + 8a b + 12a b + 4a )sinh(x) +--R + +--R 3 4 3 2 2 3 4 +--R ((8a b + 8a )cosh(x) + (16a b + 24a b + 8a )cosh(x))sinh(x) +--R + +--R 3 4 4 2 2 3 4 2 3 4 +--R (2a b + 2a )cosh(x) + (8a b + 12a b + 4a )cosh(x) + 2a b + 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 31 + +--S 32 of 526 +m0404a:= a0404.1-r0404 +--R +--R +--R (32) +--R 2 2 2 2 3 4 +--R ((2a b + 3a b)sech(x) + 2a b + 3a )sinh(x) +--R + +--R 2 2 2 2 3 3 +--R ((8a b + 12a b)cosh(x)sech(x) + (8a b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((12a b + 18a b)cosh(x) + 8b + 16a b + 6a b)sech(x) +--R + +--R 2 3 2 2 2 3 +--R (12a b + 18a )cosh(x) + 8a b + 16a b + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((8a b + 12a b)cosh(x) + (16b + 32a b + 12a b)cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 3 2 2 3 +--R (8a b + 12a )cosh(x) + (16a b + 32a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 2 +--R (2a b + 3a b)cosh(x) + (8b + 16a b + 6a b)cosh(x) + 2a b +--R + +--R 2 +--R 3a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 4 2 2 3 2 2 3 +--R (2a b + 3a )cosh(x) + (8a b + 16a b + 6a )cosh(x) + 2a b + 3a +--R * +--R +-----+ +--R | b +-----+ +--R |----- \|b + a +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4a b + 4a )sinh(x) + (8a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b + 4a )cosh(x) + 8b + 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 2a )cosh(x) + 8b + 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b + 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b + 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b + 2a)cosh(x) + a +--R + +--R 2 2 2 2 3 4 +--R ((4a b + 6a b)sech(x) + 4a b + 6a )sinh(x) +--R + +--R 2 2 2 2 3 3 +--R ((16a b + 24a b)cosh(x)sech(x) + (16a b + 24a )cosh(x))sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((24a b + 36a b)cosh(x) + 16b + 32a b + 12a b)sech(x) +--R + +--R 2 3 2 2 2 3 +--R (24a b + 36a )cosh(x) + 16a b + 32a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((16a b + 24a b)cosh(x) + (32b + 64a b + 24a b)cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 3 2 2 3 +--R (16a b + 24a )cosh(x) + (32a b + 64a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 2 +--R (4a b + 6a b)cosh(x) + (16b + 32a b + 12a b)cosh(x) + 4a b +--R + +--R 2 +--R 6a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 4 2 2 3 2 2 3 +--R (4a b + 6a )cosh(x) + (16a b + 32a b + 12a )cosh(x) + 4a b + 6a +--R * +--R +-+ +--R +-+ tanh(x)\|b +--R \|b atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 4 2 3 +--R 2a b sinh(x) + 8a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (12a b cosh(x) + 8a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 2 4 +--R (8a b cosh(x) + (16a b + 8a b)cosh(x))sinh(x) + 2a b cosh(x) +--R + +--R 2 2 2 2 +--R (8a b + 4a b)cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 3 2 2 2 2 2 +--R ((8b + 4a b )sech(x) + 8a b + 4a b)sinh(x) +--R + +--R 3 2 2 2 2 +--R ((16b + 8a b )cosh(x)sech(x) + (16a b + 8a b)cosh(x))sinh(x) +--R + +--R 3 2 2 2 2 2 2 2 2 +--R ((8b + 4a b )cosh(x) + 4a b )sech(x) + (8a b + 4a b)cosh(x) + 4a b +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 2 4 2 4 5 4 +--R ((4a b + 4a b)sech(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 +--R ((16a b + 16a b)cosh(x)sech(x) + (16a b + 16a )cosh(x))sinh(x) +--R + +--R 3 2 4 2 2 3 3 2 4 2 +--R ((24a b + 24a b)cosh(x) + 16a b + 24a b + 8a b)sech(x) +--R + +--R 4 5 2 3 2 4 5 +--R (24a b + 24a )cosh(x) + 16a b + 24a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 3 2 4 +--R ((16a b + 16a b)cosh(x) + (32a b + 48a b + 16a b)cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 4 5 3 3 2 4 5 +--R (16a b + 16a )cosh(x) + (32a b + 48a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 4 4 2 3 3 2 4 2 3 2 +--R (4a b + 4a b)cosh(x) + (16a b + 24a b + 8a b)cosh(x) + 4a b +--R + +--R 4 +--R 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 5 4 3 2 4 5 2 4 5 +--R (4a b + 4a )cosh(x) + (16a b + 24a b + 8a )cosh(x) + 4a b + 4a +--R * +--R +-----+ +--R \|b + a +--R Type: Expression(Integer) +--E 32 + +--S 33 of 526 +d0404a:= D(m0404a,x) +--R +--R +--R (33) +--R 2 3 2 3 2 8 +--R (a b sech(x) - a b )sinh(x) +--R + +--R 2 3 2 3 2 7 +--R (8a b cosh(x)sech(x) - 8a b cosh(x))sinh(x) +--R + +--R 2 3 2 4 2 3 2 3 2 2 2 3 +--R (28a b cosh(x) + 8a b + 4a b )sech(x) - 28a b cosh(x) - 8a b +--R + +--R 3 2 +--R - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 4 2 3 2 +--R (56a b cosh(x) + (48a b + 24a b )cosh(x))sech(x) +--R + +--R 3 2 3 2 3 3 2 +--R - 56a b cosh(x) + (- 48a b - 24a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 4 4 2 3 2 5 4 +--R 70a b cosh(x) + (120a b + 60a b )cosh(x) + 16b + 16a b +--R + +--R 2 3 +--R 6a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 2 3 3 2 2 4 2 3 +--R - 70a b cosh(x) + (- 120a b - 60a b )cosh(x) - 16a b - 16a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 4 2 3 3 +--R 56a b cosh(x) + (160a b + 80a b )cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 64a b + 24a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 5 2 3 3 2 3 +--R - 56a b cosh(x) + (- 160a b - 80a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 64a b - 64a b - 24a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 6 4 2 3 4 +--R 28a b cosh(x) + (120a b + 60a b )cosh(x) +--R + +--R 5 4 2 3 2 4 2 3 +--R (96b + 96a b + 36a b )cosh(x) + 8a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 6 2 3 3 2 4 +--R - 28a b cosh(x) + (- 120a b - 60a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (- 96a b - 96a b - 36a b )cosh(x) - 8a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 7 4 2 3 5 +--R 8a b cosh(x) + (48a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 4 2 3 +--R (64b + 64a b + 24a b )cosh(x) + (16a b + 8a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 7 2 3 3 2 5 +--R - 8a b cosh(x) + (- 48a b - 24a b )cosh(x) +--R + +--R 4 2 3 3 2 3 2 3 3 2 +--R (- 64a b - 64a b - 24a b )cosh(x) + (- 16a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 8 4 2 3 6 +--R a b cosh(x) + (8a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 4 4 2 3 2 2 3 +--R (16b + 16a b + 6a b )cosh(x) + (8a b + 4a b )cosh(x) + a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 8 2 3 3 2 6 +--R - a b cosh(x) + (- 8a b - 4a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 2 3 2 +--R (- 16a b - 16a b - 6a b )cosh(x) + (- 8a b - 4a b )cosh(x) - a b +--R * +--R 4 +--R tanh(x) +--R + +--R 4 2 3 4 2 3 3 2 2 3 2 4 +--R ((2a b + 3a b )sech(x) + (4a b + 5a b )sech(x) + 4a b + 4a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 4 +--R (16a b + 24a b )cosh(x)sech(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (32a b + 40a b )cosh(x)sech(x) + (32a b + 32a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 2 4 2 3 4 +--R ((56a b + 84a b )cosh(x) + 16a b + 12a b )sech(x) +--R + +--R 2 3 3 2 2 2 3 3 2 2 +--R ((112a b + 140a b )cosh(x) + 24a b + 20a b )sech(x) +--R + +--R 3 2 4 2 2 3 3 2 4 +--R (112a b + 112a b)cosh(x) + 16a b + 32a b + 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 4 2 3 4 +--R ((112a b + 168a b )cosh(x) + (96a b + 72a b )cosh(x))sech(x) +--R + +--R 2 3 3 2 3 2 3 3 2 +--R ((224a b + 280a b )cosh(x) + (144a b + 120a b )cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 3 3 2 4 +--R (224a b + 224a b)cosh(x) + (96a b + 192a b + 96a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 4 4 2 3 2 +--R (140a b + 210a b )cosh(x) + (240a b + 180a b )cosh(x) +--R + +--R 5 4 2 3 +--R 16b + 28a b + 18a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 4 2 3 3 2 2 +--R (280a b + 350a b )cosh(x) + (360a b + 300a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R 16a b + 40a b + 30a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 4 2 3 3 2 4 2 +--R (280a b + 280a b)cosh(x) + (240a b + 480a b + 240a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R 32a b + 64a b + 56a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 5 4 2 3 3 +--R (112a b + 168a b )cosh(x) + (320a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 112a b + 72a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 5 2 3 3 2 3 +--R (224a b + 280a b )cosh(x) + (480a b + 400a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (64a b + 160a b + 120a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 5 2 3 3 2 4 3 +--R (224a b + 224a b)cosh(x) + (320a b + 640a b + 320a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (128a b + 256a b + 224a b + 96a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 6 4 2 3 4 +--R (56a b + 84a b )cosh(x) + (240a b + 180a b )cosh(x) +--R + +--R 5 4 2 3 2 4 2 3 +--R (96b + 168a b + 108a b )cosh(x) + 16a b + 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 6 2 3 3 2 4 +--R (112a b + 140a b )cosh(x) + (360a b + 300a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (96a b + 240a b + 180a b )cosh(x) + 24a b + 20a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 6 2 3 3 2 4 4 +--R (112a b + 112a b)cosh(x) + (240a b + 480a b + 240a b)cosh(x) +--R + +--R 4 2 3 3 2 4 2 2 3 3 2 +--R (192a b + 384a b + 336a b + 144a b)cosh(x) + 16a b + 32a b +--R + +--R 4 +--R 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 7 4 2 3 5 +--R (16a b + 24a b )cosh(x) + (96a b + 72a b )cosh(x) +--R + +--R 5 4 2 3 3 4 2 3 +--R (64b + 112a b + 72a b )cosh(x) + (32a b + 24a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 7 2 3 3 2 5 +--R (32a b + 40a b )cosh(x) + (144a b + 120a b )cosh(x) +--R + +--R 4 2 3 3 2 3 2 3 3 2 +--R (64a b + 160a b + 120a b )cosh(x) + (48a b + 40a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 +--R (32a b + 32a b)cosh(x) + (96a b + 192a b + 96a b)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (128a b + 256a b + 224a b + 96a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (32a b + 64a b + 32a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 8 4 2 3 6 +--R (2a b + 3a b )cosh(x) + (16a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 4 4 2 3 2 +--R (16b + 28a b + 18a b )cosh(x) + (16a b + 12a b )cosh(x) +--R + +--R 4 2 3 +--R 2a b + 3a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 8 2 3 3 2 6 +--R (4a b + 5a b )cosh(x) + (24a b + 20a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 2 +--R (16a b + 40a b + 30a b )cosh(x) + (24a b + 20a b )cosh(x) +--R + +--R 2 3 3 2 +--R 4a b + 5a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 8 2 3 3 2 4 6 +--R (4a b + 4a b)cosh(x) + (16a b + 32a b + 16a b)cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (32a b + 64a b + 56a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 4 2 3 2 4 +--R (16a b + 32a b + 16a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 2 3 4 2 3 3 2 2 3 2 4 +--R ((- 2a b - 3a b )sech(x) + (- 5a b - 7a b )sech(x) - 3a b - 4a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 4 +--R (- 16a b - 24a b )cosh(x)sech(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 40a b - 56a b )cosh(x)sech(x) + (- 24a b - 32a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 2 2 3 4 +--R ((- 56a b - 84a b )cosh(x) + 4a b )sech(x) +--R + +--R 2 3 3 2 2 4 2 3 3 2 2 +--R ((- 140a b - 196a b )cosh(x) - 8a b - 12a b + 4a b )sech(x) +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 84a b - 112a b)cosh(x) - 8a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 2 3 4 +--R ((- 112a b - 168a b )cosh(x) + 24a b cosh(x))sech(x) +--R + +--R 2 3 3 2 3 +--R (- 280a b - 392a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 48a b - 72a b + 24a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 3 3 2 +--R (- 168a b - 224a b)cosh(x) + (- 48a b - 72a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 4 2 3 2 5 4 +--R (- 140a b - 210a b )cosh(x) + 60a b cosh(x) + 16b + 36a b +--R + +--R 2 3 +--R 14a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 4 +--R (- 350a b - 490a b )cosh(x) +--R + +--R 4 2 3 3 2 2 5 2 3 3 2 +--R (- 120a b - 180a b + 60a b )cosh(x) - 16b + 50a b + 22a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 4 2 3 3 2 2 4 +--R (- 210a b - 280a b)cosh(x) + (- 120a b - 180a b )cosh(x) - 16a b +--R + +--R 2 3 3 2 4 +--R - 16a b + 14a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 5 2 3 3 +--R (- 112a b - 168a b )cosh(x) + 80a b cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 144a b + 56a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 5 +--R (- 280a b - 392a b )cosh(x) +--R + +--R 4 2 3 3 2 3 +--R (- 160a b - 240a b + 80a b )cosh(x) +--R + +--R 5 2 3 3 2 +--R (- 64b + 200a b + 88a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 5 2 3 3 2 3 +--R (- 168a b - 224a b)cosh(x) + (- 160a b - 240a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 64a b - 64a b + 56a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 6 2 3 4 +--R (- 56a b - 84a b )cosh(x) + 60a b cosh(x) +--R + +--R 5 4 2 3 2 2 3 +--R (96b + 216a b + 84a b )cosh(x) + 4a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 6 +--R (- 140a b - 196a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 120a b - 180a b + 60a b )cosh(x) +--R + +--R 5 2 3 3 2 2 4 2 3 3 2 +--R (- 96b + 300a b + 132a b )cosh(x) - 8a b - 12a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 6 2 3 3 2 4 +--R (- 84a b - 112a b)cosh(x) + (- 120a b - 180a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 2 3 3 2 +--R (- 96a b - 96a b + 84a b + 48a b)cosh(x) - 8a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 7 2 3 5 +--R (- 16a b - 24a b )cosh(x) + 24a b cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (64b + 144a b + 56a b )cosh(x) + 8a b cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 7 +--R (- 40a b - 56a b )cosh(x) +--R + +--R 4 2 3 3 2 5 +--R (- 48a b - 72a b + 24a b )cosh(x) +--R + +--R 5 2 3 3 2 3 +--R (- 64b + 200a b + 88a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 16a b - 24a b + 8a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 7 2 3 3 2 5 +--R (- 24a b - 32a b)cosh(x) + (- 48a b - 72a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 64a b - 64a b + 56a b + 32a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 16a b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 8 2 3 6 +--R (- 2a b - 3a b )cosh(x) + 4a b cosh(x) +--R + +--R 5 4 2 3 4 2 3 2 4 2 3 +--R (16b + 36a b + 14a b )cosh(x) + 4a b cosh(x) - 2a b - 3a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 8 4 2 3 3 2 6 +--R (- 5a b - 7a b )cosh(x) + (- 8a b - 12a b + 4a b )cosh(x) +--R + +--R 5 2 3 3 2 4 +--R (- 16b + 50a b + 22a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (- 8a b - 12a b + 4a b )cosh(x) - 5a b - 7a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 8 2 3 3 2 6 +--R (- 3a b - 4a b)cosh(x) + (- 8a b - 12a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 2 +--R (- 16a b - 16a b + 14a b + 8a b)cosh(x) + (- 8a b - 12a b )cosh(x) +--R + +--R 3 2 4 +--R - 3a b - 4a b +--R / +--R 3 4 4 3 4 4 3 5 2 2 5 2 6 +--R ((2a b + 2a b )sech(x) + (4a b + 4a b )sech(x) + 2a b + 2a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 4 3 4 +--R (16a b + 16a b )cosh(x)sech(x) +--R + +--R 4 3 5 2 2 5 2 6 +--R (32a b + 32a b )cosh(x)sech(x) + (16a b + 16a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 2 2 5 3 4 4 3 4 +--R ((56a b + 56a b )cosh(x) + 16a b + 24a b + 8a b )sech(x) +--R + +--R 4 3 5 2 2 3 4 4 3 5 2 2 +--R ((112a b + 112a b )cosh(x) + 32a b + 48a b + 16a b )sech(x) +--R + +--R 5 2 6 2 4 3 5 2 6 +--R (56a b + 56a b)cosh(x) + 16a b + 24a b + 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 4 3 3 +--R (112a b + 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 +--R (96a b + 144a b + 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 3 +--R (224a b + 224a b )cosh(x) +--R + +--R 3 4 4 3 5 2 +--R (192a b + 288a b + 96a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 3 4 3 5 2 6 +--R (112a b + 112a b)cosh(x) + (96a b + 144a b + 48a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 4 3 4 +--R (140a b + 140a b )cosh(x) +--R + +--R 2 5 3 4 4 3 2 6 2 5 +--R (240a b + 360a b + 120a b )cosh(x) + 32a b + 64a b +--R + +--R 3 4 4 3 +--R 44a b + 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 4 +--R (280a b + 280a b )cosh(x) +--R + +--R 3 4 4 3 5 2 2 2 5 3 4 +--R (480a b + 720a b + 240a b )cosh(x) + 64a b + 128a b +--R + +--R 4 3 5 2 +--R 88a b + 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 4 4 3 5 2 6 2 +--R (140a b + 140a b)cosh(x) + (240a b + 360a b + 120a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R 32a b + 64a b + 44a b + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 +--R (112a b + 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 3 +--R (320a b + 480a b + 160a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 +--R (128a b + 256a b + 176a b + 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 5 +--R (224a b + 224a b )cosh(x) +--R + +--R 3 4 4 3 5 2 3 +--R (640a b + 960a b + 320a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (256a b + 512a b + 352a b + 96a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 5 4 3 5 2 6 3 +--R (112a b + 112a b)cosh(x) + (320a b + 480a b + 160a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (128a b + 256a b + 176a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 6 +--R (56a b + 56a b )cosh(x) +--R + +--R 2 5 3 4 4 3 4 +--R (240a b + 360a b + 120a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 2 2 5 +--R (192a b + 384a b + 264a b + 72a b )cosh(x) + 16a b +--R + +--R 3 4 4 3 +--R 24a b + 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 +--R (112a b + 112a b )cosh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (480a b + 720a b + 240a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 3 4 +--R (384a b + 768a b + 528a b + 144a b )cosh(x) + 32a b +--R + +--R 4 3 5 2 +--R 48a b + 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 6 4 3 5 2 6 4 +--R (56a b + 56a b)cosh(x) + (240a b + 360a b + 120a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 4 3 5 2 +--R (192a b + 384a b + 264a b + 72a b)cosh(x) + 16a b + 24a b +--R + +--R 6 +--R 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 7 +--R (16a b + 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 +--R (96a b + 144a b + 48a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (128a b + 256a b + 176a b + 48a b )cosh(x) +--R + +--R 2 5 3 4 4 3 +--R (32a b + 48a b + 16a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 7 +--R (32a b + 32a b )cosh(x) +--R + +--R 3 4 4 3 5 2 5 +--R (192a b + 288a b + 96a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (256a b + 512a b + 352a b + 96a b )cosh(x) +--R + +--R 3 4 4 3 5 2 +--R (64a b + 96a b + 32a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 4 3 5 2 6 5 +--R (16a b + 16a b)cosh(x) + (96a b + 144a b + 48a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 3 +--R (128a b + 256a b + 176a b + 48a b)cosh(x) +--R + +--R 4 3 5 2 6 +--R (32a b + 48a b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 8 2 5 3 4 4 3 6 +--R (2a b + 2a b )cosh(x) + (16a b + 24a b + 8a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (32a b + 64a b + 44a b + 12a b )cosh(x) +--R + +--R 2 5 3 4 4 3 2 3 4 4 3 +--R (16a b + 24a b + 8a b )cosh(x) + 2a b + 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 8 3 4 4 3 5 2 6 +--R (4a b + 4a b )cosh(x) + (32a b + 48a b + 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 4 +--R (64a b + 128a b + 88a b + 24a b )cosh(x) +--R + +--R 3 4 4 3 5 2 2 4 3 5 2 +--R (32a b + 48a b + 16a b )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 8 4 3 5 2 6 6 +--R (2a b + 2a b)cosh(x) + (16a b + 24a b + 8a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (32a b + 64a b + 44a b + 12a b)cosh(x) +--R + +--R 4 3 5 2 6 2 5 2 6 +--R (16a b + 24a b + 8a b)cosh(x) + 2a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 +--R (- 2a b - 4a b - 2a b )sech(x) + (- 4a b - 8a b - 4a b)sech(x) +--R + +--R 5 2 6 7 +--R - 2a b - 4a b - 2a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (- 16a b - 32a b - 16a b )cosh(x)sech(x) +--R + +--R 4 3 5 2 6 2 +--R (- 32a b - 64a b - 32a b)cosh(x)sech(x) +--R + +--R 5 2 6 7 +--R (- 16a b - 32a b - 16a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 2 2 5 3 4 4 3 +--R (- 56a b - 112a b - 56a b )cosh(x) - 16a b - 40a b - 32a b +--R + +--R 5 2 +--R - 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 2 3 4 4 3 5 2 +--R (- 112a b - 224a b - 112a b)cosh(x) - 32a b - 80a b - 64a b +--R + +--R 6 +--R - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 2 4 3 5 2 6 7 +--R (- 56a b - 112a b - 56a )cosh(x) - 16a b - 40a b - 32a b - 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 3 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- 96a b - 240a b - 192a b - 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 3 +--R (- 224a b - 448a b - 224a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 192a b - 480a b - 384a b - 96a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 3 +--R (- 112a b - 224a b - 112a )cosh(x) +--R + +--R 4 3 5 2 6 7 +--R (- 96a b - 240a b - 192a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (- 140a b - 280a b - 140a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 6 +--R (- 240a b - 600a b - 480a b - 120a b )cosh(x) - 32a b +--R + +--R 2 5 3 4 4 3 5 2 +--R - 96a b - 108a b - 56a b - 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 4 +--R (- 280a b - 560a b - 280a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 2 5 +--R (- 480a b - 1200a b - 960a b - 240a b)cosh(x) - 64a b +--R + +--R 3 4 4 3 5 2 6 +--R - 192a b - 216a b - 112a b - 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 4 +--R (- 140a b - 280a b - 140a )cosh(x) +--R + +--R 4 3 5 2 6 7 2 3 4 4 3 +--R (- 240a b - 600a b - 480a b - 120a )cosh(x) - 32a b - 96a b +--R + +--R 5 2 6 7 +--R - 108a b - 56a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 5 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (- 320a b - 800a b - 640a b - 160a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (- 128a b - 384a b - 432a b - 224a b - 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 5 +--R (- 224a b - 448a b - 224a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 3 +--R (- 640a b - 1600a b - 1280a b - 320a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 256a b - 768a b - 864a b - 448a b - 96a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 5 +--R (- 112a b - 224a b - 112a )cosh(x) +--R + +--R 4 3 5 2 6 7 3 +--R (- 320a b - 800a b - 640a b - 160a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (- 128a b - 384a b - 432a b - 224a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 56a b - 112a b - 56a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 4 +--R (- 240a b - 600a b - 480a b - 120a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 +--R (- 192a b - 576a b - 648a b - 336a b - 72a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 16a b - 40a b - 32a b - 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 6 +--R (- 112a b - 224a b - 112a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 480a b - 1200a b - 960a b - 240a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 +--R (- 384a b - 1152a b - 1296a b - 672a b - 144a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R - 32a b - 80a b - 64a b - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 6 +--R (- 56a b - 112a b - 56a )cosh(x) +--R + +--R 4 3 5 2 6 7 4 +--R (- 240a b - 600a b - 480a b - 120a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 4 3 +--R (- 192a b - 576a b - 648a b - 336a b - 72a )cosh(x) - 16a b +--R + +--R 5 2 6 7 +--R - 40a b - 32a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 7 +--R (- 16a b - 32a b - 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 5 +--R (- 96a b - 240a b - 192a b - 48a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (- 128a b - 384a b - 432a b - 224a b - 48a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- 32a b - 80a b - 64a b - 16a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 7 +--R (- 32a b - 64a b - 32a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 5 +--R (- 192a b - 480a b - 384a b - 96a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 256a b - 768a b - 864a b - 448a b - 96a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 64a b - 160a b - 128a b - 32a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 7 +--R (- 16a b - 32a b - 16a )cosh(x) +--R + +--R 4 3 5 2 6 7 5 +--R (- 96a b - 240a b - 192a b - 48a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (- 128a b - 384a b - 432a b - 224a b - 48a )cosh(x) +--R + +--R 4 3 5 2 6 7 +--R (- 32a b - 80a b - 64a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 8 +--R (- 2a b - 4a b - 2a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 16a b - 40a b - 32a b - 8a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (- 32a b - 96a b - 108a b - 56a b - 12a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 3 4 4 3 5 2 +--R (- 16a b - 40a b - 32a b - 8a b )cosh(x) - 2a b - 4a b - 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 8 +--R (- 4a b - 8a b - 4a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 32a b - 80a b - 64a b - 16a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 64a b - 192a b - 216a b - 112a b - 24a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 4 3 5 2 6 +--R (- 32a b - 80a b - 64a b - 16a b)cosh(x) - 4a b - 8a b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 8 +--R (- 2a b - 4a b - 2a )cosh(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 16a b - 40a b - 32a b - 8a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- 32a b - 96a b - 108a b - 56a b - 12a )cosh(x) +--R + +--R 4 3 5 2 6 7 2 5 2 6 7 +--R (- 16a b - 40a b - 32a b - 8a )cosh(x) - 2a b - 4a b - 2a +--R Type: Expression(Integer) +--E 33 + +--S 34 of 526 +m0404b:= a0404.2-r0404 +--R +--R +--R (34) +--R 2 2 2 2 3 4 +--R ((2a b + 3a b)sech(x) + 2a b + 3a )sinh(x) +--R + +--R 2 2 2 2 3 3 +--R ((8a b + 12a b)cosh(x)sech(x) + (8a b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((12a b + 18a b)cosh(x) + 8b + 16a b + 6a b)sech(x) +--R + +--R 2 3 2 2 2 3 +--R (12a b + 18a )cosh(x) + 8a b + 16a b + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((8a b + 12a b)cosh(x) + (16b + 32a b + 12a b)cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 3 2 2 3 +--R (8a b + 12a )cosh(x) + (16a b + 32a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 2 +--R (2a b + 3a b)cosh(x) + (8b + 16a b + 6a b)cosh(x) + 2a b +--R + +--R 2 +--R 3a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 4 2 2 3 2 2 3 +--R (2a b + 3a )cosh(x) + (8a b + 16a b + 6a )cosh(x) + 2a b + 3a +--R * +--R +-+ +--R +-+ tanh(x)\|b +--R \|b atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 2 2 2 3 4 +--R ((- 2a b - 3a b)sech(x) - 2a b - 3a )sinh(x) +--R + +--R 2 2 2 2 3 3 +--R ((- 8a b - 12a b)cosh(x)sech(x) + (- 8a b - 12a )cosh(x))sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((- 12a b - 18a b)cosh(x) - 8b - 16a b - 6a b)sech(x) +--R + +--R 2 3 2 2 2 3 +--R (- 12a b - 18a )cosh(x) - 8a b - 16a b - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((- 8a b - 12a b)cosh(x) + (- 16b - 32a b - 12a b)cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 3 2 2 3 +--R (- 8a b - 12a )cosh(x) + (- 16a b - 32a b - 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R (- 2a b - 3a b)cosh(x) + (- 8b - 16a b - 6a b)cosh(x) +--R + +--R 2 2 +--R - 2a b - 3a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 3 4 2 2 3 2 2 3 +--R (- 2a b - 3a )cosh(x) + (- 8a b - 16a b - 6a )cosh(x) - 2a b - 3a +--R * +--R +-------+ +--R | b +-----+ +--R |- ----- \|b + a +--R \| b + a +--R * +--R +-------+ +--R | b +--R (2b + 2a) |- ----- +--R \| b + a +--R atan(----------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b + a +--R + +--R 2 4 2 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a b cosh(x) + 4a b + 2a b)sinh(x) +--R + +--R 2 3 2 2 2 4 +--R (4a b cosh(x) + (8a b + 4a b)cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 2a b)cosh(x) + a b +--R * +--R tanh(x) +--R + +--R 3 2 2 2 2 2 +--R ((4b + 2a b )sech(x) + 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 2 2 +--R ((8b + 4a b )cosh(x)sech(x) + (8a b + 4a b)cosh(x))sinh(x) +--R + +--R 3 2 2 2 2 2 2 2 2 +--R ((4b + 2a b )cosh(x) + 2a b )sech(x) + (4a b + 2a b)cosh(x) + 2a b +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 2 4 2 4 5 4 +--R ((2a b + 2a b)sech(x) + 2a b + 2a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 +--R ((8a b + 8a b)cosh(x)sech(x) + (8a b + 8a )cosh(x))sinh(x) +--R + +--R 3 2 4 2 2 3 3 2 4 2 +--R ((12a b + 12a b)cosh(x) + 8a b + 12a b + 4a b)sech(x) +--R + +--R 4 5 2 3 2 4 5 +--R (12a b + 12a )cosh(x) + 8a b + 12a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 3 2 4 2 +--R ((8a b + 8a b)cosh(x) + (16a b + 24a b + 8a b)cosh(x))sech(x) +--R + +--R 4 5 3 3 2 4 5 +--R (8a b + 8a )cosh(x) + (16a b + 24a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 4 4 2 3 3 2 4 2 3 2 +--R (2a b + 2a b)cosh(x) + (8a b + 12a b + 4a b)cosh(x) + 2a b +--R + +--R 4 +--R 2a b +--R * +--R 2 +--R sech(x) +--R + +--R 4 5 4 3 2 4 5 2 4 5 +--R (2a b + 2a )cosh(x) + (8a b + 12a b + 4a )cosh(x) + 2a b + 2a +--R * +--R +-----+ +--R \|b + a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 526 +d0404b:= D(m0404b,x) +--R +--R +--R (35) +--R 2 3 2 3 2 8 +--R (a b sech(x) - a b )sinh(x) +--R + +--R 2 3 2 3 2 7 +--R (8a b cosh(x)sech(x) - 8a b cosh(x))sinh(x) +--R + +--R 2 3 2 4 2 3 2 3 2 2 2 3 +--R (28a b cosh(x) + 8a b + 4a b )sech(x) - 28a b cosh(x) - 8a b +--R + +--R 3 2 +--R - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 4 2 3 2 +--R (56a b cosh(x) + (48a b + 24a b )cosh(x))sech(x) +--R + +--R 3 2 3 2 3 3 2 +--R - 56a b cosh(x) + (- 48a b - 24a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 4 4 2 3 2 5 4 +--R 70a b cosh(x) + (120a b + 60a b )cosh(x) + 16b + 16a b +--R + +--R 2 3 +--R 6a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 2 3 3 2 2 4 2 3 +--R - 70a b cosh(x) + (- 120a b - 60a b )cosh(x) - 16a b - 16a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 4 2 3 3 +--R 56a b cosh(x) + (160a b + 80a b )cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 64a b + 24a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 5 2 3 3 2 3 +--R - 56a b cosh(x) + (- 160a b - 80a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 64a b - 64a b - 24a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 6 4 2 3 4 +--R 28a b cosh(x) + (120a b + 60a b )cosh(x) +--R + +--R 5 4 2 3 2 4 2 3 +--R (96b + 96a b + 36a b )cosh(x) + 8a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 6 2 3 3 2 4 +--R - 28a b cosh(x) + (- 120a b - 60a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (- 96a b - 96a b - 36a b )cosh(x) - 8a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 7 4 2 3 5 +--R 8a b cosh(x) + (48a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 4 2 3 +--R (64b + 64a b + 24a b )cosh(x) + (16a b + 8a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 7 2 3 3 2 5 +--R - 8a b cosh(x) + (- 48a b - 24a b )cosh(x) +--R + +--R 4 2 3 3 2 3 2 3 3 2 +--R (- 64a b - 64a b - 24a b )cosh(x) + (- 16a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 8 4 2 3 6 +--R a b cosh(x) + (8a b + 4a b )cosh(x) +--R + +--R 5 4 2 3 4 4 2 3 2 2 3 +--R (16b + 16a b + 6a b )cosh(x) + (8a b + 4a b )cosh(x) + a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 8 2 3 3 2 6 +--R - a b cosh(x) + (- 8a b - 4a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 2 3 2 +--R (- 16a b - 16a b - 6a b )cosh(x) + (- 8a b - 4a b )cosh(x) - a b +--R * +--R 4 +--R tanh(x) +--R + +--R 4 2 3 4 2 3 3 2 2 3 2 4 +--R ((2a b + 3a b )sech(x) + (4a b + 5a b )sech(x) + 4a b + 4a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 4 +--R (16a b + 24a b )cosh(x)sech(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (32a b + 40a b )cosh(x)sech(x) + (32a b + 32a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 2 4 2 3 4 +--R ((56a b + 84a b )cosh(x) + 16a b + 12a b )sech(x) +--R + +--R 2 3 3 2 2 2 3 3 2 2 +--R ((112a b + 140a b )cosh(x) + 24a b + 20a b )sech(x) +--R + +--R 3 2 4 2 2 3 3 2 4 +--R (112a b + 112a b)cosh(x) + 16a b + 32a b + 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 4 2 3 4 +--R ((112a b + 168a b )cosh(x) + (96a b + 72a b )cosh(x))sech(x) +--R + +--R 2 3 3 2 3 2 3 3 2 +--R ((224a b + 280a b )cosh(x) + (144a b + 120a b )cosh(x)) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 3 3 2 4 +--R (224a b + 224a b)cosh(x) + (96a b + 192a b + 96a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 4 4 2 3 2 +--R (140a b + 210a b )cosh(x) + (240a b + 180a b )cosh(x) +--R + +--R 5 4 2 3 +--R 16b + 28a b + 18a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 4 2 3 3 2 2 +--R (280a b + 350a b )cosh(x) + (360a b + 300a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R 16a b + 40a b + 30a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 4 2 3 3 2 4 2 +--R (280a b + 280a b)cosh(x) + (240a b + 480a b + 240a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R 32a b + 64a b + 56a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 5 4 2 3 3 +--R (112a b + 168a b )cosh(x) + (320a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 112a b + 72a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 5 2 3 3 2 3 +--R (224a b + 280a b )cosh(x) + (480a b + 400a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (64a b + 160a b + 120a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 5 2 3 3 2 4 3 +--R (224a b + 224a b)cosh(x) + (320a b + 640a b + 320a b)cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (128a b + 256a b + 224a b + 96a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 6 4 2 3 4 +--R (56a b + 84a b )cosh(x) + (240a b + 180a b )cosh(x) +--R + +--R 5 4 2 3 2 4 2 3 +--R (96b + 168a b + 108a b )cosh(x) + 16a b + 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 6 2 3 3 2 4 +--R (112a b + 140a b )cosh(x) + (360a b + 300a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (96a b + 240a b + 180a b )cosh(x) + 24a b + 20a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 6 2 3 3 2 4 4 +--R (112a b + 112a b)cosh(x) + (240a b + 480a b + 240a b)cosh(x) +--R + +--R 4 2 3 3 2 4 2 2 3 3 2 +--R (192a b + 384a b + 336a b + 144a b)cosh(x) + 16a b + 32a b +--R + +--R 4 +--R 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 7 4 2 3 5 +--R (16a b + 24a b )cosh(x) + (96a b + 72a b )cosh(x) +--R + +--R 5 4 2 3 3 4 2 3 +--R (64b + 112a b + 72a b )cosh(x) + (32a b + 24a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 7 2 3 3 2 5 +--R (32a b + 40a b )cosh(x) + (144a b + 120a b )cosh(x) +--R + +--R 4 2 3 3 2 3 2 3 3 2 +--R (64a b + 160a b + 120a b )cosh(x) + (48a b + 40a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 +--R (32a b + 32a b)cosh(x) + (96a b + 192a b + 96a b)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (128a b + 256a b + 224a b + 96a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (32a b + 64a b + 32a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 8 4 2 3 6 +--R (2a b + 3a b )cosh(x) + (16a b + 12a b )cosh(x) +--R + +--R 5 4 2 3 4 4 2 3 2 +--R (16b + 28a b + 18a b )cosh(x) + (16a b + 12a b )cosh(x) +--R + +--R 4 2 3 +--R 2a b + 3a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 8 2 3 3 2 6 +--R (4a b + 5a b )cosh(x) + (24a b + 20a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 2 +--R (16a b + 40a b + 30a b )cosh(x) + (24a b + 20a b )cosh(x) +--R + +--R 2 3 3 2 +--R 4a b + 5a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 8 2 3 3 2 4 6 +--R (4a b + 4a b)cosh(x) + (16a b + 32a b + 16a b)cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (32a b + 64a b + 56a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 4 2 3 2 4 +--R (16a b + 32a b + 16a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 2 3 4 2 3 3 2 2 3 2 4 +--R ((- 2a b - 3a b )sech(x) + (- 5a b - 7a b )sech(x) - 3a b - 4a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 3 4 +--R (- 16a b - 24a b )cosh(x)sech(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 40a b - 56a b )cosh(x)sech(x) + (- 24a b - 32a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 3 2 2 3 4 +--R ((- 56a b - 84a b )cosh(x) + 4a b )sech(x) +--R + +--R 2 3 3 2 2 4 2 3 3 2 2 +--R ((- 140a b - 196a b )cosh(x) - 8a b - 12a b + 4a b )sech(x) +--R + +--R 3 2 4 2 2 3 3 2 +--R (- 84a b - 112a b)cosh(x) - 8a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 3 3 2 3 4 +--R ((- 112a b - 168a b )cosh(x) + 24a b cosh(x))sech(x) +--R + +--R 2 3 3 2 3 +--R (- 280a b - 392a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 48a b - 72a b + 24a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 3 2 3 3 2 +--R (- 168a b - 224a b)cosh(x) + (- 48a b - 72a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 4 2 3 2 5 4 +--R (- 140a b - 210a b )cosh(x) + 60a b cosh(x) + 16b + 36a b +--R + +--R 2 3 +--R 14a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 4 +--R (- 350a b - 490a b )cosh(x) +--R + +--R 4 2 3 3 2 2 5 2 3 3 2 +--R (- 120a b - 180a b + 60a b )cosh(x) - 16b + 50a b + 22a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 4 2 3 3 2 2 4 +--R (- 210a b - 280a b)cosh(x) + (- 120a b - 180a b )cosh(x) - 16a b +--R + +--R 2 3 3 2 4 +--R - 16a b + 14a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 5 2 3 3 +--R (- 112a b - 168a b )cosh(x) + 80a b cosh(x) +--R + +--R 5 4 2 3 +--R (64b + 144a b + 56a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 5 +--R (- 280a b - 392a b )cosh(x) +--R + +--R 4 2 3 3 2 3 +--R (- 160a b - 240a b + 80a b )cosh(x) +--R + +--R 5 2 3 3 2 +--R (- 64b + 200a b + 88a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 5 2 3 3 2 3 +--R (- 168a b - 224a b)cosh(x) + (- 160a b - 240a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 64a b - 64a b + 56a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 6 2 3 4 +--R (- 56a b - 84a b )cosh(x) + 60a b cosh(x) +--R + +--R 5 4 2 3 2 2 3 +--R (96b + 216a b + 84a b )cosh(x) + 4a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 6 +--R (- 140a b - 196a b )cosh(x) +--R + +--R 4 2 3 3 2 4 +--R (- 120a b - 180a b + 60a b )cosh(x) +--R + +--R 5 2 3 3 2 2 4 2 3 3 2 +--R (- 96b + 300a b + 132a b )cosh(x) - 8a b - 12a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 6 2 3 3 2 4 +--R (- 84a b - 112a b)cosh(x) + (- 120a b - 180a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 2 3 3 2 +--R (- 96a b - 96a b + 84a b + 48a b)cosh(x) - 8a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 7 2 3 5 +--R (- 16a b - 24a b )cosh(x) + 24a b cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (64b + 144a b + 56a b )cosh(x) + 8a b cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 7 +--R (- 40a b - 56a b )cosh(x) +--R + +--R 4 2 3 3 2 5 +--R (- 48a b - 72a b + 24a b )cosh(x) +--R + +--R 5 2 3 3 2 3 +--R (- 64b + 200a b + 88a b )cosh(x) +--R + +--R 4 2 3 3 2 +--R (- 16a b - 24a b + 8a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 7 2 3 3 2 5 +--R (- 24a b - 32a b)cosh(x) + (- 48a b - 72a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 64a b - 64a b + 56a b + 32a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 16a b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 3 8 2 3 6 +--R (- 2a b - 3a b )cosh(x) + 4a b cosh(x) +--R + +--R 5 4 2 3 4 2 3 2 4 2 3 +--R (16b + 36a b + 14a b )cosh(x) + 4a b cosh(x) - 2a b - 3a b +--R * +--R 4 +--R sech(x) +--R + +--R 2 3 3 2 8 4 2 3 3 2 6 +--R (- 5a b - 7a b )cosh(x) + (- 8a b - 12a b + 4a b )cosh(x) +--R + +--R 5 2 3 3 2 4 +--R (- 16b + 50a b + 22a b )cosh(x) +--R + +--R 4 2 3 3 2 2 2 3 3 2 +--R (- 8a b - 12a b + 4a b )cosh(x) - 5a b - 7a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 2 4 8 2 3 3 2 6 +--R (- 3a b - 4a b)cosh(x) + (- 8a b - 12a b )cosh(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 2 +--R (- 16a b - 16a b + 14a b + 8a b)cosh(x) + (- 8a b - 12a b )cosh(x) +--R + +--R 3 2 4 +--R - 3a b - 4a b +--R / +--R 3 4 4 3 4 4 3 5 2 2 5 2 6 +--R ((2a b + 2a b )sech(x) + (4a b + 4a b )sech(x) + 2a b + 2a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 4 3 4 +--R (16a b + 16a b )cosh(x)sech(x) +--R + +--R 4 3 5 2 2 5 2 6 +--R (32a b + 32a b )cosh(x)sech(x) + (16a b + 16a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 2 2 5 3 4 4 3 4 +--R ((56a b + 56a b )cosh(x) + 16a b + 24a b + 8a b )sech(x) +--R + +--R 4 3 5 2 2 3 4 4 3 5 2 2 +--R ((112a b + 112a b )cosh(x) + 32a b + 48a b + 16a b )sech(x) +--R + +--R 5 2 6 2 4 3 5 2 6 +--R (56a b + 56a b)cosh(x) + 16a b + 24a b + 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 4 3 3 +--R (112a b + 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 +--R (96a b + 144a b + 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 3 +--R (224a b + 224a b )cosh(x) +--R + +--R 3 4 4 3 5 2 +--R (192a b + 288a b + 96a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 3 4 3 5 2 6 +--R (112a b + 112a b)cosh(x) + (96a b + 144a b + 48a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 4 3 4 +--R (140a b + 140a b )cosh(x) +--R + +--R 2 5 3 4 4 3 2 6 2 5 +--R (240a b + 360a b + 120a b )cosh(x) + 32a b + 64a b +--R + +--R 3 4 4 3 +--R 44a b + 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 4 +--R (280a b + 280a b )cosh(x) +--R + +--R 3 4 4 3 5 2 2 2 5 3 4 +--R (480a b + 720a b + 240a b )cosh(x) + 64a b + 128a b +--R + +--R 4 3 5 2 +--R 88a b + 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 4 4 3 5 2 6 2 +--R (140a b + 140a b)cosh(x) + (240a b + 360a b + 120a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R 32a b + 64a b + 44a b + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 +--R (112a b + 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 3 +--R (320a b + 480a b + 160a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 +--R (128a b + 256a b + 176a b + 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 5 +--R (224a b + 224a b )cosh(x) +--R + +--R 3 4 4 3 5 2 3 +--R (640a b + 960a b + 320a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (256a b + 512a b + 352a b + 96a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 5 4 3 5 2 6 3 +--R (112a b + 112a b)cosh(x) + (320a b + 480a b + 160a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (128a b + 256a b + 176a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 6 +--R (56a b + 56a b )cosh(x) +--R + +--R 2 5 3 4 4 3 4 +--R (240a b + 360a b + 120a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 2 2 5 +--R (192a b + 384a b + 264a b + 72a b )cosh(x) + 16a b +--R + +--R 3 4 4 3 +--R 24a b + 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 +--R (112a b + 112a b )cosh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (480a b + 720a b + 240a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 3 4 +--R (384a b + 768a b + 528a b + 144a b )cosh(x) + 32a b +--R + +--R 4 3 5 2 +--R 48a b + 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 6 4 3 5 2 6 4 +--R (56a b + 56a b)cosh(x) + (240a b + 360a b + 120a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 4 3 5 2 +--R (192a b + 384a b + 264a b + 72a b)cosh(x) + 16a b + 24a b +--R + +--R 6 +--R 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 7 +--R (16a b + 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 +--R (96a b + 144a b + 48a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (128a b + 256a b + 176a b + 48a b )cosh(x) +--R + +--R 2 5 3 4 4 3 +--R (32a b + 48a b + 16a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 7 +--R (32a b + 32a b )cosh(x) +--R + +--R 3 4 4 3 5 2 5 +--R (192a b + 288a b + 96a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (256a b + 512a b + 352a b + 96a b )cosh(x) +--R + +--R 3 4 4 3 5 2 +--R (64a b + 96a b + 32a b )cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 4 3 5 2 6 5 +--R (16a b + 16a b)cosh(x) + (96a b + 144a b + 48a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 3 +--R (128a b + 256a b + 176a b + 48a b)cosh(x) +--R + +--R 4 3 5 2 6 +--R (32a b + 48a b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 8 2 5 3 4 4 3 6 +--R (2a b + 2a b )cosh(x) + (16a b + 24a b + 8a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (32a b + 64a b + 44a b + 12a b )cosh(x) +--R + +--R 2 5 3 4 4 3 2 3 4 4 3 +--R (16a b + 24a b + 8a b )cosh(x) + 2a b + 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 8 3 4 4 3 5 2 6 +--R (4a b + 4a b )cosh(x) + (32a b + 48a b + 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 4 +--R (64a b + 128a b + 88a b + 24a b )cosh(x) +--R + +--R 3 4 4 3 5 2 2 4 3 5 2 +--R (32a b + 48a b + 16a b )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 8 4 3 5 2 6 6 +--R (2a b + 2a b)cosh(x) + (16a b + 24a b + 8a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (32a b + 64a b + 44a b + 12a b)cosh(x) +--R + +--R 4 3 5 2 6 2 5 2 6 +--R (16a b + 24a b + 8a b)cosh(x) + 2a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 +--R (- 2a b - 4a b - 2a b )sech(x) + (- 4a b - 8a b - 4a b)sech(x) +--R + +--R 5 2 6 7 +--R - 2a b - 4a b - 2a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (- 16a b - 32a b - 16a b )cosh(x)sech(x) +--R + +--R 4 3 5 2 6 2 +--R (- 32a b - 64a b - 32a b)cosh(x)sech(x) +--R + +--R 5 2 6 7 +--R (- 16a b - 32a b - 16a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 2 2 5 3 4 4 3 +--R (- 56a b - 112a b - 56a b )cosh(x) - 16a b - 40a b - 32a b +--R + +--R 5 2 +--R - 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 2 3 4 4 3 5 2 +--R (- 112a b - 224a b - 112a b)cosh(x) - 32a b - 80a b - 64a b +--R + +--R 6 +--R - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 2 4 3 5 2 6 7 +--R (- 56a b - 112a b - 56a )cosh(x) - 16a b - 40a b - 32a b - 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 3 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- 96a b - 240a b - 192a b - 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 3 +--R (- 224a b - 448a b - 224a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 192a b - 480a b - 384a b - 96a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 3 +--R (- 112a b - 224a b - 112a )cosh(x) +--R + +--R 4 3 5 2 6 7 +--R (- 96a b - 240a b - 192a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 4 +--R (- 140a b - 280a b - 140a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 6 +--R (- 240a b - 600a b - 480a b - 120a b )cosh(x) - 32a b +--R + +--R 2 5 3 4 4 3 5 2 +--R - 96a b - 108a b - 56a b - 12a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 4 +--R (- 280a b - 560a b - 280a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 2 5 +--R (- 480a b - 1200a b - 960a b - 240a b)cosh(x) - 64a b +--R + +--R 3 4 4 3 5 2 6 +--R - 192a b - 216a b - 112a b - 24a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 4 +--R (- 140a b - 280a b - 140a )cosh(x) +--R + +--R 4 3 5 2 6 7 2 3 4 4 3 +--R (- 240a b - 600a b - 480a b - 120a )cosh(x) - 32a b - 96a b +--R + +--R 5 2 6 7 +--R - 108a b - 56a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 5 +--R (- 112a b - 224a b - 112a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (- 320a b - 800a b - 640a b - 160a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (- 128a b - 384a b - 432a b - 224a b - 48a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 5 +--R (- 224a b - 448a b - 224a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 3 +--R (- 640a b - 1600a b - 1280a b - 320a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 256a b - 768a b - 864a b - 448a b - 96a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 5 +--R (- 112a b - 224a b - 112a )cosh(x) +--R + +--R 4 3 5 2 6 7 3 +--R (- 320a b - 800a b - 640a b - 160a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (- 128a b - 384a b - 432a b - 224a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 56a b - 112a b - 56a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 4 +--R (- 240a b - 600a b - 480a b - 120a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 +--R (- 192a b - 576a b - 648a b - 336a b - 72a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 16a b - 40a b - 32a b - 8a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 6 +--R (- 112a b - 224a b - 112a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 480a b - 1200a b - 960a b - 240a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 +--R (- 384a b - 1152a b - 1296a b - 672a b - 144a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R - 32a b - 80a b - 64a b - 16a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 6 +--R (- 56a b - 112a b - 56a )cosh(x) +--R + +--R 4 3 5 2 6 7 4 +--R (- 240a b - 600a b - 480a b - 120a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 2 4 3 +--R (- 192a b - 576a b - 648a b - 336a b - 72a )cosh(x) - 16a b +--R + +--R 5 2 6 7 +--R - 40a b - 32a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 4 3 5 2 7 +--R (- 16a b - 32a b - 16a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 5 +--R (- 96a b - 240a b - 192a b - 48a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (- 128a b - 384a b - 432a b - 224a b - 48a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- 32a b - 80a b - 64a b - 16a b )cosh(x) +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 7 +--R (- 32a b - 64a b - 32a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 5 +--R (- 192a b - 480a b - 384a b - 96a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 256a b - 768a b - 864a b - 448a b - 96a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 +--R (- 64a b - 160a b - 128a b - 32a b)cosh(x) +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 7 +--R (- 16a b - 32a b - 16a )cosh(x) +--R + +--R 4 3 5 2 6 7 5 +--R (- 96a b - 240a b - 192a b - 48a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (- 128a b - 384a b - 432a b - 224a b - 48a )cosh(x) +--R + +--R 4 3 5 2 6 7 +--R (- 32a b - 80a b - 64a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 8 +--R (- 2a b - 4a b - 2a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 16a b - 40a b - 32a b - 8a b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (- 32a b - 96a b - 108a b - 56a b - 12a b )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 3 4 4 3 5 2 +--R (- 16a b - 40a b - 32a b - 8a b )cosh(x) - 2a b - 4a b - 2a b +--R * +--R 4 +--R sech(x) +--R + +--R 4 3 5 2 6 8 +--R (- 4a b - 8a b - 4a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 32a b - 80a b - 64a b - 16a b)cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 64a b - 192a b - 216a b - 112a b - 24a b)cosh(x) +--R + +--R 3 4 4 3 5 2 6 2 4 3 5 2 6 +--R (- 32a b - 80a b - 64a b - 16a b)cosh(x) - 4a b - 8a b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 2 6 7 8 +--R (- 2a b - 4a b - 2a )cosh(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 16a b - 40a b - 32a b - 8a )cosh(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- 32a b - 96a b - 108a b - 56a b - 12a )cosh(x) +--R + +--R 4 3 5 2 6 7 2 5 2 6 7 +--R (- 16a b - 40a b - 32a b - 8a )cosh(x) - 2a b - 4a b - 2a +--R Type: Expression(Integer) +--E 35 + +--S 36 of 526 +t0405:= (1+sech(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (36) \|sech(x) + 1 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 526 +r0405:= asin(1/2*2^(1/2)*tanh(x))+atanh(tanh(x)/(2-tanh(x)^2)^(1/2)) +--R +--R +--R +-+ +--R tanh(x) \|2 tanh(x) +--R (37) atanh(-----------------) + asin(-----------) +--R +--------------+ 2 +--R | 2 +--R \|- tanh(x) + 2 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 526 +a0405:= integrate(t0405,x) +--R +--R +--R (38) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R 4 +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R / +--R 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 526 +m0405:= a0405-r0405 +--R +--R +--R (39) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R tanh(x) +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R + +--R 4 +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R / +--R 2 +--R + +--R +-+ +--R \|2 tanh(x) +--R - 2asin(-----------) +--R 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 526 +d0405:= D(m0405,x) +--R +--R +--R (40) +--R 14 13 2 12 +--R - sinh(x) - 6cosh(x)sinh(x) + (- 11cosh(x) - 12)sinh(x) +--R + +--R 3 11 +--R (4cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (39cosh(x) - 24cosh(x) - 66)sinh(x) +--R + +--R 5 3 9 +--R (38cosh(x) + 144cosh(x) - 156cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 27cosh(x) + 204cosh(x) + 102cosh(x) - 140)sinh(x) +--R + +--R 7 5 3 7 +--R (- 72cosh(x) - 96cosh(x) + 432cosh(x) - 288cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 27cosh(x) - 336cosh(x) - 36cosh(x) - 16cosh(x) - 301) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 38cosh(x) - 96cosh(x) - 552cosh(x) + 288cosh(x) +--R + +--R - 430cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 39cosh(x) + 204cosh(x) - 36cosh(x) + 312cosh(x) +--R + +--R 2 +--R 285cosh(x) - 328 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 4cosh(x) + 144cosh(x) + 432cosh(x) + 288cosh(x) +--R + +--R 3 +--R 828cosh(x) - 48cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 11cosh(x) - 24cosh(x) + 102cosh(x) - 16cosh(x) +--R + +--R 4 2 +--R 285cosh(x) + 560cosh(x) - 48 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 6cosh(x) - 48cosh(x) - 156cosh(x) - 288cosh(x) +--R + +--R 5 3 +--R - 430cosh(x) - 48cosh(x) - 48cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - cosh(x) - 12cosh(x) - 66cosh(x) - 140cosh(x) +--R + +--R 6 4 2 +--R - 301cosh(x) - 328cosh(x) - 48cosh(x) +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R + +--R 14 13 2 12 +--R sinh(x) + 6cosh(x)sinh(x) + (11cosh(x) + 7)sinh(x) +--R + +--R 3 11 +--R (- 4cosh(x) + 28cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 39cosh(x) + 14cosh(x) + 30)sinh(x) +--R + +--R 5 3 9 +--R (- 38cosh(x) - 84cosh(x) + 84cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (27cosh(x) - 119cosh(x) + 6cosh(x) + 114)sinh(x) +--R + +--R 7 5 3 7 +--R (72cosh(x) + 56cosh(x) - 144cosh(x) + 240cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (27cosh(x) + 196cosh(x) - 36cosh(x) + 24cosh(x) + 205) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 38cosh(x) + 56cosh(x) + 120cosh(x) - 240cosh(x) +--R + +--R 270cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 39cosh(x) - 119cosh(x) - 36cosh(x) - 276cosh(x) +--R + +--R 2 +--R - 189cosh(x) + 163 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 4cosh(x) - 84cosh(x) - 144cosh(x) - 240cosh(x) +--R + +--R 3 +--R - 508cosh(x) + 52cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 11cosh(x) + 14cosh(x) + 6cosh(x) + 24cosh(x) +--R + +--R 4 2 +--R - 189cosh(x) - 222cosh(x) + 84 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 6cosh(x) + 28cosh(x) + 84cosh(x) + 240cosh(x) +--R + +--R 5 3 +--R 270cosh(x) + 52cosh(x) + 24cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R cosh(x) + 7cosh(x) + 30cosh(x) + 114cosh(x) + 205cosh(x) +--R + +--R 4 2 +--R 163cosh(x) + 84cosh(x) + 36 +--R * +--R 2 +--R tanh(x) +--R + +--R 14 13 2 12 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 22cosh(x) - 14)sinh(x) +--R + +--R 3 11 +--R (8cosh(x) - 56cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (78cosh(x) - 28cosh(x) - 60)sinh(x) +--R + +--R 5 3 9 +--R (76cosh(x) + 168cosh(x) - 168cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 54cosh(x) + 238cosh(x) - 12cosh(x) - 228)sinh(x) +--R + +--R 7 5 3 7 +--R (- 144cosh(x) - 112cosh(x) + 288cosh(x) - 480cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (- 54cosh(x) - 392cosh(x) + 72cosh(x) - 48cosh(x) - 410)sinh(x) +--R + +--R 9 7 5 3 +--R (76cosh(x) - 112cosh(x) - 240cosh(x) + 480cosh(x) - 540cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 78cosh(x) + 238cosh(x) + 72cosh(x) + 552cosh(x) +--R + +--R 2 +--R 378cosh(x) - 326 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 8cosh(x) + 168cosh(x) + 288cosh(x) + 480cosh(x) +--R + +--R 3 +--R 1016cosh(x) - 104cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 22cosh(x) - 28cosh(x) - 12cosh(x) - 48cosh(x) +--R + +--R 4 2 +--R 378cosh(x) + 444cosh(x) - 168 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 12cosh(x) - 56cosh(x) - 168cosh(x) - 480cosh(x) +--R + +--R 5 3 +--R - 540cosh(x) - 104cosh(x) - 48cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R - 2cosh(x) - 14cosh(x) - 60cosh(x) - 228cosh(x) - 410cosh(x) +--R + +--R 4 2 +--R - 326cosh(x) - 168cosh(x) - 72 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 12 11 2 10 +--R 8sinh(x) + 48cosh(x)sinh(x) + (112cosh(x) + 90)sinh(x) +--R + +--R 3 9 +--R (112cosh(x) + 420cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 8cosh(x) + 690cosh(x) + 412)sinh(x) +--R + +--R 5 3 7 +--R (- 160cosh(x) + 240cosh(x) + 1328cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 224cosh(x) - 780cosh(x) + 1072cosh(x) + 804)sinh(x) +--R + +--R 7 5 3 5 +--R (- 160cosh(x) - 1320cosh(x) - 1072cosh(x) + 1704cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 8cosh(x) - 780cosh(x) - 2456cosh(x) + 156cosh(x) + 616) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 112cosh(x) + 240cosh(x) - 1072cosh(x) - 1488cosh(x) +--R + +--R 1120cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 112cosh(x) + 690cosh(x) + 1072cosh(x) + 156cosh(x) +--R + +--R 2 +--R 1008cosh(x) + 450 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 48cosh(x) + 420cosh(x) + 1328cosh(x) + 1704cosh(x) +--R + +--R 3 +--R 1120cosh(x) + 756cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 8cosh(x) + 90cosh(x) + 412cosh(x) + 804cosh(x) + 616cosh(x) +--R + +--R 2 +--R 450cosh(x) + 180 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R + +--R 12 11 2 10 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 112cosh(x) - 68)sinh(x) +--R + +--R 3 9 +--R (- 112cosh(x) - 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (8cosh(x) - 532cosh(x) - 224)sinh(x) +--R + +--R 5 3 7 +--R (160cosh(x) - 192cosh(x) - 744cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (224cosh(x) + 600cosh(x) - 656cosh(x) - 432)sinh(x) +--R + +--R 7 5 3 5 +--R (160cosh(x) + 1024cosh(x) + 488cosh(x) - 920cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (8cosh(x) + 600cosh(x) + 1248cosh(x) - 496cosh(x) - 592)sinh(x) +--R + +--R 9 7 5 3 +--R - 112cosh(x) - 192cosh(x) + 488cosh(x) - 16cosh(x) +--R + +--R - 1064cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 112cosh(x) - 532cosh(x) - 656cosh(x) - 496cosh(x) +--R + +--R 2 +--R - 944cosh(x) - 396 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 48cosh(x) - 320cosh(x) - 744cosh(x) - 920cosh(x) +--R + +--R 3 +--R - 1064cosh(x) - 744cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 8cosh(x) - 68cosh(x) - 224cosh(x) - 432cosh(x) - 592cosh(x) +--R + +--R 2 +--R - 396cosh(x) - 72 +--R * +--R 2 +--R tanh(x) +--R + +--R 12 11 2 10 +--R 16sinh(x) + 96cosh(x)sinh(x) + (224cosh(x) + 136)sinh(x) +--R + +--R 3 9 +--R (224cosh(x) + 640cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 16cosh(x) + 1064cosh(x) + 448)sinh(x) +--R + +--R 5 3 7 +--R (- 320cosh(x) + 384cosh(x) + 1488cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 448cosh(x) - 1200cosh(x) + 1312cosh(x) + 864)sinh(x) +--R + +--R 7 5 3 5 +--R (- 320cosh(x) - 2048cosh(x) - 976cosh(x) + 1840cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (- 16cosh(x) - 1200cosh(x) - 2496cosh(x) + 992cosh(x) + 1184)sinh(x) +--R + +--R 9 7 5 3 +--R (224cosh(x) + 384cosh(x) - 976cosh(x) + 32cosh(x) + 2128cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 224cosh(x) + 1064cosh(x) + 1312cosh(x) + 992cosh(x) +--R + +--R 2 +--R 1888cosh(x) + 792 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 96cosh(x) + 640cosh(x) + 1488cosh(x) + 1840cosh(x) +--R + +--R 3 +--R 2128cosh(x) + 1488cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 16cosh(x) + 136cosh(x) + 448cosh(x) + 864cosh(x) + 1184cosh(x) +--R + +--R 2 +--R 792cosh(x) + 144 +--R / +--R 14 13 2 12 +--R sinh(x) + 6cosh(x)sinh(x) + (11cosh(x) + 7)sinh(x) +--R + +--R 3 11 +--R (- 4cosh(x) + 28cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 39cosh(x) + 14cosh(x) + 30)sinh(x) +--R + +--R 5 3 9 +--R (- 38cosh(x) - 84cosh(x) + 84cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (27cosh(x) - 119cosh(x) + 6cosh(x) + 114)sinh(x) +--R + +--R 7 5 3 7 +--R (72cosh(x) + 56cosh(x) - 144cosh(x) + 240cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (27cosh(x) + 196cosh(x) - 36cosh(x) + 24cosh(x) + 205)sinh(x) +--R + +--R 9 7 5 3 +--R - 38cosh(x) + 56cosh(x) + 120cosh(x) - 240cosh(x) +--R + +--R 270cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 39cosh(x) - 119cosh(x) - 36cosh(x) - 276cosh(x) +--R + +--R 2 +--R - 189cosh(x) + 163 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 4cosh(x) - 84cosh(x) - 144cosh(x) - 240cosh(x) +--R + +--R 3 +--R - 508cosh(x) + 52cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 11cosh(x) + 14cosh(x) + 6cosh(x) + 24cosh(x) - 189cosh(x) +--R + +--R 2 +--R - 222cosh(x) + 84 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R 6cosh(x) + 28cosh(x) + 84cosh(x) + 240cosh(x) + 270cosh(x) +--R + +--R 3 +--R 52cosh(x) + 24cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R cosh(x) + 7cosh(x) + 30cosh(x) + 114cosh(x) + 205cosh(x) +--R + +--R 4 2 +--R 163cosh(x) + 84cosh(x) + 36 +--R * +--R +-------------------------------------+ +--R +--------------+ | 2 2 +--R | 2 | 2sinh(x) + 2cosh(x) + 6 +--R \|- tanh(x) + 2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 12 11 2 10 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 112cosh(x) - 68)sinh(x) +--R + +--R 3 9 +--R (- 112cosh(x) - 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (8cosh(x) - 532cosh(x) - 224)sinh(x) +--R + +--R 5 3 7 +--R (160cosh(x) - 192cosh(x) - 744cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (224cosh(x) + 600cosh(x) - 656cosh(x) - 432)sinh(x) +--R + +--R 7 5 3 5 +--R (160cosh(x) + 1024cosh(x) + 488cosh(x) - 920cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (8cosh(x) + 600cosh(x) + 1248cosh(x) - 496cosh(x) - 592)sinh(x) +--R + +--R 9 7 5 3 +--R - 112cosh(x) - 192cosh(x) + 488cosh(x) - 16cosh(x) +--R + +--R - 1064cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 112cosh(x) - 532cosh(x) - 656cosh(x) - 496cosh(x) +--R + +--R 2 +--R - 944cosh(x) - 396 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 48cosh(x) - 320cosh(x) - 744cosh(x) - 920cosh(x) +--R + +--R 3 +--R - 1064cosh(x) - 744cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 8cosh(x) - 68cosh(x) - 224cosh(x) - 432cosh(x) - 592cosh(x) +--R + +--R 2 +--R - 396cosh(x) - 72 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 526 +t0406:= (1-sech(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (41) \|- sech(x) + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 526 +r0406:= coth(x)*log(cosh(x))*(tanh(x)^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R (42) coth(x)log(cosh(x))\|tanh(x) +--R Type: Expression(Integer) +--E 42 + +--S 43 of 526 +a0406:= integrate(t0406,x) +--R +--R +--R 2cosh(x) +--R (43) log(- -----------------) - x +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 526 +m0406:= a0406-r0406 +--R +--R +--R +--------+ +--R | 2 2cosh(x) +--R (44) - coth(x)log(cosh(x))\|tanh(x) + log(- -----------------) - x +--R sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 44 + +--S 45 of 526 +d0406:= D(m0406,x) +--R +--R +--R (45) +--R +--------+ +--R | 2 +--R sinh(x)\|tanh(x) +--R + +--R 3 2 2 +--R cosh(x)coth(x)tanh(x) + (cosh(x)coth(x) - cosh(x))tanh(x) +--R + +--R - cosh(x)coth(x)tanh(x) +--R * +--R log(cosh(x)) +--R + +--R 2 +--R - coth(x)sinh(x)tanh(x) +--R / +--R +--------+ +--R | 2 +--R cosh(x)\|tanh(x) +--R Type: Expression(Integer) +--E 45 + +--S 46 of 526 +t0407:= (-1+sech(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (46) \|sech(x) - 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 526 +r0407:= coth(x)*log(cosh(x))*(-tanh(x)^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (47) coth(x)log(cosh(x))\|- tanh(x) +--R Type: Expression(Integer) +--E 47 + +--S 48 of 526 +a0407:= integrate(t0407,x) +--R +--R +--R (48) 0 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 526 +m0407:= a0407-r0407 +--R +--R +--R +----------+ +--R | 2 +--R (49) - coth(x)log(cosh(x))\|- tanh(x) +--R Type: Expression(Integer) +--E 49 + +--S 50 of 526 +d0407:= D(m0407,x) +--R +--R +--R (50) +--R 3 2 2 +--R - cosh(x)coth(x)tanh(x) + (- cosh(x)coth(x) + cosh(x))tanh(x) +--R + +--R cosh(x)coth(x)tanh(x) +--R * +--R log(cosh(x)) +--R + +--R 2 +--R coth(x)sinh(x)tanh(x) +--R / +--R +----------+ +--R | 2 +--R cosh(x)\|- tanh(x) +--R Type: Expression(Integer) +--E 50 + +--S 51 of 526 +t0408:= (-1-sech(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (51) \|- sech(x) - 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 526 +r0408:= -atan(tanh(x)/(-2+tanh(x)^2)^(1/2))-_ + atanh(coth(x)*(-2+tanh(x)^2)^(1/2)) +--R +--R +--R +------------+ +--R | 2 tanh(x) +--R (52) - atanh(coth(x)\|tanh(x) - 2 ) - atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 526 +a0408:= integrate(t0408,x) +--R +--R +--R (53) +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 + 2)(%e ) - \|- 1 +--R - 2log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R +---+ \|- (%e ) - 6(%e ) - 1 - \|- 1 (%e ) - \|- 1 +--R - \|- 1 log(-------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 - 2)(%e ) - \|- 1 +--R 2log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ +--R \|- 1 +--R * +--R log +--R +----------------------+ +--R +---+ x 2 +---+ | x 4 x 2 x 4 +--R (- 2\|- 1 (%e ) - 2\|- 1 )\|- (%e ) - 6(%e ) - 1 + 2(%e ) +--R + +--R x 2 +--R - 8(%e ) - 2 +--R / +--R x 4 +--R (%e ) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 526 +m0408:= a0408-r0408 +--R +--R +--R (54) +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 + 2)(%e ) - \|- 1 +--R - 2log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R +---+ \|- (%e ) - 6(%e ) - 1 - \|- 1 (%e ) - \|- 1 +--R - \|- 1 log(-------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 - 2)(%e ) - \|- 1 +--R 2log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ +--R \|- 1 +--R * +--R log +--R +----------------------+ +--R +---+ x 2 +---+ | x 4 x 2 x 4 +--R (- 2\|- 1 (%e ) - 2\|- 1 )\|- (%e ) - 6(%e ) - 1 + 2(%e ) +--R + +--R x 2 +--R - 8(%e ) - 2 +--R / +--R x 4 +--R (%e ) +--R + +--R +------------+ +--R | 2 tanh(x) +--R 2atanh(coth(x)\|tanh(x) - 2 ) + 2atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 526 +d0408:= D(m0408,x) +--R +--R +--R (55) +--R +---+ 2 x 6 +---+ 2 x 4 +--R - 9\|- 1 coth(x) (%e ) - 21\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 2 +---+ 2 +--R - 9\|- 1 coth(x) (%e ) - \|- 1 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 6 +--R (18\|- 1 coth(x) + 9\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (42\|- 1 coth(x) + 21\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (18\|- 1 coth(x) + 9\|- 1 )(%e ) + 2\|- 1 coth(x) + \|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R 2 x 8 2 x 6 2 x 4 +--R - 7coth(x) (%e ) - 48coth(x) (%e ) - 44coth(x) (%e ) +--R + +--R 2 x 2 2 +--R - 12coth(x) (%e ) - coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 8 2 x 6 +--R (14coth(x) + 7)(%e ) + (96coth(x) + 48)(%e ) +--R + +--R 2 x 4 2 x 2 2 +--R (88coth(x) + 44)(%e ) + (24coth(x) + 12)(%e ) + 2coth(x) + 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R x 6 x 4 x 2 3 +--R (7coth(x)(%e ) + 13coth(x)(%e ) + 7coth(x)(%e ) + coth(x))tanh(x) +--R + +--R 2 x 6 2 x 4 +--R (14coth(x) - 7)(%e ) + (26coth(x) - 13)(%e ) +--R + +--R 2 x 2 2 +--R (14coth(x) - 7)(%e ) + 2coth(x) - 1 +--R * +--R 2 +--R tanh(x) +--R + +--R x 6 x 4 x 2 +--R (- 7coth(x)(%e ) - 13coth(x)(%e ) - 7coth(x)(%e ) - coth(x)) +--R * +--R tanh(x) +--R + +--R 2 x 6 2 x 4 +--R (- 28coth(x) + 7)(%e ) + (- 52coth(x) + 13)(%e ) +--R + +--R 2 x 2 2 +--R (- 28coth(x) + 7)(%e ) - 4coth(x) + 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +--R - 9\|- 1 coth(x)(%e ) - 30\|- 1 coth(x)(%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R - 30\|- 1 coth(x)(%e ) - 10\|- 1 coth(x)(%e ) - \|- 1 coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 8 +--R (- 18\|- 1 coth(x) + 9\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (- 60\|- 1 coth(x) + 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 60\|- 1 coth(x) + 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 20\|- 1 coth(x) + 10\|- 1 )(%e ) - 2\|- 1 coth(x) + \|- 1 +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +--R 9\|- 1 coth(x)(%e ) + 30\|- 1 coth(x)(%e ) + 30\|- 1 coth(x)(%e ) +--R + +--R +---+ x 2 +---+ +--R 10\|- 1 coth(x)(%e ) + \|- 1 coth(x) +--R * +--R tanh(x) +--R + +--R +---+ 2 +---+ x 8 +---+ 2 +---+ x 6 +--R (36\|- 1 coth(x) - 9\|- 1 )(%e ) + (120\|- 1 coth(x) - 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (120\|- 1 coth(x) - 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (40\|- 1 coth(x) - 10\|- 1 )(%e ) + 4\|- 1 coth(x) - \|- 1 +--R / +--R 2 x 6 2 x 4 2 x 2 2 +--R (7coth(x) (%e ) + 13coth(x) (%e ) + 7coth(x) (%e ) + coth(x) ) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 6 2 x 4 +--R (- 14coth(x) - 7)(%e ) + (- 26coth(x) - 13)(%e ) +--R + +--R 2 x 2 2 +--R (- 14coth(x) - 7)(%e ) - 2coth(x) - 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ 2 x 8 +---+ 2 x 6 +--R - 9\|- 1 coth(x) (%e ) - 30\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 4 +---+ 2 x 2 +---+ 2 +--R - 30\|- 1 coth(x) (%e ) - 10\|- 1 coth(x) (%e ) - \|- 1 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 8 +--R (18\|- 1 coth(x) + 9\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (60\|- 1 coth(x) + 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (60\|- 1 coth(x) + 30\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (20\|- 1 coth(x) + 10\|- 1 )(%e ) + 2\|- 1 coth(x) + \|- 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 526 +t0409:= (a+b*sech(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (56) \|b sech(x) + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 526 +r0409:= -b^(1/2)*atan(coth(x)*(a+b*sech(x)^2)^(1/2)/b^(1/2))+_ + a^(1/2)*atanh(a^(1/2)*tanh(x)/(a+b*sech(x)^2)^(1/2)) +--R +--R +--R +--------------+ +--R +-+ | 2 +--R +-+ tanh(x)\|a +-+ coth(x)\|b sech(x) + a +--R (57) \|a atanh(-----------------) - \|b atan(------------------------) +--R +--------------+ +-+ +--R | 2 \|b +--R \|b sech(x) + a +--R Type: Expression(Integer) +--E 57 + +--S 58 of 526 +a0409:= integrate(t0409,x) +--R +--R +--R (58) +--R [ +--R - +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +---+ +-+ +--R 2\|- b \|a +--R * +--R log +--R 4 3 +--R (2b + 2a)sinh(x) + (8b + 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((12b + 12a)cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R ((8b + 8a)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (2b + 2a)cosh(x) + 2a cosh(x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (4a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) - 2b - 4a b - 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (- 8b - 16a b - 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 24a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (- 8b - 16a b - 12a )cosh(x) +--R + +--R 2 +--R (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (- 2b - 4a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 6 2 5 +--R (- 2a b - 2a )sinh(x) + (- 12a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a b - 30a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 +--R ((- 40a b - 40a )cosh(x) + (- 24a b - 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 +--R (- 30a b - 30a )cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 2a b - 2a )cosh(x) + (- 6a b - 4a )cosh(x) +--R + +--R 2 2 +--R - 2a cosh(x) +--R * +--R +---+ +--R \|- b +--R / +--R 2 4 2 3 +--R (2a b + a )sinh(x) + (8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b + 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b + 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b + a )cosh(x) + (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 30b - 30a b - 15a )cosh(x) - 2b - 6a b - 3a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 +--R (- 40b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 24a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 36a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 8b - 24a b - 12a )cosh(x) + (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b - 2a b - a )cosh(x) + (- 2b - 6a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R / +--R +-+ +--R 2\|a +--R , +--R +--R - +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R - +--R +-+ +-+ +--R 4\|a \|b +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|a \|b +--R / +--R +-+ +--R 2\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 58 + +--S 59 of 526 +m0409a:= a0409.1-r0409 +--R +--R +--R (59) +--R - +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +---+ +-+ +--R 2\|- b \|a +--R * +--R log +--R 4 3 +--R (2b + 2a)sinh(x) + (8b + 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((12b + 12a)cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R ((8b + 8a)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (2b + 2a)cosh(x) + 2a cosh(x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (4a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) - 2b - 4a b - 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (- 8b - 16a b - 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b - 15a )cosh(x) + (- 12b - 24a b - 18a )cosh(x) +--R + +--R 2 +--R - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (- 8b - 16a b - 12a )cosh(x) +--R + +--R 2 +--R (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (- 2b - 4a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 6 2 5 +--R (- 2a b - 2a )sinh(x) + (- 12a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a b - 30a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 3 +--R ((- 40a b - 40a )cosh(x) + (- 24a b - 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R (- 30a b - 30a )cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (- 2a b - 2a )cosh(x) + (- 6a b - 4a )cosh(x) - 2a cosh(x) +--R * +--R +---+ +--R \|- b +--R / +--R 2 4 2 3 +--R (2a b + a )sinh(x) + (8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b + 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b + 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b + a )cosh(x) + (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 30b - 30a b - 15a )cosh(x) - 2b - 6a b - 3a )sinh(x) +--R + +--R 2 2 3 +--R (- 40b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 24a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 36a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 8b - 24a b - 12a )cosh(x) + (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b - 2a b - a )cosh(x) + (- 2b - 6a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +--------------+ +--R +-+ | 2 +--R tanh(x)\|a +-+ +-+ coth(x)\|b sech(x) + a +--R - 2a atanh(-----------------) + 2\|a \|b atan(------------------------) +--R +--------------+ +-+ +--R | 2 \|b +--R \|b sech(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 59 + +--S 60 of 526 +--d0409a:= D(m0409a,x) +--E 60 + +--S 61 of 526 +m0409b:= a0409.2-r0409 +--R +--R +--R (60) +--R - +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +--------------+ +--R +-+ | 2 +--R tanh(x)\|a +-+ +-+ coth(x)\|b sech(x) + a +--R - 2a atanh(-----------------) + 2\|a \|b atan(------------------------) +--R +--------------+ +-+ +--R | 2 \|b +--R \|b sech(x) + a +--R + +--R - +--R +-+ +-+ +--R 4\|a \|b +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|a \|b +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 526 +--d0409b:= D(m0409b,x) +--E 62 + +--S 63 of 526 +t0410:= 1/(1+sech(x)^2)^(1/2) +--R +--R +--R 1 +--R (61) --------------- +--R +------------+ +--R | 2 +--R \|sech(x) + 1 +--R Type: Expression(Integer) +--E 63 + +--S 64 of 526 +r0410:= atanh(tanh(x)/(2-tanh(x)^2)^(1/2)) +--R +--R +--R tanh(x) +--R (62) atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 526 +a0410:= integrate(t0410,x) +--R +--R +--R (63) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 65 + +--S 66 of 526 +m0410:= a0410-r0410 +--R +--R +--R (64) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R tanh(x) +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 526 +d0410:= D(m0410,x) +--R +--R +--R (65) +--R 8 7 6 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 9sinh(x) +--R + +--R 3 5 +--R (4cosh(x) - 10cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (4cosh(x) + 9cosh(x) - 10)sinh(x) +--R + +--R 5 3 3 +--R (4cosh(x) + 20cosh(x) )sinh(x) +--R + +--R 4 2 2 +--R (9cosh(x) + 20cosh(x) - 3)sinh(x) +--R + +--R 7 5 8 +--R (- 4cosh(x) - 10cosh(x) + 6cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R - 9cosh(x) - 10cosh(x) - 3cosh(x) +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R + +--R 8 7 6 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 12sinh(x) +--R + +--R 3 5 +--R (4cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (4cosh(x) + 12cosh(x) - 18)sinh(x) +--R + +--R 5 3 3 4 2 2 +--R (4cosh(x) + 24cosh(x) )sinh(x) + (12cosh(x) + 36cosh(x) )sinh(x) +--R + +--R 7 5 8 6 4 +--R (- 4cosh(x) - 12cosh(x) )sinh(x) - 2cosh(x) - 12cosh(x) - 18cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 10 9 2 8 +--R sinh(x) + 4cosh(x)sinh(x) + (5cosh(x) + 5)sinh(x) +--R + +--R 7 4 2 6 +--R 16cosh(x)sinh(x) + (- 6cosh(x) + 12cosh(x) + 13)sinh(x) +--R + +--R 5 3 5 +--R (- 8cosh(x) - 16cosh(x) + 16cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 6cosh(x) - 34cosh(x) - 5cosh(x) + 27)sinh(x) +--R + +--R 5 3 3 +--R (- 16cosh(x) - 16cosh(x) + 24cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (5cosh(x) + 12cosh(x) - 5cosh(x) - 6cosh(x) + 18)sinh(x) +--R + +--R 9 7 5 3 +--R (4cosh(x) + 16cosh(x) + 16cosh(x) + 24cosh(x) + 36cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) + 5cosh(x) + 13cosh(x) + 27cosh(x) + 18cosh(x) +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R + +--R 10 9 2 8 +--R sinh(x) + 4cosh(x)sinh(x) + (5cosh(x) + 8)sinh(x) +--R + +--R 7 4 2 6 +--R 22cosh(x)sinh(x) + (- 6cosh(x) + 12cosh(x) + 20)sinh(x) +--R + +--R 5 3 5 +--R (- 8cosh(x) - 22cosh(x) + 34cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 6cosh(x) - 40cosh(x) - 12cosh(x) + 22)sinh(x) +--R + +--R 5 3 3 +--R (- 22cosh(x) - 52cosh(x) + 26cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (5cosh(x) + 12cosh(x) - 12cosh(x) + 8cosh(x) + 27)sinh(x) +--R + +--R 9 7 5 3 +--R (4cosh(x) + 22cosh(x) + 34cosh(x) + 26cosh(x) + 42cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) + 8cosh(x) + 20cosh(x) + 22cosh(x) + 27cosh(x) + 18 +--R / +--R 8 7 6 +--R 2sinh(x) + 4cosh(x)sinh(x) + 12sinh(x) +--R + +--R 3 5 +--R (- 4cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 4cosh(x) - 12cosh(x) + 18)sinh(x) +--R + +--R 5 3 3 +--R (- 4cosh(x) - 24cosh(x) )sinh(x) +--R + +--R 4 2 2 7 5 +--R (- 12cosh(x) - 36cosh(x) )sinh(x) + (4cosh(x) + 12cosh(x) )sinh(x) +--R + +--R 8 6 4 +--R 2cosh(x) + 12cosh(x) + 18cosh(x) +--R * +--R +-------------------------------------+ +--R +--------------+ | 2 2 +--R | 2 | 2sinh(x) + 2cosh(x) + 6 +--R \|- tanh(x) + 2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 10 9 2 8 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 5cosh(x) - 8)sinh(x) +--R + +--R 7 4 2 6 +--R - 22cosh(x)sinh(x) + (6cosh(x) - 12cosh(x) - 20)sinh(x) +--R + +--R 5 3 5 +--R (8cosh(x) + 22cosh(x) - 34cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (6cosh(x) + 40cosh(x) + 12cosh(x) - 22)sinh(x) +--R + +--R 5 3 3 +--R (22cosh(x) + 52cosh(x) - 26cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 5cosh(x) - 12cosh(x) + 12cosh(x) - 8cosh(x) - 27)sinh(x) +--R + +--R 9 7 5 3 +--R (- 4cosh(x) - 22cosh(x) - 34cosh(x) - 26cosh(x) - 42cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - cosh(x) - 8cosh(x) - 20cosh(x) - 22cosh(x) - 27cosh(x) - 18 +--R * +--R +--------------+ +--R | 2 +--R \|- tanh(x) + 2 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 526 +t0411:= 1/(1-sech(x)^2)^(1/2) +--R +--R +--R 1 +--R (66) ----------------- +--R +--------------+ +--R | 2 +--R \|- sech(x) + 1 +--R Type: Expression(Integer) +--E 68 + +--S 69 of 526 +r0411:= log(sinh(x))*tanh(x)/(tanh(x)^2)^(1/2) +--R +--R +--R tanh(x)log(sinh(x)) +--R (67) ------------------- +--R +--------+ +--R | 2 +--R \|tanh(x) +--R Type: Expression(Integer) +--E 69 + +--S 70 of 526 +a0411:= integrate(t0411,x) +--R +--R +--R 2sinh(x) +--R (68) log(- -----------------) - x +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 70 + +--S 71 of 526 +m0411:= a0411-r0411 +--R +--R +--R +--------+ +--R 2sinh(x) | 2 +--R (log(- -----------------) - x)\|tanh(x) - tanh(x)log(sinh(x)) +--R sinh(x) - cosh(x) +--R (69) --------------------------------------------------------------- +--R +--------+ +--R | 2 +--R \|tanh(x) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 526 +d0411:= D(m0411,x) +--R +--R +--R +--------+ +--R | 2 +--R cosh(x)\|tanh(x) - cosh(x)tanh(x) +--R (70) ----------------------------------- +--R +--------+ +--R | 2 +--R sinh(x)\|tanh(x) +--R Type: Expression(Integer) +--E 72 + +--S 73 of 526 +t0412:= 1/(-1+sech(x)^2)^(1/2) +--R +--R +--R 1 +--R (71) --------------- +--R +------------+ +--R | 2 +--R \|sech(x) - 1 +--R Type: Expression(Integer) +--E 73 + +--S 74 of 526 +r0412:= log(sinh(x))*tanh(x)/(-tanh(x)^2)^(1/2) +--R +--R +--R tanh(x)log(sinh(x)) +--R (72) ------------------- +--R +----------+ +--R | 2 +--R \|- tanh(x) +--R Type: Expression(Integer) +--E 74 + +--S 75 of 526 +a0412:= integrate(t0412,x) +--R +--R +--R (73) 0 +--R Type: Union(Expression(Integer),...) +--E 75 + +--S 76 of 526 +m0412:= a0412-r0412 +--R +--R +--R tanh(x)log(sinh(x)) +--R (74) - ------------------- +--R +----------+ +--R | 2 +--R \|- tanh(x) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 526 +d0412:= D(m0412,x) +--R +--R +--R cosh(x)tanh(x) +--R (75) - -------------------- +--R +----------+ +--R | 2 +--R sinh(x)\|- tanh(x) +--R Type: Expression(Integer) +--E 77 + +--S 78 of 526 +t0413:= 1/(-1-sech(x)^2)^(1/2) +--R +--R +--R 1 +--R (76) ----------------- +--R +--------------+ +--R | 2 +--R \|- sech(x) - 1 +--R Type: Expression(Integer) +--E 78 + +--S 79 of 526 +r0413:= atan(tanh(x)/(-2+tanh(x)^2)^(1/2)) +--R +--R +--R tanh(x) +--R (77) atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 526 +a0413:= integrate(t0413,x) +--R +--R +--R (78) +--R +----------------------+ +--R +---+ | x 4 x 2 x 2 +--R +---+ \|- 1 \|- (%e ) - 6(%e ) - 1 + (%e ) + 1 +--R \|- 1 log(--------------------------------------------) +--R +---+ x 2 +--R \|- 1 (%e ) +--R + +--R - +--R +---+ +--R \|- 1 +--R * +--R log +--R +----------------------+ +--R x 2 | x 4 x 2 +---+ x 4 +--R (2(%e ) + 2)\|- (%e ) - 6(%e ) - 1 + 2\|- 1 (%e ) +--R + +--R +---+ x 2 +---+ +--R - 8\|- 1 (%e ) - 2\|- 1 +--R / +--R +---+ x 4 +--R \|- 1 (%e ) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 80 + +--S 81 of 526 +m0413:= a0413-r0413 +--R +--R +--R (79) +--R +----------------------+ +--R +---+ | x 4 x 2 x 2 +--R +---+ \|- 1 \|- (%e ) - 6(%e ) - 1 + (%e ) + 1 +--R \|- 1 log(--------------------------------------------) +--R +---+ x 2 +--R \|- 1 (%e ) +--R + +--R - +--R +---+ +--R \|- 1 +--R * +--R log +--R +----------------------+ +--R x 2 | x 4 x 2 +---+ x 4 +--R (2(%e ) + 2)\|- (%e ) - 6(%e ) - 1 + 2\|- 1 (%e ) +--R + +--R +---+ x 2 +---+ +--R - 8\|- 1 (%e ) - 2\|- 1 +--R / +--R +---+ x 4 +--R \|- 1 (%e ) +--R + +--R tanh(x) +--R - 2atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 526 +d0413:= D(m0413,x) +--R +--R +--R (80) +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (5\|- 1 (%e ) + 11\|- 1 (%e ) + 7\|- 1 (%e ) + \|- 1 ) +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R 3(%e ) + 22(%e ) + 28(%e ) + 10(%e ) + 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (- 3(%e ) - 19(%e ) - 9(%e ) - 1)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R 5\|- 1 (%e ) + 36\|- 1 (%e ) + 42\|- 1 (%e ) + 12\|- 1 (%e ) + \|- 1 +--R / +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (3(%e ) + 19(%e ) + 9(%e ) + 1)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 5\|- 1 (%e ) - 36\|- 1 (%e ) - 42\|- 1 (%e ) - 12\|- 1 (%e ) +--R + +--R +---+ +--R - \|- 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 526 +t0414:= 1/(a+b*sech(x)^2)^(1/2) +--R +--R +--R 1 +--R (81) ----------------- +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R Type: Expression(Integer) +--E 83 + +--S 84 of 526 +r0414:= atanh(a^(1/2)*tanh(x)/(a+b*sech(x)^2)^(1/2))/a^(1/2) +--R +--R +--R +-+ +--R tanh(x)\|a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R (82) ------------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 84 + +--S 85 of 526 +a0414:= integrate(t0414,x) +--R +--R +--R (83) +--R - +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) + 4cosh(x) sinh(x) +--R + +--R 4 +--R cosh(x) +--R / +--R +-+ +--R 2\|a +--R Type: Union(Expression(Integer),...) +--E 85 + +--S 86 of 526 +m0414:= a0414-r0414 +--R +--R +--R (84) +--R - +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - b sinh(x) - 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 6b cosh(x) + 3b + a)sinh(x) +--R + +--R 3 4 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) - b cosh(x) +--R + +--R 2 +--R (3b + a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) + 4cosh(x) sinh(x) +--R + +--R 4 +--R cosh(x) +--R + +--R +-+ +--R tanh(x)\|a +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 526 +d0414:= D(m0414,x) +--R +--R +--R (85) +--R 8 2 2 2 6 +--R - a b sinh(x) + (4a b cosh(x) - 2b - 2a b - 2a )sinh(x) +--R + +--R 2 5 +--R (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 4 2 2 2 2 +--R - 6a b cosh(x) + (2b + 2a b + 2a )cosh(x) - 2b - 5a b +--R + +--R 2 +--R - 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 3 +--R ((8b + 8a b)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 6 2 2 4 +--R 4a b cosh(x) + (2b + 2a b + 2a )cosh(x) +--R + +--R 2 2 2 +--R (4b + 10a b)cosh(x) - 4a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 +--R ((- 4b - 4a b)cosh(x) + 4a cosh(x) + (8a b + 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 2 2 6 +--R - a b cosh(x) + (- 2b - 2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 2 +--R (- 2b - 5a b - 4a )cosh(x) + (- 4a b - 2a )cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 3 8 2 3 7 +--R (4a b + a )sinh(x) + (8a b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 3 6 +--R (8a b + 6a b + 3a )sinh(x) +--R + +--R 2 3 3 2 2 3 5 +--R ((- 8a b - 2a )cosh(x) + (16a b + 12a b + 2a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 2 3 2 2 +--R (- 8a b - 2a )cosh(x) + (- 8a b - 6a b - 3a )cosh(x) + 4a b +--R + +--R 3 +--R 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 2 2 3 3 +--R (- 8a b - 2a )cosh(x) + (- 32a b - 24a b - 4a )cosh(x) +--R + +--R 3 +--R - 2a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 4 2 3 2 2 +--R (- 8a b - 6a b - 3a )cosh(x) + (- 8a b + 2a )cosh(x) + 10a b +--R + +--R 3 +--R 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 7 2 2 3 5 +--R (8a b + 2a )cosh(x) + (16a b + 12a b + 2a )cosh(x) +--R + +--R 3 3 2 3 +--R - 2a cosh(x) + (- 4a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 8 2 2 3 6 +--R (4a b + a )cosh(x) + (8a b + 6a b + 3a )cosh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 +--R (4a b + 5a )cosh(x) + (10a b + 5a )cosh(x) + 8a b + 8a b + 2a +--R * +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R 2 3 6 +--R (- 4a b - 2a )sinh(x) +--R + +--R 2 3 2 2 2 3 4 +--R ((4a b + 2a )cosh(x) - 8a b - 8a b - 4a )sinh(x) +--R + +--R 3 3 +--R 4a cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 2 2 3 +--R ((4a b + 2a )cosh(x) + (16a b + 16a b)cosh(x) - 4a b - 2a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 3 2 3 6 +--R (4a cosh(x) + (8a b + 4a )cosh(x))sinh(x) + (- 4a b - 2a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 +--R (- 8a b - 8a b - 4a )cosh(x) + (- 4a b - 2a )cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 10 2 9 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 8 +--R (- 5a b cosh(x) - 2a b + a b + a )sinh(x) +--R + +--R 2 3 7 +--R (- 8a b + 2a )cosh(x)sinh(x) +--R + +--R 2 4 2 2 2 2 2 3 +--R (6a b cosh(x) + (- 8a b - 4a b)cosh(x) + 4a b + 9a b + 3a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 3 +--R 8a b cosh(x) + (8a b - 2a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 12a b + 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 2 3 4 +--R 6a b cosh(x) + (20a b + 6a b - 2a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 4a b - a b - 3a )cosh(x) + 14a b + 11a b + 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 2 2 3 3 +--R (8a b - 2a )cosh(x) + (- 16a b - 8a b - 4a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 8a b - 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R - 5a b cosh(x) + (- 8a b - 4a b)cosh(x) +--R + +--R 2 2 3 4 2 2 3 2 +--R (- 4a b - a b - 3a )cosh(x) + (4a b - 6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R 8b + 8a b + 12a b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 3 7 +--R - 4a b cosh(x) + (- 8a b + 2a )cosh(x) +--R + +--R 2 2 3 5 2 2 3 3 +--R (8a b + 12a b + 2a )cosh(x) + (16a b + 8a b - 2a )cosh(x) +--R + +--R 3 2 3 +--R (16b + 16a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 2 3 8 +--R - a b cosh(x) + (- 2a b + a b + a )cosh(x) +--R + +--R 2 2 3 6 2 2 3 4 +--R (4a b + 9a b + 3a )cosh(x) + (14a b + 11a b + 5a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (8b + 8a b + 12a b + 5a )cosh(x) + 8a b + 8a b + 2a +--R * +--R +-+ +--R \|a +--R / +--R 2 3 6 +--R (4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 2 3 4 +--R ((- 4a b - 2a )cosh(x) + 8a b + 8a b + 4a )sinh(x) +--R + +--R 3 3 +--R - 4a cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 2 2 +--R (- 4a b - 2a )cosh(x) + (- 16a b - 16a b)cosh(x) + 4a b +--R + +--R 3 +--R 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 3 +--R (- 4a cosh(x) + (- 8a b - 4a )cosh(x))sinh(x) +--R + +--R 2 3 6 2 2 3 4 +--R (4a b + 2a )cosh(x) + (8a b + 8a b + 4a )cosh(x) +--R + +--R 2 3 2 +--R (4a b + 2a )cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 10 2 9 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 8 +--R (5a b cosh(x) + 2a b - a b - a )sinh(x) +--R + +--R 2 3 7 +--R (8a b - 2a )cosh(x)sinh(x) +--R + +--R 2 4 2 2 2 2 2 3 +--R (- 6a b cosh(x) + (8a b + 4a b)cosh(x) - 4a b - 9a b - 3a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 3 +--R - 8a b cosh(x) + (- 8a b + 2a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 12a b - 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 2 3 4 +--R - 6a b cosh(x) + (- 20a b - 6a b + 2a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (4a b + a b + 3a )cosh(x) - 14a b - 11a b - 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 2 2 3 3 +--R (- 8a b + 2a )cosh(x) + (16a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 +--R (- 16a b - 8a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R 5a b cosh(x) + (8a b + 4a b)cosh(x) +--R + +--R 2 2 3 4 2 2 3 2 +--R (4a b + a b + 3a )cosh(x) + (- 4a b + 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 +--R - 8b - 8a b - 12a b - 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 3 7 +--R 4a b cosh(x) + (8a b - 2a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 8a b - 12a b - 2a )cosh(x) +--R + +--R 2 2 3 3 3 2 3 +--R (- 16a b - 8a b + 2a )cosh(x) + (- 16b - 16a b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 2 3 8 +--R a b cosh(x) + (2a b - a b - a )cosh(x) +--R + +--R 2 2 3 6 2 2 3 4 +--R (- 4a b - 9a b - 3a )cosh(x) + (- 14a b - 11a b - 5a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 8b - 8a b - 12a b - 5a )cosh(x) - 8a b - 8a b - 2a +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 526 +t0415:= (1+sech(x)^2)^(3/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (86) (sech(x) + 1)\|sech(x) + 1 +--R Type: Expression(Integer) +--E 88 + +--S 89 of 526 +r0415:= 2*asin(1/2*2^(1/2)*tanh(x))+atanh(tanh(x)/(2-tanh(x)^2)^(1/2))+_ + 1/2*tanh(x)*(2-tanh(x)^2)^(1/2) +--R +--R +--R (87) +--R +--------------+ +-+ +--R tanh(x) | 2 \|2 tanh(x) +--R 2atanh(-----------------) + tanh(x)\|- tanh(x) + 2 + 4asin(-----------) +--R +--------------+ 2 +--R | 2 +--R \|- tanh(x) + 2 +--R ------------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 526 +a0415:= integrate(t0415,x) +--R +--R +--R (88) +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) + 5)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) + 20cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) + 30cosh(x) + 7)sinh(x) +--R + +--R 5 3 6 +--R (6cosh(x) + 20cosh(x) + 14cosh(x))sinh(x) + cosh(x) +--R + +--R 4 2 +--R 5cosh(x) + 7cosh(x) + 3 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - sinh(x) - 8cosh(x)sinh(x) + (- 28cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (- 56cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70cosh(x) - 120cosh(x) - 18)sinh(x) +--R + +--R 5 3 3 +--R (- 56cosh(x) - 160cosh(x) - 72cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28cosh(x) - 120cosh(x) - 108cosh(x) - 16)sinh(x) +--R + +--R 7 5 3 8 +--R (- 8cosh(x) - 48cosh(x) - 72cosh(x) - 32cosh(x))sinh(x) - cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) - 18cosh(x) - 16cosh(x) - 5 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R + +--R 6 5 2 4 +--R - sinh(x) - 6cosh(x)sinh(x) + (- 15cosh(x) - 5)sinh(x) +--R + +--R 3 3 +--R (- 20cosh(x) - 20cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 15cosh(x) - 30cosh(x) - 7)sinh(x) +--R + +--R 5 3 6 +--R (- 6cosh(x) - 20cosh(x) - 14cosh(x))sinh(x) - cosh(x) +--R + +--R 4 2 +--R - 5cosh(x) - 7cosh(x) - 3 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R sinh(x) + 8cosh(x)sinh(x) + (28cosh(x) + 8)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) + 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) + 120cosh(x) + 18)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) + 160cosh(x) + 72cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) + 120cosh(x) + 108cosh(x) + 16)sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) + 48cosh(x) + 72cosh(x) + 32cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R 8cosh(x) + 18cosh(x) + 16cosh(x) + 5 +--R * +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) + 40)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) + 160cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) + 240cosh(x) + 56)sinh(x) +--R + +--R 5 3 6 +--R (48cosh(x) + 160cosh(x) + 112cosh(x))sinh(x) + 8cosh(x) +--R + +--R 4 2 +--R 40cosh(x) + 56cosh(x) + 24 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 8sinh(x) - 64cosh(x)sinh(x) + (- 224cosh(x) - 64)sinh(x) +--R + +--R 3 5 +--R (- 448cosh(x) - 384cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 560cosh(x) - 960cosh(x) - 144)sinh(x) +--R + +--R 5 3 3 +--R (- 448cosh(x) - 1280cosh(x) - 576cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 224cosh(x) - 960cosh(x) - 864cosh(x) - 128)sinh(x) +--R + +--R 7 5 3 +--R (- 64cosh(x) - 384cosh(x) - 576cosh(x) - 256cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 8cosh(x) - 64cosh(x) - 144cosh(x) - 128cosh(x) - 40 +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) - 1 +--R / +--R 2 +--R + +--R 2 2 +--R (8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) + 8) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R - 8sinh(x) - 32cosh(x)sinh(x) + (- 48cosh(x) - 32)sinh(x) +--R + +--R 3 4 2 +--R (- 32cosh(x) - 64cosh(x))sinh(x) - 8cosh(x) - 32cosh(x) - 8 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 10)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) + 40cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) + 60cosh(x) + 14)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 40cosh(x) + 28cosh(x))sinh(x) + 2cosh(x) + 10cosh(x) +--R + +--R 2 +--R 14cosh(x) + 6 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 16)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) - 96cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 240cosh(x) - 36)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) - 320cosh(x) - 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) - 240cosh(x) - 216cosh(x) - 32)sinh(x) +--R + +--R 7 5 3 8 +--R (- 16cosh(x) - 96cosh(x) - 144cosh(x) - 64cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R - 16cosh(x) - 36cosh(x) - 32cosh(x) - 10 +--R Type: Union(Expression(Integer),...) +--E 90 + +--S 91 of 526 +--m0415:= a0415-r0415 +--E 91 + +--S 92 of 526 +--d0415:= D(m0415,x) +--E 92 + +--S 93 of 526 +t0416:= (1-sech(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (89) (- sech(x) + 1)\|- sech(x) + 1 +--R Type: Expression(Integer) +--E 93 + +--S 94 of 526 +r0416:= 1/2*coth(x)*(tanh(x)^2)^(1/2)*(2*log(cosh(x))-tanh(x)^2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (2coth(x)log(cosh(x)) - coth(x)tanh(x) )\|tanh(x) +--R (90) --------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 526 +a0416:= integrate(t0416,x) +--R +--R +--R (91) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R - x sinh(x) - 4x cosh(x)sinh(x) + (- 6x cosh(x) - 2x + 2)sinh(x) +--R + +--R 3 4 +--R (- 4x cosh(x) + (- 4x + 4)cosh(x))sinh(x) - x cosh(x) +--R + +--R 2 +--R (- 2x + 2)cosh(x) - x +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 95 + +--S 96 of 526 +m0416:= a0416-r0416 +--R +--R +--R (92) +--R 4 3 +--R - 2coth(x)sinh(x) - 8cosh(x)coth(x)sinh(x) +--R + +--R 2 2 +--R (- 12cosh(x) - 4)coth(x)sinh(x) +--R + +--R 3 +--R (- 8cosh(x) - 8cosh(x))coth(x)sinh(x) +--R + +--R 4 2 +--R (- 2cosh(x) - 4cosh(x) - 2)coth(x) +--R * +--R log(cosh(x)) +--R + +--R 4 3 +--R coth(x)sinh(x) + 4cosh(x)coth(x)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) + 2)coth(x)sinh(x) +--R + +--R 3 +--R (4cosh(x) + 4cosh(x))coth(x)sinh(x) +--R + +--R 4 2 +--R (cosh(x) + 2cosh(x) + 1)coth(x) +--R * +--R 2 +--R tanh(x) +--R * +--R +--------+ +--R | 2 +--R \|tanh(x) +--R + +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) + 8cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) + 2 +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R - 2x sinh(x) - 8x cosh(x)sinh(x) + (- 12x cosh(x) - 4x + 4)sinh(x) +--R + +--R 3 4 +--R (- 8x cosh(x) + (- 8x + 8)cosh(x))sinh(x) - 2x cosh(x) +--R + +--R 2 +--R (- 4x + 4)cosh(x) - 2x +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) + 8cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) + 2 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 526 +d0416:= D(m0416,x) +--R +--R +--R (93) +--R 7 6 2 5 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 6)sinh(x) +--R + +--R 3 4 +--R (40cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (30cosh(x) + 4cosh(x) + 6)sinh(x) +--R + +--R 5 3 2 +--R (12cosh(x) - 24cosh(x) + 20cosh(x))sinh(x) +--R + +--R 6 4 2 5 +--R (2cosh(x) - 26cosh(x) + 22cosh(x) + 2)sinh(x) - 8cosh(x) +--R + +--R 3 +--R 8cosh(x) +--R * +--R +--------+ +--R | 2 +--R \|tanh(x) +--R + +--R 6 2 5 +--R 2cosh(x)coth(x)sinh(x) + 12cosh(x) coth(x)sinh(x) +--R + +--R 3 4 +--R (30cosh(x) + 6cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (40cosh(x) + 24cosh(x) )coth(x)sinh(x) +--R + +--R 5 3 2 +--R (30cosh(x) + 36cosh(x) + 6cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (12cosh(x) + 24cosh(x) + 12cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (2cosh(x) + 6cosh(x) + 6cosh(x) + 2cosh(x))coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 2 6 +--R (2cosh(x)coth(x) - 2cosh(x))sinh(x) +--R + +--R 2 2 2 5 +--R (12cosh(x) coth(x) - 12cosh(x) )sinh(x) +--R + +--R 3 2 3 4 +--R ((30cosh(x) + 6cosh(x))coth(x) - 30cosh(x) - 6cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R ((40cosh(x) + 24cosh(x) )coth(x) - 40cosh(x) - 24cosh(x) ) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (30cosh(x) + 36cosh(x) + 6cosh(x))coth(x) - 30cosh(x) +--R + +--R 3 +--R - 36cosh(x) - 6cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (12cosh(x) + 24cosh(x) + 12cosh(x) )coth(x) - 12cosh(x) +--R + +--R 4 2 +--R - 24cosh(x) - 12cosh(x) +--R * +--R sinh(x) +--R + +--R 7 5 3 2 +--R (2cosh(x) + 6cosh(x) + 6cosh(x) + 2cosh(x))coth(x) +--R + +--R 7 5 3 +--R - 2cosh(x) - 6cosh(x) - 6cosh(x) - 2cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 6 2 5 +--R - 2cosh(x)coth(x)sinh(x) - 12cosh(x) coth(x)sinh(x) +--R + +--R 3 4 +--R (- 30cosh(x) - 6cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (- 40cosh(x) - 24cosh(x) )coth(x)sinh(x) +--R + +--R 5 3 2 +--R (- 30cosh(x) - 36cosh(x) - 6cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (- 12cosh(x) - 24cosh(x) - 12cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (- 2cosh(x) - 6cosh(x) - 6cosh(x) - 2cosh(x))coth(x) +--R * +--R tanh(x) +--R * +--R log(cosh(x)) +--R + +--R 6 2 5 +--R - 3cosh(x)coth(x)sinh(x) - 18cosh(x) coth(x)sinh(x) +--R + +--R 3 4 +--R (- 45cosh(x) - 9cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (- 60cosh(x) - 36cosh(x) )coth(x)sinh(x) +--R + +--R 5 3 2 +--R (- 45cosh(x) - 54cosh(x) - 9cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (- 18cosh(x) - 36cosh(x) - 18cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (- 3cosh(x) - 9cosh(x) - 9cosh(x) - 3cosh(x))coth(x) +--R * +--R 5 +--R tanh(x) +--R + +--R 2 6 +--R (- cosh(x)coth(x) + cosh(x))sinh(x) +--R + +--R 2 2 2 5 +--R (- 6cosh(x) coth(x) + 6cosh(x) )sinh(x) +--R + +--R 3 2 3 4 +--R ((- 15cosh(x) - 3cosh(x))coth(x) + 15cosh(x) + 3cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R ((- 20cosh(x) - 12cosh(x) )coth(x) + 20cosh(x) + 12cosh(x) ) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 15cosh(x) - 18cosh(x) - 3cosh(x))coth(x) + 15cosh(x) +--R + +--R 3 +--R 18cosh(x) + 3cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- 6cosh(x) - 12cosh(x) - 6cosh(x) )coth(x) + 6cosh(x) +--R + +--R 4 2 +--R 12cosh(x) + 6cosh(x) +--R * +--R sinh(x) +--R + +--R 7 5 3 2 7 +--R (- cosh(x) - 3cosh(x) - 3cosh(x) - cosh(x))coth(x) + cosh(x) +--R + +--R 5 3 +--R 3cosh(x) + 3cosh(x) + cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 6 2 5 +--R 3cosh(x)coth(x)sinh(x) + 18cosh(x) coth(x)sinh(x) +--R + +--R 3 4 +--R (45cosh(x) + 9cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (60cosh(x) + 36cosh(x) )coth(x)sinh(x) +--R + +--R 5 3 2 +--R (45cosh(x) + 54cosh(x) + 9cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (18cosh(x) + 36cosh(x) + 18cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (3cosh(x) + 9cosh(x) + 9cosh(x) + 3cosh(x))coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 7 6 +--R - 2coth(x)sinh(x) - 12cosh(x)coth(x)sinh(x) +--R + +--R 2 5 +--R (- 30cosh(x) - 6)coth(x)sinh(x) +--R + +--R 3 4 +--R (- 40cosh(x) - 24cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (- 30cosh(x) - 36cosh(x) - 6)coth(x)sinh(x) +--R + +--R 5 3 2 +--R (- 12cosh(x) - 24cosh(x) - 12cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (- 2cosh(x) - 6cosh(x) - 6cosh(x) - 2)coth(x)sinh(x) +--R * +--R 2 +--R tanh(x) +--R / +--R 6 2 5 3 4 +--R 2cosh(x)sinh(x) + 12cosh(x) sinh(x) + (30cosh(x) + 6cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (40cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 5 3 2 +--R (30cosh(x) + 36cosh(x) + 6cosh(x))sinh(x) +--R + +--R 6 4 2 7 5 +--R (12cosh(x) + 24cosh(x) + 12cosh(x) )sinh(x) + 2cosh(x) + 6cosh(x) +--R + +--R 3 +--R 6cosh(x) + 2cosh(x) +--R * +--R +--------+ +--R | 2 +--R \|tanh(x) +--R Type: Expression(Integer) +--E 97 + +--S 98 of 526 +t0417:= (-1+sech(x)^2)^(3/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (94) (sech(x) - 1)\|sech(x) - 1 +--R Type: Expression(Integer) +--E 98 + +--S 99 of 526 +r0417:= -1/2*coth(x)*(-tanh(x)^2)^(1/2)*(2*log(cosh(x))-tanh(x)^2) +--R +--R +--R +----------+ +--R 2 | 2 +--R (- 2coth(x)log(cosh(x)) + coth(x)tanh(x) )\|- tanh(x) +--R (95) ------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 526 +a0417:= integrate(t0417,x) +--R +--R +--R (96) 0 +--R Type: Union(Expression(Integer),...) +--E 100 + +--S 101 of 526 +m0417:= a0417-r0417 +--R +--R +--R +----------+ +--R 2 | 2 +--R (2coth(x)log(cosh(x)) - coth(x)tanh(x) )\|- tanh(x) +--R (97) ----------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 526 +d0417:= D(m0417,x) +--R +--R +--R (98) +--R 3 2 2 +--R 2cosh(x)coth(x)tanh(x) + (2cosh(x)coth(x) - 2cosh(x))tanh(x) +--R + +--R - 2cosh(x)coth(x)tanh(x) +--R * +--R log(cosh(x)) +--R + +--R 5 2 4 +--R - 3cosh(x)coth(x)tanh(x) + (- cosh(x)coth(x) + cosh(x))tanh(x) +--R + +--R 3 2 +--R 3cosh(x)coth(x)tanh(x) - 2coth(x)sinh(x)tanh(x) +--R / +--R +----------+ +--R | 2 +--R 2cosh(x)\|- tanh(x) +--R Type: Expression(Integer) +--E 102 + +--S 103 of 526 +t0418:= (-1-sech(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (99) (- sech(x) - 1)\|- sech(x) - 1 +--R Type: Expression(Integer) +--E 103 + +--S 104 of 526 +r0418:= atan(tanh(x)/(-2+tanh(x)^2)^(1/2))+_ + 2*atanh(coth(x)*(-2+tanh(x)^2)^(1/2))-_ + 1/2*tanh(x)*(-2+tanh(x)^2)^(1/2) +--R +--R +--R (100) +--R +------------+ +--R | 2 tanh(x) +--R 4atanh(coth(x)\|tanh(x) - 2 ) + 2atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R +------------+ +--R | 2 +--R - tanh(x)\|tanh(x) - 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 526 +a0418:= integrate(t0418,x) +--R +--R +--R (101) +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (12(%e ) + 28(%e ) + 20(%e ) + 4)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 20\|- 1 (%e ) - 64\|- 1 (%e ) - 72\|- 1 (%e ) - 32\|- 1 (%e ) +--R + +--R +---+ +--R - 4\|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 + 2)(%e ) - \|- 1 +--R log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (3\|- 1 (%e ) + 7\|- 1 (%e ) + 5\|- 1 (%e ) + \|- 1 ) +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R 5(%e ) + 16(%e ) + 18(%e ) + 8(%e ) + 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 - \|- 1 (%e ) - \|- 1 +--R log(-------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (- 12(%e ) - 28(%e ) - 20(%e ) - 4)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R 20\|- 1 (%e ) + 64\|- 1 (%e ) + 72\|- 1 (%e ) + 32\|- 1 (%e ) +--R + +--R +---+ +--R 4\|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 - 2)(%e ) - \|- 1 +--R log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (- 3\|- 1 (%e ) - 7\|- 1 (%e ) - 5\|- 1 (%e ) - \|- 1 ) +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R - 5(%e ) - 16(%e ) - 18(%e ) - 8(%e ) - 1 +--R * +--R log +--R +----------------------+ +--R +---+ x 2 +---+ | x 4 x 2 x 4 +--R (- 2\|- 1 (%e ) - 2\|- 1 )\|- (%e ) - 6(%e ) - 1 + 2(%e ) +--R + +--R x 2 +--R - 8(%e ) - 2 +--R / +--R x 4 +--R (%e ) +--R + +--R +----------------------+ +--R +---+ x 6 +---+ x 4 | x 4 x 2 x 8 +--R (8\|- 1 (%e ) + 8\|- 1 (%e ) )\|- (%e ) - 6(%e ) - 1 + 8(%e ) +--R + +--R x 6 x 4 +--R 32(%e ) + 8(%e ) +--R / +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (6(%e ) + 14(%e ) + 10(%e ) + 2)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 10\|- 1 (%e ) - 32\|- 1 (%e ) - 36\|- 1 (%e ) - 16\|- 1 (%e ) +--R + +--R +---+ +--R - 2\|- 1 +--R Type: Union(Expression(Integer),...) +--E 105 + +--S 106 of 526 +m0418:= a0418-r0418 +--R +--R +--R (102) +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (12(%e ) + 28(%e ) + 20(%e ) + 4)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 20\|- 1 (%e ) - 64\|- 1 (%e ) - 72\|- 1 (%e ) - 32\|- 1 (%e ) +--R + +--R +---+ +--R - 4\|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 + 2)(%e ) - \|- 1 +--R log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (3\|- 1 (%e ) + 7\|- 1 (%e ) + 5\|- 1 (%e ) + \|- 1 ) +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R 5(%e ) + 16(%e ) + 18(%e ) + 8(%e ) + 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 - \|- 1 (%e ) - \|- 1 +--R log(-------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (- 12(%e ) - 28(%e ) - 20(%e ) - 4)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R 20\|- 1 (%e ) + 64\|- 1 (%e ) + 72\|- 1 (%e ) + 32\|- 1 (%e ) +--R + +--R +---+ +--R 4\|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +---+ x 2 +---+ +--R \|- (%e ) - 6(%e ) - 1 + (- \|- 1 - 2)(%e ) - \|- 1 +--R log(---------------------------------------------------------) +--R x 2 +--R (%e ) +--R + +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (- 3\|- 1 (%e ) - 7\|- 1 (%e ) - 5\|- 1 (%e ) - \|- 1 ) +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R x 8 x 6 x 4 x 2 +--R - 5(%e ) - 16(%e ) - 18(%e ) - 8(%e ) - 1 +--R * +--R log +--R +----------------------+ +--R +---+ x 2 +---+ | x 4 x 2 x 4 +--R (- 2\|- 1 (%e ) - 2\|- 1 )\|- (%e ) - 6(%e ) - 1 + 2(%e ) +--R + +--R x 2 +--R - 8(%e ) - 2 +--R / +--R x 4 +--R (%e ) +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (- 12(%e ) - 28(%e ) - 20(%e ) - 4)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R 20\|- 1 (%e ) + 64\|- 1 (%e ) + 72\|- 1 (%e ) + 32\|- 1 (%e ) +--R + +--R +---+ +--R 4\|- 1 +--R * +--R +------------+ +--R | 2 +--R atanh(coth(x)\|tanh(x) - 2 ) +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (- 6(%e ) - 14(%e ) - 10(%e ) - 2)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R 10\|- 1 (%e ) + 32\|- 1 (%e ) + 36\|- 1 (%e ) + 16\|- 1 (%e ) +--R + +--R +---+ +--R 2\|- 1 +--R * +--R tanh(x) +--R atan(---------------) +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (3(%e ) + 7(%e ) + 5(%e ) + 1)tanh(x)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 5\|- 1 (%e ) - 16\|- 1 (%e ) - 18\|- 1 (%e ) - 8\|- 1 (%e ) +--R + +--R +---+ +--R - \|- 1 +--R * +--R tanh(x) +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R +----------------------+ +--R +---+ x 6 +---+ x 4 | x 4 x 2 x 8 +--R (8\|- 1 (%e ) + 8\|- 1 (%e ) )\|- (%e ) - 6(%e ) - 1 + 8(%e ) +--R + +--R x 6 x 4 +--R 32(%e ) + 8(%e ) +--R / +--R +----------------------+ +--R x 6 x 4 x 2 | x 4 x 2 +--R (6(%e ) + 14(%e ) + 10(%e ) + 2)\|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ x 8 +---+ x 6 +---+ x 4 +---+ x 2 +--R - 10\|- 1 (%e ) - 32\|- 1 (%e ) - 36\|- 1 (%e ) - 16\|- 1 (%e ) +--R + +--R +---+ +--R - 2\|- 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 526 +d0418:= D(m0418,x) +--R +--R +--R (103) +--R +---+ 2 x 18 +---+ 2 x 16 +--R 129\|- 1 coth(x) (%e ) + 1663\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 14 +---+ 2 x 12 +--R 7290\|- 1 coth(x) (%e ) + 13482\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 10 +---+ 2 x 8 +--R 12348\|- 1 coth(x) (%e ) + 6216\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 6 +---+ 2 x 4 +--R 1806\|- 1 coth(x) (%e ) + 302\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 2 +---+ 2 +--R 27\|- 1 coth(x) (%e ) + \|- 1 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 18 +--R (- 258\|- 1 coth(x) - 129\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (- 3326\|- 1 coth(x) - 1663\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (- 14580\|- 1 coth(x) - 7290\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (- 26964\|- 1 coth(x) - 13482\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (- 24696\|- 1 coth(x) - 12348\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (- 12432\|- 1 coth(x) - 6216\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (- 3612\|- 1 coth(x) - 1806\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 604\|- 1 coth(x) - 302\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 54\|- 1 coth(x) - 27\|- 1 )(%e ) - 2\|- 1 coth(x) - \|- 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R 2 x 20 2 x 18 2 x 16 +--R 127coth(x) (%e ) + 2046coth(x) (%e ) + 11789coth(x) (%e ) +--R + +--R 2 x 14 2 x 12 +--R 30168coth(x) (%e ) + 38118coth(x) (%e ) +--R + +--R 2 x 10 2 x 8 2 x 6 +--R 26388coth(x) (%e ) + 10706coth(x) (%e ) + 2616coth(x) (%e ) +--R + +--R 2 x 4 2 x 2 2 +--R 379coth(x) (%e ) + 30coth(x) (%e ) + coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 20 2 x 18 +--R (- 254coth(x) - 127)(%e ) + (- 4092coth(x) - 2046)(%e ) +--R + +--R 2 x 16 2 x 14 +--R (- 23578coth(x) - 11789)(%e ) + (- 60336coth(x) - 30168)(%e ) +--R + +--R 2 x 12 2 x 10 +--R (- 76236coth(x) - 38118)(%e ) + (- 52776coth(x) - 26388)(%e ) +--R + +--R 2 x 8 2 x 6 +--R (- 21412coth(x) - 10706)(%e ) + (- 5232coth(x) - 2616)(%e ) +--R + +--R 2 x 4 2 x 2 2 +--R (- 758coth(x) - 379)(%e ) + (- 60coth(x) - 30)(%e ) - 2coth(x) - 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R + +--R 2 x 18 2 x 16 2 x 14 +--R - 127coth(x) (%e ) - 903coth(x) (%e ) - 2646coth(x) (%e ) +--R + +--R 2 x 12 2 x 10 2 x 8 +--R - 4210coth(x) (%e ) - 4004coth(x) (%e ) - 2352coth(x) (%e ) +--R + +--R 2 x 6 2 x 4 2 x 2 +--R - 850coth(x) (%e ) - 182coth(x) (%e ) - 21coth(x) (%e ) +--R + +--R 2 +--R - coth(x) +--R * +--R 6 +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R (508coth(x) + 127)(%e ) + (3612coth(x) + 903)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (10584coth(x) + 2646)(%e ) + (16840coth(x) + 4210)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (16016coth(x) + 4004)(%e ) + (9408coth(x) + 2352)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (3400coth(x) + 850)(%e ) + (728coth(x) + 182)(%e ) +--R + +--R 2 x 2 2 +--R (84coth(x) + 21)(%e ) + 4coth(x) + 1 +--R * +--R 4 +--R tanh(x) +--R + +--R x 18 x 16 x 14 +--R - 254coth(x)(%e ) - 1806coth(x)(%e ) - 5292coth(x)(%e ) +--R + +--R x 12 x 10 x 8 +--R - 8420coth(x)(%e ) - 8008coth(x)(%e ) - 4704coth(x)(%e ) +--R + +--R x 6 x 4 x 2 +--R - 1700coth(x)(%e ) - 364coth(x)(%e ) - 42coth(x)(%e ) - 2coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R - 1016coth(x) (%e ) - 7224coth(x) (%e ) +--R + +--R 2 x 14 2 x 12 +--R - 21168coth(x) (%e ) - 33680coth(x) (%e ) +--R + +--R 2 x 10 2 x 8 2 x 6 +--R - 32032coth(x) (%e ) - 18816coth(x) (%e ) - 6800coth(x) (%e ) +--R + +--R 2 x 4 2 x 2 2 +--R - 1456coth(x) (%e ) - 168coth(x) (%e ) - 8coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R x 18 x 16 x 14 +--R 254coth(x)(%e ) + 1806coth(x)(%e ) + 5292coth(x)(%e ) +--R + +--R x 12 x 10 x 8 +--R 8420coth(x)(%e ) + 8008coth(x)(%e ) + 4704coth(x)(%e ) +--R + +--R x 6 x 4 x 2 +--R 1700coth(x)(%e ) + 364coth(x)(%e ) + 42coth(x)(%e ) + 2coth(x) +--R * +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R (1016coth(x) - 254)(%e ) + (7224coth(x) - 1806)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (21168coth(x) - 5292)(%e ) + (33680coth(x) - 8420)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (32032coth(x) - 8008)(%e ) + (18816coth(x) - 4704)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (6800coth(x) - 1700)(%e ) + (1456coth(x) - 364)(%e ) +--R + +--R 2 x 2 2 +--R (168coth(x) - 42)(%e ) + 8coth(x) - 2 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ 2 x 20 +---+ 2 x 18 +--R 129\|- 1 coth(x) (%e ) + 1276\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 16 +---+ 2 x 14 +--R 4881\|- 1 coth(x) (%e ) + 9908\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 12 +---+ 2 x 10 +--R 11998\|- 1 coth(x) (%e ) + 9100\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 8 +---+ 2 x 6 +--R 4382\|- 1 coth(x) (%e ) + 1324\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 4 +---+ 2 x 2 +---+ 2 +--R 241\|- 1 coth(x) (%e ) + 24\|- 1 coth(x) (%e ) + \|- 1 coth(x) +--R * +--R 6 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 20 +--R (- 516\|- 1 coth(x) - 129\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 18 +--R (- 5104\|- 1 coth(x) - 1276\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (- 19524\|- 1 coth(x) - 4881\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (- 39632\|- 1 coth(x) - 9908\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (- 47992\|- 1 coth(x) - 11998\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (- 36400\|- 1 coth(x) - 9100\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (- 17528\|- 1 coth(x) - 4382\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (- 5296\|- 1 coth(x) - 1324\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 964\|- 1 coth(x) - 241\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 96\|- 1 coth(x) - 24\|- 1 )(%e ) - 4\|- 1 coth(x) - \|- 1 +--R * +--R 4 +--R tanh(x) +--R + +--R +---+ x 20 +---+ x 18 +--R 258\|- 1 coth(x)(%e ) + 2552\|- 1 coth(x)(%e ) +--R + +--R +---+ x 16 +---+ x 14 +--R 9762\|- 1 coth(x)(%e ) + 19816\|- 1 coth(x)(%e ) +--R + +--R +---+ x 12 +---+ x 10 +--R 23996\|- 1 coth(x)(%e ) + 18200\|- 1 coth(x)(%e ) +--R + +--R +---+ x 8 +---+ x 6 +--R 8764\|- 1 coth(x)(%e ) + 2648\|- 1 coth(x)(%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R 482\|- 1 coth(x)(%e ) + 48\|- 1 coth(x)(%e ) + 2\|- 1 coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R +---+ 2 x 20 +---+ 2 x 18 +--R 1032\|- 1 coth(x) (%e ) + 10208\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 16 +---+ 2 x 14 +--R 39048\|- 1 coth(x) (%e ) + 79264\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 12 +---+ 2 x 10 +--R 95984\|- 1 coth(x) (%e ) + 72800\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 8 +---+ 2 x 6 +--R 35056\|- 1 coth(x) (%e ) + 10592\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 4 +---+ 2 x 2 +---+ 2 +--R 1928\|- 1 coth(x) (%e ) + 192\|- 1 coth(x) (%e ) + 8\|- 1 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ x 20 +---+ x 18 +--R - 258\|- 1 coth(x)(%e ) - 2552\|- 1 coth(x)(%e ) +--R + +--R +---+ x 16 +---+ x 14 +--R - 9762\|- 1 coth(x)(%e ) - 19816\|- 1 coth(x)(%e ) +--R + +--R +---+ x 12 +---+ x 10 +--R - 23996\|- 1 coth(x)(%e ) - 18200\|- 1 coth(x)(%e ) +--R + +--R +---+ x 8 +---+ x 6 +--R - 8764\|- 1 coth(x)(%e ) - 2648\|- 1 coth(x)(%e ) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R - 482\|- 1 coth(x)(%e ) - 48\|- 1 coth(x)(%e ) - 2\|- 1 coth(x) +--R * +--R tanh(x) +--R + +--R +---+ 2 +---+ x 20 +--R (- 1032\|- 1 coth(x) + 258\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 18 +--R (- 10208\|- 1 coth(x) + 2552\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (- 39048\|- 1 coth(x) + 9762\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (- 79264\|- 1 coth(x) + 19816\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (- 95984\|- 1 coth(x) + 23996\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (- 72800\|- 1 coth(x) + 18200\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (- 35056\|- 1 coth(x) + 8764\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (- 10592\|- 1 coth(x) + 2648\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (- 1928\|- 1 coth(x) + 482\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (- 192\|- 1 coth(x) + 48\|- 1 )(%e ) - 8\|- 1 coth(x) + 2\|- 1 +--R / +--R 2 x 18 2 x 16 2 x 14 +--R 127coth(x) (%e ) + 903coth(x) (%e ) + 2646coth(x) (%e ) +--R + +--R 2 x 12 2 x 10 2 x 8 +--R 4210coth(x) (%e ) + 4004coth(x) (%e ) + 2352coth(x) (%e ) +--R + +--R 2 x 6 2 x 4 2 x 2 +--R 850coth(x) (%e ) + 182coth(x) (%e ) + 21coth(x) (%e ) +--R + +--R 2 +--R coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 x 18 2 x 16 +--R (- 254coth(x) - 127)(%e ) + (- 1806coth(x) - 903)(%e ) +--R + +--R 2 x 14 2 x 12 +--R (- 5292coth(x) - 2646)(%e ) + (- 8420coth(x) - 4210)(%e ) +--R + +--R 2 x 10 2 x 8 +--R (- 8008coth(x) - 4004)(%e ) + (- 4704coth(x) - 2352)(%e ) +--R + +--R 2 x 6 2 x 4 +--R (- 1700coth(x) - 850)(%e ) + (- 364coth(x) - 182)(%e ) +--R + +--R 2 x 2 2 +--R (- 42coth(x) - 21)(%e ) - 2coth(x) - 1 +--R * +--R +----------------------+ +--R | x 4 x 2 +--R \|- (%e ) - 6(%e ) - 1 +--R + +--R +---+ 2 x 20 +---+ 2 x 18 +--R - 129\|- 1 coth(x) (%e ) - 1276\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 16 +---+ 2 x 14 +--R - 4881\|- 1 coth(x) (%e ) - 9908\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 12 +---+ 2 x 10 +--R - 11998\|- 1 coth(x) (%e ) - 9100\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 8 +---+ 2 x 6 +--R - 4382\|- 1 coth(x) (%e ) - 1324\|- 1 coth(x) (%e ) +--R + +--R +---+ 2 x 4 +---+ 2 x 2 +---+ 2 +--R - 241\|- 1 coth(x) (%e ) - 24\|- 1 coth(x) (%e ) - \|- 1 coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +---+ 2 +---+ x 20 +--R (258\|- 1 coth(x) + 129\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 18 +--R (2552\|- 1 coth(x) + 1276\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 16 +--R (9762\|- 1 coth(x) + 4881\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 14 +--R (19816\|- 1 coth(x) + 9908\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 12 +--R (23996\|- 1 coth(x) + 11998\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 10 +--R (18200\|- 1 coth(x) + 9100\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 8 +--R (8764\|- 1 coth(x) + 4382\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 6 +--R (2648\|- 1 coth(x) + 1324\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 4 +--R (482\|- 1 coth(x) + 241\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ x 2 +---+ 2 +---+ +--R (48\|- 1 coth(x) + 24\|- 1 )(%e ) + 2\|- 1 coth(x) + \|- 1 +--R * +--R +------------+ +--R | 2 +--R \|tanh(x) - 2 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 526 +t0419:= (a+b*sech(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (104) (b sech(x) + a)\|b sech(x) + a +--R Type: Expression(Integer) +--E 108 + +--S 109 of 526 +r0419:= -3/2*a*b^(1/2)*atan(coth(x)*(a+b*sech(x)^2)^(1/2)/b^(1/2))-_ + 1/2*b^(3/2)*atan(coth(x)*(a+b*sech(x)^2)^(1/2)/b^(1/2))+_ + a^(3/2)*atanh(a^(1/2)*tanh(x)/(a+b*sech(x)^2)^(1/2))+_ + 1/2*b*(a+b*sech(x)^2)^(1/2)*tanh(x) +--R +--R +--R (105) +--R +-+ +--R +-+ tanh(x)\|a +--R 2a\|a atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R +--------------+ +--R | 2 +--------------+ +--R +-+ coth(x)\|b sech(x) + a | 2 +--R (- b - 3a)\|b atan(------------------------) + b tanh(x)\|b sech(x) + a +--R +-+ +--R \|b +--R / +--R 2 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 526 +a0419:= integrate(t0419,x) +--R +--R +--R (106) +--R [ +--R 2 3 6 2 3 5 +--R (- 2a b - a )sinh(x) + (- 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b - 15a )cosh(x) - 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b - 20a )cosh(x) + (- 16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b - 15a )cosh(x) + (- 24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b - 6a )cosh(x) + (- 16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b - a )cosh(x) + (- 4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b - 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b + 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b + 56a b + 28a )cosh(x) + 4a b + 8a b + 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b + 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b + 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b + 120a b + 60a )cosh(x) + 2a b + 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b + 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b + 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b + 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b + 60a b + 36a )cosh(x) + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b + 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b + 40a b + 24a )cosh(x) + (8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b + 2a b + a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b + 10a b + 6a )cosh(x) + (4a b + 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 2 6 +--R (2b + 7a b + 3a )sinh(x) +--R + +--R 2 2 5 +--R (12b + 42a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 105a b + 45a )cosh(x) + 4b + 15a b + 9a )sinh(x) +--R + +--R 2 2 3 +--R (40b + 140a b + 60a )cosh(x) +--R + +--R 2 2 +--R (16b + 60a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 105a b + 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b + 90a b + 54a )cosh(x) + 2b + 9a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (12b + 42a b + 18a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (16b + 60a b + 36a )cosh(x) + (4b + 18a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + 7a b + 3a )cosh(x) + (4b + 15a b + 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 9a b + 9a )cosh(x) + a b + 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +---+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|- b \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) - 4b - 20a b +--R + +--R 2 3 +--R - 28a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 560a b - 490a b - 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) - 2b - 16a b +--R + +--R 2 3 +--R - 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80b - 400a b - 560a b - 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 12b - 96a b - 216a b - 108a )cosh(x) - 4a b - 16a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 4b - 20a b - 28a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b - 16a b - 36a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4a b - 16a b - 12a )cosh(x) - a b - 3a +--R * +--R +---+ +--R \|- b +--R * +--R log +--R 4 3 +--R (2b + 2a)sinh(x) + (8b + 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((12b + 12a)cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R ((8b + 8a)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (2b + 2a)cosh(x) + 2a cosh(x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (4a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) - 2b - 4a b - 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (- 8b - 16a b - 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 24a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (- 8b - 16a b - 12a )cosh(x) +--R + +--R 2 +--R (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (- 2b - 4a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 6 2 5 +--R (- 2a b - 2a )sinh(x) + (- 12a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a b - 30a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 +--R ((- 40a b - 40a )cosh(x) + (- 24a b - 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 +--R (- 30a b - 30a )cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 2a b - 2a )cosh(x) + (- 6a b - 4a )cosh(x) +--R + +--R 2 2 +--R - 2a cosh(x) +--R * +--R +---+ +--R \|- b +--R / +--R 2 4 2 3 +--R (2a b + a )sinh(x) + (8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b + 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b + 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b + a )cosh(x) + (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 30b - 30a b - 15a )cosh(x) - 2b - 6a b - 3a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 +--R (- 40b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 24a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 36a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 8b - 24a b - 12a )cosh(x) + (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b - 2a b - a )cosh(x) + (- 2b - 6a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 3 6 2 3 5 +--R (2a b + a )sinh(x) + (12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b + 15a )cosh(x) + 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b + 20a )cosh(x) + (16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (30a b + 15a )cosh(x) + (24a b + 18a )cosh(x) + 2a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b + 6a )cosh(x) + (16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (2a b + a )cosh(x) + (4a b + 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (2a b + 3a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b - 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 56a b - 56a b - 28a )cosh(x) - 4a b - 8a b - 4a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b - 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b - 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b - 120a b - 60a )cosh(x) - 2a b - 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b - 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b - 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b - 60a b - 36a )cosh(x) - 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) + (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b - 2a b - a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b - 10a b - 6a )cosh(x) + (- 4a b - 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) + 6b + 2a)sinh(x) +--R + +--R 3 4 +--R (- 8b cosh(x) + (12b + 4a)cosh(x))sinh(x) - 2b cosh(x) +--R + +--R 2 +--R (6b + 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 3 2 2 6 +--R (- 2b - 4a b - 2a b)sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((- 30b - 60a b - 30a b)cosh(x) + 2b - 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 +--R (- 40b - 80a b - 40a b)cosh(x) +--R + +--R 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 30b - 60a b - 30a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b - 36a b - 24a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) + (4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 2b - 4a b - 2a b)cosh(x) + (2b - 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b - 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (2b + 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 112a b + 56a b)cosh(x) + 12b + 14a b + 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (72b + 84a b + 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (180b + 210a b + 90a b)cosh(x) - 6b + 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (240b + 280a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (180b + 210a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b + 48a b + 36a b)cosh(x) - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 32a b + 16a b)cosh(x) +--R + +--R 3 2 2 5 +--R (72b + 84a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) + (- 4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 4a b + 2a b)cosh(x) + (12b + 14a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b + 8a b + 6a b)cosh(x) + (- 2a b + 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b + 2a)sinh(x) + (24b + 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b + 30a)cosh(x) + 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b + 40a)cosh(x) + (32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b + 30a)cosh(x) + (48b + 36a)cosh(x) + 4b + 6a)sinh(x) +--R + +--R 5 3 +--R ((24b + 12a)cosh(x) + (32b + 24a)cosh(x) + (8b + 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b + 2a)cosh(x) + (8b + 6a)cosh(x) + (4b + 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b - 4a b - 2a )sinh(x) + (- 32b - 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b - 112a b - 56a )cosh(x) - 8b - 16a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b - 224a b - 112a )cosh(x) + (- 48b - 96a b - 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 280b - 280a b - 140a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) - 4b - 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 224b - 224a b - 112a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 160b - 320a b - 160a )cosh(x) + (- 16b - 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 +--R (- 112b - 112a b - 56a )cosh(x) +--R + +--R 2 2 4 +--R (- 120b - 240a b - 120a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 24b - 120a b - 72a )cosh(x) - 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b - 32a b - 16a )cosh(x) + (- 48b - 96a b - 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b - 80a b - 48a )cosh(x) + (- 16a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b - 4a b - 2a )cosh(x) + (- 8b - 16a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b - 20a b - 12a )cosh(x) + (- 8a b - 8a )cosh(x) - 2a +--R , +--R +--R 2 3 6 2 3 5 +--R (- 2a b - a )sinh(x) + (- 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b - 15a )cosh(x) - 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b - 20a )cosh(x) + (- 16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b - 15a )cosh(x) + (- 24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b - 6a )cosh(x) + (- 16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b - a )cosh(x) + (- 4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b - 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b + 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b + 56a b + 28a )cosh(x) + 4a b + 8a b + 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b + 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b + 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b + 120a b + 60a )cosh(x) + 2a b + 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b + 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b + 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b + 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b + 60a b + 36a )cosh(x) + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b + 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b + 40a b + 24a )cosh(x) + (8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b + 2a b + a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b + 10a b + 6a )cosh(x) + (4a b + 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 3 6 2 3 5 +--R (2a b + a )sinh(x) + (12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b + 15a )cosh(x) + 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b + 20a )cosh(x) + (16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (30a b + 15a )cosh(x) + (24a b + 18a )cosh(x) + 2a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b + 6a )cosh(x) + (16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (2a b + a )cosh(x) + (4a b + 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (2a b + 3a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b - 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 56a b - 56a b - 28a )cosh(x) - 4a b - 8a b - 4a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b - 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b - 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b - 120a b - 60a )cosh(x) - 2a b - 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b - 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b - 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b - 60a b - 36a )cosh(x) - 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) + (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b - 2a b - a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b - 10a b - 6a )cosh(x) + (- 4a b - 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) + 6b + 2a)sinh(x) +--R + +--R 3 4 +--R (- 8b cosh(x) + (12b + 4a)cosh(x))sinh(x) - 2b cosh(x) +--R + +--R 2 +--R (6b + 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 2 6 +--R (- 4b - 14a b - 6a )sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 84a b - 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 60b - 210a b - 90a )cosh(x) - 8b - 30a b - 18a )sinh(x) +--R + +--R 2 2 3 +--R (- 80b - 280a b - 120a )cosh(x) +--R + +--R 2 2 +--R (- 32b - 120a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 60b - 210a b - 90a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 48b - 180a b - 108a )cosh(x) - 4b - 18a b - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 84a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R (- 32b - 120a b - 72a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 4b - 14a b - 6a )cosh(x) + (- 8b - 30a b - 18a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 4b - 18a b - 18a )cosh(x) - 2a b - 6a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (4b + 16a b + 14a b + 6a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 128a b + 112a b + 48a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (112b + 448a b + 392a b + 168a )cosh(x) + 8b + 40a b +--R + +--R 2 3 +--R 56a b + 24a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (224b + 896a b + 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 +--R (48b + 240a b + 336a b + 144a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (280b + 1120a b + 980a b + 420a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (120b + 600a b + 840a b + 360a )cosh(x) + 4b + 32a b +--R + +--R 2 3 +--R 72a b + 36a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (224b + 896a b + 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (160b + 800a b + 1120a b + 480a )cosh(x) +--R + +--R 3 2 2 3 +--R (16b + 128a b + 288a b + 144a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (112b + 448a b + 392a b + 168a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (120b + 600a b + 840a b + 360a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (24b + 192a b + 432a b + 216a )cosh(x) + 8a b + 32a b +--R + +--R 3 +--R 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 128a b + 112a b + 48a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (48b + 240a b + 336a b + 144a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (16b + 128a b + 288a b + 144a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 64a b + 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (4b + 16a b + 14a b + 6a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (8b + 40a b + 56a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4b + 32a b + 72a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (8a b + 32a b + 24a )cosh(x) + 2a b + 6a +--R * +--R +-+ +--R \|b +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|a \|b +--R + +--R 3 2 2 6 +--R (- 2b - 4a b - 2a b)sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((- 30b - 60a b - 30a b)cosh(x) + 2b - 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 +--R (- 40b - 80a b - 40a b)cosh(x) +--R + +--R 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 30b - 60a b - 30a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b - 36a b - 24a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) + (4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 2b - 4a b - 2a b)cosh(x) + (2b - 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b - 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (2b + 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 112a b + 56a b)cosh(x) + 12b + 14a b + 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (72b + 84a b + 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (180b + 210a b + 90a b)cosh(x) - 6b + 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (240b + 280a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (180b + 210a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b + 48a b + 36a b)cosh(x) - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 32a b + 16a b)cosh(x) +--R + +--R 3 2 2 5 +--R (72b + 84a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) + (- 4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 4a b + 2a b)cosh(x) + (12b + 14a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b + 8a b + 6a b)cosh(x) + (- 2a b + 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b + 2a)sinh(x) + (24b + 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b + 30a)cosh(x) + 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b + 40a)cosh(x) + (32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b + 30a)cosh(x) + (48b + 36a)cosh(x) + 4b + 6a)sinh(x) +--R + +--R 5 3 +--R ((24b + 12a)cosh(x) + (32b + 24a)cosh(x) + (8b + 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b + 2a)cosh(x) + (8b + 6a)cosh(x) + (4b + 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b - 4a b - 2a )sinh(x) + (- 32b - 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b - 112a b - 56a )cosh(x) - 8b - 16a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b - 224a b - 112a )cosh(x) + (- 48b - 96a b - 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 280b - 280a b - 140a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) - 4b - 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 224b - 224a b - 112a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 160b - 320a b - 160a )cosh(x) + (- 16b - 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 +--R (- 112b - 112a b - 56a )cosh(x) +--R + +--R 2 2 4 +--R (- 120b - 240a b - 120a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 24b - 120a b - 72a )cosh(x) - 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b - 32a b - 16a )cosh(x) + (- 48b - 96a b - 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b - 80a b - 48a )cosh(x) + (- 16a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b - 4a b - 2a )cosh(x) + (- 8b - 16a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b - 20a b - 12a )cosh(x) + (- 8a b - 8a )cosh(x) - 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 110 + +--S 111 of 526 +m0419a:= a0419.1-r0419 +--R +--R +--R (107) +--R 2 3 6 2 3 5 +--R (- 2a b - a )sinh(x) + (- 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b - 15a )cosh(x) - 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b - 20a )cosh(x) + (- 16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b - 15a )cosh(x) + (- 24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b - 6a )cosh(x) + (- 16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b - a )cosh(x) + (- 4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b - 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b + 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b + 56a b + 28a )cosh(x) + 4a b + 8a b + 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b + 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b + 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b + 120a b + 60a )cosh(x) + 2a b + 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b + 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b + 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b + 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b + 60a b + 36a )cosh(x) + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b + 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b + 40a b + 24a )cosh(x) + (8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b + 2a b + a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b + 10a b + 6a )cosh(x) + (4a b + 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 2 6 2 2 5 +--R (2b + 7a b + 3a )sinh(x) + (12b + 42a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 105a b + 45a )cosh(x) + 4b + 15a b + 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 140a b + 60a )cosh(x) + (16b + 60a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 105a b + 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b + 90a b + 54a )cosh(x) + 2b + 9a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 42a b + 18a )cosh(x) + (16b + 60a b + 36a )cosh(x) +--R + +--R 2 2 +--R (4b + 18a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + 7a b + 3a )cosh(x) + (4b + 15a b + 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 9a b + 9a )cosh(x) + a b + 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +---+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|- b \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) - 4b - 20a b +--R + +--R 2 3 +--R - 28a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 560a b - 490a b - 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) - 2b - 16a b +--R + +--R 2 3 +--R - 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80b - 400a b - 560a b - 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 12b - 96a b - 216a b - 108a )cosh(x) - 4a b - 16a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 4b - 20a b - 28a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b - 16a b - 36a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4a b - 16a b - 12a )cosh(x) - a b - 3a +--R * +--R +---+ +--R \|- b +--R * +--R log +--R 4 3 +--R (2b + 2a)sinh(x) + (8b + 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((12b + 12a)cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R ((8b + 8a)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (2b + 2a)cosh(x) + 2a cosh(x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (4a b + 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) - 2b - 4a b - 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (- 8b - 16a b - 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b - 15a )cosh(x) + (- 12b - 24a b - 18a )cosh(x) +--R + +--R 2 +--R - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (- 8b - 16a b - 12a )cosh(x) +--R + +--R 2 +--R (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (- 2b - 4a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 6 2 5 +--R (- 2a b - 2a )sinh(x) + (- 12a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a b - 30a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 3 +--R ((- 40a b - 40a )cosh(x) + (- 24a b - 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R (- 30a b - 30a )cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (- 2a b - 2a )cosh(x) + (- 6a b - 4a )cosh(x) - 2a cosh(x) +--R * +--R +---+ +--R \|- b +--R / +--R 2 4 2 3 +--R (2a b + a )sinh(x) + (8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b + 6a )cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b + 4a )cosh(x) + (4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b + a )cosh(x) + (2a b + 2a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b - 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 30b - 30a b - 15a )cosh(x) - 2b - 6a b - 3a )sinh(x) +--R + +--R 2 2 3 +--R (- 40b - 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 24a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b - 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b - 36a b - 18a )cosh(x) - 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b - 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 8b - 24a b - 12a )cosh(x) + (- 8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b - 2a b - a )cosh(x) + (- 2b - 6a b - 3a )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 3a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R + +--R 2 3 6 2 3 5 +--R (2a b + a )sinh(x) + (12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b + 15a )cosh(x) + 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b + 20a )cosh(x) + (16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R ((30a b + 15a )cosh(x) + (24a b + 18a )cosh(x) + 2a b + 3a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b + 6a )cosh(x) + (16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 2 3 2 +--R (2a b + a )cosh(x) + (4a b + 3a )cosh(x) + (2a b + 3a )cosh(x) +--R + +--R 3 +--R a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b - 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((- 56a b - 56a b - 28a )cosh(x) - 4a b - 8a b - 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b - 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b - 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b - 120a b - 60a )cosh(x) - 2a b - 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b - 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b - 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b - 60a b - 36a )cosh(x) - 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) + (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b - 2a b - a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b - 10a b - 6a )cosh(x) + (- 4a b - 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) + 6b + 2a)sinh(x) +--R + +--R 3 4 +--R (- 8b cosh(x) + (12b + 4a)cosh(x))sinh(x) - 2b cosh(x) +--R + +--R 2 +--R (6b + 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 3 6 2 3 5 +--R (- 4a b - 2a )sinh(x) + (- 24a b - 12a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 60a b - 30a )cosh(x) - 8a b - 6a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 80a b - 40a )cosh(x) + (- 32a b - 24a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 60a b - 30a )cosh(x) + (- 48a b - 36a )cosh(x) - 4a b +--R + +--R 3 +--R - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 24a b - 12a )cosh(x) + (- 32a b - 24a )cosh(x) +--R + +--R 2 3 +--R (- 8a b - 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 4a b - 2a )cosh(x) + (- 8a b - 6a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 4a b - 6a )cosh(x) - 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (4a b + 4a b + 2a )sinh(x) +--R + +--R 2 2 3 7 +--R (32a b + 32a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((112a b + 112a b + 56a )cosh(x) + 8a b + 16a b + 8a )sinh(x) +--R + +--R 2 2 3 3 +--R (224a b + 224a b + 112a )cosh(x) +--R + +--R 2 2 3 +--R (48a b + 96a b + 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (280a b + 280a b + 140a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (120a b + 240a b + 120a )cosh(x) + 4a b + 20a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (224a b + 224a b + 112a )cosh(x) +--R + +--R 2 2 3 3 +--R (160a b + 320a b + 160a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 80a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 4 +--R (120a b + 240a b + 120a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (24a b + 120a b + 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (32a b + 32a b + 16a )cosh(x) +--R + +--R 2 2 3 5 +--R (48a b + 96a b + 48a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (16a b + 80a b + 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (4a b + 4a b + 2a )cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (4a b + 20a b + 12a )cosh(x) + (8a b + 8a )cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R tanh(x)\|a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R 2 2 6 2 2 5 +--R (2b + 7a b + 3a )sinh(x) + (12b + 42a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 105a b + 45a )cosh(x) + 4b + 15a b + 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 140a b + 60a )cosh(x) + (16b + 60a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 105a b + 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b + 90a b + 54a )cosh(x) + 2b + 9a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 42a b + 18a )cosh(x) + (16b + 60a b + 36a )cosh(x) +--R + +--R 2 2 +--R (4b + 18a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + 7a b + 3a )cosh(x) + (4b + 15a b + 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 9a b + 9a )cosh(x) + a b + 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) - 4b - 20a b +--R + +--R 2 3 +--R - 28a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 560a b - 490a b - 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) - 2b - 16a b +--R + +--R 2 3 +--R - 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80b - 400a b - 560a b - 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 12b - 96a b - 216a b - 108a )cosh(x) - 4a b - 16a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 4b - 20a b - 28a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b - 16a b - 36a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4a b - 16a b - 12a )cosh(x) - a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R +--------------+ +--R | 2 +--R coth(x)\|b sech(x) + a +--R atan(------------------------) +--R +-+ +--R \|b +--R + +--R 2 6 2 5 +--R (- 2b - a b)sinh(x) + (- 12b - 6a b)cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30b - 15a b)cosh(x) - 4b - 3a b)sinh(x) +--R + +--R 2 3 2 3 +--R ((- 40b - 20a b)cosh(x) + (- 16b - 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 30b - 15a b)cosh(x) + (- 24b - 18a b)cosh(x) - 2b +--R + +--R - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12b - 6a b)cosh(x) + (- 16b - 12a b)cosh(x) +--R + +--R 2 +--R (- 4b - 6a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 2b - a b)cosh(x) + (- 4b - 3a b)cosh(x) +--R + +--R 2 2 +--R (- 2b - 3a b)cosh(x) - a b +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R tanh(x)\|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (2b + 2a b + a b)sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 16a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 56a b + 28a b)cosh(x) + 4b + 8a b + 4a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 +--R (24b + 48a b + 24a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 140a b + 70a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (60b + 120a b + 60a b)cosh(x) + 2b + 10a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 +--R (80b + 160a b + 80a b)cosh(x) +--R + +--R 3 2 2 +--R (8b + 40a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 56a b + 28a b)cosh(x) +--R + +--R 3 2 2 4 +--R (60b + 120a b + 60a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b + 60a b + 36a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 16a b + 8a b)cosh(x) +--R + +--R 3 2 2 5 +--R (24b + 48a b + 24a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b + 40a b + 24a b)cosh(x) + (8a b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 2a b + a b)cosh(x) + (4b + 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 2 +--R (2b + 10a b + 6a b)cosh(x) + (4a b + 4a b)cosh(x) + a b +--R * +--R tanh(x) +--R * +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R 3 2 2 6 +--R (- 2b - 4a b - 2a b)sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((- 30b - 60a b - 30a b)cosh(x) + 2b - 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 3 2 2 +--R ((- 40b - 80a b - 40a b)cosh(x) + (8b - 24a b - 16a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 30b - 60a b - 30a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b - 36a b - 24a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) + (4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 2b - 4a b - 2a b)cosh(x) + (2b - 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b - 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (2b + 4a b + 2a b)sinh(x) + (16b + 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 112a b + 56a b)cosh(x) + 12b + 14a b + 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (72b + 84a b + 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (180b + 210a b + 90a b)cosh(x) - 6b + 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (240b + 280a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (180b + 210a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b + 48a b + 36a b)cosh(x) - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 5 +--R (16b + 32a b + 16a b)cosh(x) + (72b + 84a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) + (- 4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 4a b + 2a b)cosh(x) + (12b + 14a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b + 8a b + 6a b)cosh(x) + (- 2a b + 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b + 2a)sinh(x) + (24b + 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b + 30a)cosh(x) + 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b + 40a)cosh(x) + (32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b + 30a)cosh(x) + (48b + 36a)cosh(x) + 4b + 6a)sinh(x) +--R + +--R 5 3 +--R ((24b + 12a)cosh(x) + (32b + 24a)cosh(x) + (8b + 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b + 2a)cosh(x) + (8b + 6a)cosh(x) + (4b + 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b - 4a b - 2a )sinh(x) + (- 32b - 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b - 112a b - 56a )cosh(x) - 8b - 16a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b - 224a b - 112a )cosh(x) + (- 48b - 96a b - 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 280b - 280a b - 140a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) - 4b - 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 224b - 224a b - 112a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 160b - 320a b - 160a )cosh(x) + (- 16b - 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 +--R (- 112b - 112a b - 56a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) + (- 24b - 120a b - 72a )cosh(x) +--R + +--R 2 +--R - 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b - 32a b - 16a )cosh(x) + (- 48b - 96a b - 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b - 80a b - 48a )cosh(x) + (- 16a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b - 4a b - 2a )cosh(x) + (- 8b - 16a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b - 20a b - 12a )cosh(x) + (- 8a b - 8a )cosh(x) - 2a +--R Type: Expression(Integer) +--E 111 + +--S 112 of 526 +--d0419a:= D(m0419a,x) +--E 112 + +--S 113 of 526 +m0419b:= a0419.2-r0419 +--R +--R +--R (108) +--R 2 3 6 2 3 5 +--R (- 2a b - a )sinh(x) + (- 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b - 15a )cosh(x) - 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b - 20a )cosh(x) + (- 16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b - 15a )cosh(x) + (- 24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b - 6a )cosh(x) + (- 16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b - a )cosh(x) + (- 4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b - 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b + 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b + 56a b + 28a )cosh(x) + 4a b + 8a b + 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b + 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b + 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b + 120a b + 60a )cosh(x) + 2a b + 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b + 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b + 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b + 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b + 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b + 60a b + 36a )cosh(x) + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b + 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b + 40a b + 24a )cosh(x) + (8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b + 2a b + a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b + 10a b + 6a )cosh(x) + (4a b + 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 3 6 2 3 5 +--R (2a b + a )sinh(x) + (12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b + 15a )cosh(x) + 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b + 20a )cosh(x) + (16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R ((30a b + 15a )cosh(x) + (24a b + 18a )cosh(x) + 2a b + 3a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b + 6a )cosh(x) + (16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 2 3 2 +--R (2a b + a )cosh(x) + (4a b + 3a )cosh(x) + (2a b + 3a )cosh(x) +--R + +--R 3 +--R a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b - 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((- 56a b - 56a b - 28a )cosh(x) - 4a b - 8a b - 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b - 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b - 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b - 120a b - 60a )cosh(x) - 2a b - 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b - 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b - 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b - 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b - 60a b - 36a )cosh(x) - 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b - 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b - 40a b - 24a )cosh(x) + (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b - 2a b - a )cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b - 10a b - 6a )cosh(x) + (- 4a b - 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) + 6b + 2a)sinh(x) +--R + +--R 3 4 +--R (- 8b cosh(x) + (12b + 4a)cosh(x))sinh(x) - 2b cosh(x) +--R + +--R 2 +--R (6b + 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 3 6 2 3 5 +--R (- 4a b - 2a )sinh(x) + (- 24a b - 12a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 60a b - 30a )cosh(x) - 8a b - 6a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 80a b - 40a )cosh(x) + (- 32a b - 24a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 60a b - 30a )cosh(x) + (- 48a b - 36a )cosh(x) - 4a b +--R + +--R 3 +--R - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 24a b - 12a )cosh(x) + (- 32a b - 24a )cosh(x) +--R + +--R 2 3 +--R (- 8a b - 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 4a b - 2a )cosh(x) + (- 8a b - 6a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 4a b - 6a )cosh(x) - 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (4a b + 4a b + 2a )sinh(x) +--R + +--R 2 2 3 7 +--R (32a b + 32a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((112a b + 112a b + 56a )cosh(x) + 8a b + 16a b + 8a )sinh(x) +--R + +--R 2 2 3 3 +--R (224a b + 224a b + 112a )cosh(x) +--R + +--R 2 2 3 +--R (48a b + 96a b + 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (280a b + 280a b + 140a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (120a b + 240a b + 120a )cosh(x) + 4a b + 20a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (224a b + 224a b + 112a )cosh(x) +--R + +--R 2 2 3 3 +--R (160a b + 320a b + 160a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 80a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (112a b + 112a b + 56a )cosh(x) +--R + +--R 2 2 3 4 +--R (120a b + 240a b + 120a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (24a b + 120a b + 72a )cosh(x) + 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (32a b + 32a b + 16a )cosh(x) +--R + +--R 2 2 3 5 +--R (48a b + 96a b + 48a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (16a b + 80a b + 48a )cosh(x) + (16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (4a b + 4a b + 2a )cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (4a b + 20a b + 12a )cosh(x) + (8a b + 8a )cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R tanh(x)\|a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R 2 2 6 2 2 5 +--R (2b + 7a b + 3a )sinh(x) + (12b + 42a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b + 105a b + 45a )cosh(x) + 4b + 15a b + 9a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b + 140a b + 60a )cosh(x) + (16b + 60a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b + 105a b + 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b + 90a b + 54a )cosh(x) + 2b + 9a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b + 42a b + 18a )cosh(x) + (16b + 60a b + 36a )cosh(x) +--R + +--R 2 2 +--R (4b + 18a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b + 7a b + 3a )cosh(x) + (4b + 15a b + 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 9a b + 9a )cosh(x) + a b + 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) - 4b - 20a b +--R + +--R 2 3 +--R - 28a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b - 560a b - 490a b - 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) - 2b - 16a b +--R + +--R 2 3 +--R - 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b - 448a b - 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80b - 400a b - 560a b - 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b - 224a b - 196a b - 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60b - 300a b - 420a b - 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 12b - 96a b - 216a b - 108a )cosh(x) - 4a b - 16a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b - 64a b - 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b - 120a b - 168a b - 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b - 64a b - 144a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b - 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b - 8a b - 7a b - 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 4b - 20a b - 28a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b - 16a b - 36a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4a b - 16a b - 12a )cosh(x) - a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R +--------------+ +--R | 2 +--R coth(x)\|b sech(x) + a +--R atan(------------------------) +--R +-+ +--R \|b +--R + +--R 2 2 6 +--R (- 4b - 14a b - 6a )sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 84a b - 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 60b - 210a b - 90a )cosh(x) - 8b - 30a b - 18a )sinh(x) +--R + +--R 2 2 3 +--R (- 80b - 280a b - 120a )cosh(x) +--R + +--R 2 2 +--R (- 32b - 120a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 60b - 210a b - 90a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 48b - 180a b - 108a )cosh(x) - 4b - 18a b - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 24b - 84a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R (- 32b - 120a b - 72a )cosh(x) +--R + +--R 2 2 +--R (- 8b - 36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 4b - 14a b - 6a )cosh(x) + (- 8b - 30a b - 18a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 4b - 18a b - 18a )cosh(x) - 2a b - 6a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (4b + 16a b + 14a b + 6a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 128a b + 112a b + 48a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (112b + 448a b + 392a b + 168a )cosh(x) + 8b + 40a b +--R + +--R 2 3 +--R 56a b + 24a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (224b + 896a b + 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 +--R (48b + 240a b + 336a b + 144a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (280b + 1120a b + 980a b + 420a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (120b + 600a b + 840a b + 360a )cosh(x) + 4b + 32a b +--R + +--R 2 3 +--R 72a b + 36a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (224b + 896a b + 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (160b + 800a b + 1120a b + 480a )cosh(x) +--R + +--R 3 2 2 3 +--R (16b + 128a b + 288a b + 144a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (112b + 448a b + 392a b + 168a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (120b + 600a b + 840a b + 360a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (24b + 192a b + 432a b + 216a )cosh(x) + 8a b + 32a b +--R + +--R 3 +--R 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (32b + 128a b + 112a b + 48a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (48b + 240a b + 336a b + 144a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (16b + 128a b + 288a b + 144a )cosh(x) +--R + +--R 2 2 3 +--R (16a b + 64a b + 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (4b + 16a b + 14a b + 6a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (8b + 40a b + 56a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4b + 32a b + 72a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (8a b + 32a b + 24a )cosh(x) + 2a b + 6a +--R * +--R +-+ +--R \|b +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a 2 +--R \|a |------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2a cosh(x)sinh(x) - a cosh(x) - a +--R / +--R 2 2 +-+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|a \|b +--R + +--R 2 6 2 5 +--R (- 2b - a b)sinh(x) + (- 12b - 6a b)cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30b - 15a b)cosh(x) - 4b - 3a b)sinh(x) +--R + +--R 2 3 2 3 +--R ((- 40b - 20a b)cosh(x) + (- 16b - 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 30b - 15a b)cosh(x) + (- 24b - 18a b)cosh(x) - 2b +--R + +--R - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12b - 6a b)cosh(x) + (- 16b - 12a b)cosh(x) +--R + +--R 2 +--R (- 4b - 6a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 2b - a b)cosh(x) + (- 4b - 3a b)cosh(x) +--R + +--R 2 2 +--R (- 2b - 3a b)cosh(x) - a b +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R tanh(x)\|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (2b + 2a b + a b)sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 16a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 56a b + 28a b)cosh(x) + 4b + 8a b + 4a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 +--R (24b + 48a b + 24a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 140a b + 70a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (60b + 120a b + 60a b)cosh(x) + 2b + 10a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 +--R (80b + 160a b + 80a b)cosh(x) +--R + +--R 3 2 2 +--R (8b + 40a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 56a b + 28a b)cosh(x) +--R + +--R 3 2 2 4 +--R (60b + 120a b + 60a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b + 60a b + 36a b)cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b + 16a b + 8a b)cosh(x) +--R + +--R 3 2 2 5 +--R (24b + 48a b + 24a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b + 40a b + 24a b)cosh(x) + (8a b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 2a b + a b)cosh(x) + (4b + 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 2 +--R (2b + 10a b + 6a b)cosh(x) + (4a b + 4a b)cosh(x) + a b +--R * +--R tanh(x) +--R * +--R +--------------+ +--R | 2 +--R \|b sech(x) + a +--R + +--R 3 2 2 6 +--R (- 2b - 4a b - 2a b)sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((- 30b - 60a b - 30a b)cosh(x) + 2b - 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 3 2 2 +--R ((- 40b - 80a b - 40a b)cosh(x) + (8b - 24a b - 16a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 30b - 60a b - 30a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b - 36a b - 24a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 12b - 24a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b - 24a b - 16a b)cosh(x) + (4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 2b - 4a b - 2a b)cosh(x) + (2b - 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b - 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (2b + 4a b + 2a b)sinh(x) + (16b + 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b + 112a b + 56a b)cosh(x) + 12b + 14a b + 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (72b + 84a b + 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b + 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (180b + 210a b + 90a b)cosh(x) - 6b + 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b + 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (240b + 280a b + 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b + 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (180b + 210a b + 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b + 48a b + 36a b)cosh(x) - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 5 +--R (16b + 32a b + 16a b)cosh(x) + (72b + 84a b + 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b + 32a b + 24a b)cosh(x) + (- 4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b + 4a b + 2a b)cosh(x) + (12b + 14a b + 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b + 8a b + 6a b)cosh(x) + (- 2a b + 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b + 2a)sinh(x) + (24b + 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b + 30a)cosh(x) + 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b + 40a)cosh(x) + (32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b + 30a)cosh(x) + (48b + 36a)cosh(x) + 4b + 6a)sinh(x) +--R + +--R 5 3 +--R ((24b + 12a)cosh(x) + (32b + 24a)cosh(x) + (8b + 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b + 2a)cosh(x) + (8b + 6a)cosh(x) + (4b + 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b + 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b - 4a b - 2a )sinh(x) + (- 32b - 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b - 112a b - 56a )cosh(x) - 8b - 16a b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b - 224a b - 112a )cosh(x) + (- 48b - 96a b - 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 280b - 280a b - 140a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) - 4b - 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 224b - 224a b - 112a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 160b - 320a b - 160a )cosh(x) + (- 16b - 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 +--R (- 112b - 112a b - 56a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 120b - 240a b - 120a )cosh(x) + (- 24b - 120a b - 72a )cosh(x) +--R + +--R 2 +--R - 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b - 32a b - 16a )cosh(x) + (- 48b - 96a b - 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b - 80a b - 48a )cosh(x) + (- 16a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b - 4a b - 2a )cosh(x) + (- 8b - 16a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b - 20a b - 12a )cosh(x) + (- 8a b - 8a )cosh(x) - 2a +--R Type: Expression(Integer) +--E 113 + +--S 114 of 526 +--d0419b:= D(m0419b,x) +--E 114 + +--S 115 of 526 +t0420:= x/sech(x)^(3/2)-1/3*x*sech(x)^(1/2) +--R +--R +--R 2 +--R - x sech(x) + 3x +--R (109) ------------------ +--R +-------+ +--R 3sech(x)\|sech(x) +--R Type: Expression(Integer) +--E 115 + +--S 116 of 526 +r0420:= -2/9*(2*cosh(x)-3*x*sinh(x))/(1/cosh(x))^(1/2) +--R +--R +--R 6x sinh(x) - 4cosh(x) +--R (110) --------------------- +--R +-------+ +--R | 1 +--R 9 |------- +--R \|cosh(x) +--R Type: Expression(Integer) +--E 116 + +--S 117 of 526 +a0420:= integrate(t0420,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 117 + +--S 118 of 526 +m0420:= a0420-r0420 +--R +--R +--R +-------+ +--R | 1 +--R 9a0420 |------- - 6x sinh(x) + 4cosh(x) +--R \|cosh(x) +--R (111) ---------------------------------------- +--R +-------+ +--R | 1 +--R 9 |------- +--R \|cosh(x) +--R Type: Expression(Integer) +--E 118 + +--S 119 of 526 +d0420:= D(m0420,x) +--R +--R +--R 2 2 +--R - x sinh(x) - 2x cosh(x) +--R (112) -------------------------- +--R +-------+ +--R | 1 +--R 3cosh(x) |------- +--R \|cosh(x) +--R Type: Expression(Integer) +--E 119 + +--S 120 of 526 +t0421:= x/sech(x)^(5/2)-3/5*x/sech(x)^(1/2) +--R +--R +--R 2 +--R - 3x sech(x) + 5x +--R (113) ------------------- +--R 2 +-------+ +--R 5sech(x) \|sech(x) +--R Type: Expression(Integer) +--E 120 + +--S 121 of 526 +r0421:= -4/25/sech(x)^(5/2)+2/5*x*sinh(x)/sech(x)^(3/2) +--R +--R +--R 10x sech(x)sinh(x) - 4 +--R (114) ---------------------- +--R 2 +-------+ +--R 25sech(x) \|sech(x) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 526 +--a0421:= integrate(t0421,x) +--E 122 + +--S 123 of 526 +--m0421:= a0421-r0421 +--E 123 + +--S 124 of 526 +--d0421:= D(m0421,x) +--E 124 + +--S 125 of 526 +t0422:= x/sech(x)^(7/2)-5/21*x*sech(x)^(1/2) +--R +--R +--R 4 +--R - 5x sech(x) + 21x +--R (115) -------------------- +--R 3 +-------+ +--R 21sech(x) \|sech(x) +--R Type: Expression(Integer) +--E 125 + +--S 126 of 526 +r0422:= -2/441*(18*cosh(x)^3+70*cosh(x)-63*x*sinh(x)*cosh(x)^2-_ + 105*x*sinh(x))/(1/cosh(x))^(1/2) +--R +--R +--R 2 3 +--R (126x cosh(x) + 210x)sinh(x) - 36cosh(x) - 140cosh(x) +--R (116) ------------------------------------------------------- +--R +-------+ +--R | 1 +--R 441 |------- +--R \|cosh(x) +--R Type: Expression(Integer) +--E 126 + +--S 127 of 526 +a0422:= integrate(t0422,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 127 + +--S 128 of 526 +m0422:= a0422-r0422 +--R +--R +--R (117) +--R +-------+ +--R | 1 2 3 +--R 441a0422 |------- + (- 126x cosh(x) - 210x)sinh(x) + 36cosh(x) +--R \|cosh(x) +--R + +--R 140cosh(x) +--R / +--R +-------+ +--R | 1 +--R 441 |------- +--R \|cosh(x) +--R Type: Expression(Integer) +--E 128 + +--S 129 of 526 +d0422:= D(m0422,x) +--R +--R +--R 2 2 4 2 +--R (- 15x cosh(x) - 5x)sinh(x) - 6x cosh(x) - 10x cosh(x) +--R (118) ---------------------------------------------------------- +--R +-------+ +--R | 1 +--R 21cosh(x) |------- +--R \|cosh(x) +--R Type: Expression(Integer) +--E 129 + +--S 130 of 526 +t0423:= x^2/sech(x)^(3/2)-1/3*x^2*sech(x)^(1/2) +--R +--R +--R 2 2 2 +--R - x sech(x) + 3x +--R (119) ------------------ +--R +-------+ +--R 3sech(x)\|sech(x) +--R Type: Expression(Integer) +--E 130 + +--S 131 of 526 +r0423:= -8/9*x/sech(x)^(3/2)-16/27*%i*cosh(x)^(1/2)*_ + EllipticF(1/2*%i*x,2)*sech(x)^(1/2)+16/27*sinh(x)/sech(x)^(1/2)+_ + 2/3*x^2*sinh(x)/sech(x)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 131 + +--S 132 of 526 +--a0423:= integrate(t0423,x) +--E 132 + +--S 133 of 526 +--m0423:= a0423-r0423 +--E 133 + +--S 134 of 526 +--d0423:= D(m0423,x) +--E 134 + +--S 135 of 526 +t0424:= csch(a+b*x) +--R +--R +--R (120) csch(b x + a) +--R Type: Expression(Integer) +--E 135 + +--S 136 of 526 +r0424:= -acoth(cosh(a+b*x))/b +--R +--R +--R acoth(cosh(b x + a)) +--R (121) - -------------------- +--R b +--R Type: Expression(Integer) +--E 136 + +--S 137 of 526 +a0424:= integrate(t0424,x) +--R +--R +--R (122) +--R - log(sinh(b x + a) + cosh(b x + a) + 1) +--R + +--R log(sinh(b x + a) + cosh(b x + a) - 1) +--R / +--R b +--R Type: Union(Expression(Integer),...) +--E 137 + +--S 138 of 526 +m0424:= a0424-r0424 +--R +--R +--R (123) +--R - log(sinh(b x + a) + cosh(b x + a) + 1) +--R + +--R log(sinh(b x + a) + cosh(b x + a) - 1) + acoth(cosh(b x + a)) +--R / +--R b +--R Type: Expression(Integer) +--E 138 + +--S 139 of 526 +d0424:= D(m0424,x) +--R +--R +--R (124) +--R 3 2 +--R - sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R (cosh(b x + a) - 1)sinh(b x + a) + 2cosh(b x + a) - 2cosh(b x + a) +--R / +--R 2 2 +--R (cosh(b x + a) - 1)sinh(b x + a) +--R + +--R 3 4 +--R (2cosh(b x + a) - 2cosh(b x + a))sinh(b x + a) + cosh(b x + a) +--R + +--R 2 +--R - 2cosh(b x + a) + 1 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 526 +t0425:= csch(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (125) \|csch(b x + a) +--R Type: Expression(Integer) +--E 140 + +--S 141 of 526 +r0425:= -2*%i*csch(a+b*x)^(1/2)*EllipticF(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + (%i*sinh(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 141 + +--S 142 of 526 +a0425:= integrate(t0425,x) +--R +--R +--R x +--R ++ +--------------+ +--I (126) | \|csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 142 + +--S 143 of 526 +--m0425:= a0425-r0425 +--E 143 + +--S 144 of 526 +--d0425:= D(m0425,x) +--E 144 + +--S 145 of 526 +t0426:= csch(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (127) csch(b x + a)\|csch(b x + a) +--R Type: Expression(Integer) +--E 145 + +--S 146 of 526 +r0426:= -2*cosh(a+b*x)*csch(a+b*x)^(1/2)/b-2*%i*_ + EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b/csch(a+b*x)^(1/2)/_ + (%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 146 + +--S 147 of 526 +a0426:= integrate(t0426,x) +--R +--R +--R x +--R ++ +--------------+ +--I (128) | csch(%R b + a)\|csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 147 + +--S 148 of 526 +--m0426:= a0426-r0426 +--E 148 + +--S 149 of 526 +--d0426:= D(m0426,x) +--E 149 + +--S 150 of 526 +t0427:= csch(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (129) csch(b x + a) \|csch(b x + a) +--R Type: Expression(Integer) +--E 150 + +--S 151 of 526 +r0427:= -2/3*cosh(a+b*x)*csch(a+b*x)^(3/2)/b+2/3*%i*csch(a+b*x)^(1/2)*_ + EllipticF(-1/4*%pi+1/2*%i*(a+b*x),2)*(%i*sinh(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 151 + +--S 152 of 526 +a0427:= integrate(t0427,x) +--R +--R +--R x +--R ++ 2 +--------------+ +--I (130) | csch(%R b + a) \|csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 152 + +--S 153 of 526 +--m0427:= a0427-r0427 +--E 153 + +--S 154 of 526 +--d0427:= D(m0427,x) +--E 154 + +--S 155 of 526 +t0428:= 1/csch(a+b*x)^(1/2) +--R +--R +--R 1 +--R (131) ---------------- +--R +-------------+ +--R \|csch(b x + a) +--R Type: Expression(Integer) +--E 155 + +--S 156 of 526 +r0428:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*_ + (a+b*x),2)/b/csch(a+b*x)^(1/2)/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 156 + +--S 157 of 526 +a0428:= integrate(t0428,x) +--R +--R +--R x +--R ++ 1 +--I (132) | ----------------- d%R +--R ++ +--------------+ +--I \|csch(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 157 + +--S 158 of 526 +--m0428:= a0428-r0428 +--E 158 + +--S 159 of 526 +--d0428:= D(m0428,x) +--E 159 + +--S 160 of 526 +t0429:= 1/csch(a+b*x)^(3/2) +--R +--R +--R 1 +--R (133) ----------------------------- +--R +-------------+ +--R csch(b x + a)\|csch(b x + a) +--R Type: Expression(Integer) +--E 160 + +--S 161 of 526 +r0429:= 2/3*cosh(a+b*x)/b/csch(a+b*x)^(1/2)+2/3*%i*csch(a+b*x)^(1/2)*_ + EllipticF(-1/4*%pi+1/2*%i*(a+b*x),2)*(%i*sinh(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 161 + +--S 162 of 526 +a0429:= integrate(t0429,x) +--R +--R +--R x +--R ++ 1 +--I (134) | ------------------------------- d%R +--R ++ +--------------+ +--I csch(%R b + a)\|csch(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 162 + +--S 163 of 526 +--m0429:= a0429-r0429 +--E 163 + +--S 164 of 526 +--d0429:= D(m0429,x) +--E 164 + +--S 165 of 526 +t0430:= 1/csch(a+b*x)^(5/2) +--R +--R +--R 1 +--R (135) ------------------------------ +--R 2 +-------------+ +--R csch(b x + a) \|csch(b x + a) +--R Type: Expression(Integer) +--E 165 + +--S 166 of 526 +r0430:= 2/5*cosh(a+b*x)/b/csch(a+b*x)^(3/2)+6/5*%i*_ + EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b/csch(a+b*x)^(1/2)/_ + (%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 166 + +--S 167 of 526 +a0430:= integrate(t0430,x) +--R +--R +--R x +--R ++ 1 +--I (136) | -------------------------------- d%R +--R ++ 2 +--------------+ +--I csch(%R b + a) \|csch(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 167 + +--S 168 of 526 +--m0430:= a0430-r0430 +--E 168 + +--S 169 of 526 +--d0430:= D(m0430,x) +--E 169 + +--S 170 of 526 +t0431:= x*csch(a+b*x) +--R +--R +--R (137) x csch(b x + a) +--R Type: Expression(Integer) +--E 170 + +--S 171 of 526 +r0431:= -(2*x*atanh(exp(a+b*x))*b+polylog(2,-exp(a+b*x))-_ + polylog(2,exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 171 + +--S 172 of 526 +a0431:= integrate(t0431,x) +--R +--R +--R x +--R ++ +--I (138) | %R csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 172 + +--S 173 of 526 +--m0431:= a0431-r0431 +--E 173 + +--S 174 of 526 +--d0431:= D(m0431,x) +--E 174 + +--S 175 of 526 +t0432:= x^2*csch(a+b*x) +--R +--R +--R 2 +--R (139) x csch(b x + a) +--R Type: Expression(Integer) +--E 175 + +--S 176 of 526 +r0432:= -2*(x^2*atanh(exp(a+b*x))*b^2+polylog(2,-exp(a+b*x))*x*b-_ + polylog(2,exp(a+b*x))*x*b-polylog(3,-exp(a+b*x))+_ + polylog(3,exp(a+b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 176 + +--S 177 of 526 +a0432:= integrate(t0432,x) +--R +--R +--R x +--R ++ 2 +--I (140) | %R csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 177 + +--S 178 of 526 +--m0432:= a0432-r0432 +--E 178 + +--S 179 of 526 +--d0432:= D(m0432,x) +--E 179 + +--S 180 of 526 +t0433:= x^3*csch(a+b*x) +--R +--R +--R 3 +--R (141) x csch(b x + a) +--R Type: Expression(Integer) +--E 180 + +--S 181 of 526 +r0433:= -(2*x^3*atanh(exp(a+b*x))*b^3+3*polylog(2,-exp(a+b*x))*x^2*b^2-_ + 3*polylog(2,exp(a+b*x))*x^2*b^2-6*polylog(3,-exp(a+b*x))*x*b+_ + 6*polylog(3,exp(a+b*x))*x*b+6*polylog(4,-exp(a+b*x))-_ + 6*polylog(4,exp(a+b*x)))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 181 + +--S 182 of 526 +a0433:= integrate(t0433,x) +--R +--R +--R x +--R ++ 3 +--I (142) | %R csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 182 + +--S 183 of 526 +--m0433:= a0433-r0433 +--E 183 + +--S 184 of 526 +--d0433:= D(m0433,x) +--E 184 + +--S 185 of 526 +t0434:= x*csch(a+b*x)^2 +--R +--R +--R 2 +--R (143) x csch(b x + a) +--R Type: Expression(Integer) +--E 185 + +--S 186 of 526 +r0434:= -x*coth(a+b*x)/b+log(sinh(a+b*x))/b^2 +--R +--R +--R log(sinh(b x + a)) - b x coth(b x + a) +--R (144) -------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 186 + +--S 187 of 526 +a0434:= integrate(t0434,x) +--R +--R +--R (145) +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R - 2b x sinh(b x + a) - 4b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Union(Expression(Integer),...) +--E 187 + +--S 188 of 526 +m0434:= a0434-r0434 +--R +--R +--R (146) +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) + 1) +--R * +--R log(sinh(b x + a)) +--R + +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R (b x coth(b x + a) - 2b x)sinh(b x + a) +--R + +--R (2b x cosh(b x + a)coth(b x + a) - 4b x cosh(b x + a))sinh(b x + a) +--R + +--R 2 2 +--R (b x cosh(b x + a) - b x)coth(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Expression(Integer) +--E 188 + +--S 189 of 526 +d0434:= D(m0434,x) +--R +--R +--R (147) +--R 2 4 +--R (- b x coth(b x + a) + coth(b x + a) + b x - 1)sinh(b x + a) +--R + +--R 2 +--R - 4b x cosh(b x + a)coth(b x + a) + 4cosh(b x + a)coth(b x + a) +--R + +--R (4b x - 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 +--R (- 6b x cosh(b x + a) + 2b x)coth(b x + a) +--R + +--R 2 2 +--R (6cosh(b x + a) - 2)coth(b x + a) + (6b x - 6)cosh(b x + a) + 2b x +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 3 2 +--R (- 4b x cosh(b x + a) + 4b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R (4cosh(b x + a) - 4cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R (4b x - 4)cosh(b x + a) + 4b x cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (- b x cosh(b x + a) + 2b x cosh(b x + a) - b x)coth(b x + a) +--R + +--R 4 2 +--R (cosh(b x + a) - 2cosh(b x + a) + 1)coth(b x + a) +--R + +--R 4 2 +--R (b x - 1)cosh(b x + a) + 2b x cosh(b x + a) + b x + 1 +--R / +--R 4 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (6b cosh(b x + a) - 2b)sinh(b x + a) +--R + +--R 3 4 +--R (4b cosh(b x + a) - 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 2 +--R - 2b cosh(b x + a) + b +--R Type: Expression(Integer) +--E 189 + +--S 190 of 526 +t0435:= x^2*csch(a+b*x)^2 +--R +--R +--R 2 2 +--R (148) x csch(b x + a) +--R Type: Expression(Integer) +--E 190 + +--S 191 of 526 +r0435:= -(b^2*x^2+x^2*coth(a+b*x)*b^2-2*x*log(1-exp(2*a+2*b*x))*b-_ + polylog(2,exp(2*a+2*b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 191 + +--S 192 of 526 +a0435:= integrate(t0435,x) +--R +--R +--R x +--R ++ 2 2 +--I (149) | %R csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 192 + +--S 193 of 526 +--m0435:= a0435-r0435 +--E 193 + +--S 194 of 526 +--d0435:= D(m0435,x) +--E 194 + +--S 195 of 526 +t0436:= x^3*csch(a+b*x)^2 +--R +--R +--R 3 2 +--R (150) x csch(b x + a) +--R Type: Expression(Integer) +--E 195 + +--S 196 of 526 +r0436:= -1/2*(2*b^3*x^3+2*x^3*coth(a+b*x)*b^3-6*x^2*log(1-exp(2*a+2*b*x))*_ + b^2-6*x*polylog(2,exp(2*a+2*b*x))*b+3*polylog(3,exp(2*a+2*b*x)))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 196 + +--S 197 of 526 +a0436:= integrate(t0436,x) +--R +--R +--R x +--R ++ 3 2 +--I (151) | %R csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 197 + +--S 198 of 526 +--m0436:= a0436-r0436 +--E 198 + +--S 199 of 526 +--d0436:= D(m0436,x) +--E 199 + +--S 200 of 526 +t0437:= x*csch(a+b*x)^3 +--R +--R +--R 3 +--R (152) x csch(b x + a) +--R Type: Expression(Integer) +--E 200 + +--S 201 of 526 +r0437:= x*atanh(exp(1)^(a+b*x))/b-1/2*csch(a+b*x)/b^2-_ + 1/2*x*coth(a+b*x)*csch(a+b*x)/b+1/2*polylog(2,-exp(1)^(a+b*x))/b^2-_ + 1/2*polylog(2,exp(1)^(a+b*x))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 201 + +--S 202 of 526 +a0437:= integrate(t0437,x) +--R +--R +--R x +--R ++ 3 +--I (153) | %R csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 202 + +--S 203 of 526 +--m0437:= a0437-r0437 +--E 203 + +--S 204 of 526 +--d0437:= D(m0437,x) +--E 204 + +--S 205 of 526 +t0438:= x^2*csch(a+b*x)^3 +--R +--R +--R 2 3 +--R (154) x csch(b x + a) +--R Type: Expression(Integer) +--E 205 + +--S 206 of 526 +r0438:= -acoth(cosh(a+b*x))/b^3+x^2*atanh(exp(1)^(a+b*x))/b-_ + x*csch(a+b*x)/b^2-1/2*x^2*coth(a+b*x)*csch(a+b*x)/b+_ + x*polylog(2,-exp(1)^(a+b*x))/b^2-x*polylog(2,exp(1)^(a+b*x))/b^2-_ + polylog(3,-exp(1)^(a+b*x))/b^3+polylog(3,exp(1)^(a+b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 206 + +--S 207 of 526 +a0438:= integrate(t0438,x) +--R +--R +--R x +--R ++ 2 3 +--I (155) | %R csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 207 + +--S 208 of 526 +--m0438:= a0438-r0438 +--E 208 + +--S 209 of 526 +--d0438:= D(m0438,x) +--E 209 + +--S 210 of 526 +t0439:= (c+d*x)*csch(a+b*x) +--R +--R +--R (156) (d x + c)csch(b x + a) +--R Type: Expression(Integer) +--E 210 + +--S 211 of 526 +r0439:= -(2*atanh(exp(a+b*x))*c*b+2*atanh(exp(a+b*x))*d*x*b+_ + d*polylog(2,-exp(a+b*x))-d*polylog(2,exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 526 +a0439:= integrate(t0439,x) +--R +--R +--R x +--R ++ +--I (157) | (%R d + c)csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 212 + +--S 213 of 526 +--m0439:= a0439-r0439 +--E 213 + +--S 214 of 526 +--d0439:= D(m0439,x) +--E 214 + +--S 215 of 526 +t0440:= (c+d*x)^2*csch(a+b*x) +--R +--R +--R 2 2 2 +--R (158) (d x + 2c d x + c )csch(b x + a) +--R Type: Expression(Integer) +--E 215 + +--S 216 of 526 +r0440:= -2*(c+d*x)^2*atanh(exp(1)^(a+b*x))/b-2*d*(c+d*x)*_ + polylog(2,-exp(1)^(a+b*x))/b^2+2*d*(c+d*x)*_ + polylog(2,exp(1)^(a+b*x))/b^2+2*d^2*_ + polylog(3,-exp(1)^(a+b*x))/b^3-2*d^2*_ + polylog(3,exp(1)^(a+b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 216 + +--S 217 of 526 +a0440:= integrate(t0440,x) +--R +--R +--R x +--R ++ 2 2 2 +--I (159) | (%R d + 2%R c d + c )csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 217 + +--S 218 of 526 +--m0440:= a0440-r0440 +--E 218 + +--S 219 of 526 +--d0440:= D(m0440,x) +--E 219 + +--S 220 of 526 +t0441:= (c+d*x)^3*csch(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R (160) (d x + 3c d x + 3c d x + c )csch(b x + a) +--R Type: Expression(Integer) +--E 220 + +--S 221 of 526 +r0441:= -2*(c+d*x)^3*atanh(exp(1)^(a+b*x))/b-3*d*(c+d*x)^2*_ + polylog(2,-exp(1)^(a+b*x))/b^2+3*d*(c+d*x)^2*_ + polylog(2,exp(1)^(a+b*x))/b^2+6*d^2*(c+d*x)*_ + polylog(3,-exp(1)^(a+b*x))/b^3-6*d^2*(c+d*x)*_ + polylog(3,exp(1)^(a+b*x))/b^3-6*d^3*_ + polylog(4,-exp(1)^(a+b*x))/b^4+6*d^3*_ + polylog(4,exp(1)^(a+b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 221 + +--S 222 of 526 +a0441:= integrate(t0441,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 +--I (161) | (%R d + 3%R c d + 3%R c d + c )csch(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 222 + +--S 223 of 526 +--m0441:= a0441-r0441 +--E 223 + +--S 224 of 526 +--d0441:= D(m0441,x) +--E 224 + +--S 225 of 526 +t0442:= (c+d*x)*csch(a+b*x)^2 +--R +--R +--R 2 +--R (162) (d x + c)csch(b x + a) +--R Type: Expression(Integer) +--E 225 + +--S 226 of 526 +r0442:= -(c+d*x)*coth(a+b*x)/b+d*log(sinh(a+b*x))/b^2 +--R +--R +--R d log(sinh(b x + a)) + (- b d x - b c)coth(b x + a) +--R (163) --------------------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 226 + +--S 227 of 526 +a0442:= integrate(t0442,x) +--R +--R +--R (164) +--R 2 2 +--R d sinh(b x + a) + 2d cosh(b x + a)sinh(b x + a) + d cosh(b x + a) +--R + +--R - d +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R - 2b d x sinh(b x + a) - 4b d x cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R - 2b d x cosh(b x + a) - 2b c +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Union(Expression(Integer),...) +--E 227 + +--S 228 of 526 +m0442:= a0442-r0442 +--R +--R +--R (165) +--R 2 2 +--R - d sinh(b x + a) - 2d cosh(b x + a)sinh(b x + a) - d cosh(b x + a) +--R + +--R d +--R * +--R log(sinh(b x + a)) +--R + +--R 2 2 +--R d sinh(b x + a) + 2d cosh(b x + a)sinh(b x + a) + d cosh(b x + a) +--R + +--R - d +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R ((b d x + b c)coth(b x + a) - 2b d x)sinh(b x + a) +--R + +--R ((2b d x + 2b c)cosh(b x + a)coth(b x + a) - 4b d x cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 2 +--R ((b d x + b c)cosh(b x + a) - b d x - b c)coth(b x + a) +--R + +--R 2 +--R - 2b d x cosh(b x + a) - 2b c +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Expression(Integer) +--E 228 + +--S 229 of 526 +d0442:= D(m0442,x) +--R +--R +--R (166) +--R 2 +--R ((- b d x - b c)coth(b x + a) + d coth(b x + a) + b d x - d + b c) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 2 +--R (- 4b d x - 4b c)cosh(b x + a)coth(b x + a) +--R + +--R 4d cosh(b x + a)coth(b x + a) + (4b d x - 4d + 4b c)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 +--R ((- 6b d x - 6b c)cosh(b x + a) + 2b d x + 2b c)coth(b x + a) +--R + +--R 2 +--R (6d cosh(b x + a) - 2d)coth(b x + a) +--R + +--R 2 +--R (6b d x - 6d + 6b c)cosh(b x + a) + 2b d x + 2b c +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 3 +--R ((- 4b d x - 4b c)cosh(b x + a) + (4b d x + 4b c)cosh(b x + a)) +--R * +--R 2 +--R coth(b x + a) +--R + +--R 3 +--R (4d cosh(b x + a) - 4d cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R (4b d x - 4d + 4b c)cosh(b x + a) + (4b d x + 4b c)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 4 2 +--R (- b d x - b c)cosh(b x + a) + (2b d x + 2b c)cosh(b x + a) - b d x +--R + +--R - b c +--R * +--R 2 +--R coth(b x + a) +--R + +--R 4 2 +--R (d cosh(b x + a) - 2d cosh(b x + a) + d)coth(b x + a) +--R + +--R 4 2 +--R (b d x - d + b c)cosh(b x + a) + (2b d x + 2b c)cosh(b x + a) + b d x +--R + +--R d + b c +--R / +--R 4 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (6b cosh(b x + a) - 2b)sinh(b x + a) +--R + +--R 3 4 +--R (4b cosh(b x + a) - 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 2 +--R - 2b cosh(b x + a) + b +--R Type: Expression(Integer) +--E 229 + +--S 230 of 526 +t0443:= (c+d*x)^2*csch(a+b*x)^2 +--R +--R +--R 2 2 2 2 +--R (167) (d x + 2c d x + c )csch(b x + a) +--R Type: Expression(Integer) +--E 230 + +--S 231 of 526 +r0443:= -(c+d*x)^2/b-(c+d*x)^2*coth(a+b*x)/b+2*d*(c+d*x)*_ + log(1-exp(1)^(2*a+2*b*x))/b^2+d^2*polylog(2,exp(1)^(2*a+2*b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 231 + +--S 232 of 526 +a0443:= integrate(t0443,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--I (168) | (%R d + 2%R c d + c )csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 232 + +--S 233 of 526 +--m0443:= a0443-r0443 +--E 233 + +--S 234 of 526 +--d0443:= D(m0443,x) +--E 234 + +--S 235 of 526 +t0444:= (c+d*x)^3*csch(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 2 +--R (169) (d x + 3c d x + 3c d x + c )csch(b x + a) +--R Type: Expression(Integer) +--E 235 + +--S 236 of 526 +r0444:= -(c+d*x)^3/b-(c+d*x)^3*coth(a+b*x)/b+3*d*(c+d*x)^2*_ + log(1-exp(1)^(2*a+2*b*x))/b^2+3*d^2*(c+d*x)*_ + polylog(2,exp(1)^(2*a+2*b*x))/b^3-3/2*d^3*_ + polylog(3,exp(1)^(2*a+2*b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 236 + +--S 237 of 526 +a0444:= integrate(t0444,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 2 +--I (170) | (%R d + 3%R c d + 3%R c d + c )csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 237 + +--S 238 of 526 +--m0444:= a0444-r0444 +--E 238 + +--S 239 of 526 +--d0444:= D(m0444,x) +--E 239 + +--S 240 of 526 +t0445:= (c+d*x)*csch(a+b*x)^3 +--R +--R +--R 3 +--R (171) (d x + c)csch(b x + a) +--R Type: Expression(Integer) +--E 240 + +--S 241 of 526 +r0445:= (c+d*x)*atanh(exp(1)^(a+b*x))/b-1/2*d*csch(a+b*x)/b^2-_ + 1/2*(c+d*x)*coth(a+b*x)*csch(a+b*x)/b+1/2*d*_ + polylog(2,-exp(1)^(a+b*x))/b^2-1/2*d*_ + polylog(2,exp(1)^(a+b*x))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 241 + +--S 242 of 526 +a0445:= integrate(t0445,x) +--R +--R +--R x +--R ++ 3 +--I (172) | (%R d + c)csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 526 +--m0445:= a0445-r0445 +--E 243 + +--S 244 of 526 +--d0445:= D(m0445,x) +--E 244 + +--S 245 of 526 +t0446:= (c+d*x)^2*csch(a+b*x)^3 +--R +--R +--R 2 2 2 3 +--R (173) (d x + 2c d x + c )csch(b x + a) +--R Type: Expression(Integer) +--E 245 + +--S 246 of 526 +r0446:= -d^2*acoth(cosh(a+b*x))/b^3+(c+d*x)^2*atanh(exp(1)^(a+b*x))/b-_ + d*(c+d*x)*csch(a+b*x)/b^2-1/2*(c+d*x)^2*coth(a+b*x)*csch(a+b*x)/b+_ + d*(c+d*x)*polylog(2,-exp(1)^(a+b*x))/b^2-_ + d*(c+d*x)*polylog(2,exp(1)^(a+b*x))/b^2-_ + d^2*polylog(3,-exp(1)^(a+b*x))/b^3+_ + d^2*polylog(3,exp(1)^(a+b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 246 + +--S 247 of 526 +a0446:= integrate(t0446,x) +--R +--R +--R x +--R ++ 2 2 2 3 +--I (174) | (%R d + 2%R c d + c )csch(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 247 + +--S 248 of 526 +--m0446:= a0446-r0446 +--E 248 + +--S 249 of 526 +--d0446:= D(m0446,x) +--E 249 + +--S 250 of 526 +t0447:= csch(x)^(1/2) +--R +--R +--R +-------+ +--R (175) \|csch(x) +--R Type: Expression(Integer) +--E 250 + +--S 251 of 526 +r0447:= -2*%i*csch(x)^(1/2)*EllipticF(-1/4*%pi+1/2*%i*x,2)*(%i*sinh(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 251 + +--S 252 of 526 +a0447:= integrate(t0447,x) +--R +--R +--R x +--R ++ +--------+ +--I (176) | \|csch(%R) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 252 + +--S 253 of 526 +--m0447:= a0447-r0447 +--E 253 + +--S 254 of 526 +--d0447:= D(m0447,x) +--E 254 + +--S 255 of 526 +t0448:= (-csch(x)^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (177) \|- csch(x) +--R Type: Expression(Integer) +--E 255 + +--S 256 of 526 +r0448:= acsc(tanh(x)) +--R +--R +--R (178) acsc(tanh(x)) +--R Type: Expression(Integer) +--E 256 + +--S 257 of 526 +a0448:= integrate(t0448,x) +--R +--R +--R +---+ x +---+ x +--R (179) - \|- 1 log(%e + 1) + \|- 1 log(%e - 1) +--R Type: Union(Expression(Integer),...) +--E 257 + +--S 258 of 526 +m0448:= a0448-r0448 +--R +--R +--R +---+ x +---+ x +--R (180) - \|- 1 log(%e + 1) + \|- 1 log(%e - 1) - acsc(tanh(x)) +--R Type: Expression(Integer) +--E 258 + +--S 259 of 526 +d0448:= D(m0448,x) +--R +--R +--R (181) +--R +------------+ +--R +---+ x | 2 x 2 2 x 2 +--R 2\|- 1 %e tanh(x)\|tanh(x) - 1 + (- (%e ) + 1)tanh(x) + (%e ) - 1 +--R ---------------------------------------------------------------------- +--R +------------+ +--R x 2 | 2 +--R ((%e ) - 1)tanh(x)\|tanh(x) - 1 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 526 +t0449:= (csch(x)^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R (182) \|csch(x) +--R Type: Expression(Integer) +--E 260 + +--S 261 of 526 +r0449:= -acoth(cosh(x))*csgn(1/sinh(x)) +--R +--R There are no library operations named csgn +--R Use HyperDoc Browse or issue +--R )what op csgn +--R to learn if there is any operation containing " csgn " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named csgn +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 261 + +--S 262 of 526 +a0449:= integrate(t0449,x) +--R +--R +--R (183) - log(sinh(x) + cosh(x) + 1) + log(sinh(x) + cosh(x) - 1) +--R Type: Union(Expression(Integer),...) +--E 262 + +--S 263 of 526 +--m0449:= a0449-r0449 +--E 263 + +--S 264 of 526 +--d0449:= D(m0449,x) +--E 264 + +--S 265 of 526 +t0450:= (csch(x)^3)^(1/2) +--R +--R +--R +--------+ +--R | 3 +--R (184) \|csch(x) +--R Type: Expression(Integer) +--E 265 + +--S 266 of 526 +r0450:= -2*(csch(x)^3)^(1/2)*(coth(x)+_ + %i*EllipticE(-1/4*%pi+1/2*%i*x,2)/(%i*sinh(x))^(1/2))*sinh(x)^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 266 + +--S 267 of 526 +a0450:= integrate(t0450,x) +--R +--R +--R x +---------+ +--R ++ | 3 +--I (185) | \|csch(%R) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 267 + +--S 268 of 526 +--m0450:= a0450-r0450 +--E 268 + +--S 269 of 526 +--d0450:= D(m0450,x) +--E 269 + +--S 270 of 526 +t0451:= (csch(x)^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (186) \|csch(x) +--R Type: Expression(Integer) +--E 270 + +--S 271 of 526 +r0451:= -cosh(x)*csgn(1/sinh(x)^2)/sinh(x) +--R +--R There are no library operations named csgn +--R Use HyperDoc Browse or issue +--R )what op csgn +--R to learn if there is any operation containing " csgn " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named csgn +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 271 + +--S 272 of 526 +a0451:= integrate(t0451,x) +--R +--R +--R 2 +--R (187) - ----------------------------------------- +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 272 + +--S 273 of 526 +--m0451:= a0451-r0451 +--E 273 + +--S 274 of 526 +--d0451:= D(m0451,x) +--E 274 + +--S 275 of 526 +t0452:= 1/(a+%i*a*csch(a+b*x)) +--R +--R +--R %i +--R (188) - ---------------------- +--R a csch(b x + a) - %i a +--R Type: Expression(Complex(Integer)) +--E 275 + +--S 276 of 526 +r0452:= x/a+%i*cosh(a+b*x)/a/b/(1-%i*sinh(a+b*x)) +--R +--R +--R b x sinh(b x + a) - cosh(b x + a) + %i b x +--R (189) ------------------------------------------ +--R a b sinh(b x + a) + %i a b +--R Type: Expression(Complex(Integer)) +--E 276 + +--S 277 of 526 +a0452:= integrate(t0452,x) +--R +--R +--R b x sinh(b x + a) + b x cosh(b x + a) + %i b x + 2%i +--R (190) ---------------------------------------------------- +--R a b sinh(b x + a) + a b cosh(b x + a) + %i a b +--R Type: Union(Expression(Complex(Integer)),...) +--E 277 + +--S 278 of 526 +m0452:= a0452-r0452 +--R +--R +--R (191) +--R 2 +--R (cosh(b x + a) + 2%i)sinh(b x + a) + cosh(b x + a) + %i cosh(b x + a) - 2 +--R / +--R 2 +--R a b sinh(b x + a) + (a b cosh(b x + a) + 2%i a b)sinh(b x + a) +--R + +--R %i a b cosh(b x + a) - a b +--R Type: Expression(Complex(Integer)) +--E 278 + +--S 279 of 526 +d0452:= D(m0452,x) +--R +--R +--R (192) +--R 4 3 +--R sinh(b x + a) + (2cosh(b x + a) + %i)sinh(b x + a) +--R + +--R 2 +--R (2%i cosh(b x + a) + 1)sinh(b x + a) +--R + +--R 3 2 +--R (- 2cosh(b x + a) - %i cosh(b x + a) + 2cosh(b x + a) + %i) +--R * +--R sinh(b x + a) +--R + +--R 4 3 2 +--R - cosh(b x + a) - 2%i cosh(b x + a) + cosh(b x + a) + 2%i cosh(b x + a) +--R / +--R 4 3 +--R a sinh(b x + a) + (2a cosh(b x + a) + 4%i a)sinh(b x + a) +--R + +--R 2 2 +--R (a cosh(b x + a) + 6%i a cosh(b x + a) - 6a)sinh(b x + a) +--R + +--R 2 +--R (2%i a cosh(b x + a) - 6a cosh(b x + a) - 4%i a)sinh(b x + a) +--R + +--R 2 +--R - a cosh(b x + a) - 2%i a cosh(b x + a) + a +--R Type: Expression(Complex(Integer)) +--E 279 + +--S 280 of 526 +t0453:= 1/(a-%i*a*csch(a+b*x)) +--R +--R +--R %i +--R (193) ---------------------- +--R a csch(b x + a) + %i a +--R Type: Expression(Complex(Integer)) +--E 280 + +--S 281 of 526 +r0453:= x/a-%i*cosh(a+b*x)/a/b/(1+%i*sinh(a+b*x)) +--R +--R +--R b x sinh(b x + a) - cosh(b x + a) - %i b x +--R (194) ------------------------------------------ +--R a b sinh(b x + a) - %i a b +--R Type: Expression(Complex(Integer)) +--E 281 + +--S 282 of 526 +a0453:= integrate(t0453,x) +--R +--R +--R b x sinh(b x + a) + b x cosh(b x + a) - %i b x - 2%i +--R (195) ---------------------------------------------------- +--R a b sinh(b x + a) + a b cosh(b x + a) - %i a b +--R Type: Union(Expression(Complex(Integer)),...) +--E 282 + +--S 283 of 526 +m0453:= a0453-r0453 +--R +--R +--R (196) +--R 2 +--R (cosh(b x + a) - 2%i)sinh(b x + a) + cosh(b x + a) - %i cosh(b x + a) - 2 +--R / +--R 2 +--R a b sinh(b x + a) + (a b cosh(b x + a) - 2%i a b)sinh(b x + a) +--R + +--R - %i a b cosh(b x + a) - a b +--R Type: Expression(Complex(Integer)) +--E 283 + +--S 284 of 526 +d0453:= D(m0453,x) +--R +--R +--R (197) +--R 4 3 +--R sinh(b x + a) + (2cosh(b x + a) - %i)sinh(b x + a) +--R + +--R 2 +--R (- 2%i cosh(b x + a) + 1)sinh(b x + a) +--R + +--R 3 2 +--R (- 2cosh(b x + a) + %i cosh(b x + a) + 2cosh(b x + a) - %i) +--R * +--R sinh(b x + a) +--R + +--R 4 3 2 +--R - cosh(b x + a) + 2%i cosh(b x + a) + cosh(b x + a) - 2%i cosh(b x + a) +--R / +--R 4 3 +--R a sinh(b x + a) + (2a cosh(b x + a) - 4%i a)sinh(b x + a) +--R + +--R 2 2 +--R (a cosh(b x + a) - 6%i a cosh(b x + a) - 6a)sinh(b x + a) +--R + +--R 2 +--R (- 2%i a cosh(b x + a) - 6a cosh(b x + a) + 4%i a)sinh(b x + a) +--R + +--R 2 +--R - a cosh(b x + a) + 2%i a cosh(b x + a) + a +--R Type: Expression(Complex(Integer)) +--E 284 + +--S 285 of 526 +t0454:= (3+3*%i*csch(x))^(1/2) +--R +--R +--R +---------------+ +--R (198) \|3%i csch(x) + 3 +--R Type: Expression(Complex(Integer)) +--E 285 + +--S 286 of 526 +r0454:= 2*3^(1/2)*atan((-1+%i*csch(x))^(1/2))*_ + coth(x)/(-1+%i*csch(x))^(1/2)/(1+%i*csch(x))^(1/2) +--R +--R +--R +-+ +--------------+ +--R 2\|3 coth(x)atan(\|%i csch(x) - 1 ) +--R (199) ----------------------------------- +--R +--------------+ +--------------+ +--R \|%i csch(x) - 1 \|%i csch(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 286 + +--S 287 of 526 +a0454:= integrate(t0454,x) +--R +--R +--R (200) +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- - \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R - \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R \|3 +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) - 2%i cosh(x) +--R + +--R - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R - %i\|3 sinh(x) + (- 3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 3%i\|3 cosh(x) - 2\|3 cosh(x) + %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - %i\|3 cosh(x) - \|3 cosh(x) + %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 287 + +--S 288 of 526 +m0454:= a0454-r0454 +--R +--R +--R (201) +--R - +--R +-+ +--------------+ +--------------+ +--R \|3 \|%i csch(x) - 1 \|%i csch(x) + 1 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- - \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R - \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--------------+ +--------------+ +--R \|3 \|%i csch(x) - 1 \|%i csch(x) + 1 +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R - %i\|3 sinh(x) + (- 3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 3%i\|3 cosh(x) - 2\|3 cosh(x) + %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - %i\|3 cosh(x) - \|3 cosh(x) + %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--------------+ +--R - 2\|3 coth(x)atan(\|%i csch(x) - 1 ) +--R / +--R +--------------+ +--------------+ +--R \|%i csch(x) - 1 \|%i csch(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 288 + +--S 289 of 526 +d0454:= D(m0454,x) +--R +--R +--R (202) +--R 2 2 6 +--R (- 6csch(x) + 6coth(x) - 6)sinh(x) +--R + +--R 2 2 5 +--R (- 36cosh(x)csch(x) + 36cosh(x)coth(x) - 36cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R (- 90cosh(x) - 6)csch(x) + (90cosh(x) + 6)coth(x) +--R + +--R 2 +--R - 90cosh(x) - 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 120cosh(x) - 24cosh(x))csch(x) +--R + +--R 3 2 3 +--R (120cosh(x) + 24cosh(x))coth(x) - 120cosh(x) - 24cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 90cosh(x) - 36cosh(x) + 36)csch(x) +--R + +--R 4 2 2 4 +--R (90cosh(x) + 36cosh(x) - 36)coth(x) - 90cosh(x) +--R + +--R 2 +--R - 36cosh(x) + 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 36cosh(x) - 24cosh(x) + 72cosh(x))csch(x) +--R + +--R 5 3 2 5 +--R (36cosh(x) + 24cosh(x) - 72cosh(x))coth(x) - 36cosh(x) +--R + +--R 3 +--R - 24cosh(x) + 72cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 6cosh(x) - 6cosh(x) + 36cosh(x) - 24)csch(x) +--R + +--R 6 4 2 2 6 +--R (6cosh(x) + 6cosh(x) - 36cosh(x) + 24)coth(x) - 6cosh(x) +--R + +--R 4 2 +--R - 6cosh(x) + 36cosh(x) - 24 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 +-+ 6 +--R (6%i\|3 csch(x) - 6%i\|3 coth(x) + 6%i\|3 )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R 36%i\|3 cosh(x)csch(x) - 36%i\|3 cosh(x)coth(x) +--R + +--R +-+ +--R 36%i\|3 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 6%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (- 90%i\|3 cosh(x) + 6%i\|3 )coth(x) + 90%i\|3 cosh(x) - 6%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (120%i\|3 cosh(x) - 24%i\|3 cosh(x))csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 120%i\|3 cosh(x) + 24%i\|3 cosh(x))coth(x) +--R + +--R +-+ 3 +-+ +--R 120%i\|3 cosh(x) - 24%i\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 )coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x))coth(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 ) +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 ) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 +--R * +--R +--------------+ +--R atan(\|%i csch(x) - 1 ) +--R + +--R 2 6 +--R (- 6csch(x) - 6)sinh(x) +--R + +--R 2 5 +--R ((- 36cosh(x) + 18%i)csch(x) - 36cosh(x) + 18%i)sinh(x) +--R + +--R 2 2 2 +--R (- 90cosh(x) + 90%i cosh(x) - 3)csch(x) - 90cosh(x) +--R + +--R 90%i cosh(x) - 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 120cosh(x) + 180%i cosh(x) - 12cosh(x) - 30%i)csch(x) +--R + +--R 3 2 +--R - 120cosh(x) + 180%i cosh(x) - 12cosh(x) - 30%i +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R - 90cosh(x) + 180%i cosh(x) - 18cosh(x) - 90%i cosh(x) +--R + +--R 24 +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R - 90cosh(x) + 180%i cosh(x) - 18cosh(x) - 90%i cosh(x) + 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 36cosh(x) + 90%i cosh(x) - 12cosh(x) - 90%i cosh(x) +--R + +--R 48cosh(x) + 12%i +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 2 +--R - 36cosh(x) + 90%i cosh(x) - 12cosh(x) - 90%i cosh(x) +--R + +--R 48cosh(x) + 12%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 6cosh(x) + 18%i cosh(x) - 3cosh(x) - 30%i cosh(x) +--R + +--R 2 +--R 24cosh(x) + 12%i cosh(x) - 12 +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R - 6cosh(x) + 18%i cosh(x) - 3cosh(x) - 30%i cosh(x) +--R + +--R 2 +--R 24cosh(x) + 12%i cosh(x) - 12 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 6 +--R (3%i\|3 csch(x) + 3%i\|3 )sinh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ 5 +--R ((18%i\|3 cosh(x) + 6\|3 )csch(x) + 18%i\|3 cosh(x) + 6\|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (45%i\|3 cosh(x) + 30\|3 cosh(x) - 3%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ +-+ +--R 45%i\|3 cosh(x) + 30\|3 cosh(x) - 3%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (60%i\|3 cosh(x) + 60\|3 cosh(x) - 12%i\|3 cosh(x) - 24\|3 ) +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 60%i\|3 cosh(x) + 60\|3 cosh(x) - 12%i\|3 cosh(x) - 24\|3 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 45%i\|3 cosh(x) + 60\|3 cosh(x) - 18%i\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72\|3 cosh(x) - 18%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 45%i\|3 cosh(x) + 60\|3 cosh(x) - 18%i\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72\|3 cosh(x) - 18%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 18%i\|3 cosh(x) + 30\|3 cosh(x) - 12%i\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72\|3 cosh(x) - 36%i\|3 cosh(x) + 12\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 18%i\|3 cosh(x) + 30\|3 cosh(x) - 12%i\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72\|3 cosh(x) - 36%i\|3 cosh(x) + 12\|3 +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 3%i\|3 cosh(x) + 6\|3 cosh(x) - 3%i\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24\|3 cosh(x) - 18%i\|3 cosh(x) + 12\|3 cosh(x) + 12%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 3%i\|3 cosh(x) + 6\|3 cosh(x) - 3%i\|3 cosh(x) - 24\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 18%i\|3 cosh(x) + 12\|3 cosh(x) + 12%i\|3 +--R * +--R +--------------+ +--------------+ +--R \|%i csch(x) - 1 \|%i csch(x) + 1 +--R + +--R 2 2 6 +--R (- 3%i coth(x) csch(x) - 3coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (- 18%i cosh(x)coth(x) csch(x) - 18cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 +--R (- 45%i cosh(x) - 3%i)coth(x) csch(x) +--R + +--R 2 2 +--R (- 45cosh(x) - 3)coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 60%i cosh(x) - 12%i cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (- 60cosh(x) - 12cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 45%i cosh(x) - 18%i cosh(x) + 18%i)coth(x) csch(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) - 18cosh(x) + 18)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) - 12%i cosh(x) + 36%i cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R 5 3 2 +--R (- 18cosh(x) - 12cosh(x) + 36cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) - 3%i cosh(x) + 18%i cosh(x) - 12%i)coth(x) +--R * +--R csch(x) +--R + +--R 6 4 2 2 +--R (- 3cosh(x) - 3cosh(x) + 18cosh(x) - 12)coth(x) +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 6 +--R (- 3\|3 coth(x) csch(x) + 3%i\|3 coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 5 +--R (- 18\|3 cosh(x)coth(x) csch(x) + 18%i\|3 cosh(x)coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 45\|3 cosh(x) + 3\|3 )coth(x) csch(x) +--R + +--R +-+ 2 +-+ 2 +--R (45%i\|3 cosh(x) - 3%i\|3 )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 60\|3 cosh(x) + 12\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (60%i\|3 cosh(x) - 12%i\|3 cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 45\|3 cosh(x) + 18\|3 cosh(x) + 12\|3 )coth(x) csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (45%i\|3 cosh(x) - 18%i\|3 cosh(x) - 12%i\|3 )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 18\|3 cosh(x) + 12\|3 cosh(x) + 24\|3 cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (18%i\|3 cosh(x) - 12%i\|3 cosh(x) - 24%i\|3 cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (- 3\|3 cosh(x) + 3\|3 cosh(x) + 12\|3 cosh(x) - 12\|3 )coth(x) +--R * +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (3%i\|3 cosh(x) - 3%i\|3 cosh(x) - 12%i\|3 cosh(x) + 12%i\|3 ) +--R * +--R 2 +--R coth(x) +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R / +--R +-+ 2 +-+ 6 +--R (\|3 csch(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (6\|3 cosh(x)csch(x) + 6\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((15\|3 cosh(x) + \|3 )csch(x) + 15\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (20\|3 cosh(x) + 4\|3 cosh(x))csch(x) + 20\|3 cosh(x) +--R + +--R +-+ +--R 4\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (\|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 )csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R \|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- 3%i csch(x) - 3%i)sinh(x) +--R + +--R 2 5 +--R (- 18%i cosh(x)csch(x) - 18%i cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 45%i cosh(x) + 3%i)csch(x) - 45%i cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (- 60%i cosh(x) + 12%i cosh(x))csch(x) - 60%i cosh(x) +--R + +--R 12%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 45%i cosh(x) + 18%i cosh(x) + 12%i)csch(x) - 45%i cosh(x) +--R + +--R 2 +--R 18%i cosh(x) + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x))csch(x) +--R + +--R 5 3 +--R - 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i)csch(x) +--R + +--R 6 4 2 +--R - 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i +--R * +--R +--------------+ +--------------+ +--R \|%i csch(x) - 1 \|%i csch(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 289 + +--S 290 of 526 +t0455:= (3-3*%i*csch(x))^(1/2) +--R +--R +--R +-----------------+ +--R (203) \|- 3%i csch(x) + 3 +--R Type: Expression(Complex(Integer)) +--E 290 + +--S 291 of 526 +r0455:= 2*3^(1/2)*atan((-1-%i*csch(x))^(1/2))*_ + coth(x)/(-1-%i*csch(x))^(1/2)/(1-%i*csch(x))^(1/2) +--R +--R +--R +-+ +----------------+ +--R 2\|3 coth(x)atan(\|- %i csch(x) - 1 ) +--R (204) -------------------------------------- +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 291 + +--S 292 of 526 +a0455:= integrate(t0455,x) +--R +--R +--R (205) +--R +-+ +--R \|3 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- + \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|3 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R %i\|3 sinh(x) + (3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (3%i\|3 cosh(x) - 2\|3 cosh(x) - %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R %i\|3 cosh(x) - \|3 cosh(x) - %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 292 + +--S 293 of 526 +m0455:= a0455-r0455 +--R +--R +--R (206) +--R +-+ +----------------+ +----------------+ +--R \|3 \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- + \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +----------------+ +----------------+ +--R \|3 \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R %i\|3 sinh(x) + (3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (3%i\|3 cosh(x) - 2\|3 cosh(x) - %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R %i\|3 cosh(x) - \|3 cosh(x) - %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +----------------+ +--R - 2\|3 coth(x)atan(\|- %i csch(x) - 1 ) +--R / +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 293 + +--S 294 of 526 +d0455:= D(m0455,x) +--R +--R +--R (207) +--R 2 2 6 +--R (- 6csch(x) + 6coth(x) - 6)sinh(x) +--R + +--R 2 2 5 +--R (- 36cosh(x)csch(x) + 36cosh(x)coth(x) - 36cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R (- 90cosh(x) - 6)csch(x) + (90cosh(x) + 6)coth(x) +--R + +--R 2 +--R - 90cosh(x) - 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 120cosh(x) - 24cosh(x))csch(x) +--R + +--R 3 2 3 +--R (120cosh(x) + 24cosh(x))coth(x) - 120cosh(x) - 24cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 90cosh(x) - 36cosh(x) + 36)csch(x) +--R + +--R 4 2 2 4 +--R (90cosh(x) + 36cosh(x) - 36)coth(x) - 90cosh(x) +--R + +--R 2 +--R - 36cosh(x) + 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 36cosh(x) - 24cosh(x) + 72cosh(x))csch(x) +--R + +--R 5 3 2 5 +--R (36cosh(x) + 24cosh(x) - 72cosh(x))coth(x) - 36cosh(x) +--R + +--R 3 +--R - 24cosh(x) + 72cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 6cosh(x) - 6cosh(x) + 36cosh(x) - 24)csch(x) +--R + +--R 6 4 2 2 6 +--R (6cosh(x) + 6cosh(x) - 36cosh(x) + 24)coth(x) - 6cosh(x) +--R + +--R 4 2 +--R - 6cosh(x) + 36cosh(x) - 24 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 +-+ 6 +--R (6%i\|3 csch(x) - 6%i\|3 coth(x) + 6%i\|3 )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R 36%i\|3 cosh(x)csch(x) - 36%i\|3 cosh(x)coth(x) +--R + +--R +-+ +--R 36%i\|3 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 6%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (- 90%i\|3 cosh(x) + 6%i\|3 )coth(x) + 90%i\|3 cosh(x) - 6%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (120%i\|3 cosh(x) - 24%i\|3 cosh(x))csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 120%i\|3 cosh(x) + 24%i\|3 cosh(x))coth(x) +--R + +--R +-+ 3 +-+ +--R 120%i\|3 cosh(x) - 24%i\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 )coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x))coth(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 ) +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 ) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 +--R * +--R +----------------+ +--R atan(\|- %i csch(x) - 1 ) +--R + +--R 2 6 +--R (6csch(x) + 6)sinh(x) +--R + +--R 2 5 +--R ((36cosh(x) + 18%i)csch(x) + 36cosh(x) + 18%i)sinh(x) +--R + +--R 2 2 2 +--R (90cosh(x) + 90%i cosh(x) + 3)csch(x) + 90cosh(x) +--R + +--R 90%i cosh(x) + 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (120cosh(x) + 180%i cosh(x) + 12cosh(x) - 30%i)csch(x) +--R + +--R 3 2 +--R 120cosh(x) + 180%i cosh(x) + 12cosh(x) - 30%i +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 90cosh(x) + 180%i cosh(x) + 18cosh(x) - 90%i cosh(x) +--R + +--R - 24 +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R 90cosh(x) + 180%i cosh(x) + 18cosh(x) - 90%i cosh(x) - 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 36cosh(x) + 90%i cosh(x) + 12cosh(x) - 90%i cosh(x) +--R + +--R - 48cosh(x) + 12%i +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 2 +--R 36cosh(x) + 90%i cosh(x) + 12cosh(x) - 90%i cosh(x) +--R + +--R - 48cosh(x) + 12%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R 6cosh(x) + 18%i cosh(x) + 3cosh(x) - 30%i cosh(x) +--R + +--R 2 +--R - 24cosh(x) + 12%i cosh(x) + 12 +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R 6cosh(x) + 18%i cosh(x) + 3cosh(x) - 30%i cosh(x) +--R + +--R 2 +--R - 24cosh(x) + 12%i cosh(x) + 12 +--R * +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R + +--R 2 2 6 +--R (3%i coth(x) csch(x) - 3coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (18%i cosh(x)coth(x) csch(x) - 18cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 +--R (45%i cosh(x) + 3%i)coth(x) csch(x) +--R + +--R 2 2 +--R (- 45cosh(x) - 3)coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (60%i cosh(x) + 12%i cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (- 60cosh(x) - 12cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (45%i cosh(x) + 18%i cosh(x) - 18%i)coth(x) csch(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) - 18cosh(x) + 18)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (18%i cosh(x) + 12%i cosh(x) - 36%i cosh(x))coth(x) csch(x) +--R + +--R 5 3 2 +--R (- 18cosh(x) - 12cosh(x) + 36cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (3%i cosh(x) + 3%i cosh(x) - 18%i cosh(x) + 12%i)coth(x) +--R * +--R csch(x) +--R + +--R 6 4 2 2 +--R (- 3cosh(x) - 3cosh(x) + 18cosh(x) - 12)coth(x) +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 6 +--R (- 3%i\|3 csch(x) - 3%i\|3 )sinh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ +--R ((- 18%i\|3 cosh(x) + 6\|3 )csch(x) - 18%i\|3 cosh(x) + 6\|3 ) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (- 45%i\|3 cosh(x) + 30\|3 cosh(x) + 3%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 45%i\|3 cosh(x) + 30\|3 cosh(x) + 3%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 60%i\|3 cosh(x) + 60\|3 cosh(x) + 12%i\|3 cosh(x) +--R + +--R +-+ +--R - 24\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 60%i\|3 cosh(x) + 60\|3 cosh(x) + 12%i\|3 cosh(x) - 24\|3 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 45%i\|3 cosh(x) + 60\|3 cosh(x) + 18%i\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72\|3 cosh(x) + 18%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 45%i\|3 cosh(x) + 60\|3 cosh(x) + 18%i\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72\|3 cosh(x) + 18%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 18%i\|3 cosh(x) + 30\|3 cosh(x) + 12%i\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72\|3 cosh(x) + 36%i\|3 cosh(x) + 12\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 18%i\|3 cosh(x) + 30\|3 cosh(x) + 12%i\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72\|3 cosh(x) + 36%i\|3 cosh(x) + 12\|3 +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 3%i\|3 cosh(x) + 6\|3 cosh(x) + 3%i\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24\|3 cosh(x) + 18%i\|3 cosh(x) + 12\|3 cosh(x) - 12%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R - 3%i\|3 cosh(x) + 6\|3 cosh(x) + 3%i\|3 cosh(x) - 24\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R 18%i\|3 cosh(x) + 12\|3 cosh(x) - 12%i\|3 +--R * +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R + +--R +-+ 2 +-+ 2 6 +--R (3\|3 coth(x) csch(x) + 3%i\|3 coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 5 +--R (18\|3 cosh(x)coth(x) csch(x) + 18%i\|3 cosh(x)coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (45\|3 cosh(x) - 3\|3 )coth(x) csch(x) +--R + +--R +-+ 2 +-+ 2 +--R (45%i\|3 cosh(x) - 3%i\|3 )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (60\|3 cosh(x) - 12\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (60%i\|3 cosh(x) - 12%i\|3 cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (45\|3 cosh(x) - 18\|3 cosh(x) - 12\|3 )coth(x) csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (45%i\|3 cosh(x) - 18%i\|3 cosh(x) - 12%i\|3 )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (18\|3 cosh(x) - 12\|3 cosh(x) - 24\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (18%i\|3 cosh(x) - 12%i\|3 cosh(x) - 24%i\|3 cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (3\|3 cosh(x) - 3\|3 cosh(x) - 12\|3 cosh(x) + 12\|3 )coth(x) +--R * +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (3%i\|3 cosh(x) - 3%i\|3 cosh(x) - 12%i\|3 cosh(x) + 12%i\|3 ) +--R * +--R 2 +--R coth(x) +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R / +--R +-+ 2 +-+ 6 +--R (\|3 csch(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (6\|3 cosh(x)csch(x) + 6\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((15\|3 cosh(x) + \|3 )csch(x) + 15\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (20\|3 cosh(x) + 4\|3 cosh(x))csch(x) + 20\|3 cosh(x) +--R + +--R +-+ +--R 4\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +-+ 4 +--R (15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 )csch(x) + 15\|3 cosh(x) +--R + +--R +-+ 2 +-+ +--R 6\|3 cosh(x) - 6\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (\|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 )csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R \|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 +--R * +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- 3%i csch(x) - 3%i)sinh(x) +--R + +--R 2 5 +--R (- 18%i cosh(x)csch(x) - 18%i cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 45%i cosh(x) + 3%i)csch(x) - 45%i cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (- 60%i cosh(x) + 12%i cosh(x))csch(x) - 60%i cosh(x) +--R + +--R 12%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 45%i cosh(x) + 18%i cosh(x) + 12%i)csch(x) - 45%i cosh(x) +--R + +--R 2 +--R 18%i cosh(x) + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x))csch(x) +--R + +--R 5 3 +--R - 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i)csch(x) +--R + +--R 6 4 2 +--R - 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i +--R * +--R +----------------+ +----------------+ +--R \|- %i csch(x) - 1 \|- %i csch(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 294 + +--S 295 of 526 +t0456:= (-3+3*%i*csch(x))^(1/2) +--R +--R +--R +---------------+ +--R (208) \|3%i csch(x) - 3 +--R Type: Expression(Complex(Integer)) +--E 295 + +--S 296 of 526 +r0456:= -2*3^(1/2)*atan((-1-%i*csch(x))^(1/2))*_ + coth(x)/(-1-%i*csch(x))^(1/2)/(-1+%i*csch(x))^(1/2) +--R +--R +--R +-+ +----------------+ +--R 2\|3 coth(x)atan(\|- %i csch(x) - 1 ) +--R (209) - ------------------------------------- +--R +----------------+ +--------------+ +--R \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 296 + +--S 297 of 526 +a0456:= integrate(t0456,x) +--R +--R +--R (210) +--R +-+ +--R %i\|3 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- + \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R %i\|3 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R %i\|3 sinh(x) + (3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (3%i\|3 cosh(x) - 2\|3 cosh(x) - %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R %i\|3 cosh(x) - \|3 cosh(x) - %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 297 + +--S 298 of 526 +m0456:= a0456-r0456 +--R +--R +--R (211) +--R +-+ +----------------+ +--------------+ +--R %i\|3 \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- + \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +----------------+ +--------------+ +--R %i\|3 \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R %i\|3 sinh(x) + (3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (3%i\|3 cosh(x) - 2\|3 cosh(x) - %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R %i\|3 cosh(x) - \|3 cosh(x) - %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +----------------+ +--R 2\|3 coth(x)atan(\|- %i csch(x) - 1 ) +--R / +--R +----------------+ +--------------+ +--R \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 298 + +--S 299 of 526 +d0456:= D(m0456,x) +--R +--R +--R (212) +--R 2 2 6 +--R (6csch(x) - 6coth(x) + 6)sinh(x) +--R + +--R 2 2 5 +--R (36cosh(x)csch(x) - 36cosh(x)coth(x) + 36cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R (90cosh(x) + 6)csch(x) + (- 90cosh(x) - 6)coth(x) +--R + +--R 2 +--R 90cosh(x) + 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (120cosh(x) + 24cosh(x))csch(x) +--R + +--R 3 2 3 +--R (- 120cosh(x) - 24cosh(x))coth(x) + 120cosh(x) + 24cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (90cosh(x) + 36cosh(x) - 36)csch(x) +--R + +--R 4 2 2 4 +--R (- 90cosh(x) - 36cosh(x) + 36)coth(x) + 90cosh(x) +--R + +--R 2 +--R 36cosh(x) - 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (36cosh(x) + 24cosh(x) - 72cosh(x))csch(x) +--R + +--R 5 3 2 5 +--R (- 36cosh(x) - 24cosh(x) + 72cosh(x))coth(x) + 36cosh(x) +--R + +--R 3 +--R 24cosh(x) - 72cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (6cosh(x) + 6cosh(x) - 36cosh(x) + 24)csch(x) +--R + +--R 6 4 2 2 6 +--R (- 6cosh(x) - 6cosh(x) + 36cosh(x) - 24)coth(x) + 6cosh(x) +--R + +--R 4 2 +--R 6cosh(x) - 36cosh(x) + 24 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 +-+ 6 +--R (- 6%i\|3 csch(x) + 6%i\|3 coth(x) - 6%i\|3 )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R - 36%i\|3 cosh(x)csch(x) + 36%i\|3 cosh(x)coth(x) +--R + +--R +-+ +--R - 36%i\|3 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 6%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (90%i\|3 cosh(x) - 6%i\|3 )coth(x) - 90%i\|3 cosh(x) + 6%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 120%i\|3 cosh(x) + 24%i\|3 cosh(x))csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (120%i\|3 cosh(x) - 24%i\|3 cosh(x))coth(x) - 120%i\|3 cosh(x) +--R + +--R +-+ +--R 24%i\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 )coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x))coth(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 ) +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 ) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 +--R * +--R +----------------+ +--R atan(\|- %i csch(x) - 1 ) +--R + +--R 2 6 +--R (6%i csch(x) + 6%i)sinh(x) +--R + +--R 2 5 +--R ((36%i cosh(x) - 18)csch(x) + 36%i cosh(x) - 18)sinh(x) +--R + +--R 2 2 2 +--R (90%i cosh(x) - 90cosh(x) + 3%i)csch(x) + 90%i cosh(x) +--R + +--R - 90cosh(x) + 3%i +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (120%i cosh(x) - 180cosh(x) + 12%i cosh(x) + 30)csch(x) +--R + +--R 3 2 +--R 120%i cosh(x) - 180cosh(x) + 12%i cosh(x) + 30 +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 90%i cosh(x) - 180cosh(x) + 18%i cosh(x) + 90cosh(x) +--R + +--R - 24%i +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R 90%i cosh(x) - 180cosh(x) + 18%i cosh(x) + 90cosh(x) - 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 36%i cosh(x) - 90cosh(x) + 12%i cosh(x) + 90cosh(x) +--R + +--R - 48%i cosh(x) - 12 +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 2 +--R 36%i cosh(x) - 90cosh(x) + 12%i cosh(x) + 90cosh(x) +--R + +--R - 48%i cosh(x) - 12 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R 6%i cosh(x) - 18cosh(x) + 3%i cosh(x) + 30cosh(x) +--R + +--R 2 +--R - 24%i cosh(x) - 12cosh(x) + 12%i +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R 6%i cosh(x) - 18cosh(x) + 3%i cosh(x) + 30cosh(x) +--R + +--R 2 +--R - 24%i cosh(x) - 12cosh(x) + 12%i +--R * +--R +-----------------------------------------+ +--R +----------------+ | 3 +--R \|- %i csch(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 6 +--R (3\|3 csch(x) + 3\|3 )sinh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ +--R ((18\|3 cosh(x) + 6%i\|3 )csch(x) + 18\|3 cosh(x) + 6%i\|3 ) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (45\|3 cosh(x) + 30%i\|3 cosh(x) - 3\|3 )csch(x) +--R + +--R +-+ 2 +-+ +-+ +--R 45\|3 cosh(x) + 30%i\|3 cosh(x) - 3\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 60\|3 cosh(x) + 60%i\|3 cosh(x) - 12\|3 cosh(x) +--R + +--R +-+ +--R - 24%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 60\|3 cosh(x) + 60%i\|3 cosh(x) - 12\|3 cosh(x) - 24%i\|3 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 45\|3 cosh(x) + 60%i\|3 cosh(x) - 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72%i\|3 cosh(x) - 18\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 45\|3 cosh(x) + 60%i\|3 cosh(x) - 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72%i\|3 cosh(x) - 18\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 18\|3 cosh(x) + 30%i\|3 cosh(x) - 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72%i\|3 cosh(x) - 36\|3 cosh(x) + 12%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 18\|3 cosh(x) + 30%i\|3 cosh(x) - 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72%i\|3 cosh(x) - 36\|3 cosh(x) + 12%i\|3 +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 3\|3 cosh(x) + 6%i\|3 cosh(x) - 3\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24%i\|3 cosh(x) - 18\|3 cosh(x) + 12%i\|3 cosh(x) + 12\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 3\|3 cosh(x) + 6%i\|3 cosh(x) - 3\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24%i\|3 cosh(x) - 18\|3 cosh(x) + 12%i\|3 cosh(x) + 12\|3 +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R + +--R 2 2 6 +--R (- 3%i coth(x) csch(x) + 3coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (- 18%i cosh(x)coth(x) csch(x) + 18cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 2 2 +--R ((- 45%i cosh(x) - 3%i)coth(x) csch(x) + (45cosh(x) + 3)coth(x) ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 60%i cosh(x) - 12%i cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (60cosh(x) + 12cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 45%i cosh(x) - 18%i cosh(x) + 18%i)coth(x) csch(x) +--R + +--R 4 2 2 +--R (45cosh(x) + 18cosh(x) - 18)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) - 12%i cosh(x) + 36%i cosh(x))coth(x) csch(x) +--R + +--R 5 3 2 +--R (18cosh(x) + 12cosh(x) - 36cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) - 3%i cosh(x) + 18%i cosh(x) - 12%i)coth(x) csch(x) +--R + +--R 6 4 2 2 +--R (3cosh(x) + 3cosh(x) - 18cosh(x) + 12)coth(x) +--R * +--R +-----------------------------------------+ +--R +----------------+ | 3 +--R \|- %i csch(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 6 +--R (- 3\|3 coth(x) csch(x) - 3%i\|3 coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 5 +--R (- 18\|3 cosh(x)coth(x) csch(x) - 18%i\|3 cosh(x)coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 45\|3 cosh(x) + 3\|3 )coth(x) csch(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 45%i\|3 cosh(x) + 3%i\|3 )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 60\|3 cosh(x) + 12\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 60%i\|3 cosh(x) + 12%i\|3 cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 45\|3 cosh(x) + 18\|3 cosh(x) + 12\|3 )coth(x) csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 45%i\|3 cosh(x) + 18%i\|3 cosh(x) + 12%i\|3 )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 18\|3 cosh(x) + 12\|3 cosh(x) + 24\|3 cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 18%i\|3 cosh(x) + 12%i\|3 cosh(x) + 24%i\|3 cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (- 3\|3 cosh(x) + 3\|3 cosh(x) + 12\|3 cosh(x) - 12\|3 )coth(x) +--R * +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 3%i\|3 cosh(x) + 3%i\|3 cosh(x) + 12%i\|3 cosh(x) - 12%i\|3 ) +--R * +--R 2 +--R coth(x) +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R / +--R +-+ 2 +-+ 6 +--R (\|3 csch(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (6\|3 cosh(x)csch(x) + 6\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((15\|3 cosh(x) + \|3 )csch(x) + 15\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (20\|3 cosh(x) + 4\|3 cosh(x))csch(x) + 20\|3 cosh(x) +--R + +--R +-+ +--R 4\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (\|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 )csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R \|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 +--R * +--R +-----------------------------------------+ +--R +----------------+ | 3 +--R \|- %i csch(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- 3%i csch(x) - 3%i)sinh(x) +--R + +--R 2 5 +--R (- 18%i cosh(x)csch(x) - 18%i cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 45%i cosh(x) + 3%i)csch(x) - 45%i cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (- 60%i cosh(x) + 12%i cosh(x))csch(x) - 60%i cosh(x) +--R + +--R 12%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 45%i cosh(x) + 18%i cosh(x) + 12%i)csch(x) +--R + +--R 4 2 +--R - 45%i cosh(x) + 18%i cosh(x) + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x))csch(x) +--R + +--R 5 3 +--R - 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i)csch(x) +--R + +--R 6 4 2 +--R - 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 299 + +--S 300 of 526 +t0457:= (-3-3*%i*csch(x))^(1/2) +--R +--R +--R +-----------------+ +--R (213) \|- 3%i csch(x) - 3 +--R Type: Expression(Complex(Integer)) +--E 300 + +--S 301 of 526 +r0457:= -2*3^(1/2)*atan((-1+%i*csch(x))^(1/2))*_ + coth(x)/(-1-%i*csch(x))^(1/2)/(-1+%i*csch(x))^(1/2) +--R +--R +--R +-+ +--------------+ +--R 2\|3 coth(x)atan(\|%i csch(x) - 1 ) +--R (214) - ------------------------------------ +--R +----------------+ +--------------+ +--R \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 301 + +--S 302 of 526 +a0457:= integrate(t0457,x) +--R +--R +--R (215) +--R - +--R +-+ +--R %i\|3 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- - \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R - \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R %i\|3 +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) - 2%i cosh(x) +--R + +--R - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R - %i\|3 sinh(x) + (- 3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 3%i\|3 cosh(x) - 2\|3 cosh(x) + %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - %i\|3 cosh(x) - \|3 cosh(x) + %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 302 + +--S 303 of 526 +m0457:= a0457-r0457 +--R +--R +--R (216) +--R - +--R +-+ +----------------+ +--------------+ +--R %i\|3 \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R * +--R log +--R +-----------------------------------------+ +--R | 3 +-+ +--R |----------------------------------------- - \|3 sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R - \|3 cosh(x) - %i\|3 +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +----------------+ +--------------+ +--R %i\|3 \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 3 +-+ +-+ 2 +--R - %i\|3 sinh(x) + (- 3%i\|3 cosh(x) - \|3 )sinh(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 3%i\|3 cosh(x) - 2\|3 cosh(x) + %i\|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - %i\|3 cosh(x) - \|3 cosh(x) + %i\|3 cosh(x) + 2\|3 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--------------+ +--R 2\|3 coth(x)atan(\|%i csch(x) - 1 ) +--R / +--R +----------------+ +--------------+ +--R \|- %i csch(x) - 1 \|%i csch(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 303 + +--S 304 of 526 +d0457:= D(m0457,x) +--R +--R +--R (217) +--R 2 2 6 +--R (6csch(x) - 6coth(x) + 6)sinh(x) +--R + +--R 2 2 5 +--R (36cosh(x)csch(x) - 36cosh(x)coth(x) + 36cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R (90cosh(x) + 6)csch(x) + (- 90cosh(x) - 6)coth(x) +--R + +--R 2 +--R 90cosh(x) + 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (120cosh(x) + 24cosh(x))csch(x) +--R + +--R 3 2 3 +--R (- 120cosh(x) - 24cosh(x))coth(x) + 120cosh(x) + 24cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (90cosh(x) + 36cosh(x) - 36)csch(x) +--R + +--R 4 2 2 4 +--R (- 90cosh(x) - 36cosh(x) + 36)coth(x) + 90cosh(x) +--R + +--R 2 +--R 36cosh(x) - 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (36cosh(x) + 24cosh(x) - 72cosh(x))csch(x) +--R + +--R 5 3 2 5 +--R (- 36cosh(x) - 24cosh(x) + 72cosh(x))coth(x) + 36cosh(x) +--R + +--R 3 +--R 24cosh(x) - 72cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (6cosh(x) + 6cosh(x) - 36cosh(x) + 24)csch(x) +--R + +--R 6 4 2 2 6 +--R (- 6cosh(x) - 6cosh(x) + 36cosh(x) - 24)coth(x) + 6cosh(x) +--R + +--R 4 2 +--R 6cosh(x) - 36cosh(x) + 24 +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 2 +-+ 6 +--R (- 6%i\|3 csch(x) + 6%i\|3 coth(x) - 6%i\|3 )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R - 36%i\|3 cosh(x)csch(x) + 36%i\|3 cosh(x)coth(x) +--R + +--R +-+ +--R - 36%i\|3 cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 6%i\|3 )csch(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (90%i\|3 cosh(x) - 6%i\|3 )coth(x) - 90%i\|3 cosh(x) + 6%i\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 120%i\|3 cosh(x) + 24%i\|3 cosh(x))csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (120%i\|3 cosh(x) - 24%i\|3 cosh(x))coth(x) - 120%i\|3 cosh(x) +--R + +--R +-+ +--R 24%i\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (90%i\|3 cosh(x) - 36%i\|3 cosh(x) - 24%i\|3 )coth(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 90%i\|3 cosh(x) + 36%i\|3 cosh(x) + 24%i\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (36%i\|3 cosh(x) - 24%i\|3 cosh(x) - 48%i\|3 cosh(x))coth(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 36%i\|3 cosh(x) + 24%i\|3 cosh(x) + 48%i\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 ) +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (6%i\|3 cosh(x) - 6%i\|3 cosh(x) - 24%i\|3 cosh(x) + 24%i\|3 ) +--R * +--R 2 +--R coth(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 6%i\|3 cosh(x) + 6%i\|3 cosh(x) + 24%i\|3 cosh(x) - 24%i\|3 +--R * +--R +--------------+ +--R atan(\|%i csch(x) - 1 ) +--R + +--R 2 6 +--R (- 6%i csch(x) - 6%i)sinh(x) +--R + +--R 2 5 +--R ((- 36%i cosh(x) - 18)csch(x) - 36%i cosh(x) - 18)sinh(x) +--R + +--R 2 2 +--R (- 90%i cosh(x) - 90cosh(x) - 3%i)csch(x) +--R + +--R 2 +--R - 90%i cosh(x) - 90cosh(x) - 3%i +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 120%i cosh(x) - 180cosh(x) - 12%i cosh(x) + 30) +--R * +--R 2 +--R csch(x) +--R + +--R 3 2 +--R - 120%i cosh(x) - 180cosh(x) - 12%i cosh(x) + 30 +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R - 90%i cosh(x) - 180cosh(x) - 18%i cosh(x) +--R + +--R 90cosh(x) + 24%i +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R - 90%i cosh(x) - 180cosh(x) - 18%i cosh(x) + 90cosh(x) +--R + +--R 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R - 36%i cosh(x) - 90cosh(x) - 12%i cosh(x) +--R + +--R 2 +--R 90cosh(x) + 48%i cosh(x) - 12 +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 2 +--R - 36%i cosh(x) - 90cosh(x) - 12%i cosh(x) + 90cosh(x) +--R + +--R 48%i cosh(x) - 12 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 6%i cosh(x) - 18cosh(x) - 3%i cosh(x) + 30cosh(x) +--R + +--R 2 +--R 24%i cosh(x) - 12cosh(x) - 12%i +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R - 6%i cosh(x) - 18cosh(x) - 3%i cosh(x) + 30cosh(x) +--R + +--R 2 +--R 24%i cosh(x) - 12cosh(x) - 12%i +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R + +--R 2 2 6 +--R (3%i coth(x) csch(x) + 3coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (18%i cosh(x)coth(x) csch(x) + 18cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 +--R (45%i cosh(x) + 3%i)coth(x) csch(x) +--R + +--R 2 2 +--R (45cosh(x) + 3)coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (60%i cosh(x) + 12%i cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (60cosh(x) + 12cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (45%i cosh(x) + 18%i cosh(x) - 18%i)coth(x) csch(x) +--R + +--R 4 2 2 +--R (45cosh(x) + 18cosh(x) - 18)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (18%i cosh(x) + 12%i cosh(x) - 36%i cosh(x))coth(x) csch(x) +--R + +--R 5 3 2 +--R (18cosh(x) + 12cosh(x) - 36cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (3%i cosh(x) + 3%i cosh(x) - 18%i cosh(x) + 12%i)coth(x) +--R * +--R csch(x) +--R + +--R 6 4 2 2 +--R (3cosh(x) + 3cosh(x) - 18cosh(x) + 12)coth(x) +--R * +--R +-----------------------------------------+ +--R | 3 +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ 2 +-+ 6 +--R (- 3\|3 csch(x) - 3\|3 )sinh(x) +--R + +--R +-+ +-+ 2 +-+ +-+ +--R ((- 18\|3 cosh(x) + 6%i\|3 )csch(x) - 18\|3 cosh(x) + 6%i\|3 ) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (- 45\|3 cosh(x) + 30%i\|3 cosh(x) + 3\|3 )csch(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 45\|3 cosh(x) + 30%i\|3 cosh(x) + 3\|3 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 60\|3 cosh(x) + 60%i\|3 cosh(x) + 12\|3 cosh(x) +--R + +--R +-+ +--R - 24%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 60\|3 cosh(x) + 60%i\|3 cosh(x) + 12\|3 cosh(x) - 24%i\|3 +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 45\|3 cosh(x) + 60%i\|3 cosh(x) + 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72%i\|3 cosh(x) + 18\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 45\|3 cosh(x) + 60%i\|3 cosh(x) + 18\|3 cosh(x) +--R + +--R +-+ +-+ +--R - 72%i\|3 cosh(x) + 18\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 18\|3 cosh(x) + 30%i\|3 cosh(x) + 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72%i\|3 cosh(x) + 36\|3 cosh(x) + 12%i\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 18\|3 cosh(x) + 30%i\|3 cosh(x) + 12\|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 72%i\|3 cosh(x) + 36\|3 cosh(x) + 12%i\|3 +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 3\|3 cosh(x) + 6%i\|3 cosh(x) + 3\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24%i\|3 cosh(x) + 18\|3 cosh(x) + 12%i\|3 cosh(x) - 12\|3 +--R * +--R 2 +--R csch(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 3\|3 cosh(x) + 6%i\|3 cosh(x) + 3\|3 cosh(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24%i\|3 cosh(x) + 18\|3 cosh(x) + 12%i\|3 cosh(x) - 12\|3 +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R + +--R +-+ 2 +-+ 2 6 +--R (3\|3 coth(x) csch(x) - 3%i\|3 coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 5 +--R (18\|3 cosh(x)coth(x) csch(x) - 18%i\|3 cosh(x)coth(x) )sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (45\|3 cosh(x) - 3\|3 )coth(x) csch(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 45%i\|3 cosh(x) + 3%i\|3 )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 3 +-+ 2 +--R (60\|3 cosh(x) - 12\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 60%i\|3 cosh(x) + 12%i\|3 cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (45\|3 cosh(x) - 18\|3 cosh(x) - 12\|3 )coth(x) csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 45%i\|3 cosh(x) + 18%i\|3 cosh(x) + 12%i\|3 )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (18\|3 cosh(x) - 12\|3 cosh(x) - 24\|3 cosh(x))coth(x) csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 18%i\|3 cosh(x) + 12%i\|3 cosh(x) + 24%i\|3 cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (3\|3 cosh(x) - 3\|3 cosh(x) - 12\|3 cosh(x) + 12\|3 )coth(x) +--R * +--R csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 3%i\|3 cosh(x) + 3%i\|3 cosh(x) + 12%i\|3 cosh(x) - 12%i\|3 ) +--R * +--R 2 +--R coth(x) +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R / +--R +-+ 2 +-+ 6 +--R (\|3 csch(x) + \|3 )sinh(x) +--R + +--R +-+ 2 +-+ 5 +--R (6\|3 cosh(x)csch(x) + 6\|3 cosh(x))sinh(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ 4 +--R ((15\|3 cosh(x) + \|3 )csch(x) + 15\|3 cosh(x) + \|3 )sinh(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (20\|3 cosh(x) + 4\|3 cosh(x))csch(x) + 20\|3 cosh(x) +--R + +--R +-+ +--R 4\|3 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 )csch(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 15\|3 cosh(x) + 6\|3 cosh(x) - 6\|3 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x))csch(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 6\|3 cosh(x) + 4\|3 cosh(x) - 12\|3 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (\|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 )csch(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R \|3 cosh(x) + \|3 cosh(x) - 6\|3 cosh(x) + 4\|3 +--R * +--R +-----------------------------------------+ +--R +----------------+ | 3 +--R \|- %i csch(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- 3%i csch(x) - 3%i)sinh(x) +--R + +--R 2 5 +--R (- 18%i cosh(x)csch(x) - 18%i cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 45%i cosh(x) + 3%i)csch(x) - 45%i cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (- 60%i cosh(x) + 12%i cosh(x))csch(x) - 60%i cosh(x) +--R + +--R 12%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 45%i cosh(x) + 18%i cosh(x) + 12%i)csch(x) +--R + +--R 4 2 +--R - 45%i cosh(x) + 18%i cosh(x) + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x))csch(x) +--R + +--R 5 3 +--R - 18%i cosh(x) + 12%i cosh(x) + 24%i cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i)csch(x) +--R + +--R 6 4 2 +--R - 3%i cosh(x) + 3%i cosh(x) + 12%i cosh(x) - 12%i +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 304 + +--S 305 of 526 +t0458:= (a+%i*a*csch(x))^(1/2) +--R +--R +--R +----------------+ +--R (218) \|%i a csch(x) + a +--R Type: Expression(Complex(Integer)) +--E 305 + +--S 306 of 526 +r0458:= 2*a*atan((-1+%i*csch(x))^(1/2))*_ + coth(x)/(-1+%i*csch(x))^(1/2)/(a+%i*a*csch(x))^(1/2) +--R +--R +--R +--------------+ +--R 2a coth(x)atan(\|%i csch(x) - 1 ) +--R (219) ------------------------------------ +--R +--------------+ +----------------+ +--R \|%i csch(x) - 1 \|%i a csch(x) + a +--R Type: Expression(Complex(Integer)) +--E 306 + +--S 307 of 526 +a0458:= integrate(t0458,x) +--R +--R +--R (220) +--R - +--R +-+ +--R \|a +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +--R (- sinh(x) - cosh(x) - %i)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R \|a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) - 2%i cosh(x) +--R + +--R - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 307 + +--S 308 of 526 +m0458:= a0458-r0458 +--R +--R +--R (221) +--R - +--R +-+ +--------------+ +----------------+ +--R \|a \|%i csch(x) - 1 \|%i a csch(x) + a +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +--R (- sinh(x) - cosh(x) - %i)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--------------+ +----------------+ +--R \|a \|%i csch(x) - 1 \|%i a csch(x) + a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +--------------+ +--R - 2a coth(x)atan(\|%i csch(x) - 1 ) +--R / +--R +--------------+ +----------------+ +--R \|%i csch(x) - 1 \|%i a csch(x) + a +--R Type: Expression(Complex(Integer)) +--E 308 + +--S 309 of 526 +d0458:= D(m0458,x) +--R +--R +--R (222) +--R 2 2 6 +--R (- 2a csch(x) + 2a coth(x) - 2a)sinh(x) +--R + +--R 2 2 +--R (- 12a cosh(x)csch(x) + 12a cosh(x)coth(x) - 12a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 2 2 +--R (- 30a cosh(x) - 2a)csch(x) + (30a cosh(x) + 2a)coth(x) +--R + +--R 2 +--R - 30a cosh(x) - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 40a cosh(x) - 8a cosh(x))csch(x) +--R + +--R 3 2 3 +--R (40a cosh(x) + 8a cosh(x))coth(x) - 40a cosh(x) - 8a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 30a cosh(x) - 12a cosh(x) + 12a)csch(x) +--R + +--R 4 2 2 4 +--R (30a cosh(x) + 12a cosh(x) - 12a)coth(x) - 30a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 12a cosh(x) - 8a cosh(x) + 24a cosh(x))csch(x) +--R + +--R 5 3 2 +--R (12a cosh(x) + 8a cosh(x) - 24a cosh(x))coth(x) +--R + +--R 5 3 +--R - 12a cosh(x) - 8a cosh(x) + 24a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 2a cosh(x) - 2a cosh(x) + 12a cosh(x) - 8a)csch(x) +--R + +--R 6 4 2 2 +--R (2a cosh(x) + 2a cosh(x) - 12a cosh(x) + 8a)coth(x) +--R + +--R 6 4 2 +--R - 2a cosh(x) - 2a cosh(x) + 12a cosh(x) - 8a +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 2 2 2 2 6 +--R (2%i a csch(x) - 2%i a coth(x) + 2%i a )sinh(x) +--R + +--R 2 2 2 2 2 +--R (12%i a cosh(x)csch(x) - 12%i a cosh(x)coth(x) + 12%i a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 2 2 +--R (30%i a cosh(x) - 2%i a )csch(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 30%i a cosh(x) + 2%i a )coth(x) + 30%i a cosh(x) - 2%i a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (40%i a cosh(x) - 8%i a cosh(x))csch(x) +--R + +--R 2 3 2 2 2 3 +--R (- 40%i a cosh(x) + 8%i a cosh(x))coth(x) + 40%i a cosh(x) +--R + +--R 2 +--R - 8%i a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (30%i a cosh(x) - 12%i a cosh(x) - 8%i a )csch(x) +--R + +--R 2 4 2 2 2 2 +--R (- 30%i a cosh(x) + 12%i a cosh(x) + 8%i a )coth(x) +--R + +--R 2 4 2 2 2 +--R 30%i a cosh(x) - 12%i a cosh(x) - 8%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (12%i a cosh(x) - 8%i a cosh(x) - 16%i a cosh(x))csch(x) +--R + +--R 2 5 2 3 2 2 +--R (- 12%i a cosh(x) + 8%i a cosh(x) + 16%i a cosh(x))coth(x) +--R + +--R 2 5 2 3 2 +--R 12%i a cosh(x) - 8%i a cosh(x) - 16%i a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (2%i a cosh(x) - 2%i a cosh(x) - 8%i a cosh(x) + 8%i a )csch(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 2%i a cosh(x) + 2%i a cosh(x) + 8%i a cosh(x) - 8%i a )coth(x) +--R + +--R 2 6 2 4 2 2 2 +--R 2%i a cosh(x) - 2%i a cosh(x) - 8%i a cosh(x) + 8%i a +--R * +--R +--------------+ +--R atan(\|%i csch(x) - 1 ) +--R + +--R 2 6 +--R (- 2a csch(x) - 2a)sinh(x) +--R + +--R 2 5 +--R ((- 12a cosh(x) + 6%i a)csch(x) - 12a cosh(x) + 6%i a)sinh(x) +--R + +--R 2 2 2 +--R (- 30a cosh(x) + 30%i a cosh(x) - a)csch(x) - 30a cosh(x) +--R + +--R 30%i a cosh(x) - a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 40a cosh(x) + 60%i a cosh(x) - 4a cosh(x) - 10%i a) +--R * +--R 2 +--R csch(x) +--R + +--R 3 2 +--R - 40a cosh(x) + 60%i a cosh(x) - 4a cosh(x) - 10%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R - 30a cosh(x) + 60%i a cosh(x) - 6a cosh(x) +--R + +--R - 30%i a cosh(x) + 8a +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R - 30a cosh(x) + 60%i a cosh(x) - 6a cosh(x) +--R + +--R - 30%i a cosh(x) + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R - 12a cosh(x) + 30%i a cosh(x) - 4a cosh(x) +--R + +--R 2 +--R - 30%i a cosh(x) + 16a cosh(x) + 4%i a +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 +--R - 12a cosh(x) + 30%i a cosh(x) - 4a cosh(x) +--R + +--R 2 +--R - 30%i a cosh(x) + 16a cosh(x) + 4%i a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 2a cosh(x) + 6%i a cosh(x) - a cosh(x) - 10%i a cosh(x) +--R + +--R 2 +--R 8a cosh(x) + 4%i a cosh(x) - 4a +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R - 2a cosh(x) + 6%i a cosh(x) - a cosh(x) - 10%i a cosh(x) +--R + +--R 2 +--R 8a cosh(x) + 4%i a cosh(x) - 4a +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (%i a csch(x) + %i a)sinh(x) +--R + +--R 2 5 +--R ((6%i a cosh(x) + 2a)csch(x) + 6%i a cosh(x) + 2a)sinh(x) +--R + +--R 2 2 +--R (15%i a cosh(x) + 10a cosh(x) - %i a)csch(x) +--R + +--R 2 +--R 15%i a cosh(x) + 10a cosh(x) - %i a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 +--R (20%i a cosh(x) + 20a cosh(x) - 4%i a cosh(x) - 8a)csch(x) +--R + +--R 3 2 +--R 20%i a cosh(x) + 20a cosh(x) - 4%i a cosh(x) - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 15%i a cosh(x) + 20a cosh(x) - 6%i a cosh(x) +--R + +--R - 24a cosh(x) - 6%i a +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R 15%i a cosh(x) + 20a cosh(x) - 6%i a cosh(x) - 24a cosh(x) +--R + +--R - 6%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R 6%i a cosh(x) + 10a cosh(x) - 4%i a cosh(x) +--R + +--R 2 +--R - 24a cosh(x) - 12%i a cosh(x) + 4a +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 2 +--R 6%i a cosh(x) + 10a cosh(x) - 4%i a cosh(x) - 24a cosh(x) +--R + +--R - 12%i a cosh(x) + 4a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R %i a cosh(x) + 2a cosh(x) - %i a cosh(x) - 8a cosh(x) +--R + +--R 2 +--R - 6%i a cosh(x) + 4a cosh(x) + 4%i a +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R %i a cosh(x) + 2a cosh(x) - %i a cosh(x) - 8a cosh(x) +--R + +--R 2 +--R - 6%i a cosh(x) + 4a cosh(x) + 4%i a +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +----------------+ +--R \|%i csch(x) - 1 \|%i a csch(x) + a +--R + +--R 2 2 6 +--R (- %i a coth(x) csch(x) - a coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (- 6%i a cosh(x)coth(x) csch(x) - 6a cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 +--R (- 15%i a cosh(x) - %i a)coth(x) csch(x) +--R + +--R 2 2 +--R (- 15a cosh(x) - a)coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 20%i a cosh(x) - 4%i a cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (- 20a cosh(x) - 4a cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 15%i a cosh(x) - 6%i a cosh(x) + 6%i a)coth(x) csch(x) +--R + +--R 4 2 2 +--R (- 15a cosh(x) - 6a cosh(x) + 6a)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 +--R (- 6%i a cosh(x) - 4%i a cosh(x) + 12%i a cosh(x)) +--R * +--R 2 +--R coth(x) csch(x) +--R + +--R 5 3 2 +--R (- 6a cosh(x) - 4a cosh(x) + 12a cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (- %i a cosh(x) - %i a cosh(x) + 6%i a cosh(x) - 4%i a) +--R * +--R 2 +--R coth(x) csch(x) +--R + +--R 6 4 2 2 +--R (- a cosh(x) - a cosh(x) + 6a cosh(x) - 4a)coth(x) +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 2 2 2 6 +--R (- a coth(x) csch(x) + %i a coth(x) )sinh(x) +--R + +--R 2 2 2 2 5 +--R (- 6a cosh(x)coth(x) csch(x) + 6%i a cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 2 2 +--R (- 15a cosh(x) + a )coth(x) csch(x) +--R + +--R 2 2 2 2 +--R (15%i a cosh(x) - %i a )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 20a cosh(x) + 4a cosh(x))coth(x) csch(x) +--R + +--R 2 3 2 2 +--R (20%i a cosh(x) - 4%i a cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 15a cosh(x) + 6a cosh(x) + 4a )coth(x) csch(x) +--R + +--R 2 4 2 2 2 2 +--R (15%i a cosh(x) - 6%i a cosh(x) - 4%i a )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (- 6a cosh(x) + 4a cosh(x) + 8a cosh(x))coth(x) csch(x) +--R + +--R 2 5 2 3 2 2 +--R (6%i a cosh(x) - 4%i a cosh(x) - 8%i a cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- a cosh(x) + a cosh(x) + 4a cosh(x) - 4a )coth(x) csch(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (%i a cosh(x) - %i a cosh(x) - 4%i a cosh(x) + 4%i a )coth(x) +--R * +--R +--------------+ +--R \|%i csch(x) - 1 +--R / +--R 2 6 2 5 +--R (csch(x) + 1)sinh(x) + (6cosh(x)csch(x) + 6cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((15cosh(x) + 1)csch(x) + 15cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 3 +--R ((20cosh(x) + 4cosh(x))csch(x) + 20cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (15cosh(x) + 6cosh(x) - 6)csch(x) + 15cosh(x) + 6cosh(x) +--R + +--R - 6 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (6cosh(x) + 4cosh(x) - 12cosh(x))csch(x) + 6cosh(x) +--R + +--R 3 +--R 4cosh(x) - 12cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (cosh(x) + cosh(x) - 6cosh(x) + 4)csch(x) + cosh(x) + cosh(x) +--R + +--R 2 +--R - 6cosh(x) + 4 +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- %i a csch(x) - %i a)sinh(x) +--R + +--R 2 5 +--R (- 6%i a cosh(x)csch(x) - 6%i a cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 15%i a cosh(x) + %i a)csch(x) - 15%i a cosh(x) + %i a)sinh(x) +--R + +--R 3 2 3 +--R (- 20%i a cosh(x) + 4%i a cosh(x))csch(x) - 20%i a cosh(x) +--R + +--R 4%i a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 15%i a cosh(x) + 6%i a cosh(x) + 4%i a)csch(x) +--R + +--R 4 2 +--R - 15%i a cosh(x) + 6%i a cosh(x) + 4%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 6%i a cosh(x) + 4%i a cosh(x) + 8%i a cosh(x))csch(x) +--R + +--R 5 3 +--R - 6%i a cosh(x) + 4%i a cosh(x) + 8%i a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- %i a cosh(x) + %i a cosh(x) + 4%i a cosh(x) - 4%i a)csch(x) +--R + +--R 6 4 2 +--R - %i a cosh(x) + %i a cosh(x) + 4%i a cosh(x) - 4%i a +--R * +--R +--------------+ +----------------+ +--R \|%i csch(x) - 1 \|%i a csch(x) + a +--R Type: Expression(Complex(Integer)) +--E 309 + +--S 310 of 526 +t0459:= (a-%i*a*csch(x))^(1/2) +--R +--R +--R +------------------+ +--R (223) \|- %i a csch(x) + a +--R Type: Expression(Complex(Integer)) +--E 310 + +--S 311 of 526 +r0459:= 2*a*atan((-1-%i*csch(x))^(1/2))*_ + coth(x)/(-1-%i*csch(x))^(1/2)/(a-%i*a*csch(x))^(1/2) +--R +--R +--R +----------------+ +--R 2a coth(x)atan(\|- %i csch(x) - 1 ) +--R (224) ---------------------------------------- +--R +------------------+ +----------------+ +--R \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 311 + +--S 312 of 526 +a0459:= integrate(t0459,x) +--R +--R +--R (225) +--R +-+ +--R \|a +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +--R (sinh(x) + cosh(x) - %i)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +--R \|a +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 312 + +--S 313 of 526 +m0459:= a0459-r0459 +--R +--R +--R (226) +--R +-+ +------------------+ +----------------+ +--R \|a \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R * +--R log +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +--R (sinh(x) + cosh(x) - %i)\|a +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R +-+ +------------------+ +----------------+ +--R \|a \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +----------------+ +--R - 2a coth(x)atan(\|- %i csch(x) - 1 ) +--R / +--R +------------------+ +----------------+ +--R \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 313 + +--S 314 of 526 +d0459:= D(m0459,x) +--R +--R +--R (227) +--R 2 2 6 +--R (- 2a csch(x) + 2a coth(x) - 2a)sinh(x) +--R + +--R 2 2 +--R (- 12a cosh(x)csch(x) + 12a cosh(x)coth(x) - 12a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 2 2 +--R (- 30a cosh(x) - 2a)csch(x) + (30a cosh(x) + 2a)coth(x) +--R + +--R 2 +--R - 30a cosh(x) - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 40a cosh(x) - 8a cosh(x))csch(x) +--R + +--R 3 2 3 +--R (40a cosh(x) + 8a cosh(x))coth(x) - 40a cosh(x) - 8a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 30a cosh(x) - 12a cosh(x) + 12a)csch(x) +--R + +--R 4 2 2 4 +--R (30a cosh(x) + 12a cosh(x) - 12a)coth(x) - 30a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 12a cosh(x) - 8a cosh(x) + 24a cosh(x))csch(x) +--R + +--R 5 3 2 +--R (12a cosh(x) + 8a cosh(x) - 24a cosh(x))coth(x) +--R + +--R 5 3 +--R - 12a cosh(x) - 8a cosh(x) + 24a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 2a cosh(x) - 2a cosh(x) + 12a cosh(x) - 8a)csch(x) +--R + +--R 6 4 2 2 +--R (2a cosh(x) + 2a cosh(x) - 12a cosh(x) + 8a)coth(x) +--R + +--R 6 4 2 +--R - 2a cosh(x) - 2a cosh(x) + 12a cosh(x) - 8a +--R * +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 2 2 2 2 6 +--R (2%i a csch(x) - 2%i a coth(x) + 2%i a )sinh(x) +--R + +--R 2 2 2 2 2 +--R (12%i a cosh(x)csch(x) - 12%i a cosh(x)coth(x) + 12%i a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 2 2 +--R (30%i a cosh(x) - 2%i a )csch(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 30%i a cosh(x) + 2%i a )coth(x) + 30%i a cosh(x) - 2%i a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (40%i a cosh(x) - 8%i a cosh(x))csch(x) +--R + +--R 2 3 2 2 2 3 +--R (- 40%i a cosh(x) + 8%i a cosh(x))coth(x) + 40%i a cosh(x) +--R + +--R 2 +--R - 8%i a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (30%i a cosh(x) - 12%i a cosh(x) - 8%i a )csch(x) +--R + +--R 2 4 2 2 2 2 +--R (- 30%i a cosh(x) + 12%i a cosh(x) + 8%i a )coth(x) +--R + +--R 2 4 2 2 2 +--R 30%i a cosh(x) - 12%i a cosh(x) - 8%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (12%i a cosh(x) - 8%i a cosh(x) - 16%i a cosh(x))csch(x) +--R + +--R 2 5 2 3 2 2 +--R (- 12%i a cosh(x) + 8%i a cosh(x) + 16%i a cosh(x))coth(x) +--R + +--R 2 5 2 3 2 +--R 12%i a cosh(x) - 8%i a cosh(x) - 16%i a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (2%i a cosh(x) - 2%i a cosh(x) - 8%i a cosh(x) + 8%i a )csch(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 2%i a cosh(x) + 2%i a cosh(x) + 8%i a cosh(x) - 8%i a )coth(x) +--R + +--R 2 6 2 4 2 2 2 +--R 2%i a cosh(x) - 2%i a cosh(x) - 8%i a cosh(x) + 8%i a +--R * +--R +----------------+ +--R atan(\|- %i csch(x) - 1 ) +--R + +--R 2 6 +--R (2a csch(x) + 2a)sinh(x) +--R + +--R 2 5 +--R ((12a cosh(x) + 6%i a)csch(x) + 12a cosh(x) + 6%i a)sinh(x) +--R + +--R 2 2 2 +--R (30a cosh(x) + 30%i a cosh(x) + a)csch(x) + 30a cosh(x) +--R + +--R 30%i a cosh(x) + a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (40a cosh(x) + 60%i a cosh(x) + 4a cosh(x) - 10%i a) +--R * +--R 2 +--R csch(x) +--R + +--R 3 2 +--R 40a cosh(x) + 60%i a cosh(x) + 4a cosh(x) - 10%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 30a cosh(x) + 60%i a cosh(x) + 6a cosh(x) +--R + +--R - 30%i a cosh(x) - 8a +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R 30a cosh(x) + 60%i a cosh(x) + 6a cosh(x) - 30%i a cosh(x) +--R + +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R 12a cosh(x) + 30%i a cosh(x) + 4a cosh(x) +--R + +--R 2 +--R - 30%i a cosh(x) - 16a cosh(x) + 4%i a +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 +--R 12a cosh(x) + 30%i a cosh(x) + 4a cosh(x) +--R + +--R 2 +--R - 30%i a cosh(x) - 16a cosh(x) + 4%i a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R 2a cosh(x) + 6%i a cosh(x) + a cosh(x) - 10%i a cosh(x) +--R + +--R 2 +--R - 8a cosh(x) + 4%i a cosh(x) + 4a +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R 2a cosh(x) + 6%i a cosh(x) + a cosh(x) - 10%i a cosh(x) +--R + +--R 2 +--R - 8a cosh(x) + 4%i a cosh(x) + 4a +--R * +--R +------------------+ +--R \|- %i a csch(x) + a +--R + +--R 2 2 6 +--R (%i a coth(x) csch(x) - a coth(x) )sinh(x) +--R + +--R 2 2 5 +--R (6%i a cosh(x)coth(x) csch(x) - 6a cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 +--R (15%i a cosh(x) + %i a)coth(x) csch(x) +--R + +--R 2 2 +--R (- 15a cosh(x) - a)coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (20%i a cosh(x) + 4%i a cosh(x))coth(x) csch(x) +--R + +--R 3 2 +--R (- 20a cosh(x) - 4a cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (15%i a cosh(x) + 6%i a cosh(x) - 6%i a)coth(x) csch(x) +--R + +--R 4 2 2 +--R (- 15a cosh(x) - 6a cosh(x) + 6a)coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (6%i a cosh(x) + 4%i a cosh(x) - 12%i a cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R 5 3 2 +--R (- 6a cosh(x) - 4a cosh(x) + 12a cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (%i a cosh(x) + %i a cosh(x) - 6%i a cosh(x) + 4%i a) +--R * +--R 2 +--R coth(x) csch(x) +--R + +--R 6 4 2 2 +--R (- a cosh(x) - a cosh(x) + 6a cosh(x) - 4a)coth(x) +--R * +--R +-+ +--R \|a +--R * +--R +-----------------------------------------+ +--R +----------------+ | a +--R \|- %i csch(x) - 1 |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- %i a csch(x) - %i a)sinh(x) +--R + +--R 2 5 +--R ((- 6%i a cosh(x) + 2a)csch(x) - 6%i a cosh(x) + 2a)sinh(x) +--R + +--R 2 2 +--R (- 15%i a cosh(x) + 10a cosh(x) + %i a)csch(x) +--R + +--R 2 +--R - 15%i a cosh(x) + 10a cosh(x) + %i a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 20%i a cosh(x) + 20a cosh(x) + 4%i a cosh(x) - 8a) +--R * +--R 2 +--R csch(x) +--R + +--R 3 2 +--R - 20%i a cosh(x) + 20a cosh(x) + 4%i a cosh(x) - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R - 15%i a cosh(x) + 20a cosh(x) + 6%i a cosh(x) +--R + +--R - 24a cosh(x) + 6%i a +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R - 15%i a cosh(x) + 20a cosh(x) + 6%i a cosh(x) +--R + +--R - 24a cosh(x) + 6%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R - 6%i a cosh(x) + 10a cosh(x) + 4%i a cosh(x) +--R + +--R 2 +--R - 24a cosh(x) + 12%i a cosh(x) + 4a +--R * +--R 2 +--R csch(x) +--R + +--R 5 4 3 +--R - 6%i a cosh(x) + 10a cosh(x) + 4%i a cosh(x) +--R + +--R 2 +--R - 24a cosh(x) + 12%i a cosh(x) + 4a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - %i a cosh(x) + 2a cosh(x) + %i a cosh(x) - 8a cosh(x) +--R + +--R 2 +--R 6%i a cosh(x) + 4a cosh(x) - 4%i a +--R * +--R 2 +--R csch(x) +--R + +--R 6 5 4 3 +--R - %i a cosh(x) + 2a cosh(x) + %i a cosh(x) - 8a cosh(x) +--R + +--R 2 +--R 6%i a cosh(x) + 4a cosh(x) - 4%i a +--R * +--R +-+ +------------------+ +--R \|a \|- %i a csch(x) + a +--R + +--R 2 2 2 2 6 +--R (a coth(x) csch(x) + %i a coth(x) )sinh(x) +--R + +--R 2 2 2 2 5 +--R (6a cosh(x)coth(x) csch(x) + 6%i a cosh(x)coth(x) )sinh(x) +--R + +--R 2 2 2 2 +--R (15a cosh(x) - a )coth(x) csch(x) +--R + +--R 2 2 2 2 +--R (15%i a cosh(x) - %i a )coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (20a cosh(x) - 4a cosh(x))coth(x) csch(x) +--R + +--R 2 3 2 2 +--R (20%i a cosh(x) - 4%i a cosh(x))coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (15a cosh(x) - 6a cosh(x) - 4a )coth(x) csch(x) +--R + +--R 2 4 2 2 2 2 +--R (15%i a cosh(x) - 6%i a cosh(x) - 4%i a )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (6a cosh(x) - 4a cosh(x) - 8a cosh(x))coth(x) csch(x) +--R + +--R 2 5 2 3 2 2 +--R (6%i a cosh(x) - 4%i a cosh(x) - 8%i a cosh(x))coth(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (a cosh(x) - a cosh(x) - 4a cosh(x) + 4a )coth(x) csch(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (%i a cosh(x) - %i a cosh(x) - 4%i a cosh(x) + 4%i a )coth(x) +--R * +--R +----------------+ +--R \|- %i csch(x) - 1 +--R / +--R 2 6 2 5 +--R (csch(x) + 1)sinh(x) + (6cosh(x)csch(x) + 6cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((15cosh(x) + 1)csch(x) + 15cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 3 +--R ((20cosh(x) + 4cosh(x))csch(x) + 20cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R ((15cosh(x) + 6cosh(x) - 6)csch(x) + 15cosh(x) + 6cosh(x) - 6) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (6cosh(x) + 4cosh(x) - 12cosh(x))csch(x) + 6cosh(x) +--R + +--R 3 +--R 4cosh(x) - 12cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (cosh(x) + cosh(x) - 6cosh(x) + 4)csch(x) + cosh(x) + cosh(x) +--R + +--R 2 +--R - 6cosh(x) + 4 +--R * +--R +-+ +------------------+ +----------------+ +--R \|a \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 6 +--R (- %i a csch(x) - %i a)sinh(x) +--R + +--R 2 5 +--R (- 6%i a cosh(x)csch(x) - 6%i a cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 15%i a cosh(x) + %i a)csch(x) - 15%i a cosh(x) + %i a)sinh(x) +--R + +--R 3 2 3 +--R (- 20%i a cosh(x) + 4%i a cosh(x))csch(x) - 20%i a cosh(x) +--R + +--R 4%i a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 15%i a cosh(x) + 6%i a cosh(x) + 4%i a)csch(x) +--R + +--R 4 2 +--R - 15%i a cosh(x) + 6%i a cosh(x) + 4%i a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 6%i a cosh(x) + 4%i a cosh(x) + 8%i a cosh(x))csch(x) +--R + +--R 5 3 +--R - 6%i a cosh(x) + 4%i a cosh(x) + 8%i a cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- %i a cosh(x) + %i a cosh(x) + 4%i a cosh(x) - 4%i a)csch(x) +--R + +--R 6 4 2 +--R - %i a cosh(x) + %i a cosh(x) + 4%i a cosh(x) - 4%i a +--R * +--R +------------------+ +----------------+ +--R \|- %i a csch(x) + a \|- %i csch(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 314 + +--S 315 of 526 +t0460:= 1/(a+%i*a*csch(x))^(1/2) +--R +--R +--R 1 +--R (228) ------------------- +--R +----------------+ +--R \|%i a csch(x) + a +--R Type: Expression(Complex(Integer)) +--E 315 + +--S 316 of 526 +r0460:= -(2^(1/2)*atan(2^(1/2)*a^(1/2)/(-a+%i*a*csch(x))^(1/2))+_ + 2*atan((-a+%i*a*csch(x))^(1/2)/a^(1/2)))*(-a+%i*a*csch(x))^(1/2)*_ + (a+%i*a*csch(x))^(1/2)*tanh(x)/a^(3/2) +--R +--R +--R (229) +--R +----------------+ +--R +----------------+ +----------------+ \|%i a csch(x) - a +--R - 2tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a atan(-------------------) +--R +-+ +--R \|a +--R + +--R - +--R +-+ +----------------+ +----------------+ +--R \|2 tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(-------------------) +--R +----------------+ +--R \|%i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Complex(Integer)) +--E 316 + +--S 317 of 526 +a0460:= integrate(t0460,x) +--R +--R +--R (230) +--R [ +--R - +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R - 2sinh(x) + (- 14cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (- 42cosh(x) - 72%i cosh(x) + 10)sinh(x) +--R + +--R 3 2 +--R (- 70cosh(x) - 180%i cosh(x) + 50cosh(x) + 24%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R - 70cosh(x) - 240%i cosh(x) + 100cosh(x) +--R + +--R 96%i cosh(x) - 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 42cosh(x) - 180%i cosh(x) + 100cosh(x) +--R + +--R 2 +--R 144%i cosh(x) - 48cosh(x) - 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 14cosh(x) - 72%i cosh(x) + 50cosh(x) +--R + +--R 3 2 +--R 96%i cosh(x) - 48cosh(x) - 24%i cosh(x) + 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 +--R - 2cosh(x) - 12%i cosh(x) + 10cosh(x) +--R + +--R 4 3 2 +--R 24%i cosh(x) - 16cosh(x) - 12%i cosh(x) + 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) - 72%i cosh(x) + 20)sinh(x) +--R + +--R 3 2 +--R (- 140cosh(x) - 180%i cosh(x) + 100cosh(x) + 28%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) - 240%i cosh(x) + 200cosh(x) +--R + +--R 112%i cosh(x) - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 84cosh(x) - 180%i cosh(x) + 200cosh(x) +--R + +--R 2 +--R 168%i cosh(x) - 96cosh(x) - 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) - 72%i cosh(x) + 100cosh(x) +--R + +--R 3 2 +--R 112%i cosh(x) - 96cosh(x) - 48%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) - 12%i cosh(x) + 20cosh(x) + 28%i cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) - 24%i cosh(x) + 16cosh(x) + 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R - 3sinh(x) + (- 24cosh(x) + 4%i)sinh(x) +--R + +--R 2 6 +--R (- 84cosh(x) + 28%i cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (- 168cosh(x) + 84%i cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 +--R (- 210cosh(x) + 140%i cosh(x) - 60%i cosh(x) + 16) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 +--R - 168cosh(x) + 140%i cosh(x) - 120%i cosh(x) +--R + +--R 64cosh(x) + 24%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 +--R - 84cosh(x) + 84%i cosh(x) - 120%i cosh(x) +--R + +--R 2 +--R 96cosh(x) + 72%i cosh(x) - 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 +--R - 24cosh(x) + 28%i cosh(x) - 60%i cosh(x) +--R + +--R 3 2 +--R 64cosh(x) + 72%i cosh(x) - 40cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 5 4 +--R - 3cosh(x) + 4%i cosh(x) - 12%i cosh(x) + 16cosh(x) +--R + +--R 3 2 +--R 24%i cosh(x) - 20cosh(x) - 16%i cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) + 2%i a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) + 14%i a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 +--R - 112a cosh(x) + 42%i a cosh(x) - 12a cosh(x) +--R + +--R - 6%i a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) + 70%i a cosh(x) - 30a cosh(x) +--R + +--R - 30%i a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) + 70%i a cosh(x) - 40a cosh(x) +--R + +--R 2 +--R - 60%i a cosh(x) + 64a cosh(x) + 12%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) + 42%i a cosh(x) - 30a cosh(x) +--R + +--R 3 2 +--R - 60%i a cosh(x) + 96a cosh(x) + 36%i a cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) + 14%i a cosh(x) - 12a cosh(x) +--R + +--R 4 3 2 +--R - 30%i a cosh(x) + 64a cosh(x) + 36%i a cosh(x) +--R + +--R - 24a cosh(x) - 8%i a +--R * +--R sinh(x) +--R + +--R 8 7 6 +--R - 2a cosh(x) + 2%i a cosh(x) - 2a cosh(x) +--R + +--R 5 4 3 +--R - 6%i a cosh(x) + 16a cosh(x) + 12%i a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) - 8%i a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) - 4%i)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) - 24%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) - 60%i cosh(x) + 20cosh(x) + 12%i)sinh(x) +--R + +--R 4 3 2 +--R 140cosh(x) - 80%i cosh(x) + 40cosh(x) +--R + +--R 48%i cosh(x) - 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R 84cosh(x) - 60%i cosh(x) + 40cosh(x) +--R + +--R 2 +--R 72%i cosh(x) - 72cosh(x) - 16%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R 28cosh(x) - 24%i cosh(x) + 20cosh(x) +--R + +--R 3 2 +--R 48%i cosh(x) - 72cosh(x) - 32%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 4cosh(x) - 4%i cosh(x) + 4cosh(x) + 12%i cosh(x) +--R + +--R 3 2 +--R - 24cosh(x) - 16%i cosh(x) + 16cosh(x) + 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R sinh(x) + (8cosh(x) - 4%i)sinh(x) +--R + +--R 2 6 +--R (28cosh(x) - 28%i cosh(x) - 4)sinh(x) +--R + +--R 3 2 5 +--R (56cosh(x) - 84%i cosh(x) - 24cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R 70cosh(x) - 140%i cosh(x) - 60cosh(x) +--R + +--R 20%i cosh(x) + 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R 56cosh(x) - 140%i cosh(x) - 80cosh(x) +--R + +--R 2 +--R 40%i cosh(x) + 32cosh(x) + 16%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R 28cosh(x) - 84%i cosh(x) - 60cosh(x) +--R + +--R 3 2 +--R 40%i cosh(x) + 48cosh(x) + 48%i cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 8cosh(x) - 28%i cosh(x) - 24cosh(x) + 20%i cosh(x) +--R + +--R 3 2 +--R 32cosh(x) + 48%i cosh(x) - 24cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R cosh(x) - 4%i cosh(x) - 4cosh(x) + 4%i cosh(x) +--R + +--R 4 3 2 +--R 8cosh(x) + 16%i cosh(x) - 12cosh(x) - 16%i cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R / +--R +-+ +--R \|a +--R , +--R +--R - +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R 2%i |- \|a +--R \|a +--R * +--R atan +--R +-----------------------------------------+ +--R +-+ | a +--R %i\|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - %i a sinh(x) - %i a cosh(x) + a +--R / +--R +-+ +--R |2 +-+ +--R (a sinh(x) + a cosh(x)) |- \|a +--R \|a +--R / +--R +-+ +--R \|a +--R ] +--R Type: Union(List(Expression(Complex(Integer))),...) +--E 317 + +--S 318 of 526 +m0460a:= a0460.1-r0460 +--R +--R +--R (231) +--R - +--R a +--R * +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R a |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R - 2sinh(x) + (- 14cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (- 42cosh(x) - 72%i cosh(x) + 10)sinh(x) +--R + +--R 3 2 +--R (- 70cosh(x) - 180%i cosh(x) + 50cosh(x) + 24%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R - 70cosh(x) - 240%i cosh(x) + 100cosh(x) +--R + +--R 96%i cosh(x) - 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 42cosh(x) - 180%i cosh(x) + 100cosh(x) +--R + +--R 2 +--R 144%i cosh(x) - 48cosh(x) - 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 14cosh(x) - 72%i cosh(x) + 50cosh(x) +--R + +--R 3 2 +--R 96%i cosh(x) - 48cosh(x) - 24%i cosh(x) + 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 2cosh(x) - 12%i cosh(x) + 10cosh(x) + 24%i cosh(x) +--R + +--R 3 2 +--R - 16cosh(x) - 12%i cosh(x) + 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) - 72%i cosh(x) + 20)sinh(x) +--R + +--R 3 2 4 +--R (- 140cosh(x) - 180%i cosh(x) + 100cosh(x) + 28%i)sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) - 240%i cosh(x) + 200cosh(x) +--R + +--R 112%i cosh(x) - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 84cosh(x) - 180%i cosh(x) + 200cosh(x) +--R + +--R 2 +--R 168%i cosh(x) - 96cosh(x) - 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) - 72%i cosh(x) + 100cosh(x) +--R + +--R 3 2 +--R 112%i cosh(x) - 96cosh(x) - 48%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) - 12%i cosh(x) + 20cosh(x) + 28%i cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) - 24%i cosh(x) + 16cosh(x) + 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R - 3sinh(x) + (- 24cosh(x) + 4%i)sinh(x) +--R + +--R 2 6 +--R (- 84cosh(x) + 28%i cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (- 168cosh(x) + 84%i cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 4 +--R (- 210cosh(x) + 140%i cosh(x) - 60%i cosh(x) + 16)sinh(x) +--R + +--R 5 4 2 +--R - 168cosh(x) + 140%i cosh(x) - 120%i cosh(x) +--R + +--R 64cosh(x) + 24%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 +--R - 84cosh(x) + 84%i cosh(x) - 120%i cosh(x) +--R + +--R 2 +--R 96cosh(x) + 72%i cosh(x) - 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 +--R - 24cosh(x) + 28%i cosh(x) - 60%i cosh(x) +--R + +--R 3 2 +--R 64cosh(x) + 72%i cosh(x) - 40cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 5 4 +--R - 3cosh(x) + 4%i cosh(x) - 12%i cosh(x) + 16cosh(x) +--R + +--R 3 2 +--R 24%i cosh(x) - 20cosh(x) - 16%i cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) + 2%i a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) + 14%i a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 +--R (- 112a cosh(x) + 42%i a cosh(x) - 12a cosh(x) - 6%i a) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) + 70%i a cosh(x) - 30a cosh(x) +--R + +--R - 30%i a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) + 70%i a cosh(x) - 40a cosh(x) +--R + +--R 2 +--R - 60%i a cosh(x) + 64a cosh(x) + 12%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) + 42%i a cosh(x) - 30a cosh(x) +--R + +--R 3 2 +--R - 60%i a cosh(x) + 96a cosh(x) + 36%i a cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) + 14%i a cosh(x) - 12a cosh(x) +--R + +--R 4 3 2 +--R - 30%i a cosh(x) + 64a cosh(x) + 36%i a cosh(x) +--R + +--R - 24a cosh(x) - 8%i a +--R * +--R sinh(x) +--R + +--R 8 7 6 +--R - 2a cosh(x) + 2%i a cosh(x) - 2a cosh(x) +--R + +--R 5 4 3 +--R - 6%i a cosh(x) + 16a cosh(x) + 12%i a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) - 8%i a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) - 4%i)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) - 24%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) - 60%i cosh(x) + 20cosh(x) + 12%i)sinh(x) +--R + +--R 4 3 2 +--R 140cosh(x) - 80%i cosh(x) + 40cosh(x) + 48%i cosh(x) +--R + +--R - 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 84cosh(x) - 60%i cosh(x) + 40cosh(x) + 72%i cosh(x) +--R + +--R - 72cosh(x) - 16%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) - 24%i cosh(x) + 20cosh(x) + 48%i cosh(x) +--R + +--R 2 +--R - 72cosh(x) - 32%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 4cosh(x) - 4%i cosh(x) + 4cosh(x) + 12%i cosh(x) +--R + +--R 3 2 +--R - 24cosh(x) - 16%i cosh(x) + 16cosh(x) + 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R sinh(x) + (8cosh(x) - 4%i)sinh(x) +--R + +--R 2 6 +--R (28cosh(x) - 28%i cosh(x) - 4)sinh(x) +--R + +--R 3 2 5 +--R (56cosh(x) - 84%i cosh(x) - 24cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R 70cosh(x) - 140%i cosh(x) - 60cosh(x) + 20%i cosh(x) +--R + +--R 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) - 140%i cosh(x) - 80cosh(x) + 40%i cosh(x) +--R + +--R 32cosh(x) + 16%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) - 84%i cosh(x) - 60cosh(x) + 40%i cosh(x) +--R + +--R 2 +--R 48cosh(x) + 48%i cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 8cosh(x) - 28%i cosh(x) - 24cosh(x) + 20%i cosh(x) +--R + +--R 3 2 +--R 32cosh(x) + 48%i cosh(x) - 24cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R cosh(x) - 4%i cosh(x) - 4cosh(x) + 4%i cosh(x) +--R + +--R 4 3 2 +--R 8cosh(x) + 16%i cosh(x) - 12cosh(x) - 16%i cosh(x) + 8 +--R * +--R +-+ +--R \|a +--R + +--R +----------------+ +--R +----------------+ +----------------+ \|%i a csch(x) - a +--R 2tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a atan(-------------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +----------------+ +----------------+ \|2 \|a +--R \|2 tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a atan(-------------------) +--R +----------------+ +--R \|%i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Complex(Integer)) +--E 318 + +--S 319 of 526 +--d0460a:= D(m0460a,x) +--E 319 + +--S 320 of 526 +m0460b:= a0460.2-r0460 +--R +--R +--R (232) +--R - +--R a +--R * +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- - a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R a +--R * +--R log +--R 3 2 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 4%i cosh(x) - 1)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) - 2cosh(x) + %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +----------------+ +--R +----------------+ +----------------+ \|%i a csch(x) - a +--R 2tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a atan(-------------------) +--R +-+ +--R \|a +--R + +--R +-+ +--R |2 +-+ +--R 2%i a |- \|a +--R \|a +--R * +--R atan +--R +-----------------------------------------+ +--R +-+ | a +--R %i\|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R - %i a sinh(x) - %i a cosh(x) + a +--R / +--R +-+ +--R |2 +-+ +--R (a sinh(x) + a cosh(x)) |- \|a +--R \|a +--R + +--R +-+ +-+ +--R +-+ +----------------+ +----------------+ \|2 \|a +--R \|2 tanh(x)\|%i a csch(x) - a \|%i a csch(x) + a atan(-------------------) +--R +----------------+ +--R \|%i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Complex(Integer)) +--E 320 + +--S 321 of 526 +--d0460b:= D(m0460b,x) +--E 321 + +--S 322 of 526 +t0461:= 1/(a-%i*a*csch(x))^(1/2) +--R +--R +--R 1 +--R (233) --------------------- +--R +------------------+ +--R \|- %i a csch(x) + a +--R Type: Expression(Complex(Integer)) +--E 322 + +--S 323 of 526 +r0461:= -(2^(1/2)*atan(2^(1/2)*a^(1/2)/(-a-%i*a*csch(x))^(1/2))+_ + 2*atan((-a-%i*a*csch(x))^(1/2)/a^(1/2)))*(-a-%i*a*csch(x))^(1/2)*_ + (a-%i*a*csch(x))^(1/2)*tanh(x)/a^(3/2) +--R +--R +--R (234) +--R - +--R +------------------+ +------------------+ +--R 2tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +------------------+ +--R \|- %i a csch(x) - a +--R atan(---------------------) +--R +-+ +--R \|a +--R + +--R - +--R +-+ +------------------+ +------------------+ +--R \|2 tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(---------------------) +--R +------------------+ +--R \|- %i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Complex(Integer)) +--E 323 + +--S 324 of 526 +a0461:= integrate(t0461,x) +--R +--R +--R (235) +--R [ +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R 2sinh(x) + (14cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (42cosh(x) - 72%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 +--R (70cosh(x) - 180%i cosh(x) - 50cosh(x) + 24%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R 70cosh(x) - 240%i cosh(x) - 100cosh(x) +--R + +--R 96%i cosh(x) + 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R 42cosh(x) - 180%i cosh(x) - 100cosh(x) +--R + +--R 2 +--R 144%i cosh(x) + 48cosh(x) - 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R 14cosh(x) - 72%i cosh(x) - 50cosh(x) +--R + +--R 3 2 +--R 96%i cosh(x) + 48cosh(x) - 24%i cosh(x) - 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 2cosh(x) - 12%i cosh(x) - 10cosh(x) + 24%i cosh(x) +--R + +--R 3 2 +--R 16cosh(x) - 12%i cosh(x) - 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) + 12%i)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) + 72%i cosh(x) + 20)sinh(x) +--R + +--R 3 2 +--R (- 140cosh(x) + 180%i cosh(x) + 100cosh(x) - 28%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) + 240%i cosh(x) + 200cosh(x) +--R + +--R - 112%i cosh(x) - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 84cosh(x) + 180%i cosh(x) + 200cosh(x) +--R + +--R 2 +--R - 168%i cosh(x) - 96cosh(x) + 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) + 72%i cosh(x) + 100cosh(x) +--R + +--R 3 2 +--R - 112%i cosh(x) - 96cosh(x) + 48%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) + 12%i cosh(x) + 20cosh(x) - 28%i cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) + 24%i cosh(x) + 16cosh(x) - 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R 3sinh(x) + (24cosh(x) + 4%i)sinh(x) +--R + +--R 2 6 +--R (84cosh(x) + 28%i cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (168cosh(x) + 84%i cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 4 +--R (210cosh(x) + 140%i cosh(x) - 60%i cosh(x) - 16)sinh(x) +--R + +--R 5 4 2 +--R 168cosh(x) + 140%i cosh(x) - 120%i cosh(x) +--R + +--R - 64cosh(x) + 24%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 +--R 84cosh(x) + 84%i cosh(x) - 120%i cosh(x) +--R + +--R 2 +--R - 96cosh(x) + 72%i cosh(x) + 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 +--R 24cosh(x) + 28%i cosh(x) - 60%i cosh(x) +--R + +--R 3 2 +--R - 64cosh(x) + 72%i cosh(x) + 40cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 5 4 +--R 3cosh(x) + 4%i cosh(x) - 12%i cosh(x) - 16cosh(x) +--R + +--R 3 2 +--R 24%i cosh(x) + 20cosh(x) - 16%i cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) - 2%i a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) - 14%i a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 +--R - 112a cosh(x) - 42%i a cosh(x) - 12a cosh(x) +--R + +--R 6%i a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) - 70%i a cosh(x) - 30a cosh(x) +--R + +--R 30%i a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) - 70%i a cosh(x) - 40a cosh(x) +--R + +--R 2 +--R 60%i a cosh(x) + 64a cosh(x) - 12%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) - 42%i a cosh(x) - 30a cosh(x) +--R + +--R 3 2 +--R 60%i a cosh(x) + 96a cosh(x) - 36%i a cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) - 14%i a cosh(x) - 12a cosh(x) +--R + +--R 4 3 2 +--R 30%i a cosh(x) + 64a cosh(x) - 36%i a cosh(x) +--R + +--R - 24a cosh(x) + 8%i a +--R * +--R sinh(x) +--R + +--R 8 7 6 +--R - 2a cosh(x) - 2%i a cosh(x) - 2a cosh(x) +--R + +--R 5 4 3 +--R 6%i a cosh(x) + 16a cosh(x) - 12%i a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) + 8%i a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) + 4%i)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) + 24%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) + 60%i cosh(x) + 20cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 2 +--R 140cosh(x) + 80%i cosh(x) + 40cosh(x) +--R + +--R - 48%i cosh(x) - 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R 84cosh(x) + 60%i cosh(x) + 40cosh(x) +--R + +--R 2 +--R - 72%i cosh(x) - 72cosh(x) + 16%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R 28cosh(x) + 24%i cosh(x) + 20cosh(x) +--R + +--R 3 2 +--R - 48%i cosh(x) - 72cosh(x) + 32%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 4cosh(x) + 4%i cosh(x) + 4cosh(x) - 12%i cosh(x) +--R + +--R 3 2 +--R - 24cosh(x) + 16%i cosh(x) + 16cosh(x) - 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R - sinh(x) + (- 8cosh(x) - 4%i)sinh(x) +--R + +--R 2 6 +--R (- 28cosh(x) - 28%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 5 +--R (- 56cosh(x) - 84%i cosh(x) + 24cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R - 70cosh(x) - 140%i cosh(x) + 60cosh(x) +--R + +--R 20%i cosh(x) - 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 56cosh(x) - 140%i cosh(x) + 80cosh(x) +--R + +--R 2 +--R 40%i cosh(x) - 32cosh(x) + 16%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) - 84%i cosh(x) + 60cosh(x) +--R + +--R 3 2 +--R 40%i cosh(x) - 48cosh(x) + 48%i cosh(x) + 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 8cosh(x) - 28%i cosh(x) + 24cosh(x) +--R + +--R 4 3 2 +--R 20%i cosh(x) - 32cosh(x) + 48%i cosh(x) + 24cosh(x) +--R + +--R - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R - cosh(x) - 4%i cosh(x) + 4cosh(x) + 4%i cosh(x) +--R + +--R 4 3 2 +--R - 8cosh(x) + 16%i cosh(x) + 12cosh(x) - 16%i cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R - +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R / +--R +-+ +--R \|a +--R , +--R +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R 2%i |- \|a +--R \|a +--R * +--R atan +--R +-----------------------------------------+ +--R +-+ | a +--R %i\|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R %i a sinh(x) + %i a cosh(x) + a +--R / +--R +-+ +--R |2 +-+ +--R (a sinh(x) + a cosh(x)) |- \|a +--R \|a +--R / +--R +-+ +--R \|a +--R ] +--R Type: Union(List(Expression(Complex(Integer))),...) +--E 324 + +--S 325 of 526 +m0461a:= a0461.1-r0461 +--R +--R +--R (236) +--R a +--R * +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R a |- \|a +--R \|a +--R * +--R log +--R 7 6 +--R 2sinh(x) + (14cosh(x) - 12%i)sinh(x) +--R + +--R 2 5 +--R (42cosh(x) - 72%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 4 +--R (70cosh(x) - 180%i cosh(x) - 50cosh(x) + 24%i)sinh(x) +--R + +--R 4 3 2 +--R 70cosh(x) - 240%i cosh(x) - 100cosh(x) +--R + +--R 96%i cosh(x) + 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R 42cosh(x) - 180%i cosh(x) - 100cosh(x) +--R + +--R 2 +--R 144%i cosh(x) + 48cosh(x) - 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R 14cosh(x) - 72%i cosh(x) - 50cosh(x) +--R + +--R 3 2 +--R 96%i cosh(x) + 48cosh(x) - 24%i cosh(x) - 8 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 2cosh(x) - 12%i cosh(x) - 10cosh(x) + 24%i cosh(x) +--R + +--R 3 2 +--R 16cosh(x) - 12%i cosh(x) - 8cosh(x) +--R * +--R +-+ +--R |2 +-+ +--R |- \|a +--R \|a +--R + +--R 7 6 +--R - 4sinh(x) + (- 28cosh(x) + 12%i)sinh(x) +--R + +--R 2 5 +--R (- 84cosh(x) + 72%i cosh(x) + 20)sinh(x) +--R + +--R 3 2 4 +--R (- 140cosh(x) + 180%i cosh(x) + 100cosh(x) - 28%i)sinh(x) +--R + +--R 4 3 2 +--R - 140cosh(x) + 240%i cosh(x) + 200cosh(x) +--R + +--R - 112%i cosh(x) - 32 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 +--R - 84cosh(x) + 180%i cosh(x) + 200cosh(x) +--R + +--R 2 +--R - 168%i cosh(x) - 96cosh(x) + 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) + 72%i cosh(x) + 100cosh(x) +--R + +--R 3 2 +--R - 112%i cosh(x) - 96cosh(x) + 48%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 4cosh(x) + 12%i cosh(x) + 20cosh(x) - 28%i cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) + 24%i cosh(x) + 16cosh(x) - 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R 3sinh(x) + (24cosh(x) + 4%i)sinh(x) +--R + +--R 2 6 +--R (84cosh(x) + 28%i cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (168cosh(x) + 84%i cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 4 +--R (210cosh(x) + 140%i cosh(x) - 60%i cosh(x) - 16)sinh(x) +--R + +--R 5 4 2 +--R 168cosh(x) + 140%i cosh(x) - 120%i cosh(x) +--R + +--R - 64cosh(x) + 24%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 3 2 +--R 84cosh(x) + 84%i cosh(x) - 120%i cosh(x) - 96cosh(x) +--R + +--R 72%i cosh(x) + 20 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 4 3 +--R 24cosh(x) + 28%i cosh(x) - 60%i cosh(x) - 64cosh(x) +--R + +--R 2 +--R 72%i cosh(x) + 40cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 5 4 +--R 3cosh(x) + 4%i cosh(x) - 12%i cosh(x) - 16cosh(x) +--R + +--R 3 2 +--R 24%i cosh(x) + 20cosh(x) - 16%i cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R 8 7 +--R - 2a sinh(x) + (- 16a cosh(x) - 2%i a)sinh(x) +--R + +--R 2 6 +--R (- 56a cosh(x) - 14%i a cosh(x) - 2a)sinh(x) +--R + +--R 3 2 +--R (- 112a cosh(x) - 42%i a cosh(x) - 12a cosh(x) + 6%i a) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 +--R - 140a cosh(x) - 70%i a cosh(x) - 30a cosh(x) +--R + +--R 30%i a cosh(x) + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 112a cosh(x) - 70%i a cosh(x) - 40a cosh(x) +--R + +--R 2 +--R 60%i a cosh(x) + 64a cosh(x) - 12%i a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 56a cosh(x) - 42%i a cosh(x) - 30a cosh(x) +--R + +--R 3 2 +--R 60%i a cosh(x) + 96a cosh(x) - 36%i a cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 +--R - 16a cosh(x) - 14%i a cosh(x) - 12a cosh(x) +--R + +--R 4 3 2 +--R 30%i a cosh(x) + 64a cosh(x) - 36%i a cosh(x) +--R + +--R - 24a cosh(x) + 8%i a +--R * +--R sinh(x) +--R + +--R 8 7 6 +--R - 2a cosh(x) - 2%i a cosh(x) - 2a cosh(x) +--R + +--R 5 4 3 +--R 6%i a cosh(x) + 16a cosh(x) - 12%i a cosh(x) +--R + +--R 2 +--R - 12a cosh(x) + 8%i a cosh(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 7 6 +--R 4sinh(x) + (28cosh(x) + 4%i)sinh(x) +--R + +--R 2 5 +--R (84cosh(x) + 24%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 +--R (140cosh(x) + 60%i cosh(x) + 20cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 2 +--R 140cosh(x) + 80%i cosh(x) + 40cosh(x) - 48%i cosh(x) +--R + +--R - 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 84cosh(x) + 60%i cosh(x) + 40cosh(x) - 72%i cosh(x) +--R + +--R - 72cosh(x) + 16%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) + 24%i cosh(x) + 20cosh(x) - 48%i cosh(x) +--R + +--R 2 +--R - 72cosh(x) + 32%i cosh(x) + 16 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 4cosh(x) + 4%i cosh(x) + 4cosh(x) - 12%i cosh(x) +--R + +--R 3 2 +--R - 24cosh(x) + 16%i cosh(x) + 16cosh(x) - 8%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 8 7 +--R - sinh(x) + (- 8cosh(x) - 4%i)sinh(x) +--R + +--R 2 6 +--R (- 28cosh(x) - 28%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 5 +--R (- 56cosh(x) - 84%i cosh(x) + 24cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R - 70cosh(x) - 140%i cosh(x) + 60cosh(x) +--R + +--R 20%i cosh(x) - 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 +--R - 56cosh(x) - 140%i cosh(x) + 80cosh(x) +--R + +--R 2 +--R 40%i cosh(x) - 32cosh(x) + 16%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 +--R - 28cosh(x) - 84%i cosh(x) + 60cosh(x) +--R + +--R 3 2 +--R 40%i cosh(x) - 48cosh(x) + 48%i cosh(x) + 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 8cosh(x) - 28%i cosh(x) + 24cosh(x) + 20%i cosh(x) +--R + +--R 3 2 +--R - 32cosh(x) + 48%i cosh(x) + 24cosh(x) - 16%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R - cosh(x) - 4%i cosh(x) + 4cosh(x) + 4%i cosh(x) +--R + +--R 4 3 2 +--R - 8cosh(x) + 16%i cosh(x) + 12cosh(x) - 16%i cosh(x) - 8 +--R * +--R +-+ +--R \|a +--R + +--R - +--R a +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +------------------+ +------------------+ +--R 2tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +------------------+ +--R \|- %i a csch(x) - a +--R atan(---------------------) +--R +-+ +--R \|a +--R + +--R +-+ +------------------+ +------------------+ +--R \|2 tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(---------------------) +--R +------------------+ +--R \|- %i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Complex(Integer)) +--E 325 + +--S 326 of 526 +--d0461a:= D(m0461a,x) +--E 326 + +--S 327 of 526 +m0461b:= a0461.2-r0461 +--R +--R +--R (237) +--R a +--R * +--R log +--R +-----------------------------------------+ +--R +-+ | a +--R \|a |----------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R a cosh(x) - %i a +--R / +--R sinh(x) + cosh(x) +--R + +--R - +--R a +--R * +--R log +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 4%i cosh(x) + 1)sinh(x) - cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + cosh(x) + 2%i +--R * +--R +-----------------------------------------+ +--R | a +--R |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) - 1)sinh(x) +--R + +--R 2 3 +--R (3%i cosh(x) - 2cosh(x) - %i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 2 +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 1)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R +-+ +--R |2 +-+ +--R 2%i a |- \|a +--R \|a +--R * +--R atan +--R +-----------------------------------------+ +--R +-+ | a +--R %i\|a |----------------------------------------- +--R | 2 2 +--R \|sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R %i a sinh(x) + %i a cosh(x) + a +--R / +--R +-+ +--R |2 +-+ +--R (a sinh(x) + a cosh(x)) |- \|a +--R \|a +--R + +--R +------------------+ +------------------+ +--R 2tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +------------------+ +--R \|- %i a csch(x) - a +--R atan(---------------------) +--R +-+ +--R \|a +--R + +--R +-+ +------------------+ +------------------+ +--R \|2 tanh(x)\|- %i a csch(x) - a \|- %i a csch(x) + a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(---------------------) +--R +------------------+ +--R \|- %i a csch(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Complex(Integer)) +--E 327 + +--S 328 of 526 +--d0461b:= D(m0461b,x) +--E 328 + +--S 329 of 526 +t0462:= 1/(3+5*%i*csch(x)) +--R +--R +--R %i +--R (238) - -------------- +--R 5csch(x) - 3%i +--R Type: Expression(Complex(Integer)) +--E 329 + +--S 330 of 526 +r0462:= 1/3*x+5/6*%i*atan(-3/4+5/4*%i*tanh(1/2*x)) +--R +--R +--R 5 5 1 3 1 +--R (239) - %i atan(- %i tanh(- x) - -) + - x +--R 6 4 2 4 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 330 + +--S 331 of 526 +a0462:= integrate(t0462,x) +--R +--R +--R (240) +--R - 5log(3sinh(x) + 3cosh(x) + %i) + 5log(sinh(x) + cosh(x) + 3%i) + 4x +--R --------------------------------------------------------------------- +--R 12 +--R Type: Union(Expression(Complex(Integer)),...) +--E 331 + +--S 332 of 526 +m0462:= a0462-r0462 +--R +--R +--R (241) +--R 5 5 +--R - -- log(3sinh(x) + 3cosh(x) + %i) + -- log(sinh(x) + cosh(x) + 3%i) +--R 12 12 +--R + +--R 5 5 1 3 +--R - - %i atan(- %i tanh(- x) - -) +--R 6 4 2 4 +--R Type: Expression(Complex(Fraction(Integer))) +--E 332 + +--S 333 of 526 +d0462:= D(m0462,x) +--R +--R +--R (242) +--R 1 2 2 1 2 1 1 2 +--R (- sinh(x) + - cosh(x)sinh(x) + - cosh(x) - -)tanh(- x) +--R 3 3 3 3 2 +--R + +--R 4 4 1 1 2 2 +--R (- sinh(x) + - cosh(x))tanh(- x) - - sinh(x) - - cosh(x)sinh(x) +--R 3 3 2 3 3 +--R + +--R 1 2 1 +--R - - cosh(x) + - +--R 3 3 +--R / +--R 2 10 2 10 +--R (sinh(x) + (2cosh(x) + -- %i)sinh(x) + cosh(x) + -- %i cosh(x) - 1) +--R 3 3 +--R * +--R 1 2 +--R tanh(- x) +--R 2 +--R + +--R 6 2 12 6 2 +--R - %i sinh(x) + (-- %i cosh(x) - 4)sinh(x) + - %i cosh(x) - 4cosh(x) +--R 5 5 5 +--R + +--R 6 +--R - - %i +--R 5 +--R * +--R 1 +--R tanh(- x) +--R 2 +--R + +--R 2 10 2 10 +--R - sinh(x) + (- 2cosh(x) - -- %i)sinh(x) - cosh(x) - -- %i cosh(x) + 1 +--R 3 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 333 + +--S 334 of 526 +t0463:= 1/(a+b*csch(x)) +--R +--R +--R 1 +--R (243) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 526 +r0463:= x/a+2*b*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a/(a^2+b^2)^(1/2) +--R +--R +--R x +--R b tanh(-) - a +-------+ +--R 2 | 2 2 +--R - 2b atanh(-------------) + x\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (244) --------------------------------------- +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 526 +a0463:= integrate(t0463,x) +--R +--R +--R (245) +--R b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R +-------+ +--R | 2 2 +--R x\|b + a +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Union(Expression(Integer),...) +--E 336 + +--S 337 of 526 +m0463:= a0463-r0463 +--R +--R +--R (246) +--R b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R x +--R b tanh(-) - a +--R 2 +--R 2b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 526 +d0463:= D(m0463,x) +--R +--R +--R (247) +--R 2 2 x 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b)tanh(-) +--R 2 +--R + +--R x 2 +--R (4b sinh(x) + 4b cosh(x))tanh(-) - b sinh(x) - 2b cosh(x)sinh(x) +--R 2 +--R + +--R 2 +--R - b cosh(x) + b +--R / +--R 2 2 2 +--R a b sinh(x) + (2a b cosh(x) + 2b )sinh(x) + a b cosh(x) +--R + +--R 2 +--R 2b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 2 +--R - 2a sinh(x) + (- 4a cosh(x) - 4a b)sinh(x) - 2a cosh(x) +--R + +--R 2 +--R - 4a b cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 2 2 +--R - a b sinh(x) + (- 2a b cosh(x) - 2b )sinh(x) - a b cosh(x) +--R + +--R 2 +--R - 2b cosh(x) + a b +--R Type: Expression(Integer) +--E 338 + +--S 339 of 526 +t0464:= 1/(a+b*csch(x))^2 +--R +--R +--R 1 +--R (248) ------------------------------ +--R 2 2 2 +--R b csch(x) + 2a b csch(x) + a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 526 +r0464:= x/a^2-2*b^3*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^2/_ + (a^2+b^2)^(3/2)+4*b*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/_ + a^2/(a^2+b^2)^(1/2)-b^2*cosh(x)/a/(a^2+b^2)/(b+a*sinh(x)) +--R +--R +--R (249) +--R x +--R b tanh(-) - a +--R 3 3 4 2 2 2 +--R ((- 2a b - 4a b)sinh(x) - 2b - 4a b )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 3 2 3 2 | 2 2 +--R ((a b + a )x sinh(x) - a b cosh(x) + (b + a b)x)\|b + a +--R / +--R +-------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b + a )sinh(x) + a b + a b)\|b + a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 526 +a0464:= integrate(t0464,x) +--R +--R +--R (250) +--R 3 3 2 3 3 4 2 2 +--R (a b + 2a b)sinh(x) + ((2a b + 4a b)cosh(x) + 2b + 4a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (a b + 2a b)cosh(x) + (2b + 4a b )cosh(x) - a b - 2a b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 3 2 +--R (a b + a )x sinh(x) +--R + +--R 2 3 3 2 3 +--R ((2a b + 2a )x cosh(x) + (2b + 2a b)x + 2b )sinh(x) +--R + +--R 2 3 2 3 2 3 2 3 +--R (a b + a )x cosh(x) + ((2b + 2a b)x + 2b )cosh(x) + (- a b - a )x +--R + +--R 2 +--R - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 2 5 2 3 2 5 2 3 4 +--R (a b + a )sinh(x) + ((2a b + 2a )cosh(x) + 2a b + 2a b)sinh(x) +--R + +--R 3 2 5 2 2 3 4 3 2 5 +--R (a b + a )cosh(x) + (2a b + 2a b)cosh(x) - a b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 341 + +--S 342 of 526 +m0464:= a0464-r0464 +--R +--R +--R (251) +--R 2 3 4 3 +--R (a b + 2a b)sinh(x) +--R + +--R 2 3 4 4 3 2 2 +--R ((2a b + 4a b)cosh(x) + 3a b + 6a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 2 3 +--R (a b + 2a b)cosh(x) + (4a b + 8a b )cosh(x) + 2b + 3a b +--R + +--R 4 +--R - 2a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 5 2 3 4 3 2 +--R (a b + 2a b )cosh(x) + (2b + 4a b )cosh(x) - a b - 2a b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 3 4 3 +--R (2a b + 4a b)sinh(x) +--R + +--R 2 3 4 4 3 2 2 +--R ((4a b + 8a b)cosh(x) + 6a b + 12a b )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 2 3 +--R (2a b + 4a b)cosh(x) + (8a b + 16a b )cosh(x) + 4b + 6a b +--R + +--R 4 +--R - 4a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 5 2 3 4 3 2 +--R (2a b + 4a b )cosh(x) + (4b + 8a b )cosh(x) - 2a b - 4a b +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 3 2 +--R (a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 2 3 4 2 2 2 2 3 +--R (2a b cosh(x) + 4a b cosh(x) + 2b - 2a b )sinh(x) + a b cosh(x) +--R + +--R 3 2 4 2 2 3 +--R 2a b cosh(x) + (2b - a b )cosh(x) - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 6 3 4 2 6 3 3 5 2 +--R (a b + a )sinh(x) + ((2a b + 2a )cosh(x) + 3a b + 3a b)sinh(x) +--R + +--R 4 2 6 2 3 3 5 2 4 4 2 6 +--R ((a b + a )cosh(x) + (4a b + 4a b)cosh(x) + 2a b + a b - a ) +--R * +--R sinh(x) +--R + +--R 3 3 5 2 2 4 4 2 3 3 5 +--R (a b + a b)cosh(x) + (2a b + 2a b )cosh(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 342 + +--S 343 of 526 +d0464:= D(m0464,x) +--R +--R +--R (252) +--R 3 3 5 6 +--R (2a b + 2a b)sinh(x) +--R + +--R 3 3 5 2 4 4 2 5 +--R ((8a b + 8a b)cosh(x) + 7a b + 8a b )sinh(x) +--R + +--R 3 3 5 2 2 4 4 2 5 +--R (11a b + 12a b)cosh(x) + (24a b + 28a b )cosh(x) + 9a b +--R + +--R 3 3 5 +--R 10a b - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 4 2 2 +--R (4a b + 8a b)cosh(x) + (26a b + 36a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (24a b + 32a b - 8a b)cosh(x) + 4b + 2a b - 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 5 4 2 4 4 2 3 +--R (- 4a b + 2a b)cosh(x) + (4a b + 20a b )cosh(x) +--R + +--R 5 3 3 5 2 6 2 4 4 2 +--R (18a b + 38a b - 4a b)cosh(x) + (8b + 12a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 +--R - 2a b - 10a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 4 4 2 4 3 3 3 +--R - 4a b cosh(x) + (- 9a b + 4a b )cosh(x) + 20a b cosh(x) +--R + +--R 6 2 4 4 2 2 3 3 2 4 4 2 +--R (4b + 18a b - 8a b )cosh(x) - 16a b cosh(x) - a b + 4a b +--R * +--R sinh(x) +--R + +--R 3 3 6 2 4 5 5 3 3 4 +--R - a b cosh(x) - 4a b cosh(x) + (- 3a b + 4a b )cosh(x) +--R + +--R 2 4 3 5 3 3 2 2 4 5 3 3 +--R 8a b cosh(x) + (2a b - 5a b )cosh(x) - 4a b cosh(x) + a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 6 4 2 3 3 5 5 +--R - 2a b sinh(x) + (- 8a b cosh(x) - 2a b + 8a b)sinh(x) +--R + +--R 4 2 2 3 3 5 2 4 4 2 +--R (- 10a b cosh(x) + (- 8a b + 24a b)cosh(x) + 8a b + 28a b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 2 2 4 4 2 5 +--R (- 4a b + 24a b)cosh(x) + (24a b + 72a b )cosh(x) + 16a b +--R + +--R 3 3 5 +--R 28a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 4 3 3 5 3 +--R 10a b cosh(x) + (16a b + 8a b)cosh(x) +--R + +--R 2 4 4 2 2 5 3 3 5 6 +--R (32a b + 56a b )cosh(x) + (40a b + 64a b - 8a b)cosh(x) + 8b +--R + +--R 4 2 +--R - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 5 3 3 4 2 4 4 2 3 +--R 8a b cosh(x) + 22a b cosh(x) + (24a b + 8a b )cosh(x) +--R + +--R 5 3 3 2 6 2 4 4 2 +--R (32a b + 36a b )cosh(x) + (16b + 8a b - 16a b )cosh(x) +--R + +--R 5 3 3 +--R - 8a b - 10a b +--R * +--R sinh(x) +--R + +--R 4 2 6 3 3 5 2 4 4 2 4 +--R 2a b cosh(x) + 8a b cosh(x) + (8a b - 4a b )cosh(x) +--R + +--R 5 3 6 2 4 4 2 2 +--R 8a b cosh(x) + (8b + 8a b + 2a b )cosh(x) +--R + +--R 5 3 3 +--R (- 8a b - 8a b )cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 5 6 +--R (- 2a b - 2a b)sinh(x) +--R + +--R 3 3 5 2 4 4 2 5 +--R ((- 8a b - 8a b)cosh(x) - 7a b - 8a b )sinh(x) +--R + +--R 3 3 5 2 2 4 4 2 5 +--R (- 11a b - 12a b)cosh(x) + (- 24a b - 28a b )cosh(x) - 9a b +--R + +--R 3 3 5 +--R - 10a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 5 3 2 4 4 2 2 +--R (- 4a b - 8a b)cosh(x) + (- 26a b - 36a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 24a b - 32a b + 8a b)cosh(x) - 4b - 2a b + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 5 4 2 4 4 2 3 +--R (4a b - 2a b)cosh(x) + (- 4a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 2 6 2 4 4 2 +--R (- 18a b - 38a b + 4a b)cosh(x) + (- 8b - 12a b + 20a b )cosh(x) +--R + +--R 5 3 3 5 +--R 2a b + 10a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 4 4 2 4 3 3 3 +--R 4a b cosh(x) + (9a b - 4a b )cosh(x) - 20a b cosh(x) +--R + +--R 6 2 4 4 2 2 3 3 2 4 4 2 +--R (- 4b - 18a b + 8a b )cosh(x) + 16a b cosh(x) + a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 6 2 4 5 5 3 3 4 2 4 3 +--R a b cosh(x) + 4a b cosh(x) + (3a b - 4a b )cosh(x) - 8a b cosh(x) +--R + +--R 5 3 3 2 2 4 5 3 3 +--R (- 2a b + 5a b )cosh(x) + 4a b cosh(x) - a b - 2a b +--R / +--R 5 3 7 6 +--R (a b + a b)sinh(x) +--R + +--R 5 3 7 4 4 6 2 5 +--R ((4a b + 4a b)cosh(x) + 6a b + 6a b )sinh(x) +--R + +--R 5 3 7 2 4 4 6 2 3 5 +--R (6a b + 6a b)cosh(x) + (20a b + 20a b )cosh(x) + 13a b +--R + +--R 5 3 7 +--R 11a b - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 7 3 4 4 6 2 2 +--R (4a b + 4a b)cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 3 5 5 3 7 2 6 4 4 6 2 +--R (36a b + 32a b - 4a b)cosh(x) + 12a b + 4a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 7 4 4 4 6 2 3 +--R (a b + a b)cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 3 5 5 3 7 2 +--R (34a b + 32a b - 2a b)cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 7 +--R (28a b + 16a b - 12a b )cosh(x) + 4a b - 6a b - 9a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (2a b + 2a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (20a b + 16a b - 4a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 6 2 +--R (8a b - 4a b - 12a b )cosh(x) - 4a b - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 4 2 6 4 4 3 +--R (a b + a b )cosh(x) + (4a b + 4a b )cosh(x) +--R + +--R 7 3 5 5 3 2 2 6 4 4 3 5 +--R (4a b + 2a b - 2a b )cosh(x) + (- 4a b - 4a b )cosh(x) + a b +--R + +--R 5 3 +--R a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 2 8 6 +--R (- 2a b - 2a )sinh(x) +--R + +--R 6 2 8 5 3 7 5 +--R ((- 8a b - 8a )cosh(x) - 12a b - 12a b)sinh(x) +--R + +--R 6 2 8 2 5 3 7 4 4 +--R (- 12a b - 12a )cosh(x) + (- 40a b - 40a b)cosh(x) - 26a b +--R + +--R 6 2 8 +--R - 22a b + 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 8 3 5 3 7 2 +--R (- 8a b - 8a )cosh(x) + (- 48a b - 48a b)cosh(x) +--R + +--R 4 4 6 2 8 3 5 5 3 7 +--R (- 72a b - 64a b + 8a )cosh(x) - 24a b - 8a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 8 4 5 3 7 3 +--R (- 2a b - 2a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 4 4 6 2 8 2 +--R (- 68a b - 64a b + 4a )cosh(x) +--R + +--R 3 5 5 3 7 2 6 4 4 6 2 8 +--R (- 56a b - 32a b + 24a b)cosh(x) - 8a b + 12a b + 18a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 7 4 4 4 6 2 3 +--R (- 4a b - 4a b)cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 3 5 5 3 7 2 +--R (- 40a b - 32a b + 8a b)cosh(x) +--R + +--R 2 6 4 4 6 2 3 5 5 3 7 +--R (- 16a b + 8a b + 24a b )cosh(x) + 8a b + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (- 2a b - 2a b )cosh(x) + (- 8a b - 8a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 3 5 5 3 4 4 +--R (- 8a b - 4a b + 4a b )cosh(x) + (8a b + 8a b )cosh(x) - 2a b +--R + +--R 6 2 +--R - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 3 7 6 +--R (- a b - a b)sinh(x) +--R + +--R 5 3 7 4 4 6 2 5 +--R ((- 4a b - 4a b)cosh(x) - 6a b - 6a b )sinh(x) +--R + +--R 5 3 7 2 4 4 6 2 3 5 +--R (- 6a b - 6a b)cosh(x) + (- 20a b - 20a b )cosh(x) - 13a b +--R + +--R 5 3 7 +--R - 11a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 7 3 4 4 6 2 2 +--R (- 4a b - 4a b)cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 3 5 5 3 7 2 6 4 4 6 2 +--R (- 36a b - 32a b + 4a b)cosh(x) - 12a b - 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 7 4 4 4 6 2 3 +--R (- a b - a b)cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 3 5 5 3 7 2 +--R (- 34a b - 32a b + 2a b)cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 7 +--R (- 28a b - 16a b + 12a b )cosh(x) - 4a b + 6a b + 9a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (- 2a b - 2a b )cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 20a b - 16a b + 4a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 6 2 +--R (- 8a b + 4a b + 12a b )cosh(x) + 4a b + 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 4 2 6 4 4 3 +--R (- a b - a b )cosh(x) + (- 4a b - 4a b )cosh(x) +--R + +--R 7 3 5 5 3 2 2 6 4 4 3 5 5 3 +--R (- 4a b - 2a b + 2a b )cosh(x) + (4a b + 4a b )cosh(x) - a b - a b +--R Type: Expression(Integer) +--E 343 + +--S 344 of 526 +t0465:= 1/(a+b*csch(x))^3 +--R +--R +--R 1 +--R (253) ---------------------------------------------- +--R 3 3 2 2 2 3 +--R b csch(x) + 3a b csch(x) + 3a b csch(x) + a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 526 +r0465:= x/a^3-b^3*(a^2-2*b^2)*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/_ + a^3/(a^2+b^2)^(5/2)-6*b^3*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/_ + a^3/(a^2+b^2)^(3/2)+6*b*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/_ + a^3/(a^2+b^2)^(1/2)+1/2*b^3*cosh(x)/a^2/(a^2+b^2)/(b+a*sinh(x))^2+_ + 3/2*b^4*cosh(x)/a^2/(a^2+b^2)^2/(b+a*sinh(x))-_ + 3*b^2*cosh(x)/a^2/(a^2+b^2)/(b+a*sinh(x)) +--R +--R +--R (254) +--R 2 5 4 3 6 2 +--R (- 4a b - 10a b - 12a b)sinh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (- 8a b - 20a b - 24a b )sinh(x) - 4b - 10a b - 12a b +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 4 2 6 2 +--R (2a b + 4a b + 2a )x sinh(x) +--R + +--R 2 4 4 2 5 3 3 5 +--R ((- 3a b - 6a b )cosh(x) + (4a b + 8a b + 4a b)x)sinh(x) +--R + +--R 5 3 3 6 2 4 4 2 +--R (- 2a b - 5a b )cosh(x) + (2b + 4a b + 2a b )x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 4 7 2 9 2 4 5 6 3 8 3 6 +--R (2a b + 4a b + 2a )sinh(x) + (4a b + 8a b + 4a b)sinh(x) + 2a b +--R + +--R 5 4 7 2 +--R 4a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 345 + +--S 346 of 526 +a0465:= integrate(t0465,x) +--R +--R +--R (255) +--R 2 5 4 3 6 4 +--R (2a b + 5a b + 6a b)sinh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 3 +--R ((8a b + 20a b + 24a b)cosh(x) + 8a b + 20a b + 24a b )sinh(x) +--R + +--R 2 5 4 3 6 2 +--R (12a b + 30a b + 36a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 6 +--R (24a b + 60a b + 72a b )cosh(x) + 8b + 16a b + 14a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 3 6 3 +--R (8a b + 20a b + 24a b)cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (24a b + 60a b + 72a b )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 +--R (16b + 32a b + 28a b - 24a b)cosh(x) - 8a b - 20a b - 24a b +--R * +--R sinh(x) +--R + +--R 2 5 4 3 6 4 6 3 4 5 2 3 +--R (2a b + 5a b + 6a b)cosh(x) + (8a b + 20a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (8b + 16a b + 14a b - 12a b)cosh(x) +--R + +--R 6 3 4 5 2 2 5 4 3 6 +--R (- 8a b - 20a b - 24a b )cosh(x) + 2a b + 5a b + 6a b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 4 4 2 6 4 +--R (2a b + 4a b + 2a )x sinh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (8a b + 16a b + 8a )x cosh(x) + (8a b + 16a b + 8a b)x +--R + +--R 5 3 3 +--R 8a b + 14a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 6 2 +--R (12a b + 24a b + 12a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((24a b + 48a b + 24a b)x + 24a b + 42a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R (8b + 12a b - 4a )x + 12b + 18a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 +--R (8a b + 16a b + 8a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 2 +--R ((24a b + 48a b + 24a b)x + 24a b + 42a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 +--R ((16b + 24a b - 8a )x + 24b + 36a b - 24a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R (- 8a b - 16a b - 8a b)x - 16a b - 34a b +--R * +--R sinh(x) +--R + +--R 2 4 4 2 6 4 +--R (2a b + 4a b + 2a )x cosh(x) +--R + +--R 5 3 3 5 5 3 3 3 +--R ((8a b + 16a b + 8a b)x + 8a b + 14a b )cosh(x) +--R + +--R 6 2 4 6 6 2 4 4 2 2 +--R ((8b + 12a b - 4a )x + 12b + 18a b - 12a b )cosh(x) +--R + +--R 5 3 3 5 5 3 3 +--R ((- 8a b - 16a b - 8a b)x - 16a b - 34a b )cosh(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (2a b + 4a b + 2a )x + 6a b + 12a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 4 7 2 9 4 +--R (2a b + 4a b + 2a )sinh(x) +--R + +--R 5 4 7 2 9 4 5 6 3 8 3 +--R ((8a b + 16a b + 8a )cosh(x) + 8a b + 16a b + 8a b)sinh(x) +--R + +--R 5 4 7 2 9 2 4 5 6 3 8 +--R (12a b + 24a b + 12a )cosh(x) + (24a b + 48a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 9 +--R 8a b + 12a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 7 2 9 3 4 5 6 3 8 2 +--R (8a b + 16a b + 8a )cosh(x) + (24a b + 48a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 9 4 5 6 3 8 +--R (16a b + 24a b - 8a )cosh(x) - 8a b - 16a b - 8a b +--R * +--R sinh(x) +--R + +--R 5 4 7 2 9 4 4 5 6 3 8 3 +--R (2a b + 4a b + 2a )cosh(x) + (8a b + 16a b + 8a b)cosh(x) +--R + +--R 3 6 5 4 9 2 4 5 6 3 8 +--R (8a b + 12a b - 4a )cosh(x) + (- 8a b - 16a b - 8a b)cosh(x) +--R + +--R 5 4 7 2 9 +--R 2a b + 4a b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 346 + +--S 347 of 526 +m0465:= a0465-r0465 +--R +--R +--R (256) +--R 4 5 6 3 8 6 +--R (2a b + 5a b + 6a b)sinh(x) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 5 +--R ((8a b + 20a b + 24a b)cosh(x) + 12a b + 30a b + 36a b )sinh(x) +--R + +--R 4 5 6 3 8 2 +--R (12a b + 30a b + 36a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 +--R (40a b + 100a b + 120a b )cosh(x) + 26a b + 61a b + 68a b +--R + +--R 8 +--R - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (8a b + 20a b + 24a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (48a b + 120a b + 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 8 3 6 +--R (72a b + 172a b + 196a b - 24a b)cosh(x) + 24a b + 44a b +--R + +--R 5 4 7 2 +--R 32a b - 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (2a b + 5a b + 6a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (24a b + 60a b + 72a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (68a b + 166a b + 194a b - 12a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 4 5 +--R (56a b + 116a b + 108a b - 72a b )cosh(x) + 8b - 24a b +--R + +--R 6 3 8 +--R - 55a b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (4a b + 10a b + 12a b )cosh(x) +--R + +--R 2 7 4 5 6 3 3 +--R (24a b + 60a b + 72a b )cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (40a b + 92a b + 100a b - 24a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 +--R (16b + 16a b - 12a b - 72a b )cosh(x) - 8a b - 16a b +--R + +--R 5 4 7 2 +--R - 14a b + 12a b +--R * +--R sinh(x) +--R + +--R 2 7 4 5 6 3 4 8 3 6 5 4 3 +--R (2a b + 5a b + 6a b )cosh(x) + (8a b + 20a b + 24a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 2 +--R (8b + 16a b + 14a b - 12a b )cosh(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 +--R (- 8a b - 20a b - 24a b )cosh(x) + 2a b + 5a b + 6a b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 4 5 6 3 8 6 +--R (4a b + 10a b + 12a b)sinh(x) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 5 +--R ((16a b + 40a b + 48a b)cosh(x) + 24a b + 60a b + 72a b )sinh(x) +--R + +--R 4 5 6 3 8 2 +--R (24a b + 60a b + 72a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 +--R (80a b + 200a b + 240a b )cosh(x) + 52a b + 122a b + 136a b +--R + +--R 8 +--R - 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 6 3 8 3 +--R (16a b + 40a b + 48a b)cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (96a b + 240a b + 288a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 8 3 6 +--R (144a b + 344a b + 392a b - 48a b)cosh(x) + 48a b + 88a b +--R + +--R 5 4 7 2 +--R 64a b - 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (4a b + 10a b + 12a b)cosh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (48a b + 120a b + 144a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (136a b + 332a b + 388a b - 24a b)cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 4 5 +--R (112a b + 232a b + 216a b - 144a b )cosh(x) + 16b - 48a b +--R + +--R 6 3 8 +--R - 110a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 4 7 2 4 +--R (8a b + 20a b + 24a b )cosh(x) +--R + +--R 2 7 4 5 6 3 3 +--R (48a b + 120a b + 144a b )cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (80a b + 184a b + 200a b - 48a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 +--R (32b + 32a b - 24a b - 144a b )cosh(x) - 16a b - 32a b +--R + +--R 5 4 7 2 +--R - 28a b + 24a b +--R * +--R sinh(x) +--R + +--R 2 7 4 5 6 3 4 +--R (4a b + 10a b + 12a b )cosh(x) +--R + +--R 8 3 6 5 4 3 +--R (16a b + 40a b + 48a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 2 +--R (16b + 32a b + 28a b - 24a b )cosh(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 +--R (- 16a b - 40a b - 48a b )cosh(x) + 4a b + 10a b + 12a b +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 4 6 2 3 5 5 3 5 +--R ((3a b + 6a b )cosh(x) + 8a b + 14a b )sinh(x) +--R + +--R 4 4 6 2 2 3 5 5 3 2 6 +--R (12a b + 24a b )cosh(x) + (38a b + 71a b )cosh(x) + 28a b +--R + +--R 4 4 6 2 +--R 46a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 6 2 3 3 5 5 3 2 +--R (18a b + 36a b )cosh(x) + (68a b + 134a b )cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 +--R (92a b + 158a b - 36a b )cosh(x) + 32a b + 34a b - 58a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 6 2 4 3 5 5 3 3 +--R (12a b + 24a b )cosh(x) + (56a b + 116a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (108a b + 198a b - 36a b )cosh(x) +--R + +--R 7 3 5 5 3 8 2 6 4 4 +--R (80a b + 102a b - 116a b )cosh(x) + 12b - 14a b - 74a b +--R + +--R 6 2 +--R 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 5 3 5 5 3 4 +--R (3a b + 6a b )cosh(x) + (20a b + 44a b )cosh(x) +--R + +--R 2 6 4 4 6 2 3 +--R (52a b + 106a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (64a b + 98a b - 68a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 7 3 5 5 3 +--R (24b - 4a b - 109a b + 6a b )cosh(x) - 16a b - 22a b + 24a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 5 2 6 4 4 4 +--R (2a b + 5a b )cosh(x) + (8a b + 20a b )cosh(x) +--R + +--R 7 3 5 5 3 3 8 2 6 4 4 2 +--R (16a b + 30a b - 10a b )cosh(x) + (12b + 10a b - 32a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 +--R (- 16a b - 32a b + 5a b )cosh(x) + 6a b + 12a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 7 4 9 2 11 6 +--R (2a b + 4a b + 2a )sinh(x) +--R + +--R 7 4 9 2 11 6 5 8 3 10 5 +--R ((8a b + 16a b + 8a )cosh(x) + 12a b + 24a b + 12a b)sinh(x) +--R + +--R 7 4 9 2 11 2 +--R (12a b + 24a b + 12a )cosh(x) +--R + +--R 6 5 8 3 10 5 6 7 4 9 2 11 +--R (40a b + 80a b + 40a b)cosh(x) + 26a b + 48a b + 18a b - 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 7 4 9 2 11 3 +--R (8a b + 16a b + 8a )cosh(x) +--R + +--R 6 5 8 3 10 2 +--R (48a b + 96a b + 48a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 4 7 6 5 8 3 +--R (72a b + 136a b + 56a b - 8a )cosh(x) + 24a b + 32a b - 8a b +--R + +--R 10 +--R - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 4 9 2 11 4 6 5 8 3 10 3 +--R (2a b + 4a b + 2a )cosh(x) + (24a b + 48a b + 24a b)cosh(x) +--R + +--R 5 6 7 4 9 2 11 2 +--R (68a b + 132a b + 60a b - 4a )cosh(x) +--R + +--R 4 7 6 5 8 3 10 3 8 5 6 7 4 +--R (56a b + 88a b + 8a b - 24a b)cosh(x) + 8a b - 4a b - 30a b +--R + +--R 9 2 11 +--R - 16a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 8 3 10 4 +--R (4a b + 8a b + 4a b)cosh(x) +--R + +--R 5 6 7 4 9 2 3 +--R (24a b + 48a b + 24a b )cosh(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (40a b + 72a b + 24a b - 8a b)cosh(x) +--R + +--R 3 8 5 6 7 4 9 2 4 7 6 5 10 +--R (16a b + 8a b - 32a b - 24a b )cosh(x) - 8a b - 12a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 6 7 4 9 2 4 4 7 6 5 8 3 3 +--R (2a b + 4a b + 2a b )cosh(x) + (8a b + 16a b + 8a b )cosh(x) +--R + +--R 3 8 5 6 9 2 2 4 7 6 5 8 3 +--R (8a b + 12a b - 4a b )cosh(x) + (- 8a b - 16a b - 8a b )cosh(x) +--R + +--R 5 6 7 4 9 2 +--R 2a b + 4a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 526 +d0465:= D(m0465,x) +--R +--R +--R (257) +--R 5 5 7 3 9 9 +--R (5a b + 11a b + 6a b)sinh(x) +--R + +--R 5 5 7 3 9 4 6 6 4 8 2 8 +--R ((30a b + 66a b + 36a b)cosh(x) + 29a b + 68a b + 42a b )sinh(x) +--R + +--R 5 5 7 3 9 2 +--R (72a b + 159a b + 90a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 7 5 5 7 3 +--R (156a b + 366a b + 228a b )cosh(x) + 74a b + 173a b + 105a b +--R + +--R 9 +--R - 18a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 7 3 9 3 +--R (82a b + 184a b + 120a b)cosh(x) +--R + +--R 4 6 6 4 8 2 2 +--R (326a b + 770a b + 510a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 8 4 6 +--R (342a b + 816a b + 528a b - 72a b)cosh(x) + 98a b + 208a b +--R + +--R 6 4 8 2 +--R 92a b - 102a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 7 3 9 4 +--R (30a b + 75a b + 90a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 +--R (304a b + 736a b + 600a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (594a b + 1467a b + 1098a b - 108a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 9 3 7 +--R (384a b + 870a b + 504a b - 360a b )cosh(x) + 64a b + 94a b +--R + +--R 5 5 7 3 9 +--R - 33a b - 213a b + 18a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (- 30a b - 54a b + 36a b)cosh(x) +--R + +--R 4 6 6 4 8 2 4 +--R (60a b + 180a b + 390a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (430a b + 1144a b + 1212a b - 72a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (546a b + 1368a b + 1134a b - 468a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 10 +--R (216a b + 402a b + 102a b - 678a b + 36a b)cosh(x) + 16b +--R + +--R 2 8 4 6 6 4 8 2 +--R - 14a b - 84a b - 186a b + 78a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 7 3 9 6 +--R (- 40a b - 79a b + 6a b)cosh(x) +--R + +--R 4 6 6 4 8 2 5 +--R (- 116a b - 242a b + 132a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 4 +--R (30a b + 171a b + 753a b - 18a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (304a b + 924a b + 1316a b - 264a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (256a b + 628a b + 570a b - 789a b + 18a b)cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 9 +--R (48b + 24a b - 120a b - 594a b + 132a b )cosh(x) - 16a b +--R + +--R 3 7 5 5 7 3 9 +--R - 22a b - 53a b + 115a b - 6a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 7 3 7 +--R (- 18a b - 36a b )cosh(x) +--R + +--R 4 6 6 4 8 2 6 +--R (- 94a b - 214a b + 18a b )cosh(x) +--R + +--R 3 7 5 5 7 3 5 +--R (- 126a b - 288a b + 252a b )cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (6a b + 144a b + 804a b - 54a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (112a b + 412a b + 774a b - 396a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (48b + 108a b + 90a b - 654a b + 54a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 +--R (- 24a b - 54a b - 228a b + 180a b )cosh(x) + 6a b + 4a b +--R + +--R 6 4 8 2 +--R 64a b - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 7 3 8 4 6 6 4 7 +--R (- 3a b - 6a b )cosh(x) + (- 24a b - 60a b )cosh(x) +--R + +--R 3 7 5 5 7 3 6 +--R (- 58a b - 163a b + 36a b )cosh(x) +--R + +--R 2 8 4 6 6 4 5 +--R (- 48a b - 114a b + 228a b )cosh(x) +--R + +--R 3 7 5 5 7 3 4 +--R (78a b + 411a b - 72a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 3 +--R (16b + 88a b + 204a b - 276a b )cosh(x) +--R + +--R 3 7 5 5 7 3 2 +--R (- 18a b - 249a b + 60a b )cosh(x) +--R + +--R 4 6 6 4 3 7 5 5 7 3 +--R (- 18a b + 108a b )cosh(x) - 2a b + 4a b - 18a b +--R * +--R sinh(x) +--R + +--R 4 6 6 4 8 3 7 5 5 7 +--R (- a b - 4a b )cosh(x) + (- 6a b - 24a b )cosh(x) +--R + +--R 2 8 4 6 6 4 6 +--R (- 10a b - 40a b + 18a b )cosh(x) +--R + +--R 9 3 7 5 5 5 +--R (- 8a b - 14a b + 72a b )cosh(x) +--R + +--R 2 8 4 6 6 4 4 +--R (18a b + 78a b - 30a b )cosh(x) +--R + +--R 9 3 7 5 5 3 +--R (8a b + 14a b - 72a b )cosh(x) +--R + +--R 2 8 4 6 6 4 2 3 7 5 5 2 8 +--R (- 6a b - 32a b + 22a b )cosh(x) + (6a b + 24a b )cosh(x) - 2a b +--R + +--R 4 6 6 4 +--R - 5a b - 6a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 4 8 2 9 +--R (- 6a b - 12a b )sinh(x) +--R + +--R 6 4 8 2 5 5 7 3 9 8 +--R ((- 36a b - 72a b )cosh(x) - 22a b - 46a b + 24a b)sinh(x) +--R + +--R 6 4 8 2 2 +--R (- 84a b - 168a b )cosh(x) +--R + +--R 5 5 7 3 9 4 6 6 4 8 2 +--R (- 120a b - 252a b + 120a b)cosh(x) - 16a b - 28a b + 156a b +--R * +--R 7 +--R sinh(x) +--R + +--R 6 4 8 2 3 +--R (- 84a b - 168a b )cosh(x) +--R + +--R 5 5 7 3 9 2 +--R (- 232a b - 490a b + 240a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 7 5 5 +--R (- 60a b - 120a b + 696a b )cosh(x) + 56a b + 130a b +--R + +--R 7 3 9 +--R 362a b - 48a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 7 3 9 3 +--R (- 128a b - 272a b + 240a b)cosh(x) +--R + +--R 6 4 8 2 2 +--R (- 36a b + 1188a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 8 +--R (288a b + 612a b + 1440a b - 144a b)cosh(x) + 136a b +--R + +--R 4 6 6 4 8 2 +--R 244a b + 300a b - 228a b +--R * +--R 5 +--R sinh(x) +--R + +--R 6 4 8 2 5 5 5 7 3 9 4 +--R (84a b + 168a b )cosh(x) + (180a b + 390a b + 120a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 +--R (292a b + 544a b + 912a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (648a b + 1254a b + 2052a b - 144a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 9 +--R (552a b + 984a b + 1092a b - 600a b )cosh(x) + 112a b +--R + +--R 3 7 5 5 7 3 9 +--R 88a b - 90a b - 378a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 4 8 2 6 5 5 7 3 9 5 +--R (84a b + 168a b )cosh(x) + (328a b + 724a b + 24a b)cosh(x) +--R + +--R 4 6 6 4 8 2 4 +--R (528a b + 1116a b + 228a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (800a b + 1480a b + 1112a b - 48a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (880a b + 1528a b + 1308a b - 480a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 10 +--R (384a b + 384a b - 144a b - 876a b + 24a b)cosh(x) + 32b +--R + +--R 2 8 4 6 6 4 8 2 +--R - 80a b - 232a b - 204a b + 84a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 8 2 7 5 5 7 3 6 +--R (36a b + 72a b )cosh(x) + (200a b + 458a b )cosh(x) +--R + +--R 4 6 6 4 8 2 5 +--R (396a b + 936a b - 72a b )cosh(x) +--R + +--R 3 7 5 5 7 3 4 +--R (552a b + 1086a b - 6a b )cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (688a b + 1168a b + 468a b - 72a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (480a b + 576a b - 36a b - 546a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 9 +--R (96b - 144a b - 540a b - 480a b + 72a b )cosh(x) - 48a b +--R + +--R 3 7 5 5 7 3 +--R - 48a b + 46a b + 94a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 4 8 2 8 5 5 7 3 7 +--R (6a b + 12a b )cosh(x) + (48a b + 120a b )cosh(x) +--R + +--R 4 6 6 4 8 2 6 +--R (128a b + 356a b - 36a b )cosh(x) +--R + +--R 3 7 5 5 7 3 5 +--R (192a b + 468a b - 168a b )cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (264a b + 468a b - 120a b + 36a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (256a b + 352a b - 24a b - 24a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (96b - 48a b - 360a b - 276a b - 12a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 +--R (- 96a b - 144a b - 12a b + 72a b )cosh(x) + 24a b + 52a b +--R + +--R 6 4 +--R 34a b +--R * +--R sinh(x) +--R + +--R 5 5 7 3 8 4 6 6 4 7 +--R (2a b + 8a b )cosh(x) + (12a b + 48a b )cosh(x) +--R + +--R 3 7 5 5 7 3 6 +--R (24a b + 90a b - 24a b )cosh(x) +--R + +--R 2 8 4 6 6 4 5 +--R (40a b + 88a b - 72a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 4 +--R (48a b + 72a b - 42a b + 24a b )cosh(x) +--R + +--R 10 2 8 4 6 3 +--R (32b + 16a b - 52a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (- 48a b - 96a b - 50a b - 8a b )cosh(x) +--R + +--R 2 8 4 6 6 4 +--R (24a b + 48a b + 24a b )cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 5 7 3 9 9 +--R (- 5a b - 11a b - 6a b)sinh(x) +--R + +--R 5 5 7 3 9 4 6 6 4 8 2 8 +--R ((- 30a b - 66a b - 36a b)cosh(x) - 29a b - 68a b - 42a b )sinh(x) +--R + +--R 5 5 7 3 9 2 +--R (- 72a b - 159a b - 90a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 7 5 5 7 3 +--R (- 156a b - 366a b - 228a b )cosh(x) - 74a b - 173a b - 105a b +--R + +--R 9 +--R 18a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 5 7 3 9 3 +--R (- 82a b - 184a b - 120a b)cosh(x) +--R + +--R 4 6 6 4 8 2 2 +--R (- 326a b - 770a b - 510a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 8 4 6 +--R (- 342a b - 816a b - 528a b + 72a b)cosh(x) - 98a b - 208a b +--R + +--R 6 4 8 2 +--R - 92a b + 102a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 7 3 9 4 +--R (- 30a b - 75a b - 90a b)cosh(x) +--R + +--R 4 6 6 4 8 2 3 +--R (- 304a b - 736a b - 600a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (- 594a b - 1467a b - 1098a b + 108a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 9 3 7 +--R (- 384a b - 870a b - 504a b + 360a b )cosh(x) - 64a b - 94a b +--R + +--R 5 5 7 3 9 +--R 33a b + 213a b - 18a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 7 3 9 5 +--R (30a b + 54a b - 36a b)cosh(x) +--R + +--R 4 6 6 4 8 2 4 +--R (- 60a b - 180a b - 390a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (- 430a b - 1144a b - 1212a b + 72a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 546a b - 1368a b - 1134a b + 468a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 10 +--R (- 216a b - 402a b - 102a b + 678a b - 36a b)cosh(x) - 16b +--R + +--R 2 8 4 6 6 4 8 2 +--R 14a b + 84a b + 186a b - 78a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 7 3 9 6 +--R (40a b + 79a b - 6a b)cosh(x) +--R + +--R 4 6 6 4 8 2 5 +--R (116a b + 242a b - 132a b )cosh(x) +--R + +--R 3 7 5 5 7 3 9 4 +--R (- 30a b - 171a b - 753a b + 18a b)cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 304a b - 924a b - 1316a b + 264a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 256a b - 628a b - 570a b + 789a b - 18a b)cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 9 +--R (- 48b - 24a b + 120a b + 594a b - 132a b )cosh(x) + 16a b +--R + +--R 3 7 5 5 7 3 9 +--R 22a b + 53a b - 115a b + 6a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 7 3 7 4 6 6 4 8 2 6 +--R (18a b + 36a b )cosh(x) + (94a b + 214a b - 18a b )cosh(x) +--R + +--R 3 7 5 5 7 3 5 +--R (126a b + 288a b - 252a b )cosh(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (- 6a b - 144a b - 804a b + 54a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (- 112a b - 412a b - 774a b + 396a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (- 48b - 108a b - 90a b + 654a b - 54a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 6 4 +--R (24a b + 54a b + 228a b - 180a b )cosh(x) - 6a b - 4a b - 64a b +--R + +--R 8 2 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 7 3 8 4 6 6 4 7 +--R (3a b + 6a b )cosh(x) + (24a b + 60a b )cosh(x) +--R + +--R 3 7 5 5 7 3 6 +--R (58a b + 163a b - 36a b )cosh(x) +--R + +--R 2 8 4 6 6 4 5 +--R (48a b + 114a b - 228a b )cosh(x) +--R + +--R 3 7 5 5 7 3 4 +--R (- 78a b - 411a b + 72a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 3 +--R (- 16b - 88a b - 204a b + 276a b )cosh(x) +--R + +--R 3 7 5 5 7 3 2 4 6 6 4 +--R (18a b + 249a b - 60a b )cosh(x) + (18a b - 108a b )cosh(x) +--R + +--R 3 7 5 5 7 3 +--R 2a b - 4a b + 18a b +--R * +--R sinh(x) +--R + +--R 4 6 6 4 8 3 7 5 5 7 +--R (a b + 4a b )cosh(x) + (6a b + 24a b )cosh(x) +--R + +--R 2 8 4 6 6 4 6 9 3 7 5 5 5 +--R (10a b + 40a b - 18a b )cosh(x) + (8a b + 14a b - 72a b )cosh(x) +--R + +--R 2 8 4 6 6 4 4 +--R (- 18a b - 78a b + 30a b )cosh(x) +--R + +--R 9 3 7 5 5 3 2 8 4 6 6 4 2 +--R (- 8a b - 14a b + 72a b )cosh(x) + (6a b + 32a b - 22a b )cosh(x) +--R + +--R 3 7 5 5 2 8 4 6 6 4 +--R (- 6a b - 24a b )cosh(x) + 2a b + 5a b + 6a b +--R / +--R 8 5 10 3 12 9 +--R (2a b + 4a b + 2a b)sinh(x) +--R + +--R 8 5 10 3 12 7 6 9 4 11 2 +--R ((12a b + 24a b + 12a b)cosh(x) + 18a b + 36a b + 18a b ) +--R * +--R 8 +--R sinh(x) +--R + +--R 8 5 10 3 12 2 +--R (30a b + 60a b + 30a b)cosh(x) +--R + +--R 7 6 9 4 11 2 6 7 8 5 10 3 +--R (96a b + 192a b + 96a b )cosh(x) + 66a b + 126a b + 54a b +--R + +--R 12 +--R - 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 8 5 10 3 12 3 +--R (40a b + 80a b + 40a b)cosh(x) +--R + +--R 7 6 9 4 11 2 2 +--R (210a b + 420a b + 210a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 5 8 +--R (312a b + 600a b + 264a b - 24a b)cosh(x) + 126a b +--R + +--R 7 6 9 4 11 2 +--R 210a b + 42a b - 42a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 10 3 12 4 +--R (30a b + 60a b + 30a b)cosh(x) +--R + +--R 7 6 9 4 11 2 3 +--R (240a b + 480a b + 240a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 2 +--R (594a b + 1152a b + 522a b - 36a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 4 9 +--R (528a b + 912a b + 240a b - 144a b )cosh(x) + 132a b +--R + +--R 6 7 8 5 10 3 12 +--R 150a b - 90a b - 102a b + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 10 3 12 5 +--R (12a b + 24a b + 12a b)cosh(x) +--R + +--R 7 6 9 4 11 2 4 +--R (150a b + 300a b + 150a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 3 +--R (576a b + 1128a b + 528a b - 24a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (870a b + 1560a b + 510a b - 180a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R (492a b + 648a b - 168a b - 312a b + 12a b)cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R 72a b - 6a b - 198a b - 90a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 10 3 12 6 +--R (2a b + 4a b + 2a b)cosh(x) +--R + +--R 7 6 9 4 11 2 5 +--R (48a b + 96a b + 48a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 4 +--R (294a b + 582a b + 282a b - 6a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (704a b + 1312a b + 512a b - 96a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (696a b + 1044a b + 6a b - 336a b + 6a b)cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (240a b + 96a b - 480a b - 288a b + 48a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R 16a b - 64a b - 122a b + 10a b + 50a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 9 4 11 2 6 +--R (6a b + 12a b + 6a b )cosh(x) +--R + +--R 6 7 8 5 10 3 5 +--R (72a b + 144a b + 72a b )cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (282a b + 546a b + 246a b - 18a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (456a b + 768a b + 168a b - 144a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (288a b + 252a b - 342a b - 288a b + 18a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 3 10 +--R (48a b - 120a b - 312a b - 72a b + 72a b )cosh(x) - 24a b +--R + +--R 5 8 7 6 9 4 11 2 +--R - 6a b + 54a b + 30a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 7 8 5 10 3 6 +--R (6a b + 12a b + 6a b )cosh(x) +--R + +--R 5 8 7 6 9 4 5 +--R (48a b + 96a b + 48a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (132a b + 246a b + 96a b - 18a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (144a b + 192a b - 48a b - 96a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (48a b - 48a b - 222a b - 108a b + 18a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 4 9 6 7 +--R (- 48a b - 48a b + 48a b + 48a b )cosh(x) + 12a b + 18a b +--R + +--R 10 3 +--R - 6a b +--R * +--R sinh(x) +--R + +--R 5 8 7 6 9 4 6 4 9 6 7 8 5 5 +--R (2a b + 4a b + 2a b )cosh(x) + (12a b + 24a b + 12a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (24a b + 42a b + 12a b - 6a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 3 +--R (16a b + 8a b - 32a b - 24a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 2 +--R (- 24a b - 42a b - 12a b + 6a b )cosh(x) +--R + +--R 4 9 6 7 8 5 5 8 7 6 9 4 +--R (12a b + 24a b + 12a b )cosh(x) - 2a b - 4a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 9 4 11 2 13 9 +--R (- 4a b - 8a b - 4a )sinh(x) +--R + +--R 9 4 11 2 13 8 5 10 3 12 +--R ((- 24a b - 48a b - 24a )cosh(x) - 36a b - 72a b - 36a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 9 4 11 2 13 2 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 8 5 10 3 12 7 6 9 4 +--R (- 192a b - 384a b - 192a b)cosh(x) - 132a b - 252a b +--R + +--R 11 2 13 +--R - 108a b + 12a +--R * +--R 7 +--R sinh(x) +--R + +--R 9 4 11 2 13 3 +--R (- 80a b - 160a b - 80a )cosh(x) +--R + +--R 8 5 10 3 12 2 +--R (- 420a b - 840a b - 420a b)cosh(x) +--R + +--R 7 6 9 4 11 2 13 6 7 +--R (- 624a b - 1200a b - 528a b + 48a )cosh(x) - 252a b +--R + +--R 8 5 10 3 12 +--R - 420a b - 84a b + 84a b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 4 11 2 13 4 +--R (- 60a b - 120a b - 60a )cosh(x) +--R + +--R 8 5 10 3 12 3 +--R (- 480a b - 960a b - 480a b)cosh(x) +--R + +--R 7 6 9 4 11 2 13 2 +--R (- 1188a b - 2304a b - 1044a b + 72a )cosh(x) +--R + +--R 6 7 8 5 10 3 12 5 8 +--R (- 1056a b - 1824a b - 480a b + 288a b)cosh(x) - 264a b +--R + +--R 7 6 9 4 11 2 13 +--R - 300a b + 180a b + 204a b - 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 9 4 11 2 13 5 +--R (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 8 5 10 3 12 4 +--R (- 300a b - 600a b - 300a b)cosh(x) +--R + +--R 7 6 9 4 11 2 13 3 +--R (- 1152a b - 2256a b - 1056a b + 48a )cosh(x) +--R + +--R 6 7 8 5 10 3 12 2 +--R (- 1740a b - 3120a b - 1020a b + 360a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 13 +--R (- 984a b - 1296a b + 336a b + 624a b - 24a )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R - 144a b + 12a b + 396a b + 180a b - 60a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 4 11 2 13 6 +--R (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 8 5 10 3 12 5 +--R (- 96a b - 192a b - 96a b)cosh(x) +--R + +--R 7 6 9 4 11 2 13 4 +--R (- 588a b - 1164a b - 564a b + 12a )cosh(x) +--R + +--R 6 7 8 5 10 3 12 3 +--R (- 1408a b - 2624a b - 1024a b + 192a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 13 2 +--R (- 1392a b - 2088a b - 12a b + 672a b - 12a )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R (- 480a b - 192a b + 960a b + 576a b - 96a b)cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 13 +--R - 32a b + 128a b + 244a b - 20a b - 100a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 8 5 10 3 12 6 +--R (- 12a b - 24a b - 12a b)cosh(x) +--R + +--R 7 6 9 4 11 2 5 +--R (- 144a b - 288a b - 144a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 564a b - 1092a b - 492a b + 36a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (- 912a b - 1536a b - 336a b + 288a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 576a b - 504a b + 684a b + 576a b - 36a b)cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (- 96a b + 240a b + 624a b + 144a b - 144a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R 48a b + 12a b - 108a b - 60a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 9 4 11 2 6 +--R (- 12a b - 24a b - 12a b )cosh(x) +--R + +--R 6 7 8 5 10 3 5 +--R (- 96a b - 192a b - 96a b )cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (- 264a b - 492a b - 192a b + 36a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 288a b - 384a b + 96a b + 192a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 96a b + 96a b + 444a b + 216a b - 36a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 5 8 7 6 +--R (96a b + 96a b - 96a b - 96a b )cosh(x) - 24a b - 36a b +--R + +--R 11 2 +--R 12a b +--R * +--R sinh(x) +--R + +--R 6 7 8 5 10 3 6 +--R (- 4a b - 8a b - 4a b )cosh(x) +--R + +--R 5 8 7 6 9 4 5 +--R (- 24a b - 48a b - 24a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (- 48a b - 84a b - 24a b + 12a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 32a b - 16a b + 64a b + 48a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 2 +--R (48a b + 84a b + 24a b - 12a b )cosh(x) +--R + +--R 5 8 7 6 9 4 6 7 8 5 10 3 +--R (- 24a b - 48a b - 24a b )cosh(x) + 4a b + 8a b + 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 8 5 10 3 12 9 +--R (- 2a b - 4a b - 2a b)sinh(x) +--R + +--R 8 5 10 3 12 7 6 9 4 11 2 +--R ((- 12a b - 24a b - 12a b)cosh(x) - 18a b - 36a b - 18a b ) +--R * +--R 8 +--R sinh(x) +--R + +--R 8 5 10 3 12 2 +--R (- 30a b - 60a b - 30a b)cosh(x) +--R + +--R 7 6 9 4 11 2 6 7 8 5 10 3 +--R (- 96a b - 192a b - 96a b )cosh(x) - 66a b - 126a b - 54a b +--R + +--R 12 +--R 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 8 5 10 3 12 3 +--R (- 40a b - 80a b - 40a b)cosh(x) +--R + +--R 7 6 9 4 11 2 2 +--R (- 210a b - 420a b - 210a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 5 8 7 6 +--R (- 312a b - 600a b - 264a b + 24a b)cosh(x) - 126a b - 210a b +--R + +--R 9 4 11 2 +--R - 42a b + 42a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 5 10 3 12 4 +--R (- 30a b - 60a b - 30a b)cosh(x) +--R + +--R 7 6 9 4 11 2 3 +--R (- 240a b - 480a b - 240a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 2 +--R (- 594a b - 1152a b - 522a b + 36a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 4 9 6 7 +--R (- 528a b - 912a b - 240a b + 144a b )cosh(x) - 132a b - 150a b +--R + +--R 8 5 10 3 12 +--R 90a b + 102a b - 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 5 10 3 12 5 +--R (- 12a b - 24a b - 12a b)cosh(x) +--R + +--R 7 6 9 4 11 2 4 +--R (- 150a b - 300a b - 150a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 3 +--R (- 576a b - 1128a b - 528a b + 24a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 870a b - 1560a b - 510a b + 180a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 3 10 +--R (- 492a b - 648a b + 168a b + 312a b - 12a b)cosh(x) - 72a b +--R + +--R 5 8 7 6 9 4 11 2 +--R 6a b + 198a b + 90a b - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 10 3 12 6 +--R (- 2a b - 4a b - 2a b)cosh(x) +--R + +--R 7 6 9 4 11 2 5 +--R (- 48a b - 96a b - 48a b )cosh(x) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 294a b - 582a b - 282a b + 6a b)cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (- 704a b - 1312a b - 512a b + 96a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 696a b - 1044a b - 6a b + 336a b - 6a b)cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 11 +--R (- 240a b - 96a b + 480a b + 288a b - 48a b )cosh(x) - 16a b +--R + +--R 4 9 6 7 8 5 10 3 12 +--R 64a b + 122a b - 10a b - 50a b + 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 9 4 11 2 6 +--R (- 6a b - 12a b - 6a b )cosh(x) +--R + +--R 6 7 8 5 10 3 5 +--R (- 72a b - 144a b - 72a b )cosh(x) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (- 282a b - 546a b - 246a b + 18a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 456a b - 768a b - 168a b + 144a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 288a b - 252a b + 342a b + 288a b - 18a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 3 10 +--R (- 48a b + 120a b + 312a b + 72a b - 72a b )cosh(x) + 24a b +--R + +--R 5 8 7 6 9 4 11 2 +--R 6a b - 54a b - 30a b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 7 8 5 10 3 6 +--R (- 6a b - 12a b - 6a b )cosh(x) +--R + +--R 5 8 7 6 9 4 5 +--R (- 48a b - 96a b - 48a b )cosh(x) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (- 132a b - 246a b - 96a b + 18a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 144a b - 192a b + 48a b + 96a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 48a b + 48a b + 222a b + 108a b - 18a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 4 9 6 7 10 3 +--R (48a b + 48a b - 48a b - 48a b )cosh(x) - 12a b - 18a b + 6a b +--R * +--R sinh(x) +--R + +--R 5 8 7 6 9 4 6 4 9 6 7 8 5 5 +--R (- 2a b - 4a b - 2a b )cosh(x) + (- 12a b - 24a b - 12a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (- 24a b - 42a b - 12a b + 6a b )cosh(x) +--R + +--R 2 11 4 9 6 7 8 5 3 +--R (- 16a b - 8a b + 32a b + 24a b )cosh(x) +--R + +--R 3 10 5 8 7 6 9 4 2 +--R (24a b + 42a b + 12a b - 6a b )cosh(x) +--R + +--R 4 9 6 7 8 5 5 8 7 6 9 4 +--R (- 12a b - 24a b - 12a b )cosh(x) + 2a b + 4a b + 2a b +--R Type: Expression(Integer) +--E 348 + +--S 349 of 526 +t0466:= 1/(a+b*csch(x)^2) +--R +--R +--R 1 +--R (258) -------------- +--R 2 +--R b csch(x) + a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 526 +r0466:= x/a-b^(1/2)*atan((a-b)^(1/2)*tanh(x)/b^(1/2))/a/(a-b)^(1/2) +--R +--R +--R +-------+ +--R +-+ tanh(x)\|- b + a +-------+ +--R - \|b atan(-----------------) + x\|- b + a +--R +-+ +--R \|b +--R (259) ------------------------------------------- +--R +-------+ +--R a\|- b + a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 526 +a0466:= integrate(t0466,x) +--R +--R +--R (260) +--R [ +--R +-----+ +--R | b +--R |----- +--R \|b - a +--R * +--R log +--R 2 2 2 +--R (4a b - 4a )sinh(x) + (8a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b - 4a )cosh(x) + 8b - 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b - a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b - 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b - 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b - 2a )cosh(x) + 8b - 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b - 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b - 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b - 2a)cosh(x) + a +--R + +--R 2x +--R / +--R 2a +--R , +--R +-------+ +--R | b +--R +-------+ (2b - 2a) |- ----- +--R | b \| b - a +--R - |- ----- atan(----------------------------------------------------) + x +--R \| b - a 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b - a +--R --------------------------------------------------------------------------] +--R a +--R Type: Union(List(Expression(Integer)),...) +--E 351 + +--S 352 of 526 +m0466a:= a0466.1-r0466 +--R +--R +--R (261) +--R +-----+ +--R +-------+ | b +--R \|- b + a |----- +--R \|b - a +--R * +--R log +--R 2 2 2 +--R (4a b - 4a )sinh(x) + (8a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b - 4a )cosh(x) + 8b - 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b - a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b - 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b - 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b - 2a )cosh(x) + 8b - 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b - 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b - 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b - 2a)cosh(x) + a +--R + +--R +-------+ +--R +-+ tanh(x)\|- b + a +--R 2\|b atan(-----------------) +--R +-+ +--R \|b +--R / +--R +-------+ +--R 2a\|- b + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 526 +d0466a:= D(m0466a,x) +--R +--R +--R (262) +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (- 4b cosh(x) + 4b cosh(x))sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 2 4 2 3 +--R (a b - a )sinh(x) + (4a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6a b - 6a )cosh(x) + 4b - 6a b + 2a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4a b - 4a )cosh(x) + (8b - 12a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (a b - a )cosh(x) + (4b - 6a b + 2a )cosh(x) + a b - a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 6a b cosh(x) - 4b + 2a b)sinh(x) +--R + +--R 3 2 4 +--R (- 4a b cosh(x) + (- 8b + 4a b)cosh(x))sinh(x) - a b cosh(x) +--R + +--R 2 2 +--R (- 4b + 2a b)cosh(x) - a b +--R Type: Expression(Integer) +--E 353 + +--S 354 of 526 +m0466b:= a0466.2-r0466 +--R +--R +--R (263) +--R - +--R +-------+ +--R +-------+ | b +--R \|- b + a |- ----- +--R \| b - a +--R * +--R +-------+ +--R | b +--R (2b - 2a) |- ----- +--R \| b - a +--R atan(----------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b - a +--R + +--R +-------+ +--R +-+ tanh(x)\|- b + a +--R \|b atan(-----------------) +--R +-+ +--R \|b +--R / +--R +-------+ +--R a\|- b + a +--R Type: Expression(Integer) +--E 354 + +--S 355 of 526 +d0466b:= D(m0466b,x) +--R +--R +--R (264) +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (- 4b cosh(x) + 4b cosh(x))sinh(x) - b cosh(x) + 2b cosh(x) - b +--R / +--R 2 4 2 3 +--R (a b - a )sinh(x) + (4a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6a b - 6a )cosh(x) + 4b - 6a b + 2a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4a b - 4a )cosh(x) + (8b - 12a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (a b - a )cosh(x) + (4b - 6a b + 2a )cosh(x) + a b - a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 6a b cosh(x) - 4b + 2a b)sinh(x) +--R + +--R 3 2 4 +--R (- 4a b cosh(x) + (- 8b + 4a b)cosh(x))sinh(x) - a b cosh(x) +--R + +--R 2 2 +--R (- 4b + 2a b)cosh(x) - a b +--R Type: Expression(Integer) +--E 355 + +--S 356 of 526 +t0467:= 1/(a+b*csch(x)^2)^2 +--R +--R +--R 1 +--R (265) ------------------------------- +--R 2 4 2 2 +--R b csch(x) + 2a b csch(x) + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 526 +r0467:= x/a^2+1/2*(a-2*b)*b^(1/2)*atan((a-b)^(1/2)*_ + tanh(x)/b^(1/2))/a^2/(a-b)^(3/2)-2*b^(1/2)*atan((a-b)^(1/2)*_ + tanh(x)/b^(1/2))/a^2/(a-b)^(1/2)+1/2*b*_ + tanh(x)/a/(a-b)/(b+(a-b)*tanh(x)^2) +--R +--R +--R (266) +--R +-------+ +--R 2 2 2 2 +-+ tanh(x)\|- b + a +--R ((- 2b + 5a b - 3a )tanh(x) + 2b - 3a b)\|b atan(-----------------) +--R +-+ +--R \|b +--R + +--R 2 2 2 2 +-------+ +--R ((2b - 4a b + 2a )x tanh(x) + a b tanh(x) + (- 2b + 2a b)x)\|- b + a +--R / +--R 2 2 3 4 2 2 2 3 +-------+ +--R ((2a b - 4a b + 2a )tanh(x) - 2a b + 2a b)\|- b + a +--R Type: Expression(Integer) +--E 357 + +--S 358 of 526 +a0467:= integrate(t0467,x) +--R +--R +--R (267) +--R [ +--R 2 4 2 3 +--R (2a b - 3a )sinh(x) + (8a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((12a b - 18a )cosh(x) + 8b - 16a b + 6a )sinh(x) +--R + +--R 2 3 2 2 +--R ((8a b - 12a )cosh(x) + (16b - 32a b + 12a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (2a b - 3a )cosh(x) + (8b - 16a b + 6a )cosh(x) + 2a b - 3a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b - a +--R * +--R log +--R 2 2 2 +--R (4a b - 4a )sinh(x) + (8a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b - 4a )cosh(x) + 8b - 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b - a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b - 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b - 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b - 2a )cosh(x) + 8b - 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b - 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b - 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b - 2a)cosh(x) + a +--R + +--R 2 4 2 3 +--R (4a b - 4a )x sinh(x) + (16a b - 16a )x cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24a b - 24a )x cosh(x) + (16b - 24a b + 8a )x + 8b - 4a b)sinh(x) +--R + +--R 2 3 +--R (16a b - 16a )x cosh(x) +--R + +--R 2 2 2 +--R ((32b - 48a b + 16a )x + 16b - 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (4a b - 4a )x cosh(x) + ((16b - 24a b + 8a )x + 8b - 4a b)cosh(x) +--R + +--R 2 +--R (4a b - 4a )x + 4a b +--R / +--R 3 4 4 3 4 3 +--R (4a b - 4a )sinh(x) + (16a b - 16a )cosh(x)sinh(x) +--R + +--R 3 4 2 2 2 3 4 2 +--R ((24a b - 24a )cosh(x) + 16a b - 24a b + 8a )sinh(x) +--R + +--R 3 4 3 2 2 3 4 +--R ((16a b - 16a )cosh(x) + (32a b - 48a b + 16a )cosh(x))sinh(x) +--R + +--R 3 4 4 2 2 3 4 2 3 4 +--R (4a b - 4a )cosh(x) + (16a b - 24a b + 8a )cosh(x) + 4a b - 4a +--R , +--R +--R 2 4 2 3 +--R (- 2a b + 3a )sinh(x) + (- 8a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 12a b + 18a )cosh(x) - 8b + 16a b - 6a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 8a b + 12a )cosh(x) + (- 16b + 32a b - 12a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 2a b + 3a )cosh(x) + (- 8b + 16a b - 6a )cosh(x) - 2a b + 3a +--R * +--R +-------+ +--R | b +--R +-------+ (2b - 2a) |- ----- +--R | b \| b - a +--R |- ----- atan(----------------------------------------------------) +--R \| b - a 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b - a +--R + +--R 2 4 2 3 +--R (2a b - 2a )x sinh(x) + (8a b - 8a )x cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12a b - 12a )x cosh(x) + (8b - 12a b + 4a )x + 4b - 2a b)sinh(x) +--R + +--R 2 3 +--R (8a b - 8a )x cosh(x) +--R + +--R 2 2 2 +--R ((16b - 24a b + 8a )x + 8b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (2a b - 2a )x cosh(x) + ((8b - 12a b + 4a )x + 4b - 2a b)cosh(x) +--R + +--R 2 +--R (2a b - 2a )x + 2a b +--R / +--R 3 4 4 3 4 3 +--R (2a b - 2a )sinh(x) + (8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 4 2 2 2 3 4 2 +--R ((12a b - 12a )cosh(x) + 8a b - 12a b + 4a )sinh(x) +--R + +--R 3 4 3 2 2 3 4 +--R ((8a b - 8a )cosh(x) + (16a b - 24a b + 8a )cosh(x))sinh(x) +--R + +--R 3 4 4 2 2 3 4 2 3 4 +--R (2a b - 2a )cosh(x) + (8a b - 12a b + 4a )cosh(x) + 2a b - 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 358 + +--S 359 of 526 +m0467a:= a0467.1-r0467 +--R +--R +--R (268) +--R 2 2 3 4 +--R (2a b - 5a b + 3a )sinh(x) +--R + +--R 2 2 3 3 +--R (8a b - 20a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R ((12a b - 30a b + 18a )cosh(x) + 8b - 24a b + 22a b - 6a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 +--R (8a b - 20a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (16b - 48a b + 44a b - 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 +--R (2a b - 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (8b - 24a b + 22a b - 6a )cosh(x) + 2a b - 5a b + 3a +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b + 3a b)sinh(x) + (- 8a b + 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((- 12a b + 18a b)cosh(x) - 8b + 16a b - 6a b)sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((- 8a b + 12a b)cosh(x) + (- 16b + 32a b - 12a b)cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 2 +--R (- 2a b + 3a b)cosh(x) + (- 8b + 16a b - 6a b)cosh(x) - 2a b +--R + +--R 2 +--R 3a b +--R * +--R +-----+ +--R +-------+ | b +--R \|- b + a |----- +--R \|b - a +--R * +--R log +--R 2 2 2 +--R (4a b - 4a )sinh(x) + (8a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4a b - 4a )cosh(x) + 8b - 12a b + 4a +--R * +--R +-----+ +--R | b +--R |----- +--R \|b - a +--R + +--R 2 4 2 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6a cosh(x) + 4a b - 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (4a cosh(x) + (8a b - 4a )cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 2 2 2 +--R (4a b - 2a )cosh(x) + 8b - 8a b + a +--R / +--R 4 3 +--R a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 2 2 +--R (6a cosh(x) + 4b - 2a)sinh(x) +--R + +--R 3 4 +--R (4a cosh(x) + (8b - 4a)cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 +--R (4b - 2a)cosh(x) + a +--R + +--R 2 2 3 4 +--R (4a b - 10a b + 6a )sinh(x) +--R + +--R 2 2 3 3 +--R (16a b - 40a b + 24a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 3 2 2 +--R (24a b - 60a b + 36a )cosh(x) + 16b - 48a b + 44a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 +--R (16a b - 40a b + 24a )cosh(x) +--R + +--R 3 2 2 3 +--R (32b - 96a b + 88a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 +--R (4a b - 10a b + 6a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (16b - 48a b + 44a b - 12a )cosh(x) + 4a b - 10a b + 6a +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 4a b + 6a b)sinh(x) + (- 16a b + 24a b)cosh(x)sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((- 24a b + 36a b)cosh(x) - 16b + 32a b - 12a b)sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((- 16a b + 24a b)cosh(x) + (- 32b + 64a b - 24a b)cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 2 +--R (- 4a b + 6a b)cosh(x) + (- 16b + 32a b - 12a b)cosh(x) - 4a b +--R + +--R 2 +--R 6a b +--R * +--R +-------+ +--R +-+ tanh(x)\|- b + a +--R \|b atan(-----------------) +--R +-+ +--R \|b +--R + +--R 3 2 2 2 +--R (8b - 12a b + 4a b)sinh(x) +--R + +--R 3 2 2 +--R (16b - 24a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 2 +--R (8b - 12a b + 4a b)cosh(x) + 4a b - 4a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R - 2a b sinh(x) - 8a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 12a b cosh(x) - 8a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 +--R (- 8a b cosh(x) + (- 16a b + 8a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R - 2a b cosh(x) + (- 8a b + 4a b)cosh(x) - 2a b +--R * +--R tanh(x) +--R + +--R 3 2 2 3 2 +--R (- 8b + 4a b )sinh(x) + (- 16b + 8a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (- 8b + 4a b )cosh(x) - 4a b +--R * +--R +-------+ +--R \|- b + a +--R / +--R 3 2 4 5 4 +--R (4a b - 8a b + 4a )sinh(x) +--R + +--R 3 2 4 5 3 +--R (16a b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 3 2 4 5 2 2 3 3 2 4 5 +--R ((24a b - 48a b + 24a )cosh(x) + 16a b - 40a b + 32a b - 8a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 5 3 +--R (16a b - 32a b + 16a )cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (32a b - 80a b + 64a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 4 5 4 +--R (4a b - 8a b + 4a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 3 2 4 5 +--R (16a b - 40a b + 32a b - 8a )cosh(x) + 4a b - 8a b + 4a +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 4 4 3 2 4 3 +--R (- 4a b + 4a b)sinh(x) + (- 16a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 4 2 2 3 3 2 4 2 +--R ((- 24a b + 24a b)cosh(x) - 16a b + 24a b - 8a b)sinh(x) +--R + +--R 3 2 4 3 2 3 3 2 4 +--R ((- 16a b + 16a b)cosh(x) + (- 32a b + 48a b - 16a b)cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 4 4 2 3 3 2 4 2 3 2 +--R (- 4a b + 4a b)cosh(x) + (- 16a b + 24a b - 8a b)cosh(x) - 4a b +--R + +--R 4 +--R 4a b +--R * +--R +-------+ +--R \|- b + a +--R Type: Expression(Integer) +--E 359 + +--S 360 of 526 +d0467a:= D(m0467a,x) +--R +--R +--R (269) +--R 2 8 2 7 +--R (b - 2a b)sinh(x) + (8b - 16a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b - 56a b)cosh(x) - 4b )sinh(x) +--R + +--R 2 3 2 5 +--R ((56b - 112a b)cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((70b - 140a b)cosh(x) - 60b cosh(x) - 10b + 4a b)sinh(x) +--R + +--R 2 5 2 3 2 +--R ((56b - 112a b)cosh(x) - 80b cosh(x) + (- 40b + 16a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (28b - 56a b)cosh(x) - 60b cosh(x) + (- 60b + 24a b)cosh(x) +--R + +--R 2 +--R - 4b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (8b - 16a b)cosh(x) - 24b cosh(x) + (- 40b + 16a b)cosh(x) +--R + +--R 2 +--R - 8b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (b - 2a b)cosh(x) - 4b cosh(x) + (- 10b + 4a b)cosh(x) +--R + +--R 2 2 2 +--R - 4b cosh(x) + b - 2a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 8 2 7 +--R (- 2b + 2a b)sinh(x) + (- 16b + 16a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((- 56b + 56a b)cosh(x) + 8b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((- 112b + 112a b)cosh(x) + (48b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 140b + 140a b)cosh(x) + (120b - 120a b)cosh(x) - 12b +--R + +--R 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 112b + 112a b)cosh(x) + (160b - 160a b)cosh(x) +--R + +--R 2 +--R (- 48b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 56b + 56a b)cosh(x) + (120b - 120a b)cosh(x) +--R + +--R 2 2 2 +--R (- 72b + 72a b)cosh(x) + 8b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (- 16b + 16a b)cosh(x) + (48b - 48a b)cosh(x) +--R + +--R 2 3 2 +--R (- 48b + 48a b)cosh(x) + (16b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 +--R (- 2b + 2a b)cosh(x) + (8b - 8a b)cosh(x) +--R + +--R 2 4 2 2 2 +--R (- 12b + 12a b)cosh(x) + (8b - 8a b)cosh(x) - 2b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) - 4b )sinh(x) +--R + +--R 2 3 2 5 +--R (56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (70b cosh(x) - 60b cosh(x) + 6b )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (56b cosh(x) - 80b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (28b cosh(x) - 60b cosh(x) + 36b cosh(x) - 4b )sinh(x) +--R + +--R 2 7 2 5 2 3 2 +--R (8b cosh(x) - 24b cosh(x) + 24b cosh(x) - 8b cosh(x))sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 2 +--R b cosh(x) - 4b cosh(x) + 6b cosh(x) - 4b cosh(x) + b +--R / +--R 2 2 3 4 8 2 2 3 4 7 +--R (a b - 2a b + a )sinh(x) + (8a b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 4 2 3 2 2 3 4 +--R ((28a b - 56a b + 28a )cosh(x) + 8a b - 20a b + 16a b - 4a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 4 3 +--R (56a b - 112a b + 56a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (48a b - 120a b + 96a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 4 +--R (70a b - 140a b + 70a )cosh(x) +--R + +--R 3 2 2 3 4 2 4 3 +--R (120a b - 300a b + 240a b - 60a )cosh(x) + 16b - 48a b +--R + +--R 2 2 3 4 +--R 54a b - 28a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 4 5 +--R (56a b - 112a b + 56a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (160a b - 400a b + 320a b - 80a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (64b - 192a b + 216a b - 112a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 4 6 +--R (28a b - 56a b + 28a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (120a b - 300a b + 240a b - 60a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 3 +--R (96b - 288a b + 324a b - 168a b + 36a )cosh(x) + 8a b +--R + +--R 2 2 3 4 +--R - 20a b + 16a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 4 7 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (48a b - 120a b + 96a b - 24a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (64b - 192a b + 216a b - 112a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (16a b - 40a b + 32a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 8 3 2 2 3 4 6 +--R (a b - 2a b + a )cosh(x) + (8a b - 20a b + 16a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (16b - 48a b + 54a b - 28a b + 6a )cosh(x) +--R + +--R 3 2 2 3 4 2 2 2 3 4 +--R (8a b - 20a b + 16a b - 4a )cosh(x) + a b - 2a b + a +--R * +--R 4 +--R tanh(x) +--R + +--R 2 2 3 8 2 2 3 7 +--R (- 2a b + 2a b)sinh(x) + (- 16a b + 16a b)cosh(x)sinh(x) +--R + +--R 2 2 3 2 3 2 2 3 6 +--R ((- 56a b + 56a b)cosh(x) - 16a b + 24a b - 8a b)sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 96a b + 144a b - 48a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b + 140a b)cosh(x) +--R + +--R 3 2 2 3 2 4 3 2 2 +--R (- 240a b + 360a b - 120a b)cosh(x) - 32b + 64a b - 44a b +--R + +--R 3 +--R 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 320a b + 480a b - 160a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 128b + 256a b - 176a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 240a b + 360a b - 120a b)cosh(x) +--R + +--R 4 3 2 2 3 2 3 2 2 +--R (- 192b + 384a b - 264a b + 72a b)cosh(x) - 16a b + 24a b +--R + +--R 3 +--R - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 3 2 2 3 5 +--R (- 16a b + 16a b)cosh(x) + (- 96a b + 144a b - 48a b)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 128b + 256a b - 176a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 32a b + 48a b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 3 2 2 3 6 +--R (- 2a b + 2a b)cosh(x) + (- 16a b + 24a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 32b + 64a b - 44a b + 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 16a b + 24a b - 8a b)cosh(x) - 2a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 8 2 2 7 +--R a b sinh(x) + 8a b cosh(x)sinh(x) +--R + +--R 2 2 2 3 2 2 6 +--R (28a b cosh(x) + 8a b - 4a b )sinh(x) +--R + +--R 2 2 3 3 2 2 5 +--R (56a b cosh(x) + (48a b - 24a b )cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 4 3 2 2 +--R (70a b cosh(x) + (120a b - 60a b )cosh(x) + 16b - 16a b + 6a b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 3 2 2 3 +--R 56a b cosh(x) + (160a b - 80a b )cosh(x) +--R + +--R 4 3 2 2 +--R (64b - 64a b + 24a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 3 2 2 4 +--R 28a b cosh(x) + (120a b - 60a b )cosh(x) +--R + +--R 4 3 2 2 2 3 2 2 +--R (96b - 96a b + 36a b )cosh(x) + 8a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 3 2 2 5 +--R 8a b cosh(x) + (48a b - 24a b )cosh(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (64b - 64a b + 24a b )cosh(x) + (16a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 3 2 2 6 4 3 2 2 4 +--R a b cosh(x) + (8a b - 4a b )cosh(x) + (16b - 16a b + 6a b )cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (8a b - 4a b )cosh(x) + a b +--R Type: Expression(Integer) +--E 360 + +--S 361 of 526 +m0467b:= a0467.2-r0467 +--R +--R +--R (270) +--R 2 2 3 4 +--R (- 2a b + 5a b - 3a )sinh(x) +--R + +--R 2 2 3 3 +--R (- 8a b + 20a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 3 2 2 +--R (- 12a b + 30a b - 18a )cosh(x) - 8b + 24a b - 22a b +--R + +--R 3 +--R 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 +--R (- 8a b + 20a b - 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 16b + 48a b - 44a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 2a b + 5a b - 3a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 8b + 24a b - 22a b + 6a )cosh(x) - 2a b + 5a b - 3a +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (2a b - 3a b)sinh(x) + (8a b - 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((12a b - 18a b)cosh(x) + 8b - 16a b + 6a b)sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((8a b - 12a b)cosh(x) + (16b - 32a b + 12a b)cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 2 2 +--R (2a b - 3a b)cosh(x) + (8b - 16a b + 6a b)cosh(x) + 2a b - 3a b +--R * +--R +-------+ +--R +-------+ | b +--R \|- b + a |- ----- +--R \| b - a +--R * +--R +-------+ +--R | b +--R (2b - 2a) |- ----- +--R \| b - a +--R atan(----------------------------------------------------) +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + 2b - a +--R + +--R 2 2 3 4 +--R (2a b - 5a b + 3a )sinh(x) +--R + +--R 2 2 3 3 +--R (8a b - 20a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R ((12a b - 30a b + 18a )cosh(x) + 8b - 24a b + 22a b - 6a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 3 +--R (8a b - 20a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (16b - 48a b + 44a b - 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 +--R (2a b - 5a b + 3a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (8b - 24a b + 22a b - 6a )cosh(x) + 2a b - 5a b + 3a +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b + 3a b)sinh(x) + (- 8a b + 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R ((- 12a b + 18a b)cosh(x) - 8b + 16a b - 6a b)sinh(x) +--R + +--R 2 2 3 3 2 2 +--R ((- 8a b + 12a b)cosh(x) + (- 16b + 32a b - 12a b)cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 2 +--R (- 2a b + 3a b)cosh(x) + (- 8b + 16a b - 6a b)cosh(x) - 2a b +--R + +--R 2 +--R 3a b +--R * +--R +-------+ +--R +-+ tanh(x)\|- b + a +--R \|b atan(-----------------) +--R +-+ +--R \|b +--R + +--R 3 2 2 2 +--R (4b - 6a b + 2a b)sinh(x) +--R + +--R 3 2 2 +--R (8b - 12a b + 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 2 +--R (4b - 6a b + 2a b)cosh(x) + 2a b - 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 6a b cosh(x) - 4a b + 2a b)sinh(x) +--R + +--R 2 3 2 2 2 4 +--R (- 4a b cosh(x) + (- 8a b + 4a b)cosh(x))sinh(x) - a b cosh(x) +--R + +--R 2 2 2 2 +--R (- 4a b + 2a b)cosh(x) - a b +--R * +--R tanh(x) +--R + +--R 3 2 2 3 2 +--R (- 4b + 2a b )sinh(x) + (- 8b + 4a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (- 4b + 2a b )cosh(x) - 2a b +--R * +--R +-------+ +--R \|- b + a +--R / +--R 3 2 4 5 4 3 2 4 5 3 +--R (2a b - 4a b + 2a )sinh(x) + (8a b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 4 5 2 2 3 3 2 4 5 +--R ((12a b - 24a b + 12a )cosh(x) + 8a b - 20a b + 16a b - 4a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 5 3 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 2 3 3 2 4 5 +--R (16a b - 40a b + 32a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 4 5 4 +--R (2a b - 4a b + 2a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 3 2 4 5 +--R (8a b - 20a b + 16a b - 4a )cosh(x) + 2a b - 4a b + 2a +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 4 4 3 2 4 3 +--R (- 2a b + 2a b)sinh(x) + (- 8a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 4 2 2 3 3 2 4 2 +--R ((- 12a b + 12a b)cosh(x) - 8a b + 12a b - 4a b)sinh(x) +--R + +--R 3 2 4 3 2 3 3 2 4 +--R ((- 8a b + 8a b)cosh(x) + (- 16a b + 24a b - 8a b)cosh(x))sinh(x) +--R + +--R 3 2 4 4 2 3 3 2 4 2 3 2 +--R (- 2a b + 2a b)cosh(x) + (- 8a b + 12a b - 4a b)cosh(x) - 2a b +--R + +--R 4 +--R 2a b +--R * +--R +-------+ +--R \|- b + a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 526 +d0467b:= D(m0467b,x) +--R +--R +--R (271) +--R 2 8 2 7 +--R (b - 2a b)sinh(x) + (8b - 16a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b - 56a b)cosh(x) - 4b )sinh(x) +--R + +--R 2 3 2 5 +--R ((56b - 112a b)cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((70b - 140a b)cosh(x) - 60b cosh(x) - 10b + 4a b)sinh(x) +--R + +--R 2 5 2 3 2 +--R ((56b - 112a b)cosh(x) - 80b cosh(x) + (- 40b + 16a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (28b - 56a b)cosh(x) - 60b cosh(x) + (- 60b + 24a b)cosh(x) +--R + +--R 2 +--R - 4b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (8b - 16a b)cosh(x) - 24b cosh(x) + (- 40b + 16a b)cosh(x) +--R + +--R 2 +--R - 8b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (b - 2a b)cosh(x) - 4b cosh(x) + (- 10b + 4a b)cosh(x) +--R + +--R 2 2 2 +--R - 4b cosh(x) + b - 2a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 8 2 7 +--R (- 2b + 2a b)sinh(x) + (- 16b + 16a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((- 56b + 56a b)cosh(x) + 8b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((- 112b + 112a b)cosh(x) + (48b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 140b + 140a b)cosh(x) + (120b - 120a b)cosh(x) - 12b +--R + +--R 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 112b + 112a b)cosh(x) + (160b - 160a b)cosh(x) +--R + +--R 2 +--R (- 48b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 56b + 56a b)cosh(x) + (120b - 120a b)cosh(x) +--R + +--R 2 2 2 +--R (- 72b + 72a b)cosh(x) + 8b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (- 16b + 16a b)cosh(x) + (48b - 48a b)cosh(x) +--R + +--R 2 3 2 +--R (- 48b + 48a b)cosh(x) + (16b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 +--R (- 2b + 2a b)cosh(x) + (8b - 8a b)cosh(x) +--R + +--R 2 4 2 2 2 +--R (- 12b + 12a b)cosh(x) + (8b - 8a b)cosh(x) - 2b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) - 4b )sinh(x) +--R + +--R 2 3 2 5 +--R (56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (70b cosh(x) - 60b cosh(x) + 6b )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (56b cosh(x) - 80b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (28b cosh(x) - 60b cosh(x) + 36b cosh(x) - 4b )sinh(x) +--R + +--R 2 7 2 5 2 3 2 +--R (8b cosh(x) - 24b cosh(x) + 24b cosh(x) - 8b cosh(x))sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 2 +--R b cosh(x) - 4b cosh(x) + 6b cosh(x) - 4b cosh(x) + b +--R / +--R 2 2 3 4 8 2 2 3 4 7 +--R (a b - 2a b + a )sinh(x) + (8a b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 4 2 3 2 2 3 4 +--R ((28a b - 56a b + 28a )cosh(x) + 8a b - 20a b + 16a b - 4a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 4 3 +--R (56a b - 112a b + 56a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (48a b - 120a b + 96a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 4 +--R (70a b - 140a b + 70a )cosh(x) +--R + +--R 3 2 2 3 4 2 4 3 +--R (120a b - 300a b + 240a b - 60a )cosh(x) + 16b - 48a b +--R + +--R 2 2 3 4 +--R 54a b - 28a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 4 5 +--R (56a b - 112a b + 56a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (160a b - 400a b + 320a b - 80a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (64b - 192a b + 216a b - 112a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 4 6 +--R (28a b - 56a b + 28a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (120a b - 300a b + 240a b - 60a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 3 +--R (96b - 288a b + 324a b - 168a b + 36a )cosh(x) + 8a b +--R + +--R 2 2 3 4 +--R - 20a b + 16a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 4 7 +--R (8a b - 16a b + 8a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (48a b - 120a b + 96a b - 24a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (64b - 192a b + 216a b - 112a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (16a b - 40a b + 32a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 8 3 2 2 3 4 6 +--R (a b - 2a b + a )cosh(x) + (8a b - 20a b + 16a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (16b - 48a b + 54a b - 28a b + 6a )cosh(x) +--R + +--R 3 2 2 3 4 2 2 2 3 4 +--R (8a b - 20a b + 16a b - 4a )cosh(x) + a b - 2a b + a +--R * +--R 4 +--R tanh(x) +--R + +--R 2 2 3 8 2 2 3 7 +--R (- 2a b + 2a b)sinh(x) + (- 16a b + 16a b)cosh(x)sinh(x) +--R + +--R 2 2 3 2 3 2 2 3 6 +--R ((- 56a b + 56a b)cosh(x) - 16a b + 24a b - 8a b)sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 96a b + 144a b - 48a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b + 140a b)cosh(x) +--R + +--R 3 2 2 3 2 4 3 2 2 +--R (- 240a b + 360a b - 120a b)cosh(x) - 32b + 64a b - 44a b +--R + +--R 3 +--R 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 320a b + 480a b - 160a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 128b + 256a b - 176a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 240a b + 360a b - 120a b)cosh(x) +--R + +--R 4 3 2 2 3 2 3 2 2 +--R (- 192b + 384a b - 264a b + 72a b)cosh(x) - 16a b + 24a b +--R + +--R 3 +--R - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 3 2 2 3 5 +--R (- 16a b + 16a b)cosh(x) + (- 96a b + 144a b - 48a b)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 128b + 256a b - 176a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 32a b + 48a b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 3 2 2 3 6 +--R (- 2a b + 2a b)cosh(x) + (- 16a b + 24a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 32b + 64a b - 44a b + 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 16a b + 24a b - 8a b)cosh(x) - 2a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 8 2 2 7 +--R a b sinh(x) + 8a b cosh(x)sinh(x) +--R + +--R 2 2 2 3 2 2 6 +--R (28a b cosh(x) + 8a b - 4a b )sinh(x) +--R + +--R 2 2 3 3 2 2 5 +--R (56a b cosh(x) + (48a b - 24a b )cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 4 3 2 2 +--R (70a b cosh(x) + (120a b - 60a b )cosh(x) + 16b - 16a b + 6a b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 3 2 2 3 +--R 56a b cosh(x) + (160a b - 80a b )cosh(x) +--R + +--R 4 3 2 2 +--R (64b - 64a b + 24a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 3 2 2 4 +--R 28a b cosh(x) + (120a b - 60a b )cosh(x) +--R + +--R 4 3 2 2 2 3 2 2 +--R (96b - 96a b + 36a b )cosh(x) + 8a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 3 2 2 5 +--R 8a b cosh(x) + (48a b - 24a b )cosh(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (64b - 64a b + 24a b )cosh(x) + (16a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 3 2 2 6 4 3 2 2 4 +--R a b cosh(x) + (8a b - 4a b )cosh(x) + (16b - 16a b + 6a b )cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (8a b - 4a b )cosh(x) + a b +--R Type: Expression(Integer) +--E 362 + +--S 363 of 526 +t0468:= (1+csch(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (272) \|csch(x) + 1 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 526 +r0468:= (coth(x)^2)^(1/2)*log(sinh(x))*tanh(x) +--R +--R +--R +--------+ +--R | 2 +--R (273) tanh(x)log(sinh(x))\|coth(x) +--R Type: Expression(Integer) +--E 364 + +--S 365 of 526 +a0468:= integrate(t0468,x) +--R +--R +--R 2sinh(x) +--R (274) log(- -----------------) - x +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 365 + +--S 366 of 526 +m0468:= a0468-r0468 +--R +--R +--R +--------+ +--R | 2 2sinh(x) +--R (275) - tanh(x)log(sinh(x))\|coth(x) + log(- -----------------) - x +--R sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 366 + +--S 367 of 526 +d0468:= D(m0468,x) +--R +--R +--R (276) +--R +--------+ +--R | 2 +--R cosh(x)\|coth(x) +--R + +--R 2 2 3 +--R coth(x) sinh(x)tanh(x) + (coth(x) - coth(x))sinh(x)tanh(x) +--R + +--R 2 +--R - coth(x) sinh(x) +--R * +--R log(sinh(x)) +--R + +--R 2 +--R - cosh(x)coth(x) tanh(x) +--R / +--R +--------+ +--R | 2 +--R sinh(x)\|coth(x) +--R Type: Expression(Integer) +--E 367 + +--S 368 of 526 +t0469:= (1-csch(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (277) \|- csch(x) + 1 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 526 +r0469:= asin(1/2*2^(1/2)*coth(x))+atanh(coth(x)/(2-coth(x)^2)^(1/2)) +--R +--R +--R +-+ +--R coth(x) \|2 coth(x) +--R (278) atanh(-----------------) + asin(-----------) +--R +--------------+ 2 +--R | 2 +--R \|- coth(x) + 2 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 526 +a0469:= integrate(t0469,x) +--R +--R +--R (279) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 8cosh(x))sinh(x) + cosh(x) - 4cosh(x) - 1 +--R + +--R - +--R 4 +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R / +--R 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 370 + +--S 371 of 526 +m0469:= a0469-r0469 +--R +--R +--R (280) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 8cosh(x))sinh(x) + cosh(x) - 4cosh(x) - 1 +--R + +--R coth(x) +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R + +--R - +--R 4 +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R / +--R 2 +--R + +--R +-+ +--R \|2 coth(x) +--R - 2asin(-----------) +--R 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 526 +d0469:= D(m0469,x) +--R +--R +--R (281) +--R 14 13 2 12 +--R - sinh(x) - 6cosh(x)sinh(x) + (- 11cosh(x) + 12)sinh(x) +--R + +--R 3 11 +--R (4cosh(x) + 48cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (39cosh(x) + 24cosh(x) - 66)sinh(x) +--R + +--R 5 3 9 +--R (38cosh(x) - 144cosh(x) - 156cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 27cosh(x) - 204cosh(x) + 102cosh(x) + 140)sinh(x) +--R + +--R 7 5 3 7 +--R (- 72cosh(x) + 96cosh(x) + 432cosh(x) + 288cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 27cosh(x) + 336cosh(x) - 36cosh(x) + 16cosh(x) - 301) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 38cosh(x) + 96cosh(x) - 552cosh(x) - 288cosh(x) +--R + +--R - 430cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 39cosh(x) - 204cosh(x) - 36cosh(x) - 312cosh(x) +--R + +--R 2 +--R 285cosh(x) + 328 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 4cosh(x) - 144cosh(x) + 432cosh(x) - 288cosh(x) +--R + +--R 3 +--R 828cosh(x) + 48cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 11cosh(x) + 24cosh(x) + 102cosh(x) + 16cosh(x) +--R + +--R 4 2 +--R 285cosh(x) - 560cosh(x) - 48 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 6cosh(x) + 48cosh(x) - 156cosh(x) + 288cosh(x) +--R + +--R 5 3 +--R - 430cosh(x) + 48cosh(x) - 48cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R - cosh(x) + 12cosh(x) - 66cosh(x) + 140cosh(x) +--R + +--R 6 4 2 +--R - 301cosh(x) + 328cosh(x) - 48cosh(x) +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R + +--R 2 14 2 13 +--R (coth(x) - 2)sinh(x) + (6cosh(x)coth(x) - 12cosh(x))sinh(x) +--R + +--R 2 2 2 12 +--R ((11cosh(x) - 7)coth(x) - 22cosh(x) + 14)sinh(x) +--R + +--R 3 2 3 11 +--R ((- 4cosh(x) - 28cosh(x))coth(x) + 8cosh(x) + 56cosh(x))sinh(x) +--R + +--R 4 2 2 4 +--R (- 39cosh(x) - 14cosh(x) + 30)coth(x) + 78cosh(x) +--R + +--R 2 +--R 28cosh(x) - 60 +--R * +--R 10 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 38cosh(x) + 84cosh(x) + 84cosh(x))coth(x) + 76cosh(x) +--R + +--R 3 +--R - 168cosh(x) - 168cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (27cosh(x) + 119cosh(x) + 6cosh(x) - 114)coth(x) - 54cosh(x) +--R + +--R 4 2 +--R - 238cosh(x) - 12cosh(x) + 228 +--R * +--R 8 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (72cosh(x) - 56cosh(x) - 144cosh(x) - 240cosh(x))coth(x) +--R + +--R 7 5 3 +--R - 144cosh(x) + 112cosh(x) + 288cosh(x) + 480cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (27cosh(x) - 196cosh(x) - 36cosh(x) - 24cosh(x) + 205) +--R * +--R 2 +--R coth(x) +--R + +--R 8 6 4 2 +--R - 54cosh(x) + 392cosh(x) + 72cosh(x) + 48cosh(x) - 410 +--R * +--R 6 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 38cosh(x) - 56cosh(x) + 120cosh(x) + 240cosh(x) +--R + +--R 270cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 3 +--R 76cosh(x) + 112cosh(x) - 240cosh(x) - 480cosh(x) - 540cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 39cosh(x) + 119cosh(x) - 36cosh(x) + 276cosh(x) +--R + +--R 2 +--R - 189cosh(x) - 163 +--R * +--R 2 +--R coth(x) +--R + +--R 10 8 6 4 +--R 78cosh(x) - 238cosh(x) + 72cosh(x) - 552cosh(x) +--R + +--R 2 +--R 378cosh(x) + 326 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 4cosh(x) + 84cosh(x) - 144cosh(x) + 240cosh(x) +--R + +--R 3 +--R - 508cosh(x) - 52cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 11 9 7 5 +--R 8cosh(x) - 168cosh(x) + 288cosh(x) - 480cosh(x) +--R + +--R 3 +--R 1016cosh(x) + 104cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 11cosh(x) - 14cosh(x) + 6cosh(x) - 24cosh(x) +--R + +--R 4 2 +--R - 189cosh(x) + 222cosh(x) + 84 +--R * +--R 2 +--R coth(x) +--R + +--R 12 10 8 6 +--R - 22cosh(x) + 28cosh(x) - 12cosh(x) + 48cosh(x) +--R + +--R 4 2 +--R 378cosh(x) - 444cosh(x) - 168 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 6cosh(x) - 28cosh(x) + 84cosh(x) - 240cosh(x) +--R + +--R 5 3 +--R 270cosh(x) - 52cosh(x) + 24cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 13 11 9 7 +--R - 12cosh(x) + 56cosh(x) - 168cosh(x) + 480cosh(x) +--R + +--R 5 3 +--R - 540cosh(x) + 104cosh(x) - 48cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R cosh(x) - 7cosh(x) + 30cosh(x) - 114cosh(x) + 205cosh(x) +--R + +--R 4 2 +--R - 163cosh(x) + 84cosh(x) - 36 +--R * +--R 2 +--R coth(x) +--R + +--R 14 12 10 8 6 +--R - 2cosh(x) + 14cosh(x) - 60cosh(x) + 228cosh(x) - 410cosh(x) +--R + +--R 4 2 +--R 326cosh(x) - 168cosh(x) + 72 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 12 11 2 10 +--R 8sinh(x) + 48cosh(x)sinh(x) + (112cosh(x) - 90)sinh(x) +--R + +--R 3 9 +--R (112cosh(x) - 420cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 8cosh(x) - 690cosh(x) + 412)sinh(x) +--R + +--R 5 3 7 +--R (- 160cosh(x) - 240cosh(x) + 1328cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 224cosh(x) + 780cosh(x) + 1072cosh(x) - 804)sinh(x) +--R + +--R 7 5 3 5 +--R (- 160cosh(x) + 1320cosh(x) - 1072cosh(x) - 1704cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 8cosh(x) + 780cosh(x) - 2456cosh(x) - 156cosh(x) + 616) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 112cosh(x) - 240cosh(x) - 1072cosh(x) + 1488cosh(x) +--R + +--R 1120cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 112cosh(x) - 690cosh(x) + 1072cosh(x) - 156cosh(x) +--R + +--R 2 +--R 1008cosh(x) - 450 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 48cosh(x) - 420cosh(x) + 1328cosh(x) - 1704cosh(x) +--R + +--R 3 +--R 1120cosh(x) - 756cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 8cosh(x) - 90cosh(x) + 412cosh(x) - 804cosh(x) + 616cosh(x) +--R + +--R 2 +--R - 450cosh(x) + 180 +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R + +--R 2 12 2 11 +--R (- 8coth(x) + 16)sinh(x) + (- 48cosh(x)coth(x) + 96cosh(x))sinh(x) +--R + +--R 2 2 2 10 +--R ((- 112cosh(x) + 68)coth(x) + 224cosh(x) - 136)sinh(x) +--R + +--R 3 2 3 9 +--R ((- 112cosh(x) + 320cosh(x))coth(x) + 224cosh(x) - 640cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (8cosh(x) + 532cosh(x) - 224)coth(x) - 16cosh(x) - 1064cosh(x) +--R + +--R 448 +--R * +--R 8 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (160cosh(x) + 192cosh(x) - 744cosh(x))coth(x) - 320cosh(x) +--R + +--R 3 +--R - 384cosh(x) + 1488cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (224cosh(x) - 600cosh(x) - 656cosh(x) + 432)coth(x) - 448cosh(x) +--R + +--R 4 2 +--R 1200cosh(x) + 1312cosh(x) - 864 +--R * +--R 6 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (160cosh(x) - 1024cosh(x) + 488cosh(x) + 920cosh(x))coth(x) +--R + +--R 7 5 3 +--R - 320cosh(x) + 2048cosh(x) - 976cosh(x) - 1840cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 4 2 2 +--R (8cosh(x) - 600cosh(x) + 1248cosh(x) + 496cosh(x) - 592)coth(x) +--R + +--R 8 6 4 2 +--R - 16cosh(x) + 1200cosh(x) - 2496cosh(x) - 992cosh(x) + 1184 +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 112cosh(x) + 192cosh(x) + 488cosh(x) + 16cosh(x) +--R + +--R - 1064cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 3 +--R 224cosh(x) - 384cosh(x) - 976cosh(x) - 32cosh(x) + 2128cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 112cosh(x) + 532cosh(x) - 656cosh(x) + 496cosh(x) +--R + +--R 2 +--R - 944cosh(x) + 396 +--R * +--R 2 +--R coth(x) +--R + +--R 10 8 6 4 +--R 224cosh(x) - 1064cosh(x) + 1312cosh(x) - 992cosh(x) +--R + +--R 2 +--R 1888cosh(x) - 792 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 48cosh(x) + 320cosh(x) - 744cosh(x) + 920cosh(x) +--R + +--R 3 +--R - 1064cosh(x) + 744cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 11 9 7 5 +--R 96cosh(x) - 640cosh(x) + 1488cosh(x) - 1840cosh(x) +--R + +--R 3 +--R 2128cosh(x) - 1488cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 8cosh(x) + 68cosh(x) - 224cosh(x) + 432cosh(x) - 592cosh(x) +--R + +--R 2 +--R 396cosh(x) - 72 +--R * +--R 2 +--R coth(x) +--R + +--R 12 10 8 6 4 +--R 16cosh(x) - 136cosh(x) + 448cosh(x) - 864cosh(x) + 1184cosh(x) +--R + +--R 2 +--R - 792cosh(x) + 144 +--R / +--R 14 13 2 12 +--R sinh(x) + 6cosh(x)sinh(x) + (11cosh(x) - 7)sinh(x) +--R + +--R 3 11 +--R (- 4cosh(x) - 28cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (- 39cosh(x) - 14cosh(x) + 30)sinh(x) +--R + +--R 5 3 9 +--R (- 38cosh(x) + 84cosh(x) + 84cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (27cosh(x) + 119cosh(x) + 6cosh(x) - 114)sinh(x) +--R + +--R 7 5 3 7 +--R (72cosh(x) - 56cosh(x) - 144cosh(x) - 240cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (27cosh(x) - 196cosh(x) - 36cosh(x) - 24cosh(x) + 205)sinh(x) +--R + +--R 9 7 5 3 +--R - 38cosh(x) - 56cosh(x) + 120cosh(x) + 240cosh(x) +--R + +--R 270cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 39cosh(x) + 119cosh(x) - 36cosh(x) + 276cosh(x) +--R + +--R 2 +--R - 189cosh(x) - 163 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 4cosh(x) + 84cosh(x) - 144cosh(x) + 240cosh(x) +--R + +--R 3 +--R - 508cosh(x) - 52cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 11cosh(x) - 14cosh(x) + 6cosh(x) - 24cosh(x) - 189cosh(x) +--R + +--R 2 +--R 222cosh(x) + 84 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R 6cosh(x) - 28cosh(x) + 84cosh(x) - 240cosh(x) + 270cosh(x) +--R + +--R 3 +--R - 52cosh(x) + 24cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R cosh(x) - 7cosh(x) + 30cosh(x) - 114cosh(x) + 205cosh(x) +--R + +--R 4 2 +--R - 163cosh(x) + 84cosh(x) - 36 +--R * +--R +-------------------------------------+ +--R +--------------+ | 2 2 +--R | 2 | 2sinh(x) + 2cosh(x) - 6 +--R \|- coth(x) + 2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 12 11 2 10 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 112cosh(x) + 68)sinh(x) +--R + +--R 3 9 +--R (- 112cosh(x) + 320cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (8cosh(x) + 532cosh(x) - 224)sinh(x) +--R + +--R 5 3 7 +--R (160cosh(x) + 192cosh(x) - 744cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (224cosh(x) - 600cosh(x) - 656cosh(x) + 432)sinh(x) +--R + +--R 7 5 3 5 +--R (160cosh(x) - 1024cosh(x) + 488cosh(x) + 920cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (8cosh(x) - 600cosh(x) + 1248cosh(x) + 496cosh(x) - 592)sinh(x) +--R + +--R 9 7 5 3 +--R - 112cosh(x) + 192cosh(x) + 488cosh(x) + 16cosh(x) +--R + +--R - 1064cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 112cosh(x) + 532cosh(x) - 656cosh(x) + 496cosh(x) +--R + +--R 2 +--R - 944cosh(x) + 396 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 48cosh(x) + 320cosh(x) - 744cosh(x) + 920cosh(x) +--R + +--R 3 +--R - 1064cosh(x) + 744cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 8cosh(x) + 68cosh(x) - 224cosh(x) + 432cosh(x) - 592cosh(x) +--R + +--R 2 +--R 396cosh(x) - 72 +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 526 +t0470:= (-1+csch(x)^2)^(1/2) +--R +--R +--R +------------+ +--R | 2 +--R (282) \|csch(x) - 1 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 526 +r0470:= -atan(coth(x)/(-2+coth(x)^2)^(1/2))-_ + atanh((-2+coth(x)^2)^(1/2)*tanh(x)) +--R +--R +--R +------------+ +--R | 2 coth(x) +--R (283) - atanh(tanh(x)\|coth(x) - 2 ) - atan(---------------) +--R +------------+ +--R | 2 +--R \|coth(x) - 2 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 526 +a0470:= integrate(t0470,x) +--R +--R +--R (284) +--R - +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 2 +--R |------------------------------------- + sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 2 +--R - |------------------------------------- + sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R atan +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R - atan(-----------------------------------------) +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 375 + +--S 376 of 526 +m0470:= a0470-r0470 +--R +--R +--R (285) +--R - +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 2 +--R |------------------------------------- + sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 2 +--R - |------------------------------------- + sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +------------+ +--R | 2 +--R 2atanh(tanh(x)\|coth(x) - 2 ) +--R + +--R atan +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 coth(x) +--R - atan(-----------------------------------------) + 2atan(---------------) +--R +-------------------------------------+ +------------+ +--R | 2 2 | 2 +--R | - 2sinh(x) - 2cosh(x) + 6 \|coth(x) - 2 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 2 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 526 +d0470:= D(m0470,x) +--R +--R +--R (286) +--R 2 18 +--R (- 6coth(x) + 12)sinh(x) +--R + +--R 2 17 +--R (- 44cosh(x)coth(x) + 88cosh(x))sinh(x) +--R + +--R 2 2 2 16 +--R ((- 118cosh(x) + 78)coth(x) + 236cosh(x) - 156)sinh(x) +--R + +--R 3 2 3 +--R (- 96cosh(x) + 496cosh(x))coth(x) + 192cosh(x) +--R + +--R - 992cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (168cosh(x) + 1104cosh(x) - 62)coth(x) - 336cosh(x) +--R + +--R 2 +--R - 2208cosh(x) + 124 +--R * +--R 14 +--R sinh(x) +--R + +--R 5 3 2 +--R (432cosh(x) + 464cosh(x) - 836cosh(x))coth(x) +--R + +--R 5 3 +--R - 864cosh(x) - 928cosh(x) + 1672cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (264cosh(x) - 2296cosh(x) - 2794cosh(x) - 338)coth(x) +--R + +--R 6 4 2 +--R - 528cosh(x) + 4592cosh(x) + 5588cosh(x) + 676 +--R * +--R 12 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 160cosh(x) - 4368cosh(x) - 2216cosh(x) - 1016cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 7 5 3 +--R 320cosh(x) + 8736cosh(x) + 4432cosh(x) + 2032cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 8 6 4 +--R - 308cosh(x) - 2000cosh(x) + 4658cosh(x) +--R + +--R 2 +--R 1404cosh(x) - 434 +--R * +--R 2 +--R coth(x) +--R + +--R 8 6 4 2 +--R 616cosh(x) + 4000cosh(x) - 9316cosh(x) - 2808cosh(x) + 868 +--R * +--R 10 +--R sinh(x) +--R + +--R 9 7 5 +--R - 264cosh(x) + 3408cosh(x) + 8196cosh(x) +--R + +--R 3 +--R 8680cosh(x) - 1396cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 3 +--R 528cosh(x) - 6816cosh(x) - 16392cosh(x) - 17360cosh(x) +--R + +--R 2792cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 10 8 6 +--R - 308cosh(x) + 6228cosh(x) - 1802cosh(x) +--R + +--R 4 2 +--R 8690cosh(x) - 522cosh(x) + 994 +--R * +--R 2 +--R coth(x) +--R + +--R 10 8 6 4 +--R 616cosh(x) - 12456cosh(x) + 3604cosh(x) - 17380cosh(x) +--R + +--R 2 +--R 1044cosh(x) - 1988 +--R * +--R 8 +--R sinh(x) +--R + +--R 11 9 7 +--R - 160cosh(x) + 3408cosh(x) - 10288cosh(x) +--R + +--R 5 3 +--R - 7664cosh(x) + 3088cosh(x) + 3232cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 11 9 7 5 +--R 320cosh(x) - 6816cosh(x) + 20576cosh(x) + 15328cosh(x) +--R + +--R 3 +--R - 6176cosh(x) - 6464cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 12 10 8 +--R 264cosh(x) - 2000cosh(x) - 1802cosh(x) +--R + +--R 6 4 2 +--R - 19512cosh(x) + 5564cosh(x) - 1704cosh(x) + 950 +--R * +--R 2 +--R coth(x) +--R + +--R 12 10 8 6 +--R - 528cosh(x) + 4000cosh(x) + 3604cosh(x) + 39024cosh(x) +--R + +--R 4 2 +--R - 11128cosh(x) + 3408cosh(x) - 1900 +--R * +--R 6 +--R sinh(x) +--R + +--R 13 11 9 +--R 432cosh(x) - 4368cosh(x) + 8196cosh(x) +--R + +--R 7 5 3 +--R - 7664cosh(x) + 5832cosh(x) - 20000cosh(x) + 6756cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 13 11 9 +--R - 864cosh(x) + 8736cosh(x) - 16392cosh(x) +--R + +--R 7 5 3 +--R 15328cosh(x) - 11664cosh(x) + 40000cosh(x) - 13512cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 14 12 10 +--R 168cosh(x) - 2296cosh(x) + 4658cosh(x) +--R + +--R 8 6 4 +--R 8690cosh(x) + 5564cosh(x) - 32116cosh(x) +--R + +--R 2 +--R 18474cosh(x) - 1542 +--R * +--R 2 +--R coth(x) +--R + +--R 14 12 10 +--R - 336cosh(x) + 4592cosh(x) - 9316cosh(x) +--R + +--R 8 6 4 +--R - 17380cosh(x) - 11128cosh(x) + 64232cosh(x) +--R + +--R 2 +--R - 36948cosh(x) + 3084 +--R * +--R 4 +--R sinh(x) +--R + +--R 15 13 11 +--R - 96cosh(x) + 464cosh(x) - 2216cosh(x) +--R + +--R 9 7 5 +--R 8680cosh(x) + 3088cosh(x) - 20000cosh(x) +--R + +--R 3 +--R 25336cosh(x) - 7320cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 15 13 11 9 +--R 192cosh(x) - 928cosh(x) + 4432cosh(x) - 17360cosh(x) +--R + +--R 7 5 3 +--R - 6176cosh(x) + 40000cosh(x) - 50672cosh(x) + 14640cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 16 14 12 +--R - 118cosh(x) + 1104cosh(x) - 2794cosh(x) +--R + +--R 10 8 6 +--R 1404cosh(x) - 522cosh(x) - 1704cosh(x) +--R + +--R 4 2 +--R 18474cosh(x) - 11556cosh(x) + 576 +--R * +--R 2 +--R coth(x) +--R + +--R 16 14 12 10 +--R 236cosh(x) - 2208cosh(x) + 5588cosh(x) - 2808cosh(x) +--R + +--R 8 6 4 2 +--R 1044cosh(x) + 3408cosh(x) - 36948cosh(x) + 23112cosh(x) +--R + +--R - 1152 +--R * +--R 2 +--R sinh(x) +--R + +--R 17 15 13 +--R - 44cosh(x) + 496cosh(x) - 836cosh(x) +--R + +--R 11 9 7 +--R - 1016cosh(x) - 1396cosh(x) + 3232cosh(x) +--R + +--R 5 3 +--R 6756cosh(x) - 7320cosh(x) + 1152cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 17 15 13 11 +--R 88cosh(x) - 992cosh(x) + 1672cosh(x) + 2032cosh(x) +--R + +--R 9 7 5 3 +--R 2792cosh(x) - 6464cosh(x) - 13512cosh(x) + 14640cosh(x) +--R + +--R - 2304cosh(x) +--R * +--R sinh(x) +--R + +--R 18 16 14 12 +--R - 6cosh(x) + 78cosh(x) - 62cosh(x) - 338cosh(x) +--R + +--R 10 8 6 4 +--R - 434cosh(x) + 994cosh(x) + 950cosh(x) - 1542cosh(x) +--R + +--R 2 +--R 576cosh(x) - 216 +--R * +--R 2 +--R coth(x) +--R + +--R 18 16 14 12 +--R 12cosh(x) - 156cosh(x) + 124cosh(x) + 676cosh(x) +--R + +--R 10 8 6 4 +--R 868cosh(x) - 1988cosh(x) - 1900cosh(x) + 3084cosh(x) +--R + +--R 2 +--R - 1152cosh(x) + 432 +--R * +--R 2 +--R tanh(x) +--R + +--R 18 17 2 16 +--R 6sinh(x) + 44cosh(x)sinh(x) + (118cosh(x) - 78)sinh(x) +--R + +--R 3 15 +--R (96cosh(x) - 496cosh(x))sinh(x) +--R + +--R 4 2 14 +--R (- 168cosh(x) - 1104cosh(x) + 62)sinh(x) +--R + +--R 5 3 13 +--R (- 432cosh(x) - 464cosh(x) + 836cosh(x))sinh(x) +--R + +--R 6 4 2 12 +--R (- 264cosh(x) + 2296cosh(x) + 2794cosh(x) + 338)sinh(x) +--R + +--R 7 5 3 11 +--R (160cosh(x) + 4368cosh(x) + 2216cosh(x) + 1016cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (308cosh(x) + 2000cosh(x) - 4658cosh(x) - 1404cosh(x) + 434) +--R * +--R 10 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 264cosh(x) - 3408cosh(x) - 8196cosh(x) - 8680cosh(x) +--R + +--R 1396cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 308cosh(x) - 6228cosh(x) + 1802cosh(x) - 8690cosh(x) +--R + +--R 2 +--R 522cosh(x) - 994 +--R * +--R 8 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 160cosh(x) - 3408cosh(x) + 10288cosh(x) + 7664cosh(x) +--R + +--R 3 +--R - 3088cosh(x) - 3232cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 264cosh(x) + 2000cosh(x) + 1802cosh(x) + 19512cosh(x) +--R + +--R 4 2 +--R - 5564cosh(x) + 1704cosh(x) - 950 +--R * +--R 6 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 432cosh(x) + 4368cosh(x) - 8196cosh(x) + 7664cosh(x) +--R + +--R 5 3 +--R - 5832cosh(x) + 20000cosh(x) - 6756cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 168cosh(x) + 2296cosh(x) - 4658cosh(x) - 8690cosh(x) +--R + +--R 6 4 2 +--R - 5564cosh(x) + 32116cosh(x) - 18474cosh(x) + 1542 +--R * +--R 4 +--R sinh(x) +--R + +--R 15 13 11 9 +--R 96cosh(x) - 464cosh(x) + 2216cosh(x) - 8680cosh(x) +--R + +--R 7 5 3 +--R - 3088cosh(x) + 20000cosh(x) - 25336cosh(x) + 7320cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 16 14 12 10 +--R 118cosh(x) - 1104cosh(x) + 2794cosh(x) - 1404cosh(x) +--R + +--R 8 6 4 2 +--R 522cosh(x) + 1704cosh(x) - 18474cosh(x) + 11556cosh(x) - 576 +--R * +--R 2 +--R sinh(x) +--R + +--R 17 15 13 11 +--R 44cosh(x) - 496cosh(x) + 836cosh(x) + 1016cosh(x) +--R + +--R 9 7 5 3 +--R 1396cosh(x) - 3232cosh(x) - 6756cosh(x) + 7320cosh(x) +--R + +--R - 1152cosh(x) +--R * +--R sinh(x) +--R + +--R 18 16 14 12 10 +--R 6cosh(x) - 78cosh(x) + 62cosh(x) + 338cosh(x) + 434cosh(x) +--R + +--R 8 6 4 2 +--R - 994cosh(x) - 950cosh(x) + 1542cosh(x) - 576cosh(x) + 216 +--R * +--R +------------+ +--R | 2 +--R \|coth(x) - 2 +--R + +--R 2 22 +--R (2coth(x) - 4)sinh(x) +--R + +--R 2 21 +--R (20cosh(x)coth(x) - 40cosh(x))sinh(x) +--R + +--R 2 2 2 20 +--R ((78cosh(x) + 16)coth(x) - 156cosh(x) - 32)sinh(x) +--R + +--R 3 2 3 +--R ((120cosh(x) + 128cosh(x))coth(x) - 240cosh(x) - 256cosh(x)) +--R * +--R 19 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 90cosh(x) + 352cosh(x) + 20)coth(x) + 180cosh(x) +--R + +--R 2 +--R - 704cosh(x) - 40 +--R * +--R 18 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 636cosh(x) + 128cosh(x) + 112cosh(x))coth(x) +--R + +--R 5 3 +--R 1272cosh(x) - 256cosh(x) - 224cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 790cosh(x) - 1328cosh(x) + 116cosh(x) - 44)coth(x) +--R + +--R 6 4 2 +--R 1580cosh(x) + 2656cosh(x) - 232cosh(x) + 88 +--R * +--R 16 +--R sinh(x) +--R + +--R 7 5 3 +--R (416cosh(x) - 2560cosh(x) - 512cosh(x) - 144cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 7 5 3 +--R - 832cosh(x) + 5120cosh(x) + 1024cosh(x) + 288cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 2100cosh(x) + 128cosh(x) - 1392cosh(x) + 192cosh(x) +--R + +--R - 160 +--R * +--R 2 +--R coth(x) +--R + +--R 8 6 4 2 +--R - 4200cosh(x) - 256cosh(x) + 2784cosh(x) - 384cosh(x) + 320 +--R * +--R 14 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 1640cosh(x) + 5632cosh(x) - 192cosh(x) + 1232cosh(x) +--R + +--R - 504cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 3 +--R - 3280cosh(x) - 11264cosh(x) + 384cosh(x) - 2464cosh(x) +--R + +--R 1008cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 10 8 6 +--R - 1300cosh(x) + 5408cosh(x) + 3280cosh(x) +--R + +--R 4 2 +--R 752cosh(x) + 32cosh(x) + 196 +--R * +--R 2 +--R coth(x) +--R + +--R 10 8 6 4 +--R 2600cosh(x) - 10816cosh(x) - 6560cosh(x) - 1504cosh(x) +--R + +--R 2 +--R - 64cosh(x) - 392 +--R * +--R 12 +--R sinh(x) +--R + +--R 11 9 7 +--R - 3120cosh(x) - 3328cosh(x) + 3584cosh(x) +--R + +--R 5 3 +--R - 2832cosh(x) + 1360cosh(x) + 1168cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 11 9 7 5 +--R 6240cosh(x) + 6656cosh(x) - 7168cosh(x) + 5664cosh(x) +--R + +--R 3 +--R - 2720cosh(x) - 2336cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 12 10 8 +--R - 1300cosh(x) - 9152cosh(x) - 2024cosh(x) +--R + +--R 6 4 2 +--R - 4032cosh(x) + 352cosh(x) + 1416cosh(x) + 836 +--R * +--R 2 +--R coth(x) +--R + +--R 12 10 8 6 +--R 2600cosh(x) + 18304cosh(x) + 4048cosh(x) + 8064cosh(x) +--R + +--R 4 2 +--R - 704cosh(x) - 2832cosh(x) - 1672 +--R * +--R 10 +--R sinh(x) +--R + +--R 13 11 9 +--R 1640cosh(x) - 3328cosh(x) - 5984cosh(x) +--R + +--R 7 5 3 +--R 1744cosh(x) - 1928cosh(x) - 2480cosh(x) + 1440cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 13 11 9 +--R - 3280cosh(x) + 6656cosh(x) + 11968cosh(x) +--R + +--R 7 5 3 +--R - 3488cosh(x) + 3856cosh(x) + 4960cosh(x) - 2880cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 14 12 10 +--R 2100cosh(x) + 5408cosh(x) - 2024cosh(x) +--R + +--R 8 6 4 2 +--R 6264cosh(x) - 224cosh(x) - 5380cosh(x) - 2636cosh(x) +--R + +--R 268 +--R * +--R 2 +--R coth(x) +--R + +--R 14 12 10 +--R - 4200cosh(x) - 10816cosh(x) + 4048cosh(x) +--R + +--R 8 6 4 2 +--R - 12528cosh(x) + 448cosh(x) + 10760cosh(x) + 5272cosh(x) +--R + +--R - 536 +--R * +--R 8 +--R sinh(x) +--R + +--R 15 13 11 +--R 416cosh(x) + 5632cosh(x) + 3584cosh(x) +--R + +--R 9 7 5 3 +--R 1744cosh(x) + 2144cosh(x) + 1312cosh(x) - 5888cosh(x) +--R + +--R 400cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 15 13 11 +--R - 832cosh(x) - 11264cosh(x) - 7168cosh(x) +--R + +--R 9 7 5 3 +--R - 3488cosh(x) - 4288cosh(x) - 2624cosh(x) + 11776cosh(x) +--R + +--R - 800cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 16 14 12 +--R - 790cosh(x) + 128cosh(x) + 3280cosh(x) +--R + +--R 10 8 6 +--R - 4032cosh(x) - 224cosh(x) + 7536cosh(x) +--R + +--R 4 2 +--R 2312cosh(x) - 912cosh(x) - 1410 +--R * +--R 2 +--R coth(x) +--R + +--R 16 14 12 10 +--R 1580cosh(x) - 256cosh(x) - 6560cosh(x) + 8064cosh(x) +--R + +--R 8 6 4 2 +--R 448cosh(x) - 15072cosh(x) - 4624cosh(x) + 1824cosh(x) +--R + +--R 2820 +--R * +--R 6 +--R sinh(x) +--R + +--R 17 15 13 +--R - 636cosh(x) - 2560cosh(x) - 192cosh(x) +--R + +--R 11 9 7 +--R - 2832cosh(x) - 1928cosh(x) + 1312cosh(x) +--R + +--R 5 3 +--R 9920cosh(x) - 2960cosh(x) - 892cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 17 15 13 11 +--R 1272cosh(x) + 5120cosh(x) + 384cosh(x) + 5664cosh(x) +--R + +--R 9 7 5 3 +--R 3856cosh(x) - 2624cosh(x) - 19840cosh(x) + 5920cosh(x) +--R + +--R 1784cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 18 16 14 +--R - 90cosh(x) - 1328cosh(x) - 1392cosh(x) +--R + +--R 12 10 8 6 +--R 752cosh(x) + 352cosh(x) - 5380cosh(x) + 2312cosh(x) +--R + +--R 4 2 +--R - 3832cosh(x) + 6050cosh(x) - 516 +--R * +--R 2 +--R coth(x) +--R + +--R 18 16 14 12 +--R 180cosh(x) + 2656cosh(x) + 2784cosh(x) - 1504cosh(x) +--R + +--R 10 8 6 4 +--R - 704cosh(x) + 10760cosh(x) - 4624cosh(x) + 7664cosh(x) +--R + +--R 2 +--R - 12100cosh(x) + 1032 +--R * +--R 4 +--R sinh(x) +--R + +--R 19 17 15 +--R 120cosh(x) + 128cosh(x) - 512cosh(x) +--R + +--R 13 11 9 +--R 1232cosh(x) + 1360cosh(x) - 2480cosh(x) +--R + +--R 7 5 3 +--R - 5888cosh(x) - 2960cosh(x) + 11064cosh(x) - 3600cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 19 17 15 13 +--R - 240cosh(x) - 256cosh(x) + 1024cosh(x) - 2464cosh(x) +--R + +--R 11 9 7 5 +--R - 2720cosh(x) + 4960cosh(x) + 11776cosh(x) + 5920cosh(x) +--R + +--R 3 +--R - 22128cosh(x) + 7200cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 20 18 16 14 +--R 78cosh(x) + 352cosh(x) + 116cosh(x) + 192cosh(x) +--R + +--R 12 10 8 6 +--R 32cosh(x) + 1416cosh(x) - 2636cosh(x) - 912cosh(x) +--R + +--R 4 2 +--R 6050cosh(x) - 6168cosh(x) + 1224 +--R * +--R 2 +--R coth(x) +--R + +--R 20 18 16 14 +--R - 156cosh(x) - 704cosh(x) - 232cosh(x) - 384cosh(x) +--R + +--R 12 10 8 6 +--R - 64cosh(x) - 2832cosh(x) + 5272cosh(x) + 1824cosh(x) +--R + +--R 4 2 +--R - 12100cosh(x) + 12336cosh(x) - 2448 +--R * +--R 2 +--R sinh(x) +--R + +--R 21 19 17 15 +--R 20cosh(x) + 128cosh(x) + 112cosh(x) - 144cosh(x) +--R + +--R 13 11 9 +--R - 504cosh(x) + 1168cosh(x) + 1440cosh(x) +--R + +--R 7 5 3 +--R 400cosh(x) - 892cosh(x) - 3600cosh(x) + 1872cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 21 19 17 15 +--R - 40cosh(x) - 256cosh(x) - 224cosh(x) + 288cosh(x) +--R + +--R 13 11 9 7 +--R 1008cosh(x) - 2336cosh(x) - 2880cosh(x) - 800cosh(x) +--R + +--R 5 3 +--R 1784cosh(x) + 7200cosh(x) - 3744cosh(x) +--R * +--R sinh(x) +--R + +--R 22 20 18 16 +--R 2cosh(x) + 16cosh(x) + 20cosh(x) - 44cosh(x) +--R + +--R 14 12 10 8 +--R - 160cosh(x) + 196cosh(x) + 836cosh(x) + 268cosh(x) +--R + +--R 6 4 2 +--R - 1410cosh(x) - 516cosh(x) + 1224cosh(x) - 432 +--R * +--R 2 +--R coth(x) +--R + +--R 22 20 18 16 +--R - 4cosh(x) - 32cosh(x) - 40cosh(x) + 88cosh(x) +--R + +--R 14 12 10 8 +--R 320cosh(x) - 392cosh(x) - 1672cosh(x) - 536cosh(x) +--R + +--R 6 4 2 +--R 2820cosh(x) + 1032cosh(x) - 2448cosh(x) + 864 +--R * +--R 2 +--R tanh(x) +--R + +--R 3 22 +--R (coth(x) - coth(x))sinh(x) +--R + +--R 3 21 +--R (10cosh(x)coth(x) - 10cosh(x)coth(x))sinh(x) +--R + +--R 2 3 2 20 +--R ((39cosh(x) + 8)coth(x) + (- 39cosh(x) - 8)coth(x))sinh(x) +--R + +--R 3 3 +--R (60cosh(x) + 64cosh(x))coth(x) +--R + +--R 3 +--R (- 60cosh(x) - 64cosh(x))coth(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 4 2 3 +--R (- 45cosh(x) + 176cosh(x) + 10)coth(x) +--R + +--R 4 2 +--R (45cosh(x) - 176cosh(x) - 10)coth(x) +--R * +--R 18 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 318cosh(x) + 64cosh(x) + 56cosh(x))coth(x) +--R + +--R 5 3 +--R (318cosh(x) - 64cosh(x) - 56cosh(x))coth(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- 395cosh(x) - 664cosh(x) + 58cosh(x) - 22)coth(x) +--R + +--R 6 4 2 +--R (395cosh(x) + 664cosh(x) - 58cosh(x) + 22)coth(x) +--R * +--R 16 +--R sinh(x) +--R + +--R 7 5 3 +--R (208cosh(x) - 1280cosh(x) - 256cosh(x) - 72cosh(x)) +--R * +--R 3 +--R coth(x) +--R + +--R 7 5 3 +--R (- 208cosh(x) + 1280cosh(x) + 256cosh(x) + 72cosh(x))coth(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (1050cosh(x) + 64cosh(x) - 696cosh(x) + 96cosh(x) - 80) +--R * +--R 3 +--R coth(x) +--R + +--R 8 6 4 2 +--R - 1050cosh(x) - 64cosh(x) + 696cosh(x) - 96cosh(x) +--R + +--R 80 +--R * +--R coth(x) +--R * +--R 14 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 820cosh(x) + 2816cosh(x) - 96cosh(x) + 616cosh(x) +--R + +--R - 252cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 9 7 5 3 +--R - 820cosh(x) - 2816cosh(x) + 96cosh(x) - 616cosh(x) +--R + +--R 252cosh(x) +--R * +--R coth(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 10 8 6 +--R - 650cosh(x) + 2704cosh(x) + 1640cosh(x) +--R + +--R 4 2 +--R 376cosh(x) + 16cosh(x) + 98 +--R * +--R 3 +--R coth(x) +--R + +--R 10 8 6 4 +--R 650cosh(x) - 2704cosh(x) - 1640cosh(x) - 376cosh(x) +--R + +--R 2 +--R - 16cosh(x) - 98 +--R * +--R coth(x) +--R * +--R 12 +--R sinh(x) +--R + +--R 11 9 7 +--R - 1560cosh(x) - 1664cosh(x) + 1792cosh(x) +--R + +--R 5 3 +--R - 1416cosh(x) + 680cosh(x) + 584cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 11 9 7 +--R 1560cosh(x) + 1664cosh(x) - 1792cosh(x) +--R + +--R 5 3 +--R 1416cosh(x) - 680cosh(x) - 584cosh(x) +--R * +--R coth(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 12 10 8 +--R - 650cosh(x) - 4576cosh(x) - 1012cosh(x) +--R + +--R 6 4 2 +--R - 2016cosh(x) + 176cosh(x) + 708cosh(x) + 418 +--R * +--R 3 +--R coth(x) +--R + +--R 12 10 8 +--R 650cosh(x) + 4576cosh(x) + 1012cosh(x) +--R + +--R 6 4 2 +--R 2016cosh(x) - 176cosh(x) - 708cosh(x) - 418 +--R * +--R coth(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 820cosh(x) - 1664cosh(x) - 2992cosh(x) + 872cosh(x) +--R + +--R 5 3 +--R - 964cosh(x) - 1240cosh(x) + 720cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 13 11 9 +--R - 820cosh(x) + 1664cosh(x) + 2992cosh(x) +--R + +--R 7 5 3 +--R - 872cosh(x) + 964cosh(x) + 1240cosh(x) - 720cosh(x) +--R * +--R coth(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 14 12 10 +--R 1050cosh(x) + 2704cosh(x) - 1012cosh(x) +--R + +--R 8 6 4 2 +--R 3132cosh(x) - 112cosh(x) - 2690cosh(x) - 1318cosh(x) +--R + +--R 134 +--R * +--R 3 +--R coth(x) +--R + +--R 14 12 10 +--R - 1050cosh(x) - 2704cosh(x) + 1012cosh(x) +--R + +--R 8 6 4 +--R - 3132cosh(x) + 112cosh(x) + 2690cosh(x) +--R + +--R 2 +--R 1318cosh(x) - 134 +--R * +--R coth(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 15 13 11 +--R 208cosh(x) + 2816cosh(x) + 1792cosh(x) +--R + +--R 9 7 5 3 +--R 872cosh(x) + 1072cosh(x) + 656cosh(x) - 2944cosh(x) +--R + +--R 200cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 15 13 11 +--R - 208cosh(x) - 2816cosh(x) - 1792cosh(x) +--R + +--R 9 7 5 3 +--R - 872cosh(x) - 1072cosh(x) - 656cosh(x) + 2944cosh(x) +--R + +--R - 200cosh(x) +--R * +--R coth(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 16 14 12 +--R - 395cosh(x) + 64cosh(x) + 1640cosh(x) +--R + +--R 10 8 6 +--R - 2016cosh(x) - 112cosh(x) + 3768cosh(x) +--R + +--R 4 2 +--R 1156cosh(x) - 456cosh(x) - 705 +--R * +--R 3 +--R coth(x) +--R + +--R 16 14 12 +--R 395cosh(x) - 64cosh(x) - 1640cosh(x) +--R + +--R 10 8 6 4 +--R 2016cosh(x) + 112cosh(x) - 3768cosh(x) - 1156cosh(x) +--R + +--R 2 +--R 456cosh(x) + 705 +--R * +--R coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 17 15 13 +--R - 318cosh(x) - 1280cosh(x) - 96cosh(x) +--R + +--R 11 9 7 +--R - 1416cosh(x) - 964cosh(x) + 656cosh(x) +--R + +--R 5 3 +--R 4960cosh(x) - 1480cosh(x) - 446cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 17 15 13 +--R 318cosh(x) + 1280cosh(x) + 96cosh(x) +--R + +--R 11 9 7 5 +--R 1416cosh(x) + 964cosh(x) - 656cosh(x) - 4960cosh(x) +--R + +--R 3 +--R 1480cosh(x) + 446cosh(x) +--R * +--R coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 18 16 14 +--R - 45cosh(x) - 664cosh(x) - 696cosh(x) +--R + +--R 12 10 8 6 +--R 376cosh(x) + 176cosh(x) - 2690cosh(x) + 1156cosh(x) +--R + +--R 4 2 +--R - 1916cosh(x) + 3025cosh(x) - 258 +--R * +--R 3 +--R coth(x) +--R + +--R 18 16 14 12 +--R 45cosh(x) + 664cosh(x) + 696cosh(x) - 376cosh(x) +--R + +--R 10 8 6 +--R - 176cosh(x) + 2690cosh(x) - 1156cosh(x) +--R + +--R 4 2 +--R 1916cosh(x) - 3025cosh(x) + 258 +--R * +--R coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 19 17 15 13 +--R 60cosh(x) + 64cosh(x) - 256cosh(x) + 616cosh(x) +--R + +--R 11 9 7 5 +--R 680cosh(x) - 1240cosh(x) - 2944cosh(x) - 1480cosh(x) +--R + +--R 3 +--R 5532cosh(x) - 1800cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 19 17 15 13 +--R - 60cosh(x) - 64cosh(x) + 256cosh(x) - 616cosh(x) +--R + +--R 11 9 7 +--R - 680cosh(x) + 1240cosh(x) + 2944cosh(x) +--R + +--R 5 3 +--R 1480cosh(x) - 5532cosh(x) + 1800cosh(x) +--R * +--R coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 20 18 16 14 +--R 39cosh(x) + 176cosh(x) + 58cosh(x) + 96cosh(x) +--R + +--R 12 10 8 6 +--R 16cosh(x) + 708cosh(x) - 1318cosh(x) - 456cosh(x) +--R + +--R 4 2 +--R 3025cosh(x) - 3084cosh(x) + 612 +--R * +--R 3 +--R coth(x) +--R + +--R 20 18 16 14 +--R - 39cosh(x) - 176cosh(x) - 58cosh(x) - 96cosh(x) +--R + +--R 12 10 8 6 +--R - 16cosh(x) - 708cosh(x) + 1318cosh(x) + 456cosh(x) +--R + +--R 4 2 +--R - 3025cosh(x) + 3084cosh(x) - 612 +--R * +--R coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 21 19 17 15 +--R 10cosh(x) + 64cosh(x) + 56cosh(x) - 72cosh(x) +--R + +--R 13 11 9 7 +--R - 252cosh(x) + 584cosh(x) + 720cosh(x) + 200cosh(x) +--R + +--R 5 3 +--R - 446cosh(x) - 1800cosh(x) + 936cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 21 19 17 15 +--R - 10cosh(x) - 64cosh(x) - 56cosh(x) + 72cosh(x) +--R + +--R 13 11 9 7 +--R 252cosh(x) - 584cosh(x) - 720cosh(x) - 200cosh(x) +--R + +--R 5 3 +--R 446cosh(x) + 1800cosh(x) - 936cosh(x) +--R * +--R coth(x) +--R * +--R sinh(x) +--R + +--R 22 20 18 16 +--R cosh(x) + 8cosh(x) + 10cosh(x) - 22cosh(x) +--R + +--R 14 12 10 8 +--R - 80cosh(x) + 98cosh(x) + 418cosh(x) + 134cosh(x) +--R + +--R 6 4 2 +--R - 705cosh(x) - 258cosh(x) + 612cosh(x) - 216 +--R * +--R 3 +--R coth(x) +--R + +--R 22 20 18 16 +--R - cosh(x) - 8cosh(x) - 10cosh(x) + 22cosh(x) +--R + +--R 14 12 10 8 +--R 80cosh(x) - 98cosh(x) - 418cosh(x) - 134cosh(x) +--R + +--R 6 4 2 +--R 705cosh(x) + 258cosh(x) - 612cosh(x) + 216 +--R * +--R coth(x) +--R * +--R tanh(x) +--R + +--R 2 22 +--R (- coth(x) + 1)sinh(x) +--R + +--R 2 21 +--R (- 10cosh(x)coth(x) + 10cosh(x))sinh(x) +--R + +--R 2 2 2 20 +--R ((- 39cosh(x) - 8)coth(x) + 39cosh(x) + 8)sinh(x) +--R + +--R 3 2 3 +--R ((- 60cosh(x) - 64cosh(x))coth(x) + 60cosh(x) + 64cosh(x)) +--R * +--R 19 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (45cosh(x) - 176cosh(x) - 10)coth(x) - 45cosh(x) +--R + +--R 2 +--R 176cosh(x) + 10 +--R * +--R 18 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (318cosh(x) - 64cosh(x) - 56cosh(x))coth(x) - 318cosh(x) +--R + +--R 3 +--R 64cosh(x) + 56cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (395cosh(x) + 664cosh(x) - 58cosh(x) + 22)coth(x) +--R + +--R 6 4 2 +--R - 395cosh(x) - 664cosh(x) + 58cosh(x) - 22 +--R * +--R 16 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (- 208cosh(x) + 1280cosh(x) + 256cosh(x) + 72cosh(x))coth(x) +--R + +--R 7 5 3 +--R 208cosh(x) - 1280cosh(x) - 256cosh(x) - 72cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 1050cosh(x) - 64cosh(x) + 696cosh(x) - 96cosh(x) + 80) +--R * +--R 2 +--R coth(x) +--R + +--R 8 6 4 2 +--R 1050cosh(x) + 64cosh(x) - 696cosh(x) + 96cosh(x) - 80 +--R * +--R 14 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 820cosh(x) - 2816cosh(x) + 96cosh(x) - 616cosh(x) +--R + +--R 252cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 3 +--R 820cosh(x) + 2816cosh(x) - 96cosh(x) + 616cosh(x) - 252cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 650cosh(x) - 2704cosh(x) - 1640cosh(x) - 376cosh(x) +--R + +--R 2 +--R - 16cosh(x) - 98 +--R * +--R 2 +--R coth(x) +--R + +--R 10 8 6 4 +--R - 650cosh(x) + 2704cosh(x) + 1640cosh(x) + 376cosh(x) +--R + +--R 2 +--R 16cosh(x) + 98 +--R * +--R 12 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 1560cosh(x) + 1664cosh(x) - 1792cosh(x) + 1416cosh(x) +--R + +--R 3 +--R - 680cosh(x) - 584cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 11 9 7 5 +--R - 1560cosh(x) - 1664cosh(x) + 1792cosh(x) - 1416cosh(x) +--R + +--R 3 +--R 680cosh(x) + 584cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 650cosh(x) + 4576cosh(x) + 1012cosh(x) + 2016cosh(x) +--R + +--R 4 2 +--R - 176cosh(x) - 708cosh(x) - 418 +--R * +--R 2 +--R coth(x) +--R + +--R 12 10 8 6 +--R - 650cosh(x) - 4576cosh(x) - 1012cosh(x) - 2016cosh(x) +--R + +--R 4 2 +--R 176cosh(x) + 708cosh(x) + 418 +--R * +--R 10 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 820cosh(x) + 1664cosh(x) + 2992cosh(x) - 872cosh(x) +--R + +--R 5 3 +--R 964cosh(x) + 1240cosh(x) - 720cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 13 11 9 7 +--R 820cosh(x) - 1664cosh(x) - 2992cosh(x) + 872cosh(x) +--R + +--R 5 3 +--R - 964cosh(x) - 1240cosh(x) + 720cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 14 12 10 +--R - 1050cosh(x) - 2704cosh(x) + 1012cosh(x) +--R + +--R 8 6 4 2 +--R - 3132cosh(x) + 112cosh(x) + 2690cosh(x) + 1318cosh(x) +--R + +--R - 134 +--R * +--R 2 +--R coth(x) +--R + +--R 14 12 10 8 +--R 1050cosh(x) + 2704cosh(x) - 1012cosh(x) + 3132cosh(x) +--R + +--R 6 4 2 +--R - 112cosh(x) - 2690cosh(x) - 1318cosh(x) + 134 +--R * +--R 8 +--R sinh(x) +--R + +--R 15 13 11 9 +--R - 208cosh(x) - 2816cosh(x) - 1792cosh(x) - 872cosh(x) +--R + +--R 7 5 3 +--R - 1072cosh(x) - 656cosh(x) + 2944cosh(x) - 200cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 15 13 11 9 +--R 208cosh(x) + 2816cosh(x) + 1792cosh(x) + 872cosh(x) +--R + +--R 7 5 3 +--R 1072cosh(x) + 656cosh(x) - 2944cosh(x) + 200cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 16 14 12 10 +--R 395cosh(x) - 64cosh(x) - 1640cosh(x) + 2016cosh(x) +--R + +--R 8 6 4 2 +--R 112cosh(x) - 3768cosh(x) - 1156cosh(x) + 456cosh(x) + 705 +--R * +--R 2 +--R coth(x) +--R + +--R 16 14 12 10 +--R - 395cosh(x) + 64cosh(x) + 1640cosh(x) - 2016cosh(x) +--R + +--R 8 6 4 2 +--R - 112cosh(x) + 3768cosh(x) + 1156cosh(x) - 456cosh(x) - 705 +--R * +--R 6 +--R sinh(x) +--R + +--R 17 15 13 11 +--R 318cosh(x) + 1280cosh(x) + 96cosh(x) + 1416cosh(x) +--R + +--R 9 7 5 3 +--R 964cosh(x) - 656cosh(x) - 4960cosh(x) + 1480cosh(x) +--R + +--R 446cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 17 15 13 11 +--R - 318cosh(x) - 1280cosh(x) - 96cosh(x) - 1416cosh(x) +--R + +--R 9 7 5 3 +--R - 964cosh(x) + 656cosh(x) + 4960cosh(x) - 1480cosh(x) +--R + +--R - 446cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 18 16 14 12 +--R 45cosh(x) + 664cosh(x) + 696cosh(x) - 376cosh(x) +--R + +--R 10 8 6 4 +--R - 176cosh(x) + 2690cosh(x) - 1156cosh(x) + 1916cosh(x) +--R + +--R 2 +--R - 3025cosh(x) + 258 +--R * +--R 2 +--R coth(x) +--R + +--R 18 16 14 12 +--R - 45cosh(x) - 664cosh(x) - 696cosh(x) + 376cosh(x) +--R + +--R 10 8 6 4 +--R 176cosh(x) - 2690cosh(x) + 1156cosh(x) - 1916cosh(x) +--R + +--R 2 +--R 3025cosh(x) - 258 +--R * +--R 4 +--R sinh(x) +--R + +--R 19 17 15 13 +--R - 60cosh(x) - 64cosh(x) + 256cosh(x) - 616cosh(x) +--R + +--R 11 9 7 5 +--R - 680cosh(x) + 1240cosh(x) + 2944cosh(x) + 1480cosh(x) +--R + +--R 3 +--R - 5532cosh(x) + 1800cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 19 17 15 13 +--R 60cosh(x) + 64cosh(x) - 256cosh(x) + 616cosh(x) +--R + +--R 11 9 7 5 +--R 680cosh(x) - 1240cosh(x) - 2944cosh(x) - 1480cosh(x) +--R + +--R 3 +--R 5532cosh(x) - 1800cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 20 18 16 14 +--R - 39cosh(x) - 176cosh(x) - 58cosh(x) - 96cosh(x) +--R + +--R 12 10 8 6 +--R - 16cosh(x) - 708cosh(x) + 1318cosh(x) + 456cosh(x) +--R + +--R 4 2 +--R - 3025cosh(x) + 3084cosh(x) - 612 +--R * +--R 2 +--R coth(x) +--R + +--R 20 18 16 14 +--R 39cosh(x) + 176cosh(x) + 58cosh(x) + 96cosh(x) +--R + +--R 12 10 8 6 +--R 16cosh(x) + 708cosh(x) - 1318cosh(x) - 456cosh(x) +--R + +--R 4 2 +--R 3025cosh(x) - 3084cosh(x) + 612 +--R * +--R 2 +--R sinh(x) +--R + +--R 21 19 17 15 +--R - 10cosh(x) - 64cosh(x) - 56cosh(x) + 72cosh(x) +--R + +--R 13 11 9 7 +--R 252cosh(x) - 584cosh(x) - 720cosh(x) - 200cosh(x) +--R + +--R 5 3 +--R 446cosh(x) + 1800cosh(x) - 936cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 21 19 17 15 +--R 10cosh(x) + 64cosh(x) + 56cosh(x) - 72cosh(x) +--R + +--R 13 11 9 7 +--R - 252cosh(x) + 584cosh(x) + 720cosh(x) + 200cosh(x) +--R + +--R 5 3 +--R - 446cosh(x) - 1800cosh(x) + 936cosh(x) +--R * +--R sinh(x) +--R + +--R 22 20 18 16 +--R - cosh(x) - 8cosh(x) - 10cosh(x) + 22cosh(x) +--R + +--R 14 12 10 8 +--R 80cosh(x) - 98cosh(x) - 418cosh(x) - 134cosh(x) +--R + +--R 6 4 2 +--R 705cosh(x) + 258cosh(x) - 612cosh(x) + 216 +--R * +--R 2 +--R coth(x) +--R + +--R 22 20 18 16 14 +--R cosh(x) + 8cosh(x) + 10cosh(x) - 22cosh(x) - 80cosh(x) +--R + +--R 12 10 8 6 4 +--R 98cosh(x) + 418cosh(x) + 134cosh(x) - 705cosh(x) - 258cosh(x) +--R + +--R 2 +--R 612cosh(x) - 216 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 2 22 2 21 +--R (coth(x) - 2)sinh(x) + (10cosh(x)coth(x) - 20cosh(x))sinh(x) +--R + +--R 2 2 2 20 +--R ((39cosh(x) + 8)coth(x) - 78cosh(x) - 16)sinh(x) +--R + +--R 3 2 3 +--R ((60cosh(x) + 64cosh(x))coth(x) - 120cosh(x) - 128cosh(x)) +--R * +--R 19 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (- 45cosh(x) + 176cosh(x) + 10)coth(x) + 90cosh(x) +--R + +--R 2 +--R - 352cosh(x) - 20 +--R * +--R 18 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 318cosh(x) + 64cosh(x) + 56cosh(x))coth(x) + 636cosh(x) +--R + +--R 3 +--R - 128cosh(x) - 112cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 395cosh(x) - 664cosh(x) + 58cosh(x) - 22)coth(x) +--R + +--R 6 4 2 +--R 790cosh(x) + 1328cosh(x) - 116cosh(x) + 44 +--R * +--R 16 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (208cosh(x) - 1280cosh(x) - 256cosh(x) - 72cosh(x))coth(x) +--R + +--R 7 5 3 +--R - 416cosh(x) + 2560cosh(x) + 512cosh(x) + 144cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (1050cosh(x) + 64cosh(x) - 696cosh(x) + 96cosh(x) - 80) +--R * +--R 2 +--R coth(x) +--R + +--R 8 6 4 2 +--R - 2100cosh(x) - 128cosh(x) + 1392cosh(x) - 192cosh(x) + 160 +--R * +--R 14 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 820cosh(x) + 2816cosh(x) - 96cosh(x) + 616cosh(x) +--R + +--R - 252cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 3 +--R - 1640cosh(x) - 5632cosh(x) + 192cosh(x) - 1232cosh(x) +--R + +--R 504cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 650cosh(x) + 2704cosh(x) + 1640cosh(x) + 376cosh(x) +--R + +--R 2 +--R 16cosh(x) + 98 +--R * +--R 2 +--R coth(x) +--R + +--R 10 8 6 4 +--R 1300cosh(x) - 5408cosh(x) - 3280cosh(x) - 752cosh(x) +--R + +--R 2 +--R - 32cosh(x) - 196 +--R * +--R 12 +--R sinh(x) +--R + +--R 11 9 7 +--R - 1560cosh(x) - 1664cosh(x) + 1792cosh(x) +--R + +--R 5 3 +--R - 1416cosh(x) + 680cosh(x) + 584cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 11 9 7 5 +--R 3120cosh(x) + 3328cosh(x) - 3584cosh(x) + 2832cosh(x) +--R + +--R 3 +--R - 1360cosh(x) - 1168cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 12 10 8 +--R - 650cosh(x) - 4576cosh(x) - 1012cosh(x) +--R + +--R 6 4 2 +--R - 2016cosh(x) + 176cosh(x) + 708cosh(x) + 418 +--R * +--R 2 +--R coth(x) +--R + +--R 12 10 8 6 +--R 1300cosh(x) + 9152cosh(x) + 2024cosh(x) + 4032cosh(x) +--R + +--R 4 2 +--R - 352cosh(x) - 1416cosh(x) - 836 +--R * +--R 10 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 820cosh(x) - 1664cosh(x) - 2992cosh(x) + 872cosh(x) +--R + +--R 5 3 +--R - 964cosh(x) - 1240cosh(x) + 720cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 13 11 9 7 +--R - 1640cosh(x) + 3328cosh(x) + 5984cosh(x) - 1744cosh(x) +--R + +--R 5 3 +--R 1928cosh(x) + 2480cosh(x) - 1440cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 14 12 10 +--R 1050cosh(x) + 2704cosh(x) - 1012cosh(x) +--R + +--R 8 6 4 2 +--R 3132cosh(x) - 112cosh(x) - 2690cosh(x) - 1318cosh(x) +--R + +--R 134 +--R * +--R 2 +--R coth(x) +--R + +--R 14 12 10 8 +--R - 2100cosh(x) - 5408cosh(x) + 2024cosh(x) - 6264cosh(x) +--R + +--R 6 4 2 +--R 224cosh(x) + 5380cosh(x) + 2636cosh(x) - 268 +--R * +--R 8 +--R sinh(x) +--R + +--R 15 13 11 9 +--R 208cosh(x) + 2816cosh(x) + 1792cosh(x) + 872cosh(x) +--R + +--R 7 5 3 +--R 1072cosh(x) + 656cosh(x) - 2944cosh(x) + 200cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 15 13 11 9 +--R - 416cosh(x) - 5632cosh(x) - 3584cosh(x) - 1744cosh(x) +--R + +--R 7 5 3 +--R - 2144cosh(x) - 1312cosh(x) + 5888cosh(x) - 400cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 16 14 12 +--R - 395cosh(x) + 64cosh(x) + 1640cosh(x) +--R + +--R 10 8 6 4 +--R - 2016cosh(x) - 112cosh(x) + 3768cosh(x) + 1156cosh(x) +--R + +--R 2 +--R - 456cosh(x) - 705 +--R * +--R 2 +--R coth(x) +--R + +--R 16 14 12 10 +--R 790cosh(x) - 128cosh(x) - 3280cosh(x) + 4032cosh(x) +--R + +--R 8 6 4 2 +--R 224cosh(x) - 7536cosh(x) - 2312cosh(x) + 912cosh(x) + 1410 +--R * +--R 6 +--R sinh(x) +--R + +--R 17 15 13 +--R - 318cosh(x) - 1280cosh(x) - 96cosh(x) +--R + +--R 11 9 7 5 +--R - 1416cosh(x) - 964cosh(x) + 656cosh(x) + 4960cosh(x) +--R + +--R 3 +--R - 1480cosh(x) - 446cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 17 15 13 11 +--R 636cosh(x) + 2560cosh(x) + 192cosh(x) + 2832cosh(x) +--R + +--R 9 7 5 3 +--R 1928cosh(x) - 1312cosh(x) - 9920cosh(x) + 2960cosh(x) +--R + +--R 892cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 18 16 14 12 +--R - 45cosh(x) - 664cosh(x) - 696cosh(x) + 376cosh(x) +--R + +--R 10 8 6 4 +--R 176cosh(x) - 2690cosh(x) + 1156cosh(x) - 1916cosh(x) +--R + +--R 2 +--R 3025cosh(x) - 258 +--R * +--R 2 +--R coth(x) +--R + +--R 18 16 14 12 +--R 90cosh(x) + 1328cosh(x) + 1392cosh(x) - 752cosh(x) +--R + +--R 10 8 6 4 +--R - 352cosh(x) + 5380cosh(x) - 2312cosh(x) + 3832cosh(x) +--R + +--R 2 +--R - 6050cosh(x) + 516 +--R * +--R 4 +--R sinh(x) +--R + +--R 19 17 15 13 +--R 60cosh(x) + 64cosh(x) - 256cosh(x) + 616cosh(x) +--R + +--R 11 9 7 5 +--R 680cosh(x) - 1240cosh(x) - 2944cosh(x) - 1480cosh(x) +--R + +--R 3 +--R 5532cosh(x) - 1800cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 19 17 15 13 +--R - 120cosh(x) - 128cosh(x) + 512cosh(x) - 1232cosh(x) +--R + +--R 11 9 7 5 +--R - 1360cosh(x) + 2480cosh(x) + 5888cosh(x) + 2960cosh(x) +--R + +--R 3 +--R - 11064cosh(x) + 3600cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 20 18 16 14 +--R 39cosh(x) + 176cosh(x) + 58cosh(x) + 96cosh(x) +--R + +--R 12 10 8 6 +--R 16cosh(x) + 708cosh(x) - 1318cosh(x) - 456cosh(x) +--R + +--R 4 2 +--R 3025cosh(x) - 3084cosh(x) + 612 +--R * +--R 2 +--R coth(x) +--R + +--R 20 18 16 14 +--R - 78cosh(x) - 352cosh(x) - 116cosh(x) - 192cosh(x) +--R + +--R 12 10 8 6 +--R - 32cosh(x) - 1416cosh(x) + 2636cosh(x) + 912cosh(x) +--R + +--R 4 2 +--R - 6050cosh(x) + 6168cosh(x) - 1224 +--R * +--R 2 +--R sinh(x) +--R + +--R 21 19 17 15 +--R 10cosh(x) + 64cosh(x) + 56cosh(x) - 72cosh(x) +--R + +--R 13 11 9 7 +--R - 252cosh(x) + 584cosh(x) + 720cosh(x) + 200cosh(x) +--R + +--R 5 3 +--R - 446cosh(x) - 1800cosh(x) + 936cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 21 19 17 15 +--R - 20cosh(x) - 128cosh(x) - 112cosh(x) + 144cosh(x) +--R + +--R 13 11 9 7 +--R 504cosh(x) - 1168cosh(x) - 1440cosh(x) - 400cosh(x) +--R + +--R 5 3 +--R 892cosh(x) + 3600cosh(x) - 1872cosh(x) +--R * +--R sinh(x) +--R + +--R 22 20 18 16 +--R cosh(x) + 8cosh(x) + 10cosh(x) - 22cosh(x) +--R + +--R 14 12 10 8 +--R - 80cosh(x) + 98cosh(x) + 418cosh(x) + 134cosh(x) +--R + +--R 6 4 2 +--R - 705cosh(x) - 258cosh(x) + 612cosh(x) - 216 +--R * +--R 2 +--R coth(x) +--R + +--R 22 20 18 16 +--R - 2cosh(x) - 16cosh(x) - 20cosh(x) + 44cosh(x) +--R + +--R 14 12 10 8 +--R 160cosh(x) - 196cosh(x) - 836cosh(x) - 268cosh(x) +--R + +--R 6 4 2 +--R 1410cosh(x) + 516cosh(x) - 1224cosh(x) + 432 +--R * +--R 2 +--R tanh(x) +--R + +--R 22 21 2 20 +--R - sinh(x) - 10cosh(x)sinh(x) + (- 39cosh(x) - 8)sinh(x) +--R + +--R 3 19 +--R (- 60cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 18 +--R (45cosh(x) - 176cosh(x) - 10)sinh(x) +--R + +--R 5 3 17 +--R (318cosh(x) - 64cosh(x) - 56cosh(x))sinh(x) +--R + +--R 6 4 2 16 +--R (395cosh(x) + 664cosh(x) - 58cosh(x) + 22)sinh(x) +--R + +--R 7 5 3 15 +--R (- 208cosh(x) + 1280cosh(x) + 256cosh(x) + 72cosh(x))sinh(x) +--R + +--R 8 6 4 2 14 +--R (- 1050cosh(x) - 64cosh(x) + 696cosh(x) - 96cosh(x) + 80)sinh(x) +--R + +--R 9 7 5 3 +--R - 820cosh(x) - 2816cosh(x) + 96cosh(x) - 616cosh(x) +--R + +--R 252cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 650cosh(x) - 2704cosh(x) - 1640cosh(x) - 376cosh(x) +--R + +--R 2 +--R - 16cosh(x) - 98 +--R * +--R 12 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 1560cosh(x) + 1664cosh(x) - 1792cosh(x) + 1416cosh(x) +--R + +--R 3 +--R - 680cosh(x) - 584cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 650cosh(x) + 4576cosh(x) + 1012cosh(x) + 2016cosh(x) +--R + +--R 4 2 +--R - 176cosh(x) - 708cosh(x) - 418 +--R * +--R 10 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 820cosh(x) + 1664cosh(x) + 2992cosh(x) - 872cosh(x) +--R + +--R 5 3 +--R 964cosh(x) + 1240cosh(x) - 720cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 1050cosh(x) - 2704cosh(x) + 1012cosh(x) - 3132cosh(x) +--R + +--R 6 4 2 +--R 112cosh(x) + 2690cosh(x) + 1318cosh(x) - 134 +--R * +--R 8 +--R sinh(x) +--R + +--R 15 13 11 9 +--R - 208cosh(x) - 2816cosh(x) - 1792cosh(x) - 872cosh(x) +--R + +--R 7 5 3 +--R - 1072cosh(x) - 656cosh(x) + 2944cosh(x) - 200cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 16 14 12 10 +--R 395cosh(x) - 64cosh(x) - 1640cosh(x) + 2016cosh(x) +--R + +--R 8 6 4 2 +--R 112cosh(x) - 3768cosh(x) - 1156cosh(x) + 456cosh(x) + 705 +--R * +--R 6 +--R sinh(x) +--R + +--R 17 15 13 11 +--R 318cosh(x) + 1280cosh(x) + 96cosh(x) + 1416cosh(x) +--R + +--R 9 7 5 3 +--R 964cosh(x) - 656cosh(x) - 4960cosh(x) + 1480cosh(x) + 446cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 18 16 14 12 +--R 45cosh(x) + 664cosh(x) + 696cosh(x) - 376cosh(x) +--R + +--R 10 8 6 4 +--R - 176cosh(x) + 2690cosh(x) - 1156cosh(x) + 1916cosh(x) +--R + +--R 2 +--R - 3025cosh(x) + 258 +--R * +--R 4 +--R sinh(x) +--R + +--R 19 17 15 13 +--R - 60cosh(x) - 64cosh(x) + 256cosh(x) - 616cosh(x) +--R + +--R 11 9 7 5 +--R - 680cosh(x) + 1240cosh(x) + 2944cosh(x) + 1480cosh(x) +--R + +--R 3 +--R - 5532cosh(x) + 1800cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 20 18 16 14 +--R - 39cosh(x) - 176cosh(x) - 58cosh(x) - 96cosh(x) +--R + +--R 12 10 8 6 +--R - 16cosh(x) - 708cosh(x) + 1318cosh(x) + 456cosh(x) +--R + +--R 4 2 +--R - 3025cosh(x) + 3084cosh(x) - 612 +--R * +--R 2 +--R sinh(x) +--R + +--R 21 19 17 15 +--R - 10cosh(x) - 64cosh(x) - 56cosh(x) + 72cosh(x) +--R + +--R 13 11 9 7 +--R 252cosh(x) - 584cosh(x) - 720cosh(x) - 200cosh(x) +--R + +--R 5 3 +--R 446cosh(x) + 1800cosh(x) - 936cosh(x) +--R * +--R sinh(x) +--R + +--R 22 20 18 16 14 +--R - cosh(x) - 8cosh(x) - 10cosh(x) + 22cosh(x) + 80cosh(x) +--R + +--R 12 10 8 6 4 +--R - 98cosh(x) - 418cosh(x) - 134cosh(x) + 705cosh(x) + 258cosh(x) +--R + +--R 2 +--R - 612cosh(x) + 216 +--R * +--R +-------------------------------------+ +--R | 2 2 +------------+ +--R | - 2sinh(x) - 2cosh(x) + 6 | 2 +--R |------------------------------------- \|coth(x) - 2 +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 377 + +--S 378 of 526 +t0471:= (-1-csch(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (287) \|- csch(x) - 1 +--R Type: Expression(Integer) +--E 378 + +--S 379 of 526 +r0471:= (-coth(x)^2)^(1/2)*log(sinh(x))*tanh(x) +--R +--R +--R +----------+ +--R | 2 +--R (288) tanh(x)log(sinh(x))\|- coth(x) +--R Type: Expression(Integer) +--E 379 + +--S 380 of 526 +a0471:= integrate(t0471,x) +--R +--R +--R +---+ x 2 +---+ +--R (289) \|- 1 log((%e ) - 1) - x\|- 1 +--R Type: Union(Expression(Integer),...) +--E 380 + +--S 381 of 526 +m0471:= a0471-r0471 +--R +--R +--R +----------+ +--R | 2 +---+ x 2 +---+ +--R (290) - tanh(x)log(sinh(x))\|- coth(x) + \|- 1 log((%e ) - 1) - x\|- 1 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 526 +d0471:= D(m0471,x) +--R +--R +--R (291) +--R +----------+ +--R +---+ x 2 +---+ | 2 +--R (\|- 1 (%e ) + \|- 1 )sinh(x)\|- coth(x) +--R + +--R 2 x 2 2 2 +--R (- coth(x) (%e ) + coth(x) )sinh(x)tanh(x) +--R + +--R 3 x 2 3 +--R ((- coth(x) + coth(x))(%e ) + coth(x) - coth(x))sinh(x)tanh(x) +--R + +--R 2 x 2 2 +--R (coth(x) (%e ) - coth(x) )sinh(x) +--R * +--R log(sinh(x)) +--R + +--R 2 x 2 2 +--R (cosh(x)coth(x) (%e ) - cosh(x)coth(x) )tanh(x) +--R / +--R +----------+ +--R x 2 | 2 +--R ((%e ) - 1)sinh(x)\|- coth(x) +--R Type: Expression(Integer) +--E 382 + +--S 383 of 526 +t0472:= (a+b*csch(x)^2)^(1/2) +--R +--R +--R +--------------+ +--R | 2 +--R (292) \|b csch(x) + a +--R Type: Expression(Integer) +--E 383 + +--S 384 of 526 +r0472:= a^(1/2)*atanh(a^(1/2)*coth(x)/(a+b*csch(x)^2)^(1/2))-_ + b^(1/2)*atanh((a+b*csch(x)^2)^(1/2)*tanh(x)/b^(1/2)) +--R +--R +--R +--------------+ +--R | 2 +-+ +--R +-+ tanh(x)\|b csch(x) + a +-+ coth(x)\|a +--R (293) - \|b atanh(------------------------) + \|a atanh(-----------------) +--R +-+ +--------------+ +--R \|b | 2 +--R \|b csch(x) + a +--R Type: Expression(Integer) +--E 384 + +--S 385 of 526 +a0472:= integrate(t0472,x) +--R +--R +--R (294) +--R [ +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ +--R 2\|a \|b +--R * +--R log +--R 4 3 +--R (- 2b + 2a)sinh(x) + (- 8b + 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((- 12b + 12a)cosh(x) - 2a)sinh(x) +--R + +--R 3 +--R ((- 8b + 8a)cosh(x) - 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (- 2b + 2a)cosh(x) - 2a cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R + +--R 2 4 2 3 +--R - a sinh(x) - 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 6a cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R (- 4a cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R - a cosh(x) + (- 2a b + 2a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 6 2 5 +--R (- 2a b + 2a )sinh(x) + (- 12a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a b + 30a )cosh(x) + 6a b - 4a )sinh(x) +--R + +--R 2 3 2 3 +--R ((- 40a b + 40a )cosh(x) + (24a b - 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R (- 30a b + 30a )cosh(x) + (36a b - 24a )cosh(x) +--R + +--R 2 +--R 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12a b + 12a )cosh(x) + (24a b - 16a )cosh(x) +--R + +--R 2 +--R 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (- 2a b + 2a )cosh(x) + (6a b - 4a )cosh(x) + 2a cosh(x) +--R * +--R +-+ +--R \|b +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) + 2b - 4a b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (8b - 16a b + 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b - 15a )cosh(x) + (12b - 24a b + 18a )cosh(x) +--R + +--R 2 +--R 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (8b - 16a b + 12a )cosh(x) +--R + +--R 2 +--R (8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (2b - 4a b + 3a )cosh(x) +--R + +--R 2 2 2 +--R (4a b - 3a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 2 4 2 3 +--R (2a b - a )sinh(x) + (8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b - 6a )cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b - 4a )cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b - a )cosh(x) + (- 2a b + 2a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b + 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 30b + 30a b - 15a )cosh(x) + 2b - 6a b + 3a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 +--R (- 40b + 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (8b - 24a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b + 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (12b - 36a b + 18a )cosh(x) + 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (8b - 24a b + 12a )cosh(x) + (8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b + 2a b - a )cosh(x) + (2b - 6a b + 3a )cosh(x) +--R + +--R 2 2 2 +--R (4a b - 3a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R + +--R - +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 3b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (6b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (3b - a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R / +--R +-+ +--R 2\|a +--R , +--R +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 3b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (6b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (3b - a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R - +--R +---+ +-+ +--R 4\|- b \|a +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +---+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|a +--R / +--R +-+ +--R 2\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 385 + +--S 386 of 526 +m0472a:= a0472.1-r0472 +--R +--R +--R (295) +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-+ +-+ +--R 2\|a \|b +--R * +--R log +--R 4 3 +--R (- 2b + 2a)sinh(x) + (- 8b + 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((- 12b + 12a)cosh(x) - 2a)sinh(x) +--R + +--R 3 +--R ((- 8b + 8a)cosh(x) - 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (- 2b + 2a)cosh(x) - 2a cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R + +--R 2 4 2 3 +--R - a sinh(x) - 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 6a cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (- 4a cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) - a cosh(x) +--R + +--R 2 2 2 +--R (- 2a b + 2a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 6 2 5 +--R (- 2a b + 2a )sinh(x) + (- 12a b + 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30a b + 30a )cosh(x) + 6a b - 4a )sinh(x) +--R + +--R 2 3 2 3 +--R ((- 40a b + 40a )cosh(x) + (24a b - 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R ((- 30a b + 30a )cosh(x) + (36a b - 24a )cosh(x) + 2a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (- 12a b + 12a )cosh(x) + (24a b - 16a )cosh(x) +--R + +--R 2 +--R 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (- 2a b + 2a )cosh(x) + (6a b - 4a )cosh(x) + 2a cosh(x) +--R * +--R +-+ +--R \|b +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) + 2b - 4a b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (8b - 16a b + 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b - 15a )cosh(x) + (12b - 24a b + 18a )cosh(x) +--R + +--R 2 +--R 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (8b - 16a b + 12a )cosh(x) +--R + +--R 2 +--R (8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (2b - 4a b + 3a )cosh(x) +--R + +--R 2 2 2 +--R (4a b - 3a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 2 4 2 3 +--R (2a b - a )sinh(x) + (8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b - 6a )cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b - 4a )cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b - a )cosh(x) + (- 2a b + 2a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b + 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 30b + 30a b - 15a )cosh(x) + 2b - 6a b + 3a )sinh(x) +--R + +--R 2 2 3 +--R (- 40b + 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (8b - 24a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b + 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (12b - 36a b + 18a )cosh(x) + 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (8b - 24a b + 12a )cosh(x) + (8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b + 2a b - a )cosh(x) + (2b - 6a b + 3a )cosh(x) +--R + +--R 2 2 2 +--R (4a b - 3a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R + +--R - +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 3b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (6b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (3b - a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +--------------+ +--R | 2 +-+ +--R +-+ +-+ tanh(x)\|b csch(x) + a coth(x)\|a +--R 2\|a \|b atanh(------------------------) - 2a atanh(-----------------) +--R +-+ +--------------+ +--R \|b | 2 +--R \|b csch(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 386 + +--S 387 of 526 +--d0472a:= D(m0472a,x) +--E 387 + +--S 388 of 526 +m0472b:= a0472.2-r0472 +--R +--R +--R (296) +--R a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R a +--R * +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 3b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (6b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (3b - a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +--------------+ +--R | 2 +-+ +--R +-+ +-+ tanh(x)\|b csch(x) + a coth(x)\|a +--R 2\|a \|b atanh(------------------------) - 2a atanh(-----------------) +--R +-+ +--------------+ +--R \|b | 2 +--R \|b csch(x) + a +--R + +--R - +--R +---+ +-+ +--R 4\|- b \|a +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +---+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 388 + +--S 389 of 526 +--d0472b:= D(m0472b,x) +--E 389 + +--S 390 of 526 +t0473:= 1/(1+csch(x)^2)^(1/2) +--R +--R +--R 1 +--R (297) --------------- +--R +------------+ +--R | 2 +--R \|csch(x) + 1 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 526 +r0473:= coth(x)*log(cosh(x))/(coth(x)^2)^(1/2) +--R +--R +--R coth(x)log(cosh(x)) +--R (298) ------------------- +--R +--------+ +--R | 2 +--R \|coth(x) +--R Type: Expression(Integer) +--E 391 + +--S 392 of 526 +a0473:= integrate(t0473,x) +--R +--R +--R 2cosh(x) +--R (299) log(- -----------------) - x +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 392 + +--S 393 of 526 +m0473:= a0473-r0473 +--R +--R +--R +--------+ +--R 2cosh(x) | 2 +--R (log(- -----------------) - x)\|coth(x) - coth(x)log(cosh(x)) +--R sinh(x) - cosh(x) +--R (300) --------------------------------------------------------------- +--R +--------+ +--R | 2 +--R \|coth(x) +--R Type: Expression(Integer) +--E 393 + +--S 394 of 526 +d0473:= D(m0473,x) +--R +--R +--R +--------+ +--R | 2 +--R sinh(x)\|coth(x) - coth(x)sinh(x) +--R (301) ----------------------------------- +--R +--------+ +--R | 2 +--R cosh(x)\|coth(x) +--R Type: Expression(Integer) +--E 394 + +--S 395 of 526 +t0474:= 1/(1-csch(x)^2)^(1/2) +--R +--R +--R 1 +--R (302) ----------------- +--R +--------------+ +--R | 2 +--R \|- csch(x) + 1 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 526 +r0474:= atanh(coth(x)/(2-coth(x)^2)^(1/2)) +--R +--R +--R coth(x) +--R (303) atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 526 +a0474:= integrate(t0474,x) +--R +--R +--R (304) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 8cosh(x))sinh(x) + cosh(x) - 4cosh(x) - 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 397 + +--S 398 of 526 +m0474:= a0474-r0474 +--R +--R +--R (305) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R + +--R - +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 8cosh(x))sinh(x) + cosh(x) - 4cosh(x) - 1 +--R + +--R coth(x) +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 526 +d0474:= D(m0474,x) +--R +--R +--R (306) +--R 8 7 6 +--R - 2sinh(x) - 4cosh(x)sinh(x) + 9sinh(x) +--R + +--R 3 5 +--R (4cosh(x) + 10cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (4cosh(x) - 9cosh(x) - 10)sinh(x) +--R + +--R 5 3 3 +--R (4cosh(x) - 20cosh(x) )sinh(x) +--R + +--R 4 2 2 +--R (- 9cosh(x) + 20cosh(x) + 3)sinh(x) +--R + +--R 7 5 8 +--R (- 4cosh(x) + 10cosh(x) - 6cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R 9cosh(x) - 10cosh(x) + 3cosh(x) +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R + +--R 8 7 6 +--R - 2sinh(x) - 4cosh(x)sinh(x) + 12sinh(x) +--R + +--R 3 5 +--R (4cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (4cosh(x) - 12cosh(x) - 18)sinh(x) +--R + +--R 5 3 3 +--R (4cosh(x) - 24cosh(x) )sinh(x) +--R + +--R 4 2 2 +--R (- 12cosh(x) + 36cosh(x) )sinh(x) +--R + +--R 7 5 8 6 4 +--R (- 4cosh(x) + 12cosh(x) )sinh(x) - 2cosh(x) + 12cosh(x) - 18cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 10 9 2 8 +--R sinh(x) + 4cosh(x)sinh(x) + (5cosh(x) - 5)sinh(x) +--R + +--R 7 4 2 6 +--R - 16cosh(x)sinh(x) + (- 6cosh(x) - 12cosh(x) + 13)sinh(x) +--R + +--R 5 3 5 +--R (- 8cosh(x) + 16cosh(x) + 16cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 6cosh(x) + 34cosh(x) - 5cosh(x) - 27)sinh(x) +--R + +--R 5 3 3 +--R (16cosh(x) - 16cosh(x) - 24cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (5cosh(x) - 12cosh(x) - 5cosh(x) + 6cosh(x) + 18)sinh(x) +--R + +--R 9 7 5 3 +--R (4cosh(x) - 16cosh(x) + 16cosh(x) - 24cosh(x) + 36cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) - 5cosh(x) + 13cosh(x) - 27cosh(x) + 18cosh(x) +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R + +--R 10 9 2 8 +--R sinh(x) + 4cosh(x)sinh(x) + (5cosh(x) - 8)sinh(x) +--R + +--R 7 4 2 6 +--R - 22cosh(x)sinh(x) + (- 6cosh(x) - 12cosh(x) + 20)sinh(x) +--R + +--R 5 3 5 +--R (- 8cosh(x) + 22cosh(x) + 34cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 6cosh(x) + 40cosh(x) - 12cosh(x) - 22)sinh(x) +--R + +--R 5 3 3 +--R (22cosh(x) - 52cosh(x) - 26cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (5cosh(x) - 12cosh(x) - 12cosh(x) - 8cosh(x) + 27)sinh(x) +--R + +--R 9 7 5 3 +--R (4cosh(x) - 22cosh(x) + 34cosh(x) - 26cosh(x) + 42cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) - 8cosh(x) + 20cosh(x) - 22cosh(x) + 27cosh(x) - 18 +--R / +--R 8 7 6 +--R 2sinh(x) + 4cosh(x)sinh(x) - 12sinh(x) +--R + +--R 3 5 +--R (- 4cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 4cosh(x) + 12cosh(x) + 18)sinh(x) +--R + +--R 5 3 3 +--R (- 4cosh(x) + 24cosh(x) )sinh(x) +--R + +--R 4 2 2 7 5 +--R (12cosh(x) - 36cosh(x) )sinh(x) + (4cosh(x) - 12cosh(x) )sinh(x) +--R + +--R 8 6 4 +--R 2cosh(x) - 12cosh(x) + 18cosh(x) +--R * +--R +-------------------------------------+ +--R +--------------+ | 2 2 +--R | 2 | 2sinh(x) + 2cosh(x) - 6 +--R \|- coth(x) + 2 |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 10 9 2 8 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 5cosh(x) + 8)sinh(x) +--R + +--R 7 4 2 6 +--R 22cosh(x)sinh(x) + (6cosh(x) + 12cosh(x) - 20)sinh(x) +--R + +--R 5 3 5 +--R (8cosh(x) - 22cosh(x) - 34cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (6cosh(x) - 40cosh(x) + 12cosh(x) + 22)sinh(x) +--R + +--R 5 3 3 +--R (- 22cosh(x) + 52cosh(x) + 26cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 5cosh(x) + 12cosh(x) + 12cosh(x) + 8cosh(x) - 27)sinh(x) +--R + +--R 9 7 5 3 +--R (- 4cosh(x) + 22cosh(x) - 34cosh(x) + 26cosh(x) - 42cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - cosh(x) + 8cosh(x) - 20cosh(x) + 22cosh(x) - 27cosh(x) + 18 +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 526 +t0475:= 1/(-1+csch(x)^2)^(1/2) +--R +--R +--R 1 +--R (307) --------------- +--R +------------+ +--R | 2 +--R \|csch(x) - 1 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 526 +r0475:= atan(coth(x)/(-2+coth(x)^2)^(1/2)) +--R +--R +--R coth(x) +--R (308) atan(---------------) +--R +------------+ +--R | 2 +--R \|coth(x) - 2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 526 +a0475:= integrate(t0475,x) +--R +--R +--R (309) +--R - +--R atan +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 402 + +--S 403 of 526 +m0475:= a0475-r0475 +--R +--R +--R (310) +--R - +--R atan +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 coth(x) +--R atan(-----------------------------------------) - 2atan(---------------) +--R +-------------------------------------+ +------------+ +--R | 2 2 | 2 +--R | - 2sinh(x) - 2cosh(x) + 6 \|coth(x) - 2 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 2 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 526 +d0475:= D(m0475,x) +--R +--R +--R (311) +--R 14 13 2 12 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 22cosh(x) + 6)sinh(x) +--R + +--R 3 11 +--R (8cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (78cosh(x) + 252cosh(x) - 32)sinh(x) +--R + +--R 5 3 9 +--R (76cosh(x) + 448cosh(x) - 136cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 54cosh(x) + 218cosh(x) - 192cosh(x) + 68)sinh(x) +--R + +--R 7 5 3 7 +--R (- 144cosh(x) - 512cosh(x) - 32cosh(x) + 232cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (- 54cosh(x) - 952cosh(x) + 224cosh(x) + 32cosh(x) + 134)sinh(x) +--R + +--R 9 7 5 3 +--R (76cosh(x) - 512cosh(x) + 336cosh(x) - 872cosh(x) + 604cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 78cosh(x) + 218cosh(x) + 224cosh(x) - 1480cosh(x) +--R + +--R 2 +--R 1210cosh(x) - 138 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 8cosh(x) + 448cosh(x) - 32cosh(x) - 872cosh(x) +--R + +--R 3 +--R 1480cosh(x) - 552cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 22cosh(x) + 252cosh(x) - 192cosh(x) + 32cosh(x) +--R + +--R 4 2 +--R 1210cosh(x) - 828cosh(x) - 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 12cosh(x) + 64cosh(x) - 136cosh(x) + 232cosh(x) +--R + +--R 5 3 +--R 604cosh(x) - 552cosh(x) - 72cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R - 2cosh(x) + 6cosh(x) - 32cosh(x) + 68cosh(x) + 134cosh(x) +--R + +--R 4 2 +--R - 138cosh(x) - 36cosh(x) +--R * +--R +------------+ +--R | 2 +--R \|coth(x) - 2 +--R + +--R 16 15 2 14 +--R - sinh(x) - 8cosh(x)sinh(x) + (- 24cosh(x) - 6)sinh(x) +--R + +--R 3 13 +--R (- 24cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (36cosh(x) - 66cosh(x) + 5)sinh(x) +--R + +--R 5 3 11 +--R (120cosh(x) + 24cosh(x) + 28cosh(x))sinh(x) +--R + +--R 6 4 2 10 +--R (88cosh(x) + 234cosh(x) + 58cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 9 +--R (- 88cosh(x) + 228cosh(x) + 44cosh(x) + 16cosh(x))sinh(x) +--R + +--R 8 6 4 2 8 +--R (- 198cosh(x) - 162cosh(x) - 21cosh(x) - 200cosh(x) - 19)sinh(x) +--R + +--R 9 7 5 3 +--R (- 88cosh(x) - 432cosh(x) - 72cosh(x) - 320cosh(x) - 32cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R 88cosh(x) - 162cosh(x) - 84cosh(x) + 176cosh(x) - 4cosh(x) +--R + +--R - 102 +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 120cosh(x) + 228cosh(x) - 72cosh(x) + 608cosh(x) +--R + +--R 3 +--R - 32cosh(x) - 148cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 36cosh(x) + 234cosh(x) - 21cosh(x) + 176cosh(x) +--R + +--R 4 2 +--R - 82cosh(x) + 326cosh(x) - 13 +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 24cosh(x) + 24cosh(x) + 44cosh(x) - 320cosh(x) +--R + +--R 5 3 +--R - 32cosh(x) + 744cosh(x) - 244cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 24cosh(x) - 66cosh(x) + 58cosh(x) - 200cosh(x) +--R + +--R 6 4 2 +--R - 4cosh(x) + 326cosh(x) - 462cosh(x) + 84 +--R * +--R 2 +--R sinh(x) +--R + +--R 15 13 11 9 +--R - 8cosh(x) - 36cosh(x) + 28cosh(x) + 16cosh(x) +--R + +--R 7 5 3 +--R - 32cosh(x) - 148cosh(x) - 244cosh(x) + 168cosh(x) +--R * +--R sinh(x) +--R + +--R 16 14 12 10 8 +--R - cosh(x) - 6cosh(x) + 5cosh(x) + 24cosh(x) - 19cosh(x) +--R + +--R 6 4 2 +--R - 102cosh(x) - 13cosh(x) + 84cosh(x) - 36 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 16 15 2 14 +--R sinh(x) + 8cosh(x)sinh(x) + (24cosh(x) + 6)sinh(x) +--R + +--R 3 13 +--R (24cosh(x) + 36cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (- 36cosh(x) + 66cosh(x) - 5)sinh(x) +--R + +--R 5 3 11 +--R (- 120cosh(x) - 24cosh(x) - 28cosh(x))sinh(x) +--R + +--R 6 4 2 10 +--R (- 88cosh(x) - 234cosh(x) - 58cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 9 +--R (88cosh(x) - 228cosh(x) - 44cosh(x) - 16cosh(x))sinh(x) +--R + +--R 8 6 4 2 8 +--R (198cosh(x) + 162cosh(x) + 21cosh(x) + 200cosh(x) + 19)sinh(x) +--R + +--R 9 7 5 3 +--R (88cosh(x) + 432cosh(x) + 72cosh(x) + 320cosh(x) + 32cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 88cosh(x) + 162cosh(x) + 84cosh(x) - 176cosh(x) + 4cosh(x) +--R + +--R 102 +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 120cosh(x) - 228cosh(x) + 72cosh(x) - 608cosh(x) +--R + +--R 3 +--R 32cosh(x) + 148cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 36cosh(x) - 234cosh(x) + 21cosh(x) - 176cosh(x) +--R + +--R 4 2 +--R 82cosh(x) - 326cosh(x) + 13 +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R 24cosh(x) - 24cosh(x) - 44cosh(x) + 320cosh(x) + 32cosh(x) +--R + +--R 3 +--R - 744cosh(x) + 244cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R 24cosh(x) + 66cosh(x) - 58cosh(x) + 200cosh(x) + 4cosh(x) +--R + +--R 4 2 +--R - 326cosh(x) + 462cosh(x) - 84 +--R * +--R 2 +--R sinh(x) +--R + +--R 15 13 11 9 7 +--R 8cosh(x) + 36cosh(x) - 28cosh(x) - 16cosh(x) + 32cosh(x) +--R + +--R 5 3 +--R 148cosh(x) + 244cosh(x) - 168cosh(x) +--R * +--R sinh(x) +--R + +--R 16 14 12 10 8 +--R cosh(x) + 6cosh(x) - 5cosh(x) - 24cosh(x) + 19cosh(x) +--R + +--R 6 4 2 +--R 102cosh(x) + 13cosh(x) - 84cosh(x) + 36 +--R * +--R +-------------------------------------+ +--R | 2 2 +------------+ +--R | - 2sinh(x) - 2cosh(x) + 6 | 2 +--R |------------------------------------- \|coth(x) - 2 +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 404 + +--S 405 of 526 +t0476:= 1/(-1-csch(x)^2)^(1/2) +--R +--R +--R 1 +--R (312) ----------------- +--R +--------------+ +--R | 2 +--R \|- csch(x) - 1 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 526 +r0476:= coth(x)*log(cosh(x))/(-coth(x)^2)^(1/2) +--R +--R +--R coth(x)log(cosh(x)) +--R (313) ------------------- +--R +----------+ +--R | 2 +--R \|- coth(x) +--R Type: Expression(Integer) +--E 406 + +--S 407 of 526 +a0476:= integrate(t0476,x) +--R +--R +--R x 2 +--R log((%e ) + 1) - x +--R (314) ------------------- +--R +---+ +--R \|- 1 +--R Type: Union(Expression(Integer),...) +--E 407 + +--S 408 of 526 +m0476:= a0476-r0476 +--R +--R +--R +----------+ +--R x 2 | 2 +---+ +--R (log((%e ) + 1) - x)\|- coth(x) - \|- 1 coth(x)log(cosh(x)) +--R (315) -------------------------------------------------------------- +--R +----------+ +--R +---+ | 2 +--R \|- 1 \|- coth(x) +--R Type: Expression(Integer) +--E 408 + +--S 409 of 526 +d0476:= D(m0476,x) +--R +--R +--R (316) +--R +----------+ +--R +---+ x 2 +---+ | 2 +--R (- \|- 1 cosh(x)(%e ) + \|- 1 cosh(x))\|- coth(x) +--R + +--R x 2 +--R (- coth(x)(%e ) - coth(x))sinh(x) +--R / +--R +----------+ +--R x 2 | 2 +--R (cosh(x)(%e ) + cosh(x))\|- coth(x) +--R Type: Expression(Integer) +--E 409 + +--S 410 of 526 +t0477:= 1/(a+b*csch(x)^2)^(1/2) +--R +--R +--R 1 +--R (317) ----------------- +--R +--------------+ +--R | 2 +--R \|b csch(x) + a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 526 +r0477:= atanh(a^(1/2)*coth(x)/(a+b*csch(x)^2)^(1/2))/a^(1/2) +--R +--R +--R +-+ +--R coth(x)\|a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b csch(x) + a +--R (318) ------------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 411 + +--S 412 of 526 +a0477:= integrate(t0477,x) +--R +--R +--R (319) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 3b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (6b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (3b - a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R / +--R +-+ +--R 2\|a +--R Type: Union(Expression(Integer),...) +--E 412 + +--S 413 of 526 +m0477:= a0477-r0477 +--R +--R +--R (320) +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R - +--R log +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 3b - a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (6b - 2a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (3b - a)cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R + +--R +-+ +--R coth(x)\|a +--R - 2atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b csch(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 526 +d0477:= D(m0477,x) +--R +--R +--R (321) +--R 8 2 2 2 6 +--R - a b sinh(x) + (4a b cosh(x) - 2b + 2a b - 2a )sinh(x) +--R + +--R 2 5 +--R (- 4b + 4a b)cosh(x)sinh(x) +--R + +--R 4 2 2 2 2 +--R - 6a b cosh(x) + (2b - 2a b + 2a )cosh(x) + 2b - 5a b +--R + +--R 2 +--R 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 3 +--R ((8b - 8a b)cosh(x) - 4a cosh(x))sinh(x) +--R + +--R 6 2 2 4 +--R 4a b cosh(x) + (2b - 2a b + 2a )cosh(x) +--R + +--R 2 2 2 +--R (- 4b + 10a b)cosh(x) + 4a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 +--R ((- 4b + 4a b)cosh(x) - 4a cosh(x) + (- 8a b + 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 2 2 6 +--R - a b cosh(x) + (- 2b + 2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 2 +--R (2b - 5a b + 4a )cosh(x) + (4a b - 2a )cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 3 8 2 3 7 +--R (4a b - a )sinh(x) + (8a b - 2a )cosh(x)sinh(x) +--R + +--R 2 2 3 6 +--R (8a b - 6a b + 3a )sinh(x) +--R + +--R 2 3 3 2 2 3 5 +--R ((- 8a b + 2a )cosh(x) + (16a b - 12a b + 2a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 2 3 2 2 +--R (- 8a b + 2a )cosh(x) + (- 8a b + 6a b - 3a )cosh(x) + 4a b +--R + +--R 3 +--R - 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 2 2 3 3 +--R (- 8a b + 2a )cosh(x) + (- 32a b + 24a b - 4a )cosh(x) +--R + +--R 3 +--R 2a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 4 2 3 2 2 +--R (- 8a b + 6a b - 3a )cosh(x) + (- 8a b - 2a )cosh(x) - 10a b +--R + +--R 3 +--R 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 7 2 2 3 5 +--R (8a b - 2a )cosh(x) + (16a b - 12a b + 2a )cosh(x) +--R + +--R 3 3 2 3 +--R 2a cosh(x) + (4a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 8 2 2 3 6 +--R (4a b - a )cosh(x) + (8a b - 6a b + 3a )cosh(x) +--R + +--R 2 3 4 2 3 2 2 2 3 +--R (4a b - 5a )cosh(x) + (- 10a b + 5a )cosh(x) - 8a b + 8a b - 2a +--R * +--R +--------------+ +--R | 2 +--R \|b csch(x) + a +--R + +--R 2 3 6 +--R (- 4a b + 2a )sinh(x) +--R + +--R 2 3 2 2 2 3 4 +--R ((4a b - 2a )cosh(x) - 8a b + 8a b - 4a )sinh(x) +--R + +--R 3 3 +--R 4a cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 2 2 3 +--R ((4a b - 2a )cosh(x) + (16a b - 16a b)cosh(x) - 4a b + 2a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 3 2 3 6 +--R (4a cosh(x) + (8a b - 4a )cosh(x))sinh(x) + (- 4a b + 2a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 +--R (- 8a b + 8a b - 4a )cosh(x) + (- 4a b + 2a )cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 10 2 9 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 8 +--R (- 5a b cosh(x) - 2a b - a b + a )sinh(x) +--R + +--R 2 3 7 +--R (- 8a b + 2a )cosh(x)sinh(x) +--R + +--R 2 4 2 2 2 2 2 3 +--R (6a b cosh(x) + (- 8a b + 4a b)cosh(x) - 4a b + 9a b - 3a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 3 +--R 8a b cosh(x) + (8a b - 2a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b + 12a b - 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 2 3 4 +--R 6a b cosh(x) + (20a b - 6a b - 2a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (4a b - a b + 3a )cosh(x) + 14a b - 11a b + 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 2 2 3 3 +--R (8a b - 2a )cosh(x) + (16a b - 8a b + 4a )cosh(x) +--R + +--R 2 2 3 +--R (16a b - 8a b - 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R - 5a b cosh(x) + (- 8a b + 4a b)cosh(x) +--R + +--R 2 2 3 4 2 2 3 2 3 +--R (4a b - a b + 3a )cosh(x) + (4a b + 6a b + 2a )cosh(x) + 8b +--R + +--R 2 2 3 +--R - 8a b + 12a b - 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 3 7 +--R - 4a b cosh(x) + (- 8a b + 2a )cosh(x) +--R + +--R 2 2 3 5 2 2 3 3 +--R (- 8a b + 12a b - 2a )cosh(x) + (16a b - 8a b - 2a )cosh(x) +--R + +--R 3 2 3 +--R (16b - 16a b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 2 3 8 +--R - a b cosh(x) + (- 2a b - a b + a )cosh(x) +--R + +--R 2 2 3 6 2 2 3 4 +--R (- 4a b + 9a b - 3a )cosh(x) + (14a b - 11a b + 5a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (8b - 8a b + 12a b - 5a )cosh(x) + 8a b - 8a b + 2a +--R * +--R +-+ +--R \|a +--R / +--R 2 3 6 +--R (4a b - 2a )sinh(x) +--R + +--R 2 3 2 2 2 3 4 +--R ((- 4a b + 2a )cosh(x) + 8a b - 8a b + 4a )sinh(x) +--R + +--R 3 3 +--R - 4a cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 2 2 +--R (- 4a b + 2a )cosh(x) + (- 16a b + 16a b)cosh(x) + 4a b +--R + +--R 3 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 2 3 +--R (- 4a cosh(x) + (- 8a b + 4a )cosh(x))sinh(x) +--R + +--R 2 3 6 2 2 3 4 +--R (4a b - 2a )cosh(x) + (8a b - 8a b + 4a )cosh(x) +--R + +--R 2 3 2 +--R (4a b - 2a )cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 10 2 9 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 8 +--R (5a b cosh(x) + 2a b + a b - a )sinh(x) +--R + +--R 2 3 7 +--R (8a b - 2a )cosh(x)sinh(x) +--R + +--R 2 4 2 2 2 2 2 3 +--R (- 6a b cosh(x) + (8a b - 4a b)cosh(x) + 4a b - 9a b + 3a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 3 +--R - 8a b cosh(x) + (- 8a b + 2a )cosh(x) +--R + +--R 2 2 3 +--R (8a b - 12a b + 2a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 2 3 4 +--R - 6a b cosh(x) + (- 20a b + 6a b + 2a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 4a b + a b - 3a )cosh(x) - 14a b + 11a b - 5a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 5 2 2 3 3 +--R (- 8a b + 2a )cosh(x) + (- 16a b + 8a b - 4a )cosh(x) +--R + +--R 2 2 3 +--R (- 16a b + 8a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R 5a b cosh(x) + (8a b - 4a b)cosh(x) +--R + +--R 2 2 3 4 2 2 3 2 +--R (- 4a b + a b - 3a )cosh(x) + (- 4a b - 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 +--R - 8b + 8a b - 12a b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 3 7 +--R 4a b cosh(x) + (8a b - 2a )cosh(x) +--R + +--R 2 2 3 5 2 2 3 3 +--R (8a b - 12a b + 2a )cosh(x) + (- 16a b + 8a b + 2a )cosh(x) +--R + +--R 3 2 3 +--R (- 16b + 16a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 2 3 8 +--R a b cosh(x) + (2a b + a b - a )cosh(x) +--R + +--R 2 2 3 6 2 2 3 4 +--R (4a b - 9a b + 3a )cosh(x) + (- 14a b + 11a b - 5a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 8b + 8a b - 12a b + 5a )cosh(x) - 8a b + 8a b - 2a +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R | 2 +--R \|b csch(x) + a +--R Type: Expression(Integer) +--E 414 + +--S 415 of 526 +t0478:= (1+csch(x)^2)^(3/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (322) (csch(x) + 1)\|csch(x) + 1 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 526 +r0478:= -1/2*(coth(x)^2)^(1/2)*(coth(x)^2-2*log(sinh(x)))*tanh(x) +--R +--R +--R +--------+ +--R 2 | 2 +--R (2tanh(x)log(sinh(x)) - coth(x) tanh(x))\|coth(x) +--R (323) --------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 526 +a0478:= integrate(t0478,x) +--R +--R +--R (324) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R - x sinh(x) - 4x cosh(x)sinh(x) + (- 6x cosh(x) + 2x - 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4x cosh(x) + (4x - 4)cosh(x))sinh(x) - x cosh(x) + (2x - 2)cosh(x) +--R + +--R - x +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 417 + +--S 418 of 526 +m0478:= a0478-r0478 +--R +--R +--R (325) +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) + 8cosh(x))sinh(x) - 2cosh(x) + 4cosh(x) - 2 +--R * +--R tanh(x)log(sinh(x)) +--R + +--R 2 4 2 3 +--R coth(x) sinh(x) + 4cosh(x)coth(x) sinh(x) +--R + +--R 2 2 2 +--R (6cosh(x) - 2)coth(x) sinh(x) +--R + +--R 3 2 +--R (4cosh(x) - 4cosh(x))coth(x) sinh(x) +--R + +--R 4 2 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x) +--R * +--R tanh(x) +--R * +--R +--------+ +--R | 2 +--R \|coth(x) +--R + +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R - 2x sinh(x) - 8x cosh(x)sinh(x) + (- 12x cosh(x) + 4x - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 8x cosh(x) + (8x - 8)cosh(x))sinh(x) - 2x cosh(x) + (4x - 4)cosh(x) +--R + +--R - 2x +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 526 +--d0478:= D(m0478,x) +--E 419 + +--S 420 of 526 +t0479:= (1-csch(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (326) (- csch(x) + 1)\|- csch(x) + 1 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 526 +r0479:= 2*asin(1/2*2^(1/2)*coth(x))+atanh(coth(x)/(2-coth(x)^2)^(1/2))+_ + 1/2*coth(x)*(2-coth(x)^2)^(1/2) +--R +--R +--R (327) +--R +--------------+ +-+ +--R coth(x) | 2 \|2 coth(x) +--R 2atanh(-----------------) + coth(x)\|- coth(x) + 2 + 4asin(-----------) +--R +--------------+ 2 +--R | 2 +--R \|- coth(x) + 2 +--R ------------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 526 +a0479:= integrate(t0479,x) +--R +--R +--R (328) +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 5)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 20cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 30cosh(x) + 7)sinh(x) +--R + +--R 5 3 6 +--R (6cosh(x) - 20cosh(x) + 14cosh(x))sinh(x) + cosh(x) +--R + +--R 4 2 +--R - 5cosh(x) + 7cosh(x) - 3 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - sinh(x) - 8cosh(x)sinh(x) + (- 28cosh(x) + 8)sinh(x) +--R + +--R 3 5 +--R (- 56cosh(x) + 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70cosh(x) + 120cosh(x) - 18)sinh(x) +--R + +--R 5 3 3 +--R (- 56cosh(x) + 160cosh(x) - 72cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28cosh(x) + 120cosh(x) - 108cosh(x) + 16)sinh(x) +--R + +--R 7 5 3 8 +--R (- 8cosh(x) + 48cosh(x) - 72cosh(x) + 32cosh(x))sinh(x) - cosh(x) +--R + +--R 6 4 2 +--R 8cosh(x) - 18cosh(x) + 16cosh(x) - 5 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R + +--R 6 5 2 4 +--R - sinh(x) - 6cosh(x)sinh(x) + (- 15cosh(x) + 5)sinh(x) +--R + +--R 3 3 +--R (- 20cosh(x) + 20cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 15cosh(x) + 30cosh(x) - 7)sinh(x) +--R + +--R 5 3 6 +--R (- 6cosh(x) + 20cosh(x) - 14cosh(x))sinh(x) - cosh(x) +--R + +--R 4 2 +--R 5cosh(x) - 7cosh(x) + 3 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R sinh(x) + 8cosh(x)sinh(x) + (28cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) - 120cosh(x) + 18)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) - 160cosh(x) + 72cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) - 120cosh(x) + 108cosh(x) - 16)sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) - 48cosh(x) + 72cosh(x) - 32cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) + 18cosh(x) - 16cosh(x) + 5 +--R * +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 8cosh(x))sinh(x) + cosh(x) - 4cosh(x) - 1 +--R + +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) + 40)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) + 160cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) + 240cosh(x) - 56)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) + 160cosh(x) - 112cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R 40cosh(x) - 56cosh(x) + 24 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R 8sinh(x) + 64cosh(x)sinh(x) + (224cosh(x) - 64)sinh(x) +--R + +--R 3 5 +--R (448cosh(x) - 384cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (560cosh(x) - 960cosh(x) + 144)sinh(x) +--R + +--R 5 3 3 +--R (448cosh(x) - 1280cosh(x) + 576cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (224cosh(x) - 960cosh(x) + 864cosh(x) - 128)sinh(x) +--R + +--R 7 5 3 +--R (64cosh(x) - 384cosh(x) + 576cosh(x) - 256cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 8cosh(x) - 64cosh(x) + 144cosh(x) - 128cosh(x) + 40 +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R / +--R 2 +--R + +--R 2 2 +--R (8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) - 8) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R - 8sinh(x) - 32cosh(x)sinh(x) + (- 48cosh(x) + 32)sinh(x) +--R + +--R 3 4 2 +--R (- 32cosh(x) + 64cosh(x))sinh(x) - 8cosh(x) + 32cosh(x) - 8 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) - 10)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) - 40cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 60cosh(x) + 14)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) - 40cosh(x) + 28cosh(x))sinh(x) + 2cosh(x) - 10cosh(x) +--R + +--R 2 +--R 14cosh(x) - 6 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) + 16)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) + 96cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) + 240cosh(x) - 36)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) + 320cosh(x) - 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) + 240cosh(x) - 216cosh(x) + 32)sinh(x) +--R + +--R 7 5 3 8 +--R (- 16cosh(x) + 96cosh(x) - 144cosh(x) + 64cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R 16cosh(x) - 36cosh(x) + 32cosh(x) - 10 +--R Type: Union(Expression(Integer),...) +--E 422 + +--S 423 of 526 +m0479:= a0479-r0479 +--R +--R +--R (329) +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 5)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 20cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 30cosh(x) + 7)sinh(x) +--R + +--R 5 3 6 +--R (6cosh(x) - 20cosh(x) + 14cosh(x))sinh(x) + cosh(x) +--R + +--R 4 2 +--R - 5cosh(x) + 7cosh(x) - 3 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - sinh(x) - 8cosh(x)sinh(x) + (- 28cosh(x) + 8)sinh(x) +--R + +--R 3 5 +--R (- 56cosh(x) + 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70cosh(x) + 120cosh(x) - 18)sinh(x) +--R + +--R 5 3 3 +--R (- 56cosh(x) + 160cosh(x) - 72cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28cosh(x) + 120cosh(x) - 108cosh(x) + 16)sinh(x) +--R + +--R 7 5 3 8 +--R (- 8cosh(x) + 48cosh(x) - 72cosh(x) + 32cosh(x))sinh(x) - cosh(x) +--R + +--R 6 4 2 +--R 8cosh(x) - 18cosh(x) + 16cosh(x) - 5 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R + +--R 6 5 2 4 +--R - sinh(x) - 6cosh(x)sinh(x) + (- 15cosh(x) + 5)sinh(x) +--R + +--R 3 3 +--R (- 20cosh(x) + 20cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 15cosh(x) + 30cosh(x) - 7)sinh(x) +--R + +--R 5 3 6 +--R (- 6cosh(x) + 20cosh(x) - 14cosh(x))sinh(x) - cosh(x) +--R + +--R 4 2 +--R 5cosh(x) - 7cosh(x) + 3 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R sinh(x) + 8cosh(x)sinh(x) + (28cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) - 120cosh(x) + 18)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) - 160cosh(x) + 72cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) - 120cosh(x) + 108cosh(x) - 16)sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) - 48cosh(x) + 72cosh(x) - 32cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) + 18cosh(x) - 16cosh(x) + 5 +--R * +--R log +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 8cosh(x))sinh(x) + cosh(x) - 4cosh(x) - 1 +--R + +--R 6 5 2 4 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 30cosh(x) + 10)sinh(x) +--R + +--R 3 3 +--R (- 40cosh(x) + 40cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30cosh(x) + 60cosh(x) - 14)sinh(x) +--R + +--R 5 3 6 +--R (- 12cosh(x) + 40cosh(x) - 28cosh(x))sinh(x) - 2cosh(x) +--R + +--R 4 2 +--R 10cosh(x) - 14cosh(x) + 6 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) - 16)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) - 96cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) - 240cosh(x) + 36)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) - 320cosh(x) + 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 240cosh(x) + 216cosh(x) - 32)sinh(x) +--R + +--R 7 5 3 +--R (16cosh(x) - 96cosh(x) + 144cosh(x) - 64cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 2cosh(x) - 16cosh(x) + 36cosh(x) - 32cosh(x) + 10 +--R * +--R coth(x) +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R + +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) + 40)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) + 160cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) + 240cosh(x) - 56)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) + 160cosh(x) - 112cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R 40cosh(x) - 56cosh(x) + 24 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R 8sinh(x) + 64cosh(x)sinh(x) + (224cosh(x) - 64)sinh(x) +--R + +--R 3 5 +--R (448cosh(x) - 384cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (560cosh(x) - 960cosh(x) + 144)sinh(x) +--R + +--R 5 3 3 +--R (448cosh(x) - 1280cosh(x) + 576cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (224cosh(x) - 960cosh(x) + 864cosh(x) - 128)sinh(x) +--R + +--R 7 5 3 +--R (64cosh(x) - 384cosh(x) + 576cosh(x) - 256cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 8cosh(x) - 64cosh(x) + 144cosh(x) - 128cosh(x) + 40 +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 2 +--R |------------------------------------- - sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R / +--R 2 +--R + +--R 6 5 +--R - coth(x)sinh(x) - 6cosh(x)coth(x)sinh(x) +--R + +--R 2 4 +--R (- 15cosh(x) + 5)coth(x)sinh(x) +--R + +--R 3 3 +--R (- 20cosh(x) + 20cosh(x))coth(x)sinh(x) +--R + +--R 4 2 2 +--R (- 15cosh(x) + 30cosh(x) - 7)coth(x)sinh(x) +--R + +--R 5 3 +--R (- 6cosh(x) + 20cosh(x) - 14cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (- cosh(x) + 5cosh(x) - 7cosh(x) + 3)coth(x) +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R + +--R 6 5 2 4 +--R - 4sinh(x) - 24cosh(x)sinh(x) + (- 60cosh(x) + 20)sinh(x) +--R + +--R 3 3 +--R (- 80cosh(x) + 80cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 60cosh(x) + 120cosh(x) - 28)sinh(x) +--R + +--R 5 3 6 +--R (- 24cosh(x) + 80cosh(x) - 56cosh(x))sinh(x) - 4cosh(x) +--R + +--R 4 2 +--R 20cosh(x) - 28cosh(x) + 12 +--R * +--R +-+ +--R \|2 coth(x) +--R asin(-----------) +--R 2 +--R + +--R 2 2 +--R 8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) - 8 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 +--R coth(x)sinh(x) + 8cosh(x)coth(x)sinh(x) +--R + +--R 2 6 +--R (28cosh(x) - 8)coth(x)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) - 48cosh(x))coth(x)sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) - 120cosh(x) + 18)coth(x)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) - 160cosh(x) + 72cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) - 120cosh(x) + 108cosh(x) - 16)coth(x)sinh(x) +--R + +--R 7 5 3 +--R (8cosh(x) - 48cosh(x) + 72cosh(x) - 32cosh(x))coth(x)sinh(x) +--R + +--R 8 6 4 2 +--R (cosh(x) - 8cosh(x) + 18cosh(x) - 16cosh(x) + 5)coth(x) +--R * +--R +--------------+ +--R | 2 +--R \|- coth(x) + 2 +--R + +--R 8 7 2 6 +--R 4sinh(x) + 32cosh(x)sinh(x) + (112cosh(x) - 32)sinh(x) +--R + +--R 3 5 +--R (224cosh(x) - 192cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (280cosh(x) - 480cosh(x) + 72)sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) - 640cosh(x) + 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (112cosh(x) - 480cosh(x) + 432cosh(x) - 64)sinh(x) +--R + +--R 7 5 3 +--R (32cosh(x) - 192cosh(x) + 288cosh(x) - 128cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 4cosh(x) - 32cosh(x) + 72cosh(x) - 64cosh(x) + 20 +--R * +--R +-+ +--R \|2 coth(x) +--R asin(-----------) +--R 2 +--R + +--R 4 3 2 2 +--R - 8sinh(x) - 32cosh(x)sinh(x) + (- 48cosh(x) + 32)sinh(x) +--R + +--R 3 4 2 +--R (- 32cosh(x) + 64cosh(x))sinh(x) - 8cosh(x) + 32cosh(x) - 8 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) - 10)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) - 40cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 60cosh(x) + 14)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) - 40cosh(x) + 28cosh(x))sinh(x) + 2cosh(x) - 10cosh(x) +--R + +--R 2 +--R 14cosh(x) - 6 +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2sinh(x) + 2cosh(x) - 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) + 16)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) + 96cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) + 240cosh(x) - 36)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) + 320cosh(x) - 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) + 240cosh(x) - 216cosh(x) + 32)sinh(x) +--R + +--R 7 5 3 8 +--R (- 16cosh(x) + 96cosh(x) - 144cosh(x) + 64cosh(x))sinh(x) - 2cosh(x) +--R + +--R 6 4 2 +--R 16cosh(x) - 36cosh(x) + 32cosh(x) - 10 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 526 +--d0479:= D(m0479,x) +--E 424 + +--S 425 of 526 +t0480:= (-1+csch(x)^2)^(3/2) +--R +--R +--R +------------+ +--R 2 | 2 +--R (330) (csch(x) - 1)\|csch(x) - 1 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 526 +r0480:= atan(coth(x)/(-2+coth(x)^2)^(1/2))+2*atanh((-2+coth(x)^2)^(1/2)*_ + tanh(x))-1/2*coth(x)*(-2+coth(x)^2)^(1/2) +--R +--R +--R (331) +--R +------------+ +--R | 2 coth(x) +--R 4atanh(tanh(x)\|coth(x) - 2 ) + 2atan(---------------) +--R +------------+ +--R | 2 +--R \|coth(x) - 2 +--R + +--R +------------+ +--R | 2 +--R - coth(x)\|coth(x) - 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 526 +a0480:= integrate(t0480,x) +--R +--R +--R (332) +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 2 +--R |------------------------------------- + sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) + 8cosh(x))sinh(x) - 2cosh(x) + 4cosh(x) - 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 2 +--R - |------------------------------------- + sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - cosh(x) + 2cosh(x) - 1 +--R * +--R atan +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 427 + +--S 428 of 526 +m0480:= a0480-r0480 +--R +--R +--R (333) +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 2 +--R |------------------------------------- + sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) + 8cosh(x))sinh(x) - 2cosh(x) + 4cosh(x) - 2 +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 2 +--R - |------------------------------------- + sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) + 1 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 8)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 16cosh(x))sinh(x) - 4cosh(x) + 8cosh(x) - 4 +--R * +--R +------------+ +--R | 2 +--R atanh(tanh(x)\|coth(x) - 2 ) +--R + +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - cosh(x) + 2cosh(x) - 1 +--R * +--R atan +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + cosh(x) + 4cosh(x) - 1 +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R atan(-----------------------------------------) +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) + 8cosh(x))sinh(x) - 2cosh(x) + 4cosh(x) - 2 +--R * +--R coth(x) +--R atan(---------------) +--R +------------+ +--R | 2 +--R \|coth(x) - 2 +--R + +--R 4 3 +--R coth(x)sinh(x) + 4cosh(x)coth(x)sinh(x) +--R + +--R 2 2 3 +--R (6cosh(x) - 2)coth(x)sinh(x) + (4cosh(x) - 4cosh(x))coth(x)sinh(x) +--R + +--R 4 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x) +--R * +--R +------------+ +--R | 2 +--R \|coth(x) - 2 +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | - 2sinh(x) - 2cosh(x) + 6 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 526 +--d0480:= D(m0480,x) +--E 429 + +--S 430 of 526 +t0481:= (-1-csch(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (334) (- csch(x) - 1)\|- csch(x) - 1 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 526 +r0481:= 1/2*(-coth(x)^2)^(1/2)*(coth(x)^2-2*log(sinh(x)))*tanh(x) +--R +--R +--R +----------+ +--R 2 | 2 +--R (- 2tanh(x)log(sinh(x)) + coth(x) tanh(x))\|- coth(x) +--R (335) ------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 526 +a0481:= integrate(t0481,x) +--R +--R +--R (336) +--R +---+ x 4 +---+ x 2 +---+ x 2 +---+ x 4 +--R (- \|- 1 (%e ) + 2\|- 1 (%e ) - \|- 1 )log((%e ) - 1) + x\|- 1 (%e ) +--R + +--R +---+ x 2 +---+ +--R (- 2x + 2)\|- 1 (%e ) + x\|- 1 +--R / +--R x 4 x 2 +--R (%e ) - 2(%e ) + 1 +--R Type: Union(Expression(Integer),...) +--E 432 + +--S 433 of 526 +m0481:= a0481-r0481 +--R +--R +--R (337) +--R x 4 x 2 +--R (2(%e ) - 4(%e ) + 2)tanh(x)log(sinh(x)) +--R + +--R 2 x 4 2 x 2 2 +--R (- coth(x) (%e ) + 2coth(x) (%e ) - coth(x) )tanh(x) +--R * +--R +----------+ +--R | 2 +--R \|- coth(x) +--R + +--R +---+ x 4 +---+ x 2 +---+ x 2 +--R (- 2\|- 1 (%e ) + 4\|- 1 (%e ) - 2\|- 1 )log((%e ) - 1) +--R + +--R +---+ x 4 +---+ x 2 +---+ +--R 2x\|- 1 (%e ) + (- 4x + 4)\|- 1 (%e ) + 2x\|- 1 +--R / +--R x 4 x 2 +--R 2(%e ) - 4(%e ) + 2 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 526 +d0481:= D(m0481,x) +--R +--R +--R (338) +--R +---+ x 6 +---+ x 4 +---+ x 2 +---+ +--R (- 2\|- 1 (%e ) - 6\|- 1 (%e ) - 6\|- 1 (%e ) - 2\|- 1 )sinh(x) +--R * +--R +----------+ +--R | 2 +--R \|- coth(x) +--R + +--R 2 x 6 2 x 4 2 x 2 2 +--R (2coth(x) (%e ) - 6coth(x) (%e ) + 6coth(x) (%e ) - 2coth(x) ) +--R * +--R 2 +--R sinh(x)tanh(x) +--R + +--R 3 x 6 3 x 4 +--R (2coth(x) - 2coth(x))(%e ) + (- 6coth(x) + 6coth(x))(%e ) +--R + +--R 3 x 2 3 +--R (6coth(x) - 6coth(x))(%e ) - 2coth(x) + 2coth(x) +--R * +--R sinh(x)tanh(x) +--R + +--R 2 x 6 2 x 4 2 x 2 2 +--R (- 2coth(x) (%e ) + 6coth(x) (%e ) - 6coth(x) (%e ) + 2coth(x) ) +--R * +--R sinh(x) +--R * +--R log(sinh(x)) +--R + +--R 4 x 6 4 x 4 4 x 2 4 +--R (- coth(x) (%e ) + 3coth(x) (%e ) - 3coth(x) (%e ) + coth(x) ) +--R * +--R 2 +--R sinh(x)tanh(x) +--R + +--R 5 3 x 6 5 3 x 4 +--R (- 3coth(x) + 3coth(x) )(%e ) + (9coth(x) - 9coth(x) )(%e ) +--R + +--R 5 3 x 2 5 3 +--R (- 9coth(x) + 9coth(x) )(%e ) + 3coth(x) - 3coth(x) +--R * +--R sinh(x) +--R + +--R 2 x 6 2 x 4 +--R - 2cosh(x)coth(x) (%e ) + 6cosh(x)coth(x) (%e ) +--R + +--R 2 x 2 2 +--R - 6cosh(x)coth(x) (%e ) + 2cosh(x)coth(x) +--R * +--R tanh(x) +--R + +--R 4 x 6 4 x 4 4 x 2 4 +--R (coth(x) (%e ) - 3coth(x) (%e ) + 3coth(x) (%e ) - coth(x) )sinh(x) +--R / +--R +----------+ +--R x 6 x 4 x 2 | 2 +--R (2(%e ) - 6(%e ) + 6(%e ) - 2)sinh(x)\|- coth(x) +--R Type: Expression(Integer) +--E 434 + +--S 435 of 526 +t0482:= (a+b*csch(x)^2)^(3/2) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (339) (b csch(x) + a)\|b csch(x) + a +--R Type: Expression(Integer) +--E 435 + +--S 436 of 526 +r0482:= a^(3/2)*atanh(a^(1/2)*coth(x)/(a+b*csch(x)^2)^(1/2))-_ + 3/2*a*b^(1/2)*atanh((a+b*csch(x)^2)^(1/2)*tanh(x)/b^(1/2))+_ + 1/2*b^(3/2)*atanh((a+b*csch(x)^2)^(1/2)*tanh(x)/b^(1/2))-_ + 1/2*b*coth(x)*(a+b*csch(x)^2)^(1/2) +--R +--R +--R (340) +--R +--------------+ +--R | 2 +--R +-+ tanh(x)\|b csch(x) + a +--R (b - 3a)\|b atanh(------------------------) +--R +-+ +--R \|b +--R + +--R +-+ +--------------+ +--R +-+ coth(x)\|a | 2 +--R 2a\|a atanh(-----------------) - b coth(x)\|b csch(x) + a +--R +--------------+ +--R | 2 +--R \|b csch(x) + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 526 +a0482:= integrate(t0482,x) +--R +--R +--R (341) +--R [ +--R 2 3 6 2 3 5 +--R (2a b - a )sinh(x) + (12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b - 15a )cosh(x) - 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b - 20a )cosh(x) + (- 16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (30a b - 15a )cosh(x) + (- 24a b + 18a )cosh(x) + 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b - 6a )cosh(x) + (- 16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (2a b - a )cosh(x) + (- 4a b + 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (2a b - 3a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b + 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 56a b + 56a b - 28a )cosh(x) + 4a b - 8a b + 4a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b + 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b - 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b + 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b - 120a b + 60a )cosh(x) - 2a b + 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b + 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b - 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b + 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b + 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b - 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b + 60a b - 36a )cosh(x) - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b - 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b + 40a b - 24a )cosh(x) + (- 8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b + 2a b - a )cosh(x) + (4a b - 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b + 10a b - 6a )cosh(x) + (- 4a b + 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 2 6 +--R (2b - 7a b + 3a )sinh(x) +--R + +--R 2 2 5 +--R (12b - 42a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 105a b + 45a )cosh(x) - 4b + 15a b - 9a )sinh(x) +--R + +--R 2 2 3 +--R (40b - 140a b + 60a )cosh(x) +--R + +--R 2 2 +--R (- 16b + 60a b - 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b - 105a b + 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 24b + 90a b - 54a )cosh(x) + 2b - 9a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (12b - 42a b + 18a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 16b + 60a b - 36a )cosh(x) + (4b - 18a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - 7a b + 3a )cosh(x) + (- 4b + 15a b - 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (2b - 9a b + 9a )cosh(x) + a b - 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b + 8a b - 7a b + 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b + 64a b - 56a b + 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 56b + 224a b - 196a b + 84a )cosh(x) + 4b - 20a b +--R + +--R 2 3 +--R 28a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b + 448a b - 392a b + 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (24b - 120a b + 168a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b + 560a b - 490a b + 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (60b - 300a b + 420a b - 180a )cosh(x) - 2b + 16a b +--R + +--R 2 3 +--R - 36a b + 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b + 448a b - 392a b + 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (80b - 400a b + 560a b - 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b + 64a b - 144a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b + 224a b - 196a b + 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (60b - 300a b + 420a b - 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 12b + 96a b - 216a b + 108a )cosh(x) - 4a b + 16a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b + 64a b - 56a b + 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (24b - 120a b + 168a b - 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b + 64a b - 144a b + 72a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b + 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b + 8a b - 7a b + 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (4b - 20a b + 28a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b + 16a b - 36a b + 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4a b + 16a b - 12a )cosh(x) - a b + 3a +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 3 +--R (2b - 2a)sinh(x) + (8b - 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((12b - 12a)cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R ((8b - 8a)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (2b - 2a)cosh(x) + 2a cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R + +--R 2 4 2 3 +--R - a sinh(x) - 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 6a cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R (- 4a cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R - a cosh(x) + (- 2a b + 2a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 6 2 5 +--R (2a b - 2a )sinh(x) + (12a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((30a b - 30a )cosh(x) - 6a b + 4a )sinh(x) +--R + +--R 2 3 2 3 +--R ((40a b - 40a )cosh(x) + (- 24a b + 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R (30a b - 30a )cosh(x) + (- 36a b + 24a )cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (12a b - 12a )cosh(x) + (- 24a b + 16a )cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (2a b - 2a )cosh(x) + (- 6a b + 4a )cosh(x) - 2a cosh(x) +--R * +--R +-+ +--R \|b +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) + 2b - 4a b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (8b - 16a b + 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b - 15a )cosh(x) + (12b - 24a b + 18a )cosh(x) +--R + +--R 2 +--R 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (8b - 16a b + 12a )cosh(x) +--R + +--R 2 +--R (8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (2b - 4a b + 3a )cosh(x) +--R + +--R 2 2 2 +--R (4a b - 3a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 2 4 2 3 +--R (2a b - a )sinh(x) + (8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b - 6a )cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b - 4a )cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b - a )cosh(x) + (- 2a b + 2a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b + 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 30b + 30a b - 15a )cosh(x) + 2b - 6a b + 3a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 +--R (- 40b + 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (8b - 24a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b + 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (12b - 36a b + 18a )cosh(x) + 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (8b - 24a b + 12a )cosh(x) + (8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b + 2a b - a )cosh(x) + (2b - 6a b + 3a )cosh(x) +--R + +--R 2 2 2 +--R (4a b - 3a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R + +--R 2 3 6 2 3 5 +--R (- 2a b + a )sinh(x) + (- 12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b + 15a )cosh(x) + 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b + 20a )cosh(x) + (16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b + 15a )cosh(x) + (24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b + 6a )cosh(x) + (16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b + a )cosh(x) + (4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b + 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b - 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b - 56a b + 28a )cosh(x) - 4a b + 8a b - 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b - 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b + 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b - 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b + 120a b - 60a )cosh(x) + 2a b - 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b - 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b + 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b - 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b - 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b + 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b - 60a b + 36a )cosh(x) + 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b - 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b + 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b - 40a b + 24a )cosh(x) + (8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b - 2a b + a )cosh(x) + (- 4a b + 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b - 10a b + 6a )cosh(x) + (4a b - 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) + 6b - 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (12b - 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (6b - 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 3 2 2 6 +--R (2b - 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 5 +--R (12b - 24a b + 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((30b - 60a b + 30a b)cosh(x) + 2b + 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 3 2 2 +--R ((40b - 80a b + 40a b)cosh(x) + (8b + 24a b - 16a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (30b - 60a b + 30a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b + 36a b - 24a b)cosh(x) + 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (12b - 24a b + 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b + 24a b - 16a b)cosh(x) + (4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (2b - 4a b + 2a b)cosh(x) + (2b + 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (2b - 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 7 +--R (16b - 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b - 112a b + 56a b)cosh(x) - 12b + 14a b - 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b - 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (- 72b + 84a b - 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b - 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 180b + 210a b - 90a b)cosh(x) - 6b - 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b - 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 240b + 280a b - 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b - 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b - 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (- 180b + 210a b - 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b - 48a b + 36a b)cosh(x) - 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b - 32a b + 16a b)cosh(x) +--R + +--R 3 2 2 5 +--R (- 72b + 84a b - 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b - 32a b + 24a b)cosh(x) + (- 4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b - 4a b + 2a b)cosh(x) + (- 12b + 14a b - 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b - 8a b + 6a b)cosh(x) + (- 2a b - 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b - 2a)sinh(x) + (24b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b - 30a)cosh(x) - 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b - 40a)cosh(x) + (- 32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b - 30a)cosh(x) + (- 48b + 36a)cosh(x) + 4b - 6a)sinh(x) +--R + +--R 5 3 +--R ((24b - 12a)cosh(x) + (- 32b + 24a)cosh(x) + (8b - 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b - 2a)cosh(x) + (- 8b + 6a)cosh(x) + (4b - 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b + 4a b - 2a )sinh(x) + (- 32b + 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b + 112a b - 56a )cosh(x) + 8b - 16a b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b + 224a b - 112a )cosh(x) + (48b - 96a b + 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 280b + 280a b - 140a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (120b - 240a b + 120a )cosh(x) - 4b + 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 224b + 224a b - 112a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (160b - 320a b + 160a )cosh(x) + (- 16b + 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 +--R (- 112b + 112a b - 56a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (120b - 240a b + 120a )cosh(x) + (- 24b + 120a b - 72a )cosh(x) +--R + +--R 2 +--R - 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b + 32a b - 16a )cosh(x) + (48b - 96a b + 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b + 80a b - 48a )cosh(x) + (- 16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b + 4a b - 2a )cosh(x) + (8b - 16a b + 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b + 20a b - 12a )cosh(x) + (- 8a b + 8a )cosh(x) - 2a +--R , +--R +--R 2 3 6 2 3 5 +--R (2a b - a )sinh(x) + (12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b - 15a )cosh(x) - 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b - 20a )cosh(x) + (- 16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (30a b - 15a )cosh(x) + (- 24a b + 18a )cosh(x) + 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b - 6a )cosh(x) + (- 16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (2a b - a )cosh(x) + (- 4a b + 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (2a b - 3a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b + 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 56a b + 56a b - 28a )cosh(x) + 4a b - 8a b + 4a ) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b + 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b - 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b + 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b - 120a b + 60a )cosh(x) - 2a b + 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b + 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b - 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b + 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b + 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b - 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b + 60a b - 36a )cosh(x) - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b - 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b + 40a b - 24a )cosh(x) + (- 8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b + 2a b - a )cosh(x) + (4a b - 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b + 10a b - 6a )cosh(x) + (- 4a b + 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 3 6 2 3 5 +--R (- 2a b + a )sinh(x) + (- 12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b + 15a )cosh(x) + 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b + 20a )cosh(x) + (16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b + 15a )cosh(x) + (24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b + 6a )cosh(x) + (16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b + a )cosh(x) + (4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b + 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b - 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b - 56a b + 28a )cosh(x) - 4a b + 8a b - 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b - 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b + 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b - 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b + 120a b - 60a )cosh(x) + 2a b - 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b - 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b + 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b - 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b - 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b + 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b - 60a b + 36a )cosh(x) + 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b - 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b + 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b - 40a b + 24a )cosh(x) + (8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b - 2a b + a )cosh(x) + (- 4a b + 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b - 10a b + 6a )cosh(x) + (4a b - 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) + 6b - 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (12b - 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (6b - 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 2 6 +--R (4b - 14a b + 6a )sinh(x) +--R + +--R 2 2 5 +--R (24b - 84a b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((60b - 210a b + 90a )cosh(x) - 8b + 30a b - 18a )sinh(x) +--R + +--R 2 2 3 +--R (80b - 280a b + 120a )cosh(x) +--R + +--R 2 2 +--R (- 32b + 120a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (60b - 210a b + 90a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 48b + 180a b - 108a )cosh(x) + 4b - 18a b + 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (24b - 84a b + 36a )cosh(x) +--R + +--R 2 2 3 +--R (- 32b + 120a b - 72a )cosh(x) +--R + +--R 2 2 +--R (8b - 36a b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (4b - 14a b + 6a )cosh(x) + (- 8b + 30a b - 18a )cosh(x) +--R + +--R 2 2 2 2 +--R (4b - 18a b + 18a )cosh(x) + 2a b - 6a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +---+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|- b \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 4b + 16a b - 14a b + 6a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 32b + 128a b - 112a b + 48a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 112b + 448a b - 392a b + 168a )cosh(x) + 8b - 40a b +--R + +--R 2 3 +--R 56a b - 24a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 224b + 896a b - 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 +--R (48b - 240a b + 336a b - 144a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 280b + 1120a b - 980a b + 420a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (120b - 600a b + 840a b - 360a )cosh(x) - 4b + 32a b +--R + +--R 2 3 +--R - 72a b + 36a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 224b + 896a b - 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (160b - 800a b + 1120a b - 480a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 16b + 128a b - 288a b + 144a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 112b + 448a b - 392a b + 168a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (120b - 600a b + 840a b - 360a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 24b + 192a b - 432a b + 216a )cosh(x) - 8a b + 32a b +--R + +--R 3 +--R - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 32b + 128a b - 112a b + 48a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (48b - 240a b + 336a b - 144a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 16b + 128a b - 288a b + 144a )cosh(x) +--R + +--R 2 2 3 +--R (- 16a b + 64a b - 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 4b + 16a b - 14a b + 6a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (8b - 40a b + 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 4b + 32a b - 72a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 8a b + 32a b - 24a )cosh(x) - 2a b + 6a +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +---+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|a +--R + +--R 3 2 2 6 +--R (2b - 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 5 +--R (12b - 24a b + 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((30b - 60a b + 30a b)cosh(x) + 2b + 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 3 2 2 +--R ((40b - 80a b + 40a b)cosh(x) + (8b + 24a b - 16a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (30b - 60a b + 30a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (12b + 36a b - 24a b)cosh(x) + 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (12b - 24a b + 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (8b + 24a b - 16a b)cosh(x) + (4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (2b - 4a b + 2a b)cosh(x) + (2b + 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (2b - 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 7 +--R (16b - 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b - 112a b + 56a b)cosh(x) - 12b + 14a b - 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b - 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (- 72b + 84a b - 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b - 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 180b + 210a b - 90a b)cosh(x) - 6b - 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b - 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 240b + 280a b - 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b - 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b - 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (- 180b + 210a b - 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b - 48a b + 36a b)cosh(x) - 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b - 32a b + 16a b)cosh(x) +--R + +--R 3 2 2 5 +--R (- 72b + 84a b - 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b - 32a b + 24a b)cosh(x) + (- 4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b - 4a b + 2a b)cosh(x) + (- 12b + 14a b - 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b - 8a b + 6a b)cosh(x) + (- 2a b - 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b - 2a)sinh(x) + (24b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b - 30a)cosh(x) - 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b - 40a)cosh(x) + (- 32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b - 30a)cosh(x) + (- 48b + 36a)cosh(x) + 4b - 6a)sinh(x) +--R + +--R 5 3 +--R ((24b - 12a)cosh(x) + (- 32b + 24a)cosh(x) + (8b - 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b - 2a)cosh(x) + (- 8b + 6a)cosh(x) + (4b - 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b + 4a b - 2a )sinh(x) + (- 32b + 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b + 112a b - 56a )cosh(x) + 8b - 16a b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b + 224a b - 112a )cosh(x) + (48b - 96a b + 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 280b + 280a b - 140a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (120b - 240a b + 120a )cosh(x) - 4b + 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 224b + 224a b - 112a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (160b - 320a b + 160a )cosh(x) + (- 16b + 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 +--R (- 112b + 112a b - 56a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (120b - 240a b + 120a )cosh(x) + (- 24b + 120a b - 72a )cosh(x) +--R + +--R 2 +--R - 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b + 32a b - 16a )cosh(x) + (48b - 96a b + 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b + 80a b - 48a )cosh(x) + (- 16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b + 4a b - 2a )cosh(x) + (8b - 16a b + 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b + 20a b - 12a )cosh(x) + (- 8a b + 8a )cosh(x) - 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 437 + +--S 438 of 526 +m0482a:= a0482.1-r0482 +--R +--R +--R (342) +--R 2 3 6 2 3 5 +--R (2a b - a )sinh(x) + (12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b - 15a )cosh(x) - 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b - 20a )cosh(x) + (- 16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (30a b - 15a )cosh(x) + (- 24a b + 18a )cosh(x) + 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b - 6a )cosh(x) + (- 16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (2a b - a )cosh(x) + (- 4a b + 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (2a b - 3a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b + 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((- 56a b + 56a b - 28a )cosh(x) + 4a b - 8a b + 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b + 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b - 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b + 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b - 120a b + 60a )cosh(x) - 2a b + 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b + 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b - 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b + 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b + 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b - 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b + 60a b - 36a )cosh(x) - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b - 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b + 40a b - 24a )cosh(x) + (- 8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b + 2a b - a )cosh(x) + (4a b - 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b + 10a b - 6a )cosh(x) + (- 4a b + 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 2 6 2 2 5 +--R (2b - 7a b + 3a )sinh(x) + (12b - 42a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 105a b + 45a )cosh(x) - 4b + 15a b - 9a )sinh(x) +--R + +--R 2 2 3 +--R (40b - 140a b + 60a )cosh(x) +--R + +--R 2 2 +--R (- 16b + 60a b - 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (30b - 105a b + 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 24b + 90a b - 54a )cosh(x) + 2b - 9a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (12b - 42a b + 18a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 16b + 60a b - 36a )cosh(x) + (4b - 18a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - 7a b + 3a )cosh(x) + (- 4b + 15a b - 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (2b - 9a b + 9a )cosh(x) + a b - 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b + 8a b - 7a b + 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b + 64a b - 56a b + 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 56b + 224a b - 196a b + 84a )cosh(x) + 4b - 20a b +--R + +--R 2 3 +--R 28a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b + 448a b - 392a b + 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (24b - 120a b + 168a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 140b + 560a b - 490a b + 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (60b - 300a b + 420a b - 180a )cosh(x) - 2b + 16a b +--R + +--R 2 3 +--R - 36a b + 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 112b + 448a b - 392a b + 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (80b - 400a b + 560a b - 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b + 64a b - 144a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 56b + 224a b - 196a b + 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (60b - 300a b + 420a b - 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 12b + 96a b - 216a b + 108a )cosh(x) - 4a b + 16a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 16b + 64a b - 56a b + 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (24b - 120a b + 168a b - 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 8b + 64a b - 144a b + 72a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b + 32a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 2b + 8a b - 7a b + 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (4b - 20a b + 28a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 2b + 16a b - 36a b + 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4a b + 16a b - 12a )cosh(x) - a b + 3a +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 3 +--R (2b - 2a)sinh(x) + (8b - 8a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((12b - 12a)cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R ((8b - 8a)cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 2 +--R (2b - 2a)cosh(x) + 2a cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R + +--R 2 4 2 3 +--R - a sinh(x) - 4a cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 6a cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 4 +--R (- 4a cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) - a cosh(x) +--R + +--R 2 2 2 +--R (- 2a b + 2a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 6 2 5 +--R (2a b - 2a )sinh(x) + (12a b - 12a )cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((30a b - 30a )cosh(x) - 6a b + 4a )sinh(x) +--R + +--R 2 3 2 3 +--R ((40a b - 40a )cosh(x) + (- 24a b + 16a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R ((30a b - 30a )cosh(x) + (- 36a b + 24a )cosh(x) - 2a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (12a b - 12a )cosh(x) + (- 24a b + 16a )cosh(x) +--R + +--R 2 +--R - 4a cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (2a b - 2a )cosh(x) + (- 6a b + 4a )cosh(x) - 2a cosh(x) +--R * +--R +-+ +--R \|b +--R + +--R 2 2 6 2 2 5 +--R (2b - a )sinh(x) + (12b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((30b - 15a )cosh(x) + 2b - 4a b + 3a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((40b - 20a )cosh(x) + (8b - 16a b + 12a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (30b - 15a )cosh(x) + (12b - 24a b + 18a )cosh(x) +--R + +--R 2 +--R 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (12b - 6a )cosh(x) + (8b - 16a b + 12a )cosh(x) +--R + +--R 2 +--R (8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (2b - a )cosh(x) + (2b - 4a b + 3a )cosh(x) +--R + +--R 2 2 2 +--R (4a b - 3a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R / +--R 2 4 2 3 +--R (2a b - a )sinh(x) + (8a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R ((12a b - 6a )cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 2 +--R ((8a b - 4a )cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2a b - a )cosh(x) + (- 2a b + 2a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 6 +--R (- 2b + 2a b - a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 30b + 30a b - 15a )cosh(x) + 2b - 6a b + 3a )sinh(x) +--R + +--R 2 2 3 +--R (- 40b + 40a b - 20a )cosh(x) +--R + +--R 2 2 +--R (8b - 24a b + 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b + 30a b - 15a )cosh(x) +--R + +--R 2 2 2 2 +--R (12b - 36a b + 18a )cosh(x) + 4a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 12a b - 6a )cosh(x) +--R + +--R 2 2 3 2 +--R (8b - 24a b + 12a )cosh(x) + (8a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b + 2a b - a )cosh(x) + (2b - 6a b + 3a )cosh(x) +--R + +--R 2 2 2 +--R (4a b - 3a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R + +--R 2 3 6 2 3 5 +--R (- 2a b + a )sinh(x) + (- 12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b + 15a )cosh(x) + 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b + 20a )cosh(x) + (16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b + 15a )cosh(x) + (24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b + 6a )cosh(x) + (16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b + a )cosh(x) + (4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b + 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b - 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b - 56a b + 28a )cosh(x) - 4a b + 8a b - 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b - 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b + 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b - 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b + 120a b - 60a )cosh(x) + 2a b - 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b - 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b + 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b - 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b - 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b + 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b - 60a b + 36a )cosh(x) + 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b - 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b + 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b - 40a b + 24a )cosh(x) + (8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b - 2a b + a )cosh(x) + (- 4a b + 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b - 10a b + 6a )cosh(x) + (4a b - 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) + 6b - 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (12b - 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (6b - 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 2 6 +--R (- 2b + 7a b - 3a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 42a b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 30b + 105a b - 45a )cosh(x) + 4b - 15a b + 9a )sinh(x) +--R + +--R 2 2 3 +--R (- 40b + 140a b - 60a )cosh(x) +--R + +--R 2 2 +--R (16b - 60a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b + 105a b - 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b - 90a b + 54a )cosh(x) - 2b + 9a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 42a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (16b - 60a b + 36a )cosh(x) + (- 4b + 18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b + 7a b - 3a )cosh(x) + (4b - 15a b + 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 9a b - 9a )cosh(x) - a b + 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (2b - 8a b + 7a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b - 64a b + 56a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (56b - 224a b + 196a b - 84a )cosh(x) - 4b + 20a b +--R + +--R 2 3 +--R - 28a b + 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (112b - 448a b + 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b + 120a b - 168a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (140b - 560a b + 490a b - 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 60b + 300a b - 420a b + 180a )cosh(x) + 2b - 16a b +--R + +--R 2 3 +--R 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (112b - 448a b + 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80b + 400a b - 560a b + 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (8b - 64a b + 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (56b - 224a b + 196a b - 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60b + 300a b - 420a b + 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (12b - 96a b + 216a b - 108a )cosh(x) + 4a b - 16a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b - 64a b + 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b + 120a b - 168a b + 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (8b - 64a b + 144a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (8a b - 32a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (2b - 8a b + 7a b - 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 4b + 20a b - 28a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (2b - 16a b + 36a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4a b - 16a b + 12a )cosh(x) + a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R +--------------+ +--R | 2 +--R tanh(x)\|b csch(x) + a +--R atanh(------------------------) +--R +-+ +--R \|b +--R + +--R 2 3 6 2 3 5 +--R (- 4a b + 2a )sinh(x) + (- 24a b + 12a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 60a b + 30a )cosh(x) + 8a b - 6a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 80a b + 40a )cosh(x) + (32a b - 24a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 60a b + 30a )cosh(x) + (48a b - 36a )cosh(x) - 4a b +--R + +--R 3 +--R 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 24a b + 12a )cosh(x) + (32a b - 24a )cosh(x) +--R + +--R 2 3 +--R (- 8a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 4a b + 2a )cosh(x) + (8a b - 6a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 4a b + 6a )cosh(x) - 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (4a b - 4a b + 2a )sinh(x) +--R + +--R 2 2 3 7 +--R (32a b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((112a b - 112a b + 56a )cosh(x) - 8a b + 16a b - 8a )sinh(x) +--R + +--R 2 2 3 3 +--R (224a b - 224a b + 112a )cosh(x) +--R + +--R 2 2 3 +--R (- 48a b + 96a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (280a b - 280a b + 140a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 120a b + 240a b - 120a )cosh(x) + 4a b - 20a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (224a b - 224a b + 112a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 160a b + 320a b - 160a )cosh(x) +--R + +--R 2 2 3 +--R (16a b - 80a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (112a b - 112a b + 56a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 120a b + 240a b - 120a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (24a b - 120a b + 72a )cosh(x) + 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (32a b - 32a b + 16a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 48a b + 96a b - 48a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (16a b - 80a b + 48a )cosh(x) + (16a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (4a b - 4a b + 2a )cosh(x) + (- 8a b + 16a b - 8a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (4a b - 20a b + 12a )cosh(x) + (8a b - 8a )cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R coth(x)\|a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b csch(x) + a +--R + +--R 2 6 2 5 +--R (2b - a b)coth(x)sinh(x) + (12b - 6a b)cosh(x)coth(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((30b - 15a b)cosh(x) - 4b + 3a b)coth(x)sinh(x) +--R + +--R 2 3 2 3 +--R ((40b - 20a b)cosh(x) + (- 16b + 12a b)cosh(x))coth(x)sinh(x) +--R + +--R 2 4 2 2 2 +--R (30b - 15a b)cosh(x) + (- 24b + 18a b)cosh(x) + 2b +--R + +--R - 3a b +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 2 5 2 3 +--R (12b - 6a b)cosh(x) + (- 16b + 12a b)cosh(x) +--R + +--R 2 +--R (4b - 6a b)cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 2 6 2 4 +--R (2b - a b)cosh(x) + (- 4b + 3a b)cosh(x) +--R + +--R 2 2 +--R (2b - 3a b)cosh(x) + a b +--R * +--R coth(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (- 2b + 2a b - a b)coth(x)sinh(x) +--R + +--R 3 2 2 7 +--R (- 16b + 16a b - 8a b)cosh(x)coth(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R ((- 56b + 56a b - 28a b)cosh(x) + 4b - 8a b + 4a b)coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 112b + 112a b - 56a b)cosh(x) +--R + +--R 3 2 2 +--R (24b - 48a b + 24a b)cosh(x) +--R * +--R 5 +--R coth(x)sinh(x) +--R + +--R 3 2 2 4 +--R (- 140b + 140a b - 70a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (60b - 120a b + 60a b)cosh(x) - 2b + 10a b - 6a b +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 3 2 2 5 +--R (- 112b + 112a b - 56a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (80b - 160a b + 80a b)cosh(x) + (- 8b + 40a b - 24a b)cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 3 2 2 6 +--R (- 56b + 56a b - 28a b)cosh(x) +--R + +--R 3 2 2 4 +--R (60b - 120a b + 60a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 12b + 60a b - 36a b)cosh(x) - 4a b + 4a b +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 3 2 2 7 +--R (- 16b + 16a b - 8a b)cosh(x) +--R + +--R 3 2 2 5 +--R (24b - 48a b + 24a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 8b + 40a b - 24a b)cosh(x) + (- 8a b + 8a b)cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (- 2b + 2a b - a b)cosh(x) + (4b - 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 2 +--R (- 2b + 10a b - 6a b)cosh(x) + (- 4a b + 4a b)cosh(x) - a b +--R * +--R coth(x) +--R * +--R +--------------+ +--R | 2 +--R \|b csch(x) + a +--R + +--R 3 2 2 6 3 2 2 5 +--R (2b - 4a b + 2a b)sinh(x) + (12b - 24a b + 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((30b - 60a b + 30a b)cosh(x) + 2b + 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 3 2 2 +--R ((40b - 80a b + 40a b)cosh(x) + (8b + 24a b - 16a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (30b - 60a b + 30a b)cosh(x) + (12b + 36a b - 24a b)cosh(x) +--R + +--R 2 2 +--R 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 3 2 2 3 +--R (12b - 24a b + 12a b)cosh(x) + (8b + 24a b - 16a b)cosh(x) +--R + +--R 2 2 +--R (4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (2b - 4a b + 2a b)cosh(x) + (2b + 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (2b - 4a b + 2a b)sinh(x) + (16b - 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b - 112a b + 56a b)cosh(x) - 12b + 14a b - 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b - 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (- 72b + 84a b - 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b - 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 180b + 210a b - 90a b)cosh(x) - 6b - 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b - 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 240b + 280a b - 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b - 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b - 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (- 180b + 210a b - 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b - 48a b + 36a b)cosh(x) - 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b - 32a b + 16a b)cosh(x) +--R + +--R 3 2 2 5 +--R (- 72b + 84a b - 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b - 32a b + 24a b)cosh(x) + (- 4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b - 4a b + 2a b)cosh(x) + (- 12b + 14a b - 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b - 8a b + 6a b)cosh(x) + (- 2a b - 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b - 2a)sinh(x) + (24b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b - 30a)cosh(x) - 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b - 40a)cosh(x) + (- 32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b - 30a)cosh(x) + (- 48b + 36a)cosh(x) + 4b - 6a)sinh(x) +--R + +--R 5 3 +--R ((24b - 12a)cosh(x) + (- 32b + 24a)cosh(x) + (8b - 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b - 2a)cosh(x) + (- 8b + 6a)cosh(x) + (4b - 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b + 4a b - 2a )sinh(x) + (- 32b + 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b + 112a b - 56a )cosh(x) + 8b - 16a b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b + 224a b - 112a )cosh(x) + (48b - 96a b + 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 280b + 280a b - 140a )cosh(x) + (120b - 240a b + 120a )cosh(x) +--R + +--R 2 2 +--R - 4b + 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 224b + 224a b - 112a )cosh(x) + (160b - 320a b + 160a )cosh(x) +--R + +--R 2 2 +--R (- 16b + 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 112b + 112a b - 56a )cosh(x) + (120b - 240a b + 120a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 24b + 120a b - 72a )cosh(x) - 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b + 32a b - 16a )cosh(x) + (48b - 96a b + 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b + 80a b - 48a )cosh(x) + (- 16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b + 4a b - 2a )cosh(x) + (8b - 16a b + 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b + 20a b - 12a )cosh(x) + (- 8a b + 8a )cosh(x) - 2a +--R Type: Expression(Integer) +--E 438 + +--S 439 of 526 +--d0482a:= D(m0482a,x) +--E 439 + +--S 440 of 526 +m0482b:= a0482.2-r0482 +--R +--R +--R (343) +--R 2 3 6 2 3 5 +--R (2a b - a )sinh(x) + (12a b - 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((30a b - 15a )cosh(x) - 4a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((40a b - 20a )cosh(x) + (- 16a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (30a b - 15a )cosh(x) + (- 24a b + 18a )cosh(x) + 2a b +--R + +--R 3 +--R - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (12a b - 6a )cosh(x) + (- 16a b + 12a )cosh(x) +--R + +--R 2 3 +--R (4a b - 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (2a b - a )cosh(x) + (- 4a b + 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (2a b - 3a )cosh(x) + a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (- 2a b + 2a b - a )sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 16a b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((- 56a b + 56a b - 28a )cosh(x) + 4a b - 8a b + 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (- 112a b + 112a b - 56a )cosh(x) +--R + +--R 2 2 3 +--R (24a b - 48a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 140a b + 140a b - 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (60a b - 120a b + 60a )cosh(x) - 2a b + 10a b - 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 112a b + 112a b - 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (80a b - 160a b + 80a )cosh(x) +--R + +--R 2 2 3 +--R (- 8a b + 40a b - 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (- 56a b + 56a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (60a b - 120a b + 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 12a b + 60a b - 36a )cosh(x) - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 16a b - 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (24a b - 48a b + 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (- 8a b + 40a b - 24a )cosh(x) + (- 8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (- 2a b + 2a b - a )cosh(x) + (4a b - 8a b + 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (- 2a b + 10a b - 6a )cosh(x) + (- 4a b + 4a )cosh(x) - a +--R * +--R +-+ +--R \|a +--R * +--R log +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +-+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) )\|a +--R + +--R 2 3 6 2 3 5 +--R (- 2a b + a )sinh(x) + (- 12a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 30a b + 15a )cosh(x) + 4a b - 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 40a b + 20a )cosh(x) + (16a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 30a b + 15a )cosh(x) + (24a b - 18a )cosh(x) - 2a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 12a b + 6a )cosh(x) + (16a b - 12a )cosh(x) +--R + +--R 2 3 +--R (- 4a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b + a )cosh(x) + (4a b - 3a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 2a b + 3a )cosh(x) - a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (2a b - 2a b + a )sinh(x) +--R + +--R 2 2 3 7 +--R (16a b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((56a b - 56a b + 28a )cosh(x) - 4a b + 8a b - 4a )sinh(x) +--R + +--R 2 2 3 3 +--R (112a b - 112a b + 56a )cosh(x) +--R + +--R 2 2 3 +--R (- 24a b + 48a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (140a b - 140a b + 70a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 60a b + 120a b - 60a )cosh(x) + 2a b - 10a b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (112a b - 112a b + 56a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 80a b + 160a b - 80a )cosh(x) +--R + +--R 2 2 3 +--R (8a b - 40a b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (56a b - 56a b + 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 60a b + 120a b - 60a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (12a b - 60a b + 36a )cosh(x) + 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (16a b - 16a b + 8a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 24a b + 48a b - 24a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (8a b - 40a b + 24a )cosh(x) + (8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (2a b - 2a b + a )cosh(x) + (- 4a b + 8a b - 4a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (2a b - 10a b + 6a )cosh(x) + (4a b - 4a )cosh(x) + a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2a) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 4 3 +--R 2b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (12b cosh(x) + 6b - 2a)sinh(x) +--R + +--R 3 4 +--R (8b cosh(x) + (12b - 4a)cosh(x))sinh(x) + 2b cosh(x) +--R + +--R 2 +--R (6b - 2a)cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R 4cosh(x) sinh(x) + cosh(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 2 6 +--R (- 2b + 7a b - 3a )sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 42a b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 30b + 105a b - 45a )cosh(x) + 4b - 15a b + 9a )sinh(x) +--R + +--R 2 2 3 +--R (- 40b + 140a b - 60a )cosh(x) +--R + +--R 2 2 +--R (16b - 60a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (- 30b + 105a b - 45a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (24b - 90a b + 54a )cosh(x) - 2b + 9a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (- 12b + 42a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (16b - 60a b + 36a )cosh(x) + (- 4b + 18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 2b + 7a b - 3a )cosh(x) + (4b - 15a b + 9a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 9a b - 9a )cosh(x) - a b + 3a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a \|b |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (2b - 8a b + 7a b - 3a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b - 64a b + 56a b - 24a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (56b - 224a b + 196a b - 84a )cosh(x) - 4b + 20a b +--R + +--R 2 3 +--R - 28a b + 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (112b - 448a b + 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b + 120a b - 168a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (140b - 560a b + 490a b - 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 60b + 300a b - 420a b + 180a )cosh(x) + 2b - 16a b +--R + +--R 2 3 +--R 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (112b - 448a b + 392a b - 168a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 80b + 400a b - 560a b + 240a )cosh(x) +--R + +--R 3 2 2 3 +--R (8b - 64a b + 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (56b - 224a b + 196a b - 84a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 60b + 300a b - 420a b + 180a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (12b - 96a b + 216a b - 108a )cosh(x) + 4a b - 16a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (16b - 64a b + 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b + 120a b - 168a b + 72a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (8b - 64a b + 144a b - 72a )cosh(x) +--R + +--R 2 2 3 +--R (8a b - 32a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (2b - 8a b + 7a b - 3a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 4b + 20a b - 28a b + 12a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (2b - 16a b + 36a b - 18a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4a b - 16a b + 12a )cosh(x) + a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R +--------------+ +--R | 2 +--R tanh(x)\|b csch(x) + a +--R atanh(------------------------) +--R +-+ +--R \|b +--R + +--R 2 3 6 2 3 5 +--R (- 4a b + 2a )sinh(x) + (- 24a b + 12a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 60a b + 30a )cosh(x) + 8a b - 6a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 80a b + 40a )cosh(x) + (32a b - 24a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 60a b + 30a )cosh(x) + (48a b - 36a )cosh(x) - 4a b +--R + +--R 3 +--R 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 24a b + 12a )cosh(x) + (32a b - 24a )cosh(x) +--R + +--R 2 3 +--R (- 8a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 4a b + 2a )cosh(x) + (8a b - 6a )cosh(x) +--R + +--R 2 3 2 3 +--R (- 4a b + 6a )cosh(x) - 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 3 8 +--R (4a b - 4a b + 2a )sinh(x) +--R + +--R 2 2 3 7 +--R (32a b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 3 2 2 2 3 6 +--R ((112a b - 112a b + 56a )cosh(x) - 8a b + 16a b - 8a )sinh(x) +--R + +--R 2 2 3 3 +--R (224a b - 224a b + 112a )cosh(x) +--R + +--R 2 2 3 +--R (- 48a b + 96a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (280a b - 280a b + 140a )cosh(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 120a b + 240a b - 120a )cosh(x) + 4a b - 20a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (224a b - 224a b + 112a )cosh(x) +--R + +--R 2 2 3 3 +--R (- 160a b + 320a b - 160a )cosh(x) +--R + +--R 2 2 3 +--R (16a b - 80a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 +--R (112a b - 112a b + 56a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 120a b + 240a b - 120a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (24a b - 120a b + 72a )cosh(x) + 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 +--R (32a b - 32a b + 16a )cosh(x) +--R + +--R 2 2 3 5 +--R (- 48a b + 96a b - 48a )cosh(x) +--R + +--R 2 2 3 3 2 3 +--R (16a b - 80a b + 48a )cosh(x) + (16a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 8 2 2 3 6 +--R (4a b - 4a b + 2a )cosh(x) + (- 8a b + 16a b - 8a )cosh(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (4a b - 20a b + 12a )cosh(x) + (8a b - 8a )cosh(x) + 2a +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R coth(x)\|a +--R atanh(-----------------) +--R +--------------+ +--R | 2 +--R \|b csch(x) + a +--R + +--R 2 2 6 +--R (4b - 14a b + 6a )sinh(x) +--R + +--R 2 2 5 +--R (24b - 84a b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((60b - 210a b + 90a )cosh(x) - 8b + 30a b - 18a )sinh(x) +--R + +--R 2 2 3 +--R (80b - 280a b + 120a )cosh(x) +--R + +--R 2 2 +--R (- 32b + 120a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 +--R (60b - 210a b + 90a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 48b + 180a b - 108a )cosh(x) + 4b - 18a b + 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (24b - 84a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 +--R (- 32b + 120a b - 72a )cosh(x) + (8b - 36a b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (4b - 14a b + 6a )cosh(x) + (- 8b + 30a b - 18a )cosh(x) +--R + +--R 2 2 2 2 +--R (4b - 18a b + 18a )cosh(x) + 2a b - 6a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +---+ +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|- b \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 4b + 16a b - 14a b + 6a )sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 32b + 128a b - 112a b + 48a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 112b + 448a b - 392a b + 168a )cosh(x) + 8b - 40a b +--R + +--R 2 3 +--R 56a b - 24a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 224b + 896a b - 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 +--R (48b - 240a b + 336a b - 144a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 280b + 1120a b - 980a b + 420a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (120b - 600a b + 840a b - 360a )cosh(x) - 4b + 32a b +--R + +--R 2 3 +--R - 72a b + 36a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 224b + 896a b - 784a b + 336a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (160b - 800a b + 1120a b - 480a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 16b + 128a b - 288a b + 144a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (- 112b + 448a b - 392a b + 168a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (120b - 600a b + 840a b - 360a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (- 24b + 192a b - 432a b + 216a )cosh(x) - 8a b + 32a b +--R + +--R 3 +--R - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (- 32b + 128a b - 112a b + 48a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (48b - 240a b + 336a b - 144a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 16b + 128a b - 288a b + 144a )cosh(x) +--R + +--R 2 2 3 +--R (- 16a b + 64a b - 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 8 +--R (- 4b + 16a b - 14a b + 6a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (8b - 40a b + 56a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 4b + 32a b - 72a b + 36a )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (- 8a b + 32a b - 24a )cosh(x) - 2a b + 6a +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a 2 +--R \|a |------------------------------------- + a sinh(x) +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) - a +--R / +--R 2 2 +---+ +-+ +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )\|- b \|a +--R + +--R 2 6 2 5 +--R (2b - a b)coth(x)sinh(x) + (12b - 6a b)cosh(x)coth(x)sinh(x) +--R + +--R 2 2 2 4 +--R ((30b - 15a b)cosh(x) - 4b + 3a b)coth(x)sinh(x) +--R + +--R 2 3 2 3 +--R ((40b - 20a b)cosh(x) + (- 16b + 12a b)cosh(x))coth(x)sinh(x) +--R + +--R 2 4 2 2 2 +--R (30b - 15a b)cosh(x) + (- 24b + 18a b)cosh(x) + 2b +--R + +--R - 3a b +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 2 5 2 3 +--R (12b - 6a b)cosh(x) + (- 16b + 12a b)cosh(x) +--R + +--R 2 +--R (4b - 6a b)cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 2 6 2 4 +--R (2b - a b)cosh(x) + (- 4b + 3a b)cosh(x) +--R + +--R 2 2 +--R (2b - 3a b)cosh(x) + a b +--R * +--R coth(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 +--R (- 2b + 2a b - a b)coth(x)sinh(x) +--R + +--R 3 2 2 7 +--R (- 16b + 16a b - 8a b)cosh(x)coth(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R ((- 56b + 56a b - 28a b)cosh(x) + 4b - 8a b + 4a b)coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 112b + 112a b - 56a b)cosh(x) +--R + +--R 3 2 2 +--R (24b - 48a b + 24a b)cosh(x) +--R * +--R 5 +--R coth(x)sinh(x) +--R + +--R 3 2 2 4 +--R (- 140b + 140a b - 70a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (60b - 120a b + 60a b)cosh(x) - 2b + 10a b - 6a b +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 3 2 2 5 +--R (- 112b + 112a b - 56a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (80b - 160a b + 80a b)cosh(x) + (- 8b + 40a b - 24a b)cosh(x) +--R * +--R 3 +--R coth(x)sinh(x) +--R + +--R 3 2 2 6 +--R (- 56b + 56a b - 28a b)cosh(x) +--R + +--R 3 2 2 4 +--R (60b - 120a b + 60a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 12b + 60a b - 36a b)cosh(x) - 4a b + 4a b +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 3 2 2 7 +--R (- 16b + 16a b - 8a b)cosh(x) +--R + +--R 3 2 2 5 +--R (24b - 48a b + 24a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 8b + 40a b - 24a b)cosh(x) + (- 8a b + 8a b)cosh(x) +--R * +--R coth(x)sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (- 2b + 2a b - a b)cosh(x) + (4b - 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 2 +--R (- 2b + 10a b - 6a b)cosh(x) + (- 4a b + 4a b)cosh(x) - a b +--R * +--R coth(x) +--R * +--R +--------------+ +--R | 2 +--R \|b csch(x) + a +--R + +--R 3 2 2 6 3 2 2 5 +--R (2b - 4a b + 2a b)sinh(x) + (12b - 24a b + 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 4 +--R ((30b - 60a b + 30a b)cosh(x) + 2b + 6a b - 4a b)sinh(x) +--R + +--R 3 2 2 3 3 2 2 +--R ((40b - 80a b + 40a b)cosh(x) + (8b + 24a b - 16a b)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (30b - 60a b + 30a b)cosh(x) + (12b + 36a b - 24a b)cosh(x) +--R + +--R 2 2 +--R 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 5 3 2 2 3 +--R (12b - 24a b + 12a b)cosh(x) + (8b + 24a b - 16a b)cosh(x) +--R + +--R 2 2 +--R (4a b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (2b - 4a b + 2a b)cosh(x) + (2b + 6a b - 4a b)cosh(x) +--R + +--R 2 2 2 +--R (2a b + 2a b)cosh(x) +--R * +--R +-------------------------------------+ +--R | 2 2 +--R | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (2b - 4a b + 2a b)sinh(x) + (16b - 32a b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 6 +--R ((56b - 112a b + 56a b)cosh(x) - 12b + 14a b - 6a b)sinh(x) +--R + +--R 3 2 2 3 +--R (112b - 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 +--R (- 72b + 84a b - 36a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (140b - 280a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 180b + 210a b - 90a b)cosh(x) - 6b - 8a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (112b - 224a b + 112a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 240b + 280a b - 120a b)cosh(x) +--R + +--R 3 2 2 +--R (- 24b - 32a b + 24a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (56b - 112a b + 56a b)cosh(x) +--R + +--R 3 2 2 4 +--R (- 180b + 210a b - 90a b)cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (- 36b - 48a b + 36a b)cosh(x) - 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 +--R (16b - 32a b + 16a b)cosh(x) +--R + +--R 3 2 2 5 +--R (- 72b + 84a b - 36a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 24b - 32a b + 24a b)cosh(x) + (- 4a b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 6 +--R (2b - 4a b + 2a b)cosh(x) + (- 12b + 14a b - 6a b)cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (- 6b - 8a b + 6a b)cosh(x) + (- 2a b - 2a b)cosh(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 5 +--R (4b - 2a)sinh(x) + (24b - 12a)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((60b - 30a)cosh(x) - 8b + 6a)sinh(x) +--R + +--R 3 3 +--R ((80b - 40a)cosh(x) + (- 32b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((60b - 30a)cosh(x) + (- 48b + 36a)cosh(x) + 4b - 6a)sinh(x) +--R + +--R 5 3 +--R ((24b - 12a)cosh(x) + (- 32b + 24a)cosh(x) + (8b - 12a)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (4b - 2a)cosh(x) + (- 8b + 6a)cosh(x) + (4b - 6a)cosh(x) + 2a +--R * +--R +-------------------------------------+ +--R | 2 2 +--R +-+ | 2a sinh(x) + 2a cosh(x) + 4b - 2a +--R \|a |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 4b + 4a b - 2a )sinh(x) + (- 32b + 32a b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((- 112b + 112a b - 56a )cosh(x) + 8b - 16a b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 224b + 224a b - 112a )cosh(x) + (48b - 96a b + 48a )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 280b + 280a b - 140a )cosh(x) + (120b - 240a b + 120a )cosh(x) +--R + +--R 2 2 +--R - 4b + 20a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 224b + 224a b - 112a )cosh(x) + (160b - 320a b + 160a )cosh(x) +--R + +--R 2 2 +--R (- 16b + 80a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 112b + 112a b - 56a )cosh(x) + (120b - 240a b + 120a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 24b + 120a b - 72a )cosh(x) - 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 32b + 32a b - 16a )cosh(x) + (48b - 96a b + 48a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 16b + 80a b - 48a )cosh(x) + (- 16a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (- 4b + 4a b - 2a )cosh(x) + (8b - 16a b + 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 4b + 20a b - 12a )cosh(x) + (- 8a b + 8a )cosh(x) - 2a +--R Type: Expression(Integer) +--E 440 + +--S 441 of 526 +--d0482b:= D(m0482b,x) +--E 441 + +--S 442 of 526 +t0483:= x/csch(x)^(3/2)+1/3*x*csch(x)^(1/2) +--R +--R +--R 2 +--R x csch(x) + 3x +--R (344) ------------------ +--R +-------+ +--R 3csch(x)\|csch(x) +--R Type: Expression(Integer) +--E 442 + +--S 443 of 526 +r0483:= -2/9*(2*sinh(x)-3*x*cosh(x))/(1/sinh(x))^(1/2) +--R +--R +--R - 4sinh(x) + 6x cosh(x) +--R (345) ----------------------- +--R +-------+ +--R | 1 +--R 9 |------- +--R \|sinh(x) +--R Type: Expression(Integer) +--E 443 + +--S 444 of 526 +a0483:= integrate(t0483,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 444 + +--S 445 of 526 +m0483:= a0483-r0483 +--R +--R +--R +-------+ +--R | 1 +--R 9a0483 |------- + 4sinh(x) - 6x cosh(x) +--R \|sinh(x) +--R (346) ---------------------------------------- +--R +-------+ +--R | 1 +--R 9 |------- +--R \|sinh(x) +--R Type: Expression(Integer) +--E 445 + +--S 446 of 526 +d0483:= D(m0483,x) +--R +--R +--R 2 2 +--R - 2x sinh(x) - x cosh(x) +--R (347) -------------------------- +--R +-------+ +--R | 1 +--R 3sinh(x) |------- +--R \|sinh(x) +--R Type: Expression(Integer) +--E 446 + +--S 447 of 526 +t0484:= x/csch(x)^(5/2)+3/5*x/csch(x)^(1/2) +--R +--R +--R 2 +--R 3x csch(x) + 5x +--R (348) ------------------- +--R 2 +-------+ +--R 5csch(x) \|csch(x) +--R Type: Expression(Integer) +--E 447 + +--S 448 of 526 +r0484:= -4/25/csch(x)^(5/2)+2/5*x*cosh(x)/csch(x)^(3/2) +--R +--R +--R 10x cosh(x)csch(x) - 4 +--R (349) ---------------------- +--R 2 +-------+ +--R 25csch(x) \|csch(x) +--R Type: Expression(Integer) +--E 448 + +--S 449 of 526 +a0484:= integrate(t0484,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 449 + +--S 450 of 526 +--m0484:= a0484-r0484 +--E 450 + +--S 451 of 526 +--d0484:= D(m0484,x) +--E 451 + +--S 452 of 526 +t0485:= x/csch(x)^(7/2)-5/21*x*csch(x)^(1/2) +--R +--R +--R 4 +--R - 5x csch(x) + 21x +--R (350) -------------------- +--R 3 +-------+ +--R 21csch(x) \|csch(x) +--R Type: Expression(Integer) +--E 452 + +--S 453 of 526 +r0485:= -2/441*(-88*sinh(x)+18*sinh(x)*cosh(x)^2+168*x*cosh(x)-_ + 63*x*cosh(x)^3)/(1/sinh(x))^(1/2) +--R +--R +--R 2 3 +--R (- 36cosh(x) + 176)sinh(x) + 126x cosh(x) - 336x cosh(x) +--R (351) ---------------------------------------------------------- +--R +-------+ +--R | 1 +--R 441 |------- +--R \|sinh(x) +--R Type: Expression(Integer) +--E 453 + +--S 454 of 526 +a0485:= integrate(t0485,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 454 + +--S 455 of 526 +--m0485:= a0485-r0485 +--E 455 + +--S 456 of 526 +--d0485:= D(m0485,x) +--E 456 + +--S 457 of 526 +t0486:= x^2/csch(x)^(3/2)+1/3*x^2*csch(x)^(1/2) +--R +--R +--R 2 2 2 +--R x csch(x) + 3x +--R (352) ------------------ +--R +-------+ +--R 3csch(x)\|csch(x) +--R Type: Expression(Integer) +--E 457 + +--S 458 of 526 +r0486:= 2/27*(12*x-12*x*cosh(x)^2+8*cosh(x)*sinh(x)+9*x^2*cosh(x)*sinh(x)+_ + 8*%i*EllipticF(-1/4*%pi+1/2*%i*x,2)*_ + (%i*sinh(x))^(1/2))/sinh(x)/(1/sinh(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 458 + +--S 459 of 526 +a0486:= integrate(t0486,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 459 + +--S 460 of 526 +--m0486:= a0486-r0486 +--E 460 + +--S 461 of 526 +--d0486:= D(m0486,x) +--E 461 + +--S 462 of 526 +t0487:= sinh(x)/(a+b*sinh(x)) +--R +--R +--R sinh(x) +--R (353) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 462 + +--S 463 of 526 +r0487:= x/b+2*a*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/b/(a^2+b^2)^(1/2) +--R +--R +--R x +--R a tanh(-) - b +-------+ +--R 2 | 2 2 +--R - 2a atanh(-------------) + x\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (354) --------------------------------------- +--R +-------+ +--R | 2 2 +--R b\|b + a +--R Type: Expression(Integer) +--E 463 + +--S 464 of 526 +a0487:= integrate(t0487,x) +--R +--R +--R (355) +--R a +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R +-------+ +--R | 2 2 +--R x\|b + a +--R / +--R +-------+ +--R | 2 2 +--R b\|b + a +--R Type: Union(Expression(Integer),...) +--E 464 + +--S 465 of 526 +m0487:= a0487-r0487 +--R +--R +--R (356) +--R a +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R x +--R a tanh(-) - b +--R 2 +--R 2a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R | 2 2 +--R b\|b + a +--R Type: Expression(Integer) +--E 465 + +--S 466 of 526 +d0487:= D(m0487,x) +--R +--R +--R (357) +--R 2 2 x 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a)tanh(-) +--R 2 +--R + +--R x 2 +--R (4a sinh(x) + 4a cosh(x))tanh(-) - a sinh(x) - 2a cosh(x)sinh(x) +--R 2 +--R + +--R 2 +--R - a cosh(x) + a +--R / +--R 2 2 2 +--R a b sinh(x) + (2a b cosh(x) + 2a )sinh(x) + a b cosh(x) +--R + +--R 2 +--R 2a cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 2 +--R - 2b sinh(x) + (- 4b cosh(x) - 4a b)sinh(x) - 2b cosh(x) +--R + +--R 2 +--R - 4a b cosh(x) + 2b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 2 2 +--R - a b sinh(x) + (- 2a b cosh(x) - 2a )sinh(x) - a b cosh(x) +--R + +--R 2 +--R - 2a cosh(x) + a b +--R Type: Expression(Integer) +--E 466 + +--S 467 of 526 +t0488:= sinh(x)^2/(a+b*sinh(x)) +--R +--R +--R 2 +--R sinh(x) +--R (358) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 526 +r0488:= -a*x/b^2-2*a^2*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/_ + b^2/(a^2+b^2)^(1/2)+cosh(x)/b +--R +--R +--R x +--R a tanh(-) - b +-------+ +--R 2 2 | 2 2 +--R 2a atanh(-------------) + (b cosh(x) - a x)\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (359) ----------------------------------------------------- +--R +-------+ +--R 2 | 2 2 +--R b \|b + a +--R Type: Expression(Integer) +--E 468 + +--S 469 of 526 +a0488:= integrate(t0488,x) +--R +--R +--R (360) +--R 2 2 +--R (2a sinh(x) + 2a cosh(x)) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 2 +--R b sinh(x) + (2b cosh(x) - 2a x)sinh(x) + b cosh(x) - 2a x cosh(x) +--R + +--R b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|b + a +--R Type: Union(Expression(Integer),...) +--E 469 + +--S 470 of 526 +m0488:= a0488-r0488 +--R +--R +--R (361) +--R 2 2 +--R (2a sinh(x) + 2a cosh(x)) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R x +--R a tanh(-) - b +--R 2 2 2 +--R (- 4a sinh(x) - 4a cosh(x))atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (b sinh(x) - b cosh(x) + b)\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|b + a +--R Type: Expression(Integer) +--E 470 + +--S 471 of 526 +d0488:= D(m0488,x) +--R +--R +--R (362) +--R 4 2 3 2 2 +--R - a b sinh(x) + (- 2a b cosh(x) - 4a )sinh(x) - 8a cosh(x)sinh(x) +--R + +--R 3 2 2 4 +--R (2a b cosh(x) - 4a cosh(x) - 2a b cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R 2b sinh(x) + (4b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 +--R (4a b cosh(x) - 8a )sinh(x) +--R + +--R 2 3 2 2 2 +--R (- 4b cosh(x) - 4a b cosh(x) + (4b - 16a )cosh(x) + 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 +--R - 2b cosh(x) - 4a b cosh(x) + (4b - 8a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - 2b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 3 2 2 +--R a b sinh(x) + (2a b cosh(x) + 4a )sinh(x) + 8a cosh(x)sinh(x) +--R + +--R 3 2 2 4 +--R (- 2a b cosh(x) + 4a cosh(x) + 2a b cosh(x))sinh(x) - a b cosh(x) +--R + +--R 2 +--R 2a b cosh(x) - a b +--R / +--R 2 3 2 2 2 +--R 2a b sinh(x) + (6a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (6a b cosh(x) + 8a b cosh(x) - 2a b )sinh(x) + 2a b cosh(x) +--R + +--R 2 2 2 +--R 4a b cosh(x) - 2a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 3 2 2 +--R - 4b sinh(x) + (- 12b cosh(x) - 8a b )sinh(x) +--R + +--R 3 2 2 3 3 3 +--R (- 12b cosh(x) - 16a b cosh(x) + 4b )sinh(x) - 4b cosh(x) +--R + +--R 2 2 3 +--R - 8a b cosh(x) + 4b cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3 2 2 2 +--R - 2a b sinh(x) + (- 6a b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 6a b cosh(x) - 8a b cosh(x) + 2a b )sinh(x) - 2a b cosh(x) +--R + +--R 2 2 2 +--R - 4a b cosh(x) + 2a b cosh(x) +--R Type: Expression(Integer) +--E 471 + +--S 472 of 526 +t0489:= sinh(x)^3/(a+b*sinh(x)) +--R +--R +--R 3 +--R sinh(x) +--R (363) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 526 +r0489:= a^2*x/b^3-1/2*x/b+2*a^3*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/_ + b^3/(a^2+b^2)^(1/2)-a*cosh(x)/b^2+1/2*cosh(x)*sinh(x)/b +--R +--R +--R (364) +--R x +--R a tanh(-) - b +--R 3 2 +--R - 4a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (b cosh(x)sinh(x) - 2a b cosh(x) + (- b + 2a )x)\|b + a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2b \|b + a +--R Type: Expression(Integer) +--E 473 + +--S 474 of 526 +a0489:= integrate(t0489,x) +--R +--R +--R (365) +--R 3 2 3 3 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 4 2 3 +--R b sinh(x) + (4b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6b cosh(x) - 12a b cosh(x) + (- 4b + 8a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4b cosh(x) - 12a b cosh(x) + (- 8b + 16a )x cosh(x) - 4a b) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 +--R b cosh(x) - 4a b cosh(x) + (- 4b + 8a )x cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R - b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b + a +--R Type: Union(Expression(Integer),...) +--E 474 + +--S 475 of 526 +m0489:= a0489-r0489 +--R +--R +--R (366) +--R 3 2 3 3 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R x +--R a tanh(-) - b +--R 3 2 3 3 2 2 +--R (16a sinh(x) + 32a cosh(x)sinh(x) + 16a cosh(x) )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 3 2 2 2 +--R b sinh(x) - 4a b sinh(x) + (- 2b cosh(x) - 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (4a b cosh(x) - 4a b)sinh(x) + b cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - 4a b cosh(x) - b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b + a +--R Type: Expression(Integer) +--E 475 + +--S 476 of 526 +d0489:= D(m0489,x) +--R +--R +--R (367) +--R 2 6 2 5 +--R - a b sinh(x) - 2a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 4 +--R (a b cosh(x) + 4a b cosh(x) + a b + 8a )sinh(x) +--R + +--R 2 3 2 2 3 3 +--R (4a b cosh(x) + 8a b cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 2 4 2 3 2 2 2 +--R (a b cosh(x) + (- 2a b + 24a )cosh(x) + 4a b cosh(x) + a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 3 3 2 2 +--R - 2a b cosh(x) - 8a b cosh(x) + 8a cosh(x) + 8a b cosh(x) +--R + +--R 2 +--R 2a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - a b cosh(x) - 4a b cosh(x) + a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 +--R a b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 5 +--R 2b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (- 2b cosh(x) - 8a b cosh(x) - 2b - 8a b)sinh(x) +--R + +--R 3 3 2 2 2 3 3 +--R (- 8b cosh(x) - 16a b cosh(x) - 16a b cosh(x) + 16a )sinh(x) +--R + +--R 3 4 3 2 2 3 3 +--R - 2b cosh(x) + 4b cosh(x) + (- 8a b + 48a )cosh(x) - 2b +--R + +--R 2 +--R - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 +--R 4b cosh(x) + 16a b cosh(x) + 16a b cosh(x) +--R + +--R 2 3 2 3 2 +--R (- 16a b + 48a )cosh(x) + (- 4b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R 2b cosh(x) + 8a b cosh(x) + (- 2b + 8a b)cosh(x) +--R + +--R 2 3 3 3 2 2 3 +--R (- 8a b + 16a )cosh(x) + (- 2b - 8a b)cosh(x) + 2b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 5 +--R a b sinh(x) + 2a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 4 +--R (- a b cosh(x) - 4a b cosh(x) - a b - 8a )sinh(x) +--R + +--R 2 3 2 2 3 3 +--R (- 4a b cosh(x) - 8a b cosh(x) - 24a cosh(x))sinh(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- a b cosh(x) + (2a b - 24a )cosh(x) - 4a b cosh(x) - a b )sinh(x) +--R + +--R 2 5 2 4 3 3 2 2 +--R 2a b cosh(x) + 8a b cosh(x) - 8a cosh(x) - 8a b cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R a b cosh(x) + 4a b cosh(x) - a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 +--R - a b cosh(x) + a b +--R / +--R 3 4 3 2 2 3 +--R 4a b sinh(x) + (16a b cosh(x) + 8a b )sinh(x) +--R + +--R 3 2 2 2 3 2 +--R (24a b cosh(x) + 24a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R (16a b cosh(x) + 24a b cosh(x) - 8a b cosh(x))sinh(x) +--R + +--R 3 4 2 2 3 3 2 +--R 4a b cosh(x) + 8a b cosh(x) - 4a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 4 4 3 3 +--R - 8b sinh(x) + (- 32b cosh(x) - 16a b )sinh(x) +--R + +--R 4 2 3 4 2 +--R (- 48b cosh(x) - 48a b cosh(x) + 8b )sinh(x) +--R + +--R 4 3 3 2 4 4 4 +--R (- 32b cosh(x) - 48a b cosh(x) + 16b cosh(x))sinh(x) - 8b cosh(x) +--R + +--R 3 3 4 2 +--R - 16a b cosh(x) + 8b cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 4 3 2 2 3 +--R - 4a b sinh(x) + (- 16a b cosh(x) - 8a b )sinh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 24a b cosh(x) - 24a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 3 2 2 2 3 3 4 +--R (- 16a b cosh(x) - 24a b cosh(x) + 8a b cosh(x))sinh(x) - 4a b cosh(x) +--R + +--R 2 2 3 3 2 +--R - 8a b cosh(x) + 4a b cosh(x) +--R Type: Expression(Integer) +--E 476 + +--S 477 of 526 +t0490:= sinh(x)^4/(a+b*sinh(x)) +--R +--R +--R 4 +--R sinh(x) +--R (368) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 526 +r0490:= -a^3*x/b^4+1/2*a*x/b^2-2*a^4*atanh((b-a*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/b^4/(a^2+b^2)^(1/2)+a^2*cosh(x)/b^3-_ + cosh(x)/b+1/3*cosh(x)^3/b-1/2*a*cosh(x)*sinh(x)/b^2 +--R +--R +--R (369) +--R x +--R a tanh(-) - b +--R 4 2 +--R 12a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 3 3 2 +--R - 3a b cosh(x)sinh(x) + 2b cosh(x) + (- 6b + 6a b)cosh(x) +--R + +--R 2 3 +--R (3a b - 6a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6b \|b + a +--R Type: Expression(Integer) +--E 478 + +--S 479 of 526 +a0490:= integrate(t0490,x) +--R +--R +--R (370) +--R 4 3 4 2 4 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 4 3 +--R 24a cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 6 3 2 5 +--R b sinh(x) + (6b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (15b cosh(x) - 15a b cosh(x) - 9b + 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 +--R 20b cosh(x) - 30a b cosh(x) + (- 36b + 48a b)cosh(x) +--R + +--R 2 3 +--R (12a b - 24a )x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 15b cosh(x) - 30a b cosh(x) + (- 54b + 72a b)cosh(x) +--R + +--R 2 3 3 2 +--R (36a b - 72a )x cosh(x) - 9b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 15a b cosh(x) + (- 36b + 48a b)cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (36a b - 72a )x cosh(x) + (- 18b + 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R b cosh(x) - 3a b cosh(x) + (- 9b + 12a b)cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (12a b - 24a )x cosh(x) + (- 9b + 12a b)cosh(x) + 3a b cosh(x) + b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 479 + +--S 480 of 526 +m0490:= a0490-r0490 +--R +--R +--R (371) +--R 4 3 4 2 4 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 4 3 +--R 24a cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 3 4 2 4 2 +--R - 48a sinh(x) - 144a cosh(x)sinh(x) - 144a cosh(x) sinh(x) +--R + +--R 4 3 +--R - 48a cosh(x) +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 6 3 2 5 +--R b sinh(x) + (6b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (15b cosh(x) - 3a b cosh(x) - 9b + 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 3 +--R (12b cosh(x) + 6a b cosh(x) + (- 12b + 24a b)cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 3 2 2 +--R (- 9b cosh(x) + 6a b cosh(x) + 18b cosh(x) - 9b + 12a b)sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R - 18b cosh(x) - 3a b cosh(x) + (36b - 24a b)cosh(x) +--R + +--R 3 2 2 +--R (- 18b + 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R - 7b cosh(x) - 3a b cosh(x) + (15b - 12a b)cosh(x) +--R + +--R 3 2 2 2 3 +--R (- 9b + 12a b)cosh(x) + 3a b cosh(x) + b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 480 + +--S 481 of 526 +d0490:= D(m0490,x) +--R +--R +--R (372) +--R 3 8 3 2 2 7 +--R a b sinh(x) + (8a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 2 2 2 3 6 +--R (20a b cosh(x) + 20a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 3 2 2 2 3 3 2 2 +--R 16a b cosh(x) + 28a b cosh(x) + (16a b - 8a b)cosh(x) + 8a b +--R + +--R 4 +--R - 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R - 10a b cosh(x) - 4a b cosh(x) + (28a b - 24a b)cosh(x) +--R + +--R 2 2 4 3 +--R (32a b - 64a )cosh(x) - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 2 2 4 3 3 3 +--R - 24a b cosh(x) - 36a b cosh(x) + (24a b - 16a b)cosh(x) +--R + +--R 2 2 4 2 3 2 2 +--R (40a b - 96a )cosh(x) - 8a b cosh(x) + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 2 2 5 3 3 4 +--R - 12a b cosh(x) - 20a b cosh(x) + (4a b + 16a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 2 2 +--R (8a b - 64a )cosh(x) + (12a b - 24a b)cosh(x) + 12a b cosh(x) +--R + +--R 3 +--R - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 6 3 3 5 +--R 4a b cosh(x) + (- 8a b + 24a b)cosh(x) +--R + +--R 2 2 4 4 3 3 3 +--R (- 16a b - 16a )cosh(x) + (16a b - 24a b)cosh(x) +--R + +--R 2 2 2 3 +--R 12a b cosh(x) - 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 2 2 7 3 3 6 +--R a b cosh(x) + 4a b cosh(x) + (- 4a b + 8a b)cosh(x) +--R + +--R 2 2 5 3 3 4 2 2 3 +--R - 8a b cosh(x) + (6a b - 8a b)cosh(x) + 4a b cosh(x) +--R + +--R 3 2 3 +--R - 4a b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 8 4 3 7 +--R - 2b sinh(x) + (- 16b cosh(x) - 8a b )sinh(x) +--R + +--R 4 2 3 4 6 +--R (- 40b cosh(x) - 40a b cosh(x) - 8b )sinh(x) +--R + +--R 4 3 3 2 4 2 2 +--R - 32b cosh(x) - 56a b cosh(x) + (- 32b + 16a b )cosh(x) +--R + +--R 3 3 +--R - 16a b + 16a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 4 2 2 2 +--R 20b cosh(x) + 8a b cosh(x) + (- 56b + 48a b )cosh(x) +--R + +--R 3 3 4 4 +--R (- 64a b + 48a b)cosh(x) + 4b - 32a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 4 2 2 3 +--R 48b cosh(x) + 72a b cosh(x) + (- 48b + 32a b )cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (- 80a b + 32a b)cosh(x) + (16a b - 128a )cosh(x) - 8a b +--R + +--R 3 +--R 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 4 2 2 4 +--R 24b cosh(x) + 40a b cosh(x) + (- 8b - 32a b )cosh(x) +--R + +--R 3 3 3 4 2 2 4 2 +--R (- 16a b - 32a b)cosh(x) + (- 24b + 48a b - 192a )cosh(x) +--R + +--R 3 3 4 +--R (- 24a b + 48a b)cosh(x) + 8b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 4 2 2 5 +--R - 8a b cosh(x) + (16b - 48a b )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (32a b - 48a b)cosh(x) + (- 32b + 48a b - 128a )cosh(x) +--R + +--R 3 3 2 4 +--R (- 24a b + 48a b)cosh(x) + 16b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 8 3 7 4 2 2 6 +--R - 2b cosh(x) - 8a b cosh(x) + (8b - 16a b )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (16a b - 16a b)cosh(x) + (- 12b + 16a b - 32a )cosh(x) +--R + +--R 3 3 3 4 2 4 +--R (- 8a b + 16a b)cosh(x) + 8b cosh(x) - 2b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 8 3 2 2 7 +--R - a b sinh(x) + (- 8a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 2 2 2 3 6 +--R (- 20a b cosh(x) - 20a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 2 2 2 3 3 2 2 +--R - 16a b cosh(x) - 28a b cosh(x) + (- 16a b + 8a b)cosh(x) - 8a b +--R + +--R 4 +--R 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R 10a b cosh(x) + 4a b cosh(x) + (- 28a b + 24a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 32a b + 64a )cosh(x) + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 2 2 4 3 3 3 +--R 24a b cosh(x) + 36a b cosh(x) + (- 24a b + 16a b)cosh(x) +--R + +--R 2 2 4 2 3 2 2 +--R (- 40a b + 96a )cosh(x) + 8a b cosh(x) - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 2 2 5 3 3 4 +--R 12a b cosh(x) + 20a b cosh(x) + (- 4a b - 16a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 2 2 +--R (- 8a b + 64a )cosh(x) + (- 12a b + 24a b)cosh(x) - 12a b cosh(x) +--R + +--R 3 +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 6 3 3 5 2 2 4 4 +--R - 4a b cosh(x) + (8a b - 24a b)cosh(x) + (16a b + 16a )cosh(x) +--R + +--R 3 3 3 2 2 2 3 +--R (- 16a b + 24a b)cosh(x) - 12a b cosh(x) + 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 2 2 7 3 3 6 2 2 5 +--R - a b cosh(x) - 4a b cosh(x) + (4a b - 8a b)cosh(x) + 8a b cosh(x) +--R + +--R 3 3 4 2 2 3 3 2 3 +--R (- 6a b + 8a b)cosh(x) - 4a b cosh(x) + 4a b cosh(x) - a b +--R / +--R 4 5 4 2 3 4 +--R 8a b sinh(x) + (40a b cosh(x) + 16a b )sinh(x) +--R + +--R 4 2 2 3 4 3 +--R (80a b cosh(x) + 64a b cosh(x) - 8a b )sinh(x) +--R + +--R 4 3 2 3 2 4 2 +--R (80a b cosh(x) + 96a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 4 4 2 3 3 4 2 +--R (40a b cosh(x) + 64a b cosh(x) - 24a b cosh(x) )sinh(x) +--R + +--R 4 5 2 3 4 4 3 +--R 8a b cosh(x) + 16a b cosh(x) - 8a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 5 5 4 4 +--R - 16b sinh(x) + (- 80b cosh(x) - 32a b )sinh(x) +--R + +--R 5 2 4 5 3 +--R (- 160b cosh(x) - 128a b cosh(x) + 16b )sinh(x) +--R + +--R 5 3 4 2 5 2 +--R (- 160b cosh(x) - 192a b cosh(x) + 48b cosh(x))sinh(x) +--R + +--R 5 4 4 3 5 2 +--R (- 80b cosh(x) - 128a b cosh(x) + 48b cosh(x) )sinh(x) +--R + +--R 5 5 4 4 5 3 +--R - 16b cosh(x) - 32a b cosh(x) + 16b cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 5 4 2 3 4 +--R - 8a b sinh(x) + (- 40a b cosh(x) - 16a b )sinh(x) +--R + +--R 4 2 2 3 4 3 +--R (- 80a b cosh(x) - 64a b cosh(x) + 8a b )sinh(x) +--R + +--R 4 3 2 3 2 4 2 +--R (- 80a b cosh(x) - 96a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 4 4 2 3 3 4 2 +--R (- 40a b cosh(x) - 64a b cosh(x) + 24a b cosh(x) )sinh(x) +--R + +--R 4 5 2 3 4 4 3 +--R - 8a b cosh(x) - 16a b cosh(x) + 8a b cosh(x) +--R Type: Expression(Integer) +--E 481 + +--S 482 of 526 +t0491:= sinh(x)/(%i+sinh(x)) +--R +--R +--R sinh(x) +--R (373) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 482 + +--S 483 of 526 +r0491:= x+%i*cosh(x)/(1-%i*sinh(x)) +--R +--R +--R x sinh(x) - cosh(x) + %i x +--R (374) -------------------------- +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 483 + +--S 484 of 526 +a0491:= integrate(t0491,x) +--R +--R +--R x sinh(x) + x cosh(x) + %i x + 2%i +--R (375) ---------------------------------- +--R sinh(x) + cosh(x) + %i +--R Type: Union(Expression(Complex(Integer)),...) +--E 484 + +--S 485 of 526 +m0491:= a0491-r0491 +--R +--R +--R 2 +--R (cosh(x) + 2%i)sinh(x) + cosh(x) + %i cosh(x) - 2 +--R (376) -------------------------------------------------- +--R 2 +--R sinh(x) + (cosh(x) + 2%i)sinh(x) + %i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 485 + +--S 486 of 526 +d0491:= D(m0491,x) +--R +--R +--R (377) +--R 4 3 2 +--R sinh(x) + (2cosh(x) + %i)sinh(x) + (2%i cosh(x) + 1)sinh(x) +--R + +--R 3 2 4 +--R (- 2cosh(x) - %i cosh(x) + 2cosh(x) + %i)sinh(x) - cosh(x) +--R + +--R 3 2 +--R - 2%i cosh(x) + cosh(x) + 2%i cosh(x) +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) + 4%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) + 6%i cosh(x) - 6)sinh(x) +--R + +--R 2 2 +--R (2%i cosh(x) - 6cosh(x) - 4%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 486 + +--S 487 of 526 +t0492:= sinh(x)^2/(%i+sinh(x)) +--R +--R +--R 2 +--R sinh(x) +--R (378) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 487 + +--S 488 of 526 +r0492:= -%i*x+cosh(x)+cosh(x)/(1-%i*sinh(x)) +--R +--R +--R (cosh(x) - %i x)sinh(x) + 2%i cosh(x) + x +--R (379) ----------------------------------------- +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 488 + +--S 489 of 526 +a0492:= integrate(t0492,x) +--R +--R +--R (380) +--R 2 2 +--R sinh(x) + (2cosh(x) - 2%i x)sinh(x) + cosh(x) + (- 2%i x + 2%i)cosh(x) +--R + +--R 2x + 5 +--R / +--R 2sinh(x) + 2cosh(x) + 2%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 489 + +--S 490 of 526 +m0492:= a0492-r0492 +--R +--R +--R (381) +--R 3 2 2 +--R sinh(x) + %i sinh(x) + (- cosh(x) - 2%i cosh(x) + 5)sinh(x) +--R + +--R 2 +--R - 3%i cosh(x) + 2cosh(x) + 5%i +--R / +--R 2 +--R 2sinh(x) + (2cosh(x) + 4%i)sinh(x) + 2%i cosh(x) - 2 +--R Type: Expression(Complex(Integer)) +--E 490 + +--S 491 of 526 +d0492:= D(m0492,x) +--R +--R +--R (382) +--R 5 4 +--R - sinh(x) + (- cosh(x) - 4%i)sinh(x) +--R + +--R 2 3 +--R (cosh(x) - 6%i cosh(x) + 2)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) + 2%i cosh(x) + 4cosh(x) - 4%i)sinh(x) +--R + +--R 3 2 4 +--R (6%i cosh(x) - 3cosh(x) - 6%i cosh(x) + 3)sinh(x) + 2%i cosh(x) +--R + +--R 3 2 +--R - 5cosh(x) - 2%i cosh(x) + 5cosh(x) +--R / +--R 4 3 +--R 2sinh(x) + (4cosh(x) + 8%i)sinh(x) +--R + +--R 2 2 +--R (2cosh(x) + 12%i cosh(x) - 12)sinh(x) +--R + +--R 2 2 +--R (4%i cosh(x) - 12cosh(x) - 8%i)sinh(x) - 2cosh(x) - 4%i cosh(x) + 2 +--R Type: Expression(Complex(Integer)) +--E 491 + +--S 492 of 526 +t0493:= sinh(x)^3/(%i+sinh(x)) +--R +--R +--R 3 +--R sinh(x) +--R (383) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 492 + +--S 493 of 526 +r0493:= -3/2*x-%i*cosh(x)-%i*cosh(x)/(1-%i*sinh(x))+1/2*cosh(x)*sinh(x) +--R +--R +--R 2 +--R cosh(x)sinh(x) + (- %i cosh(x) - 3x)sinh(x) + 4cosh(x) - 3%i x +--R (384) --------------------------------------------------------------- +--R 2sinh(x) + 2%i +--R Type: Expression(Complex(Integer)) +--E 493 + +--S 494 of 526 +a0493:= integrate(t0493,x) +--R +--R +--R (385) +--R 3 2 +--R sinh(x) + (3cosh(x) - 4%i)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4%i cosh(x) - 12x + 1)sinh(x) + cosh(x) - 4%i cosh(x) +--R + +--R (- 12x + 7)cosh(x) - 12%i x - 20%i +--R / +--R 8sinh(x) + 8cosh(x) + 8%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 494 + +--S 495 of 526 +m0493:= a0493-r0493 +--R +--R +--R (386) +--R 4 3 +--R sinh(x) + (- cosh(x) - 3%i)sinh(x) +--R + +--R 2 2 +--R (- cosh(x) - %i cosh(x) + 5)sinh(x) +--R + +--R 3 2 3 +--R (cosh(x) + 3%i cosh(x) - 9cosh(x) - 19%i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - 12cosh(x) - 9%i cosh(x) + 20 +--R / +--R 2 +--R 8sinh(x) + (8cosh(x) + 16%i)sinh(x) + 8%i cosh(x) - 8 +--R Type: Expression(Complex(Integer)) +--E 495 + +--S 496 of 526 +d0493:= D(m0493,x) +--R +--R +--R (387) +--R 6 5 2 4 +--R - 2sinh(x) - %i sinh(x) + (4cosh(x) + 5%i cosh(x) - 14)sinh(x) +--R + +--R 2 3 +--R (5%i cosh(x) - 26cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 2 2 +--R (- 2cosh(x) - 5%i cosh(x) + 4cosh(x) - 16%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R (- 4%i cosh(x) + 26cosh(x) + 15%i cosh(x) - 26cosh(x) - 11%i)sinh(x) +--R + +--R 4 3 2 +--R 10cosh(x) + 21%i cosh(x) - 10cosh(x) - 21%i cosh(x) +--R / +--R 4 3 +--R 8sinh(x) + (16cosh(x) + 32%i)sinh(x) +--R + +--R 2 2 +--R (8cosh(x) + 48%i cosh(x) - 48)sinh(x) +--R + +--R 2 2 +--R (16%i cosh(x) - 48cosh(x) - 32%i)sinh(x) - 8cosh(x) - 16%i cosh(x) + 8 +--R Type: Expression(Complex(Integer)) +--E 496 + +--S 497 of 526 +t0494:= sinh(x)^4/(%i+sinh(x)) +--R +--R +--R 4 +--R sinh(x) +--R (388) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 497 + +--S 498 of 526 +r0494:= 3/2*%i*x-2*cosh(x)+1/3*cosh(x)^3-cosh(x)/(1-%i*sinh(x))-_ + 1/2*%i*cosh(x)*sinh(x) +--R +--R +--R (389) +--R 1 2 1 3 3 3 +--R - - %i cosh(x)sinh(x) + (- cosh(x) - - cosh(x) + - %i x)sinh(x) +--R 2 3 2 2 +--R + +--R 1 3 3 +--R - %i cosh(x) - 3%i cosh(x) - - x +--R 3 2 +--R / +--R sinh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 498 + +--S 499 of 526 +a0494:= integrate(t0494,x) +--R +--R +--R (390) +--R 4 3 +--R sinh(x) + (4cosh(x) - 3%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) - 3%i cosh(x) - 20)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 9%i cosh(x) - 32cosh(x) + 36%i x - 3%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R - %i cosh(x) - 20cosh(x) + (36%i x - 39%i)cosh(x) - 36x - 69 +--R / +--R 24sinh(x) + 24cosh(x) + 24%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 499 + +--S 500 of 526 +m0494:= a0494-r0494 +--R +--R +--R (391) +--R 1 5 1 1 4 +--R -- sinh(x) + (- cosh(x) - -- %i)sinh(x) +--R 24 6 12 +--R + +--R 1 2 13 17 3 +--R (- cosh(x) + -- %i cosh(x) - --)sinh(x) +--R 4 24 24 +--R + +--R 1 3 3 2 5 23 2 +--R (- - cosh(x) + - %i cosh(x) - -- cosh(x) - -- %i)sinh(x) +--R 6 8 24 24 +--R + +--R 7 4 13 3 25 2 37 11 +--R (- -- cosh(x) - -- %i cosh(x) + -- cosh(x) + -- %i cosh(x) - --) +--R 24 24 24 24 4 +--R * +--R sinh(x) +--R + +--R 7 4 3 3 13 2 11 23 +--R - -- %i cosh(x) + - cosh(x) + -- %i cosh(x) - -- cosh(x) - -- %i +--R 24 8 6 8 8 +--R / +--R 2 +--R sinh(x) + (cosh(x) + 2%i)sinh(x) + %i cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 500 + +--S 501 of 526 +d0494:= D(m0494,x) +--R +--R +--R (392) +--R 1 7 5 11 6 +--R - sinh(x) + (- cosh(x) + -- %i)sinh(x) +--R 8 8 12 +--R + +--R 1 2 23 5 5 +--R (- cosh(x) + -- %i cosh(x) - -)sinh(x) +--R 4 12 6 +--R + +--R 3 3 1 2 1 9 4 +--R (- - cosh(x) - - %i cosh(x) - - cosh(x) + - %i)sinh(x) +--R 4 2 3 4 +--R + +--R 3 4 13 3 13 2 21 59 +--R (- - cosh(x) - -- %i cosh(x) + -- cosh(x) + -- %i cosh(x) - --) +--R 8 6 8 4 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 5 5 4 23 3 5 2 +--R - cosh(x) - -- %i cosh(x) + -- cosh(x) + -- %i cosh(x) +--R 8 12 24 12 +--R + +--R 95 4 +--R - -- cosh(x) + - %i +--R 24 3 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 5 7 4 43 3 43 2 +--R - %i cosh(x) - -- cosh(x) - -- %i cosh(x) + -- cosh(x) +--R 4 24 12 24 +--R + +--R 10 3 +--R -- %i cosh(x) - - +--R 3 2 +--R * +--R sinh(x) +--R + +--R 1 5 4 4 25 3 4 2 +--R - - cosh(x) - - %i cosh(x) + -- cosh(x) + - %i cosh(x) - 3cosh(x) +--R 8 3 8 3 +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) + 4%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) + 6%i cosh(x) - 6)sinh(x) +--R + +--R 2 2 +--R (2%i cosh(x) - 6cosh(x) - 4%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 501 + +--S 502 of 526 +t0495:= cosh(x)^2/(a+b*sinh(x)) +--R +--R +--R 2 +--R cosh(x) +--R (393) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 502 + +--S 503 of 526 +r0495:= -a*x/b^2-2*(a^2+b^2)^(1/2)*atanh((b-a*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/b^2+cosh(x)/b +--R +--R +--R x +--R +-------+ a tanh(-) - b +--R | 2 2 2 +--R 2\|b + a atanh(-------------) + b cosh(x) - a x +--R +-------+ +--R | 2 2 +--R \|b + a +--R (394) ------------------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 503 + +--S 504 of 526 +a0495:= integrate(t0495,x) +--R +--R +--R (395) +--R +-------+ +--R | 2 2 +--R (2sinh(x) + 2cosh(x))\|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 2 +--R b sinh(x) + (2b cosh(x) - 2a x)sinh(x) + b cosh(x) - 2a x cosh(x) + b +--R / +--R 2 2 +--R 2b sinh(x) + 2b cosh(x) +--R Type: Union(Expression(Integer),...) +--E 504 + +--S 505 of 526 +m0495:= a0495-r0495 +--R +--R +--R (396) +--R +-------+ +--R | 2 2 +--R (2sinh(x) + 2cosh(x))\|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R x +--R +-------+ a tanh(-) - b +--R | 2 2 2 2 +--R (- 4sinh(x) - 4cosh(x))\|b + a atanh(-------------) + b sinh(x) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 +--R - b cosh(x) + b +--R / +--R 2 2 +--R 2b sinh(x) + 2b cosh(x) +--R Type: Expression(Integer) +--E 505 + +--S 506 of 526 +d0495:= D(m0495,x) +--R +--R +--R (397) +--R 4 2 2 3 +--R - a b sinh(x) + (- 2a b cosh(x) - 2b - 4a )sinh(x) +--R + +--R 2 2 2 +--R (- 6b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 +--R (2a b cosh(x) + (- 6b - 4a )cosh(x) - 2a b cosh(x) + 2b )sinh(x) +--R + +--R 4 2 3 2 2 +--R a b cosh(x) - 2b cosh(x) - 2a b cosh(x) + 2b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R 2b sinh(x) + (4b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 +--R (4a b cosh(x) - 8b - 8a )sinh(x) +--R + +--R 2 3 2 2 2 +--R (- 4b cosh(x) - 4a b cosh(x) + (- 12b - 16a )cosh(x) + 4a b) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 +--R - 2b cosh(x) - 4a b cosh(x) + (- 4b - 8a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - 2b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 2 3 +--R a b sinh(x) + (2a b cosh(x) + 2b + 4a )sinh(x) +--R + +--R 2 2 2 +--R (6b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 +--R (- 2a b cosh(x) + (6b + 4a )cosh(x) + 2a b cosh(x) - 2b )sinh(x) +--R + +--R 4 2 3 2 2 +--R - a b cosh(x) + 2b cosh(x) + 2a b cosh(x) - 2b cosh(x) - a b +--R / +--R 2 3 2 2 2 +--R 2a b sinh(x) + (6a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (6a b cosh(x) + 8a b cosh(x) - 2a b )sinh(x) + 2a b cosh(x) +--R + +--R 2 2 2 +--R 4a b cosh(x) - 2a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 3 2 2 +--R - 4b sinh(x) + (- 12b cosh(x) - 8a b )sinh(x) +--R + +--R 3 2 2 3 3 3 +--R (- 12b cosh(x) - 16a b cosh(x) + 4b )sinh(x) - 4b cosh(x) +--R + +--R 2 2 3 +--R - 8a b cosh(x) + 4b cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3 2 2 2 +--R - 2a b sinh(x) + (- 6a b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 6a b cosh(x) - 8a b cosh(x) + 2a b )sinh(x) - 2a b cosh(x) +--R + +--R 2 2 2 +--R - 4a b cosh(x) + 2a b cosh(x) +--R Type: Expression(Integer) +--E 506 + +--S 507 of 526 +t0496:= cosh(x)^3/(a+b*sinh(x)) +--R +--R +--R 3 +--R cosh(x) +--R (398) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 507 + +--S 508 of 526 +r0496:= (a^2+b^2)*log(a+b*sinh(x))/b^3-a*sinh(x)/b^2+1/2*sinh(x)^2/b +--R +--R +--R 2 2 2 2 +--R (2b + 2a )log(b sinh(x) + a) + b sinh(x) - 2a b sinh(x) +--R (399) --------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 508 + +--S 509 of 526 +a0496:= integrate(t0496,x) +--R +--R +--R (400) +--R 2 2 2 2 2 +--R (8b + 8a )sinh(x) + (16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (8b + 8a )cosh(x) +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 4 2 3 +--R b sinh(x) + (4b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6b cosh(x) - 12a b cosh(x) + (- 8b - 8a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4b cosh(x) - 12a b cosh(x) + (- 16b - 16a )x cosh(x) + 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R b cosh(x) - 4a b cosh(x) + (- 8b - 8a )x cosh(x) + 4a b cosh(x) + b +--R / +--R 3 2 3 3 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R Type: Union(Expression(Integer),...) +--E 509 + +--S 510 of 526 +m0496:= a0496-r0496 +--R +--R +--R (401) +--R 2 2 2 2 2 +--R (- 8b - 8a )sinh(x) + (- 16b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 8b - 8a )cosh(x) +--R * +--R log(b sinh(x) + a) +--R + +--R 2 2 2 2 2 +--R (8b + 8a )sinh(x) + (16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (8b + 8a )cosh(x) +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 4 2 3 +--R - 3b sinh(x) + (- 4b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 4a b cosh(x) + (- 8b - 8a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4b cosh(x) - 4a b cosh(x) + (- 16b - 16a )x cosh(x) + 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R b cosh(x) - 4a b cosh(x) + (- 8b - 8a )x cosh(x) + 4a b cosh(x) + b +--R / +--R 3 2 3 3 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R Type: Expression(Integer) +--E 510 + +--S 511 of 526 +d0496:= D(m0496,x) +--R +--R +--R (402) +--R 4 3 2 2 +--R b sinh(x) - 2a sinh(x) + (- 2b cosh(x) - 2a cosh(x))sinh(x) +--R + +--R 2 4 3 +--R (2a cosh(x) - 2a)sinh(x) + b cosh(x) + 2a cosh(x) - 2a cosh(x) - b +--R / +--R 2 2 2 2 2 +--R 4b sinh(x) + 8b cosh(x)sinh(x) + 4b cosh(x) +--R Type: Expression(Integer) +--E 511 + +--S 512 of 526 +t0497:= cosh(x)^4/(a+b*sinh(x)) +--R +--R +--R 4 +--R cosh(x) +--R (403) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 512 + +--S 513 of 526 +r0497:= -a^3*x/b^4-3/2*a*x/b^2-2*(a^2+b^2)^(3/2)*_ + atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/b^4+_ + a^2*cosh(x)/b^3+cosh(x)/b+1/3*cosh(x)^3/b-_ + 1/2*a*cosh(x)*sinh(x)/b^2 +--R +--R +--R (404) +--R x +--R +-------+ a tanh(-) - b +--R 2 2 | 2 2 2 2 +--R (12b + 12a )\|b + a atanh(-------------) - 3a b cosh(x)sinh(x) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 3 3 2 2 3 +--R 2b cosh(x) + (6b + 6a b)cosh(x) + (- 9a b - 6a )x +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 513 + +--S 514 of 526 +a0497:= integrate(t0497,x) +--R +--R +--R (405) +--R 2 2 3 2 2 2 +--R (24b + 24a )sinh(x) + (72b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (72b + 72a )cosh(x) sinh(x) + (24b + 24a )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 6 3 2 5 +--R b sinh(x) + (6b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (15b cosh(x) - 15a b cosh(x) + 15b + 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 +--R 20b cosh(x) - 30a b cosh(x) + (60b + 48a b)cosh(x) +--R + +--R 2 3 +--R (- 36a b - 24a )x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 15b cosh(x) - 30a b cosh(x) + (90b + 72a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 108a b - 72a )x cosh(x) + 15b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 15a b cosh(x) + (60b + 48a b)cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (- 108a b - 72a )x cosh(x) + (30b + 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R b cosh(x) - 3a b cosh(x) + (15b + 12a b)cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (- 36a b - 24a )x cosh(x) + (15b + 12a b)cosh(x) + 3a b cosh(x) + b +--R / +--R 4 3 4 2 4 2 4 3 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) +--R Type: Union(Expression(Integer),...) +--E 514 + +--S 515 of 526 +m0497:= a0497-r0497 +--R +--R +--R (406) +--R 2 2 3 2 2 2 +--R (24b + 24a )sinh(x) + (72b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (72b + 72a )cosh(x) sinh(x) + (24b + 24a )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 2 3 2 2 2 +--R (- 48b - 48a )sinh(x) + (- 144b - 144a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 144b - 144a )cosh(x) sinh(x) + (- 48b - 48a )cosh(x) +--R * +--R x +--R +-------+ a tanh(-) - b +--R | 2 2 2 +--R \|b + a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 6 3 2 5 +--R b sinh(x) + (6b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (15b cosh(x) - 3a b cosh(x) + 15b + 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 3 +--R (12b cosh(x) + 6a b cosh(x) + (36b + 24a b)cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 3 2 2 +--R (- 9b cosh(x) + 6a b cosh(x) + 18b cosh(x) + 15b + 12a b)sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R - 18b cosh(x) - 3a b cosh(x) + (- 12b - 24a b)cosh(x) +--R + +--R 3 2 2 +--R (30b + 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R - 7b cosh(x) - 3a b cosh(x) + (- 9b - 12a b)cosh(x) +--R + +--R 3 2 2 2 3 +--R (15b + 12a b)cosh(x) + 3a b cosh(x) + b +--R / +--R 4 3 4 2 4 2 4 3 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) +--R Type: Expression(Integer) +--E 515 + +--S 516 of 526 +d0497:= D(m0497,x) +--R +--R +--R (407) +--R 3 8 3 2 2 7 +--R a b sinh(x) + (8a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 2 2 2 3 6 +--R (20a b cosh(x) + 20a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 2 2 2 3 3 4 +--R 16a b cosh(x) + 28a b cosh(x) + (- 16a b - 8a b)cosh(x) - 8b +--R + +--R 2 2 4 +--R - 24a b - 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R - 10a b cosh(x) - 4a b cosh(x) + (- 12a b - 24a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (- 40b - 96a b - 64a )cosh(x) - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 2 2 4 3 3 3 +--R - 24a b cosh(x) - 36a b cosh(x) + (24a b - 16a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 80b - 152a b - 96a )cosh(x) + (- 16a b - 8a b)cosh(x) +--R + +--R 4 2 2 +--R 8b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 2 2 5 3 3 4 +--R - 12a b cosh(x) - 20a b cosh(x) + (44a b + 16a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 80b - 120a b - 64a )cosh(x) + (- 36a b - 24a b)cosh(x) +--R + +--R 4 2 2 3 +--R (24b + 12a b )cosh(x) + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 6 3 3 5 +--R 4a b cosh(x) + (24a b + 24a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 40b - 48a b - 16a )cosh(x) + (- 32a b - 24a b)cosh(x) +--R + +--R 4 2 2 2 3 +--R (24b + 12a b )cosh(x) + 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 2 2 7 3 3 6 +--R a b cosh(x) + 4a b cosh(x) + (4a b + 8a b)cosh(x) +--R + +--R 4 2 2 5 3 3 4 +--R (- 8b - 8a b )cosh(x) + (- 10a b - 8a b)cosh(x) +--R + +--R 4 2 2 3 3 2 3 +--R (8b + 4a b )cosh(x) + 4a b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 8 4 3 7 +--R - 2b sinh(x) + (- 16b cosh(x) - 8a b )sinh(x) +--R + +--R 4 2 3 4 6 +--R (- 40b cosh(x) - 40a b cosh(x) + 8b )sinh(x) +--R + +--R 4 3 3 2 4 2 2 3 +--R - 32b cosh(x) - 56a b cosh(x) + (32b + 16a b )cosh(x) + 16a b +--R + +--R 3 +--R 16a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 4 2 2 2 +--R 20b cosh(x) + 8a b cosh(x) + (24b + 48a b )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (32a b + 48a b)cosh(x) - 28b - 64a b - 32a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 4 2 2 3 +--R 48b cosh(x) + 72a b cosh(x) + (- 48b + 32a b )cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 16a b + 32a b)cosh(x) + (- 96b - 240a b - 128a )cosh(x) +--R + +--R 3 3 +--R 24a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 4 2 2 4 +--R 24b cosh(x) + 40a b cosh(x) + (- 88b - 32a b )cosh(x) +--R + +--R 3 3 3 4 2 2 4 2 +--R (- 80a b - 32a b)cosh(x) + (- 120b - 336a b - 192a )cosh(x) +--R + +--R 3 3 4 +--R (72a b + 48a b)cosh(x) - 8b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 4 2 2 5 +--R - 8a b cosh(x) + (- 48b - 48a b )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (- 64a b - 48a b)cosh(x) + (- 64b - 208a b - 128a )cosh(x) +--R + +--R 3 3 2 4 +--R (72a b + 48a b)cosh(x) - 16b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 8 3 7 4 2 2 6 +--R - 2b cosh(x) - 8a b cosh(x) + (- 8b - 16a b )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 16a b - 16a b)cosh(x) + (- 12b - 48a b - 32a )cosh(x) +--R + +--R 3 3 3 4 2 4 +--R (24a b + 16a b)cosh(x) - 8b cosh(x) - 2b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 8 3 2 2 7 +--R - a b sinh(x) + (- 8a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 2 2 2 3 6 +--R (- 20a b cosh(x) - 20a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 3 2 2 2 3 3 4 +--R - 16a b cosh(x) - 28a b cosh(x) + (16a b + 8a b)cosh(x) + 8b +--R + +--R 2 2 4 +--R 24a b + 16a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R 10a b cosh(x) + 4a b cosh(x) + (12a b + 24a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (40b + 96a b + 64a )cosh(x) + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 2 2 4 3 3 3 +--R 24a b cosh(x) + 36a b cosh(x) + (- 24a b + 16a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 2 2 +--R (80b + 152a b + 96a )cosh(x) + (16a b + 8a b)cosh(x) - 8b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 2 2 5 3 3 4 +--R 12a b cosh(x) + 20a b cosh(x) + (- 44a b - 16a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (80b + 120a b + 64a )cosh(x) + (36a b + 24a b)cosh(x) +--R + +--R 4 2 2 3 +--R (- 24b - 12a b )cosh(x) - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 6 3 3 5 +--R - 4a b cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (40b + 48a b + 16a )cosh(x) + (32a b + 24a b)cosh(x) +--R + +--R 4 2 2 2 3 +--R (- 24b - 12a b )cosh(x) - 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 2 2 7 3 3 6 +--R - a b cosh(x) - 4a b cosh(x) + (- 4a b - 8a b)cosh(x) +--R + +--R 4 2 2 5 3 3 4 4 2 2 3 +--R (8b + 8a b )cosh(x) + (10a b + 8a b)cosh(x) + (- 8b - 4a b )cosh(x) +--R + +--R 3 2 3 +--R - 4a b cosh(x) - a b +--R / +--R 4 5 4 2 3 4 +--R 8a b sinh(x) + (40a b cosh(x) + 16a b )sinh(x) +--R + +--R 4 2 2 3 4 3 +--R (80a b cosh(x) + 64a b cosh(x) - 8a b )sinh(x) +--R + +--R 4 3 2 3 2 4 2 +--R (80a b cosh(x) + 96a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 4 4 2 3 3 4 2 +--R (40a b cosh(x) + 64a b cosh(x) - 24a b cosh(x) )sinh(x) +--R + +--R 4 5 2 3 4 4 3 +--R 8a b cosh(x) + 16a b cosh(x) - 8a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 5 5 4 4 +--R - 16b sinh(x) + (- 80b cosh(x) - 32a b )sinh(x) +--R + +--R 5 2 4 5 3 +--R (- 160b cosh(x) - 128a b cosh(x) + 16b )sinh(x) +--R + +--R 5 3 4 2 5 2 +--R (- 160b cosh(x) - 192a b cosh(x) + 48b cosh(x))sinh(x) +--R + +--R 5 4 4 3 5 2 +--R (- 80b cosh(x) - 128a b cosh(x) + 48b cosh(x) )sinh(x) +--R + +--R 5 5 4 4 5 3 +--R - 16b cosh(x) - 32a b cosh(x) + 16b cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 5 4 2 3 4 +--R - 8a b sinh(x) + (- 40a b cosh(x) - 16a b )sinh(x) +--R + +--R 4 2 2 3 4 3 +--R (- 80a b cosh(x) - 64a b cosh(x) + 8a b )sinh(x) +--R + +--R 4 3 2 3 2 4 2 +--R (- 80a b cosh(x) - 96a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 4 4 2 3 3 4 2 +--R (- 40a b cosh(x) - 64a b cosh(x) + 24a b cosh(x) )sinh(x) +--R + +--R 4 5 2 3 4 4 3 +--R - 8a b cosh(x) - 16a b cosh(x) + 8a b cosh(x) +--R Type: Expression(Integer) +--E 516 + +--S 517 of 526 +t0498:= cosh(x)^2/(%i+sinh(x)) +--R +--R +--R 2 +--R cosh(x) +--R (408) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 517 + +--S 518 of 526 +r0498:= -%i*x+cosh(x) +--R +--R +--R (409) cosh(x) - %i x +--R Type: Expression(Complex(Integer)) +--E 518 + +--S 519 of 526 +a0498:= integrate(t0498,x) +--R +--R +--R (410) cosh(x) - %i x +--R Type: Union(Expression(Complex(Integer)),...) +--E 519 + +--S 520 of 526 +m0498:= a0498-r0498 +--R +--R +--R (411) 0 +--R Type: Expression(Complex(Integer)) +--E 520 + +--S 521 of 526 +d0498:= D(m0498,x) +--R +--R +--R (412) 0 +--R Type: Expression(Complex(Integer)) +--E 521 + +--S 522 of 526 +t0499:= cosh(x)^4/(%i+sinh(x)) +--R +--R +--R 4 +--R cosh(x) +--R (413) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 522 + +--S 523 of 526 +r0499:= -1/2*%i*x+1/3*cosh(x)^3-1/2*%i*cosh(x)*sinh(x) +--R +--R +--R 1 1 3 1 +--R (414) - - %i cosh(x)sinh(x) + - cosh(x) - - %i x +--R 2 3 2 +--R Type: Expression(Complex(Fraction(Integer))) +--E 523 + +--S 524 of 526 +a0499:= integrate(t0499,x) +--R +--R +--R 2 3 +--R 3cosh(x)sinh(x) - 6%i cosh(x)sinh(x) + cosh(x) + 3cosh(x) - 6%i x +--R (415) ------------------------------------------------------------------- +--R 12 +--R Type: Union(Expression(Complex(Integer)),...) +--E 524 + +--S 525 of 526 +m0499:= a0499-r0499 +--R +--R +--R 1 2 1 3 1 +--R (416) - cosh(x)sinh(x) - - cosh(x) + - cosh(x) +--R 4 4 4 +--R Type: Expression(Complex(Fraction(Integer))) +--E 525 + +--S 526 of 526 +d0499:= D(m0499,x) +--R +--R +--R 1 3 1 2 1 +--R (417) - sinh(x) + (- - cosh(x) + -)sinh(x) +--R 4 4 4 +--R Type: Expression(Complex(Fraction(Integer))) +--E 526 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper400-499.input.pdf b/src/axiom-website/CATS/richhyper400-499.input.pdf new file mode 100644 index 0000000..afaa206 Binary files /dev/null and b/src/axiom-website/CATS/richhyper400-499.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper500-599.input.pamphlet b/src/axiom-website/CATS/richhyper500-599.input.pamphlet new file mode 100644 index 0000000..8938fea --- /dev/null +++ b/src/axiom-website/CATS/richhyper500-599.input.pamphlet @@ -0,0 +1,49087 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper500-599.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper500-599.output +)spool richhyper500-599.output +)set message auto off +)clear all + +--S 1 of 530 +t0500:= tanh(x)/(a+b*sinh(x)) +--R +--R +--R tanh(x) +--R (1) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 530 +r0500:= 1/2*(2*b*atan(sinh(x))+a*log(cosh(x)^2)-2*a*log(a+b*sinh(x)))/(a^2+b^2) +--R +--R +--R 2 +--R - 2a log(b sinh(x) + a) + a log(cosh(x) ) + 2b atan(sinh(x)) +--R (2) ------------------------------------------------------------ +--R 2 2 +--R 2b + 2a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 530 +a0500:= integrate(t0500,x) +--R +--R +--R (3) +--R 2cosh(x) - 2b sinh(x) - 2a +--R a log(- -----------------) - a log(-----------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R + +--R 2b atan(sinh(x) + cosh(x)) +--R / +--R 2 2 +--R b + a +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 530 +m0500:= a0500-r0500 +--R +--R +--R (4) +--R 2 2cosh(x) +--R 2a log(b sinh(x) + a) - a log(cosh(x) ) + 2a log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2b sinh(x) - 2a +--R - 2a log(-----------------) + 4b atan(sinh(x) + cosh(x)) - 2b atan(sinh(x)) +--R sinh(x) - cosh(x) +--R / +--R 2 2 +--R 2b + 2a +--R Type: Expression(Integer) +--E 4 + +--S 5 of 530 +d0500:= D(m0500,x) +--R +--R +--R (5) +--R 3 2 2 +--R 2b sinh(x) + b cosh(x)sinh(x) + (- 2b cosh(x) + 2b)sinh(x) +--R + +--R 3 +--R - b cosh(x) + b cosh(x) +--R / +--R 2 2 4 2 2 3 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((b + a )cosh(x) + 2b + 2a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b + a )cosh(x) + b + a +--R Type: Expression(Integer) +--E 5 + +--S 6 of 530 +t0501:= tanh(x)^2/(a+b*sinh(x)) +--R +--R +--R 2 +--R tanh(x) +--R (6) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 530 +r0501:= -2*a^2*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ + b*sech(x)/(a^2+b^2)-a*tanh(x)/(a^2+b^2) +--R +--R +--R x +--R a tanh(-) - b +-------+ +--R 2 2 | 2 2 +--R 2a atanh(-------------) + (- a tanh(x) - b sech(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (7) ------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 7 + +--S 8 of 530 +a0501:= integrate(t0501,x) +--R +--R +--R (8) +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R +-------+ +--R | 2 2 +--R (- 2b sinh(x) - 2b cosh(x) + 2a)\|b + a +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) + b +--R + +--R 2 +--R a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 530 +m0501:= a0501-r0501 +--R +--R +--R (9) +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 2 2 2 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a ) +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a)tanh(x) +--R + +--R 2 +--R b sech(x)sinh(x) + (2b cosh(x)sech(x) - 2b)sinh(x) +--R + +--R 2 +--R (b cosh(x) + b)sech(x) - 2b cosh(x) + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) + b +--R + +--R 2 +--R a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 9 + +--S 10 of 530 +d0501:= D(m0501,x) +--R +--R +--R (10) +--R 2 6 2 3 5 +--R - a b sinh(x) + (- 6a b cosh(x) - 2a )sinh(x) +--R + +--R 2 2 3 2 4 +--R (- 15a b cosh(x) - 10a cosh(x) - a b)sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (- 20a b cosh(x) - 20a cosh(x) - 4a b cosh(x) - 4a )sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R - 15a b cosh(x) - 20a cosh(x) - 6a b cosh(x) - 12a cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R - 6a b cosh(x) - 10a cosh(x) - 4a b cosh(x) - 12a cosh(x) +--R + +--R 2 3 +--R 2a b cosh(x) - 2a +--R * +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R - a b cosh(x) - 2a cosh(x) - a b cosh(x) - 4a cosh(x) +--R + +--R 2 2 3 2 +--R a b cosh(x) - 2a cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R 2a b sinh(x) + (12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 4 +--R (30a b cosh(x) + 20a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (40a b cosh(x) + 40a b cosh(x) + 8a b cosh(x) + 8a b)sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 30a b cosh(x) + 40a b cosh(x) + 12a b cosh(x) +--R + +--R 2 2 +--R 24a b cosh(x) - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 12a b cosh(x) + 20a b cosh(x) + 8a b cosh(x) +--R + +--R 2 2 2 2 +--R 24a b cosh(x) - 4a b cosh(x) + 4a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 2a b cosh(x) + 4a b cosh(x) + 2a b cosh(x) + 8a b cosh(x) +--R + +--R 2 2 2 2 +--R - 2a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 3 5 +--R a b sinh(x) + (6a b cosh(x) + 2a )sinh(x) +--R + +--R 2 2 3 2 4 +--R (15a b cosh(x) + 10a cosh(x) + a b)sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (20a b cosh(x) + 20a cosh(x) + 4a b cosh(x) + 4a )sinh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R (15a b cosh(x) + 20a cosh(x) + 6a b cosh(x) + 12a cosh(x) - a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 6a b cosh(x) + 10a cosh(x) + 4a b cosh(x) + 12a cosh(x) +--R + +--R 2 3 +--R - 2a b cosh(x) + 2a +--R * +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R a b cosh(x) + 2a cosh(x) + a b cosh(x) + 4a cosh(x) +--R + +--R 2 2 3 2 +--R - a b cosh(x) + 2a cosh(x) - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 2 5 +--R - a b sech(x)sinh(x) + (- 6a b cosh(x) - 2a b)sech(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 15a b cosh(x) - 10a b cosh(x) - a b )sech(x)sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (- 20a b cosh(x) - 20a b cosh(x) - 4a b cosh(x) - 4a b) +--R * +--R 3 +--R sech(x)sinh(x) +--R + +--R 2 4 2 3 2 2 +--R - 15a b cosh(x) - 20a b cosh(x) - 6a b cosh(x) +--R + +--R 2 2 +--R - 12a b cosh(x) + a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 2 4 2 3 +--R - 6a b cosh(x) - 10a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 2 +--R - 12a b cosh(x) + 2a b cosh(x) - 2a b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - a b cosh(x) - 2a b cosh(x) - a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 2 +--R a b cosh(x) - 2a b cosh(x) + a b +--R * +--R sech(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 2 5 +--R 2b sech(x)sinh(x) + (12b cosh(x) + 4a b )sech(x)sinh(x) +--R + +--R 3 2 2 3 4 +--R (30b cosh(x) + 20a b cosh(x) + 2b )sech(x)sinh(x) +--R + +--R 3 3 2 2 3 2 +--R (40b cosh(x) + 40a b cosh(x) + 8b cosh(x) + 8a b )sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 30b cosh(x) + 40a b cosh(x) + 12b cosh(x) + 24a b cosh(x) +--R + +--R 3 +--R - 2b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 3 5 2 4 3 3 2 2 +--R 12b cosh(x) + 20a b cosh(x) + 8b cosh(x) + 24a b cosh(x) +--R + +--R 3 2 +--R - 4b cosh(x) + 4a b +--R * +--R sech(x)sinh(x) +--R + +--R 3 6 2 5 3 4 2 3 +--R 2b cosh(x) + 4a b cosh(x) + 2b cosh(x) + 8a b cosh(x) +--R + +--R 3 2 2 3 +--R - 2b cosh(x) + 4a b cosh(x) - 2b +--R * +--R sech(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R a b sech(x)sinh(x) + (6a b cosh(x) + 2a b)sech(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (15a b cosh(x) + 10a b cosh(x) + a b )sech(x)sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (20a b cosh(x) + 20a b cosh(x) + 4a b cosh(x) + 4a b)sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 2 +--R 15a b cosh(x) + 20a b cosh(x) + 6a b cosh(x) + 12a b cosh(x) +--R + +--R 2 +--R - a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 6a b cosh(x) + 10a b cosh(x) + 4a b cosh(x) + 12a b cosh(x) +--R + +--R 2 2 +--R - 2a b cosh(x) + 2a b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 2 +--R - a b cosh(x) + 2a b cosh(x) - a b +--R * +--R sech(x) +--R * +--R tanh(x) +--R + +--R 2 3 5 2 3 4 +--R (2a b + 2a )sinh(x) + (10a b + 10a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 3 +--R ((20a b + 20a )cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 2 +--R ((20a b + 20a )cosh(x) + (- 12a b - 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R ((10a b + 10a )cosh(x) + (- 12a b - 12a )cosh(x) + 2a b + 2a ) +--R * +--R sinh(x) +--R + +--R 2 3 5 2 3 3 2 3 +--R (2a b + 2a )cosh(x) + (- 4a b - 4a )cosh(x) + (2a b + 2a )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 3 2 5 +--R - 2a b sinh(x) + (- 12a b cosh(x) - 4b - 8a b)sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (- 30a b cosh(x) + (- 20b - 40a b)cosh(x) - 2a b )sinh(x) +--R + +--R 2 3 3 2 2 2 3 +--R (- 40a b cosh(x) + (- 40b - 80a b)cosh(x) - 8a b cosh(x) + 8b ) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 2 3 2 2 +--R - 30a b cosh(x) + (- 40b - 80a b)cosh(x) - 12a b cosh(x) +--R + +--R 3 2 +--R 24b cosh(x) + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 2 4 2 3 +--R - 12a b cosh(x) + (- 20b - 40a b)cosh(x) - 8a b cosh(x) +--R + +--R 3 2 2 3 2 +--R 24b cosh(x) + 4a b cosh(x) - 4b - 8a b +--R * +--R sinh(x) +--R + +--R 2 6 3 2 5 2 4 +--R - 2a b cosh(x) + (- 4b - 8a b)cosh(x) - 2a b cosh(x) +--R + +--R 3 3 2 2 3 2 2 +--R 8b cosh(x) + 2a b cosh(x) + (- 4b - 8a b)cosh(x) + 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3 5 2 3 4 +--R (- 2a b - 2a )sinh(x) + (- 10a b - 10a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 3 +--R ((- 20a b - 20a )cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 2 3 3 2 3 2 +--R ((- 20a b - 20a )cosh(x) + (12a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R ((- 10a b - 10a )cosh(x) + (12a b + 12a )cosh(x) - 2a b - 2a ) +--R * +--R sinh(x) +--R + +--R 2 3 5 2 3 3 2 3 +--R (- 2a b - 2a )cosh(x) + (4a b + 4a )cosh(x) + (- 2a b - 2a )cosh(x) +--R / +--R 3 3 6 3 3 2 2 4 5 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R ((15a b + 15a b)cosh(x) + (10a b + 10a )cosh(x) + a b + a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (20a b + 20a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (4a b + 4a b)cosh(x) + 4a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (15a b + 15a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (6a b + 6a b)cosh(x) + (12a b + 12a )cosh(x) - a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 2 4 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (4a b + 4a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (- 2a b - 2a b)cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 3 6 2 2 4 5 3 3 4 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) + (a b + a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 2 2 4 +--R (4a b + 4a )cosh(x) + (- a b - a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 3 3 +--R - a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 2 6 +--R (- 2b - 2a b )sinh(x) +--R + +--R 4 2 2 3 3 5 +--R ((- 12b - 12a b )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 +--R (- 30b - 30a b )cosh(x) + (- 20a b - 20a b)cosh(x) - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 40b - 40a b )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 4 2 2 3 3 +--R (- 8b - 8a b )cosh(x) - 8a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 30b - 30a b )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (- 12b - 12a b )cosh(x) + (- 24a b - 24a b)cosh(x) + 2b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 5 3 3 4 +--R (- 12b - 12a b )cosh(x) + (- 20a b - 20a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 8b - 8a b )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 4 2 2 3 3 +--R (4b + 4a b )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 4 2 2 6 3 3 5 +--R (- 2b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 2b - 2a b )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (2b + 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) + 2b + 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 6 3 3 2 2 4 5 +--R (- a b - a b)sinh(x) + ((- 6a b - 6a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R ((- 15a b - 15a b)cosh(x) + (- 10a b - 10a )cosh(x) - a b - a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (- 20a b - 20a b)cosh(x) + (- 20a b - 20a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (- 4a b - 4a b)cosh(x) - 4a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (- 15a b - 15a b)cosh(x) + (- 20a b - 20a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 6a b - 6a b)cosh(x) + (- 12a b - 12a )cosh(x) + a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 2 4 4 +--R (- 6a b - 6a b)cosh(x) + (- 10a b - 10a )cosh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (- 4a b - 4a b)cosh(x) + (- 12a b - 12a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (2a b + 2a b)cosh(x) - 2a b - 2a +--R * +--R sinh(x) +--R + +--R 3 3 6 2 2 4 5 3 3 4 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) + (- a b - a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 2 2 4 +--R (- 4a b - 4a )cosh(x) + (a b + a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 3 3 +--R a b + a b +--R Type: Expression(Integer) +--E 10 + +--S 11 of 530 +t0502:= tanh(x)^3/(a+b*sinh(x)) +--R +--R +--R 3 +--R tanh(x) +--R (11) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 530 +r0502:= 1/2*(3*b*atan(sinh(x))*a^2*cosh(x)^2+b^3*atan(sinh(x))*cosh(x)^2+_ + a^3*log(cosh(x)^2)*cosh(x)^2-2*a^3*log(a+b*sinh(x))*cosh(x)^2+_ + a^3+b^2*a-a^2*b*sinh(x)-b^3*sinh(x))/cosh(x)^2/(a^2+b^2)^2 +--R +--R +--R (12) +--R 3 2 3 2 2 +--R - 2a cosh(x) log(b sinh(x) + a) + a cosh(x) log(cosh(x) ) +--R + +--R 3 2 2 3 2 2 3 +--R (b + 3a b)cosh(x) atan(sinh(x)) + (- b - a b)sinh(x) + a b + a +--R / +--R 4 2 2 4 2 +--R (2b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 12 + +--S 13 of 530 +a0502:= integrate(t0502,x) +--R +--R +--R (13) +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 4 3 3 3 2 3 2 +--R - a sinh(x) - 4a cosh(x)sinh(x) + (- 6a cosh(x) - 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (- 4a cosh(x) - 4a cosh(x))sinh(x) - a cosh(x) - 2a cosh(x) - a +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 4 3 2 3 +--R (b + 3a b)sinh(x) + (4b + 12a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 +--R ((6b + 18a b)cosh(x) + 2b + 6a b)sinh(x) +--R + +--R 3 2 3 3 2 +--R ((4b + 12a b)cosh(x) + (4b + 12a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R (b + 3a b)cosh(x) + (2b + 6a b)cosh(x) + b + 3a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 2 3 3 2 2 3 2 +--R (- b - a b)sinh(x) + ((- 3b - 3a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R ((- 3b - 3a b)cosh(x) + (4a b + 4a )cosh(x) + b + a b)sinh(x) +--R + +--R 3 2 3 2 3 2 3 2 +--R (- b - a b)cosh(x) + (2a b + 2a )cosh(x) + (b + a b)cosh(x) +--R / +--R 4 2 2 4 4 4 2 2 4 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 2 +--R ((6b + 12a b + 6a )cosh(x) + 2b + 4a b + 2a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((4b + 8a b + 4a )cosh(x) + (4b + 8a b + 4a )cosh(x))sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 4 2 2 4 +--R (b + 2a b + a )cosh(x) + (2b + 4a b + 2a )cosh(x) + b + 2a b + a +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 530 +m0502:= a0502-r0502 +--R +--R +--R (14) +--R 3 2 4 3 3 3 +--R 2a cosh(x) sinh(x) + 8a cosh(x) sinh(x) +--R + +--R 3 4 3 2 2 +--R (12a cosh(x) + 4a cosh(x) )sinh(x) +--R + +--R 3 5 3 3 3 6 3 4 +--R (8a cosh(x) + 8a cosh(x) )sinh(x) + 2a cosh(x) + 4a cosh(x) +--R + +--R 3 2 +--R 2a cosh(x) +--R * +--R log(b sinh(x) + a) +--R + +--R 3 2 4 3 3 3 +--R - a cosh(x) sinh(x) - 4a cosh(x) sinh(x) +--R + +--R 3 4 3 2 2 +--R (- 6a cosh(x) - 2a cosh(x) )sinh(x) +--R + +--R 3 5 3 3 3 6 3 4 +--R (- 4a cosh(x) - 4a cosh(x) )sinh(x) - a cosh(x) - 2a cosh(x) +--R + +--R 3 2 +--R - a cosh(x) +--R * +--R 2 +--R log(cosh(x) ) +--R + +--R 3 2 4 3 3 3 +--R 2a cosh(x) sinh(x) + 8a cosh(x) sinh(x) +--R + +--R 3 4 3 2 2 +--R (12a cosh(x) + 4a cosh(x) )sinh(x) +--R + +--R 3 5 3 3 3 6 3 4 +--R (8a cosh(x) + 8a cosh(x) )sinh(x) + 2a cosh(x) + 4a cosh(x) +--R + +--R 3 2 +--R 2a cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 4 3 3 3 +--R - 2a cosh(x) sinh(x) - 8a cosh(x) sinh(x) +--R + +--R 3 4 3 2 2 +--R (- 12a cosh(x) - 4a cosh(x) )sinh(x) +--R + +--R 3 5 3 3 3 6 3 4 +--R (- 8a cosh(x) - 8a cosh(x) )sinh(x) - 2a cosh(x) - 4a cosh(x) +--R + +--R 3 2 +--R - 2a cosh(x) +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 4 3 2 3 3 +--R (2b + 6a b)cosh(x) sinh(x) + (8b + 24a b)cosh(x) sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R ((12b + 36a b)cosh(x) + (4b + 12a b)cosh(x) )sinh(x) +--R + +--R 3 2 5 3 2 3 +--R ((8b + 24a b)cosh(x) + (8b + 24a b)cosh(x) )sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (2b + 6a b)cosh(x) + (4b + 12a b)cosh(x) + (2b + 6a b)cosh(x) +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 2 2 4 3 2 3 3 +--R (- b - 3a b)cosh(x) sinh(x) + (- 4b - 12a b)cosh(x) sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R ((- 6b - 18a b)cosh(x) + (- 2b - 6a b)cosh(x) )sinh(x) +--R + +--R 3 2 5 3 2 3 +--R ((- 4b - 12a b)cosh(x) + (- 4b - 12a b)cosh(x) )sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (- b - 3a b)cosh(x) + (- 2b - 6a b)cosh(x) + (- b - 3a b)cosh(x) +--R * +--R atan(sinh(x)) +--R + +--R 3 2 5 3 2 2 3 4 +--R (b + a b)sinh(x) + ((4b + 4a b)cosh(x) - a b - a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 3 +--R ((4b + 4a b)cosh(x) + (- 4a b - 4a )cosh(x) + 2b + 2a b)sinh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 2b - 2a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b + 4a b)cosh(x) - 2a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 2 3 3 3 2 2 +--R (- 5b - 5a b)cosh(x) + (4a b + 4a )cosh(x) + (4b + 4a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 4a b - 4a )cosh(x) + b + a b +--R * +--R sinh(x) +--R + +--R 3 2 5 2 3 4 3 2 3 +--R (- 2b - 2a b)cosh(x) + (3a b + 3a )cosh(x) + (2b + 2a b)cosh(x) +--R + +--R 2 3 2 2 3 +--R (- 2a b - 2a )cosh(x) - a b - a +--R / +--R 4 2 2 4 2 4 +--R (2b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 3 3 +--R (8b + 16a b + 8a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 2 +--R ((12b + 24a b + 12a )cosh(x) + (4b + 8a b + 4a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R ((8b + 16a b + 8a )cosh(x) + (8b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (2b + 4a b + 2a )cosh(x) + (4b + 8a b + 4a )cosh(x) +--R + +--R 4 2 2 4 2 +--R (2b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 14 + +--S 15 of 530 +d0502:= D(m0502,x) +--R +--R +--R (15) +--R 3 2 10 3 2 2 3 9 +--R (- 2b - 2a b)sinh(x) + ((- 12b - 12a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 8 +--R ((- 29b - 29a b)cosh(x) + (12a b + 12a )cosh(x) - 8b - 8a b)sinh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 30b - 26a b)cosh(x) + (30a b + 30a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 36b - 36a b)cosh(x) + 8a b + 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 2 3 3 +--R (4b + 22a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 62b - 62a b)cosh(x) + (36a b + 36a )cosh(x) - 12b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 5 2 3 4 +--R (42b + 70a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 50b - 38a b)cosh(x) + (66a b + 66a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 36b - 36a b)cosh(x) + 12a b + 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 6 2 3 5 +--R (38b + 48a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 10b + 28a b)cosh(x) + (64a b + 64a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 36b - 36a b)cosh(x) + (36a b + 36a )cosh(x) - 8b - 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 7 2 3 6 +--R (6b - 14a b)cosh(x) + (- 30a b - 30a )cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (24b + 64a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 10b + 2a b)cosh(x) + (42a b + 42a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b - 12a b)cosh(x) + 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 8 2 3 7 +--R (- 10b - 36a b)cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 3 2 6 2 3 5 +--R (30b + 42a b)cosh(x) + (- 28a b - 28a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 8b + 14a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 2b - 2a b)cosh(x) + (12a b + 12a )cosh(x) - 2b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 9 3 2 7 +--R (- 6b - 18a b)cosh(x) + (14b + 10a b)cosh(x) +--R + +--R 2 3 6 3 2 5 +--R (- 30a b - 30a )cosh(x) + (- 18b - 6a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (22a b + 22a )cosh(x) + (10b + 14a b)cosh(x) +--R + +--R 2 3 2 2 3 +--R (6a b + 6a )cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 10 3 8 2 3 7 +--R (- b - 3a b)cosh(x) + 2b cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 3 2 6 2 3 5 3 2 4 +--R (- 8b - 6a b)cosh(x) + (8a b + 8a )cosh(x) + (6b + 8a b)cosh(x) +--R + +--R 3 2 2 +--R (b + a b)cosh(x) +--R / +--R 4 2 2 4 3 8 +--R (2b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 4 7 +--R (12b + 24a b + 12a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 6 +--R ((30b + 60a b + 30a )cosh(x) + (8b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 5 +--R ((40b + 80a b + 40a )cosh(x) + (36b + 72a b + 36a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 7 4 2 2 4 5 +--R (30b + 60a b + 30a )cosh(x) + (66b + 132a b + 66a )cosh(x) +--R + +--R 4 2 2 4 3 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (64b + 128a b + 64a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (36b + 72a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (42b + 84a b + 42a )cosh(x) + (8b + 16a b + 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (24b + 48a b + 24a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (6b + 12a b + 6a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (6b + 12a b + 6a )cosh(x) + (2b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 15 + +--S 16 of 530 +t0503:= tanh(x)^4/(a+b*sinh(x)) +--R +--R +--R 4 +--R tanh(x) +--R (16) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 530 +r0503:= -2*a^4*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ + b*(2*a^2+b^2)*sech(x)/(a^2+b^2)^2+b*sech(x)^3/(3*a^2+3*b^2)+_ + a*tanh(x)/(a^2+b^2)-a*(2*a^2+b^2)*tanh(x)/(a^2+b^2)^2-_ + a*tanh(x)^3/(3*a^2+3*b^2) +--R +--R +--R (17) +--R x +--R a tanh(-) - b +--R 4 2 +--R 6a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 3 3 3 2 3 +--R (- a b - a )tanh(x) - 3a tanh(x) + (b + a b)sech(x) +--R + +--R 3 2 +--R (- 3b - 6a b)sech(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 17 + +--S 18 of 530 +a0503:= integrate(t0503,x) +--R +--R +--R (18) +--R 4 6 4 5 4 2 4 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) + 9a )sinh(x) +--R + +--R 4 3 4 3 +--R (60a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45a cosh(x) + 54a cosh(x) + 9a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18a cosh(x) + 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 4 4 4 2 4 +--R 9a cosh(x) + 9a cosh(x) + 3a +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 2 5 +--R (- 6b - 12a b)sinh(x) +--R + +--R 3 2 2 3 4 +--R ((- 30b - 60a b)cosh(x) + 6a b + 12a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R ((- 60b - 120a b)cosh(x) + (24a b + 48a )cosh(x) - 4b - 16a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 60b - 120a b)cosh(x) + (36a b + 72a )cosh(x) +--R + +--R 3 2 3 +--R (- 12b - 48a b)cosh(x) + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 30b - 60a b)cosh(x) + (24a b + 48a )cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 12b - 48a b)cosh(x) + 24a cosh(x) - 6b - 12a b +--R * +--R sinh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 6b - 12a b)cosh(x) + (6a b + 12a )cosh(x) +--R + +--R 3 2 3 3 2 3 2 +--R (- 4b - 16a b)cosh(x) + 12a cosh(x) + (- 6b - 12a b)cosh(x) +--R + +--R 2 3 +--R 2a b + 8a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 2 4 6 4 2 2 4 5 +--R (3b + 6a b + 3a )sinh(x) + (18b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 4 +--R ((45b + 90a b + 45a )cosh(x) + 9b + 18a b + 9a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((60b + 120a b + 60a )cosh(x) + (36b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (45b + 90a b + 45a )cosh(x) + (54b + 108a b + 54a )cosh(x) +--R + +--R 4 2 2 4 +--R 9b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (18b + 36a b + 18a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 +--R (18b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (3b + 6a b + 3a )cosh(x) + (9b + 18a b + 9a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (9b + 18a b + 9a )cosh(x) + 3b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 530 +m0503:= a0503-r0503 +--R +--R +--R (19) +--R 4 6 4 5 4 2 4 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) + 9a )sinh(x) +--R + +--R 4 3 4 3 +--R (60a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45a cosh(x) + 54a cosh(x) + 9a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18a cosh(x) + 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 4 4 4 2 4 +--R 9a cosh(x) + 9a cosh(x) + 3a +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 6 4 5 4 2 4 4 +--R - 6a sinh(x) - 36a cosh(x)sinh(x) + (- 90a cosh(x) - 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (- 120a cosh(x) - 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (- 90a cosh(x) - 108a cosh(x) - 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (- 36a cosh(x) - 72a cosh(x) - 36a cosh(x))sinh(x) - 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R - 18a cosh(x) - 18a cosh(x) - 6a +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 6 2 3 5 +--R (a b + a )sinh(x) + (6a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((15a b + 15a )cosh(x) + 3a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((20a b + 20a )cosh(x) + (12a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (15a b + 15a )cosh(x) + (18a b + 18a )cosh(x) + 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (6a b + 6a )cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 3 +--R (6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (a b + a )cosh(x) + (3a b + 3a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (3a b + 3a )cosh(x) + a b + a +--R * +--R 3 +--R tanh(x) +--R + +--R 3 6 3 5 3 2 3 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) + 9a )sinh(x) +--R + +--R 3 3 3 3 +--R (60a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (45a cosh(x) + 54a cosh(x) + 9a )sinh(x) +--R + +--R 3 5 3 3 3 3 6 +--R (18a cosh(x) + 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 3 4 3 2 3 +--R 9a cosh(x) + 9a cosh(x) + 3a +--R * +--R tanh(x) +--R + +--R 3 2 3 3 2 6 +--R ((- b - a b)sech(x) + (3b + 6a b)sech(x))sinh(x) +--R + +--R 3 2 3 3 2 +--R (- 6b - 6a b)cosh(x)sech(x) + (18b + 36a b)cosh(x)sech(x) +--R + +--R 3 2 +--R - 6b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 2 3 +--R ((- 15b - 15a b)cosh(x) - 3b - 3a b)sech(x) +--R + +--R 3 2 2 3 2 +--R ((45b + 90a b)cosh(x) + 9b + 18a b)sech(x) +--R + +--R 3 2 2 3 +--R (- 30b - 60a b)cosh(x) + 6a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 20b - 20a b)cosh(x) + (- 12b - 12a b)cosh(x))sech(x) +--R + +--R 3 2 3 3 2 +--R ((60b + 120a b)cosh(x) + (36b + 72a b)cosh(x))sech(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 60b - 120a b)cosh(x) + (24a b + 48a )cosh(x) - 4b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 15b - 15a b)cosh(x) + (- 18b - 18a b)cosh(x) - 3b +--R + +--R 2 +--R - 3a b +--R * +--R 3 +--R sech(x) +--R + +--R 3 2 4 3 2 2 3 +--R (45b + 90a b)cosh(x) + (54b + 108a b)cosh(x) + 9b +--R + +--R 2 +--R 18a b +--R * +--R sech(x) +--R + +--R 3 2 3 2 3 2 +--R (- 60b - 120a b)cosh(x) + (36a b + 72a )cosh(x) +--R + +--R 3 2 3 +--R (- 12b - 48a b)cosh(x) + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 6b - 6a b)cosh(x) + (- 12b - 12a b)cosh(x) +--R + +--R 3 2 +--R (- 6b - 6a b)cosh(x) +--R * +--R 3 +--R sech(x) +--R + +--R 3 2 5 3 2 3 +--R (18b + 36a b)cosh(x) + (36b + 72a b)cosh(x) +--R + +--R 3 2 +--R (18b + 36a b)cosh(x) +--R * +--R sech(x) +--R + +--R 3 2 4 2 3 3 +--R (- 30b - 60a b)cosh(x) + (24a b + 48a )cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 12b - 48a b)cosh(x) + 24a cosh(x) - 6b - 12a b +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- b - a b)cosh(x) + (- 3b - 3a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 3b - 3a b)cosh(x) - b - a b +--R * +--R 3 +--R sech(x) +--R + +--R 3 2 6 3 2 4 +--R (3b + 6a b)cosh(x) + (9b + 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (9b + 18a b)cosh(x) + 3b + 6a b +--R * +--R sech(x) +--R + +--R 3 2 5 2 3 4 +--R (- 6b - 12a b)cosh(x) + (6a b + 12a )cosh(x) +--R + +--R 3 2 3 3 2 3 2 +--R (- 4b - 16a b)cosh(x) + 12a cosh(x) + (- 6b - 12a b)cosh(x) +--R + +--R 2 3 +--R 2a b + 8a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 2 4 6 4 2 2 4 5 +--R (3b + 6a b + 3a )sinh(x) + (18b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 4 +--R ((45b + 90a b + 45a )cosh(x) + 9b + 18a b + 9a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((60b + 120a b + 60a )cosh(x) + (36b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (45b + 90a b + 45a )cosh(x) + (54b + 108a b + 54a )cosh(x) +--R + +--R 4 2 2 4 +--R 9b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (18b + 36a b + 18a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 +--R (18b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (3b + 6a b + 3a )cosh(x) + (9b + 18a b + 9a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (9b + 18a b + 9a )cosh(x) + 3b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 530 +--d0503:= D(m0503,x) +--E 20 + +--S 21 of 530 +t0504:= tanh(x)/(%i+sinh(x)) +--R +--R +--R tanh(x) +--R (20) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 21 + +--S 22 of 530 +r0504:= 1/2*atan(sinh(x))-1/(2*%i+2*sinh(x)) +--R +--R +--R (sinh(x) + %i)atan(sinh(x)) - 1 +--R (21) ------------------------------- +--R 2sinh(x) + 2%i +--R Type: Expression(Complex(Integer)) +--E 22 + +--S 23 of 530 +a0504:= integrate(t0504,x) +--R +--R +--R (22) +--R 2 2 +--R (%i sinh(x) + (2%i cosh(x) - 2)sinh(x) + %i cosh(x) - 2cosh(x) - %i) +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R - 2sinh(x) - 2cosh(x) +--R / +--R 2 2 +--R 2sinh(x) + (4cosh(x) + 4%i)sinh(x) + 2cosh(x) + 4%i cosh(x) - 2 +--R Type: Union(Expression(Complex(Integer)),...) +--E 23 + +--S 24 of 530 +m0504:= a0504-r0504 +--R +--R +--R (23) +--R 3 2 +--R %i sinh(x) + (2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (%i cosh(x) - 4cosh(x) - 3%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1 +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 3 2 +--R - sinh(x) + (- 2cosh(x) - 3%i)sinh(x) +--R + +--R 2 2 +--R (- cosh(x) - 4%i cosh(x) + 3)sinh(x) - %i cosh(x) + 2cosh(x) + %i +--R * +--R atan(sinh(x)) +--R + +--R 2 2 +--R - sinh(x) + cosh(x) - 1 +--R / +--R 3 2 +--R 2sinh(x) + (4cosh(x) + 6%i)sinh(x) +--R + +--R 2 2 +--R (2cosh(x) + 8%i cosh(x) - 6)sinh(x) + 2%i cosh(x) - 4cosh(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 24 + +--S 25 of 530 +d0504:= D(m0504,x) +--R +--R +--R (24) +--R 6 5 2 4 +--R 2sinh(x) + (5cosh(x) + 2%i)sinh(x) + (2cosh(x) + 4%i cosh(x))sinh(x) +--R + +--R 3 3 +--R (- 4cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 3 2 2 +--R (- 4cosh(x) - 4%i cosh(x) + 6cosh(x) + 2%i cosh(x) - 2)sinh(x) +--R + +--R 5 4 3 2 +--R (- cosh(x) - 2%i cosh(x) + 2cosh(x) + 4%i cosh(x) - cosh(x) - 2%i) +--R * +--R sinh(x) +--R + +--R 3 +--R 2%i cosh(x) - 2%i cosh(x) +--R / +--R 7 6 +--R sinh(x) + (4cosh(x) + 3%i)sinh(x) +--R + +--R 2 5 +--R (6cosh(x) + 10%i cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 12%i cosh(x) - 2cosh(x) + 5%i)sinh(x) +--R + +--R 4 3 3 +--R (cosh(x) + 6%i cosh(x) + 12%i cosh(x) - 5)sinh(x) +--R + +--R 4 3 2 2 +--R (%i cosh(x) + 2cosh(x) + 12%i cosh(x) - 8cosh(x) + %i)sinh(x) +--R + +--R 4 3 2 +--R (cosh(x) + 6%i cosh(x) - 6cosh(x) + 2%i cosh(x) - 3)sinh(x) +--R + +--R 4 3 +--R %i cosh(x) - 2cosh(x) - 2cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 25 + +--S 26 of 530 +t0505:= tanh(x)^3/(%i+sinh(x)) +--R +--R +--R 3 +--R tanh(x) +--R (25) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 26 + +--S 27 of 530 +r0505:= 3/8*atan(sinh(x))+1/(8*%i-8*sinh(x))+1/8*%i/(%i+sinh(x))^2-_ + 1/(2*%i+2*sinh(x)) +--R +--R +--R (26) +--R 3 2 2 +--R (3sinh(x) + 3%i sinh(x) + 3sinh(x) + 3%i)atan(sinh(x)) - 5sinh(x) +--R + +--R - %i sinh(x) - 2 +--R / +--R 3 2 +--R 8sinh(x) + 8%i sinh(x) + 8sinh(x) + 8%i +--R Type: Expression(Complex(Integer)) +--E 27 + +--S 28 of 530 +a0505:= integrate(t0505,x) +--R +--R +--R (27) +--R 6 5 +--R 3%i sinh(x) + (18%i cosh(x) - 6)sinh(x) +--R + +--R 2 4 +--R (45%i cosh(x) - 30cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (60%i cosh(x) - 60cosh(x) + 12%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R (45%i cosh(x) - 60cosh(x) + 18%i cosh(x) - 36cosh(x) - 3%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 18%i cosh(x) - 30cosh(x) + 12%i cosh(x) - 36cosh(x) +--R + +--R - 6%i cosh(x) - 6 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 3%i cosh(x) - 6cosh(x) + 3%i cosh(x) - 12cosh(x) - 3%i cosh(x) +--R + +--R - 6cosh(x) - 3%i +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 5 4 +--R - 10sinh(x) + (- 50cosh(x) - 4%i)sinh(x) +--R + +--R 2 3 +--R (- 100cosh(x) - 16%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 2 +--R (- 100cosh(x) - 24%i cosh(x) + 12cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R (- 50cosh(x) - 16%i cosh(x) + 12cosh(x) + 8%i cosh(x) - 10)sinh(x) +--R + +--R 5 4 3 2 +--R - 10cosh(x) - 4%i cosh(x) + 4cosh(x) + 4%i cosh(x) - 10cosh(x) +--R / +--R 6 5 +--R 8sinh(x) + (48cosh(x) + 16%i)sinh(x) +--R + +--R 2 4 +--R (120cosh(x) + 80%i cosh(x) + 8)sinh(x) +--R + +--R 3 2 3 +--R (160cosh(x) + 160%i cosh(x) + 32cosh(x) + 32%i)sinh(x) +--R + +--R 4 3 2 2 +--R (120cosh(x) + 160%i cosh(x) + 48cosh(x) + 96%i cosh(x) - 8)sinh(x) +--R + +--R 5 4 3 2 +--R 48cosh(x) + 80%i cosh(x) + 32cosh(x) + 96%i cosh(x) - 16cosh(x) +--R + +--R 16%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 8cosh(x) + 16%i cosh(x) + 8cosh(x) + 32%i cosh(x) - 8cosh(x) +--R + +--R 16%i cosh(x) - 8 +--R Type: Union(Expression(Complex(Integer)),...) +--E 28 + +--S 29 of 530 +m0505:= a0505-r0505 +--R +--R +--R (28) +--R 9 8 +--R 3%i sinh(x) + (18%i cosh(x) - 9)sinh(x) +--R + +--R 2 7 +--R (45%i cosh(x) - 48cosh(x))sinh(x) +--R + +--R 3 2 6 +--R (60%i cosh(x) - 105cosh(x) - 24)sinh(x) +--R + +--R 4 3 2 +--R (45%i cosh(x) - 120cosh(x) + 3%i cosh(x) - 96cosh(x) - 18%i) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 18%i cosh(x) - 75cosh(x) + 12%i cosh(x) - 159cosh(x) +--R + +--R - 60%i cosh(x) - 18 +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 3%i cosh(x) - 24cosh(x) + 18%i cosh(x) - 144cosh(x) +--R + +--R 2 +--R - 81%i cosh(x) - 48cosh(x) - 24%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 3cosh(x) + 12%i cosh(x) - 78cosh(x) - 60%i cosh(x) +--R + +--R 2 +--R - 51cosh(x) - 48%i cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 3%i cosh(x) - 24cosh(x) - 27%i cosh(x) - 24cosh(x) +--R + +--R 2 +--R - 39%i cosh(x) - 9%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 3cosh(x) - 6%i cosh(x) - 3cosh(x) - 12%i cosh(x) + 3cosh(x) +--R + +--R - 6%i cosh(x) + 3 +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 9 8 +--R - 3sinh(x) + (- 18cosh(x) - 9%i)sinh(x) +--R + +--R 2 7 +--R (- 45cosh(x) - 48%i cosh(x))sinh(x) +--R + +--R 3 2 6 +--R (- 60cosh(x) - 105%i cosh(x) - 24%i)sinh(x) +--R + +--R 4 3 2 +--R (- 45cosh(x) - 120%i cosh(x) - 3cosh(x) - 96%i cosh(x) + 18) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 18cosh(x) - 75%i cosh(x) - 12cosh(x) - 159%i cosh(x) +--R + +--R 60cosh(x) - 18%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 3cosh(x) - 24%i cosh(x) - 18cosh(x) - 144%i cosh(x) +--R + +--R 2 +--R 81cosh(x) - 48%i cosh(x) + 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 3%i cosh(x) - 12cosh(x) - 78%i cosh(x) + 60cosh(x) +--R + +--R 2 +--R - 51%i cosh(x) + 48cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 3cosh(x) - 24%i cosh(x) + 27cosh(x) - 24%i cosh(x) +--R + +--R 2 +--R 39cosh(x) + 9 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 3%i cosh(x) + 6cosh(x) - 3%i cosh(x) + 12cosh(x) + 3%i cosh(x) +--R + +--R 6cosh(x) + 3%i +--R * +--R atan(sinh(x)) +--R + +--R 8 7 +--R - 5sinh(x) + (- 20cosh(x) - 3%i)sinh(x) +--R + +--R 2 6 +--R (- 25cosh(x) - 10%i cosh(x) + 3)sinh(x) +--R + +--R 2 5 +--R (- 9%i cosh(x) + 19%i)sinh(x) +--R + +--R 4 3 2 4 +--R (25cosh(x) + 4%i cosh(x) - 24cosh(x) + 38%i cosh(x) - 13)sinh(x) +--R + +--R 5 4 3 2 +--R 20cosh(x) + 11%i cosh(x) - 40cosh(x) - 2%i cosh(x) - 4cosh(x) +--R + +--R 15%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 5cosh(x) + 6%i cosh(x) - 21cosh(x) - 48%i cosh(x) + 27cosh(x) +--R + +--R 42%i cosh(x) - 23 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 4 3 2 +--R %i cosh(x) - 33%i cosh(x) + 24cosh(x) + 39%i cosh(x) - 24cosh(x) +--R + +--R - 7%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 2cosh(x) - 6%i cosh(x) + 6cosh(x) + 12%i cosh(x) - 6cosh(x) +--R + +--R - 6%i cosh(x) - 2 +--R / +--R 9 8 +--R 8sinh(x) + (48cosh(x) + 24%i)sinh(x) +--R + +--R 2 7 +--R (120cosh(x) + 128%i cosh(x))sinh(x) +--R + +--R 3 2 6 +--R (160cosh(x) + 280%i cosh(x) + 64%i)sinh(x) +--R + +--R 4 3 2 5 +--R (120cosh(x) + 320%i cosh(x) + 8cosh(x) + 256%i cosh(x) - 48)sinh(x) +--R + +--R 5 4 3 2 +--R 48cosh(x) + 200%i cosh(x) + 32cosh(x) + 424%i cosh(x) +--R + +--R - 160cosh(x) + 48%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 8cosh(x) + 64%i cosh(x) + 48cosh(x) + 384%i cosh(x) - 216cosh(x) +--R + +--R 128%i cosh(x) - 64 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 8%i cosh(x) + 32cosh(x) + 208%i cosh(x) - 160cosh(x) +--R + +--R 2 +--R 136%i cosh(x) - 128cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 8cosh(x) + 64%i cosh(x) - 72cosh(x) + 64%i cosh(x) - 104cosh(x) +--R + +--R - 24 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 8%i cosh(x) - 16cosh(x) + 8%i cosh(x) - 32cosh(x) - 8%i cosh(x) +--R + +--R - 16cosh(x) - 8%i +--R Type: Expression(Complex(Integer)) +--E 29 + +--S 30 of 530 +d0505:= D(m0505,x) +--R +--R +--R (29) +--R 12 11 +--R 2sinh(x) + (13cosh(x) + 2%i)sinh(x) +--R + +--R 2 10 +--R (34cosh(x) + 12%i cosh(x) - 2)sinh(x) +--R + +--R 3 2 9 +--R (42cosh(x) + 28%i cosh(x) - 4cosh(x) - 2%i)sinh(x) +--R + +--R 4 3 2 8 +--R (14cosh(x) + 28%i cosh(x) + 12cosh(x) - 8%i cosh(x) - 4)sinh(x) +--R + +--R 5 3 2 7 +--R (- 28cosh(x) + 50cosh(x) - 6%i cosh(x) - 28cosh(x) - 4%i)sinh(x) +--R + +--R 6 5 4 3 +--R - 42cosh(x) - 28%i cosh(x) + 70cosh(x) + 20%i cosh(x) +--R + +--R 2 +--R - 60cosh(x) - 34%i cosh(x) + 4 +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 26cosh(x) - 28%i cosh(x) + 48cosh(x) + 50%i cosh(x) +--R + +--R 3 2 +--R - 44cosh(x) - 78%i cosh(x) + 6cosh(x) + 4%i +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 8cosh(x) - 12%i cosh(x) + 16cosh(x) + 48%i cosh(x) + 10cosh(x) +--R + +--R 3 2 +--R - 62%i cosh(x) - 20cosh(x) + 2%i cosh(x) + 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R - cosh(x) - 2%i cosh(x) + 2cosh(x) + 22%i cosh(x) + 30cosh(x) +--R + +--R 4 3 2 +--R 4%i cosh(x) - 46cosh(x) - 26%i cosh(x) + 15cosh(x) + 2%i +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 4%i cosh(x) + 14cosh(x) + 30%i cosh(x) - 30cosh(x) +--R + +--R 3 2 +--R - 48%i cosh(x) + 18cosh(x) + 14%i cosh(x) - 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 2cosh(x) + 14%i cosh(x) - 6cosh(x) - 30%i cosh(x) + 6cosh(x) +--R + +--R 2 +--R 18%i cosh(x) - 2cosh(x) - 2%i +--R * +--R sinh(x) +--R + +--R 7 5 3 +--R 2%i cosh(x) - 6%i cosh(x) + 6%i cosh(x) - 2%i cosh(x) +--R / +--R 13 12 +--R sinh(x) + (8cosh(x) + 3%i)sinh(x) +--R + +--R 2 11 +--R (28cosh(x) + 22%i cosh(x) + 2)sinh(x) +--R + +--R 3 2 10 +--R (56cosh(x) + 70%i cosh(x) + 14cosh(x) + 14%i)sinh(x) +--R + +--R 4 3 2 9 +--R (70cosh(x) + 126%i cosh(x) + 44cosh(x) + 86%i cosh(x) - 5)sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) + 140%i cosh(x) + 82cosh(x) + 230%i cosh(x) - 26cosh(x) +--R + +--R 25%i +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) + 98%i cosh(x) + 100cosh(x) + 352%i cosh(x) +--R + +--R 2 +--R - 56cosh(x) + 124%i cosh(x) - 20 +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 8cosh(x) + 42%i cosh(x) + 82cosh(x) + 340%i cosh(x) - 64cosh(x) +--R + +--R 2 +--R 268%i cosh(x) - 84cosh(x) + 20%i +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 10%i cosh(x) + 44cosh(x) + 214%i cosh(x) - 40cosh(x) +--R + +--R 3 2 +--R 332%i cosh(x) - 152cosh(x) + 76%i cosh(x) - 25 +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R %i cosh(x) + 14cosh(x) + 86%i cosh(x) - 10cosh(x) +--R + +--R 4 3 2 +--R 260%i cosh(x) - 156cosh(x) + 124%i cosh(x) - 76cosh(x) + 5%i +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 2cosh(x) + 20%i cosh(x) + 4cosh(x) + 134%i cosh(x) - 100cosh(x) +--R + +--R 3 2 +--R 112%i cosh(x) - 100cosh(x) + 14%i cosh(x) - 14 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 2%i cosh(x) + 4cosh(x) + 46%i cosh(x) - 42cosh(x) + 60%i cosh(x) +--R + +--R 3 2 +--R - 72cosh(x) + 14%i cosh(x) - 26cosh(x) - 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 10%i cosh(x) - 12cosh(x) + 18%i cosh(x) - 30cosh(x) +--R + +--R 3 2 +--R 6%i cosh(x) - 20cosh(x) - 2%i cosh(x) - 3 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 3 +--R %i cosh(x) - 2cosh(x) + 2%i cosh(x) - 6cosh(x) - 6cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - 2cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 30 + +--S 31 of 530 +t0506:= tanh(x)^4/(%i+sinh(x)) +--R +--R +--R 4 +--R tanh(x) +--R (30) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 31 + +--S 32 of 530 +r0506:= -1/15*(-4*sinh(x)+12*sinh(x)*cosh(x)^2-%i+6*%i*cosh(x)^2+_ + 3*%i*cosh(x)^4)/cosh(x)^3/(%i+sinh(x)) +--R +--R +--R 2 4 2 +--R (- 12cosh(x) + 4)sinh(x) - 3%i cosh(x) - 6%i cosh(x) + %i +--R (31) ------------------------------------------------------------ +--R 3 3 +--R 15cosh(x) sinh(x) + 15%i cosh(x) +--R Type: Expression(Complex(Integer)) +--E 32 + +--S 33 of 530 +a0506:= integrate(t0506,x) +--R +--R +--R (32) +--R 4 3 +--R - 30sinh(x) + (- 120cosh(x) - 24%i)sinh(x) +--R + +--R 2 2 +--R (- 180cosh(x) - 108%i cosh(x) + 8)sinh(x) +--R + +--R 3 2 4 +--R (- 120cosh(x) - 72%i cosh(x) - 56cosh(x) - 8%i)sinh(x) - 30cosh(x) +--R + +--R 3 2 +--R - 36%i cosh(x) + 8cosh(x) - 92%i cosh(x) - 26 +--R / +--R 5 4 +--R 15sinh(x) + (75cosh(x) + 30%i)sinh(x) +--R + +--R 2 3 +--R (150cosh(x) + 120%i cosh(x) + 45)sinh(x) +--R + +--R 3 2 2 +--R (150cosh(x) + 180%i cosh(x) + 45cosh(x) + 120%i)sinh(x) +--R + +--R 4 3 2 +--R (75cosh(x) + 120%i cosh(x) + 135cosh(x) + 120%i cosh(x) + 30)sinh(x) +--R + +--R 5 4 3 2 +--R 15cosh(x) + 30%i cosh(x) + 15cosh(x) + 120%i cosh(x) - 30cosh(x) + 90%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 33 + +--S 34 of 530 +m0506:= a0506-r0506 +--R +--R +--R (33) +--R 2 6 +--R (12cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 5 +--R (3%i cosh(x) + 30cosh(x) + 30%i cosh(x) - 20cosh(x) - 9%i)sinh(x) +--R + +--R 5 4 3 2 +--R 15%i cosh(x) - 6cosh(x) + 72%i cosh(x) - 16cosh(x) - 37%i cosh(x) +--R + +--R - 10 +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 30%i cosh(x) - 84cosh(x) - 15%i cosh(x) - 20cosh(x) +--R + +--R 2 +--R 56%i cosh(x) - 4cosh(x) - 35%i +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 30%i cosh(x) - 96cosh(x) - 87%i cosh(x) + 44cosh(x) +--R + +--R 3 2 +--R 72%i cosh(x) - 48cosh(x) - 35%i cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 15%i cosh(x) - 42cosh(x) - 75%i cosh(x) + 16cosh(x) +--R + +--R 4 3 2 +--R - 5%i cosh(x) - 86cosh(x) + 43%i cosh(x) + 16cosh(x) - 26%i +--R * +--R sinh(x) +--R + +--R 9 8 7 5 4 +--R 3%i cosh(x) - 6cosh(x) - 21%i cosh(x) + 7%i cosh(x) + 28cosh(x) +--R + +--R 3 2 +--R - 39%i cosh(x) - 28cosh(x) + 2%i cosh(x) + 6 +--R / +--R 3 6 4 3 5 +--R 15cosh(x) sinh(x) + (75cosh(x) + 45%i cosh(x) )sinh(x) +--R + +--R 5 4 3 4 +--R (150cosh(x) + 195%i cosh(x) + 15cosh(x) )sinh(x) +--R + +--R 6 5 4 3 3 +--R (150cosh(x) + 330%i cosh(x) - 75cosh(x) + 165%i cosh(x) )sinh(x) +--R + +--R 7 6 5 4 +--R 75cosh(x) + 270%i cosh(x) - 45cosh(x) + 165%i cosh(x) +--R + +--R 3 +--R - 90cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 15cosh(x) + 105%i cosh(x) - 105cosh(x) + 255%i cosh(x) +--R + +--R 4 3 +--R - 150cosh(x) + 120%i cosh(x) +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 15%i cosh(x) - 30cosh(x) + 15%i cosh(x) - 120cosh(x) - 30%i cosh(x) +--R + +--R 3 +--R - 90cosh(x) +--R Type: Expression(Complex(Integer)) +--E 34 + +--S 35 of 530 +d0506:= D(m0506,x) +--R +--R +--R (34) +--R 2 13 +--R (- 12cosh(x) + 12)sinh(x) +--R + +--R 4 3 2 12 +--R (3%i cosh(x) - 120cosh(x) - 66%i cosh(x) + 120cosh(x) + 63%i)sinh(x) +--R + +--R 5 4 3 2 +--R 30%i cosh(x) - 525cosh(x) - 612%i cosh(x) + 594cosh(x) +--R + +--R 582%i cosh(x) - 39 +--R * +--R 11 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 132%i cosh(x) - 1308cosh(x) - 2466%i cosh(x) + 2100cosh(x) +--R + +--R 2 +--R 2052%i cosh(x) - 522cosh(x) + 354%i +--R * +--R 10 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 330%i cosh(x) - 1995cosh(x) - 5304%i cosh(x) + 4920cosh(x) +--R + +--R 3 2 +--R 4074%i cosh(x) - 1587cosh(x) + 1824%i cosh(x) - 654 +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 495%i cosh(x) - 1764cosh(x) - 6072%i cosh(x) + 7068cosh(x) +--R + +--R 4 3 2 +--R 3030%i cosh(x) - 1092cosh(x) + 4140%i cosh(x) - 3864cosh(x) + 447%i +--R * +--R 8 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 396%i cosh(x) - 450cosh(x) - 2232%i cosh(x) + 4578cosh(x) +--R + +--R 5 4 3 2 +--R - 2670%i cosh(x) + 5719cosh(x) + 7860%i cosh(x) - 7290cosh(x) +--R + +--R - 198%i cosh(x) - 1875 +--R * +--R 7 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 1080cosh(x) + 3708%i cosh(x) - 3594cosh(x) - 7518%i cosh(x) +--R + +--R 5 4 3 2 +--R 15590cosh(x) + 9580%i cosh(x) - 9000cosh(x) + 258%i cosh(x) +--R + +--R - 5010cosh(x) - 528%i +--R * +--R 6 +--R sinh(x) +--R + +--R 11 10 9 8 +--R - 396%i cosh(x) + 1854cosh(x) + 6816%i cosh(x) - 11142cosh(x) +--R + +--R 7 6 5 4 +--R - 10542%i cosh(x) + 14611cosh(x) + 10556%i cosh(x) - 98cosh(x) +--R + +--R 3 2 +--R 978%i cosh(x) - 6501cosh(x) - 3468%i cosh(x) - 1896 +--R * +--R 5 +--R sinh(x) +--R + +--R 12 11 10 9 +--R - 495%i cosh(x) + 1680cosh(x) + 5646%i cosh(x) - 11202cosh(x) +--R + +--R 8 7 6 5 +--R - 12195%i cosh(x) + 7634cosh(x) + 6228%i cosh(x) + 5360cosh(x) +--R + +--R 4 3 2 +--R 6264%i cosh(x) - 5496cosh(x) - 2508%i cosh(x) - 1116cosh(x) - 1296%i +--R * +--R 4 +--R sinh(x) +--R + +--R 13 12 11 10 +--R - 330%i cosh(x) + 1023cosh(x) + 2748%i cosh(x) - 6012cosh(x) +--R + +--R 9 8 7 6 +--R - 8736%i cosh(x) + 5188cosh(x) + 492%i cosh(x) + 1464cosh(x) +--R + +--R 5 4 3 2 +--R 9654%i cosh(x) - 1235cosh(x) - 1968%i cosh(x) - 1272cosh(x) +--R + +--R - 1956%i cosh(x) - 516 +--R * +--R 3 +--R sinh(x) +--R + +--R 14 13 12 11 +--R - 132%i cosh(x) + 420cosh(x) + 774%i cosh(x) - 1794cosh(x) +--R + +--R 10 9 8 7 +--R - 3078%i cosh(x) + 3404cosh(x) + 842%i cosh(x) + 1278cosh(x) +--R + +--R 6 5 4 3 +--R 926%i cosh(x) - 4420cosh(x) + 1868%i cosh(x) + 120cosh(x) +--R + +--R 2 +--R - 636%i cosh(x) + 672cosh(x) - 612%i +--R * +--R 2 +--R sinh(x) +--R + +--R 15 14 13 12 +--R - 30%i cosh(x) + 105cosh(x) + 120%i cosh(x) - 246cosh(x) +--R + +--R 11 10 9 8 +--R - 372%i cosh(x) + 1164cosh(x) + 484%i cosh(x) - 550cosh(x) +--R + +--R 7 6 5 4 +--R 286%i cosh(x) - 225cosh(x) - 788%i cosh(x) - 488cosh(x) +--R + +--R 3 2 +--R 228%i cosh(x) + 132cosh(x) + 72%i cosh(x) + 108 +--R * +--R sinh(x) +--R + +--R 16 15 14 13 +--R - 3%i cosh(x) + 12cosh(x) + 12%i cosh(x) + 6cosh(x) +--R + +--R 12 11 10 9 +--R - 18%i cosh(x) + 42cosh(x) + 264%i cosh(x) + 10cosh(x) +--R + +--R 8 7 6 5 +--R - 183%i cosh(x) + 18cosh(x) - 240%i cosh(x) - 16cosh(x) +--R + +--R 4 3 2 +--R 60%i cosh(x) - 72cosh(x) + 108%i cosh(x) +--R / +--R 4 12 5 4 11 +--R 15cosh(x) sinh(x) + (150cosh(x) + 90%i cosh(x) )sinh(x) +--R + +--R 6 5 4 10 +--R (675cosh(x) + 840%i cosh(x) - 105cosh(x) )sinh(x) +--R + +--R 7 6 5 4 9 +--R (1800cosh(x) + 3510%i cosh(x) - 1170cosh(x) + 420%i cosh(x) )sinh(x) +--R + +--R 8 7 6 5 +--R 3150cosh(x) + 8640%i cosh(x) - 5055cosh(x) + 1920%i cosh(x) +--R + +--R 4 +--R - 1155cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 3780cosh(x) + 13860%i cosh(x) - 12060cosh(x) + 3900%i cosh(x) +--R + +--R 5 4 +--R - 6630cosh(x) + 30%i cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 3150cosh(x) + 15120%i cosh(x) - 18270cosh(x) + 4620%i cosh(x) +--R + +--R 6 5 4 +--R - 16335cosh(x) - 3420%i cosh(x) - 2895cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 1800cosh(x) + 11340%i cosh(x) - 18720cosh(x) + 2820%i cosh(x) +--R + +--R 7 6 5 4 +--R - 25680cosh(x) - 8610%i cosh(x) - 6870cosh(x) - 2280%i cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 11 10 9 +--R 675cosh(x) + 5760%i cosh(x) - 13170cosh(x) - 660%i cosh(x) +--R + +--R 8 7 6 5 +--R - 25035cosh(x) - 16980%i cosh(x) - 11925cosh(x) - 8880%i cosh(x) +--R + +--R 4 +--R - 2280cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 13 12 11 10 +--R 150cosh(x) + 1890%i cosh(x) - 6180cosh(x) - 2700%i cosh(x) +--R + +--R 9 8 7 6 +--R - 15630cosh(x) - 15990%i cosh(x) - 7380cosh(x) - 13380%i cosh(x) +--R + +--R 5 4 +--R 720cosh(x) - 3420%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 13 12 11 +--R 15cosh(x) + 360%i cosh(x) - 1785cosh(x) - 1980%i cosh(x) +--R + +--R 10 9 8 7 +--R - 5025cosh(x) - 10980%i cosh(x) - 2985cosh(x) - 12660%i cosh(x) +--R + +--R 6 5 4 +--R 60cosh(x) - 4020%i cosh(x) + 120cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 14 13 12 11 +--R 30%i cosh(x) - 270cosh(x) - 600%i cosh(x) - 540cosh(x) +--R + +--R 10 9 8 7 +--R - 3270%i cosh(x) + 1770cosh(x) - 5700%i cosh(x) + 4440cosh(x) +--R + +--R 6 5 4 +--R - 4380%i cosh(x) + 2280cosh(x) - 1440%i cosh(x) +--R * +--R sinh(x) +--R + +--R 14 13 12 11 +--R - 15cosh(x) - 60%i cosh(x) + 30cosh(x) - 300%i cosh(x) +--R + +--R 10 9 8 7 +--R 525cosh(x) - 300%i cosh(x) + 1380cosh(x) + 300%i cosh(x) +--R + +--R 6 5 4 +--R 1380cosh(x) + 360%i cosh(x) + 540cosh(x) +--R Type: Expression(Complex(Integer)) +--E 35 + +--S 36 of 530 +t0507:= coth(x)/(a+b*sinh(x)) +--R +--R +--R coth(x) +--R (35) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 36 + +--S 37 of 530 +r0507:= -(-log(sinh(x))+log(a+b*sinh(x)))/a +--R +--R +--R - log(b sinh(x) + a) + log(sinh(x)) +--R (36) ----------------------------------- +--R a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 530 +a0507:= integrate(t0507,x) +--R +--R +--R 2sinh(x) - 2b sinh(x) - 2a +--R log(- -----------------) - log(-----------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R (37) ------------------------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 530 +m0507:= a0507-r0507 +--R +--R +--R (38) +--R 2sinh(x) +--R log(b sinh(x) + a) - log(sinh(x)) + log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2b sinh(x) - 2a +--R - log(-----------------) +--R sinh(x) - cosh(x) +--R / +--R a +--R Type: Expression(Integer) +--E 39 + +--S 40 of 530 +d0507:= D(m0507,x) +--R +--R +--R (39) 0 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 530 +t0508:= coth(x)^2/(a+b*sinh(x)) +--R +--R +--R 2 +--R coth(x) +--R (40) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 41 + +--S 42 of 530 +r0508:= b*acoth(cosh(x))/a^2-2*(a^2+b^2)^(1/2)*_ + atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^2-coth(x)/a +--R +--R +--R x +--R +-------+ a tanh(-) - b +--R | 2 2 2 +--R 2\|b + a atanh(-------------) + b acoth(cosh(x)) - a coth(x) +--R +-------+ +--R | 2 2 +--R \|b + a +--R (41) -------------------------------------------------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 42 + +--S 43 of 530 +a0508:= integrate(t0508,x) +--R +--R +--R (42) +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) + b) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R - 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 530 +m0508:= a0508-r0508 +--R +--R +--R (43) +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) + b) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2)\|b + a +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) + b)acoth(cosh(x)) +--R + +--R 2 2 +--R a coth(x)sinh(x) + 2a cosh(x)coth(x)sinh(x) + (a cosh(x) - a)coth(x) - 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a +--R Type: Expression(Integer) +--E 44 + +--S 45 of 530 +d0508:= D(m0508,x) +--R +--R +--R (44) +--R 2 7 +--R a b sinh(x) +--R + +--R 2 2 2 2 3 2 2 3 +--R (- a b cosh(x) + a b)coth(x) - b cosh(x) + 6a b cosh(x) + b +--R + +--R 2 +--R 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (- 6a b cosh(x) - 2a cosh(x) + 6a b cosh(x) + 2a )coth(x) +--R + +--R 3 3 2 3 2 3 2 +--R - 6b cosh(x) + (13a b + 2a )cosh(x) + (6b + 10a b)cosh(x) +--R + +--R 2 3 +--R - a b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 +--R - 15a b cosh(x) - 10a cosh(x) + 18a b cosh(x) +--R + +--R 3 2 +--R 10a cosh(x) - 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 4 2 3 3 3 2 2 +--R - 15b cosh(x) + (10a b + 10a )cosh(x) + (18b + 20a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 2a b - 10a )cosh(x) - 3b - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 +--R - 20a b cosh(x) - 20a cosh(x) + 32a b cosh(x) +--R + +--R 3 2 2 3 +--R 24a cosh(x) - 12a b cosh(x) - 4a +--R * +--R 2 +--R coth(x) +--R + +--R 3 5 2 3 4 +--R - 20b cosh(x) + (- 5a b + 20a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (32b + 20a b)cosh(x) + (6a b - 16a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b - 12a b)cosh(x) - a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 2 4 +--R - 15a b cosh(x) - 20a cosh(x) + 33a b cosh(x) +--R + +--R 3 3 2 2 3 2 +--R 32a cosh(x) - 21a b cosh(x) - 12a cosh(x) + 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 6 2 3 5 +--R - 15b cosh(x) + (- 14a b + 20a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (33b + 10a b)cosh(x) + (20a b - 8a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 21b - 12a b)cosh(x) + (- 6a b - 12a )cosh(x) + 3b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 2 5 +--R - 6a b cosh(x) - 10a cosh(x) + 18a b cosh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 22a cosh(x) - 18a b cosh(x) - 14a cosh(x) + 6a b cosh(x) +--R + +--R 3 +--R 2a +--R * +--R 2 +--R coth(x) +--R + +--R 3 7 2 3 6 3 2 5 +--R - 6b cosh(x) + (- 9a b + 10a )cosh(x) + (18b + 2a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (19a b + 2a )cosh(x) + (- 18b - 4a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 11a b - 10a )cosh(x) + (6b + 2a b)cosh(x) + a b - 2a +--R * +--R sinh(x) +--R + +--R 2 8 3 7 2 6 3 5 +--R - a b cosh(x) - 2a cosh(x) + 4a b cosh(x) + 6a cosh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R - 6a b cosh(x) - 6a cosh(x) + 4a b cosh(x) + 2a cosh(x) - a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 8 2 3 7 3 6 +--R - b cosh(x) + (- 2a b + 2a )cosh(x) + 4b cosh(x) +--R + +--R 2 3 5 3 4 2 3 3 +--R (6a b + 2a )cosh(x) - 6b cosh(x) + (- 6a b - 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R 4b cosh(x) + (2a b - 2a )cosh(x) - b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 7 +--R - 2b sinh(x) +--R + +--R 2 2 2 2 2 2 3 +--R (2a b cosh(x) - 2a b )coth(x) - 2a b cosh(x) - 12b cosh(x) +--R + +--R 2 +--R - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 2 2 2 2 2 +--R (12a b cosh(x) + 4a b cosh(x) - 12a b cosh(x) - 4a b)coth(x) +--R + +--R 2 3 3 2 2 2 3 +--R - 12a b cosh(x) + (- 30b - 8a b)cosh(x) - 8a b cosh(x) + 6b +--R + +--R 2 +--R 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 30a b cosh(x) + 20a b cosh(x) - 36a b cosh(x) +--R + +--R 2 2 +--R - 20a b cosh(x) + 6a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 2 3 2 2 +--R - 30a b cosh(x) + (- 40b - 40a b)cosh(x) - 4a b cosh(x) +--R + +--R 3 2 2 +--R (24b + 40a b)cosh(x) + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 40a b cosh(x) + 40a b cosh(x) - 64a b cosh(x) +--R + +--R 2 2 2 2 +--R - 48a b cosh(x) + 24a b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 2 4 2 3 +--R - 40a b cosh(x) + (- 30b - 80a b)cosh(x) + 24a b cosh(x) +--R + +--R 3 2 2 3 +--R (36b + 80a b)cosh(x) - 6b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 5 2 4 +--R 30a b cosh(x) + 40a b cosh(x) - 66a b cosh(x) +--R + +--R 2 3 2 2 2 2 +--R - 64a b cosh(x) + 42a b cosh(x) + 24a b cosh(x) - 6a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 6 3 2 5 2 4 +--R - 30a b cosh(x) + (- 12b - 80a b)cosh(x) + 46a b cosh(x) +--R + +--R 3 2 3 2 2 3 2 +--R (24b + 80a b)cosh(x) - 18a b cosh(x) - 12b cosh(x) + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 6 2 5 +--R 12a b cosh(x) + 20a b cosh(x) - 36a b cosh(x) +--R + +--R 2 4 2 3 2 2 +--R - 44a b cosh(x) + 36a b cosh(x) + 28a b cosh(x) +--R + +--R 2 2 +--R - 12a b cosh(x) - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 7 3 2 6 2 5 +--R - 12a b cosh(x) + (- 2b - 40a b)cosh(x) + 32a b cosh(x) +--R + +--R 3 2 4 2 3 3 2 2 +--R (6b + 40a b)cosh(x) - 28a b cosh(x) + (- 6b - 8a b)cosh(x) +--R + +--R 2 3 2 +--R 8a b cosh(x) + 2b + 8a b +--R * +--R sinh(x) +--R + +--R 2 8 2 7 2 6 2 5 +--R 2a b cosh(x) + 4a b cosh(x) - 8a b cosh(x) - 12a b cosh(x) +--R + +--R 2 4 2 3 2 2 2 +--R 12a b cosh(x) + 12a b cosh(x) - 8a b cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 8 2 7 2 6 2 5 +--R - 2a b cosh(x) - 8a b cosh(x) + 8a b cosh(x) + 8a b cosh(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R - 12a b cosh(x) - 8a b cosh(x) + 8a b cosh(x) + 8a b cosh(x) - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 7 +--R - a b sinh(x) +--R + +--R 2 2 2 2 3 2 2 3 2 +--R ((a b cosh(x) - a b)coth(x) + b cosh(x) - 6a b cosh(x) - b - 2a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (6a b cosh(x) + 2a cosh(x) - 6a b cosh(x) - 2a )coth(x) +--R + +--R 3 3 2 3 2 3 2 +--R 6b cosh(x) + (- 13a b - 2a )cosh(x) + (- 6b - 10a b)cosh(x) +--R + +--R 2 3 +--R a b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R 15a b cosh(x) + 10a cosh(x) - 18a b cosh(x) - 10a cosh(x) +--R + +--R 2 +--R 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 4 2 3 3 3 2 2 +--R 15b cosh(x) + (- 10a b - 10a )cosh(x) + (- 18b - 20a b)cosh(x) +--R + +--R 2 3 3 2 +--R (2a b + 10a )cosh(x) + 3b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 20a b cosh(x) + 20a cosh(x) - 32a b cosh(x) - 24a cosh(x) +--R + +--R 2 3 +--R 12a b cosh(x) + 4a +--R * +--R 2 +--R coth(x) +--R + +--R 3 5 2 3 4 3 2 3 +--R 20b cosh(x) + (5a b - 20a )cosh(x) + (- 32b - 20a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 6a b + 16a )cosh(x) + (12b + 12a b)cosh(x) + a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R 15a b cosh(x) + 20a cosh(x) - 33a b cosh(x) - 32a cosh(x) +--R + +--R 2 2 3 2 +--R 21a b cosh(x) + 12a cosh(x) - 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 6 2 3 5 3 2 4 +--R 15b cosh(x) + (14a b - 20a )cosh(x) + (- 33b - 10a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (- 20a b + 8a )cosh(x) + (21b + 12a b)cosh(x) +--R + +--R 2 3 3 2 +--R (6a b + 12a )cosh(x) - 3b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 2 5 3 4 +--R 6a b cosh(x) + 10a cosh(x) - 18a b cosh(x) - 22a cosh(x) +--R + +--R 2 3 3 2 2 3 +--R 18a b cosh(x) + 14a cosh(x) - 6a b cosh(x) - 2a +--R * +--R 2 +--R coth(x) +--R + +--R 3 7 2 3 6 3 2 5 +--R 6b cosh(x) + (9a b - 10a )cosh(x) + (- 18b - 2a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (- 19a b - 2a )cosh(x) + (18b + 4a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (11a b + 10a )cosh(x) + (- 6b - 2a b)cosh(x) - a b + 2a +--R * +--R sinh(x) +--R + +--R 2 8 3 7 2 6 3 5 +--R a b cosh(x) + 2a cosh(x) - 4a b cosh(x) - 6a cosh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R 6a b cosh(x) + 6a cosh(x) - 4a b cosh(x) - 2a cosh(x) + a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 8 2 3 7 3 6 +--R b cosh(x) + (2a b - 2a )cosh(x) - 4b cosh(x) +--R + +--R 2 3 5 3 4 2 3 3 +--R (- 6a b - 2a )cosh(x) + 6b cosh(x) + (6a b + 2a )cosh(x) +--R + +--R 3 2 2 3 3 +--R - 4b cosh(x) + (- 2a b + 2a )cosh(x) + b +--R / +--R 3 2 3 6 +--R (a b cosh(x) - a b)sinh(x) +--R + +--R 3 3 4 2 3 4 5 +--R (6a b cosh(x) + 2a cosh(x) - 6a b cosh(x) - 2a )sinh(x) +--R + +--R 3 4 4 3 3 2 4 +--R 15a b cosh(x) + 10a cosh(x) - 18a b cosh(x) - 10a cosh(x) +--R + +--R 3 +--R 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R 20a b cosh(x) + 20a cosh(x) - 32a b cosh(x) - 24a cosh(x) +--R + +--R 3 4 +--R 12a b cosh(x) + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R 15a b cosh(x) + 20a cosh(x) - 33a b cosh(x) - 32a cosh(x) +--R + +--R 3 2 4 3 +--R 21a b cosh(x) + 12a cosh(x) - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 4 4 +--R 6a b cosh(x) + 10a cosh(x) - 18a b cosh(x) - 22a cosh(x) +--R + +--R 3 3 4 2 3 4 +--R 18a b cosh(x) + 14a cosh(x) - 6a b cosh(x) - 2a +--R * +--R sinh(x) +--R + +--R 3 8 4 7 3 6 4 5 +--R a b cosh(x) + 2a cosh(x) - 4a b cosh(x) - 6a cosh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R 6a b cosh(x) + 6a cosh(x) - 4a b cosh(x) - 2a cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 2 6 +--R (- 2a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 3 3 2 2 2 3 5 +--R (- 12a b cosh(x) - 4a b cosh(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R - 30a b cosh(x) - 20a b cosh(x) + 36a b cosh(x) +--R + +--R 3 2 2 +--R 20a b cosh(x) - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R - 40a b cosh(x) - 40a b cosh(x) + 64a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 48a b cosh(x) - 24a b cosh(x) - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R - 30a b cosh(x) - 40a b cosh(x) + 66a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 64a b cosh(x) - 42a b cosh(x) - 24a b cosh(x) + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R - 12a b cosh(x) - 20a b cosh(x) + 36a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 2 2 +--R 44a b cosh(x) - 36a b cosh(x) - 28a b cosh(x) + 12a b cosh(x) +--R + +--R 3 +--R 4a b +--R * +--R sinh(x) +--R + +--R 2 2 8 3 7 2 2 6 3 5 +--R - 2a b cosh(x) - 4a b cosh(x) + 8a b cosh(x) + 12a b cosh(x) +--R + +--R 2 2 4 3 3 2 2 2 3 +--R - 12a b cosh(x) - 12a b cosh(x) + 8a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 +--R - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 3 6 +--R (- a b cosh(x) + a b)sinh(x) +--R + +--R 3 3 4 2 3 4 5 +--R (- 6a b cosh(x) - 2a cosh(x) + 6a b cosh(x) + 2a )sinh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R (- 15a b cosh(x) - 10a cosh(x) + 18a b cosh(x) + 10a cosh(x) - 3a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R - 20a b cosh(x) - 20a cosh(x) + 32a b cosh(x) + 24a cosh(x) +--R + +--R 3 4 +--R - 12a b cosh(x) - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R - 15a b cosh(x) - 20a cosh(x) + 33a b cosh(x) + 32a cosh(x) +--R + +--R 3 2 4 3 +--R - 21a b cosh(x) - 12a cosh(x) + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 4 4 +--R - 6a b cosh(x) - 10a cosh(x) + 18a b cosh(x) + 22a cosh(x) +--R + +--R 3 3 4 2 3 4 +--R - 18a b cosh(x) - 14a cosh(x) + 6a b cosh(x) + 2a +--R * +--R sinh(x) +--R + +--R 3 8 4 7 3 6 4 5 +--R - a b cosh(x) - 2a cosh(x) + 4a b cosh(x) + 6a cosh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R - 6a b cosh(x) - 6a cosh(x) + 4a b cosh(x) + 2a cosh(x) - a b +--R Type: Expression(Integer) +--E 45 + +--S 46 of 530 +t0509:= coth(x)^3/(a+b*sinh(x)) +--R +--R +--R 3 +--R coth(x) +--R (45) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 530 +r0509:= b*csch(x)/a^2-1/2*csch(x)^2/a+(a^2+b^2)*log(sinh(x))/a^3-_ + (a^2+b^2)*log(a+b*sinh(x))/a^3 +--R +--R +--R (46) +--R 2 2 2 2 2 2 +--R (- 2b - 2a )log(b sinh(x) + a) + (2b + 2a )log(sinh(x)) - a csch(x) +--R + +--R 2a b csch(x) +--R / +--R 3 +--R 2a +--R Type: Expression(Integer) +--E 47 + +--S 48 of 530 +a0509:= integrate(t0509,x) +--R +--R +--R (47) +--R 2 2 4 2 2 3 +--R (b + a )sinh(x) + (4b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 6a )cosh(x) - 2b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 4a )cosh(x) + (- 4b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + a )cosh(x) + (- 2b - 2a )cosh(x) + b + a +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- b - a )sinh(x) + (- 4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b - 6a )cosh(x) + 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b - 4a )cosh(x) + (4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b - a )cosh(x) + (2b + 2a )cosh(x) - b - a +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 +--R 2a b sinh(x) + (6a b cosh(x) - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R (6a b cosh(x) - 4a cosh(x) - 2a b)sinh(x) + 2a b cosh(x) - 2a cosh(x) +--R + +--R - 2a b cosh(x) +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) - 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) - 4a cosh(x))sinh(x) + a cosh(x) - 2a cosh(x) + a +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 530 +m0509:= a0509-r0509 +--R +--R +--R (48) +--R 2 2 4 2 2 3 +--R (2b + 2a )sinh(x) + (8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 12a )cosh(x) - 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 8a )cosh(x) + (- 8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + 2a )cosh(x) + (- 4b - 4a )cosh(x) + 2b + 2a +--R * +--R log(b sinh(x) + a) +--R + +--R 2 2 4 2 2 3 +--R (- 2b - 2a )sinh(x) + (- 8b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b - 12a )cosh(x) + 4b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b - 8a )cosh(x) + (8b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b - 2a )cosh(x) + (4b + 4a )cosh(x) - 2b - 2a +--R * +--R log(sinh(x)) +--R + +--R 2 2 4 2 2 3 +--R (2b + 2a )sinh(x) + (8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 12a )cosh(x) - 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 8a )cosh(x) + (- 8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + 2a )cosh(x) + (- 4b - 4a )cosh(x) + 2b + 2a +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2b - 2a )sinh(x) + (- 8b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b - 12a )cosh(x) + 4b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b - 8a )cosh(x) + (8b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b - 2a )cosh(x) + (4b + 4a )cosh(x) - 2b - 2a +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 +--R (a csch(x) - 2a b csch(x))sinh(x) +--R + +--R 2 2 3 +--R (4a cosh(x)csch(x) - 8a b cosh(x)csch(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 2a )csch(x) + (- 12a b cosh(x) + 4a b)csch(x) +--R + +--R 2 +--R 12a b cosh(x) - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4a cosh(x) - 4a cosh(x))csch(x) +--R + +--R 3 2 2 +--R (- 8a b cosh(x) + 8a b cosh(x))csch(x) + 12a b cosh(x) - 8a cosh(x) +--R + +--R - 4a b +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (a cosh(x) - 2a cosh(x) + a )csch(x) +--R + +--R 4 2 3 +--R (- 2a b cosh(x) + 4a b cosh(x) - 2a b)csch(x) + 4a b cosh(x) +--R + +--R 2 2 +--R - 4a cosh(x) - 4a b cosh(x) +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) - 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) - 8a cosh(x))sinh(x) + 2a cosh(x) - 4a cosh(x) + 2a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 530 +d0509:= D(m0509,x) +--R +--R +--R (49) +--R 2 6 +--R (- a coth(x)csch(x) + b coth(x)csch(x))sinh(x) +--R + +--R 2 5 +--R (- 6a cosh(x)coth(x)csch(x) + 6b cosh(x)coth(x)csch(x) - 2b)sinh(x) +--R + +--R 2 2 +--R (- 15a cosh(x) + 3a)coth(x)csch(x) +--R + +--R 2 +--R (15b cosh(x) - 3b)coth(x)csch(x) - 10b cosh(x) + 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 20a cosh(x) + 12a cosh(x))coth(x)csch(x) +--R + +--R 3 2 +--R (20b cosh(x) - 12b cosh(x))coth(x)csch(x) - 20b cosh(x) + 16a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 15a cosh(x) + 18a cosh(x) - 3a)coth(x)csch(x) +--R + +--R 4 2 3 +--R (15b cosh(x) - 18b cosh(x) + 3b)coth(x)csch(x) - 20b cosh(x) +--R + +--R 2 +--R 24a cosh(x) + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 6a cosh(x) + 12a cosh(x) - 6a cosh(x))coth(x)csch(x) +--R + +--R 5 3 +--R (6b cosh(x) - 12b cosh(x) + 6b cosh(x))coth(x)csch(x) +--R + +--R 4 3 +--R - 10b cosh(x) + 16a cosh(x) + 8a cosh(x) + 2b +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- a cosh(x) + 3a cosh(x) - 3a cosh(x) + a)coth(x)csch(x) +--R + +--R 6 4 2 5 +--R (b cosh(x) - 3b cosh(x) + 3b cosh(x) - b)coth(x)csch(x) - 2b cosh(x) +--R + +--R 4 2 +--R 4a cosh(x) + 4a cosh(x) + 2b cosh(x) +--R / +--R 2 6 2 5 2 2 2 4 +--R a sinh(x) + 6a cosh(x)sinh(x) + (15a cosh(x) - 3a )sinh(x) +--R + +--R 2 3 2 3 +--R (20a cosh(x) - 12a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (15a cosh(x) - 18a cosh(x) + 3a )sinh(x) +--R + +--R 2 5 2 3 2 2 6 +--R (6a cosh(x) - 12a cosh(x) + 6a cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 4 2 2 2 +--R - 3a cosh(x) + 3a cosh(x) - a +--R Type: Expression(Integer) +--E 50 + +--S 51 of 530 +t0510:= coth(x)^4/(a+b*sinh(x)) +--R +--R +--R 4 +--R coth(x) +--R (50) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 530 +r0510:= 3/2*b*acoth(cosh(x))/a^2+b^3*acoth(cosh(x))/a^4-_ + 2*(a^2+b^2)^(3/2)*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^4-_ + coth(x)/a-b^2*coth(x)/a^3-1/3*coth(x)^3/a+1/2*b*coth(x)*csch(x)/a^2 +--R +--R +--R (51) +--R x +--R +-------+ a tanh(-) - b +--R 2 2 | 2 2 2 3 2 +--R (12b + 12a )\|b + a atanh(-------------) + (6b + 9a b)acoth(cosh(x)) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 3 2 3 +--R 3a b coth(x)csch(x) - 2a coth(x) + (- 6a b - 6a )coth(x) +--R / +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 530 +a0510:= integrate(t0510,x) +--R +--R +--R (52) +--R 3 2 6 3 2 5 +--R (6b + 9a b)sinh(x) + (36b + 54a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b + 135a b)cosh(x) - 18b - 27a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b + 180a b)cosh(x) + (- 72b - 108a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (90b + 135a b)cosh(x) + (- 108b - 162a b)cosh(x) + 18b +--R + +--R 2 +--R 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b + 54a b)cosh(x) + (- 72b - 108a b)cosh(x) +--R + +--R 3 2 +--R (36b + 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (6b + 9a b)cosh(x) + (- 18b - 27a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (18b + 27a b)cosh(x) - 6b - 9a b +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 6 3 2 5 +--R (- 6b - 9a b)sinh(x) + (- 36b - 54a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b - 135a b)cosh(x) + 18b + 27a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b - 180a b)cosh(x) + (72b + 108a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b - 135a b)cosh(x) + (108b + 162a b)cosh(x) - 18b +--R + +--R 2 +--R - 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b - 54a b)cosh(x) + (72b + 108a b)cosh(x) +--R + +--R 3 2 +--R (- 36b - 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b - 9a b)cosh(x) + (18b + 27a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b - 27a b)cosh(x) + 6b + 9a b +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 6 2 2 5 +--R (6b + 6a )sinh(x) + (36b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((90b + 90a )cosh(x) - 18b - 18a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((120b + 120a )cosh(x) + (- 72b - 72a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R ((90b + 90a )cosh(x) + (- 108b - 108a )cosh(x) + 18b + 18a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (36b + 36a )cosh(x) + (- 72b - 72a )cosh(x) +--R + +--R 2 2 +--R (36b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 2 2 2 +--R (6b + 6a )cosh(x) + (- 18b - 18a )cosh(x) + (18b + 18a )cosh(x) +--R + +--R 2 2 +--R - 6b - 6a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 5 2 2 3 4 +--R 6a b sinh(x) + (30a b cosh(x) - 12a b - 24a )sinh(x) +--R + +--R 2 2 2 3 3 +--R (60a b cosh(x) + (- 48a b - 96a )cosh(x))sinh(x) +--R + +--R 2 3 2 3 2 2 3 2 +--R (60a b cosh(x) + (- 72a b - 144a )cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 2 4 2 3 3 2 3 +--R 30a b cosh(x) + (- 48a b - 96a )cosh(x) + (48a b + 48a )cosh(x) +--R + +--R 2 +--R - 6a b +--R * +--R sinh(x) +--R + +--R 2 5 2 3 4 2 3 2 +--R 6a b cosh(x) + (- 12a b - 24a )cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 2 2 3 +--R - 6a b cosh(x) - 12a b - 16a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) - 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) - 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) - 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) - 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R - 18a cosh(x) + 18a cosh(x) - 6a +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 530 +m0510:= a0510-r0510 +--R +--R +--R (53) +--R 3 2 6 3 2 5 +--R (6b + 9a b)sinh(x) + (36b + 54a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b + 135a b)cosh(x) - 18b - 27a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b + 180a b)cosh(x) + (- 72b - 108a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (90b + 135a b)cosh(x) + (- 108b - 162a b)cosh(x) + 18b +--R + +--R 2 +--R 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b + 54a b)cosh(x) + (- 72b - 108a b)cosh(x) +--R + +--R 3 2 +--R (36b + 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (6b + 9a b)cosh(x) + (- 18b - 27a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (18b + 27a b)cosh(x) - 6b - 9a b +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 6 3 2 5 +--R (- 6b - 9a b)sinh(x) + (- 36b - 54a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b - 135a b)cosh(x) + 18b + 27a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b - 180a b)cosh(x) + (72b + 108a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b - 135a b)cosh(x) + (108b + 162a b)cosh(x) - 18b +--R + +--R 2 +--R - 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b - 54a b)cosh(x) + (72b + 108a b)cosh(x) +--R + +--R 3 2 +--R (- 36b - 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b - 9a b)cosh(x) + (18b + 27a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b - 27a b)cosh(x) + 6b + 9a b +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 6 2 2 5 +--R (6b + 6a )sinh(x) + (36b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((90b + 90a )cosh(x) - 18b - 18a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((120b + 120a )cosh(x) + (- 72b - 72a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R ((90b + 90a )cosh(x) + (- 108b - 108a )cosh(x) + 18b + 18a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (36b + 36a )cosh(x) + (- 72b - 72a )cosh(x) +--R + +--R 2 2 +--R (36b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 2 2 2 +--R (6b + 6a )cosh(x) + (- 18b - 18a )cosh(x) + (18b + 18a )cosh(x) +--R + +--R 2 2 +--R - 6b - 6a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 2 6 2 2 5 +--R (- 12b - 12a )sinh(x) + (- 72b - 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 180b - 180a )cosh(x) + 36b + 36a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 240b - 240a )cosh(x) + (144b + 144a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R ((- 180b - 180a )cosh(x) + (216b + 216a )cosh(x) - 36b - 36a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 72b - 72a )cosh(x) + (144b + 144a )cosh(x) +--R + +--R 2 2 +--R (- 72b - 72a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 12b - 12a )cosh(x) + (36b + 36a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 36b - 36a )cosh(x) + 12b + 12a +--R * +--R x +--R +-------+ a tanh(-) - b +--R | 2 2 2 +--R \|b + a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 6 3 2 5 +--R (- 6b - 9a b)sinh(x) + (- 36b - 54a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b - 135a b)cosh(x) + 18b + 27a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b - 180a b)cosh(x) + (72b + 108a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b - 135a b)cosh(x) + (108b + 162a b)cosh(x) - 18b +--R + +--R 2 +--R - 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b - 54a b)cosh(x) + (72b + 108a b)cosh(x) +--R + +--R 3 2 +--R (- 36b - 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b - 9a b)cosh(x) + (18b + 27a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b - 27a b)cosh(x) + 6b + 9a b +--R * +--R acoth(cosh(x)) +--R + +--R 2 3 3 2 3 6 +--R (- 3a b coth(x)csch(x) + 2a coth(x) + (6a b + 6a )coth(x))sinh(x) +--R + +--R 2 3 3 +--R - 18a b cosh(x)coth(x)csch(x) + 12a cosh(x)coth(x) +--R + +--R 2 3 2 +--R (36a b + 36a )cosh(x)coth(x) + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 2 +--R (- 45a b cosh(x) + 9a b)coth(x)csch(x) +--R + +--R 3 2 3 3 +--R (30a cosh(x) - 6a )coth(x) +--R + +--R 2 3 2 2 3 2 +--R ((90a b + 90a )cosh(x) - 18a b - 18a )coth(x) + 30a b cosh(x) +--R + +--R 2 3 +--R - 12a b - 24a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 +--R (- 60a b cosh(x) + 36a b cosh(x))coth(x)csch(x) +--R + +--R 3 3 3 3 +--R (40a cosh(x) - 24a cosh(x))coth(x) +--R + +--R 2 3 3 2 3 +--R ((120a b + 120a )cosh(x) + (- 72a b - 72a )cosh(x))coth(x) +--R + +--R 2 2 2 3 +--R 60a b cosh(x) + (- 48a b - 96a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 45a b cosh(x) + 54a b cosh(x) - 9a b)coth(x)csch(x) +--R + +--R 3 4 3 2 3 3 +--R (30a cosh(x) - 36a cosh(x) + 6a )coth(x) +--R + +--R 2 3 4 2 3 2 2 +--R (90a b + 90a )cosh(x) + (- 108a b - 108a )cosh(x) + 18a b +--R + +--R 3 +--R 18a +--R * +--R coth(x) +--R + +--R 2 3 2 3 2 2 3 +--R 60a b cosh(x) + (- 72a b - 144a )cosh(x) + 24a b + 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 +--R (- 18a b cosh(x) + 36a b cosh(x) - 18a b cosh(x))coth(x)csch(x) +--R + +--R 3 5 3 3 3 3 +--R (12a cosh(x) - 24a cosh(x) + 12a cosh(x))coth(x) +--R + +--R 2 3 5 2 3 3 +--R (36a b + 36a )cosh(x) + (- 72a b - 72a )cosh(x) +--R + +--R 2 3 +--R (36a b + 36a )cosh(x) +--R * +--R coth(x) +--R + +--R 2 4 2 3 3 2 3 +--R 30a b cosh(x) + (- 48a b - 96a )cosh(x) + (48a b + 48a )cosh(x) +--R + +--R 2 +--R - 6a b +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (- 3a b cosh(x) + 9a b cosh(x) - 9a b cosh(x) + 3a b)coth(x)csch(x) +--R + +--R 3 6 3 4 3 2 3 3 +--R (2a cosh(x) - 6a cosh(x) + 6a cosh(x) - 2a )coth(x) +--R + +--R 2 3 6 2 3 4 +--R (6a b + 6a )cosh(x) + (- 18a b - 18a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (18a b + 18a )cosh(x) - 6a b - 6a +--R * +--R coth(x) +--R + +--R 2 5 2 3 4 2 3 2 +--R 6a b cosh(x) + (- 12a b - 24a )cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 2 2 3 +--R - 6a b cosh(x) - 12a b - 16a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) - 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) - 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) - 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) - 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R - 18a cosh(x) + 18a cosh(x) - 6a +--R Type: Expression(Integer) +--E 54 + +--S 55 of 530 +d0510:= D(m0510,x) +--R +--R +--R (54) +--R 4 3 2 11 +--R (2a b + 3a b )sinh(x) +--R + +--R 3 2 2 3 2 2 3 2 2 3 2 +--R ((2a b cosh(x) - 2a b )coth(x) - a b cosh(x) + a b )csch(x) +--R + +--R 4 2 4 4 +--R (- 2a b cosh(x) + 2a b)coth(x) +--R + +--R 2 3 2 2 3 2 5 2 3 2 +--R (- 2a b cosh(x) + 2a b )coth(x) + (- 2b - 2a b )cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (20a b + 30a b )cosh(x) + 2b + 6a b + 6a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 3 4 2 3 2 4 +--R (20a b cosh(x) + 4a b cosh(x) - 20a b cosh(x) - 4a b) +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 3 4 2 3 2 4 +--R - 10a b cosh(x) - 2a b cosh(x) + 10a b cosh(x) + 2a b +--R * +--R csch(x) +--R + +--R 4 3 5 2 4 5 4 +--R (- 20a b cosh(x) - 4a cosh(x) + 20a b cosh(x) + 4a )coth(x) +--R + +--R 2 3 3 3 2 2 2 3 3 2 +--R (- 20a b cosh(x) - 4a b cosh(x) + 20a b cosh(x) + 4a b ) +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 3 4 3 2 5 2 +--R (- 20b - 20a b )cosh(x) + (86a b + 131a b + 4a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (20b + 56a b + 54a b)cosh(x) - 6a b - 11a b - 4a +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 4 3 3 2 2 +--R 90a b cosh(x) + 36a b cosh(x) - 100a b cosh(x) +--R + +--R 4 3 2 +--R - 36a b cosh(x) + 10a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 4 4 3 3 2 2 +--R - 45a b cosh(x) - 18a b cosh(x) + 50a b cosh(x) +--R + +--R 4 3 2 +--R 18a b cosh(x) - 5a b +--R * +--R csch(x) +--R + +--R 4 4 5 3 4 2 +--R - 90a b cosh(x) - 36a cosh(x) + 100a b cosh(x) +--R + +--R 5 4 +--R 36a cosh(x) - 10a b +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 4 3 2 3 2 3 2 +--R - 90a b cosh(x) - 36a b cosh(x) + 100a b cosh(x) +--R + +--R 3 2 2 3 +--R 36a b cosh(x) - 10a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 4 4 3 2 5 3 +--R (- 90b - 90a b )cosh(x) + (204a b + 324a b + 36a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (100b + 244a b + 216a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 44a b - 84a b - 36a )cosh(x) - 10b - 26a b - 24a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R 240a b cosh(x) + 144a b cosh(x) - 320a b cosh(x) +--R + +--R 4 2 3 2 4 +--R - 160a b cosh(x) + 80a b cosh(x) + 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R - 120a b cosh(x) - 72a b cosh(x) + 160a b cosh(x) +--R + +--R 4 2 3 2 4 +--R 80a b cosh(x) - 40a b cosh(x) - 8a b +--R * +--R csch(x) +--R + +--R 4 5 5 4 4 3 +--R - 240a b cosh(x) - 144a cosh(x) + 320a b cosh(x) +--R + +--R 5 2 4 5 +--R 160a cosh(x) - 80a b cosh(x) - 16a +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R - 240a b cosh(x) - 144a b cosh(x) + 320a b cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R 160a b cosh(x) - 80a b cosh(x) - 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 5 4 3 2 5 4 +--R (- 240b - 240a b )cosh(x) + (276a b + 486a b + 144a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (320b + 656a b + 504a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 120a b - 260a b - 128a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 80b - 192a b - 168a b)cosh(x) + 4a b + 14a b - 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 6 4 5 3 2 4 +--R 420a b cosh(x) + 336a b cosh(x) - 700a b cosh(x) +--R + +--R 4 3 3 2 2 4 +--R - 448a b cosh(x) + 300a b cosh(x) + 112a b cosh(x) +--R + +--R 3 2 +--R - 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 6 4 5 3 2 4 +--R - 210a b cosh(x) - 168a b cosh(x) + 350a b cosh(x) +--R + +--R 4 3 3 2 2 4 3 2 +--R 224a b cosh(x) - 150a b cosh(x) - 56a b cosh(x) + 10a b +--R * +--R csch(x) +--R + +--R 4 6 5 5 4 4 +--R - 420a b cosh(x) - 336a cosh(x) + 700a b cosh(x) +--R + +--R 5 3 4 2 5 4 +--R 448a cosh(x) - 300a b cosh(x) - 112a cosh(x) + 20a b +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 6 3 2 5 2 3 4 +--R - 420a b cosh(x) - 336a b cosh(x) + 700a b cosh(x) +--R + +--R 3 2 3 2 3 2 3 2 2 3 +--R 448a b cosh(x) - 300a b cosh(x) - 112a b cosh(x) + 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 6 4 3 2 5 5 +--R (- 420b - 420a b )cosh(x) + (168a b + 420a b + 336a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (700b + 1204a b + 756a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (- 112a b - 392a b - 224a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (- 300b - 636a b - 504a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (8a b + 68a b - 112a )cosh(x) + 20b + 44a b + 36a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 7 4 6 3 2 5 +--R 504a b cosh(x) + 504a b cosh(x) - 1064a b cosh(x) +--R + +--R 4 4 3 2 3 4 2 +--R - 840a b cosh(x) + 680a b cosh(x) + 360a b cosh(x) +--R + +--R 3 2 4 +--R - 120a b cosh(x) - 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 7 4 6 3 2 5 +--R - 252a b cosh(x) - 252a b cosh(x) + 532a b cosh(x) +--R + +--R 4 4 3 2 3 4 2 +--R 420a b cosh(x) - 340a b cosh(x) - 180a b cosh(x) +--R + +--R 3 2 4 +--R 60a b cosh(x) + 12a b +--R * +--R csch(x) +--R + +--R 4 7 5 6 4 5 +--R - 504a b cosh(x) - 504a cosh(x) + 1064a b cosh(x) +--R + +--R 5 4 4 3 5 2 +--R 840a cosh(x) - 680a b cosh(x) - 360a cosh(x) +--R + +--R 4 5 +--R 120a b cosh(x) + 24a +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 7 3 2 6 2 3 5 +--R - 504a b cosh(x) - 504a b cosh(x) + 1064a b cosh(x) +--R + +--R 3 2 4 2 3 3 3 2 2 +--R 840a b cosh(x) - 680a b cosh(x) - 360a b cosh(x) +--R + +--R 2 3 3 2 +--R 120a b cosh(x) + 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 7 +--R (- 504b - 504a b )cosh(x) +--R + +--R 4 3 2 5 6 +--R (- 84a b + 126a b + 504a )cosh(x) +--R + +--R 5 2 3 4 5 +--R (1064b + 1568a b + 756a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (140a b - 210a b - 168a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 680b - 1240a b - 840a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 60a b + 90a b - 312a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (120b + 240a b + 180a b)cosh(x) + 4a b - 6a b - 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 8 4 7 3 2 6 +--R 420a b cosh(x) + 504a b cosh(x) - 1120a b cosh(x) +--R + +--R 4 5 3 2 4 4 3 +--R - 1064a b cosh(x) + 1000a b cosh(x) + 680a b cosh(x) +--R + +--R 3 2 2 4 3 2 +--R - 320a b cosh(x) - 120a b cosh(x) + 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 8 4 7 3 2 6 +--R - 210a b cosh(x) - 252a b cosh(x) + 560a b cosh(x) +--R + +--R 4 5 3 2 4 4 3 +--R 532a b cosh(x) - 500a b cosh(x) - 340a b cosh(x) +--R + +--R 3 2 2 4 3 2 +--R 160a b cosh(x) + 60a b cosh(x) - 10a b +--R * +--R csch(x) +--R + +--R 4 8 5 7 4 6 +--R - 420a b cosh(x) - 504a cosh(x) + 1120a b cosh(x) +--R + +--R 5 5 4 4 5 3 +--R 1064a cosh(x) - 1000a b cosh(x) - 680a cosh(x) +--R + +--R 4 2 5 4 +--R 320a b cosh(x) + 120a cosh(x) - 20a b +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 8 3 2 7 2 3 6 +--R - 420a b cosh(x) - 504a b cosh(x) + 1120a b cosh(x) +--R + +--R 3 2 5 2 3 4 3 2 3 +--R 1064a b cosh(x) - 1000a b cosh(x) - 680a b cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R 320a b cosh(x) + 120a b cosh(x) - 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 8 +--R (- 420b - 420a b )cosh(x) +--R + +--R 4 3 2 5 7 +--R (- 264a b - 144a b + 504a )cosh(x) +--R + +--R 5 2 3 4 6 +--R (1120b + 1456a b + 504a b)cosh(x) +--R + +--R 4 3 2 5 5 +--R (504a b + 224a b + 56a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (- 1000b - 1560a b - 840a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (- 280a b - 80a b - 440a )cosh(x) +--R + +--R 5 2 3 4 2 4 5 +--R (320b + 560a b + 360a b)cosh(x) + (40a b - 120a )cosh(x) +--R + +--R 5 2 3 4 +--R - 20b - 36a b - 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 9 4 8 3 2 7 +--R 240a b cosh(x) + 336a b cosh(x) - 800a b cosh(x) +--R + +--R 4 6 3 2 5 4 4 +--R - 896a b cosh(x) + 960a b cosh(x) + 800a b cosh(x) +--R + +--R 3 2 3 4 2 3 2 4 +--R - 480a b cosh(x) - 256a b cosh(x) + 80a b cosh(x) + 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 9 4 8 3 2 7 +--R - 120a b cosh(x) - 168a b cosh(x) + 400a b cosh(x) +--R + +--R 4 6 3 2 5 4 4 +--R 448a b cosh(x) - 480a b cosh(x) - 400a b cosh(x) +--R + +--R 3 2 3 4 2 3 2 4 +--R 240a b cosh(x) + 128a b cosh(x) - 40a b cosh(x) - 8a b +--R * +--R csch(x) +--R + +--R 4 9 5 8 4 7 +--R - 240a b cosh(x) - 336a cosh(x) + 800a b cosh(x) +--R + +--R 5 6 4 5 5 4 +--R 896a cosh(x) - 960a b cosh(x) - 800a cosh(x) +--R + +--R 4 3 5 2 4 5 +--R 480a b cosh(x) + 256a cosh(x) - 80a b cosh(x) - 16a +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 9 3 2 8 2 3 7 +--R - 240a b cosh(x) - 336a b cosh(x) + 800a b cosh(x) +--R + +--R 3 2 6 2 3 5 3 2 4 +--R 896a b cosh(x) - 960a b cosh(x) - 800a b cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 3 2 +--R 480a b cosh(x) + 256a b cosh(x) - 80a b cosh(x) - 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 9 +--R (- 240b - 240a b )cosh(x) +--R + +--R 4 3 2 5 8 +--R (- 246a b - 201a b + 336a )cosh(x) +--R + +--R 5 2 3 4 7 +--R (800b + 944a b + 216a b)cosh(x) +--R + +--R 4 3 2 5 6 +--R (616a b + 476a b + 224a )cosh(x) +--R + +--R 5 2 3 4 5 +--R (- 960b - 1296a b - 504a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (- 500a b - 350a b - 320a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (480b + 720a b + 360a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (136a b + 76a b - 224a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 80b - 128a b - 72a b)cosh(x) - 6a b - a b - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 10 4 9 3 2 8 +--R 90a b cosh(x) + 144a b cosh(x) - 370a b cosh(x) +--R + +--R 4 7 3 2 6 4 5 +--R - 480a b cosh(x) + 580a b cosh(x) + 576a b cosh(x) +--R + +--R 3 2 4 4 3 3 2 2 +--R - 420a b cosh(x) - 288a b cosh(x) + 130a b cosh(x) +--R + +--R 4 3 2 +--R 48a b cosh(x) - 10a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 10 4 9 3 2 8 +--R - 45a b cosh(x) - 72a b cosh(x) + 185a b cosh(x) +--R + +--R 4 7 3 2 6 4 5 +--R 240a b cosh(x) - 290a b cosh(x) - 288a b cosh(x) +--R + +--R 3 2 4 4 3 3 2 2 +--R 210a b cosh(x) + 144a b cosh(x) - 65a b cosh(x) +--R + +--R 4 3 2 +--R - 24a b cosh(x) + 5a b +--R * +--R csch(x) +--R + +--R 4 10 5 9 4 8 +--R - 90a b cosh(x) - 144a cosh(x) + 370a b cosh(x) +--R + +--R 5 7 4 6 5 5 +--R 480a cosh(x) - 580a b cosh(x) - 576a cosh(x) +--R + +--R 4 4 5 3 4 2 +--R 420a b cosh(x) + 288a cosh(x) - 130a b cosh(x) +--R + +--R 5 4 +--R - 48a cosh(x) + 10a b +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 10 3 2 9 2 3 8 +--R - 90a b cosh(x) - 144a b cosh(x) + 370a b cosh(x) +--R + +--R 3 2 7 2 3 6 3 2 5 +--R 480a b cosh(x) - 580a b cosh(x) - 576a b cosh(x) +--R + +--R 2 3 4 3 2 3 2 3 2 +--R 420a b cosh(x) + 288a b cosh(x) - 130a b cosh(x) +--R + +--R 3 2 2 3 +--R - 48a b cosh(x) + 10a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 10 +--R (- 90b - 90a b )cosh(x) +--R + +--R 4 3 2 5 9 +--R (- 124a b - 114a b + 144a )cosh(x) +--R + +--R 5 2 3 4 8 +--R (370b + 406a b + 54a b)cosh(x) +--R + +--R 4 3 2 5 7 +--R (400a b + 360a b + 192a )cosh(x) +--R + +--R 5 2 3 4 6 +--R (- 580b - 692a b - 168a b)cosh(x) +--R + +--R 4 3 2 5 5 +--R (- 456a b - 396a b - 96a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (420b + 540a b + 180a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (208a b + 168a b - 192a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (- 130b - 178a b - 72a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 28a b - 18a b - 48a )cosh(x) + 10b + 14a b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 11 4 10 3 2 9 +--R 20a b cosh(x) + 36a b cosh(x) - 100a b cosh(x) +--R + +--R 4 8 3 2 7 4 6 +--R - 148a b cosh(x) + 200a b cosh(x) + 232a b cosh(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R - 200a b cosh(x) - 168a b cosh(x) + 100a b cosh(x) +--R + +--R 4 2 3 2 4 +--R 52a b cosh(x) - 20a b cosh(x) - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 11 4 10 3 2 9 +--R - 10a b cosh(x) - 18a b cosh(x) + 50a b cosh(x) +--R + +--R 4 8 3 2 7 4 6 +--R 74a b cosh(x) - 100a b cosh(x) - 116a b cosh(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R 100a b cosh(x) + 84a b cosh(x) - 50a b cosh(x) +--R + +--R 4 2 3 2 4 +--R - 26a b cosh(x) + 10a b cosh(x) + 2a b +--R * +--R csch(x) +--R + +--R 4 11 5 10 4 9 +--R - 20a b cosh(x) - 36a cosh(x) + 100a b cosh(x) +--R + +--R 5 8 4 7 5 6 +--R 148a cosh(x) - 200a b cosh(x) - 232a cosh(x) +--R + +--R 4 5 5 4 4 3 +--R 200a b cosh(x) + 168a cosh(x) - 100a b cosh(x) +--R + +--R 5 2 4 5 +--R - 52a cosh(x) + 20a b cosh(x) + 4a +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 11 3 2 10 2 3 9 +--R - 20a b cosh(x) - 36a b cosh(x) + 100a b cosh(x) +--R + +--R 3 2 8 2 3 7 3 2 6 +--R 148a b cosh(x) - 200a b cosh(x) - 232a b cosh(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R 200a b cosh(x) + 168a b cosh(x) - 100a b cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R - 52a b cosh(x) + 20a b cosh(x) + 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 11 4 3 2 5 10 +--R (- 20b - 20a b )cosh(x) + (- 34a b - 33a b + 36a )cosh(x) +--R + +--R 5 2 3 4 9 +--R (100b + 104a b + 6a b)cosh(x) +--R + +--R 4 3 2 5 8 +--R (138a b + 133a b + 76a )cosh(x) +--R + +--R 5 2 3 4 7 +--R (- 200b - 216a b - 24a b)cosh(x) +--R + +--R 4 3 2 5 6 +--R (- 212a b - 202a b + 8a )cosh(x) +--R + +--R 5 2 3 4 5 +--R (200b + 224a b + 36a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (148a b + 138a b - 72a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 100b - 116a b - 24a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 42a b - 37a b - 44a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (20b + 24a b + 6a b)cosh(x) + 2a b + a b - 4a +--R * +--R sinh(x) +--R + +--R 3 2 12 4 11 3 2 10 +--R 2a b cosh(x) + 4a b cosh(x) - 12a b cosh(x) +--R + +--R 4 9 3 2 8 4 7 +--R - 20a b cosh(x) + 30a b cosh(x) + 40a b cosh(x) +--R + +--R 3 2 6 4 5 3 2 4 +--R - 40a b cosh(x) - 40a b cosh(x) + 30a b cosh(x) +--R + +--R 4 3 3 2 2 4 3 2 +--R 20a b cosh(x) - 12a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 12 4 11 3 2 10 +--R - a b cosh(x) - 2a b cosh(x) + 6a b cosh(x) +--R + +--R 4 9 3 2 8 4 7 3 2 6 +--R 10a b cosh(x) - 15a b cosh(x) - 20a b cosh(x) + 20a b cosh(x) +--R + +--R 4 5 3 2 4 4 3 3 2 2 +--R 20a b cosh(x) - 15a b cosh(x) - 10a b cosh(x) + 6a b cosh(x) +--R + +--R 4 3 2 +--R 2a b cosh(x) - a b +--R * +--R csch(x) +--R + +--R 4 12 5 11 4 10 5 9 +--R - 2a b cosh(x) - 4a cosh(x) + 12a b cosh(x) + 20a cosh(x) +--R + +--R 4 8 5 7 4 6 5 5 +--R - 30a b cosh(x) - 40a cosh(x) + 40a b cosh(x) + 40a cosh(x) +--R + +--R 4 4 5 3 4 2 5 +--R - 30a b cosh(x) - 20a cosh(x) + 12a b cosh(x) + 4a cosh(x) +--R + +--R 4 +--R - 2a b +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 12 3 2 11 2 3 10 +--R - 2a b cosh(x) - 4a b cosh(x) + 12a b cosh(x) +--R + +--R 3 2 9 2 3 8 3 2 7 2 3 6 +--R 20a b cosh(x) - 30a b cosh(x) - 40a b cosh(x) + 40a b cosh(x) +--R + +--R 3 2 5 2 3 4 3 2 3 2 3 2 +--R 40a b cosh(x) - 30a b cosh(x) - 20a b cosh(x) + 12a b cosh(x) +--R + +--R 3 2 2 3 +--R 4a b cosh(x) - 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 12 4 3 2 5 11 +--R (- 2b - 2a b )cosh(x) + (- 4a b - 4a b + 4a )cosh(x) +--R + +--R 5 2 3 10 4 3 2 5 9 +--R (12b + 12a b )cosh(x) + (20a b + 20a b + 12a )cosh(x) +--R + +--R 5 2 3 8 4 3 2 5 7 +--R (- 30b - 30a b )cosh(x) + (- 40a b - 40a b + 8a )cosh(x) +--R + +--R 5 2 3 6 4 3 2 5 5 +--R (40b + 40a b )cosh(x) + (40a b + 40a b - 8a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 3 +--R (- 30b - 30a b )cosh(x) + (- 20a b - 20a b - 12a )cosh(x) +--R + +--R 5 2 3 2 4 3 2 5 5 2 3 +--R (12b + 12a b )cosh(x) + (4a b + 4a b - 4a )cosh(x) - 2b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 2 3 11 +--R (- 4b - 6a b )sinh(x) +--R + +--R 2 3 2 2 3 2 2 3 2 2 3 +--R ((- 4a b cosh(x) + 4a b )coth(x) + 2a b cosh(x) - 2a b ) +--R * +--R csch(x) +--R + +--R 3 2 2 3 2 4 4 2 4 2 +--R (4a b cosh(x) - 4a b )coth(x) + (4a b cosh(x) - 4a b )coth(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (- 4a b - 4a b )cosh(x) + (- 40b - 60a b )cosh(x) - 4a b +--R + +--R 3 2 +--R - 8a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 3 2 2 2 3 3 2 +--R (- 40a b cosh(x) - 8a b cosh(x) + 40a b cosh(x) + 8a b ) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 3 2 2 2 3 3 2 +--R 20a b cosh(x) + 4a b cosh(x) - 20a b cosh(x) - 4a b +--R * +--R csch(x) +--R + +--R 3 2 3 4 2 3 2 4 4 +--R (40a b cosh(x) + 8a b cosh(x) - 40a b cosh(x) - 8a b)coth(x) +--R + +--R 4 3 2 3 2 4 2 3 2 +--R (40a b cosh(x) + 8a b cosh(x) - 40a b cosh(x) - 8a b )coth(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (- 40a b - 40a b )cosh(x) + (- 180b - 278a b - 16a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (- 32a b - 68a b )cosh(x) + 20b + 38a b + 16a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 2 3 2 +--R - 180a b cosh(x) - 72a b cosh(x) + 200a b cosh(x) +--R + +--R 3 2 2 3 +--R 72a b cosh(x) - 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 4 3 2 3 2 3 2 +--R 90a b cosh(x) + 36a b cosh(x) - 100a b cosh(x) +--R + +--R 3 2 2 3 +--R - 36a b cosh(x) + 10a b +--R * +--R csch(x) +--R + +--R 3 2 4 4 3 3 2 2 +--R 180a b cosh(x) + 72a b cosh(x) - 200a b cosh(x) +--R + +--R 4 3 2 +--R - 72a b cosh(x) + 20a b +--R * +--R 4 +--R coth(x) +--R + +--R 4 4 2 3 3 4 2 +--R 180a b cosh(x) + 72a b cosh(x) - 200a b cosh(x) +--R + +--R 2 3 4 +--R - 72a b cosh(x) + 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 4 +--R (- 180a b - 180a b )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 480b - 792a b - 144a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (- 88a b - 232a b )cosh(x) + (160b + 312a b + 144a b)cosh(x) +--R + +--R 4 3 2 +--R 12a b + 28a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R - 480a b cosh(x) - 288a b cosh(x) + 640a b cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R 320a b cosh(x) - 160a b cosh(x) - 32a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R 240a b cosh(x) + 144a b cosh(x) - 320a b cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R - 160a b cosh(x) + 80a b cosh(x) + 16a b +--R * +--R csch(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R 480a b cosh(x) + 288a b cosh(x) - 640a b cosh(x) +--R + +--R 4 2 3 2 4 +--R - 320a b cosh(x) + 160a b cosh(x) + 32a b +--R * +--R 4 +--R coth(x) +--R + +--R 4 5 2 3 4 4 3 +--R 480a b cosh(x) + 288a b cosh(x) - 640a b cosh(x) +--R + +--R 2 3 2 4 2 3 +--R - 320a b cosh(x) + 160a b cosh(x) + 32a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 5 +--R (- 480a b - 480a b )cosh(x) +--R + +--R 5 2 3 4 4 +--R (- 840b - 1548a b - 576a b)cosh(x) +--R + +--R 4 3 2 3 +--R (- 32a b - 368a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 +--R (560b + 1160a b + 576a b)cosh(x) + (64a b + 176a b )cosh(x) +--R + +--R 5 2 3 +--R - 40b - 92a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 6 3 2 5 2 3 4 +--R - 840a b cosh(x) - 672a b cosh(x) + 1400a b cosh(x) +--R + +--R 3 2 3 2 3 2 3 2 2 3 +--R 896a b cosh(x) - 600a b cosh(x) - 224a b cosh(x) + 40a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 6 3 2 5 2 3 4 +--R 420a b cosh(x) + 336a b cosh(x) - 700a b cosh(x) +--R + +--R 3 2 3 2 3 2 3 2 2 3 +--R - 448a b cosh(x) + 300a b cosh(x) + 112a b cosh(x) - 20a b +--R * +--R csch(x) +--R + +--R 3 2 6 4 5 3 2 4 +--R 840a b cosh(x) + 672a b cosh(x) - 1400a b cosh(x) +--R + +--R 4 3 3 2 2 4 3 2 +--R - 896a b cosh(x) + 600a b cosh(x) + 224a b cosh(x) - 40a b +--R * +--R 4 +--R coth(x) +--R + +--R 4 6 2 3 5 4 4 +--R 840a b cosh(x) + 672a b cosh(x) - 1400a b cosh(x) +--R + +--R 2 3 3 4 2 2 3 4 +--R - 896a b cosh(x) + 600a b cosh(x) + 224a b cosh(x) - 40a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 6 +--R (- 840a b - 840a b )cosh(x) +--R + +--R 5 2 3 4 5 +--R (- 1008b - 2184a b - 1344a b)cosh(x) +--R + +--R 4 3 2 4 +--R (392a b - 112a b )cosh(x) +--R + +--R 5 2 3 4 3 +--R (1120b + 2576a b + 1344a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (72a b + 408a b )cosh(x) + (- 240b - 584a b )cosh(x) - 8a b +--R + +--R 3 2 +--R - 32a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 7 3 2 6 2 3 5 +--R - 1008a b cosh(x) - 1008a b cosh(x) + 2128a b cosh(x) +--R + +--R 3 2 4 2 3 3 3 2 2 +--R 1680a b cosh(x) - 1360a b cosh(x) - 720a b cosh(x) +--R + +--R 2 3 3 2 +--R 240a b cosh(x) + 48a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 7 3 2 6 2 3 5 +--R 504a b cosh(x) + 504a b cosh(x) - 1064a b cosh(x) +--R + +--R 3 2 4 2 3 3 3 2 2 +--R - 840a b cosh(x) + 680a b cosh(x) + 360a b cosh(x) +--R + +--R 2 3 3 2 +--R - 120a b cosh(x) - 24a b +--R * +--R csch(x) +--R + +--R 3 2 7 4 6 3 2 5 +--R 1008a b cosh(x) + 1008a b cosh(x) - 2128a b cosh(x) +--R + +--R 4 4 3 2 3 4 2 +--R - 1680a b cosh(x) + 1360a b cosh(x) + 720a b cosh(x) +--R + +--R 3 2 4 +--R - 240a b cosh(x) - 48a b +--R * +--R 4 +--R coth(x) +--R + +--R 4 7 2 3 6 4 5 +--R 1008a b cosh(x) + 1008a b cosh(x) - 2128a b cosh(x) +--R + +--R 2 3 4 4 3 2 3 2 +--R - 1680a b cosh(x) + 1360a b cosh(x) + 720a b cosh(x) +--R + +--R 4 2 3 +--R - 240a b cosh(x) - 48a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 7 +--R (- 1008a b - 1008a b )cosh(x) +--R + +--R 5 2 3 4 6 +--R (- 840b - 2268a b - 2016a b)cosh(x) +--R + +--R 4 3 2 5 +--R (1120a b + 616a b )cosh(x) +--R + +--R 5 2 3 4 4 +--R (1400b + 3780a b + 2016a b)cosh(x) +--R + +--R 4 3 2 3 +--R (- 240a b + 320a b )cosh(x) +--R + +--R 5 2 3 4 2 3 2 5 +--R (- 600b - 1620a b - 96a b)cosh(x) - 120a b cosh(x) + 40b +--R + +--R 2 3 4 +--R 108a b + 96a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 8 3 2 7 2 3 6 +--R - 840a b cosh(x) - 1008a b cosh(x) + 2240a b cosh(x) +--R + +--R 3 2 5 2 3 4 3 2 3 +--R 2128a b cosh(x) - 2000a b cosh(x) - 1360a b cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R 640a b cosh(x) + 240a b cosh(x) - 40a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 8 3 2 7 2 3 6 +--R 420a b cosh(x) + 504a b cosh(x) - 1120a b cosh(x) +--R + +--R 3 2 5 2 3 4 3 2 3 +--R - 1064a b cosh(x) + 1000a b cosh(x) + 680a b cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R - 320a b cosh(x) - 120a b cosh(x) + 20a b +--R * +--R csch(x) +--R + +--R 3 2 8 4 7 3 2 6 +--R 840a b cosh(x) + 1008a b cosh(x) - 2240a b cosh(x) +--R + +--R 4 5 3 2 4 4 3 +--R - 2128a b cosh(x) + 2000a b cosh(x) + 1360a b cosh(x) +--R + +--R 3 2 2 4 3 2 +--R - 640a b cosh(x) - 240a b cosh(x) + 40a b +--R * +--R 4 +--R coth(x) +--R + +--R 4 8 2 3 7 4 6 +--R 840a b cosh(x) + 1008a b cosh(x) - 2240a b cosh(x) +--R + +--R 2 3 5 4 4 2 3 3 +--R - 2128a b cosh(x) + 2000a b cosh(x) + 1360a b cosh(x) +--R + +--R 4 2 2 3 4 +--R - 640a b cosh(x) - 240a b cosh(x) + 40a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 8 +--R (- 840a b - 840a b )cosh(x) +--R + +--R 5 2 3 4 7 +--R (- 480b - 1728a b - 2016a b)cosh(x) +--R + +--R 4 3 2 6 +--R (1568a b + 1232a b )cosh(x) +--R + +--R 5 2 3 4 5 +--R (1120b + 3808a b + 2016a b)cosh(x) +--R + +--R 4 3 2 4 +--R (- 880a b - 320a b )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 800b - 2560a b - 480a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (160a b - 80a b )cosh(x) + (160b + 480a b + 480a b)cosh(x) +--R + +--R 4 3 2 +--R - 8a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 9 3 2 8 2 3 7 +--R - 480a b cosh(x) - 672a b cosh(x) + 1600a b cosh(x) +--R + +--R 3 2 6 2 3 5 3 2 4 +--R 1792a b cosh(x) - 1920a b cosh(x) - 1600a b cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 3 2 +--R 960a b cosh(x) + 512a b cosh(x) - 160a b cosh(x) - 32a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 9 3 2 8 2 3 7 +--R 240a b cosh(x) + 336a b cosh(x) - 800a b cosh(x) +--R + +--R 3 2 6 2 3 5 3 2 4 +--R - 896a b cosh(x) + 960a b cosh(x) + 800a b cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 3 2 +--R - 480a b cosh(x) - 256a b cosh(x) + 80a b cosh(x) + 16a b +--R * +--R csch(x) +--R + +--R 3 2 9 4 8 3 2 7 +--R 480a b cosh(x) + 672a b cosh(x) - 1600a b cosh(x) +--R + +--R 4 6 3 2 5 4 4 +--R - 1792a b cosh(x) + 1920a b cosh(x) + 1600a b cosh(x) +--R + +--R 3 2 3 4 2 3 2 4 +--R - 960a b cosh(x) - 512a b cosh(x) + 160a b cosh(x) + 32a b +--R * +--R 4 +--R coth(x) +--R + +--R 4 9 2 3 8 4 7 +--R 480a b cosh(x) + 672a b cosh(x) - 1600a b cosh(x) +--R + +--R 2 3 6 4 5 2 3 4 +--R - 1792a b cosh(x) + 1920a b cosh(x) + 1600a b cosh(x) +--R + +--R 4 3 2 3 2 4 2 3 +--R - 960a b cosh(x) - 512a b cosh(x) + 160a b cosh(x) + 32a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 9 +--R (- 480a b - 480a b )cosh(x) +--R + +--R 5 2 3 4 8 +--R (- 180b - 942a b - 1344a b)cosh(x) +--R + +--R 4 3 2 7 +--R (1312a b + 1168a b )cosh(x) +--R + +--R 5 2 3 4 6 +--R (560b + 2632a b + 1344a b)cosh(x) +--R + +--R 4 3 2 5 +--R (- 1248a b - 912a b )cosh(x) +--R + +--R 5 2 3 4 4 +--R (- 600b - 2500a b - 960a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (480a b + 240a b )cosh(x) + (240b + 872a b + 960a b)cosh(x) +--R + +--R 4 3 2 5 2 3 +--R (- 64a b - 16a b )cosh(x) - 20b - 62a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 10 3 2 9 2 3 8 +--R - 180a b cosh(x) - 288a b cosh(x) + 740a b cosh(x) +--R + +--R 3 2 7 2 3 6 3 2 5 +--R 960a b cosh(x) - 1160a b cosh(x) - 1152a b cosh(x) +--R + +--R 2 3 4 3 2 3 2 3 2 +--R 840a b cosh(x) + 576a b cosh(x) - 260a b cosh(x) +--R + +--R 3 2 2 3 +--R - 96a b cosh(x) + 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 10 3 2 9 2 3 8 +--R 90a b cosh(x) + 144a b cosh(x) - 370a b cosh(x) +--R + +--R 3 2 7 2 3 6 3 2 5 +--R - 480a b cosh(x) + 580a b cosh(x) + 576a b cosh(x) +--R + +--R 2 3 4 3 2 3 2 3 2 +--R - 420a b cosh(x) - 288a b cosh(x) + 130a b cosh(x) +--R + +--R 3 2 2 3 +--R 48a b cosh(x) - 10a b +--R * +--R csch(x) +--R + +--R 3 2 10 4 9 3 2 8 +--R 180a b cosh(x) + 288a b cosh(x) - 740a b cosh(x) +--R + +--R 4 7 3 2 6 4 5 +--R - 960a b cosh(x) + 1160a b cosh(x) + 1152a b cosh(x) +--R + +--R 3 2 4 4 3 3 2 2 +--R - 840a b cosh(x) - 576a b cosh(x) + 260a b cosh(x) +--R + +--R 4 3 2 +--R 96a b cosh(x) - 20a b +--R * +--R 4 +--R coth(x) +--R + +--R 4 10 2 3 9 4 8 +--R 180a b cosh(x) + 288a b cosh(x) - 740a b cosh(x) +--R + +--R 2 3 7 4 6 2 3 5 +--R - 960a b cosh(x) + 1160a b cosh(x) + 1152a b cosh(x) +--R + +--R 4 4 2 3 3 4 2 +--R - 840a b cosh(x) - 576a b cosh(x) + 260a b cosh(x) +--R + +--R 2 3 4 +--R 96a b cosh(x) - 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 10 +--R (- 180a b - 180a b )cosh(x) +--R + +--R 5 2 3 4 9 4 3 2 8 +--R (- 40b - 348a b - 576a b)cosh(x) + (668a b + 632a b )cosh(x) +--R + +--R 5 2 3 4 7 +--R (160b + 1200a b + 576a b)cosh(x) +--R + +--R 4 3 2 6 +--R (- 936a b - 824a b )cosh(x) +--R + +--R 5 2 3 4 5 +--R (- 240b - 1512a b - 960a b)cosh(x) +--R + +--R 4 3 2 4 5 2 3 4 3 +--R (600a b + 480a b )cosh(x) + (160b + 816a b + 960a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 +--R (- 164a b - 116a b )cosh(x) + (- 40b - 156a b )cosh(x) +--R + +--R 4 3 2 +--R 12a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 11 3 2 10 2 3 9 +--R - 40a b cosh(x) - 72a b cosh(x) + 200a b cosh(x) +--R + +--R 3 2 8 2 3 7 3 2 6 +--R 296a b cosh(x) - 400a b cosh(x) - 464a b cosh(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R 400a b cosh(x) + 336a b cosh(x) - 200a b cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R - 104a b cosh(x) + 40a b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 11 3 2 10 2 3 9 +--R 20a b cosh(x) + 36a b cosh(x) - 100a b cosh(x) +--R + +--R 3 2 8 2 3 7 3 2 6 +--R - 148a b cosh(x) + 200a b cosh(x) + 232a b cosh(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R - 200a b cosh(x) - 168a b cosh(x) + 100a b cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R 52a b cosh(x) - 20a b cosh(x) - 4a b +--R * +--R csch(x) +--R + +--R 3 2 11 4 10 3 2 9 +--R 40a b cosh(x) + 72a b cosh(x) - 200a b cosh(x) +--R + +--R 4 8 3 2 7 4 6 +--R - 296a b cosh(x) + 400a b cosh(x) + 464a b cosh(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R - 400a b cosh(x) - 336a b cosh(x) + 200a b cosh(x) +--R + +--R 4 2 3 2 4 +--R 104a b cosh(x) - 40a b cosh(x) - 8a b +--R * +--R 4 +--R coth(x) +--R + +--R 4 11 2 3 10 4 9 +--R 40a b cosh(x) + 72a b cosh(x) - 200a b cosh(x) +--R + +--R 2 3 8 4 7 2 3 6 +--R - 296a b cosh(x) + 400a b cosh(x) + 464a b cosh(x) +--R + +--R 4 5 2 3 4 4 3 +--R - 400a b cosh(x) - 336a b cosh(x) + 200a b cosh(x) +--R + +--R 2 3 2 4 2 3 +--R 104a b cosh(x) - 40a b cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 11 5 2 3 4 10 +--R (- 40a b - 40a b )cosh(x) + (- 4b - 78a b - 144a b)cosh(x) +--R + +--R 4 3 2 9 5 2 3 4 8 +--R (192a b + 188a b )cosh(x) + (20b + 326a b + 144a b)cosh(x) +--R + +--R 4 3 2 7 +--R (- 368a b - 352a b )cosh(x) +--R + +--R 5 2 3 4 6 4 3 2 5 +--R (- 40b - 524a b - 480a b)cosh(x) + (352a b + 328a b )cosh(x) +--R + +--R 5 2 3 4 4 4 3 2 3 +--R (40b + 396a b + 480a b)cosh(x) + (- 168a b - 152a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 +--R (- 20b - 134a b - 16a b)cosh(x) + (32a b + 28a b )cosh(x) +--R + +--R 5 2 3 4 +--R 4b + 14a b + 16a b +--R * +--R sinh(x) +--R + +--R 2 3 12 3 2 11 2 3 10 +--R - 4a b cosh(x) - 8a b cosh(x) + 24a b cosh(x) +--R + +--R 3 2 9 2 3 8 3 2 7 +--R 40a b cosh(x) - 60a b cosh(x) - 80a b cosh(x) +--R + +--R 2 3 6 3 2 5 2 3 4 +--R 80a b cosh(x) + 80a b cosh(x) - 60a b cosh(x) +--R + +--R 3 2 3 2 3 2 3 2 2 3 +--R - 40a b cosh(x) + 24a b cosh(x) + 8a b cosh(x) - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 12 3 2 11 2 3 10 +--R 2a b cosh(x) + 4a b cosh(x) - 12a b cosh(x) +--R + +--R 3 2 9 2 3 8 3 2 7 +--R - 20a b cosh(x) + 30a b cosh(x) + 40a b cosh(x) +--R + +--R 2 3 6 3 2 5 2 3 4 +--R - 40a b cosh(x) - 40a b cosh(x) + 30a b cosh(x) +--R + +--R 3 2 3 2 3 2 3 2 2 3 +--R 20a b cosh(x) - 12a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R csch(x) +--R + +--R 3 2 12 4 11 3 2 10 +--R 4a b cosh(x) + 8a b cosh(x) - 24a b cosh(x) +--R + +--R 4 9 3 2 8 4 7 +--R - 40a b cosh(x) + 60a b cosh(x) + 80a b cosh(x) +--R + +--R 3 2 6 4 5 3 2 4 +--R - 80a b cosh(x) - 80a b cosh(x) + 60a b cosh(x) +--R + +--R 4 3 3 2 2 4 3 2 +--R 40a b cosh(x) - 24a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R 4 +--R coth(x) +--R + +--R 4 12 2 3 11 4 10 +--R 4a b cosh(x) + 8a b cosh(x) - 24a b cosh(x) +--R + +--R 2 3 9 4 8 2 3 7 +--R - 40a b cosh(x) + 60a b cosh(x) + 80a b cosh(x) +--R + +--R 4 6 2 3 5 4 4 +--R - 80a b cosh(x) - 80a b cosh(x) + 60a b cosh(x) +--R + +--R 2 3 3 4 2 2 3 4 +--R 40a b cosh(x) - 24a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 12 2 3 4 11 +--R (- 4a b - 4a b )cosh(x) + (- 8a b - 16a b)cosh(x) +--R + +--R 4 3 2 10 2 3 4 9 +--R (24a b + 24a b )cosh(x) + (40a b + 16a b)cosh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (- 60a b - 60a b )cosh(x) + (- 80a b - 96a b)cosh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (80a b + 80a b )cosh(x) + (80a b + 96a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 60a b - 60a b )cosh(x) + (- 40a b - 16a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (24a b + 24a b )cosh(x) + (8a b + 16a b)cosh(x) - 4a b - 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 2 11 +--R (- 2a b - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 2 3 2 2 3 2 +--R ((- 2a b cosh(x) + 2a b )coth(x) + a b cosh(x) - a b )csch(x) +--R + +--R 4 2 4 4 2 3 2 2 3 2 +--R (2a b cosh(x) - 2a b)coth(x) + (2a b cosh(x) - 2a b )coth(x) +--R + +--R 5 2 3 2 4 3 2 5 2 3 4 +--R (2b + 2a b )cosh(x) + (- 20a b - 30a b )cosh(x) - 2b - 6a b - 6a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 3 4 2 3 2 4 2 +--R (- 20a b cosh(x) - 4a b cosh(x) + 20a b cosh(x) + 4a b)coth(x) +--R + +--R 3 2 3 4 2 3 2 4 +--R 10a b cosh(x) + 2a b cosh(x) - 10a b cosh(x) - 2a b +--R * +--R csch(x) +--R + +--R 4 3 5 2 4 5 4 +--R (20a b cosh(x) + 4a cosh(x) - 20a b cosh(x) - 4a )coth(x) +--R + +--R 2 3 3 3 2 2 2 3 3 2 2 +--R (20a b cosh(x) + 4a b cosh(x) - 20a b cosh(x) - 4a b )coth(x) +--R + +--R 5 2 3 3 4 3 2 5 2 +--R (20b + 20a b )cosh(x) + (- 86a b - 131a b - 4a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 20b - 56a b - 54a b)cosh(x) + 6a b + 11a b + 4a +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 4 3 3 2 2 +--R - 90a b cosh(x) - 36a b cosh(x) + 100a b cosh(x) +--R + +--R 4 3 2 +--R 36a b cosh(x) - 10a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 4 4 3 3 2 2 4 +--R 45a b cosh(x) + 18a b cosh(x) - 50a b cosh(x) - 18a b cosh(x) +--R + +--R 3 2 +--R 5a b +--R * +--R csch(x) +--R + +--R 4 4 5 3 4 2 5 +--R 90a b cosh(x) + 36a cosh(x) - 100a b cosh(x) - 36a cosh(x) +--R + +--R 4 +--R 10a b +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 4 3 2 3 2 3 2 3 2 +--R 90a b cosh(x) + 36a b cosh(x) - 100a b cosh(x) - 36a b cosh(x) +--R + +--R 2 3 +--R 10a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 4 4 3 2 5 3 +--R (90b + 90a b )cosh(x) + (- 204a b - 324a b - 36a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (- 100b - 244a b - 216a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (44a b + 84a b + 36a )cosh(x) + 10b + 26a b + 24a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R - 240a b cosh(x) - 144a b cosh(x) + 320a b cosh(x) +--R + +--R 4 2 3 2 4 +--R 160a b cosh(x) - 80a b cosh(x) - 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R 120a b cosh(x) + 72a b cosh(x) - 160a b cosh(x) +--R + +--R 4 2 3 2 4 +--R - 80a b cosh(x) + 40a b cosh(x) + 8a b +--R * +--R csch(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R 240a b cosh(x) + 144a cosh(x) - 320a b cosh(x) - 160a cosh(x) +--R + +--R 4 5 +--R 80a b cosh(x) + 16a +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R 240a b cosh(x) + 144a b cosh(x) - 320a b cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R - 160a b cosh(x) + 80a b cosh(x) + 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 5 4 3 2 5 4 +--R (240b + 240a b )cosh(x) + (- 276a b - 486a b - 144a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 320b - 656a b - 504a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (120a b + 260a b + 128a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (80b + 192a b + 168a b)cosh(x) - 4a b - 14a b + 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 6 4 5 3 2 4 +--R - 420a b cosh(x) - 336a b cosh(x) + 700a b cosh(x) +--R + +--R 4 3 3 2 2 4 3 2 +--R 448a b cosh(x) - 300a b cosh(x) - 112a b cosh(x) + 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 6 4 5 3 2 4 +--R 210a b cosh(x) + 168a b cosh(x) - 350a b cosh(x) +--R + +--R 4 3 3 2 2 4 3 2 +--R - 224a b cosh(x) + 150a b cosh(x) + 56a b cosh(x) - 10a b +--R * +--R csch(x) +--R + +--R 4 6 5 5 4 4 5 3 +--R 420a b cosh(x) + 336a cosh(x) - 700a b cosh(x) - 448a cosh(x) +--R + +--R 4 2 5 4 +--R 300a b cosh(x) + 112a cosh(x) - 20a b +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 6 3 2 5 2 3 4 +--R 420a b cosh(x) + 336a b cosh(x) - 700a b cosh(x) +--R + +--R 3 2 3 2 3 2 3 2 2 3 +--R - 448a b cosh(x) + 300a b cosh(x) + 112a b cosh(x) - 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 6 4 3 2 5 5 +--R (420b + 420a b )cosh(x) + (- 168a b - 420a b - 336a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (- 700b - 1204a b - 756a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (112a b + 392a b + 224a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (300b + 636a b + 504a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 8a b - 68a b + 112a )cosh(x) - 20b - 44a b - 36a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 7 4 6 3 2 5 +--R - 504a b cosh(x) - 504a b cosh(x) + 1064a b cosh(x) +--R + +--R 4 4 3 2 3 4 2 +--R 840a b cosh(x) - 680a b cosh(x) - 360a b cosh(x) +--R + +--R 3 2 4 +--R 120a b cosh(x) + 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 7 4 6 3 2 5 +--R 252a b cosh(x) + 252a b cosh(x) - 532a b cosh(x) +--R + +--R 4 4 3 2 3 4 2 +--R - 420a b cosh(x) + 340a b cosh(x) + 180a b cosh(x) +--R + +--R 3 2 4 +--R - 60a b cosh(x) - 12a b +--R * +--R csch(x) +--R + +--R 4 7 5 6 4 5 +--R 504a b cosh(x) + 504a cosh(x) - 1064a b cosh(x) +--R + +--R 5 4 4 3 5 2 +--R - 840a cosh(x) + 680a b cosh(x) + 360a cosh(x) +--R + +--R 4 5 +--R - 120a b cosh(x) - 24a +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 7 3 2 6 2 3 5 +--R 504a b cosh(x) + 504a b cosh(x) - 1064a b cosh(x) +--R + +--R 3 2 4 2 3 3 3 2 2 +--R - 840a b cosh(x) + 680a b cosh(x) + 360a b cosh(x) +--R + +--R 2 3 3 2 +--R - 120a b cosh(x) - 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 7 4 3 2 5 6 +--R (504b + 504a b )cosh(x) + (84a b - 126a b - 504a )cosh(x) +--R + +--R 5 2 3 4 5 +--R (- 1064b - 1568a b - 756a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (- 140a b + 210a b + 168a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (680b + 1240a b + 840a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (60a b - 90a b + 312a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 120b - 240a b - 180a b)cosh(x) - 4a b + 6a b + 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 8 4 7 3 2 6 +--R - 420a b cosh(x) - 504a b cosh(x) + 1120a b cosh(x) +--R + +--R 4 5 3 2 4 4 3 +--R 1064a b cosh(x) - 1000a b cosh(x) - 680a b cosh(x) +--R + +--R 3 2 2 4 3 2 +--R 320a b cosh(x) + 120a b cosh(x) - 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 8 4 7 3 2 6 +--R 210a b cosh(x) + 252a b cosh(x) - 560a b cosh(x) +--R + +--R 4 5 3 2 4 4 3 +--R - 532a b cosh(x) + 500a b cosh(x) + 340a b cosh(x) +--R + +--R 3 2 2 4 3 2 +--R - 160a b cosh(x) - 60a b cosh(x) + 10a b +--R * +--R csch(x) +--R + +--R 4 8 5 7 4 6 +--R 420a b cosh(x) + 504a cosh(x) - 1120a b cosh(x) +--R + +--R 5 5 4 4 5 3 +--R - 1064a cosh(x) + 1000a b cosh(x) + 680a cosh(x) +--R + +--R 4 2 5 4 +--R - 320a b cosh(x) - 120a cosh(x) + 20a b +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 8 3 2 7 2 3 6 +--R 420a b cosh(x) + 504a b cosh(x) - 1120a b cosh(x) +--R + +--R 3 2 5 2 3 4 3 2 3 +--R - 1064a b cosh(x) + 1000a b cosh(x) + 680a b cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R - 320a b cosh(x) - 120a b cosh(x) + 20a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 8 4 3 2 5 7 +--R (420b + 420a b )cosh(x) + (264a b + 144a b - 504a )cosh(x) +--R + +--R 5 2 3 4 6 +--R (- 1120b - 1456a b - 504a b)cosh(x) +--R + +--R 4 3 2 5 5 +--R (- 504a b - 224a b - 56a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (1000b + 1560a b + 840a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (280a b + 80a b + 440a )cosh(x) +--R + +--R 5 2 3 4 2 4 5 +--R (- 320b - 560a b - 360a b)cosh(x) + (- 40a b + 120a )cosh(x) +--R + +--R 5 2 3 4 +--R 20b + 36a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 9 4 8 3 2 7 +--R - 240a b cosh(x) - 336a b cosh(x) + 800a b cosh(x) +--R + +--R 4 6 3 2 5 4 4 +--R 896a b cosh(x) - 960a b cosh(x) - 800a b cosh(x) +--R + +--R 3 2 3 4 2 3 2 4 +--R 480a b cosh(x) + 256a b cosh(x) - 80a b cosh(x) - 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 9 4 8 3 2 7 +--R 120a b cosh(x) + 168a b cosh(x) - 400a b cosh(x) +--R + +--R 4 6 3 2 5 4 4 +--R - 448a b cosh(x) + 480a b cosh(x) + 400a b cosh(x) +--R + +--R 3 2 3 4 2 3 2 4 +--R - 240a b cosh(x) - 128a b cosh(x) + 40a b cosh(x) + 8a b +--R * +--R csch(x) +--R + +--R 4 9 5 8 4 7 5 6 +--R 240a b cosh(x) + 336a cosh(x) - 800a b cosh(x) - 896a cosh(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R 960a b cosh(x) + 800a cosh(x) - 480a b cosh(x) - 256a cosh(x) +--R + +--R 4 5 +--R 80a b cosh(x) + 16a +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 9 3 2 8 2 3 7 +--R 240a b cosh(x) + 336a b cosh(x) - 800a b cosh(x) +--R + +--R 3 2 6 2 3 5 3 2 4 +--R - 896a b cosh(x) + 960a b cosh(x) + 800a b cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 3 2 +--R - 480a b cosh(x) - 256a b cosh(x) + 80a b cosh(x) + 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 9 4 3 2 5 8 +--R (240b + 240a b )cosh(x) + (246a b + 201a b - 336a )cosh(x) +--R + +--R 5 2 3 4 7 +--R (- 800b - 944a b - 216a b)cosh(x) +--R + +--R 4 3 2 5 6 +--R (- 616a b - 476a b - 224a )cosh(x) +--R + +--R 5 2 3 4 5 +--R (960b + 1296a b + 504a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (500a b + 350a b + 320a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 480b - 720a b - 360a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 136a b - 76a b + 224a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (80b + 128a b + 72a b)cosh(x) + 6a b + a b + 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 10 4 9 3 2 8 +--R - 90a b cosh(x) - 144a b cosh(x) + 370a b cosh(x) +--R + +--R 4 7 3 2 6 4 5 +--R 480a b cosh(x) - 580a b cosh(x) - 576a b cosh(x) +--R + +--R 3 2 4 4 3 3 2 2 +--R 420a b cosh(x) + 288a b cosh(x) - 130a b cosh(x) +--R + +--R 4 3 2 +--R - 48a b cosh(x) + 10a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 10 4 9 3 2 8 +--R 45a b cosh(x) + 72a b cosh(x) - 185a b cosh(x) +--R + +--R 4 7 3 2 6 4 5 +--R - 240a b cosh(x) + 290a b cosh(x) + 288a b cosh(x) +--R + +--R 3 2 4 4 3 3 2 2 +--R - 210a b cosh(x) - 144a b cosh(x) + 65a b cosh(x) +--R + +--R 4 3 2 +--R 24a b cosh(x) - 5a b +--R * +--R csch(x) +--R + +--R 4 10 5 9 4 8 5 7 +--R 90a b cosh(x) + 144a cosh(x) - 370a b cosh(x) - 480a cosh(x) +--R + +--R 4 6 5 5 4 4 5 3 +--R 580a b cosh(x) + 576a cosh(x) - 420a b cosh(x) - 288a cosh(x) +--R + +--R 4 2 5 4 +--R 130a b cosh(x) + 48a cosh(x) - 10a b +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 10 3 2 9 2 3 8 +--R 90a b cosh(x) + 144a b cosh(x) - 370a b cosh(x) +--R + +--R 3 2 7 2 3 6 3 2 5 +--R - 480a b cosh(x) + 580a b cosh(x) + 576a b cosh(x) +--R + +--R 2 3 4 3 2 3 2 3 2 +--R - 420a b cosh(x) - 288a b cosh(x) + 130a b cosh(x) +--R + +--R 3 2 2 3 +--R 48a b cosh(x) - 10a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 10 4 3 2 5 9 +--R (90b + 90a b )cosh(x) + (124a b + 114a b - 144a )cosh(x) +--R + +--R 5 2 3 4 8 +--R (- 370b - 406a b - 54a b)cosh(x) +--R + +--R 4 3 2 5 7 +--R (- 400a b - 360a b - 192a )cosh(x) +--R + +--R 5 2 3 4 6 +--R (580b + 692a b + 168a b)cosh(x) +--R + +--R 4 3 2 5 5 +--R (456a b + 396a b + 96a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (- 420b - 540a b - 180a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (- 208a b - 168a b + 192a )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (130b + 178a b + 72a b)cosh(x) + (28a b + 18a b + 48a )cosh(x) +--R + +--R 5 2 3 4 +--R - 10b - 14a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 11 4 10 3 2 9 +--R - 20a b cosh(x) - 36a b cosh(x) + 100a b cosh(x) +--R + +--R 4 8 3 2 7 4 6 +--R 148a b cosh(x) - 200a b cosh(x) - 232a b cosh(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R 200a b cosh(x) + 168a b cosh(x) - 100a b cosh(x) +--R + +--R 4 2 3 2 4 +--R - 52a b cosh(x) + 20a b cosh(x) + 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 11 4 10 3 2 9 +--R 10a b cosh(x) + 18a b cosh(x) - 50a b cosh(x) +--R + +--R 4 8 3 2 7 4 6 +--R - 74a b cosh(x) + 100a b cosh(x) + 116a b cosh(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R - 100a b cosh(x) - 84a b cosh(x) + 50a b cosh(x) +--R + +--R 4 2 3 2 4 +--R 26a b cosh(x) - 10a b cosh(x) - 2a b +--R * +--R csch(x) +--R + +--R 4 11 5 10 4 9 5 8 +--R 20a b cosh(x) + 36a cosh(x) - 100a b cosh(x) - 148a cosh(x) +--R + +--R 4 7 5 6 4 5 5 4 +--R 200a b cosh(x) + 232a cosh(x) - 200a b cosh(x) - 168a cosh(x) +--R + +--R 4 3 5 2 4 5 +--R 100a b cosh(x) + 52a cosh(x) - 20a b cosh(x) - 4a +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 11 3 2 10 2 3 9 +--R 20a b cosh(x) + 36a b cosh(x) - 100a b cosh(x) +--R + +--R 3 2 8 2 3 7 3 2 6 +--R - 148a b cosh(x) + 200a b cosh(x) + 232a b cosh(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R - 200a b cosh(x) - 168a b cosh(x) + 100a b cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R 52a b cosh(x) - 20a b cosh(x) - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 11 4 3 2 5 10 +--R (20b + 20a b )cosh(x) + (34a b + 33a b - 36a )cosh(x) +--R + +--R 5 2 3 4 9 +--R (- 100b - 104a b - 6a b)cosh(x) +--R + +--R 4 3 2 5 8 +--R (- 138a b - 133a b - 76a )cosh(x) +--R + +--R 5 2 3 4 7 4 3 2 5 6 +--R (200b + 216a b + 24a b)cosh(x) + (212a b + 202a b - 8a )cosh(x) +--R + +--R 5 2 3 4 5 +--R (- 200b - 224a b - 36a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (- 148a b - 138a b + 72a )cosh(x) +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (100b + 116a b + 24a b)cosh(x) + (42a b + 37a b + 44a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 20b - 24a b - 6a b)cosh(x) - 2a b - a b + 4a +--R * +--R sinh(x) +--R + +--R 3 2 12 4 11 3 2 10 +--R - 2a b cosh(x) - 4a b cosh(x) + 12a b cosh(x) +--R + +--R 4 9 3 2 8 4 7 3 2 6 +--R 20a b cosh(x) - 30a b cosh(x) - 40a b cosh(x) + 40a b cosh(x) +--R + +--R 4 5 3 2 4 4 3 3 2 2 +--R 40a b cosh(x) - 30a b cosh(x) - 20a b cosh(x) + 12a b cosh(x) +--R + +--R 4 3 2 +--R 4a b cosh(x) - 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 12 4 11 3 2 10 4 9 +--R a b cosh(x) + 2a b cosh(x) - 6a b cosh(x) - 10a b cosh(x) +--R + +--R 3 2 8 4 7 3 2 6 4 5 +--R 15a b cosh(x) + 20a b cosh(x) - 20a b cosh(x) - 20a b cosh(x) +--R + +--R 3 2 4 4 3 3 2 2 4 3 2 +--R 15a b cosh(x) + 10a b cosh(x) - 6a b cosh(x) - 2a b cosh(x) + a b +--R * +--R csch(x) +--R + +--R 4 12 5 11 4 10 5 9 +--R 2a b cosh(x) + 4a cosh(x) - 12a b cosh(x) - 20a cosh(x) +--R + +--R 4 8 5 7 4 6 5 5 +--R 30a b cosh(x) + 40a cosh(x) - 40a b cosh(x) - 40a cosh(x) +--R + +--R 4 4 5 3 4 2 5 4 +--R 30a b cosh(x) + 20a cosh(x) - 12a b cosh(x) - 4a cosh(x) + 2a b +--R * +--R 4 +--R coth(x) +--R + +--R 2 3 12 3 2 11 2 3 10 3 2 9 +--R 2a b cosh(x) + 4a b cosh(x) - 12a b cosh(x) - 20a b cosh(x) +--R + +--R 2 3 8 3 2 7 2 3 6 3 2 5 +--R 30a b cosh(x) + 40a b cosh(x) - 40a b cosh(x) - 40a b cosh(x) +--R + +--R 2 3 4 3 2 3 2 3 2 3 2 2 3 +--R 30a b cosh(x) + 20a b cosh(x) - 12a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 5 2 3 12 4 3 2 5 11 +--R (2b + 2a b )cosh(x) + (4a b + 4a b - 4a )cosh(x) +--R + +--R 5 2 3 10 4 3 2 5 9 +--R (- 12b - 12a b )cosh(x) + (- 20a b - 20a b - 12a )cosh(x) +--R + +--R 5 2 3 8 4 3 2 5 7 +--R (30b + 30a b )cosh(x) + (40a b + 40a b - 8a )cosh(x) +--R + +--R 5 2 3 6 4 3 2 5 5 +--R (- 40b - 40a b )cosh(x) + (- 40a b - 40a b + 8a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 3 +--R (30b + 30a b )cosh(x) + (20a b + 20a b + 12a )cosh(x) +--R + +--R 5 2 3 2 4 3 2 5 5 2 3 +--R (- 12b - 12a b )cosh(x) + (- 4a b - 4a b + 4a )cosh(x) + 2b + 2a b +--R / +--R 5 2 5 10 +--R (2a b cosh(x) - 2a b)sinh(x) +--R + +--R 5 3 6 2 5 6 9 +--R (20a b cosh(x) + 4a cosh(x) - 20a b cosh(x) - 4a )sinh(x) +--R + +--R 5 4 6 3 5 2 6 +--R 90a b cosh(x) + 36a cosh(x) - 100a b cosh(x) - 36a cosh(x) +--R + +--R 5 +--R 10a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 5 6 4 5 3 6 2 +--R 240a b cosh(x) + 144a cosh(x) - 320a b cosh(x) - 160a cosh(x) +--R + +--R 5 6 +--R 80a b cosh(x) + 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 5 6 6 5 5 4 6 3 +--R 420a b cosh(x) + 336a cosh(x) - 700a b cosh(x) - 448a cosh(x) +--R + +--R 5 2 6 5 +--R 300a b cosh(x) + 112a cosh(x) - 20a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 7 6 6 5 5 +--R 504a b cosh(x) + 504a cosh(x) - 1064a b cosh(x) +--R + +--R 6 4 5 3 6 2 +--R - 840a cosh(x) + 680a b cosh(x) + 360a cosh(x) +--R + +--R 5 6 +--R - 120a b cosh(x) - 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 5 8 6 7 5 6 +--R 420a b cosh(x) + 504a cosh(x) - 1120a b cosh(x) +--R + +--R 6 5 5 4 6 3 +--R - 1064a cosh(x) + 1000a b cosh(x) + 680a cosh(x) +--R + +--R 5 2 6 5 +--R - 320a b cosh(x) - 120a cosh(x) + 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 9 6 8 5 7 6 6 +--R 240a b cosh(x) + 336a cosh(x) - 800a b cosh(x) - 896a cosh(x) +--R + +--R 5 5 6 4 5 3 6 2 +--R 960a b cosh(x) + 800a cosh(x) - 480a b cosh(x) - 256a cosh(x) +--R + +--R 5 6 +--R 80a b cosh(x) + 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 10 6 9 5 8 6 7 +--R 90a b cosh(x) + 144a cosh(x) - 370a b cosh(x) - 480a cosh(x) +--R + +--R 5 6 6 5 5 4 6 3 +--R 580a b cosh(x) + 576a cosh(x) - 420a b cosh(x) - 288a cosh(x) +--R + +--R 5 2 6 5 +--R 130a b cosh(x) + 48a cosh(x) - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 11 6 10 5 9 6 8 +--R 20a b cosh(x) + 36a cosh(x) - 100a b cosh(x) - 148a cosh(x) +--R + +--R 5 7 6 6 5 5 6 4 +--R 200a b cosh(x) + 232a cosh(x) - 200a b cosh(x) - 168a cosh(x) +--R + +--R 5 3 6 2 5 6 +--R 100a b cosh(x) + 52a cosh(x) - 20a b cosh(x) - 4a +--R * +--R sinh(x) +--R + +--R 5 12 6 11 5 10 6 9 +--R 2a b cosh(x) + 4a cosh(x) - 12a b cosh(x) - 20a cosh(x) +--R + +--R 5 8 6 7 5 6 6 5 +--R 30a b cosh(x) + 40a cosh(x) - 40a b cosh(x) - 40a cosh(x) +--R + +--R 5 4 6 3 5 2 6 5 +--R 30a b cosh(x) + 20a cosh(x) - 12a b cosh(x) - 4a cosh(x) + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 2 4 2 10 +--R (- 4a b cosh(x) + 4a b )sinh(x) +--R + +--R 4 2 3 5 2 4 2 5 9 +--R (- 40a b cosh(x) - 8a b cosh(x) + 40a b cosh(x) + 8a b)sinh(x) +--R + +--R 4 2 4 5 3 4 2 2 +--R - 180a b cosh(x) - 72a b cosh(x) + 200a b cosh(x) +--R + +--R 5 4 2 +--R 72a b cosh(x) - 20a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 5 5 4 4 2 3 +--R - 480a b cosh(x) - 288a b cosh(x) + 640a b cosh(x) +--R + +--R 5 2 4 2 5 +--R 320a b cosh(x) - 160a b cosh(x) - 32a b +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 6 5 5 4 2 4 +--R - 840a b cosh(x) - 672a b cosh(x) + 1400a b cosh(x) +--R + +--R 5 3 4 2 2 5 4 2 +--R 896a b cosh(x) - 600a b cosh(x) - 224a b cosh(x) + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 7 5 6 4 2 5 +--R - 1008a b cosh(x) - 1008a b cosh(x) + 2128a b cosh(x) +--R + +--R 5 4 4 2 3 5 2 +--R 1680a b cosh(x) - 1360a b cosh(x) - 720a b cosh(x) +--R + +--R 4 2 5 +--R 240a b cosh(x) + 48a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 8 5 7 4 2 6 +--R - 840a b cosh(x) - 1008a b cosh(x) + 2240a b cosh(x) +--R + +--R 5 5 4 2 4 5 3 +--R 2128a b cosh(x) - 2000a b cosh(x) - 1360a b cosh(x) +--R + +--R 4 2 2 5 4 2 +--R 640a b cosh(x) + 240a b cosh(x) - 40a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 9 5 8 4 2 7 +--R - 480a b cosh(x) - 672a b cosh(x) + 1600a b cosh(x) +--R + +--R 5 6 4 2 5 5 4 +--R 1792a b cosh(x) - 1920a b cosh(x) - 1600a b cosh(x) +--R + +--R 4 2 3 5 2 4 2 5 +--R 960a b cosh(x) + 512a b cosh(x) - 160a b cosh(x) - 32a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 10 5 9 4 2 8 +--R - 180a b cosh(x) - 288a b cosh(x) + 740a b cosh(x) +--R + +--R 5 7 4 2 6 5 5 +--R 960a b cosh(x) - 1160a b cosh(x) - 1152a b cosh(x) +--R + +--R 4 2 4 5 3 4 2 2 +--R 840a b cosh(x) + 576a b cosh(x) - 260a b cosh(x) +--R + +--R 5 4 2 +--R - 96a b cosh(x) + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 11 5 10 4 2 9 +--R - 40a b cosh(x) - 72a b cosh(x) + 200a b cosh(x) +--R + +--R 5 8 4 2 7 5 6 +--R 296a b cosh(x) - 400a b cosh(x) - 464a b cosh(x) +--R + +--R 4 2 5 5 4 4 2 3 +--R 400a b cosh(x) + 336a b cosh(x) - 200a b cosh(x) +--R + +--R 5 2 4 2 5 +--R - 104a b cosh(x) + 40a b cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 2 12 5 11 4 2 10 5 9 +--R - 4a b cosh(x) - 8a b cosh(x) + 24a b cosh(x) + 40a b cosh(x) +--R + +--R 4 2 8 5 7 4 2 6 5 5 +--R - 60a b cosh(x) - 80a b cosh(x) + 80a b cosh(x) + 80a b cosh(x) +--R + +--R 4 2 4 5 3 4 2 2 5 +--R - 60a b cosh(x) - 40a b cosh(x) + 24a b cosh(x) + 8a b cosh(x) +--R + +--R 4 2 +--R - 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 2 5 10 +--R (- 2a b cosh(x) + 2a b)sinh(x) +--R + +--R 5 3 6 2 5 6 9 +--R (- 20a b cosh(x) - 4a cosh(x) + 20a b cosh(x) + 4a )sinh(x) +--R + +--R 5 4 6 3 5 2 6 +--R - 90a b cosh(x) - 36a cosh(x) + 100a b cosh(x) + 36a cosh(x) +--R + +--R 5 +--R - 10a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 5 6 4 5 3 6 2 +--R - 240a b cosh(x) - 144a cosh(x) + 320a b cosh(x) + 160a cosh(x) +--R + +--R 5 6 +--R - 80a b cosh(x) - 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 5 6 6 5 5 4 6 3 +--R - 420a b cosh(x) - 336a cosh(x) + 700a b cosh(x) + 448a cosh(x) +--R + +--R 5 2 6 5 +--R - 300a b cosh(x) - 112a cosh(x) + 20a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 7 6 6 5 5 6 4 +--R - 504a b cosh(x) - 504a cosh(x) + 1064a b cosh(x) + 840a cosh(x) +--R + +--R 5 3 6 2 5 6 +--R - 680a b cosh(x) - 360a cosh(x) + 120a b cosh(x) + 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 5 8 6 7 5 6 6 5 +--R - 420a b cosh(x) - 504a cosh(x) + 1120a b cosh(x) + 1064a cosh(x) +--R + +--R 5 4 6 3 5 2 6 +--R - 1000a b cosh(x) - 680a cosh(x) + 320a b cosh(x) + 120a cosh(x) +--R + +--R 5 +--R - 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 9 6 8 5 7 6 6 +--R - 240a b cosh(x) - 336a cosh(x) + 800a b cosh(x) + 896a cosh(x) +--R + +--R 5 5 6 4 5 3 6 2 +--R - 960a b cosh(x) - 800a cosh(x) + 480a b cosh(x) + 256a cosh(x) +--R + +--R 5 6 +--R - 80a b cosh(x) - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 10 6 9 5 8 6 7 +--R - 90a b cosh(x) - 144a cosh(x) + 370a b cosh(x) + 480a cosh(x) +--R + +--R 5 6 6 5 5 4 6 3 +--R - 580a b cosh(x) - 576a cosh(x) + 420a b cosh(x) + 288a cosh(x) +--R + +--R 5 2 6 5 +--R - 130a b cosh(x) - 48a cosh(x) + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 11 6 10 5 9 6 8 +--R - 20a b cosh(x) - 36a cosh(x) + 100a b cosh(x) + 148a cosh(x) +--R + +--R 5 7 6 6 5 5 6 4 +--R - 200a b cosh(x) - 232a cosh(x) + 200a b cosh(x) + 168a cosh(x) +--R + +--R 5 3 6 2 5 6 +--R - 100a b cosh(x) - 52a cosh(x) + 20a b cosh(x) + 4a +--R * +--R sinh(x) +--R + +--R 5 12 6 11 5 10 6 9 +--R - 2a b cosh(x) - 4a cosh(x) + 12a b cosh(x) + 20a cosh(x) +--R + +--R 5 8 6 7 5 6 6 5 +--R - 30a b cosh(x) - 40a cosh(x) + 40a b cosh(x) + 40a cosh(x) +--R + +--R 5 4 6 3 5 2 6 5 +--R - 30a b cosh(x) - 20a cosh(x) + 12a b cosh(x) + 4a cosh(x) - 2a b +--R Type: Expression(Integer) +--E 55 + +--S 56 of 530 +t0511:= coth(x)/(%i+sinh(x)) +--R +--R +--R coth(x) +--R (55) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 56 + +--S 57 of 530 +r0511:= -%i*log(sinh(x))+%i*log(%i+sinh(x)) +--R +--R +--R (56) %i log(sinh(x) + %i) - %i log(sinh(x)) +--R Type: Expression(Complex(Integer)) +--E 57 + +--S 58 of 530 +a0511:= integrate(t0511,x) +--R +--R +--R 2sinh(x) +--R (57) 2%i log(sinh(x) + cosh(x) + %i) - %i log(- -----------------) +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 58 + +--S 59 of 530 +m0511:= a0511-r0511 +--R +--R +--R (58) +--R 2%i log(sinh(x) + cosh(x) + %i) - %i log(sinh(x) + %i) + %i log(sinh(x)) +--R + +--R 2sinh(x) +--R - %i log(- -----------------) +--R sinh(x) - cosh(x) +--R Type: Expression(Complex(Integer)) +--E 59 + +--S 60 of 530 +d0511:= D(m0511,x) +--R +--R +--R 2 2 +--R %i sinh(x) - %i cosh(x) + %i +--R (59) -------------------------------------------------- +--R 2 +--R sinh(x) + (cosh(x) + 2%i)sinh(x) + %i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 60 + +--S 61 of 530 +t0512:= coth(x)^2/(%i+sinh(x)) +--R +--R +--R 2 +--R coth(x) +--R (60) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 61 + +--S 62 of 530 +r0512:= -acoth(cosh(x))+%i*coth(x) +--R +--R +--R (61) - acoth(cosh(x)) + %i coth(x) +--R Type: Expression(Complex(Integer)) +--E 62 + +--S 63 of 530 +a0512:= integrate(t0512,x) +--R +--R +--R (62) +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)log(sinh(x) + cosh(x) - 1) + 2%i +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 63 + +--S 64 of 530 +m0512:= a0512-r0512 +--R +--R +--R (63) +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)acoth(cosh(x)) +--R + +--R 2 +--R - %i coth(x)sinh(x) - 2%i cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (- %i cosh(x) + %i)coth(x) + 2%i +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 64 + +--S 65 of 530 +d0512:= D(m0512,x) +--R +--R +--R (64) +--R 5 +--R - sinh(x) +--R + +--R 2 2 2 4 +--R ((%i cosh(x) - %i)coth(x) - %i cosh(x) - 4cosh(x) + %i)sinh(x) +--R + +--R 3 2 3 2 +--R (4%i cosh(x) - 4%i cosh(x))coth(x) - 4%i cosh(x) - 4cosh(x) +--R + +--R 4%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 +--R (6%i cosh(x) - 8%i cosh(x) + 2%i)coth(x) - 6%i cosh(x) +--R + +--R 3 2 +--R 2cosh(x) + 4%i cosh(x) - 2cosh(x) + 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (4%i cosh(x) - 8%i cosh(x) + 4%i cosh(x))coth(x) - 4%i cosh(x) +--R + +--R 4 2 +--R 5cosh(x) - 6cosh(x) + 4%i cosh(x) + 1 +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (%i cosh(x) - 3%i cosh(x) + 3%i cosh(x) - %i)coth(x) - %i cosh(x) +--R + +--R 5 4 3 2 +--R 2cosh(x) - %i cosh(x) - 4cosh(x) + %i cosh(x) + 2cosh(x) + %i +--R / +--R 2 4 3 3 +--R (cosh(x) - 1)sinh(x) + (4cosh(x) - 4cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (6cosh(x) - 8cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (4cosh(x) - 8cosh(x) + 4cosh(x))sinh(x) + cosh(x) - 3cosh(x) +--R + +--R 2 +--R 3cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 65 + +--S 66 of 530 +t0513:= coth(x)^3/(%i+sinh(x)) +--R +--R +--R 3 +--R coth(x) +--R (65) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 66 + +--S 67 of 530 +r0513:= -csch(x)+1/2*%i*csch(x)^2 +--R +--R +--R 1 2 +--R (66) - %i csch(x) - csch(x) +--R 2 +--R Type: Expression(Complex(Fraction(Integer))) +--E 67 + +--S 68 of 530 +a0513:= integrate(t0513,x) +--R +--R +--R (67) +--R 2 2 +--R - 2sinh(x) + (- 4cosh(x) + 2%i)sinh(x) - 2cosh(x) + 2%i cosh(x) + 2 +--R ------------------------------------------------------------------------- +--R 3 2 2 3 +--R sinh(x) + 3cosh(x)sinh(x) + (3cosh(x) - 3)sinh(x) + cosh(x) - cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 68 + +--S 69 of 530 +m0513:= a0513-r0513 +--R +--R +--R (68) +--R 1 2 3 +--R (- - %i csch(x) + csch(x))sinh(x) +--R 2 +--R + +--R 3 2 2 +--R (- - %i cosh(x)csch(x) + 3cosh(x)csch(x) - 2)sinh(x) +--R 2 +--R + +--R 3 2 3 2 2 +--R (- - %i cosh(x) + - %i)csch(x) + (3cosh(x) - 3)csch(x) - 4cosh(x) +--R 2 2 +--R + +--R 2%i +--R * +--R sinh(x) +--R + +--R 1 3 1 2 3 +--R (- - %i cosh(x) + - %i cosh(x))csch(x) + (cosh(x) - cosh(x))csch(x) +--R 2 2 +--R + +--R 2 +--R - 2cosh(x) + 2%i cosh(x) + 2 +--R / +--R 3 2 2 3 +--R sinh(x) + 3cosh(x)sinh(x) + (3cosh(x) - 3)sinh(x) + cosh(x) - cosh(x) +--R Type: Expression(Complex(Fraction(Integer))) +--E 69 + +--S 70 of 530 +d0513:= D(m0513,x) +--R +--R +--R (69) +--R 2 6 +--R (%i coth(x)csch(x) - coth(x)csch(x))sinh(x) +--R + +--R 2 5 +--R (6%i cosh(x)coth(x)csch(x) - 6cosh(x)coth(x)csch(x) + 2)sinh(x) +--R + +--R 2 2 +--R (15%i cosh(x) - 6%i)coth(x)csch(x) +--R + +--R 2 +--R (- 15cosh(x) + 6)coth(x)csch(x) + 10cosh(x) - 4%i +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (20%i cosh(x) - 20%i cosh(x))coth(x)csch(x) +--R + +--R 3 2 +--R (- 20cosh(x) + 20cosh(x))coth(x)csch(x) + 20cosh(x) - 16%i cosh(x) +--R + +--R 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (15%i cosh(x) - 24%i cosh(x) + 9%i)coth(x)csch(x) +--R + +--R 4 2 3 +--R (- 15cosh(x) + 24cosh(x) - 9)coth(x)csch(x) + 20cosh(x) +--R + +--R 2 +--R - 24%i cosh(x) - 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (6%i cosh(x) - 12%i cosh(x) + 6%i cosh(x))coth(x)csch(x) +--R + +--R 5 3 4 +--R (- 6cosh(x) + 12cosh(x) - 6cosh(x))coth(x)csch(x) + 10cosh(x) +--R + +--R 3 2 +--R - 16%i cosh(x) - 12cosh(x) + 2 +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (%i cosh(x) - 2%i cosh(x) + %i cosh(x) )coth(x)csch(x) +--R + +--R 6 4 2 5 +--R (- cosh(x) + 2cosh(x) - cosh(x) )coth(x)csch(x) + 2cosh(x) +--R + +--R 4 3 2 +--R - 4%i cosh(x) - 8cosh(x) + 4%i cosh(x) + 6cosh(x) +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 6)sinh(x) +--R + +--R 3 3 4 2 2 +--R (20cosh(x) - 20cosh(x))sinh(x) + (15cosh(x) - 24cosh(x) + 9)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 12cosh(x) + 6cosh(x))sinh(x) + cosh(x) - 2cosh(x) +--R + +--R 2 +--R cosh(x) +--R Type: Expression(Complex(Fraction(Integer))) +--E 70 + +--S 71 of 530 +t0514:= coth(x)^4/(%i+sinh(x)) +--R +--R +--R 4 +--R coth(x) +--R (70) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 71 + +--S 72 of 530 +r0514:= -1/2*acoth(cosh(x))+1/3*%i*coth(x)^3-1/2*coth(x)*csch(x) +--R +--R +--R 1 1 1 3 +--R (71) - - acoth(cosh(x)) - - coth(x)csch(x) + - %i coth(x) +--R 2 2 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 72 + +--S 73 of 530 +a0514:= integrate(t0514,x) +--R +--R +--R (72) +--R 6 5 2 4 +--R - 3sinh(x) - 18cosh(x)sinh(x) + (- 45cosh(x) + 9)sinh(x) +--R + +--R 3 3 +--R (- 60cosh(x) + 36cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) + 54cosh(x) - 9)sinh(x) +--R + +--R 5 3 6 +--R (- 18cosh(x) + 36cosh(x) - 18cosh(x))sinh(x) - 3cosh(x) +--R + +--R 4 2 +--R 9cosh(x) - 9cosh(x) + 3 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 6 5 2 4 +--R 3sinh(x) + 18cosh(x)sinh(x) + (45cosh(x) - 9)sinh(x) +--R + +--R 3 3 +--R (60cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (45cosh(x) - 54cosh(x) + 9)sinh(x) +--R + +--R 5 3 6 4 +--R (18cosh(x) - 36cosh(x) + 18cosh(x))sinh(x) + 3cosh(x) - 9cosh(x) +--R + +--R 2 +--R 9cosh(x) - 3 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 5 4 +--R - 6sinh(x) + (- 30cosh(x) + 12%i)sinh(x) +--R + +--R 2 3 +--R (- 60cosh(x) + 48%i cosh(x))sinh(x) +--R + +--R 3 2 2 +--R (- 60cosh(x) + 72%i cosh(x) )sinh(x) +--R + +--R 4 3 5 4 +--R (- 30cosh(x) + 48%i cosh(x) + 6)sinh(x) - 6cosh(x) + 12%i cosh(x) +--R + +--R 6cosh(x) + 4%i +--R / +--R 6 5 2 4 +--R 6sinh(x) + 36cosh(x)sinh(x) + (90cosh(x) - 18)sinh(x) +--R + +--R 3 3 +--R (120cosh(x) - 72cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (90cosh(x) - 108cosh(x) + 18)sinh(x) +--R + +--R 5 3 6 4 +--R (36cosh(x) - 72cosh(x) + 36cosh(x))sinh(x) + 6cosh(x) - 18cosh(x) +--R + +--R 2 +--R 18cosh(x) - 6 +--R Type: Union(Expression(Complex(Integer)),...) +--E 73 + +--S 74 of 530 +m0514:= a0514-r0514 +--R +--R +--R (73) +--R 1 6 5 15 2 3 4 +--R - - sinh(x) - 3cosh(x)sinh(x) + (- -- cosh(x) + -)sinh(x) +--R 2 2 2 +--R + +--R 3 3 +--R (- 10cosh(x) + 6cosh(x))sinh(x) +--R + +--R 15 4 2 3 2 +--R (- -- cosh(x) + 9cosh(x) - -)sinh(x) +--R 2 2 +--R + +--R 5 3 1 6 3 4 +--R (- 3cosh(x) + 6cosh(x) - 3cosh(x))sinh(x) - - cosh(x) + - cosh(x) +--R 2 2 +--R + +--R 3 2 1 +--R - - cosh(x) + - +--R 2 2 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 1 6 5 15 2 3 4 +--R - sinh(x) + 3cosh(x)sinh(x) + (-- cosh(x) - -)sinh(x) +--R 2 2 2 +--R + +--R 3 3 +--R (10cosh(x) - 6cosh(x))sinh(x) +--R + +--R 15 4 2 3 2 +--R (-- cosh(x) - 9cosh(x) + -)sinh(x) +--R 2 2 +--R + +--R 5 3 1 6 3 4 +--R (3cosh(x) - 6cosh(x) + 3cosh(x))sinh(x) + - cosh(x) - - cosh(x) +--R 2 2 +--R + +--R 3 2 1 +--R - cosh(x) - - +--R 2 2 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 1 6 5 15 2 3 4 +--R - sinh(x) + 3cosh(x)sinh(x) + (-- cosh(x) - -)sinh(x) +--R 2 2 2 +--R + +--R 3 3 +--R (10cosh(x) - 6cosh(x))sinh(x) +--R + +--R 15 4 2 3 2 +--R (-- cosh(x) - 9cosh(x) + -)sinh(x) +--R 2 2 +--R + +--R 5 3 1 6 3 4 +--R (3cosh(x) - 6cosh(x) + 3cosh(x))sinh(x) + - cosh(x) - - cosh(x) +--R 2 2 +--R + +--R 3 2 1 +--R - cosh(x) - - +--R 2 2 +--R * +--R acoth(cosh(x)) +--R + +--R 1 1 3 6 +--R (- coth(x)csch(x) - - %i coth(x) )sinh(x) +--R 2 3 +--R + +--R 3 5 +--R (3cosh(x)coth(x)csch(x) - 2%i cosh(x)coth(x) - 1)sinh(x) +--R + +--R 15 2 3 2 3 +--R (-- cosh(x) - -)coth(x)csch(x) + (- 5%i cosh(x) + %i)coth(x) +--R 2 2 +--R + +--R - 5cosh(x) + 2%i +--R * +--R 4 +--R sinh(x) +--R + +--R 3 +--R (10cosh(x) - 6cosh(x))coth(x)csch(x) +--R + +--R 20 3 3 2 +--R (- -- %i cosh(x) + 4%i cosh(x))coth(x) - 10cosh(x) + 8%i cosh(x) +--R 3 +--R * +--R 3 +--R sinh(x) +--R + +--R 15 4 2 3 +--R (-- cosh(x) - 9cosh(x) + -)coth(x)csch(x) +--R 2 2 +--R + +--R 4 2 3 3 +--R (- 5%i cosh(x) + 6%i cosh(x) - %i)coth(x) - 10cosh(x) +--R + +--R 2 +--R 12%i cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 +--R (3cosh(x) - 6cosh(x) + 3cosh(x))coth(x)csch(x) +--R + +--R 5 3 3 4 +--R (- 2%i cosh(x) + 4%i cosh(x) - 2%i cosh(x))coth(x) - 5cosh(x) +--R + +--R 3 +--R 8%i cosh(x) + 1 +--R * +--R sinh(x) +--R + +--R 1 6 3 4 3 2 1 +--R (- cosh(x) - - cosh(x) + - cosh(x) - -)coth(x)csch(x) +--R 2 2 2 2 +--R + +--R 1 6 4 2 1 3 5 +--R (- - %i cosh(x) + %i cosh(x) - %i cosh(x) + - %i)coth(x) - cosh(x) +--R 3 3 +--R + +--R 4 2 +--R 2%i cosh(x) + cosh(x) + - %i +--R 3 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 3)sinh(x) +--R + +--R 3 3 4 2 2 +--R (20cosh(x) - 12cosh(x))sinh(x) + (15cosh(x) - 18cosh(x) + 3)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 12cosh(x) + 6cosh(x))sinh(x) + cosh(x) - 3cosh(x) +--R + +--R 2 +--R 3cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 74 + +--S 75 of 530 +d0514:= D(m0514,x) +--R +--R +--R (74) +--R 1 9 +--R - - sinh(x) +--R 2 +--R + +--R 2 2 1 2 1 +--R ((- cosh(x) + 1)coth(x) + - cosh(x) - -)csch(x) +--R 2 2 +--R + +--R 2 4 2 2 +--R (%i cosh(x) - %i)coth(x) + (- %i cosh(x) + %i)coth(x) - 4cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 3 +--R ((- 8cosh(x) + 8cosh(x))coth(x) + 4cosh(x) - 4cosh(x))csch(x) +--R + +--R 3 4 +--R (8%i cosh(x) - 8%i cosh(x))coth(x) +--R + +--R 3 2 2 +--R (- 8%i cosh(x) + 8%i cosh(x))coth(x) - 12cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 2 4 2 +--R (- 28cosh(x) + 32cosh(x) - 4)coth(x) + 14cosh(x) - 16cosh(x) +--R + +--R 2 +--R * +--R csch(x) +--R + +--R 4 2 4 +--R (28%i cosh(x) - 32%i cosh(x) + 4%i)coth(x) +--R + +--R 4 2 2 3 +--R (- 28%i cosh(x) + 32%i cosh(x) - 4%i)coth(x) - 14cosh(x) +--R + +--R 2 +--R - 4%i cosh(x) - 2cosh(x) + 4%i +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 56cosh(x) + 80cosh(x) - 24cosh(x))coth(x) + 28cosh(x) +--R + +--R 3 +--R - 40cosh(x) + 12cosh(x) +--R * +--R csch(x) +--R + +--R 5 3 4 +--R (56%i cosh(x) - 80%i cosh(x) + 24%i cosh(x))coth(x) +--R + +--R 5 3 2 4 +--R (- 56%i cosh(x) + 80%i cosh(x) - 24%i cosh(x))coth(x) + 7cosh(x) +--R + +--R 3 2 +--R - 24%i cosh(x) - 10cosh(x) + 24%i cosh(x) - 5 +--R * +--R 5 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 70cosh(x) + 130cosh(x) - 66cosh(x) + 6)coth(x) +--R + +--R 6 4 2 +--R 35cosh(x) - 65cosh(x) + 33cosh(x) - 3 +--R * +--R csch(x) +--R + +--R 6 4 2 4 +--R (70%i cosh(x) - 130%i cosh(x) + 66%i cosh(x) - 6%i)coth(x) +--R + +--R 6 4 2 2 +--R (- 70%i cosh(x) + 130%i cosh(x) - 66%i cosh(x) + 6%i)coth(x) +--R + +--R 5 4 3 2 +--R 42cosh(x) - 60%i cosh(x) - 20cosh(x) + 52%i cosh(x) - 22cosh(x) +--R + +--R 8%i +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (- 56cosh(x) + 136cosh(x) - 104cosh(x) + 24cosh(x))coth(x) +--R + +--R 7 5 3 +--R 28cosh(x) - 68cosh(x) + 52cosh(x) - 12cosh(x) +--R * +--R csch(x) +--R + +--R 7 5 3 +--R (56%i cosh(x) - 136%i cosh(x) + 104%i cosh(x) - 24%i cosh(x)) +--R * +--R 4 +--R coth(x) +--R + +--R 7 5 3 +--R (- 56%i cosh(x) + 136%i cosh(x) - 104%i cosh(x) + 24%i cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 2 +--R 56cosh(x) - 80%i cosh(x) - 20cosh(x) + 48%i cosh(x) - 40cosh(x) +--R + +--R 32%i cosh(x) + 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 28cosh(x) + 88cosh(x) - 96cosh(x) + 40cosh(x) - 4)coth(x) +--R + +--R 8 6 4 2 +--R 14cosh(x) - 44cosh(x) + 48cosh(x) - 20cosh(x) + 2 +--R * +--R csch(x) +--R + +--R 8 6 4 2 +--R 28%i cosh(x) - 88%i cosh(x) + 96%i cosh(x) - 40%i cosh(x) +--R + +--R 4%i +--R * +--R 4 +--R coth(x) +--R + +--R 8 6 4 2 +--R - 28%i cosh(x) + 88%i cosh(x) - 96%i cosh(x) + 40%i cosh(x) +--R + +--R - 4%i +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 3 +--R 38cosh(x) - 60%i cosh(x) - 10cosh(x) + 12%i cosh(x) - 38cosh(x) +--R + +--R 2 +--R 44%i cosh(x) + 10cosh(x) + 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (- 8cosh(x) + 32cosh(x) - 48cosh(x) + 32cosh(x) - 8cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 3 +--R 4cosh(x) - 16cosh(x) + 24cosh(x) - 16cosh(x) + 4cosh(x) +--R * +--R csch(x) +--R + +--R 9 7 5 3 +--R 8%i cosh(x) - 32%i cosh(x) + 48%i cosh(x) - 32%i cosh(x) +--R + +--R 8%i cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 9 7 5 3 +--R - 8%i cosh(x) + 32%i cosh(x) - 48%i cosh(x) + 32%i cosh(x) +--R + +--R - 8%i cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 27 8 7 6 5 4 +--R -- cosh(x) - 24%i cosh(x) - 2cosh(x) - 8%i cosh(x) - 19cosh(x) +--R 2 +--R + +--R 3 2 3 +--R 24%i cosh(x) + 6cosh(x) + 8%i cosh(x) + - +--R 2 +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R (- cosh(x) + 5cosh(x) - 10cosh(x) + 10cosh(x) - 5cosh(x) + 1) +--R * +--R 2 +--R coth(x) +--R + +--R 1 10 5 8 6 4 5 2 1 +--R - cosh(x) - - cosh(x) + 5cosh(x) - 5cosh(x) + - cosh(x) - - +--R 2 2 2 2 +--R * +--R csch(x) +--R + +--R 10 8 6 4 +--R %i cosh(x) - 5%i cosh(x) + 10%i cosh(x) - 10%i cosh(x) +--R + +--R 2 +--R 5%i cosh(x) - %i +--R * +--R 4 +--R coth(x) +--R + +--R 10 8 6 4 +--R - %i cosh(x) + 5%i cosh(x) - 10%i cosh(x) + 10%i cosh(x) +--R + +--R 2 +--R - 5%i cosh(x) + %i +--R * +--R 2 +--R coth(x) +--R + +--R 9 8 6 5 4 +--R 2cosh(x) - 4%i cosh(x) - 4%i cosh(x) - 4cosh(x) + 4%i cosh(x) +--R + +--R 2 +--R 4%i cosh(x) + 2cosh(x) +--R / +--R 2 8 3 7 +--R (cosh(x) - 1)sinh(x) + (8cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (28cosh(x) - 32cosh(x) + 4)sinh(x) +--R + +--R 5 3 5 +--R (56cosh(x) - 80cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (70cosh(x) - 130cosh(x) + 66cosh(x) - 6)sinh(x) +--R + +--R 7 5 3 3 +--R (56cosh(x) - 136cosh(x) + 104cosh(x) - 24cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (28cosh(x) - 88cosh(x) + 96cosh(x) - 40cosh(x) + 4)sinh(x) +--R + +--R 9 7 5 3 +--R (8cosh(x) - 32cosh(x) + 48cosh(x) - 32cosh(x) + 8cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) - 5cosh(x) + 10cosh(x) - 10cosh(x) + 5cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 75 + +--S 76 of 530 +t0515:= sech(x)/(a+b*sinh(x)) +--R +--R +--R sech(x) +--R (75) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 530 +r0515:= 1/2*(2*a*atan(sinh(x))-b*log(cosh(x)^2)+2*b*log(a+b*sinh(x)))/(a^2+b^2) +--R +--R +--R 2 +--R 2b log(b sinh(x) + a) - b log(cosh(x) ) + 2a atan(sinh(x)) +--R (76) ---------------------------------------------------------- +--R 2 2 +--R 2b + 2a +--R Type: Expression(Integer) +--E 77 + +--S 78 of 530 +a0515:= integrate(t0515,x) +--R +--R +--R (77) +--R 2cosh(x) - 2b sinh(x) - 2a +--R - b log(- -----------------) + b log(-----------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R + +--R 2a atan(sinh(x) + cosh(x)) +--R / +--R 2 2 +--R b + a +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 530 +m0515:= a0515-r0515 +--R +--R +--R (78) +--R 2 2cosh(x) +--R - 2b log(b sinh(x) + a) + b log(cosh(x) ) - 2b log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2b sinh(x) - 2a +--R 2b log(-----------------) + 4a atan(sinh(x) + cosh(x)) - 2a atan(sinh(x)) +--R sinh(x) - cosh(x) +--R / +--R 2 2 +--R 2b + 2a +--R Type: Expression(Integer) +--E 79 + +--S 80 of 530 +d0515:= D(m0515,x) +--R +--R +--R (79) +--R 3 2 2 +--R 2a sinh(x) + a cosh(x)sinh(x) + (- 2a cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R - a cosh(x) + a cosh(x) +--R / +--R 2 2 4 2 2 3 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((b + a )cosh(x) + 2b + 2a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b + a )cosh(x) + b + a +--R Type: Expression(Integer) +--E 80 + +--S 81 of 530 +t0516:= sech(x)^2/(a+b*sinh(x)) +--R +--R +--R 2 +--R sech(x) +--R (80) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 530 +r0516:= -2*b^2*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+_ + b*sech(x)/(a^2+b^2)+a*tanh(x)/(a^2+b^2) +--R +--R +--R x +--R a tanh(-) - b +-------+ +--R 2 2 | 2 2 +--R 2b atanh(-------------) + (a tanh(x) + b sech(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (81) ----------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 82 + +--S 83 of 530 +a0516:= integrate(t0516,x) +--R +--R +--R (82) +--R 2 2 2 2 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R +-------+ +--R | 2 2 +--R (2b sinh(x) + 2b cosh(x) - 2a)\|b + a +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) + b +--R + +--R 2 +--R a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 530 +m0516:= a0516-r0516 +--R +--R +--R (83) +--R 2 2 2 2 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 2 2 2 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2b ) +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a)tanh(x) +--R + +--R 2 +--R - b sech(x)sinh(x) + (- 2b cosh(x)sech(x) + 2b)sinh(x) +--R + +--R 2 +--R (- b cosh(x) - b)sech(x) + 2b cosh(x) - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) + b +--R + +--R 2 +--R a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 84 + +--S 85 of 530 +d0516:= D(m0516,x) +--R +--R +--R (84) +--R 2 6 2 3 5 +--R a b sinh(x) + (6a b cosh(x) + 2a )sinh(x) +--R + +--R 2 2 3 2 4 +--R (15a b cosh(x) + 10a cosh(x) + a b)sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (20a b cosh(x) + 20a cosh(x) + 4a b cosh(x) + 4a )sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R 15a b cosh(x) + 20a cosh(x) + 6a b cosh(x) + 12a cosh(x) +--R + +--R 2 +--R - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 6a b cosh(x) + 10a cosh(x) + 4a b cosh(x) + 12a cosh(x) +--R + +--R 2 3 +--R - 2a b cosh(x) + 2a +--R * +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R a b cosh(x) + 2a cosh(x) + a b cosh(x) + 4a cosh(x) +--R + +--R 2 2 3 2 +--R - a b cosh(x) + 2a cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R - 2a b sinh(x) + (- 12a b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 30a b cosh(x) - 20a b cosh(x) - 2a b )sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (- 40a b cosh(x) - 40a b cosh(x) - 8a b cosh(x) - 8a b)sinh(x) +--R + +--R 2 4 2 3 2 2 +--R - 30a b cosh(x) - 40a b cosh(x) - 12a b cosh(x) +--R + +--R 2 2 +--R - 24a b cosh(x) + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R - 12a b cosh(x) - 20a b cosh(x) - 8a b cosh(x) +--R + +--R 2 2 2 2 +--R - 24a b cosh(x) + 4a b cosh(x) - 4a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 2a b cosh(x) - 4a b cosh(x) - 2a b cosh(x) - 8a b cosh(x) +--R + +--R 2 2 2 2 +--R 2a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 3 5 +--R - a b sinh(x) + (- 6a b cosh(x) - 2a )sinh(x) +--R + +--R 2 2 3 2 4 +--R (- 15a b cosh(x) - 10a cosh(x) - a b)sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (- 20a b cosh(x) - 20a cosh(x) - 4a b cosh(x) - 4a )sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R - 15a b cosh(x) - 20a cosh(x) - 6a b cosh(x) - 12a cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R - 6a b cosh(x) - 10a cosh(x) - 4a b cosh(x) - 12a cosh(x) +--R + +--R 2 3 +--R 2a b cosh(x) - 2a +--R * +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R - a b cosh(x) - 2a cosh(x) - a b cosh(x) - 4a cosh(x) +--R + +--R 2 2 3 2 +--R a b cosh(x) - 2a cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 2 5 +--R a b sech(x)sinh(x) + (6a b cosh(x) + 2a b)sech(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (15a b cosh(x) + 10a b cosh(x) + a b )sech(x)sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (20a b cosh(x) + 20a b cosh(x) + 4a b cosh(x) + 4a b)sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 15a b cosh(x) + 20a b cosh(x) + 6a b cosh(x) +--R + +--R 2 2 +--R 12a b cosh(x) - a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 6a b cosh(x) + 10a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 2 +--R 12a b cosh(x) - 2a b cosh(x) + 2a b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 2 +--R - a b cosh(x) + 2a b cosh(x) - a b +--R * +--R sech(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 2 5 +--R - 2b sech(x)sinh(x) + (- 12b cosh(x) - 4a b )sech(x)sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 30b cosh(x) - 20a b cosh(x) - 2b )sech(x)sinh(x) +--R + +--R 3 3 2 2 3 2 +--R (- 40b cosh(x) - 40a b cosh(x) - 8b cosh(x) - 8a b )sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 +--R - 30b cosh(x) - 40a b cosh(x) - 12b cosh(x) +--R + +--R 2 3 +--R - 24a b cosh(x) + 2b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 3 5 2 4 3 3 +--R - 12b cosh(x) - 20a b cosh(x) - 8b cosh(x) +--R + +--R 2 2 3 2 +--R - 24a b cosh(x) + 4b cosh(x) - 4a b +--R * +--R sech(x)sinh(x) +--R + +--R 3 6 2 5 3 4 2 3 +--R - 2b cosh(x) - 4a b cosh(x) - 2b cosh(x) - 8a b cosh(x) +--R + +--R 3 2 2 3 +--R 2b cosh(x) - 4a b cosh(x) + 2b +--R * +--R sech(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R - a b sech(x)sinh(x) + (- 6a b cosh(x) - 2a b)sech(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 15a b cosh(x) - 10a b cosh(x) - a b )sech(x)sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (- 20a b cosh(x) - 20a b cosh(x) - 4a b cosh(x) - 4a b)sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 2 +--R - 15a b cosh(x) - 20a b cosh(x) - 6a b cosh(x) - 12a b cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 6a b cosh(x) - 10a b cosh(x) - 4a b cosh(x) - 12a b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - 2a b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - a b cosh(x) - 2a b cosh(x) - a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 2 +--R a b cosh(x) - 2a b cosh(x) + a b +--R * +--R sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 6 3 2 2 3 5 +--R (- b - a b)sinh(x) + ((- 6b - 6a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R ((- 15b - 15a b)cosh(x) + (- 10a b - 10a )cosh(x) - b - a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 20b - 20a b)cosh(x) + (- 20a b - 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b - 4a b)cosh(x) + 4a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 15b - 15a b)cosh(x) + (- 20a b - 20a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 6b - 6a b)cosh(x) + (12a b + 12a )cosh(x) + b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 6b - 6a b)cosh(x) + (- 10a b - 10a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 4b - 4a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (2b + 2a b)cosh(x) - 2a b - 2a +--R * +--R sinh(x) +--R + +--R 3 2 6 2 3 5 3 2 4 +--R (- b - a b)cosh(x) + (- 2a b - 2a )cosh(x) + (- b - a b)cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (4a b + 4a )cosh(x) + (b + a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 3 2 +--R b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R 2a b sinh(x) + (12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 4 +--R (30a b cosh(x) + 20a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R (40a b cosh(x) + 40a b cosh(x) + 8a b cosh(x) - 16b - 8a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 30a b cosh(x) + 40a b cosh(x) + 12a b cosh(x) +--R + +--R 3 2 2 +--R (- 48b - 24a b)cosh(x) - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 12a b cosh(x) + 20a b cosh(x) + 8a b cosh(x) +--R + +--R 3 2 2 2 2 +--R (- 48b - 24a b)cosh(x) - 4a b cosh(x) + 4a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 +--R 2a b cosh(x) + 4a b cosh(x) + 2a b cosh(x) +--R + +--R 3 2 3 2 2 2 2 +--R (- 16b - 8a b)cosh(x) - 2a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 6 3 2 2 3 5 +--R (b + a b)sinh(x) + ((6b + 6a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 4 +--R ((15b + 15a b)cosh(x) + (10a b + 10a )cosh(x) + b + a b)sinh(x) +--R + +--R 3 2 3 2 3 2 +--R (20b + 20a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (4b + 4a b)cosh(x) - 4a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 2 3 3 +--R (15b + 15a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (6b + 6a b)cosh(x) + (- 12a b - 12a )cosh(x) - b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 2 3 4 3 2 3 +--R (6b + 6a b)cosh(x) + (10a b + 10a )cosh(x) + (4b + 4a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 12a b - 12a )cosh(x) + (- 2b - 2a b)cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 6 2 3 5 3 2 4 +--R (b + a b)cosh(x) + (2a b + 2a )cosh(x) + (b + a b)cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (- 4a b - 4a )cosh(x) + (- b - a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 3 2 +--R - b - a b +--R / +--R 3 3 6 3 3 2 2 4 5 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R ((15a b + 15a b)cosh(x) + (10a b + 10a )cosh(x) + a b + a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (20a b + 20a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (4a b + 4a b)cosh(x) + 4a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (15a b + 15a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (6a b + 6a b)cosh(x) + (12a b + 12a )cosh(x) - a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 2 4 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (4a b + 4a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (- 2a b - 2a b)cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 3 6 2 2 4 5 3 3 4 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) + (a b + a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 2 2 4 +--R (4a b + 4a )cosh(x) + (- a b - a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 3 3 +--R - a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 2 6 +--R (- 2b - 2a b )sinh(x) +--R + +--R 4 2 2 3 3 5 +--R ((- 12b - 12a b )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 +--R (- 30b - 30a b )cosh(x) + (- 20a b - 20a b)cosh(x) - 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 40b - 40a b )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 4 2 2 3 3 +--R (- 8b - 8a b )cosh(x) - 8a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 30b - 30a b )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (- 12b - 12a b )cosh(x) + (- 24a b - 24a b)cosh(x) + 2b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 5 3 3 4 +--R (- 12b - 12a b )cosh(x) + (- 20a b - 20a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 8b - 8a b )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 4 2 2 3 3 +--R (4b + 4a b )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 4 2 2 6 3 3 5 +--R (- 2b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 2b - 2a b )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (2b + 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) + 2b + 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 6 3 3 2 2 4 5 +--R (- a b - a b)sinh(x) + ((- 6a b - 6a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R ((- 15a b - 15a b)cosh(x) + (- 10a b - 10a )cosh(x) - a b - a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (- 20a b - 20a b)cosh(x) + (- 20a b - 20a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (- 4a b - 4a b)cosh(x) - 4a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (- 15a b - 15a b)cosh(x) + (- 20a b - 20a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 6a b - 6a b)cosh(x) + (- 12a b - 12a )cosh(x) + a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 2 4 4 +--R (- 6a b - 6a b)cosh(x) + (- 10a b - 10a )cosh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (- 4a b - 4a b)cosh(x) + (- 12a b - 12a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (2a b + 2a b)cosh(x) - 2a b - 2a +--R * +--R sinh(x) +--R + +--R 3 3 6 2 2 4 5 3 3 4 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) + (- a b - a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 2 2 4 +--R (- 4a b - 4a )cosh(x) + (a b + a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 3 3 +--R a b + a b +--R Type: Expression(Integer) +--E 85 + +--S 86 of 530 +t0517:= sech(x)^3/(a+b*sinh(x)) +--R +--R +--R 3 +--R sech(x) +--R (85) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 530 +r0517:= 1/2*(3*a*b^2*atan(sinh(x))*cosh(x)^2+a^3*atan(sinh(x))*cosh(x)^2-_ + b^3*log(cosh(x)^2)*cosh(x)^2+2*b^3*log(a+b*sinh(x))*cosh(x)^2+_ + a^2*b+b^3+sinh(x)*a^3+sinh(x)*b^2*a)/cosh(x)^2/(a^2+b^2)^2 +--R +--R +--R (86) +--R 3 2 3 2 2 +--R 2b cosh(x) log(b sinh(x) + a) - b cosh(x) log(cosh(x) ) +--R + +--R 2 3 2 2 3 3 2 +--R (3a b + a )cosh(x) atan(sinh(x)) + (a b + a )sinh(x) + b + a b +--R / +--R 4 2 2 4 2 +--R (2b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 87 + +--S 88 of 530 +a0517:= integrate(t0517,x) +--R +--R +--R (87) +--R 3 4 3 3 3 2 3 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) - 2b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (- 4b cosh(x) - 4b cosh(x))sinh(x) - b cosh(x) - 2b cosh(x) - b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 4 3 3 3 2 3 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 4 2 3 3 +--R (3a b + a )sinh(x) + (12a b + 4a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b + 6a )cosh(x) + 6a b + 2a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b + 4a )cosh(x) + (12a b + 4a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b + a )cosh(x) + (6a b + 2a )cosh(x) + 3a b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 3 2 3 3 2 2 +--R (a b + a )sinh(x) + ((3a b + 3a )cosh(x) + 2b + 2a b)sinh(x) +--R + +--R 2 3 2 3 2 2 3 +--R ((3a b + 3a )cosh(x) + (4b + 4a b)cosh(x) - a b - a )sinh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (a b + a )cosh(x) + (2b + 2a b)cosh(x) + (- a b - a )cosh(x) +--R / +--R 4 2 2 4 4 4 2 2 4 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 2 +--R ((6b + 12a b + 6a )cosh(x) + 2b + 4a b + 2a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((4b + 8a b + 4a )cosh(x) + (4b + 8a b + 4a )cosh(x))sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 4 2 2 4 +--R (b + 2a b + a )cosh(x) + (2b + 4a b + 2a )cosh(x) + b + 2a b + a +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 530 +m0517:= a0517-r0517 +--R +--R +--R (88) +--R 3 2 4 3 3 3 +--R - 2b cosh(x) sinh(x) - 8b cosh(x) sinh(x) +--R + +--R 3 4 3 2 2 +--R (- 12b cosh(x) - 4b cosh(x) )sinh(x) +--R + +--R 3 5 3 3 3 6 3 4 +--R (- 8b cosh(x) - 8b cosh(x) )sinh(x) - 2b cosh(x) - 4b cosh(x) +--R + +--R 3 2 +--R - 2b cosh(x) +--R * +--R log(b sinh(x) + a) +--R + +--R 3 2 4 3 3 3 +--R b cosh(x) sinh(x) + 4b cosh(x) sinh(x) +--R + +--R 3 4 3 2 2 +--R (6b cosh(x) + 2b cosh(x) )sinh(x) +--R + +--R 3 5 3 3 3 6 3 4 +--R (4b cosh(x) + 4b cosh(x) )sinh(x) + b cosh(x) + 2b cosh(x) +--R + +--R 3 2 +--R b cosh(x) +--R * +--R 2 +--R log(cosh(x) ) +--R + +--R 3 2 4 3 3 3 +--R - 2b cosh(x) sinh(x) - 8b cosh(x) sinh(x) +--R + +--R 3 4 3 2 2 +--R (- 12b cosh(x) - 4b cosh(x) )sinh(x) +--R + +--R 3 5 3 3 3 6 3 4 +--R (- 8b cosh(x) - 8b cosh(x) )sinh(x) - 2b cosh(x) - 4b cosh(x) +--R + +--R 3 2 +--R - 2b cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 4 3 3 3 +--R 2b cosh(x) sinh(x) + 8b cosh(x) sinh(x) +--R + +--R 3 4 3 2 2 +--R (12b cosh(x) + 4b cosh(x) )sinh(x) +--R + +--R 3 5 3 3 3 6 3 4 +--R (8b cosh(x) + 8b cosh(x) )sinh(x) + 2b cosh(x) + 4b cosh(x) +--R + +--R 3 2 +--R 2b cosh(x) +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 4 2 3 3 3 +--R (6a b + 2a )cosh(x) sinh(x) + (24a b + 8a )cosh(x) sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R ((36a b + 12a )cosh(x) + (12a b + 4a )cosh(x) )sinh(x) +--R + +--R 2 3 5 2 3 3 +--R ((24a b + 8a )cosh(x) + (24a b + 8a )cosh(x) )sinh(x) +--R + +--R 2 3 6 2 3 4 2 3 2 +--R (6a b + 2a )cosh(x) + (12a b + 4a )cosh(x) + (6a b + 2a )cosh(x) +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 4 2 3 3 3 +--R (- 3a b - a )cosh(x) sinh(x) + (- 12a b - 4a )cosh(x) sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R ((- 18a b - 6a )cosh(x) + (- 6a b - 2a )cosh(x) )sinh(x) +--R + +--R 2 3 5 2 3 3 +--R ((- 12a b - 4a )cosh(x) + (- 12a b - 4a )cosh(x) )sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 3a b - a )cosh(x) + (- 6a b - 2a )cosh(x) +--R + +--R 2 3 2 +--R (- 3a b - a )cosh(x) +--R * +--R atan(sinh(x)) +--R + +--R 2 3 5 2 3 3 2 4 +--R (- a b - a )sinh(x) + ((- 4a b - 4a )cosh(x) - b - a b)sinh(x) +--R + +--R 2 3 2 3 2 2 3 3 +--R ((- 4a b - 4a )cosh(x) + (- 4b - 4a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 3 3 3 2 2 +--R (2a b + 2a )cosh(x) + (- 2b - 2a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 4a b - 4a )cosh(x) - 2b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 +--R (5a b + 5a )cosh(x) + (4b + 4a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 4a b - 4a )cosh(x) + (- 4b - 4a b)cosh(x) - a b - a +--R * +--R sinh(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R (2a b + 2a )cosh(x) + (3b + 3a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 2b - 2a b)cosh(x) - b - a b +--R / +--R 4 2 2 4 2 4 +--R (2b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 3 3 +--R (8b + 16a b + 8a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 2 +--R ((12b + 24a b + 12a )cosh(x) + (4b + 8a b + 4a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R ((8b + 16a b + 8a )cosh(x) + (8b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (2b + 4a b + 2a )cosh(x) + (4b + 8a b + 4a )cosh(x) +--R + +--R 4 2 2 4 2 +--R (2b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 89 + +--S 90 of 530 +d0517:= D(m0517,x) +--R +--R +--R (89) +--R 2 3 10 2 3 3 2 9 +--R (2a b + 2a )sinh(x) + ((12a b + 12a )cosh(x) + 2b + 2a b)sinh(x) +--R + +--R 2 3 2 3 2 2 3 8 +--R ((29a b + 29a )cosh(x) + (12b + 12a b)cosh(x) + 8a b + 8a )sinh(x) +--R + +--R 2 3 3 3 2 2 +--R (38a b + 34a )cosh(x) + (30b + 30a b)cosh(x) +--R + +--R 2 3 3 2 +--R (36a b + 36a )cosh(x) + 8b + 8a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 +--R (32a b + 14a )cosh(x) + (32b + 32a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (62a b + 62a )cosh(x) + (36b + 36a b)cosh(x) + 12a b + 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 5 3 2 4 +--R (14a b - 14a )cosh(x) + (- 2b - 2a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (74a b + 62a )cosh(x) + (66b + 66a b)cosh(x) +--R + +--R 2 3 3 2 +--R (36a b + 36a )cosh(x) + 12b + 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 6 3 2 5 +--R (- 18a b - 28a )cosh(x) + (- 36b - 36a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (86a b + 48a )cosh(x) + (64b + 64a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (36a b + 36a )cosh(x) + (36b + 36a b)cosh(x) + 8a b + 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 7 3 2 6 +--R (- 46a b - 26a )cosh(x) + (- 30b - 30a b)cosh(x) +--R + +--R 2 3 5 3 2 4 +--R (56a b + 16a )cosh(x) + (20b + 20a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (34a b + 22a )cosh(x) + (42b + 42a b)cosh(x) +--R + +--R 2 3 3 2 +--R (12a b + 12a )cosh(x) + 8b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 8 3 2 7 +--R (- 42a b - 16a )cosh(x) + (- 8b - 8a b)cosh(x) +--R + +--R 2 3 6 3 2 5 +--R (- 6a b - 18a )cosh(x) + (- 28b - 28a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (52a b + 30a )cosh(x) + (32b + 32a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (2a b + 2a )cosh(x) + (12b + 12a b)cosh(x) + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 9 2 3 7 +--R (- 18a b - 6a )cosh(x) + (- 22a b - 18a )cosh(x) +--R + +--R 3 2 6 2 3 5 +--R (- 30b - 30a b)cosh(x) + (42a b + 30a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (22b + 22a b)cosh(x) + (- 2a b - 6a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b + 6a b)cosh(x) + 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 3 10 2 3 8 +--R (- 3a b - a )cosh(x) + (- 6a b - 4a )cosh(x) +--R + +--R 3 2 7 2 3 6 3 2 5 +--R (- 8b - 8a b)cosh(x) + (12a b + 10a )cosh(x) + (8b + 8a b)cosh(x) +--R + +--R 2 3 4 2 3 2 +--R (- 2a b - 4a )cosh(x) + (- a b - a )cosh(x) +--R / +--R 4 2 2 4 3 8 +--R (2b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 4 7 +--R (12b + 24a b + 12a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 6 +--R ((30b + 60a b + 30a )cosh(x) + (8b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 5 +--R ((40b + 80a b + 40a )cosh(x) + (36b + 72a b + 36a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 7 4 2 2 4 5 +--R (30b + 60a b + 30a )cosh(x) + (66b + 132a b + 66a )cosh(x) +--R + +--R 4 2 2 4 3 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (64b + 128a b + 64a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (36b + 72a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (42b + 84a b + 42a )cosh(x) + (8b + 16a b + 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (24b + 48a b + 24a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (6b + 12a b + 6a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (6b + 12a b + 6a )cosh(x) + (2b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 90 + +--S 91 of 530 +t0518:= sech(x)^4/(a+b*sinh(x)) +--R +--R +--R 4 +--R sech(x) +--R (90) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 91 + +--S 92 of 530 +r0518:= -2*b^4*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)+_ + b^3*sech(x)/(a^2+b^2)^2+b*sech(x)^3/(3*a^2+3*b^2)+_ + a*b^2*tanh(x)/(a^2+b^2)^2+a*tanh(x)/(a^2+b^2)-a*tanh(x)^3/(3*a^2+3*b^2) +--R +--R +--R (91) +--R x +--R a tanh(-) - b +--R 4 2 +--R 6b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 3 2 3 3 2 3 +--R (- a b - a )tanh(x) + (6a b + 3a )tanh(x) + (b + a b)sech(x) +--R + +--R 3 +--R 3b sech(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 92 + +--S 93 of 530 +a0518:= integrate(t0518,x) +--R +--R +--R (92) +--R 4 6 4 5 4 2 4 4 +--R 3b sinh(x) + 18b cosh(x)sinh(x) + (45b cosh(x) + 9b )sinh(x) +--R + +--R 4 3 4 3 +--R (60b cosh(x) + 36b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45b cosh(x) + 54b cosh(x) + 9b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18b cosh(x) + 36b cosh(x) + 18b cosh(x))sinh(x) + 3b cosh(x) +--R + +--R 4 4 4 2 4 +--R 9b cosh(x) + 9b cosh(x) + 3b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 5 3 2 4 +--R 6b sinh(x) + (30b cosh(x) - 6a b )sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (60b cosh(x) - 24a b cosh(x) + 20b + 8a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R 60b cosh(x) - 36a b cosh(x) + (60b + 24a b)cosh(x) - 24a b +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 30b cosh(x) - 24a b cosh(x) + (60b + 24a b)cosh(x) +--R + +--R 2 3 3 +--R (- 48a b - 24a )cosh(x) + 6b +--R * +--R sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 6a b cosh(x) + (20b + 8a b)cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 24a b - 12a )cosh(x) + 6b cosh(x) - 10a b - 4a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 2 4 6 4 2 2 4 5 +--R (3b + 6a b + 3a )sinh(x) + (18b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 4 +--R ((45b + 90a b + 45a )cosh(x) + 9b + 18a b + 9a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((60b + 120a b + 60a )cosh(x) + (36b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (45b + 90a b + 45a )cosh(x) + (54b + 108a b + 54a )cosh(x) +--R + +--R 4 2 2 4 +--R 9b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (18b + 36a b + 18a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 +--R (18b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (3b + 6a b + 3a )cosh(x) + (9b + 18a b + 9a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (9b + 18a b + 9a )cosh(x) + 3b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 530 +m0518:= a0518-r0518 +--R +--R +--R (93) +--R 4 6 4 5 4 2 4 4 +--R 3b sinh(x) + 18b cosh(x)sinh(x) + (45b cosh(x) + 9b )sinh(x) +--R + +--R 4 3 4 3 +--R (60b cosh(x) + 36b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45b cosh(x) + 54b cosh(x) + 9b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18b cosh(x) + 36b cosh(x) + 18b cosh(x))sinh(x) + 3b cosh(x) +--R + +--R 4 4 4 2 4 +--R 9b cosh(x) + 9b cosh(x) + 3b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 6 4 5 4 2 4 4 +--R - 6b sinh(x) - 36b cosh(x)sinh(x) + (- 90b cosh(x) - 18b )sinh(x) +--R + +--R 4 3 4 3 +--R (- 120b cosh(x) - 72b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (- 90b cosh(x) - 108b cosh(x) - 18b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (- 36b cosh(x) - 72b cosh(x) - 36b cosh(x))sinh(x) - 6b cosh(x) +--R + +--R 4 4 4 2 4 +--R - 18b cosh(x) - 18b cosh(x) - 6b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 6 2 3 5 +--R (a b + a )sinh(x) + (6a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((15a b + 15a )cosh(x) + 3a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((20a b + 20a )cosh(x) + (12a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (15a b + 15a )cosh(x) + (18a b + 18a )cosh(x) + 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (6a b + 6a )cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 3 +--R (6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (a b + a )cosh(x) + (3a b + 3a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (3a b + 3a )cosh(x) + a b + a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 3 6 2 3 5 +--R (- 6a b - 3a )sinh(x) + (- 36a b - 18a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((- 90a b - 45a )cosh(x) - 18a b - 9a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((- 120a b - 60a )cosh(x) + (- 72a b - 36a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 +--R (- 90a b - 45a )cosh(x) + (- 108a b - 54a )cosh(x) +--R + +--R 2 3 +--R - 18a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (- 36a b - 18a )cosh(x) + (- 72a b - 36a )cosh(x) +--R + +--R 2 3 +--R (- 36a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 6a b - 3a )cosh(x) + (- 18a b - 9a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (- 18a b - 9a )cosh(x) - 6a b - 3a +--R * +--R tanh(x) +--R + +--R 3 2 3 3 6 +--R ((- b - a b)sech(x) - 3b sech(x))sinh(x) +--R + +--R 3 2 3 3 3 5 +--R ((- 6b - 6a b)cosh(x)sech(x) - 18b cosh(x)sech(x) + 6b )sinh(x) +--R + +--R 3 2 2 3 2 3 +--R ((- 15b - 15a b)cosh(x) - 3b - 3a b)sech(x) +--R + +--R 3 2 3 3 2 +--R (- 45b cosh(x) - 9b )sech(x) + 30b cosh(x) - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 20b - 20a b)cosh(x) + (- 12b - 12a b)cosh(x))sech(x) +--R + +--R 3 3 3 3 2 +--R (- 60b cosh(x) - 36b cosh(x))sech(x) + 60b cosh(x) +--R + +--R 2 3 2 +--R - 24a b cosh(x) + 20b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 15b - 15a b)cosh(x) + (- 18b - 18a b)cosh(x) - 3b +--R + +--R 2 +--R - 3a b +--R * +--R 3 +--R sech(x) +--R + +--R 3 4 3 2 3 3 3 +--R (- 45b cosh(x) - 54b cosh(x) - 9b )sech(x) + 60b cosh(x) +--R + +--R 2 2 3 2 2 3 +--R - 36a b cosh(x) + (60b + 24a b)cosh(x) - 24a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 6b - 6a b)cosh(x) + (- 12b - 12a b)cosh(x) +--R + +--R 3 2 +--R (- 6b - 6a b)cosh(x) +--R * +--R 3 +--R sech(x) +--R + +--R 3 5 3 3 3 +--R (- 18b cosh(x) - 36b cosh(x) - 18b cosh(x))sech(x) +--R + +--R 3 4 2 3 3 2 2 +--R 30b cosh(x) - 24a b cosh(x) + (60b + 24a b)cosh(x) +--R + +--R 2 3 3 +--R (- 48a b - 24a )cosh(x) + 6b +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- b - a b)cosh(x) + (- 3b - 3a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 3b - 3a b)cosh(x) - b - a b +--R * +--R 3 +--R sech(x) +--R + +--R 3 6 3 4 3 2 3 +--R (- 3b cosh(x) - 9b cosh(x) - 9b cosh(x) - 3b )sech(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 6a b cosh(x) + (20b + 8a b)cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 24a b - 12a )cosh(x) + 6b cosh(x) - 10a b - 4a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 2 4 6 4 2 2 4 5 +--R (3b + 6a b + 3a )sinh(x) + (18b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 4 +--R ((45b + 90a b + 45a )cosh(x) + 9b + 18a b + 9a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((60b + 120a b + 60a )cosh(x) + (36b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (45b + 90a b + 45a )cosh(x) + (54b + 108a b + 54a )cosh(x) +--R + +--R 4 2 2 4 +--R 9b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (18b + 36a b + 18a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 +--R (18b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (3b + 6a b + 3a )cosh(x) + (9b + 18a b + 9a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (9b + 18a b + 9a )cosh(x) + 3b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 530 +d0518:= D(m0518,x) +--R +--R +--R (94) +--R 2 3 4 10 +--R (- a b - a b)sinh(x) +--R + +--R 2 3 4 3 2 5 9 +--R ((- 10a b - 10a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (- 45a b - 45a b)cosh(x) + (- 18a b - 18a )cosh(x) - 3a b +--R + +--R 4 +--R - 3a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (- 120a b - 120a b)cosh(x) + (- 72a b - 72a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 24a b - 24a b)cosh(x) - 8a b - 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (- 210a b - 210a b)cosh(x) + (- 168a b - 168a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (- 84a b - 84a b)cosh(x) + (- 56a b - 56a )cosh(x) - 2a b +--R + +--R 4 +--R - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (- 252a b - 252a b)cosh(x) + (- 252a b - 252a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (- 168a b - 168a b)cosh(x) + (- 168a b - 168a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 12a b - 12a b)cosh(x) - 12a b - 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (- 210a b - 210a b)cosh(x) + (- 252a b - 252a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (- 210a b - 210a b)cosh(x) + (- 280a b - 280a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (- 30a b - 30a b)cosh(x) + (- 60a b - 60a )cosh(x) + 2a b +--R + +--R 4 +--R 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 7 3 2 5 6 +--R (- 120a b - 120a b)cosh(x) + (- 168a b - 168a )cosh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (- 168a b - 168a b)cosh(x) + (- 280a b - 280a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (- 40a b - 40a b)cosh(x) + (- 120a b - 120a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (8a b + 8a b)cosh(x) - 8a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 8 3 2 5 7 +--R (- 45a b - 45a b)cosh(x) + (- 72a b - 72a )cosh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (- 84a b - 84a b)cosh(x) + (- 168a b - 168a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (- 30a b - 30a b)cosh(x) + (- 120a b - 120a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (12a b + 12a b)cosh(x) + (- 24a b - 24a )cosh(x) + 3a b +--R + +--R 4 +--R 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 9 3 2 5 8 +--R (- 10a b - 10a b)cosh(x) + (- 18a b - 18a )cosh(x) +--R + +--R 2 3 4 7 3 2 5 6 +--R (- 24a b - 24a b)cosh(x) + (- 56a b - 56a )cosh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (- 12a b - 12a b)cosh(x) + (- 60a b - 60a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (8a b + 8a b)cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (6a b + 6a b)cosh(x) - 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 3 4 10 3 2 5 9 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 2 3 4 8 3 2 5 7 +--R (- 3a b - 3a b)cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (- 2a b - 2a b)cosh(x) + (- 12a b - 12a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (2a b + 2a b)cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (3a b + 3a b)cosh(x) + (- 2a b - 2a )cosh(x) + a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 10 +--R (2a b + 2a b )sinh(x) +--R + +--R 4 3 2 2 3 4 9 +--R ((20a b + 20a b )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (90a b + 90a b )cosh(x) + (36a b + 36a b)cosh(x) + 6a b +--R + +--R 3 2 +--R 6a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (240a b + 240a b )cosh(x) + (144a b + 144a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (48a b + 48a b )cosh(x) + 16a b + 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (420a b + 420a b )cosh(x) + (336a b + 336a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (168a b + 168a b )cosh(x) + (112a b + 112a b)cosh(x) +--R + +--R 4 3 2 +--R 4a b + 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (504a b + 504a b )cosh(x) + (504a b + 504a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (336a b + 336a b )cosh(x) + (336a b + 336a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (24a b + 24a b )cosh(x) + 24a b + 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (420a b + 420a b )cosh(x) + (504a b + 504a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (420a b + 420a b )cosh(x) + (560a b + 560a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (60a b + 60a b )cosh(x) + (120a b + 120a b)cosh(x) - 4a b +--R + +--R 3 2 +--R - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (240a b + 240a b )cosh(x) + (336a b + 336a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (336a b + 336a b )cosh(x) + (560a b + 560a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (80a b + 80a b )cosh(x) + (240a b + 240a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 16a b - 16a b )cosh(x) + 16a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (90a b + 90a b )cosh(x) + (144a b + 144a b)cosh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (168a b + 168a b )cosh(x) + (336a b + 336a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (60a b + 60a b )cosh(x) + (240a b + 240a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (- 24a b - 24a b )cosh(x) + (48a b + 48a b)cosh(x) - 6a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 9 2 3 4 8 +--R (20a b + 20a b )cosh(x) + (36a b + 36a b)cosh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (48a b + 48a b )cosh(x) + (112a b + 112a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (24a b + 24a b )cosh(x) + (120a b + 120a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 16a b - 16a b )cosh(x) + (48a b + 48a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 12a b - 12a b )cosh(x) + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 4 3 2 10 2 3 4 9 +--R (2a b + 2a b )cosh(x) + (4a b + 4a b)cosh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (6a b + 6a b )cosh(x) + (16a b + 16a b)cosh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (4a b + 4a b )cosh(x) + (24a b + 24a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 4a b - 4a b )cosh(x) + (16a b + 16a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 6a b - 6a b )cosh(x) + (4a b + 4a b)cosh(x) - 2a b - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3 4 10 +--R (a b + a b)sinh(x) +--R + +--R 2 3 4 3 2 5 9 +--R ((10a b + 10a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R ((45a b + 45a b)cosh(x) + (18a b + 18a )cosh(x) + 3a b + 3a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (120a b + 120a b)cosh(x) + (72a b + 72a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (24a b + 24a b)cosh(x) + 8a b + 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (210a b + 210a b)cosh(x) + (168a b + 168a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (84a b + 84a b)cosh(x) + (56a b + 56a )cosh(x) + 2a b + 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (252a b + 252a b)cosh(x) + (252a b + 252a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (168a b + 168a b)cosh(x) + (168a b + 168a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (12a b + 12a b)cosh(x) + 12a b + 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (210a b + 210a b)cosh(x) + (252a b + 252a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (210a b + 210a b)cosh(x) + (280a b + 280a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (30a b + 30a b)cosh(x) + (60a b + 60a )cosh(x) - 2a b - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 7 3 2 5 6 +--R (120a b + 120a b)cosh(x) + (168a b + 168a )cosh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (168a b + 168a b)cosh(x) + (280a b + 280a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (40a b + 40a b)cosh(x) + (120a b + 120a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 8a b - 8a b)cosh(x) + 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 8 3 2 5 7 +--R (45a b + 45a b)cosh(x) + (72a b + 72a )cosh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (84a b + 84a b)cosh(x) + (168a b + 168a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (30a b + 30a b)cosh(x) + (120a b + 120a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (- 12a b - 12a b)cosh(x) + (24a b + 24a )cosh(x) - 3a b - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 9 3 2 5 8 +--R (10a b + 10a b)cosh(x) + (18a b + 18a )cosh(x) +--R + +--R 2 3 4 7 3 2 5 6 +--R (24a b + 24a b)cosh(x) + (56a b + 56a )cosh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (12a b + 12a b)cosh(x) + (60a b + 60a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (- 8a b - 8a b)cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 6a b - 6a b)cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 2 3 4 10 3 2 5 9 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 3 4 8 3 2 5 7 +--R (3a b + 3a b)cosh(x) + (8a b + 8a )cosh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (2a b + 2a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (- 2a b - 2a b)cosh(x) + (8a b + 8a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (- 3a b - 3a b)cosh(x) + (2a b + 2a )cosh(x) - a b - a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 3 4 10 +--R (3a b + 2a b)sinh(x) +--R + +--R 2 3 4 3 2 5 9 +--R ((30a b + 20a b)cosh(x) + 6a b + 4a )sinh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (135a b + 90a b)cosh(x) + (54a b + 36a )cosh(x) + 9a b +--R + +--R 4 +--R 6a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (360a b + 240a b)cosh(x) + (216a b + 144a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (72a b + 48a b)cosh(x) + 24a b + 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (630a b + 420a b)cosh(x) + (504a b + 336a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (252a b + 168a b)cosh(x) + (168a b + 112a )cosh(x) + 6a b +--R + +--R 4 +--R 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (756a b + 504a b)cosh(x) + (756a b + 504a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (504a b + 336a b)cosh(x) + (504a b + 336a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (36a b + 24a b)cosh(x) + 36a b + 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (630a b + 420a b)cosh(x) + (756a b + 504a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (630a b + 420a b)cosh(x) + (840a b + 560a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (90a b + 60a b)cosh(x) + (180a b + 120a )cosh(x) - 6a b +--R + +--R 4 +--R - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 7 3 2 5 6 +--R (360a b + 240a b)cosh(x) + (504a b + 336a )cosh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (504a b + 336a b)cosh(x) + (840a b + 560a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (120a b + 80a b)cosh(x) + (360a b + 240a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 24a b - 16a b)cosh(x) + 24a b + 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 8 3 2 5 7 +--R (135a b + 90a b)cosh(x) + (216a b + 144a )cosh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (252a b + 168a b)cosh(x) + (504a b + 336a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (90a b + 60a b)cosh(x) + (360a b + 240a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (- 36a b - 24a b)cosh(x) + (72a b + 48a )cosh(x) - 9a b +--R + +--R 4 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 9 3 2 5 8 +--R (30a b + 20a b)cosh(x) + (54a b + 36a )cosh(x) +--R + +--R 2 3 4 7 3 2 5 6 +--R (72a b + 48a b)cosh(x) + (168a b + 112a )cosh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (36a b + 24a b)cosh(x) + (180a b + 120a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (- 24a b - 16a b)cosh(x) + (72a b + 48a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 18a b - 12a b)cosh(x) + 6a b + 4a +--R * +--R sinh(x) +--R + +--R 2 3 4 10 3 2 5 9 +--R (3a b + 2a b)cosh(x) + (6a b + 4a )cosh(x) +--R + +--R 2 3 4 8 3 2 5 7 +--R (9a b + 6a b)cosh(x) + (24a b + 16a )cosh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (6a b + 4a b)cosh(x) + (36a b + 24a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (- 6a b - 4a b)cosh(x) + (24a b + 16a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (- 9a b - 6a b)cosh(x) + (6a b + 4a )cosh(x) - 3a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 10 +--R (- 6a b - 4a b )sinh(x) +--R + +--R 4 3 2 2 3 4 9 +--R ((- 60a b - 40a b )cosh(x) - 12a b - 8a b)sinh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (- 270a b - 180a b )cosh(x) + (- 108a b - 72a b)cosh(x) +--R + +--R 4 3 2 +--R - 18a b - 12a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 720a b - 480a b )cosh(x) + (- 432a b - 288a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 144a b - 96a b )cosh(x) - 48a b - 32a b +--R * +--R 7 +--R sinh(x) +--R + +--R 4 3 2 4 +--R (- 1260a b - 840a b )cosh(x) +--R + +--R 2 3 4 3 4 3 2 2 +--R (- 1008a b - 672a b)cosh(x) + (- 504a b - 336a b )cosh(x) +--R + +--R 2 3 4 4 3 2 +--R (- 336a b - 224a b)cosh(x) - 12a b - 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 5 +--R (- 1512a b - 1008a b )cosh(x) +--R + +--R 2 3 4 4 +--R (- 1512a b - 1008a b)cosh(x) +--R + +--R 4 3 2 3 +--R (- 1008a b - 672a b )cosh(x) +--R + +--R 2 3 4 2 4 3 2 +--R (- 1008a b - 672a b)cosh(x) + (- 72a b - 48a b )cosh(x) +--R + +--R 2 3 4 +--R - 72a b - 48a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 6 +--R (- 1260a b - 840a b )cosh(x) +--R + +--R 2 3 4 5 +--R (- 1512a b - 1008a b)cosh(x) +--R + +--R 4 3 2 4 +--R (- 1260a b - 840a b )cosh(x) +--R + +--R 2 3 4 3 +--R (- 1680a b - 1120a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (- 180a b - 120a b )cosh(x) + (- 360a b - 240a b)cosh(x) +--R + +--R 4 3 2 +--R 12a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (- 720a b - 480a b )cosh(x) + (- 1008a b - 672a b)cosh(x) +--R + +--R 4 3 2 5 +--R (- 1008a b - 672a b )cosh(x) +--R + +--R 2 3 4 4 +--R (- 1680a b - 1120a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 240a b - 160a b )cosh(x) + (- 720a b - 480a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (48a b + 32a b )cosh(x) - 48a b - 32a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (- 270a b - 180a b )cosh(x) + (- 432a b - 288a b)cosh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (- 504a b - 336a b )cosh(x) + (- 1008a b - 672a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 180a b - 120a b )cosh(x) + (- 720a b - 480a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (72a b + 48a b )cosh(x) + (- 144a b - 96a b)cosh(x) +--R + +--R 4 3 2 +--R 18a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 9 2 3 4 8 +--R (- 60a b - 40a b )cosh(x) + (- 108a b - 72a b)cosh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (- 144a b - 96a b )cosh(x) + (- 336a b - 224a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (- 72a b - 48a b )cosh(x) + (- 360a b - 240a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (48a b + 32a b )cosh(x) + (- 144a b - 96a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (36a b + 24a b )cosh(x) - 12a b - 8a b +--R * +--R sinh(x) +--R + +--R 4 3 2 10 2 3 4 9 +--R (- 6a b - 4a b )cosh(x) + (- 12a b - 8a b)cosh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (- 18a b - 12a b )cosh(x) + (- 48a b - 32a b)cosh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (- 12a b - 8a b )cosh(x) + (- 72a b - 48a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (12a b + 8a b )cosh(x) + (- 48a b - 32a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (18a b + 12a b )cosh(x) + (- 12a b - 8a b)cosh(x) + 6a b +--R + +--R 3 2 +--R 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3 4 10 +--R (- 3a b - 2a b)sinh(x) +--R + +--R 2 3 4 3 2 5 9 +--R ((- 30a b - 20a b)cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (- 135a b - 90a b)cosh(x) + (- 54a b - 36a )cosh(x) - 9a b +--R + +--R 4 +--R - 6a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (- 360a b - 240a b)cosh(x) + (- 216a b - 144a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 72a b - 48a b)cosh(x) - 24a b - 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (- 630a b - 420a b)cosh(x) + (- 504a b - 336a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (- 252a b - 168a b)cosh(x) + (- 168a b - 112a )cosh(x) - 6a b +--R + +--R 4 +--R - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (- 756a b - 504a b)cosh(x) + (- 756a b - 504a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (- 504a b - 336a b)cosh(x) + (- 504a b - 336a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 36a b - 24a b)cosh(x) - 36a b - 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (- 630a b - 420a b)cosh(x) + (- 756a b - 504a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (- 630a b - 420a b)cosh(x) + (- 840a b - 560a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (- 90a b - 60a b)cosh(x) + (- 180a b - 120a )cosh(x) + 6a b +--R + +--R 4 +--R 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 7 3 2 5 6 +--R (- 360a b - 240a b)cosh(x) + (- 504a b - 336a )cosh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (- 504a b - 336a b)cosh(x) + (- 840a b - 560a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (- 120a b - 80a b)cosh(x) + (- 360a b - 240a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (24a b + 16a b)cosh(x) - 24a b - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 8 3 2 5 7 +--R (- 135a b - 90a b)cosh(x) + (- 216a b - 144a )cosh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (- 252a b - 168a b)cosh(x) + (- 504a b - 336a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (- 90a b - 60a b)cosh(x) + (- 360a b - 240a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (36a b + 24a b)cosh(x) + (- 72a b - 48a )cosh(x) + 9a b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 9 3 2 5 8 +--R (- 30a b - 20a b)cosh(x) + (- 54a b - 36a )cosh(x) +--R + +--R 2 3 4 7 3 2 5 6 +--R (- 72a b - 48a b)cosh(x) + (- 168a b - 112a )cosh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (- 36a b - 24a b)cosh(x) + (- 180a b - 120a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (24a b + 16a b)cosh(x) + (- 72a b - 48a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (18a b + 12a b)cosh(x) - 6a b - 4a +--R * +--R sinh(x) +--R + +--R 2 3 4 10 3 2 5 9 +--R (- 3a b - 2a b)cosh(x) + (- 6a b - 4a )cosh(x) +--R + +--R 2 3 4 8 3 2 5 7 +--R (- 9a b - 6a b)cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (- 6a b - 4a b)cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (6a b + 4a b)cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (9a b + 6a b)cosh(x) + (- 6a b - 4a )cosh(x) + 3a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 3 4 10 +--R ((a b + a b )sech(x) + a b sech(x))sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R ((10a b + 10a b )cosh(x) + 2a b + 2a b)sech(x) +--R + +--R 4 2 3 +--R (10a b cosh(x) + 2a b )sech(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (45a b + 45a b )cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 4 3 2 +--R 3a b + 3a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 2 2 3 4 +--R (45a b cosh(x) + 18a b cosh(x) + 3a b )sech(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (120a b + 120a b )cosh(x) + (72a b + 72a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (24a b + 24a b )cosh(x) + 8a b + 8a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 3 2 3 2 4 2 3 +--R (120a b cosh(x) + 72a b cosh(x) + 24a b cosh(x) + 8a b ) +--R * +--R sech(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (210a b + 210a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (84a b + 84a b )cosh(x) + (56a b + 56a b)cosh(x) +--R + +--R 4 3 2 +--R 2a b + 2a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 4 2 3 3 4 2 +--R 210a b cosh(x) + 168a b cosh(x) + 84a b cosh(x) +--R + +--R 2 3 4 +--R 56a b cosh(x) + 2a b +--R * +--R sech(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (252a b + 252a b )cosh(x) + (252a b + 252a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (168a b + 168a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (12a b + 12a b )cosh(x) + 12a b + 12a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 5 2 3 4 4 3 +--R 252a b cosh(x) + 252a b cosh(x) + 168a b cosh(x) +--R + +--R 2 3 2 4 2 3 +--R 168a b cosh(x) + 12a b cosh(x) + 12a b +--R * +--R sech(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (210a b + 210a b )cosh(x) + (252a b + 252a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (210a b + 210a b )cosh(x) + (280a b + 280a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (30a b + 30a b )cosh(x) + (60a b + 60a b)cosh(x) +--R + +--R 4 3 2 +--R - 2a b - 2a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 6 2 3 5 4 4 +--R 210a b cosh(x) + 252a b cosh(x) + 210a b cosh(x) +--R + +--R 2 3 3 4 2 2 3 4 +--R 280a b cosh(x) + 30a b cosh(x) + 60a b cosh(x) - 2a b +--R * +--R sech(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (120a b + 120a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (168a b + 168a b )cosh(x) + (280a b + 280a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (40a b + 40a b )cosh(x) + (120a b + 120a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 8a b - 8a b )cosh(x) + 8a b + 8a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 7 2 3 6 4 5 +--R 120a b cosh(x) + 168a b cosh(x) + 168a b cosh(x) +--R + +--R 2 3 4 4 3 2 3 2 +--R 280a b cosh(x) + 40a b cosh(x) + 120a b cosh(x) +--R + +--R 4 2 3 +--R - 8a b cosh(x) + 8a b +--R * +--R sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (45a b + 45a b )cosh(x) + (72a b + 72a b)cosh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (84a b + 84a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (30a b + 30a b )cosh(x) + (120a b + 120a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (- 12a b - 12a b )cosh(x) + (24a b + 24a b)cosh(x) +--R + +--R 4 3 2 +--R - 3a b - 3a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 8 2 3 7 4 6 +--R 45a b cosh(x) + 72a b cosh(x) + 84a b cosh(x) +--R + +--R 2 3 5 4 4 2 3 3 +--R 168a b cosh(x) + 30a b cosh(x) + 120a b cosh(x) +--R + +--R 4 2 2 3 4 +--R - 12a b cosh(x) + 24a b cosh(x) - 3a b +--R * +--R sech(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 9 2 3 4 8 +--R (10a b + 10a b )cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (24a b + 24a b )cosh(x) + (56a b + 56a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (12a b + 12a b )cosh(x) + (60a b + 60a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 8a b - 8a b )cosh(x) + (24a b + 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 6a b - 6a b )cosh(x) + 2a b + 2a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 9 2 3 8 4 7 +--R 10a b cosh(x) + 18a b cosh(x) + 24a b cosh(x) +--R + +--R 2 3 6 4 5 2 3 4 +--R 56a b cosh(x) + 12a b cosh(x) + 60a b cosh(x) +--R + +--R 4 3 2 3 2 4 2 3 +--R - 8a b cosh(x) + 24a b cosh(x) - 6a b cosh(x) + 2a b +--R * +--R sech(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 10 2 3 4 9 +--R (a b + a b )cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (3a b + 3a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (2a b + 2a b )cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 2a b - 2a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 3a b - 3a b )cosh(x) + (2a b + 2a b)cosh(x) - a b - a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 10 2 3 9 4 8 2 3 7 +--R a b cosh(x) + 2a b cosh(x) + 3a b cosh(x) + 8a b cosh(x) +--R + +--R 4 6 2 3 5 4 4 +--R 2a b cosh(x) + 12a b cosh(x) - 2a b cosh(x) +--R + +--R 2 3 3 4 2 2 3 4 +--R 8a b cosh(x) - 3a b cosh(x) + 2a b cosh(x) - a b +--R * +--R sech(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 2 3 3 5 10 +--R ((- 2b - 2a b )sech(x) - 2b sech(x))sinh(x) +--R + +--R 5 2 3 4 3 2 3 +--R ((- 20b - 20a b )cosh(x) - 4a b - 4a b )sech(x) +--R + +--R 5 4 +--R (- 20b cosh(x) - 4a b )sech(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 5 2 3 2 4 3 2 +--R (- 90b - 90a b )cosh(x) + (- 36a b - 36a b )cosh(x) +--R + +--R 5 2 3 +--R - 6b - 6a b +--R * +--R 3 +--R sech(x) +--R + +--R 5 2 4 5 +--R (- 90b cosh(x) - 36a b cosh(x) - 6b )sech(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 3 3 +--R (- 240b - 240a b )cosh(x) +--R + +--R 4 3 2 2 5 2 3 +--R (- 144a b - 144a b )cosh(x) + (- 48b - 48a b )cosh(x) +--R + +--R 4 3 2 +--R - 16a b - 16a b +--R * +--R 3 +--R sech(x) +--R + +--R 5 3 4 2 5 4 +--R (- 240b cosh(x) - 144a b cosh(x) - 48b cosh(x) - 16a b ) +--R * +--R sech(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 2 3 4 +--R (- 420b - 420a b )cosh(x) +--R + +--R 4 3 2 3 +--R (- 336a b - 336a b )cosh(x) +--R + +--R 5 2 3 2 +--R (- 168b - 168a b )cosh(x) +--R + +--R 4 3 2 5 2 3 +--R (- 112a b - 112a b )cosh(x) - 4b - 4a b +--R * +--R 3 +--R sech(x) +--R + +--R 5 4 4 3 5 2 +--R - 420b cosh(x) - 336a b cosh(x) - 168b cosh(x) +--R + +--R 4 5 +--R - 112a b cosh(x) - 4b +--R * +--R sech(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 3 5 +--R (- 504b - 504a b )cosh(x) +--R + +--R 4 3 2 4 +--R (- 504a b - 504a b )cosh(x) +--R + +--R 5 2 3 3 +--R (- 336b - 336a b )cosh(x) +--R + +--R 4 3 2 2 5 2 3 +--R (- 336a b - 336a b )cosh(x) + (- 24b - 24a b )cosh(x) +--R + +--R 4 3 2 +--R - 24a b - 24a b +--R * +--R 3 +--R sech(x) +--R + +--R 5 5 4 4 5 3 +--R - 504b cosh(x) - 504a b cosh(x) - 336b cosh(x) +--R + +--R 4 2 5 4 +--R - 336a b cosh(x) - 24b cosh(x) - 24a b +--R * +--R sech(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 3 6 +--R (- 420b - 420a b )cosh(x) +--R + +--R 4 3 2 5 +--R (- 504a b - 504a b )cosh(x) +--R + +--R 5 2 3 4 +--R (- 420b - 420a b )cosh(x) +--R + +--R 4 3 2 3 5 2 3 2 +--R (- 560a b - 560a b )cosh(x) + (- 60b - 60a b )cosh(x) +--R + +--R 4 3 2 5 2 3 +--R (- 120a b - 120a b )cosh(x) + 4b + 4a b +--R * +--R 3 +--R sech(x) +--R + +--R 5 6 4 5 5 4 +--R - 420b cosh(x) - 504a b cosh(x) - 420b cosh(x) +--R + +--R 4 3 5 2 4 5 +--R - 560a b cosh(x) - 60b cosh(x) - 120a b cosh(x) + 4b +--R * +--R sech(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 3 7 +--R (- 240b - 240a b )cosh(x) +--R + +--R 4 3 2 6 +--R (- 336a b - 336a b )cosh(x) +--R + +--R 5 2 3 5 +--R (- 336b - 336a b )cosh(x) +--R + +--R 4 3 2 4 5 2 3 3 +--R (- 560a b - 560a b )cosh(x) + (- 80b - 80a b )cosh(x) +--R + +--R 4 3 2 2 5 2 3 +--R (- 240a b - 240a b )cosh(x) + (16b + 16a b )cosh(x) +--R + +--R 4 3 2 +--R - 16a b - 16a b +--R * +--R 3 +--R sech(x) +--R + +--R 5 7 4 6 5 5 +--R - 240b cosh(x) - 336a b cosh(x) - 336b cosh(x) +--R + +--R 4 4 5 3 4 2 +--R - 560a b cosh(x) - 80b cosh(x) - 240a b cosh(x) +--R + +--R 5 4 +--R 16b cosh(x) - 16a b +--R * +--R sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 8 4 3 2 7 +--R (- 90b - 90a b )cosh(x) + (- 144a b - 144a b )cosh(x) +--R + +--R 5 2 3 6 +--R (- 168b - 168a b )cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 336a b - 336a b )cosh(x) + (- 60b - 60a b )cosh(x) +--R + +--R 4 3 2 3 5 2 3 2 +--R (- 240a b - 240a b )cosh(x) + (24b + 24a b )cosh(x) +--R + +--R 4 3 2 5 2 3 +--R (- 48a b - 48a b )cosh(x) + 6b + 6a b +--R * +--R 3 +--R sech(x) +--R + +--R 5 8 4 7 5 6 +--R - 90b cosh(x) - 144a b cosh(x) - 168b cosh(x) +--R + +--R 4 5 5 4 4 3 +--R - 336a b cosh(x) - 60b cosh(x) - 240a b cosh(x) +--R + +--R 5 2 4 5 +--R 24b cosh(x) - 48a b cosh(x) + 6b +--R * +--R sech(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 9 4 3 2 8 +--R (- 20b - 20a b )cosh(x) + (- 36a b - 36a b )cosh(x) +--R + +--R 5 2 3 7 4 3 2 6 +--R (- 48b - 48a b )cosh(x) + (- 112a b - 112a b )cosh(x) +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 24b - 24a b )cosh(x) + (- 120a b - 120a b )cosh(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (16b + 16a b )cosh(x) + (- 48a b - 48a b )cosh(x) +--R + +--R 5 2 3 4 3 2 +--R (12b + 12a b )cosh(x) - 4a b - 4a b +--R * +--R 3 +--R sech(x) +--R + +--R 5 9 4 8 5 7 +--R - 20b cosh(x) - 36a b cosh(x) - 48b cosh(x) +--R + +--R 4 6 5 5 4 4 +--R - 112a b cosh(x) - 24b cosh(x) - 120a b cosh(x) +--R + +--R 5 3 4 2 5 4 +--R 16b cosh(x) - 48a b cosh(x) + 12b cosh(x) - 4a b +--R * +--R sech(x) +--R * +--R sinh(x) +--R + +--R 5 2 3 10 4 3 2 9 +--R (- 2b - 2a b )cosh(x) + (- 4a b - 4a b )cosh(x) +--R + +--R 5 2 3 8 4 3 2 7 +--R (- 6b - 6a b )cosh(x) + (- 16a b - 16a b )cosh(x) +--R + +--R 5 2 3 6 4 3 2 5 +--R (- 4b - 4a b )cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (4b + 4a b )cosh(x) + (- 16a b - 16a b )cosh(x) +--R + +--R 5 2 3 2 4 3 2 5 2 3 +--R (6b + 6a b )cosh(x) + (- 4a b - 4a b )cosh(x) + 2b + 2a b +--R * +--R 3 +--R sech(x) +--R + +--R 5 10 4 9 5 8 4 7 +--R - 2b cosh(x) - 4a b cosh(x) - 6b cosh(x) - 16a b cosh(x) +--R + +--R 5 6 4 5 5 4 4 3 +--R - 4b cosh(x) - 24a b cosh(x) + 4b cosh(x) - 16a b cosh(x) +--R + +--R 5 2 4 5 +--R 6b cosh(x) - 4a b cosh(x) + 2b +--R * +--R sech(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 2 3 4 10 +--R ((- a b - a b )sech(x) - a b sech(x))sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R ((- 10a b - 10a b )cosh(x) - 2a b - 2a b)sech(x) +--R + +--R 4 2 3 +--R (- 10a b cosh(x) - 2a b )sech(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (- 45a b - 45a b )cosh(x) + (- 18a b - 18a b)cosh(x) +--R + +--R 4 3 2 +--R - 3a b - 3a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 2 2 3 4 +--R (- 45a b cosh(x) - 18a b cosh(x) - 3a b )sech(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 120a b - 120a b )cosh(x) + (- 72a b - 72a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 24a b - 24a b )cosh(x) - 8a b - 8a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 3 2 3 2 4 2 3 +--R (- 120a b cosh(x) - 72a b cosh(x) - 24a b cosh(x) - 8a b )sech(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 210a b - 210a b )cosh(x) + (- 168a b - 168a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (- 84a b - 84a b )cosh(x) + (- 56a b - 56a b)cosh(x) +--R + +--R 4 3 2 +--R - 2a b - 2a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 4 2 3 3 4 2 +--R - 210a b cosh(x) - 168a b cosh(x) - 84a b cosh(x) +--R + +--R 2 3 4 +--R - 56a b cosh(x) - 2a b +--R * +--R sech(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (- 252a b - 252a b )cosh(x) + (- 252a b - 252a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 168a b - 168a b )cosh(x) + (- 168a b - 168a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 12a b - 12a b )cosh(x) - 12a b - 12a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 5 2 3 4 4 3 +--R - 252a b cosh(x) - 252a b cosh(x) - 168a b cosh(x) +--R + +--R 2 3 2 4 2 3 +--R - 168a b cosh(x) - 12a b cosh(x) - 12a b +--R * +--R sech(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (- 210a b - 210a b )cosh(x) + (- 252a b - 252a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 210a b - 210a b )cosh(x) + (- 280a b - 280a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (- 30a b - 30a b )cosh(x) + (- 60a b - 60a b)cosh(x) +--R + +--R 4 3 2 +--R 2a b + 2a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 6 2 3 5 4 4 +--R - 210a b cosh(x) - 252a b cosh(x) - 210a b cosh(x) +--R + +--R 2 3 3 4 2 2 3 4 +--R - 280a b cosh(x) - 30a b cosh(x) - 60a b cosh(x) + 2a b +--R * +--R sech(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (- 120a b - 120a b )cosh(x) + (- 168a b - 168a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (- 168a b - 168a b )cosh(x) + (- 280a b - 280a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 40a b - 40a b )cosh(x) + (- 120a b - 120a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (8a b + 8a b )cosh(x) - 8a b - 8a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 7 2 3 6 4 5 +--R - 120a b cosh(x) - 168a b cosh(x) - 168a b cosh(x) +--R + +--R 2 3 4 4 3 2 3 2 +--R - 280a b cosh(x) - 40a b cosh(x) - 120a b cosh(x) +--R + +--R 4 2 3 +--R 8a b cosh(x) - 8a b +--R * +--R sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (- 45a b - 45a b )cosh(x) + (- 72a b - 72a b)cosh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (- 84a b - 84a b )cosh(x) + (- 168a b - 168a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 30a b - 30a b )cosh(x) + (- 120a b - 120a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (12a b + 12a b )cosh(x) + (- 24a b - 24a b)cosh(x) + 3a b +--R + +--R 3 2 +--R 3a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 8 2 3 7 4 6 +--R - 45a b cosh(x) - 72a b cosh(x) - 84a b cosh(x) +--R + +--R 2 3 5 4 4 2 3 3 +--R - 168a b cosh(x) - 30a b cosh(x) - 120a b cosh(x) +--R + +--R 4 2 2 3 4 +--R 12a b cosh(x) - 24a b cosh(x) + 3a b +--R * +--R sech(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 9 2 3 4 8 +--R (- 10a b - 10a b )cosh(x) + (- 18a b - 18a b)cosh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (- 24a b - 24a b )cosh(x) + (- 56a b - 56a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (- 12a b - 12a b )cosh(x) + (- 60a b - 60a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (8a b + 8a b )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (6a b + 6a b )cosh(x) - 2a b - 2a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 9 2 3 8 4 7 +--R - 10a b cosh(x) - 18a b cosh(x) - 24a b cosh(x) +--R + +--R 2 3 6 4 5 2 3 4 +--R - 56a b cosh(x) - 12a b cosh(x) - 60a b cosh(x) +--R + +--R 4 3 2 3 2 4 2 3 +--R 8a b cosh(x) - 24a b cosh(x) + 6a b cosh(x) - 2a b +--R * +--R sech(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 10 2 3 4 9 +--R (- a b - a b )cosh(x) + (- 2a b - 2a b)cosh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (- 3a b - 3a b )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (- 2a b - 2a b )cosh(x) + (- 12a b - 12a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (2a b + 2a b )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (3a b + 3a b )cosh(x) + (- 2a b - 2a b)cosh(x) + a b + a b +--R * +--R 3 +--R sech(x) +--R + +--R 4 10 2 3 9 4 8 2 3 7 +--R - a b cosh(x) - 2a b cosh(x) - 3a b cosh(x) - 8a b cosh(x) +--R + +--R 4 6 2 3 5 4 4 2 3 3 +--R - 2a b cosh(x) - 12a b cosh(x) + 2a b cosh(x) - 8a b cosh(x) +--R + +--R 4 2 2 3 4 +--R 3a b cosh(x) - 2a b cosh(x) + a b +--R * +--R sech(x) +--R * +--R tanh(x) +--R + +--R 5 2 3 4 10 +--R (- b - 2a b - a b)sinh(x) +--R + +--R 5 2 3 4 4 3 2 5 9 +--R ((- 10b - 20a b - 10a b)cosh(x) - 2a b - 4a b - 2a )sinh(x) +--R + +--R 5 2 3 4 2 +--R (- 45b - 90a b - 45a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 18a b - 36a b - 18a )cosh(x) - 3b - 6a b - 3a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 3 4 3 +--R (- 120b - 240a b - 120a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 72a b - 144a b - 72a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 24b - 48a b - 24a b)cosh(x) - 8a b - 16a b - 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 5 2 3 4 4 +--R (- 210b - 420a b - 210a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (- 168a b - 336a b - 168a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (- 84b - 168a b - 84a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 56a b - 112a b - 56a )cosh(x) - 2b - 4a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 3 4 5 +--R (- 252b - 504a b - 252a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (- 252a b - 504a b - 252a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 168b - 336a b - 168a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 168a b - 336a b - 168a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 12b - 24a b - 12a b)cosh(x) + 20a b + 40a b + 20a +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 3 4 6 +--R (- 210b - 420a b - 210a b)cosh(x) +--R + +--R 4 3 2 5 5 +--R (- 252a b - 504a b - 252a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (- 210b - 420a b - 210a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (- 280a b - 560a b - 280a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (- 30b - 60a b - 30a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (100a b + 200a b + 100a )cosh(x) + 2b + 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 3 4 7 +--R (- 120b - 240a b - 120a b)cosh(x) +--R + +--R 4 3 2 5 6 +--R (- 168a b - 336a b - 168a )cosh(x) +--R + +--R 5 2 3 4 5 +--R (- 168b - 336a b - 168a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (- 280a b - 560a b - 280a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 40b - 80a b - 40a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (200a b + 400a b + 200a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (8b + 16a b + 8a b)cosh(x) - 8a b - 16a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 4 8 +--R (- 45b - 90a b - 45a b)cosh(x) +--R + +--R 4 3 2 5 7 +--R (- 72a b - 144a b - 72a )cosh(x) +--R + +--R 5 2 3 4 6 +--R (- 84b - 168a b - 84a b)cosh(x) +--R + +--R 4 3 2 5 5 +--R (- 168a b - 336a b - 168a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (- 30b - 60a b - 30a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (200a b + 400a b + 200a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (12b + 24a b + 12a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 24a b - 48a b - 24a )cosh(x) + 3b + 6a b + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 4 9 +--R (- 10b - 20a b - 10a b)cosh(x) +--R + +--R 4 3 2 5 8 +--R (- 18a b - 36a b - 18a )cosh(x) +--R + +--R 5 2 3 4 7 +--R (- 24b - 48a b - 24a b)cosh(x) +--R + +--R 4 3 2 5 6 +--R (- 56a b - 112a b - 56a )cosh(x) +--R + +--R 5 2 3 4 5 +--R (- 12b - 24a b - 12a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (100a b + 200a b + 100a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (8b + 16a b + 8a b)cosh(x) +--R + +--R 4 3 2 5 2 5 2 3 4 +--R (- 24a b - 48a b - 24a )cosh(x) + (6b + 12a b + 6a b)cosh(x) +--R + +--R 4 3 2 5 +--R - 2a b - 4a b - 2a +--R * +--R sinh(x) +--R + +--R 5 2 3 4 10 4 3 2 5 9 +--R (- b - 2a b - a b)cosh(x) + (- 2a b - 4a b - 2a )cosh(x) +--R + +--R 5 2 3 4 8 4 3 2 5 7 +--R (- 3b - 6a b - 3a b)cosh(x) + (- 8a b - 16a b - 8a )cosh(x) +--R + +--R 5 2 3 4 6 4 3 2 5 5 +--R (- 2b - 4a b - 2a b)cosh(x) + (20a b + 40a b + 20a )cosh(x) +--R + +--R 5 2 3 4 4 4 3 2 5 3 +--R (2b + 4a b + 2a b)cosh(x) + (- 8a b - 16a b - 8a )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 5 +--R (3b + 6a b + 3a b)cosh(x) + (- 2a b - 4a b - 2a )cosh(x) + b +--R + +--R 2 3 4 +--R 2a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 10 +--R (4a b + 2a b )sinh(x) +--R + +--R 4 3 2 2 3 4 9 +--R ((40a b + 20a b )cosh(x) + 8a b + 4a b)sinh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (180a b + 90a b )cosh(x) + (72a b + 36a b)cosh(x) + 12a b +--R + +--R 3 2 +--R 6a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (480a b + 240a b )cosh(x) + (288a b + 144a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (96a b + 48a b )cosh(x) + 32a b + 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (840a b + 420a b )cosh(x) + (672a b + 336a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (336a b + 168a b )cosh(x) + (224a b + 112a b)cosh(x) + 8a b +--R + +--R 3 2 +--R 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (1008a b + 504a b )cosh(x) + (1008a b + 504a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (672a b + 336a b )cosh(x) + (672a b + 336a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (48a b + 24a b )cosh(x) - 64b - 80a b - 40a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (840a b + 420a b )cosh(x) + (1008a b + 504a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (840a b + 420a b )cosh(x) + (1120a b + 560a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (120a b + 60a b )cosh(x) + (- 320b - 400a b - 200a b)cosh(x) +--R + +--R 4 3 2 +--R - 8a b - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (480a b + 240a b )cosh(x) + (672a b + 336a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (672a b + 336a b )cosh(x) + (1120a b + 560a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (160a b + 80a b )cosh(x) + (- 640b - 800a b - 400a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 32a b - 16a b )cosh(x) + 32a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (180a b + 90a b )cosh(x) + (288a b + 144a b)cosh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (336a b + 168a b )cosh(x) + (672a b + 336a b)cosh(x) +--R + +--R 4 3 2 4 5 2 3 4 3 +--R (120a b + 60a b )cosh(x) + (- 640b - 800a b - 400a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (- 48a b - 24a b )cosh(x) + (96a b + 48a b)cosh(x) - 12a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 9 2 3 4 8 +--R (40a b + 20a b )cosh(x) + (72a b + 36a b)cosh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (96a b + 48a b )cosh(x) + (224a b + 112a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 4 +--R (48a b + 24a b )cosh(x) + (- 320b - 400a b - 200a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 32a b - 16a b )cosh(x) + (96a b + 48a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 24a b - 12a b )cosh(x) + 8a b + 4a b +--R * +--R sinh(x) +--R + +--R 4 3 2 10 2 3 4 9 +--R (4a b + 2a b )cosh(x) + (8a b + 4a b)cosh(x) +--R + +--R 4 3 2 8 2 3 4 7 +--R (12a b + 6a b )cosh(x) + (32a b + 16a b)cosh(x) +--R + +--R 4 3 2 6 5 2 3 4 5 +--R (8a b + 4a b )cosh(x) + (- 64b - 80a b - 40a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 8a b - 4a b )cosh(x) + (32a b + 16a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 12a b - 6a b )cosh(x) + (8a b + 4a b)cosh(x) - 4a b - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 2 3 4 10 +--R (b + 2a b + a b)sinh(x) +--R + +--R 5 2 3 4 4 3 2 5 9 +--R ((10b + 20a b + 10a b)cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (45b + 90a b + 45a b)cosh(x) + (18a b + 36a b + 18a )cosh(x) +--R + +--R 5 2 3 4 +--R 3b + 6a b + 3a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 2 3 4 3 +--R (120b + 240a b + 120a b)cosh(x) +--R + +--R 4 3 2 5 2 5 2 3 4 +--R (72a b + 144a b + 72a )cosh(x) + (24b + 48a b + 24a b)cosh(x) +--R + +--R 4 3 2 5 +--R 8a b + 16a b + 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 5 2 3 4 4 +--R (210b + 420a b + 210a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (168a b + 336a b + 168a )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (84b + 168a b + 84a b)cosh(x) + (56a b + 112a b + 56a )cosh(x) +--R + +--R 5 2 3 4 +--R 2b + 4a b + 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 2 3 4 5 +--R (252b + 504a b + 252a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (252a b + 504a b + 252a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (168b + 336a b + 168a b)cosh(x) +--R + +--R 4 3 2 5 2 5 2 3 4 +--R (168a b + 336a b + 168a )cosh(x) + (12b + 24a b + 12a b)cosh(x) +--R + +--R 4 3 2 5 +--R - 20a b - 40a b - 20a +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 3 4 6 +--R (210b + 420a b + 210a b)cosh(x) +--R + +--R 4 3 2 5 5 +--R (252a b + 504a b + 252a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (210b + 420a b + 210a b)cosh(x) +--R + +--R 4 3 2 5 3 5 2 3 4 2 +--R (280a b + 560a b + 280a )cosh(x) + (30b + 60a b + 30a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 100a b - 200a b - 100a )cosh(x) - 2b - 4a b - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 3 4 7 +--R (120b + 240a b + 120a b)cosh(x) +--R + +--R 4 3 2 5 6 +--R (168a b + 336a b + 168a )cosh(x) +--R + +--R 5 2 3 4 5 +--R (168b + 336a b + 168a b)cosh(x) +--R + +--R 4 3 2 5 4 5 2 3 4 3 +--R (280a b + 560a b + 280a )cosh(x) + (40b + 80a b + 40a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 200a b - 400a b - 200a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 8b - 16a b - 8a b)cosh(x) + 8a b + 16a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 4 8 4 3 2 5 7 +--R (45b + 90a b + 45a b)cosh(x) + (72a b + 144a b + 72a )cosh(x) +--R + +--R 5 2 3 4 6 +--R (84b + 168a b + 84a b)cosh(x) +--R + +--R 4 3 2 5 5 5 2 3 4 4 +--R (168a b + 336a b + 168a )cosh(x) + (30b + 60a b + 30a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (- 200a b - 400a b - 200a )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (- 12b - 24a b - 12a b)cosh(x) + (24a b + 48a b + 24a )cosh(x) +--R + +--R 5 2 3 4 +--R - 3b - 6a b - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 4 9 4 3 2 5 8 +--R (10b + 20a b + 10a b)cosh(x) + (18a b + 36a b + 18a )cosh(x) +--R + +--R 5 2 3 4 7 4 3 2 5 6 +--R (24b + 48a b + 24a b)cosh(x) + (56a b + 112a b + 56a )cosh(x) +--R + +--R 5 2 3 4 5 +--R (12b + 24a b + 12a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (- 100a b - 200a b - 100a )cosh(x) +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 8b - 16a b - 8a b)cosh(x) + (24a b + 48a b + 24a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 6b - 12a b - 6a b)cosh(x) + 2a b + 4a b + 2a +--R * +--R sinh(x) +--R + +--R 5 2 3 4 10 4 3 2 5 9 +--R (b + 2a b + a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) +--R + +--R 5 2 3 4 8 4 3 2 5 7 +--R (3b + 6a b + 3a b)cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R + +--R 5 2 3 4 6 4 3 2 5 5 +--R (2b + 4a b + 2a b)cosh(x) + (- 20a b - 40a b - 20a )cosh(x) +--R + +--R 5 2 3 4 4 4 3 2 5 3 +--R (- 2b - 4a b - 2a b)cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 5 +--R (- 3b - 6a b - 3a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) - b +--R + +--R 2 3 4 +--R - 2a b - a b +--R / +--R 5 3 3 5 10 +--R (a b + 2a b + a b)sinh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 9 +--R ((10a b + 20a b + 10a b)cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 5 3 3 5 2 +--R (45a b + 90a b + 45a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (18a b + 36a b + 18a )cosh(x) + 3a b + 6a b + 3a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 3 3 5 3 +--R (120a b + 240a b + 120a b)cosh(x) +--R + +--R 2 4 4 2 6 2 +--R (72a b + 144a b + 72a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (24a b + 48a b + 24a b)cosh(x) + 8a b + 16a b + 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 3 5 4 +--R (210a b + 420a b + 210a b)cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (168a b + 336a b + 168a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (84a b + 168a b + 84a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (56a b + 112a b + 56a )cosh(x) + 2a b + 4a b + 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 3 5 5 +--R (252a b + 504a b + 252a b)cosh(x) +--R + +--R 2 4 4 2 6 4 +--R (252a b + 504a b + 252a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (168a b + 336a b + 168a b)cosh(x) +--R + +--R 2 4 4 2 6 2 +--R (168a b + 336a b + 168a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (12a b + 24a b + 12a b)cosh(x) + 12a b + 24a b + 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 5 6 +--R (210a b + 420a b + 210a b)cosh(x) +--R + +--R 2 4 4 2 6 5 +--R (252a b + 504a b + 252a )cosh(x) +--R + +--R 5 3 3 5 4 +--R (210a b + 420a b + 210a b)cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (280a b + 560a b + 280a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (30a b + 60a b + 30a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (60a b + 120a b + 60a )cosh(x) - 2a b - 4a b - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 5 7 +--R (120a b + 240a b + 120a b)cosh(x) +--R + +--R 2 4 4 2 6 6 +--R (168a b + 336a b + 168a )cosh(x) +--R + +--R 5 3 3 5 5 +--R (168a b + 336a b + 168a b)cosh(x) +--R + +--R 2 4 4 2 6 4 +--R (280a b + 560a b + 280a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (40a b + 80a b + 40a b)cosh(x) +--R + +--R 2 4 4 2 6 2 +--R (120a b + 240a b + 120a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (- 8a b - 16a b - 8a b)cosh(x) + 8a b + 16a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 3 5 8 +--R (45a b + 90a b + 45a b)cosh(x) +--R + +--R 2 4 4 2 6 7 +--R (72a b + 144a b + 72a )cosh(x) +--R + +--R 5 3 3 5 6 +--R (84a b + 168a b + 84a b)cosh(x) +--R + +--R 2 4 4 2 6 5 +--R (168a b + 336a b + 168a )cosh(x) +--R + +--R 5 3 3 5 4 +--R (30a b + 60a b + 30a b)cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (120a b + 240a b + 120a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 12a b - 24a b - 12a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (24a b + 48a b + 24a )cosh(x) - 3a b - 6a b - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 3 5 9 +--R (10a b + 20a b + 10a b)cosh(x) +--R + +--R 2 4 4 2 6 8 +--R (18a b + 36a b + 18a )cosh(x) +--R + +--R 5 3 3 5 7 +--R (24a b + 48a b + 24a b)cosh(x) +--R + +--R 2 4 4 2 6 6 +--R (56a b + 112a b + 56a )cosh(x) +--R + +--R 5 3 3 5 5 +--R (12a b + 24a b + 12a b)cosh(x) +--R + +--R 2 4 4 2 6 4 +--R (60a b + 120a b + 60a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 8a b - 16a b - 8a b)cosh(x) +--R + +--R 2 4 4 2 6 2 +--R (24a b + 48a b + 24a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (- 6a b - 12a b - 6a b)cosh(x) + 2a b + 4a b + 2a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 10 2 4 4 2 6 9 +--R (a b + 2a b + a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) +--R + +--R 5 3 3 5 8 2 4 4 2 6 7 +--R (3a b + 6a b + 3a b)cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 5 +--R (2a b + 4a b + 2a b)cosh(x) + (12a b + 24a b + 12a )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 6 3 +--R (- 2a b - 4a b - 2a b)cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 6 +--R (- 3a b - 6a b - 3a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) +--R + +--R 5 3 3 5 +--R - a b - 2a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 2 4 4 2 10 +--R (- 2b - 4a b - 2a b )sinh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 9 +--R ((- 20b - 40a b - 20a b )cosh(x) - 4a b - 8a b - 4a b)sinh(x) +--R + +--R 6 2 4 4 2 2 +--R (- 90b - 180a b - 90a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 36a b - 72a b - 36a b)cosh(x) - 6b - 12a b - 6a b +--R * +--R 8 +--R sinh(x) +--R + +--R 6 2 4 4 2 3 +--R (- 240b - 480a b - 240a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 144a b - 288a b - 144a b)cosh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 +--R (- 48b - 96a b - 48a b )cosh(x) - 16a b - 32a b - 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 6 2 4 4 2 4 +--R (- 420b - 840a b - 420a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 336a b - 672a b - 336a b)cosh(x) +--R + +--R 6 2 4 4 2 2 +--R (- 168b - 336a b - 168a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 112a b - 224a b - 112a b)cosh(x) - 4b - 8a b - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 2 4 4 2 5 +--R (- 504b - 1008a b - 504a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 504a b - 1008a b - 504a b)cosh(x) +--R + +--R 6 2 4 4 2 3 +--R (- 336b - 672a b - 336a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 336a b - 672a b - 336a b)cosh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 +--R (- 24b - 48a b - 24a b )cosh(x) - 24a b - 48a b - 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 6 2 4 4 2 6 +--R (- 420b - 840a b - 420a b )cosh(x) +--R + +--R 5 3 3 5 5 +--R (- 504a b - 1008a b - 504a b)cosh(x) +--R + +--R 6 2 4 4 2 4 +--R (- 420b - 840a b - 420a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 560a b - 1120a b - 560a b)cosh(x) +--R + +--R 6 2 4 4 2 2 +--R (- 60b - 120a b - 60a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 120a b - 240a b - 120a b)cosh(x) + 4b + 8a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 4 4 2 7 +--R (- 240b - 480a b - 240a b )cosh(x) +--R + +--R 5 3 3 5 6 +--R (- 336a b - 672a b - 336a b)cosh(x) +--R + +--R 6 2 4 4 2 5 +--R (- 336b - 672a b - 336a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 560a b - 1120a b - 560a b)cosh(x) +--R + +--R 6 2 4 4 2 3 +--R (- 80b - 160a b - 80a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 240a b - 480a b - 240a b)cosh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 +--R (16b + 32a b + 16a b )cosh(x) - 16a b - 32a b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 4 2 8 +--R (- 90b - 180a b - 90a b )cosh(x) +--R + +--R 5 3 3 5 7 +--R (- 144a b - 288a b - 144a b)cosh(x) +--R + +--R 6 2 4 4 2 6 +--R (- 168b - 336a b - 168a b )cosh(x) +--R + +--R 5 3 3 5 5 +--R (- 336a b - 672a b - 336a b)cosh(x) +--R + +--R 6 2 4 4 2 4 +--R (- 60b - 120a b - 60a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 240a b - 480a b - 240a b)cosh(x) +--R + +--R 6 2 4 4 2 2 +--R (24b + 48a b + 24a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 48a b - 96a b - 48a b)cosh(x) + 6b + 12a b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 4 2 9 +--R (- 20b - 40a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 8 +--R (- 36a b - 72a b - 36a b)cosh(x) +--R + +--R 6 2 4 4 2 7 +--R (- 48b - 96a b - 48a b )cosh(x) +--R + +--R 5 3 3 5 6 +--R (- 112a b - 224a b - 112a b)cosh(x) +--R + +--R 6 2 4 4 2 5 +--R (- 24b - 48a b - 24a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 120a b - 240a b - 120a b)cosh(x) +--R + +--R 6 2 4 4 2 3 +--R (16b + 32a b + 16a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 48a b - 96a b - 48a b)cosh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 +--R (12b + 24a b + 12a b )cosh(x) - 4a b - 8a b - 4a b +--R * +--R sinh(x) +--R + +--R 6 2 4 4 2 10 5 3 3 5 9 +--R (- 2b - 4a b - 2a b )cosh(x) + (- 4a b - 8a b - 4a b)cosh(x) +--R + +--R 6 2 4 4 2 8 +--R (- 6b - 12a b - 6a b )cosh(x) +--R + +--R 5 3 3 5 7 6 2 4 4 2 6 +--R (- 16a b - 32a b - 16a b)cosh(x) + (- 4b - 8a b - 4a b )cosh(x) +--R + +--R 5 3 3 5 5 6 2 4 4 2 4 +--R (- 24a b - 48a b - 24a b)cosh(x) + (4b + 8a b + 4a b )cosh(x) +--R + +--R 5 3 3 5 3 6 2 4 4 2 2 +--R (- 16a b - 32a b - 16a b)cosh(x) + (6b + 12a b + 6a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 4a b - 8a b - 4a b)cosh(x) + 2b + 4a b + 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 3 3 5 10 +--R (- a b - 2a b - a b)sinh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 9 +--R ((- 10a b - 20a b - 10a b)cosh(x) - 2a b - 4a b - 2a )sinh(x) +--R + +--R 5 3 3 5 2 +--R (- 45a b - 90a b - 45a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (- 18a b - 36a b - 18a )cosh(x) - 3a b - 6a b - 3a b +--R * +--R 8 +--R sinh(x) +--R + +--R 5 3 3 5 3 +--R (- 120a b - 240a b - 120a b)cosh(x) +--R + +--R 2 4 4 2 6 2 +--R (- 72a b - 144a b - 72a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (- 24a b - 48a b - 24a b)cosh(x) - 8a b - 16a b - 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 3 5 4 +--R (- 210a b - 420a b - 210a b)cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (- 168a b - 336a b - 168a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 84a b - 168a b - 84a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (- 56a b - 112a b - 56a )cosh(x) - 2a b - 4a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 3 5 5 +--R (- 252a b - 504a b - 252a b)cosh(x) +--R + +--R 2 4 4 2 6 4 +--R (- 252a b - 504a b - 252a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 168a b - 336a b - 168a b)cosh(x) +--R + +--R 2 4 4 2 6 2 +--R (- 168a b - 336a b - 168a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (- 12a b - 24a b - 12a b)cosh(x) - 12a b - 24a b - 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 5 6 +--R (- 210a b - 420a b - 210a b)cosh(x) +--R + +--R 2 4 4 2 6 5 +--R (- 252a b - 504a b - 252a )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 210a b - 420a b - 210a b)cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (- 280a b - 560a b - 280a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 30a b - 60a b - 30a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (- 60a b - 120a b - 60a )cosh(x) + 2a b + 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 5 7 +--R (- 120a b - 240a b - 120a b)cosh(x) +--R + +--R 2 4 4 2 6 6 +--R (- 168a b - 336a b - 168a )cosh(x) +--R + +--R 5 3 3 5 5 +--R (- 168a b - 336a b - 168a b)cosh(x) +--R + +--R 2 4 4 2 6 4 +--R (- 280a b - 560a b - 280a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 40a b - 80a b - 40a b)cosh(x) +--R + +--R 2 4 4 2 6 2 +--R (- 120a b - 240a b - 120a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (8a b + 16a b + 8a b)cosh(x) - 8a b - 16a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 3 5 8 +--R (- 45a b - 90a b - 45a b)cosh(x) +--R + +--R 2 4 4 2 6 7 +--R (- 72a b - 144a b - 72a )cosh(x) +--R + +--R 5 3 3 5 6 +--R (- 84a b - 168a b - 84a b)cosh(x) +--R + +--R 2 4 4 2 6 5 +--R (- 168a b - 336a b - 168a )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 30a b - 60a b - 30a b)cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (- 120a b - 240a b - 120a )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 6 +--R (12a b + 24a b + 12a b)cosh(x) + (- 24a b - 48a b - 24a )cosh(x) +--R + +--R 5 3 3 5 +--R 3a b + 6a b + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 3 5 9 +--R (- 10a b - 20a b - 10a b)cosh(x) +--R + +--R 2 4 4 2 6 8 +--R (- 18a b - 36a b - 18a )cosh(x) +--R + +--R 5 3 3 5 7 +--R (- 24a b - 48a b - 24a b)cosh(x) +--R + +--R 2 4 4 2 6 6 +--R (- 56a b - 112a b - 56a )cosh(x) +--R + +--R 5 3 3 5 5 +--R (- 12a b - 24a b - 12a b)cosh(x) +--R + +--R 2 4 4 2 6 4 5 3 3 5 3 +--R (- 60a b - 120a b - 60a )cosh(x) + (8a b + 16a b + 8a b)cosh(x) +--R + +--R 2 4 4 2 6 2 5 3 3 5 +--R (- 24a b - 48a b - 24a )cosh(x) + (6a b + 12a b + 6a b)cosh(x) +--R + +--R 2 4 4 2 6 +--R - 2a b - 4a b - 2a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 10 2 4 4 2 6 9 +--R (- a b - 2a b - a b)cosh(x) + (- 2a b - 4a b - 2a )cosh(x) +--R + +--R 5 3 3 5 8 2 4 4 2 6 7 +--R (- 3a b - 6a b - 3a b)cosh(x) + (- 8a b - 16a b - 8a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 5 +--R (- 2a b - 4a b - 2a b)cosh(x) + (- 12a b - 24a b - 12a )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 6 3 +--R (2a b + 4a b + 2a b)cosh(x) + (- 8a b - 16a b - 8a )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 6 5 +--R (3a b + 6a b + 3a b)cosh(x) + (- 2a b - 4a b - 2a )cosh(x) + a b +--R + +--R 3 3 5 +--R 2a b + a b +--R Type: Expression(Integer) +--E 95 + +--S 96 of 530 +t0519:= sech(x)/(%i+sinh(x)) +--R +--R +--R sech(x) +--R (95) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 96 + +--S 97 of 530 +r0519:= -1/2*%i*atan(sinh(x))-%i/(2*%i+2*sinh(x)) +--R +--R +--R 1 1 1 +--R (- - %i sinh(x) + -)atan(sinh(x)) - - %i +--R 2 2 2 +--R (96) ---------------------------------------- +--R sinh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 97 + +--S 98 of 530 +a0519:= integrate(t0519,x) +--R +--R +--R (97) +--R 2 2 +--R (sinh(x) + (2cosh(x) + 2%i)sinh(x) + cosh(x) + 2%i cosh(x) - 1) +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 2 2 +--R (- sinh(x) + (- 2cosh(x) - 2%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1) +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R - 2%i sinh(x) - 2%i cosh(x) +--R / +--R 2 2 +--R 2sinh(x) + (4cosh(x) + 4%i)sinh(x) + 2cosh(x) + 4%i cosh(x) - 2 +--R Type: Union(Expression(Complex(Integer)),...) +--E 98 + +--S 99 of 530 +m0519:= a0519-r0519 +--R +--R +--R (98) +--R 1 3 3 2 +--R - sinh(x) + (cosh(x) + - %i)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 1 +--R (- cosh(x) + 2%i cosh(x) - -)sinh(x) + - %i cosh(x) - cosh(x) - - %i +--R 2 2 2 2 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 1 3 3 2 +--R - - sinh(x) + (- cosh(x) - - %i)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 +--R (- - cosh(x) - 2%i cosh(x) + -)sinh(x) - - %i cosh(x) + cosh(x) +--R 2 2 2 +--R + +--R 1 +--R - %i +--R 2 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 1 3 3 2 +--R - %i sinh(x) + (%i cosh(x) - -)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 1 +--R (- %i cosh(x) - 2cosh(x) - - %i)sinh(x) - - cosh(x) - %i cosh(x) + - +--R 2 2 2 2 +--R * +--R atan(sinh(x)) +--R + +--R 1 2 1 2 1 +--R - - %i sinh(x) + - %i cosh(x) - - %i +--R 2 2 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) + 3%i)sinh(x) + (cosh(x) + 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R %i cosh(x) - 2cosh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 99 + +--S 100 of 530 +d0519:= D(m0519,x) +--R +--R +--R (99) +--R 5 4 3 +--R 4sinh(x) + (7cosh(x) + 4%i)sinh(x) + (6%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 2 +--R (- 6cosh(x) - 2%i cosh(x) + 8cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 5 +--R (- 4cosh(x) - 6%i cosh(x) + 4cosh(x) + 6%i cosh(x))sinh(x) - cosh(x) +--R + +--R 4 2 +--R - 2%i cosh(x) + 2%i cosh(x) + cosh(x) +--R / +--R 7 6 +--R sinh(x) + (4cosh(x) + 3%i)sinh(x) +--R + +--R 2 5 +--R (6cosh(x) + 10%i cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 12%i cosh(x) - 2cosh(x) + 5%i)sinh(x) +--R + +--R 4 3 3 +--R (cosh(x) + 6%i cosh(x) + 12%i cosh(x) - 5)sinh(x) +--R + +--R 4 3 2 2 +--R (%i cosh(x) + 2cosh(x) + 12%i cosh(x) - 8cosh(x) + %i)sinh(x) +--R + +--R 4 3 2 +--R (cosh(x) + 6%i cosh(x) - 6cosh(x) + 2%i cosh(x) - 3)sinh(x) +--R + +--R 4 3 +--R %i cosh(x) - 2cosh(x) - 2cosh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 100 + +--S 101 of 530 +t0520:= sech(x)^2/(%i+sinh(x)) +--R +--R +--R 2 +--R sech(x) +--R (100) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 101 + +--S 102 of 530 +r0520:= -1/3/cosh(x)^3*(2*%i*sinh(x)*cosh(x)^2+%i*sinh(x)+1) +--R +--R +--R 2 +--R (- 2%i cosh(x) - %i)sinh(x) - 1 +--R (101) -------------------------------- +--R 3 +--R 3cosh(x) +--R Type: Expression(Complex(Integer)) +--E 102 + +--S 103 of 530 +a0520:= integrate(t0520,x) +--R +--R +--R (102) +--R - 8sinh(x) - 8cosh(x) - 4%i +--R / +--R 4 3 +--R 3sinh(x) + (12cosh(x) + 6%i)sinh(x) +--R + +--R 2 2 +--R (18cosh(x) + 18%i cosh(x))sinh(x) +--R + +--R 3 2 4 3 +--R (12cosh(x) + 18%i cosh(x) + 6%i)sinh(x) + 3cosh(x) + 6%i cosh(x) +--R + +--R 6%i cosh(x) - 3 +--R Type: Union(Expression(Complex(Integer)),...) +--E 103 + +--S 104 of 530 +m0520:= a0520-r0520 +--R +--R +--R (103) +--R 2 5 +--R (2%i cosh(x) + %i)sinh(x) +--R + +--R 3 2 4 +--R (8%i cosh(x) - 4cosh(x) + 4%i cosh(x) - 1)sinh(x) +--R + +--R 4 3 2 3 +--R (12%i cosh(x) - 12cosh(x) + 6%i cosh(x) - 2cosh(x) + 2%i)sinh(x) +--R + +--R 5 4 3 2 +--R 8%i cosh(x) - 12cosh(x) + 4%i cosh(x) - 4cosh(x) + 6%i cosh(x) +--R + +--R - 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 2%i cosh(x) - 4cosh(x) + %i cosh(x) - 10cosh(x) + 4%i cosh(x) +--R + +--R - 2cosh(x) + %i +--R * +--R sinh(x) +--R + +--R 4 3 +--R - 7cosh(x) - 2%i cosh(x) + 2%i cosh(x) - 1 +--R / +--R 3 4 4 3 3 +--R 3cosh(x) sinh(x) + (12cosh(x) + 6%i cosh(x) )sinh(x) +--R + +--R 5 4 2 +--R (18cosh(x) + 18%i cosh(x) )sinh(x) +--R + +--R 6 5 3 7 +--R (12cosh(x) + 18%i cosh(x) + 6%i cosh(x) )sinh(x) + 3cosh(x) +--R + +--R 6 4 3 +--R 6%i cosh(x) + 6%i cosh(x) - 3cosh(x) +--R Type: Expression(Complex(Integer)) +--E 104 + +--S 105 of 530 +d0520:= D(m0520,x) +--R +--R +--R (104) +--R 2 8 +--R (- 2%i cosh(x) - 3%i)sinh(x) +--R + +--R 3 2 7 +--R (- 12%i cosh(x) + 4cosh(x) - 18%i cosh(x) + 3)sinh(x) +--R + +--R 4 3 2 6 +--R (- 28%i cosh(x) + 20cosh(x) - 46%i cosh(x) + 12cosh(x) - 9%i)sinh(x) +--R + +--R 5 4 3 2 +--R - 28%i cosh(x) + 36cosh(x) - 62%i cosh(x) + 21cosh(x) +--R + +--R - 42%i cosh(x) + 9 +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 20cosh(x) - 40%i cosh(x) + 14cosh(x) - 75%i cosh(x) + 24cosh(x) +--R + +--R - 9%i +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 28%i cosh(x) - 20cosh(x) + 2%i cosh(x) + 5cosh(x) - 64%i cosh(x) +--R + +--R 2 +--R 18cosh(x) - 30%i cosh(x) + 9 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 28%i cosh(x) - 36cosh(x) + 22%i cosh(x) + 24cosh(x) +--R + +--R 4 3 2 +--R - 27%i cosh(x) - 8cosh(x) - 32%i cosh(x) + 12cosh(x) - 3%i +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 12%i cosh(x) - 20cosh(x) + 14%i cosh(x) + 35cosh(x) +--R + +--R 5 4 3 2 +--R - 6%i cosh(x) - 19cosh(x) - 14%i cosh(x) + cosh(x) - 6%i cosh(x) +--R + +--R 3 +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R 2%i cosh(x) - 4cosh(x) + 3%i cosh(x) + 14cosh(x) - %i cosh(x) +--R + +--R 5 4 3 2 +--R - 8cosh(x) - 3%i cosh(x) - 2cosh(x) - %i cosh(x) +--R / +--R 4 6 5 4 5 +--R 3cosh(x) sinh(x) + (18cosh(x) + 6%i cosh(x) )sinh(x) +--R + +--R 6 5 4 4 +--R (45cosh(x) + 30%i cosh(x) + 3cosh(x) )sinh(x) +--R + +--R 7 6 5 4 3 +--R (60cosh(x) + 60%i cosh(x) + 12cosh(x) + 12%i cosh(x) )sinh(x) +--R + +--R 8 7 6 5 4 +--R (45cosh(x) + 60%i cosh(x) + 18cosh(x) + 36%i cosh(x) - 3cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R 18cosh(x) + 30%i cosh(x) + 12cosh(x) + 36%i cosh(x) - 6cosh(x) +--R + +--R 4 +--R 6%i cosh(x) +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R 3cosh(x) + 6%i cosh(x) + 3cosh(x) + 12%i cosh(x) - 3cosh(x) +--R + +--R 5 4 +--R 6%i cosh(x) - 3cosh(x) +--R Type: Expression(Complex(Integer)) +--E 105 + +--S 106 of 530 +t0521:= sech(x)^3/(%i+sinh(x)) +--R +--R +--R 3 +--R sech(x) +--R (105) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 106 + +--S 107 of 530 +r0521:= -3/8*%i*atan(sinh(x))+%i/(8*%i-8*sinh(x))+_ + 1/8/(%i+sinh(x))^2-%i/(4*%i+4*sinh(x)) +--R +--R +--R (106) +--R 3 3 3 2 3 3 +--R (- - %i sinh(x) + - sinh(x) - - %i sinh(x) + -)atan(sinh(x)) +--R 8 8 8 8 +--R + +--R 3 2 3 1 +--R - - %i sinh(x) + - sinh(x) - - %i +--R 8 8 4 +--R / +--R 3 2 +--R sinh(x) + %i sinh(x) + sinh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 107 + +--S 108 of 530 +a0521:= integrate(t0521,x) +--R +--R +--R (107) +--R 6 5 +--R 3sinh(x) + (18cosh(x) + 6%i)sinh(x) +--R + +--R 2 4 +--R (45cosh(x) + 30%i cosh(x) + 3)sinh(x) +--R + +--R 3 2 3 +--R (60cosh(x) + 60%i cosh(x) + 12cosh(x) + 12%i)sinh(x) +--R + +--R 4 3 2 2 +--R (45cosh(x) + 60%i cosh(x) + 18cosh(x) + 36%i cosh(x) - 3)sinh(x) +--R + +--R 5 4 3 2 +--R 18cosh(x) + 30%i cosh(x) + 12cosh(x) + 36%i cosh(x) +--R + +--R - 6cosh(x) + 6%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 3cosh(x) + 6%i cosh(x) + 3cosh(x) + 12%i cosh(x) - 3cosh(x) +--R + +--R 6%i cosh(x) - 3 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 6 5 +--R - 3sinh(x) + (- 18cosh(x) - 6%i)sinh(x) +--R + +--R 2 4 +--R (- 45cosh(x) - 30%i cosh(x) - 3)sinh(x) +--R + +--R 3 2 3 +--R (- 60cosh(x) - 60%i cosh(x) - 12cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 2 +--R (- 45cosh(x) - 60%i cosh(x) - 18cosh(x) - 36%i cosh(x) + 3) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 18cosh(x) - 30%i cosh(x) - 12cosh(x) - 36%i cosh(x) +--R + +--R 6cosh(x) - 6%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 3cosh(x) - 6%i cosh(x) - 3cosh(x) - 12%i cosh(x) + 3cosh(x) +--R + +--R - 6%i cosh(x) + 3 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 5 4 +--R - 6%i sinh(x) + (- 30%i cosh(x) + 12)sinh(x) +--R + +--R 2 3 +--R (- 60%i cosh(x) + 48cosh(x) - 4%i)sinh(x) +--R + +--R 3 2 2 +--R (- 60%i cosh(x) + 72cosh(x) - 12%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R (- 30%i cosh(x) + 48cosh(x) - 12%i cosh(x) - 24cosh(x) - 6%i)sinh(x) +--R + +--R 5 4 3 2 +--R - 6%i cosh(x) + 12cosh(x) - 4%i cosh(x) - 12cosh(x) - 6%i cosh(x) +--R / +--R 6 5 +--R 8sinh(x) + (48cosh(x) + 16%i)sinh(x) +--R + +--R 2 4 +--R (120cosh(x) + 80%i cosh(x) + 8)sinh(x) +--R + +--R 3 2 3 +--R (160cosh(x) + 160%i cosh(x) + 32cosh(x) + 32%i)sinh(x) +--R + +--R 4 3 2 2 +--R (120cosh(x) + 160%i cosh(x) + 48cosh(x) + 96%i cosh(x) - 8)sinh(x) +--R + +--R 5 4 3 2 +--R 48cosh(x) + 80%i cosh(x) + 32cosh(x) + 96%i cosh(x) - 16cosh(x) +--R + +--R 16%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 8cosh(x) + 16%i cosh(x) + 8cosh(x) + 32%i cosh(x) - 8cosh(x) +--R + +--R 16%i cosh(x) - 8 +--R Type: Union(Expression(Complex(Integer)),...) +--E 108 + +--S 109 of 530 +m0521:= a0521-r0521 +--R +--R +--R (108) +--R 3 9 9 9 8 +--R - sinh(x) + (- cosh(x) + - %i)sinh(x) +--R 8 4 8 +--R + +--R 45 2 7 +--R (-- cosh(x) + 6%i cosh(x))sinh(x) +--R 8 +--R + +--R 15 3 105 2 6 +--R (-- cosh(x) + --- %i cosh(x) + 3%i)sinh(x) +--R 2 8 +--R + +--R 45 4 3 3 2 9 5 +--R (-- cosh(x) + 15%i cosh(x) + - cosh(x) + 12%i cosh(x) - -)sinh(x) +--R 8 8 4 +--R + +--R 9 5 75 4 3 3 159 2 +--R - cosh(x) + -- %i cosh(x) + - cosh(x) + --- %i cosh(x) +--R 4 8 2 8 +--R + +--R 15 9 +--R - -- cosh(x) + - %i +--R 2 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 6 5 9 4 3 +--R - cosh(x) + 3%i cosh(x) + - cosh(x) + 18%i cosh(x) +--R 8 4 +--R + +--R 81 2 +--R - -- cosh(x) + 6%i cosh(x) - 3 +--R 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 5 39 4 15 3 +--R - %i cosh(x) + - cosh(x) + -- %i cosh(x) - -- cosh(x) +--R 8 2 4 2 +--R + +--R 51 2 +--R -- %i cosh(x) - 6cosh(x) +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 27 4 3 +--R - cosh(x) + 3%i cosh(x) - -- cosh(x) + 3%i cosh(x) +--R 8 8 +--R + +--R 39 2 9 +--R - -- cosh(x) - - +--R 8 8 +--R * +--R sinh(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R - %i cosh(x) - - cosh(x) + - %i cosh(x) - - cosh(x) +--R 8 4 8 2 +--R + +--R 3 2 3 3 +--R - - %i cosh(x) - - cosh(x) - - %i +--R 8 4 8 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 3 9 9 9 8 +--R - - sinh(x) + (- - cosh(x) - - %i)sinh(x) +--R 8 4 8 +--R + +--R 45 2 7 +--R (- -- cosh(x) - 6%i cosh(x))sinh(x) +--R 8 +--R + +--R 15 3 105 2 6 +--R (- -- cosh(x) - --- %i cosh(x) - 3%i)sinh(x) +--R 2 8 +--R + +--R 45 4 3 3 2 9 +--R (- -- cosh(x) - 15%i cosh(x) - - cosh(x) - 12%i cosh(x) + -) +--R 8 8 4 +--R * +--R 5 +--R sinh(x) +--R + +--R 9 5 75 4 3 3 159 2 +--R - - cosh(x) - -- %i cosh(x) - - cosh(x) - --- %i cosh(x) +--R 4 8 2 8 +--R + +--R 15 9 +--R -- cosh(x) - - %i +--R 2 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 6 5 9 4 3 +--R - - cosh(x) - 3%i cosh(x) - - cosh(x) - 18%i cosh(x) +--R 8 4 +--R + +--R 81 2 +--R -- cosh(x) - 6%i cosh(x) + 3 +--R 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 5 39 4 15 3 +--R - - %i cosh(x) - - cosh(x) - -- %i cosh(x) + -- cosh(x) +--R 8 2 4 2 +--R + +--R 51 2 +--R - -- %i cosh(x) + 6cosh(x) +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 27 4 3 +--R - - cosh(x) - 3%i cosh(x) + -- cosh(x) - 3%i cosh(x) +--R 8 8 +--R + +--R 39 2 9 +--R -- cosh(x) + - +--R 8 8 +--R * +--R sinh(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R - - %i cosh(x) + - cosh(x) - - %i cosh(x) + - cosh(x) +--R 8 4 8 2 +--R + +--R 3 2 3 3 +--R - %i cosh(x) + - cosh(x) + - %i +--R 8 4 8 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 3 9 9 9 8 +--R - %i sinh(x) + (- %i cosh(x) - -)sinh(x) +--R 8 4 8 +--R + +--R 45 2 7 +--R (-- %i cosh(x) - 6cosh(x))sinh(x) +--R 8 +--R + +--R 15 3 105 2 6 +--R (-- %i cosh(x) - --- cosh(x) - 3)sinh(x) +--R 2 8 +--R + +--R 45 4 3 3 2 9 +--R (-- %i cosh(x) - 15cosh(x) + - %i cosh(x) - 12cosh(x) - - %i) +--R 8 8 4 +--R * +--R 5 +--R sinh(x) +--R + +--R 9 5 75 4 3 3 159 2 +--R - %i cosh(x) - -- cosh(x) + - %i cosh(x) - --- cosh(x) +--R 4 8 2 8 +--R + +--R 15 9 +--R - -- %i cosh(x) - - +--R 2 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 6 5 9 4 3 +--R - %i cosh(x) - 3cosh(x) + - %i cosh(x) - 18cosh(x) +--R 8 4 +--R + +--R 81 2 +--R - -- %i cosh(x) - 6cosh(x) - 3%i +--R 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 5 39 4 15 3 +--R - - cosh(x) + - %i cosh(x) - -- cosh(x) - -- %i cosh(x) +--R 8 2 4 2 +--R + +--R 51 2 +--R - -- cosh(x) - 6%i cosh(x) +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 27 4 3 +--R - %i cosh(x) - 3cosh(x) - -- %i cosh(x) - 3cosh(x) +--R 8 8 +--R + +--R 39 2 9 +--R - -- %i cosh(x) - - %i +--R 8 8 +--R * +--R sinh(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R - - cosh(x) - - %i cosh(x) - - cosh(x) - - %i cosh(x) +--R 8 4 8 2 +--R + +--R 3 2 3 3 +--R - cosh(x) - - %i cosh(x) + - +--R 8 4 8 +--R * +--R atan(sinh(x)) +--R + +--R 3 8 3 9 7 +--R - - %i sinh(x) + (- - %i cosh(x) + -)sinh(x) +--R 8 2 8 +--R + +--R 15 2 15 1 6 +--R (- -- %i cosh(x) + -- cosh(x) + - %i)sinh(x) +--R 8 4 8 +--R + +--R 27 2 9 5 +--R (-- cosh(x) - -)sinh(x) +--R 8 8 +--R + +--R 15 4 3 3 3 2 1 23 4 +--R (-- %i cosh(x) - - cosh(x) - - %i cosh(x) - - cosh(x) - -- %i)sinh(x) +--R 8 2 2 4 8 +--R + +--R 3 5 33 4 3 19 2 +--R - %i cosh(x) - -- cosh(x) - 3%i cosh(x) + -- cosh(x) +--R 2 8 4 +--R + +--R 7 13 +--R - - %i cosh(x) - -- +--R 2 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 9 5 15 4 3 +--R - %i cosh(x) - - cosh(x) - -- %i cosh(x) + 6cosh(x) +--R 8 4 8 +--R + +--R 21 2 15 29 +--R -- %i cosh(x) - -- cosh(x) - -- %i +--R 8 4 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 19 4 3 21 2 +--R - - cosh(x) + -- cosh(x) + 5%i cosh(x) - -- cosh(x) - 5%i cosh(x) +--R 8 8 8 +--R + +--R 5 +--R - +--R 8 +--R * +--R sinh(x) +--R + +--R 1 6 1 5 7 4 1 3 7 2 +--R - %i cosh(x) + - cosh(x) + - %i cosh(x) - - cosh(x) - - %i cosh(x) +--R 4 4 4 2 4 +--R + +--R 1 1 +--R - cosh(x) - - %i +--R 4 4 +--R / +--R 9 8 2 7 +--R sinh(x) + (6cosh(x) + 3%i)sinh(x) + (15cosh(x) + 16%i cosh(x))sinh(x) +--R + +--R 3 2 6 +--R (20cosh(x) + 35%i cosh(x) + 8%i)sinh(x) +--R + +--R 4 3 2 5 +--R (15cosh(x) + 40%i cosh(x) + cosh(x) + 32%i cosh(x) - 6)sinh(x) +--R + +--R 5 4 3 2 +--R 6cosh(x) + 25%i cosh(x) + 4cosh(x) + 53%i cosh(x) - 20cosh(x) +--R + +--R 6%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) + 8%i cosh(x) + 6cosh(x) + 48%i cosh(x) - 27cosh(x) +--R + +--R 16%i cosh(x) - 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R %i cosh(x) + 4cosh(x) + 26%i cosh(x) - 20cosh(x) + 17%i cosh(x) +--R + +--R - 16cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R (cosh(x) + 8%i cosh(x) - 9cosh(x) + 8%i cosh(x) - 13cosh(x) - 3) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R %i cosh(x) - 2cosh(x) + %i cosh(x) - 4cosh(x) - %i cosh(x) +--R + +--R - 2cosh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 109 + +--S 110 of 530 +d0521:= D(m0521,x) +--R +--R +--R (109) +--R 9 8 +--R 16sinh(x) + (63cosh(x) + 16%i)sinh(x) +--R + +--R 2 7 +--R (88cosh(x) + 62%i cosh(x) + 32)sinh(x) +--R + +--R 3 2 6 +--R (36cosh(x) + 82%i cosh(x) + 126cosh(x) + 32%i)sinh(x) +--R + +--R 4 3 2 5 +--R (- 40cosh(x) + 22%i cosh(x) + 180cosh(x) + 122%i cosh(x) + 16)sinh(x) +--R + +--R 5 4 3 2 +--R - 70cosh(x) - 54%i cosh(x) + 98cosh(x) + 162%i cosh(x) +--R + +--R 64cosh(x) + 16%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 56cosh(x) - 70%i cosh(x) - 8cosh(x) + 68%i cosh(x) + 96cosh(x) +--R + +--R 58%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 28cosh(x) - 42%i cosh(x) - 30cosh(x) - 28%i cosh(x) +--R + +--R 3 2 +--R 64cosh(x) + 78%i cosh(x) + 2cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 8cosh(x) - 14%i cosh(x) - 12cosh(x) - 30%i cosh(x) + 16cosh(x) +--R + +--R 3 2 +--R 46%i cosh(x) + 4cosh(x) - 2%i cosh(x) +--R * +--R sinh(x) +--R + +--R 9 8 7 6 4 +--R - cosh(x) - 2%i cosh(x) - 2cosh(x) - 6%i cosh(x) + 10%i cosh(x) +--R + +--R 3 2 +--R 2cosh(x) - 2%i cosh(x) + cosh(x) +--R / +--R 13 12 +--R sinh(x) + (8cosh(x) + 3%i)sinh(x) +--R + +--R 2 11 +--R (28cosh(x) + 22%i cosh(x) + 2)sinh(x) +--R + +--R 3 2 10 +--R (56cosh(x) + 70%i cosh(x) + 14cosh(x) + 14%i)sinh(x) +--R + +--R 4 3 2 9 +--R (70cosh(x) + 126%i cosh(x) + 44cosh(x) + 86%i cosh(x) - 5)sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) + 140%i cosh(x) + 82cosh(x) + 230%i cosh(x) - 26cosh(x) +--R + +--R 25%i +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) + 98%i cosh(x) + 100cosh(x) + 352%i cosh(x) +--R + +--R 2 +--R - 56cosh(x) + 124%i cosh(x) - 20 +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 8cosh(x) + 42%i cosh(x) + 82cosh(x) + 340%i cosh(x) - 64cosh(x) +--R + +--R 2 +--R 268%i cosh(x) - 84cosh(x) + 20%i +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 10%i cosh(x) + 44cosh(x) + 214%i cosh(x) - 40cosh(x) +--R + +--R 3 2 +--R 332%i cosh(x) - 152cosh(x) + 76%i cosh(x) - 25 +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R %i cosh(x) + 14cosh(x) + 86%i cosh(x) - 10cosh(x) +--R + +--R 4 3 2 +--R 260%i cosh(x) - 156cosh(x) + 124%i cosh(x) - 76cosh(x) + 5%i +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 2cosh(x) + 20%i cosh(x) + 4cosh(x) + 134%i cosh(x) - 100cosh(x) +--R + +--R 3 2 +--R 112%i cosh(x) - 100cosh(x) + 14%i cosh(x) - 14 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 2%i cosh(x) + 4cosh(x) + 46%i cosh(x) - 42cosh(x) + 60%i cosh(x) +--R + +--R 3 2 +--R - 72cosh(x) + 14%i cosh(x) - 26cosh(x) - 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 10%i cosh(x) - 12cosh(x) + 18%i cosh(x) - 30cosh(x) +--R + +--R 3 2 +--R 6%i cosh(x) - 20cosh(x) - 2%i cosh(x) - 3 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 3 +--R %i cosh(x) - 2cosh(x) + 2%i cosh(x) - 6cosh(x) - 6cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) - 2cosh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 110 + +--S 111 of 530 +t0522:= sech(x)^4/(%i+sinh(x)) +--R +--R +--R 4 +--R sech(x) +--R (110) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 111 + +--S 112 of 530 +r0522:= -1/15/cosh(x)^5*(8*%i*cosh(x)^4*sinh(x)+_ + 4*%i*sinh(x)*cosh(x)^2+3*%i*sinh(x)+3) +--R +--R +--R 4 2 +--R (- 8%i cosh(x) - 4%i cosh(x) - 3%i)sinh(x) - 3 +--R (111) ------------------------------------------------ +--R 5 +--R 15cosh(x) +--R Type: Expression(Complex(Integer)) +--E 112 + +--S 113 of 530 +a0522:= integrate(t0522,x) +--R +--R +--R (112) +--R 2 2 +--R - 96sinh(x) + (- 192cosh(x) - 16%i)sinh(x) - 96cosh(x) - 48%i cosh(x) +--R + +--R - 32 +--R / +--R 7 6 +--R 15sinh(x) + (105cosh(x) + 30%i)sinh(x) +--R + +--R 2 5 +--R (315cosh(x) + 180%i cosh(x) + 30)sinh(x) +--R + +--R 3 2 4 +--R (525cosh(x) + 450%i cosh(x) + 150cosh(x) + 90%i)sinh(x) +--R + +--R 4 3 2 3 +--R (525cosh(x) + 600%i cosh(x) + 300cosh(x) + 360%i cosh(x))sinh(x) +--R + +--R 5 4 3 2 +--R (315cosh(x) + 450%i cosh(x) + 300cosh(x) + 540%i cosh(x) + 90%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 105cosh(x) + 180%i cosh(x) + 150cosh(x) + 360%i cosh(x) +--R + +--R 180%i cosh(x) - 15 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 2 +--R 15cosh(x) + 30%i cosh(x) + 30cosh(x) + 90%i cosh(x) + 90%i cosh(x) +--R + +--R - 45cosh(x) + 30%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 113 + +--S 114 of 530 +m0522:= a0522-r0522 +--R +--R +--R (113) +--R 4 2 8 +--R (8%i cosh(x) + 4%i cosh(x) + 3%i)sinh(x) +--R + +--R 5 4 3 2 +--R 56%i cosh(x) - 16cosh(x) + 28%i cosh(x) - 8cosh(x) + 21%i cosh(x) +--R + +--R - 3 +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 168%i cosh(x) - 96cosh(x) + 100%i cosh(x) - 48cosh(x) +--R + +--R 2 +--R 71%i cosh(x) - 15cosh(x) + 12%i +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 280%i cosh(x) - 240cosh(x) + 220%i cosh(x) - 168cosh(x) +--R + +--R 3 2 +--R 145%i cosh(x) - 51cosh(x) + 66%i cosh(x) - 12 +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 280%i cosh(x) - 320cosh(x) + 300%i cosh(x) - 352cosh(x) +--R + +--R 4 3 2 +--R 185%i cosh(x) - 111cosh(x) + 150%i cosh(x) - 42cosh(x) + 18%i +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 168%i cosh(x) - 240cosh(x) + 244%i cosh(x) - 408cosh(x) +--R + +--R 5 4 3 2 +--R 143%i cosh(x) - 177cosh(x) + 180%i cosh(x) - 72cosh(x) +--R + +--R 72%i cosh(x) - 18 +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 56%i cosh(x) - 96cosh(x) + 108%i cosh(x) - 240cosh(x) +--R + +--R 6 5 4 3 +--R 61%i cosh(x) - 261cosh(x) + 112%i cosh(x) - 60cosh(x) +--R + +--R 2 +--R 104%i cosh(x) - 36cosh(x) + 15%i +--R * +--R 2 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 8%i cosh(x) - 16cosh(x) + 20%i cosh(x) - 56cosh(x) +--R + +--R 7 6 5 4 +--R 11%i cosh(x) - 249cosh(x) + 2%i cosh(x) - 28cosh(x) +--R + +--R 3 2 +--R 60%i cosh(x) - 26cosh(x) + 27%i cosh(x) - 9 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 2 +--R - 93cosh(x) - 42%i cosh(x) - 26cosh(x) + 18%i cosh(x) + 18%i cosh(x) +--R + +--R - 9cosh(x) + 6%i +--R / +--R 5 7 6 5 6 +--R 15cosh(x) sinh(x) + (105cosh(x) + 30%i cosh(x) )sinh(x) +--R + +--R 7 6 5 5 +--R (315cosh(x) + 180%i cosh(x) + 30cosh(x) )sinh(x) +--R + +--R 8 7 6 5 4 +--R (525cosh(x) + 450%i cosh(x) + 150cosh(x) + 90%i cosh(x) )sinh(x) +--R + +--R 9 8 7 6 3 +--R (525cosh(x) + 600%i cosh(x) + 300cosh(x) + 360%i cosh(x) )sinh(x) +--R + +--R 10 9 8 7 +--R 315cosh(x) + 450%i cosh(x) + 300cosh(x) + 540%i cosh(x) +--R + +--R 5 +--R 90%i cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 105cosh(x) + 180%i cosh(x) + 150cosh(x) + 360%i cosh(x) +--R + +--R 6 5 +--R 180%i cosh(x) - 15cosh(x) +--R * +--R sinh(x) +--R + +--R 12 11 10 9 +--R 15cosh(x) + 30%i cosh(x) + 30cosh(x) + 90%i cosh(x) +--R + +--R 7 6 5 +--R 90%i cosh(x) - 45cosh(x) + 30%i cosh(x) +--R Type: Expression(Complex(Integer)) +--E 114 + +--S 115 of 530 +d0522:= D(m0522,x) +--R +--R +--R (114) +--R 4 2 16 +--R (- 8%i cosh(x) - 12%i cosh(x) - 15%i)sinh(x) +--R + +--R 5 4 3 2 +--R - 112%i cosh(x) + 32cosh(x) - 168%i cosh(x) + 48cosh(x) +--R + +--R - 210%i cosh(x) + 45 +--R * +--R 15 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 720%i cosh(x) + 416cosh(x) - 1088%i cosh(x) + 624cosh(x) +--R + +--R 2 +--R - 1362%i cosh(x) + 570cosh(x) - 60%i +--R * +--R 14 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 2800%i cosh(x) + 2464cosh(x) - 4312%i cosh(x) + 3888cosh(x) +--R + +--R 3 2 +--R - 5418%i cosh(x) + 3543cosh(x) - 780%i cosh(x) + 300 +--R * +--R 13 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 7280%i cosh(x) + 8736cosh(x) - 11648%i cosh(x) + 15280cosh(x) +--R + +--R 4 3 2 +--R - 14582%i cosh(x) + 14184cosh(x) - 4440%i cosh(x) + 3300cosh(x) +--R * +--R 12 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - 13104%i cosh(x) + 20384cosh(x) - 22568%i cosh(x) + 41712cosh(x) +--R + +--R 5 4 3 2 +--R - 27338%i cosh(x) + 40357cosh(x) - 14760%i cosh(x) + 16872cosh(x) +--R + +--R - 300%i cosh(x) + 840 +--R * +--R 11 +--R sinh(x) +--R + +--R 10 9 8 +--R - 16016%i cosh(x) + 32032cosh(x) - 32032%i cosh(x) +--R + +--R 7 6 5 4 +--R 81840cosh(x) - 35002%i cosh(x) + 85070cosh(x) - 31684%i cosh(x) +--R + +--R 3 2 +--R 52728cosh(x) - 2316%i cosh(x) + 7860cosh(x) + 390%i +--R * +--R 10 +--R sinh(x) +--R + +--R 11 10 9 +--R - 11440%i cosh(x) + 32032cosh(x) - 33176%i cosh(x) +--R + +--R 8 7 6 5 +--R 114928cosh(x) - 27874%i cosh(x) + 134695cosh(x) - 45220%i cosh(x) +--R + +--R 4 3 2 +--R 111300cosh(x) - 8100%i cosh(x) + 33120cosh(x) + 2640%i cosh(x) +--R + +--R 1290 +--R * +--R 9 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 13728cosh(x) - 24024%i cosh(x) + 109296cosh(x) - 9636%i cosh(x) +--R + +--R 7 6 5 4 +--R 159636cosh(x) - 41712%i cosh(x) + 164972cosh(x) - 17108%i cosh(x) +--R + +--R 3 2 +--R 82308cosh(x) + 7842%i cosh(x) + 9900cosh(x) + 900%i +--R * +--R 8 +--R sinh(x) +--R + +--R 13 12 11 +--R 11440%i cosh(x) - 13728cosh(x) - 10296%i cosh(x) +--R + +--R 10 9 8 7 +--R 55440cosh(x) + 1386%i cosh(x) + 139263cosh(x) - 20720%i cosh(x) +--R + +--R 6 5 4 3 +--R 172208cosh(x) - 25432%i cosh(x) + 132496cosh(x) + 12624%i cosh(x) +--R + +--R 2 +--R 33180cosh(x) + 5280%i cosh(x) + 1200 +--R * +--R 7 +--R sinh(x) +--R + +--R 14 13 11 +--R 16016%i cosh(x) - 32032cosh(x) - 14256cosh(x) +--R + +--R 10 9 8 7 +--R - 6006%i cosh(x) + 86934cosh(x) + 3196%i cosh(x) + 122576cosh(x) +--R + +--R 6 5 4 3 +--R - 30168%i cosh(x) + 142216cosh(x) + 9612%i cosh(x) + 63132cosh(x) +--R + +--R 2 +--R 13128%i cosh(x) + 7020cosh(x) + 960%i +--R * +--R 6 +--R sinh(x) +--R + +--R 15 14 13 +--R 13104%i cosh(x) - 32032cosh(x) + 3640%i cosh(x) +--R + +--R 12 11 10 +--R - 54384cosh(x) - 20574%i cosh(x) + 37725cosh(x) +--R + +--R 9 8 7 6 +--R 18156%i cosh(x) + 53812cosh(x) - 29032%i cosh(x) + 100256cosh(x) +--R + +--R 5 4 3 2 +--R - 3536%i cosh(x) + 74320cosh(x) + 16944%i cosh(x) + 17328cosh(x) +--R + +--R 4260%i cosh(x) + 720 +--R * +--R 5 +--R sinh(x) +--R + +--R 16 15 14 13 +--R 7280%i cosh(x) - 20384cosh(x) + 2912%i cosh(x) - 51696cosh(x) +--R + +--R 12 11 10 +--R - 24762%i cosh(x) + 12000cosh(x) + 22760%i cosh(x) +--R + +--R 9 8 7 6 +--R 9340cosh(x) - 18440%i cosh(x) + 42600cosh(x) - 17452%i cosh(x) +--R + +--R 5 4 3 2 +--R 55268cosh(x) + 10264%i cosh(x) + 23052cosh(x) + 7536%i cosh(x) +--R + +--R 2700cosh(x) + 525%i +--R * +--R 4 +--R sinh(x) +--R + +--R 17 16 15 14 +--R 2800%i cosh(x) - 8736cosh(x) + 1288%i cosh(x) - 28592cosh(x) +--R + +--R 13 12 11 +--R - 16718%i cosh(x) + 4143cosh(x) + 18968%i cosh(x) +--R + +--R 10 9 8 7 +--R - 3608cosh(x) - 2748%i cosh(x) + 6568cosh(x) - 19856%i cosh(x) +--R + +--R 6 5 4 3 +--R 25636cosh(x) - 624%i cosh(x) + 17776cosh(x) + 6144%i cosh(x) +--R + +--R 2 +--R 4128cosh(x) + 1530%i cosh(x) + 285 +--R * +--R 3 +--R sinh(x) +--R + +--R 18 17 16 15 +--R 720%i cosh(x) - 2464cosh(x) + 352%i cosh(x) - 9840cosh(x) +--R + +--R 14 13 12 +--R - 6782%i cosh(x) + 1954cosh(x) + 10500%i cosh(x) +--R + +--R 11 10 9 8 +--R - 2632cosh(x) + 5668%i cosh(x) - 3964cosh(x) - 11378%i cosh(x) +--R + +--R 7 6 5 4 +--R 7540cosh(x) - 5224%i cosh(x) + 8004cosh(x) + 1680%i cosh(x) +--R + +--R 3 2 +--R 3096cosh(x) + 1464%i cosh(x) + 450cosh(x) + 120%i +--R * +--R 2 +--R sinh(x) +--R + +--R 19 18 17 16 +--R 112%i cosh(x) - 416cosh(x) + 56%i cosh(x) - 1968cosh(x) +--R + +--R 15 14 13 12 +--R - 1558%i cosh(x) + 677cosh(x) + 3396%i cosh(x) - 676cosh(x) +--R + +--R 11 10 9 8 +--R 4172%i cosh(x) - 2944cosh(x) - 3136%i cosh(x) + 1766cosh(x) +--R + +--R 7 6 5 4 +--R - 3168%i cosh(x) + 2096cosh(x) - 468%i cosh(x) + 1168cosh(x) +--R + +--R 3 2 +--R 414%i cosh(x) + 237cosh(x) + 180%i cosh(x) + 60 +--R * +--R sinh(x) +--R + +--R 20 19 18 17 +--R 8%i cosh(x) - 32cosh(x) + 4%i cosh(x) - 176cosh(x) +--R + +--R 16 15 14 13 +--R - 157%i cosh(x) + 100cosh(x) + 480%i cosh(x) - 76cosh(x) +--R + +--R 12 11 10 9 +--R 924%i cosh(x) - 684cosh(x) - 278%i cosh(x) + 352cosh(x) +--R + +--R 8 7 6 5 +--R - 636%i cosh(x) + 324cosh(x) - 272%i cosh(x) + 156cosh(x) +--R + +--R 4 3 2 +--R - 61%i cosh(x) + 36cosh(x) - 12%i cosh(x) +--R / +--R 6 14 7 6 13 +--R 15cosh(x) sinh(x) + (210cosh(x) + 60%i cosh(x) )sinh(x) +--R + +--R 8 7 12 +--R (1365cosh(x) + 780%i cosh(x) )sinh(x) +--R + +--R 9 8 6 11 +--R (5460cosh(x) + 4680%i cosh(x) + 300%i cosh(x) )sinh(x) +--R + +--R 10 9 7 6 +--R (15015cosh(x) + 17160%i cosh(x) + 3300%i cosh(x) - 300cosh(x) ) +--R * +--R 10 +--R sinh(x) +--R + +--R 11 10 8 7 +--R 30030cosh(x) + 42900%i cosh(x) + 16500%i cosh(x) - 3000cosh(x) +--R + +--R 6 +--R 540%i cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 12 11 9 8 +--R 45045cosh(x) + 77220%i cosh(x) + 49500%i cosh(x) - 13500cosh(x) +--R + +--R 7 6 +--R 4860%i cosh(x) - 930cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 13 12 10 +--R 51480cosh(x) + 102960%i cosh(x) + 99000%i cosh(x) +--R + +--R 9 8 7 6 +--R - 36000cosh(x) + 19440%i cosh(x) - 7500cosh(x) + 360%i cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 14 13 11 +--R 45045cosh(x) + 102960%i cosh(x) + 138600%i cosh(x) +--R + +--R 10 9 8 7 +--R - 63000cosh(x) + 45360%i cosh(x) - 26460cosh(x) + 2400%i cosh(x) +--R + +--R 6 +--R - 1260cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 15 14 12 +--R 30030cosh(x) + 77220%i cosh(x) + 138600%i cosh(x) +--R + +--R 11 10 9 +--R - 75600cosh(x) + 68040%i cosh(x) - 53340cosh(x) +--R + +--R 8 7 6 +--R 6840%i cosh(x) - 7680cosh(x) - 60%i cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 16 15 13 +--R 15015cosh(x) + 42900%i cosh(x) + 99000%i cosh(x) +--R + +--R 12 11 10 +--R - 63000cosh(x) + 68040%i cosh(x) - 67200cosh(x) +--R + +--R 9 8 7 6 +--R 10800%i cosh(x) - 19500cosh(x) - 660%i cosh(x) - 900cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 17 16 14 +--R 5460cosh(x) + 17160%i cosh(x) + 49500%i cosh(x) +--R + +--R 13 12 11 +--R - 36000cosh(x) + 45360%i cosh(x) - 54180cosh(x) +--R + +--R 10 9 8 7 +--R 10200%i cosh(x) - 26400cosh(x) - 2040%i cosh(x) - 3600cosh(x) +--R + +--R 6 +--R - 180%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 18 17 15 14 +--R 1365cosh(x) + 4680%i cosh(x) + 16500%i cosh(x) - 13500cosh(x) +--R + +--R 13 12 11 +--R 19440%i cosh(x) - 27300cosh(x) + 5760%i cosh(x) +--R + +--R 10 9 8 7 +--R - 20100cosh(x) - 2760%i cosh(x) - 5400cosh(x) - 900%i cosh(x) +--R + +--R 6 +--R - 345cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 19 18 16 15 +--R 210cosh(x) + 780%i cosh(x) + 3300%i cosh(x) - 3000cosh(x) +--R + +--R 14 13 12 11 +--R 4860%i cosh(x) - 7860cosh(x) + 1800%i cosh(x) - 8160cosh(x) +--R + +--R 10 9 8 7 +--R - 1740%i cosh(x) - 3600cosh(x) - 1260%i cosh(x) - 630cosh(x) +--R + +--R 6 +--R - 60%i cosh(x) +--R * +--R sinh(x) +--R + +--R 20 19 17 16 +--R 15cosh(x) + 60%i cosh(x) + 300%i cosh(x) - 300cosh(x) +--R + +--R 15 14 13 12 +--R 540%i cosh(x) - 990cosh(x) + 240%i cosh(x) - 1380cosh(x) +--R + +--R 11 10 9 8 +--R - 420%i cosh(x) - 900cosh(x) - 540%i cosh(x) - 225cosh(x) +--R + +--R 7 6 +--R - 180%i cosh(x) - 60cosh(x) +--R Type: Expression(Complex(Integer)) +--E 115 + +--S 116 of 530 +t0523:= csch(x)^2/(a+b*sinh(x)) +--R +--R +--R 2 +--R csch(x) +--R (115) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 116 + +--S 117 of 530 +r0523:= b*acoth(cosh(x))/a^2-_ + 2*b^2*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^2/_ + (a^2+b^2)^(1/2)-coth(x)/a +--R +--R +--R (116) +--R x +--R a tanh(-) - b +-------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R 2b atanh(-------------) + b\|b + a acoth(cosh(x)) - a coth(x)\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R ------------------------------------------------------------------------- +--R +-------+ +--R 2 | 2 2 +--R a \|b + a +--R Type: Expression(Integer) +--E 117 + +--S 118 of 530 +a0523:= integrate(t0523,x) +--R +--R +--R (117) +--R 2 2 2 2 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b)\|b + a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) + b)\|b + a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R +-------+ +--R | 2 2 +--R - 2a\|b + a +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 530 +m0523:= a0523-r0523 +--R +--R +--R (118) +--R 2 2 2 2 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b)\|b + a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) + b)\|b + a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 2 2 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) + 2b ) +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) + b)\|b + a +--R * +--R acoth(cosh(x)) +--R + +--R 2 +--R a coth(x)sinh(x) + 2a cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (a cosh(x) - a)coth(x) - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a )\|b + a +--R Type: Expression(Integer) +--E 119 + +--S 120 of 530 +d0523:= D(m0523,x) +--R +--R +--R (119) +--R 2 7 +--R a b sinh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- a b cosh(x) + a b)coth(x) + (- b + a b)cosh(x) +--R + +--R 2 3 2 +--R 6a b cosh(x) + b + a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (- 6a b cosh(x) - 2a cosh(x) + 6a b cosh(x) + 2a )coth(x) +--R + +--R 3 2 3 2 3 2 +--R (- 6b + 6a b)cosh(x) + (13a b + 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b + 4a b)cosh(x) - a b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 +--R - 15a b cosh(x) - 10a cosh(x) + 18a b cosh(x) +--R + +--R 3 2 +--R 10a cosh(x) - 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 4 2 3 3 +--R (- 15b + 15a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (18b + 2a b)cosh(x) + (- 2a b - 10a )cosh(x) - 3b - a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 +--R - 20a b cosh(x) - 20a cosh(x) + 32a b cosh(x) +--R + +--R 3 2 2 3 +--R 24a cosh(x) - 12a b cosh(x) - 4a +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 5 2 3 4 +--R (- 20b + 20a b)cosh(x) + (- 5a b + 20a )cosh(x) +--R + +--R 3 2 3 2 3 2 3 +--R (32b - 12a b)cosh(x) + (6a b - 16a )cosh(x) - 12b cosh(x) +--R + +--R 2 3 +--R - a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 2 4 +--R - 15a b cosh(x) - 20a cosh(x) + 33a b cosh(x) +--R + +--R 3 3 2 2 3 2 +--R 32a cosh(x) - 21a b cosh(x) - 12a cosh(x) + 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 6 2 3 5 +--R (- 15b + 15a b)cosh(x) + (- 14a b + 20a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (33b - 23a b)cosh(x) + (20a b - 8a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 21b + 9a b)cosh(x) + (- 6a b - 12a )cosh(x) + 3b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 2 5 +--R - 6a b cosh(x) - 10a cosh(x) + 18a b cosh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 22a cosh(x) - 18a b cosh(x) - 14a cosh(x) + 6a b cosh(x) +--R + +--R 3 +--R 2a +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 7 2 3 6 +--R (- 6b + 6a b)cosh(x) + (- 9a b + 10a )cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (18b - 16a b)cosh(x) + (19a b + 2a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 18b + 14a b)cosh(x) + (- 11a b - 10a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 4a b)cosh(x) + a b - 2a +--R * +--R sinh(x) +--R + +--R 2 8 3 7 2 6 3 5 +--R - a b cosh(x) - 2a cosh(x) + 4a b cosh(x) + 6a cosh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R - 6a b cosh(x) - 6a cosh(x) + 4a b cosh(x) + 2a cosh(x) - a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 8 2 3 7 3 2 6 +--R (- b + a b)cosh(x) + (- 2a b + 2a )cosh(x) + (4b - 4a b)cosh(x) +--R + +--R 2 3 5 3 2 4 +--R (6a b + 2a )cosh(x) + (- 6b + 6a b)cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (- 6a b - 2a )cosh(x) + (4b - 4a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 3 2 +--R - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 7 +--R - 2b sinh(x) +--R + +--R 2 2 2 2 2 2 3 +--R (2a b cosh(x) - 2a b )coth(x) - 2a b cosh(x) - 12b cosh(x) +--R + +--R 2 +--R - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 2 2 2 2 2 +--R (12a b cosh(x) + 4a b cosh(x) - 12a b cosh(x) - 4a b)coth(x) +--R + +--R 2 3 3 2 2 2 3 +--R - 12a b cosh(x) + (- 30b - 4a b)cosh(x) - 8a b cosh(x) + 6b +--R + +--R 2 +--R 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 30a b cosh(x) + 20a b cosh(x) - 36a b cosh(x) +--R + +--R 2 2 +--R - 20a b cosh(x) + 6a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 2 3 2 2 +--R - 30a b cosh(x) + (- 40b - 20a b)cosh(x) - 4a b cosh(x) +--R + +--R 3 2 2 +--R (24b + 20a b)cosh(x) + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 40a b cosh(x) + 40a b cosh(x) - 64a b cosh(x) +--R + +--R 2 2 2 2 +--R - 48a b cosh(x) + 24a b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 2 4 2 3 +--R - 40a b cosh(x) + (- 30b - 40a b)cosh(x) + 24a b cosh(x) +--R + +--R 3 2 2 3 2 +--R (36b + 32a b)cosh(x) - 6b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 5 2 4 +--R 30a b cosh(x) + 40a b cosh(x) - 66a b cosh(x) +--R + +--R 2 3 2 2 2 2 +--R - 64a b cosh(x) + 42a b cosh(x) + 24a b cosh(x) - 6a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 6 3 2 5 2 4 +--R - 30a b cosh(x) + (- 12b - 40a b)cosh(x) + 46a b cosh(x) +--R + +--R 3 2 3 2 2 3 2 +--R (24b + 16a b)cosh(x) - 18a b cosh(x) + (- 12b + 24a b)cosh(x) +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 6 2 5 +--R 12a b cosh(x) + 20a b cosh(x) - 36a b cosh(x) +--R + +--R 2 4 2 3 2 2 +--R - 44a b cosh(x) + 36a b cosh(x) + 28a b cosh(x) +--R + +--R 2 2 +--R - 12a b cosh(x) - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 7 3 2 6 2 5 +--R - 12a b cosh(x) + (- 2b - 20a b)cosh(x) + 32a b cosh(x) +--R + +--R 3 2 4 2 3 3 2 2 +--R (6b - 4a b)cosh(x) - 28a b cosh(x) + (- 6b + 20a b)cosh(x) +--R + +--R 2 3 2 +--R 8a b cosh(x) + 2b + 4a b +--R * +--R sinh(x) +--R + +--R 2 8 2 7 2 6 2 5 +--R 2a b cosh(x) + 4a b cosh(x) - 8a b cosh(x) - 12a b cosh(x) +--R + +--R 2 4 2 3 2 2 2 +--R 12a b cosh(x) + 12a b cosh(x) - 8a b cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 8 2 7 2 6 2 5 +--R - 2a b cosh(x) - 4a b cosh(x) + 8a b cosh(x) - 4a b cosh(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R - 12a b cosh(x) + 4a b cosh(x) + 8a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 7 +--R - a b sinh(x) +--R + +--R 2 2 2 2 3 2 2 2 3 +--R (a b cosh(x) - a b)coth(x) + (b - a b)cosh(x) - 6a b cosh(x) - b +--R + +--R 2 +--R - a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (6a b cosh(x) + 2a cosh(x) - 6a b cosh(x) - 2a )coth(x) +--R + +--R 3 2 3 2 3 2 +--R (6b - 6a b)cosh(x) + (- 13a b - 2a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 6b - 4a b)cosh(x) + a b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R 15a b cosh(x) + 10a cosh(x) - 18a b cosh(x) - 10a cosh(x) +--R + +--R 2 +--R 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 4 2 3 3 +--R (15b - 15a b)cosh(x) + (- 10a b - 10a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 18b - 2a b)cosh(x) + (2a b + 10a )cosh(x) + 3b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 20a b cosh(x) + 20a cosh(x) - 32a b cosh(x) - 24a cosh(x) +--R + +--R 2 3 +--R 12a b cosh(x) + 4a +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 5 2 3 4 +--R (20b - 20a b)cosh(x) + (5a b - 20a )cosh(x) +--R + +--R 3 2 3 2 3 2 3 +--R (- 32b + 12a b)cosh(x) + (- 6a b + 16a )cosh(x) + 12b cosh(x) +--R + +--R 2 3 +--R a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R 15a b cosh(x) + 20a cosh(x) - 33a b cosh(x) - 32a cosh(x) +--R + +--R 2 2 3 2 +--R 21a b cosh(x) + 12a cosh(x) - 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 6 2 3 5 +--R (15b - 15a b)cosh(x) + (14a b - 20a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 33b + 23a b)cosh(x) + (- 20a b + 8a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (21b - 9a b)cosh(x) + (6a b + 12a )cosh(x) - 3b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 2 5 3 4 +--R 6a b cosh(x) + 10a cosh(x) - 18a b cosh(x) - 22a cosh(x) +--R + +--R 2 3 3 2 2 3 +--R 18a b cosh(x) + 14a cosh(x) - 6a b cosh(x) - 2a +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 7 2 3 6 +--R (6b - 6a b)cosh(x) + (9a b - 10a )cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 18b + 16a b)cosh(x) + (- 19a b - 2a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (18b - 14a b)cosh(x) + (11a b + 10a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 6b + 4a b)cosh(x) - a b + 2a +--R * +--R sinh(x) +--R + +--R 2 8 3 7 2 6 3 5 +--R a b cosh(x) + 2a cosh(x) - 4a b cosh(x) - 6a cosh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R 6a b cosh(x) + 6a cosh(x) - 4a b cosh(x) - 2a cosh(x) + a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 8 2 3 7 3 2 6 +--R (b - a b)cosh(x) + (2a b - 2a )cosh(x) + (- 4b + 4a b)cosh(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R (- 6a b - 2a )cosh(x) + (6b - 6a b)cosh(x) + (6a b + 2a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 4b + 4a b)cosh(x) + (- 2a b + 2a )cosh(x) + b - a b +--R / +--R 3 2 3 6 +--R (a b cosh(x) - a b)sinh(x) +--R + +--R 3 3 4 2 3 4 5 +--R (6a b cosh(x) + 2a cosh(x) - 6a b cosh(x) - 2a )sinh(x) +--R + +--R 3 4 4 3 3 2 4 +--R 15a b cosh(x) + 10a cosh(x) - 18a b cosh(x) - 10a cosh(x) +--R + +--R 3 +--R 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R 20a b cosh(x) + 20a cosh(x) - 32a b cosh(x) - 24a cosh(x) +--R + +--R 3 4 +--R 12a b cosh(x) + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R 15a b cosh(x) + 20a cosh(x) - 33a b cosh(x) - 32a cosh(x) +--R + +--R 3 2 4 3 +--R 21a b cosh(x) + 12a cosh(x) - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 4 4 +--R 6a b cosh(x) + 10a cosh(x) - 18a b cosh(x) - 22a cosh(x) +--R + +--R 3 3 4 2 3 4 +--R 18a b cosh(x) + 14a cosh(x) - 6a b cosh(x) - 2a +--R * +--R sinh(x) +--R + +--R 3 8 4 7 3 6 4 5 +--R a b cosh(x) + 2a cosh(x) - 4a b cosh(x) - 6a cosh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R 6a b cosh(x) + 6a cosh(x) - 4a b cosh(x) - 2a cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 2 6 +--R (- 2a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 3 3 2 2 2 3 5 +--R (- 12a b cosh(x) - 4a b cosh(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R - 30a b cosh(x) - 20a b cosh(x) + 36a b cosh(x) +--R + +--R 3 2 2 +--R 20a b cosh(x) - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R - 40a b cosh(x) - 40a b cosh(x) + 64a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 48a b cosh(x) - 24a b cosh(x) - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R - 30a b cosh(x) - 40a b cosh(x) + 66a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 64a b cosh(x) - 42a b cosh(x) - 24a b cosh(x) + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R - 12a b cosh(x) - 20a b cosh(x) + 36a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 2 2 +--R 44a b cosh(x) - 36a b cosh(x) - 28a b cosh(x) + 12a b cosh(x) +--R + +--R 3 +--R 4a b +--R * +--R sinh(x) +--R + +--R 2 2 8 3 7 2 2 6 3 5 +--R - 2a b cosh(x) - 4a b cosh(x) + 8a b cosh(x) + 12a b cosh(x) +--R + +--R 2 2 4 3 3 2 2 2 3 +--R - 12a b cosh(x) - 12a b cosh(x) + 8a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 +--R - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 3 6 +--R (- a b cosh(x) + a b)sinh(x) +--R + +--R 3 3 4 2 3 4 5 +--R (- 6a b cosh(x) - 2a cosh(x) + 6a b cosh(x) + 2a )sinh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R (- 15a b cosh(x) - 10a cosh(x) + 18a b cosh(x) + 10a cosh(x) - 3a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R - 20a b cosh(x) - 20a cosh(x) + 32a b cosh(x) + 24a cosh(x) +--R + +--R 3 4 +--R - 12a b cosh(x) - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R - 15a b cosh(x) - 20a cosh(x) + 33a b cosh(x) + 32a cosh(x) +--R + +--R 3 2 4 3 +--R - 21a b cosh(x) - 12a cosh(x) + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 4 4 +--R - 6a b cosh(x) - 10a cosh(x) + 18a b cosh(x) + 22a cosh(x) +--R + +--R 3 3 4 2 3 4 +--R - 18a b cosh(x) - 14a cosh(x) + 6a b cosh(x) + 2a +--R * +--R sinh(x) +--R + +--R 3 8 4 7 3 6 4 5 +--R - a b cosh(x) - 2a cosh(x) + 4a b cosh(x) + 6a cosh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R - 6a b cosh(x) - 6a cosh(x) + 4a b cosh(x) + 2a cosh(x) - a b +--R Type: Expression(Integer) +--E 120 + +--S 121 of 530 +t0524:= csch(x)^3/(a+b*sinh(x)) +--R +--R +--R 3 +--R csch(x) +--R (120) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 530 +r0524:= 1/2*acoth(cosh(x))/a-b^2*acoth(cosh(x))/a^3+_ + 2*b^3*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^3/(a^2+b^2)^(1/2)+_ + b*coth(x)/a^2-1/2*coth(x)*csch(x)/a +--R +--R +--R (121) +--R x +--R a tanh(-) - b +-------+ +--R 3 2 2 2 | 2 2 +--R - 4b atanh(-------------) + (- 2b + a )\|b + a acoth(cosh(x)) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 | 2 2 +--R (- a coth(x)csch(x) + 2a b coth(x))\|b + a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2a \|b + a +--R Type: Expression(Integer) +--E 122 + +--S 123 of 530 +a0524:= integrate(t0524,x) +--R +--R +--R (122) +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) - 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) - 8b cosh(x))sinh(x) + 2b cosh(x) - 4b cosh(x) + 2b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) + 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (4b - 2a )cosh(x) - 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (- 4b + 2a )cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 2 3 2 2 +--R - 2a sinh(x) + (- 6a cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 6a cosh(x) + 8a b cosh(x) - 2a )sinh(x) - 2a cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2a cosh(x) - 4a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) - 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) - 8a cosh(x))sinh(x) + 2a cosh(x) - 4a cosh(x) + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 530 +m0524:= a0524-r0524 +--R +--R +--R (123) +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) - 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) - 8b cosh(x))sinh(x) + 2b cosh(x) - 4b cosh(x) + 2b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) + 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (4b - 2a )cosh(x) - 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (- 4b + 2a )cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 3 4 3 3 3 2 3 2 +--R 4b sinh(x) + 16b cosh(x)sinh(x) + (24b cosh(x) - 8b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (16b cosh(x) - 16b cosh(x))sinh(x) + 4b cosh(x) - 8b cosh(x) + 4b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (- 4b + 2a )cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a acoth(cosh(x)) +--R + +--R 2 4 +--R (a coth(x)csch(x) - 2a b coth(x))sinh(x) +--R + +--R 2 2 3 +--R (4a cosh(x)coth(x)csch(x) - 8a b cosh(x)coth(x) - 2a )sinh(x) +--R + +--R 2 2 2 +--R (6a cosh(x) - 2a )coth(x)csch(x) +--R + +--R 2 2 +--R (- 12a b cosh(x) + 4a b)coth(x) - 6a cosh(x) + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (4a cosh(x) - 4a cosh(x))coth(x)csch(x) +--R + +--R 3 2 2 +--R (- 8a b cosh(x) + 8a b cosh(x))coth(x) - 6a cosh(x) +--R + +--R 2 +--R 8a b cosh(x) - 2a +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (a cosh(x) - 2a cosh(x) + a )coth(x)csch(x) +--R + +--R 4 2 2 3 +--R (- 2a b cosh(x) + 4a b cosh(x) - 2a b)coth(x) - 2a cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2a cosh(x) - 4a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) - 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) - 8a cosh(x))sinh(x) + 2a cosh(x) - 4a cosh(x) + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 124 + +--S 125 of 530 +d0524:= D(m0524,x) +--R +--R +--R (124) +--R 3 3 9 +--R (- 2a b + a b)sinh(x) +--R + +--R 3 2 3 2 3 2 3 +--R ((- 2a b cosh(x) + 2a b)coth(x) + a b cosh(x) - a b)csch(x) +--R + +--R 2 2 2 2 2 2 4 2 2 2 +--R (2a b cosh(x) - 2a b )coth(x) + (2b - 2a b )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 16a b + 8a b)cosh(x) - 2b - 2a b + 2a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 3 4 2 3 4 +--R (- 16a b cosh(x) - 4a cosh(x) + 16a b cosh(x) + 4a ) +--R * +--R 2 +--R coth(x) +--R + +--R 3 3 4 2 3 4 +--R 8a b cosh(x) + 2a cosh(x) - 8a b cosh(x) - 2a +--R * +--R csch(x) +--R + +--R 2 2 3 3 2 2 2 3 2 +--R (16a b cosh(x) + 4a b cosh(x) - 16a b cosh(x) - 4a b)coth(x) +--R + +--R 4 2 2 3 3 3 2 +--R (16b - 16a b )cosh(x) + (- 52a b + 24a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (- 16b - 12a b + 14a )cosh(x) + 4a b +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 3 2 +--R - 56a b cosh(x) - 28a cosh(x) + 64a b cosh(x) +--R + +--R 4 3 +--R 28a cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 4 4 3 3 2 4 +--R 28a b cosh(x) + 14a cosh(x) - 32a b cosh(x) - 14a cosh(x) +--R + +--R 3 +--R 4a b +--R * +--R csch(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R 56a b cosh(x) + 28a b cosh(x) - 64a b cosh(x) +--R + +--R 3 2 2 +--R - 28a b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 4 3 3 3 +--R (56b - 56a b )cosh(x) + (- 84a b + 28a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (- 64b - 20a b + 42a )cosh(x) + (20a b + 4a b)cosh(x) + 8b +--R + +--R 2 2 4 +--R 4a b - 6a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 +--R - 112a b cosh(x) - 84a cosh(x) + 160a b cosh(x) +--R + +--R 4 2 3 4 +--R 96a cosh(x) - 48a b cosh(x) - 12a +--R * +--R 2 +--R coth(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R 56a b cosh(x) + 42a cosh(x) - 80a b cosh(x) - 48a cosh(x) +--R + +--R 3 4 +--R 24a b cosh(x) + 6a +--R * +--R csch(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R 112a b cosh(x) + 84a b cosh(x) - 160a b cosh(x) +--R + +--R 3 2 2 2 3 +--R - 96a b cosh(x) + 48a b cosh(x) + 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 5 3 3 4 +--R (112b - 112a b )cosh(x) + (- 56a b - 14a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 160b + 20a b + 70a )cosh(x) + (24a b + 36a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (48b + 12a b - 30a )cosh(x) - 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 +--R - 140a b cosh(x) - 140a cosh(x) + 260a b cosh(x) +--R + +--R 4 3 3 2 4 3 +--R 200a cosh(x) - 132a b cosh(x) - 60a cosh(x) + 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 6 4 5 3 4 +--R 70a b cosh(x) + 70a cosh(x) - 130a b cosh(x) +--R + +--R 4 3 3 2 4 3 +--R - 100a cosh(x) + 66a b cosh(x) + 30a cosh(x) - 6a b +--R * +--R csch(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R 140a b cosh(x) + 140a b cosh(x) - 260a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R - 200a b cosh(x) + 132a b cosh(x) + 60a b cosh(x) - 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 6 3 3 5 +--R (140b - 140a b )cosh(x) + (28a b - 84a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 260b + 120a b + 70a )cosh(x) + (- 40a b + 120a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (132b - 12a b - 28a )cosh(x) + (12a b - 36a b)cosh(x) - 12b +--R + +--R 4 +--R - 26a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 +--R - 112a b cosh(x) - 140a cosh(x) + 272a b cosh(x) +--R + +--R 4 4 3 3 4 2 +--R 260a cosh(x) - 208a b cosh(x) - 132a cosh(x) +--R + +--R 3 4 +--R 48a b cosh(x) + 12a +--R * +--R 2 +--R coth(x) +--R + +--R 3 7 4 6 3 5 +--R 56a b cosh(x) + 70a cosh(x) - 136a b cosh(x) +--R + +--R 4 4 3 3 4 2 +--R - 130a cosh(x) + 104a b cosh(x) + 66a cosh(x) +--R + +--R 3 4 +--R - 24a b cosh(x) - 6a +--R * +--R csch(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R 112a b cosh(x) + 140a b cosh(x) - 272a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 +--R - 260a b cosh(x) + 208a b cosh(x) + 132a b cosh(x) +--R + +--R 2 2 3 +--R - 48a b cosh(x) - 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 7 3 3 6 +--R (112b - 112a b )cosh(x) + (84a b - 112a b)cosh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (- 272b + 188a b + 42a )cosh(x) + (- 140a b + 200a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (208b - 88a b + 68a )cosh(x) + (60a b - 96a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- 48b + 12a b - 110a )cosh(x) - 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 8 4 7 3 6 +--R - 56a b cosh(x) - 84a cosh(x) + 176a b cosh(x) +--R + +--R 4 5 3 4 4 3 +--R 204a cosh(x) - 192a b cosh(x) - 156a cosh(x) +--R + +--R 3 2 4 3 +--R 80a b cosh(x) + 36a cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 8 4 7 3 6 +--R 28a b cosh(x) + 42a cosh(x) - 88a b cosh(x) +--R + +--R 4 5 3 4 4 3 +--R - 102a cosh(x) + 96a b cosh(x) + 78a cosh(x) +--R + +--R 3 2 4 3 +--R - 40a b cosh(x) - 18a cosh(x) + 4a b +--R * +--R csch(x) +--R + +--R 2 2 8 3 7 2 2 6 +--R 56a b cosh(x) + 84a b cosh(x) - 176a b cosh(x) +--R + +--R 3 5 2 2 4 3 3 +--R - 204a b cosh(x) + 192a b cosh(x) + 156a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R - 80a b cosh(x) - 36a b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 8 3 3 7 +--R (56b - 56a b )cosh(x) + (68a b - 76a b)cosh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (- 176b + 148a b + 14a )cosh(x) + (- 156a b + 180a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (192b - 132a b + 162a )cosh(x) + (108a b - 132a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 80b + 44a b - 174a )cosh(x) + (- 20a b + 28a b)cosh(x) +--R + +--R 4 2 2 4 +--R 8b - 4a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 9 4 8 3 7 +--R - 16a b cosh(x) - 28a cosh(x) + 64a b cosh(x) +--R + +--R 4 6 3 5 4 4 +--R 88a cosh(x) - 96a b cosh(x) - 96a cosh(x) +--R + +--R 3 3 4 2 3 4 +--R 64a b cosh(x) + 40a cosh(x) - 16a b cosh(x) - 4a +--R * +--R 2 +--R coth(x) +--R + +--R 3 9 4 8 3 7 4 6 +--R 8a b cosh(x) + 14a cosh(x) - 32a b cosh(x) - 44a cosh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R 48a b cosh(x) + 48a cosh(x) - 32a b cosh(x) - 20a cosh(x) +--R + +--R 3 4 +--R 8a b cosh(x) + 2a +--R * +--R csch(x) +--R + +--R 2 2 9 3 8 2 2 7 +--R 16a b cosh(x) + 28a b cosh(x) - 64a b cosh(x) +--R + +--R 3 6 2 2 5 3 4 +--R - 88a b cosh(x) + 96a b cosh(x) + 96a b cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R - 64a b cosh(x) - 40a b cosh(x) + 16a b cosh(x) + 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 9 3 3 8 +--R (16b - 16a b )cosh(x) + (26a b - 27a b)cosh(x) +--R + +--R 4 2 2 4 7 3 3 6 +--R (- 64b + 60a b + 2a )cosh(x) + (- 80a b + 84a b)cosh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (96b - 84a b + 122a )cosh(x) + (84a b - 90a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 64b + 52a b - 122a )cosh(x) + (- 32a b + 36a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (16b - 12a b - 2a )cosh(x) + 2a b - 3a b +--R * +--R sinh(x) +--R + +--R 3 10 4 9 3 8 +--R - 2a b cosh(x) - 4a cosh(x) + 10a b cosh(x) +--R + +--R 4 7 3 6 4 5 3 4 +--R 16a cosh(x) - 20a b cosh(x) - 24a cosh(x) + 20a b cosh(x) +--R + +--R 4 3 3 2 4 3 +--R 16a cosh(x) - 10a b cosh(x) - 4a cosh(x) + 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 10 4 9 3 8 4 7 +--R a b cosh(x) + 2a cosh(x) - 5a b cosh(x) - 8a cosh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R 10a b cosh(x) + 12a cosh(x) - 10a b cosh(x) - 8a cosh(x) +--R + +--R 3 2 4 3 +--R 5a b cosh(x) + 2a cosh(x) - a b +--R * +--R csch(x) +--R + +--R 2 2 10 3 9 2 2 8 3 7 +--R 2a b cosh(x) + 4a b cosh(x) - 10a b cosh(x) - 16a b cosh(x) +--R + +--R 2 2 6 3 5 2 2 4 3 3 +--R 20a b cosh(x) + 24a b cosh(x) - 20a b cosh(x) - 16a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R 10a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 10 3 3 9 +--R (2b - 2a b )cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 4 2 2 8 3 3 7 +--R (- 10b + 10a b )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (20b - 20a b + 32a )cosh(x) + (24a b - 24a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 20b + 20a b - 32a )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (10b - 10a b )cosh(x) + (4a b - 4a b)cosh(x) - 2b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 2 9 +--R (4b - 2a b )sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R ((4a b cosh(x) - 4a b )coth(x) - 2a b cosh(x) + 2a b )csch(x) +--R + +--R 3 2 3 2 3 2 +--R (- 4a b cosh(x) + 4a b )coth(x) + 4a b cosh(x) +--R + +--R 4 2 2 3 3 +--R (32b - 16a b )cosh(x) + 4a b - 4a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R (32a b cosh(x) + 8a b cosh(x) - 32a b cosh(x) - 8a b) +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R - 16a b cosh(x) - 4a b cosh(x) + 16a b cosh(x) + 4a b +--R * +--R csch(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 32a b cosh(x) - 8a b cosh(x) + 32a b cosh(x) + 8a b ) +--R * +--R 2 +--R coth(x) +--R + +--R 3 3 4 2 2 2 +--R 32a b cosh(x) + (112b - 48a b )cosh(x) +--R + +--R 3 3 4 +--R (24a b - 28a b)cosh(x) - 16b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R 112a b cosh(x) + 56a b cosh(x) - 128a b cosh(x) +--R + +--R 3 2 2 +--R - 56a b cosh(x) + 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R - 56a b cosh(x) - 28a b cosh(x) + 64a b cosh(x) +--R + +--R 3 2 2 +--R 28a b cosh(x) - 8a b +--R * +--R csch(x) +--R + +--R 3 4 2 2 3 3 2 +--R - 112a b cosh(x) - 56a b cosh(x) + 128a b cosh(x) +--R + +--R 2 2 3 +--R 56a b cosh(x) - 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 4 4 2 2 3 +--R 112a b cosh(x) + (224b - 56a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (40a b - 84a b)cosh(x) + (- 96b - 8a b )cosh(x) - 8a b + 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R 224a b cosh(x) + 168a b cosh(x) - 320a b cosh(x) +--R + +--R 3 2 2 2 3 +--R - 192a b cosh(x) + 96a b cosh(x) + 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R - 112a b cosh(x) - 84a b cosh(x) + 160a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 96a b cosh(x) - 48a b cosh(x) - 12a b +--R * +--R csch(x) +--R + +--R 3 5 2 2 4 3 3 +--R - 224a b cosh(x) - 168a b cosh(x) + 320a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R 192a b cosh(x) - 96a b cosh(x) - 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 5 4 2 2 4 +--R 224a b cosh(x) + (280b + 28a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (- 40a b - 140a b)cosh(x) + (- 240b - 72a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 24a b + 60a b)cosh(x) + 24b + 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R 280a b cosh(x) + 280a b cosh(x) - 520a b cosh(x) +--R + +--R 3 3 2 2 2 3 +--R - 400a b cosh(x) + 264a b cosh(x) + 120a b cosh(x) +--R + +--R 2 2 +--R - 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R - 140a b cosh(x) - 140a b cosh(x) + 260a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 200a b cosh(x) - 132a b cosh(x) - 60a b cosh(x) + 12a b +--R * +--R csch(x) +--R + +--R 3 6 2 2 5 3 4 +--R - 280a b cosh(x) - 280a b cosh(x) + 520a b cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R 400a b cosh(x) - 264a b cosh(x) - 120a b cosh(x) + 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 6 4 2 2 5 +--R 280a b cosh(x) + (224b + 168a b )cosh(x) +--R + +--R 3 3 4 4 2 2 3 +--R (- 240a b - 140a b)cosh(x) + (- 320b - 240a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 +--R (24a b + 56a b)cosh(x) + (96b + 72a b )cosh(x) + 52a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R 224a b cosh(x) + 280a b cosh(x) - 544a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 +--R - 520a b cosh(x) + 416a b cosh(x) + 264a b cosh(x) +--R + +--R 2 2 3 +--R - 96a b cosh(x) - 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R - 112a b cosh(x) - 140a b cosh(x) + 272a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 +--R 260a b cosh(x) - 208a b cosh(x) - 132a b cosh(x) +--R + +--R 2 2 3 +--R 48a b cosh(x) + 12a b +--R * +--R csch(x) +--R + +--R 3 7 2 2 6 3 5 +--R - 224a b cosh(x) - 280a b cosh(x) + 544a b cosh(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R 520a b cosh(x) - 416a b cosh(x) - 264a b cosh(x) +--R + +--R 3 2 2 +--R 96a b cosh(x) + 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 7 4 2 2 6 +--R 224a b cosh(x) + (112b + 224a b )cosh(x) +--R + +--R 3 3 5 4 2 2 4 +--R (- 376a b - 84a b)cosh(x) + (- 240b - 400a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (176a b - 136a b)cosh(x) + (144b + 192a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 24a b + 220a b)cosh(x) - 16b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 8 3 7 2 2 6 +--R 112a b cosh(x) + 168a b cosh(x) - 352a b cosh(x) +--R + +--R 3 5 2 2 4 3 3 +--R - 408a b cosh(x) + 384a b cosh(x) + 312a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R - 160a b cosh(x) - 72a b cosh(x) + 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 8 3 7 2 2 6 +--R - 56a b cosh(x) - 84a b cosh(x) + 176a b cosh(x) +--R + +--R 3 5 2 2 4 3 3 +--R 204a b cosh(x) - 192a b cosh(x) - 156a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R 80a b cosh(x) + 36a b cosh(x) - 8a b +--R * +--R csch(x) +--R + +--R 3 8 2 2 7 3 6 +--R - 112a b cosh(x) - 168a b cosh(x) + 352a b cosh(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R 408a b cosh(x) - 384a b cosh(x) - 312a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 160a b cosh(x) + 72a b cosh(x) - 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 8 4 2 2 7 +--R 112a b cosh(x) + (32b + 152a b )cosh(x) +--R + +--R 3 3 6 4 2 2 5 +--R (- 296a b - 28a b)cosh(x) + (- 96b - 360a b )cosh(x) +--R + +--R 3 3 4 4 2 2 3 +--R (264a b - 324a b)cosh(x) + (96b + 264a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 +--R (- 88a b + 348a b)cosh(x) + (- 32b - 56a b )cosh(x) + 8a b +--R + +--R 3 +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 9 3 8 2 2 7 +--R 32a b cosh(x) + 56a b cosh(x) - 128a b cosh(x) +--R + +--R 3 6 2 2 5 3 4 +--R - 176a b cosh(x) + 192a b cosh(x) + 192a b cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R - 128a b cosh(x) - 80a b cosh(x) + 32a b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 9 3 8 2 2 7 +--R - 16a b cosh(x) - 28a b cosh(x) + 64a b cosh(x) +--R + +--R 3 6 2 2 5 3 4 +--R 88a b cosh(x) - 96a b cosh(x) - 96a b cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R 64a b cosh(x) + 40a b cosh(x) - 16a b cosh(x) - 4a b +--R * +--R csch(x) +--R + +--R 3 9 2 2 8 3 7 +--R - 32a b cosh(x) - 56a b cosh(x) + 128a b cosh(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R 176a b cosh(x) - 192a b cosh(x) - 192a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 128a b cosh(x) + 80a b cosh(x) - 32a b cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 9 4 2 2 8 +--R 32a b cosh(x) + (4b + 54a b )cosh(x) +--R + +--R 3 3 7 4 2 2 6 +--R (- 120a b - 4a b)cosh(x) + (- 16b - 168a b )cosh(x) +--R + +--R 3 3 5 4 2 2 4 +--R (168a b - 244a b)cosh(x) + (24b + 180a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (- 104a b + 244a b)cosh(x) + (- 16b - 72a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (24a b + 4a b)cosh(x) + 4b + 6a b +--R * +--R sinh(x) +--R + +--R 2 2 10 3 9 2 2 8 +--R 4a b cosh(x) + 8a b cosh(x) - 20a b cosh(x) +--R + +--R 3 7 2 2 6 3 5 +--R - 32a b cosh(x) + 40a b cosh(x) + 48a b cosh(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R - 40a b cosh(x) - 32a b cosh(x) + 20a b cosh(x) +--R + +--R 3 2 2 +--R 8a b cosh(x) - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 10 3 9 2 2 8 +--R - 2a b cosh(x) - 4a b cosh(x) + 10a b cosh(x) +--R + +--R 3 7 2 2 6 3 5 2 2 4 +--R 16a b cosh(x) - 20a b cosh(x) - 24a b cosh(x) + 20a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 16a b cosh(x) - 10a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R csch(x) +--R + +--R 3 10 2 2 9 3 8 +--R - 4a b cosh(x) - 8a b cosh(x) + 20a b cosh(x) +--R + +--R 2 2 7 3 6 2 2 5 3 4 +--R 32a b cosh(x) - 40a b cosh(x) - 48a b cosh(x) + 40a b cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R 32a b cosh(x) - 20a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 10 2 2 9 3 8 2 2 7 +--R 4a b cosh(x) + 8a b cosh(x) - 20a b cosh(x) - 32a b cosh(x) +--R + +--R 3 3 6 2 2 5 +--R (40a b - 64a b)cosh(x) + 48a b cosh(x) +--R + +--R 3 3 4 2 2 3 3 2 +--R (- 40a b + 64a b)cosh(x) - 32a b cosh(x) + 20a b cosh(x) +--R + +--R 2 2 3 +--R 8a b cosh(x) - 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 9 +--R (2a b - a b)sinh(x) +--R + +--R 3 2 3 2 3 2 3 +--R ((2a b cosh(x) - 2a b)coth(x) - a b cosh(x) + a b)csch(x) +--R + +--R 2 2 2 2 2 2 4 2 2 2 +--R (- 2a b cosh(x) + 2a b )coth(x) + (- 2b + 2a b )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (16a b - 8a b)cosh(x) + 2b + 2a b - 2a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 3 4 2 3 4 2 +--R (16a b cosh(x) + 4a cosh(x) - 16a b cosh(x) - 4a )coth(x) +--R + +--R 3 3 4 2 3 4 +--R - 8a b cosh(x) - 2a cosh(x) + 8a b cosh(x) + 2a +--R * +--R csch(x) +--R + +--R 2 2 3 3 2 2 2 3 2 +--R (- 16a b cosh(x) - 4a b cosh(x) + 16a b cosh(x) + 4a b)coth(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 16b + 16a b )cosh(x) + (52a b - 24a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (16b + 12a b - 14a )cosh(x) - 4a b +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 3 2 4 +--R 56a b cosh(x) + 28a cosh(x) - 64a b cosh(x) - 28a cosh(x) +--R + +--R 3 +--R 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 4 4 3 3 2 4 +--R - 28a b cosh(x) - 14a cosh(x) + 32a b cosh(x) + 14a cosh(x) +--R + +--R 3 +--R - 4a b +--R * +--R csch(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R - 56a b cosh(x) - 28a b cosh(x) + 64a b cosh(x) +--R + +--R 3 2 2 +--R 28a b cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 56b + 56a b )cosh(x) + (84a b - 28a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (64b + 20a b - 42a )cosh(x) + (- 20a b - 4a b)cosh(x) - 8b +--R + +--R 2 2 4 +--R - 4a b + 6a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 +--R 112a b cosh(x) + 84a cosh(x) - 160a b cosh(x) +--R + +--R 4 2 3 4 +--R - 96a cosh(x) + 48a b cosh(x) + 12a +--R * +--R 2 +--R coth(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R - 56a b cosh(x) - 42a cosh(x) + 80a b cosh(x) + 48a cosh(x) +--R + +--R 3 4 +--R - 24a b cosh(x) - 6a +--R * +--R csch(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R - 112a b cosh(x) - 84a b cosh(x) + 160a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 96a b cosh(x) - 48a b cosh(x) - 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 5 3 3 4 +--R (- 112b + 112a b )cosh(x) + (56a b + 14a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (160b - 20a b - 70a )cosh(x) + (- 24a b - 36a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (- 48b - 12a b + 30a )cosh(x) + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 +--R 140a b cosh(x) + 140a cosh(x) - 260a b cosh(x) +--R + +--R 4 3 3 2 4 3 +--R - 200a cosh(x) + 132a b cosh(x) + 60a cosh(x) - 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R - 70a b cosh(x) - 70a cosh(x) + 130a b cosh(x) + 100a cosh(x) +--R + +--R 3 2 4 3 +--R - 66a b cosh(x) - 30a cosh(x) + 6a b +--R * +--R csch(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R - 140a b cosh(x) - 140a b cosh(x) + 260a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 200a b cosh(x) - 132a b cosh(x) - 60a b cosh(x) + 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 6 3 3 5 +--R (- 140b + 140a b )cosh(x) + (- 28a b + 84a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (260b - 120a b - 70a )cosh(x) + (40a b - 120a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (- 132b + 12a b + 28a )cosh(x) + (- 12a b + 36a b)cosh(x) + 12b +--R + +--R 4 +--R 26a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 +--R 112a b cosh(x) + 140a cosh(x) - 272a b cosh(x) +--R + +--R 4 4 3 3 4 2 +--R - 260a cosh(x) + 208a b cosh(x) + 132a cosh(x) +--R + +--R 3 4 +--R - 48a b cosh(x) - 12a +--R * +--R 2 +--R coth(x) +--R + +--R 3 7 4 6 3 5 4 4 +--R - 56a b cosh(x) - 70a cosh(x) + 136a b cosh(x) + 130a cosh(x) +--R + +--R 3 3 4 2 3 4 +--R - 104a b cosh(x) - 66a cosh(x) + 24a b cosh(x) + 6a +--R * +--R csch(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R - 112a b cosh(x) - 140a b cosh(x) + 272a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 +--R 260a b cosh(x) - 208a b cosh(x) - 132a b cosh(x) +--R + +--R 2 2 3 +--R 48a b cosh(x) + 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 7 3 3 6 +--R (- 112b + 112a b )cosh(x) + (- 84a b + 112a b)cosh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (272b - 188a b - 42a )cosh(x) + (140a b - 200a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 208b + 88a b - 68a )cosh(x) + (- 60a b + 96a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (48b - 12a b + 110a )cosh(x) + 4a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 8 4 7 3 6 +--R 56a b cosh(x) + 84a cosh(x) - 176a b cosh(x) +--R + +--R 4 5 3 4 4 3 +--R - 204a cosh(x) + 192a b cosh(x) + 156a cosh(x) +--R + +--R 3 2 4 3 +--R - 80a b cosh(x) - 36a cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 8 4 7 3 6 4 5 +--R - 28a b cosh(x) - 42a cosh(x) + 88a b cosh(x) + 102a cosh(x) +--R + +--R 3 4 4 3 3 2 4 +--R - 96a b cosh(x) - 78a cosh(x) + 40a b cosh(x) + 18a cosh(x) +--R + +--R 3 +--R - 4a b +--R * +--R csch(x) +--R + +--R 2 2 8 3 7 2 2 6 +--R - 56a b cosh(x) - 84a b cosh(x) + 176a b cosh(x) +--R + +--R 3 5 2 2 4 3 3 +--R 204a b cosh(x) - 192a b cosh(x) - 156a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R 80a b cosh(x) + 36a b cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 8 3 3 7 +--R (- 56b + 56a b )cosh(x) + (- 68a b + 76a b)cosh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (176b - 148a b - 14a )cosh(x) + (156a b - 180a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 192b + 132a b - 162a )cosh(x) + (- 108a b + 132a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (80b - 44a b + 174a )cosh(x) + (20a b - 28a b)cosh(x) - 8b +--R + +--R 2 2 4 +--R 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 9 4 8 3 7 4 6 +--R 16a b cosh(x) + 28a cosh(x) - 64a b cosh(x) - 88a cosh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R 96a b cosh(x) + 96a cosh(x) - 64a b cosh(x) - 40a cosh(x) +--R + +--R 3 4 +--R 16a b cosh(x) + 4a +--R * +--R 2 +--R coth(x) +--R + +--R 3 9 4 8 3 7 4 6 +--R - 8a b cosh(x) - 14a cosh(x) + 32a b cosh(x) + 44a cosh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R - 48a b cosh(x) - 48a cosh(x) + 32a b cosh(x) + 20a cosh(x) +--R + +--R 3 4 +--R - 8a b cosh(x) - 2a +--R * +--R csch(x) +--R + +--R 2 2 9 3 8 2 2 7 +--R - 16a b cosh(x) - 28a b cosh(x) + 64a b cosh(x) +--R + +--R 3 6 2 2 5 3 4 2 2 3 +--R 88a b cosh(x) - 96a b cosh(x) - 96a b cosh(x) + 64a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 40a b cosh(x) - 16a b cosh(x) - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 9 3 3 8 +--R (- 16b + 16a b )cosh(x) + (- 26a b + 27a b)cosh(x) +--R + +--R 4 2 2 4 7 3 3 6 +--R (64b - 60a b - 2a )cosh(x) + (80a b - 84a b)cosh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (- 96b + 84a b - 122a )cosh(x) + (- 84a b + 90a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (64b - 52a b + 122a )cosh(x) + (32a b - 36a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- 16b + 12a b + 2a )cosh(x) - 2a b + 3a b +--R * +--R sinh(x) +--R + +--R 3 10 4 9 3 8 4 7 +--R 2a b cosh(x) + 4a cosh(x) - 10a b cosh(x) - 16a cosh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R 20a b cosh(x) + 24a cosh(x) - 20a b cosh(x) - 16a cosh(x) +--R + +--R 3 2 4 3 +--R 10a b cosh(x) + 4a cosh(x) - 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 10 4 9 3 8 4 7 +--R - a b cosh(x) - 2a cosh(x) + 5a b cosh(x) + 8a cosh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R - 10a b cosh(x) - 12a cosh(x) + 10a b cosh(x) + 8a cosh(x) +--R + +--R 3 2 4 3 +--R - 5a b cosh(x) - 2a cosh(x) + a b +--R * +--R csch(x) +--R + +--R 2 2 10 3 9 2 2 8 3 7 +--R - 2a b cosh(x) - 4a b cosh(x) + 10a b cosh(x) + 16a b cosh(x) +--R + +--R 2 2 6 3 5 2 2 4 3 3 +--R - 20a b cosh(x) - 24a b cosh(x) + 20a b cosh(x) + 16a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R - 10a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 2 2 10 3 3 9 +--R (- 2b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 4 2 2 8 3 3 7 +--R (10b - 10a b )cosh(x) + (16a b - 16a b)cosh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (- 20b + 20a b - 32a )cosh(x) + (- 24a b + 24a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (20b - 20a b + 32a )cosh(x) + (16a b - 16a b)cosh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (- 10b + 10a b )cosh(x) + (- 4a b + 4a b)cosh(x) + 2b - 2a b +--R / +--R 4 2 4 8 +--R (2a b cosh(x) - 2a b)sinh(x) +--R + +--R 4 3 5 2 4 5 7 +--R (16a b cosh(x) + 4a cosh(x) - 16a b cosh(x) - 4a )sinh(x) +--R + +--R 4 4 5 3 4 2 5 +--R 56a b cosh(x) + 28a cosh(x) - 64a b cosh(x) - 28a cosh(x) +--R + +--R 4 +--R 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R 112a b cosh(x) + 84a cosh(x) - 160a b cosh(x) - 96a cosh(x) +--R + +--R 4 5 +--R 48a b cosh(x) + 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 5 5 4 4 5 3 +--R 140a b cosh(x) + 140a cosh(x) - 260a b cosh(x) - 200a cosh(x) +--R + +--R 4 2 5 4 +--R 132a b cosh(x) + 60a cosh(x) - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 5 6 4 5 5 4 +--R 112a b cosh(x) + 140a cosh(x) - 272a b cosh(x) - 260a cosh(x) +--R + +--R 4 3 5 2 4 5 +--R 208a b cosh(x) + 132a cosh(x) - 48a b cosh(x) - 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 5 7 4 6 5 5 +--R 56a b cosh(x) + 84a cosh(x) - 176a b cosh(x) - 204a cosh(x) +--R + +--R 4 4 5 3 4 2 5 +--R 192a b cosh(x) + 156a cosh(x) - 80a b cosh(x) - 36a cosh(x) +--R + +--R 4 +--R 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 5 8 4 7 5 6 +--R 16a b cosh(x) + 28a cosh(x) - 64a b cosh(x) - 88a cosh(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R 96a b cosh(x) + 96a cosh(x) - 64a b cosh(x) - 40a cosh(x) +--R + +--R 4 5 +--R 16a b cosh(x) + 4a +--R * +--R sinh(x) +--R + +--R 4 10 5 9 4 8 5 7 +--R 2a b cosh(x) + 4a cosh(x) - 10a b cosh(x) - 16a cosh(x) +--R + +--R 4 6 5 5 4 4 5 3 +--R 20a b cosh(x) + 24a cosh(x) - 20a b cosh(x) - 16a cosh(x) +--R + +--R 4 2 5 4 +--R 10a b cosh(x) + 4a cosh(x) - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 8 +--R (- 4a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 2 3 4 2 3 2 4 7 +--R (- 32a b cosh(x) - 8a b cosh(x) + 32a b cosh(x) + 8a b)sinh(x) +--R + +--R 3 2 4 4 3 3 2 2 +--R - 112a b cosh(x) - 56a b cosh(x) + 128a b cosh(x) +--R + +--R 4 3 2 +--R 56a b cosh(x) - 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 5 4 4 3 2 3 +--R - 224a b cosh(x) - 168a b cosh(x) + 320a b cosh(x) +--R + +--R 4 2 3 2 4 +--R 192a b cosh(x) - 96a b cosh(x) - 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 6 4 5 3 2 4 +--R - 280a b cosh(x) - 280a b cosh(x) + 520a b cosh(x) +--R + +--R 4 3 3 2 2 4 3 2 +--R 400a b cosh(x) - 264a b cosh(x) - 120a b cosh(x) + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 7 4 6 3 2 5 +--R - 224a b cosh(x) - 280a b cosh(x) + 544a b cosh(x) +--R + +--R 4 4 3 2 3 4 2 +--R 520a b cosh(x) - 416a b cosh(x) - 264a b cosh(x) +--R + +--R 3 2 4 +--R 96a b cosh(x) + 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 8 4 7 3 2 6 +--R - 112a b cosh(x) - 168a b cosh(x) + 352a b cosh(x) +--R + +--R 4 5 3 2 4 4 3 +--R 408a b cosh(x) - 384a b cosh(x) - 312a b cosh(x) +--R + +--R 3 2 2 4 3 2 +--R 160a b cosh(x) + 72a b cosh(x) - 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 9 4 8 3 2 7 +--R - 32a b cosh(x) - 56a b cosh(x) + 128a b cosh(x) +--R + +--R 4 6 3 2 5 4 4 +--R 176a b cosh(x) - 192a b cosh(x) - 192a b cosh(x) +--R + +--R 3 2 3 4 2 3 2 4 +--R 128a b cosh(x) + 80a b cosh(x) - 32a b cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 3 2 10 4 9 3 2 8 4 7 +--R - 4a b cosh(x) - 8a b cosh(x) + 20a b cosh(x) + 32a b cosh(x) +--R + +--R 3 2 6 4 5 3 2 4 4 3 +--R - 40a b cosh(x) - 48a b cosh(x) + 40a b cosh(x) + 32a b cosh(x) +--R + +--R 3 2 2 4 3 2 +--R - 20a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 4 8 +--R (- 2a b cosh(x) + 2a b)sinh(x) +--R + +--R 4 3 5 2 4 5 7 +--R (- 16a b cosh(x) - 4a cosh(x) + 16a b cosh(x) + 4a )sinh(x) +--R + +--R 4 4 5 3 4 2 5 4 +--R (- 56a b cosh(x) - 28a cosh(x) + 64a b cosh(x) + 28a cosh(x) - 8a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R - 112a b cosh(x) - 84a cosh(x) + 160a b cosh(x) + 96a cosh(x) +--R + +--R 4 5 +--R - 48a b cosh(x) - 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 5 5 4 4 5 3 +--R - 140a b cosh(x) - 140a cosh(x) + 260a b cosh(x) + 200a cosh(x) +--R + +--R 4 2 5 4 +--R - 132a b cosh(x) - 60a cosh(x) + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 5 6 4 5 5 4 +--R - 112a b cosh(x) - 140a cosh(x) + 272a b cosh(x) + 260a cosh(x) +--R + +--R 4 3 5 2 4 5 +--R - 208a b cosh(x) - 132a cosh(x) + 48a b cosh(x) + 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 5 7 4 6 5 5 +--R - 56a b cosh(x) - 84a cosh(x) + 176a b cosh(x) + 204a cosh(x) +--R + +--R 4 4 5 3 4 2 5 4 +--R - 192a b cosh(x) - 156a cosh(x) + 80a b cosh(x) + 36a cosh(x) - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 5 8 4 7 5 6 +--R - 16a b cosh(x) - 28a cosh(x) + 64a b cosh(x) + 88a cosh(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R - 96a b cosh(x) - 96a cosh(x) + 64a b cosh(x) + 40a cosh(x) +--R + +--R 4 5 +--R - 16a b cosh(x) - 4a +--R * +--R sinh(x) +--R + +--R 4 10 5 9 4 8 5 7 +--R - 2a b cosh(x) - 4a cosh(x) + 10a b cosh(x) + 16a cosh(x) +--R + +--R 4 6 5 5 4 4 5 3 +--R - 20a b cosh(x) - 24a cosh(x) + 20a b cosh(x) + 16a cosh(x) +--R + +--R 4 2 5 4 +--R - 10a b cosh(x) - 4a cosh(x) + 2a b +--R Type: Expression(Integer) +--E 125 + +--S 126 of 530 +t0525:= csch(x)^4/(a+b*sinh(x)) +--R +--R +--R 4 +--R csch(x) +--R (125) ------------- +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 530 +r0525:= -1/2*b*acoth(cosh(x))/a^2+b^3*acoth(cosh(x))/a^4-_ + 2*b^4*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^4/(a^2+b^2)^(1/2)+_ + coth(x)/a-b^2*coth(x)/a^3-1/3*coth(x)^3/a+1/2*b*coth(x)*csch(x)/a^2 +--R +--R +--R (126) +--R x +--R a tanh(-) - b +-------+ +--R 4 2 3 2 | 2 2 +--R 12b atanh(-------------) + (6b - 3a b)\|b + a acoth(cosh(x)) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 3 3 2 3 | 2 2 +--R (3a b coth(x)csch(x) - 2a coth(x) + (- 6a b + 6a )coth(x))\|b + a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6a \|b + a +--R Type: Expression(Integer) +--E 127 + +--S 128 of 530 +a0525:= integrate(t0525,x) +--R +--R +--R (127) +--R 4 6 4 5 4 2 4 4 +--R 6b sinh(x) + 36b cosh(x)sinh(x) + (90b cosh(x) - 18b )sinh(x) +--R + +--R 4 3 4 3 +--R (120b cosh(x) - 72b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90b cosh(x) - 108b cosh(x) + 18b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36b cosh(x) - 72b cosh(x) + 36b cosh(x))sinh(x) + 6b cosh(x) +--R + +--R 4 4 4 2 4 +--R - 18b cosh(x) + 18b cosh(x) - 6b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 2 6 3 2 5 +--R (6b - 3a b)sinh(x) + (36b - 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b - 45a b)cosh(x) - 18b + 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b - 60a b)cosh(x) + (- 72b + 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((90b - 45a b)cosh(x) + (- 108b + 54a b)cosh(x) + 18b - 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b - 18a b)cosh(x) + (- 72b + 36a b)cosh(x) +--R + +--R 3 2 +--R (36b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (6b - 3a b)cosh(x) + (- 18b + 9a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (18b - 9a b)cosh(x) - 6b + 3a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 6 3 2 5 +--R (- 6b + 3a b)sinh(x) + (- 36b + 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 45a b)cosh(x) + 18b - 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 60a b)cosh(x) + (72b - 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((- 90b + 45a b)cosh(x) + (108b - 54a b)cosh(x) - 18b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 18a b)cosh(x) + (72b - 36a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 3a b)cosh(x) + (18b - 9a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 9a b)cosh(x) + 6b - 3a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 2 5 2 2 4 +--R 6a b sinh(x) + (30a b cosh(x) - 12a b )sinh(x) +--R + +--R 2 2 2 3 +--R (60a b cosh(x) - 48a b cosh(x))sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R (60a b cosh(x) - 72a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 2 4 2 3 2 3 2 +--R (30a b cosh(x) - 48a b cosh(x) + (48a b - 48a )cosh(x) - 6a b) +--R * +--R sinh(x) +--R + +--R 2 5 2 4 2 3 2 +--R 6a b cosh(x) - 12a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R - 6a b cosh(x) - 12a b + 8a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) - 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) - 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) - 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) - 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R - 18a cosh(x) + 18a cosh(x) - 6a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 530 +m0525:= a0525-r0525 +--R +--R +--R (128) +--R 4 6 4 5 4 2 4 4 +--R 6b sinh(x) + 36b cosh(x)sinh(x) + (90b cosh(x) - 18b )sinh(x) +--R + +--R 4 3 4 3 +--R (120b cosh(x) - 72b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90b cosh(x) - 108b cosh(x) + 18b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36b cosh(x) - 72b cosh(x) + 36b cosh(x))sinh(x) + 6b cosh(x) +--R + +--R 4 4 4 2 4 +--R - 18b cosh(x) + 18b cosh(x) - 6b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 2 6 3 2 5 +--R (6b - 3a b)sinh(x) + (36b - 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b - 45a b)cosh(x) - 18b + 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b - 60a b)cosh(x) + (- 72b + 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((90b - 45a b)cosh(x) + (- 108b + 54a b)cosh(x) + 18b - 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b - 18a b)cosh(x) + (- 72b + 36a b)cosh(x) +--R + +--R 3 2 +--R (36b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (6b - 3a b)cosh(x) + (- 18b + 9a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (18b - 9a b)cosh(x) - 6b + 3a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 6 3 2 5 +--R (- 6b + 3a b)sinh(x) + (- 36b + 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 45a b)cosh(x) + 18b - 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 60a b)cosh(x) + (72b - 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((- 90b + 45a b)cosh(x) + (108b - 54a b)cosh(x) - 18b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 18a b)cosh(x) + (72b - 36a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 3a b)cosh(x) + (18b - 9a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 9a b)cosh(x) + 6b - 3a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 4 6 4 5 +--R - 12b sinh(x) - 72b cosh(x)sinh(x) +--R + +--R 4 2 4 4 +--R (- 180b cosh(x) + 36b )sinh(x) +--R + +--R 4 3 4 3 +--R (- 240b cosh(x) + 144b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (- 180b cosh(x) + 216b cosh(x) - 36b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (- 72b cosh(x) + 144b cosh(x) - 72b cosh(x))sinh(x) - 12b cosh(x) +--R + +--R 4 4 4 2 4 +--R 36b cosh(x) - 36b cosh(x) + 12b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 6 3 2 5 +--R (- 6b + 3a b)sinh(x) + (- 36b + 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 45a b)cosh(x) + 18b - 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 60a b)cosh(x) + (72b - 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((- 90b + 45a b)cosh(x) + (108b - 54a b)cosh(x) - 18b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 18a b)cosh(x) + (72b - 36a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 3a b)cosh(x) + (18b - 9a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 9a b)cosh(x) + 6b - 3a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a acoth(cosh(x)) +--R + +--R 2 3 3 2 3 6 +--R (- 3a b coth(x)csch(x) + 2a coth(x) + (6a b - 6a )coth(x))sinh(x) +--R + +--R 2 3 3 +--R - 18a b cosh(x)coth(x)csch(x) + 12a cosh(x)coth(x) +--R + +--R 2 3 2 +--R (36a b - 36a )cosh(x)coth(x) + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 2 +--R (- 45a b cosh(x) + 9a b)coth(x)csch(x) +--R + +--R 3 2 3 3 +--R (30a cosh(x) - 6a )coth(x) +--R + +--R 2 3 2 2 3 2 +--R ((90a b - 90a )cosh(x) - 18a b + 18a )coth(x) + 30a b cosh(x) +--R + +--R 2 +--R - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 +--R (- 60a b cosh(x) + 36a b cosh(x))coth(x)csch(x) +--R + +--R 3 3 3 3 +--R (40a cosh(x) - 24a cosh(x))coth(x) +--R + +--R 2 3 3 2 3 +--R ((120a b - 120a )cosh(x) + (- 72a b + 72a )cosh(x))coth(x) +--R + +--R 2 2 2 +--R 60a b cosh(x) - 48a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 45a b cosh(x) + 54a b cosh(x) - 9a b)coth(x)csch(x) +--R + +--R 3 4 3 2 3 3 +--R (30a cosh(x) - 36a cosh(x) + 6a )coth(x) +--R + +--R 2 3 4 2 3 2 +--R (90a b - 90a )cosh(x) + (- 108a b + 108a )cosh(x) +--R + +--R 2 3 +--R 18a b - 18a +--R * +--R coth(x) +--R + +--R 2 3 2 2 2 3 +--R 60a b cosh(x) - 72a b cosh(x) + 24a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 +--R (- 18a b cosh(x) + 36a b cosh(x) - 18a b cosh(x))coth(x)csch(x) +--R + +--R 3 5 3 3 3 3 +--R (12a cosh(x) - 24a cosh(x) + 12a cosh(x))coth(x) +--R + +--R 2 3 5 2 3 3 +--R (36a b - 36a )cosh(x) + (- 72a b + 72a )cosh(x) +--R + +--R 2 3 +--R (36a b - 36a )cosh(x) +--R * +--R coth(x) +--R + +--R 2 4 2 3 2 3 2 +--R 30a b cosh(x) - 48a b cosh(x) + (48a b - 48a )cosh(x) - 6a b +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (- 3a b cosh(x) + 9a b cosh(x) - 9a b cosh(x) + 3a b)coth(x) +--R * +--R csch(x) +--R + +--R 3 6 3 4 3 2 3 3 +--R (2a cosh(x) - 6a cosh(x) + 6a cosh(x) - 2a )coth(x) +--R + +--R 2 3 6 2 3 4 +--R (6a b - 6a )cosh(x) + (- 18a b + 18a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (18a b - 18a )cosh(x) - 6a b + 6a +--R * +--R coth(x) +--R + +--R 2 5 2 4 2 3 2 +--R 6a b cosh(x) - 12a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R - 6a b cosh(x) - 12a b + 8a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) - 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) - 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) - 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) - 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R - 18a cosh(x) + 18a cosh(x) - 6a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 129 + +--S 130 of 530 +--d0525:= D(m0525,x) +--E 130 + +--S 131 of 530 +t0526:= csch(x)^2/(%i+sinh(x)) +--R +--R +--R 2 +--R csch(x) +--R (129) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 131 + +--S 132 of 530 +r0526:= -acoth(cosh(x))+%i*coth(x)+cosh(x)/(1-%i*sinh(x)) +--R +--R +--R (130) +--R (- sinh(x) - %i)acoth(cosh(x)) + %i coth(x)sinh(x) - coth(x) + %i cosh(x) +--R ------------------------------------------------------------------------- +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 132 + +--S 133 of 530 +a0526:= integrate(t0526,x) +--R +--R +--R (131) +--R 3 2 +--R - sinh(x) + (- 3cosh(x) - %i)sinh(x) +--R + +--R 2 3 2 +--R (- 3cosh(x) - 2%i cosh(x) + 1)sinh(x) - cosh(x) - %i cosh(x) +--R + +--R cosh(x) + %i +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 +--R sinh(x) + (3cosh(x) + %i)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) + 2%i cosh(x) - 1)sinh(x) + cosh(x) + %i cosh(x) +--R + +--R - cosh(x) - %i +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R 2sinh(x) + (4cosh(x) + 2%i)sinh(x) + 2cosh(x) + 2%i cosh(x) - 4 +--R / +--R 3 2 2 +--R sinh(x) + (3cosh(x) + %i)sinh(x) + (3cosh(x) + 2%i cosh(x) - 1)sinh(x) +--R + +--R 3 2 +--R cosh(x) + %i cosh(x) - cosh(x) - %i +--R Type: Union(Expression(Complex(Integer)),...) +--E 133 + +--S 134 of 530 +m0526:= a0526-r0526 +--R +--R +--R (132) +--R 4 3 +--R - sinh(x) + (- 3cosh(x) - 2%i)sinh(x) +--R + +--R 2 2 +--R (- 3cosh(x) - 5%i cosh(x) + 2)sinh(x) +--R + +--R 3 2 3 +--R (- cosh(x) - 4%i cosh(x) + 3cosh(x) + 2%i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R cosh(x) + %i cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 +--R sinh(x) + (3cosh(x) + 2%i)sinh(x) +--R + +--R 2 2 +--R (3cosh(x) + 5%i cosh(x) - 2)sinh(x) +--R + +--R 3 2 3 +--R (cosh(x) + 4%i cosh(x) - 3cosh(x) - 2%i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 3 +--R sinh(x) + (3cosh(x) + 2%i)sinh(x) +--R + +--R 2 2 +--R (3cosh(x) + 5%i cosh(x) - 2)sinh(x) +--R + +--R 3 2 3 +--R (cosh(x) + 4%i cosh(x) - 3cosh(x) - 2%i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 1 +--R * +--R acoth(cosh(x)) +--R + +--R 4 +--R - %i coth(x)sinh(x) +--R + +--R 3 +--R ((- 3%i cosh(x) + 2)coth(x) - %i cosh(x) + 2)sinh(x) +--R + +--R 2 2 +--R (- 3%i cosh(x) + 5cosh(x) + 2%i)coth(x) - 3%i cosh(x) + 5cosh(x) +--R + +--R 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3 +--R (- %i cosh(x) + 4cosh(x) + 3%i cosh(x) - 2)coth(x) - 3%i cosh(x) +--R + +--R 2 +--R 4cosh(x) + 7%i cosh(x) - 6 +--R * +--R sinh(x) +--R + +--R 3 2 4 3 +--R (cosh(x) + %i cosh(x) - cosh(x) - %i)coth(x) - %i cosh(x) + cosh(x) +--R + +--R 2 +--R 3%i cosh(x) - 3cosh(x) - 4%i +--R / +--R 4 3 +--R sinh(x) + (3cosh(x) + 2%i)sinh(x) +--R + +--R 2 2 +--R (3cosh(x) + 5%i cosh(x) - 2)sinh(x) +--R + +--R 3 2 3 +--R (cosh(x) + 4%i cosh(x) - 3cosh(x) - 2%i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 134 + +--S 135 of 530 +d0526:= D(m0526,x) +--R +--R +--R (133) +--R 9 +--R - sinh(x) +--R + +--R 2 2 2 8 +--R ((%i cosh(x) - %i)coth(x) - 2%i cosh(x) - 6cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 2 3 +--R (6%i cosh(x) - 4cosh(x) - 6%i cosh(x) + 4)coth(x) - 12%i cosh(x) +--R + +--R 2 +--R - 8cosh(x) - 10%i cosh(x) + 1 +--R * +--R 7 +--R sinh(x) +--R + +--R 4 3 2 +--R (15%i cosh(x) - 22cosh(x) - 23%i cosh(x) + 22cosh(x) + 8%i) +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 +--R - 29%i cosh(x) + 18cosh(x) - 8%i cosh(x) - %i +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 20%i cosh(x) - 50cosh(x) - 58%i cosh(x) + 62cosh(x) +--R + +--R 38%i cosh(x) - 12 +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 2 +--R - 34%i cosh(x) + 68cosh(x) + 34%i cosh(x) - 21cosh(x) +--R + +--R - 14%i cosh(x) - 3 +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 15%i cosh(x) - 60cosh(x) - 88%i cosh(x) + 106cosh(x) +--R + +--R 2 +--R 87%i cosh(x) - 46cosh(x) - 14%i +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 +--R - 15%i cosh(x) + 84cosh(x) + 83%i cosh(x) - 64cosh(x) +--R + +--R 2 +--R - 45%i cosh(x) + 4cosh(x) - 7%i +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 6%i cosh(x) - 40cosh(x) - 78%i cosh(x) + 108cosh(x) +--R + +--R 3 2 +--R 114%i cosh(x) - 80cosh(x) - 42%i cosh(x) + 12 +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R 8%i cosh(x) + 44cosh(x) + 70%i cosh(x) - 77cosh(x) +--R + +--R 3 2 +--R - 56%i cosh(x) + 34cosh(x) - 14%i cosh(x) - 1 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R %i cosh(x) - 14cosh(x) - 39%i cosh(x) + 62cosh(x) +--R + +--R 4 3 2 +--R 83%i cosh(x) - 74cosh(x) - 53%i cosh(x) + 26cosh(x) + 8%i +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 +--R 13%i cosh(x) + 2cosh(x) + 18%i cosh(x) - 36cosh(x) +--R + +--R 4 3 2 +--R - 26%i cosh(x) + 34cosh(x) + 2%i cosh(x) - 7%i +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 2cosh(x) - 10%i cosh(x) + 18cosh(x) + 30%i cosh(x) +--R + +--R 4 3 2 +--R - 34cosh(x) - 30%i cosh(x) + 22cosh(x) + 10%i cosh(x) - 4 +--R * +--R 2 +--R coth(x) +--R + +--R 9 8 7 6 4 +--R 6%i cosh(x) - 7cosh(x) - 6%i cosh(x) + cosh(x) - cosh(x) +--R + +--R 3 2 +--R 10%i cosh(x) + 3cosh(x) - 10%i cosh(x) + 4 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - %i cosh(x) + 2cosh(x) + 4%i cosh(x) - 6cosh(x) - 6%i cosh(x) +--R + +--R 3 2 +--R 6cosh(x) + 4%i cosh(x) - 2cosh(x) - %i +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 6 +--R %i cosh(x) - 2cosh(x) - 3%i cosh(x) + 4cosh(x) + 2%i cosh(x) +--R + +--R 5 4 3 2 +--R - 8cosh(x) + 2%i cosh(x) + 4cosh(x) - 3%i cosh(x) + 2cosh(x) + %i +--R / +--R 2 8 +--R (cosh(x) - 1)sinh(x) +--R + +--R 3 2 7 +--R (6cosh(x) + 4%i cosh(x) - 6cosh(x) - 4%i)sinh(x) +--R + +--R 4 3 2 6 +--R (15cosh(x) + 22%i cosh(x) - 23cosh(x) - 22%i cosh(x) + 8)sinh(x) +--R + +--R 5 4 3 2 +--R 20cosh(x) + 50%i cosh(x) - 58cosh(x) - 62%i cosh(x) + 38cosh(x) +--R + +--R 12%i +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 15cosh(x) + 60%i cosh(x) - 88cosh(x) - 106%i cosh(x) + 87cosh(x) +--R + +--R 46%i cosh(x) - 14 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) + 40%i cosh(x) - 78cosh(x) - 108%i cosh(x) + 114cosh(x) +--R + +--R 2 +--R 80%i cosh(x) - 42cosh(x) - 12%i +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 14%i cosh(x) - 39cosh(x) - 62%i cosh(x) + 83cosh(x) +--R + +--R 3 2 +--R 74%i cosh(x) - 53cosh(x) - 26%i cosh(x) + 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 2%i cosh(x) - 10cosh(x) - 18%i cosh(x) + 30cosh(x) +--R + +--R 4 3 2 +--R 34%i cosh(x) - 30cosh(x) - 22%i cosh(x) + 10cosh(x) + 4%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) - 2%i cosh(x) + 4cosh(x) + 6%i cosh(x) - 6cosh(x) +--R + +--R 3 2 +--R - 6%i cosh(x) + 4cosh(x) + 2%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 135 + +--S 136 of 530 +t0527:= csch(x)^3/(%i+sinh(x)) +--R +--R +--R 3 +--R csch(x) +--R (134) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 136 + +--S 137 of 530 +r0527:= -3/2*%i*acoth(cosh(x))-coth(x)+1/2*%i*coth(x)*csch(x)+_ + %i*cosh(x)/(1-%i*sinh(x)) +--R +--R +--R (135) +--R 3 3 +--R (- - %i sinh(x) + -)acoth(cosh(x)) +--R 2 2 +--R + +--R 1 1 +--R (- %i coth(x)csch(x) - coth(x))sinh(x) - - coth(x)csch(x) - %i coth(x) +--R 2 2 +--R + +--R - cosh(x) +--R / +--R sinh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 137 + +--S 138 of 530 +a0527:= integrate(t0527,x) +--R +--R +--R (136) +--R 5 4 +--R 3%i sinh(x) + (15%i cosh(x) - 3)sinh(x) +--R + +--R 2 3 +--R (30%i cosh(x) - 12cosh(x) - 6%i)sinh(x) +--R + +--R 3 2 2 +--R (30%i cosh(x) - 18cosh(x) - 18%i cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 +--R (15%i cosh(x) - 12cosh(x) - 18%i cosh(x) + 12cosh(x) + 3%i)sinh(x) +--R + +--R 5 4 3 2 +--R 3%i cosh(x) - 3cosh(x) - 6%i cosh(x) + 6cosh(x) + 3%i cosh(x) - 3 +--R * +--R sinh(x) + cosh(x) - 1 +--R log(---------------------) +--R sinh(x) + cosh(x) + 1 +--R + +--R 4 3 +--R 6%i sinh(x) + (24%i cosh(x) - 6)sinh(x) +--R + +--R 2 2 +--R (36%i cosh(x) - 18cosh(x) - 10%i)sinh(x) +--R + +--R 3 2 4 +--R (24%i cosh(x) - 18cosh(x) - 20%i cosh(x) + 2)sinh(x) + 6%i cosh(x) +--R + +--R 3 2 +--R - 6cosh(x) - 10%i cosh(x) + 2cosh(x) + 8%i +--R / +--R 5 4 +--R 2sinh(x) + (10cosh(x) + 2%i)sinh(x) +--R + +--R 2 3 +--R (20cosh(x) + 8%i cosh(x) - 4)sinh(x) +--R + +--R 3 2 2 +--R (20cosh(x) + 12%i cosh(x) - 12cosh(x) - 4%i)sinh(x) +--R + +--R 4 3 2 +--R (10cosh(x) + 8%i cosh(x) - 12cosh(x) - 8%i cosh(x) + 2)sinh(x) +--R + +--R 5 4 3 2 +--R 2cosh(x) + 2%i cosh(x) - 4cosh(x) - 4%i cosh(x) + 2cosh(x) + 2%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 138 + +--S 139 of 530 +m0527:= a0527-r0527 +--R +--R +--R (137) +--R 3 6 15 5 +--R - %i sinh(x) + (-- %i cosh(x) - 3)sinh(x) +--R 2 2 +--R + +--R 2 27 9 4 +--R (15%i cosh(x) - -- cosh(x) - - %i)sinh(x) +--R 2 2 +--R + +--R 3 2 3 +--R (15%i cosh(x) - 24cosh(x) - 15%i cosh(x) + 6)sinh(x) +--R + +--R 15 4 3 2 9 +--R (-- %i cosh(x) - 21cosh(x) - 18%i cosh(x) + 15cosh(x) + - %i) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 3 2 +--R - %i cosh(x) - 9cosh(x) - 9%i cosh(x) + 12cosh(x) +--R 2 +--R + +--R 15 +--R -- %i cosh(x) - 3 +--R 2 +--R * +--R sinh(x) +--R + +--R 3 5 3 4 3 2 3 +--R - - cosh(x) - - %i cosh(x) + 3cosh(x) + 3%i cosh(x) - - cosh(x) +--R 2 2 2 +--R + +--R 3 +--R - - %i +--R 2 +--R * +--R sinh(x) + cosh(x) - 1 +--R log(---------------------) +--R sinh(x) + cosh(x) + 1 +--R + +--R 3 6 15 5 +--R - %i sinh(x) + (-- %i cosh(x) - 3)sinh(x) +--R 2 2 +--R + +--R 2 27 9 4 +--R (15%i cosh(x) - -- cosh(x) - - %i)sinh(x) +--R 2 2 +--R + +--R 3 2 3 +--R (15%i cosh(x) - 24cosh(x) - 15%i cosh(x) + 6)sinh(x) +--R + +--R 15 4 3 2 9 +--R (-- %i cosh(x) - 21cosh(x) - 18%i cosh(x) + 15cosh(x) + - %i) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 3 2 +--R - %i cosh(x) - 9cosh(x) - 9%i cosh(x) + 12cosh(x) +--R 2 +--R + +--R 15 +--R -- %i cosh(x) - 3 +--R 2 +--R * +--R sinh(x) +--R + +--R 3 5 3 4 3 2 3 +--R - - cosh(x) - - %i cosh(x) + 3cosh(x) + 3%i cosh(x) - - cosh(x) +--R 2 2 2 +--R + +--R 3 +--R - - %i +--R 2 +--R * +--R acoth(cosh(x)) +--R + +--R 1 6 +--R (- - %i coth(x)csch(x) + coth(x))sinh(x) +--R 2 +--R + +--R 5 +--R (- - %i cosh(x) + 1)coth(x)csch(x) + (5cosh(x) + 2%i)coth(x) +--R 2 +--R + +--R cosh(x) + 3%i +--R * +--R 5 +--R sinh(x) +--R + +--R 2 9 3 +--R (- 5%i cosh(x) + - cosh(x) + - %i)coth(x)csch(x) +--R 2 2 +--R + +--R 2 2 +--R (10cosh(x) + 9%i cosh(x) - 3)coth(x) + 5cosh(x) + 13%i cosh(x) - 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (- 5%i cosh(x) + 8cosh(x) + 5%i cosh(x) - 2)coth(x)csch(x) +--R + +--R 3 2 3 +--R (10cosh(x) + 16%i cosh(x) - 10cosh(x) - 4%i)coth(x) + 10cosh(x) +--R + +--R 2 +--R 22%i cosh(x) - 23cosh(x) - 8%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 3 +--R (- - %i cosh(x) + 7cosh(x) + 6%i cosh(x) - 5cosh(x) - - %i) +--R 2 2 +--R * +--R coth(x)csch(x) +--R + +--R 4 3 2 +--R (5cosh(x) + 14%i cosh(x) - 12cosh(x) - 10%i cosh(x) + 3)coth(x) +--R + +--R 4 3 2 +--R 10cosh(x) + 18%i cosh(x) - 33cosh(x) - 21%i cosh(x) + 6 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 5 4 3 2 +--R - - %i cosh(x) + 3cosh(x) + 3%i cosh(x) - 4cosh(x) +--R 2 +--R + +--R 5 +--R - - %i cosh(x) + 1 +--R 2 +--R * +--R coth(x)csch(x) +--R + +--R 5 4 3 2 +--R cosh(x) + 6%i cosh(x) - 6cosh(x) - 8%i cosh(x) + 5cosh(x) +--R + +--R 2%i +--R * +--R coth(x) +--R + +--R 5 4 3 2 +--R 5cosh(x) + 7%i cosh(x) - 21cosh(x) - 18%i cosh(x) + 12cosh(x) + 5%i +--R * +--R sinh(x) +--R + +--R 1 5 1 4 3 2 1 +--R - cosh(x) + - %i cosh(x) - cosh(x) - %i cosh(x) + - cosh(x) +--R 2 2 2 +--R + +--R 1 +--R - %i +--R 2 +--R * +--R coth(x)csch(x) +--R + +--R 5 4 3 2 +--R (%i cosh(x) - cosh(x) - 2%i cosh(x) + 2cosh(x) + %i cosh(x) - 1) +--R * +--R coth(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) + %i cosh(x) - 5cosh(x) - 5%i cosh(x) + 6cosh(x) +--R + +--R 2%i cosh(x) - 4 +--R / +--R 6 5 +--R sinh(x) + (5cosh(x) + 2%i)sinh(x) +--R + +--R 2 4 +--R (10cosh(x) + 9%i cosh(x) - 3)sinh(x) +--R + +--R 3 2 3 +--R (10cosh(x) + 16%i cosh(x) - 10cosh(x) - 4%i)sinh(x) +--R + +--R 4 3 2 2 +--R (5cosh(x) + 14%i cosh(x) - 12cosh(x) - 10%i cosh(x) + 3)sinh(x) +--R + +--R 5 4 3 2 +--R (cosh(x) + 6%i cosh(x) - 6cosh(x) - 8%i cosh(x) + 5cosh(x) + 2%i) +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R %i cosh(x) - cosh(x) - 2%i cosh(x) + 2cosh(x) + %i cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 139 + +--S 140 of 530 +d0527:= D(m0527,x) +--R +--R +--R (138) +--R 3 11 +--R - - %i sinh(x) +--R 2 +--R + +--R 2 2 1 2 1 +--R ((%i cosh(x) - %i)coth(x) - - %i cosh(x) + - %i)csch(x) +--R 2 2 +--R + +--R 2 2 2 +--R (- cosh(x) + 1)coth(x) + 2cosh(x) - 12%i cosh(x) + 4 +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 2 +--R (8%i cosh(x) - 4cosh(x) - 8%i cosh(x) + 4)coth(x) +--R + +--R 3 2 +--R - 4%i cosh(x) + 2cosh(x) + 4%i cosh(x) - 2 +--R * +--R csch(x) +--R + +--R 3 2 2 3 +--R (- 8cosh(x) - 4%i cosh(x) + 8cosh(x) + 4%i)coth(x) + 16cosh(x) +--R + +--R 2 13 +--R - 35%i cosh(x) + 29cosh(x) + -- %i +--R 2 +--R * +--R 9 +--R sinh(x) +--R + +--R 4 3 2 +--R (28%i cosh(x) - 30cosh(x) - 37%i cosh(x) + 30cosh(x) + 9%i) +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 37 2 9 +--R - 14%i cosh(x) + 15cosh(x) + -- %i cosh(x) - 15cosh(x) - - %i +--R 2 2 +--R * +--R csch(x) +--R + +--R 4 3 2 +--R (- 28cosh(x) - 30%i cosh(x) + 37cosh(x) + 30%i cosh(x) - 9) +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 +--R 55cosh(x) - 32%i cosh(x) + 77cosh(x) + 38%i cosh(x) - 9 +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 56%i cosh(x) - 98cosh(x) - 116%i cosh(x) + 114cosh(x) +--R + +--R 60%i cosh(x) - 16 +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 2 +--R - 28%i cosh(x) + 49cosh(x) + 58%i cosh(x) - 57cosh(x) +--R + +--R - 30%i cosh(x) + 8 +--R * +--R csch(x) +--R + +--R 5 4 3 2 +--R - 56cosh(x) - 98%i cosh(x) + 116cosh(x) + 114%i cosh(x) +--R + +--R - 60cosh(x) - 16%i +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 2 +--R 104cosh(x) + 61%i cosh(x) + 71cosh(x) + 66%i cosh(x) - 40cosh(x) +--R + +--R - 7%i +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 70%i cosh(x) - 182cosh(x) - 242%i cosh(x) + 274cosh(x) +--R + +--R 2 +--R 194%i cosh(x) - 92cosh(x) - 22%i +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 +--R - 35%i cosh(x) + 91cosh(x) + 121%i cosh(x) - 137cosh(x) +--R + +--R 2 +--R - 97%i cosh(x) + 46cosh(x) + 11%i +--R * +--R csch(x) +--R + +--R 6 5 4 3 +--R - 70cosh(x) - 182%i cosh(x) + 242cosh(x) + 274%i cosh(x) +--R + +--R 2 +--R - 194cosh(x) - 92%i cosh(x) + 22 +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 +--R 112cosh(x) + 210%i cosh(x) - 67cosh(x) - 26%i cosh(x) +--R + +--R 2 +--R - 13cosh(x) - 16%i cosh(x) - 14 +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 56%i cosh(x) - 210cosh(x) - 332%i cosh(x) + 432cosh(x) +--R + +--R 3 2 +--R 384%i cosh(x) - 246cosh(x) - 108%i cosh(x) + 24 +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R - 28%i cosh(x) + 105cosh(x) + 166%i cosh(x) - 216cosh(x) +--R + +--R 3 2 +--R - 192%i cosh(x) + 123cosh(x) + 54%i cosh(x) - 12 +--R * +--R csch(x) +--R + +--R 7 6 5 4 +--R - 56cosh(x) - 210%i cosh(x) + 332cosh(x) + 432%i cosh(x) +--R + +--R 3 2 +--R - 384cosh(x) - 246%i cosh(x) + 108cosh(x) + 24%i +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R 56cosh(x) + 266%i cosh(x) - 227cosh(x) - 239%i cosh(x) +--R + +--R 3 2 +--R 193cosh(x) + 80%i cosh(x) - 82cosh(x) - 35%i +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 28%i cosh(x) - 154cosh(x) - 298%i cosh(x) + 444cosh(x) +--R + +--R 4 3 2 +--R 486%i cosh(x) - 386cosh(x) - 238%i cosh(x) + 96cosh(x) +--R + +--R 22%i +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 +--R - 14%i cosh(x) + 77cosh(x) + 149%i cosh(x) - 222cosh(x) +--R + +--R 4 3 2 +--R - 243%i cosh(x) + 193cosh(x) + 119%i cosh(x) - 48cosh(x) - 11%i +--R * +--R csch(x) +--R + +--R 8 7 6 5 +--R - 28cosh(x) - 154%i cosh(x) + 298cosh(x) + 444%i cosh(x) +--R + +--R 4 3 2 +--R - 486cosh(x) - 386%i cosh(x) + 238cosh(x) + 96%i cosh(x) - 22 +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 +--R - 14cosh(x) + 170%i cosh(x) - 221cosh(x) - 336%i cosh(x) +--R + +--R 4 3 2 +--R 412cosh(x) + 330%i cosh(x) - 225cosh(x) - 164%i cosh(x) + 24 +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 8%i cosh(x) - 70cosh(x) - 172%i cosh(x) + 290cosh(x) +--R + +--R 5 4 3 2 +--R 388%i cosh(x) - 370cosh(x) - 292%i cosh(x) + 166cosh(x) +--R + +--R 68%i cosh(x) - 16 +--R * +--R 2 +--R coth(x) +--R + +--R 9 8 7 6 +--R - 4%i cosh(x) + 35cosh(x) + 86%i cosh(x) - 145cosh(x) +--R + +--R 5 4 3 2 +--R - 194%i cosh(x) + 185cosh(x) + 146%i cosh(x) - 83cosh(x) +--R + +--R - 34%i cosh(x) + 8 +--R * +--R csch(x) +--R + +--R 9 8 7 6 +--R - 8cosh(x) - 70%i cosh(x) + 172cosh(x) + 290%i cosh(x) +--R + +--R 5 4 3 2 +--R - 388cosh(x) - 370%i cosh(x) + 292cosh(x) + 166%i cosh(x) +--R + +--R - 68cosh(x) - 16%i +--R * +--R 2 +--R coth(x) +--R + +--R 9 81 8 7 6 +--R - 40cosh(x) + -- %i cosh(x) - 83cosh(x) - 202%i cosh(x) +--R 2 +--R + +--R 5 4 3 2 +--R 354cosh(x) + 451%i cosh(x) - 335cosh(x) - 298%i cosh(x) +--R + +--R 17 +--R 104cosh(x) + -- %i +--R 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R %i cosh(x) - 18cosh(x) - 61%i cosh(x) + 114cosh(x) +--R + +--R 6 5 4 3 +--R 186%i cosh(x) - 210cosh(x) - 202%i cosh(x) + 150cosh(x) +--R + +--R 2 +--R 85%i cosh(x) - 36cosh(x) - 9%i +--R * +--R 2 +--R coth(x) +--R + +--R 1 10 9 61 8 7 +--R - - %i cosh(x) + 9cosh(x) + -- %i cosh(x) - 57cosh(x) +--R 2 2 +--R + +--R 6 5 4 3 +--R - 93%i cosh(x) + 105cosh(x) + 101%i cosh(x) - 75cosh(x) +--R + +--R 85 2 9 +--R - -- %i cosh(x) + 18cosh(x) + - %i +--R 2 2 +--R * +--R csch(x) +--R + +--R 10 9 8 7 +--R - cosh(x) - 18%i cosh(x) + 61cosh(x) + 114%i cosh(x) +--R + +--R 6 5 4 3 +--R - 186cosh(x) - 210%i cosh(x) + 202cosh(x) + 150%i cosh(x) +--R + +--R 2 +--R - 85cosh(x) - 36%i cosh(x) + 9 +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 +--R - 26cosh(x) - 14%i cosh(x) + 11cosh(x) - 34%i cosh(x) +--R + +--R 6 5 4 3 +--R 127cosh(x) + 266%i cosh(x) - 269cosh(x) - 246%i cosh(x) +--R + +--R 2 +--R 163cosh(x) + 28%i cosh(x) - 6 +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 2cosh(x) - 12%i cosh(x) + 24cosh(x) + 48%i cosh(x) +--R + +--R 6 5 4 3 +--R - 64cosh(x) - 72%i cosh(x) + 68cosh(x) + 48%i cosh(x) +--R + +--R 2 +--R - 30cosh(x) - 12%i cosh(x) + 4 +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 +--R cosh(x) + 6%i cosh(x) - 12cosh(x) - 24%i cosh(x) +--R + +--R 6 5 4 3 +--R 32cosh(x) + 36%i cosh(x) - 34cosh(x) - 24%i cosh(x) +--R + +--R 2 +--R 15cosh(x) + 6%i cosh(x) - 2 +--R * +--R csch(x) +--R + +--R 10 9 8 7 +--R - 2%i cosh(x) + 12cosh(x) + 24%i cosh(x) - 48cosh(x) +--R + +--R 6 5 4 3 +--R - 64%i cosh(x) + 72cosh(x) + 68%i cosh(x) - 48cosh(x) +--R + +--R 2 +--R - 30%i cosh(x) + 12cosh(x) + 4%i +--R * +--R 2 +--R coth(x) +--R + +--R 11 10 9 33 8 +--R - 8cosh(x) - 11%i cosh(x) + 18cosh(x) + -- %i cosh(x) +--R 2 +--R + +--R 7 6 5 4 3 +--R 5cosh(x) + 52%i cosh(x) - 107cosh(x) - 81%i cosh(x) + 103cosh(x) +--R + +--R 2 7 +--R 27%i cosh(x) - 11cosh(x) - - %i +--R 2 +--R * +--R sinh(x) +--R + +--R 10 9 8 7 +--R - %i cosh(x) + 2cosh(x) + 5%i cosh(x) - 8cosh(x) +--R + +--R 6 5 4 3 +--R - 10%i cosh(x) + 12cosh(x) + 10%i cosh(x) - 8cosh(x) +--R + +--R 2 +--R - 5%i cosh(x) + 2cosh(x) + %i +--R * +--R 2 +--R coth(x) +--R + +--R 1 10 9 5 8 7 6 +--R - %i cosh(x) - cosh(x) - - %i cosh(x) + 4cosh(x) + 5%i cosh(x) +--R 2 2 +--R + +--R 5 4 3 5 2 1 +--R - 6cosh(x) - 5%i cosh(x) + 4cosh(x) + - %i cosh(x) - cosh(x) - - %i +--R 2 2 +--R * +--R csch(x) +--R + +--R 10 9 8 7 6 +--R cosh(x) + 2%i cosh(x) - 5cosh(x) - 8%i cosh(x) + 10cosh(x) +--R + +--R 5 4 3 2 +--R 12%i cosh(x) - 10cosh(x) - 8%i cosh(x) + 5cosh(x) + 2%i cosh(x) - 1 +--R * +--R 2 +--R coth(x) +--R + +--R 12 11 10 9 8 +--R - cosh(x) - 2%i cosh(x) + 4cosh(x) + 6%i cosh(x) - 5cosh(x) +--R + +--R 7 6 5 4 3 +--R - 4%i cosh(x) - 16cosh(x) - 4%i cosh(x) + 21cosh(x) + 6%i cosh(x) +--R + +--R 2 +--R - 4cosh(x) - 2%i cosh(x) + 1 +--R / +--R 2 10 +--R (cosh(x) - 1)sinh(x) +--R + +--R 3 2 9 +--R (8cosh(x) + 4%i cosh(x) - 8cosh(x) - 4%i)sinh(x) +--R + +--R 4 3 2 8 +--R (28cosh(x) + 30%i cosh(x) - 37cosh(x) - 30%i cosh(x) + 9)sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) + 98%i cosh(x) - 116cosh(x) - 114%i cosh(x) + 60cosh(x) +--R + +--R 16%i +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 70cosh(x) + 182%i cosh(x) - 242cosh(x) - 274%i cosh(x) +--R + +--R 2 +--R 194cosh(x) + 92%i cosh(x) - 22 +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 56cosh(x) + 210%i cosh(x) - 332cosh(x) - 432%i cosh(x) +--R + +--R 3 2 +--R 384cosh(x) + 246%i cosh(x) - 108cosh(x) - 24%i +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 28cosh(x) + 154%i cosh(x) - 298cosh(x) - 444%i cosh(x) +--R + +--R 4 3 2 +--R 486cosh(x) + 386%i cosh(x) - 238cosh(x) - 96%i cosh(x) + 22 +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 8cosh(x) + 70%i cosh(x) - 172cosh(x) - 290%i cosh(x) +--R + +--R 5 4 3 2 +--R 388cosh(x) + 370%i cosh(x) - 292cosh(x) - 166%i cosh(x) +--R + +--R 68cosh(x) + 16%i +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R cosh(x) + 18%i cosh(x) - 61cosh(x) - 114%i cosh(x) + 186cosh(x) +--R + +--R 5 4 3 2 +--R 210%i cosh(x) - 202cosh(x) - 150%i cosh(x) + 85cosh(x) +--R + +--R 36%i cosh(x) - 9 +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 2%i cosh(x) - 12cosh(x) - 24%i cosh(x) + 48cosh(x) +--R + +--R 6 5 4 3 +--R 64%i cosh(x) - 72cosh(x) - 68%i cosh(x) + 48cosh(x) +--R + +--R 2 +--R 30%i cosh(x) - 12cosh(x) - 4%i +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R - cosh(x) - 2%i cosh(x) + 5cosh(x) + 8%i cosh(x) - 10cosh(x) +--R + +--R 5 4 3 2 +--R - 12%i cosh(x) + 10cosh(x) + 8%i cosh(x) - 5cosh(x) - 2%i cosh(x) + 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 140 + +--S 141 of 530 +t0528:= csch(x)^4/(%i+sinh(x)) +--R +--R +--R 4 +--R csch(x) +--R (139) ------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 141 + +--S 142 of 530 +r0528:= 3/2*acoth(cosh(x))-2*%i*coth(x)+1/3*%i*coth(x)^3-_ + 1/2*coth(x)*csch(x)-cosh(x)/(1-%i*sinh(x)) +--R +--R +--R (140) +--R 3 3 +--R (- sinh(x) + - %i)acoth(cosh(x)) +--R 2 2 +--R + +--R 1 1 3 +--R (- - coth(x)csch(x) + - %i coth(x) - 2%i coth(x))sinh(x) +--R 2 3 +--R + +--R 1 1 3 +--R - - %i coth(x)csch(x) - - coth(x) + 2coth(x) - %i cosh(x) +--R 2 3 +--R / +--R sinh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 142 + +--S 143 of 530 +a0528:= integrate(t0528,x) +--R +--R +--R (141) +--R 7 6 +--R 9sinh(x) + (63cosh(x) + 9%i)sinh(x) +--R + +--R 2 5 +--R (189cosh(x) + 54%i cosh(x) - 27)sinh(x) +--R + +--R 3 2 4 +--R (315cosh(x) + 135%i cosh(x) - 135cosh(x) - 27%i)sinh(x) +--R + +--R 4 3 2 +--R (315cosh(x) + 180%i cosh(x) - 270cosh(x) - 108%i cosh(x) + 27) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 189cosh(x) + 135%i cosh(x) - 270cosh(x) - 162%i cosh(x) +--R + +--R 81cosh(x) + 27%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 63cosh(x) + 54%i cosh(x) - 135cosh(x) - 108%i cosh(x) +--R + +--R 2 +--R 81cosh(x) + 54%i cosh(x) - 9 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 9cosh(x) + 9%i cosh(x) - 27cosh(x) - 27%i cosh(x) + 27cosh(x) +--R + +--R 2 +--R 27%i cosh(x) - 9cosh(x) - 9%i +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 7 6 +--R - 9sinh(x) + (- 63cosh(x) - 9%i)sinh(x) +--R + +--R 2 5 +--R (- 189cosh(x) - 54%i cosh(x) + 27)sinh(x) +--R + +--R 3 2 4 +--R (- 315cosh(x) - 135%i cosh(x) + 135cosh(x) + 27%i)sinh(x) +--R + +--R 4 3 2 +--R (- 315cosh(x) - 180%i cosh(x) + 270cosh(x) + 108%i cosh(x) - 27) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 189cosh(x) - 135%i cosh(x) + 270cosh(x) + 162%i cosh(x) +--R + +--R - 81cosh(x) - 27%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 63cosh(x) - 54%i cosh(x) + 135cosh(x) + 108%i cosh(x) +--R + +--R 2 +--R - 81cosh(x) - 54%i cosh(x) + 9 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 9cosh(x) - 9%i cosh(x) + 27cosh(x) + 27%i cosh(x) - 27cosh(x) +--R + +--R 2 +--R - 27%i cosh(x) + 9cosh(x) + 9%i +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 6 5 +--R - 18sinh(x) + (- 108cosh(x) - 18%i)sinh(x) +--R + +--R 2 4 +--R (- 270cosh(x) - 90%i cosh(x) + 48)sinh(x) +--R + +--R 3 2 3 +--R (- 360cosh(x) - 180%i cosh(x) + 192cosh(x) + 48%i)sinh(x) +--R + +--R 4 3 2 +--R (- 270cosh(x) - 180%i cosh(x) + 288cosh(x) + 144%i cosh(x) - 78) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 108cosh(x) - 90%i cosh(x) + 192cosh(x) + 144%i cosh(x) +--R + +--R - 156cosh(x) - 14%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 18cosh(x) - 18%i cosh(x) + 48cosh(x) + 48%i cosh(x) - 78cosh(x) +--R + +--R - 14%i cosh(x) + 32 +--R / +--R 7 6 +--R 6sinh(x) + (42cosh(x) + 6%i)sinh(x) +--R + +--R 2 5 +--R (126cosh(x) + 36%i cosh(x) - 18)sinh(x) +--R + +--R 3 2 4 +--R (210cosh(x) + 90%i cosh(x) - 90cosh(x) - 18%i)sinh(x) +--R + +--R 4 3 2 3 +--R (210cosh(x) + 120%i cosh(x) - 180cosh(x) - 72%i cosh(x) + 18)sinh(x) +--R + +--R 5 4 3 2 +--R 126cosh(x) + 90%i cosh(x) - 180cosh(x) - 108%i cosh(x) +--R + +--R 54cosh(x) + 18%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 42cosh(x) + 36%i cosh(x) - 90cosh(x) - 72%i cosh(x) + 54cosh(x) +--R + +--R 36%i cosh(x) - 6 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) + 6%i cosh(x) - 18cosh(x) - 18%i cosh(x) + 18cosh(x) +--R + +--R 2 +--R 18%i cosh(x) - 6cosh(x) - 6%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 143 + +--S 144 of 530 +m0528:= a0528-r0528 +--R +--R +--R (142) +--R 3 8 21 7 +--R - sinh(x) + (-- cosh(x) + 3%i)sinh(x) +--R 2 2 +--R + +--R 63 2 39 6 +--R (-- cosh(x) + -- %i cosh(x) - 6)sinh(x) +--R 2 2 +--R + +--R 105 3 2 63 5 +--R (--- cosh(x) + 54%i cosh(x) - -- cosh(x) - 9%i)sinh(x) +--R 2 2 +--R + +--R 105 4 165 3 135 2 81 +--R (--- cosh(x) + --- %i cosh(x) - --- cosh(x) - -- %i cosh(x) + 9) +--R 2 2 2 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 63 5 4 3 2 +--R -- cosh(x) + 75%i cosh(x) - 75cosh(x) - 72%i cosh(x) +--R 2 +--R + +--R 63 +--R -- cosh(x) + 9%i +--R 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 21 6 81 5 4 3 +--R -- cosh(x) + -- %i cosh(x) - 45cosh(x) - 63%i cosh(x) +--R 2 2 +--R + +--R 81 2 45 +--R -- cosh(x) + -- %i cosh(x) - 6 +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 6 27 5 4 +--R - cosh(x) + 12%i cosh(x) - -- cosh(x) - 27%i cosh(x) +--R 2 2 +--R + +--R 45 3 2 21 +--R -- cosh(x) + 18%i cosh(x) - -- cosh(x) - 3%i +--R 2 2 +--R * +--R sinh(x) +--R + +--R 3 7 3 6 9 5 9 4 +--R - %i cosh(x) - - cosh(x) - - %i cosh(x) + - cosh(x) +--R 2 2 2 2 +--R + +--R 9 3 9 2 3 3 +--R - %i cosh(x) - - cosh(x) - - %i cosh(x) + - +--R 2 2 2 2 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 8 21 7 +--R - - sinh(x) + (- -- cosh(x) - 3%i)sinh(x) +--R 2 2 +--R + +--R 63 2 39 6 +--R (- -- cosh(x) - -- %i cosh(x) + 6)sinh(x) +--R 2 2 +--R + +--R 105 3 2 63 5 +--R (- --- cosh(x) - 54%i cosh(x) + -- cosh(x) + 9%i)sinh(x) +--R 2 2 +--R + +--R 105 4 165 3 135 2 81 +--R - --- cosh(x) - --- %i cosh(x) + --- cosh(x) + -- %i cosh(x) +--R 2 2 2 2 +--R + +--R - 9 +--R * +--R 4 +--R sinh(x) +--R + +--R 63 5 4 3 2 +--R - -- cosh(x) - 75%i cosh(x) + 75cosh(x) + 72%i cosh(x) +--R 2 +--R + +--R 63 +--R - -- cosh(x) - 9%i +--R 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 21 6 81 5 4 3 +--R - -- cosh(x) - -- %i cosh(x) + 45cosh(x) + 63%i cosh(x) +--R 2 2 +--R + +--R 81 2 45 +--R - -- cosh(x) - -- %i cosh(x) + 6 +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 6 27 5 4 +--R - - cosh(x) - 12%i cosh(x) + -- cosh(x) + 27%i cosh(x) +--R 2 2 +--R + +--R 45 3 2 21 +--R - -- cosh(x) - 18%i cosh(x) + -- cosh(x) + 3%i +--R 2 2 +--R * +--R sinh(x) +--R + +--R 3 7 3 6 9 5 9 4 +--R - - %i cosh(x) + - cosh(x) + - %i cosh(x) - - cosh(x) +--R 2 2 2 2 +--R + +--R 9 3 9 2 3 3 +--R - - %i cosh(x) + - cosh(x) + - %i cosh(x) - - +--R 2 2 2 2 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 8 21 7 +--R - - sinh(x) + (- -- cosh(x) - 3%i)sinh(x) +--R 2 2 +--R + +--R 63 2 39 6 +--R (- -- cosh(x) - -- %i cosh(x) + 6)sinh(x) +--R 2 2 +--R + +--R 105 3 2 63 5 +--R (- --- cosh(x) - 54%i cosh(x) + -- cosh(x) + 9%i)sinh(x) +--R 2 2 +--R + +--R 105 4 165 3 135 2 81 +--R - --- cosh(x) - --- %i cosh(x) + --- cosh(x) + -- %i cosh(x) +--R 2 2 2 2 +--R + +--R - 9 +--R * +--R 4 +--R sinh(x) +--R + +--R 63 5 4 3 2 +--R - -- cosh(x) - 75%i cosh(x) + 75cosh(x) + 72%i cosh(x) +--R 2 +--R + +--R 63 +--R - -- cosh(x) - 9%i +--R 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 21 6 81 5 4 3 +--R - -- cosh(x) - -- %i cosh(x) + 45cosh(x) + 63%i cosh(x) +--R 2 2 +--R + +--R 81 2 45 +--R - -- cosh(x) - -- %i cosh(x) + 6 +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 6 27 5 4 +--R - - cosh(x) - 12%i cosh(x) + -- cosh(x) + 27%i cosh(x) +--R 2 2 +--R + +--R 45 3 2 21 +--R - -- cosh(x) - 18%i cosh(x) + -- cosh(x) + 3%i +--R 2 2 +--R * +--R sinh(x) +--R + +--R 3 7 3 6 9 5 9 4 +--R - - %i cosh(x) + - cosh(x) + - %i cosh(x) - - cosh(x) +--R 2 2 2 2 +--R + +--R 9 3 9 2 3 3 +--R - - %i cosh(x) + - cosh(x) + - %i cosh(x) - - +--R 2 2 2 2 +--R * +--R acoth(cosh(x)) +--R + +--R 1 1 3 8 +--R (- coth(x)csch(x) - - %i coth(x) + 2%i coth(x))sinh(x) +--R 2 3 +--R + +--R 7 7 2 3 +--R (- cosh(x) + %i)coth(x)csch(x) + (- - %i cosh(x) + -)coth(x) +--R 2 3 3 +--R + +--R (14%i cosh(x) - 4)coth(x) + %i cosh(x) - 3 +--R * +--R 7 +--R sinh(x) +--R + +--R 21 2 13 +--R (-- cosh(x) + -- %i cosh(x) - 2)coth(x)csch(x) +--R 2 2 +--R + +--R 2 13 4 3 +--R (- 7%i cosh(x) + -- cosh(x) + - %i)coth(x) +--R 3 3 +--R + +--R 2 2 +--R (42%i cosh(x) - 26cosh(x) - 8%i)coth(x) + 7%i cosh(x) - 19cosh(x) +--R + +--R - 6%i +--R * +--R 6 +--R sinh(x) +--R + +--R 35 3 2 21 +--R (-- cosh(x) + 18%i cosh(x) - -- cosh(x) - 3%i)coth(x)csch(x) +--R 2 2 +--R + +--R 35 3 2 3 +--R (- -- %i cosh(x) + 12cosh(x) + 7%i cosh(x) - 2)coth(x) +--R 3 +--R + +--R 3 2 +--R (70%i cosh(x) - 72cosh(x) - 42%i cosh(x) + 12)coth(x) +--R + +--R 3 2 +--R 21%i cosh(x) - 51cosh(x) - 36%i cosh(x) + 11 +--R * +--R 5 +--R sinh(x) +--R + +--R 35 4 55 3 45 2 27 +--R (-- cosh(x) + -- %i cosh(x) - -- cosh(x) - -- %i cosh(x) + 3) +--R 2 2 2 2 +--R * +--R coth(x)csch(x) +--R + +--R 35 4 55 3 2 +--R (- -- %i cosh(x) + -- cosh(x) + 15%i cosh(x) - 9cosh(x) - 2%i) +--R 3 3 +--R * +--R 3 +--R coth(x) +--R + +--R 4 3 2 +--R (70%i cosh(x) - 110cosh(x) - 90%i cosh(x) + 54cosh(x) + 12%i) +--R * +--R coth(x) +--R + +--R 4 3 2 +--R 35%i cosh(x) - 75cosh(x) - 90%i cosh(x) + 50cosh(x) + 16%i +--R * +--R 4 +--R sinh(x) +--R + +--R 21 5 4 3 2 +--R -- cosh(x) + 25%i cosh(x) - 25cosh(x) - 24%i cosh(x) +--R 2 +--R + +--R 21 +--R -- cosh(x) + 3%i +--R 2 +--R * +--R coth(x)csch(x) +--R + +--R 5 50 4 50 3 2 +--R - 7%i cosh(x) + -- cosh(x) + -- %i cosh(x) - 16cosh(x) +--R 3 3 +--R + +--R - 7%i cosh(x) + 2 +--R * +--R 3 +--R coth(x) +--R + +--R 5 4 3 2 +--R 42%i cosh(x) - 100cosh(x) - 100%i cosh(x) + 96cosh(x) +--R + +--R 42%i cosh(x) - 12 +--R * +--R coth(x) +--R + +--R 5 4 3 2 +--R 35%i cosh(x) - 65cosh(x) - 120%i cosh(x) + 90cosh(x) +--R + +--R 59%i cosh(x) - 21 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 27 5 4 3 +--R - cosh(x) + -- %i cosh(x) - 15cosh(x) - 21%i cosh(x) +--R 2 2 +--R + +--R 27 2 15 +--R -- cosh(x) + -- %i cosh(x) - 2 +--R 2 2 +--R * +--R coth(x)csch(x) +--R + +--R 7 6 5 4 3 +--R - - %i cosh(x) + 9cosh(x) + 10%i cosh(x) - 14cosh(x) +--R 3 +--R + +--R 2 4 +--R - 9%i cosh(x) + 5cosh(x) + - %i +--R 3 +--R * +--R 3 +--R coth(x) +--R + +--R 6 5 4 3 +--R 14%i cosh(x) - 54cosh(x) - 60%i cosh(x) + 84cosh(x) +--R + +--R 2 +--R 54%i cosh(x) - 30cosh(x) - 8%i +--R * +--R coth(x) +--R + +--R 6 5 4 3 +--R 21%i cosh(x) - 33cosh(x) - 90%i cosh(x) + 80cosh(x) +--R + +--R 2 46 +--R 81%i cosh(x) - 53cosh(x) - -- %i +--R 3 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 7 6 9 5 4 +--R - cosh(x) + 4%i cosh(x) - - cosh(x) - 9%i cosh(x) +--R 2 2 +--R + +--R 15 3 2 7 +--R -- cosh(x) + 6%i cosh(x) - - cosh(x) - %i +--R 2 2 +--R * +--R coth(x)csch(x) +--R + +--R 1 7 8 6 5 4 +--R - - %i cosh(x) + - cosh(x) + 3%i cosh(x) - 6cosh(x) +--R 3 3 +--R + +--R 3 2 7 2 +--R - 5%i cosh(x) + 4cosh(x) + - %i cosh(x) - - +--R 3 3 +--R * +--R 3 +--R coth(x) +--R + +--R 7 6 5 4 +--R 2%i cosh(x) - 16cosh(x) - 18%i cosh(x) + 36cosh(x) +--R + +--R 3 2 +--R 30%i cosh(x) - 24cosh(x) - 14%i cosh(x) + 4 +--R * +--R coth(x) +--R + +--R 7 6 5 4 3 +--R 7%i cosh(x) - 9cosh(x) - 36%i cosh(x) + 35cosh(x) + 49%i cosh(x) +--R + +--R 2 88 23 +--R - 43cosh(x) - -- %i cosh(x) + -- +--R 3 3 +--R * +--R sinh(x) +--R + +--R 1 7 1 6 3 5 3 4 +--R - %i cosh(x) - - cosh(x) - - %i cosh(x) + - cosh(x) +--R 2 2 2 2 +--R + +--R 3 3 3 2 1 1 +--R - %i cosh(x) - - cosh(x) - - %i cosh(x) + - +--R 2 2 2 2 +--R * +--R coth(x)csch(x) +--R + +--R 1 7 1 6 5 4 3 +--R - cosh(x) + - %i cosh(x) - cosh(x) - %i cosh(x) + cosh(x) +--R 3 3 +--R + +--R 2 1 1 +--R %i cosh(x) - - cosh(x) - - %i +--R 3 3 +--R * +--R 3 +--R coth(x) +--R + +--R 7 6 5 4 3 +--R - 2cosh(x) - 2%i cosh(x) + 6cosh(x) + 6%i cosh(x) - 6cosh(x) +--R + +--R 2 +--R - 6%i cosh(x) + 2cosh(x) + 2%i +--R * +--R coth(x) +--R + +--R 8 7 6 5 4 +--R %i cosh(x) - cosh(x) - 6%i cosh(x) + 6cosh(x) + 11%i cosh(x) +--R + +--R 3 2 10 16 +--R - 11cosh(x) - 14%i cosh(x) + -- cosh(x) + -- %i +--R 3 3 +--R / +--R 8 7 +--R sinh(x) + (7cosh(x) + 2%i)sinh(x) +--R + +--R 2 6 +--R (21cosh(x) + 13%i cosh(x) - 4)sinh(x) +--R + +--R 3 2 5 +--R (35cosh(x) + 36%i cosh(x) - 21cosh(x) - 6%i)sinh(x) +--R + +--R 4 3 2 4 +--R (35cosh(x) + 55%i cosh(x) - 45cosh(x) - 27%i cosh(x) + 6)sinh(x) +--R + +--R 5 4 3 2 +--R 21cosh(x) + 50%i cosh(x) - 50cosh(x) - 48%i cosh(x) + 21cosh(x) +--R + +--R 6%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 7cosh(x) + 27%i cosh(x) - 30cosh(x) - 42%i cosh(x) + 27cosh(x) +--R + +--R 15%i cosh(x) - 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R cosh(x) + 8%i cosh(x) - 9cosh(x) - 18%i cosh(x) + 15cosh(x) +--R + +--R 2 +--R 12%i cosh(x) - 7cosh(x) - 2%i +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R %i cosh(x) - cosh(x) - 3%i cosh(x) + 3cosh(x) + 3%i cosh(x) +--R + +--R 2 +--R - 3cosh(x) - %i cosh(x) + 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 144 + +--S 145 of 530 +d0528:= D(m0528,x) +--R +--R +--R (143) +--R 3 13 +--R - sinh(x) +--R 2 +--R + +--R 2 2 1 2 1 +--R ((- cosh(x) + 1)coth(x) + - cosh(x) - -)csch(x) +--R 2 2 +--R + +--R 2 4 2 2 +--R (%i cosh(x) - %i)coth(x) + (- 3%i cosh(x) + 3%i)coth(x) +--R + +--R 2 +--R 3%i cosh(x) + 15cosh(x) + 3%i +--R * +--R 12 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 10cosh(x) - 4%i cosh(x) + 10cosh(x) + 4%i)coth(x) +--R + +--R 3 2 +--R 5cosh(x) + 2%i cosh(x) - 5cosh(x) - 2%i +--R * +--R csch(x) +--R + +--R 3 2 4 +--R (10%i cosh(x) - 4cosh(x) - 10%i cosh(x) + 4)coth(x) +--R + +--R 3 2 2 +--R (- 30%i cosh(x) + 12cosh(x) + 30%i cosh(x) - 12)coth(x) +--R + +--R 3 113 2 +--R 30%i cosh(x) + --- cosh(x) + 27%i cosh(x) - 4 +--R 2 +--R * +--R 11 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 45cosh(x) - 38%i cosh(x) + 55cosh(x) + 38%i cosh(x) - 10) +--R * +--R 2 +--R coth(x) +--R + +--R 45 4 3 55 2 +--R -- cosh(x) + 19%i cosh(x) - -- cosh(x) - 19%i cosh(x) + 5 +--R 2 2 +--R * +--R csch(x) +--R + +--R 4 3 2 +--R (45%i cosh(x) - 38cosh(x) - 55%i cosh(x) + 38cosh(x) + 10%i) +--R * +--R 4 +--R coth(x) +--R + +--R 4 3 2 +--R - 135%i cosh(x) + 114cosh(x) + 165%i cosh(x) - 114cosh(x) +--R + +--R - 30%i +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 +--R 134%i cosh(x) + 76cosh(x) + 82%i cosh(x) - 25cosh(x) - 3%i +--R * +--R 10 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 120cosh(x) - 162%i cosh(x) + 206cosh(x) + 182%i cosh(x) +--R + +--R - 86cosh(x) - 20%i +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 2 +--R 60cosh(x) + 81%i cosh(x) - 103cosh(x) - 91%i cosh(x) +--R + +--R 43cosh(x) + 10%i +--R * +--R csch(x) +--R + +--R 5 4 3 2 +--R 120%i cosh(x) - 162cosh(x) - 206%i cosh(x) + 182cosh(x) +--R + +--R 86%i cosh(x) - 20 +--R * +--R 4 +--R coth(x) +--R + +--R 5 4 3 2 +--R - 360%i cosh(x) + 486cosh(x) + 618%i cosh(x) - 546cosh(x) +--R + +--R - 258%i cosh(x) + 60 +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 3 2 +--R 350%i cosh(x) - 124cosh(x) + 32%i cosh(x) - - cosh(x) +--R 2 +--R + +--R 13 +--R - %i cosh(x) - -- +--R 2 +--R * +--R 9 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 210cosh(x) - 408%i cosh(x) + 539cosh(x) + 562%i cosh(x) +--R + +--R 2 +--R - 360cosh(x) - 154%i cosh(x) + 31 +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 539 4 3 +--R 105cosh(x) + 204%i cosh(x) - --- cosh(x) - 281%i cosh(x) +--R 2 +--R + +--R 2 31 +--R 180cosh(x) + 77%i cosh(x) - -- +--R 2 +--R * +--R csch(x) +--R + +--R 6 5 4 3 +--R 210%i cosh(x) - 408cosh(x) - 539%i cosh(x) + 562cosh(x) +--R + +--R 2 +--R 360%i cosh(x) - 154cosh(x) - 31%i +--R * +--R 4 +--R coth(x) +--R + +--R 6 5 4 3 +--R - 630%i cosh(x) + 1224cosh(x) + 1617%i cosh(x) - 1686cosh(x) +--R + +--R 2 +--R - 1080%i cosh(x) + 462cosh(x) + 93%i +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 +--R 585%i cosh(x) - 708cosh(x) - 442%i cosh(x) + 386cosh(x) +--R + +--R 2 +--R 165%i cosh(x) - 86cosh(x) - 20%i +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 5 +--R - 252cosh(x) - 672%i cosh(x) + 988cosh(x) +--R + +--R 4 3 2 +--R 1192%i cosh(x) - 948cosh(x) - 560%i cosh(x) + 212cosh(x) +--R + +--R 40%i +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R 126cosh(x) + 336%i cosh(x) - 494cosh(x) - 596%i cosh(x) +--R + +--R 3 2 +--R 474cosh(x) + 280%i cosh(x) - 106cosh(x) - 20%i +--R * +--R csch(x) +--R + +--R 7 6 5 4 +--R 252%i cosh(x) - 672cosh(x) - 988%i cosh(x) + 1192cosh(x) +--R + +--R 3 2 +--R 948%i cosh(x) - 560cosh(x) - 212%i cosh(x) + 40 +--R * +--R 4 +--R coth(x) +--R + +--R 7 6 5 4 +--R - 756%i cosh(x) + 2016cosh(x) + 2964%i cosh(x) - 3576cosh(x) +--R + +--R 3 2 +--R - 2844%i cosh(x) + 1680cosh(x) + 636%i cosh(x) - 120 +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R 636%i cosh(x) - 1419cosh(x) - 1382%i cosh(x) + 1478cosh(x) +--R + +--R 3 2 +--R 908%i cosh(x) - 471cosh(x) - 186%i cosh(x) + 4 +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 6 +--R - 210cosh(x) - 756%i cosh(x) + 1274cosh(x) +--R + +--R 5 4 3 +--R 1764%i cosh(x) - 1690cosh(x) - 1244%i cosh(x) +--R + +--R 2 +--R 670cosh(x) + 236%i cosh(x) - 44 +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 +--R 105cosh(x) + 378%i cosh(x) - 637cosh(x) - 882%i cosh(x) +--R + +--R 4 3 2 +--R 845cosh(x) + 622%i cosh(x) - 335cosh(x) - 118%i cosh(x) + 22 +--R * +--R csch(x) +--R + +--R 8 7 6 5 +--R 210%i cosh(x) - 756cosh(x) - 1274%i cosh(x) + 1764cosh(x) +--R + +--R 4 3 2 +--R 1690%i cosh(x) - 1244cosh(x) - 670%i cosh(x) + 236cosh(x) + 44%i +--R * +--R 4 +--R coth(x) +--R + +--R 8 7 6 5 +--R - 630%i cosh(x) + 2268cosh(x) + 3822%i cosh(x) - 5292cosh(x) +--R + +--R 4 3 2 +--R - 5070%i cosh(x) + 3732cosh(x) + 2010%i cosh(x) - 708cosh(x) +--R + +--R - 132%i +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 +--R 420%i cosh(x) - 1668cosh(x) - 2128%i cosh(x) + 2814cosh(x) +--R + +--R 4 3 2 +--R 2302%i cosh(x) - 1392cosh(x) - 724%i cosh(x) + 102cosh(x) - 14%i +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 7 +--R - 120cosh(x) - 588%i cosh(x) + 1156cosh(x) +--R + +--R 6 5 4 +--R 1820%i cosh(x) - 2076cosh(x) - 1820%i cosh(x) +--R + +--R 3 2 +--R 1260cosh(x) + 628%i cosh(x) - 220cosh(x) - 40%i +--R * +--R 2 +--R coth(x) +--R + +--R 9 8 7 6 +--R 60cosh(x) + 294%i cosh(x) - 578cosh(x) - 910%i cosh(x) +--R + +--R 5 4 3 2 +--R 1038cosh(x) + 910%i cosh(x) - 630cosh(x) - 314%i cosh(x) +--R + +--R 110cosh(x) + 20%i +--R * +--R csch(x) +--R + +--R 9 8 7 6 +--R 120%i cosh(x) - 588cosh(x) - 1156%i cosh(x) + 1820cosh(x) +--R + +--R 5 4 3 2 +--R 2076%i cosh(x) - 1820cosh(x) - 1260%i cosh(x) + 628cosh(x) +--R + +--R 220%i cosh(x) - 40 +--R * +--R 4 +--R coth(x) +--R + +--R 9 8 7 6 +--R - 360%i cosh(x) + 1764cosh(x) + 3468%i cosh(x) - 5460cosh(x) +--R + +--R 5 4 3 2 +--R - 6228%i cosh(x) + 5460cosh(x) + 3780%i cosh(x) - 1884cosh(x) +--R + +--R - 660%i cosh(x) + 120 +--R * +--R 2 +--R coth(x) +--R + +--R 9 2469 8 7 6 +--R 108%i cosh(x) - ---- cosh(x) - 1964%i cosh(x) + 3199cosh(x) +--R 2 +--R + +--R 5 4 3 2 +--R 3354%i cosh(x) - 2450cosh(x) - 1520%i cosh(x) + 505cosh(x) +--R + +--R 39 +--R - 26%i cosh(x) - -- +--R 2 +--R * +--R 5 +--R sinh(x) +--R + +--R 10 9 8 +--R - 45cosh(x) - 312%i cosh(x) + 731cosh(x) +--R + +--R 7 6 5 +--R 1292%i cosh(x) - 1746cosh(x) - 1780%i cosh(x) +--R + +--R 4 3 2 +--R 1510cosh(x) + 964%i cosh(x) - 481cosh(x) - 164%i cosh(x) +--R + +--R 31 +--R * +--R 2 +--R coth(x) +--R + +--R 45 10 9 731 8 7 +--R -- cosh(x) + 156%i cosh(x) - --- cosh(x) - 646%i cosh(x) +--R 2 2 +--R + +--R 6 5 4 3 +--R 873cosh(x) + 890%i cosh(x) - 755cosh(x) - 482%i cosh(x) +--R + +--R 481 2 31 +--R --- cosh(x) + 82%i cosh(x) - -- +--R 2 2 +--R * +--R csch(x) +--R + +--R 10 9 8 7 +--R 45%i cosh(x) - 312cosh(x) - 731%i cosh(x) + 1292cosh(x) +--R + +--R 6 5 4 3 +--R 1746%i cosh(x) - 1780cosh(x) - 1510%i cosh(x) + 964cosh(x) +--R + +--R 2 +--R 481%i cosh(x) - 164cosh(x) - 31%i +--R * +--R 4 +--R coth(x) +--R + +--R 10 9 8 7 +--R - 135%i cosh(x) + 936cosh(x) + 2193%i cosh(x) - 3876cosh(x) +--R + +--R 6 5 4 3 +--R - 5238%i cosh(x) + 5340cosh(x) + 4530%i cosh(x) - 2892cosh(x) +--R + +--R 2 +--R - 1443%i cosh(x) + 492cosh(x) + 93%i +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 +--R - 75%i cosh(x) - 549cosh(x) - 1093%i cosh(x) + 2236cosh(x) +--R + +--R 6 5 4 3 +--R 2974%i cosh(x) - 2654cosh(x) - 1870%i cosh(x) + 1052cosh(x) +--R + +--R 2 +--R 109%i cosh(x) - 85cosh(x) - 45%i +--R * +--R 4 +--R sinh(x) +--R + +--R 11 10 9 +--R - 10cosh(x) - 108%i cosh(x) + 314cosh(x) +--R + +--R 8 7 6 5 +--R 612%i cosh(x) - 980cosh(x) - 1144%i cosh(x) + 1156cosh(x) +--R + +--R 4 3 2 +--R 904%i cosh(x) - 578cosh(x) - 284%i cosh(x) + 98cosh(x) +--R + +--R 20%i +--R * +--R 2 +--R coth(x) +--R + +--R 11 10 9 8 +--R 5cosh(x) + 54%i cosh(x) - 157cosh(x) - 306%i cosh(x) +--R + +--R 7 6 5 4 +--R 490cosh(x) + 572%i cosh(x) - 578cosh(x) - 452%i cosh(x) +--R + +--R 3 2 +--R 289cosh(x) + 142%i cosh(x) - 49cosh(x) - 10%i +--R * +--R csch(x) +--R + +--R 11 10 9 8 +--R 10%i cosh(x) - 108cosh(x) - 314%i cosh(x) + 612cosh(x) +--R + +--R 7 6 5 4 +--R 980%i cosh(x) - 1144cosh(x) - 1156%i cosh(x) + 904cosh(x) +--R + +--R 3 2 +--R 578%i cosh(x) - 284cosh(x) - 98%i cosh(x) + 20 +--R * +--R 4 +--R coth(x) +--R + +--R 11 10 9 8 +--R - 30%i cosh(x) + 324cosh(x) + 942%i cosh(x) - 1836cosh(x) +--R + +--R 7 6 5 4 +--R - 2940%i cosh(x) + 3432cosh(x) + 3468%i cosh(x) - 2712cosh(x) +--R + +--R 3 2 +--R - 1734%i cosh(x) + 852cosh(x) + 294%i cosh(x) - 60 +--R * +--R 2 +--R coth(x) +--R + +--R 11 219 10 9 8 +--R - 90%i cosh(x) - --- cosh(x) - 317%i cosh(x) + 906cosh(x) +--R 2 +--R + +--R 7 6 5 4 +--R 1580%i cosh(x) - 1741cosh(x) - 1370%i cosh(x) + 1074cosh(x) +--R + +--R 3 323 2 +--R 358%i cosh(x) - --- cosh(x) - 161%i cosh(x) + 32 +--R 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 12 11 10 9 +--R - cosh(x) - 22%i cosh(x) + 87cosh(x) + 182%i cosh(x) +--R + +--R 8 7 6 5 +--R - 348cosh(x) - 460%i cosh(x) + 542cosh(x) + 508%i cosh(x) +--R + +--R 4 3 2 +--R - 393cosh(x) - 254%i cosh(x) + 123cosh(x) + 46%i cosh(x) +--R + +--R - 10 +--R * +--R 2 +--R coth(x) +--R + +--R 1 12 11 87 10 9 +--R - cosh(x) + 11%i cosh(x) - -- cosh(x) - 91%i cosh(x) +--R 2 2 +--R + +--R 8 7 6 5 +--R 174cosh(x) + 230%i cosh(x) - 271cosh(x) - 254%i cosh(x) +--R + +--R 393 4 3 123 2 +--R --- cosh(x) + 127%i cosh(x) - --- cosh(x) - 23%i cosh(x) + 5 +--R 2 2 +--R * +--R csch(x) +--R + +--R 12 11 10 9 +--R %i cosh(x) - 22cosh(x) - 87%i cosh(x) + 182cosh(x) +--R + +--R 8 7 6 5 +--R 348%i cosh(x) - 460cosh(x) - 542%i cosh(x) + 508cosh(x) +--R + +--R 4 3 2 +--R 393%i cosh(x) - 254cosh(x) - 123%i cosh(x) + 46cosh(x) + 10%i +--R * +--R 4 +--R coth(x) +--R + +--R 12 11 10 9 +--R - 3%i cosh(x) + 66cosh(x) + 261%i cosh(x) - 546cosh(x) +--R + +--R 8 7 6 5 +--R - 1044%i cosh(x) + 1380cosh(x) + 1626%i cosh(x) - 1524cosh(x) +--R + +--R 4 3 2 +--R - 1179%i cosh(x) + 762cosh(x) + 369%i cosh(x) - 138cosh(x) +--R + +--R - 30%i +--R * +--R 2 +--R coth(x) +--R + +--R 12 11 10 9 +--R - 42%i cosh(x) + 16cosh(x) - 10%i cosh(x) + 163cosh(x) +--R + +--R 8 7 6 5 +--R 453%i cosh(x) - 636cosh(x) - 576%i cosh(x) + 514cosh(x) +--R + +--R 4 3 2 +--R 380%i cosh(x) - 140cosh(x) - 222%i cosh(x) + 83cosh(x) + 17%i +--R * +--R 2 +--R sinh(x) +--R + +--R 12 11 10 9 +--R - 2%i cosh(x) + 14cosh(x) + 30%i cosh(x) - 70cosh(x) +--R + +--R 8 7 6 5 +--R - 104%i cosh(x) + 140cosh(x) + 156%i cosh(x) - 140cosh(x) +--R + +--R 4 3 2 +--R - 114%i cosh(x) + 70cosh(x) + 38%i cosh(x) - 14cosh(x) - 4%i +--R * +--R 2 +--R coth(x) +--R + +--R 12 11 10 9 +--R %i cosh(x) - 7cosh(x) - 15%i cosh(x) + 35cosh(x) +--R + +--R 8 7 6 5 +--R 52%i cosh(x) - 70cosh(x) - 78%i cosh(x) + 70cosh(x) +--R + +--R 4 3 2 +--R 57%i cosh(x) - 35cosh(x) - 19%i cosh(x) + 7cosh(x) + 2%i +--R * +--R csch(x) +--R + +--R 12 11 10 9 +--R - 2cosh(x) - 14%i cosh(x) + 30cosh(x) + 70%i cosh(x) +--R + +--R 8 7 6 5 +--R - 104cosh(x) - 140%i cosh(x) + 156cosh(x) + 140%i cosh(x) +--R + +--R 4 3 2 +--R - 114cosh(x) - 70%i cosh(x) + 38cosh(x) + 14%i cosh(x) - 4 +--R * +--R 4 +--R coth(x) +--R + +--R 12 11 10 9 +--R 6cosh(x) + 42%i cosh(x) - 90cosh(x) - 210%i cosh(x) +--R + +--R 8 7 6 5 +--R 312cosh(x) + 420%i cosh(x) - 468cosh(x) - 420%i cosh(x) +--R + +--R 4 3 2 +--R 342cosh(x) + 210%i cosh(x) - 114cosh(x) - 42%i cosh(x) + 12 +--R * +--R 2 +--R coth(x) +--R + +--R 13 12 11 19 10 +--R - 10%i cosh(x) + 13cosh(x) + 20%i cosh(x) - -- cosh(x) +--R 2 +--R + +--R 9 199 8 7 6 +--R 47%i cosh(x) - --- cosh(x) - 124%i cosh(x) + 73cosh(x) +--R 2 +--R + +--R 5 4 3 145 2 +--R 168%i cosh(x) - 42cosh(x) - 128%i cosh(x) + --- cosh(x) +--R 2 +--R + +--R 15 +--R 27%i cosh(x) - -- +--R 2 +--R * +--R sinh(x) +--R + +--R 12 11 10 9 +--R cosh(x) + 2%i cosh(x) - 6cosh(x) - 10%i cosh(x) +--R + +--R 8 7 6 5 +--R 15cosh(x) + 20%i cosh(x) - 20cosh(x) - 20%i cosh(x) +--R + +--R 4 3 2 +--R 15cosh(x) + 10%i cosh(x) - 6cosh(x) - 2%i cosh(x) + 1 +--R * +--R 2 +--R coth(x) +--R + +--R 1 12 11 10 9 +--R - - cosh(x) - %i cosh(x) + 3cosh(x) + 5%i cosh(x) +--R 2 +--R + +--R 15 8 7 6 5 +--R - -- cosh(x) - 10%i cosh(x) + 10cosh(x) + 10%i cosh(x) +--R 2 +--R + +--R 15 4 3 2 1 +--R - -- cosh(x) - 5%i cosh(x) + 3cosh(x) + %i cosh(x) - - +--R 2 2 +--R * +--R csch(x) +--R + +--R 12 11 10 9 +--R - %i cosh(x) + 2cosh(x) + 6%i cosh(x) - 10cosh(x) +--R + +--R 8 7 6 5 +--R - 15%i cosh(x) + 20cosh(x) + 20%i cosh(x) - 20cosh(x) +--R + +--R 4 3 2 +--R - 15%i cosh(x) + 10cosh(x) + 6%i cosh(x) - 2cosh(x) - %i +--R * +--R 4 +--R coth(x) +--R + +--R 12 11 10 9 +--R 3%i cosh(x) - 6cosh(x) - 18%i cosh(x) + 30cosh(x) +--R + +--R 8 7 6 5 +--R 45%i cosh(x) - 60cosh(x) - 60%i cosh(x) + 60cosh(x) +--R + +--R 4 3 2 +--R 45%i cosh(x) - 30cosh(x) - 18%i cosh(x) + 6cosh(x) + 3%i +--R * +--R 2 +--R coth(x) +--R + +--R 14 13 12 11 10 +--R - %i cosh(x) + 2cosh(x) + 4%i cosh(x) - 6cosh(x) - 3%i cosh(x) +--R + +--R 8 7 6 5 4 +--R - 10%i cosh(x) - 12cosh(x) + 25%i cosh(x) + 2cosh(x) - 24%i cosh(x) +--R + +--R 3 2 +--R 18cosh(x) + 11%i cosh(x) - 4cosh(x) - 2%i +--R / +--R 2 12 +--R (cosh(x) - 1)sinh(x) +--R + +--R 3 2 11 +--R (10cosh(x) + 4%i cosh(x) - 10cosh(x) - 4%i)sinh(x) +--R + +--R 4 3 2 10 +--R (45cosh(x) + 38%i cosh(x) - 55cosh(x) - 38%i cosh(x) + 10)sinh(x) +--R + +--R 5 4 3 2 +--R 120cosh(x) + 162%i cosh(x) - 206cosh(x) - 182%i cosh(x) +--R + +--R 86cosh(x) + 20%i +--R * +--R 9 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 210cosh(x) + 408%i cosh(x) - 539cosh(x) - 562%i cosh(x) +--R + +--R 2 +--R 360cosh(x) + 154%i cosh(x) - 31 +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 252cosh(x) + 672%i cosh(x) - 988cosh(x) - 1192%i cosh(x) +--R + +--R 3 2 +--R 948cosh(x) + 560%i cosh(x) - 212cosh(x) - 40%i +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 210cosh(x) + 756%i cosh(x) - 1274cosh(x) - 1764%i cosh(x) +--R + +--R 4 3 2 +--R 1690cosh(x) + 1244%i cosh(x) - 670cosh(x) - 236%i cosh(x) + 44 +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 120cosh(x) + 588%i cosh(x) - 1156cosh(x) - 1820%i cosh(x) +--R + +--R 5 4 3 2 +--R 2076cosh(x) + 1820%i cosh(x) - 1260cosh(x) - 628%i cosh(x) +--R + +--R 220cosh(x) + 40%i +--R * +--R 5 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 45cosh(x) + 312%i cosh(x) - 731cosh(x) - 1292%i cosh(x) +--R + +--R 6 5 4 3 +--R 1746cosh(x) + 1780%i cosh(x) - 1510cosh(x) - 964%i cosh(x) +--R + +--R 2 +--R 481cosh(x) + 164%i cosh(x) - 31 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 10cosh(x) + 108%i cosh(x) - 314cosh(x) - 612%i cosh(x) +--R + +--R 7 6 5 4 +--R 980cosh(x) + 1144%i cosh(x) - 1156cosh(x) - 904%i cosh(x) +--R + +--R 3 2 +--R 578cosh(x) + 284%i cosh(x) - 98cosh(x) - 20%i +--R * +--R 3 +--R sinh(x) +--R + +--R 12 11 10 9 +--R cosh(x) + 22%i cosh(x) - 87cosh(x) - 182%i cosh(x) +--R + +--R 8 7 6 5 +--R 348cosh(x) + 460%i cosh(x) - 542cosh(x) - 508%i cosh(x) +--R + +--R 4 3 2 +--R 393cosh(x) + 254%i cosh(x) - 123cosh(x) - 46%i cosh(x) + 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 12 11 10 9 +--R 2%i cosh(x) - 14cosh(x) - 30%i cosh(x) + 70cosh(x) +--R + +--R 8 7 6 5 +--R 104%i cosh(x) - 140cosh(x) - 156%i cosh(x) + 140cosh(x) +--R + +--R 4 3 2 +--R 114%i cosh(x) - 70cosh(x) - 38%i cosh(x) + 14cosh(x) + 4%i +--R * +--R sinh(x) +--R + +--R 12 11 10 9 8 +--R - cosh(x) - 2%i cosh(x) + 6cosh(x) + 10%i cosh(x) - 15cosh(x) +--R + +--R 7 6 5 4 3 +--R - 20%i cosh(x) + 20cosh(x) + 20%i cosh(x) - 15cosh(x) - 10%i cosh(x) +--R + +--R 2 +--R 6cosh(x) + 2%i cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 145 + +--S 146 of 530 +t0529:= sinh(x)^2/(a+b*cosh(x)) +--R +--R +--R 2 +--R sinh(x) +--R (144) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 530 +r0529:= (-a*x+2*(a^2-b^2)^(1/2)*_ + atanh((a-b)*(cosh(x)-1)/sinh(x)/(a^2-b^2)^(1/2))+b*sinh(x))/b^2 +--R +--R +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a +--R - 2\|- b + a atanh(----------------------) + b sinh(x) - a x +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R (145) -------------------------------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 147 + +--S 148 of 530 +a0529:= integrate(t0529,x) +--R +--R +--R (146) +--R [ +--R +---------+ +--R | 2 2 +--R (2sinh(x) + 2cosh(x))\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|- b + a + b sinh(x) +--R + +--R 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) - b +--R + +--R 2 +--R 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 2 2 +--R b sinh(x) + (2b cosh(x) - 2a x)sinh(x) + b cosh(x) - 2a x cosh(x) - b +--R / +--R 2 2 +--R 2b sinh(x) + 2b cosh(x) +--R , +--R +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 \|b - a +--R (4sinh(x) + 4cosh(x))\|b - a atan(-------------------------) +--R b sinh(x) + b cosh(x) + a +--R + +--R 2 2 +--R b sinh(x) + (2b cosh(x) - 2a x)sinh(x) + b cosh(x) - 2a x cosh(x) - b +--R / +--R 2 2 +--R 2b sinh(x) + 2b cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 148 + +--S 149 of 530 +m0529a:= a0529.1-r0529 +--R +--R +--R (147) +--R +---------+ +--R | 2 2 +--R (2sinh(x) + 2cosh(x))\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|- b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) - b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a +--R (4sinh(x) + 4cosh(x))\|- b + a atanh(----------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R + +--R 2 2 +--R - b sinh(x) + b cosh(x) - b +--R / +--R 2 2 +--R 2b sinh(x) + 2b cosh(x) +--R Type: Expression(Integer) +--E 149 + +--S 150 of 530 +d0529a:= D(m0529a,x) +--R +--R +--R (148) +--R 3 2 6 3 2 3 2 2 5 +--R (b + a b )sinh(x) + ((2b + 2a b )cosh(x) + 4b + 2a b - 2a b)sinh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (b - a b )cosh(x) + (10b + 4a b - 10a b)cosh(x) - b + 5a b +--R + +--R 2 3 +--R 4a b - 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 2 2 +--R - 4a b cosh(x) + (4b + 4a b - 12a b)cosh(x) +--R + +--R 2 2 3 3 2 2 +--R (4a b + 8a b - 8a )cosh(x) + 4b + 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 +--R (- b - a b )cosh(x) + (- 8b + 4a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (6b - 6a b )cosh(x) + (8b + 8a b - 12a b)cosh(x) - b + 3a b +--R + +--R 2 3 +--R 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 4 +--R (- 2b + 2a b )cosh(x) + (- 8b - 6a b + 14a b)cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 2 +--R (4b - 4a b - 8a b + 8a )cosh(x) + (8b + 4a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 2b + 2a b + 8a b - 8a )cosh(x) + 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 5 +--R (- b + a b )cosh(x) + (- 2b - 4a b + 6a b)cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (- b + a b - 4a b + 4a )cosh(x) + (4b - 4a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b - a b + 4a b - 4a )cosh(x) + (- 2b + 4a b - 2a b)cosh(x) + b +--R + +--R 2 +--R - a b +--R / +--R 4 3 5 4 3 3 2 2 4 +--R (2b + 2a b )sinh(x) + ((6b + 6a b )cosh(x) + 4a b + 4a b )sinh(x) +--R + +--R 4 3 2 4 3 2 2 4 3 +--R ((8b + 4a b )cosh(x) + (- 4b + 12a b + 8a b )cosh(x) + 4b )sinh(x) +--R + +--R 4 3 3 4 3 2 +--R (8b - 4a b )cosh(x) + (- 12b + 20a b )cosh(x) +--R + +--R 4 3 2 2 3 2 2 +--R (8b - 12a b + 8a b )cosh(x) + 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 4 4 3 2 2 3 +--R (6b - 6a b )cosh(x) + (- 12b + 20a b - 8a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (8b - 24a b + 16a b )cosh(x) + (- 4b + 12a b - 8a b )cosh(x) +--R + +--R 4 3 +--R 2b - 2a b +--R * +--R sinh(x) +--R + +--R 4 3 5 4 3 2 2 4 +--R (2b - 2a b )cosh(x) + (- 4b + 8a b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 2 +--R (4b - 12a b + 8a b )cosh(x) + (- 4b + 8a b - 4a b )cosh(x) +--R + +--R 4 3 +--R (2b - 2a b )cosh(x) +--R Type: Expression(Integer) +--E 150 + +--S 151 of 530 +m0529b:= a0529.2-r0529 +--R +--R +--R (149) +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a +--R (4sinh(x) + 4cosh(x))\|- b + a atanh(----------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 \|b - a +--R (4sinh(x) + 4cosh(x))\|b - a atan(-------------------------) +--R b sinh(x) + b cosh(x) + a +--R + +--R 2 2 +--R - b sinh(x) + b cosh(x) - b +--R / +--R 2 2 +--R 2b sinh(x) + 2b cosh(x) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 530 +d0529b:= D(m0529b,x) +--R +--R +--R (150) +--R 3 2 6 3 2 3 2 2 5 +--R (b + a b )sinh(x) + ((2b + 2a b )cosh(x) + 4b + 2a b - 2a b)sinh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (b - a b )cosh(x) + (10b + 4a b - 10a b)cosh(x) - b + 5a b +--R + +--R 2 3 +--R 4a b - 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 2 2 +--R - 4a b cosh(x) + (4b + 4a b - 12a b)cosh(x) +--R + +--R 2 2 3 3 2 2 +--R (4a b + 8a b - 8a )cosh(x) + 4b + 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 3 2 3 +--R (- b - a b )cosh(x) + (- 8b + 4a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (6b - 6a b )cosh(x) + (8b + 8a b - 12a b)cosh(x) - b + 3a b +--R + +--R 2 3 +--R 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 4 +--R (- 2b + 2a b )cosh(x) + (- 8b - 6a b + 14a b)cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 2 +--R (4b - 4a b - 8a b + 8a )cosh(x) + (8b + 4a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 2 +--R (- 2b + 2a b + 8a b - 8a )cosh(x) + 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 5 +--R (- b + a b )cosh(x) + (- 2b - 4a b + 6a b)cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (- b + a b - 4a b + 4a )cosh(x) + (4b - 4a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b - a b + 4a b - 4a )cosh(x) + (- 2b + 4a b - 2a b)cosh(x) + b +--R + +--R 2 +--R - a b +--R / +--R 4 3 5 4 3 3 2 2 4 +--R (2b + 2a b )sinh(x) + ((6b + 6a b )cosh(x) + 4a b + 4a b )sinh(x) +--R + +--R 4 3 2 4 3 2 2 4 3 +--R ((8b + 4a b )cosh(x) + (- 4b + 12a b + 8a b )cosh(x) + 4b )sinh(x) +--R + +--R 4 3 3 4 3 2 +--R (8b - 4a b )cosh(x) + (- 12b + 20a b )cosh(x) +--R + +--R 4 3 2 2 3 2 2 +--R (8b - 12a b + 8a b )cosh(x) + 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 4 4 3 2 2 3 +--R (6b - 6a b )cosh(x) + (- 12b + 20a b - 8a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (8b - 24a b + 16a b )cosh(x) + (- 4b + 12a b - 8a b )cosh(x) +--R + +--R 4 3 +--R 2b - 2a b +--R * +--R sinh(x) +--R + +--R 4 3 5 4 3 2 2 4 +--R (2b - 2a b )cosh(x) + (- 4b + 8a b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 2 +--R (4b - 12a b + 8a b )cosh(x) + (- 4b + 8a b - 4a b )cosh(x) +--R + +--R 4 3 +--R (2b - 2a b )cosh(x) +--R Type: Expression(Integer) +--E 152 + +--S 153 of 530 +t0530:= sinh(x)^3/(a+b*cosh(x)) +--R +--R +--R 3 +--R sinh(x) +--R (151) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 153 + +--S 154 of 530 +r0530:= -a*cosh(x)/b^2+1/2*cosh(x)^2/b+(a^2-b^2)*log(a+b*cosh(x))/b^3 +--R +--R +--R 2 2 2 2 +--R (- 2b + 2a )log(b cosh(x) + a) + b cosh(x) - 2a b cosh(x) +--R (152) ----------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 154 + +--S 155 of 530 +a0530:= integrate(t0530,x) +--R +--R +--R (153) +--R 2 2 2 2 2 +--R (- 8b + 8a )sinh(x) + (- 16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 8b + 8a )cosh(x) +--R * +--R - 2b cosh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 4 2 3 +--R b sinh(x) + (4b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6b cosh(x) - 12a b cosh(x) + (8b - 8a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4b cosh(x) - 12a b cosh(x) + (16b - 16a )x cosh(x) - 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R b cosh(x) - 4a b cosh(x) + (8b - 8a )x cosh(x) - 4a b cosh(x) + b +--R / +--R 3 2 3 3 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R Type: Union(Expression(Integer),...) +--E 155 + +--S 156 of 530 +m0530:= a0530-r0530 +--R +--R +--R (154) +--R 2 2 2 2 2 +--R (8b - 8a )sinh(x) + (16b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (8b - 8a )cosh(x) +--R * +--R log(b cosh(x) + a) +--R + +--R 2 2 2 2 2 +--R (- 8b + 8a )sinh(x) + (- 16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 8b + 8a )cosh(x) +--R * +--R - 2b cosh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 4 2 3 +--R b sinh(x) + (4b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) - 4a b cosh(x) + (8b - 8a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (- 4b cosh(x) + 4a b cosh(x) + (16b - 16a )x cosh(x) - 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R - 3b cosh(x) + 4a b cosh(x) + (8b - 8a )x cosh(x) - 4a b cosh(x) + b +--R / +--R 3 2 3 3 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R Type: Expression(Integer) +--E 156 + +--S 157 of 530 +d0530:= D(m0530,x) +--R +--R +--R (155) +--R 4 3 2 2 +--R b sinh(x) + 2a sinh(x) + (- 2b cosh(x) + 2a cosh(x))sinh(x) +--R + +--R 2 4 3 +--R (- 2a cosh(x) + 2a)sinh(x) + b cosh(x) - 2a cosh(x) + 2a cosh(x) - b +--R / +--R 2 2 2 2 2 +--R 4b sinh(x) + 8b cosh(x)sinh(x) + 4b cosh(x) +--R Type: Expression(Integer) +--E 157 + +--S 158 of 530 +t0531:= sinh(x)^4/(a+b*cosh(x)) +--R +--R +--R 4 +--R sinh(x) +--R (156) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 158 + +--S 159 of 530 +r0531:= -a^3*x/b^4+3/2*a*x/b^2+2*(a^2-b^2)^(3/2)*_ + atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/b^4+a^2*sinh(x)/b^3-_ + sinh(x)/b-1/2*a*cosh(x)*sinh(x)/b^2+1/3*sinh(x)^3/b +--R +--R +--R (157) +--R x +--R +---------+ (b - a)tanh(-) +--R 2 2 | 2 2 2 3 3 +--R (12b - 12a )\|- b + a atanh(--------------) + 2b sinh(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 +--R (- 3a b cosh(x) - 6b + 6a b)sinh(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 159 + +--S 160 of 530 +a0531:= integrate(t0531,x) +--R +--R +--R (158) +--R [ +--R 2 2 3 2 2 2 +--R (24b - 24a )sinh(x) + (72b - 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (72b - 72a )cosh(x) sinh(x) + (24b - 24a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 2 +--R (2b sinh(x) + 2b cosh(x) + 2a)\|- b + a + b sinh(x) +--R + +--R 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) - b +--R + +--R 2 +--R 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 3 6 3 2 5 +--R b sinh(x) + (6b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (15b cosh(x) - 15a b cosh(x) - 15b + 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 +--R 20b cosh(x) - 30a b cosh(x) + (- 60b + 48a b)cosh(x) +--R + +--R 2 3 +--R (36a b - 24a )x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 15b cosh(x) - 30a b cosh(x) + (- 90b + 72a b)cosh(x) +--R + +--R 2 3 3 2 +--R (108a b - 72a )x cosh(x) + 15b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 15a b cosh(x) + (- 60b + 48a b)cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (108a b - 72a )x cosh(x) + (30b - 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R b cosh(x) - 3a b cosh(x) + (- 15b + 12a b)cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (36a b - 24a )x cosh(x) + (15b - 12a b)cosh(x) + 3a b cosh(x) - b +--R / +--R 4 3 4 2 4 2 4 3 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) +--R , +--R +--R 2 2 3 2 2 2 +--R (- 48b + 48a )sinh(x) + (- 144b + 144a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 144b + 144a )cosh(x) sinh(x) + (- 48b + 48a )cosh(x) +--R * +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 \|b - a +--R \|b - a atan(-------------------------) +--R b sinh(x) + b cosh(x) + a +--R + +--R 3 6 3 2 5 +--R b sinh(x) + (6b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (15b cosh(x) - 15a b cosh(x) - 15b + 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 +--R 20b cosh(x) - 30a b cosh(x) + (- 60b + 48a b)cosh(x) +--R + +--R 2 3 +--R (36a b - 24a )x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 15b cosh(x) - 30a b cosh(x) + (- 90b + 72a b)cosh(x) +--R + +--R 2 3 3 2 +--R (108a b - 72a )x cosh(x) + 15b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 15a b cosh(x) + (- 60b + 48a b)cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (108a b - 72a )x cosh(x) + (30b - 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R b cosh(x) - 3a b cosh(x) + (- 15b + 12a b)cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (36a b - 24a )x cosh(x) + (15b - 12a b)cosh(x) + 3a b cosh(x) - b +--R / +--R 4 3 4 2 4 2 4 3 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 160 + +--S 161 of 530 +m0531a:= a0531.1-r0531 +--R +--R +--R (159) +--R 2 2 3 2 2 2 +--R (24b - 24a )sinh(x) + (72b - 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (72b - 72a )cosh(x) sinh(x) + (24b - 24a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 2 +--R (2b sinh(x) + 2b cosh(x) + 2a)\|- b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) - b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R 2 2 3 2 2 2 +--R (- 48b + 48a )sinh(x) + (- 144b + 144a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 144b + 144a )cosh(x) sinh(x) + (- 48b + 48a )cosh(x) +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 6 3 2 5 +--R - 7b sinh(x) + (- 18b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (- 9b cosh(x) - 3a b cosh(x) + 9b - 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 3 +--R (12b cosh(x) + 6a b cosh(x) + (12b - 24a b)cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 3 2 2 +--R (15b cosh(x) + 6a b cosh(x) - 18b cosh(x) + 15b - 12a b)sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 3a b cosh(x) + (- 36b + 24a b)cosh(x) +--R + +--R 3 2 2 +--R (30b - 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R b cosh(x) - 3a b cosh(x) + (- 15b + 12a b)cosh(x) +--R + +--R 3 2 2 2 3 +--R (15b - 12a b)cosh(x) + 3a b cosh(x) - b +--R / +--R 4 3 4 2 4 2 4 3 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) +--R Type: Expression(Integer) +--E 161 + +--S 162 of 530 +d0531a:= D(m0531a,x) +--R +--R +--R (160) +--R 4 3 8 3 2 2 7 +--R (b - a b )sinh(x) + (4a b - 4a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R (- 12b + 12a b )cosh(x) + (4a b - 4a b )cosh(x) - 4b + 4a b +--R + +--R 2 2 3 +--R 8a b - 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 3 3 2 2 2 +--R (- 24b + 24a b )cosh(x) + (- 20a b + 20a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 24b + 24a b + 24a b - 24a b)cosh(x) + 8b - 8a b - 8a b +--R + +--R 3 +--R 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 +--R (- 10b + 10a b )cosh(x) + (- 36a b + 36a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 44b + 44a b + 16a b - 16a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 3 +--R (40b - 32a b - 48a b + 24a b + 16a )cosh(x) + 6b + 10a b +--R + +--R 2 2 3 4 +--R - 24a b - 8a b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 3 2 2 4 +--R (16b - 16a b )cosh(x) + (- 4a b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 24b + 24a b - 16a b + 16a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (80b - 40a b - 120a b + 16a b + 64a )cosh(x) +--R + +--R 4 3 2 2 3 4 4 3 +--R (32b + 32a b - 104a b - 24a b + 64a )cosh(x) + 8b - 12a b +--R + +--R 2 2 3 +--R - 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 3 2 2 5 +--R (20b - 20a b )cosh(x) + (28a b - 28a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (12b - 12a b - 24a b + 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (80b - 8a b - 152a b - 16a b + 96a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (60b + 36a b - 168a b - 24a b + 96a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (24b - 36a b - 12a b + 24a b)cosh(x) - 4b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 3 2 2 6 +--R (8b - 8a b )cosh(x) + (20a b - 20a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (16b - 16a b - 8a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (40b + 16a b - 96a b - 24a b + 64a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (48b + 16a b - 120a b - 8a b + 64a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (24b - 36a b - 12a b + 24a b)cosh(x) + (- 8b + 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 3 2 2 7 4 3 6 +--R (b - a b )cosh(x) + (4a b - 4a b )cosh(x) + (4b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (8b + 8a b - 24a b - 8a b + 16a )cosh(x) +--R + +--R 4 3 2 2 4 4 +--R (14b + 2a b - 32a b + 16a )cosh(x) +--R + +--R 4 3 2 2 3 3 4 3 2 4 +--R (8b - 12a b - 4a b + 8a b)cosh(x) + (- 4b + 4a b )cosh(x) + b +--R + +--R 3 +--R - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 8 3 2 2 7 +--R (b + a b )sinh(x) + (4a b + 4a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R (- 12b - 12a b )cosh(x) + (4a b + 4a b )cosh(x) - 4b - 4a b +--R + +--R 2 2 3 +--R 8a b + 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 3 3 2 2 2 +--R (- 24b - 24a b )cosh(x) + (- 20a b - 20a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (- 24b - 24a b + 24a b + 24a b)cosh(x) - 8b - 8a b + 8a b + 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 +--R (- 10b - 10a b )cosh(x) + (- 36a b - 36a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 44b - 44a b + 16a b + 16a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 3 +--R (- 40b - 32a b + 48a b + 24a b - 16a )cosh(x) + 6b - 10a b +--R + +--R 2 2 3 4 +--R - 24a b + 8a b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 3 2 2 4 +--R (16b + 16a b )cosh(x) + (- 4a b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 24b - 24a b - 16a b - 16a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 80b - 40a b + 120a b + 16a b - 64a )cosh(x) +--R + +--R 4 3 2 2 3 4 4 3 +--R (32b - 32a b - 104a b + 24a b + 64a )cosh(x) - 8b - 12a b +--R + +--R 2 2 3 +--R 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 3 2 2 5 +--R (20b + 20a b )cosh(x) + (28a b + 28a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (12b + 12a b - 24a b - 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 80b - 8a b + 152a b - 16a b - 96a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (60b - 36a b - 168a b + 24a b + 96a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 24b - 36a b + 12a b + 24a b)cosh(x) - 4b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 3 2 2 6 +--R (8b + 8a b )cosh(x) + (20a b + 20a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (16b + 16a b - 8a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 40b + 16a b + 96a b - 24a b - 64a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (48b - 16a b - 120a b + 8a b + 64a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 24b - 36a b + 12a b + 24a b)cosh(x) + (- 8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 3 2 2 7 4 3 6 +--R (b + a b )cosh(x) + (4a b + 4a b )cosh(x) + (4b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 8b + 8a b + 24a b - 8a b - 16a )cosh(x) +--R + +--R 4 3 2 2 4 4 +--R (14b - 2a b - 32a b + 16a )cosh(x) +--R + +--R 4 3 2 2 3 3 4 3 2 4 +--R (- 8b - 12a b + 4a b + 8a b)cosh(x) + (- 4b - 4a b )cosh(x) + b +--R + +--R 3 +--R a b +--R / +--R 5 4 5 +--R (8b - 8a b )sinh(x) +--R + +--R 5 4 4 2 3 4 +--R ((40b - 40a b )cosh(x) + 16a b - 16a b )sinh(x) +--R + +--R 5 4 2 4 2 3 5 4 +--R ((80b - 80a b )cosh(x) + (64a b - 64a b )cosh(x) + 8b - 8a b ) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 4 2 3 2 +--R (80b - 80a b )cosh(x) + (96a b - 96a b )cosh(x) +--R + +--R 5 4 +--R (24b - 24a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 4 4 2 3 3 +--R (40b - 40a b )cosh(x) + (64a b - 64a b )cosh(x) +--R + +--R 5 4 2 +--R (24b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 5 4 2 3 4 +--R (8b - 8a b )cosh(x) + (16a b - 16a b )cosh(x) +--R + +--R 5 4 3 +--R (8b - 8a b )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 4 5 +--R (8b + 8a b )sinh(x) +--R + +--R 5 4 4 2 3 4 +--R ((40b + 40a b )cosh(x) + 16a b + 16a b )sinh(x) +--R + +--R 5 4 2 4 2 3 5 4 +--R ((80b + 80a b )cosh(x) + (64a b + 64a b )cosh(x) + 8b + 8a b ) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 4 2 3 2 +--R (80b + 80a b )cosh(x) + (96a b + 96a b )cosh(x) +--R + +--R 5 4 +--R (24b + 24a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 4 4 2 3 3 +--R (40b + 40a b )cosh(x) + (64a b + 64a b )cosh(x) +--R + +--R 5 4 2 +--R (24b + 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 5 4 2 3 4 5 4 3 +--R (8b + 8a b )cosh(x) + (16a b + 16a b )cosh(x) + (8b + 8a b )cosh(x) +--R Type: Expression(Integer) +--E 162 + +--S 163 of 530 +m0531b:= a0531.2-r0531 +--R +--R +--R (161) +--R 2 2 3 2 2 2 +--R (- 48b + 48a )sinh(x) + (- 144b + 144a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 144b + 144a )cosh(x) sinh(x) + (- 48b + 48a )cosh(x) +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 2 2 2 +--R (- 48b + 48a )sinh(x) + (- 144b + 144a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 144b + 144a )cosh(x) sinh(x) + (- 48b + 48a )cosh(x) +--R * +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 \|b - a +--R \|b - a atan(-------------------------) +--R b sinh(x) + b cosh(x) + a +--R + +--R 3 6 3 2 5 +--R - 7b sinh(x) + (- 18b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (- 9b cosh(x) - 3a b cosh(x) + 9b - 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 3 +--R (12b cosh(x) + 6a b cosh(x) + (12b - 24a b)cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 3 2 2 +--R (15b cosh(x) + 6a b cosh(x) - 18b cosh(x) + 15b - 12a b)sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 3a b cosh(x) + (- 36b + 24a b)cosh(x) +--R + +--R 3 2 2 +--R (30b - 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R b cosh(x) - 3a b cosh(x) + (- 15b + 12a b)cosh(x) +--R + +--R 3 2 2 2 3 +--R (15b - 12a b)cosh(x) + 3a b cosh(x) - b +--R / +--R 4 3 4 2 4 2 4 3 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) +--R Type: Expression(Integer) +--E 163 + +--S 164 of 530 +d0531b:= D(m0531b,x) +--R +--R +--R (162) +--R 4 3 8 3 2 2 7 +--R (b - a b )sinh(x) + (4a b - 4a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R (- 12b + 12a b )cosh(x) + (4a b - 4a b )cosh(x) - 4b + 4a b +--R + +--R 2 2 3 +--R 8a b - 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 3 3 2 2 2 +--R (- 24b + 24a b )cosh(x) + (- 20a b + 20a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 24b + 24a b + 24a b - 24a b)cosh(x) + 8b - 8a b - 8a b +--R + +--R 3 +--R 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 +--R (- 10b + 10a b )cosh(x) + (- 36a b + 36a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 44b + 44a b + 16a b - 16a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 3 +--R (40b - 32a b - 48a b + 24a b + 16a )cosh(x) + 6b + 10a b +--R + +--R 2 2 3 4 +--R - 24a b - 8a b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 3 2 2 4 +--R (16b - 16a b )cosh(x) + (- 4a b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 24b + 24a b - 16a b + 16a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (80b - 40a b - 120a b + 16a b + 64a )cosh(x) +--R + +--R 4 3 2 2 3 4 4 3 +--R (32b + 32a b - 104a b - 24a b + 64a )cosh(x) + 8b - 12a b +--R + +--R 2 2 3 +--R - 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 3 2 2 5 +--R (20b - 20a b )cosh(x) + (28a b - 28a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (12b - 12a b - 24a b + 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (80b - 8a b - 152a b - 16a b + 96a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (60b + 36a b - 168a b - 24a b + 96a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (24b - 36a b - 12a b + 24a b)cosh(x) - 4b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 3 2 2 6 +--R (8b - 8a b )cosh(x) + (20a b - 20a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (16b - 16a b - 8a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (40b + 16a b - 96a b - 24a b + 64a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (48b + 16a b - 120a b - 8a b + 64a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (24b - 36a b - 12a b + 24a b)cosh(x) + (- 8b + 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 3 2 2 7 4 3 6 +--R (b - a b )cosh(x) + (4a b - 4a b )cosh(x) + (4b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (8b + 8a b - 24a b - 8a b + 16a )cosh(x) +--R + +--R 4 3 2 2 4 4 +--R (14b + 2a b - 32a b + 16a )cosh(x) +--R + +--R 4 3 2 2 3 3 4 3 2 4 +--R (8b - 12a b - 4a b + 8a b)cosh(x) + (- 4b + 4a b )cosh(x) + b +--R + +--R 3 +--R - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 8 3 2 2 7 +--R (b + a b )sinh(x) + (4a b + 4a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R (- 12b - 12a b )cosh(x) + (4a b + 4a b )cosh(x) - 4b - 4a b +--R + +--R 2 2 3 +--R 8a b + 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 3 3 2 2 2 +--R (- 24b - 24a b )cosh(x) + (- 20a b - 20a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (- 24b - 24a b + 24a b + 24a b)cosh(x) - 8b - 8a b + 8a b + 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 +--R (- 10b - 10a b )cosh(x) + (- 36a b - 36a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 44b - 44a b + 16a b + 16a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 3 +--R (- 40b - 32a b + 48a b + 24a b - 16a )cosh(x) + 6b - 10a b +--R + +--R 2 2 3 4 +--R - 24a b + 8a b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 3 2 2 4 +--R (16b + 16a b )cosh(x) + (- 4a b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 24b - 24a b - 16a b - 16a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 80b - 40a b + 120a b + 16a b - 64a )cosh(x) +--R + +--R 4 3 2 2 3 4 4 3 +--R (32b - 32a b - 104a b + 24a b + 64a )cosh(x) - 8b - 12a b +--R + +--R 2 2 3 +--R 4a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 3 2 2 5 +--R (20b + 20a b )cosh(x) + (28a b + 28a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (12b + 12a b - 24a b - 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 80b - 8a b + 152a b - 16a b - 96a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (60b - 36a b - 168a b + 24a b + 96a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 24b - 36a b + 12a b + 24a b)cosh(x) - 4b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 3 2 2 6 +--R (8b + 8a b )cosh(x) + (20a b + 20a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (16b + 16a b - 8a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 40b + 16a b + 96a b - 24a b - 64a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (48b - 16a b - 120a b + 8a b + 64a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 24b - 36a b + 12a b + 24a b)cosh(x) + (- 8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 3 2 2 7 4 3 6 +--R (b + a b )cosh(x) + (4a b + 4a b )cosh(x) + (4b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 8b + 8a b + 24a b - 8a b - 16a )cosh(x) +--R + +--R 4 3 2 2 4 4 +--R (14b - 2a b - 32a b + 16a )cosh(x) +--R + +--R 4 3 2 2 3 3 4 3 2 4 +--R (- 8b - 12a b + 4a b + 8a b)cosh(x) + (- 4b - 4a b )cosh(x) + b +--R + +--R 3 +--R a b +--R / +--R 5 4 5 +--R (8b - 8a b )sinh(x) +--R + +--R 5 4 4 2 3 4 +--R ((40b - 40a b )cosh(x) + 16a b - 16a b )sinh(x) +--R + +--R 5 4 2 4 2 3 5 4 +--R ((80b - 80a b )cosh(x) + (64a b - 64a b )cosh(x) + 8b - 8a b ) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 4 2 3 2 +--R (80b - 80a b )cosh(x) + (96a b - 96a b )cosh(x) +--R + +--R 5 4 +--R (24b - 24a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 4 4 2 3 3 +--R (40b - 40a b )cosh(x) + (64a b - 64a b )cosh(x) +--R + +--R 5 4 2 +--R (24b - 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 5 4 2 3 4 +--R (8b - 8a b )cosh(x) + (16a b - 16a b )cosh(x) +--R + +--R 5 4 3 +--R (8b - 8a b )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 4 5 +--R (8b + 8a b )sinh(x) +--R + +--R 5 4 4 2 3 4 +--R ((40b + 40a b )cosh(x) + 16a b + 16a b )sinh(x) +--R + +--R 5 4 2 4 2 3 5 4 +--R ((80b + 80a b )cosh(x) + (64a b + 64a b )cosh(x) + 8b + 8a b ) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 4 2 3 2 +--R (80b + 80a b )cosh(x) + (96a b + 96a b )cosh(x) +--R + +--R 5 4 +--R (24b + 24a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 4 4 2 3 3 +--R (40b + 40a b )cosh(x) + (64a b + 64a b )cosh(x) +--R + +--R 5 4 2 +--R (24b + 24a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 5 4 2 3 4 5 4 3 +--R (8b + 8a b )cosh(x) + (16a b + 16a b )cosh(x) + (8b + 8a b )cosh(x) +--R Type: Expression(Integer) +--E 164 + +--S 165 of 530 +t0532:= sinh(x)^2/(a+a*cosh(x)) +--R +--R +--R 2 +--R sinh(x) +--R (163) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 165 + +--S 166 of 530 +r0532:= (-x+sinh(x))/a +--R +--R +--R sinh(x) - x +--R (164) ----------- +--R a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 530 +a0532:= integrate(t0532,x) +--R +--R +--R sinh(x) - x +--R (165) ----------- +--R a +--R Type: Union(Expression(Integer),...) +--E 167 + +--S 168 of 530 +m0532:= a0532-r0532 +--R +--R +--R (166) 0 +--R Type: Expression(Integer) +--E 168 + +--S 169 of 530 +d0532:= D(m0532,x) +--R +--R +--R (167) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 530 +t0533:= sinh(x)^3/(a+a*cosh(x)) +--R +--R +--R 3 +--R sinh(x) +--R (168) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 170 + +--S 171 of 530 +r0533:= 1/2*cosh(x)*(cosh(x)-2)/a +--R +--R +--R 2 +--R cosh(x) - 2cosh(x) +--R (169) ------------------- +--R 2a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 530 +a0533:= integrate(t0533,x) +--R +--R +--R 2 2 +--R sinh(x) + cosh(x) - 4cosh(x) +--R (170) ------------------------------ +--R 4a +--R Type: Union(Expression(Integer),...) +--E 172 + +--S 173 of 530 +m0533:= a0533-r0533 +--R +--R +--R 2 2 +--R sinh(x) - cosh(x) +--R (171) ------------------- +--R 4a +--R Type: Expression(Integer) +--E 173 + +--S 174 of 530 +d0533:= D(m0533,x) +--R +--R +--R (172) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 530 +t0534:= sinh(x)^4/(a+a*cosh(x)) +--R +--R +--R 4 +--R sinh(x) +--R (173) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 175 + +--S 176 of 530 +r0534:= 1/6/a*(-3*cosh(x)*sinh(x)-2*sinh(x)+2*sinh(x)*cosh(x)^2+3*x) +--R +--R +--R 2 +--R (2cosh(x) - 3cosh(x) - 2)sinh(x) + 3x +--R (174) -------------------------------------- +--R 6a +--R Type: Expression(Integer) +--E 176 + +--S 177 of 530 +a0534:= integrate(t0534,x) +--R +--R +--R 3 2 +--R sinh(x) + (3cosh(x) - 6cosh(x) - 3)sinh(x) + 6x +--R (175) ------------------------------------------------- +--R 12a +--R Type: Union(Expression(Integer),...) +--E 177 + +--S 178 of 530 +m0534:= a0534-r0534 +--R +--R +--R 3 2 +--R sinh(x) + (- cosh(x) + 1)sinh(x) +--R (176) ---------------------------------- +--R 12a +--R Type: Expression(Integer) +--E 178 + +--S 179 of 530 +d0534:= D(m0534,x) +--R +--R +--R 2 3 +--R cosh(x)sinh(x) - cosh(x) + cosh(x) +--R (177) ------------------------------------ +--R 12a +--R Type: Expression(Integer) +--E 179 + +--S 180 of 530 +t0535:= cosh(x)/(a+b*cosh(x)) +--R +--R +--R cosh(x) +--R (178) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 180 + +--S 181 of 530 +r0535:= x/b-2*a*atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/b/(a^2-b^2)^(1/2) +--R +--R +--R x +--R (b - a)tanh(-) +---------+ +--R 2 | 2 2 +--R 2a atanh(--------------) + x\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (179) ---------------------------------------- +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R Type: Expression(Integer) +--E 181 + +--S 182 of 530 +a0535:= integrate(t0535,x) +--R +--R +--R (180) +--R [ +--R a +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + (- 2b + 2a b)cosh(x) - 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R +---------+ +--R | 2 2 +--R x\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R , +--R +-------+ +--R | 2 2 +-------+ +--R (b sinh(x) + b cosh(x) + a)\|b - a | 2 2 +--R - 2a atan(-------------------------------------) + x\|b - a +--R 2 2 +--R b - a +--R --------------------------------------------------------------] +--R +-------+ +--R | 2 2 +--R b\|b - a +--R Type: Union(List(Expression(Integer)),...) +--E 182 + +--S 183 of 530 +m0535a:= a0535.1-r0535 +--R +--R +--R (181) +--R a +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + (- 2b + 2a b)cosh(x) - 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R x +--R (b - a)tanh(-) +--R 2 +--R - 2a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R Type: Expression(Integer) +--E 183 + +--S 184 of 530 +d0535a:= D(m0535a,x) +--R +--R +--R (182) +--R 2 2 +--R - a sinh(x) + (- 2a cosh(x) - 2a)sinh(x) - a cosh(x) - 2a cosh(x) +--R + +--R - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 +--R a sinh(x) + (2a cosh(x) - 2a)sinh(x) + a cosh(x) - 2a cosh(x) + a +--R / +--R 2 2 2 2 +--R (b - a b)sinh(x) + ((2b - 2a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 2 2 2 +--R (b - a b)cosh(x) + (2a b - 2a )cosh(x) + b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 +--R (b + a b)sinh(x) + ((2b + 2a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 2 2 +--R (b + a b)cosh(x) + (2a b + 2a )cosh(x) + b + a b +--R Type: Expression(Integer) +--E 184 + +--S 185 of 530 +m0535b:= a0535.2-r0535 +--R +--R +--R (183) +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R - 2a\|b - a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sinh(x) + b cosh(x) + a)\|b - a +--R - 2a\|- b + a atan(-------------------------------------) +--R 2 2 +--R b - a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R b\|- b + a \|b - a +--R Type: Expression(Integer) +--E 185 + +--S 186 of 530 +d0535b:= D(m0535b,x) +--R +--R +--R (184) +--R 2 2 +--R - a sinh(x) + (- 2a cosh(x) - 2a)sinh(x) - a cosh(x) - 2a cosh(x) +--R + +--R - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 +--R a sinh(x) + (2a cosh(x) - 2a)sinh(x) + a cosh(x) - 2a cosh(x) + a +--R / +--R 2 2 2 2 +--R (b - a b)sinh(x) + ((2b - 2a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 2 2 2 +--R (b - a b)cosh(x) + (2a b - 2a )cosh(x) + b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 +--R (b + a b)sinh(x) + ((2b + 2a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 2 2 +--R (b + a b)cosh(x) + (2a b + 2a )cosh(x) + b + a b +--R Type: Expression(Integer) +--E 186 + +--S 187 of 530 +t0536:= cosh(x)^2/(a+b*cosh(x)) +--R +--R +--R 2 +--R cosh(x) +--R (185) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 187 + +--S 188 of 530 +r0536:= -a*x/b^2+2*a^2*atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/_ + b^2/(a^2-b^2)^(1/2)+sinh(x)/b +--R +--R +--R x +--R (b - a)tanh(-) +---------+ +--R 2 2 | 2 2 +--R - 2a atanh(--------------) + (b sinh(x) - a x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (186) ---------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 188 + +--S 189 of 530 +a0536:= integrate(t0536,x) +--R +--R +--R (187) +--R [ +--R 2 2 +--R (2a sinh(x) + 2a cosh(x)) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)sinh(x) + (2b - 2a b)cosh(x) + 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 2 2 +--R b sinh(x) + (2b cosh(x) - 2a x)sinh(x) + b cosh(x) - 2a x cosh(x) +--R + +--R - b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 2 2 (b sinh(x) + b cosh(x) + a)\|b - a +--R (4a sinh(x) + 4a cosh(x))atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 +--R b sinh(x) + (2b cosh(x) - 2a x)sinh(x) + b cosh(x) - 2a x cosh(x) +--R + +--R - b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 189 + +--S 190 of 530 +m0536a:= a0536.1-r0536 +--R +--R +--R (188) +--R 2 2 +--R (2a sinh(x) + 2a cosh(x)) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)sinh(x) + (2b - 2a b)cosh(x) + 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R x +--R (b - a)tanh(-) +--R 2 2 2 +--R (4a sinh(x) + 4a cosh(x))atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- b sinh(x) + b cosh(x) - b)\|- b + a +--R / +--R +---------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 530 +d0536a:= D(m0536a,x) +--R +--R +--R (189) +--R 2 4 2 3 +--R (b - a b)sinh(x) + ((2b - 2a b)cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((2a b + 4a )cosh(x) + 2b - 2a b + 4a )sinh(x) +--R + +--R 2 3 2 2 +--R (- 2b + 2a b)cosh(x) + (- 2a b + 8a )cosh(x) +--R + +--R 2 2 +--R (2b - 2a b + 8a )cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (- b + a b)cosh(x) + (- 2a b + 4a )cosh(x) + 4a cosh(x) +--R + +--R 2 +--R 2a b cosh(x) + b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (b + a b)sinh(x) + ((2b + 2a b)cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((2a b - 4a )cosh(x) + 2b + 2a b + 4a )sinh(x) +--R + +--R 2 3 2 2 +--R (- 2b - 2a b)cosh(x) + (- 2a b - 8a )cosh(x) +--R + +--R 2 2 +--R (2b + 2a b + 8a )cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (- b - a b)cosh(x) + (- 2a b - 4a )cosh(x) + 4a cosh(x) +--R + +--R 2 +--R 2a b cosh(x) + b + a b +--R / +--R 3 2 3 3 2 2 2 2 +--R (2b - 2a b )sinh(x) + ((6b - 6a b )cosh(x) + 4a b - 4a b)sinh(x) +--R + +--R 3 2 2 2 2 3 2 +--R ((6b - 6a b )cosh(x) + (8a b - 8a b)cosh(x) + 2b - 2a b )sinh(x) +--R + +--R 3 2 3 2 2 2 3 2 +--R (2b - 2a b )cosh(x) + (4a b - 4a b)cosh(x) + (2b - 2a b )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 3 3 2 2 2 2 +--R (2b + 2a b )sinh(x) + ((6b + 6a b )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 3 2 2 2 2 3 2 +--R ((6b + 6a b )cosh(x) + (8a b + 8a b)cosh(x) + 2b + 2a b )sinh(x) +--R + +--R 3 2 3 2 2 2 3 2 +--R (2b + 2a b )cosh(x) + (4a b + 4a b)cosh(x) + (2b + 2a b )cosh(x) +--R Type: Expression(Integer) +--E 191 + +--S 192 of 530 +m0536b:= a0536.2-r0536 +--R +--R +--R (190) +--R x +--R +-------+ (b - a)tanh(-) +--R 2 2 | 2 2 2 +--R (4a sinh(x) + 4a cosh(x))\|b - a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (4a sinh(x) + 4a cosh(x))\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (- b sinh(x) + b cosh(x) - b)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|- b + a \|b - a +--R Type: Expression(Integer) +--E 192 + +--S 193 of 530 +d0536b:= D(m0536b,x) +--R +--R +--R (191) +--R 2 4 2 3 +--R (b - a b)sinh(x) + ((2b - 2a b)cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((2a b + 4a )cosh(x) + 2b - 2a b + 4a )sinh(x) +--R + +--R 2 3 2 2 +--R (- 2b + 2a b)cosh(x) + (- 2a b + 8a )cosh(x) +--R + +--R 2 2 +--R (2b - 2a b + 8a )cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (- b + a b)cosh(x) + (- 2a b + 4a )cosh(x) + 4a cosh(x) +--R + +--R 2 +--R 2a b cosh(x) + b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (b + a b)sinh(x) + ((2b + 2a b)cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((2a b - 4a )cosh(x) + 2b + 2a b + 4a )sinh(x) +--R + +--R 2 3 2 2 +--R (- 2b - 2a b)cosh(x) + (- 2a b - 8a )cosh(x) +--R + +--R 2 2 +--R (2b + 2a b + 8a )cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (- b - a b)cosh(x) + (- 2a b - 4a )cosh(x) + 4a cosh(x) +--R + +--R 2 +--R 2a b cosh(x) + b + a b +--R / +--R 3 2 3 3 2 2 2 2 +--R (2b - 2a b )sinh(x) + ((6b - 6a b )cosh(x) + 4a b - 4a b)sinh(x) +--R + +--R 3 2 2 2 2 3 2 +--R ((6b - 6a b )cosh(x) + (8a b - 8a b)cosh(x) + 2b - 2a b )sinh(x) +--R + +--R 3 2 3 2 2 2 3 2 +--R (2b - 2a b )cosh(x) + (4a b - 4a b)cosh(x) + (2b - 2a b )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 3 3 2 2 2 2 +--R (2b + 2a b )sinh(x) + ((6b + 6a b )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 3 2 2 2 2 3 2 +--R ((6b + 6a b )cosh(x) + (8a b + 8a b)cosh(x) + 2b + 2a b )sinh(x) +--R + +--R 3 2 3 2 2 2 3 2 +--R (2b + 2a b )cosh(x) + (4a b + 4a b)cosh(x) + (2b + 2a b )cosh(x) +--R Type: Expression(Integer) +--E 193 + +--S 194 of 530 +t0537:= cosh(x)^3/(a+b*cosh(x)) +--R +--R +--R 3 +--R cosh(x) +--R (192) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 194 + +--S 195 of 530 +r0537:= a^2*x/b^3+1/2*x/b-2*a^3*atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/_ + b^3/(a^2-b^2)^(1/2)-a*sinh(x)/b^2+1/2*cosh(x)*sinh(x)/b +--R +--R +--R (193) +--R x +--R (b - a)tanh(-) +--R 3 2 +--R 4a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R ((b cosh(x) - 2a b)sinh(x) + (b + 2a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression(Integer) +--E 195 + +--S 196 of 530 +a0537:= integrate(t0537,x) +--R +--R +--R (194) +--R [ +--R 3 2 3 3 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + (- 2b + 2a b)cosh(x) - 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 2 4 2 3 +--R b sinh(x) + (4b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6b cosh(x) - 12a b cosh(x) + (4b + 8a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4b cosh(x) - 12a b cosh(x) + (8b + 16a )x cosh(x) + 4a b) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 +--R b cosh(x) - 4a b cosh(x) + (4b + 8a )x cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 3 3 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|- b + a +--R , +--R +--R 3 2 3 3 2 +--R (- 16a sinh(x) - 32a cosh(x)sinh(x) - 16a cosh(x) ) +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 4 2 3 +--R b sinh(x) + (4b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6b cosh(x) - 12a b cosh(x) + (4b + 8a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4b cosh(x) - 12a b cosh(x) + (8b + 16a )x cosh(x) + 4a b) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 +--R b cosh(x) - 4a b cosh(x) + (4b + 8a )x cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 196 + +--S 197 of 530 +m0537a:= a0537.1-r0537 +--R +--R +--R (195) +--R 3 2 3 3 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + (- 2b + 2a b)cosh(x) - 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R x +--R (b - a)tanh(-) +--R 3 2 3 3 2 2 +--R (- 16a sinh(x) - 32a cosh(x)sinh(x) - 16a cosh(x) )atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 3 2 2 2 +--R b sinh(x) + 4a b sinh(x) + (- 2b cosh(x) + 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (- 4a b cosh(x) + 4a b)sinh(x) + b cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) - b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 3 3 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|- b + a +--R Type: Expression(Integer) +--E 197 + +--S 198 of 530 +d0537a:= D(m0537a,x) +--R +--R +--R (196) +--R 3 2 6 +--R (- b + a b )sinh(x) +--R + +--R 3 2 2 2 5 +--R ((- 2b + 2a b )cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 3 2 2 2 2 3 2 2 +--R ((b - a b )cosh(x) + (- 8a b + 8a b)cosh(x) - b + a b - 4a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 2 3 2 2 +--R (4b - 4a b )cosh(x) + (- 8a b - 8a )cosh(x) - 4a b + 4a b +--R + +--R 3 +--R - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 2 2 3 +--R (b - a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 3 2 3 2 2 2 3 +--R (2b - 2a b - 24a )cosh(x) + (- 8a b + 8a b - 24a )cosh(x) +--R + +--R 3 2 2 +--R b - a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 2 2 4 +--R (- 2b + 2a b )cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (8a b - 24a )cosh(x) + (- 4a b + 4a b - 24a )cosh(x) +--R + +--R 3 2 2 +--R (2b - 2a b - 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 3 4 +--R (- b + a b )cosh(x) + (- b + a b + 4a b - 8a )cosh(x) +--R + +--R 3 3 3 2 2 2 3 2 +--R - 8a cosh(x) + (b - a b - 4a b)cosh(x) + b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 6 3 2 2 2 5 +--R (- b - a b )sinh(x) + ((- 2b - 2a b )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 3 2 2 2 2 3 2 2 +--R ((b + a b )cosh(x) + (- 8a b - 8a b)cosh(x) - b - a b - 4a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R ((4b + 4a b )cosh(x) + (- 8a b + 8a )cosh(x) - 4a b - 4a b - 8a ) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 2 2 3 +--R (b + a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 3 2 3 2 2 2 3 3 +--R (2b + 2a b + 24a )cosh(x) + (- 8a b - 8a b - 24a )cosh(x) + b +--R + +--R 2 2 +--R a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 2 2 4 +--R (- 2b - 2a b )cosh(x) + (4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (8a b + 24a )cosh(x) + (- 4a b - 4a b - 24a )cosh(x) +--R + +--R 3 2 2 +--R (2b + 2a b - 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 3 4 3 3 +--R (- b - a b )cosh(x) + (- b - a b + 4a b + 8a )cosh(x) - 8a cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (b + a b - 4a b)cosh(x) + b + a b +--R / +--R 4 3 4 +--R (4b - 4a b )sinh(x) +--R + +--R 4 3 3 2 2 3 +--R ((16b - 16a b )cosh(x) + 8a b - 8a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R ((24b - 24a b )cosh(x) + (24a b - 24a b )cosh(x) + 4b - 4a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 3 3 2 2 2 +--R (16b - 16a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 4 3 +--R (8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 4 3 2 +--R (4b - 4a b )cosh(x) + (8a b - 8a b )cosh(x) + (4b - 4a b )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 4 4 3 3 2 2 3 +--R (4b + 4a b )sinh(x) + ((16b + 16a b )cosh(x) + 8a b + 8a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R ((24b + 24a b )cosh(x) + (24a b + 24a b )cosh(x) + 4b + 4a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 3 3 2 2 2 +--R (16b + 16a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 4 3 +--R (8b + 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 4 3 2 +--R (4b + 4a b )cosh(x) + (8a b + 8a b )cosh(x) + (4b + 4a b )cosh(x) +--R Type: Expression(Integer) +--E 198 + +--S 199 of 530 +m0537b:= a0537.2-r0537 +--R +--R +--R (197) +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (- 16a sinh(x) - 32a cosh(x)sinh(x) - 16a cosh(x) )\|b - a +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 2 3 3 2 | 2 2 +--R (- 16a sinh(x) - 32a cosh(x)sinh(x) - 16a cosh(x) )\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 4 3 2 2 2 +--R b sinh(x) + 4a b sinh(x) + (- 2b cosh(x) + 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (- 4a b cosh(x) + 4a b)sinh(x) + b cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) - b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 3 3 2 | 2 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 530 +d0537b:= D(m0537b,x) +--R +--R +--R (198) +--R 3 2 6 +--R (- b + a b )sinh(x) +--R + +--R 3 2 2 2 5 +--R ((- 2b + 2a b )cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 3 2 2 2 2 3 2 2 +--R ((b - a b )cosh(x) + (- 8a b + 8a b)cosh(x) - b + a b - 4a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 2 3 2 2 +--R (4b - 4a b )cosh(x) + (- 8a b - 8a )cosh(x) - 4a b + 4a b +--R + +--R 3 +--R - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 2 2 3 +--R (b - a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 3 2 3 2 2 2 3 +--R (2b - 2a b - 24a )cosh(x) + (- 8a b + 8a b - 24a )cosh(x) +--R + +--R 3 2 2 +--R b - a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 2 2 4 +--R (- 2b + 2a b )cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (8a b - 24a )cosh(x) + (- 4a b + 4a b - 24a )cosh(x) +--R + +--R 3 2 2 +--R (2b - 2a b - 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 3 4 +--R (- b + a b )cosh(x) + (- b + a b + 4a b - 8a )cosh(x) +--R + +--R 3 3 3 2 2 2 3 2 +--R - 8a cosh(x) + (b - a b - 4a b)cosh(x) + b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 6 3 2 2 2 5 +--R (- b - a b )sinh(x) + ((- 2b - 2a b )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 3 2 2 2 2 3 2 2 +--R ((b + a b )cosh(x) + (- 8a b - 8a b)cosh(x) - b - a b - 4a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R ((4b + 4a b )cosh(x) + (- 8a b + 8a )cosh(x) - 4a b - 4a b - 8a ) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 2 2 3 +--R (b + a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 3 2 3 2 2 2 3 3 +--R (2b + 2a b + 24a )cosh(x) + (- 8a b - 8a b - 24a )cosh(x) + b +--R + +--R 2 2 +--R a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 2 2 4 +--R (- 2b - 2a b )cosh(x) + (4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (8a b + 24a )cosh(x) + (- 4a b - 4a b - 24a )cosh(x) +--R + +--R 3 2 2 +--R (2b + 2a b - 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 3 4 3 3 +--R (- b - a b )cosh(x) + (- b - a b + 4a b + 8a )cosh(x) - 8a cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (b + a b - 4a b)cosh(x) + b + a b +--R / +--R 4 3 4 +--R (4b - 4a b )sinh(x) +--R + +--R 4 3 3 2 2 3 +--R ((16b - 16a b )cosh(x) + 8a b - 8a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R ((24b - 24a b )cosh(x) + (24a b - 24a b )cosh(x) + 4b - 4a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 3 3 2 2 2 +--R (16b - 16a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 4 3 +--R (8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 4 3 2 +--R (4b - 4a b )cosh(x) + (8a b - 8a b )cosh(x) + (4b - 4a b )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 4 4 3 3 2 2 3 +--R (4b + 4a b )sinh(x) + ((16b + 16a b )cosh(x) + 8a b + 8a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R ((24b + 24a b )cosh(x) + (24a b + 24a b )cosh(x) + 4b + 4a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 3 3 2 2 2 +--R (16b + 16a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 4 3 +--R (8b + 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 4 3 2 +--R (4b + 4a b )cosh(x) + (8a b + 8a b )cosh(x) + (4b + 4a b )cosh(x) +--R Type: Expression(Integer) +--E 200 + +--S 201 of 530 +t0538:= cosh(x)^4/(a+b*cosh(x)) +--R +--R +--R 4 +--R cosh(x) +--R (199) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 201 + +--S 202 of 530 +r0538:= -a^3*x/b^4-1/2*a*x/b^2+_ + 2*a^4*atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/b^4/(a^2-b^2)^(1/2)+_ + a^2*sinh(x)/b^3+sinh(x)/b-1/2*a*cosh(x)*sinh(x)/b^2+1/3*sinh(x)^3/b +--R +--R +--R (200) +--R x +--R (b - a)tanh(-) +--R 4 2 +--R - 12a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 2 3 2 2 3 +--R (2b sinh(x) + (- 3a b cosh(x) + 6b + 6a b)sinh(x) + (- 3a b - 6a )x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6b \|- b + a +--R Type: Expression(Integer) +--E 202 + +--S 203 of 530 +a0538:= integrate(t0538,x) +--R +--R +--R (201) +--R [ +--R 4 3 4 2 4 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 4 3 +--R 24a cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)sinh(x) + (2b - 2a b)cosh(x) + 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 3 6 3 2 5 +--R b sinh(x) + (6b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (15b cosh(x) - 15a b cosh(x) + 9b + 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 +--R 20b cosh(x) - 30a b cosh(x) + (36b + 48a b)cosh(x) +--R + +--R 2 3 +--R (- 12a b - 24a )x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 15b cosh(x) - 30a b cosh(x) + (54b + 72a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 36a b - 72a )x cosh(x) - 9b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 15a b cosh(x) + (36b + 48a b)cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (- 36a b - 72a )x cosh(x) + (- 18b - 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R b cosh(x) - 3a b cosh(x) + (9b + 12a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (- 12a b - 24a )x cosh(x) + (- 9b - 12a b)cosh(x) +--R + +--R 2 3 +--R 3a b cosh(x) - b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 4 2 4 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 4 3 +--R 24b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 4 3 4 2 4 2 +--R 48a sinh(x) + 144a cosh(x)sinh(x) + 144a cosh(x) sinh(x) +--R + +--R 4 3 +--R 48a cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 3 6 3 2 5 +--R b sinh(x) + (6b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (15b cosh(x) - 15a b cosh(x) + 9b + 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 +--R 20b cosh(x) - 30a b cosh(x) + (36b + 48a b)cosh(x) +--R + +--R 2 3 +--R (- 12a b - 24a )x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 15b cosh(x) - 30a b cosh(x) + (54b + 72a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 36a b - 72a )x cosh(x) - 9b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 15a b cosh(x) + (36b + 48a b)cosh(x) +--R + +--R 2 3 2 3 2 2 +--R (- 36a b - 72a )x cosh(x) + (- 18b - 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R b cosh(x) - 3a b cosh(x) + (9b + 12a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (- 12a b - 24a )x cosh(x) + (- 9b - 12a b)cosh(x) +--R + +--R 2 3 +--R 3a b cosh(x) - b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 3 4 2 4 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 4 3 +--R 24b cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 203 + +--S 204 of 530 +m0538:= a0538.1-r0538 +--R +--R +--R (202) +--R 4 3 4 2 4 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 4 3 +--R 24a cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)sinh(x) + (2b - 2a b)cosh(x) + 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R 4 3 4 2 4 2 +--R 48a sinh(x) + 144a cosh(x)sinh(x) + 144a cosh(x) sinh(x) +--R + +--R 4 3 +--R 48a cosh(x) +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 6 3 2 5 +--R - 7b sinh(x) + (- 18b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (- 9b cosh(x) - 3a b cosh(x) - 15b - 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 3 +--R (12b cosh(x) + 6a b cosh(x) + (- 36b - 24a b)cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 3 2 2 +--R (15b cosh(x) + 6a b cosh(x) - 18b cosh(x) - 9b - 12a b)sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 3a b cosh(x) + (12b + 24a b)cosh(x) +--R + +--R 3 2 2 +--R (- 18b - 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R b cosh(x) - 3a b cosh(x) + (9b + 12a b)cosh(x) +--R + +--R 3 2 2 2 3 +--R (- 9b - 12a b)cosh(x) + 3a b cosh(x) - b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 204 + +--S 205 of 530 +d0538:= D(m0538a,x) +--R +--R +--R (203) 0 +--R Type: Polynomial(Integer) +--E 205 + +--S 206 of 530 +m0538:= a0538.2-r0538 +--R +--R +--R (204) +--R 4 3 4 2 4 2 +--R 48a sinh(x) + 144a cosh(x)sinh(x) + 144a cosh(x) sinh(x) +--R + +--R 4 3 +--R 48a cosh(x) +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 4 2 4 2 +--R 48a sinh(x) + 144a cosh(x)sinh(x) + 144a cosh(x) sinh(x) +--R + +--R 4 3 +--R 48a cosh(x) +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sinh(x) + b cosh(x) + a)\|b - a +--R \|- b + a atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 3 6 3 2 5 +--R - 7b sinh(x) + (- 18b cosh(x) - 3a b )sinh(x) +--R + +--R 3 2 2 3 2 4 +--R (- 9b cosh(x) - 3a b cosh(x) - 15b - 12a b)sinh(x) +--R + +--R 3 3 2 2 3 2 3 +--R (12b cosh(x) + 6a b cosh(x) + (- 36b - 24a b)cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 3 2 2 +--R (15b cosh(x) + 6a b cosh(x) - 18b cosh(x) - 9b - 12a b)sinh(x) +--R + +--R 3 5 2 4 3 2 3 +--R 6b cosh(x) - 3a b cosh(x) + (12b + 24a b)cosh(x) +--R + +--R 3 2 2 +--R (- 18b - 24a b)cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 4 +--R b cosh(x) - 3a b cosh(x) + (9b + 12a b)cosh(x) +--R + +--R 3 2 2 2 3 +--R (- 9b - 12a b)cosh(x) + 3a b cosh(x) - b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 206 + +--S 207 of 530 +d0538:= D(m0538b,x) +--R +--R +--R (205) 0 +--R Type: Polynomial(Integer) +--E 207 + +--S 208 of 530 +t0539:= cosh(x)/(a+a*cosh(x)) +--R +--R +--R cosh(x) +--R (206) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 208 + +--S 209 of 530 +r0539:= x/a-sinh(x)/a/(1+cosh(x)) +--R +--R +--R - sinh(x) + x cosh(x) + x +--R (207) ------------------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 209 + +--S 210 of 530 +a0539:= integrate(t0539,x) +--R +--R +--R x sinh(x) + x cosh(x) + x + 2 +--R (208) ----------------------------- +--R a sinh(x) + a cosh(x) + a +--R Type: Union(Expression(Integer),...) +--E 210 + +--S 211 of 530 +m0539:= a0539-r0539 +--R +--R +--R 2 +--R sinh(x) + (cosh(x) + 1)sinh(x) + 2cosh(x) + 2 +--R (209) ---------------------------------------------------- +--R 2 +--R (a cosh(x) + a)sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression(Integer) +--E 211 + +--S 212 of 530 +d0539:= D(m0539,x) +--R +--R +--R (210) +--R 4 3 2 +--R - sinh(x) + (- 2cosh(x) - 2)sinh(x) + (- cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 3 +--R (2cosh(x) + 2cosh(x) - 2cosh(x) - 2)sinh(x) + cosh(x) + cosh(x) +--R + +--R 2 +--R - cosh(x) - cosh(x) +--R / +--R 2 2 +--R (a cosh(x) + 2a cosh(x) + a)sinh(x) +--R + +--R 3 2 4 +--R (2a cosh(x) + 6a cosh(x) + 6a cosh(x) + 2a)sinh(x) + a cosh(x) +--R + +--R 3 2 +--R 4a cosh(x) + 6a cosh(x) + 4a cosh(x) + a +--R Type: Expression(Integer) +--E 212 + +--S 213 of 530 +t0540:= cosh(x)^2/(a+a*cosh(x)) +--R +--R +--R 2 +--R cosh(x) +--R (211) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 213 + +--S 214 of 530 +r0540:= -x/a+sinh(x)/a+sinh(x)/a/(1+cosh(x)) +--R +--R +--R (cosh(x) + 2)sinh(x) - x cosh(x) - x +--R (212) ------------------------------------ +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 530 +a0540:= integrate(t0540,x) +--R +--R +--R (213) +--R 2 2 +--R sinh(x) + (2cosh(x) - 2x + 2)sinh(x) + cosh(x) - 2x cosh(x) - 2x - 5 +--R ---------------------------------------------------------------------- +--R 2a sinh(x) + 2a cosh(x) + 2a +--R Type: Union(Expression(Integer),...) +--E 215 + +--S 216 of 530 +m0540:= a0540-r0540 +--R +--R +--R (214) +--R 2 3 2 +--R (- cosh(x) - 3)sinh(x) + (- 2cosh(x) - 2)sinh(x) + cosh(x) + cosh(x) +--R + +--R - 5cosh(x) - 5 +--R / +--R 2 +--R (2a cosh(x) + 2a)sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R Type: Expression(Integer) +--E 216 + +--S 217 of 530 +d0540:= D(m0540,x) +--R +--R +--R (215) +--R 4 2 3 +--R 2sinh(x) + (cosh(x) + 6cosh(x) + 5)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) + 2cosh(x) + 3cosh(x) + 2)sinh(x) +--R + +--R 4 3 2 5 +--R (- cosh(x) - 6cosh(x) - 4cosh(x) + 6cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 4 3 2 +--R - 4cosh(x) - 2cosh(x) + 4cosh(x) + 3cosh(x) +--R / +--R 2 2 +--R (2a cosh(x) + 4a cosh(x) + 2a)sinh(x) +--R + +--R 3 2 4 +--R (4a cosh(x) + 12a cosh(x) + 12a cosh(x) + 4a)sinh(x) + 2a cosh(x) +--R + +--R 3 2 +--R 8a cosh(x) + 12a cosh(x) + 8a cosh(x) + 2a +--R Type: Expression(Integer) +--E 217 + +--S 218 of 530 +t0541:= cosh(x)^3/(a+a*cosh(x)) +--R +--R +--R 3 +--R cosh(x) +--R (216) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 218 + +--S 219 of 530 +r0541:= 1/2*(3*x+3*x*cosh(x)-4*sinh(x)-cosh(x)*sinh(x)+_ + sinh(x)*cosh(x)^2)/a/(1+cosh(x)) +--R +--R +--R 2 +--R (cosh(x) - cosh(x) - 4)sinh(x) + 3x cosh(x) + 3x +--R (217) ------------------------------------------------- +--R 2a cosh(x) + 2a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 530 +a0541:= integrate(t0541,x) +--R +--R +--R (218) +--R 3 2 +--R sinh(x) + (3cosh(x) - 4)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4cosh(x) + 12x - 7)sinh(x) + cosh(x) - 4cosh(x) +--R + +--R (12x - 1)cosh(x) + 12x + 20 +--R / +--R 8a sinh(x) + 8a cosh(x) + 8a +--R Type: Union(Expression(Integer),...) +--E 220 + +--S 221 of 530 +m0541:= a0541-r0541 +--R +--R +--R (219) +--R 3 2 2 +--R (cosh(x) + 1)sinh(x) + (- cosh(x) + 3cosh(x) + 12)sinh(x) +--R + +--R 3 2 4 3 +--R (- cosh(x) - cosh(x) + 9cosh(x) + 9)sinh(x) + cosh(x) - 3cosh(x) +--R + +--R 2 +--R - 5cosh(x) + 19cosh(x) + 20 +--R / +--R 2 +--R (8a cosh(x) + 8a)sinh(x) + 8a cosh(x) + 16a cosh(x) + 8a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 530 +d0541:= D(m0541,x) +--R +--R +--R (220) +--R 2 4 +--R (- 2cosh(x) - 4cosh(x) - 10)sinh(x) +--R + +--R 2 3 +--R (- 5cosh(x) - 26cosh(x) - 21)sinh(x) +--R + +--R 4 3 2 2 +--R (4cosh(x) + 5cosh(x) - 4cosh(x) - 15cosh(x) - 10)sinh(x) +--R + +--R 4 3 2 6 +--R (5cosh(x) + 26cosh(x) + 16cosh(x) - 26cosh(x) - 21)sinh(x) - 2cosh(x) +--R + +--R 5 4 3 2 +--R - cosh(x) + 14cosh(x) + 12cosh(x) - 12cosh(x) - 11cosh(x) +--R / +--R 2 2 +--R (8a cosh(x) + 16a cosh(x) + 8a)sinh(x) +--R + +--R 3 2 4 +--R (16a cosh(x) + 48a cosh(x) + 48a cosh(x) + 16a)sinh(x) + 8a cosh(x) +--R + +--R 3 2 +--R 32a cosh(x) + 48a cosh(x) + 32a cosh(x) + 8a +--R Type: Expression(Integer) +--E 222 + +--S 223 of 530 +t0542:= cosh(x)^4/(a+a*cosh(x)) +--R +--R +--R 4 +--R cosh(x) +--R (221) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 223 + +--S 224 of 530 +r0542:= 1/6*(7*cosh(x)*sinh(x)-sinh(x)*cosh(x)^2+_ + 16*sinh(x)+2*cosh(x)^3*sinh(x)-9*x*cosh(x)-9*x)/a/(1+cosh(x)) +--R +--R +--R 3 2 +--R (2cosh(x) - cosh(x) + 7cosh(x) + 16)sinh(x) - 9x cosh(x) - 9x +--R (222) --------------------------------------------------------------- +--R 6a cosh(x) + 6a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 530 +a0542:= integrate(t0542,x) +--R +--R +--R (223) +--R 4 3 2 2 +--R sinh(x) + (4cosh(x) - 1)sinh(x) + (6cosh(x) - 9cosh(x) + 20)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 3cosh(x) + 32cosh(x) - 36x + 39)sinh(x) + cosh(x) +--R + +--R 3 2 +--R - 3cosh(x) + 20cosh(x) + (- 36x + 3)cosh(x) - 36x - 69 +--R / +--R 24a sinh(x) + 24a cosh(x) + 24a +--R Type: Union(Expression(Integer),...) +--E 225 + +--S 226 of 530 +m0542:= a0542-r0542 +--R +--R +--R (224) +--R 4 2 3 +--R (cosh(x) + 1)sinh(x) + (4cosh(x) + 3cosh(x) - 1)sinh(x) +--R + +--R 3 2 2 +--R (- 2cosh(x) + cosh(x) - 17cosh(x) - 44)sinh(x) +--R + +--R 4 3 2 5 +--R (- 4cosh(x) - 3cosh(x) + 5cosh(x) - 21cosh(x) - 25)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R - 2cosh(x) + 17cosh(x) + 23cosh(x) - 66cosh(x) - 69 +--R / +--R 2 +--R (24a cosh(x) + 24a)sinh(x) + 24a cosh(x) + 48a cosh(x) + 24a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 530 +d0542:= D(m0542,x) +--R +--R +--R (225) +--R 2 5 +--R (3cosh(x) + 6cosh(x) + 3)sinh(x) +--R + +--R 3 2 4 +--R (- cosh(x) + 6cosh(x) + 15cosh(x) + 32)sinh(x) +--R + +--R 4 3 2 3 +--R (- 2cosh(x) - 4cosh(x) + 25cosh(x) + 102cosh(x) + 75)sinh(x) +--R + +--R 5 4 3 2 2 +--R (6cosh(x) + 4cosh(x) + 9cosh(x) + 38cosh(x) + 59cosh(x) + 32)sinh(x) +--R + +--R 6 5 4 3 2 +--R - cosh(x) - 2cosh(x) - 24cosh(x) - 94cosh(x) - 47cosh(x) +--R + +--R 96cosh(x) + 72 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 5cosh(x) - 10cosh(x) - 20cosh(x) - 54cosh(x) - 19cosh(x) +--R + +--R 2 +--R 64cosh(x) + 44cosh(x) +--R / +--R 2 2 +--R (24a cosh(x) + 48a cosh(x) + 24a)sinh(x) +--R + +--R 3 2 4 +--R (48a cosh(x) + 144a cosh(x) + 144a cosh(x) + 48a)sinh(x) + 24a cosh(x) +--R + +--R 3 2 +--R 96a cosh(x) + 144a cosh(x) + 96a cosh(x) + 24a +--R Type: Expression(Integer) +--E 227 + +--S 228 of 530 +t0543:= tanh(x)/(a+b*cosh(x)) +--R +--R +--R tanh(x) +--R (226) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 228 + +--S 229 of 530 +r0543:= (log(cosh(x))-log(a+b*cosh(x)))/a +--R +--R +--R - log(b cosh(x) + a) + log(cosh(x)) +--R (227) ----------------------------------- +--R a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 530 +a0543:= integrate(t0543,x) +--R +--R +--R 2cosh(x) - 2b cosh(x) - 2a +--R log(- -----------------) - log(-----------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R (228) ------------------------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 230 + +--S 231 of 530 +m0543:= a0543-r0543 +--R +--R +--R (229) +--R 2cosh(x) +--R log(b cosh(x) + a) - log(cosh(x)) + log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2b cosh(x) - 2a +--R - log(-----------------) +--R sinh(x) - cosh(x) +--R / +--R a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 530 +d0543:= D(m0543,x) +--R +--R +--R (230) 0 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 530 +t0544:= tanh(x)^2/(a+b*cosh(x)) +--R +--R +--R 2 +--R tanh(x) +--R (231) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 530 +r0544:= b*atan(sinh(x))/a^2+2*(a^2-b^2)^(1/2)*_ + atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a^2-tanh(x)/a +--R +--R +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R - 2\|- b + a atanh(--------------) + b atan(sinh(x)) - a tanh(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (232) ------------------------------------------------------------------ +--R 2 +--R a +--R Type: Expression(Integer) +--E 234 + +--S 235 of 530 +a0544:= integrate(t0544,x) +--R +--R +--R (233) +--R [ +--R +---------+ +--R 2 2 | 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|- b + a + b sinh(x) +--R + +--R 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) - b +--R + +--R 2 +--R 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) + 2b) +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R , +--R +--R +-------+ +--R 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)\|b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R atan(-------------------------) +--R b sinh(x) + b cosh(x) + a +--R + +--R 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) + 2b) +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 235 + +--S 236 of 530 +m0544a:= a0544.1-r0544 +--R +--R +--R (234) +--R +---------+ +--R 2 2 | 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|- b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) - b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)\|- b + a +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) + 2b) +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b)atan(sinh(x)) +--R + +--R 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a)tanh(x) + 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 530 +d0544a:= D(m0544a,x) +--R +--R +--R (235) +--R 2 2 8 +--R (- a b + a b)sinh(x) +--R + +--R 2 2 2 3 7 +--R ((- 6a b + 6a b)cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (- 15a b + 15a b)cosh(x) + (- 10a b + 10a )cosh(x) - 4a b +--R + +--R 2 +--R 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 20a b + 20a b)cosh(x) + (- 20a b + 20a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 18a b + 18a b)cosh(x) - 6a b + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 15a b + 15a b)cosh(x) + (- 20a b + 20a )cosh(x) +--R + +--R 2 2 2 2 3 2 +--R (- 33a b + 33a b)cosh(x) + (- 22a b + 22a )cosh(x) - 6a b +--R + +--R 2 +--R 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (- 6a b + 6a b)cosh(x) + (- 10a b + 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 32a b + 32a b)cosh(x) + (- 32a b + 32a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 18a b + 18a b)cosh(x) - 6a b + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (- a b + a b)cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 18a b + 18a b)cosh(x) + (- 24a b + 24a )cosh(x) +--R + +--R 2 2 2 2 3 2 +--R (- 21a b + 21a b)cosh(x) + (- 14a b + 14a )cosh(x) - 4a b +--R + +--R 2 +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (- 6a b + 6a b)cosh(x) + (- 10a b + 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 12a b + 12a b)cosh(x) + (- 12a b + 12a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 6a b + 6a b)cosh(x) - 2a b + 2a +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (- a b + a b)cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 3a b + 3a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 3a b + 3a b)cosh(x) + (- 2a b + 2a )cosh(x) - a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 8 +--R (- a b - a b)sinh(x) +--R + +--R 2 2 2 3 7 +--R ((- 6a b - 6a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (- 15a b - 15a b)cosh(x) + (- 10a b - 10a )cosh(x) - 4a b +--R + +--R 2 +--R - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 20a b - 20a b)cosh(x) + (- 20a b - 20a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 18a b - 18a b)cosh(x) - 6a b - 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 15a b - 15a b)cosh(x) + (- 20a b - 20a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 33a b - 33a b)cosh(x) + (- 22a b - 22a )cosh(x) - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (- 6a b - 6a b)cosh(x) + (- 10a b - 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 32a b - 32a b)cosh(x) + (- 32a b - 32a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 18a b - 18a b)cosh(x) - 6a b - 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 18a b - 18a b)cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 21a b - 21a b)cosh(x) + (- 14a b - 14a )cosh(x) - 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (- 6a b - 6a b)cosh(x) + (- 10a b - 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 12a b - 12a b)cosh(x) + (- 12a b - 12a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 6a b - 6a b)cosh(x) - 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 3a b - 3a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 3a b - 3a b)cosh(x) + (- 2a b - 2a )cosh(x) - a b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 8 +--R (- b + a b )sinh(x) +--R + +--R 3 2 2 2 3 7 +--R ((- 6b + 6a b )cosh(x) - 2a b + 4a b - 2a )sinh(x) +--R + +--R 3 2 2 3 2 2 3 +--R (- 15b + 15a b )cosh(x) + (- b - 9a b + 20a b - 10a )cosh(x) +--R + +--R 3 2 +--R - 4b + 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 3 +--R (- 20b + 20a b )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 6b - 14a b + 40a b - 20a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 18b + 16a b + 2a b)cosh(x) - 6a b + 4a b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 +--R (- 15b + 15a b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 15b - 5a b + 40a b - 20a )cosh(x) +--R + +--R 3 2 2 2 +--R (- 33b + 23a b + 10a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 3b - 19a b + 20a b + 2a )cosh(x) - 6b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 5 +--R (- 6b + 6a b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 20b + 10a b + 20a b - 10a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 32b + 12a b + 20a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 12b - 20a b + 40a b - 8a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 18b + 14a b + 4a b)cosh(x) - 6a b + 4a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 3 5 +--R (- b + a b )cosh(x) + (- 15b + 13a b + 4a b - 2a )cosh(x) +--R + +--R 3 2 2 4 +--R (- 18b - 2a b + 20a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 18b - 6a b + 40a b - 16a )cosh(x) +--R + +--R 3 2 2 2 +--R (- 21b + 9a b + 12a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 3b - 11a b + 4a b + 10a )cosh(x) - 4b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 5 +--R (- 6b + 6a b )cosh(x) + (- 6b - 4a b + 10a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12b + 2a b + 20a b - 10a )cosh(x) +--R + +--R 3 2 3 3 2 3 2 +--R (- 12b + 12a b)cosh(x) + (- 6b - 6a b + 12a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 6b + 4a b + 2a b)cosh(x) - 2a b + 4a b - 2a +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (- b + a b )cosh(x) + (- b - a b + 2a b)cosh(x) +--R + +--R 3 2 2 3 5 3 2 2 4 +--R (- 3b + a b + 4a b - 2a )cosh(x) + (- 3b - a b + 4a b)cosh(x) +--R + +--R 3 2 3 3 3 2 2 2 +--R (- 3b - a b + 4a )cosh(x) + (- 3b + a b + 2a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- b - a b + 4a b - 2a )cosh(x) - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 8 3 2 2 2 3 7 +--R (b + a b )sinh(x) + ((6b + 6a b )cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 3 2 2 3 2 2 3 3 +--R (15b + 15a b )cosh(x) + (- b + 9a b + 20a b + 10a )cosh(x) + 4b +--R + +--R 2 +--R 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 3 3 2 2 3 2 +--R (20b + 20a b )cosh(x) + (- 6b + 14a b + 40a b + 20a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (18b + 16a b - 2a b)cosh(x) + 6a b + 4a b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 3 3 +--R (15b + 15a b )cosh(x) + (- 15b + 5a b + 40a b + 20a )cosh(x) +--R + +--R 3 2 2 2 +--R (33b + 23a b - 10a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 3b + 19a b + 20a b - 2a )cosh(x) + 6b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 4 +--R (6b + 6a b )cosh(x) + (- 20b - 10a b + 20a b + 10a )cosh(x) +--R + +--R 3 2 2 3 +--R (32b + 12a b - 20a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 12b + 20a b + 40a b + 8a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (18b + 14a b - 4a b)cosh(x) + 6a b + 4a b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 3 5 +--R (b + a b )cosh(x) + (- 15b - 13a b + 4a b + 2a )cosh(x) +--R + +--R 3 2 2 4 +--R (18b - 2a b - 20a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 18b + 6a b + 40a b + 16a )cosh(x) +--R + +--R 3 2 2 2 +--R (21b + 9a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 3b + 11a b + 4a b - 10a )cosh(x) + 4b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 5 +--R (- 6b - 6a b )cosh(x) + (6b - 4a b - 10a b)cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (- 12b - 2a b + 20a b + 10a )cosh(x) + (12b - 12a b)cosh(x) +--R + +--R 3 2 3 2 3 2 2 2 +--R (- 6b + 6a b - 12a )cosh(x) + (6b + 4a b - 2a b)cosh(x) + 2a b +--R + +--R 2 3 +--R 4a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (- b - a b )cosh(x) + (b - a b - 2a b)cosh(x) +--R + +--R 3 2 2 3 5 3 2 2 4 +--R (- 3b - a b + 4a b + 2a )cosh(x) + (3b - a b - 4a b)cosh(x) +--R + +--R 3 2 3 3 3 2 2 2 +--R (- 3b + a b - 4a )cosh(x) + (3b + a b - 2a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- b + a b + 4a b + 2a )cosh(x) + b + a b +--R / +--R 2 2 3 8 2 2 3 3 4 7 +--R (a b - a b)sinh(x) + ((6a b - 6a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R ((15a b - 15a b)cosh(x) + (10a b - 10a )cosh(x) + 4a b - 4a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20a b - 20a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15a b - 15a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33a b - 33a b)cosh(x) + (22a b - 22a )cosh(x) + 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32a b - 32a b)cosh(x) + (32a b - 32a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18a b - 18a b)cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21a b - 21a b)cosh(x) + (14a b - 14a )cosh(x) + 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12a b - 12a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6a b - 6a b)cosh(x) + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) + (3a b - 3a b)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4a b - 4a )cosh(x) + (3a b - 3a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 3 +--R a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 8 2 2 3 3 4 7 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 6 +--R ((15a b + 15a b)cosh(x) + (10a b + 10a )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20a b + 20a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15a b + 15a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33a b + 33a b)cosh(x) + (22a b + 22a )cosh(x) + 6a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32a b + 32a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18a b + 18a b)cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21a b + 21a b)cosh(x) + (14a b + 14a )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12a b + 12a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6a b + 6a b)cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4a b + 4a )cosh(x) + (3a b + 3a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 3 +--R a b + a b +--R Type: Expression(Integer) +--E 237 + +--S 238 of 530 +m0544b:= a0544.2-r0544 +--R +--R +--R (236) +--R +---------+ +--R 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)\|- b + a +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)\|b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R atan(-------------------------) +--R b sinh(x) + b cosh(x) + a +--R + +--R 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) + 2b) +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b)atan(sinh(x)) +--R + +--R 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a)tanh(x) + 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 530 +d0544b:= D(m0544b,x) +--R +--R +--R (237) +--R 2 2 8 +--R (- a b + a b)sinh(x) +--R + +--R 2 2 2 3 7 +--R ((- 6a b + 6a b)cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (- 15a b + 15a b)cosh(x) + (- 10a b + 10a )cosh(x) - 4a b +--R + +--R 2 +--R 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 20a b + 20a b)cosh(x) + (- 20a b + 20a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 18a b + 18a b)cosh(x) - 6a b + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 15a b + 15a b)cosh(x) + (- 20a b + 20a )cosh(x) +--R + +--R 2 2 2 2 3 2 +--R (- 33a b + 33a b)cosh(x) + (- 22a b + 22a )cosh(x) - 6a b +--R + +--R 2 +--R 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (- 6a b + 6a b)cosh(x) + (- 10a b + 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 32a b + 32a b)cosh(x) + (- 32a b + 32a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 18a b + 18a b)cosh(x) - 6a b + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (- a b + a b)cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 18a b + 18a b)cosh(x) + (- 24a b + 24a )cosh(x) +--R + +--R 2 2 2 2 3 2 +--R (- 21a b + 21a b)cosh(x) + (- 14a b + 14a )cosh(x) - 4a b +--R + +--R 2 +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (- 6a b + 6a b)cosh(x) + (- 10a b + 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 12a b + 12a b)cosh(x) + (- 12a b + 12a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 6a b + 6a b)cosh(x) - 2a b + 2a +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (- a b + a b)cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 3a b + 3a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 3a b + 3a b)cosh(x) + (- 2a b + 2a )cosh(x) - a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 8 +--R (- a b - a b)sinh(x) +--R + +--R 2 2 2 3 7 +--R ((- 6a b - 6a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (- 15a b - 15a b)cosh(x) + (- 10a b - 10a )cosh(x) - 4a b +--R + +--R 2 +--R - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 20a b - 20a b)cosh(x) + (- 20a b - 20a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 18a b - 18a b)cosh(x) - 6a b - 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 15a b - 15a b)cosh(x) + (- 20a b - 20a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 33a b - 33a b)cosh(x) + (- 22a b - 22a )cosh(x) - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (- 6a b - 6a b)cosh(x) + (- 10a b - 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 32a b - 32a b)cosh(x) + (- 32a b - 32a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 18a b - 18a b)cosh(x) - 6a b - 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 18a b - 18a b)cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 21a b - 21a b)cosh(x) + (- 14a b - 14a )cosh(x) - 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (- 6a b - 6a b)cosh(x) + (- 10a b - 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 12a b - 12a b)cosh(x) + (- 12a b - 12a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 6a b - 6a b)cosh(x) - 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (- 3a b - 3a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- 3a b - 3a b)cosh(x) + (- 2a b - 2a )cosh(x) - a b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 8 +--R (- b + a b )sinh(x) +--R + +--R 3 2 2 2 3 7 +--R ((- 6b + 6a b )cosh(x) - 2a b + 4a b - 2a )sinh(x) +--R + +--R 3 2 2 3 2 2 3 +--R (- 15b + 15a b )cosh(x) + (- b - 9a b + 20a b - 10a )cosh(x) +--R + +--R 3 2 +--R - 4b + 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 3 +--R (- 20b + 20a b )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 6b - 14a b + 40a b - 20a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 18b + 16a b + 2a b)cosh(x) - 6a b + 4a b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 +--R (- 15b + 15a b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 15b - 5a b + 40a b - 20a )cosh(x) +--R + +--R 3 2 2 2 +--R (- 33b + 23a b + 10a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 3b - 19a b + 20a b + 2a )cosh(x) - 6b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 5 +--R (- 6b + 6a b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 20b + 10a b + 20a b - 10a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 32b + 12a b + 20a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 12b - 20a b + 40a b - 8a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 18b + 14a b + 4a b)cosh(x) - 6a b + 4a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 3 5 +--R (- b + a b )cosh(x) + (- 15b + 13a b + 4a b - 2a )cosh(x) +--R + +--R 3 2 2 4 +--R (- 18b - 2a b + 20a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 18b - 6a b + 40a b - 16a )cosh(x) +--R + +--R 3 2 2 2 +--R (- 21b + 9a b + 12a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 3b - 11a b + 4a b + 10a )cosh(x) - 4b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 5 +--R (- 6b + 6a b )cosh(x) + (- 6b - 4a b + 10a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12b + 2a b + 20a b - 10a )cosh(x) +--R + +--R 3 2 3 3 2 3 2 +--R (- 12b + 12a b)cosh(x) + (- 6b - 6a b + 12a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 6b + 4a b + 2a b)cosh(x) - 2a b + 4a b - 2a +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (- b + a b )cosh(x) + (- b - a b + 2a b)cosh(x) +--R + +--R 3 2 2 3 5 3 2 2 4 +--R (- 3b + a b + 4a b - 2a )cosh(x) + (- 3b - a b + 4a b)cosh(x) +--R + +--R 3 2 3 3 3 2 2 2 +--R (- 3b - a b + 4a )cosh(x) + (- 3b + a b + 2a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- b - a b + 4a b - 2a )cosh(x) - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 8 3 2 2 2 3 7 +--R (b + a b )sinh(x) + ((6b + 6a b )cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 3 2 2 3 2 2 3 3 +--R (15b + 15a b )cosh(x) + (- b + 9a b + 20a b + 10a )cosh(x) + 4b +--R + +--R 2 +--R 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 3 3 2 2 3 2 +--R (20b + 20a b )cosh(x) + (- 6b + 14a b + 40a b + 20a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (18b + 16a b - 2a b)cosh(x) + 6a b + 4a b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 3 3 +--R (15b + 15a b )cosh(x) + (- 15b + 5a b + 40a b + 20a )cosh(x) +--R + +--R 3 2 2 2 +--R (33b + 23a b - 10a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 3b + 19a b + 20a b - 2a )cosh(x) + 6b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 4 +--R (6b + 6a b )cosh(x) + (- 20b - 10a b + 20a b + 10a )cosh(x) +--R + +--R 3 2 2 3 +--R (32b + 12a b - 20a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 12b + 20a b + 40a b + 8a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (18b + 14a b - 4a b)cosh(x) + 6a b + 4a b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 3 5 +--R (b + a b )cosh(x) + (- 15b - 13a b + 4a b + 2a )cosh(x) +--R + +--R 3 2 2 4 +--R (18b - 2a b - 20a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 18b + 6a b + 40a b + 16a )cosh(x) +--R + +--R 3 2 2 2 +--R (21b + 9a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 3b + 11a b + 4a b - 10a )cosh(x) + 4b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 5 +--R (- 6b - 6a b )cosh(x) + (6b - 4a b - 10a b)cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (- 12b - 2a b + 20a b + 10a )cosh(x) + (12b - 12a b)cosh(x) +--R + +--R 3 2 3 2 3 2 2 2 +--R (- 6b + 6a b - 12a )cosh(x) + (6b + 4a b - 2a b)cosh(x) + 2a b +--R + +--R 2 3 +--R 4a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (- b - a b )cosh(x) + (b - a b - 2a b)cosh(x) +--R + +--R 3 2 2 3 5 3 2 2 4 +--R (- 3b - a b + 4a b + 2a )cosh(x) + (3b - a b - 4a b)cosh(x) +--R + +--R 3 2 3 3 3 2 2 2 +--R (- 3b + a b - 4a )cosh(x) + (3b + a b - 2a b)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- b + a b + 4a b + 2a )cosh(x) + b + a b +--R / +--R 2 2 3 8 2 2 3 3 4 7 +--R (a b - a b)sinh(x) + ((6a b - 6a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R ((15a b - 15a b)cosh(x) + (10a b - 10a )cosh(x) + 4a b - 4a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20a b - 20a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15a b - 15a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33a b - 33a b)cosh(x) + (22a b - 22a )cosh(x) + 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32a b - 32a b)cosh(x) + (32a b - 32a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18a b - 18a b)cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21a b - 21a b)cosh(x) + (14a b - 14a )cosh(x) + 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12a b - 12a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6a b - 6a b)cosh(x) + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) + (3a b - 3a b)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4a b - 4a )cosh(x) + (3a b - 3a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 3 +--R a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 8 2 2 3 3 4 7 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 6 +--R ((15a b + 15a b)cosh(x) + (10a b + 10a )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20a b + 20a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15a b + 15a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33a b + 33a b)cosh(x) + (22a b + 22a )cosh(x) + 6a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32a b + 32a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18a b + 18a b)cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21a b + 21a b)cosh(x) + (14a b + 14a )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12a b + 12a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6a b + 6a b)cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4a b + 4a )cosh(x) + (3a b + 3a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 3 +--R a b + a b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 530 +t0545:= tanh(x)^3/(a+b*cosh(x)) +--R +--R +--R 3 +--R tanh(x) +--R (238) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 240 + +--S 241 of 530 +r0545:= (a^2-b^2)*log(cosh(x))/a^3-(a^2-b^2)*_ + log(a+b*cosh(x))/a^3-b*sech(x)/a^2+1/2*sech(x)^2/a +--R +--R +--R (239) +--R 2 2 2 2 2 2 +--R (2b - 2a )log(b cosh(x) + a) + (- 2b + 2a )log(cosh(x)) + a sech(x) +--R + +--R - 2a b sech(x) +--R / +--R 3 +--R 2a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 530 +a0545:= integrate(t0545,x) +--R +--R +--R (240) +--R 2 2 4 2 2 3 +--R (- b + a )sinh(x) + (- 4b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b + 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b + 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b + a )cosh(x) + (- 2b + 2a )cosh(x) - b + a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b - 6a )cosh(x) + 2b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 2 2 4 +--R ((4b - 4a )cosh(x) + (4b - 4a )cosh(x))sinh(x) + (b - a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (2b - 2a )cosh(x) + b - a +--R * +--R - 2b cosh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 +--R - 2a b sinh(x) + (- 6a b cosh(x) + 2a )sinh(x) +--R + +--R 2 2 3 +--R (- 6a b cosh(x) + 4a cosh(x) - 2a b)sinh(x) - 2a b cosh(x) +--R + +--R 2 2 +--R 2a cosh(x) - 2a b cosh(x) +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 530 +m0545:= a0545-r0545 +--R +--R +--R (241) +--R 2 2 4 2 2 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + (- 4b + 4a )cosh(x) - 2b + 2a +--R * +--R log(b cosh(x) + a) +--R + +--R 2 2 4 2 2 3 +--R (2b - 2a )sinh(x) + (8b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - 2a )cosh(x) + (4b - 4a )cosh(x) + 2b - 2a +--R * +--R log(cosh(x)) +--R + +--R 2 2 4 2 2 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + (- 4b + 4a )cosh(x) - 2b + 2a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (2b - 2a )sinh(x) + (8b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - 2a )cosh(x) + (4b - 4a )cosh(x) + 2b - 2a +--R * +--R - 2b cosh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 +--R (- a sech(x) + 2a b sech(x))sinh(x) +--R + +--R 2 2 3 +--R (- 4a cosh(x)sech(x) + 8a b cosh(x)sech(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 6a cosh(x) - 2a )sech(x) + (12a b cosh(x) + 4a b)sech(x) +--R + +--R 2 +--R - 12a b cosh(x) + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 4a cosh(x) - 4a cosh(x))sech(x) +--R + +--R 3 2 2 +--R (8a b cosh(x) + 8a b cosh(x))sech(x) - 12a b cosh(x) + 8a cosh(x) +--R + +--R - 4a b +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- a cosh(x) - 2a cosh(x) - a )sech(x) +--R + +--R 4 2 3 +--R (2a b cosh(x) + 4a b cosh(x) + 2a b)sech(x) - 4a b cosh(x) +--R + +--R 2 2 +--R 4a cosh(x) - 4a b cosh(x) +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R Type: Expression(Integer) +--E 243 + +--S 244 of 530 +d0545:= D(m0545,x) +--R +--R +--R (242) +--R 2 6 +--R (a sech(x) - b sech(x))sinh(x) +--R + +--R 2 5 +--R (6a cosh(x)sech(x) - 6b cosh(x)sech(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((15a cosh(x) + 3a)sech(x) + (- 15b cosh(x) - 3b)sech(x))sinh(x) +--R + +--R 3 2 +--R (20a cosh(x) + 12a cosh(x))sech(x) +--R + +--R 3 +--R (- 20b cosh(x) - 12b cosh(x))sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (15a cosh(x) + 18a cosh(x) + 3a)sech(x) +--R + +--R 4 2 +--R (- 15b cosh(x) - 18b cosh(x) - 3b)sech(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (6a cosh(x) + 12a cosh(x) + 6a cosh(x))sech(x) +--R + +--R 5 3 +--R (- 6b cosh(x) - 12b cosh(x) - 6b cosh(x))sech(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (a cosh(x) + 3a cosh(x) + 3a cosh(x) + a)sech(x) +--R + +--R 6 4 2 +--R (- b cosh(x) - 3b cosh(x) - 3b cosh(x) - b)sech(x) +--R * +--R tanh(x) +--R + +--R 5 4 +--R 2b sinh(x) + (10b cosh(x) - 4a)sinh(x) +--R + +--R 2 3 +--R (20b cosh(x) - 16a cosh(x))sinh(x) +--R + +--R 3 2 2 +--R (20b cosh(x) - 24a cosh(x) + 4a)sinh(x) +--R + +--R 4 3 5 +--R (10b cosh(x) - 16a cosh(x) + 8a cosh(x) - 2b)sinh(x) + 2b cosh(x) +--R + +--R 4 2 +--R - 4a cosh(x) + 4a cosh(x) - 2b cosh(x) +--R / +--R 2 6 2 5 2 2 2 4 +--R a sinh(x) + 6a cosh(x)sinh(x) + (15a cosh(x) + 3a )sinh(x) +--R + +--R 2 3 2 3 +--R (20a cosh(x) + 12a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (15a cosh(x) + 18a cosh(x) + 3a )sinh(x) +--R + +--R 2 5 2 3 2 2 6 +--R (6a cosh(x) + 12a cosh(x) + 6a cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 4 2 2 2 +--R 3a cosh(x) + 3a cosh(x) + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 530 +t0546:= tanh(x)^4/(a+b*cosh(x)) +--R +--R +--R 4 +--R tanh(x) +--R (243) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 245 + +--S 246 of 530 +r0546:= 3/2*b*atan(sinh(x))/a^2-b^3*atan(sinh(x))/a^4+_ + 2*(a^2-b^2)^(3/2)*atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a^4-_ + tanh(x)/a+b^2*tanh(x)/a^3-1/2*b*sech(x)*tanh(x)/a^2-1/3*tanh(x)^3/a +--R +--R +--R (244) +--R x +--R +---------+ (b - a)tanh(-) +--R 2 2 | 2 2 2 +--R (12b - 12a )\|- b + a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 3 +--R (- 6b + 9a b)atan(sinh(x)) - 2a tanh(x) +--R + +--R 2 2 3 +--R (- 3a b sech(x) + 6a b - 6a )tanh(x) +--R / +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 246 + +--S 247 of 530 +a0546:= integrate(t0546,x) +--R +--R +--R (245) +--R [ +--R 2 2 6 2 2 5 +--R (3b - 3a )sinh(x) + (18b - 18a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((45b - 45a )cosh(x) + 9b - 9a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((60b - 60a )cosh(x) + (36b - 36a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 2 +--R ((45b - 45a )cosh(x) + (54b - 54a )cosh(x) + 9b - 9a )sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (18b - 18a )cosh(x) + (36b - 36a )cosh(x) +--R + +--R 2 2 +--R (18b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 2 2 2 +--R (3b - 3a )cosh(x) + (9b - 9a )cosh(x) + (9b - 9a )cosh(x) +--R + +--R 2 2 +--R 3b - 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 2 +--R (2b sinh(x) + 2b cosh(x) + 2a)\|- b + a + b sinh(x) +--R + +--R 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) - b +--R + +--R 2 +--R 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 3 2 6 3 2 5 +--R (- 6b + 9a b)sinh(x) + (- 36b + 54a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 135a b)cosh(x) - 18b + 27a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 180a b)cosh(x) + (- 72b + 108a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b + 135a b)cosh(x) + (- 108b + 162a b)cosh(x) - 18b +--R + +--R 2 +--R 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 54a b)cosh(x) + (- 72b + 108a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 9a b)cosh(x) + (- 18b + 27a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 27a b)cosh(x) - 6b + 9a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 5 2 2 3 4 +--R - 3a b sinh(x) + (- 15a b cosh(x) - 6a b + 12a )sinh(x) +--R + +--R 2 2 2 3 3 +--R (- 30a b cosh(x) + (- 24a b + 48a )cosh(x))sinh(x) +--R + +--R 2 3 2 3 2 2 3 2 +--R (- 30a b cosh(x) + (- 36a b + 72a )cosh(x) - 12a b + 12a )sinh(x) +--R + +--R 2 4 2 3 3 +--R - 15a b cosh(x) + (- 24a b + 48a )cosh(x) +--R + +--R 2 3 2 +--R (- 24a b + 24a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 2 5 2 3 4 2 3 2 +--R - 3a b cosh(x) + (- 6a b + 12a )cosh(x) + (- 12a b + 12a )cosh(x) +--R + +--R 2 2 3 +--R 3a b cosh(x) - 6a b + 8a +--R / +--R 4 6 4 5 4 2 4 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) + 9a )sinh(x) +--R + +--R 4 3 4 3 +--R (60a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45a cosh(x) + 54a cosh(x) + 9a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18a cosh(x) + 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 4 4 4 2 4 +--R 9a cosh(x) + 9a cosh(x) + 3a +--R , +--R +--R 2 2 6 2 2 5 +--R (- 6b + 6a )sinh(x) + (- 36b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 90b + 90a )cosh(x) - 18b + 18a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 120b + 120a )cosh(x) + (- 72b + 72a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (- 90b + 90a )cosh(x) + (- 108b + 108a )cosh(x) - 18b +--R + +--R 2 +--R 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 36b + 36a )cosh(x) + (- 72b + 72a )cosh(x) +--R + +--R 2 2 +--R (- 36b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 6b + 6a )cosh(x) + (- 18b + 18a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 18b + 18a )cosh(x) - 6b + 6a +--R * +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 \|b - a +--R \|b - a atan(-------------------------) +--R b sinh(x) + b cosh(x) + a +--R + +--R 3 2 6 3 2 5 +--R (- 6b + 9a b)sinh(x) + (- 36b + 54a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 135a b)cosh(x) - 18b + 27a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 180a b)cosh(x) + (- 72b + 108a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b + 135a b)cosh(x) + (- 108b + 162a b)cosh(x) - 18b +--R + +--R 2 +--R 27a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 54a b)cosh(x) + (- 72b + 108a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 9a b)cosh(x) + (- 18b + 27a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 27a b)cosh(x) - 6b + 9a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 5 2 2 3 4 +--R - 3a b sinh(x) + (- 15a b cosh(x) - 6a b + 12a )sinh(x) +--R + +--R 2 2 2 3 3 +--R (- 30a b cosh(x) + (- 24a b + 48a )cosh(x))sinh(x) +--R + +--R 2 3 2 3 2 2 3 2 +--R (- 30a b cosh(x) + (- 36a b + 72a )cosh(x) - 12a b + 12a )sinh(x) +--R + +--R 2 4 2 3 3 +--R - 15a b cosh(x) + (- 24a b + 48a )cosh(x) +--R + +--R 2 3 2 +--R (- 24a b + 24a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 2 5 2 3 4 2 3 2 +--R - 3a b cosh(x) + (- 6a b + 12a )cosh(x) + (- 12a b + 12a )cosh(x) +--R + +--R 2 2 3 +--R 3a b cosh(x) - 6a b + 8a +--R / +--R 4 6 4 5 4 2 4 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) + 9a )sinh(x) +--R + +--R 4 3 4 3 +--R (60a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45a cosh(x) + 54a cosh(x) + 9a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18a cosh(x) + 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 4 4 4 2 4 +--R 9a cosh(x) + 9a cosh(x) + 3a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 247 + +--S 248 of 530 +m0546a:= a0546.1-r0546 +--R +--R +--R (246) +--R 2 2 6 2 2 5 +--R (6b - 6a )sinh(x) + (36b - 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((90b - 90a )cosh(x) + 18b - 18a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((120b - 120a )cosh(x) + (72b - 72a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R ((90b - 90a )cosh(x) + (108b - 108a )cosh(x) + 18b - 18a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (36b - 36a )cosh(x) + (72b - 72a )cosh(x) +--R + +--R 2 2 +--R (36b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 2 2 2 +--R (6b - 6a )cosh(x) + (18b - 18a )cosh(x) + (18b - 18a )cosh(x) +--R + +--R 2 2 +--R 6b - 6a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 2 +--R (2b sinh(x) + 2b cosh(x) + 2a)\|- b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) - b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R 2 2 6 2 2 5 +--R (- 12b + 12a )sinh(x) + (- 72b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 180b + 180a )cosh(x) - 36b + 36a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 240b + 240a )cosh(x) + (- 144b + 144a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (- 180b + 180a )cosh(x) + (- 216b + 216a )cosh(x) - 36b +--R + +--R 2 +--R 36a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 72b + 72a )cosh(x) + (- 144b + 144a )cosh(x) +--R + +--R 2 2 +--R (- 72b + 72a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 12b + 12a )cosh(x) + (- 36b + 36a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 36b + 36a )cosh(x) - 12b + 12a +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 6 3 2 5 +--R (- 12b + 18a b)sinh(x) + (- 72b + 108a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 180b + 270a b)cosh(x) - 36b + 54a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 240b + 360a b)cosh(x) + (- 144b + 216a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 180b + 270a b)cosh(x) + (- 216b + 324a b)cosh(x) - 36b +--R + +--R 2 +--R 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 72b + 108a b)cosh(x) + (- 144b + 216a b)cosh(x) +--R + +--R 3 2 +--R (- 72b + 108a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 12b + 18a b)cosh(x) + (- 36b + 54a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 36b + 54a b)cosh(x) - 12b + 18a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 2 6 3 2 5 +--R (6b - 9a b)sinh(x) + (36b - 54a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b - 135a b)cosh(x) + 18b - 27a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b - 180a b)cosh(x) + (72b - 108a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((90b - 135a b)cosh(x) + (108b - 162a b)cosh(x) + 18b - 27a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b - 54a b)cosh(x) + (72b - 108a b)cosh(x) +--R + +--R 3 2 +--R (36b - 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (6b - 9a b)cosh(x) + (18b - 27a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (18b - 27a b)cosh(x) + 6b - 9a b +--R * +--R atan(sinh(x)) +--R + +--R 3 6 3 5 3 2 3 4 +--R 2a sinh(x) + 12a cosh(x)sinh(x) + (30a cosh(x) + 6a )sinh(x) +--R + +--R 3 3 3 3 +--R (40a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (30a cosh(x) + 36a cosh(x) + 6a )sinh(x) +--R + +--R 3 5 3 3 3 3 6 +--R (12a cosh(x) + 24a cosh(x) + 12a cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 3 4 3 2 3 +--R 6a cosh(x) + 6a cosh(x) + 2a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 2 3 6 +--R (3a b sech(x) - 6a b + 6a )sinh(x) +--R + +--R 2 2 3 5 +--R (18a b cosh(x)sech(x) + (- 36a b + 36a )cosh(x))sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (45a b cosh(x) + 9a b)sech(x) + (- 90a b + 90a )cosh(x) +--R + +--R 2 3 +--R - 18a b + 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 +--R (60a b cosh(x) + 36a b cosh(x))sech(x) +--R + +--R 2 3 3 2 3 +--R (- 120a b + 120a )cosh(x) + (- 72a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (45a b cosh(x) + 54a b cosh(x) + 9a b)sech(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 90a b + 90a )cosh(x) + (- 108a b + 108a )cosh(x) - 18a b +--R + +--R 3 +--R 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 +--R (18a b cosh(x) + 36a b cosh(x) + 18a b cosh(x))sech(x) +--R + +--R 2 3 5 2 3 3 +--R (- 36a b + 36a )cosh(x) + (- 72a b + 72a )cosh(x) +--R + +--R 2 3 +--R (- 36a b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (3a b cosh(x) + 9a b cosh(x) + 9a b cosh(x) + 3a b)sech(x) +--R + +--R 2 3 6 2 3 4 +--R (- 6a b + 6a )cosh(x) + (- 18a b + 18a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (- 18a b + 18a )cosh(x) - 6a b + 6a +--R * +--R tanh(x) +--R + +--R 2 5 2 2 3 4 +--R - 6a b sinh(x) + (- 30a b cosh(x) - 12a b + 24a )sinh(x) +--R + +--R 2 2 2 3 3 +--R (- 60a b cosh(x) + (- 48a b + 96a )cosh(x))sinh(x) +--R + +--R 2 3 2 3 2 2 3 2 +--R (- 60a b cosh(x) + (- 72a b + 144a )cosh(x) - 24a b + 24a )sinh(x) +--R + +--R 2 4 2 3 3 +--R - 30a b cosh(x) + (- 48a b + 96a )cosh(x) +--R + +--R 2 3 2 +--R (- 48a b + 48a )cosh(x) + 6a b +--R * +--R sinh(x) +--R + +--R 2 5 2 3 4 2 3 2 +--R - 6a b cosh(x) + (- 12a b + 24a )cosh(x) + (- 24a b + 24a )cosh(x) +--R + +--R 2 2 3 +--R 6a b cosh(x) - 12a b + 16a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) + 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) + 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) + 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) + 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R 18a cosh(x) + 18a cosh(x) + 6a +--R Type: Expression(Integer) +--E 248 + +--S 249 of 530 +d0546a:= D(m0546a,x) +--R +--R +--R (247) +--R 3 2 4 12 +--R (- 2a b + 2a b)sinh(x) +--R + +--R 3 2 4 4 5 11 +--R ((- 20a b + 20a b)cosh(x) - 4a b + 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 90a b + 90a b)cosh(x) + (- 36a b + 36a )cosh(x) - 12a b +--R + +--R 4 +--R 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 240a b + 240a b)cosh(x) + (- 144a b + 144a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b + 100a b)cosh(x) - 20a b + 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 420a b + 420a b)cosh(x) + (- 336a b + 336a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 370a b + 370a b)cosh(x) + (- 148a b + 148a )cosh(x) +--R + +--R 3 2 4 +--R - 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 504a b + 504a b)cosh(x) + (- 504a b + 504a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 800a b + 800a b)cosh(x) + (- 480a b + 480a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b + 200a b)cosh(x) - 40a b + 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 420a b + 420a b)cosh(x) + (- 504a b + 504a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1120a b + 1120a b)cosh(x) + (- 896a b + 896a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 580a b + 580a b)cosh(x) + (- 232a b + 232a )cosh(x) +--R + +--R 3 2 4 +--R - 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 240a b + 240a b)cosh(x) + (- 336a b + 336a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 1064a b + 1064a b)cosh(x) + (- 1064a b + 1064a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 960a b + 960a b)cosh(x) + (- 576a b + 576a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b + 200a b)cosh(x) - 40a b + 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 90a b + 90a b)cosh(x) + (- 144a b + 144a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 700a b + 700a b)cosh(x) + (- 840a b + 840a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1000a b + 1000a b)cosh(x) + (- 800a b + 800a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 420a b + 420a b)cosh(x) + (- 168a b + 168a )cosh(x) +--R + +--R 3 2 4 +--R - 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b + 20a b)cosh(x) + (- 36a b + 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 320a b + 320a b)cosh(x) + (- 448a b + 448a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 680a b + 680a b)cosh(x) + (- 680a b + 680a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 480a b + 480a b)cosh(x) + (- 288a b + 288a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b + 100a b)cosh(x) - 20a b + 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 100a b + 100a b)cosh(x) + (- 160a b + 160a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 300a b + 300a b)cosh(x) + (- 360a b + 360a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 320a b + 320a b)cosh(x) + (- 256a b + 256a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 130a b + 130a b)cosh(x) + (- 52a b + 52a )cosh(x) +--R + +--R 3 2 4 +--R - 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b + 20a b)cosh(x) + (- 36a b + 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 80a b + 80a b)cosh(x) + (- 112a b + 112a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 120a b + 120a b)cosh(x) + (- 120a b + 120a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 80a b + 80a b)cosh(x) + (- 48a b + 48a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 20a b + 20a b)cosh(x) - 4a b + 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 10a b + 10a b)cosh(x) + (- 16a b + 16a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 20a b + 20a b)cosh(x) + (- 24a b + 24a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 20a b + 20a b)cosh(x) + (- 16a b + 16a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (- 10a b + 10a b)cosh(x) + (- 4a b + 4a )cosh(x) - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 4 12 +--R (- 2a b - 2a b)sinh(x) +--R + +--R 3 2 4 4 5 11 +--R ((- 20a b - 20a b)cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 90a b - 90a b)cosh(x) + (- 36a b - 36a )cosh(x) - 12a b +--R + +--R 4 +--R - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 240a b - 240a b)cosh(x) + (- 144a b - 144a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b - 100a b)cosh(x) - 20a b - 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 420a b - 420a b)cosh(x) + (- 336a b - 336a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 370a b - 370a b)cosh(x) + (- 148a b - 148a )cosh(x) - 30a b +--R + +--R 4 +--R - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 504a b - 504a b)cosh(x) + (- 504a b - 504a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 800a b - 800a b)cosh(x) + (- 480a b - 480a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b - 200a b)cosh(x) - 40a b - 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 420a b - 420a b)cosh(x) + (- 504a b - 504a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1120a b - 1120a b)cosh(x) + (- 896a b - 896a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 580a b - 580a b)cosh(x) + (- 232a b - 232a )cosh(x) - 40a b +--R + +--R 4 +--R - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 240a b - 240a b)cosh(x) + (- 336a b - 336a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 1064a b - 1064a b)cosh(x) + (- 1064a b - 1064a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 960a b - 960a b)cosh(x) + (- 576a b - 576a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b - 200a b)cosh(x) - 40a b - 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 90a b - 90a b)cosh(x) + (- 144a b - 144a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 700a b - 700a b)cosh(x) + (- 840a b - 840a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1000a b - 1000a b)cosh(x) + (- 800a b - 800a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 420a b - 420a b)cosh(x) + (- 168a b - 168a )cosh(x) - 30a b +--R + +--R 4 +--R - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b - 20a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 320a b - 320a b)cosh(x) + (- 448a b - 448a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 680a b - 680a b)cosh(x) + (- 680a b - 680a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 480a b - 480a b)cosh(x) + (- 288a b - 288a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b - 100a b)cosh(x) - 20a b - 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b - 2a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 100a b - 100a b)cosh(x) + (- 160a b - 160a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 300a b - 300a b)cosh(x) + (- 360a b - 360a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 320a b - 320a b)cosh(x) + (- 256a b - 256a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 130a b - 130a b)cosh(x) + (- 52a b - 52a )cosh(x) - 12a b +--R + +--R 4 +--R - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b - 20a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 80a b - 80a b)cosh(x) + (- 112a b - 112a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 120a b - 120a b)cosh(x) + (- 120a b - 120a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 80a b - 80a b)cosh(x) + (- 48a b - 48a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 20a b - 20a b)cosh(x) - 4a b - 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b - 2a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 10a b - 10a b)cosh(x) + (- 16a b - 16a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 20a b - 20a b)cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 20a b - 20a b)cosh(x) + (- 16a b - 16a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (- 10a b - 10a b)cosh(x) + (- 4a b - 4a )cosh(x) - 2a b - 2a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 3 3 2 4 2 3 12 +--R ((- 2a b + 2a b )sech(x) + 2a b - 2a b )sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((- 20a b + 20a b )cosh(x) - 4a b + 4a b)sech(x) +--R + +--R 4 2 3 2 3 3 2 +--R (20a b - 20a b )cosh(x) + 4a b - 4a b +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 90a b + 90a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b + 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (90a b - 90a b )cosh(x) + (36a b - 36a b )cosh(x) + 12a b +--R + +--R 2 3 +--R - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 +--R (- 240a b + 240a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b + 100a b )cosh(x) - 20a b + 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (240a b - 240a b )cosh(x) + (144a b - 144a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 336a b + 336a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 370a b + 370a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 148a b + 148a b)cosh(x) - 30a b + 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (420a b - 420a b )cosh(x) + (336a b - 336a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 +--R (370a b - 370a b )cosh(x) + (148a b - 148a b )cosh(x) +--R + +--R 4 2 3 +--R 30a b - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 +--R (- 504a b + 504a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 504a b + 504a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 800a b + 800a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 480a b + 480a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b + 200a b )cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (504a b - 504a b )cosh(x) + (504a b - 504a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (800a b - 800a b )cosh(x) + (480a b - 480a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (200a b - 200a b )cosh(x) + 40a b - 40a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 504a b + 504a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1120a b + 1120a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 896a b + 896a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 580a b + 580a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 232a b + 232a b)cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (420a b - 420a b )cosh(x) + (504a b - 504a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (1120a b - 1120a b )cosh(x) + (896a b - 896a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 +--R (580a b - 580a b )cosh(x) + (232a b - 232a b )cosh(x) +--R + +--R 4 2 3 +--R 40a b - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 +--R (- 240a b + 240a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 336a b + 336a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 1064a b + 1064a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 1064a b + 1064a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 960a b + 960a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 576a b + 576a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b + 200a b )cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (240a b - 240a b )cosh(x) + (336a b - 336a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (1064a b - 1064a b )cosh(x) + (1064a b - 1064a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (960a b - 960a b )cosh(x) + (576a b - 576a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (200a b - 200a b )cosh(x) + 40a b - 40a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 +--R (- 90a b + 90a b )cosh(x) +--R + +--R 3 2 4 7 +--R (- 144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 6 +--R (- 700a b + 700a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 840a b + 840a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1000a b + 1000a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 800a b + 800a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 168a b + 168a b)cosh(x) - 30a b + 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (90a b - 90a b )cosh(x) + (144a b - 144a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (700a b - 700a b )cosh(x) + (840a b - 840a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (1000a b - 1000a b )cosh(x) + (800a b - 800a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 +--R (420a b - 420a b )cosh(x) + (168a b - 168a b )cosh(x) +--R + +--R 4 2 3 +--R 30a b - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b + 20a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 7 +--R (- 320a b + 320a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 448a b + 448a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 680a b + 680a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 680a b + 680a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 480a b + 480a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 288a b + 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b + 100a b )cosh(x) - 20a b + 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 9 2 3 3 2 8 +--R (20a b - 20a b )cosh(x) + (36a b - 36a b )cosh(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (320a b - 320a b )cosh(x) + (448a b - 448a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (680a b - 680a b )cosh(x) + (680a b - 680a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (480a b - 480a b )cosh(x) + (288a b - 288a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 8 +--R (- 100a b + 100a b )cosh(x) +--R + +--R 3 2 4 7 +--R (- 160a b + 160a b)cosh(x) +--R + +--R 2 3 3 2 6 +--R (- 300a b + 300a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 360a b + 360a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 320a b + 320a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 256a b + 256a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 130a b + 130a b )cosh(x) + (- 52a b + 52a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b + 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 10 2 3 3 2 9 +--R (2a b - 2a b )cosh(x) + (4a b - 4a b )cosh(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (100a b - 100a b )cosh(x) + (160a b - 160a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (300a b - 300a b )cosh(x) + (360a b - 360a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (320a b - 320a b )cosh(x) + (256a b - 256a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 +--R (130a b - 130a b )cosh(x) + (52a b - 52a b )cosh(x) +--R + +--R 4 2 3 +--R 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b + 20a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 7 +--R (- 80a b + 80a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 112a b + 112a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 120a b + 120a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 120a b + 120a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 80a b + 80a b )cosh(x) + (- 48a b + 48a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 20a b + 20a b )cosh(x) - 4a b + 4a b +--R * +--R sech(x) +--R + +--R 4 2 3 9 2 3 3 2 8 +--R (20a b - 20a b )cosh(x) + (36a b - 36a b )cosh(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (80a b - 80a b )cosh(x) + (112a b - 112a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (120a b - 120a b )cosh(x) + (120a b - 120a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (80a b - 80a b )cosh(x) + (48a b - 48a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (20a b - 20a b )cosh(x) + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 10a b + 10a b )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 20a b + 20a b )cosh(x) + (- 24a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 20a b + 20a b )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (- 10a b + 10a b )cosh(x) + (- 4a b + 4a b)cosh(x) - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R sech(x) +--R + +--R 4 2 3 10 2 3 3 2 9 +--R (2a b - 2a b )cosh(x) + (4a b - 4a b )cosh(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (10a b - 10a b )cosh(x) + (16a b - 16a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (20a b - 20a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (20a b - 20a b )cosh(x) + (16a b - 16a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 2 3 +--R (10a b - 10a b )cosh(x) + (4a b - 4a b )cosh(x) + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 4 2 3 12 +--R ((- 2a b - 2a b )sech(x) + 2a b + 2a b )sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((- 20a b - 20a b )cosh(x) - 4a b - 4a b)sech(x) +--R + +--R 4 2 3 2 3 3 2 +--R (20a b + 20a b )cosh(x) + 4a b + 4a b +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 90a b - 90a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b - 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (90a b + 90a b )cosh(x) + (36a b + 36a b )cosh(x) + 12a b +--R + +--R 2 3 +--R 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 240a b - 240a b )cosh(x) + (- 144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b - 100a b )cosh(x) - 20a b - 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (240a b + 240a b )cosh(x) + (144a b + 144a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 420a b - 420a b )cosh(x) + (- 336a b - 336a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 370a b - 370a b )cosh(x) + (- 148a b - 148a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 30a b - 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (420a b + 420a b )cosh(x) + (336a b + 336a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (370a b + 370a b )cosh(x) + (148a b + 148a b )cosh(x) + 30a b +--R + +--R 2 3 +--R 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 504a b - 504a b )cosh(x) + (- 504a b - 504a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 800a b - 800a b )cosh(x) + (- 480a b - 480a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b - 200a b )cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (504a b + 504a b )cosh(x) + (504a b + 504a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (800a b + 800a b )cosh(x) + (480a b + 480a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (200a b + 200a b )cosh(x) + 40a b + 40a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 420a b - 420a b )cosh(x) + (- 504a b - 504a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1120a b - 1120a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 896a b - 896a b)cosh(x) + (- 580a b - 580a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 232a b - 232a b)cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (420a b + 420a b )cosh(x) + (504a b + 504a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (1120a b + 1120a b )cosh(x) + (896a b + 896a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (580a b + 580a b )cosh(x) + (232a b + 232a b )cosh(x) + 40a b +--R + +--R 2 3 +--R 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 240a b - 240a b )cosh(x) + (- 336a b - 336a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 1064a b - 1064a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 1064a b - 1064a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 960a b - 960a b )cosh(x) + (- 576a b - 576a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b - 200a b )cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (240a b + 240a b )cosh(x) + (336a b + 336a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (1064a b + 1064a b )cosh(x) + (1064a b + 1064a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (960a b + 960a b )cosh(x) + (576a b + 576a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (200a b + 200a b )cosh(x) + 40a b + 40a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 90a b - 90a b )cosh(x) + (- 144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 700a b - 700a b )cosh(x) + (- 840a b - 840a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1000a b - 1000a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 800a b - 800a b)cosh(x) + (- 420a b - 420a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 168a b - 168a b)cosh(x) - 30a b - 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (90a b + 90a b )cosh(x) + (144a b + 144a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (700a b + 700a b )cosh(x) + (840a b + 840a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (1000a b + 1000a b )cosh(x) + (800a b + 800a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (420a b + 420a b )cosh(x) + (168a b + 168a b )cosh(x) + 30a b +--R + +--R 2 3 +--R 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b - 20a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 320a b - 320a b )cosh(x) + (- 448a b - 448a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 680a b - 680a b )cosh(x) + (- 680a b - 680a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 480a b - 480a b )cosh(x) + (- 288a b - 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b - 100a b )cosh(x) - 20a b - 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 9 2 3 3 2 8 +--R (20a b + 20a b )cosh(x) + (36a b + 36a b )cosh(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (320a b + 320a b )cosh(x) + (448a b + 448a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (680a b + 680a b )cosh(x) + (680a b + 680a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (480a b + 480a b )cosh(x) + (288a b + 288a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 100a b - 100a b )cosh(x) + (- 160a b - 160a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 300a b - 300a b )cosh(x) + (- 360a b - 360a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 320a b - 320a b )cosh(x) + (- 256a b - 256a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 130a b - 130a b )cosh(x) + (- 52a b - 52a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b - 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 10 2 3 3 2 9 +--R (2a b + 2a b )cosh(x) + (4a b + 4a b )cosh(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (100a b + 100a b )cosh(x) + (160a b + 160a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (300a b + 300a b )cosh(x) + (360a b + 360a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (320a b + 320a b )cosh(x) + (256a b + 256a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (130a b + 130a b )cosh(x) + (52a b + 52a b )cosh(x) + 12a b +--R + +--R 2 3 +--R 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b - 20a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 80a b - 80a b )cosh(x) + (- 112a b - 112a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 120a b - 120a b )cosh(x) + (- 120a b - 120a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 80a b - 80a b )cosh(x) + (- 48a b - 48a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 20a b - 20a b )cosh(x) - 4a b - 4a b +--R * +--R sech(x) +--R + +--R 4 2 3 9 2 3 3 2 8 +--R (20a b + 20a b )cosh(x) + (36a b + 36a b )cosh(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (80a b + 80a b )cosh(x) + (112a b + 112a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (120a b + 120a b )cosh(x) + (120a b + 120a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (80a b + 80a b )cosh(x) + (48a b + 48a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (20a b + 20a b )cosh(x) + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 10a b - 10a b )cosh(x) + (- 16a b - 16a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 20a b - 20a b )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 20a b - 20a b )cosh(x) + (- 16a b - 16a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (- 10a b - 10a b )cosh(x) + (- 4a b - 4a b)cosh(x) - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R sech(x) +--R + +--R 4 2 3 10 2 3 3 2 9 +--R (2a b + 2a b )cosh(x) + (4a b + 4a b )cosh(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (10a b + 10a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (20a b + 20a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (20a b + 20a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 2 3 +--R (10a b + 10a b )cosh(x) + (4a b + 4a b )cosh(x) + 2a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 3 2 5 4 2 3 3 2 12 +--R ((a b - a b )sech(x) + 2b - 2a b - 2a b + 2a b )sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((10a b - 10a b )cosh(x) + 2a b - 2a b)sech(x) +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 +--R (20b - 20a b - 20a b + 20a b )cosh(x) + 4a b - 4a b - 4a b +--R + +--R 4 5 +--R 8a b - 4a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (45a b - 45a b )cosh(x) + (18a b - 18a b)cosh(x) + 6a b +--R + +--R 3 2 +--R - 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 2 +--R (90b - 90a b - 90a b + 90a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b + 34a b - 39a b - 33a b + 72a b - 36a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 +--R - 12a b - 12a b + 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (120a b - 120a b )cosh(x) + (72a b - 72a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b - 50a b )cosh(x) + 10a b - 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 3 +--R (240b - 240a b - 240a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b + 124a b - 174a b - 114a b + 288a b - 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (100b - 96a b - 104a b + 94a b + 6a b)cosh(x) + 20a b +--R + +--R 2 3 3 2 4 5 +--R - 20a b - 20a b + 8a b + 12a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (210a b - 210a b )cosh(x) + (168a b - 168a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (185a b - 185a b )cosh(x) + (74a b - 74a b)cosh(x) +--R + +--R 2 3 3 2 +--R 15a b - 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 +--R (420b - 420a b - 420a b + 420a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (90b + 246a b - 471a b - 201a b + 672a b - 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (370b - 334a b - 406a b + 316a b + 54a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b + 138a b - 163a b - 133a b + 72a b + 76a )cosh(x) + 30b +--R + +--R 4 2 3 3 2 +--R - 30a b - 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (252a b - 252a b )cosh(x) + (252a b - 252a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (400a b - 400a b )cosh(x) + (240a b - 240a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 5 +--R (504b - 504a b - 504a b + 504a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (240b + 264a b - 864a b - 144a b + 1008a b - 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (800b - 656a b - 944a b + 584a b + 216a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b + 400a b - 600a b - 360a b + 288a b + 192a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (200b - 184a b - 216a b + 176a b + 24a b)cosh(x) + 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b - 40a b + 48a b - 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (210a b - 210a b )cosh(x) + (252a b - 252a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (560a b - 560a b )cosh(x) + (448a b - 448a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (290a b - 290a b )cosh(x) + (116a b - 116a b)cosh(x) +--R + +--R 2 3 3 2 +--R 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 6 +--R (420b - 420a b - 420a b + 420a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (420b + 84a b - 1134a b + 126a b + 1008a b - 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (1120b - 784a b - 1456a b + 616a b + 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (280b + 616a b - 1316a b - 476a b + 672a b + 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (580b - 468a b - 692a b + 412a b + 168a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b + 212a b - 262a b - 202a b + 240a b - 8a )cosh(x) + 40b +--R + +--R 4 2 3 3 2 +--R - 40a b - 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (120a b - 120a b )cosh(x) + (168a b - 168a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (532a b - 532a b )cosh(x) + (532a b - 532a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (480a b - 480a b )cosh(x) + (288a b - 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 7 +--R (240b - 240a b - 240a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (504b - 168a b - 1092a b + 420a b + 672a b - 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (1064b - 560a b - 1568a b + 308a b + 756a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (560b + 504a b - 1904a b - 224a b + 1008a b + 56a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (960b - 624a b - 1296a b + 456a b + 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (120b + 456a b - 756a b - 396a b + 480a b + 96a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (200b - 176a b - 224a b + 164a b + 36a b)cosh(x) + 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b - 40a b + 48a b - 8a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (45a b - 45a b )cosh(x) + (72a b - 72a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (350a b - 350a b )cosh(x) + (420a b - 420a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (500a b - 500a b )cosh(x) + (400a b - 400a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (210a b - 210a b )cosh(x) + (84a b - 84a b)cosh(x) +--R + +--R 2 3 3 2 +--R 15a b - 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 8 +--R (90b - 90a b - 90a b + 90a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (420b - 276a b - 774a b + 486a b + 288a b - 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (700b - 196a b - 1204a b - 56a b + 756a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (700b + 140a b - 1890a b + 210a b + 1008a b - 168a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (1000b - 440a b - 1560a b + 160a b + 840a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (300b + 500a b - 1250a b - 350a b + 480a b + 320a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (420b - 300a b - 540a b + 240a b + 180a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (20b + 148a b - 198a b - 138a b + 240a b - 72a )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R 30b - 30a b - 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b - 10a b )cosh(x) + (18a b - 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (160a b - 160a b )cosh(x) + (224a b - 224a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (340a b - 340a b )cosh(x) + (340a b - 340a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (240a b - 240a b )cosh(x) + (144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b - 50a b )cosh(x) + 10a b - 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 9 +--R (20b - 20a b - 20a b + 20a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (240b - 204a b - 396a b + 324a b + 72a b - 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (320b + 16a b - 656a b - 184a b + 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (560b - 112a b - 1288a b + 392a b + 672a b - 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (680b - 120a b - 1240a b - 160a b + 840a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (400b + 280a b - 1280a b - 80a b + 240a b + 440a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (480b - 240a b - 720a b + 120a b + 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b + 208a b - 408a b - 168a b + 480a b - 192a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (100b - 84a b - 116a b + 76a b + 24a b)cosh(x) + 20a b +--R + +--R 2 3 3 2 4 5 +--R - 20a b - 20a b + 8a b + 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b - a b )cosh(x) + (2a b - 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (50a b - 50a b )cosh(x) + (80a b - 80a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (150a b - 150a b )cosh(x) + (180a b - 180a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (160a b - 160a b )cosh(x) + (128a b - 128a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (65a b - 65a b )cosh(x) + (26a b - 26a b)cosh(x) + 6a b +--R + +--R 3 2 +--R - 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (2b - 2a b - 2a b + 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (90b - 86a b - 139a b + 131a b + 8a b - 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (100b + 44a b - 244a b - 116a b + 216a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (280b - 120a b - 580a b + 260a b + 288a b - 128a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (300b + 36a b - 636a b - 204a b + 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (300b + 60a b - 810a b + 90a b + 48a b + 312a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (320b - 80a b - 560a b - 40a b + 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (120b + 136a b - 436a b - 76a b + 480a b - 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (130b - 82a b - 178a b + 58a b + 72a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b + 42a b - 67a b - 37a b + 8a b + 44a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 +--R - 12a b - 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b - 10a b )cosh(x) + (18a b - 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (40a b - 40a b )cosh(x) + (56a b - 56a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (60a b - 60a b )cosh(x) + (60a b - 60a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (40a b - 40a b )cosh(x) + (24a b - 24a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (10a b - 10a b )cosh(x) + 2a b - 2a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (20b - 20a b - 30a b + 30a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (20b + 16a b - 56a b - 34a b + 54a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (80b - 44a b - 156a b + 84a b + 72a b - 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (80b + 32a b - 192a b - 88a b + 168a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 6 +--R (120b - 8a b - 292a b + 68a b + 112a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 +--R (120b - 240a b - 60a b + 180a b)cosh(x) +--R + +--R 5 4 2 3 4 5 4 +--R (80b + 40a b - 240a b + 240a b - 120a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (80b - 32a b - 128a b + 8a b + 72a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (20b + 28a b - 78a b - 18a b + 48a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (20b - 16a b - 24a b + 14a b + 6a b)cosh(x) + 4a b - 4a b +--R + +--R 3 2 4 5 +--R - 4a b + 8a b - 4a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b - a b )cosh(x) + (2a b - 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (5a b - 5a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (10a b - 10a b )cosh(x) + (12a b - 12a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (10a b - 10a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (5a b - 5a b )cosh(x) + (2a b - 2a b)cosh(x) + a b - a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 11 +--R (2b - 2a b - 3a b + 3a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (2b + 2a b - 6a b - 4a b + 6a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (10b - 6a b - 19a b + 11a b + 8a b - 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (10b + 6a b - 26a b - 14a b + 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 7 +--R (20b - 4a b - 46a b + 14a b + 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (20b + 4a b - 44a b - 16a b + 36a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b + 4a b - 54a b + 6a b + 48a b - 24a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (20b - 4a b - 36a b - 4a b + 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 3 +--R (10b + 6a b - 31a b - a b + 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (10b - 6a b - 14a b + 4a b + 6a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 +--R (2b + 2a b - 7a b - a b + 8a b - 4a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 +--R - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 5 4 2 3 3 2 12 +--R ((a b + a b )sech(x) - 2b - 2a b + 2a b + 2a b )sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((10a b + 10a b )cosh(x) + 2a b + 2a b)sech(x) +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 +--R (- 20b - 20a b + 20a b + 20a b )cosh(x) - 4a b - 4a b + 4a b +--R + +--R 4 5 +--R 8a b + 4a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (45a b + 45a b )cosh(x) + (18a b + 18a b)cosh(x) + 6a b +--R + +--R 3 2 +--R 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 2 +--R (- 90b - 90a b + 90a b + 90a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b - 34a b - 39a b + 33a b + 72a b + 36a )cosh(x) - 12b +--R + +--R 4 2 3 3 2 +--R - 12a b + 12a b + 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (120a b + 120a b )cosh(x) + (72a b + 72a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b + 50a b )cosh(x) + 10a b + 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 240b - 240a b + 240a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b - 124a b - 174a b + 114a b + 288a b + 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 100b - 96a b + 104a b + 94a b - 6a b)cosh(x) - 20a b - 20a b +--R + +--R 3 2 4 5 +--R 20a b + 8a b - 12a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (210a b + 210a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (185a b + 185a b )cosh(x) + (74a b + 74a b)cosh(x) + 15a b +--R + +--R 3 2 +--R 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 420b - 420a b + 420a b + 420a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (90b - 246a b - 471a b + 201a b + 672a b + 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 370b - 334a b + 406a b + 316a b - 54a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b - 138a b - 163a b + 133a b + 72a b - 76a )cosh(x) - 30b +--R + +--R 4 2 3 3 2 +--R - 30a b + 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (252a b + 252a b )cosh(x) + (252a b + 252a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (400a b + 400a b )cosh(x) + (240a b + 240a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 504b - 504a b + 504a b + 504a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (240b - 264a b - 864a b + 144a b + 1008a b + 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 800b - 656a b + 944a b + 584a b - 216a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b - 400a b - 600a b + 360a b + 288a b - 192a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 200b - 184a b + 216a b + 176a b - 24a b)cosh(x) - 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b + 40a b + 48a b + 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (210a b + 210a b )cosh(x) + (252a b + 252a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (560a b + 560a b )cosh(x) + (448a b + 448a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (290a b + 290a b )cosh(x) + (116a b + 116a b)cosh(x) + 20a b +--R + +--R 3 2 +--R 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 420b - 420a b + 420a b + 420a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (420b - 84a b - 1134a b - 126a b + 1008a b + 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 1120b - 784a b + 1456a b + 616a b - 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (280b - 616a b - 1316a b + 476a b + 672a b - 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 580b - 468a b + 692a b + 412a b - 168a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 212a b - 262a b + 202a b + 240a b + 8a )cosh(x) - 40b +--R + +--R 4 2 3 3 2 +--R - 40a b + 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (120a b + 120a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (532a b + 532a b )cosh(x) + (532a b + 532a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (480a b + 480a b )cosh(x) + (288a b + 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 240b - 240a b + 240a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (504b + 168a b - 1092a b - 420a b + 672a b + 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 1064b - 560a b + 1568a b + 308a b - 756a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (560b - 504a b - 1904a b + 224a b + 1008a b - 56a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 960b - 624a b + 1296a b + 456a b - 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (120b - 456a b - 756a b + 396a b + 480a b - 96a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 200b - 176a b + 224a b + 164a b - 36a b)cosh(x) - 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b + 40a b + 48a b + 8a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (45a b + 45a b )cosh(x) + (72a b + 72a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (350a b + 350a b )cosh(x) + (420a b + 420a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (500a b + 500a b )cosh(x) + (400a b + 400a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (210a b + 210a b )cosh(x) + (84a b + 84a b)cosh(x) + 15a b +--R + +--R 3 2 +--R 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 90b - 90a b + 90a b + 90a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (420b + 276a b - 774a b - 486a b + 288a b + 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 700b - 196a b + 1204a b - 56a b - 756a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (700b - 140a b - 1890a b - 210a b + 1008a b + 168a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 1000b - 440a b + 1560a b + 160a b - 840a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (300b - 500a b - 1250a b + 350a b + 480a b - 320a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 420b - 300a b + 540a b + 240a b - 180a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 148a b - 198a b + 138a b + 240a b + 72a )cosh(x) - 30b +--R + +--R 4 2 3 3 2 +--R - 30a b + 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b + 10a b )cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (160a b + 160a b )cosh(x) + (224a b + 224a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (340a b + 340a b )cosh(x) + (340a b + 340a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (240a b + 240a b )cosh(x) + (144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b + 50a b )cosh(x) + 10a b + 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 9 +--R (- 20b - 20a b + 20a b + 20a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (240b + 204a b - 396a b - 324a b + 72a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 320b + 16a b + 656a b - 184a b - 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (560b + 112a b - 1288a b - 392a b + 672a b + 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 680b - 120a b + 1240a b - 160a b - 840a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (400b - 280a b - 1280a b + 80a b + 240a b - 440a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 480b - 240a b + 720a b + 120a b - 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b - 208a b - 408a b + 168a b + 480a b + 192a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 100b - 84a b + 116a b + 76a b - 24a b)cosh(x) - 20a b +--R + +--R 2 3 3 2 4 5 +--R - 20a b + 20a b + 8a b - 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b + a b )cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (50a b + 50a b )cosh(x) + (80a b + 80a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (150a b + 150a b )cosh(x) + (180a b + 180a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (160a b + 160a b )cosh(x) + (128a b + 128a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (65a b + 65a b )cosh(x) + (26a b + 26a b)cosh(x) + 6a b + 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (- 2b - 2a b + 2a b + 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (90b + 86a b - 139a b - 131a b + 8a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 100b + 44a b + 244a b - 116a b - 216a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (280b + 120a b - 580a b - 260a b + 288a b + 128a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 300b + 36a b + 636a b - 204a b - 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (300b - 60a b - 810a b - 90a b + 48a b - 312a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 320b - 80a b + 560a b - 40a b - 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (120b - 136a b - 436a b + 76a b + 480a b + 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 130b - 82a b + 178a b + 58a b - 72a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b - 42a b - 67a b + 37a b + 8a b - 44a )cosh(x) - 12b +--R + +--R 4 2 3 3 2 +--R - 12a b + 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b + 10a b )cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (40a b + 40a b )cosh(x) + (56a b + 56a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (60a b + 60a b )cosh(x) + (60a b + 60a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (40a b + 40a b )cosh(x) + (24a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (10a b + 10a b )cosh(x) + 2a b + 2a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (20b + 20a b - 30a b - 30a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (- 20b + 16a b + 56a b - 34a b - 54a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (80b + 44a b - 156a b - 84a b + 72a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 80b + 32a b + 192a b - 88a b - 168a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 6 +--R (120b + 8a b - 292a b - 68a b - 112a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 +--R (- 120b + 240a b - 60a b - 180a b)cosh(x) +--R + +--R 5 4 2 3 4 5 4 +--R (80b - 40a b - 240a b + 240a b + 120a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 80b - 32a b + 128a b + 8a b - 72a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (20b - 28a b - 78a b + 18a b - 48a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 20b - 16a b + 24a b + 14a b - 6a b)cosh(x) - 4a b - 4a b +--R + +--R 3 2 4 5 +--R 4a b + 8a b + 4a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b + a b )cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (5a b + 5a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (10a b + 10a b )cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (10a b + 10a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (5a b + 5a b )cosh(x) + (2a b + 2a b)cosh(x) + a b + a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 11 +--R (2b + 2a b - 3a b - 3a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (- 2b + 2a b + 6a b - 4a b - 6a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (10b + 6a b - 19a b - 11a b + 8a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 10b + 6a b + 26a b - 14a b - 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 7 +--R (20b + 4a b - 46a b - 14a b - 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 20b + 4a b + 44a b - 16a b - 36a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 4a b - 54a b - 6a b + 48a b + 24a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 20b - 4a b + 36a b - 4a b - 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 3 +--R (10b - 6a b - 31a b + a b - 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 10b - 6a b + 14a b + 4a b - 6a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 2 3 +--R (2b - 2a b - 7a b + a b + 8a b + 4a )cosh(x) - 2b - 2a b + 2a b +--R + +--R 3 2 +--R 2a b +--R / +--R 4 2 5 12 +--R (2a b - 2a b)sinh(x) +--R + +--R 4 2 5 5 6 11 +--R ((20a b - 20a b)cosh(x) + 4a b - 4a )sinh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R ((90a b - 90a b)cosh(x) + (36a b - 36a )cosh(x) + 12a b - 12a b) +--R * +--R 10 +--R sinh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (240a b - 240a b)cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b - 100a b)cosh(x) + 20a b - 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (420a b - 420a b)cosh(x) + (336a b - 336a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (370a b - 370a b)cosh(x) + (148a b - 148a )cosh(x) + 30a b +--R + +--R 5 +--R - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (504a b - 504a b)cosh(x) + (504a b - 504a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (800a b - 800a b)cosh(x) + (480a b - 480a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b - 200a b)cosh(x) + 40a b - 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (420a b - 420a b)cosh(x) + (504a b - 504a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1120a b - 1120a b)cosh(x) + (896a b - 896a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (580a b - 580a b)cosh(x) + (232a b - 232a )cosh(x) + 40a b +--R + +--R 5 +--R - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (240a b - 240a b)cosh(x) + (336a b - 336a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (1064a b - 1064a b)cosh(x) + (1064a b - 1064a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (960a b - 960a b)cosh(x) + (576a b - 576a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b - 200a b)cosh(x) + 40a b - 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (90a b - 90a b)cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (700a b - 700a b)cosh(x) + (840a b - 840a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1000a b - 1000a b)cosh(x) + (800a b - 800a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (420a b - 420a b)cosh(x) + (168a b - 168a )cosh(x) + 30a b +--R + +--R 5 +--R - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b - 20a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (320a b - 320a b)cosh(x) + (448a b - 448a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (680a b - 680a b)cosh(x) + (680a b - 680a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (480a b - 480a b)cosh(x) + (288a b - 288a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b - 100a b)cosh(x) + 20a b - 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (100a b - 100a b)cosh(x) + (160a b - 160a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (300a b - 300a b)cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (320a b - 320a b)cosh(x) + (256a b - 256a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (130a b - 130a b)cosh(x) + (52a b - 52a )cosh(x) + 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b - 20a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (80a b - 80a b)cosh(x) + (112a b - 112a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (120a b - 120a b)cosh(x) + (120a b - 120a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (80a b - 80a b)cosh(x) + (48a b - 48a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (20a b - 20a b)cosh(x) + 4a b - 4a +--R * +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (10a b - 10a b)cosh(x) + (16a b - 16a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (20a b - 20a b)cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (20a b - 20a b)cosh(x) + (16a b - 16a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (10a b - 10a b)cosh(x) + (4a b - 4a )cosh(x) + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 5 12 4 2 5 5 6 11 +--R (2a b + 2a b)sinh(x) + ((20a b + 20a b)cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R ((90a b + 90a b)cosh(x) + (36a b + 36a )cosh(x) + 12a b + 12a b) +--R * +--R 10 +--R sinh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (240a b + 240a b)cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b + 100a b)cosh(x) + 20a b + 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (420a b + 420a b)cosh(x) + (336a b + 336a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (370a b + 370a b)cosh(x) + (148a b + 148a )cosh(x) + 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (504a b + 504a b)cosh(x) + (504a b + 504a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (800a b + 800a b)cosh(x) + (480a b + 480a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b + 200a b)cosh(x) + 40a b + 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (420a b + 420a b)cosh(x) + (504a b + 504a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1120a b + 1120a b)cosh(x) + (896a b + 896a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (580a b + 580a b)cosh(x) + (232a b + 232a )cosh(x) + 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (240a b + 240a b)cosh(x) + (336a b + 336a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (1064a b + 1064a b)cosh(x) + (1064a b + 1064a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (960a b + 960a b)cosh(x) + (576a b + 576a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b + 200a b)cosh(x) + 40a b + 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (90a b + 90a b)cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (700a b + 700a b)cosh(x) + (840a b + 840a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1000a b + 1000a b)cosh(x) + (800a b + 800a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (420a b + 420a b)cosh(x) + (168a b + 168a )cosh(x) + 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b + 20a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (320a b + 320a b)cosh(x) + (448a b + 448a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (680a b + 680a b)cosh(x) + (680a b + 680a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (480a b + 480a b)cosh(x) + (288a b + 288a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b + 100a b)cosh(x) + 20a b + 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (100a b + 100a b)cosh(x) + (160a b + 160a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (300a b + 300a b)cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (320a b + 320a b)cosh(x) + (256a b + 256a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (130a b + 130a b)cosh(x) + (52a b + 52a )cosh(x) + 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b + 20a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (80a b + 80a b)cosh(x) + (112a b + 112a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (120a b + 120a b)cosh(x) + (120a b + 120a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (80a b + 80a b)cosh(x) + (48a b + 48a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (20a b + 20a b)cosh(x) + 4a b + 4a +--R * +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 4 2 5 8 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) + (10a b + 10a b)cosh(x) +--R + +--R 5 6 7 4 2 5 6 +--R (16a b + 16a )cosh(x) + (20a b + 20a b)cosh(x) +--R + +--R 5 6 5 4 2 5 4 +--R (24a b + 24a )cosh(x) + (20a b + 20a b)cosh(x) +--R + +--R 5 6 3 4 2 5 2 5 6 +--R (16a b + 16a )cosh(x) + (10a b + 10a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 4 2 5 +--R 2a b + 2a b +--R Type: Expression(Integer) +--E 249 + +--S 250 of 530 +m0546b:= a0546.2-r0546 +--R +--R +--R (248) +--R 2 2 6 2 2 5 +--R (- 12b + 12a )sinh(x) + (- 72b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 180b + 180a )cosh(x) - 36b + 36a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 240b + 240a )cosh(x) + (- 144b + 144a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (- 180b + 180a )cosh(x) + (- 216b + 216a )cosh(x) - 36b +--R + +--R 2 +--R 36a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 72b + 72a )cosh(x) + (- 144b + 144a )cosh(x) +--R + +--R 2 2 +--R (- 72b + 72a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 12b + 12a )cosh(x) + (- 36b + 36a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 36b + 36a )cosh(x) - 12b + 12a +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 6 2 2 5 +--R (- 12b + 12a )sinh(x) + (- 72b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((- 180b + 180a )cosh(x) - 36b + 36a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 240b + 240a )cosh(x) + (- 144b + 144a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (- 180b + 180a )cosh(x) + (- 216b + 216a )cosh(x) - 36b +--R + +--R 2 +--R 36a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (- 72b + 72a )cosh(x) + (- 144b + 144a )cosh(x) +--R + +--R 2 2 +--R (- 72b + 72a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 12b + 12a )cosh(x) + (- 36b + 36a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 36b + 36a )cosh(x) - 12b + 12a +--R * +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 \|b - a +--R \|b - a atan(-------------------------) +--R b sinh(x) + b cosh(x) + a +--R + +--R 3 2 6 3 2 5 +--R (- 12b + 18a b)sinh(x) + (- 72b + 108a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 180b + 270a b)cosh(x) - 36b + 54a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 240b + 360a b)cosh(x) + (- 144b + 216a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 180b + 270a b)cosh(x) + (- 216b + 324a b)cosh(x) - 36b +--R + +--R 2 +--R 54a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 72b + 108a b)cosh(x) + (- 144b + 216a b)cosh(x) +--R + +--R 3 2 +--R (- 72b + 108a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 12b + 18a b)cosh(x) + (- 36b + 54a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 36b + 54a b)cosh(x) - 12b + 18a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 2 6 3 2 5 +--R (6b - 9a b)sinh(x) + (36b - 54a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b - 135a b)cosh(x) + 18b - 27a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b - 180a b)cosh(x) + (72b - 108a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((90b - 135a b)cosh(x) + (108b - 162a b)cosh(x) + 18b - 27a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b - 54a b)cosh(x) + (72b - 108a b)cosh(x) +--R + +--R 3 2 +--R (36b - 54a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (6b - 9a b)cosh(x) + (18b - 27a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (18b - 27a b)cosh(x) + 6b - 9a b +--R * +--R atan(sinh(x)) +--R + +--R 3 6 3 5 3 2 3 4 +--R 2a sinh(x) + 12a cosh(x)sinh(x) + (30a cosh(x) + 6a )sinh(x) +--R + +--R 3 3 3 3 +--R (40a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (30a cosh(x) + 36a cosh(x) + 6a )sinh(x) +--R + +--R 3 5 3 3 3 3 6 +--R (12a cosh(x) + 24a cosh(x) + 12a cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 3 4 3 2 3 +--R 6a cosh(x) + 6a cosh(x) + 2a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 2 3 6 +--R (3a b sech(x) - 6a b + 6a )sinh(x) +--R + +--R 2 2 3 5 +--R (18a b cosh(x)sech(x) + (- 36a b + 36a )cosh(x))sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (45a b cosh(x) + 9a b)sech(x) + (- 90a b + 90a )cosh(x) +--R + +--R 2 3 +--R - 18a b + 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 +--R (60a b cosh(x) + 36a b cosh(x))sech(x) +--R + +--R 2 3 3 2 3 +--R (- 120a b + 120a )cosh(x) + (- 72a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (45a b cosh(x) + 54a b cosh(x) + 9a b)sech(x) +--R + +--R 2 3 4 2 3 2 2 +--R (- 90a b + 90a )cosh(x) + (- 108a b + 108a )cosh(x) - 18a b +--R + +--R 3 +--R 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 +--R (18a b cosh(x) + 36a b cosh(x) + 18a b cosh(x))sech(x) +--R + +--R 2 3 5 2 3 3 +--R (- 36a b + 36a )cosh(x) + (- 72a b + 72a )cosh(x) +--R + +--R 2 3 +--R (- 36a b + 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (3a b cosh(x) + 9a b cosh(x) + 9a b cosh(x) + 3a b)sech(x) +--R + +--R 2 3 6 2 3 4 +--R (- 6a b + 6a )cosh(x) + (- 18a b + 18a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (- 18a b + 18a )cosh(x) - 6a b + 6a +--R * +--R tanh(x) +--R + +--R 2 5 2 2 3 4 +--R - 6a b sinh(x) + (- 30a b cosh(x) - 12a b + 24a )sinh(x) +--R + +--R 2 2 2 3 3 +--R (- 60a b cosh(x) + (- 48a b + 96a )cosh(x))sinh(x) +--R + +--R 2 3 2 3 2 2 3 2 +--R (- 60a b cosh(x) + (- 72a b + 144a )cosh(x) - 24a b + 24a )sinh(x) +--R + +--R 2 4 2 3 3 +--R - 30a b cosh(x) + (- 48a b + 96a )cosh(x) +--R + +--R 2 3 2 +--R (- 48a b + 48a )cosh(x) + 6a b +--R * +--R sinh(x) +--R + +--R 2 5 2 3 4 2 3 2 +--R - 6a b cosh(x) + (- 12a b + 24a )cosh(x) + (- 24a b + 24a )cosh(x) +--R + +--R 2 2 3 +--R 6a b cosh(x) - 12a b + 16a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) + 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) + 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) + 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) + 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R 18a cosh(x) + 18a cosh(x) + 6a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 530 +d0546b:= D(m0546b,x) +--R +--R +--R (249) +--R 3 2 4 12 +--R (- 2a b + 2a b)sinh(x) +--R + +--R 3 2 4 4 5 11 +--R ((- 20a b + 20a b)cosh(x) - 4a b + 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 90a b + 90a b)cosh(x) + (- 36a b + 36a )cosh(x) - 12a b +--R + +--R 4 +--R 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 240a b + 240a b)cosh(x) + (- 144a b + 144a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b + 100a b)cosh(x) - 20a b + 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 420a b + 420a b)cosh(x) + (- 336a b + 336a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 370a b + 370a b)cosh(x) + (- 148a b + 148a )cosh(x) +--R + +--R 3 2 4 +--R - 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 504a b + 504a b)cosh(x) + (- 504a b + 504a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 800a b + 800a b)cosh(x) + (- 480a b + 480a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b + 200a b)cosh(x) - 40a b + 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 420a b + 420a b)cosh(x) + (- 504a b + 504a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1120a b + 1120a b)cosh(x) + (- 896a b + 896a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 580a b + 580a b)cosh(x) + (- 232a b + 232a )cosh(x) +--R + +--R 3 2 4 +--R - 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 240a b + 240a b)cosh(x) + (- 336a b + 336a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 1064a b + 1064a b)cosh(x) + (- 1064a b + 1064a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 960a b + 960a b)cosh(x) + (- 576a b + 576a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b + 200a b)cosh(x) - 40a b + 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 90a b + 90a b)cosh(x) + (- 144a b + 144a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 700a b + 700a b)cosh(x) + (- 840a b + 840a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1000a b + 1000a b)cosh(x) + (- 800a b + 800a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 420a b + 420a b)cosh(x) + (- 168a b + 168a )cosh(x) +--R + +--R 3 2 4 +--R - 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b + 20a b)cosh(x) + (- 36a b + 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 320a b + 320a b)cosh(x) + (- 448a b + 448a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 680a b + 680a b)cosh(x) + (- 680a b + 680a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 480a b + 480a b)cosh(x) + (- 288a b + 288a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b + 100a b)cosh(x) - 20a b + 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 100a b + 100a b)cosh(x) + (- 160a b + 160a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 300a b + 300a b)cosh(x) + (- 360a b + 360a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 320a b + 320a b)cosh(x) + (- 256a b + 256a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 130a b + 130a b)cosh(x) + (- 52a b + 52a )cosh(x) +--R + +--R 3 2 4 +--R - 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b + 20a b)cosh(x) + (- 36a b + 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 80a b + 80a b)cosh(x) + (- 112a b + 112a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 120a b + 120a b)cosh(x) + (- 120a b + 120a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 80a b + 80a b)cosh(x) + (- 48a b + 48a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 20a b + 20a b)cosh(x) - 4a b + 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 10a b + 10a b)cosh(x) + (- 16a b + 16a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 20a b + 20a b)cosh(x) + (- 24a b + 24a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 20a b + 20a b)cosh(x) + (- 16a b + 16a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (- 10a b + 10a b)cosh(x) + (- 4a b + 4a )cosh(x) - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 4 12 +--R (- 2a b - 2a b)sinh(x) +--R + +--R 3 2 4 4 5 11 +--R ((- 20a b - 20a b)cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 90a b - 90a b)cosh(x) + (- 36a b - 36a )cosh(x) - 12a b +--R + +--R 4 +--R - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 240a b - 240a b)cosh(x) + (- 144a b - 144a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b - 100a b)cosh(x) - 20a b - 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 420a b - 420a b)cosh(x) + (- 336a b - 336a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 370a b - 370a b)cosh(x) + (- 148a b - 148a )cosh(x) - 30a b +--R + +--R 4 +--R - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 504a b - 504a b)cosh(x) + (- 504a b - 504a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 800a b - 800a b)cosh(x) + (- 480a b - 480a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b - 200a b)cosh(x) - 40a b - 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 420a b - 420a b)cosh(x) + (- 504a b - 504a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1120a b - 1120a b)cosh(x) + (- 896a b - 896a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 580a b - 580a b)cosh(x) + (- 232a b - 232a )cosh(x) - 40a b +--R + +--R 4 +--R - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 240a b - 240a b)cosh(x) + (- 336a b - 336a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 1064a b - 1064a b)cosh(x) + (- 1064a b - 1064a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 960a b - 960a b)cosh(x) + (- 576a b - 576a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b - 200a b)cosh(x) - 40a b - 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 90a b - 90a b)cosh(x) + (- 144a b - 144a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 700a b - 700a b)cosh(x) + (- 840a b - 840a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1000a b - 1000a b)cosh(x) + (- 800a b - 800a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 420a b - 420a b)cosh(x) + (- 168a b - 168a )cosh(x) - 30a b +--R + +--R 4 +--R - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b - 20a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 320a b - 320a b)cosh(x) + (- 448a b - 448a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 680a b - 680a b)cosh(x) + (- 680a b - 680a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 480a b - 480a b)cosh(x) + (- 288a b - 288a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b - 100a b)cosh(x) - 20a b - 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b - 2a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 100a b - 100a b)cosh(x) + (- 160a b - 160a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 300a b - 300a b)cosh(x) + (- 360a b - 360a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 320a b - 320a b)cosh(x) + (- 256a b - 256a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 130a b - 130a b)cosh(x) + (- 52a b - 52a )cosh(x) - 12a b +--R + +--R 4 +--R - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b - 20a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 80a b - 80a b)cosh(x) + (- 112a b - 112a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 120a b - 120a b)cosh(x) + (- 120a b - 120a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 80a b - 80a b)cosh(x) + (- 48a b - 48a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 20a b - 20a b)cosh(x) - 4a b - 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b - 2a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 10a b - 10a b)cosh(x) + (- 16a b - 16a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 20a b - 20a b)cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 20a b - 20a b)cosh(x) + (- 16a b - 16a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (- 10a b - 10a b)cosh(x) + (- 4a b - 4a )cosh(x) - 2a b - 2a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 3 3 2 4 2 3 12 +--R ((- 2a b + 2a b )sech(x) + 2a b - 2a b )sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((- 20a b + 20a b )cosh(x) - 4a b + 4a b)sech(x) +--R + +--R 4 2 3 2 3 3 2 +--R (20a b - 20a b )cosh(x) + 4a b - 4a b +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 90a b + 90a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b + 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (90a b - 90a b )cosh(x) + (36a b - 36a b )cosh(x) + 12a b +--R + +--R 2 3 +--R - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 +--R (- 240a b + 240a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b + 100a b )cosh(x) - 20a b + 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (240a b - 240a b )cosh(x) + (144a b - 144a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 336a b + 336a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 370a b + 370a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 148a b + 148a b)cosh(x) - 30a b + 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (420a b - 420a b )cosh(x) + (336a b - 336a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 +--R (370a b - 370a b )cosh(x) + (148a b - 148a b )cosh(x) +--R + +--R 4 2 3 +--R 30a b - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 +--R (- 504a b + 504a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 504a b + 504a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 800a b + 800a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 480a b + 480a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b + 200a b )cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (504a b - 504a b )cosh(x) + (504a b - 504a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (800a b - 800a b )cosh(x) + (480a b - 480a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (200a b - 200a b )cosh(x) + 40a b - 40a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 504a b + 504a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1120a b + 1120a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 896a b + 896a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 580a b + 580a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 232a b + 232a b)cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (420a b - 420a b )cosh(x) + (504a b - 504a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (1120a b - 1120a b )cosh(x) + (896a b - 896a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 +--R (580a b - 580a b )cosh(x) + (232a b - 232a b )cosh(x) +--R + +--R 4 2 3 +--R 40a b - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 +--R (- 240a b + 240a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 336a b + 336a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 1064a b + 1064a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 1064a b + 1064a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 960a b + 960a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 576a b + 576a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b + 200a b )cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (240a b - 240a b )cosh(x) + (336a b - 336a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (1064a b - 1064a b )cosh(x) + (1064a b - 1064a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (960a b - 960a b )cosh(x) + (576a b - 576a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (200a b - 200a b )cosh(x) + 40a b - 40a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 +--R (- 90a b + 90a b )cosh(x) +--R + +--R 3 2 4 7 +--R (- 144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 6 +--R (- 700a b + 700a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 840a b + 840a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1000a b + 1000a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 800a b + 800a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 168a b + 168a b)cosh(x) - 30a b + 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (90a b - 90a b )cosh(x) + (144a b - 144a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (700a b - 700a b )cosh(x) + (840a b - 840a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (1000a b - 1000a b )cosh(x) + (800a b - 800a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 +--R (420a b - 420a b )cosh(x) + (168a b - 168a b )cosh(x) +--R + +--R 4 2 3 +--R 30a b - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b + 20a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 7 +--R (- 320a b + 320a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 448a b + 448a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 680a b + 680a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 680a b + 680a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 480a b + 480a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 288a b + 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b + 100a b )cosh(x) - 20a b + 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 9 2 3 3 2 8 +--R (20a b - 20a b )cosh(x) + (36a b - 36a b )cosh(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (320a b - 320a b )cosh(x) + (448a b - 448a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (680a b - 680a b )cosh(x) + (680a b - 680a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (480a b - 480a b )cosh(x) + (288a b - 288a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 8 +--R (- 100a b + 100a b )cosh(x) +--R + +--R 3 2 4 7 +--R (- 160a b + 160a b)cosh(x) +--R + +--R 2 3 3 2 6 +--R (- 300a b + 300a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 360a b + 360a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 320a b + 320a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 256a b + 256a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 130a b + 130a b )cosh(x) + (- 52a b + 52a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b + 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 10 2 3 3 2 9 +--R (2a b - 2a b )cosh(x) + (4a b - 4a b )cosh(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (100a b - 100a b )cosh(x) + (160a b - 160a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (300a b - 300a b )cosh(x) + (360a b - 360a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (320a b - 320a b )cosh(x) + (256a b - 256a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 +--R (130a b - 130a b )cosh(x) + (52a b - 52a b )cosh(x) +--R + +--R 4 2 3 +--R 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b + 20a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 7 +--R (- 80a b + 80a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 112a b + 112a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 120a b + 120a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 120a b + 120a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 80a b + 80a b )cosh(x) + (- 48a b + 48a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 20a b + 20a b )cosh(x) - 4a b + 4a b +--R * +--R sech(x) +--R + +--R 4 2 3 9 2 3 3 2 8 +--R (20a b - 20a b )cosh(x) + (36a b - 36a b )cosh(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (80a b - 80a b )cosh(x) + (112a b - 112a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (120a b - 120a b )cosh(x) + (120a b - 120a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (80a b - 80a b )cosh(x) + (48a b - 48a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (20a b - 20a b )cosh(x) + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 10a b + 10a b )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 20a b + 20a b )cosh(x) + (- 24a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 20a b + 20a b )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (- 10a b + 10a b )cosh(x) + (- 4a b + 4a b)cosh(x) - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R sech(x) +--R + +--R 4 2 3 10 2 3 3 2 9 +--R (2a b - 2a b )cosh(x) + (4a b - 4a b )cosh(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (10a b - 10a b )cosh(x) + (16a b - 16a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (20a b - 20a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (20a b - 20a b )cosh(x) + (16a b - 16a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 2 3 +--R (10a b - 10a b )cosh(x) + (4a b - 4a b )cosh(x) + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 4 2 3 12 +--R ((- 2a b - 2a b )sech(x) + 2a b + 2a b )sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((- 20a b - 20a b )cosh(x) - 4a b - 4a b)sech(x) +--R + +--R 4 2 3 2 3 3 2 +--R (20a b + 20a b )cosh(x) + 4a b + 4a b +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 90a b - 90a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b - 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (90a b + 90a b )cosh(x) + (36a b + 36a b )cosh(x) + 12a b +--R + +--R 2 3 +--R 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 240a b - 240a b )cosh(x) + (- 144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b - 100a b )cosh(x) - 20a b - 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (240a b + 240a b )cosh(x) + (144a b + 144a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 420a b - 420a b )cosh(x) + (- 336a b - 336a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 370a b - 370a b )cosh(x) + (- 148a b - 148a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 30a b - 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (420a b + 420a b )cosh(x) + (336a b + 336a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (370a b + 370a b )cosh(x) + (148a b + 148a b )cosh(x) + 30a b +--R + +--R 2 3 +--R 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 504a b - 504a b )cosh(x) + (- 504a b - 504a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 800a b - 800a b )cosh(x) + (- 480a b - 480a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b - 200a b )cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (504a b + 504a b )cosh(x) + (504a b + 504a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (800a b + 800a b )cosh(x) + (480a b + 480a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (200a b + 200a b )cosh(x) + 40a b + 40a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 420a b - 420a b )cosh(x) + (- 504a b - 504a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1120a b - 1120a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 896a b - 896a b)cosh(x) + (- 580a b - 580a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 232a b - 232a b)cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (420a b + 420a b )cosh(x) + (504a b + 504a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (1120a b + 1120a b )cosh(x) + (896a b + 896a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (580a b + 580a b )cosh(x) + (232a b + 232a b )cosh(x) + 40a b +--R + +--R 2 3 +--R 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 240a b - 240a b )cosh(x) + (- 336a b - 336a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 1064a b - 1064a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 1064a b - 1064a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 960a b - 960a b )cosh(x) + (- 576a b - 576a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b - 200a b )cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (240a b + 240a b )cosh(x) + (336a b + 336a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (1064a b + 1064a b )cosh(x) + (1064a b + 1064a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (960a b + 960a b )cosh(x) + (576a b + 576a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (200a b + 200a b )cosh(x) + 40a b + 40a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 90a b - 90a b )cosh(x) + (- 144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 700a b - 700a b )cosh(x) + (- 840a b - 840a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1000a b - 1000a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 800a b - 800a b)cosh(x) + (- 420a b - 420a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 168a b - 168a b)cosh(x) - 30a b - 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (90a b + 90a b )cosh(x) + (144a b + 144a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (700a b + 700a b )cosh(x) + (840a b + 840a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (1000a b + 1000a b )cosh(x) + (800a b + 800a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (420a b + 420a b )cosh(x) + (168a b + 168a b )cosh(x) + 30a b +--R + +--R 2 3 +--R 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b - 20a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 320a b - 320a b )cosh(x) + (- 448a b - 448a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 680a b - 680a b )cosh(x) + (- 680a b - 680a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 480a b - 480a b )cosh(x) + (- 288a b - 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b - 100a b )cosh(x) - 20a b - 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 9 2 3 3 2 8 +--R (20a b + 20a b )cosh(x) + (36a b + 36a b )cosh(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (320a b + 320a b )cosh(x) + (448a b + 448a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (680a b + 680a b )cosh(x) + (680a b + 680a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (480a b + 480a b )cosh(x) + (288a b + 288a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 100a b - 100a b )cosh(x) + (- 160a b - 160a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 300a b - 300a b )cosh(x) + (- 360a b - 360a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 320a b - 320a b )cosh(x) + (- 256a b - 256a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 130a b - 130a b )cosh(x) + (- 52a b - 52a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b - 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 10 2 3 3 2 9 +--R (2a b + 2a b )cosh(x) + (4a b + 4a b )cosh(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (100a b + 100a b )cosh(x) + (160a b + 160a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (300a b + 300a b )cosh(x) + (360a b + 360a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (320a b + 320a b )cosh(x) + (256a b + 256a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 +--R (130a b + 130a b )cosh(x) + (52a b + 52a b )cosh(x) + 12a b +--R + +--R 2 3 +--R 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b - 20a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 80a b - 80a b )cosh(x) + (- 112a b - 112a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 120a b - 120a b )cosh(x) + (- 120a b - 120a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 80a b - 80a b )cosh(x) + (- 48a b - 48a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 20a b - 20a b )cosh(x) - 4a b - 4a b +--R * +--R sech(x) +--R + +--R 4 2 3 9 2 3 3 2 8 +--R (20a b + 20a b )cosh(x) + (36a b + 36a b )cosh(x) +--R + +--R 4 2 3 7 2 3 3 2 6 +--R (80a b + 80a b )cosh(x) + (112a b + 112a b )cosh(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (120a b + 120a b )cosh(x) + (120a b + 120a b )cosh(x) +--R + +--R 4 2 3 3 2 3 3 2 2 +--R (80a b + 80a b )cosh(x) + (48a b + 48a b )cosh(x) +--R + +--R 4 2 3 2 3 3 2 +--R (20a b + 20a b )cosh(x) + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 10a b - 10a b )cosh(x) + (- 16a b - 16a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 20a b - 20a b )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 20a b - 20a b )cosh(x) + (- 16a b - 16a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (- 10a b - 10a b )cosh(x) + (- 4a b - 4a b)cosh(x) - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R sech(x) +--R + +--R 4 2 3 10 2 3 3 2 9 +--R (2a b + 2a b )cosh(x) + (4a b + 4a b )cosh(x) +--R + +--R 4 2 3 8 2 3 3 2 7 +--R (10a b + 10a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 4 2 3 6 2 3 3 2 5 +--R (20a b + 20a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 4 2 3 4 2 3 3 2 3 +--R (20a b + 20a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 4 2 3 2 2 3 3 2 4 2 3 +--R (10a b + 10a b )cosh(x) + (4a b + 4a b )cosh(x) + 2a b + 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 3 2 5 4 2 3 3 2 12 +--R ((a b - a b )sech(x) + 2b - 2a b - 2a b + 2a b )sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((10a b - 10a b )cosh(x) + 2a b - 2a b)sech(x) +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 +--R (20b - 20a b - 20a b + 20a b )cosh(x) + 4a b - 4a b - 4a b +--R + +--R 4 5 +--R 8a b - 4a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (45a b - 45a b )cosh(x) + (18a b - 18a b)cosh(x) + 6a b +--R + +--R 3 2 +--R - 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 2 +--R (90b - 90a b - 90a b + 90a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b + 34a b - 39a b - 33a b + 72a b - 36a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 +--R - 12a b - 12a b + 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (120a b - 120a b )cosh(x) + (72a b - 72a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b - 50a b )cosh(x) + 10a b - 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 3 +--R (240b - 240a b - 240a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b + 124a b - 174a b - 114a b + 288a b - 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (100b - 96a b - 104a b + 94a b + 6a b)cosh(x) + 20a b +--R + +--R 2 3 3 2 4 5 +--R - 20a b - 20a b + 8a b + 12a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (210a b - 210a b )cosh(x) + (168a b - 168a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (185a b - 185a b )cosh(x) + (74a b - 74a b)cosh(x) +--R + +--R 2 3 3 2 +--R 15a b - 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 +--R (420b - 420a b - 420a b + 420a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (90b + 246a b - 471a b - 201a b + 672a b - 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (370b - 334a b - 406a b + 316a b + 54a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b + 138a b - 163a b - 133a b + 72a b + 76a )cosh(x) + 30b +--R + +--R 4 2 3 3 2 +--R - 30a b - 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (252a b - 252a b )cosh(x) + (252a b - 252a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (400a b - 400a b )cosh(x) + (240a b - 240a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 5 +--R (504b - 504a b - 504a b + 504a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (240b + 264a b - 864a b - 144a b + 1008a b - 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (800b - 656a b - 944a b + 584a b + 216a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b + 400a b - 600a b - 360a b + 288a b + 192a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (200b - 184a b - 216a b + 176a b + 24a b)cosh(x) + 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b - 40a b + 48a b - 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (210a b - 210a b )cosh(x) + (252a b - 252a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (560a b - 560a b )cosh(x) + (448a b - 448a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (290a b - 290a b )cosh(x) + (116a b - 116a b)cosh(x) +--R + +--R 2 3 3 2 +--R 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 6 +--R (420b - 420a b - 420a b + 420a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (420b + 84a b - 1134a b + 126a b + 1008a b - 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (1120b - 784a b - 1456a b + 616a b + 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (280b + 616a b - 1316a b - 476a b + 672a b + 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (580b - 468a b - 692a b + 412a b + 168a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b + 212a b - 262a b - 202a b + 240a b - 8a )cosh(x) + 40b +--R + +--R 4 2 3 3 2 +--R - 40a b - 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (120a b - 120a b )cosh(x) + (168a b - 168a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (532a b - 532a b )cosh(x) + (532a b - 532a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (480a b - 480a b )cosh(x) + (288a b - 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 7 +--R (240b - 240a b - 240a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (504b - 168a b - 1092a b + 420a b + 672a b - 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (1064b - 560a b - 1568a b + 308a b + 756a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (560b + 504a b - 1904a b - 224a b + 1008a b + 56a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (960b - 624a b - 1296a b + 456a b + 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (120b + 456a b - 756a b - 396a b + 480a b + 96a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (200b - 176a b - 224a b + 164a b + 36a b)cosh(x) + 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b - 40a b + 48a b - 8a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (45a b - 45a b )cosh(x) + (72a b - 72a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (350a b - 350a b )cosh(x) + (420a b - 420a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (500a b - 500a b )cosh(x) + (400a b - 400a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (210a b - 210a b )cosh(x) + (84a b - 84a b)cosh(x) +--R + +--R 2 3 3 2 +--R 15a b - 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 8 +--R (90b - 90a b - 90a b + 90a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (420b - 276a b - 774a b + 486a b + 288a b - 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (700b - 196a b - 1204a b - 56a b + 756a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (700b + 140a b - 1890a b + 210a b + 1008a b - 168a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (1000b - 440a b - 1560a b + 160a b + 840a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (300b + 500a b - 1250a b - 350a b + 480a b + 320a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (420b - 300a b - 540a b + 240a b + 180a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (20b + 148a b - 198a b - 138a b + 240a b - 72a )cosh(x) +--R + +--R 5 4 2 3 3 2 +--R 30b - 30a b - 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b - 10a b )cosh(x) + (18a b - 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (160a b - 160a b )cosh(x) + (224a b - 224a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (340a b - 340a b )cosh(x) + (340a b - 340a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (240a b - 240a b )cosh(x) + (144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b - 50a b )cosh(x) + 10a b - 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 9 +--R (20b - 20a b - 20a b + 20a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (240b - 204a b - 396a b + 324a b + 72a b - 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (320b + 16a b - 656a b - 184a b + 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (560b - 112a b - 1288a b + 392a b + 672a b - 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (680b - 120a b - 1240a b - 160a b + 840a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (400b + 280a b - 1280a b - 80a b + 240a b + 440a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (480b - 240a b - 720a b + 120a b + 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b + 208a b - 408a b - 168a b + 480a b - 192a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (100b - 84a b - 116a b + 76a b + 24a b)cosh(x) + 20a b +--R + +--R 2 3 3 2 4 5 +--R - 20a b - 20a b + 8a b + 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b - a b )cosh(x) + (2a b - 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (50a b - 50a b )cosh(x) + (80a b - 80a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (150a b - 150a b )cosh(x) + (180a b - 180a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (160a b - 160a b )cosh(x) + (128a b - 128a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (65a b - 65a b )cosh(x) + (26a b - 26a b)cosh(x) + 6a b +--R + +--R 3 2 +--R - 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (2b - 2a b - 2a b + 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (90b - 86a b - 139a b + 131a b + 8a b - 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (100b + 44a b - 244a b - 116a b + 216a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (280b - 120a b - 580a b + 260a b + 288a b - 128a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (300b + 36a b - 636a b - 204a b + 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (300b + 60a b - 810a b + 90a b + 48a b + 312a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (320b - 80a b - 560a b - 40a b + 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (120b + 136a b - 436a b - 76a b + 480a b - 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (130b - 82a b - 178a b + 58a b + 72a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b + 42a b - 67a b - 37a b + 8a b + 44a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 +--R - 12a b - 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b - 10a b )cosh(x) + (18a b - 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (40a b - 40a b )cosh(x) + (56a b - 56a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (60a b - 60a b )cosh(x) + (60a b - 60a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (40a b - 40a b )cosh(x) + (24a b - 24a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (10a b - 10a b )cosh(x) + 2a b - 2a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (20b - 20a b - 30a b + 30a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (20b + 16a b - 56a b - 34a b + 54a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (80b - 44a b - 156a b + 84a b + 72a b - 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (80b + 32a b - 192a b - 88a b + 168a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 6 +--R (120b - 8a b - 292a b + 68a b + 112a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 +--R (120b - 240a b - 60a b + 180a b)cosh(x) +--R + +--R 5 4 2 3 4 5 4 +--R (80b + 40a b - 240a b + 240a b - 120a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (80b - 32a b - 128a b + 8a b + 72a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (20b + 28a b - 78a b - 18a b + 48a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (20b - 16a b - 24a b + 14a b + 6a b)cosh(x) + 4a b - 4a b +--R + +--R 3 2 4 5 +--R - 4a b + 8a b - 4a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b - a b )cosh(x) + (2a b - 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (5a b - 5a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (10a b - 10a b )cosh(x) + (12a b - 12a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (10a b - 10a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (5a b - 5a b )cosh(x) + (2a b - 2a b)cosh(x) + a b - a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 11 +--R (2b - 2a b - 3a b + 3a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (2b + 2a b - 6a b - 4a b + 6a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (10b - 6a b - 19a b + 11a b + 8a b - 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (10b + 6a b - 26a b - 14a b + 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 7 +--R (20b - 4a b - 46a b + 14a b + 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (20b + 4a b - 44a b - 16a b + 36a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b + 4a b - 54a b + 6a b + 48a b - 24a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (20b - 4a b - 36a b - 4a b + 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 3 +--R (10b + 6a b - 31a b - a b + 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (10b - 6a b - 14a b + 4a b + 6a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 +--R (2b + 2a b - 7a b - a b + 8a b - 4a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 +--R - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 5 4 2 3 3 2 12 +--R ((a b + a b )sech(x) - 2b - 2a b + 2a b + 2a b )sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((10a b + 10a b )cosh(x) + 2a b + 2a b)sech(x) +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 +--R (- 20b - 20a b + 20a b + 20a b )cosh(x) - 4a b - 4a b + 4a b +--R + +--R 4 5 +--R 8a b + 4a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (45a b + 45a b )cosh(x) + (18a b + 18a b)cosh(x) + 6a b +--R + +--R 3 2 +--R 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 2 +--R (- 90b - 90a b + 90a b + 90a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b - 34a b - 39a b + 33a b + 72a b + 36a )cosh(x) - 12b +--R + +--R 4 2 3 3 2 +--R - 12a b + 12a b + 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (120a b + 120a b )cosh(x) + (72a b + 72a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b + 50a b )cosh(x) + 10a b + 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 240b - 240a b + 240a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b - 124a b - 174a b + 114a b + 288a b + 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 100b - 96a b + 104a b + 94a b - 6a b)cosh(x) - 20a b - 20a b +--R + +--R 3 2 4 5 +--R 20a b + 8a b - 12a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (210a b + 210a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (185a b + 185a b )cosh(x) + (74a b + 74a b)cosh(x) + 15a b +--R + +--R 3 2 +--R 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 420b - 420a b + 420a b + 420a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (90b - 246a b - 471a b + 201a b + 672a b + 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 370b - 334a b + 406a b + 316a b - 54a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b - 138a b - 163a b + 133a b + 72a b - 76a )cosh(x) - 30b +--R + +--R 4 2 3 3 2 +--R - 30a b + 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (252a b + 252a b )cosh(x) + (252a b + 252a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (400a b + 400a b )cosh(x) + (240a b + 240a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 504b - 504a b + 504a b + 504a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (240b - 264a b - 864a b + 144a b + 1008a b + 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 800b - 656a b + 944a b + 584a b - 216a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b - 400a b - 600a b + 360a b + 288a b - 192a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 200b - 184a b + 216a b + 176a b - 24a b)cosh(x) - 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b + 40a b + 48a b + 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (210a b + 210a b )cosh(x) + (252a b + 252a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (560a b + 560a b )cosh(x) + (448a b + 448a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (290a b + 290a b )cosh(x) + (116a b + 116a b)cosh(x) + 20a b +--R + +--R 3 2 +--R 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 420b - 420a b + 420a b + 420a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (420b - 84a b - 1134a b - 126a b + 1008a b + 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 1120b - 784a b + 1456a b + 616a b - 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (280b - 616a b - 1316a b + 476a b + 672a b - 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 580b - 468a b + 692a b + 412a b - 168a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 212a b - 262a b + 202a b + 240a b + 8a )cosh(x) - 40b +--R + +--R 4 2 3 3 2 +--R - 40a b + 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (120a b + 120a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (532a b + 532a b )cosh(x) + (532a b + 532a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (480a b + 480a b )cosh(x) + (288a b + 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 7 +--R (- 240b - 240a b + 240a b + 240a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (504b + 168a b - 1092a b - 420a b + 672a b + 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 1064b - 560a b + 1568a b + 308a b - 756a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (560b - 504a b - 1904a b + 224a b + 1008a b - 56a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 960b - 624a b + 1296a b + 456a b - 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (120b - 456a b - 756a b + 396a b + 480a b - 96a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 200b - 176a b + 224a b + 164a b - 36a b)cosh(x) - 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b + 40a b + 48a b + 8a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (45a b + 45a b )cosh(x) + (72a b + 72a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (350a b + 350a b )cosh(x) + (420a b + 420a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (500a b + 500a b )cosh(x) + (400a b + 400a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (210a b + 210a b )cosh(x) + (84a b + 84a b)cosh(x) + 15a b +--R + +--R 3 2 +--R 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 90b - 90a b + 90a b + 90a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (420b + 276a b - 774a b - 486a b + 288a b + 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 700b - 196a b + 1204a b - 56a b - 756a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (700b - 140a b - 1890a b - 210a b + 1008a b + 168a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 1000b - 440a b + 1560a b + 160a b - 840a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (300b - 500a b - 1250a b + 350a b + 480a b - 320a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 420b - 300a b + 540a b + 240a b - 180a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 148a b - 198a b + 138a b + 240a b + 72a )cosh(x) - 30b +--R + +--R 4 2 3 3 2 +--R - 30a b + 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b + 10a b )cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (160a b + 160a b )cosh(x) + (224a b + 224a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (340a b + 340a b )cosh(x) + (340a b + 340a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (240a b + 240a b )cosh(x) + (144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b + 50a b )cosh(x) + 10a b + 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 9 +--R (- 20b - 20a b + 20a b + 20a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (240b + 204a b - 396a b - 324a b + 72a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 320b + 16a b + 656a b - 184a b - 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (560b + 112a b - 1288a b - 392a b + 672a b + 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 680b - 120a b + 1240a b - 160a b - 840a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (400b - 280a b - 1280a b + 80a b + 240a b - 440a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 480b - 240a b + 720a b + 120a b - 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b - 208a b - 408a b + 168a b + 480a b + 192a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 100b - 84a b + 116a b + 76a b - 24a b)cosh(x) - 20a b +--R + +--R 2 3 3 2 4 5 +--R - 20a b + 20a b + 8a b - 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b + a b )cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (50a b + 50a b )cosh(x) + (80a b + 80a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (150a b + 150a b )cosh(x) + (180a b + 180a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (160a b + 160a b )cosh(x) + (128a b + 128a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (65a b + 65a b )cosh(x) + (26a b + 26a b)cosh(x) + 6a b + 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (- 2b - 2a b + 2a b + 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (90b + 86a b - 139a b - 131a b + 8a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 100b + 44a b + 244a b - 116a b - 216a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (280b + 120a b - 580a b - 260a b + 288a b + 128a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 300b + 36a b + 636a b - 204a b - 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (300b - 60a b - 810a b - 90a b + 48a b - 312a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 320b - 80a b + 560a b - 40a b - 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (120b - 136a b - 436a b + 76a b + 480a b + 224a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 130b - 82a b + 178a b + 58a b - 72a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b - 42a b - 67a b + 37a b + 8a b - 44a )cosh(x) - 12b +--R + +--R 4 2 3 3 2 +--R - 12a b + 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b + 10a b )cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (40a b + 40a b )cosh(x) + (56a b + 56a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (60a b + 60a b )cosh(x) + (60a b + 60a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (40a b + 40a b )cosh(x) + (24a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (10a b + 10a b )cosh(x) + 2a b + 2a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (20b + 20a b - 30a b - 30a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (- 20b + 16a b + 56a b - 34a b - 54a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (80b + 44a b - 156a b - 84a b + 72a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 80b + 32a b + 192a b - 88a b - 168a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 6 +--R (120b + 8a b - 292a b - 68a b - 112a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 +--R (- 120b + 240a b - 60a b - 180a b)cosh(x) +--R + +--R 5 4 2 3 4 5 4 +--R (80b - 40a b - 240a b + 240a b + 120a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 80b - 32a b + 128a b + 8a b - 72a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (20b - 28a b - 78a b + 18a b - 48a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 20b - 16a b + 24a b + 14a b - 6a b)cosh(x) - 4a b - 4a b +--R + +--R 3 2 4 5 +--R 4a b + 8a b + 4a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b + a b )cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (5a b + 5a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (10a b + 10a b )cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (10a b + 10a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (5a b + 5a b )cosh(x) + (2a b + 2a b)cosh(x) + a b + a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 11 +--R (2b + 2a b - 3a b - 3a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (- 2b + 2a b + 6a b - 4a b - 6a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (10b + 6a b - 19a b - 11a b + 8a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 10b + 6a b + 26a b - 14a b - 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 7 +--R (20b + 4a b - 46a b - 14a b - 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 20b + 4a b + 44a b - 16a b - 36a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 4a b - 54a b - 6a b + 48a b + 24a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 20b - 4a b + 36a b - 4a b - 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 5 3 +--R (10b - 6a b - 31a b + a b - 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 10b - 6a b + 14a b + 4a b - 6a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 2 3 +--R (2b - 2a b - 7a b + a b + 8a b + 4a )cosh(x) - 2b - 2a b + 2a b +--R + +--R 3 2 +--R 2a b +--R / +--R 4 2 5 12 +--R (2a b - 2a b)sinh(x) +--R + +--R 4 2 5 5 6 11 +--R ((20a b - 20a b)cosh(x) + 4a b - 4a )sinh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R ((90a b - 90a b)cosh(x) + (36a b - 36a )cosh(x) + 12a b - 12a b) +--R * +--R 10 +--R sinh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (240a b - 240a b)cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b - 100a b)cosh(x) + 20a b - 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (420a b - 420a b)cosh(x) + (336a b - 336a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (370a b - 370a b)cosh(x) + (148a b - 148a )cosh(x) + 30a b +--R + +--R 5 +--R - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (504a b - 504a b)cosh(x) + (504a b - 504a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (800a b - 800a b)cosh(x) + (480a b - 480a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b - 200a b)cosh(x) + 40a b - 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (420a b - 420a b)cosh(x) + (504a b - 504a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1120a b - 1120a b)cosh(x) + (896a b - 896a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (580a b - 580a b)cosh(x) + (232a b - 232a )cosh(x) + 40a b +--R + +--R 5 +--R - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (240a b - 240a b)cosh(x) + (336a b - 336a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (1064a b - 1064a b)cosh(x) + (1064a b - 1064a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (960a b - 960a b)cosh(x) + (576a b - 576a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b - 200a b)cosh(x) + 40a b - 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (90a b - 90a b)cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (700a b - 700a b)cosh(x) + (840a b - 840a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1000a b - 1000a b)cosh(x) + (800a b - 800a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (420a b - 420a b)cosh(x) + (168a b - 168a )cosh(x) + 30a b +--R + +--R 5 +--R - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b - 20a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (320a b - 320a b)cosh(x) + (448a b - 448a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (680a b - 680a b)cosh(x) + (680a b - 680a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (480a b - 480a b)cosh(x) + (288a b - 288a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b - 100a b)cosh(x) + 20a b - 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (100a b - 100a b)cosh(x) + (160a b - 160a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (300a b - 300a b)cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (320a b - 320a b)cosh(x) + (256a b - 256a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (130a b - 130a b)cosh(x) + (52a b - 52a )cosh(x) + 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b - 20a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (80a b - 80a b)cosh(x) + (112a b - 112a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (120a b - 120a b)cosh(x) + (120a b - 120a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (80a b - 80a b)cosh(x) + (48a b - 48a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (20a b - 20a b)cosh(x) + 4a b - 4a +--R * +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (10a b - 10a b)cosh(x) + (16a b - 16a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (20a b - 20a b)cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (20a b - 20a b)cosh(x) + (16a b - 16a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (10a b - 10a b)cosh(x) + (4a b - 4a )cosh(x) + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 5 12 4 2 5 5 6 11 +--R (2a b + 2a b)sinh(x) + ((20a b + 20a b)cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R ((90a b + 90a b)cosh(x) + (36a b + 36a )cosh(x) + 12a b + 12a b) +--R * +--R 10 +--R sinh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (240a b + 240a b)cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b + 100a b)cosh(x) + 20a b + 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (420a b + 420a b)cosh(x) + (336a b + 336a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (370a b + 370a b)cosh(x) + (148a b + 148a )cosh(x) + 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (504a b + 504a b)cosh(x) + (504a b + 504a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (800a b + 800a b)cosh(x) + (480a b + 480a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b + 200a b)cosh(x) + 40a b + 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (420a b + 420a b)cosh(x) + (504a b + 504a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1120a b + 1120a b)cosh(x) + (896a b + 896a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (580a b + 580a b)cosh(x) + (232a b + 232a )cosh(x) + 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (240a b + 240a b)cosh(x) + (336a b + 336a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (1064a b + 1064a b)cosh(x) + (1064a b + 1064a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (960a b + 960a b)cosh(x) + (576a b + 576a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b + 200a b)cosh(x) + 40a b + 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (90a b + 90a b)cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (700a b + 700a b)cosh(x) + (840a b + 840a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1000a b + 1000a b)cosh(x) + (800a b + 800a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (420a b + 420a b)cosh(x) + (168a b + 168a )cosh(x) + 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b + 20a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (320a b + 320a b)cosh(x) + (448a b + 448a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (680a b + 680a b)cosh(x) + (680a b + 680a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (480a b + 480a b)cosh(x) + (288a b + 288a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b + 100a b)cosh(x) + 20a b + 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (100a b + 100a b)cosh(x) + (160a b + 160a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (300a b + 300a b)cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (320a b + 320a b)cosh(x) + (256a b + 256a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (130a b + 130a b)cosh(x) + (52a b + 52a )cosh(x) + 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b + 20a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (80a b + 80a b)cosh(x) + (112a b + 112a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (120a b + 120a b)cosh(x) + (120a b + 120a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (80a b + 80a b)cosh(x) + (48a b + 48a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (20a b + 20a b)cosh(x) + 4a b + 4a +--R * +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 4 2 5 8 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) + (10a b + 10a b)cosh(x) +--R + +--R 5 6 7 4 2 5 6 +--R (16a b + 16a )cosh(x) + (20a b + 20a b)cosh(x) +--R + +--R 5 6 5 4 2 5 4 +--R (24a b + 24a )cosh(x) + (20a b + 20a b)cosh(x) +--R + +--R 5 6 3 4 2 5 2 5 6 +--R (16a b + 16a )cosh(x) + (10a b + 10a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 4 2 5 +--R 2a b + 2a b +--R Type: Expression(Integer) +--E 251 + +--S 252 of 530 +t0547:= tanh(x)^2/(a+a*cosh(x)) +--R +--R +--R 2 +--R tanh(x) +--R (250) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 252 + +--S 253 of 530 +r0547:= atan(sinh(x))/a-tanh(x)/a +--R +--R +--R atan(sinh(x)) - tanh(x) +--R (251) ----------------------- +--R a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 530 +a0547:= integrate(t0547,x) +--R +--R +--R (252) +--R 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)atan(sinh(x) + cosh(x)) + 2 +--R ------------------------------------------------------------------------ +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Union(Expression(Integer),...) +--E 254 + +--S 255 of 530 +m0547:= a0547-r0547 +--R +--R +--R (253) +--R 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)atan(sinh(x)) +--R + +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)tanh(x) + 2 +--R / +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Expression(Integer) +--E 255 + +--S 256 of 530 +d0547:= D(m0547,x) +--R +--R +--R (254) +--R 6 5 2 4 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) - 3)sinh(x) +--R + +--R 3 3 +--R (- 4cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- cosh(x) - 8cosh(x) - 3)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) - 4cosh(x))sinh(x) - cosh(x) - 2cosh(x) - 1 +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 2 4 +--R sinh(x) + (4cosh(x) + 2)sinh(x) + (6cosh(x) + 5cosh(x) - 1)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) + 2cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) - 4cosh(x) + 4cosh(x) + 6cosh(x) - 1)sinh(x) +--R + +--R 4 3 2 5 +--R (- 4cosh(x) + 4cosh(x) + 2cosh(x) - 4cosh(x) + 2)sinh(x) - cosh(x) +--R + +--R 4 2 +--R cosh(x) - 2cosh(x) + cosh(x) + 1 +--R / +--R 6 5 2 4 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 3a)sinh(x) +--R + +--R 3 3 +--R (4a cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (a cosh(x) + 8a cosh(x) + 3a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 530 +t0548:= tanh(x)^3/(a+a*cosh(x)) +--R +--R +--R 3 +--R tanh(x) +--R (255) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 257 + +--S 258 of 530 +r0548:= -1/2*(2*cosh(x)-1)/a/cosh(x)^2 +--R +--R +--R - 2cosh(x) + 1 +--R (256) -------------- +--R 2 +--R 2a cosh(x) +--R Type: Expression(Integer) +--E 258 + +--S 259 of 530 +a0548:= integrate(t0548,x) +--R +--R +--R (257) +--R 2 2 +--R - 2sinh(x) + (- 4cosh(x) + 2)sinh(x) - 2cosh(x) + 2cosh(x) - 2 +--R / +--R 3 2 2 3 +--R a sinh(x) + 3a cosh(x)sinh(x) + (3a cosh(x) + a)sinh(x) + a cosh(x) +--R + +--R 3a cosh(x) +--R Type: Union(Expression(Integer),...) +--E 259 + +--S 260 of 530 +m0548:= a0548-r0548 +--R +--R +--R (258) +--R 3 2 2 +--R (2cosh(x) - 1)sinh(x) + (2cosh(x) - 3cosh(x))sinh(x) +--R + +--R 3 2 4 3 +--R (- 2cosh(x) + cosh(x) + 2cosh(x) - 1)sinh(x) - 2cosh(x) + 3cosh(x) +--R + +--R 2 +--R 2cosh(x) - 3cosh(x) +--R / +--R 2 3 3 2 +--R 2a cosh(x) sinh(x) + 6a cosh(x) sinh(x) +--R + +--R 4 2 5 3 +--R (6a cosh(x) + 2a cosh(x) )sinh(x) + 2a cosh(x) + 6a cosh(x) +--R Type: Expression(Integer) +--E 260 + +--S 261 of 530 +d0548:= D(m0548,x) +--R +--R +--R (259) +--R 7 2 6 +--R (- cosh(x) + 1)sinh(x) + (- 6cosh(x) + 6cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (- 13cosh(x) + 15cosh(x) - 2cosh(x) + 2)sinh(x) +--R + +--R 4 3 2 4 +--R (- 10cosh(x) + 16cosh(x) - 12cosh(x) + 12cosh(x))sinh(x) +--R + +--R 5 4 3 2 3 +--R (5cosh(x) - cosh(x) - 16cosh(x) + 24cosh(x) - cosh(x) + 1)sinh(x) +--R + +--R 6 5 4 3 2 +--R 14cosh(x) - 18cosh(x) - 8cosh(x) + 16cosh(x) - 6cosh(x) +--R + +--R 6cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 9cosh(x) - 15cosh(x) - 6cosh(x) + 6cosh(x) - 3cosh(x) +--R + +--R 2 +--R 9cosh(x) +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 2cosh(x) - 4cosh(x) - 4cosh(x) + 4cosh(x) + 2cosh(x) +--R / +--R 3 6 4 5 +--R a cosh(x) sinh(x) + 6a cosh(x) sinh(x) +--R + +--R 5 3 4 +--R (15a cosh(x) + 2a cosh(x) )sinh(x) +--R + +--R 6 4 3 +--R (20a cosh(x) + 12a cosh(x) )sinh(x) +--R + +--R 7 5 3 2 +--R (15a cosh(x) + 24a cosh(x) + a cosh(x) )sinh(x) +--R + +--R 8 6 4 9 +--R (6a cosh(x) + 20a cosh(x) + 6a cosh(x) )sinh(x) + a cosh(x) +--R + +--R 7 5 +--R 6a cosh(x) + 9a cosh(x) +--R Type: Expression(Integer) +--E 261 + +--S 262 of 530 +t0549:= tanh(x)^4/(a+a*cosh(x)) +--R +--R +--R 4 +--R tanh(x) +--R (260) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 262 + +--S 263 of 530 +r0549:= 1/2*atan(sinh(x))/a-1/2*sech(x)*tanh(x)/a-1/3*tanh(x)^3/a +--R +--R +--R 3 +--R 3atan(sinh(x)) - 2tanh(x) - 3sech(x)tanh(x) +--R (261) -------------------------------------------- +--R 6a +--R Type: Expression(Integer) +--E 263 + +--S 264 of 530 +a0549:= integrate(t0549,x) +--R +--R +--R (262) +--R 6 5 2 4 +--R 3sinh(x) + 18cosh(x)sinh(x) + (45cosh(x) + 9)sinh(x) +--R + +--R 3 3 +--R (60cosh(x) + 36cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (45cosh(x) + 54cosh(x) + 9)sinh(x) +--R + +--R 5 3 6 4 +--R (18cosh(x) + 36cosh(x) + 18cosh(x))sinh(x) + 3cosh(x) + 9cosh(x) +--R + +--R 2 +--R 9cosh(x) + 3 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 5 4 +--R - 3sinh(x) + (- 15cosh(x) + 6)sinh(x) +--R + +--R 2 3 3 2 2 +--R (- 30cosh(x) + 24cosh(x))sinh(x) + (- 30cosh(x) + 36cosh(x) )sinh(x) +--R + +--R 4 3 5 4 +--R (- 15cosh(x) + 24cosh(x) + 3)sinh(x) - 3cosh(x) + 6cosh(x) + 3cosh(x) +--R + +--R 2 +--R / +--R 6 5 2 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) + 9a)sinh(x) +--R + +--R 3 3 +--R (60a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (45a cosh(x) + 54a cosh(x) + 9a)sinh(x) +--R + +--R 5 3 6 +--R (18a cosh(x) + 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 4 2 +--R 9a cosh(x) + 9a cosh(x) + 3a +--R Type: Union(Expression(Integer),...) +--E 264 + +--S 265 of 530 +m0549:= a0549-r0549 +--R +--R +--R (263) +--R 6 5 2 4 +--R 6sinh(x) + 36cosh(x)sinh(x) + (90cosh(x) + 18)sinh(x) +--R + +--R 3 3 +--R (120cosh(x) + 72cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (90cosh(x) + 108cosh(x) + 18)sinh(x) +--R + +--R 5 3 6 4 +--R (36cosh(x) + 72cosh(x) + 36cosh(x))sinh(x) + 6cosh(x) + 18cosh(x) +--R + +--R 2 +--R 18cosh(x) + 6 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 6 5 2 4 +--R - 3sinh(x) - 18cosh(x)sinh(x) + (- 45cosh(x) - 9)sinh(x) +--R + +--R 3 3 +--R (- 60cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) - 54cosh(x) - 9)sinh(x) +--R + +--R 5 3 6 +--R (- 18cosh(x) - 36cosh(x) - 18cosh(x))sinh(x) - 3cosh(x) +--R + +--R 4 2 +--R - 9cosh(x) - 9cosh(x) - 3 +--R * +--R atan(sinh(x)) +--R + +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 6)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) + 24cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) + 36cosh(x) + 6)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 24cosh(x) + 12cosh(x))sinh(x) + 2cosh(x) + 6cosh(x) +--R + +--R 2 +--R 6cosh(x) + 2 +--R * +--R 3 +--R tanh(x) +--R + +--R 6 5 +--R 3sech(x)sinh(x) + 18cosh(x)sech(x)sinh(x) +--R + +--R 2 4 +--R (45cosh(x) + 9)sech(x)sinh(x) +--R + +--R 3 3 +--R (60cosh(x) + 36cosh(x))sech(x)sinh(x) +--R + +--R 4 2 2 +--R (45cosh(x) + 54cosh(x) + 9)sech(x)sinh(x) +--R + +--R 5 3 +--R (18cosh(x) + 36cosh(x) + 18cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 +--R (3cosh(x) + 9cosh(x) + 9cosh(x) + 3)sech(x) +--R * +--R tanh(x) +--R + +--R 5 4 +--R - 6sinh(x) + (- 30cosh(x) + 12)sinh(x) +--R + +--R 2 3 3 2 2 +--R (- 60cosh(x) + 48cosh(x))sinh(x) + (- 60cosh(x) + 72cosh(x) )sinh(x) +--R + +--R 4 3 5 4 +--R (- 30cosh(x) + 48cosh(x) + 6)sinh(x) - 6cosh(x) + 12cosh(x) +--R + +--R 6cosh(x) + 4 +--R / +--R 6 5 2 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) + 18a)sinh(x) +--R + +--R 3 3 +--R (120a cosh(x) + 72a cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (90a cosh(x) + 108a cosh(x) + 18a)sinh(x) +--R + +--R 5 3 6 +--R (36a cosh(x) + 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 2 +--R 18a cosh(x) + 18a cosh(x) + 6a +--R Type: Expression(Integer) +--E 265 + +--S 266 of 530 +d0549:= D(m0549,x) +--R +--R +--R (264) +--R 10 9 2 8 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 10)sinh(x) +--R + +--R 3 7 +--R (- 112cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 140cosh(x) - 176cosh(x) - 20)sinh(x) +--R + +--R 5 3 5 +--R (- 112cosh(x) - 272cosh(x) - 96cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 56cosh(x) - 260cosh(x) - 192cosh(x) - 20)sinh(x) +--R + +--R 7 5 3 3 +--R (- 16cosh(x) - 160cosh(x) - 208cosh(x) - 64cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 2cosh(x) - 64cosh(x) - 132cosh(x) - 80cosh(x) - 10)sinh(x) +--R + +--R 7 5 3 +--R (- 16cosh(x) - 48cosh(x) - 48cosh(x) - 16cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 2cosh(x) - 8cosh(x) - 12cosh(x) - 8cosh(x) - 2 +--R * +--R 4 +--R tanh(x) +--R + +--R 10 9 +--R (- 2sech(x) + 2)sinh(x) + (- 16cosh(x)sech(x) + 16cosh(x))sinh(x) +--R + +--R 2 2 8 +--R ((- 56cosh(x) - 10)sech(x) + 56cosh(x) + 10)sinh(x) +--R + +--R 3 3 +--R ((- 112cosh(x) - 64cosh(x))sech(x) + 112cosh(x) + 64cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 176cosh(x) - 20)sech(x) + 140cosh(x) +--R + +--R 2 +--R 176cosh(x) + 20 +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 5 +--R (- 112cosh(x) - 272cosh(x) - 96cosh(x))sech(x) + 112cosh(x) +--R + +--R 3 +--R 272cosh(x) + 96cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 4 2 +--R (- 56cosh(x) - 260cosh(x) - 192cosh(x) - 20)sech(x) +--R + +--R 6 4 2 +--R 56cosh(x) + 260cosh(x) + 192cosh(x) + 20 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 16cosh(x) - 160cosh(x) - 208cosh(x) - 64cosh(x))sech(x) +--R + +--R 7 5 3 +--R 16cosh(x) + 160cosh(x) + 208cosh(x) + 64cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 2cosh(x) - 64cosh(x) - 132cosh(x) - 80cosh(x) - 10)sech(x) +--R + +--R 8 6 4 2 +--R 2cosh(x) + 64cosh(x) + 132cosh(x) + 80cosh(x) + 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 16cosh(x) - 48cosh(x) - 48cosh(x) - 16cosh(x))sech(x) +--R + +--R 7 5 3 +--R 16cosh(x) + 48cosh(x) + 48cosh(x) + 16cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 2cosh(x) - 8cosh(x) - 12cosh(x) - 8cosh(x) - 2)sech(x) +--R + +--R 8 6 4 2 +--R 2cosh(x) + 8cosh(x) + 12cosh(x) + 8cosh(x) + 2 +--R * +--R 2 +--R tanh(x) +--R + +--R 10 9 +--R sech(x)sinh(x) + (8cosh(x)sech(x) + 4)sinh(x) +--R + +--R 2 8 +--R ((28cosh(x) + 5)sech(x) + 27cosh(x) - 8)sinh(x) +--R + +--R 3 2 7 +--R ((56cosh(x) + 32cosh(x))sech(x) + 76cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 3 2 +--R (70cosh(x) + 88cosh(x) + 10)sech(x) + 112cosh(x) - 120cosh(x) +--R + +--R 4cosh(x) + 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 4 +--R (56cosh(x) + 136cosh(x) + 48cosh(x))sech(x) + 84cosh(x) +--R + +--R 3 2 +--R - 160cosh(x) + 20cosh(x) + 16cosh(x) - 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 6 4 2 5 +--R (28cosh(x) + 130cosh(x) + 96cosh(x) + 10)sech(x) + 14cosh(x) +--R + +--R 4 3 2 +--R - 120cosh(x) + 40cosh(x) - 24cosh(x) - 38cosh(x) + 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 3 +--R (8cosh(x) + 80cosh(x) + 104cosh(x) + 32cosh(x))sech(x) +--R + +--R 6 5 4 3 2 +--R - 28cosh(x) - 48cosh(x) + 40cosh(x) - 96cosh(x) - 76cosh(x) +--R + +--R 48cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (cosh(x) + 32cosh(x) + 66cosh(x) + 40cosh(x) + 5)sech(x) +--R + +--R 7 6 5 4 3 +--R - 24cosh(x) - 8cosh(x) + 20cosh(x) - 104cosh(x) - 80cosh(x) +--R + +--R 2 +--R 88cosh(x) - 12cosh(x) - 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) + 24cosh(x) + 24cosh(x) + 8cosh(x))sech(x) - 8cosh(x) +--R + +--R 6 5 4 3 2 +--R 4cosh(x) - 48cosh(x) - 44cosh(x) + 64cosh(x) - 20cosh(x) +--R + +--R - 16cosh(x) + 4 +--R * +--R sinh(x) +--R + +--R 8 6 4 2 9 +--R (cosh(x) + 4cosh(x) + 6cosh(x) + 4cosh(x) + 1)sech(x) - cosh(x) +--R + +--R 6 5 4 3 2 +--R - 8cosh(x) - 10cosh(x) + 16cosh(x) - 8cosh(x) - 8cosh(x) + 3cosh(x) +--R / +--R 10 9 2 8 +--R 2a sinh(x) + 16a cosh(x)sinh(x) + (56a cosh(x) + 10a)sinh(x) +--R + +--R 3 7 +--R (112a cosh(x) + 64a cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (140a cosh(x) + 176a cosh(x) + 20a)sinh(x) +--R + +--R 5 3 5 +--R (112a cosh(x) + 272a cosh(x) + 96a cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (56a cosh(x) + 260a cosh(x) + 192a cosh(x) + 20a)sinh(x) +--R + +--R 7 5 3 3 +--R (16a cosh(x) + 160a cosh(x) + 208a cosh(x) + 64a cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (2a cosh(x) + 64a cosh(x) + 132a cosh(x) + 80a cosh(x) + 10a)sinh(x) +--R + +--R 7 5 3 +--R (16a cosh(x) + 48a cosh(x) + 48a cosh(x) + 16a cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 2a cosh(x) + 8a cosh(x) + 12a cosh(x) + 8a cosh(x) + 2a +--R Type: Expression(Integer) +--E 266 + +--S 267 of 530 +t0550:= sech(x)^2/(a+b*cosh(x)) +--R +--R +--R 2 +--R sech(x) +--R (265) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 267 + +--S 268 of 530 +r0550:= -b*atan(sinh(x))/a^2+2*b^2*atanh((a-b)*_ + tanh(1/2*x)/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)+tanh(x)/a +--R +--R +--R (266) +--R x +--R (b - a)tanh(-) +---------+ +--R 2 2 | 2 2 +--R - 2b atanh(--------------) - b\|- b + a atan(sinh(x)) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R a tanh(x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 268 + +--S 269 of 530 +a0550:= integrate(t0550,x) +--R +--R +--R (267) +--R [ +--R 2 2 2 2 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)sinh(x) + (2b - 2a b)cosh(x) + 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2b)\|- b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +--R | 2 2 +--R - 2a\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a )\|- b + a +--R , +--R +--R 2 2 2 2 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) + 2b ) +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2b)\|b - a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R +-------+ +--R | 2 2 +--R - 2a\|b - a +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a )\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 269 + +--S 270 of 530 +m0550a:= a0550.1-r0550 +--R +--R +--R (268) +--R 2 2 2 2 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)sinh(x) + (2b - 2a b)cosh(x) + 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R 2 2 2 2 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) + 2b ) +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2b)\|- b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b)\|- b + a +--R * +--R atan(sinh(x)) +--R + +--R 2 2 +--R ((- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a)tanh(x) - 2a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a )\|- b + a +--R Type: Expression(Integer) +--E 270 + +--S 271 of 530 +d0550a:= D(m0550a,x) +--R +--R +--R (269) +--R 2 2 8 +--R (a b - a b)sinh(x) +--R + +--R 2 2 2 3 7 +--R ((6a b - 6a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (15a b - 15a b)cosh(x) + (10a b - 10a )cosh(x) + 4a b +--R + +--R 2 +--R - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (20a b - 20a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 2 3 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (15a b - 15a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (33a b - 33a b)cosh(x) + (22a b - 22a )cosh(x) + 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (32a b - 32a b)cosh(x) + (32a b - 32a )cosh(x) +--R + +--R 2 2 2 3 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (18a b - 18a b)cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (21a b - 21a b)cosh(x) + (14a b - 14a )cosh(x) + 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (12a b - 12a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 2 2 2 3 +--R (6a b - 6a b)cosh(x) + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (3a b - 3a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (3a b - 3a b)cosh(x) + (2a b - 2a )cosh(x) + a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 8 2 2 2 3 7 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((15a b + 15a b)cosh(x) + (10a b + 10a )cosh(x) + 4a b + 4a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (20a b + 20a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 2 3 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (15a b + 15a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (33a b + 33a b)cosh(x) + (22a b + 22a )cosh(x) + 6a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (32a b + 32a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 2 2 2 3 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (18a b + 18a b)cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (21a b + 21a b)cosh(x) + (14a b + 14a )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (12a b + 12a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 2 3 +--R (6a b + 6a b)cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 2 2 4 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (4a b + 4a )cosh(x) + (3a b + 3a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 +--R a b + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 2 8 +--R (b - a b + a b)sinh(x) +--R + +--R 3 2 2 2 2 3 7 +--R ((6b - 6a b + 6a b)cosh(x) + 2a b - 2a b + 2a )sinh(x) +--R + +--R 3 2 2 2 +--R (15b - 15a b + 15a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (b + 9a b - 10a b + 10a )cosh(x) + 4b - 4a b + 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (20b - 20a b + 20a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b + 14a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (18b - 16a b + 16a b)cosh(x) + 6a b + 2a b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (15b - 15a b + 15a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (15b + 5a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 2 +--R (33b - 23a b + 23a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (3b + 19a b + 2a b - 2a )cosh(x) + 6b - 6a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (6b - 6a b + 6a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (20b - 10a b - 10a b + 10a )cosh(x) +--R + +--R 3 2 2 3 +--R (32b - 12a b + 12a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (12b + 20a b - 8a b + 8a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (18b - 14a b + 14a b)cosh(x) + 6a b + 2a b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 3 5 +--R (b - a b + a b)cosh(x) + (15b - 13a b - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 4 +--R (18b + 2a b - 2a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (18b + 6a b - 16a b + 16a )cosh(x) +--R + +--R 3 2 2 2 +--R (21b - 9a b + 9a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (3b + 11a b + 10a b - 10a )cosh(x) + 4b - 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 5 +--R (6b - 6a b )cosh(x) + (6b + 4a b - 4a b)cosh(x) +--R + +--R 3 2 2 3 4 3 3 +--R (12b - 2a b - 10a b + 10a )cosh(x) + 12b cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b + 6a b + 12a b - 12a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (6b - 4a b + 4a b)cosh(x) + 2a b - 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (b - a b )cosh(x) + (b + a b - a b)cosh(x) +--R + +--R 3 2 2 3 5 3 2 2 4 +--R (3b - a b - 2a b + 2a )cosh(x) + (3b + a b - a b)cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 2 +--R (3b + a b + 4a b - 4a )cosh(x) + (3b - a b + a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (b + a b - 2a b + 2a )cosh(x) + b - a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 8 +--R (- b - a b - a b)sinh(x) +--R + +--R 3 2 2 2 2 3 7 +--R ((- 6b - 6a b - 6a b)cosh(x) - 2a b - 2a b - 2a )sinh(x) +--R + +--R 3 2 2 2 +--R (- 15b - 15a b - 15a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (b - 9a b - 10a b - 10a )cosh(x) - 4b - 4a b - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 20b - 20a b - 20a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b - 14a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 18b - 16a b - 16a b)cosh(x) - 6a b + 2a b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 15b - 15a b - 15a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (15b - 5a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 2 +--R (- 33b - 23a b - 23a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (3b - 19a b + 2a b + 2a )cosh(x) - 6b - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 6b - 6a b - 6a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (20b + 10a b - 10a b - 10a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 32b - 12a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (12b - 20a b - 8a b - 8a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 18b - 14a b - 14a b)cosh(x) - 6a b + 2a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 3 5 +--R (- b - a b - a b)cosh(x) + (15b + 13a b - 2a b - 2a )cosh(x) +--R + +--R 3 2 2 4 +--R (- 18b + 2a b + 2a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (18b - 6a b - 16a b - 16a )cosh(x) +--R + +--R 3 2 2 2 +--R (- 21b - 9a b - 9a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (3b - 11a b + 10a b + 10a )cosh(x) - 4b - 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 5 +--R (6b + 6a b )cosh(x) + (- 6b + 4a b + 4a b)cosh(x) +--R + +--R 3 2 2 3 4 3 3 +--R (12b + 2a b - 10a b - 10a )cosh(x) - 12b cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (6b - 6a b + 12a b + 12a )cosh(x) + (- 6b - 4a b - 4a b)cosh(x) +--R + +--R 2 2 3 +--R - 2a b - 2a b - 2a +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (b + a b )cosh(x) + (- b + a b + a b)cosh(x) +--R + +--R 3 2 2 3 5 3 2 2 4 +--R (3b + a b - 2a b - 2a )cosh(x) + (- 3b + a b + a b)cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 2 +--R (3b - a b + 4a b + 4a )cosh(x) + (- 3b - a b - a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (b - a b - 2a b - 2a )cosh(x) - b - a b - a b +--R / +--R 2 2 3 8 2 2 3 3 4 7 +--R (a b - a b)sinh(x) + ((6a b - 6a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R ((15a b - 15a b)cosh(x) + (10a b - 10a )cosh(x) + 4a b - 4a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20a b - 20a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15a b - 15a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33a b - 33a b)cosh(x) + (22a b - 22a )cosh(x) + 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32a b - 32a b)cosh(x) + (32a b - 32a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18a b - 18a b)cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21a b - 21a b)cosh(x) + (14a b - 14a )cosh(x) + 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12a b - 12a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6a b - 6a b)cosh(x) + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) + (3a b - 3a b)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4a b - 4a )cosh(x) + (3a b - 3a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 3 +--R a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 8 2 2 3 3 4 7 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 6 +--R ((15a b + 15a b)cosh(x) + (10a b + 10a )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20a b + 20a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15a b + 15a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33a b + 33a b)cosh(x) + (22a b + 22a )cosh(x) + 6a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32a b + 32a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18a b + 18a b)cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21a b + 21a b)cosh(x) + (14a b + 14a )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12a b + 12a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6a b + 6a b)cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4a b + 4a )cosh(x) + (3a b + 3a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 3 +--R a b + a b +--R Type: Expression(Integer) +--E 271 + +--S 272 of 530 +m0550b:= a0550.2-r0550 +--R +--R +--R (270) +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) + 2b )\|b - a +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) + 2b )\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- 2b sinh(x) - 4b cosh(x)sinh(x) - 2b cosh(x) - 2b)\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b)\|- b + a \|b - a +--R * +--R atan(sinh(x)) +--R + +--R 2 2 +--R ((- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a)tanh(x) - 2a) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 2 2 | 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 272 + +--S 273 of 530 +d0550b:= D(m0550b,x) +--R +--R +--R (271) +--R 2 2 8 +--R (a b - a b)sinh(x) +--R + +--R 2 2 2 3 7 +--R ((6a b - 6a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (15a b - 15a b)cosh(x) + (10a b - 10a )cosh(x) + 4a b +--R + +--R 2 +--R - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (20a b - 20a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 2 3 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (15a b - 15a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (33a b - 33a b)cosh(x) + (22a b - 22a )cosh(x) + 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (32a b - 32a b)cosh(x) + (32a b - 32a )cosh(x) +--R + +--R 2 2 2 3 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (18a b - 18a b)cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (21a b - 21a b)cosh(x) + (14a b - 14a )cosh(x) + 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (12a b - 12a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 2 2 2 3 +--R (6a b - 6a b)cosh(x) + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (3a b - 3a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (3a b - 3a b)cosh(x) + (2a b - 2a )cosh(x) + a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 8 2 2 2 3 7 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((15a b + 15a b)cosh(x) + (10a b + 10a )cosh(x) + 4a b + 4a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (20a b + 20a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 2 3 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (15a b + 15a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (33a b + 33a b)cosh(x) + (22a b + 22a )cosh(x) + 6a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (32a b + 32a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 2 2 2 3 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (18a b + 18a b)cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (21a b + 21a b)cosh(x) + (14a b + 14a )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (12a b + 12a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 2 3 +--R (6a b + 6a b)cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 2 2 4 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (4a b + 4a )cosh(x) + (3a b + 3a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 +--R a b + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 2 8 +--R (b - a b + a b)sinh(x) +--R + +--R 3 2 2 2 2 3 7 +--R ((6b - 6a b + 6a b)cosh(x) + 2a b - 2a b + 2a )sinh(x) +--R + +--R 3 2 2 2 +--R (15b - 15a b + 15a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (b + 9a b - 10a b + 10a )cosh(x) + 4b - 4a b + 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (20b - 20a b + 20a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b + 14a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (18b - 16a b + 16a b)cosh(x) + 6a b + 2a b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (15b - 15a b + 15a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (15b + 5a b - 20a b + 20a )cosh(x) +--R + +--R 3 2 2 2 +--R (33b - 23a b + 23a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (3b + 19a b + 2a b - 2a )cosh(x) + 6b - 6a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (6b - 6a b + 6a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (20b - 10a b - 10a b + 10a )cosh(x) +--R + +--R 3 2 2 3 +--R (32b - 12a b + 12a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (12b + 20a b - 8a b + 8a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (18b - 14a b + 14a b)cosh(x) + 6a b + 2a b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 3 5 +--R (b - a b + a b)cosh(x) + (15b - 13a b - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 4 +--R (18b + 2a b - 2a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (18b + 6a b - 16a b + 16a )cosh(x) +--R + +--R 3 2 2 2 +--R (21b - 9a b + 9a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (3b + 11a b + 10a b - 10a )cosh(x) + 4b - 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 5 +--R (6b - 6a b )cosh(x) + (6b + 4a b - 4a b)cosh(x) +--R + +--R 3 2 2 3 4 3 3 +--R (12b - 2a b - 10a b + 10a )cosh(x) + 12b cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b + 6a b + 12a b - 12a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (6b - 4a b + 4a b)cosh(x) + 2a b - 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (b - a b )cosh(x) + (b + a b - a b)cosh(x) +--R + +--R 3 2 2 3 5 3 2 2 4 +--R (3b - a b - 2a b + 2a )cosh(x) + (3b + a b - a b)cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 2 +--R (3b + a b + 4a b - 4a )cosh(x) + (3b - a b + a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (b + a b - 2a b + 2a )cosh(x) + b - a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 8 +--R (- b - a b - a b)sinh(x) +--R + +--R 3 2 2 2 2 3 7 +--R ((- 6b - 6a b - 6a b)cosh(x) - 2a b - 2a b - 2a )sinh(x) +--R + +--R 3 2 2 2 +--R (- 15b - 15a b - 15a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (b - 9a b - 10a b - 10a )cosh(x) - 4b - 4a b - 4a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 20b - 20a b - 20a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b - 14a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 18b - 16a b - 16a b)cosh(x) - 6a b + 2a b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 15b - 15a b - 15a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (15b - 5a b - 20a b - 20a )cosh(x) +--R + +--R 3 2 2 2 +--R (- 33b - 23a b - 23a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (3b - 19a b + 2a b + 2a )cosh(x) - 6b - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 6b - 6a b - 6a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (20b + 10a b - 10a b - 10a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 32b - 12a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (12b - 20a b - 8a b - 8a )cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 18b - 14a b - 14a b)cosh(x) - 6a b + 2a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 3 5 +--R (- b - a b - a b)cosh(x) + (15b + 13a b - 2a b - 2a )cosh(x) +--R + +--R 3 2 2 4 +--R (- 18b + 2a b + 2a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (18b - 6a b - 16a b - 16a )cosh(x) +--R + +--R 3 2 2 2 +--R (- 21b - 9a b - 9a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (3b - 11a b + 10a b + 10a )cosh(x) - 4b - 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 5 +--R (6b + 6a b )cosh(x) + (- 6b + 4a b + 4a b)cosh(x) +--R + +--R 3 2 2 3 4 3 3 +--R (12b + 2a b - 10a b - 10a )cosh(x) - 12b cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (6b - 6a b + 12a b + 12a )cosh(x) + (- 6b - 4a b - 4a b)cosh(x) +--R + +--R 2 2 3 +--R - 2a b - 2a b - 2a +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (b + a b )cosh(x) + (- b + a b + a b)cosh(x) +--R + +--R 3 2 2 3 5 3 2 2 4 +--R (3b + a b - 2a b - 2a )cosh(x) + (- 3b + a b + a b)cosh(x) +--R + +--R 3 2 2 3 3 3 2 2 2 +--R (3b - a b + 4a b + 4a )cosh(x) + (- 3b - a b - a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 +--R (b - a b - 2a b - 2a )cosh(x) - b - a b - a b +--R / +--R 2 2 3 8 2 2 3 3 4 7 +--R (a b - a b)sinh(x) + ((6a b - 6a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R ((15a b - 15a b)cosh(x) + (10a b - 10a )cosh(x) + 4a b - 4a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20a b - 20a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15a b - 15a b)cosh(x) + (20a b - 20a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33a b - 33a b)cosh(x) + (22a b - 22a )cosh(x) + 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32a b - 32a b)cosh(x) + (32a b - 32a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b - 18a b)cosh(x) + 6a b - 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18a b - 18a b)cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21a b - 21a b)cosh(x) + (14a b - 14a )cosh(x) + 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b - 6a b)cosh(x) + (10a b - 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12a b - 12a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6a b - 6a b)cosh(x) + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) + (3a b - 3a b)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4a b - 4a )cosh(x) + (3a b - 3a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 3 +--R a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 8 2 2 3 3 4 7 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 6 +--R ((15a b + 15a b)cosh(x) + (10a b + 10a )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20a b + 20a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15a b + 15a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33a b + 33a b)cosh(x) + (22a b + 22a )cosh(x) + 6a b + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32a b + 32a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18a b + 18a b)cosh(x) + 6a b + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18a b + 18a b)cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21a b + 21a b)cosh(x) + (14a b + 14a )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6a b + 6a b)cosh(x) + (10a b + 10a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12a b + 12a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6a b + 6a b)cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4a b + 4a )cosh(x) + (3a b + 3a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 2 3 +--R a b + a b +--R Type: Expression(Integer) +--E 273 + +--S 274 of 530 +t0551:= sech(x)^3/(a+b*cosh(x)) +--R +--R +--R 3 +--R sech(x) +--R (272) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 274 + +--S 275 of 530 +r0551:= 1/2*atan(sinh(x))/a+b^2*atan(sinh(x))/a^3-_ + 2*b^3*atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)-_ + b*tanh(x)/a^2+1/2*sech(x)*tanh(x)/a +--R +--R +--R (273) +--R x +--R (b - a)tanh(-) +---------+ +--R 3 2 2 2 | 2 2 +--R 4b atanh(--------------) + (2b + a )\|- b + a atan(sinh(x)) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (a sech(x) - 2a b)tanh(x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 530 +a0551:= integrate(t0551,x) +--R +--R +--R (274) +--R [ +--R 3 4 3 3 3 2 3 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + (- 2b + 2a b)cosh(x) - 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 2 2 4 2 2 3 +--R (2b + a )sinh(x) + (8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 6a )cosh(x) + 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 4a )cosh(x) + (8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + a )cosh(x) + (4b + 2a )cosh(x) + 2b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R a sinh(x) + (3a cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (3a cosh(x) + 4a b cosh(x) - a )sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - a cosh(x) + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 3 4 3 3 3 2 3 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 4 2 2 3 +--R (2b + a )sinh(x) + (8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 6a )cosh(x) + 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 4a )cosh(x) + (8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + a )cosh(x) + (4b + 2a )cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R a sinh(x) + (3a cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (3a cosh(x) + 4a b cosh(x) - a )sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - a cosh(x) + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 276 + +--S 277 of 530 +m0551a:= a0551.1-r0551 +--R +--R +--R (275) +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) + 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) + 8b cosh(x))sinh(x) + 2b cosh(x) + 4b cosh(x) + 2b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + (- 2b + 2a b)cosh(x) - 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R 3 4 3 3 3 2 3 2 +--R - 4b sinh(x) - 16b cosh(x)sinh(x) + (- 24b cosh(x) - 8b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (- 16b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) - 8b cosh(x) - 4b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 2 2 3 +--R (4b + 2a )sinh(x) + (16b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b + 12a )cosh(x) + 8b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b + 8a )cosh(x) + (16b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b + 2a )cosh(x) + (8b + 4a )cosh(x) + 4b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x) + cosh(x)) +--R + +--R 2 2 4 2 2 3 +--R (- 2b - a )sinh(x) + (- 8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b - 6a )cosh(x) - 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b - 4a )cosh(x) + (- 8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b - a )cosh(x) + (- 4b - 2a )cosh(x) - 2b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x)) +--R + +--R 2 4 +--R (- a sech(x) + 2a b)sinh(x) +--R + +--R 2 3 +--R (- 4a cosh(x)sech(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6a cosh(x) - 2a )sech(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 3 +--R (- 4a cosh(x) - 4a cosh(x))sech(x) + 8a b cosh(x) +--R + +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- a cosh(x) - 2a cosh(x) - a )sech(x) + 2a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 2 3 2 2 +--R 2a sinh(x) + (6a cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (6a cosh(x) + 8a b cosh(x) - 2a )sinh(x) + 2a cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2a cosh(x) + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 530 +d0551a:= D(m0551a,x) +--R +--R +--R (276) +--R 2 2 3 3 2 2 10 +--R ((2a b - 2a b)sech(x) - 2a b + 2a b )sinh(x) +--R + +--R 2 2 3 3 4 +--R ((16a b - 16a b)cosh(x) + 4a b - 4a )sech(x) +--R + +--R 3 2 2 2 2 3 +--R (- 16a b + 16a b )cosh(x) - 4a b + 4a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (56a b - 56a b)cosh(x) + (28a b - 28a )cosh(x) + 10a b +--R + +--R 3 +--R - 10a b +--R * +--R sech(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 56a b + 56a b )cosh(x) + (- 28a b + 28a b)cosh(x) +--R + +--R 3 2 2 +--R - 10a b + 10a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (112a b - 112a b)cosh(x) + (84a b - 84a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (64a b - 64a b)cosh(x) + 16a b - 16a +--R * +--R sech(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 112a b + 112a b )cosh(x) + (- 84a b + 84a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 64a b + 64a b )cosh(x) - 16a b + 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (140a b - 140a b)cosh(x) + (140a b - 140a )cosh(x) +--R + +--R 2 2 3 2 3 4 +--R (176a b - 176a b)cosh(x) + (88a b - 88a )cosh(x) +--R + +--R 2 2 3 +--R 20a b - 20a b +--R * +--R sech(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 140a b + 140a b )cosh(x) + (- 140a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 176a b + 176a b )cosh(x) + (- 88a b + 88a b)cosh(x) +--R + +--R 3 2 2 +--R - 20a b + 20a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (112a b - 112a b)cosh(x) + (140a b - 140a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (272a b - 272a b)cosh(x) + (204a b - 204a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (96a b - 96a b)cosh(x) + 24a b - 24a +--R * +--R sech(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 112a b + 112a b )cosh(x) + (- 140a b + 140a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 272a b + 272a b )cosh(x) + (- 204a b + 204a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 96a b + 96a b )cosh(x) - 24a b + 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (56a b - 56a b)cosh(x) + (84a b - 84a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (260a b - 260a b)cosh(x) + (260a b - 260a )cosh(x) +--R + +--R 2 2 3 2 3 4 +--R (192a b - 192a b)cosh(x) + (96a b - 96a )cosh(x) +--R + +--R 2 2 3 +--R 20a b - 20a b +--R * +--R sech(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 56a b + 56a b )cosh(x) + (- 84a b + 84a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 260a b + 260a b )cosh(x) + (- 260a b + 260a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 192a b + 192a b )cosh(x) + (- 96a b + 96a b)cosh(x) +--R + +--R 3 2 2 +--R - 20a b + 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (16a b - 16a b)cosh(x) + (28a b - 28a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (160a b - 160a b)cosh(x) + (200a b - 200a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (208a b - 208a b)cosh(x) + (156a b - 156a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (64a b - 64a b)cosh(x) + 16a b - 16a +--R * +--R sech(x) +--R + +--R 3 2 2 7 2 2 3 6 +--R (- 16a b + 16a b )cosh(x) + (- 28a b + 28a b)cosh(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 160a b + 160a b )cosh(x) + (- 200a b + 200a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 208a b + 208a b )cosh(x) + (- 156a b + 156a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 64a b + 64a b )cosh(x) - 16a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (64a b - 64a b)cosh(x) + (96a b - 96a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (132a b - 132a b)cosh(x) + (132a b - 132a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (80a b - 80a b)cosh(x) + (40a b - 40a )cosh(x) + 10a b +--R + +--R 3 +--R - 10a b +--R * +--R sech(x) +--R + +--R 3 2 2 8 2 2 3 7 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 64a b + 64a b )cosh(x) + (- 96a b + 96a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 132a b + 132a b )cosh(x) + (- 132a b + 132a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 80a b + 80a b )cosh(x) + (- 40a b + 40a b)cosh(x) +--R + +--R 3 2 2 +--R - 10a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (16a b - 16a b)cosh(x) + (28a b - 28a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (48a b - 48a b)cosh(x) + (60a b - 60a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (48a b - 48a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (16a b - 16a b)cosh(x) + 4a b - 4a +--R * +--R sech(x) +--R + +--R 3 2 2 7 2 2 3 6 +--R (- 16a b + 16a b )cosh(x) + (- 28a b + 28a b)cosh(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 48a b + 48a b )cosh(x) + (- 60a b + 60a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 48a b + 48a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 16a b + 16a b )cosh(x) - 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (8a b - 8a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (12a b - 12a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (8a b - 8a b)cosh(x) + (4a b - 4a )cosh(x) + 2a b - 2a b +--R * +--R sech(x) +--R + +--R 3 2 2 8 2 2 3 7 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 8a b + 8a b )cosh(x) + (- 12a b + 12a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 12a b + 12a b )cosh(x) + (- 12a b + 12a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 3 2 2 +--R (- 8a b + 8a b )cosh(x) + (- 4a b + 4a b)cosh(x) - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 3 2 2 10 +--R ((2a b + 2a b)sech(x) - 2a b - 2a b )sinh(x) +--R + +--R 2 2 3 3 4 +--R ((16a b + 16a b)cosh(x) + 4a b + 4a )sech(x) +--R + +--R 3 2 2 2 2 3 +--R (- 16a b - 16a b )cosh(x) - 4a b - 4a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (56a b + 56a b)cosh(x) + (28a b + 28a )cosh(x) + 10a b +--R + +--R 3 +--R 10a b +--R * +--R sech(x) +--R + +--R 3 2 2 2 2 2 3 3 +--R (- 56a b - 56a b )cosh(x) + (- 28a b - 28a b)cosh(x) - 10a b +--R + +--R 2 2 +--R - 10a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (112a b + 112a b)cosh(x) + (84a b + 84a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (64a b + 64a b)cosh(x) + 16a b + 16a +--R * +--R sech(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 112a b - 112a b )cosh(x) + (- 84a b - 84a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 64a b - 64a b )cosh(x) - 16a b - 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (140a b + 140a b)cosh(x) + (140a b + 140a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (176a b + 176a b)cosh(x) + (88a b + 88a )cosh(x) + 20a b +--R + +--R 3 +--R 20a b +--R * +--R sech(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 140a b - 140a b )cosh(x) + (- 140a b - 140a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 176a b - 176a b )cosh(x) + (- 88a b - 88a b)cosh(x) +--R + +--R 3 2 2 +--R - 20a b - 20a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (112a b + 112a b)cosh(x) + (140a b + 140a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (272a b + 272a b)cosh(x) + (204a b + 204a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (96a b + 96a b)cosh(x) + 24a b + 24a +--R * +--R sech(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 112a b - 112a b )cosh(x) + (- 140a b - 140a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 272a b - 272a b )cosh(x) + (- 204a b - 204a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 96a b - 96a b )cosh(x) - 24a b - 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (56a b + 56a b)cosh(x) + (84a b + 84a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (260a b + 260a b)cosh(x) + (260a b + 260a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (192a b + 192a b)cosh(x) + (96a b + 96a )cosh(x) + 20a b +--R + +--R 3 +--R 20a b +--R * +--R sech(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 56a b - 56a b )cosh(x) + (- 84a b - 84a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 260a b - 260a b )cosh(x) + (- 260a b - 260a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 192a b - 192a b )cosh(x) + (- 96a b - 96a b)cosh(x) +--R + +--R 3 2 2 +--R - 20a b - 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (16a b + 16a b)cosh(x) + (28a b + 28a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (160a b + 160a b)cosh(x) + (200a b + 200a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (208a b + 208a b)cosh(x) + (156a b + 156a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (64a b + 64a b)cosh(x) + 16a b + 16a +--R * +--R sech(x) +--R + +--R 3 2 2 7 2 2 3 6 +--R (- 16a b - 16a b )cosh(x) + (- 28a b - 28a b)cosh(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 160a b - 160a b )cosh(x) + (- 200a b - 200a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 208a b - 208a b )cosh(x) + (- 156a b - 156a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 64a b - 64a b )cosh(x) - 16a b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (64a b + 64a b)cosh(x) + (96a b + 96a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (132a b + 132a b)cosh(x) + (132a b + 132a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (80a b + 80a b)cosh(x) + (40a b + 40a )cosh(x) + 10a b +--R + +--R 3 +--R 10a b +--R * +--R sech(x) +--R + +--R 3 2 2 8 2 2 3 7 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 64a b - 64a b )cosh(x) + (- 96a b - 96a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 132a b - 132a b )cosh(x) + (- 132a b - 132a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 3 +--R (- 80a b - 80a b )cosh(x) + (- 40a b - 40a b)cosh(x) - 10a b +--R + +--R 2 2 +--R - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (16a b + 16a b)cosh(x) + (28a b + 28a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (48a b + 48a b)cosh(x) + (60a b + 60a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (48a b + 48a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (16a b + 16a b)cosh(x) + 4a b + 4a +--R * +--R sech(x) +--R + +--R 3 2 2 7 2 2 3 6 +--R (- 16a b - 16a b )cosh(x) + (- 28a b - 28a b)cosh(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 48a b - 48a b )cosh(x) + (- 60a b - 60a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 48a b - 48a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 16a b - 16a b )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (8a b + 8a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (12a b + 12a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (8a b + 8a b)cosh(x) + (4a b + 4a )cosh(x) + 2a b + 2a b +--R * +--R sech(x) +--R + +--R 3 2 2 8 2 2 3 7 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 8a b - 8a b )cosh(x) + (- 12a b - 12a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 12a b - 12a b )cosh(x) + (- 12a b - 12a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 3 2 2 +--R (- 8a b - 8a b )cosh(x) + (- 4a b - 4a b)cosh(x) - 2a b - 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 3 4 3 2 2 10 +--R ((- a b + a b)sech(x) - 2b + 2a b - 2a b )sinh(x) +--R + +--R 2 2 3 3 4 +--R ((- 8a b + 8a b)cosh(x) - 2a b + 2a )sech(x) +--R + +--R 4 3 2 2 3 2 2 3 +--R (- 16b + 16a b - 16a b )cosh(x) - 4a b + 4a b - 4a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 28a b + 28a b)cosh(x) + (- 14a b + 14a )cosh(x) - 5a b +--R + +--R 3 +--R 5a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 2 +--R (- 56b + 56a b - 56a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 2b - 26a b + 27a b - 27a b)cosh(x) - 10b + 10a b - 10a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 56a b + 56a b)cosh(x) + (- 42a b + 42a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 32a b + 32a b)cosh(x) - 8a b + 8a +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 +--R (- 112b + 112a b - 112a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 16b - 68a b + 76a b - 76a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 64b + 60a b - 60a b - 2a b + 2a )cosh(x) - 16a b + 16a b +--R + +--R 3 +--R - 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 70a b + 70a b)cosh(x) + (- 70a b + 70a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 88a b + 88a b)cosh(x) + (- 44a b + 44a )cosh(x) - 10a b +--R + +--R 3 +--R 10a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 4 +--R (- 140b + 140a b - 140a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 56b - 84a b + 112a b - 112a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 176b + 148a b - 148a b - 14a b + 14a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b - 80a b + 84a b - 84a b)cosh(x) - 20b + 20a b - 20a b +--R + +--R 3 4 +--R 32a b - 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 56a b + 56a b)cosh(x) + (- 70a b + 70a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 136a b + 136a b)cosh(x) + (- 102a b + 102a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 48a b + 48a b)cosh(x) - 12a b + 12a +--R * +--R sech(x) +--R + +--R 4 3 2 2 5 +--R (- 112b + 112a b - 112a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 112b - 28a b + 84a b - 84a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 272b + 188a b - 188a b - 42a b + 42a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 48b - 156a b + 180a b - 180a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 96b + 84a b - 84a b + 122a b - 122a )cosh(x) - 24a b +--R + +--R 2 2 3 +--R 24a b - 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 28a b + 28a b)cosh(x) + (- 42a b + 42a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 130a b + 130a b)cosh(x) + (- 130a b + 130a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 96a b + 96a b)cosh(x) + (- 48a b + 48a )cosh(x) - 10a b +--R + +--R 3 +--R 10a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 6 +--R (- 56b + 56a b - 56a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 140b + 56a b + 14a b - 14a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 260b + 120a b - 120a b - 70a b + 70a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 120b - 140a b + 200a b - 200a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 192b + 132a b - 132a b + 162a b - 162a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 12b - 84a b + 90a b - 90a b)cosh(x) - 20b + 20a b +--R + +--R 2 2 3 4 +--R - 20a b + 32a b - 32a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (- 8a b + 8a b)cosh(x) + (- 14a b + 14a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 80a b + 80a b)cosh(x) + (- 100a b + 100a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 104a b + 104a b)cosh(x) + (- 78a b + 78a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 32a b + 32a b)cosh(x) - 8a b + 8a +--R * +--R sech(x) +--R + +--R 4 3 2 2 7 +--R (- 16b + 16a b - 16a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 112b + 84a b - 28a b + 28a b)cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 160b + 20a b - 20a b - 70a b + 70a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 160b - 40a b + 120a b - 120a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 208b + 88a b - 88a b + 68a b - 68a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 48b - 108a b + 132a b - 132a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 64b + 52a b - 52a b + 122a b - 122a )cosh(x) - 16a b +--R + +--R 2 2 3 +--R 16a b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (- a b + a b)cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 32a b + 32a b)cosh(x) + (- 48a b + 48a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 66a b + 66a b)cosh(x) + (- 66a b + 66a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 40a b + 40a b)cosh(x) + (- 20a b + 20a )cosh(x) - 5a b +--R + +--R 3 +--R 5a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 8 +--R (- 2b + 2a b - 2a b )cosh(x) +--R + +--R 4 3 2 2 3 7 +--R (- 56b + 52a b - 24a b + 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 64b - 20a b + 20a b - 42a b + 42a )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 120b + 24a b + 36a b - 36a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 132b + 12a b - 12a b - 28a b + 28a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 72b - 60a b + 96a b - 96a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 80b + 44a b - 44a b + 174a b - 174a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b - 32a b + 36a b - 36a b)cosh(x) - 10b + 10a b - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (- 8a b + 8a b)cosh(x) + (- 14a b + 14a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 24a b + 24a b)cosh(x) + (- 30a b + 30a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 24a b + 24a b)cosh(x) + (- 18a b + 18a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 8a b + 8a b)cosh(x) - 2a b + 2a +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 8 +--R (- 16b + 16a b - 8a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 16b - 12a b + 12a b - 14a b + 14a )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 48b + 20a b + 4a b - 4a b)cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 48b - 12a b + 12a b - 30a b + 30a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 48b - 12a b + 36a b - 36a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 48b + 12a b - 12a b + 110a b - 110a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 16b - 20a b + 28a b - 28a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 16b + 12a b - 12a b - 2a b + 2a )cosh(x) - 4a b + 4a b +--R + +--R 3 +--R - 4a b +--R * +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (- a b + a b)cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 4a b + 4a b)cosh(x) + (- 6a b + 6a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 6a b + 6a b)cosh(x) + (- 6a b + 6a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (- 4a b + 4a b)cosh(x) + (- 2a b + 2a )cosh(x) - a b + a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 9 +--R (- 2b + 2a b - a b + a b)cosh(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 2b - 2a b + 2a b - 2a b + 2a )cosh(x) +--R + +--R 4 3 7 +--R (- 8b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 8b - 4a b + 4a b - 6a b + 6a )cosh(x) +--R + +--R 4 2 2 3 5 4 3 4 4 +--R (- 12b + 6a b - 6a b)cosh(x) + (- 12b + 26a b - 26a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 8b - 4a b + 8a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 8b + 4a b - 4a b - 2a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 2b - 2a b + 3a b - 3a b)cosh(x) - 2b + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 4 3 2 2 10 +--R ((- a b - a b)sech(x) + 2b + 2a b + 2a b )sinh(x) +--R + +--R 2 2 3 3 4 +--R ((- 8a b - 8a b)cosh(x) - 2a b - 2a )sech(x) +--R + +--R 4 3 2 2 3 2 2 3 +--R (16b + 16a b + 16a b )cosh(x) + 4a b + 4a b + 4a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 28a b - 28a b)cosh(x) + (- 14a b - 14a )cosh(x) - 5a b +--R + +--R 3 +--R - 5a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 2 +--R (56b + 56a b + 56a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 2b + 26a b + 27a b + 27a b)cosh(x) + 10b + 10a b + 10a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 56a b - 56a b)cosh(x) + (- 42a b - 42a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 32a b - 32a b)cosh(x) - 8a b - 8a +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 +--R (112b + 112a b + 112a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 16b + 68a b + 76a b + 76a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (64b + 60a b + 60a b - 2a b - 2a )cosh(x) + 16a b + 16a b + 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 70a b - 70a b)cosh(x) + (- 70a b - 70a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 88a b - 88a b)cosh(x) + (- 44a b - 44a )cosh(x) - 10a b +--R + +--R 3 +--R - 10a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 4 +--R (140b + 140a b + 140a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 56b + 84a b + 112a b + 112a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (176b + 148a b + 148a b - 14a b - 14a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b + 80a b + 84a b + 84a b)cosh(x) + 20b + 20a b + 20a b +--R + +--R 3 4 +--R 32a b + 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 56a b - 56a b)cosh(x) + (- 70a b - 70a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 136a b - 136a b)cosh(x) + (- 102a b - 102a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 48a b - 48a b)cosh(x) - 12a b - 12a +--R * +--R sech(x) +--R + +--R 4 3 2 2 5 +--R (112b + 112a b + 112a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 112b + 28a b + 84a b + 84a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (272b + 188a b + 188a b - 42a b - 42a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 48b + 156a b + 180a b + 180a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (96b + 84a b + 84a b + 122a b + 122a )cosh(x) + 24a b + 24a b +--R + +--R 3 +--R 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 28a b - 28a b)cosh(x) + (- 42a b - 42a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 130a b - 130a b)cosh(x) + (- 130a b - 130a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 96a b - 96a b)cosh(x) + (- 48a b - 48a )cosh(x) - 10a b +--R + +--R 3 +--R - 10a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 6 +--R (56b + 56a b + 56a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 140b - 56a b + 14a b + 14a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (260b + 120a b + 120a b - 70a b - 70a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 120b + 140a b + 200a b + 200a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (192b + 132a b + 132a b + 162a b + 162a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 12b + 84a b + 90a b + 90a b)cosh(x) + 20b + 20a b + 20a b +--R + +--R 3 4 +--R 32a b + 32a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (- 8a b - 8a b)cosh(x) + (- 14a b - 14a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 80a b - 80a b)cosh(x) + (- 100a b - 100a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 104a b - 104a b)cosh(x) + (- 78a b - 78a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 32a b - 32a b)cosh(x) - 8a b - 8a +--R * +--R sech(x) +--R + +--R 4 3 2 2 7 +--R (16b + 16a b + 16a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 112b - 84a b - 28a b - 28a b)cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (160b + 20a b + 20a b - 70a b - 70a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 160b + 40a b + 120a b + 120a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (208b + 88a b + 88a b + 68a b + 68a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 48b + 108a b + 132a b + 132a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (64b + 52a b + 52a b + 122a b + 122a )cosh(x) + 16a b + 16a b +--R + +--R 3 +--R 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 32a b - 32a b)cosh(x) + (- 48a b - 48a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 66a b - 66a b)cosh(x) + (- 66a b - 66a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (- 40a b - 40a b)cosh(x) + (- 20a b - 20a )cosh(x) - 5a b - 5a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 8 +--R (2b + 2a b + 2a b )cosh(x) +--R + +--R 4 3 2 2 3 7 +--R (- 56b - 52a b - 24a b - 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (64b - 20a b - 20a b - 42a b - 42a )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 120b - 24a b + 36a b + 36a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (132b + 12a b + 12a b - 28a b - 28a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 72b + 60a b + 96a b + 96a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (80b + 44a b + 44a b + 174a b + 174a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b + 32a b + 36a b + 36a b)cosh(x) + 10b + 10a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (- 8a b - 8a b)cosh(x) + (- 14a b - 14a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 24a b - 24a b)cosh(x) + (- 30a b - 30a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 24a b - 24a b)cosh(x) + (- 18a b - 18a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 8a b - 8a b)cosh(x) - 2a b - 2a +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 8 +--R (- 16b - 16a b - 8a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (16b - 12a b - 12a b - 14a b - 14a )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 48b - 20a b + 4a b + 4a b)cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (48b - 12a b - 12a b - 30a b - 30a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 48b + 12a b + 36a b + 36a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (48b + 12a b + 12a b + 110a b + 110a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 16b + 20a b + 28a b + 28a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (16b + 12a b + 12a b - 2a b - 2a )cosh(x) + 4a b + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 4a b - 4a b)cosh(x) + (- 6a b - 6a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 6a b - 6a b)cosh(x) + (- 6a b - 6a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (- 4a b - 4a b)cosh(x) + (- 2a b - 2a )cosh(x) - a b - a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 9 +--R (- 2b - 2a b - a b - a b)cosh(x) +--R + +--R 4 3 2 2 3 4 8 4 3 7 +--R (2b - 2a b - 2a b - 2a b - 2a )cosh(x) + (- 8b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (8b - 4a b - 4a b - 6a b - 6a )cosh(x) +--R + +--R 4 2 2 3 5 4 3 4 4 +--R (- 12b + 6a b + 6a b)cosh(x) + (12b + 26a b + 26a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 8b + 4a b + 8a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (8b + 4a b + 4a b - 2a b - 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 2b + 2a b + 3a b + 3a b)cosh(x) + 2b + 2a b + 2a b +--R / +--R 3 2 4 10 +--R (2a b - 2a b)sinh(x) +--R + +--R 3 2 4 4 5 9 +--R ((16a b - 16a b)cosh(x) + 4a b - 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R ((56a b - 56a b)cosh(x) + (28a b - 28a )cosh(x) + 10a b - 10a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (112a b - 112a b)cosh(x) + (84a b - 84a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (64a b - 64a b)cosh(x) + 16a b - 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (140a b - 140a b)cosh(x) + (140a b - 140a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (176a b - 176a b)cosh(x) + (88a b - 88a )cosh(x) + 20a b - 20a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (112a b - 112a b)cosh(x) + (140a b - 140a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (272a b - 272a b)cosh(x) + (204a b - 204a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (96a b - 96a b)cosh(x) + 24a b - 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (56a b - 56a b)cosh(x) + (84a b - 84a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (260a b - 260a b)cosh(x) + (260a b - 260a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (192a b - 192a b)cosh(x) + (96a b - 96a )cosh(x) + 20a b - 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (16a b - 16a b)cosh(x) + (28a b - 28a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (160a b - 160a b)cosh(x) + (200a b - 200a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (208a b - 208a b)cosh(x) + (156a b - 156a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (64a b - 64a b)cosh(x) + 16a b - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (64a b - 64a b)cosh(x) + (96a b - 96a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (132a b - 132a b)cosh(x) + (132a b - 132a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (80a b - 80a b)cosh(x) + (40a b - 40a )cosh(x) + 10a b - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (16a b - 16a b)cosh(x) + (28a b - 28a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (48a b - 48a b)cosh(x) + (60a b - 60a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (48a b - 48a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (16a b - 16a b)cosh(x) + 4a b - 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (8a b - 8a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (12a b - 12a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (8a b - 8a b)cosh(x) + (4a b - 4a )cosh(x) + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 4 10 3 2 4 4 5 9 +--R (2a b + 2a b)sinh(x) + ((16a b + 16a b)cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R ((56a b + 56a b)cosh(x) + (28a b + 28a )cosh(x) + 10a b + 10a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (112a b + 112a b)cosh(x) + (84a b + 84a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (64a b + 64a b)cosh(x) + 16a b + 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (140a b + 140a b)cosh(x) + (140a b + 140a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (176a b + 176a b)cosh(x) + (88a b + 88a )cosh(x) + 20a b + 20a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (112a b + 112a b)cosh(x) + (140a b + 140a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (272a b + 272a b)cosh(x) + (204a b + 204a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (96a b + 96a b)cosh(x) + 24a b + 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (56a b + 56a b)cosh(x) + (84a b + 84a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (260a b + 260a b)cosh(x) + (260a b + 260a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (192a b + 192a b)cosh(x) + (96a b + 96a )cosh(x) + 20a b + 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (16a b + 16a b)cosh(x) + (28a b + 28a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (160a b + 160a b)cosh(x) + (200a b + 200a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (208a b + 208a b)cosh(x) + (156a b + 156a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (64a b + 64a b)cosh(x) + 16a b + 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (64a b + 64a b)cosh(x) + (96a b + 96a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (132a b + 132a b)cosh(x) + (132a b + 132a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (80a b + 80a b)cosh(x) + (40a b + 40a )cosh(x) + 10a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (16a b + 16a b)cosh(x) + (28a b + 28a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (48a b + 48a b)cosh(x) + (60a b + 60a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (48a b + 48a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (16a b + 16a b)cosh(x) + 4a b + 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 3 2 4 6 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 4 5 5 3 2 4 4 +--R (12a b + 12a )cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 4 5 3 3 2 4 2 4 5 +--R (12a b + 12a )cosh(x) + (8a b + 8a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 4 +--R 2a b + 2a b +--R Type: Expression(Integer) +--E 278 + +--S 279 of 530 +m0551b:= a0551.2-r0551 +--R +--R +--R (277) +--R 3 4 3 3 3 2 3 2 +--R - 4b sinh(x) - 16b cosh(x)sinh(x) + (- 24b cosh(x) - 8b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (- 16b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) - 8b cosh(x) - 4b +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 4 3 3 3 2 3 2 +--R - 4b sinh(x) - 16b cosh(x)sinh(x) + (- 24b cosh(x) - 8b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (- 16b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) - 8b cosh(x) - 4b +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sinh(x) + b cosh(x) + a)\|b - a +--R \|- b + a atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 4 2 2 3 +--R (4b + 2a )sinh(x) + (16b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b + 12a )cosh(x) + 8b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b + 8a )cosh(x) + (16b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b + 2a )cosh(x) + (8b + 4a )cosh(x) + 4b + 2a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atan(sinh(x) + cosh(x)) +--R + +--R 2 2 4 2 2 3 +--R (- 2b - a )sinh(x) + (- 8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b - 6a )cosh(x) - 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b - 4a )cosh(x) + (- 8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b - a )cosh(x) + (- 4b - 2a )cosh(x) - 2b - a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atan(sinh(x)) +--R + +--R 2 4 +--R (- a sech(x) + 2a b)sinh(x) +--R + +--R 2 3 +--R (- 4a cosh(x)sech(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6a cosh(x) - 2a )sech(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 3 +--R (- 4a cosh(x) - 4a cosh(x))sech(x) + 8a b cosh(x) +--R + +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- a cosh(x) - 2a cosh(x) - a )sech(x) + 2a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 2 3 2 2 +--R 2a sinh(x) + (6a cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (6a cosh(x) + 8a b cosh(x) - 2a )sinh(x) + 2a cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2a cosh(x) + 4a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 279 + +--S 280 of 530 +d0551b:= D(m0551b,x) +--R +--R +--R (278) +--R 2 2 3 3 2 2 10 +--R ((2a b - 2a b)sech(x) - 2a b + 2a b )sinh(x) +--R + +--R 2 2 3 3 4 +--R ((16a b - 16a b)cosh(x) + 4a b - 4a )sech(x) +--R + +--R 3 2 2 2 2 3 +--R (- 16a b + 16a b )cosh(x) - 4a b + 4a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (56a b - 56a b)cosh(x) + (28a b - 28a )cosh(x) + 10a b +--R + +--R 3 +--R - 10a b +--R * +--R sech(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 56a b + 56a b )cosh(x) + (- 28a b + 28a b)cosh(x) +--R + +--R 3 2 2 +--R - 10a b + 10a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (112a b - 112a b)cosh(x) + (84a b - 84a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (64a b - 64a b)cosh(x) + 16a b - 16a +--R * +--R sech(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 112a b + 112a b )cosh(x) + (- 84a b + 84a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 64a b + 64a b )cosh(x) - 16a b + 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (140a b - 140a b)cosh(x) + (140a b - 140a )cosh(x) +--R + +--R 2 2 3 2 3 4 +--R (176a b - 176a b)cosh(x) + (88a b - 88a )cosh(x) +--R + +--R 2 2 3 +--R 20a b - 20a b +--R * +--R sech(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 140a b + 140a b )cosh(x) + (- 140a b + 140a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 176a b + 176a b )cosh(x) + (- 88a b + 88a b)cosh(x) +--R + +--R 3 2 2 +--R - 20a b + 20a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (112a b - 112a b)cosh(x) + (140a b - 140a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (272a b - 272a b)cosh(x) + (204a b - 204a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (96a b - 96a b)cosh(x) + 24a b - 24a +--R * +--R sech(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 112a b + 112a b )cosh(x) + (- 140a b + 140a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 272a b + 272a b )cosh(x) + (- 204a b + 204a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 96a b + 96a b )cosh(x) - 24a b + 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (56a b - 56a b)cosh(x) + (84a b - 84a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (260a b - 260a b)cosh(x) + (260a b - 260a )cosh(x) +--R + +--R 2 2 3 2 3 4 +--R (192a b - 192a b)cosh(x) + (96a b - 96a )cosh(x) +--R + +--R 2 2 3 +--R 20a b - 20a b +--R * +--R sech(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 56a b + 56a b )cosh(x) + (- 84a b + 84a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 260a b + 260a b )cosh(x) + (- 260a b + 260a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 192a b + 192a b )cosh(x) + (- 96a b + 96a b)cosh(x) +--R + +--R 3 2 2 +--R - 20a b + 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (16a b - 16a b)cosh(x) + (28a b - 28a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (160a b - 160a b)cosh(x) + (200a b - 200a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (208a b - 208a b)cosh(x) + (156a b - 156a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (64a b - 64a b)cosh(x) + 16a b - 16a +--R * +--R sech(x) +--R + +--R 3 2 2 7 2 2 3 6 +--R (- 16a b + 16a b )cosh(x) + (- 28a b + 28a b)cosh(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 160a b + 160a b )cosh(x) + (- 200a b + 200a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 208a b + 208a b )cosh(x) + (- 156a b + 156a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 64a b + 64a b )cosh(x) - 16a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (64a b - 64a b)cosh(x) + (96a b - 96a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (132a b - 132a b)cosh(x) + (132a b - 132a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (80a b - 80a b)cosh(x) + (40a b - 40a )cosh(x) + 10a b +--R + +--R 3 +--R - 10a b +--R * +--R sech(x) +--R + +--R 3 2 2 8 2 2 3 7 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 64a b + 64a b )cosh(x) + (- 96a b + 96a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 132a b + 132a b )cosh(x) + (- 132a b + 132a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 80a b + 80a b )cosh(x) + (- 40a b + 40a b)cosh(x) +--R + +--R 3 2 2 +--R - 10a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (16a b - 16a b)cosh(x) + (28a b - 28a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (48a b - 48a b)cosh(x) + (60a b - 60a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (48a b - 48a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (16a b - 16a b)cosh(x) + 4a b - 4a +--R * +--R sech(x) +--R + +--R 3 2 2 7 2 2 3 6 +--R (- 16a b + 16a b )cosh(x) + (- 28a b + 28a b)cosh(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 48a b + 48a b )cosh(x) + (- 60a b + 60a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 48a b + 48a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 16a b + 16a b )cosh(x) - 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (8a b - 8a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (12a b - 12a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (8a b - 8a b)cosh(x) + (4a b - 4a )cosh(x) + 2a b - 2a b +--R * +--R sech(x) +--R + +--R 3 2 2 8 2 2 3 7 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 8a b + 8a b )cosh(x) + (- 12a b + 12a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 12a b + 12a b )cosh(x) + (- 12a b + 12a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 3 2 2 +--R (- 8a b + 8a b )cosh(x) + (- 4a b + 4a b)cosh(x) - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 3 2 2 10 +--R ((2a b + 2a b)sech(x) - 2a b - 2a b )sinh(x) +--R + +--R 2 2 3 3 4 +--R ((16a b + 16a b)cosh(x) + 4a b + 4a )sech(x) +--R + +--R 3 2 2 2 2 3 +--R (- 16a b - 16a b )cosh(x) - 4a b - 4a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (56a b + 56a b)cosh(x) + (28a b + 28a )cosh(x) + 10a b +--R + +--R 3 +--R 10a b +--R * +--R sech(x) +--R + +--R 3 2 2 2 2 2 3 3 +--R (- 56a b - 56a b )cosh(x) + (- 28a b - 28a b)cosh(x) - 10a b +--R + +--R 2 2 +--R - 10a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (112a b + 112a b)cosh(x) + (84a b + 84a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (64a b + 64a b)cosh(x) + 16a b + 16a +--R * +--R sech(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 112a b - 112a b )cosh(x) + (- 84a b - 84a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 64a b - 64a b )cosh(x) - 16a b - 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (140a b + 140a b)cosh(x) + (140a b + 140a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (176a b + 176a b)cosh(x) + (88a b + 88a )cosh(x) + 20a b +--R + +--R 3 +--R 20a b +--R * +--R sech(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 140a b - 140a b )cosh(x) + (- 140a b - 140a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 176a b - 176a b )cosh(x) + (- 88a b - 88a b)cosh(x) +--R + +--R 3 2 2 +--R - 20a b - 20a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (112a b + 112a b)cosh(x) + (140a b + 140a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (272a b + 272a b)cosh(x) + (204a b + 204a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (96a b + 96a b)cosh(x) + 24a b + 24a +--R * +--R sech(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 112a b - 112a b )cosh(x) + (- 140a b - 140a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 272a b - 272a b )cosh(x) + (- 204a b - 204a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 96a b - 96a b )cosh(x) - 24a b - 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (56a b + 56a b)cosh(x) + (84a b + 84a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (260a b + 260a b)cosh(x) + (260a b + 260a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (192a b + 192a b)cosh(x) + (96a b + 96a )cosh(x) + 20a b +--R + +--R 3 +--R 20a b +--R * +--R sech(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 56a b - 56a b )cosh(x) + (- 84a b - 84a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 260a b - 260a b )cosh(x) + (- 260a b - 260a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 +--R (- 192a b - 192a b )cosh(x) + (- 96a b - 96a b)cosh(x) +--R + +--R 3 2 2 +--R - 20a b - 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (16a b + 16a b)cosh(x) + (28a b + 28a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (160a b + 160a b)cosh(x) + (200a b + 200a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (208a b + 208a b)cosh(x) + (156a b + 156a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (64a b + 64a b)cosh(x) + 16a b + 16a +--R * +--R sech(x) +--R + +--R 3 2 2 7 2 2 3 6 +--R (- 16a b - 16a b )cosh(x) + (- 28a b - 28a b)cosh(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 160a b - 160a b )cosh(x) + (- 200a b - 200a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 208a b - 208a b )cosh(x) + (- 156a b - 156a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 64a b - 64a b )cosh(x) - 16a b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (64a b + 64a b)cosh(x) + (96a b + 96a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (132a b + 132a b)cosh(x) + (132a b + 132a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (80a b + 80a b)cosh(x) + (40a b + 40a )cosh(x) + 10a b +--R + +--R 3 +--R 10a b +--R * +--R sech(x) +--R + +--R 3 2 2 8 2 2 3 7 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 64a b - 64a b )cosh(x) + (- 96a b - 96a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 132a b - 132a b )cosh(x) + (- 132a b - 132a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 3 +--R (- 80a b - 80a b )cosh(x) + (- 40a b - 40a b)cosh(x) - 10a b +--R + +--R 2 2 +--R - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (16a b + 16a b)cosh(x) + (28a b + 28a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (48a b + 48a b)cosh(x) + (60a b + 60a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (48a b + 48a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (16a b + 16a b)cosh(x) + 4a b + 4a +--R * +--R sech(x) +--R + +--R 3 2 2 7 2 2 3 6 +--R (- 16a b - 16a b )cosh(x) + (- 28a b - 28a b)cosh(x) +--R + +--R 3 2 2 5 2 2 3 4 +--R (- 48a b - 48a b )cosh(x) + (- 60a b - 60a b)cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (- 48a b - 48a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 3 2 2 2 2 3 +--R (- 16a b - 16a b )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (8a b + 8a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (12a b + 12a b)cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (8a b + 8a b)cosh(x) + (4a b + 4a )cosh(x) + 2a b + 2a b +--R * +--R sech(x) +--R + +--R 3 2 2 8 2 2 3 7 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 3 2 2 6 2 2 3 5 +--R (- 8a b - 8a b )cosh(x) + (- 12a b - 12a b)cosh(x) +--R + +--R 3 2 2 4 2 2 3 3 +--R (- 12a b - 12a b )cosh(x) + (- 12a b - 12a b)cosh(x) +--R + +--R 3 2 2 2 2 2 3 3 2 2 +--R (- 8a b - 8a b )cosh(x) + (- 4a b - 4a b)cosh(x) - 2a b - 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 3 4 3 2 2 10 +--R ((- a b + a b)sech(x) - 2b + 2a b - 2a b )sinh(x) +--R + +--R 2 2 3 3 4 +--R ((- 8a b + 8a b)cosh(x) - 2a b + 2a )sech(x) +--R + +--R 4 3 2 2 3 2 2 3 +--R (- 16b + 16a b - 16a b )cosh(x) - 4a b + 4a b - 4a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 28a b + 28a b)cosh(x) + (- 14a b + 14a )cosh(x) - 5a b +--R + +--R 3 +--R 5a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 2 +--R (- 56b + 56a b - 56a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 2b - 26a b + 27a b - 27a b)cosh(x) - 10b + 10a b - 10a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 56a b + 56a b)cosh(x) + (- 42a b + 42a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 32a b + 32a b)cosh(x) - 8a b + 8a +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 +--R (- 112b + 112a b - 112a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 16b - 68a b + 76a b - 76a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 64b + 60a b - 60a b - 2a b + 2a )cosh(x) - 16a b + 16a b +--R + +--R 3 +--R - 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 70a b + 70a b)cosh(x) + (- 70a b + 70a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 88a b + 88a b)cosh(x) + (- 44a b + 44a )cosh(x) - 10a b +--R + +--R 3 +--R 10a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 4 +--R (- 140b + 140a b - 140a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 56b - 84a b + 112a b - 112a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 176b + 148a b - 148a b - 14a b + 14a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b - 80a b + 84a b - 84a b)cosh(x) - 20b + 20a b - 20a b +--R + +--R 3 4 +--R 32a b - 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 56a b + 56a b)cosh(x) + (- 70a b + 70a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 136a b + 136a b)cosh(x) + (- 102a b + 102a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 48a b + 48a b)cosh(x) - 12a b + 12a +--R * +--R sech(x) +--R + +--R 4 3 2 2 5 +--R (- 112b + 112a b - 112a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 112b - 28a b + 84a b - 84a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 272b + 188a b - 188a b - 42a b + 42a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 48b - 156a b + 180a b - 180a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 96b + 84a b - 84a b + 122a b - 122a )cosh(x) - 24a b +--R + +--R 2 2 3 +--R 24a b - 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 28a b + 28a b)cosh(x) + (- 42a b + 42a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 130a b + 130a b)cosh(x) + (- 130a b + 130a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 96a b + 96a b)cosh(x) + (- 48a b + 48a )cosh(x) - 10a b +--R + +--R 3 +--R 10a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 6 +--R (- 56b + 56a b - 56a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 140b + 56a b + 14a b - 14a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 260b + 120a b - 120a b - 70a b + 70a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 120b - 140a b + 200a b - 200a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 192b + 132a b - 132a b + 162a b - 162a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 12b - 84a b + 90a b - 90a b)cosh(x) - 20b + 20a b +--R + +--R 2 2 3 4 +--R - 20a b + 32a b - 32a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (- 8a b + 8a b)cosh(x) + (- 14a b + 14a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 80a b + 80a b)cosh(x) + (- 100a b + 100a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 104a b + 104a b)cosh(x) + (- 78a b + 78a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 32a b + 32a b)cosh(x) - 8a b + 8a +--R * +--R sech(x) +--R + +--R 4 3 2 2 7 +--R (- 16b + 16a b - 16a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 112b + 84a b - 28a b + 28a b)cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 160b + 20a b - 20a b - 70a b + 70a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 160b - 40a b + 120a b - 120a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 208b + 88a b - 88a b + 68a b - 68a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 48b - 108a b + 132a b - 132a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 64b + 52a b - 52a b + 122a b - 122a )cosh(x) - 16a b +--R + +--R 2 2 3 +--R 16a b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (- a b + a b)cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 32a b + 32a b)cosh(x) + (- 48a b + 48a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 66a b + 66a b)cosh(x) + (- 66a b + 66a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 40a b + 40a b)cosh(x) + (- 20a b + 20a )cosh(x) - 5a b +--R + +--R 3 +--R 5a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 8 +--R (- 2b + 2a b - 2a b )cosh(x) +--R + +--R 4 3 2 2 3 7 +--R (- 56b + 52a b - 24a b + 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 64b - 20a b + 20a b - 42a b + 42a )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 120b + 24a b + 36a b - 36a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 132b + 12a b - 12a b - 28a b + 28a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 72b - 60a b + 96a b - 96a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 80b + 44a b - 44a b + 174a b - 174a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b - 32a b + 36a b - 36a b)cosh(x) - 10b + 10a b - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (- 8a b + 8a b)cosh(x) + (- 14a b + 14a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 24a b + 24a b)cosh(x) + (- 30a b + 30a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 24a b + 24a b)cosh(x) + (- 18a b + 18a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 8a b + 8a b)cosh(x) - 2a b + 2a +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 8 +--R (- 16b + 16a b - 8a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 16b - 12a b + 12a b - 14a b + 14a )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 48b + 20a b + 4a b - 4a b)cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 48b - 12a b + 12a b - 30a b + 30a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 48b - 12a b + 36a b - 36a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 48b + 12a b - 12a b + 110a b - 110a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 16b - 20a b + 28a b - 28a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 16b + 12a b - 12a b - 2a b + 2a )cosh(x) - 4a b + 4a b +--R + +--R 3 +--R - 4a b +--R * +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (- a b + a b)cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 4a b + 4a b)cosh(x) + (- 6a b + 6a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 6a b + 6a b)cosh(x) + (- 6a b + 6a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (- 4a b + 4a b)cosh(x) + (- 2a b + 2a )cosh(x) - a b + a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 9 +--R (- 2b + 2a b - a b + a b)cosh(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 2b - 2a b + 2a b - 2a b + 2a )cosh(x) +--R + +--R 4 3 7 +--R (- 8b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 8b - 4a b + 4a b - 6a b + 6a )cosh(x) +--R + +--R 4 2 2 3 5 4 3 4 4 +--R (- 12b + 6a b - 6a b)cosh(x) + (- 12b + 26a b - 26a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 8b - 4a b + 8a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 8b + 4a b - 4a b - 2a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 2b - 2a b + 3a b - 3a b)cosh(x) - 2b + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 4 3 2 2 10 +--R ((- a b - a b)sech(x) + 2b + 2a b + 2a b )sinh(x) +--R + +--R 2 2 3 3 4 +--R ((- 8a b - 8a b)cosh(x) - 2a b - 2a )sech(x) +--R + +--R 4 3 2 2 3 2 2 3 +--R (16b + 16a b + 16a b )cosh(x) + 4a b + 4a b + 4a b +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 28a b - 28a b)cosh(x) + (- 14a b - 14a )cosh(x) - 5a b +--R + +--R 3 +--R - 5a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 2 +--R (56b + 56a b + 56a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 2b + 26a b + 27a b + 27a b)cosh(x) + 10b + 10a b + 10a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 56a b - 56a b)cosh(x) + (- 42a b - 42a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 32a b - 32a b)cosh(x) - 8a b - 8a +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 +--R (112b + 112a b + 112a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 16b + 68a b + 76a b + 76a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (64b + 60a b + 60a b - 2a b - 2a )cosh(x) + 16a b + 16a b + 16a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 70a b - 70a b)cosh(x) + (- 70a b - 70a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 88a b - 88a b)cosh(x) + (- 44a b - 44a )cosh(x) - 10a b +--R + +--R 3 +--R - 10a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 4 +--R (140b + 140a b + 140a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 56b + 84a b + 112a b + 112a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (176b + 148a b + 148a b - 14a b - 14a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b + 80a b + 84a b + 84a b)cosh(x) + 20b + 20a b + 20a b +--R + +--R 3 4 +--R 32a b + 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 56a b - 56a b)cosh(x) + (- 70a b - 70a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 136a b - 136a b)cosh(x) + (- 102a b - 102a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 48a b - 48a b)cosh(x) - 12a b - 12a +--R * +--R sech(x) +--R + +--R 4 3 2 2 5 +--R (112b + 112a b + 112a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 112b + 28a b + 84a b + 84a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (272b + 188a b + 188a b - 42a b - 42a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 48b + 156a b + 180a b + 180a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (96b + 84a b + 84a b + 122a b + 122a )cosh(x) + 24a b + 24a b +--R + +--R 3 +--R 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 28a b - 28a b)cosh(x) + (- 42a b - 42a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 130a b - 130a b)cosh(x) + (- 130a b - 130a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 +--R (- 96a b - 96a b)cosh(x) + (- 48a b - 48a )cosh(x) - 10a b +--R + +--R 3 +--R - 10a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 6 +--R (56b + 56a b + 56a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 140b - 56a b + 14a b + 14a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (260b + 120a b + 120a b - 70a b - 70a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 120b + 140a b + 200a b + 200a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (192b + 132a b + 132a b + 162a b + 162a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 12b + 84a b + 90a b + 90a b)cosh(x) + 20b + 20a b + 20a b +--R + +--R 3 4 +--R 32a b + 32a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (- 8a b - 8a b)cosh(x) + (- 14a b - 14a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 80a b - 80a b)cosh(x) + (- 100a b - 100a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 104a b - 104a b)cosh(x) + (- 78a b - 78a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 32a b - 32a b)cosh(x) - 8a b - 8a +--R * +--R sech(x) +--R + +--R 4 3 2 2 7 +--R (16b + 16a b + 16a b )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 112b - 84a b - 28a b - 28a b)cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (160b + 20a b + 20a b - 70a b - 70a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 160b + 40a b + 120a b + 120a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (208b + 88a b + 88a b + 68a b + 68a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 48b + 108a b + 132a b + 132a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (64b + 52a b + 52a b + 122a b + 122a )cosh(x) + 16a b + 16a b +--R + +--R 3 +--R 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 32a b - 32a b)cosh(x) + (- 48a b - 48a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 66a b - 66a b)cosh(x) + (- 66a b - 66a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (- 40a b - 40a b)cosh(x) + (- 20a b - 20a )cosh(x) - 5a b - 5a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 8 +--R (2b + 2a b + 2a b )cosh(x) +--R + +--R 4 3 2 2 3 7 +--R (- 56b - 52a b - 24a b - 24a b)cosh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (64b - 20a b - 20a b - 42a b - 42a )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 120b - 24a b + 36a b + 36a b)cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (132b + 12a b + 12a b - 28a b - 28a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 72b + 60a b + 96a b + 96a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (80b + 44a b + 44a b + 174a b + 174a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b + 32a b + 36a b + 36a b)cosh(x) + 10b + 10a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 7 3 4 6 +--R (- 8a b - 8a b)cosh(x) + (- 14a b - 14a )cosh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (- 24a b - 24a b)cosh(x) + (- 30a b - 30a )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (- 24a b - 24a b)cosh(x) + (- 18a b - 18a )cosh(x) +--R + +--R 2 2 3 3 4 +--R (- 8a b - 8a b)cosh(x) - 2a b - 2a +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 8 +--R (- 16b - 16a b - 8a b - 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (16b - 12a b - 12a b - 14a b - 14a )cosh(x) +--R + +--R 4 3 2 2 3 6 +--R (- 48b - 20a b + 4a b + 4a b)cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (48b - 12a b - 12a b - 30a b - 30a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 48b + 12a b + 36a b + 36a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (48b + 12a b + 12a b + 110a b + 110a )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 16b + 20a b + 28a b + 28a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (16b + 12a b + 12a b - 2a b - 2a )cosh(x) + 4a b + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 2 2 3 8 3 4 7 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (- 4a b - 4a b)cosh(x) + (- 6a b - 6a )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (- 6a b - 6a b)cosh(x) + (- 6a b - 6a )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (- 4a b - 4a b)cosh(x) + (- 2a b - 2a )cosh(x) - a b - a b +--R * +--R sech(x) +--R + +--R 4 3 2 2 3 9 +--R (- 2b - 2a b - a b - a b)cosh(x) +--R + +--R 4 3 2 2 3 4 8 4 3 7 +--R (2b - 2a b - 2a b - 2a b - 2a )cosh(x) + (- 8b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (8b - 4a b - 4a b - 6a b - 6a )cosh(x) +--R + +--R 4 2 2 3 5 4 3 4 4 +--R (- 12b + 6a b + 6a b)cosh(x) + (12b + 26a b + 26a )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 8b + 4a b + 8a b + 8a b)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (8b + 4a b + 4a b - 2a b - 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 2b + 2a b + 3a b + 3a b)cosh(x) + 2b + 2a b + 2a b +--R / +--R 3 2 4 10 +--R (2a b - 2a b)sinh(x) +--R + +--R 3 2 4 4 5 9 +--R ((16a b - 16a b)cosh(x) + 4a b - 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R ((56a b - 56a b)cosh(x) + (28a b - 28a )cosh(x) + 10a b - 10a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (112a b - 112a b)cosh(x) + (84a b - 84a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (64a b - 64a b)cosh(x) + 16a b - 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (140a b - 140a b)cosh(x) + (140a b - 140a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (176a b - 176a b)cosh(x) + (88a b - 88a )cosh(x) + 20a b - 20a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (112a b - 112a b)cosh(x) + (140a b - 140a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (272a b - 272a b)cosh(x) + (204a b - 204a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (96a b - 96a b)cosh(x) + 24a b - 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (56a b - 56a b)cosh(x) + (84a b - 84a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (260a b - 260a b)cosh(x) + (260a b - 260a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (192a b - 192a b)cosh(x) + (96a b - 96a )cosh(x) + 20a b - 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (16a b - 16a b)cosh(x) + (28a b - 28a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (160a b - 160a b)cosh(x) + (200a b - 200a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (208a b - 208a b)cosh(x) + (156a b - 156a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (64a b - 64a b)cosh(x) + 16a b - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (64a b - 64a b)cosh(x) + (96a b - 96a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (132a b - 132a b)cosh(x) + (132a b - 132a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (80a b - 80a b)cosh(x) + (40a b - 40a )cosh(x) + 10a b - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (16a b - 16a b)cosh(x) + (28a b - 28a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (48a b - 48a b)cosh(x) + (60a b - 60a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (48a b - 48a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (16a b - 16a b)cosh(x) + 4a b - 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (8a b - 8a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (12a b - 12a b)cosh(x) + (12a b - 12a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (8a b - 8a b)cosh(x) + (4a b - 4a )cosh(x) + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 4 10 3 2 4 4 5 9 +--R (2a b + 2a b)sinh(x) + ((16a b + 16a b)cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R ((56a b + 56a b)cosh(x) + (28a b + 28a )cosh(x) + 10a b + 10a b) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (112a b + 112a b)cosh(x) + (84a b + 84a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (64a b + 64a b)cosh(x) + 16a b + 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (140a b + 140a b)cosh(x) + (140a b + 140a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (176a b + 176a b)cosh(x) + (88a b + 88a )cosh(x) + 20a b + 20a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (112a b + 112a b)cosh(x) + (140a b + 140a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (272a b + 272a b)cosh(x) + (204a b + 204a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (96a b + 96a b)cosh(x) + 24a b + 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (56a b + 56a b)cosh(x) + (84a b + 84a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (260a b + 260a b)cosh(x) + (260a b + 260a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (192a b + 192a b)cosh(x) + (96a b + 96a )cosh(x) + 20a b + 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (16a b + 16a b)cosh(x) + (28a b + 28a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (160a b + 160a b)cosh(x) + (200a b + 200a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (208a b + 208a b)cosh(x) + (156a b + 156a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (64a b + 64a b)cosh(x) + 16a b + 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (64a b + 64a b)cosh(x) + (96a b + 96a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (132a b + 132a b)cosh(x) + (132a b + 132a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (80a b + 80a b)cosh(x) + (40a b + 40a )cosh(x) + 10a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (16a b + 16a b)cosh(x) + (28a b + 28a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (48a b + 48a b)cosh(x) + (60a b + 60a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (48a b + 48a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (16a b + 16a b)cosh(x) + 4a b + 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 3 2 4 6 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 4 5 5 3 2 4 4 +--R (12a b + 12a )cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 4 5 3 3 2 4 2 4 5 +--R (12a b + 12a )cosh(x) + (8a b + 8a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 3 2 4 +--R 2a b + 2a b +--R Type: Expression(Integer) +--E 280 + +--S 281 of 530 +t0552:= sech(x)^4/(a+b*cosh(x)) +--R +--R +--R 4 +--R sech(x) +--R (279) ------------- +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 281 + +--S 282 of 530 +r0552:= -1/2*b*atan(sinh(x))/a^2-b^3*atan(sinh(x))/a^4+_ + 2*b^4*atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)+_ + tanh(x)/a+b^2*tanh(x)/a^3-1/2*b*sech(x)*tanh(x)/a^2-1/3*tanh(x)^3/a +--R +--R +--R (280) +--R x +--R (b - a)tanh(-) +---------+ +--R 4 2 3 2 | 2 2 +--R - 12b atanh(--------------) + (- 6b - 3a b)\|- b + a atan(sinh(x)) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 3 2 2 3 | 2 2 +--R (- 2a tanh(x) + (- 3a b sech(x) + 6a b + 6a )tanh(x))\|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 530 +a0552:= integrate(t0552,x) +--R +--R +--R (281) +--R [ +--R 4 6 4 5 4 2 4 4 +--R 3b sinh(x) + 18b cosh(x)sinh(x) + (45b cosh(x) + 9b )sinh(x) +--R + +--R 4 3 4 3 +--R (60b cosh(x) + 36b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45b cosh(x) + 54b cosh(x) + 9b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18b cosh(x) + 36b cosh(x) + 18b cosh(x))sinh(x) + 3b cosh(x) +--R + +--R 4 4 4 2 4 +--R 9b cosh(x) + 9b cosh(x) + 3b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)sinh(x) + (2b - 2a b)cosh(x) + 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 3 2 6 3 2 5 +--R (- 6b - 3a b)sinh(x) + (- 36b - 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b - 45a b)cosh(x) - 18b - 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b - 60a b)cosh(x) + (- 72b - 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b - 45a b)cosh(x) + (- 108b - 54a b)cosh(x) - 18b +--R + +--R 2 +--R - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b - 18a b)cosh(x) + (- 72b - 36a b)cosh(x) +--R + +--R 3 2 +--R (- 36b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b - 3a b)cosh(x) + (- 18b - 9a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b - 9a b)cosh(x) - 6b - 3a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x) + cosh(x)) +--R + +--R 2 5 2 2 4 +--R - 3a b sinh(x) + (- 15a b cosh(x) - 6a b )sinh(x) +--R + +--R 2 2 2 3 +--R (- 30a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R (- 30a b cosh(x) - 36a b cosh(x) - 12a b - 12a )sinh(x) +--R + +--R 2 4 2 3 2 3 +--R - 15a b cosh(x) - 24a b cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 2 +--R 3a b +--R * +--R sinh(x) +--R + +--R 2 5 2 4 2 3 2 +--R - 3a b cosh(x) - 6a b cosh(x) + (- 12a b - 12a )cosh(x) +--R + +--R 2 2 3 +--R 3a b cosh(x) - 6a b - 4a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 6 4 5 4 2 4 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) + 9a )sinh(x) +--R + +--R 4 3 4 3 +--R (60a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45a cosh(x) + 54a cosh(x) + 9a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18a cosh(x) + 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 4 4 4 2 4 +--R 9a cosh(x) + 9a cosh(x) + 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 4 6 4 5 4 2 4 4 +--R 6b sinh(x) + 36b cosh(x)sinh(x) + (90b cosh(x) + 18b )sinh(x) +--R + +--R 4 3 4 3 +--R (120b cosh(x) + 72b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90b cosh(x) + 108b cosh(x) + 18b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36b cosh(x) + 72b cosh(x) + 36b cosh(x))sinh(x) + 6b cosh(x) +--R + +--R 4 4 4 2 4 +--R 18b cosh(x) + 18b cosh(x) + 6b +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 3 2 6 3 2 5 +--R (- 6b - 3a b)sinh(x) + (- 36b - 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b - 45a b)cosh(x) - 18b - 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b - 60a b)cosh(x) + (- 72b - 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b - 45a b)cosh(x) + (- 108b - 54a b)cosh(x) - 18b +--R + +--R 2 +--R - 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b - 18a b)cosh(x) + (- 72b - 36a b)cosh(x) +--R + +--R 3 2 +--R (- 36b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b - 3a b)cosh(x) + (- 18b - 9a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b - 9a b)cosh(x) - 6b - 3a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a atan(sinh(x) + cosh(x)) +--R + +--R 2 5 2 2 4 +--R - 3a b sinh(x) + (- 15a b cosh(x) - 6a b )sinh(x) +--R + +--R 2 2 2 3 +--R (- 30a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R (- 30a b cosh(x) - 36a b cosh(x) - 12a b - 12a )sinh(x) +--R + +--R 2 4 2 3 2 3 +--R - 15a b cosh(x) - 24a b cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 2 +--R 3a b +--R * +--R sinh(x) +--R + +--R 2 5 2 4 2 3 2 +--R - 3a b cosh(x) - 6a b cosh(x) + (- 12a b - 12a )cosh(x) +--R + +--R 2 2 3 +--R 3a b cosh(x) - 6a b - 4a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 6 4 5 4 2 4 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) + 9a )sinh(x) +--R + +--R 4 3 4 3 +--R (60a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45a cosh(x) + 54a cosh(x) + 9a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18a cosh(x) + 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 4 4 4 2 4 +--R 9a cosh(x) + 9a cosh(x) + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 283 + +--S 284 of 530 +m0552a:= a0552.1-r0552 +--R +--R +--R (282) +--R 4 6 4 5 4 2 4 4 +--R 6b sinh(x) + 36b cosh(x)sinh(x) + (90b cosh(x) + 18b )sinh(x) +--R + +--R 4 3 4 3 +--R (120b cosh(x) + 72b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90b cosh(x) + 108b cosh(x) + 18b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36b cosh(x) + 72b cosh(x) + 36b cosh(x))sinh(x) + 6b cosh(x) +--R + +--R 4 4 4 2 4 +--R 18b cosh(x) + 18b cosh(x) + 6b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)sinh(x) + (2b - 2a b)cosh(x) + 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R 4 6 4 5 4 2 4 4 +--R 12b sinh(x) + 72b cosh(x)sinh(x) + (180b cosh(x) + 36b )sinh(x) +--R + +--R 4 3 4 3 +--R (240b cosh(x) + 144b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (180b cosh(x) + 216b cosh(x) + 36b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (72b cosh(x) + 144b cosh(x) + 72b cosh(x))sinh(x) + 12b cosh(x) +--R + +--R 4 4 4 2 4 +--R 36b cosh(x) + 36b cosh(x) + 12b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 6 3 2 5 +--R (- 12b - 6a b)sinh(x) + (- 72b - 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 180b - 90a b)cosh(x) - 36b - 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 240b - 120a b)cosh(x) + (- 144b - 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 180b - 90a b)cosh(x) + (- 216b - 108a b)cosh(x) - 36b +--R + +--R 2 +--R - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 72b - 36a b)cosh(x) + (- 144b - 72a b)cosh(x) +--R + +--R 3 2 +--R (- 72b - 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 12b - 6a b)cosh(x) + (- 36b - 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 36b - 18a b)cosh(x) - 12b - 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x) + cosh(x)) +--R + +--R 3 2 6 3 2 5 +--R (6b + 3a b)sinh(x) + (36b + 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b + 45a b)cosh(x) + 18b + 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b + 60a b)cosh(x) + (72b + 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((90b + 45a b)cosh(x) + (108b + 54a b)cosh(x) + 18b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b + 18a b)cosh(x) + (72b + 36a b)cosh(x) +--R + +--R 3 2 +--R (36b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (6b + 3a b)cosh(x) + (18b + 9a b)cosh(x) + (18b + 9a b)cosh(x) +--R + +--R 3 2 +--R 6b + 3a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x)) +--R + +--R 3 6 3 5 3 2 3 4 +--R 2a sinh(x) + 12a cosh(x)sinh(x) + (30a cosh(x) + 6a )sinh(x) +--R + +--R 3 3 3 3 +--R (40a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (30a cosh(x) + 36a cosh(x) + 6a )sinh(x) +--R + +--R 3 5 3 3 3 3 6 +--R (12a cosh(x) + 24a cosh(x) + 12a cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 3 4 3 2 3 +--R 6a cosh(x) + 6a cosh(x) + 2a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 2 3 6 +--R (3a b sech(x) - 6a b - 6a )sinh(x) +--R + +--R 2 2 3 5 +--R (18a b cosh(x)sech(x) + (- 36a b - 36a )cosh(x))sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (45a b cosh(x) + 9a b)sech(x) + (- 90a b - 90a )cosh(x) +--R + +--R 2 3 +--R - 18a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 +--R (60a b cosh(x) + 36a b cosh(x))sech(x) +--R + +--R 2 3 3 2 3 +--R (- 120a b - 120a )cosh(x) + (- 72a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (45a b cosh(x) + 54a b cosh(x) + 9a b)sech(x) +--R + +--R 2 3 4 2 3 2 +--R (- 90a b - 90a )cosh(x) + (- 108a b - 108a )cosh(x) +--R + +--R 2 3 +--R - 18a b - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 +--R (18a b cosh(x) + 36a b cosh(x) + 18a b cosh(x))sech(x) +--R + +--R 2 3 5 2 3 3 +--R (- 36a b - 36a )cosh(x) + (- 72a b - 72a )cosh(x) +--R + +--R 2 3 +--R (- 36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (3a b cosh(x) + 9a b cosh(x) + 9a b cosh(x) + 3a b)sech(x) +--R + +--R 2 3 6 2 3 4 +--R (- 6a b - 6a )cosh(x) + (- 18a b - 18a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (- 18a b - 18a )cosh(x) - 6a b - 6a +--R * +--R tanh(x) +--R + +--R 2 5 2 2 4 +--R - 6a b sinh(x) + (- 30a b cosh(x) - 12a b )sinh(x) +--R + +--R 2 2 2 3 +--R (- 60a b cosh(x) - 48a b cosh(x))sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R (- 60a b cosh(x) - 72a b cosh(x) - 24a b - 24a )sinh(x) +--R + +--R 2 4 2 3 2 3 +--R - 30a b cosh(x) - 48a b cosh(x) + (- 48a b - 48a )cosh(x) +--R + +--R 2 +--R 6a b +--R * +--R sinh(x) +--R + +--R 2 5 2 4 2 3 2 +--R - 6a b cosh(x) - 12a b cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R 6a b cosh(x) - 12a b - 8a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) + 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) + 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) + 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) + 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R 18a cosh(x) + 18a cosh(x) + 6a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 530 +d0552a:= D(m0552a,x) +--R +--R +--R (283) +--R 3 2 4 12 +--R (- 2a b + 2a b)sinh(x) +--R + +--R 3 2 4 4 5 11 +--R ((- 20a b + 20a b)cosh(x) - 4a b + 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 90a b + 90a b)cosh(x) + (- 36a b + 36a )cosh(x) - 12a b +--R + +--R 4 +--R 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 240a b + 240a b)cosh(x) + (- 144a b + 144a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b + 100a b)cosh(x) - 20a b + 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 420a b + 420a b)cosh(x) + (- 336a b + 336a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 370a b + 370a b)cosh(x) + (- 148a b + 148a )cosh(x) +--R + +--R 3 2 4 +--R - 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 504a b + 504a b)cosh(x) + (- 504a b + 504a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 800a b + 800a b)cosh(x) + (- 480a b + 480a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b + 200a b)cosh(x) - 40a b + 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 420a b + 420a b)cosh(x) + (- 504a b + 504a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1120a b + 1120a b)cosh(x) + (- 896a b + 896a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 580a b + 580a b)cosh(x) + (- 232a b + 232a )cosh(x) +--R + +--R 3 2 4 +--R - 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 240a b + 240a b)cosh(x) + (- 336a b + 336a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 1064a b + 1064a b)cosh(x) + (- 1064a b + 1064a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 960a b + 960a b)cosh(x) + (- 576a b + 576a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b + 200a b)cosh(x) - 40a b + 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 90a b + 90a b)cosh(x) + (- 144a b + 144a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 700a b + 700a b)cosh(x) + (- 840a b + 840a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1000a b + 1000a b)cosh(x) + (- 800a b + 800a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 420a b + 420a b)cosh(x) + (- 168a b + 168a )cosh(x) +--R + +--R 3 2 4 +--R - 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b + 20a b)cosh(x) + (- 36a b + 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 320a b + 320a b)cosh(x) + (- 448a b + 448a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 680a b + 680a b)cosh(x) + (- 680a b + 680a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 480a b + 480a b)cosh(x) + (- 288a b + 288a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b + 100a b)cosh(x) - 20a b + 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 100a b + 100a b)cosh(x) + (- 160a b + 160a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 300a b + 300a b)cosh(x) + (- 360a b + 360a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 320a b + 320a b)cosh(x) + (- 256a b + 256a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 130a b + 130a b)cosh(x) + (- 52a b + 52a )cosh(x) +--R + +--R 3 2 4 +--R - 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b + 20a b)cosh(x) + (- 36a b + 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 80a b + 80a b)cosh(x) + (- 112a b + 112a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 120a b + 120a b)cosh(x) + (- 120a b + 120a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 80a b + 80a b)cosh(x) + (- 48a b + 48a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 20a b + 20a b)cosh(x) - 4a b + 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 10a b + 10a b)cosh(x) + (- 16a b + 16a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 20a b + 20a b)cosh(x) + (- 24a b + 24a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 20a b + 20a b)cosh(x) + (- 16a b + 16a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (- 10a b + 10a b)cosh(x) + (- 4a b + 4a )cosh(x) - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 4 12 +--R (- 2a b - 2a b)sinh(x) +--R + +--R 3 2 4 4 5 11 +--R ((- 20a b - 20a b)cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 90a b - 90a b)cosh(x) + (- 36a b - 36a )cosh(x) - 12a b +--R + +--R 4 +--R - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 240a b - 240a b)cosh(x) + (- 144a b - 144a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b - 100a b)cosh(x) - 20a b - 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 420a b - 420a b)cosh(x) + (- 336a b - 336a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 370a b - 370a b)cosh(x) + (- 148a b - 148a )cosh(x) - 30a b +--R + +--R 4 +--R - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 504a b - 504a b)cosh(x) + (- 504a b - 504a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 800a b - 800a b)cosh(x) + (- 480a b - 480a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b - 200a b)cosh(x) - 40a b - 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 420a b - 420a b)cosh(x) + (- 504a b - 504a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1120a b - 1120a b)cosh(x) + (- 896a b - 896a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 580a b - 580a b)cosh(x) + (- 232a b - 232a )cosh(x) - 40a b +--R + +--R 4 +--R - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 240a b - 240a b)cosh(x) + (- 336a b - 336a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 1064a b - 1064a b)cosh(x) + (- 1064a b - 1064a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 960a b - 960a b)cosh(x) + (- 576a b - 576a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b - 200a b)cosh(x) - 40a b - 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 90a b - 90a b)cosh(x) + (- 144a b - 144a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 700a b - 700a b)cosh(x) + (- 840a b - 840a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1000a b - 1000a b)cosh(x) + (- 800a b - 800a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 420a b - 420a b)cosh(x) + (- 168a b - 168a )cosh(x) - 30a b +--R + +--R 4 +--R - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b - 20a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 320a b - 320a b)cosh(x) + (- 448a b - 448a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 680a b - 680a b)cosh(x) + (- 680a b - 680a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 480a b - 480a b)cosh(x) + (- 288a b - 288a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b - 100a b)cosh(x) - 20a b - 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b - 2a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 100a b - 100a b)cosh(x) + (- 160a b - 160a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 300a b - 300a b)cosh(x) + (- 360a b - 360a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 320a b - 320a b)cosh(x) + (- 256a b - 256a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 130a b - 130a b)cosh(x) + (- 52a b - 52a )cosh(x) - 12a b +--R + +--R 4 +--R - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b - 20a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 80a b - 80a b)cosh(x) + (- 112a b - 112a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 120a b - 120a b)cosh(x) + (- 120a b - 120a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 80a b - 80a b)cosh(x) + (- 48a b - 48a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 20a b - 20a b)cosh(x) - 4a b - 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b - 2a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 10a b - 10a b)cosh(x) + (- 16a b - 16a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 20a b - 20a b)cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 20a b - 20a b)cosh(x) + (- 16a b - 16a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (- 10a b - 10a b)cosh(x) + (- 4a b - 4a )cosh(x) - 2a b - 2a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 3 3 2 4 2 3 3 2 4 +--R ((- 2a b + 2a b )sech(x) + 2a b - 2a b + 4a b - 4a b) +--R * +--R 12 +--R sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((- 20a b + 20a b )cosh(x) - 4a b + 4a b)sech(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) + 4a b - 4a b +--R + +--R 4 5 +--R 8a b - 8a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 90a b + 90a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b + 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 2 +--R (90a b - 90a b + 180a b - 180a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (36a b - 36a b + 72a b - 72a )cosh(x) + 12a b - 12a b +--R + +--R 3 2 4 +--R 24a b - 24a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 +--R (- 240a b + 240a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b + 100a b )cosh(x) - 20a b + 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 3 +--R (240a b - 240a b + 480a b - 480a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (144a b - 144a b + 288a b - 288a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 +--R (100a b - 100a b + 200a b - 200a b)cosh(x) + 20a b +--R + +--R 3 2 4 5 +--R - 20a b + 40a b - 40a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 336a b + 336a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 370a b + 370a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 148a b + 148a b)cosh(x) - 30a b + 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 4 +--R (420a b - 420a b + 840a b - 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (336a b - 336a b + 672a b - 672a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (370a b - 370a b + 740a b - 740a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (148a b - 148a b + 296a b - 296a )cosh(x) + 30a b - 30a b +--R + +--R 3 2 4 +--R 60a b - 60a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 +--R (- 504a b + 504a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 504a b + 504a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 800a b + 800a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 480a b + 480a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b + 200a b )cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 5 +--R (504a b - 504a b + 1008a b - 1008a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (504a b - 504a b + 1008a b - 1008a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (800a b - 800a b + 1600a b - 1600a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (480a b - 480a b + 960a b - 960a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 +--R (200a b - 200a b + 400a b - 400a b)cosh(x) + 40a b +--R + +--R 3 2 4 5 +--R - 40a b + 80a b - 80a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 504a b + 504a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1120a b + 1120a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 896a b + 896a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 580a b + 580a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 232a b + 232a b)cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 6 +--R (420a b - 420a b + 840a b - 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (504a b - 504a b + 1008a b - 1008a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (1120a b - 1120a b + 2240a b - 2240a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (896a b - 896a b + 1792a b - 1792a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (580a b - 580a b + 1160a b - 1160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (232a b - 232a b + 464a b - 464a )cosh(x) + 40a b - 40a b +--R + +--R 3 2 4 +--R 80a b - 80a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 +--R (- 240a b + 240a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 336a b + 336a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 1064a b + 1064a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 1064a b + 1064a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 960a b + 960a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 576a b + 576a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b + 200a b )cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 7 +--R (240a b - 240a b + 480a b - 480a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (336a b - 336a b + 672a b - 672a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (1064a b - 1064a b + 2128a b - 2128a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (1064a b - 1064a b + 2128a b - 2128a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (960a b - 960a b + 1920a b - 1920a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (576a b - 576a b + 1152a b - 1152a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 +--R (200a b - 200a b + 400a b - 400a b)cosh(x) + 40a b +--R + +--R 3 2 4 5 +--R - 40a b + 80a b - 80a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 +--R (- 90a b + 90a b )cosh(x) +--R + +--R 3 2 4 7 +--R (- 144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 6 +--R (- 700a b + 700a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 840a b + 840a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1000a b + 1000a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 800a b + 800a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 168a b + 168a b)cosh(x) - 30a b + 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 8 +--R (90a b - 90a b + 180a b - 180a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (144a b - 144a b + 288a b - 288a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (700a b - 700a b + 1400a b - 1400a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (840a b - 840a b + 1680a b - 1680a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (1000a b - 1000a b + 2000a b - 2000a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (800a b - 800a b + 1600a b - 1600a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (420a b - 420a b + 840a b - 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (168a b - 168a b + 336a b - 336a )cosh(x) + 30a b - 30a b +--R + +--R 3 2 4 +--R 60a b - 60a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b + 20a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 7 +--R (- 320a b + 320a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 448a b + 448a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 680a b + 680a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 680a b + 680a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 480a b + 480a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 288a b + 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b + 100a b )cosh(x) - 20a b + 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 9 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (36a b - 36a b + 72a b - 72a )cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (320a b - 320a b + 640a b - 640a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (448a b - 448a b + 896a b - 896a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (680a b - 680a b + 1360a b - 1360a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (680a b - 680a b + 1360a b - 1360a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (480a b - 480a b + 960a b - 960a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (288a b - 288a b + 576a b - 576a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 +--R (100a b - 100a b + 200a b - 200a b)cosh(x) + 20a b +--R + +--R 3 2 4 5 +--R - 20a b + 40a b - 40a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 8 +--R (- 100a b + 100a b )cosh(x) +--R + +--R 3 2 4 7 +--R (- 160a b + 160a b)cosh(x) +--R + +--R 2 3 3 2 6 +--R (- 300a b + 300a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 360a b + 360a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 320a b + 320a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 256a b + 256a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 130a b + 130a b )cosh(x) + (- 52a b + 52a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b + 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 10 +--R (2a b - 2a b + 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (4a b - 4a b + 8a b - 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (100a b - 100a b + 200a b - 200a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (160a b - 160a b + 320a b - 320a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (300a b - 300a b + 600a b - 600a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (360a b - 360a b + 720a b - 720a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (320a b - 320a b + 640a b - 640a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (256a b - 256a b + 512a b - 512a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (130a b - 130a b + 260a b - 260a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (52a b - 52a b + 104a b - 104a )cosh(x) + 12a b - 12a b +--R + +--R 3 2 4 +--R 24a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b + 20a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 7 +--R (- 80a b + 80a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 112a b + 112a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 120a b + 120a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 120a b + 120a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 80a b + 80a b )cosh(x) + (- 48a b + 48a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 20a b + 20a b )cosh(x) - 4a b + 4a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 9 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (36a b - 36a b + 72a b - 72a )cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (80a b - 80a b + 160a b - 160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (112a b - 112a b + 224a b - 224a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (120a b - 120a b + 240a b - 240a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (120a b - 120a b + 240a b - 240a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (80a b - 80a b + 160a b - 160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (48a b - 48a b + 96a b - 96a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) + 4a b - 4a b +--R + +--R 4 5 +--R 8a b - 8a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 10a b + 10a b )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 20a b + 20a b )cosh(x) + (- 24a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 20a b + 20a b )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (- 10a b + 10a b )cosh(x) + (- 4a b + 4a b)cosh(x) - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 10 +--R (2a b - 2a b + 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (4a b - 4a b + 8a b - 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (10a b - 10a b + 20a b - 20a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (16a b - 16a b + 32a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (24a b - 24a b + 48a b - 48a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (16a b - 16a b + 32a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (10a b - 10a b + 20a b - 20a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R (4a b - 4a b + 8a b - 8a )cosh(x) + 2a b - 2a b + 4a b - 4a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 4 2 3 3 2 4 12 +--R ((- 2a b - 2a b )sech(x) + 2a b + 2a b + 4a b + 4a b)sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((- 20a b - 20a b )cosh(x) - 4a b - 4a b)sech(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) + 4a b + 4a b + 8a b +--R + +--R 5 +--R 8a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 90a b - 90a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b - 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 2 +--R (90a b + 90a b + 180a b + 180a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (36a b + 36a b + 72a b + 72a )cosh(x) + 12a b + 12a b +--R + +--R 3 2 4 +--R 24a b + 24a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 240a b - 240a b )cosh(x) + (- 144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b - 100a b )cosh(x) - 20a b - 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 3 +--R (240a b + 240a b + 480a b + 480a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (144a b + 144a b + 288a b + 288a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (100a b + 100a b + 200a b + 200a b)cosh(x) + 20a b + 20a b +--R + +--R 4 5 +--R 40a b + 40a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 420a b - 420a b )cosh(x) + (- 336a b - 336a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 370a b - 370a b )cosh(x) + (- 148a b - 148a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 30a b - 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 4 +--R (420a b + 420a b + 840a b + 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (336a b + 336a b + 672a b + 672a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (370a b + 370a b + 740a b + 740a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (148a b + 148a b + 296a b + 296a )cosh(x) + 30a b + 30a b +--R + +--R 3 2 4 +--R 60a b + 60a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 504a b - 504a b )cosh(x) + (- 504a b - 504a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 800a b - 800a b )cosh(x) + (- 480a b - 480a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b - 200a b )cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 5 +--R (504a b + 504a b + 1008a b + 1008a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (504a b + 504a b + 1008a b + 1008a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (800a b + 800a b + 1600a b + 1600a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (480a b + 480a b + 960a b + 960a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (200a b + 200a b + 400a b + 400a b)cosh(x) + 40a b + 40a b +--R + +--R 4 5 +--R 80a b + 80a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 420a b - 420a b )cosh(x) + (- 504a b - 504a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1120a b - 1120a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 896a b - 896a b)cosh(x) + (- 580a b - 580a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 232a b - 232a b)cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 6 +--R (420a b + 420a b + 840a b + 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (504a b + 504a b + 1008a b + 1008a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (1120a b + 1120a b + 2240a b + 2240a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (896a b + 896a b + 1792a b + 1792a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (580a b + 580a b + 1160a b + 1160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (232a b + 232a b + 464a b + 464a )cosh(x) + 40a b + 40a b +--R + +--R 3 2 4 +--R 80a b + 80a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 240a b - 240a b )cosh(x) + (- 336a b - 336a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 1064a b - 1064a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 1064a b - 1064a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 960a b - 960a b )cosh(x) + (- 576a b - 576a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b - 200a b )cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 7 +--R (240a b + 240a b + 480a b + 480a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (336a b + 336a b + 672a b + 672a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (1064a b + 1064a b + 2128a b + 2128a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (1064a b + 1064a b + 2128a b + 2128a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (960a b + 960a b + 1920a b + 1920a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (576a b + 576a b + 1152a b + 1152a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (200a b + 200a b + 400a b + 400a b)cosh(x) + 40a b + 40a b +--R + +--R 4 5 +--R 80a b + 80a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 90a b - 90a b )cosh(x) + (- 144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 700a b - 700a b )cosh(x) + (- 840a b - 840a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1000a b - 1000a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 800a b - 800a b)cosh(x) + (- 420a b - 420a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 168a b - 168a b)cosh(x) - 30a b - 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 8 +--R (90a b + 90a b + 180a b + 180a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (144a b + 144a b + 288a b + 288a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (700a b + 700a b + 1400a b + 1400a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (840a b + 840a b + 1680a b + 1680a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (1000a b + 1000a b + 2000a b + 2000a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (800a b + 800a b + 1600a b + 1600a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (420a b + 420a b + 840a b + 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (168a b + 168a b + 336a b + 336a )cosh(x) + 30a b + 30a b +--R + +--R 3 2 4 +--R 60a b + 60a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b - 20a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 320a b - 320a b )cosh(x) + (- 448a b - 448a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 680a b - 680a b )cosh(x) + (- 680a b - 680a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 480a b - 480a b )cosh(x) + (- 288a b - 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b - 100a b )cosh(x) - 20a b - 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 9 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (36a b + 36a b + 72a b + 72a )cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (320a b + 320a b + 640a b + 640a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (448a b + 448a b + 896a b + 896a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (680a b + 680a b + 1360a b + 1360a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (680a b + 680a b + 1360a b + 1360a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (480a b + 480a b + 960a b + 960a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (288a b + 288a b + 576a b + 576a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (100a b + 100a b + 200a b + 200a b)cosh(x) + 20a b + 20a b +--R + +--R 4 5 +--R 40a b + 40a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 100a b - 100a b )cosh(x) + (- 160a b - 160a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 300a b - 300a b )cosh(x) + (- 360a b - 360a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 320a b - 320a b )cosh(x) + (- 256a b - 256a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 130a b - 130a b )cosh(x) + (- 52a b - 52a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b - 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 10 +--R (2a b + 2a b + 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (4a b + 4a b + 8a b + 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (100a b + 100a b + 200a b + 200a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (160a b + 160a b + 320a b + 320a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (300a b + 300a b + 600a b + 600a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (360a b + 360a b + 720a b + 720a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (320a b + 320a b + 640a b + 640a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (256a b + 256a b + 512a b + 512a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (130a b + 130a b + 260a b + 260a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (52a b + 52a b + 104a b + 104a )cosh(x) + 12a b + 12a b +--R + +--R 3 2 4 +--R 24a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b - 20a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 80a b - 80a b )cosh(x) + (- 112a b - 112a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 120a b - 120a b )cosh(x) + (- 120a b - 120a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 80a b - 80a b )cosh(x) + (- 48a b - 48a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 20a b - 20a b )cosh(x) - 4a b - 4a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 9 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (36a b + 36a b + 72a b + 72a )cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (80a b + 80a b + 160a b + 160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (112a b + 112a b + 224a b + 224a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (120a b + 120a b + 240a b + 240a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (120a b + 120a b + 240a b + 240a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (80a b + 80a b + 160a b + 160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (48a b + 48a b + 96a b + 96a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) + 4a b + 4a b + 8a b +--R + +--R 5 +--R 8a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 10a b - 10a b )cosh(x) + (- 16a b - 16a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 20a b - 20a b )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 20a b - 20a b )cosh(x) + (- 16a b - 16a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (- 10a b - 10a b )cosh(x) + (- 4a b - 4a b)cosh(x) - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 10 +--R (2a b + 2a b + 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (4a b + 4a b + 8a b + 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (10a b + 10a b + 20a b + 20a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (16a b + 16a b + 32a b + 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (24a b + 24a b + 48a b + 48a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (16a b + 16a b + 32a b + 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (10a b + 10a b + 20a b + 20a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R (4a b + 4a b + 8a b + 8a )cosh(x) + 2a b + 2a b + 4a b + 4a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 3 2 5 4 2 3 3 2 4 12 +--R ((a b - a b )sech(x) + 2b - 2a b + 2a b - 2a b + 2a b)sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((10a b - 10a b )cosh(x) + 2a b - 2a b)sech(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (20b - 20a b + 20a b - 20a b + 20a b)cosh(x) + 4a b - 4a b +--R + +--R 3 2 4 5 +--R 4a b - 4a b + 4a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (45a b - 45a b )cosh(x) + (18a b - 18a b)cosh(x) + 6a b +--R + +--R 3 2 +--R - 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (90b - 90a b + 90a b - 90a b + 90a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b + 34a b - 35a b + 35a b - 36a b + 36a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 4 +--R - 12a b + 12a b - 12a b + 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (120a b - 120a b )cosh(x) + (72a b - 72a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b - 50a b )cosh(x) + 10a b - 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (240b - 240a b + 240a b - 240a b + 240a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b + 124a b - 134a b + 134a b - 144a b + 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (100b - 96a b + 96a b - 98a b + 98a b)cosh(x) + 20a b +--R + +--R 2 3 3 2 4 5 +--R - 20a b + 20a b - 20a b + 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (210a b - 210a b )cosh(x) + (168a b - 168a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (185a b - 185a b )cosh(x) + (74a b - 74a b)cosh(x) +--R + +--R 2 3 3 2 +--R 15a b - 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (420b - 420a b + 420a b - 420a b + 420a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (90b + 246a b - 291a b + 291a b - 336a b + 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (370b - 334a b + 334a b - 352a b + 352a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (10b + 138a b - 143a b + 143a b - 148a b + 148a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 30b - 30a b + 30a b - 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (252a b - 252a b )cosh(x) + (252a b - 252a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (400a b - 400a b )cosh(x) + (240a b - 240a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (504b - 504a b + 504a b - 504a b + 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (240b + 264a b - 384a b + 384a b - 504a b + 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (800b - 656a b + 656a b - 728a b + 728a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b + 400a b - 440a b + 440a b - 480a b + 480a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (200b - 184a b + 184a b - 192a b + 192a b)cosh(x) + 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b + 40a b + 24a b - 24a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (210a b - 210a b )cosh(x) + (252a b - 252a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (560a b - 560a b )cosh(x) + (448a b - 448a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (290a b - 290a b )cosh(x) + (116a b - 116a b)cosh(x) +--R + +--R 2 3 3 2 +--R 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (420b - 420a b + 420a b - 420a b + 420a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (420b + 84a b - 294a b + 294a b - 504a b + 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (1120b - 784a b + 784a b - 952a b + 952a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (280b + 616a b - 756a b + 756a b - 896a b + 896a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (580b - 468a b + 468a b - 524a b + 524a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b + 212a b - 222a b + 222a b + 88a b - 88a )cosh(x) + 40b +--R + +--R 4 2 3 3 2 4 +--R - 40a b + 40a b - 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (120a b - 120a b )cosh(x) + (168a b - 168a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (532a b - 532a b )cosh(x) + (532a b - 532a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (480a b - 480a b )cosh(x) + (288a b - 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (240b - 240a b + 240a b - 240a b + 240a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (504b - 168a b - 84a b + 84a b - 336a b + 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (1064b - 560a b + 560a b - 812a b + 812a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (560b + 504a b - 784a b + 784a b - 1064a b + 1064a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (960b - 624a b + 624a b - 792a b + 792a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (120b + 456a b - 516a b + 516a b + 64a b - 64a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (200b - 176a b + 176a b - 188a b + 188a b)cosh(x) + 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b + 40a b + 24a b - 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (45a b - 45a b )cosh(x) + (72a b - 72a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (350a b - 350a b )cosh(x) + (420a b - 420a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (500a b - 500a b )cosh(x) + (400a b - 400a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (210a b - 210a b )cosh(x) + (84a b - 84a b)cosh(x) +--R + +--R 2 3 3 2 +--R 15a b - 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (90b - 90a b + 90a b - 90a b + 90a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (420b - 276a b + 66a b - 66a b - 144a b + 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (700b - 196a b + 196a b - 448a b + 448a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (700b + 140a b - 490a b + 490a b - 840a b + 840a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (1000b - 440a b + 440a b - 720a b + 720a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (300b + 500a b - 650a b + 650a b - 160a b + 160a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (420b - 300a b + 300a b - 360a b + 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (20b + 148a b - 158a b + 158a b + 152a b - 152a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 30b - 30a b + 30a b - 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b - 10a b )cosh(x) + (18a b - 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (160a b - 160a b )cosh(x) + (224a b - 224a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (340a b - 340a b )cosh(x) + (340a b - 340a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (240a b - 240a b )cosh(x) + (144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b - 50a b )cosh(x) + 10a b - 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (20b - 20a b + 20a b - 20a b + 20a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (240b - 204a b + 84a b - 84a b - 36a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (320b + 16a b - 16a b - 152a b + 152a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (560b - 112a b - 168a b + 168a b - 448a b + 448a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (680b - 120a b + 120a b - 400a b + 400a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (400b + 280a b - 480a b + 480a b - 360a b + 360a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (480b - 240a b + 240a b - 360a b + 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b + 208a b - 248a b + 248a b + 352a b - 352a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (100b - 84a b + 84a b - 92a b + 92a b)cosh(x) + 20a b +--R + +--R 2 3 3 2 4 5 +--R - 20a b + 20a b - 20a b + 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b - a b )cosh(x) + (2a b - 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (50a b - 50a b )cosh(x) + (80a b - 80a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (150a b - 150a b )cosh(x) + (180a b - 180a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (160a b - 160a b )cosh(x) + (128a b - 128a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (65a b - 65a b )cosh(x) + (26a b - 26a b)cosh(x) + 6a b +--R + +--R 3 2 +--R - 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (2b - 2a b + 2a b - 2a b + 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (90b - 86a b + 41a b - 41a b - 4a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (100b + 44a b - 44a b - 28a b + 28a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (280b - 120a b - 20a b + 20a b - 160a b + 160a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (300b + 36a b - 36a b - 132a b + 132a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (300b + 60a b - 210a b + 210a b - 296a b + 296a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (320b - 80a b + 80a b - 200a b + 200a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (120b + 136a b - 196a b + 196a b + 384a b - 384a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (130b - 82a b + 82a b - 106a b + 106a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b + 42a b - 47a b + 47a b - 52a b + 52a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 4 +--R - 12a b + 12a b - 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b - 10a b )cosh(x) + (18a b - 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (40a b - 40a b )cosh(x) + (56a b - 56a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (60a b - 60a b )cosh(x) + (60a b - 60a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (40a b - 40a b )cosh(x) + (24a b - 24a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (10a b - 10a b )cosh(x) + 2a b - 2a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (20b - 20a b + 10a b - 10a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (20b + 16a b - 16a b - 2a b + 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (80b - 44a b + 4a b - 4a b - 36a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (80b + 32a b - 32a b - 24a b + 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (120b - 8a b - 52a b + 52a b - 112a b + 112a )cosh(x) +--R + +--R 5 3 2 4 5 +--R (120b - 60a b + 60a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (80b + 40a b - 80a b + 80a b + 200a b - 200a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (80b - 32a b + 32a b - 56a b + 56a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b + 28a b - 38a b + 38a b - 48a b + 48a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (20b - 16a b + 16a b - 18a b + 18a b)cosh(x) + 4a b - 4a b +--R + +--R 3 2 4 5 +--R 4a b - 4a b + 4a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b - a b )cosh(x) + (2a b - 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (5a b - 5a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (10a b - 10a b )cosh(x) + (12a b - 12a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (10a b - 10a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (5a b - 5a b )cosh(x) + (2a b - 2a b)cosh(x) + a b - a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 11 5 4 2 3 10 +--R (2b - 2a b + a b - a b )cosh(x) + (2b + 2a b - 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (10b - 6a b + a b - a b - 4a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (10b + 6a b - 6a b - 2a b + 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (20b - 4a b - 6a b + 6a b - 16a b + 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (20b + 4a b - 4a b - 8a b + 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b + 4a b - 14a b + 14a b + 40a b - 40a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (20b - 4a b + 4a b - 12a b + 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (10b + 6a b - 11a b + 11a b - 16a b + 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (10b - 6a b + 6a b - 8a b + 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 +--R (2b + 2a b - 3a b + 3a b - 4a b + 4a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 +--R 2a b - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 5 4 2 3 3 2 4 12 +--R ((a b + a b )sech(x) - 2b - 2a b - 2a b - 2a b - 2a b)sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((10a b + 10a b )cosh(x) + 2a b + 2a b)sech(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 20b - 20a b - 20a b - 20a b - 20a b)cosh(x) - 4a b - 4a b +--R + +--R 3 2 4 5 +--R - 4a b - 4a b - 4a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (45a b + 45a b )cosh(x) + (18a b + 18a b)cosh(x) + 6a b +--R + +--R 3 2 +--R 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 90b - 90a b - 90a b - 90a b - 90a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b - 34a b - 35a b - 35a b - 36a b - 36a )cosh(x) - 12b +--R + +--R 4 2 3 3 2 4 +--R - 12a b - 12a b - 12a b - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (120a b + 120a b )cosh(x) + (72a b + 72a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b + 50a b )cosh(x) + 10a b + 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 240b - 240a b - 240a b - 240a b - 240a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b - 124a b - 134a b - 134a b - 144a b - 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 100b - 96a b - 96a b - 98a b - 98a b)cosh(x) - 20a b - 20a b +--R + +--R 3 2 4 5 +--R - 20a b - 20a b - 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (210a b + 210a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (185a b + 185a b )cosh(x) + (74a b + 74a b)cosh(x) + 15a b +--R + +--R 3 2 +--R 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 420b - 420a b - 420a b - 420a b - 420a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (90b - 246a b - 291a b - 291a b - 336a b - 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 370b - 334a b - 334a b - 352a b - 352a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b - 138a b - 143a b - 143a b - 148a b - 148a )cosh(x) - 30b +--R + +--R 4 2 3 3 2 4 +--R - 30a b - 30a b - 30a b - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (252a b + 252a b )cosh(x) + (252a b + 252a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (400a b + 400a b )cosh(x) + (240a b + 240a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 504b - 504a b - 504a b - 504a b - 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (240b - 264a b - 384a b - 384a b - 504a b - 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 800b - 656a b - 656a b - 728a b - 728a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b - 400a b - 440a b - 440a b - 480a b - 480a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 200b - 184a b - 184a b - 192a b - 192a b)cosh(x) - 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b - 40a b + 24a b + 24a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (210a b + 210a b )cosh(x) + (252a b + 252a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (560a b + 560a b )cosh(x) + (448a b + 448a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (290a b + 290a b )cosh(x) + (116a b + 116a b)cosh(x) + 20a b +--R + +--R 3 2 +--R 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 420b - 420a b - 420a b - 420a b - 420a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (420b - 84a b - 294a b - 294a b - 504a b - 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 1120b - 784a b - 784a b - 952a b - 952a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (280b - 616a b - 756a b - 756a b - 896a b - 896a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 580b - 468a b - 468a b - 524a b - 524a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 212a b - 222a b - 222a b + 88a b + 88a )cosh(x) - 40b +--R + +--R 4 2 3 3 2 4 +--R - 40a b - 40a b - 40a b - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (120a b + 120a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (532a b + 532a b )cosh(x) + (532a b + 532a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (480a b + 480a b )cosh(x) + (288a b + 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 240b - 240a b - 240a b - 240a b - 240a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (504b + 168a b - 84a b - 84a b - 336a b - 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 1064b - 560a b - 560a b - 812a b - 812a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (560b - 504a b - 784a b - 784a b - 1064a b - 1064a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 960b - 624a b - 624a b - 792a b - 792a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (120b - 456a b - 516a b - 516a b + 64a b + 64a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 200b - 176a b - 176a b - 188a b - 188a b)cosh(x) - 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b - 40a b + 24a b + 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (45a b + 45a b )cosh(x) + (72a b + 72a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (350a b + 350a b )cosh(x) + (420a b + 420a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (500a b + 500a b )cosh(x) + (400a b + 400a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (210a b + 210a b )cosh(x) + (84a b + 84a b)cosh(x) + 15a b +--R + +--R 3 2 +--R 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 90b - 90a b - 90a b - 90a b - 90a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (420b + 276a b + 66a b + 66a b - 144a b - 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 700b - 196a b - 196a b - 448a b - 448a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (700b - 140a b - 490a b - 490a b - 840a b - 840a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 1000b - 440a b - 440a b - 720a b - 720a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (300b - 500a b - 650a b - 650a b - 160a b - 160a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 420b - 300a b - 300a b - 360a b - 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 148a b - 158a b - 158a b + 152a b + 152a )cosh(x) - 30b +--R + +--R 4 2 3 3 2 4 +--R - 30a b - 30a b - 30a b - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b + 10a b )cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (160a b + 160a b )cosh(x) + (224a b + 224a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (340a b + 340a b )cosh(x) + (340a b + 340a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (240a b + 240a b )cosh(x) + (144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b + 50a b )cosh(x) + 10a b + 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (- 20b - 20a b - 20a b - 20a b - 20a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (240b + 204a b + 84a b + 84a b - 36a b - 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 320b + 16a b + 16a b - 152a b - 152a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (560b + 112a b - 168a b - 168a b - 448a b - 448a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 680b - 120a b - 120a b - 400a b - 400a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (400b - 280a b - 480a b - 480a b - 360a b - 360a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 480b - 240a b - 240a b - 360a b - 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b - 208a b - 248a b - 248a b + 352a b + 352a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 100b - 84a b - 84a b - 92a b - 92a b)cosh(x) - 20a b - 20a b +--R + +--R 3 2 4 5 +--R - 20a b - 20a b - 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b + a b )cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (50a b + 50a b )cosh(x) + (80a b + 80a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (150a b + 150a b )cosh(x) + (180a b + 180a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (160a b + 160a b )cosh(x) + (128a b + 128a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (65a b + 65a b )cosh(x) + (26a b + 26a b)cosh(x) + 6a b + 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (- 2b - 2a b - 2a b - 2a b - 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (90b + 86a b + 41a b + 41a b - 4a b - 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 100b + 44a b + 44a b - 28a b - 28a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (280b + 120a b - 20a b - 20a b - 160a b - 160a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 300b + 36a b + 36a b - 132a b - 132a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (300b - 60a b - 210a b - 210a b - 296a b - 296a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 320b - 80a b - 80a b - 200a b - 200a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (120b - 136a b - 196a b - 196a b + 384a b + 384a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 130b - 82a b - 82a b - 106a b - 106a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b - 42a b - 47a b - 47a b - 52a b - 52a )cosh(x) - 12b +--R + +--R 4 2 3 3 2 4 +--R - 12a b - 12a b - 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b + 10a b )cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (40a b + 40a b )cosh(x) + (56a b + 56a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (60a b + 60a b )cosh(x) + (60a b + 60a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (40a b + 40a b )cosh(x) + (24a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (10a b + 10a b )cosh(x) + 2a b + 2a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (20b + 20a b + 10a b + 10a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (- 20b + 16a b + 16a b - 2a b - 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (80b + 44a b + 4a b + 4a b - 36a b - 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 80b + 32a b + 32a b - 24a b - 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (120b + 8a b - 52a b - 52a b - 112a b - 112a )cosh(x) +--R + +--R 5 3 2 4 5 +--R (- 120b - 60a b - 60a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (80b - 40a b - 80a b - 80a b + 200a b + 200a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 80b - 32a b - 32a b - 56a b - 56a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b - 28a b - 38a b - 38a b - 48a b - 48a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 20b - 16a b - 16a b - 18a b - 18a b)cosh(x) - 4a b - 4a b +--R + +--R 3 2 4 5 +--R - 4a b - 4a b - 4a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b + a b )cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (5a b + 5a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (10a b + 10a b )cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (10a b + 10a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (5a b + 5a b )cosh(x) + (2a b + 2a b)cosh(x) + a b + a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 11 5 4 2 3 10 +--R (2b + 2a b + a b + a b )cosh(x) + (- 2b + 2a b + 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (10b + 6a b + a b + a b - 4a b - 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 10b + 6a b + 6a b - 2a b - 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (20b + 4a b - 6a b - 6a b - 16a b - 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 20b + 4a b + 4a b - 8a b - 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 4a b - 14a b - 14a b + 40a b + 40a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 20b - 4a b - 4a b - 12a b - 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (10b - 6a b - 11a b - 11a b - 16a b - 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 10b - 6a b - 6a b - 8a b - 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 2 3 +--R (2b - 2a b - 3a b - 3a b - 4a b - 4a )cosh(x) - 2b - 2a b - 2a b +--R + +--R 3 2 4 +--R - 2a b - 2a b +--R / +--R 4 2 5 12 +--R (2a b - 2a b)sinh(x) +--R + +--R 4 2 5 5 6 11 +--R ((20a b - 20a b)cosh(x) + 4a b - 4a )sinh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R ((90a b - 90a b)cosh(x) + (36a b - 36a )cosh(x) + 12a b - 12a b) +--R * +--R 10 +--R sinh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (240a b - 240a b)cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b - 100a b)cosh(x) + 20a b - 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (420a b - 420a b)cosh(x) + (336a b - 336a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (370a b - 370a b)cosh(x) + (148a b - 148a )cosh(x) + 30a b +--R + +--R 5 +--R - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (504a b - 504a b)cosh(x) + (504a b - 504a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (800a b - 800a b)cosh(x) + (480a b - 480a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b - 200a b)cosh(x) + 40a b - 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (420a b - 420a b)cosh(x) + (504a b - 504a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1120a b - 1120a b)cosh(x) + (896a b - 896a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (580a b - 580a b)cosh(x) + (232a b - 232a )cosh(x) + 40a b +--R + +--R 5 +--R - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (240a b - 240a b)cosh(x) + (336a b - 336a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (1064a b - 1064a b)cosh(x) + (1064a b - 1064a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (960a b - 960a b)cosh(x) + (576a b - 576a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b - 200a b)cosh(x) + 40a b - 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (90a b - 90a b)cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (700a b - 700a b)cosh(x) + (840a b - 840a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1000a b - 1000a b)cosh(x) + (800a b - 800a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (420a b - 420a b)cosh(x) + (168a b - 168a )cosh(x) + 30a b +--R + +--R 5 +--R - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b - 20a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (320a b - 320a b)cosh(x) + (448a b - 448a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (680a b - 680a b)cosh(x) + (680a b - 680a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (480a b - 480a b)cosh(x) + (288a b - 288a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b - 100a b)cosh(x) + 20a b - 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (100a b - 100a b)cosh(x) + (160a b - 160a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (300a b - 300a b)cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (320a b - 320a b)cosh(x) + (256a b - 256a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (130a b - 130a b)cosh(x) + (52a b - 52a )cosh(x) + 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b - 20a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (80a b - 80a b)cosh(x) + (112a b - 112a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (120a b - 120a b)cosh(x) + (120a b - 120a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (80a b - 80a b)cosh(x) + (48a b - 48a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (20a b - 20a b)cosh(x) + 4a b - 4a +--R * +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (10a b - 10a b)cosh(x) + (16a b - 16a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (20a b - 20a b)cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (20a b - 20a b)cosh(x) + (16a b - 16a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (10a b - 10a b)cosh(x) + (4a b - 4a )cosh(x) + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 5 12 4 2 5 5 6 11 +--R (2a b + 2a b)sinh(x) + ((20a b + 20a b)cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R ((90a b + 90a b)cosh(x) + (36a b + 36a )cosh(x) + 12a b + 12a b) +--R * +--R 10 +--R sinh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (240a b + 240a b)cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b + 100a b)cosh(x) + 20a b + 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (420a b + 420a b)cosh(x) + (336a b + 336a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (370a b + 370a b)cosh(x) + (148a b + 148a )cosh(x) + 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (504a b + 504a b)cosh(x) + (504a b + 504a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (800a b + 800a b)cosh(x) + (480a b + 480a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b + 200a b)cosh(x) + 40a b + 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (420a b + 420a b)cosh(x) + (504a b + 504a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1120a b + 1120a b)cosh(x) + (896a b + 896a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (580a b + 580a b)cosh(x) + (232a b + 232a )cosh(x) + 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (240a b + 240a b)cosh(x) + (336a b + 336a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (1064a b + 1064a b)cosh(x) + (1064a b + 1064a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (960a b + 960a b)cosh(x) + (576a b + 576a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b + 200a b)cosh(x) + 40a b + 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (90a b + 90a b)cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (700a b + 700a b)cosh(x) + (840a b + 840a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1000a b + 1000a b)cosh(x) + (800a b + 800a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (420a b + 420a b)cosh(x) + (168a b + 168a )cosh(x) + 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b + 20a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (320a b + 320a b)cosh(x) + (448a b + 448a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (680a b + 680a b)cosh(x) + (680a b + 680a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (480a b + 480a b)cosh(x) + (288a b + 288a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b + 100a b)cosh(x) + 20a b + 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (100a b + 100a b)cosh(x) + (160a b + 160a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (300a b + 300a b)cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (320a b + 320a b)cosh(x) + (256a b + 256a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (130a b + 130a b)cosh(x) + (52a b + 52a )cosh(x) + 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b + 20a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (80a b + 80a b)cosh(x) + (112a b + 112a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (120a b + 120a b)cosh(x) + (120a b + 120a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (80a b + 80a b)cosh(x) + (48a b + 48a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (20a b + 20a b)cosh(x) + 4a b + 4a +--R * +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 4 2 5 8 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) + (10a b + 10a b)cosh(x) +--R + +--R 5 6 7 4 2 5 6 +--R (16a b + 16a )cosh(x) + (20a b + 20a b)cosh(x) +--R + +--R 5 6 5 4 2 5 4 +--R (24a b + 24a )cosh(x) + (20a b + 20a b)cosh(x) +--R + +--R 5 6 3 4 2 5 2 5 6 +--R (16a b + 16a )cosh(x) + (10a b + 10a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 4 2 5 +--R 2a b + 2a b +--R Type: Expression(Integer) +--E 285 + +--S 286 of 530 +m0552b:= a0552.2-r0552 +--R +--R +--R (284) +--R 4 6 4 5 4 2 4 4 +--R 12b sinh(x) + 72b cosh(x)sinh(x) + (180b cosh(x) + 36b )sinh(x) +--R + +--R 4 3 4 3 +--R (240b cosh(x) + 144b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (180b cosh(x) + 216b cosh(x) + 36b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (72b cosh(x) + 144b cosh(x) + 72b cosh(x))sinh(x) + 12b cosh(x) +--R + +--R 4 4 4 2 4 +--R 36b cosh(x) + 36b cosh(x) + 12b +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 6 4 5 4 2 4 4 +--R 12b sinh(x) + 72b cosh(x)sinh(x) + (180b cosh(x) + 36b )sinh(x) +--R + +--R 4 3 4 3 +--R (240b cosh(x) + 144b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (180b cosh(x) + 216b cosh(x) + 36b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (72b cosh(x) + 144b cosh(x) + 72b cosh(x))sinh(x) + 12b cosh(x) +--R + +--R 4 4 4 2 4 +--R 36b cosh(x) + 36b cosh(x) + 12b +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sinh(x) + b cosh(x) + a)\|b - a +--R \|- b + a atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 3 2 6 3 2 5 +--R (- 12b - 6a b)sinh(x) + (- 72b - 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 180b - 90a b)cosh(x) - 36b - 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 240b - 120a b)cosh(x) + (- 144b - 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 180b - 90a b)cosh(x) + (- 216b - 108a b)cosh(x) - 36b +--R + +--R 2 +--R - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 72b - 36a b)cosh(x) + (- 144b - 72a b)cosh(x) +--R + +--R 3 2 +--R (- 72b - 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 12b - 6a b)cosh(x) + (- 36b - 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 36b - 18a b)cosh(x) - 12b - 6a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atan(sinh(x) + cosh(x)) +--R + +--R 3 2 6 3 2 5 +--R (6b + 3a b)sinh(x) + (36b + 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b + 45a b)cosh(x) + 18b + 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b + 60a b)cosh(x) + (72b + 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((90b + 45a b)cosh(x) + (108b + 54a b)cosh(x) + 18b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b + 18a b)cosh(x) + (72b + 36a b)cosh(x) +--R + +--R 3 2 +--R (36b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (6b + 3a b)cosh(x) + (18b + 9a b)cosh(x) + (18b + 9a b)cosh(x) +--R + +--R 3 2 +--R 6b + 3a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atan(sinh(x)) +--R + +--R 3 6 3 5 3 2 3 4 +--R 2a sinh(x) + 12a cosh(x)sinh(x) + (30a cosh(x) + 6a )sinh(x) +--R + +--R 3 3 3 3 +--R (40a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (30a cosh(x) + 36a cosh(x) + 6a )sinh(x) +--R + +--R 3 5 3 3 3 3 6 +--R (12a cosh(x) + 24a cosh(x) + 12a cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 3 4 3 2 3 +--R 6a cosh(x) + 6a cosh(x) + 2a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 2 3 6 +--R (3a b sech(x) - 6a b - 6a )sinh(x) +--R + +--R 2 2 3 5 +--R (18a b cosh(x)sech(x) + (- 36a b - 36a )cosh(x))sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (45a b cosh(x) + 9a b)sech(x) + (- 90a b - 90a )cosh(x) +--R + +--R 2 3 +--R - 18a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 +--R (60a b cosh(x) + 36a b cosh(x))sech(x) +--R + +--R 2 3 3 2 3 +--R (- 120a b - 120a )cosh(x) + (- 72a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (45a b cosh(x) + 54a b cosh(x) + 9a b)sech(x) +--R + +--R 2 3 4 2 3 2 +--R (- 90a b - 90a )cosh(x) + (- 108a b - 108a )cosh(x) +--R + +--R 2 3 +--R - 18a b - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 +--R (18a b cosh(x) + 36a b cosh(x) + 18a b cosh(x))sech(x) +--R + +--R 2 3 5 2 3 3 +--R (- 36a b - 36a )cosh(x) + (- 72a b - 72a )cosh(x) +--R + +--R 2 3 +--R (- 36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (3a b cosh(x) + 9a b cosh(x) + 9a b cosh(x) + 3a b)sech(x) +--R + +--R 2 3 6 2 3 4 +--R (- 6a b - 6a )cosh(x) + (- 18a b - 18a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (- 18a b - 18a )cosh(x) - 6a b - 6a +--R * +--R tanh(x) +--R + +--R 2 5 2 2 4 +--R - 6a b sinh(x) + (- 30a b cosh(x) - 12a b )sinh(x) +--R + +--R 2 2 2 3 +--R (- 60a b cosh(x) - 48a b cosh(x))sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R (- 60a b cosh(x) - 72a b cosh(x) - 24a b - 24a )sinh(x) +--R + +--R 2 4 2 3 2 3 +--R - 30a b cosh(x) - 48a b cosh(x) + (- 48a b - 48a )cosh(x) +--R + +--R 2 +--R 6a b +--R * +--R sinh(x) +--R + +--R 2 5 2 4 2 3 2 +--R - 6a b cosh(x) - 12a b cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R 6a b cosh(x) - 12a b - 8a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) + 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) + 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) + 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) + 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R 18a cosh(x) + 18a cosh(x) + 6a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 530 +d0552b:= D(m0552b,x) +--R +--R +--R (285) +--R 3 2 4 12 +--R (- 2a b + 2a b)sinh(x) +--R + +--R 3 2 4 4 5 11 +--R ((- 20a b + 20a b)cosh(x) - 4a b + 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 90a b + 90a b)cosh(x) + (- 36a b + 36a )cosh(x) - 12a b +--R + +--R 4 +--R 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 240a b + 240a b)cosh(x) + (- 144a b + 144a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b + 100a b)cosh(x) - 20a b + 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 420a b + 420a b)cosh(x) + (- 336a b + 336a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 370a b + 370a b)cosh(x) + (- 148a b + 148a )cosh(x) +--R + +--R 3 2 4 +--R - 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 504a b + 504a b)cosh(x) + (- 504a b + 504a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 800a b + 800a b)cosh(x) + (- 480a b + 480a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b + 200a b)cosh(x) - 40a b + 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 420a b + 420a b)cosh(x) + (- 504a b + 504a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1120a b + 1120a b)cosh(x) + (- 896a b + 896a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 580a b + 580a b)cosh(x) + (- 232a b + 232a )cosh(x) +--R + +--R 3 2 4 +--R - 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 240a b + 240a b)cosh(x) + (- 336a b + 336a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 1064a b + 1064a b)cosh(x) + (- 1064a b + 1064a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 960a b + 960a b)cosh(x) + (- 576a b + 576a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b + 200a b)cosh(x) - 40a b + 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 90a b + 90a b)cosh(x) + (- 144a b + 144a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 700a b + 700a b)cosh(x) + (- 840a b + 840a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1000a b + 1000a b)cosh(x) + (- 800a b + 800a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 420a b + 420a b)cosh(x) + (- 168a b + 168a )cosh(x) +--R + +--R 3 2 4 +--R - 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b + 20a b)cosh(x) + (- 36a b + 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 320a b + 320a b)cosh(x) + (- 448a b + 448a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 680a b + 680a b)cosh(x) + (- 680a b + 680a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 480a b + 480a b)cosh(x) + (- 288a b + 288a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b + 100a b)cosh(x) - 20a b + 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 100a b + 100a b)cosh(x) + (- 160a b + 160a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 300a b + 300a b)cosh(x) + (- 360a b + 360a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 320a b + 320a b)cosh(x) + (- 256a b + 256a )cosh(x) +--R + +--R 3 2 4 2 4 5 +--R (- 130a b + 130a b)cosh(x) + (- 52a b + 52a )cosh(x) +--R + +--R 3 2 4 +--R - 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b + 20a b)cosh(x) + (- 36a b + 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 80a b + 80a b)cosh(x) + (- 112a b + 112a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 120a b + 120a b)cosh(x) + (- 120a b + 120a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 80a b + 80a b)cosh(x) + (- 48a b + 48a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 20a b + 20a b)cosh(x) - 4a b + 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 10a b + 10a b)cosh(x) + (- 16a b + 16a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 20a b + 20a b)cosh(x) + (- 24a b + 24a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 20a b + 20a b)cosh(x) + (- 16a b + 16a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (- 10a b + 10a b)cosh(x) + (- 4a b + 4a )cosh(x) - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 4 12 +--R (- 2a b - 2a b)sinh(x) +--R + +--R 3 2 4 4 5 11 +--R ((- 20a b - 20a b)cosh(x) - 4a b - 4a )sinh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 90a b - 90a b)cosh(x) + (- 36a b - 36a )cosh(x) - 12a b +--R + +--R 4 +--R - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 240a b - 240a b)cosh(x) + (- 144a b - 144a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b - 100a b)cosh(x) - 20a b - 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 420a b - 420a b)cosh(x) + (- 336a b - 336a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 370a b - 370a b)cosh(x) + (- 148a b - 148a )cosh(x) - 30a b +--R + +--R 4 +--R - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 504a b - 504a b)cosh(x) + (- 504a b - 504a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 800a b - 800a b)cosh(x) + (- 480a b - 480a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b - 200a b)cosh(x) - 40a b - 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 420a b - 420a b)cosh(x) + (- 504a b - 504a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1120a b - 1120a b)cosh(x) + (- 896a b - 896a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 580a b - 580a b)cosh(x) + (- 232a b - 232a )cosh(x) - 40a b +--R + +--R 4 +--R - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 240a b - 240a b)cosh(x) + (- 336a b - 336a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 1064a b - 1064a b)cosh(x) + (- 1064a b - 1064a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 960a b - 960a b)cosh(x) + (- 576a b - 576a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 200a b - 200a b)cosh(x) - 40a b - 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 90a b - 90a b)cosh(x) + (- 144a b - 144a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 700a b - 700a b)cosh(x) + (- 840a b - 840a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 1000a b - 1000a b)cosh(x) + (- 800a b - 800a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 420a b - 420a b)cosh(x) + (- 168a b - 168a )cosh(x) - 30a b +--R + +--R 4 +--R - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b - 20a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 320a b - 320a b)cosh(x) + (- 448a b - 448a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 680a b - 680a b)cosh(x) + (- 680a b - 680a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 480a b - 480a b)cosh(x) + (- 288a b - 288a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 100a b - 100a b)cosh(x) - 20a b - 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b - 2a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 100a b - 100a b)cosh(x) + (- 160a b - 160a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 300a b - 300a b)cosh(x) + (- 360a b - 360a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 320a b - 320a b)cosh(x) + (- 256a b - 256a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 +--R (- 130a b - 130a b)cosh(x) + (- 52a b - 52a )cosh(x) - 12a b +--R + +--R 4 +--R - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 9 4 5 8 +--R (- 20a b - 20a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 7 4 5 6 +--R (- 80a b - 80a b)cosh(x) + (- 112a b - 112a )cosh(x) +--R + +--R 3 2 4 5 4 5 4 +--R (- 120a b - 120a b)cosh(x) + (- 120a b - 120a )cosh(x) +--R + +--R 3 2 4 3 4 5 2 +--R (- 80a b - 80a b)cosh(x) + (- 48a b - 48a )cosh(x) +--R + +--R 3 2 4 4 5 +--R (- 20a b - 20a b)cosh(x) - 4a b - 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 10 4 5 9 +--R (- 2a b - 2a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 4 8 4 5 7 +--R (- 10a b - 10a b)cosh(x) + (- 16a b - 16a )cosh(x) +--R + +--R 3 2 4 6 4 5 5 +--R (- 20a b - 20a b)cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 3 2 4 4 4 5 3 +--R (- 20a b - 20a b)cosh(x) + (- 16a b - 16a )cosh(x) +--R + +--R 3 2 4 2 4 5 3 2 4 +--R (- 10a b - 10a b)cosh(x) + (- 4a b - 4a )cosh(x) - 2a b - 2a b +--R * +--R 4 +--R tanh(x) +--R + +--R 2 3 3 2 4 2 3 3 2 4 +--R ((- 2a b + 2a b )sech(x) + 2a b - 2a b + 4a b - 4a b) +--R * +--R 12 +--R sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((- 20a b + 20a b )cosh(x) - 4a b + 4a b)sech(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) + 4a b - 4a b +--R + +--R 4 5 +--R 8a b - 8a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 90a b + 90a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b + 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 2 +--R (90a b - 90a b + 180a b - 180a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (36a b - 36a b + 72a b - 72a )cosh(x) + 12a b - 12a b +--R + +--R 3 2 4 +--R 24a b - 24a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 +--R (- 240a b + 240a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b + 100a b )cosh(x) - 20a b + 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 3 +--R (240a b - 240a b + 480a b - 480a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (144a b - 144a b + 288a b - 288a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 +--R (100a b - 100a b + 200a b - 200a b)cosh(x) + 20a b +--R + +--R 3 2 4 5 +--R - 20a b + 40a b - 40a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 336a b + 336a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 370a b + 370a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 148a b + 148a b)cosh(x) - 30a b + 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 4 +--R (420a b - 420a b + 840a b - 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (336a b - 336a b + 672a b - 672a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (370a b - 370a b + 740a b - 740a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (148a b - 148a b + 296a b - 296a )cosh(x) + 30a b - 30a b +--R + +--R 3 2 4 +--R 60a b - 60a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 +--R (- 504a b + 504a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 504a b + 504a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 800a b + 800a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 480a b + 480a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b + 200a b )cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 5 +--R (504a b - 504a b + 1008a b - 1008a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (504a b - 504a b + 1008a b - 1008a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (800a b - 800a b + 1600a b - 1600a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (480a b - 480a b + 960a b - 960a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 +--R (200a b - 200a b + 400a b - 400a b)cosh(x) + 40a b +--R + +--R 3 2 4 5 +--R - 40a b + 80a b - 80a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 504a b + 504a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1120a b + 1120a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 896a b + 896a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 580a b + 580a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 232a b + 232a b)cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 6 +--R (420a b - 420a b + 840a b - 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (504a b - 504a b + 1008a b - 1008a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (1120a b - 1120a b + 2240a b - 2240a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (896a b - 896a b + 1792a b - 1792a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (580a b - 580a b + 1160a b - 1160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (232a b - 232a b + 464a b - 464a )cosh(x) + 40a b - 40a b +--R + +--R 3 2 4 +--R 80a b - 80a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 +--R (- 240a b + 240a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 336a b + 336a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 1064a b + 1064a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 1064a b + 1064a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 960a b + 960a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 576a b + 576a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b + 200a b )cosh(x) - 40a b + 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 7 +--R (240a b - 240a b + 480a b - 480a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (336a b - 336a b + 672a b - 672a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (1064a b - 1064a b + 2128a b - 2128a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (1064a b - 1064a b + 2128a b - 2128a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (960a b - 960a b + 1920a b - 1920a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (576a b - 576a b + 1152a b - 1152a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 +--R (200a b - 200a b + 400a b - 400a b)cosh(x) + 40a b +--R + +--R 3 2 4 5 +--R - 40a b + 80a b - 80a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 +--R (- 90a b + 90a b )cosh(x) +--R + +--R 3 2 4 7 +--R (- 144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 6 +--R (- 700a b + 700a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 840a b + 840a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1000a b + 1000a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 800a b + 800a b)cosh(x) +--R + +--R 2 3 3 2 2 +--R (- 420a b + 420a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 168a b + 168a b)cosh(x) - 30a b + 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 8 +--R (90a b - 90a b + 180a b - 180a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (144a b - 144a b + 288a b - 288a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (700a b - 700a b + 1400a b - 1400a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (840a b - 840a b + 1680a b - 1680a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (1000a b - 1000a b + 2000a b - 2000a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (800a b - 800a b + 1600a b - 1600a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (420a b - 420a b + 840a b - 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (168a b - 168a b + 336a b - 336a )cosh(x) + 30a b - 30a b +--R + +--R 3 2 4 +--R 60a b - 60a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b + 20a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 7 +--R (- 320a b + 320a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 448a b + 448a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 680a b + 680a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 680a b + 680a b)cosh(x) +--R + +--R 2 3 3 2 3 +--R (- 480a b + 480a b )cosh(x) +--R + +--R 3 2 4 2 +--R (- 288a b + 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b + 100a b )cosh(x) - 20a b + 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 9 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (36a b - 36a b + 72a b - 72a )cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (320a b - 320a b + 640a b - 640a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (448a b - 448a b + 896a b - 896a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (680a b - 680a b + 1360a b - 1360a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (680a b - 680a b + 1360a b - 1360a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (480a b - 480a b + 960a b - 960a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (288a b - 288a b + 576a b - 576a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 +--R (100a b - 100a b + 200a b - 200a b)cosh(x) + 20a b +--R + +--R 3 2 4 5 +--R - 20a b + 40a b - 40a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 8 +--R (- 100a b + 100a b )cosh(x) +--R + +--R 3 2 4 7 +--R (- 160a b + 160a b)cosh(x) +--R + +--R 2 3 3 2 6 +--R (- 300a b + 300a b )cosh(x) +--R + +--R 3 2 4 5 +--R (- 360a b + 360a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 320a b + 320a b )cosh(x) +--R + +--R 3 2 4 3 +--R (- 256a b + 256a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 130a b + 130a b )cosh(x) + (- 52a b + 52a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b + 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 10 +--R (2a b - 2a b + 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (4a b - 4a b + 8a b - 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (100a b - 100a b + 200a b - 200a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (160a b - 160a b + 320a b - 320a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (300a b - 300a b + 600a b - 600a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (360a b - 360a b + 720a b - 720a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (320a b - 320a b + 640a b - 640a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (256a b - 256a b + 512a b - 512a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (130a b - 130a b + 260a b - 260a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (52a b - 52a b + 104a b - 104a )cosh(x) + 12a b - 12a b +--R + +--R 3 2 4 +--R 24a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b + 20a b )cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 3 2 7 +--R (- 80a b + 80a b )cosh(x) +--R + +--R 3 2 4 6 +--R (- 112a b + 112a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 120a b + 120a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 120a b + 120a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 80a b + 80a b )cosh(x) + (- 48a b + 48a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 20a b + 20a b )cosh(x) - 4a b + 4a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 9 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (36a b - 36a b + 72a b - 72a )cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (80a b - 80a b + 160a b - 160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (112a b - 112a b + 224a b - 224a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (120a b - 120a b + 240a b - 240a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (120a b - 120a b + 240a b - 240a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (80a b - 80a b + 160a b - 160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (48a b - 48a b + 96a b - 96a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) + 4a b - 4a b +--R + +--R 4 5 +--R 8a b - 8a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b + 2a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 10a b + 10a b )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 20a b + 20a b )cosh(x) + (- 24a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 20a b + 20a b )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (- 10a b + 10a b )cosh(x) + (- 4a b + 4a b)cosh(x) - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 10 +--R (2a b - 2a b + 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (4a b - 4a b + 8a b - 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (10a b - 10a b + 20a b - 20a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (16a b - 16a b + 32a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (24a b - 24a b + 48a b - 48a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (20a b - 20a b + 40a b - 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (16a b - 16a b + 32a b - 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (10a b - 10a b + 20a b - 20a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R (4a b - 4a b + 8a b - 8a )cosh(x) + 2a b - 2a b + 4a b - 4a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 4 2 3 3 2 4 12 +--R ((- 2a b - 2a b )sech(x) + 2a b + 2a b + 4a b + 4a b)sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((- 20a b - 20a b )cosh(x) - 4a b - 4a b)sech(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) + 4a b + 4a b + 8a b +--R + +--R 5 +--R 8a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 90a b - 90a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b - 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 2 +--R (90a b + 90a b + 180a b + 180a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (36a b + 36a b + 72a b + 72a )cosh(x) + 12a b + 12a b +--R + +--R 3 2 4 +--R 24a b + 24a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 240a b - 240a b )cosh(x) + (- 144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b - 100a b )cosh(x) - 20a b - 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 3 +--R (240a b + 240a b + 480a b + 480a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (144a b + 144a b + 288a b + 288a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (100a b + 100a b + 200a b + 200a b)cosh(x) + 20a b + 20a b +--R + +--R 4 5 +--R 40a b + 40a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 420a b - 420a b )cosh(x) + (- 336a b - 336a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 370a b - 370a b )cosh(x) + (- 148a b - 148a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 30a b - 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 4 +--R (420a b + 420a b + 840a b + 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (336a b + 336a b + 672a b + 672a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (370a b + 370a b + 740a b + 740a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (148a b + 148a b + 296a b + 296a )cosh(x) + 30a b + 30a b +--R + +--R 3 2 4 +--R 60a b + 60a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 504a b - 504a b )cosh(x) + (- 504a b - 504a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 800a b - 800a b )cosh(x) + (- 480a b - 480a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b - 200a b )cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 5 +--R (504a b + 504a b + 1008a b + 1008a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (504a b + 504a b + 1008a b + 1008a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (800a b + 800a b + 1600a b + 1600a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (480a b + 480a b + 960a b + 960a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (200a b + 200a b + 400a b + 400a b)cosh(x) + 40a b + 40a b +--R + +--R 4 5 +--R 80a b + 80a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 420a b - 420a b )cosh(x) + (- 504a b - 504a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1120a b - 1120a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 896a b - 896a b)cosh(x) + (- 580a b - 580a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 232a b - 232a b)cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 6 +--R (420a b + 420a b + 840a b + 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (504a b + 504a b + 1008a b + 1008a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (1120a b + 1120a b + 2240a b + 2240a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (896a b + 896a b + 1792a b + 1792a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (580a b + 580a b + 1160a b + 1160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (232a b + 232a b + 464a b + 464a )cosh(x) + 40a b + 40a b +--R + +--R 3 2 4 +--R 80a b + 80a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 240a b - 240a b )cosh(x) + (- 336a b - 336a b)cosh(x) +--R + +--R 2 3 3 2 5 +--R (- 1064a b - 1064a b )cosh(x) +--R + +--R 3 2 4 4 +--R (- 1064a b - 1064a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 960a b - 960a b )cosh(x) + (- 576a b - 576a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 200a b - 200a b )cosh(x) - 40a b - 40a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 7 +--R (240a b + 240a b + 480a b + 480a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (336a b + 336a b + 672a b + 672a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (1064a b + 1064a b + 2128a b + 2128a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (1064a b + 1064a b + 2128a b + 2128a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (960a b + 960a b + 1920a b + 1920a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (576a b + 576a b + 1152a b + 1152a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (200a b + 200a b + 400a b + 400a b)cosh(x) + 40a b + 40a b +--R + +--R 4 5 +--R 80a b + 80a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 90a b - 90a b )cosh(x) + (- 144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 700a b - 700a b )cosh(x) + (- 840a b - 840a b)cosh(x) +--R + +--R 2 3 3 2 4 +--R (- 1000a b - 1000a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 800a b - 800a b)cosh(x) + (- 420a b - 420a b )cosh(x) +--R + +--R 3 2 4 2 3 3 2 +--R (- 168a b - 168a b)cosh(x) - 30a b - 30a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 8 +--R (90a b + 90a b + 180a b + 180a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (144a b + 144a b + 288a b + 288a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (700a b + 700a b + 1400a b + 1400a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (840a b + 840a b + 1680a b + 1680a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (1000a b + 1000a b + 2000a b + 2000a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (800a b + 800a b + 1600a b + 1600a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (420a b + 420a b + 840a b + 840a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (168a b + 168a b + 336a b + 336a )cosh(x) + 30a b + 30a b +--R + +--R 3 2 4 +--R 60a b + 60a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b - 20a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 320a b - 320a b )cosh(x) + (- 448a b - 448a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 680a b - 680a b )cosh(x) + (- 680a b - 680a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 480a b - 480a b )cosh(x) + (- 288a b - 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 100a b - 100a b )cosh(x) - 20a b - 20a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 9 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (36a b + 36a b + 72a b + 72a )cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (320a b + 320a b + 640a b + 640a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (448a b + 448a b + 896a b + 896a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (680a b + 680a b + 1360a b + 1360a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (680a b + 680a b + 1360a b + 1360a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (480a b + 480a b + 960a b + 960a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (288a b + 288a b + 576a b + 576a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (100a b + 100a b + 200a b + 200a b)cosh(x) + 20a b + 20a b +--R + +--R 4 5 +--R 40a b + 40a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 100a b - 100a b )cosh(x) + (- 160a b - 160a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 300a b - 300a b )cosh(x) + (- 360a b - 360a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 320a b - 320a b )cosh(x) + (- 256a b - 256a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (- 130a b - 130a b )cosh(x) + (- 52a b - 52a b)cosh(x) +--R + +--R 2 3 3 2 +--R - 12a b - 12a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 10 +--R (2a b + 2a b + 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (4a b + 4a b + 8a b + 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (100a b + 100a b + 200a b + 200a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (160a b + 160a b + 320a b + 320a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (300a b + 300a b + 600a b + 600a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (360a b + 360a b + 720a b + 720a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (320a b + 320a b + 640a b + 640a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (256a b + 256a b + 512a b + 512a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (130a b + 130a b + 260a b + 260a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 +--R (52a b + 52a b + 104a b + 104a )cosh(x) + 12a b + 12a b +--R + +--R 3 2 4 +--R 24a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (- 20a b - 20a b )cosh(x) + (- 36a b - 36a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (- 80a b - 80a b )cosh(x) + (- 112a b - 112a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (- 120a b - 120a b )cosh(x) + (- 120a b - 120a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (- 80a b - 80a b )cosh(x) + (- 48a b - 48a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (- 20a b - 20a b )cosh(x) - 4a b - 4a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 9 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 8 +--R (36a b + 36a b + 72a b + 72a )cosh(x) +--R + +--R 4 2 3 3 2 4 7 +--R (80a b + 80a b + 160a b + 160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 6 +--R (112a b + 112a b + 224a b + 224a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (120a b + 120a b + 240a b + 240a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (120a b + 120a b + 240a b + 240a )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (80a b + 80a b + 160a b + 160a b)cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (48a b + 48a b + 96a b + 96a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) + 4a b + 4a b + 8a b +--R + +--R 5 +--R 8a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (- 10a b - 10a b )cosh(x) + (- 16a b - 16a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (- 20a b - 20a b )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (- 20a b - 20a b )cosh(x) + (- 16a b - 16a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (- 10a b - 10a b )cosh(x) + (- 4a b - 4a b)cosh(x) - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R sech(x) +--R + +--R 4 2 3 3 2 4 10 +--R (2a b + 2a b + 4a b + 4a b)cosh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (4a b + 4a b + 8a b + 8a )cosh(x) +--R + +--R 4 2 3 3 2 4 8 +--R (10a b + 10a b + 20a b + 20a b)cosh(x) +--R + +--R 2 3 3 2 4 5 7 +--R (16a b + 16a b + 32a b + 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 6 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (24a b + 24a b + 48a b + 48a )cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (20a b + 20a b + 40a b + 40a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (16a b + 16a b + 32a b + 32a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (10a b + 10a b + 20a b + 20a b)cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R (4a b + 4a b + 8a b + 8a )cosh(x) + 2a b + 2a b + 4a b + 4a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 3 2 5 4 2 3 3 2 4 12 +--R ((a b - a b )sech(x) + 2b - 2a b + 2a b - 2a b + 2a b)sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((10a b - 10a b )cosh(x) + 2a b - 2a b)sech(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (20b - 20a b + 20a b - 20a b + 20a b)cosh(x) + 4a b - 4a b +--R + +--R 3 2 4 5 +--R 4a b - 4a b + 4a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (45a b - 45a b )cosh(x) + (18a b - 18a b)cosh(x) + 6a b +--R + +--R 3 2 +--R - 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (90b - 90a b + 90a b - 90a b + 90a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b + 34a b - 35a b + 35a b - 36a b + 36a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 4 +--R - 12a b + 12a b - 12a b + 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (120a b - 120a b )cosh(x) + (72a b - 72a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b - 50a b )cosh(x) + 10a b - 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (240b - 240a b + 240a b - 240a b + 240a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b + 124a b - 134a b + 134a b - 144a b + 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (100b - 96a b + 96a b - 98a b + 98a b)cosh(x) + 20a b +--R + +--R 2 3 3 2 4 5 +--R - 20a b + 20a b - 20a b + 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (210a b - 210a b )cosh(x) + (168a b - 168a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (185a b - 185a b )cosh(x) + (74a b - 74a b)cosh(x) +--R + +--R 2 3 3 2 +--R 15a b - 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (420b - 420a b + 420a b - 420a b + 420a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (90b + 246a b - 291a b + 291a b - 336a b + 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (370b - 334a b + 334a b - 352a b + 352a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (10b + 138a b - 143a b + 143a b - 148a b + 148a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 30b - 30a b + 30a b - 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (252a b - 252a b )cosh(x) + (252a b - 252a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (400a b - 400a b )cosh(x) + (240a b - 240a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (504b - 504a b + 504a b - 504a b + 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (240b + 264a b - 384a b + 384a b - 504a b + 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (800b - 656a b + 656a b - 728a b + 728a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b + 400a b - 440a b + 440a b - 480a b + 480a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (200b - 184a b + 184a b - 192a b + 192a b)cosh(x) + 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b + 40a b + 24a b - 24a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (210a b - 210a b )cosh(x) + (252a b - 252a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (560a b - 560a b )cosh(x) + (448a b - 448a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (290a b - 290a b )cosh(x) + (116a b - 116a b)cosh(x) +--R + +--R 2 3 3 2 +--R 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (420b - 420a b + 420a b - 420a b + 420a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (420b + 84a b - 294a b + 294a b - 504a b + 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (1120b - 784a b + 784a b - 952a b + 952a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (280b + 616a b - 756a b + 756a b - 896a b + 896a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (580b - 468a b + 468a b - 524a b + 524a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b + 212a b - 222a b + 222a b + 88a b - 88a )cosh(x) + 40b +--R + +--R 4 2 3 3 2 4 +--R - 40a b + 40a b - 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (120a b - 120a b )cosh(x) + (168a b - 168a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (532a b - 532a b )cosh(x) + (532a b - 532a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (480a b - 480a b )cosh(x) + (288a b - 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b - 100a b )cosh(x) + 20a b - 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (240b - 240a b + 240a b - 240a b + 240a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (504b - 168a b - 84a b + 84a b - 336a b + 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (1064b - 560a b + 560a b - 812a b + 812a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (560b + 504a b - 784a b + 784a b - 1064a b + 1064a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (960b - 624a b + 624a b - 792a b + 792a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (120b + 456a b - 516a b + 516a b + 64a b - 64a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (200b - 176a b + 176a b - 188a b + 188a b)cosh(x) + 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b + 40a b + 24a b - 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (45a b - 45a b )cosh(x) + (72a b - 72a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (350a b - 350a b )cosh(x) + (420a b - 420a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (500a b - 500a b )cosh(x) + (400a b - 400a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 +--R (210a b - 210a b )cosh(x) + (84a b - 84a b)cosh(x) +--R + +--R 2 3 3 2 +--R 15a b - 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (90b - 90a b + 90a b - 90a b + 90a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (420b - 276a b + 66a b - 66a b - 144a b + 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (700b - 196a b + 196a b - 448a b + 448a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (700b + 140a b - 490a b + 490a b - 840a b + 840a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (1000b - 440a b + 440a b - 720a b + 720a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (300b + 500a b - 650a b + 650a b - 160a b + 160a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (420b - 300a b + 300a b - 360a b + 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (20b + 148a b - 158a b + 158a b + 152a b - 152a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 30b - 30a b + 30a b - 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b - 10a b )cosh(x) + (18a b - 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (160a b - 160a b )cosh(x) + (224a b - 224a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (340a b - 340a b )cosh(x) + (340a b - 340a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (240a b - 240a b )cosh(x) + (144a b - 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b - 50a b )cosh(x) + 10a b - 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (20b - 20a b + 20a b - 20a b + 20a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (240b - 204a b + 84a b - 84a b - 36a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (320b + 16a b - 16a b - 152a b + 152a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (560b - 112a b - 168a b + 168a b - 448a b + 448a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (680b - 120a b + 120a b - 400a b + 400a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (400b + 280a b - 480a b + 480a b - 360a b + 360a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (480b - 240a b + 240a b - 360a b + 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b + 208a b - 248a b + 248a b + 352a b - 352a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (100b - 84a b + 84a b - 92a b + 92a b)cosh(x) + 20a b +--R + +--R 2 3 3 2 4 5 +--R - 20a b + 20a b - 20a b + 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b - a b )cosh(x) + (2a b - 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (50a b - 50a b )cosh(x) + (80a b - 80a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (150a b - 150a b )cosh(x) + (180a b - 180a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (160a b - 160a b )cosh(x) + (128a b - 128a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (65a b - 65a b )cosh(x) + (26a b - 26a b)cosh(x) + 6a b +--R + +--R 3 2 +--R - 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (2b - 2a b + 2a b - 2a b + 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (90b - 86a b + 41a b - 41a b - 4a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (100b + 44a b - 44a b - 28a b + 28a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (280b - 120a b - 20a b + 20a b - 160a b + 160a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (300b + 36a b - 36a b - 132a b + 132a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (300b + 60a b - 210a b + 210a b - 296a b + 296a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (320b - 80a b + 80a b - 200a b + 200a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (120b + 136a b - 196a b + 196a b + 384a b - 384a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (130b - 82a b + 82a b - 106a b + 106a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b + 42a b - 47a b + 47a b - 52a b + 52a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 4 +--R - 12a b + 12a b - 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b - 10a b )cosh(x) + (18a b - 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (40a b - 40a b )cosh(x) + (56a b - 56a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (60a b - 60a b )cosh(x) + (60a b - 60a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (40a b - 40a b )cosh(x) + (24a b - 24a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (10a b - 10a b )cosh(x) + 2a b - 2a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (20b - 20a b + 10a b - 10a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (20b + 16a b - 16a b - 2a b + 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (80b - 44a b + 4a b - 4a b - 36a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (80b + 32a b - 32a b - 24a b + 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (120b - 8a b - 52a b + 52a b - 112a b + 112a )cosh(x) +--R + +--R 5 3 2 4 5 +--R (120b - 60a b + 60a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (80b + 40a b - 80a b + 80a b + 200a b - 200a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (80b - 32a b + 32a b - 56a b + 56a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b + 28a b - 38a b + 38a b - 48a b + 48a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (20b - 16a b + 16a b - 18a b + 18a b)cosh(x) + 4a b - 4a b +--R + +--R 3 2 4 5 +--R 4a b - 4a b + 4a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b - a b )cosh(x) + (2a b - 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (5a b - 5a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (10a b - 10a b )cosh(x) + (12a b - 12a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (10a b - 10a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (5a b - 5a b )cosh(x) + (2a b - 2a b)cosh(x) + a b - a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 11 5 4 2 3 10 +--R (2b - 2a b + a b - a b )cosh(x) + (2b + 2a b - 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (10b - 6a b + a b - a b - 4a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (10b + 6a b - 6a b - 2a b + 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (20b - 4a b - 6a b + 6a b - 16a b + 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (20b + 4a b - 4a b - 8a b + 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b + 4a b - 14a b + 14a b + 40a b - 40a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (20b - 4a b + 4a b - 12a b + 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (10b + 6a b - 11a b + 11a b - 16a b + 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (10b - 6a b + 6a b - 8a b + 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 +--R (2b + 2a b - 3a b + 3a b - 4a b + 4a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 +--R 2a b - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 5 4 2 3 3 2 4 12 +--R ((a b + a b )sech(x) - 2b - 2a b - 2a b - 2a b - 2a b)sinh(x) +--R + +--R 2 3 3 2 3 2 4 +--R ((10a b + 10a b )cosh(x) + 2a b + 2a b)sech(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 20b - 20a b - 20a b - 20a b - 20a b)cosh(x) - 4a b - 4a b +--R + +--R 3 2 4 5 +--R - 4a b - 4a b - 4a +--R * +--R 11 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (45a b + 45a b )cosh(x) + (18a b + 18a b)cosh(x) + 6a b +--R + +--R 3 2 +--R 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 90b - 90a b - 90a b - 90a b - 90a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b - 34a b - 35a b - 35a b - 36a b - 36a )cosh(x) - 12b +--R + +--R 4 2 3 3 2 4 +--R - 12a b - 12a b - 12a b - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (120a b + 120a b )cosh(x) + (72a b + 72a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b + 50a b )cosh(x) + 10a b + 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 240b - 240a b - 240a b - 240a b - 240a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b - 124a b - 134a b - 134a b - 144a b - 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 100b - 96a b - 96a b - 98a b - 98a b)cosh(x) - 20a b - 20a b +--R + +--R 3 2 4 5 +--R - 20a b - 20a b - 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (210a b + 210a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (185a b + 185a b )cosh(x) + (74a b + 74a b)cosh(x) + 15a b +--R + +--R 3 2 +--R 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 420b - 420a b - 420a b - 420a b - 420a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (90b - 246a b - 291a b - 291a b - 336a b - 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 370b - 334a b - 334a b - 352a b - 352a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b - 138a b - 143a b - 143a b - 148a b - 148a )cosh(x) - 30b +--R + +--R 4 2 3 3 2 4 +--R - 30a b - 30a b - 30a b - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (252a b + 252a b )cosh(x) + (252a b + 252a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (400a b + 400a b )cosh(x) + (240a b + 240a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 504b - 504a b - 504a b - 504a b - 504a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (240b - 264a b - 384a b - 384a b - 504a b - 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 800b - 656a b - 656a b - 728a b - 728a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b - 400a b - 440a b - 440a b - 480a b - 480a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 200b - 184a b - 184a b - 192a b - 192a b)cosh(x) - 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b - 40a b + 24a b + 24a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (210a b + 210a b )cosh(x) + (252a b + 252a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (560a b + 560a b )cosh(x) + (448a b + 448a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (290a b + 290a b )cosh(x) + (116a b + 116a b)cosh(x) + 20a b +--R + +--R 3 2 +--R 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 420b - 420a b - 420a b - 420a b - 420a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (420b - 84a b - 294a b - 294a b - 504a b - 504a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 1120b - 784a b - 784a b - 952a b - 952a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (280b - 616a b - 756a b - 756a b - 896a b - 896a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 580b - 468a b - 468a b - 524a b - 524a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 212a b - 222a b - 222a b + 88a b + 88a )cosh(x) - 40b +--R + +--R 4 2 3 3 2 4 +--R - 40a b - 40a b - 40a b - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (120a b + 120a b )cosh(x) + (168a b + 168a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (532a b + 532a b )cosh(x) + (532a b + 532a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (480a b + 480a b )cosh(x) + (288a b + 288a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (100a b + 100a b )cosh(x) + 20a b + 20a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 240b - 240a b - 240a b - 240a b - 240a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (504b + 168a b - 84a b - 84a b - 336a b - 336a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 1064b - 560a b - 560a b - 812a b - 812a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (560b - 504a b - 784a b - 784a b - 1064a b - 1064a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 960b - 624a b - 624a b - 792a b - 792a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (120b - 456a b - 516a b - 516a b + 64a b + 64a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 200b - 176a b - 176a b - 188a b - 188a b)cosh(x) - 40a b +--R + +--R 2 3 3 2 4 5 +--R - 40a b - 40a b + 24a b + 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (45a b + 45a b )cosh(x) + (72a b + 72a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (350a b + 350a b )cosh(x) + (420a b + 420a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (500a b + 500a b )cosh(x) + (400a b + 400a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 +--R (210a b + 210a b )cosh(x) + (84a b + 84a b)cosh(x) + 15a b +--R + +--R 3 2 +--R 15a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 90b - 90a b - 90a b - 90a b - 90a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (420b + 276a b + 66a b + 66a b - 144a b - 144a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 700b - 196a b - 196a b - 448a b - 448a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (700b - 140a b - 490a b - 490a b - 840a b - 840a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 1000b - 440a b - 440a b - 720a b - 720a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (300b - 500a b - 650a b - 650a b - 160a b - 160a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 420b - 300a b - 300a b - 360a b - 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 148a b - 158a b - 158a b + 152a b + 152a )cosh(x) - 30b +--R + +--R 4 2 3 3 2 4 +--R - 30a b - 30a b - 30a b - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b + 10a b )cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (160a b + 160a b )cosh(x) + (224a b + 224a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (340a b + 340a b )cosh(x) + (340a b + 340a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (240a b + 240a b )cosh(x) + (144a b + 144a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (50a b + 50a b )cosh(x) + 10a b + 10a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (- 20b - 20a b - 20a b - 20a b - 20a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (240b + 204a b + 84a b + 84a b - 36a b - 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 320b + 16a b + 16a b - 152a b - 152a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (560b + 112a b - 168a b - 168a b - 448a b - 448a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 680b - 120a b - 120a b - 400a b - 400a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (400b - 280a b - 480a b - 480a b - 360a b - 360a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 480b - 240a b - 240a b - 360a b - 360a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (80b - 208a b - 248a b - 248a b + 352a b + 352a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 100b - 84a b - 84a b - 92a b - 92a b)cosh(x) - 20a b - 20a b +--R + +--R 3 2 4 5 +--R - 20a b - 20a b - 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b + a b )cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (50a b + 50a b )cosh(x) + (80a b + 80a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (150a b + 150a b )cosh(x) + (180a b + 180a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (160a b + 160a b )cosh(x) + (128a b + 128a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (65a b + 65a b )cosh(x) + (26a b + 26a b)cosh(x) + 6a b + 6a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 4 10 +--R (- 2b - 2a b - 2a b - 2a b - 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (90b + 86a b + 41a b + 41a b - 4a b - 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 100b + 44a b + 44a b - 28a b - 28a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (280b + 120a b - 20a b - 20a b - 160a b - 160a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 300b + 36a b + 36a b - 132a b - 132a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (300b - 60a b - 210a b - 210a b - 296a b - 296a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 320b - 80a b - 80a b - 200a b - 200a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (120b - 136a b - 196a b - 196a b + 384a b + 384a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 130b - 82a b - 82a b - 106a b - 106a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (10b - 42a b - 47a b - 47a b - 52a b - 52a )cosh(x) - 12b +--R + +--R 4 2 3 3 2 4 +--R - 12a b - 12a b - 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 9 3 2 4 8 +--R (10a b + 10a b )cosh(x) + (18a b + 18a b)cosh(x) +--R + +--R 2 3 3 2 7 3 2 4 6 +--R (40a b + 40a b )cosh(x) + (56a b + 56a b)cosh(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R (60a b + 60a b )cosh(x) + (60a b + 60a b)cosh(x) +--R + +--R 2 3 3 2 3 3 2 4 2 +--R (40a b + 40a b )cosh(x) + (24a b + 24a b)cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (10a b + 10a b )cosh(x) + 2a b + 2a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 10 +--R (20b + 20a b + 10a b + 10a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (- 20b + 16a b + 16a b - 2a b - 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (80b + 44a b + 4a b + 4a b - 36a b - 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 80b + 32a b + 32a b - 24a b - 24a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (120b + 8a b - 52a b - 52a b - 112a b - 112a )cosh(x) +--R + +--R 5 3 2 4 5 +--R (- 120b - 60a b - 60a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (80b - 40a b - 80a b - 80a b + 200a b + 200a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 80b - 32a b - 32a b - 56a b - 56a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (20b - 28a b - 38a b - 38a b - 48a b - 48a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (- 20b - 16a b - 16a b - 18a b - 18a b)cosh(x) - 4a b - 4a b +--R + +--R 3 2 4 5 +--R - 4a b - 4a b - 4a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 10 3 2 4 9 +--R (a b + a b )cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 2 3 3 2 8 3 2 4 7 +--R (5a b + 5a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 2 3 3 2 6 3 2 4 5 +--R (10a b + 10a b )cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 2 3 3 2 4 3 2 4 3 +--R (10a b + 10a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 2 3 3 2 2 3 2 4 2 3 3 2 +--R (5a b + 5a b )cosh(x) + (2a b + 2a b)cosh(x) + a b + a b +--R * +--R sech(x) +--R + +--R 5 4 2 3 3 2 11 5 4 2 3 10 +--R (2b + 2a b + a b + a b )cosh(x) + (- 2b + 2a b + 2a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (10b + 6a b + a b + a b - 4a b - 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 10b + 6a b + 6a b - 2a b - 2a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (20b + 4a b - 6a b - 6a b - 16a b - 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 20b + 4a b + 4a b - 8a b - 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (20b - 4a b - 14a b - 14a b + 40a b + 40a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 20b - 4a b - 4a b - 12a b - 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (10b - 6a b - 11a b - 11a b - 16a b - 16a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 10b - 6a b - 6a b - 8a b - 8a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 2 3 +--R (2b - 2a b - 3a b - 3a b - 4a b - 4a )cosh(x) - 2b - 2a b - 2a b +--R + +--R 3 2 4 +--R - 2a b - 2a b +--R / +--R 4 2 5 12 +--R (2a b - 2a b)sinh(x) +--R + +--R 4 2 5 5 6 11 +--R ((20a b - 20a b)cosh(x) + 4a b - 4a )sinh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R ((90a b - 90a b)cosh(x) + (36a b - 36a )cosh(x) + 12a b - 12a b) +--R * +--R 10 +--R sinh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (240a b - 240a b)cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b - 100a b)cosh(x) + 20a b - 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (420a b - 420a b)cosh(x) + (336a b - 336a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (370a b - 370a b)cosh(x) + (148a b - 148a )cosh(x) + 30a b +--R + +--R 5 +--R - 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (504a b - 504a b)cosh(x) + (504a b - 504a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (800a b - 800a b)cosh(x) + (480a b - 480a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b - 200a b)cosh(x) + 40a b - 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (420a b - 420a b)cosh(x) + (504a b - 504a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1120a b - 1120a b)cosh(x) + (896a b - 896a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (580a b - 580a b)cosh(x) + (232a b - 232a )cosh(x) + 40a b +--R + +--R 5 +--R - 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (240a b - 240a b)cosh(x) + (336a b - 336a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (1064a b - 1064a b)cosh(x) + (1064a b - 1064a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (960a b - 960a b)cosh(x) + (576a b - 576a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b - 200a b)cosh(x) + 40a b - 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (90a b - 90a b)cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (700a b - 700a b)cosh(x) + (840a b - 840a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1000a b - 1000a b)cosh(x) + (800a b - 800a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 +--R (420a b - 420a b)cosh(x) + (168a b - 168a )cosh(x) + 30a b +--R + +--R 5 +--R - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b - 20a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (320a b - 320a b)cosh(x) + (448a b - 448a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (680a b - 680a b)cosh(x) + (680a b - 680a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (480a b - 480a b)cosh(x) + (288a b - 288a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b - 100a b)cosh(x) + 20a b - 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (100a b - 100a b)cosh(x) + (160a b - 160a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (300a b - 300a b)cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (320a b - 320a b)cosh(x) + (256a b - 256a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (130a b - 130a b)cosh(x) + (52a b - 52a )cosh(x) + 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b - 20a b)cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (80a b - 80a b)cosh(x) + (112a b - 112a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (120a b - 120a b)cosh(x) + (120a b - 120a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (80a b - 80a b)cosh(x) + (48a b - 48a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (20a b - 20a b)cosh(x) + 4a b - 4a +--R * +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (10a b - 10a b)cosh(x) + (16a b - 16a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (20a b - 20a b)cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (20a b - 20a b)cosh(x) + (16a b - 16a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (10a b - 10a b)cosh(x) + (4a b - 4a )cosh(x) + 2a b - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 2 5 12 4 2 5 5 6 11 +--R (2a b + 2a b)sinh(x) + ((20a b + 20a b)cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R ((90a b + 90a b)cosh(x) + (36a b + 36a )cosh(x) + 12a b + 12a b) +--R * +--R 10 +--R sinh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (240a b + 240a b)cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b + 100a b)cosh(x) + 20a b + 20a +--R * +--R 9 +--R sinh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (420a b + 420a b)cosh(x) + (336a b + 336a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (370a b + 370a b)cosh(x) + (148a b + 148a )cosh(x) + 30a b + 30a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (504a b + 504a b)cosh(x) + (504a b + 504a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (800a b + 800a b)cosh(x) + (480a b + 480a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b + 200a b)cosh(x) + 40a b + 40a +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (420a b + 420a b)cosh(x) + (504a b + 504a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1120a b + 1120a b)cosh(x) + (896a b + 896a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (580a b + 580a b)cosh(x) + (232a b + 232a )cosh(x) + 40a b + 40a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (240a b + 240a b)cosh(x) + (336a b + 336a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (1064a b + 1064a b)cosh(x) + (1064a b + 1064a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (960a b + 960a b)cosh(x) + (576a b + 576a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (200a b + 200a b)cosh(x) + 40a b + 40a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (90a b + 90a b)cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (700a b + 700a b)cosh(x) + (840a b + 840a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (1000a b + 1000a b)cosh(x) + (800a b + 800a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (420a b + 420a b)cosh(x) + (168a b + 168a )cosh(x) + 30a b + 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b + 20a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (320a b + 320a b)cosh(x) + (448a b + 448a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (680a b + 680a b)cosh(x) + (680a b + 680a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (480a b + 480a b)cosh(x) + (288a b + 288a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (100a b + 100a b)cosh(x) + 20a b + 20a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 4 2 5 8 5 6 7 +--R (100a b + 100a b)cosh(x) + (160a b + 160a )cosh(x) +--R + +--R 4 2 5 6 5 6 5 +--R (300a b + 300a b)cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 4 2 5 4 5 6 3 +--R (320a b + 320a b)cosh(x) + (256a b + 256a )cosh(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (130a b + 130a b)cosh(x) + (52a b + 52a )cosh(x) + 12a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 5 9 5 6 8 +--R (20a b + 20a b)cosh(x) + (36a b + 36a )cosh(x) +--R + +--R 4 2 5 7 5 6 6 +--R (80a b + 80a b)cosh(x) + (112a b + 112a )cosh(x) +--R + +--R 4 2 5 5 5 6 4 +--R (120a b + 120a b)cosh(x) + (120a b + 120a )cosh(x) +--R + +--R 4 2 5 3 5 6 2 +--R (80a b + 80a b)cosh(x) + (48a b + 48a )cosh(x) +--R + +--R 4 2 5 5 6 +--R (20a b + 20a b)cosh(x) + 4a b + 4a +--R * +--R sinh(x) +--R + +--R 4 2 5 10 5 6 9 4 2 5 8 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) + (10a b + 10a b)cosh(x) +--R + +--R 5 6 7 4 2 5 6 +--R (16a b + 16a )cosh(x) + (20a b + 20a b)cosh(x) +--R + +--R 5 6 5 4 2 5 4 +--R (24a b + 24a )cosh(x) + (20a b + 20a b)cosh(x) +--R + +--R 5 6 3 4 2 5 2 5 6 +--R (16a b + 16a )cosh(x) + (10a b + 10a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 4 2 5 +--R 2a b + 2a b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 530 +t0553:= sech(x)^2/(a+a*cosh(x)) +--R +--R +--R 2 +--R sech(x) +--R (286) ------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 288 + +--S 289 of 530 +r0553:= -atan(sinh(x))/a+sinh(x)/a/(1+cosh(x))+tanh(x)/a +--R +--R +--R (- cosh(x) - 1)atan(sinh(x)) + (cosh(x) + 1)tanh(x) + sinh(x) +--R (287) ------------------------------------------------------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 530 +a0553:= integrate(t0553,x) +--R +--R +--R (288) +--R 3 2 +--R - 2sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (- 6cosh(x) - 4cosh(x) - 2)sinh(x) - 2cosh(x) - 2cosh(x) +--R + +--R - 2cosh(x) - 2 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R - 2sinh(x) + (- 4cosh(x) - 2)sinh(x) - 2cosh(x) - 2cosh(x) - 4 +--R / +--R 3 2 +--R a sinh(x) + (3a cosh(x) + a)sinh(x) +--R + +--R 2 3 2 +--R (3a cosh(x) + 2a cosh(x) + a)sinh(x) + a cosh(x) + a cosh(x) +--R + +--R a cosh(x) + a +--R Type: Union(Expression(Integer),...) +--E 290 + +--S 291 of 530 +m0553:= a0553-r0553 +--R +--R +--R (289) +--R 3 2 2 +--R (- 2cosh(x) - 2)sinh(x) + (- 6cosh(x) - 8cosh(x) - 2)sinh(x) +--R + +--R 3 2 4 +--R (- 6cosh(x) - 10cosh(x) - 6cosh(x) - 2)sinh(x) - 2cosh(x) +--R + +--R 3 2 +--R - 4cosh(x) - 4cosh(x) - 4cosh(x) - 2 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 2 2 +--R (cosh(x) + 1)sinh(x) + (3cosh(x) + 4cosh(x) + 1)sinh(x) +--R + +--R 3 2 4 3 +--R (3cosh(x) + 5cosh(x) + 3cosh(x) + 1)sinh(x) + cosh(x) + 2cosh(x) +--R + +--R 2 +--R 2cosh(x) + 2cosh(x) + 1 +--R * +--R atan(sinh(x)) +--R + +--R 3 2 2 +--R (- cosh(x) - 1)sinh(x) + (- 3cosh(x) - 4cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 +--R (- 3cosh(x) - 5cosh(x) - 3cosh(x) - 1)sinh(x) - cosh(x) +--R + +--R 3 2 +--R - 2cosh(x) - 2cosh(x) - 2cosh(x) - 1 +--R * +--R tanh(x) +--R + +--R 4 3 +--R - sinh(x) + (- 3cosh(x) - 1)sinh(x) +--R + +--R 2 2 +--R (- 3cosh(x) - 4cosh(x) - 3)sinh(x) +--R + +--R 3 2 3 2 +--R (- cosh(x) - 5cosh(x) - 7cosh(x) - 3)sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R - 6cosh(x) - 4 +--R / +--R 3 2 2 +--R (a cosh(x) + a)sinh(x) + (3a cosh(x) + 4a cosh(x) + a)sinh(x) +--R + +--R 3 2 4 +--R (3a cosh(x) + 5a cosh(x) + 3a cosh(x) + a)sinh(x) + a cosh(x) +--R + +--R 3 2 +--R 2a cosh(x) + 2a cosh(x) + 2a cosh(x) + a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 530 +d0553:= D(m0553,x) +--R +--R +--R (290) +--R 2 8 +--R (cosh(x) + 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 7 +--R (6cosh(x) + 14cosh(x) + 10cosh(x) + 2)sinh(x) +--R + +--R 4 3 2 6 +--R (15cosh(x) + 40cosh(x) + 39cosh(x) + 18cosh(x) + 4)sinh(x) +--R + +--R 5 4 3 2 +--R (20cosh(x) + 60cosh(x) + 78cosh(x) + 62cosh(x) + 30cosh(x) + 6) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 15cosh(x) + 50cosh(x) + 88cosh(x) + 108cosh(x) + 83cosh(x) +--R + +--R 34cosh(x) + 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) + 22cosh(x) + 58cosh(x) + 106cosh(x) + 114cosh(x) +--R + +--R 2 +--R 74cosh(x) + 30cosh(x) + 6 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 4cosh(x) + 23cosh(x) + 62cosh(x) + 87cosh(x) +--R + +--R 3 2 +--R 80cosh(x) + 53cosh(x) + 22cosh(x) + 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) + 22cosh(x) + 38cosh(x) + 46cosh(x) + 42cosh(x) +--R + +--R 2 +--R 26cosh(x) + 10cosh(x) + 2 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 4cosh(x) + 8cosh(x) + 12cosh(x) + 14cosh(x) +--R + +--R 3 2 +--R 12cosh(x) + 8cosh(x) + 4cosh(x) + 1 +--R * +--R 2 +--R tanh(x) +--R + +--R 10 9 2 8 +--R sinh(x) + (6cosh(x) + 2)sinh(x) + (13cosh(x) + 7cosh(x) + 3)sinh(x) +--R + +--R 3 2 7 +--R (8cosh(x) - 2cosh(x) + 6cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 6 +--R (- 15cosh(x) - 44cosh(x) - 18cosh(x) + cosh(x) + 2)sinh(x) +--R + +--R 5 4 3 2 5 +--R (- 34cosh(x) - 84cosh(x) - 70cosh(x) - 36cosh(x) + 8)sinh(x) +--R + +--R 6 5 4 3 2 +--R - 29cosh(x) - 68cosh(x) - 83cosh(x) - 77cosh(x) - 26cosh(x) +--R + +--R cosh(x) - 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 12cosh(x) - 18cosh(x) - 34cosh(x) - 64cosh(x) - 56cosh(x) +--R + +--R 2 +--R - 34cosh(x) - 10cosh(x) + 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 2cosh(x) + 8cosh(x) + 8cosh(x) - 21cosh(x) - 45cosh(x) +--R + +--R 3 2 +--R - 34cosh(x) - 2cosh(x) + 3cosh(x) - 3 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R 6cosh(x) + 10cosh(x) - 14cosh(x) - 4cosh(x) + 14cosh(x) +--R + +--R - 10cosh(x) - 2 +--R * +--R sinh(x) +--R + +--R 9 8 7 6 5 4 +--R cosh(x) + 2cosh(x) + cosh(x) - cosh(x) + 3cosh(x) + 7cosh(x) +--R + +--R 3 2 +--R - cosh(x) - 7cosh(x) - 4cosh(x) - 1 +--R / +--R 2 8 +--R (a cosh(x) + 2a cosh(x) + a)sinh(x) +--R + +--R 3 2 7 +--R (6a cosh(x) + 14a cosh(x) + 10a cosh(x) + 2a)sinh(x) +--R + +--R 4 3 2 6 +--R (15a cosh(x) + 40a cosh(x) + 39a cosh(x) + 18a cosh(x) + 4a)sinh(x) +--R + +--R 5 4 3 2 +--R 20a cosh(x) + 60a cosh(x) + 78a cosh(x) + 62a cosh(x) +--R + +--R 30a cosh(x) + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 15a cosh(x) + 50a cosh(x) + 88a cosh(x) + 108a cosh(x) +--R + +--R 2 +--R 83a cosh(x) + 34a cosh(x) + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 6a cosh(x) + 22a cosh(x) + 58a cosh(x) + 106a cosh(x) +--R + +--R 3 2 +--R 114a cosh(x) + 74a cosh(x) + 30a cosh(x) + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R a cosh(x) + 4a cosh(x) + 23a cosh(x) + 62a cosh(x) + 87a cosh(x) +--R + +--R 3 2 +--R 80a cosh(x) + 53a cosh(x) + 22a cosh(x) + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 6a cosh(x) + 22a cosh(x) + 38a cosh(x) + 46a cosh(x) +--R + +--R 3 2 +--R 42a cosh(x) + 26a cosh(x) + 10a cosh(x) + 2a +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R a cosh(x) + 4a cosh(x) + 8a cosh(x) + 12a cosh(x) + 14a cosh(x) +--R + +--R 3 2 +--R 12a cosh(x) + 8a cosh(x) + 4a cosh(x) + a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 530 +t0554:= sinh(x)/(a+b*tanh(x)) +--R +--R +--R sinh(x) +--R (291) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 293 + +--S 294 of 530 +r0554:= a*b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ + a*cosh(x)/(a^2-b^2)-b*sinh(x)/(a^2-b^2) +--R +--R +--R (292) +--R +---------+ +--R a sinh(x) + b cosh(x) | 2 2 +--R - a b atan(---------------------) + (b sinh(x) - a cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ----------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 530 +a0554:= integrate(t0554,x) +--R +--R +--R (293) +--R [ +--R (2a b sinh(x) + 2a b cosh(x)) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) - b - a) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R (4a b sinh(x) + 4a b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) - b - a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 295 + +--S 296 of 530 +m0554a:= a0554.1-r0554 +--R +--R +--R (294) +--R +---------+ +--R | 2 2 +--R (2a b sinh(x) + 2a b cosh(x))\|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R (2a b sinh(x) + 2a b cosh(x))\|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R ((- b - a)sinh(x) + (b + a)cosh(x) - b - a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 | 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a \|b - a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 530 +d0554a:= D(m0554a,x) +--R +--R +--R (295) +--R 2 2 3 4 6 3 2 2 3 4 5 +--R (a b + 2a b + a )sinh(x) + (2a b + 6a b + 6a b + 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 4 +--R ((b + 6a b + 9a b + 4a b)cosh(x) - b + 2a b + 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (2b + 4a b - 4a b - 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b + 2a b + 6a b + 6a b + 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 4a b - 9a b - 6a b - a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 4 +--R (8a b + 8a b + 8a b)cosh(x) - a b - 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 2b - 6a b - 6a b - 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 4 4 +--R (4b + 6a b + 6a b + 2a b - 2a )cosh(x) + (- 2b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 2 2 4 4 +--R (- b - 2a b - a b )cosh(x) + (3b + 2a b - a )cosh(x) +--R + +--R 4 3 2 2 2 4 2 2 4 +--R (- 3b + 2a b + a b )cosh(x) + b - 2a b + a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 297 + +--S 298 of 530 +m0554b:= a0554.2-r0554 +--R +--R +--R (296) +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R (4a b sinh(x) + 4a b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R a sinh(x) + b cosh(x) +--R (2a b sinh(x) + 2a b cosh(x))atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((- b - a)sinh(x) + (b + a)cosh(x) - b - a)\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 530 +d0554b:= D(m0554b,x) +--R +--R +--R (297) +--R 2 2 3 4 6 3 2 2 3 4 5 +--R (a b + 2a b + a )sinh(x) + (2a b + 6a b + 6a b + 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 4 +--R ((b + 6a b + 9a b + 4a b)cosh(x) - b + 2a b + 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (2b + 4a b - 4a b - 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b + 2a b + 6a b + 6a b + 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 4a b - 9a b - 6a b - a )cosh(x) +--R + +--R 3 2 2 3 2 2 2 3 4 +--R (8a b + 8a b + 8a b)cosh(x) - a b - 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 2b - 6a b - 6a b - 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 4 4 +--R (4b + 6a b + 6a b + 2a b - 2a )cosh(x) + (- 2b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 2 2 4 4 +--R (- b - 2a b - a b )cosh(x) + (3b + 2a b - a )cosh(x) +--R + +--R 4 3 2 2 2 4 2 2 4 +--R (- 3b + 2a b + a b )cosh(x) + b - 2a b + a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 299 + +--S 300 of 530 +t0555:= sinh(x)^2/(a+b*tanh(x)) +--R +--R +--R 2 +--R sinh(x) +--R (298) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 300 + +--S 301 of 530 +r0555:= 1/2*(-a^3*x+sinh(x)*a^3*cosh(x)-b*cosh(x)^2*a^2+_ + 2*a^2*b*log(a*cosh(x)+b*sinh(x))-sinh(x)*b^2*a*cosh(x)-_ + a*b^2*x+b^3*cosh(x)^2)/(b^4+a^4-2*a^2*b^2) +--R +--R +--R (299) +--R 2 2 3 +--R 2a b log(b sinh(x) + a cosh(x)) + (- a b + a )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (b - a b)cosh(x) + (- a b - a )x +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 530 +a0555:= integrate(t0555,x) +--R +--R +--R (300) +--R 2 2 2 2 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 2 3 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (- 4a b - 8a b - 4a )x)sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (- 8a b - 16a b - 8a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 2 2 3 2 3 +--R (b - a b - a b + a )cosh(x) + (- 4a b - 8a b - 4a )x cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 302 + +--S 303 of 530 +m0555:= a0555-r0555 +--R +--R +--R (301) +--R 2 2 2 2 2 +--R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 2 2 2 2 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (b - a b - a b + a )sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 2 +--R ((2b + 2a b - 2a b - 2a )cosh(x) - 8a b x)sinh(x) +--R + +--R 3 2 3 2 +--R ((- 4b + 4a b)cosh(x) - 16a b x cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 2 2 3 2 2 3 +--R (- 3b - a b + 3a b + a )cosh(x) - 8a b x cosh(x) + b + a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 303 + +--S 304 of 530 +d0555:= D(m0555,x) +--R +--R +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 +--R (302) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression(Integer) +--E 304 + +--S 305 of 530 +t0556:= sinh(x)^4/(a+b*tanh(x)) +--R +--R +--R 4 +--R sinh(x) +--R (303) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 530 +r0556:= -1/8*(-6*a^3*b^2*x+12*a^2*b^3*cosh(x)^2+a*x*b^4-_ + 8*a^4*b*cosh(x)^2-6*a^3*b^2*sinh(x)*cosh(x)+_ + a*b^4*sinh(x)*cosh(x)+8*a^4*b*log(a*cosh(x)+b*sinh(x))+_ + 2*b^5*cosh(x)^4-2*a^5*sinh(x)*cosh(x)^3+2*a^4*b*cosh(x)^4-_ + 4*a^2*b^3*cosh(x)^4-3*a^5*x+4*a^3*b^2*sinh(x)*cosh(x)^3-_ + 2*a*b^4*sinh(x)*cosh(x)^3+5*a^5*sinh(x)*cosh(x)-_ + 4*b^5*cosh(x)^2)/(3*b^4*a^2-b^6+a^6-3*b^2*a^4) +--R +--R +--R (304) +--R 4 +--R 8a b log(b sinh(x) + a cosh(x)) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((- 2a b + 4a b - 2a )cosh(x) + (a b - 6a b + 5a )cosh(x))sinh(x) +--R + +--R 5 2 3 4 4 5 2 3 4 2 +--R (2b - 4a b + 2a b)cosh(x) + (- 4b + 12a b - 8a b)cosh(x) +--R + +--R 4 3 2 5 +--R (a b - 6a b - 3a )x +--R / +--R 6 2 4 4 2 6 +--R 8b - 24a b + 24a b - 8a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 530 +a0556:= integrate(t0556,x) +--R +--R +--R (305) +--R 4 4 4 3 4 2 2 +--R 64a b sinh(x) + 256a b cosh(x)sinh(x) + 384a b cosh(x) sinh(x) +--R + +--R 4 3 4 4 +--R 256a b cosh(x) sinh(x) + 64a b cosh(x) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) - 4b +--R + +--R 2 3 3 2 4 5 +--R 16a b - 8a b - 12a b + 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (56b - 56a b - 112a b + 112a b + 56a b - 56a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 +--R (- 24b + 96a b - 48a b - 72a b + 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (70b - 70a b - 140a b + 140a b + 70a b - 70a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (- 60b + 240a b - 120a b - 180a b + 120a )cosh(x) +--R + +--R 4 3 2 4 5 +--R (8a b - 48a b - 64a b - 24a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (56b - 56a b - 112a b + 112a b + 56a b - 56a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 80b + 320a b - 160a b - 240a b + 160a )cosh(x) +--R + +--R 4 3 2 4 5 +--R (32a b - 192a b - 256a b - 96a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (- 60b + 240a b - 120a b - 180a b + 120a )cosh(x) +--R + +--R 4 3 2 4 5 2 5 2 3 3 2 +--R (48a b - 288a b - 384a b - 144a )x cosh(x) - 4b + 16a b + 8a b +--R + +--R 4 5 +--R - 12a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (- 24b + 96a b - 48a b - 72a b + 48a )cosh(x) +--R + +--R 4 3 2 4 5 3 +--R (32a b - 192a b - 256a b - 96a )x cosh(x) +--R + +--R 5 2 3 3 2 4 5 +--R (- 8b + 32a b + 16a b - 24a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 6 +--R (- 4b + 16a b - 8a b - 12a b + 8a )cosh(x) +--R + +--R 4 3 2 4 5 4 +--R (8a b - 48a b - 64a b - 24a )x cosh(x) +--R + +--R 5 2 3 3 2 4 5 2 5 4 2 3 +--R (- 4b + 16a b + 8a b - 12a b - 8a )cosh(x) + b + a b - 2a b +--R + +--R 3 2 4 5 +--R - 2a b + a b + a +--R / +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x)sinh(x) +--R + +--R 6 2 4 4 2 6 2 2 +--R (384b - 1152a b + 1152a b - 384a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 307 + +--S 308 of 530 +m0556:= a0556-r0556 +--R +--R +--R (306) +--R 4 4 4 3 4 2 2 +--R - 64a b sinh(x) - 256a b cosh(x)sinh(x) - 384a b cosh(x) sinh(x) +--R + +--R 4 3 4 4 +--R - 256a b cosh(x) sinh(x) - 64a b cosh(x) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 4 4 4 3 4 2 2 +--R 64a b sinh(x) + 256a b cosh(x)sinh(x) + 384a b cosh(x) sinh(x) +--R + +--R 4 3 4 4 +--R 256a b cosh(x) sinh(x) + 64a b cosh(x) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) - 4b +--R + +--R 2 3 3 2 4 5 +--R 16a b - 8a b - 12a b + 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (56b - 40a b - 112a b + 80a b + 56a b - 40a )cosh(x) +--R + +--R 5 4 2 3 4 5 +--R (- 24b - 8a b + 96a b - 72a b + 8a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (54b - 6a b - 108a b + 12a b + 54a b - 6a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 4 +--R (- 28b - 32a b + 144a b + 72a b - 116a b - 40a )cosh(x) - 64a b x +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 8b + 40a b + 16a b - 80a b - 8a b + 40a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (48b - 48a b - 64a b + 128a b + 16a b - 80a )cosh(x) +--R + +--R 4 +--R - 256a b x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 68b + 36a b + 136a b - 72a b - 68a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (132b - 32a b - 336a b + 72a b + 204a b - 40a )cosh(x) +--R + +--R 4 2 5 2 3 3 2 4 5 +--R - 384a b x cosh(x) - 4b + 16a b + 8a b - 12a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 56b + 8a b + 112a b - 16a b - 56a b + 8a )cosh(x) +--R + +--R 5 4 2 3 4 5 5 4 3 +--R (104b - 8a b - 288a b + 184a b + 8a )cosh(x) - 256a b x cosh(x) +--R + +--R 5 2 3 3 2 4 5 +--R (- 8b + 32a b + 16a b - 24a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 15b - a b + 30a b + 2a b - 15a b - a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 6 4 4 +--R (28b - 80a b - 8a b + 52a b + 8a )cosh(x) - 64a b x cosh(x) +--R + +--R 5 2 3 3 2 4 5 2 5 4 2 3 +--R (- 4b + 16a b + 8a b - 12a b - 8a )cosh(x) + b + a b - 2a b +--R + +--R 3 2 4 5 +--R - 2a b + a b + a +--R / +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x)sinh(x) +--R + +--R 6 2 4 4 2 6 2 2 +--R (384b - 1152a b + 1152a b - 384a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )cosh(x) +--R Type: Expression(Integer) +--E 308 + +--S 309 of 530 +d0556:= D(m0556,x) +--R +--R +--R (307) +--R 2 2 8 2 2 7 +--R (b - 2a b + a )sinh(x) + (8b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((28b - 44a b + 16a )cosh(x) - 2b + 6a )sinh(x) +--R + +--R 2 2 3 2 2 5 +--R ((40b - 48a b + 8a )cosh(x) + (4b - 12a b + 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 4 +--R ((6b - 6a )cosh(x) + (34b - 48a b + 10a )cosh(x) )sinh(x) +--R + +--R 2 2 5 2 3 3 +--R ((- 40b + 48a b - 8a )cosh(x) + (56b - 72a b)cosh(x) )sinh(x) +--R + +--R 2 2 6 2 2 4 2 +--R (- 36b + 44a b - 8a )cosh(x) + (34b - 48a b + 10a )cosh(x) + 2b +--R + +--R 2 +--R - 2a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 8b + 16a b - 8a )cosh(x) + (4b - 12a b + 16a )cosh(x) +--R + +--R 2 2 +--R (4b - 4a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (b + 2a b - 3a )cosh(x) + (- 2b + 6a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (2b - 2a b - 4a )cosh(x) - b + a +--R / +--R 3 2 2 3 4 +--R (16b - 16a b - 16a b + 16a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (64b - 64a b - 64a b + 64a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (96b - 96a b - 96a b + 96a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 +--R (64b - 64a b - 64a b + 64a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (16b - 16a b - 16a b + 16a )cosh(x) +--R Type: Expression(Integer) +--E 309 + +--S 310 of 530 +t0557:= sinh(x)/(1+tanh(x)) +--R +--R +--R sinh(x) +--R (308) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 310 + +--S 311 of 530 +r0557:= 1/3*cosh(x)^3-1/3*sinh(x)^3 +--R +--R +--R 3 3 +--R - sinh(x) + cosh(x) +--R (309) --------------------- +--R 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 530 +a0557:= integrate(t0557,x) +--R +--R +--R 2 2 +--R sinh(x) + cosh(x)sinh(x) + cosh(x) +--R (310) ------------------------------------ +--R 3sinh(x) + 3cosh(x) +--R Type: Union(Expression(Integer),...) +--E 312 + +--S 313 of 530 +m0557:= a0557-r0557 +--R +--R +--R (311) +--R 4 3 2 3 +--R sinh(x) + cosh(x)sinh(x) + sinh(x) + (- cosh(x) + cosh(x))sinh(x) +--R + +--R 4 2 +--R - cosh(x) + cosh(x) +--R / +--R 3sinh(x) + 3cosh(x) +--R Type: Expression(Integer) +--E 313 + +--S 314 of 530 +d0557:= D(m0557,x) +--R +--R +--R 3 3 +--R cosh(x)sinh(x) + (- cosh(x) + cosh(x))sinh(x) +--R (312) ----------------------------------------------- +--R sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 314 + +--S 315 of 530 +t0558:= sinh(x)^2/(1+tanh(x)) +--R +--R +--R 2 +--R sinh(x) +--R (313) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 530 +r0558:= -1/8*x-1/8*cosh(x)*sinh(x)+1/4*cosh(x)^3*sinh(x)-1/4*sinh(x)^4 +--R +--R +--R 4 3 +--R - 2sinh(x) + (2cosh(x) - cosh(x))sinh(x) - x +--R (314) ---------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 530 +a0558:= integrate(t0558,x) +--R +--R +--R (315) +--R 3 2 2 3 +--R 3sinh(x) + 3cosh(x)sinh(x) + (9cosh(x) - 4x - 2)sinh(x) + cosh(x) +--R + +--R (- 4x + 2)cosh(x) +--R / +--R 32sinh(x) + 32cosh(x) +--R Type: Union(Expression(Integer),...) +--E 317 + +--S 318 of 530 +m0558:= a0558-r0558 +--R +--R +--R (316) +--R 5 4 3 +--R 8sinh(x) + 8cosh(x)sinh(x) + 3sinh(x) +--R + +--R 3 2 4 2 +--R (- 8cosh(x) + 7cosh(x))sinh(x) + (- 8cosh(x) + 13cosh(x) - 2)sinh(x) +--R + +--R 3 +--R cosh(x) + 2cosh(x) +--R / +--R 32sinh(x) + 32cosh(x) +--R Type: Expression(Integer) +--E 318 + +--S 319 of 530 +d0558:= D(m0558,x) +--R +--R +--R (317) +--R 4 2 3 +--R 8cosh(x)sinh(x) + (2cosh(x) + 1)sinh(x) +--R + +--R 3 2 4 2 +--R (- 6cosh(x) + 7cosh(x))sinh(x) + (- 2cosh(x) + cosh(x) + 1)sinh(x) +--R + +--R 5 3 +--R - 2cosh(x) + 3cosh(x) - cosh(x) +--R / +--R 8sinh(x) + 8cosh(x) +--R Type: Expression(Integer) +--E 319 + +--S 320 of 530 +t0559:= sinh(x)^3/(1+tanh(x)) +--R +--R +--R 3 +--R sinh(x) +--R (318) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 530 +r0559:= -1/3*cosh(x)^3+1/5*cosh(x)^5-1/5*sinh(x)^5 +--R +--R +--R 5 5 3 +--R - 3sinh(x) + 3cosh(x) - 5cosh(x) +--R (319) ----------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 530 +a0559:= integrate(t0559,x) +--R +--R +--R (320) +--R 4 3 2 2 +--R sinh(x) + cosh(x)sinh(x) + (6cosh(x) - 5)sinh(x) +--R + +--R 3 4 2 +--R (cosh(x) - 5cosh(x))sinh(x) + cosh(x) - 5cosh(x) +--R / +--R 30sinh(x) + 30cosh(x) +--R Type: Union(Expression(Integer),...) +--E 322 + +--S 323 of 530 +m0559:= a0559-r0559 +--R +--R +--R (321) +--R 6 5 4 3 +--R 6sinh(x) + 6cosh(x)sinh(x) + sinh(x) + cosh(x)sinh(x) +--R + +--R 2 2 5 3 +--R (6cosh(x) - 5)sinh(x) + (- 6cosh(x) + 11cosh(x) - 5cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 6cosh(x) + 11cosh(x) - 5cosh(x) +--R / +--R 30sinh(x) + 30cosh(x) +--R Type: Expression(Integer) +--E 323 + +--S 324 of 530 +d0559:= D(m0559,x) +--R +--R +--R (322) +--R 5 2 4 3 +--R 2cosh(x)sinh(x) + 2cosh(x) sinh(x) + cosh(x)sinh(x) +--R + +--R 4 2 2 +--R (- 2cosh(x) + 2cosh(x) )sinh(x) +--R + +--R 5 3 +--R (- 2cosh(x) + 3cosh(x) - cosh(x))sinh(x) +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 324 + +--S 325 of 530 +t0560:= sinh(x)^4/(1+tanh(x)) +--R +--R +--R 4 +--R sinh(x) +--R (323) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 530 +r0560:= 1/16*x+1/16*cosh(x)*sinh(x)-1/8*cosh(x)^3*sinh(x)+_ + 1/6*cosh(x)^3*sinh(x)^3-1/6*sinh(x)^6 +--R +--R +--R (324) +--R 6 3 3 3 +--R - 8sinh(x) + 8cosh(x) sinh(x) + (- 6cosh(x) + 3cosh(x))sinh(x) + 3x +--R ---------------------------------------------------------------------- +--R 48 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 530 +a0560:= integrate(t0560,x) +--R +--R +--R (325) +--R 5 4 2 3 +--R 5sinh(x) + 5cosh(x)sinh(x) + (50cosh(x) - 27)sinh(x) +--R + +--R 3 2 +--R (10cosh(x) - 27cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (25cosh(x) - 81cosh(x) + 24x + 12)sinh(x) + cosh(x) - 9cosh(x) +--R + +--R (24x - 12)cosh(x) +--R / +--R 384sinh(x) + 384cosh(x) +--R Type: Union(Expression(Integer),...) +--E 327 + +--S 328 of 530 +m0560:= a0560-r0560 +--R +--R +--R (326) +--R 7 6 5 +--R 64sinh(x) + 64cosh(x)sinh(x) + 5sinh(x) +--R + +--R 3 4 +--R (- 64cosh(x) + 5cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (- 64cosh(x) + 50cosh(x) - 27)sinh(x) +--R + +--R 3 2 4 2 +--R (58cosh(x) - 51cosh(x))sinh(x) + (73cosh(x) - 105cosh(x) + 12)sinh(x) +--R + +--R 5 3 +--R cosh(x) - 9cosh(x) - 12cosh(x) +--R / +--R 384sinh(x) + 384cosh(x) +--R Type: Expression(Integer) +--E 328 + +--S 329 of 530 +d0560:= D(m0560,x) +--R +--R +--R (327) +--R 6 2 5 3 4 +--R 16cosh(x)sinh(x) + 8cosh(x) sinh(x) + (- 8cosh(x) + 5cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (- 8cosh(x) + 6cosh(x) - 1)sinh(x) +--R + +--R 5 3 2 +--R (- 8cosh(x) + 16cosh(x) - 10cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (2cosh(x) - cosh(x) - 1)sinh(x) + 3cosh(x) - 4cosh(x) + cosh(x) +--R / +--R 16sinh(x) + 16cosh(x) +--R Type: Expression(Integer) +--E 329 + +--S 330 of 530 +t0561:= cosh(x)/(a+b*tanh(x)) +--R +--R +--R cosh(x) +--R (328) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 530 +r0561:= -b^2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ + b*cosh(x)/(a^2-b^2)+a*sinh(x)/(a^2-b^2) +--R +--R +--R (329) +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R b atan(---------------------) + (- a sinh(x) + b cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R --------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 530 +a0561:= integrate(t0561,x) +--R +--R +--R (330) +--R [ +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|- b + a +--R (- 4b sinh(x) - 4b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 332 + +--S 333 of 530 +m0561a:= a0561.1-r0561 +--R +--R +--R (331) +--R +---------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R +-------+ +--R 2 2 | 2 2 a sinh(x) + b cosh(x) +--R (- 2b sinh(x) - 2b cosh(x))\|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 | 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a \|b - a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 530 +d0561a:= D(m0561a,x) +--R +--R +--R (332) +--R 2 2 3 4 6 +--R (- a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 4 +--R ((- b - 6a b - 9a b - 4a b)cosh(x) - b + 4a b - 4a b - 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 3 4 +--R (- 4b + 4a b - 12a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4a b + 9a b + 6a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 +--R (- 2b - 2a b - 14a b - 6a b)cosh(x) - 2b + 7a b - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b - 12a b - 12a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 4b + 6a b + 6a b - 6a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 3 2 2 3 4 4 +--R (b + 2a b + a b )cosh(x) + (b - 6a b - 2a b + 2a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 +--R (- b + 4a b - a b - 2a b)cosh(x) - b + 2a b - a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 334 + +--S 335 of 530 +m0561b:= a0561.2-r0561 +--R +--R +--R (333) +--R +---------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|- b + a +--R (- 4b sinh(x) - 4b cosh(x))atan(-------------------------------) +--R b - a +--R + +--R 2 2 a sinh(x) + b cosh(x) +--R (- 2b sinh(x) - 2b cosh(x))atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 530 +d0561b:= D(m0561b,x) +--R +--R +--R (334) +--R 2 2 3 4 6 +--R (- a b - 2a b - a )sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 4 +--R ((- b - 6a b - 9a b - 4a b)cosh(x) - b + 4a b - 4a b - 3a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 3 4 +--R (- 4b + 4a b - 12a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4a b + 9a b + 6a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 4 +--R (- 2b - 2a b - 14a b - 6a b)cosh(x) - 2b + 7a b - 2a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 5 +--R (2b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2b - 12a b - 12a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 4b + 6a b + 6a b - 6a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 6 4 3 2 2 3 4 4 +--R (b + 2a b + a b )cosh(x) + (b - 6a b - 2a b + 2a b + a )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 +--R (- b + 4a b - a b - 2a b)cosh(x) - b + 2a b - a +--R / +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) - 2b - 2a b +--R + +--R 2 3 3 2 5 +--R 2a b + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 10a b + 14a b + 18a b - 8a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 8b - 8a b + 18a b + 14a b - 10a b - 6a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 4b + 6a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 336 + +--S 337 of 530 +t0562:= cosh(x)^2/(a+b*tanh(x)) +--R +--R +--R 2 +--R cosh(x) +--R (335) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 530 +r0562:= 1/2*(sinh(x)*a^3*cosh(x)+a^3*x-a^2*b*cosh(x)^2-3*a*b^2*x-_ + sinh(x)*a*cosh(x)*b^2+cosh(x)^2*b^3+_ + 2*b^3*log(a*cosh(x)+b*sinh(x)))/(b^4+a^4-2*a^2*b^2) +--R +--R +--R (336) +--R 3 2 3 +--R 2b log(b sinh(x) + a cosh(x)) + (- a b + a )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (b - a b)cosh(x) + (- 3a b + a )x +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 530 +a0562:= integrate(t0562,x) +--R +--R +--R (337) +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 3 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (- 8b - 12a b + 4a )x)sinh(x) +--R + +--R 3 2 2 3 3 3 2 3 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (- 16b - 24a b + 8a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 3 2 3 +--R (b - a b - a b + a )cosh(x) + (- 8b - 12a b + 4a )x cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 339 + +--S 340 of 530 +m0562:= a0562-r0562 +--R +--R +--R (338) +--R 3 2 3 3 2 +--R (- 8b sinh(x) - 16b cosh(x)sinh(x) - 8b cosh(x) ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (b - a b - a b + a )sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R ((2b + 2a b - 2a b - 2a )cosh(x) - 8b x)sinh(x) +--R + +--R 3 2 3 3 +--R ((- 4b + 4a b)cosh(x) - 16b x cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 3 2 3 2 2 3 +--R (- 3b - a b + 3a b + a )cosh(x) - 8b x cosh(x) + b + a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 340 + +--S 341 of 530 +d0562:= D(m0562,x) +--R +--R +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 +--R (339) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 530 +t0563:= cosh(x)^4/(a+b*tanh(x)) +--R +--R +--R 4 +--R cosh(x) +--R (340) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 342 + +--S 343 of 530 +r0563:= 1/8*(15*x*b^4*a-10*x*a^3*b^2-4*b^5*cosh(x)^2-_ + 10*a^3*b^2*sinh(x)*cosh(x)+7*b^4*a*sinh(x)*cosh(x)-_ + 8*b^5*log(a*cosh(x)+b*sinh(x))+3*x*a^5+3*a^5*sinh(x)*cosh(x)-_ + 2*b^5*cosh(x)^4-4*a^3*cosh(x)^3*b^2*sinh(x)+4*a^2*b^3*cosh(x)^2+_ + 2*a^5*sinh(x)*cosh(x)^3-2*a^4*b*cosh(x)^4+4*a^2*b^3*cosh(x)^4+_ + 2*a*b^4*sinh(x)*cosh(x)^3)/(3*b^4*a^2-b^6+a^6-3*b^2*a^4) +--R +--R +--R (341) +--R 5 +--R 8b log(b sinh(x) + a cosh(x)) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((- 2a b + 4a b - 2a )cosh(x) + (- 7a b + 10a b - 3a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 5 2 3 4 4 5 2 3 2 +--R (2b - 4a b + 2a b)cosh(x) + (4b - 4a b )cosh(x) +--R + +--R 4 3 2 5 +--R (- 15a b + 10a b - 3a )x +--R / +--R 6 2 4 4 2 6 +--R 8b - 24a b + 24a b - 8a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 530 +a0563:= integrate(t0563,x) +--R +--R +--R (342) +--R 5 4 5 3 5 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 4 5 +--R - 16a b - 16a b + 24a b + 4a b - 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (56b - 56a b - 112a b + 112a b + 56a b - 56a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (72b - 96a b - 96a b + 144a b + 24a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (70b - 70a b - 140a b + 140a b + 70a b - 70a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (180b - 240a b - 240a b + 360a b + 60a b - 120a )cosh(x) +--R + +--R 5 4 3 2 5 +--R (- 64b - 120a b + 80a b - 24a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (56b - 56a b - 112a b + 112a b + 56a b - 56a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (240b - 320a b - 320a b + 480a b + 80a b - 160a )cosh(x) +--R + +--R 5 4 3 2 5 +--R (- 256b - 480a b + 320a b - 96a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (180b - 240a b - 240a b + 360a b + 60a b - 120a )cosh(x) +--R + +--R 5 4 3 2 5 2 5 4 +--R (- 384b - 720a b + 480a b - 144a )x cosh(x) + 12b + 16a b +--R + +--R 2 3 3 2 4 5 +--R - 16a b - 24a b + 4a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (72b - 96a b - 96a b + 144a b + 24a b - 48a )cosh(x) +--R + +--R 5 4 3 2 5 3 +--R (- 256b - 480a b + 320a b - 96a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (24b + 32a b - 32a b - 48a b + 8a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (12b - 16a b - 16a b + 24a b + 4a b - 8a )cosh(x) +--R + +--R 5 4 3 2 5 4 +--R (- 64b - 120a b + 80a b - 24a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (12b + 16a b - 16a b - 24a b + 4a b + 8a )cosh(x) + b + a b +--R + +--R 2 3 3 2 4 5 +--R - 2a b - 2a b + a b + a +--R / +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x)sinh(x) +--R + +--R 6 2 4 4 2 6 2 2 +--R (384b - 1152a b + 1152a b - 384a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 344 + +--S 345 of 530 +m0563:= a0563-r0563 +--R +--R +--R (343) +--R 5 4 5 3 5 2 2 +--R - 64b sinh(x) - 256b cosh(x)sinh(x) - 384b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R - 256b cosh(x) sinh(x) - 64b cosh(x) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 5 4 5 3 5 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 4 5 +--R - 16a b - 16a b + 24a b + 4a b - 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (56b - 40a b - 112a b + 80a b + 56a b - 40a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (72b - 40a b - 96a b + 64a b + 24a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (54b - 6a b - 108a b + 12a b + 54a b - 6a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (148b - 16a b - 208a b + 40a b + 60a b - 24a )cosh(x) - 64b x +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 8b + 40a b + 16a b - 80a b - 8a b + 40a )cosh(x) +--R + +--R 5 4 2 3 4 5 3 5 +--R (112b + 16a b - 192a b + 80a b - 16a )cosh(x) - 256b x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 68b + 36a b + 136a b - 72a b - 68a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 12b - 16a b - 48a b + 40a b + 60a b - 24a )cosh(x) +--R + +--R 5 2 5 4 2 3 3 2 4 5 +--R - 384b x cosh(x) + 12b + 16a b - 16a b - 24a b + 4a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 56b + 8a b + 112a b - 16a b - 56a b + 8a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 56b - 40a b + 32a b + 64a b + 24a b - 24a )cosh(x) +--R + +--R 5 3 +--R - 256b x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (24b + 32a b - 32a b - 48a b + 8a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 15b - a b + 30a b + 2a b - 15a b - a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 5 4 +--R (- 20b - 16a b + 16a b + 24a b + 4a b - 8a )cosh(x) - 64b x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (12b + 16a b - 16a b - 24a b + 4a b + 8a )cosh(x) + b + a b +--R + +--R 2 3 3 2 4 5 +--R - 2a b - 2a b + a b + a +--R / +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x)sinh(x) +--R + +--R 6 2 4 4 2 6 2 2 +--R (384b - 1152a b + 1152a b - 384a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )cosh(x) +--R Type: Expression(Integer) +--E 345 + +--S 346 of 530 +d0563:= D(m0563,x) +--R +--R +--R (344) +--R 2 2 8 2 2 7 +--R (b - 2a b + a )sinh(x) + (8b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((28b - 44a b + 16a )cosh(x) + 6b - 2a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((40b - 48a b + 8a )cosh(x) + (20b - 12a b)cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 4 +--R ((6b - 6a )cosh(x) + (26b - 48a b + 18a )cosh(x) )sinh(x) +--R + +--R 2 2 5 2 2 3 3 +--R ((- 40b + 48a b - 8a )cosh(x) + (24b - 72a b + 32a )cosh(x) )sinh(x) +--R + +--R 2 2 6 2 2 4 2 +--R (- 36b + 44a b - 8a )cosh(x) + (26b - 48a b + 18a )cosh(x) - 6b +--R + +--R 2 +--R - 2a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 +--R (- 8b + 16a b - 8a )cosh(x) + (20b - 12a b)cosh(x) +--R + +--R 2 2 +--R (- 12b - 4a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (b + 2a b - 3a )cosh(x) + (6b - 2a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 6b - 2a b + 4a )cosh(x) - b + a +--R / +--R 3 2 2 3 4 +--R (16b - 16a b - 16a b + 16a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (64b - 64a b - 64a b + 64a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (96b - 96a b - 96a b + 96a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 +--R (64b - 64a b - 64a b + 64a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (16b - 16a b - 16a b + 16a )cosh(x) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 530 +t0564:= cosh(x)/(1+tanh(x)) +--R +--R +--R cosh(x) +--R (345) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 530 +r0564:= -1/3*cosh(x)^3+sinh(x)+1/3*sinh(x)^3 +--R +--R +--R 3 3 +--R sinh(x) + 3sinh(x) - cosh(x) +--R (346) ------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 348 + +--S 349 of 530 +a0564:= integrate(t0564,x) +--R +--R +--R 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + cosh(x) - 3 +--R (347) ----------------------------------------- +--R 6sinh(x) + 6cosh(x) +--R Type: Union(Expression(Integer),...) +--E 349 + +--S 350 of 530 +m0564:= a0564-r0564 +--R +--R +--R (348) +--R 4 3 2 +--R - 2sinh(x) - 2cosh(x)sinh(x) - 5sinh(x) +--R + +--R 3 4 2 +--R (2cosh(x) - 2cosh(x))sinh(x) + 2cosh(x) + cosh(x) - 3 +--R / +--R 6sinh(x) + 6cosh(x) +--R Type: Expression(Integer) +--E 350 + +--S 351 of 530 +d0564:= D(m0564,x) +--R +--R +--R (349) +--R 3 2 3 2 +--R - 2cosh(x)sinh(x) + sinh(x) + (2cosh(x) - 2cosh(x))sinh(x) - cosh(x) + 1 +--R ---------------------------------------------------------------------------- +--R 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 351 + +--S 352 of 530 +t0565:= cosh(x)^2/(1+tanh(x)) +--R +--R +--R 2 +--R cosh(x) +--R (350) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 530 +r0565:= 3/8*x-1/4*cosh(x)^4+3/8*cosh(x)*sinh(x)+1/4*cosh(x)^3*sinh(x) +--R +--R +--R 3 4 +--R (2cosh(x) + 3cosh(x))sinh(x) - 2cosh(x) + 3x +--R (351) ---------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 530 +a0565:= integrate(t0565,x) +--R +--R +--R (352) +--R 3 2 2 3 +--R 3sinh(x) + 3cosh(x)sinh(x) + (9cosh(x) + 12x + 6)sinh(x) + cosh(x) +--R + +--R (12x - 6)cosh(x) +--R / +--R 32sinh(x) + 32cosh(x) +--R Type: Union(Expression(Integer),...) +--E 354 + +--S 355 of 530 +m0565:= a0565-r0565 +--R +--R +--R (353) +--R 3 3 2 2 +--R 3sinh(x) + (- 8cosh(x) - 9cosh(x))sinh(x) + (- 3cosh(x) + 6)sinh(x) +--R + +--R 5 3 +--R 8cosh(x) + cosh(x) - 6cosh(x) +--R / +--R 32sinh(x) + 32cosh(x) +--R Type: Expression(Integer) +--E 355 + +--S 356 of 530 +d0565:= D(m0565,x) +--R +--R +--R (354) +--R 2 3 3 2 +--R (- 6cosh(x) - 3)sinh(x) + (2cosh(x) + 3cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (6cosh(x) - 3cosh(x) - 3)sinh(x) - 2cosh(x) - cosh(x) + 3cosh(x) +--R / +--R 8sinh(x) + 8cosh(x) +--R Type: Expression(Integer) +--E 356 + +--S 357 of 530 +t0566:= cosh(x)^3/(1+tanh(x)) +--R +--R +--R 3 +--R cosh(x) +--R (355) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 530 +r0566:= -1/5*cosh(x)^5+sinh(x)+2/3*sinh(x)^3+1/5*sinh(x)^5 +--R +--R +--R 5 3 5 +--R 3sinh(x) + 10sinh(x) + 15sinh(x) - 3cosh(x) +--R (356) ---------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 530 +a0566:= integrate(t0566,x) +--R +--R +--R (357) +--R 4 3 2 2 +--R sinh(x) + 16cosh(x)sinh(x) + (6cosh(x) + 20)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 80cosh(x))sinh(x) + cosh(x) + 20cosh(x) - 45 +--R / +--R 120sinh(x) + 120cosh(x) +--R Type: Union(Expression(Integer),...) +--E 359 + +--S 360 of 530 +m0566:= a0566-r0566 +--R +--R +--R (358) +--R 6 5 4 3 +--R - 24sinh(x) - 24cosh(x)sinh(x) - 79sinh(x) - 64cosh(x)sinh(x) +--R + +--R 2 2 5 3 +--R (6cosh(x) - 100)sinh(x) + (24cosh(x) + 16cosh(x) - 40cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 24cosh(x) + cosh(x) + 20cosh(x) - 45 +--R / +--R 120sinh(x) + 120cosh(x) +--R Type: Expression(Integer) +--E 360 + +--S 361 of 530 +d0566:= D(m0566,x) +--R +--R +--R (359) +--R 5 2 4 3 +--R - 8cosh(x)sinh(x) + (- 8cosh(x) + 1)sinh(x) - 16cosh(x)sinh(x) +--R + +--R 4 2 2 5 +--R (8cosh(x) - 10cosh(x) + 4)sinh(x) + (8cosh(x) - 8cosh(x))sinh(x) +--R + +--R 4 2 +--R cosh(x) - 4cosh(x) + 3 +--R / +--R 8sinh(x) + 8cosh(x) +--R Type: Expression(Integer) +--E 361 + +--S 362 of 530 +t0567:= cosh(x)^4/(1+tanh(x)) +--R +--R +--R 4 +--R cosh(x) +--R (360) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 530 +r0567:= 5/16*x-1/6*cosh(x)^6+5/16*cosh(x)*sinh(x)+5/24*cosh(x)^3*sinh(x)+_ + 1/6*cosh(x)^5*sinh(x) +--R +--R +--R 5 3 6 +--R (8cosh(x) + 10cosh(x) + 15cosh(x))sinh(x) - 8cosh(x) + 15x +--R (361) ------------------------------------------------------------- +--R 48 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 530 +a0567:= integrate(t0567,x) +--R +--R +--R (362) +--R 5 4 2 3 +--R 5sinh(x) + 5cosh(x)sinh(x) + (50cosh(x) + 45)sinh(x) +--R + +--R 3 2 +--R (10cosh(x) + 45cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (25cosh(x) + 135cosh(x) + 120x + 60)sinh(x) + cosh(x) + 15cosh(x) +--R + +--R (120x - 60)cosh(x) +--R / +--R 384sinh(x) + 384cosh(x) +--R Type: Union(Expression(Integer),...) +--E 364 + +--S 365 of 530 +m0567:= a0567-r0567 +--R +--R +--R (363) +--R 5 4 2 3 +--R 5sinh(x) + 5cosh(x)sinh(x) + (50cosh(x) + 45)sinh(x) +--R + +--R 5 3 2 +--R (- 64cosh(x) - 70cosh(x) - 75cosh(x))sinh(x) +--R + +--R 4 2 7 5 +--R (- 55cosh(x) + 15cosh(x) + 60)sinh(x) + 64cosh(x) + cosh(x) +--R + +--R 3 +--R 15cosh(x) - 60cosh(x) +--R / +--R 384sinh(x) + 384cosh(x) +--R Type: Expression(Integer) +--E 365 + +--S 366 of 530 +d0567:= D(m0567,x) +--R +--R +--R (364) +--R 4 4 2 3 +--R 15cosh(x)sinh(x) + (- 40cosh(x) - 30cosh(x) - 15)sinh(x) +--R + +--R 5 2 +--R (8cosh(x) + 30cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (40cosh(x) - 10cosh(x) - 15cosh(x) - 15)sinh(x) - 8cosh(x) +--R + +--R 5 +--R - 7cosh(x) + 15cosh(x) +--R / +--R 48sinh(x) + 48cosh(x) +--R Type: Expression(Integer) +--E 366 + +--S 367 of 530 +t0568:= tanh(x)/(a+b*tanh(x)) +--R +--R +--R tanh(x) +--R (365) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 367 + +--S 368 of 530 +r0568:= (-b*x+a*log(a*cosh(x)+b*sinh(x)))/(a^2-b^2) +--R +--R +--R - a log(b sinh(x) + a cosh(x)) + b x +--R (366) ------------------------------------ +--R 2 2 +--R b - a +--R Type: Expression(Integer) +--E 368 + +--S 369 of 530 +a0568:= integrate(t0568,x) +--R +--R +--R - 2b sinh(x) - 2a cosh(x) +--R - a log(-------------------------) + (b + a)x +--R sinh(x) - cosh(x) +--R (367) --------------------------------------------- +--R 2 2 +--R b - a +--R Type: Union(Expression(Integer),...) +--E 369 + +--S 370 of 530 +m0568:= a0568-r0568 +--R +--R +--R (368) +--R - 2b sinh(x) - 2a cosh(x) +--R a log(b sinh(x) + a cosh(x)) - a log(-------------------------) + a x +--R sinh(x) - cosh(x) +--R --------------------------------------------------------------------- +--R 2 2 +--R b - a +--R Type: Expression(Integer) +--E 370 + +--S 371 of 530 +d0568:= D(m0568,x) +--R +--R +--R (369) 0 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 530 +t0569:= tanh(x)/(1+tanh(x)) +--R +--R +--R tanh(x) +--R (370) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 530 +r0569:= 1/2*x-1/(2+2*coth(x)) +--R +--R +--R x coth(x) + x - 1 +--R (371) ----------------- +--R 2coth(x) + 2 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 530 +a0569:= integrate(t0569,x) +--R +--R +--R (2x - 1)sinh(x) + (2x + 1)cosh(x) +--R (372) --------------------------------- +--R 4sinh(x) + 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 374 + +--S 375 of 530 +m0569:= a0569-r0569 +--R +--R +--R (- coth(x) + 1)sinh(x) + cosh(x)coth(x) + 3cosh(x) +--R (373) -------------------------------------------------- +--R (4coth(x) + 4)sinh(x) + 4cosh(x)coth(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 375 + +--S 376 of 530 +d0569:= D(m0569,x) +--R +--R +--R coth(x)sinh(x) - cosh(x) +--R (374) ----------------------------------------------- +--R (coth(x) + 1)sinh(x) + cosh(x)coth(x) + cosh(x) +--R Type: Expression(Integer) +--E 376 + +--S 377 of 530 +t0570:= tanh(x)^2/(1+tanh(x)) +--R +--R +--R 2 +--R tanh(x) +--R (375) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 530 +r0570:= -1/2*x+log(cosh(x))-1/(2+2*tanh(x)) +--R +--R +--R (2tanh(x) + 2)log(cosh(x)) - x tanh(x) - x - 1 +--R (376) ---------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 378 + +--S 379 of 530 +a0570:= integrate(t0570,x) +--R +--R +--R (377) +--R 2 2 2cosh(x) +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 6x sinh(x) - 12x cosh(x)sinh(x) - 6x cosh(x) - 1 +--R / +--R 2 2 +--R 4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 379 + +--S 380 of 530 +m0570:= a0570-r0570 +--R +--R +--R (378) +--R 2 2 2 +--R (- 4sinh(x) - 8cosh(x)sinh(x) - 4cosh(x) )tanh(x) - 4sinh(x) +--R + +--R 2 +--R - 8cosh(x)sinh(x) - 4cosh(x) +--R * +--R log(cosh(x)) +--R + +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 4x sinh(x) - 8x cosh(x)sinh(x) - 4x cosh(x) - 1)tanh(x) +--R + +--R 2 2 +--R (- 4x + 2)sinh(x) + (- 8x + 4)cosh(x)sinh(x) + (- 4x + 2)cosh(x) - 1 +--R / +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 380 + +--S 381 of 530 +d0570:= D(m0570,x) +--R +--R +--R (379) +--R 2 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)tanh(x) - sinh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R / +--R 2 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )tanh(x) + 2sinh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 381 + +--S 382 of 530 +t0571:= tanh(x)^3/(1+tanh(x)) +--R +--R +--R 3 +--R tanh(x) +--R (380) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 530 +r0571:= 3/2*x-log(cosh(x))-tanh(x)+1/(2+2*tanh(x)) +--R +--R +--R 2 +--R (- 2tanh(x) - 2)log(cosh(x)) - 2tanh(x) + (3x - 2)tanh(x) + 3x + 1 +--R (381) ------------------------------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 530 +a0571:= integrate(t0571,x) +--R +--R +--R (382) +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) - 8cosh(x))sinh(x) - 4cosh(x) - 4cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R 10x sinh(x) + 40x cosh(x)sinh(x) + (60x cosh(x) + 10x + 9)sinh(x) +--R + +--R 3 4 +--R (40x cosh(x) + (20x + 18)cosh(x))sinh(x) + 10x cosh(x) +--R + +--R 2 +--R (10x + 9)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 384 + +--S 385 of 530 +m0571:= a0571-r0571 +--R +--R +--R (383) +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R log(cosh(x)) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) - 8cosh(x))sinh(x) - 4cosh(x) - 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) - 8cosh(x))sinh(x) - 4cosh(x) - 4cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R (4x + 4)sinh(x) + (16x + 16)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((24x + 24)cosh(x) + 4x + 13)sinh(x) +--R + +--R 3 4 +--R ((16x + 16)cosh(x) + (8x + 26)cosh(x))sinh(x) + (4x + 4)cosh(x) +--R + +--R 2 +--R (4x + 13)cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 4 3 +--R (4x - 2)sinh(x) + (16x - 8)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((24x - 12)cosh(x) + 4x + 7)sinh(x) +--R + +--R 3 4 +--R ((16x - 8)cosh(x) + (8x + 14)cosh(x))sinh(x) + (4x - 2)cosh(x) +--R + +--R 2 +--R (4x + 7)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 385 + +--S 3886 of 530 +d0571:= D(m0571,x) +--R +--R +--R (384) +--R 6 5 2 4 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (- 40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30cosh(x) - 24cosh(x) - 2)sinh(x) +--R + +--R 5 3 6 4 +--R (- 12cosh(x) - 16cosh(x) - 4cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R - 2cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (- 40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30cosh(x) - 24cosh(x) - 2)sinh(x) +--R + +--R 5 3 6 4 +--R (- 12cosh(x) - 16cosh(x) - 4cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R - 2cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 7)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 28cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 42cosh(x) - 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 28cosh(x) - 2cosh(x))sinh(x) + cosh(x) - 7cosh(x) +--R + +--R 2 +--R - cosh(x) - 1 +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 3sinh(x) + 18cosh(x)sinh(x) + (45cosh(x) - 3)sinh(x) +--R + +--R 3 3 4 2 2 +--R (60cosh(x) - 12cosh(x))sinh(x) + (45cosh(x) - 18cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (18cosh(x) - 12cosh(x) + 2cosh(x))sinh(x) + 3cosh(x) - 3cosh(x) +--R + +--R 2 +--R cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) + 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 4)sinh(x) +--R + +--R 3 3 4 2 2 +--R (40cosh(x) + 16cosh(x))sinh(x) + (30cosh(x) + 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R Type: Expression(Integer) +--E 3886 + +--S 387 of 530 +t0572:= coth(x)/(a+b*tanh(x)) +--R +--R +--R coth(x) +--R (385) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 387 + +--S 388 of 530 +r0572:= (-a*b*x+log(sinh(x))*a^2-log(sinh(x))*b^2+_ + b^2*log(a*cosh(x)+b*sinh(x)))/a/(a^2-b^2) +--R +--R +--R 2 2 2 +--R - b log(b sinh(x) + a cosh(x)) + (b - a )log(sinh(x)) + a b x +--R (386) -------------------------------------------------------------- +--R 2 3 +--R a b - a +--R Type: Expression(Integer) +--E 388 + +--S 389 of 530 +a0572:= integrate(t0572,x) +--R +--R +--R (387) +--R 2 2 2sinh(x) 2 - 2b sinh(x) - 2a cosh(x) +--R (b - a )log(- -----------------) - b log(-------------------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R + +--R 2 +--R (a b + a )x +--R / +--R 2 3 +--R a b - a +--R Type: Union(Expression(Integer),...) +--E 389 + +--S 390 of 530 +m0572:= a0572-r0572 +--R +--R +--R (388) +--R 2 2 2 +--R b log(b sinh(x) + a cosh(x)) + (- b + a )log(sinh(x)) +--R + +--R 2 2 2sinh(x) 2 - 2b sinh(x) - 2a cosh(x) 2 +--R (b - a )log(- -----------------) - b log(-------------------------) + a x +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R / +--R 2 3 +--R a b - a +--R Type: Expression(Integer) +--E 390 + +--S 391 of 530 +d0572:= D(m0572,x) +--R +--R +--R (389) 0 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 530 +t0573:= coth(x)^2/(a+b*tanh(x)) +--R +--R +--R 2 +--R coth(x) +--R (390) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 392 + +--S 393 of 530 +r0573:= a*x/(a^2-b^2)-coth(x)/a-b*log(sinh(x))/a^2-b^3*log(a*cosh(x)+_ + b*sinh(x))/a^2/(a^2-b^2) +--R +--R +--R (391) +--R 3 3 2 +--R b log(b sinh(x) + a cosh(x)) + (- b + a b)log(sinh(x)) +--R + +--R 2 3 3 +--R (- a b + a )coth(x) - a x +--R / +--R 2 2 4 +--R a b - a +--R Type: Expression(Integer) +--E 393 + +--S 394 of 530 +a0573:= integrate(t0573,x) +--R +--R +--R (392) +--R 3 2 2 3 2 +--R (- b + a b)sinh(x) + (- 2b + 2a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 +--R (- b + a b)cosh(x) + b - a b +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 3 +--R (- a b - a )x sinh(x) + (- 2a b - 2a )x cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- a b - a )x cosh(x) + (a b + a )x - 2a b + 2a +--R / +--R 2 2 4 2 2 2 4 2 2 4 2 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) + (a b - a )cosh(x) +--R + +--R 2 2 4 +--R - a b + a +--R Type: Union(Expression(Integer),...) +--E 394 + +--S 395 of 530 +m0573:= a0573-r0573 +--R +--R +--R (393) +--R 3 2 3 3 2 3 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) + b ) +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 3 2 2 3 2 3 2 2 +--R (b - a b)sinh(x) + (2b - 2a b)cosh(x)sinh(x) + (b - a b)cosh(x) +--R + +--R 3 2 +--R - b + a b +--R * +--R log(sinh(x)) +--R + +--R 3 2 2 3 2 +--R (- b + a b)sinh(x) + (- 2b + 2a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 +--R (- b + a b)cosh(x) + b - a b +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b ) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 +--R ((a b - a )coth(x) - a b x)sinh(x) +--R + +--R 2 3 2 +--R ((2a b - 2a )cosh(x)coth(x) - 2a b x cosh(x))sinh(x) +--R + +--R 2 3 2 2 3 2 2 2 2 +--R ((a b - a )cosh(x) - a b + a )coth(x) - a b x cosh(x) + a b x - 2a b +--R + +--R 3 +--R 2a +--R / +--R 2 2 4 2 2 2 4 2 2 4 2 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) + (a b - a )cosh(x) +--R + +--R 2 2 4 +--R - a b + a +--R Type: Expression(Integer) +--E 395 + +--S 396 of 530 +d0573:= D(m0573,x) +--R +--R +--R (394) +--R 2 4 2 3 +--R (- coth(x) + 1)sinh(x) + (- 4cosh(x)coth(x) + 4cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R ((- 6cosh(x) + 2)coth(x) + 6cosh(x) + 2)sinh(x) +--R + +--R 3 2 3 +--R ((- 4cosh(x) + 4cosh(x))coth(x) + 4cosh(x) + 4cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (- cosh(x) + 2cosh(x) - 1)coth(x) + cosh(x) + 2cosh(x) + 1 +--R / +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) - 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) - 4a cosh(x))sinh(x) + a cosh(x) - 2a cosh(x) + a +--R Type: Expression(Integer) +--E 396 + +--S 397 of 530 +t0574:= coth(x)^3/(a+b*tanh(x)) +--R +--R +--R 3 +--R coth(x) +--R (395) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 530 +r0574:= -b*x/a^2-b^3*x/a^2/(a^2-b^2)+b*coth(x)/a^2-1/2*coth(x)^2/a+_ + log(sinh(x))/a+b^2*log(sinh(x))/a^3+b^4*log(a*cosh(x)+_ + b*sinh(x))/a^3/(a^2-b^2) +--R +--R +--R (396) +--R 4 4 4 +--R - 2b log(b sinh(x) + a cosh(x)) + (2b - 2a )log(sinh(x)) +--R + +--R 2 2 4 2 3 3 3 +--R (- a b + a )coth(x) + (2a b - 2a b)coth(x) + 2a b x +--R / +--R 3 2 5 +--R 2a b - 2a +--R Type: Expression(Integer) +--E 398 + +--S 399 of 530 +a0574:= integrate(t0574,x) +--R +--R +--R (397) +--R 4 4 4 4 4 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 4 4 2 4 4 2 +--R ((6b - 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 4 4 3 4 4 +--R ((4b - 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 4 4 4 4 4 2 4 4 +--R (b - a )cosh(x) + (- 2b + 2a )cosh(x) + b - a +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 4 4 3 4 2 4 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) + 2b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (- 4b cosh(x) + 4b cosh(x))sinh(x) - b cosh(x) + 2b cosh(x) - b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 4 4 3 4 3 +--R (a b + a )x sinh(x) + (4a b + 4a )x cosh(x)sinh(x) +--R + +--R 3 4 2 3 4 3 2 2 3 4 +--R ((6a b + 6a )x cosh(x) + (- 2a b - 2a )x + 2a b - 2a b - 2a b + 2a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 +--R (4a b + 4a )x cosh(x) +--R + +--R 3 4 3 2 2 3 4 +--R ((- 4a b - 4a )x + 4a b - 4a b - 4a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 +--R (a b + a )x cosh(x) +--R + +--R 3 4 3 2 2 3 4 2 3 4 +--R ((- 2a b - 2a )x + 2a b - 2a b - 2a b + 2a )cosh(x) + (a b + a )x +--R + +--R 3 3 +--R - 2a b + 2a b +--R / +--R 3 2 5 4 3 2 5 3 +--R (a b - a )sinh(x) + (4a b - 4a )cosh(x)sinh(x) +--R + +--R 3 2 5 2 3 2 5 2 +--R ((6a b - 6a )cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 3 2 5 3 3 2 5 +--R ((4a b - 4a )cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R (a b - a )cosh(x) + (- 2a b + 2a )cosh(x) + a b - a +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 530 +m0574:= a0574-r0574 +--R +--R +--R (398) +--R 4 4 4 3 4 2 4 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) - 4b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (8b cosh(x) - 8b cosh(x))sinh(x) + 2b cosh(x) - 4b cosh(x) + 2b +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 4 4 4 4 4 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 4 4 2 4 4 2 +--R ((- 12b + 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 4 4 3 4 4 +--R ((- 8b + 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 4 4 4 4 4 2 4 4 +--R (- 2b + 2a )cosh(x) + (4b - 4a )cosh(x) - 2b + 2a +--R * +--R log(sinh(x)) +--R + +--R 4 4 4 4 4 3 +--R (2b - 2a )sinh(x) + (8b - 8a )cosh(x)sinh(x) +--R + +--R 4 4 2 4 4 2 +--R ((12b - 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 4 4 3 4 4 +--R ((8b - 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 4 4 4 4 4 2 4 4 +--R (2b - 2a )cosh(x) + (- 4b + 4a )cosh(x) + 2b - 2a +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 4 4 3 4 2 4 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) + 4b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (- 8b cosh(x) + 8b cosh(x))sinh(x) - 2b cosh(x) + 4b cosh(x) - 2b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 3 3 4 4 +--R ((a b - a )coth(x) + (- 2a b + 2a b)coth(x) + 2a x)sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (4a b - 4a )cosh(x)coth(x) + (- 8a b + 8a b)cosh(x)coth(x) +--R + +--R 4 +--R 8a x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 4 2 +--R ((6a b - 6a )cosh(x) - 2a b + 2a )coth(x) +--R + +--R 3 3 2 3 3 4 2 +--R ((- 12a b + 12a b)cosh(x) + 4a b - 4a b)coth(x) + 12a x cosh(x) +--R + +--R 4 3 2 2 3 4 +--R - 4a x + 4a b - 4a b - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 3 2 2 4 2 +--R ((4a b - 4a )cosh(x) + (- 4a b + 4a )cosh(x))coth(x) +--R + +--R 3 3 3 3 3 +--R ((- 8a b + 8a b)cosh(x) + (8a b - 8a b)cosh(x))coth(x) +--R + +--R 4 3 4 3 2 2 3 4 +--R 8a x cosh(x) + (- 8a x + 8a b - 8a b - 8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 2 +--R ((a b - a )cosh(x) + (- 2a b + 2a )cosh(x) + a b - a )coth(x) +--R + +--R 3 3 4 3 3 2 3 3 +--R ((- 2a b + 2a b)cosh(x) + (4a b - 4a b)cosh(x) - 2a b + 2a b)coth(x) +--R + +--R 4 4 4 3 2 2 3 4 2 4 +--R 2a x cosh(x) + (- 4a x + 4a b - 4a b - 4a b + 4a )cosh(x) + 2a x +--R + +--R 3 3 +--R - 4a b + 4a b +--R / +--R 3 2 5 4 3 2 5 3 +--R (2a b - 2a )sinh(x) + (8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 5 2 3 2 5 2 +--R ((12a b - 12a )cosh(x) - 4a b + 4a )sinh(x) +--R + +--R 3 2 5 3 3 2 5 +--R ((8a b - 8a )cosh(x) + (- 8a b + 8a )cosh(x))sinh(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R (2a b - 2a )cosh(x) + (- 4a b + 4a )cosh(x) + 2a b - 2a +--R Type: Expression(Integer) +--E 400 + +--S 401 of 530 +d0574:= D(m0574,x) +--R +--R +--R (399) +--R 3 2 6 +--R (- a coth(x) + b coth(x) + a coth(x) - b)sinh(x) +--R + +--R 3 2 +--R - 6a cosh(x)coth(x) + 6b cosh(x)coth(x) + 6a cosh(x)coth(x) +--R + +--R - 6b cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 15a cosh(x) + 3a)coth(x) + (15b cosh(x) - 3b)coth(x) +--R + +--R 2 2 +--R (15a cosh(x) - 3a)coth(x) - 15b cosh(x) - b + 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 +--R (- 20a cosh(x) + 12a cosh(x))coth(x) +--R + +--R 3 2 +--R (20b cosh(x) - 12b cosh(x))coth(x) +--R + +--R 3 3 +--R (20a cosh(x) - 12a cosh(x))coth(x) - 20b cosh(x) +--R + +--R (- 4b + 16a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 +--R (- 15a cosh(x) + 18a cosh(x) - 3a)coth(x) +--R + +--R 4 2 2 +--R (15b cosh(x) - 18b cosh(x) + 3b)coth(x) +--R + +--R 4 2 4 +--R (15a cosh(x) - 18a cosh(x) + 3a)coth(x) - 15b cosh(x) +--R + +--R 2 +--R (- 6b + 24a)cosh(x) + b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 6a cosh(x) + 12a cosh(x) - 6a cosh(x))coth(x) +--R + +--R 5 3 2 +--R (6b cosh(x) - 12b cosh(x) + 6b cosh(x))coth(x) +--R + +--R 5 3 5 +--R (6a cosh(x) - 12a cosh(x) + 6a cosh(x))coth(x) - 6b cosh(x) +--R + +--R 3 +--R (- 4b + 16a)cosh(x) + (2b + 8a)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- a cosh(x) + 3a cosh(x) - 3a cosh(x) + a)coth(x) +--R + +--R 6 4 2 2 +--R (b cosh(x) - 3b cosh(x) + 3b cosh(x) - b)coth(x) +--R + +--R 6 4 2 6 +--R (a cosh(x) - 3a cosh(x) + 3a cosh(x) - a)coth(x) - b cosh(x) +--R + +--R 4 2 +--R (- b + 4a)cosh(x) + (b + 4a)cosh(x) + b +--R / +--R 2 6 2 5 2 2 2 4 +--R a sinh(x) + 6a cosh(x)sinh(x) + (15a cosh(x) - 3a )sinh(x) +--R + +--R 2 3 2 3 +--R (20a cosh(x) - 12a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (15a cosh(x) - 18a cosh(x) + 3a )sinh(x) +--R + +--R 2 5 2 3 2 2 6 +--R (6a cosh(x) - 12a cosh(x) + 6a cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 4 2 2 2 +--R - 3a cosh(x) + 3a cosh(x) - a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 530 +t0575:= coth(x)^4/(a+b*tanh(x)) +--R +--R +--R 4 +--R coth(x) +--R (400) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 402 + +--S 403 of 530 +r0575:= x/a+b^2*x/a^3+b^4*x/a^3/(a^2-b^2)-coth(x)/a-b^2*coth(x)/a^3+_ + 1/2*b*coth(x)^2/a^2-1/3*coth(x)^3/a-b*log(sinh(x))/a^2-_ + b^3*log(sinh(x))/a^4-b^5*log(a*cosh(x)+b*sinh(x))/a^4/(a^2-b^2) +--R +--R +--R (401) +--R 5 5 4 +--R 6b log(b sinh(x) + a cosh(x)) + (- 6b + 6a b)log(sinh(x)) +--R + +--R 3 2 5 3 2 3 4 2 4 5 +--R (- 2a b + 2a )coth(x) + (3a b - 3a b)coth(x) + (- 6a b + 6a )coth(x) +--R + +--R 5 +--R - 6a x +--R / +--R 4 2 6 +--R 6a b - 6a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 530 +a0575:= integrate(t0575,x) +--R +--R +--R (402) +--R 5 4 6 5 4 5 +--R (- 3b + 3a b)sinh(x) + (- 18b + 18a b)cosh(x)sinh(x) +--R + +--R 5 4 2 5 4 4 +--R ((- 45b + 45a b)cosh(x) + 9b - 9a b)sinh(x) +--R + +--R 5 4 3 5 4 3 +--R ((- 60b + 60a b)cosh(x) + (36b - 36a b)cosh(x))sinh(x) +--R + +--R 5 4 4 5 4 2 5 4 +--R ((- 45b + 45a b)cosh(x) + (54b - 54a b)cosh(x) - 9b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 5 4 3 +--R (- 18b + 18a b)cosh(x) + (36b - 36a b)cosh(x) +--R + +--R 5 4 +--R (- 18b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 6 5 4 4 +--R (- 3b + 3a b)cosh(x) + (9b - 9a b)cosh(x) +--R + +--R 5 4 2 5 4 +--R (- 9b + 9a b)cosh(x) + 3b - 3a b +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 5 6 5 5 5 2 5 4 +--R 3b sinh(x) + 18b cosh(x)sinh(x) + (45b cosh(x) - 9b )sinh(x) +--R + +--R 5 3 5 3 +--R (60b cosh(x) - 36b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (45b cosh(x) - 54b cosh(x) + 9b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (18b cosh(x) - 36b cosh(x) + 18b cosh(x))sinh(x) + 3b cosh(x) +--R + +--R 5 4 5 2 5 +--R - 9b cosh(x) + 9b cosh(x) - 3b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 4 5 6 4 5 5 +--R (- 3a b - 3a )x sinh(x) + (- 18a b - 18a )x cosh(x)sinh(x) +--R + +--R 4 5 2 4 5 4 2 3 3 2 +--R (- 45a b - 45a )x cosh(x) + (9a b + 9a )x - 6a b + 6a b - 6a b +--R + +--R 4 5 +--R - 6a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 +--R (- 60a b - 60a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 +--R ((36a b + 36a )x - 24a b + 24a b - 24a b - 24a b + 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 4 +--R (- 45a b - 45a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 2 +--R ((54a b + 54a )x - 36a b + 36a b - 36a b - 36a b + 72a )cosh(x) +--R + +--R 4 5 4 2 3 4 5 +--R (- 9a b - 9a )x + 12a b - 6a b + 6a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 5 +--R (- 18a b - 18a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 3 +--R ((36a b + 36a )x - 24a b + 24a b - 24a b - 24a b + 48a )cosh(x) +--R + +--R 4 5 4 2 3 4 5 +--R ((- 18a b - 18a )x + 24a b - 12a b + 12a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 5 6 +--R (- 3a b - 3a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 4 +--R ((9a b + 9a )x - 6a b + 6a b - 6a b - 6a b + 12a )cosh(x) +--R + +--R 4 5 4 2 3 4 5 2 4 5 +--R ((- 9a b - 9a )x + 12a b - 6a b + 6a b - 12a )cosh(x) + (3a b + 3a )x +--R + +--R 4 3 2 5 +--R - 6a b - 2a b + 8a +--R / +--R 4 2 6 6 4 2 6 5 +--R (3a b - 3a )sinh(x) + (18a b - 18a )cosh(x)sinh(x) +--R + +--R 4 2 6 2 4 2 6 4 +--R ((45a b - 45a )cosh(x) - 9a b + 9a )sinh(x) +--R + +--R 4 2 6 3 4 2 6 3 +--R ((60a b - 60a )cosh(x) + (- 36a b + 36a )cosh(x))sinh(x) +--R + +--R 4 2 6 4 4 2 6 2 4 2 6 +--R ((45a b - 45a )cosh(x) + (- 54a b + 54a )cosh(x) + 9a b - 9a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 6 5 4 2 6 3 +--R (18a b - 18a )cosh(x) + (- 36a b + 36a )cosh(x) +--R + +--R 4 2 6 +--R (18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 6 6 4 2 6 4 4 2 6 2 +--R (3a b - 3a )cosh(x) + (- 9a b + 9a )cosh(x) + (9a b - 9a )cosh(x) +--R + +--R 4 2 6 +--R - 3a b + 3a +--R Type: Union(Expression(Integer),...) +--E 404 + +--S 405 of 530 +m0575:= a0575-r0575 +--R +--R +--R (403) +--R 5 6 5 5 5 2 5 4 +--R - 6b sinh(x) - 36b cosh(x)sinh(x) + (- 90b cosh(x) + 18b )sinh(x) +--R + +--R 5 3 5 3 +--R (- 120b cosh(x) + 72b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (- 90b cosh(x) + 108b cosh(x) - 18b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (- 36b cosh(x) + 72b cosh(x) - 36b cosh(x))sinh(x) - 6b cosh(x) +--R + +--R 5 4 5 2 5 +--R 18b cosh(x) - 18b cosh(x) + 6b +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 5 4 6 5 4 5 +--R (6b - 6a b)sinh(x) + (36b - 36a b)cosh(x)sinh(x) +--R + +--R 5 4 2 5 4 4 +--R ((90b - 90a b)cosh(x) - 18b + 18a b)sinh(x) +--R + +--R 5 4 3 5 4 3 +--R ((120b - 120a b)cosh(x) + (- 72b + 72a b)cosh(x))sinh(x) +--R + +--R 5 4 4 5 4 2 5 +--R (90b - 90a b)cosh(x) + (- 108b + 108a b)cosh(x) + 18b +--R + +--R 4 +--R - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 5 4 3 +--R (36b - 36a b)cosh(x) + (- 72b + 72a b)cosh(x) +--R + +--R 5 4 +--R (36b - 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 6 5 4 4 +--R (6b - 6a b)cosh(x) + (- 18b + 18a b)cosh(x) +--R + +--R 5 4 2 5 4 +--R (18b - 18a b)cosh(x) - 6b + 6a b +--R * +--R log(sinh(x)) +--R + +--R 5 4 6 5 4 5 +--R (- 6b + 6a b)sinh(x) + (- 36b + 36a b)cosh(x)sinh(x) +--R + +--R 5 4 2 5 4 4 +--R ((- 90b + 90a b)cosh(x) + 18b - 18a b)sinh(x) +--R + +--R 5 4 3 5 4 3 +--R ((- 120b + 120a b)cosh(x) + (72b - 72a b)cosh(x))sinh(x) +--R + +--R 5 4 4 5 4 2 5 +--R (- 90b + 90a b)cosh(x) + (108b - 108a b)cosh(x) - 18b +--R + +--R 4 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 5 4 3 +--R (- 36b + 36a b)cosh(x) + (72b - 72a b)cosh(x) +--R + +--R 5 4 +--R (- 36b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 6 5 4 4 +--R (- 6b + 6a b)cosh(x) + (18b - 18a b)cosh(x) +--R + +--R 5 4 2 5 4 +--R (- 18b + 18a b)cosh(x) + 6b - 6a b +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 5 6 5 5 5 2 5 4 +--R 6b sinh(x) + 36b cosh(x)sinh(x) + (90b cosh(x) - 18b )sinh(x) +--R + +--R 5 3 5 3 +--R (120b cosh(x) - 72b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (90b cosh(x) - 108b cosh(x) + 18b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (36b cosh(x) - 72b cosh(x) + 36b cosh(x))sinh(x) + 6b cosh(x) +--R + +--R 5 4 5 2 5 +--R - 18b cosh(x) + 18b cosh(x) - 6b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 5 3 2 3 4 2 +--R (2a b - 2a )coth(x) + (- 3a b + 3a b)coth(x) +--R + +--R 4 5 4 +--R (6a b - 6a )coth(x) - 6a b x +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 4 2 +--R (12a b - 12a )cosh(x)coth(x) + (- 18a b + 18a b)cosh(x)coth(x) +--R + +--R 4 5 4 +--R (36a b - 36a )cosh(x)coth(x) - 36a b x cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 5 2 3 2 5 3 +--R ((30a b - 30a )cosh(x) - 6a b + 6a )coth(x) +--R + +--R 2 3 4 2 2 3 4 2 +--R ((- 45a b + 45a b)cosh(x) + 9a b - 9a b)coth(x) +--R + +--R 4 5 2 4 5 4 2 +--R ((90a b - 90a )cosh(x) - 18a b + 18a )coth(x) - 90a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 +--R 18a b x - 12a b + 12a b - 12a b - 12a b + 24a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 5 3 3 2 5 3 +--R ((40a b - 40a )cosh(x) + (- 24a b + 24a )cosh(x))coth(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R ((- 60a b + 60a b)cosh(x) + (36a b - 36a b)cosh(x))coth(x) +--R + +--R 4 5 3 4 5 +--R ((120a b - 120a )cosh(x) + (- 72a b + 72a )cosh(x))coth(x) +--R + +--R 4 3 +--R - 120a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 +--R (72a b x - 48a b + 48a b - 48a b - 48a b + 96a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R ((30a b - 30a )cosh(x) + (- 36a b + 36a )cosh(x) + 6a b - 6a ) +--R * +--R 3 +--R coth(x) +--R + +--R 2 3 4 4 2 3 4 2 2 3 +--R (- 45a b + 45a b)cosh(x) + (54a b - 54a b)cosh(x) - 9a b +--R + +--R 4 +--R 9a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 5 4 4 5 2 4 +--R (90a b - 90a )cosh(x) + (- 108a b + 108a )cosh(x) + 18a b +--R + +--R 5 +--R - 18a +--R * +--R coth(x) +--R + +--R 4 4 +--R - 90a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 2 +--R (108a b x - 72a b + 72a b - 72a b - 72a b + 144a )cosh(x) +--R + +--R 4 4 2 3 4 5 +--R - 18a b x + 24a b - 12a b + 12a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 5 3 2 5 3 +--R (12a b - 12a )cosh(x) + (- 24a b + 24a )cosh(x) +--R + +--R 3 2 5 +--R (12a b - 12a )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 2 3 4 5 2 3 4 3 +--R (- 18a b + 18a b)cosh(x) + (36a b - 36a b)cosh(x) +--R + +--R 2 3 4 +--R (- 18a b + 18a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 4 5 5 4 5 3 +--R (36a b - 36a )cosh(x) + (- 72a b + 72a )cosh(x) +--R + +--R 4 5 +--R (36a b - 36a )cosh(x) +--R * +--R coth(x) +--R + +--R 4 5 +--R - 36a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 3 +--R (72a b x - 48a b + 48a b - 48a b - 48a b + 96a )cosh(x) +--R + +--R 4 4 2 3 4 5 +--R (- 36a b x + 48a b - 24a b + 24a b - 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 5 6 3 2 5 4 +--R (2a b - 2a )cosh(x) + (- 6a b + 6a )cosh(x) +--R + +--R 3 2 5 2 3 2 5 +--R (6a b - 6a )cosh(x) - 2a b + 2a +--R * +--R 3 +--R coth(x) +--R + +--R 2 3 4 6 2 3 4 4 +--R (- 3a b + 3a b)cosh(x) + (9a b - 9a b)cosh(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 9a b + 9a b)cosh(x) + 3a b - 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 4 5 6 4 5 4 +--R (6a b - 6a )cosh(x) + (- 18a b + 18a )cosh(x) +--R + +--R 4 5 2 4 5 +--R (18a b - 18a )cosh(x) - 6a b + 6a +--R * +--R coth(x) +--R + +--R 4 6 +--R - 6a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 4 +--R (18a b x - 12a b + 12a b - 12a b - 12a b + 24a )cosh(x) +--R + +--R 4 4 2 3 4 5 2 4 4 +--R (- 18a b x + 24a b - 12a b + 12a b - 24a )cosh(x) + 6a b x - 12a b +--R + +--R 3 2 5 +--R - 4a b + 16a +--R / +--R 4 2 6 6 4 2 6 5 +--R (6a b - 6a )sinh(x) + (36a b - 36a )cosh(x)sinh(x) +--R + +--R 4 2 6 2 4 2 6 4 +--R ((90a b - 90a )cosh(x) - 18a b + 18a )sinh(x) +--R + +--R 4 2 6 3 4 2 6 3 +--R ((120a b - 120a )cosh(x) + (- 72a b + 72a )cosh(x))sinh(x) +--R + +--R 4 2 6 4 4 2 6 2 4 2 6 +--R ((90a b - 90a )cosh(x) + (- 108a b + 108a )cosh(x) + 18a b - 18a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 6 5 4 2 6 3 +--R (36a b - 36a )cosh(x) + (- 72a b + 72a )cosh(x) +--R + +--R 4 2 6 +--R (36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 6 6 4 2 6 4 +--R (6a b - 6a )cosh(x) + (- 18a b + 18a )cosh(x) +--R + +--R 4 2 6 2 4 2 6 +--R (18a b - 18a )cosh(x) - 6a b + 6a +--R Type: Expression(Integer) +--E 405 + +--S 406 of 530 +d0575:= D(m0575,x) +--R +--R +--R (404) +--R 2 4 3 2 2 2 2 +--R (- a coth(x) + a b coth(x) - b coth(x) - a b coth(x) + b + a ) +--R * +--R 8 +--R sinh(x) +--R + +--R 2 4 3 2 2 +--R - 8a cosh(x)coth(x) + 8a b cosh(x)coth(x) - 8b cosh(x)coth(x) +--R + +--R 2 2 +--R - 8a b cosh(x)coth(x) + (8b + 8a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 2 4 2 3 +--R (- 28a cosh(x) + 4a )coth(x) + (28a b cosh(x) - 4a b)coth(x) +--R + +--R 2 2 2 2 2 +--R (- 28b cosh(x) + 4b )coth(x) + (- 28a b cosh(x) + 4a b)coth(x) +--R + +--R 2 2 2 2 +--R (28b + 28a )cosh(x) - 4a b + 4a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 2 4 +--R (- 56a cosh(x) + 24a cosh(x))coth(x) +--R + +--R 3 3 +--R (56a b cosh(x) - 24a b cosh(x))coth(x) +--R + +--R 2 3 2 2 +--R (- 56b cosh(x) + 24b cosh(x))coth(x) +--R + +--R 3 2 2 3 +--R (- 56a b cosh(x) + 24a b cosh(x))coth(x) + (56b + 56a )cosh(x) +--R + +--R 2 +--R (- 24a b + 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- 70a cosh(x) + 60a cosh(x) - 6a )coth(x) +--R + +--R 4 2 3 +--R (70a b cosh(x) - 60a b cosh(x) + 6a b)coth(x) +--R + +--R 2 4 2 2 2 2 +--R (- 70b cosh(x) + 60b cosh(x) - 6b )coth(x) +--R + +--R 4 2 +--R (- 70a b cosh(x) + 60a b cosh(x) - 6a b)coth(x) +--R + +--R 2 2 4 2 2 2 2 +--R (70b + 70a )cosh(x) + (- 60a b + 60a )cosh(x) - 2b + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 2 4 +--R (- 56a cosh(x) + 80a cosh(x) - 24a cosh(x))coth(x) +--R + +--R 5 3 3 +--R (56a b cosh(x) - 80a b cosh(x) + 24a b cosh(x))coth(x) +--R + +--R 2 5 2 3 2 2 +--R (- 56b cosh(x) + 80b cosh(x) - 24b cosh(x))coth(x) +--R + +--R 5 3 +--R (- 56a b cosh(x) + 80a b cosh(x) - 24a b cosh(x))coth(x) +--R + +--R 2 2 5 2 3 +--R (56b + 56a )cosh(x) + (- 80a b + 80a )cosh(x) +--R + +--R 2 2 +--R (- 8b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 2 4 +--R (- 28a cosh(x) + 60a cosh(x) - 36a cosh(x) + 4a )coth(x) +--R + +--R 6 4 2 3 +--R (28a b cosh(x) - 60a b cosh(x) + 36a b cosh(x) - 4a b)coth(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 28b cosh(x) + 60b cosh(x) - 36b cosh(x) + 4b )coth(x) +--R + +--R 6 4 2 +--R (- 28a b cosh(x) + 60a b cosh(x) - 36a b cosh(x) + 4a b)coth(x) +--R + +--R 2 2 6 2 4 +--R (28b + 28a )cosh(x) + (- 60a b + 60a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b + 36a )cosh(x) + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 2 4 +--R (- 8a cosh(x) + 24a cosh(x) - 24a cosh(x) + 8a cosh(x))coth(x) +--R + +--R 7 5 3 +--R (8a b cosh(x) - 24a b cosh(x) + 24a b cosh(x) - 8a b cosh(x)) +--R * +--R 3 +--R coth(x) +--R + +--R 2 7 2 5 2 3 2 2 +--R (- 8b cosh(x) + 24b cosh(x) - 24b cosh(x) + 8b cosh(x))coth(x) +--R + +--R 7 5 3 +--R (- 8a b cosh(x) + 24a b cosh(x) - 24a b cosh(x) + 8a b cosh(x)) +--R * +--R coth(x) +--R + +--R 2 2 7 2 5 +--R (8b + 8a )cosh(x) + (- 24a b + 24a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 8b + 24a )cosh(x) + (8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 2 4 +--R (- a cosh(x) + 4a cosh(x) - 6a cosh(x) + 4a cosh(x) - a )coth(x) +--R + +--R 8 6 4 2 +--R (a b cosh(x) - 4a b cosh(x) + 6a b cosh(x) - 4a b cosh(x) + a b) +--R * +--R 3 +--R coth(x) +--R + +--R 2 8 2 6 2 4 2 2 2 2 +--R (- b cosh(x) + 4b cosh(x) - 6b cosh(x) + 4b cosh(x) - b )coth(x) +--R + +--R 8 6 4 2 +--R (- a b cosh(x) + 4a b cosh(x) - 6a b cosh(x) + 4a b cosh(x) - a b) +--R * +--R coth(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (b + a )cosh(x) + (- 4a b + 4a )cosh(x) + (- 2b + 6a )cosh(x) +--R + +--R 2 2 2 2 +--R (4a b + 4a )cosh(x) + b + a +--R / +--R 3 8 3 7 3 2 3 6 +--R a sinh(x) + 8a cosh(x)sinh(x) + (28a cosh(x) - 4a )sinh(x) +--R + +--R 3 3 3 5 +--R (56a cosh(x) - 24a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 4 +--R (70a cosh(x) - 60a cosh(x) + 6a )sinh(x) +--R + +--R 3 5 3 3 3 3 +--R (56a cosh(x) - 80a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 2 +--R (28a cosh(x) - 60a cosh(x) + 36a cosh(x) - 4a )sinh(x) +--R + +--R 3 7 3 5 3 3 3 +--R (8a cosh(x) - 24a cosh(x) + 24a cosh(x) - 8a cosh(x))sinh(x) +--R + +--R 3 8 3 6 3 4 3 2 3 +--R a cosh(x) - 4a cosh(x) + 6a cosh(x) - 4a cosh(x) + a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 530 +t0576:= coth(x)/(1+tanh(x)) +--R +--R +--R coth(x) +--R (405) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 530 +r0576:= -1/2*x+log(sinh(x))+1/(2+2*tanh(x)) +--R +--R +--R (2tanh(x) + 2)log(sinh(x)) - x tanh(x) - x + 1 +--R (406) ---------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 530 +a0576:= integrate(t0576,x) +--R +--R +--R (407) +--R 2 2 2sinh(x) +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 6x sinh(x) - 12x cosh(x)sinh(x) - 6x cosh(x) + 1 +--R / +--R 2 2 +--R 4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 409 + +--S 410 of 530 +m0576:= a0576-r0576 +--R +--R +--R (408) +--R 2 2 2 +--R (- 4sinh(x) - 8cosh(x)sinh(x) - 4cosh(x) )tanh(x) - 4sinh(x) +--R + +--R 2 +--R - 8cosh(x)sinh(x) - 4cosh(x) +--R * +--R log(sinh(x)) +--R + +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 4x sinh(x) - 8x cosh(x)sinh(x) - 4x cosh(x) + 1)tanh(x) +--R + +--R 2 2 +--R (- 4x - 2)sinh(x) + (- 8x - 4)cosh(x)sinh(x) + (- 4x - 2)cosh(x) + 1 +--R / +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 410 + +--S 411 of 530 +d0576:= D(m0576,x) +--R +--R +--R (409) +--R 2 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)tanh(x) + sinh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 2 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )tanh(x) + 2sinh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 411 + +--S 412 of 530 +t0577:= coth(x)^2/(1+tanh(x)) +--R +--R +--R 2 +--R coth(x) +--R (410) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 530 +r0577:= 3/2*x-coth(x)-log(sinh(x))-1/(2+2*tanh(x)) +--R +--R +--R (411) +--R (- 2tanh(x) - 2)log(sinh(x)) + (- 2coth(x) + 3x)tanh(x) - 2coth(x) + 3x - 1 +--R --------------------------------------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 530 +a0577:= integrate(t0577,x) +--R +--R +--R (412) +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 8cosh(x))sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R 10x sinh(x) + 40x cosh(x)sinh(x) + (60x cosh(x) - 10x - 9)sinh(x) +--R + +--R 3 4 +--R (40x cosh(x) + (- 20x - 18)cosh(x))sinh(x) + 10x cosh(x) +--R + +--R 2 +--R (- 10x - 9)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 414 + +--S 415 of 530 +m0577:= a0577-r0577 +--R +--R +--R (413) +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R log(sinh(x)) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 8cosh(x))sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 8cosh(x))sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 +--R (4coth(x) + 4x)sinh(x) + (16cosh(x)coth(x) + 16x cosh(x))sinh(x) +--R + +--R 2 2 2 +--R ((24cosh(x) - 4)coth(x) + 24x cosh(x) - 4x - 9)sinh(x) +--R + +--R 3 3 +--R (16cosh(x) - 8cosh(x))coth(x) + 16x cosh(x) +--R + +--R (- 8x - 18)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 4 2 +--R (4cosh(x) - 4cosh(x) )coth(x) + 4x cosh(x) + (- 4x - 9)cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 4 +--R (4coth(x) + 4x + 2)sinh(x) +--R + +--R 3 +--R (16cosh(x)coth(x) + (16x + 8)cosh(x))sinh(x) +--R + +--R 2 2 2 +--R ((24cosh(x) - 4)coth(x) + (24x + 12)cosh(x) - 4x - 11)sinh(x) +--R + +--R 3 3 +--R (16cosh(x) - 8cosh(x))coth(x) + (16x + 8)cosh(x) +--R + +--R (- 8x - 22)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 4 2 +--R (4cosh(x) - 4cosh(x) )coth(x) + (4x + 2)cosh(x) + (- 4x - 11)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R Type: Expression(Integer) +--E 415 + +--S 416 of 530 +d0577:= D(m0577,x) +--R +--R +--R (414) +--R 2 6 2 5 +--R (- 2coth(x) + 3)sinh(x) + (- 12cosh(x)coth(x) + 18cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30cosh(x) + 4)coth(x) + 45cosh(x) + 3)sinh(x) +--R + +--R 3 2 3 3 +--R ((- 40cosh(x) + 16cosh(x))coth(x) + 60cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (- 30cosh(x) + 24cosh(x) - 2)coth(x) + 45cosh(x) + 18cosh(x) +--R + +--R 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 12cosh(x) + 16cosh(x) - 4cosh(x))coth(x) + 18cosh(x) +--R + +--R 3 +--R 12cosh(x) + 2cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (- 2cosh(x) + 4cosh(x) - 2cosh(x) )coth(x) + 3cosh(x) + 3cosh(x) +--R + +--R 2 +--R cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 2 6 2 5 +--R (- 2coth(x) + 1)sinh(x) + (- 12cosh(x)coth(x) + 6cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30cosh(x) + 4)coth(x) + 15cosh(x) + 7)sinh(x) +--R + +--R 3 2 3 3 +--R ((- 40cosh(x) + 16cosh(x))coth(x) + 20cosh(x) + 28cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R ((- 30cosh(x) + 24cosh(x) - 2)coth(x) + 15cosh(x) + 42cosh(x) - 1) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 12cosh(x) + 16cosh(x) - 4cosh(x))coth(x) + 6cosh(x) +--R + +--R 3 +--R 28cosh(x) - 2cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (- 2cosh(x) + 4cosh(x) - 2cosh(x) )coth(x) + cosh(x) + 7cosh(x) +--R + +--R 2 +--R - cosh(x) + 1 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) - 4)sinh(x) +--R + +--R 3 3 4 2 2 +--R (40cosh(x) - 16cosh(x))sinh(x) + (30cosh(x) - 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R Type: Expression(Integer) +--E 416 + +--S 417 of 530 +t0578:= coth(x)^3/(1+tanh(x)) +--R +--R +--R 3 +--R coth(x) +--R (415) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 530 +r0578:= -3/2*x+coth(x)-1/2*coth(x)^2+2*log(sinh(x))+1/(2+2*tanh(x)) +--R +--R +--R (416) +--R 2 +--R (4tanh(x) + 4)log(sinh(x)) + (- coth(x) + 2coth(x) - 3x)tanh(x) +--R + +--R 2 +--R - coth(x) + 2coth(x) - 3x + 1 +--R / +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 530 +a0578:= integrate(t0578,x) +--R +--R +--R (417) +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) - 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (48cosh(x) - 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) - 16cosh(x) +--R + +--R 2 +--R 8cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 5 +--R - 14x sinh(x) - 84x cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 210x cosh(x) + 28x + 1)sinh(x) +--R + +--R 3 3 +--R (- 280x cosh(x) + (112x + 4)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 210x cosh(x) + (168x + 6)cosh(x) - 14x - 10)sinh(x) +--R + +--R 5 3 +--R (- 84x cosh(x) + (112x + 4)cosh(x) + (- 28x - 20)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 14x cosh(x) + (28x + 1)cosh(x) + (- 14x - 10)cosh(x) + 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 8)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) - 32cosh(x))sinh(x) + (60cosh(x) - 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 419 + +--S 420 of 530 +m0578:= a0578-r0578 +--R +--R +--R (418) +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) + 96cosh(x) - 8)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) + 64cosh(x) - 16cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R 16cosh(x) - 8cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) + 96cosh(x) - 8)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) + 64cosh(x) - 16cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R 16cosh(x) - 8cosh(x) +--R * +--R log(sinh(x)) +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) - 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 +--R (48cosh(x) - 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) +--R + +--R 4 2 +--R - 16cosh(x) + 8cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) - 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (48cosh(x) - 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) - 16cosh(x) +--R + +--R 2 +--R 8cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 6 +--R (2coth(x) - 4coth(x) - 8x)sinh(x) +--R + +--R 2 5 +--R (12cosh(x)coth(x) - 24cosh(x)coth(x) - 48x cosh(x))sinh(x) +--R + +--R 2 2 2 +--R (30cosh(x) - 4)coth(x) + (- 60cosh(x) + 8)coth(x) +--R + +--R 2 +--R - 120x cosh(x) + 16x + 1 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (40cosh(x) - 16cosh(x))coth(x) +--R + +--R 3 3 +--R (- 80cosh(x) + 32cosh(x))coth(x) - 160x cosh(x) +--R + +--R (64x + 4)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 24cosh(x) + 2)coth(x) +--R + +--R 4 2 4 +--R (- 60cosh(x) + 48cosh(x) - 4)coth(x) - 120x cosh(x) +--R + +--R 2 +--R (96x + 6)cosh(x) - 8x - 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))coth(x) +--R + +--R 5 3 5 +--R (- 24cosh(x) + 32cosh(x) - 8cosh(x))coth(x) - 48x cosh(x) +--R + +--R 3 +--R (64x + 4)cosh(x) + (- 16x - 20)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (2cosh(x) - 4cosh(x) + 2cosh(x) )coth(x) +--R + +--R 6 4 2 6 +--R (- 4cosh(x) + 8cosh(x) - 4cosh(x) )coth(x) - 8x cosh(x) +--R + +--R 4 2 +--R (16x + 1)cosh(x) + (- 8x - 10)cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 2 6 +--R (2coth(x) - 4coth(x) - 8x - 2)sinh(x) +--R + +--R 2 5 +--R (12cosh(x)coth(x) - 24cosh(x)coth(x) + (- 48x - 12)cosh(x))sinh(x) +--R + +--R 2 2 2 +--R (30cosh(x) - 4)coth(x) + (- 60cosh(x) + 8)coth(x) +--R + +--R 2 +--R (- 120x - 30)cosh(x) + 16x + 5 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 +--R (40cosh(x) - 16cosh(x))coth(x) + (- 80cosh(x) + 32cosh(x))coth(x) +--R + +--R 3 +--R (- 160x - 40)cosh(x) + (64x + 20)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 24cosh(x) + 2)coth(x) +--R + +--R 4 2 4 +--R (- 60cosh(x) + 48cosh(x) - 4)coth(x) + (- 120x - 30)cosh(x) +--R + +--R 2 +--R (96x + 30)cosh(x) - 8x - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))coth(x) +--R + +--R 5 3 5 +--R (- 24cosh(x) + 32cosh(x) - 8cosh(x))coth(x) + (- 48x - 12)cosh(x) +--R + +--R 3 +--R (64x + 20)cosh(x) + (- 16x - 24)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (2cosh(x) - 4cosh(x) + 2cosh(x) )coth(x) +--R + +--R 6 4 2 6 +--R (- 4cosh(x) + 8cosh(x) - 4cosh(x) )coth(x) + (- 8x - 2)cosh(x) +--R + +--R 4 2 +--R (16x + 5)cosh(x) + (- 8x - 12)cosh(x) + 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 8)sinh(x) +--R + +--R 3 3 +--R (80cosh(x) - 32cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (60cosh(x) - 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 8)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) - 32cosh(x))sinh(x) + (60cosh(x) - 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R Type: Expression(Integer) +--E 420 + +--S 421 of 530 +d0578:= D(m0578,x) +--R +--R +--R (419) +--R 3 2 8 +--R (- 2coth(x) + 2coth(x) + 2coth(x) - 3)sinh(x) +--R + +--R 3 2 +--R - 16cosh(x)coth(x) + 16cosh(x)coth(x) + 16cosh(x)coth(x) +--R + +--R - 24cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 56cosh(x) + 6)coth(x) + (56cosh(x) - 6)coth(x) +--R + +--R 2 2 +--R (56cosh(x) - 6)coth(x) - 84cosh(x) + 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 +--R (- 112cosh(x) + 36cosh(x))coth(x) +--R + +--R 3 2 +--R (112cosh(x) - 36cosh(x))coth(x) +--R + +--R 3 3 +--R (112cosh(x) - 36cosh(x))coth(x) - 168cosh(x) + 48cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 +--R (- 140cosh(x) + 90cosh(x) - 6)coth(x) +--R + +--R 4 2 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) +--R + +--R 4 2 4 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) - 210cosh(x) + 120cosh(x) +--R + +--R 10 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) + 120cosh(x) - 24cosh(x))coth(x) +--R + +--R 5 3 2 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) +--R + +--R 5 3 5 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) - 168cosh(x) +--R + +--R 3 +--R 160cosh(x) + 40cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- 56cosh(x) + 90cosh(x) - 36cosh(x) + 2)coth(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) +--R + +--R 6 4 2 6 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) - 84cosh(x) +--R + +--R 4 2 +--R 120cosh(x) + 60cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 3 +--R (- 16cosh(x) + 36cosh(x) - 24cosh(x) + 4cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) +--R + +--R 7 5 3 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) +--R + +--R 7 5 3 +--R - 24cosh(x) + 48cosh(x) + 40cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (- 2cosh(x) + 6cosh(x) - 6cosh(x) + 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 2 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 8 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) - 3cosh(x) +--R + +--R 6 4 +--R 8cosh(x) + 10cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 3 2 8 +--R (- 2coth(x) + 2coth(x) + 2coth(x) - 1)sinh(x) +--R + +--R 3 2 +--R (- 16cosh(x)coth(x) + 16cosh(x)coth(x) + 16cosh(x)coth(x) - 8cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 56cosh(x) + 6)coth(x) + (56cosh(x) - 6)coth(x) +--R + +--R 2 2 +--R (56cosh(x) - 6)coth(x) - 28cosh(x) + 2 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 +--R (- 112cosh(x) + 36cosh(x))coth(x) +--R + +--R 3 2 3 +--R (112cosh(x) - 36cosh(x))coth(x) + (112cosh(x) - 36cosh(x))coth(x) +--R + +--R 3 +--R - 56cosh(x) + 12cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 +--R (- 140cosh(x) + 90cosh(x) - 6)coth(x) +--R + +--R 4 2 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) +--R + +--R 4 2 4 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) - 70cosh(x) + 30cosh(x) + 16 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) + 120cosh(x) - 24cosh(x))coth(x) +--R + +--R 5 3 2 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) +--R + +--R 5 3 5 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) - 56cosh(x) +--R + +--R 3 +--R 40cosh(x) + 64cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- 56cosh(x) + 90cosh(x) - 36cosh(x) + 2)coth(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) +--R + +--R 6 4 2 6 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) - 28cosh(x) +--R + +--R 4 2 +--R 30cosh(x) + 96cosh(x) - 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 3 +--R (- 16cosh(x) + 36cosh(x) - 24cosh(x) + 4cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) +--R + +--R 7 5 3 7 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) - 8cosh(x) +--R + +--R 5 3 +--R 12cosh(x) + 64cosh(x) - 4cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (- 2cosh(x) + 6cosh(x) - 6cosh(x) + 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 2 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 8 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) - cosh(x) +--R + +--R 6 4 2 +--R 2cosh(x) + 16cosh(x) - 2cosh(x) + 1 +--R / +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) - 6)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) - 90cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 6cosh(x) + 6cosh(x) - 2cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) - 6)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) - 90cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 6cosh(x) + 6cosh(x) - 2cosh(x) +--R Type: Expression(Integer) +--E 421 + +--S 422 of 530 +t0579:= coth(x)^4/(1+tanh(x)) +--R +--R +--R 4 +--R coth(x) +--R (420) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 530 +r0579:= 5/2*x-2*coth(x)+1/2*coth(x)^2-1/3*coth(x)^3-2*log(sinh(x))-_ + 1/(2+2*tanh(x)) +--R +--R +--R (421) +--R (- 12tanh(x) - 12)log(sinh(x)) +--R + +--R 3 2 3 +--R (- 2coth(x) + 3coth(x) - 12coth(x) + 15x)tanh(x) - 2coth(x) +--R + +--R 2 +--R 3coth(x) - 12coth(x) + 15x - 3 +--R / +--R 6tanh(x) + 6 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 530 +a0579:= integrate(t0579,x) +--R +--R +--R (422) +--R 8 7 2 6 +--R - 24sinh(x) - 192cosh(x)sinh(x) + (- 672cosh(x) + 72)sinh(x) +--R + +--R 3 5 +--R (- 1344cosh(x) + 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1680cosh(x) + 1080cosh(x) - 72)sinh(x) +--R + +--R 5 3 3 +--R (- 1344cosh(x) + 1440cosh(x) - 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 672cosh(x) + 1080cosh(x) - 432cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 +--R (- 192cosh(x) + 432cosh(x) - 288cosh(x) + 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 24cosh(x) + 72cosh(x) - 72cosh(x) + 24cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 8 7 +--R 54x sinh(x) + 432x cosh(x)sinh(x) +--R + +--R 2 6 +--R (1512x cosh(x) - 162x - 51)sinh(x) +--R + +--R 3 5 +--R (3024x cosh(x) + (- 972x - 306)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (3780x cosh(x) + (- 2430x - 765)cosh(x) + 162x + 81)sinh(x) +--R + +--R 5 3 3 +--R (3024x cosh(x) + (- 3240x - 1020)cosh(x) + (648x + 324)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 1512x cosh(x) + (- 2430x - 765)cosh(x) + (972x + 486)cosh(x) - 54x +--R + +--R - 65 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R 432x cosh(x) + (- 972x - 306)cosh(x) + (648x + 324)cosh(x) +--R + +--R (- 108x - 130)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 +--R 54x cosh(x) + (- 162x - 51)cosh(x) + (162x + 81)cosh(x) +--R + +--R 2 +--R (- 54x - 65)cosh(x) + 3 +--R / +--R 8 7 2 6 +--R 12sinh(x) + 96cosh(x)sinh(x) + (336cosh(x) - 36)sinh(x) +--R + +--R 3 5 +--R (672cosh(x) - 216cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (840cosh(x) - 540cosh(x) + 36)sinh(x) +--R + +--R 5 3 3 +--R (672cosh(x) - 720cosh(x) + 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (336cosh(x) - 540cosh(x) + 216cosh(x) - 12)sinh(x) +--R + +--R 7 5 3 8 +--R (96cosh(x) - 216cosh(x) + 144cosh(x) - 24cosh(x))sinh(x) + 12cosh(x) +--R + +--R 6 4 2 +--R - 36cosh(x) + 36cosh(x) - 12cosh(x) +--R Type: Union(Expression(Integer),...) +--E 424 + +--S 425 of 530 +m0579:= a0579-r0579 +--R +--R +--R (423) +--R 8 7 2 6 +--R 24sinh(x) + 192cosh(x)sinh(x) + (672cosh(x) - 72)sinh(x) +--R + +--R 3 5 +--R (1344cosh(x) - 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1680cosh(x) - 1080cosh(x) + 72)sinh(x) +--R + +--R 5 3 3 +--R (1344cosh(x) - 1440cosh(x) + 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (672cosh(x) - 1080cosh(x) + 432cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 +--R (192cosh(x) - 432cosh(x) + 288cosh(x) - 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 24cosh(x) - 72cosh(x) + 72cosh(x) - 24cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 24sinh(x) + 192cosh(x)sinh(x) + (672cosh(x) - 72)sinh(x) +--R + +--R 3 5 +--R (1344cosh(x) - 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1680cosh(x) - 1080cosh(x) + 72)sinh(x) +--R + +--R 5 3 3 +--R (1344cosh(x) - 1440cosh(x) + 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (672cosh(x) - 1080cosh(x) + 432cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 +--R (192cosh(x) - 432cosh(x) + 288cosh(x) - 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 24cosh(x) - 72cosh(x) + 72cosh(x) - 24cosh(x) +--R * +--R log(sinh(x)) +--R + +--R 8 7 2 6 +--R - 24sinh(x) - 192cosh(x)sinh(x) + (- 672cosh(x) + 72)sinh(x) +--R + +--R 3 5 +--R (- 1344cosh(x) + 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1680cosh(x) + 1080cosh(x) - 72)sinh(x) +--R + +--R 5 3 3 +--R (- 1344cosh(x) + 1440cosh(x) - 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 672cosh(x) + 1080cosh(x) - 432cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 +--R (- 192cosh(x) + 432cosh(x) - 288cosh(x) + 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 24cosh(x) + 72cosh(x) - 72cosh(x) + 24cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 24sinh(x) - 192cosh(x)sinh(x) + (- 672cosh(x) + 72)sinh(x) +--R + +--R 3 5 +--R (- 1344cosh(x) + 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1680cosh(x) + 1080cosh(x) - 72)sinh(x) +--R + +--R 5 3 3 +--R (- 1344cosh(x) + 1440cosh(x) - 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 672cosh(x) + 1080cosh(x) - 432cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 +--R (- 192cosh(x) + 432cosh(x) - 288cosh(x) + 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 24cosh(x) + 72cosh(x) - 72cosh(x) + 24cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 8 +--R (4coth(x) - 6coth(x) + 24coth(x) + 24x)sinh(x) +--R + +--R 3 2 +--R 32cosh(x)coth(x) - 48cosh(x)coth(x) + 192cosh(x)coth(x) +--R + +--R 192x cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (112cosh(x) - 12)coth(x) + (- 168cosh(x) + 18)coth(x) +--R + +--R 2 2 +--R (672cosh(x) - 72)coth(x) + 672x cosh(x) - 72x - 51 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 +--R (224cosh(x) - 72cosh(x))coth(x) +--R + +--R 3 2 +--R (- 336cosh(x) + 108cosh(x))coth(x) +--R + +--R 3 3 +--R (1344cosh(x) - 432cosh(x))coth(x) + 1344x cosh(x) +--R + +--R (- 432x - 306)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 +--R (280cosh(x) - 180cosh(x) + 12)coth(x) +--R + +--R 4 2 2 +--R (- 420cosh(x) + 270cosh(x) - 18)coth(x) +--R + +--R 4 2 4 +--R (1680cosh(x) - 1080cosh(x) + 72)coth(x) + 1680x cosh(x) +--R + +--R 2 +--R (- 1080x - 765)cosh(x) + 72x + 81 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) - 240cosh(x) + 48cosh(x))coth(x) +--R + +--R 5 3 2 +--R (- 336cosh(x) + 360cosh(x) - 72cosh(x))coth(x) +--R + +--R 5 3 +--R (1344cosh(x) - 1440cosh(x) + 288cosh(x))coth(x) +--R + +--R 5 3 +--R 1344x cosh(x) + (- 1440x - 1020)cosh(x) + (288x + 324)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (112cosh(x) - 180cosh(x) + 72cosh(x) - 4)coth(x) +--R + +--R 6 4 2 2 +--R (- 168cosh(x) + 270cosh(x) - 108cosh(x) + 6)coth(x) +--R + +--R 6 4 2 +--R (672cosh(x) - 1080cosh(x) + 432cosh(x) - 24)coth(x) +--R + +--R 6 4 2 +--R 672x cosh(x) + (- 1080x - 765)cosh(x) + (432x + 486)cosh(x) +--R + +--R - 24x - 65 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 3 +--R (32cosh(x) - 72cosh(x) + 48cosh(x) - 8cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (- 48cosh(x) + 108cosh(x) - 72cosh(x) + 12cosh(x))coth(x) +--R + +--R 7 5 3 +--R (192cosh(x) - 432cosh(x) + 288cosh(x) - 48cosh(x))coth(x) +--R + +--R 7 5 3 +--R 192x cosh(x) + (- 432x - 306)cosh(x) + (288x + 324)cosh(x) +--R + +--R (- 48x - 130)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (4cosh(x) - 12cosh(x) + 12cosh(x) - 4cosh(x) )coth(x) +--R + +--R 8 6 4 2 2 +--R (- 6cosh(x) + 18cosh(x) - 18cosh(x) + 6cosh(x) )coth(x) +--R + +--R 8 6 4 2 +--R (24cosh(x) - 72cosh(x) + 72cosh(x) - 24cosh(x) )coth(x) +--R + +--R 8 6 4 +--R 24x cosh(x) + (- 72x - 51)cosh(x) + (72x + 81)cosh(x) +--R + +--R 2 +--R (- 24x - 65)cosh(x) + 3 +--R * +--R tanh(x) +--R + +--R 3 2 8 +--R (4coth(x) - 6coth(x) + 24coth(x) + 24x + 6)sinh(x) +--R + +--R 3 2 +--R 32cosh(x)coth(x) - 48cosh(x)coth(x) + 192cosh(x)coth(x) +--R + +--R (192x + 48)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (112cosh(x) - 12)coth(x) + (- 168cosh(x) + 18)coth(x) +--R + +--R 2 2 +--R (672cosh(x) - 72)coth(x) + (672x + 168)cosh(x) - 72x - 69 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 +--R (224cosh(x) - 72cosh(x))coth(x) +--R + +--R 3 2 +--R (- 336cosh(x) + 108cosh(x))coth(x) +--R + +--R 3 3 +--R (1344cosh(x) - 432cosh(x))coth(x) + (1344x + 336)cosh(x) +--R + +--R (- 432x - 414)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 +--R (280cosh(x) - 180cosh(x) + 12)coth(x) +--R + +--R 4 2 2 +--R (- 420cosh(x) + 270cosh(x) - 18)coth(x) +--R + +--R 4 2 4 +--R (1680cosh(x) - 1080cosh(x) + 72)coth(x) + (1680x + 420)cosh(x) +--R + +--R 2 +--R (- 1080x - 1035)cosh(x) + 72x + 99 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) - 240cosh(x) + 48cosh(x))coth(x) +--R + +--R 5 3 2 +--R (- 336cosh(x) + 360cosh(x) - 72cosh(x))coth(x) +--R + +--R 5 3 +--R (1344cosh(x) - 1440cosh(x) + 288cosh(x))coth(x) +--R + +--R 5 3 +--R (1344x + 336)cosh(x) + (- 1440x - 1380)cosh(x) + (288x + 396)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (112cosh(x) - 180cosh(x) + 72cosh(x) - 4)coth(x) +--R + +--R 6 4 2 2 +--R (- 168cosh(x) + 270cosh(x) - 108cosh(x) + 6)coth(x) +--R + +--R 6 4 2 +--R (672cosh(x) - 1080cosh(x) + 432cosh(x) - 24)coth(x) +--R + +--R 6 4 +--R (672x + 168)cosh(x) + (- 1080x - 1035)cosh(x) +--R + +--R 2 +--R (432x + 594)cosh(x) - 24x - 71 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 3 +--R (32cosh(x) - 72cosh(x) + 48cosh(x) - 8cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (- 48cosh(x) + 108cosh(x) - 72cosh(x) + 12cosh(x))coth(x) +--R + +--R 7 5 3 +--R (192cosh(x) - 432cosh(x) + 288cosh(x) - 48cosh(x))coth(x) +--R + +--R 7 5 3 +--R (192x + 48)cosh(x) + (- 432x - 414)cosh(x) + (288x + 396)cosh(x) +--R + +--R (- 48x - 142)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (4cosh(x) - 12cosh(x) + 12cosh(x) - 4cosh(x) )coth(x) +--R + +--R 8 6 4 2 2 +--R (- 6cosh(x) + 18cosh(x) - 18cosh(x) + 6cosh(x) )coth(x) +--R + +--R 8 6 4 2 +--R (24cosh(x) - 72cosh(x) + 72cosh(x) - 24cosh(x) )coth(x) +--R + +--R 8 6 4 +--R (24x + 6)cosh(x) + (- 72x - 69)cosh(x) + (72x + 99)cosh(x) +--R + +--R 2 +--R (- 24x - 71)cosh(x) + 3 +--R / +--R 8 7 2 6 +--R 12sinh(x) + 96cosh(x)sinh(x) + (336cosh(x) - 36)sinh(x) +--R + +--R 3 5 +--R (672cosh(x) - 216cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (840cosh(x) - 540cosh(x) + 36)sinh(x) +--R + +--R 5 3 3 +--R (672cosh(x) - 720cosh(x) + 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (336cosh(x) - 540cosh(x) + 216cosh(x) - 12)sinh(x) +--R + +--R 7 5 3 +--R (96cosh(x) - 216cosh(x) + 144cosh(x) - 24cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 12cosh(x) - 36cosh(x) + 36cosh(x) - 12cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 12sinh(x) + 96cosh(x)sinh(x) + (336cosh(x) - 36)sinh(x) +--R + +--R 3 5 +--R (672cosh(x) - 216cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (840cosh(x) - 540cosh(x) + 36)sinh(x) +--R + +--R 5 3 3 +--R (672cosh(x) - 720cosh(x) + 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (336cosh(x) - 540cosh(x) + 216cosh(x) - 12)sinh(x) +--R + +--R 7 5 3 8 +--R (96cosh(x) - 216cosh(x) + 144cosh(x) - 24cosh(x))sinh(x) + 12cosh(x) +--R + +--R 6 4 2 +--R - 36cosh(x) + 36cosh(x) - 12cosh(x) +--R Type: Expression(Integer) +--E 425 + +--S 426 of 530 +d0579:= D(m0579,x) +--R +--R +--R (424) +--R 4 3 2 10 +--R (- 2coth(x) + 2coth(x) - 2coth(x) - 2coth(x) + 5)sinh(x) +--R + +--R 4 3 2 +--R - 20cosh(x)coth(x) + 20cosh(x)coth(x) - 20cosh(x)coth(x) +--R + +--R - 20cosh(x)coth(x) + 50cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 4 2 3 +--R (- 90cosh(x) + 8)coth(x) + (90cosh(x) - 8)coth(x) +--R + +--R 2 2 2 +--R (- 90cosh(x) + 8)coth(x) + (- 90cosh(x) + 8)coth(x) +--R + +--R 2 +--R 225cosh(x) - 3 +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 +--R (- 240cosh(x) + 64cosh(x))coth(x) +--R + +--R 3 3 +--R (240cosh(x) - 64cosh(x))coth(x) +--R + +--R 3 2 +--R (- 240cosh(x) + 64cosh(x))coth(x) +--R + +--R 3 3 +--R (- 240cosh(x) + 64cosh(x))coth(x) + 600cosh(x) - 24cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 4 +--R (- 420cosh(x) + 224cosh(x) - 12)coth(x) +--R + +--R 4 2 3 +--R (420cosh(x) - 224cosh(x) + 12)coth(x) +--R + +--R 4 2 2 +--R (- 420cosh(x) + 224cosh(x) - 12)coth(x) +--R + +--R 4 2 4 +--R (- 420cosh(x) + 224cosh(x) - 12)coth(x) + 1050cosh(x) +--R + +--R 2 +--R - 84cosh(x) + 10 +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 4 +--R (- 504cosh(x) + 448cosh(x) - 72cosh(x))coth(x) +--R + +--R 5 3 3 +--R (504cosh(x) - 448cosh(x) + 72cosh(x))coth(x) +--R + +--R 5 3 2 +--R (- 504cosh(x) + 448cosh(x) - 72cosh(x))coth(x) +--R + +--R 5 3 5 +--R (- 504cosh(x) + 448cosh(x) - 72cosh(x))coth(x) + 1260cosh(x) +--R + +--R 3 +--R - 168cosh(x) + 60cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 4 2 4 +--R (- 420cosh(x) + 560cosh(x) - 180cosh(x) + 8)coth(x) +--R + +--R 6 4 2 3 +--R (420cosh(x) - 560cosh(x) + 180cosh(x) - 8)coth(x) +--R + +--R 6 4 2 2 +--R (- 420cosh(x) + 560cosh(x) - 180cosh(x) + 8)coth(x) +--R + +--R 6 4 2 +--R (- 420cosh(x) + 560cosh(x) - 180cosh(x) + 8)coth(x) +--R + +--R 6 4 2 +--R 1050cosh(x) - 210cosh(x) + 150cosh(x) + 18 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 3 4 +--R (- 240cosh(x) + 448cosh(x) - 240cosh(x) + 32cosh(x))coth(x) +--R + +--R 7 5 3 3 +--R (240cosh(x) - 448cosh(x) + 240cosh(x) - 32cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (- 240cosh(x) + 448cosh(x) - 240cosh(x) + 32cosh(x))coth(x) +--R + +--R 7 5 3 +--R (- 240cosh(x) + 448cosh(x) - 240cosh(x) + 32cosh(x))coth(x) +--R + +--R 7 5 3 +--R 600cosh(x) - 168cosh(x) + 200cosh(x) + 72cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 90cosh(x) + 224cosh(x) - 180cosh(x) + 48cosh(x) - 2) +--R * +--R 4 +--R coth(x) +--R + +--R 8 6 4 2 3 +--R (90cosh(x) - 224cosh(x) + 180cosh(x) - 48cosh(x) + 2)coth(x) +--R + +--R 8 6 4 2 +--R (- 90cosh(x) + 224cosh(x) - 180cosh(x) + 48cosh(x) - 2) +--R * +--R 2 +--R coth(x) +--R + +--R 8 6 4 2 +--R (- 90cosh(x) + 224cosh(x) - 180cosh(x) + 48cosh(x) - 2) +--R * +--R coth(x) +--R + +--R 8 6 4 2 +--R 225cosh(x) - 84cosh(x) + 150cosh(x) + 108cosh(x) + 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 20cosh(x) + 64cosh(x) - 72cosh(x) + 32cosh(x) +--R + +--R - 4cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 9 7 5 3 +--R (20cosh(x) - 64cosh(x) + 72cosh(x) - 32cosh(x) + 4cosh(x)) +--R * +--R 3 +--R coth(x) +--R + +--R 9 7 5 3 +--R - 20cosh(x) + 64cosh(x) - 72cosh(x) + 32cosh(x) +--R + +--R - 4cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 3 +--R - 20cosh(x) + 64cosh(x) - 72cosh(x) + 32cosh(x) +--R + +--R - 4cosh(x) +--R * +--R coth(x) +--R + +--R 9 7 5 3 +--R 50cosh(x) - 24cosh(x) + 60cosh(x) + 72cosh(x) + 2cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R (- 2cosh(x) + 8cosh(x) - 12cosh(x) + 8cosh(x) - 2cosh(x) ) +--R * +--R 4 +--R coth(x) +--R + +--R 10 8 6 4 2 3 +--R (2cosh(x) - 8cosh(x) + 12cosh(x) - 8cosh(x) + 2cosh(x) )coth(x) +--R + +--R 10 8 6 4 2 +--R (- 2cosh(x) + 8cosh(x) - 12cosh(x) + 8cosh(x) - 2cosh(x) ) +--R * +--R 2 +--R coth(x) +--R + +--R 10 8 6 4 2 +--R (- 2cosh(x) + 8cosh(x) - 12cosh(x) + 8cosh(x) - 2cosh(x) ) +--R * +--R coth(x) +--R + +--R 10 8 6 4 2 +--R 5cosh(x) - 3cosh(x) + 10cosh(x) + 18cosh(x) + cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 4 3 2 10 +--R (- 2coth(x) + 2coth(x) - 2coth(x) - 2coth(x) + 3)sinh(x) +--R + +--R 4 3 2 +--R - 20cosh(x)coth(x) + 20cosh(x)coth(x) - 20cosh(x)coth(x) +--R + +--R - 20cosh(x)coth(x) + 30cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 4 2 3 +--R (- 90cosh(x) + 8)coth(x) + (90cosh(x) - 8)coth(x) +--R + +--R 2 2 2 2 +--R (- 90cosh(x) + 8)coth(x) + (- 90cosh(x) + 8)coth(x) + 135cosh(x) +--R + +--R 5 +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 +--R (- 240cosh(x) + 64cosh(x))coth(x) +--R + +--R 3 3 +--R (240cosh(x) - 64cosh(x))coth(x) +--R + +--R 3 2 +--R (- 240cosh(x) + 64cosh(x))coth(x) +--R + +--R 3 3 +--R (- 240cosh(x) + 64cosh(x))coth(x) + 360cosh(x) + 40cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 4 +--R (- 420cosh(x) + 224cosh(x) - 12)coth(x) +--R + +--R 4 2 3 +--R (420cosh(x) - 224cosh(x) + 12)coth(x) +--R + +--R 4 2 2 +--R (- 420cosh(x) + 224cosh(x) - 12)coth(x) +--R + +--R 4 2 4 2 +--R (- 420cosh(x) + 224cosh(x) - 12)coth(x) + 630cosh(x) + 140cosh(x) +--R + +--R - 2 +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 4 +--R (- 504cosh(x) + 448cosh(x) - 72cosh(x))coth(x) +--R + +--R 5 3 3 +--R (504cosh(x) - 448cosh(x) + 72cosh(x))coth(x) +--R + +--R 5 3 2 +--R (- 504cosh(x) + 448cosh(x) - 72cosh(x))coth(x) +--R + +--R 5 3 5 +--R (- 504cosh(x) + 448cosh(x) - 72cosh(x))coth(x) + 756cosh(x) +--R + +--R 3 +--R 280cosh(x) - 12cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 4 2 4 +--R (- 420cosh(x) + 560cosh(x) - 180cosh(x) + 8)coth(x) +--R + +--R 6 4 2 3 +--R (420cosh(x) - 560cosh(x) + 180cosh(x) - 8)coth(x) +--R + +--R 6 4 2 2 +--R (- 420cosh(x) + 560cosh(x) - 180cosh(x) + 8)coth(x) +--R + +--R 6 4 2 6 +--R (- 420cosh(x) + 560cosh(x) - 180cosh(x) + 8)coth(x) + 630cosh(x) +--R + +--R 4 2 +--R 350cosh(x) - 30cosh(x) + 26 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 3 4 +--R (- 240cosh(x) + 448cosh(x) - 240cosh(x) + 32cosh(x))coth(x) +--R + +--R 7 5 3 3 +--R (240cosh(x) - 448cosh(x) + 240cosh(x) - 32cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (- 240cosh(x) + 448cosh(x) - 240cosh(x) + 32cosh(x))coth(x) +--R + +--R 7 5 3 +--R (- 240cosh(x) + 448cosh(x) - 240cosh(x) + 32cosh(x))coth(x) +--R + +--R 7 5 3 +--R 360cosh(x) + 280cosh(x) - 40cosh(x) + 104cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 6 4 2 4 +--R (- 90cosh(x) + 224cosh(x) - 180cosh(x) + 48cosh(x) - 2)coth(x) +--R + +--R 8 6 4 2 3 +--R (90cosh(x) - 224cosh(x) + 180cosh(x) - 48cosh(x) + 2)coth(x) +--R + +--R 8 6 4 2 2 +--R (- 90cosh(x) + 224cosh(x) - 180cosh(x) + 48cosh(x) - 2)coth(x) +--R + +--R 8 6 4 2 +--R (- 90cosh(x) + 224cosh(x) - 180cosh(x) + 48cosh(x) - 2)coth(x) +--R + +--R 8 6 4 2 +--R 135cosh(x) + 140cosh(x) - 30cosh(x) + 156cosh(x) - 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (- 20cosh(x) + 64cosh(x) - 72cosh(x) + 32cosh(x) - 4cosh(x)) +--R * +--R 4 +--R coth(x) +--R + +--R 9 7 5 3 +--R (20cosh(x) - 64cosh(x) + 72cosh(x) - 32cosh(x) + 4cosh(x)) +--R * +--R 3 +--R coth(x) +--R + +--R 9 7 5 3 +--R (- 20cosh(x) + 64cosh(x) - 72cosh(x) + 32cosh(x) - 4cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 3 +--R (- 20cosh(x) + 64cosh(x) - 72cosh(x) + 32cosh(x) - 4cosh(x)) +--R * +--R coth(x) +--R + +--R 9 7 5 3 +--R 30cosh(x) + 40cosh(x) - 12cosh(x) + 104cosh(x) - 2cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 4 +--R (- 2cosh(x) + 8cosh(x) - 12cosh(x) + 8cosh(x) - 2cosh(x) )coth(x) +--R + +--R 10 8 6 4 2 3 +--R (2cosh(x) - 8cosh(x) + 12cosh(x) - 8cosh(x) + 2cosh(x) )coth(x) +--R + +--R 10 8 6 4 2 2 +--R (- 2cosh(x) + 8cosh(x) - 12cosh(x) + 8cosh(x) - 2cosh(x) )coth(x) +--R + +--R 10 8 6 4 2 +--R (- 2cosh(x) + 8cosh(x) - 12cosh(x) + 8cosh(x) - 2cosh(x) )coth(x) +--R + +--R 10 8 6 4 2 +--R 3cosh(x) + 5cosh(x) - 2cosh(x) + 26cosh(x) - cosh(x) + 1 +--R / +--R 10 9 2 8 +--R 2sinh(x) + 20cosh(x)sinh(x) + (90cosh(x) - 8)sinh(x) +--R + +--R 3 7 +--R (240cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (420cosh(x) - 224cosh(x) + 12)sinh(x) +--R + +--R 5 3 5 +--R (504cosh(x) - 448cosh(x) + 72cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (420cosh(x) - 560cosh(x) + 180cosh(x) - 8)sinh(x) +--R + +--R 7 5 3 3 +--R (240cosh(x) - 448cosh(x) + 240cosh(x) - 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (90cosh(x) - 224cosh(x) + 180cosh(x) - 48cosh(x) + 2)sinh(x) +--R + +--R 9 7 5 3 +--R (20cosh(x) - 64cosh(x) + 72cosh(x) - 32cosh(x) + 4cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R 2cosh(x) - 8cosh(x) + 12cosh(x) - 8cosh(x) + 2cosh(x) +--R * +--R tanh(x) +--R + +--R 10 9 2 8 +--R 2sinh(x) + 20cosh(x)sinh(x) + (90cosh(x) - 8)sinh(x) +--R + +--R 3 7 +--R (240cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (420cosh(x) - 224cosh(x) + 12)sinh(x) +--R + +--R 5 3 5 +--R (504cosh(x) - 448cosh(x) + 72cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (420cosh(x) - 560cosh(x) + 180cosh(x) - 8)sinh(x) +--R + +--R 7 5 3 3 +--R (240cosh(x) - 448cosh(x) + 240cosh(x) - 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (90cosh(x) - 224cosh(x) + 180cosh(x) - 48cosh(x) + 2)sinh(x) +--R + +--R 9 7 5 3 +--R (20cosh(x) - 64cosh(x) + 72cosh(x) - 32cosh(x) + 4cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R 2cosh(x) - 8cosh(x) + 12cosh(x) - 8cosh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 426 + +--S 427 of 530 +t0580:= sech(x)^2/(a+b*tanh(x)) +--R +--R +--R 2 +--R sech(x) +--R (425) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 530 +r0580:= log(a+b*tanh(x))/b +--R +--R +--R log(b tanh(x) + a) +--R (426) ------------------ +--R b +--R Type: Expression(Integer) +--E 428 + +--S 429 of 530 +a0580:= integrate(t0580,x) +--R +--R +--R 2cosh(x) - 2b sinh(x) - 2a cosh(x) +--R - log(- -----------------) + log(-------------------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R (427) ----------------------------------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 429 + +--S 430 of 530 +m0580:= a0580-r0580 +--R +--R +--R (428) +--R 2cosh(x) +--R - log(b tanh(x) + a) - log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R / +--R b +--R Type: Expression(Integer) +--E 430 + +--S 431 of 530 +d0580:= D(m0580,x) +--R +--R +--R (429) +--R 2 2 +--R (b cosh(x)sinh(x) + a cosh(x) )tanh(x) +--R + +--R 2 2 2 +--R (- b sinh(x) + b cosh(x) )tanh(x) - a sinh(x) - b cosh(x)sinh(x) +--R / +--R 2 2 2 2 +--R (b cosh(x)sinh(x) + a b cosh(x) )tanh(x) + a b cosh(x)sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 431 + +--S 432 of 530 +t0581:= sech(x)^4/(a+b*tanh(x)) +--R +--R +--R 4 +--R sech(x) +--R (430) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 530 +r0581:= -(a^2-b^2)*log(a+b*tanh(x))/b^3+a*tanh(x)/b^2-1/2*tanh(x)^2/b +--R +--R +--R 2 2 2 2 +--R (2b - 2a )log(b tanh(x) + a) - b tanh(x) + 2a b tanh(x) +--R (431) --------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 433 + +--S 434 of 530 +a0581:= integrate(t0581,x) +--R +--R +--R (432) +--R 2 2 4 2 2 3 +--R (- b + a )sinh(x) + (- 4b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b + 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b + 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b + a )cosh(x) + (- 2b + 2a )cosh(x) - b + a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b - 6a )cosh(x) + 2b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 2 2 4 +--R ((4b - 4a )cosh(x) + (4b - 4a )cosh(x))sinh(x) + (b - a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (2b - 2a )cosh(x) + b - a +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 +--R (2b - 2a b)sinh(x) + (4b - 4a b)cosh(x)sinh(x) + (2b - 2a b)cosh(x) +--R + +--R - 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R Type: Union(Expression(Integer),...) +--E 434 + +--S 435 of 530 +m0581:= a0581-r0581 +--R +--R +--R (433) +--R 2 2 4 2 2 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + (- 4b + 4a )cosh(x) - 2b + 2a +--R * +--R log(b tanh(x) + a) +--R + +--R 2 2 4 2 2 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + (- 4b + 4a )cosh(x) - 2b + 2a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (2b - 2a )sinh(x) + (8b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - 2a )cosh(x) + (4b - 4a )cosh(x) + 2b - 2a +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b )sinh(x) +--R + +--R 2 3 2 2 4 2 2 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R - 2a b sinh(x) - 8a b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 4 +--R (- 8a b cosh(x) - 8a b cosh(x))sinh(x) - 2a b cosh(x) +--R + +--R 2 +--R - 4a b cosh(x) - 2a b +--R * +--R tanh(x) +--R + +--R 2 2 2 2 2 +--R (4b - 4a b)sinh(x) + (8b - 8a b)cosh(x)sinh(x) + (4b - 4a b)cosh(x) +--R + +--R - 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) + 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) + 8b cosh(x))sinh(x) + 2b cosh(x) + 4b cosh(x) + 2b +--R Type: Expression(Integer) +--E 435 + +--S 436 of 530 +d0581:= D(m0581,x) +--R +--R +--R (434) +--R 3 7 3 2 2 6 +--R - b cosh(x)sinh(x) + (- 6b - a b )cosh(x) sinh(x) +--R + +--R 3 2 3 3 5 +--R ((- 15b - 6a b )cosh(x) - 3b cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 4 +--R ((- 20b - 15a b )cosh(x) + (- 12b - 3a b )cosh(x) )sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 15b - 20a b )cosh(x) + (- 18b - 12a b )cosh(x) +--R + +--R 3 +--R - 3b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b - 15a b )cosh(x) + (- 12b - 18a b )cosh(x) +--R + +--R 3 2 2 +--R (- 6b - 3a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 7 3 2 5 +--R (- b - 6a b )cosh(x) + (- 3b - 12a b )cosh(x) +--R + +--R 3 2 3 3 +--R (- 3b - 6a b )cosh(x) - b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 +--R - a b cosh(x) - 3a b cosh(x) - 3a b cosh(x) - a b cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 3 7 3 2 2 6 +--R 2b cosh(x)sinh(x) + (12b + 2a b )cosh(x) sinh(x) +--R + +--R 3 2 3 3 5 +--R ((30b + 12a b )cosh(x) + 6b cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 4 +--R ((40b + 30a b )cosh(x) + (24b + 6a b )cosh(x) )sinh(x) +--R + +--R 3 2 5 3 2 3 3 +--R ((30b + 40a b )cosh(x) + (36b + 24a b )cosh(x) + 6b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (12b + 30a b )cosh(x) + (24b + 36a b )cosh(x) +--R + +--R 3 2 2 +--R (12b + 6a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 7 3 2 5 +--R (2b + 12a b )cosh(x) + (6b + 24a b )cosh(x) +--R + +--R 3 2 3 3 +--R (6b + 12a b )cosh(x) + 2b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 +--R 2a b cosh(x) + 6a b cosh(x) + 6a b cosh(x) + 2a b cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 8 3 2 7 +--R (- b + a b)sinh(x) + (- 6b + 6a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 6 +--R ((- 14b + 14a b)cosh(x) - 3b + 3a b)sinh(x) +--R + +--R 3 2 3 3 2 2 5 +--R ((- 14b + 14a b)cosh(x) + (- 16b + 4a b + 12a b)cosh(x))sinh(x) +--R + +--R 3 2 2 2 3 2 4 +--R ((- 31b + 12a b + 19a b)cosh(x) - 3b + 3a b)sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (14b - 14a b)cosh(x) + (- 24b + 8a b + 16a b)cosh(x) +--R + +--R 3 2 2 +--R (- 2b + 4a b + 6a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (14b - 14a b)cosh(x) + (- b - 8a b + 9a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (8b + 12a b + 4a b)cosh(x) - b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 7 3 2 2 5 +--R (6b - 6a b)cosh(x) + (8b - 12a b + 4a b)cosh(x) +--R + +--R 3 2 2 3 +--R (10b + 12a b + 2a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 8 3 2 2 6 +--R (b - a b)cosh(x) + (3b - 4a b + a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 +--R (3b + 4a b + a b)cosh(x) + (b - a b)cosh(x) +--R * +--R tanh(x) +--R + +--R 2 3 8 3 2 3 7 +--R (- a b + a )sinh(x) + (- b - 6a b + 6a )cosh(x)sinh(x) +--R + +--R 3 2 3 2 2 3 6 +--R ((- 6b - 15a b + 14a )cosh(x) - 3a b + 3a )sinh(x) +--R + +--R 3 2 3 3 +--R (- 15b - 20a b + 14a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 3b - 16a b + 4a b + 12a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R (- 20b - 15a b )cosh(x) + (- 12b - 34a b + 12a b + 19a )cosh(x) +--R + +--R 2 3 +--R - 3a b + 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 5 +--R (- 15b - 6a b - 14a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 18b - 36a b + 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 3b - 2a b + 4a b + 6a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3 6 +--R (- 6b - a b - 14a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12b - 19a b - 8a b + 9a )cosh(x) +--R + +--R 3 2 2 3 2 2 3 +--R (- 6b + 5a b + 12a b + 4a )cosh(x) - a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 7 3 2 2 3 5 +--R (- b - 6a )cosh(x) + (- 3b - 4a b - 12a b + 4a )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R (- 3b + 4a b + 12a b + 2a )cosh(x) - b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 2 3 6 2 3 4 3 2 +--R - a cosh(x) + (- 4a b + a )cosh(x) + (4a b + a )cosh(x) - a cosh(x) +--R / +--R 4 7 4 3 2 6 +--R b cosh(x)sinh(x) + (6b + a b )cosh(x) sinh(x) +--R + +--R 4 3 3 4 5 +--R ((15b + 6a b )cosh(x) + 3b cosh(x))sinh(x) +--R + +--R 4 3 4 4 3 2 4 +--R ((20b + 15a b )cosh(x) + (12b + 3a b )cosh(x) )sinh(x) +--R + +--R 4 3 5 4 3 3 4 +--R ((15b + 20a b )cosh(x) + (18b + 12a b )cosh(x) + 3b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 4 3 4 +--R (6b + 15a b )cosh(x) + (12b + 18a b )cosh(x) +--R + +--R 4 3 2 +--R (6b + 3a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 4 3 5 +--R (b + 6a b )cosh(x) + (3b + 12a b )cosh(x) +--R + +--R 4 3 3 4 +--R (3b + 6a b )cosh(x) + b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 3 6 3 4 3 2 +--R a b cosh(x) + 3a b cosh(x) + 3a b cosh(x) + a b cosh(x) +--R * +--R tanh(x) +--R + +--R 3 7 3 2 2 2 6 +--R a b cosh(x)sinh(x) + (6a b + a b )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 5 +--R ((15a b + 6a b )cosh(x) + 3a b cosh(x))sinh(x) +--R + +--R 3 2 2 4 3 2 2 2 4 +--R ((20a b + 15a b )cosh(x) + (12a b + 3a b )cosh(x) )sinh(x) +--R + +--R 3 2 2 5 3 2 2 3 3 +--R ((15a b + 20a b )cosh(x) + (18a b + 12a b )cosh(x) + 3a b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (6a b + 15a b )cosh(x) + (12a b + 18a b )cosh(x) +--R + +--R 3 2 2 2 +--R (6a b + 3a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 5 +--R (a b + 6a b )cosh(x) + (3a b + 12a b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (3a b + 6a b )cosh(x) + a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 2 2 4 2 2 2 +--R a b cosh(x) + 3a b cosh(x) + 3a b cosh(x) + a b cosh(x) +--R Type: Expression(Integer) +--E 436 + +--S 437 of 530 +t0582:= sech(x)^2/(1+tanh(x)) +--R +--R +--R 2 +--R sech(x) +--R (435) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 530 +r0582:= log(1+tanh(x)) +--R +--R +--R (436) log(tanh(x) + 1) +--R Type: Expression(Integer) +--E 438 + +--S 439 of 530 +a0582:= integrate(t0582,x) +--R +--R +--R 2cosh(x) +--R (437) - log(- -----------------) + 2x +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 439 + +--S 440 of 530 +m0582:= a0582-r0582 +--R +--R +--R 2cosh(x) +--R (438) - log(tanh(x) + 1) - log(- -----------------) + 2x +--R sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 440 + +--S 441 of 530 +d0582:= D(m0582,x) +--R +--R +--R cosh(x)tanh(x) - sinh(x) +--R (439) ------------------------ +--R cosh(x) +--R Type: Expression(Integer) +--E 441 + +--S 442 of 530 +t0583:= sech(x)^3/(1+tanh(x)) +--R +--R +--R 3 +--R sech(x) +--R (440) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 530 +r0583:= atan(sinh(x))+sech(x) +--R +--R +--R (441) atan(sinh(x)) + sech(x) +--R Type: Expression(Integer) +--E 443 + +--S 444 of 530 +a0583:= integrate(t0583,x) +--R +--R +--R (442) +--R 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)atan(sinh(x) + cosh(x)) +--R + +--R 2sinh(x) + 2cosh(x) +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 444 + +--S 445 of 530 +m0583:= a0583-r0583 +--R +--R +--R (443) +--R 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) + 2)atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)atan(sinh(x)) +--R + +--R 2 +--R - sech(x)sinh(x) + (- 2cosh(x)sech(x) + 2)sinh(x) +--R + +--R 2 +--R (- cosh(x) - 1)sech(x) + 2cosh(x) +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 530 +d0583:= D(m0583,x) +--R +--R +--R (444) +--R 6 5 +--R sech(x)sinh(x) + 4cosh(x)sech(x)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) + 3)sech(x)sinh(x) +--R + +--R 3 3 +--R (4cosh(x) + 8cosh(x))sech(x)sinh(x) +--R + +--R 4 2 2 +--R (cosh(x) + 8cosh(x) + 3)sech(x)sinh(x) +--R + +--R 3 +--R (4cosh(x) + 4cosh(x))sech(x)sinh(x) +--R + +--R 4 2 +--R (cosh(x) + 2cosh(x) + 1)sech(x) +--R * +--R tanh(x) +--R + +--R 4 2 3 +--R - cosh(x)sinh(x) + (- 4cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 2 +--R (- 6cosh(x) + 2cosh(x))sinh(x) + (- 4cosh(x) - 4cosh(x) + 4)sinh(x) +--R + +--R 5 3 +--R - cosh(x) - 2cosh(x) + 3cosh(x) +--R / +--R 6 5 2 4 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 3)sinh(x) +--R + +--R 3 3 4 2 2 +--R (4cosh(x) + 8cosh(x))sinh(x) + (cosh(x) + 8cosh(x) + 3)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 530 +t0584:= csch(x)^2/(a+b*tanh(x)) +--R +--R +--R 2 +--R csch(x) +--R (445) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 447 + +--S 448 of 530 +r0584:= (-a*coth(x)+b*log(b+a*coth(x)))/a^2 +--R +--R +--R b log(a coth(x) + b) - a coth(x) +--R (446) -------------------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 448 + +--S 449 of 530 +a0584:= integrate(t0584,x) +--R +--R +--R (447) +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) + b) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R - 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a +--R Type: Union(Expression(Integer),...) +--E 449 + +--S 450 of 530 +m0584:= a0584-r0584 +--R +--R +--R (448) +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) + b)log(a coth(x) + b) +--R + +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) + b) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R a coth(x)sinh(x) + 2a cosh(x)coth(x)sinh(x) + (a cosh(x) - a)coth(x) - 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a +--R Type: Expression(Integer) +--E 450 + +--S 451 of 530 +d0584:= D(m0584,x) +--R +--R +--R (449) +--R 3 2 6 +--R (- a b coth(x) + 2a b coth(x) + b )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4a b - a )cosh(x)coth(x) + (8a b + a )cosh(x)coth(x) + 4b cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 +--R ((- 6a b - 4a )cosh(x) + 2a b)coth(x) +--R + +--R 2 2 2 2 2 +--R (11a b + 4a )cosh(x) coth(x) + 5b cosh(x) + 2b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 3 +--R ((- 4a b - 6a )cosh(x) + (4a b + 2a )cosh(x))coth(x) +--R + +--R 2 3 2 2 +--R ((4a b + 6a )cosh(x) + 2a cosh(x))coth(x) + (4b + 4a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 3 +--R ((- a b - 4a )cosh(x) + (2a b + 4a )cosh(x) - a b)coth(x) +--R + +--R 2 4 2 2 +--R ((- 4a b + 4a )cosh(x) + (2a b + 4a )cosh(x) + 2a b)coth(x) +--R + +--R 2 4 2 2 2 +--R - 5b cosh(x) + (4b + 8a b)cosh(x) + b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (- a cosh(x) + 2a cosh(x) - a cosh(x))coth(x) +--R + +--R 2 5 2 3 2 +--R ((- 4a b + a )cosh(x) + (4a b + 2a )cosh(x) + a cosh(x))coth(x) +--R + +--R 2 5 2 3 +--R - 4b cosh(x) + (4b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- a b cosh(x) + 2a b cosh(x) - a b cosh(x) )coth(x) - b cosh(x) +--R + +--R 2 4 2 2 +--R 2b cosh(x) - b cosh(x) +--R / +--R 2 2 6 +--R (a b coth(x) + a b )sinh(x) +--R + +--R 2 3 2 2 5 +--R ((4a b + a )cosh(x)coth(x) + (4a b + a b)cosh(x))sinh(x) +--R + +--R 2 3 2 2 2 2 2 2 +--R (((6a b + 4a )cosh(x) - 2a b)coth(x) + (6a b + 4a b)cosh(x) - 2a b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 2 3 +--R ((4a b + 6a )cosh(x) + (- 4a b - 2a )cosh(x))coth(x) +--R + +--R 2 2 3 2 2 +--R (4a b + 6a b)cosh(x) + (- 4a b - 2a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R ((a b + 4a )cosh(x) + (- 2a b - 4a )cosh(x) + a b)coth(x) +--R + +--R 2 2 4 2 2 2 2 +--R (a b + 4a b)cosh(x) + (- 2a b - 4a b)cosh(x) + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 3 3 3 2 5 +--R (a cosh(x) - 2a cosh(x) + a cosh(x))coth(x) + a b cosh(x) +--R + +--R 2 3 2 +--R - 2a b cosh(x) + a b cosh(x) +--R * +--R sinh(x) +--R Type: Expression(Integer) +--E 451 + +--S 452 of 530 +t0585:= csch(x)^4/(a+b*tanh(x)) +--R +--R +--R 4 +--R csch(x) +--R (450) ------------- +--R b tanh(x) + a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 530 +r0585:= (a^2-b^2)*coth(x)/a^3+1/2*b*coth(x)^2/a^2-1/3*coth(x)^3/a-_ + b*(a^2-b^2)*log(b+a*coth(x))/a^4 +--R +--R +--R (451) +--R 3 2 3 3 2 2 +--R (6b - 6a b)log(a coth(x) + b) - 2a coth(x) + 3a b coth(x) +--R + +--R 2 3 +--R (- 6a b + 6a )coth(x) +--R / +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 453 + +--S 454 of 530 +a0585:= integrate(t0585,x) +--R +--R +--R (452) +--R 3 2 6 3 2 5 +--R (- 3b + 3a b)sinh(x) + (- 18b + 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 45b + 45a b)cosh(x) + 9b - 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 60b + 60a b)cosh(x) + (36b - 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((- 45b + 45a b)cosh(x) + (54b - 54a b)cosh(x) - 9b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 18b + 18a b)cosh(x) + (36b - 36a b)cosh(x) +--R + +--R 3 2 +--R (- 18b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 3b + 3a b)cosh(x) + (9b - 9a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 9b + 9a b)cosh(x) + 3b - 3a b +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 6 3 2 5 +--R (3b - 3a b)sinh(x) + (18b - 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((45b - 45a b)cosh(x) - 9b + 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((60b - 60a b)cosh(x) + (- 36b + 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((45b - 45a b)cosh(x) + (- 54b + 54a b)cosh(x) + 9b - 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (18b - 18a b)cosh(x) + (- 36b + 36a b)cosh(x) +--R + +--R 3 2 +--R (18b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (3b - 3a b)cosh(x) + (- 9b + 9a b)cosh(x) + (9b - 9a b)cosh(x) +--R + +--R 3 2 +--R - 3b + 3a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 6a b + 6a b)sinh(x) + (- 24a b + 24a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((- 36a b + 36a b)cosh(x) + 12a b - 6a b - 12a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((- 24a b + 24a b)cosh(x) + (24a b - 12a b - 24a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 3 +--R (- 6a b + 6a b)cosh(x) + (12a b - 6a b - 12a )cosh(x) - 6a b + 4a +--R / +--R 4 6 4 5 4 2 4 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) - 9a )sinh(x) +--R + +--R 4 3 4 3 +--R (60a cosh(x) - 36a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45a cosh(x) - 54a cosh(x) + 9a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18a cosh(x) - 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 4 4 4 2 4 +--R - 9a cosh(x) + 9a cosh(x) - 3a +--R Type: Union(Expression(Integer),...) +--E 454 + +--S 455 of 530 +m0585:= a0585-r0585 +--R +--R +--R (453) +--R 3 2 6 3 2 5 +--R (- 6b + 6a b)sinh(x) + (- 36b + 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 90a b)cosh(x) + 18b - 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 120a b)cosh(x) + (72b - 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b + 90a b)cosh(x) + (108b - 108a b)cosh(x) - 18b +--R + +--R 2 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 36a b)cosh(x) + (72b - 72a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 6a b)cosh(x) + (18b - 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 18a b)cosh(x) + 6b - 6a b +--R * +--R log(a coth(x) + b) +--R + +--R 3 2 6 3 2 5 +--R (- 6b + 6a b)sinh(x) + (- 36b + 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 90a b)cosh(x) + 18b - 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 120a b)cosh(x) + (72b - 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b + 90a b)cosh(x) + (108b - 108a b)cosh(x) - 18b +--R + +--R 2 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 36a b)cosh(x) + (72b - 72a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 6a b)cosh(x) + (18b - 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 18a b)cosh(x) + 6b - 6a b +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 6 3 2 5 +--R (6b - 6a b)sinh(x) + (36b - 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b - 90a b)cosh(x) - 18b + 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b - 120a b)cosh(x) + (- 72b + 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (90b - 90a b)cosh(x) + (- 108b + 108a b)cosh(x) + 18b +--R + +--R 2 +--R - 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b - 36a b)cosh(x) + (- 72b + 72a b)cosh(x) +--R + +--R 3 2 +--R (36b - 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (6b - 6a b)cosh(x) + (- 18b + 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (18b - 18a b)cosh(x) - 6b + 6a b +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 2 2 2 3 6 +--R (2a coth(x) - 3a b coth(x) + (6a b - 6a )coth(x))sinh(x) +--R + +--R 3 3 2 2 +--R 12a cosh(x)coth(x) - 18a b cosh(x)coth(x) +--R + +--R 2 3 +--R (36a b - 36a )cosh(x)coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 3 3 2 2 2 2 +--R (30a cosh(x) - 6a )coth(x) + (- 45a b cosh(x) + 9a b)coth(x) +--R + +--R 2 3 2 2 3 2 2 +--R ((90a b - 90a )cosh(x) - 18a b + 18a )coth(x) - 12a b + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 3 +--R (40a cosh(x) - 24a cosh(x))coth(x) +--R + +--R 2 3 2 2 +--R (- 60a b cosh(x) + 36a b cosh(x))coth(x) +--R + +--R 2 3 3 2 3 +--R ((120a b - 120a )cosh(x) + (- 72a b + 72a )cosh(x))coth(x) +--R + +--R 2 2 +--R (- 48a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 3 2 3 3 +--R (30a cosh(x) - 36a cosh(x) + 6a )coth(x) +--R + +--R 2 4 2 2 2 2 +--R (- 45a b cosh(x) + 54a b cosh(x) - 9a b)coth(x) +--R + +--R 2 3 4 2 3 2 2 +--R (90a b - 90a )cosh(x) + (- 108a b + 108a )cosh(x) + 18a b +--R + +--R 3 +--R - 18a +--R * +--R coth(x) +--R + +--R 2 2 2 2 2 3 +--R (- 72a b + 72a b)cosh(x) + 24a b - 12a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 3 3 3 3 +--R (12a cosh(x) - 24a cosh(x) + 12a cosh(x))coth(x) +--R + +--R 2 5 2 3 2 2 +--R (- 18a b cosh(x) + 36a b cosh(x) - 18a b cosh(x))coth(x) +--R + +--R 2 3 5 2 3 3 +--R (36a b - 36a )cosh(x) + (- 72a b + 72a )cosh(x) +--R + +--R 2 3 +--R (36a b - 36a )cosh(x) +--R * +--R coth(x) +--R + +--R 2 2 3 2 2 3 +--R (- 48a b + 48a b)cosh(x) + (48a b - 24a b - 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 6 3 4 3 2 3 3 +--R (2a cosh(x) - 6a cosh(x) + 6a cosh(x) - 2a )coth(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 3a b cosh(x) + 9a b cosh(x) - 9a b cosh(x) + 3a b)coth(x) +--R + +--R 2 3 6 2 3 4 +--R (6a b - 6a )cosh(x) + (- 18a b + 18a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (18a b - 18a )cosh(x) - 6a b + 6a +--R * +--R coth(x) +--R + +--R 2 2 4 2 2 3 2 2 3 +--R (- 12a b + 12a b)cosh(x) + (24a b - 12a b - 24a )cosh(x) - 12a b + 8a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) - 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) - 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) - 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) - 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R - 18a cosh(x) + 18a cosh(x) - 6a +--R Type: Expression(Integer) +--E 455 + +--S 456 of 530 +d0585:= D(m0585,x) +--R +--R +--R (454) +--R 3 5 3 3 3 3 4 2 2 +--R (- a b coth(x) + 2a b coth(x) + (a b - 2a b)coth(x) + b - a b ) +--R * +--R 10 +--R sinh(x) +--R + +--R 3 4 5 3 4 3 +--R (- 8a b - a )cosh(x)coth(x) + (16a b + 2a )cosh(x)coth(x) +--R + +--R 3 3 4 4 2 2 +--R (8a b - 16a b - a )cosh(x)coth(x) + (8b - 8a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 3 4 2 3 5 +--R ((- 28a b - 8a )cosh(x) + 4a b)coth(x) +--R + +--R 3 4 2 3 3 +--R ((56a b + 16a )cosh(x) - 8a b)coth(x) +--R + +--R 3 3 4 2 2 2 3 +--R ((27a b - 55a b - 8a )cosh(x) - 4a b + 8a b)coth(x) +--R + +--R 4 2 2 2 3 2 2 +--R (27b - 27a b )cosh(x) - 4a b + 4a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 3 3 4 5 +--R ((- 56a b - 28a )cosh(x) + (24a b + 4a )cosh(x))coth(x) +--R + +--R 3 4 3 3 4 3 +--R ((112a b + 56a )cosh(x) + (- 48a b - 8a )cosh(x))coth(x) +--R + +--R 3 3 4 3 +--R (48a b - 104a b - 28a )cosh(x) +--R + +--R 2 2 3 4 +--R (- 20a b + 44a b + 4a )cosh(x) +--R * +--R coth(x) +--R + +--R 4 2 2 3 3 2 2 +--R (48b - 48a b )cosh(x) + (- 20a b + 20a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 4 2 3 5 +--R ((- 70a b - 56a )cosh(x) + (60a b + 24a )cosh(x) - 6a b)coth(x) +--R + +--R 3 4 4 3 4 2 3 +--R ((140a b + 112a )cosh(x) + (- 120a b - 48a )cosh(x) + 12a b) +--R * +--R 3 +--R coth(x) +--R + +--R 3 3 4 4 +--R (42a b - 112a b - 56a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (4a b - 36a b + 92a b + 24a )cosh(x) - 2a b + 4a b +--R * +--R coth(x) +--R + +--R 4 2 2 4 4 3 2 2 2 4 +--R (42b - 42a b )cosh(x) + (4b - 36a b + 32a b )cosh(x) - 2b +--R + +--R 2 2 +--R 10a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 5 3 4 3 +--R (- 56a b - 70a )cosh(x) + (80a b + 60a )cosh(x) +--R + +--R 3 4 +--R (- 24a b - 6a )cosh(x) +--R * +--R 5 +--R coth(x) +--R + +--R 3 4 5 3 4 3 +--R (112a b + 140a )cosh(x) + (- 160a b - 120a )cosh(x) +--R + +--R 3 4 +--R (48a b + 12a )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 3 4 5 +--R (- 56a b - 70a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (24a b - 20a b + 76a b + 60a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 8a b - 8a b + 16a b + 10a )cosh(x) +--R * +--R coth(x) +--R + +--R 4 3 2 2 3 +--R (24b - 20a b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 8b - 8a b + 40a b + 16a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 6 3 4 4 +--R (- 28a b - 56a )cosh(x) + (60a b + 80a )cosh(x) +--R + +--R 3 4 2 3 +--R (- 36a b - 24a )cosh(x) + 4a b +--R * +--R 5 +--R coth(x) +--R + +--R 3 4 6 3 4 4 +--R (56a b + 112a )cosh(x) + (- 120a b - 160a )cosh(x) +--R + +--R 3 4 2 3 +--R (72a b + 48a )cosh(x) - 8a b +--R * +--R 3 +--R coth(x) +--R + +--R 3 3 4 6 +--R (- 42a b + 14a b - 56a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (60a b + 20a b - 20a b + 80a )cosh(x) +--R + +--R 3 2 2 3 4 2 2 2 3 +--R (- 18a b - 32a b + 30a b + 40a )cosh(x) + 4a b + 8a b +--R * +--R coth(x) +--R + +--R 4 2 2 6 4 3 2 2 4 +--R (- 42b + 42a b )cosh(x) + (60b + 20a b - 80a b )cosh(x) +--R + +--R 4 3 2 2 3 2 3 2 2 +--R (- 18b - 32a b + 66a b + 64a b)cosh(x) + 4a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 7 3 4 5 +--R (- 8a b - 28a )cosh(x) + (24a b + 60a )cosh(x) +--R + +--R 3 4 3 3 4 +--R (- 24a b - 36a )cosh(x) + (8a b + 4a )cosh(x) +--R * +--R 5 +--R coth(x) +--R + +--R 3 4 7 3 4 5 +--R (16a b + 56a )cosh(x) + (- 48a b - 120a )cosh(x) +--R + +--R 3 4 3 3 4 +--R (48a b + 72a )cosh(x) + (- 16a b - 8a )cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 3 3 4 7 +--R (- 48a b + 40a b - 28a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (80a b + 36a b - 92a b + 60a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 32a b - 48a b + 40a b + 60a )cosh(x) +--R + +--R 2 2 3 4 +--R (12a b + 20a b + 4a )cosh(x) +--R * +--R coth(x) +--R + +--R 4 2 2 7 4 3 2 2 5 +--R (- 48b + 48a b )cosh(x) + (80b + 36a b - 116a b )cosh(x) +--R + +--R 4 3 2 2 3 3 3 2 2 +--R (- 32b - 48a b + 64a b + 96a b)cosh(x) + (12a b + 12a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 8 3 4 6 +--R (- a b - 8a )cosh(x) + (4a b + 24a )cosh(x) +--R + +--R 3 4 4 3 4 2 3 +--R (- 6a b - 24a )cosh(x) + (4a b + 8a )cosh(x) - a b +--R * +--R 5 +--R coth(x) +--R + +--R 3 4 8 3 4 6 +--R (2a b + 16a )cosh(x) + (- 8a b - 48a )cosh(x) +--R + +--R 3 4 4 3 4 2 3 +--R (12a b + 48a )cosh(x) + (- 8a b - 16a )cosh(x) + 2a b +--R * +--R 3 +--R coth(x) +--R + +--R 3 3 4 8 +--R (- 27a b + 26a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 6 +--R (60a b + 20a b - 76a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 38a b - 32a b + 40a b + 40a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (4a b + 12a b + 12a b + 8a )cosh(x) + a b - 2a b +--R * +--R coth(x) +--R + +--R 4 2 2 8 4 3 2 2 6 +--R (- 27b + 27a b )cosh(x) + (60b + 20a b - 80a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 38b - 32a b + 46a b + 64a b)cosh(x) +--R + +--R 4 3 2 2 2 4 2 2 +--R (4b + 12a b + 8a b )cosh(x) + b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 4 7 4 5 4 3 +--R - a cosh(x) + 4a cosh(x) - 6a cosh(x) + 4a cosh(x) +--R + +--R 4 +--R - a cosh(x) +--R * +--R 5 +--R coth(x) +--R + +--R 4 9 4 7 4 5 4 3 +--R 2a cosh(x) - 8a cosh(x) + 12a cosh(x) - 8a cosh(x) +--R + +--R 4 +--R 2a cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 3 3 4 9 +--R (- 8a b + 8a b - a )cosh(x) +--R + +--R 3 2 2 3 4 7 +--R (24a b + 4a b - 28a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 24a b - 8a b + 24a b + 10a )cosh(x) +--R + +--R 3 2 2 3 4 3 4 +--R (8a b + 4a b - 4a b + 4a )cosh(x) - a cosh(x) +--R * +--R coth(x) +--R + +--R 4 2 2 9 4 3 2 2 7 +--R (- 8b + 8a b )cosh(x) + (24b + 4a b - 28a b )cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 24b - 8a b + 24a b + 16a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (8b + 4a b - 4a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 10 3 3 8 +--R (- a b + a b)cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 3 3 6 3 3 4 +--R (- 6a b + 6a b)cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 3 3 2 +--R (- a b + a b)cosh(x) +--R * +--R coth(x) +--R + +--R 4 2 2 10 4 2 2 8 4 2 2 6 +--R (- b + a b )cosh(x) + (4b - 4a b )cosh(x) + (- 6b + 6a b )cosh(x) +--R + +--R 4 2 2 4 4 2 2 2 +--R (4b - 4a b )cosh(x) + (- b + a b )cosh(x) +--R / +--R 4 3 2 10 +--R (a b coth(x) + a b )sinh(x) +--R + +--R 4 5 3 2 4 9 +--R ((8a b + a )cosh(x)coth(x) + (8a b + a b)cosh(x))sinh(x) +--R + +--R 4 5 2 4 3 2 4 2 +--R ((28a b + 8a )cosh(x) - 4a b)coth(x) + (28a b + 8a b)cosh(x) +--R + +--R 3 2 +--R - 4a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 5 3 4 5 +--R ((56a b + 28a )cosh(x) + (- 24a b - 4a )cosh(x))coth(x) +--R + +--R 3 2 4 3 3 2 4 +--R (56a b + 28a b)cosh(x) + (- 24a b - 4a b)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 5 4 4 5 2 4 +--R ((70a b + 56a )cosh(x) + (- 60a b - 24a )cosh(x) + 6a b)coth(x) +--R + +--R 3 2 4 4 3 2 4 2 3 2 +--R (70a b + 56a b)cosh(x) + (- 60a b - 24a b)cosh(x) + 6a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 5 4 5 3 +--R (56a b + 70a )cosh(x) + (- 80a b - 60a )cosh(x) +--R + +--R 4 5 +--R (24a b + 6a )cosh(x) +--R * +--R coth(x) +--R + +--R 3 2 4 5 3 2 4 3 +--R (56a b + 70a b)cosh(x) + (- 80a b - 60a b)cosh(x) +--R + +--R 3 2 4 +--R (24a b + 6a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 5 6 4 5 4 +--R (28a b + 56a )cosh(x) + (- 60a b - 80a )cosh(x) +--R + +--R 4 5 2 4 +--R (36a b + 24a )cosh(x) - 4a b +--R * +--R coth(x) +--R + +--R 3 2 4 6 3 2 4 4 +--R (28a b + 56a b)cosh(x) + (- 60a b - 80a b)cosh(x) +--R + +--R 3 2 4 2 3 2 +--R (36a b + 24a b)cosh(x) - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 7 4 5 5 +--R (8a b + 28a )cosh(x) + (- 24a b - 60a )cosh(x) +--R + +--R 4 5 3 4 5 +--R (24a b + 36a )cosh(x) + (- 8a b - 4a )cosh(x) +--R * +--R coth(x) +--R + +--R 3 2 4 7 3 2 4 5 +--R (8a b + 28a b)cosh(x) + (- 24a b - 60a b)cosh(x) +--R + +--R 3 2 4 3 3 2 4 +--R (24a b + 36a b)cosh(x) + (- 8a b - 4a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 8 4 5 6 +--R (a b + 8a )cosh(x) + (- 4a b - 24a )cosh(x) +--R + +--R 4 5 4 4 5 2 4 +--R (6a b + 24a )cosh(x) + (- 4a b - 8a )cosh(x) + a b +--R * +--R coth(x) +--R + +--R 3 2 4 8 3 2 4 6 +--R (a b + 8a b)cosh(x) + (- 4a b - 24a b)cosh(x) +--R + +--R 3 2 4 4 3 2 4 2 3 2 +--R (6a b + 24a b)cosh(x) + (- 4a b - 8a b)cosh(x) + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 9 5 7 5 5 5 3 5 +--R (a cosh(x) - 4a cosh(x) + 6a cosh(x) - 4a cosh(x) + a cosh(x)) +--R * +--R coth(x) +--R + +--R 4 9 4 7 4 5 4 3 +--R a b cosh(x) - 4a b cosh(x) + 6a b cosh(x) - 4a b cosh(x) +--R + +--R 4 +--R a b cosh(x) +--R * +--R sinh(x) +--R Type: Expression(Integer) +--E 456 + +--S 457 of 530 +t0586:= csch(x)/(1+tanh(x)) +--R +--R +--R csch(x) +--R (455) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 530 +r0586:= -acoth(cosh(x))+cosh(x)-sinh(x) +--R +--R +--R (456) - acoth(cosh(x)) - sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 458 + +--S 459 of 530 +a0586:= integrate(t0586,x) +--R +--R +--R (457) +--R (- sinh(x) - cosh(x))log(sinh(x) + cosh(x) + 1) +--R + +--R (sinh(x) + cosh(x))log(sinh(x) + cosh(x) - 1) + 1 +--R / +--R sinh(x) + cosh(x) +--R Type: Union(Expression(Integer),...) +--E 459 + +--S 460 of 530 +m0586:= a0586-r0586 +--R +--R +--R (458) +--R (- sinh(x) - cosh(x))log(sinh(x) + cosh(x) + 1) +--R + +--R (sinh(x) + cosh(x))log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R (sinh(x) + cosh(x))acoth(cosh(x)) + sinh(x) - cosh(x) + 1 +--R / +--R sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 460 + +--S 461 of 530 +d0586:= D(m0586,x) +--R +--R +--R (459) +--R 2 4 3 3 +--R - cosh(x) sinh(x) + (- 2cosh(x) - cosh(x))sinh(x) +--R + +--R 2 2 5 3 +--R (- cosh(x) - 1)sinh(x) + (2cosh(x) - cosh(x) - cosh(x))sinh(x) +--R + +--R 6 4 2 +--R cosh(x) - cosh(x) + cosh(x) - 1 +--R / +--R 2 3 3 2 +--R (cosh(x) - 1)sinh(x) + (3cosh(x) - 3cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (3cosh(x) - 4cosh(x) + 1)sinh(x) + cosh(x) - 2cosh(x) + cosh(x) +--R Type: Expression(Integer) +--E 461 + +--S 462 of 530 +t0587:= csch(x)^2/(1+tanh(x)) +--R +--R +--R 2 +--R csch(x) +--R (460) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 530 +r0587:= -coth(x)+log(1+coth(x)) +--R +--R +--R (461) log(coth(x) + 1) - coth(x) +--R Type: Expression(Integer) +--E 463 + +--S 464 of 530 +a0587:= integrate(t0587,x) +--R +--R +--R (462) +--R 2 2 2sinh(x) +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R 2x sinh(x) + 4x cosh(x)sinh(x) + 2x cosh(x) - 2x - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 464 + +--S 465 of 530 +m0587:= a0587-r0587 +--R +--R +--R (463) +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(coth(x) + 1) +--R + +--R 2 2 2sinh(x) +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (coth(x) + 2x)sinh(x) + (2cosh(x)coth(x) + 4x cosh(x))sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 1)coth(x) + 2x cosh(x) - 2x - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression(Integer) +--E 465 + +--S 466 of 530 +d0587:= D(m0587,x) +--R +--R +--R (464) +--R 2 5 +--R (- coth(x) + coth(x) + 1)sinh(x) +--R + +--R 2 4 +--R (- 4cosh(x)coth(x) + 4cosh(x)coth(x) + 3cosh(x))sinh(x) +--R + +--R 2 2 2 2 +--R ((- 6cosh(x) + 2)coth(x) + (6cosh(x) - 2)coth(x) + 2cosh(x) + 2) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 3 +--R (- 4cosh(x) + 4cosh(x))coth(x) + (4cosh(x) - 4cosh(x))coth(x) +--R + +--R 3 +--R - 2cosh(x) + 6cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 +--R (- cosh(x) + 2cosh(x) - 1)coth(x) +--R + +--R 4 2 4 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x) - 3cosh(x) + 6cosh(x) + 1 +--R * +--R sinh(x) +--R + +--R 5 3 +--R - cosh(x) + 2cosh(x) - cosh(x) +--R / +--R 5 4 2 3 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 2 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + (cosh(x) - 2cosh(x) + 1)sinh(x) +--R Type: Expression(Integer) +--E 466 + +--S 467 of 530 +t0588:= csch(x)^3/(1+tanh(x)) +--R +--R +--R 3 +--R csch(x) +--R (465) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 530 +r0588:= -1/2*acoth(cosh(x))+csch(x)-1/2*coth(x)*csch(x) +--R +--R +--R - acoth(cosh(x)) + (- coth(x) + 2)csch(x) +--R (466) ----------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 530 +a0588:= integrate(t0588,x) +--R +--R +--R (467) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - cosh(x) + 2cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 2 2 3 +--R 2sinh(x) + 6cosh(x)sinh(x) + (6cosh(x) - 6)sinh(x) + 2cosh(x) +--R + +--R - 6cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 469 + +--S 470 of 530 +m0588:= a0588-r0588 +--R +--R +--R (468) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - cosh(x) + 2cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R acoth(cosh(x)) +--R + +--R 4 +--R (coth(x) - 2)csch(x)sinh(x) +--R + +--R 3 +--R ((4cosh(x)coth(x) - 8cosh(x))csch(x) + 2)sinh(x) +--R + +--R 2 2 2 +--R (((6cosh(x) - 2)coth(x) - 12cosh(x) + 4)csch(x) + 6cosh(x))sinh(x) +--R + +--R 3 3 +--R ((4cosh(x) - 4cosh(x))coth(x) - 8cosh(x) + 8cosh(x))csch(x) +--R + +--R 2 +--R 6cosh(x) - 6 +--R * +--R sinh(x) +--R + +--R 4 2 4 2 +--R ((cosh(x) - 2cosh(x) + 1)coth(x) - 2cosh(x) + 4cosh(x) - 2)csch(x) +--R + +--R 3 +--R 2cosh(x) - 6cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 530 +d0588:= D(m0588,x) +--R +--R +--R (469) +--R 7 +--R - sinh(x) +--R + +--R 2 2 2 2 +--R ((- 2cosh(x) + 2)coth(x) + (2cosh(x) - 2)coth(x) + cosh(x) - 1) +--R * +--R csch(x) +--R + +--R - 6cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 +--R (- 12cosh(x) + 12cosh(x))coth(x) +--R + +--R 3 3 +--R (12cosh(x) - 12cosh(x))coth(x) + 6cosh(x) - 6cosh(x) +--R * +--R csch(x) +--R + +--R 2 +--R - 15cosh(x) + 3 +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 +--R (- 30cosh(x) + 36cosh(x) - 6)coth(x) +--R + +--R 4 2 4 2 +--R (30cosh(x) - 36cosh(x) + 6)coth(x) + 15cosh(x) - 18cosh(x) + 3 +--R * +--R csch(x) +--R + +--R 3 +--R - 20cosh(x) + 12cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 40cosh(x) + 64cosh(x) - 24cosh(x))coth(x) +--R + +--R 5 3 5 +--R (40cosh(x) - 64cosh(x) + 24cosh(x))coth(x) + 20cosh(x) +--R + +--R 3 +--R - 32cosh(x) + 12cosh(x) +--R * +--R csch(x) +--R + +--R 4 2 +--R - 15cosh(x) + 26cosh(x) - 11 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 30cosh(x) + 66cosh(x) - 42cosh(x) + 6)coth(x) +--R + +--R 6 4 2 6 +--R (30cosh(x) - 66cosh(x) + 42cosh(x) - 6)coth(x) + 15cosh(x) +--R + +--R 4 2 +--R - 33cosh(x) + 21cosh(x) - 3 +--R * +--R csch(x) +--R + +--R 5 3 +--R - 6cosh(x) + 36cosh(x) - 30cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (- 12cosh(x) + 36cosh(x) - 36cosh(x) + 12cosh(x))coth(x) +--R + +--R 7 5 3 +--R (12cosh(x) - 36cosh(x) + 36cosh(x) - 12cosh(x))coth(x) +--R + +--R 7 5 3 +--R 6cosh(x) - 18cosh(x) + 18cosh(x) - 6cosh(x) +--R * +--R csch(x) +--R + +--R 6 4 2 +--R - cosh(x) + 27cosh(x) - 19cosh(x) - 7 +--R * +--R sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 2cosh(x) + 8cosh(x) - 12cosh(x) + 8cosh(x) - 2)coth(x) +--R + +--R 8 6 4 2 +--R (2cosh(x) - 8cosh(x) + 12cosh(x) - 8cosh(x) + 2)coth(x) +--R + +--R 8 6 4 2 +--R cosh(x) - 4cosh(x) + 6cosh(x) - 4cosh(x) + 1 +--R * +--R csch(x) +--R + +--R 5 +--R 8cosh(x) - 8cosh(x) +--R / +--R 2 6 3 5 +--R (2cosh(x) - 2)sinh(x) + (12cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (30cosh(x) - 36cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (40cosh(x) - 64cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (30cosh(x) - 66cosh(x) + 42cosh(x) - 6)sinh(x) +--R + +--R 7 5 3 8 +--R (12cosh(x) - 36cosh(x) + 36cosh(x) - 12cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) + 12cosh(x) - 8cosh(x) + 2 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 530 +t0589:= csch(x)^4/(1+tanh(x)) +--R +--R +--R 4 +--R csch(x) +--R (470) ----------- +--R tanh(x) + 1 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 530 +r0589:= -1/6*coth(x)^2*(-3+2*coth(x)) +--R +--R +--R 3 2 +--R - 2coth(x) + 3coth(x) +--R (471) ----------------------- +--R 6 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 530 +a0589:= integrate(t0589,x) +--R +--R +--R (472) +--R - 4sinh(x) - 8cosh(x) +--R / +--R 5 4 2 3 +--R 3sinh(x) + 15cosh(x)sinh(x) + (30cosh(x) - 9)sinh(x) +--R + +--R 3 2 4 2 +--R (30cosh(x) - 27cosh(x))sinh(x) + (15cosh(x) - 27cosh(x) + 12)sinh(x) +--R + +--R 5 3 +--R 3cosh(x) - 9cosh(x) + 6cosh(x) +--R Type: Union(Expression(Integer),...) +--E 474 + +--S 475 of 530 +m0589:= a0589-r0589 +--R +--R +--R (473) +--R 3 2 5 +--R (2coth(x) - 3coth(x) )sinh(x) +--R + +--R 3 2 4 +--R (10cosh(x)coth(x) - 15cosh(x)coth(x) )sinh(x) +--R + +--R 2 3 2 2 3 +--R ((20cosh(x) - 6)coth(x) + (- 30cosh(x) + 9)coth(x) )sinh(x) +--R + +--R 3 3 3 2 +--R ((20cosh(x) - 18cosh(x))coth(x) + (- 30cosh(x) + 27cosh(x))coth(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 +--R (10cosh(x) - 18cosh(x) + 8)coth(x) +--R + +--R 4 2 2 +--R (- 15cosh(x) + 27cosh(x) - 12)coth(x) - 8 +--R * +--R sinh(x) +--R + +--R 5 3 3 +--R (2cosh(x) - 6cosh(x) + 4cosh(x))coth(x) +--R + +--R 5 3 2 +--R (- 3cosh(x) + 9cosh(x) - 6cosh(x))coth(x) - 16cosh(x) +--R / +--R 5 4 2 3 +--R 6sinh(x) + 30cosh(x)sinh(x) + (60cosh(x) - 18)sinh(x) +--R + +--R 3 2 4 2 +--R (60cosh(x) - 54cosh(x))sinh(x) + (30cosh(x) - 54cosh(x) + 24)sinh(x) +--R + +--R 5 3 +--R 6cosh(x) - 18cosh(x) + 12cosh(x) +--R Type: Expression(Integer) +--E 475 + +--S 476 of 530 +d0589:= D(m0589,x) +--R +--R +--R (474) +--R 4 3 2 10 +--R (- coth(x) + coth(x) + coth(x) - coth(x))sinh(x) +--R + +--R 4 3 2 +--R - 10cosh(x)coth(x) + 10cosh(x)coth(x) + 10cosh(x)coth(x) +--R + +--R - 10cosh(x)coth(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 4 2 3 +--R (- 45cosh(x) + 6)coth(x) + (45cosh(x) - 6)coth(x) +--R + +--R 2 2 2 +--R (45cosh(x) - 6)coth(x) + (- 45cosh(x) + 6)coth(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 +--R (- 120cosh(x) + 48cosh(x))coth(x) +--R + +--R 3 3 3 2 +--R (120cosh(x) - 48cosh(x))coth(x) + (120cosh(x) - 48cosh(x))coth(x) +--R + +--R 3 +--R (- 120cosh(x) + 48cosh(x))coth(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 2 4 +--R (- 210cosh(x) + 168cosh(x) - 17)coth(x) +--R + +--R 4 2 3 +--R (210cosh(x) - 168cosh(x) + 17)coth(x) +--R + +--R 4 2 2 +--R (210cosh(x) - 168cosh(x) + 17)coth(x) +--R + +--R 4 2 +--R (- 210cosh(x) + 168cosh(x) - 17)coth(x) + 4 +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 4 +--R (- 252cosh(x) + 336cosh(x) - 98cosh(x))coth(x) +--R + +--R 5 3 3 +--R (252cosh(x) - 336cosh(x) + 98cosh(x))coth(x) +--R + +--R 5 3 2 +--R (252cosh(x) - 336cosh(x) + 98cosh(x))coth(x) +--R + +--R 5 3 +--R (- 252cosh(x) + 336cosh(x) - 98cosh(x))coth(x) + 32cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 4 2 4 +--R (- 210cosh(x) + 420cosh(x) - 235cosh(x) + 24)coth(x) +--R + +--R 6 4 2 3 +--R (210cosh(x) - 420cosh(x) + 235cosh(x) - 24)coth(x) +--R + +--R 6 4 2 2 +--R (210cosh(x) - 420cosh(x) + 235cosh(x) - 24)coth(x) +--R + +--R 6 4 2 2 +--R (- 210cosh(x) + 420cosh(x) - 235cosh(x) + 24)coth(x) + 100cosh(x) +--R + +--R - 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 3 4 +--R (- 120cosh(x) + 336cosh(x) - 300cosh(x) + 84cosh(x))coth(x) +--R + +--R 7 5 3 3 +--R (120cosh(x) - 336cosh(x) + 300cosh(x) - 84cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (120cosh(x) - 336cosh(x) + 300cosh(x) - 84cosh(x))coth(x) +--R + +--R 7 5 3 +--R (- 120cosh(x) + 336cosh(x) - 300cosh(x) + 84cosh(x))coth(x) +--R + +--R 3 +--R 160cosh(x) - 32cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 6 4 2 4 +--R (- 45cosh(x) + 168cosh(x) - 215cosh(x) + 108cosh(x) - 16)coth(x) +--R + +--R 8 6 4 2 3 +--R (45cosh(x) - 168cosh(x) + 215cosh(x) - 108cosh(x) + 16)coth(x) +--R + +--R 8 6 4 2 2 +--R (45cosh(x) - 168cosh(x) + 215cosh(x) - 108cosh(x) + 16)coth(x) +--R + +--R 8 6 4 2 +--R (- 45cosh(x) + 168cosh(x) - 215cosh(x) + 108cosh(x) - 16)coth(x) +--R + +--R 4 2 +--R 140cosh(x) - 72cosh(x) - 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (- 10cosh(x) + 48cosh(x) - 82cosh(x) + 60cosh(x) - 16cosh(x)) +--R * +--R 4 +--R coth(x) +--R + +--R 9 7 5 3 +--R (10cosh(x) - 48cosh(x) + 82cosh(x) - 60cosh(x) + 16cosh(x)) +--R * +--R 3 +--R coth(x) +--R + +--R 9 7 5 3 +--R (10cosh(x) - 48cosh(x) + 82cosh(x) - 60cosh(x) + 16cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 9 7 5 3 +--R (- 10cosh(x) + 48cosh(x) - 82cosh(x) + 60cosh(x) - 16cosh(x)) +--R * +--R coth(x) +--R + +--R 5 3 +--R 64cosh(x) - 64cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 4 +--R (- cosh(x) + 6cosh(x) - 13cosh(x) + 12cosh(x) - 4cosh(x) )coth(x) +--R + +--R 10 8 6 4 2 3 +--R (cosh(x) - 6cosh(x) + 13cosh(x) - 12cosh(x) + 4cosh(x) )coth(x) +--R + +--R 10 8 6 4 2 2 +--R (cosh(x) - 6cosh(x) + 13cosh(x) - 12cosh(x) + 4cosh(x) )coth(x) +--R + +--R 10 8 6 4 2 +--R (- cosh(x) + 6cosh(x) - 13cosh(x) + 12cosh(x) - 4cosh(x) )coth(x) +--R + +--R 6 4 2 +--R 12cosh(x) - 20cosh(x) + 8cosh(x) +--R / +--R 10 9 2 8 +--R sinh(x) + 10cosh(x)sinh(x) + (45cosh(x) - 6)sinh(x) +--R + +--R 3 7 +--R (120cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (210cosh(x) - 168cosh(x) + 17)sinh(x) +--R + +--R 5 3 5 +--R (252cosh(x) - 336cosh(x) + 98cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (210cosh(x) - 420cosh(x) + 235cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 3 +--R (120cosh(x) - 336cosh(x) + 300cosh(x) - 84cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (45cosh(x) - 168cosh(x) + 215cosh(x) - 108cosh(x) + 16)sinh(x) +--R + +--R 9 7 5 3 +--R (10cosh(x) - 48cosh(x) + 82cosh(x) - 60cosh(x) + 16cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) - 6cosh(x) + 13cosh(x) - 12cosh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 476 + +--S 477 of 530 +t0590:= sinh(x)/(a+b*coth(x)) +--R +--R +--R sinh(x) +--R (475) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 530 +r0590:= -b^2*atanh((a*cosh(x)+b*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ + a*cosh(x)/(a^2-b^2)-b*sinh(x)/(a^2-b^2) +--R +--R +--R +---------+ +--R 2 b sinh(x) + a cosh(x) | 2 2 +--R b atanh(---------------------) + (b sinh(x) - a cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (476) -------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression(Integer) +--E 478 + +--S 479 of 530 +a0590:= integrate(t0590,x) +--R +--R +--R (477) +--R [ +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) - b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) - b - a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 2 2 (sinh(x) + cosh(x))\|b - a +--R (- 4b sinh(x) - 4b cosh(x))atan(-----------------------------) +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) - b - a) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 479 + +--S 480 of 530 +m0590a:= a0590.1-r0590 +--R +--R +--R (478) +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) + b +--R + +--R - a +--R + +--R 2 2 b sinh(x) + a cosh(x) +--R (- 2b sinh(x) - 2b cosh(x))atanh(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((- b - a)sinh(x) + (b + a)cosh(x) - b - a)\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 480 + +--S 481 of 530 +d0590a:= D(m0590a,x) +--R +--R +--R (479) +--R 4 3 2 2 6 4 3 2 2 3 5 +--R (b + 2a b + a b )sinh(x) + (2b + 6a b + 6a b + 2a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 4 3 2 2 3 4 +--R ((4a b + 9a b + 6a b + a )cosh(x) - b + 6a b + 2a b - 2a b - a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b + 12a b + 12a b - 4a b - 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 +--R (- b - 6a b - 9a b - 4a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (2b + 2a b + 14a b + 6a b)cosh(x) - b + 4a b - a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x) +--R + +--R 4 3 3 4 3 +--R (4b - 4a b + 12a b + 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 4b + 6a b + 6a b - 6a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 6 4 2 2 3 4 4 +--R (- a b - 2a b - a )cosh(x) + (b - 4a b + 4a b + 3a )cosh(x) +--R + +--R 4 2 2 3 4 2 4 2 2 4 +--R (- 2b + 7a b - 2a b - 3a )cosh(x) + b - 2a b + a +--R / +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 2 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) + 4b - 6a b +--R + +--R 3 2 4 5 +--R - 2a b + 2a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b + 8a b - 18a b - 14a b + 10a b + 6a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (6b + 10a b - 14a b - 18a b + 8a b + 8a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 5 3 +--R (2b + 2a b - 2a b - 6a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 481 + +--S 482 of 530 +m0590b:= a0590.2-r0590 +--R +--R +--R (480) +--R +-------+ +--R 2 2 | 2 2 b sinh(x) + a cosh(x) +--R (- 2b sinh(x) - 2b cosh(x))\|b - a atanh(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- 4b sinh(x) - 4b cosh(x))\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|b - a +--R atan(-----------------------------) +--R b - a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R ((- b - a)sinh(x) + (b + a)cosh(x) - b - a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 | 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a \|b - a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 530 +d0590b:= D(m0590b,x) +--R +--R +--R (481) +--R 4 3 2 2 6 4 3 2 2 3 5 +--R (b + 2a b + a b )sinh(x) + (2b + 6a b + 6a b + 2a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 4 3 2 2 3 4 +--R ((4a b + 9a b + 6a b + a )cosh(x) - b + 6a b + 2a b - 2a b - a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 3 4 3 +--R (- 2b - 4a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b + 12a b + 12a b - 4a b - 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 +--R (- b - 6a b - 9a b - 4a b)cosh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (2b + 2a b + 14a b + 6a b)cosh(x) - b + 4a b - a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 2a b - 6a b - 6a b - 2a )cosh(x) +--R + +--R 4 3 3 4 3 +--R (4b - 4a b + 12a b + 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 4b + 6a b + 6a b - 6a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 3 4 6 4 2 2 3 4 4 +--R (- a b - 2a b - a )cosh(x) + (b - 4a b + 4a b + 3a )cosh(x) +--R + +--R 4 2 2 3 4 2 4 2 2 4 +--R (- 2b + 7a b - 2a b - 3a )cosh(x) + b - 2a b + a +--R / +--R 5 4 2 3 3 2 5 +--R (2b + 2a b - 2a b - 2a b )sinh(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (6b + 10a b - 2a b - 10a b - 4a b)cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 2 3 +--R (6b + 18a b + 8a b - 16a b - 14a b - 2a )cosh(x) + 4b - 6a b +--R + +--R 3 2 4 5 +--R - 2a b + 2a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (2b + 14a b + 16a b - 8a b - 18a b - 6a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b + 8a b - 18a b - 14a b + 10a b + 6a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (4a b + 10a b + 2a b - 10a b - 6a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (6b + 10a b - 14a b - 18a b + 8a b + 8a )cosh(x) + 2b - 2a b +--R + +--R 2 3 3 2 4 5 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (2a b + 2a b - 2a b - 2a )cosh(x) +--R + +--R 5 4 2 3 3 2 5 3 +--R (2b + 2a b - 2a b - 6a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 483 + +--S 484 of 530 +t0591:= sinh(x)^2/(a+b*coth(x)) +--R +--R +--R 2 +--R sinh(x) +--R (482) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 484 + +--S 485 of 530 +r0591:= -1/2*(a^3*x-sinh(x)*a^3*cosh(x)+b*cosh(x)^2*a^2-3*a*b^2*x+_ + a*sinh(x)*b^2*cosh(x)+2*b^3*log(b*cosh(x)+a*sinh(x))-_ + b^3*cosh(x)^2)/(b^4+a^4-2*a^2*b^2) +--R +--R +--R (483) +--R 3 2 3 +--R - 2b log(a sinh(x) + b cosh(x)) + (- a b + a )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (b - a b)cosh(x) + (3a b - a )x +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression(Integer) +--E 485 + +--S 486 of 530 +a0591:= integrate(t0591,x) +--R +--R +--R (484) +--R 3 2 3 3 2 +--R (- 8b sinh(x) - 16b cosh(x)sinh(x) - 8b cosh(x) ) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 3 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (8b + 12a b - 4a )x)sinh(x) +--R + +--R 3 2 2 3 3 3 2 3 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (16b + 24a b - 8a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 3 2 3 +--R (b - a b - a b + a )cosh(x) + (8b + 12a b - 4a )x cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 530 +m0591:= a0591-r0591 +--R +--R +--R (485) +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 3 2 3 3 2 +--R (- 8b sinh(x) - 16b cosh(x)sinh(x) - 8b cosh(x) ) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (b - a b - a b + a )sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R ((2b + 2a b - 2a b - 2a )cosh(x) + 8b x)sinh(x) +--R + +--R 3 2 3 3 +--R ((- 4b + 4a b)cosh(x) + 16b x cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 3 2 3 2 2 3 +--R (- 3b - a b + 3a b + a )cosh(x) + 8b x cosh(x) + b + a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 487 + +--S 488 of 530 +d0591:= D(m0591,x) +--R +--R +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 +--R (486) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression(Integer) +--E 488 + +--S 489 of 530 +t0592:= sinh(x)^4/(a+b*coth(x)) +--R +--R +--R 4 +--R sinh(x) +--R (487) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 489 + +--S 490 of 530 +r0592:= -1/8*(-3*a^5*x-8*b^5*cosh(x)^2-2*a*b^4*sinh(x)*cosh(x)^3+_ + 4*a^3*b^2*sinh(x)*cosh(x)^3+5*a^5*sinh(x)*cosh(x)-_ + 4*a^2*b^3*cosh(x)^4-2*a^5*sinh(x)*cosh(x)^3-4*a^4*b*cosh(x)^2-_ + 15*a*x*b^4+12*a^2*b^3*cosh(x)^2+10*a^3*x*b^2+8*b^5*log(b*cosh(x)+_ + a*sinh(x))+2*b^5*cosh(x)^4+2*a^4*b*cosh(x)^4+_ + 9*a*b^4*sinh(x)*cosh(x)-14*a^3*b^2*sinh(x)*cosh(x))/_ + (3*b^4*a^2-b^6+a^6-3*b^2*a^4) +--R +--R +--R (488) +--R 5 +--R 8b log(a sinh(x) + b cosh(x)) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((- 2a b + 4a b - 2a )cosh(x) + (9a b - 14a b + 5a )cosh(x))sinh(x) +--R + +--R 5 2 3 4 4 5 2 3 4 2 +--R (2b - 4a b + 2a b)cosh(x) + (- 8b + 12a b - 4a b)cosh(x) +--R + +--R 4 3 2 5 +--R (- 15a b + 10a b - 3a )x +--R / +--R 6 2 4 4 2 6 +--R 8b - 24a b + 24a b - 8a +--R Type: Expression(Integer) +--E 490 + +--S 491 of 530 +a0592:= integrate(t0592,x) +--R +--R +--R (489) +--R 5 4 5 3 5 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) - 12b +--R + +--R 4 2 3 3 2 4 5 +--R 16a b + 16a b - 24a b - 4a b + 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (56b - 56a b - 112a b + 112a b + 56a b - 56a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 72b + 96a b + 96a b - 144a b - 24a b + 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (70b - 70a b - 140a b + 140a b + 70a b - 70a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 180b + 240a b + 240a b - 360a b - 60a b + 120a )cosh(x) +--R + +--R 5 4 3 2 5 +--R (- 64b - 120a b + 80a b - 24a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (56b - 56a b - 112a b + 112a b + 56a b - 56a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 240b + 320a b + 320a b - 480a b - 80a b + 160a )cosh(x) +--R + +--R 5 4 3 2 5 +--R (- 256b - 480a b + 320a b - 96a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 180b + 240a b + 240a b - 360a b - 60a b + 120a )cosh(x) +--R + +--R 5 4 3 2 5 2 5 4 +--R (- 384b - 720a b + 480a b - 144a )x cosh(x) - 12b - 16a b +--R + +--R 2 3 3 2 4 5 +--R 16a b + 24a b - 4a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 72b + 96a b + 96a b - 144a b - 24a b + 48a )cosh(x) +--R + +--R 5 4 3 2 5 3 +--R (- 256b - 480a b + 320a b - 96a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 24b - 32a b + 32a b + 48a b - 8a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b + 16a b + 16a b - 24a b - 4a b + 8a )cosh(x) +--R + +--R 5 4 3 2 5 4 +--R (- 64b - 120a b + 80a b - 24a )x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 12b - 16a b + 16a b + 24a b - 4a b - 8a )cosh(x) + b + a b +--R + +--R 2 3 3 2 4 5 +--R - 2a b - 2a b + a b + a +--R / +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x)sinh(x) +--R + +--R 6 2 4 4 2 6 2 2 +--R (384b - 1152a b + 1152a b - 384a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 530 +m0592:= a0592-r0592 +--R +--R +--R (490) +--R 5 4 5 3 5 2 2 +--R - 64b sinh(x) - 256b cosh(x)sinh(x) - 384b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R - 256b cosh(x) sinh(x) - 64b cosh(x) +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 5 4 5 3 5 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) - 12b +--R + +--R 4 2 3 3 2 4 5 +--R 16a b + 16a b - 24a b - 4a b + 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (56b - 40a b - 112a b + 80a b + 56a b - 40a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 72b + 24a b + 96a b - 32a b - 24a b + 8a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (54b - 6a b - 108a b + 12a b + 54a b - 6a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (- 116b - 48a b + 144a b + 88a b - 28a b - 40a )cosh(x) - 64b x +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 8b + 40a b + 16a b - 80a b - 8a b + 40a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (16b - 112a b - 64a b + 192a b + 48a b - 80a )cosh(x) +--R + +--R 5 +--R - 256b x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 68b + 36a b + 136a b - 72a b - 68a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (204b - 48a b - 336a b + 88a b + 132a b - 40a )cosh(x) +--R + +--R 5 2 5 4 2 3 3 2 4 5 +--R - 384b x cosh(x) - 12b - 16a b + 16a b + 24a b - 4a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 56b + 8a b + 112a b - 16a b - 56a b + 8a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (184b + 24a b - 288a b - 32a b + 104a b + 8a )cosh(x) +--R + +--R 5 3 +--R - 256b x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 24b - 32a b + 32a b + 48a b - 8a b - 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 15b - a b + 30a b + 2a b - 15a b - a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 5 4 +--R (52b + 16a b - 80a b - 24a b + 28a b + 8a )cosh(x) - 64b x cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 12b - 16a b + 16a b + 24a b - 4a b - 8a )cosh(x) + b + a b +--R + +--R 2 3 3 2 4 5 +--R - 2a b - 2a b + a b + a +--R / +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x)sinh(x) +--R + +--R 6 2 4 4 2 6 2 2 +--R (384b - 1152a b + 1152a b - 384a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )cosh(x) +--R Type: Expression(Integer) +--E 492 + +--S 493 of 530 +d0592:= D(m0592,x) +--R +--R +--R (491) +--R 2 2 8 2 2 7 +--R (b - 2a b + a )sinh(x) + (8b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((28b - 44a b + 16a )cosh(x) - 6b - 4a b + 6a )sinh(x) +--R + +--R 2 2 3 2 2 5 +--R ((40b - 48a b + 8a )cosh(x) + (- 4b - 20a b + 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 4 +--R ((6b - 6a )cosh(x) + (38b - 44a b + 10a )cosh(x) )sinh(x) +--R + +--R 2 2 5 2 3 3 +--R ((- 40b + 48a b - 8a )cosh(x) + (72b - 56a b)cosh(x) )sinh(x) +--R + +--R 2 2 6 2 2 4 2 +--R (- 36b + 44a b - 8a )cosh(x) + (38b - 44a b + 10a )cosh(x) + 6b +--R + +--R 2 +--R 2a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 2 5 +--R (- 8b + 16a b - 8a )cosh(x) + (- 4b - 20a b + 16a )cosh(x) +--R + +--R 2 2 +--R (12b + 4a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (b + 2a b - 3a )cosh(x) + (- 6b - 4a b + 6a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (6b + 2a b - 4a )cosh(x) - b + a +--R / +--R 3 2 2 3 4 +--R (16b - 16a b - 16a b + 16a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (64b - 64a b - 64a b + 64a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (96b - 96a b - 96a b + 96a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 +--R (64b - 64a b - 64a b + 64a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (16b - 16a b - 16a b + 16a )cosh(x) +--R Type: Expression(Integer) +--E 493 + +--S 494 of 530 +t0593:= sinh(x)/(1+coth(x)) +--R +--R +--R sinh(x) +--R (492) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 530 +r0593:= cosh(x)-1/3*cosh(x)^3+1/3*sinh(x)^3 +--R +--R +--R 3 3 +--R sinh(x) - cosh(x) + 3cosh(x) +--R (493) ------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 495 + +--S 496 of 530 +a0593:= integrate(t0593,x) +--R +--R +--R 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + cosh(x) + 3 +--R (494) ----------------------------------------- +--R 6sinh(x) + 6cosh(x) +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 530 +m0593:= a0593-r0593 +--R +--R +--R (495) +--R 4 3 2 3 +--R - 2sinh(x) - 2cosh(x)sinh(x) + sinh(x) + (2cosh(x) - 2cosh(x))sinh(x) +--R + +--R 4 2 +--R 2cosh(x) - 5cosh(x) + 3 +--R / +--R 6sinh(x) + 6cosh(x) +--R Type: Expression(Integer) +--E 497 + +--S 498 of 530 +d0593:= D(m0593,x) +--R +--R +--R (496) +--R 3 2 3 2 +--R - 2cosh(x)sinh(x) - sinh(x) + (2cosh(x) - 2cosh(x))sinh(x) + cosh(x) - 1 +--R ---------------------------------------------------------------------------- +--R 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 498 + +--S 499 of 530 +t0594:= sinh(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R sinh(x) +--R (497) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 530 +r0594:= -3/8*x+3/8*cosh(x)*sinh(x)-1/4*cosh(x)*sinh(x)^3+1/4*sinh(x)^4 +--R +--R +--R 4 3 +--R 2sinh(x) - 2cosh(x)sinh(x) + 3cosh(x)sinh(x) - 3x +--R (498) --------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 500 + +--S 501 of 530 +a0594:= integrate(t0594,x) +--R +--R +--R (499) +--R 3 2 2 3 +--R sinh(x) + 9cosh(x)sinh(x) + (3cosh(x) - 12x + 6)sinh(x) + 3cosh(x) +--R + +--R (- 12x - 6)cosh(x) +--R / +--R 32sinh(x) + 32cosh(x) +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 530 +m0594:= a0594-r0594 +--R +--R +--R (500) +--R 5 2 3 2 +--R - 8sinh(x) + (8cosh(x) + 1)sinh(x) - 3cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 9cosh(x) + 6)sinh(x) + 3cosh(x) - 6cosh(x) +--R / +--R 32sinh(x) + 32cosh(x) +--R Type: Expression(Integer) +--E 502 + +--S 503 of 530 +d0594:= D(m0594,x) +--R +--R +--R (501) +--R 5 4 2 3 +--R 2sinh(x) - 6cosh(x)sinh(x) + (- 2cosh(x) - 1)sinh(x) +--R + +--R 3 2 2 3 +--R (6cosh(x) - 3cosh(x))sinh(x) + (3cosh(x) - 3)sinh(x) - 3cosh(x) +--R + +--R 3cosh(x) +--R / +--R 8sinh(x) + 8cosh(x) +--R Type: Expression(Integer) +--E 503 + +--S 504 of 530 +t0595:= sinh(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R sinh(x) +--R (502) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 530 +r0595:= -cosh(x)+2/3*cosh(x)^3-1/5*cosh(x)^5+1/5*sinh(x)^5 +--R +--R +--R 5 5 3 +--R 3sinh(x) - 3cosh(x) + 10cosh(x) - 15cosh(x) +--R (503) ---------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 530 +a0595:= integrate(t0595,x) +--R +--R +--R (504) +--R 4 3 2 2 +--R sinh(x) + 16cosh(x)sinh(x) + (6cosh(x) - 20)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 80cosh(x))sinh(x) + cosh(x) - 20cosh(x) - 45 +--R / +--R 120sinh(x) + 120cosh(x) +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 530 +m0595:= a0595-r0595 +--R +--R +--R (505) +--R 6 5 4 3 +--R - 24sinh(x) - 24cosh(x)sinh(x) + sinh(x) + 16cosh(x)sinh(x) +--R + +--R 2 2 5 3 +--R (6cosh(x) - 20)sinh(x) + (24cosh(x) - 64cosh(x) + 40cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 24cosh(x) - 79cosh(x) + 100cosh(x) - 45 +--R / +--R 120sinh(x) + 120cosh(x) +--R Type: Expression(Integer) +--E 507 + +--S 508 of 530 +d0595:= D(m0595,x) +--R +--R +--R (506) +--R 5 2 4 +--R - 8cosh(x)sinh(x) + (- 8cosh(x) + 1)sinh(x) +--R + +--R 4 2 2 +--R (8cosh(x) - 10cosh(x) + 4)sinh(x) +--R + +--R 5 3 4 2 +--R (8cosh(x) - 16cosh(x) + 8cosh(x))sinh(x) + cosh(x) - 4cosh(x) + 3 +--R / +--R 8sinh(x) + 8cosh(x) +--R Type: Expression(Integer) +--E 508 + +--S 509 of 530 +t0596:= sinh(x)^4/(1+coth(x)) +--R +--R +--R 4 +--R sinh(x) +--R (507) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 530 +r0596:= 5/16*x-5/16*cosh(x)*sinh(x)+5/24*cosh(x)*sinh(x)^3-_ + 1/6*cosh(x)*sinh(x)^5+1/6*sinh(x)^6 +--R +--R +--R (508) +--R 6 5 3 +--R 8sinh(x) - 8cosh(x)sinh(x) + 10cosh(x)sinh(x) - 15cosh(x)sinh(x) + 15x +--R ------------------------------------------------------------------------- +--R 48 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 530 +a0596:= integrate(t0596,x) +--R +--R +--R (509) +--R 5 4 2 3 +--R sinh(x) + 25cosh(x)sinh(x) + (10cosh(x) - 15)sinh(x) +--R + +--R 3 2 +--R (50cosh(x) - 135cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (5cosh(x) - 45cosh(x) + 120x - 60)sinh(x) + 5cosh(x) - 45cosh(x) +--R + +--R (120x + 60)cosh(x) +--R / +--R 384sinh(x) + 384cosh(x) +--R Type: Union(Expression(Integer),...) +--E 511 + +--S 512 of 530 +m0596:= a0596-r0596 +--R +--R +--R (510) +--R 7 2 5 4 +--R - 64sinh(x) + (64cosh(x) + 1)sinh(x) - 55cosh(x)sinh(x) +--R + +--R 2 3 3 2 +--R (- 70cosh(x) - 15)sinh(x) + (50cosh(x) - 15cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (5cosh(x) + 75cosh(x) - 60)sinh(x) + 5cosh(x) - 45cosh(x) + 60cosh(x) +--R / +--R 384sinh(x) + 384cosh(x) +--R Type: Expression(Integer) +--E 512 + +--S 513 of 530 +d0596:= D(m0596,x) +--R +--R +--R (511) +--R 7 6 2 5 +--R 8sinh(x) - 40cosh(x)sinh(x) + (- 8cosh(x) - 7)sinh(x) +--R + +--R 3 4 3 2 +--R (40cosh(x) - 10cosh(x))sinh(x) + (- 30cosh(x) + 15cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (15cosh(x) - 30cosh(x) + 15)sinh(x) + 15cosh(x) - 15cosh(x) +--R / +--R 48sinh(x) + 48cosh(x) +--R Type: Expression(Integer) +--E 513 + +--S 514 of 530 +t0597:= cosh(x)/(a+b*coth(x)) +--R +--R +--R cosh(x) +--R (512) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 514 + +--S 515 of 530 +r0597:= 2*a*b*atanh((a+b*tanh(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ + b*cosh(x)/(a^2-b^2)+a*sinh(x)/(a^2-b^2) +--R +--R +--R x +--R b tanh(-) + a +---------+ +--R 2 | 2 2 +--R - 2a b atanh(-------------) + (- a sinh(x) + b cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (513) ------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression(Integer) +--E 515 + +--S 516 of 530 +a0597:= integrate(t0597,x) +--R +--R +--R (514) +--R [ +--R (2a b sinh(x) + 2a b cosh(x)) +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) - b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|b - a +--R (4a b sinh(x) + 4a b cosh(x))atan(-----------------------------) +--R b - a +--R + +--R 2 2 +--R ((b - a)sinh(x) + (2b - 2a)cosh(x)sinh(x) + (b - a)cosh(x) + b + a) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 516 + +--S 517 of 530 +m0597a:= a0597.1-r0597 +--R +--R +--R (515) +--R (2a b sinh(x) + 2a b cosh(x)) +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) + b +--R + +--R - a +--R + +--R x +--R b tanh(-) + a +--R 2 +--R (4a b sinh(x) + 4a b cosh(x))atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 517 + +--S 518 of 530 +d0597a:= D(m0597a,x) +--R +--R +--R (516) +--R 3 2 2 4 +--R (- b - 2a b - a b)sinh(x) +--R + +--R 3 2 2 2 2 3 +--R ((- 2b - 4a b - 2a b)cosh(x) + 2a b + 2a b)sinh(x) +--R + +--R 2 2 3 2 2 +--R ((6a b + 6a b)cosh(x) - 2b + 2a b )sinh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (2b + 4a b + 2a b)cosh(x) + (6a b + 6a b)cosh(x) +--R + +--R 3 2 2 2 2 +--R (- 2b + 4a b - 2a b)cosh(x) + 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 4 2 2 3 +--R (b + 2a b + a b)cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 2 2 2 2 2 3 2 +--R (2a b - 2a b)cosh(x) + (2a b - 2a b)cosh(x) - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 4 +--R (- 2a b - 4a b - 2a )sinh(x) +--R + +--R 2 2 3 3 2 2 2 +--R (- 4a b - 8a b - 4a )cosh(x)sinh(x) + (- 4a b + 4a b)sinh(x) +--R + +--R 2 2 3 3 2 2 3 +--R ((4a b + 8a b + 4a )cosh(x) + (- 4a b + 8a b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 3 4 2 3 2 2 3 +--R (2a b + 4a b + 2a )cosh(x) + (4a b - 4a )cosh(x) - 2a b + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 4 +--R (- b - 2a b - a b)sinh(x) +--R + +--R 3 2 2 2 2 3 +--R ((- 2b - 4a b - 2a b)cosh(x) - 2a b - 2a b)sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 6a b - 6a b)cosh(x) - 2b + 2a b )sinh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (2b + 4a b + 2a b)cosh(x) + (- 6a b - 6a b)cosh(x) +--R + +--R 3 2 2 2 2 +--R (- 2b + 4a b - 2a b)cosh(x) - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 4 2 2 3 +--R (b + 2a b + a b)cosh(x) + (- 2a b - 2a b)cosh(x) +--R + +--R 2 2 2 2 2 3 2 +--R (2a b - 2a b)cosh(x) + (- 2a b + 2a b)cosh(x) - b + a b +--R / +--R 4 3 2 2 3 3 +--R (2b + 2a b - 2a b - 2a b)sinh(x) +--R + +--R 4 3 2 2 3 2 +--R (6b + 6a b - 6a b - 6a b)cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R ((6b + 6a b - 6a b - 6a b)cosh(x) + 2b - 2a b - 2a b + 2a b) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 3 +--R (2b + 2a b - 2a b - 2a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (2b - 2a b - 2a b + 2a b)cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 4 3 +--R (4a b + 4a b - 4a b - 4a )sinh(x) +--R + +--R 3 2 2 3 4 2 +--R (12a b + 12a b - 12a b - 12a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (12a b + 12a b - 12a b - 12a )cosh(x) + 4a b - 4a b - 4a b +--R + +--R 4 +--R 4a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (4a b + 4a b - 4a b - 4a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 3 +--R (2b + 2a b - 2a b - 2a b)sinh(x) +--R + +--R 4 3 2 2 3 2 +--R (6b + 6a b - 6a b - 6a b)cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R ((6b + 6a b - 6a b - 6a b)cosh(x) + 2b - 2a b - 2a b + 2a b) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 3 4 3 2 2 3 +--R (2b + 2a b - 2a b - 2a b)cosh(x) + (2b - 2a b - 2a b + 2a b)cosh(x) +--R Type: Expression(Integer) +--E 518 + +--S 519 of 530 +m0597b:= a0597.2-r0597 +--R +--R +--R (517) +--R x +--R +-------+ b tanh(-) + a +--R | 2 2 2 +--R (4a b sinh(x) + 4a b cosh(x))\|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R (4a b sinh(x) + 4a b cosh(x))\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|b - a +--R atan(-----------------------------) +--R b - a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R ((b + a)sinh(x) + (- b - a)cosh(x) + b + a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 | 2 2 | 2 2 +--R ((2b - 2a )sinh(x) + (2b - 2a )cosh(x))\|- b + a \|b - a +--R Type: Expression(Integer) +--E 519 + +--S 520 of 530 +d0597b:= D(m0597b,x) +--R +--R +--R (518) +--R 3 2 2 4 +--R (- b - 2a b - a b)sinh(x) +--R + +--R 3 2 2 2 2 3 +--R ((- 2b - 4a b - 2a b)cosh(x) + 2a b + 2a b)sinh(x) +--R + +--R 2 2 3 2 2 +--R ((6a b + 6a b)cosh(x) - 2b + 2a b )sinh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (2b + 4a b + 2a b)cosh(x) + (6a b + 6a b)cosh(x) +--R + +--R 3 2 2 2 2 +--R (- 2b + 4a b - 2a b)cosh(x) + 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 4 2 2 3 +--R (b + 2a b + a b)cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 2 2 2 2 2 3 2 +--R (2a b - 2a b)cosh(x) + (2a b - 2a b)cosh(x) - b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 4 +--R (- 2a b - 4a b - 2a )sinh(x) +--R + +--R 2 2 3 3 2 2 2 +--R (- 4a b - 8a b - 4a )cosh(x)sinh(x) + (- 4a b + 4a b)sinh(x) +--R + +--R 2 2 3 3 2 2 3 +--R ((4a b + 8a b + 4a )cosh(x) + (- 4a b + 8a b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 3 4 2 3 2 2 3 +--R (2a b + 4a b + 2a )cosh(x) + (4a b - 4a )cosh(x) - 2a b + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 4 +--R (- b - 2a b - a b)sinh(x) +--R + +--R 3 2 2 2 2 3 +--R ((- 2b - 4a b - 2a b)cosh(x) - 2a b - 2a b)sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 6a b - 6a b)cosh(x) - 2b + 2a b )sinh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (2b + 4a b + 2a b)cosh(x) + (- 6a b - 6a b)cosh(x) +--R + +--R 3 2 2 2 2 +--R (- 2b + 4a b - 2a b)cosh(x) - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 2 2 4 2 2 3 +--R (b + 2a b + a b)cosh(x) + (- 2a b - 2a b)cosh(x) +--R + +--R 2 2 2 2 2 3 2 +--R (2a b - 2a b)cosh(x) + (- 2a b + 2a b)cosh(x) - b + a b +--R / +--R 4 3 2 2 3 3 +--R (2b + 2a b - 2a b - 2a b)sinh(x) +--R + +--R 4 3 2 2 3 2 +--R (6b + 6a b - 6a b - 6a b)cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R ((6b + 6a b - 6a b - 6a b)cosh(x) + 2b - 2a b - 2a b + 2a b) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 3 +--R (2b + 2a b - 2a b - 2a b)cosh(x) +--R + +--R 4 3 2 2 3 +--R (2b - 2a b - 2a b + 2a b)cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 4 3 +--R (4a b + 4a b - 4a b - 4a )sinh(x) +--R + +--R 3 2 2 3 4 2 +--R (12a b + 12a b - 12a b - 12a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (12a b + 12a b - 12a b - 12a )cosh(x) + 4a b - 4a b - 4a b +--R + +--R 4 +--R 4a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (4a b + 4a b - 4a b - 4a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 3 +--R (2b + 2a b - 2a b - 2a b)sinh(x) +--R + +--R 4 3 2 2 3 2 +--R (6b + 6a b - 6a b - 6a b)cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R ((6b + 6a b - 6a b - 6a b)cosh(x) + 2b - 2a b - 2a b + 2a b) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 3 4 3 2 2 3 +--R (2b + 2a b - 2a b - 2a b)cosh(x) + (2b - 2a b - 2a b + 2a b)cosh(x) +--R Type: Expression(Integer) +--E 520 + +--S 521 of 530 +t0598:= cosh(x)^2/(a+b*coth(x)) +--R +--R +--R 2 +--R cosh(x) +--R (519) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 521 + +--S 522 of 530 +r0598:= -1/2*(-cosh(x)*a^3*sinh(x)-a^3*x+cosh(x)^2*b*a^2+_ + 2*a^2*b*log(b*cosh(x)+a*sinh(x))+cosh(x)*b^2*a*sinh(x)-_ + a*b^2*x-cosh(x)^2*b^3)/(b^4+a^4-2*a^2*b^2) +--R +--R +--R (520) +--R 2 2 3 +--R - 2a b log(a sinh(x) + b cosh(x)) + (- a b + a )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (b - a b)cosh(x) + (a b + a )x +--R / +--R 4 2 2 4 +--R 2b - 4a b + 2a +--R Type: Expression(Integer) +--E 522 + +--S 523 of 530 +a0598:= integrate(t0598,x) +--R +--R +--R (521) +--R 2 2 2 2 2 +--R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 +--R (b - a b - a b + a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b - 4a b + 4a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 2 3 2 +--R ((6b - 6a b - 6a b + 6a )cosh(x) + (4a b + 8a b + 4a )x)sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((4b - 4a b - 4a b + 4a )cosh(x) + (8a b + 16a b + 8a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 2 2 3 2 3 +--R (b - a b - a b + a )cosh(x) + (4a b + 8a b + 4a )x cosh(x) + b +--R + +--R 2 2 3 +--R a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 530 +m0598:= a0598-r0598 +--R +--R +--R (522) +--R 2 2 2 2 2 +--R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 2 2 2 2 2 +--R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (b - a b - a b + a )sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 2 +--R ((2b + 2a b - 2a b - 2a )cosh(x) + 8a b x)sinh(x) +--R + +--R 3 2 3 2 +--R ((- 4b + 4a b)cosh(x) + 16a b x cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 2 2 3 2 2 3 +--R (- 3b - a b + 3a b + a )cosh(x) + 8a b x cosh(x) + b + a b - a b - a +--R / +--R 4 2 2 4 2 4 2 2 4 +--R (8b - 16a b + 8a )sinh(x) + (16b - 32a b + 16a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 +--R (8b - 16a b + 8a )cosh(x) +--R Type: Expression(Integer) +--E 524 + +--S 525 of 530 +d0598:= D(m0598,x) +--R +--R +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 +--R (523) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R Type: Expression(Integer) +--E 525 + +--S 526 of 530 +t0599:= cosh(x)^4/(a+b*coth(x)) +--R +--R +--R 4 +--R cosh(x) +--R (524) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 526 + +--S 527 of 530 +r0599:= -1/8*(8*a^4*b*log(b*cosh(x)+a*sinh(x))+2*a^4*b*cosh(x)^4-_ + 2*a^5*sinh(x)*cosh(x)^3+2*b^5*cosh(x)^4-4*a^2*b^3*cosh(x)^4-_ + 3*a^5*sinh(x)*cosh(x)-3*x*a^5+4*a^4*b*cosh(x)^2-_ + 4*a^2*b^3*cosh(x)^2+2*a^3*b^2*sinh(x)*cosh(x)+_ + b^4*a*sinh(x)*cosh(x)-6*x*a^3*b^2+x*b^4*a+_ + 4*a^3*b^2*cosh(x)^3*sinh(x)-_ + 2*b^4*a*sinh(x)*cosh(x)^3)/(3*b^4*a^2-b^6+a^6-3*b^2*a^4) +--R +--R +--R (525) +--R 4 +--R 8a b log(a sinh(x) + b cosh(x)) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((- 2a b + 4a b - 2a )cosh(x) + (a b + 2a b - 3a )cosh(x))sinh(x) +--R + +--R 5 2 3 4 4 2 3 4 2 +--R (2b - 4a b + 2a b)cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 4 3 2 5 +--R (a b - 6a b - 3a )x +--R / +--R 6 2 4 4 2 6 +--R 8b - 24a b + 24a b - 8a +--R Type: Expression(Integer) +--E 527 + +--S 528 of 530 +a0599:= integrate(t0599,x) +--R +--R +--R (526) +--R 4 4 4 3 4 2 2 +--R 64a b sinh(x) + 256a b cosh(x)sinh(x) + 384a b cosh(x) sinh(x) +--R + +--R 4 3 4 4 +--R 256a b cosh(x) sinh(x) + 64a b cosh(x) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) + 4b +--R + +--R 2 3 3 2 4 5 +--R - 16a b + 8a b + 12a b - 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (56b - 56a b - 112a b + 112a b + 56a b - 56a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 +--R (24b - 96a b + 48a b + 72a b - 48a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (70b - 70a b - 140a b + 140a b + 70a b - 70a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (60b - 240a b + 120a b + 180a b - 120a )cosh(x) +--R + +--R 4 3 2 4 5 +--R (8a b - 48a b - 64a b - 24a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (56b - 56a b - 112a b + 112a b + 56a b - 56a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (80b - 320a b + 160a b + 240a b - 160a )cosh(x) +--R + +--R 4 3 2 4 5 +--R (32a b - 192a b - 256a b - 96a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (60b - 240a b + 120a b + 180a b - 120a )cosh(x) +--R + +--R 4 3 2 4 5 2 5 2 3 3 2 +--R (48a b - 288a b - 384a b - 144a )x cosh(x) + 4b - 16a b - 8a b +--R + +--R 4 5 +--R 12a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (24b - 96a b + 48a b + 72a b - 48a )cosh(x) +--R + +--R 4 3 2 4 5 3 +--R (32a b - 192a b - 256a b - 96a )x cosh(x) +--R + +--R 5 2 3 3 2 4 5 +--R (8b - 32a b - 16a b + 24a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 6 +--R (4b - 16a b + 8a b + 12a b - 8a )cosh(x) +--R + +--R 4 3 2 4 5 4 +--R (8a b - 48a b - 64a b - 24a )x cosh(x) +--R + +--R 5 2 3 3 2 4 5 2 5 4 2 3 3 2 +--R (4b - 16a b - 8a b + 12a b + 8a )cosh(x) + b + a b - 2a b - 2a b +--R + +--R 4 5 +--R a b + a +--R / +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x)sinh(x) +--R + +--R 6 2 4 4 2 6 2 2 +--R (384b - 1152a b + 1152a b - 384a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 530 +m0599:= a0599-r0599 +--R +--R +--R (527) +--R 4 4 4 3 4 2 2 +--R - 64a b sinh(x) - 256a b cosh(x)sinh(x) - 384a b cosh(x) sinh(x) +--R + +--R 4 3 4 4 +--R - 256a b cosh(x) sinh(x) - 64a b cosh(x) +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 4 4 4 3 4 2 2 +--R 64a b sinh(x) + 256a b cosh(x)sinh(x) + 384a b cosh(x) sinh(x) +--R + +--R 4 3 4 4 +--R 256a b cosh(x) sinh(x) + 64a b cosh(x) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (b - a b - 2a b + 2a b + a b - a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 16a b + 16a b + 8a b - 8a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (28b - 28a b - 56a b + 56a b + 28a b - 28a )cosh(x) + 4b +--R + +--R 2 3 3 2 4 5 +--R - 16a b + 8a b + 12a b - 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (56b - 40a b - 112a b + 80a b + 56a b - 40a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (24b - 8a b - 96a b + 32a b + 72a b - 24a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (54b - 6a b - 108a b + 12a b + 54a b - 6a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 4 +--R (60b - 32a b - 208a b + 56a b + 148a b - 24a )cosh(x) - 64a b x +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 8b + 40a b + 16a b - 80a b - 8a b + 40a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (80b - 48a b - 192a b + 64a b + 112a b - 16a )cosh(x) +--R + +--R 4 +--R - 256a b x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 68b + 36a b + 136a b - 72a b - 68a b + 36a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (60b - 32a b - 48a b + 56a b - 12a b - 24a )cosh(x) +--R + +--R 4 2 5 2 3 3 2 4 5 +--R - 384a b x cosh(x) + 4b - 16a b - 8a b + 12a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 56b + 8a b + 112a b - 16a b - 56a b + 8a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (24b - 8a b + 32a b + 32a b - 56a b - 24a )cosh(x) +--R + +--R 4 3 5 2 3 3 2 4 5 +--R - 256a b x cosh(x) + (8b - 32a b - 16a b + 24a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 15b - a b + 30a b + 2a b - 15a b - a )cosh(x) +--R + +--R 5 2 3 3 2 4 5 6 4 4 +--R (4b + 16a b + 8a b - 20a b - 8a )cosh(x) - 64a b x cosh(x) +--R + +--R 5 2 3 3 2 4 5 2 5 4 2 3 3 2 +--R (4b - 16a b - 8a b + 12a b + 8a )cosh(x) + b + a b - 2a b - 2a b +--R + +--R 4 5 +--R a b + a +--R / +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x)sinh(x) +--R + +--R 6 2 4 4 2 6 2 2 +--R (384b - 1152a b + 1152a b - 384a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (256b - 768a b + 768a b - 256a )cosh(x) sinh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (64b - 192a b + 192a b - 64a )cosh(x) +--R Type: Expression(Integer) +--E 529 + +--S 530 of 530 +d0599:= D(m0599,x) +--R +--R +--R (528) +--R 2 2 8 2 2 7 +--R (b - 2a b + a )sinh(x) + (8b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 6 +--R ((28b - 44a b + 16a )cosh(x) + 2b - 4a b - 2a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((40b - 48a b + 8a )cosh(x) + (12b - 20a b)cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 4 +--R ((6b - 6a )cosh(x) + (30b - 44a b + 18a )cosh(x) )sinh(x) +--R + +--R 2 2 5 2 2 3 3 +--R ((- 40b + 48a b - 8a )cosh(x) + (40b - 56a b + 32a )cosh(x) )sinh(x) +--R + +--R 2 2 6 2 2 4 2 +--R (- 36b + 44a b - 8a )cosh(x) + (30b - 44a b + 18a )cosh(x) - 2b +--R + +--R 2 +--R 2a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 +--R (- 8b + 16a b - 8a )cosh(x) + (12b - 20a b)cosh(x) +--R + +--R 2 2 +--R (- 4b + 4a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 2 6 +--R (b + 2a b - 3a )cosh(x) + (2b - 4a b - 2a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b + 2a b + 4a )cosh(x) - b + a +--R / +--R 3 2 2 3 4 +--R (16b - 16a b - 16a b + 16a )sinh(x) +--R + +--R 3 2 2 3 3 +--R (64b - 64a b - 64a b + 64a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (96b - 96a b - 96a b + 96a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 +--R (64b - 64a b - 64a b + 64a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (16b - 16a b - 16a b + 16a )cosh(x) +--R Type: Expression(Integer) +--E 530 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper500-599.input.pdf b/src/axiom-website/CATS/richhyper500-599.input.pdf new file mode 100644 index 0000000..870f2f7 Binary files /dev/null and b/src/axiom-website/CATS/richhyper500-599.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper600-699.input.pamphlet b/src/axiom-website/CATS/richhyper600-699.input.pamphlet new file mode 100644 index 0000000..e11e0ad --- /dev/null +++ b/src/axiom-website/CATS/richhyper600-699.input.pamphlet @@ -0,0 +1,25568 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper600-699.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper600-699.output +)spool richhyper600-699.output +)set message auto off +)clear all + +--S 1 of 526 +t0600:= cosh(x)/(1+coth(x)) +--R +--R +--R cosh(x) +--R (1) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 526 +r0600:= 1/3*cosh(x)^3-1/3*sinh(x)^3 +--R +--R +--R 3 3 +--R - sinh(x) + cosh(x) +--R (2) --------------------- +--R 3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 526 +a0600:= integrate(t0600,x) +--R +--R +--R 2 2 +--R sinh(x) + cosh(x)sinh(x) + cosh(x) +--R (3) ------------------------------------ +--R 3sinh(x) + 3cosh(x) +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 526 +m0600:= a0600-r0600 +--R +--R +--R (4) +--R 4 3 2 3 +--R sinh(x) + cosh(x)sinh(x) + sinh(x) + (- cosh(x) + cosh(x))sinh(x) +--R + +--R 4 2 +--R - cosh(x) + cosh(x) +--R / +--R 3sinh(x) + 3cosh(x) +--R Type: Expression(Integer) +--E 4 + +--S 5 of 526 +d0600:= D(m0600,x) +--R +--R +--R 3 3 +--R cosh(x)sinh(x) + (- cosh(x) + cosh(x))sinh(x) +--R (5) ----------------------------------------------- +--R sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 5 + +--S 6 of 526 +t0601:= cosh(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R cosh(x) +--R (6) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 526 +r0601:= 1/8*x+1/4*cosh(x)^4+1/8*cosh(x)*sinh(x)-1/4*cosh(x)^3*sinh(x) +--R +--R +--R 3 4 +--R (- 2cosh(x) + cosh(x))sinh(x) + 2cosh(x) + x +--R (7) ---------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 526 +a0601:= integrate(t0601,x) +--R +--R +--R (8) +--R 3 2 2 3 +--R sinh(x) + 9cosh(x)sinh(x) + (3cosh(x) + 4x - 2)sinh(x) + 3cosh(x) +--R + +--R (4x + 2)cosh(x) +--R / +--R 32sinh(x) + 32cosh(x) +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 526 +m0601:= a0601-r0601 +--R +--R +--R (9) +--R 3 3 2 2 +--R sinh(x) + (8cosh(x) + 5cosh(x))sinh(x) + (- cosh(x) - 2)sinh(x) +--R + +--R 5 3 +--R - 8cosh(x) + 3cosh(x) + 2cosh(x) +--R / +--R 32sinh(x) + 32cosh(x) +--R Type: Expression(Integer) +--E 9 + +--S 10 of 526 +d0601:= D(m0601,x) +--R +--R +--R (10) +--R 2 3 3 2 +--R (6cosh(x) + 1)sinh(x) + (- 2cosh(x) - cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (- 6cosh(x) + 5cosh(x) + 1)sinh(x) + 2cosh(x) - cosh(x) - cosh(x) +--R / +--R 8sinh(x) + 8cosh(x) +--R Type: Expression(Integer) +--E 10 + +--S 11 of 526 +t0602:= cosh(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R cosh(x) +--R (11) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 526 +r0602:= 1/5*cosh(x)^5-1/3*sinh(x)^3-1/5*sinh(x)^5 +--R +--R +--R 5 3 5 +--R - 3sinh(x) - 5sinh(x) + 3cosh(x) +--R (12) ----------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 526 +a0602:= integrate(t0602,x) +--R +--R +--R (13) +--R 4 3 2 2 +--R sinh(x) + cosh(x)sinh(x) + (6cosh(x) + 5)sinh(x) +--R + +--R 3 4 2 +--R (cosh(x) + 5cosh(x))sinh(x) + cosh(x) + 5cosh(x) +--R / +--R 30sinh(x) + 30cosh(x) +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 526 +m0602:= a0602-r0602 +--R +--R +--R (14) +--R 6 5 4 3 +--R 6sinh(x) + 6cosh(x)sinh(x) + 11sinh(x) + 11cosh(x)sinh(x) +--R + +--R 2 2 5 3 +--R (6cosh(x) + 5)sinh(x) + (- 6cosh(x) + cosh(x) + 5cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 6cosh(x) + cosh(x) + 5cosh(x) +--R / +--R 30sinh(x) + 30cosh(x) +--R Type: Expression(Integer) +--E 14 + +--S 15 of 526 +d0602:= D(m0602,x) +--R +--R +--R (15) +--R 5 2 4 3 +--R 2cosh(x)sinh(x) + 2cosh(x) sinh(x) + 3cosh(x)sinh(x) +--R + +--R 4 2 2 +--R (- 2cosh(x) + 2cosh(x) )sinh(x) +--R + +--R 5 3 +--R (- 2cosh(x) + cosh(x) + cosh(x))sinh(x) +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 15 + +--S 16 of 526 +t0603:= cosh(x)^4/(1+coth(x)) +--R +--R +--R 4 +--R cosh(x) +--R (16) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 526 +r0603:= 1/16*x+1/6*cosh(x)^6+1/16*cosh(x)*sinh(x)+1/24*cosh(x)^3*sinh(x)-_ + 1/6*cosh(x)^5*sinh(x) +--R +--R +--R 5 3 6 +--R (- 8cosh(x) + 2cosh(x) + 3cosh(x))sinh(x) + 8cosh(x) + 3x +--R (17) ------------------------------------------------------------ +--R 48 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 526 +a0603:= integrate(t0603,x) +--R +--R +--R (18) +--R 5 4 2 3 +--R sinh(x) + 25cosh(x)sinh(x) + (10cosh(x) + 9)sinh(x) +--R + +--R 3 2 +--R (50cosh(x) + 81cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (5cosh(x) + 27cosh(x) + 24x - 12)sinh(x) + 5cosh(x) + 27cosh(x) +--R + +--R (24x + 12)cosh(x) +--R / +--R 384sinh(x) + 384cosh(x) +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 526 +m0603:= a0603-r0603 +--R +--R +--R (19) +--R 5 4 2 3 +--R sinh(x) + 25cosh(x)sinh(x) + (10cosh(x) + 9)sinh(x) +--R + +--R 5 3 2 +--R (64cosh(x) + 34cosh(x) + 57cosh(x))sinh(x) +--R + +--R 4 2 7 5 +--R (- 11cosh(x) + 3cosh(x) - 12)sinh(x) - 64cosh(x) + 5cosh(x) +--R + +--R 3 +--R 27cosh(x) + 12cosh(x) +--R / +--R 384sinh(x) + 384cosh(x) +--R Type: Expression(Integer) +--E 19 + +--S 20 of 526 +d0603:= D(m0603,x) +--R +--R +--R (20) +--R 5 4 2 3 +--R 3sinh(x) + (40cosh(x) + 24cosh(x) + 6)sinh(x) +--R + +--R 5 3 2 +--R (- 8cosh(x) - 6cosh(x) - 3cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (- 40cosh(x) + 13cosh(x) + 24cosh(x) + 3)sinh(x) + 8cosh(x) +--R + +--R 5 3 +--R - 2cosh(x) - 3cosh(x) - 3cosh(x) +--R / +--R 48sinh(x) + 48cosh(x) +--R Type: Expression(Integer) +--E 20 + +--S 21 of 526 +t0604:= tanh(x)/(a+b*coth(x)) +--R +--R +--R tanh(x) +--R (21) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 21 + +--S 22 of 526 +r0604:= (-a*b*x+log(cosh(x))*a^2-log(cosh(x))*b^2+_ + b^2*log(b*cosh(x)+a*sinh(x)))/a/(a^2-b^2) +--R +--R +--R 2 2 2 +--R - b log(a sinh(x) + b cosh(x)) + (b - a )log(cosh(x)) + a b x +--R (22) -------------------------------------------------------------- +--R 2 3 +--R a b - a +--R Type: Expression(Integer) +--E 22 + +--S 23 of 526 +a0604:= integrate(t0604,x) +--R +--R +--R (23) +--R 2 2 2cosh(x) 2 - 2a sinh(x) - 2b cosh(x) +--R (b - a )log(- -----------------) - b log(-------------------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R + +--R 2 +--R (a b + a )x +--R / +--R 2 3 +--R a b - a +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 526 +m0604:= a0604-r0604 +--R +--R +--R (24) +--R 2 2 2 +--R b log(a sinh(x) + b cosh(x)) + (- b + a )log(cosh(x)) +--R + +--R 2 2 2cosh(x) 2 - 2a sinh(x) - 2b cosh(x) 2 +--R (b - a )log(- -----------------) - b log(-------------------------) + a x +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R / +--R 2 3 +--R a b - a +--R Type: Expression(Integer) +--E 24 + +--S 25 of 526 +d0604:= D(m0604,x) +--R +--R +--R (25) 0 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 526 +t0605:= tanh(x)^2/(a+b*coth(x)) +--R +--R +--R 2 +--R tanh(x) +--R (26) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 526 +r0605:= a*x/(a^2-b^2)-b*log(cosh(x))/a^2-_ + b^3*log(b*cosh(x)+a*sinh(x))/a^2/(a^2-b^2)-tanh(x)/a +--R +--R +--R (27) +--R 3 3 2 +--R b log(a sinh(x) + b cosh(x)) + (- b + a b)log(cosh(x)) +--R + +--R 2 3 3 +--R (- a b + a )tanh(x) - a x +--R / +--R 2 2 4 +--R a b - a +--R Type: Expression(Integer) +--E 27 + +--S 28 of 526 +a0605:= integrate(t0605,x) +--R +--R +--R (28) +--R 3 2 2 3 2 +--R (- b + a b)sinh(x) + (- 2b + 2a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 +--R (- b + a b)cosh(x) - b + a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 3 +--R (- a b - a )x sinh(x) + (- 2a b - 2a )x cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- a b - a )x cosh(x) + (- a b - a )x + 2a b - 2a +--R / +--R 2 2 4 2 2 2 4 2 2 4 2 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) + (a b - a )cosh(x) +--R + +--R 2 2 4 +--R a b - a +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 526 +m0605:= a0605-r0605 +--R +--R +--R (29) +--R 3 2 3 3 2 3 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b ) +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 3 2 2 3 2 3 2 2 +--R (b - a b)sinh(x) + (2b - 2a b)cosh(x)sinh(x) + (b - a b)cosh(x) +--R + +--R 3 2 +--R b - a b +--R * +--R log(cosh(x)) +--R + +--R 3 2 2 3 2 +--R (- b + a b)sinh(x) + (- 2b + 2a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 +--R (- b + a b)cosh(x) - b + a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )cosh(x) + a b - a +--R * +--R tanh(x) +--R + +--R 2 2 2 2 2 2 2 +--R - a b x sinh(x) - 2a b x cosh(x)sinh(x) - a b x cosh(x) - a b x + 2a b +--R + +--R 3 +--R - 2a +--R / +--R 2 2 4 2 2 2 4 2 2 4 2 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) + (a b - a )cosh(x) +--R + +--R 2 2 4 +--R a b - a +--R Type: Expression(Integer) +--E 29 + +--S 30 of 526 +d0605:= D(m0605,x) +--R +--R +--R (30) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) - 4cosh(x))sinh(x) - cosh(x) - 2cosh(x) - 1 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R / +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression(Integer) +--E 30 + +--S 31 of 526 +t0606:= tanh(x)^3/(a+b*coth(x)) +--R +--R +--R 3 +--R tanh(x) +--R (31) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 31 + +--S 32 of 526 +r0606:= -b*x/a^2-b^3*x/a^4-b^5*x/a^4/(a^2-b^2)+log(cosh(x))/a+_ + b^2*log(cosh(x))/a^3+b^4*log(b*cosh(x)+a*sinh(x))/a^3/(a^2-b^2)+_ + b*tanh(x)/a^2-1/2*tanh(x)^2/a +--R +--R +--R (32) +--R 4 4 4 +--R - 2b log(a sinh(x) + b cosh(x)) + (2b - 2a )log(cosh(x)) +--R + +--R 2 2 4 2 3 3 3 +--R (- a b + a )tanh(x) + (2a b - 2a b)tanh(x) + 2a b x +--R / +--R 3 2 5 +--R 2a b - 2a +--R Type: Expression(Integer) +--E 32 + +--S 33 of 526 +a0606:= integrate(t0606,x) +--R +--R +--R (33) +--R 4 4 4 4 4 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 4 4 2 4 4 2 +--R ((6b - 6a )cosh(x) + 2b - 2a )sinh(x) +--R + +--R 4 4 3 4 4 4 4 4 +--R ((4b - 4a )cosh(x) + (4b - 4a )cosh(x))sinh(x) + (b - a )cosh(x) +--R + +--R 4 4 2 4 4 +--R (2b - 2a )cosh(x) + b - a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 4 4 3 4 2 4 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) - 2b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (- 4b cosh(x) - 4b cosh(x))sinh(x) - b cosh(x) - 2b cosh(x) - b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 4 4 3 4 3 +--R (a b + a )x sinh(x) + (4a b + 4a )x cosh(x)sinh(x) +--R + +--R 3 4 2 3 4 3 2 2 3 4 +--R ((6a b + 6a )x cosh(x) + (2a b + 2a )x - 2a b + 2a b + 2a b - 2a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 +--R (4a b + 4a )x cosh(x) +--R + +--R 3 4 3 2 2 3 4 +--R ((4a b + 4a )x - 4a b + 4a b + 4a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 +--R (a b + a )x cosh(x) +--R + +--R 3 4 3 2 2 3 4 2 3 4 +--R ((2a b + 2a )x - 2a b + 2a b + 2a b - 2a )cosh(x) + (a b + a )x +--R + +--R 3 3 +--R - 2a b + 2a b +--R / +--R 3 2 5 4 3 2 5 3 +--R (a b - a )sinh(x) + (4a b - 4a )cosh(x)sinh(x) +--R + +--R 3 2 5 2 3 2 5 2 +--R ((6a b - 6a )cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 3 2 5 3 3 2 5 +--R ((4a b - 4a )cosh(x) + (4a b - 4a )cosh(x))sinh(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R (a b - a )cosh(x) + (2a b - 2a )cosh(x) + a b - a +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 526 +m0606:= a0606-r0606 +--R +--R +--R (34) +--R 4 4 4 3 4 2 4 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) + 4b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (8b cosh(x) + 8b cosh(x))sinh(x) + 2b cosh(x) + 4b cosh(x) + 2b +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 4 4 4 4 4 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 4 4 2 4 4 2 +--R ((- 12b + 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 4 4 3 4 4 +--R ((- 8b + 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 4 4 4 4 4 2 4 4 +--R (- 2b + 2a )cosh(x) + (- 4b + 4a )cosh(x) - 2b + 2a +--R * +--R log(cosh(x)) +--R + +--R 4 4 4 4 4 3 +--R (2b - 2a )sinh(x) + (8b - 8a )cosh(x)sinh(x) +--R + +--R 4 4 2 4 4 2 +--R ((12b - 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 4 4 3 4 4 +--R ((8b - 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 4 4 4 4 4 2 4 4 +--R (2b - 2a )cosh(x) + (4b - 4a )cosh(x) + 2b - 2a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 4 4 3 4 2 4 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 4 2 2 4 3 +--R (a b - a )sinh(x) + (4a b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 4 2 2 2 4 2 +--R ((6a b - 6a )cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 2 4 3 2 2 4 +--R ((4a b - 4a )cosh(x) + (4a b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 +--R (a b - a )cosh(x) + (2a b - 2a )cosh(x) + a b - a +--R * +--R 2 +--R tanh(x) +--R + +--R 3 3 4 3 3 3 +--R (- 2a b + 2a b)sinh(x) + (- 8a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 2 +--R ((- 12a b + 12a b)cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 3 3 3 3 3 +--R ((- 8a b + 8a b)cosh(x) + (- 8a b + 8a b)cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 3 3 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a b)cosh(x) - 2a b + 2a b +--R * +--R tanh(x) +--R + +--R 4 4 4 3 +--R 2a x sinh(x) + 8a x cosh(x)sinh(x) +--R + +--R 4 2 4 3 2 2 3 4 2 +--R (12a x cosh(x) + 4a x - 4a b + 4a b + 4a b - 4a )sinh(x) +--R + +--R 4 3 4 3 2 2 3 4 +--R (8a x cosh(x) + (8a x - 8a b + 8a b + 8a b - 8a )cosh(x))sinh(x) +--R + +--R 4 4 4 3 2 2 3 4 2 4 +--R 2a x cosh(x) + (4a x - 4a b + 4a b + 4a b - 4a )cosh(x) + 2a x +--R + +--R 3 3 +--R - 4a b + 4a b +--R / +--R 3 2 5 4 3 2 5 3 +--R (2a b - 2a )sinh(x) + (8a b - 8a )cosh(x)sinh(x) +--R + +--R 3 2 5 2 3 2 5 2 +--R ((12a b - 12a )cosh(x) + 4a b - 4a )sinh(x) +--R + +--R 3 2 5 3 3 2 5 +--R ((8a b - 8a )cosh(x) + (8a b - 8a )cosh(x))sinh(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R (2a b - 2a )cosh(x) + (4a b - 4a )cosh(x) + 2a b - 2a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 526 +d0606:= D(m0606,x) +--R +--R +--R (35) +--R 6 5 2 4 +--R - a sinh(x) - 6a cosh(x)sinh(x) + (- 15a cosh(x) - 3a)sinh(x) +--R + +--R 3 3 +--R (- 20a cosh(x) - 12a cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 15a cosh(x) - 18a cosh(x) - 3a)sinh(x) +--R + +--R 5 3 6 +--R (- 6a cosh(x) - 12a cosh(x) - 6a cosh(x))sinh(x) - a cosh(x) +--R + +--R 4 2 +--R - 3a cosh(x) - 3a cosh(x) - a +--R * +--R 3 +--R tanh(x) +--R + +--R 6 5 2 4 +--R b sinh(x) + 6b cosh(x)sinh(x) + (15b cosh(x) + 3b)sinh(x) +--R + +--R 3 3 +--R (20b cosh(x) + 12b cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) + 18b cosh(x) + 3b)sinh(x) +--R + +--R 5 3 6 +--R (6b cosh(x) + 12b cosh(x) + 6b cosh(x))sinh(x) + b cosh(x) +--R + +--R 4 2 +--R 3b cosh(x) + 3b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 2 4 +--R a sinh(x) + 6a cosh(x)sinh(x) + (15a cosh(x) + 3a)sinh(x) +--R + +--R 3 3 +--R (20a cosh(x) + 12a cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15a cosh(x) + 18a cosh(x) + 3a)sinh(x) +--R + +--R 5 3 6 +--R (6a cosh(x) + 12a cosh(x) + 6a cosh(x))sinh(x) + a cosh(x) +--R + +--R 4 2 +--R 3a cosh(x) + 3a cosh(x) + a +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R - b sinh(x) - 6b cosh(x)sinh(x) + (- 15b cosh(x) + b - 4a)sinh(x) +--R + +--R 3 3 +--R (- 20b cosh(x) + (4b - 16a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 15b cosh(x) + (6b - 24a)cosh(x) + b + 4a)sinh(x) +--R + +--R 5 3 +--R (- 6b cosh(x) + (4b - 16a)cosh(x) + (2b + 8a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - b cosh(x) + (b - 4a)cosh(x) + (b + 4a)cosh(x) - b +--R / +--R 2 6 2 5 2 2 2 4 +--R a sinh(x) + 6a cosh(x)sinh(x) + (15a cosh(x) + 3a )sinh(x) +--R + +--R 2 3 2 3 +--R (20a cosh(x) + 12a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (15a cosh(x) + 18a cosh(x) + 3a )sinh(x) +--R + +--R 2 5 2 3 2 2 6 +--R (6a cosh(x) + 12a cosh(x) + 6a cosh(x))sinh(x) + a cosh(x) +--R + +--R 2 4 2 2 2 +--R 3a cosh(x) + 3a cosh(x) + a +--R Type: Expression(Integer) +--E 35 + +--S 36 of 526 +t0607:= tanh(x)^4/(a+b*coth(x)) +--R +--R +--R 4 +--R tanh(x) +--R (36) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 36 + +--S 37 of 526 +r0607:= x/a+b^2*x/a^3+b^4*x/a^5+b^6*x/a^5/(a^2-b^2)-b*log(cosh(x))/a^2-_ + b^3*log(cosh(x))/a^4-b^5*log(b*cosh(x)+a*sinh(x))/a^4/(a^2-b^2)-_ + tanh(x)/a-b^2*tanh(x)/a^3+1/2*b*tanh(x)^2/a^2-1/3*tanh(x)^3/a +--R +--R +--R (37) +--R 5 5 4 +--R 6b log(a sinh(x) + b cosh(x)) + (- 6b + 6a b)log(cosh(x)) +--R + +--R 3 2 5 3 2 3 4 2 4 5 +--R (- 2a b + 2a )tanh(x) + (3a b - 3a b)tanh(x) + (- 6a b + 6a )tanh(x) +--R + +--R 5 +--R - 6a x +--R / +--R 4 2 6 +--R 6a b - 6a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 526 +a0607:= integrate(t0607,x) +--R +--R +--R (38) +--R 5 4 6 5 4 5 +--R (- 3b + 3a b)sinh(x) + (- 18b + 18a b)cosh(x)sinh(x) +--R + +--R 5 4 2 5 4 4 +--R ((- 45b + 45a b)cosh(x) - 9b + 9a b)sinh(x) +--R + +--R 5 4 3 5 4 3 +--R ((- 60b + 60a b)cosh(x) + (- 36b + 36a b)cosh(x))sinh(x) +--R + +--R 5 4 4 5 4 2 5 4 +--R ((- 45b + 45a b)cosh(x) + (- 54b + 54a b)cosh(x) - 9b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 5 4 3 +--R (- 18b + 18a b)cosh(x) + (- 36b + 36a b)cosh(x) +--R + +--R 5 4 +--R (- 18b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 6 5 4 4 +--R (- 3b + 3a b)cosh(x) + (- 9b + 9a b)cosh(x) +--R + +--R 5 4 2 5 4 +--R (- 9b + 9a b)cosh(x) - 3b + 3a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 5 6 5 5 5 2 5 4 +--R 3b sinh(x) + 18b cosh(x)sinh(x) + (45b cosh(x) + 9b )sinh(x) +--R + +--R 5 3 5 3 +--R (60b cosh(x) + 36b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (45b cosh(x) + 54b cosh(x) + 9b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (18b cosh(x) + 36b cosh(x) + 18b cosh(x))sinh(x) + 3b cosh(x) +--R + +--R 5 4 5 2 5 +--R 9b cosh(x) + 9b cosh(x) + 3b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 4 5 6 4 5 5 +--R (- 3a b - 3a )x sinh(x) + (- 18a b - 18a )x cosh(x)sinh(x) +--R + +--R 4 5 2 4 5 4 2 3 3 2 +--R (- 45a b - 45a )x cosh(x) + (- 9a b - 9a )x + 6a b - 6a b + 6a b +--R + +--R 4 5 +--R 6a b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 +--R (- 60a b - 60a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 +--R ((- 36a b - 36a )x + 24a b - 24a b + 24a b + 24a b - 48a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 4 +--R (- 45a b - 45a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 2 +--R ((- 54a b - 54a )x + 36a b - 36a b + 36a b + 36a b - 72a )cosh(x) +--R + +--R 4 5 4 2 3 4 5 +--R (- 9a b - 9a )x + 12a b - 6a b + 6a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 5 +--R (- 18a b - 18a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 3 +--R ((- 36a b - 36a )x + 24a b - 24a b + 24a b + 24a b - 48a )cosh(x) +--R + +--R 4 5 4 2 3 4 5 +--R ((- 18a b - 18a )x + 24a b - 12a b + 12a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 5 6 +--R (- 3a b - 3a )x cosh(x) +--R + +--R 4 5 4 2 3 3 2 4 5 4 +--R ((- 9a b - 9a )x + 6a b - 6a b + 6a b + 6a b - 12a )cosh(x) +--R + +--R 4 5 4 2 3 4 5 2 +--R ((- 9a b - 9a )x + 12a b - 6a b + 6a b - 12a )cosh(x) +--R + +--R 4 5 4 3 2 5 +--R (- 3a b - 3a )x + 6a b + 2a b - 8a +--R / +--R 4 2 6 6 4 2 6 5 +--R (3a b - 3a )sinh(x) + (18a b - 18a )cosh(x)sinh(x) +--R + +--R 4 2 6 2 4 2 6 4 +--R ((45a b - 45a )cosh(x) + 9a b - 9a )sinh(x) +--R + +--R 4 2 6 3 4 2 6 3 +--R ((60a b - 60a )cosh(x) + (36a b - 36a )cosh(x))sinh(x) +--R + +--R 4 2 6 4 4 2 6 2 4 2 6 2 +--R ((45a b - 45a )cosh(x) + (54a b - 54a )cosh(x) + 9a b - 9a )sinh(x) +--R + +--R 4 2 6 5 4 2 6 3 +--R (18a b - 18a )cosh(x) + (36a b - 36a )cosh(x) +--R + +--R 4 2 6 +--R (18a b - 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 6 6 4 2 6 4 4 2 6 2 +--R (3a b - 3a )cosh(x) + (9a b - 9a )cosh(x) + (9a b - 9a )cosh(x) +--R + +--R 4 2 6 +--R 3a b - 3a +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 526 +m0607:= a0607-r0607 +--R +--R +--R (39) +--R 5 6 5 5 5 2 5 4 +--R - 6b sinh(x) - 36b cosh(x)sinh(x) + (- 90b cosh(x) - 18b )sinh(x) +--R + +--R 5 3 5 3 +--R (- 120b cosh(x) - 72b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (- 90b cosh(x) - 108b cosh(x) - 18b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (- 36b cosh(x) - 72b cosh(x) - 36b cosh(x))sinh(x) - 6b cosh(x) +--R + +--R 5 4 5 2 5 +--R - 18b cosh(x) - 18b cosh(x) - 6b +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 5 4 6 5 4 5 +--R (6b - 6a b)sinh(x) + (36b - 36a b)cosh(x)sinh(x) +--R + +--R 5 4 2 5 4 4 +--R ((90b - 90a b)cosh(x) + 18b - 18a b)sinh(x) +--R + +--R 5 4 3 5 4 3 +--R ((120b - 120a b)cosh(x) + (72b - 72a b)cosh(x))sinh(x) +--R + +--R 5 4 4 5 4 2 5 4 +--R ((90b - 90a b)cosh(x) + (108b - 108a b)cosh(x) + 18b - 18a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 5 4 3 +--R (36b - 36a b)cosh(x) + (72b - 72a b)cosh(x) +--R + +--R 5 4 +--R (36b - 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 6 5 4 4 +--R (6b - 6a b)cosh(x) + (18b - 18a b)cosh(x) +--R + +--R 5 4 2 5 4 +--R (18b - 18a b)cosh(x) + 6b - 6a b +--R * +--R log(cosh(x)) +--R + +--R 5 4 6 5 4 5 +--R (- 6b + 6a b)sinh(x) + (- 36b + 36a b)cosh(x)sinh(x) +--R + +--R 5 4 2 5 4 4 +--R ((- 90b + 90a b)cosh(x) - 18b + 18a b)sinh(x) +--R + +--R 5 4 3 5 4 3 +--R ((- 120b + 120a b)cosh(x) + (- 72b + 72a b)cosh(x))sinh(x) +--R + +--R 5 4 4 5 4 2 5 +--R (- 90b + 90a b)cosh(x) + (- 108b + 108a b)cosh(x) - 18b +--R + +--R 4 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 5 4 3 +--R (- 36b + 36a b)cosh(x) + (- 72b + 72a b)cosh(x) +--R + +--R 5 4 +--R (- 36b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 6 5 4 4 +--R (- 6b + 6a b)cosh(x) + (- 18b + 18a b)cosh(x) +--R + +--R 5 4 2 5 4 +--R (- 18b + 18a b)cosh(x) - 6b + 6a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 5 6 5 5 5 2 5 4 +--R 6b sinh(x) + 36b cosh(x)sinh(x) + (90b cosh(x) + 18b )sinh(x) +--R + +--R 5 3 5 3 +--R (120b cosh(x) + 72b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (90b cosh(x) + 108b cosh(x) + 18b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (36b cosh(x) + 72b cosh(x) + 36b cosh(x))sinh(x) + 6b cosh(x) +--R + +--R 5 4 5 2 5 +--R 18b cosh(x) + 18b cosh(x) + 6b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (2a b - 2a )sinh(x) + (12a b - 12a )cosh(x)sinh(x) +--R + +--R 3 2 5 2 3 2 5 4 +--R ((30a b - 30a )cosh(x) + 6a b - 6a )sinh(x) +--R + +--R 3 2 5 3 3 2 5 3 +--R ((40a b - 40a )cosh(x) + (24a b - 24a )cosh(x))sinh(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R ((30a b - 30a )cosh(x) + (36a b - 36a )cosh(x) + 6a b - 6a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 5 3 2 5 3 +--R (12a b - 12a )cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 2 5 +--R (12a b - 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 5 6 3 2 5 4 3 2 5 2 +--R (2a b - 2a )cosh(x) + (6a b - 6a )cosh(x) + (6a b - 6a )cosh(x) +--R + +--R 3 2 5 +--R 2a b - 2a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 3a b + 3a b)sinh(x) + (- 18a b + 18a b)cosh(x)sinh(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R ((- 45a b + 45a b)cosh(x) - 9a b + 9a b)sinh(x) +--R + +--R 2 3 4 3 2 3 4 3 +--R ((- 60a b + 60a b)cosh(x) + (- 36a b + 36a b)cosh(x))sinh(x) +--R + +--R 2 3 4 4 2 3 4 2 2 3 +--R (- 45a b + 45a b)cosh(x) + (- 54a b + 54a b)cosh(x) - 9a b +--R + +--R 4 +--R 9a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 5 2 3 4 3 +--R (- 18a b + 18a b)cosh(x) + (- 36a b + 36a b)cosh(x) +--R + +--R 2 3 4 +--R (- 18a b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 4 6 2 3 4 4 +--R (- 3a b + 3a b)cosh(x) + (- 9a b + 9a b)cosh(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 9a b + 9a b)cosh(x) - 3a b + 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 5 6 4 5 5 +--R (6a b - 6a )sinh(x) + (36a b - 36a )cosh(x)sinh(x) +--R + +--R 4 5 2 4 5 4 +--R ((90a b - 90a )cosh(x) + 18a b - 18a )sinh(x) +--R + +--R 4 5 3 4 5 3 +--R ((120a b - 120a )cosh(x) + (72a b - 72a )cosh(x))sinh(x) +--R + +--R 4 5 4 4 5 2 4 +--R (90a b - 90a )cosh(x) + (108a b - 108a )cosh(x) + 18a b +--R + +--R 5 +--R - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 5 4 5 3 +--R (36a b - 36a )cosh(x) + (72a b - 72a )cosh(x) +--R + +--R 4 5 +--R (36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 5 6 4 5 4 +--R (6a b - 6a )cosh(x) + (18a b - 18a )cosh(x) +--R + +--R 4 5 2 4 5 +--R (18a b - 18a )cosh(x) + 6a b - 6a +--R * +--R tanh(x) +--R + +--R 4 6 4 5 +--R - 6a b x sinh(x) - 36a b x cosh(x)sinh(x) +--R + +--R 4 2 4 4 2 3 3 2 4 +--R - 90a b x cosh(x) - 18a b x + 12a b - 12a b + 12a b + 12a b +--R + +--R 5 +--R - 24a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 +--R - 120a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 +--R (- 72a b x + 48a b - 48a b + 48a b + 48a b - 96a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 +--R - 90a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 2 +--R (- 108a b x + 72a b - 72a b + 72a b + 72a b - 144a )cosh(x) +--R + +--R 4 4 2 3 4 5 +--R - 18a b x + 24a b - 12a b + 12a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 +--R - 36a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 3 +--R (- 72a b x + 48a b - 48a b + 48a b + 48a b - 96a )cosh(x) +--R + +--R 4 4 2 3 4 5 +--R (- 36a b x + 48a b - 24a b + 24a b - 48a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 6 +--R - 6a b x cosh(x) +--R + +--R 4 4 2 3 3 2 4 5 4 +--R (- 18a b x + 12a b - 12a b + 12a b + 12a b - 24a )cosh(x) +--R + +--R 4 4 2 3 4 5 2 4 4 +--R (- 18a b x + 24a b - 12a b + 12a b - 24a )cosh(x) - 6a b x + 12a b +--R + +--R 3 2 5 +--R 4a b - 16a +--R / +--R 4 2 6 6 4 2 6 5 +--R (6a b - 6a )sinh(x) + (36a b - 36a )cosh(x)sinh(x) +--R + +--R 4 2 6 2 4 2 6 4 +--R ((90a b - 90a )cosh(x) + 18a b - 18a )sinh(x) +--R + +--R 4 2 6 3 4 2 6 3 +--R ((120a b - 120a )cosh(x) + (72a b - 72a )cosh(x))sinh(x) +--R + +--R 4 2 6 4 4 2 6 2 4 2 6 +--R ((90a b - 90a )cosh(x) + (108a b - 108a )cosh(x) + 18a b - 18a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 6 5 4 2 6 3 +--R (36a b - 36a )cosh(x) + (72a b - 72a )cosh(x) +--R + +--R 4 2 6 +--R (36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 6 6 4 2 6 4 4 2 6 2 +--R (6a b - 6a )cosh(x) + (18a b - 18a )cosh(x) + (18a b - 18a )cosh(x) +--R + +--R 4 2 6 +--R 6a b - 6a +--R Type: Expression(Integer) +--E 39 + +--S 40 of 526 +d0607:= D(m0607,x) +--R +--R +--R (40) +--R 2 8 2 7 2 2 2 6 +--R - a sinh(x) - 8a cosh(x)sinh(x) + (- 28a cosh(x) - 4a )sinh(x) +--R + +--R 2 3 2 5 +--R (- 56a cosh(x) - 24a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- 70a cosh(x) - 60a cosh(x) - 6a )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (- 56a cosh(x) - 80a cosh(x) - 24a cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 28a cosh(x) - 60a cosh(x) - 36a cosh(x) - 4a )sinh(x) +--R + +--R 2 7 2 5 2 3 2 +--R (- 8a cosh(x) - 24a cosh(x) - 24a cosh(x) - 8a cosh(x))sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 2 +--R - a cosh(x) - 4a cosh(x) - 6a cosh(x) - 4a cosh(x) - a +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R a b sinh(x) + 8a b cosh(x)sinh(x) + (28a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 5 +--R (56a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70a b cosh(x) + 60a b cosh(x) + 6a b)sinh(x) +--R + +--R 5 3 3 +--R (56a b cosh(x) + 80a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28a b cosh(x) + 60a b cosh(x) + 36a b cosh(x) + 4a b)sinh(x) +--R + +--R 7 5 3 +--R (8a b cosh(x) + 24a b cosh(x) + 24a b cosh(x) + 8a b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R a b cosh(x) + 4a b cosh(x) + 6a b cosh(x) + 4a b cosh(x) + a b +--R * +--R 3 +--R tanh(x) +--R + +--R 2 8 2 7 2 2 2 6 +--R - b sinh(x) - 8b cosh(x)sinh(x) + (- 28b cosh(x) - 4b )sinh(x) +--R + +--R 2 3 2 5 +--R (- 56b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- 70b cosh(x) - 60b cosh(x) - 6b )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (- 56b cosh(x) - 80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 28b cosh(x) - 60b cosh(x) - 36b cosh(x) - 4b )sinh(x) +--R + +--R 2 7 2 5 2 3 2 +--R (- 8b cosh(x) - 24b cosh(x) - 24b cosh(x) - 8b cosh(x))sinh(x) +--R + +--R 2 8 2 6 2 4 2 2 2 +--R - b cosh(x) - 4b cosh(x) - 6b cosh(x) - 4b cosh(x) - b +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R - a b sinh(x) - 8a b cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 28a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 5 +--R (- 56a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 70a b cosh(x) - 60a b cosh(x) - 6a b)sinh(x) +--R + +--R 5 3 3 +--R (- 56a b cosh(x) - 80a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 28a b cosh(x) - 60a b cosh(x) - 36a b cosh(x) - 4a b)sinh(x) +--R + +--R 7 5 3 +--R (- 8a b cosh(x) - 24a b cosh(x) - 24a b cosh(x) - 8a b cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - a b cosh(x) - 4a b cosh(x) - 6a b cosh(x) - 4a b cosh(x) - a b +--R * +--R tanh(x) +--R + +--R 2 2 8 2 2 7 +--R (b + a )sinh(x) + (8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((28b + 28a )cosh(x) + 4a b - 4a )sinh(x) +--R + +--R 2 2 3 2 5 +--R ((56b + 56a )cosh(x) + (24a b - 24a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 4 +--R ((70b + 70a )cosh(x) + (60a b - 60a )cosh(x) - 2b + 6a )sinh(x) +--R + +--R 2 2 5 2 3 +--R (56b + 56a )cosh(x) + (80a b - 80a )cosh(x) +--R + +--R 2 2 +--R (- 8b + 24a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 4 +--R (28b + 28a )cosh(x) + (60a b - 60a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 12b + 36a )cosh(x) - 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 2 5 2 2 3 +--R (8b + 8a )cosh(x) + (24a b - 24a )cosh(x) + (- 8b + 24a )cosh(x) +--R + +--R 2 +--R (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 8 2 6 2 2 4 +--R (b + a )cosh(x) + (4a b - 4a )cosh(x) + (- 2b + 6a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 4a b - 4a )cosh(x) + b + a +--R / +--R 3 8 3 7 3 2 3 6 +--R a sinh(x) + 8a cosh(x)sinh(x) + (28a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 5 +--R (56a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 4 +--R (70a cosh(x) + 60a cosh(x) + 6a )sinh(x) +--R + +--R 3 5 3 3 3 3 +--R (56a cosh(x) + 80a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 2 +--R (28a cosh(x) + 60a cosh(x) + 36a cosh(x) + 4a )sinh(x) +--R + +--R 3 7 3 5 3 3 3 +--R (8a cosh(x) + 24a cosh(x) + 24a cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 3 8 3 6 3 4 3 2 3 +--R a cosh(x) + 4a cosh(x) + 6a cosh(x) + 4a cosh(x) + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 526 +t0608:= tanh(x)/(1+coth(x)) +--R +--R +--R tanh(x) +--R (41) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 526 +r0608:= -1/2*x+log(cosh(x))-1/(2+2*tanh(x)) +--R +--R +--R (2tanh(x) + 2)log(cosh(x)) - x tanh(x) - x - 1 +--R (42) ---------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 526 +a0608:= integrate(t0608,x) +--R +--R +--R (43) +--R 2 2 2cosh(x) +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 6x sinh(x) - 12x cosh(x)sinh(x) - 6x cosh(x) - 1 +--R / +--R 2 2 +--R 4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 526 +m0608:= a0608-r0608 +--R +--R +--R (44) +--R 2 2 2 +--R (- 4sinh(x) - 8cosh(x)sinh(x) - 4cosh(x) )tanh(x) - 4sinh(x) +--R + +--R 2 +--R - 8cosh(x)sinh(x) - 4cosh(x) +--R * +--R log(cosh(x)) +--R + +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 4x sinh(x) - 8x cosh(x)sinh(x) - 4x cosh(x) - 1)tanh(x) +--R + +--R 2 2 +--R (- 4x + 2)sinh(x) + (- 8x + 4)cosh(x)sinh(x) + (- 4x + 2)cosh(x) - 1 +--R / +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 44 + +--S 45 of 526 +d0608:= D(m0608,x) +--R +--R +--R (45) +--R 2 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)tanh(x) - sinh(x) +--R + +--R 2 +--R - 2cosh(x)sinh(x) - cosh(x) + 1 +--R / +--R 2 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )tanh(x) + 2sinh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 45 + +--S 46 of 526 +t0609:= tanh(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R tanh(x) +--R (46) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 526 +r0609:= 3/2*x-log(cosh(x))-tanh(x)+1/(2+2*tanh(x)) +--R +--R +--R 2 +--R (- 2tanh(x) - 2)log(cosh(x)) - 2tanh(x) + (3x - 2)tanh(x) + 3x + 1 +--R (47) ------------------------------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 526 +a0609:= integrate(t0609,x) +--R +--R +--R (48) +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) - 8cosh(x))sinh(x) - 4cosh(x) - 4cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R 10x sinh(x) + 40x cosh(x)sinh(x) + (60x cosh(x) + 10x + 9)sinh(x) +--R + +--R 3 4 +--R (40x cosh(x) + (20x + 18)cosh(x))sinh(x) + 10x cosh(x) +--R + +--R 2 +--R (10x + 9)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 526 +m0609:= a0609-r0609 +--R +--R +--R (49) +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R log(cosh(x)) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) - 8cosh(x))sinh(x) - 4cosh(x) - 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) - 8cosh(x))sinh(x) - 4cosh(x) - 4cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R (4x + 4)sinh(x) + (16x + 16)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((24x + 24)cosh(x) + 4x + 13)sinh(x) +--R + +--R 3 4 +--R ((16x + 16)cosh(x) + (8x + 26)cosh(x))sinh(x) + (4x + 4)cosh(x) +--R + +--R 2 +--R (4x + 13)cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 4 3 +--R (4x - 2)sinh(x) + (16x - 8)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((24x - 12)cosh(x) + 4x + 7)sinh(x) +--R + +--R 3 4 +--R ((16x - 8)cosh(x) + (8x + 14)cosh(x))sinh(x) + (4x - 2)cosh(x) +--R + +--R 2 +--R (4x + 7)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 49 + +--S 50 of 526 +d0609:= D(m0609,x) +--R +--R +--R (50) +--R 6 5 2 4 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (- 40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30cosh(x) - 24cosh(x) - 2)sinh(x) +--R + +--R 5 3 6 4 +--R (- 12cosh(x) - 16cosh(x) - 4cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R - 2cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (- 40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30cosh(x) - 24cosh(x) - 2)sinh(x) +--R + +--R 5 3 6 4 +--R (- 12cosh(x) - 16cosh(x) - 4cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R - 2cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 7)sinh(x) +--R + +--R 3 3 +--R (20cosh(x) - 28cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 42cosh(x) - 1)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 28cosh(x) - 2cosh(x))sinh(x) + cosh(x) - 7cosh(x) +--R + +--R 2 +--R - cosh(x) - 1 +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 3sinh(x) + 18cosh(x)sinh(x) + (45cosh(x) - 3)sinh(x) +--R + +--R 3 3 4 2 2 +--R (60cosh(x) - 12cosh(x))sinh(x) + (45cosh(x) - 18cosh(x) + 1)sinh(x) +--R + +--R 5 3 6 4 +--R (18cosh(x) - 12cosh(x) + 2cosh(x))sinh(x) + 3cosh(x) - 3cosh(x) +--R + +--R 2 +--R cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) + 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 4)sinh(x) +--R + +--R 3 3 4 2 2 +--R (40cosh(x) + 16cosh(x))sinh(x) + (30cosh(x) + 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R Type: Expression(Integer) +--E 50 + +--S 51 of 526 +t0610:= tanh(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R tanh(x) +--R (51) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 526 +r0610:= -3/2*x+2*log(cosh(x))+tanh(x)-1/2*tanh(x)^2-1/(2+2*tanh(x)) +--R +--R +--R (52) +--R 3 2 +--R (4tanh(x) + 4)log(cosh(x)) - tanh(x) + tanh(x) + (- 3x + 2)tanh(x) - 3x - 1 +--R ----------------------------------------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 526 +a0610:= integrate(t0610,x) +--R +--R +--R (53) +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) + 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (48cosh(x) + 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) + 16cosh(x) +--R + +--R 2 +--R 8cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 5 +--R - 14x sinh(x) - 84x cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 210x cosh(x) - 28x - 1)sinh(x) +--R + +--R 3 3 +--R (- 280x cosh(x) + (- 112x - 4)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 210x cosh(x) + (- 168x - 6)cosh(x) - 14x - 10)sinh(x) +--R + +--R 5 3 +--R (- 84x cosh(x) + (- 112x - 4)cosh(x) + (- 28x - 20)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 14x cosh(x) + (- 28x - 1)cosh(x) + (- 14x - 10)cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) + 8)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) + 32cosh(x))sinh(x) + (60cosh(x) + 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) + 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 526 +m0610:= a0610-r0610 +--R +--R +--R (54) +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) - 96cosh(x) - 8)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) - 64cosh(x) - 16cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R - 16cosh(x) - 8cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) - 96cosh(x) - 8)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) - 64cosh(x) - 16cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R - 16cosh(x) - 8cosh(x) +--R * +--R log(cosh(x)) +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) + 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 +--R (48cosh(x) + 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) +--R + +--R 4 2 +--R 16cosh(x) + 8cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) + 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (48cosh(x) + 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) + 16cosh(x) +--R + +--R 2 +--R 8cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) + 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) + 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 2sinh(x) - 12cosh(x)sinh(x) + (- 30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (- 40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 30cosh(x) - 24cosh(x) - 2)sinh(x) +--R + +--R 5 3 6 4 +--R (- 12cosh(x) - 16cosh(x) - 4cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R - 2cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 6 5 +--R (- 8x - 4)sinh(x) + (- 48x - 24)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((- 120x - 60)cosh(x) - 16x - 9)sinh(x) +--R + +--R 3 3 +--R ((- 160x - 80)cosh(x) + (- 64x - 36)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((- 120x - 60)cosh(x) + (- 96x - 54)cosh(x) - 8x - 14)sinh(x) +--R + +--R 5 3 +--R ((- 48x - 24)cosh(x) + (- 64x - 36)cosh(x) + (- 16x - 28)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (- 8x - 4)cosh(x) + (- 16x - 9)cosh(x) + (- 8x - 14)cosh(x) - 1 +--R * +--R tanh(x) +--R + +--R 6 5 +--R (- 8x + 2)sinh(x) + (- 48x + 12)cosh(x)sinh(x) +--R + +--R 2 4 +--R ((- 120x + 30)cosh(x) - 16x + 3)sinh(x) +--R + +--R 3 3 +--R ((- 160x + 40)cosh(x) + (- 64x + 12)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R ((- 120x + 30)cosh(x) + (- 96x + 18)cosh(x) - 8x - 8)sinh(x) +--R + +--R 5 3 +--R ((- 48x + 12)cosh(x) + (- 64x + 12)cosh(x) + (- 16x - 16)cosh(x)) +--R * +--R sinh(x) +--R + +--R 6 4 2 +--R (- 8x + 2)cosh(x) + (- 16x + 3)cosh(x) + (- 8x - 8)cosh(x) - 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) + 8)sinh(x) +--R + +--R 3 3 +--R (80cosh(x) + 32cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (60cosh(x) + 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) + 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) + 8)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) + 32cosh(x))sinh(x) + (60cosh(x) + 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) + 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) + 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R Type: Expression(Integer) +--E 54 + +--S 55 of 526 +d0610:= D(m0610,x) +--R +--R +--R (55) +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 6)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 90cosh(x) - 6)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) - 120cosh(x) - 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) - 90cosh(x) - 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 +--R (- 16cosh(x) - 36cosh(x) - 24cosh(x) - 4cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 2cosh(x) - 6cosh(x) - 6cosh(x) - 2cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 4sinh(x) + 32cosh(x)sinh(x) + (112cosh(x) + 12)sinh(x) +--R + +--R 3 5 +--R (224cosh(x) + 72cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (280cosh(x) + 180cosh(x) + 12)sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) + 240cosh(x) + 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (112cosh(x) + 180cosh(x) + 72cosh(x) + 4)sinh(x) +--R + +--R 7 5 3 8 +--R (32cosh(x) + 72cosh(x) + 48cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) +--R + +--R 6 4 2 +--R 12cosh(x) + 12cosh(x) + 4cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R sinh(x) + 8cosh(x)sinh(x) + (28cosh(x) + 4)sinh(x) +--R + +--R 3 5 +--R (56cosh(x) + 24cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (70cosh(x) + 60cosh(x) + 22)sinh(x) +--R + +--R 5 3 3 +--R (56cosh(x) + 80cosh(x) + 88cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (28cosh(x) + 60cosh(x) + 132cosh(x) + 4)sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) + 24cosh(x) + 88cosh(x) + 8cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R 4cosh(x) + 22cosh(x) + 4cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 3sinh(x) - 24cosh(x)sinh(x) + (- 84cosh(x) - 8)sinh(x) +--R + +--R 3 5 +--R (- 168cosh(x) - 48cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 210cosh(x) - 120cosh(x) + 10)sinh(x) +--R + +--R 5 3 3 +--R (- 168cosh(x) - 160cosh(x) + 40cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 84cosh(x) - 120cosh(x) + 60cosh(x) )sinh(x) +--R + +--R 7 5 3 8 6 +--R (- 24cosh(x) - 48cosh(x) + 40cosh(x) )sinh(x) - 3cosh(x) - 8cosh(x) +--R + +--R 4 +--R 10cosh(x) + 1 +--R / +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) + 6)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) + 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) + 90cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) + 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) + 90cosh(x) + 36cosh(x) + 2)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) + 36cosh(x) + 24cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R 6cosh(x) + 6cosh(x) + 2cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) + 6)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) + 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) + 90cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) + 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) + 90cosh(x) + 36cosh(x) + 2)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) + 36cosh(x) + 24cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R 6cosh(x) + 6cosh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 526 +t0611:= tanh(x)^4/(1+coth(x)) +--R +--R +--R 4 +--R tanh(x) +--R (56) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 526 +r0611:= 5/2*x-2*log(cosh(x))-2*tanh(x)+1/2*tanh(x)^2-1/3*tanh(x)^3+_ + 1/(2+2*tanh(x)) +--R +--R +--R (57) +--R 4 3 2 +--R (- 12tanh(x) - 12)log(cosh(x)) - 2tanh(x) + tanh(x) - 9tanh(x) +--R + +--R (15x - 12)tanh(x) + 15x + 3 +--R / +--R 6tanh(x) + 6 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 526 +a0611:= integrate(t0611,x) +--R +--R +--R (58) +--R 8 7 2 6 +--R - 24sinh(x) - 192cosh(x)sinh(x) + (- 672cosh(x) - 72)sinh(x) +--R + +--R 3 5 +--R (- 1344cosh(x) - 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1680cosh(x) - 1080cosh(x) - 72)sinh(x) +--R + +--R 5 3 3 +--R (- 1344cosh(x) - 1440cosh(x) - 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 672cosh(x) - 1080cosh(x) - 432cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 +--R (- 192cosh(x) - 432cosh(x) - 288cosh(x) - 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 24cosh(x) - 72cosh(x) - 72cosh(x) - 24cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 8 7 +--R 54x sinh(x) + 432x cosh(x)sinh(x) +--R + +--R 2 6 +--R (1512x cosh(x) + 162x + 51)sinh(x) +--R + +--R 3 5 +--R (3024x cosh(x) + (972x + 306)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (3780x cosh(x) + (2430x + 765)cosh(x) + 162x + 81)sinh(x) +--R + +--R 5 3 3 +--R (3024x cosh(x) + (3240x + 1020)cosh(x) + (648x + 324)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 1512x cosh(x) + (2430x + 765)cosh(x) + (972x + 486)cosh(x) + 54x +--R + +--R 65 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R 432x cosh(x) + (972x + 306)cosh(x) + (648x + 324)cosh(x) +--R + +--R (108x + 130)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 +--R 54x cosh(x) + (162x + 51)cosh(x) + (162x + 81)cosh(x) +--R + +--R 2 +--R (54x + 65)cosh(x) + 3 +--R / +--R 8 7 2 6 +--R 12sinh(x) + 96cosh(x)sinh(x) + (336cosh(x) + 36)sinh(x) +--R + +--R 3 5 +--R (672cosh(x) + 216cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (840cosh(x) + 540cosh(x) + 36)sinh(x) +--R + +--R 5 3 3 +--R (672cosh(x) + 720cosh(x) + 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (336cosh(x) + 540cosh(x) + 216cosh(x) + 12)sinh(x) +--R + +--R 7 5 3 8 +--R (96cosh(x) + 216cosh(x) + 144cosh(x) + 24cosh(x))sinh(x) + 12cosh(x) +--R + +--R 6 4 2 +--R 36cosh(x) + 36cosh(x) + 12cosh(x) +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 526 +m0611:= a0611-r0611 +--R +--R +--R (59) +--R 8 7 2 6 +--R 24sinh(x) + 192cosh(x)sinh(x) + (672cosh(x) + 72)sinh(x) +--R + +--R 3 5 +--R (1344cosh(x) + 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1680cosh(x) + 1080cosh(x) + 72)sinh(x) +--R + +--R 5 3 3 +--R (1344cosh(x) + 1440cosh(x) + 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (672cosh(x) + 1080cosh(x) + 432cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 +--R (192cosh(x) + 432cosh(x) + 288cosh(x) + 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 24cosh(x) + 72cosh(x) + 72cosh(x) + 24cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 24sinh(x) + 192cosh(x)sinh(x) + (672cosh(x) + 72)sinh(x) +--R + +--R 3 5 +--R (1344cosh(x) + 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1680cosh(x) + 1080cosh(x) + 72)sinh(x) +--R + +--R 5 3 3 +--R (1344cosh(x) + 1440cosh(x) + 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (672cosh(x) + 1080cosh(x) + 432cosh(x) + 24)sinh(x) +--R + +--R 7 5 3 +--R (192cosh(x) + 432cosh(x) + 288cosh(x) + 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 24cosh(x) + 72cosh(x) + 72cosh(x) + 24cosh(x) +--R * +--R log(cosh(x)) +--R + +--R 8 7 2 6 +--R - 24sinh(x) - 192cosh(x)sinh(x) + (- 672cosh(x) - 72)sinh(x) +--R + +--R 3 5 +--R (- 1344cosh(x) - 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1680cosh(x) - 1080cosh(x) - 72)sinh(x) +--R + +--R 5 3 3 +--R (- 1344cosh(x) - 1440cosh(x) - 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 672cosh(x) - 1080cosh(x) - 432cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 +--R (- 192cosh(x) - 432cosh(x) - 288cosh(x) - 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 24cosh(x) - 72cosh(x) - 72cosh(x) - 24cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 24sinh(x) - 192cosh(x)sinh(x) + (- 672cosh(x) - 72)sinh(x) +--R + +--R 3 5 +--R (- 1344cosh(x) - 432cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1680cosh(x) - 1080cosh(x) - 72)sinh(x) +--R + +--R 5 3 3 +--R (- 1344cosh(x) - 1440cosh(x) - 288cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 672cosh(x) - 1080cosh(x) - 432cosh(x) - 24)sinh(x) +--R + +--R 7 5 3 +--R (- 192cosh(x) - 432cosh(x) - 288cosh(x) - 48cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 24cosh(x) - 72cosh(x) - 72cosh(x) - 24cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 8 7 2 6 +--R 4sinh(x) + 32cosh(x)sinh(x) + (112cosh(x) + 12)sinh(x) +--R + +--R 3 5 +--R (224cosh(x) + 72cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (280cosh(x) + 180cosh(x) + 12)sinh(x) +--R + +--R 5 3 3 +--R (224cosh(x) + 240cosh(x) + 48cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (112cosh(x) + 180cosh(x) + 72cosh(x) + 4)sinh(x) +--R + +--R 7 5 3 8 +--R (32cosh(x) + 72cosh(x) + 48cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) +--R + +--R 6 4 2 +--R 12cosh(x) + 12cosh(x) + 4cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) + (- 56cosh(x) - 6)sinh(x) +--R + +--R 3 5 +--R (- 112cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 140cosh(x) - 90cosh(x) - 6)sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) - 120cosh(x) - 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 56cosh(x) - 90cosh(x) - 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 +--R (- 16cosh(x) - 36cosh(x) - 24cosh(x) - 4cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 2cosh(x) - 6cosh(x) - 6cosh(x) - 2cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 18sinh(x) + 144cosh(x)sinh(x) + (504cosh(x) + 54)sinh(x) +--R + +--R 3 5 +--R (1008cosh(x) + 324cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1260cosh(x) + 810cosh(x) + 54)sinh(x) +--R + +--R 5 3 3 +--R (1008cosh(x) + 1080cosh(x) + 216cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (504cosh(x) + 810cosh(x) + 324cosh(x) + 18)sinh(x) +--R + +--R 7 5 3 +--R (144cosh(x) + 324cosh(x) + 216cosh(x) + 36cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 18cosh(x) + 54cosh(x) + 54cosh(x) + 18cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R (24x + 24)sinh(x) + (192x + 192)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((672x + 672)cosh(x) + 72x + 123)sinh(x) +--R + +--R 3 5 +--R ((1344x + 1344)cosh(x) + (432x + 738)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R ((1680x + 1680)cosh(x) + (1080x + 1845)cosh(x) + 72x + 153)sinh(x) +--R + +--R 5 3 +--R (1344x + 1344)cosh(x) + (1440x + 2460)cosh(x) +--R + +--R (288x + 612)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 +--R (672x + 672)cosh(x) + (1080x + 1845)cosh(x) +--R + +--R 2 +--R (432x + 918)cosh(x) + 24x + 89 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 +--R (192x + 192)cosh(x) + (432x + 738)cosh(x) +--R + +--R 3 +--R (288x + 612)cosh(x) + (48x + 178)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 +--R (24x + 24)cosh(x) + (72x + 123)cosh(x) + (72x + 153)cosh(x) +--R + +--R 2 +--R (24x + 89)cosh(x) + 3 +--R * +--R tanh(x) +--R + +--R 8 7 +--R (24x - 6)sinh(x) + (192x - 48)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((672x - 168)cosh(x) + 72x + 33)sinh(x) +--R + +--R 3 5 +--R ((1344x - 336)cosh(x) + (432x + 198)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R ((1680x - 420)cosh(x) + (1080x + 495)cosh(x) + 72x + 63)sinh(x) +--R + +--R 5 3 +--R ((1344x - 336)cosh(x) + (1440x + 660)cosh(x) + (288x + 252)cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 +--R (672x - 168)cosh(x) + (1080x + 495)cosh(x) + (432x + 378)cosh(x) +--R + +--R 24x + 59 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R (192x - 48)cosh(x) + (432x + 198)cosh(x) + (288x + 252)cosh(x) +--R + +--R (48x + 118)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 +--R (24x - 6)cosh(x) + (72x + 33)cosh(x) + (72x + 63)cosh(x) +--R + +--R 2 +--R (24x + 59)cosh(x) + 3 +--R / +--R 8 7 2 6 +--R 12sinh(x) + 96cosh(x)sinh(x) + (336cosh(x) + 36)sinh(x) +--R + +--R 3 5 +--R (672cosh(x) + 216cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (840cosh(x) + 540cosh(x) + 36)sinh(x) +--R + +--R 5 3 3 +--R (672cosh(x) + 720cosh(x) + 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (336cosh(x) + 540cosh(x) + 216cosh(x) + 12)sinh(x) +--R + +--R 7 5 3 +--R (96cosh(x) + 216cosh(x) + 144cosh(x) + 24cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 12cosh(x) + 36cosh(x) + 36cosh(x) + 12cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 12sinh(x) + 96cosh(x)sinh(x) + (336cosh(x) + 36)sinh(x) +--R + +--R 3 5 +--R (672cosh(x) + 216cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (840cosh(x) + 540cosh(x) + 36)sinh(x) +--R + +--R 5 3 3 +--R (672cosh(x) + 720cosh(x) + 144cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (336cosh(x) + 540cosh(x) + 216cosh(x) + 12)sinh(x) +--R + +--R 7 5 3 8 +--R (96cosh(x) + 216cosh(x) + 144cosh(x) + 24cosh(x))sinh(x) + 12cosh(x) +--R + +--R 6 4 2 +--R 36cosh(x) + 36cosh(x) + 12cosh(x) +--R Type: Expression(Integer) +--E 59 + +--S 60 of 526 +d0611:= D(m0611,x) +--R +--R +--R (60) +--R 10 9 2 8 +--R - 2sinh(x) - 20cosh(x)sinh(x) + (- 90cosh(x) - 8)sinh(x) +--R + +--R 3 7 +--R (- 240cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 420cosh(x) - 224cosh(x) - 12)sinh(x) +--R + +--R 5 3 5 +--R (- 504cosh(x) - 448cosh(x) - 72cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 420cosh(x) - 560cosh(x) - 180cosh(x) - 8)sinh(x) +--R + +--R 7 5 3 3 +--R (- 240cosh(x) - 448cosh(x) - 240cosh(x) - 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 90cosh(x) - 224cosh(x) - 180cosh(x) - 48cosh(x) - 2)sinh(x) +--R + +--R 9 7 5 3 +--R (- 20cosh(x) - 64cosh(x) - 72cosh(x) - 32cosh(x) - 4cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 2cosh(x) - 8cosh(x) - 12cosh(x) - 8cosh(x) - 2cosh(x) +--R * +--R 5 +--R tanh(x) +--R + +--R 10 9 2 8 +--R - 4sinh(x) - 40cosh(x)sinh(x) + (- 180cosh(x) - 16)sinh(x) +--R + +--R 3 7 +--R (- 480cosh(x) - 128cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 840cosh(x) - 448cosh(x) - 24)sinh(x) +--R + +--R 5 3 5 +--R (- 1008cosh(x) - 896cosh(x) - 144cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 840cosh(x) - 1120cosh(x) - 360cosh(x) - 16)sinh(x) +--R + +--R 7 5 3 3 +--R (- 480cosh(x) - 896cosh(x) - 480cosh(x) - 64cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 180cosh(x) - 448cosh(x) - 360cosh(x) - 96cosh(x) - 4)sinh(x) +--R + +--R 9 7 5 3 +--R (- 40cosh(x) - 128cosh(x) - 144cosh(x) - 64cosh(x) - 8cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 4cosh(x) - 16cosh(x) - 24cosh(x) - 16cosh(x) - 4cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 10 9 2 8 +--R sinh(x) + 10cosh(x)sinh(x) + (45cosh(x) - 13)sinh(x) +--R + +--R 3 7 +--R (120cosh(x) - 104cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (210cosh(x) - 364cosh(x) - 14)sinh(x) +--R + +--R 5 3 5 +--R (252cosh(x) - 728cosh(x) - 84cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (210cosh(x) - 910cosh(x) - 210cosh(x) - 34)sinh(x) +--R + +--R 7 5 3 3 +--R (120cosh(x) - 728cosh(x) - 280cosh(x) - 136cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (45cosh(x) - 364cosh(x) - 210cosh(x) - 204cosh(x) - 3)sinh(x) +--R + +--R 9 7 5 3 +--R (10cosh(x) - 104cosh(x) - 84cosh(x) - 136cosh(x) - 6cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) - 13cosh(x) - 14cosh(x) - 34cosh(x) - 3cosh(x) - 1 +--R * +--R tanh(x) +--R + +--R 10 9 2 8 +--R 5sinh(x) + 50cosh(x)sinh(x) + (225cosh(x) + 3)sinh(x) +--R + +--R 3 7 +--R (600cosh(x) + 24cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (1050cosh(x) + 84cosh(x) + 10)sinh(x) +--R + +--R 5 3 5 +--R (1260cosh(x) + 168cosh(x) + 60cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (1050cosh(x) + 210cosh(x) + 150cosh(x) - 18)sinh(x) +--R + +--R 7 5 3 3 +--R (600cosh(x) + 168cosh(x) + 200cosh(x) - 72cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (225cosh(x) + 84cosh(x) + 150cosh(x) - 108cosh(x) + 1)sinh(x) +--R + +--R 9 7 5 3 +--R (50cosh(x) + 24cosh(x) + 60cosh(x) - 72cosh(x) + 2cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R 5cosh(x) + 3cosh(x) + 10cosh(x) - 18cosh(x) + cosh(x) - 1 +--R / +--R 10 9 2 8 +--R 2sinh(x) + 20cosh(x)sinh(x) + (90cosh(x) + 8)sinh(x) +--R + +--R 3 7 +--R (240cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (420cosh(x) + 224cosh(x) + 12)sinh(x) +--R + +--R 5 3 5 +--R (504cosh(x) + 448cosh(x) + 72cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (420cosh(x) + 560cosh(x) + 180cosh(x) + 8)sinh(x) +--R + +--R 7 5 3 3 +--R (240cosh(x) + 448cosh(x) + 240cosh(x) + 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (90cosh(x) + 224cosh(x) + 180cosh(x) + 48cosh(x) + 2)sinh(x) +--R + +--R 9 7 5 3 +--R (20cosh(x) + 64cosh(x) + 72cosh(x) + 32cosh(x) + 4cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R 2cosh(x) + 8cosh(x) + 12cosh(x) + 8cosh(x) + 2cosh(x) +--R * +--R tanh(x) +--R + +--R 10 9 2 8 +--R 2sinh(x) + 20cosh(x)sinh(x) + (90cosh(x) + 8)sinh(x) +--R + +--R 3 7 +--R (240cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (420cosh(x) + 224cosh(x) + 12)sinh(x) +--R + +--R 5 3 5 +--R (504cosh(x) + 448cosh(x) + 72cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (420cosh(x) + 560cosh(x) + 180cosh(x) + 8)sinh(x) +--R + +--R 7 5 3 3 +--R (240cosh(x) + 448cosh(x) + 240cosh(x) + 32cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (90cosh(x) + 224cosh(x) + 180cosh(x) + 48cosh(x) + 2)sinh(x) +--R + +--R 9 7 5 3 +--R (20cosh(x) + 64cosh(x) + 72cosh(x) + 32cosh(x) + 4cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R 2cosh(x) + 8cosh(x) + 12cosh(x) + 8cosh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 60 + +--S 61 of 526 +t0612:= coth(x)/(a+b*coth(x)) +--R +--R +--R coth(x) +--R (61) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 526 +r0612:= (-b*x+a*log(b*cosh(x)+a*sinh(x)))/(a^2-b^2) +--R +--R +--R - a log(a sinh(x) + b cosh(x)) + b x +--R (62) ------------------------------------ +--R 2 2 +--R b - a +--R Type: Expression(Integer) +--E 62 + +--S 63 of 526 +a0612:= integrate(t0612,x) +--R +--R +--R - 2a sinh(x) - 2b cosh(x) +--R - a log(-------------------------) + (b + a)x +--R sinh(x) - cosh(x) +--R (63) --------------------------------------------- +--R 2 2 +--R b - a +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 526 +m0612:= a0612-r0612 +--R +--R +--R - 2a sinh(x) - 2b cosh(x) +--R a log(a sinh(x) + b cosh(x)) - a log(-------------------------) + a x +--R sinh(x) - cosh(x) +--R (64) --------------------------------------------------------------------- +--R 2 2 +--R b - a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 526 +d0612:= D(m0612,x) +--R +--R +--R (65) 0 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 526 +t0613:= coth(x)/(1+coth(x)) +--R +--R +--R coth(x) +--R (66) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 526 +r0613:= 1/2*x-1/(2+2*tanh(x)) +--R +--R +--R x tanh(x) + x - 1 +--R (67) ----------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 526 +a0613:= integrate(t0613,x) +--R +--R +--R (2x + 1)sinh(x) + (2x - 1)cosh(x) +--R (68) --------------------------------- +--R 4sinh(x) + 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 526 +m0613:= a0613-r0613 +--R +--R +--R (sinh(x) - cosh(x))tanh(x) + 3sinh(x) + cosh(x) +--R (69) -------------------------------------------------- +--R (4sinh(x) + 4cosh(x))tanh(x) + 4sinh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 69 + +--S 70 of 526 +d0613:= D(m0613,x) +--R +--R +--R cosh(x)tanh(x) - sinh(x) +--R (70) ---------------------------------------------- +--R (sinh(x) + cosh(x))tanh(x) + sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 70 + +--S 71 of 526 +t0614:= coth(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R coth(x) +--R (71) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 526 +r0614:= -1/2*x+log(sinh(x))+1/(2+2*tanh(x)) +--R +--R +--R (2tanh(x) + 2)log(sinh(x)) - x tanh(x) - x + 1 +--R (72) ---------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 526 +a0614:= integrate(t0614,x) +--R +--R +--R (73) +--R 2 2 2sinh(x) +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 6x sinh(x) - 12x cosh(x)sinh(x) - 6x cosh(x) + 1 +--R / +--R 2 2 +--R 4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 526 +m0614:= a0614-r0614 +--R +--R +--R (74) +--R 2 2 2 +--R (- 4sinh(x) - 8cosh(x)sinh(x) - 4cosh(x) )tanh(x) - 4sinh(x) +--R + +--R 2 +--R - 8cosh(x)sinh(x) - 4cosh(x) +--R * +--R log(sinh(x)) +--R + +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 4x sinh(x) - 8x cosh(x)sinh(x) - 4x cosh(x) + 1)tanh(x) +--R + +--R 2 2 +--R (- 4x - 2)sinh(x) + (- 8x - 4)cosh(x)sinh(x) + (- 4x - 2)cosh(x) + 1 +--R / +--R 2 2 2 +--R (4sinh(x) + 8cosh(x)sinh(x) + 4cosh(x) )tanh(x) + 4sinh(x) +--R + +--R 2 +--R 8cosh(x)sinh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 74 + +--S 75 of 526 +d0614:= D(m0614,x) +--R +--R +--R (75) +--R 2 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)tanh(x) + sinh(x) +--R + +--R 2 +--R 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 2 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) )tanh(x) + 2sinh(x) +--R + +--R 2 +--R 4cosh(x)sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 75 + +--S 76 of 526 +t0615:= coth(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R coth(x) +--R (76) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 526 +r0615:= 3/2*x-coth(x)-log(sinh(x))-1/(2+2*tanh(x)) +--R +--R +--R (77) +--R (- 2tanh(x) - 2)log(sinh(x)) + (- 2coth(x) + 3x)tanh(x) - 2coth(x) + 3x - 1 +--R --------------------------------------------------------------------------- +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 526 +a0615:= integrate(t0615,x) +--R +--R +--R (78) +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 8cosh(x))sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 2 +--R 10x sinh(x) + 40x cosh(x)sinh(x) + (60x cosh(x) - 10x - 9)sinh(x) +--R + +--R 3 4 +--R (40x cosh(x) + (- 20x - 18)cosh(x))sinh(x) + 10x cosh(x) +--R + +--R 2 +--R (- 10x - 9)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 526 +m0615:= a0615-r0615 +--R +--R +--R (79) +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R log(sinh(x)) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 8cosh(x))sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 8cosh(x))sinh(x) - 4cosh(x) + 4cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 +--R (4coth(x) + 4x)sinh(x) + (16cosh(x)coth(x) + 16x cosh(x))sinh(x) +--R + +--R 2 2 2 +--R ((24cosh(x) - 4)coth(x) + 24x cosh(x) - 4x - 9)sinh(x) +--R + +--R 3 3 +--R (16cosh(x) - 8cosh(x))coth(x) + 16x cosh(x) +--R + +--R (- 8x - 18)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 4 2 +--R (4cosh(x) - 4cosh(x) )coth(x) + 4x cosh(x) + (- 4x - 9)cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 4 +--R (4coth(x) + 4x + 2)sinh(x) +--R + +--R 3 +--R (16cosh(x)coth(x) + (16x + 8)cosh(x))sinh(x) +--R + +--R 2 2 2 +--R ((24cosh(x) - 4)coth(x) + (24x + 12)cosh(x) - 4x - 11)sinh(x) +--R + +--R 3 3 +--R (16cosh(x) - 8cosh(x))coth(x) + (16x + 8)cosh(x) +--R + +--R (- 8x - 22)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 4 2 +--R (4cosh(x) - 4cosh(x) )coth(x) + (4x + 2)cosh(x) + (- 4x - 11)cosh(x) + 1 +--R / +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R * +--R tanh(x) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 8cosh(x))sinh(x) + 4cosh(x) - 4cosh(x) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 526 +d0615:= D(m0615,x) +--R +--R +--R (80) +--R 2 6 2 5 +--R (- 2coth(x) + 3)sinh(x) + (- 12cosh(x)coth(x) + 18cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30cosh(x) + 4)coth(x) + 45cosh(x) + 3)sinh(x) +--R + +--R 3 2 3 3 +--R ((- 40cosh(x) + 16cosh(x))coth(x) + 60cosh(x) + 12cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (- 30cosh(x) + 24cosh(x) - 2)coth(x) + 45cosh(x) + 18cosh(x) +--R + +--R 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 12cosh(x) + 16cosh(x) - 4cosh(x))coth(x) + 18cosh(x) +--R + +--R 3 +--R 12cosh(x) + 2cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (- 2cosh(x) + 4cosh(x) - 2cosh(x) )coth(x) + 3cosh(x) + 3cosh(x) +--R + +--R 2 +--R cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 2 6 2 5 +--R (- 2coth(x) + 1)sinh(x) + (- 12cosh(x)coth(x) + 6cosh(x))sinh(x) +--R + +--R 2 2 2 4 +--R ((- 30cosh(x) + 4)coth(x) + 15cosh(x) + 7)sinh(x) +--R + +--R 3 2 3 3 +--R ((- 40cosh(x) + 16cosh(x))coth(x) + 20cosh(x) + 28cosh(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R ((- 30cosh(x) + 24cosh(x) - 2)coth(x) + 15cosh(x) + 42cosh(x) - 1) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 12cosh(x) + 16cosh(x) - 4cosh(x))coth(x) + 6cosh(x) +--R + +--R 3 +--R 28cosh(x) - 2cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 6 4 +--R (- 2cosh(x) + 4cosh(x) - 2cosh(x) )coth(x) + cosh(x) + 7cosh(x) +--R + +--R 2 +--R - cosh(x) + 1 +--R / +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) - 4)sinh(x) +--R + +--R 3 3 +--R (40cosh(x) - 16cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) - 4)sinh(x) +--R + +--R 3 3 4 2 2 +--R (40cosh(x) - 16cosh(x))sinh(x) + (30cosh(x) - 24cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) +--R + +--R 2 +--R 2cosh(x) +--R Type: Expression(Integer) +--E 80 + +--S 81 of 526 +t0616:= coth(x)^4/(1+coth(x)) +--R +--R +--R 4 +--R coth(x) +--R (81) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 526 +r0616:= -3/2*x+coth(x)-1/2*coth(x)^2+2*log(sinh(x))+1/(2+2*tanh(x)) +--R +--R +--R (82) +--R 2 +--R (4tanh(x) + 4)log(sinh(x)) + (- coth(x) + 2coth(x) - 3x)tanh(x) +--R + +--R 2 +--R - coth(x) + 2coth(x) - 3x + 1 +--R / +--R 2tanh(x) + 2 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 526 +a0616:= integrate(t0616,x) +--R +--R +--R (83) +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) - 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (48cosh(x) - 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) - 16cosh(x) +--R + +--R 2 +--R 8cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 5 +--R - 14x sinh(x) - 84x cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 210x cosh(x) + 28x + 1)sinh(x) +--R + +--R 3 3 +--R (- 280x cosh(x) + (112x + 4)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 210x cosh(x) + (168x + 6)cosh(x) - 14x - 10)sinh(x) +--R + +--R 5 3 +--R (- 84x cosh(x) + (112x + 4)cosh(x) + (- 28x - 20)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 14x cosh(x) + (28x + 1)cosh(x) + (- 14x - 10)cosh(x) + 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 8)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) - 32cosh(x))sinh(x) + (60cosh(x) - 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 526 +m0616:= a0616-r0616 +--R +--R +--R (84) +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) + 96cosh(x) - 8)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) + 64cosh(x) - 16cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R 16cosh(x) - 8cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R - 8sinh(x) - 48cosh(x)sinh(x) + (- 120cosh(x) + 16)sinh(x) +--R + +--R 3 3 +--R (- 160cosh(x) + 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 120cosh(x) + 96cosh(x) - 8)sinh(x) +--R + +--R 5 3 6 +--R (- 48cosh(x) + 64cosh(x) - 16cosh(x))sinh(x) - 8cosh(x) +--R + +--R 4 2 +--R 16cosh(x) - 8cosh(x) +--R * +--R log(sinh(x)) +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) - 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 +--R (48cosh(x) - 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) +--R + +--R 4 2 +--R - 16cosh(x) + 8cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 8sinh(x) + 48cosh(x)sinh(x) + (120cosh(x) - 16)sinh(x) +--R + +--R 3 3 +--R (160cosh(x) - 64cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (120cosh(x) - 96cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (48cosh(x) - 64cosh(x) + 16cosh(x))sinh(x) + 8cosh(x) - 16cosh(x) +--R + +--R 2 +--R 8cosh(x) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 6 +--R (2coth(x) - 4coth(x) - 8x)sinh(x) +--R + +--R 2 5 +--R (12cosh(x)coth(x) - 24cosh(x)coth(x) - 48x cosh(x))sinh(x) +--R + +--R 2 2 2 +--R (30cosh(x) - 4)coth(x) + (- 60cosh(x) + 8)coth(x) +--R + +--R 2 +--R - 120x cosh(x) + 16x + 1 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (40cosh(x) - 16cosh(x))coth(x) +--R + +--R 3 3 +--R (- 80cosh(x) + 32cosh(x))coth(x) - 160x cosh(x) +--R + +--R (64x + 4)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 24cosh(x) + 2)coth(x) +--R + +--R 4 2 4 +--R (- 60cosh(x) + 48cosh(x) - 4)coth(x) - 120x cosh(x) +--R + +--R 2 +--R (96x + 6)cosh(x) - 8x - 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))coth(x) +--R + +--R 5 3 5 +--R (- 24cosh(x) + 32cosh(x) - 8cosh(x))coth(x) - 48x cosh(x) +--R + +--R 3 +--R (64x + 4)cosh(x) + (- 16x - 20)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (2cosh(x) - 4cosh(x) + 2cosh(x) )coth(x) +--R + +--R 6 4 2 6 +--R (- 4cosh(x) + 8cosh(x) - 4cosh(x) )coth(x) - 8x cosh(x) +--R + +--R 4 2 +--R (16x + 1)cosh(x) + (- 8x - 10)cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 2 6 +--R (2coth(x) - 4coth(x) - 8x - 2)sinh(x) +--R + +--R 2 5 +--R (12cosh(x)coth(x) - 24cosh(x)coth(x) + (- 48x - 12)cosh(x))sinh(x) +--R + +--R 2 2 2 +--R (30cosh(x) - 4)coth(x) + (- 60cosh(x) + 8)coth(x) +--R + +--R 2 +--R (- 120x - 30)cosh(x) + 16x + 5 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 +--R (40cosh(x) - 16cosh(x))coth(x) + (- 80cosh(x) + 32cosh(x))coth(x) +--R + +--R 3 +--R (- 160x - 40)cosh(x) + (64x + 20)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 +--R (30cosh(x) - 24cosh(x) + 2)coth(x) +--R + +--R 4 2 4 +--R (- 60cosh(x) + 48cosh(x) - 4)coth(x) + (- 120x - 30)cosh(x) +--R + +--R 2 +--R (96x + 30)cosh(x) - 8x - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 2 +--R (12cosh(x) - 16cosh(x) + 4cosh(x))coth(x) +--R + +--R 5 3 5 +--R (- 24cosh(x) + 32cosh(x) - 8cosh(x))coth(x) + (- 48x - 12)cosh(x) +--R + +--R 3 +--R (64x + 20)cosh(x) + (- 16x - 24)cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 2 +--R (2cosh(x) - 4cosh(x) + 2cosh(x) )coth(x) +--R + +--R 6 4 2 6 +--R (- 4cosh(x) + 8cosh(x) - 4cosh(x) )coth(x) + (- 8x - 2)cosh(x) +--R + +--R 4 2 +--R (16x + 5)cosh(x) + (- 8x - 12)cosh(x) + 1 +--R / +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 8)sinh(x) +--R + +--R 3 3 +--R (80cosh(x) - 32cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (60cosh(x) - 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R * +--R tanh(x) +--R + +--R 6 5 2 4 +--R 4sinh(x) + 24cosh(x)sinh(x) + (60cosh(x) - 8)sinh(x) +--R + +--R 3 3 4 2 2 +--R (80cosh(x) - 32cosh(x))sinh(x) + (60cosh(x) - 48cosh(x) + 4)sinh(x) +--R + +--R 5 3 6 4 +--R (24cosh(x) - 32cosh(x) + 8cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) +--R + +--R 2 +--R 4cosh(x) +--R Type: Expression(Integer) +--E 84 + +--S 85 of 526 +d0616:= D(m0616,x) +--R +--R +--R (85) +--R 3 2 8 +--R (- 2coth(x) + 2coth(x) + 2coth(x) - 3)sinh(x) +--R + +--R 3 2 +--R - 16cosh(x)coth(x) + 16cosh(x)coth(x) + 16cosh(x)coth(x) +--R + +--R - 24cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 56cosh(x) + 6)coth(x) + (56cosh(x) - 6)coth(x) +--R + +--R 2 2 +--R (56cosh(x) - 6)coth(x) - 84cosh(x) + 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 +--R (- 112cosh(x) + 36cosh(x))coth(x) +--R + +--R 3 2 +--R (112cosh(x) - 36cosh(x))coth(x) +--R + +--R 3 3 +--R (112cosh(x) - 36cosh(x))coth(x) - 168cosh(x) + 48cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 +--R (- 140cosh(x) + 90cosh(x) - 6)coth(x) +--R + +--R 4 2 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) +--R + +--R 4 2 4 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) - 210cosh(x) + 120cosh(x) +--R + +--R 10 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) + 120cosh(x) - 24cosh(x))coth(x) +--R + +--R 5 3 2 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) +--R + +--R 5 3 5 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) - 168cosh(x) +--R + +--R 3 +--R 160cosh(x) + 40cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- 56cosh(x) + 90cosh(x) - 36cosh(x) + 2)coth(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) +--R + +--R 6 4 2 6 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) - 84cosh(x) +--R + +--R 4 2 +--R 120cosh(x) + 60cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 3 +--R (- 16cosh(x) + 36cosh(x) - 24cosh(x) + 4cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) +--R + +--R 7 5 3 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) +--R + +--R 7 5 3 +--R - 24cosh(x) + 48cosh(x) + 40cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (- 2cosh(x) + 6cosh(x) - 6cosh(x) + 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 2 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 8 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) - 3cosh(x) +--R + +--R 6 4 +--R 8cosh(x) + 10cosh(x) + 1 +--R * +--R tanh(x) +--R + +--R 3 2 8 +--R (- 2coth(x) + 2coth(x) + 2coth(x) - 1)sinh(x) +--R + +--R 3 2 +--R (- 16cosh(x)coth(x) + 16cosh(x)coth(x) + 16cosh(x)coth(x) - 8cosh(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 56cosh(x) + 6)coth(x) + (56cosh(x) - 6)coth(x) +--R + +--R 2 2 +--R (56cosh(x) - 6)coth(x) - 28cosh(x) + 2 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 3 +--R (- 112cosh(x) + 36cosh(x))coth(x) +--R + +--R 3 2 3 +--R (112cosh(x) - 36cosh(x))coth(x) + (112cosh(x) - 36cosh(x))coth(x) +--R + +--R 3 +--R - 56cosh(x) + 12cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 +--R (- 140cosh(x) + 90cosh(x) - 6)coth(x) +--R + +--R 4 2 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) +--R + +--R 4 2 4 2 +--R (140cosh(x) - 90cosh(x) + 6)coth(x) - 70cosh(x) + 30cosh(x) + 16 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 112cosh(x) + 120cosh(x) - 24cosh(x))coth(x) +--R + +--R 5 3 2 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) +--R + +--R 5 3 5 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))coth(x) - 56cosh(x) +--R + +--R 3 +--R 40cosh(x) + 64cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- 56cosh(x) + 90cosh(x) - 36cosh(x) + 2)coth(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) +--R + +--R 6 4 2 6 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)coth(x) - 28cosh(x) +--R + +--R 4 2 +--R 30cosh(x) + 96cosh(x) - 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 3 +--R (- 16cosh(x) + 36cosh(x) - 24cosh(x) + 4cosh(x))coth(x) +--R + +--R 7 5 3 2 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) +--R + +--R 7 5 3 7 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))coth(x) - 8cosh(x) +--R + +--R 5 3 +--R 12cosh(x) + 64cosh(x) - 4cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (- 2cosh(x) + 6cosh(x) - 6cosh(x) + 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 2 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) +--R + +--R 8 6 4 2 8 +--R (2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) )coth(x) - cosh(x) +--R + +--R 6 4 2 +--R 2cosh(x) + 16cosh(x) - 2cosh(x) + 1 +--R / +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) - 6)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) - 90cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 6cosh(x) + 6cosh(x) - 2cosh(x) +--R * +--R tanh(x) +--R + +--R 8 7 2 6 +--R 2sinh(x) + 16cosh(x)sinh(x) + (56cosh(x) - 6)sinh(x) +--R + +--R 3 5 +--R (112cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (140cosh(x) - 90cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (112cosh(x) - 120cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (56cosh(x) - 90cosh(x) + 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 8 +--R (16cosh(x) - 36cosh(x) + 24cosh(x) - 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 6cosh(x) + 6cosh(x) - 2cosh(x) +--R Type: Expression(Integer) +--E 85 + +--S 86 of 526 +t0617:= sech(x)^2/(a+b*coth(x)) +--R +--R +--R 2 +--R sech(x) +--R (86) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 526 +r0617:= -b*log(b+a*tanh(x))/a^2+tanh(x)/a +--R +--R +--R - b log(a tanh(x) + b) + a tanh(x) +--R (87) ---------------------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 526 +a0617:= integrate(t0617,x) +--R +--R +--R (88) +--R 2 2 2cosh(x) +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R - 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 526 +m0617:= a0617-r0617 +--R +--R +--R (89) +--R 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b)log(a tanh(x) + b) +--R + +--R 2 2 2cosh(x) +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b) +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a)tanh(x) - 2a +--R / +--R 2 2 2 2 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Expression(Integer) +--E 89 + +--S 90 of 526 +d0617:= D(m0617,x) +--R +--R +--R (90) +--R 2 5 2 2 4 +--R a cosh(x)sinh(x) + (a b + 4a )cosh(x) sinh(x) +--R + +--R 2 3 2 3 +--R ((4a b + 6a )cosh(x) + 2a cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R ((6a b + 4a )cosh(x) + (2a b + 4a )cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((4a b + a )cosh(x) + (4a b + 2a )cosh(x) + a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 6 2 5 +--R a b sinh(x) + (4a b - a )cosh(x)sinh(x) +--R + +--R 2 2 4 +--R ((4a b - 4a )cosh(x) + 2a b)sinh(x) +--R + +--R 2 3 2 3 +--R ((- 4a b - 6a )cosh(x) + (4a b + 2a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R ((- 11a b - 4a )cosh(x) + (2a b + 4a )cosh(x) + a b)sinh(x) +--R + +--R 2 5 2 3 2 +--R ((- 8a b - a )cosh(x) + 2a cosh(x) - a cosh(x))sinh(x) +--R + +--R 6 2 +--R - 2a b cosh(x) - 2a b cosh(x) +--R * +--R tanh(x) +--R + +--R 2 6 2 5 2 2 2 4 +--R b sinh(x) + 4b cosh(x)sinh(x) + (5b cosh(x) + 2b )sinh(x) +--R + +--R 2 3 +--R (4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 5b cosh(x) + (4b + 8a b)cosh(x) + b )sinh(x) +--R + +--R 2 5 2 3 2 6 2 4 +--R (- 4b cosh(x) + (4b + 4a b)cosh(x) )sinh(x) - b cosh(x) + 2b cosh(x) +--R + +--R 2 2 +--R - b cosh(x) +--R / +--R 3 5 2 3 2 4 +--R a cosh(x)sinh(x) + (a b + 4a )cosh(x) sinh(x) +--R + +--R 2 3 3 3 3 +--R ((4a b + 6a )cosh(x) + 2a cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R ((6a b + 4a )cosh(x) + (2a b + 4a )cosh(x) )sinh(x) +--R + +--R 2 3 5 2 3 3 3 +--R ((4a b + a )cosh(x) + (4a b + 2a )cosh(x) + a cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) +--R * +--R tanh(x) +--R + +--R 2 5 2 2 2 4 +--R a b cosh(x)sinh(x) + (a b + 4a b)cosh(x) sinh(x) +--R + +--R 2 2 3 2 3 +--R ((4a b + 6a b)cosh(x) + 2a b cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R ((6a b + 4a b)cosh(x) + (2a b + 4a b)cosh(x) )sinh(x) +--R + +--R 2 2 5 2 2 3 2 +--R ((4a b + a b)cosh(x) + (4a b + 2a b)cosh(x) + a b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) +--R Type: Expression(Integer) +--E 90 + +--S 91 of 526 +t0618:= sech(x)^3/(a+b*coth(x)) +--R +--R +--R 3 +--R sech(x) +--R (91) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 91 + +--S 92 of 526 +r0618:= atan(tanh(1/2*x))/a-2*b^2*atan(tanh(1/2*x))/a^3+_ + 2*b*(a^2-b^2)^(1/2)*atanh((a+b*tanh(1/2*x))/(a^2-b^2)^(1/2))/a^3+_ + 2*tanh(1/2*x)/a/(1+tanh(1/2*x)^2)^2-2*b/a^2/(1+tanh(1/2*x)^2)-_ + tanh(1/2*x)/a/(1+tanh(1/2*x)^2) +--R +--R +--R (92) +--R x +--R +---------+ b tanh(-) + a +--R x 4 x 2 | 2 2 2 +--R (2b tanh(-) + 4b tanh(-) + 2b)\|- b + a atanh(-------------) +--R 2 2 +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 x 4 2 2 x 2 2 2 x +--R ((- 2b + a )tanh(-) + (- 4b + 2a )tanh(-) - 2b + a )atan(tanh(-)) +--R 2 2 2 +--R + +--R 2 x 3 x 2 2 x +--R - a tanh(-) - 2a b tanh(-) + a tanh(-) - 2a b +--R 2 2 2 +--R / +--R 3 x 4 3 x 2 3 +--R a tanh(-) + 2a tanh(-) + a +--R 2 2 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 526 +a0618:= integrate(t0618,x) +--R +--R +--R (93) +--R [ +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- b + a + (b + a)sinh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b + a +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R (- 2a b + a )sinh(x) + (- 6a b + 3a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 +--R ((- 6a b + 3a )cosh(x) - 2a b - a )sinh(x) + (- 2a b + a )cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R , +--R +--R 4 3 2 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 \|b - a +--R \|b - a atan(-------------------------------) +--R (b + a)sinh(x) + (b + a)cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R (- 2a b + a )sinh(x) + (- 6a b + 3a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 +--R ((- 6a b + 3a )cosh(x) - 2a b - a )sinh(x) + (- 2a b + a )cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 93 + +--S 94 of 526 +m0618a:= a0618.1-r0618 +--R +--R +--R (94) +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) + 4b)sinh(x) +--R + +--R 3 4 2 +--R (8b cosh(x) + 8b cosh(x))sinh(x) + 2b cosh(x) + 4b cosh(x) + 2b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- b + a + (b + a)sinh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b + a +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) + b +--R + +--R - a +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) +--R + +--R - 2b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - 4b sinh(x) - 16b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 24b cosh(x) - 8b)sinh(x) +--R + +--R 3 4 2 +--R (- 16b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) - 8b cosh(x) +--R + +--R - 4b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R x +--R +---------+ b tanh(-) + a +--R | 2 2 2 +--R \|- b + a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) + 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (4b - 2a )cosh(x) + 2b - a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (4b - 2a )sinh(x) + (16b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b - 12a )cosh(x) + 8b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b - 8a )cosh(x) + (16b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b - 2a )cosh(x) + (8b - 4a )cosh(x) + 4b - 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) + 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (4b - 2a )cosh(x) + 2b - a +--R * +--R x +--R atan(tanh(-)) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 4b + 2a )sinh(x) + (- 16b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 24b + 12a )cosh(x) - 8b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 16b + 8a )cosh(x) + (- 16b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 4b + 2a )cosh(x) + (- 8b + 4a )cosh(x) - 4b + 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R (- 2a b + a )sinh(x) + (- 6a b + 3a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 +--R ((- 6a b + 3a )cosh(x) - 2a b - a )sinh(x) + (- 2a b + a )cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 2 2 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 2 3 2 2 4 2 2 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2a b sinh(x) + (8a b cosh(x) - 4a b + 2a )sinh(x) +--R + +--R 2 2 2 +--R (12a b cosh(x) + (- 12a b + 6a )cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 +--R 8a b cosh(x) + (- 12a b + 6a )cosh(x) + 8a b cosh(x) - 4a b +--R + +--R 2 +--R - 2a +--R * +--R sinh(x) +--R + +--R 4 2 3 2 +--R 2a b cosh(x) + (- 4a b + 2a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R (- 4a b - 2a )cosh(x) + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 2 2 2 2 +--R - a sinh(x) - 4a cosh(x)sinh(x) + (- 6a cosh(x) - 2a )sinh(x) +--R + +--R 2 3 2 2 4 2 2 2 +--R (- 4a cosh(x) - 4a cosh(x))sinh(x) - a cosh(x) - 2a cosh(x) - a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2a b sinh(x) + (8a b cosh(x) - 2a b + a )sinh(x) +--R + +--R 2 2 2 +--R (12a b cosh(x) + (- 6a b + 3a )cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 2 +--R (8a b cosh(x) + (- 6a b + 3a )cosh(x) + 8a b cosh(x) - 2a b - a ) +--R * +--R sinh(x) +--R + +--R 4 2 3 2 +--R 2a b cosh(x) + (- 2a b + a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) + 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 526 +d0618a:= D(m0618a,x) +--R +--R +--R (95) +--R 5 4 2 3 +--R 8b sinh(x) + 40b cosh(x)sinh(x) + (80b cosh(x) - 8b)sinh(x) +--R + +--R 3 2 +--R (80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (40b cosh(x) - 24b cosh(x) )sinh(x) + 8b cosh(x) - 8b cosh(x) +--R * +--R x 8 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (2b + 2a)sinh(x) + (16b + 16a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((56b + 56a)cosh(x) + 8b + 4a)sinh(x) +--R + +--R 3 5 +--R ((112b + 112a)cosh(x) + (48b + 24a)cosh(x) + 16a)sinh(x) +--R + +--R 4 2 +--R ((140b + 140a)cosh(x) + (120b + 60a)cosh(x) + 80a cosh(x) + 12b) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (112b + 112a)cosh(x) + (160b + 80a)cosh(x) + 160a cosh(x) +--R + +--R 48b cosh(x) - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (56b + 56a)cosh(x) + (120b + 60a)cosh(x) + 160a cosh(x) +--R + +--R 2 +--R 72b cosh(x) - 48a cosh(x) + 8b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (16b + 16a)cosh(x) + (48b + 24a)cosh(x) + 80a cosh(x) +--R + +--R 3 2 +--R 48b cosh(x) - 48a cosh(x) + (16b - 8a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 4 +--R (2b + 2a)cosh(x) + (8b + 4a)cosh(x) + 16a cosh(x) + 12b cosh(x) +--R + +--R 3 2 +--R - 16a cosh(x) + (8b - 4a)cosh(x) + 2b - 2a +--R * +--R x 7 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 32b sinh(x) + 160b cosh(x)sinh(x) + (320b cosh(x) - 32b)sinh(x) +--R + +--R 3 2 +--R (320b cosh(x) - 96b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (160b cosh(x) - 96b cosh(x) )sinh(x) + 32b cosh(x) - 32b cosh(x) +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (- 6b - 6a)sinh(x) + (- 48b - 48a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((- 168b - 168a)cosh(x) - 24b - 12a)sinh(x) +--R + +--R 3 5 +--R ((- 336b - 336a)cosh(x) + (- 144b - 72a)cosh(x) + 48a)sinh(x) +--R + +--R 4 2 +--R (- 420b - 420a)cosh(x) + (- 360b - 180a)cosh(x) + 240a cosh(x) +--R + +--R - 36b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 336b - 336a)cosh(x) + (- 480b - 240a)cosh(x) + 480a cosh(x) +--R + +--R - 144b cosh(x) - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (- 168b - 168a)cosh(x) + (- 360b - 180a)cosh(x) + 480a cosh(x) +--R + +--R 2 +--R - 216b cosh(x) - 144a cosh(x) - 24b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (- 48b - 48a)cosh(x) + (- 144b - 72a)cosh(x) + 240a cosh(x) +--R + +--R 3 2 +--R - 144b cosh(x) - 144a cosh(x) + (- 48b + 24a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 +--R (- 6b - 6a)cosh(x) + (- 24b - 12a)cosh(x) + 48a cosh(x) +--R + +--R 4 3 2 +--R - 36b cosh(x) - 48a cosh(x) + (- 24b + 12a)cosh(x) - 6b + 6a +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 48b sinh(x) + 240b cosh(x)sinh(x) + (480b cosh(x) - 48b)sinh(x) +--R + +--R 3 2 +--R (480b cosh(x) - 144b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (240b cosh(x) - 144b cosh(x) )sinh(x) + 48b cosh(x) - 48b cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (6b + 6a)sinh(x) + (48b + 48a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((168b + 168a)cosh(x) + 24b + 12a)sinh(x) +--R + +--R 3 5 +--R ((336b + 336a)cosh(x) + (144b + 72a)cosh(x) + 48a)sinh(x) +--R + +--R 4 2 +--R (420b + 420a)cosh(x) + (360b + 180a)cosh(x) + 240a cosh(x) +--R + +--R 36b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (336b + 336a)cosh(x) + (480b + 240a)cosh(x) + 480a cosh(x) +--R + +--R 144b cosh(x) - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (168b + 168a)cosh(x) + (360b + 180a)cosh(x) + 480a cosh(x) +--R + +--R 2 +--R 216b cosh(x) - 144a cosh(x) + 24b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (48b + 48a)cosh(x) + (144b + 72a)cosh(x) + 240a cosh(x) +--R + +--R 3 2 +--R 144b cosh(x) - 144a cosh(x) + (48b - 24a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 4 +--R (6b + 6a)cosh(x) + (24b + 12a)cosh(x) + 48a cosh(x) + 36b cosh(x) +--R + +--R 3 2 +--R - 48a cosh(x) + (24b - 12a)cosh(x) + 6b - 6a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 32b sinh(x) + 160b cosh(x)sinh(x) + (320b cosh(x) - 32b)sinh(x) +--R + +--R 3 2 +--R (320b cosh(x) - 96b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (160b cosh(x) - 96b cosh(x) )sinh(x) + 32b cosh(x) - 32b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (- 2b - 2a)sinh(x) + (- 16b - 16a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((- 56b - 56a)cosh(x) - 8b - 4a)sinh(x) +--R + +--R 3 5 +--R ((- 112b - 112a)cosh(x) + (- 48b - 24a)cosh(x) + 16a)sinh(x) +--R + +--R 4 2 +--R (- 140b - 140a)cosh(x) + (- 120b - 60a)cosh(x) + 80a cosh(x) +--R + +--R - 12b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 112b - 112a)cosh(x) + (- 160b - 80a)cosh(x) + 160a cosh(x) +--R + +--R - 48b cosh(x) - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (- 56b - 56a)cosh(x) + (- 120b - 60a)cosh(x) + 160a cosh(x) +--R + +--R 2 +--R - 72b cosh(x) - 48a cosh(x) - 8b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (- 16b - 16a)cosh(x) + (- 48b - 24a)cosh(x) + 80a cosh(x) +--R + +--R 3 2 +--R - 48b cosh(x) - 48a cosh(x) + (- 16b + 8a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 +--R (- 2b - 2a)cosh(x) + (- 8b - 4a)cosh(x) + 16a cosh(x) +--R + +--R 4 3 2 +--R - 12b cosh(x) - 16a cosh(x) + (- 8b + 4a)cosh(x) - 2b + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 8b sinh(x) + 40b cosh(x)sinh(x) + (80b cosh(x) - 8b)sinh(x) +--R + +--R 3 2 +--R (80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (40b cosh(x) - 24b cosh(x) )sinh(x) + 8b cosh(x) - 8b cosh(x) +--R / +--R 2 8 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b + 56a b)cosh(x) + (24b + 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((70b + 70a b)cosh(x) + (60b + 30a b)cosh(x) + 6b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((56b + 56a b)cosh(x) + (80b + 40a b)cosh(x) + 24b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (28b + 28a b)cosh(x) + (60b + 30a b)cosh(x) + 36b cosh(x) +--R + +--R 2 +--R 4b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (8b + 8a b)cosh(x) + (24b + 12a b)cosh(x) + 24b cosh(x) +--R + +--R 2 +--R (8b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (b + a b)cosh(x) + (4b + 2a b)cosh(x) + 6b cosh(x) +--R + +--R 2 2 2 +--R (4b - 2a b)cosh(x) + b - a b +--R * +--R x 8 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (2a b + 2a )sinh(x) + (16a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((56a b + 56a )cosh(x) + 8a b + 4a )sinh(x) +--R + +--R 2 3 2 5 +--R ((112a b + 112a )cosh(x) + (48a b + 24a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((140a b + 140a )cosh(x) + (120a b + 60a )cosh(x) + 12a b)sinh(x) +--R + +--R 2 5 2 3 +--R (112a b + 112a )cosh(x) + (160a b + 80a )cosh(x) +--R + +--R 48a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 +--R (56a b + 56a )cosh(x) + (120a b + 60a )cosh(x) + 72a b cosh(x) +--R + +--R 2 +--R 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 3 +--R (16a b + 16a )cosh(x) + (48a b + 24a )cosh(x) + 48a b cosh(x) +--R + +--R 2 +--R (16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (2a b + 2a )cosh(x) + (8a b + 4a )cosh(x) + 12a b cosh(x) +--R + +--R 2 2 2 +--R (8a b - 4a )cosh(x) + 2a b - 2a +--R * +--R x 7 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (4b + 4a b)sinh(x) + (32b + 32a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((112b + 112a b)cosh(x) + 16b + 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((224b + 224a b)cosh(x) + (96b + 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((280b + 280a b)cosh(x) + (240b + 120a b)cosh(x) + 24b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((224b + 224a b)cosh(x) + (320b + 160a b)cosh(x) + 96b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (112b + 112a b)cosh(x) + (240b + 120a b)cosh(x) +--R + +--R 2 2 2 +--R 144b cosh(x) + 16b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (32b + 32a b)cosh(x) + (96b + 48a b)cosh(x) + 96b cosh(x) +--R + +--R 2 +--R (32b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (4b + 4a b)cosh(x) + (16b + 8a b)cosh(x) + 24b cosh(x) +--R + +--R 2 2 2 +--R (16b - 8a b)cosh(x) + 4b - 4a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6a b + 6a )sinh(x) + (48a b + 48a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168a b + 168a )cosh(x) + 24a b + 12a )sinh(x) +--R + +--R 2 3 2 5 +--R ((336a b + 336a )cosh(x) + (144a b + 72a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((420a b + 420a )cosh(x) + (360a b + 180a )cosh(x) + 36a b)sinh(x) +--R + +--R 2 5 2 3 +--R (336a b + 336a )cosh(x) + (480a b + 240a )cosh(x) +--R + +--R 144a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168a b + 168a )cosh(x) + (360a b + 180a )cosh(x) +--R + +--R 2 2 +--R 216a b cosh(x) + 24a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (48a b + 48a )cosh(x) + (144a b + 72a )cosh(x) +--R + +--R 3 2 +--R 144a b cosh(x) + (48a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (6a b + 6a )cosh(x) + (24a b + 12a )cosh(x) + 36a b cosh(x) +--R + +--R 2 2 2 +--R (24a b - 12a )cosh(x) + 6a b - 6a +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6b + 6a b)sinh(x) + (48b + 48a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168b + 168a b)cosh(x) + 24b + 12a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((336b + 336a b)cosh(x) + (144b + 72a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((420b + 420a b)cosh(x) + (360b + 180a b)cosh(x) + 36b )sinh(x) +--R + +--R 2 5 2 3 +--R (336b + 336a b)cosh(x) + (480b + 240a b)cosh(x) +--R + +--R 2 +--R 144b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168b + 168a b)cosh(x) + (360b + 180a b)cosh(x) +--R + +--R 2 2 2 +--R 216b cosh(x) + 24b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (48b + 48a b)cosh(x) + (144b + 72a b)cosh(x) + 144b cosh(x) +--R + +--R 2 +--R (48b - 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (6b + 6a b)cosh(x) + (24b + 12a b)cosh(x) + 36b cosh(x) +--R + +--R 2 2 2 +--R (24b - 12a b)cosh(x) + 6b - 6a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6a b + 6a )sinh(x) + (48a b + 48a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168a b + 168a )cosh(x) + 24a b + 12a )sinh(x) +--R + +--R 2 3 2 5 +--R ((336a b + 336a )cosh(x) + (144a b + 72a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((420a b + 420a )cosh(x) + (360a b + 180a )cosh(x) + 36a b)sinh(x) +--R + +--R 2 5 2 3 +--R (336a b + 336a )cosh(x) + (480a b + 240a )cosh(x) +--R + +--R 144a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168a b + 168a )cosh(x) + (360a b + 180a )cosh(x) +--R + +--R 2 2 +--R 216a b cosh(x) + 24a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (48a b + 48a )cosh(x) + (144a b + 72a )cosh(x) +--R + +--R 3 2 +--R 144a b cosh(x) + (48a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (6a b + 6a )cosh(x) + (24a b + 12a )cosh(x) + 36a b cosh(x) +--R + +--R 2 2 2 +--R (24a b - 12a )cosh(x) + 6a b - 6a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (4b + 4a b)sinh(x) + (32b + 32a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((112b + 112a b)cosh(x) + 16b + 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((224b + 224a b)cosh(x) + (96b + 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((280b + 280a b)cosh(x) + (240b + 120a b)cosh(x) + 24b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((224b + 224a b)cosh(x) + (320b + 160a b)cosh(x) + 96b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (112b + 112a b)cosh(x) + (240b + 120a b)cosh(x) +--R + +--R 2 2 2 +--R 144b cosh(x) + 16b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (32b + 32a b)cosh(x) + (96b + 48a b)cosh(x) + 96b cosh(x) +--R + +--R 2 +--R (32b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (4b + 4a b)cosh(x) + (16b + 8a b)cosh(x) + 24b cosh(x) +--R + +--R 2 2 2 +--R (16b - 8a b)cosh(x) + 4b - 4a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (2a b + 2a )sinh(x) + (16a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((56a b + 56a )cosh(x) + 8a b + 4a )sinh(x) +--R + +--R 2 3 2 5 +--R ((112a b + 112a )cosh(x) + (48a b + 24a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((140a b + 140a )cosh(x) + (120a b + 60a )cosh(x) + 12a b)sinh(x) +--R + +--R 2 5 2 3 +--R (112a b + 112a )cosh(x) + (160a b + 80a )cosh(x) +--R + +--R 48a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 +--R (56a b + 56a )cosh(x) + (120a b + 60a )cosh(x) + 72a b cosh(x) +--R + +--R 2 +--R 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 3 +--R (16a b + 16a )cosh(x) + (48a b + 24a )cosh(x) + 48a b cosh(x) +--R + +--R 2 +--R (16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (2a b + 2a )cosh(x) + (8a b + 4a )cosh(x) + 12a b cosh(x) +--R + +--R 2 2 2 +--R (8a b - 4a )cosh(x) + 2a b - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b + 56a b)cosh(x) + (24b + 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((70b + 70a b)cosh(x) + (60b + 30a b)cosh(x) + 6b )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R ((56b + 56a b)cosh(x) + (80b + 40a b)cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (28b + 28a b)cosh(x) + (60b + 30a b)cosh(x) + 36b cosh(x) + 4b +--R + +--R - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (8b + 8a b)cosh(x) + (24b + 12a b)cosh(x) + 24b cosh(x) +--R + +--R 2 +--R (8b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (b + a b)cosh(x) + (4b + 2a b)cosh(x) + 6b cosh(x) +--R + +--R 2 2 2 +--R (4b - 2a b)cosh(x) + b - a b +--R Type: Expression(Integer) +--E 95 + +--S 96 of 526 +m0618b:= a0618.2-r0618 +--R +--R +--R (96) +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) +--R + +--R - 2b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - 4b sinh(x) - 16b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 24b cosh(x) - 8b)sinh(x) +--R + +--R 3 4 2 +--R (- 16b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) - 8b cosh(x) +--R + +--R - 4b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R x +--R +---------+ b tanh(-) + a +--R | 2 2 2 +--R \|- b + a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) +--R + +--R - 2b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 +--R - 4b sinh(x) - 16b cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 24b cosh(x) - 8b)sinh(x) +--R + +--R 3 4 2 +--R (- 16b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) - 8b cosh(x) +--R + +--R - 4b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) + (- 12b cosh(x) - 4b)sinh(x) +--R + +--R 3 4 2 +--R (- 8b cosh(x) - 8b cosh(x))sinh(x) - 2b cosh(x) - 4b cosh(x) - 2b +--R * +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 \|b - a +--R \|b - a atan(-------------------------------) +--R (b + a)sinh(x) + (b + a)cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) + 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (4b - 2a )cosh(x) + 2b - a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (4b - 2a )sinh(x) + (16b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b - 12a )cosh(x) + 8b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b - 8a )cosh(x) + (16b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b - 2a )cosh(x) + (8b - 4a )cosh(x) + 4b - 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (2b - a )sinh(x) + (8b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 6a )cosh(x) + 4b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 4a )cosh(x) + (8b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - a )cosh(x) + (4b - 2a )cosh(x) + 2b - a +--R * +--R x +--R atan(tanh(-)) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 4b + 2a )sinh(x) + (- 16b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 24b + 12a )cosh(x) - 8b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 16b + 8a )cosh(x) + (- 16b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 4b + 2a )cosh(x) + (- 8b + 4a )cosh(x) - 4b + 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a )sinh(x) + (- 8b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 6a )cosh(x) - 4b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 4a )cosh(x) + (- 8b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + a )cosh(x) + (- 4b + 2a )cosh(x) - 2b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R (- 2a b + a )sinh(x) + (- 6a b + 3a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 3 +--R ((- 6a b + 3a )cosh(x) - 2a b - a )sinh(x) + (- 2a b + a )cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 2 2 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 2 3 2 2 4 2 2 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2a b sinh(x) + (8a b cosh(x) - 4a b + 2a )sinh(x) +--R + +--R 2 2 2 +--R (12a b cosh(x) + (- 12a b + 6a )cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 +--R 8a b cosh(x) + (- 12a b + 6a )cosh(x) + 8a b cosh(x) - 4a b +--R + +--R 2 +--R - 2a +--R * +--R sinh(x) +--R + +--R 4 2 3 2 +--R 2a b cosh(x) + (- 4a b + 2a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R (- 4a b - 2a )cosh(x) + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 2 2 2 2 +--R - a sinh(x) - 4a cosh(x)sinh(x) + (- 6a cosh(x) - 2a )sinh(x) +--R + +--R 2 3 2 2 4 2 2 2 +--R (- 4a cosh(x) - 4a cosh(x))sinh(x) - a cosh(x) - 2a cosh(x) - a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 3 +--R 2a b sinh(x) + (8a b cosh(x) - 2a b + a )sinh(x) +--R + +--R 2 2 2 +--R (12a b cosh(x) + (- 6a b + 3a )cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 2 +--R (8a b cosh(x) + (- 6a b + 3a )cosh(x) + 8a b cosh(x) - 2a b - a ) +--R * +--R sinh(x) +--R + +--R 4 2 3 2 +--R 2a b cosh(x) + (- 2a b + a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R (- 2a b - a )cosh(x) + 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression(Integer) +--E 96 + +--S 97 of 526 +d0618b:= D(m0618b,x) +--R +--R +--R (97) +--R 5 4 2 3 +--R 8b sinh(x) + 40b cosh(x)sinh(x) + (80b cosh(x) - 8b)sinh(x) +--R + +--R 3 2 +--R (80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (40b cosh(x) - 24b cosh(x) )sinh(x) + 8b cosh(x) - 8b cosh(x) +--R * +--R x 8 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (2b + 2a)sinh(x) + (16b + 16a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((56b + 56a)cosh(x) + 8b + 4a)sinh(x) +--R + +--R 3 5 +--R ((112b + 112a)cosh(x) + (48b + 24a)cosh(x) + 16a)sinh(x) +--R + +--R 4 2 +--R ((140b + 140a)cosh(x) + (120b + 60a)cosh(x) + 80a cosh(x) + 12b) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (112b + 112a)cosh(x) + (160b + 80a)cosh(x) + 160a cosh(x) +--R + +--R 48b cosh(x) - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (56b + 56a)cosh(x) + (120b + 60a)cosh(x) + 160a cosh(x) +--R + +--R 2 +--R 72b cosh(x) - 48a cosh(x) + 8b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (16b + 16a)cosh(x) + (48b + 24a)cosh(x) + 80a cosh(x) +--R + +--R 3 2 +--R 48b cosh(x) - 48a cosh(x) + (16b - 8a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 4 +--R (2b + 2a)cosh(x) + (8b + 4a)cosh(x) + 16a cosh(x) + 12b cosh(x) +--R + +--R 3 2 +--R - 16a cosh(x) + (8b - 4a)cosh(x) + 2b - 2a +--R * +--R x 7 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 32b sinh(x) + 160b cosh(x)sinh(x) + (320b cosh(x) - 32b)sinh(x) +--R + +--R 3 2 +--R (320b cosh(x) - 96b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (160b cosh(x) - 96b cosh(x) )sinh(x) + 32b cosh(x) - 32b cosh(x) +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (- 6b - 6a)sinh(x) + (- 48b - 48a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((- 168b - 168a)cosh(x) - 24b - 12a)sinh(x) +--R + +--R 3 5 +--R ((- 336b - 336a)cosh(x) + (- 144b - 72a)cosh(x) + 48a)sinh(x) +--R + +--R 4 2 +--R (- 420b - 420a)cosh(x) + (- 360b - 180a)cosh(x) + 240a cosh(x) +--R + +--R - 36b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 336b - 336a)cosh(x) + (- 480b - 240a)cosh(x) + 480a cosh(x) +--R + +--R - 144b cosh(x) - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (- 168b - 168a)cosh(x) + (- 360b - 180a)cosh(x) + 480a cosh(x) +--R + +--R 2 +--R - 216b cosh(x) - 144a cosh(x) - 24b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (- 48b - 48a)cosh(x) + (- 144b - 72a)cosh(x) + 240a cosh(x) +--R + +--R 3 2 +--R - 144b cosh(x) - 144a cosh(x) + (- 48b + 24a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 +--R (- 6b - 6a)cosh(x) + (- 24b - 12a)cosh(x) + 48a cosh(x) +--R + +--R 4 3 2 +--R - 36b cosh(x) - 48a cosh(x) + (- 24b + 12a)cosh(x) - 6b + 6a +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 48b sinh(x) + 240b cosh(x)sinh(x) + (480b cosh(x) - 48b)sinh(x) +--R + +--R 3 2 +--R (480b cosh(x) - 144b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (240b cosh(x) - 144b cosh(x) )sinh(x) + 48b cosh(x) - 48b cosh(x) +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (6b + 6a)sinh(x) + (48b + 48a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((168b + 168a)cosh(x) + 24b + 12a)sinh(x) +--R + +--R 3 5 +--R ((336b + 336a)cosh(x) + (144b + 72a)cosh(x) + 48a)sinh(x) +--R + +--R 4 2 +--R (420b + 420a)cosh(x) + (360b + 180a)cosh(x) + 240a cosh(x) +--R + +--R 36b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (336b + 336a)cosh(x) + (480b + 240a)cosh(x) + 480a cosh(x) +--R + +--R 144b cosh(x) - 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (168b + 168a)cosh(x) + (360b + 180a)cosh(x) + 480a cosh(x) +--R + +--R 2 +--R 216b cosh(x) - 144a cosh(x) + 24b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (48b + 48a)cosh(x) + (144b + 72a)cosh(x) + 240a cosh(x) +--R + +--R 3 2 +--R 144b cosh(x) - 144a cosh(x) + (48b - 24a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 4 +--R (6b + 6a)cosh(x) + (24b + 12a)cosh(x) + 48a cosh(x) + 36b cosh(x) +--R + +--R 3 2 +--R - 48a cosh(x) + (24b - 12a)cosh(x) + 6b - 6a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 32b sinh(x) + 160b cosh(x)sinh(x) + (320b cosh(x) - 32b)sinh(x) +--R + +--R 3 2 +--R (320b cosh(x) - 96b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (160b cosh(x) - 96b cosh(x) )sinh(x) + 32b cosh(x) - 32b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 7 +--R (- 2b - 2a)sinh(x) + (- 16b - 16a)cosh(x)sinh(x) +--R + +--R 2 6 +--R ((- 56b - 56a)cosh(x) - 8b - 4a)sinh(x) +--R + +--R 3 5 +--R ((- 112b - 112a)cosh(x) + (- 48b - 24a)cosh(x) + 16a)sinh(x) +--R + +--R 4 2 +--R (- 140b - 140a)cosh(x) + (- 120b - 60a)cosh(x) + 80a cosh(x) +--R + +--R - 12b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 112b - 112a)cosh(x) + (- 160b - 80a)cosh(x) + 160a cosh(x) +--R + +--R - 48b cosh(x) - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 3 +--R (- 56b - 56a)cosh(x) + (- 120b - 60a)cosh(x) + 160a cosh(x) +--R + +--R 2 +--R - 72b cosh(x) - 48a cosh(x) - 8b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 4 +--R (- 16b - 16a)cosh(x) + (- 48b - 24a)cosh(x) + 80a cosh(x) +--R + +--R 3 2 +--R - 48b cosh(x) - 48a cosh(x) + (- 16b + 8a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 5 +--R (- 2b - 2a)cosh(x) + (- 8b - 4a)cosh(x) + 16a cosh(x) +--R + +--R 4 3 2 +--R - 12b cosh(x) - 16a cosh(x) + (- 8b + 4a)cosh(x) - 2b + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 +--R 8b sinh(x) + 40b cosh(x)sinh(x) + (80b cosh(x) - 8b)sinh(x) +--R + +--R 3 2 +--R (80b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (40b cosh(x) - 24b cosh(x) )sinh(x) + 8b cosh(x) - 8b cosh(x) +--R / +--R 2 8 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b + 56a b)cosh(x) + (24b + 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((70b + 70a b)cosh(x) + (60b + 30a b)cosh(x) + 6b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((56b + 56a b)cosh(x) + (80b + 40a b)cosh(x) + 24b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (28b + 28a b)cosh(x) + (60b + 30a b)cosh(x) + 36b cosh(x) +--R + +--R 2 +--R 4b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (8b + 8a b)cosh(x) + (24b + 12a b)cosh(x) + 24b cosh(x) +--R + +--R 2 +--R (8b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (b + a b)cosh(x) + (4b + 2a b)cosh(x) + 6b cosh(x) +--R + +--R 2 2 2 +--R (4b - 2a b)cosh(x) + b - a b +--R * +--R x 8 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (2a b + 2a )sinh(x) + (16a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((56a b + 56a )cosh(x) + 8a b + 4a )sinh(x) +--R + +--R 2 3 2 5 +--R ((112a b + 112a )cosh(x) + (48a b + 24a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((140a b + 140a )cosh(x) + (120a b + 60a )cosh(x) + 12a b)sinh(x) +--R + +--R 2 5 2 3 +--R (112a b + 112a )cosh(x) + (160a b + 80a )cosh(x) +--R + +--R 48a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 +--R (56a b + 56a )cosh(x) + (120a b + 60a )cosh(x) + 72a b cosh(x) +--R + +--R 2 +--R 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 3 +--R (16a b + 16a )cosh(x) + (48a b + 24a )cosh(x) + 48a b cosh(x) +--R + +--R 2 +--R (16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (2a b + 2a )cosh(x) + (8a b + 4a )cosh(x) + 12a b cosh(x) +--R + +--R 2 2 2 +--R (8a b - 4a )cosh(x) + 2a b - 2a +--R * +--R x 7 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (4b + 4a b)sinh(x) + (32b + 32a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((112b + 112a b)cosh(x) + 16b + 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((224b + 224a b)cosh(x) + (96b + 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((280b + 280a b)cosh(x) + (240b + 120a b)cosh(x) + 24b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((224b + 224a b)cosh(x) + (320b + 160a b)cosh(x) + 96b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (112b + 112a b)cosh(x) + (240b + 120a b)cosh(x) +--R + +--R 2 2 2 +--R 144b cosh(x) + 16b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (32b + 32a b)cosh(x) + (96b + 48a b)cosh(x) + 96b cosh(x) +--R + +--R 2 +--R (32b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (4b + 4a b)cosh(x) + (16b + 8a b)cosh(x) + 24b cosh(x) +--R + +--R 2 2 2 +--R (16b - 8a b)cosh(x) + 4b - 4a b +--R * +--R x 6 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6a b + 6a )sinh(x) + (48a b + 48a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168a b + 168a )cosh(x) + 24a b + 12a )sinh(x) +--R + +--R 2 3 2 5 +--R ((336a b + 336a )cosh(x) + (144a b + 72a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((420a b + 420a )cosh(x) + (360a b + 180a )cosh(x) + 36a b)sinh(x) +--R + +--R 2 5 2 3 +--R (336a b + 336a )cosh(x) + (480a b + 240a )cosh(x) +--R + +--R 144a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168a b + 168a )cosh(x) + (360a b + 180a )cosh(x) +--R + +--R 2 2 +--R 216a b cosh(x) + 24a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (48a b + 48a )cosh(x) + (144a b + 72a )cosh(x) +--R + +--R 3 2 +--R 144a b cosh(x) + (48a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (6a b + 6a )cosh(x) + (24a b + 12a )cosh(x) + 36a b cosh(x) +--R + +--R 2 2 2 +--R (24a b - 12a )cosh(x) + 6a b - 6a +--R * +--R x 5 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6b + 6a b)sinh(x) + (48b + 48a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168b + 168a b)cosh(x) + 24b + 12a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((336b + 336a b)cosh(x) + (144b + 72a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((420b + 420a b)cosh(x) + (360b + 180a b)cosh(x) + 36b )sinh(x) +--R + +--R 2 5 2 3 +--R (336b + 336a b)cosh(x) + (480b + 240a b)cosh(x) +--R + +--R 2 +--R 144b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168b + 168a b)cosh(x) + (360b + 180a b)cosh(x) +--R + +--R 2 2 2 +--R 216b cosh(x) + 24b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (48b + 48a b)cosh(x) + (144b + 72a b)cosh(x) + 144b cosh(x) +--R + +--R 2 +--R (48b - 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (6b + 6a b)cosh(x) + (24b + 12a b)cosh(x) + 36b cosh(x) +--R + +--R 2 2 2 +--R (24b - 12a b)cosh(x) + 6b - 6a b +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (6a b + 6a )sinh(x) + (48a b + 48a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((168a b + 168a )cosh(x) + 24a b + 12a )sinh(x) +--R + +--R 2 3 2 5 +--R ((336a b + 336a )cosh(x) + (144a b + 72a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((420a b + 420a )cosh(x) + (360a b + 180a )cosh(x) + 36a b)sinh(x) +--R + +--R 2 5 2 3 +--R (336a b + 336a )cosh(x) + (480a b + 240a )cosh(x) +--R + +--R 144a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (168a b + 168a )cosh(x) + (360a b + 180a )cosh(x) +--R + +--R 2 2 +--R 216a b cosh(x) + 24a b - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R (48a b + 48a )cosh(x) + (144a b + 72a )cosh(x) +--R + +--R 3 2 +--R 144a b cosh(x) + (48a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (6a b + 6a )cosh(x) + (24a b + 12a )cosh(x) + 36a b cosh(x) +--R + +--R 2 2 2 +--R (24a b - 12a )cosh(x) + 6a b - 6a +--R * +--R x 3 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (4b + 4a b)sinh(x) + (32b + 32a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((112b + 112a b)cosh(x) + 16b + 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((224b + 224a b)cosh(x) + (96b + 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((280b + 280a b)cosh(x) + (240b + 120a b)cosh(x) + 24b )sinh(x) +--R + +--R 2 5 2 3 2 +--R ((224b + 224a b)cosh(x) + (320b + 160a b)cosh(x) + 96b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (112b + 112a b)cosh(x) + (240b + 120a b)cosh(x) +--R + +--R 2 2 2 +--R 144b cosh(x) + 16b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (32b + 32a b)cosh(x) + (96b + 48a b)cosh(x) + 96b cosh(x) +--R + +--R 2 +--R (32b - 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (4b + 4a b)cosh(x) + (16b + 8a b)cosh(x) + 24b cosh(x) +--R + +--R 2 2 2 +--R (16b - 8a b)cosh(x) + 4b - 4a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (2a b + 2a )sinh(x) + (16a b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((56a b + 56a )cosh(x) + 8a b + 4a )sinh(x) +--R + +--R 2 3 2 5 +--R ((112a b + 112a )cosh(x) + (48a b + 24a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R ((140a b + 140a )cosh(x) + (120a b + 60a )cosh(x) + 12a b)sinh(x) +--R + +--R 2 5 2 3 +--R (112a b + 112a )cosh(x) + (160a b + 80a )cosh(x) +--R + +--R 48a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 2 +--R (56a b + 56a )cosh(x) + (120a b + 60a )cosh(x) + 72a b cosh(x) +--R + +--R 2 +--R 8a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 3 +--R (16a b + 16a )cosh(x) + (48a b + 24a )cosh(x) + 48a b cosh(x) +--R + +--R 2 +--R (16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 4 +--R (2a b + 2a )cosh(x) + (8a b + 4a )cosh(x) + 12a b cosh(x) +--R + +--R 2 2 2 +--R (8a b - 4a )cosh(x) + 2a b - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 8 2 7 +--R (b + a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R ((28b + 28a b)cosh(x) + 4b + 2a b)sinh(x) +--R + +--R 2 3 2 5 +--R ((56b + 56a b)cosh(x) + (24b + 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 4 +--R ((70b + 70a b)cosh(x) + (60b + 30a b)cosh(x) + 6b )sinh(x) +--R + +--R 2 5 2 3 2 3 +--R ((56b + 56a b)cosh(x) + (80b + 40a b)cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R (28b + 28a b)cosh(x) + (60b + 30a b)cosh(x) + 36b cosh(x) + 4b +--R + +--R - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 2 3 +--R (8b + 8a b)cosh(x) + (24b + 12a b)cosh(x) + 24b cosh(x) +--R + +--R 2 +--R (8b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 4 +--R (b + a b)cosh(x) + (4b + 2a b)cosh(x) + 6b cosh(x) +--R + +--R 2 2 2 +--R (4b - 2a b)cosh(x) + b - a b +--R Type: Expression(Integer) +--E 97 + +--S 98 of 526 +t0619:= sech(x)^4/(a+b*coth(x)) +--R +--R +--R 4 +--R sech(x) +--R (98) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 98 + +--S 99 of 526 +r0619:= -b*(a^2-b^2)*log(b+a*tanh(x))/a^4+(a^2-b^2)*tanh(x)/a^3+_ + 1/2*b*tanh(x)^2/a^2-1/3*tanh(x)^3/a +--R +--R +--R (99) +--R 3 2 3 3 2 2 +--R (6b - 6a b)log(a tanh(x) + b) - 2a tanh(x) + 3a b tanh(x) +--R + +--R 2 3 +--R (- 6a b + 6a )tanh(x) +--R / +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 99 + +--S 100 of 526 +a0619:= integrate(t0619,x) +--R +--R +--R (100) +--R 3 2 6 3 2 5 +--R (- 3b + 3a b)sinh(x) + (- 18b + 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 45b + 45a b)cosh(x) - 9b + 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 60b + 60a b)cosh(x) + (- 36b + 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((- 45b + 45a b)cosh(x) + (- 54b + 54a b)cosh(x) - 9b + 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 18b + 18a b)cosh(x) + (- 36b + 36a b)cosh(x) +--R + +--R 3 2 +--R (- 18b + 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 3b + 3a b)cosh(x) + (- 9b + 9a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 9b + 9a b)cosh(x) - 3b + 3a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 6 3 2 5 +--R (3b - 3a b)sinh(x) + (18b - 18a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((45b - 45a b)cosh(x) + 9b - 9a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((60b - 60a b)cosh(x) + (36b - 36a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((45b - 45a b)cosh(x) + (54b - 54a b)cosh(x) + 9b - 9a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (18b - 18a b)cosh(x) + (36b - 36a b)cosh(x) +--R + +--R 3 2 +--R (18b - 18a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (3b - 3a b)cosh(x) + (9b - 9a b)cosh(x) + (9b - 9a b)cosh(x) +--R + +--R 3 2 +--R 3b - 3a b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (6a b - 6a b)sinh(x) + (24a b - 24a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((36a b - 36a b)cosh(x) + 12a b - 6a b - 12a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((24a b - 24a b)cosh(x) + (24a b - 12a b - 24a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 3 +--R (6a b - 6a b)cosh(x) + (12a b - 6a b - 12a )cosh(x) + 6a b - 4a +--R / +--R 4 6 4 5 4 2 4 4 +--R 3a sinh(x) + 18a cosh(x)sinh(x) + (45a cosh(x) + 9a )sinh(x) +--R + +--R 4 3 4 3 +--R (60a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (45a cosh(x) + 54a cosh(x) + 9a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (18a cosh(x) + 36a cosh(x) + 18a cosh(x))sinh(x) + 3a cosh(x) +--R + +--R 4 4 4 2 4 +--R 9a cosh(x) + 9a cosh(x) + 3a +--R Type: Union(Expression(Integer),...) +--E 100 + +--S 101 of 526 +m0619:= a0619-r0619 +--R +--R +--R (101) +--R 3 2 6 3 2 5 +--R (- 6b + 6a b)sinh(x) + (- 36b + 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 90a b)cosh(x) - 18b + 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 120a b)cosh(x) + (- 72b + 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b + 90a b)cosh(x) + (- 108b + 108a b)cosh(x) - 18b +--R + +--R 2 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 36a b)cosh(x) + (- 72b + 72a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 6a b)cosh(x) + (- 18b + 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 18a b)cosh(x) - 6b + 6a b +--R * +--R log(a tanh(x) + b) +--R + +--R 3 2 6 3 2 5 +--R (- 6b + 6a b)sinh(x) + (- 36b + 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 90b + 90a b)cosh(x) - 18b + 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 120b + 120a b)cosh(x) + (- 72b + 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 90b + 90a b)cosh(x) + (- 108b + 108a b)cosh(x) - 18b +--R + +--R 2 +--R 18a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 36b + 36a b)cosh(x) + (- 72b + 72a b)cosh(x) +--R + +--R 3 2 +--R (- 36b + 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b + 6a b)cosh(x) + (- 18b + 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 18b + 18a b)cosh(x) - 6b + 6a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 6 3 2 5 +--R (6b - 6a b)sinh(x) + (36b - 36a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((90b - 90a b)cosh(x) + 18b - 18a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((120b - 120a b)cosh(x) + (72b - 72a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((90b - 90a b)cosh(x) + (108b - 108a b)cosh(x) + 18b - 18a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (36b - 36a b)cosh(x) + (72b - 72a b)cosh(x) +--R + +--R 3 2 +--R (36b - 36a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (6b - 6a b)cosh(x) + (18b - 18a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (18b - 18a b)cosh(x) + 6b - 6a b +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 3 6 3 5 3 2 3 4 +--R 2a sinh(x) + 12a cosh(x)sinh(x) + (30a cosh(x) + 6a )sinh(x) +--R + +--R 3 3 3 3 +--R (40a cosh(x) + 24a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (30a cosh(x) + 36a cosh(x) + 6a )sinh(x) +--R + +--R 3 5 3 3 3 3 6 +--R (12a cosh(x) + 24a cosh(x) + 12a cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 3 4 3 2 3 +--R 6a cosh(x) + 6a cosh(x) + 2a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 6 2 5 +--R - 3a b sinh(x) - 18a b cosh(x)sinh(x) +--R + +--R 2 2 2 4 +--R (- 45a b cosh(x) - 9a b)sinh(x) +--R + +--R 2 3 2 3 +--R (- 60a b cosh(x) - 36a b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 45a b cosh(x) - 54a b cosh(x) - 9a b)sinh(x) +--R + +--R 2 5 2 3 2 +--R (- 18a b cosh(x) - 36a b cosh(x) - 18a b cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R - 3a b cosh(x) - 9a b cosh(x) - 9a b cosh(x) - 3a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 6 2 3 5 +--R (6a b - 6a )sinh(x) + (36a b - 36a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((90a b - 90a )cosh(x) + 18a b - 18a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((120a b - 120a )cosh(x) + (72a b - 72a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (90a b - 90a )cosh(x) + (108a b - 108a )cosh(x) + 18a b +--R + +--R 3 +--R - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (36a b - 36a )cosh(x) + (72a b - 72a )cosh(x) +--R + +--R 2 3 +--R (36a b - 36a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (6a b - 6a )cosh(x) + (18a b - 18a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (18a b - 18a )cosh(x) + 6a b - 6a +--R * +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (12a b - 12a b)sinh(x) + (48a b - 48a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((72a b - 72a b)cosh(x) + 24a b - 12a b - 24a )sinh(x) +--R + +--R 2 2 3 2 2 3 +--R ((48a b - 48a b)cosh(x) + (48a b - 24a b - 48a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 3 2 2 3 +--R (12a b - 12a b)cosh(x) + (24a b - 12a b - 24a )cosh(x) + 12a b - 8a +--R / +--R 4 6 4 5 4 2 4 4 +--R 6a sinh(x) + 36a cosh(x)sinh(x) + (90a cosh(x) + 18a )sinh(x) +--R + +--R 4 3 4 3 +--R (120a cosh(x) + 72a cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (90a cosh(x) + 108a cosh(x) + 18a )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (36a cosh(x) + 72a cosh(x) + 36a cosh(x))sinh(x) + 6a cosh(x) +--R + +--R 4 4 4 2 4 +--R 18a cosh(x) + 18a cosh(x) + 6a +--R Type: Expression(Integer) +--E 101 + +--S 102 of 526 +d0619:= D(m0619,x) +--R +--R +--R (102) +--R 4 9 3 4 2 8 +--R - a cosh(x)sinh(x) + (- a b - 8a )cosh(x) sinh(x) +--R + +--R 3 4 3 4 7 +--R ((- 8a b - 28a )cosh(x) - 4a cosh(x))sinh(x) +--R + +--R 3 4 4 3 4 2 6 +--R ((- 28a b - 56a )cosh(x) + (- 4a b - 24a )cosh(x) )sinh(x) +--R + +--R 3 4 5 3 4 3 4 +--R ((- 56a b - 70a )cosh(x) + (- 24a b - 60a )cosh(x) - 6a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 6 3 4 4 +--R (- 70a b - 56a )cosh(x) + (- 60a b - 80a )cosh(x) +--R + +--R 3 4 2 +--R (- 6a b - 24a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 7 3 4 5 +--R (- 56a b - 28a )cosh(x) + (- 80a b - 60a )cosh(x) +--R + +--R 3 4 3 4 +--R (- 24a b - 36a )cosh(x) - 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 8 3 4 6 +--R (- 28a b - 8a )cosh(x) + (- 60a b - 24a )cosh(x) +--R + +--R 3 4 4 3 4 2 +--R (- 36a b - 24a )cosh(x) + (- 4a b - 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 9 3 4 7 +--R (- 8a b - a )cosh(x) + (- 24a b - 4a )cosh(x) +--R + +--R 3 4 5 3 4 3 4 +--R (- 24a b - 6a )cosh(x) + (- 8a b - 4a )cosh(x) - a cosh(x) +--R * +--R sinh(x) +--R + +--R 3 10 3 8 3 6 3 4 +--R - a b cosh(x) - 4a b cosh(x) - 6a b cosh(x) - 4a b cosh(x) +--R + +--R 3 2 +--R - a b cosh(x) +--R * +--R 5 +--R tanh(x) +--R + +--R 4 9 3 4 2 8 +--R 2a cosh(x)sinh(x) + (2a b + 16a )cosh(x) sinh(x) +--R + +--R 3 4 3 4 7 +--R ((16a b + 56a )cosh(x) + 8a cosh(x))sinh(x) +--R + +--R 3 4 4 3 4 2 6 +--R ((56a b + 112a )cosh(x) + (8a b + 48a )cosh(x) )sinh(x) +--R + +--R 3 4 5 3 4 3 4 +--R ((112a b + 140a )cosh(x) + (48a b + 120a )cosh(x) + 12a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 6 3 4 4 +--R (140a b + 112a )cosh(x) + (120a b + 160a )cosh(x) +--R + +--R 3 4 2 +--R (12a b + 48a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 7 3 4 5 +--R (112a b + 56a )cosh(x) + (160a b + 120a )cosh(x) +--R + +--R 3 4 3 4 +--R (48a b + 72a )cosh(x) + 8a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 8 3 4 6 +--R (56a b + 16a )cosh(x) + (120a b + 48a )cosh(x) +--R + +--R 3 4 4 3 4 2 +--R (72a b + 48a )cosh(x) + (8a b + 16a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 9 3 4 7 +--R (16a b + 2a )cosh(x) + (48a b + 8a )cosh(x) +--R + +--R 3 4 5 3 4 3 4 +--R (48a b + 12a )cosh(x) + (16a b + 8a )cosh(x) + 2a cosh(x) +--R * +--R sinh(x) +--R + +--R 3 10 3 8 3 6 3 4 +--R 2a b cosh(x) + 8a b cosh(x) + 12a b cosh(x) + 8a b cosh(x) +--R + +--R 3 2 +--R 2a b cosh(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 3 3 10 3 3 4 9 +--R (- a b + a b)sinh(x) + (- 8a b + 8a b - a )cosh(x)sinh(x) +--R + +--R 3 3 4 2 3 3 8 +--R ((- 27a b + 26a b - 8a )cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 3 3 4 3 +--R (- 48a b + 40a b - 28a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 24a b - 4a b + 28a b - 4a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 3 4 4 +--R (- 42a b + 14a b - 56a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (- 60a b - 20a b + 76a b - 24a )cosh(x) - 6a b + 6a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 5 +--R (- 56a b - 70a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 80a b - 36a b + 92a b - 60a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 24a b - 8a b + 24a b + 10a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 3 4 6 +--R (42a b - 112a b - 56a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 60a b - 20a b + 20a b - 80a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (- 38a b - 32a b + 40a b + 40a )cosh(x) - 4a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 4 7 +--R (48a b - 104a b - 28a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 24a b + 20a b - 76a b - 60a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 32a b - 48a b + 40a b + 60a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 8a b - 4a b + 4a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 8 +--R (27a b - 55a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 6 +--R (- 4a b + 36a b - 92a b - 24a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 18a b - 32a b + 30a b + 40a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (- 4a b - 12a b - 12a b - 8a )cosh(x) - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 9 2 2 3 4 7 +--R (8a b - 16a b - a )cosh(x) + (20a b - 44a b - 4a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 8a b - 8a b + 16a b + 10a )cosh(x) +--R + +--R 2 2 3 4 3 4 +--R (- 12a b - 20a b - 4a )cosh(x) - a cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 10 2 2 3 8 +--R (a b - 2a b)cosh(x) + (4a b - 8a b)cosh(x) +--R + +--R 3 3 6 2 2 3 4 +--R (- 2a b + 4a b)cosh(x) + (- 4a b - 8a b)cosh(x) +--R + +--R 3 3 2 +--R (a b - 2a b)cosh(x) +--R * +--R tanh(x) +--R + +--R 4 2 2 10 4 2 2 9 +--R (- b + a b )sinh(x) + (- 8b + 8a b )cosh(x)sinh(x) +--R + +--R 4 2 2 2 4 2 2 8 +--R ((- 27b + 27a b )cosh(x) - 4b + 4a b )sinh(x) +--R + +--R 4 2 2 3 4 3 2 2 7 +--R ((- 48b + 48a b )cosh(x) + (- 24b - 4a b + 28a b )cosh(x))sinh(x) +--R + +--R 4 2 2 4 4 3 2 2 2 4 +--R (- 42b + 42a b )cosh(x) + (- 60b - 20a b + 80a b )cosh(x) - 6b +--R + +--R 2 2 +--R 6a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 +--R (- 80b - 36a b + 116a b )cosh(x) +--R + +--R 4 3 2 2 3 +--R (- 24b - 8a b + 24a b + 16a b)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 6 4 3 2 2 4 +--R (42b - 42a b )cosh(x) + (- 60b - 20a b + 80a b )cosh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (- 38b - 32a b + 46a b + 64a b)cosh(x) - 4b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 7 4 3 2 2 5 +--R (48b - 48a b )cosh(x) + (- 24b + 20a b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 32b - 48a b + 64a b + 96a b)cosh(x) +--R + +--R 4 3 2 2 +--R (- 8b - 4a b + 4a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 8 4 3 2 2 6 +--R (27b - 27a b )cosh(x) + (- 4b + 36a b - 32a b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 18b - 32a b + 66a b + 64a b)cosh(x) +--R + +--R 4 3 2 2 2 4 2 2 +--R (- 4b - 12a b - 8a b )cosh(x) - b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 9 3 2 2 7 +--R (8b - 8a b )cosh(x) + (20a b - 20a b )cosh(x) +--R + +--R 4 3 2 2 3 5 3 2 2 3 +--R (- 8b - 8a b + 40a b + 16a b)cosh(x) + (- 12a b - 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 10 3 2 2 8 4 2 2 6 +--R (b - a b )cosh(x) + (4a b - 4a b )cosh(x) + (- 2b + 10a b )cosh(x) +--R + +--R 3 2 2 4 4 2 2 2 +--R (- 4a b - 4a b )cosh(x) + (b - a b )cosh(x) +--R / +--R 5 9 4 5 2 8 +--R a cosh(x)sinh(x) + (a b + 8a )cosh(x) sinh(x) +--R + +--R 4 5 3 5 7 +--R ((8a b + 28a )cosh(x) + 4a cosh(x))sinh(x) +--R + +--R 4 5 4 4 5 2 6 +--R ((28a b + 56a )cosh(x) + (4a b + 24a )cosh(x) )sinh(x) +--R + +--R 4 5 5 4 5 3 5 +--R ((56a b + 70a )cosh(x) + (24a b + 60a )cosh(x) + 6a cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 5 6 4 5 4 +--R (70a b + 56a )cosh(x) + (60a b + 80a )cosh(x) +--R + +--R 4 5 2 +--R (6a b + 24a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 7 4 5 5 +--R (56a b + 28a )cosh(x) + (80a b + 60a )cosh(x) +--R + +--R 4 5 3 5 +--R (24a b + 36a )cosh(x) + 4a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 8 4 5 6 +--R (28a b + 8a )cosh(x) + (60a b + 24a )cosh(x) +--R + +--R 4 5 4 4 5 2 +--R (36a b + 24a )cosh(x) + (4a b + 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 9 4 5 7 +--R (8a b + a )cosh(x) + (24a b + 4a )cosh(x) +--R + +--R 4 5 5 4 5 3 5 +--R (24a b + 6a )cosh(x) + (8a b + 4a )cosh(x) + a cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 4 8 4 6 4 4 +--R a b cosh(x) + 4a b cosh(x) + 6a b cosh(x) + 4a b cosh(x) +--R + +--R 4 2 +--R a b cosh(x) +--R * +--R tanh(x) +--R + +--R 4 9 3 2 4 2 8 +--R a b cosh(x)sinh(x) + (a b + 8a b)cosh(x) sinh(x) +--R + +--R 3 2 4 3 4 7 +--R ((8a b + 28a b)cosh(x) + 4a b cosh(x))sinh(x) +--R + +--R 3 2 4 4 3 2 4 2 6 +--R ((28a b + 56a b)cosh(x) + (4a b + 24a b)cosh(x) )sinh(x) +--R + +--R 3 2 4 5 3 2 4 3 4 +--R ((56a b + 70a b)cosh(x) + (24a b + 60a b)cosh(x) + 6a b cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 6 3 2 4 4 +--R (70a b + 56a b)cosh(x) + (60a b + 80a b)cosh(x) +--R + +--R 3 2 4 2 +--R (6a b + 24a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 4 7 3 2 4 5 +--R (56a b + 28a b)cosh(x) + (80a b + 60a b)cosh(x) +--R + +--R 3 2 4 3 4 +--R (24a b + 36a b)cosh(x) + 4a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 8 3 2 4 6 +--R (28a b + 8a b)cosh(x) + (60a b + 24a b)cosh(x) +--R + +--R 3 2 4 4 3 2 4 2 +--R (36a b + 24a b)cosh(x) + (4a b + 8a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 9 3 2 4 7 +--R (8a b + a b)cosh(x) + (24a b + 4a b)cosh(x) +--R + +--R 3 2 4 5 3 2 4 3 4 +--R (24a b + 6a b)cosh(x) + (8a b + 4a b)cosh(x) + a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 10 3 2 8 3 2 6 3 2 4 +--R a b cosh(x) + 4a b cosh(x) + 6a b cosh(x) + 4a b cosh(x) +--R + +--R 3 2 2 +--R a b cosh(x) +--R Type: Expression(Integer) +--E 102 + +--S 103 of 526 +t0620:= sech(x)/(1+coth(x)) +--R +--R +--R sech(x) +--R (103) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 103 + +--S 104 of 526 +r0620:= atan(sinh(x))+cosh(x)-sinh(x) +--R +--R +--R (104) atan(sinh(x)) - sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 104 + +--S 105 of 526 +a0620:= integrate(t0620,x) +--R +--R +--R (2sinh(x) + 2cosh(x))atan(sinh(x) + cosh(x)) + 1 +--R (105) ------------------------------------------------ +--R sinh(x) + cosh(x) +--R Type: Union(Expression(Integer),...) +--E 105 + +--S 106 of 526 +m0620:= a0620-r0620 +--R +--R +--R (106) +--R (2sinh(x) + 2cosh(x))atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R (- sinh(x) - cosh(x))atan(sinh(x)) + sinh(x) - cosh(x) + 1 +--R / +--R sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 526 +d0620:= D(m0620,x) +--R +--R +--R (107) +--R 6 5 4 3 3 +--R - sinh(x) - 2cosh(x)sinh(x) - sinh(x) + (2cosh(x) - cosh(x))sinh(x) +--R + +--R 4 2 2 3 +--R (cosh(x) - cosh(x) - 1)sinh(x) + (- cosh(x) + cosh(x))sinh(x) +--R + +--R 2 +--R cosh(x) - 1 +--R / +--R 5 4 2 3 +--R sinh(x) + 3cosh(x)sinh(x) + (3cosh(x) + 2)sinh(x) +--R + +--R 3 2 2 3 +--R (cosh(x) + 4cosh(x))sinh(x) + (3cosh(x) + 1)sinh(x) + cosh(x) + cosh(x) +--R Type: Expression(Integer) +--E 107 + +--S 108 of 526 +t0621:= sech(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R sech(x) +--R (108) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 108 + +--S 109 of 526 +r0621:= -log(1+tanh(x))+tanh(x) +--R +--R +--R (109) - log(tanh(x) + 1) + tanh(x) +--R Type: Expression(Integer) +--E 109 + +--S 110 of 526 +a0621:= integrate(t0621,x) +--R +--R +--R (110) +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 2x sinh(x) - 4x cosh(x)sinh(x) - 2x cosh(x) - 2x - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 110 + +--S 111 of 526 +m0621:= a0621-r0621 +--R +--R +--R (111) +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(tanh(x) + 1) +--R + +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)tanh(x) - 2x sinh(x) +--R + +--R 2 +--R - 4x cosh(x)sinh(x) - 2x cosh(x) - 2x - 2 +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 526 +d0621:= D(m0621,x) +--R +--R +--R (112) +--R 4 2 3 3 2 +--R cosh(x)sinh(x) + 4cosh(x) sinh(x) + (6cosh(x) + 2cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (4cosh(x) + 4cosh(x) )sinh(x) + cosh(x) + 2cosh(x) + cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 2 3 +--R - cosh(x)sinh(x) - 4cosh(x) sinh(x) +--R + +--R 3 2 4 2 +--R (- 6cosh(x) - 2cosh(x))sinh(x) + (- 4cosh(x) - 4cosh(x) )sinh(x) +--R + +--R 5 3 +--R - cosh(x) - 2cosh(x) - cosh(x) +--R * +--R tanh(x) +--R + +--R 5 4 2 3 +--R sinh(x) + 3cosh(x)sinh(x) + (2cosh(x) + 2)sinh(x) +--R + +--R 3 2 4 2 +--R (- 2cosh(x) + 6cosh(x))sinh(x) + (- 3cosh(x) + 6cosh(x) + 1)sinh(x) +--R + +--R 5 3 +--R - cosh(x) + 2cosh(x) - cosh(x) +--R / +--R 4 2 3 3 2 +--R cosh(x)sinh(x) + 4cosh(x) sinh(x) + (6cosh(x) + 2cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (4cosh(x) + 4cosh(x) )sinh(x) + cosh(x) + 2cosh(x) + cosh(x) +--R Type: Expression(Integer) +--E 112 + +--S 113 of 526 +t0622:= sech(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R sech(x) +--R (113) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 113 + +--S 114 of 526 +r0622:= -1/2*atan(sinh(x))-sech(x)+1/2*sech(x)*tanh(x) +--R +--R +--R - atan(sinh(x)) + sech(x)tanh(x) - 2sech(x) +--R (114) ------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 526 +a0622:= integrate(t0622,x) +--R +--R +--R (115) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) - 4cosh(x))sinh(x) - cosh(x) - 2cosh(x) - 1 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 2 2 3 +--R - sinh(x) - 3cosh(x)sinh(x) + (- 3cosh(x) - 3)sinh(x) - cosh(x) +--R + +--R - 3cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 115 + +--S 116 of 526 +m0622:= a0622-r0622 +--R +--R +--R (116) +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) - 8cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) - 2 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R * +--R atan(sinh(x)) +--R + +--R 4 3 +--R - sech(x)sinh(x) - 4cosh(x)sech(x)sinh(x) +--R + +--R 2 2 +--R (- 6cosh(x) - 2)sech(x)sinh(x) +--R + +--R 3 +--R (- 4cosh(x) - 4cosh(x))sech(x)sinh(x) +--R + +--R 4 2 +--R (- cosh(x) - 2cosh(x) - 1)sech(x) +--R * +--R tanh(x) +--R + +--R 4 3 +--R 2sech(x)sinh(x) + (8cosh(x)sech(x) - 2)sinh(x) +--R + +--R 2 2 +--R ((12cosh(x) + 4)sech(x) - 6cosh(x))sinh(x) +--R + +--R 3 2 +--R ((8cosh(x) + 8cosh(x))sech(x) - 6cosh(x) - 6)sinh(x) +--R + +--R 4 2 3 +--R (2cosh(x) + 4cosh(x) + 2)sech(x) - 2cosh(x) - 6cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) + 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) + 8cosh(x))sinh(x) + 2cosh(x) + 4cosh(x) + 2 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 526 +d0622:= D(m0622,x) +--R +--R +--R (117) +--R 8 7 +--R 2sech(x)sinh(x) + 12cosh(x)sech(x)sinh(x) +--R + +--R 2 6 +--R (30cosh(x) + 8)sech(x)sinh(x) +--R + +--R 3 5 +--R (40cosh(x) + 36cosh(x))sech(x)sinh(x) +--R + +--R 4 2 4 +--R (30cosh(x) + 66cosh(x) + 12)sech(x)sinh(x) +--R + +--R 5 3 3 +--R (12cosh(x) + 64cosh(x) + 36cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 2 +--R (2cosh(x) + 36cosh(x) + 42cosh(x) + 8)sech(x)sinh(x) +--R + +--R 5 3 +--R (12cosh(x) + 24cosh(x) + 12cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 +--R (2cosh(x) + 6cosh(x) + 6cosh(x) + 2)sech(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R - 2sech(x)sinh(x) - 12cosh(x)sech(x)sinh(x) +--R + +--R 2 6 +--R (- 30cosh(x) - 8)sech(x)sinh(x) +--R + +--R 3 5 +--R (- 40cosh(x) - 36cosh(x))sech(x)sinh(x) +--R + +--R 4 2 4 +--R (- 30cosh(x) - 66cosh(x) - 12)sech(x)sinh(x) +--R + +--R 5 3 3 +--R (- 12cosh(x) - 64cosh(x) - 36cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 2 +--R (- 2cosh(x) - 36cosh(x) - 42cosh(x) - 8)sech(x)sinh(x) +--R + +--R 5 3 +--R (- 12cosh(x) - 24cosh(x) - 12cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 +--R (- 2cosh(x) - 6cosh(x) - 6cosh(x) - 2)sech(x) +--R * +--R tanh(x) +--R + +--R 8 7 +--R - sech(x)sinh(x) - 6cosh(x)sech(x)sinh(x) +--R + +--R 2 6 +--R ((- 15cosh(x) - 4)sech(x) + cosh(x))sinh(x) +--R + +--R 3 2 5 +--R ((- 20cosh(x) - 18cosh(x))sech(x) + 6cosh(x) + 8)sinh(x) +--R + +--R 4 2 3 4 +--R ((- 15cosh(x) - 33cosh(x) - 6)sech(x) + 15cosh(x) + 27cosh(x))sinh(x) +--R + +--R 5 3 4 +--R (- 6cosh(x) - 32cosh(x) - 18cosh(x))sech(x) + 20cosh(x) +--R + +--R 2 +--R 36cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 5 +--R (- cosh(x) - 18cosh(x) - 21cosh(x) - 4)sech(x) + 15cosh(x) +--R + +--R 3 +--R 26cosh(x) + 19cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 4 +--R (- 6cosh(x) - 12cosh(x) - 6cosh(x))sech(x) + 6cosh(x) + 12cosh(x) +--R + +--R 2 +--R 30cosh(x) - 8 +--R * +--R sinh(x) +--R + +--R 6 4 2 7 5 +--R (- cosh(x) - 3cosh(x) - 3cosh(x) - 1)sech(x) + cosh(x) + 3cosh(x) +--R + +--R 3 +--R 11cosh(x) - 7cosh(x) +--R / +--R 8 7 2 6 +--R 2sinh(x) + 12cosh(x)sinh(x) + (30cosh(x) + 8)sinh(x) +--R + +--R 3 5 4 2 4 +--R (40cosh(x) + 36cosh(x))sinh(x) + (30cosh(x) + 66cosh(x) + 12)sinh(x) +--R + +--R 5 3 3 +--R (12cosh(x) + 64cosh(x) + 36cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (2cosh(x) + 36cosh(x) + 42cosh(x) + 8)sinh(x) +--R + +--R 5 3 6 4 +--R (12cosh(x) + 24cosh(x) + 12cosh(x))sinh(x) + 2cosh(x) + 6cosh(x) +--R + +--R 2 +--R 6cosh(x) + 2 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 526 +t0623:= sech(x)/(%i+2*coth(x)) +--R +--R +--R sech(x) +--R (118) ------------- +--R 2coth(x) + %i +--R Type: Expression(Complex(Integer)) +--E 118 + +--S 119 of 526 +r0623:= -%i*atan(sinh(x))+2/5*%i*atan(1/5*(%i*cosh(x)+_ + 2*sinh(x))*5^(1/2))*5^(1/2) +--R +--R +--R 2 +-+ 2 +-+ 1 +-+ +--R (119) - %i\|5 atan(- \|5 sinh(x) + - %i\|5 cosh(x)) - %i atan(sinh(x)) +--R 5 5 5 +--R Type: Expression(Complex(Fraction(Integer))) +--E 119 + +--S 120 of 526 +a0623:= integrate(t0623,x) +--R +--R +--R (120) +--R +-+ +-+ +--R \|5 log(sinh(x) + cosh(x) + %i) - \|5 log(sinh(x) + cosh(x) - %i) +--R + +--R +-+ +-+ +--R - 2%i\|5 sinh(x) + \|5 cosh(x) - 5 +--R 2log(----------------------------------) +--R sinh(x) - 2%i cosh(x) +--R / +--R +-+ +--R \|5 +--R Type: Union(Expression(Complex(Integer)),...) +--E 120 + +--S 121 of 526 +m0623:= a0623-r0623 +--R +--R +--R (121) +--R +-+ +-+ +--R \|5 log(sinh(x) + cosh(x) + %i) - \|5 log(sinh(x) + cosh(x) - %i) +--R + +--R +-+ +-+ +--R - 2%i\|5 sinh(x) + \|5 cosh(x) - 5 +--R 2log(----------------------------------) +--R sinh(x) - 2%i cosh(x) +--R + +--R 2 +-+ 1 +-+ +-+ +--R - 2%i atan(- \|5 sinh(x) + - %i\|5 cosh(x)) + %i\|5 atan(sinh(x)) +--R 5 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Complex(Fraction(Integer))) +--E 121 + +--S 122 of 526 +d0623:= D(m0623,x) +--R +--R +--R (122) +--R 8 5 +-+ 7 +--R 5%i sinh(x) + ((- 5 + 10%i)cosh(x) + (- - 2%i)\|5 )sinh(x) +--R 2 +--R + +--R 5 2 1 +-+ 6 +--R ((- 10 - - %i)cosh(x) + (4 + - %i)\|5 cosh(x) - 5 + 15%i)sinh(x) +--R 4 4 +--R + +--R 25 3 1 +-+ 2 35 +--R - -- %i cosh(x) - - \|5 cosh(x) + (- -- + 25%i)cosh(x) +--R 2 2 2 +--R + +--R 15 9 +-+ +--R (-- - - %i)\|5 +--R 2 2 +--R * +--R 5 +--R sinh(x) +--R + +--R 4 5 5 +-+ 3 95 5 2 +--R (10 - 5%i)cosh(x) + (- - - - %i)\|5 cosh(x) + (- -- - - %i)cosh(x) +--R 4 4 4 4 +--R + +--R 21 3 +-+ 45 +--R (-- + - %i)\|5 cosh(x) - -- + 15%i +--R 4 2 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 5 5 5 +-+ 4 +--R (5 + - %i)cosh(x) + (- - + - %i)\|5 cosh(x) +--R 2 8 2 +--R + +--R 15 45 3 19 1 +-+ 2 +--R (- -- - -- %i)cosh(x) + (- -- + - %i)\|5 cosh(x) +--R 8 2 8 2 +--R + +--R 165 55 15 5 +-+ +--R (- --- + -- %i)cosh(x) + (-- - - %i)\|5 +--R 8 2 2 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 6 11 5 +-+ 5 75 35 4 +--R - %i cosh(x) + (- -- + - %i)\|5 cosh(x) + (-- - -- %i)cosh(x) +--R 4 4 4 4 4 +--R + +--R 3 9 +-+ 3 25 2 5 5 +-+ +--R (- - - %i)\|5 cosh(x) + (- -- + 5%i)cosh(x) + (- + - %i)\|5 cosh(x) +--R 2 4 2 4 2 +--R + +--R 25 +--R - -- + 5%i +--R 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 1 +-+ 6 75 5 +--R (- -- - - %i)\|5 cosh(x) + (-- + 5%i)cosh(x) +--R 8 2 8 +--R + +--R 3 1 +-+ 4 5 35 3 15 +-+ 2 +--R (- + - %i)\|5 cosh(x) + (- - - -- %i)cosh(x) - -- \|5 cosh(x) +--R 4 2 4 2 8 +--R + +--R 65 25 5 +-+ +--R (- -- + -- %i)cosh(x) + - \|5 +--R 8 2 2 +--R * +--R sinh(x) +--R + +--R 1 +-+ 7 5 6 1 +-+ 5 15 4 +--R - - %i\|5 cosh(x) + - %i cosh(x) + - %i\|5 cosh(x) - -- %i cosh(x) +--R 4 2 4 2 +--R + +--R 5 +-+ 3 2 5 +-+ +--R - - %i\|5 cosh(x) + 5%i cosh(x) + - %i\|5 cosh(x) +--R 4 4 +--R / +--R +-+ 8 1 +-+ 5 7 +--R \|5 sinh(x) + ((2 - - %i)\|5 cosh(x) - - %i)sinh(x) +--R 2 2 +--R + +--R 13 +-+ 2 5 13 +-+ 6 +--R ((-- - %i)\|5 cosh(x) + (- - - 5%i)cosh(x) + -- \|5 )sinh(x) +--R 4 2 4 +--R + +--R 9 7 +-+ 3 55 2 +--R (- + - %i)\|5 cosh(x) + (- 5 - -- %i)cosh(x) +--R 2 8 8 +--R + +--R 9 23 +-+ 65 +--R (- - -- %i)\|5 cosh(x) - -- %i +--R 2 8 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 11 +-+ 4 5 35 3 +--R (2 + -- %i)\|5 cosh(x) + (- - - -- %i)cosh(x) +--R 4 4 4 +--R + +--R 19 +-+ 2 45 45 7 +-+ +--R (8 - -- %i)\|5 cosh(x) + (- -- - -- %i)cosh(x) + - \|5 +--R 4 4 4 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 1 11 +-+ 5 5 35 4 +--R (- - + -- %i)\|5 cosh(x) + (- - -- %i)cosh(x) +--R 2 8 2 8 +--R + +--R 3 +-+ 3 35 115 2 +--R (7 + - %i)\|5 cosh(x) + (- -- - --- %i)cosh(x) +--R 8 2 8 +--R + +--R 5 17 +-+ 35 +--R (- - -- %i)\|5 cosh(x) - -- %i +--R 2 4 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 +-+ 6 5 5 11 +-+ 4 +--R - - \|5 cosh(x) + - cosh(x) + (3 + -- %i)\|5 cosh(x) +--R 4 4 4 +--R + +--R 25 35 3 15 +-+ 2 +--R (- -- - -- %i)cosh(x) + (6 - -- %i)\|5 cosh(x) +--R 4 4 4 +--R + +--R 25 5 +-+ +--R (- 15 - -- %i)cosh(x) + - \|5 +--R 4 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 11 +-+ 5 5 35 4 +--R (- - + -- %i)\|5 cosh(x) + (- - -- %i)cosh(x) +--R 2 8 2 8 +--R + +--R 5 1 +-+ 3 25 15 2 15 +-+ +--R (- - - %i)\|5 cosh(x) + (- -- - -- %i)cosh(x) - -- %i\|5 cosh(x) +--R 2 2 2 2 8 +--R + +--R 25 +--R - -- %i +--R 8 +--R * +--R sinh(x) +--R + +--R 1 +-+ 6 5 5 +-+ 4 3 5 +-+ 2 +--R - - \|5 cosh(x) + - cosh(x) + \|5 cosh(x) - 5cosh(x) + - \|5 cosh(x) +--R 4 4 4 +--R + +--R 25 +--R - -- cosh(x) +--R 4 +--R Type: Expression(Complex(Fraction(Integer))) +--E 122 + +--S 123 of 526 +t0624:= csch(x)^2/(a+b*coth(x)) +--R +--R +--R 2 +--R csch(x) +--R (123) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 123 + +--S 124 of 526 +r0624:= -log(a+b*coth(x))/b +--R +--R +--R log(b coth(x) + a) +--R (124) - ------------------ +--R b +--R Type: Expression(Integer) +--E 124 + +--S 125 of 526 +a0624:= integrate(t0624,x) +--R +--R +--R 2sinh(x) - 2a sinh(x) - 2b cosh(x) +--R log(- -----------------) - log(-------------------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R (125) --------------------------------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 125 + +--S 126 of 526 +m0624:= a0624-r0624 +--R +--R +--R (126) +--R 2sinh(x) +--R log(b coth(x) + a) + log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2a sinh(x) - 2b cosh(x) +--R - log(-------------------------) +--R sinh(x) - cosh(x) +--R / +--R b +--R Type: Expression(Integer) +--E 126 + +--S 127 of 526 +d0624:= D(m0624,x) +--R +--R +--R (127) +--R 2 2 +--R (- a coth(x) - b coth(x))sinh(x) +--R + +--R 2 2 2 +--R (- b cosh(x)coth(x) + b cosh(x))sinh(x) + b cosh(x) coth(x) + a cosh(x) +--R / +--R 2 2 2 +--R (a b coth(x) + a )sinh(x) + (b cosh(x)coth(x) + a b cosh(x))sinh(x) +--R Type: Expression(Integer) +--E 127 + +--S 128 of 526 +t0625:= csch(x)^3/(a+b*coth(x)) +--R +--R +--R 3 +--R csch(x) +--R (128) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 128 + +--S 129 of 526 +r0625:= -(2*(a^2-b^2)^(1/2)*atanh(1/(a^2-b^2)^(1/2)*(a*sinh(x)+_ + b*cosh(x)-b)/sinh(x))*sinh(x)+b+_ + a*log((cosh(x)-1)/sinh(x))*sinh(x))/sinh(x)/b^2 +--R +--R +--R (129) +--R cosh(x) - 1 +--R - a sinh(x)log(-----------) +--R sinh(x) +--R + +--R +---------+ +--R | 2 2 a sinh(x) + b cosh(x) - b +--R - 2sinh(x)\|- b + a atanh(-------------------------) - b +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R / +--R 2 +--R b sinh(x) +--R Type: Expression(Integer) +--E 129 + +--S 130 of 526 +a0625:= integrate(t0625,x) +--R +--R +--R (130) +--R [ +--R 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 +--R (- 2sinh(x) - 2cosh(x))\|- b + a + (b + a)sinh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b + a +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R + +--R - 2b sinh(x) - 2b cosh(x) +--R / +--R 2 2 2 2 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b +--R , +--R +--R 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 2)\|b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R atan(-------------------------------) +--R (b + a)sinh(x) + (b + a)cosh(x) +--R + +--R - 2b sinh(x) - 2b cosh(x) +--R / +--R 2 2 2 2 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 130 + +--S 131 of 526 +m0625a:= a0625.1-r0625 +--R +--R +--R (131) +--R 3 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + (a cosh(x) - a)sinh(x)) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) + (- a cosh(x) + a)sinh(x)) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + (a cosh(x) - a)sinh(x)) +--R * +--R cosh(x) - 1 +--R log(-----------) +--R sinh(x) +--R + +--R +---------+ +--R 3 2 2 | 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + (cosh(x) - 1)sinh(x))\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 2 +--R (- 2sinh(x) - 2cosh(x))\|- b + a + (b + a)sinh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b + a +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) + b +--R + +--R - a +--R + +--R +---------+ +--R 3 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + (2cosh(x) - 2)sinh(x))\|- b + a +--R * +--R a sinh(x) + b cosh(x) - b +--R atanh(-------------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R + +--R 2 2 +--R - b sinh(x) + b cosh(x) - b +--R / +--R 2 3 2 2 2 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + (b cosh(x) - b )sinh(x) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 526 +d0625a:= D(m0625a,x) +--R +--R +--R (132) +--R 2 11 2 2 2 10 +--R (a b + a )sinh(x) + ((2b + 8a b + 6a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 27a b + 15a )cosh(x) + (- 12b - 13a b - a )cosh(x) - 2a ) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 2 2 +--R (28b + 48a b + 20a )cosh(x) + (- 27b - 33a b - 6a )cosh(x) +--R + +--R 2 2 2 +--R (- 3b - 5a b - 6a )cosh(x) + 2b + 6a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 4 2 2 3 +--R (28b + 42a b + 14a )cosh(x) + (- 22b - 36a b - 14a )cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (- 14b - 20a b - 2a )cosh(x) + (16b + 24a b + 2a )cosh(x) - 8b +--R + +--R - 2a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 4 2 2 3 +--R (14b - 14a )cosh(x) + (- 22b - 20a b + 14a )cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (30b + 38a b + 6a )cosh(x) + (- 24b - 28a b - 6a )cosh(x) + 2b +--R + +--R 10a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 6 2 5 +--R (- 28b - 42a b - 14a )cosh(x) + (42b + 42a b)cosh(x) +--R + +--R 2 2 4 2 3 +--R (- 2b + 28a b + 30a )cosh(x) + (10b + 8a b)cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (- 42b - 74a b - 18a )cosh(x) + (28b + 38a b)cosh(x) - 8b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 7 2 2 6 +--R (- 28b - 48a b - 20a )cosh(x) + (28b + 42a b + 14a )cosh(x) +--R + +--R 2 2 5 2 2 4 +--R (40b + 90a b + 38a )cosh(x) + (- 28b - 62a b - 20a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 62b - 80a b - 24a )cosh(x) + (74b + 66a b + 6a )cosh(x) +--R + +--R 2 2 2 +--R (- 22b - 10a b + 6a )cosh(x) - 2b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 12b - 27a b - 15a )cosh(x) + (- 2b + 12a b + 14a )cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (62b + 100a b + 34a )cosh(x) + (- 44b - 88a b - 30a )cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 56b - 54a b - 24a )cosh(x) + (78b + 76a b + 18a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 26b - 20a b + 6a )cosh(x) - 2a cosh(x) + a b - a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 9 2 2 8 +--R (- 2b - 8a b - 6a )cosh(x) + (- 12b - 6a b + 6a )cosh(x) +--R + +--R 2 2 7 2 2 6 +--R (46b + 60a b + 18a )cosh(x) + (- 34b - 46a b - 18a )cosh(x) +--R + +--R 2 2 5 2 2 4 +--R (- 24b - 44a b - 18a )cosh(x) + (40b + 62a b + 18a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 18b - 12a b + 6a )cosh(x) + (6b - 10a b - 6a )cosh(x) +--R + +--R 2 +--R (- 2b + 4a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 10 2 2 9 +--R (- a b - a )cosh(x) + (- 6b - 5a b + a )cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (18b + 20a b + 4a )cosh(x) + (- 14b - 8a b - 4a )cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (- 6b - 30a b - 6a )cosh(x) + (14b + 30a b + 6a )cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 10b + 4a b + 4a )cosh(x) + (6b - 16a b - 4a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 7a b - a )cosh(x) + (- a b + a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 9 2 8 +--R (- b - a b)cosh(x) + (3b + 3a b)cosh(x) - 2b cosh(x) +--R + +--R 2 7 2 6 2 5 +--R (- 2b - 8a b)cosh(x) + (4b + 6a b)cosh(x) + (- 4b + 6a b)cosh(x) +--R + +--R 2 4 2 3 2 2 +--R (2b - 8a b)cosh(x) + 2b cosh(x) + (- 3b + 3a b)cosh(x) +--R + +--R 2 +--R (b - a b)cosh(x) +--R / +--R 3 2 3 2 10 +--R ((b + a b )cosh(x) - b - a b )sinh(x) +--R + +--R 3 2 2 2 3 2 2 2 +--R (6b + 8a b + 2a b)cosh(x) + (- 6b - 10a b - 4a b)cosh(x) + 2a b +--R + +--R 2 +--R 2a b +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (16b + 28a b + 12a b)cosh(x) + (- 18b - 42a b - 24a b)cosh(x) +--R + +--R 3 2 2 2 +--R (2b + 12a b + 12a b)cosh(x) + 2a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (26b + 56a b + 30a b)cosh(x) + (- 38b - 98a b - 60a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (14b + 34a b + 24a b)cosh(x) + (- 2b + 10a b + 12a b)cosh(x) +--R + +--R 2 2 +--R - 2a b - 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (30b + 70a b + 40a b)cosh(x) + (- 60b - 140a b - 80a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (38b + 56a b + 16a b)cosh(x) + (- 6b + 28a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b - 14a b - 24a b)cosh(x) + 2b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (26b + 56a b + 30a b)cosh(x) + (- 66b - 126a b - 60a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (52b + 54a b - 6a b)cosh(x) + (- 4b + 52a b + 72a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 14b - 44a b - 30a b)cosh(x) + (6b + 10a b - 12a b)cosh(x) +--R + +--R 2 2 +--R - 2a b + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 6 +--R (16b + 28a b + 12a b)cosh(x) + (- 46b - 70a b - 24a b)cosh(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (38b + 28a b - 12a b)cosh(x) + (4b + 58a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (- 20b - 60a b - 12a b)cosh(x) + (10b + 14a b - 24a b)cosh(x) +--R + +--R 3 2 2 2 +--R (- 2b + 4a b + 12a b)cosh(x) - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (6b + 8a b + 2a b)cosh(x) + (- 18b - 22a b - 4a b)cosh(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (14b + 6a b - 4a b)cosh(x) + (6b + 34a b + 12a b)cosh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 14b - 34a b )cosh(x) + (10b - 2a b - 12a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 6b + 18a b + 4a b)cosh(x) + (2b - 10a b + 4a b)cosh(x) +--R + +--R 2 2 +--R 2a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 9 3 2 8 3 7 +--R (b + a b )cosh(x) + (- 3b - 3a b )cosh(x) + 2b cosh(x) +--R + +--R 3 2 6 3 2 5 +--R (2b + 8a b )cosh(x) + (- 4b - 6a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 +--R (4b - 6a b )cosh(x) + (- 2b + 8a b )cosh(x) - 2b cosh(x) +--R + +--R 3 2 3 2 +--R (3b - 3a b )cosh(x) - b + a b +--R * +--R 2 +--R sinh(x) +--R Type: Expression(Integer) +--E 132 + +--S 133 of 526 +m0625b:= a0625.2-r0625 +--R +--R +--R (133) +--R 3 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + (a cosh(x) - a)sinh(x)) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) + (- a cosh(x) + a)sinh(x)) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + (a cosh(x) - a)sinh(x)) +--R * +--R cosh(x) - 1 +--R log(-----------) +--R sinh(x) +--R + +--R +---------+ +--R 3 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + (2cosh(x) - 2)sinh(x))\|- b + a +--R * +--R a sinh(x) + b cosh(x) - b +--R atanh(-------------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R + +--R +-------+ +--R 3 2 2 | 2 2 +--R (2sinh(x) + 4cosh(x)sinh(x) + (2cosh(x) - 2)sinh(x))\|b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R atan(-------------------------------) +--R (b + a)sinh(x) + (b + a)cosh(x) +--R + +--R 2 2 +--R - b sinh(x) + b cosh(x) - b +--R / +--R 2 3 2 2 2 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + (b cosh(x) - b )sinh(x) +--R Type: Expression(Integer) +--E 133 + +--S 134 of 526 +d0625b:= D(m0625b,x) +--R +--R +--R (134) +--R 2 11 2 2 2 10 +--R (a b + a )sinh(x) + ((2b + 8a b + 6a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 27a b + 15a )cosh(x) + (- 12b - 13a b - a )cosh(x) - 2a ) +--R * +--R 9 +--R sinh(x) +--R + +--R 2 2 3 2 2 2 +--R (28b + 48a b + 20a )cosh(x) + (- 27b - 33a b - 6a )cosh(x) +--R + +--R 2 2 2 +--R (- 3b - 5a b - 6a )cosh(x) + 2b + 6a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 4 2 2 3 +--R (28b + 42a b + 14a )cosh(x) + (- 22b - 36a b - 14a )cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (- 14b - 20a b - 2a )cosh(x) + (16b + 24a b + 2a )cosh(x) - 8b +--R + +--R - 2a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 4 2 2 3 +--R (14b - 14a )cosh(x) + (- 22b - 20a b + 14a )cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (30b + 38a b + 6a )cosh(x) + (- 24b - 28a b - 6a )cosh(x) + 2b +--R + +--R 10a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 6 2 5 +--R (- 28b - 42a b - 14a )cosh(x) + (42b + 42a b)cosh(x) +--R + +--R 2 2 4 2 3 +--R (- 2b + 28a b + 30a )cosh(x) + (10b + 8a b)cosh(x) +--R + +--R 2 2 2 2 2 2 +--R (- 42b - 74a b - 18a )cosh(x) + (28b + 38a b)cosh(x) - 8b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 7 2 2 6 +--R (- 28b - 48a b - 20a )cosh(x) + (28b + 42a b + 14a )cosh(x) +--R + +--R 2 2 5 2 2 4 +--R (40b + 90a b + 38a )cosh(x) + (- 28b - 62a b - 20a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 62b - 80a b - 24a )cosh(x) + (74b + 66a b + 6a )cosh(x) +--R + +--R 2 2 2 +--R (- 22b - 10a b + 6a )cosh(x) - 2b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 8 2 2 7 +--R (- 12b - 27a b - 15a )cosh(x) + (- 2b + 12a b + 14a )cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (62b + 100a b + 34a )cosh(x) + (- 44b - 88a b - 30a )cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 56b - 54a b - 24a )cosh(x) + (78b + 76a b + 18a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 26b - 20a b + 6a )cosh(x) - 2a cosh(x) + a b - a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 9 2 2 8 +--R (- 2b - 8a b - 6a )cosh(x) + (- 12b - 6a b + 6a )cosh(x) +--R + +--R 2 2 7 2 2 6 +--R (46b + 60a b + 18a )cosh(x) + (- 34b - 46a b - 18a )cosh(x) +--R + +--R 2 2 5 2 2 4 +--R (- 24b - 44a b - 18a )cosh(x) + (40b + 62a b + 18a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 18b - 12a b + 6a )cosh(x) + (6b - 10a b - 6a )cosh(x) +--R + +--R 2 +--R (- 2b + 4a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 10 2 2 9 +--R (- a b - a )cosh(x) + (- 6b - 5a b + a )cosh(x) +--R + +--R 2 2 8 2 2 7 +--R (18b + 20a b + 4a )cosh(x) + (- 14b - 8a b - 4a )cosh(x) +--R + +--R 2 2 6 2 2 5 +--R (- 6b - 30a b - 6a )cosh(x) + (14b + 30a b + 6a )cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 10b + 4a b + 4a )cosh(x) + (6b - 16a b - 4a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 7a b - a )cosh(x) + (- a b + a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 9 2 8 +--R (- b - a b)cosh(x) + (3b + 3a b)cosh(x) - 2b cosh(x) +--R + +--R 2 7 2 6 2 5 +--R (- 2b - 8a b)cosh(x) + (4b + 6a b)cosh(x) + (- 4b + 6a b)cosh(x) +--R + +--R 2 4 2 3 2 2 +--R (2b - 8a b)cosh(x) + 2b cosh(x) + (- 3b + 3a b)cosh(x) +--R + +--R 2 +--R (b - a b)cosh(x) +--R / +--R 3 2 3 2 10 +--R ((b + a b )cosh(x) - b - a b )sinh(x) +--R + +--R 3 2 2 2 3 2 2 2 +--R (6b + 8a b + 2a b)cosh(x) + (- 6b - 10a b - 4a b)cosh(x) + 2a b +--R + +--R 2 +--R 2a b +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (16b + 28a b + 12a b)cosh(x) + (- 18b - 42a b - 24a b)cosh(x) +--R + +--R 3 2 2 2 +--R (2b + 12a b + 12a b)cosh(x) + 2a b +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (26b + 56a b + 30a b)cosh(x) + (- 38b - 98a b - 60a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (14b + 34a b + 24a b)cosh(x) + (- 2b + 10a b + 12a b)cosh(x) +--R + +--R 2 2 +--R - 2a b - 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (30b + 70a b + 40a b)cosh(x) + (- 60b - 140a b - 80a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (38b + 56a b + 16a b)cosh(x) + (- 6b + 28a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 4b - 14a b - 24a b)cosh(x) + 2b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (26b + 56a b + 30a b)cosh(x) + (- 66b - 126a b - 60a b)cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (52b + 54a b - 6a b)cosh(x) + (- 4b + 52a b + 72a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 14b - 44a b - 30a b)cosh(x) + (6b + 10a b - 12a b)cosh(x) +--R + +--R 2 2 +--R - 2a b + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 7 3 2 2 6 +--R (16b + 28a b + 12a b)cosh(x) + (- 46b - 70a b - 24a b)cosh(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (38b + 28a b - 12a b)cosh(x) + (4b + 58a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 2 +--R (- 20b - 60a b - 12a b)cosh(x) + (10b + 14a b - 24a b)cosh(x) +--R + +--R 3 2 2 2 +--R (- 2b + 4a b + 12a b)cosh(x) - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 8 3 2 2 7 +--R (6b + 8a b + 2a b)cosh(x) + (- 18b - 22a b - 4a b)cosh(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (14b + 6a b - 4a b)cosh(x) + (6b + 34a b + 12a b)cosh(x) +--R + +--R 3 2 4 3 2 2 3 +--R (- 14b - 34a b )cosh(x) + (10b - 2a b - 12a b)cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 6b + 18a b + 4a b)cosh(x) + (2b - 10a b + 4a b)cosh(x) +--R + +--R 2 2 +--R 2a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 9 3 2 8 3 7 +--R (b + a b )cosh(x) + (- 3b - 3a b )cosh(x) + 2b cosh(x) +--R + +--R 3 2 6 3 2 5 +--R (2b + 8a b )cosh(x) + (- 4b - 6a b )cosh(x) +--R + +--R 3 2 4 3 2 3 3 2 +--R (4b - 6a b )cosh(x) + (- 2b + 8a b )cosh(x) - 2b cosh(x) +--R + +--R 3 2 3 2 +--R (3b - 3a b )cosh(x) - b + a b +--R * +--R 2 +--R sinh(x) +--R Type: Expression(Integer) +--E 134 + +--S 135 of 526 +t0626:= csch(x)^4/(a+b*coth(x)) +--R +--R +--R 4 +--R csch(x) +--R (135) ------------- +--R b coth(x) + a +--R Type: Expression(Integer) +--E 135 + +--S 136 of 526 +r0626:= a*coth(x)/b^2-1/2*coth(x)^2/b-(a^2-b^2)*log(a+b*coth(x))/b^3 +--R +--R +--R 2 2 2 2 +--R (2b - 2a )log(b coth(x) + a) - b coth(x) + 2a b coth(x) +--R (136) --------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 136 + +--S 137 of 526 +a0626:= integrate(t0626,x) +--R +--R +--R (137) +--R 2 2 4 2 2 3 +--R (- b + a )sinh(x) + (- 4b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b + 6a )cosh(x) + 2b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b + 4a )cosh(x) + (4b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b + a )cosh(x) + (2b - 2a )cosh(x) - b + a +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b - 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b - 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b - a )cosh(x) + (- 2b + 2a )cosh(x) + b - a +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 +--R (- 2b + 2a b)sinh(x) + (- 4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 +--R (- 2b + 2a b)cosh(x) - 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) - 2b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4b cosh(x) - 4b cosh(x))sinh(x) + b cosh(x) - 2b cosh(x) + b +--R Type: Union(Expression(Integer),...) +--E 137 + +--S 138 of 526 +m0626:= a0626-r0626 +--R +--R +--R (138) +--R 2 2 4 2 2 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + (4b - 4a )cosh(x) - 2b + 2a +--R * +--R log(b coth(x) + a) +--R + +--R 2 2 4 2 2 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + (4b - 4a )cosh(x) - 2b + 2a +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 2 3 +--R (2b - 2a )sinh(x) + (8b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - 2a )cosh(x) + (- 4b + 4a )cosh(x) + 2b - 2a +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 +--R (b coth(x) - 2a b coth(x))sinh(x) +--R + +--R 2 2 3 +--R (4b cosh(x)coth(x) - 8a b cosh(x)coth(x))sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (6b cosh(x) - 2b )coth(x) + (- 12a b cosh(x) + 4a b)coth(x) - 4b +--R + +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4b cosh(x) - 4b cosh(x))coth(x) +--R + +--R 3 2 +--R (- 8a b cosh(x) + 8a b cosh(x))coth(x) + (- 8b + 8a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b cosh(x) - 2b cosh(x) + b )coth(x) +--R + +--R 4 2 2 2 +--R (- 2a b cosh(x) + 4a b cosh(x) - 2a b)coth(x) + (- 4b + 4a b)cosh(x) +--R + +--R - 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) - 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) - 8b cosh(x))sinh(x) + 2b cosh(x) - 4b cosh(x) + 2b +--R Type: Expression(Integer) +--E 138 + +--S 139 of 526 +d0626:= D(m0626,x) +--R +--R +--R (139) +--R 2 4 2 2 3 2 3 8 +--R (- a b coth(x) + 2a b coth(x) + (b - a b)coth(x) - a )sinh(x) +--R + +--R 3 2 4 3 2 2 +--R (- b - 6a b )cosh(x)coth(x) + (2b + 12a b )cosh(x)coth(x) +--R + +--R 3 2 3 3 +--R (6b - 6a b)cosh(x)coth(x) + (- b - 6a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 2 4 +--R ((- 6b - 15a b )cosh(x) + 3a b )coth(x) +--R + +--R 3 2 2 2 2 +--R ((12b + 30a b )cosh(x) - 6a b )coth(x) +--R + +--R 3 2 2 3 2 2 +--R ((14b - 14a b)cosh(x) - 3b + 4a b - a b)coth(x) +--R + +--R 3 2 3 2 2 3 +--R (- 6b - a b - 14a )cosh(x) + 4a b - a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 3 3 2 4 +--R ((- 15b - 20a b )cosh(x) + (3b + 12a b )cosh(x))coth(x) +--R + +--R 3 2 3 3 2 2 +--R ((30b + 40a b )cosh(x) + (- 6b - 24a b )cosh(x))coth(x) +--R + +--R 3 2 3 3 2 2 +--R ((14b - 14a b)cosh(x) + (- 8b + 12a b - 4a b)cosh(x))coth(x) +--R + +--R 3 2 3 3 3 2 2 3 +--R (- 15b - 6a b - 14a )cosh(x) + (3b + 4a b + 12a b - 4a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 2 4 +--R ((- 20b - 15a b )cosh(x) + (12b + 18a b )cosh(x) - 3a b )coth(x) +--R + +--R 3 2 4 3 2 2 2 2 +--R ((40b + 30a b )cosh(x) + (- 24b - 36a b )cosh(x) + 6a b )coth(x) +--R + +--R 3 2 2 2 3 2 2 +--R ((b + 8a b - 9a b)cosh(x) + 3b + 4a b + a b)coth(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R (- 20b - 15a b )cosh(x) + (12b + 19a b + 8a b - 9a )cosh(x) +--R + +--R 2 3 +--R 4a b + a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 15b - 6a b )cosh(x) + (18b + 12a b )cosh(x) +--R + +--R 3 2 +--R (- 3b - 6a b )cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 3 2 5 3 2 3 +--R (30b + 12a b )cosh(x) + (- 36b - 24a b )cosh(x) +--R + +--R 3 2 +--R (6b + 12a b )cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 5 3 2 2 3 +--R (- 14b + 14a b)cosh(x) + (24b - 8a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (10b + 12a b + 2a b)cosh(x) +--R * +--R coth(x) +--R + +--R 3 2 3 5 +--R (- 15b - 20a b + 14a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (18b + 36a b - 8a b - 16a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 3b + 4a b + 12a b + 2a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 6 3 2 4 +--R (- 6b - a b )cosh(x) + (12b + 3a b )cosh(x) +--R + +--R 3 2 2 2 +--R (- 6b - 3a b )cosh(x) + a b +--R * +--R 4 +--R coth(x) +--R + +--R 3 2 6 3 2 4 +--R (12b + 2a b )cosh(x) + (- 24b - 6a b )cosh(x) +--R + +--R 3 2 2 2 +--R (12b + 6a b )cosh(x) - 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 14b + 14a b)cosh(x) + (31b - 12a b - 19a b)cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (8b + 12a b + 4a b)cosh(x) - b + a b +--R * +--R coth(x) +--R + +--R 3 2 3 6 +--R (- 6b - 15a b + 14a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (12b + 34a b - 12a b - 19a )cosh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 6b + 5a b + 12a b + 4a )cosh(x) + a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 5 3 3 3 4 +--R (- b cosh(x) + 3b cosh(x) - 3b cosh(x) + b cosh(x))coth(x) +--R + +--R 3 7 3 5 3 3 3 2 +--R (2b cosh(x) - 6b cosh(x) + 6b cosh(x) - 2b cosh(x))coth(x) +--R + +--R 3 2 7 3 2 2 5 +--R (- 6b + 6a b)cosh(x) + (16b - 4a b - 12a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 2b + 4a b + 6a b)cosh(x) +--R * +--R coth(x) +--R + +--R 3 2 3 7 3 2 2 3 5 +--R (- b - 6a b + 6a )cosh(x) + (3b + 16a b - 4a b - 12a )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R (- 3b - 2a b + 4a b + 6a )cosh(x) + b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 8 3 2 6 3 2 4 +--R (- b + a b)cosh(x) + (3b - 3a b)cosh(x) + (- 3b + 3a b)cosh(x) +--R + +--R 3 2 2 +--R (b - a b)cosh(x) +--R * +--R coth(x) +--R + +--R 2 3 8 2 3 6 2 3 4 +--R (- a b + a )cosh(x) + (3a b - 3a )cosh(x) + (- 3a b + 3a )cosh(x) +--R + +--R 2 3 2 +--R (a b - a )cosh(x) +--R / +--R 3 2 2 8 +--R (a b coth(x) + a b )sinh(x) +--R + +--R 4 3 3 2 2 7 +--R ((b + 6a b )cosh(x)coth(x) + (a b + 6a b )cosh(x))sinh(x) +--R + +--R 4 3 2 3 3 2 2 2 +--R ((6b + 15a b )cosh(x) - 3a b )coth(x) + (6a b + 15a b )cosh(x) +--R + +--R 2 2 +--R - 3a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 3 4 3 +--R ((15b + 20a b )cosh(x) + (- 3b - 12a b )cosh(x))coth(x) +--R + +--R 3 2 2 3 3 2 2 +--R (15a b + 20a b )cosh(x) + (- 3a b - 12a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 4 3 2 3 +--R ((20b + 15a b )cosh(x) + (- 12b - 18a b )cosh(x) + 3a b )coth(x) +--R + +--R 3 2 2 4 3 2 2 2 2 2 +--R (20a b + 15a b )cosh(x) + (- 12a b - 18a b )cosh(x) + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 4 3 3 +--R (15b + 6a b )cosh(x) + (- 18b - 12a b )cosh(x) +--R + +--R 4 3 +--R (3b + 6a b )cosh(x) +--R * +--R coth(x) +--R + +--R 3 2 2 5 3 2 2 3 +--R (15a b + 6a b )cosh(x) + (- 18a b - 12a b )cosh(x) +--R + +--R 3 2 2 +--R (3a b + 6a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 4 3 4 +--R (6b + a b )cosh(x) + (- 12b - 3a b )cosh(x) +--R + +--R 4 3 2 3 +--R (6b + 3a b )cosh(x) - a b +--R * +--R coth(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (6a b + a b )cosh(x) + (- 12a b - 3a b )cosh(x) +--R + +--R 3 2 2 2 2 2 +--R (6a b + 3a b )cosh(x) - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 4 5 4 3 4 +--R (b cosh(x) - 3b cosh(x) + 3b cosh(x) - b cosh(x))coth(x) +--R + +--R 3 7 3 5 3 3 3 +--R a b cosh(x) - 3a b cosh(x) + 3a b cosh(x) - a b cosh(x) +--R * +--R sinh(x) +--R Type: Expression(Integer) +--E 139 + +--S 140 of 526 +t0627:= csch(x)^2/(1+coth(x)) +--R +--R +--R 2 +--R csch(x) +--R (140) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 140 + +--S 141 of 526 +r0627:= -log(1+coth(x)) +--R +--R +--R (141) - log(coth(x) + 1) +--R Type: Expression(Integer) +--E 141 + +--S 142 of 526 +a0627:= integrate(t0627,x) +--R +--R +--R 2sinh(x) +--R (142) log(- -----------------) - 2x +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 142 + +--S 143 of 526 +m0627:= a0627-r0627 +--R +--R +--R 2sinh(x) +--R (143) log(coth(x) + 1) + log(- -----------------) - 2x +--R sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 143 + +--S 144 of 526 +d0627:= D(m0627,x) +--R +--R +--R - coth(x)sinh(x) + cosh(x) +--R (144) -------------------------- +--R sinh(x) +--R Type: Expression(Integer) +--E 144 + +--S 145 of 526 +t0628:= csch(x)^3/(1+coth(x)) +--R +--R +--R 3 +--R csch(x) +--R (145) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 145 + +--S 146 of 526 +r0628:= acoth(cosh(x))-csch(x) +--R +--R +--R (146) acoth(cosh(x)) - csch(x) +--R Type: Expression(Integer) +--E 146 + +--S 147 of 526 +a0628:= integrate(t0628,x) +--R +--R +--R (147) +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(sinh(x) + cosh(x) - 1) +--R + +--R - 2sinh(x) - 2cosh(x) +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 147 + +--S 148 of 526 +m0628:= a0628-r0628 +--R +--R +--R (148) +--R 2 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)acoth(cosh(x)) +--R + +--R 2 2 +--R csch(x)sinh(x) + (2cosh(x)csch(x) - 2)sinh(x) + (cosh(x) - 1)csch(x) +--R + +--R - 2cosh(x) +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression(Integer) +--E 148 + +--S 149 of 526 +d0628:= D(m0628,x) +--R +--R +--R (149) +--R 5 2 4 +--R sinh(x) + ((- cosh(x) + 1)coth(x)csch(x) + 4cosh(x))sinh(x) +--R + +--R 3 2 3 +--R ((- 4cosh(x) + 4cosh(x))coth(x)csch(x) + 6cosh(x) - 2)sinh(x) +--R + +--R 4 2 3 +--R ((- 6cosh(x) + 8cosh(x) - 2)coth(x)csch(x) + 4cosh(x) - 4cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 4 +--R (- 4cosh(x) + 8cosh(x) - 4cosh(x))coth(x)csch(x) + cosh(x) +--R + +--R 2 +--R 2cosh(x) - 3 +--R * +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- cosh(x) + 3cosh(x) - 3cosh(x) + 1)coth(x)csch(x) + 4cosh(x) +--R + +--R - 4cosh(x) +--R / +--R 2 4 3 3 +--R (cosh(x) - 1)sinh(x) + (4cosh(x) - 4cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (6cosh(x) - 8cosh(x) + 2)sinh(x) +--R + +--R 5 3 6 4 +--R (4cosh(x) - 8cosh(x) + 4cosh(x))sinh(x) + cosh(x) - 3cosh(x) +--R + +--R 2 +--R 3cosh(x) - 1 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 526 +t0629:= csch(x)^4/(1+coth(x)) +--R +--R +--R 4 +--R csch(x) +--R (150) ----------- +--R coth(x) + 1 +--R Type: Expression(Integer) +--E 150 + +--S 151 of 526 +r0629:= -1/2*coth(x)*(-2+coth(x)) +--R +--R +--R 2 +--R - coth(x) + 2coth(x) +--R (151) --------------------- +--R 2 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 526 +a0629:= integrate(t0629,x) +--R +--R +--R (152) +--R - +--R 2 +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 152 + +--S 153 of 526 +m0629:= a0629-r0629 +--R +--R +--R (153) +--R 2 4 +--R (coth(x) - 2coth(x))sinh(x) +--R + +--R 2 3 +--R (4cosh(x)coth(x) - 8cosh(x)coth(x))sinh(x) +--R + +--R 2 2 2 2 +--R ((6cosh(x) - 2)coth(x) + (- 12cosh(x) + 4)coth(x))sinh(x) +--R + +--R 3 2 3 +--R ((4cosh(x) - 4cosh(x))coth(x) + (- 8cosh(x) + 8cosh(x))coth(x))sinh(x) +--R + +--R 4 2 2 4 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x) + (- 2cosh(x) + 4cosh(x) - 2)coth(x) +--R + +--R - 4 +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Expression(Integer) +--E 153 + +--S 154 of 526 +d0629:= D(m0629,x) +--R +--R +--R (154) +--R 3 2 6 +--R (- coth(x) + coth(x) + coth(x) - 1)sinh(x) +--R + +--R 3 2 +--R (- 6cosh(x)coth(x) + 6cosh(x)coth(x) + 6cosh(x)coth(x) - 6cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 15cosh(x) + 3)coth(x) + (15cosh(x) - 3)coth(x) +--R + +--R 2 2 +--R (15cosh(x) - 3)coth(x) - 15cosh(x) + 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 +--R (- 20cosh(x) + 12cosh(x))coth(x) + (20cosh(x) - 12cosh(x))coth(x) +--R + +--R 3 3 +--R (20cosh(x) - 12cosh(x))coth(x) - 20cosh(x) + 12cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 +--R (- 15cosh(x) + 18cosh(x) - 3)coth(x) +--R + +--R 4 2 2 +--R (15cosh(x) - 18cosh(x) + 3)coth(x) +--R + +--R 4 2 4 2 +--R (15cosh(x) - 18cosh(x) + 3)coth(x) - 15cosh(x) + 18cosh(x) + 5 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 6cosh(x) + 12cosh(x) - 6cosh(x))coth(x) +--R + +--R 5 3 2 +--R (6cosh(x) - 12cosh(x) + 6cosh(x))coth(x) +--R + +--R 5 3 5 3 +--R (6cosh(x) - 12cosh(x) + 6cosh(x))coth(x) - 6cosh(x) + 12cosh(x) +--R + +--R 10cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- cosh(x) + 3cosh(x) - 3cosh(x) + 1)coth(x) +--R + +--R 6 4 2 2 +--R (cosh(x) - 3cosh(x) + 3cosh(x) - 1)coth(x) +--R + +--R 6 4 2 6 4 +--R (cosh(x) - 3cosh(x) + 3cosh(x) - 1)coth(x) - cosh(x) + 3cosh(x) +--R + +--R 2 +--R 5cosh(x) + 1 +--R / +--R 6 5 2 4 +--R sinh(x) + 6cosh(x)sinh(x) + (15cosh(x) - 3)sinh(x) +--R + +--R 3 3 4 2 2 +--R (20cosh(x) - 12cosh(x))sinh(x) + (15cosh(x) - 18cosh(x) + 3)sinh(x) +--R + +--R 5 3 6 4 +--R (6cosh(x) - 12cosh(x) + 6cosh(x))sinh(x) + cosh(x) - 3cosh(x) +--R + +--R 2 +--R 3cosh(x) - 1 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 526 +t0630:= sinh(x)/(a+b*sech(x)) +--R +--R +--R sinh(x) +--R (155) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 155 + +--S 156 of 526 +r0630:= cosh(x)/a-b*log(b+a*cosh(x))/a^2 +--R +--R +--R - b log(a cosh(x) + b) + a cosh(x) +--R (156) ---------------------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 526 +a0630:= integrate(t0630,x) +--R +--R +--R (157) +--R - 2a cosh(x) - 2b 2 +--R (- 2b sinh(x) - 2b cosh(x))log(-----------------) + a sinh(x) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (2a cosh(x) + 2b x)sinh(x) + a cosh(x) + 2b x cosh(x) + a +--R / +--R 2 2 +--R 2a sinh(x) + 2a cosh(x) +--R Type: Union(Expression(Integer),...) +--E 157 + +--S 158 of 526 +m0630:= a0630-r0630 +--R +--R +--R (158) +--R (2b sinh(x) + 2b cosh(x))log(a cosh(x) + b) +--R + +--R - 2a cosh(x) - 2b 2 +--R (- 2b sinh(x) - 2b cosh(x))log(-----------------) + a sinh(x) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R 2b x sinh(x) - a cosh(x) + 2b x cosh(x) + a +--R / +--R 2 2 +--R 2a sinh(x) + 2a cosh(x) +--R Type: Expression(Integer) +--E 158 + +--S 159 of 526 +d0630:= D(m0630,x) +--R +--R +--R 2 2 +--R - sinh(x) + cosh(x) - 1 +--R (159) ------------------------- +--R 2a sinh(x) + 2a cosh(x) +--R Type: Expression(Integer) +--E 159 + +--S 160 of 526 +t0631:= sinh(x)^2/(a+b*sech(x)) +--R +--R +--R 2 +--R sinh(x) +--R (160) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 160 + +--S 161 of 526 +r0631:= 1/2*(-a^2*x+2*b^2*x+4*b*(a^2-b^2)^(1/2)*_ + atan((a-b)*(cosh(x)-1)/sinh(x)/(a^2-b^2)^(1/2))-_ + 2*a*b*sinh(x)+a^2*cosh(x)*sinh(x))/a^3 +--R +--R +--R (161) +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a 2 +--R - 4b\|- b + a atan(----------------------) + (a cosh(x) - 2a b)sinh(x) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R + +--R 2 2 +--R (2b - a )x +--R / +--R 3 +--R 2a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 526 +a0631:= integrate(t0631,x) +--R +--R +--R (162) +--R [ +--R +-------+ +--R 2 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b +--R + +--R 2 +--R - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b - 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b - 8a )x cosh(x) + 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b - 4a )x cosh(x) + 4a b cosh(x) - a +--R / +--R 3 2 3 3 2 +--R 8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) +--R , +--R +--R +---------+ +--R 2 2 | 2 2 +--R (- 16b sinh(x) - 32b cosh(x)sinh(x) - 16b cosh(x) )\|- b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b - 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b - 8a )x cosh(x) + 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b - 4a )x cosh(x) + 4a b cosh(x) - a +--R / +--R 3 2 3 3 2 +--R 8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 162 + +--S 163 of 526 +m0631a:= a06311.1-r0631 +--R +--R There are no library operations named a06311 +--R Use HyperDoc Browse or issue +--R )what op a06311 +--R to learn if there is any operation containing " a06311 " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R a06311 with argument type(s) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 163 + +--S 164 of 526 +d0631a:= D(m0631a,x) +--R +--R +--R (163) 0 +--R Type: Polynomial(Integer) +--E 164 + +--S 165 of 526 +m0631b:= a0631.2-r0631 +--R +--R +--R (164) +--R +---------+ +--R 2 2 | 2 2 +--R (- 16b sinh(x) - 32b cosh(x)sinh(x) - 16b cosh(x) )\|- b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (16b sinh(x) + 32b cosh(x)sinh(x) + 16b cosh(x) )\|- b + a +--R * +--R (b - a)cosh(x) - b + a +--R atan(----------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R + +--R 2 4 3 2 2 2 +--R a sinh(x) + 4a b sinh(x) + (- 2a cosh(x) + 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (- 4a b cosh(x) + 4a b)sinh(x) + a cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) - a +--R / +--R 3 2 3 3 2 +--R 8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) +--R Type: Expression(Integer) +--E 165 + +--S 166 of 526 +d0631b:= D(m0631b,x) +--R +--R +--R (165) +--R 3 4 8 3 4 2 2 3 7 +--R (- a b - a )sinh(x) + ((- 2a b - 2a )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 3 2 2 2 3 4 3 2 2 3 +--R 2a b cosh(x) + (- 8a b - 10a b + 2a )cosh(x) + 4a b - 4a b - 8a b +--R + +--R 4 +--R - 2a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 4 2 +--R (6a b + 2a )cosh(x) + (4a b - 8a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 +--R (24a b - 16a b - 22a b - 2a )cosh(x) + 8b - 8a b - 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 2 2 3 4 3 +--R 2a cosh(x) + (16a b + 2a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 2 +--R (44a b - 20a b - 22a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (24b - 24a b - 16a b - 2a b + 2a )cosh(x) + 8a b - 8a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 5 2 2 3 4 4 +--R (- 6a b + 2a )cosh(x) + (4a b + 12a b - 8a )cosh(x) +--R + +--R 3 3 4 3 4 3 3 2 +--R (16a b - 4a b + 4a )cosh(x) + (16b - 16a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 +--R (32a b - 24a b - 22a b + 2a )cosh(x) + 8b - 8a b - 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 2 2 3 4 5 +--R - 2a b cosh(x) + (- 8a b + 10a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 36a b + 20a b + 20a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 16b + 16a b + 16a b - 12a b - 4a )cosh(x) +--R + +--R 3 2 2 3 4 2 +--R (48a b - 24a b - 34a b + 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 4 +--R (24b - 24a b - 8a b + 10a b - 2a )cosh(x) + 4a b - 4a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 7 2 2 4 6 +--R (2a b - 2a )cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 40a b + 16a b + 26a b - 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 24b + 24a b + 8a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (32a b - 8a b - 26a b + 2a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (24b - 24a b - 4a b + 8a b - 4a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (8a b - 8a b - 2a b + 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 8 3 4 7 +--R (a b - a )cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 6 +--R (- 12a b + 4a b + 10a b - 2a )cosh(x) +--R + +--R 4 3 3 4 5 3 3 4 +--R (- 8b + 8a b - 2a b + 2a )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 4 3 3 4 3 3 2 2 3 4 2 +--R (8b - 8a b + 2a b - 2a )cosh(x) + (4a b - 4a b - 2a b + 2a )cosh(x) +--R + +--R 3 4 3 4 +--R (2a b - 2a )cosh(x) - a b + a +--R / +--R 4 5 6 4 5 3 2 4 5 +--R (4a b + 4a )sinh(x) + ((16a b + 16a )cosh(x) + 8a b + 8a b)sinh(x) +--R + +--R 4 5 2 3 2 4 5 5 4 +--R ((20a b + 28a )cosh(x) + (24a b + 32a b - 8a )cosh(x) + 8a )sinh(x) +--R + +--R 5 3 3 2 4 5 2 +--R 32a cosh(x) + (16a b + 64a b - 32a )cosh(x) +--R + +--R 3 2 4 5 3 2 4 +--R (16a b - 24a b + 24a )cosh(x) - 8a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 4 3 2 4 5 3 +--R (- 20a b + 28a )cosh(x) + (- 16a b + 80a b - 48a )cosh(x) +--R + +--R 3 2 4 5 2 3 2 4 5 +--R (48a b - 72a b + 32a )cosh(x) + (- 24a b + 32a b - 8a )cosh(x) +--R + +--R 4 5 +--R - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 5 3 2 4 5 4 +--R (- 16a b + 16a )cosh(x) + (- 24a b + 56a b - 32a )cosh(x) +--R + +--R 3 2 4 5 3 3 2 4 5 2 +--R (48a b - 72a b + 24a )cosh(x) + (- 24a b + 40a b - 16a )cosh(x) +--R + +--R 4 5 +--R (- 8a b + 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 5 6 3 2 4 5 5 +--R (- 4a b + 4a )cosh(x) + (- 8a b + 16a b - 8a )cosh(x) +--R + +--R 3 2 4 5 4 3 2 4 5 3 +--R (16a b - 24a b + 8a )cosh(x) + (- 8a b + 16a b - 8a )cosh(x) +--R + +--R 4 5 2 +--R (- 4a b + 4a )cosh(x) +--R Type: Expression(Integer) +--E 166 + +--S 167 of 526 +t0632:= sinh(x)^3/(a+b*sech(x)) +--R +--R +--R 3 +--R sinh(x) +--R (166) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 526 +r0632:= -(a^2-b^2)*cosh(x)/a^3-1/2*b*cosh(x)^2/a^2+1/3*cosh(x)^3/a+_ + b*(a^2-b^2)*log(b+a*cosh(x))/a^4 +--R +--R +--R (167) +--R 3 2 3 3 2 2 +--R (- 6b + 6a b)log(a cosh(x) + b) + 2a cosh(x) - 3a b cosh(x) +--R + +--R 2 3 +--R (6a b - 6a )cosh(x) +--R / +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 168 + +--S 169 of 526 +a0632:= integrate(t0632,x) +--R +--R +--R (168) +--R 3 2 3 3 2 2 +--R (- 24b + 24a b)sinh(x) + (- 72b + 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 72b + 72a b)cosh(x) sinh(x) + (- 24b + 24a b)cosh(x) +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b - 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 20a cosh(x) - 30a b cosh(x) + (48a b - 36a )cosh(x) +--R + +--R 3 2 +--R (24b - 24a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 15a cosh(x) - 30a b cosh(x) + (72a b - 54a )cosh(x) +--R + +--R 3 2 2 3 +--R (72b - 72a b)x cosh(x) + 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (48a b - 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (72b - 72a b)x cosh(x) + (24a b - 18a )cosh(x) - 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b - 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R (24b - 24a b)x cosh(x) + (12a b - 9a )cosh(x) - 3a b cosh(x) + a +--R / +--R 4 3 4 2 4 2 4 3 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) +--R Type: Union(Expression(Integer),...) +--E 169 + +--S 170 of 526 +m0632:= a0632-r0632 +--R +--R +--R (169) +--R 3 2 3 3 2 2 +--R (24b - 24a b)sinh(x) + (72b - 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (72b - 72a b)cosh(x) sinh(x) + (24b - 24a b)cosh(x) +--R * +--R log(a cosh(x) + b) +--R + +--R 3 2 3 3 2 2 +--R (- 24b + 24a b)sinh(x) + (- 72b + 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 72b + 72a b)cosh(x) sinh(x) + (- 24b + 24a b)cosh(x) +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b - 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 12a cosh(x) - 18a b cosh(x) + (24a b - 12a )cosh(x) +--R + +--R 3 2 +--R (24b - 24a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 +--R - 9a cosh(x) + 6a b cosh(x) + 18a cosh(x) +--R + +--R 3 2 2 3 +--R (72b - 72a b)x cosh(x) + 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R - 18a cosh(x) + 21a b cosh(x) + (- 24a b + 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (72b - 72a b)x cosh(x) + (24a b - 18a )cosh(x) - 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R - 7a cosh(x) + 9a b cosh(x) + (- 12a b + 15a )cosh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R (24b - 24a b)x cosh(x) + (12a b - 9a )cosh(x) - 3a b cosh(x) + a +--R / +--R 4 3 4 2 4 2 4 3 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) +--R Type: Expression(Integer) +--E 170 + +--S 171 of 526 +d0632:= D(m0632,x) +--R +--R +--R (170) +--R 2 6 2 5 +--R a sinh(x) + (6a cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 4 +--R (7a cosh(x) - 2a b cosh(x) - 4b + 5a )sinh(x) +--R + +--R 2 3 2 2 2 3 +--R (- 4a cosh(x) + 4a b cosh(x) + (- 8b + 12a )cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 2 2 +--R (- 9a cosh(x) + 4a b cosh(x) + 6a cosh(x) - 4b + 3a )sinh(x) +--R + +--R 2 5 4 2 2 3 +--R - 2a cosh(x) - 2a b cosh(x) + (8b - 4a )cosh(x) +--R + +--R 2 2 +--R (- 8b + 6a )cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 6 5 2 2 4 2 2 2 +--R a cosh(x) - 2a b cosh(x) + (4b - 3a )cosh(x) + (- 4b + 3a )cosh(x) +--R + +--R 2 +--R 2a b cosh(x) - a +--R / +--R 3 3 3 2 3 2 3 3 +--R 8a sinh(x) + 24a cosh(x)sinh(x) + 24a cosh(x) sinh(x) + 8a cosh(x) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 526 +t0633:= sinh(x)^4/(a+b*sech(x)) +--R +--R +--R 4 +--R sinh(x) +--R (171) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 526 +r0633:= -5/8*x/a+1/2*b^2*x/a^3+(a^2-b^2)^2*x/a^5-2*b*(a^2-b^2)^(3/2)*_ + atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a^5+b*sinh(x)/a^2-_ + b^3*sinh(x)/a^4-5/8*cosh(x)*sinh(x)/a+1/2*b^2*cosh(x)*sinh(x)/a^3+_ + 1/4*cosh(x)^3*sinh(x)/a-1/3*b*sinh(x)^3/a^2 +--R +--R +--R (172) +--R x +--R +---------+ (b - a)tanh(-) +--R 3 2 | 2 2 2 3 3 +--R (- 48b + 48a b)\|- b + a atan(--------------) - 8a b sinh(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 2 2 4 3 3 +--R (6a cosh(x) + (12a b - 15a )cosh(x) - 24a b + 24a b)sinh(x) +--R + +--R 4 2 2 4 +--R (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R Type: Expression(Integer) +--E 173 + +--S 174 of 526 +a0633:= integrate(t0633,x) +--R +--R +--R (173) +--R [ +--R 3 2 4 3 2 3 +--R (192b - 192a b)sinh(x) + (768b - 768a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (1152b - 1152a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (768b - 768a b)cosh(x) sinh(x) + (192b - 192a b)cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b +--R + +--R 2 +--R - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 168a cosh(x) - 168a b cosh(x) + (144a b - 144a )cosh(x) - 96a b +--R + +--R 3 +--R 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b + 600a b)cosh(x) + (192b - 288a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b - 480a )cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 960a b + 1200a b)cosh(x) + (768b - 1152a b + 288a )x cosh(x) +--R + +--R 3 3 +--R 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 3 +--R (- 960a b + 1200a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (1152b - 1728a b + 432a )x cosh(x) + (288a b - 360a b)cosh(x) +--R + +--R 2 2 4 +--R - 24a b + 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (- 480a b + 600a b)cosh(x) + (768b - 1152a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (288a b - 360a b)cosh(x) + (- 48a b + 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b + 120a b)cosh(x) + (192b - 288a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (96a b - 120a b)cosh(x) + (- 24a b + 24a )cosh(x) + 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R , +--R +--R 3 2 4 3 2 3 +--R (- 384b + 384a b)sinh(x) + (- 1536b + 1536a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (- 2304b + 2304a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (- 1536b + 1536a b)cosh(x) sinh(x) + (- 384b + 384a b)cosh(x) +--R * +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R \|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 168a cosh(x) - 168a b cosh(x) + (144a b - 144a )cosh(x) - 96a b +--R + +--R 3 +--R 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b + 600a b)cosh(x) + (192b - 288a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b - 480a )cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 960a b + 1200a b)cosh(x) + (768b - 1152a b + 288a )x cosh(x) +--R + +--R 3 3 +--R 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 3 +--R (- 960a b + 1200a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (1152b - 1728a b + 432a )x cosh(x) + (288a b - 360a b)cosh(x) +--R + +--R 2 2 4 +--R - 24a b + 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (- 480a b + 600a b)cosh(x) + (768b - 1152a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (288a b - 360a b)cosh(x) + (- 48a b + 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b + 120a b)cosh(x) + (192b - 288a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (96a b - 120a b)cosh(x) + (- 24a b + 24a )cosh(x) + 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 174 + +--S 175 of 526 +m0633:= a0633.1-r0633 +--R +--R +--R (174) +--R 3 2 4 3 2 3 +--R (192b - 192a b)sinh(x) + (768b - 768a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 3 +--R (1152b - 1152a b)cosh(x) sinh(x) + (768b - 768a b)cosh(x) sinh(x) +--R + +--R 3 2 4 +--R (192b - 192a b)cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 3 2 4 3 2 3 +--R (384b - 384a b)sinh(x) + (1536b - 1536a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (2304b - 2304a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (1536b - 1536a b)cosh(x) sinh(x) + (384b - 384a b)cosh(x) +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) + 56a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) + 200a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 120a cosh(x) + 216a b cosh(x) + (48a b - 24a )cosh(x) + 96a b +--R + +--R 3 +--R - 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 24a b cosh(x) + (- 24a b + 120a )cosh(x) +--R + +--R 3 3 +--R (288a b - 168a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R - 120a cosh(x) - 216a b cosh(x) + (- 96a b + 240a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (192a b + 48a b)cosh(x) + 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R - 108a cosh(x) - 168a b cosh(x) + (- 24a b + 120a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 +--R (- 192a b + 432a b)cosh(x) + (288a b - 360a b)cosh(x) - 24a b +--R + +--R 4 +--R 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R - 24a cosh(x) - 56a b cosh(x) + (48a b - 24a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (- 288a b + 408a b)cosh(x) + (288a b - 360a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b + 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (- 96a b + 120a b)cosh(x) + (96a b - 120a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b + 24a )cosh(x) + 8a b cosh(x) - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R Type: Expression(Integer) +--E 175 + +--S 176 of 526 +d0633:= D(m0633a,x) +--R +--R +--R (175) 0 +--R Type: Polynomial(Integer) +--E 176 + +--S 177 of 526 +m0633:= a0633.2-r0633 +--R +--R +--R (176) +--R 3 2 4 3 2 3 +--R (- 384b + 384a b)sinh(x) + (- 1536b + 1536a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (- 2304b + 2304a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (- 1536b + 1536a b)cosh(x) sinh(x) + (- 384b + 384a b)cosh(x) +--R * +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R \|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R 3 2 4 3 2 3 +--R (384b - 384a b)sinh(x) + (1536b - 1536a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (2304b - 2304a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (1536b - 1536a b)cosh(x) sinh(x) + (384b - 384a b)cosh(x) +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) + 56a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) + 200a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 120a cosh(x) + 216a b cosh(x) + (48a b - 24a )cosh(x) + 96a b +--R + +--R 3 +--R - 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 24a b cosh(x) + (- 24a b + 120a )cosh(x) +--R + +--R 3 3 +--R (288a b - 168a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R - 120a cosh(x) - 216a b cosh(x) + (- 96a b + 240a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (192a b + 48a b)cosh(x) + 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R - 108a cosh(x) - 168a b cosh(x) + (- 24a b + 120a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 +--R (- 192a b + 432a b)cosh(x) + (288a b - 360a b)cosh(x) - 24a b +--R + +--R 4 +--R 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R - 24a cosh(x) - 56a b cosh(x) + (48a b - 24a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (- 288a b + 408a b)cosh(x) + (288a b - 360a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b + 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (- 96a b + 120a b)cosh(x) + (96a b - 120a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b + 24a )cosh(x) + 8a b cosh(x) - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R Type: Expression(Integer) +--E 177 + +--S 178 of 526 +d0633:= D(m0633b,x) +--R +--R +--R (177) 0 +--R Type: Polynomial(Integer) +--E 178 + +--S 179 of 526 +t0634:= sinh(x)/(a+a*sech(x)) +--R +--R +--R sinh(x) +--R (178) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 179 + +--S 180 of 526 +r0634:= -(-cosh(x)+log(1+cosh(x)))/a +--R +--R +--R - log(cosh(x) + 1) + cosh(x) +--R (179) ---------------------------- +--R a +--R Type: Expression(Integer) +--E 180 + +--S 181 of 526 +a0634:= integrate(t0634,x) +--R +--R +--R (180) +--R 2 +--R (- 4sinh(x) - 4cosh(x))log(sinh(x) + cosh(x) + 1) + sinh(x) +--R + +--R 2 +--R (2cosh(x) + 2x)sinh(x) + cosh(x) + 2x cosh(x) + 1 +--R / +--R 2a sinh(x) + 2a cosh(x) +--R Type: Union(Expression(Integer),...) +--E 181 + +--S 182 of 526 +m0634:= a0634-r0634 +--R +--R +--R (181) +--R (- 4sinh(x) - 4cosh(x))log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (2sinh(x) + 2cosh(x))log(cosh(x) + 1) + sinh(x) + 2x sinh(x) - cosh(x) +--R + +--R 2x cosh(x) + 1 +--R / +--R 2a sinh(x) + 2a cosh(x) +--R Type: Expression(Integer) +--E 182 + +--S 183 of 526 +d0634:= D(m0634,x) +--R +--R +--R (182) +--R 3 2 2 +--R (- cosh(x) + 1)sinh(x) + (- cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 +--R (cosh(x) - cosh(x) - cosh(x) + 1)sinh(x) + cosh(x) - 1 +--R / +--R 2 2 +--R (2a cosh(x) + 2a)sinh(x) + (4a cosh(x) + 6a cosh(x) + 2a)sinh(x) +--R + +--R 3 2 +--R 2a cosh(x) + 4a cosh(x) + 2a cosh(x) +--R Type: Expression(Integer) +--E 183 + +--S 184 of 526 +t0635:= sinh(x)^2/(a+a*sech(x)) +--R +--R +--R 2 +--R sinh(x) +--R (183) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 184 + +--S 185 of 526 +r0635:= 1/2*(x-2*sinh(x)+cosh(x)*sinh(x))/a +--R +--R +--R (cosh(x) - 2)sinh(x) + x +--R (184) ------------------------ +--R 2a +--R Type: Expression(Integer) +--E 185 + +--S 186 of 526 +a0635:= integrate(t0635,x) +--R +--R +--R (cosh(x) - 2)sinh(x) + x +--R (185) ------------------------ +--R 2a +--R Type: Union(Expression(Integer),...) +--E 186 + +--S 187 of 526 +m0635:= a0635-r0635 +--R +--R +--R (186) 0 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 526 +d0635:= D(m0635,x) +--R +--R +--R (187) 0 +--R Type: Expression(Integer) +--E 188 + +--S 189 of 526 +t0636:= sinh(x)^3/(a+a*sech(x)) +--R +--R +--R 3 +--R sinh(x) +--R (188) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 189 + +--S 190 of 526 +r0636:= 1/6*cosh(x)^2*(-3+2*cosh(x))/a +--R +--R +--R 3 2 +--R 2cosh(x) - 3cosh(x) +--R (189) --------------------- +--R 6a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 526 +a0636:= integrate(t0636,x) +--R +--R +--R 2 3 2 +--R (3cosh(x) - 3)sinh(x) + cosh(x) - 3cosh(x) + 3cosh(x) +--R (190) -------------------------------------------------------- +--R 12a +--R Type: Union(Expression(Integer),...) +--E 191 + +--S 192 of 526 +m0636:= a0636-r0636 +--R +--R +--R 2 3 2 +--R (cosh(x) - 1)sinh(x) - cosh(x) + cosh(x) + cosh(x) +--R (191) ----------------------------------------------------- +--R 4a +--R Type: Expression(Integer) +--E 192 + +--S 193 of 526 +d0636:= D(m0636,x) +--R +--R +--R 3 2 +--R sinh(x) + (- cosh(x) + 1)sinh(x) +--R (192) ---------------------------------- +--R 4a +--R Type: Expression(Integer) +--E 193 + +--S 194 of 526 +t0637:= sinh(x)^4/(a+a*sech(x)) +--R +--R +--R 4 +--R sinh(x) +--R (193) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 194 + +--S 195 of 526 +r0637:= 1/24/a*(-3*cosh(x)*sinh(x)+6*cosh(x)^3*sinh(x)+8*sinh(x)-_ + 8*sinh(x)*cosh(x)^2-3*x) +--R +--R +--R 3 2 +--R (6cosh(x) - 8cosh(x) - 3cosh(x) + 8)sinh(x) - 3x +--R (194) -------------------------------------------------- +--R 24a +--R Type: Expression(Integer) +--E 195 + +--S 196 of 526 +a0637:= integrate(t0637,x) +--R +--R +--R 3 3 2 +--R (3cosh(x) - 2)sinh(x) + (3cosh(x) - 6cosh(x) + 6)sinh(x) - 3x +--R (195) ---------------------------------------------------------------- +--R 24a +--R Type: Union(Expression(Integer),...) +--E 196 + +--S 197 of 526 +m0637:= a0637-r0637 +--R +--R +--R (196) +--R 3 3 2 +--R (3cosh(x) - 2)sinh(x) + (- 3cosh(x) + 2cosh(x) + 3cosh(x) - 2)sinh(x) +--R ------------------------------------------------------------------------ +--R 24a +--R Type: Expression(Integer) +--E 197 + +--S 198 of 526 +d0637:= D(m0637,x) +--R +--R +--R (197) +--R 4 2 4 3 2 +--R 3sinh(x) + (- 2cosh(x) + 3)sinh(x) - 3cosh(x) + 2cosh(x) + 3cosh(x) +--R + +--R - 2cosh(x) +--R / +--R 24a +--R Type: Expression(Integer) +--E 198 + +--S 199 of 526 +t0638:= cosh(x)/(a+b*sech(x)) +--R +--R +--R cosh(x) +--R (198) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 526 +r0638:= -b*x/a^2+2*b^2*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/_ + a^2/(a^2-b^2)^(1/2)+sinh(x)/a +--R +--R +--R x +--R (b - a)tanh(-) +---------+ +--R 2 2 | 2 2 +--R - 2b atan(--------------) + (a sinh(x) - b x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (199) --------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 200 + +--S 201 of 526 +a0638:= integrate(t0638,x) +--R +--R +--R (200) +--R [ +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 2 +--R a sinh(x) + (2a cosh(x) - 2b x)sinh(x) + a cosh(x) - 2b x cosh(x) +--R + +--R - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|b - a +--R , +--R +--R 2 2 +--R (- 4b sinh(x) - 4b cosh(x)) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 +--R a sinh(x) + (2a cosh(x) - 2b x)sinh(x) + a cosh(x) - 2b x cosh(x) +--R + +--R - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 201 + +--S 202 of 526 +m0638a:= a0638.1-r0638 +--R +--R +--R (201) +--R +---------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2b cosh(x))\|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R x +--R +-------+ (b - a)tanh(-) +--R 2 2 | 2 2 2 +--R (4b sinh(x) + 4b cosh(x))\|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (- a sinh(x) + a cosh(x) - a)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|- b + a \|b - a +--R Type: Expression(Integer) +--E 202 + +--S 203 of 526 +d0638a:= D(m0638a,x) +--R +--R +--R (202) +--R 2 4 2 3 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((- 4b - 2a b)cosh(x) - 4b + 2a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R (- 2a b + 2a )cosh(x) + (- 8b + 2a b)cosh(x) +--R + +--R 2 2 +--R (- 8b + 2a b - 2a )cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (- a b + a )cosh(x) + (- 4b + 2a b)cosh(x) - 4b cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (- a b - a )sinh(x) + ((- 2a b - 2a )cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((4b - 2a b)cosh(x) - 4b - 2a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R (2a b + 2a )cosh(x) + (8b + 2a b)cosh(x) +--R + +--R 2 2 +--R (- 8b - 2a b - 2a )cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (a b + a )cosh(x) + (4b + 2a b)cosh(x) - 4b cosh(x) - 2a b cosh(x) +--R + +--R 2 +--R - a b - a +--R / +--R 2 3 3 2 3 2 2 2 +--R (2a b - 2a )sinh(x) + ((6a b - 6a )cosh(x) + 4a b - 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R ((6a b - 6a )cosh(x) + (8a b - 8a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (2a b - 2a )cosh(x) + (4a b - 4a b)cosh(x) + (2a b - 2a )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 3 2 2 2 +--R (- 2a b - 2a )sinh(x) + ((- 6a b - 6a )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R ((- 6a b - 6a )cosh(x) + (- 8a b - 8a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (- 2a b - 2a )cosh(x) + (- 4a b - 4a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 203 + +--S 204 of 526 +m0638b:= a0638.2-r0638 +--R +--R +--R (203) +--R +---------+ +--R | 2 2 +--R 2 2 (a sinh(x) + a cosh(x) + b)\|- b + a +--R (- 4b sinh(x) - 4b cosh(x))atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R x +--R (b - a)tanh(-) +--R 2 2 2 +--R (4b sinh(x) + 4b cosh(x))atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- a sinh(x) + a cosh(x) - a)\|- b + a +--R / +--R +---------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|- b + a +--R Type: Expression(Integer) +--E 204 + +--S 205 of 526 +d0638b:= D(m0638b,x) +--R +--R +--R (204) +--R 2 4 2 3 +--R (a b - a )sinh(x) + ((2a b - 2a )cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((- 4b - 2a b)cosh(x) - 4b + 2a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R (- 2a b + 2a )cosh(x) + (- 8b + 2a b)cosh(x) +--R + +--R 2 2 +--R (- 8b + 2a b - 2a )cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (- a b + a )cosh(x) + (- 4b + 2a b)cosh(x) - 4b cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R (- a b - a )sinh(x) + ((- 2a b - 2a )cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R ((4b - 2a b)cosh(x) - 4b - 2a b - 2a )sinh(x) +--R + +--R 2 3 2 2 +--R (2a b + 2a )cosh(x) + (8b + 2a b)cosh(x) +--R + +--R 2 2 +--R (- 8b - 2a b - 2a )cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R (a b + a )cosh(x) + (4b + 2a b)cosh(x) - 4b cosh(x) - 2a b cosh(x) +--R + +--R 2 +--R - a b - a +--R / +--R 2 3 3 2 3 2 2 2 +--R (2a b - 2a )sinh(x) + ((6a b - 6a )cosh(x) + 4a b - 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R ((6a b - 6a )cosh(x) + (8a b - 8a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (2a b - 2a )cosh(x) + (4a b - 4a b)cosh(x) + (2a b - 2a )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 3 2 3 2 2 2 +--R (- 2a b - 2a )sinh(x) + ((- 6a b - 6a )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R ((- 6a b - 6a )cosh(x) + (- 8a b - 8a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (- 2a b - 2a )cosh(x) + (- 4a b - 4a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R Type: Expression(Integer) +--E 205 + +--S 206 of 526 +t0639:= cosh(x)^2/(a+b*sech(x)) +--R +--R +--R 2 +--R cosh(x) +--R (205) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 206 + +--S 207 of 526 +r0639:= 1/2*x/a+b^2*x/a^3-2*b^3*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/_ + a^3/(a^2-b^2)^(1/2)-b*sinh(x)/a^2+1/2*cosh(x)*sinh(x)/a +--R +--R +--R (206) +--R x +--R (b - a)tanh(-) +--R 3 2 +--R 4b atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R ((a cosh(x) - 2a b)sinh(x) + (2b + a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression(Integer) +--E 207 + +--S 208 of 526 +a0639:= integrate(t0639,x) +--R +--R +--R (207) +--R [ +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b + 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b + 8a )x cosh(x) + 4a b) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b + 4a )x cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|b - a +--R , +--R +--R 3 2 3 3 2 +--R (16b sinh(x) + 32b cosh(x)sinh(x) + 16b cosh(x) ) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b + 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b + 8a )x cosh(x) + 4a b) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b + 4a )x cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 3 3 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 208 + +--S 209 of 526 +m0639a:= a0639.1-r0639 +--R +--R +--R (208) +--R +---------+ +--R 3 2 3 3 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (- 16b sinh(x) - 32b cosh(x)sinh(x) - 16b cosh(x) )\|b - a +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 3 2 2 2 +--R a sinh(x) + 4a b sinh(x) + (- 2a cosh(x) + 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (- 4a b cosh(x) + 4a b)sinh(x) + a cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) - a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 3 3 2 | 2 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 209 + +--S 210 of 526 +d0639a:= D(m0639a,x) +--R +--R +--R (209) +--R 2 3 6 2 3 2 2 5 +--R (- a b + a )sinh(x) + ((- 2a b + 2a )cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 2 3 +--R ((a b - a )cosh(x) + (- 8a b + 8a b)cosh(x) + 4a b - a b + a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 3 2 3 2 2 +--R ((4a b - 4a )cosh(x) + (8b + 8a b )cosh(x) + 8b - 4a b + 4a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 2 3 +--R (a b - a )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 3 2 3 2 3 2 2 +--R (24b + 2a b - 2a )cosh(x) + (24b - 8a b + 8a b)cosh(x) +--R + +--R 2 2 3 +--R 4a b + a b - a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 2 4 +--R (- 2a b + 2a )cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 3 2 3 3 2 2 2 +--R (24b - 8a b )cosh(x) + (24b - 4a b + 4a b)cosh(x) +--R + +--R 2 2 3 +--R (8a b + 2a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 3 2 2 3 4 3 3 +--R (- a b + a )cosh(x) + (8b - 4a b - a b + a )cosh(x) + 8b cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4a b + a b - a )cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 6 2 3 2 2 5 +--R (a b + a )sinh(x) + ((2a b + 2a )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 2 3 4 +--R ((- a b - a )cosh(x) + (8a b + 8a b)cosh(x) + 4a b + a b + a )sinh(x) +--R + +--R 2 3 3 3 2 3 2 2 +--R ((- 4a b - 4a )cosh(x) + (- 8b + 8a b )cosh(x) + 8b + 4a b + 4a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 2 3 +--R (- a b - a )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 3 2 3 2 3 2 2 2 +--R (- 24b - 2a b - 2a )cosh(x) + (24b + 8a b + 8a b)cosh(x) + 4a b +--R + +--R 2 3 +--R - a b - a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 2 4 +--R (2a b + 2a )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 3 2 3 3 2 2 2 +--R (- 24b - 8a b )cosh(x) + (24b + 4a b + 4a b)cosh(x) +--R + +--R 2 2 3 +--R (8a b - 2a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 3 2 2 3 4 3 3 +--R (a b + a )cosh(x) + (- 8b - 4a b + a b + a )cosh(x) + 8b cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4a b - a b - a )cosh(x) - a b - a +--R / +--R 3 4 4 3 4 2 2 3 3 +--R (4a b - 4a )sinh(x) + ((16a b - 16a )cosh(x) + 8a b - 8a b)sinh(x) +--R + +--R 3 4 2 2 2 3 3 4 +--R ((24a b - 24a )cosh(x) + (24a b - 24a b)cosh(x) + 4a b - 4a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R (16a b - 16a )cosh(x) + (24a b - 24a b)cosh(x) +--R + +--R 3 4 +--R (8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 2 2 3 3 3 4 2 +--R (4a b - 4a )cosh(x) + (8a b - 8a b)cosh(x) + (4a b - 4a )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 4 4 3 4 2 2 3 3 +--R (- 4a b - 4a )sinh(x) + ((- 16a b - 16a )cosh(x) - 8a b - 8a b)sinh(x) +--R + +--R 3 4 2 2 2 3 3 4 +--R ((- 24a b - 24a )cosh(x) + (- 24a b - 24a b)cosh(x) - 4a b - 4a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R (- 16a b - 16a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 3 4 +--R (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 2 2 3 3 3 4 2 +--R (- 4a b - 4a )cosh(x) + (- 8a b - 8a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R Type: Expression(Integer) +--E 210 + +--S 211 of 526 +m0639b:= a0639.2-r0639 +--R +--R +--R (210) +--R 3 2 3 3 2 +--R (16b sinh(x) + 32b cosh(x)sinh(x) + 16b cosh(x) ) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R x +--R (b - a)tanh(-) +--R 3 2 3 3 2 2 +--R (- 16b sinh(x) - 32b cosh(x)sinh(x) - 16b cosh(x) )atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 3 2 2 2 +--R a sinh(x) + 4a b sinh(x) + (- 2a cosh(x) + 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (- 4a b cosh(x) + 4a b)sinh(x) + a cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 3 3 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|- b + a +--R Type: Expression(Integer) +--E 211 + +--S 212 of 526 +d0639b:= D(m0639b,x) +--R +--R +--R (211) +--R 2 3 6 2 3 2 2 5 +--R (- a b + a )sinh(x) + ((- 2a b + 2a )cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 2 3 +--R ((a b - a )cosh(x) + (- 8a b + 8a b)cosh(x) + 4a b - a b + a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 3 3 2 3 2 2 +--R ((4a b - 4a )cosh(x) + (8b + 8a b )cosh(x) + 8b - 4a b + 4a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 2 3 +--R (a b - a )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 3 2 3 2 3 2 2 +--R (24b + 2a b - 2a )cosh(x) + (24b - 8a b + 8a b)cosh(x) +--R + +--R 2 2 3 +--R 4a b + a b - a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 2 4 +--R (- 2a b + 2a )cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 3 2 3 3 2 2 2 +--R (24b - 8a b )cosh(x) + (24b - 4a b + 4a b)cosh(x) +--R + +--R 2 2 3 +--R (8a b + 2a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 3 2 2 3 4 3 3 +--R (- a b + a )cosh(x) + (8b - 4a b - a b + a )cosh(x) + 8b cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4a b + a b - a )cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 6 2 3 2 2 5 +--R (a b + a )sinh(x) + ((2a b + 2a )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 2 3 2 2 2 2 2 3 4 +--R ((- a b - a )cosh(x) + (8a b + 8a b)cosh(x) + 4a b + a b + a )sinh(x) +--R + +--R 2 3 3 3 2 3 2 2 +--R ((- 4a b - 4a )cosh(x) + (- 8b + 8a b )cosh(x) + 8b + 4a b + 4a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 2 2 3 +--R (- a b - a )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 3 2 3 2 3 2 2 2 +--R (- 24b - 2a b - 2a )cosh(x) + (24b + 8a b + 8a b)cosh(x) + 4a b +--R + +--R 2 3 +--R - a b - a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 2 4 +--R (2a b + 2a )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 3 2 3 3 2 2 2 +--R (- 24b - 8a b )cosh(x) + (24b + 4a b + 4a b)cosh(x) +--R + +--R 2 2 3 +--R (8a b - 2a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 3 2 2 3 4 3 3 +--R (a b + a )cosh(x) + (- 8b - 4a b + a b + a )cosh(x) + 8b cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (4a b - a b - a )cosh(x) - a b - a +--R / +--R 3 4 4 3 4 2 2 3 3 +--R (4a b - 4a )sinh(x) + ((16a b - 16a )cosh(x) + 8a b - 8a b)sinh(x) +--R + +--R 3 4 2 2 2 3 3 4 +--R ((24a b - 24a )cosh(x) + (24a b - 24a b)cosh(x) + 4a b - 4a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R (16a b - 16a )cosh(x) + (24a b - 24a b)cosh(x) +--R + +--R 3 4 +--R (8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 2 2 3 3 3 4 2 +--R (4a b - 4a )cosh(x) + (8a b - 8a b)cosh(x) + (4a b - 4a )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 4 4 3 4 2 2 3 3 +--R (- 4a b - 4a )sinh(x) + ((- 16a b - 16a )cosh(x) - 8a b - 8a b)sinh(x) +--R + +--R 3 4 2 2 2 3 3 4 +--R ((- 24a b - 24a )cosh(x) + (- 24a b - 24a b)cosh(x) - 4a b - 4a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 2 +--R (- 16a b - 16a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 3 4 +--R (- 8a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 4 4 2 2 3 3 3 4 2 +--R (- 4a b - 4a )cosh(x) + (- 8a b - 8a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R Type: Expression(Integer) +--E 212 + +--S 213 of 526 +t0640:= cosh(x)^3/(a+b*sech(x)) +--R +--R +--R 3 +--R cosh(x) +--R (212) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 213 + +--S 214 of 526 +r0640:= -1/2*b*x/a^2-b^3*x/a^4+2*b^4*atan((a-b)*tanh(1/2*x)/_ + (a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)+sinh(x)/a+_ + b^2*sinh(x)/a^3-1/2*b*cosh(x)*sinh(x)/a^2+1/3*sinh(x)^3/a +--R +--R +--R (213) +--R x +--R (b - a)tanh(-) +--R 4 2 +--R - 12b atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 2 2 3 3 2 +--R (2a sinh(x) + (- 3a b cosh(x) + 6a b + 6a )sinh(x) + (- 6b - 3a b)x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 526 +a0640:= integrate(t0640,x) +--R +--R +--R (214) +--R [ +--R 4 3 4 2 4 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 4 3 +--R 24b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b + 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 20a cosh(x) - 30a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 +--R (- 24b - 12a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 15a cosh(x) - 30a b cosh(x) + (72a b + 54a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 72b - 36a b)x cosh(x) - 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 72b - 36a b)x cosh(x) + (- 24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 24b - 12a b)x cosh(x) + (- 12a b - 9a )cosh(x) +--R + +--R 2 3 +--R 3a b cosh(x) - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 3 4 2 4 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 4 3 +--R 24a cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 4 3 4 2 4 2 +--R - 48b sinh(x) - 144b cosh(x)sinh(x) - 144b cosh(x) sinh(x) +--R + +--R 4 3 +--R - 48b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b + 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 20a cosh(x) - 30a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 +--R (- 24b - 12a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 15a cosh(x) - 30a b cosh(x) + (72a b + 54a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 72b - 36a b)x cosh(x) - 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 72b - 36a b)x cosh(x) + (- 24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 24b - 12a b)x cosh(x) + (- 12a b - 9a )cosh(x) +--R + +--R 2 3 +--R 3a b cosh(x) - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 4 2 4 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 4 3 +--R 24a cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 215 + +--S 216 of 526 +m0640:= a0640.1-r0640 +--R +--R +--R (215) +--R 4 3 4 2 4 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 4 3 +--R 24b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 4 3 4 2 4 2 +--R 48b sinh(x) + 144b cosh(x)sinh(x) + 144b cosh(x) sinh(x) +--R + +--R 4 3 +--R 48b cosh(x) +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 6 3 2 5 +--R - 7a sinh(x) + (- 18a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (- 9a cosh(x) - 3a b cosh(x) - 12a b - 15a )sinh(x) +--R + +--R 3 3 2 2 2 3 3 +--R (12a cosh(x) + 6a b cosh(x) + (- 24a b - 36a )cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 2 3 2 +--R (15a cosh(x) + 6a b cosh(x) - 18a cosh(x) - 12a b - 9a )sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 3a b cosh(x) + (24a b + 12a )cosh(x) +--R + +--R 2 3 2 +--R (- 24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (- 12a b - 9a )cosh(x) + 3a b cosh(x) - a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) ) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 216 + +--S 217 of 526 +d0640:= D(m0640a,x) +--R +--R +--R (216) 0 +--R Type: Polynomial(Integer) +--E 217 + +--S 218 of 526 +m0640:= a0640.2-r0640 +--R +--R +--R (217) +--R 4 3 4 2 4 2 +--R - 48b sinh(x) - 144b cosh(x)sinh(x) - 144b cosh(x) sinh(x) +--R + +--R 4 3 +--R - 48b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 4 3 4 2 4 2 +--R 48b sinh(x) + 144b cosh(x)sinh(x) + 144b cosh(x) sinh(x) +--R + +--R 4 3 +--R 48b cosh(x) +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 6 3 2 5 +--R - 7a sinh(x) + (- 18a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (- 9a cosh(x) - 3a b cosh(x) - 12a b - 15a )sinh(x) +--R + +--R 3 3 2 2 2 3 3 +--R (12a cosh(x) + 6a b cosh(x) + (- 24a b - 36a )cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 2 3 2 +--R (15a cosh(x) + 6a b cosh(x) - 18a cosh(x) - 12a b - 9a )sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 3a b cosh(x) + (24a b + 12a )cosh(x) +--R + +--R 2 3 2 +--R (- 24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (- 12a b - 9a )cosh(x) + 3a b cosh(x) - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) ) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 218 + +--S 219 of 526 +d0640:= D(m0640b,x) +--R +--R +--R (218) 0 +--R Type: Polynomial(Integer) +--E 219 + +--S 220 of 526 +t0641:= cosh(x)^4/(a+b*sech(x)) +--R +--R +--R 4 +--R cosh(x) +--R (219) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 220 + +--S 221 of 526 +r0641:= 3/8*x/a+1/2*b^2*x/a^3+b^4*x/a^5-2*b^5*atan((a-b)*tanh(1/2*x)/_ + (a^2-b^2)^(1/2))/a^5/(a^2-b^2)^(1/2)-b*sinh(x)/a^2-_ + b^3*sinh(x)/a^4+3/8*cosh(x)*sinh(x)/a+1/2*b^2*cosh(x)*sinh(x)/a^3+_ + 1/4*cosh(x)^3*sinh(x)/a-1/3*b*sinh(x)^3/a^2 +--R +--R +--R (220) +--R x +--R (b - a)tanh(-) +--R 5 2 +--R 48b atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 +--R - 8a b sinh(x) +--R + +--R 4 3 2 2 4 3 3 +--R (6a cosh(x) + (12a b + 9a )cosh(x) - 24a b - 24a b)sinh(x) +--R + +--R 4 2 2 4 +--R (24b + 12a b + 9a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 24a \|- b + a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 526 +a0641:= integrate(t0641,x) +--R +--R +--R (221) +--R [ +--R 5 4 5 3 5 2 2 +--R 192b sinh(x) + 768b cosh(x)sinh(x) + 1152b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768b cosh(x) sinh(x) + 192b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 +--R 168a cosh(x) - 168a b cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 3 3 +--R - 96a b - 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b - 360a b)cosh(x) + (192b + 96a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b + 480a )cosh(x) +--R + +--R 3 3 2 +--R (- 960a b - 720a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (768b + 384a b + 288a )x cosh(x) + 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 3 +--R (- 960a b - 720a b)cosh(x) +--R + +--R 4 2 2 4 2 +--R (1152b + 576a b + 432a )x cosh(x) +--R + +--R 3 3 2 2 4 +--R (288a b + 216a b)cosh(x) - 24a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 3 3 4 +--R (- 480a b - 360a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (768b + 384a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (288a b + 216a b)cosh(x) + (- 48a b - 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b - 72a b)cosh(x) + (192b + 96a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (96a b + 72a b)cosh(x) + (- 24a b - 24a )cosh(x) + 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 5 4 5 3 5 2 2 +--R 384b sinh(x) + 1536b cosh(x)sinh(x) + 2304b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 1536b cosh(x) sinh(x) + 384b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 +--R 168a cosh(x) - 168a b cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 3 3 +--R - 96a b - 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b - 360a b)cosh(x) + (192b + 96a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b + 480a )cosh(x) +--R + +--R 3 3 2 +--R (- 960a b - 720a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (768b + 384a b + 288a )x cosh(x) + 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 3 +--R (- 960a b - 720a b)cosh(x) +--R + +--R 4 2 2 4 2 +--R (1152b + 576a b + 432a )x cosh(x) +--R + +--R 3 3 2 2 4 +--R (288a b + 216a b)cosh(x) - 24a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 3 3 4 +--R (- 480a b - 360a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (768b + 384a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (288a b + 216a b)cosh(x) + (- 48a b - 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b - 72a b)cosh(x) + (192b + 96a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (96a b + 72a b)cosh(x) + (- 24a b - 24a )cosh(x) + 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 222 + +--S 223 of 526 +m0641:= a0641.1-r0641 +--R +--R +--R (222) +--R 5 4 5 3 5 2 2 +--R 192b sinh(x) + 768b cosh(x)sinh(x) + 1152b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768b cosh(x) sinh(x) + 192b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 5 4 5 3 5 2 2 +--R - 384b sinh(x) - 1536b cosh(x)sinh(x) - 2304b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R - 1536b cosh(x) sinh(x) - 384b cosh(x) +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) + 56a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) + 200a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 120a cosh(x) + 216a b cosh(x) + (48a b + 72a )cosh(x) + 96a b +--R + +--R 3 +--R 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 24a b cosh(x) + (- 24a b + 72a )cosh(x) +--R + +--R 3 3 +--R (288a b + 408a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R - 120a cosh(x) - 216a b cosh(x) + (- 96a b + 48a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (192a b + 432a b)cosh(x) + 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R - 108a cosh(x) - 168a b cosh(x) + (- 24a b + 72a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 +--R (- 192a b + 48a b)cosh(x) + (288a b + 216a b)cosh(x) - 24a b +--R + +--R 4 +--R - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R - 24a cosh(x) - 56a b cosh(x) + (48a b + 72a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (- 288a b - 168a b)cosh(x) + (288a b + 216a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b - 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (- 96a b - 72a b)cosh(x) + (96a b + 72a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b - 24a )cosh(x) + 8a b cosh(x) - 3a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 223 + +--S 224 of 526 +d0641:= D(m0641a,x) +--R +--R +--R (223) 0 +--R Type: Polynomial(Integer) +--E 224 + +--S 225 of 526 +m0641:= a0641.2-r0641 +--R +--R +--R (224) +--R 5 4 5 3 5 2 2 +--R 384b sinh(x) + 1536b cosh(x)sinh(x) + 2304b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 1536b cosh(x) sinh(x) + 384b cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 5 4 5 3 5 2 2 +--R - 384b sinh(x) - 1536b cosh(x)sinh(x) - 2304b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R - 1536b cosh(x) sinh(x) - 384b cosh(x) +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) + 56a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) + 200a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 120a cosh(x) + 216a b cosh(x) + (48a b + 72a )cosh(x) + 96a b +--R + +--R 3 +--R 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 24a b cosh(x) + (- 24a b + 72a )cosh(x) +--R + +--R 3 3 +--R (288a b + 408a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R - 120a cosh(x) - 216a b cosh(x) + (- 96a b + 48a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (192a b + 432a b)cosh(x) + 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R - 108a cosh(x) - 168a b cosh(x) + (- 24a b + 72a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 +--R (- 192a b + 48a b)cosh(x) + (288a b + 216a b)cosh(x) - 24a b +--R + +--R 4 +--R - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R - 24a cosh(x) - 56a b cosh(x) + (48a b + 72a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (- 288a b - 168a b)cosh(x) + (288a b + 216a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b - 48a )cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (- 96a b - 72a b)cosh(x) + (96a b + 72a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b - 24a )cosh(x) + 8a b cosh(x) - 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 225 + +--S 226 of 526 +d0641:= D(m0641b,x) +--R +--R +--R (225) 0 +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 526 +t0642:= cosh(x)/(a+a*sech(x)) +--R +--R +--R cosh(x) +--R (226) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 227 + +--S 228 of 526 +r0642:= -x/a+sinh(x)/a+sinh(x)/a/(1+cosh(x)) +--R +--R +--R (cosh(x) + 2)sinh(x) - x cosh(x) - x +--R (227) ------------------------------------ +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 228 + +--S 229 of 526 +a0642:= integrate(t0642,x) +--R +--R +--R (228) +--R 2 2 +--R sinh(x) + (2cosh(x) - 2x + 2)sinh(x) + cosh(x) - 2x cosh(x) - 2x - 5 +--R ---------------------------------------------------------------------- +--R 2a sinh(x) + 2a cosh(x) + 2a +--R Type: Union(Expression(Integer),...) +--E 229 + +--S 230 of 526 +m0642:= a0642-r0642 +--R +--R +--R (229) +--R 2 3 2 +--R (- cosh(x) - 3)sinh(x) + (- 2cosh(x) - 2)sinh(x) + cosh(x) + cosh(x) +--R + +--R - 5cosh(x) - 5 +--R / +--R 2 +--R (2a cosh(x) + 2a)sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R Type: Expression(Integer) +--E 230 + +--S 231 of 526 +d0642:= D(m0642,x) +--R +--R +--R (230) +--R 4 2 3 +--R 2sinh(x) + (cosh(x) + 6cosh(x) + 5)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) + 2cosh(x) + 3cosh(x) + 2)sinh(x) +--R + +--R 4 3 2 5 +--R (- cosh(x) - 6cosh(x) - 4cosh(x) + 6cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 4 3 2 +--R - 4cosh(x) - 2cosh(x) + 4cosh(x) + 3cosh(x) +--R / +--R 2 2 +--R (2a cosh(x) + 4a cosh(x) + 2a)sinh(x) +--R + +--R 3 2 4 +--R (4a cosh(x) + 12a cosh(x) + 12a cosh(x) + 4a)sinh(x) + 2a cosh(x) +--R + +--R 3 2 +--R 8a cosh(x) + 12a cosh(x) + 8a cosh(x) + 2a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 526 +t0643:= cosh(x)^2/(a+a*sech(x)) +--R +--R +--R 2 +--R cosh(x) +--R (231) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 232 + +--S 233 of 526 +r0643:= 1/2*(3*x+3*x*cosh(x)-4*sinh(x)-cosh(x)*sinh(x)+_ + sinh(x)*cosh(x)^2)/a/(1+cosh(x)) +--R +--R +--R 2 +--R (cosh(x) - cosh(x) - 4)sinh(x) + 3x cosh(x) + 3x +--R (232) ------------------------------------------------- +--R 2a cosh(x) + 2a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 526 +a0643:= integrate(t0643,x) +--R +--R +--R (233) +--R 3 2 +--R sinh(x) + (3cosh(x) - 4)sinh(x) +--R + +--R 2 3 2 +--R (3cosh(x) - 4cosh(x) + 12x - 7)sinh(x) + cosh(x) - 4cosh(x) +--R + +--R (12x - 1)cosh(x) + 12x + 20 +--R / +--R 8a sinh(x) + 8a cosh(x) + 8a +--R Type: Union(Expression(Integer),...) +--E 234 + +--S 235 of 526 +m0643:= a0643-r0643 +--R +--R +--R (234) +--R 3 2 2 +--R (cosh(x) + 1)sinh(x) + (- cosh(x) + 3cosh(x) + 12)sinh(x) +--R + +--R 3 2 4 3 +--R (- cosh(x) - cosh(x) + 9cosh(x) + 9)sinh(x) + cosh(x) - 3cosh(x) +--R + +--R 2 +--R - 5cosh(x) + 19cosh(x) + 20 +--R / +--R 2 +--R (8a cosh(x) + 8a)sinh(x) + 8a cosh(x) + 16a cosh(x) + 8a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 526 +d0643:= D(m0643,x) +--R +--R +--R (235) +--R 2 4 +--R (- 2cosh(x) - 4cosh(x) - 10)sinh(x) +--R + +--R 2 3 +--R (- 5cosh(x) - 26cosh(x) - 21)sinh(x) +--R + +--R 4 3 2 2 +--R (4cosh(x) + 5cosh(x) - 4cosh(x) - 15cosh(x) - 10)sinh(x) +--R + +--R 4 3 2 6 +--R (5cosh(x) + 26cosh(x) + 16cosh(x) - 26cosh(x) - 21)sinh(x) - 2cosh(x) +--R + +--R 5 4 3 2 +--R - cosh(x) + 14cosh(x) + 12cosh(x) - 12cosh(x) - 11cosh(x) +--R / +--R 2 2 +--R (8a cosh(x) + 16a cosh(x) + 8a)sinh(x) +--R + +--R 3 2 4 +--R (16a cosh(x) + 48a cosh(x) + 48a cosh(x) + 16a)sinh(x) + 8a cosh(x) +--R + +--R 3 2 +--R 32a cosh(x) + 48a cosh(x) + 32a cosh(x) + 8a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 526 +t0644:= cosh(x)^3/(a+a*sech(x)) +--R +--R +--R 3 +--R cosh(x) +--R (236) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 237 + +--S 238 of 526 +r0644:= 1/6*(7*cosh(x)*sinh(x)-sinh(x)*cosh(x)^2+_ + 16*sinh(x)+2*cosh(x)^3*sinh(x)-9*x*cosh(x)-9*x)/a/(1+cosh(x)) +--R +--R +--R 3 2 +--R (2cosh(x) - cosh(x) + 7cosh(x) + 16)sinh(x) - 9x cosh(x) - 9x +--R (237) --------------------------------------------------------------- +--R 6a cosh(x) + 6a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 526 +a0644:= integrate(t0644,x) +--R +--R +--R (238) +--R 4 3 2 2 +--R sinh(x) + (4cosh(x) - 1)sinh(x) + (6cosh(x) - 9cosh(x) + 20)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 3cosh(x) + 32cosh(x) - 36x + 39)sinh(x) + cosh(x) +--R + +--R 3 2 +--R - 3cosh(x) + 20cosh(x) + (- 36x + 3)cosh(x) - 36x - 69 +--R / +--R 24a sinh(x) + 24a cosh(x) + 24a +--R Type: Union(Expression(Integer),...) +--E 239 + +--S 240 of 526 +m0644:= a0644-r0644 +--R +--R +--R (239) +--R 4 2 3 +--R (cosh(x) + 1)sinh(x) + (4cosh(x) + 3cosh(x) - 1)sinh(x) +--R + +--R 3 2 2 +--R (- 2cosh(x) + cosh(x) - 17cosh(x) - 44)sinh(x) +--R + +--R 4 3 2 5 +--R (- 4cosh(x) - 3cosh(x) + 5cosh(x) - 21cosh(x) - 25)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R - 2cosh(x) + 17cosh(x) + 23cosh(x) - 66cosh(x) - 69 +--R / +--R 2 +--R (24a cosh(x) + 24a)sinh(x) + 24a cosh(x) + 48a cosh(x) + 24a +--R Type: Expression(Integer) +--E 240 + +--S 241 of 526 +d0644:= D(m0644,x) +--R +--R +--R (240) +--R 2 5 +--R (3cosh(x) + 6cosh(x) + 3)sinh(x) +--R + +--R 3 2 4 +--R (- cosh(x) + 6cosh(x) + 15cosh(x) + 32)sinh(x) +--R + +--R 4 3 2 3 +--R (- 2cosh(x) - 4cosh(x) + 25cosh(x) + 102cosh(x) + 75)sinh(x) +--R + +--R 5 4 3 2 2 +--R (6cosh(x) + 4cosh(x) + 9cosh(x) + 38cosh(x) + 59cosh(x) + 32)sinh(x) +--R + +--R 6 5 4 3 2 +--R - cosh(x) - 2cosh(x) - 24cosh(x) - 94cosh(x) - 47cosh(x) +--R + +--R 96cosh(x) + 72 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 5cosh(x) - 10cosh(x) - 20cosh(x) - 54cosh(x) - 19cosh(x) +--R + +--R 2 +--R 64cosh(x) + 44cosh(x) +--R / +--R 2 2 +--R (24a cosh(x) + 48a cosh(x) + 24a)sinh(x) +--R + +--R 3 2 4 +--R (48a cosh(x) + 144a cosh(x) + 144a cosh(x) + 48a)sinh(x) + 24a cosh(x) +--R + +--R 3 2 +--R 96a cosh(x) + 144a cosh(x) + 96a cosh(x) + 24a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 526 +t0645:= cosh(x)^4/(a+a*sech(x)) +--R +--R +--R 4 +--R cosh(x) +--R (241) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 242 + +--S 243 of 526 +r0645:= 1/24*(-64*sinh(x)-2*cosh(x)^3*sinh(x)+6*cosh(x)^4*sinh(x)-_ + 19*cosh(x)*sinh(x)+13*sinh(x)*cosh(x)^2+45*x+_ + 45*x*cosh(x))/a/(1+cosh(x)) +--R +--R +--R (242) +--R 4 3 2 +--R (6cosh(x) - 2cosh(x) + 13cosh(x) - 19cosh(x) - 64)sinh(x) +--R + +--R 45x cosh(x) + 45x +--R / +--R 24a cosh(x) + 24a +--R Type: Expression(Integer) +--E 243 + +--S 244 of 526 +a0645:= integrate(t0645,x) +--R +--R +--R (243) +--R 5 4 +--R 3sinh(x) + (15cosh(x) - 8)sinh(x) +--R + +--R 2 3 +--R (30cosh(x) - 8cosh(x) + 35)sinh(x) +--R + +--R 3 2 2 +--R (30cosh(x) - 48cosh(x) + 135cosh(x) - 160)sinh(x) +--R + +--R 4 3 2 +--R (15cosh(x) - 8cosh(x) + 105cosh(x) - 160cosh(x) + 360x - 288)sinh(x) +--R + +--R 5 4 3 2 +--R 3cosh(x) - 8cosh(x) + 45cosh(x) - 160cosh(x) + (360x - 48)cosh(x) +--R + +--R 360x + 552 +--R / +--R 192a sinh(x) + 192a cosh(x) + 192a +--R Type: Union(Expression(Integer),...) +--E 244 + +--S 245 of 526 +m0645:= a0645-r0645 +--R +--R +--R (244) +--R 5 2 4 +--R (3cosh(x) + 3)sinh(x) + (15cosh(x) + 7cosh(x) - 8)sinh(x) +--R + +--R 3 2 3 +--R (30cosh(x) + 22cosh(x) + 27cosh(x) + 35)sinh(x) +--R + +--R 4 3 2 2 +--R (- 18cosh(x) - 2cosh(x) - 17cosh(x) + 127cosh(x) + 352)sinh(x) +--R + +--R 5 4 3 2 +--R (- 33cosh(x) - 25cosh(x) + 9cosh(x) - 7cosh(x) + 216cosh(x) + 224) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 3cosh(x) - 5cosh(x) + 37cosh(x) - 115cosh(x) - 208cosh(x) +--R + +--R 504cosh(x) + 552 +--R / +--R 2 +--R (192a cosh(x) + 192a)sinh(x) + 192a cosh(x) + 384a cosh(x) + 192a +--R Type: Expression(Integer) +--E 245 + +--S 246 of 526 +d0645:= D(m0645,x) +--R +--R +--R (245) +--R 2 6 +--R (12cosh(x) + 24cosh(x) + 12)sinh(x) +--R + +--R 3 2 5 +--R (72cosh(x) + 159cosh(x) + 102cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 4 +--R (36cosh(x) + 155cosh(x) + 126cosh(x) - 69cosh(x) - 268)sinh(x) +--R + +--R 5 4 3 2 +--R - 48cosh(x) - 98cosh(x) + 20cosh(x) - 59cosh(x) - 714cosh(x) +--R + +--R - 585 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 12cosh(x) - 90cosh(x) + 64cosh(x) + 297cosh(x) + 14cosh(x) +--R + +--R - 421cosh(x) - 280 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 24cosh(x) - 61cosh(x) - 26cosh(x) + 264cosh(x) + 866cosh(x) +--R + +--R 2 +--R 397cosh(x) - 816cosh(x) - 600 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 36cosh(x) - 89cosh(x) - 106cosh(x) + 64cosh(x) + 534cosh(x) +--R + +--R 3 2 +--R 353cosh(x) - 392cosh(x) - 328cosh(x) +--R / +--R 2 2 +--R (192a cosh(x) + 384a cosh(x) + 192a)sinh(x) +--R + +--R 3 2 +--R (384a cosh(x) + 1152a cosh(x) + 1152a cosh(x) + 384a)sinh(x) +--R + +--R 4 3 2 +--R 192a cosh(x) + 768a cosh(x) + 1152a cosh(x) + 768a cosh(x) + 192a +--R Type: Expression(Integer) +--E 246 + +--S 247 of 526 +t0646:= tanh(x)/(a+b*sech(x)) +--R +--R +--R tanh(x) +--R (246) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 526 +r0646:= log(b+a*cosh(x))/a +--R +--R +--R log(a cosh(x) + b) +--R (247) ------------------ +--R a +--R Type: Expression(Integer) +--E 248 + +--S 249 of 526 +a0646:= integrate(t0646,x) +--R +--R +--R - 2a cosh(x) - 2b +--R log(-----------------) - x +--R sinh(x) - cosh(x) +--R (248) -------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 249 + +--S 250 of 526 +m0646:= a0646-r0646 +--R +--R +--R - 2a cosh(x) - 2b +--R - log(a cosh(x) + b) + log(-----------------) - x +--R sinh(x) - cosh(x) +--R (249) ------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 526 +d0646:= D(m0646,x) +--R +--R +--R (250) 0 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 526 +t0647:= tanh(x)^2/(a+b*sech(x)) +--R +--R +--R 2 +--R tanh(x) +--R (251) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 252 + +--S 253 of 526 +r0647:= (b*x-atan(sinh(x))*a+2*(a^2-b^2)^(1/2)*_ + atan((a-b)*(cosh(x)-1)/sinh(x)/(a^2-b^2)^(1/2)))/a/b +--R +--R +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a +--R - a atan(sinh(x)) - 2\|- b + a atan(----------------------) + b x +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R (252) ------------------------------------------------------------------- +--R a b +--R Type: Expression(Integer) +--E 253 + +--S 254 of 526 +a0647:= integrate(t0647,x) +--R +--R +--R (253) +--R [ +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b +--R + +--R 2 +--R - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R - 2a atan(sinh(x) + cosh(x)) + b x +--R / +--R a b +--R , +--R +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R - 2\|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R - 2a atan(sinh(x) + cosh(x)) + b x +--R / +--R a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 254 + +--S 255 of 526 +m0647:= a0647.1-r0647 +--R +--R +--R (254) +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R - 2a atan(sinh(x) + cosh(x)) + a atan(sinh(x)) +--R + +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a +--R 2\|- b + a atan(----------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R / +--R a b +--R Type: Expression(Integer) +--E 255 + +--S 256 of 526 +d0647:= D(m0647a,x) +--R +--R +--R (255) 0 +--R Type: Polynomial(Integer) +--E 256 + +--S 257 of 526 +m0647:= a0647.2-r0647 +--R +--R +--R (256) +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R - 2\|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R - 2a atan(sinh(x) + cosh(x)) + a atan(sinh(x)) +--R + +--R +---------+ +--R | 2 2 (b - a)cosh(x) - b + a +--R 2\|- b + a atan(----------------------) +--R +---------+ +--R | 2 2 +--R sinh(x)\|- b + a +--R / +--R a b +--R Type: Expression(Integer) +--E 257 + +--S 258 of 526 +d0647:= D(m0647b,x) +--R +--R +--R (257) 0 +--R Type: Polynomial(Integer) +--E 258 + +--S 259 of 526 +t0648:= tanh(x)^3/(a+b*sech(x)) +--R +--R +--R 3 +--R tanh(x) +--R (258) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 526 +r0648:= a*log(cosh(x))/b^2-(a^2-b^2)*log(b+a*cosh(x))/b^2/a+sech(x)/b +--R +--R +--R 2 2 2 +--R (b - a )log(a cosh(x) + b) + a log(cosh(x)) + a b sech(x) +--R (259) ---------------------------------------------------------- +--R 2 +--R a b +--R Type: Expression(Integer) +--E 260 + +--S 261 of 526 +a0648:= integrate(t0648,x) +--R +--R +--R (260) +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a ) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (b - a )sinh(x) + (2b - 2a )cosh(x)sinh(x) + (b - a )cosh(x) +--R + +--R 2 2 +--R b - a +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 +--R - b x sinh(x) + (- 2b x cosh(x) + 2a b)sinh(x) - b x cosh(x) +--R + +--R 2 +--R 2a b cosh(x) - b x +--R / +--R 2 2 2 2 2 2 +--R a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) + a b +--R Type: Union(Expression(Integer),...) +--E 261 + +--S 262 of 526 +m0648:= a0648-r0648 +--R +--R +--R (261) +--R 2 2 2 2 2 +--R (- b + a )sinh(x) + (- 2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- b + a )cosh(x) - b + a +--R * +--R log(a cosh(x) + b) +--R + +--R 2 2 2 2 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a )log(cosh(x)) +--R + +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a ) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (b - a )sinh(x) + (2b - 2a )cosh(x)sinh(x) + (b - a )cosh(x) +--R + +--R 2 2 +--R b - a +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- a b sech(x) - b x)sinh(x) +--R + +--R 2 +--R (- 2a b cosh(x)sech(x) - 2b x cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (- a b cosh(x) - a b)sech(x) - b x cosh(x) + 2a b cosh(x) - b x +--R / +--R 2 2 2 2 2 2 +--R a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) + a b +--R Type: Expression(Integer) +--E 262 + +--S 263 of 526 +d0648:= D(m0648,x) +--R +--R +--R (262) +--R 4 3 +--R sech(x)sinh(x) + 4cosh(x)sech(x)sinh(x) +--R + +--R 2 2 3 +--R (6cosh(x) + 2)sech(x)sinh(x) + (4cosh(x) + 4cosh(x))sech(x)sinh(x) +--R + +--R 4 2 +--R (cosh(x) + 2cosh(x) + 1)sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 2 3 +--R - 2sinh(x) - 6cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) - 2cosh(x) +--R + +--R 2cosh(x) +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R Type: Expression(Integer) +--E 263 + +--S 264 of 526 +t0649:= tanh(x)^4/(a+b*sech(x)) +--R +--R +--R 4 +--R tanh(x) +--R (263) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 264 + +--S 265 of 526 +r0649:= x/a+a^2*atan(sinh(x))/b^3-3/2*atan(sinh(x))/b-_ + 2*(a^2-b^2)^(3/2)*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a/b^3-_ + a*tanh(x)/b^2+1/2*sech(x)*tanh(x)/b +--R +--R +--R (264) +--R 2 3 +--R (- 3a b + 2a )atan(sinh(x)) +--R + +--R x +--R +---------+ (b - a)tanh(-) +--R 2 2 | 2 2 2 +--R (- 4b + 4a )\|- b + a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 +--R (a b sech(x) - 2a b)tanh(x) + 2b x +--R / +--R 3 +--R 2a b +--R Type: Expression(Integer) +--E 265 + +--S 266 of 526 +a0649:= integrate(t0649,x) +--R +--R +--R (265) +--R [ +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b - 6a )cosh(x) + 2b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b - 4a )cosh(x) + (4b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b - a )cosh(x) + (2b - 2a )cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b +--R + +--R 2 +--R - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 3 4 2 3 3 +--R (- 3a b + 2a )sinh(x) + (- 12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 18a b + 12a )cosh(x) - 6a b + 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 12a b + 8a )cosh(x) + (- 12a b + 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 3a b + 2a )cosh(x) + (- 6a b + 4a )cosh(x) - 3a b + 2a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 4 3 2 3 +--R b x sinh(x) + (4b x cosh(x) + a b )sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (6b x cosh(x) + 3a b cosh(x) + 2b x + 2a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (4b x cosh(x) + 3a b cosh(x) + (4b x + 4a b)cosh(x) - a b )sinh(x) +--R + +--R 3 4 2 3 3 2 2 2 3 +--R b x cosh(x) + a b cosh(x) + (2b x + 2a b)cosh(x) - a b cosh(x) + b x +--R + +--R 2 +--R 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R a b sinh(x) + 4a b cosh(x)sinh(x) + (6a b cosh(x) + 2a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (4a b cosh(x) + 4a b cosh(x))sinh(x) + a b cosh(x) + 2a b cosh(x) +--R + +--R 3 +--R a b +--R , +--R +--R 2 2 4 2 2 3 +--R (- 2b + 2a )sinh(x) + (- 8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 12b + 12a )cosh(x) - 4b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 8b + 8a )cosh(x) + (- 8b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + (- 4b + 4a )cosh(x) - 2b + 2a +--R * +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R \|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R 2 3 4 2 3 3 +--R (- 3a b + 2a )sinh(x) + (- 12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 18a b + 12a )cosh(x) - 6a b + 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 12a b + 8a )cosh(x) + (- 12a b + 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 3a b + 2a )cosh(x) + (- 6a b + 4a )cosh(x) - 3a b + 2a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 4 3 2 3 +--R b x sinh(x) + (4b x cosh(x) + a b )sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (6b x cosh(x) + 3a b cosh(x) + 2b x + 2a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (4b x cosh(x) + 3a b cosh(x) + (4b x + 4a b)cosh(x) - a b )sinh(x) +--R + +--R 3 4 2 3 3 2 2 2 3 +--R b x cosh(x) + a b cosh(x) + (2b x + 2a b)cosh(x) - a b cosh(x) + b x +--R + +--R 2 +--R 2a b +--R / +--R 3 4 3 3 3 2 3 2 +--R a b sinh(x) + 4a b cosh(x)sinh(x) + (6a b cosh(x) + 2a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (4a b cosh(x) + 4a b cosh(x))sinh(x) + a b cosh(x) + 2a b cosh(x) +--R + +--R 3 +--R a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 266 + +--S 267 of 526 +m0649:= a0649.1-r0649 +--R +--R +--R (266) +--R 2 2 4 2 2 3 +--R (2b - 2a )sinh(x) + (8b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b - 12a )cosh(x) + 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b - 8a )cosh(x) + (8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b - 2a )cosh(x) + (4b - 4a )cosh(x) + 2b - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b - a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b - a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 2 3 4 2 3 3 +--R (- 6a b + 4a )sinh(x) + (- 24a b + 16a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 36a b + 24a )cosh(x) - 12a b + 8a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 24a b + 16a )cosh(x) + (- 24a b + 16a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 6a b + 4a )cosh(x) + (- 12a b + 8a )cosh(x) - 6a b + 4a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 4 2 3 3 +--R (3a b - 2a )sinh(x) + (12a b - 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b - 12a )cosh(x) + 6a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b - 8a )cosh(x) + (12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b - 2a )cosh(x) + (6a b - 4a )cosh(x) + 3a b - 2a +--R * +--R atan(sinh(x)) +--R + +--R 2 2 4 2 2 3 +--R (4b - 4a )sinh(x) + (16b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b - 24a )cosh(x) + 8b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b - 16a )cosh(x) + (16b - 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b - 4a )cosh(x) + (8b - 8a )cosh(x) + 4b - 4a +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 +--R (- a b sech(x) + 2a b)sinh(x) +--R + +--R 2 2 3 +--R (- 4a b cosh(x)sech(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 2 +--R ((- 6a b cosh(x) - 2a b )sech(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (- 4a b cosh(x) - 4a b cosh(x))sech(x) + 8a b cosh(x) +--R + +--R 2 +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 4 +--R (- a b cosh(x) - 2a b cosh(x) - a b )sech(x) + 2a b cosh(x) +--R + +--R 2 2 2 +--R 4a b cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 2 3 2 2 2 +--R 2a b sinh(x) + (6a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (6a b cosh(x) + 8a b cosh(x) - 2a b )sinh(x) + 2a b cosh(x) +--R + +--R 2 2 2 2 +--R 4a b cosh(x) - 2a b cosh(x) + 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a b sinh(x) + 8a b cosh(x)sinh(x) + (12a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (8a b cosh(x) + 8a b cosh(x))sinh(x) + 2a b cosh(x) + 4a b cosh(x) +--R + +--R 3 +--R 2a b +--R Type: Expression(Integer) +--E 267 + +--S 268 of 526 +d0649:= D(m0649a,x) +--R +--R +--R (267) 0 +--R Type: Polynomial(Integer) +--E 268 + +--S 269 of 526 +m0649:= a0649.2-r0649 +--R +--R +--R (268) +--R 2 2 4 2 2 3 +--R (- 4b + 4a )sinh(x) + (- 16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 24b + 24a )cosh(x) - 8b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 16b + 16a )cosh(x) + (- 16b + 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 4b + 4a )cosh(x) + (- 8b + 8a )cosh(x) - 4b + 4a +--R * +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 \|- b + a +--R \|- b + a atan(-------------------------) +--R a sinh(x) + a cosh(x) + b +--R + +--R 2 3 4 2 3 3 +--R (- 6a b + 4a )sinh(x) + (- 24a b + 16a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 36a b + 24a )cosh(x) - 12a b + 8a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 24a b + 16a )cosh(x) + (- 24a b + 16a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 6a b + 4a )cosh(x) + (- 12a b + 8a )cosh(x) - 6a b + 4a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 4 2 3 3 +--R (3a b - 2a )sinh(x) + (12a b - 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b - 12a )cosh(x) + 6a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b - 8a )cosh(x) + (12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b - 2a )cosh(x) + (6a b - 4a )cosh(x) + 3a b - 2a +--R * +--R atan(sinh(x)) +--R + +--R 2 2 4 2 2 3 +--R (4b - 4a )sinh(x) + (16b - 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b - 24a )cosh(x) + 8b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b - 16a )cosh(x) + (16b - 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b - 4a )cosh(x) + (8b - 8a )cosh(x) + 4b - 4a +--R * +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|- b + a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 +--R (- a b sech(x) + 2a b)sinh(x) +--R + +--R 2 2 3 +--R (- 4a b cosh(x)sech(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 2 +--R ((- 6a b cosh(x) - 2a b )sech(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (- 4a b cosh(x) - 4a b cosh(x))sech(x) + 8a b cosh(x) +--R + +--R 2 +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 4 +--R (- a b cosh(x) - 2a b cosh(x) - a b )sech(x) + 2a b cosh(x) +--R + +--R 2 2 2 +--R 4a b cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 2 3 2 2 2 +--R 2a b sinh(x) + (6a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (6a b cosh(x) + 8a b cosh(x) - 2a b )sinh(x) + 2a b cosh(x) +--R + +--R 2 2 2 2 +--R 4a b cosh(x) - 2a b cosh(x) + 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a b sinh(x) + 8a b cosh(x)sinh(x) + (12a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (8a b cosh(x) + 8a b cosh(x))sinh(x) + 2a b cosh(x) + 4a b cosh(x) +--R + +--R 3 +--R 2a b +--R Type: Expression(Integer) +--E 269 + +--S 270 of 526 +d0649:= D(m0649b,x) +--R +--R +--R (269) 0 +--R Type: Polynomial(Integer) +--E 270 + +--S 271 of 526 +t0650:= tanh(x)/(a+a*sech(x)) +--R +--R +--R tanh(x) +--R (270) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 526 +r0650:= log(1+cosh(x))/a +--R +--R +--R log(cosh(x) + 1) +--R (271) ---------------- +--R a +--R Type: Expression(Integer) +--E 272 + +--S 273 of 526 +a0650:= integrate(t0650,x) +--R +--R +--R 2log(sinh(x) + cosh(x) + 1) - x +--R (272) ------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 526 +m0650:= a0650-r0650 +--R +--R +--R 2log(sinh(x) + cosh(x) + 1) - log(cosh(x) + 1) - x +--R (273) -------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 274 + +--S 275 of 526 +d0650:= D(m0650,x) +--R +--R +--R 2 2 +--R - sinh(x) + cosh(x) - 1 +--R (274) ---------------------------------------------------- +--R 2 +--R (a cosh(x) + a)sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 526 +t0651:= tanh(x)^2/(a+a*sech(x)) +--R +--R +--R 2 +--R tanh(x) +--R (275) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 276 + +--S 277 of 526 +r0651:= -(-x+atan(sinh(x)))/a +--R +--R +--R - atan(sinh(x)) + x +--R (276) ------------------- +--R a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 526 +a0651:= integrate(t0651,x) +--R +--R +--R - 2atan(sinh(x) + cosh(x)) + x +--R (277) ------------------------------ +--R a +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 526 +m0651:= a0651-r0651 +--R +--R +--R - 2atan(sinh(x) + cosh(x)) + atan(sinh(x)) +--R (278) ------------------------------------------ +--R a +--R Type: Expression(Integer) +--E 279 + +--S 280 of 526 +d0651:= D(m0651,x) +--R +--R +--R (279) +--R 3 2 2 3 +--R - 2sinh(x) - cosh(x)sinh(x) + (2cosh(x) - 2)sinh(x) + cosh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + (a cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 526 +t0652:= tanh(x)^3/(a+a*sech(x)) +--R +--R +--R 3 +--R tanh(x) +--R (280) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 281 + +--S 282 of 526 +r0652:= log(cosh(x))/a+sech(x)/a +--R +--R +--R log(cosh(x)) + sech(x) +--R (281) ---------------------- +--R a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 526 +a0652:= integrate(t0652,x) +--R +--R +--R (282) +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - x sinh(x) + (- 2x cosh(x) + 2)sinh(x) - x cosh(x) + 2cosh(x) - x +--R / +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 526 +m0652:= a0652-r0652 +--R +--R +--R (283) +--R 2 2 +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)log(cosh(x)) +--R + +--R 2 2 2cosh(x) +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (- sech(x) - x)sinh(x) + (- 2cosh(x)sech(x) - 2x cosh(x) + 2)sinh(x) +--R + +--R 2 2 +--R (- cosh(x) - 1)sech(x) - x cosh(x) + 2cosh(x) - x +--R / +--R 2 2 +--R a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 526 +d0652:= D(m0652,x) +--R +--R +--R (284) +--R 4 3 +--R sech(x)sinh(x) + 4cosh(x)sech(x)sinh(x) +--R + +--R 2 2 3 +--R (6cosh(x) + 2)sech(x)sinh(x) + (4cosh(x) + 4cosh(x))sech(x)sinh(x) +--R + +--R 4 2 +--R (cosh(x) + 2cosh(x) + 1)sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 2 3 +--R - 2sinh(x) - 6cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) - 2cosh(x) +--R + +--R 2cosh(x) +--R / +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression(Integer) +--E 285 + +--S 286 of 526 +t0653:= tanh(x)^4/(a+a*sech(x)) +--R +--R +--R 4 +--R tanh(x) +--R (285) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 526 +r0653:= x/a-1/2*atan(sinh(x))/a-tanh(x)/a+1/2*sech(x)*tanh(x)/a +--R +--R +--R - atan(sinh(x)) + (sech(x) - 2)tanh(x) + 2x +--R (286) ------------------------------------------- +--R 2a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 526 +a0653:= integrate(t0653,x) +--R +--R +--R (287) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) - 4cosh(x))sinh(x) - cosh(x) - 2cosh(x) - 1 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 4 3 +--R x sinh(x) + (4x cosh(x) + 1)sinh(x) +--R + +--R 2 2 +--R (6x cosh(x) + 3cosh(x) + 2x + 2)sinh(x) +--R + +--R 3 2 4 +--R (4x cosh(x) + 3cosh(x) + (4x + 4)cosh(x) - 1)sinh(x) + x cosh(x) +--R + +--R 3 2 +--R cosh(x) + (2x + 2)cosh(x) - cosh(x) + x + 2 +--R / +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 526 +m0653:= a0653-r0653 +--R +--R +--R (288) +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) - 8cosh(x))sinh(x) - 2cosh(x) - 4cosh(x) - 2 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 4cosh(x))sinh(x) + cosh(x) + 2cosh(x) + 1 +--R * +--R atan(sinh(x)) +--R + +--R 4 3 +--R (- sech(x) + 2)sinh(x) + (- 4cosh(x)sech(x) + 8cosh(x))sinh(x) +--R + +--R 2 2 2 +--R ((- 6cosh(x) - 2)sech(x) + 12cosh(x) + 4)sinh(x) +--R + +--R 3 3 +--R ((- 4cosh(x) - 4cosh(x))sech(x) + 8cosh(x) + 8cosh(x))sinh(x) +--R + +--R 4 2 4 2 +--R (- cosh(x) - 2cosh(x) - 1)sech(x) + 2cosh(x) + 4cosh(x) + 2 +--R * +--R tanh(x) +--R + +--R 3 2 2 +--R 2sinh(x) + (6cosh(x) + 4)sinh(x) + (6cosh(x) + 8cosh(x) - 2)sinh(x) +--R + +--R 3 2 +--R 2cosh(x) + 4cosh(x) - 2cosh(x) + 4 +--R / +--R 4 3 2 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a)sinh(x) +--R + +--R 3 4 2 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 526 +d0653:= D(m0653,x) +--R +--R +--R (289) +--R 8 7 +--R (2sech(x) - 2)sinh(x) + (12cosh(x)sech(x) - 12cosh(x))sinh(x) +--R + +--R 2 2 6 +--R ((30cosh(x) + 8)sech(x) - 30cosh(x) - 8)sinh(x) +--R + +--R 3 3 5 +--R ((40cosh(x) + 36cosh(x))sech(x) - 40cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 4 2 +--R (30cosh(x) + 66cosh(x) + 12)sech(x) - 30cosh(x) - 66cosh(x) +--R + +--R - 12 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 5 +--R (12cosh(x) + 64cosh(x) + 36cosh(x))sech(x) - 12cosh(x) +--R + +--R 3 +--R - 64cosh(x) - 36cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 6 +--R (2cosh(x) + 36cosh(x) + 42cosh(x) + 8)sech(x) - 2cosh(x) +--R + +--R 4 2 +--R - 36cosh(x) - 42cosh(x) - 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 5 +--R (12cosh(x) + 24cosh(x) + 12cosh(x))sech(x) - 12cosh(x) +--R + +--R 3 +--R - 24cosh(x) - 12cosh(x) +--R * +--R sinh(x) +--R + +--R 6 4 2 6 +--R (2cosh(x) + 6cosh(x) + 6cosh(x) + 2)sech(x) - 2cosh(x) +--R + +--R 4 2 +--R - 6cosh(x) - 6cosh(x) - 2 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R (- sech(x) + 2)sinh(x) + (- 6cosh(x)sech(x) + 12cosh(x) - 4)sinh(x) +--R + +--R 2 2 6 +--R ((- 15cosh(x) - 4)sech(x) + 30cosh(x) - 19cosh(x))sinh(x) +--R + +--R 3 3 2 +--R (- 20cosh(x) - 18cosh(x))sech(x) + 40cosh(x) - 34cosh(x) +--R + +--R 4cosh(x) + 4 +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 4 3 +--R (- 15cosh(x) - 33cosh(x) - 6)sech(x) + 30cosh(x) - 25cosh(x) +--R + +--R 2 +--R 18cosh(x) + 7cosh(x) - 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 5 +--R (- 6cosh(x) - 32cosh(x) - 18cosh(x))sech(x) + 12cosh(x) +--R + +--R 3 2 +--R 32cosh(x) - 4cosh(x) - 12cosh(x) + 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 6 +--R (- cosh(x) - 18cosh(x) - 21cosh(x) - 4)sech(x) + 2cosh(x) +--R + +--R 5 4 3 2 +--R 11cosh(x) + 28cosh(x) - 14cosh(x) - 14cosh(x) + 23cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 6 5 +--R (- 6cosh(x) - 12cosh(x) - 6cosh(x))sech(x) + 6cosh(x) + 12cosh(x) +--R + +--R 4 3 2 +--R - 8cosh(x) - 8cosh(x) + 30cosh(x) - 4cosh(x) - 4 +--R * +--R sinh(x) +--R + +--R 6 4 2 7 6 +--R (- cosh(x) - 3cosh(x) - 3cosh(x) - 1)sech(x) + cosh(x) + 2cosh(x) +--R + +--R 5 4 3 2 +--R - cosh(x) - 2cosh(x) + 11cosh(x) - 2cosh(x) - 3cosh(x) + 2 +--R / +--R 8 7 2 6 +--R 2a sinh(x) + 12a cosh(x)sinh(x) + (30a cosh(x) + 8a)sinh(x) +--R + +--R 3 5 +--R (40a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (30a cosh(x) + 66a cosh(x) + 12a)sinh(x) +--R + +--R 5 3 3 +--R (12a cosh(x) + 64a cosh(x) + 36a cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (2a cosh(x) + 36a cosh(x) + 42a cosh(x) + 8a)sinh(x) +--R + +--R 5 3 6 +--R (12a cosh(x) + 24a cosh(x) + 12a cosh(x))sinh(x) + 2a cosh(x) +--R + +--R 4 2 +--R 6a cosh(x) + 6a cosh(x) + 2a +--R Type: Expression(Integer) +--E 290 + +--S 291 of 526 +t0654:= coth(x)/(a+b*sech(x)) +--R +--R +--R coth(x) +--R (290) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 526 +r0654:= log(1-cosh(x))/(2*a+2*b)+log(1+cosh(x))/(2*a-2*b)-_ + b^2*log(b+a*cosh(x))/a/(a^2-b^2) +--R +--R +--R (291) +--R 2 2 +--R 2b log(a cosh(x) + b) + (- a b - a )log(cosh(x) + 1) +--R + +--R 2 +--R (a b - a )log(- cosh(x) + 1) +--R / +--R 2 3 +--R 2a b - 2a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 526 +a0654:= integrate(t0654,x) +--R +--R +--R (292) +--R 2 +--R (- a b - a )log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 - 2a cosh(x) - 2b +--R (a b - a )log(sinh(x) + cosh(x) - 1) + b log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- b + a )x +--R / +--R 2 3 +--R a b - a +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 526 +m0654:= a0654-r0654 +--R +--R +--R (293) +--R 2 +--R (- 2a b - 2a )log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (2a b - 2a )log(sinh(x) + cosh(x) - 1) - 2b log(a cosh(x) + b) +--R + +--R 2 2 - 2a cosh(x) - 2b +--R (a b + a )log(cosh(x) + 1) + 2b log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 +--R (- a b + a )log(- cosh(x) + 1) + (- 2b + 2a )x +--R / +--R 2 3 +--R 2a b - 2a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 526 +d0654:= D(m0654,x) +--R +--R +--R (294) +--R 3 2 2 +--R (a cosh(x) - b)sinh(x) + (a cosh(x) - 2b cosh(x) + a)sinh(x) +--R + +--R 3 2 4 +--R (- a cosh(x) + b cosh(x) + a cosh(x) - b)sinh(x) - a cosh(x) +--R + +--R 3 +--R 2b cosh(x) - 2b cosh(x) + a +--R / +--R 2 2 2 2 2 2 +--R ((b - a )cosh(x) - b + a )sinh(x) +--R + +--R 2 2 3 2 2 2 2 4 +--R ((2b - 2a )cosh(x) + (- 2b + 2a )cosh(x))sinh(x) + (b - a )cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b + 2a )cosh(x) + b - a +--R Type: Expression(Integer) +--E 295 + +--S 296 of 526 +t0655:= coth(x)^2/(a+b*sech(x)) +--R +--R +--R 2 +--R coth(x) +--R (295) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 526 +r0655:= x/a+2*b^3*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(3/2)+_ + 1/2*sinh(x)/(a+b)/(1-cosh(x))-1/2*sinh(x)/(a-b)/(1+cosh(x)) +--R +--R +--R (296) +--R x +--R (b - a)tanh(-) +--R 3 2 3 2 +--R (2b cosh(x) - 2b )atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R ((a cosh(x) - a b)sinh(x) + (b - a )x cosh(x) + (- b + a )x)\|- b + a +--R / +--R +---------+ +--R 2 3 2 2 3 | 2 2 +--R ((a b - a )cosh(x) - a b + a )\|- b + a +--R Type: Expression(Integer) +--E 297 + +--S 298 of 526 +a0655:= integrate(t0655,x) +--R +--R +--R (297) +--R [ +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 2 2 2 2 +--R (b - a )x sinh(x) + ((2b - 2a )x cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (b - a )x cosh(x) - 2a b cosh(x) + (- b + a )x + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 2 3 2 2 3 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )cosh(x) - a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 2 3 3 2 3 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) - 2b ) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 2 2 2 +--R (b - a )x sinh(x) + ((2b - 2a )x cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (b - a )x cosh(x) - 2a b cosh(x) + (- b + a )x + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 3 2 2 3 +--R (a b - a )sinh(x) + (2a b - 2a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )cosh(x) - a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 298 + +--S 299 of 526 +m0655:= a0655.1-r0655 +--R +--R +--R (298) +--R 3 2 3 2 3 3 3 +--R (b cosh(x) - b )sinh(x) + (2b cosh(x) - 2b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 +--R b cosh(x) - 2b cosh(x) + b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 3 2 3 2 3 3 3 +--R (- 2b cosh(x) + 2b )sinh(x) + (- 4b cosh(x) + 4b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 +--R - 2b cosh(x) + 4b cosh(x) - 2b +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 2 +--R (- a cosh(x) + a b)sinh(x) + (- 2a cosh(x) + 2a b cosh(x))sinh(x) +--R + +--R 2 3 2 2 +--R (- a cosh(x) - a b cosh(x) + a cosh(x) + a b)sinh(x) +--R + +--R 3 2 2 2 +--R - 2a b cosh(x) + 2a cosh(x) + 2a b cosh(x) - 2a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 2 3 2 2 3 2 +--R ((a b - a )cosh(x) - a b + a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((2a b - 2a )cosh(x) + (- 2a b + 2a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (a b - a )cosh(x) + (- 2a b + 2a )cosh(x) + a b - a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 299 + +--S 300 of 526 +d0655:= D(m0655a,x) +--R +--R +--R (299) 0 +--R Type: Polynomial(Integer) +--E 300 + +--S 301 of 526 +m0655:= a0655.2-r0655 +--R +--R +--R (300) +--R 3 2 3 2 3 3 3 +--R (2b cosh(x) - 2b )sinh(x) + (4b cosh(x) - 4b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 +--R 2b cosh(x) - 4b cosh(x) + 2b +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 3 2 3 2 3 3 3 +--R (- 2b cosh(x) + 2b )sinh(x) + (- 4b cosh(x) + 4b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 +--R - 2b cosh(x) + 4b cosh(x) - 2b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 2 +--R (- a cosh(x) + a b)sinh(x) + (- 2a cosh(x) + 2a b cosh(x))sinh(x) +--R + +--R 2 3 2 2 +--R (- a cosh(x) - a b cosh(x) + a cosh(x) + a b)sinh(x) +--R + +--R 3 2 2 2 +--R - 2a b cosh(x) + 2a cosh(x) + 2a b cosh(x) - 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 3 2 2 3 2 +--R ((a b - a )cosh(x) - a b + a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((2a b - 2a )cosh(x) + (- 2a b + 2a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (a b - a )cosh(x) + (- 2a b + 2a )cosh(x) + a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 526 +d0655:= D(m0655b,x) +--R +--R +--R (301) 0 +--R Type: Polynomial(Integer) +--E 302 + +--S 303 of 526 +t0656:= coth(x)^3/(a+b*sech(x)) +--R +--R +--R 3 +--R coth(x) +--R (302) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 303 + +--S 304 of 526 +r0656:= 1/4/(a+b)/(1-cosh(x))+1/4/(a-b)/(1+cosh(x))+_ + 1/4*(2*a+3*b)*log(1-cosh(x))/(a+b)^2+_ + 1/4*(2*a-3*b)*log(1+cosh(x))/(a-b)^2+_ + b^4*log(b+a*cosh(x))/a/(a^2-b^2)^2 +--R +--R +--R (303) +--R 4 2 4 +--R (4b cosh(x) - 4b )log(a cosh(x) + b) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R ((- 3a b - 4a b + a b + 2a )cosh(x) + 3a b + 4a b - a b - 2a ) +--R * +--R log(cosh(x) + 1) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R ((3a b - 4a b - a b + 2a )cosh(x) - 3a b + 4a b + a b - 2a ) +--R * +--R log(- cosh(x) + 1) +--R + +--R 3 3 2 2 4 +--R (- 2a b + 2a b)cosh(x) + 2a b - 2a +--R / +--R 4 3 2 5 2 4 3 2 5 +--R (4a b - 8a b + 4a )cosh(x) - 4a b + 8a b - 4a +--R Type: Expression(Integer) +--E 304 + +--S 305 of 526 +a0656:= integrate(t0656,x) +--R +--R +--R (304) +--R 3 2 2 3 4 4 +--R (- 3a b - 4a b + a b + 2a )sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 12a b - 16a b + 4a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (- 18a b - 24a b + 6a b + 12a )cosh(x) + 6a b + 8a b - 2a b +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 12a b - 16a b + 4a b + 8a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (12a b + 16a b - 4a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 3a b - 4a b + a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (6a b + 8a b - 2a b - 4a )cosh(x) - 3a b - 4a b + a b + 2a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 2 3 4 4 +--R (3a b - 4a b - a b + 2a )sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (12a b - 16a b - 4a b + 8a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (18a b - 24a b - 6a b + 12a )cosh(x) - 6a b + 8a b + 2a b +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (12a b - 16a b - 4a b + 8a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12a b + 16a b + 4a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (3a b - 4a b - a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 6a b + 8a b + 2a b - 4a )cosh(x) + 3a b - 4a b - a b + 2a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 4 4 3 4 2 4 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) - 4b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (8b cosh(x) - 8b cosh(x))sinh(x) + 2b cosh(x) - 4b cosh(x) + 2b +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 2 2 4 4 +--R (- 2b + 4a b - 2a )x sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R ((- 8b + 16a b - 8a )x cosh(x) - 2a b + 2a b)sinh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 12b + 24a b - 12a )x cosh(x) + (- 6a b + 6a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 +--R (4b - 8a b + 4a )x + 4a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 8b + 16a b - 8a )x cosh(x) + (- 6a b + 6a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((8b - 16a b + 8a )x + 8a b - 8a )cosh(x) - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 2b + 4a b - 2a )x cosh(x) + (- 2a b + 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 3 3 +--R ((4b - 8a b + 4a )x + 4a b - 4a )cosh(x) + (- 2a b + 2a b)cosh(x) +--R + +--R 4 2 2 4 +--R (- 2b + 4a b - 2a )x +--R / +--R 4 3 2 5 4 4 3 2 5 3 +--R (2a b - 4a b + 2a )sinh(x) + (8a b - 16a b + 8a )cosh(x)sinh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 2 +--R ((12a b - 24a b + 12a )cosh(x) - 4a b + 8a b - 4a )sinh(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((8a b - 16a b + 8a )cosh(x) + (- 8a b + 16a b - 8a )cosh(x))sinh(x) +--R + +--R 4 3 2 5 4 4 3 2 5 2 4 +--R (2a b - 4a b + 2a )cosh(x) + (- 4a b + 8a b - 4a )cosh(x) + 2a b +--R + +--R 3 2 5 +--R - 4a b + 2a +--R Type: Union(Expression(Integer),...) +--E 305 + +--S 306 of 526 +m0656:= a0656-r0656 +--R +--R +--R (305) +--R 3 2 2 3 4 2 3 2 2 3 +--R (- 6a b - 8a b + 2a b + 4a )cosh(x) + 6a b + 8a b - 2a b +--R + +--R 4 +--R - 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 24a b - 32a b + 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (24a b + 32a b - 8a b - 16a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 36a b - 48a b + 12a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (48a b + 64a b - 16a b - 32a )cosh(x) - 12a b - 16a b + 4a b +--R + +--R 4 +--R 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 24a b - 32a b + 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (48a b + 64a b - 16a b - 32a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 24a b - 32a b + 8a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 6 +--R (- 6a b - 8a b + 2a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (18a b + 24a b - 6a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 18a b - 24a b + 6a b + 12a )cosh(x) + 6a b + 8a b - 2a b - 4a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R ((6a b - 8a b - 2a b + 4a )cosh(x) - 6a b + 8a b + 2a b - 4a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (24a b - 32a b - 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 24a b + 32a b + 8a b - 16a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (36a b - 48a b - 12a b + 24a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 +--R (- 48a b + 64a b + 16a b - 32a )cosh(x) + 12a b - 16a b +--R + +--R 3 4 +--R - 4a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (24a b - 32a b - 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 48a b + 64a b + 16a b - 32a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (24a b - 32a b - 8a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 6 +--R (6a b - 8a b - 2a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 18a b + 24a b + 6a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (18a b - 24a b - 6a b + 12a )cosh(x) - 6a b + 8a b + 2a b - 4a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 2 4 4 +--R (- 4b cosh(x) + 4b )sinh(x) +--R + +--R 4 3 4 3 +--R (- 16b cosh(x) + 16b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (- 24b cosh(x) + 32b cosh(x) - 8b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (- 16b cosh(x) + 32b cosh(x) - 16b cosh(x))sinh(x) - 4b cosh(x) +--R + +--R 4 4 4 2 4 +--R 12b cosh(x) - 12b cosh(x) + 4b +--R * +--R log(a cosh(x) + b) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R ((3a b + 4a b - a b - 2a )cosh(x) - 3a b - 4a b + a b + 2a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (12a b + 16a b - 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12a b - 16a b + 4a b + 8a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (18a b + 24a b - 6a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (- 24a b - 32a b + 8a b + 16a )cosh(x) + 6a b + 8a b - 2a b +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (12a b + 16a b - 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 24a b - 32a b + 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (12a b + 16a b - 4a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 6 +--R (3a b + 4a b - a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 9a b - 12a b + 3a b + 6a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (9a b + 12a b - 3a b - 6a )cosh(x) - 3a b - 4a b + a b + 2a +--R * +--R log(cosh(x) + 1) +--R + +--R 4 2 4 4 4 3 4 3 +--R (4b cosh(x) - 4b )sinh(x) + (16b cosh(x) - 16b cosh(x))sinh(x) +--R + +--R 4 4 4 2 4 2 +--R (24b cosh(x) - 32b cosh(x) + 8b )sinh(x) +--R + +--R 4 5 4 3 4 4 6 +--R (16b cosh(x) - 32b cosh(x) + 16b cosh(x))sinh(x) + 4b cosh(x) +--R + +--R 4 4 4 2 4 +--R - 12b cosh(x) + 12b cosh(x) - 4b +--R * +--R - 2a cosh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R ((- 3a b + 4a b + a b - 2a )cosh(x) + 3a b - 4a b - a b + 2a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 12a b + 16a b + 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (12a b - 16a b - 4a b + 8a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 18a b + 24a b + 6a b - 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (24a b - 32a b - 8a b + 16a )cosh(x) - 6a b + 8a b + 2a b +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 12a b + 16a b + 4a b - 8a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (24a b - 32a b - 8a b + 16a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12a b + 16a b + 4a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 6 +--R (- 3a b + 4a b + a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (9a b - 12a b - 3a b + 6a )cosh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 9a b + 12a b + 3a b - 6a )cosh(x) + 3a b - 4a b - a b + 2a +--R * +--R log(- cosh(x) + 1) +--R + +--R 4 2 2 4 2 3 3 +--R (- 4b + 8a b - 4a )x cosh(x) + (2a b - 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 +--R (4b - 8a b + 4a )x - 2a b + 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 16b + 32a b - 16a )x cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((16b - 32a b + 16a )x - 8a b + 8a )cosh(x) + 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 +--R (- 24b + 48a b - 24a )x cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 +--R ((32b - 64a b + 32a )x - 4a b + 4a )cosh(x) +--R + +--R 3 3 4 2 2 4 2 2 4 +--R (8a b - 8a b)cosh(x) + (- 8b + 16a b - 8a )x - 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (- 16b + 32a b - 16a )x cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 +--R ((32b - 64a b + 32a )x + 8a b - 8a )cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((- 16b + 32a b - 16a )x - 8a b + 8a )cosh(x) + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (- 4b + 8a b - 4a )x cosh(x) + (- 2a b + 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 4 +--R ((12b - 24a b + 12a )x + 6a b - 6a )cosh(x) +--R + +--R 3 3 3 +--R (- 4a b + 4a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 3 3 +--R ((- 12b + 24a b - 12a )x - 4a b + 4a )cosh(x) + (6a b - 6a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 +--R (4b - 8a b + 4a )x - 2a b + 2a +--R / +--R 4 3 2 5 2 4 3 2 5 4 +--R ((4a b - 8a b + 4a )cosh(x) - 4a b + 8a b - 4a )sinh(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((16a b - 32a b + 16a )cosh(x) + (- 16a b + 32a b - 16a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 5 4 4 3 2 5 2 +--R (24a b - 48a b + 24a )cosh(x) + (- 32a b + 64a b - 32a )cosh(x) +--R + +--R 4 3 2 5 +--R 8a b - 16a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 5 5 4 3 2 5 3 +--R (16a b - 32a b + 16a )cosh(x) + (- 32a b + 64a b - 32a )cosh(x) +--R + +--R 4 3 2 5 +--R (16a b - 32a b + 16a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 5 6 4 3 2 5 4 +--R (4a b - 8a b + 4a )cosh(x) + (- 12a b + 24a b - 12a )cosh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (12a b - 24a b + 12a )cosh(x) - 4a b + 8a b - 4a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 526 +d0656:= D(m0656,x) +--R +--R +--R (306) +--R 2 3 3 3 2 2 2 3 7 +--R ((2a b - a )cosh(x) + (- 2b + a b)cosh(x) - a b cosh(x) + b )sinh(x) +--R + +--R 2 3 4 3 2 3 +--R (10a b - 5a )cosh(x) + (- 12b + 6a b)cosh(x) +--R + +--R 2 3 2 3 2 3 +--R (- 2a b - 2a )cosh(x) + 6b cosh(x) - 2a b + a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 5 3 2 4 +--R (18a b - 9a )cosh(x) + (- 26b + 13a b)cosh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (3a b - 9a )cosh(x) + (13b + a b)cosh(x) + (- 9a b + 6a )cosh(x) +--R + +--R 3 2 +--R b - 2a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 6 3 2 5 +--R (10a b - 5a )cosh(x) + (- 20b + 10a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (14a b - 15a )cosh(x) + (4b + 8a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 14a b + 9a )cosh(x) + (8b - 10a b)cosh(x) - 2a b + 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 7 3 2 6 +--R (- 10a b + 5a )cosh(x) + (10b - 5a b)cosh(x) +--R + +--R 2 3 5 3 2 4 3 3 +--R (21a b - 10a )cosh(x) + (- 29b + 18a b)cosh(x) - 7a cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (16b - 9a b)cosh(x) + (- 11a b + 12a )cosh(x) + 3b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 8 3 2 7 2 6 +--R (- 18a b + 9a )cosh(x) + (28b - 14a b)cosh(x) + 18a b cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 50b + 16a b)cosh(x) + (16a b - 24a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (16b + 10a b)cosh(x) + (- 14a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 12a b)cosh(x) - 2a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 9 3 2 8 +--R (- 10a b + 5a )cosh(x) + (18b - 9a b)cosh(x) +--R + +--R 2 3 7 3 2 6 +--R (9a b + 3a )cosh(x) + (- 33b + 5a b)cosh(x) +--R + +--R 2 3 5 3 2 4 +--R (9a b - 15a )cosh(x) + (15b + 15a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (- 5a b + a )cosh(x) + (- 3b - 9a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 3a b + 6a )cosh(x) + 3b - 2a b +--R * +--R sinh(x) +--R + +--R 2 3 10 3 2 9 2 3 8 +--R (- 2a b + a )cosh(x) + (4b - 2a b)cosh(x) + (2a b + a )cosh(x) +--R + +--R 3 7 3 6 3 2 5 3 4 +--R - 8b cosh(x) - 2a cosh(x) + (8b + 4a b)cosh(x) - 2a cosh(x) +--R + +--R 3 3 2 3 2 3 2 2 3 +--R - 8b cosh(x) + (2a b + a )cosh(x) + (4b - 2a b)cosh(x) - 2a b + a +--R / +--R 4 2 2 4 4 4 2 2 4 2 4 +--R (b - 2a b + a )cosh(x) + (- 2b + 4a b - 2a )cosh(x) + b +--R + +--R 2 2 4 +--R - 2a b + a +--R * +--R 6 +--R sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (6b - 12a b + 6a )cosh(x) + (- 12b + 24a b - 12a )cosh(x) +--R + +--R 4 2 2 4 +--R (6b - 12a b + 6a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (15b - 30a b + 15a )cosh(x) + (- 33b + 66a b - 33a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (21b - 42a b + 21a )cosh(x) - 3b + 6a b - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 7 4 2 2 4 5 +--R (20b - 40a b + 20a )cosh(x) + (- 52b + 104a b - 52a )cosh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R (44b - 88a b + 44a )cosh(x) + (- 12b + 24a b - 12a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (15b - 30a b + 15a )cosh(x) + (- 48b + 96a b - 48a )cosh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (54b - 108a b + 54a )cosh(x) + (- 24b + 48a b - 24a )cosh(x) +--R + +--R 4 2 2 4 +--R 3b - 6a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (6b - 12a b + 6a )cosh(x) + (- 24b + 48a b - 24a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (36b - 72a b + 36a )cosh(x) + (- 24b + 48a b - 24a )cosh(x) +--R + +--R 4 2 2 4 +--R (6b - 12a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 10 4 2 2 4 8 +--R (b - 2a b + a )cosh(x) + (- 5b + 10a b - 5a )cosh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (10b - 20a b + 10a )cosh(x) + (- 10b + 20a b - 10a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (5b - 10a b + 5a )cosh(x) - b + 2a b - a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 526 +t0657:= coth(x)^2/(a+a*sech(x)) +--R +--R +--R 2 +--R coth(x) +--R (307) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 526 +r0657:= 1/3*(2-cosh(x)-4*cosh(x)^2+3*x*cosh(x)*sinh(x)+_ + 3*x*sinh(x))/sinh(x)/a/(1+cosh(x)) +--R +--R +--R 2 +--R (3x cosh(x) + 3x)sinh(x) - 4cosh(x) - cosh(x) + 2 +--R (308) -------------------------------------------------- +--R (3a cosh(x) + 3a)sinh(x) +--R Type: Expression(Integer) +--E 309 + +--S 310 of 526 +a0657:= integrate(t0657,x) +--R +--R +--R (309) +--R 2 2 +--R - 2sinh(x) + ((3x + 4)cosh(x) + 3x + 4)sinh(x) - 2cosh(x) - cosh(x) +--R --------------------------------------------------------------------- +--R (3a cosh(x) + 3a)sinh(x) +--R Type: Union(Expression(Integer),...) +--E 310 + +--S 311 of 526 +m0657:= a0657-r0657 +--R +--R +--R 2 2 +--R - 2sinh(x) + (4cosh(x) + 4)sinh(x) + 2cosh(x) - 2 +--R (310) --------------------------------------------------- +--R (3a cosh(x) + 3a)sinh(x) +--R Type: Expression(Integer) +--E 311 + +--S 312 of 526 +d0657:= D(m0657,x) +--R +--R +--R (311) +--R 4 2 4 3 2 +--R 2sinh(x) + (2cosh(x) + 2)sinh(x) - 2cosh(x) - 2cosh(x) + 2cosh(x) +--R + +--R 2cosh(x) +--R / +--R 2 2 +--R (3a cosh(x) + 6a cosh(x) + 3a)sinh(x) +--R Type: Expression(Integer) +--E 312 + +--S 313 of 526 +t0658:= coth(x)^4/(a+a*sech(x)) +--R +--R +--R 4 +--R coth(x) +--R (312) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 313 + +--S 314 of 526 +r0658:= 1/15*(-8+7*cosh(x)+27*cosh(x)^2-8*cosh(x)^3-_ + 23*cosh(x)^4+15*sinh(x)*x*cosh(x)^3+_ + 15*sinh(x)*cosh(x)^2*x-15*x*cosh(x)*sinh(x)-_ + 15*x*sinh(x))/sinh(x)^3/a/(1+cosh(x)) +--R +--R +--R (313) +--R 3 2 4 +--R (15x cosh(x) + 15x cosh(x) - 15x cosh(x) - 15x)sinh(x) - 23cosh(x) +--R + +--R 3 2 +--R - 8cosh(x) + 27cosh(x) + 7cosh(x) - 8 +--R / +--R 3 +--R (15a cosh(x) + 15a)sinh(x) +--R Type: Expression(Integer) +--E 314 + +--S 315 of 526 +a0658:= integrate(t0658,x) +--R +--R +--R (314) +--R 4 3 +--R - 23sinh(x) + ((60x + 92)cosh(x) + 30x + 46)sinh(x) +--R + +--R 2 2 +--R (- 138cosh(x) - 48cosh(x) + 16)sinh(x) +--R + +--R 3 2 +--R (60x + 92)cosh(x) + (90x + 138)cosh(x) + (- 60x - 92)cosh(x) - 90x +--R + +--R - 138 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R - 23cosh(x) - 16cosh(x) + 16cosh(x) + 8cosh(x) - 25 +--R / +--R 3 +--R (60a cosh(x) + 30a)sinh(x) +--R + +--R 3 2 +--R (60a cosh(x) + 90a cosh(x) - 60a cosh(x) - 90a)sinh(x) +--R Type: Union(Expression(Integer),...) +--E 315 + +--S 316 of 526 +m0658:= a0658-r0658 +--R +--R +--R (315) +--R 6 +--R (- 23cosh(x) - 23)sinh(x) +--R + +--R 2 5 +--R ((60x + 92)cosh(x) + (90x + 138)cosh(x) + 30x + 46)sinh(x) +--R + +--R 3 2 4 +--R (- 138cosh(x) - 186cosh(x) - 32cosh(x) + 16)sinh(x) +--R + +--R 4 3 2 +--R 92cosh(x) + (60x + 230)cosh(x) + (60x + 46)cosh(x) +--R + +--R (- 60x - 230)cosh(x) - 60x - 138 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 2 +--R (69cosh(x) + 39cosh(x) - 92cosh(x) - 58cosh(x) + cosh(x) - 9)sinh(x) +--R + +--R 6 5 4 3 +--R - 60x cosh(x) - 150x cosh(x) + 30x cosh(x) + 300x cosh(x) +--R + +--R 2 +--R 120x cosh(x) - 150x cosh(x) - 90x +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 92cosh(x) + 170cosh(x) - 152cosh(x) - 360cosh(x) + 50cosh(x) +--R + +--R 2 +--R 238cosh(x) + 10cosh(x) - 48 +--R / +--R 2 5 +--R (60a cosh(x) + 90a cosh(x) + 30a)sinh(x) +--R + +--R 4 3 2 3 +--R (60a cosh(x) + 150a cosh(x) + 30a cosh(x) - 150a cosh(x) - 90a)sinh(x) +--R Type: Expression(Integer) +--E 316 + +--S 317 of 526 +d0658:= D(m0658,x) +--R +--R +--R (316) +--R 2 10 +--R (46cosh(x) + 92cosh(x) + 46)sinh(x) +--R + +--R 4 3 2 8 +--R (- 64cosh(x) - 169cosh(x) - 242cosh(x) - 233cosh(x) - 96)sinh(x) +--R + +--R 5 4 3 2 +--R - 240x cosh(x) - 720x cosh(x) - 780x cosh(x) - 360x cosh(x) +--R + +--R - 60x cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 948cosh(x) + 2631cosh(x) + 2712cosh(x) + 1762cosh(x) +--R + +--R 2 +--R 1208cosh(x) + 535cosh(x) + 54 +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 240x cosh(x) - 1200x cosh(x) - 1740x cosh(x) - 120x cosh(x) +--R + +--R 3 2 +--R 1680x cosh(x) + 1320x cosh(x) + 300x cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 248cosh(x) + 1429cosh(x) + 1700cosh(x) - 1099cosh(x) +--R + +--R 4 3 2 +--R - 2634cosh(x) - 153cosh(x) + 1740cosh(x) + 1073cosh(x) + 196 +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 240x cosh(x) + 720x cosh(x) + 60x cosh(x) - 1560x cosh(x) +--R + +--R 5 4 3 2 +--R - 1020x cosh(x) + 960x cosh(x) + 900x cosh(x) - 120x cosh(x) +--R + +--R - 180x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 626cosh(x) - 1583cosh(x) + 386cosh(x) + 3212cosh(x) +--R + +--R 6 5 4 3 2 +--R 604cosh(x) - 2394cosh(x) - 362cosh(x) + 984cosh(x) - 2cosh(x) +--R + +--R - 219cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 240x cosh(x) + 1200x cosh(x) + 1500x cosh(x) - 1800x cosh(x) +--R + +--R 7 6 5 4 +--R - 5400x cosh(x) - 1800x cosh(x) + 4800x cosh(x) + 4200x cosh(x) +--R + +--R 3 2 +--R - 600x cosh(x) - 1800x cosh(x) - 540x cosh(x) +--R * +--R sinh(x) +--R + +--R 12 11 10 9 +--R - 552cosh(x) - 2400cosh(x) - 1914cosh(x) + 5310cosh(x) +--R + +--R 8 7 6 5 4 +--R 8934cosh(x) - 1848cosh(x) - 10548cosh(x) - 3066cosh(x) + 4710cosh(x) +--R + +--R 3 2 +--R 2436cosh(x) - 630cosh(x) - 432cosh(x) +--R / +--R 4 3 2 +--R (120a cosh(x) + 360a cosh(x) + 390a cosh(x) + 180a cosh(x) + 30a) +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 240a cosh(x) + 960a cosh(x) + 1140a cosh(x) - 120a cosh(x) +--R + +--R 2 +--R - 1200a cosh(x) - 840a cosh(x) - 180a +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 120a cosh(x) + 600a cosh(x) + 870a cosh(x) - 300a cosh(x) +--R + +--R 4 3 2 +--R - 1830a cosh(x) - 1200a cosh(x) + 570a cosh(x) + 900a cosh(x) + 270a +--R * +--R 4 +--R sinh(x) +--R Type: Expression(Integer) +--E 317 + +--S 318 of 526 +t0659:= sech(x)^3/(a+b*sech(x)) +--R +--R +--R 3 +--R sech(x) +--R (317) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 526 +r0659:= -a*atan(sinh(x))/b^2+2*a^2*atan((a-b)*tanh(1/2*x)/_ + (a^2-b^2)^(1/2))/b^2/(a^2-b^2)^(1/2)+tanh(x)/b +--R +--R +--R (318) +--R x +--R +---------+ (b - a)tanh(-) +--R | 2 2 2 2 +--R - a\|- b + a atan(sinh(x)) - 2a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R b tanh(x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 526 +a0659:= integrate(t0659,x) +--R +--R +--R (319) +--R [ +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)\|b - a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R +-------+ +--R | 2 2 +--R - 2b\|b - a +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b )\|b - a +--R , +--R +--R 2 2 2 2 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)\|- b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +--R | 2 2 +--R - 2b\|- b + a +--R / +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b )\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 320 + +--S 321 of 526 +m0659:= a0659.1-r0659 +--R +--R +--R (320) +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a )\|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b + 2a )sinh(x) + (- 2a b + 2a )cosh(x) - 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a)\|- b + a \|b - a +--R * +--R atan(sinh(x)) +--R + +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) + 2a )\|b - a +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 +--R ((- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b)tanh(x) - 2b) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 2 2 2 2 | 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 321 + +--S 322 of 526 +d0659:= D(m0659a,x) +--R +--R +--R (321) 0 +--R Type: Polynomial(Integer) +--E 322 + +--S 323 of 526 +m0659:= a0659.2-r0659 +--R +--R +--R (322) +--R 2 2 2 2 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) - 2a)\|- b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a)\|- b + a +--R * +--R atan(sinh(x)) +--R + +--R x +--R (b - a)tanh(-) +--R 2 2 2 2 2 2 2 +--R (2a sinh(x) + 4a cosh(x)sinh(x) + 2a cosh(x) + 2a )atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 +--R ((- b sinh(x) - 2b cosh(x)sinh(x) - b cosh(x) - b)tanh(x) - 2b) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b )\|- b + a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 526 +d0659:= D(m0659b,x) +--R +--R +--R (323) 0 +--R Type: Polynomial(Integer) +--E 324 + +--S 325 of 526 +t0660:= sech(x)^4/(a+b*sech(x)) +--R +--R +--R 4 +--R sech(x) +--R (324) ------------- +--R b sech(x) + a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 526 +r0660:= a^2*atan(sinh(x))/b^3+1/2*atan(sinh(x))/b-_ + 2*a^3*atan((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(1/2)-_ + a*tanh(x)/b^2+1/2*sech(x)*tanh(x)/b +--R +--R +--R (325) +--R x +--R +---------+ (b - a)tanh(-) +--R 2 2 | 2 2 3 2 +--R (b + 2a )\|- b + a atan(sinh(x)) + 4a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (b sech(x) - 2a b)tanh(x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 526 +a0660:= integrate(t0660,x) +--R +--R +--R (326) +--R [ +--R 3 4 3 3 3 2 3 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) +--R + +--R 2b cosh(x) + a +--R + +--R 2 2 4 2 2 3 +--R (b + 2a )sinh(x) + (4b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a )cosh(x) + 2b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a )cosh(x) + (4b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + 2a )cosh(x) + (2b + 4a )cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R b sinh(x) + (3b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (3b cosh(x) + 4a b cosh(x) - b )sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b cosh(x) + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 3 4 3 3 3 2 3 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 4 2 2 3 +--R (b + 2a )sinh(x) + (4b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a )cosh(x) + 2b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a )cosh(x) + (4b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + 2a )cosh(x) + (2b + 4a )cosh(x) + b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 2 +--R b sinh(x) + (3b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (3b cosh(x) + 4a b cosh(x) - b )sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b cosh(x) + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 4 3 3 3 2 3 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 327 + +--S 328 of 526 +m0660:= a0660.1-r0660 +--R +--R +--R (327) +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) + 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) + 8a cosh(x))sinh(x) + 2a cosh(x) + 4a cosh(x) + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 3 2 +--R (2a b - 2a )sinh(x) + (2a b - 2a )cosh(x) + 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R a +--R + +--R 2 2 4 2 2 3 +--R (2b + 4a )sinh(x) + (8b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 24a )cosh(x) + 4b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 16a )cosh(x) + (8b + 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + 4a )cosh(x) + (4b + 8a )cosh(x) + 2b + 4a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atan(sinh(x) + cosh(x)) +--R + +--R 2 2 4 2 2 3 +--R (- b - 2a )sinh(x) + (- 4b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b - 12a )cosh(x) - 2b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b - 8a )cosh(x) + (- 4b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b - 2a )cosh(x) + (- 2b - 4a )cosh(x) - b - 2a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atan(sinh(x)) +--R + +--R 3 4 3 3 3 2 3 2 +--R - 4a sinh(x) - 16a cosh(x)sinh(x) + (- 24a cosh(x) - 8a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (- 16a cosh(x) - 16a cosh(x))sinh(x) - 4a cosh(x) - 8a cosh(x) - 4a +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 +--R (- b sech(x) + 2a b)sinh(x) +--R + +--R 2 3 +--R (- 4b cosh(x)sech(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b cosh(x) - 2b )sech(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 3 +--R (- 4b cosh(x) - 4b cosh(x))sech(x) + 8a b cosh(x) +--R + +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- b cosh(x) - 2b cosh(x) - b )sech(x) + 2a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 2 3 2 2 +--R 2b sinh(x) + (6b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (6b cosh(x) + 8a b cosh(x) - 2b )sinh(x) + 2b cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2b cosh(x) + 4a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) + 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) + 8b cosh(x))sinh(x) + 2b cosh(x) + 4b cosh(x) + 2b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 526 +d0660:= D(m0660a,x) +--R +--R +--R (328) 0 +--R Type: Polynomial(Integer) +--E 329 + +--S 330 of 526 +m0660:= a0660.2-r0660 +--R +--R +--R (329) +--R 3 4 3 3 3 2 3 2 +--R 4a sinh(x) + 16a cosh(x)sinh(x) + (24a cosh(x) + 8a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (16a cosh(x) + 16a cosh(x))sinh(x) + 4a cosh(x) + 8a cosh(x) + 4a +--R * +--R +---------+ +--R | 2 2 +--R (a sinh(x) + a cosh(x) + b)\|- b + a +--R atan(---------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 4 2 2 3 +--R (2b + 4a )sinh(x) + (8b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 24a )cosh(x) + 4b + 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 16a )cosh(x) + (8b + 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + 4a )cosh(x) + (4b + 8a )cosh(x) + 2b + 4a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x) + cosh(x)) +--R + +--R 2 2 4 2 2 3 +--R (- b - 2a )sinh(x) + (- 4b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b - 12a )cosh(x) - 2b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b - 8a )cosh(x) + (- 4b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b - 2a )cosh(x) + (- 2b - 4a )cosh(x) - b - 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atan(sinh(x)) +--R + +--R 3 4 3 3 3 2 3 2 +--R - 4a sinh(x) - 16a cosh(x)sinh(x) + (- 24a cosh(x) - 8a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (- 16a cosh(x) - 16a cosh(x))sinh(x) - 4a cosh(x) - 8a cosh(x) - 4a +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atan(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 +--R (- b sech(x) + 2a b)sinh(x) +--R + +--R 2 3 +--R (- 4b cosh(x)sech(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b cosh(x) - 2b )sech(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 3 +--R (- 4b cosh(x) - 4b cosh(x))sech(x) + 8a b cosh(x) +--R + +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 4 +--R (- b cosh(x) - 2b cosh(x) - b )sech(x) + 2a b cosh(x) +--R + +--R 2 +--R 4a b cosh(x) + 2a b +--R * +--R tanh(x) +--R + +--R 2 3 2 2 +--R 2b sinh(x) + (6b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (6b cosh(x) + 8a b cosh(x) - 2b )sinh(x) + 2b cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2b cosh(x) + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) + 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) + 8b cosh(x))sinh(x) + 2b cosh(x) + 4b cosh(x) + 2b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 526 +d0660:= D(m0660b,x) +--R +--R +--R (330) 0 +--R Type: Polynomial(Integer) +--E 331 + +--S 332 of 526 +t0661:= sech(x)^3/(a+a*sech(x)) +--R +--R +--R 3 +--R sech(x) +--R (331) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 526 +r0661:= -atan(sinh(x))/a+sinh(x)/a/(1+cosh(x))+tanh(x)/a +--R +--R +--R (- cosh(x) - 1)atan(sinh(x)) + (cosh(x) + 1)tanh(x) + sinh(x) +--R (332) ------------------------------------------------------------- +--R a cosh(x) + a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 526 +a0661:= integrate(t0661,x) +--R +--R +--R (333) +--R 3 2 +--R - 2sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (- 6cosh(x) - 4cosh(x) - 2)sinh(x) - 2cosh(x) - 2cosh(x) +--R + +--R - 2cosh(x) - 2 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R - 2sinh(x) + (- 4cosh(x) - 2)sinh(x) - 2cosh(x) - 2cosh(x) - 4 +--R / +--R 3 2 +--R a sinh(x) + (3a cosh(x) + a)sinh(x) +--R + +--R 2 3 2 +--R (3a cosh(x) + 2a cosh(x) + a)sinh(x) + a cosh(x) + a cosh(x) +--R + +--R a cosh(x) + a +--R Type: Union(Expression(Integer),...) +--E 334 + +--S 335 of 526 +m0661:= a0661-r0661 +--R +--R +--R (334) +--R 3 2 2 +--R (- 2cosh(x) - 2)sinh(x) + (- 6cosh(x) - 8cosh(x) - 2)sinh(x) +--R + +--R 3 2 4 +--R (- 6cosh(x) - 10cosh(x) - 6cosh(x) - 2)sinh(x) - 2cosh(x) +--R + +--R 3 2 +--R - 4cosh(x) - 4cosh(x) - 4cosh(x) - 2 +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 2 2 +--R (cosh(x) + 1)sinh(x) + (3cosh(x) + 4cosh(x) + 1)sinh(x) +--R + +--R 3 2 4 3 +--R (3cosh(x) + 5cosh(x) + 3cosh(x) + 1)sinh(x) + cosh(x) + 2cosh(x) +--R + +--R 2 +--R 2cosh(x) + 2cosh(x) + 1 +--R * +--R atan(sinh(x)) +--R + +--R 3 2 2 +--R (- cosh(x) - 1)sinh(x) + (- 3cosh(x) - 4cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 +--R (- 3cosh(x) - 5cosh(x) - 3cosh(x) - 1)sinh(x) - cosh(x) +--R + +--R 3 2 +--R - 2cosh(x) - 2cosh(x) - 2cosh(x) - 1 +--R * +--R tanh(x) +--R + +--R 4 3 +--R - sinh(x) + (- 3cosh(x) - 1)sinh(x) +--R + +--R 2 2 +--R (- 3cosh(x) - 4cosh(x) - 3)sinh(x) +--R + +--R 3 2 3 2 +--R (- cosh(x) - 5cosh(x) - 7cosh(x) - 3)sinh(x) - 2cosh(x) - 4cosh(x) +--R + +--R - 6cosh(x) - 4 +--R / +--R 3 2 2 +--R (a cosh(x) + a)sinh(x) + (3a cosh(x) + 4a cosh(x) + a)sinh(x) +--R + +--R 3 2 4 +--R (3a cosh(x) + 5a cosh(x) + 3a cosh(x) + a)sinh(x) + a cosh(x) +--R + +--R 3 2 +--R 2a cosh(x) + 2a cosh(x) + 2a cosh(x) + a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 526 +d0661:= D(m0661,x) +--R +--R +--R (335) +--R 2 8 +--R (cosh(x) + 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 7 +--R (6cosh(x) + 14cosh(x) + 10cosh(x) + 2)sinh(x) +--R + +--R 4 3 2 6 +--R (15cosh(x) + 40cosh(x) + 39cosh(x) + 18cosh(x) + 4)sinh(x) +--R + +--R 5 4 3 2 +--R (20cosh(x) + 60cosh(x) + 78cosh(x) + 62cosh(x) + 30cosh(x) + 6) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 15cosh(x) + 50cosh(x) + 88cosh(x) + 108cosh(x) + 83cosh(x) +--R + +--R 34cosh(x) + 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) + 22cosh(x) + 58cosh(x) + 106cosh(x) + 114cosh(x) +--R + +--R 2 +--R 74cosh(x) + 30cosh(x) + 6 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 4cosh(x) + 23cosh(x) + 62cosh(x) + 87cosh(x) +--R + +--R 3 2 +--R 80cosh(x) + 53cosh(x) + 22cosh(x) + 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) + 22cosh(x) + 38cosh(x) + 46cosh(x) + 42cosh(x) +--R + +--R 2 +--R 26cosh(x) + 10cosh(x) + 2 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 4cosh(x) + 8cosh(x) + 12cosh(x) + 14cosh(x) +--R + +--R 3 2 +--R 12cosh(x) + 8cosh(x) + 4cosh(x) + 1 +--R * +--R 2 +--R tanh(x) +--R + +--R 10 9 2 8 +--R sinh(x) + (6cosh(x) + 2)sinh(x) + (13cosh(x) + 7cosh(x) + 3)sinh(x) +--R + +--R 3 2 7 +--R (8cosh(x) - 2cosh(x) + 6cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 6 +--R (- 15cosh(x) - 44cosh(x) - 18cosh(x) + cosh(x) + 2)sinh(x) +--R + +--R 5 4 3 2 5 +--R (- 34cosh(x) - 84cosh(x) - 70cosh(x) - 36cosh(x) + 8)sinh(x) +--R + +--R 6 5 4 3 2 +--R - 29cosh(x) - 68cosh(x) - 83cosh(x) - 77cosh(x) - 26cosh(x) +--R + +--R cosh(x) - 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 12cosh(x) - 18cosh(x) - 34cosh(x) - 64cosh(x) - 56cosh(x) +--R + +--R 2 +--R - 34cosh(x) - 10cosh(x) + 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 2cosh(x) + 8cosh(x) + 8cosh(x) - 21cosh(x) - 45cosh(x) +--R + +--R 3 2 +--R - 34cosh(x) - 2cosh(x) + 3cosh(x) - 3 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R 6cosh(x) + 10cosh(x) - 14cosh(x) - 4cosh(x) + 14cosh(x) +--R + +--R - 10cosh(x) - 2 +--R * +--R sinh(x) +--R + +--R 9 8 7 6 5 4 +--R cosh(x) + 2cosh(x) + cosh(x) - cosh(x) + 3cosh(x) + 7cosh(x) +--R + +--R 3 2 +--R - cosh(x) - 7cosh(x) - 4cosh(x) - 1 +--R / +--R 2 8 +--R (a cosh(x) + 2a cosh(x) + a)sinh(x) +--R + +--R 3 2 7 +--R (6a cosh(x) + 14a cosh(x) + 10a cosh(x) + 2a)sinh(x) +--R + +--R 4 3 2 6 +--R (15a cosh(x) + 40a cosh(x) + 39a cosh(x) + 18a cosh(x) + 4a)sinh(x) +--R + +--R 5 4 3 2 +--R 20a cosh(x) + 60a cosh(x) + 78a cosh(x) + 62a cosh(x) +--R + +--R 30a cosh(x) + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 15a cosh(x) + 50a cosh(x) + 88a cosh(x) + 108a cosh(x) +--R + +--R 2 +--R 83a cosh(x) + 34a cosh(x) + 6a +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 6a cosh(x) + 22a cosh(x) + 58a cosh(x) + 106a cosh(x) +--R + +--R 3 2 +--R 114a cosh(x) + 74a cosh(x) + 30a cosh(x) + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R a cosh(x) + 4a cosh(x) + 23a cosh(x) + 62a cosh(x) + 87a cosh(x) +--R + +--R 3 2 +--R 80a cosh(x) + 53a cosh(x) + 22a cosh(x) + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 6a cosh(x) + 22a cosh(x) + 38a cosh(x) + 46a cosh(x) +--R + +--R 3 2 +--R 42a cosh(x) + 26a cosh(x) + 10a cosh(x) + 2a +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R a cosh(x) + 4a cosh(x) + 8a cosh(x) + 12a cosh(x) + 14a cosh(x) +--R + +--R 3 2 +--R 12a cosh(x) + 8a cosh(x) + 4a cosh(x) + a +--R Type: Expression(Integer) +--E 336 + +--S 337 of 526 +t0662:= csch(x)^3/(a+a*sech(x)) +--R +--R +--R 3 +--R csch(x) +--R (336) ------------- +--R a sech(x) + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 526 +r0662:= 1/8*atanh(cosh(x))/a+1/8/a/(1-cosh(x))+1/8/a/(1+cosh(x))^2 +--R +--R +--R (337) +--R 3 2 2 +--R (cosh(x) + cosh(x) - cosh(x) - 1)atanh(cosh(x)) - cosh(x) - cosh(x) - 2 +--R -------------------------------------------------------------------------- +--R 3 2 +--R 8a cosh(x) + 8a cosh(x) - 8a cosh(x) - 8a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 526 +a0662:= integrate(t0662,x) +--R +--R +--R (338) +--R 6 5 +--R sinh(x) + (6cosh(x) + 2)sinh(x) +--R + +--R 2 4 +--R (15cosh(x) + 10cosh(x) - 1)sinh(x) +--R + +--R 3 2 3 +--R (20cosh(x) + 20cosh(x) - 4cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 2 +--R (15cosh(x) + 20cosh(x) - 6cosh(x) - 12cosh(x) - 1)sinh(x) +--R + +--R 5 4 3 2 +--R (6cosh(x) + 10cosh(x) - 4cosh(x) - 12cosh(x) - 2cosh(x) + 2) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) + 2cosh(x) - cosh(x) - 4cosh(x) - cosh(x) + 2cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 6 5 +--R - sinh(x) + (- 6cosh(x) - 2)sinh(x) +--R + +--R 2 4 +--R (- 15cosh(x) - 10cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 +--R (- 20cosh(x) - 20cosh(x) + 4cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 2 +--R (- 15cosh(x) - 20cosh(x) + 6cosh(x) + 12cosh(x) + 1)sinh(x) +--R + +--R 5 4 3 2 +--R (- 6cosh(x) - 10cosh(x) + 4cosh(x) + 12cosh(x) + 2cosh(x) - 2) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - cosh(x) - 2cosh(x) + cosh(x) + 4cosh(x) + cosh(x) - 2cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 5 4 +--R - 2sinh(x) + (- 10cosh(x) - 4)sinh(x) +--R + +--R 2 3 +--R (- 20cosh(x) - 16cosh(x) - 20)sinh(x) +--R + +--R 3 2 2 +--R (- 20cosh(x) - 24cosh(x) - 60cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 +--R (- 10cosh(x) - 16cosh(x) - 60cosh(x) - 8cosh(x) - 2)sinh(x) +--R + +--R 5 4 3 2 +--R - 2cosh(x) - 4cosh(x) - 20cosh(x) - 4cosh(x) - 2cosh(x) +--R / +--R 6 5 +--R 8a sinh(x) + (48a cosh(x) + 16a)sinh(x) +--R + +--R 2 4 +--R (120a cosh(x) + 80a cosh(x) - 8a)sinh(x) +--R + +--R 3 2 3 +--R (160a cosh(x) + 160a cosh(x) - 32a cosh(x) - 32a)sinh(x) +--R + +--R 4 3 2 2 +--R (120a cosh(x) + 160a cosh(x) - 48a cosh(x) - 96a cosh(x) - 8a)sinh(x) +--R + +--R 5 4 3 2 +--R 48a cosh(x) + 80a cosh(x) - 32a cosh(x) - 96a cosh(x) +--R + +--R - 16a cosh(x) + 16a +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 8a cosh(x) + 16a cosh(x) - 8a cosh(x) - 32a cosh(x) - 8a cosh(x) +--R + +--R 16a cosh(x) + 8a +--R Type: Union(Expression(Integer),...) +--E 339 + +--S 340 of 526 +m0662:= a0662-r0662 +--R +--R +--R (339) +--R 3 2 6 +--R (cosh(x) + cosh(x) - cosh(x) - 1)sinh(x) +--R + +--R 4 3 2 5 +--R (6cosh(x) + 8cosh(x) - 4cosh(x) - 8cosh(x) - 2)sinh(x) +--R + +--R 5 4 3 2 +--R (15cosh(x) + 25cosh(x) - 6cosh(x) - 26cosh(x) - 9cosh(x) + 1) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 20cosh(x) + 40cosh(x) - 4cosh(x) - 48cosh(x) - 20cosh(x) +--R + +--R 8cosh(x) + 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 15cosh(x) + 35cosh(x) - cosh(x) - 53cosh(x) - 27cosh(x) +--R + +--R 2 +--R 17cosh(x) + 13cosh(x) + 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R 6cosh(x) + 16cosh(x) - 32cosh(x) - 20cosh(x) + 16cosh(x) +--R + +--R 2 +--R 16cosh(x) - 2 +--R * +--R sinh(x) +--R + +--R 9 8 6 5 4 3 +--R cosh(x) + 3cosh(x) - 8cosh(x) - 6cosh(x) + 6cosh(x) + 8cosh(x) +--R + +--R - 3cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 6 +--R (- cosh(x) - cosh(x) + cosh(x) + 1)sinh(x) +--R + +--R 4 3 2 5 +--R (- 6cosh(x) - 8cosh(x) + 4cosh(x) + 8cosh(x) + 2)sinh(x) +--R + +--R 5 4 3 2 +--R (- 15cosh(x) - 25cosh(x) + 6cosh(x) + 26cosh(x) + 9cosh(x) - 1) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 20cosh(x) - 40cosh(x) + 4cosh(x) + 48cosh(x) + 20cosh(x) +--R + +--R - 8cosh(x) - 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 15cosh(x) - 35cosh(x) + cosh(x) + 53cosh(x) + 27cosh(x) +--R + +--R 2 +--R - 17cosh(x) - 13cosh(x) - 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R - 6cosh(x) - 16cosh(x) + 32cosh(x) + 20cosh(x) - 16cosh(x) +--R + +--R 2 +--R - 16cosh(x) + 2 +--R * +--R sinh(x) +--R + +--R 9 8 6 5 4 +--R - cosh(x) - 3cosh(x) + 8cosh(x) + 6cosh(x) - 6cosh(x) +--R + +--R 3 +--R - 8cosh(x) + 3cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 2 6 +--R (- cosh(x) - cosh(x) + cosh(x) + 1)sinh(x) +--R + +--R 4 3 2 5 +--R (- 6cosh(x) - 8cosh(x) + 4cosh(x) + 8cosh(x) + 2)sinh(x) +--R + +--R 5 4 3 2 +--R (- 15cosh(x) - 25cosh(x) + 6cosh(x) + 26cosh(x) + 9cosh(x) - 1) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 20cosh(x) - 40cosh(x) + 4cosh(x) + 48cosh(x) + 20cosh(x) +--R + +--R - 8cosh(x) - 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 15cosh(x) - 35cosh(x) + cosh(x) + 53cosh(x) + 27cosh(x) +--R + +--R 2 +--R - 17cosh(x) - 13cosh(x) - 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 3 +--R - 6cosh(x) - 16cosh(x) + 32cosh(x) + 20cosh(x) - 16cosh(x) +--R + +--R 2 +--R - 16cosh(x) + 2 +--R * +--R sinh(x) +--R + +--R 9 8 6 5 4 +--R - cosh(x) - 3cosh(x) + 8cosh(x) + 6cosh(x) - 6cosh(x) +--R + +--R 3 +--R - 8cosh(x) + 3cosh(x) + 1 +--R * +--R atanh(cosh(x)) +--R + +--R 2 6 +--R (cosh(x) + cosh(x) + 2)sinh(x) +--R + +--R 3 2 5 +--R (4cosh(x) + 6cosh(x) + 16cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) + 11cosh(x) + 45cosh(x) + 33cosh(x) + 2)sinh(x) +--R + +--R 4 3 2 3 +--R (4cosh(x) + 40cosh(x) + 48cosh(x) + 24cosh(x) + 12)sinh(x) +--R + +--R 6 5 4 3 2 +--R - 5cosh(x) - 9cosh(x) - 20cosh(x) + 2cosh(x) + 55cosh(x) +--R + +--R 39cosh(x) + 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 4cosh(x) - 10cosh(x) - 48cosh(x) - 38cosh(x) + 44cosh(x) +--R + +--R 2 +--R 42cosh(x) + 8cosh(x) + 6 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) - 3cosh(x) - 19cosh(x) - 19cosh(x) + 11cosh(x) +--R + +--R 3 2 +--R 15cosh(x) + 7cosh(x) + 7cosh(x) + 2 +--R / +--R 3 2 6 +--R (8a cosh(x) + 8a cosh(x) - 8a cosh(x) - 8a)sinh(x) +--R + +--R 4 3 2 5 +--R (48a cosh(x) + 64a cosh(x) - 32a cosh(x) - 64a cosh(x) - 16a)sinh(x) +--R + +--R 5 4 3 2 +--R 120a cosh(x) + 200a cosh(x) - 48a cosh(x) - 208a cosh(x) +--R + +--R - 72a cosh(x) + 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 160a cosh(x) + 320a cosh(x) - 32a cosh(x) - 384a cosh(x) +--R + +--R 2 +--R - 160a cosh(x) + 64a cosh(x) + 32a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 120a cosh(x) + 280a cosh(x) - 8a cosh(x) - 424a cosh(x) +--R + +--R 3 2 +--R - 216a cosh(x) + 136a cosh(x) + 104a cosh(x) + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 5 4 +--R 48a cosh(x) + 128a cosh(x) - 256a cosh(x) - 160a cosh(x) +--R + +--R 3 2 +--R 128a cosh(x) + 128a cosh(x) - 16a +--R * +--R sinh(x) +--R + +--R 9 8 6 5 4 +--R 8a cosh(x) + 24a cosh(x) - 64a cosh(x) - 48a cosh(x) + 48a cosh(x) +--R + +--R 3 +--R 64a cosh(x) - 24a cosh(x) - 8a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 526 +d0662:= D(m0662,x) +--R +--R +--R (340) +--R 9 2 8 +--R - cosh(x)sinh(x) + (- 8cosh(x) - 2cosh(x))sinh(x) +--R + +--R 3 2 7 +--R (- 28cosh(x) - 14cosh(x) + 2cosh(x))sinh(x) +--R + +--R 4 3 2 6 +--R (- 56cosh(x) - 42cosh(x) + 12cosh(x) + 6cosh(x))sinh(x) +--R + +--R 5 4 3 2 +--R (- 62cosh(x) - 62cosh(x) + 14cosh(x) + 14cosh(x) + 8cosh(x) + 8) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 16cosh(x) - 30cosh(x) - 40cosh(x) - 20cosh(x) + 40cosh(x) +--R + +--R 34cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 52cosh(x) + 38cosh(x) - 122cosh(x) - 92cosh(x) + 64cosh(x) +--R + +--R 2 +--R 46cosh(x) + 6cosh(x) + 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 72cosh(x) + 66cosh(x) - 124cosh(x) - 106cosh(x) + 32cosh(x) +--R + +--R 3 2 +--R 14cosh(x) + 20cosh(x) + 26cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R 39cosh(x) + 38cosh(x) - 54cosh(x) - 50cosh(x) - 8cosh(x) +--R + +--R 4 3 2 +--R - 14cosh(x) + 22cosh(x) + 26cosh(x) + cosh(x) +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 5 +--R 8cosh(x) + 8cosh(x) - 8cosh(x) - 8cosh(x) - 8cosh(x) - 8cosh(x) +--R + +--R 4 3 +--R 8cosh(x) + 8cosh(x) +--R / +--R 5 4 3 2 +--R (a cosh(x) + a cosh(x) - 2a cosh(x) - 2a cosh(x) + a cosh(x) + a) +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 8a cosh(x) + 10a cosh(x) - 14a cosh(x) - 20a cosh(x) +--R + +--R 2 +--R 4a cosh(x) + 10a cosh(x) + 2a +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 28a cosh(x) + 42a cosh(x) - 44a cosh(x) - 86a cosh(x) +--R + +--R 3 2 +--R 4a cosh(x) + 46a cosh(x) + 12a cosh(x) - 2a +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 56a cosh(x) + 98a cosh(x) - 82a cosh(x) - 214a cosh(x) +--R + +--R 4 3 2 +--R - 10a cosh(x) + 134a cosh(x) + 42a cosh(x) - 18a cosh(x) - 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 70a cosh(x) + 140a cosh(x) - 100a cosh(x) - 340a cosh(x) +--R + +--R 5 4 3 2 +--R - 40a cosh(x) + 260a cosh(x) + 100a cosh(x) - 60a cosh(x) +--R + +--R - 30a cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 56a cosh(x) + 126a cosh(x) - 82a cosh(x) - 352a cosh(x) +--R + +--R 6 5 4 3 +--R - 64a cosh(x) + 332a cosh(x) + 156a cosh(x) - 112a cosh(x) +--R + +--R 2 +--R - 72a cosh(x) + 6a cosh(x) + 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 28a cosh(x) + 70a cosh(x) - 44a cosh(x) - 230a cosh(x) +--R + +--R 7 6 5 4 +--R - 56a cosh(x) + 268a cosh(x) + 152a cosh(x) - 124a cosh(x) +--R + +--R 3 2 +--R - 100a cosh(x) + 14a cosh(x) + 20a cosh(x) + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 12 11 10 9 +--R 8a cosh(x) + 22a cosh(x) - 14a cosh(x) - 86a cosh(x) +--R + +--R 8 7 6 5 +--R - 26a cosh(x) + 124a cosh(x) + 84a cosh(x) - 76a cosh(x) +--R + +--R 4 3 2 +--R - 76a cosh(x) + 14a cosh(x) + 26a cosh(x) + 2a cosh(x) - 2a +--R * +--R sinh(x) +--R + +--R 13 12 11 10 9 +--R a cosh(x) + 3a cosh(x) - 2a cosh(x) - 14a cosh(x) - 5a cosh(x) +--R + +--R 8 7 6 5 4 +--R 25a cosh(x) + 20a cosh(x) - 20a cosh(x) - 25a cosh(x) + 5a cosh(x) +--R + +--R 3 2 +--R 14a cosh(x) + 2a cosh(x) - 3a cosh(x) - a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 526 +t0663:= sinh(x)/(a+b*csch(x)) +--R +--R +--R sinh(x) +--R (341) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 342 + +--S 343 of 526 +r0663:= -b*x/a^2-2*b^2*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/_ + a^2/(a^2+b^2)^(1/2)+cosh(x)/a +--R +--R +--R x +--R b tanh(-) - a +-------+ +--R 2 2 | 2 2 +--R 2b atanh(-------------) + (a cosh(x) - b x)\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (342) ----------------------------------------------------- +--R +-------+ +--R 2 | 2 2 +--R a \|b + a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 526 +a0663:= integrate(t0663,x) +--R +--R +--R (343) +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b - 2a )sinh(x) + (- 2a b - 2a )cosh(x) - 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 2 +--R a sinh(x) + (2a cosh(x) - 2b x)sinh(x) + a cosh(x) - 2b x cosh(x) +--R + +--R a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|b + a +--R Type: Union(Expression(Integer),...) +--E 344 + +--S 345 of 526 +m0663:= a0663-r0663 +--R +--R +--R (344) +--R 2 2 +--R (2b sinh(x) + 2b cosh(x)) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b - 2a )sinh(x) + (- 2a b - 2a )cosh(x) - 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R x +--R b tanh(-) - a +--R 2 2 2 +--R (- 4b sinh(x) - 4b cosh(x))atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (a sinh(x) - a cosh(x) + a)\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (2a sinh(x) + 2a cosh(x))\|b + a +--R Type: Expression(Integer) +--E 345 + +--S 346 of 526 +d0663:= D(m0663,x) +--R +--R +--R (345) +--R 4 2 3 2 2 +--R - a b sinh(x) + (- 2a b cosh(x) - 4b )sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 3 2 2 4 +--R (2a b cosh(x) - 4b cosh(x) - 2a b cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 2 3 +--R 2a sinh(x) + (4a cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 +--R (4a b cosh(x) - 8b )sinh(x) +--R + +--R 2 3 2 2 2 +--R (- 4a cosh(x) - 4a b cosh(x) + (- 16b + 4a )cosh(x) + 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 +--R - 2a cosh(x) - 4a b cosh(x) + (- 8b + 4a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 3 2 2 +--R a b sinh(x) + (2a b cosh(x) + 4b )sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 3 2 2 4 +--R (- 2a b cosh(x) + 4b cosh(x) + 2a b cosh(x))sinh(x) - a b cosh(x) +--R + +--R 2 +--R 2a b cosh(x) - a b +--R / +--R 2 3 2 2 2 +--R 2a b sinh(x) + (6a b cosh(x) + 4a b )sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (6a b cosh(x) + 8a b cosh(x) - 2a b)sinh(x) + 2a b cosh(x) +--R + +--R 2 2 2 +--R 4a b cosh(x) - 2a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 3 2 2 +--R - 4a sinh(x) + (- 12a cosh(x) - 8a b)sinh(x) +--R + +--R 3 2 2 3 3 3 +--R (- 12a cosh(x) - 16a b cosh(x) + 4a )sinh(x) - 4a cosh(x) +--R + +--R 2 2 3 +--R - 8a b cosh(x) + 4a cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 3 2 2 2 +--R - 2a b sinh(x) + (- 6a b cosh(x) - 4a b )sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (- 6a b cosh(x) - 8a b cosh(x) + 2a b)sinh(x) - 2a b cosh(x) +--R + +--R 2 2 2 +--R - 4a b cosh(x) + 2a b cosh(x) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 526 +t0664:= sinh(x)^2/(a+b*csch(x)) +--R +--R +--R 2 +--R sinh(x) +--R (346) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 526 +r0664:= -1/2*x/a+b^2*x/a^3+2*b^3*atanh((a-b*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/a^3/(a^2+b^2)^(1/2)-b*cosh(x)/a^2+_ + 1/2*cosh(x)*sinh(x)/a +--R +--R +--R (347) +--R x +--R b tanh(-) - a +--R 3 2 +--R - 4b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (a cosh(x)sinh(x) - 2a b cosh(x) + (2b - a )x)\|b + a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2a \|b + a +--R Type: Expression(Integer) +--E 348 + +--S 349 of 526 +a0664:= integrate(t0664,x) +--R +--R +--R (348) +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b - 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b - 8a )x cosh(x) - 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b - 4a )x cosh(x) - 4a b cosh(x) - a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|b + a +--R Type: Union(Expression(Integer),...) +--E 349 + +--S 350 of 526 +m0664:= a0664-r0664 +--R +--R +--R (349) +--R 3 2 3 3 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R x +--R b tanh(-) - a +--R 3 2 3 3 2 2 +--R (16b sinh(x) + 32b cosh(x)sinh(x) + 16b cosh(x) )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 3 2 2 2 +--R a sinh(x) - 4a b sinh(x) + (- 2a cosh(x) - 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (4a b cosh(x) - 4a b)sinh(x) + a cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R - 4a b cosh(x) - a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 3 2 3 3 2 | 2 2 +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) )\|b + a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 526 +d0664:= D(m0664,x) +--R +--R +--R (350) +--R 2 6 2 5 +--R - a b sinh(x) - 2a b cosh(x)sinh(x) +--R + +--R 2 2 2 3 2 4 +--R (a b cosh(x) + 4a b cosh(x) + 8b + a b)sinh(x) +--R + +--R 2 3 2 2 3 3 +--R (4a b cosh(x) + 8a b cosh(x) + 24b cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 2 2 +--R (a b cosh(x) + (24b - 2a b)cosh(x) + 4a b cosh(x) + a b)sinh(x) +--R + +--R 2 5 2 4 3 3 2 2 +--R - 2a b cosh(x) - 8a b cosh(x) + 8b cosh(x) + 8a b cosh(x) +--R + +--R 2 +--R 2a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - a b cosh(x) - 4a b cosh(x) + a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 +--R a b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 5 +--R 2a sinh(x) + 4a cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (- 2a cosh(x) - 8a b cosh(x) - 8a b - 2a )sinh(x) +--R + +--R 3 3 2 2 2 3 3 +--R (- 8a cosh(x) - 16a b cosh(x) - 16a b cosh(x) + 16b )sinh(x) +--R + +--R 3 4 3 2 3 2 2 3 +--R (- 2a cosh(x) + 4a cosh(x) + (48b - 8a b)cosh(x) - 8a b - 2a ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 +--R 4a cosh(x) + 16a b cosh(x) + 16a b cosh(x) +--R + +--R 3 2 2 2 3 +--R (48b - 16a b)cosh(x) + (- 16a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R 2a cosh(x) + 8a b cosh(x) + (8a b - 2a )cosh(x) +--R + +--R 3 2 3 2 3 2 3 +--R (16b - 8a b)cosh(x) + (- 8a b - 2a )cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 5 +--R a b sinh(x) + 2a b cosh(x)sinh(x) +--R + +--R 2 2 2 3 2 4 +--R (- a b cosh(x) - 4a b cosh(x) - 8b - a b)sinh(x) +--R + +--R 2 3 2 2 3 3 +--R (- 4a b cosh(x) - 8a b cosh(x) - 24b cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 2 2 +--R (- a b cosh(x) + (- 24b + 2a b)cosh(x) - 4a b cosh(x) - a b)sinh(x) +--R + +--R 2 5 2 4 3 3 2 2 +--R 2a b cosh(x) + 8a b cosh(x) - 8b cosh(x) - 8a b cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R a b cosh(x) + 4a b cosh(x) - a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 +--R - a b cosh(x) + a b +--R / +--R 3 4 3 2 2 3 +--R 4a b sinh(x) + (16a b cosh(x) + 8a b )sinh(x) +--R + +--R 3 2 2 2 3 2 +--R (24a b cosh(x) + 24a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 3 2 2 2 3 +--R (16a b cosh(x) + 24a b cosh(x) - 8a b cosh(x))sinh(x) +--R + +--R 3 4 2 2 3 3 2 +--R 4a b cosh(x) + 8a b cosh(x) - 4a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 4 4 3 3 +--R - 8a sinh(x) + (- 32a cosh(x) - 16a b)sinh(x) +--R + +--R 4 2 3 4 2 +--R (- 48a cosh(x) - 48a b cosh(x) + 8a )sinh(x) +--R + +--R 4 3 3 2 4 4 4 +--R (- 32a cosh(x) - 48a b cosh(x) + 16a cosh(x))sinh(x) - 8a cosh(x) +--R + +--R 3 3 4 2 +--R - 16a b cosh(x) + 8a cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 4 3 2 2 3 +--R - 4a b sinh(x) + (- 16a b cosh(x) - 8a b )sinh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 24a b cosh(x) - 24a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 3 2 2 2 3 3 4 +--R (- 16a b cosh(x) - 24a b cosh(x) + 8a b cosh(x))sinh(x) - 4a b cosh(x) +--R + +--R 2 2 3 3 2 +--R - 8a b cosh(x) + 4a b cosh(x) +--R Type: Expression(Integer) +--E 351 + +--S 352 of 526 +t0665:= sinh(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R sinh(x) +--R (351) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 526 +r0665:= 1/2*b*x/a^2-b^3*x/a^4-2*b^4*atanh((a-b*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/a^4/(a^2+b^2)^(1/2)-cosh(x)/a+_ + b^2*cosh(x)/a^3+1/3*cosh(x)^3/a-1/2*b*cosh(x)*sinh(x)/a^2 +--R +--R +--R (352) +--R x +--R b tanh(-) - a +--R 4 2 +--R 12b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 3 2 3 +--R - 3a b cosh(x)sinh(x) + 2a cosh(x) + (6a b - 6a )cosh(x) +--R + +--R 3 2 +--R (- 6b + 3a b)x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6a \|b + a +--R Type: Expression(Integer) +--E 353 + +--S 354 of 526 +a0665:= integrate(t0665,x) +--R +--R +--R (353) +--R 4 3 4 2 4 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 4 3 +--R 24b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b - 2a )sinh(x) + (- 2a b - 2a )cosh(x) - 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b - 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 20a cosh(x) - 30a b cosh(x) + (48a b - 36a )cosh(x) +--R + +--R 3 2 +--R (- 24b + 12a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 15a cosh(x) - 30a b cosh(x) + (72a b - 54a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 72b + 36a b)x cosh(x) + 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (48a b - 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 72b + 36a b)x cosh(x) + (24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b - 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R (- 24b + 12a b)x cosh(x) + (12a b - 9a )cosh(x) + 3a b cosh(x) + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) ) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 354 + +--S 355 of 526 +m0665:= a0665-r0665 +--R +--R +--R (354) +--R 4 3 4 2 4 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 4 3 +--R 24b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b - 2a )sinh(x) + (- 2a b - 2a )cosh(x) - 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 4 3 4 2 4 2 +--R - 48b sinh(x) - 144b cosh(x)sinh(x) - 144b cosh(x) sinh(x) +--R + +--R 4 3 +--R - 48b cosh(x) +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 3a b cosh(x) + 12a b - 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 3 +--R (12a cosh(x) + 6a b cosh(x) + (24a b - 12a )cosh(x))sinh(x) +--R + +--R 3 4 2 3 3 2 2 3 2 +--R (- 9a cosh(x) + 6a b cosh(x) + 18a cosh(x) + 12a b - 9a )sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R - 18a cosh(x) - 3a b cosh(x) + (- 24a b + 36a )cosh(x) +--R + +--R 2 3 2 +--R (24a b - 18a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R - 7a cosh(x) - 3a b cosh(x) + (- 12a b + 15a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (12a b - 9a )cosh(x) + 3a b cosh(x) + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 4 2 4 2 4 3 +--R (24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) ) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 355 + +--S 356 of 526 +d0665:= D(m0665,x) +--R +--R +--R (355) +--R 3 8 3 2 2 7 +--R a b sinh(x) + (8a b cosh(x) + 4a b )sinh(x) +--R + +--R 3 2 2 2 3 6 +--R (20a b cosh(x) + 20a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 3 2 2 2 3 3 4 +--R 16a b cosh(x) + 28a b cosh(x) + (- 8a b + 16a b)cosh(x) - 16b +--R + +--R 2 2 +--R 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R - 10a b cosh(x) - 4a b cosh(x) + (- 24a b + 28a b)cosh(x) +--R + +--R 4 2 2 3 +--R (- 64b + 32a b )cosh(x) - 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 2 2 4 3 3 3 +--R - 24a b cosh(x) - 36a b cosh(x) + (- 16a b + 24a b)cosh(x) +--R + +--R 4 2 2 2 3 2 2 +--R (- 96b + 40a b )cosh(x) - 8a b cosh(x) + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 2 2 5 3 3 4 +--R - 12a b cosh(x) - 20a b cosh(x) + (16a b + 4a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 64b + 8a b )cosh(x) + (- 24a b + 12a b)cosh(x) +--R + +--R 2 2 3 +--R 12a b cosh(x) - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 6 3 3 5 +--R 4a b cosh(x) + (24a b - 8a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 16b - 16a b )cosh(x) + (- 24a b + 16a b)cosh(x) +--R + +--R 2 2 2 3 +--R 12a b cosh(x) - 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 2 2 7 3 3 6 2 2 5 +--R a b cosh(x) + 4a b cosh(x) + (8a b - 4a b)cosh(x) - 8a b cosh(x) +--R + +--R 3 3 4 2 2 3 3 2 3 +--R (- 8a b + 6a b)cosh(x) + 4a b cosh(x) - 4a b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 8 4 3 7 +--R - 2a sinh(x) + (- 16a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 4 6 +--R (- 40a cosh(x) - 40a b cosh(x) - 8a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R - 32a cosh(x) - 56a b cosh(x) + (16a b - 32a )cosh(x) + 16a b +--R + +--R 3 +--R - 16a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 20a cosh(x) + 8a b cosh(x) + (48a b - 56a )cosh(x) +--R + +--R 3 3 4 4 +--R (48a b - 64a b)cosh(x) - 32b + 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 48a cosh(x) + 72a b cosh(x) + (32a b - 48a )cosh(x) +--R + +--R 3 3 2 4 2 2 3 +--R (32a b - 80a b)cosh(x) + (- 128b + 16a b )cosh(x) + 16a b +--R + +--R 3 +--R - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 24a cosh(x) + 40a b cosh(x) + (- 32a b - 8a )cosh(x) +--R + +--R 3 3 3 4 2 2 4 2 +--R (- 32a b - 16a b)cosh(x) + (- 192b + 48a b - 24a )cosh(x) +--R + +--R 3 3 4 +--R (48a b - 24a b)cosh(x) + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 2 2 4 5 +--R - 8a b cosh(x) + (- 48a b + 16a )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (- 48a b + 32a b)cosh(x) + (- 128b + 48a b - 32a )cosh(x) +--R + +--R 3 3 2 4 +--R (48a b - 24a b)cosh(x) + 16a cosh(x) +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R - 2a cosh(x) - 8a b cosh(x) + (- 16a b + 8a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 16a b + 16a b)cosh(x) + (- 32b + 16a b - 12a )cosh(x) +--R + +--R 3 3 3 4 2 4 +--R (16a b - 8a b)cosh(x) + 8a cosh(x) - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 8 3 2 2 7 +--R - a b sinh(x) + (- 8a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 2 2 2 3 6 +--R (- 20a b cosh(x) - 20a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 3 2 2 2 3 3 4 +--R - 16a b cosh(x) - 28a b cosh(x) + (8a b - 16a b)cosh(x) + 16b +--R + +--R 2 2 +--R - 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R 10a b cosh(x) + 4a b cosh(x) + (24a b - 28a b)cosh(x) +--R + +--R 4 2 2 3 +--R (64b - 32a b )cosh(x) + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 2 2 4 3 3 3 +--R 24a b cosh(x) + 36a b cosh(x) + (16a b - 24a b)cosh(x) +--R + +--R 4 2 2 2 3 2 2 +--R (96b - 40a b )cosh(x) + 8a b cosh(x) - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 2 2 5 3 3 4 +--R 12a b cosh(x) + 20a b cosh(x) + (- 16a b - 4a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 2 2 +--R (64b - 8a b )cosh(x) + (24a b - 12a b)cosh(x) - 12a b cosh(x) +--R + +--R 3 +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 6 3 3 5 4 2 2 4 +--R - 4a b cosh(x) + (- 24a b + 8a b)cosh(x) + (16b + 16a b )cosh(x) +--R + +--R 3 3 3 2 2 2 3 +--R (24a b - 16a b)cosh(x) - 12a b cosh(x) + 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 8 2 2 7 3 3 6 2 2 5 +--R - a b cosh(x) - 4a b cosh(x) + (- 8a b + 4a b)cosh(x) + 8a b cosh(x) +--R + +--R 3 3 4 2 2 3 3 2 3 +--R (8a b - 6a b)cosh(x) - 4a b cosh(x) + 4a b cosh(x) - a b +--R / +--R 4 5 4 3 2 4 +--R 8a b sinh(x) + (40a b cosh(x) + 16a b )sinh(x) +--R + +--R 4 2 3 2 4 3 +--R (80a b cosh(x) + 64a b cosh(x) - 8a b)sinh(x) +--R + +--R 4 3 3 2 2 4 2 +--R (80a b cosh(x) + 96a b cosh(x) - 24a b cosh(x))sinh(x) +--R + +--R 4 4 3 2 3 4 2 +--R (40a b cosh(x) + 64a b cosh(x) - 24a b cosh(x) )sinh(x) +--R + +--R 4 5 3 2 4 4 3 +--R 8a b cosh(x) + 16a b cosh(x) - 8a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 5 5 4 4 +--R - 16a sinh(x) + (- 80a cosh(x) - 32a b)sinh(x) +--R + +--R 5 2 4 5 3 +--R (- 160a cosh(x) - 128a b cosh(x) + 16a )sinh(x) +--R + +--R 5 3 4 2 5 2 +--R (- 160a cosh(x) - 192a b cosh(x) + 48a cosh(x))sinh(x) +--R + +--R 5 4 4 3 5 2 +--R (- 80a cosh(x) - 128a b cosh(x) + 48a cosh(x) )sinh(x) +--R + +--R 5 5 4 4 5 3 +--R - 16a cosh(x) - 32a b cosh(x) + 16a cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 5 4 3 2 4 +--R - 8a b sinh(x) + (- 40a b cosh(x) - 16a b )sinh(x) +--R + +--R 4 2 3 2 4 3 +--R (- 80a b cosh(x) - 64a b cosh(x) + 8a b)sinh(x) +--R + +--R 4 3 3 2 2 4 2 +--R (- 80a b cosh(x) - 96a b cosh(x) + 24a b cosh(x))sinh(x) +--R + +--R 4 4 3 2 3 4 2 +--R (- 40a b cosh(x) - 64a b cosh(x) + 24a b cosh(x) )sinh(x) +--R + +--R 4 5 3 2 4 4 3 +--R - 8a b cosh(x) - 16a b cosh(x) + 8a b cosh(x) +--R Type: Expression(Integer) +--E 356 + +--S 357 of 526 +t0666:= sinh(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R sinh(x) +--R (356) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 357 + +--S 358 of 526 +r0666:= 3/8*x/a-1/2*b^2*x/a^3+b^4*x/a^5+_ + 2*b^5*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^5/(a^2+b^2)^(1/2)+_ + b*cosh(x)/a^2-b^3*cosh(x)/a^4-1/3*b*cosh(x)^3/a^2-_ + 3/8*cosh(x)*sinh(x)/a+1/2*b^2*cosh(x)*sinh(x)/a^3+_ + 1/4*cosh(x)*sinh(x)^3/a +--R +--R +--R (357) +--R x +--R b tanh(-) - a +--R 5 2 +--R - 48b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 3 2 2 4 3 3 +--R 6a cosh(x)sinh(x) + (12a b - 9a )cosh(x)sinh(x) - 8a b cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 24a b + 24a b)cosh(x) + (24b - 12a b + 9a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 5 | 2 2 +--R 24a \|b + a +--R Type: Expression(Integer) +--E 358 + +--S 359 of 526 +a0666:= integrate(t0666,x) +--R +--R +--R (358) +--R 5 4 5 3 5 2 2 +--R 192b sinh(x) + 768b cosh(x)sinh(x) + 1152b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768b cosh(x) sinh(x) + 192b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 +--R 168a cosh(x) - 168a b cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 3 3 +--R - 96a b + 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b + 360a b)cosh(x) + (192b - 96a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b - 480a )cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 960a b + 720a b)cosh(x) + (768b - 384a b + 288a )x cosh(x) +--R + +--R 3 3 +--R - 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b - 360a )cosh(x) +--R + +--R 3 3 3 +--R (- 960a b + 720a b)cosh(x) +--R + +--R 4 2 2 4 2 +--R (1152b - 576a b + 432a )x cosh(x) +--R + +--R 3 3 2 2 4 +--R (- 288a b + 216a b)cosh(x) - 24a b + 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b - 144a )cosh(x) +--R + +--R 3 3 4 +--R (- 480a b + 360a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (768b - 384a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (- 288a b + 216a b)cosh(x) + (- 48a b + 48a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b + 72a b)cosh(x) + (192b - 96a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (- 96a b + 72a b)cosh(x) + (- 24a b + 24a )cosh(x) - 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 359 + +--S 360 of 526 +m0666:= a0666-r0666 +--R +--R +--R (359) +--R 5 4 5 3 5 2 2 +--R 192b sinh(x) + 768b cosh(x)sinh(x) + 1152b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768b cosh(x) sinh(x) + 192b cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 5 4 5 3 5 2 2 +--R 384b sinh(x) + 1536b cosh(x)sinh(x) + 2304b cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 1536b cosh(x) sinh(x) + 384b cosh(x) +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (- 24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (- 108a cosh(x) - 56a b cosh(x) + 24a b - 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 +--R - 120a cosh(x) - 168a b cosh(x) + (48a b - 72a )cosh(x) +--R + +--R 3 3 +--R - 96a b + 72a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 216a b cosh(x) + (- 24a b - 72a )cosh(x) +--R + +--R 3 3 +--R (- 288a b + 168a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 120a cosh(x) - 24a b cosh(x) + (- 96a b - 48a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (- 192a b - 48a b)cosh(x) - 96a b + 72a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) + 216a b cosh(x) + (- 24a b - 72a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 +--R (192a b - 432a b)cosh(x) + (- 288a b + 216a b)cosh(x) - 24a b +--R + +--R 4 +--R 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) + 200a b cosh(x) + (48a b - 72a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (288a b - 408a b)cosh(x) + (- 288a b + 216a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b + 48a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) + 56a b cosh(x) + (24a b - 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (96a b - 120a b)cosh(x) + (- 96a b + 72a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b + 24a )cosh(x) - 8a b cosh(x) - 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 360 + +--S 361 of 526 +d0666:= D(m0666,x) +--R +--R +--R (360) +--R 4 10 4 3 2 9 +--R - 3a b sinh(x) + (- 14a b cosh(x) - 8a b )sinh(x) +--R + +--R 4 2 3 2 2 3 4 8 +--R (- 27a b cosh(x) - 40a b cosh(x) - 8a b + 5a b)sinh(x) +--R + +--R 4 3 3 2 2 2 3 4 +--R - 32a b cosh(x) - 88a b cosh(x) + (- 48a b + 12a b)cosh(x) +--R + +--R 3 2 +--R - 4a b +--R * +--R 7 +--R sinh(x) +--R + +--R 4 4 3 2 3 2 3 4 2 +--R - 30a b cosh(x) - 104a b cosh(x) + (- 96a b - 8a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (16a b - 36a b )cosh(x) + 32b - 16a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 3 2 4 2 3 4 3 +--R - 12a b cosh(x) - 40a b cosh(x) + (- 48a b - 60a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 3 2 +--R (64a b - 124a b )cosh(x) + (160b - 80a b )cosh(x) + 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 3 2 5 2 3 4 4 +--R 26a b cosh(x) + 72a b cosh(x) + (80a b - 94a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (80a b - 204a b )cosh(x) + (320b - 144a b + 18a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (16a b + 4a b )cosh(x) - 8a b - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 3 2 6 2 3 4 5 +--R 48a b cosh(x) + 120a b cosh(x) + (112a b - 76a b)cosh(x) +--R + +--R 3 2 4 5 2 3 4 3 +--R - 156a b cosh(x) + (320b - 96a b + 32a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (64a b - 24a b )cosh(x) + (- 32a b - 16a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 3 2 7 2 3 4 6 +--R 33a b cosh(x) + 72a b cosh(x) + (32a b - 32a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 4 +--R (- 80a b - 28a b )cosh(x) + (160b + 16a b + 18a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 4 +--R (96a b - 56a b )cosh(x) + (- 48a b - 24a b)cosh(x) + 5a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 3 2 8 2 3 4 7 +--R 10a b cosh(x) + 16a b cosh(x) + (- 16a b - 4a b)cosh(x) +--R + +--R 4 3 2 6 5 2 3 5 +--R (- 64a b + 28a b )cosh(x) + (32b + 48a b )cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (64a b - 44a b )cosh(x) + (- 32a b - 16a b)cosh(x) +--R + +--R 4 +--R 10a b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 2 3 4 8 4 3 2 7 +--R a b cosh(x) + (- 8a b + a b)cosh(x) + (- 16a b + 12a b )cosh(x) +--R + +--R 2 3 4 6 4 3 2 5 +--R (16a b - 2a b)cosh(x) + (16a b - 12a b )cosh(x) +--R + +--R 2 3 4 4 4 2 4 +--R (- 8a b - 4a b)cosh(x) + 5a b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 10 5 4 9 +--R 6a sinh(x) + (28a cosh(x) + 16a b)sinh(x) +--R + +--R 5 2 4 3 2 5 8 +--R (54a cosh(x) + 80a b cosh(x) + 16a b - 10a )sinh(x) +--R + +--R 5 3 4 2 3 2 5 4 +--R (64a cosh(x) + 176a b cosh(x) + (96a b - 24a )cosh(x) + 8a b) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 4 3 3 2 5 2 +--R 60a cosh(x) + 208a b cosh(x) + (192a b + 16a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 32a b + 72a b)cosh(x) - 32a b + 32a b + 4a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 4 4 3 2 5 3 +--R 24a cosh(x) + 80a b cosh(x) + (96a b + 120a )cosh(x) +--R + +--R 2 3 4 2 4 3 2 +--R (- 128a b + 248a b)cosh(x) + (- 128a b + 160a b )cosh(x) +--R + +--R 5 4 +--R 64b - 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 6 4 5 3 2 5 4 +--R - 52a cosh(x) - 144a b cosh(x) + (- 160a b + 188a )cosh(x) +--R + +--R 2 3 4 3 +--R (- 160a b + 408a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 160a b + 288a b - 36a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (320b - 32a b - 8a b)cosh(x) - 32a b + 16a b + 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 7 4 6 3 2 5 5 +--R - 96a cosh(x) - 240a b cosh(x) + (- 224a b + 152a )cosh(x) +--R + +--R 4 4 3 2 5 3 +--R 312a b cosh(x) + (192a b - 64a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (640b - 128a b + 48a b)cosh(x) +--R + +--R 4 3 2 5 +--R (- 128a b + 64a b + 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 8 4 7 3 2 5 6 +--R - 66a cosh(x) - 144a b cosh(x) + (- 64a b + 64a )cosh(x) +--R + +--R 2 3 4 5 4 3 2 5 4 +--R (160a b + 56a b)cosh(x) + (160a b - 32a b - 36a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (640b - 192a b + 112a b)cosh(x) +--R + +--R 4 3 2 5 2 5 +--R (- 192a b + 96a b + 48a )cosh(x) - 10a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 9 4 8 3 2 5 7 +--R - 20a cosh(x) - 32a b cosh(x) + (32a b + 8a )cosh(x) +--R + +--R 2 3 4 6 4 3 2 5 +--R (128a b - 56a b)cosh(x) + (128a b - 96a b )cosh(x) +--R + +--R 5 2 3 4 4 +--R (320b - 128a b + 88a b)cosh(x) +--R + +--R 4 3 2 5 3 5 +--R (- 128a b + 64a b + 32a )cosh(x) - 20a cosh(x) +--R * +--R sinh(x) +--R + +--R 5 10 3 2 5 8 2 3 4 7 +--R - 2a cosh(x) + (16a b - 2a )cosh(x) + (32a b - 24a b)cosh(x) +--R + +--R 4 3 2 5 6 5 2 3 4 5 +--R (32a b - 32a b + 4a )cosh(x) + (64b - 32a b + 24a b)cosh(x) +--R + +--R 4 3 2 5 4 5 2 5 +--R (- 32a b + 16a b + 8a )cosh(x) - 10a cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 10 4 3 2 9 +--R 3a b sinh(x) + (14a b cosh(x) + 8a b )sinh(x) +--R + +--R 4 2 3 2 2 3 4 8 +--R (27a b cosh(x) + 40a b cosh(x) + 8a b - 5a b)sinh(x) +--R + +--R 4 3 3 2 2 2 3 4 3 2 +--R (32a b cosh(x) + 88a b cosh(x) + (48a b - 12a b)cosh(x) + 4a b ) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 4 3 2 3 2 3 4 2 +--R 30a b cosh(x) + 104a b cosh(x) + (96a b + 8a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (- 16a b + 36a b )cosh(x) - 32b + 16a b + 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 3 2 4 2 3 4 3 +--R 12a b cosh(x) + 40a b cosh(x) + (48a b + 60a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 3 2 +--R (- 64a b + 124a b )cosh(x) + (- 160b + 80a b )cosh(x) - 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 3 2 5 2 3 4 4 +--R - 26a b cosh(x) - 72a b cosh(x) + (- 80a b + 94a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (- 80a b + 204a b )cosh(x) + (- 320b + 144a b - 18a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 16a b - 4a b )cosh(x) + 8a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 3 2 6 2 3 4 5 +--R - 48a b cosh(x) - 120a b cosh(x) + (- 112a b + 76a b)cosh(x) +--R + +--R 3 2 4 5 2 3 4 3 +--R 156a b cosh(x) + (- 320b + 96a b - 32a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (- 64a b + 24a b )cosh(x) + (32a b + 16a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 3 2 7 2 3 4 6 +--R - 33a b cosh(x) - 72a b cosh(x) + (- 32a b + 32a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 4 +--R (80a b + 28a b )cosh(x) + (- 160b - 16a b - 18a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 4 +--R (- 96a b + 56a b )cosh(x) + (48a b + 24a b)cosh(x) - 5a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 3 2 8 2 3 4 7 +--R - 10a b cosh(x) - 16a b cosh(x) + (16a b + 4a b)cosh(x) +--R + +--R 4 3 2 6 5 2 3 5 +--R (64a b - 28a b )cosh(x) + (- 32b - 48a b )cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 4 +--R (- 64a b + 44a b )cosh(x) + (32a b + 16a b)cosh(x) - 10a b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 2 3 4 8 4 3 2 7 +--R - a b cosh(x) + (8a b - a b)cosh(x) + (16a b - 12a b )cosh(x) +--R + +--R 2 3 4 6 4 3 2 5 +--R (- 16a b + 2a b)cosh(x) + (- 16a b + 12a b )cosh(x) +--R + +--R 2 3 4 4 4 2 4 +--R (8a b + 4a b)cosh(x) - 5a b cosh(x) + a b +--R / +--R 5 6 5 4 2 5 +--R 16a b sinh(x) + (96a b cosh(x) + 32a b )sinh(x) +--R + +--R 5 2 4 2 5 4 +--R (240a b cosh(x) + 160a b cosh(x) - 16a b)sinh(x) +--R + +--R 5 3 4 2 2 5 3 +--R (320a b cosh(x) + 320a b cosh(x) - 64a b cosh(x))sinh(x) +--R + +--R 5 4 4 2 3 5 2 2 +--R (240a b cosh(x) + 320a b cosh(x) - 96a b cosh(x) )sinh(x) +--R + +--R 5 5 4 2 4 5 3 +--R (96a b cosh(x) + 160a b cosh(x) - 64a b cosh(x) )sinh(x) +--R + +--R 5 6 4 2 5 5 4 +--R 16a b cosh(x) + 32a b cosh(x) - 16a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 6 6 5 5 +--R - 32a sinh(x) + (- 192a cosh(x) - 64a b)sinh(x) +--R + +--R 6 2 5 6 4 +--R (- 480a cosh(x) - 320a b cosh(x) + 32a )sinh(x) +--R + +--R 6 3 5 2 6 3 +--R (- 640a cosh(x) - 640a b cosh(x) + 128a cosh(x))sinh(x) +--R + +--R 6 4 5 3 6 2 2 +--R (- 480a cosh(x) - 640a b cosh(x) + 192a cosh(x) )sinh(x) +--R + +--R 6 5 5 4 6 3 +--R (- 192a cosh(x) - 320a b cosh(x) + 128a cosh(x) )sinh(x) +--R + +--R 6 6 5 5 6 4 +--R - 32a cosh(x) - 64a b cosh(x) + 32a cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 6 5 4 2 5 +--R - 16a b sinh(x) + (- 96a b cosh(x) - 32a b )sinh(x) +--R + +--R 5 2 4 2 5 4 +--R (- 240a b cosh(x) - 160a b cosh(x) + 16a b)sinh(x) +--R + +--R 5 3 4 2 2 5 3 +--R (- 320a b cosh(x) - 320a b cosh(x) + 64a b cosh(x))sinh(x) +--R + +--R 5 4 4 2 3 5 2 2 +--R (- 240a b cosh(x) - 320a b cosh(x) + 96a b cosh(x) )sinh(x) +--R + +--R 5 5 4 2 4 5 3 +--R (- 96a b cosh(x) - 160a b cosh(x) + 64a b cosh(x) )sinh(x) +--R + +--R 5 6 4 2 5 5 4 +--R - 16a b cosh(x) - 32a b cosh(x) + 16a b cosh(x) +--R Type: Expression(Integer) +--E 361 + +--S 362 of 526 +t0667:= sinh(x)/(%i+csch(x)) +--R +--R +--R sinh(x) +--R (361) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 362 + +--S 363 of 526 +r0667:= x-%i*cosh(x)-%i*cosh(x)/(1+%i*sinh(x)) +--R +--R +--R (- %i cosh(x) + x)sinh(x) - 2cosh(x) - %i x +--R (362) ------------------------------------------- +--R sinh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 363 + +--S 364 of 526 +a0667:= integrate(t0667,x) +--R +--R +--R (363) +--R 2 2 +--R - %i sinh(x) + (- 2%i cosh(x) + 2x)sinh(x) - %i cosh(x) +--R + +--R (2x - 2)cosh(x) - 2%i x - 5%i +--R / +--R 2sinh(x) + 2cosh(x) - 2%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 364 + +--S 365 of 526 +m0667:= a0667-r0667 +--R +--R +--R (364) +--R 3 2 2 +--R - %i sinh(x) - sinh(x) + (%i cosh(x) + 2cosh(x) - 5%i)sinh(x) +--R + +--R 2 +--R 3cosh(x) - 2%i cosh(x) - 5 +--R / +--R 2 +--R 2sinh(x) + (2cosh(x) - 4%i)sinh(x) - 2%i cosh(x) - 2 +--R Type: Expression(Complex(Integer)) +--E 365 + +--S 366 of 526 +d0667:= D(m0667,x) +--R +--R +--R (365) +--R 5 4 +--R %i sinh(x) + (%i cosh(x) + 4)sinh(x) +--R + +--R 2 3 +--R (- %i cosh(x) + 6cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 2 +--R (- %i cosh(x) - 2cosh(x) - 4%i cosh(x) + 4)sinh(x) +--R + +--R 3 2 4 +--R (- 6cosh(x) + 3%i cosh(x) + 6cosh(x) - 3%i)sinh(x) - 2cosh(x) +--R + +--R 3 2 +--R 5%i cosh(x) + 2cosh(x) - 5%i cosh(x) +--R / +--R 4 3 +--R 2sinh(x) + (4cosh(x) - 8%i)sinh(x) +--R + +--R 2 2 +--R (2cosh(x) - 12%i cosh(x) - 12)sinh(x) +--R + +--R 2 2 +--R (- 4%i cosh(x) - 12cosh(x) + 8%i)sinh(x) - 2cosh(x) + 4%i cosh(x) + 2 +--R Type: Expression(Complex(Integer)) +--E 366 + +--S 367 of 526 +t0668:= sinh(x)^2/(%i+csch(x)) +--R +--R +--R 2 +--R sinh(x) +--R (366) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 367 + +--S 368 of 526 +r0668:= 3/2*%i*x+cosh(x)+cosh(x)/(1+%i*sinh(x))-1/2*%i*cosh(x)*sinh(x) +--R +--R +--R (367) +--R 1 2 1 3 3 +--R - - %i cosh(x)sinh(x) + (- cosh(x) + - %i x)sinh(x) - 2%i cosh(x) + - x +--R 2 2 2 2 +--R ------------------------------------------------------------------------ +--R sinh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 368 + +--S 369 of 526 +a0668:= integrate(t0668,x) +--R +--R +--R (368) +--R 3 2 +--R - %i sinh(x) + (- 3%i cosh(x) + 4)sinh(x) +--R + +--R 2 3 +--R (- 3%i cosh(x) + 4cosh(x) + 12%i x - %i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R 4cosh(x) + (12%i x - 7%i)cosh(x) + 12x + 20 +--R / +--R 8sinh(x) + 8cosh(x) - 8%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 369 + +--S 370 of 526 +m0668:= a0668-r0668 +--R +--R +--R (369) +--R 1 4 1 3 3 +--R - - %i sinh(x) + (- %i cosh(x) + -)sinh(x) +--R 8 8 8 +--R + +--R 1 2 1 5 2 +--R (- %i cosh(x) + - cosh(x) - - %i)sinh(x) +--R 8 8 8 +--R + +--R 1 3 3 2 9 19 1 3 +--R (- - %i cosh(x) - - cosh(x) + - %i cosh(x) + --)sinh(x) - - cosh(x) +--R 8 8 8 8 8 +--R + +--R 3 2 9 5 +--R - %i cosh(x) + - cosh(x) - - %i +--R 2 8 2 +--R / +--R 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) - %i cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 370 + +--S 371 of 526 +d0668:= D(m0668,x) +--R +--R +--R (370) +--R 1 6 1 5 1 2 5 7 4 +--R - %i sinh(x) + - sinh(x) + (- - %i cosh(x) - - cosh(x) + - %i)sinh(x) +--R 4 8 2 8 4 +--R + +--R 5 2 13 3 3 +--R (- - cosh(x) + -- %i cosh(x) + -)sinh(x) +--R 8 4 2 +--R + +--R 1 4 5 3 1 2 3 2 +--R (- %i cosh(x) + - cosh(x) - - %i cosh(x) + 2cosh(x) + - %i)sinh(x) +--R 4 8 2 2 +--R + +--R 1 4 13 3 15 2 13 11 +--R (- cosh(x) - -- %i cosh(x) - -- cosh(x) + -- %i cosh(x) + --)sinh(x) +--R 2 4 8 4 8 +--R + +--R 5 4 21 3 5 2 21 +--R - - %i cosh(x) - -- cosh(x) + - %i cosh(x) + -- cosh(x) +--R 4 8 4 8 +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 6%i cosh(x) - 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) - 6cosh(x) + 4%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 371 + +--S 372 of 526 +t0669:= sinh(x)^3/(%i+csch(x)) +--R +--R +--R 3 +--R sinh(x) +--R (371) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 372 + +--S 373 of 526 +r0669:= -3/2*x+2*%i*cosh(x)-1/3*%i*cosh(x)^3+%i*cosh(x)/(1+%i*sinh(x))+_ + 1/2*cosh(x)*sinh(x) +--R +--R +--R (372) +--R 1 2 1 3 3 3 +--R - cosh(x)sinh(x) + (- - %i cosh(x) + - %i cosh(x) - - x)sinh(x) +--R 2 3 2 2 +--R + +--R 1 3 3 +--R - - cosh(x) + 3cosh(x) + - %i x +--R 3 2 +--R / +--R sinh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 373 + +--S 374 of 526 +a0669:= integrate(t0669,x) +--R +--R +--R (373) +--R 4 3 +--R - %i sinh(x) + (- 4%i cosh(x) + 3)sinh(x) +--R + +--R 2 2 +--R (- 6%i cosh(x) + 3cosh(x) + 20%i)sinh(x) +--R + +--R 3 2 +--R (- 4%i cosh(x) + 9cosh(x) + 32%i cosh(x) - 36x + 3)sinh(x) +--R + +--R 4 3 2 +--R - %i cosh(x) + cosh(x) + 20%i cosh(x) + (- 36x + 39)cosh(x) + 36%i x +--R + +--R 69%i +--R / +--R 24sinh(x) + 24cosh(x) - 24%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 374 + +--S 375 of 526 +m0669:= a0669-r0669 +--R +--R +--R (374) +--R 1 5 1 1 4 +--R - -- %i sinh(x) + (- - %i cosh(x) + --)sinh(x) +--R 24 6 12 +--R + +--R 1 2 13 17 3 +--R (- - %i cosh(x) - -- cosh(x) + -- %i)sinh(x) +--R 4 24 24 +--R + +--R 1 3 3 2 5 23 2 +--R (- %i cosh(x) - - cosh(x) + -- %i cosh(x) + --)sinh(x) +--R 6 8 24 24 +--R + +--R 7 4 13 3 25 2 37 11 +--R (-- %i cosh(x) + -- cosh(x) - -- %i cosh(x) - -- cosh(x) + -- %i) +--R 24 24 24 24 4 +--R * +--R sinh(x) +--R + +--R 7 4 3 3 13 2 11 23 +--R -- cosh(x) - - %i cosh(x) - -- cosh(x) + -- %i cosh(x) + -- +--R 24 8 6 8 8 +--R / +--R 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) - %i cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 375 + +--S 376 of 526 +d0669:= D(m0669,x) +--R +--R +--R (375) +--R 1 7 5 11 6 +--R - - %i sinh(x) + (- - %i cosh(x) - --)sinh(x) +--R 8 8 12 +--R + +--R 1 2 23 5 5 +--R (- - %i cosh(x) - -- cosh(x) + - %i)sinh(x) +--R 4 12 6 +--R + +--R 3 3 1 2 1 9 4 +--R (- %i cosh(x) + - cosh(x) + - %i cosh(x) - -)sinh(x) +--R 4 2 3 4 +--R + +--R 3 4 13 3 13 2 21 59 +--R (- %i cosh(x) + -- cosh(x) - -- %i cosh(x) - -- cosh(x) + -- %i) +--R 8 6 8 4 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 5 5 4 23 3 5 2 +--R - - %i cosh(x) + -- cosh(x) - -- %i cosh(x) - -- cosh(x) +--R 8 12 24 12 +--R + +--R 95 4 +--R -- %i cosh(x) - - +--R 24 3 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 5 7 4 43 3 43 2 +--R - - cosh(x) + -- %i cosh(x) + -- cosh(x) - -- %i cosh(x) +--R 4 24 12 24 +--R + +--R 10 3 +--R - -- cosh(x) + - %i +--R 3 2 +--R * +--R sinh(x) +--R + +--R 1 5 4 4 25 3 4 2 +--R - %i cosh(x) + - cosh(x) - -- %i cosh(x) - - cosh(x) + 3%i cosh(x) +--R 8 3 8 3 +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 6%i cosh(x) - 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) - 6cosh(x) + 4%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 376 + +--S 377 of 526 +t0670:= sinh(x)^4/(%i+csch(x)) +--R +--R +--R 4 +--R sinh(x) +--R (376) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 377 + +--S 378 of 526 +r0670:= -15/8*%i*x-2*cosh(x)+1/3*cosh(x)^3-cosh(x)/(1+%i*sinh(x))+_ + 7/8*%i*cosh(x)*sinh(x)-1/4*%i*cosh(x)*sinh(x)^3 +--R +--R +--R (377) +--R 1 4 1 3 7 2 +--R - - %i cosh(x)sinh(x) - - cosh(x)sinh(x) + - %i cosh(x)sinh(x) +--R 4 4 8 +--R + +--R 1 3 9 15 1 3 +--R (- cosh(x) - - cosh(x) - -- %i x)sinh(x) - - %i cosh(x) + 3%i cosh(x) +--R 3 8 8 3 +--R + +--R 15 +--R - -- x +--R 8 +--R / +--R sinh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 378 + +--S 379 of 526 +a0670:= integrate(t0670,x) +--R +--R +--R (378) +--R 5 4 +--R - 3%i sinh(x) + (- 15%i cosh(x) + 8)sinh(x) +--R + +--R 2 3 +--R (- 30%i cosh(x) + 8cosh(x) + 45%i)sinh(x) +--R + +--R 3 2 2 +--R (- 30%i cosh(x) + 48cosh(x) + 105%i cosh(x) - 160)sinh(x) +--R + +--R 4 3 2 +--R - 15%i cosh(x) + 8cosh(x) + 135%i cosh(x) - 160cosh(x) - 360%i x +--R + +--R 48%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3%i cosh(x) + 8cosh(x) + 35%i cosh(x) - 160cosh(x) +--R + +--R (- 360%i x + 288%i)cosh(x) - 360x - 552 +--R / +--R 192sinh(x) + 192cosh(x) - 192%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 379 + +--S 380 of 526 +m0670:= a0670-r0670 +--R +--R +--R (379) +--R 1 6 11 5 5 +--R - -- %i sinh(x) + (-- %i cosh(x) + ---)sinh(x) +--R 64 64 192 +--R + +--R 3 2 89 37 4 +--R (-- %i cosh(x) + --- cosh(x) + --- %i)sinh(x) +--R 32 192 192 +--R + +--R 5 3 11 2 119 115 3 +--R (- -- %i cosh(x) + -- cosh(x) - --- %i cosh(x) - ---)sinh(x) +--R 32 32 192 192 +--R + +--R 5 4 43 3 27 2 7 13 +--R (- -- %i cosh(x) - -- cosh(x) - -- %i cosh(x) - --- cosh(x) + -- %i) +--R 64 96 64 192 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 5 71 4 155 3 191 2 +--R - -- %i cosh(x) - --- cosh(x) + --- %i cosh(x) + --- cosh(x) +--R 64 192 192 192 +--R + +--R 43 21 +--R - -- %i cosh(x) - -- +--R 24 8 +--R * +--R sinh(x) +--R + +--R 1 5 7 4 33 3 13 2 3 +--R - -- cosh(x) + -- %i cosh(x) + -- cosh(x) - -- %i cosh(x) - - cosh(x) +--R 64 24 64 6 2 +--R + +--R 23 +--R -- %i +--R 8 +--R / +--R 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) - %i cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 380 + +--S 381 of 526 +d0670:= D(m0670,x) +--R +--R +--R (380) +--R 3 8 1 51 7 +--R -- %i sinh(x) + (- %i cosh(x) + --)sinh(x) +--R 16 8 64 +--R + +--R 1 2 63 181 6 +--R (-- %i cosh(x) + -- cosh(x) - --- %i)sinh(x) +--R 16 64 96 +--R + +--R 1 3 15 2 205 4 5 +--R (- %i cosh(x) + -- cosh(x) - --- %i cosh(x) - -)sinh(x) +--R 4 32 96 3 +--R + +--R 3 4 5 3 2 1 89 +--R (- -- %i cosh(x) - -- cosh(x) + %i cosh(x) + -- cosh(x) - -- %i) +--R 16 32 24 32 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 73 4 101 3 227 2 +--R - - %i cosh(x) - -- cosh(x) + --- %i cosh(x) + --- cosh(x) +--R 8 64 48 64 +--R + +--R 187 673 +--R - --- %i cosh(x) - --- +--R 32 192 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 6 53 5 127 4 325 3 +--R - -- %i cosh(x) - -- cosh(x) + --- %i cosh(x) + --- cosh(x) +--R 16 64 96 192 +--R + +--R 199 2 781 17 +--R - --- %i cosh(x) - --- cosh(x) - -- %i +--R 96 192 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 6 17 5 5 4 293 3 +--R - - cosh(x) + -- %i cosh(x) - --- cosh(x) + --- %i cosh(x) +--R 8 32 192 96 +--R + +--R 293 2 43 11 +--R --- cosh(x) - -- %i cosh(x) - -- +--R 192 12 8 +--R * +--R sinh(x) +--R + +--R 1 6 5 5 67 4 195 3 +--R -- %i cosh(x) + -- cosh(x) + -- %i cosh(x) + --- cosh(x) +--R 16 64 48 64 +--R + +--R 35 2 25 +--R - -- %i cosh(x) - -- cosh(x) +--R 24 8 +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 6%i cosh(x) - 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) - 6cosh(x) + 4%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 381 + +--S 382 of 526 +t0671:= cosh(x)/(a+b*csch(x)) +--R +--R +--R cosh(x) +--R (381) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 382 + +--S 383 of 526 +r0671:= -b*log(b+a*sinh(x))/a^2+sinh(x)/a +--R +--R +--R - b log(a sinh(x) + b) + a sinh(x) +--R (382) ---------------------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 383 + +--S 384 of 526 +a0671:= integrate(t0671,x) +--R +--R +--R (383) +--R - 2a sinh(x) - 2b 2 +--R (- 2b sinh(x) - 2b cosh(x))log(-----------------) + a sinh(x) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (2a cosh(x) + 2b x)sinh(x) + a cosh(x) + 2b x cosh(x) - a +--R / +--R 2 2 +--R 2a sinh(x) + 2a cosh(x) +--R Type: Union(Expression(Integer),...) +--E 384 + +--S 385 of 526 +m0671:= a0671-r0671 +--R +--R +--R (384) +--R (2b sinh(x) + 2b cosh(x))log(a sinh(x) + b) +--R + +--R - 2a sinh(x) - 2b 2 +--R (- 2b sinh(x) - 2b cosh(x))log(-----------------) - a sinh(x) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R 2b x sinh(x) + a cosh(x) + 2b x cosh(x) - a +--R / +--R 2 2 +--R 2a sinh(x) + 2a cosh(x) +--R Type: Expression(Integer) +--E 385 + +--S 386 of 526 +d0671:= D(m0671,x) +--R +--R +--R 2 2 +--R sinh(x) - cosh(x) + 1 +--R (385) ----------------------- +--R 2a sinh(x) + 2a cosh(x) +--R Type: Expression(Integer) +--E 386 + +--S 387 of 526 +t0672:= cosh(x)^2/(a+b*csch(x)) +--R +--R +--R 2 +--R cosh(x) +--R (386) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 387 + +--S 388 of 526 +r0672:= 1/2/a^3*(a^2*x+2*b^2*x+4*b*(a^2+b^2)^(1/2)*_ + atanh(1/(a^2+b^2)^(1/2)*(-b*cosh(x)+b+a*sinh(x))/sinh(x))-_ + 2*a*b*cosh(x)+a^2*cosh(x)*sinh(x)) +--R +--R +--R (387) +--R +-------+ +--R | 2 2 a sinh(x) - b cosh(x) + b 2 +--R 4b\|b + a atanh(-------------------------) + a cosh(x)sinh(x) +--R +-------+ +--R | 2 2 +--R sinh(x)\|b + a +--R + +--R 2 2 +--R - 2a b cosh(x) + (2b + a )x +--R / +--R 3 +--R 2a +--R Type: Expression(Integer) +--E 388 + +--S 389 of 526 +a0672:= integrate(t0672,x) +--R +--R +--R (388) +--R +-------+ +--R 2 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 4 2 3 +--R a sinh(x) + (4a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a cosh(x) - 12a b cosh(x) + (8b + 4a )x)sinh(x) +--R + +--R 2 3 2 2 2 +--R (4a cosh(x) - 12a b cosh(x) + (16b + 8a )x cosh(x) - 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R a cosh(x) - 4a b cosh(x) + (8b + 4a )x cosh(x) - 4a b cosh(x) - a +--R / +--R 3 2 3 3 2 +--R 8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) +--R Type: Union(Expression(Integer),...) +--E 389 + +--S 390 of 526 +m0672:= a0672-r0672 +--R +--R +--R (389) +--R +-------+ +--R 2 2 | 2 2 +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- 16b sinh(x) - 32b cosh(x)sinh(x) - 16b cosh(x) )\|b + a +--R * +--R a sinh(x) - b cosh(x) + b +--R atanh(-------------------------) +--R +-------+ +--R | 2 2 +--R sinh(x)\|b + a +--R + +--R 2 4 3 2 2 2 +--R a sinh(x) - 4a b sinh(x) + (- 2a cosh(x) - 4a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 +--R (4a b cosh(x) - 4a b)sinh(x) + a cosh(x) + 4a b cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R - a +--R / +--R 3 2 3 3 2 +--R 8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) +--R Type: Expression(Integer) +--E 390 + +--S 391 of 526 +d0672:= D(m0672,x) +--R +--R +--R (390) +--R 3 8 3 4 4 7 +--R - a b sinh(x) + ((- 2a b - 2a )cosh(x) + 2a )sinh(x) +--R + +--R 3 4 2 2 2 3 4 3 3 +--R ((2a b - 4a )cosh(x) + (4a b - 2a b + 4a )cosh(x) + 12a b + 10a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 3 2 2 3 4 2 +--R (6a b + 2a )cosh(x) + (8a b + 4a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 4 4 +--R (40a b + 8a b + 26a b + 2a )cosh(x) + 8b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 2 2 3 4 3 +--R 8a cosh(x) + (- 4a b + 18a b - 8a )cosh(x) +--R + +--R 3 2 2 3 2 4 2 2 3 +--R (36a b + 24a b + 20a b)cosh(x) + (24b + 8a b - 6a b)cosh(x) +--R + +--R 3 3 +--R 8a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 5 2 2 3 4 4 +--R (- 6a b + 2a )cosh(x) + (- 16a b + 8a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 16a b + 16a b - 4a b - 4a )cosh(x) +--R + +--R 4 2 2 3 4 2 +--R (16b + 16a b - 8a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 4 4 +--R (32a b + 8a b + 26a b + 2a )cosh(x) + 8b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 6 2 2 3 4 5 +--R (- 2a b - 4a )cosh(x) + (- 4a b - 14a b + 4a )cosh(x) +--R + +--R 3 2 2 3 4 4 3 3 +--R (- 44a b - 16a b - 22a b)cosh(x) + (- 16b + 12a b)cosh(x) +--R + +--R 3 2 2 3 4 2 +--R (48a b + 24a b + 34a b + 4a )cosh(x) +--R + +--R 4 2 2 3 4 3 3 +--R (24b + 4a b - 6a b - 4a )cosh(x) - 4a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 7 2 2 3 4 6 +--R (2a b - 2a )cosh(x) + (8a b - 12a b + 2a )cosh(x) +--R + +--R 3 2 2 3 4 5 +--R (- 24a b - 24a b - 22a b + 2a )cosh(x) +--R + +--R 4 2 2 3 4 4 +--R (- 24b - 16a b + 24a b - 2a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (32a b + 24a b + 22a b + 2a )cosh(x) +--R + +--R 4 2 2 3 4 2 3 3 4 +--R (24b + 8a b - 12a b - 2a )cosh(x) + (- 8a b - 2a b - 2a )cosh(x) +--R + +--R 4 +--R 2a +--R * +--R sinh(x) +--R + +--R 3 8 2 2 3 7 3 2 2 3 6 +--R a b cosh(x) + (4a b - 2a b)cosh(x) + (- 4a b - 8a b - 8a b)cosh(x) +--R + +--R 4 2 2 3 5 3 2 2 3 4 +--R (- 8b - 8a b + 10a b)cosh(x) + (8a b + 8a b + 6a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 3 3 +--R (8b + 4a b - 6a b)cosh(x) - 4a b cosh(x) - 2a b cosh(x) + a b +--R / +--R 4 6 4 5 3 2 5 5 +--R 4a b sinh(x) + ((16a b + 8a )cosh(x) + 8a b - 8a )sinh(x) +--R + +--R 4 5 2 3 2 4 5 4 4 +--R ((20a b + 32a )cosh(x) + (24a b + 24a b - 32a )cosh(x) - 24a b)sinh(x) +--R + +--R 5 3 3 2 4 5 2 +--R 48a cosh(x) + (16a b + 80a b - 48a )cosh(x) +--R + +--R 3 2 4 5 3 2 5 +--R (16a b - 72a b - 8a )cosh(x) - 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 4 3 2 4 5 3 +--R (- 20a b + 32a )cosh(x) + (- 16a b + 96a b - 32a )cosh(x) +--R + +--R 3 2 4 5 2 3 2 4 5 +--R (48a b - 72a b - 16a )cosh(x) + (- 24a b - 8a b + 16a )cosh(x) +--R + +--R 4 +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 5 3 2 4 5 4 +--R (- 16a b + 8a )cosh(x) + (- 24a b + 48a b - 8a )cosh(x) +--R + +--R 3 2 4 5 3 3 2 4 5 2 +--R (48a b - 24a b - 8a )cosh(x) + (- 24a b - 16a b + 8a )cosh(x) +--R + +--R 4 +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 6 3 2 4 5 3 2 4 +--R - 4a b cosh(x) + (- 8a b + 8a b)cosh(x) + 16a b cosh(x) +--R + +--R 3 2 4 3 4 2 +--R (- 8a b - 8a b)cosh(x) + 4a b cosh(x) +--R Type: Expression(Integer) +--E 391 + +--S 392 of 526 +t0673:= cosh(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R cosh(x) +--R (391) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 392 + +--S 393 of 526 +r0673:= -b*(a^2+b^2)*log(b+a*sinh(x))/a^4+(a^2+b^2)*sinh(x)/a^3-_ + 1/2*b*sinh(x)^2/a^2+1/3*sinh(x)^3/a +--R +--R +--R (392) +--R 3 2 3 3 2 2 +--R (- 6b - 6a b)log(a sinh(x) + b) + 2a sinh(x) - 3a b sinh(x) +--R + +--R 2 3 +--R (6a b + 6a )sinh(x) +--R / +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 393 + +--S 394 of 526 +a0673:= integrate(t0673,x) +--R +--R +--R (393) +--R 3 2 3 3 2 2 +--R (- 24b - 24a b)sinh(x) + (- 72b - 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 72b - 72a b)cosh(x) sinh(x) + (- 24b - 24a b)cosh(x) +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 6 3 2 5 +--R a sinh(x) + (6a cosh(x) - 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (15a cosh(x) - 15a b cosh(x) + 12a b + 9a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 20a cosh(x) - 30a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 +--R (24b + 24a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 15a cosh(x) - 30a b cosh(x) + (72a b + 54a )cosh(x) +--R + +--R 3 2 2 3 +--R (72b + 72a b)x cosh(x) - 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (72b + 72a b)x cosh(x) + (- 24a b - 18a )cosh(x) - 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R (24b + 24a b)x cosh(x) + (- 12a b - 9a )cosh(x) - 3a b cosh(x) - a +--R / +--R 4 3 4 2 4 2 4 3 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) +--R Type: Union(Expression(Integer),...) +--E 394 + +--S 395 of 526 +m0673:= a0673-r0673 +--R +--R +--R (394) +--R 3 2 3 3 2 2 +--R (24b + 24a b)sinh(x) + (72b + 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (72b + 72a b)cosh(x) sinh(x) + (24b + 24a b)cosh(x) +--R * +--R log(a sinh(x) + b) +--R + +--R 3 2 3 3 2 2 +--R (- 24b - 24a b)sinh(x) + (- 72b - 72a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 72b - 72a b)cosh(x) sinh(x) + (- 24b - 24a b)cosh(x) +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 6 3 2 5 +--R - 7a sinh(x) + (- 18a cosh(x) + 9a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (- 9a cosh(x) + 21a b cosh(x) - 12a b - 15a )sinh(x) +--R + +--R 3 3 2 2 2 3 +--R 12a cosh(x) + 6a b cosh(x) + (- 24a b - 36a )cosh(x) +--R + +--R 3 2 +--R (24b + 24a b)x +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 +--R 15a cosh(x) - 18a b cosh(x) - 18a cosh(x) +--R + +--R 3 2 2 3 +--R (72b + 72a b)x cosh(x) - 12a b - 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 6a cosh(x) - 15a b cosh(x) + (24a b + 12a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (72b + 72a b)x cosh(x) + (- 24a b - 18a )cosh(x) - 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R a cosh(x) - 3a b cosh(x) + (12a b + 9a )cosh(x) +--R + +--R 3 2 3 2 3 2 2 3 +--R (24b + 24a b)x cosh(x) + (- 12a b - 9a )cosh(x) - 3a b cosh(x) - a +--R / +--R 4 3 4 2 4 2 4 3 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) + 24a cosh(x) +--R Type: Expression(Integer) +--E 395 + +--S 396 of 526 +d0673:= D(m0673,x) +--R +--R +--R (395) +--R 2 6 2 5 +--R a sinh(x) + (- 2a cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 9a cosh(x) - 2a b cosh(x) + 4b + 3a )sinh(x) +--R + +--R 2 3 2 2 2 3 +--R (- 4a cosh(x) + 4a b cosh(x) + (8b + 4a )cosh(x))sinh(x) +--R + +--R 2 4 3 2 2 2 2 2 +--R (7a cosh(x) + 4a b cosh(x) - 6a cosh(x) + 4b + 3a )sinh(x) +--R + +--R 2 5 4 2 2 3 +--R 6a cosh(x) - 2a b cosh(x) + (- 8b - 12a )cosh(x) +--R + +--R 2 2 +--R (8b + 6a )cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 6 5 2 2 4 2 2 2 +--R a cosh(x) - 2a b cosh(x) + (- 4b - 5a )cosh(x) + (4b + 3a )cosh(x) +--R + +--R 2 +--R 2a b cosh(x) + a +--R / +--R 3 3 3 2 3 2 3 3 +--R 8a sinh(x) + 24a cosh(x)sinh(x) + 24a cosh(x) sinh(x) + 8a cosh(x) +--R Type: Expression(Integer) +--E 396 + +--S 397 of 526 +t0674:= cosh(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R cosh(x) +--R (396) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 526 +r0674:= -5/8*x/a-1/2*b^2*x/a^3+(a^2+b^2)^2*x/a^5+_ + 2*b*(a^2+b^2)^(3/2)*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^5-_ + b*cosh(x)/a^2-b^3*cosh(x)/a^4-1/3*b*cosh(x)^3/a^2+_ + 5/8*cosh(x)*sinh(x)/a+1/2*b^2*cosh(x)*sinh(x)/a^3+_ + 1/4*cosh(x)*sinh(x)^3/a +--R +--R +--R (397) +--R x +--R +-------+ b tanh(-) - a +--R 3 2 | 2 2 2 4 3 +--R (- 48b - 48a b)\|b + a atanh(-------------) + 6a cosh(x)sinh(x) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 4 3 3 3 3 +--R (12a b + 15a )cosh(x)sinh(x) - 8a b cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 4 2 2 4 +--R (24b + 36a b + 9a )x +--R / +--R 5 +--R 24a +--R Type: Expression(Integer) +--E 398 + +--S 399 of 526 +a0674:= integrate(t0674,x) +--R +--R +--R (398) +--R 3 2 4 3 2 3 +--R (192b + 192a b)sinh(x) + (768b + 768a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 3 +--R (1152b + 1152a b)cosh(x) sinh(x) + (768b + 768a b)cosh(x) sinh(x) +--R + +--R 3 2 4 +--R (192b + 192a b)cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (84a cosh(x) - 56a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R 168a cosh(x) - 168a b cosh(x) + (144a b + 144a )cosh(x) - 96a b +--R + +--R 3 +--R - 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 210a cosh(x) - 280a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 480a b - 600a b)cosh(x) + (192b + 288a b + 72a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 168a cosh(x) - 280a b cosh(x) + (480a b + 480a )cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 960a b - 1200a b)cosh(x) + (768b + 1152a b + 288a )x cosh(x) +--R + +--R 3 3 +--R - 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) - 168a b cosh(x) + (360a b + 360a )cosh(x) +--R + +--R 3 3 3 4 2 2 4 2 +--R (- 960a b - 1200a b)cosh(x) + (1152b + 1728a b + 432a )x cosh(x) +--R + +--R 3 3 2 2 4 +--R (- 288a b - 360a b)cosh(x) - 24a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) - 56a b cosh(x) + (144a b + 144a )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (- 480a b - 600a b)cosh(x) + (768b + 1152a b + 288a )x cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (- 288a b - 360a b)cosh(x) + (- 48a b - 48a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) - 8a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 4 2 2 4 4 +--R (- 96a b - 120a b)cosh(x) + (192b + 288a b + 72a )x cosh(x) +--R + +--R 3 3 3 2 2 4 2 3 +--R (- 96a b - 120a b)cosh(x) + (- 24a b - 24a )cosh(x) - 8a b cosh(x) +--R + +--R 4 +--R - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 526 +m0674:= a0674-r0674 +--R +--R +--R (399) +--R 3 2 4 3 2 3 +--R (192b + 192a b)sinh(x) + (768b + 768a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 3 +--R (1152b + 1152a b)cosh(x) sinh(x) + (768b + 768a b)cosh(x) sinh(x) +--R + +--R 3 2 4 +--R (192b + 192a b)cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 3 2 4 3 2 3 +--R (384b + 384a b)sinh(x) + (1536b + 1536a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 +--R (2304b + 2304a b)cosh(x) sinh(x) +--R + +--R 3 2 3 3 2 4 +--R (1536b + 1536a b)cosh(x) sinh(x) + (384b + 384a b)cosh(x) +--R * +--R x +--R +-------+ b tanh(-) - a +--R | 2 2 2 +--R \|b + a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 8 4 3 7 +--R 3a sinh(x) + (- 24a cosh(x) - 8a b)sinh(x) +--R + +--R 4 2 3 2 2 4 6 +--R (- 108a cosh(x) - 56a b cosh(x) + 24a b + 24a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 +--R - 120a cosh(x) - 168a b cosh(x) + (48a b + 24a )cosh(x) - 96a b +--R + +--R 3 +--R - 120a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R 18a cosh(x) - 216a b cosh(x) + (- 24a b - 120a )cosh(x) +--R + +--R 3 3 +--R (- 288a b - 408a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 2 2 4 3 +--R 120a cosh(x) - 24a b cosh(x) + (- 96a b - 240a )cosh(x) +--R + +--R 3 3 2 3 3 +--R (- 192a b - 432a b)cosh(x) - 96a b - 120a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 2 2 4 4 +--R 84a cosh(x) + 216a b cosh(x) + (- 24a b - 120a )cosh(x) +--R + +--R 3 3 3 3 3 2 2 4 +--R (192a b - 48a b)cosh(x) + (- 288a b - 360a b)cosh(x) - 24a b - 24a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 7 3 6 2 2 4 5 +--R 24a cosh(x) + 200a b cosh(x) + (48a b + 24a )cosh(x) +--R + +--R 3 3 4 3 3 2 +--R (288a b + 168a b)cosh(x) + (- 288a b - 360a b)cosh(x) +--R + +--R 2 2 4 3 +--R (- 48a b - 48a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 8 3 7 2 2 4 6 +--R 3a cosh(x) + 56a b cosh(x) + (24a b + 24a )cosh(x) +--R + +--R 3 3 5 3 3 3 +--R (96a b + 72a b)cosh(x) + (- 96a b - 120a b)cosh(x) +--R + +--R 2 2 4 2 3 4 +--R (- 24a b - 24a )cosh(x) - 8a b cosh(x) - 3a +--R / +--R 5 4 5 3 5 2 2 +--R 192a sinh(x) + 768a cosh(x)sinh(x) + 1152a cosh(x) sinh(x) +--R + +--R 5 3 5 4 +--R 768a cosh(x) sinh(x) + 192a cosh(x) +--R Type: Expression(Integer) +--E 400 + +--S 401 of 526 +d0674:= D(m0674,x) +--R +--R +--R (400) +--R 4 10 4 3 2 9 +--R - 3a b sinh(x) + (- 14a b cosh(x) - 8a b )sinh(x) +--R + +--R 4 2 3 2 2 3 4 8 +--R (- 27a b cosh(x) - 40a b cosh(x) - 8a b - 3a b)sinh(x) +--R + +--R 4 3 3 2 2 2 3 4 +--R - 32a b cosh(x) - 88a b cosh(x) + (- 48a b - 20a b)cosh(x) +--R + +--R 3 2 +--R - 4a b +--R * +--R 7 +--R sinh(x) +--R + +--R 4 4 3 2 3 2 3 4 2 +--R - 30a b cosh(x) - 104a b cosh(x) + (- 96a b - 40a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (16a b - 4a b )cosh(x) + 32b + 48a b + 22a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 3 2 4 2 3 4 3 +--R - 12a b cosh(x) - 40a b cosh(x) + (- 48a b - 28a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (64a b + 4a b )cosh(x) + (160b + 240a b + 112a b)cosh(x) +--R + +--R 3 2 +--R 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 3 2 5 2 3 4 4 +--R 26a b cosh(x) + 72a b cosh(x) + (80a b - 14a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (80a b - 44a b )cosh(x) + (320b + 496a b + 250a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (16a b + 36a b )cosh(x) - 8a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 3 2 6 2 3 4 5 +--R 48a b cosh(x) + 120a b cosh(x) + (112a b - 44a b)cosh(x) +--R + +--R 3 2 4 5 2 3 4 3 +--R - 156a b cosh(x) + (320b + 544a b + 320a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (64a b + 104a b )cosh(x) + (- 32a b - 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 3 2 7 2 3 4 6 +--R 33a b cosh(x) + 72a b cosh(x) + (32a b - 64a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 4 +--R (- 80a b - 188a b )cosh(x) + (160b + 336a b + 250a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 4 +--R (96a b + 136a b )cosh(x) + (- 48a b - 72a b)cosh(x) - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 3 2 8 2 3 4 7 +--R 10a b cosh(x) + 16a b cosh(x) + (- 16a b - 36a b)cosh(x) +--R + +--R 4 3 2 6 5 2 3 4 5 +--R (- 64a b - 100a b )cosh(x) + (32b + 112a b + 112a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (64a b + 84a b )cosh(x) + (- 32a b - 48a b)cosh(x) +--R + +--R 4 +--R - 6a b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 2 3 4 8 +--R a b cosh(x) + (- 8a b - 7a b)cosh(x) +--R + +--R 4 3 2 7 2 3 4 6 +--R (- 16a b - 20a b )cosh(x) + (16a b + 22a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 4 2 +--R (16a b + 20a b )cosh(x) + (- 8a b - 12a b)cosh(x) - 3a b cosh(x) +--R + +--R 4 +--R - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 10 5 4 9 +--R 6a sinh(x) + (28a cosh(x) + 16a b)sinh(x) +--R + +--R 5 2 4 3 2 5 8 +--R (54a cosh(x) + 80a b cosh(x) + 16a b + 6a )sinh(x) +--R + +--R 5 3 4 2 3 2 5 4 +--R (64a cosh(x) + 176a b cosh(x) + (96a b + 40a )cosh(x) + 8a b) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 4 3 3 2 5 2 +--R 60a cosh(x) + 208a b cosh(x) + (192a b + 80a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 32a b + 8a b)cosh(x) - 32a b - 32a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 4 4 3 2 5 3 +--R 24a cosh(x) + 80a b cosh(x) + (96a b + 56a )cosh(x) +--R + +--R 2 3 4 2 4 3 2 5 +--R (- 128a b - 8a b)cosh(x) + (- 128a b - 96a b - 32a )cosh(x) +--R + +--R 5 2 3 4 +--R 64b + 128a b + 56a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 6 4 5 3 2 5 4 +--R - 52a cosh(x) - 144a b cosh(x) + (- 160a b + 28a )cosh(x) +--R + +--R 2 3 4 3 4 3 2 5 2 +--R (- 160a b + 88a b)cosh(x) + (- 160a b - 32a b - 20a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (320b + 608a b + 248a b)cosh(x) - 32a b - 48a b - 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 7 4 6 3 2 5 5 +--R - 96a cosh(x) - 240a b cosh(x) + (- 224a b + 88a )cosh(x) +--R + +--R 4 4 3 2 3 +--R 312a b cosh(x) + 192a b cosh(x) +--R + +--R 5 2 3 4 2 +--R (640b + 1152a b + 432a b)cosh(x) +--R + +--R 4 3 2 5 +--R (- 128a b - 192a b - 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 8 4 7 3 2 5 6 +--R - 66a cosh(x) - 144a b cosh(x) + (- 64a b + 128a )cosh(x) +--R + +--R 2 3 4 5 4 3 2 5 4 +--R (160a b + 376a b)cosh(x) + (160a b + 288a b - 20a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (640b + 1088a b + 368a b)cosh(x) +--R + +--R 4 3 2 5 2 5 +--R (- 192a b - 288a b - 48a )cosh(x) + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 9 4 8 3 2 5 7 +--R - 20a cosh(x) - 32a b cosh(x) + (32a b + 72a )cosh(x) +--R + +--R 2 3 4 6 4 3 2 5 5 +--R (128a b + 200a b)cosh(x) + (128a b + 160a b - 32a )cosh(x) +--R + +--R 5 2 3 4 4 +--R (320b + 512a b + 152a b)cosh(x) +--R + +--R 4 3 2 5 3 5 +--R (- 128a b - 192a b - 32a )cosh(x) + 12a cosh(x) +--R * +--R sinh(x) +--R + +--R 5 10 3 2 5 8 2 3 4 7 +--R - 2a cosh(x) + (16a b + 14a )cosh(x) + (32a b + 40a b)cosh(x) +--R + +--R 4 3 2 5 6 5 2 3 4 5 +--R (32a b + 32a b - 12a )cosh(x) + (64b + 96a b + 24a b)cosh(x) +--R + +--R 4 3 2 5 4 5 2 5 +--R (- 32a b - 48a b - 8a )cosh(x) + 6a cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 10 4 3 2 9 +--R 3a b sinh(x) + (14a b cosh(x) + 8a b )sinh(x) +--R + +--R 4 2 3 2 2 3 4 8 +--R (27a b cosh(x) + 40a b cosh(x) + 8a b + 3a b)sinh(x) +--R + +--R 4 3 3 2 2 2 3 4 3 2 +--R (32a b cosh(x) + 88a b cosh(x) + (48a b + 20a b)cosh(x) + 4a b ) +--R * +--R 7 +--R sinh(x) +--R + +--R 4 4 3 2 3 2 3 4 2 +--R 30a b cosh(x) + 104a b cosh(x) + (96a b + 40a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (- 16a b + 4a b )cosh(x) - 32b - 48a b - 22a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 3 2 4 2 3 4 3 +--R 12a b cosh(x) + 40a b cosh(x) + (48a b + 28a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (- 64a b - 4a b )cosh(x) + (- 160b - 240a b - 112a b)cosh(x) +--R + +--R 3 2 +--R - 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 3 2 5 2 3 4 4 +--R - 26a b cosh(x) - 72a b cosh(x) + (- 80a b + 14a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (- 80a b + 44a b )cosh(x) + (- 320b - 496a b - 250a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 16a b - 36a b )cosh(x) + 8a b + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 3 2 6 2 3 4 5 +--R - 48a b cosh(x) - 120a b cosh(x) + (- 112a b + 44a b)cosh(x) +--R + +--R 3 2 4 5 2 3 4 3 +--R 156a b cosh(x) + (- 320b - 544a b - 320a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 +--R (- 64a b - 104a b )cosh(x) + (32a b + 48a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 3 2 7 2 3 4 6 +--R - 33a b cosh(x) - 72a b cosh(x) + (- 32a b + 64a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 4 +--R (80a b + 188a b )cosh(x) + (- 160b - 336a b - 250a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 4 +--R (- 96a b - 136a b )cosh(x) + (48a b + 72a b)cosh(x) + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 3 2 8 2 3 4 7 +--R - 10a b cosh(x) - 16a b cosh(x) + (16a b + 36a b)cosh(x) +--R + +--R 4 3 2 6 5 2 3 4 5 +--R (64a b + 100a b )cosh(x) + (- 32b - 112a b - 112a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 4 +--R (- 64a b - 84a b )cosh(x) + (32a b + 48a b)cosh(x) + 6a b cosh(x) +--R * +--R sinh(x) +--R + +--R 4 10 2 3 4 8 4 3 2 7 +--R - a b cosh(x) + (8a b + 7a b)cosh(x) + (16a b + 20a b )cosh(x) +--R + +--R 2 3 4 6 4 3 2 5 +--R (- 16a b - 22a b)cosh(x) + (- 16a b - 20a b )cosh(x) +--R + +--R 2 3 4 4 4 2 4 +--R (8a b + 12a b)cosh(x) + 3a b cosh(x) + a b +--R / +--R 5 6 5 4 2 5 +--R 16a b sinh(x) + (96a b cosh(x) + 32a b )sinh(x) +--R + +--R 5 2 4 2 5 4 +--R (240a b cosh(x) + 160a b cosh(x) - 16a b)sinh(x) +--R + +--R 5 3 4 2 2 5 3 +--R (320a b cosh(x) + 320a b cosh(x) - 64a b cosh(x))sinh(x) +--R + +--R 5 4 4 2 3 5 2 2 +--R (240a b cosh(x) + 320a b cosh(x) - 96a b cosh(x) )sinh(x) +--R + +--R 5 5 4 2 4 5 3 +--R (96a b cosh(x) + 160a b cosh(x) - 64a b cosh(x) )sinh(x) +--R + +--R 5 6 4 2 5 5 4 +--R 16a b cosh(x) + 32a b cosh(x) - 16a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 6 6 5 5 +--R - 32a sinh(x) + (- 192a cosh(x) - 64a b)sinh(x) +--R + +--R 6 2 5 6 4 +--R (- 480a cosh(x) - 320a b cosh(x) + 32a )sinh(x) +--R + +--R 6 3 5 2 6 3 +--R (- 640a cosh(x) - 640a b cosh(x) + 128a cosh(x))sinh(x) +--R + +--R 6 4 5 3 6 2 2 +--R (- 480a cosh(x) - 640a b cosh(x) + 192a cosh(x) )sinh(x) +--R + +--R 6 5 5 4 6 3 +--R (- 192a cosh(x) - 320a b cosh(x) + 128a cosh(x) )sinh(x) +--R + +--R 6 6 5 5 6 4 +--R - 32a cosh(x) - 64a b cosh(x) + 32a cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 6 5 4 2 5 +--R - 16a b sinh(x) + (- 96a b cosh(x) - 32a b )sinh(x) +--R + +--R 5 2 4 2 5 4 +--R (- 240a b cosh(x) - 160a b cosh(x) + 16a b)sinh(x) +--R + +--R 5 3 4 2 2 5 3 +--R (- 320a b cosh(x) - 320a b cosh(x) + 64a b cosh(x))sinh(x) +--R + +--R 5 4 4 2 3 5 2 2 +--R (- 240a b cosh(x) - 320a b cosh(x) + 96a b cosh(x) )sinh(x) +--R + +--R 5 5 4 2 4 5 3 +--R (- 96a b cosh(x) - 160a b cosh(x) + 64a b cosh(x) )sinh(x) +--R + +--R 5 6 4 2 5 5 4 +--R - 16a b cosh(x) - 32a b cosh(x) + 16a b cosh(x) +--R Type: Expression(Integer) +--E 401 + +--S 402 of 526 +t0675:= cosh(x)/(%i+csch(x)) +--R +--R +--R cosh(x) +--R (401) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 402 + +--S 403 of 526 +r0675:= log(-%i+sinh(x))-%i*sinh(x) +--R +--R +--R (402) log(sinh(x) - %i) - %i sinh(x) +--R Type: Expression(Complex(Integer)) +--E 403 + +--S 404 of 526 +a0675:= integrate(t0675,x) +--R +--R +--R (403) +--R 2 +--R (4sinh(x) + 4cosh(x))log(sinh(x) + cosh(x) - %i) - %i sinh(x) +--R + +--R 2 +--R (- 2%i cosh(x) - 2x)sinh(x) - %i cosh(x) - 2x cosh(x) + %i +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 404 + +--S 405 of 526 +m0675:= a0675-r0675 +--R +--R +--R (404) +--R (4sinh(x) + 4cosh(x))log(sinh(x) + cosh(x) - %i) +--R + +--R 2 +--R (- 2sinh(x) - 2cosh(x))log(sinh(x) - %i) + %i sinh(x) - 2x sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2x cosh(x) + %i +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Expression(Complex(Integer)) +--E 405 + +--S 406 of 526 +d0675:= D(m0675,x) +--R +--R +--R (405) +--R 4 3 2 2 +--R - %i sinh(x) - %i cosh(x)sinh(x) + (%i cosh(x) + cosh(x))sinh(x) +--R + +--R 3 3 2 +--R (%i cosh(x) - %i cosh(x))sinh(x) - cosh(x) - %i cosh(x) + cosh(x) + %i +--R / +--R 3 2 +--R 2sinh(x) + (4cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (2cosh(x) - 6%i cosh(x) - 2)sinh(x) - 2%i cosh(x) - 2cosh(x) +--R Type: Expression(Complex(Integer)) +--E 406 + +--S 407 of 526 +t0676:= cosh(x)^2/(%i+csch(x)) +--R +--R +--R 2 +--R cosh(x) +--R (406) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 407 + +--S 408 of 526 +r0676:= 1/2*%i*x+cosh(x)-1/2*%i*cosh(x)*sinh(x) +--R +--R +--R 1 1 +--R (407) - - %i cosh(x)sinh(x) + cosh(x) + - %i x +--R 2 2 +--R Type: Expression(Complex(Fraction(Integer))) +--E 408 + +--S 409 of 526 +a0676:= integrate(t0676,x) +--R +--R +--R - %i cosh(x)sinh(x) + 2cosh(x) + %i x +--R (408) ------------------------------------- +--R 2 +--R Type: Union(Expression(Complex(Integer)),...) +--E 409 + +--S 410 of 526 +m0676:= a0676-r0676 +--R +--R +--R (409) 0 +--R Type: Expression(Complex(Fraction(Integer))) +--E 410 + +--S 411 of 526 +d0676:= D(m0676,x) +--R +--R +--R (410) 0 +--R Type: Expression(Complex(Fraction(Integer))) +--E 411 + +--S 412 of 526 +t0677:= cosh(x)^4/(%i+csch(x)) +--R +--R +--R 4 +--R cosh(x) +--R (411) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 412 + +--S 413 of 526 +r0677:= 1/8*%i*x+1/3*cosh(x)^3-1/8*%i*cosh(x)*sinh(x)-1/4*%i*cosh(x)*sinh(x)^3 +--R +--R +--R 1 3 1 1 3 1 +--R (412) - - %i cosh(x)sinh(x) - - %i cosh(x)sinh(x) + - cosh(x) + - %i x +--R 4 8 3 8 +--R Type: Expression(Complex(Fraction(Integer))) +--E 413 + +--S 414 of 526 +a0677:= integrate(t0677,x) +--R +--R +--R (413) +--R 3 2 3 +--R - 3%i cosh(x)sinh(x) + 6cosh(x)sinh(x) - 3%i cosh(x) sinh(x) +--R + +--R 3 +--R 2cosh(x) + 6cosh(x) + 3%i x +--R / +--R 24 +--R Type: Union(Expression(Complex(Integer)),...) +--E 414 + +--S 415 of 526 +m0677:= a0677-r0677 +--R +--R +--R (414) +--R 1 3 1 2 +--R - %i cosh(x)sinh(x) + - cosh(x)sinh(x) +--R 8 4 +--R + +--R 1 3 1 1 3 1 +--R (- - %i cosh(x) + - %i cosh(x))sinh(x) - - cosh(x) + - cosh(x) +--R 8 8 4 4 +--R Type: Expression(Complex(Fraction(Integer))) +--E 415 + +--S 416 of 526 +d0677:= D(m0677,x) +--R +--R +--R (415) +--R 1 4 1 3 1 2 1 2 1 +--R - %i sinh(x) + - sinh(x) + - %i sinh(x) + (- - cosh(x) + -)sinh(x) +--R 8 4 8 4 4 +--R + +--R 1 4 1 2 +--R - - %i cosh(x) + - %i cosh(x) +--R 8 8 +--R Type: Expression(Complex(Fraction(Integer))) +--E 416 + +--S 417 of 526 +t0678:= tanh(x)/(a+b*csch(x)) +--R +--R +--R tanh(x) +--R (416) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 417 + +--S 418 of 526 +r0678:= -1/2*(2*a*b*atan(sinh(x))-a^2*log(cosh(x)^2)-_ + 2*b^2*log(b+a*sinh(x)))/a/(a^2+b^2) +--R +--R +--R 2 2 2 +--R 2b log(a sinh(x) + b) + a log(cosh(x) ) - 2a b atan(sinh(x)) +--R (417) ------------------------------------------------------------ +--R 2 3 +--R 2a b + 2a +--R Type: Expression(Integer) +--E 418 + +--S 419 of 526 +a0678:= integrate(t0678,x) +--R +--R +--R (418) +--R 2 2cosh(x) 2 - 2a sinh(x) - 2b +--R a log(- -----------------) + b log(-----------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 2a b atan(sinh(x) + cosh(x)) + (- b - a )x +--R / +--R 2 3 +--R a b + a +--R Type: Union(Expression(Integer),...) +--E 419 + +--S 420 of 526 +m0678:= a0678-r0678 +--R +--R +--R (419) +--R 2 2 2 2 2cosh(x) +--R - 2b log(a sinh(x) + b) - a log(cosh(x) ) + 2a log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 - 2a sinh(x) - 2b +--R 2b log(-----------------) - 4a b atan(sinh(x) + cosh(x)) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R 2a b atan(sinh(x)) + (- 2b - 2a )x +--R / +--R 2 3 +--R 2a b + 2a +--R Type: Expression(Integer) +--E 420 + +--S 421 of 526 +d0678:= D(m0678,x) +--R +--R +--R (420) +--R 3 2 2 +--R - 2b sinh(x) - b cosh(x)sinh(x) + (2b cosh(x) - 2b)sinh(x) +--R + +--R 3 +--R b cosh(x) - b cosh(x) +--R / +--R 2 2 4 2 2 3 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((b + a )cosh(x) + 2b + 2a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b + a )cosh(x) + b + a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 526 +t0679:= tanh(x)^2/(a+b*csch(x)) +--R +--R +--R 2 +--R tanh(x) +--R (421) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 526 +r0679:= x/a+2*b^3*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a/_ + (a^2+b^2)^(3/2)+b*sech(x)/(a^2+b^2)-a*tanh(x)/(a^2+b^2) +--R +--R +--R (422) +--R x +--R b tanh(-) - a +--R 3 2 +--R - 2b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (- a tanh(x) + a b sech(x) + (b + a )x)\|b + a +--R / +--R +-------+ +--R 2 3 | 2 2 +--R (a b + a )\|b + a +--R Type: Expression(Integer) +--E 423 + +--S 424 of 526 +a0679:= integrate(t0679,x) +--R +--R +--R (423) +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 2 2 2 2 +--R (b + a )x sinh(x) + ((2b + 2a )x cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (b + a )x cosh(x) + 2a b cosh(x) + (b + a )x + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 2 2 3 2 3 2 +--R (a b + a )sinh(x) + (2a b + 2a )cosh(x)sinh(x) + (a b + a )cosh(x) +--R + +--R 2 3 +--R a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 424 + +--S 425 of 526 +m0679:= a0679-r0679 +--R +--R +--R (424) +--R 3 2 3 3 2 3 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R x +--R b tanh(-) - a +--R 3 2 3 3 2 3 2 +--R (2b sinh(x) + 4b cosh(x)sinh(x) + 2b cosh(x) + 2b )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) + a )tanh(x) +--R + +--R 2 +--R - a b sech(x)sinh(x) + (- 2a b cosh(x)sech(x) + 2a b)sinh(x) +--R + +--R 2 2 +--R (- a b cosh(x) - a b)sech(x) + 2a b cosh(x) + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 2 2 3 2 3 2 +--R (a b + a )sinh(x) + (2a b + 2a )cosh(x)sinh(x) + (a b + a )cosh(x) +--R + +--R 2 3 +--R a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 425 + +--S 426 of 526 +d0679:= D(m0679,x) +--R +--R +--R (425) +--R 2 6 2 2 5 +--R - a b sinh(x) + (- 6a b cosh(x) - 2a b )sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 15a b cosh(x) - 10a b cosh(x) - a b)sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (- 20a b cosh(x) - 20a b cosh(x) - 4a b cosh(x) - 4a b ) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R - 15a b cosh(x) - 20a b cosh(x) - 6a b cosh(x) +--R + +--R 2 2 +--R - 12a b cosh(x) + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R - 6a b cosh(x) - 10a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 2 +--R - 12a b cosh(x) + 2a b cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - a b cosh(x) - 2a b cosh(x) - a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 2 +--R a b cosh(x) - 2a b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 2 5 +--R 2a sinh(x) + (12a cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 3 4 +--R (30a cosh(x) + 20a b cosh(x) + 2a )sinh(x) +--R + +--R 3 3 2 2 3 2 3 +--R (40a cosh(x) + 40a b cosh(x) + 8a cosh(x) + 8a b)sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 30a cosh(x) + 40a b cosh(x) + 12a cosh(x) + 24a b cosh(x) +--R + +--R 3 +--R - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 3 3 2 2 +--R 12a cosh(x) + 20a b cosh(x) + 8a cosh(x) + 24a b cosh(x) +--R + +--R 3 2 +--R - 4a cosh(x) + 4a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 4 2 3 +--R 2a cosh(x) + 4a b cosh(x) + 2a cosh(x) + 8a b cosh(x) +--R + +--R 3 2 2 3 +--R - 2a cosh(x) + 4a b cosh(x) - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R a b sinh(x) + (6a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 2 2 4 +--R (15a b cosh(x) + 10a b cosh(x) + a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (20a b cosh(x) + 20a b cosh(x) + 4a b cosh(x) + 4a b )sinh(x) +--R + +--R 2 4 2 3 2 2 2 +--R 15a b cosh(x) + 20a b cosh(x) + 6a b cosh(x) + 12a b cosh(x) +--R + +--R 2 +--R - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 6a b cosh(x) + 10a b cosh(x) + 4a b cosh(x) + 12a b cosh(x) +--R + +--R 2 2 +--R - 2a b cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 2 +--R - a b cosh(x) + 2a b cosh(x) - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 3 5 +--R a b sech(x)sinh(x) + (6a b cosh(x) + 2b )sech(x)sinh(x) +--R + +--R 2 2 3 2 4 +--R (15a b cosh(x) + 10b cosh(x) + a b )sech(x)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (20a b cosh(x) + 20b cosh(x) + 4a b cosh(x) + 4b )sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R 15a b cosh(x) + 20b cosh(x) + 6a b cosh(x) + 12b cosh(x) +--R + +--R 2 +--R - a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 6a b cosh(x) + 10b cosh(x) + 4a b cosh(x) + 12b cosh(x) +--R + +--R 2 3 +--R - 2a b cosh(x) + 2b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R a b cosh(x) + 2b cosh(x) + a b cosh(x) + 4b cosh(x) +--R + +--R 2 2 3 2 +--R - a b cosh(x) + 2b cosh(x) - a b +--R * +--R sech(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R - 2a b sech(x)sinh(x) + (- 12a b cosh(x) - 4a b )sech(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 30a b cosh(x) - 20a b cosh(x) - 2a b)sech(x)sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (- 40a b cosh(x) - 40a b cosh(x) - 8a b cosh(x) - 8a b ) +--R * +--R 3 +--R sech(x)sinh(x) +--R + +--R 2 4 2 3 2 2 +--R - 30a b cosh(x) - 40a b cosh(x) - 12a b cosh(x) +--R + +--R 2 2 +--R - 24a b cosh(x) + 2a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 2 4 2 3 +--R - 12a b cosh(x) - 20a b cosh(x) - 8a b cosh(x) +--R + +--R 2 2 2 2 +--R - 24a b cosh(x) + 4a b cosh(x) - 4a b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 2 5 2 4 +--R - 2a b cosh(x) - 4a b cosh(x) - 2a b cosh(x) +--R + +--R 2 3 2 2 2 2 +--R - 8a b cosh(x) + 2a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R sech(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 3 5 +--R - a b sech(x)sinh(x) + (- 6a b cosh(x) - 2b )sech(x)sinh(x) +--R + +--R 2 2 3 2 4 +--R (- 15a b cosh(x) - 10b cosh(x) - a b )sech(x)sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (- 20a b cosh(x) - 20b cosh(x) - 4a b cosh(x) - 4b )sech(x)sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R - 15a b cosh(x) - 20b cosh(x) - 6a b cosh(x) - 12b cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R - 6a b cosh(x) - 10b cosh(x) - 4a b cosh(x) - 12b cosh(x) +--R + +--R 2 3 +--R 2a b cosh(x) - 2b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R - a b cosh(x) - 2b cosh(x) - a b cosh(x) - 4b cosh(x) +--R + +--R 2 2 3 2 +--R a b cosh(x) - 2b cosh(x) + a b +--R * +--R sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 6 3 2 5 +--R (b + a b)sinh(x) + (6b + 6a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((15b + 15a b)cosh(x) - 3b - 3a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((20b + 20a b)cosh(x) + (- 12b - 12a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((15b + 15a b)cosh(x) + (- 18b - 18a b)cosh(x) + 3b + 3a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (6b + 6a b)cosh(x) + (- 12b - 12a b)cosh(x) +--R + +--R 3 2 +--R (6b + 6a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (b + a b)cosh(x) + (- 3b - 3a b)cosh(x) + (3b + 3a b)cosh(x) +--R + +--R 3 2 +--R - b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 3 5 +--R - 2a sinh(x) + (- 12a cosh(x) + 4b )sinh(x) +--R + +--R 3 2 3 2 3 4 +--R (- 30a cosh(x) + 20b cosh(x) + 8a b + 6a )sinh(x) +--R + +--R 3 3 3 2 2 3 3 +--R (- 40a cosh(x) + 40b cosh(x) + (32a b + 24a )cosh(x) + 8b ) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 3 3 2 3 2 +--R - 30a cosh(x) + 40b cosh(x) + (48a b + 36a )cosh(x) +--R + +--R 3 2 3 +--R 24b cosh(x) - 8a b - 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 3 4 2 3 3 +--R - 12a cosh(x) + 20b cosh(x) + (32a b + 24a )cosh(x) +--R + +--R 3 2 2 3 3 +--R 24b cosh(x) + (- 16a b - 12a )cosh(x) + 4b +--R * +--R sinh(x) +--R + +--R 3 6 3 5 2 3 4 3 3 +--R - 2a cosh(x) + 4b cosh(x) + (8a b + 6a )cosh(x) + 8b cosh(x) +--R + +--R 2 3 2 3 3 +--R (- 8a b - 6a )cosh(x) + 4b cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 6 3 2 5 +--R (- b - a b)sinh(x) + (- 6b - 6a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 4 +--R ((- 15b - 15a b)cosh(x) + 3b + 3a b)sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((- 20b - 20a b)cosh(x) + (12b + 12a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R ((- 15b - 15a b)cosh(x) + (18b + 18a b)cosh(x) - 3b - 3a b)sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (- 6b - 6a b)cosh(x) + (12b + 12a b)cosh(x) +--R + +--R 3 2 +--R (- 6b - 6a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 3 +--R (- b - a b)cosh(x) + (3b + 3a b)cosh(x) + (- 3b - 3a b)cosh(x) + b +--R + +--R 2 +--R a b +--R / +--R 3 3 6 3 3 4 2 2 5 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2b + 2a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R ((15a b + 15a b)cosh(x) + (10b + 10a b )cosh(x) + a b + a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (20a b + 20a b)cosh(x) + (20b + 20a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (4a b + 4a b)cosh(x) + 4b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 4 2 2 3 +--R (15a b + 15a b)cosh(x) + (20b + 20a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (6a b + 6a b)cosh(x) + (12b + 12a b )cosh(x) - a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 4 2 2 4 +--R (6a b + 6a b)cosh(x) + (10b + 10a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (4a b + 4a b)cosh(x) + (12b + 12a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 2a b - 2a b)cosh(x) + 2b + 2a b +--R * +--R sinh(x) +--R + +--R 3 3 6 4 2 2 5 3 3 4 +--R (a b + a b)cosh(x) + (2b + 2a b )cosh(x) + (a b + a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 4 2 2 +--R (4b + 4a b )cosh(x) + (- a b - a b)cosh(x) + (2b + 2a b )cosh(x) +--R + +--R 3 3 +--R - a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 6 +--R (- 2a b - 2a )sinh(x) +--R + +--R 2 2 4 3 3 5 +--R ((- 12a b - 12a )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 2 2 4 2 3 3 2 2 +--R (- 30a b - 30a )cosh(x) + (- 20a b - 20a b)cosh(x) - 2a b +--R + +--R 4 +--R - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 4 3 3 3 2 +--R (- 40a b - 40a )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 8a b - 8a )cosh(x) - 8a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 4 3 3 3 +--R (- 30a b - 30a )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 2 2 4 2 3 3 2 2 4 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 24a b)cosh(x) + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 5 3 3 4 +--R (- 12a b - 12a )cosh(x) + (- 20a b - 20a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 +--R (- 8a b - 8a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (4a b + 4a )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 2 4 6 3 3 5 +--R (- 2a b - 2a )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 2 4 4 3 3 3 +--R (- 2a b - 2a )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 2 2 4 2 3 3 2 2 4 +--R (2a b + 2a )cosh(x) + (- 4a b - 4a b)cosh(x) + 2a b + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 6 3 3 4 2 2 5 +--R (- a b - a b)sinh(x) + ((- 6a b - 6a b)cosh(x) - 2b - 2a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R ((- 15a b - 15a b)cosh(x) + (- 10b - 10a b )cosh(x) - a b - a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (- 20a b - 20a b)cosh(x) + (- 20b - 20a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 4a b - 4a b)cosh(x) - 4b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 4 2 2 3 +--R (- 15a b - 15a b)cosh(x) + (- 20b - 20a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (- 6a b - 6a b)cosh(x) + (- 12b - 12a b )cosh(x) + a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 4 2 2 4 +--R (- 6a b - 6a b)cosh(x) + (- 10b - 10a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (- 4a b - 4a b)cosh(x) + (- 12b - 12a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (2a b + 2a b)cosh(x) - 2b - 2a b +--R * +--R sinh(x) +--R + +--R 3 3 6 4 2 2 5 3 3 4 +--R (- a b - a b)cosh(x) + (- 2b - 2a b )cosh(x) + (- a b - a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 4 2 2 +--R (- 4b - 4a b )cosh(x) + (a b + a b)cosh(x) + (- 2b - 2a b )cosh(x) +--R + +--R 3 3 +--R a b + a b +--R Type: Expression(Integer) +--E 426 + +--S 427 of 526 +t0680:= tanh(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R tanh(x) +--R (426) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 526 +r0680:= -1/2*(b*atan(sinh(x))*a^3*cosh(x)^2+3*b^3*atan(sinh(x))*a*cosh(x)^2-_ + a^4*log(cosh(x)^2)*cosh(x)^2-2*a^2*log(cosh(x)^2)*b^2*cosh(x)^2-_ + 2*b^4*log(b+a*sinh(x))*cosh(x)^2-a^4-a^2*b^2-b*sinh(x)*a^3-_ + b^3*sinh(x)*a)/cosh(x)^2/a/(a^2+b^2)^2 +--R +--R +--R (427) +--R 4 2 2 2 4 2 2 +--R 2b cosh(x) log(a sinh(x) + b) + (2a b + a )cosh(x) log(cosh(x) ) +--R + +--R 3 3 2 3 3 2 2 4 +--R (- 3a b - a b)cosh(x) atan(sinh(x)) + (a b + a b)sinh(x) + a b + a +--R / +--R 4 3 2 5 2 +--R (2a b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 428 + +--S 429 of 526 +a0680:= integrate(t0680,x) +--R +--R +--R (428) +--R 2 2 4 4 2 2 4 3 +--R (2a b + a )sinh(x) + (8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 4 2 2 2 4 2 +--R ((12a b + 6a )cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 2 4 3 2 2 4 +--R ((8a b + 4a )cosh(x) + (8a b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 +--R (2a b + a )cosh(x) + (4a b + 2a )cosh(x) + 2a b + a +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 4 4 3 4 2 4 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b )sinh(x) +--R + +--R 4 3 4 4 4 4 2 4 +--R (4b cosh(x) + 4b cosh(x))sinh(x) + b cosh(x) + 2b cosh(x) + b +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 4 3 3 3 +--R (- 3a b - a b)sinh(x) + (- 12a b - 4a b)cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 2 +--R ((- 18a b - 6a b)cosh(x) - 6a b - 2a b)sinh(x) +--R + +--R 3 3 3 3 3 +--R ((- 12a b - 4a b)cosh(x) + (- 12a b - 4a b)cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 3 3 +--R (- 3a b - a b)cosh(x) + (- 6a b - 2a b)cosh(x) - 3a b - a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 4 2 2 4 4 +--R (- b - 2a b - a )x sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R ((- 4b - 8a b - 4a )x cosh(x) + a b + a b)sinh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 6b - 12a b - 6a )x cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- 2b - 4a b - 2a )x + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 4b - 8a b - 4a )x cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((- 4b - 8a b - 4a )x + 4a b + 4a )cosh(x) - a b - a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- b - 2a b - a )x cosh(x) + (a b + a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 3 3 +--R ((- 2b - 4a b - 2a )x + 2a b + 2a )cosh(x) + (- a b - a b)cosh(x) +--R + +--R 4 2 2 4 +--R (- b - 2a b - a )x +--R / +--R 4 3 2 5 4 4 3 2 5 3 +--R (a b + 2a b + a )sinh(x) + (4a b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 2 +--R ((6a b + 12a b + 6a )cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((4a b + 8a b + 4a )cosh(x) + (4a b + 8a b + 4a )cosh(x))sinh(x) +--R + +--R 4 3 2 5 4 4 3 2 5 2 4 +--R (a b + 2a b + a )cosh(x) + (2a b + 4a b + 2a )cosh(x) + a b +--R + +--R 3 2 5 +--R 2a b + a +--R Type: Union(Expression(Integer),...) +--E 429 + +--S 430 of 526 +m0680:= a0680-r0680 +--R +--R +--R (429) +--R 4 2 4 4 3 3 +--R - 2b cosh(x) sinh(x) - 8b cosh(x) sinh(x) +--R + +--R 4 4 4 2 2 +--R (- 12b cosh(x) - 4b cosh(x) )sinh(x) +--R + +--R 4 5 4 3 4 6 4 4 +--R (- 8b cosh(x) - 8b cosh(x) )sinh(x) - 2b cosh(x) - 4b cosh(x) +--R + +--R 4 2 +--R - 2b cosh(x) +--R * +--R log(a sinh(x) + b) +--R + +--R 2 2 4 2 4 2 2 4 3 3 +--R (- 2a b - a )cosh(x) sinh(x) + (- 8a b - 4a )cosh(x) sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((- 12a b - 6a )cosh(x) + (- 4a b - 2a )cosh(x) )sinh(x) +--R + +--R 2 2 4 5 2 2 4 3 +--R ((- 8a b - 4a )cosh(x) + (- 8a b - 4a )cosh(x) )sinh(x) +--R + +--R 2 2 4 6 2 2 4 4 +--R (- 2a b - a )cosh(x) + (- 4a b - 2a )cosh(x) +--R + +--R 2 2 4 2 +--R (- 2a b - a )cosh(x) +--R * +--R 2 +--R log(cosh(x) ) +--R + +--R 2 2 4 2 4 2 2 4 3 3 +--R (4a b + 2a )cosh(x) sinh(x) + (16a b + 8a )cosh(x) sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((24a b + 12a )cosh(x) + (8a b + 4a )cosh(x) )sinh(x) +--R + +--R 2 2 4 5 2 2 4 3 +--R ((16a b + 8a )cosh(x) + (16a b + 8a )cosh(x) )sinh(x) +--R + +--R 2 2 4 6 2 2 4 4 2 2 4 2 +--R (4a b + 2a )cosh(x) + (8a b + 4a )cosh(x) + (4a b + 2a )cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 2 4 4 3 3 +--R 2b cosh(x) sinh(x) + 8b cosh(x) sinh(x) +--R + +--R 4 4 4 2 2 +--R (12b cosh(x) + 4b cosh(x) )sinh(x) +--R + +--R 4 5 4 3 4 6 4 4 +--R (8b cosh(x) + 8b cosh(x) )sinh(x) + 2b cosh(x) + 4b cosh(x) +--R + +--R 4 2 +--R 2b cosh(x) +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 2 4 3 3 3 3 +--R (- 6a b - 2a b)cosh(x) sinh(x) + (- 24a b - 8a b)cosh(x) sinh(x) +--R + +--R 3 3 4 3 3 2 2 +--R ((- 36a b - 12a b)cosh(x) + (- 12a b - 4a b)cosh(x) )sinh(x) +--R + +--R 3 3 5 3 3 3 +--R ((- 24a b - 8a b)cosh(x) + (- 24a b - 8a b)cosh(x) )sinh(x) +--R + +--R 3 3 6 3 3 4 +--R (- 6a b - 2a b)cosh(x) + (- 12a b - 4a b)cosh(x) +--R + +--R 3 3 2 +--R (- 6a b - 2a b)cosh(x) +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 3 2 4 3 3 3 3 +--R (3a b + a b)cosh(x) sinh(x) + (12a b + 4a b)cosh(x) sinh(x) +--R + +--R 3 3 4 3 3 2 2 +--R ((18a b + 6a b)cosh(x) + (6a b + 2a b)cosh(x) )sinh(x) +--R + +--R 3 3 5 3 3 3 +--R ((12a b + 4a b)cosh(x) + (12a b + 4a b)cosh(x) )sinh(x) +--R + +--R 3 3 6 3 3 4 3 3 2 +--R (3a b + a b)cosh(x) + (6a b + 2a b)cosh(x) + (3a b + a b)cosh(x) +--R * +--R atan(sinh(x)) +--R + +--R 3 3 5 +--R (- a b - a b)sinh(x) +--R + +--R 4 2 2 4 2 3 3 2 2 4 +--R ((- 2b - 4a b - 2a )x cosh(x) + (- 4a b - 4a b)cosh(x) - a b - a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 8b - 16a b - 8a )x cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 4a b - 4a )cosh(x) - 2a b - 2a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 12b - 24a b - 12a )x cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 +--R ((- 4b - 8a b - 4a )x - 2a b - 2a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (- 4a b - 4a b)cosh(x) - 2a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (- 8b - 16a b - 8a )x cosh(x) + (5a b + 5a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 +--R ((- 8b - 16a b - 8a )x + 4a b + 4a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 4a b - 4a b)cosh(x) + (- 4a b - 4a )cosh(x) - a b - a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (- 2b - 4a b - 2a )x cosh(x) + (2a b + 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 4 3 3 3 +--R ((- 4b - 8a b - 4a )x + 3a b + 3a )cosh(x) + (- 2a b - 2a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 2 2 4 +--R ((- 2b - 4a b - 2a )x - 2a b - 2a )cosh(x) - a b - a +--R / +--R 4 3 2 5 2 4 +--R (2a b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 3 2 5 3 3 +--R (8a b + 16a b + 8a )cosh(x) sinh(x) +--R + +--R 4 3 2 5 4 4 3 2 5 2 +--R ((12a b + 24a b + 12a )cosh(x) + (4a b + 8a b + 4a )cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 5 5 4 3 2 5 3 +--R ((8a b + 16a b + 8a )cosh(x) + (8a b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 3 2 5 6 4 3 2 5 4 +--R (2a b + 4a b + 2a )cosh(x) + (4a b + 8a b + 4a )cosh(x) +--R + +--R 4 3 2 5 2 +--R (2a b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 430 + +--S 431 of 526 +d0680:= D(m0680,x) +--R +--R +--R (430) +--R 3 2 10 3 2 2 3 9 +--R (2b + 2a b)sinh(x) + ((12b + 12a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 8 +--R ((29b + 29a b)cosh(x) + (12a b + 12a )cosh(x) + 8b + 8a b)sinh(x) +--R + +--R 3 2 3 2 3 2 +--R (26b + 30a b)cosh(x) + (30a b + 30a )cosh(x) +--R + +--R 3 2 2 3 +--R (36b + 36a b)cosh(x) + 8a b + 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 22b - 4a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (62b + 62a b)cosh(x) + (36a b + 36a )cosh(x) + 12b + 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 70b - 42a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (38b + 50a b)cosh(x) + (66a b + 66a )cosh(x) +--R + +--R 3 2 2 3 +--R (36b + 36a b)cosh(x) + 12a b + 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 6 2 3 5 +--R (- 48b - 38a b)cosh(x) + (- 36a b - 36a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 28b + 10a b)cosh(x) + (64a b + 64a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (36b + 36a b)cosh(x) + (36a b + 36a )cosh(x) + 8b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 7 2 3 6 +--R (14b - 6a b)cosh(x) + (- 30a b - 30a )cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 64b - 24a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 2b + 10a b)cosh(x) + (42a b + 42a )cosh(x) +--R + +--R 3 2 2 3 +--R (12b + 12a b)cosh(x) + 8a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 8 2 3 7 +--R (36b + 10a b)cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 3 2 6 2 3 5 +--R (- 42b - 30a b)cosh(x) + (- 28a b - 28a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 14b + 8a b)cosh(x) + (32a b + 32a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (2b + 2a b)cosh(x) + (12a b + 12a )cosh(x) + 2b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 9 3 2 7 +--R (18b + 6a b)cosh(x) + (- 10b - 14a b)cosh(x) +--R + +--R 2 3 6 3 2 5 +--R (- 30a b - 30a )cosh(x) + (6b + 18a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (22a b + 22a )cosh(x) + (- 14b - 10a b)cosh(x) +--R + +--R 2 3 2 2 3 +--R (6a b + 6a )cosh(x) + 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 10 2 8 2 3 7 +--R (3b + a b)cosh(x) - 2a b cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 3 2 6 2 3 5 3 2 4 +--R (6b + 8a b)cosh(x) + (8a b + 8a )cosh(x) + (- 8b - 6a b)cosh(x) +--R + +--R 3 2 2 +--R (- b - a b)cosh(x) +--R / +--R 4 2 2 4 3 8 +--R (2b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 4 7 +--R (12b + 24a b + 12a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 6 +--R ((30b + 60a b + 30a )cosh(x) + (8b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 5 +--R ((40b + 80a b + 40a )cosh(x) + (36b + 72a b + 36a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 7 4 2 2 4 5 +--R (30b + 60a b + 30a )cosh(x) + (66b + 132a b + 66a )cosh(x) +--R + +--R 4 2 2 4 3 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (64b + 128a b + 64a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (36b + 72a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (42b + 84a b + 42a )cosh(x) + (8b + 16a b + 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (24b + 48a b + 24a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (6b + 12a b + 6a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (6b + 12a b + 6a )cosh(x) + (2b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 431 + +--S 432 of 526 +t0681:= tanh(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R tanh(x) +--R (431) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 526 +r0681:= x/a+2*b^5*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a/_ + (a^2+b^2)^(5/2)+b*(a^2+2*b^2)*sech(x)/(a^2+b^2)^2-_ + b*sech(x)^3/(3*a^2+3*b^2)+a*tanh(x)/(a^2+b^2)-_ + a*(2*a^2+3*b^2)*tanh(x)/(a^2+b^2)^2-a*tanh(x)^3/(3*a^2+3*b^2) +--R +--R +--R (432) +--R x +--R b tanh(-) - a +--R 5 2 +--R - 6b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 4 3 2 2 4 +--R (- a b - a )tanh(x) + (- 6a b - 3a )tanh(x) +--R + +--R 3 3 3 3 3 4 2 2 4 +--R (- a b - a b)sech(x) + (6a b + 3a b)sech(x) + (3b + 6a b + 3a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 3 2 5 | 2 2 +--R (3a b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 433 + +--S 434 of 526 +a0681:= integrate(t0681,x) +--R +--R +--R (433) +--R 5 6 5 5 5 2 5 4 +--R 3b sinh(x) + 18b cosh(x)sinh(x) + (45b cosh(x) + 9b )sinh(x) +--R + +--R 5 3 5 3 +--R (60b cosh(x) + 36b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (45b cosh(x) + 54b cosh(x) + 9b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (18b cosh(x) + 36b cosh(x) + 18b cosh(x))sinh(x) + 3b cosh(x) +--R + +--R 5 4 5 2 5 +--R 9b cosh(x) + 9b cosh(x) + 3b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 4 2 2 4 6 +--R (3b + 6a b + 3a )x sinh(x) +--R + +--R 4 2 2 4 3 3 5 +--R ((18b + 36a b + 18a )x cosh(x) + 12a b + 6a b)sinh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (45b + 90a b + 45a )x cosh(x) + (60a b + 30a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 +--R (9b + 18a b + 9a )x + 18a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (60b + 120a b + 60a )x cosh(x) + (120a b + 60a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((36b + 72a b + 36a )x + 72a b + 48a )cosh(x) + 16a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (45b + 90a b + 45a )x cosh(x) + (120a b + 60a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 +--R ((54b + 108a b + 54a )x + 108a b + 72a )cosh(x) +--R + +--R 3 3 4 2 2 4 2 2 4 +--R (48a b + 12a b)cosh(x) + (9b + 18a b + 9a )x + 24a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (18b + 36a b + 18a )x cosh(x) + (60a b + 30a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 +--R ((36b + 72a b + 36a )x + 72a b + 48a )cosh(x) +--R + +--R 3 3 2 +--R (48a b + 12a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((18b + 36a b + 18a )x + 48a b + 24a )cosh(x) + 12a b + 6a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (3b + 6a b + 3a )x cosh(x) + (12a b + 6a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 4 +--R ((9b + 18a b + 9a )x + 18a b + 12a )cosh(x) +--R + +--R 3 3 3 +--R (16a b + 4a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 +--R ((9b + 18a b + 9a )x + 24a b + 12a )cosh(x) +--R + +--R 3 3 4 2 2 4 2 2 4 +--R (12a b + 6a b)cosh(x) + (3b + 6a b + 3a )x + 14a b + 8a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 2 5 6 4 3 2 5 5 +--R (3a b + 6a b + 3a )sinh(x) + (18a b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R ((45a b + 90a b + 45a )cosh(x) + 9a b + 18a b + 9a )sinh(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((60a b + 120a b + 60a )cosh(x) + (36a b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 5 4 +--R (45a b + 90a b + 45a )cosh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (54a b + 108a b + 54a )cosh(x) + 9a b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 5 5 4 3 2 5 3 +--R (18a b + 36a b + 18a )cosh(x) + (36a b + 72a b + 36a )cosh(x) +--R + +--R 4 3 2 5 +--R (18a b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 5 6 4 3 2 5 4 +--R (3a b + 6a b + 3a )cosh(x) + (9a b + 18a b + 9a )cosh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (9a b + 18a b + 9a )cosh(x) + 3a b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 434 + +--S 435 of 526 +m0681:= a0681-r0681 +--R +--R +--R (434) +--R 5 6 5 5 5 2 5 4 +--R 3b sinh(x) + 18b cosh(x)sinh(x) + (45b cosh(x) + 9b )sinh(x) +--R + +--R 5 3 5 3 +--R (60b cosh(x) + 36b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (45b cosh(x) + 54b cosh(x) + 9b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (18b cosh(x) + 36b cosh(x) + 18b cosh(x))sinh(x) + 3b cosh(x) +--R + +--R 5 4 5 2 5 +--R 9b cosh(x) + 9b cosh(x) + 3b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 5 6 5 5 5 2 5 4 +--R 6b sinh(x) + 36b cosh(x)sinh(x) + (90b cosh(x) + 18b )sinh(x) +--R + +--R 5 3 5 3 +--R (120b cosh(x) + 72b cosh(x))sinh(x) +--R + +--R 5 4 5 2 5 2 +--R (90b cosh(x) + 108b cosh(x) + 18b )sinh(x) +--R + +--R 5 5 5 3 5 5 6 +--R (36b cosh(x) + 72b cosh(x) + 36b cosh(x))sinh(x) + 6b cosh(x) +--R + +--R 5 4 5 2 5 +--R 18b cosh(x) + 18b cosh(x) + 6b +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 4 6 2 2 4 5 +--R (a b + a )sinh(x) + (6a b + 6a )cosh(x)sinh(x) +--R + +--R 2 2 4 2 2 2 4 4 +--R ((15a b + 15a )cosh(x) + 3a b + 3a )sinh(x) +--R + +--R 2 2 4 3 2 2 4 3 +--R ((20a b + 20a )cosh(x) + (12a b + 12a )cosh(x))sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 +--R (15a b + 15a )cosh(x) + (18a b + 18a )cosh(x) + 3a b +--R + +--R 4 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 5 2 2 4 3 +--R (6a b + 6a )cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 2 4 +--R (6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 6 2 2 4 4 +--R (a b + a )cosh(x) + (3a b + 3a )cosh(x) +--R + +--R 2 2 4 2 2 2 4 +--R (3a b + 3a )cosh(x) + a b + a +--R * +--R 3 +--R tanh(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (6a b + 3a )sinh(x) + (36a b + 18a )cosh(x)sinh(x) +--R + +--R 2 2 4 2 2 2 4 4 +--R ((90a b + 45a )cosh(x) + 18a b + 9a )sinh(x) +--R + +--R 2 2 4 3 2 2 4 3 +--R ((120a b + 60a )cosh(x) + (72a b + 36a )cosh(x))sinh(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 +--R (90a b + 45a )cosh(x) + (108a b + 54a )cosh(x) + 18a b +--R + +--R 4 +--R 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 5 2 2 4 3 +--R (36a b + 18a )cosh(x) + (72a b + 36a )cosh(x) +--R + +--R 2 2 4 +--R (36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 4 6 2 2 4 4 +--R (6a b + 3a )cosh(x) + (18a b + 9a )cosh(x) +--R + +--R 2 2 4 2 2 2 4 +--R (18a b + 9a )cosh(x) + 6a b + 3a +--R * +--R tanh(x) +--R + +--R 3 3 3 3 3 6 +--R ((a b + a b)sech(x) + (- 6a b - 3a b)sech(x))sinh(x) +--R + +--R 3 3 3 3 3 +--R (6a b + 6a b)cosh(x)sech(x) + (- 36a b - 18a b)cosh(x)sech(x) +--R + +--R 3 3 +--R 12a b + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 3 2 3 3 3 +--R ((15a b + 15a b)cosh(x) + 3a b + 3a b)sech(x) +--R + +--R 3 3 2 3 3 +--R ((- 90a b - 45a b)cosh(x) - 18a b - 9a b)sech(x) +--R + +--R 3 3 2 2 4 +--R (60a b + 30a b)cosh(x) + 18a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 3 3 3 +--R ((20a b + 20a b)cosh(x) + (12a b + 12a b)cosh(x))sech(x) +--R + +--R 3 3 3 3 3 +--R ((- 120a b - 60a b)cosh(x) + (- 72a b - 36a b)cosh(x))sech(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (120a b + 60a b)cosh(x) + (72a b + 48a )cosh(x) + 16a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 3 3 2 3 +--R (15a b + 15a b)cosh(x) + (18a b + 18a b)cosh(x) + 3a b +--R + +--R 3 +--R 3a b +--R * +--R 3 +--R sech(x) +--R + +--R 3 3 4 3 3 2 +--R (- 90a b - 45a b)cosh(x) + (- 108a b - 54a b)cosh(x) +--R + +--R 3 3 +--R - 18a b - 9a b +--R * +--R sech(x) +--R + +--R 3 3 3 2 2 4 2 +--R (120a b + 60a b)cosh(x) + (108a b + 72a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (48a b + 12a b)cosh(x) + 24a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 3 3 3 +--R (6a b + 6a b)cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 3 3 +--R (6a b + 6a b)cosh(x) +--R * +--R 3 +--R sech(x) +--R + +--R 3 3 5 3 3 3 +--R (- 36a b - 18a b)cosh(x) + (- 72a b - 36a b)cosh(x) +--R + +--R 3 3 +--R (- 36a b - 18a b)cosh(x) +--R * +--R sech(x) +--R + +--R 3 3 4 2 2 4 3 +--R (60a b + 30a b)cosh(x) + (72a b + 48a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (48a b + 12a b)cosh(x) + (48a b + 24a )cosh(x) + 12a b + 6a b +--R * +--R sinh(x) +--R + +--R 3 3 6 3 3 4 +--R (a b + a b)cosh(x) + (3a b + 3a b)cosh(x) +--R + +--R 3 3 2 3 3 +--R (3a b + 3a b)cosh(x) + a b + a b +--R * +--R 3 +--R sech(x) +--R + +--R 3 3 6 3 3 4 +--R (- 6a b - 3a b)cosh(x) + (- 18a b - 9a b)cosh(x) +--R + +--R 3 3 2 3 3 +--R (- 18a b - 9a b)cosh(x) - 6a b - 3a b +--R * +--R sech(x) +--R + +--R 3 3 5 2 2 4 4 +--R (12a b + 6a b)cosh(x) + (18a b + 12a )cosh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (16a b + 4a b)cosh(x) + (24a b + 12a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (12a b + 6a b)cosh(x) + 14a b + 8a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 2 5 6 4 3 2 5 5 +--R (3a b + 6a b + 3a )sinh(x) + (18a b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R ((45a b + 90a b + 45a )cosh(x) + 9a b + 18a b + 9a )sinh(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((60a b + 120a b + 60a )cosh(x) + (36a b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 5 4 +--R (45a b + 90a b + 45a )cosh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (54a b + 108a b + 54a )cosh(x) + 9a b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 5 5 4 3 2 5 3 +--R (18a b + 36a b + 18a )cosh(x) + (36a b + 72a b + 36a )cosh(x) +--R + +--R 4 3 2 5 +--R (18a b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 5 6 4 3 2 5 4 +--R (3a b + 6a b + 3a )cosh(x) + (9a b + 18a b + 9a )cosh(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (9a b + 18a b + 9a )cosh(x) + 3a b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 435 + +--S 436 of 526 +--d0681:= D(m0681,x) +--E 436 + +--S 437 of 526 +t0682:= tanh(x)/(%i+csch(x)) +--R +--R +--R tanh(x) +--R (435) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 437 + +--S 438 of 526 +r0682:= -3/4*%i*log(-%i+sinh(x))-1/4*%i*log(%i+sinh(x))+1/(2*%i-2*sinh(x)) +--R +--R +--R (436) +--R 1 1 +--R (- - %i sinh(x) - -)log(sinh(x) + %i) +--R 4 4 +--R + +--R 3 3 1 +--R (- - %i sinh(x) - -)log(sinh(x) - %i) - - +--R 4 4 2 +--R / +--R sinh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 438 + +--S 439 of 526 +a0682:= integrate(t0682,x) +--R +--R +--R (437) +--R 2 2 +--R (%i sinh(x) + (2%i cosh(x) + 2)sinh(x) + %i cosh(x) + 2cosh(x) - %i) +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 2 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) - 4)sinh(x) - 2%i cosh(x) - 4cosh(x) +--R + +--R 2%i +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R 2%i x sinh(x) + (4%i x cosh(x) + 4x - 2)sinh(x) + 2%i x cosh(x) +--R + +--R (4x - 2)cosh(x) - 2%i x +--R / +--R 2 2 +--R 2sinh(x) + (4cosh(x) - 4%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2 +--R Type: Union(Expression(Complex(Integer)),...) +--E 439 + +--S 440 of 526 +m0682:= a0682-r0682 +--R +--R +--R (438) +--R 1 3 1 3 2 +--R - %i sinh(x) + (- %i cosh(x) + -)sinh(x) +--R 4 2 4 +--R + +--R 1 2 3 1 2 1 1 +--R (- %i cosh(x) + cosh(x) - - %i)sinh(x) + - cosh(x) - - %i cosh(x) - - +--R 4 4 4 2 4 +--R * +--R log(sinh(x) + %i) +--R + +--R 3 3 3 9 2 +--R - %i sinh(x) + (- %i cosh(x) + -)sinh(x) +--R 4 2 4 +--R + +--R 3 2 9 3 2 3 +--R (- %i cosh(x) + 3cosh(x) - - %i)sinh(x) + - cosh(x) - - %i cosh(x) +--R 4 4 4 2 +--R + +--R 3 +--R - - +--R 4 +--R * +--R log(sinh(x) - %i) +--R + +--R 1 3 3 2 +--R - %i sinh(x) + (%i cosh(x) + -)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 1 +--R (- %i cosh(x) + 2cosh(x) - - %i)sinh(x) + - cosh(x) - %i cosh(x) - - +--R 2 2 2 2 +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 3 2 +--R - %i sinh(x) + (- 2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (- %i cosh(x) - 4cosh(x) + 3%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 1 2 +--R %i x sinh(x) + (2%i x cosh(x) + 3x - -)sinh(x) +--R 2 +--R + +--R 2 1 2 +--R (%i x cosh(x) + 4x cosh(x) - 3%i x)sinh(x) + (x + -)cosh(x) +--R 2 +--R + +--R 1 +--R - 2%i x cosh(x) - x - - +--R 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) - 3%i)sinh(x) + (cosh(x) - 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2cosh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 440 + +--S 441 of 526 +d0682:= D(m0682,x) +--R +--R +--R (439) +--R 8 7 +--R - %i sinh(x) + (- 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 6 2 5 +--R (- 5%i cosh(x) - 8cosh(x) + %i)sinh(x) + (- 4cosh(x) - 5)sinh(x) +--R + +--R 4 3 2 4 +--R (5%i cosh(x) + 6cosh(x) - 6%i cosh(x) - 12cosh(x) + 5%i)sinh(x) +--R + +--R 5 4 3 2 +--R (4%i cosh(x) + 7cosh(x) - 8%i cosh(x) - 6cosh(x) + 8%i cosh(x) - 1) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R %i cosh(x) + 2cosh(x) - 3%i cosh(x) + 2cosh(x) + %i cosh(x) +--R + +--R - 4cosh(x) + 3%i +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (cosh(x) - 4%i cosh(x) - 2cosh(x) + 4%i cosh(x) + 1)sinh(x) +--R + +--R 4 2 +--R - 2%i cosh(x) + 2%i cosh(x) +--R / +--R 7 2 6 +--R cosh(x)sinh(x) + (4cosh(x) - 3%i cosh(x))sinh(x) +--R + +--R 3 2 5 +--R (6cosh(x) - 10%i cosh(x) - cosh(x))sinh(x) +--R + +--R 4 3 2 4 +--R (4cosh(x) - 12%i cosh(x) - 2cosh(x) - 5%i cosh(x))sinh(x) +--R + +--R 5 4 2 3 +--R (cosh(x) - 6%i cosh(x) - 12%i cosh(x) - 5cosh(x))sinh(x) +--R + +--R 5 4 3 2 +--R (- %i cosh(x) + 2cosh(x) - 12%i cosh(x) - 8cosh(x) - %i cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R (cosh(x) - 6%i cosh(x) - 6cosh(x) - 2%i cosh(x) - 3cosh(x))sinh(x) +--R + +--R 5 4 2 +--R - %i cosh(x) - 2cosh(x) - 2cosh(x) + %i cosh(x) +--R Type: Expression(Complex(Fraction(Integer))) +--E 441 + +--S 442 of 526 +t0683:= tanh(x)^2/(%i+csch(x)) +--R +--R +--R 2 +--R tanh(x) +--R (440) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 442 + +--S 443 of 526 +r0683:= 1/3/cosh(x)^3*(4*%i*sinh(x)*cosh(x)^2-_ + %i*sinh(x)+1-3*%i*x*cosh(x)^3-3*cosh(x)^2) +--R +--R +--R 2 3 2 +--R (4%i cosh(x) - %i)sinh(x) - 3%i x cosh(x) - 3cosh(x) + 1 +--R (441) ----------------------------------------------------------- +--R 3 +--R 3cosh(x) +--R Type: Expression(Complex(Integer)) +--E 443 + +--S 444 of 526 +a0683:= integrate(t0683,x) +--R +--R +--R (442) +--R 2 2 +--R 2%i sinh(x) + ((- 3%i x - 4%i)cosh(x) + 1)sinh(x) + 2%i cosh(x) +--R + +--R (- 3x - 4)cosh(x) +--R / +--R 3cosh(x)sinh(x) - 3%i cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 444 + +--S 445 of 526 +m0683:= a0683-r0683 +--R +--R +--R (443) +--R 2 2 3 4 +--R (- 2%i cosh(x) + %i)sinh(x) - 4%i cosh(x) sinh(x) + 2%i cosh(x) +--R + +--R 3 2 +--R - 4cosh(x) - 3%i cosh(x) + %i +--R / +--R 3 3 +--R 3cosh(x) sinh(x) - 3%i cosh(x) +--R Type: Expression(Complex(Integer)) +--E 445 + +--S 446 of 526 +d0683:= D(m0683,x) +--R +--R +--R (444) +--R 2 4 2 3 +--R (2%i cosh(x) - 3%i)sinh(x) + (2cosh(x) - 3)sinh(x) +--R + +--R 2 2 4 2 +--R (4%i cosh(x) - 3%i)sinh(x) + (- 2cosh(x) + 5cosh(x) - 3)sinh(x) +--R + +--R 6 4 2 +--R - 2%i cosh(x) + 3%i cosh(x) - %i cosh(x) +--R / +--R 4 2 4 4 +--R 3cosh(x) sinh(x) - 6%i cosh(x) sinh(x) - 3cosh(x) +--R Type: Expression(Complex(Integer)) +--E 446 + +--S 447 of 526 +t0684:= tanh(x)^3/(%i+csch(x)) +--R +--R +--R 3 +--R tanh(x) +--R (445) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 447 + +--S 448 of 526 +r0684:= -11/16*%i*log(-%i+sinh(x))-5/16*%i*log(%i+sinh(x))-_ + 1/8*%i/(%i-sinh(x))^2+3/(4*%i-4*sinh(x))+1/(8*%i+8*sinh(x)) +--R +--R +--R (446) +--R 5 3 5 2 5 5 +--R (- -- %i sinh(x) - -- sinh(x) - -- %i sinh(x) - --)log(sinh(x) + %i) +--R 16 16 16 16 +--R + +--R 11 3 11 2 11 11 +--R (- -- %i sinh(x) - -- sinh(x) - -- %i sinh(x) - --)log(sinh(x) - %i) +--R 16 16 16 16 +--R + +--R 5 2 3 3 +--R - - sinh(x) - - %i sinh(x) - - +--R 8 8 4 +--R / +--R 3 2 +--R sinh(x) - %i sinh(x) + sinh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 448 + +--S 449 of 526 +a0684:= integrate(t0684,x) +--R +--R +--R (447) +--R 6 5 +--R 3%i sinh(x) + (18%i cosh(x) + 6)sinh(x) +--R + +--R 2 4 +--R (45%i cosh(x) + 30cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 3 +--R (60%i cosh(x) + 60cosh(x) + 12%i cosh(x) + 12)sinh(x) +--R + +--R 4 3 2 +--R (45%i cosh(x) + 60cosh(x) + 18%i cosh(x) + 36cosh(x) - 3%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 18%i cosh(x) + 30cosh(x) + 12%i cosh(x) + 36cosh(x) +--R + +--R - 6%i cosh(x) + 6 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 3%i cosh(x) + 6cosh(x) + 3%i cosh(x) + 12cosh(x) - 3%i cosh(x) +--R + +--R 6cosh(x) - 3%i +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 6 5 +--R - 8%i sinh(x) + (- 48%i cosh(x) - 16)sinh(x) +--R + +--R 2 4 +--R (- 120%i cosh(x) - 80cosh(x) - 8%i)sinh(x) +--R + +--R 3 2 3 +--R (- 160%i cosh(x) - 160cosh(x) - 32%i cosh(x) - 32)sinh(x) +--R + +--R 4 3 2 +--R (- 120%i cosh(x) - 160cosh(x) - 48%i cosh(x) - 96cosh(x) + 8%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 48%i cosh(x) - 80cosh(x) - 32%i cosh(x) - 96cosh(x) +--R + +--R 16%i cosh(x) - 16 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 8%i cosh(x) - 16cosh(x) - 8%i cosh(x) - 32cosh(x) +--R + +--R 2 +--R 8%i cosh(x) - 16cosh(x) + 8%i +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 5 +--R 8%i x sinh(x) + (48%i x cosh(x) + 16x - 10)sinh(x) +--R + +--R 2 4 +--R (120%i x cosh(x) + (80x - 50)cosh(x) + 8%i x - 12%i)sinh(x) +--R + +--R 3 2 +--R 160%i x cosh(x) + (160x - 100)cosh(x) + (32%i x - 48%i)cosh(x) +--R + +--R 32x - 28 +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R 120%i x cosh(x) + (160x - 100)cosh(x) + (48%i x - 72%i)cosh(x) +--R + +--R (96x - 84)cosh(x) - 8%i x + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R 48%i x cosh(x) + (80x - 50)cosh(x) + (32%i x - 48%i)cosh(x) +--R + +--R 2 +--R (96x - 84)cosh(x) + (- 16%i x + 24%i)cosh(x) + 16x - 10 +--R * +--R sinh(x) +--R + +--R 6 5 4 +--R 8%i x cosh(x) + (16x - 10)cosh(x) + (8%i x - 12%i)cosh(x) +--R + +--R 3 2 +--R (32x - 28)cosh(x) + (- 8%i x + 12%i)cosh(x) + (16x - 10)cosh(x) - 8%i x +--R / +--R 6 5 +--R 8sinh(x) + (48cosh(x) - 16%i)sinh(x) +--R + +--R 2 4 +--R (120cosh(x) - 80%i cosh(x) + 8)sinh(x) +--R + +--R 3 2 3 +--R (160cosh(x) - 160%i cosh(x) + 32cosh(x) - 32%i)sinh(x) +--R + +--R 4 3 2 2 +--R (120cosh(x) - 160%i cosh(x) + 48cosh(x) - 96%i cosh(x) - 8)sinh(x) +--R + +--R 5 4 3 2 +--R 48cosh(x) - 80%i cosh(x) + 32cosh(x) - 96%i cosh(x) - 16cosh(x) +--R + +--R - 16%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 8cosh(x) - 16%i cosh(x) + 8cosh(x) - 32%i cosh(x) - 8cosh(x) +--R + +--R - 16%i cosh(x) - 8 +--R Type: Union(Expression(Complex(Integer)),...) +--E 449 + +--S 450 of 526 +m0684:= a0684-r0684 +--R +--R +--R (448) +--R 5 9 15 15 8 +--R -- %i sinh(x) + (-- %i cosh(x) + --)sinh(x) +--R 16 8 16 +--R + +--R 75 2 7 +--R (-- %i cosh(x) + 5cosh(x))sinh(x) +--R 16 +--R + +--R 25 3 175 2 5 6 +--R (-- %i cosh(x) + --- cosh(x) + -)sinh(x) +--R 4 16 2 +--R + +--R 75 4 25 3 5 2 15 +--R (-- %i cosh(x) + -- cosh(x) + -- %i cosh(x) + 10cosh(x) - -- %i) +--R 16 2 16 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 15 5 125 4 5 3 265 2 +--R -- %i cosh(x) + --- cosh(x) + - %i cosh(x) + --- cosh(x) +--R 8 16 4 16 +--R + +--R 25 15 +--R - -- %i cosh(x) + -- +--R 4 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 5 6 5 5 15 4 3 +--R -- %i cosh(x) + - cosh(x) + -- %i cosh(x) + 15cosh(x) +--R 16 2 8 +--R + +--R 135 2 5 +--R - --- %i cosh(x) + 5cosh(x) - - %i +--R 16 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 6 5 5 65 4 25 3 +--R -- cosh(x) + - %i cosh(x) + -- cosh(x) - -- %i cosh(x) +--R 16 4 8 4 +--R + +--R 85 2 +--R -- cosh(x) - 5%i cosh(x) +--R 16 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 6 5 5 45 4 5 3 +--R -- %i cosh(x) + - cosh(x) - -- %i cosh(x) + - cosh(x) +--R 16 2 16 2 +--R + +--R 65 2 15 +--R - -- %i cosh(x) - -- %i +--R 16 16 +--R * +--R sinh(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R -- cosh(x) - - %i cosh(x) + -- cosh(x) - - %i cosh(x) +--R 16 8 16 4 +--R + +--R 5 2 5 5 +--R - -- cosh(x) - - %i cosh(x) - -- +--R 16 8 16 +--R * +--R log(sinh(x) + %i) +--R + +--R 11 9 33 33 8 +--R -- %i sinh(x) + (-- %i cosh(x) + --)sinh(x) +--R 16 8 16 +--R + +--R 165 2 7 +--R (--- %i cosh(x) + 11cosh(x))sinh(x) +--R 16 +--R + +--R 55 3 385 2 11 6 +--R (-- %i cosh(x) + --- cosh(x) + --)sinh(x) +--R 4 16 2 +--R + +--R 165 4 55 3 11 2 +--R --- %i cosh(x) + -- cosh(x) + -- %i cosh(x) + 22cosh(x) +--R 16 2 16 +--R + +--R 33 +--R - -- %i +--R 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 33 5 275 4 11 3 583 2 +--R -- %i cosh(x) + --- cosh(x) + -- %i cosh(x) + --- cosh(x) +--R 8 16 4 16 +--R + +--R 55 33 +--R - -- %i cosh(x) + -- +--R 4 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 6 11 5 33 4 3 +--R -- %i cosh(x) + -- cosh(x) + -- %i cosh(x) + 33cosh(x) +--R 16 2 8 +--R + +--R 297 2 11 +--R - --- %i cosh(x) + 11cosh(x) - -- %i +--R 16 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 11 6 11 5 143 4 55 3 +--R -- cosh(x) + -- %i cosh(x) + --- cosh(x) - -- %i cosh(x) +--R 16 4 8 4 +--R + +--R 187 2 +--R --- cosh(x) - 11%i cosh(x) +--R 16 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 6 11 5 99 4 11 3 +--R -- %i cosh(x) + -- cosh(x) - -- %i cosh(x) + -- cosh(x) +--R 16 2 16 2 +--R + +--R 143 2 33 +--R - --- %i cosh(x) - -- %i +--R 16 16 +--R * +--R sinh(x) +--R + +--R 11 6 11 5 11 4 11 3 +--R -- cosh(x) - -- %i cosh(x) + -- cosh(x) - -- %i cosh(x) +--R 16 8 16 4 +--R + +--R 11 2 11 11 +--R - -- cosh(x) - -- %i cosh(x) - -- +--R 16 8 16 +--R * +--R log(sinh(x) - %i) +--R + +--R 3 9 9 9 8 +--R - %i sinh(x) + (- %i cosh(x) + -)sinh(x) +--R 8 4 8 +--R + +--R 45 2 7 +--R (-- %i cosh(x) + 6cosh(x))sinh(x) +--R 8 +--R + +--R 15 3 105 2 6 +--R (-- %i cosh(x) + --- cosh(x) + 3)sinh(x) +--R 2 8 +--R + +--R 45 4 3 3 2 9 +--R (-- %i cosh(x) + 15cosh(x) + - %i cosh(x) + 12cosh(x) - - %i) +--R 8 8 4 +--R * +--R 5 +--R sinh(x) +--R + +--R 9 5 75 4 3 3 159 2 +--R - %i cosh(x) + -- cosh(x) + - %i cosh(x) + --- cosh(x) +--R 4 8 2 8 +--R + +--R 15 9 +--R - -- %i cosh(x) + - +--R 2 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 3 6 5 9 4 3 +--R - %i cosh(x) + 3cosh(x) + - %i cosh(x) + 18cosh(x) +--R 8 4 +--R + +--R 81 2 +--R - -- %i cosh(x) + 6cosh(x) - 3%i +--R 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 5 39 4 15 3 +--R - cosh(x) + - %i cosh(x) + -- cosh(x) - -- %i cosh(x) +--R 8 2 4 2 +--R + +--R 51 2 +--R -- cosh(x) - 6%i cosh(x) +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 27 4 3 +--R - %i cosh(x) + 3cosh(x) - -- %i cosh(x) + 3cosh(x) +--R 8 8 +--R + +--R 39 2 9 +--R - -- %i cosh(x) - - %i +--R 8 8 +--R * +--R sinh(x) +--R + +--R 3 6 3 5 3 4 3 3 3 2 +--R - cosh(x) - - %i cosh(x) + - cosh(x) - - %i cosh(x) - - cosh(x) +--R 8 4 8 2 8 +--R + +--R 3 3 +--R - - %i cosh(x) - - +--R 4 8 +--R * +--R sinh(x) + cosh(x) + %i +--R log(----------------------) +--R sinh(x) + cosh(x) - %i +--R + +--R 9 8 +--R - %i sinh(x) + (- 6%i cosh(x) - 3)sinh(x) +--R + +--R 2 7 +--R (- 15%i cosh(x) - 16cosh(x))sinh(x) +--R + +--R 3 2 6 +--R (- 20%i cosh(x) - 35cosh(x) - 8)sinh(x) +--R + +--R 4 3 2 +--R (- 15%i cosh(x) - 40cosh(x) - %i cosh(x) - 32cosh(x) + 6%i) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 6%i cosh(x) - 25cosh(x) - 4%i cosh(x) - 53cosh(x) +--R + +--R 20%i cosh(x) - 6 +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - %i cosh(x) - 8cosh(x) - 6%i cosh(x) - 48cosh(x) +--R + +--R 2 +--R 27%i cosh(x) - 16cosh(x) + 8%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - cosh(x) - 4%i cosh(x) - 26cosh(x) + 20%i cosh(x) +--R + +--R 2 +--R - 17cosh(x) + 16%i cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - %i cosh(x) - 8cosh(x) + 9%i cosh(x) - 8cosh(x) +--R + +--R 2 +--R 13%i cosh(x) + 3%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - cosh(x) + 2%i cosh(x) - cosh(x) + 4%i cosh(x) + cosh(x) +--R + +--R 2%i cosh(x) + 1 +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 9 5 8 +--R %i x sinh(x) + (6%i x cosh(x) + 3x - -)sinh(x) +--R 8 +--R + +--R 2 5 9 7 +--R (15%i x cosh(x) + (16x - -)cosh(x) - - %i)sinh(x) +--R 2 8 +--R + +--R 3 25 2 15 33 6 +--R (20%i x cosh(x) + (35x - --)cosh(x) - -- %i cosh(x) + 8x - --)sinh(x) +--R 8 4 8 +--R + +--R 4 3 27 2 +--R 15%i x cosh(x) + 40x cosh(x) + (%i x - -- %i)cosh(x) +--R 8 +--R + +--R 9 +--R (32x - 12)cosh(x) - 6%i x + - %i +--R 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 5 25 4 3 3 +--R 6%i x cosh(x) + (25x + --)cosh(x) + (4%i x + - %i)cosh(x) +--R 8 2 +--R + +--R 19 2 1 25 +--R (53x - --)cosh(x) + (- 20%i x + - %i)cosh(x) + 6x - -- +--R 2 4 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 5 33 4 +--R %i x cosh(x) + (8x + -)cosh(x) + (6%i x + -- %i)cosh(x) +--R 2 8 +--R + +--R 3 19 2 17 +--R (48x + 3)cosh(x) + (- 27%i x - -- %i)cosh(x) + (16x - --)cosh(x) +--R 4 2 +--R + +--R 13 +--R - 8%i x + -- %i +--R 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 6 9 5 63 4 +--R (x + -)cosh(x) + (4%i x + - %i)cosh(x) + (26x + --)cosh(x) +--R 8 4 8 +--R + +--R 3 77 2 +--R (- 20%i x - 6%i)cosh(x) + (17x - --)cosh(x) +--R 8 +--R + +--R 15 3 +--R (- 16%i x + -- %i)cosh(x) - - +--R 4 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 19 4 +--R (%i x + - %i)cosh(x) + (8x + 4)cosh(x) + (- 9%i x - -- %i)cosh(x) +--R 8 8 +--R + +--R 3 21 2 5 +--R (8x - 5)cosh(x) + (- 13%i x + -- %i)cosh(x) + cosh(x) - 3%i x - - %i +--R 8 8 +--R * +--R sinh(x) +--R + +--R 3 6 1 5 3 4 +--R (x + -)cosh(x) + (- 2%i x - - %i)cosh(x) + (x - -)cosh(x) +--R 4 4 4 +--R + +--R 1 3 3 2 1 +--R (- 4%i x + - %i)cosh(x) + (- x + -)cosh(x) + (- 2%i x - - %i)cosh(x) +--R 2 4 4 +--R + +--R 3 +--R - x - - +--R 4 +--R / +--R 9 8 2 7 +--R sinh(x) + (6cosh(x) - 3%i)sinh(x) + (15cosh(x) - 16%i cosh(x))sinh(x) +--R + +--R 3 2 6 +--R (20cosh(x) - 35%i cosh(x) - 8%i)sinh(x) +--R + +--R 4 3 2 5 +--R (15cosh(x) - 40%i cosh(x) + cosh(x) - 32%i cosh(x) - 6)sinh(x) +--R + +--R 5 4 3 2 +--R 6cosh(x) - 25%i cosh(x) + 4cosh(x) - 53%i cosh(x) - 20cosh(x) +--R + +--R - 6%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) - 8%i cosh(x) + 6cosh(x) - 48%i cosh(x) - 27cosh(x) +--R + +--R - 16%i cosh(x) - 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - %i cosh(x) + 4cosh(x) - 26%i cosh(x) - 20cosh(x) +--R + +--R 2 +--R - 17%i cosh(x) - 16cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R (cosh(x) - 8%i cosh(x) - 9cosh(x) - 8%i cosh(x) - 13cosh(x) - 3) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - %i cosh(x) - 2cosh(x) - %i cosh(x) - 4cosh(x) + %i cosh(x) +--R + +--R - 2cosh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 450 + +--S 451 of 526 +d0684:= D(m0684,x) +--R +--R +--R (449) +--R 14 13 +--R - %i sinh(x) + (- 8%i cosh(x) - 3)sinh(x) +--R + +--R 2 12 +--R (- 27%i cosh(x) - 20cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 11 +--R (- 48%i cosh(x) - 54cosh(x) - 12%i cosh(x) - 14)sinh(x) +--R + +--R 4 3 2 10 +--R (- 42%i cosh(x) - 70cosh(x) - 32%i cosh(x) - 76cosh(x) + 5%i)sinh(x) +--R + +--R 4 3 2 9 +--R (- 28cosh(x) - 52%i cosh(x) - 162cosh(x) + 20%i cosh(x) - 25)sinh(x) +--R + +--R 6 5 4 3 +--R 42%i cosh(x) + 42cosh(x) - 60%i cosh(x) - 158cosh(x) +--R + +--R 2 +--R 34%i cosh(x) - 120cosh(x) + 20%i +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 48%i cosh(x) + 70cosh(x) - 52%i cosh(x) - 40cosh(x) +--R + +--R 3 2 +--R 32%i cosh(x) - 218cosh(x) + 72%i cosh(x) - 20 +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 27%i cosh(x) + 46cosh(x) - 32%i cosh(x) + 56cosh(x) +--R + +--R 4 3 2 +--R 8%i cosh(x) - 166cosh(x) + 90%i cosh(x) - 88cosh(x) + 25%i +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 8%i cosh(x) + 15cosh(x) - 12%i cosh(x) + 54cosh(x) +--R + +--R 5 4 3 2 +--R - 28%i cosh(x) - 6cosh(x) + 44%i cosh(x) - 158cosh(x) +--R + +--R 80%i cosh(x) - 5 +--R * +--R 5 +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R %i cosh(x) + 2cosh(x) - 2%i cosh(x) + 18cosh(x) - 42%i cosh(x) +--R + +--R 5 4 3 2 +--R 74cosh(x) + 6%i cosh(x) - 134cosh(x) + 87%i cosh(x) - 20cosh(x) +--R + +--R 14%i +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 2cosh(x) - 24%i cosh(x) + 48cosh(x) - 4%i cosh(x) - 28cosh(x) +--R + +--R 3 2 +--R 24%i cosh(x) - 40cosh(x) + 36%i cosh(x) + 2 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 5%i cosh(x) + 12cosh(x) - 10%i cosh(x) + 36cosh(x) +--R + +--R 4 3 2 +--R - 18%i cosh(x) - 52cosh(x) + 38%i cosh(x) + 4cosh(x) + 3%i +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) - 8%i cosh(x) + 24cosh(x) - 12%i cosh(x) - 34cosh(x) +--R + +--R 3 2 +--R 16%i cosh(x) + 8cosh(x) + 4%i cosh(x) + 1 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 2%i cosh(x) + 4cosh(x) - 2%i cosh(x) - 8cosh(x) + 2%i cosh(x) +--R + +--R 3 2 +--R 4cosh(x) + 2%i cosh(x) +--R / +--R 13 2 12 +--R cosh(x)sinh(x) + (8cosh(x) - 3%i cosh(x))sinh(x) +--R + +--R 3 2 11 +--R (28cosh(x) - 22%i cosh(x) + 2cosh(x))sinh(x) +--R + +--R 4 3 2 10 +--R (56cosh(x) - 70%i cosh(x) + 14cosh(x) - 14%i cosh(x))sinh(x) +--R + +--R 5 4 3 2 +--R (70cosh(x) - 126%i cosh(x) + 44cosh(x) - 86%i cosh(x) - 5cosh(x)) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 56cosh(x) - 140%i cosh(x) + 82cosh(x) - 230%i cosh(x) +--R + +--R 2 +--R - 26cosh(x) - 25%i cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 28cosh(x) - 98%i cosh(x) + 100cosh(x) - 352%i cosh(x) +--R + +--R 3 2 +--R - 56cosh(x) - 124%i cosh(x) - 20cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 8cosh(x) - 42%i cosh(x) + 82cosh(x) - 340%i cosh(x) - 64cosh(x) +--R + +--R 3 2 +--R - 268%i cosh(x) - 84cosh(x) - 20%i cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R cosh(x) - 10%i cosh(x) + 44cosh(x) - 214%i cosh(x) - 40cosh(x) +--R + +--R 4 3 2 +--R - 332%i cosh(x) - 152cosh(x) - 76%i cosh(x) - 25cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - %i cosh(x) + 14cosh(x) - 86%i cosh(x) - 10cosh(x) +--R + +--R 5 4 3 2 +--R - 260%i cosh(x) - 156cosh(x) - 124%i cosh(x) - 76cosh(x) +--R + +--R - 5%i cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R 2cosh(x) - 20%i cosh(x) + 4cosh(x) - 134%i cosh(x) - 100cosh(x) +--R + +--R 4 3 2 +--R - 112%i cosh(x) - 100cosh(x) - 14%i cosh(x) - 14cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - 2%i cosh(x) + 4cosh(x) - 46%i cosh(x) - 42cosh(x) +--R + +--R 5 4 3 2 +--R - 60%i cosh(x) - 72cosh(x) - 14%i cosh(x) - 26cosh(x) + 2%i cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R cosh(x) - 10%i cosh(x) - 12cosh(x) - 18%i cosh(x) - 30cosh(x) +--R + +--R 4 3 2 +--R - 6%i cosh(x) - 20cosh(x) + 2%i cosh(x) - 3cosh(x) +--R * +--R sinh(x) +--R + +--R 9 8 7 6 4 +--R - %i cosh(x) - 2cosh(x) - 2%i cosh(x) - 6cosh(x) - 6cosh(x) +--R + +--R 3 2 +--R 2%i cosh(x) - 2cosh(x) + %i cosh(x) +--R Type: Expression(Complex(Fraction(Integer))) +--E 451 + +--S 452 of 526 +t0685:= tanh(x)^4/(%i+csch(x)) +--R +--R +--R 4 +--R tanh(x) +--R (450) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 452 + +--S 453 of 526 +r0685:= 1/15/cosh(x)^5*(23*%i*cosh(x)^4*sinh(x)-11*%i*cosh(x)^2*sinh(x)+_ + 3*%i*sinh(x)+10*cosh(x)^2-3-15*cosh(x)^4-15*%i*x*cosh(x)^5) +--R +--R +--R (451) +--R 4 2 5 +--R (23%i cosh(x) - 11%i cosh(x) + 3%i)sinh(x) - 15%i x cosh(x) +--R + +--R 4 2 +--R - 15cosh(x) + 10cosh(x) - 3 +--R / +--R 5 +--R 15cosh(x) +--R Type: Expression(Complex(Integer)) +--E 453 + +--S 454 of 526 +a0685:= integrate(t0685,x) +--R +--R +--R (452) +--R 4 3 +--R 23%i sinh(x) + ((- 60%i x - 92%i)cosh(x) + 16)sinh(x) +--R + +--R 2 2 +--R (138%i cosh(x) + (- 90x - 138)cosh(x) + 16%i)sinh(x) +--R + +--R 3 2 +--R ((- 60%i x - 92%i)cosh(x) + 48cosh(x) + (- 60%i x - 92%i)cosh(x) + 8) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R 23%i cosh(x) + (- 30x - 46)cosh(x) + 16%i cosh(x) +--R + +--R (- 90x - 138)cosh(x) + 25%i +--R / +--R 3 2 +--R 60cosh(x)sinh(x) - 90%i cosh(x)sinh(x) +--R + +--R 3 3 +--R (60cosh(x) + 60cosh(x))sinh(x) - 30%i cosh(x) - 90%i cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 454 + +--S 455 of 526 +m0685:= a0685-r0685 +--R +--R +--R (453) +--R 4 2 4 +--R (- 69%i cosh(x) + 44%i cosh(x) - 12%i)sinh(x) +--R + +--R 5 4 2 3 +--R (- 92%i cosh(x) - 62cosh(x) + 26cosh(x) - 6)sinh(x) +--R + +--R 6 5 4 2 +--R (46%i cosh(x) - 138cosh(x) - 122%i cosh(x) + 92%i cosh(x) - 30%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 92%i cosh(x) + 62cosh(x) - 92%i cosh(x) - 88cosh(x) +--R + +--R 2 +--R 32cosh(x) - 6 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 23%i cosh(x) - 46cosh(x) - 14%i cosh(x) - 138cosh(x) - 45%i cosh(x) +--R + +--R 2 +--R 54%i cosh(x) - 18%i +--R / +--R 5 3 5 2 +--R 60cosh(x) sinh(x) - 90%i cosh(x) sinh(x) +--R + +--R 7 5 7 5 +--R (60cosh(x) + 60cosh(x) )sinh(x) - 30%i cosh(x) - 90%i cosh(x) +--R Type: Expression(Complex(Integer)) +--E 455 + +--S 456 of 526 +d0685:= D(m0685,x) +--R +--R +--R (454) +--R 4 2 8 +--R (138%i cosh(x) - 264%i cosh(x) + 120%i)sinh(x) +--R + +--R 4 2 7 +--R (331cosh(x) - 552cosh(x) + 240)sinh(x) +--R + +--R 6 4 2 6 +--R (368%i cosh(x) - 156%i cosh(x) - 438%i cosh(x) + 330%i)sinh(x) +--R + +--R 6 4 2 5 +--R (427cosh(x) + 657cosh(x) - 1476cosh(x) + 750)sinh(x) +--R + +--R 8 6 4 2 +--R - 460%i cosh(x) + 704%i cosh(x) - 976%i cosh(x) + 30%i cosh(x) +--R + +--R 300%i +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (- 735cosh(x) + 670cosh(x) + 329cosh(x) - 1356cosh(x) + 780)sinh(x) +--R + +--R 8 6 4 2 +--R 532%i cosh(x) + 218%i cosh(x) - 874%i cosh(x) + 258%i cosh(x) +--R + +--R 90%i +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 23cosh(x) + 337cosh(x) - 185cosh(x) + 33cosh(x) - 432cosh(x) +--R + +--R 270 +--R * +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 46%i cosh(x) - 80%i cosh(x) + 20%i cosh(x) + 214%i cosh(x) +--R + +--R 4 2 +--R - 162%i cosh(x) + 54%i cosh(x) +--R / +--R 6 6 6 5 +--R 120cosh(x) sinh(x) - 360%i cosh(x) sinh(x) +--R + +--R 8 6 4 +--R (240cosh(x) - 30cosh(x) )sinh(x) +--R + +--R 8 6 3 +--R (- 480%i cosh(x) - 720%i cosh(x) )sinh(x) +--R + +--R 10 8 6 2 +--R (120cosh(x) + 60cosh(x) - 420cosh(x) )sinh(x) +--R + +--R 10 8 6 +--R (- 120%i cosh(x) - 480%i cosh(x) - 360%i cosh(x) )sinh(x) +--R + +--R 10 8 6 +--R - 30cosh(x) - 180cosh(x) - 270cosh(x) +--R Type: Expression(Complex(Integer)) +--E 456 + +--S 457 of 526 +t0686:= coth(x)/(a+b*csch(x)) +--R +--R +--R coth(x) +--R (455) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 526 +r0686:= log(b+a*sinh(x))/a +--R +--R +--R log(a sinh(x) + b) +--R (456) ------------------ +--R a +--R Type: Expression(Integer) +--E 458 + +--S 459 of 526 +a0686:= integrate(t0686,x) +--R +--R +--R - 2a sinh(x) - 2b +--R log(-----------------) - x +--R sinh(x) - cosh(x) +--R (457) -------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 459 + +--S 460 of 526 +m0686:= a0686-r0686 +--R +--R +--R - 2a sinh(x) - 2b +--R - log(a sinh(x) + b) + log(-----------------) - x +--R sinh(x) - cosh(x) +--R (458) ------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 460 + +--S 461 of 526 +d0686:= D(m0686,x) +--R +--R +--R (459) 0 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 526 +t0687:= coth(x)^2/(a+b*csch(x)) +--R +--R +--R 2 +--R coth(x) +--R (460) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 462 + +--S 463 of 526 +r0687:= x/a-acoth(cosh(x))/b+_ + 2*(a^2+b^2)^(1/2)*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a/b +--R +--R +--R x +--R +-------+ b tanh(-) - a +--R | 2 2 2 +--R - 2\|b + a atanh(-------------) - a acoth(cosh(x)) + b x +--R +-------+ +--R | 2 2 +--R \|b + a +--R (461) ---------------------------------------------------------- +--R a b +--R Type: Expression(Integer) +--E 463 + +--S 464 of 526 +a0687:= integrate(t0687,x) +--R +--R +--R (462) +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R - a log(sinh(x) + cosh(x) + 1) + a log(sinh(x) + cosh(x) - 1) + b x +--R / +--R a b +--R Type: Union(Expression(Integer),...) +--E 464 + +--S 465 of 526 +m0687:= a0687-r0687 +--R +--R +--R (463) +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R - a log(sinh(x) + cosh(x) + 1) + a log(sinh(x) + cosh(x) - 1) +--R + +--R x +--R +-------+ b tanh(-) - a +--R | 2 2 2 +--R 2\|b + a atanh(-------------) + a acoth(cosh(x)) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R a b +--R Type: Expression(Integer) +--E 465 + +--S 466 of 526 +d0687:= D(m0687,x) +--R +--R +--R (464) +--R 5 +--R - a b sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((b + a )cosh(x) - 4a b cosh(x) - 3b - a )sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((4b + 4a )cosh(x) - 4a b cosh(x) + (- 10b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R (6b + 6a )cosh(x) + 2a b cosh(x) + (- 10b - 8a )cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 4 2 2 3 +--R (4b + 4a )cosh(x) + 5a b cosh(x) + (- 2b - 8a )cosh(x) +--R + +--R 2 2 2 +--R - 6a b cosh(x) + (- 2b + 4a )cosh(x) + a b +--R * +--R sinh(x) +--R + +--R 2 2 6 5 2 2 4 +--R (b + a )cosh(x) + 2a b cosh(x) + (b - 3a )cosh(x) +--R + +--R 3 2 2 2 2 2 +--R - 4a b cosh(x) + (- b + 3a )cosh(x) + 2a b cosh(x) - b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 5 2 4 +--R 2a sinh(x) + (8a cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R ((4b + 12a )cosh(x) + 12a b cosh(x) - 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 2 +--R (12b + 8a )cosh(x) + 4a b cosh(x) + (- 12b - 8a )cosh(x) +--R + +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R (12b + 2a )cosh(x) - 12a b cosh(x) + (- 16b - 4a )cosh(x) +--R + +--R 2 2 +--R 12a b cosh(x) + 4b + 2a +--R * +--R sinh(x) +--R + +--R 2 5 4 2 3 2 2 +--R 4b cosh(x) - 8a b cosh(x) - 8b cosh(x) + 8a b cosh(x) + 4b cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 2 2 2 2 2 4 +--R a b sinh(x) + ((- b - a )cosh(x) + 4a b cosh(x) + 3b + a )sinh(x) +--R + +--R 2 2 3 2 2 2 3 +--R ((- 4b - 4a )cosh(x) + 4a b cosh(x) + (10b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R (- 6b - 6a )cosh(x) - 2a b cosh(x) + (10b + 8a )cosh(x) +--R + +--R 2 +--R 2a b cosh(x) - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 4 2 2 3 +--R (- 4b - 4a )cosh(x) - 5a b cosh(x) + (2b + 8a )cosh(x) +--R + +--R 2 2 2 +--R 6a b cosh(x) + (2b - 4a )cosh(x) - a b +--R * +--R sinh(x) +--R + +--R 2 2 6 5 2 2 4 +--R (- b - a )cosh(x) - 2a b cosh(x) + (- b + 3a )cosh(x) +--R + +--R 3 2 2 2 2 2 +--R 4a b cosh(x) + (b - 3a )cosh(x) - 2a b cosh(x) + b + a +--R / +--R 2 2 2 4 +--R (a b cosh(x) - a b )sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (4a b cosh(x) + 2b cosh(x) - 4a b cosh(x) - 2b )sinh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R (6a b cosh(x) + 6b cosh(x) - 8a b cosh(x) - 6b cosh(x) + 2a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 4a b cosh(x) + 6b cosh(x) - 8a b cosh(x) - 8b cosh(x) +--R + +--R 2 3 +--R 4a b cosh(x) + 2b +--R * +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R a b cosh(x) + 2b cosh(x) - 3a b cosh(x) - 4b cosh(x) +--R + +--R 2 2 3 2 +--R 3a b cosh(x) + 2b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 4 +--R (- 2a b cosh(x) + 2a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (- 8a b cosh(x) - 4a b cosh(x) + 8a b cosh(x) + 4a b )sinh(x) +--R + +--R 2 4 2 3 2 2 +--R - 12a b cosh(x) - 12a b cosh(x) + 16a b cosh(x) +--R + +--R 2 2 +--R 12a b cosh(x) - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R - 8a b cosh(x) - 12a b cosh(x) + 16a b cosh(x) +--R + +--R 2 2 2 2 +--R 16a b cosh(x) - 8a b cosh(x) - 4a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 2a b cosh(x) - 4a b cosh(x) + 6a b cosh(x) + 8a b cosh(x) +--R + +--R 2 2 2 2 +--R - 6a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 2 2 4 +--R (- a b cosh(x) + a b )sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (- 4a b cosh(x) - 2b cosh(x) + 4a b cosh(x) + 2b )sinh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R (- 6a b cosh(x) - 6b cosh(x) + 8a b cosh(x) + 6b cosh(x) - 2a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R - 4a b cosh(x) - 6b cosh(x) + 8a b cosh(x) + 8b cosh(x) +--R + +--R 2 3 +--R - 4a b cosh(x) - 2b +--R * +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R - a b cosh(x) - 2b cosh(x) + 3a b cosh(x) + 4b cosh(x) +--R + +--R 2 2 3 2 +--R - 3a b cosh(x) - 2b cosh(x) + a b +--R Type: Expression(Integer) +--E 466 + +--S 467 of 526 +t0688:= coth(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R coth(x) +--R (465) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 526 +r0688:= -csch(x)/b-a*log(sinh(x))/b^2+(a^2+b^2)*log(b+a*sinh(x))/b^2/a +--R +--R +--R 2 2 2 +--R (b + a )log(a sinh(x) + b) - a log(sinh(x)) - a b csch(x) +--R (466) ---------------------------------------------------------- +--R 2 +--R a b +--R Type: Expression(Integer) +--E 468 + +--S 469 of 526 +a0688:= integrate(t0688,x) +--R +--R +--R (467) +--R 2 2 2 2 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a ) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) +--R + +--R 2 2 +--R - b - a +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 +--R - b x sinh(x) + (- 2b x cosh(x) - 2a b)sinh(x) - b x cosh(x) +--R + +--R 2 +--R - 2a b cosh(x) + b x +--R / +--R 2 2 2 2 2 2 +--R a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) - a b +--R Type: Union(Expression(Integer),...) +--E 469 + +--S 470 of 526 +m0688:= a0688-r0688 +--R +--R +--R (468) +--R 2 2 2 2 2 +--R (- b - a )sinh(x) + (- 2b - 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- b - a )cosh(x) + b + a +--R * +--R log(a sinh(x) + b) +--R + +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a )log(sinh(x)) +--R + +--R 2 2 2 2 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a ) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) +--R + +--R 2 2 +--R - b - a +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (a b csch(x) - b x)sinh(x) +--R + +--R 2 +--R (2a b cosh(x)csch(x) - 2b x cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 +--R (a b cosh(x) - a b)csch(x) - b x cosh(x) - 2a b cosh(x) + b x +--R / +--R 2 2 2 2 2 2 +--R a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) - a b +--R Type: Expression(Integer) +--E 470 + +--S 471 of 526 +d0688:= D(m0688,x) +--R +--R +--R (469) +--R 4 3 +--R - coth(x)csch(x)sinh(x) + (- 4cosh(x)coth(x)csch(x) + 2)sinh(x) +--R + +--R 2 2 +--R ((- 6cosh(x) + 2)coth(x)csch(x) + 6cosh(x))sinh(x) +--R + +--R 3 2 +--R ((- 4cosh(x) + 4cosh(x))coth(x)csch(x) + 6cosh(x) + 2)sinh(x) +--R + +--R 4 2 3 +--R (- cosh(x) + 2cosh(x) - 1)coth(x)csch(x) + 2cosh(x) + 2cosh(x) +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) - 2b)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) - 4b cosh(x))sinh(x) + b cosh(x) - 2b cosh(x) + b +--R Type: Expression(Integer) +--E 471 + +--S 472 of 526 +t0689:= coth(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R coth(x) +--R (470) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 526 +r0689:= x/a-a^2*acoth(cosh(x))/b^3-3/2*acoth(cosh(x))/b+_ + 2*(a^2+b^2)^(3/2)*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/a/b^3+_ + a*coth(x)/b^2-1/2*coth(x)*csch(x)/b +--R +--R +--R (471) +--R x +--R +-------+ b tanh(-) - a +--R 2 2 | 2 2 2 +--R (- 4b - 4a )\|b + a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 2 3 +--R (- 3a b - 2a )acoth(cosh(x)) - a b coth(x)csch(x) + 2a b coth(x) + 2b x +--R / +--R 3 +--R 2a b +--R Type: Expression(Integer) +--E 473 + +--S 474 of 526 +a0689:= integrate(t0689,x) +--R +--R +--R (472) +--R 2 2 4 2 2 3 +--R (2b + 2a )sinh(x) + (8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 12a )cosh(x) - 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 8a )cosh(x) + (- 8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + 2a )cosh(x) + (- 4b - 4a )cosh(x) + 2b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 3 4 2 3 3 +--R (- 3a b - 2a )sinh(x) + (- 12a b - 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 18a b - 12a )cosh(x) + 6a b + 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 12a b - 8a )cosh(x) + (12a b + 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 3a b - 2a )cosh(x) + (6a b + 4a )cosh(x) - 3a b - 2a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 3 4 2 3 3 +--R (3a b + 2a )sinh(x) + (12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b + 12a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b + 8a )cosh(x) + (- 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b + 2a )cosh(x) + (- 6a b - 4a )cosh(x) + 3a b + 2a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 3 4 3 2 3 +--R 2b x sinh(x) + (8b x cosh(x) - 2a b )sinh(x) +--R + +--R 3 2 2 3 2 2 +--R (12b x cosh(x) - 6a b cosh(x) - 4b x + 4a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (8b x cosh(x) - 6a b cosh(x) + (- 8b x + 8a b)cosh(x) - 2a b )sinh(x) +--R + +--R 3 4 2 3 3 2 2 2 +--R 2b x cosh(x) - 2a b cosh(x) + (- 4b x + 4a b)cosh(x) - 2a b cosh(x) +--R + +--R 3 2 +--R 2b x - 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a b sinh(x) + 8a b cosh(x)sinh(x) + (12a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (8a b cosh(x) - 8a b cosh(x))sinh(x) + 2a b cosh(x) - 4a b cosh(x) +--R + +--R 3 +--R 2a b +--R Type: Union(Expression(Integer),...) +--E 474 + +--S 475 of 526 +m0689:= a0689-r0689 +--R +--R +--R (473) +--R 2 2 4 2 2 3 +--R (2b + 2a )sinh(x) + (8b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((12b + 12a )cosh(x) - 4b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8b + 8a )cosh(x) + (- 8b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (2b + 2a )cosh(x) + (- 4b - 4a )cosh(x) + 2b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2a sinh(x) + 2a cosh(x) + 2b)\|b + a + a sinh(x) +--R + +--R 2 2 2 2 2 +--R (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) + 2b + a +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 3 4 2 3 3 +--R (- 3a b - 2a )sinh(x) + (- 12a b - 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 18a b - 12a )cosh(x) + 6a b + 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 12a b - 8a )cosh(x) + (12a b + 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- 3a b - 2a )cosh(x) + (6a b + 4a )cosh(x) - 3a b - 2a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 3 4 2 3 3 +--R (3a b + 2a )sinh(x) + (12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b + 12a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b + 8a )cosh(x) + (- 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b + 2a )cosh(x) + (- 6a b - 4a )cosh(x) + 3a b + 2a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 4 2 2 3 +--R (4b + 4a )sinh(x) + (16b + 16a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((24b + 24a )cosh(x) - 8b - 8a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((16b + 16a )cosh(x) + (- 16b - 16a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (4b + 4a )cosh(x) + (- 8b - 8a )cosh(x) + 4b + 4a +--R * +--R x +--R +-------+ b tanh(-) - a +--R | 2 2 2 +--R \|b + a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 4 2 3 3 +--R (3a b + 2a )sinh(x) + (12a b + 8a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((18a b + 12a )cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((12a b + 8a )cosh(x) + (- 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (3a b + 2a )cosh(x) + (- 6a b - 4a )cosh(x) + 3a b + 2a +--R * +--R acoth(cosh(x)) +--R + +--R 2 2 4 +--R (a b coth(x)csch(x) - 2a b coth(x))sinh(x) +--R + +--R 2 2 2 3 +--R (4a b cosh(x)coth(x)csch(x) - 8a b cosh(x)coth(x) - 2a b )sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) - 2a b )coth(x)csch(x) +--R + +--R 2 2 2 2 2 +--R (- 12a b cosh(x) + 4a b)coth(x) - 6a b cosh(x) + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (4a b cosh(x) - 4a b cosh(x))coth(x)csch(x) +--R + +--R 2 3 2 2 2 +--R (- 8a b cosh(x) + 8a b cosh(x))coth(x) - 6a b cosh(x) +--R + +--R 2 2 +--R 8a b cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (a b cosh(x) - 2a b cosh(x) + a b )coth(x)csch(x) +--R + +--R 2 4 2 2 2 2 3 +--R (- 2a b cosh(x) + 4a b cosh(x) - 2a b)coth(x) - 2a b cosh(x) +--R + +--R 2 2 2 2 +--R 4a b cosh(x) - 2a b cosh(x) - 4a b +--R / +--R 3 4 3 3 3 2 3 2 +--R 2a b sinh(x) + 8a b cosh(x)sinh(x) + (12a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 +--R (8a b cosh(x) - 8a b cosh(x))sinh(x) + 2a b cosh(x) - 4a b cosh(x) +--R + +--R 3 +--R 2a b +--R Type: Expression(Integer) +--E 475 + +--S 476 of 526 +--d0689:= D(m0689,x) +--E 476 + +--S 477 of 526 +t0690:= coth(x)/(%i+csch(x)) +--R +--R +--R coth(x) +--R (474) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 477 + +--S 478 of 526 +r0690:= -%i*log(1+%i*sinh(x)) +--R +--R +--R (475) - %i log(%i sinh(x) + 1) +--R Type: Expression(Complex(Integer)) +--E 478 + +--S 479 of 526 +a0690:= integrate(t0690,x) +--R +--R +--R (476) - 2%i log(sinh(x) + cosh(x) - %i) + %i x +--R Type: Union(Expression(Complex(Integer)),...) +--E 479 + +--S 480 of 526 +m0690:= a0690-r0690 +--R +--R +--R (477) - 2%i log(sinh(x) + cosh(x) - %i) + %i log(%i sinh(x) + 1) + %i x +--R Type: Expression(Complex(Integer)) +--E 480 + +--S 481 of 526 +d0690:= D(m0690,x) +--R +--R +--R 2 2 +--R - %i sinh(x) + %i cosh(x) - %i +--R (478) -------------------------------------------------- +--R 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) - %i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 481 + +--S 482 of 526 +t0691:= coth(x)^2/(%i+csch(x)) +--R +--R +--R 2 +--R coth(x) +--R (479) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 482 + +--S 483 of 526 +r0691:= -%i*x-acoth(cosh(x)) +--R +--R +--R (480) - acoth(cosh(x)) - %i x +--R Type: Expression(Complex(Integer)) +--E 483 + +--S 484 of 526 +a0691:= integrate(t0691,x) +--R +--R +--R (481) - log(sinh(x) + cosh(x) + 1) + log(sinh(x) + cosh(x) - 1) - %i x +--R Type: Union(Expression(Complex(Integer)),...) +--E 484 + +--S 485 of 526 +m0691:= a0691-r0691 +--R +--R +--R (482) +--R - log(sinh(x) + cosh(x) + 1) + log(sinh(x) + cosh(x) - 1) + acoth(cosh(x)) +--R Type: Expression(Complex(Integer)) +--E 485 + +--S 486 of 526 +d0691:= D(m0691,x) +--R +--R +--R (483) +--R 3 2 2 3 +--R - sinh(x) - 2cosh(x)sinh(x) + (cosh(x) - 1)sinh(x) + 2cosh(x) +--R + +--R - 2cosh(x) +--R / +--R 2 2 3 4 +--R (cosh(x) - 1)sinh(x) + (2cosh(x) - 2cosh(x))sinh(x) + cosh(x) +--R + +--R 2 +--R - 2cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 486 + +--S 487 of 526 +t0692:= coth(x)^3/(%i+csch(x)) +--R +--R +--R 3 +--R coth(x) +--R (484) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 487 + +--S 488 of 526 +r0692:= -csch(x)-%i*log(sinh(x)) +--R +--R +--R (485) - %i log(sinh(x)) - csch(x) +--R Type: Expression(Complex(Integer)) +--E 488 + +--S 489 of 526 +a0692:= integrate(t0692,x) +--R +--R +--R (486) +--R 2 2 +--R (- %i sinh(x) - 2%i cosh(x)sinh(x) - %i cosh(x) + %i) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R %i x sinh(x) + (2%i x cosh(x) - 2)sinh(x) + %i x cosh(x) - 2cosh(x) +--R + +--R - %i x +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 489 + +--S 490 of 526 +m0692:= a0692-r0692 +--R +--R +--R (487) +--R 2 2 +--R (%i sinh(x) + 2%i cosh(x)sinh(x) + %i cosh(x) - %i)log(sinh(x)) +--R + +--R 2 2 +--R (- %i sinh(x) - 2%i cosh(x)sinh(x) - %i cosh(x) + %i) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (csch(x) + %i x)sinh(x) + (2cosh(x)csch(x) + 2%i x cosh(x) - 2)sinh(x) +--R + +--R 2 2 +--R (cosh(x) - 1)csch(x) + %i x cosh(x) - 2cosh(x) - %i x +--R / +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 490 + +--S 491 of 526 +d0692:= D(m0692,x) +--R +--R +--R (488) +--R 4 3 +--R - coth(x)csch(x)sinh(x) + (- 4cosh(x)coth(x)csch(x) + 2)sinh(x) +--R + +--R 2 2 +--R ((- 6cosh(x) + 2)coth(x)csch(x) + 6cosh(x))sinh(x) +--R + +--R 3 2 +--R ((- 4cosh(x) + 4cosh(x))coth(x)csch(x) + 6cosh(x) + 2)sinh(x) +--R + +--R 4 2 3 +--R (- cosh(x) + 2cosh(x) - 1)coth(x)csch(x) + 2cosh(x) + 2cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 491 + +--S 492 of 526 +t0693:= coth(x)^4/(%i+csch(x)) +--R +--R +--R 4 +--R coth(x) +--R (489) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 492 + +--S 493 of 526 +r0693:= -%i*x-1/2*acoth(cosh(x))+%i*coth(x)-1/2*coth(x)*csch(x) +--R +--R +--R - acoth(cosh(x)) - coth(x)csch(x) + 2%i coth(x) - 2%i x +--R (490) ------------------------------------------------------- +--R 2 +--R Type: Expression(Complex(Integer)) +--E 493 + +--S 494 of 526 +a0693:= integrate(t0693,x) +--R +--R +--R (491) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - cosh(x) + 2cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 3 +--R - 2%i x sinh(x) + (- 8%i x cosh(x) - 2)sinh(x) +--R + +--R 2 2 +--R (- 12%i x cosh(x) - 6cosh(x) + 4%i x + 4%i)sinh(x) +--R + +--R 3 2 +--R (- 8%i x cosh(x) - 6cosh(x) + (8%i x + 8%i)cosh(x) - 2)sinh(x) +--R + +--R 4 3 2 +--R - 2%i x cosh(x) - 2cosh(x) + (4%i x + 4%i)cosh(x) - 2cosh(x) - 2%i x +--R + +--R - 4%i +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Union(Expression(Complex(Integer)),...) +--E 494 + +--S 495 of 526 +m0693:= a0693-r0693 +--R +--R +--R (492) +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 2)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 4cosh(x))sinh(x) - cosh(x) + 2cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R * +--R acoth(cosh(x)) +--R + +--R 4 +--R (coth(x)csch(x) - 2%i coth(x))sinh(x) +--R + +--R 3 +--R (4cosh(x)coth(x)csch(x) - 8%i cosh(x)coth(x) - 2)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) - 2)coth(x)csch(x) + (- 12%i cosh(x) + 4%i)coth(x) +--R + +--R - 6cosh(x) + 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 3 +--R (4cosh(x) - 4cosh(x))coth(x)csch(x) +--R + +--R 3 2 +--R (- 8%i cosh(x) + 8%i cosh(x))coth(x) - 6cosh(x) + 8%i cosh(x) - 2 +--R * +--R sinh(x) +--R + +--R 4 2 +--R (cosh(x) - 2cosh(x) + 1)coth(x)csch(x) +--R + +--R 4 2 3 2 +--R (- 2%i cosh(x) + 4%i cosh(x) - 2%i)coth(x) - 2cosh(x) + 4%i cosh(x) +--R + +--R - 2cosh(x) - 4%i +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Expression(Complex(Integer)) +--E 495 + +--S 496 of 526 +d0693:= D(m0693,x) +--R +--R +--R (493) +--R 7 +--R - sinh(x) +--R + +--R 2 2 2 +--R ((- 2cosh(x) + 2)coth(x) + cosh(x) - 1)csch(x) +--R + +--R 2 2 2 +--R (2%i cosh(x) - 2%i)coth(x) - 2%i cosh(x) - 6cosh(x) + 2%i +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 3 +--R ((- 12cosh(x) + 12cosh(x))coth(x) + 6cosh(x) - 6cosh(x))csch(x) +--R + +--R 3 2 3 2 +--R (12%i cosh(x) - 12%i cosh(x))coth(x) - 12%i cosh(x) - 11cosh(x) +--R + +--R 12%i cosh(x) - 1 +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 4 2 +--R (- 30cosh(x) + 36cosh(x) - 6)coth(x) + 15cosh(x) - 18cosh(x) +--R + +--R 3 +--R * +--R csch(x) +--R + +--R 4 2 2 4 +--R (30%i cosh(x) - 36%i cosh(x) + 6%i)coth(x) - 30%i cosh(x) +--R + +--R 2 +--R 28%i cosh(x) - 8cosh(x) + 2%i +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 2 5 +--R (- 40cosh(x) + 64cosh(x) - 24cosh(x))coth(x) + 20cosh(x) +--R + +--R 3 +--R - 32cosh(x) + 12cosh(x) +--R * +--R csch(x) +--R + +--R 5 3 2 +--R (40%i cosh(x) - 64%i cosh(x) + 24%i cosh(x))coth(x) +--R + +--R 5 4 3 2 +--R - 40%i cosh(x) + 25cosh(x) + 32%i cosh(x) - 14cosh(x) +--R + +--R 8%i cosh(x) - 11 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 2 6 +--R (- 30cosh(x) + 66cosh(x) - 42cosh(x) + 6)coth(x) + 15cosh(x) +--R + +--R 4 2 +--R - 33cosh(x) + 21cosh(x) - 3 +--R * +--R csch(x) +--R + +--R 6 4 2 2 +--R (30%i cosh(x) - 66%i cosh(x) + 42%i cosh(x) - 6%i)coth(x) +--R + +--R 6 5 4 3 +--R - 30%i cosh(x) + 34cosh(x) + 18%i cosh(x) - 4cosh(x) +--R + +--R 2 +--R 14%i cosh(x) - 30cosh(x) - 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (- 12cosh(x) + 36cosh(x) - 36cosh(x) + 12cosh(x))coth(x) +--R + +--R 7 5 3 +--R 6cosh(x) - 18cosh(x) + 18cosh(x) - 6cosh(x) +--R * +--R csch(x) +--R + +--R 7 5 3 +--R (12%i cosh(x) - 36%i cosh(x) + 36%i cosh(x) - 12%i cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R - 12%i cosh(x) + 19cosh(x) + 4%i cosh(x) + 7cosh(x) +--R + +--R 3 2 +--R 12%i cosh(x) - 23cosh(x) - 4%i cosh(x) - 3 +--R * +--R sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 2cosh(x) + 8cosh(x) - 12cosh(x) + 8cosh(x) - 2)coth(x) +--R + +--R 8 6 4 2 +--R cosh(x) - 4cosh(x) + 6cosh(x) - 4cosh(x) + 1 +--R * +--R csch(x) +--R + +--R 8 6 4 2 +--R (2%i cosh(x) - 8%i cosh(x) + 12%i cosh(x) - 8%i cosh(x) + 2%i) +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 5 4 3 +--R - 2%i cosh(x) + 4cosh(x) + 4cosh(x) + 4%i cosh(x) - 4cosh(x) +--R + +--R - 4cosh(x) - 2%i +--R / +--R 2 6 3 5 +--R (2cosh(x) - 2)sinh(x) + (12cosh(x) - 12cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (30cosh(x) - 36cosh(x) + 6)sinh(x) +--R + +--R 5 3 3 +--R (40cosh(x) - 64cosh(x) + 24cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (30cosh(x) - 66cosh(x) + 42cosh(x) - 6)sinh(x) +--R + +--R 7 5 3 8 +--R (12cosh(x) - 36cosh(x) + 36cosh(x) - 12cosh(x))sinh(x) + 2cosh(x) +--R + +--R 6 4 2 +--R - 8cosh(x) + 12cosh(x) - 8cosh(x) + 2 +--R Type: Expression(Complex(Integer)) +--E 496 + +--S 497 of 526 +t0694:= sech(x)/(a+b*csch(x)) +--R +--R +--R sech(x) +--R (494) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 497 + +--S 498 of 526 +r0694:= 1/2*(2*a*atan(sinh(x))+b*log(cosh(x)^2)-2*b*log(b+a*sinh(x)))/(a^2+b^2) +--R +--R +--R 2 +--R - 2b log(a sinh(x) + b) + b log(cosh(x) ) + 2a atan(sinh(x)) +--R (495) ------------------------------------------------------------ +--R 2 2 +--R 2b + 2a +--R Type: Expression(Integer) +--E 498 + +--S 499 of 526 +a0694:= integrate(t0694,x) +--R +--R +--R (496) +--R 2cosh(x) - 2a sinh(x) - 2b +--R b log(- -----------------) - b log(-----------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R + +--R 2a atan(sinh(x) + cosh(x)) +--R / +--R 2 2 +--R b + a +--R Type: Union(Expression(Integer),...) +--E 499 + +--S 500 of 526 +m0694:= a0694-r0694 +--R +--R +--R (497) +--R 2 2cosh(x) +--R 2b log(a sinh(x) + b) - b log(cosh(x) ) + 2b log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2a sinh(x) - 2b +--R - 2b log(-----------------) + 4a atan(sinh(x) + cosh(x)) - 2a atan(sinh(x)) +--R sinh(x) - cosh(x) +--R / +--R 2 2 +--R 2b + 2a +--R Type: Expression(Integer) +--E 500 + +--S 501 of 526 +d0694:= D(m0694,x) +--R +--R +--R (498) +--R 3 2 2 +--R 2a sinh(x) + a cosh(x)sinh(x) + (- 2a cosh(x) + 2a)sinh(x) +--R + +--R 3 +--R - a cosh(x) + a cosh(x) +--R / +--R 2 2 4 2 2 3 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((b + a )cosh(x) + 2b + 2a )sinh(x) + (2b + 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b + a )cosh(x) + b + a +--R Type: Expression(Integer) +--E 501 + +--S 502 of 526 +t0695:= sech(x)^2/(a+b*csch(x)) +--R +--R +--R 2 +--R sech(x) +--R (499) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 502 + +--S 503 of 526 +r0695:= 2*a*b*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ + b*sech(x)/(a^2+b^2)+a*tanh(x)/(a^2+b^2) +--R +--R +--R x +--R b tanh(-) - a +-------+ +--R 2 | 2 2 +--R - 2a b atanh(-------------) + (a tanh(x) - b sech(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (500) --------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 526 +a0695:= integrate(t0695,x) +--R +--R +--R (501) +--R 2 2 +--R (a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) + a b) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R +-------+ +--R | 2 2 +--R (- 2b sinh(x) - 2b cosh(x) - 2a)\|b + a +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) + b +--R + +--R 2 +--R a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 504 + +--S 505 of 526 +m0695:= a0695-r0695 +--R +--R +--R (502) +--R 2 2 +--R (a b sinh(x) + 2a b cosh(x)sinh(x) + a b cosh(x) + a b) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 2 +--R (2a b sinh(x) + 4a b cosh(x)sinh(x) + 2a b cosh(x) + 2a b) +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) - a)tanh(x) +--R + +--R 2 +--R b sech(x)sinh(x) + (2b cosh(x)sech(x) - 2b)sinh(x) +--R + +--R 2 +--R (b cosh(x) + b)sech(x) - 2b cosh(x) - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (b + a )sinh(x) + (2b + 2a )cosh(x)sinh(x) + (b + a )cosh(x) + b +--R + +--R 2 +--R a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 505 + +--S 506 of 526 +d0695:= D(m0695,x) +--R +--R +--R (503) +--R 2 6 2 2 5 +--R a b sinh(x) + (6a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 2 2 4 +--R (15a b cosh(x) + 10a b cosh(x) + a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (20a b cosh(x) + 20a b cosh(x) + 4a b cosh(x) + 4a b )sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 15a b cosh(x) + 20a b cosh(x) + 6a b cosh(x) +--R + +--R 2 2 +--R 12a b cosh(x) - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 6a b cosh(x) + 10a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 2 +--R 12a b cosh(x) - 2a b cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R a b cosh(x) + 2a b cosh(x) + a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 2 2 +--R - a b cosh(x) + 2a b cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 2 5 +--R - 2a sinh(x) + (- 12a cosh(x) - 4a b)sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 30a cosh(x) - 20a b cosh(x) - 2a )sinh(x) +--R + +--R 3 3 2 2 3 2 3 +--R (- 40a cosh(x) - 40a b cosh(x) - 8a cosh(x) - 8a b)sinh(x) +--R + +--R 3 4 2 3 3 2 +--R - 30a cosh(x) - 40a b cosh(x) - 12a cosh(x) +--R + +--R 2 3 +--R - 24a b cosh(x) + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 3 3 +--R - 12a cosh(x) - 20a b cosh(x) - 8a cosh(x) +--R + +--R 2 2 3 2 +--R - 24a b cosh(x) + 4a cosh(x) - 4a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 4 2 3 +--R - 2a cosh(x) - 4a b cosh(x) - 2a cosh(x) - 8a b cosh(x) +--R + +--R 3 2 2 3 +--R 2a cosh(x) - 4a b cosh(x) + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R - a b sinh(x) + (- 6a b cosh(x) - 2a b )sinh(x) +--R + +--R 2 2 2 2 4 +--R (- 15a b cosh(x) - 10a b cosh(x) - a b)sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (- 20a b cosh(x) - 20a b cosh(x) - 4a b cosh(x) - 4a b )sinh(x) +--R + +--R 2 4 2 3 2 2 2 +--R - 15a b cosh(x) - 20a b cosh(x) - 6a b cosh(x) - 12a b cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 6a b cosh(x) - 10a b cosh(x) - 4a b cosh(x) - 12a b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - a b cosh(x) - 2a b cosh(x) - a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 2 2 +--R a b cosh(x) - 2a b cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 3 5 +--R - a b sech(x)sinh(x) + (- 6a b cosh(x) - 2b )sech(x)sinh(x) +--R + +--R 2 2 3 2 4 +--R (- 15a b cosh(x) - 10b cosh(x) - a b )sech(x)sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (- 20a b cosh(x) - 20b cosh(x) - 4a b cosh(x) - 4b )sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R - 15a b cosh(x) - 20b cosh(x) - 6a b cosh(x) - 12b cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R - 6a b cosh(x) - 10b cosh(x) - 4a b cosh(x) - 12b cosh(x) +--R + +--R 2 3 +--R 2a b cosh(x) - 2b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R - a b cosh(x) - 2b cosh(x) - a b cosh(x) - 4b cosh(x) +--R + +--R 2 2 3 2 +--R a b cosh(x) - 2b cosh(x) + a b +--R * +--R sech(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 2 5 +--R 2a b sech(x)sinh(x) + (12a b cosh(x) + 4a b )sech(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (30a b cosh(x) + 20a b cosh(x) + 2a b)sech(x)sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (40a b cosh(x) + 40a b cosh(x) + 8a b cosh(x) + 8a b )sech(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 30a b cosh(x) + 40a b cosh(x) + 12a b cosh(x) +--R + +--R 2 2 +--R 24a b cosh(x) - 2a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 12a b cosh(x) + 20a b cosh(x) + 8a b cosh(x) +--R + +--R 2 2 2 2 +--R 24a b cosh(x) - 4a b cosh(x) + 4a b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 2a b cosh(x) + 4a b cosh(x) + 2a b cosh(x) + 8a b cosh(x) +--R + +--R 2 2 2 2 +--R - 2a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R sech(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 6 2 3 5 +--R a b sech(x)sinh(x) + (6a b cosh(x) + 2b )sech(x)sinh(x) +--R + +--R 2 2 3 2 4 +--R (15a b cosh(x) + 10b cosh(x) + a b )sech(x)sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (20a b cosh(x) + 20b cosh(x) + 4a b cosh(x) + 4b )sech(x)sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R 15a b cosh(x) + 20b cosh(x) + 6a b cosh(x) + 12b cosh(x) +--R + +--R 2 +--R - a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 6a b cosh(x) + 10b cosh(x) + 4a b cosh(x) + 12b cosh(x) +--R + +--R 2 3 +--R - 2a b cosh(x) + 2b +--R * +--R sech(x)sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R a b cosh(x) + 2b cosh(x) + a b cosh(x) + 4b cosh(x) +--R + +--R 2 2 3 2 +--R - a b cosh(x) + 2b cosh(x) - a b +--R * +--R sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 4 3 2 3 +--R (4b + 4a b)sinh(x) + (16b + 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 +--R ((24b + 24a b)cosh(x) - 4b - 4a b)sinh(x) +--R + +--R 3 2 3 3 2 +--R ((16b + 16a b)cosh(x) + (- 8b - 8a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 +--R (4b + 4a b)cosh(x) + (- 4b - 4a b)cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 6 3 2 5 +--R 2a sinh(x) + (12a cosh(x) + 4a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (30a cosh(x) + 20a b cosh(x) - 8a b - 6a )sinh(x) +--R + +--R 3 3 2 2 2 3 2 +--R (40a cosh(x) + 40a b cosh(x) + (- 32a b - 24a )cosh(x) + 8a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 2 3 2 +--R 30a cosh(x) + 40a b cosh(x) + (- 48a b - 36a )cosh(x) +--R + +--R 2 2 3 +--R 24a b cosh(x) + 8a b + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R 12a cosh(x) + 20a b cosh(x) + (- 32a b - 24a )cosh(x) +--R + +--R 2 2 2 3 2 +--R 24a b cosh(x) + (16a b + 12a )cosh(x) + 4a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 2 3 +--R 2a cosh(x) + 4a b cosh(x) + (- 8a b - 6a )cosh(x) + 8a b cosh(x) +--R + +--R 2 3 2 2 3 +--R (8a b + 6a )cosh(x) + 4a b cosh(x) - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 4 3 2 3 +--R (- 4b - 4a b)sinh(x) + (- 16b - 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 +--R ((- 24b - 24a b)cosh(x) + 4b + 4a b)sinh(x) +--R + +--R 3 2 3 3 2 +--R ((- 16b - 16a b)cosh(x) + (8b + 8a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 +--R (- 4b - 4a b)cosh(x) + (4b + 4a b)cosh(x) +--R / +--R 3 3 6 3 3 4 2 2 5 +--R (a b + a b)sinh(x) + ((6a b + 6a b)cosh(x) + 2b + 2a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R ((15a b + 15a b)cosh(x) + (10b + 10a b )cosh(x) + a b + a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (20a b + 20a b)cosh(x) + (20b + 20a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (4a b + 4a b)cosh(x) + 4b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 4 2 2 3 +--R (15a b + 15a b)cosh(x) + (20b + 20a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (6a b + 6a b)cosh(x) + (12b + 12a b )cosh(x) - a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 4 2 2 4 +--R (6a b + 6a b)cosh(x) + (10b + 10a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (4a b + 4a b)cosh(x) + (12b + 12a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 2a b - 2a b)cosh(x) + 2b + 2a b +--R * +--R sinh(x) +--R + +--R 3 3 6 4 2 2 5 3 3 4 +--R (a b + a b)cosh(x) + (2b + 2a b )cosh(x) + (a b + a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 4 2 2 +--R (4b + 4a b )cosh(x) + (- a b - a b)cosh(x) + (2b + 2a b )cosh(x) +--R + +--R 3 3 +--R - a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 6 +--R (- 2a b - 2a )sinh(x) +--R + +--R 2 2 4 3 3 5 +--R ((- 12a b - 12a )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 2 2 4 2 3 3 2 2 +--R (- 30a b - 30a )cosh(x) + (- 20a b - 20a b)cosh(x) - 2a b +--R + +--R 4 +--R - 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 4 3 3 3 2 +--R (- 40a b - 40a )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 8a b - 8a )cosh(x) - 8a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 4 3 3 3 +--R (- 30a b - 30a )cosh(x) + (- 40a b - 40a b)cosh(x) +--R + +--R 2 2 4 2 3 3 2 2 4 +--R (- 12a b - 12a )cosh(x) + (- 24a b - 24a b)cosh(x) + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 5 3 3 4 +--R (- 12a b - 12a )cosh(x) + (- 20a b - 20a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 +--R (- 8a b - 8a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (4a b + 4a )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 2 4 6 3 3 5 +--R (- 2a b - 2a )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 2 4 4 3 3 3 +--R (- 2a b - 2a )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 2 2 4 2 3 3 2 2 4 +--R (2a b + 2a )cosh(x) + (- 4a b - 4a b)cosh(x) + 2a b + 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 6 3 3 4 2 2 5 +--R (- a b - a b)sinh(x) + ((- 6a b - 6a b)cosh(x) - 2b - 2a b )sinh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R ((- 15a b - 15a b)cosh(x) + (- 10b - 10a b )cosh(x) - a b - a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (- 20a b - 20a b)cosh(x) + (- 20b - 20a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 4a b - 4a b)cosh(x) - 4b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 4 2 2 3 +--R (- 15a b - 15a b)cosh(x) + (- 20b - 20a b )cosh(x) +--R + +--R 3 3 2 4 2 2 3 3 +--R (- 6a b - 6a b)cosh(x) + (- 12b - 12a b )cosh(x) + a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 4 2 2 4 +--R (- 6a b - 6a b)cosh(x) + (- 10b - 10a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (- 4a b - 4a b)cosh(x) + (- 12b - 12a b )cosh(x) +--R + +--R 3 3 4 2 2 +--R (2a b + 2a b)cosh(x) - 2b - 2a b +--R * +--R sinh(x) +--R + +--R 3 3 6 4 2 2 5 3 3 4 +--R (- a b - a b)cosh(x) + (- 2b - 2a b )cosh(x) + (- a b - a b)cosh(x) +--R + +--R 4 2 2 3 3 3 2 4 2 2 +--R (- 4b - 4a b )cosh(x) + (a b + a b)cosh(x) + (- 2b - 2a b )cosh(x) +--R + +--R 3 3 +--R a b + a b +--R Type: Expression(Integer) +--E 506 + +--S 507 of 526 +t0696:= sech(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R sech(x) +--R (504) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 507 + +--S 508 of 526 +r0696:= 1/2*(-a*b^2*atan(sinh(x))*cosh(x)^2+a^3*atan(sinh(x))*cosh(x)^2+_ + a^2*b*log(cosh(x)^2)*cosh(x)^2-2*a^2*b*log(b+a*sinh(x))*cosh(x)^2-_ + a^2*b-b^3+a^3*sinh(x)+b^2*a*sinh(x))/cosh(x)^2/(a^2+b^2)^2 +--R +--R +--R (505) +--R 2 2 2 2 2 +--R - 2a b cosh(x) log(a sinh(x) + b) + a b cosh(x) log(cosh(x) ) +--R + +--R 2 3 2 2 3 3 2 +--R (- a b + a )cosh(x) atan(sinh(x)) + (a b + a )sinh(x) - b - a b +--R / +--R 4 2 2 4 2 +--R (2b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 508 + +--S 509 of 526 +a0696:= integrate(t0696,x) +--R +--R +--R (506) +--R 2 4 2 3 2 2 2 2 +--R a b sinh(x) + 4a b cosh(x)sinh(x) + (6a b cosh(x) + 2a b)sinh(x) +--R + +--R 2 3 2 2 4 2 2 +--R (4a b cosh(x) + 4a b cosh(x))sinh(x) + a b cosh(x) + 2a b cosh(x) +--R + +--R 2 +--R a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 4 2 3 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 6a b cosh(x) - 2a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (- 4a b cosh(x) - 4a b cosh(x))sinh(x) - a b cosh(x) +--R + +--R 2 2 2 +--R - 2a b cosh(x) - a b +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 4 2 3 3 +--R (- a b + a )sinh(x) + (- 4a b + 4a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 6a b + 6a )cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 3 3 2 3 +--R ((- 4a b + 4a )cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R (- a b + a )cosh(x) + (- 2a b + 2a )cosh(x) - a b + a +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 3 2 3 3 2 2 +--R (a b + a )sinh(x) + ((3a b + 3a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 3 2 3 2 2 3 +--R ((3a b + 3a )cosh(x) + (- 4b - 4a b)cosh(x) - a b - a )sinh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (a b + a )cosh(x) + (- 2b - 2a b)cosh(x) + (- a b - a )cosh(x) +--R / +--R 4 2 2 4 4 4 2 2 4 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 2 +--R ((6b + 12a b + 6a )cosh(x) + 2b + 4a b + 2a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((4b + 8a b + 4a )cosh(x) + (4b + 8a b + 4a )cosh(x))sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 4 2 2 4 +--R (b + 2a b + a )cosh(x) + (2b + 4a b + 2a )cosh(x) + b + 2a b + a +--R Type: Union(Expression(Integer),...) +--E 509 + +--S 510 of 526 +m0696:= a0696-r0696 +--R +--R +--R (507) +--R 2 2 4 2 3 3 +--R 2a b cosh(x) sinh(x) + 8a b cosh(x) sinh(x) +--R + +--R 2 4 2 2 2 +--R (12a b cosh(x) + 4a b cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 6 +--R (8a b cosh(x) + 8a b cosh(x) )sinh(x) + 2a b cosh(x) +--R + +--R 2 4 2 2 +--R 4a b cosh(x) + 2a b cosh(x) +--R * +--R log(a sinh(x) + b) +--R + +--R 2 2 4 2 3 3 +--R - a b cosh(x) sinh(x) - 4a b cosh(x) sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 6a b cosh(x) - 2a b cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 6 +--R (- 4a b cosh(x) - 4a b cosh(x) )sinh(x) - a b cosh(x) +--R + +--R 2 4 2 2 +--R - 2a b cosh(x) - a b cosh(x) +--R * +--R 2 +--R log(cosh(x) ) +--R + +--R 2 2 4 2 3 3 +--R 2a b cosh(x) sinh(x) + 8a b cosh(x) sinh(x) +--R + +--R 2 4 2 2 2 +--R (12a b cosh(x) + 4a b cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 6 +--R (8a b cosh(x) + 8a b cosh(x) )sinh(x) + 2a b cosh(x) +--R + +--R 2 4 2 2 +--R 4a b cosh(x) + 2a b cosh(x) +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 4 2 3 3 +--R - 2a b cosh(x) sinh(x) - 8a b cosh(x) sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 12a b cosh(x) - 4a b cosh(x) )sinh(x) +--R + +--R 2 5 2 3 2 6 +--R (- 8a b cosh(x) - 8a b cosh(x) )sinh(x) - 2a b cosh(x) +--R + +--R 2 4 2 2 +--R - 4a b cosh(x) - 2a b cosh(x) +--R * +--R - 2a sinh(x) - 2b +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 4 2 3 3 3 +--R (- 2a b + 2a )cosh(x) sinh(x) + (- 8a b + 8a )cosh(x) sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R ((- 12a b + 12a )cosh(x) + (- 4a b + 4a )cosh(x) )sinh(x) +--R + +--R 2 3 5 2 3 3 +--R ((- 8a b + 8a )cosh(x) + (- 8a b + 8a )cosh(x) )sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (- 2a b + 2a )cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 2 3 2 +--R (- 2a b + 2a )cosh(x) +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 4 2 3 3 3 +--R (a b - a )cosh(x) sinh(x) + (4a b - 4a )cosh(x) sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R ((6a b - 6a )cosh(x) + (2a b - 2a )cosh(x) )sinh(x) +--R + +--R 2 3 5 2 3 3 +--R ((4a b - 4a )cosh(x) + (4a b - 4a )cosh(x) )sinh(x) +--R + +--R 2 3 6 2 3 4 2 3 2 +--R (a b - a )cosh(x) + (2a b - 2a )cosh(x) + (a b - a )cosh(x) +--R * +--R atan(sinh(x)) +--R + +--R 2 3 5 2 3 3 2 4 +--R (- a b - a )sinh(x) + ((- 4a b - 4a )cosh(x) + b + a b)sinh(x) +--R + +--R 2 3 2 3 2 2 3 3 +--R ((- 4a b - 4a )cosh(x) + (4b + 4a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 2 3 3 3 2 2 2 3 +--R (2a b + 2a )cosh(x) + (2b + 2a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 2 +--R 2b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 +--R (5a b + 5a )cosh(x) + (- 4b - 4a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 4a b - 4a )cosh(x) + (4b + 4a b)cosh(x) - a b - a +--R * +--R sinh(x) +--R + +--R 2 3 5 3 2 4 2 3 3 +--R (2a b + 2a )cosh(x) + (- 3b - 3a b)cosh(x) + (- 2a b - 2a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (2b + 2a b)cosh(x) + b + a b +--R / +--R 4 2 2 4 2 4 +--R (2b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 3 3 +--R (8b + 16a b + 8a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 2 +--R ((12b + 24a b + 12a )cosh(x) + (4b + 8a b + 4a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R ((8b + 16a b + 8a )cosh(x) + (8b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (2b + 4a b + 2a )cosh(x) + (4b + 8a b + 4a )cosh(x) +--R + +--R 4 2 2 4 2 +--R (2b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 510 + +--S 511 of 526 +d0696:= D(m0696,x) +--R +--R +--R (508) +--R 2 3 10 2 3 3 2 9 +--R (2a b + 2a )sinh(x) + ((12a b + 12a )cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 2 3 2 3 2 2 3 8 +--R ((29a b + 29a )cosh(x) + (- 12b - 12a b)cosh(x) + 8a b + 8a )sinh(x) +--R + +--R 2 3 3 3 2 2 +--R (30a b + 34a )cosh(x) + (- 30b - 30a b)cosh(x) +--R + +--R 2 3 3 2 +--R (36a b + 36a )cosh(x) - 8b - 8a b +--R * +--R 7 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 +--R (- 4a b + 14a )cosh(x) + (- 32b - 32a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (62a b + 62a )cosh(x) + (- 36b - 36a b)cosh(x) + 12a b + 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 5 3 2 4 +--R (- 42a b - 14a )cosh(x) + (2b + 2a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (50a b + 62a )cosh(x) + (- 66b - 66a b)cosh(x) +--R + +--R 2 3 3 2 +--R (36a b + 36a )cosh(x) - 12b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 6 3 2 5 +--R (- 38a b - 28a )cosh(x) + (36b + 36a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (10a b + 48a )cosh(x) + (- 64b - 64a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (36a b + 36a )cosh(x) + (- 36b - 36a b)cosh(x) + 8a b + 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 7 3 2 6 +--R (- 6a b - 26a )cosh(x) + (30b + 30a b)cosh(x) +--R + +--R 2 3 5 3 2 4 +--R (- 24a b + 16a )cosh(x) + (- 20b - 20a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (10a b + 22a )cosh(x) + (- 42b - 42a b)cosh(x) +--R + +--R 2 3 3 2 +--R (12a b + 12a )cosh(x) - 8b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 8 3 2 7 +--R (10a b - 16a )cosh(x) + (8b + 8a b)cosh(x) +--R + +--R 2 3 6 3 2 5 +--R (- 30a b - 18a )cosh(x) + (28b + 28a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (8a b + 30a )cosh(x) + (- 32b - 32a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (2a b + 2a )cosh(x) + (- 12b - 12a b)cosh(x) + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 9 2 3 7 +--R (6a b - 6a )cosh(x) + (- 14a b - 18a )cosh(x) +--R + +--R 3 2 6 2 3 5 +--R (30b + 30a b)cosh(x) + (18a b + 30a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 22b - 22a b)cosh(x) + (- 10a b - 6a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 6b - 6a b)cosh(x) - 2b - 2a b +--R * +--R sinh(x) +--R + +--R 2 3 10 2 3 8 3 2 7 +--R (a b - a )cosh(x) + (- 2a b - 4a )cosh(x) + (8b + 8a b)cosh(x) +--R + +--R 2 3 6 3 2 5 2 3 4 +--R (8a b + 10a )cosh(x) + (- 8b - 8a b)cosh(x) + (- 6a b - 4a )cosh(x) +--R + +--R 2 3 2 +--R (- a b - a )cosh(x) +--R / +--R 4 2 2 4 3 8 +--R (2b + 4a b + 2a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 4 7 +--R (12b + 24a b + 12a )cosh(x) sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 6 +--R ((30b + 60a b + 30a )cosh(x) + (8b + 16a b + 8a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 5 +--R ((40b + 80a b + 40a )cosh(x) + (36b + 72a b + 36a )cosh(x) )sinh(x) +--R + +--R 4 2 2 4 7 4 2 2 4 5 +--R (30b + 60a b + 30a )cosh(x) + (66b + 132a b + 66a )cosh(x) +--R + +--R 4 2 2 4 3 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (64b + 128a b + 64a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (36b + 72a b + 36a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (42b + 84a b + 42a )cosh(x) + (8b + 16a b + 8a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 8 4 2 2 4 6 +--R (12b + 24a b + 12a )cosh(x) + (24b + 48a b + 24a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (12b + 24a b + 12a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 9 4 2 2 4 7 +--R (2b + 4a b + 2a )cosh(x) + (6b + 12a b + 6a )cosh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (6b + 12a b + 6a )cosh(x) + (2b + 4a b + 2a )cosh(x) +--R Type: Expression(Integer) +--E 511 + +--S 512 of 526 +t0697:= sech(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R sech(x) +--R (509) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 512 + +--S 513 of 526 +r0697:= 2*a^3*b*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ + a^2*b*sech(x)/(a^2+b^2)^2-b*sech(x)^3/(3*a^2+3*b^2)-_ + a*b^2*tanh(x)/(a^2+b^2)^2+a*tanh(x)/(a^2+b^2)-a*tanh(x)^3/(3*a^2+3*b^2) +--R +--R +--R (510) +--R x +--R b tanh(-) - a +--R 3 2 +--R - 6a b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 3 3 3 2 3 +--R (- a b - a )tanh(x) + 3a tanh(x) + (- b - a b)sech(x) +--R + +--R 2 +--R - 3a b sech(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 513 + +--S 514 of 526 +a0697:= integrate(t0697,x) +--R +--R +--R (511) +--R 3 6 3 5 +--R 3a b sinh(x) + 18a b cosh(x)sinh(x) +--R + +--R 3 2 3 4 +--R (45a b cosh(x) + 9a b)sinh(x) +--R + +--R 3 3 3 3 +--R (60a b cosh(x) + 36a b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (45a b cosh(x) + 54a b cosh(x) + 9a b)sinh(x) +--R + +--R 3 5 3 3 3 +--R (18a b cosh(x) + 36a b cosh(x) + 18a b cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 +--R 3a b cosh(x) + 9a b cosh(x) + 9a b cosh(x) + 3a b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 5 2 2 4 +--R - 6a b sinh(x) + (- 30a b cosh(x) + 6a b )sinh(x) +--R + +--R 2 2 2 3 2 3 +--R (- 60a b cosh(x) + 24a b cosh(x) - 8b - 20a b)sinh(x) +--R + +--R 2 3 2 2 3 2 +--R - 60a b cosh(x) + 36a b cosh(x) + (- 24b - 60a b)cosh(x) +--R + +--R 3 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 3 3 2 2 +--R - 30a b cosh(x) + 24a b cosh(x) + (- 24b - 60a b)cosh(x) +--R + +--R 3 2 +--R - 24a cosh(x) - 6a b +--R * +--R sinh(x) +--R + +--R 2 5 2 4 3 2 3 +--R - 6a b cosh(x) + 6a b cosh(x) + (- 8b - 20a b)cosh(x) +--R + +--R 3 2 2 2 3 +--R - 12a cosh(x) - 6a b cosh(x) + 2a b - 4a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 2 4 6 4 2 2 4 5 +--R (3b + 6a b + 3a )sinh(x) + (18b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 4 +--R ((45b + 90a b + 45a )cosh(x) + 9b + 18a b + 9a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((60b + 120a b + 60a )cosh(x) + (36b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (45b + 90a b + 45a )cosh(x) + (54b + 108a b + 54a )cosh(x) +--R + +--R 4 2 2 4 +--R 9b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (18b + 36a b + 18a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 +--R (18b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (3b + 6a b + 3a )cosh(x) + (9b + 18a b + 9a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (9b + 18a b + 9a )cosh(x) + 3b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 514 + +--S 515 of 526 +m0697:= a0697-r0697 +--R +--R +--R (512) +--R 3 6 3 5 +--R 3a b sinh(x) + 18a b cosh(x)sinh(x) +--R + +--R 3 2 3 4 +--R (45a b cosh(x) + 9a b)sinh(x) +--R + +--R 3 3 3 3 +--R (60a b cosh(x) + 36a b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (45a b cosh(x) + 54a b cosh(x) + 9a b)sinh(x) +--R + +--R 3 5 3 3 3 +--R (18a b cosh(x) + 36a b cosh(x) + 18a b cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 +--R 3a b cosh(x) + 9a b cosh(x) + 9a b cosh(x) + 3a b +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 3 6 3 5 +--R 6a b sinh(x) + 36a b cosh(x)sinh(x) +--R + +--R 3 2 3 4 +--R (90a b cosh(x) + 18a b)sinh(x) +--R + +--R 3 3 3 3 +--R (120a b cosh(x) + 72a b cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (90a b cosh(x) + 108a b cosh(x) + 18a b)sinh(x) +--R + +--R 3 5 3 3 3 +--R (36a b cosh(x) + 72a b cosh(x) + 36a b cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 +--R 6a b cosh(x) + 18a b cosh(x) + 18a b cosh(x) + 6a b +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 6 2 3 5 +--R (a b + a )sinh(x) + (6a b + 6a )cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 4 +--R ((15a b + 15a )cosh(x) + 3a b + 3a )sinh(x) +--R + +--R 2 3 3 2 3 3 +--R ((20a b + 20a )cosh(x) + (12a b + 12a )cosh(x))sinh(x) +--R + +--R 2 3 4 2 3 2 2 +--R (15a b + 15a )cosh(x) + (18a b + 18a )cosh(x) + 3a b +--R + +--R 3 +--R 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 2 3 3 +--R (6a b + 6a )cosh(x) + (12a b + 12a )cosh(x) +--R + +--R 2 3 +--R (6a b + 6a )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 6 2 3 4 +--R (a b + a )cosh(x) + (3a b + 3a )cosh(x) +--R + +--R 2 3 2 2 3 +--R (3a b + 3a )cosh(x) + a b + a +--R * +--R 3 +--R tanh(x) +--R + +--R 3 6 3 5 +--R - 3a sinh(x) - 18a cosh(x)sinh(x) +--R + +--R 3 2 3 4 +--R (- 45a cosh(x) - 9a )sinh(x) +--R + +--R 3 3 3 3 +--R (- 60a cosh(x) - 36a cosh(x))sinh(x) +--R + +--R 3 4 3 2 3 2 +--R (- 45a cosh(x) - 54a cosh(x) - 9a )sinh(x) +--R + +--R 3 5 3 3 3 +--R (- 18a cosh(x) - 36a cosh(x) - 18a cosh(x))sinh(x) +--R + +--R 3 6 3 4 3 2 3 +--R - 3a cosh(x) - 9a cosh(x) - 9a cosh(x) - 3a +--R * +--R tanh(x) +--R + +--R 3 2 3 2 6 +--R ((b + a b)sech(x) + 3a b sech(x))sinh(x) +--R + +--R 3 2 3 2 2 5 +--R ((6b + 6a b)cosh(x)sech(x) + 18a b cosh(x)sech(x) - 6a b)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R ((15b + 15a b)cosh(x) + 3b + 3a b)sech(x) +--R + +--R 2 2 2 2 2 +--R (45a b cosh(x) + 9a b)sech(x) - 30a b cosh(x) + 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 3 2 3 +--R ((20b + 20a b)cosh(x) + (12b + 12a b)cosh(x))sech(x) +--R + +--R 2 3 2 2 2 +--R (60a b cosh(x) + 36a b cosh(x))sech(x) - 60a b cosh(x) +--R + +--R 2 3 2 +--R 24a b cosh(x) - 8b - 20a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R ((15b + 15a b)cosh(x) + (18b + 18a b)cosh(x) + 3b + 3a b) +--R * +--R 3 +--R sech(x) +--R + +--R 2 4 2 2 2 2 3 +--R (45a b cosh(x) + 54a b cosh(x) + 9a b)sech(x) - 60a b cosh(x) +--R + +--R 2 2 3 2 3 +--R 36a b cosh(x) + (- 24b - 60a b)cosh(x) - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 3 +--R (6b + 6a b)cosh(x) + (12b + 12a b)cosh(x) +--R + +--R 3 2 +--R (6b + 6a b)cosh(x) +--R * +--R 3 +--R sech(x) +--R + +--R 2 5 2 3 2 +--R (18a b cosh(x) + 36a b cosh(x) + 18a b cosh(x))sech(x) +--R + +--R 2 4 2 3 3 2 2 +--R - 30a b cosh(x) + 24a b cosh(x) + (- 24b - 60a b)cosh(x) +--R + +--R 3 2 +--R - 24a cosh(x) - 6a b +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R (b + a b)cosh(x) + (3b + 3a b)cosh(x) + (3b + 3a b)cosh(x) +--R + +--R 3 2 +--R b + a b +--R * +--R 3 +--R sech(x) +--R + +--R 2 6 2 4 2 2 2 +--R (3a b cosh(x) + 9a b cosh(x) + 9a b cosh(x) + 3a b)sech(x) +--R + +--R 2 5 2 4 3 2 3 +--R - 6a b cosh(x) + 6a b cosh(x) + (- 8b - 20a b)cosh(x) +--R + +--R 3 2 2 2 3 +--R - 12a cosh(x) - 6a b cosh(x) + 2a b - 4a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 2 2 4 6 4 2 2 4 5 +--R (3b + 6a b + 3a )sinh(x) + (18b + 36a b + 18a )cosh(x)sinh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 4 +--R ((45b + 90a b + 45a )cosh(x) + 9b + 18a b + 9a )sinh(x) +--R + +--R 4 2 2 4 3 4 2 2 4 +--R ((60b + 120a b + 60a )cosh(x) + (36b + 72a b + 36a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (45b + 90a b + 45a )cosh(x) + (54b + 108a b + 54a )cosh(x) +--R + +--R 4 2 2 4 +--R 9b + 18a b + 9a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 5 4 2 2 4 3 +--R (18b + 36a b + 18a )cosh(x) + (36b + 72a b + 36a )cosh(x) +--R + +--R 4 2 2 4 +--R (18b + 36a b + 18a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 2 4 6 4 2 2 4 4 +--R (3b + 6a b + 3a )cosh(x) + (9b + 18a b + 9a )cosh(x) +--R + +--R 4 2 2 4 2 4 2 2 4 +--R (9b + 18a b + 9a )cosh(x) + 3b + 6a b + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 515 + +--S 516 of 526 +--d0697:= D(m0697,x) +--E 516 + +--S 517 of 526 +t0698:= sech(x)/(%i+csch(x)) +--R +--R +--R sech(x) +--R (513) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 517 + +--S 518 of 526 +r0698:= -1/2*%i*atan(sinh(x))-%i/(2*%i-2*sinh(x)) +--R +--R +--R 1 1 1 +--R (- - %i sinh(x) - -)atan(sinh(x)) + - %i +--R 2 2 2 +--R (514) ---------------------------------------- +--R sinh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 518 + +--S 519 of 526 +a0698:= integrate(t0698,x) +--R +--R +--R (515) +--R 2 2 +--R (sinh(x) + (2cosh(x) - 2%i)sinh(x) + cosh(x) - 2%i cosh(x) - 1) +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 2 2 +--R (- sinh(x) + (- 2cosh(x) + 2%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1) +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 2%i sinh(x) + 2%i cosh(x) +--R / +--R 2 2 +--R 2sinh(x) + (4cosh(x) - 4%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2 +--R Type: Union(Expression(Complex(Integer)),...) +--E 519 + +--S 520 of 526 +m0698:= a0698-r0698 +--R +--R +--R (516) +--R 1 3 3 2 +--R - sinh(x) + (cosh(x) - - %i)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 1 +--R (- cosh(x) - 2%i cosh(x) - -)sinh(x) - - %i cosh(x) - cosh(x) + - %i +--R 2 2 2 2 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 1 3 3 2 +--R - - sinh(x) + (- cosh(x) + - %i)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 +--R (- - cosh(x) + 2%i cosh(x) + -)sinh(x) + - %i cosh(x) + cosh(x) +--R 2 2 2 +--R + +--R 1 +--R - - %i +--R 2 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 1 3 3 2 +--R - %i sinh(x) + (%i cosh(x) + -)sinh(x) +--R 2 2 +--R + +--R 1 2 3 1 2 1 +--R (- %i cosh(x) + 2cosh(x) - - %i)sinh(x) + - cosh(x) - %i cosh(x) - - +--R 2 2 2 2 +--R * +--R atan(sinh(x)) +--R + +--R 1 2 1 2 1 +--R - %i sinh(x) - - %i cosh(x) + - %i +--R 2 2 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) - 3%i)sinh(x) + (cosh(x) - 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2cosh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 520 + +--S 521 of 526 +d0698:= D(m0698,x) +--R +--R +--R (517) +--R 6 5 +--R - 2%i sinh(x) + (- 5%i cosh(x) - 2)sinh(x) +--R + +--R 2 4 +--R (- 2%i cosh(x) - 4cosh(x))sinh(x) +--R + +--R 3 3 +--R (4%i cosh(x) - 4%i cosh(x))sinh(x) +--R + +--R 4 3 2 2 +--R (4%i cosh(x) + 4cosh(x) - 6%i cosh(x) - 2cosh(x) + 2%i)sinh(x) +--R + +--R 5 4 3 2 +--R (%i cosh(x) + 2cosh(x) - 2%i cosh(x) - 4cosh(x) + %i cosh(x) + 2) +--R * +--R sinh(x) +--R + +--R 3 +--R - 2cosh(x) + 2cosh(x) +--R / +--R 7 6 +--R sinh(x) + (4cosh(x) - 3%i)sinh(x) +--R + +--R 2 5 +--R (6cosh(x) - 10%i cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 12%i cosh(x) - 2cosh(x) - 5%i)sinh(x) +--R + +--R 4 3 3 +--R (cosh(x) - 6%i cosh(x) - 12%i cosh(x) - 5)sinh(x) +--R + +--R 4 3 2 2 +--R (- %i cosh(x) + 2cosh(x) - 12%i cosh(x) - 8cosh(x) - %i)sinh(x) +--R + +--R 4 3 2 +--R (cosh(x) - 6%i cosh(x) - 6cosh(x) - 2%i cosh(x) - 3)sinh(x) +--R + +--R 4 3 +--R - %i cosh(x) - 2cosh(x) - 2cosh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 521 + +--S 522 of 526 +t0699:= sech(x)^2/(%i+csch(x)) +--R +--R +--R 2 +--R sech(x) +--R (518) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 522 + +--S 523 of 526 +r0699:= -1/3/cosh(x)^3*(%i*sinh(x)*cosh(x)^2-%i*sinh(x)+1) +--R +--R +--R 2 +--R (- %i cosh(x) + %i)sinh(x) - 1 +--R (519) ------------------------------- +--R 3 +--R 3cosh(x) +--R Type: Expression(Complex(Integer)) +--E 523 + +--S 524 of 526 +a0699:= integrate(t0699,x) +--R +--R +--R (520) +--R 8%i sinh(x) + 4%i cosh(x) + 4 +--R / +--R 3 2 +--R 3sinh(x) + (9cosh(x) - 6%i)sinh(x) +--R + +--R 2 3 2 +--R (9cosh(x) - 12%i cosh(x) + 3)sinh(x) + 3cosh(x) - 6%i cosh(x) +--R + +--R - 3cosh(x) - 6%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 524 + +--S 525 of 526 +m0699:= a0699-r0699 +--R +--R +--R (521) +--R 2 4 +--R (%i cosh(x) - %i)sinh(x) +--R + +--R 3 2 3 +--R (3%i cosh(x) + 2cosh(x) - 3%i cosh(x) - 1)sinh(x) +--R + +--R 4 3 2 2 +--R (3%i cosh(x) + 4cosh(x) - 2%i cosh(x) - cosh(x) - 3%i)sinh(x) +--R + +--R 5 4 3 2 +--R (%i cosh(x) + 2cosh(x) + 6%i cosh(x) + 3cosh(x) - 3%i cosh(x) - 1) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R 4%i cosh(x) + 5cosh(x) - 2%i cosh(x) - cosh(x) - 2%i +--R / +--R 3 3 4 3 2 +--R 3cosh(x) sinh(x) + (9cosh(x) - 6%i cosh(x) )sinh(x) +--R + +--R 5 4 3 6 5 +--R (9cosh(x) - 12%i cosh(x) + 3cosh(x) )sinh(x) + 3cosh(x) - 6%i cosh(x) +--R + +--R 4 3 +--R - 3cosh(x) - 6%i cosh(x) +--R Type: Expression(Complex(Integer)) +--E 525 + +--S 526 of 526 +d0699:= D(m0699,x) +--R +--R +--R (522) +--R 2 8 +--R (- %i cosh(x) + 3%i)sinh(x) +--R + +--R 3 2 7 +--R (- 6%i cosh(x) - 4cosh(x) + 18%i cosh(x) + 9)sinh(x) +--R + +--R 4 3 2 6 +--R (- 14%i cosh(x) - 20cosh(x) + 46%i cosh(x) + 42cosh(x) + 6%i)sinh(x) +--R + +--R 5 4 3 2 +--R - 14%i cosh(x) - 36cosh(x) + 66%i cosh(x) + 63cosh(x) +--R + +--R 24%i cosh(x) + 30 +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 20cosh(x) + 32%i cosh(x) + 24cosh(x) + 57%i cosh(x) + 84cosh(x) +--R + +--R 3%i +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 14%i cosh(x) + 20cosh(x) - 58%i cosh(x) - 61cosh(x) +--R + +--R 3 2 +--R 90%i cosh(x) + 84cosh(x) - 6%i cosh(x) + 33 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 14%i cosh(x) + 36cosh(x) - 102%i cosh(x) - 114cosh(x) +--R + +--R 4 3 2 +--R 94%i cosh(x) + 48cosh(x) + 14%i cosh(x) + 42cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 6%i cosh(x) + 20cosh(x) - 58%i cosh(x) - 75cosh(x) +--R + +--R 5 4 3 2 +--R 46%i cosh(x) + 26cosh(x) + 18%i cosh(x) + 17cosh(x) +--R + +--R - 12%i cosh(x) + 12 +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R %i cosh(x) + 4cosh(x) - 11%i cosh(x) - 16cosh(x) + 3%i cosh(x) +--R + +--R 5 4 3 2 +--R 8cosh(x) + 3%i cosh(x) + 4cosh(x) + 4%i cosh(x) +--R / +--R 4 6 5 4 5 +--R 3cosh(x) sinh(x) + (18cosh(x) - 12%i cosh(x) )sinh(x) +--R + +--R 6 5 4 4 +--R (45cosh(x) - 60%i cosh(x) - 6cosh(x) )sinh(x) +--R + +--R 7 6 5 4 3 +--R (60cosh(x) - 120%i cosh(x) - 36cosh(x) - 24%i cosh(x) )sinh(x) +--R + +--R 8 7 6 5 4 +--R (45cosh(x) - 120%i cosh(x) - 72cosh(x) - 48%i cosh(x) - 21cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R 18cosh(x) - 60%i cosh(x) - 60cosh(x) - 24%i cosh(x) - 54cosh(x) +--R + +--R 4 +--R - 12%i cosh(x) +--R * +--R sinh(x) +--R + +--R 10 9 8 6 5 +--R 3cosh(x) - 12%i cosh(x) - 18cosh(x) - 21cosh(x) + 12%i cosh(x) +--R + +--R 4 +--R - 12cosh(x) +--R Type: Expression(Complex(Integer)) +--E 526 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper600-699.input.pdf b/src/axiom-website/CATS/richhyper600-699.input.pdf new file mode 100644 index 0000000..3e9a480 Binary files /dev/null and b/src/axiom-website/CATS/richhyper600-699.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper700-799.input.pamphlet b/src/axiom-website/CATS/richhyper700-799.input.pamphlet new file mode 100644 index 0000000..15537ca --- /dev/null +++ b/src/axiom-website/CATS/richhyper700-799.input.pamphlet @@ -0,0 +1,46214 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper700-799.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper700-799.output +)spool richhyper700-799.output +)set message auto off +)clear all + +--S 1 of 552 +t0700:= sech(x)^3/(%i+csch(x)) +--R +--R +--R 3 +--R sech(x) +--R (1) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 1 + +--S 2 of 552 +r0700:= -1/8*%i*atan(sinh(x))+1/8/(%i-sinh(x))^2-%i/(8*%i+8*sinh(x)) +--R +--R +--R (2) +--R 1 3 1 2 1 1 +--R (- - %i sinh(x) - - sinh(x) - - %i sinh(x) - -)atan(sinh(x)) +--R 8 8 8 8 +--R + +--R 1 2 1 1 +--R - - %i sinh(x) - - sinh(x) + - %i +--R 8 8 4 +--R / +--R 3 2 +--R sinh(x) - %i sinh(x) + sinh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 2 + +--S 3 of 552 +a0700:= integrate(t0700,x) +--R +--R +--R (3) +--R 6 5 +--R sinh(x) + (6cosh(x) - 2%i)sinh(x) +--R + +--R 2 4 +--R (15cosh(x) - 10%i cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 +--R (20cosh(x) - 20%i cosh(x) + 4cosh(x) - 4%i)sinh(x) +--R + +--R 4 3 2 2 +--R (15cosh(x) - 20%i cosh(x) + 6cosh(x) - 12%i cosh(x) - 1)sinh(x) +--R + +--R 5 4 3 2 +--R 6cosh(x) - 10%i cosh(x) + 4cosh(x) - 12%i cosh(x) - 2cosh(x) +--R + +--R - 2%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) - 2%i cosh(x) + cosh(x) - 4%i cosh(x) - cosh(x) +--R + +--R - 2%i cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 6 5 +--R - sinh(x) + (- 6cosh(x) + 2%i)sinh(x) +--R + +--R 2 4 +--R (- 15cosh(x) + 10%i cosh(x) - 1)sinh(x) +--R + +--R 3 2 3 +--R (- 20cosh(x) + 20%i cosh(x) - 4cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 2 +--R (- 15cosh(x) + 20%i cosh(x) - 6cosh(x) + 12%i cosh(x) + 1)sinh(x) +--R + +--R 5 4 3 2 +--R - 6cosh(x) + 10%i cosh(x) - 4cosh(x) + 12%i cosh(x) +--R + +--R 2cosh(x) + 2%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - cosh(x) + 2%i cosh(x) - cosh(x) + 4%i cosh(x) + cosh(x) +--R + +--R 2%i cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 5 4 +--R - 2%i sinh(x) + (- 10%i cosh(x) - 4)sinh(x) +--R + +--R 2 3 +--R (- 20%i cosh(x) - 16cosh(x) + 20%i)sinh(x) +--R + +--R 3 2 2 +--R (- 20%i cosh(x) - 24cosh(x) + 60%i cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 +--R (- 10%i cosh(x) - 16cosh(x) + 60%i cosh(x) + 8cosh(x) - 2%i)sinh(x) +--R + +--R 5 4 3 2 +--R - 2%i cosh(x) - 4cosh(x) + 20%i cosh(x) + 4cosh(x) - 2%i cosh(x) +--R / +--R 6 5 +--R 8sinh(x) + (48cosh(x) - 16%i)sinh(x) +--R + +--R 2 4 +--R (120cosh(x) - 80%i cosh(x) + 8)sinh(x) +--R + +--R 3 2 3 +--R (160cosh(x) - 160%i cosh(x) + 32cosh(x) - 32%i)sinh(x) +--R + +--R 4 3 2 2 +--R (120cosh(x) - 160%i cosh(x) + 48cosh(x) - 96%i cosh(x) - 8)sinh(x) +--R + +--R 5 4 3 2 +--R 48cosh(x) - 80%i cosh(x) + 32cosh(x) - 96%i cosh(x) - 16cosh(x) +--R + +--R - 16%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 8cosh(x) - 16%i cosh(x) + 8cosh(x) - 32%i cosh(x) - 8cosh(x) +--R + +--R - 16%i cosh(x) - 8 +--R Type: Union(Expression(Complex(Integer)),...) +--E 3 + +--S 4 of 552 +m0700:= a0700-r0700 +--R +--R +--R (4) +--R 1 9 3 3 8 +--R - sinh(x) + (- cosh(x) - - %i)sinh(x) +--R 8 4 8 +--R + +--R 15 2 7 +--R (-- cosh(x) - 2%i cosh(x))sinh(x) +--R 8 +--R + +--R 5 3 35 2 6 +--R (- cosh(x) - -- %i cosh(x) - %i)sinh(x) +--R 2 8 +--R + +--R 15 4 3 1 2 3 5 +--R (-- cosh(x) - 5%i cosh(x) + - cosh(x) - 4%i cosh(x) - -)sinh(x) +--R 8 8 4 +--R + +--R 3 5 25 4 1 3 53 2 +--R - cosh(x) - -- %i cosh(x) + - cosh(x) - -- %i cosh(x) +--R 4 8 2 8 +--R + +--R 5 3 +--R - - cosh(x) - - %i +--R 2 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 1 6 5 3 4 3 +--R - cosh(x) - %i cosh(x) + - cosh(x) - 6%i cosh(x) +--R 8 4 +--R + +--R 27 2 +--R - -- cosh(x) - 2%i cosh(x) - 1 +--R 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 6 1 5 13 4 5 3 +--R - - %i cosh(x) + - cosh(x) - -- %i cosh(x) - - cosh(x) +--R 8 2 4 2 +--R + +--R 17 2 +--R - -- %i cosh(x) - 2cosh(x) +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 6 5 9 4 3 13 2 +--R - cosh(x) - %i cosh(x) - - cosh(x) - %i cosh(x) - -- cosh(x) +--R 8 8 8 +--R + +--R 3 +--R - - +--R 8 +--R * +--R sinh(x) +--R + +--R 1 6 1 5 1 4 1 3 +--R - - %i cosh(x) - - cosh(x) - - %i cosh(x) - - cosh(x) +--R 8 4 8 2 +--R + +--R 1 2 1 1 +--R - %i cosh(x) - - cosh(x) + - %i +--R 8 4 8 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 1 9 3 3 8 +--R - - sinh(x) + (- - cosh(x) + - %i)sinh(x) +--R 8 4 8 +--R + +--R 15 2 7 +--R (- -- cosh(x) + 2%i cosh(x))sinh(x) +--R 8 +--R + +--R 5 3 35 2 6 +--R (- - cosh(x) + -- %i cosh(x) + %i)sinh(x) +--R 2 8 +--R + +--R 15 4 3 1 2 3 5 +--R (- -- cosh(x) + 5%i cosh(x) - - cosh(x) + 4%i cosh(x) + -)sinh(x) +--R 8 8 4 +--R + +--R 3 5 25 4 1 3 53 2 +--R - - cosh(x) + -- %i cosh(x) - - cosh(x) + -- %i cosh(x) +--R 4 8 2 8 +--R + +--R 5 3 +--R - cosh(x) + - %i +--R 2 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 1 6 5 3 4 3 +--R - - cosh(x) + %i cosh(x) - - cosh(x) + 6%i cosh(x) +--R 8 4 +--R + +--R 27 2 +--R -- cosh(x) + 2%i cosh(x) + 1 +--R 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 6 1 5 13 4 5 3 +--R - %i cosh(x) - - cosh(x) + -- %i cosh(x) + - cosh(x) +--R 8 2 4 2 +--R + +--R 17 2 +--R -- %i cosh(x) + 2cosh(x) +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 6 5 9 4 3 +--R - - cosh(x) + %i cosh(x) + - cosh(x) + %i cosh(x) +--R 8 8 +--R + +--R 13 2 3 +--R -- cosh(x) + - +--R 8 8 +--R * +--R sinh(x) +--R + +--R 1 6 1 5 1 4 1 3 +--R - %i cosh(x) + - cosh(x) + - %i cosh(x) + - cosh(x) +--R 8 4 8 2 +--R + +--R 1 2 1 1 +--R - - %i cosh(x) + - cosh(x) - - %i +--R 8 4 8 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 1 9 3 3 8 +--R - %i sinh(x) + (- %i cosh(x) + -)sinh(x) +--R 8 4 8 +--R + +--R 15 2 7 +--R (-- %i cosh(x) + 2cosh(x))sinh(x) +--R 8 +--R + +--R 5 3 35 2 6 +--R (- %i cosh(x) + -- cosh(x) + 1)sinh(x) +--R 2 8 +--R + +--R 15 4 3 1 2 3 +--R (-- %i cosh(x) + 5cosh(x) + - %i cosh(x) + 4cosh(x) - - %i) +--R 8 8 4 +--R * +--R 5 +--R sinh(x) +--R + +--R 3 5 25 4 1 3 53 2 +--R - %i cosh(x) + -- cosh(x) + - %i cosh(x) + -- cosh(x) +--R 4 8 2 8 +--R + +--R 5 3 +--R - - %i cosh(x) + - +--R 2 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 1 6 5 3 4 3 +--R - %i cosh(x) + cosh(x) + - %i cosh(x) + 6cosh(x) +--R 8 4 +--R + +--R 27 2 +--R - -- %i cosh(x) + 2cosh(x) - %i +--R 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 6 1 5 13 4 5 3 +--R - cosh(x) + - %i cosh(x) + -- cosh(x) - - %i cosh(x) +--R 8 2 4 2 +--R + +--R 17 2 +--R -- cosh(x) - 2%i cosh(x) +--R 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 6 5 9 4 3 +--R - %i cosh(x) + cosh(x) - - %i cosh(x) + cosh(x) +--R 8 8 +--R + +--R 13 2 3 +--R - -- %i cosh(x) - - %i +--R 8 8 +--R * +--R sinh(x) +--R + +--R 1 6 1 5 1 4 1 3 1 2 +--R - cosh(x) - - %i cosh(x) + - cosh(x) - - %i cosh(x) - - cosh(x) +--R 8 4 8 2 8 +--R + +--R 1 1 +--R - - %i cosh(x) - - +--R 4 8 +--R * +--R atan(sinh(x)) +--R + +--R 1 8 1 3 7 +--R - - %i sinh(x) + (- - %i cosh(x) - -)sinh(x) +--R 8 2 8 +--R + +--R 5 2 5 19 6 +--R (- - %i cosh(x) - - cosh(x) + -- %i)sinh(x) +--R 8 4 8 +--R + +--R 9 2 19 5 +--R (- - cosh(x) + 6%i cosh(x) + --)sinh(x) +--R 8 8 +--R + +--R 5 4 1 3 5 2 19 11 4 +--R (- %i cosh(x) + - cosh(x) + - %i cosh(x) + -- cosh(x) + -- %i)sinh(x) +--R 8 2 2 4 8 +--R + +--R 1 5 11 4 3 1 2 +--R - %i cosh(x) + -- cosh(x) - 5%i cosh(x) - - cosh(x) +--R 2 8 4 +--R + +--R 11 15 +--R -- %i cosh(x) + -- +--R 2 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 6 3 5 45 4 3 +--R - %i cosh(x) + - cosh(x) - -- %i cosh(x) - 6cosh(x) +--R 8 4 8 +--R + +--R 55 2 21 7 +--R -- %i cosh(x) + -- cosh(x) - - %i +--R 8 4 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 6 5 33 4 3 39 2 +--R - cosh(x) - 2%i cosh(x) - -- cosh(x) + 3%i cosh(x) + -- cosh(x) +--R 8 8 8 +--R + +--R 7 +--R - %i cosh(x) - - +--R 8 +--R * +--R sinh(x) +--R + +--R 1 6 3 5 1 4 3 3 1 2 +--R - - %i cosh(x) - - cosh(x) + - %i cosh(x) + - cosh(x) - - %i cosh(x) +--R 4 4 4 2 4 +--R + +--R 3 1 +--R - - cosh(x) + - %i +--R 4 4 +--R / +--R 9 8 2 7 +--R sinh(x) + (6cosh(x) - 3%i)sinh(x) + (15cosh(x) - 16%i cosh(x))sinh(x) +--R + +--R 3 2 6 +--R (20cosh(x) - 35%i cosh(x) - 8%i)sinh(x) +--R + +--R 4 3 2 5 +--R (15cosh(x) - 40%i cosh(x) + cosh(x) - 32%i cosh(x) - 6)sinh(x) +--R + +--R 5 4 3 2 +--R 6cosh(x) - 25%i cosh(x) + 4cosh(x) - 53%i cosh(x) - 20cosh(x) +--R + +--R - 6%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) - 8%i cosh(x) + 6cosh(x) - 48%i cosh(x) - 27cosh(x) +--R + +--R - 16%i cosh(x) - 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - %i cosh(x) + 4cosh(x) - 26%i cosh(x) - 20cosh(x) +--R + +--R 2 +--R - 17%i cosh(x) - 16cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R (cosh(x) - 8%i cosh(x) - 9cosh(x) - 8%i cosh(x) - 13cosh(x) - 3) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - %i cosh(x) - 2cosh(x) - %i cosh(x) - 4cosh(x) + %i cosh(x) +--R + +--R - 2cosh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 4 + +--S 5 of 552 +d0700:= D(m0700,x) +--R +--R +--R (5) +--R 10 9 +--R - 8%i sinh(x) + (- 39%i cosh(x) - 8)sinh(x) +--R + +--R 2 8 +--R (- 72%i cosh(x) - 38cosh(x) - 8%i)sinh(x) +--R + +--R 3 2 7 +--R (- 52%i cosh(x) - 66cosh(x) - 54%i cosh(x) - 8)sinh(x) +--R + +--R 4 3 2 6 +--R (16%i cosh(x) - 38cosh(x) - 124%i cosh(x) - 50cosh(x) + 8%i)sinh(x) +--R + +--R 5 4 3 2 +--R 62%i cosh(x) + 30cosh(x) - 122%i cosh(x) - 106cosh(x) +--R + +--R 8%i cosh(x) + 8 +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 56%i cosh(x) + 62cosh(x) - 40%i cosh(x) - 92cosh(x) +--R + +--R 2 +--R - 32%i cosh(x) + 14cosh(x) + 8%i +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 28%i cosh(x) + 42cosh(x) + 14%i cosh(x) - 20cosh(x) +--R + +--R 3 2 +--R - 64%i cosh(x) - 14cosh(x) + 22%i cosh(x) + 8 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 8%i cosh(x) + 14cosh(x) + 12%i cosh(x) + 14cosh(x) +--R + +--R 4 3 2 +--R - 40%i cosh(x) - 46cosh(x) + 20%i cosh(x) + 26cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R %i cosh(x) + 2cosh(x) + 2%i cosh(x) + 6cosh(x) - 8%i cosh(x) +--R + +--R 4 3 2 +--R - 34cosh(x) + 6%i cosh(x) + 26cosh(x) - %i cosh(x) +--R * +--R sinh(x) +--R + +--R 5 3 +--R - 8cosh(x) + 8cosh(x) +--R / +--R 13 12 +--R sinh(x) + (8cosh(x) - 3%i)sinh(x) +--R + +--R 2 11 +--R (28cosh(x) - 22%i cosh(x) + 2)sinh(x) +--R + +--R 3 2 10 +--R (56cosh(x) - 70%i cosh(x) + 14cosh(x) - 14%i)sinh(x) +--R + +--R 4 3 2 9 +--R (70cosh(x) - 126%i cosh(x) + 44cosh(x) - 86%i cosh(x) - 5)sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) - 140%i cosh(x) + 82cosh(x) - 230%i cosh(x) - 26cosh(x) +--R + +--R - 25%i +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) - 98%i cosh(x) + 100cosh(x) - 352%i cosh(x) +--R + +--R 2 +--R - 56cosh(x) - 124%i cosh(x) - 20 +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 8cosh(x) - 42%i cosh(x) + 82cosh(x) - 340%i cosh(x) - 64cosh(x) +--R + +--R 2 +--R - 268%i cosh(x) - 84cosh(x) - 20%i +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) - 10%i cosh(x) + 44cosh(x) - 214%i cosh(x) - 40cosh(x) +--R + +--R 3 2 +--R - 332%i cosh(x) - 152cosh(x) - 76%i cosh(x) - 25 +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - %i cosh(x) + 14cosh(x) - 86%i cosh(x) - 10cosh(x) +--R + +--R 4 3 2 +--R - 260%i cosh(x) - 156cosh(x) - 124%i cosh(x) - 76cosh(x) - 5%i +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 2cosh(x) - 20%i cosh(x) + 4cosh(x) - 134%i cosh(x) - 100cosh(x) +--R + +--R 3 2 +--R - 112%i cosh(x) - 100cosh(x) - 14%i cosh(x) - 14 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 2%i cosh(x) + 4cosh(x) - 46%i cosh(x) - 42cosh(x) +--R + +--R 4 3 2 +--R - 60%i cosh(x) - 72cosh(x) - 14%i cosh(x) - 26cosh(x) + 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) - 10%i cosh(x) - 12cosh(x) - 18%i cosh(x) - 30cosh(x) +--R + +--R 3 2 +--R - 6%i cosh(x) - 20cosh(x) + 2%i cosh(x) - 3 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 3 +--R - %i cosh(x) - 2cosh(x) - 2%i cosh(x) - 6cosh(x) - 6cosh(x) +--R + +--R 2 +--R 2%i cosh(x) - 2cosh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 5 + +--S 6 of 552 +t0701:= sech(x)^4/(%i+csch(x)) +--R +--R +--R 4 +--R sech(x) +--R (6) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 6 + +--S 7 of 552 +r0701:= -1/15/cosh(x)^5*(2*%i*cosh(x)^4*sinh(x)+%i*sinh(x)*cosh(x)^2-_ + 3*%i*sinh(x)+3) +--R +--R +--R 4 2 +--R (- 2%i cosh(x) - %i cosh(x) + 3%i)sinh(x) - 3 +--R (7) ----------------------------------------------- +--R 5 +--R 15cosh(x) +--R Type: Expression(Complex(Integer)) +--E 7 + +--S 8 of 552 +a0701:= integrate(t0701,x) +--R +--R +--R (8) +--R 2 2 +--R 56%i sinh(x) + (128%i cosh(x) + 16)sinh(x) + 56%i cosh(x) + 32cosh(x) +--R + +--R - 8%i +--R / +--R 6 5 +--R 15sinh(x) + (90cosh(x) - 30%i)sinh(x) +--R + +--R 2 4 +--R (225cosh(x) - 150%i cosh(x) + 30)sinh(x) +--R + +--R 3 2 3 +--R (300cosh(x) - 300%i cosh(x) + 120cosh(x) - 90%i)sinh(x) +--R + +--R 4 3 2 2 +--R (225cosh(x) - 300%i cosh(x) + 180cosh(x) - 270%i cosh(x) - 15)sinh(x) +--R + +--R 5 4 3 2 +--R 90cosh(x) - 150%i cosh(x) + 120cosh(x) - 270%i cosh(x) +--R + +--R 30cosh(x) - 60%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 15cosh(x) - 30%i cosh(x) + 30cosh(x) - 90%i cosh(x) - 15cosh(x) +--R + +--R - 120%i cosh(x) - 30 +--R Type: Union(Expression(Complex(Integer)),...) +--E 8 + +--S 9 of 552 +m0701:= a0701-r0701 +--R +--R +--R (9) +--R 4 2 7 +--R (2%i cosh(x) + %i cosh(x) - 3%i)sinh(x) +--R + +--R 5 4 3 2 +--R 12%i cosh(x) + 4cosh(x) + 6%i cosh(x) + 2cosh(x) - 18%i cosh(x) +--R + +--R - 3 +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 30%i cosh(x) + 20cosh(x) + 19%i cosh(x) + 10cosh(x) +--R + +--R 2 +--R - 43%i cosh(x) - 12cosh(x) - 12%i +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 40%i cosh(x) + 40cosh(x) + 36%i cosh(x) + 32cosh(x) +--R + +--R 3 2 +--R - 52%i cosh(x) - 9cosh(x) - 54%i cosh(x) - 12 +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 30%i cosh(x) + 40cosh(x) + 39%i cosh(x) + 56cosh(x) +--R + +--R 4 3 2 +--R - 35%i cosh(x) + 18cosh(x) - 97%i cosh(x) - 30cosh(x) - 15%i +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 12%i cosh(x) + 20cosh(x) + 22%i cosh(x) + 46cosh(x) +--R + +--R 5 4 3 2 +--R 50%i cosh(x) + 41cosh(x) - 82%i cosh(x) - 14cosh(x) +--R + +--R - 60%i cosh(x) - 15 +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 2%i cosh(x) + 4cosh(x) + 5%i cosh(x) + 14cosh(x) +--R + +--R 6 5 4 3 +--R 125%i cosh(x) + 50cosh(x) - 41%i cosh(x) + 14cosh(x) +--R + +--R 2 +--R - 53%i cosh(x) - 18cosh(x) - 6%i +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 56%i cosh(x) + 35cosh(x) - 14%i cosh(x) + 6cosh(x) - 18%i cosh(x) +--R + +--R 2 +--R - 3cosh(x) - 24%i cosh(x) - 6 +--R / +--R 5 6 6 5 5 +--R 15cosh(x) sinh(x) + (90cosh(x) - 30%i cosh(x) )sinh(x) +--R + +--R 7 6 5 4 +--R (225cosh(x) - 150%i cosh(x) + 30cosh(x) )sinh(x) +--R + +--R 8 7 6 5 3 +--R (300cosh(x) - 300%i cosh(x) + 120cosh(x) - 90%i cosh(x) )sinh(x) +--R + +--R 9 8 7 6 +--R 225cosh(x) - 300%i cosh(x) + 180cosh(x) - 270%i cosh(x) +--R + +--R 5 +--R - 15cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 90cosh(x) - 150%i cosh(x) + 120cosh(x) - 270%i cosh(x) +--R + +--R 6 5 +--R 30cosh(x) - 60%i cosh(x) +--R * +--R sinh(x) +--R + +--R 11 10 9 8 7 +--R 15cosh(x) - 30%i cosh(x) + 30cosh(x) - 90%i cosh(x) - 15cosh(x) +--R + +--R 6 5 +--R - 120%i cosh(x) - 30cosh(x) +--R Type: Expression(Complex(Integer)) +--E 9 + +--S 10 of 552 +d0701:= D(m0701,x) +--R +--R +--R (10) +--R 4 2 14 +--R (- 2%i cosh(x) - 3%i cosh(x) + 15%i)sinh(x) +--R + +--R 5 4 3 2 +--R - 24%i cosh(x) - 8cosh(x) - 36%i cosh(x) - 12cosh(x) +--R + +--R 180%i cosh(x) + 45 +--R * +--R 13 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 130%i cosh(x) - 88cosh(x) - 197%i cosh(x) - 132cosh(x) +--R + +--R 2 +--R 987%i cosh(x) + 480cosh(x) + 60%i +--R * +--R 12 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 416%i cosh(x) - 432cosh(x) - 648%i cosh(x) - 696cosh(x) +--R + +--R 3 2 +--R 3264%i cosh(x) + 2238cosh(x) + 660%i cosh(x) + 300 +--R * +--R 11 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 858%i cosh(x) - 1232cosh(x) - 1419%i cosh(x) - 2296cosh(x) +--R + +--R 4 3 2 +--R 7271%i cosh(x) + 5928cosh(x) + 3366%i cosh(x) + 2700cosh(x) - 30%i +--R * +--R 10 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - 1144%i cosh(x) - 2200cosh(x) - 2156%i cosh(x) - 5140cosh(x) +--R + +--R 5 4 3 2 +--R 11556%i cosh(x) + 9519cosh(x) + 10404%i cosh(x) + 10656cosh(x) +--R + +--R 180%i cosh(x) + 750 +--R * +--R 9 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 858%i cosh(x) - 2376cosh(x) - 2277%i cosh(x) - 7884cosh(x) +--R + +--R 6 5 4 3 +--R 13259%i cosh(x) + 8560cosh(x) + 21602%i cosh(x) + 24000cosh(x) +--R + +--R 2 +--R 2526%i cosh(x) + 5820cosh(x) - 480%i +--R * +--R 8 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 1056cosh(x) - 1584%i cosh(x) - 7824cosh(x) + 9600%i cosh(x) +--R + +--R 6 5 4 3 +--R 1316cosh(x) + 31608%i cosh(x) + 33528cosh(x) + 10104%i cosh(x) +--R + +--R 2 +--R 19188cosh(x) - 2100%i cosh(x) + 840 +--R * +--R 7 +--R sinh(x) +--R + +--R 12 11 10 9 +--R 858%i cosh(x) + 1056cosh(x) - 561%i cosh(x) - 3792cosh(x) +--R + +--R 8 7 6 5 +--R - 315%i cosh(x) - 8496cosh(x) + 32956%i cosh(x) + 29112cosh(x) +--R + +--R 4 3 2 +--R 21602%i cosh(x) + 34788cosh(x) - 2655%i cosh(x) + 6060cosh(x) +--R + +--R - 885%i +--R * +--R 6 +--R sinh(x) +--R + +--R 13 12 11 10 +--R 1144%i cosh(x) + 2376cosh(x) + 132%i cosh(x) + 1548cosh(x) +--R + +--R 9 8 7 6 +--R - 12644%i cosh(x) - 16277cosh(x) + 23544%i cosh(x) + 13888cosh(x) +--R + +--R 5 4 3 2 +--R 28440%i cosh(x) + 37608cosh(x) + 1848%i cosh(x) + 16368cosh(x) +--R + +--R - 3480%i cosh(x) + 345 +--R * +--R 5 +--R sinh(x) +--R + +--R 14 13 12 11 +--R 858%i cosh(x) + 2200cosh(x) + 297%i cosh(x) + 4260cosh(x) +--R + +--R 10 9 8 7 +--R - 19239%i cosh(x) - 19456cosh(x) + 9856%i cosh(x) + 64cosh(x) +--R + +--R 6 5 4 3 +--R 23650%i cosh(x) + 24308cosh(x) + 8699%i cosh(x) + 22044cosh(x) +--R + +--R 2 +--R - 4389%i cosh(x) + 3060cosh(x) - 660%i +--R * +--R 4 +--R sinh(x) +--R + +--R 15 14 13 12 +--R 416%i cosh(x) + 1232cosh(x) + 184%i cosh(x) + 3528cosh(x) +--R + +--R 11 10 9 8 +--R - 15936%i cosh(x) - 16450cosh(x) + 820%i cosh(x) - 5988cosh(x) +--R + +--R 7 6 5 4 +--R 12840%i cosh(x) + 8588cosh(x) + 10236%i cosh(x) + 15960cosh(x) +--R + +--R 3 2 +--R - 1536%i cosh(x) + 6534cosh(x) - 2160%i cosh(x) - 60 +--R * +--R 3 +--R sinh(x) +--R + +--R 16 15 14 13 +--R 130%i cosh(x) + 432cosh(x) + 63%i cosh(x) + 1608cosh(x) +--R + +--R 12 11 10 9 +--R - 7867%i cosh(x) - 9144cosh(x) - 1250%i cosh(x) - 5444cosh(x) +--R + +--R 8 7 6 5 +--R 5156%i cosh(x) + 1948cosh(x) + 5439%i cosh(x) + 6052cosh(x) +--R + +--R 4 3 2 +--R 1417%i cosh(x) + 5292cosh(x) - 1596%i cosh(x) + 600cosh(x) - 180%i +--R * +--R 2 +--R sinh(x) +--R + +--R 17 16 15 14 +--R 24%i cosh(x) + 88cosh(x) + 12%i cosh(x) + 404cosh(x) +--R + +--R 13 12 11 10 +--R - 2164%i cosh(x) - 2919cosh(x) - 476%i cosh(x) - 2336cosh(x) +--R + +--R 9 8 7 6 +--R 1428%i cosh(x) + 1418cosh(x) + 816%i cosh(x) + 784cosh(x) +--R + +--R 5 4 3 2 +--R 1224%i cosh(x) + 1673cosh(x) - 384%i cosh(x) + 948cosh(x) +--R + +--R - 480%i cosh(x) - 60 +--R * +--R sinh(x) +--R + +--R 18 17 16 15 14 +--R 2%i cosh(x) + 8cosh(x) + %i cosh(x) + 44cosh(x) - 255%i cosh(x) +--R + +--R 13 12 11 10 +--R - 400cosh(x) - 30%i cosh(x) - 384cosh(x) + 88%i cosh(x) +--R + +--R 9 8 7 6 5 +--R 688cosh(x) - 235%i cosh(x) - 140cosh(x) + 257%i cosh(x) + 88cosh(x) +--R + +--R 4 3 2 +--R 184%i cosh(x) + 96cosh(x) - 12%i cosh(x) +--R / +--R 6 12 7 6 11 +--R 15cosh(x) sinh(x) + (180cosh(x) - 60%i cosh(x) )sinh(x) +--R + +--R 8 7 10 +--R (990cosh(x) - 660%i cosh(x) )sinh(x) +--R + +--R 9 8 6 9 +--R (3300cosh(x) - 3300%i cosh(x) - 300%i cosh(x) )sinh(x) +--R + +--R 10 9 7 6 8 +--R (7425cosh(x) - 9900%i cosh(x) - 2700%i cosh(x) - 330cosh(x) )sinh(x) +--R + +--R 11 10 8 7 +--R 11880cosh(x) - 19800%i cosh(x) - 10800%i cosh(x) - 2520cosh(x) +--R + +--R 6 +--R - 420%i cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 12 11 9 8 +--R 13860cosh(x) - 27720%i cosh(x) - 25200%i cosh(x) - 8520cosh(x) +--R + +--R 7 6 +--R - 3300%i cosh(x) - 900cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 13 12 10 +--R 11880cosh(x) - 27720%i cosh(x) - 37800%i cosh(x) +--R + +--R 9 8 7 6 +--R - 16680cosh(x) - 10740%i cosh(x) - 5400cosh(x) + 60%i cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 14 13 11 +--R 7425cosh(x) - 19800%i cosh(x) - 37800%i cosh(x) +--R + +--R 10 9 8 7 +--R - 20700cosh(x) - 18900%i cosh(x) - 13740cosh(x) - 660%i cosh(x) +--R + +--R 6 +--R - 825cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 15 14 12 11 +--R 3300cosh(x) - 9900%i cosh(x) - 25200%i cosh(x) - 16680cosh(x) +--R + +--R 10 9 8 7 +--R - 19500%i cosh(x) - 18960cosh(x) - 2520%i cosh(x) - 4140cosh(x) +--R + +--R 6 +--R 480%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 16 15 13 12 +--R 990cosh(x) - 3300%i cosh(x) - 10800%i cosh(x) - 8520cosh(x) +--R + +--R 11 10 9 8 +--R - 11820%i cosh(x) - 14940cosh(x) - 3000%i cosh(x) - 7110cosh(x) +--R + +--R 7 6 +--R 1080%i cosh(x) - 180cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 17 16 14 13 +--R 180cosh(x) - 660%i cosh(x) - 2700%i cosh(x) - 2520cosh(x) +--R + +--R 12 11 10 9 +--R - 3900%i cosh(x) - 6360cosh(x) - 1380%i cosh(x) - 5580cosh(x) +--R + +--R 8 7 6 +--R 720%i cosh(x) - 1080cosh(x) + 240%i cosh(x) +--R * +--R sinh(x) +--R + +--R 18 17 15 14 +--R 15cosh(x) - 60%i cosh(x) - 300%i cosh(x) - 330cosh(x) +--R + +--R 13 12 11 10 +--R - 540%i cosh(x) - 1140cosh(x) - 180%i cosh(x) - 1545cosh(x) +--R + +--R 9 8 7 6 +--R 600%i cosh(x) - 900cosh(x) + 480%i cosh(x) + 60cosh(x) +--R Type: Expression(Complex(Integer)) +--E 10 + +--S 11 of 552 +t0702:= csch(x)^3/(a+b*csch(x)) +--R +--R +--R 3 +--R csch(x) +--R (11) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 552 +r0702:= a*acoth(cosh(x))/b^2-2*a^2*atanh((a-b*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/b^2/(a^2+b^2)^(1/2)-coth(x)/b +--R +--R +--R (12) +--R x +--R b tanh(-) - a +-------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R 2a atanh(-------------) + a\|b + a acoth(cosh(x)) - b coth(x)\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R ------------------------------------------------------------------------- +--R +-------+ +--R 2 | 2 2 +--R b \|b + a +--R Type: Expression(Integer) +--E 12 + +--S 13 of 552 +a0702:= integrate(t0702,x) +--R +--R +--R (13) +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b - 2a )sinh(x) + (- 2a b - 2a )cosh(x) - 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a)\|b + a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a)\|b + a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R +-------+ +--R | 2 2 +--R - 2b\|b + a +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b )\|b + a +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 552 +m0702:= a0702-r0702 +--R +--R +--R (14) +--R 2 2 2 2 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a ) +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (- 2a b - 2a )sinh(x) + (- 2a b - 2a )cosh(x) - 2b - 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (a sinh(x) + 2a cosh(x)sinh(x) + a cosh(x) - a)\|b + a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a)\|b + a +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 2 2 2 2 +--R (- 2a sinh(x) - 4a cosh(x)sinh(x) - 2a cosh(x) + 2a ) +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- a sinh(x) - 2a cosh(x)sinh(x) - a cosh(x) + a)\|b + a +--R * +--R acoth(cosh(x)) +--R + +--R 2 +--R b coth(x)sinh(x) + 2b cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (b cosh(x) - b)coth(x) - 2b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b )\|b + a +--R Type: Expression(Integer) +--E 14 + +--S 15 of 552 +d0702:= D(m0702,x) +--R +--R +--R (15) +--R 2 7 +--R a b sinh(x) +--R + +--R 2 2 2 2 2 3 2 +--R (- a b cosh(x) + a b )coth(x) + (a b - a )cosh(x) +--R + +--R 2 2 3 +--R 6a b cosh(x) + a b + a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (- 6a b cosh(x) - 2b cosh(x) + 6a b cosh(x) + 2b )coth(x) +--R + +--R 2 3 3 3 2 2 +--R (6a b - 6a )cosh(x) + (2b + 13a b)cosh(x) +--R + +--R 2 3 3 2 +--R (4a b + 6a )cosh(x) - 2b - a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 +--R - 15a b cosh(x) - 10b cosh(x) + 18a b cosh(x) +--R + +--R 3 2 +--R 10b cosh(x) - 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 4 3 2 3 +--R (15a b - 15a )cosh(x) + (10b + 10a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (2a b + 18a )cosh(x) + (- 10b - 2a b)cosh(x) - a b - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 +--R - 20a b cosh(x) - 20b cosh(x) + 32a b cosh(x) +--R + +--R 3 2 2 3 +--R 24b cosh(x) - 12a b cosh(x) - 4b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 5 3 2 4 +--R (20a b - 20a )cosh(x) + (20b - 5a b)cosh(x) +--R + +--R 2 3 3 3 2 2 3 +--R (- 12a b + 32a )cosh(x) + (- 16b + 6a b)cosh(x) - 12a cosh(x) +--R + +--R 3 2 +--R - 4b - a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 2 4 +--R - 15a b cosh(x) - 20b cosh(x) + 33a b cosh(x) +--R + +--R 3 3 2 2 3 2 +--R 32b cosh(x) - 21a b cosh(x) - 12b cosh(x) + 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 6 3 2 5 +--R (15a b - 15a )cosh(x) + (20b - 14a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (- 23a b + 33a )cosh(x) + (- 8b + 20a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (9a b - 21a )cosh(x) + (- 12b - 6a b)cosh(x) - a b + 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 2 5 +--R - 6a b cosh(x) - 10b cosh(x) + 18a b cosh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 22b cosh(x) - 18a b cosh(x) - 14b cosh(x) + 6a b cosh(x) +--R + +--R 3 +--R 2b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 7 3 2 6 +--R (6a b - 6a )cosh(x) + (10b - 9a b)cosh(x) +--R + +--R 2 3 5 3 2 4 +--R (- 16a b + 18a )cosh(x) + (2b + 19a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (14a b - 18a )cosh(x) + (- 10b - 11a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 4a b + 6a )cosh(x) - 2b + a b +--R * +--R sinh(x) +--R + +--R 2 8 3 7 2 6 3 5 +--R - a b cosh(x) - 2b cosh(x) + 4a b cosh(x) + 6b cosh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R - 6a b cosh(x) - 6b cosh(x) + 4a b cosh(x) + 2b cosh(x) - a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 8 3 2 7 2 3 6 +--R (a b - a )cosh(x) + (2b - 2a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R + +--R 3 2 5 2 3 4 3 2 3 +--R (2b + 6a b)cosh(x) + (6a b - 6a )cosh(x) + (- 2b - 6a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 4a b + 4a )cosh(x) + (- 2b + 2a b)cosh(x) + a b - a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 7 +--R - 2a sinh(x) +--R + +--R 2 2 2 2 2 2 3 +--R (2a b cosh(x) - 2a b)coth(x) - 2a b cosh(x) - 12a cosh(x) +--R + +--R 2 +--R - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 2 2 2 2 2 +--R (12a b cosh(x) + 4a b cosh(x) - 12a b cosh(x) - 4a b )coth(x) +--R + +--R 2 3 2 3 2 2 +--R - 12a b cosh(x) + (- 4a b - 30a )cosh(x) - 8a b cosh(x) +--R + +--R 2 3 +--R 4a b + 6a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 30a b cosh(x) + 20a b cosh(x) - 36a b cosh(x) +--R + +--R 2 2 +--R - 20a b cosh(x) + 6a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 2 3 3 2 2 +--R - 30a b cosh(x) + (- 20a b - 40a )cosh(x) - 4a b cosh(x) +--R + +--R 2 3 2 +--R (20a b + 24a )cosh(x) + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 40a b cosh(x) + 40a b cosh(x) - 64a b cosh(x) +--R + +--R 2 2 2 2 +--R - 48a b cosh(x) + 24a b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 2 3 4 2 3 +--R - 40a b cosh(x) + (- 40a b - 30a )cosh(x) + 24a b cosh(x) +--R + +--R 2 3 2 2 3 +--R (32a b + 36a )cosh(x) + 8a b - 6a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 5 2 4 +--R 30a b cosh(x) + 40a b cosh(x) - 66a b cosh(x) +--R + +--R 2 3 2 2 2 2 +--R - 64a b cosh(x) + 42a b cosh(x) + 24a b cosh(x) - 6a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 6 2 3 5 2 4 +--R - 30a b cosh(x) + (- 40a b - 12a )cosh(x) + 46a b cosh(x) +--R + +--R 2 3 3 2 2 2 3 +--R (16a b + 24a )cosh(x) - 18a b cosh(x) + (24a b - 12a )cosh(x) +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 6 2 5 +--R 12a b cosh(x) + 20a b cosh(x) - 36a b cosh(x) +--R + +--R 2 4 2 3 2 2 +--R - 44a b cosh(x) + 36a b cosh(x) + 28a b cosh(x) +--R + +--R 2 2 +--R - 12a b cosh(x) - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 7 2 3 6 2 5 +--R - 12a b cosh(x) + (- 20a b - 2a )cosh(x) + 32a b cosh(x) +--R + +--R 2 3 4 2 3 2 3 2 +--R (- 4a b + 6a )cosh(x) - 28a b cosh(x) + (20a b - 6a )cosh(x) +--R + +--R 2 2 3 +--R 8a b cosh(x) + 4a b + 2a +--R * +--R sinh(x) +--R + +--R 2 8 2 7 2 6 2 5 +--R 2a b cosh(x) + 4a b cosh(x) - 8a b cosh(x) - 12a b cosh(x) +--R + +--R 2 4 2 3 2 2 2 +--R 12a b cosh(x) + 12a b cosh(x) - 8a b cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 8 2 7 2 6 2 5 +--R - 2a b cosh(x) - 4a b cosh(x) + 8a b cosh(x) - 4a b cosh(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R - 12a b cosh(x) + 4a b cosh(x) + 8a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 7 +--R - a b sinh(x) +--R + +--R 2 2 2 2 2 3 2 2 +--R (a b cosh(x) - a b )coth(x) + (- a b + a )cosh(x) - 6a b cosh(x) +--R + +--R 2 3 +--R - a b - a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (6a b cosh(x) + 2b cosh(x) - 6a b cosh(x) - 2b )coth(x) +--R + +--R 2 3 3 3 2 2 +--R (- 6a b + 6a )cosh(x) + (- 2b - 13a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 4a b - 6a )cosh(x) + 2b + a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 3 +--R 15a b cosh(x) + 10b cosh(x) - 18a b cosh(x) - 10b cosh(x) +--R + +--R 2 +--R 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 4 3 2 3 +--R (- 15a b + 15a )cosh(x) + (- 10b - 10a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 2a b - 18a )cosh(x) + (10b + 2a b)cosh(x) + a b + 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 20a b cosh(x) + 20b cosh(x) - 32a b cosh(x) - 24b cosh(x) +--R + +--R 2 3 +--R 12a b cosh(x) + 4b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 5 3 2 4 +--R (- 20a b + 20a )cosh(x) + (- 20b + 5a b)cosh(x) +--R + +--R 2 3 3 3 2 2 3 3 +--R (12a b - 32a )cosh(x) + (16b - 6a b)cosh(x) + 12a cosh(x) + 4b +--R + +--R 2 +--R a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R 15a b cosh(x) + 20b cosh(x) - 33a b cosh(x) - 32b cosh(x) +--R + +--R 2 2 3 2 +--R 21a b cosh(x) + 12b cosh(x) - 3a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 6 3 2 5 +--R (- 15a b + 15a )cosh(x) + (- 20b + 14a b)cosh(x) +--R + +--R 2 3 4 3 2 3 +--R (23a b - 33a )cosh(x) + (8b - 20a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 9a b + 21a )cosh(x) + (12b + 6a b)cosh(x) + a b - 3a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 2 5 3 4 +--R 6a b cosh(x) + 10b cosh(x) - 18a b cosh(x) - 22b cosh(x) +--R + +--R 2 3 3 2 2 3 +--R 18a b cosh(x) + 14b cosh(x) - 6a b cosh(x) - 2b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 7 3 2 6 +--R (- 6a b + 6a )cosh(x) + (- 10b + 9a b)cosh(x) +--R + +--R 2 3 5 3 2 4 +--R (16a b - 18a )cosh(x) + (- 2b - 19a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (- 14a b + 18a )cosh(x) + (10b + 11a b)cosh(x) +--R + +--R 2 3 3 2 +--R (4a b - 6a )cosh(x) + 2b - a b +--R * +--R sinh(x) +--R + +--R 2 8 3 7 2 6 3 5 +--R a b cosh(x) + 2b cosh(x) - 4a b cosh(x) - 6b cosh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R 6a b cosh(x) + 6b cosh(x) - 4a b cosh(x) - 2b cosh(x) + a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 8 3 2 7 2 3 6 +--R (- a b + a )cosh(x) + (- 2b + 2a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 3 2 5 2 3 4 3 2 3 +--R (- 2b - 6a b)cosh(x) + (- 6a b + 6a )cosh(x) + (2b + 6a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 +--R (4a b - 4a )cosh(x) + (2b - 2a b)cosh(x) - a b + a +--R / +--R 3 2 3 6 +--R (a b cosh(x) - a b )sinh(x) +--R + +--R 3 3 4 2 3 4 5 +--R (6a b cosh(x) + 2b cosh(x) - 6a b cosh(x) - 2b )sinh(x) +--R + +--R 3 4 4 3 3 2 4 +--R 15a b cosh(x) + 10b cosh(x) - 18a b cosh(x) - 10b cosh(x) +--R + +--R 3 +--R 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R 20a b cosh(x) + 20b cosh(x) - 32a b cosh(x) - 24b cosh(x) +--R + +--R 3 4 +--R 12a b cosh(x) + 4b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R 15a b cosh(x) + 20b cosh(x) - 33a b cosh(x) - 32b cosh(x) +--R + +--R 3 2 4 3 +--R 21a b cosh(x) + 12b cosh(x) - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 4 4 +--R 6a b cosh(x) + 10b cosh(x) - 18a b cosh(x) - 22b cosh(x) +--R + +--R 3 3 4 2 3 4 +--R 18a b cosh(x) + 14b cosh(x) - 6a b cosh(x) - 2b +--R * +--R sinh(x) +--R + +--R 3 8 4 7 3 6 4 5 +--R a b cosh(x) + 2b cosh(x) - 4a b cosh(x) - 6b cosh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R 6a b cosh(x) + 6b cosh(x) - 4a b cosh(x) - 2b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 2 6 +--R (- 2a b cosh(x) + 2a b )sinh(x) +--R + +--R 2 2 3 3 2 2 2 3 5 +--R (- 12a b cosh(x) - 4a b cosh(x) + 12a b cosh(x) + 4a b )sinh(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R - 30a b cosh(x) - 20a b cosh(x) + 36a b cosh(x) +--R + +--R 3 2 2 +--R 20a b cosh(x) - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R - 40a b cosh(x) - 40a b cosh(x) + 64a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 48a b cosh(x) - 24a b cosh(x) - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R - 30a b cosh(x) - 40a b cosh(x) + 66a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 64a b cosh(x) - 42a b cosh(x) - 24a b cosh(x) + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R - 12a b cosh(x) - 20a b cosh(x) + 36a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 2 2 +--R 44a b cosh(x) - 36a b cosh(x) - 28a b cosh(x) + 12a b cosh(x) +--R + +--R 3 +--R 4a b +--R * +--R sinh(x) +--R + +--R 2 2 8 3 7 2 2 6 3 5 +--R - 2a b cosh(x) - 4a b cosh(x) + 8a b cosh(x) + 12a b cosh(x) +--R + +--R 2 2 4 3 3 2 2 2 3 +--R - 12a b cosh(x) - 12a b cosh(x) + 8a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 +--R - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 3 6 +--R (- a b cosh(x) + a b )sinh(x) +--R + +--R 3 3 4 2 3 4 5 +--R (- 6a b cosh(x) - 2b cosh(x) + 6a b cosh(x) + 2b )sinh(x) +--R + +--R 3 4 4 3 3 2 4 +--R - 15a b cosh(x) - 10b cosh(x) + 18a b cosh(x) + 10b cosh(x) +--R + +--R 3 +--R - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R - 20a b cosh(x) - 20b cosh(x) + 32a b cosh(x) + 24b cosh(x) +--R + +--R 3 4 +--R - 12a b cosh(x) - 4b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R - 15a b cosh(x) - 20b cosh(x) + 33a b cosh(x) + 32b cosh(x) +--R + +--R 3 2 4 3 +--R - 21a b cosh(x) - 12b cosh(x) + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 4 4 +--R - 6a b cosh(x) - 10b cosh(x) + 18a b cosh(x) + 22b cosh(x) +--R + +--R 3 3 4 2 3 4 +--R - 18a b cosh(x) - 14b cosh(x) + 6a b cosh(x) + 2b +--R * +--R sinh(x) +--R + +--R 3 8 4 7 3 6 4 5 +--R - a b cosh(x) - 2b cosh(x) + 4a b cosh(x) + 6b cosh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R - 6a b cosh(x) - 6b cosh(x) + 4a b cosh(x) + 2b cosh(x) - a b +--R Type: Expression(Integer) +--E 15 + +--S 16 of 552 +t0703:= csch(x)^4/(a+b*csch(x)) +--R +--R +--R 4 +--R csch(x) +--R (16) ------------- +--R b csch(x) + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 552 +r0703:= -a^2*acoth(cosh(x))/b^3+1/2*acoth(cosh(x))/b+_ + 2*a^3*atanh((a-b*tanh(1/2*x))/(a^2+b^2)^(1/2))/b^3/(a^2+b^2)^(1/2)+_ + a*coth(x)/b^2-1/2*coth(x)*csch(x)/b +--R +--R +--R (17) +--R x +--R b tanh(-) - a +-------+ +--R 3 2 2 2 | 2 2 +--R - 4a atanh(-------------) + (b - 2a )\|b + a acoth(cosh(x)) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 | 2 2 +--R (- b coth(x)csch(x) + 2a b coth(x))\|b + a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2b \|b + a +--R Type: Expression(Integer) +--E 17 + +--S 18 of 552 +a0703:= integrate(t0703,x) +--R +--R +--R (18) +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) - 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) - 8a cosh(x))sinh(x) + 2a cosh(x) - 4a cosh(x) + 2a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 2 4 2 2 3 +--R (b - 2a )sinh(x) + (4b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b - 12a )cosh(x) - 2b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b - 8a )cosh(x) + (- 4b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b - 2a )cosh(x) + (- 2b + 4a )cosh(x) + b - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 4 2 2 3 +--R (- b + 2a )sinh(x) + (- 4b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b + 12a )cosh(x) + 2b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b + 8a )cosh(x) + (4b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b + 2a )cosh(x) + (2b - 4a )cosh(x) - b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 2 3 2 2 +--R - 2b sinh(x) + (- 6b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 6b cosh(x) + 8a b cosh(x) - 2b )sinh(x) - 2b cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2b cosh(x) - 4a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) - 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) - 8b cosh(x))sinh(x) + 2b cosh(x) - 4b cosh(x) + 2b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 552 +m0703:= a0703-r0703 +--R +--R +--R (19) +--R 3 4 3 3 3 2 3 2 +--R 2a sinh(x) + 8a cosh(x)sinh(x) + (12a cosh(x) - 4a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8a cosh(x) - 8a cosh(x))sinh(x) + 2a cosh(x) - 4a cosh(x) + 2a +--R * +--R log +--R 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + 2b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 2 3 3 2 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) + 2b + 2a b +--R / +--R 2 2 +--R a sinh(x) + (2a cosh(x) + 2b)sinh(x) + a cosh(x) + 2b cosh(x) +--R + +--R - a +--R + +--R 2 2 4 2 2 3 +--R (b - 2a )sinh(x) + (4b - 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b - 12a )cosh(x) - 2b + 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b - 8a )cosh(x) + (- 4b + 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b - 2a )cosh(x) + (- 2b + 4a )cosh(x) + b - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 4 2 2 3 +--R (- b + 2a )sinh(x) + (- 4b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b + 12a )cosh(x) + 2b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b + 8a )cosh(x) + (4b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b + 2a )cosh(x) + (2b - 4a )cosh(x) - b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 3 4 3 3 3 2 3 2 +--R 4a sinh(x) + 16a cosh(x)sinh(x) + (24a cosh(x) - 8a )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (16a cosh(x) - 16a cosh(x))sinh(x) + 4a cosh(x) - 8a cosh(x) + 4a +--R * +--R x +--R b tanh(-) - a +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 4 2 2 3 +--R (- b + 2a )sinh(x) + (- 4b + 8a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b + 12a )cosh(x) + 2b - 4a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b + 8a )cosh(x) + (4b - 8a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- b + 2a )cosh(x) + (2b - 4a )cosh(x) - b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a acoth(cosh(x)) +--R + +--R 2 4 +--R (b coth(x)csch(x) - 2a b coth(x))sinh(x) +--R + +--R 2 2 3 +--R (4b cosh(x)coth(x)csch(x) - 8a b cosh(x)coth(x) - 2b )sinh(x) +--R + +--R 2 2 2 +--R (6b cosh(x) - 2b )coth(x)csch(x) +--R + +--R 2 2 +--R (- 12a b cosh(x) + 4a b)coth(x) - 6b cosh(x) + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 2 +--R (4b cosh(x) - 4b cosh(x))coth(x)csch(x) +--R + +--R 3 2 2 +--R (- 8a b cosh(x) + 8a b cosh(x))coth(x) - 6b cosh(x) +--R + +--R 2 +--R 8a b cosh(x) - 2b +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (b cosh(x) - 2b cosh(x) + b )coth(x)csch(x) +--R + +--R 4 2 2 3 +--R (- 2a b cosh(x) + 4a b cosh(x) - 2a b)coth(x) - 2b cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2b cosh(x) - 4a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 4 3 3 3 2 3 2 +--R 2b sinh(x) + 8b cosh(x)sinh(x) + (12b cosh(x) - 4b )sinh(x) +--R + +--R 3 3 3 3 4 3 2 3 +--R (8b cosh(x) - 8b cosh(x))sinh(x) + 2b cosh(x) - 4b cosh(x) + 2b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 552 +d0703:= D(m0703,x) +--R +--R +--R (20) +--R 3 3 9 +--R (a b - 2a b)sinh(x) +--R + +--R 3 2 3 2 3 2 3 +--R ((- 2a b cosh(x) + 2a b )coth(x) + a b cosh(x) - a b )csch(x) +--R + +--R 2 2 2 2 2 2 2 2 4 2 +--R (2a b cosh(x) - 2a b )coth(x) + (- 2a b + 2a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (8a b - 16a b)cosh(x) + 2b - 2a b - 2a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 3 4 2 3 4 +--R (- 16a b cosh(x) - 4b cosh(x) + 16a b cosh(x) + 4b ) +--R * +--R 2 +--R coth(x) +--R + +--R 3 3 4 2 3 4 +--R 8a b cosh(x) + 2b cosh(x) - 8a b cosh(x) - 2b +--R * +--R csch(x) +--R + +--R 2 2 3 3 2 2 2 3 2 +--R (16a b cosh(x) + 4a b cosh(x) - 16a b cosh(x) - 4a b )coth(x) +--R + +--R 2 2 4 3 3 3 2 +--R (- 16a b + 16a )cosh(x) + (24a b - 52a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (14b - 12a b - 16a )cosh(x) + 4a b +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 3 2 +--R - 56a b cosh(x) - 28b cosh(x) + 64a b cosh(x) +--R + +--R 4 3 +--R 28b cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 4 4 3 3 2 4 +--R 28a b cosh(x) + 14b cosh(x) - 32a b cosh(x) - 14b cosh(x) +--R + +--R 3 +--R 4a b +--R * +--R csch(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R 56a b cosh(x) + 28a b cosh(x) - 64a b cosh(x) +--R + +--R 3 2 2 +--R - 28a b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 4 3 3 3 +--R (- 56a b + 56a )cosh(x) + (28a b - 84a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (42b - 20a b - 64a )cosh(x) + (4a b + 20a b)cosh(x) - 6b +--R + +--R 2 2 4 +--R 4a b + 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 +--R - 112a b cosh(x) - 84b cosh(x) + 160a b cosh(x) +--R + +--R 4 2 3 4 +--R 96b cosh(x) - 48a b cosh(x) - 12b +--R * +--R 2 +--R coth(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R 56a b cosh(x) + 42b cosh(x) - 80a b cosh(x) - 48b cosh(x) +--R + +--R 3 4 +--R 24a b cosh(x) + 6b +--R * +--R csch(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R 112a b cosh(x) + 84a b cosh(x) - 160a b cosh(x) +--R + +--R 3 2 2 2 3 +--R - 96a b cosh(x) + 48a b cosh(x) + 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 5 3 3 4 +--R (- 112a b + 112a )cosh(x) + (- 14a b - 56a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (70b + 20a b - 160a )cosh(x) + (36a b + 24a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (- 30b + 12a b + 48a )cosh(x) - 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 +--R - 140a b cosh(x) - 140b cosh(x) + 260a b cosh(x) +--R + +--R 4 3 3 2 4 3 +--R 200b cosh(x) - 132a b cosh(x) - 60b cosh(x) + 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 6 4 5 3 4 +--R 70a b cosh(x) + 70b cosh(x) - 130a b cosh(x) +--R + +--R 4 3 3 2 4 3 +--R - 100b cosh(x) + 66a b cosh(x) + 30b cosh(x) - 6a b +--R * +--R csch(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R 140a b cosh(x) + 140a b cosh(x) - 260a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R - 200a b cosh(x) + 132a b cosh(x) + 60a b cosh(x) - 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 6 3 3 5 +--R (- 140a b + 140a )cosh(x) + (- 84a b + 28a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (70b + 120a b - 260a )cosh(x) + (120a b - 40a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 28b - 12a b + 132a )cosh(x) + (- 36a b + 12a b)cosh(x) +--R + +--R 4 4 +--R - 26b - 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 +--R - 112a b cosh(x) - 140b cosh(x) + 272a b cosh(x) +--R + +--R 4 4 3 3 4 2 +--R 260b cosh(x) - 208a b cosh(x) - 132b cosh(x) +--R + +--R 3 4 +--R 48a b cosh(x) + 12b +--R * +--R 2 +--R coth(x) +--R + +--R 3 7 4 6 3 5 +--R 56a b cosh(x) + 70b cosh(x) - 136a b cosh(x) +--R + +--R 4 4 3 3 4 2 +--R - 130b cosh(x) + 104a b cosh(x) + 66b cosh(x) +--R + +--R 3 4 +--R - 24a b cosh(x) - 6b +--R * +--R csch(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R 112a b cosh(x) + 140a b cosh(x) - 272a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 +--R - 260a b cosh(x) + 208a b cosh(x) + 132a b cosh(x) +--R + +--R 2 2 3 +--R - 48a b cosh(x) - 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 7 3 3 6 +--R (- 112a b + 112a )cosh(x) + (- 112a b + 84a b)cosh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (42b + 188a b - 272a )cosh(x) + (200a b - 140a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (68b - 88a b + 208a )cosh(x) + (- 96a b + 60a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- 110b + 12a b - 48a )cosh(x) + 8a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 8 4 7 3 6 +--R - 56a b cosh(x) - 84b cosh(x) + 176a b cosh(x) +--R + +--R 4 5 3 4 4 3 +--R 204b cosh(x) - 192a b cosh(x) - 156b cosh(x) +--R + +--R 3 2 4 3 +--R 80a b cosh(x) + 36b cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 8 4 7 3 6 +--R 28a b cosh(x) + 42b cosh(x) - 88a b cosh(x) +--R + +--R 4 5 3 4 4 3 +--R - 102b cosh(x) + 96a b cosh(x) + 78b cosh(x) +--R + +--R 3 2 4 3 +--R - 40a b cosh(x) - 18b cosh(x) + 4a b +--R * +--R csch(x) +--R + +--R 2 2 8 3 7 2 2 6 +--R 56a b cosh(x) + 84a b cosh(x) - 176a b cosh(x) +--R + +--R 3 5 2 2 4 3 3 +--R - 204a b cosh(x) + 192a b cosh(x) + 156a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R - 80a b cosh(x) - 36a b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 8 3 3 7 +--R (- 56a b + 56a )cosh(x) + (- 76a b + 68a b)cosh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (14b + 148a b - 176a )cosh(x) + (180a b - 156a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (162b - 132a b + 192a )cosh(x) + (- 132a b + 108a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (- 174b + 44a b - 80a )cosh(x) + (28a b - 20a b)cosh(x) - 2b +--R + +--R 2 2 4 +--R - 4a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 9 4 8 3 7 +--R - 16a b cosh(x) - 28b cosh(x) + 64a b cosh(x) +--R + +--R 4 6 3 5 4 4 +--R 88b cosh(x) - 96a b cosh(x) - 96b cosh(x) +--R + +--R 3 3 4 2 3 4 +--R 64a b cosh(x) + 40b cosh(x) - 16a b cosh(x) - 4b +--R * +--R 2 +--R coth(x) +--R + +--R 3 9 4 8 3 7 4 6 +--R 8a b cosh(x) + 14b cosh(x) - 32a b cosh(x) - 44b cosh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R 48a b cosh(x) + 48b cosh(x) - 32a b cosh(x) - 20b cosh(x) +--R + +--R 3 4 +--R 8a b cosh(x) + 2b +--R * +--R csch(x) +--R + +--R 2 2 9 3 8 2 2 7 +--R 16a b cosh(x) + 28a b cosh(x) - 64a b cosh(x) +--R + +--R 3 6 2 2 5 3 4 +--R - 88a b cosh(x) + 96a b cosh(x) + 96a b cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R - 64a b cosh(x) - 40a b cosh(x) + 16a b cosh(x) + 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 9 3 3 8 +--R (- 16a b + 16a )cosh(x) + (- 27a b + 26a b)cosh(x) +--R + +--R 4 2 2 4 7 3 3 6 +--R (2b + 60a b - 64a )cosh(x) + (84a b - 80a b)cosh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (122b - 84a b + 96a )cosh(x) + (- 90a b + 84a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 122b + 52a b - 64a )cosh(x) + (36a b - 32a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- 2b - 12a b + 16a )cosh(x) - 3a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 10 4 9 3 8 +--R - 2a b cosh(x) - 4b cosh(x) + 10a b cosh(x) +--R + +--R 4 7 3 6 4 5 3 4 +--R 16b cosh(x) - 20a b cosh(x) - 24b cosh(x) + 20a b cosh(x) +--R + +--R 4 3 3 2 4 3 +--R 16b cosh(x) - 10a b cosh(x) - 4b cosh(x) + 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 10 4 9 3 8 4 7 +--R a b cosh(x) + 2b cosh(x) - 5a b cosh(x) - 8b cosh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R 10a b cosh(x) + 12b cosh(x) - 10a b cosh(x) - 8b cosh(x) +--R + +--R 3 2 4 3 +--R 5a b cosh(x) + 2b cosh(x) - a b +--R * +--R csch(x) +--R + +--R 2 2 10 3 9 2 2 8 3 7 +--R 2a b cosh(x) + 4a b cosh(x) - 10a b cosh(x) - 16a b cosh(x) +--R + +--R 2 2 6 3 5 2 2 4 3 3 +--R 20a b cosh(x) + 24a b cosh(x) - 20a b cosh(x) - 16a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R 10a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 10 3 3 9 +--R (- 2a b + 2a )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 2 2 4 8 3 3 7 +--R (10a b - 10a )cosh(x) + (16a b - 16a b)cosh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (32b - 20a b + 20a )cosh(x) + (- 24a b + 24a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 32b + 20a b - 20a )cosh(x) + (16a b - 16a b)cosh(x) +--R + +--R 2 2 4 2 3 3 2 2 4 +--R (- 10a b + 10a )cosh(x) + (- 4a b + 4a b)cosh(x) + 2a b - 2a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 4 9 +--R (- 2a b + 4a )sinh(x) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R ((4a b cosh(x) - 4a b )coth(x) - 2a b cosh(x) + 2a b )csch(x) +--R + +--R 3 2 3 2 3 2 +--R (- 4a b cosh(x) + 4a b)coth(x) + 4a b cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 16a b + 32a )cosh(x) - 4a b + 4a b +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R (32a b cosh(x) + 8a b cosh(x) - 32a b cosh(x) - 8a b ) +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R - 16a b cosh(x) - 4a b cosh(x) + 16a b cosh(x) + 4a b +--R * +--R csch(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 32a b cosh(x) - 8a b cosh(x) + 32a b cosh(x) + 8a b ) +--R * +--R 2 +--R coth(x) +--R + +--R 3 3 2 2 4 2 +--R 32a b cosh(x) + (- 48a b + 112a )cosh(x) +--R + +--R 3 3 4 +--R (- 28a b + 24a b)cosh(x) - 16a +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R 112a b cosh(x) + 56a b cosh(x) - 128a b cosh(x) +--R + +--R 3 2 2 +--R - 56a b cosh(x) + 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R - 56a b cosh(x) - 28a b cosh(x) + 64a b cosh(x) +--R + +--R 3 2 2 +--R 28a b cosh(x) - 8a b +--R * +--R csch(x) +--R + +--R 3 4 2 2 3 3 2 +--R - 112a b cosh(x) - 56a b cosh(x) + 128a b cosh(x) +--R + +--R 2 2 3 +--R 56a b cosh(x) - 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 4 2 2 4 3 +--R 112a b cosh(x) + (- 56a b + 224a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (- 84a b + 40a b)cosh(x) + (- 8a b - 96a )cosh(x) + 12a b +--R + +--R 3 +--R - 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R 224a b cosh(x) + 168a b cosh(x) - 320a b cosh(x) +--R + +--R 3 2 2 2 3 +--R - 192a b cosh(x) + 96a b cosh(x) + 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R - 112a b cosh(x) - 84a b cosh(x) + 160a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 96a b cosh(x) - 48a b cosh(x) - 12a b +--R * +--R csch(x) +--R + +--R 3 5 2 2 4 3 3 +--R - 224a b cosh(x) - 168a b cosh(x) + 320a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R 192a b cosh(x) - 96a b cosh(x) - 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 5 2 2 4 4 +--R 224a b cosh(x) + (28a b + 280a )cosh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (- 140a b - 40a b)cosh(x) + (- 72a b - 240a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (60a b - 24a b)cosh(x) + 12a b + 24a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R 280a b cosh(x) + 280a b cosh(x) - 520a b cosh(x) +--R + +--R 3 3 2 2 2 3 +--R - 400a b cosh(x) + 264a b cosh(x) + 120a b cosh(x) +--R + +--R 2 2 +--R - 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R - 140a b cosh(x) - 140a b cosh(x) + 260a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 200a b cosh(x) - 132a b cosh(x) - 60a b cosh(x) + 12a b +--R * +--R csch(x) +--R + +--R 3 6 2 2 5 3 4 +--R - 280a b cosh(x) - 280a b cosh(x) + 520a b cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R 400a b cosh(x) - 264a b cosh(x) - 120a b cosh(x) + 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 6 2 2 4 5 +--R 280a b cosh(x) + (168a b + 224a )cosh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (- 140a b - 240a b)cosh(x) + (- 240a b - 320a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (56a b + 24a b)cosh(x) + (72a b + 96a )cosh(x) + 52a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R 224a b cosh(x) + 280a b cosh(x) - 544a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 +--R - 520a b cosh(x) + 416a b cosh(x) + 264a b cosh(x) +--R + +--R 2 2 3 +--R - 96a b cosh(x) - 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R - 112a b cosh(x) - 140a b cosh(x) + 272a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 +--R 260a b cosh(x) - 208a b cosh(x) - 132a b cosh(x) +--R + +--R 2 2 3 +--R 48a b cosh(x) + 12a b +--R * +--R csch(x) +--R + +--R 3 7 2 2 6 3 5 +--R - 224a b cosh(x) - 280a b cosh(x) + 544a b cosh(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R 520a b cosh(x) - 416a b cosh(x) - 264a b cosh(x) +--R + +--R 3 2 2 +--R 96a b cosh(x) + 24a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 7 2 2 4 6 +--R 224a b cosh(x) + (224a b + 112a )cosh(x) +--R + +--R 3 3 5 2 2 4 4 +--R (- 84a b - 376a b)cosh(x) + (- 400a b - 240a )cosh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (- 136a b + 176a b)cosh(x) + (192a b + 144a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (220a b - 24a b)cosh(x) - 16a b - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 8 3 7 2 2 6 +--R 112a b cosh(x) + 168a b cosh(x) - 352a b cosh(x) +--R + +--R 3 5 2 2 4 3 3 +--R - 408a b cosh(x) + 384a b cosh(x) + 312a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R - 160a b cosh(x) - 72a b cosh(x) + 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 8 3 7 2 2 6 +--R - 56a b cosh(x) - 84a b cosh(x) + 176a b cosh(x) +--R + +--R 3 5 2 2 4 3 3 +--R 204a b cosh(x) - 192a b cosh(x) - 156a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R 80a b cosh(x) + 36a b cosh(x) - 8a b +--R * +--R csch(x) +--R + +--R 3 8 2 2 7 3 6 +--R - 112a b cosh(x) - 168a b cosh(x) + 352a b cosh(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R 408a b cosh(x) - 384a b cosh(x) - 312a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 160a b cosh(x) + 72a b cosh(x) - 16a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 8 2 2 4 7 +--R 112a b cosh(x) + (152a b + 32a )cosh(x) +--R + +--R 3 3 6 2 2 4 5 +--R (- 28a b - 296a b)cosh(x) + (- 360a b - 96a )cosh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (- 324a b + 264a b)cosh(x) + (264a b + 96a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (348a b - 88a b)cosh(x) + (- 56a b - 32a )cosh(x) + 4a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 9 3 8 2 2 7 +--R 32a b cosh(x) + 56a b cosh(x) - 128a b cosh(x) +--R + +--R 3 6 2 2 5 3 4 +--R - 176a b cosh(x) + 192a b cosh(x) + 192a b cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R - 128a b cosh(x) - 80a b cosh(x) + 32a b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 9 3 8 2 2 7 +--R - 16a b cosh(x) - 28a b cosh(x) + 64a b cosh(x) +--R + +--R 3 6 2 2 5 3 4 +--R 88a b cosh(x) - 96a b cosh(x) - 96a b cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R 64a b cosh(x) + 40a b cosh(x) - 16a b cosh(x) - 4a b +--R * +--R csch(x) +--R + +--R 3 9 2 2 8 3 7 +--R - 32a b cosh(x) - 56a b cosh(x) + 128a b cosh(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R 176a b cosh(x) - 192a b cosh(x) - 192a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 128a b cosh(x) + 80a b cosh(x) - 32a b cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 9 2 2 4 8 +--R 32a b cosh(x) + (54a b + 4a )cosh(x) +--R + +--R 3 3 7 2 2 4 6 +--R (- 4a b - 120a b)cosh(x) + (- 168a b - 16a )cosh(x) +--R + +--R 3 3 5 2 2 4 4 +--R (- 244a b + 168a b)cosh(x) + (180a b + 24a )cosh(x) +--R + +--R 3 3 3 2 2 4 2 +--R (244a b - 104a b)cosh(x) + (- 72a b - 16a )cosh(x) +--R + +--R 3 3 2 2 4 +--R (4a b + 24a b)cosh(x) + 6a b + 4a +--R * +--R sinh(x) +--R + +--R 2 2 10 3 9 2 2 8 +--R 4a b cosh(x) + 8a b cosh(x) - 20a b cosh(x) +--R + +--R 3 7 2 2 6 3 5 +--R - 32a b cosh(x) + 40a b cosh(x) + 48a b cosh(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R - 40a b cosh(x) - 32a b cosh(x) + 20a b cosh(x) +--R + +--R 3 2 2 +--R 8a b cosh(x) - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 10 3 9 2 2 8 +--R - 2a b cosh(x) - 4a b cosh(x) + 10a b cosh(x) +--R + +--R 3 7 2 2 6 3 5 2 2 4 +--R 16a b cosh(x) - 20a b cosh(x) - 24a b cosh(x) + 20a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 16a b cosh(x) - 10a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R csch(x) +--R + +--R 3 10 2 2 9 3 8 +--R - 4a b cosh(x) - 8a b cosh(x) + 20a b cosh(x) +--R + +--R 2 2 7 3 6 2 2 5 3 4 +--R 32a b cosh(x) - 40a b cosh(x) - 48a b cosh(x) + 40a b cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R 32a b cosh(x) - 20a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 10 2 2 9 3 8 2 2 7 +--R 4a b cosh(x) + 8a b cosh(x) - 20a b cosh(x) - 32a b cosh(x) +--R + +--R 3 3 6 2 2 5 +--R (- 64a b + 40a b)cosh(x) + 48a b cosh(x) +--R + +--R 3 3 4 2 2 3 3 2 +--R (64a b - 40a b)cosh(x) - 32a b cosh(x) + 20a b cosh(x) +--R + +--R 2 2 3 +--R 8a b cosh(x) - 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 3 9 +--R (- a b + 2a b)sinh(x) +--R + +--R 3 2 3 2 3 2 3 +--R ((2a b cosh(x) - 2a b )coth(x) - a b cosh(x) + a b )csch(x) +--R + +--R 2 2 2 2 2 2 2 2 4 2 +--R (- 2a b cosh(x) + 2a b )coth(x) + (2a b - 2a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 8a b + 16a b)cosh(x) - 2b + 2a b + 2a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 3 4 2 3 4 2 +--R (16a b cosh(x) + 4b cosh(x) - 16a b cosh(x) - 4b )coth(x) +--R + +--R 3 3 4 2 3 4 +--R - 8a b cosh(x) - 2b cosh(x) + 8a b cosh(x) + 2b +--R * +--R csch(x) +--R + +--R 2 2 3 3 2 2 2 3 2 +--R (- 16a b cosh(x) - 4a b cosh(x) + 16a b cosh(x) + 4a b )coth(x) +--R + +--R 2 2 4 3 3 3 2 +--R (16a b - 16a )cosh(x) + (- 24a b + 52a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (- 14b + 12a b + 16a )cosh(x) - 4a b +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 4 3 3 2 4 +--R 56a b cosh(x) + 28b cosh(x) - 64a b cosh(x) - 28b cosh(x) +--R + +--R 3 +--R 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 4 4 3 3 2 4 +--R - 28a b cosh(x) - 14b cosh(x) + 32a b cosh(x) + 14b cosh(x) +--R + +--R 3 +--R - 4a b +--R * +--R csch(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R - 56a b cosh(x) - 28a b cosh(x) + 64a b cosh(x) +--R + +--R 3 2 2 +--R 28a b cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 4 3 3 3 +--R (56a b - 56a )cosh(x) + (- 28a b + 84a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (- 42b + 20a b + 64a )cosh(x) + (- 4a b - 20a b)cosh(x) + 6b +--R + +--R 2 2 4 +--R - 4a b - 8a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 +--R 112a b cosh(x) + 84b cosh(x) - 160a b cosh(x) +--R + +--R 4 2 3 4 +--R - 96b cosh(x) + 48a b cosh(x) + 12b +--R * +--R 2 +--R coth(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R - 56a b cosh(x) - 42b cosh(x) + 80a b cosh(x) + 48b cosh(x) +--R + +--R 3 4 +--R - 24a b cosh(x) - 6b +--R * +--R csch(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R - 112a b cosh(x) - 84a b cosh(x) + 160a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 96a b cosh(x) - 48a b cosh(x) - 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 5 3 3 4 +--R (112a b - 112a )cosh(x) + (14a b + 56a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 70b - 20a b + 160a )cosh(x) + (- 36a b - 24a b)cosh(x) +--R + +--R 4 2 2 4 3 +--R (30b - 12a b - 48a )cosh(x) + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 +--R 140a b cosh(x) + 140b cosh(x) - 260a b cosh(x) +--R + +--R 4 3 3 2 4 3 +--R - 200b cosh(x) + 132a b cosh(x) + 60b cosh(x) - 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R - 70a b cosh(x) - 70b cosh(x) + 130a b cosh(x) + 100b cosh(x) +--R + +--R 3 2 4 3 +--R - 66a b cosh(x) - 30b cosh(x) + 6a b +--R * +--R csch(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R - 140a b cosh(x) - 140a b cosh(x) + 260a b cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 200a b cosh(x) - 132a b cosh(x) - 60a b cosh(x) + 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 6 3 3 5 +--R (140a b - 140a )cosh(x) + (84a b - 28a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 70b - 120a b + 260a )cosh(x) + (- 120a b + 40a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 4 +--R (28b + 12a b - 132a )cosh(x) + (36a b - 12a b)cosh(x) + 26b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 +--R 112a b cosh(x) + 140b cosh(x) - 272a b cosh(x) +--R + +--R 4 4 3 3 4 2 +--R - 260b cosh(x) + 208a b cosh(x) + 132b cosh(x) +--R + +--R 3 4 +--R - 48a b cosh(x) - 12b +--R * +--R 2 +--R coth(x) +--R + +--R 3 7 4 6 3 5 4 4 +--R - 56a b cosh(x) - 70b cosh(x) + 136a b cosh(x) + 130b cosh(x) +--R + +--R 3 3 4 2 3 4 +--R - 104a b cosh(x) - 66b cosh(x) + 24a b cosh(x) + 6b +--R * +--R csch(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R - 112a b cosh(x) - 140a b cosh(x) + 272a b cosh(x) +--R + +--R 3 4 2 2 3 3 2 +--R 260a b cosh(x) - 208a b cosh(x) - 132a b cosh(x) +--R + +--R 2 2 3 +--R 48a b cosh(x) + 12a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 7 3 3 6 +--R (112a b - 112a )cosh(x) + (112a b - 84a b)cosh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (- 42b - 188a b + 272a )cosh(x) + (- 200a b + 140a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 68b + 88a b - 208a )cosh(x) + (96a b - 60a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (110b - 12a b + 48a )cosh(x) - 8a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 8 4 7 3 6 +--R 56a b cosh(x) + 84b cosh(x) - 176a b cosh(x) +--R + +--R 4 5 3 4 4 3 +--R - 204b cosh(x) + 192a b cosh(x) + 156b cosh(x) +--R + +--R 3 2 4 3 +--R - 80a b cosh(x) - 36b cosh(x) + 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 8 4 7 3 6 4 5 +--R - 28a b cosh(x) - 42b cosh(x) + 88a b cosh(x) + 102b cosh(x) +--R + +--R 3 4 4 3 3 2 4 +--R - 96a b cosh(x) - 78b cosh(x) + 40a b cosh(x) + 18b cosh(x) +--R + +--R 3 +--R - 4a b +--R * +--R csch(x) +--R + +--R 2 2 8 3 7 2 2 6 +--R - 56a b cosh(x) - 84a b cosh(x) + 176a b cosh(x) +--R + +--R 3 5 2 2 4 3 3 +--R 204a b cosh(x) - 192a b cosh(x) - 156a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R 80a b cosh(x) + 36a b cosh(x) - 8a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 8 3 3 7 +--R (56a b - 56a )cosh(x) + (76a b - 68a b)cosh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (- 14b - 148a b + 176a )cosh(x) + (- 180a b + 156a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 162b + 132a b - 192a )cosh(x) + (132a b - 108a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (174b - 44a b + 80a )cosh(x) + (- 28a b + 20a b)cosh(x) + 2b +--R + +--R 2 2 4 +--R 4a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 9 4 8 3 7 4 6 +--R 16a b cosh(x) + 28b cosh(x) - 64a b cosh(x) - 88b cosh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R 96a b cosh(x) + 96b cosh(x) - 64a b cosh(x) - 40b cosh(x) +--R + +--R 3 4 +--R 16a b cosh(x) + 4b +--R * +--R 2 +--R coth(x) +--R + +--R 3 9 4 8 3 7 4 6 +--R - 8a b cosh(x) - 14b cosh(x) + 32a b cosh(x) + 44b cosh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R - 48a b cosh(x) - 48b cosh(x) + 32a b cosh(x) + 20b cosh(x) +--R + +--R 3 4 +--R - 8a b cosh(x) - 2b +--R * +--R csch(x) +--R + +--R 2 2 9 3 8 2 2 7 +--R - 16a b cosh(x) - 28a b cosh(x) + 64a b cosh(x) +--R + +--R 3 6 2 2 5 3 4 2 2 3 +--R 88a b cosh(x) - 96a b cosh(x) - 96a b cosh(x) + 64a b cosh(x) +--R + +--R 3 2 2 2 3 +--R 40a b cosh(x) - 16a b cosh(x) - 4a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 9 3 3 8 +--R (16a b - 16a )cosh(x) + (27a b - 26a b)cosh(x) +--R + +--R 4 2 2 4 7 3 3 6 +--R (- 2b - 60a b + 64a )cosh(x) + (- 84a b + 80a b)cosh(x) +--R + +--R 4 2 2 4 5 3 3 4 +--R (- 122b + 84a b - 96a )cosh(x) + (90a b - 84a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (122b - 52a b + 64a )cosh(x) + (- 36a b + 32a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (2b + 12a b - 16a )cosh(x) + 3a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 10 4 9 3 8 4 7 +--R 2a b cosh(x) + 4b cosh(x) - 10a b cosh(x) - 16b cosh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R 20a b cosh(x) + 24b cosh(x) - 20a b cosh(x) - 16b cosh(x) +--R + +--R 3 2 4 3 +--R 10a b cosh(x) + 4b cosh(x) - 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 10 4 9 3 8 4 7 +--R - a b cosh(x) - 2b cosh(x) + 5a b cosh(x) + 8b cosh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R - 10a b cosh(x) - 12b cosh(x) + 10a b cosh(x) + 8b cosh(x) +--R + +--R 3 2 4 3 +--R - 5a b cosh(x) - 2b cosh(x) + a b +--R * +--R csch(x) +--R + +--R 2 2 10 3 9 2 2 8 3 7 +--R - 2a b cosh(x) - 4a b cosh(x) + 10a b cosh(x) + 16a b cosh(x) +--R + +--R 2 2 6 3 5 2 2 4 3 3 +--R - 20a b cosh(x) - 24a b cosh(x) + 20a b cosh(x) + 16a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R - 10a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 10 3 3 9 +--R (2a b - 2a )cosh(x) + (4a b - 4a b)cosh(x) +--R + +--R 2 2 4 8 3 3 7 +--R (- 10a b + 10a )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 4 2 2 4 6 3 3 5 +--R (- 32b + 20a b - 20a )cosh(x) + (24a b - 24a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (32b - 20a b + 20a )cosh(x) + (- 16a b + 16a b)cosh(x) +--R + +--R 2 2 4 2 3 3 2 2 4 +--R (10a b - 10a )cosh(x) + (4a b - 4a b)cosh(x) - 2a b + 2a +--R / +--R 4 2 4 8 +--R (2a b cosh(x) - 2a b )sinh(x) +--R + +--R 4 3 5 2 4 5 7 +--R (16a b cosh(x) + 4b cosh(x) - 16a b cosh(x) - 4b )sinh(x) +--R + +--R 4 4 5 3 4 2 5 +--R 56a b cosh(x) + 28b cosh(x) - 64a b cosh(x) - 28b cosh(x) +--R + +--R 4 +--R 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R 112a b cosh(x) + 84b cosh(x) - 160a b cosh(x) - 96b cosh(x) +--R + +--R 4 5 +--R 48a b cosh(x) + 12b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 5 5 4 4 5 3 +--R 140a b cosh(x) + 140b cosh(x) - 260a b cosh(x) - 200b cosh(x) +--R + +--R 4 2 5 4 +--R 132a b cosh(x) + 60b cosh(x) - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 5 6 4 5 5 4 +--R 112a b cosh(x) + 140b cosh(x) - 272a b cosh(x) - 260b cosh(x) +--R + +--R 4 3 5 2 4 5 +--R 208a b cosh(x) + 132b cosh(x) - 48a b cosh(x) - 12b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 5 7 4 6 5 5 +--R 56a b cosh(x) + 84b cosh(x) - 176a b cosh(x) - 204b cosh(x) +--R + +--R 4 4 5 3 4 2 5 +--R 192a b cosh(x) + 156b cosh(x) - 80a b cosh(x) - 36b cosh(x) +--R + +--R 4 +--R 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 5 8 4 7 5 6 +--R 16a b cosh(x) + 28b cosh(x) - 64a b cosh(x) - 88b cosh(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R 96a b cosh(x) + 96b cosh(x) - 64a b cosh(x) - 40b cosh(x) +--R + +--R 4 5 +--R 16a b cosh(x) + 4b +--R * +--R sinh(x) +--R + +--R 4 10 5 9 4 8 5 7 +--R 2a b cosh(x) + 4b cosh(x) - 10a b cosh(x) - 16b cosh(x) +--R + +--R 4 6 5 5 4 4 5 3 +--R 20a b cosh(x) + 24b cosh(x) - 20a b cosh(x) - 16b cosh(x) +--R + +--R 4 2 5 4 +--R 10a b cosh(x) + 4b cosh(x) - 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 3 2 2 3 8 +--R (- 4a b cosh(x) + 4a b )sinh(x) +--R + +--R 2 3 3 4 2 2 3 4 7 +--R (- 32a b cosh(x) - 8a b cosh(x) + 32a b cosh(x) + 8a b )sinh(x) +--R + +--R 2 3 4 4 3 2 3 2 +--R - 112a b cosh(x) - 56a b cosh(x) + 128a b cosh(x) +--R + +--R 4 2 3 +--R 56a b cosh(x) - 16a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 5 4 4 2 3 3 +--R - 224a b cosh(x) - 168a b cosh(x) + 320a b cosh(x) +--R + +--R 4 2 2 3 4 +--R 192a b cosh(x) - 96a b cosh(x) - 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 3 6 4 5 2 3 4 +--R - 280a b cosh(x) - 280a b cosh(x) + 520a b cosh(x) +--R + +--R 4 3 2 3 2 4 2 3 +--R 400a b cosh(x) - 264a b cosh(x) - 120a b cosh(x) + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 7 4 6 2 3 5 +--R - 224a b cosh(x) - 280a b cosh(x) + 544a b cosh(x) +--R + +--R 4 4 2 3 3 4 2 +--R 520a b cosh(x) - 416a b cosh(x) - 264a b cosh(x) +--R + +--R 2 3 4 +--R 96a b cosh(x) + 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 8 4 7 2 3 6 +--R - 112a b cosh(x) - 168a b cosh(x) + 352a b cosh(x) +--R + +--R 4 5 2 3 4 4 3 +--R 408a b cosh(x) - 384a b cosh(x) - 312a b cosh(x) +--R + +--R 2 3 2 4 2 3 +--R 160a b cosh(x) + 72a b cosh(x) - 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 9 4 8 2 3 7 +--R - 32a b cosh(x) - 56a b cosh(x) + 128a b cosh(x) +--R + +--R 4 6 2 3 5 4 4 +--R 176a b cosh(x) - 192a b cosh(x) - 192a b cosh(x) +--R + +--R 2 3 3 4 2 2 3 4 +--R 128a b cosh(x) + 80a b cosh(x) - 32a b cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 2 3 10 4 9 2 3 8 4 7 +--R - 4a b cosh(x) - 8a b cosh(x) + 20a b cosh(x) + 32a b cosh(x) +--R + +--R 2 3 6 4 5 2 3 4 4 3 +--R - 40a b cosh(x) - 48a b cosh(x) + 40a b cosh(x) + 32a b cosh(x) +--R + +--R 2 3 2 4 2 3 +--R - 20a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 4 8 +--R (- 2a b cosh(x) + 2a b )sinh(x) +--R + +--R 4 3 5 2 4 5 7 +--R (- 16a b cosh(x) - 4b cosh(x) + 16a b cosh(x) + 4b )sinh(x) +--R + +--R 4 4 5 3 4 2 5 +--R - 56a b cosh(x) - 28b cosh(x) + 64a b cosh(x) + 28b cosh(x) +--R + +--R 4 +--R - 8a b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R - 112a b cosh(x) - 84b cosh(x) + 160a b cosh(x) + 96b cosh(x) +--R + +--R 4 5 +--R - 48a b cosh(x) - 12b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 6 5 5 4 4 5 3 +--R - 140a b cosh(x) - 140b cosh(x) + 260a b cosh(x) + 200b cosh(x) +--R + +--R 4 2 5 4 +--R - 132a b cosh(x) - 60b cosh(x) + 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 7 5 6 4 5 5 4 +--R - 112a b cosh(x) - 140b cosh(x) + 272a b cosh(x) + 260b cosh(x) +--R + +--R 4 3 5 2 4 5 +--R - 208a b cosh(x) - 132b cosh(x) + 48a b cosh(x) + 12b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 8 5 7 4 6 5 5 +--R - 56a b cosh(x) - 84b cosh(x) + 176a b cosh(x) + 204b cosh(x) +--R + +--R 4 4 5 3 4 2 5 +--R - 192a b cosh(x) - 156b cosh(x) + 80a b cosh(x) + 36b cosh(x) +--R + +--R 4 +--R - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 9 5 8 4 7 5 6 +--R - 16a b cosh(x) - 28b cosh(x) + 64a b cosh(x) + 88b cosh(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R - 96a b cosh(x) - 96b cosh(x) + 64a b cosh(x) + 40b cosh(x) +--R + +--R 4 5 +--R - 16a b cosh(x) - 4b +--R * +--R sinh(x) +--R + +--R 4 10 5 9 4 8 5 7 +--R - 2a b cosh(x) - 4b cosh(x) + 10a b cosh(x) + 16b cosh(x) +--R + +--R 4 6 5 5 4 4 5 3 +--R - 20a b cosh(x) - 24b cosh(x) + 20a b cosh(x) + 16b cosh(x) +--R + +--R 4 2 5 4 +--R - 10a b cosh(x) - 4b cosh(x) + 2a b +--R Type: Expression(Integer) +--E 20 + +--S 21 of 552 +t0704:= csch(x)^3/(%i+csch(x)) +--R +--R +--R 3 +--R csch(x) +--R (21) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 21 + +--S 22 of 552 +r0704:= %i*acoth(cosh(x))-coth(x)-%i*cosh(x)/(1+%i*sinh(x)) +--R +--R +--R (22) +--R (%i sinh(x) + 1)acoth(cosh(x)) - coth(x)sinh(x) + %i coth(x) - cosh(x) +--R ---------------------------------------------------------------------- +--R sinh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 22 + +--S 23 of 552 +a0704:= integrate(t0704,x) +--R +--R +--R (23) +--R 3 2 +--R %i sinh(x) + (3%i cosh(x) + 1)sinh(x) +--R + +--R 2 3 2 +--R (3%i cosh(x) + 2cosh(x) - %i)sinh(x) + %i cosh(x) + cosh(x) +--R + +--R - %i cosh(x) - 1 +--R * +--R sinh(x) + cosh(x) + 1 +--R log(---------------------) +--R sinh(x) + cosh(x) - 1 +--R + +--R 2 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) - 2)sinh(x) - 2%i cosh(x) - 2cosh(x) + 4%i +--R / +--R 3 2 2 +--R sinh(x) + (3cosh(x) - %i)sinh(x) + (3cosh(x) - 2%i cosh(x) - 1)sinh(x) +--R + +--R 3 2 +--R cosh(x) - %i cosh(x) - cosh(x) + %i +--R Type: Union(Expression(Complex(Integer)),...) +--E 23 + +--S 24 of 552 +m0704:= a0704-r0704 +--R +--R +--R (24) +--R 4 3 +--R %i sinh(x) + (3%i cosh(x) + 2)sinh(x) +--R + +--R 2 2 +--R (3%i cosh(x) + 5cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 3 +--R (%i cosh(x) + 4cosh(x) - 3%i cosh(x) - 2)sinh(x) + cosh(x) +--R + +--R 2 +--R - %i cosh(x) - cosh(x) + %i +--R * +--R sinh(x) + cosh(x) + 1 +--R log(---------------------) +--R sinh(x) + cosh(x) - 1 +--R + +--R 4 3 +--R - %i sinh(x) + (- 3%i cosh(x) - 2)sinh(x) +--R + +--R 2 2 +--R (- 3%i cosh(x) - 5cosh(x) + 2%i)sinh(x) +--R + +--R 3 2 3 +--R (- %i cosh(x) - 4cosh(x) + 3%i cosh(x) + 2)sinh(x) - cosh(x) +--R + +--R 2 +--R %i cosh(x) + cosh(x) - %i +--R * +--R acoth(cosh(x)) +--R + +--R 4 3 +--R coth(x)sinh(x) + ((3cosh(x) - 2%i)coth(x) + cosh(x) - 2%i)sinh(x) +--R + +--R 2 2 +--R ((3cosh(x) - 5%i cosh(x) - 2)coth(x) + 3cosh(x) - 5%i cosh(x) - 4) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3 +--R (cosh(x) - 4%i cosh(x) - 3cosh(x) + 2%i)coth(x) + 3cosh(x) +--R + +--R 2 +--R - 4%i cosh(x) - 7cosh(x) + 6%i +--R * +--R sinh(x) +--R + +--R 3 2 4 +--R (- %i cosh(x) - cosh(x) + %i cosh(x) + 1)coth(x) + cosh(x) +--R + +--R 3 2 +--R - %i cosh(x) - 3cosh(x) + 3%i cosh(x) + 4 +--R / +--R 4 3 +--R sinh(x) + (3cosh(x) - 2%i)sinh(x) +--R + +--R 2 2 +--R (3cosh(x) - 5%i cosh(x) - 2)sinh(x) +--R + +--R 3 2 3 +--R (cosh(x) - 4%i cosh(x) - 3cosh(x) + 2%i)sinh(x) - %i cosh(x) +--R + +--R 2 +--R - cosh(x) + %i cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 24 + +--S 25 of 552 +d0704:= D(m0704,x) +--R +--R +--R (25) +--R 9 +--R %i sinh(x) +--R + +--R 2 2 2 8 +--R ((- cosh(x) + 1)coth(x) + 2cosh(x) + 6%i cosh(x) + 2)sinh(x) +--R + +--R 3 2 2 3 +--R (- 6cosh(x) + 4%i cosh(x) + 6cosh(x) - 4%i)coth(x) + 12cosh(x) +--R + +--R 2 +--R 8%i cosh(x) + 10cosh(x) - %i +--R * +--R 7 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 15cosh(x) + 22%i cosh(x) + 23cosh(x) - 22%i cosh(x) - 8) +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 +--R 29cosh(x) - 18%i cosh(x) + 8cosh(x) + 1 +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 20cosh(x) + 50%i cosh(x) + 58cosh(x) - 62%i cosh(x) +--R + +--R - 38cosh(x) + 12%i +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 2 +--R 34cosh(x) - 68%i cosh(x) - 34cosh(x) + 21%i cosh(x) + 14cosh(x) +--R + +--R 3%i +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 15cosh(x) + 60%i cosh(x) + 88cosh(x) - 106%i cosh(x) +--R + +--R 2 +--R - 87cosh(x) + 46%i cosh(x) + 14 +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 2 +--R 15cosh(x) - 84%i cosh(x) - 83cosh(x) + 64%i cosh(x) + 45cosh(x) +--R + +--R - 4%i cosh(x) + 7 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 6cosh(x) + 40%i cosh(x) + 78cosh(x) - 108%i cosh(x) +--R + +--R 3 2 +--R - 114cosh(x) + 80%i cosh(x) + 42cosh(x) - 12%i +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 3 +--R - 8cosh(x) - 44%i cosh(x) - 70cosh(x) + 77%i cosh(x) + 56cosh(x) +--R + +--R 2 +--R - 34%i cosh(x) + 14cosh(x) + %i +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - cosh(x) + 14%i cosh(x) + 39cosh(x) - 62%i cosh(x) +--R + +--R 4 3 2 +--R - 83cosh(x) + 74%i cosh(x) + 53cosh(x) - 26%i cosh(x) - 8 +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 4 +--R - 13cosh(x) - 2%i cosh(x) - 18cosh(x) + 36%i cosh(x) + 26cosh(x) +--R + +--R 3 2 +--R - 34%i cosh(x) - 2cosh(x) + 7 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 2%i cosh(x) + 10cosh(x) - 18%i cosh(x) - 30cosh(x) +--R + +--R 4 3 2 +--R 34%i cosh(x) + 30cosh(x) - 22%i cosh(x) - 10cosh(x) + 4%i +--R * +--R 2 +--R coth(x) +--R + +--R 9 8 7 6 4 +--R - 6cosh(x) + 7%i cosh(x) + 6cosh(x) - %i cosh(x) + %i cosh(x) +--R + +--R 3 2 +--R - 10cosh(x) - 3%i cosh(x) + 10cosh(x) - 4%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) - 2%i cosh(x) - 4cosh(x) + 6%i cosh(x) + 6cosh(x) +--R + +--R 3 2 +--R - 6%i cosh(x) - 4cosh(x) + 2%i cosh(x) + 1 +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 6 +--R - cosh(x) + 2%i cosh(x) + 3cosh(x) - 4%i cosh(x) - 2cosh(x) +--R + +--R 5 4 3 2 +--R 8%i cosh(x) - 2cosh(x) - 4%i cosh(x) + 3cosh(x) - 2%i cosh(x) - 1 +--R / +--R 2 8 +--R (cosh(x) - 1)sinh(x) +--R + +--R 3 2 7 +--R (6cosh(x) - 4%i cosh(x) - 6cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 6 +--R (15cosh(x) - 22%i cosh(x) - 23cosh(x) + 22%i cosh(x) + 8)sinh(x) +--R + +--R 5 4 3 2 +--R 20cosh(x) - 50%i cosh(x) - 58cosh(x) + 62%i cosh(x) + 38cosh(x) +--R + +--R - 12%i +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 15cosh(x) - 60%i cosh(x) - 88cosh(x) + 106%i cosh(x) + 87cosh(x) +--R + +--R - 46%i cosh(x) - 14 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) - 40%i cosh(x) - 78cosh(x) + 108%i cosh(x) + 114cosh(x) +--R + +--R 2 +--R - 80%i cosh(x) - 42cosh(x) + 12%i +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) - 14%i cosh(x) - 39cosh(x) + 62%i cosh(x) + 83cosh(x) +--R + +--R 3 2 +--R - 74%i cosh(x) - 53cosh(x) + 26%i cosh(x) + 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 2%i cosh(x) - 10cosh(x) + 18%i cosh(x) + 30cosh(x) +--R + +--R 4 3 2 +--R - 34%i cosh(x) - 30cosh(x) + 22%i cosh(x) + 10cosh(x) - 4%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) + 2%i cosh(x) + 4cosh(x) - 6%i cosh(x) - 6cosh(x) +--R + +--R 3 2 +--R 6%i cosh(x) + 4cosh(x) - 2%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 25 + +--S 26 of 552 +t0705:= csch(x)^4/(%i+csch(x)) +--R +--R +--R 4 +--R csch(x) +--R (26) ------------ +--R csch(x) + %i +--R Type: Expression(Complex(Integer)) +--E 26 + +--S 27 of 552 +r0705:= 3/2*acoth(cosh(x))+%i*coth(x)-1/2*coth(x)*csch(x)-_ + cosh(x)/(1+%i*sinh(x)) +--R +--R +--R (27) +--R (3sinh(x) - 3%i)acoth(cosh(x)) + (- coth(x)csch(x) + 2%i coth(x))sinh(x) +--R + +--R %i coth(x)csch(x) + 2coth(x) + 2%i cosh(x) +--R / +--R 2sinh(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 27 + +--S 28 of 552 +a0705:= integrate(t0705,x) +--R +--R +--R (28) +--R 5 4 +--R 3sinh(x) + (15cosh(x) - 3%i)sinh(x) +--R + +--R 2 3 +--R (30cosh(x) - 12%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 2 +--R (30cosh(x) - 18%i cosh(x) - 18cosh(x) + 6%i)sinh(x) +--R + +--R 4 3 2 +--R (15cosh(x) - 12%i cosh(x) - 18cosh(x) + 12%i cosh(x) + 3)sinh(x) +--R + +--R 5 4 3 2 +--R 3cosh(x) - 3%i cosh(x) - 6cosh(x) + 6%i cosh(x) + 3cosh(x) - 3%i +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 5 4 +--R - 3sinh(x) + (- 15cosh(x) + 3%i)sinh(x) +--R + +--R 2 3 +--R (- 30cosh(x) + 12%i cosh(x) + 6)sinh(x) +--R + +--R 3 2 2 +--R (- 30cosh(x) + 18%i cosh(x) + 18cosh(x) - 6%i)sinh(x) +--R + +--R 4 3 2 +--R (- 15cosh(x) + 12%i cosh(x) + 18cosh(x) - 12%i cosh(x) - 3)sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) + 3%i cosh(x) + 6cosh(x) - 6%i cosh(x) - 3cosh(x) + 3%i +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 3 +--R - 6sinh(x) + (- 24cosh(x) + 6%i)sinh(x) +--R + +--R 2 2 +--R (- 36cosh(x) + 18%i cosh(x) + 10)sinh(x) +--R + +--R 3 2 4 +--R (- 24cosh(x) + 18%i cosh(x) + 20cosh(x) - 2%i)sinh(x) - 6cosh(x) +--R + +--R 3 2 +--R 6%i cosh(x) + 10cosh(x) - 2%i cosh(x) - 8 +--R / +--R 5 4 +--R 2sinh(x) + (10cosh(x) - 2%i)sinh(x) +--R + +--R 2 3 +--R (20cosh(x) - 8%i cosh(x) - 4)sinh(x) +--R + +--R 3 2 2 +--R (20cosh(x) - 12%i cosh(x) - 12cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R (10cosh(x) - 8%i cosh(x) - 12cosh(x) + 8%i cosh(x) + 2)sinh(x) +--R + +--R 5 4 3 2 +--R 2cosh(x) - 2%i cosh(x) - 4cosh(x) + 4%i cosh(x) + 2cosh(x) - 2%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 28 + +--S 29 of 552 +m0705:= a0705-r0705 +--R +--R +--R (29) +--R 6 5 +--R 3sinh(x) + (15cosh(x) - 6%i)sinh(x) +--R + +--R 2 4 +--R (30cosh(x) - 27%i cosh(x) - 9)sinh(x) +--R + +--R 3 2 3 +--R (30cosh(x) - 48%i cosh(x) - 30cosh(x) + 12%i)sinh(x) +--R + +--R 4 3 2 2 +--R (15cosh(x) - 42%i cosh(x) - 36cosh(x) + 30%i cosh(x) + 9)sinh(x) +--R + +--R 5 4 3 2 +--R 3cosh(x) - 18%i cosh(x) - 18cosh(x) + 24%i cosh(x) +--R + +--R 15cosh(x) - 6%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3%i cosh(x) - 3cosh(x) + 6%i cosh(x) + 6cosh(x) - 3%i cosh(x) - 3 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 6 5 +--R - 3sinh(x) + (- 15cosh(x) + 6%i)sinh(x) +--R + +--R 2 4 +--R (- 30cosh(x) + 27%i cosh(x) + 9)sinh(x) +--R + +--R 3 2 3 +--R (- 30cosh(x) + 48%i cosh(x) + 30cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 2 +--R (- 15cosh(x) + 42%i cosh(x) + 36cosh(x) - 30%i cosh(x) - 9) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) + 18%i cosh(x) + 18cosh(x) - 24%i cosh(x) +--R + +--R - 15cosh(x) + 6%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R 3%i cosh(x) + 3cosh(x) - 6%i cosh(x) - 6cosh(x) + 3%i cosh(x) + 3 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 6 5 +--R - 3sinh(x) + (- 15cosh(x) + 6%i)sinh(x) +--R + +--R 2 4 +--R (- 30cosh(x) + 27%i cosh(x) + 9)sinh(x) +--R + +--R 3 2 3 +--R (- 30cosh(x) + 48%i cosh(x) + 30cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 2 +--R (- 15cosh(x) + 42%i cosh(x) + 36cosh(x) - 30%i cosh(x) - 9) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) + 18%i cosh(x) + 18cosh(x) - 24%i cosh(x) +--R + +--R - 15cosh(x) + 6%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R 3%i cosh(x) + 3cosh(x) - 6%i cosh(x) - 6cosh(x) + 3%i cosh(x) + 3 +--R * +--R acoth(cosh(x)) +--R + +--R 6 +--R (coth(x)csch(x) - 2%i coth(x))sinh(x) +--R + +--R (5cosh(x) - 2%i)coth(x)csch(x) + (- 10%i cosh(x) - 4)coth(x) +--R + +--R - 2%i cosh(x) - 6 +--R * +--R 5 +--R sinh(x) +--R + +--R 2 +--R (10cosh(x) - 9%i cosh(x) - 3)coth(x)csch(x) +--R + +--R 2 2 +--R (- 20%i cosh(x) - 18cosh(x) + 6%i)coth(x) - 10%i cosh(x) +--R + +--R - 26cosh(x) + 12%i +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 +--R (10cosh(x) - 16%i cosh(x) - 10cosh(x) + 4%i)coth(x)csch(x) +--R + +--R 3 2 +--R (- 20%i cosh(x) - 32cosh(x) + 20%i cosh(x) + 8)coth(x) +--R + +--R 3 2 +--R - 20%i cosh(x) - 44cosh(x) + 46%i cosh(x) + 16 +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 +--R (5cosh(x) - 14%i cosh(x) - 12cosh(x) + 10%i cosh(x) + 3)coth(x) +--R * +--R csch(x) +--R + +--R 4 3 2 +--R (- 10%i cosh(x) - 28cosh(x) + 24%i cosh(x) + 20cosh(x) - 6%i) +--R * +--R coth(x) +--R + +--R 4 3 2 +--R - 20%i cosh(x) - 36cosh(x) + 66%i cosh(x) + 42cosh(x) - 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R cosh(x) - 6%i cosh(x) - 6cosh(x) + 8%i cosh(x) + 5cosh(x) +--R + +--R - 2%i +--R * +--R coth(x)csch(x) +--R + +--R 5 4 3 2 +--R - 2%i cosh(x) - 12cosh(x) + 12%i cosh(x) + 16cosh(x) +--R + +--R - 10%i cosh(x) - 4 +--R * +--R coth(x) +--R + +--R 5 4 3 2 +--R - 10%i cosh(x) - 14cosh(x) + 42%i cosh(x) + 36cosh(x) +--R + +--R - 24%i cosh(x) - 10 +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R (- %i cosh(x) - cosh(x) + 2%i cosh(x) + 2cosh(x) - %i cosh(x) - 1) +--R * +--R coth(x)csch(x) +--R + +--R 5 4 3 2 +--R - 2cosh(x) + 2%i cosh(x) + 4cosh(x) - 4%i cosh(x) - 2cosh(x) +--R + +--R 2%i +--R * +--R coth(x) +--R + +--R 6 5 4 3 2 +--R - 2%i cosh(x) - 2cosh(x) + 10%i cosh(x) + 10cosh(x) - 12%i cosh(x) +--R + +--R - 4cosh(x) + 8%i +--R / +--R 6 5 +--R 2sinh(x) + (10cosh(x) - 4%i)sinh(x) +--R + +--R 2 4 +--R (20cosh(x) - 18%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 3 +--R (20cosh(x) - 32%i cosh(x) - 20cosh(x) + 8%i)sinh(x) +--R + +--R 4 3 2 2 +--R (10cosh(x) - 28%i cosh(x) - 24cosh(x) + 20%i cosh(x) + 6)sinh(x) +--R + +--R 5 4 3 2 +--R 2cosh(x) - 12%i cosh(x) - 12cosh(x) + 16%i cosh(x) + 10cosh(x) +--R + +--R - 4%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 2%i cosh(x) - 2cosh(x) + 4%i cosh(x) + 4cosh(x) - 2%i cosh(x) - 2 +--R Type: Expression(Complex(Integer)) +--E 29 + +--S 30 of 552 +d0705:= D(m0705,x) +--R +--R +--R (30) +--R 11 +--R 3sinh(x) +--R + +--R 2 2 2 +--R ((- 2cosh(x) + 2)coth(x) + cosh(x) - 1)csch(x) +--R + +--R 2 2 2 +--R (2%i cosh(x) - 2%i)coth(x) - 4%i cosh(x) + 24cosh(x) - 8%i +--R * +--R 10 +--R sinh(x) +--R + +--R 3 2 2 +--R (- 16cosh(x) + 8%i cosh(x) + 16cosh(x) - 8%i)coth(x) +--R + +--R 3 2 +--R 8cosh(x) - 4%i cosh(x) - 8cosh(x) + 4%i +--R * +--R csch(x) +--R + +--R 3 2 2 +--R (16%i cosh(x) + 8cosh(x) - 16%i cosh(x) - 8)coth(x) +--R + +--R 3 2 +--R - 32%i cosh(x) + 70cosh(x) - 58%i cosh(x) - 13 +--R * +--R 9 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 56cosh(x) + 60%i cosh(x) + 74cosh(x) - 60%i cosh(x) - 18) +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 +--R 28cosh(x) - 30%i cosh(x) - 37cosh(x) + 30%i cosh(x) + 9 +--R * +--R csch(x) +--R + +--R 4 3 2 +--R (56%i cosh(x) + 60cosh(x) - 74%i cosh(x) - 60cosh(x) + 18%i) +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 +--R - 110%i cosh(x) + 64cosh(x) - 154%i cosh(x) - 76cosh(x) + 18%i +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 112cosh(x) + 196%i cosh(x) + 232cosh(x) - 228%i cosh(x) +--R + +--R - 120cosh(x) + 32%i +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) - 98%i cosh(x) - 116cosh(x) + 114%i cosh(x) +--R + +--R 60cosh(x) - 16%i +--R * +--R csch(x) +--R + +--R 5 4 3 2 +--R 112%i cosh(x) + 196cosh(x) - 232%i cosh(x) - 228cosh(x) +--R + +--R 120%i cosh(x) + 32 +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 2 +--R - 208%i cosh(x) - 122cosh(x) - 142%i cosh(x) - 132cosh(x) +--R + +--R 80%i cosh(x) + 14 +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 140cosh(x) + 364%i cosh(x) + 484cosh(x) - 548%i cosh(x) +--R + +--R 2 +--R - 388cosh(x) + 184%i cosh(x) + 44 +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 +--R 70cosh(x) - 182%i cosh(x) - 242cosh(x) + 274%i cosh(x) +--R + +--R 2 +--R 194cosh(x) - 92%i cosh(x) - 22 +--R * +--R csch(x) +--R + +--R 6 5 4 3 +--R 140%i cosh(x) + 364cosh(x) - 484%i cosh(x) - 548cosh(x) +--R + +--R 2 +--R 388%i cosh(x) + 184cosh(x) - 44%i +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 +--R - 224%i cosh(x) - 420cosh(x) + 134%i cosh(x) + 52cosh(x) +--R + +--R 2 +--R 26%i cosh(x) + 32cosh(x) + 28%i +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 112cosh(x) + 420%i cosh(x) + 664cosh(x) - 864%i cosh(x) +--R + +--R 3 2 +--R - 768cosh(x) + 492%i cosh(x) + 216cosh(x) - 48%i +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R 56cosh(x) - 210%i cosh(x) - 332cosh(x) + 432%i cosh(x) +--R + +--R 3 2 +--R 384cosh(x) - 246%i cosh(x) - 108cosh(x) + 24%i +--R * +--R csch(x) +--R + +--R 7 6 5 4 +--R 112%i cosh(x) + 420cosh(x) - 664%i cosh(x) - 864cosh(x) +--R + +--R 3 2 +--R 768%i cosh(x) + 492cosh(x) - 216%i cosh(x) - 48 +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R - 112%i cosh(x) - 532cosh(x) + 454%i cosh(x) + 478cosh(x) +--R + +--R 3 2 +--R - 386%i cosh(x) - 160cosh(x) + 164%i cosh(x) + 70 +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 56cosh(x) + 308%i cosh(x) + 596cosh(x) - 888%i cosh(x) +--R + +--R 4 3 2 +--R - 972cosh(x) + 772%i cosh(x) + 476cosh(x) - 192%i cosh(x) +--R + +--R - 44 +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 +--R 28cosh(x) - 154%i cosh(x) - 298cosh(x) + 444%i cosh(x) +--R + +--R 4 3 2 +--R 486cosh(x) - 386%i cosh(x) - 238cosh(x) + 96%i cosh(x) + 22 +--R * +--R csch(x) +--R + +--R 8 7 6 5 +--R 56%i cosh(x) + 308cosh(x) - 596%i cosh(x) - 888cosh(x) +--R + +--R 4 3 2 +--R 972%i cosh(x) + 772cosh(x) - 476%i cosh(x) - 192cosh(x) + 44%i +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 +--R 28%i cosh(x) - 340cosh(x) + 442%i cosh(x) + 672cosh(x) +--R + +--R 4 3 2 +--R - 824%i cosh(x) - 660cosh(x) + 450%i cosh(x) + 328cosh(x) - 48%i +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - 16cosh(x) + 140%i cosh(x) + 344cosh(x) - 580%i cosh(x) +--R + +--R 5 4 3 2 +--R - 776cosh(x) + 740%i cosh(x) + 584cosh(x) - 332%i cosh(x) +--R + +--R - 136cosh(x) + 32%i +--R * +--R 2 +--R coth(x) +--R + +--R 9 8 7 6 +--R 8cosh(x) - 70%i cosh(x) - 172cosh(x) + 290%i cosh(x) +--R + +--R 5 4 3 2 +--R 388cosh(x) - 370%i cosh(x) - 292cosh(x) + 166%i cosh(x) +--R + +--R 68cosh(x) - 16%i +--R * +--R csch(x) +--R + +--R 9 8 7 6 +--R 16%i cosh(x) + 140cosh(x) - 344%i cosh(x) - 580cosh(x) +--R + +--R 5 4 3 2 +--R 776%i cosh(x) + 740cosh(x) - 584%i cosh(x) - 332cosh(x) +--R + +--R 136%i cosh(x) + 32 +--R * +--R 2 +--R coth(x) +--R + +--R 9 8 7 6 +--R 80%i cosh(x) - 81cosh(x) + 166%i cosh(x) + 404cosh(x) +--R + +--R 5 4 3 2 +--R - 708%i cosh(x) - 902cosh(x) + 670%i cosh(x) + 596cosh(x) +--R + +--R - 208%i cosh(x) - 17 +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 2cosh(x) + 36%i cosh(x) + 122cosh(x) - 228%i cosh(x) +--R + +--R 6 5 4 3 +--R - 372cosh(x) + 420%i cosh(x) + 404cosh(x) - 300%i cosh(x) +--R + +--R 2 +--R - 170cosh(x) + 72%i cosh(x) + 18 +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 +--R cosh(x) - 18%i cosh(x) - 61cosh(x) + 114%i cosh(x) +--R + +--R 6 5 4 3 +--R 186cosh(x) - 210%i cosh(x) - 202cosh(x) + 150%i cosh(x) +--R + +--R 2 +--R 85cosh(x) - 36%i cosh(x) - 9 +--R * +--R csch(x) +--R + +--R 10 9 8 7 +--R 2%i cosh(x) + 36cosh(x) - 122%i cosh(x) - 228cosh(x) +--R + +--R 6 5 4 3 +--R 372%i cosh(x) + 420cosh(x) - 404%i cosh(x) - 300cosh(x) +--R + +--R 2 +--R 170%i cosh(x) + 72cosh(x) - 18%i +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 +--R 52%i cosh(x) + 28cosh(x) - 22%i cosh(x) + 68cosh(x) +--R + +--R 6 5 4 3 +--R - 254%i cosh(x) - 532cosh(x) + 538%i cosh(x) + 492cosh(x) +--R + +--R 2 +--R - 326%i cosh(x) - 56cosh(x) + 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 4%i cosh(x) + 24cosh(x) - 48%i cosh(x) - 96cosh(x) +--R + +--R 6 5 4 3 +--R 128%i cosh(x) + 144cosh(x) - 136%i cosh(x) - 96cosh(x) +--R + +--R 2 +--R 60%i cosh(x) + 24cosh(x) - 8%i +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 +--R - 2%i cosh(x) - 12cosh(x) + 24%i cosh(x) + 48cosh(x) +--R + +--R 6 5 4 3 +--R - 64%i cosh(x) - 72cosh(x) + 68%i cosh(x) + 48cosh(x) +--R + +--R 2 +--R - 30%i cosh(x) - 12cosh(x) + 4%i +--R * +--R csch(x) +--R + +--R 10 9 8 7 +--R 4cosh(x) - 24%i cosh(x) - 48cosh(x) + 96%i cosh(x) +--R + +--R 6 5 4 3 +--R 128cosh(x) - 144%i cosh(x) - 136cosh(x) + 96%i cosh(x) +--R + +--R 2 +--R 60cosh(x) - 24%i cosh(x) - 8 +--R * +--R 2 +--R coth(x) +--R + +--R 11 10 9 8 +--R 16%i cosh(x) + 22cosh(x) - 36%i cosh(x) - 33cosh(x) +--R + +--R 7 6 5 4 +--R - 10%i cosh(x) - 104cosh(x) + 214%i cosh(x) + 162cosh(x) +--R + +--R 3 2 +--R - 206%i cosh(x) - 54cosh(x) + 22%i cosh(x) + 7 +--R * +--R sinh(x) +--R + +--R 10 9 8 7 +--R 2cosh(x) - 4%i cosh(x) - 10cosh(x) + 16%i cosh(x) +--R + +--R 6 5 4 3 +--R 20cosh(x) - 24%i cosh(x) - 20cosh(x) + 16%i cosh(x) +--R + +--R 2 +--R 10cosh(x) - 4%i cosh(x) - 2 +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 6 +--R - cosh(x) + 2%i cosh(x) + 5cosh(x) - 8%i cosh(x) - 10cosh(x) +--R + +--R 5 4 3 2 +--R 12%i cosh(x) + 10cosh(x) - 8%i cosh(x) - 5cosh(x) + 2%i cosh(x) + 1 +--R * +--R csch(x) +--R + +--R 10 9 8 7 +--R - 2%i cosh(x) - 4cosh(x) + 10%i cosh(x) + 16cosh(x) +--R + +--R 6 5 4 3 +--R - 20%i cosh(x) - 24cosh(x) + 20%i cosh(x) + 16cosh(x) +--R + +--R 2 +--R - 10%i cosh(x) - 4cosh(x) + 2%i +--R * +--R 2 +--R coth(x) +--R + +--R 12 11 10 9 8 +--R 2%i cosh(x) + 4cosh(x) - 8%i cosh(x) - 12cosh(x) + 10%i cosh(x) +--R + +--R 7 6 5 4 3 +--R 8cosh(x) + 32%i cosh(x) + 8cosh(x) - 42%i cosh(x) - 12cosh(x) +--R + +--R 2 +--R 8%i cosh(x) + 4cosh(x) - 2%i +--R / +--R 2 10 +--R (2cosh(x) - 2)sinh(x) +--R + +--R 3 2 9 +--R (16cosh(x) - 8%i cosh(x) - 16cosh(x) + 8%i)sinh(x) +--R + +--R 4 3 2 8 +--R (56cosh(x) - 60%i cosh(x) - 74cosh(x) + 60%i cosh(x) + 18)sinh(x) +--R + +--R 5 4 3 2 +--R 112cosh(x) - 196%i cosh(x) - 232cosh(x) + 228%i cosh(x) +--R + +--R 120cosh(x) - 32%i +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 140cosh(x) - 364%i cosh(x) - 484cosh(x) + 548%i cosh(x) +--R + +--R 2 +--R 388cosh(x) - 184%i cosh(x) - 44 +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 112cosh(x) - 420%i cosh(x) - 664cosh(x) + 864%i cosh(x) +--R + +--R 3 2 +--R 768cosh(x) - 492%i cosh(x) - 216cosh(x) + 48%i +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 56cosh(x) - 308%i cosh(x) - 596cosh(x) + 888%i cosh(x) +--R + +--R 4 3 2 +--R 972cosh(x) - 772%i cosh(x) - 476cosh(x) + 192%i cosh(x) + 44 +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 16cosh(x) - 140%i cosh(x) - 344cosh(x) + 580%i cosh(x) +--R + +--R 5 4 3 2 +--R 776cosh(x) - 740%i cosh(x) - 584cosh(x) + 332%i cosh(x) +--R + +--R 136cosh(x) - 32%i +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 2cosh(x) - 36%i cosh(x) - 122cosh(x) + 228%i cosh(x) +--R + +--R 6 5 4 3 +--R 372cosh(x) - 420%i cosh(x) - 404cosh(x) + 300%i cosh(x) +--R + +--R 2 +--R 170cosh(x) - 72%i cosh(x) - 18 +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 4%i cosh(x) - 24cosh(x) + 48%i cosh(x) + 96cosh(x) +--R + +--R 6 5 4 3 +--R - 128%i cosh(x) - 144cosh(x) + 136%i cosh(x) + 96cosh(x) +--R + +--R 2 +--R - 60%i cosh(x) - 24cosh(x) + 8%i +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R - 2cosh(x) + 4%i cosh(x) + 10cosh(x) - 16%i cosh(x) - 20cosh(x) +--R + +--R 5 4 3 2 +--R 24%i cosh(x) + 20cosh(x) - 16%i cosh(x) - 10cosh(x) + 4%i cosh(x) + 2 +--R Type: Expression(Complex(Integer)) +--E 30 + +--S 31 of 552 +t0706:= sinh(x)/(a+b*sinh(x))^2 +--R +--R +--R sinh(x) +--R (31) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 31 + +--S 32 of 552 +r0706:= -2*b*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+_ + a*cosh(x)/(a^2+b^2)/(a+b*sinh(x)) +--R +--R +--R x +--R a tanh(-) - b +-------+ +--R 2 2 | 2 2 +--R (2b sinh(x) + 2a b)atanh(-------------) + a cosh(x)\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (32) ------------------------------------------------------------- +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b + a b)sinh(x) + a b + a )\|b + a +--R Type: Expression(Integer) +--E 32 + +--S 33 of 552 +a0706:= integrate(t0706,x) +--R +--R +--R (33) +--R 3 2 3 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b )sinh(x) + b cosh(x) + 2a b cosh(x) +--R + +--R 3 +--R - b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- 2a sinh(x) - 2a cosh(x) + 2a b)\|b + a +--R / +--R 4 2 2 2 4 2 2 3 3 +--R (b + a b )sinh(x) + ((2b + 2a b )cosh(x) + 2a b + 2a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (b + a b )cosh(x) + (2a b + 2a b)cosh(x) - b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 552 +m0706:= a0706-r0706 +--R +--R +--R (34) +--R 4 3 4 3 2 +--R b sinh(x) + (2b cosh(x) + 3a b )sinh(x) +--R + +--R 4 2 3 4 2 2 3 2 +--R (b cosh(x) + 4a b cosh(x) - b + 2a b )sinh(x) + a b cosh(x) +--R + +--R 2 2 3 +--R 2a b cosh(x) - a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 3 4 3 2 +--R - 2b sinh(x) + (- 4b cosh(x) - 6a b )sinh(x) +--R + +--R 4 2 3 4 2 2 3 2 +--R (- 2b cosh(x) - 8a b cosh(x) + 2b - 4a b )sinh(x) - 2a b cosh(x) +--R + +--R 2 2 3 +--R - 4a b cosh(x) + 2a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 2 +--R (- a b cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 2 3 2 3 +--R (- 2a b cosh(x) - 4a b cosh(x) + 2a b - 2a )sinh(x) - a b cosh(x) +--R + +--R 2 2 2 3 2 +--R - 2a b cosh(x) + (a b - 2a )cosh(x) + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 2 3 3 5 2 3 4 3 2 2 +--R (b + a b )sinh(x) + ((2b + 2a b )cosh(x) + 3a b + 3a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 2 3 4 +--R ((b + a b )cosh(x) + (4a b + 4a b )cosh(x) - b + a b + 2a b) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (a b + a b )cosh(x) + (2a b + 2a b)cosh(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 552 +d0706:= D(m0706,x) +--R +--R +--R (35) +--R 5 2 3 6 +--R (- b - a b )sinh(x) +--R + +--R 5 2 3 4 3 2 5 +--R ((- 4b - 4a b )cosh(x) - 4a b - 3a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 +--R (- 6b - 5a b )cosh(x) + (- 14a b - 10a b )cosh(x) + 2b +--R + +--R 2 3 4 +--R - 7a b - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 4 3 2 2 +--R - 4b cosh(x) + (- 18a b - 8a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (4b - 20a b - 8a b)cosh(x) + 6a b - 6a b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (- b + 5a b )cosh(x) + (- 10a b + 6a b )cosh(x) +--R + +--R 5 2 3 2 4 3 2 5 5 +--R (2b - 22a b )cosh(x) + (10a b - 16a b - 2a )cosh(x) - b +--R + +--R 2 3 4 +--R 5a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 4 3 2 4 +--R 4a b cosh(x) + (- 2a b + 11a b )cosh(x) +--R + +--R 2 3 4 3 4 3 2 5 2 +--R (- 12a b + 8a b)cosh(x) + (4a b - 16a b + 2a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (8a b - 8a b)cosh(x) - 2a b + a b - 2a +--R * +--R sinh(x) +--R + +--R 2 3 6 3 2 5 2 3 4 4 +--R a b cosh(x) + 4a b cosh(x) + (- 3a b + 4a b)cosh(x) +--R + +--R 3 2 5 3 2 3 4 2 +--R (- 6a b + 2a )cosh(x) + (3a b - 4a b)cosh(x) +--R + +--R 3 2 5 2 3 +--R (2a b - 2a )cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 6 4 5 2 3 5 +--R 2a b sinh(x) + (8a b cosh(x) - 4b + 6a b )sinh(x) +--R + +--R 4 2 5 2 3 4 3 2 4 +--R (10a b cosh(x) + (- 12b + 20a b )cosh(x) - 12a b + 8a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 +--R (- 12b + 16a b )cosh(x) + (- 32a b + 16a b )cosh(x) + 4b +--R + +--R 2 3 4 +--R - 12a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 5 2 3 3 4 2 +--R - 10a b cosh(x) + (- 4b - 12a b )cosh(x) - 24a b cosh(x) +--R + +--R 5 2 3 4 4 +--R (4b - 24a b + 4a b)cosh(x) + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 2 3 4 3 2 3 +--R - 8a b cosh(x) - 22a b cosh(x) - 16a b cosh(x) +--R + +--R 2 3 4 2 4 2 3 4 +--R (- 8a b - 4a b)cosh(x) + 8a b cosh(x) + 6a b + 4a b +--R * +--R sinh(x) +--R + +--R 4 6 2 3 5 4 3 2 4 +--R - 2a b cosh(x) - 8a b cosh(x) + (4a b - 8a b )cosh(x) +--R + +--R 2 3 4 3 4 2 2 3 4 +--R (4a b - 4a b)cosh(x) - 2a b cosh(x) + (4a b + 4a b)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 2 3 6 5 2 3 4 3 2 5 +--R (b + a b )sinh(x) + ((4b + 4a b )cosh(x) + 4a b + 3a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 2 3 4 +--R ((6b + 5a b )cosh(x) + (14a b + 10a b )cosh(x) - 2b + 7a b + 4a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 4 3 2 2 +--R 4b cosh(x) + (18a b + 8a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 4b + 20a b + 8a b)cosh(x) - 6a b + 6a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (b - 5a b )cosh(x) + (10a b - 6a b )cosh(x) +--R + +--R 5 2 3 2 4 3 2 5 5 +--R (- 2b + 22a b )cosh(x) + (- 10a b + 16a b + 2a )cosh(x) + b +--R + +--R 2 3 4 +--R - 5a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 5 4 3 2 4 2 3 4 3 +--R - 4a b cosh(x) + (2a b - 11a b )cosh(x) + (12a b - 8a b)cosh(x) +--R + +--R 4 3 2 5 2 2 3 4 4 +--R (- 4a b + 16a b - 2a )cosh(x) + (- 8a b + 8a b)cosh(x) + 2a b +--R + +--R 3 2 5 +--R - a b + 2a +--R * +--R sinh(x) +--R + +--R 2 3 6 3 2 5 2 3 4 4 +--R - a b cosh(x) - 4a b cosh(x) + (3a b - 4a b)cosh(x) +--R + +--R 3 2 5 3 2 3 4 2 3 2 5 +--R (6a b - 2a )cosh(x) + (- 3a b + 4a b)cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 3 +--R a b +--R / +--R 6 3 4 6 +--R (a b + a b )sinh(x) +--R + +--R 6 3 4 2 5 4 3 5 +--R ((4a b + 4a b )cosh(x) + 6a b + 6a b )sinh(x) +--R + +--R 6 3 4 2 2 5 4 3 6 +--R (6a b + 6a b )cosh(x) + (20a b + 20a b )cosh(x) - 2a b +--R + +--R 3 4 5 2 +--R 11a b + 13a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 3 4 3 2 5 4 3 2 +--R (4a b + 4a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 6 3 4 5 2 2 5 4 3 6 +--R (- 4a b + 32a b + 36a b )cosh(x) - 8a b + 4a b + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 3 4 4 2 5 4 3 3 +--R (a b + a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (- 2a b + 32a b + 34a b )cosh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 7 +--R (- 12a b + 16a b + 28a b)cosh(x) + a b - 9a b - 6a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 3 4 3 4 5 2 3 +--R (2a b + 2a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 2 5 4 3 6 2 +--R (- 4a b + 16a b + 20a b)cosh(x) +--R + +--R 3 4 5 2 7 2 5 4 3 6 +--R (- 12a b - 4a b + 8a )cosh(x) + 2a b - 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 4 5 2 4 4 3 6 3 +--R (a b + a b )cosh(x) + (4a b + 4a b)cosh(x) +--R + +--R 3 4 5 2 7 2 4 3 6 3 4 5 2 +--R (- 2a b + 2a b + 4a )cosh(x) + (- 4a b - 4a b)cosh(x) + a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 7 2 5 6 +--R (- 2b - 2a b )sinh(x) +--R + +--R 7 2 5 6 3 4 5 +--R ((- 8b - 8a b )cosh(x) - 12a b - 12a b )sinh(x) +--R + +--R 7 2 5 2 6 3 4 7 +--R (- 12b - 12a b )cosh(x) + (- 40a b - 40a b )cosh(x) + 4b +--R + +--R 2 5 4 3 +--R - 22a b - 26a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 5 3 6 3 4 2 +--R (- 8b - 8a b )cosh(x) + (- 48a b - 48a b )cosh(x) +--R + +--R 7 2 5 4 3 6 3 4 5 2 +--R (8b - 64a b - 72a b )cosh(x) + 16a b - 8a b - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 5 4 6 3 4 3 +--R (- 2b - 2a b )cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 7 2 5 4 3 2 +--R (4b - 64a b - 68a b )cosh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 6 +--R (24a b - 32a b - 56a b )cosh(x) - 2b + 18a b + 12a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 3 4 4 2 5 4 3 3 +--R (- 4a b - 4a b )cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (8a b - 32a b - 40a b )cosh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 +--R (24a b + 8a b - 16a b)cosh(x) - 4a b + 4a b + 8a b +--R * +--R sinh(x) +--R + +--R 2 5 4 3 4 3 4 5 2 3 +--R (- 2a b - 2a b )cosh(x) + (- 8a b - 8a b )cosh(x) +--R + +--R 2 5 4 3 6 2 3 4 5 2 2 5 4 3 +--R (4a b - 4a b - 8a b)cosh(x) + (8a b + 8a b )cosh(x) - 2a b - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 6 3 4 6 +--R (- a b - a b )sinh(x) +--R + +--R 6 3 4 2 5 4 3 5 +--R ((- 4a b - 4a b )cosh(x) - 6a b - 6a b )sinh(x) +--R + +--R 6 3 4 2 2 5 4 3 6 +--R (- 6a b - 6a b )cosh(x) + (- 20a b - 20a b )cosh(x) + 2a b +--R + +--R 3 4 5 2 +--R - 11a b - 13a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 3 4 3 2 5 4 3 2 +--R (- 4a b - 4a b )cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 6 3 4 5 2 2 5 4 3 6 +--R (4a b - 32a b - 36a b )cosh(x) + 8a b - 4a b - 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 3 4 4 2 5 4 3 3 +--R (- a b - a b )cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 6 3 4 5 2 2 2 5 4 3 6 +--R (2a b - 32a b - 34a b )cosh(x) + (12a b - 16a b - 28a b)cosh(x) +--R + +--R 6 3 4 5 2 7 +--R - a b + 9a b + 6a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 3 4 3 4 5 2 3 +--R (- 2a b - 2a b )cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 2 5 4 3 6 2 3 4 5 2 7 +--R (4a b - 16a b - 20a b)cosh(x) + (12a b + 4a b - 8a )cosh(x) +--R + +--R 2 5 4 3 6 +--R - 2a b + 2a b + 4a b +--R * +--R sinh(x) +--R + +--R 3 4 5 2 4 4 3 6 3 +--R (- a b - a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 3 4 5 2 7 2 4 3 6 3 4 5 2 +--R (2a b - 2a b - 4a )cosh(x) + (4a b + 4a b)cosh(x) - a b - a b +--R Type: Expression(Integer) +--E 35 + +--S 36 of 552 +t0707:= sinh(x)^2/(a+b*sinh(x))^2 +--R +--R +--R 2 +--R sinh(x) +--R (36) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 36 + +--S 37 of 552 +r0707:= x/b^2-2*a^3*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/b^2/_ + (a^2+b^2)^(3/2)+4*a*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/_ + b^2/(a^2+b^2)^(1/2)-a^2*cosh(x)/b/(a^2+b^2)/(a+b*sinh(x)) +--R +--R +--R (37) +--R x +--R a tanh(-) - b +--R 3 3 2 2 4 2 +--R ((- 4a b - 2a b)sinh(x) - 4a b - 2a )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 3 2 2 2 3 | 2 2 +--R ((b + a b)x sinh(x) - a b cosh(x) + (a b + a )x)\|b + a +--R / +--R +-------+ +--R 5 2 3 4 3 2 | 2 2 +--R ((b + a b )sinh(x) + a b + a b )\|b + a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 552 +a0707:= integrate(t0707,x) +--R +--R +--R (38) +--R 3 3 2 3 3 2 2 4 +--R (2a b + a b)sinh(x) + ((4a b + 2a b)cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (2a b + a b)cosh(x) + (4a b + 2a )cosh(x) - 2a b - a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 2 2 +--R (b + a b)x sinh(x) +--R + +--R 3 2 2 3 3 +--R ((2b + 2a b)x cosh(x) + (2a b + 2a )x + 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 3 2 +--R (b + a b)x cosh(x) + ((2a b + 2a )x + 2a )cosh(x) + (- b - a b)x +--R + +--R 2 +--R - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 2 3 2 5 2 3 4 3 2 +--R (b + a b )sinh(x) + ((2b + 2a b )cosh(x) + 2a b + 2a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 2 3 +--R (b + a b )cosh(x) + (2a b + 2a b )cosh(x) - b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 552 +m0707:= a0707-r0707 +--R +--R +--R (39) +--R 4 3 2 3 +--R (2a b + a b )sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R ((4a b + 2a b )cosh(x) + 6a b + 3a b)sinh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (2a b + a b )cosh(x) + (8a b + 4a b)cosh(x) - 2a b + 3a b +--R + +--R 5 +--R 2a +--R * +--R sinh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (2a b + a b)cosh(x) + (4a b + 2a )cosh(x) - 2a b - a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 3 2 3 +--R (4a b + 2a b )sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R ((8a b + 4a b )cosh(x) + 12a b + 6a b)sinh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (4a b + 2a b )cosh(x) + (16a b + 8a b)cosh(x) - 4a b + 6a b +--R + +--R 5 +--R 4a +--R * +--R sinh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (4a b + 2a b)cosh(x) + (8a b + 4a )cosh(x) - 4a b - 2a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 3 2 +--R (a b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 3 2 2 4 2 2 3 +--R (2a b cosh(x) + 4a b cosh(x) - 2a b + 2a )sinh(x) + a b cosh(x) +--R + +--R 3 2 2 2 4 3 +--R 2a b cosh(x) + (- a b + 2a )cosh(x) - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 6 2 4 3 6 2 4 5 3 3 2 +--R (b + a b )sinh(x) + ((2b + 2a b )cosh(x) + 3a b + 3a b )sinh(x) +--R + +--R 6 2 4 2 5 3 3 6 2 4 4 2 +--R ((b + a b )cosh(x) + (4a b + 4a b )cosh(x) - b + a b + 2a b ) +--R * +--R sinh(x) +--R + +--R 5 3 3 2 2 4 4 2 5 3 3 +--R (a b + a b )cosh(x) + (2a b + 2a b )cosh(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 39 + +--S 40 of 552 +d0707:= D(m0707,x) +--R +--R +--R (40) +--R 5 3 3 6 +--R (2a b + 2a b )sinh(x) +--R + +--R 5 3 3 2 4 4 2 5 +--R ((8a b + 8a b )cosh(x) + 8a b + 7a b )sinh(x) +--R + +--R 5 3 3 2 2 4 4 2 5 +--R (12a b + 11a b )cosh(x) + (28a b + 24a b )cosh(x) - 4a b +--R + +--R 3 3 5 +--R 10a b + 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 3 2 4 4 2 2 +--R (8a b + 4a b )cosh(x) + (36a b + 26a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (- 8a b + 32a b + 24a b)cosh(x) - 12a b + 2a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (2a b - 4a b )cosh(x) + (20a b + 4a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 4a b + 38a b + 18a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (- 20a b + 12a b + 8a )cosh(x) + 2a b - 10a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 4 4 2 4 3 3 3 +--R - 4a b cosh(x) + (4a b - 9a b )cosh(x) + 20a b cosh(x) +--R + +--R 2 4 4 2 6 2 3 3 2 4 4 2 +--R (- 8a b + 18a b + 4a )cosh(x) - 16a b cosh(x) + 4a b - a b +--R * +--R sinh(x) +--R + +--R 3 3 6 4 2 5 3 3 5 4 +--R - a b cosh(x) - 4a b cosh(x) + (4a b - 3a b)cosh(x) +--R + +--R 4 2 3 3 3 5 2 4 2 3 3 5 +--R 8a b cosh(x) + (- 5a b + 2a b)cosh(x) - 4a b cosh(x) + 2a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 4 6 2 4 5 3 3 5 +--R - 2a b sinh(x) + (- 8a b cosh(x) + 8a b - 2a b )sinh(x) +--R + +--R 2 4 2 5 3 3 2 4 4 2 4 +--R (- 10a b cosh(x) + (24a b - 8a b )cosh(x) + 28a b + 8a b )sinh(x) +--R + +--R 5 3 3 2 2 4 4 2 5 +--R (24a b - 4a b )cosh(x) + (72a b + 24a b )cosh(x) - 8a b +--R + +--R 3 3 5 +--R 28a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 5 3 3 3 +--R 10a b cosh(x) + (8a b + 16a b )cosh(x) +--R + +--R 2 4 4 2 2 5 3 3 5 +--R (56a b + 32a b )cosh(x) + (- 8a b + 64a b + 40a b)cosh(x) +--R + +--R 2 4 6 +--R - 18a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 5 3 3 4 2 4 4 2 3 +--R 8a b cosh(x) + 22a b cosh(x) + (8a b + 24a b )cosh(x) +--R + +--R 3 3 5 2 2 4 4 2 6 +--R (36a b + 32a b)cosh(x) + (- 16a b + 8a b + 16a )cosh(x) +--R + +--R 3 3 5 +--R - 10a b - 8a b +--R * +--R sinh(x) +--R + +--R 2 4 6 3 3 5 2 4 4 2 4 +--R 2a b cosh(x) + 8a b cosh(x) + (- 4a b + 8a b )cosh(x) +--R + +--R 5 3 2 4 4 2 6 2 3 3 5 +--R 8a b cosh(x) + (2a b + 8a b + 8a )cosh(x) + (- 8a b - 8a b)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 3 3 6 +--R (- 2a b - 2a b )sinh(x) +--R + +--R 5 3 3 2 4 4 2 5 +--R ((- 8a b - 8a b )cosh(x) - 8a b - 7a b )sinh(x) +--R + +--R 5 3 3 2 2 4 4 2 5 +--R (- 12a b - 11a b )cosh(x) + (- 28a b - 24a b )cosh(x) + 4a b +--R + +--R 3 3 5 +--R - 10a b - 9a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 3 2 4 4 2 2 +--R (- 8a b - 4a b )cosh(x) + (- 36a b - 26a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (8a b - 32a b - 24a b)cosh(x) + 12a b - 2a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (- 2a b + 4a b )cosh(x) + (- 20a b - 4a b )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 6 +--R (4a b - 38a b - 18a b)cosh(x) + (20a b - 12a b - 8a )cosh(x) +--R + +--R 5 3 3 5 +--R - 2a b + 10a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 4 4 2 4 3 3 3 +--R 4a b cosh(x) + (- 4a b + 9a b )cosh(x) - 20a b cosh(x) +--R + +--R 2 4 4 2 6 2 3 3 2 4 4 2 +--R (8a b - 18a b - 4a )cosh(x) + 16a b cosh(x) - 4a b + a b +--R * +--R sinh(x) +--R + +--R 3 3 6 4 2 5 3 3 5 4 4 2 3 +--R a b cosh(x) + 4a b cosh(x) + (- 4a b + 3a b)cosh(x) - 8a b cosh(x) +--R + +--R 3 3 5 2 4 2 3 3 5 +--R (5a b - 2a b)cosh(x) + 4a b cosh(x) - 2a b - a b +--R / +--R 7 3 5 6 +--R (a b + a b )sinh(x) +--R + +--R 7 3 5 2 6 4 4 5 +--R ((4a b + 4a b )cosh(x) + 6a b + 6a b )sinh(x) +--R + +--R 7 3 5 2 2 6 4 4 7 +--R (6a b + 6a b )cosh(x) + (20a b + 20a b )cosh(x) - 2a b +--R + +--R 3 5 5 3 +--R 11a b + 13a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 3 5 3 2 6 4 4 2 +--R (4a b + 4a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 6 2 +--R (- 4a b + 32a b + 36a b )cosh(x) - 8a b + 4a b + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 3 5 4 2 6 4 4 3 +--R (a b + a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (- 2a b + 32a b + 34a b )cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 7 +--R (- 12a b + 16a b + 28a b )cosh(x) + a b - 9a b - 6a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 4 4 4 3 5 5 3 3 +--R (2a b + 2a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 4a b + 16a b + 20a b )cosh(x) +--R + +--R 3 5 5 3 7 2 6 4 4 6 2 +--R (- 12a b - 4a b + 8a b)cosh(x) + 2a b - 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 4 4 4 6 2 3 +--R (a b + a b )cosh(x) + (4a b + 4a b )cosh(x) +--R + +--R 3 5 5 3 7 2 4 4 6 2 3 5 +--R (- 2a b + 2a b + 4a b)cosh(x) + (- 4a b - 4a b )cosh(x) + a b +--R + +--R 5 3 +--R a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 2 6 6 +--R (- 2b - 2a b )sinh(x) +--R + +--R 8 2 6 7 3 5 5 +--R ((- 8b - 8a b )cosh(x) - 12a b - 12a b )sinh(x) +--R + +--R 8 2 6 2 7 3 5 8 +--R (- 12b - 12a b )cosh(x) + (- 40a b - 40a b )cosh(x) + 4b +--R + +--R 2 6 4 4 +--R - 22a b - 26a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 2 6 3 7 3 5 2 +--R (- 8b - 8a b )cosh(x) + (- 48a b - 48a b )cosh(x) +--R + +--R 8 2 6 4 4 7 3 5 5 3 +--R (8b - 64a b - 72a b )cosh(x) + 16a b - 8a b - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 6 4 7 3 5 3 +--R (- 2b - 2a b )cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 8 2 6 4 4 2 +--R (4b - 64a b - 68a b )cosh(x) +--R + +--R 7 3 5 5 3 8 2 6 4 4 6 2 +--R (24a b - 32a b - 56a b )cosh(x) - 2b + 18a b + 12a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 3 5 4 2 6 4 4 3 +--R (- 4a b - 4a b )cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (8a b - 32a b - 40a b )cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 5 3 +--R (24a b + 8a b - 16a b )cosh(x) - 4a b + 4a b + 8a b +--R * +--R sinh(x) +--R + +--R 2 6 4 4 4 3 5 5 3 3 +--R (- 2a b - 2a b )cosh(x) + (- 8a b - 8a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 3 5 5 3 2 6 +--R (4a b - 4a b - 8a b )cosh(x) + (8a b + 8a b )cosh(x) - 2a b +--R + +--R 4 4 +--R - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 7 3 5 6 +--R (- a b - a b )sinh(x) +--R + +--R 7 3 5 2 6 4 4 5 +--R ((- 4a b - 4a b )cosh(x) - 6a b - 6a b )sinh(x) +--R + +--R 7 3 5 2 2 6 4 4 7 +--R (- 6a b - 6a b )cosh(x) + (- 20a b - 20a b )cosh(x) + 2a b +--R + +--R 3 5 5 3 +--R - 11a b - 13a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 3 5 3 2 6 4 4 2 +--R (- 4a b - 4a b )cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 6 2 +--R (4a b - 32a b - 36a b )cosh(x) + 8a b - 4a b - 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 3 5 4 2 6 4 4 3 +--R (- a b - a b )cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 7 3 5 5 3 2 2 6 4 4 6 2 +--R (2a b - 32a b - 34a b )cosh(x) + (12a b - 16a b - 28a b )cosh(x) +--R + +--R 7 3 5 5 3 7 +--R - a b + 9a b + 6a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 4 4 4 3 5 5 3 3 +--R (- 2a b - 2a b )cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 3 5 5 3 7 +--R (4a b - 16a b - 20a b )cosh(x) + (12a b + 4a b - 8a b)cosh(x) +--R + +--R 2 6 4 4 6 2 +--R - 2a b + 2a b + 4a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 4 4 4 6 2 3 +--R (- a b - a b )cosh(x) + (- 4a b - 4a b )cosh(x) +--R + +--R 3 5 5 3 7 2 4 4 6 2 3 5 5 3 +--R (2a b - 2a b - 4a b)cosh(x) + (4a b + 4a b )cosh(x) - a b - a b +--R Type: Expression(Integer) +--E 40 + +--S 41 of 552 +t0708:= sinh(x)^3/(a+b*sinh(x))^2 +--R +--R +--R 3 +--R sinh(x) +--R (41) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 41 + +--S 42 of 552 +r0708:= -2*a*x/b^3+2*a^4*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/b^3/_ + (a^2+b^2)^(3/2)-6*a^2*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/_ + b^3/(a^2+b^2)^(1/2)+cosh(x)/b^2+a^3*cosh(x)/b^2/(a^2+b^2)/_ + (a+b*sinh(x)) +--R +--R +--R (42) +--R x +--R a tanh(-) - b +--R 2 3 4 3 2 5 2 +--R ((6a b + 4a b)sinh(x) + 6a b + 4a )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 2 2 3 3 +--R ((b + a b )cosh(x) + (- 2a b - 2a b)x)sinh(x) +--R + +--R 3 3 2 2 4 +--R (a b + 2a b)cosh(x) + (- 2a b - 2a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 6 2 4 5 3 3 | 2 2 +--R ((b + a b )sinh(x) + a b + a b )\|b + a +--R Type: Expression(Integer) +--E 42 + +--S 43 of 552 +a0708:= integrate(t0708,x) +--R +--R +--R (43) +--R 2 3 4 3 +--R (6a b + 4a b)sinh(x) +--R + +--R 2 3 4 3 2 5 2 +--R ((18a b + 12a b)cosh(x) + 12a b + 8a )sinh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R ((18a b + 12a b)cosh(x) + (24a b + 16a )cosh(x) - 6a b - 4a b) +--R * +--R sinh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (6a b + 4a b)cosh(x) + (12a b + 8a )cosh(x) +--R + +--R 2 3 4 +--R (- 6a b - 4a b)cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 2 2 4 +--R (b + a b )sinh(x) +--R + +--R 4 2 2 3 3 3 3 3 +--R ((4b + 4a b )cosh(x) + (- 4a b - 4a b)x + 2a b + 2a b)sinh(x) +--R + +--R 4 2 2 2 +--R (6b + 6a b )cosh(x) +--R + +--R 3 3 3 3 2 2 4 +--R ((- 12a b - 12a b)x + 6a b + 6a b)cosh(x) + (- 8a b - 8a )x +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 3 +--R (4b + 4a b )cosh(x) +--R + +--R 3 3 3 3 2 +--R ((- 12a b - 12a b)x + 6a b + 6a b)cosh(x) +--R + +--R 2 2 4 4 3 3 3 3 +--R ((- 16a b - 16a )x - 8a )cosh(x) + (4a b + 4a b)x + 2a b + 6a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 3 3 +--R (b + a b )cosh(x) + ((- 4a b - 4a b)x + 2a b + 2a b)cosh(x) +--R + +--R 2 2 4 4 2 +--R ((- 8a b - 8a )x - 4a )cosh(x) +--R + +--R 3 3 3 3 4 2 2 +--R ((4a b + 4a b)x + 2a b + 6a b)cosh(x) - b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 6 2 4 3 6 2 4 5 3 3 2 +--R (2b + 2a b )sinh(x) + ((6b + 6a b )cosh(x) + 4a b + 4a b )sinh(x) +--R + +--R 6 2 4 2 5 3 3 6 2 4 +--R ((6b + 6a b )cosh(x) + (8a b + 8a b )cosh(x) - 2b - 2a b )sinh(x) +--R + +--R 6 2 4 3 5 3 3 2 6 2 4 +--R (2b + 2a b )cosh(x) + (4a b + 4a b )cosh(x) + (- 2b - 2a b )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 552 +m0708:= a0708-r0708 +--R +--R +--R (44) +--R 2 4 4 2 4 +--R (6a b + 4a b )sinh(x) +--R + +--R 2 4 4 2 3 3 5 3 +--R ((18a b + 12a b )cosh(x) + 18a b + 12a b)sinh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 +--R (18a b + 12a b )cosh(x) + (42a b + 28a b)cosh(x) - 6a b +--R + +--R 4 2 6 +--R 8a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 3 3 3 5 2 +--R (6a b + 4a b )cosh(x) + (30a b + 20a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (- 6a b + 20a b + 16a )cosh(x) - 6a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 5 3 4 2 6 2 +--R (6a b + 4a b)cosh(x) + (12a b + 8a )cosh(x) +--R + +--R 3 3 5 +--R (- 6a b - 4a b)cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 4 4 2 4 +--R (- 12a b - 8a b )sinh(x) +--R + +--R 2 4 4 2 3 3 5 3 +--R ((- 36a b - 24a b )cosh(x) - 36a b - 24a b)sinh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 +--R (- 36a b - 24a b )cosh(x) + (- 84a b - 56a b)cosh(x) + 12a b +--R + +--R 4 2 6 +--R - 16a b - 16a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 3 3 3 5 2 +--R (- 12a b - 8a b )cosh(x) + (- 60a b - 40a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (12a b - 40a b - 32a )cosh(x) + 12a b + 8a b +--R * +--R sinh(x) +--R + +--R 3 3 5 3 4 2 6 2 +--R (- 12a b - 8a b)cosh(x) + (- 24a b - 16a )cosh(x) +--R + +--R 3 3 5 +--R (12a b + 8a b)cosh(x) +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 5 2 3 5 5 2 3 4 3 2 4 +--R (b + a b )sinh(x) + ((2b + 2a b )cosh(x) + 3a b + 3a b )sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R ((4a b + 2a b )cosh(x) + 2a b - 2a b)sinh(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (- 2b - 2a b )cosh(x) + (- 2a b - 8a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (2b + 4a b - 10a b)cosh(x) + 2a b + 6a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (- b - a b )cosh(x) + (- 4a b - 10a b )cosh(x) +--R + +--R 5 4 2 4 3 2 5 5 2 3 +--R (2b - 14a b)cosh(x) + (4a b + 10a b - 8a )cosh(x) - b + a b +--R + +--R 4 +--R 6a b +--R * +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- a b - 3a b )cosh(x) + (- 2a b - 6a b)cosh(x) +--R + +--R 4 3 2 5 2 2 3 4 4 3 2 +--R (2a b + 4a b - 4a )cosh(x) + (2a b + 6a b)cosh(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 7 2 5 4 7 2 5 6 3 4 3 +--R (2b + 2a b )sinh(x) + ((6b + 6a b )cosh(x) + 6a b + 6a b )sinh(x) +--R + +--R 7 2 5 2 6 3 4 7 2 5 +--R (6b + 6a b )cosh(x) + (14a b + 14a b )cosh(x) - 2b + 2a b +--R + +--R 4 3 +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 3 6 3 4 2 +--R (2b + 2a b )cosh(x) + (10a b + 10a b )cosh(x) +--R + +--R 7 2 5 4 3 6 3 4 +--R (- 2b + 6a b + 8a b )cosh(x) - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 6 3 4 3 2 5 4 3 2 +--R (2a b + 2a b )cosh(x) + (4a b + 4a b )cosh(x) +--R + +--R 6 3 4 +--R (- 2a b - 2a b )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 44 + +--S 45 of 552 +d0708:= D(m0708,x) +--R +--R +--R (45) +--R 6 3 4 8 +--R (- a b - a b )sinh(x) +--R + +--R 6 3 4 2 5 4 3 7 +--R ((- 4a b - 4a b )cosh(x) - 12a b - 12a b )sinh(x) +--R + +--R 6 3 4 2 2 5 4 3 6 +--R (- 5a b - 5a b )cosh(x) + (- 50a b - 50a b )cosh(x) + a b +--R + +--R 3 4 5 2 +--R - 36a b - 35a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 4 3 2 3 4 5 2 +--R (- 78a b - 76a b )cosh(x) + (- 144a b - 134a b )cosh(x) +--R + +--R 2 5 4 3 6 +--R 14a b - 36a b - 40a b +--R * +--R 5 +--R sinh(x) +--R + +--R 6 3 4 4 2 5 4 3 3 +--R (5a b + 5a b )cosh(x) + (- 52a b - 42a b )cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (- 6a b - 219a b - 185a b )cosh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 7 +--R (28a b - 150a b - 136a b)cosh(x) + a b + 34a b - 3a b - 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 3 4 5 2 5 4 3 4 +--R (4a b + 4a b )cosh(x) + (- 8a b + 12a b )cosh(x) +--R + +--R 6 3 4 5 2 3 +--R (- 8a b - 152a b - 92a b )cosh(x) +--R + +--R 2 5 4 3 6 2 +--R (8a b - 232a b - 160a b)cosh(x) +--R + +--R 6 3 4 5 2 7 4 3 6 +--R (4a b + 76a b - 44a b - 48a )cosh(x) + 28a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 3 4 6 2 5 4 3 5 +--R (a b + a b )cosh(x) + (6a b + 26a b )cosh(x) +--R + +--R 6 3 4 5 2 4 +--R (- 3a b - 42a b + 19a b )cosh(x) +--R + +--R 2 5 4 3 6 3 +--R (- 12a b - 164a b - 64a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 +--R (3a b + 45a b - 98a b - 48a )cosh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 +--R (6a b + 66a b + 8a b)cosh(x) - a b - 4a b + 7a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 3 6 5 2 5 +--R (2a b + 12a b )cosh(x) + 34a b cosh(x) +--R + +--R 2 5 4 3 6 4 5 2 7 3 +--R (- 6a b - 52a b + 8a b)cosh(x) + (- 76a b - 16a )cosh(x) +--R + +--R 2 5 4 3 6 2 5 2 2 5 4 3 +--R (6a b + 44a b - 8a b)cosh(x) + 18a b cosh(x) - 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 4 3 7 3 4 5 2 6 4 3 6 5 +--R 2a b cosh(x) + (a b + 9a b )cosh(x) + (- 6a b + 8a b)cosh(x) +--R + +--R 3 4 5 2 4 4 3 6 3 +--R (- 3a b - 19a b )cosh(x) + (6a b - 8a b)cosh(x) +--R + +--R 3 4 5 2 2 4 3 3 4 5 2 +--R (3a b + 11a b )cosh(x) - 2a b cosh(x) - a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 7 2 5 8 +--R (2b + 2a b )sinh(x) +--R + +--R 7 2 5 6 3 4 7 +--R ((8b + 8a b )cosh(x) + 12a b + 16a b )sinh(x) +--R + +--R 7 2 5 2 6 3 4 7 4 3 +--R ((10b + 10a b )cosh(x) + (40a b + 60a b )cosh(x) - 2b + 22a b ) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 3 4 2 2 5 4 3 6 +--R (36a b + 72a b )cosh(x) + (- 24a b + 60a b )cosh(x) - 4a b +--R + +--R 3 4 5 2 +--R - 68a b - 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 7 2 5 4 6 3 4 3 +--R (- 10b - 10a b )cosh(x) + (- 16a b + 4a b )cosh(x) +--R + +--R 7 2 5 4 3 2 +--R (12b - 90a b + 18a b )cosh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 6 +--R (16a b - 240a b - 120a b )cosh(x) - 2b + 28a b - 74a b - 64a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 5 5 6 3 4 4 +--R (- 8b - 8a b )cosh(x) + (- 44a b - 64a b )cosh(x) +--R + +--R 7 2 5 4 3 3 +--R (16b - 128a b - 104a b )cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (56a b - 328a b - 240a b )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 +--R (- 8b + 88a b - 232a b - 224a b)cosh(x) - 12a b + 56a b +--R + +--R 5 2 7 +--R 16a b - 32a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 5 6 6 3 4 5 +--R (- 2b - 2a b )cosh(x) + (- 24a b - 60a b )cosh(x) +--R + +--R 7 2 5 4 3 4 +--R (6b - 84a b - 150a b )cosh(x) +--R + +--R 6 3 4 5 2 3 +--R (48a b - 208a b - 240a b )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- 6b + 102a b - 252a b - 288a b)cosh(x) +--R + +--R 6 3 4 5 2 7 7 2 5 +--R (- 24a b + 124a b + 16a b - 96a )cosh(x) + 2b - 16a b +--R + +--R 4 3 6 +--R 18a b + 32a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 3 4 6 2 5 4 3 5 +--R (- 4a b - 24a b )cosh(x) + (- 24a b - 84a b )cosh(x) +--R + +--R 6 3 4 5 2 4 +--R (12a b - 52a b - 120a b )cosh(x) +--R + +--R 2 5 4 3 6 3 +--R (48a b - 104a b - 160a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 12a b + 80a b - 16a b - 96a )cosh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 +--R (- 24a b + 44a b + 64a b)cosh(x) + 4a b - 4a b - 8a b +--R * +--R sinh(x) +--R + +--R 3 4 7 2 5 4 3 6 5 2 5 +--R - 4a b cosh(x) + (- 2a b - 18a b )cosh(x) - 24a b cosh(x) +--R + +--R 2 5 4 3 6 4 3 4 5 2 7 3 +--R (6a b - 10a b - 32a b)cosh(x) + (12a b - 16a b - 32a )cosh(x) +--R + +--R 2 5 4 3 6 2 3 4 5 2 2 5 +--R (- 6a b + 26a b + 32a b)cosh(x) + (- 8a b - 8a b )cosh(x) + 2a b +--R + +--R 4 3 +--R 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 6 3 4 8 +--R (a b + a b )sinh(x) +--R + +--R 6 3 4 2 5 4 3 7 +--R ((4a b + 4a b )cosh(x) + 12a b + 12a b )sinh(x) +--R + +--R 6 3 4 2 2 5 4 3 6 3 4 +--R (5a b + 5a b )cosh(x) + (50a b + 50a b )cosh(x) - a b + 36a b +--R + +--R 5 2 +--R 35a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 4 3 2 3 4 5 2 2 5 +--R (78a b + 76a b )cosh(x) + (144a b + 134a b )cosh(x) - 14a b +--R + +--R 4 3 6 +--R 36a b + 40a b +--R * +--R 5 +--R sinh(x) +--R + +--R 6 3 4 4 2 5 4 3 3 +--R (- 5a b - 5a b )cosh(x) + (52a b + 42a b )cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (6a b + 219a b + 185a b )cosh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 7 +--R (- 28a b + 150a b + 136a b)cosh(x) - a b - 34a b + 3a b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 3 4 5 2 5 4 3 4 +--R (- 4a b - 4a b )cosh(x) + (8a b - 12a b )cosh(x) +--R + +--R 6 3 4 5 2 3 +--R (8a b + 152a b + 92a b )cosh(x) +--R + +--R 2 5 4 3 6 2 +--R (- 8a b + 232a b + 160a b)cosh(x) +--R + +--R 6 3 4 5 2 7 4 3 6 +--R (- 4a b - 76a b + 44a b + 48a )cosh(x) - 28a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 3 4 6 2 5 4 3 5 +--R (- a b - a b )cosh(x) + (- 6a b - 26a b )cosh(x) +--R + +--R 6 3 4 5 2 4 +--R (3a b + 42a b - 19a b )cosh(x) +--R + +--R 2 5 4 3 6 3 +--R (12a b + 164a b + 64a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 3a b - 45a b + 98a b + 48a )cosh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 +--R (- 6a b - 66a b - 8a b)cosh(x) + a b + 4a b - 7a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 3 6 5 2 5 +--R (- 2a b - 12a b )cosh(x) - 34a b cosh(x) +--R + +--R 2 5 4 3 6 4 5 2 7 3 +--R (6a b + 52a b - 8a b)cosh(x) + (76a b + 16a )cosh(x) +--R + +--R 2 5 4 3 6 2 5 2 2 5 4 3 +--R (- 6a b - 44a b + 8a b)cosh(x) - 18a b cosh(x) + 2a b + 4a b +--R * +--R sinh(x) +--R + +--R 4 3 7 3 4 5 2 6 4 3 6 5 +--R - 2a b cosh(x) + (- a b - 9a b )cosh(x) + (6a b - 8a b)cosh(x) +--R + +--R 3 4 5 2 4 4 3 6 3 +--R (3a b + 19a b )cosh(x) + (- 6a b + 8a b)cosh(x) +--R + +--R 3 4 5 2 2 4 3 3 4 5 2 +--R (- 3a b - 11a b )cosh(x) + 2a b cosh(x) + a b + a b +--R / +--R 8 3 6 7 +--R (2a b + 2a b )sinh(x) +--R + +--R 8 3 6 2 7 4 5 6 +--R ((10a b + 10a b )cosh(x) + 12a b + 12a b )sinh(x) +--R + +--R 8 3 6 2 2 7 4 5 8 +--R (20a b + 20a b )cosh(x) + (52a b + 52a b )cosh(x) - 4a b +--R + +--R 3 6 5 4 +--R 22a b + 26a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 3 6 3 2 7 4 5 2 +--R (20a b + 20a b )cosh(x) + (88a b + 88a b )cosh(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 +--R (- 12a b + 86a b + 98a b )cosh(x) - 16a b + 8a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 3 6 4 2 7 4 5 3 +--R (10a b + 10a b )cosh(x) + (72a b + 72a b )cosh(x) +--R + +--R 8 3 6 5 4 2 +--R (- 12a b + 128a b + 140a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (- 40a b + 40a b + 80a b )cosh(x) + 2a b - 18a b - 12a b +--R + +--R 7 2 +--R 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 3 6 5 2 7 4 5 4 +--R (2a b + 2a b )cosh(x) + (28a b + 28a b )cosh(x) +--R + +--R 8 3 6 5 4 3 +--R (- 4a b + 88a b + 92a b )cosh(x) +--R + +--R 2 7 4 5 6 3 2 +--R (- 32a b + 64a b + 96a b )cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 +--R (2a b - 42a b - 20a b + 24a b )cosh(x) + 4a b - 4a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 4 5 5 3 6 5 4 4 +--R (4a b + 4a b )cosh(x) + (26a b + 26a b )cosh(x) +--R + +--R 2 7 4 5 6 3 3 +--R (- 8a b + 40a b + 48a b )cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 28a b - 4a b + 24a b )cosh(x) +--R + +--R 2 7 4 5 6 3 3 6 5 4 +--R (4a b - 12a b - 16a b )cosh(x) + 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 6 5 4 5 4 5 6 3 4 +--R (2a b + 2a b )cosh(x) + (8a b + 8a b )cosh(x) +--R + +--R 3 6 5 4 7 2 3 4 5 6 3 2 +--R (- 4a b + 4a b + 8a b )cosh(x) + (- 8a b - 8a b )cosh(x) +--R + +--R 3 6 5 4 +--R (2a b + 2a b )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 9 2 7 7 +--R (- 4b - 4a b )sinh(x) +--R + +--R 9 2 7 8 3 6 6 +--R ((- 20b - 20a b )cosh(x) - 24a b - 24a b )sinh(x) +--R + +--R 9 2 7 2 8 3 6 9 +--R (- 40b - 40a b )cosh(x) + (- 104a b - 104a b )cosh(x) + 8b +--R + +--R 2 7 4 5 +--R - 44a b - 52a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 2 7 3 8 3 6 2 +--R (- 40b - 40a b )cosh(x) + (- 176a b - 176a b )cosh(x) +--R + +--R 9 2 7 4 5 8 3 6 5 4 +--R (24b - 172a b - 196a b )cosh(x) + 32a b - 16a b - 48a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 2 7 4 8 3 6 3 +--R (- 20b - 20a b )cosh(x) + (- 144a b - 144a b )cosh(x) +--R + +--R 9 2 7 4 5 2 +--R (24b - 256a b - 280a b )cosh(x) +--R + +--R 8 3 6 5 4 9 2 7 4 5 6 3 +--R (80a b - 80a b - 160a b )cosh(x) - 4b + 36a b + 24a b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 9 2 7 5 8 3 6 4 +--R (- 4b - 4a b )cosh(x) + (- 56a b - 56a b )cosh(x) +--R + +--R 9 2 7 4 5 3 +--R (8b - 176a b - 184a b )cosh(x) +--R + +--R 8 3 6 5 4 2 +--R (64a b - 128a b - 192a b )cosh(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 5 4 +--R (- 4b + 84a b + 40a b - 48a b )cosh(x) - 8a b + 8a b + 16a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 3 6 5 2 7 4 5 4 +--R (- 8a b - 8a b )cosh(x) + (- 52a b - 52a b )cosh(x) +--R + +--R 8 3 6 5 4 3 +--R (16a b - 80a b - 96a b )cosh(x) +--R + +--R 2 7 4 5 6 3 2 +--R (56a b + 8a b - 48a b )cosh(x) +--R + +--R 8 3 6 5 4 2 7 4 5 +--R (- 8a b + 24a b + 32a b )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 7 4 5 5 3 6 5 4 4 +--R (- 4a b - 4a b )cosh(x) + (- 16a b - 16a b )cosh(x) +--R + +--R 2 7 4 5 6 3 3 3 6 5 4 2 +--R (8a b - 8a b - 16a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 2 7 4 5 +--R (- 4a b - 4a b )cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 8 3 6 7 +--R (- 2a b - 2a b )sinh(x) +--R + +--R 8 3 6 2 7 4 5 6 +--R ((- 10a b - 10a b )cosh(x) - 12a b - 12a b )sinh(x) +--R + +--R 8 3 6 2 2 7 4 5 8 +--R (- 20a b - 20a b )cosh(x) + (- 52a b - 52a b )cosh(x) + 4a b +--R + +--R 3 6 5 4 +--R - 22a b - 26a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 3 6 3 2 7 4 5 2 +--R (- 20a b - 20a b )cosh(x) + (- 88a b - 88a b )cosh(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 +--R (12a b - 86a b - 98a b )cosh(x) + 16a b - 8a b - 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 3 6 4 2 7 4 5 3 +--R (- 10a b - 10a b )cosh(x) + (- 72a b - 72a b )cosh(x) +--R + +--R 8 3 6 5 4 2 +--R (12a b - 128a b - 140a b )cosh(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 7 2 +--R (40a b - 40a b - 80a b )cosh(x) - 2a b + 18a b + 12a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 3 6 5 2 7 4 5 4 +--R (- 2a b - 2a b )cosh(x) + (- 28a b - 28a b )cosh(x) +--R + +--R 8 3 6 5 4 3 +--R (4a b - 88a b - 92a b )cosh(x) +--R + +--R 2 7 4 5 6 3 2 +--R (32a b - 64a b - 96a b )cosh(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 +--R (- 2a b + 42a b + 20a b - 24a b )cosh(x) - 4a b + 4a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 4 5 5 3 6 5 4 4 +--R (- 4a b - 4a b )cosh(x) + (- 26a b - 26a b )cosh(x) +--R + +--R 2 7 4 5 6 3 3 3 6 5 4 7 2 2 +--R (8a b - 40a b - 48a b )cosh(x) + (28a b + 4a b - 24a b )cosh(x) +--R + +--R 2 7 4 5 6 3 3 6 5 4 +--R (- 4a b + 12a b + 16a b )cosh(x) - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 6 5 4 5 4 5 6 3 4 +--R (- 2a b - 2a b )cosh(x) + (- 8a b - 8a b )cosh(x) +--R + +--R 3 6 5 4 7 2 3 4 5 6 3 2 +--R (4a b - 4a b - 8a b )cosh(x) + (8a b + 8a b )cosh(x) +--R + +--R 3 6 5 4 +--R (- 2a b - 2a b )cosh(x) +--R Type: Expression(Integer) +--E 45 + +--S 46 of 552 +t0709:= sinh(x)^4/(a+b*sinh(x))^2 +--R +--R +--R 4 +--R sinh(x) +--R (46) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 552 +r0709:= 3*a^2*x/b^4-1/2*x/b^2-2*a^5*atanh((b-a*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/b^4/(a^2+b^2)^(3/2)+_ + 8*a^3*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/b^4/(a^2+b^2)^(1/2)-_ + 2*a*cosh(x)/b^3+1/2*cosh(x)*sinh(x)/b^2-_ + a^4*cosh(x)/b^3/(a^2+b^2)/(a+b*sinh(x)) +--R +--R +--R (47) +--R x +--R a tanh(-) - b +--R 3 3 5 4 2 6 2 +--R ((- 16a b - 12a b)sinh(x) - 16a b - 12a )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 5 2 3 2 +--R (b + a b )cosh(x)sinh(x) +--R + +--R 4 3 2 5 2 3 4 +--R ((- 3a b - 3a b )cosh(x) + (- b + 5a b + 6a b)x)sinh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 4a b - 6a b)cosh(x) + (- a b + 5a b + 6a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 7 2 5 6 3 4 | 2 2 +--R ((2b + 2a b )sinh(x) + 2a b + 2a b )\|b + a +--R Type: Expression(Integer) +--E 47 + +--S 48 of 552 +a0709:= integrate(t0709,x) +--R +--R +--R (48) +--R 3 3 5 4 +--R (32a b + 24a b)sinh(x) +--R + +--R 3 3 5 4 2 6 3 +--R ((128a b + 96a b)cosh(x) + 64a b + 48a )sinh(x) +--R + +--R 3 3 5 2 4 2 6 3 3 +--R (192a b + 144a b)cosh(x) + (192a b + 144a )cosh(x) - 32a b +--R + +--R 5 +--R - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 3 4 2 6 2 +--R (128a b + 96a b)cosh(x) + (192a b + 144a )cosh(x) +--R + +--R 3 3 5 +--R (- 64a b - 48a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 3 3 5 4 4 2 6 3 +--R (32a b + 24a b)cosh(x) + (64a b + 48a )cosh(x) +--R + +--R 3 3 5 2 +--R (- 32a b - 24a b)cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 5 2 3 6 5 2 3 4 3 2 5 +--R (b + a b )sinh(x) + ((6b + 6a b )cosh(x) - 6a b - 6a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 +--R (15b + 15a b )cosh(x) + (- 30a b - 30a b )cosh(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R (- 4b + 20a b + 24a b)x - b - 17a b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (20b + 20a b )cosh(x) + (- 60a b - 60a b )cosh(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R ((- 16b + 80a b + 96a b)x - 4b - 68a b - 64a b)cosh(x) +--R + +--R 4 3 2 5 5 +--R (- 8a b + 40a b + 48a )x + 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (15b + 15a b )cosh(x) + (- 60a b - 60a b )cosh(x) +--R + +--R 5 2 3 4 5 2 3 4 2 +--R ((- 24b + 120a b + 144a b)x - 6b - 102a b - 96a b)cosh(x) +--R + +--R 4 3 2 5 5 +--R ((- 24a b + 120a b + 144a )x + 48a )cosh(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R (4b - 20a b - 24a b)x - b - 17a b - 32a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 5 4 3 2 4 +--R (6b + 6a b )cosh(x) + (- 30a b - 30a b )cosh(x) +--R + +--R 5 2 3 4 5 2 3 4 3 +--R ((- 16b + 80a b + 96a b)x - 4b - 68a b - 64a b)cosh(x) +--R + +--R 4 3 2 5 5 2 +--R ((- 24a b + 120a b + 144a )x + 48a )cosh(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R ((8b - 40a b - 48a b)x - 2b - 34a b - 64a b)cosh(x) + 6a b +--R + +--R 3 2 +--R 6a b +--R * +--R sinh(x) +--R + +--R 5 2 3 6 4 3 2 5 +--R (b + a b )cosh(x) + (- 6a b - 6a b )cosh(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R ((- 4b + 20a b + 24a b)x - b - 17a b - 16a b)cosh(x) +--R + +--R 4 3 2 5 5 3 +--R ((- 8a b + 40a b + 48a )x + 16a )cosh(x) +--R + +--R 5 2 3 4 5 2 3 4 2 +--R ((4b - 20a b - 24a b)x - b - 17a b - 32a b)cosh(x) +--R + +--R 4 3 2 5 2 3 +--R (6a b + 6a b )cosh(x) + b + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 7 2 5 4 +--R (8b + 8a b )sinh(x) +--R + +--R 7 2 5 6 3 4 3 +--R ((32b + 32a b )cosh(x) + 16a b + 16a b )sinh(x) +--R + +--R 7 2 5 2 6 3 4 7 2 5 +--R ((48b + 48a b )cosh(x) + (48a b + 48a b )cosh(x) - 8b - 8a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 3 6 3 4 2 +--R (32b + 32a b )cosh(x) + (48a b + 48a b )cosh(x) +--R + +--R 7 2 5 +--R (- 16b - 16a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 2 5 4 6 3 4 3 +--R (8b + 8a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 7 2 5 2 +--R (- 8b - 8a b )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 552 +m0709:= a0709-r0709 +--R +--R +--R (49) +--R 3 4 5 2 5 +--R (32a b + 24a b )sinh(x) +--R + +--R 3 4 5 2 4 3 6 4 +--R ((128a b + 96a b )cosh(x) + 96a b + 72a b)sinh(x) +--R + +--R 3 4 5 2 2 4 3 6 3 4 +--R (192a b + 144a b )cosh(x) + (320a b + 240a b)cosh(x) - 32a b +--R + +--R 5 2 7 +--R 40a b + 48a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 5 2 3 4 3 6 2 +--R (128a b + 96a b )cosh(x) + (384a b + 288a b)cosh(x) +--R + +--R 3 4 5 2 7 4 3 6 +--R (- 64a b + 144a b + 144a )cosh(x) - 32a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 5 2 4 4 3 6 3 +--R (32a b + 24a b )cosh(x) + (192a b + 144a b)cosh(x) +--R + +--R 3 4 5 2 7 2 4 3 6 +--R (- 32a b + 168a b + 144a )cosh(x) + (- 64a b - 48a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 6 4 5 2 7 3 +--R (32a b + 24a b)cosh(x) + (64a b + 48a )cosh(x) +--R + +--R 4 3 6 2 +--R (- 32a b - 24a b)cosh(x) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 4 5 2 5 +--R (64a b + 48a b )sinh(x) +--R + +--R 3 4 5 2 4 3 6 4 +--R ((256a b + 192a b )cosh(x) + 192a b + 144a b)sinh(x) +--R + +--R 3 4 5 2 2 4 3 6 3 4 +--R (384a b + 288a b )cosh(x) + (640a b + 480a b)cosh(x) - 64a b +--R + +--R 5 2 7 +--R 80a b + 96a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 5 2 3 4 3 6 2 +--R (256a b + 192a b )cosh(x) + (768a b + 576a b)cosh(x) +--R + +--R 3 4 5 2 7 4 3 6 +--R (- 128a b + 288a b + 288a )cosh(x) - 64a b - 48a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 5 2 4 4 3 6 3 +--R (64a b + 48a b )cosh(x) + (384a b + 288a b)cosh(x) +--R + +--R 3 4 5 2 7 2 4 3 6 +--R (- 64a b + 336a b + 288a )cosh(x) + (- 128a b - 96a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 6 4 5 2 7 3 +--R (64a b + 48a b)cosh(x) + (128a b + 96a )cosh(x) +--R + +--R 4 3 6 2 +--R (- 64a b - 48a b)cosh(x) +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 6 2 4 7 6 2 4 5 3 3 6 +--R (b + a b )sinh(x) + ((2b + 2a b )cosh(x) - 5a b - 5a b )sinh(x) +--R + +--R 6 2 4 2 5 3 3 6 2 4 +--R (- b - a b )cosh(x) + (- 20a b - 20a b )cosh(x) - b - 23a b +--R + +--R 4 2 +--R - 22a b +--R * +--R 5 +--R sinh(x) +--R + +--R 6 2 4 3 5 3 3 2 +--R (- 4b - 4a b )cosh(x) + (- 21a b - 21a b )cosh(x) +--R + +--R 2 4 4 2 5 3 3 +--R (- 54a b - 46a b )cosh(x) - a b - 17a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 4 4 5 3 3 3 +--R (- b - a b )cosh(x) + (8a b + 8a b )cosh(x) +--R + +--R 6 2 4 4 2 2 +--R (2b - 18a b + 12a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (- 16a b - 48a b + 32a b)cosh(x) - b - 17a b - 32a b + 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 5 5 3 3 4 +--R (2b + 2a b )cosh(x) + (25a b + 25a b )cosh(x) +--R + +--R 2 4 4 2 3 5 3 3 5 2 +--R (44a b + 92a b )cosh(x) + (- 30a b - 30a b + 96a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 +--R (- 2b - 50a b - 88a b + 48a )cosh(x) + 5a b - 11a b - 32a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 6 5 3 3 5 +--R (b + a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 6 2 4 4 2 4 +--R (- b + 41a b + 74a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 16a b + 16a b + 96a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- b - 49a b - 80a b + 48a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (4a b - 28a b - 64a b)cosh(x) + b + 7a b + 6a b +--R * +--R sinh(x) +--R + +--R 5 3 3 6 2 4 4 2 5 +--R (a b + a b )cosh(x) + (10a b + 18a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- a b + 15a b + 32a b)cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (- 16a b - 24a b + 16a )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 5 +--R (- a b - 17a b - 32a b)cosh(x) + (6a b + 6a b )cosh(x) + a b +--R + +--R 3 3 +--R a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 8 2 6 5 +--R (8b + 8a b )sinh(x) +--R + +--R 8 2 6 7 3 5 4 +--R ((32b + 32a b )cosh(x) + 24a b + 24a b )sinh(x) +--R + +--R 8 2 6 2 7 3 5 8 2 6 +--R (48b + 48a b )cosh(x) + (80a b + 80a b )cosh(x) - 8b + 8a b +--R + +--R 4 4 +--R 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 6 3 7 3 5 2 +--R (32b + 32a b )cosh(x) + (96a b + 96a b )cosh(x) +--R + +--R 8 2 6 4 4 7 3 5 +--R (- 16b + 32a b + 48a b )cosh(x) - 8a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 2 6 4 7 3 5 3 +--R (8b + 8a b )cosh(x) + (48a b + 48a b )cosh(x) +--R + +--R 8 2 6 4 4 2 7 3 5 +--R (- 8b + 40a b + 48a b )cosh(x) + (- 16a b - 16a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 7 3 5 4 2 6 4 4 3 +--R (8a b + 8a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 7 3 5 2 +--R (- 8a b - 8a b )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 552 +d0709:= D(m0709,x) +--R +--R +--R (50) +--R 7 3 5 10 +--R (- a b - a b )sinh(x) +--R + +--R 7 3 5 2 6 4 4 9 +--R ((- 4a b - 4a b )cosh(x) - 2a b - 2a b )sinh(x) +--R + +--R 7 3 5 2 7 3 5 5 3 8 +--R ((- 4a b - 4a b )cosh(x) + 2a b + 29a b + 27a b )sinh(x) +--R + +--R 7 3 5 3 2 6 4 4 2 +--R (4a b + 4a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 6 2 +--R (4a b + 168a b + 164a b )cosh(x) + 4a b + 108a b + 100a b +--R * +--R 7 +--R sinh(x) +--R + +--R 7 3 5 4 2 6 4 4 3 +--R (10a b + 10a b )cosh(x) + (48a b + 48a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (- 2a b + 382a b + 380a b )cosh(x) +--R + +--R 2 6 4 4 6 2 3 5 5 3 7 +--R (8a b + 528a b + 496a b )cosh(x) - 30a b + 110a b + 120a b +--R * +--R 6 +--R sinh(x) +--R + +--R 7 3 5 5 2 6 4 4 4 +--R (4a b + 4a b )cosh(x) + (20a b + 20a b )cosh(x) +--R + +--R 7 3 5 5 3 3 +--R (- 8a b + 412a b + 396a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (12a b + 1044a b + 956a b )cosh(x) +--R + +--R 7 3 5 5 3 7 4 4 6 2 8 +--R (4a b - 88a b + 540a b + 528a b)cosh(x) - 80a b + 8a b + 48a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 3 5 6 2 6 4 4 5 +--R (- 4a b - 4a b )cosh(x) + (- 32a b - 32a b )cosh(x) +--R + +--R 7 3 5 5 3 4 +--R (- 2a b + 172a b + 114a b )cosh(x) +--R + +--R 2 6 4 4 6 2 3 +--R (32a b + 1032a b + 840a b )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (8a b - 58a b + 1066a b + 888a b)cosh(x) +--R + +--R 4 4 6 2 8 7 3 5 5 3 +--R (- 240a b + 128a b + 192a )cosh(x) - 2a b + 2a b - 60a b +--R + +--R 7 +--R - 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 3 5 7 2 6 4 4 6 +--R (- 4a b - 4a b )cosh(x) + (- 40a b - 40a b )cosh(x) +--R + +--R 7 3 5 5 3 5 +--R (4a b - 48a b - 132a b )cosh(x) +--R + +--R 2 6 4 4 6 2 4 +--R (44a b + 484a b + 220a b )cosh(x) +--R + +--R 7 3 5 5 3 7 3 +--R (4a b + 60a b + 1064a b + 672a b)cosh(x) +--R + +--R 4 4 6 2 8 2 +--R (- 224a b + 384a b + 288a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 +--R (- 4a b - 8a b - 196a b - 48a b)cosh(x) - 4a b + 4a b - 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 3 5 8 2 6 4 4 7 +--R (- a b - a b )cosh(x) + (- 16a b - 16a b )cosh(x) +--R + +--R 7 3 5 5 3 6 +--R (2a b - 70a b - 132a b )cosh(x) +--R + +--R 2 6 4 4 6 2 5 +--R (24a b + 48a b - 160a b )cosh(x) +--R + +--R 3 5 5 3 7 4 +--R (94a b + 546a b + 168a b)cosh(x) +--R + +--R 4 4 6 2 8 3 +--R (- 32a b + 464a b + 192a )cosh(x) +--R + +--R 7 3 5 5 3 2 2 6 6 2 +--R (- 2a b - 22a b - 216a b )cosh(x) + (- 8a b - 48a b )cosh(x) +--R + +--R 7 3 5 5 3 +--R a b - a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 4 4 8 3 5 5 3 7 +--R (- 2a b - 2a b )cosh(x) + (- 20a b - 44a b )cosh(x) +--R + +--R 2 6 4 4 6 2 6 +--R (4a b - 36a b - 124a b )cosh(x) +--R + +--R 3 5 5 3 7 5 +--R (36a b + 124a b - 48a b)cosh(x) +--R + +--R 4 4 6 2 8 4 +--R (48a b + 248a b + 48a )cosh(x) +--R + +--R 3 5 5 3 7 3 +--R (- 12a b - 84a b + 48a b)cosh(x) +--R + +--R 2 6 4 4 6 2 2 3 5 5 3 +--R (- 4a b - 12a b - 60a b )cosh(x) + (- 4a b + 4a b )cosh(x) +--R + +--R 2 6 4 4 +--R 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 8 4 4 6 2 7 +--R (- a b - 5a b )cosh(x) + (- 8a b - 24a b )cosh(x) +--R + +--R 3 5 5 3 7 6 4 4 6 2 5 +--R (2a b + 6a b - 24a b)cosh(x) + (16a b + 48a b )cosh(x) +--R + +--R 5 3 7 4 4 4 6 2 3 +--R (- 4a b + 24a b)cosh(x) + (- 8a b - 24a b )cosh(x) +--R + +--R 3 5 5 3 2 3 5 5 3 +--R (- 2a b + 2a b )cosh(x) + a b + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 2 6 10 +--R (2b + 2a b )sinh(x) +--R + +--R 8 2 6 7 3 5 9 +--R ((8b + 8a b )cosh(x) + 4a b + 4a b )sinh(x) +--R + +--R 8 2 6 2 8 2 6 4 4 8 +--R ((8b + 8a b )cosh(x) - 4b - 26a b - 30a b )sinh(x) +--R + +--R 8 2 6 3 7 3 5 2 +--R (- 8b - 8a b )cosh(x) + (- 48a b - 48a b )cosh(x) +--R + +--R 8 2 6 4 4 7 3 5 5 3 +--R (- 8b - 144a b - 184a b )cosh(x) - 8a b - 24a b - 56a b +--R * +--R 7 +--R sinh(x) +--R + +--R 8 2 6 4 7 3 5 3 +--R (- 20b - 20a b )cosh(x) + (- 96a b - 96a b )cosh(x) +--R + +--R 8 2 6 4 4 2 +--R (4b - 284a b - 400a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 6 2 +--R (- 16a b - 32a b - 224a b )cosh(x) - 4a b + 148a b + 72a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 2 6 5 7 3 5 4 +--R (- 8b - 8a b )cosh(x) + (- 40a b - 40a b )cosh(x) +--R + +--R 8 2 6 4 4 3 +--R (16b - 184a b - 312a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (- 24a b + 152a b - 232a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 3 5 5 3 +--R (- 8b - 80a b + 712a b + 432a b )cosh(x) - 96a b + 176a b +--R + +--R 7 +--R 192a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 2 6 6 7 3 5 5 +--R (8b + 8a b )cosh(x) + (64a b + 64a b )cosh(x) +--R + +--R 8 2 6 4 4 4 +--R (4b + 136a b + 132a b )cosh(x) +--R + +--R 7 3 5 5 3 3 +--R (- 64a b + 496a b + 240a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 16b - 268a b + 1388a b + 1080a b )cosh(x) +--R + +--R 3 5 5 3 7 8 2 6 4 4 +--R (- 416a b + 736a b + 864a b)cosh(x) + 4b + 28a b - 176a b +--R + +--R 6 2 8 +--R - 64a b + 96a +--R * +--R 4 +--R sinh(x) +--R + +--R 8 2 6 7 7 3 5 6 +--R (8b + 8a b )cosh(x) + (80a b + 80a b )cosh(x) +--R + +--R 8 2 6 4 4 5 +--R (- 8b + 288a b + 408a b )cosh(x) +--R + +--R 7 3 5 5 3 4 +--R (- 88a b + 632a b + 760a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 8b - 376a b + 1392a b + 1440a b )cosh(x) +--R + +--R 3 5 5 3 7 2 +--R (- 704a b + 1184a b + 1536a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 7 +--R (8b + 80a b - 584a b - 160a b + 384a )cosh(x) + 8a b +--R + +--R 3 5 5 3 7 +--R 56a b - 56a b - 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 6 8 7 3 5 7 +--R (2b + 2a b )cosh(x) + (32a b + 32a b )cosh(x) +--R + +--R 8 2 6 4 4 6 +--R (- 4b + 172a b + 288a b )cosh(x) +--R + +--R 7 3 5 5 3 5 +--R (- 48a b + 416a b + 704a b )cosh(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 252a b + 748a b + 1080a b )cosh(x) +--R + +--R 3 5 5 3 7 3 +--R (- 576a b + 896a b + 1344a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (4b + 76a b - 696a b - 96a b + 576a )cosh(x) +--R + +--R 7 3 5 5 3 7 8 2 6 +--R (16a b + 128a b - 192a b - 288a b)cosh(x) - 2b + 2a b +--R + +--R 4 4 6 2 +--R 28a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 3 5 8 2 6 4 4 7 +--R (4a b + 4a b )cosh(x) + (40a b + 88a b )cosh(x) +--R + +--R 7 3 5 5 3 6 +--R (- 8a b + 136a b + 296a b )cosh(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 72a b + 200a b + 432a b )cosh(x) +--R + +--R 3 5 5 3 7 4 +--R (- 224a b + 304a b + 576a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (24a b - 344a b + 32a b + 384a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (8a b + 88a b - 216a b - 288a b)cosh(x) +--R + +--R 2 6 4 4 6 2 7 3 5 +--R (8a b + 56a b + 48a b )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 6 4 4 8 3 5 5 3 7 +--R (2a b + 10a b )cosh(x) + (16a b + 48a b )cosh(x) +--R + +--R 2 6 4 4 6 2 6 +--R (- 4a b + 20a b + 72a b )cosh(x) +--R + +--R 3 5 5 3 7 5 +--R (- 32a b + 32a b + 96a b)cosh(x) +--R + +--R 4 4 6 2 8 4 +--R (- 56a b + 32a b + 96a )cosh(x) +--R + +--R 3 5 5 3 7 3 2 6 4 4 6 2 2 +--R (16a b - 80a b - 96a b)cosh(x) + (4a b + 28a b + 24a b )cosh(x) +--R + +--R 2 6 4 4 +--R - 2a b - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 7 3 5 10 7 3 5 2 6 4 4 9 +--R (a b + a b )sinh(x) + ((4a b + 4a b )cosh(x) + 2a b + 2a b )sinh(x) +--R + +--R 7 3 5 2 7 3 5 5 3 8 +--R ((4a b + 4a b )cosh(x) - 2a b - 29a b - 27a b )sinh(x) +--R + +--R 7 3 5 3 2 6 4 4 2 +--R (- 4a b - 4a b )cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 7 3 5 5 3 2 6 4 4 6 2 +--R (- 4a b - 168a b - 164a b )cosh(x) - 4a b - 108a b - 100a b +--R * +--R 7 +--R sinh(x) +--R + +--R 7 3 5 4 2 6 4 4 3 +--R (- 10a b - 10a b )cosh(x) + (- 48a b - 48a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (2a b - 382a b - 380a b )cosh(x) +--R + +--R 2 6 4 4 6 2 3 5 5 3 7 +--R (- 8a b - 528a b - 496a b )cosh(x) + 30a b - 110a b - 120a b +--R * +--R 6 +--R sinh(x) +--R + +--R 7 3 5 5 2 6 4 4 4 +--R (- 4a b - 4a b )cosh(x) + (- 20a b - 20a b )cosh(x) +--R + +--R 7 3 5 5 3 3 +--R (8a b - 412a b - 396a b )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 12a b - 1044a b - 956a b )cosh(x) +--R + +--R 7 3 5 5 3 7 4 4 6 2 8 +--R (- 4a b + 88a b - 540a b - 528a b)cosh(x) + 80a b - 8a b - 48a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 3 5 6 2 6 4 4 5 +--R (4a b + 4a b )cosh(x) + (32a b + 32a b )cosh(x) +--R + +--R 7 3 5 5 3 4 +--R (2a b - 172a b - 114a b )cosh(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 32a b - 1032a b - 840a b )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 8a b + 58a b - 1066a b - 888a b)cosh(x) +--R + +--R 4 4 6 2 8 7 3 5 5 3 7 +--R (240a b - 128a b - 192a )cosh(x) + 2a b - 2a b + 60a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 3 5 7 2 6 4 4 6 +--R (4a b + 4a b )cosh(x) + (40a b + 40a b )cosh(x) +--R + +--R 7 3 5 5 3 5 +--R (- 4a b + 48a b + 132a b )cosh(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 44a b - 484a b - 220a b )cosh(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 4a b - 60a b - 1064a b - 672a b)cosh(x) +--R + +--R 4 4 6 2 8 2 +--R (224a b - 384a b - 288a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 +--R (4a b + 8a b + 196a b + 48a b)cosh(x) + 4a b - 4a b + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 3 5 8 2 6 4 4 7 +--R (a b + a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 7 3 5 5 3 6 +--R (- 2a b + 70a b + 132a b )cosh(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 24a b - 48a b + 160a b )cosh(x) +--R + +--R 3 5 5 3 7 4 +--R (- 94a b - 546a b - 168a b)cosh(x) +--R + +--R 4 4 6 2 8 3 +--R (32a b - 464a b - 192a )cosh(x) +--R + +--R 7 3 5 5 3 2 2 6 6 2 7 +--R (2a b + 22a b + 216a b )cosh(x) + (8a b + 48a b )cosh(x) - a b +--R + +--R 3 5 5 3 +--R a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 4 4 8 3 5 5 3 7 +--R (2a b + 2a b )cosh(x) + (20a b + 44a b )cosh(x) +--R + +--R 2 6 4 4 6 2 6 +--R (- 4a b + 36a b + 124a b )cosh(x) +--R + +--R 3 5 5 3 7 5 +--R (- 36a b - 124a b + 48a b)cosh(x) +--R + +--R 4 4 6 2 8 4 +--R (- 48a b - 248a b - 48a )cosh(x) +--R + +--R 3 5 5 3 7 3 2 6 4 4 6 2 2 +--R (12a b + 84a b - 48a b)cosh(x) + (4a b + 12a b + 60a b )cosh(x) +--R + +--R 3 5 5 3 2 6 4 4 +--R (4a b - 4a b )cosh(x) - 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 3 5 5 3 8 4 4 6 2 7 +--R (a b + 5a b )cosh(x) + (8a b + 24a b )cosh(x) +--R + +--R 3 5 5 3 7 6 4 4 6 2 5 +--R (- 2a b - 6a b + 24a b)cosh(x) + (- 16a b - 48a b )cosh(x) +--R + +--R 5 3 7 4 4 4 6 2 3 +--R (4a b - 24a b)cosh(x) + (8a b + 24a b )cosh(x) +--R + +--R 3 5 5 3 2 3 5 5 3 +--R (2a b - 2a b )cosh(x) - a b - a b +--R / +--R 9 3 7 8 +--R (4a b + 4a b )sinh(x) +--R + +--R 9 3 7 2 8 4 6 7 +--R ((24a b + 24a b )cosh(x) + 24a b + 24a b )sinh(x) +--R + +--R 9 3 7 2 2 8 4 6 9 +--R (60a b + 60a b )cosh(x) + (128a b + 128a b )cosh(x) - 8a b +--R + +--R 3 7 5 5 +--R 44a b + 52a b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 3 7 3 2 8 4 6 2 +--R (80a b + 80a b )cosh(x) + (280a b + 280a b )cosh(x) +--R + +--R 9 3 7 5 5 2 8 4 6 6 4 +--R (- 32a b + 216a b + 248a b )cosh(x) - 32a b + 16a b + 48a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 3 7 4 2 8 4 6 3 +--R (60a b + 60a b )cosh(x) + (320a b + 320a b )cosh(x) +--R + +--R 9 3 7 5 5 2 +--R (- 48a b + 428a b + 476a b )cosh(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 +--R (- 112a b + 96a b + 208a b )cosh(x) + 4a b - 36a b - 24a b +--R + +--R 7 3 +--R 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 3 7 5 2 8 4 6 4 +--R (24a b + 24a b )cosh(x) + (200a b + 200a b )cosh(x) +--R + +--R 9 3 7 5 5 3 +--R (- 32a b + 432a b + 464a b )cosh(x) +--R + +--R 2 8 4 6 6 4 2 +--R (- 144a b + 208a b + 352a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 6 4 +--R (8a b - 120a b - 64a b + 64a b )cosh(x) + 8a b - 8a b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 9 3 7 6 2 8 4 6 5 +--R (4a b + 4a b )cosh(x) + (64a b + 64a b )cosh(x) +--R + +--R 9 3 7 5 5 4 +--R (- 8a b + 228a b + 236a b )cosh(x) +--R + +--R 2 8 4 6 6 4 3 +--R (- 80a b + 208a b + 288a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (4a b - 140a b - 48a b + 96a b )cosh(x) +--R + +--R 2 8 4 6 6 4 3 7 5 5 +--R (16a b - 32a b - 48a b )cosh(x) + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 4 6 6 3 7 5 5 5 +--R (8a b + 8a b )cosh(x) + (56a b + 56a b )cosh(x) +--R + +--R 2 8 4 6 6 4 4 +--R (- 16a b + 96a b + 112a b )cosh(x) +--R + +--R 3 7 7 3 3 2 8 4 6 6 4 2 +--R (- 64a b + 64a b )cosh(x) + (8a b - 40a b - 48a b )cosh(x) +--R + +--R 3 7 5 5 +--R (8a b + 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 7 5 5 6 4 6 6 4 5 +--R (4a b + 4a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 3 7 5 5 7 3 4 4 6 6 4 3 +--R (- 8a b + 8a b + 16a b )cosh(x) + (- 16a b - 16a b )cosh(x) +--R + +--R 3 7 5 5 2 +--R (4a b + 4a b )cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 10 2 8 8 +--R (- 8b - 8a b )sinh(x) +--R + +--R 10 2 8 9 3 7 7 +--R ((- 48b - 48a b )cosh(x) - 48a b - 48a b )sinh(x) +--R + +--R 10 2 8 2 9 3 7 +--R (- 120b - 120a b )cosh(x) + (- 256a b - 256a b )cosh(x) +--R + +--R 10 2 8 4 6 +--R 16b - 88a b - 104a b +--R * +--R 6 +--R sinh(x) +--R + +--R 10 2 8 3 9 3 7 2 +--R (- 160b - 160a b )cosh(x) + (- 560a b - 560a b )cosh(x) +--R + +--R 10 2 8 4 6 9 3 7 5 5 +--R (64b - 432a b - 496a b )cosh(x) + 64a b - 32a b - 96a b +--R * +--R 5 +--R sinh(x) +--R + +--R 10 2 8 4 9 3 7 3 +--R (- 120b - 120a b )cosh(x) + (- 640a b - 640a b )cosh(x) +--R + +--R 10 2 8 4 6 2 +--R (96b - 856a b - 952a b )cosh(x) +--R + +--R 9 3 7 5 5 10 2 8 4 6 +--R (224a b - 192a b - 416a b )cosh(x) - 8b + 72a b + 48a b +--R + +--R 6 4 +--R - 32a b +--R * +--R 4 +--R sinh(x) +--R + +--R 10 2 8 5 9 3 7 4 +--R (- 48b - 48a b )cosh(x) + (- 400a b - 400a b )cosh(x) +--R + +--R 10 2 8 4 6 3 +--R (64b - 864a b - 928a b )cosh(x) +--R + +--R 9 3 7 5 5 2 +--R (288a b - 416a b - 704a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 9 3 7 +--R (- 16b + 240a b + 128a b - 128a b )cosh(x) - 16a b + 16a b +--R + +--R 5 5 +--R 32a b +--R * +--R 3 +--R sinh(x) +--R + +--R 10 2 8 6 9 3 7 5 +--R (- 8b - 8a b )cosh(x) + (- 128a b - 128a b )cosh(x) +--R + +--R 10 2 8 4 6 4 +--R (16b - 456a b - 472a b )cosh(x) +--R + +--R 9 3 7 5 5 3 +--R (160a b - 416a b - 576a b )cosh(x) +--R + +--R 10 2 8 4 6 6 4 2 +--R (- 8b + 280a b + 96a b - 192a b )cosh(x) +--R + +--R 9 3 7 5 5 2 8 4 6 +--R (- 32a b + 64a b + 96a b )cosh(x) - 8a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 9 3 7 6 2 8 4 6 5 +--R (- 16a b - 16a b )cosh(x) + (- 112a b - 112a b )cosh(x) +--R + +--R 9 3 7 5 5 4 +--R (32a b - 192a b - 224a b )cosh(x) +--R + +--R 2 8 6 4 3 +--R (128a b - 128a b )cosh(x) +--R + +--R 9 3 7 5 5 2 2 8 4 6 +--R (- 16a b + 80a b + 96a b )cosh(x) + (- 16a b - 16a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 4 6 6 3 7 5 5 5 +--R (- 8a b - 8a b )cosh(x) + (- 32a b - 32a b )cosh(x) +--R + +--R 2 8 4 6 6 4 4 3 7 5 5 3 +--R (16a b - 16a b - 32a b )cosh(x) + (32a b + 32a b )cosh(x) +--R + +--R 2 8 4 6 2 +--R (- 8a b - 8a b )cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 9 3 7 8 +--R (- 4a b - 4a b )sinh(x) +--R + +--R 9 3 7 2 8 4 6 7 +--R ((- 24a b - 24a b )cosh(x) - 24a b - 24a b )sinh(x) +--R + +--R 9 3 7 2 2 8 4 6 9 +--R (- 60a b - 60a b )cosh(x) + (- 128a b - 128a b )cosh(x) + 8a b +--R + +--R 3 7 5 5 +--R - 44a b - 52a b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 3 7 3 2 8 4 6 2 +--R (- 80a b - 80a b )cosh(x) + (- 280a b - 280a b )cosh(x) +--R + +--R 9 3 7 5 5 2 8 4 6 6 4 +--R (32a b - 216a b - 248a b )cosh(x) + 32a b - 16a b - 48a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 3 7 4 2 8 4 6 3 +--R (- 60a b - 60a b )cosh(x) + (- 320a b - 320a b )cosh(x) +--R + +--R 9 3 7 5 5 2 +--R (48a b - 428a b - 476a b )cosh(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 7 3 +--R (112a b - 96a b - 208a b )cosh(x) - 4a b + 36a b + 24a b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 3 7 5 2 8 4 6 4 +--R (- 24a b - 24a b )cosh(x) + (- 200a b - 200a b )cosh(x) +--R + +--R 9 3 7 5 5 3 +--R (32a b - 432a b - 464a b )cosh(x) +--R + +--R 2 8 4 6 6 4 2 +--R (144a b - 208a b - 352a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 6 4 +--R (- 8a b + 120a b + 64a b - 64a b )cosh(x) - 8a b + 8a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 9 3 7 6 2 8 4 6 5 +--R (- 4a b - 4a b )cosh(x) + (- 64a b - 64a b )cosh(x) +--R + +--R 9 3 7 5 5 4 +--R (8a b - 228a b - 236a b )cosh(x) +--R + +--R 2 8 4 6 6 4 3 +--R (80a b - 208a b - 288a b )cosh(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (- 4a b + 140a b + 48a b - 96a b )cosh(x) +--R + +--R 2 8 4 6 6 4 3 7 5 5 +--R (- 16a b + 32a b + 48a b )cosh(x) - 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 4 6 6 3 7 5 5 5 +--R (- 8a b - 8a b )cosh(x) + (- 56a b - 56a b )cosh(x) +--R + +--R 2 8 4 6 6 4 4 3 7 7 3 3 +--R (16a b - 96a b - 112a b )cosh(x) + (64a b - 64a b )cosh(x) +--R + +--R 2 8 4 6 6 4 2 3 7 5 5 +--R (- 8a b + 40a b + 48a b )cosh(x) + (- 8a b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 7 5 5 6 4 6 6 4 5 +--R (- 4a b - 4a b )cosh(x) + (- 16a b - 16a b )cosh(x) +--R + +--R 3 7 5 5 7 3 4 4 6 6 4 3 +--R (8a b - 8a b - 16a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 3 7 5 5 2 +--R (- 4a b - 4a b )cosh(x) +--R Type: Expression(Integer) +--E 50 + +--S 51 of 552 +t0710:= sinh(x)^2/(%i+sinh(x))^2 +--R +--R +--R 2 +--R sinh(x) +--R (51) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 51 + +--S 52 of 552 +r0710:= x+5*%i*cosh(x)/(3-3*%i*sinh(x))+1/3*%i*cosh(x)/(%i+sinh(x))^2 +--R +--R +--R 2 5 4 +--R x sinh(x) + (- - cosh(x) + 2%i x)sinh(x) - - %i cosh(x) - x +--R 3 3 +--R (52) ------------------------------------------------------------ +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 52 + +--S 53 of 552 +a0710:= integrate(t0710,x) +--R +--R +--R (53) +--R 2 2 +--R 3x sinh(x) + (6x cosh(x) + 12%i x + 22%i)sinh(x) + 3x cosh(x) +--R + +--R (6%i x + 2%i)cosh(x) - 9x - 18 +--R / +--R 2 2 +--R 3sinh(x) + (6cosh(x) + 12%i)sinh(x) + 3cosh(x) + 6%i cosh(x) - 9 +--R Type: Union(Expression(Complex(Integer)),...) +--E 53 + +--S 54 of 552 +m0710:= a0710-r0710 +--R +--R +--R (54) +--R 5 22 3 10 2 26 62 2 +--R (- cosh(x) + -- %i)sinh(x) + (-- cosh(x) + -- %i cosh(x) - --)sinh(x) +--R 3 3 3 3 3 +--R + +--R 5 3 2 35 58 4 3 +--R (- cosh(x) + 6%i cosh(x) - -- cosh(x) - -- %i)sinh(x) + - %i cosh(x) +--R 3 3 3 3 +--R + +--R 8 2 14 +--R - - cosh(x) - -- %i cosh(x) + 6 +--R 3 3 +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) + 6%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) + 6%i cosh(x) - 12)sinh(x) +--R + +--R 2 2 +--R (2%i cosh(x) - 6cosh(x) - 10%i)sinh(x) - cosh(x) - 2%i cosh(x) + 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 54 + +--S 55 of 552 +d0710:= D(m0710,x) +--R +--R +--R (55) +--R 5 7 20 7 6 +--R - sinh(x) + (-- cosh(x) + - %i)sinh(x) +--R 3 3 3 +--R + +--R 25 2 70 5 +--R (-- cosh(x) + -- %i cosh(x) + 4)sinh(x) +--R 3 3 +--R + +--R 85 2 22 4 +--R (-- %i cosh(x) - 22cosh(x) + -- %i)sinh(x) +--R 3 3 +--R + +--R 25 4 38 3 2 28 1 3 +--R (- -- cosh(x) - -- %i cosh(x) - 22cosh(x) + -- %i cosh(x) + -)sinh(x) +--R 3 3 3 3 +--R + +--R 20 5 89 4 94 3 50 2 +--R - -- cosh(x) - -- %i cosh(x) + -- cosh(x) + -- %i cosh(x) +--R 3 3 3 3 +--R + +--R 80 +--R - -- cosh(x) + 5%i +--R 3 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 6 32 5 94 4 74 3 +--R - - cosh(x) - -- %i cosh(x) + -- cosh(x) + -- %i cosh(x) +--R 3 3 3 3 +--R + +--R 83 2 +--R - -- cosh(x) - 14%i cosh(x) - 2 +--R 3 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - %i cosh(x) + 4cosh(x) + 10%i cosh(x) - 6cosh(x) - 9%i cosh(x) +--R + +--R 2cosh(x) +--R / +--R 7 6 +--R sinh(x) + (4cosh(x) + 11%i)sinh(x) +--R + +--R 2 5 +--R (6cosh(x) + 32%i cosh(x) - 49)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 34%i cosh(x) - 100cosh(x) - 115%i)sinh(x) +--R + +--R 4 3 2 3 +--R (cosh(x) + 16%i cosh(x) - 76cosh(x) - 160%i cosh(x) + 155)sinh(x) +--R + +--R 4 3 2 2 +--R (3%i cosh(x) - 24cosh(x) - 84%i cosh(x) + 140cosh(x) + 121%i)sinh(x) +--R + +--R 4 3 2 +--R (- 3cosh(x) - 16%i cosh(x) + 46cosh(x) + 64%i cosh(x) - 51)sinh(x) +--R + +--R 4 3 2 +--R - %i cosh(x) + 4cosh(x) + 10%i cosh(x) - 12cosh(x) - 9%i +--R Type: Expression(Complex(Fraction(Integer))) +--E 55 + +--S 56 of 552 +t0711:= sinh(x)^3/(%i+sinh(x))^2 +--R +--R +--R 3 +--R sinh(x) +--R (56) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 56 + +--S 57 of 552 +r0711:= -2*%i*x+cosh(x)+8*cosh(x)/(3-3*%i*sinh(x))+1/3*cosh(x)/(%i+sinh(x))^2 +--R +--R +--R (57) +--R 2 +--R (3cosh(x) - 6%i x)sinh(x) + (14%i cosh(x) + 12x)sinh(x) - 10cosh(x) + 6%i x +--R ---------------------------------------------------------------------------- +--R 2 +--R 3sinh(x) + 6%i sinh(x) - 3 +--R Type: Expression(Complex(Integer)) +--E 57 + +--S 58 of 552 +a0711:= integrate(t0711,x) +--R +--R +--R (58) +--R 3 2 +--R 3sinh(x) + (9cosh(x) - 12%i x + 6%i)sinh(x) +--R + +--R 2 3 +--R (9cosh(x) + (- 24%i x + 24%i)cosh(x) + 48x + 71)sinh(x) + 3cosh(x) +--R + +--R 2 +--R (- 12%i x + 6%i)cosh(x) + (24x - 11)cosh(x) + 36%i x + 66%i +--R / +--R 2 2 +--R 6sinh(x) + (12cosh(x) + 24%i)sinh(x) + 6cosh(x) + 12%i cosh(x) - 18 +--R Type: Union(Expression(Complex(Integer)),...) +--E 58 + +--S 59 of 552 +m0711:= a0711-r0711 +--R +--R +--R (59) +--R 5 4 +--R 3sinh(x) + (3cosh(x) + 12%i)sinh(x) +--R + +--R 2 3 +--R (- 3cosh(x) - 10%i cosh(x) + 56)sinh(x) +--R + +--R 3 2 2 +--R (- 3cosh(x) - 44%i cosh(x) + 82cosh(x) + 202%i)sinh(x) +--R + +--R 3 2 3 +--R (- 22%i cosh(x) + 75cosh(x) + 118%i cosh(x) - 203)sinh(x) + 17cosh(x) +--R + +--R 2 +--R 34%i cosh(x) - 49cosh(x) - 66%i +--R / +--R 4 3 +--R 6sinh(x) + (12cosh(x) + 36%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) + 36%i cosh(x) - 72)sinh(x) +--R + +--R 2 2 +--R (12%i cosh(x) - 36cosh(x) - 60%i)sinh(x) - 6cosh(x) - 12%i cosh(x) + 18 +--R Type: Expression(Complex(Integer)) +--E 59 + +--S 60 of 552 +d0711:= D(m0711,x) +--R +--R +--R (60) +--R 8 7 +--R - 3sinh(x) + (- 9cosh(x) - 31%i)sinh(x) +--R + +--R 2 6 +--R (- 6cosh(x) - 115%i cosh(x) + 53)sinh(x) +--R + +--R 3 2 5 +--R (6cosh(x) - 110%i cosh(x) + 341cosh(x) - 15%i)sinh(x) +--R + +--R 4 3 2 4 +--R (9cosh(x) + 42%i cosh(x) + 326cosh(x) + 327%i cosh(x) + 83)sinh(x) +--R + +--R 5 4 3 2 +--R 3cosh(x) + 125%i cosh(x) - 232cosh(x) + 228%i cosh(x) +--R + +--R 101cosh(x) + 31%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 73%i cosh(x) - 379cosh(x) - 464%i cosh(x) + 238cosh(x) +--R + +--R 391%i cosh(x) + 27 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 16%i cosh(x) - 121cosh(x) - 401%i cosh(x) + 370cosh(x) +--R + +--R 2 +--R 370%i cosh(x) - 249cosh(x) + 15%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 12cosh(x) - 51%i cosh(x) + 138cosh(x) + 102%i cosh(x) - 126cosh(x) +--R + +--R - 51%i cosh(x) +--R / +--R 7 6 +--R 6sinh(x) + (24cosh(x) + 66%i)sinh(x) +--R + +--R 2 5 +--R (36cosh(x) + 192%i cosh(x) - 294)sinh(x) +--R + +--R 3 2 4 +--R (24cosh(x) + 204%i cosh(x) - 600cosh(x) - 690%i)sinh(x) +--R + +--R 4 3 2 3 +--R (6cosh(x) + 96%i cosh(x) - 456cosh(x) - 960%i cosh(x) + 930)sinh(x) +--R + +--R 4 3 2 +--R (18%i cosh(x) - 144cosh(x) - 504%i cosh(x) + 840cosh(x) + 726%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 18cosh(x) - 96%i cosh(x) + 276cosh(x) + 384%i cosh(x) - 306)sinh(x) +--R + +--R 4 3 2 +--R - 6%i cosh(x) + 24cosh(x) + 60%i cosh(x) - 72cosh(x) - 54%i +--R Type: Expression(Complex(Integer)) +--E 60 + +--S 61 of 552 +t0712:= sinh(x)^4/(%i+sinh(x))^2 +--R +--R +--R 4 +--R sinh(x) +--R (61) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 61 + +--S 62 of 552 +r0712:= -7/2*x-2*%i*cosh(x)-11*%i*cosh(x)/(3-3*%i*sinh(x))+_ + 1/2*cosh(x)*sinh(x)-1/3*%i*cosh(x)/(%i+sinh(x))^2 +--R +--R +--R (62) +--R 1 3 7 2 +--R - cosh(x)sinh(x) + (- %i cosh(x) - - x)sinh(x) +--R 2 2 +--R + +--R 43 16 7 +--R (-- cosh(x) - 7%i x)sinh(x) + -- %i cosh(x) + - x +--R 6 3 2 +--R / +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 62 + +--S 63 of 552 +a0712:= integrate(t0712,x) +--R +--R +--R (63) +--R 4 3 +--R 3sinh(x) + (12cosh(x) - 18%i)sinh(x) +--R + +--R 2 2 +--R (18cosh(x) - 36%i cosh(x) - 84x + 48)sinh(x) +--R + +--R 3 2 +--R (12cosh(x) - 54%i cosh(x) + (- 168x + 156)cosh(x) - 336%i x - 386%i) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R 3cosh(x) - 12%i cosh(x) + (- 84x + 48)cosh(x) +--R + +--R (- 168%i x + 92%i)cosh(x) + 252x + 381 +--R / +--R 2 2 +--R 24sinh(x) + (48cosh(x) + 96%i)sinh(x) + 24cosh(x) + 48%i cosh(x) - 72 +--R Type: Union(Expression(Complex(Integer)),...) +--E 63 + +--S 64 of 552 +m0712:= a0712-r0712 +--R +--R +--R (64) +--R 1 6 1 5 1 2 3 27 4 +--R - sinh(x) - - %i sinh(x) + (- - cosh(x) - - %i cosh(x) + --)sinh(x) +--R 8 2 4 2 8 +--R + +--R 1 2 2 34 3 +--R (- %i cosh(x) - - cosh(x) - -- %i)sinh(x) +--R 4 3 3 +--R + +--R 1 4 3 3 127 2 56 1105 +--R (- cosh(x) + - %i cosh(x) - --- cosh(x) - -- %i cosh(x) + ----) +--R 8 2 12 3 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 4 20 3 75 2 86 287 +--R (- %i cosh(x) - -- cosh(x) - -- %i cosh(x) + -- cosh(x) + --- %i) +--R 4 3 4 3 6 +--R * +--R sinh(x) +--R + +--R 1 4 29 3 26 2 73 127 +--R - - cosh(x) - -- %i cosh(x) + -- cosh(x) + -- %i cosh(x) - --- +--R 8 6 3 6 8 +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) + 6%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) + 6%i cosh(x) - 12)sinh(x) +--R + +--R 2 2 +--R (2%i cosh(x) - 6cosh(x) - 10%i)sinh(x) - cosh(x) - 2%i cosh(x) + 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 64 + +--S 65 of 552 +d0712:= D(m0712,x) +--R +--R +--R (65) +--R 1 9 1 8 +--R - - sinh(x) + (- - cosh(x) - %i)sinh(x) +--R 4 2 +--R + +--R 1 2 1 5 7 +--R (- cosh(x) + - %i cosh(x) - -)sinh(x) +--R 4 4 3 +--R + +--R 3 23 2 317 10 6 +--R (cosh(x) + -- %i cosh(x) - --- cosh(x) - -- %i)sinh(x) +--R 4 12 3 +--R + +--R 1 4 3 517 2 1051 17 5 +--R (- cosh(x) + 4%i cosh(x) - --- cosh(x) - ---- %i cosh(x) - --)sinh(x) +--R 4 12 12 2 +--R + +--R 1 5 4 3 1255 2 +--R - - cosh(x) - 4%i cosh(x) + 2cosh(x) - ---- %i cosh(x) +--R 2 12 +--R + +--R 363 43 +--R --- cosh(x) - -- %i +--R 4 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 1 6 17 5 121 4 170 3 +--R - - cosh(x) - -- %i cosh(x) + --- cosh(x) + --- %i cosh(x) +--R 4 4 3 3 +--R + +--R 279 2 223 7 +--R --- cosh(x) - --- %i cosh(x) - - +--R 4 12 3 +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 293 5 655 4 379 3 +--R - - %i cosh(x) + --- cosh(x) + --- %i cosh(x) - --- cosh(x) +--R 4 12 6 3 +--R + +--R 773 2 1217 +--R - --- %i cosh(x) + ---- cosh(x) - 12%i +--R 12 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 53 6 425 5 1339 4 314 3 +--R -- cosh(x) + --- %i cosh(x) - ---- cosh(x) - --- %i cosh(x) +--R 12 12 12 3 +--R + +--R 1229 2 277 19 +--R ---- cosh(x) + --- %i cosh(x) + -- +--R 12 4 4 +--R * +--R sinh(x) +--R + +--R 13 6 59 5 77 4 3 +--R -- %i cosh(x) - -- cosh(x) - -- %i cosh(x) + 30cosh(x) +--R 4 4 2 +--R + +--R 141 2 61 +--R --- %i cosh(x) - -- cosh(x) +--R 4 4 +--R / +--R 7 6 +--R sinh(x) + (4cosh(x) + 11%i)sinh(x) +--R + +--R 2 5 +--R (6cosh(x) + 32%i cosh(x) - 49)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 34%i cosh(x) - 100cosh(x) - 115%i)sinh(x) +--R + +--R 4 3 2 3 +--R (cosh(x) + 16%i cosh(x) - 76cosh(x) - 160%i cosh(x) + 155)sinh(x) +--R + +--R 4 3 2 2 +--R (3%i cosh(x) - 24cosh(x) - 84%i cosh(x) + 140cosh(x) + 121%i)sinh(x) +--R + +--R 4 3 2 +--R (- 3cosh(x) - 16%i cosh(x) + 46cosh(x) + 64%i cosh(x) - 51)sinh(x) +--R + +--R 4 3 2 +--R - %i cosh(x) + 4cosh(x) + 10%i cosh(x) - 12cosh(x) - 9%i +--R Type: Expression(Complex(Fraction(Integer))) +--E 65 + +--S 66 of 552 +t0713:= cosh(x)^2/(a+b*sinh(x))^2 +--R +--R +--R 2 +--R cosh(x) +--R (66) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 552 +r0713:= x/b^2+2*a*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/b^2/_ + (a^2+b^2)^(1/2)-cosh(x)/b/(a+b*sinh(x)) +--R +--R +--R (67) +--R x +--R a tanh(-) - b +--R 2 2 +--R (- 2a b sinh(x) - 2a )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R | 2 2 +--R (b x sinh(x) - b cosh(x) + a x)\|b + a +--R / +--R +-------+ +--R 3 2 | 2 2 +--R (b sinh(x) + a b )\|b + a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 552 +a0713:= integrate(t0713,x) +--R +--R +--R (68) +--R 2 2 2 +--R a b sinh(x) + (2a b cosh(x) + 2a )sinh(x) + a b cosh(x) +--R + +--R 2 +--R 2a cosh(x) - a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 2 +--R b x sinh(x) + (2b x cosh(x) + 2a x + 2a)sinh(x) + b x cosh(x) +--R + +--R (2a x + 2a)cosh(x) - b x - 2b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 2 3 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b )sinh(x) + b cosh(x) + 2a b cosh(x) +--R + +--R 3 +--R - b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 552 +m0713:= a0713-r0713 +--R +--R +--R (69) +--R 2 3 2 2 2 +--R a b sinh(x) + (2a b cosh(x) + 3a b)sinh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (a b cosh(x) + 4a b cosh(x) - a b + 2a )sinh(x) + a b cosh(x) +--R + +--R 3 2 +--R 2a cosh(x) - a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 3 2 2 2 +--R 2a b sinh(x) + (4a b cosh(x) + 6a b)sinh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (2a b cosh(x) + 8a b cosh(x) - 2a b + 4a )sinh(x) + 2a b cosh(x) +--R + +--R 3 2 +--R 4a cosh(x) - 2a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 +--R (b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (2b cosh(x) + 4a b cosh(x) - 2b + 2a )sinh(x) + b cosh(x) +--R + +--R 2 2 2 +--R 2a b cosh(x) + (- b + 2a )cosh(x) - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 4 3 2 +--R b sinh(x) + (2b cosh(x) + 3a b )sinh(x) +--R + +--R 4 2 3 4 2 2 3 2 +--R (b cosh(x) + 4a b cosh(x) - b + 2a b )sinh(x) + a b cosh(x) +--R + +--R 2 2 3 +--R 2a b cosh(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 69 + +--S 70 of 552 +d0713:= D(m0713,x) +--R +--R +--R (70) +--R 3 6 3 2 2 5 +--R 2a b sinh(x) + (8a b cosh(x) + 7a b )sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (11a b cosh(x) + 24a b cosh(x) + 9a b)sinh(x) +--R + +--R 3 3 2 2 2 3 2 2 4 +--R (4a b cosh(x) + 26a b cosh(x) + 24a b cosh(x) - 2a b + 4a ) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R - 4a b cosh(x) + 4a b cosh(x) + (2a b + 18a b)cosh(x) +--R + +--R 4 3 3 +--R 8a cosh(x) + 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 2 4 3 3 +--R - 4a b cosh(x) - 9a b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (6a b + 4a )cosh(x) + 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 2 5 3 3 4 +--R - a b cosh(x) - 4a b cosh(x) + (2a b - 3a b)cosh(x) +--R + +--R 2 2 3 3 3 2 3 +--R 4a b cosh(x) + (- a b + 2a b)cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 6 4 3 5 +--R - 2b sinh(x) + (- 8b cosh(x) - 2a b )sinh(x) +--R + +--R 4 2 3 4 2 2 4 +--R (- 10b cosh(x) - 8a b cosh(x) - 4b + 8a b )sinh(x) +--R + +--R 3 2 4 2 2 3 3 3 +--R (- 4a b cosh(x) + (- 8b + 24a b )cosh(x) - 12a b + 16a b)sinh(x) +--R + +--R 4 4 3 3 4 2 2 2 +--R 10b cosh(x) + 16a b cosh(x) + (- 8b + 32a b )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 24a b + 40a b)cosh(x) - 2b - 16a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 3 4 4 2 2 3 +--R 8b cosh(x) + 22a b cosh(x) + (- 8b + 24a b )cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (- 20a b + 32a b)cosh(x) + (- 24a b + 16a )cosh(x) - 2a b +--R + +--R 3 +--R - 8a b +--R * +--R sinh(x) +--R + +--R 4 6 3 5 4 2 2 4 +--R 2b cosh(x) + 8a b cosh(x) + (- 4b + 8a b )cosh(x) +--R + +--R 3 3 3 4 2 2 4 2 3 +--R (- 8a b + 8a b)cosh(x) + (2b - 8a b + 8a )cosh(x) - 8a b cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 6 3 2 2 5 +--R - 2a b sinh(x) + (- 8a b cosh(x) - 7a b )sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (- 11a b cosh(x) - 24a b cosh(x) - 9a b)sinh(x) +--R + +--R 3 3 2 2 2 3 2 2 4 3 +--R (- 4a b cosh(x) - 26a b cosh(x) - 24a b cosh(x) + 2a b - 4a )sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R 4a b cosh(x) - 4a b cosh(x) + (- 2a b - 18a b)cosh(x) +--R + +--R 4 3 3 +--R - 8a cosh(x) - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 2 4 3 3 +--R 4a b cosh(x) + 9a b cosh(x) - 4a b cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 6a b - 4a )cosh(x) - 3a b +--R * +--R sinh(x) +--R + +--R 3 6 2 2 5 3 3 4 2 2 3 +--R a b cosh(x) + 4a b cosh(x) + (- 2a b + 3a b)cosh(x) - 4a b cosh(x) +--R + +--R 3 3 2 3 +--R (a b - 2a b)cosh(x) - a b +--R / +--R 5 6 5 2 4 5 +--R a b sinh(x) + (4a b cosh(x) + 6a b )sinh(x) +--R + +--R 5 2 2 4 5 3 3 4 +--R (6a b cosh(x) + 20a b cosh(x) - 2a b + 13a b )sinh(x) +--R + +--R 5 3 2 4 2 5 3 3 +--R 4a b cosh(x) + 24a b cosh(x) + (- 4a b + 36a b )cosh(x) +--R + +--R 2 4 4 2 +--R - 8a b + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 4 3 5 3 3 2 +--R a b cosh(x) + 12a b cosh(x) + (- 2a b + 34a b )cosh(x) +--R + +--R 2 4 4 2 5 3 3 5 +--R (- 12a b + 28a b )cosh(x) + a b - 10a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 3 3 3 2 4 4 2 2 +--R 2a b cosh(x) + 12a b cosh(x) + (- 4a b + 20a b )cosh(x) +--R + +--R 3 3 5 2 4 4 2 +--R (- 12a b + 8a b)cosh(x) + 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 3 4 4 2 3 3 3 5 2 +--R a b cosh(x) + 4a b cosh(x) + (- 2a b + 4a b)cosh(x) +--R + +--R 4 2 3 3 +--R - 4a b cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 6 6 5 5 +--R - 2b sinh(x) + (- 8b cosh(x) - 12a b )sinh(x) +--R + +--R 6 2 5 6 2 4 4 +--R (- 12b cosh(x) - 40a b cosh(x) + 4b - 26a b )sinh(x) +--R + +--R 6 3 5 2 6 2 4 5 +--R - 8b cosh(x) - 48a b cosh(x) + (8b - 72a b )cosh(x) + 16a b +--R + +--R 3 3 +--R - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 5 3 6 2 4 2 +--R - 2b cosh(x) - 24a b cosh(x) + (4b - 68a b )cosh(x) +--R + +--R 5 3 3 6 2 4 4 2 +--R (24a b - 56a b )cosh(x) - 2b + 20a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 4 3 5 3 3 2 +--R - 4a b cosh(x) - 24a b cosh(x) + (8a b - 40a b )cosh(x) +--R + +--R 2 4 4 2 5 3 3 +--R (24a b - 16a b )cosh(x) - 4a b + 8a b +--R * +--R sinh(x) +--R + +--R 2 4 4 3 3 3 2 4 4 2 2 +--R - 2a b cosh(x) - 8a b cosh(x) + (4a b - 8a b )cosh(x) +--R + +--R 3 3 2 4 +--R 8a b cosh(x) - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 6 5 2 4 5 +--R - a b sinh(x) + (- 4a b cosh(x) - 6a b )sinh(x) +--R + +--R 5 2 2 4 5 3 3 4 +--R (- 6a b cosh(x) - 20a b cosh(x) + 2a b - 13a b )sinh(x) +--R + +--R 5 3 2 4 2 5 3 3 2 4 +--R - 4a b cosh(x) - 24a b cosh(x) + (4a b - 36a b )cosh(x) + 8a b +--R + +--R 4 2 +--R - 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 4 3 5 3 3 2 +--R - a b cosh(x) - 12a b cosh(x) + (2a b - 34a b )cosh(x) +--R + +--R 2 4 4 2 5 3 3 5 +--R (12a b - 28a b )cosh(x) - a b + 10a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 3 3 3 2 4 4 2 2 +--R - 2a b cosh(x) - 12a b cosh(x) + (4a b - 20a b )cosh(x) +--R + +--R 3 3 5 2 4 4 2 +--R (12a b - 8a b)cosh(x) - 2a b + 4a b +--R * +--R sinh(x) +--R + +--R 3 3 4 4 2 3 3 3 5 2 4 2 +--R - a b cosh(x) - 4a b cosh(x) + (2a b - 4a b)cosh(x) + 4a b cosh(x) +--R + +--R 3 3 +--R - a b +--R Type: Expression(Integer) +--E 70 + +--S 71 of 552 +t0714:= cosh(x)^3/(a+b*sinh(x))^2 +--R +--R +--R 3 +--R cosh(x) +--R (71) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 552 +r0714:= -2*a*log(a+b*sinh(x))/b^3+sinh(x)/b^2-(a^2+b^2)/b^3/(a+b*sinh(x)) +--R +--R +--R (72) +--R 2 2 2 2 2 +--R (- 2a b sinh(x) - 2a )log(b sinh(x) + a) + b sinh(x) + a b sinh(x) - b - a +--R ----------------------------------------------------------------------------- +--R 4 3 +--R b sinh(x) + a b +--R Type: Expression(Integer) +--E 72 + +--S 73 of 552 +a0714:= integrate(t0714,x) +--R +--R +--R (73) +--R 3 2 2 +--R - 4a b sinh(x) + (- 12a b cosh(x) - 8a )sinh(x) +--R + +--R 2 2 3 +--R (- 12a b cosh(x) - 16a cosh(x) + 4a b)sinh(x) - 4a b cosh(x) +--R + +--R 2 2 +--R - 8a cosh(x) + 4a b cosh(x) +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 4 2 3 +--R b sinh(x) + (4b cosh(x) + 4a b x + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (6b cosh(x) + (12a b x + 6a b)cosh(x) + 8a x - 6b - 4a )sinh(x) +--R + +--R 2 3 2 2 2 2 +--R 4b cosh(x) + (12a b x + 6a b)cosh(x) + (16a x - 12b - 8a )cosh(x) +--R + +--R - 4a b x - 2a b +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 2 +--R b cosh(x) + (4a b x + 2a b)cosh(x) + (8a x - 6b - 4a )cosh(x) +--R + +--R 2 +--R (- 4a b x - 2a b)cosh(x) + b +--R / +--R 4 3 4 3 2 +--R 2b sinh(x) + (6b cosh(x) + 4a b )sinh(x) +--R + +--R 4 2 3 4 4 3 3 2 +--R (6b cosh(x) + 8a b cosh(x) - 2b )sinh(x) + 2b cosh(x) + 4a b cosh(x) +--R + +--R 4 +--R - 2b cosh(x) +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 552 +m0714:= a0714-r0714 +--R +--R +--R (74) +--R 2 4 2 2 3 +--R 4a b sinh(x) + (12a b cosh(x) + 12a b)sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (12a b cosh(x) + 28a b cosh(x) - 4a b + 8a )sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R (4a b cosh(x) + 20a b cosh(x) + (- 4a b + 16a )cosh(x) - 4a b) +--R * +--R sinh(x) +--R + +--R 2 3 3 2 2 +--R 4a b cosh(x) + 8a cosh(x) - 4a b cosh(x) +--R * +--R log(b sinh(x) + a) +--R + +--R 2 4 2 2 3 +--R - 4a b sinh(x) + (- 12a b cosh(x) - 12a b)sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (- 12a b cosh(x) - 28a b cosh(x) + 4a b - 8a )sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R (- 4a b cosh(x) - 20a b cosh(x) + (4a b - 16a )cosh(x) + 4a b) +--R * +--R sinh(x) +--R + +--R 2 3 3 2 2 +--R - 4a b cosh(x) - 8a cosh(x) + 4a b cosh(x) +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 5 3 2 2 4 +--R - b sinh(x) + (- 2b cosh(x) + 4a b x - 3a b )sinh(x) +--R + +--R 2 2 2 3 2 3 +--R ((12a b x - 4a b )cosh(x) + 12a b x - 2b - 4a b)sinh(x) +--R + +--R 3 3 2 2 2 +--R 2b cosh(x) + (12a b x + 2a b )cosh(x) +--R + +--R 2 3 2 2 3 2 +--R (28a b x - 4b - 4a b)cosh(x) + (- 4a b + 8a )x - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 2 3 2 2 2 +--R b cosh(x) + (4a b x + 4a b )cosh(x) + (20a b x + 4a b)cosh(x) +--R + +--R 2 3 2 2 3 2 +--R ((- 4a b + 16a )x - 4a b )cosh(x) - 4a b x - b - 4a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 3 3 2 2 +--R a b cosh(x) + (4a b x + 2b + 4a b)cosh(x) + (8a x - 2a b )cosh(x) +--R + +--R 2 3 2 2 +--R (- 4a b x - 2b - 4a b)cosh(x) + a b +--R / +--R 5 4 5 4 3 +--R 2b sinh(x) + (6b cosh(x) + 6a b )sinh(x) +--R + +--R 5 2 4 5 2 3 2 +--R (6b cosh(x) + 14a b cosh(x) - 2b + 4a b )sinh(x) +--R + +--R 5 3 4 2 5 2 3 4 +--R (2b cosh(x) + 10a b cosh(x) + (- 2b + 8a b )cosh(x) - 2a b )sinh(x) +--R + +--R 4 3 2 3 2 4 +--R 2a b cosh(x) + 4a b cosh(x) - 2a b cosh(x) +--R Type: Expression(Integer) +--E 74 + +--S 75 of 552 +d0714:= D(m0714,x) +--R +--R +--R (75) +--R 4 8 4 3 7 +--R b sinh(x) + (4b cosh(x) + 6a b )sinh(x) +--R + +--R 4 2 3 4 2 2 6 +--R (5b cosh(x) + 20a b cosh(x) + 3b + 17a b )sinh(x) +--R + +--R 3 2 4 2 2 3 3 5 +--R (18a b cosh(x) + (14b + 50a b )cosh(x) + 6a b + 20a b)sinh(x) +--R + +--R 4 4 3 3 4 2 2 2 +--R - 5b cosh(x) - 8a b cosh(x) + (20b + 35a b )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (32a b + 52a b)cosh(x) + 3b + 11a b + 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 5 3 4 4 2 2 3 +--R - 4b cosh(x) - 22a b cosh(x) + (4b - 28a b )cosh(x) +--R + +--R 3 3 2 4 2 2 4 3 3 +--R (44a b + 24a b)cosh(x) + (8b + 44a b + 16a )cosh(x) + 2a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 6 3 5 4 2 2 4 +--R - b cosh(x) - 12a b cosh(x) + (- 13b - 49a b )cosh(x) +--R + +--R 3 3 3 4 2 2 2 +--R (8a b - 40a b)cosh(x) + (13b + 58a b )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (12a b + 48a b)cosh(x) + b - 5a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 4 2 2 5 +--R - 2a b cosh(x) + (- 10b - 22a b )cosh(x) +--R + +--R 3 3 4 4 2 2 4 3 +--R (- 18a b - 44a b)cosh(x) + (12b + 28a b - 16a )cosh(x) +--R + +--R 3 3 2 4 2 2 4 3 3 +--R (18a b + 48a b)cosh(x) + (- 2b - 6a b + 16a )cosh(x) + 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 4 2 2 6 3 3 5 +--R (- 2b - 3a b )cosh(x) + (- 8a b - 12a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (4b + 3a b - 8a )cosh(x) + (8a b + 16a b)cosh(x) +--R + +--R 4 2 2 4 2 3 2 2 +--R (- 2b - a b + 8a )cosh(x) - 4a b cosh(x) + a b +--R / +--R 6 7 6 5 6 +--R 2b sinh(x) + (10b cosh(x) + 12a b )sinh(x) +--R + +--R 6 2 5 6 2 4 5 +--R (20b cosh(x) + 52a b cosh(x) - 4b + 26a b )sinh(x) +--R + +--R 6 3 5 2 6 2 4 5 +--R 20b cosh(x) + 88a b cosh(x) + (- 12b + 98a b )cosh(x) - 16a b +--R + +--R 3 3 +--R 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 4 5 3 6 2 4 2 +--R 10b cosh(x) + 72a b cosh(x) + (- 12b + 140a b )cosh(x) +--R + +--R 5 3 3 6 2 4 4 2 +--R (- 40a b + 80a b )cosh(x) + 2b - 20a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 5 4 6 2 4 3 +--R 2b cosh(x) + 28a b cosh(x) + (- 4b + 92a b )cosh(x) +--R + +--R 5 3 3 2 6 2 4 4 2 5 +--R (- 32a b + 96a b )cosh(x) + (2b - 44a b + 24a b )cosh(x) + 4a b +--R + +--R 3 3 +--R - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 5 2 4 4 5 3 3 3 +--R 4a b cosh(x) + 26a b cosh(x) + (- 8a b + 48a b )cosh(x) +--R + +--R 2 4 4 2 2 5 3 3 2 4 +--R (- 28a b + 24a b )cosh(x) + (4a b - 16a b )cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 5 3 3 4 2 4 4 2 3 3 3 2 +--R 2a b cosh(x) + 8a b cosh(x) + (- 4a b + 8a b )cosh(x) - 8a b cosh(x) +--R + +--R 2 4 +--R 2a b cosh(x) +--R Type: Expression(Integer) +--E 75 + +--S 76 of 552 +t0715:= cosh(x)^4/(a+b*sinh(x))^2 +--R +--R +--R 4 +--R cosh(x) +--R (76) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 552 +r0715:= 3*a^2*x/b^4+3/2*x/b^2+6*a*(a^2+b^2)^(1/2)*_ + atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/b^4-_ + 2*a*cosh(x)/b^3+1/2*cosh(x)*sinh(x)/b^2-_ + (a^2+b^2)*cosh(x)/b^3/(a+b*sinh(x)) +--R +--R +--R (77) +--R x +--R +-------+ a tanh(-) - b +--R 2 | 2 2 2 +--R (- 12a b sinh(x) - 12a )\|b + a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 2 3 2 +--R b cosh(x)sinh(x) + (- 3a b cosh(x) + (3b + 6a b)x)sinh(x) +--R + +--R 3 2 2 3 +--R (- 2b - 6a b)cosh(x) + (3a b + 6a )x +--R / +--R 5 4 +--R 2b sinh(x) + 2a b +--R Type: Expression(Integer) +--E 77 + +--S 78 of 552 +a0715:= integrate(t0715,x) +--R +--R +--R (78) +--R 4 2 3 +--R 24a b sinh(x) + (96a b cosh(x) + 48a )sinh(x) +--R + +--R 2 2 2 +--R (144a b cosh(x) + 144a cosh(x) - 24a b)sinh(x) +--R + +--R 3 2 2 +--R (96a b cosh(x) + 144a cosh(x) - 48a b cosh(x))sinh(x) +--R + +--R 4 2 3 2 +--R 24a b cosh(x) + 48a cosh(x) - 24a b cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2b sinh(x) + 2b cosh(x) + 2a)\|b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 6 3 2 5 +--R b sinh(x) + (6b cosh(x) - 6a b )sinh(x) +--R + +--R 3 2 2 3 2 3 2 4 +--R (15b cosh(x) - 30a b cosh(x) + (12b + 24a b)x - b - 16a b)sinh(x) +--R + +--R 3 3 2 2 +--R 20b cosh(x) - 60a b cosh(x) +--R + +--R 3 2 3 2 2 3 2 +--R ((48b + 96a b)x - 4b - 64a b)cosh(x) + (24a b + 48a )x + 16a b +--R + +--R 3 +--R 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 3 +--R 15b cosh(x) - 60a b cosh(x) +--R + +--R 3 2 3 2 2 +--R ((72b + 144a b)x - 6b - 96a b)cosh(x) +--R + +--R 2 3 2 3 3 2 3 +--R ((72a b + 144a )x + 48a b + 48a )cosh(x) + (- 12b - 24a b)x - 17b +--R + +--R 2 +--R - 32a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 +--R 6b cosh(x) - 30a b cosh(x) +--R + +--R 3 2 3 2 3 +--R ((48b + 96a b)x - 4b - 64a b)cosh(x) +--R + +--R 2 3 2 3 2 +--R ((72a b + 144a )x + 48a b + 48a )cosh(x) +--R + +--R 3 2 3 2 2 +--R ((- 24b - 48a b)x - 34b - 64a b)cosh(x) + 6a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 3 2 3 2 4 +--R b cosh(x) - 6a b cosh(x) + ((12b + 24a b)x - b - 16a b)cosh(x) +--R + +--R 2 3 2 3 3 +--R ((24a b + 48a )x + 16a b + 16a )cosh(x) +--R + +--R 3 2 3 2 2 2 3 +--R ((- 12b - 24a b)x - 17b - 32a b)cosh(x) + 6a b cosh(x) + b +--R / +--R 5 4 5 4 3 +--R 8b sinh(x) + (32b cosh(x) + 16a b )sinh(x) +--R + +--R 5 2 4 5 2 +--R (48b cosh(x) + 48a b cosh(x) - 8b )sinh(x) +--R + +--R 5 3 4 2 5 5 4 +--R (32b cosh(x) + 48a b cosh(x) - 16b cosh(x))sinh(x) + 8b cosh(x) +--R + +--R 4 3 5 2 +--R 16a b cosh(x) - 8b cosh(x) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 552 +m0715:= a0715-r0715 +--R +--R +--R (79) +--R 2 5 2 2 4 +--R 24a b sinh(x) + (96a b cosh(x) + 72a b)sinh(x) +--R + +--R 2 2 2 2 3 3 +--R (144a b cosh(x) + 240a b cosh(x) - 24a b + 48a )sinh(x) +--R + +--R 2 3 2 2 2 3 +--R 96a b cosh(x) + 288a b cosh(x) + (- 48a b + 144a )cosh(x) +--R + +--R 2 +--R - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 3 2 3 2 +--R 24a b cosh(x) + 144a b cosh(x) + (- 24a b + 144a )cosh(x) +--R + +--R 2 +--R - 48a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 2 2 +--R 24a b cosh(x) + 48a cosh(x) - 24a b cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (2b sinh(x) + 2b cosh(x) + 2a)\|b + a + b sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 5 2 2 4 +--R 48a b sinh(x) + (192a b cosh(x) + 144a b)sinh(x) +--R + +--R 2 2 2 2 3 3 +--R (288a b cosh(x) + 480a b cosh(x) - 48a b + 96a )sinh(x) +--R + +--R 2 3 2 2 2 3 +--R 192a b cosh(x) + 576a b cosh(x) + (- 96a b + 288a )cosh(x) +--R + +--R 2 +--R - 48a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 3 2 3 2 +--R 48a b cosh(x) + 288a b cosh(x) + (- 48a b + 288a )cosh(x) +--R + +--R 2 +--R - 96a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 3 2 2 +--R 48a b cosh(x) + 96a cosh(x) - 48a b cosh(x) +--R * +--R x +--R +-------+ a tanh(-) - b +--R | 2 2 2 +--R \|b + a atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 7 4 3 6 +--R b sinh(x) + (2b cosh(x) - 5a b )sinh(x) +--R + +--R 4 2 3 4 2 2 5 +--R (- b cosh(x) - 20a b cosh(x) - b - 22a b )sinh(x) +--R + +--R 4 3 3 2 4 2 2 3 4 +--R (- 4b cosh(x) - 21a b cosh(x) + (8b - 46a b )cosh(x) + 15a b )sinh(x) +--R + +--R 4 4 3 3 4 2 2 2 +--R - b cosh(x) + 8a b cosh(x) + (34b + 12a b )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (48a b + 32a b)cosh(x) - 17b - 16a b + 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 3 4 4 2 2 3 +--R 2b cosh(x) + 25a b cosh(x) + (48b + 92a b )cosh(x) +--R + +--R 3 3 2 4 2 2 4 3 +--R (66a b + 96a b)cosh(x) + (- 42b - 40a b + 48a )cosh(x) - 11a b +--R + +--R 3 +--R - 32a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 6 3 5 4 2 2 4 +--R b cosh(x) + 12a b cosh(x) + (31b + 74a b )cosh(x) +--R + +--R 3 3 3 4 2 2 4 2 +--R (48a b + 96a b)cosh(x) + (- 33b - 32a b + 48a )cosh(x) +--R + +--R 3 3 4 2 2 +--R (- 28a b - 64a b)cosh(x) + b + 6a b +--R * +--R sinh(x) +--R + +--R 3 6 4 2 2 5 3 3 4 +--R a b cosh(x) + (8b + 18a b )cosh(x) + (15a b + 32a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 8b - 8a b + 16a )cosh(x) + (- 17a b - 32a b)cosh(x) +--R + +--R 2 2 3 +--R 6a b cosh(x) + a b +--R / +--R 6 5 6 5 4 +--R 8b sinh(x) + (32b cosh(x) + 24a b )sinh(x) +--R + +--R 6 2 5 6 2 4 3 +--R (48b cosh(x) + 80a b cosh(x) - 8b + 16a b )sinh(x) +--R + +--R 6 3 5 2 6 2 4 5 +--R (32b cosh(x) + 96a b cosh(x) + (- 16b + 48a b )cosh(x) - 8a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 4 5 3 6 2 4 2 +--R 8b cosh(x) + 48a b cosh(x) + (- 8b + 48a b )cosh(x) +--R + +--R 5 +--R - 16a b cosh(x) +--R * +--R sinh(x) +--R + +--R 5 4 2 4 3 5 2 +--R 8a b cosh(x) + 16a b cosh(x) - 8a b cosh(x) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 552 +d0715:= D(m0715,x) +--R +--R +--R (80) +--R 5 10 5 2 4 9 +--R - a b sinh(x) + (- 4a b cosh(x) - 2a b )sinh(x) +--R + +--R 5 2 5 3 3 8 +--R (- 4a b cosh(x) + 18a b + 27a b )sinh(x) +--R + +--R 5 3 2 4 2 5 3 3 +--R 4a b cosh(x) + 24a b cosh(x) + (100a b + 164a b )cosh(x) +--R + +--R 2 4 4 2 +--R 64a b + 100a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 4 3 5 3 3 2 +--R 10a b cosh(x) + 48a b cosh(x) + (234a b + 380a b )cosh(x) +--R + +--R 2 4 4 2 5 3 3 5 +--R (336a b + 496a b )cosh(x) - 16a b + 62a b + 120a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 2 4 4 5 3 3 3 +--R 4a b cosh(x) + 20a b cosh(x) + (288a b + 396a b )cosh(x) +--R + +--R 2 4 4 2 2 +--R (736a b + 956a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (- 60a b + 348a b + 528a b)cosh(x) - 56a b - 8a b + 48a +--R * +--R 5 +--R sinh(x) +--R + +--R 5 6 2 4 5 5 3 3 4 +--R - 4a b cosh(x) - 32a b cosh(x) + (178a b + 114a b )cosh(x) +--R + +--R 2 4 4 2 3 +--R (832a b + 840a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 80a b + 778a b + 888a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (- 192a b + 64a b + 192a )cosh(x) + 14a b - 52a b - 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 7 2 4 6 5 3 3 5 +--R - 4a b cosh(x) - 40a b cosh(x) + (20a b - 132a b )cosh(x) +--R + +--R 2 4 4 2 4 +--R (464a b + 220a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 28a b + 872a b + 672a b)cosh(x) +--R + +--R 2 4 4 2 6 2 +--R (- 224a b + 288a b + 288a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (28a b - 180a b - 48a b)cosh(x) + 24a b - 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 8 2 4 7 5 3 3 6 +--R - a b cosh(x) - 16a b cosh(x) + (- 42a b - 132a b )cosh(x) +--R + +--R 2 4 4 2 5 5 3 3 5 4 +--R (64a b - 160a b )cosh(x) + (32a b + 498a b + 168a b)cosh(x) +--R + +--R 2 4 4 2 6 3 5 3 3 2 +--R (- 80a b + 400a b + 192a )cosh(x) + (10a b - 216a b )cosh(x) +--R + +--R 2 4 4 2 5 3 3 +--R (48a b - 48a b )cosh(x) + a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 8 5 3 3 7 +--R - 2a b cosh(x) + (- 24a b - 44a b )cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 5 +--R (- 48a b - 124a b )cosh(x) + (32a b + 124a b - 48a b)cosh(x) +--R + +--R 2 4 4 2 6 4 +--R (24a b + 232a b + 48a )cosh(x) +--R + +--R 5 3 3 5 3 2 4 4 2 2 +--R (- 8a b - 100a b + 48a b)cosh(x) + (24a b - 60a b )cosh(x) +--R + +--R 3 3 2 4 +--R 20a b cosh(x) + 2a b +--R * +--R sinh(x) +--R + +--R 5 3 3 8 2 4 4 2 7 +--R (- 4a b - 5a b )cosh(x) + (- 16a b - 24a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 5 +--R (8a b + 6a b - 24a b)cosh(x) + (16a b + 48a b )cosh(x) +--R + +--R 5 3 3 5 4 4 2 3 3 3 2 +--R (- 4a b - 12a b + 24a b)cosh(x) - 24a b cosh(x) + 10a b cosh(x) +--R + +--R 3 3 +--R a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 10 6 5 9 +--R 2b sinh(x) + (8b cosh(x) + 4a b )sinh(x) +--R + +--R 6 2 6 2 4 8 +--R (8b cosh(x) - 12b - 30a b )sinh(x) +--R + +--R 6 3 5 2 6 2 4 +--R - 8b cosh(x) - 48a b cosh(x) + (- 56b - 184a b )cosh(x) +--R + +--R 5 3 3 +--R 16a b - 56a b +--R * +--R 7 +--R sinh(x) +--R + +--R 6 4 5 3 6 2 4 2 +--R - 20b cosh(x) - 96a b cosh(x) + (- 108b - 400a b )cosh(x) +--R + +--R 5 3 3 6 2 4 4 2 +--R (96a b - 224a b )cosh(x) - 16b + 140a b + 72a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 5 4 6 2 4 3 +--R - 8b cosh(x) - 40a b cosh(x) + (- 96b - 312a b )cosh(x) +--R + +--R 5 3 3 2 6 2 4 4 2 +--R (208a b - 232a b )cosh(x) + (- 72b + 600a b + 432a b )cosh(x) +--R + +--R 5 3 3 5 +--R - 80a b + 112a b + 192a b +--R * +--R 5 +--R sinh(x) +--R + +--R 6 6 5 5 6 2 4 4 +--R 8b cosh(x) + 64a b cosh(x) + (4b + 132a b )cosh(x) +--R + +--R 5 3 3 3 +--R (256a b + 240a b )cosh(x) +--R + +--R 6 2 4 4 2 2 +--R (- 128b + 1012a b + 1080a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 288a b + 448a b + 864a b)cosh(x) - 4b - 112a b - 96a b +--R + +--R 6 +--R 96a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 7 5 6 6 2 4 5 +--R 8b cosh(x) + 80a b cosh(x) + (104b + 408a b )cosh(x) +--R + +--R 5 3 3 4 +--R (272a b + 760a b )cosh(x) +--R + +--R 6 2 4 4 2 3 +--R (- 136b + 848a b + 1440a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 416a b + 672a b + 1536a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 3 5 +--R (- 8b - 360a b - 288a b + 384a )cosh(x) - 24a b - 96a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 8 5 7 6 2 4 6 +--R 2b cosh(x) + 32a b cosh(x) + (108b + 288a b )cosh(x) +--R + +--R 5 3 3 5 +--R (256a b + 704a b )cosh(x) +--R + +--R 6 2 4 4 2 4 +--R (- 112b + 372a b + 1080a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 320a b + 448a b + 1344a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (4b - 408a b - 288a b + 576a )cosh(x) +--R + +--R 3 3 5 6 2 4 4 2 +--R (- 96a b - 288a b)cosh(x) - 2b + 4a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 8 6 2 4 7 +--R 4a b cosh(x) + (48b + 88a b )cosh(x) +--R + +--R 5 3 3 6 6 2 4 4 2 5 +--R (144a b + 296a b )cosh(x) + (- 64b + 88a b + 432a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 144a b + 112a b + 576a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (16b - 184a b - 96a b + 384a )cosh(x) +--R + +--R 3 3 5 2 2 4 4 2 5 +--R (- 120a b - 288a b)cosh(x) + (8a b + 48a b )cosh(x) - 4a b +--R * +--R sinh(x) +--R + +--R 6 2 4 8 5 3 3 7 +--R (8b + 10a b )cosh(x) + (32a b + 48a b )cosh(x) +--R + +--R 6 2 4 4 2 6 5 5 5 +--R (- 16b + 12a b + 72a b )cosh(x) + (- 32a b + 96a b)cosh(x) +--R + +--R 6 2 4 6 4 3 3 5 3 +--R (8b - 24a b + 96a )cosh(x) + (- 48a b - 96a b)cosh(x) +--R + +--R 2 4 4 2 2 2 4 +--R (4a b + 24a b )cosh(x) - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 10 5 2 4 9 +--R a b sinh(x) + (4a b cosh(x) + 2a b )sinh(x) +--R + +--R 5 2 5 3 3 8 +--R (4a b cosh(x) - 18a b - 27a b )sinh(x) +--R + +--R 5 3 2 4 2 5 3 3 +--R - 4a b cosh(x) - 24a b cosh(x) + (- 100a b - 164a b )cosh(x) +--R + +--R 2 4 4 2 +--R - 64a b - 100a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 4 3 5 3 3 2 +--R - 10a b cosh(x) - 48a b cosh(x) + (- 234a b - 380a b )cosh(x) +--R + +--R 2 4 4 2 5 3 3 5 +--R (- 336a b - 496a b )cosh(x) + 16a b - 62a b - 120a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 5 2 4 4 5 3 3 3 +--R - 4a b cosh(x) - 20a b cosh(x) + (- 288a b - 396a b )cosh(x) +--R + +--R 2 4 4 2 2 5 3 3 5 +--R (- 736a b - 956a b )cosh(x) + (60a b - 348a b - 528a b)cosh(x) +--R + +--R 2 4 4 2 6 +--R 56a b + 8a b - 48a +--R * +--R 5 +--R sinh(x) +--R + +--R 5 6 2 4 5 5 3 3 4 +--R 4a b cosh(x) + 32a b cosh(x) + (- 178a b - 114a b )cosh(x) +--R + +--R 2 4 4 2 3 5 3 3 5 2 +--R (- 832a b - 840a b )cosh(x) + (80a b - 778a b - 888a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (192a b - 64a b - 192a )cosh(x) - 14a b + 52a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 7 2 4 6 5 3 3 5 +--R 4a b cosh(x) + 40a b cosh(x) + (- 20a b + 132a b )cosh(x) +--R + +--R 2 4 4 2 4 5 3 3 5 3 +--R (- 464a b - 220a b )cosh(x) + (28a b - 872a b - 672a b)cosh(x) +--R + +--R 2 4 4 2 6 2 +--R (224a b - 288a b - 288a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 28a b + 180a b + 48a b)cosh(x) - 24a b + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 8 2 4 7 5 3 3 6 +--R a b cosh(x) + 16a b cosh(x) + (42a b + 132a b )cosh(x) +--R + +--R 2 4 4 2 5 5 3 3 5 4 +--R (- 64a b + 160a b )cosh(x) + (- 32a b - 498a b - 168a b)cosh(x) +--R + +--R 2 4 4 2 6 3 5 3 3 2 +--R (80a b - 400a b - 192a )cosh(x) + (- 10a b + 216a b )cosh(x) +--R + +--R 2 4 4 2 5 3 3 +--R (- 48a b + 48a b )cosh(x) - a b - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 8 5 3 3 7 +--R 2a b cosh(x) + (24a b + 44a b )cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 5 +--R (48a b + 124a b )cosh(x) + (- 32a b - 124a b + 48a b)cosh(x) +--R + +--R 2 4 4 2 6 4 +--R (- 24a b - 232a b - 48a )cosh(x) +--R + +--R 5 3 3 5 3 2 4 4 2 2 +--R (8a b + 100a b - 48a b)cosh(x) + (- 24a b + 60a b )cosh(x) +--R + +--R 3 3 2 4 +--R - 20a b cosh(x) - 2a b +--R * +--R sinh(x) +--R + +--R 5 3 3 8 2 4 4 2 7 +--R (4a b + 5a b )cosh(x) + (16a b + 24a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 5 +--R (- 8a b - 6a b + 24a b)cosh(x) + (- 16a b - 48a b )cosh(x) +--R + +--R 5 3 3 5 4 4 2 3 3 3 2 3 3 +--R (4a b + 12a b - 24a b)cosh(x) + 24a b cosh(x) - 10a b cosh(x) - a b +--R / +--R 7 8 7 2 6 7 +--R 4a b sinh(x) + (24a b cosh(x) + 24a b )sinh(x) +--R + +--R 7 2 2 6 7 3 5 6 +--R (60a b cosh(x) + 128a b cosh(x) - 8a b + 52a b )sinh(x) +--R + +--R 7 3 2 6 2 7 3 5 +--R 80a b cosh(x) + 280a b cosh(x) + (- 32a b + 248a b )cosh(x) +--R + +--R 2 6 4 4 +--R - 32a b + 48a b +--R * +--R 5 +--R sinh(x) +--R + +--R 7 4 2 6 3 7 3 5 2 +--R 60a b cosh(x) + 320a b cosh(x) + (- 48a b + 476a b )cosh(x) +--R + +--R 2 6 4 4 7 3 5 5 3 +--R (- 112a b + 208a b )cosh(x) + 4a b - 40a b + 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 2 6 4 7 3 5 3 +--R 24a b cosh(x) + 200a b cosh(x) + (- 32a b + 464a b )cosh(x) +--R + +--R 2 6 4 4 2 7 3 5 5 3 +--R (- 144a b + 352a b )cosh(x) + (8a b - 128a b + 64a b )cosh(x) +--R + +--R 2 6 4 4 +--R 8a b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 6 5 7 3 5 4 +--R 4a b cosh(x) + 64a b cosh(x) + (- 8a b + 236a b )cosh(x) +--R + +--R 2 6 4 4 3 7 3 5 5 3 2 +--R (- 80a b + 288a b )cosh(x) + (4a b - 144a b + 96a b )cosh(x) +--R + +--R 2 6 4 4 3 5 +--R (16a b - 48a b )cosh(x) + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 6 3 5 5 2 6 4 4 4 +--R 8a b cosh(x) + 56a b cosh(x) + (- 16a b + 112a b )cosh(x) +--R + +--R 3 5 5 3 3 2 6 4 4 2 +--R (- 64a b + 64a b )cosh(x) + (8a b - 48a b )cosh(x) +--R + +--R 3 5 +--R 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 5 6 4 4 5 3 5 5 3 4 +--R 4a b cosh(x) + 16a b cosh(x) + (- 8a b + 16a b )cosh(x) +--R + +--R 4 4 3 3 5 2 +--R - 16a b cosh(x) + 4a b cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 8 8 8 7 7 +--R - 8b sinh(x) + (- 48b cosh(x) - 48a b )sinh(x) +--R + +--R 8 2 7 8 2 6 6 +--R (- 120b cosh(x) - 256a b cosh(x) + 16b - 104a b )sinh(x) +--R + +--R 8 3 7 2 8 2 6 +--R - 160b cosh(x) - 560a b cosh(x) + (64b - 496a b )cosh(x) +--R + +--R 7 3 5 +--R 64a b - 96a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 4 7 3 8 2 6 2 +--R - 120b cosh(x) - 640a b cosh(x) + (96b - 952a b )cosh(x) +--R + +--R 7 3 5 8 2 6 4 4 +--R (224a b - 416a b )cosh(x) - 8b + 80a b - 32a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 5 7 4 8 2 6 3 +--R - 48b cosh(x) - 400a b cosh(x) + (64b - 928a b )cosh(x) +--R + +--R 7 3 5 2 8 2 6 4 4 +--R (288a b - 704a b )cosh(x) + (- 16b + 256a b - 128a b )cosh(x) +--R + +--R 7 3 5 +--R - 16a b + 32a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 6 7 5 8 2 6 4 +--R - 8b cosh(x) - 128a b cosh(x) + (16b - 472a b )cosh(x) +--R + +--R 7 3 5 3 8 2 6 4 4 2 +--R (160a b - 576a b )cosh(x) + (- 8b + 288a b - 192a b )cosh(x) +--R + +--R 7 3 5 2 6 +--R (- 32a b + 96a b )cosh(x) - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 6 5 7 3 5 4 +--R - 16a b cosh(x) - 112a b cosh(x) + (32a b - 224a b )cosh(x) +--R + +--R 2 6 4 4 3 7 3 5 2 +--R (128a b - 128a b )cosh(x) + (- 16a b + 96a b )cosh(x) +--R + +--R 2 6 +--R - 16a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 6 3 5 5 2 6 4 4 4 +--R - 8a b cosh(x) - 32a b cosh(x) + (16a b - 32a b )cosh(x) +--R + +--R 3 5 3 2 6 2 +--R 32a b cosh(x) - 8a b cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 7 8 7 2 6 7 +--R - 4a b sinh(x) + (- 24a b cosh(x) - 24a b )sinh(x) +--R + +--R 7 2 2 6 7 3 5 6 +--R (- 60a b cosh(x) - 128a b cosh(x) + 8a b - 52a b )sinh(x) +--R + +--R 7 3 2 6 2 7 3 5 +--R - 80a b cosh(x) - 280a b cosh(x) + (32a b - 248a b )cosh(x) +--R + +--R 2 6 4 4 +--R 32a b - 48a b +--R * +--R 5 +--R sinh(x) +--R + +--R 7 4 2 6 3 7 3 5 2 +--R - 60a b cosh(x) - 320a b cosh(x) + (48a b - 476a b )cosh(x) +--R + +--R 2 6 4 4 7 3 5 5 3 +--R (112a b - 208a b )cosh(x) - 4a b + 40a b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 5 2 6 4 7 3 5 3 +--R - 24a b cosh(x) - 200a b cosh(x) + (32a b - 464a b )cosh(x) +--R + +--R 2 6 4 4 2 7 3 5 5 3 +--R (144a b - 352a b )cosh(x) + (- 8a b + 128a b - 64a b )cosh(x) +--R + +--R 2 6 4 4 +--R - 8a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 6 5 7 3 5 4 +--R - 4a b cosh(x) - 64a b cosh(x) + (8a b - 236a b )cosh(x) +--R + +--R 2 6 4 4 3 7 3 5 5 3 2 +--R (80a b - 288a b )cosh(x) + (- 4a b + 144a b - 96a b )cosh(x) +--R + +--R 2 6 4 4 3 5 +--R (- 16a b + 48a b )cosh(x) - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 6 3 5 5 2 6 4 4 4 +--R - 8a b cosh(x) - 56a b cosh(x) + (16a b - 112a b )cosh(x) +--R + +--R 3 5 5 3 3 2 6 4 4 2 3 5 +--R (64a b - 64a b )cosh(x) + (- 8a b + 48a b )cosh(x) - 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 3 5 6 4 4 5 3 5 5 3 4 +--R - 4a b cosh(x) - 16a b cosh(x) + (8a b - 16a b )cosh(x) +--R + +--R 4 4 3 3 5 2 +--R 16a b cosh(x) - 4a b cosh(x) +--R Type: Expression(Integer) +--E 80 + +--S 81 of 552 +t0716:= cosh(x)^2/(%i+sinh(x))^2 +--R +--R +--R 2 +--R cosh(x) +--R (81) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 81 + +--S 82 of 552 +r0716:= x+2*%i*cosh(x)/(1-%i*sinh(x)) +--R +--R +--R x sinh(x) - 2cosh(x) + %i x +--R (82) --------------------------- +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 82 + +--S 83 of 552 +a0716:= integrate(t0716,x) +--R +--R +--R x sinh(x) + x cosh(x) + %i x + 4%i +--R (83) ---------------------------------- +--R sinh(x) + cosh(x) + %i +--R Type: Union(Expression(Complex(Integer)),...) +--E 83 + +--S 84 of 552 +m0716:= a0716-r0716 +--R +--R +--R 2 +--R (2cosh(x) + 4%i)sinh(x) + 2cosh(x) + 2%i cosh(x) - 4 +--R (84) ----------------------------------------------------- +--R 2 +--R sinh(x) + (cosh(x) + 2%i)sinh(x) + %i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 84 + +--S 85 of 552 +d0716:= D(m0716,x) +--R +--R +--R (85) +--R 4 3 2 +--R 2sinh(x) + (4cosh(x) + 2%i)sinh(x) + (4%i cosh(x) + 2)sinh(x) +--R + +--R 3 2 4 +--R (- 4cosh(x) - 2%i cosh(x) + 4cosh(x) + 2%i)sinh(x) - 2cosh(x) +--R + +--R 3 2 +--R - 4%i cosh(x) + 2cosh(x) + 4%i cosh(x) +--R / +--R 4 3 +--R sinh(x) + (2cosh(x) + 4%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) + 6%i cosh(x) - 6)sinh(x) +--R + +--R 2 2 +--R (2%i cosh(x) - 6cosh(x) - 4%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 85 + +--S 86 of 552 +t0717:= cosh(x)^3/(%i+sinh(x))^2 +--R +--R +--R 3 +--R cosh(x) +--R (86) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 86 + +--S 87 of 552 +r0717:= -2*%i*log(%i+sinh(x))+sinh(x) +--R +--R +--R (87) - 2%i log(sinh(x) + %i) + sinh(x) +--R Type: Expression(Complex(Integer)) +--E 87 + +--S 88 of 552 +a0717:= integrate(t0717,x) +--R +--R +--R (88) +--R 2 +--R (- 8%i sinh(x) - 8%i cosh(x))log(sinh(x) + cosh(x) + %i) + sinh(x) +--R + +--R 2 +--R (2cosh(x) + 4%i x)sinh(x) + cosh(x) + 4%i x cosh(x) - 1 +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 88 + +--S 89 of 552 +m0717:= a0717-r0717 +--R +--R +--R (89) +--R (- 8%i sinh(x) - 8%i cosh(x))log(sinh(x) + cosh(x) + %i) +--R + +--R 2 +--R (4%i sinh(x) + 4%i cosh(x))log(sinh(x) + %i) - sinh(x) + 4%i x sinh(x) +--R + +--R 2 +--R cosh(x) + 4%i x cosh(x) - 1 +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Expression(Complex(Integer)) +--E 89 + +--S 90 of 552 +d0717:= D(m0717,x) +--R +--R +--R (90) +--R 4 3 2 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) + (- cosh(x) - 3%i cosh(x))sinh(x) +--R + +--R 3 2 3 +--R (- cosh(x) + 2%i cosh(x) + cosh(x) - 2%i)sinh(x) + 3%i cosh(x) +--R + +--R 2 +--R cosh(x) - 3%i cosh(x) - 1 +--R / +--R 3 2 +--R 2sinh(x) + (4cosh(x) + 4%i)sinh(x) +--R + +--R 2 2 +--R (2cosh(x) + 6%i cosh(x) - 2)sinh(x) + 2%i cosh(x) - 2cosh(x) +--R Type: Expression(Complex(Integer)) +--E 90 + +--S 91 of 552 +t0718:= cosh(x)^4/(%i+sinh(x))^2 +--R +--R +--R 4 +--R cosh(x) +--R (91) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 91 + +--S 92 of 552 +r0718:= -3/2*x-2*%i*cosh(x)+1/2*cosh(x)*sinh(x) +--R +--R +--R cosh(x)sinh(x) - 4%i cosh(x) - 3x +--R (92) --------------------------------- +--R 2 +--R Type: Expression(Complex(Integer)) +--E 92 + +--S 93 of 552 +a0718:= integrate(t0718,x) +--R +--R +--R cosh(x)sinh(x) - 4%i cosh(x) - 3x +--R (93) --------------------------------- +--R 2 +--R Type: Union(Expression(Complex(Integer)),...) +--E 93 + +--S 94 of 552 +m0718:= a0718-r0718 +--R +--R +--R (94) 0 +--R Type: Expression(Complex(Integer)) +--E 94 + +--S 95 of 552 +d0718:= D(m0718,x) +--R +--R +--R (95) 0 +--R Type: Expression(Complex(Integer)) +--E 95 + +--S 96 of 552 +t0719:= tanh(x)/(a+b*sinh(x))^2 +--R +--R +--R tanh(x) +--R (96) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 96 + +--S 97 of 552 +r0719:= 2*a*b*atan(sinh(x))/(a^2+b^2)^2+_ + 1/2*(a^2-b^2)*log(cosh(x)^2)/(a^2+b^2)^2-_ + (a^2-b^2)*log(a+b*sinh(x))/(a^2+b^2)^2+a/(a^2+b^2)/(a+b*sinh(x)) +--R +--R +--R (97) +--R 3 2 2 3 +--R ((2b - 2a b)sinh(x) + 2a b - 2a )log(b sinh(x) + a) +--R + +--R 3 2 2 3 2 +--R ((- b + a b)sinh(x) - a b + a )log(cosh(x) ) +--R + +--R 2 2 2 3 +--R (4a b sinh(x) + 4a b)atan(sinh(x)) + 2a b + 2a +--R / +--R 5 2 3 4 4 3 2 5 +--R (2b + 4a b + 2a b)sinh(x) + 2a b + 4a b + 2a +--R Type: Expression(Integer) +--E 97 + +--S 98 of 552 +a0719:= integrate(t0719,x) +--R +--R +--R (98) +--R 3 2 2 3 2 2 3 +--R (- b + a b)sinh(x) + ((- 2b + 2a b)cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- b + a b)cosh(x) + (- 2a b + 2a )cosh(x) + b - a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 2 2 3 +--R (b - a b)sinh(x) + ((2b - 2a b)cosh(x) + 2a b - 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (b - a b)cosh(x) + (2a b - 2a )cosh(x) - b + a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 +--R 4a b sinh(x) + (8a b cosh(x) + 8a b)sinh(x) + 4a b cosh(x) +--R + +--R 2 2 +--R 8a b cosh(x) - 4a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 2 3 2 3 +--R (2a b + 2a )sinh(x) + (2a b + 2a )cosh(x) +--R / +--R 5 2 3 4 2 +--R (b + 2a b + a b)sinh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R ((2b + 4a b + 2a b)cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 5 2 3 +--R (b + 2a b + a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) - b - 2a b +--R + +--R 4 +--R - a b +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 552 +m0719:= a0719-r0719 +--R +--R +--R (99) +--R 4 2 2 3 +--R (- 2b + 2a b )sinh(x) +--R + +--R 4 2 2 3 3 2 +--R ((- 4b + 4a b )cosh(x) - 6a b + 6a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (- 2b + 2a b )cosh(x) + (- 8a b + 8a b)cosh(x) + 2b - 6a b +--R + +--R 4 +--R 4a +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) + 2a b - 2a b +--R * +--R log(b sinh(x) + a) +--R + +--R 4 2 2 3 4 2 2 3 3 2 +--R (b - a b )sinh(x) + ((2b - 2a b )cosh(x) + 3a b - 3a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 4 +--R ((b - a b )cosh(x) + (4a b - 4a b)cosh(x) - b + 3a b - 2a ) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) - a b + a b +--R * +--R 2 +--R log(cosh(x) ) +--R + +--R 4 2 2 3 +--R (- 2b + 2a b )sinh(x) +--R + +--R 4 2 2 3 3 2 +--R ((- 4b + 4a b )cosh(x) - 6a b + 6a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (- 2b + 2a b )cosh(x) + (- 8a b + 8a b)cosh(x) + 2b - 6a b +--R + +--R 4 +--R 4a +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) + 2a b - 2a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 2 2 3 4 2 2 3 3 2 +--R (2b - 2a b )sinh(x) + ((4b - 4a b )cosh(x) + 6a b - 6a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 4 +--R ((2b - 2a b )cosh(x) + (8a b - 8a b)cosh(x) - 2b + 6a b - 4a ) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (2a b - 2a b)cosh(x) + (4a b - 4a )cosh(x) - 2a b + 2a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 3 2 2 2 +--R 8a b sinh(x) + (16a b cosh(x) + 24a b )sinh(x) +--R + +--R 3 2 2 2 3 3 +--R (8a b cosh(x) + 32a b cosh(x) - 8a b + 16a b)sinh(x) +--R + +--R 2 2 2 3 2 2 +--R 8a b cosh(x) + 16a b cosh(x) - 8a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 3 3 2 2 2 +--R - 4a b sinh(x) + (- 8a b cosh(x) - 12a b )sinh(x) +--R + +--R 3 2 2 2 3 3 +--R (- 4a b cosh(x) - 16a b cosh(x) + 4a b - 8a b)sinh(x) +--R + +--R 2 2 2 3 2 2 +--R - 4a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R atan(sinh(x)) +--R + +--R 3 3 2 3 3 2 3 3 +--R (2a b + 2a b)sinh(x) + (- 2a b - 2a b)cosh(x) + 2a b + 2a b +--R / +--R 6 2 4 4 2 3 +--R (2b + 4a b + 2a b )sinh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 2 +--R ((4b + 8a b + 4a b )cosh(x) + 6a b + 12a b + 6a b)sinh(x) +--R + +--R 6 2 4 4 2 2 5 3 3 5 6 +--R (2b + 4a b + 2a b )cosh(x) + (8a b + 16a b + 8a b)cosh(x) - 2b +--R + +--R 4 2 6 +--R 6a b + 4a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 6 5 +--R (2a b + 4a b + 2a b)cosh(x) + (4a b + 8a b + 4a )cosh(x) - 2a b +--R + +--R 3 3 5 +--R - 4a b - 2a b +--R Type: Expression(Integer) +--E 99 + +--S 100 of 552 +d0719:= D(m0719,x) +--R +--R +--R (100) +--R 5 3 3 9 +--R (2a b - 2a b )sinh(x) +--R + +--R 5 3 3 2 4 4 2 8 +--R ((9a b - 9a b )cosh(x) + 20a b - 4a b )sinh(x) +--R + +--R 5 3 3 2 2 4 4 2 5 +--R (14a b - 14a b )cosh(x) + (76a b - 16a b )cosh(x) - 10a b +--R + +--R 3 3 5 +--R 44a b - 2a b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 3 3 2 4 4 2 2 +--R (5a b - 5a b )cosh(x) + (92a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 24a b + 142a b - 6a b)cosh(x) - 20a b + 36a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 3 4 2 4 3 +--R (- 10a b + 10a b )cosh(x) + 4a b cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 +--R (- 6a b + 122a b - 4a b)cosh(x) + (- 12a b + 96a b )cosh(x) +--R + +--R 5 5 +--R - 10a b + 10a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 5 2 4 4 2 4 +--R (- 13a b + 13a b )cosh(x) + (- 84a b + 20a b )cosh(x) +--R + +--R 5 3 3 5 3 2 4 4 2 2 +--R (29a b - 65a b + 4a b)cosh(x) + (84a b + 44a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 34a b + 72a b + 26a b)cosh(x) - 36a b + 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 6 2 4 4 2 5 +--R (- 6a b + 6a b )cosh(x) + (- 76a b + 16a b )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 3 +--R (34a b - 168a b + 6a b)cosh(x) + (144a b - 88a b )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 +--R (- 38a b + 190a b + 8a b)cosh(x) + (- 92a b + 80a b )cosh(x) +--R + +--R 5 3 3 5 +--R 2a b - 44a b + 10a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 3 7 2 4 4 2 6 +--R (- a b + a b )cosh(x) + (- 28a b + 4a b )cosh(x) +--R + +--R 5 3 3 5 5 2 4 4 2 4 +--R (18a b - 100a b + 2a b)cosh(x) + (92a b - 108a b )cosh(x) +--R + +--R 5 3 3 5 3 2 4 4 2 2 +--R (- 17a b + 173a b - 28a b)cosh(x) + (- 76a b + 116a b )cosh(x) +--R + +--R 3 3 5 2 4 4 2 +--R (- 78a b + 30a b)cosh(x) + 4a b - 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 7 5 3 3 6 +--R - 4a b cosh(x) + (6a b - 22a b )cosh(x) +--R + +--R 2 4 4 2 5 5 3 3 5 4 +--R (28a b - 40a b )cosh(x) + (- 4a b + 62a b - 26a b)cosh(x) +--R + +--R 2 4 4 2 3 5 3 3 5 2 +--R (- 20a b + 72a b )cosh(x) + (- 2a b - 42a b + 28a b)cosh(x) +--R + +--R 2 4 4 2 3 3 5 +--R (- 4a b - 32a b )cosh(x) + 2a b - 2a b +--R * +--R sinh(x) +--R + +--R 5 3 3 7 2 4 4 2 6 +--R (a b - a b )cosh(x) + (4a b - 4a b )cosh(x) +--R + +--R 5 3 3 5 5 4 2 4 +--R (- a b + 7a b - 6a b)cosh(x) + 16a b cosh(x) +--R + +--R 5 3 3 5 3 2 4 4 2 2 +--R (- a b - 7a b + 8a b)cosh(x) + (- 4a b - 12a b )cosh(x) +--R + +--R 5 3 3 5 +--R (a b + a b - 2a b)cosh(x) +--R / +--R 8 2 6 4 4 10 +--R (b + 2a b + a b )sinh(x) +--R + +--R 8 2 6 4 4 7 3 5 5 3 9 +--R ((6b + 12a b + 6a b )cosh(x) + 6a b + 12a b + 6a b )sinh(x) +--R + +--R 8 2 6 4 4 2 7 3 5 5 3 +--R (15b + 30a b + 15a b )cosh(x) + (32a b + 64a b + 32a b )cosh(x) +--R + +--R 2 6 4 4 6 2 +--R 13a b + 26a b + 13a b +--R * +--R 8 +--R sinh(x) +--R + +--R 8 2 6 4 4 3 +--R (20b + 40a b + 20a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (70a b + 140a b + 70a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 7 3 5 5 3 +--R (2b + 66a b + 126a b + 62a b )cosh(x) + 4a b + 20a b + 28a b +--R + +--R 7 +--R 12a b +--R * +--R 7 +--R sinh(x) +--R + +--R 8 2 6 4 4 4 +--R (15b + 30a b + 15a b )cosh(x) +--R + +--R 7 3 5 5 3 3 +--R (80a b + 160a b + 80a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (9b + 137a b + 247a b + 119a b )cosh(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 +--R (24a b + 100a b + 128a b + 52a b)cosh(x) - 2b + 12a b + 34a b +--R + +--R 6 2 8 +--R 24a b + 4a +--R * +--R 6 +--R sinh(x) +--R + +--R 8 2 6 4 4 5 7 3 5 5 3 4 +--R (6b + 12a b + 6a b )cosh(x) + (50a b + 100a b + 50a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (16b + 148a b + 248a b + 116a b )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (58a b + 204a b + 234a b + 88a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 7 3 5 +--R (- 6b + 54a b + 142a b + 98a b + 16a )cosh(x) - 8a b + 4a b +--R + +--R 5 3 7 +--R 32a b + 20a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 7 3 5 5 3 5 +--R (b + 2a b + a b )cosh(x) + (16a b + 32a b + 16a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (14b + 87a b + 132a b + 59a b )cosh(x) +--R + +--R 7 3 5 5 3 7 3 +--R (72a b + 216a b + 216a b + 72a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- 7b + 103a b + 251a b + 165a b + 24a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 +--R (- 16a b + 36a b + 120a b + 68a b)cosh(x) - 6a b - 4a b + 10a b +--R + +--R 8 +--R 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 7 3 5 5 3 6 +--R (2a b + 4a b + 2a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (6b + 26a b + 34a b + 14a b )cosh(x) +--R + +--R 7 3 5 5 3 7 4 +--R (48a b + 124a b + 104a b + 28a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (- 4b + 104a b + 236a b + 144a b + 16a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 14a b + 68a b + 178a b + 96a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 7 3 5 +--R (- 2b - 10a b + 10a b + 42a b + 24a )cosh(x) - 4a b - 4a b +--R + +--R 5 3 7 +--R 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (b + 3a b + 3a b + a b )cosh(x) +--R + +--R 7 3 5 5 3 7 5 +--R (16a b + 36a b + 24a b + 4a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- b + 56a b + 119a b + 66a b + 4a )cosh(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 8a b + 56a b + 136a b + 72a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- b - 5a b + 21a b + 53a b + 28a )cosh(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 8 +--R (- 8a b - 4a b + 16a b + 12a b)cosh(x) + b - 6a b - 11a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 3 5 5 3 6 2 6 4 4 6 2 5 +--R (2a b + 4a b + 2a b )cosh(x) + (14a b + 28a b + 14a b )cosh(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 2a b + 24a b + 54a b + 28a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 4a b + 8a b + 28a b + 16a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 2a b + 4a b + 14a b + 8a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 7 5 3 7 +--R (- 10a b - 12a b + 6a b + 8a )cosh(x) + 2a b - 6a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 6 4 4 6 2 6 3 5 5 3 7 5 +--R (a b + 2a b + a b )cosh(x) + (4a b + 8a b + 4a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- a b + 2a b + 7a b + 4a )cosh(x) +--R + +--R 2 6 4 4 6 2 8 2 3 5 5 3 7 +--R (- a b + 2a b + 7a b + 4a )cosh(x) + (- 4a b - 8a b - 4a b)cosh(x) +--R + +--R 2 6 4 4 6 2 +--R a b + 2a b + a b +--R Type: Expression(Integer) +--E 100 + +--S 101 of 552 +t0720:= tanh(x)^2/(a+b*sinh(x))^2 +--R +--R +--R 2 +--R tanh(x) +--R (101) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 101 + +--S 102 of 552 +r0720:= -2*a^3*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)+_ + 4*a*b^2*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ + 2*a*b*sech(x)/(a^2+b^2)^2-a^2*b*cosh(x)/(a^2+b^2)^2/(a+b*sinh(x))-_ + (a^2-b^2)*tanh(x)/(a^2+b^2)^2 +--R +--R +--R (102) +--R x +--R a tanh(-) - b +--R 3 3 2 2 4 2 +--R ((- 4a b + 2a b)sinh(x) - 4a b + 2a )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 2 3 2 +--R ((b - a b)sinh(x) + a b - a )tanh(x) - 2a b sech(x)sinh(x) +--R + +--R 2 2 +--R - 2a b sech(x) - a b cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 5 2 3 4 4 3 2 5 | 2 2 +--R ((b + 2a b + a b)sinh(x) + a b + 2a b + a )\|b + a +--R Type: Expression(Integer) +--E 102 + +--S 103 of 552 +a0720:= integrate(t0720,x) +--R +--R +--R (103) +--R 3 3 4 3 3 2 2 4 3 +--R (2a b - a b)sinh(x) + ((8a b - 4a b)cosh(x) + 4a b - 2a )sinh(x) +--R + +--R 3 3 2 2 2 4 2 +--R ((12a b - 6a b)cosh(x) + (12a b - 6a )cosh(x))sinh(x) +--R + +--R 3 3 3 2 2 4 2 2 2 4 +--R ((8a b - 4a b)cosh(x) + (12a b - 6a )cosh(x) + 4a b - 2a ) +--R * +--R sinh(x) +--R + +--R 3 3 4 2 2 4 3 2 2 4 +--R (2a b - a b)cosh(x) + (4a b - 2a )cosh(x) + (4a b - 2a )cosh(x) +--R + +--R 3 3 +--R - 2a b + a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 3 3 +--R (- 4a b + 2a )sinh(x) +--R + +--R 2 3 3 2 2 +--R ((- 12a b + 6a )cosh(x) - 2b - 8a b)sinh(x) +--R + +--R 2 3 2 3 2 3 +--R ((- 12a b + 6a )cosh(x) + (- 4b - 16a b)cosh(x) + 6a )sinh(x) +--R + +--R 2 3 3 3 2 2 3 3 +--R (- 4a b + 2a )cosh(x) + (- 2b - 8a b)cosh(x) + 6a cosh(x) + 2b +--R + +--R 2 +--R - 4a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 2 3 4 4 +--R (b + 2a b + a b)sinh(x) +--R + +--R 5 2 3 4 4 3 2 5 3 +--R ((4b + 8a b + 4a b)cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 2 +--R ((6b + 12a b + 6a b)cosh(x) + (6a b + 12a b + 6a )cosh(x))sinh(x) +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (4b + 8a b + 4a b)cosh(x) + (6a b + 12a b + 6a )cosh(x) +--R + +--R 4 3 2 5 +--R 2a b + 4a b + 2a +--R * +--R sinh(x) +--R + +--R 5 2 3 4 4 4 3 2 5 3 +--R (b + 2a b + a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (2a b + 4a b + 2a )cosh(x) - b - 2a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 552 +m0720:= a0720-r0720 +--R +--R +--R (104) +--R 4 3 2 5 +--R (2a b - a b )sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R ((8a b - 4a b )cosh(x) + 6a b - 3a b)sinh(x) +--R + +--R 4 3 2 2 2 3 4 3 2 5 +--R ((12a b - 6a b )cosh(x) + (20a b - 10a b)cosh(x) + 4a b - 2a ) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (8a b - 4a b )cosh(x) + (24a b - 12a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (12a b - 6a )cosh(x) + 4a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (2a b - a b )cosh(x) + (12a b - 6a b)cosh(x) +--R + +--R 3 2 5 2 2 3 4 4 3 2 +--R (12a b - 6a )cosh(x) + (4a b - 2a b)cosh(x) - 2a b + 5a b +--R + +--R 5 +--R - 2a +--R * +--R sinh(x) +--R + +--R 2 3 4 4 3 2 5 3 3 2 5 +--R (2a b - a b)cosh(x) + (4a b - 2a )cosh(x) + (4a b - 2a )cosh(x) +--R + +--R 2 3 4 +--R - 2a b + a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 3 2 5 +--R (4a b - 2a b )sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R ((16a b - 8a b )cosh(x) + 12a b - 6a b)sinh(x) +--R + +--R 4 3 2 2 2 3 4 3 2 5 +--R ((24a b - 12a b )cosh(x) + (40a b - 20a b)cosh(x) + 8a b - 4a ) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (16a b - 8a b )cosh(x) + (48a b - 24a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (24a b - 12a )cosh(x) + 8a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (4a b - 2a b )cosh(x) + (24a b - 12a b)cosh(x) +--R + +--R 3 2 5 2 2 3 4 4 3 2 +--R (24a b - 12a )cosh(x) + (8a b - 4a b)cosh(x) - 4a b + 10a b +--R + +--R 5 +--R - 4a +--R * +--R sinh(x) +--R + +--R 2 3 4 4 3 2 5 3 3 2 5 +--R (4a b - 2a b)cosh(x) + (8a b - 4a )cosh(x) + (8a b - 4a )cosh(x) +--R + +--R 2 3 4 +--R - 4a b + 2a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 2 2 5 +--R (- b + a b )sinh(x) +--R + +--R 4 2 2 3 3 4 +--R ((- 4b + 4a b )cosh(x) - 3a b + 3a b)sinh(x) +--R + +--R 4 2 2 2 3 3 2 2 +--R (- 6b + 6a b )cosh(x) + (- 10a b + 10a b)cosh(x) - 2a b +--R + +--R 4 +--R 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 4b + 4a b )cosh(x) + (- 12a b + 12a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 6a b + 6a )cosh(x) - 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- b + a b )cosh(x) + (- 6a b + 6a b)cosh(x) +--R + +--R 2 2 4 2 3 3 4 +--R (- 6a b + 6a )cosh(x) + (- 2a b + 2a b)cosh(x) + b +--R + +--R 2 2 4 +--R - 3a b + 2a +--R * +--R sinh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (- a b + a b)cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 2a b + 2a )cosh(x) + a b - a b +--R * +--R tanh(x) +--R + +--R 3 5 +--R 2a b sech(x)sinh(x) +--R + +--R 3 2 2 2 2 3 3 4 +--R ((8a b cosh(x) + 6a b )sech(x) + a b cosh(x) - 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 2 +--R (12a b cosh(x) + 20a b cosh(x) + 4a b)sech(x) + 4a b cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 12a b + 8a b)cosh(x) - 2b - 12a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R (8a b cosh(x) + 24a b cosh(x) + 12a b cosh(x) + 4a b )sech(x) +--R + +--R 2 2 3 3 3 2 +--R 6a b cosh(x) + (- 12a b + 12a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- 4b - 28a b + 6a )cosh(x) - 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 2 +--R 2a b cosh(x) + 12a b cosh(x) + 12a b cosh(x) +--R + +--R 2 2 3 3 +--R 4a b cosh(x) - 2a b + 4a b +--R * +--R sech(x) +--R + +--R 2 2 4 3 3 3 +--R 4a b cosh(x) + (- 4a b + 8a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (- 2b - 20a b + 6a )cosh(x) + (- 4a b - 8a b)cosh(x) + 2b +--R + +--R 2 2 4 +--R - 4a b + 6a +--R * +--R sinh(x) +--R + +--R 2 2 4 3 3 3 2 2 +--R (2a b cosh(x) + 4a b cosh(x) + 4a b cosh(x) - 2a b )sech(x) +--R + +--R 2 2 5 3 4 2 2 4 3 +--R a b cosh(x) + 2a b cosh(x) + (- 4a b + 2a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 2a b - 6a b)cosh(x) + (- a b + 6a )cosh(x) + 2a b - 4a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 6 2 4 4 2 5 +--R (b + 2a b + a b )sinh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 4 +--R ((4b + 8a b + 4a b )cosh(x) + 3a b + 6a b + 3a b)sinh(x) +--R + +--R 6 2 4 4 2 2 5 3 3 5 +--R (6b + 12a b + 6a b )cosh(x) + (10a b + 20a b + 10a b)cosh(x) +--R + +--R 2 4 4 2 6 +--R 2a b + 4a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 4 2 3 5 3 3 5 2 +--R (4b + 8a b + 4a b )cosh(x) + (12a b + 24a b + 12a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (6a b + 12a b + 6a )cosh(x) + 2a b + 4a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (b + 2a b + a b )cosh(x) + (6a b + 12a b + 6a b)cosh(x) +--R + +--R 2 4 4 2 6 2 5 3 3 5 6 +--R (6a b + 12a b + 6a )cosh(x) + (2a b + 4a b + 2a b)cosh(x) - b +--R + +--R 4 2 6 +--R 3a b + 2a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 6 3 +--R (a b + 2a b + a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (2a b + 4a b + 2a )cosh(x) - a b - 2a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 104 + +--S 105 of 552 +--d0720:= D(m0720,x) +--E 105 + +--S 106 of 552 +t0721:= tanh(x)^3/(a+b*sinh(x))^2 +--R +--R +--R 3 +--R tanh(x) +--R (105) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 106 + +--S 107 of 552 +r0721:= 4*a^3*b*atan(sinh(x))/(a^2+b^2)^3-a*b*atan(sinh(x))/(a^2+b^2)^2+_ + 1/2*a^2*(a^2-3*b^2)*log(cosh(x)^2)/(a^2+b^2)^3-_ + a^2*(a^2-3*b^2)*log(a+b*sinh(x))/(a^2+b^2)^3+_ + 1/2*(a^2-b^2)*sech(x)^2/(a^2+b^2)^2+a^3/(a^2+b^2)^2/(a+b*sinh(x))-_ + a*b*sech(x)*tanh(x)/(a^2+b^2)^2 +--R +--R +--R (106) +--R 2 3 4 3 2 5 +--R ((6a b - 2a b)sinh(x) + 6a b - 2a )log(b sinh(x) + a) +--R + +--R 2 3 4 3 2 5 2 +--R ((- 3a b + a b)sinh(x) - 3a b + a )log(cosh(x) ) +--R + +--R 4 3 2 2 3 4 +--R ((- 2a b + 6a b )sinh(x) - 2a b + 6a b)atan(sinh(x)) +--R + +--R 4 3 2 2 3 4 +--R ((- 2a b - 2a b )sech(x)sinh(x) + (- 2a b - 2a b)sech(x))tanh(x) +--R + +--R 5 4 2 4 5 2 3 2 5 +--R (- b + a b)sech(x) sinh(x) + (- a b + a )sech(x) + 2a b + 2a +--R / +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R (2b + 6a b + 6a b + 2a b)sinh(x) + 2a b + 6a b + 6a b + 2a +--R Type: Expression(Integer) +--E 107 + +--S 108 of 552 +a0721:= integrate(t0721,x) +--R +--R +--R (107) +--R 2 3 4 6 +--R (- 3a b + a b)sinh(x) +--R + +--R 2 3 4 3 2 5 5 +--R ((- 18a b + 6a b)cosh(x) - 6a b + 2a )sinh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 +--R (- 45a b + 15a b)cosh(x) + (- 30a b + 10a )cosh(x) - 3a b +--R + +--R 4 +--R a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (- 60a b + 20a b)cosh(x) + (- 60a b + 20a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 12a b + 4a b)cosh(x) - 12a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (- 45a b + 15a b)cosh(x) + (- 60a b + 20a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (- 18a b + 6a b)cosh(x) + (- 36a b + 12a )cosh(x) + 3a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (- 18a b + 6a b)cosh(x) + (- 30a b + 10a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (- 12a b + 4a b)cosh(x) + (- 36a b + 12a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (6a b - 2a b)cosh(x) - 6a b + 2a +--R * +--R sinh(x) +--R + +--R 2 3 4 6 3 2 5 5 +--R (- 3a b + a b)cosh(x) + (- 6a b + 2a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (- 3a b + a b)cosh(x) + (- 12a b + 4a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (3a b - a b)cosh(x) + (- 6a b + 2a )cosh(x) + 3a b - a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 4 6 +--R (3a b - a b)sinh(x) +--R + +--R 2 3 4 3 2 5 5 +--R ((18a b - 6a b)cosh(x) + 6a b - 2a )sinh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R ((45a b - 15a b)cosh(x) + (30a b - 10a )cosh(x) + 3a b - a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (60a b - 20a b)cosh(x) + (60a b - 20a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (12a b - 4a b)cosh(x) + 12a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (45a b - 15a b)cosh(x) + (60a b - 20a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (18a b - 6a b)cosh(x) + (36a b - 12a )cosh(x) - 3a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 5 3 2 5 4 +--R (18a b - 6a b)cosh(x) + (30a b - 10a )cosh(x) +--R + +--R 2 3 4 3 3 2 5 2 +--R (12a b - 4a b)cosh(x) + (36a b - 12a )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 6a b + 2a b)cosh(x) + 6a b - 2a +--R * +--R sinh(x) +--R + +--R 2 3 4 6 3 2 5 5 2 3 4 4 +--R (3a b - a b)cosh(x) + (6a b - 2a )cosh(x) + (3a b - a b)cosh(x) +--R + +--R 3 2 5 3 2 3 4 2 +--R (12a b - 4a )cosh(x) + (- 3a b + a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (6a b - 2a )cosh(x) - 3a b + a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 3 2 6 +--R (- 2a b + 6a b )sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R ((- 12a b + 36a b )cosh(x) - 4a b + 12a b)sinh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (- 30a b + 90a b )cosh(x) + (- 20a b + 60a b)cosh(x) - 2a b +--R + +--R 3 2 +--R 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 40a b + 120a b )cosh(x) + (- 40a b + 120a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 8a b + 24a b )cosh(x) - 8a b + 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 30a b + 90a b )cosh(x) + (- 40a b + 120a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (- 12a b + 36a b )cosh(x) + (- 24a b + 72a b)cosh(x) + 2a b +--R + +--R 3 2 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (- 12a b + 36a b )cosh(x) + (- 20a b + 60a b)cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (- 8a b + 24a b )cosh(x) + (- 24a b + 72a b)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (4a b - 12a b )cosh(x) - 4a b + 12a b +--R * +--R sinh(x) +--R + +--R 4 3 2 6 2 3 4 5 +--R (- 2a b + 6a b )cosh(x) + (- 4a b + 12a b)cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 2a b + 6a b )cosh(x) + (- 8a b + 24a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (2a b - 6a b )cosh(x) + (- 4a b + 12a b)cosh(x) + 2a b - 6a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 4 5 5 +--R (- 2a b + 2a )sinh(x) +--R + +--R 4 5 5 2 3 4 4 +--R ((- 10a b + 10a )cosh(x) - 2b - 4a b - 2a b)sinh(x) +--R + +--R 4 5 2 5 2 3 4 3 2 +--R (- 20a b + 20a )cosh(x) + (- 8b - 16a b - 8a b)cosh(x) + 8a b +--R + +--R 5 +--R 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 5 3 5 2 3 4 2 +--R (- 20a b + 20a )cosh(x) + (- 12b - 24a b - 12a b)cosh(x) +--R + +--R 3 2 5 5 2 3 4 +--R (24a b + 24a )cosh(x) + 2b + 4a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 4 5 2 3 4 3 +--R (- 10a b + 10a )cosh(x) + (- 8b - 16a b - 8a b)cosh(x) +--R + +--R 3 2 5 2 5 2 3 4 4 5 +--R (24a b + 24a )cosh(x) + (4b + 8a b + 4a b)cosh(x) - 2a b + 2a +--R * +--R sinh(x) +--R + +--R 4 5 5 5 2 3 4 4 +--R (- 2a b + 2a )cosh(x) + (- 2b - 4a b - 2a b)cosh(x) +--R + +--R 3 2 5 3 5 2 3 4 2 +--R (8a b + 8a )cosh(x) + (2b + 4a b + 2a b)cosh(x) +--R + +--R 4 5 +--R (- 2a b + 2a )cosh(x) +--R / +--R 7 2 5 4 3 6 6 +--R (b + 3a b + 3a b + a b)sinh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((6b + 18a b + 18a b + 6a b)cosh(x) + 2a b + 6a b + 6a b + 2a ) +--R * +--R 5 +--R sinh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (15b + 45a b + 45a b + 15a b)cosh(x) +--R + +--R 6 3 4 5 2 7 7 2 5 4 3 6 +--R (10a b + 30a b + 30a b + 10a )cosh(x) + b + 3a b + 3a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 5 4 3 6 3 +--R (20b + 60a b + 60a b + 20a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 +--R (20a b + 60a b + 60a b + 20a )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R (4b + 12a b + 12a b + 4a b)cosh(x) + 4a b + 12a b + 12a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 5 4 3 6 4 +--R (15b + 45a b + 45a b + 15a b)cosh(x) +--R + +--R 6 3 4 5 2 7 3 +--R (20a b + 60a b + 60a b + 20a )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (6b + 18a b + 18a b + 6a b)cosh(x) +--R + +--R 6 3 4 5 2 7 7 2 5 4 3 6 +--R (12a b + 36a b + 36a b + 12a )cosh(x) - b - 3a b - 3a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 4 3 6 5 +--R (6b + 18a b + 18a b + 6a b)cosh(x) +--R + +--R 6 3 4 5 2 7 4 +--R (10a b + 30a b + 30a b + 10a )cosh(x) +--R + +--R 7 2 5 4 3 6 3 +--R (4b + 12a b + 12a b + 4a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 +--R (12a b + 36a b + 36a b + 12a )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R (- 2b - 6a b - 6a b - 2a b)cosh(x) + 2a b + 6a b + 6a b + 2a +--R * +--R sinh(x) +--R + +--R 7 2 5 4 3 6 6 +--R (b + 3a b + 3a b + a b)cosh(x) +--R + +--R 6 3 4 5 2 7 5 +--R (2a b + 6a b + 6a b + 2a )cosh(x) +--R + +--R 7 2 5 4 3 6 4 +--R (b + 3a b + 3a b + a b)cosh(x) +--R + +--R 6 3 4 5 2 7 3 +--R (4a b + 12a b + 12a b + 4a )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- b - 3a b - 3a b - a b)cosh(x) +--R + +--R 6 3 4 5 2 7 7 2 5 4 3 6 +--R (2a b + 6a b + 6a b + 2a )cosh(x) - b - 3a b - 3a b - a b +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 552 +m0721:= a0721-r0721 +--R +--R +--R (108) +--R 2 4 4 2 7 +--R (- 6a b + 2a b )sinh(x) +--R + +--R 2 4 4 2 3 3 5 6 +--R ((- 36a b + 12a b )cosh(x) - 18a b + 6a b)sinh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 +--R (- 90a b + 30a b )cosh(x) + (- 96a b + 32a b)cosh(x) - 6a b +--R + +--R 4 2 6 +--R - 10a b + 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 4 2 3 3 3 5 2 +--R (- 120a b + 40a b )cosh(x) + (- 210a b + 70a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (- 24a b - 52a b + 20a )cosh(x) - 30a b + 10a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (- 90a b + 30a b )cosh(x) + (- 240a b + 80a b)cosh(x) +--R + +--R 2 4 4 2 6 2 3 3 5 +--R (- 36a b - 108a b + 40a )cosh(x) + (- 96a b + 32a b)cosh(x) +--R + +--R 2 4 4 2 6 +--R 6a b - 26a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 5 3 3 5 4 +--R (- 36a b + 12a b )cosh(x) + (- 150a b + 50a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 3 5 2 +--R (- 24a b - 112a b + 40a )cosh(x) + (- 108a b + 36a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (12a b - 76a b + 24a )cosh(x) - 6a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 3 5 5 +--R (- 6a b + 2a b )cosh(x) + (- 48a b + 16a b)cosh(x) +--R + +--R 2 4 4 2 6 4 3 3 5 3 +--R (- 6a b - 58a b + 20a )cosh(x) + (- 48a b + 16a b)cosh(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (6a b - 74a b + 24a )cosh(x) + 6a b - 14a b + 4a +--R * +--R sinh(x) +--R + +--R 3 3 5 6 4 2 6 5 +--R (- 6a b + 2a b)cosh(x) + (- 12a b + 4a )cosh(x) +--R + +--R 3 3 5 4 4 2 6 3 +--R (- 6a b + 2a b)cosh(x) + (- 24a b + 8a )cosh(x) +--R + +--R 3 3 5 2 4 2 6 3 3 5 +--R (6a b - 2a b)cosh(x) + (- 12a b + 4a )cosh(x) + 6a b - 2a b +--R * +--R log(b sinh(x) + a) +--R + +--R 2 4 4 2 7 +--R (3a b - a b )sinh(x) +--R + +--R 2 4 4 2 3 3 5 6 +--R ((18a b - 6a b )cosh(x) + 9a b - 3a b)sinh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 +--R (45a b - 15a b )cosh(x) + (48a b - 16a b)cosh(x) + 3a b +--R + +--R 4 2 6 +--R 5a b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 4 2 3 3 3 5 2 +--R (60a b - 20a b )cosh(x) + (105a b - 35a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (12a b + 26a b - 10a )cosh(x) + 15a b - 5a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (45a b - 15a b )cosh(x) + (120a b - 40a b)cosh(x) +--R + +--R 2 4 4 2 6 2 3 3 5 +--R (18a b + 54a b - 20a )cosh(x) + (48a b - 16a b)cosh(x) +--R + +--R 2 4 4 2 6 +--R - 3a b + 13a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 5 3 3 5 4 +--R (18a b - 6a b )cosh(x) + (75a b - 25a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 3 5 2 +--R (12a b + 56a b - 20a )cosh(x) + (54a b - 18a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (- 6a b + 38a b - 12a )cosh(x) + 3a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 3 5 5 +--R (3a b - a b )cosh(x) + (24a b - 8a b)cosh(x) +--R + +--R 2 4 4 2 6 4 3 3 5 3 +--R (3a b + 29a b - 10a )cosh(x) + (24a b - 8a b)cosh(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (- 3a b + 37a b - 12a )cosh(x) - 3a b + 7a b - 2a +--R * +--R sinh(x) +--R + +--R 3 3 5 6 4 2 6 5 3 3 5 4 +--R (3a b - a b)cosh(x) + (6a b - 2a )cosh(x) + (3a b - a b)cosh(x) +--R + +--R 4 2 6 3 3 3 5 2 +--R (12a b - 4a )cosh(x) + (- 3a b + a b)cosh(x) +--R + +--R 4 2 6 3 3 5 +--R (6a b - 2a )cosh(x) - 3a b + a b +--R * +--R 2 +--R log(cosh(x) ) +--R + +--R 2 4 4 2 7 +--R (- 6a b + 2a b )sinh(x) +--R + +--R 2 4 4 2 3 3 5 6 +--R ((- 36a b + 12a b )cosh(x) - 18a b + 6a b)sinh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 +--R (- 90a b + 30a b )cosh(x) + (- 96a b + 32a b)cosh(x) - 6a b +--R + +--R 4 2 6 +--R - 10a b + 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 4 2 3 3 3 5 2 +--R (- 120a b + 40a b )cosh(x) + (- 210a b + 70a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (- 24a b - 52a b + 20a )cosh(x) - 30a b + 10a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (- 90a b + 30a b )cosh(x) + (- 240a b + 80a b)cosh(x) +--R + +--R 2 4 4 2 6 2 3 3 5 +--R (- 36a b - 108a b + 40a )cosh(x) + (- 96a b + 32a b)cosh(x) +--R + +--R 2 4 4 2 6 +--R 6a b - 26a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 5 3 3 5 4 +--R (- 36a b + 12a b )cosh(x) + (- 150a b + 50a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 3 5 2 +--R (- 24a b - 112a b + 40a )cosh(x) + (- 108a b + 36a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (12a b - 76a b + 24a )cosh(x) - 6a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 3 5 5 +--R (- 6a b + 2a b )cosh(x) + (- 48a b + 16a b)cosh(x) +--R + +--R 2 4 4 2 6 4 3 3 5 3 +--R (- 6a b - 58a b + 20a )cosh(x) + (- 48a b + 16a b)cosh(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (6a b - 74a b + 24a )cosh(x) + 6a b - 14a b + 4a +--R * +--R sinh(x) +--R + +--R 3 3 5 6 4 2 6 5 +--R (- 6a b + 2a b)cosh(x) + (- 12a b + 4a )cosh(x) +--R + +--R 3 3 5 4 4 2 6 3 +--R (- 6a b + 2a b)cosh(x) + (- 24a b + 8a )cosh(x) +--R + +--R 3 3 5 2 4 2 6 3 3 5 +--R (6a b - 2a b)cosh(x) + (- 12a b + 4a )cosh(x) + 6a b - 2a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 4 4 2 7 +--R (6a b - 2a b )sinh(x) +--R + +--R 2 4 4 2 3 3 5 6 +--R ((36a b - 12a b )cosh(x) + 18a b - 6a b)sinh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 +--R (90a b - 30a b )cosh(x) + (96a b - 32a b)cosh(x) + 6a b +--R + +--R 4 2 6 +--R 10a b - 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 4 2 3 3 3 5 2 +--R (120a b - 40a b )cosh(x) + (210a b - 70a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (24a b + 52a b - 20a )cosh(x) + 30a b - 10a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (90a b - 30a b )cosh(x) + (240a b - 80a b)cosh(x) +--R + +--R 2 4 4 2 6 2 3 3 5 +--R (36a b + 108a b - 40a )cosh(x) + (96a b - 32a b)cosh(x) +--R + +--R 2 4 4 2 6 +--R - 6a b + 26a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 5 3 3 5 4 +--R (36a b - 12a b )cosh(x) + (150a b - 50a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 3 5 2 +--R (24a b + 112a b - 40a )cosh(x) + (108a b - 36a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (- 12a b + 76a b - 24a )cosh(x) + 6a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 3 5 5 +--R (6a b - 2a b )cosh(x) + (48a b - 16a b)cosh(x) +--R + +--R 2 4 4 2 6 4 3 3 5 3 +--R (6a b + 58a b - 20a )cosh(x) + (48a b - 16a b)cosh(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (- 6a b + 74a b - 24a )cosh(x) - 6a b + 14a b - 4a +--R * +--R sinh(x) +--R + +--R 3 3 5 6 4 2 6 5 +--R (6a b - 2a b)cosh(x) + (12a b - 4a )cosh(x) +--R + +--R 3 3 5 4 4 2 6 3 +--R (6a b - 2a b)cosh(x) + (24a b - 8a )cosh(x) +--R + +--R 3 3 5 2 4 2 6 3 3 5 +--R (- 6a b + 2a b)cosh(x) + (12a b - 4a )cosh(x) - 6a b + 2a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 5 3 3 7 +--R (- 4a b + 12a b )sinh(x) +--R + +--R 5 3 3 2 4 4 2 6 +--R ((- 24a b + 72a b )cosh(x) - 12a b + 36a b )sinh(x) +--R + +--R 5 3 3 2 2 4 4 2 +--R (- 60a b + 180a b )cosh(x) + (- 64a b + 192a b )cosh(x) +--R + +--R 5 3 3 5 +--R - 4a b + 4a b + 24a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 3 2 4 4 2 2 +--R (- 80a b + 240a b )cosh(x) + (- 140a b + 420a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 16a b + 8a b + 120a b)cosh(x) - 20a b + 60a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (- 60a b + 180a b )cosh(x) + (- 160a b + 480a b )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 +--R (- 24a b - 8a b + 240a b)cosh(x) + (- 64a b + 192a b )cosh(x) +--R + +--R 5 3 3 5 +--R 4a b - 28a b + 48a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 3 5 2 4 4 2 4 +--R (- 24a b + 72a b )cosh(x) + (- 100a b + 300a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 16a b - 32a b + 240a b)cosh(x) +--R + +--R 2 4 4 2 2 5 3 3 5 +--R (- 72a b + 216a b )cosh(x) + (8a b - 72a b + 144a b)cosh(x) +--R + +--R 2 4 4 2 +--R - 4a b + 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 3 6 2 4 4 2 5 +--R (- 4a b + 12a b )cosh(x) + (- 32a b + 96a b )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 3 +--R (- 4a b - 28a b + 120a b)cosh(x) + (- 32a b + 96a b )cosh(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (4a b - 60a b + 144a b)cosh(x) + 4a b - 20a b + 24a b +--R * +--R sinh(x) +--R + +--R 2 4 4 2 6 3 3 5 5 +--R (- 4a b + 12a b )cosh(x) + (- 8a b + 24a b)cosh(x) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (- 4a b + 12a b )cosh(x) + (- 16a b + 48a b)cosh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 4 2 +--R (4a b - 12a b )cosh(x) + (- 8a b + 24a b)cosh(x) + 4a b - 12a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 5 3 3 7 +--R (2a b - 6a b )sinh(x) +--R + +--R 5 3 3 2 4 4 2 6 +--R ((12a b - 36a b )cosh(x) + 6a b - 18a b )sinh(x) +--R + +--R 5 3 3 2 2 4 4 2 5 +--R (30a b - 90a b )cosh(x) + (32a b - 96a b )cosh(x) + 2a b +--R + +--R 3 3 5 +--R - 2a b - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 3 2 4 4 2 2 +--R (40a b - 120a b )cosh(x) + (70a b - 210a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (8a b - 4a b - 60a b)cosh(x) + 10a b - 30a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (30a b - 90a b )cosh(x) + (80a b - 240a b )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 +--R (12a b + 4a b - 120a b)cosh(x) + (32a b - 96a b )cosh(x) +--R + +--R 5 3 3 5 +--R - 2a b + 14a b - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 3 5 2 4 4 2 4 +--R (12a b - 36a b )cosh(x) + (50a b - 150a b )cosh(x) +--R + +--R 5 3 3 5 3 2 4 4 2 2 +--R (8a b + 16a b - 120a b)cosh(x) + (36a b - 108a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 4a b + 36a b - 72a b)cosh(x) + 2a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 3 6 2 4 4 2 5 +--R (2a b - 6a b )cosh(x) + (16a b - 48a b )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 3 +--R (2a b + 14a b - 60a b)cosh(x) + (16a b - 48a b )cosh(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 2a b + 30a b - 72a b)cosh(x) - 2a b + 10a b - 12a b +--R * +--R sinh(x) +--R + +--R 2 4 4 2 6 3 3 5 5 +--R (2a b - 6a b )cosh(x) + (4a b - 12a b)cosh(x) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (2a b - 6a b )cosh(x) + (8a b - 24a b)cosh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 4 2 +--R (- 2a b + 6a b )cosh(x) + (4a b - 12a b)cosh(x) - 2a b + 6a b +--R * +--R atan(sinh(x)) +--R + +--R 5 3 3 7 +--R (2a b + 2a b )sech(x)sinh(x) +--R + +--R 5 3 3 2 4 4 2 6 +--R ((12a b + 12a b )cosh(x) + 6a b + 6a b )sech(x)sinh(x) +--R + +--R 5 3 3 2 2 4 4 2 5 +--R (30a b + 30a b )cosh(x) + (32a b + 32a b )cosh(x) + 2a b +--R + +--R 3 3 5 +--R 6a b + 4a b +--R * +--R 5 +--R sech(x)sinh(x) +--R + +--R 5 3 3 3 2 4 4 2 2 +--R (40a b + 40a b )cosh(x) + (70a b + 70a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (8a b + 28a b + 20a b)cosh(x) + 10a b + 10a b +--R * +--R 4 +--R sech(x)sinh(x) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (30a b + 30a b )cosh(x) + (80a b + 80a b )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 +--R (12a b + 52a b + 40a b)cosh(x) + (32a b + 32a b )cosh(x) +--R + +--R 5 3 3 5 +--R - 2a b + 6a b + 8a b +--R * +--R 3 +--R sech(x)sinh(x) +--R + +--R 5 3 3 5 2 4 4 2 4 +--R (12a b + 12a b )cosh(x) + (50a b + 50a b )cosh(x) +--R + +--R 5 3 3 5 3 2 4 4 2 2 +--R (8a b + 48a b + 40a b)cosh(x) + (36a b + 36a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 4a b + 20a b + 24a b)cosh(x) + 2a b + 2a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 5 3 3 6 2 4 4 2 5 +--R (2a b + 2a b )cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 3 +--R (2a b + 22a b + 20a b)cosh(x) + (16a b + 16a b )cosh(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 2a b + 22a b + 24a b)cosh(x) - 2a b + 2a b + 4a b +--R * +--R sech(x)sinh(x) +--R + +--R 2 4 4 2 6 3 3 5 5 +--R (2a b + 2a b )cosh(x) + (4a b + 4a b)cosh(x) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (2a b + 2a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 4 2 +--R (- 2a b - 2a b )cosh(x) + (4a b + 4a b)cosh(x) - 2a b - 2a b +--R * +--R sech(x) +--R * +--R tanh(x) +--R + +--R 6 4 2 2 7 +--R (b - a b )sech(x) sinh(x) +--R + +--R 6 4 2 5 5 2 5 3 3 5 +--R (((6b - 6a b )cosh(x) + 3a b - 3a b)sech(x) - 4a b - 2a b + 2a b) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 2 5 5 6 2 4 +--R (15b - 15a b )cosh(x) + (16a b - 16a b)cosh(x) + b + 2a b +--R + +--R 4 2 6 +--R - a b - 2a +--R * +--R 2 +--R sech(x) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (- 20a b - 12a b + 8a b)cosh(x) - 4b - 12a b - 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 6 4 2 3 5 5 2 +--R (20b - 20a b )cosh(x) + (35a b - 35a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 5 +--R (4b + 10a b - 4a b - 10a )cosh(x) + 5a b - 5a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 3 3 5 2 +--R (- 40a b - 30a b + 10a b)cosh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 +--R (- 16b - 52a b - 36a b )cosh(x) - 4a b + 6a b + 10a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 4 2 4 5 5 3 +--R (15b - 15a b )cosh(x) + (40a b - 40a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 5 5 +--R (6b + 20a b - 6a b - 20a )cosh(x) + (16a b - 16a b)cosh(x) +--R + +--R 6 2 4 4 2 6 +--R - b + 4a b + a b - 4a +--R * +--R 2 +--R sech(x) +--R + +--R 5 3 3 3 6 2 4 4 2 2 +--R (- 40a b - 40a b )cosh(x) + (- 24b - 88a b - 64a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (- 16a b + 8a b + 24a b)cosh(x) + 4b + 8a b + 12a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 4 2 5 5 5 4 +--R (6b - 6a b )cosh(x) + (25a b - 25a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 5 5 2 +--R (4b + 20a b - 4a b - 20a )cosh(x) + (18a b - 18a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 5 +--R (- 2b + 12a b + 2a b - 12a )cosh(x) + a b - a b +--R * +--R 2 +--R sech(x) +--R + +--R 5 3 3 5 4 +--R (- 20a b - 30a b - 10a b)cosh(x) +--R + +--R 6 2 4 4 2 3 +--R (- 16b - 72a b - 56a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 24a b - 12a b + 12a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 3 5 +--R (8b + 16a b + 32a b + 24a )cosh(x) + 10a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 4 2 6 5 5 5 +--R (b - a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 4 5 5 3 +--R (b + 10a b - a b - 10a )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (- b + 12a b + a b - 12a )cosh(x) - b + 2a b + a b - 2a +--R * +--R 2 +--R sech(x) +--R + +--R 5 3 3 5 5 6 2 4 4 2 4 +--R (- 4a b - 12a b - 8a b)cosh(x) + (- 4b - 28a b - 24a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 16a b - 24a b - 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (4b + 8a b + 28a b + 24a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (4a b + 20a b + 16a b)cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 5 5 6 2 4 6 5 5 5 4 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) + (a b - a b)cosh(x) +--R + +--R 2 4 6 3 5 5 2 2 4 6 +--R (4a b - 4a )cosh(x) + (- a b + a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 5 5 +--R - a b + a b +--R * +--R 2 +--R sech(x) +--R + +--R 3 3 5 6 2 4 4 2 5 +--R (- 2a b - 2a b)cosh(x) + (- 4a b - 4a b )cosh(x) +--R + +--R 5 3 3 5 4 4 2 6 3 +--R (- 4a b - 10a b - 6a b)cosh(x) + (8a b + 8a )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 3 3 5 +--R (4a b + 10a b + 6a b)cosh(x) + (- 4a b - 4a b )cosh(x) + 2a b + 2a b +--R / +--R 8 2 6 4 4 6 2 7 +--R (2b + 6a b + 6a b + 2a b )sinh(x) +--R + +--R 8 2 6 4 4 6 2 7 3 5 5 3 +--R (12b + 36a b + 36a b + 12a b )cosh(x) + 6a b + 18a b + 18a b +--R + +--R 7 +--R 6a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (30b + 90a b + 90a b + 30a b )cosh(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 +--R (32a b + 96a b + 96a b + 32a b)cosh(x) + 2b + 10a b + 18a b +--R + +--R 6 2 8 +--R 14a b + 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (40b + 120a b + 120a b + 40a b )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (70a b + 210a b + 210a b + 70a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 7 3 5 +--R (8b + 44a b + 84a b + 68a b + 20a )cosh(x) + 10a b + 30a b +--R + +--R 5 3 7 +--R 30a b + 10a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (30b + 90a b + 90a b + 30a b )cosh(x) +--R + +--R 7 3 5 5 3 7 3 +--R (80a b + 240a b + 240a b + 80a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (12b + 76a b + 156a b + 132a b + 40a )cosh(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 +--R (32a b + 96a b + 96a b + 32a b)cosh(x) - 2b + 2a b + 18a b +--R + +--R 6 2 8 +--R 22a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (12b + 36a b + 36a b + 12a b )cosh(x) +--R + +--R 7 3 5 5 3 7 4 +--R (50a b + 150a b + 150a b + 50a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (8b + 64a b + 144a b + 128a b + 40a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (36a b + 108a b + 108a b + 36a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 7 3 5 +--R (- 4b + 12a b + 60a b + 68a b + 24a )cosh(x) + 2a b + 6a b +--R + +--R 5 3 7 +--R 6a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (2b + 6a b + 6a b + 2a b )cosh(x) +--R + +--R 7 3 5 5 3 7 5 +--R (16a b + 48a b + 48a b + 16a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (2b + 26a b + 66a b + 62a b + 20a )cosh(x) +--R + +--R 7 3 5 5 3 7 3 +--R (16a b + 48a b + 48a b + 16a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 8 2 6 +--R (- 2b + 18a b + 66a b + 70a b + 24a )cosh(x) - 2b - 2a b +--R + +--R 4 4 6 2 8 +--R 6a b + 10a b + 4a +--R * +--R sinh(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (4a b + 12a b + 12a b + 4a )cosh(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (8a b + 24a b + 24a b + 8a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 2a b - 6a b - 6a b - 2a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 7 3 5 5 3 7 +--R (4a b + 12a b + 12a b + 4a )cosh(x) - 2a b - 6a b - 6a b - 2a b +--R Type: Expression(Integer) +--E 109 + +--S 110 of 552 +--d0721:= D(m0721,x) +--E 110 + +--S 111 of 552 +t0722:= tanh(x)/(%i+sinh(x))^2 +--R +--R +--R tanh(x) +--R (109) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 111 + +--S 112 of 552 +r0722:= -1/4*%i*atan(sinh(x))-1/4/(%i+sinh(x))^2-%i/(4*%i+4*sinh(x)) +--R +--R +--R 1 2 1 1 1 +--R (- - %i sinh(x) + - sinh(x) + - %i)atan(sinh(x)) - - %i sinh(x) +--R 4 2 4 4 +--R (110) ---------------------------------------------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 112 + +--S 113 of 552 +a0722:= integrate(t0722,x) +--R +--R +--R (111) +--R 4 3 +--R sinh(x) + (4cosh(x) + 4%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) + 12%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 12%i cosh(x) - 12cosh(x) - 4%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R 4%i cosh(x) - 6cosh(x) - 4%i cosh(x) + 1 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 4 3 +--R - sinh(x) + (- 4cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (- 6cosh(x) - 12%i cosh(x) + 6)sinh(x) +--R + +--R 3 2 4 +--R (- 4cosh(x) - 12%i cosh(x) + 12cosh(x) + 4%i)sinh(x) - cosh(x) +--R + +--R 3 2 +--R - 4%i cosh(x) + 6cosh(x) + 4%i cosh(x) - 1 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 3 2 2 +--R - 2%i sinh(x) - 6%i cosh(x)sinh(x) + (- 6%i cosh(x) + 2%i)sinh(x) +--R + +--R 3 +--R - 2%i cosh(x) + 2%i cosh(x) +--R / +--R 4 3 +--R 4sinh(x) + (16cosh(x) + 16%i)sinh(x) +--R + +--R 2 2 +--R (24cosh(x) + 48%i cosh(x) - 24)sinh(x) +--R + +--R 3 2 4 +--R (16cosh(x) + 48%i cosh(x) - 48cosh(x) - 16%i)sinh(x) + 4cosh(x) +--R + +--R 3 2 +--R 16%i cosh(x) - 24cosh(x) - 16%i cosh(x) + 4 +--R Type: Union(Expression(Complex(Integer)),...) +--E 113 + +--S 114 of 552 +m0722:= a0722-r0722 +--R +--R +--R (112) +--R 1 6 3 5 +--R - sinh(x) + (cosh(x) + - %i)sinh(x) +--R 4 2 +--R + +--R 3 2 15 4 +--R (- cosh(x) + 5%i cosh(x) - --)sinh(x) +--R 2 4 +--R + +--R 3 2 3 +--R (cosh(x) + 6%i cosh(x) - 10cosh(x) - 5%i)sinh(x) +--R + +--R 1 4 3 2 15 2 +--R (- cosh(x) + 3%i cosh(x) - 9cosh(x) - 10%i cosh(x) + --)sinh(x) +--R 4 4 +--R + +--R 1 4 3 2 3 +--R (- %i cosh(x) - 3cosh(x) - 6%i cosh(x) + 5cosh(x) + - %i)sinh(x) +--R 2 2 +--R + +--R 1 4 3 3 2 1 +--R - - cosh(x) - %i cosh(x) + - cosh(x) + %i cosh(x) - - +--R 4 2 4 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 1 6 3 5 +--R - - sinh(x) + (- cosh(x) - - %i)sinh(x) +--R 4 2 +--R + +--R 3 2 15 4 +--R (- - cosh(x) - 5%i cosh(x) + --)sinh(x) +--R 2 4 +--R + +--R 3 2 3 +--R (- cosh(x) - 6%i cosh(x) + 10cosh(x) + 5%i)sinh(x) +--R + +--R 1 4 3 2 15 2 +--R (- - cosh(x) - 3%i cosh(x) + 9cosh(x) + 10%i cosh(x) - --)sinh(x) +--R 4 4 +--R + +--R 1 4 3 2 3 +--R (- - %i cosh(x) + 3cosh(x) + 6%i cosh(x) - 5cosh(x) - - %i)sinh(x) +--R 2 2 +--R + +--R 1 4 3 3 2 1 +--R - cosh(x) + %i cosh(x) - - cosh(x) - %i cosh(x) + - +--R 4 2 4 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 1 6 3 5 +--R - %i sinh(x) + (%i cosh(x) - -)sinh(x) +--R 4 2 +--R + +--R 3 2 15 4 +--R (- %i cosh(x) - 5cosh(x) - -- %i)sinh(x) +--R 2 4 +--R + +--R 3 2 3 +--R (%i cosh(x) - 6cosh(x) - 10%i cosh(x) + 5)sinh(x) +--R + +--R 1 4 3 2 15 +--R (- %i cosh(x) - 3cosh(x) - 9%i cosh(x) + 10cosh(x) + -- %i) +--R 4 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 4 3 2 3 +--R (- - cosh(x) - 3%i cosh(x) + 6cosh(x) + 5%i cosh(x) - -)sinh(x) +--R 2 2 +--R + +--R 1 4 3 3 2 1 +--R - - %i cosh(x) + cosh(x) + - %i cosh(x) - cosh(x) - - %i +--R 4 2 4 +--R * +--R atan(sinh(x)) +--R + +--R 1 5 1 4 1 3 +--R - - %i sinh(x) - - %i cosh(x)sinh(x) - - %i sinh(x) +--R 4 2 2 +--R + +--R 1 3 2 1 4 1 +--R (- %i cosh(x) - %i cosh(x))sinh(x) + (- %i cosh(x) - - %i)sinh(x) +--R 2 4 4 +--R + +--R 1 3 1 +--R - %i cosh(x) - - %i cosh(x) +--R 2 2 +--R / +--R 6 5 +--R sinh(x) + (4cosh(x) + 6%i)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) + 20%i cosh(x) - 15)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) + 24%i cosh(x) - 40cosh(x) - 20%i)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) + 12%i cosh(x) - 36cosh(x) - 40%i cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 +--R (2%i cosh(x) - 12cosh(x) - 24%i cosh(x) + 20cosh(x) + 6%i)sinh(x) +--R + +--R 4 3 2 +--R - cosh(x) - 4%i cosh(x) + 6cosh(x) + 4%i cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 114 + +--S 115 of 552 +d0722:= D(m0722,x) +--R +--R +--R (113) +--R 8 7 +--R 4sinh(x) + (15cosh(x) + 8%i)sinh(x) +--R + +--R 2 6 +--R (18cosh(x) + 28%i cosh(x) - 4)sinh(x) +--R + +--R 3 2 5 +--R (cosh(x) + 28%i cosh(x) - 3cosh(x))sinh(x) +--R + +--R 4 3 2 4 +--R (- 16cosh(x) - 8%i cosh(x) + 16cosh(x) + 16%i cosh(x) - 4)sinh(x) +--R + +--R 5 4 3 2 +--R - 15cosh(x) - 32%i cosh(x) + 30cosh(x) + 40%i cosh(x) - 11cosh(x) +--R + +--R - 8%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 6cosh(x) - 20%i cosh(x) + 20cosh(x) + 32%i cosh(x) - 14cosh(x) +--R + +--R - 12%i cosh(x) + 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - cosh(x) - 4%i cosh(x) + 5cosh(x) + 8%i cosh(x) - 11cosh(x) +--R + +--R 2 +--R - 4%i cosh(x) + 7cosh(x) +--R * +--R sinh(x) +--R + +--R 4 2 +--R - 4cosh(x) + 4cosh(x) +--R / +--R 10 9 +--R sinh(x) + (6cosh(x) + 6%i)sinh(x) +--R + +--R 2 8 +--R (15cosh(x) + 32%i cosh(x) - 13)sinh(x) +--R + +--R 3 2 7 +--R (20cosh(x) + 70%i cosh(x) - 60cosh(x) - 8%i)sinh(x) +--R + +--R 4 3 2 6 +--R (15cosh(x) + 80%i cosh(x) - 110cosh(x) - 28%i cosh(x) - 14)sinh(x) +--R + +--R 5 4 3 2 +--R 6cosh(x) + 50%i cosh(x) - 100cosh(x) - 30%i cosh(x) - 56cosh(x) +--R + +--R - 28%i +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 2 +--R cosh(x) + 16%i cosh(x) - 45cosh(x) - 100cosh(x) - 84%i cosh(x) +--R + +--R 14 +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 2%i cosh(x) - 8cosh(x) + 20%i cosh(x) - 100cosh(x) +--R + +--R 2 +--R - 110%i cosh(x) + 28cosh(x) - 8%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 12%i cosh(x) - 55cosh(x) - 80%i cosh(x) + 30cosh(x) +--R + +--R - 20%i cosh(x) + 13 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 2%i cosh(x) - 14cosh(x) - 30%i cosh(x) + 20cosh(x) +--R + +--R 2 +--R - 10%i cosh(x) + 18cosh(x) + 6%i +--R * +--R sinh(x) +--R + +--R 6 5 4 2 +--R - cosh(x) - 4%i cosh(x) + 5cosh(x) + 5cosh(x) + 4%i cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 115 + +--S 116 of 552 +t0723:= tanh(x)^2/(%i+sinh(x))^2 +--R +--R +--R 2 +--R tanh(x) +--R (114) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 116 + +--S 117 of 552 +r0723:= 1/15/cosh(x)^5*(cosh(x)^4*sinh(x)-7*sinh(x)*cosh(x)^2+_ + 6*sinh(x)+10*%i*cosh(x)^2-6*%i) +--R +--R +--R 4 2 2 +--R (cosh(x) - 7cosh(x) + 6)sinh(x) + 10%i cosh(x) - 6%i +--R (115) ------------------------------------------------------- +--R 5 +--R 15cosh(x) +--R Type: Expression(Complex(Integer)) +--E 117 + +--S 118 of 552 +a0723:= integrate(t0723,x) +--R +--R +--R (116) +--R 2 2 +--R - 32sinh(x) + (- 56cosh(x) - 48%i)sinh(x) - 32cosh(x) - 32%i cosh(x) + 40 +--R / +--R 4 3 +--R 15sinh(x) + (60cosh(x) + 60%i)sinh(x) +--R + +--R 2 2 +--R (90cosh(x) + 180%i cosh(x) - 60)sinh(x) +--R + +--R 3 2 4 +--R (60cosh(x) + 180%i cosh(x) - 180cosh(x) + 60%i)sinh(x) + 15cosh(x) +--R + +--R 3 2 +--R 60%i cosh(x) - 60cosh(x) - 60%i cosh(x) - 75 +--R Type: Union(Expression(Complex(Integer)),...) +--E 118 + +--S 119 of 552 +m0723:= a0723-r0723 +--R +--R +--R (117) +--R 4 2 5 +--R (- cosh(x) + 7cosh(x) - 6)sinh(x) +--R + +--R 5 4 3 2 +--R - 4cosh(x) - 4%i cosh(x) + 28cosh(x) + 18%i cosh(x) - 24cosh(x) +--R + +--R - 18%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 6cosh(x) - 12%i cosh(x) + 46cosh(x) + 44%i cosh(x) - 24cosh(x) +--R + +--R - 48%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 4cosh(x) - 12%i cosh(x) + 8cosh(x) + 20%i cosh(x) + 12cosh(x) +--R + +--R 2 +--R 32%i cosh(x) - 48%i +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) - 4%i cosh(x) - 45cosh(x) - 56%i cosh(x) + 91cosh(x) +--R + +--R 3 2 +--R 92%i cosh(x) - 43cosh(x) - 48%i cosh(x) + 6 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 32cosh(x) - 42%i cosh(x) + 80cosh(x) + 46%i cosh(x) - 64cosh(x) +--R + +--R 2 +--R 26%i cosh(x) + 24cosh(x) - 30%i +--R / +--R 5 4 6 5 3 +--R 15cosh(x) sinh(x) + (60cosh(x) + 60%i cosh(x) )sinh(x) +--R + +--R 7 6 5 2 +--R (90cosh(x) + 180%i cosh(x) - 60cosh(x) )sinh(x) +--R + +--R 8 7 6 5 +--R (60cosh(x) + 180%i cosh(x) - 180cosh(x) + 60%i cosh(x) )sinh(x) +--R + +--R 9 8 7 6 5 +--R 15cosh(x) + 60%i cosh(x) - 60cosh(x) - 60%i cosh(x) - 75cosh(x) +--R Type: Expression(Complex(Integer)) +--E 119 + +--S 120 of 552 +d0723:= D(m0723,x) +--R +--R +--R (118) +--R 4 2 10 +--R (cosh(x) - 21cosh(x) + 30)sinh(x) +--R + +--R 5 4 3 2 +--R 8cosh(x) + 8%i cosh(x) - 168cosh(x) - 138%i cosh(x) + 240cosh(x) +--R + +--R 210%i +--R * +--R 9 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 27cosh(x) + 56%i cosh(x) - 605cosh(x) - 936%i cosh(x) +--R + +--R 2 +--R 1098cosh(x) + 1440%i cosh(x) - 480 +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 48cosh(x) + 160%i cosh(x) - 1272cosh(x) - 2656%i cosh(x) +--R + +--R 3 2 +--R 3144cosh(x) + 3936%i cosh(x) - 2880cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 42cosh(x) + 224%i cosh(x) - 1570cosh(x) - 3976%i cosh(x) +--R + +--R 4 3 2 +--R 4930cosh(x) + 5352%i cosh(x) - 5310cosh(x) - 480%i cosh(x) - 1500 +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 112%i cosh(x) - 776cosh(x) - 2660%i cosh(x) + 2960cosh(x) +--R + +--R 4 3 2 +--R 1692%i cosh(x) - 1320cosh(x) + 636%i cosh(x) - 5280cosh(x) - 1380%i +--R * +--R 5 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 42cosh(x) - 112%i cosh(x) + 790cosh(x) + 1208%i cosh(x) +--R + +--R 6 5 4 3 +--R - 3118cosh(x) - 6448%i cosh(x) + 8398cosh(x) + 7512%i cosh(x) +--R + +--R 2 +--R - 6708cosh(x) - 5280%i cosh(x) - 1440 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 10 9 8 +--R - 48cosh(x) - 224%i cosh(x) + 1752cosh(x) + 4208%i cosh(x) +--R + +--R 7 6 5 4 +--R - 7688cosh(x) - 12128%i cosh(x) + 14184cosh(x) + 11792%i cosh(x) +--R + +--R 3 2 +--R - 6984cosh(x) - 3168%i cosh(x) - 960cosh(x) - 1920%i +--R * +--R 3 +--R sinh(x) +--R + +--R 12 11 10 9 +--R - 27cosh(x) - 160%i cosh(x) + 1431cosh(x) + 3880%i cosh(x) +--R + +--R 8 7 6 5 +--R - 6696cosh(x) - 9976%i cosh(x) + 10886cosh(x) + 8472%i cosh(x) +--R + +--R 4 3 2 +--R - 4667cosh(x) + 984%i cosh(x) - 429cosh(x) - 3360%i cosh(x) - 450 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 12 11 10 +--R - 8cosh(x) - 56%i cosh(x) + 592cosh(x) + 1758%i cosh(x) +--R + +--R 9 8 7 6 +--R - 3136cosh(x) - 3982%i cosh(x) + 4320cosh(x) + 3124%i cosh(x) +--R + +--R 5 4 3 2 +--R - 616cosh(x) - 364%i cosh(x) - 2352cosh(x) + 270%i cosh(x) +--R + +--R 1200cosh(x) - 750%i +--R * +--R sinh(x) +--R + +--R 14 13 12 11 +--R - cosh(x) - 8%i cosh(x) + 103cosh(x) + 336%i cosh(x) +--R + +--R 10 9 8 7 +--R - 724cosh(x) - 640%i cosh(x) + 826cosh(x) + 224%i cosh(x) +--R + +--R 6 5 4 3 2 +--R - 85cosh(x) + 328%i cosh(x) + 31cosh(x) - 240%i cosh(x) - 150cosh(x) +--R / +--R 6 8 7 6 7 +--R 15cosh(x) sinh(x) + (120cosh(x) + 120%i cosh(x) )sinh(x) +--R + +--R 8 7 6 6 +--R (420cosh(x) + 840%i cosh(x) - 360cosh(x) )sinh(x) +--R + +--R 9 8 7 6 5 +--R (840cosh(x) + 2520%i cosh(x) - 2280cosh(x) - 360%i cosh(x) )sinh(x) +--R + +--R 10 9 8 7 +--R 1050cosh(x) + 4200%i cosh(x) - 5880cosh(x) - 2520%i cosh(x) +--R + +--R 6 +--R - 390cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 840cosh(x) + 4200%i cosh(x) - 7920cosh(x) - 6000%i cosh(x) +--R + +--R 7 6 +--R - 120cosh(x) - 1080%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 11 10 9 +--R 420cosh(x) + 2520%i cosh(x) - 5880cosh(x) - 6480%i cosh(x) +--R + +--R 8 7 6 +--R 1740cosh(x) - 2760%i cosh(x) + 360cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 13 12 11 10 +--R 120cosh(x) + 840%i cosh(x) - 2280cosh(x) - 3240%i cosh(x) +--R + +--R 9 8 7 6 +--R 1800cosh(x) - 840%i cosh(x) + 2280cosh(x) - 600%i cosh(x) +--R * +--R sinh(x) +--R + +--R 14 13 12 11 +--R 15cosh(x) + 120%i cosh(x) - 360cosh(x) - 600%i cosh(x) +--R + +--R 10 9 8 7 6 +--R 570cosh(x) - 120%i cosh(x) + 360cosh(x) + 600%i cosh(x) + 375cosh(x) +--R Type: Expression(Complex(Integer)) +--E 120 + +--S 121 of 552 +t0724:= tanh(x)^3/(%i+sinh(x))^2 +--R +--R +--R 3 +--R tanh(x) +--R (119) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 121 + +--S 122 of 552 +r0724:= -1/8*%i*atan(sinh(x))-%i/(16*%i-16*sinh(x))+_ + 1/12*%i/(%i+sinh(x))^3-1/4/(%i+sinh(x))^2-3*%i/(16*%i+16*sinh(x)) +--R +--R +--R (120) +--R 1 4 1 3 1 1 +--R (- - %i sinh(x) + - sinh(x) + - sinh(x) + - %i)atan(sinh(x)) +--R 8 4 4 8 +--R + +--R 1 3 1 2 7 1 +--R - - %i sinh(x) - - sinh(x) - -- %i sinh(x) + -- +--R 8 4 24 12 +--R / +--R 4 3 +--R sinh(x) + 2%i sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 122 + +--S 123 of 552 +a0724:= integrate(t0724,x) +--R +--R +--R (121) +--R 8 7 +--R 3sinh(x) + (24cosh(x) + 12%i)sinh(x) +--R + +--R 2 6 +--R (84cosh(x) + 84%i cosh(x) - 12)sinh(x) +--R + +--R 3 2 5 +--R (168cosh(x) + 252%i cosh(x) - 72cosh(x) + 12%i)sinh(x) +--R + +--R 4 3 2 +--R (210cosh(x) + 420%i cosh(x) - 180cosh(x) + 60%i cosh(x) - 30) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 168cosh(x) + 420%i cosh(x) - 240cosh(x) + 120%i cosh(x) +--R + +--R - 120cosh(x) - 12%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 84cosh(x) + 252%i cosh(x) - 180cosh(x) + 120%i cosh(x) +--R + +--R 2 +--R - 180cosh(x) - 36%i cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 24cosh(x) + 84%i cosh(x) - 72cosh(x) + 60%i cosh(x) +--R + +--R 3 2 +--R - 120cosh(x) - 36%i cosh(x) - 24cosh(x) - 12%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 3cosh(x) + 12%i cosh(x) - 12cosh(x) + 12%i cosh(x) - 30cosh(x) +--R + +--R 3 2 +--R - 12%i cosh(x) - 12cosh(x) - 12%i cosh(x) + 3 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 8 7 +--R - 3sinh(x) + (- 24cosh(x) - 12%i)sinh(x) +--R + +--R 2 6 +--R (- 84cosh(x) - 84%i cosh(x) + 12)sinh(x) +--R + +--R 3 2 5 +--R (- 168cosh(x) - 252%i cosh(x) + 72cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 2 +--R (- 210cosh(x) - 420%i cosh(x) + 180cosh(x) - 60%i cosh(x) + 30) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 168cosh(x) - 420%i cosh(x) + 240cosh(x) - 120%i cosh(x) +--R + +--R 120cosh(x) + 12%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 84cosh(x) - 252%i cosh(x) + 180cosh(x) - 120%i cosh(x) +--R + +--R 2 +--R 180cosh(x) + 36%i cosh(x) + 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 24cosh(x) - 84%i cosh(x) + 72cosh(x) - 60%i cosh(x) +--R + +--R 3 2 +--R 120cosh(x) + 36%i cosh(x) + 24cosh(x) + 12%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 3cosh(x) - 12%i cosh(x) + 12cosh(x) - 12%i cosh(x) + 30cosh(x) +--R + +--R 3 2 +--R 12%i cosh(x) + 12cosh(x) + 12%i cosh(x) - 3 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 7 6 +--R - 6%i sinh(x) + (- 42%i cosh(x) - 24)sinh(x) +--R + +--R 2 5 +--R (- 126%i cosh(x) - 144cosh(x) - 38%i)sinh(x) +--R + +--R 3 2 4 +--R (- 210%i cosh(x) - 360cosh(x) - 190%i cosh(x) + 80)sinh(x) +--R + +--R 4 3 2 +--R (- 210%i cosh(x) - 480cosh(x) - 380%i cosh(x) + 320cosh(x) + 38%i) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 126%i cosh(x) - 360cosh(x) - 380%i cosh(x) + 480cosh(x) +--R + +--R 114%i cosh(x) - 24 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 42%i cosh(x) - 144cosh(x) - 190%i cosh(x) + 320cosh(x) +--R + +--R 2 +--R 114%i cosh(x) - 48cosh(x) + 6%i +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 6%i cosh(x) - 24cosh(x) - 38%i cosh(x) + 80cosh(x) + 38%i cosh(x) +--R + +--R 2 +--R - 24cosh(x) + 6%i cosh(x) +--R / +--R 8 7 +--R 24sinh(x) + (192cosh(x) + 96%i)sinh(x) +--R + +--R 2 6 +--R (672cosh(x) + 672%i cosh(x) - 96)sinh(x) +--R + +--R 3 2 5 +--R (1344cosh(x) + 2016%i cosh(x) - 576cosh(x) + 96%i)sinh(x) +--R + +--R 4 3 2 +--R (1680cosh(x) + 3360%i cosh(x) - 1440cosh(x) + 480%i cosh(x) - 240) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 1344cosh(x) + 3360%i cosh(x) - 1920cosh(x) + 960%i cosh(x) +--R + +--R - 960cosh(x) - 96%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 672cosh(x) + 2016%i cosh(x) - 1440cosh(x) + 960%i cosh(x) +--R + +--R 2 +--R - 1440cosh(x) - 288%i cosh(x) - 96 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 192cosh(x) + 672%i cosh(x) - 576cosh(x) + 480%i cosh(x) +--R + +--R 3 2 +--R - 960cosh(x) - 288%i cosh(x) - 192cosh(x) - 96%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 24cosh(x) + 96%i cosh(x) - 96cosh(x) + 96%i cosh(x) - 240cosh(x) +--R + +--R 3 2 +--R - 96%i cosh(x) - 96cosh(x) - 96%i cosh(x) + 24 +--R Type: Union(Expression(Complex(Integer)),...) +--E 123 + +--S 124 of 552 +m0724:= a0724-r0724 +--R +--R +--R (122) +--R 1 12 3 11 +--R - sinh(x) + (cosh(x) + - %i)sinh(x) +--R 8 4 +--R + +--R 7 2 11 3 10 +--R (- cosh(x) + -- %i cosh(x) - -)sinh(x) +--R 2 2 2 +--R + +--R 3 35 2 1 9 +--R (7cosh(x) + -- %i cosh(x) - 10cosh(x) - - %i)sinh(x) +--R 2 4 +--R + +--R 35 4 63 3 57 2 3 27 +--R (-- cosh(x) + -- %i cosh(x) - -- cosh(x) - - %i cosh(x) - --) +--R 4 2 2 2 8 +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 7cosh(x) + 35%i cosh(x) - 45cosh(x) - 3%i cosh(x) - 18cosh(x) +--R + +--R 9 +--R - - %i +--R 2 +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 49 5 85 4 3 +--R - cosh(x) + -- %i cosh(x) - -- cosh(x) - %i cosh(x) +--R 2 2 2 +--R + +--R 2 +--R - 42cosh(x) - 21%i cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 21 6 5 4 +--R cosh(x) + -- %i cosh(x) - 24cosh(x) + 5%i cosh(x) +--R 2 +--R + +--R 3 2 9 +--R - 57cosh(x) - 42%i cosh(x) - - %i +--R 2 +--R * +--R 5 +--R sinh(x) +--R + +--R 1 8 5 7 15 6 17 5 +--R - cosh(x) + - %i cosh(x) - -- cosh(x) + -- %i cosh(x) +--R 8 2 2 2 +--R + +--R 4 3 27 +--R - 50cosh(x) - 48%i cosh(x) - 15%i cosh(x) + -- +--R 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 1 8 7 6 5 +--R - %i cosh(x) - cosh(x) + 6%i cosh(x) - 29cosh(x) +--R 4 +--R + +--R 4 3 2 1 +--R - 35%i cosh(x) + cosh(x) - 21%i cosh(x) + 9cosh(x) - - %i +--R 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 21 6 33 5 5 4 +--R 2%i cosh(x) - -- cosh(x) - -- %i cosh(x) + - cosh(x) +--R 2 2 2 +--R + +--R 3 21 2 1 3 +--R - 15%i cosh(x) + -- cosh(x) - - %i cosh(x) + - +--R 2 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 8 7 9 6 5 +--R - %i cosh(x) - 2cosh(x) - - %i cosh(x) + 2cosh(x) +--R 4 2 +--R + +--R 4 3 1 2 3 +--R - 5%i cosh(x) + 6cosh(x) + - %i cosh(x) + 2cosh(x) + - %i +--R 2 4 +--R * +--R sinh(x) +--R + +--R 1 8 1 7 1 6 1 5 +--R - - cosh(x) - - %i cosh(x) + - cosh(x) - - %i cosh(x) +--R 8 2 2 2 +--R + +--R 5 4 1 3 1 2 1 1 +--R - cosh(x) + - %i cosh(x) + - cosh(x) + - %i cosh(x) - - +--R 4 2 2 2 8 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 1 12 3 11 +--R - - sinh(x) + (- cosh(x) - - %i)sinh(x) +--R 8 4 +--R + +--R 7 2 11 3 10 +--R (- - cosh(x) - -- %i cosh(x) + -)sinh(x) +--R 2 2 2 +--R + +--R 3 35 2 1 9 +--R (- 7cosh(x) - -- %i cosh(x) + 10cosh(x) + - %i)sinh(x) +--R 2 4 +--R + +--R 35 4 63 3 57 2 3 27 +--R (- -- cosh(x) - -- %i cosh(x) + -- cosh(x) + - %i cosh(x) + --) +--R 4 2 2 2 8 +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 7cosh(x) - 35%i cosh(x) + 45cosh(x) + 3%i cosh(x) +--R + +--R 9 +--R 18cosh(x) + - %i +--R 2 +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 49 5 85 4 3 +--R - - cosh(x) - -- %i cosh(x) + -- cosh(x) + %i cosh(x) +--R 2 2 2 +--R + +--R 2 +--R 42cosh(x) + 21%i cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 21 6 5 4 +--R - cosh(x) - -- %i cosh(x) + 24cosh(x) - 5%i cosh(x) +--R 2 +--R + +--R 3 2 9 +--R 57cosh(x) + 42%i cosh(x) + - %i +--R 2 +--R * +--R 5 +--R sinh(x) +--R + +--R 1 8 5 7 15 6 17 5 +--R - - cosh(x) - - %i cosh(x) + -- cosh(x) - -- %i cosh(x) +--R 8 2 2 2 +--R + +--R 4 3 27 +--R 50cosh(x) + 48%i cosh(x) + 15%i cosh(x) - -- +--R 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 1 8 7 6 5 +--R - - %i cosh(x) + cosh(x) - 6%i cosh(x) + 29cosh(x) +--R 4 +--R + +--R 4 3 2 1 +--R 35%i cosh(x) - cosh(x) + 21%i cosh(x) - 9cosh(x) + - %i +--R 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 21 6 33 5 5 4 +--R - 2%i cosh(x) + -- cosh(x) + -- %i cosh(x) - - cosh(x) +--R 2 2 2 +--R + +--R 3 21 2 1 3 +--R 15%i cosh(x) - -- cosh(x) + - %i cosh(x) - - +--R 2 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 8 7 9 6 5 +--R - - %i cosh(x) + 2cosh(x) + - %i cosh(x) - 2cosh(x) +--R 4 2 +--R + +--R 4 3 1 2 3 +--R 5%i cosh(x) - 6cosh(x) - - %i cosh(x) - 2cosh(x) - - %i +--R 2 4 +--R * +--R sinh(x) +--R + +--R 1 8 1 7 1 6 1 5 5 4 +--R - cosh(x) + - %i cosh(x) - - cosh(x) + - %i cosh(x) - - cosh(x) +--R 8 2 2 2 4 +--R + +--R 1 3 1 2 1 1 +--R - - %i cosh(x) - - cosh(x) - - %i cosh(x) + - +--R 2 2 2 8 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 1 12 3 11 +--R - %i sinh(x) + (%i cosh(x) - -)sinh(x) +--R 8 4 +--R + +--R 7 2 11 3 10 +--R (- %i cosh(x) - -- cosh(x) - - %i)sinh(x) +--R 2 2 2 +--R + +--R 3 35 2 1 9 +--R (7%i cosh(x) - -- cosh(x) - 10%i cosh(x) + -)sinh(x) +--R 2 4 +--R + +--R 35 4 63 3 57 2 3 27 +--R (-- %i cosh(x) - -- cosh(x) - -- %i cosh(x) + - cosh(x) - -- %i) +--R 4 2 2 2 8 +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 7%i cosh(x) - 35cosh(x) - 45%i cosh(x) + 3cosh(x) +--R + +--R 9 +--R - 18%i cosh(x) + - +--R 2 +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 49 5 85 4 3 +--R - %i cosh(x) - -- cosh(x) - -- %i cosh(x) + cosh(x) +--R 2 2 2 +--R + +--R 2 +--R - 42%i cosh(x) + 21cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 21 6 5 4 +--R %i cosh(x) - -- cosh(x) - 24%i cosh(x) - 5cosh(x) +--R 2 +--R + +--R 3 2 9 +--R - 57%i cosh(x) + 42cosh(x) + - +--R 2 +--R * +--R 5 +--R sinh(x) +--R + +--R 1 8 5 7 15 6 17 5 +--R - %i cosh(x) - - cosh(x) - -- %i cosh(x) - -- cosh(x) +--R 8 2 2 2 +--R + +--R 4 3 27 +--R - 50%i cosh(x) + 48cosh(x) + 15cosh(x) + -- %i +--R 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 1 8 7 6 5 +--R - - cosh(x) - %i cosh(x) - 6cosh(x) - 29%i cosh(x) +--R 4 +--R + +--R 4 3 2 1 +--R 35cosh(x) + %i cosh(x) + 21cosh(x) + 9%i cosh(x) + - +--R 4 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 21 6 33 5 5 4 +--R - 2cosh(x) - -- %i cosh(x) + -- cosh(x) + - %i cosh(x) +--R 2 2 2 +--R + +--R 3 21 2 1 3 +--R 15cosh(x) + -- %i cosh(x) + - cosh(x) + - %i +--R 2 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 1 8 7 9 6 5 +--R - - cosh(x) - 2%i cosh(x) + - cosh(x) + 2%i cosh(x) +--R 4 2 +--R + +--R 4 3 1 2 3 +--R 5cosh(x) + 6%i cosh(x) - - cosh(x) + 2%i cosh(x) - - +--R 2 4 +--R * +--R sinh(x) +--R + +--R 1 8 1 7 1 6 1 5 +--R - - %i cosh(x) + - cosh(x) + - %i cosh(x) + - cosh(x) +--R 8 2 2 2 +--R + +--R 5 4 1 3 1 2 1 1 +--R - %i cosh(x) - - cosh(x) + - %i cosh(x) - - cosh(x) - - %i +--R 4 2 2 2 8 +--R * +--R atan(sinh(x)) +--R + +--R 1 11 3 3 10 +--R - - %i sinh(x) + (- - %i cosh(x) - -)sinh(x) +--R 8 4 4 +--R + +--R 7 2 67 9 +--R (- - %i cosh(x) - 4cosh(x) - -- %i)sinh(x) +--R 4 24 +--R + +--R 7 3 2 163 17 8 +--R (- - %i cosh(x) - 8cosh(x) - --- %i cosh(x) + --)sinh(x) +--R 4 12 4 +--R + +--R 3 145 2 46 19 7 +--R (- 6cosh(x) - --- %i cosh(x) + -- cosh(x) + -- %i)sinh(x) +--R 6 3 4 +--R + +--R 7 5 5 4 29 3 46 2 +--R - %i cosh(x) + - cosh(x) - -- %i cosh(x) + -- cosh(x) +--R 4 2 2 3 +--R + +--R 71 17 +--R -- %i cosh(x) - -- +--R 6 6 +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 3 2 +--R - %i cosh(x) + 8cosh(x) + 10%i cosh(x) - 8cosh(x) - 2%i cosh(x) +--R 4 +--R + +--R 7 +--R - 2cosh(x) + - %i +--R 4 +--R * +--R 5 +--R sinh(x) +--R + +--R 3 7 6 83 5 55 4 +--R - %i cosh(x) + 6cosh(x) + -- %i cosh(x) - -- cosh(x) +--R 4 4 2 +--R + +--R 3 2 27 11 +--R - 33%i cosh(x) + 16cosh(x) + -- %i cosh(x) - -- +--R 2 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 1 8 7 38 6 5 +--R - %i cosh(x) + 2cosh(x) + -- %i cosh(x) - 22cosh(x) +--R 8 3 +--R + +--R 4 3 59 2 127 +--R - 40%i cosh(x) + 34cosh(x) + -- %i cosh(x) - 18cosh(x) - --- %i +--R 2 24 +--R * +--R 3 +--R sinh(x) +--R + +--R 1 8 10 7 6 79 5 +--R - cosh(x) + -- %i cosh(x) - 8cosh(x) - -- %i cosh(x) +--R 4 3 4 +--R + +--R 55 4 53 3 2 133 9 +--R -- cosh(x) + -- %i cosh(x) - 22cosh(x) - --- %i cosh(x) + - +--R 2 2 12 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 8 4 7 15 6 5 +--R -- %i cosh(x) - - cosh(x) - -- %i cosh(x) + 10cosh(x) +--R 24 3 4 +--R + +--R 4 3 83 2 10 3 +--R 10%i cosh(x) - 12cosh(x) - -- %i cosh(x) + -- cosh(x) + - %i +--R 12 3 8 +--R * +--R sinh(x) +--R + +--R 1 8 1 7 4 6 5 5 5 4 +--R - -- cosh(x) - -- %i cosh(x) + - cosh(x) + - %i cosh(x) - - cosh(x) +--R 12 12 3 4 2 +--R + +--R 5 3 4 2 1 1 +--R - - %i cosh(x) + - cosh(x) + -- %i cosh(x) - -- +--R 4 3 12 12 +--R / +--R 12 11 +--R sinh(x) + (8cosh(x) + 6%i)sinh(x) +--R + +--R 2 10 +--R (28cosh(x) + 44%i cosh(x) - 12)sinh(x) +--R + +--R 3 2 9 +--R (56cosh(x) + 140%i cosh(x) - 80cosh(x) - 2%i)sinh(x) +--R + +--R 4 3 2 8 +--R (70cosh(x) + 252%i cosh(x) - 228cosh(x) - 12%i cosh(x) - 27)sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) + 280%i cosh(x) - 360cosh(x) - 24%i cosh(x) +--R + +--R - 144cosh(x) - 36%i +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 28cosh(x) + 196%i cosh(x) - 340cosh(x) - 8%i cosh(x) +--R + +--R 2 +--R - 336cosh(x) - 168%i cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 8cosh(x) + 84%i cosh(x) - 192cosh(x) + 40%i cosh(x) - 456cosh(x) +--R + +--R 2 +--R - 336%i cosh(x) - 36%i +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 20%i cosh(x) - 60cosh(x) + 68%i cosh(x) - 400cosh(x) +--R + +--R 3 +--R - 384%i cosh(x) - 120%i cosh(x) + 27 +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 2%i cosh(x) - 8cosh(x) + 48%i cosh(x) - 232cosh(x) +--R + +--R 4 3 2 +--R - 280%i cosh(x) + 8cosh(x) - 168%i cosh(x) + 72cosh(x) - 2%i +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 16%i cosh(x) - 84cosh(x) - 132%i cosh(x) + 20cosh(x) +--R + +--R 3 2 +--R - 120%i cosh(x) + 84cosh(x) - 4%i cosh(x) + 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 2%i cosh(x) - 16cosh(x) - 36%i cosh(x) + 16cosh(x) +--R + +--R 4 3 2 +--R - 40%i cosh(x) + 48cosh(x) + 4%i cosh(x) + 16cosh(x) + 6%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) - 4%i cosh(x) + 4cosh(x) - 4%i cosh(x) + 10cosh(x) +--R + +--R 3 2 +--R 4%i cosh(x) + 4cosh(x) + 4%i cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 124 + +--S 125 of 552 +d0724:= D(m0724,x) +--R +--R +--R (123) +--R 14 13 +--R 4sinh(x) + (31cosh(x) + 8%i)sinh(x) +--R + +--R 2 12 +--R (102cosh(x) + 60%i cosh(x) - 8)sinh(x) +--R + +--R 3 2 11 +--R (179cosh(x) + 188%i cosh(x) - 37cosh(x) - 8%i)sinh(x) +--R + +--R 4 3 2 10 +--R (160cosh(x) + 304%i cosh(x) - 44cosh(x) - 24%i cosh(x) - 4)sinh(x) +--R + +--R 5 4 3 2 +--R 14cosh(x) + 224%i cosh(x) + 68cosh(x) + 32%i cosh(x) - 42cosh(x) +--R + +--R - 16%i +--R * +--R 9 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 140cosh(x) - 56%i cosh(x) + 268cosh(x) + 248%i cosh(x) +--R + +--R 2 +--R - 136cosh(x) - 128%i cosh(x) + 16 +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 178cosh(x) - 280%i cosh(x) + 362cosh(x) + 480%i cosh(x) +--R + +--R 3 2 +--R - 206cosh(x) - 352%i cosh(x) + 94cosh(x) + 16%i +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 116cosh(x) - 272%i cosh(x) + 268cosh(x) + 472%i cosh(x) +--R + +--R 4 3 2 +--R - 168cosh(x) - 416%i cosh(x) + 192cosh(x) + 40%i cosh(x) - 4 +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - 45cosh(x) - 136%i cosh(x) + 116cosh(x) + 256%i cosh(x) +--R + +--R 5 4 3 2 +--R - 86cosh(x) - 136%i cosh(x) + 148cosh(x) - 56%i cosh(x) +--R + +--R 19cosh(x) + 8%i +--R * +--R 5 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 10cosh(x) - 36%i cosh(x) + 28cosh(x) + 72%i cosh(x) +--R + +--R 6 5 4 3 +--R - 40cosh(x) + 160%i cosh(x) - 32cosh(x) - 264%i cosh(x) +--R + +--R 2 +--R 110cosh(x) + 68%i cosh(x) - 8 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 10 9 8 7 +--R - cosh(x) - 4%i cosh(x) + 3cosh(x) + 8%i cosh(x) - 18cosh(x) +--R + +--R 6 5 4 3 +--R 176%i cosh(x) - 138cosh(x) - 304%i cosh(x) + 195cosh(x) +--R + +--R 2 +--R 132%i cosh(x) - 41cosh(x) - 8%i +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 4cosh(x) + 64%i cosh(x) - 100cosh(x) - 144%i cosh(x) +--R + +--R 4 3 2 +--R 168cosh(x) + 96%i cosh(x) - 68cosh(x) - 16%i cosh(x) + 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 8%i cosh(x) - 32cosh(x) - 24%i cosh(x) + 72cosh(x) +--R + +--R 4 3 2 +--R 24%i cosh(x) - 48cosh(x) - 8%i cosh(x) + 8cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - 4cosh(x) + 12cosh(x) - 12cosh(x) + 4cosh(x) +--R / +--R 16 15 +--R sinh(x) + (10cosh(x) + 6%i)sinh(x) +--R + +--R 2 14 +--R (45cosh(x) + 56%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 13 +--R (120cosh(x) + 234%i cosh(x) - 86cosh(x) + 10%i)sinh(x) +--R + +--R 4 3 2 12 +--R (210cosh(x) + 576%i cosh(x) - 327cosh(x) + 84%i cosh(x) - 50)sinh(x) +--R + +--R 5 4 3 2 +--R 252cosh(x) + 924%i cosh(x) - 720cosh(x) + 324%i cosh(x) +--R + +--R - 374cosh(x) - 34%i +--R * +--R 11 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 210cosh(x) + 1008%i cosh(x) - 1008cosh(x) + 760%i cosh(x) +--R + +--R 2 +--R - 1251cosh(x) - 224%i cosh(x) - 66 +--R * +--R 10 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 120cosh(x) + 756%i cosh(x) - 924cosh(x) + 1204%i cosh(x) +--R + +--R 3 2 +--R - 2472cosh(x) - 642%i cosh(x) - 422cosh(x) - 110%i +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 45cosh(x) + 384%i cosh(x) - 546cosh(x) + 1344%i cosh(x) +--R + +--R 4 3 2 +--R - 3206cosh(x) - 1048%i cosh(x) - 1215cosh(x) - 612%i cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 10cosh(x) + 126%i cosh(x) - 192cosh(x) + 1064%i cosh(x) +--R + +--R 5 4 3 2 +--R - 2856cosh(x) - 1064%i cosh(x) - 2080cosh(x) - 1512%i cosh(x) +--R + +--R - 18cosh(x) - 110%i +--R * +--R 7 +--R sinh(x) +--R + +--R 10 9 8 7 +--R cosh(x) + 24%i cosh(x) - 30cosh(x) + 584%i cosh(x) +--R + +--R 6 5 4 3 +--R - 1764cosh(x) - 672%i cosh(x) - 2352cosh(x) - 2192%i cosh(x) +--R + +--R 2 +--R - 81cosh(x) - 488%i cosh(x) + 66 +--R * +--R 6 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 2%i cosh(x) + 2cosh(x) + 210%i cosh(x) - 736cosh(x) +--R + +--R 6 5 4 3 +--R - 224%i cosh(x) - 1848cosh(x) - 2072%i cosh(x) - 152cosh(x) +--R + +--R 2 +--R - 954%i cosh(x) + 238cosh(x) - 34%i +--R * +--R 5 +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R cosh(x) + 44%i cosh(x) - 192cosh(x) + 8%i cosh(x) - 1036cosh(x) +--R + +--R 5 4 3 2 +--R - 1344%i cosh(x) - 154cosh(x) - 1072%i cosh(x) + 387cosh(x) +--R + +--R - 116%i cosh(x) + 50 +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 4%i cosh(x) - 26cosh(x) + 42%i cosh(x) - 416cosh(x) +--R + +--R 6 5 4 3 +--R - 616%i cosh(x) - 84cosh(x) - 756%i cosh(x) + 368cosh(x) +--R + +--R 2 +--R - 156%i cosh(x) + 126cosh(x) + 10%i +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - cosh(x) + 16%i cosh(x) - 114cosh(x) - 200%i cosh(x) +--R + +--R 6 5 4 3 +--R - 14cosh(x) - 336%i cosh(x) + 224cosh(x) - 104%i cosh(x) +--R + +--R 2 +--R 135cosh(x) + 16%i cosh(x) + 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 2%i cosh(x) - 18cosh(x) - 42%i cosh(x) + 8cosh(x) +--R + +--R 6 5 4 3 +--R - 84%i cosh(x) + 84cosh(x) - 28%i cosh(x) + 72cosh(x) +--R + +--R 2 +--R 18%i cosh(x) + 14cosh(x) + 6%i +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R - cosh(x) - 4%i cosh(x) + 3cosh(x) - 8%i cosh(x) + 14cosh(x) +--R + +--R 4 3 2 +--R 14cosh(x) + 8%i cosh(x) + 3cosh(x) + 4%i cosh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 125 + +--S 126 of 552 +t0725:= coth(x)/(a+b*sinh(x))^2 +--R +--R +--R coth(x) +--R (124) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 552 +r0725:= log(sinh(x))/a^2-log(a+b*sinh(x))/a^2+1/a/(a+b*sinh(x)) +--R +--R +--R (125) +--R (- b sinh(x) - a)log(b sinh(x) + a) + (b sinh(x) + a)log(sinh(x)) + a +--R --------------------------------------------------------------------- +--R 2 3 +--R a b sinh(x) + a +--R Type: Expression(Integer) +--E 127 + +--S 128 of 552 +a0725:= integrate(t0725,x) +--R +--R +--R (126) +--R 2 2 +--R (b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) - b) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - b sinh(x) + (- 2b cosh(x) - 2a)sinh(x) - b cosh(x) - 2a cosh(x) +--R + +--R b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2a sinh(x) + 2a cosh(x) +--R / +--R 2 2 2 3 2 2 3 +--R a b sinh(x) + (2a b cosh(x) + 2a )sinh(x) + a b cosh(x) + 2a cosh(x) +--R + +--R 2 +--R - a b +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 552 +m0725:= a0725-r0725 +--R +--R +--R (127) +--R 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 3a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b cosh(x) + 4a b cosh(x) - b + 2a )sinh(x) + a b cosh(x) +--R + +--R 2 +--R 2a cosh(x) - a b +--R * +--R log(b sinh(x) + a) +--R + +--R 2 3 2 2 +--R - b sinh(x) + (- 2b cosh(x) - 3a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- b cosh(x) - 4a b cosh(x) + b - 2a )sinh(x) - a b cosh(x) +--R + +--R 2 +--R - 2a cosh(x) + a b +--R * +--R log(sinh(x)) +--R + +--R 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 3a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b cosh(x) + 4a b cosh(x) - b + 2a )sinh(x) + a b cosh(x) +--R + +--R 2 +--R 2a cosh(x) - a b +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 +--R - b sinh(x) + (- 2b cosh(x) - 3a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- b cosh(x) - 4a b cosh(x) + b - 2a )sinh(x) - a b cosh(x) +--R + +--R 2 +--R - 2a cosh(x) + a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R a b sinh(x) - a b cosh(x) + a b +--R / +--R 2 2 3 2 2 3 2 +--R a b sinh(x) + (2a b cosh(x) + 3a b)sinh(x) +--R + +--R 2 2 2 3 2 2 4 3 2 +--R (a b cosh(x) + 4a b cosh(x) - a b + 2a )sinh(x) + a b cosh(x) +--R + +--R 4 3 +--R 2a cosh(x) - a b +--R Type: Expression(Integer) +--E 129 + +--S 130 of 552 +d0725:= D(m0725,x) +--R +--R +--R (128) +--R 3 5 3 2 4 +--R - 2b sinh(x) + (- 5b cosh(x) - 4a b )sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 2b cosh(x) - 8a b cosh(x) - 2b - 2a b)sinh(x) +--R + +--R 3 3 3 2 2 2 +--R (4b cosh(x) + (- 4b - 2a b)cosh(x) - 4a b )sinh(x) +--R + +--R 3 4 2 3 3 2 2 2 +--R 4b cosh(x) + 8a b cosh(x) + (- 4b + 2a b)cosh(x) - 8a b cosh(x) +--R + +--R 2 +--R - 2a b +--R * +--R sinh(x) +--R + +--R 3 5 2 4 3 2 3 2 2 +--R b cosh(x) + 4a b cosh(x) + (- 2b + 2a b)cosh(x) - 4a b cosh(x) +--R + +--R 3 2 +--R (b - 2a b)cosh(x) +--R / +--R 4 6 4 2 3 5 +--R a b sinh(x) + (4a b cosh(x) + 6a b )sinh(x) +--R + +--R 4 2 2 3 4 3 2 4 +--R (6a b cosh(x) + 20a b cosh(x) - 2a b + 13a b )sinh(x) +--R + +--R 4 3 2 3 2 4 3 2 2 3 +--R 4a b cosh(x) + 24a b cosh(x) + (- 4a b + 36a b )cosh(x) - 8a b +--R + +--R 4 +--R 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R a b cosh(x) + 12a b cosh(x) + (- 2a b + 34a b )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 12a b + 28a b)cosh(x) + a b - 10a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 2 3 4 2 +--R 2a b cosh(x) + 12a b cosh(x) + (- 4a b + 20a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 12a b + 8a )cosh(x) + 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 2 4 4 3 3 2 5 2 4 +--R a b cosh(x) + 4a b cosh(x) + (- 2a b + 4a )cosh(x) - 4a b cosh(x) +--R + +--R 3 2 +--R a b +--R Type: Expression(Integer) +--E 130 + +--S 131 of 552 +t0726:= coth(x)^2/(a+b*sinh(x))^2 +--R +--R +--R 2 +--R coth(x) +--R (129) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 131 + +--S 132 of 552 +r0726:= 2*b*acoth(cosh(x))/a^3-2*atanh((b-a*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/a/(a^2+b^2)^(1/2)-4*b^2*atanh((b-a*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/a^3/(a^2+b^2)^(1/2)-_ + coth(x)/a^2-b*cosh(x)/a^2/(a+b*sinh(x)) +--R +--R +--R (130) +--R x +--R a tanh(-) - b +--R 3 2 2 3 2 +--R ((4b + 2a b)sinh(x) + 4a b + 2a )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 | 2 2 +--R (2b sinh(x) + 2a b)\|b + a acoth(cosh(x)) +--R + +--R +-------+ +--R 2 | 2 2 +--R (- a b coth(x)sinh(x) - a coth(x) - a b cosh(x))\|b + a +--R / +--R +-------+ +--R 3 4 | 2 2 +--R (a b sinh(x) + a )\|b + a +--R Type: Expression(Integer) +--E 132 + +--S 133 of 552 +a0726:= integrate(t0726,x) +--R +--R +--R (131) +--R 3 2 4 3 2 2 3 3 +--R (2b + a b)sinh(x) + ((8b + 4a b)cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 2 +--R ((12b + 6a b)cosh(x) + (12a b + 6a )cosh(x) - 4b - 2a b)sinh(x) +--R + +--R 3 2 3 2 3 2 +--R (8b + 4a b)cosh(x) + (12a b + 6a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 8b - 4a b)cosh(x) - 4a b - 2a +--R * +--R sinh(x) +--R + +--R 3 2 4 2 3 3 3 2 2 +--R (2b + a b)cosh(x) + (4a b + 2a )cosh(x) + (- 4b - 2a b)cosh(x) +--R + +--R 2 3 3 2 +--R (- 4a b - 2a )cosh(x) + 2b + a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 4 2 3 +--R 2b sinh(x) + (8b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 +--R (12b cosh(x) + 12a b cosh(x) - 4b )sinh(x) +--R + +--R 2 3 2 2 +--R (8b cosh(x) + 12a b cosh(x) - 8b cosh(x) - 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 +--R 2b cosh(x) + 4a b cosh(x) - 4b cosh(x) - 4a b cosh(x) + 2b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 2 4 2 3 +--R - 2b sinh(x) + (- 8b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 +--R (- 12b cosh(x) - 12a b cosh(x) + 4b )sinh(x) +--R + +--R 2 3 2 2 +--R (- 8b cosh(x) - 12a b cosh(x) + 8b cosh(x) + 4a b)sinh(x) +--R + +--R 2 4 3 2 2 2 +--R - 2b cosh(x) - 4a b cosh(x) + 4b cosh(x) + 4a b cosh(x) - 2b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 2 3 2 2 +--R 2a sinh(x) + (6a cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (6a cosh(x) - 8a b cosh(x) - 6a )sinh(x) + 2a cosh(x) +--R + +--R 2 2 +--R - 4a b cosh(x) - 6a cosh(x) + 4a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 4 3 4 3 +--R a b sinh(x) + (4a b cosh(x) + 2a )sinh(x) +--R + +--R 3 2 4 3 2 +--R (6a b cosh(x) + 6a cosh(x) - 2a b)sinh(x) +--R + +--R 3 3 4 2 3 4 +--R (4a b cosh(x) + 6a cosh(x) - 4a b cosh(x) - 2a )sinh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R a b cosh(x) + 2a cosh(x) - 2a b cosh(x) - 2a cosh(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 552 +m0726:= a0726-r0726 +--R +--R +--R (132) +--R 4 2 2 5 4 2 2 3 3 4 +--R (2b + a b )sinh(x) + ((8b + 4a b )cosh(x) + 6a b + 3a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (12b + 6a b )cosh(x) + (20a b + 10a b)cosh(x) - 4b + 2a b +--R + +--R 4 +--R 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (8b + 4a b )cosh(x) + (24a b + 12a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- 8b + 8a b + 6a )cosh(x) - 8a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (2b + a b )cosh(x) + (12a b + 6a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (- 4b + 10a b + 6a )cosh(x) + (- 12a b - 6a b)cosh(x) + 2b +--R + +--R 2 2 4 +--R - 3a b - 2a +--R * +--R sinh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (2a b + a b)cosh(x) + (4a b + 2a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 4a b - 2a b)cosh(x) + (- 4a b - 2a )cosh(x) + 2a b + a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 5 3 2 4 +--R 2b sinh(x) + (8b cosh(x) + 6a b )sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (12b cosh(x) + 20a b cosh(x) - 4b + 4a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (8b cosh(x) + 24a b cosh(x) + (- 8b + 12a b)cosh(x) - 8a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R 2b cosh(x) + 12a b cosh(x) + (- 4b + 12a b)cosh(x) +--R + +--R 2 3 2 +--R - 12a b cosh(x) + 2b - 4a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R 2a b cosh(x) + 4a b cosh(x) - 4a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 3 5 3 2 4 +--R - 2b sinh(x) + (- 8b cosh(x) - 6a b )sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 12b cosh(x) - 20a b cosh(x) + 4b - 4a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (- 8b cosh(x) - 24a b cosh(x) + (8b - 12a b)cosh(x) + 8a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R - 2b cosh(x) - 12a b cosh(x) + (4b - 12a b)cosh(x) +--R + +--R 2 3 2 +--R 12a b cosh(x) - 2b + 4a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R - 2a b cosh(x) - 4a b cosh(x) + 4a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 4 2 2 5 +--R (- 4b - 2a b )sinh(x) +--R + +--R 4 2 2 3 3 4 +--R ((- 16b - 8a b )cosh(x) - 12a b - 6a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 +--R (- 24b - 12a b )cosh(x) + (- 40a b - 20a b)cosh(x) + 8b +--R + +--R 2 2 4 +--R - 4a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 16b - 8a b )cosh(x) + (- 48a b - 24a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (16b - 16a b - 12a )cosh(x) + 16a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 4b - 2a b )cosh(x) + (- 24a b - 12a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (8b - 20a b - 12a )cosh(x) + (24a b + 12a b)cosh(x) - 4b +--R + +--R 2 2 4 +--R 6a b + 4a +--R * +--R sinh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (- 4a b - 2a b)cosh(x) + (- 8a b - 4a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (8a b + 4a b)cosh(x) + (8a b + 4a )cosh(x) - 4a b - 2a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 5 3 2 4 +--R - 2b sinh(x) + (- 8b cosh(x) - 6a b )sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 12b cosh(x) - 20a b cosh(x) + 4b - 4a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R (- 8b cosh(x) - 24a b cosh(x) + (8b - 12a b)cosh(x) + 8a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 3 3 2 2 +--R - 2b cosh(x) - 12a b cosh(x) + (4b - 12a b)cosh(x) +--R + +--R 2 3 2 +--R 12a b cosh(x) - 2b + 4a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R - 2a b cosh(x) - 4a b cosh(x) + 4a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a acoth(cosh(x)) +--R + +--R 2 5 +--R a b coth(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R ((4a b cosh(x) + 3a b)coth(x) + a b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (6a b cosh(x) + 10a b cosh(x) - 2a b + 2a )coth(x) +--R + +--R 2 2 2 2 3 +--R 4a b cosh(x) + 8a b cosh(x) - 4a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 2 2 2 3 +--R 4a b cosh(x) + 12a b cosh(x) + (- 4a b + 6a )cosh(x) +--R + +--R 2 +--R - 4a b +--R * +--R coth(x) +--R + +--R 2 3 2 2 2 3 2 +--R 6a b cosh(x) + 12a b cosh(x) + (- 10a b + 6a )cosh(x) - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 3 2 3 2 +--R a b cosh(x) + 6a b cosh(x) + (- 2a b + 6a )cosh(x) +--R + +--R 2 2 3 +--R - 6a b cosh(x) + a b - 2a +--R * +--R coth(x) +--R + +--R 2 4 2 3 2 3 2 +--R 4a b cosh(x) + 8a b cosh(x) + (- 8a b + 6a )cosh(x) +--R + +--R 2 2 3 +--R - 16a b cosh(x) + 4a b - 6a +--R * +--R sinh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R (a b cosh(x) + 2a cosh(x) - 2a b cosh(x) - 2a cosh(x) + a b) +--R * +--R coth(x) +--R + +--R 2 5 2 4 2 3 3 +--R a b cosh(x) + 2a b cosh(x) + (- 2a b + 2a )cosh(x) +--R + +--R 2 2 2 3 2 +--R - 6a b cosh(x) + (a b - 6a )cosh(x) + 4a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 2 5 3 2 4 4 +--R a b sinh(x) + (4a b cosh(x) + 3a b)sinh(x) +--R + +--R 3 2 2 4 3 2 5 3 +--R (6a b cosh(x) + 10a b cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 3 2 3 4 2 3 2 5 4 +--R (4a b cosh(x) + 12a b cosh(x) + (- 4a b + 6a )cosh(x) - 4a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 4 4 3 3 2 5 2 +--R a b cosh(x) + 6a b cosh(x) + (- 2a b + 6a )cosh(x) +--R + +--R 4 3 2 5 +--R - 6a b cosh(x) + a b - 2a +--R * +--R sinh(x) +--R + +--R 4 4 5 3 4 2 5 4 +--R a b cosh(x) + 2a cosh(x) - 2a b cosh(x) - 2a cosh(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 134 + +--S 135 of 552 +--d0726:= D(m0726,x) +--E 135 + +--S 136 of 552 +t0727:= coth(x)^3/(a+b*sinh(x))^2 +--R +--R +--R 3 +--R coth(x) +--R (133) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 136 + +--S 137 of 552 +r0727:= 2*b*csch(x)/a^3-1/2*csch(x)^2/a^2+(a^2+3*b^2)*log(sinh(x))/a^4-_ + (a^2+3*b^2)*log(a+b*sinh(x))/a^4+(a^2+b^2)/a^3/(a+b*sinh(x)) +--R +--R +--R (134) +--R 3 2 2 3 +--R ((- 6b - 2a b)sinh(x) - 6a b - 2a )log(b sinh(x) + a) +--R + +--R 3 2 2 3 +--R ((6b + 2a b)sinh(x) + 6a b + 2a )log(sinh(x)) +--R + +--R 2 2 2 3 2 2 +--R (- a b csch(x) + 4a b csch(x))sinh(x) - a csch(x) + 4a b csch(x) +--R + +--R 2 3 +--R 2a b + 2a +--R / +--R 4 5 +--R 2a b sinh(x) + 2a +--R Type: Expression(Integer) +--E 137 + +--S 138 of 552 +a0727:= integrate(t0727,x) +--R +--R +--R (135) +--R 3 2 6 3 2 2 3 5 +--R (3b + a b)sinh(x) + ((18b + 6a b)cosh(x) + 6a b + 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R ((45b + 15a b)cosh(x) + (30a b + 10a )cosh(x) - 9b - 3a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 2 3 2 +--R (60b + 20a b)cosh(x) + (60a b + 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 36b - 12a b)cosh(x) - 12a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 2 3 3 +--R (45b + 15a b)cosh(x) + (60a b + 20a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 54b - 18a b)cosh(x) + (- 36a b - 12a )cosh(x) + 9b + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 2 3 4 +--R (18b + 6a b)cosh(x) + (30a b + 10a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 36b - 12a b)cosh(x) + (- 36a b - 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (18b + 6a b)cosh(x) + 6a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 6 2 3 5 3 2 4 +--R (3b + a b)cosh(x) + (6a b + 2a )cosh(x) + (- 9b - 3a b)cosh(x) +--R + +--R 2 3 3 3 2 2 +--R (- 12a b - 4a )cosh(x) + (9b + 3a b)cosh(x) +--R + +--R 2 3 3 2 +--R (6a b + 2a )cosh(x) - 3b - a b +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 6 +--R (- 3b - a b)sinh(x) +--R + +--R 3 2 2 3 5 +--R ((- 18b - 6a b)cosh(x) - 6a b - 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R ((- 45b - 15a b)cosh(x) + (- 30a b - 10a )cosh(x) + 9b + 3a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 60b - 20a b)cosh(x) + (- 60a b - 20a )cosh(x) +--R + +--R 3 2 2 3 +--R (36b + 12a b)cosh(x) + 12a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 45b - 15a b)cosh(x) + (- 60a b - 20a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (54b + 18a b)cosh(x) + (36a b + 12a )cosh(x) - 9b - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 18b - 6a b)cosh(x) + (- 30a b - 10a )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (36b + 12a b)cosh(x) + (36a b + 12a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 18b - 6a b)cosh(x) - 6a b - 2a +--R * +--R sinh(x) +--R + +--R 3 2 6 2 3 5 +--R (- 3b - a b)cosh(x) + (- 6a b - 2a )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (9b + 3a b)cosh(x) + (12a b + 4a )cosh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 9b - 3a b)cosh(x) + (- 6a b - 2a )cosh(x) + 3b + a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 5 2 3 2 4 +--R (6a b + 2a )sinh(x) + ((30a b + 10a )cosh(x) + 6a b)sinh(x) +--R + +--R 2 3 2 2 2 3 3 +--R ((60a b + 20a )cosh(x) + 24a b cosh(x) - 12a b - 8a )sinh(x) +--R + +--R 2 3 3 2 2 2 3 +--R (60a b + 20a )cosh(x) + 36a b cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 +--R - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 2 3 2 3 2 +--R (30a b + 10a )cosh(x) + 24a b cosh(x) + (- 36a b - 24a )cosh(x) +--R + +--R 2 2 3 +--R - 12a b cosh(x) + 6a b + 2a +--R * +--R sinh(x) +--R + +--R 2 3 5 2 4 2 3 3 +--R (6a b + 2a )cosh(x) + 6a b cosh(x) + (- 12a b - 8a )cosh(x) +--R + +--R 2 2 2 3 +--R - 6a b cosh(x) + (6a b + 2a )cosh(x) +--R / +--R 4 6 4 5 5 +--R a b sinh(x) + (6a b cosh(x) + 2a )sinh(x) +--R + +--R 4 2 5 4 4 +--R (15a b cosh(x) + 10a cosh(x) - 3a b)sinh(x) +--R + +--R 4 3 5 2 4 5 3 +--R (20a b cosh(x) + 20a cosh(x) - 12a b cosh(x) - 4a )sinh(x) +--R + +--R 4 4 5 3 4 2 5 4 +--R (15a b cosh(x) + 20a cosh(x) - 18a b cosh(x) - 12a cosh(x) + 3a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 5 4 4 3 5 2 +--R 6a b cosh(x) + 10a cosh(x) - 12a b cosh(x) - 12a cosh(x) +--R + +--R 4 5 +--R 6a b cosh(x) + 2a +--R * +--R sinh(x) +--R + +--R 4 6 5 5 4 4 5 3 4 2 +--R a b cosh(x) + 2a cosh(x) - 3a b cosh(x) - 4a cosh(x) + 3a b cosh(x) +--R + +--R 5 4 +--R 2a cosh(x) - a b +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 552 +m0727:= a0727-r0727 +--R +--R +--R (136) +--R 4 2 2 7 +--R (6b + 2a b )sinh(x) +--R + +--R 4 2 2 3 3 6 +--R ((36b + 12a b )cosh(x) + 18a b + 6a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (90b + 30a b )cosh(x) + (96a b + 32a b)cosh(x) - 18b + 6a b +--R + +--R 4 +--R 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (120b + 40a b )cosh(x) + (210a b + 70a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- 72b + 36a b + 20a )cosh(x) - 42a b - 14a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (90b + 30a b )cosh(x) + (240a b + 80a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 108b + 84a b + 40a )cosh(x) + (- 144a b - 48a b)cosh(x) +--R + +--R 4 2 2 4 +--R 18b - 18a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 5 3 3 4 +--R (36b + 12a b )cosh(x) + (150a b + 50a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 72b + 96a b + 40a )cosh(x) + (- 180a b - 60a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (36b - 60a b - 24a )cosh(x) + 30a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 6 3 3 5 +--R (6b + 2a b )cosh(x) + (48a b + 16a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 18b + 54a b + 20a )cosh(x) + (- 96a b - 32a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (18b - 66a b - 24a )cosh(x) + (48a b + 16a b)cosh(x) - 6b +--R + +--R 2 2 4 +--R 10a b + 4a +--R * +--R sinh(x) +--R + +--R 3 3 6 2 2 4 5 +--R (6a b + 2a b)cosh(x) + (12a b + 4a )cosh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (- 18a b - 6a b)cosh(x) + (- 24a b - 8a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (18a b + 6a b)cosh(x) + (12a b + 4a )cosh(x) - 6a b - 2a b +--R * +--R log(b sinh(x) + a) +--R + +--R 4 2 2 7 +--R (- 6b - 2a b )sinh(x) +--R + +--R 4 2 2 3 3 6 +--R ((- 36b - 12a b )cosh(x) - 18a b - 6a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 +--R (- 90b - 30a b )cosh(x) + (- 96a b - 32a b)cosh(x) + 18b +--R + +--R 2 2 4 +--R - 6a b - 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 120b - 40a b )cosh(x) + (- 210a b - 70a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (72b - 36a b - 20a )cosh(x) + 42a b + 14a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 90b - 30a b )cosh(x) + (- 240a b - 80a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (108b - 84a b - 40a )cosh(x) + (144a b + 48a b)cosh(x) - 18b +--R + +--R 2 2 4 +--R 18a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 5 3 3 4 +--R (- 36b - 12a b )cosh(x) + (- 150a b - 50a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (72b - 96a b - 40a )cosh(x) + (180a b + 60a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- 36b + 60a b + 24a )cosh(x) - 30a b - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 6 3 3 5 +--R (- 6b - 2a b )cosh(x) + (- 48a b - 16a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (18b - 54a b - 20a )cosh(x) + (96a b + 32a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 18b + 66a b + 24a )cosh(x) + (- 48a b - 16a b)cosh(x) +--R + +--R 4 2 2 4 +--R 6b - 10a b - 4a +--R * +--R sinh(x) +--R + +--R 3 3 6 2 2 4 5 +--R (- 6a b - 2a b)cosh(x) + (- 12a b - 4a )cosh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (18a b + 6a b)cosh(x) + (24a b + 8a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 18a b - 6a b)cosh(x) + (- 12a b - 4a )cosh(x) + 6a b + 2a b +--R * +--R log(sinh(x)) +--R + +--R 4 2 2 7 +--R (6b + 2a b )sinh(x) +--R + +--R 4 2 2 3 3 6 +--R ((36b + 12a b )cosh(x) + 18a b + 6a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (90b + 30a b )cosh(x) + (96a b + 32a b)cosh(x) - 18b + 6a b +--R + +--R 4 +--R 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (120b + 40a b )cosh(x) + (210a b + 70a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- 72b + 36a b + 20a )cosh(x) - 42a b - 14a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (90b + 30a b )cosh(x) + (240a b + 80a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 108b + 84a b + 40a )cosh(x) + (- 144a b - 48a b)cosh(x) +--R + +--R 4 2 2 4 +--R 18b - 18a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 5 3 3 4 +--R (36b + 12a b )cosh(x) + (150a b + 50a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (- 72b + 96a b + 40a )cosh(x) + (- 180a b - 60a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (36b - 60a b - 24a )cosh(x) + 30a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 6 3 3 5 +--R (6b + 2a b )cosh(x) + (48a b + 16a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (- 18b + 54a b + 20a )cosh(x) + (- 96a b - 32a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (18b - 66a b - 24a )cosh(x) + (48a b + 16a b)cosh(x) - 6b +--R + +--R 2 2 4 +--R 10a b + 4a +--R * +--R sinh(x) +--R + +--R 3 3 6 2 2 4 5 +--R (6a b + 2a b)cosh(x) + (12a b + 4a )cosh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (- 18a b - 6a b)cosh(x) + (- 24a b - 8a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (18a b + 6a b)cosh(x) + (12a b + 4a )cosh(x) - 6a b - 2a b +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 2 2 7 +--R (- 6b - 2a b )sinh(x) +--R + +--R 4 2 2 3 3 6 +--R ((- 36b - 12a b )cosh(x) - 18a b - 6a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 +--R (- 90b - 30a b )cosh(x) + (- 96a b - 32a b)cosh(x) + 18b +--R + +--R 2 2 4 +--R - 6a b - 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 120b - 40a b )cosh(x) + (- 210a b - 70a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (72b - 36a b - 20a )cosh(x) + 42a b + 14a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 90b - 30a b )cosh(x) + (- 240a b - 80a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 4 +--R (108b - 84a b - 40a )cosh(x) + (144a b + 48a b)cosh(x) - 18b +--R + +--R 2 2 4 +--R 18a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 5 3 3 4 +--R (- 36b - 12a b )cosh(x) + (- 150a b - 50a b)cosh(x) +--R + +--R 4 2 2 4 3 3 3 2 +--R (72b - 96a b - 40a )cosh(x) + (180a b + 60a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- 36b + 60a b + 24a )cosh(x) - 30a b - 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 6 3 3 5 +--R (- 6b - 2a b )cosh(x) + (- 48a b - 16a b)cosh(x) +--R + +--R 4 2 2 4 4 3 3 3 +--R (18b - 54a b - 20a )cosh(x) + (96a b + 32a b)cosh(x) +--R + +--R 4 2 2 4 2 3 3 +--R (- 18b + 66a b + 24a )cosh(x) + (- 48a b - 16a b)cosh(x) +--R + +--R 4 2 2 4 +--R 6b - 10a b - 4a +--R * +--R sinh(x) +--R + +--R 3 3 6 2 2 4 5 +--R (- 6a b - 2a b)cosh(x) + (- 12a b - 4a )cosh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (18a b + 6a b)cosh(x) + (24a b + 8a )cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 18a b - 6a b)cosh(x) + (- 12a b - 4a )cosh(x) + 6a b + 2a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 3 7 +--R (a b csch(x) - 4a b csch(x))sinh(x) +--R + +--R 2 2 3 2 3 2 2 +--R (6a b cosh(x) + 3a b)csch(x) + (- 24a b cosh(x) - 12a b )csch(x) +--R + +--R 3 3 +--R 10a b + 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 2 3 2 2 4 2 +--R (15a b cosh(x) + 16a b cosh(x) - 3a b + 2a )csch(x) +--R + +--R 3 2 2 2 3 3 +--R (- 60a b cosh(x) - 64a b cosh(x) + 12a b - 8a b)csch(x) +--R + +--R 3 3 2 2 +--R (48a b + 8a b)cosh(x) + 20a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 3 2 2 2 4 3 +--R (20a b cosh(x) + 35a b cosh(x) + (- 12a b + 10a )cosh(x) - 7a b) +--R * +--R 2 +--R csch(x) +--R + +--R 3 3 2 2 2 3 3 +--R - 80a b cosh(x) - 140a b cosh(x) + (48a b - 40a b)cosh(x) +--R + +--R 2 2 +--R 28a b +--R * +--R csch(x) +--R + +--R 3 3 2 2 2 3 3 +--R (90a b + 10a b)cosh(x) + 88a b cosh(x) - 18a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 4 3 3 2 2 4 2 +--R 15a b cosh(x) + 40a b cosh(x) + (- 18a b + 20a )cosh(x) +--R + +--R 3 2 2 4 +--R - 24a b cosh(x) + 3a b - 4a +--R * +--R 2 +--R csch(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R - 60a b cosh(x) - 160a b cosh(x) + (72a b - 80a b)cosh(x) +--R + +--R 2 2 3 3 +--R 96a b cosh(x) - 12a b + 16a b +--R * +--R csch(x) +--R + +--R 3 3 2 2 2 3 3 2 2 +--R 80a b cosh(x) + 152a b cosh(x) + (- 48a b + 24a b)cosh(x) - 28a b +--R + +--R 4 +--R - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 5 3 4 2 2 4 3 +--R 6a b cosh(x) + 25a b cosh(x) + (- 12a b + 20a )cosh(x) +--R + +--R 3 2 2 2 4 3 +--R - 30a b cosh(x) + (6a b - 12a )cosh(x) + 5a b +--R * +--R 2 +--R csch(x) +--R + +--R 3 5 2 2 4 3 3 3 +--R - 24a b cosh(x) - 100a b cosh(x) + (48a b - 80a b)cosh(x) +--R + +--R 2 2 2 3 3 2 2 +--R 120a b cosh(x) + (- 24a b + 48a b)cosh(x) - 20a b +--R * +--R csch(x) +--R + +--R 3 3 4 2 2 3 +--R (30a b - 10a b)cosh(x) + 128a b cosh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 36a b + 60a b)cosh(x) + (- 72a b - 24a )cosh(x) + 6a b - 14a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 6 3 5 2 2 4 4 +--R a b cosh(x) + 8a b cosh(x) + (- 3a b + 10a )cosh(x) +--R + +--R 3 3 2 2 4 2 3 2 2 +--R - 16a b cosh(x) + (3a b - 12a )cosh(x) + 8a b cosh(x) - a b +--R + +--R 4 +--R 2a +--R * +--R 2 +--R csch(x) +--R + +--R 3 6 2 2 5 3 3 4 +--R - 4a b cosh(x) - 32a b cosh(x) + (12a b - 40a b)cosh(x) +--R + +--R 2 2 3 3 3 2 2 2 +--R 64a b cosh(x) + (- 12a b + 48a b)cosh(x) - 32a b cosh(x) +--R + +--R 3 3 +--R 4a b - 8a b +--R * +--R csch(x) +--R + +--R 3 5 2 2 4 3 3 +--R - 8a b cosh(x) + 52a b cosh(x) + 56a b cosh(x) +--R + +--R 2 2 4 2 3 2 2 +--R (- 60a b - 24a )cosh(x) - 32a b cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R a b cosh(x) + 2a cosh(x) - 3a b cosh(x) - 4a cosh(x) +--R + +--R 3 2 4 3 +--R 3a b cosh(x) + 2a cosh(x) - a b +--R * +--R 2 +--R csch(x) +--R + +--R 2 2 6 3 5 2 2 4 3 3 +--R - 4a b cosh(x) - 8a b cosh(x) + 12a b cosh(x) + 16a b cosh(x) +--R + +--R 2 2 2 3 2 2 +--R - 12a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R csch(x) +--R + +--R 3 3 6 2 2 5 3 3 4 +--R (- 2a b - 2a b)cosh(x) + 8a b cosh(x) + (6a b + 18a b)cosh(x) +--R + +--R 2 2 4 3 3 3 2 2 2 +--R (- 16a b - 8a )cosh(x) + (- 6a b - 18a b)cosh(x) + 8a b cosh(x) +--R + +--R 3 3 +--R 2a b + 2a b +--R / +--R 4 2 7 4 2 5 6 +--R 2a b sinh(x) + (12a b cosh(x) + 6a b)sinh(x) +--R + +--R 4 2 2 5 4 2 6 5 +--R (30a b cosh(x) + 32a b cosh(x) - 6a b + 4a )sinh(x) +--R + +--R 4 2 3 5 2 4 2 6 5 +--R (40a b cosh(x) + 70a b cosh(x) + (- 24a b + 20a )cosh(x) - 14a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 4 5 3 4 2 6 2 +--R 30a b cosh(x) + 80a b cosh(x) + (- 36a b + 40a )cosh(x) +--R + +--R 5 4 2 6 +--R - 48a b cosh(x) + 6a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 5 5 4 4 2 6 3 +--R 12a b cosh(x) + 50a b cosh(x) + (- 24a b + 40a )cosh(x) +--R + +--R 5 2 4 2 6 5 +--R - 60a b cosh(x) + (12a b - 24a )cosh(x) + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 6 5 5 4 2 6 4 +--R 2a b cosh(x) + 16a b cosh(x) + (- 6a b + 20a )cosh(x) +--R + +--R 5 3 4 2 6 2 5 4 2 6 +--R - 32a b cosh(x) + (6a b - 24a )cosh(x) + 16a b cosh(x) - 2a b + 4a +--R * +--R sinh(x) +--R + +--R 5 6 6 5 5 4 6 3 5 2 +--R 2a b cosh(x) + 4a cosh(x) - 6a b cosh(x) - 8a cosh(x) + 6a b cosh(x) +--R + +--R 6 5 +--R 4a cosh(x) - 2a b +--R Type: Expression(Integer) +--E 139 + +--S 140 of 552 +d0727:= D(m0727,x) +--R +--R +--R (137) +--R 4 2 5 12 +--R (- a b coth(x)csch(x) + 2b coth(x)csch(x))sinh(x) +--R + +--R 4 2 3 2 +--R (- 10a b cosh(x) - 6a b )coth(x)csch(x) +--R + +--R 5 4 5 2 3 +--R (20b cosh(x) + 12a b )coth(x)csch(x) - 6b - 2a b +--R * +--R 11 +--R sinh(x) +--R + +--R 4 2 2 3 4 3 2 2 +--R (- 45a b cosh(x) - 56a b cosh(x) + 5a b - 13a b )coth(x)csch(x) +--R + +--R 5 2 4 5 2 3 +--R (90b cosh(x) + 112a b cosh(x) - 10b + 26a b )coth(x)csch(x) +--R + +--R 5 2 3 4 3 2 +--R (- 53b - 17a b )cosh(x) - 24a b - 4a b +--R * +--R 10 +--R sinh(x) +--R + +--R 4 3 2 3 2 4 3 2 +--R - 120a b cosh(x) - 234a b cosh(x) + (40a b - 114a b )cosh(x) +--R + +--R 2 3 4 +--R 26a b - 12a b +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 5 3 4 2 5 2 3 +--R 240b cosh(x) + 468a b cosh(x) + (- 80b + 228a b )cosh(x) +--R + +--R 4 3 2 +--R - 52a b + 24a b +--R * +--R coth(x)csch(x) +--R + +--R 5 2 3 2 4 3 2 5 +--R (- 206b - 62a b )cosh(x) + (- 200a b - 32a b )cosh(x) + 12b +--R + +--R 2 3 4 +--R - 26a b - 2a b +--R * +--R 9 +--R sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R - 210a b cosh(x) - 576a b cosh(x) + (140a b - 445a b )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (192a b - 100a b)cosh(x) - 10a b + 49a b - 4a +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 5 4 4 3 5 2 3 2 +--R 420b cosh(x) + 1152a b cosh(x) + (- 280b + 890a b )cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (- 384a b + 200a b )cosh(x) + 20b - 98a b + 8a b +--R * +--R coth(x)csch(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (- 459b - 123a b )cosh(x) + (- 732a b - 108a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (79b - 219a b - 14a b)cosh(x) + 36a b + 12a b +--R * +--R 8 +--R sinh(x) +--R + +--R 4 5 2 3 4 +--R - 252a b cosh(x) - 924a b cosh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (280a b - 1016a b )cosh(x) + (616a b - 368a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (- 60a b + 336a b - 32a )cosh(x) - 44a b + 40a b +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 5 5 4 4 5 2 3 3 +--R 504b cosh(x) + 1848a b cosh(x) + (- 560b + 2032a b )cosh(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (- 1232a b + 736a b )cosh(x) + (120b - 672a b + 64a b)cosh(x) +--R + +--R 4 3 2 +--R 88a b - 80a b +--R * +--R coth(x)csch(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (- 636b - 132a b )cosh(x) + (- 1536a b - 192a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 +--R (212b - 812a b - 40a b)cosh(x) + (224a b + 40a b )cosh(x) +--R + +--R 2 3 4 +--R 36a b + 36a b +--R * +--R 7 +--R sinh(x) +--R + +--R 4 6 2 3 5 +--R - 210a b cosh(x) - 1008a b cosh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (350a b - 1498a b )cosh(x) + (1120a b - 784a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 150a b + 992a b - 112a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 240a b + 256a b)cosh(x) + 10a b - 70a b + 12a +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 5 6 4 5 5 2 3 4 +--R 420b cosh(x) + 2016a b cosh(x) + (- 700b + 2996a b )cosh(x) +--R + +--R 4 3 2 3 +--R (- 2240a b + 1568a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 +--R (300b - 1984a b + 224a b)cosh(x) + (480a b - 512a b )cosh(x) +--R + +--R 5 2 3 4 +--R - 20b + 140a b - 24a b +--R * +--R coth(x)csch(x) +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 546b - 42a b )cosh(x) + (- 2016a b - 168a b )cosh(x) +--R + +--R 5 2 3 4 3 4 3 2 2 +--R (280b - 1736a b - 56a b)cosh(x) + (572a b - 40a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (10b + 226a b + 208a b)cosh(x) + 12a b + 28a b + 16a +--R * +--R 6 +--R sinh(x) +--R + +--R 4 7 2 3 6 +--R - 120a b cosh(x) - 756a b cosh(x) +--R + +--R 4 3 2 5 2 3 4 4 +--R (280a b - 1484a b )cosh(x) + (1260a b - 1064a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (- 200a b + 1640a b - 224a )cosh(x) +--R + +--R 2 3 4 2 4 3 2 5 +--R (- 540a b + 696a b)cosh(x) + (40a b - 348a b + 72a )cosh(x) +--R + +--R 2 3 4 +--R 36a b - 48a b +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 5 7 4 6 5 2 3 5 +--R 240b cosh(x) + 1512a b cosh(x) + (- 560b + 2968a b )cosh(x) +--R + +--R 4 3 2 4 +--R (- 2520a b + 2128a b )cosh(x) +--R + +--R 5 2 3 4 3 +--R (400b - 3280a b + 448a b)cosh(x) +--R + +--R 4 3 2 2 +--R (1080a b - 1392a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (- 80b + 696a b - 144a b)cosh(x) - 72a b + 96a b +--R * +--R coth(x)csch(x) +--R + +--R 5 2 3 6 4 5 +--R (- 252b + 84a b )cosh(x) - 1680a b cosh(x) +--R + +--R 5 2 3 4 4 4 3 2 3 +--R (140b - 2352a b - 28a b)cosh(x) + (744a b - 408a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (60b + 600a b + 492a b)cosh(x) + (72a b + 160a b + 96a )cosh(x) +--R + +--R 5 2 3 4 +--R - 12b + 20a b + 32a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 8 2 3 7 4 3 2 6 +--R - 45a b cosh(x) - 384a b cosh(x) + (140a b - 994a b )cosh(x) +--R + +--R 2 3 4 5 +--R (896a b - 952a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (- 150a b + 1650a b - 280a )cosh(x) +--R + +--R 2 3 4 3 +--R (- 640a b + 1040a b)cosh(x) +--R + +--R 4 3 2 5 2 2 3 4 +--R (60a b - 702a b + 180a )cosh(x) + (128a b - 216a b)cosh(x) +--R + +--R 4 3 2 5 +--R - 5a b + 46a b - 12a +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 5 8 4 7 5 2 3 6 +--R 90b cosh(x) + 768a b cosh(x) + (- 280b + 1988a b )cosh(x) +--R + +--R 4 3 2 5 +--R (- 1792a b + 1904a b )cosh(x) +--R + +--R 5 2 3 4 4 +--R (300b - 3300a b + 560a b)cosh(x) +--R + +--R 4 3 2 3 +--R (1280a b - 2080a b )cosh(x) +--R + +--R 5 2 3 4 2 +--R (- 120b + 1404a b - 360a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (- 256a b + 432a b )cosh(x) + 10b - 92a b + 24a b +--R * +--R coth(x)csch(x) +--R + +--R 5 2 3 7 4 3 2 6 +--R (- 6b + 138a b )cosh(x) + (- 840a b + 168a b )cosh(x) +--R + +--R 5 2 3 4 5 4 3 2 4 +--R (- 98b - 2086a b + 28a b)cosh(x) + (460a b - 880a b )cosh(x) +--R + +--R 5 2 3 4 3 +--R (150b + 870a b + 600a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (192a b + 396a b + 240a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 46b + 86a b + 140a b)cosh(x) - 36a b + 4a b + 16a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 9 2 3 8 4 3 2 7 +--R - 10a b cosh(x) - 126a b cosh(x) + (40a b - 440a b )cosh(x) +--R + +--R 2 3 4 6 +--R (392a b - 560a b)cosh(x) +--R + +--R 4 3 2 5 5 +--R (- 60a b + 1024a b - 224a )cosh(x) +--R + +--R 2 3 4 4 4 3 2 5 3 +--R (- 420a b + 920a b)cosh(x) + (40a b - 728a b + 240a )cosh(x) +--R + +--R 2 3 4 2 4 3 2 5 +--R (168a b - 384a b)cosh(x) + (- 10a b + 144a b - 48a )cosh(x) +--R + +--R 2 3 4 +--R - 14a b + 24a b +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 5 9 4 8 5 2 3 7 +--R 20b cosh(x) + 252a b cosh(x) + (- 80b + 880a b )cosh(x) +--R + +--R 4 3 2 6 +--R (- 784a b + 1120a b )cosh(x) +--R + +--R 5 2 3 4 5 +--R (120b - 2048a b + 448a b)cosh(x) +--R + +--R 4 3 2 4 +--R (840a b - 1840a b )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 80b + 1456a b - 480a b)cosh(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (- 336a b + 768a b )cosh(x) + (20b - 288a b + 96a b)cosh(x) +--R + +--R 4 3 2 +--R 28a b - 48a b +--R * +--R coth(x)csch(x) +--R + +--R 5 2 3 8 4 3 2 7 +--R (66b + 102a b )cosh(x) + (- 192a b + 192a b )cosh(x) +--R + +--R 5 2 3 4 6 4 3 2 5 +--R (- 196b - 1204a b + 56a b)cosh(x) + (16a b - 968a b )cosh(x) +--R + +--R 5 2 3 4 4 +--R (200b + 740a b + 380a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (288a b + 544a b + 320a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (- 76b + 140a b + 240a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 112a b + 8a b + 64a )cosh(x) + 6b - 34a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 10 2 3 9 4 3 2 8 +--R - a b cosh(x) - 24a b cosh(x) + (5a b - 121a b )cosh(x) +--R + +--R 2 3 4 7 4 3 2 5 6 +--R (96a b - 208a b)cosh(x) + (- 10a b + 376a b - 112a )cosh(x) +--R + +--R 2 3 4 5 4 3 2 5 4 +--R (- 144a b + 480a b)cosh(x) + (10a b - 402a b + 180a )cosh(x) +--R + +--R 2 3 4 3 4 3 2 5 2 +--R (96a b - 336a b)cosh(x) + (- 5a b + 160a b - 72a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 24a b + 64a b)cosh(x) + a b - 13a b + 4a +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 5 10 4 9 5 2 3 8 +--R 2b cosh(x) + 48a b cosh(x) + (- 10b + 242a b )cosh(x) +--R + +--R 4 3 2 7 5 2 3 4 6 +--R (- 192a b + 416a b )cosh(x) + (20b - 752a b + 224a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 4 +--R (288a b - 960a b )cosh(x) + (- 20b + 804a b - 360a b)cosh(x) +--R + +--R 4 3 2 3 5 2 3 4 2 +--R (- 192a b + 672a b )cosh(x) + (10b - 320a b + 144a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (48a b - 128a b )cosh(x) - 2b + 26a b - 8a b +--R * +--R coth(x)csch(x) +--R + +--R 5 2 3 9 4 3 2 8 +--R (39b + 43a b )cosh(x) + (24a b + 108a b )cosh(x) +--R + +--R 5 2 3 4 7 4 3 2 6 +--R (- 128b - 432a b + 40a b)cosh(x) + (- 156a b - 600a b )cosh(x) +--R + +--R 5 2 3 4 5 +--R (150b + 366a b + 96a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (252a b + 436a b + 240a )cosh(x) +--R + +--R 5 2 3 4 3 4 5 2 +--R (- 72b + 104a b + 200a b)cosh(x) + (- 132a b + 96a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (11b - 81a b - 16a b)cosh(x) + 12a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 10 3 2 9 2 3 4 8 +--R - 2a b cosh(x) - 18a b cosh(x) + (10a b - 44a b)cosh(x) +--R + +--R 3 2 5 7 2 3 4 6 +--R (72a b - 32a )cosh(x) + (- 20a b + 136a b)cosh(x) +--R + +--R 3 2 5 5 2 3 4 4 +--R (- 108a b + 72a )cosh(x) + (20a b - 144a b)cosh(x) +--R + +--R 3 2 5 3 2 3 4 2 +--R (72a b - 48a )cosh(x) + (- 10a b + 56a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 18a b + 8a )cosh(x) + 2a b - 4a b +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 4 10 2 3 9 4 3 2 8 +--R 4a b cosh(x) + 36a b cosh(x) + (- 20a b + 88a b )cosh(x) +--R + +--R 2 3 4 7 4 3 2 6 +--R (- 144a b + 64a b)cosh(x) + (40a b - 272a b )cosh(x) +--R + +--R 2 3 4 5 4 3 2 4 +--R (216a b - 144a b)cosh(x) + (- 40a b + 288a b )cosh(x) +--R + +--R 2 3 4 3 4 3 2 2 +--R (- 144a b + 96a b)cosh(x) + (20a b - 112a b )cosh(x) +--R + +--R 2 3 4 4 3 2 +--R (36a b - 16a b)cosh(x) - 4a b + 8a b +--R * +--R coth(x)csch(x) +--R + +--R 5 2 3 10 4 3 2 9 +--R (10b + 10a b )cosh(x) + (24a b + 32a b )cosh(x) +--R + +--R 5 2 3 4 8 4 3 2 7 +--R (- 40b - 86a b + 14a b)cosh(x) + (- 88a b - 200a b )cosh(x) +--R + +--R 5 2 3 4 6 4 3 2 5 5 +--R (60b + 96a b - 12a b)cosh(x) + (120a b + 192a b + 96a )cosh(x) +--R + +--R 5 2 3 4 4 4 3 2 5 3 +--R (- 40b + 32a b + 80a b)cosh(x) + (- 72a b - 8a b + 64a )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 2 3 +--R (10b - 58a b - 20a b)cosh(x) + (16a b - 16a b )cosh(x) + 6a b +--R + +--R 4 +--R 2a b +--R * +--R sinh(x) +--R + +--R 3 2 10 4 9 3 2 5 8 +--R - a b cosh(x) - 4a b cosh(x) + (5a b - 4a )cosh(x) +--R + +--R 4 7 3 2 5 6 4 5 +--R 16a b cosh(x) + (- 10a b + 12a )cosh(x) - 24a b cosh(x) +--R + +--R 3 2 5 4 4 3 3 2 5 2 +--R (10a b - 12a )cosh(x) + 16a b cosh(x) + (- 5a b + 4a )cosh(x) +--R + +--R 4 3 2 +--R - 4a b cosh(x) + a b +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 2 3 10 3 2 9 2 3 4 8 +--R 2a b cosh(x) + 8a b cosh(x) + (- 10a b + 8a b)cosh(x) +--R + +--R 3 2 7 2 3 4 6 3 2 5 +--R - 32a b cosh(x) + (20a b - 24a b)cosh(x) + 48a b cosh(x) +--R + +--R 2 3 4 4 3 2 3 2 3 4 2 +--R (- 20a b + 24a b)cosh(x) - 32a b cosh(x) + (10a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 +--R 8a b cosh(x) - 2a b +--R * +--R coth(x)csch(x) +--R + +--R 5 2 3 11 4 3 2 10 +--R (b + a b )cosh(x) + (4a b + 4a b )cosh(x) +--R + +--R 5 2 3 4 9 4 3 2 8 +--R (- 5b - 7a b + 2a b)cosh(x) + (- 16a b - 28a b )cosh(x) +--R + +--R 5 2 3 4 7 4 3 2 5 6 +--R (10b + 10a b - 8a b)cosh(x) + (24a b + 36a b + 16a )cosh(x) +--R + +--R 5 2 3 4 5 4 3 2 5 4 +--R (- 10b + 2a b + 12a b)cosh(x) + (- 16a b - 4a b + 16a )cosh(x) +--R + +--R 5 2 3 4 3 4 3 2 2 +--R (5b - 11a b - 8a b)cosh(x) + (4a b - 8a b )cosh(x) +--R + +--R 5 2 3 4 +--R (- b + 5a b + 2a b)cosh(x) +--R / +--R 3 4 12 3 4 4 3 11 +--R a b sinh(x) + (10a b cosh(x) + 6a b )sinh(x) +--R + +--R 3 4 2 4 3 3 4 5 2 10 +--R (45a b cosh(x) + 56a b cosh(x) - 5a b + 13a b )sinh(x) +--R + +--R 3 4 3 4 3 2 3 4 5 2 +--R 120a b cosh(x) + 234a b cosh(x) + (- 40a b + 114a b )cosh(x) +--R + +--R 4 3 6 +--R - 26a b + 12a b +--R * +--R 9 +--R sinh(x) +--R + +--R 3 4 4 4 3 3 3 4 5 2 2 +--R 210a b cosh(x) + 576a b cosh(x) + (- 140a b + 445a b )cosh(x) +--R + +--R 4 3 6 3 4 5 2 7 +--R (- 192a b + 100a b)cosh(x) + 10a b - 49a b + 4a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 4 5 4 3 4 3 4 5 2 3 +--R 252a b cosh(x) + 924a b cosh(x) + (- 280a b + 1016a b )cosh(x) +--R + +--R 4 3 6 2 3 4 5 2 7 +--R (- 616a b + 368a b)cosh(x) + (60a b - 336a b + 32a )cosh(x) +--R + +--R 4 3 6 +--R 44a b - 40a b +--R * +--R 7 +--R sinh(x) +--R + +--R 3 4 6 4 3 5 3 4 5 2 4 +--R 210a b cosh(x) + 1008a b cosh(x) + (- 350a b + 1498a b )cosh(x) +--R + +--R 4 3 6 3 3 4 5 2 7 2 +--R (- 1120a b + 784a b)cosh(x) + (150a b - 992a b + 112a )cosh(x) +--R + +--R 4 3 6 3 4 5 2 7 +--R (240a b - 256a b)cosh(x) - 10a b + 70a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 4 7 4 3 6 3 4 5 2 5 +--R 120a b cosh(x) + 756a b cosh(x) + (- 280a b + 1484a b )cosh(x) +--R + +--R 4 3 6 4 3 4 5 2 7 3 +--R (- 1260a b + 1064a b)cosh(x) + (200a b - 1640a b + 224a )cosh(x) +--R + +--R 4 3 6 2 3 4 5 2 7 +--R (540a b - 696a b)cosh(x) + (- 40a b + 348a b - 72a )cosh(x) +--R + +--R 4 3 6 +--R - 36a b + 48a b +--R * +--R 5 +--R sinh(x) +--R + +--R 3 4 8 4 3 7 3 4 5 2 6 +--R 45a b cosh(x) + 384a b cosh(x) + (- 140a b + 994a b )cosh(x) +--R + +--R 4 3 6 5 3 4 5 2 7 4 +--R (- 896a b + 952a b)cosh(x) + (150a b - 1650a b + 280a )cosh(x) +--R + +--R 4 3 6 3 3 4 5 2 7 2 +--R (640a b - 1040a b)cosh(x) + (- 60a b + 702a b - 180a )cosh(x) +--R + +--R 4 3 6 3 4 5 2 7 +--R (- 128a b + 216a b)cosh(x) + 5a b - 46a b + 12a +--R * +--R 4 +--R sinh(x) +--R + +--R 3 4 9 4 3 8 3 4 5 2 7 +--R 10a b cosh(x) + 126a b cosh(x) + (- 40a b + 440a b )cosh(x) +--R + +--R 4 3 6 6 3 4 5 2 7 5 +--R (- 392a b + 560a b)cosh(x) + (60a b - 1024a b + 224a )cosh(x) +--R + +--R 4 3 6 4 3 4 5 2 7 3 +--R (420a b - 920a b)cosh(x) + (- 40a b + 728a b - 240a )cosh(x) +--R + +--R 4 3 6 2 3 4 5 2 7 +--R (- 168a b + 384a b)cosh(x) + (10a b - 144a b + 48a )cosh(x) +--R + +--R 4 3 6 +--R 14a b - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 10 4 3 9 3 4 5 2 8 +--R a b cosh(x) + 24a b cosh(x) + (- 5a b + 121a b )cosh(x) +--R + +--R 4 3 6 7 3 4 5 2 7 6 +--R (- 96a b + 208a b)cosh(x) + (10a b - 376a b + 112a )cosh(x) +--R + +--R 4 3 6 5 3 4 5 2 7 4 +--R (144a b - 480a b)cosh(x) + (- 10a b + 402a b - 180a )cosh(x) +--R + +--R 4 3 6 3 3 4 5 2 7 2 +--R (- 96a b + 336a b)cosh(x) + (5a b - 160a b + 72a )cosh(x) +--R + +--R 4 3 6 3 4 5 2 7 +--R (24a b - 64a b)cosh(x) - a b + 13a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 10 5 2 9 4 3 6 8 +--R 2a b cosh(x) + 18a b cosh(x) + (- 10a b + 44a b)cosh(x) +--R + +--R 5 2 7 7 4 3 6 6 +--R (- 72a b + 32a )cosh(x) + (20a b - 136a b)cosh(x) +--R + +--R 5 2 7 5 4 3 6 4 +--R (108a b - 72a )cosh(x) + (- 20a b + 144a b)cosh(x) +--R + +--R 5 2 7 3 4 3 6 2 +--R (- 72a b + 48a )cosh(x) + (10a b - 56a b)cosh(x) +--R + +--R 5 2 7 4 3 6 +--R (18a b - 8a )cosh(x) - 2a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 2 10 6 9 5 2 7 8 6 7 +--R a b cosh(x) + 4a b cosh(x) + (- 5a b + 4a )cosh(x) - 16a b cosh(x) +--R + +--R 5 2 7 6 6 5 5 2 7 4 +--R (10a b - 12a )cosh(x) + 24a b cosh(x) + (- 10a b + 12a )cosh(x) +--R + +--R 6 3 5 2 7 2 6 5 2 +--R - 16a b cosh(x) + (5a b - 4a )cosh(x) + 4a b cosh(x) - a b +--R Type: Expression(Integer) +--E 140 + +--S 141 of 552 +t0728:= coth(x)/(%i+sinh(x))^2 +--R +--R +--R coth(x) +--R (138) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 141 + +--S 142 of 552 +r0728:= -log(sinh(x))+log(%i+sinh(x))-%i/(%i+sinh(x)) +--R +--R +--R (sinh(x) + %i)log(sinh(x) + %i) + (- sinh(x) - %i)log(sinh(x)) - %i +--R (139) ------------------------------------------------------------------- +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 142 + +--S 143 of 552 +a0728:= integrate(t0728,x) +--R +--R +--R (140) +--R 2 2 +--R (2sinh(x) + (4cosh(x) + 4%i)sinh(x) + 2cosh(x) + 4%i cosh(x) - 2) +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 2 2 +--R (- sinh(x) + (- 2cosh(x) - 2%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1) +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2%i sinh(x) - 2%i cosh(x) +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2%i)sinh(x) + cosh(x) + 2%i cosh(x) - 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 143 + +--S 144 of 552 +m0728:= a0728-r0728 +--R +--R +--R (141) +--R 3 2 +--R 2sinh(x) + (4cosh(x) + 6%i)sinh(x) +--R + +--R 2 2 +--R (2cosh(x) + 8%i cosh(x) - 6)sinh(x) + 2%i cosh(x) - 4cosh(x) - 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 3 2 +--R - sinh(x) + (- 2cosh(x) - 3%i)sinh(x) +--R + +--R 2 2 +--R (- cosh(x) - 4%i cosh(x) + 3)sinh(x) - %i cosh(x) + 2cosh(x) + %i +--R * +--R log(sinh(x) + %i) +--R + +--R 3 2 +--R sinh(x) + (2cosh(x) + 3%i)sinh(x) +--R + +--R 2 2 +--R (cosh(x) + 4%i cosh(x) - 3)sinh(x) + %i cosh(x) - 2cosh(x) - %i +--R * +--R log(sinh(x)) +--R + +--R 3 2 +--R - sinh(x) + (- 2cosh(x) - 3%i)sinh(x) +--R + +--R 2 2 +--R (- cosh(x) - 4%i cosh(x) + 3)sinh(x) - %i cosh(x) + 2cosh(x) + %i +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - %i sinh(x) + %i cosh(x) - %i +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) + 3%i)sinh(x) + (cosh(x) + 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R %i cosh(x) - 2cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 144 + +--S 145 of 552 +d0728:= D(m0728,x) +--R +--R +--R (142) +--R 5 4 3 +--R sinh(x) + (2cosh(x) + 5%i)sinh(x) + (7%i cosh(x) - 4)sinh(x) +--R + +--R 3 2 2 +--R (- 2cosh(x) - 3%i cosh(x) - 3cosh(x) + 4%i)sinh(x) +--R + +--R 4 3 2 +--R (- cosh(x) - 7%i cosh(x) + 6cosh(x) + 7%i cosh(x) - 5)sinh(x) +--R + +--R 4 3 2 +--R - 2%i cosh(x) + 5cosh(x) + 3%i cosh(x) - 5cosh(x) - %i +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) + 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) + 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) + 9%i cosh(x) - 18cosh(x) - 10%i)sinh(x) +--R + +--R 3 2 3 +--R (2%i cosh(x) - 9cosh(x) - 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R - 3%i cosh(x) + 3cosh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 145 + +--S 146 of 552 +t0729:= coth(x)^2/(%i+sinh(x))^2 +--R +--R +--R 2 +--R coth(x) +--R (143) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 146 + +--S 147 of 552 +r0729:= 2*%i*acoth(cosh(x))+coth(x)-2*%i*cosh(x)/(1-%i*sinh(x)) +--R +--R +--R (144) +--R (2%i sinh(x) - 2)acoth(cosh(x)) + coth(x)sinh(x) + %i coth(x) + 2cosh(x) +--R ------------------------------------------------------------------------ +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 147 + +--S 148 of 552 +a0729:= integrate(t0729,x) +--R +--R +--R (145) +--R 3 2 +--R 2%i sinh(x) + (6%i cosh(x) - 2)sinh(x) +--R + +--R 2 3 2 +--R (6%i cosh(x) - 4cosh(x) - 2%i)sinh(x) + 2%i cosh(x) - 2cosh(x) +--R + +--R - 2%i cosh(x) + 2 +--R * +--R sinh(x) + cosh(x) + 1 +--R log(---------------------) +--R sinh(x) + cosh(x) - 1 +--R + +--R 2 2 +--R - 4%i sinh(x) + (- 8%i cosh(x) + 2)sinh(x) - 4%i cosh(x) + 2cosh(x) + 6%i +--R / +--R 3 2 2 +--R sinh(x) + (3cosh(x) + %i)sinh(x) + (3cosh(x) + 2%i cosh(x) - 1)sinh(x) +--R + +--R 3 2 +--R cosh(x) + %i cosh(x) - cosh(x) - %i +--R Type: Union(Expression(Complex(Integer)),...) +--E 148 + +--S 149 of 552 +m0729:= a0729-r0729 +--R +--R +--R (146) +--R 4 3 +--R 2%i sinh(x) + (6%i cosh(x) - 4)sinh(x) +--R + +--R 2 2 +--R (6%i cosh(x) - 10cosh(x) - 4%i)sinh(x) +--R + +--R 3 2 3 +--R (2%i cosh(x) - 8cosh(x) - 6%i cosh(x) + 4)sinh(x) - 2cosh(x) +--R + +--R 2 +--R - 2%i cosh(x) + 2cosh(x) + 2%i +--R * +--R sinh(x) + cosh(x) + 1 +--R log(---------------------) +--R sinh(x) + cosh(x) - 1 +--R + +--R 4 3 +--R - 2%i sinh(x) + (- 6%i cosh(x) + 4)sinh(x) +--R + +--R 2 2 +--R (- 6%i cosh(x) + 10cosh(x) + 4%i)sinh(x) +--R + +--R 3 2 3 +--R (- 2%i cosh(x) + 8cosh(x) + 6%i cosh(x) - 4)sinh(x) + 2cosh(x) +--R + +--R 2 +--R 2%i cosh(x) - 2cosh(x) - 2%i +--R * +--R acoth(cosh(x)) +--R + +--R 4 3 +--R - coth(x)sinh(x) + ((- 3cosh(x) - 2%i)coth(x) - 2cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R ((- 3cosh(x) - 5%i cosh(x) + 2)coth(x) - 6cosh(x) - 10%i cosh(x) + 6) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3 +--R (- cosh(x) - 4%i cosh(x) + 3cosh(x) + 2%i)coth(x) - 6cosh(x) +--R + +--R 2 +--R - 8%i cosh(x) + 12cosh(x) + 8%i +--R * +--R sinh(x) +--R + +--R 3 2 4 +--R (- %i cosh(x) + cosh(x) + %i cosh(x) - 1)coth(x) - 2cosh(x) +--R + +--R 3 2 +--R - 2%i cosh(x) + 6cosh(x) + 4%i cosh(x) - 6 +--R / +--R 4 3 +--R sinh(x) + (3cosh(x) + 2%i)sinh(x) +--R + +--R 2 2 +--R (3cosh(x) + 5%i cosh(x) - 2)sinh(x) +--R + +--R 3 2 3 +--R (cosh(x) + 4%i cosh(x) - 3cosh(x) - 2%i)sinh(x) + %i cosh(x) +--R + +--R 2 +--R - cosh(x) - %i cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 149 + +--S 150 of 552 +d0729:= D(m0729,x) +--R +--R +--R (147) +--R 9 +--R 2%i sinh(x) +--R + +--R 2 2 2 8 +--R ((cosh(x) - 1)coth(x) - 3cosh(x) + 12%i cosh(x) - 5)sinh(x) +--R + +--R 3 2 2 3 +--R (6cosh(x) + 4%i cosh(x) - 6cosh(x) - 4%i)coth(x) - 18cosh(x) +--R + +--R 2 +--R 20%i cosh(x) - 26cosh(x) - 6%i +--R * +--R 7 +--R sinh(x) +--R + +--R 4 3 2 2 +--R (15cosh(x) + 22%i cosh(x) - 23cosh(x) - 22%i cosh(x) + 8)coth(x) +--R + +--R 4 3 2 +--R - 43cosh(x) - 14%i cosh(x) - 35cosh(x) - 22%i cosh(x) + 2 +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 20cosh(x) + 50%i cosh(x) - 58cosh(x) - 62%i cosh(x) +--R + +--R 38cosh(x) + 12%i +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 2 +--R - 48cosh(x) - 86%i cosh(x) + 26cosh(x) - 4%i cosh(x) - 6cosh(x) +--R + +--R 2%i +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 15cosh(x) + 60%i cosh(x) - 88cosh(x) - 106%i cosh(x) +--R + +--R 2 +--R 87cosh(x) + 46%i cosh(x) - 14 +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 +--R - 15cosh(x) - 108%i cosh(x) + 102cosh(x) + 78%i cosh(x) +--R + +--R 2 +--R - 51cosh(x) - 18%i cosh(x) - 4 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 6cosh(x) + 40%i cosh(x) - 78cosh(x) - 108%i cosh(x) +--R + +--R 3 2 +--R 114cosh(x) + 80%i cosh(x) - 42cosh(x) - 12%i +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 3 +--R 22cosh(x) - 48%i cosh(x) + 78cosh(x) + 118%i cosh(x) - 86cosh(x) +--R + +--R 2 +--R - 76%i cosh(x) + 2cosh(x) + 6%i +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R cosh(x) + 14%i cosh(x) - 39cosh(x) - 62%i cosh(x) +--R + +--R 4 3 2 +--R 83cosh(x) + 74%i cosh(x) - 53cosh(x) - 26%i cosh(x) + 8 +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 4 +--R 27cosh(x) + 10%i cosh(x) + cosh(x) + 50%i cosh(x) - 49cosh(x) +--R + +--R 3 2 +--R - 74%i cosh(x) + 31cosh(x) + 14%i cosh(x) - 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 2%i cosh(x) - 10cosh(x) - 18%i cosh(x) + 30cosh(x) +--R + +--R 4 3 2 +--R 34%i cosh(x) - 30cosh(x) - 22%i cosh(x) + 10cosh(x) + 4%i +--R * +--R 2 +--R coth(x) +--R + +--R 9 8 7 6 5 +--R 12cosh(x) + 16%i cosh(x) - 22cosh(x) - 12%i cosh(x) - 2cosh(x) +--R + +--R 4 3 2 +--R - 4%i cosh(x) + 30cosh(x) + 4%i cosh(x) - 18cosh(x) - 4%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) - 2%i cosh(x) + 4cosh(x) + 6%i cosh(x) - 6cosh(x) +--R + +--R 3 2 +--R - 6%i cosh(x) + 4cosh(x) + 2%i cosh(x) - 1 +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 6 +--R 2cosh(x) + 4%i cosh(x) - 7cosh(x) - 10%i cosh(x) + 4cosh(x) +--R + +--R 5 4 3 2 +--R 14%i cosh(x) + 6cosh(x) - 6%i cosh(x) - 6cosh(x) - 2%i cosh(x) + 1 +--R / +--R 2 8 +--R (cosh(x) - 1)sinh(x) +--R + +--R 3 2 7 +--R (6cosh(x) + 4%i cosh(x) - 6cosh(x) - 4%i)sinh(x) +--R + +--R 4 3 2 6 +--R (15cosh(x) + 22%i cosh(x) - 23cosh(x) - 22%i cosh(x) + 8)sinh(x) +--R + +--R 5 4 3 2 +--R 20cosh(x) + 50%i cosh(x) - 58cosh(x) - 62%i cosh(x) + 38cosh(x) +--R + +--R 12%i +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 15cosh(x) + 60%i cosh(x) - 88cosh(x) - 106%i cosh(x) + 87cosh(x) +--R + +--R 46%i cosh(x) - 14 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) + 40%i cosh(x) - 78cosh(x) - 108%i cosh(x) + 114cosh(x) +--R + +--R 2 +--R 80%i cosh(x) - 42cosh(x) - 12%i +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R cosh(x) + 14%i cosh(x) - 39cosh(x) - 62%i cosh(x) + 83cosh(x) +--R + +--R 3 2 +--R 74%i cosh(x) - 53cosh(x) - 26%i cosh(x) + 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 2%i cosh(x) - 10cosh(x) - 18%i cosh(x) + 30cosh(x) +--R + +--R 4 3 2 +--R 34%i cosh(x) - 30cosh(x) - 22%i cosh(x) + 10cosh(x) + 4%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) - 2%i cosh(x) + 4cosh(x) + 6%i cosh(x) - 6cosh(x) +--R + +--R 3 2 +--R - 6%i cosh(x) + 4cosh(x) + 2%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 150 + +--S 151 of 552 +t0730:= coth(x)^3/(%i+sinh(x))^2 +--R +--R +--R 3 +--R coth(x) +--R (148) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 151 + +--S 152 of 552 +r0730:= 2*%i*csch(x)+1/2*csch(x)^2+2*log(sinh(x))-2*log(%i+sinh(x)) +--R +--R +--R 2 +--R - 4log(sinh(x) + %i) + 4log(sinh(x)) + csch(x) + 4%i csch(x) +--R (149) ------------------------------------------------------------- +--R 2 +--R Type: Expression(Complex(Integer)) +--E 152 + +--S 153 of 552 +a0730:= integrate(t0730,x) +--R +--R +--R (150) +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 8)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 16cosh(x))sinh(x) - 4cosh(x) + 8cosh(x) - 4 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 +--R 4%i sinh(x) + (12%i cosh(x) + 2)sinh(x) +--R + +--R 2 3 2 +--R (12%i cosh(x) + 4cosh(x) - 4%i)sinh(x) + 4%i cosh(x) + 2cosh(x) +--R + +--R - 4%i cosh(x) +--R / +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 2)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 4cosh(x))sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 153 + +--S 154 of 552 +m0730:= a0730-r0730 +--R +--R +--R (151) +--R 4 3 2 2 +--R - 8sinh(x) - 32cosh(x)sinh(x) + (- 48cosh(x) + 16)sinh(x) +--R + +--R 3 4 2 +--R (- 32cosh(x) + 32cosh(x))sinh(x) - 8cosh(x) + 16cosh(x) - 8 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 8)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 16cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) + 4 +--R * +--R log(sinh(x) + %i) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) + 8)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) + 16cosh(x))sinh(x) - 4cosh(x) + 8cosh(x) - 4 +--R * +--R log(sinh(x)) +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 8)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 16cosh(x))sinh(x) + 4cosh(x) - 8cosh(x) + 4 +--R * +--R 2sinh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 4 +--R (- csch(x) - 4%i csch(x))sinh(x) +--R + +--R 2 3 +--R (- 4cosh(x)csch(x) - 16%i cosh(x)csch(x) + 8%i)sinh(x) +--R + +--R 2 2 2 +--R (- 6cosh(x) + 2)csch(x) + (- 24%i cosh(x) + 8%i)csch(x) +--R + +--R 24%i cosh(x) + 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 +--R (- 4cosh(x) + 4cosh(x))csch(x) +--R + +--R 3 2 +--R (- 16%i cosh(x) + 16%i cosh(x))csch(x) + 24%i cosh(x) + 8cosh(x) +--R + +--R - 8%i +--R * +--R sinh(x) +--R + +--R 4 2 2 +--R (- cosh(x) + 2cosh(x) - 1)csch(x) +--R + +--R 4 2 3 2 +--R (- 4%i cosh(x) + 8%i cosh(x) - 4%i)csch(x) + 8%i cosh(x) + 4cosh(x) +--R + +--R - 8%i cosh(x) +--R / +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 4)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 8cosh(x))sinh(x) + 2cosh(x) - 4cosh(x) + 2 +--R Type: Expression(Complex(Integer)) +--E 154 + +--S 155 of 552 +d0730:= D(m0730,x) +--R +--R +--R (152) +--R 2 8 +--R (coth(x)csch(x) + 2%i coth(x)csch(x) - 2)sinh(x) +--R + +--R 2 +--R (7cosh(x) + 2%i)coth(x)csch(x) + (14%i cosh(x) - 4)coth(x)csch(x) +--R + +--R - 12cosh(x) - 4%i +--R * +--R 7 +--R sinh(x) +--R + +--R 2 2 +--R (21cosh(x) + 13%i cosh(x) - 4)coth(x)csch(x) +--R + +--R 2 2 +--R (42%i cosh(x) - 26cosh(x) - 8%i)coth(x)csch(x) - 28cosh(x) +--R + +--R - 24%i cosh(x) + 8 +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 +--R (35cosh(x) + 36%i cosh(x) - 21cosh(x) - 6%i)coth(x)csch(x) +--R + +--R 3 2 +--R (70%i cosh(x) - 72cosh(x) - 42%i cosh(x) + 12)coth(x)csch(x) +--R + +--R 3 2 +--R - 28cosh(x) - 60%i cosh(x) + 36cosh(x) - 4%i +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 +--R (35cosh(x) + 55%i cosh(x) - 45cosh(x) - 27%i cosh(x) + 6)coth(x) +--R * +--R 2 +--R csch(x) +--R + +--R 4 3 2 +--R (70%i cosh(x) - 110cosh(x) - 90%i cosh(x) + 54cosh(x) + 12%i) +--R * +--R coth(x)csch(x) +--R + +--R 3 2 +--R - 80%i cosh(x) + 60cosh(x) - 16%i cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 21cosh(x) + 50%i cosh(x) - 50cosh(x) - 48%i cosh(x) +--R + +--R 21cosh(x) + 6%i +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 5 4 3 2 +--R 42%i cosh(x) - 100cosh(x) - 100%i cosh(x) + 96cosh(x) +--R + +--R 42%i cosh(x) - 12 +--R * +--R coth(x)csch(x) +--R + +--R 5 4 3 2 +--R 28cosh(x) - 60%i cosh(x) + 40cosh(x) - 24%i cosh(x) + 16cosh(x) +--R + +--R - 4%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 7cosh(x) + 27%i cosh(x) - 30cosh(x) - 42%i cosh(x) +--R + +--R 2 +--R 27cosh(x) + 15%i cosh(x) - 4 +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 6 5 4 3 +--R 14%i cosh(x) - 54cosh(x) - 60%i cosh(x) + 84cosh(x) +--R + +--R 2 +--R 54%i cosh(x) - 30cosh(x) - 8%i +--R * +--R coth(x)csch(x) +--R + +--R 6 5 3 2 +--R 28cosh(x) - 24%i cosh(x) - 16%i cosh(x) + 48cosh(x) +--R + +--R - 12%i cosh(x) - 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R cosh(x) + 8%i cosh(x) - 9cosh(x) - 18%i cosh(x) + 15cosh(x) +--R + +--R 2 +--R 12%i cosh(x) - 7cosh(x) - 2%i +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 7 6 5 4 +--R 2%i cosh(x) - 16cosh(x) - 18%i cosh(x) + 36cosh(x) +--R + +--R 3 2 +--R 30%i cosh(x) - 24cosh(x) - 14%i cosh(x) + 4 +--R * +--R coth(x)csch(x) +--R + +--R 7 6 5 4 3 +--R 12cosh(x) - 4%i cosh(x) - 12cosh(x) - 4%i cosh(x) + 48cosh(x) +--R + +--R 2 +--R - 12%i cosh(x) - 16cosh(x) - 4%i +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R %i cosh(x) - cosh(x) - 3%i cosh(x) + 3cosh(x) + 3%i cosh(x) +--R + +--R 2 +--R - 3cosh(x) - %i cosh(x) + 1 +--R * +--R 2 +--R coth(x)csch(x) +--R + +--R 7 6 5 4 3 +--R - 2cosh(x) - 2%i cosh(x) + 6cosh(x) + 6%i cosh(x) - 6cosh(x) +--R + +--R 2 +--R - 6%i cosh(x) + 2cosh(x) + 2%i +--R * +--R coth(x)csch(x) +--R + +--R 8 6 4 3 2 +--R 2cosh(x) - 4cosh(x) + 16cosh(x) - 4%i cosh(x) - 8cosh(x) +--R + +--R - 4%i cosh(x) + 2 +--R / +--R 8 7 +--R sinh(x) + (7cosh(x) + 2%i)sinh(x) +--R + +--R 2 6 +--R (21cosh(x) + 13%i cosh(x) - 4)sinh(x) +--R + +--R 3 2 5 +--R (35cosh(x) + 36%i cosh(x) - 21cosh(x) - 6%i)sinh(x) +--R + +--R 4 3 2 4 +--R (35cosh(x) + 55%i cosh(x) - 45cosh(x) - 27%i cosh(x) + 6)sinh(x) +--R + +--R 5 4 3 2 +--R 21cosh(x) + 50%i cosh(x) - 50cosh(x) - 48%i cosh(x) + 21cosh(x) +--R + +--R 6%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 7cosh(x) + 27%i cosh(x) - 30cosh(x) - 42%i cosh(x) + 27cosh(x) +--R + +--R 15%i cosh(x) - 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R cosh(x) + 8%i cosh(x) - 9cosh(x) - 18%i cosh(x) + 15cosh(x) +--R + +--R 2 +--R 12%i cosh(x) - 7cosh(x) - 2%i +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R %i cosh(x) - cosh(x) - 3%i cosh(x) + 3cosh(x) + 3%i cosh(x) +--R + +--R 2 +--R - 3cosh(x) - %i cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 155 + +--S 156 of 552 +t0731:= sech(x)/(a+b*sinh(x))^2 +--R +--R +--R sech(x) +--R (153) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 552 +r0731:= (a^2-b^2)*atan(sinh(x))/(a^2+b^2)^2-_ + a*b*log(cosh(x)^2)/(a^2+b^2)^2+_ + 2*a*b*log(a+b*sinh(x))/(a^2+b^2)^2-b/(a^2+b^2)/(a+b*sinh(x)) +--R +--R +--R (154) +--R 2 2 +--R (2a b sinh(x) + 2a b)log(b sinh(x) + a) +--R + +--R 2 2 2 +--R (- a b sinh(x) - a b)log(cosh(x) ) +--R + +--R 3 2 2 3 3 2 +--R ((- b + a b)sinh(x) - a b + a )atan(sinh(x)) - b - a b +--R / +--R 5 2 3 4 4 3 2 5 +--R (b + 2a b + a b)sinh(x) + a b + 2a b + a +--R Type: Expression(Integer) +--E 157 + +--S 158 of 552 +a0731:= integrate(t0731,x) +--R +--R +--R (155) +--R 2 2 2 2 2 2 +--R - 2a b sinh(x) + (- 4a b cosh(x) - 4a b)sinh(x) - 2a b cosh(x) +--R + +--R 2 2 +--R - 4a b cosh(x) + 2a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 2 +--R 2a b sinh(x) + (4a b cosh(x) + 4a b)sinh(x) + 2a b cosh(x) +--R + +--R 2 2 +--R 4a b cosh(x) - 2a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 2 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + ((- 4b + 4a b)cosh(x) - 4a b + 4a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- 2b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) + 2b - 2a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 3 2 3 2 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) +--R / +--R 5 2 3 4 2 +--R (b + 2a b + a b)sinh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R ((2b + 4a b + 2a b)cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 5 2 3 +--R (b + 2a b + a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) - b - 2a b +--R + +--R 4 +--R - a b +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 552 +m0731:= a0731-r0731 +--R +--R +--R (156) +--R 3 3 3 2 2 2 +--R - 2a b sinh(x) + (- 4a b cosh(x) - 6a b )sinh(x) +--R + +--R 3 2 2 2 3 3 +--R (- 2a b cosh(x) - 8a b cosh(x) + 2a b - 4a b)sinh(x) +--R + +--R 2 2 2 3 2 2 +--R - 2a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R log(b sinh(x) + a) +--R + +--R 3 3 3 2 2 2 +--R a b sinh(x) + (2a b cosh(x) + 3a b )sinh(x) +--R + +--R 3 2 2 2 3 3 2 2 2 +--R (a b cosh(x) + 4a b cosh(x) - a b + 2a b)sinh(x) + a b cosh(x) +--R + +--R 3 2 2 +--R 2a b cosh(x) - a b +--R * +--R 2 +--R log(cosh(x) ) +--R + +--R 3 3 3 2 2 2 +--R - 2a b sinh(x) + (- 4a b cosh(x) - 6a b )sinh(x) +--R + +--R 3 2 2 2 3 3 +--R (- 2a b cosh(x) - 8a b cosh(x) + 2a b - 4a b)sinh(x) +--R + +--R 2 2 2 3 2 2 +--R - 2a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 3 3 3 2 2 2 +--R 2a b sinh(x) + (4a b cosh(x) + 6a b )sinh(x) +--R + +--R 3 2 2 2 3 3 2 2 2 +--R (2a b cosh(x) + 8a b cosh(x) - 2a b + 4a b)sinh(x) + 2a b cosh(x) +--R + +--R 3 2 2 +--R 4a b cosh(x) - 2a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 2 2 3 +--R (- 2b + 2a b )sinh(x) +--R + +--R 4 2 2 3 3 2 +--R ((- 4b + 4a b )cosh(x) - 6a b + 6a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (- 2b + 2a b )cosh(x) + (- 8a b + 8a b)cosh(x) + 2b - 6a b +--R + +--R 4 +--R 4a +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- 2a b + 2a b)cosh(x) + (- 4a b + 4a )cosh(x) + 2a b - 2a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 4 2 2 3 4 2 2 3 3 2 +--R (b - a b )sinh(x) + ((2b - 2a b )cosh(x) + 3a b - 3a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 4 +--R ((b - a b )cosh(x) + (4a b - 4a b)cosh(x) - b + 3a b - 2a ) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) - a b + a b +--R * +--R atan(sinh(x)) +--R + +--R 4 2 2 2 4 2 2 2 4 2 2 +--R (- b - a b )sinh(x) + (b + a b )cosh(x) - b - a b +--R / +--R 6 2 4 4 2 3 +--R (b + 2a b + a b )sinh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 2 +--R ((2b + 4a b + 2a b )cosh(x) + 3a b + 6a b + 3a b)sinh(x) +--R + +--R 6 2 4 4 2 2 5 3 3 5 6 +--R (b + 2a b + a b )cosh(x) + (4a b + 8a b + 4a b)cosh(x) - b +--R + +--R 4 2 6 +--R 3a b + 2a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 6 5 +--R (a b + 2a b + a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) - a b +--R + +--R 3 3 5 +--R - 2a b - a b +--R Type: Expression(Integer) +--E 159 + +--S 160 of 552 +d0731:= D(m0731,x) +--R +--R +--R (157) +--R 2 4 9 2 4 5 3 3 8 +--R 4a b sinh(x) + (18a b cosh(x) - 8a b + 16a b )sinh(x) +--R + +--R 2 4 2 5 3 3 6 2 4 4 2 +--R (28a b cosh(x) + (- 30a b + 62a b )cosh(x) + 8b - 20a b + 28a b ) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 4 3 5 3 3 2 +--R 10a b cosh(x) + (- 36a b + 76a b )cosh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 +--R (23b - 58a b + 91a b )cosh(x) + 16a b - 16a b + 24a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 4 5 3 3 3 +--R - 20a b cosh(x) + (- 2a b + 2a b )cosh(x) +--R + +--R 6 2 4 4 2 2 5 3 3 5 +--R (18b - 32a b + 82a b )cosh(x) + (26a b - 14a b + 68a b)cosh(x) +--R + +--R 6 2 4 4 2 6 +--R 8b + 4a b + 4a b + 8a +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 5 5 3 3 4 +--R - 26a b cosh(x) + (32a b - 72a b )cosh(x) +--R + +--R 6 2 4 4 2 3 +--R (- 7b + 60a b - 31a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 20a b + 64a b + 44a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 +--R (25b - 30a b + 45a b + 20a )cosh(x) + 24a b - 16a b + 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 6 5 3 3 5 +--R - 12a b cosh(x) + (30a b - 62a b )cosh(x) +--R + +--R 6 2 4 4 2 4 +--R (- 20b + 92a b - 96a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 68a b + 124a b - 40a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (28b - 92a b + 108a b + 8a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (62a b - 54a b + 56a b)cosh(x) + 28a b - 20a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 7 5 3 3 6 +--R - 2a b cosh(x) + (12a b - 20a b )cosh(x) +--R + +--R 6 2 4 4 2 5 +--R (- 15b + 46a b - 59a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 56a b + 80a b - 64a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (14b - 86a b + 102a b - 16a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (52a b - 68a b + 72a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 3 5 +--R (b + 46a b - 43a b + 20a )cosh(x) + 16a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 3 7 6 2 4 4 2 6 +--R (2a b - 2a b )cosh(x) + (- 6b + 8a b - 14a b )cosh(x) +--R + +--R 5 3 3 5 5 +--R (- 22a b + 18a b - 28a b)cosh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (4b - 32a b + 40a b - 16a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (14a b - 38a b + 40a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (2b + 24a b - 30a b + 16a )cosh(x) +--R + +--R 5 3 3 5 4 2 +--R (6a b + 22a b - 12a b)cosh(x) + 4a b +--R * +--R sinh(x) +--R + +--R 6 4 2 7 5 5 6 +--R (- b - a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 4 +--R (b - 4a b + 5a b - 4a )cosh(x) + (- 8a b + 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 5 3 3 5 2 +--R (b + 4a b - 7a b + 4a )cosh(x) + (4a b + 8a b - 4a b)cosh(x) +--R + +--R 6 4 2 +--R (- b + 3a b )cosh(x) +--R / +--R 8 2 6 4 4 10 +--R (b + 2a b + a b )sinh(x) +--R + +--R 8 2 6 4 4 7 3 5 5 3 9 +--R ((6b + 12a b + 6a b )cosh(x) + 6a b + 12a b + 6a b )sinh(x) +--R + +--R 8 2 6 4 4 2 7 3 5 5 3 +--R (15b + 30a b + 15a b )cosh(x) + (32a b + 64a b + 32a b )cosh(x) +--R + +--R 2 6 4 4 6 2 +--R 13a b + 26a b + 13a b +--R * +--R 8 +--R sinh(x) +--R + +--R 8 2 6 4 4 3 +--R (20b + 40a b + 20a b )cosh(x) +--R + +--R 7 3 5 5 3 2 +--R (70a b + 140a b + 70a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 7 3 5 5 3 +--R (2b + 66a b + 126a b + 62a b )cosh(x) + 4a b + 20a b + 28a b +--R + +--R 7 +--R 12a b +--R * +--R 7 +--R sinh(x) +--R + +--R 8 2 6 4 4 4 +--R (15b + 30a b + 15a b )cosh(x) +--R + +--R 7 3 5 5 3 3 +--R (80a b + 160a b + 80a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (9b + 137a b + 247a b + 119a b )cosh(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 +--R (24a b + 100a b + 128a b + 52a b)cosh(x) - 2b + 12a b + 34a b +--R + +--R 6 2 8 +--R 24a b + 4a +--R * +--R 6 +--R sinh(x) +--R + +--R 8 2 6 4 4 5 7 3 5 5 3 4 +--R (6b + 12a b + 6a b )cosh(x) + (50a b + 100a b + 50a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (16b + 148a b + 248a b + 116a b )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (58a b + 204a b + 234a b + 88a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 7 3 5 +--R (- 6b + 54a b + 142a b + 98a b + 16a )cosh(x) - 8a b + 4a b +--R + +--R 5 3 7 +--R 32a b + 20a b +--R * +--R 5 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 7 3 5 5 3 5 +--R (b + 2a b + a b )cosh(x) + (16a b + 32a b + 16a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (14b + 87a b + 132a b + 59a b )cosh(x) +--R + +--R 7 3 5 5 3 7 3 +--R (72a b + 216a b + 216a b + 72a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- 7b + 103a b + 251a b + 165a b + 24a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 +--R (- 16a b + 36a b + 120a b + 68a b)cosh(x) - 6a b - 4a b + 10a b +--R + +--R 8 +--R 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 7 3 5 5 3 6 +--R (2a b + 4a b + 2a b )cosh(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (6b + 26a b + 34a b + 14a b )cosh(x) +--R + +--R 7 3 5 5 3 7 4 +--R (48a b + 124a b + 104a b + 28a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (- 4b + 104a b + 236a b + 144a b + 16a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 14a b + 68a b + 178a b + 96a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 7 3 5 +--R (- 2b - 10a b + 10a b + 42a b + 24a )cosh(x) - 4a b - 4a b +--R + +--R 5 3 7 +--R 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (b + 3a b + 3a b + a b )cosh(x) +--R + +--R 7 3 5 5 3 7 5 +--R (16a b + 36a b + 24a b + 4a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- b + 56a b + 119a b + 66a b + 4a )cosh(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 8a b + 56a b + 136a b + 72a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- b - 5a b + 21a b + 53a b + 28a )cosh(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 8 +--R (- 8a b - 4a b + 16a b + 12a b)cosh(x) + b - 6a b - 11a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 3 5 5 3 6 2 6 4 4 6 2 5 +--R (2a b + 4a b + 2a b )cosh(x) + (14a b + 28a b + 14a b )cosh(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 2a b + 24a b + 54a b + 28a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 4a b + 8a b + 28a b + 16a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 2a b + 4a b + 14a b + 8a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 7 5 3 7 +--R (- 10a b - 12a b + 6a b + 8a )cosh(x) + 2a b - 6a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 6 4 4 6 2 6 3 5 5 3 7 5 +--R (a b + 2a b + a b )cosh(x) + (4a b + 8a b + 4a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- a b + 2a b + 7a b + 4a )cosh(x) +--R + +--R 2 6 4 4 6 2 8 2 3 5 5 3 7 +--R (- a b + 2a b + 7a b + 4a )cosh(x) + (- 4a b - 8a b - 4a b)cosh(x) +--R + +--R 2 6 4 4 6 2 +--R a b + 2a b + a b +--R Type: Expression(Integer) +--E 160 + +--S 161 of 552 +t0732:= sech(x)^2/(a+b*sinh(x))^2 +--R +--R +--R 2 +--R sech(x) +--R (158) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 552 +r0732:= -6*a*b^2*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)+_ + 2*a*b*sech(x)/(a^2+b^2)^2-b^3*cosh(x)/(a^2+b^2)^2/(a+b*sinh(x))+_ + (a^2-b^2)*tanh(x)/(a^2+b^2)^2 +--R +--R +--R (159) +--R x +--R a tanh(-) - b +--R 3 2 2 2 +--R (6a b sinh(x) + 6a b )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 2 3 2 +--R ((- b + a b)sinh(x) - a b + a )tanh(x) + 2a b sech(x)sinh(x) +--R + +--R 2 3 +--R 2a b sech(x) - b cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 5 2 3 4 4 3 2 5 | 2 2 +--R ((b + 2a b + a b)sinh(x) + a b + 2a b + a )\|b + a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 552 +a0732:= integrate(t0732,x) +--R +--R +--R (160) +--R 3 4 3 2 2 3 +--R 3a b sinh(x) + (12a b cosh(x) + 6a b )sinh(x) +--R + +--R 3 2 2 2 2 +--R (18a b cosh(x) + 18a b cosh(x))sinh(x) +--R + +--R 3 3 2 2 2 2 2 3 4 +--R (12a b cosh(x) + 18a b cosh(x) + 6a b )sinh(x) + 3a b cosh(x) +--R + +--R 2 2 3 2 2 3 +--R 6a b cosh(x) + 6a b cosh(x) - 3a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 3 2 2 2 +--R 6a b sinh(x) + (18a b cosh(x) + 6a b)sinh(x) +--R + +--R 2 2 2 2 3 2 3 +--R (18a b cosh(x) + 12a b cosh(x) + 2a b - 4a )sinh(x) + 6a b cosh(x) +--R + +--R 2 2 2 3 3 2 +--R 6a b cosh(x) + (2a b - 4a )cosh(x) - 4b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 2 3 4 4 +--R (b + 2a b + a b)sinh(x) +--R + +--R 5 2 3 4 4 3 2 5 3 +--R ((4b + 8a b + 4a b)cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 2 +--R ((6b + 12a b + 6a b)cosh(x) + (6a b + 12a b + 6a )cosh(x))sinh(x) +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (4b + 8a b + 4a b)cosh(x) + (6a b + 12a b + 6a )cosh(x) +--R + +--R 4 3 2 5 +--R 2a b + 4a b + 2a +--R * +--R sinh(x) +--R + +--R 5 2 3 4 4 4 3 2 5 3 +--R (b + 2a b + a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (2a b + 4a b + 2a )cosh(x) - b - 2a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 552 +m0732:= a0732-r0732 +--R +--R +--R (161) +--R 4 5 4 2 3 4 +--R 3a b sinh(x) + (12a b cosh(x) + 9a b )sinh(x) +--R + +--R 4 2 2 3 3 2 3 +--R (18a b cosh(x) + 30a b cosh(x) + 6a b )sinh(x) +--R + +--R 4 3 2 3 2 3 2 2 3 2 +--R (12a b cosh(x) + 36a b cosh(x) + 18a b cosh(x) + 6a b )sinh(x) +--R + +--R 4 4 2 3 3 3 2 2 2 3 +--R 3a b cosh(x) + 18a b cosh(x) + 18a b cosh(x) + 6a b cosh(x) +--R + +--R 4 3 2 +--R - 3a b + 6a b +--R * +--R sinh(x) +--R + +--R 2 3 4 3 2 3 3 2 2 3 +--R 3a b cosh(x) + 6a b cosh(x) + 6a b cosh(x) - 3a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 5 4 2 3 4 +--R - 6a b sinh(x) + (- 24a b cosh(x) - 18a b )sinh(x) +--R + +--R 4 2 2 3 3 2 3 +--R (- 36a b cosh(x) - 60a b cosh(x) - 12a b )sinh(x) +--R + +--R 4 3 2 3 2 3 2 2 3 2 +--R (- 24a b cosh(x) - 72a b cosh(x) - 36a b cosh(x) - 12a b )sinh(x) +--R + +--R 4 4 2 3 3 3 2 2 2 3 +--R - 6a b cosh(x) - 36a b cosh(x) - 36a b cosh(x) - 12a b cosh(x) +--R + +--R 4 3 2 +--R 6a b - 12a b +--R * +--R sinh(x) +--R + +--R 2 3 4 3 2 3 3 2 2 3 +--R - 6a b cosh(x) - 12a b cosh(x) - 12a b cosh(x) + 6a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 2 2 5 +--R (b - a b )sinh(x) +--R + +--R 4 2 2 3 3 4 +--R ((4b - 4a b )cosh(x) + 3a b - 3a b)sinh(x) +--R + +--R 4 2 2 2 3 3 2 2 4 +--R ((6b - 6a b )cosh(x) + (10a b - 10a b)cosh(x) + 2a b - 2a ) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (4b - 4a b )cosh(x) + (12a b - 12a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (6a b - 6a )cosh(x) + 2a b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (b - a b )cosh(x) + (6a b - 6a b)cosh(x) +--R + +--R 2 2 4 2 3 3 4 2 2 +--R (6a b - 6a )cosh(x) + (2a b - 2a b)cosh(x) - b + 3a b +--R + +--R 4 +--R - 2a +--R * +--R sinh(x) +--R + +--R 3 3 4 2 2 4 3 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 2 2 4 3 3 +--R (2a b - 2a )cosh(x) - a b + a b +--R * +--R tanh(x) +--R + +--R 3 5 +--R - 2a b sech(x)sinh(x) +--R + +--R 3 2 2 4 3 4 +--R ((- 8a b cosh(x) - 6a b )sech(x) + b cosh(x) + 6a b )sinh(x) +--R + +--R 3 2 2 2 3 4 2 +--R (- 12a b cosh(x) - 20a b cosh(x) - 4a b)sech(x) + 4b cosh(x) +--R + +--R 3 2 2 +--R 20a b cosh(x) + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R (- 8a b cosh(x) - 24a b cosh(x) - 12a b cosh(x) - 4a b )sech(x) +--R + +--R 4 3 3 2 2 2 3 3 +--R 6b cosh(x) + 24a b cosh(x) + 30a b cosh(x) + 2a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 2 +--R - 2a b cosh(x) - 12a b cosh(x) - 12a b cosh(x) +--R + +--R 2 2 3 3 +--R - 4a b cosh(x) + 2a b - 4a b +--R * +--R sech(x) +--R + +--R 4 4 3 3 2 2 2 +--R 4b cosh(x) + 12a b cosh(x) + 24a b cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (4a b + 8a b)cosh(x) - 4b + 4a b - 4a +--R * +--R sinh(x) +--R + +--R 2 2 4 3 3 3 2 2 +--R (- 2a b cosh(x) - 4a b cosh(x) - 4a b cosh(x) + 2a b )sech(x) +--R + +--R 4 5 3 4 2 2 3 3 3 2 +--R b cosh(x) + 2a b cosh(x) + 6a b cosh(x) + (2a b + 6a b)cosh(x) +--R + +--R 4 2 2 4 3 3 +--R (- b + 2a b - 4a )cosh(x) - 4a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 6 2 4 4 2 5 +--R (b + 2a b + a b )sinh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 4 +--R ((4b + 8a b + 4a b )cosh(x) + 3a b + 6a b + 3a b)sinh(x) +--R + +--R 6 2 4 4 2 2 5 3 3 5 +--R (6b + 12a b + 6a b )cosh(x) + (10a b + 20a b + 10a b)cosh(x) +--R + +--R 2 4 4 2 6 +--R 2a b + 4a b + 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 4 2 3 5 3 3 5 2 +--R (4b + 8a b + 4a b )cosh(x) + (12a b + 24a b + 12a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (6a b + 12a b + 6a )cosh(x) + 2a b + 4a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (b + 2a b + a b )cosh(x) + (6a b + 12a b + 6a b)cosh(x) +--R + +--R 2 4 4 2 6 2 5 3 3 5 6 +--R (6a b + 12a b + 6a )cosh(x) + (2a b + 4a b + 2a b)cosh(x) - b +--R + +--R 4 2 6 +--R 3a b + 2a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 6 3 +--R (a b + 2a b + a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (2a b + 4a b + 2a )cosh(x) - a b - 2a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 164 + +--S 165 of 552 +--d0732:= D(m0732,x) +--E 165 + +--S 166 of 552 +t0733:= sech(x)^3/(a+b*sinh(x))^2 +--R +--R +--R 3 +--R sech(x) +--R (162) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 552 +r0733:= b^2*(3*a^2-b^2)*atan(sinh(x))/(a^2+b^2)^3+_ + 1/2*(a^2-b^2)*atan(sinh(x))/(a^2+b^2)^2-_ + 2*a*b^3*log(cosh(x)^2)/(a^2+b^2)^3+_ + 4*a*b^3*log(a+b*sinh(x))/(a^2+b^2)^3+_ + a*b*sech(x)^2/(a^2+b^2)^2-b^3/(a^2+b^2)^2/(a+b*sinh(x))+_ + 1/2*(a^2-b^2)*sech(x)*tanh(x)/(a^2+b^2)^2 +--R +--R +--R (163) +--R 4 2 3 +--R (8a b sinh(x) + 8a b )log(b sinh(x) + a) +--R + +--R 4 2 3 2 +--R (- 4a b sinh(x) - 4a b )log(cosh(x) ) +--R + +--R 5 2 3 4 4 3 2 5 +--R ((- 3b + 6a b + a b)sinh(x) - 3a b + 6a b + a )atan(sinh(x)) +--R + +--R 5 4 4 5 +--R ((- b + a b)sech(x)sinh(x) + (- a b + a )sech(x))tanh(x) +--R + +--R 4 3 2 2 2 3 4 2 5 2 3 +--R (2a b + 2a b )sech(x) sinh(x) + (2a b + 2a b)sech(x) - 2b - 2a b +--R / +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R (2b + 6a b + 6a b + 2a b)sinh(x) + 2a b + 6a b + 6a b + 2a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 552 +a0733:= integrate(t0733,x) +--R +--R +--R (164) +--R 4 6 4 2 3 5 +--R - 4a b sinh(x) + (- 24a b cosh(x) - 8a b )sinh(x) +--R + +--R 4 2 2 3 4 4 +--R (- 60a b cosh(x) - 40a b cosh(x) - 4a b )sinh(x) +--R + +--R 4 3 2 3 2 4 2 3 3 +--R (- 80a b cosh(x) - 80a b cosh(x) - 16a b cosh(x) - 16a b )sinh(x) +--R + +--R 4 4 2 3 3 4 2 +--R - 60a b cosh(x) - 80a b cosh(x) - 24a b cosh(x) +--R + +--R 2 3 4 +--R - 48a b cosh(x) + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 2 3 4 4 3 +--R - 24a b cosh(x) - 40a b cosh(x) - 16a b cosh(x) +--R + +--R 2 3 2 4 2 3 +--R - 48a b cosh(x) + 8a b cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 6 2 3 5 4 4 2 3 3 +--R - 4a b cosh(x) - 8a b cosh(x) - 4a b cosh(x) - 16a b cosh(x) +--R + +--R 4 2 2 3 4 +--R 4a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 4 6 4 2 3 5 +--R 4a b sinh(x) + (24a b cosh(x) + 8a b )sinh(x) +--R + +--R 4 2 2 3 4 4 +--R (60a b cosh(x) + 40a b cosh(x) + 4a b )sinh(x) +--R + +--R 4 3 2 3 2 4 2 3 3 +--R (80a b cosh(x) + 80a b cosh(x) + 16a b cosh(x) + 16a b )sinh(x) +--R + +--R 4 4 2 3 3 4 2 2 3 +--R 60a b cosh(x) + 80a b cosh(x) + 24a b cosh(x) + 48a b cosh(x) +--R + +--R 4 +--R - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 2 3 4 4 3 2 3 2 +--R 24a b cosh(x) + 40a b cosh(x) + 16a b cosh(x) + 48a b cosh(x) +--R + +--R 4 2 3 +--R - 8a b cosh(x) + 8a b +--R * +--R sinh(x) +--R + +--R 4 6 2 3 5 4 4 2 3 3 +--R 4a b cosh(x) + 8a b cosh(x) + 4a b cosh(x) + 16a b cosh(x) +--R + +--R 4 2 2 3 4 +--R - 4a b cosh(x) + 8a b cosh(x) - 4a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 5 2 3 4 6 +--R (- 3b + 6a b + a b)sinh(x) +--R + +--R 5 2 3 4 4 3 2 5 5 +--R ((- 18b + 36a b + 6a b)cosh(x) - 6a b + 12a b + 2a )sinh(x) +--R + +--R 5 2 3 4 2 +--R (- 45b + 90a b + 15a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 30a b + 60a b + 10a )cosh(x) - 3b + 6a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 3 4 3 +--R (- 60b + 120a b + 20a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 60a b + 120a b + 20a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 12b + 24a b + 4a b)cosh(x) - 12a b + 24a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 4 4 +--R (- 45b + 90a b + 15a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (- 60a b + 120a b + 20a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (- 18b + 36a b + 6a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 36a b + 72a b + 12a )cosh(x) + 3b - 6a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 4 5 +--R (- 18b + 36a b + 6a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (- 30a b + 60a b + 10a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 12b + 24a b + 4a b)cosh(x) +--R + +--R 4 3 2 5 2 5 2 3 4 +--R (- 36a b + 72a b + 12a )cosh(x) + (6b - 12a b - 2a b)cosh(x) +--R + +--R 4 3 2 5 +--R - 6a b + 12a b + 2a +--R * +--R sinh(x) +--R + +--R 5 2 3 4 6 4 3 2 5 5 +--R (- 3b + 6a b + a b)cosh(x) + (- 6a b + 12a b + 2a )cosh(x) +--R + +--R 5 2 3 4 4 4 3 2 5 3 +--R (- 3b + 6a b + a b)cosh(x) + (- 12a b + 24a b + 4a )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 5 +--R (3b - 6a b - a b)cosh(x) + (- 6a b + 12a b + 2a )cosh(x) + 3b +--R + +--R 2 3 4 +--R - 6a b - a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 5 2 3 4 5 +--R (- 3b - 2a b + a b)sinh(x) +--R + +--R 5 2 3 4 4 3 2 5 4 +--R ((- 15b - 10a b + 5a b)cosh(x) + 2a b + 4a b + 2a )sinh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (- 30b - 20a b + 10a b)cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R + +--R 5 2 3 4 +--R - 2b + 4a b + 6a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 30b - 20a b + 10a b)cosh(x) + (12a b + 24a b + 12a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 6b + 12a b + 18a b)cosh(x) - 2a b - 4a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 4 4 4 3 2 5 3 +--R (- 15b - 10a b + 5a b)cosh(x) + (8a b + 16a b + 8a )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (- 6b + 12a b + 18a b)cosh(x) + (- 4a b - 8a b - 4a )cosh(x) +--R + +--R 5 2 3 4 +--R - 3b - 2a b + a b +--R * +--R sinh(x) +--R + +--R 5 2 3 4 5 4 3 2 5 4 +--R (- 3b - 2a b + a b)cosh(x) + (2a b + 4a b + 2a )cosh(x) +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2b + 4a b + 6a b)cosh(x) + (- 2a b - 4a b - 2a )cosh(x) +--R + +--R 5 2 3 4 +--R (- 3b - 2a b + a b)cosh(x) +--R / +--R 7 2 5 4 3 6 6 +--R (b + 3a b + 3a b + a b)sinh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((6b + 18a b + 18a b + 6a b)cosh(x) + 2a b + 6a b + 6a b + 2a ) +--R * +--R 5 +--R sinh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (15b + 45a b + 45a b + 15a b)cosh(x) +--R + +--R 6 3 4 5 2 7 7 2 5 4 3 6 +--R (10a b + 30a b + 30a b + 10a )cosh(x) + b + 3a b + 3a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 5 4 3 6 3 +--R (20b + 60a b + 60a b + 20a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 +--R (20a b + 60a b + 60a b + 20a )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R (4b + 12a b + 12a b + 4a b)cosh(x) + 4a b + 12a b + 12a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 5 4 3 6 4 +--R (15b + 45a b + 45a b + 15a b)cosh(x) +--R + +--R 6 3 4 5 2 7 3 +--R (20a b + 60a b + 60a b + 20a )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (6b + 18a b + 18a b + 6a b)cosh(x) +--R + +--R 6 3 4 5 2 7 7 2 5 4 3 6 +--R (12a b + 36a b + 36a b + 12a )cosh(x) - b - 3a b - 3a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 4 3 6 5 +--R (6b + 18a b + 18a b + 6a b)cosh(x) +--R + +--R 6 3 4 5 2 7 4 +--R (10a b + 30a b + 30a b + 10a )cosh(x) +--R + +--R 7 2 5 4 3 6 3 +--R (4b + 12a b + 12a b + 4a b)cosh(x) +--R + +--R 6 3 4 5 2 7 2 +--R (12a b + 36a b + 36a b + 12a )cosh(x) +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R (- 2b - 6a b - 6a b - 2a b)cosh(x) + 2a b + 6a b + 6a b + 2a +--R * +--R sinh(x) +--R + +--R 7 2 5 4 3 6 6 +--R (b + 3a b + 3a b + a b)cosh(x) +--R + +--R 6 3 4 5 2 7 5 +--R (2a b + 6a b + 6a b + 2a )cosh(x) +--R + +--R 7 2 5 4 3 6 4 +--R (b + 3a b + 3a b + a b)cosh(x) +--R + +--R 6 3 4 5 2 7 3 +--R (4a b + 12a b + 12a b + 4a )cosh(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- b - 3a b - 3a b - a b)cosh(x) +--R + +--R 6 3 4 5 2 7 7 2 5 4 3 6 +--R (2a b + 6a b + 6a b + 2a )cosh(x) - b - 3a b - 3a b - a b +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 552 +m0733:= a0733-r0733 +--R +--R +--R (165) +--R 5 7 5 2 4 6 +--R - 8a b sinh(x) + (- 48a b cosh(x) - 24a b )sinh(x) +--R + +--R 5 2 2 4 5 3 3 5 +--R (- 120a b cosh(x) - 128a b cosh(x) - 8a b - 16a b )sinh(x) +--R + +--R 5 3 2 4 2 5 3 3 +--R - 160a b cosh(x) - 280a b cosh(x) + (- 32a b - 80a b )cosh(x) +--R + +--R 2 4 +--R - 40a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 4 3 +--R - 120a b cosh(x) - 320a b cosh(x) +--R + +--R 5 3 3 2 2 4 5 3 3 +--R (- 48a b - 160a b )cosh(x) - 128a b cosh(x) + 8a b - 32a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 2 4 4 5 3 3 3 +--R - 48a b cosh(x) - 200a b cosh(x) + (- 32a b - 160a b )cosh(x) +--R + +--R 2 4 2 5 3 3 2 4 +--R - 144a b cosh(x) + (16a b - 96a b )cosh(x) - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 6 2 4 5 5 3 3 4 +--R - 8a b cosh(x) - 64a b cosh(x) + (- 8a b - 80a b )cosh(x) +--R + +--R 2 4 3 5 3 3 2 5 3 3 +--R - 64a b cosh(x) + (8a b - 96a b )cosh(x) + 8a b - 16a b +--R * +--R sinh(x) +--R + +--R 2 4 6 3 3 5 2 4 4 3 3 3 +--R - 8a b cosh(x) - 16a b cosh(x) - 8a b cosh(x) - 32a b cosh(x) +--R + +--R 2 4 2 3 3 2 4 +--R 8a b cosh(x) - 16a b cosh(x) + 8a b +--R * +--R log(b sinh(x) + a) +--R + +--R 5 7 5 2 4 6 +--R 4a b sinh(x) + (24a b cosh(x) + 12a b )sinh(x) +--R + +--R 5 2 2 4 5 3 3 5 +--R (60a b cosh(x) + 64a b cosh(x) + 4a b + 8a b )sinh(x) +--R + +--R 5 3 2 4 2 5 3 3 +--R 80a b cosh(x) + 140a b cosh(x) + (16a b + 40a b )cosh(x) +--R + +--R 2 4 +--R 20a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 4 3 5 3 3 2 +--R 60a b cosh(x) + 160a b cosh(x) + (24a b + 80a b )cosh(x) +--R + +--R 2 4 5 3 3 +--R 64a b cosh(x) - 4a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 2 4 4 5 3 3 3 +--R 24a b cosh(x) + 100a b cosh(x) + (16a b + 80a b )cosh(x) +--R + +--R 2 4 2 5 3 3 2 4 +--R 72a b cosh(x) + (- 8a b + 48a b )cosh(x) + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 6 2 4 5 5 3 3 4 +--R 4a b cosh(x) + 32a b cosh(x) + (4a b + 40a b )cosh(x) +--R + +--R 2 4 3 5 3 3 2 5 3 3 +--R 32a b cosh(x) + (- 4a b + 48a b )cosh(x) - 4a b + 8a b +--R * +--R sinh(x) +--R + +--R 2 4 6 3 3 5 2 4 4 3 3 3 +--R 4a b cosh(x) + 8a b cosh(x) + 4a b cosh(x) + 16a b cosh(x) +--R + +--R 2 4 2 3 3 2 4 +--R - 4a b cosh(x) + 8a b cosh(x) - 4a b +--R * +--R 2 +--R log(cosh(x) ) +--R + +--R 5 7 5 2 4 6 +--R - 8a b sinh(x) + (- 48a b cosh(x) - 24a b )sinh(x) +--R + +--R 5 2 2 4 5 3 3 5 +--R (- 120a b cosh(x) - 128a b cosh(x) - 8a b - 16a b )sinh(x) +--R + +--R 5 3 2 4 2 5 3 3 +--R - 160a b cosh(x) - 280a b cosh(x) + (- 32a b - 80a b )cosh(x) +--R + +--R 2 4 +--R - 40a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 4 3 +--R - 120a b cosh(x) - 320a b cosh(x) +--R + +--R 5 3 3 2 2 4 5 3 3 +--R (- 48a b - 160a b )cosh(x) - 128a b cosh(x) + 8a b - 32a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 2 4 4 5 3 3 3 +--R - 48a b cosh(x) - 200a b cosh(x) + (- 32a b - 160a b )cosh(x) +--R + +--R 2 4 2 5 3 3 2 4 +--R - 144a b cosh(x) + (16a b - 96a b )cosh(x) - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 6 2 4 5 5 3 3 4 +--R - 8a b cosh(x) - 64a b cosh(x) + (- 8a b - 80a b )cosh(x) +--R + +--R 2 4 3 5 3 3 2 5 3 3 +--R - 64a b cosh(x) + (8a b - 96a b )cosh(x) + 8a b - 16a b +--R * +--R sinh(x) +--R + +--R 2 4 6 3 3 5 2 4 4 3 3 3 +--R - 8a b cosh(x) - 16a b cosh(x) - 8a b cosh(x) - 32a b cosh(x) +--R + +--R 2 4 2 3 3 2 4 +--R 8a b cosh(x) - 16a b cosh(x) + 8a b +--R * +--R 2cosh(x) +--R log(- -----------------) +--R sinh(x) - cosh(x) +--R + +--R 5 7 5 2 4 6 +--R 8a b sinh(x) + (48a b cosh(x) + 24a b )sinh(x) +--R + +--R 5 2 2 4 5 3 3 5 +--R (120a b cosh(x) + 128a b cosh(x) + 8a b + 16a b )sinh(x) +--R + +--R 5 3 2 4 2 5 3 3 +--R 160a b cosh(x) + 280a b cosh(x) + (32a b + 80a b )cosh(x) +--R + +--R 2 4 +--R 40a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 4 3 5 3 3 2 +--R 120a b cosh(x) + 320a b cosh(x) + (48a b + 160a b )cosh(x) +--R + +--R 2 4 5 3 3 +--R 128a b cosh(x) - 8a b + 32a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 5 2 4 4 5 3 3 3 +--R 48a b cosh(x) + 200a b cosh(x) + (32a b + 160a b )cosh(x) +--R + +--R 2 4 2 5 3 3 2 4 +--R 144a b cosh(x) + (- 16a b + 96a b )cosh(x) + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 6 2 4 5 5 3 3 4 +--R 8a b cosh(x) + 64a b cosh(x) + (8a b + 80a b )cosh(x) +--R + +--R 2 4 3 5 3 3 2 5 3 3 +--R 64a b cosh(x) + (- 8a b + 96a b )cosh(x) - 8a b + 16a b +--R * +--R sinh(x) +--R + +--R 2 4 6 3 3 5 2 4 4 3 3 3 +--R 8a b cosh(x) + 16a b cosh(x) + 8a b cosh(x) + 32a b cosh(x) +--R + +--R 2 4 2 3 3 2 4 +--R - 8a b cosh(x) + 16a b cosh(x) - 8a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 2 4 4 2 7 +--R (- 6b + 12a b + 2a b )sinh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 6 +--R ((- 36b + 72a b + 12a b )cosh(x) - 18a b + 36a b + 6a b)sinh(x) +--R + +--R 6 2 4 4 2 2 +--R (- 90b + 180a b + 30a b )cosh(x) +--R + +--R 5 3 3 5 6 4 2 6 +--R (- 96a b + 192a b + 32a b)cosh(x) - 6b + 26a b + 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 6 2 4 4 2 3 +--R (- 120b + 240a b + 40a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 210a b + 420a b + 70a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 +--R (- 24b - 12a b + 128a b + 20a )cosh(x) - 30a b + 60a b + 10a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 4 4 2 4 +--R (- 90b + 180a b + 30a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 240a b + 480a b + 80a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- 36b - 48a b + 252a b + 40a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (- 96a b + 192a b + 32a b)cosh(x) + 6b - 36a b + 46a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 4 2 5 +--R (- 36b + 72a b + 12a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 150a b + 300a b + 50a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (- 24b - 72a b + 248a b + 40a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 108a b + 216a b + 36a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 +--R (12b - 96a b + 140a b + 24a )cosh(x) - 6a b + 12a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 4 2 6 +--R (- 6b + 12a b + 2a b )cosh(x) +--R + +--R 5 3 3 5 5 +--R (- 48a b + 96a b + 16a b)cosh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 6b - 48a b + 122a b + 20a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 48a b + 96a b + 16a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 +--R (6b - 84a b + 142a b + 24a )cosh(x) + 6b - 24a b + 22a b +--R + +--R 6 +--R 4a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 5 +--R (- 6a b + 12a b + 2a b)cosh(x) + (- 12a b + 24a b + 4a )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 6 3 +--R (- 6a b + 12a b + 2a b)cosh(x) + (- 24a b + 48a b + 8a )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 6 +--R (6a b - 12a b - 2a b)cosh(x) + (- 12a b + 24a b + 4a )cosh(x) +--R + +--R 5 3 3 5 +--R 6a b - 12a b - 2a b +--R * +--R atan(sinh(x) + cosh(x)) +--R + +--R 6 2 4 4 2 7 +--R (3b - 6a b - a b )sinh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 6 +--R ((18b - 36a b - 6a b )cosh(x) + 9a b - 18a b - 3a b)sinh(x) +--R + +--R 6 2 4 4 2 2 +--R (45b - 90a b - 15a b )cosh(x) +--R + +--R 5 3 3 5 6 4 2 6 +--R (48a b - 96a b - 16a b)cosh(x) + 3b - 13a b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 6 2 4 4 2 3 +--R (60b - 120a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (105a b - 210a b - 35a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 +--R (12b + 6a b - 64a b - 10a )cosh(x) + 15a b - 30a b - 5a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 4 4 2 4 +--R (45b - 90a b - 15a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (120a b - 240a b - 40a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (18b + 24a b - 126a b - 20a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (48a b - 96a b - 16a b)cosh(x) - 3b + 18a b - 23a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 4 2 5 +--R (18b - 36a b - 6a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (75a b - 150a b - 25a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (12b + 36a b - 124a b - 20a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (54a b - 108a b - 18a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 +--R (- 6b + 48a b - 70a b - 12a )cosh(x) + 3a b - 6a b - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 5 +--R (3b - 6a b - a b )cosh(x) + (24a b - 48a b - 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (3b + 24a b - 61a b - 10a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (24a b - 48a b - 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 +--R (- 3b + 42a b - 71a b - 12a )cosh(x) - 3b + 12a b - 11a b +--R + +--R 6 +--R - 2a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 5 +--R (3a b - 6a b - a b)cosh(x) + (6a b - 12a b - 2a )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 6 3 +--R (3a b - 6a b - a b)cosh(x) + (12a b - 24a b - 4a )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 6 +--R (- 3a b + 6a b + a b)cosh(x) + (6a b - 12a b - 2a )cosh(x) +--R + +--R 5 3 3 5 +--R - 3a b + 6a b + a b +--R * +--R atan(sinh(x)) +--R + +--R 6 4 2 7 +--R (b - a b )sech(x)sinh(x) +--R + +--R 6 4 2 5 5 6 +--R ((6b - 6a b )cosh(x) + 3a b - 3a b)sech(x)sinh(x) +--R + +--R 6 4 2 2 5 5 6 2 4 +--R (15b - 15a b )cosh(x) + (16a b - 16a b)cosh(x) + b + 2a b +--R + +--R 4 2 6 +--R - a b - 2a +--R * +--R 5 +--R sech(x)sinh(x) +--R + +--R 6 4 2 3 5 5 2 +--R (20b - 20a b )cosh(x) + (35a b - 35a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 5 +--R (4b + 10a b - 4a b - 10a )cosh(x) + 5a b - 5a b +--R * +--R 4 +--R sech(x)sinh(x) +--R + +--R 6 4 2 4 5 5 3 +--R (15b - 15a b )cosh(x) + (40a b - 40a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 5 5 +--R (6b + 20a b - 6a b - 20a )cosh(x) + (16a b - 16a b)cosh(x) +--R + +--R 6 2 4 4 2 6 +--R - b + 4a b + a b - 4a +--R * +--R 3 +--R sech(x)sinh(x) +--R + +--R 6 4 2 5 5 5 4 +--R (6b - 6a b )cosh(x) + (25a b - 25a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 5 5 2 +--R (4b + 20a b - 4a b - 20a )cosh(x) + (18a b - 18a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 5 +--R (- 2b + 12a b + 2a b - 12a )cosh(x) + a b - a b +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 6 4 2 6 5 5 5 +--R (b - a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 4 5 5 3 +--R (b + 10a b - a b - 10a )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (- b + 12a b + a b - 12a )cosh(x) - b + 2a b + a b - 2a +--R * +--R sech(x)sinh(x) +--R + +--R 5 5 6 2 4 6 5 +--R (a b - a b)cosh(x) + (2a b - 2a )cosh(x) +--R + +--R 5 5 4 2 4 6 3 +--R (a b - a b)cosh(x) + (4a b - 4a )cosh(x) +--R + +--R 5 5 2 2 4 6 5 5 +--R (- a b + a b)cosh(x) + (2a b - 2a )cosh(x) - a b + a b +--R * +--R sech(x) +--R * +--R tanh(x) +--R + +--R 5 3 3 2 7 +--R (- 2a b - 2a b )sech(x) sinh(x) +--R + +--R 5 3 3 2 4 4 2 2 6 2 4 +--R ((- 12a b - 12a b )cosh(x) - 6a b - 6a b )sech(x) - 4b - 2a b +--R + +--R 4 2 +--R 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 5 3 3 2 2 4 4 2 5 +--R (- 30a b - 30a b )cosh(x) + (- 32a b - 32a b )cosh(x) - 2a b +--R + +--R 3 3 5 +--R - 6a b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 2 4 4 2 5 3 3 5 +--R (- 18b - 8a b + 10a b )cosh(x) + 2a b + 8a b + 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 3 2 4 4 2 2 +--R (- 40a b - 40a b )cosh(x) + (- 70a b - 70a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 8a b - 28a b - 20a b)cosh(x) - 10a b - 10a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 2 4 4 2 2 5 3 3 5 +--R (- 30b - 10a b + 20a b )cosh(x) + (6a b + 32a b + 26a b)cosh(x) +--R + +--R 6 2 4 4 2 6 +--R - 2b + 14a b + 20a b + 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (- 30a b - 30a b )cosh(x) + (- 80a b - 80a b )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 +--R (- 12a b - 52a b - 40a b)cosh(x) + (- 32a b - 32a b )cosh(x) +--R + +--R 5 3 3 5 +--R 2a b - 6a b - 8a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 4 2 3 5 3 3 5 2 +--R (- 20b + 20a b )cosh(x) + (4a b + 48a b + 44a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 3 5 +--R (- 4b + 48a b + 68a b + 16a )cosh(x) + 8a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 3 3 5 2 4 4 2 4 +--R (- 12a b - 12a b )cosh(x) + (- 50a b - 50a b )cosh(x) +--R + +--R 5 3 3 5 3 2 4 4 2 2 +--R (- 8a b - 48a b - 40a b)cosh(x) + (- 36a b - 36a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (4a b - 20a b - 24a b)cosh(x) - 2a b - 2a b +--R * +--R 2 +--R sech(x) +--R + +--R 2 4 4 2 4 5 3 3 5 3 +--R (10a b + 10a b )cosh(x) + (- 4a b + 32a b + 36a b)cosh(x) +--R + +--R 2 4 4 2 6 2 5 3 3 5 +--R (60a b + 84a b + 24a )cosh(x) + (4a b + 32a b + 28a b)cosh(x) +--R + +--R 6 2 4 4 2 6 +--R - 8b - 10a b - 6a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 3 6 2 4 4 2 5 +--R (- 2a b - 2a b )cosh(x) + (- 16a b - 16a b )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 3 +--R (- 2a b - 22a b - 20a b)cosh(x) + (- 16a b - 16a b )cosh(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (2a b - 22a b - 24a b)cosh(x) + 2a b - 2a b - 4a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 2 4 4 2 5 5 3 3 5 4 +--R (6b + 8a b + 2a b )cosh(x) + (- 6a b + 8a b + 14a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (4b + 32a b + 44a b + 16a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (8a b + 40a b + 32a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 5 +--R (- 10b - 16a b - 14a b - 8a )cosh(x) - 2a b + 2a b +--R * +--R sinh(x) +--R + +--R 2 4 4 2 6 3 3 5 5 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (- 2a b - 2a b )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 4 2 +--R (2a b + 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) + 2a b + 2a b +--R * +--R 2 +--R sech(x) +--R + +--R 6 2 4 6 5 5 5 +--R (2b + 2a b )cosh(x) + (- 2a b + 2a b)cosh(x) +--R + +--R 6 2 4 4 2 6 4 5 3 3 5 3 +--R (2b + 6a b + 8a b + 4a )cosh(x) + (4a b + 16a b + 12a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 5 5 6 +--R (- 2b - 6a b - 8a b - 4a )cosh(x) + (- 2a b + 2a b)cosh(x) - 2b +--R + +--R 2 4 +--R - 2a b +--R / +--R 8 2 6 4 4 6 2 7 +--R (2b + 6a b + 6a b + 2a b )sinh(x) +--R + +--R 8 2 6 4 4 6 2 7 3 5 5 3 +--R (12b + 36a b + 36a b + 12a b )cosh(x) + 6a b + 18a b + 18a b +--R + +--R 7 +--R 6a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (30b + 90a b + 90a b + 30a b )cosh(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 +--R (32a b + 96a b + 96a b + 32a b)cosh(x) + 2b + 10a b + 18a b +--R + +--R 6 2 8 +--R 14a b + 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (40b + 120a b + 120a b + 40a b )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (70a b + 210a b + 210a b + 70a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 7 3 5 +--R (8b + 44a b + 84a b + 68a b + 20a )cosh(x) + 10a b + 30a b +--R + +--R 5 3 7 +--R 30a b + 10a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (30b + 90a b + 90a b + 30a b )cosh(x) +--R + +--R 7 3 5 5 3 7 3 +--R (80a b + 240a b + 240a b + 80a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (12b + 76a b + 156a b + 132a b + 40a )cosh(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 +--R (32a b + 96a b + 96a b + 32a b)cosh(x) - 2b + 2a b + 18a b +--R + +--R 6 2 8 +--R 22a b + 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (12b + 36a b + 36a b + 12a b )cosh(x) +--R + +--R 7 3 5 5 3 7 4 +--R (50a b + 150a b + 150a b + 50a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (8b + 64a b + 144a b + 128a b + 40a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (36a b + 108a b + 108a b + 36a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 7 3 5 +--R (- 4b + 12a b + 60a b + 68a b + 24a )cosh(x) + 2a b + 6a b +--R + +--R 5 3 7 +--R 6a b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (2b + 6a b + 6a b + 2a b )cosh(x) +--R + +--R 7 3 5 5 3 7 5 +--R (16a b + 48a b + 48a b + 16a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (2b + 26a b + 66a b + 62a b + 20a )cosh(x) +--R + +--R 7 3 5 5 3 7 3 +--R (16a b + 48a b + 48a b + 16a b)cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 8 2 6 +--R (- 2b + 18a b + 66a b + 70a b + 24a )cosh(x) - 2b - 2a b +--R + +--R 4 4 6 2 8 +--R 6a b + 10a b + 4a +--R * +--R sinh(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (4a b + 12a b + 12a b + 4a )cosh(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b + 6a b + 6a b + 2a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (8a b + 24a b + 24a b + 8a )cosh(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 2a b - 6a b - 6a b - 2a b)cosh(x) +--R + +--R 2 6 4 4 6 2 8 7 3 5 5 3 7 +--R (4a b + 12a b + 12a b + 4a )cosh(x) - 2a b - 6a b - 6a b - 2a b +--R Type: Expression(Integer) +--E 169 + +--S 170 of 552 +--d0733:= D(m0733,x) +--E 170 + +--S 171 of 552 +t0734:= sech(x)/(%i+sinh(x))^2 +--R +--R +--R sech(x) +--R (166) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 171 + +--S 172 of 552 +r0734:= -1/4*atan(sinh(x))-1/4*%i/(%i+sinh(x))^2-1/(4*%i+4*sinh(x)) +--R +--R +--R 2 +--R (- sinh(x) - 2%i sinh(x) + 1)atan(sinh(x)) - sinh(x) - 2%i +--R (167) ----------------------------------------------------------- +--R 2 +--R 4sinh(x) + 8%i sinh(x) - 4 +--R Type: Expression(Complex(Integer)) +--E 172 + +--S 173 of 552 +a0734:= integrate(t0734,x) +--R +--R +--R (168) +--R 4 3 +--R %i sinh(x) + (4%i cosh(x) - 4)sinh(x) +--R + +--R 2 2 +--R (6%i cosh(x) - 12cosh(x) - 6%i)sinh(x) +--R + +--R 3 2 4 +--R (4%i cosh(x) - 12cosh(x) - 12%i cosh(x) + 4)sinh(x) + %i cosh(x) +--R + +--R 3 2 +--R - 4cosh(x) - 6%i cosh(x) + 4cosh(x) + %i +--R * +--R sinh(x) + cosh(x) - %i +--R log(----------------------) +--R sinh(x) + cosh(x) + %i +--R + +--R 3 2 +--R - 2sinh(x) + (- 6cosh(x) - 8%i)sinh(x) +--R + +--R 2 3 2 +--R (- 6cosh(x) - 16%i cosh(x) + 2)sinh(x) - 2cosh(x) - 8%i cosh(x) +--R + +--R 2cosh(x) +--R / +--R 4 3 +--R 4sinh(x) + (16cosh(x) + 16%i)sinh(x) +--R + +--R 2 2 +--R (24cosh(x) + 48%i cosh(x) - 24)sinh(x) +--R + +--R 3 2 4 +--R (16cosh(x) + 48%i cosh(x) - 48cosh(x) - 16%i)sinh(x) + 4cosh(x) +--R + +--R 3 2 +--R 16%i cosh(x) - 24cosh(x) - 16%i cosh(x) + 4 +--R Type: Union(Expression(Complex(Integer)),...) +--E 173 + +--S 174 of 552 +m0734:= a0734-r0734 +--R +--R +--R (169) +--R 6 5 +--R %i sinh(x) + (4%i cosh(x) - 6)sinh(x) +--R + +--R 2 4 +--R (6%i cosh(x) - 20cosh(x) - 15%i)sinh(x) +--R + +--R 3 2 3 +--R (4%i cosh(x) - 24cosh(x) - 40%i cosh(x) + 20)sinh(x) +--R + +--R 4 3 2 2 +--R (%i cosh(x) - 12cosh(x) - 36%i cosh(x) + 40cosh(x) + 15%i)sinh(x) +--R + +--R 4 3 2 +--R (- 2cosh(x) - 12%i cosh(x) + 24cosh(x) + 20%i cosh(x) - 6)sinh(x) +--R + +--R 4 3 2 +--R - %i cosh(x) + 4cosh(x) + 6%i cosh(x) - 4cosh(x) - %i +--R * +--R sinh(x) + cosh(x) - %i +--R log(----------------------) +--R sinh(x) + cosh(x) + %i +--R + +--R 6 5 +--R sinh(x) + (4cosh(x) + 6%i)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) + 20%i cosh(x) - 15)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) + 24%i cosh(x) - 40cosh(x) - 20%i)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) + 12%i cosh(x) - 36cosh(x) - 40%i cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 +--R (2%i cosh(x) - 12cosh(x) - 24%i cosh(x) + 20cosh(x) + 6%i)sinh(x) +--R + +--R 4 3 2 +--R - cosh(x) - 4%i cosh(x) + 6cosh(x) + 4%i cosh(x) - 1 +--R * +--R atan(sinh(x)) +--R + +--R 5 4 3 +--R - sinh(x) + (- 2cosh(x) - 6%i)sinh(x) + (- 8%i cosh(x) + 6)sinh(x) +--R + +--R 3 2 2 +--R (2cosh(x) + 4%i cosh(x) + 4cosh(x) - 4%i)sinh(x) +--R + +--R 4 3 2 +--R (cosh(x) + 8%i cosh(x) - 8cosh(x) - 8%i cosh(x) + 7)sinh(x) +--R + +--R 4 3 2 +--R 2%i cosh(x) - 6cosh(x) - 4%i cosh(x) + 6cosh(x) + 2%i +--R / +--R 6 5 +--R 4sinh(x) + (16cosh(x) + 24%i)sinh(x) +--R + +--R 2 4 +--R (24cosh(x) + 80%i cosh(x) - 60)sinh(x) +--R + +--R 3 2 3 +--R (16cosh(x) + 96%i cosh(x) - 160cosh(x) - 80%i)sinh(x) +--R + +--R 4 3 2 2 +--R (4cosh(x) + 48%i cosh(x) - 144cosh(x) - 160%i cosh(x) + 60)sinh(x) +--R + +--R 4 3 2 +--R (8%i cosh(x) - 48cosh(x) - 96%i cosh(x) + 80cosh(x) + 24%i)sinh(x) +--R + +--R 4 3 2 +--R - 4cosh(x) - 16%i cosh(x) + 24cosh(x) + 16%i cosh(x) - 4 +--R Type: Expression(Complex(Integer)) +--E 174 + +--S 175 of 552 +d0734:= D(m0734,x) +--R +--R +--R (170) +--R 7 6 +--R 8sinh(x) + (23cosh(x) + 16%i)sinh(x) +--R + +--R 2 5 +--R (18cosh(x) + 44%i cosh(x))sinh(x) +--R + +--R 3 2 4 +--R (- 7cosh(x) + 28%i cosh(x) + 5cosh(x) + 16%i)sinh(x) +--R + +--R 4 3 2 3 +--R (- 20cosh(x) - 24%i cosh(x) + 20cosh(x) + 48%i cosh(x) - 8)sinh(x) +--R + +--R 5 4 3 2 +--R (- 15cosh(x) - 40%i cosh(x) + 30cosh(x) + 48%i cosh(x) - 19cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 6cosh(x) - 20%i cosh(x) + 20cosh(x) + 16%i cosh(x) - 14cosh(x) +--R + +--R 4%i cosh(x) +--R * +--R sinh(x) +--R + +--R 7 6 5 3 2 +--R - cosh(x) - 4%i cosh(x) + 5cosh(x) - 3cosh(x) + 4%i cosh(x) - cosh(x) +--R / +--R 10 9 +--R sinh(x) + (6cosh(x) + 6%i)sinh(x) +--R + +--R 2 8 +--R (15cosh(x) + 32%i cosh(x) - 13)sinh(x) +--R + +--R 3 2 7 +--R (20cosh(x) + 70%i cosh(x) - 60cosh(x) - 8%i)sinh(x) +--R + +--R 4 3 2 6 +--R (15cosh(x) + 80%i cosh(x) - 110cosh(x) - 28%i cosh(x) - 14)sinh(x) +--R + +--R 5 4 3 2 +--R 6cosh(x) + 50%i cosh(x) - 100cosh(x) - 30%i cosh(x) - 56cosh(x) +--R + +--R - 28%i +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 4 2 +--R cosh(x) + 16%i cosh(x) - 45cosh(x) - 100cosh(x) - 84%i cosh(x) +--R + +--R 14 +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 2%i cosh(x) - 8cosh(x) + 20%i cosh(x) - 100cosh(x) +--R + +--R 2 +--R - 110%i cosh(x) + 28cosh(x) - 8%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 12%i cosh(x) - 55cosh(x) - 80%i cosh(x) + 30cosh(x) +--R + +--R - 20%i cosh(x) + 13 +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 2%i cosh(x) - 14cosh(x) - 30%i cosh(x) + 20cosh(x) +--R + +--R 2 +--R - 10%i cosh(x) + 18cosh(x) + 6%i +--R * +--R sinh(x) +--R + +--R 6 5 4 2 +--R - cosh(x) - 4%i cosh(x) + 5cosh(x) + 5cosh(x) + 4%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 175 + +--S 176 of 552 +t0735:= sech(x)^2/(%i+sinh(x))^2 +--R +--R +--R 2 +--R sech(x) +--R (171) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 176 + +--S 177 of 552 +r0735:= 1/5/cosh(x)^5*(-2*cosh(x)^4*sinh(x)-sinh(x)*cosh(x)^2-2*sinh(x)+2*%i) +--R +--R +--R 4 2 +--R (- 2cosh(x) - cosh(x) - 2)sinh(x) + 2%i +--R (172) ----------------------------------------- +--R 5 +--R 5cosh(x) +--R Type: Expression(Complex(Integer)) +--E 177 + +--S 178 of 552 +a0735:= integrate(t0735,x) +--R +--R +--R (173) +--R - 24sinh(x) - 16cosh(x) - 16%i +--R / +--R 5 4 +--R 5sinh(x) + (25cosh(x) + 20%i)sinh(x) +--R + +--R 2 3 +--R (50cosh(x) + 80%i cosh(x) - 25)sinh(x) +--R + +--R 3 2 2 +--R (50cosh(x) + 120%i cosh(x) - 75cosh(x))sinh(x) +--R + +--R 4 3 2 5 +--R (25cosh(x) + 80%i cosh(x) - 75cosh(x) - 30)sinh(x) + 5cosh(x) +--R + +--R 4 3 +--R 20%i cosh(x) - 25cosh(x) - 20cosh(x) - 20%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 178 + +--S 179 of 552 +m0735:= a0735-r0735 +--R +--R +--R (174) +--R 4 2 6 +--R (2cosh(x) + cosh(x) + 2)sinh(x) +--R + +--R 5 4 3 2 +--R 10cosh(x) + 8%i cosh(x) + 5cosh(x) + 4%i cosh(x) + 10cosh(x) +--R + +--R 6%i +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 3 2 +--R 20cosh(x) + 32%i cosh(x) + 16%i cosh(x) + 15cosh(x) +--R + +--R 22%i cosh(x) - 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 20cosh(x) + 48%i cosh(x) - 20cosh(x) + 24%i cosh(x) + 5cosh(x) +--R + +--R 2 +--R 28%i cosh(x) + 2cosh(x) + 10%i +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 10cosh(x) + 32%i cosh(x) - 25cosh(x) + 16%i cosh(x) - 17cosh(x) +--R + +--R 3 2 +--R 12%i cosh(x) + 12cosh(x) + 30%i cosh(x) - 12 +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 7 6 5 +--R 2cosh(x) + 8%i cosh(x) - 9cosh(x) + 4%i cosh(x) - 35cosh(x) +--R + +--R 4 3 2 +--R - 10%i cosh(x) + 18cosh(x) + 26%i cosh(x) - 8cosh(x) + 4%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 16cosh(x) - 18%i cosh(x) + 8cosh(x) + 10%i cosh(x) + 8%i cosh(x) - 8 +--R / +--R 5 5 6 5 4 +--R 5cosh(x) sinh(x) + (25cosh(x) + 20%i cosh(x) )sinh(x) +--R + +--R 7 6 5 3 +--R (50cosh(x) + 80%i cosh(x) - 25cosh(x) )sinh(x) +--R + +--R 8 7 6 2 +--R (50cosh(x) + 120%i cosh(x) - 75cosh(x) )sinh(x) +--R + +--R 9 8 7 5 +--R (25cosh(x) + 80%i cosh(x) - 75cosh(x) - 30cosh(x) )sinh(x) +--R + +--R 10 9 8 6 5 +--R 5cosh(x) + 20%i cosh(x) - 25cosh(x) - 20cosh(x) - 20%i cosh(x) +--R Type: Expression(Complex(Integer)) +--E 179 + +--S 180 of 552 +d0735:= D(m0735,x) +--R +--R +--R (175) +--R 4 2 12 +--R (- 2cosh(x) - 3cosh(x) - 10)sinh(x) +--R + +--R 5 4 3 2 +--R - 20cosh(x) - 16%i cosh(x) - 30cosh(x) - 24%i cosh(x) +--R + +--R - 100cosh(x) - 70%i +--R * +--R 11 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 88cosh(x) - 144%i cosh(x) - 82cosh(x) - 216%i cosh(x) +--R + +--R 2 +--R - 370cosh(x) - 620%i cosh(x) + 180 +--R * +--R 10 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 220cosh(x) - 560%i cosh(x) + 66cosh(x) - 776%i cosh(x) +--R + +--R 3 2 +--R - 556cosh(x) - 2294%i cosh(x) + 1360cosh(x) + 140%i +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 330cosh(x) - 1200%i cosh(x) + 819cosh(x) - 1384%i cosh(x) +--R + +--R 4 3 2 +--R 122cosh(x) - 4536%i cosh(x) + 4309cosh(x) + 720%i cosh(x) + 270 +--R * +--R 8 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - 264cosh(x) - 1440%i cosh(x) + 1860cosh(x) - 1136%i cosh(x) +--R + +--R 5 4 3 2 +--R 1716cosh(x) - 4812%i cosh(x) + 7178cosh(x) + 1208%i cosh(x) +--R + +--R 1980cosh(x) + 690%i +--R * +--R 7 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - 672%i cosh(x) + 1764cosh(x) - 112%i cosh(x) + 2752cosh(x) +--R + +--R 5 4 3 2 +--R - 1768%i cosh(x) + 5848cosh(x) - 328%i cosh(x) + 6000cosh(x) +--R + +--R 3460%i cosh(x) - 360 +--R * +--R 6 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 264cosh(x) + 672%i cosh(x) - 108cosh(x) + 112%i cosh(x) +--R + +--R 7 6 5 4 +--R 2356cosh(x) + 2036%i cosh(x) + 54cosh(x) - 4528%i cosh(x) +--R + +--R 3 2 +--R 10120cosh(x) + 6878%i cosh(x) - 840cosh(x) + 520%i +--R * +--R 5 +--R sinh(x) +--R + +--R 12 11 10 9 +--R 330cosh(x) + 1440%i cosh(x) - 2109cosh(x) - 976%i cosh(x) +--R + +--R 8 7 6 5 +--R 1614cosh(x) + 3696%i cosh(x) - 4906cosh(x) - 8072%i cosh(x) +--R + +--R 4 3 2 +--R 10624cosh(x) + 6752%i cosh(x) + 116cosh(x) + 2280%i cosh(x) - 760 +--R * +--R 4 +--R sinh(x) +--R + +--R 13 12 11 10 +--R 220cosh(x) + 1200%i cosh(x) - 2406cosh(x) - 1784%i cosh(x) +--R + +--R 9 8 7 6 +--R 1312cosh(x) + 3314%i cosh(x) - 5610cosh(x) - 7528%i cosh(x) +--R + +--R 5 4 3 2 +--R 7348cosh(x) + 3102%i cosh(x) + 2112cosh(x) + 3656%i cosh(x) +--R + +--R - 1680cosh(x) - 120%i +--R * +--R 3 +--R sinh(x) +--R + +--R 14 13 12 11 +--R 88cosh(x) + 560%i cosh(x) - 1362cosh(x) - 1336%i cosh(x) +--R + +--R 10 9 8 7 +--R 946cosh(x) + 2068%i cosh(x) - 3628cosh(x) - 4264%i cosh(x) +--R + +--R 6 5 4 3 +--R 3416cosh(x) + 388%i cosh(x) + 2444cosh(x) + 2824%i cosh(x) +--R + +--R 2 +--R - 1240cosh(x) + 160%i cosh(x) - 320 +--R * +--R 2 +--R sinh(x) +--R + +--R 15 14 13 12 +--R 20cosh(x) + 144%i cosh(x) - 406cosh(x) - 488%i cosh(x) +--R + +--R 11 10 9 8 +--R 392cosh(x) + 802%i cosh(x) - 1446cosh(x) - 1516%i cosh(x) +--R + +--R 7 6 5 4 +--R 1000cosh(x) - 46%i cosh(x) + 1064cosh(x) + 1008%i cosh(x) +--R + +--R 3 2 +--R - 304cosh(x) + 256%i cosh(x) - 320cosh(x) - 160%i +--R * +--R sinh(x) +--R + +--R 16 15 14 13 12 +--R 2cosh(x) + 16%i cosh(x) - 51cosh(x) - 72%i cosh(x) + 66cosh(x) +--R + +--R 11 10 9 8 +--R 136%i cosh(x) - 267cosh(x) - 280%i cosh(x) + 138cosh(x) +--R + +--R 7 6 5 4 3 +--R 24%i cosh(x) + 128cosh(x) + 112%i cosh(x) + 16cosh(x) + 64%i cosh(x) +--R + +--R 2 +--R - 32cosh(x) +--R / +--R 6 10 7 6 9 +--R 5cosh(x) sinh(x) + (50cosh(x) + 40%i cosh(x) )sinh(x) +--R + +--R 8 7 6 8 +--R (225cosh(x) + 360%i cosh(x) - 130cosh(x) )sinh(x) +--R + +--R 9 8 7 6 7 +--R (600cosh(x) + 1440%i cosh(x) - 1040cosh(x) - 200%i cosh(x) )sinh(x) +--R + +--R 10 9 8 7 +--R 1050cosh(x) + 3360%i cosh(x) - 3640cosh(x) - 1400%i cosh(x) +--R + +--R 6 +--R 65cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 1260cosh(x) + 5040%i cosh(x) - 7280cosh(x) - 4200%i cosh(x) +--R + +--R 7 6 +--R 410cosh(x) - 280%i cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 11 10 9 +--R 1050cosh(x) + 5040%i cosh(x) - 9100cosh(x) - 7000%i cosh(x) +--R + +--R 8 7 6 +--R 1075cosh(x) - 1320%i cosh(x) + 460cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 13 12 11 10 +--R 600cosh(x) + 3360%i cosh(x) - 7280cosh(x) - 7000%i cosh(x) +--R + +--R 9 8 7 6 +--R 1500cosh(x) - 2480%i cosh(x) + 1740cosh(x) + 200%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 13 12 11 +--R 225cosh(x) + 1440%i cosh(x) - 3640cosh(x) - 4200%i cosh(x) +--R + +--R 10 9 8 7 +--R 1175cosh(x) - 2320%i cosh(x) + 2460cosh(x) + 600%i cosh(x) +--R + +--R 6 +--R 180cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 15 14 13 12 +--R 50cosh(x) + 360%i cosh(x) - 1040cosh(x) - 1400%i cosh(x) +--R + +--R 11 10 9 8 +--R 490cosh(x) - 1080%i cosh(x) + 1540cosh(x) + 600%i cosh(x) +--R + +--R 7 6 +--R 240cosh(x) + 240%i cosh(x) +--R * +--R sinh(x) +--R + +--R 16 15 14 13 +--R 5cosh(x) + 40%i cosh(x) - 130cosh(x) - 200%i cosh(x) +--R + +--R 12 11 10 9 +--R 85cosh(x) - 200%i cosh(x) + 360cosh(x) + 200%i cosh(x) +--R + +--R 8 7 6 +--R 80cosh(x) + 160%i cosh(x) - 80cosh(x) +--R Type: Expression(Complex(Integer)) +--E 180 + +--S 181 of 552 +t0736:= sech(x)^3/(%i+sinh(x))^2 +--R +--R +--R 3 +--R sech(x) +--R (176) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 181 + +--S 182 of 552 +r0736:= -1/4*atan(sinh(x))+1/(16*%i-16*sinh(x))+1/12/(%i+sinh(x))^3-_ + 1/8*%i/(%i+sinh(x))^2-3/(16*%i+16*sinh(x)) +--R +--R +--R (177) +--R 4 3 3 +--R (- 3sinh(x) - 6%i sinh(x) - 6%i sinh(x) + 3)atan(sinh(x)) - 3sinh(x) +--R + +--R 2 +--R - 6%i sinh(x) + sinh(x) - 4%i +--R / +--R 4 3 +--R 12sinh(x) + 24%i sinh(x) + 24%i sinh(x) - 12 +--R Type: Expression(Complex(Integer)) +--E 182 + +--S 183 of 552 +a0736:= integrate(t0736,x) +--R +--R +--R (178) +--R 8 7 +--R 3%i sinh(x) + (24%i cosh(x) - 12)sinh(x) +--R + +--R 2 6 +--R (84%i cosh(x) - 84cosh(x) - 12%i)sinh(x) +--R + +--R 3 2 5 +--R (168%i cosh(x) - 252cosh(x) - 72%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R (210%i cosh(x) - 420cosh(x) - 180%i cosh(x) - 60cosh(x) - 30%i) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 168%i cosh(x) - 420cosh(x) - 240%i cosh(x) - 120cosh(x) +--R + +--R - 120%i cosh(x) + 12 +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 84%i cosh(x) - 252cosh(x) - 180%i cosh(x) - 120cosh(x) +--R + +--R 2 +--R - 180%i cosh(x) + 36cosh(x) - 12%i +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 24%i cosh(x) - 84cosh(x) - 72%i cosh(x) - 60cosh(x) +--R + +--R 3 2 +--R - 120%i cosh(x) + 36cosh(x) - 24%i cosh(x) + 12 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R 3%i cosh(x) - 12cosh(x) - 12%i cosh(x) - 12cosh(x) +--R + +--R 4 3 2 +--R - 30%i cosh(x) + 12cosh(x) - 12%i cosh(x) + 12cosh(x) + 3%i +--R * +--R sinh(x) + cosh(x) - %i +--R log(----------------------) +--R sinh(x) + cosh(x) + %i +--R + +--R 7 6 +--R - 6sinh(x) + (- 42cosh(x) - 24%i)sinh(x) +--R + +--R 2 5 +--R (- 126cosh(x) - 144%i cosh(x) + 26)sinh(x) +--R + +--R 3 2 4 +--R (- 210cosh(x) - 360%i cosh(x) + 130cosh(x) - 16%i)sinh(x) +--R + +--R 4 3 2 +--R (- 210cosh(x) - 480%i cosh(x) + 260cosh(x) - 64%i cosh(x) - 26) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 126cosh(x) - 360%i cosh(x) + 260cosh(x) - 96%i cosh(x) +--R + +--R - 78cosh(x) - 24%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 42cosh(x) - 144%i cosh(x) + 130cosh(x) - 64%i cosh(x) +--R + +--R 2 +--R - 78cosh(x) - 48%i cosh(x) + 6 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 6cosh(x) - 24%i cosh(x) + 26cosh(x) - 16%i cosh(x) - 26cosh(x) +--R + +--R 2 +--R - 24%i cosh(x) + 6cosh(x) +--R / +--R 8 7 +--R 12sinh(x) + (96cosh(x) + 48%i)sinh(x) +--R + +--R 2 6 +--R (336cosh(x) + 336%i cosh(x) - 48)sinh(x) +--R + +--R 3 2 5 +--R (672cosh(x) + 1008%i cosh(x) - 288cosh(x) + 48%i)sinh(x) +--R + +--R 4 3 2 +--R (840cosh(x) + 1680%i cosh(x) - 720cosh(x) + 240%i cosh(x) - 120) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 672cosh(x) + 1680%i cosh(x) - 960cosh(x) + 480%i cosh(x) +--R + +--R - 480cosh(x) - 48%i +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 336cosh(x) + 1008%i cosh(x) - 720cosh(x) + 480%i cosh(x) +--R + +--R 2 +--R - 720cosh(x) - 144%i cosh(x) - 48 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 96cosh(x) + 336%i cosh(x) - 288cosh(x) + 240%i cosh(x) +--R + +--R 3 2 +--R - 480cosh(x) - 144%i cosh(x) - 96cosh(x) - 48%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 12cosh(x) + 48%i cosh(x) - 48cosh(x) + 48%i cosh(x) - 120cosh(x) +--R + +--R 3 2 +--R - 48%i cosh(x) - 48cosh(x) - 48%i cosh(x) + 12 +--R Type: Union(Expression(Complex(Integer)),...) +--E 183 + +--S 184 of 552 +m0736:= a0736-r0736 +--R +--R +--R (179) +--R 12 11 +--R 3%i sinh(x) + (24%i cosh(x) - 18)sinh(x) +--R + +--R 2 10 +--R (84%i cosh(x) - 132cosh(x) - 36%i)sinh(x) +--R + +--R 3 2 9 +--R (168%i cosh(x) - 420cosh(x) - 240%i cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 +--R (210%i cosh(x) - 756cosh(x) - 684%i cosh(x) + 36cosh(x) - 81%i) +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 168%i cosh(x) - 840cosh(x) - 1080%i cosh(x) + 72cosh(x) +--R + +--R - 432%i cosh(x) + 108 +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 84%i cosh(x) - 588cosh(x) - 1020%i cosh(x) + 24cosh(x) +--R + +--R 2 +--R - 1008%i cosh(x) + 504cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 24%i cosh(x) - 252cosh(x) - 576%i cosh(x) - 120cosh(x) +--R + +--R 3 2 +--R - 1368%i cosh(x) + 1008cosh(x) + 108 +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 3%i cosh(x) - 60cosh(x) - 180%i cosh(x) - 204cosh(x) +--R + +--R 4 3 +--R - 1200%i cosh(x) + 1152cosh(x) + 360cosh(x) + 81%i +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 6cosh(x) - 24%i cosh(x) - 144cosh(x) - 696%i cosh(x) +--R + +--R 4 3 2 +--R 840cosh(x) + 24%i cosh(x) + 504cosh(x) + 216%i cosh(x) + 6 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 48cosh(x) - 252%i cosh(x) + 396cosh(x) + 60%i cosh(x) +--R + +--R 3 2 +--R 360cosh(x) + 252%i cosh(x) + 12cosh(x) + 36%i +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 6cosh(x) - 48%i cosh(x) + 108cosh(x) + 48%i cosh(x) +--R + +--R 4 3 2 +--R 120cosh(x) + 144%i cosh(x) - 12cosh(x) + 48%i cosh(x) - 18 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 3%i cosh(x) + 12cosh(x) + 12%i cosh(x) + 12cosh(x) +--R + +--R 4 3 2 +--R 30%i cosh(x) - 12cosh(x) + 12%i cosh(x) - 12cosh(x) - 3%i +--R * +--R sinh(x) + cosh(x) - %i +--R log(----------------------) +--R sinh(x) + cosh(x) + %i +--R + +--R 12 11 +--R 3sinh(x) + (24cosh(x) + 18%i)sinh(x) +--R + +--R 2 10 +--R (84cosh(x) + 132%i cosh(x) - 36)sinh(x) +--R + +--R 3 2 9 +--R (168cosh(x) + 420%i cosh(x) - 240cosh(x) - 6%i)sinh(x) +--R + +--R 4 3 2 +--R (210cosh(x) + 756%i cosh(x) - 684cosh(x) - 36%i cosh(x) - 81) +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 168cosh(x) + 840%i cosh(x) - 1080cosh(x) - 72%i cosh(x) +--R + +--R - 432cosh(x) - 108%i +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 84cosh(x) + 588%i cosh(x) - 1020cosh(x) - 24%i cosh(x) +--R + +--R 2 +--R - 1008cosh(x) - 504%i cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 24cosh(x) + 252%i cosh(x) - 576cosh(x) + 120%i cosh(x) +--R + +--R 3 2 +--R - 1368cosh(x) - 1008%i cosh(x) - 108%i +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 3cosh(x) + 60%i cosh(x) - 180cosh(x) + 204%i cosh(x) +--R + +--R 4 3 +--R - 1200cosh(x) - 1152%i cosh(x) - 360%i cosh(x) + 81 +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 6%i cosh(x) - 24cosh(x) + 144%i cosh(x) - 696cosh(x) +--R + +--R 4 3 2 +--R - 840%i cosh(x) + 24cosh(x) - 504%i cosh(x) + 216cosh(x) - 6%i +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 48%i cosh(x) - 252cosh(x) - 396%i cosh(x) + 60cosh(x) +--R + +--R 3 2 +--R - 360%i cosh(x) + 252cosh(x) - 12%i cosh(x) + 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 6%i cosh(x) - 48cosh(x) - 108%i cosh(x) + 48cosh(x) +--R + +--R 4 3 2 +--R - 120%i cosh(x) + 144cosh(x) + 12%i cosh(x) + 48cosh(x) + 18%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 3cosh(x) - 12%i cosh(x) + 12cosh(x) - 12%i cosh(x) + 30cosh(x) +--R + +--R 3 2 +--R 12%i cosh(x) + 12cosh(x) + 12%i cosh(x) - 3 +--R * +--R atan(sinh(x)) +--R + +--R 11 10 +--R - 3sinh(x) + (- 18cosh(x) - 18%i)sinh(x) +--R + +--R 2 9 +--R (- 42cosh(x) - 96%i cosh(x) + 37)sinh(x) +--R + +--R 3 2 8 +--R (- 42cosh(x) - 192%i cosh(x) + 170cosh(x) + 12%i)sinh(x) +--R + +--R 3 2 7 +--R (- 144%i cosh(x) + 268cosh(x) + 32%i cosh(x) - 6)sinh(x) +--R + +--R 5 4 3 2 +--R 42cosh(x) + 60%i cosh(x) + 84cosh(x) - 40%i cosh(x) + 52cosh(x) +--R + +--R - 92%i +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 42cosh(x) + 192%i cosh(x) - 240cosh(x) - 240%i cosh(x) +--R + +--R 2 +--R 264cosh(x) - 192%i cosh(x) + 66 +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 18cosh(x) + 144%i cosh(x) - 318cosh(x) - 336%i cosh(x) +--R + +--R 3 2 +--R 432cosh(x) + 24%i cosh(x) + 108cosh(x) - 96%i +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 3cosh(x) + 48%i cosh(x) - 160cosh(x) - 192%i cosh(x) +--R + +--R 4 3 2 +--R 312cosh(x) + 336%i cosh(x) - 60cosh(x) - 288%i cosh(x) + 121 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 6%i cosh(x) - 32cosh(x) - 24%i cosh(x) + 78cosh(x) +--R + +--R 4 3 2 +--R 300%i cosh(x) - 228cosh(x) - 312%i cosh(x) + 254cosh(x) + 30%i +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - cosh(x) + 16%i cosh(x) - 18cosh(x) + 96%i cosh(x) - 168cosh(x) +--R + +--R 3 2 +--R - 144%i cosh(x) + 178cosh(x) + 32%i cosh(x) + 9 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R 4%i cosh(x) - 10cosh(x) + 8%i cosh(x) - 42cosh(x) - 24%i cosh(x) +--R + +--R 3 2 +--R 42cosh(x) + 8%i cosh(x) + 10cosh(x) + 4%i +--R / +--R 12 11 +--R 12sinh(x) + (96cosh(x) + 72%i)sinh(x) +--R + +--R 2 10 +--R (336cosh(x) + 528%i cosh(x) - 144)sinh(x) +--R + +--R 3 2 9 +--R (672cosh(x) + 1680%i cosh(x) - 960cosh(x) - 24%i)sinh(x) +--R + +--R 4 3 2 +--R (840cosh(x) + 3024%i cosh(x) - 2736cosh(x) - 144%i cosh(x) - 324) +--R * +--R 8 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 672cosh(x) + 3360%i cosh(x) - 4320cosh(x) - 288%i cosh(x) +--R + +--R - 1728cosh(x) - 432%i +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 336cosh(x) + 2352%i cosh(x) - 4080cosh(x) - 96%i cosh(x) +--R + +--R 2 +--R - 4032cosh(x) - 2016%i cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 96cosh(x) + 1008%i cosh(x) - 2304cosh(x) + 480%i cosh(x) +--R + +--R 3 2 +--R - 5472cosh(x) - 4032%i cosh(x) - 432%i +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 12cosh(x) + 240%i cosh(x) - 720cosh(x) + 816%i cosh(x) +--R + +--R 4 3 +--R - 4800cosh(x) - 4608%i cosh(x) - 1440%i cosh(x) + 324 +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 24%i cosh(x) - 96cosh(x) + 576%i cosh(x) - 2784cosh(x) +--R + +--R 4 3 2 +--R - 3360%i cosh(x) + 96cosh(x) - 2016%i cosh(x) + 864cosh(x) - 24%i +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 192%i cosh(x) - 1008cosh(x) - 1584%i cosh(x) + 240cosh(x) +--R + +--R 3 2 +--R - 1440%i cosh(x) + 1008cosh(x) - 48%i cosh(x) + 144 +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 24%i cosh(x) - 192cosh(x) - 432%i cosh(x) + 192cosh(x) +--R + +--R 4 3 2 +--R - 480%i cosh(x) + 576cosh(x) + 48%i cosh(x) + 192cosh(x) + 72%i +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 12cosh(x) - 48%i cosh(x) + 48cosh(x) - 48%i cosh(x) + 120cosh(x) +--R + +--R 3 2 +--R 48%i cosh(x) + 48cosh(x) + 48%i cosh(x) - 12 +--R Type: Expression(Complex(Integer)) +--E 184 + +--S 185 of 552 +d0736:= D(m0736,x) +--R +--R +--R (180) +--R 11 10 +--R 32sinh(x) + (159cosh(x) + 64%i)sinh(x) +--R + +--R 2 9 +--R (310cosh(x) + 316%i cosh(x) + 32)sinh(x) +--R + +--R 3 2 8 +--R (275cosh(x) + 604%i cosh(x) + 163cosh(x) + 128%i)sinh(x) +--R + +--R 4 3 2 7 +--R (40cosh(x) + 496%i cosh(x) + 344cosh(x) + 632%i cosh(x) - 32)sinh(x) +--R + +--R 5 4 3 2 +--R - 178cosh(x) - 16%i cosh(x) + 404cosh(x) + 1224%i cosh(x) +--R + +--R - 146cosh(x) + 64%i +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 252cosh(x) - 440%i cosh(x) + 328cosh(x) + 1112%i cosh(x) +--R + +--R 2 +--R - 236cosh(x) + 320%i cosh(x) - 32 +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 210cosh(x) - 504%i cosh(x) + 242cosh(x) + 360%i cosh(x) +--R + +--R 3 2 +--R - 110cosh(x) + 640%i cosh(x) - 146cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 120cosh(x) - 336%i cosh(x) + 168cosh(x) - 152%i cosh(x) +--R + +--R 4 3 2 +--R 120cosh(x) + 640%i cosh(x) - 264cosh(x) + 8%i cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - 45cosh(x) - 144%i cosh(x) + 84cosh(x) - 168%i cosh(x) +--R + +--R 5 4 3 2 +--R 178cosh(x) + 320%i cosh(x) - 236cosh(x) + 24%i cosh(x) + 3cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 10cosh(x) - 36%i cosh(x) + 24cosh(x) - 56%i cosh(x) +--R + +--R 6 5 4 3 2 +--R 84cosh(x) + 64%i cosh(x) - 104cosh(x) + 24%i cosh(x) + 6cosh(x) +--R + +--R 4%i cosh(x) +--R * +--R sinh(x) +--R + +--R 11 10 9 8 7 +--R - cosh(x) - 4%i cosh(x) + 3cosh(x) - 8%i cosh(x) + 14cosh(x) +--R + +--R 5 4 3 2 +--R - 18cosh(x) + 8%i cosh(x) + 3cosh(x) + 4%i cosh(x) - cosh(x) +--R / +--R 16 15 +--R sinh(x) + (10cosh(x) + 6%i)sinh(x) +--R + +--R 2 14 +--R (45cosh(x) + 56%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 13 +--R (120cosh(x) + 234%i cosh(x) - 86cosh(x) + 10%i)sinh(x) +--R + +--R 4 3 2 12 +--R (210cosh(x) + 576%i cosh(x) - 327cosh(x) + 84%i cosh(x) - 50)sinh(x) +--R + +--R 5 4 3 2 +--R 252cosh(x) + 924%i cosh(x) - 720cosh(x) + 324%i cosh(x) +--R + +--R - 374cosh(x) - 34%i +--R * +--R 11 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 210cosh(x) + 1008%i cosh(x) - 1008cosh(x) + 760%i cosh(x) +--R + +--R 2 +--R - 1251cosh(x) - 224%i cosh(x) - 66 +--R * +--R 10 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 120cosh(x) + 756%i cosh(x) - 924cosh(x) + 1204%i cosh(x) +--R + +--R 3 2 +--R - 2472cosh(x) - 642%i cosh(x) - 422cosh(x) - 110%i +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 45cosh(x) + 384%i cosh(x) - 546cosh(x) + 1344%i cosh(x) +--R + +--R 4 3 2 +--R - 3206cosh(x) - 1048%i cosh(x) - 1215cosh(x) - 612%i cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 10cosh(x) + 126%i cosh(x) - 192cosh(x) + 1064%i cosh(x) +--R + +--R 5 4 3 2 +--R - 2856cosh(x) - 1064%i cosh(x) - 2080cosh(x) - 1512%i cosh(x) +--R + +--R - 18cosh(x) - 110%i +--R * +--R 7 +--R sinh(x) +--R + +--R 10 9 8 7 +--R cosh(x) + 24%i cosh(x) - 30cosh(x) + 584%i cosh(x) +--R + +--R 6 5 4 3 +--R - 1764cosh(x) - 672%i cosh(x) - 2352cosh(x) - 2192%i cosh(x) +--R + +--R 2 +--R - 81cosh(x) - 488%i cosh(x) + 66 +--R * +--R 6 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 2%i cosh(x) + 2cosh(x) + 210%i cosh(x) - 736cosh(x) +--R + +--R 6 5 4 3 +--R - 224%i cosh(x) - 1848cosh(x) - 2072%i cosh(x) - 152cosh(x) +--R + +--R 2 +--R - 954%i cosh(x) + 238cosh(x) - 34%i +--R * +--R 5 +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R cosh(x) + 44%i cosh(x) - 192cosh(x) + 8%i cosh(x) - 1036cosh(x) +--R + +--R 5 4 3 2 +--R - 1344%i cosh(x) - 154cosh(x) - 1072%i cosh(x) + 387cosh(x) +--R + +--R - 116%i cosh(x) + 50 +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 4%i cosh(x) - 26cosh(x) + 42%i cosh(x) - 416cosh(x) +--R + +--R 6 5 4 3 +--R - 616%i cosh(x) - 84cosh(x) - 756%i cosh(x) + 368cosh(x) +--R + +--R 2 +--R - 156%i cosh(x) + 126cosh(x) + 10%i +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - cosh(x) + 16%i cosh(x) - 114cosh(x) - 200%i cosh(x) +--R + +--R 6 5 4 3 +--R - 14cosh(x) - 336%i cosh(x) + 224cosh(x) - 104%i cosh(x) +--R + +--R 2 +--R 135cosh(x) + 16%i cosh(x) + 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 2%i cosh(x) - 18cosh(x) - 42%i cosh(x) + 8cosh(x) +--R + +--R 6 5 4 3 +--R - 84%i cosh(x) + 84cosh(x) - 28%i cosh(x) + 72cosh(x) +--R + +--R 2 +--R 18%i cosh(x) + 14cosh(x) + 6%i +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R - cosh(x) - 4%i cosh(x) + 3cosh(x) - 8%i cosh(x) + 14cosh(x) +--R + +--R 4 3 2 +--R 14cosh(x) + 8%i cosh(x) + 3cosh(x) + 4%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 185 + +--S 186 of 552 +t0737:= csch(x)/(a+b*sinh(x))^2 +--R +--R +--R csch(x) +--R (181) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 186 + +--S 187 of 552 +r0737:= -acoth(cosh(x))/a^2+2*b*atanh((b-a*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+2*b*_ + atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^2/(a^2+b^2)^(1/2)+_ + b^2*cosh(x)/a/(a^2+b^2)/(a+b*sinh(x)) +--R +--R +--R (182) +--R x +--R a tanh(-) - b +--R 4 2 2 3 3 2 +--R ((- 2b - 4a b )sinh(x) - 2a b - 4a b)atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((- b - a b)sinh(x) - a b - a )\|b + a acoth(cosh(x)) +--R + +--R +-------+ +--R 2 | 2 2 +--R a b cosh(x)\|b + a +--R / +--R +-------+ +--R 2 3 4 3 2 5 | 2 2 +--R ((a b + a b)sinh(x) + a b + a )\|b + a +--R Type: Expression(Integer) +--E 187 + +--S 188 of 552 +a0737:= integrate(t0737,x) +--R +--R +--R (183) +--R 4 2 2 2 4 2 2 3 3 +--R (b + 2a b )sinh(x) + ((2b + 4a b )cosh(x) + 2a b + 4a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (b + 2a b )cosh(x) + (2a b + 4a b)cosh(x) - b - 2a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 2 2 3 2 2 3 +--R (- b - a b)sinh(x) + ((- 2b - 2a b)cosh(x) - 2a b - 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- b - a b)cosh(x) + (- 2a b - 2a )cosh(x) + b + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 2 3 2 2 3 +--R (b + a b)sinh(x) + ((2b + 2a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 2 3 3 2 +--R (b + a b)cosh(x) + (2a b + 2a )cosh(x) - b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (- 2a b sinh(x) - 2a b cosh(x) + 2a b )\|b + a +--R / +--R 2 3 4 2 2 3 4 3 2 5 +--R (a b + a b)sinh(x) + ((2a b + 2a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 552 +m0737:= a0737-r0737 +--R +--R +--R (184) +--R 5 2 3 3 5 2 3 4 3 2 2 +--R (b + 2a b )sinh(x) + ((2b + 4a b )cosh(x) + 3a b + 6a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 4 +--R ((b + 2a b )cosh(x) + (4a b + 8a b )cosh(x) - b + 4a b)sinh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (a b + 2a b )cosh(x) + (2a b + 4a b)cosh(x) - a b - 2a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 2 2 3 +--R (- b - a b )sinh(x) +--R + +--R 4 2 2 3 3 2 +--R ((- 2b - 2a b )cosh(x) - 3a b - 3a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 4 +--R ((- b - a b )cosh(x) + (- 4a b - 4a b)cosh(x) + b - a b - 2a ) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (- a b - a b)cosh(x) + (- 2a b - 2a )cosh(x) + a b + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 4 2 2 3 4 2 2 3 3 2 +--R (b + a b )sinh(x) + ((2b + 2a b )cosh(x) + 3a b + 3a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 4 +--R ((b + a b )cosh(x) + (4a b + 4a b)cosh(x) - b + a b + 2a ) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 5 2 3 3 +--R (2b + 4a b )sinh(x) +--R + +--R 5 2 3 4 3 2 2 +--R ((4b + 8a b )cosh(x) + 6a b + 12a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 4 +--R ((2b + 4a b )cosh(x) + (8a b + 16a b )cosh(x) - 2b + 8a b)sinh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (2a b + 4a b )cosh(x) + (4a b + 8a b)cosh(x) - 2a b - 4a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 2 2 3 4 2 2 3 3 2 +--R (b + a b )sinh(x) + ((2b + 2a b )cosh(x) + 3a b + 3a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 4 +--R ((b + a b )cosh(x) + (4a b + 4a b)cosh(x) - b + a b + 2a ) +--R * +--R sinh(x) +--R + +--R 3 3 2 2 2 4 3 3 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a acoth(cosh(x)) +--R + +--R 3 2 2 2 +--R (- a b cosh(x) - 2a b )sinh(x) +--R + +--R 3 2 2 2 3 3 3 3 +--R (- 2a b cosh(x) - 4a b cosh(x) + 2a b - 2a b)sinh(x) - a b cosh(x) +--R + +--R 2 2 2 3 3 2 2 +--R - 2a b cosh(x) + (a b - 2a b)cosh(x) + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 4 4 2 3 2 4 4 2 3 3 5 2 +--R (a b + a b )sinh(x) + ((2a b + 2a b )cosh(x) + 3a b + 3a b)sinh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 4 2 6 +--R ((a b + a b )cosh(x) + (4a b + 4a b)cosh(x) - a b + a b + 2a ) +--R * +--R sinh(x) +--R + +--R 3 3 5 2 4 2 6 3 3 5 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 189 + +--S 190 of 552 +--d0737:= D(m0737,x) +--E 190 + +--S 191 of 552 +t0738:= csch(x)^2/(a+b*sinh(x))^2 +--R +--R +--R 2 +--R csch(x) +--R (185) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 191 + +--S 192 of 552 +r0738:= 2*b*acoth(cosh(x))/a^3-2*b^2*atanh((b-a*tanh(1/2*x))/_ + (a^2+b^2)^(1/2))/a/(a^2+b^2)^(3/2)-_ + 4*b^2*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^3/(a^2+b^2)^(1/2)-_ + coth(x)/a^2-b^3*cosh(x)/a^2/(a^2+b^2)/(a+b*sinh(x)) +--R +--R +--R (186) +--R x +--R a tanh(-) - b +--R 5 2 3 4 3 2 2 +--R ((4b + 6a b )sinh(x) + 4a b + 6a b )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 4 2 2 3 3 | 2 2 +--R ((2b + 2a b )sinh(x) + 2a b + 2a b)\|b + a acoth(cosh(x)) +--R + +--R 3 3 2 2 4 3 +--R ((- a b - a b)coth(x)sinh(x) + (- a b - a )coth(x) - a b cosh(x)) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 3 3 5 4 2 6 | 2 2 +--R ((a b + a b)sinh(x) + a b + a )\|b + a +--R Type: Expression(Integer) +--E 192 + +--S 193 of 552 +a0738:= integrate(t0738,x) +--R +--R +--R (187) +--R 5 2 3 4 +--R (2b + 3a b )sinh(x) +--R + +--R 5 2 3 4 3 2 3 +--R ((8b + 12a b )cosh(x) + 4a b + 6a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 2 3 +--R ((12b + 18a b )cosh(x) + (12a b + 18a b )cosh(x) - 4b - 6a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (8b + 12a b )cosh(x) + (12a b + 18a b )cosh(x) +--R + +--R 5 2 3 4 3 2 +--R (- 8b - 12a b )cosh(x) - 4a b - 6a b +--R * +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (2b + 3a b )cosh(x) + (4a b + 6a b )cosh(x) +--R + +--R 5 2 3 2 4 3 2 5 2 3 +--R (- 4b - 6a b )cosh(x) + (- 4a b - 6a b )cosh(x) + 2b + 3a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 2 2 4 4 2 2 3 3 3 +--R (2b + 2a b )sinh(x) + ((8b + 8a b )cosh(x) + 4a b + 4a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R ((12b + 12a b )cosh(x) + (12a b + 12a b)cosh(x) - 4b - 4a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (8b + 8a b )cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 4 2 2 3 3 +--R (- 8b - 8a b )cosh(x) - 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (2b + 2a b )cosh(x) + (4a b + 4a b)cosh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (- 4b - 4a b )cosh(x) + (- 4a b - 4a b)cosh(x) + 2b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 4 2 2 4 +--R (- 2b - 2a b )sinh(x) +--R + +--R 4 2 2 3 3 3 +--R ((- 8b - 8a b )cosh(x) - 4a b - 4a b)sinh(x) +--R + +--R 4 2 2 2 3 3 4 +--R (- 12b - 12a b )cosh(x) + (- 12a b - 12a b)cosh(x) + 4b +--R + +--R 2 2 +--R 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 3 3 3 2 +--R (- 8b - 8a b )cosh(x) + (- 12a b - 12a b)cosh(x) +--R + +--R 4 2 2 3 3 +--R (8b + 8a b )cosh(x) + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 4 2 2 4 3 3 3 +--R (- 2b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 4 2 2 2 3 3 4 2 2 +--R (4b + 4a b )cosh(x) + (4a b + 4a b)cosh(x) - 2b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 3 2 2 3 3 2 +--R 2a b sinh(x) + (6a b cosh(x) - 4a b - 2a b)sinh(x) +--R + +--R 2 2 2 3 3 2 2 4 +--R (6a b cosh(x) + (- 8a b - 4a b)cosh(x) - 6a b - 4a )sinh(x) +--R + +--R 2 2 3 3 3 2 2 2 4 +--R 2a b cosh(x) + (- 4a b - 2a b)cosh(x) + (- 6a b - 4a )cosh(x) +--R + +--R 3 3 +--R 4a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 3 5 4 3 3 5 4 2 6 3 +--R (a b + a b)sinh(x) + ((4a b + 4a b)cosh(x) + 2a b + 2a )sinh(x) +--R + +--R 3 3 5 2 4 2 6 3 3 5 2 +--R ((6a b + 6a b)cosh(x) + (6a b + 6a )cosh(x) - 2a b - 2a b)sinh(x) +--R + +--R 3 3 5 3 4 2 6 2 +--R (4a b + 4a b)cosh(x) + (6a b + 6a )cosh(x) +--R + +--R 3 3 5 4 2 6 +--R (- 4a b - 4a b)cosh(x) - 2a b - 2a +--R * +--R sinh(x) +--R + +--R 3 3 5 4 4 2 6 3 3 3 5 2 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) + (- 2a b - 2a b)cosh(x) +--R + +--R 4 2 6 3 3 5 +--R (- 2a b - 2a )cosh(x) + a b + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 552 +m0738:= a0738-r0738 +--R +--R +--R (188) +--R 6 2 4 5 +--R (2b + 3a b )sinh(x) +--R + +--R 6 2 4 5 3 3 4 +--R ((8b + 12a b )cosh(x) + 6a b + 9a b )sinh(x) +--R + +--R 6 2 4 2 5 3 3 6 2 4 +--R (12b + 18a b )cosh(x) + (20a b + 30a b )cosh(x) - 4b - 2a b +--R + +--R 4 2 +--R 6a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 3 5 3 3 2 +--R (8b + 12a b )cosh(x) + (24a b + 36a b )cosh(x) +--R + +--R 6 4 2 5 3 3 +--R (- 8b + 18a b )cosh(x) - 8a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 4 5 3 3 3 +--R (2b + 3a b )cosh(x) + (12a b + 18a b )cosh(x) +--R + +--R 6 2 4 4 2 2 5 3 3 +--R (- 4b + 6a b + 18a b )cosh(x) + (- 12a b - 18a b )cosh(x) +--R + +--R 6 2 4 4 2 +--R 2b - a b - 6a b +--R * +--R sinh(x) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (2a b + 3a b )cosh(x) + (4a b + 6a b )cosh(x) +--R + +--R 5 3 3 2 2 4 4 2 5 3 3 +--R (- 4a b - 6a b )cosh(x) + (- 4a b - 6a b )cosh(x) + 2a b + 3a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 5 2 3 5 +--R (2b + 2a b )sinh(x) +--R + +--R 5 2 3 4 3 2 4 +--R ((8b + 8a b )cosh(x) + 6a b + 6a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 4 +--R ((12b + 12a b )cosh(x) + (20a b + 20a b )cosh(x) - 4b + 4a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (8b + 8a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (- 8b + 4a b + 12a b)cosh(x) - 8a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (2b + 2a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 +--R (- 4b + 8a b + 12a b)cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 5 2 3 4 +--R 2b - 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (2a b + 2a b )cosh(x) + (4a b + 4a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 4a b - 4a b )cosh(x) + (- 4a b - 4a b)cosh(x) + 2a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 5 2 3 5 +--R (- 2b - 2a b )sinh(x) +--R + +--R 5 2 3 4 3 2 4 +--R ((- 8b - 8a b )cosh(x) - 6a b - 6a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 +--R (- 12b - 12a b )cosh(x) + (- 20a b - 20a b )cosh(x) + 4b +--R + +--R 4 +--R - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (- 8b - 8a b )cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (8b - 4a b - 12a b)cosh(x) + 8a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (- 2b - 2a b )cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (4b - 8a b - 12a b)cosh(x) + (12a b + 12a b )cosh(x) - 2b +--R + +--R 2 3 4 +--R 2a b + 4a b +--R * +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (4a b + 4a b )cosh(x) + (4a b + 4a b)cosh(x) - 2a b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 6 2 4 5 +--R (- 4b - 6a b )sinh(x) +--R + +--R 6 2 4 5 3 3 4 +--R ((- 16b - 24a b )cosh(x) - 12a b - 18a b )sinh(x) +--R + +--R 6 2 4 2 5 3 3 6 +--R (- 24b - 36a b )cosh(x) + (- 40a b - 60a b )cosh(x) + 8b +--R + +--R 2 4 4 2 +--R 4a b - 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 3 5 3 3 2 +--R (- 16b - 24a b )cosh(x) + (- 48a b - 72a b )cosh(x) +--R + +--R 6 4 2 5 3 3 +--R (16b - 36a b )cosh(x) + 16a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 4 5 3 3 3 +--R (- 4b - 6a b )cosh(x) + (- 24a b - 36a b )cosh(x) +--R + +--R 6 2 4 4 2 2 5 3 3 6 +--R (8b - 12a b - 36a b )cosh(x) + (24a b + 36a b )cosh(x) - 4b +--R + +--R 2 4 4 2 +--R 2a b + 12a b +--R * +--R sinh(x) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (- 4a b - 6a b )cosh(x) + (- 8a b - 12a b )cosh(x) +--R + +--R 5 3 3 2 2 4 4 2 5 3 3 +--R (8a b + 12a b )cosh(x) + (8a b + 12a b )cosh(x) - 4a b - 6a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 5 2 3 5 +--R (- 2b - 2a b )sinh(x) +--R + +--R 5 2 3 4 3 2 4 +--R ((- 8b - 8a b )cosh(x) - 6a b - 6a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 +--R (- 12b - 12a b )cosh(x) + (- 20a b - 20a b )cosh(x) + 4b +--R + +--R 4 +--R - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (- 8b - 8a b )cosh(x) + (- 24a b - 24a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (8b - 4a b - 12a b)cosh(x) + 8a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (- 2b - 2a b )cosh(x) + (- 12a b - 12a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (4b - 8a b - 12a b)cosh(x) + (12a b + 12a b )cosh(x) - 2b +--R + +--R 2 3 4 +--R 2a b + 4a b +--R * +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (- 2a b - 2a b )cosh(x) + (- 4a b - 4a b)cosh(x) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (4a b + 4a b )cosh(x) + (4a b + 4a b)cosh(x) - 2a b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a acoth(cosh(x)) +--R + +--R 4 3 2 5 +--R (a b + a b )coth(x)sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R ((4a b + 4a b )cosh(x) + 3a b + 3a b)coth(x) + a b cosh(x) +--R + +--R 2 3 +--R 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 2 3 4 4 +--R (6a b + 6a b )cosh(x) + (10a b + 10a b)cosh(x) - 2a b +--R + +--R 5 +--R 2a +--R * +--R coth(x) +--R + +--R 4 2 2 3 4 +--R 4a b cosh(x) + 8a b cosh(x) - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 3 2 3 4 2 +--R (4a b + 4a b )cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (- 4a b + 2a b + 6a )cosh(x) - 4a b - 4a b +--R * +--R coth(x) +--R + +--R 4 3 2 3 2 4 3 2 +--R 6a b cosh(x) + 12a b cosh(x) + (- 10a b + 2a b )cosh(x) +--R + +--R 2 3 4 +--R - 10a b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 4 2 3 4 3 +--R (a b + a b )cosh(x) + (6a b + 6a b)cosh(x) +--R + +--R 4 3 2 5 2 2 3 4 +--R (- 2a b + 4a b + 6a )cosh(x) + (- 6a b - 6a b)cosh(x) +--R + +--R 4 3 2 5 +--R a b - a b - 2a +--R * +--R coth(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R 4a b cosh(x) + 8a b cosh(x) + (- 8a b + 4a b )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 16a b - 8a b)cosh(x) + 4a b - 4a b - 4a +--R * +--R sinh(x) +--R + +--R 2 3 4 4 3 2 5 3 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 2 3 4 2 3 2 5 2 3 4 +--R (- 2a b - 2a b)cosh(x) + (- 2a b - 2a )cosh(x) + a b + a b +--R * +--R coth(x) +--R + +--R 4 5 2 3 4 4 3 2 3 +--R a b cosh(x) + 2a b cosh(x) + (- 2a b + 2a b )cosh(x) +--R + +--R 2 3 4 2 4 3 2 5 2 3 4 +--R (- 6a b - 2a b)cosh(x) + (a b - 6a b - 4a )cosh(x) + 4a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 4 5 2 5 3 4 5 2 4 3 6 4 +--R (a b + a b )sinh(x) + ((4a b + 4a b )cosh(x) + 3a b + 3a b)sinh(x) +--R + +--R 3 4 5 2 2 4 3 6 3 4 7 +--R ((6a b + 6a b )cosh(x) + (10a b + 10a b)cosh(x) - 2a b + 2a ) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 5 2 3 4 3 6 2 +--R (4a b + 4a b )cosh(x) + (12a b + 12a b)cosh(x) +--R + +--R 3 4 5 2 7 4 3 6 +--R (- 4a b + 2a b + 6a )cosh(x) - 4a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 5 2 4 4 3 6 3 +--R (a b + a b )cosh(x) + (6a b + 6a b)cosh(x) +--R + +--R 3 4 5 2 7 2 4 3 6 3 4 +--R (- 2a b + 4a b + 6a )cosh(x) + (- 6a b - 6a b)cosh(x) + a b +--R + +--R 5 2 7 +--R - a b - 2a +--R * +--R sinh(x) +--R + +--R 4 3 6 4 5 2 7 3 4 3 6 2 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) + (- 2a b - 2a b)cosh(x) +--R + +--R 5 2 7 4 3 6 +--R (- 2a b - 2a )cosh(x) + a b + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 194 + +--S 195 of 552 +--d0738:= D(m0738,x) +--E 195 + +--S 196 of 552 +t0739:= csch(x)^3/(a+b*sinh(x))^2 +--R +--R +--R 3 +--R csch(x) +--R (189) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 196 + +--S 197 of 552 +r0739:= 1/2*acoth(cosh(x))/a^2-3*b^2*acoth(cosh(x))/a^4+_ + 2*b^3*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^2/(a^2+b^2)^(3/2)+_ + 6*b^3*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/a^4/(a^2+b^2)^(1/2)+_ + 2*b*coth(x)/a^3-1/2*coth(x)*csch(x)/a^2+_ + b^4*cosh(x)/a^3/(a^2+b^2)/(a+b*sinh(x)) +--R +--R +--R (190) +--R x +--R a tanh(-) - b +--R 6 2 4 5 3 3 2 +--R ((- 12b - 16a b )sinh(x) - 12a b - 16a b )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 5 2 3 4 4 3 2 5 | 2 2 +--R ((- 6b - 5a b + a b)sinh(x) - 6a b - 5a b + a )\|b + a +--R * +--R acoth(cosh(x)) +--R + +--R 2 3 4 4 3 2 +--R ((- a b - a b)coth(x)csch(x) + (4a b + 4a b )coth(x))sinh(x) +--R + +--R 3 2 5 2 3 4 4 +--R (- a b - a )coth(x)csch(x) + (4a b + 4a b)coth(x) + 2a b cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 3 6 5 2 7 | 2 2 +--R ((2a b + 2a b)sinh(x) + 2a b + 2a )\|b + a +--R Type: Expression(Integer) +--E 197 + +--S 198 of 552 +a0739:= integrate(t0739,x) +--R +--R +--R (191) +--R 6 2 4 6 +--R (6b + 8a b )sinh(x) +--R + +--R 6 2 4 5 3 3 5 +--R ((36b + 48a b )cosh(x) + 12a b + 16a b )sinh(x) +--R + +--R 6 2 4 2 5 3 3 6 +--R (90b + 120a b )cosh(x) + (60a b + 80a b )cosh(x) - 18b +--R + +--R 2 4 +--R - 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 4 3 5 3 3 2 +--R (120b + 160a b )cosh(x) + (120a b + 160a b )cosh(x) +--R + +--R 6 2 4 5 3 3 +--R (- 72b - 96a b )cosh(x) - 24a b - 32a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 4 5 3 3 3 +--R (90b + 120a b )cosh(x) + (120a b + 160a b )cosh(x) +--R + +--R 6 2 4 2 5 3 3 6 +--R (- 108b - 144a b )cosh(x) + (- 72a b - 96a b )cosh(x) + 18b +--R + +--R 2 4 +--R 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 5 5 3 3 4 +--R (36b + 48a b )cosh(x) + (60a b + 80a b )cosh(x) +--R + +--R 6 2 4 3 5 3 3 2 +--R (- 72b - 96a b )cosh(x) + (- 72a b - 96a b )cosh(x) +--R + +--R 6 2 4 5 3 3 +--R (36b + 48a b )cosh(x) + 12a b + 16a b +--R * +--R sinh(x) +--R + +--R 6 2 4 6 5 3 3 5 +--R (6b + 8a b )cosh(x) + (12a b + 16a b )cosh(x) +--R + +--R 6 2 4 4 5 3 3 3 +--R (- 18b - 24a b )cosh(x) + (- 24a b - 32a b )cosh(x) +--R + +--R 6 2 4 2 5 3 3 6 2 4 +--R (18b + 24a b )cosh(x) + (12a b + 16a b )cosh(x) - 6b - 8a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 5 2 3 4 6 +--R (- 6b - 5a b + a b)sinh(x) +--R + +--R 5 2 3 4 4 3 2 5 5 +--R ((- 36b - 30a b + 6a b)cosh(x) - 12a b - 10a b + 2a )sinh(x) +--R + +--R 5 2 3 4 2 +--R (- 90b - 75a b + 15a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 60a b - 50a b + 10a )cosh(x) + 18b + 15a b - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 3 4 3 +--R (- 120b - 100a b + 20a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 120a b - 100a b + 20a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (72b + 60a b - 12a b)cosh(x) + 24a b + 20a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 4 4 +--R (- 90b - 75a b + 15a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (- 120a b - 100a b + 20a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (108b + 90a b - 18a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (72a b + 60a b - 12a )cosh(x) - 18b - 15a b + 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 4 5 +--R (- 36b - 30a b + 6a b)cosh(x) +--R + +--R 4 3 2 5 4 +--R (- 60a b - 50a b + 10a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (72b + 60a b - 12a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (72a b + 60a b - 12a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 36b - 30a b + 6a b)cosh(x) - 12a b - 10a b + 2a +--R * +--R sinh(x) +--R + +--R 5 2 3 4 6 4 3 2 5 5 +--R (- 6b - 5a b + a b)cosh(x) + (- 12a b - 10a b + 2a )cosh(x) +--R + +--R 5 2 3 4 4 4 3 2 5 3 +--R (18b + 15a b - 3a b)cosh(x) + (24a b + 20a b - 4a )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (- 18b - 15a b + 3a b)cosh(x) + (- 12a b - 10a b + 2a )cosh(x) +--R + +--R 5 2 3 4 +--R 6b + 5a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 5 2 3 4 6 +--R (6b + 5a b - a b)sinh(x) +--R + +--R 5 2 3 4 4 3 2 5 5 +--R ((36b + 30a b - 6a b)cosh(x) + 12a b + 10a b - 2a )sinh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (90b + 75a b - 15a b)cosh(x) + (60a b + 50a b - 10a )cosh(x) +--R + +--R 5 2 3 4 +--R - 18b - 15a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 3 4 3 +--R (120b + 100a b - 20a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (120a b + 100a b - 20a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 72b - 60a b + 12a b)cosh(x) - 24a b - 20a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 3 4 4 +--R (90b + 75a b - 15a b)cosh(x) +--R + +--R 4 3 2 5 3 +--R (120a b + 100a b - 20a )cosh(x) +--R + +--R 5 2 3 4 2 +--R (- 108b - 90a b + 18a b)cosh(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 72a b - 60a b + 12a )cosh(x) + 18b + 15a b - 3a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 4 5 4 3 2 5 4 +--R (36b + 30a b - 6a b)cosh(x) + (60a b + 50a b - 10a )cosh(x) +--R + +--R 5 2 3 4 3 +--R (- 72b - 60a b + 12a b)cosh(x) +--R + +--R 4 3 2 5 2 +--R (- 72a b - 60a b + 12a )cosh(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (36b + 30a b - 6a b)cosh(x) + 12a b + 10a b - 2a +--R * +--R sinh(x) +--R + +--R 5 2 3 4 6 4 3 2 5 5 +--R (6b + 5a b - a b)cosh(x) + (12a b + 10a b - 2a )cosh(x) +--R + +--R 5 2 3 4 4 4 3 2 5 3 +--R (- 18b - 15a b + 3a b)cosh(x) + (- 24a b - 20a b + 4a )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 5 +--R (18b + 15a b - 3a b)cosh(x) + (12a b + 10a b - 2a )cosh(x) - 6b +--R + +--R 2 3 4 +--R - 5a b + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 2 3 4 5 +--R (- 6a b - 2a b)sinh(x) +--R + +--R 2 3 4 4 3 2 5 4 +--R ((- 30a b - 10a b)cosh(x) + 12a b + 4a b - 4a )sinh(x) +--R + +--R 2 3 4 2 4 3 2 5 +--R (- 60a b - 20a b)cosh(x) + (48a b + 16a b - 16a )cosh(x) +--R + +--R 2 3 4 +--R 24a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 4 3 4 3 2 5 2 +--R (- 60a b - 20a b)cosh(x) + (72a b + 24a b - 24a )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (72a b + 48a b)cosh(x) - 24a b - 20a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 4 4 3 2 5 3 +--R (- 30a b - 10a b)cosh(x) + (48a b + 16a b - 16a )cosh(x) +--R + +--R 2 3 4 2 4 3 2 5 +--R (72a b + 48a b)cosh(x) + (- 48a b - 40a b - 8a )cosh(x) +--R + +--R 2 3 4 +--R - 18a b - 14a b +--R * +--R sinh(x) +--R + +--R 2 3 4 5 4 3 2 5 4 +--R (- 6a b - 2a b)cosh(x) + (12a b + 4a b - 4a )cosh(x) +--R + +--R 2 3 4 3 4 3 2 5 2 +--R (24a b + 16a b)cosh(x) + (- 24a b - 20a b - 4a )cosh(x) +--R + +--R 2 3 4 4 3 2 +--R (- 18a b - 14a b)cosh(x) + 12a b + 8a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 6 6 +--R (2a b + 2a b)sinh(x) +--R + +--R 4 3 6 5 2 7 5 +--R ((12a b + 12a b)cosh(x) + 4a b + 4a )sinh(x) +--R + +--R 4 3 6 2 5 2 7 4 3 6 +--R ((30a b + 30a b)cosh(x) + (20a b + 20a )cosh(x) - 6a b - 6a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 6 3 5 2 7 2 +--R (40a b + 40a b)cosh(x) + (40a b + 40a )cosh(x) +--R + +--R 4 3 6 5 2 7 +--R (- 24a b - 24a b)cosh(x) - 8a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 4 5 2 7 3 +--R (30a b + 30a b)cosh(x) + (40a b + 40a )cosh(x) +--R + +--R 4 3 6 2 5 2 7 4 3 6 +--R (- 36a b - 36a b)cosh(x) + (- 24a b - 24a )cosh(x) + 6a b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 6 5 5 2 7 4 +--R (12a b + 12a b)cosh(x) + (20a b + 20a )cosh(x) +--R + +--R 4 3 6 3 5 2 7 2 +--R (- 24a b - 24a b)cosh(x) + (- 24a b - 24a )cosh(x) +--R + +--R 4 3 6 5 2 7 +--R (12a b + 12a b)cosh(x) + 4a b + 4a +--R * +--R sinh(x) +--R + +--R 4 3 6 6 5 2 7 5 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 4 3 6 4 5 2 7 3 +--R (- 6a b - 6a b)cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 4 3 6 2 5 2 7 4 3 6 +--R (6a b + 6a b)cosh(x) + (4a b + 4a )cosh(x) - 2a b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 552 +m0739:= a0739-r0739 +--R +--R +--R (192) +--R 7 2 5 7 +--R (6b + 8a b )sinh(x) +--R + +--R 7 2 5 6 3 4 6 +--R ((36b + 48a b )cosh(x) + 18a b + 24a b )sinh(x) +--R + +--R 7 2 5 2 6 3 4 7 +--R (90b + 120a b )cosh(x) + (96a b + 128a b )cosh(x) - 18b +--R + +--R 2 5 4 3 +--R - 12a b + 16a b +--R * +--R 5 +--R sinh(x) +--R + +--R 7 2 5 3 6 3 4 2 +--R (120b + 160a b )cosh(x) + (210a b + 280a b )cosh(x) +--R + +--R 7 2 5 4 3 6 3 4 +--R (- 72b - 36a b + 80a b )cosh(x) - 42a b - 56a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 5 4 6 3 4 3 +--R (90b + 120a b )cosh(x) + (240a b + 320a b )cosh(x) +--R + +--R 7 2 5 4 3 2 +--R (- 108b - 24a b + 160a b )cosh(x) +--R + +--R 6 3 4 7 4 3 +--R (- 144a b - 192a b )cosh(x) + 18b - 32a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 5 5 6 3 4 4 +--R (36b + 48a b )cosh(x) + (150a b + 200a b )cosh(x) +--R + +--R 7 2 5 4 3 3 +--R (- 72b + 24a b + 160a b )cosh(x) +--R + +--R 6 3 4 2 7 2 5 4 3 +--R (- 180a b - 240a b )cosh(x) + (36b - 24a b - 96a b )cosh(x) +--R + +--R 6 3 4 +--R 30a b + 40a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 6 6 3 4 5 +--R (6b + 8a b )cosh(x) + (48a b + 64a b )cosh(x) +--R + +--R 7 2 5 4 3 4 6 3 4 3 +--R (- 18b + 36a b + 80a b )cosh(x) + (- 96a b - 128a b )cosh(x) +--R + +--R 7 2 5 4 3 2 6 3 4 7 +--R (18b - 48a b - 96a b )cosh(x) + (48a b + 64a b )cosh(x) - 6b +--R + +--R 2 5 4 3 +--R 4a b + 16a b +--R * +--R sinh(x) +--R + +--R 6 3 4 6 2 5 4 3 5 +--R (6a b + 8a b )cosh(x) + (12a b + 16a b )cosh(x) +--R + +--R 6 3 4 4 2 5 4 3 3 +--R (- 18a b - 24a b )cosh(x) + (- 24a b - 32a b )cosh(x) +--R + +--R 6 3 4 2 2 5 4 3 6 3 4 +--R (18a b + 24a b )cosh(x) + (12a b + 16a b )cosh(x) - 6a b - 8a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (2b + 2a b)sinh(x) + (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 6 2 4 4 2 7 +--R (- 6b - 5a b + a b )sinh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 6 +--R ((- 36b - 30a b + 6a b )cosh(x) - 18a b - 15a b + 3a b)sinh(x) +--R + +--R 6 2 4 4 2 2 +--R (- 90b - 75a b + 15a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (- 96a b - 80a b + 16a b)cosh(x) + 18b + 3a b - 13a b + 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 6 2 4 4 2 3 +--R (- 120b - 100a b + 20a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 210a b - 175a b + 35a b)cosh(x) +--R + +--R 6 4 2 6 5 3 3 5 +--R (72b - 62a b + 10a )cosh(x) + 42a b + 35a b - 7a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 4 4 2 4 +--R (- 90b - 75a b + 15a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 240a b - 200a b + 40a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (108b - 30a b - 118a b + 20a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (144a b + 120a b - 24a b)cosh(x) - 18b + 9a b + 23a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 4 2 5 +--R (- 36b - 30a b + 6a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 150a b - 125a b + 25a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (72b - 60a b - 112a b + 20a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (180a b + 150a b - 30a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 +--R (- 36b + 42a b + 66a b - 12a )cosh(x) - 30a b - 25a b + 5a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 4 2 6 +--R (- 6b - 5a b + a b )cosh(x) +--R + +--R 5 3 3 5 5 +--R (- 48a b - 40a b + 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (18b - 45a b - 53a b + 10a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (96a b + 80a b - 16a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- 18b + 57a b + 63a b - 12a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (- 48a b - 40a b + 8a b)cosh(x) + 6b - 7a b - 11a b + 2a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 5 +--R (- 6a b - 5a b + a b)cosh(x) + (- 12a b - 10a b + 2a )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 6 3 +--R (18a b + 15a b - 3a b)cosh(x) + (24a b + 20a b - 4a )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 6 +--R (- 18a b - 15a b + 3a b)cosh(x) + (- 12a b - 10a b + 2a )cosh(x) +--R + +--R 5 3 3 5 +--R 6a b + 5a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) + 1) +--R + +--R 6 2 4 4 2 7 +--R (6b + 5a b - a b )sinh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 6 +--R ((36b + 30a b - 6a b )cosh(x) + 18a b + 15a b - 3a b)sinh(x) +--R + +--R 6 2 4 4 2 2 +--R (90b + 75a b - 15a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (96a b + 80a b - 16a b)cosh(x) - 18b - 3a b + 13a b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 6 2 4 4 2 3 +--R (120b + 100a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (210a b + 175a b - 35a b)cosh(x) +--R + +--R 6 4 2 6 5 3 3 5 +--R (- 72b + 62a b - 10a )cosh(x) - 42a b - 35a b + 7a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 4 4 2 4 +--R (90b + 75a b - 15a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (240a b + 200a b - 40a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- 108b + 30a b + 118a b - 20a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (- 144a b - 120a b + 24a b)cosh(x) + 18b - 9a b - 23a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 4 2 5 +--R (36b + 30a b - 6a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (150a b + 125a b - 25a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (- 72b + 60a b + 112a b - 20a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 180a b - 150a b + 30a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 +--R (36b - 42a b - 66a b + 12a )cosh(x) + 30a b + 25a b - 5a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 5 +--R (6b + 5a b - a b )cosh(x) + (48a b + 40a b - 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 18b + 45a b + 53a b - 10a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 96a b - 80a b + 16a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (18b - 57a b - 63a b + 12a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (48a b + 40a b - 8a b)cosh(x) - 6b + 7a b + 11a b - 2a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 5 +--R (6a b + 5a b - a b)cosh(x) + (12a b + 10a b - 2a )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b - 15a b + 3a b)cosh(x) +--R + +--R 2 4 4 2 6 3 5 3 3 5 2 +--R (- 24a b - 20a b + 4a )cosh(x) + (18a b + 15a b - 3a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (12a b + 10a b - 2a )cosh(x) - 6a b - 5a b + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a log(sinh(x) + cosh(x) - 1) +--R + +--R 7 2 5 7 +--R (12b + 16a b )sinh(x) +--R + +--R 7 2 5 6 3 4 6 +--R ((72b + 96a b )cosh(x) + 36a b + 48a b )sinh(x) +--R + +--R 7 2 5 2 6 3 4 7 +--R (180b + 240a b )cosh(x) + (192a b + 256a b )cosh(x) - 36b +--R + +--R 2 5 4 3 +--R - 24a b + 32a b +--R * +--R 5 +--R sinh(x) +--R + +--R 7 2 5 3 6 3 4 2 +--R (240b + 320a b )cosh(x) + (420a b + 560a b )cosh(x) +--R + +--R 7 2 5 4 3 6 3 4 +--R (- 144b - 72a b + 160a b )cosh(x) - 84a b - 112a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 5 4 6 3 4 3 +--R (180b + 240a b )cosh(x) + (480a b + 640a b )cosh(x) +--R + +--R 7 2 5 4 3 2 +--R (- 216b - 48a b + 320a b )cosh(x) +--R + +--R 6 3 4 7 4 3 +--R (- 288a b - 384a b )cosh(x) + 36b - 64a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 5 5 6 3 4 4 +--R (72b + 96a b )cosh(x) + (300a b + 400a b )cosh(x) +--R + +--R 7 2 5 4 3 3 +--R (- 144b + 48a b + 320a b )cosh(x) +--R + +--R 6 3 4 2 7 2 5 4 3 +--R (- 360a b - 480a b )cosh(x) + (72b - 48a b - 192a b )cosh(x) +--R + +--R 6 3 4 +--R 60a b + 80a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 6 6 3 4 5 +--R (12b + 16a b )cosh(x) + (96a b + 128a b )cosh(x) +--R + +--R 7 2 5 4 3 4 +--R (- 36b + 72a b + 160a b )cosh(x) +--R + +--R 6 3 4 3 7 2 5 4 3 2 +--R (- 192a b - 256a b )cosh(x) + (36b - 96a b - 192a b )cosh(x) +--R + +--R 6 3 4 7 2 5 4 3 +--R (96a b + 128a b )cosh(x) - 12b + 8a b + 32a b +--R * +--R sinh(x) +--R + +--R 6 3 4 6 2 5 4 3 5 +--R (12a b + 16a b )cosh(x) + (24a b + 32a b )cosh(x) +--R + +--R 6 3 4 4 2 5 4 3 3 +--R (- 36a b - 48a b )cosh(x) + (- 48a b - 64a b )cosh(x) +--R + +--R 6 3 4 2 2 5 4 3 6 3 4 +--R (36a b + 48a b )cosh(x) + (24a b + 32a b )cosh(x) - 12a b - 16a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 6 2 4 4 2 7 +--R (6b + 5a b - a b )sinh(x) +--R + +--R 6 2 4 4 2 5 3 3 5 6 +--R ((36b + 30a b - 6a b )cosh(x) + 18a b + 15a b - 3a b)sinh(x) +--R + +--R 6 2 4 4 2 2 +--R (90b + 75a b - 15a b )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (96a b + 80a b - 16a b)cosh(x) - 18b - 3a b + 13a b - 2a +--R * +--R 5 +--R sinh(x) +--R + +--R 6 2 4 4 2 3 +--R (120b + 100a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (210a b + 175a b - 35a b)cosh(x) +--R + +--R 6 4 2 6 5 3 3 5 +--R (- 72b + 62a b - 10a )cosh(x) - 42a b - 35a b + 7a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 4 4 2 4 +--R (90b + 75a b - 15a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (240a b + 200a b - 40a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- 108b + 30a b + 118a b - 20a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (- 144a b - 120a b + 24a b)cosh(x) + 18b - 9a b - 23a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 4 2 5 +--R (36b + 30a b - 6a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (150a b + 125a b - 25a b)cosh(x) +--R + +--R 6 2 4 4 2 6 3 +--R (- 72b + 60a b + 112a b - 20a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 180a b - 150a b + 30a b)cosh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 +--R (36b - 42a b - 66a b + 12a )cosh(x) + 30a b + 25a b - 5a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 4 2 6 5 3 3 5 5 +--R (6b + 5a b - a b )cosh(x) + (48a b + 40a b - 8a b)cosh(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 18b + 45a b + 53a b - 10a )cosh(x) +--R + +--R 5 3 3 5 3 +--R (- 96a b - 80a b + 16a b)cosh(x) +--R + +--R 6 2 4 4 2 6 2 +--R (18b - 57a b - 63a b + 12a )cosh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 +--R (48a b + 40a b - 8a b)cosh(x) - 6b + 7a b + 11a b - 2a +--R * +--R sinh(x) +--R + +--R 5 3 3 5 6 2 4 4 2 6 5 +--R (6a b + 5a b - a b)cosh(x) + (12a b + 10a b - 2a )cosh(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b - 15a b + 3a b)cosh(x) +--R + +--R 2 4 4 2 6 3 5 3 3 5 2 +--R (- 24a b - 20a b + 4a )cosh(x) + (18a b + 15a b - 3a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (12a b + 10a b - 2a )cosh(x) - 6a b - 5a b + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a acoth(cosh(x)) +--R + +--R 2 4 4 2 5 3 3 7 +--R ((a b + a b )coth(x)csch(x) + (- 4a b - 4a b )coth(x))sinh(x) +--R + +--R 2 4 4 2 3 3 5 +--R ((6a b + 6a b )cosh(x) + 3a b + 3a b)coth(x)csch(x) +--R + +--R 5 3 3 2 4 4 2 +--R ((- 24a b - 24a b )cosh(x) - 12a b - 12a b )coth(x) +--R + +--R 5 2 4 4 2 +--R - 2a b cosh(x) - 6a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 +--R (15a b + 15a b )cosh(x) + (16a b + 16a b)cosh(x) - 3a b +--R + +--R 4 2 6 +--R - a b + 2a +--R * +--R coth(x)csch(x) +--R + +--R 5 3 3 2 2 4 4 2 +--R (- 60a b - 60a b )cosh(x) + (- 64a b - 64a b )cosh(x) +--R + +--R 5 3 3 5 +--R 12a b + 4a b - 8a b +--R * +--R coth(x) +--R + +--R 5 2 2 4 4 2 5 3 3 +--R - 12a b cosh(x) + (- 34a b - 10a b )cosh(x) + 12a b - 2a b +--R + +--R 5 +--R - 6a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 4 2 3 3 3 5 2 +--R (20a b + 20a b )cosh(x) + (35a b + 35a b)cosh(x) +--R + +--R 2 4 4 2 6 3 3 5 +--R (- 12a b - 2a b + 10a )cosh(x) - 7a b - 7a b +--R * +--R coth(x)csch(x) +--R + +--R 5 3 3 3 2 4 4 2 2 +--R (- 80a b - 80a b )cosh(x) + (- 140a b - 140a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (48a b + 8a b - 40a b)cosh(x) + 28a b + 28a b +--R * +--R coth(x) +--R + +--R 5 3 2 4 4 2 2 +--R - 30a b cosh(x) + (- 80a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (54a b - 14a b - 26a b)cosh(x) + 36a b + 20a b - 4a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (15a b + 15a b )cosh(x) + (40a b + 40a b)cosh(x) +--R + +--R 2 4 4 2 6 2 3 3 5 +--R (- 18a b + 2a b + 20a )cosh(x) + (- 24a b - 24a b)cosh(x) +--R + +--R 2 4 4 2 6 +--R 3a b - a b - 4a +--R * +--R coth(x)csch(x) +--R + +--R 5 3 3 4 2 4 4 2 3 +--R (- 60a b - 60a b )cosh(x) + (- 160a b - 160a b )cosh(x) +--R + +--R 5 3 3 5 2 2 4 4 2 +--R (72a b - 8a b - 80a b)cosh(x) + (96a b + 96a b )cosh(x) +--R + +--R 5 3 3 5 +--R - 12a b + 4a b + 16a b +--R * +--R coth(x) +--R + +--R 5 4 2 4 4 2 3 +--R - 40a b cosh(x) + (- 100a b - 20a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (96a b - 36a b - 44a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (128a b + 64a b - 16a )cosh(x) - 24a b + 4a b + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 4 2 5 3 3 5 4 +--R (6a b + 6a b )cosh(x) + (25a b + 25a b)cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (- 12a b + 8a b + 20a )cosh(x) +--R + +--R 3 3 5 2 2 4 4 2 6 +--R (- 30a b - 30a b)cosh(x) + (6a b - 6a b - 12a )cosh(x) +--R + +--R 3 3 5 +--R 5a b + 5a b +--R * +--R coth(x)csch(x) +--R + +--R 5 3 3 5 2 4 4 2 4 +--R (- 24a b - 24a b )cosh(x) + (- 100a b - 100a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (48a b - 32a b - 80a b)cosh(x) +--R + +--R 2 4 4 2 2 +--R (120a b + 120a b )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 +--R (- 24a b + 24a b + 48a b)cosh(x) - 20a b - 20a b +--R * +--R coth(x) +--R + +--R 5 5 2 4 4 2 4 +--R - 30a b cosh(x) + (- 70a b - 10a b )cosh(x) +--R + +--R 5 3 3 5 3 +--R (84a b - 44a b - 36a b)cosh(x) +--R + +--R 2 4 4 2 6 2 +--R (168a b + 72a b - 24a )cosh(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (- 54a b + 32a b + 40a b)cosh(x) - 42a b - 34a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 3 5 5 +--R (a b + a b )cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 2 4 4 2 6 4 3 3 5 3 +--R (- 3a b + 7a b + 10a )cosh(x) + (- 16a b - 16a b)cosh(x) +--R + +--R 2 4 4 2 6 2 3 3 5 2 4 +--R (3a b - 9a b - 12a )cosh(x) + (8a b + 8a b)cosh(x) - a b +--R + +--R 4 2 6 +--R a b + 2a +--R * +--R coth(x)csch(x) +--R + +--R 5 3 3 6 2 4 4 2 5 +--R (- 4a b - 4a b )cosh(x) + (- 32a b - 32a b )cosh(x) +--R + +--R 5 3 3 5 4 2 4 4 2 3 +--R (12a b - 28a b - 40a b)cosh(x) + (64a b + 64a b )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 12a b + 36a b + 48a b)cosh(x) +--R + +--R 2 4 4 2 5 3 3 5 +--R (- 32a b - 32a b )cosh(x) + 4a b - 4a b - 8a b +--R * +--R coth(x) +--R + +--R 5 6 2 4 4 2 5 +--R - 12a b cosh(x) + (- 26a b - 2a b )cosh(x) +--R + +--R 5 3 3 5 4 +--R (36a b - 26a b - 14a b)cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (96a b + 32a b - 16a )cosh(x) +--R + +--R 5 3 3 5 2 +--R (- 36a b + 52a b + 44a b)cosh(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (- 70a b - 54a b - 8a )cosh(x) + 12a b - 10a b - 14a b +--R * +--R sinh(x) +--R + +--R 3 3 5 6 4 2 6 5 +--R (a b + a b)cosh(x) + (2a b + 2a )cosh(x) +--R + +--R 3 3 5 4 4 2 6 3 +--R (- 3a b - 3a b)cosh(x) + (- 4a b - 4a )cosh(x) +--R + +--R 3 3 5 2 4 2 6 3 3 5 +--R (3a b + 3a b)cosh(x) + (2a b + 2a )cosh(x) - a b - a b +--R * +--R coth(x)csch(x) +--R + +--R 2 4 4 2 6 3 3 5 5 +--R (- 4a b - 4a b )cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 2 4 4 2 4 3 3 5 3 +--R (12a b + 12a b )cosh(x) + (16a b + 16a b)cosh(x) +--R + +--R 2 4 4 2 2 3 3 5 2 4 +--R (- 12a b - 12a b )cosh(x) + (- 8a b - 8a b)cosh(x) + 4a b +--R + +--R 4 2 +--R 4a b +--R * +--R coth(x) +--R + +--R 5 7 2 4 6 5 3 3 5 5 +--R - 2a b cosh(x) - 4a b cosh(x) + (6a b - 6a b - 2a b)cosh(x) +--R + +--R 2 4 4 2 6 4 5 3 3 5 3 +--R (20a b + 4a b - 4a )cosh(x) + (- 6a b + 24a b + 16a b)cosh(x) +--R + +--R 2 4 4 2 6 2 5 3 3 5 +--R (- 28a b - 20a b - 4a )cosh(x) + (2a b - 18a b - 14a b)cosh(x) +--R + +--R 2 4 4 2 +--R 12a b + 8a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 4 6 2 7 +--R (2a b + 2a b )sinh(x) +--R + +--R 4 4 6 2 5 3 7 6 +--R ((12a b + 12a b )cosh(x) + 6a b + 6a b)sinh(x) +--R + +--R 4 4 6 2 2 5 3 7 4 4 6 2 +--R (30a b + 30a b )cosh(x) + (32a b + 32a b)cosh(x) - 6a b - 2a b +--R + +--R 8 +--R 4a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 4 6 2 3 5 3 7 2 +--R (40a b + 40a b )cosh(x) + (70a b + 70a b)cosh(x) +--R + +--R 4 4 6 2 8 5 3 7 +--R (- 24a b - 4a b + 20a )cosh(x) - 14a b - 14a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 4 6 2 4 5 3 7 3 +--R (30a b + 30a b )cosh(x) + (80a b + 80a b)cosh(x) +--R + +--R 4 4 6 2 8 2 5 3 7 +--R (- 36a b + 4a b + 40a )cosh(x) + (- 48a b - 48a b)cosh(x) +--R + +--R 4 4 6 2 8 +--R 6a b - 2a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 6 2 5 5 3 7 4 +--R (12a b + 12a b )cosh(x) + (50a b + 50a b)cosh(x) +--R + +--R 4 4 6 2 8 3 5 3 7 2 +--R (- 24a b + 16a b + 40a )cosh(x) + (- 60a b - 60a b)cosh(x) +--R + +--R 4 4 6 2 8 5 3 7 +--R (12a b - 12a b - 24a )cosh(x) + 10a b + 10a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 6 5 3 7 5 +--R (2a b + 2a b )cosh(x) + (16a b + 16a b)cosh(x) +--R + +--R 4 4 6 2 8 4 5 3 7 3 +--R (- 6a b + 14a b + 20a )cosh(x) + (- 32a b - 32a b)cosh(x) +--R + +--R 4 4 6 2 8 2 5 3 7 4 4 +--R (6a b - 18a b - 24a )cosh(x) + (16a b + 16a b)cosh(x) - 2a b +--R + +--R 6 2 8 +--R 2a b + 4a +--R * +--R sinh(x) +--R + +--R 5 3 7 6 6 2 8 5 +--R (2a b + 2a b)cosh(x) + (4a b + 4a )cosh(x) +--R + +--R 5 3 7 4 6 2 8 3 +--R (- 6a b - 6a b)cosh(x) + (- 8a b - 8a )cosh(x) +--R + +--R 5 3 7 2 6 2 8 5 3 7 +--R (6a b + 6a b)cosh(x) + (4a b + 4a )cosh(x) - 2a b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 552 +--d0739:= D(m0739,x) +--E 200 + +--S 201 of 552 +t0740:= csch(x)/(%i+sinh(x))^2 +--R +--R +--R csch(x) +--R (193) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 201 + +--S 202 of 552 +r0740:= acoth(cosh(x))-4*cosh(x)/(3-3*%i*sinh(x))+1/3*cosh(x)/(%i+sinh(x))^2 +--R +--R +--R (194) +--R 2 +--R (3sinh(x) + 6%i sinh(x) - 3)acoth(cosh(x)) - 4%i cosh(x)sinh(x) + 5cosh(x) +--R --------------------------------------------------------------------------- +--R 2 +--R 3sinh(x) + 6%i sinh(x) - 3 +--R Type: Expression(Complex(Integer)) +--E 202 + +--S 203 of 552 +a0740:= integrate(t0740,x) +--R +--R +--R (195) +--R 3 2 +--R 3sinh(x) + (9cosh(x) + 9%i)sinh(x) +--R + +--R 2 3 2 +--R (9cosh(x) + 18%i cosh(x) - 9)sinh(x) + 3cosh(x) + 9%i cosh(x) +--R + +--R - 9cosh(x) - 3%i +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 3 2 +--R - 3sinh(x) + (- 9cosh(x) - 9%i)sinh(x) +--R + +--R 2 3 2 +--R (- 9cosh(x) - 18%i cosh(x) + 9)sinh(x) - 3cosh(x) - 9%i cosh(x) +--R + +--R 9cosh(x) + 3%i +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R - 6sinh(x) + (- 12cosh(x) - 18%i)sinh(x) - 6cosh(x) - 18%i cosh(x) + 8 +--R / +--R 3 2 +--R 3sinh(x) + (9cosh(x) + 9%i)sinh(x) +--R + +--R 2 3 2 +--R (9cosh(x) + 18%i cosh(x) - 9)sinh(x) + 3cosh(x) + 9%i cosh(x) +--R + +--R - 9cosh(x) - 3%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 203 + +--S 204 of 552 +m0740:= a0740-r0740 +--R +--R +--R (196) +--R 5 4 +--R 3sinh(x) + (9cosh(x) + 15%i)sinh(x) +--R + +--R 2 3 +--R (9cosh(x) + 36%i cosh(x) - 30)sinh(x) +--R + +--R 3 2 2 +--R (3cosh(x) + 27%i cosh(x) - 54cosh(x) - 30%i)sinh(x) +--R + +--R 3 2 3 +--R (6%i cosh(x) - 27cosh(x) - 36%i cosh(x) + 15)sinh(x) - 3cosh(x) +--R + +--R 2 +--R - 9%i cosh(x) + 9cosh(x) + 3%i +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 5 4 +--R - 3sinh(x) + (- 9cosh(x) - 15%i)sinh(x) +--R + +--R 2 3 +--R (- 9cosh(x) - 36%i cosh(x) + 30)sinh(x) +--R + +--R 3 2 2 +--R (- 3cosh(x) - 27%i cosh(x) + 54cosh(x) + 30%i)sinh(x) +--R + +--R 3 2 3 +--R (- 6%i cosh(x) + 27cosh(x) + 36%i cosh(x) - 15)sinh(x) + 3cosh(x) +--R + +--R 2 +--R 9%i cosh(x) - 9cosh(x) - 3%i +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 5 4 +--R - 3sinh(x) + (- 9cosh(x) - 15%i)sinh(x) +--R + +--R 2 3 +--R (- 9cosh(x) - 36%i cosh(x) + 30)sinh(x) +--R + +--R 3 2 2 +--R (- 3cosh(x) - 27%i cosh(x) + 54cosh(x) + 30%i)sinh(x) +--R + +--R 3 2 3 +--R (- 6%i cosh(x) + 27cosh(x) + 36%i cosh(x) - 15)sinh(x) + 3cosh(x) +--R + +--R 2 +--R 9%i cosh(x) - 9cosh(x) - 3%i +--R * +--R acoth(cosh(x)) +--R + +--R 4 2 3 +--R (4%i cosh(x) - 6)sinh(x) + (12%i cosh(x) - 29cosh(x) - 30%i)sinh(x) +--R + +--R 3 2 2 +--R (12%i cosh(x) - 45cosh(x) - 69%i cosh(x) + 50)sinh(x) +--R + +--R 4 3 2 +--R (4%i cosh(x) - 27cosh(x) - 54%i cosh(x) + 67cosh(x) + 34%i)sinh(x) +--R + +--R 4 3 2 +--R - 5cosh(x) - 15%i cosh(x) + 21cosh(x) + 23%i cosh(x) - 8 +--R / +--R 5 4 +--R 3sinh(x) + (9cosh(x) + 15%i)sinh(x) +--R + +--R 2 3 +--R (9cosh(x) + 36%i cosh(x) - 30)sinh(x) +--R + +--R 3 2 2 +--R (3cosh(x) + 27%i cosh(x) - 54cosh(x) - 30%i)sinh(x) +--R + +--R 3 2 3 +--R (6%i cosh(x) - 27cosh(x) - 36%i cosh(x) + 15)sinh(x) - 3cosh(x) +--R + +--R 2 +--R - 9%i cosh(x) + 9cosh(x) + 3%i +--R Type: Expression(Complex(Integer)) +--E 204 + +--S 205 of 552 +d0740:= D(m0740,x) +--R +--R +--R (197) +--R 10 2 9 +--R 3sinh(x) + (4%i cosh(x) + 18cosh(x) + 17%i)sinh(x) +--R + +--R 3 2 8 +--R (24%i cosh(x) + 20cosh(x) + 90%i cosh(x) - 41)sinh(x) +--R + +--R 4 3 2 7 +--R (56%i cosh(x) - 74cosh(x) + 130%i cosh(x) - 184cosh(x) - 57%i)sinh(x) +--R + +--R 5 4 3 2 +--R 56%i cosh(x) - 228cosh(x) - 78%i cosh(x) - 209cosh(x) +--R + +--R - 200%i cosh(x) + 29 +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 206cosh(x) - 356%i cosh(x) + 120cosh(x) - 97%i cosh(x) +--R + +--R 50cosh(x) - 39%i +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 56%i cosh(x) + 38cosh(x) - 218%i cosh(x) + 301cosh(x) +--R + +--R 3 2 +--R 272%i cosh(x) - 128cosh(x) - 190%i cosh(x) + 65 +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 56%i cosh(x) + 210cosh(x) + 190%i cosh(x) - 56cosh(x) +--R + +--R 4 3 2 +--R 181%i cosh(x) - 278cosh(x) - 288%i cosh(x) + 244cosh(x) + 33%i +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 7 6 +--R - 24%i cosh(x) + 161cosh(x) + 310%i cosh(x) - 355cosh(x) +--R + +--R 5 4 3 2 +--R - 256%i cosh(x) - 33cosh(x) - 106%i cosh(x) + 235cosh(x) +--R + +--R 100%i cosh(x) - 8 +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 4%i cosh(x) + 52cosh(x) + 147%i cosh(x) - 232cosh(x) +--R + +--R 6 5 4 3 +--R - 283%i cosh(x) + 180cosh(x) + 79%i cosh(x) + 8cosh(x) +--R + +--R 2 +--R 63%i cosh(x) - 8cosh(x) - 2%i +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R 6cosh(x) + 24%i cosh(x) - 48cosh(x) - 72%i cosh(x) + 84cosh(x) +--R + +--R 5 4 2 +--R 48%i cosh(x) - 48cosh(x) + 6cosh(x) +--R / +--R 2 9 +--R (3cosh(x) - 3)sinh(x) +--R + +--R 3 2 8 +--R (18cosh(x) + 21%i cosh(x) - 18cosh(x) - 21%i)sinh(x) +--R + +--R 4 3 2 7 +--R (45cosh(x) + 114%i cosh(x) - 111cosh(x) - 114%i cosh(x) + 66)sinh(x) +--R + +--R 5 4 3 2 +--R 60cosh(x) + 255%i cosh(x) - 378cosh(x) - 381%i cosh(x) +--R + +--R 318cosh(x) + 126%i +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 45cosh(x) + 300%i cosh(x) - 666cosh(x) - 822%i cosh(x) +--R + +--R 2 +--R 789cosh(x) + 522%i cosh(x) - 168 +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 18cosh(x) + 195%i cosh(x) - 642cosh(x) - 1050%i cosh(x) +--R + +--R 3 2 +--R 1194cosh(x) + 1023%i cosh(x) - 570cosh(x) - 168%i +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 3cosh(x) + 66%i cosh(x) - 339cosh(x) - 762%i cosh(x) +--R + +--R 4 3 2 +--R 1071cosh(x) + 1134%i cosh(x) - 861cosh(x) - 438%i cosh(x) + 126 +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 9%i cosh(x) - 90cosh(x) - 297%i cosh(x) + 534cosh(x) +--R + +--R 4 3 2 +--R 693%i cosh(x) - 678cosh(x) - 471%i cosh(x) + 234cosh(x) + 66%i +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 6 5 +--R - 9cosh(x) - 54%i cosh(x) + 132cosh(x) + 210%i cosh(x) +--R + +--R 4 3 2 +--R - 258cosh(x) - 234%i cosh(x) + 156cosh(x) + 78%i cosh(x) - 21 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 +--R - 3%i cosh(x) + 12cosh(x) + 24%i cosh(x) - 36cosh(x) - 42%i cosh(x) +--R + +--R 3 2 +--R 36cosh(x) + 24%i cosh(x) - 12cosh(x) - 3%i +--R Type: Expression(Complex(Integer)) +--E 205 + +--S 206 of 552 +t0741:= csch(x)^2/(%i+sinh(x))^2 +--R +--R +--R 2 +--R csch(x) +--R (198) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 206 + +--S 207 of 552 +r0741:= 2*%i*acoth(cosh(x))+coth(x)-7*%i*cosh(x)/(3-3*%i*sinh(x))+_ + 1/3*%i*cosh(x)/(%i+sinh(x))^2 +--R +--R +--R (199) +--R 2 2 +--R (2%i sinh(x) - 4sinh(x) - 2%i)acoth(cosh(x)) + coth(x)sinh(x) +--R + +--R 7 8 +--R (2%i coth(x) + - cosh(x))sinh(x) - coth(x) + - %i cosh(x) +--R 3 3 +--R / +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 207 + +--S 208 of 552 +a0741:= integrate(t0741,x) +--R +--R +--R (200) +--R 5 4 +--R 6%i sinh(x) + (30%i cosh(x) - 18)sinh(x) +--R + +--R 2 3 +--R (60%i cosh(x) - 72cosh(x) - 24%i)sinh(x) +--R + +--R 3 2 2 +--R (60%i cosh(x) - 108cosh(x) - 72%i cosh(x) + 24)sinh(x) +--R + +--R 4 3 2 +--R (30%i cosh(x) - 72cosh(x) - 72%i cosh(x) + 48cosh(x) + 18%i) +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R 6%i cosh(x) - 18cosh(x) - 24%i cosh(x) + 24cosh(x) + 18%i cosh(x) +--R + +--R - 6 +--R * +--R sinh(x) + cosh(x) + 1 +--R log(---------------------) +--R sinh(x) + cosh(x) - 1 +--R + +--R 4 3 +--R - 12%i sinh(x) + (- 48%i cosh(x) + 36)sinh(x) +--R + +--R 2 2 +--R (- 72%i cosh(x) + 108cosh(x) + 44%i)sinh(x) +--R + +--R 3 2 +--R (- 48%i cosh(x) + 108cosh(x) + 88%i cosh(x) - 48)sinh(x) +--R + +--R 4 3 2 +--R - 12%i cosh(x) + 36cosh(x) + 44%i cosh(x) - 48cosh(x) - 20%i +--R / +--R 5 4 +--R 3sinh(x) + (15cosh(x) + 9%i)sinh(x) +--R + +--R 2 3 +--R (30cosh(x) + 36%i cosh(x) - 12)sinh(x) +--R + +--R 3 2 2 +--R (30cosh(x) + 54%i cosh(x) - 36cosh(x) - 12%i)sinh(x) +--R + +--R 4 3 2 +--R (15cosh(x) + 36%i cosh(x) - 36cosh(x) - 24%i cosh(x) + 9)sinh(x) +--R + +--R 5 4 3 2 +--R 3cosh(x) + 9%i cosh(x) - 12cosh(x) - 12%i cosh(x) + 9cosh(x) + 3%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 208 + +--S 209 of 552 +m0741:= a0741-r0741 +--R +--R +--R (201) +--R 7 6 +--R 2%i sinh(x) + (10%i cosh(x) - 10)sinh(x) +--R + +--R 2 5 +--R (20%i cosh(x) - 44cosh(x) - 22%i)sinh(x) +--R + +--R 3 2 4 +--R (20%i cosh(x) - 76cosh(x) - 82%i cosh(x) + 30)sinh(x) +--R + +--R 4 3 2 +--R (10%i cosh(x) - 64cosh(x) - 116%i cosh(x) + 88cosh(x) + 30%i) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 2%i cosh(x) - 26cosh(x) - 76%i cosh(x) + 92cosh(x) +--R + +--R 62%i cosh(x) - 22 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 4cosh(x) - 22%i cosh(x) + 40cosh(x) + 40%i cosh(x) +--R + +--R - 28cosh(x) - 10%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 2%i cosh(x) + 6cosh(x) + 8%i cosh(x) - 8cosh(x) - 6%i cosh(x) + 2 +--R * +--R sinh(x) + cosh(x) + 1 +--R log(---------------------) +--R sinh(x) + cosh(x) - 1 +--R + +--R 7 6 +--R - 2%i sinh(x) + (- 10%i cosh(x) + 10)sinh(x) +--R + +--R 2 5 +--R (- 20%i cosh(x) + 44cosh(x) + 22%i)sinh(x) +--R + +--R 3 2 4 +--R (- 20%i cosh(x) + 76cosh(x) + 82%i cosh(x) - 30)sinh(x) +--R + +--R 4 3 2 +--R (- 10%i cosh(x) + 64cosh(x) + 116%i cosh(x) - 88cosh(x) - 30%i) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 2%i cosh(x) + 26cosh(x) + 76%i cosh(x) - 92cosh(x) +--R + +--R - 62%i cosh(x) + 22 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 4cosh(x) + 22%i cosh(x) - 40cosh(x) - 40%i cosh(x) +--R + +--R 28cosh(x) + 10%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R 2%i cosh(x) - 6cosh(x) - 8%i cosh(x) + 8cosh(x) + 6%i cosh(x) - 2 +--R * +--R acoth(cosh(x)) +--R + +--R 7 7 6 +--R - coth(x)sinh(x) + ((- 5cosh(x) - 5%i)coth(x) - - cosh(x) - 4%i)sinh(x) +--R 3 +--R + +--R 2 35 2 +--R (- 10cosh(x) - 22%i cosh(x) + 11)coth(x) - -- cosh(x) +--R 3 +--R + +--R 77 +--R - -- %i cosh(x) + 20 +--R 3 +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 +--R (- 10cosh(x) - 38%i cosh(x) + 41cosh(x) + 15%i)coth(x) +--R + +--R 70 3 196 2 256 128 +--R - -- cosh(x) - --- %i cosh(x) + --- cosh(x) + --- %i +--R 3 3 3 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 5cosh(x) - 32%i cosh(x) + 58cosh(x) + 44%i cosh(x) - 15)coth(x) +--R + +--R 70 4 254 3 2 412 172 +--R - -- cosh(x) - --- %i cosh(x) + 144cosh(x) + --- %i cosh(x) - --- +--R 3 3 3 3 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - cosh(x) - 13%i cosh(x) + 38cosh(x) + 46%i cosh(x) +--R + +--R - 31cosh(x) - 11%i +--R * +--R coth(x) +--R + +--R 35 5 176 4 3 484 2 +--R - -- cosh(x) - --- %i cosh(x) + 120cosh(x) + --- %i cosh(x) +--R 3 3 3 +--R + +--R 385 160 +--R - --- cosh(x) - --- %i +--R 3 3 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 2%i cosh(x) + 11cosh(x) + 20%i cosh(x) - 20cosh(x) +--R + +--R - 14%i cosh(x) + 5 +--R * +--R coth(x) +--R + +--R 7 6 61 5 148 4 244 3 +--R - - cosh(x) - -- %i cosh(x) + --- cosh(x) + --- %i cosh(x) +--R 3 3 3 3 +--R + +--R 281 2 215 88 +--R - --- cosh(x) - --- %i cosh(x) + -- +--R 3 3 3 +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R (cosh(x) + 3%i cosh(x) - 4cosh(x) - 4%i cosh(x) + 3cosh(x) + %i) +--R * +--R coth(x) +--R + +--R 8 6 5 44 4 68 3 +--R - - %i cosh(x) + 8cosh(x) + -- %i cosh(x) - -- cosh(x) +--R 3 3 3 +--R + +--R 68 2 56 20 +--R - -- %i cosh(x) + -- cosh(x) + -- %i +--R 3 3 3 +--R / +--R 7 6 +--R sinh(x) + (5cosh(x) + 5%i)sinh(x) +--R + +--R 2 5 +--R (10cosh(x) + 22%i cosh(x) - 11)sinh(x) +--R + +--R 3 2 4 +--R (10cosh(x) + 38%i cosh(x) - 41cosh(x) - 15%i)sinh(x) +--R + +--R 4 3 2 3 +--R (5cosh(x) + 32%i cosh(x) - 58cosh(x) - 44%i cosh(x) + 15)sinh(x) +--R + +--R 5 4 3 2 +--R cosh(x) + 13%i cosh(x) - 38cosh(x) - 46%i cosh(x) + 31cosh(x) +--R + +--R 11%i +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 2%i cosh(x) - 11cosh(x) - 20%i cosh(x) + 20cosh(x) + 14%i cosh(x) +--R + +--R - 5 +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R - cosh(x) - 3%i cosh(x) + 4cosh(x) + 4%i cosh(x) - 3cosh(x) - %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 209 + +--S 210 of 552 +d0741:= D(m0741,x) +--R +--R +--R (202) +--R 12 +--R 2%i sinh(x) +--R + +--R 2 2 10 2 32 11 +--R ((cosh(x) - 1)coth(x) - -- cosh(x) + 16%i cosh(x) - --)sinh(x) +--R 3 3 +--R + +--R 3 2 2 80 3 +--R (8cosh(x) + 7%i cosh(x) - 8cosh(x) - 7%i)coth(x) - -- cosh(x) +--R 3 +--R + +--R 104 2 232 74 +--R --- %i cosh(x) - --- cosh(x) - -- %i +--R 3 3 3 +--R * +--R 10 +--R sinh(x) +--R + +--R 4 3 2 2 +--R (28cosh(x) + 52%i cosh(x) - 51cosh(x) - 52%i cosh(x) + 23)coth(x) +--R + +--R 4 136 3 542 2 464 101 +--R - 91cosh(x) - --- %i cosh(x) - --- cosh(x) - --- %i cosh(x) + --- +--R 3 3 3 3 +--R * +--R 9 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) + 168%i cosh(x) - 212cosh(x) - 217%i cosh(x) +--R + +--R 156cosh(x) + 49%i +--R * +--R 2 +--R coth(x) +--R + +--R 5 1055 4 56 3 878 2 +--R - 168cosh(x) - ---- %i cosh(x) - -- cosh(x) - --- %i cosh(x) +--R 3 3 3 +--R + +--R 488 85 +--R --- cosh(x) + -- %i +--R 3 3 +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 70cosh(x) + 308%i cosh(x) - 526cosh(x) - 604%i cosh(x) +--R + +--R 2 +--R 534cosh(x) + 296%i cosh(x) - 78 +--R * +--R 2 +--R coth(x) +--R + +--R 6 2140 5 4 3 +--R - 168cosh(x) - ---- %i cosh(x) + 668cosh(x) + 80%i cosh(x) +--R 3 +--R + +--R 2 196 +--R 144cosh(x) + --- %i cosh(x) - 20 +--R 3 +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 56cosh(x) + 350%i cosh(x) - 804cosh(x) - 1110%i cosh(x) +--R + +--R 3 2 +--R 1156cosh(x) + 858%i cosh(x) - 408cosh(x) - 98%i +--R * +--R 2 +--R coth(x) +--R + +--R 7 2072 6 3980 5 3176 4 +--R - 56cosh(x) - ---- %i cosh(x) + ---- cosh(x) + ---- %i cosh(x) +--R 3 3 3 +--R + +--R 1576 3 2 116 +--R - ---- cosh(x) - 216%i cosh(x) + --- cosh(x) - 16%i +--R 3 3 +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 28cosh(x) + 252%i cosh(x) - 778cosh(x) - 1328%i cosh(x) +--R + +--R 4 3 2 +--R 1638cosh(x) + 1508%i cosh(x) - 986cosh(x) - 432%i cosh(x) + 98 +--R * +--R 2 +--R coth(x) +--R + +--R 8 652 7 3272 6 4628 5 +--R 70cosh(x) - --- %i cosh(x) + ---- cosh(x) + ---- %i cosh(x) +--R 3 3 3 +--R + +--R 4 2812 3 1408 2 +--R - 1404cosh(x) - ---- %i cosh(x) + ---- cosh(x) + 60%i cosh(x) - 10 +--R 3 3 +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 8cosh(x) + 112%i cosh(x) - 476cosh(x) - 1022%i cosh(x) +--R + +--R 5 4 3 2 +--R 1504cosh(x) + 1678%i cosh(x) - 1388cosh(x) - 846%i cosh(x) +--R + +--R 352cosh(x) + 78%i +--R * +--R 2 +--R coth(x) +--R + +--R 9 664 8 7 6 +--R 104cosh(x) + --- %i cosh(x) + 196cosh(x) + 812%i cosh(x) +--R 3 +--R + +--R 3740 5 3688 4 2836 3 1204 2 +--R - ---- cosh(x) - ---- %i cosh(x) + ---- cosh(x) + ---- %i cosh(x) +--R 3 3 3 3 +--R + +--R 284 136 +--R - --- cosh(x) - --- %i +--R 3 3 +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 8 7 +--R cosh(x) + 28%i cosh(x) - 177cosh(x) - 492%i cosh(x) +--R + +--R 6 5 4 3 +--R 870cosh(x) + 1164%i cosh(x) - 1182cosh(x) - 916%i cosh(x) +--R + +--R 2 +--R 537cosh(x) + 216%i cosh(x) - 49 +--R * +--R 2 +--R coth(x) +--R + +--R 10 860 9 1076 8 488 7 +--R 62cosh(x) + --- %i cosh(x) - ---- cosh(x) - --- %i cosh(x) +--R 3 3 3 +--R + +--R 6 5 1976 4 1720 3 +--R - 212cosh(x) - 552%i cosh(x) + ---- cosh(x) + ---- %i cosh(x) +--R 3 3 +--R + +--R 686 2 436 140 +--R - --- cosh(x) - --- %i cosh(x) + --- +--R 3 3 3 +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 3%i cosh(x) - 36cosh(x) - 139%i cosh(x) + 300cosh(x) +--R + +--R 6 5 4 3 +--R 478%i cosh(x) - 588cosh(x) - 558%i cosh(x) + 420cosh(x) +--R + +--R 2 +--R 239%i cosh(x) - 96cosh(x) - 23%i +--R * +--R 2 +--R coth(x) +--R + +--R 56 11 424 10 916 9 1190 8 +--R -- cosh(x) + --- %i cosh(x) - --- cosh(x) - ---- %i cosh(x) +--R 3 3 3 3 +--R + +--R 1096 7 496 6 32 5 620 4 +--R ---- cosh(x) + --- %i cosh(x) - -- cosh(x) + --- %i cosh(x) +--R 3 3 3 3 +--R + +--R 512 3 424 2 308 74 +--R - --- cosh(x) - --- %i cosh(x) + --- cosh(x) + -- %i +--R 3 3 3 3 +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 3cosh(x) - 20%i cosh(x) + 55cosh(x) + 104%i cosh(x) +--R + +--R 6 5 4 3 +--R - 154cosh(x) - 176%i cosh(x) + 162cosh(x) + 120%i cosh(x) +--R + +--R 2 +--R - 67cosh(x) - 28%i cosh(x) + 7 +--R * +--R 2 +--R coth(x) +--R + +--R 7 12 100 11 298 10 524 9 +--R - cosh(x) + --- %i cosh(x) - --- cosh(x) - --- %i cosh(x) +--R 3 3 3 3 +--R + +--R 715 8 688 7 572 6 304 5 +--R --- cosh(x) + --- %i cosh(x) - --- cosh(x) - --- %i cosh(x) +--R 3 3 3 3 +--R + +--R 11 4 52 3 182 2 92 23 +--R - -- cosh(x) - -- %i cosh(x) + --- cosh(x) + -- %i cosh(x) - -- +--R 3 3 3 3 3 +--R * +--R sinh(x) +--R + +--R 10 9 8 7 +--R - %i cosh(x) + 4cosh(x) + 9%i cosh(x) - 16cosh(x) +--R + +--R 6 5 4 3 +--R - 22%i cosh(x) + 24cosh(x) + 22%i cosh(x) - 16cosh(x) +--R + +--R 2 +--R - 9%i cosh(x) + 4cosh(x) + %i +--R * +--R 2 +--R coth(x) +--R + +--R 12 11 10 9 8 +--R 3%i cosh(x) - 12cosh(x) - 26%i cosh(x) + 44cosh(x) + 57%i cosh(x) +--R + +--R 7 6 5 4 3 +--R - 56cosh(x) - 60%i cosh(x) + 24cosh(x) + 21%i cosh(x) + 4cosh(x) +--R + +--R 2 +--R 6%i cosh(x) - 4cosh(x) - %i +--R / +--R 2 11 +--R (cosh(x) - 1)sinh(x) +--R + +--R 3 2 10 +--R (8cosh(x) + 7%i cosh(x) - 8cosh(x) - 7%i)sinh(x) +--R + +--R 4 3 2 9 +--R (28cosh(x) + 52%i cosh(x) - 51cosh(x) - 52%i cosh(x) + 23)sinh(x) +--R + +--R 5 4 3 2 +--R 56cosh(x) + 168%i cosh(x) - 212cosh(x) - 217%i cosh(x) +--R + +--R 156cosh(x) + 49%i +--R * +--R 8 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 70cosh(x) + 308%i cosh(x) - 526cosh(x) - 604%i cosh(x) +--R + +--R 2 +--R 534cosh(x) + 296%i cosh(x) - 78 +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 56cosh(x) + 350%i cosh(x) - 804cosh(x) - 1110%i cosh(x) +--R + +--R 3 2 +--R 1156cosh(x) + 858%i cosh(x) - 408cosh(x) - 98%i +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 28cosh(x) + 252%i cosh(x) - 778cosh(x) - 1328%i cosh(x) +--R + +--R 4 3 2 +--R 1638cosh(x) + 1508%i cosh(x) - 986cosh(x) - 432%i cosh(x) + 98 +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 8cosh(x) + 112%i cosh(x) - 476cosh(x) - 1022%i cosh(x) +--R + +--R 5 4 3 2 +--R 1504cosh(x) + 1678%i cosh(x) - 1388cosh(x) - 846%i cosh(x) +--R + +--R 352cosh(x) + 78%i +--R * +--R 4 +--R sinh(x) +--R + +--R 10 9 8 7 +--R cosh(x) + 28%i cosh(x) - 177cosh(x) - 492%i cosh(x) +--R + +--R 6 5 4 3 +--R 870cosh(x) + 1164%i cosh(x) - 1182cosh(x) - 916%i cosh(x) +--R + +--R 2 +--R 537cosh(x) + 216%i cosh(x) - 49 +--R * +--R 3 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 3%i cosh(x) - 36cosh(x) - 139%i cosh(x) + 300cosh(x) +--R + +--R 6 5 4 3 +--R 478%i cosh(x) - 588cosh(x) - 558%i cosh(x) + 420cosh(x) +--R + +--R 2 +--R 239%i cosh(x) - 96cosh(x) - 23%i +--R * +--R 2 +--R sinh(x) +--R + +--R 10 9 8 7 +--R - 3cosh(x) - 20%i cosh(x) + 55cosh(x) + 104%i cosh(x) +--R + +--R 6 5 4 3 +--R - 154cosh(x) - 176%i cosh(x) + 162cosh(x) + 120%i cosh(x) +--R + +--R 2 +--R - 67cosh(x) - 28%i cosh(x) + 7 +--R * +--R sinh(x) +--R + +--R 10 9 8 7 6 +--R - %i cosh(x) + 4cosh(x) + 9%i cosh(x) - 16cosh(x) - 22%i cosh(x) +--R + +--R 5 4 3 2 +--R 24cosh(x) + 22%i cosh(x) - 16cosh(x) - 9%i cosh(x) + 4cosh(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 210 + +--S 211 of 552 +t0742:= csch(x)^3/(%i+sinh(x))^2 +--R +--R +--R 3 +--R csch(x) +--R (203) -------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 211 + +--S 212 of 552 +r0742:= -7/2*acoth(cosh(x))+2*%i*coth(x)+1/2*coth(x)*csch(x)+_ + 10*cosh(x)/(3-3*%i*sinh(x))-1/3*cosh(x)/(%i+sinh(x))^2 +--R +--R +--R (204) +--R 2 +--R (- 21sinh(x) - 42%i sinh(x) + 21)acoth(cosh(x)) +--R + +--R 2 +--R (3coth(x)csch(x) + 12%i coth(x))sinh(x) +--R + +--R (6%i coth(x)csch(x) - 24coth(x) + 20%i cosh(x))sinh(x) - 3coth(x)csch(x) +--R + +--R - 12%i coth(x) - 22cosh(x) +--R / +--R 2 +--R 6sinh(x) + 12%i sinh(x) - 6 +--R Type: Expression(Complex(Integer)) +--E 212 + +--S 213 of 552 +a0742:= integrate(t0742,x) +--R +--R +--R (205) +--R 7 6 +--R - 21sinh(x) + (- 147cosh(x) - 63%i)sinh(x) +--R + +--R 2 5 +--R (- 441cosh(x) - 378%i cosh(x) + 105)sinh(x) +--R + +--R 3 2 4 +--R (- 735cosh(x) - 945%i cosh(x) + 525cosh(x) + 147%i)sinh(x) +--R + +--R 4 3 2 +--R - 735cosh(x) - 1260%i cosh(x) + 1050cosh(x) + 588%i cosh(x) +--R + +--R - 147 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 441cosh(x) - 945%i cosh(x) + 1050cosh(x) + 882%i cosh(x) +--R + +--R - 441cosh(x) - 105%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 147cosh(x) - 378%i cosh(x) + 525cosh(x) + 588%i cosh(x) +--R + +--R 2 +--R - 441cosh(x) - 210%i cosh(x) + 63 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 21cosh(x) - 63%i cosh(x) + 105cosh(x) + 147%i cosh(x) +--R + +--R 3 2 +--R - 147cosh(x) - 105%i cosh(x) + 63cosh(x) + 21%i +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 7 6 +--R 21sinh(x) + (147cosh(x) + 63%i)sinh(x) +--R + +--R 2 5 +--R (441cosh(x) + 378%i cosh(x) - 105)sinh(x) +--R + +--R 3 2 4 +--R (735cosh(x) + 945%i cosh(x) - 525cosh(x) - 147%i)sinh(x) +--R + +--R 4 3 2 +--R 735cosh(x) + 1260%i cosh(x) - 1050cosh(x) - 588%i cosh(x) +--R + +--R 147 +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 441cosh(x) + 945%i cosh(x) - 1050cosh(x) - 882%i cosh(x) +--R + +--R 441cosh(x) + 105%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 147cosh(x) + 378%i cosh(x) - 525cosh(x) - 588%i cosh(x) +--R + +--R 2 +--R 441cosh(x) + 210%i cosh(x) - 63 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 21cosh(x) + 63%i cosh(x) - 105cosh(x) - 147%i cosh(x) +--R + +--R 3 2 +--R 147cosh(x) + 105%i cosh(x) - 63cosh(x) - 21%i +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 6 5 +--R 42sinh(x) + (252cosh(x) + 126%i)sinh(x) +--R + +--R 2 4 +--R (630cosh(x) + 630%i cosh(x) - 196)sinh(x) +--R + +--R 3 2 3 +--R (840cosh(x) + 1260%i cosh(x) - 784cosh(x) - 252%i)sinh(x) +--R + +--R 4 3 2 +--R (630cosh(x) + 1260%i cosh(x) - 1176cosh(x) - 756%i cosh(x) + 194) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 252cosh(x) + 630%i cosh(x) - 784cosh(x) - 756%i cosh(x) +--R + +--R 388cosh(x) + 150%i +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 42cosh(x) + 126%i cosh(x) - 196cosh(x) - 252%i cosh(x) + 194cosh(x) +--R + +--R 150%i cosh(x) - 64 +--R / +--R 7 6 +--R 6sinh(x) + (42cosh(x) + 18%i)sinh(x) +--R + +--R 2 5 +--R (126cosh(x) + 108%i cosh(x) - 30)sinh(x) +--R + +--R 3 2 4 +--R (210cosh(x) + 270%i cosh(x) - 150cosh(x) - 42%i)sinh(x) +--R + +--R 4 3 2 3 +--R (210cosh(x) + 360%i cosh(x) - 300cosh(x) - 168%i cosh(x) + 42)sinh(x) +--R + +--R 5 4 3 2 +--R 126cosh(x) + 270%i cosh(x) - 300cosh(x) - 252%i cosh(x) +--R + +--R 126cosh(x) + 30%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 42cosh(x) + 108%i cosh(x) - 150cosh(x) - 168%i cosh(x) +--R + +--R 2 +--R 126cosh(x) + 60%i cosh(x) - 18 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 6cosh(x) + 18%i cosh(x) - 30cosh(x) - 42%i cosh(x) + 42cosh(x) +--R + +--R 2 +--R 30%i cosh(x) - 18cosh(x) - 6%i +--R Type: Union(Expression(Complex(Integer)),...) +--E 213 + +--S 214 of 552 +m0742:= a0742-r0742 +--R +--R +--R (206) +--R 9 8 +--R - 21sinh(x) + (- 147cosh(x) - 105%i)sinh(x) +--R + +--R 2 7 +--R (- 441cosh(x) - 672%i cosh(x) + 252)sinh(x) +--R + +--R 3 2 6 +--R (- 735cosh(x) - 1827%i cosh(x) + 1428cosh(x) + 420%i)sinh(x) +--R + +--R 4 3 2 +--R - 735cosh(x) - 2730%i cosh(x) + 3381cosh(x) + 2016%i cosh(x) +--R + +--R - 546 +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 441cosh(x) - 2415%i cosh(x) + 4305cosh(x) + 3927%i cosh(x) +--R + +--R - 2142cosh(x) - 546%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 147cosh(x) - 1260%i cosh(x) + 3150cosh(x) + 3948%i cosh(x) +--R + +--R 2 +--R - 3255cosh(x) - 1680%i cosh(x) + 420 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 21cosh(x) - 357%i cosh(x) + 1302cosh(x) + 2142%i cosh(x) +--R + +--R 3 2 +--R - 2373cosh(x) - 1869%i cosh(x) + 924cosh(x) + 252%i +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 42%i cosh(x) + 273cosh(x) + 588%i cosh(x) - 819cosh(x) +--R + +--R 3 2 +--R - 882%i cosh(x) + 651cosh(x) + 336%i cosh(x) - 105 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R 21cosh(x) + 63%i cosh(x) - 105cosh(x) - 147%i cosh(x) +--R + +--R 3 2 +--R 147cosh(x) + 105%i cosh(x) - 63cosh(x) - 21%i +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 9 8 +--R 21sinh(x) + (147cosh(x) + 105%i)sinh(x) +--R + +--R 2 7 +--R (441cosh(x) + 672%i cosh(x) - 252)sinh(x) +--R + +--R 3 2 6 +--R (735cosh(x) + 1827%i cosh(x) - 1428cosh(x) - 420%i)sinh(x) +--R + +--R 4 3 2 +--R 735cosh(x) + 2730%i cosh(x) - 3381cosh(x) - 2016%i cosh(x) +--R + +--R 546 +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 441cosh(x) + 2415%i cosh(x) - 4305cosh(x) - 3927%i cosh(x) +--R + +--R 2142cosh(x) + 546%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 147cosh(x) + 1260%i cosh(x) - 3150cosh(x) - 3948%i cosh(x) +--R + +--R 2 +--R 3255cosh(x) + 1680%i cosh(x) - 420 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 21cosh(x) + 357%i cosh(x) - 1302cosh(x) - 2142%i cosh(x) +--R + +--R 3 2 +--R 2373cosh(x) + 1869%i cosh(x) - 924cosh(x) - 252%i +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 42%i cosh(x) - 273cosh(x) - 588%i cosh(x) + 819cosh(x) +--R + +--R 3 2 +--R 882%i cosh(x) - 651cosh(x) - 336%i cosh(x) + 105 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 21cosh(x) - 63%i cosh(x) + 105cosh(x) + 147%i cosh(x) +--R + +--R 3 2 +--R - 147cosh(x) - 105%i cosh(x) + 63cosh(x) + 21%i +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 9 8 +--R 21sinh(x) + (147cosh(x) + 105%i)sinh(x) +--R + +--R 2 7 +--R (441cosh(x) + 672%i cosh(x) - 252)sinh(x) +--R + +--R 3 2 6 +--R (735cosh(x) + 1827%i cosh(x) - 1428cosh(x) - 420%i)sinh(x) +--R + +--R 4 3 2 +--R 735cosh(x) + 2730%i cosh(x) - 3381cosh(x) - 2016%i cosh(x) +--R + +--R 546 +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 441cosh(x) + 2415%i cosh(x) - 4305cosh(x) - 3927%i cosh(x) +--R + +--R 2142cosh(x) + 546%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 147cosh(x) + 1260%i cosh(x) - 3150cosh(x) - 3948%i cosh(x) +--R + +--R 2 +--R 3255cosh(x) + 1680%i cosh(x) - 420 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 21cosh(x) + 357%i cosh(x) - 1302cosh(x) - 2142%i cosh(x) +--R + +--R 3 2 +--R 2373cosh(x) + 1869%i cosh(x) - 924cosh(x) - 252%i +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 42%i cosh(x) - 273cosh(x) - 588%i cosh(x) + 819cosh(x) +--R + +--R 3 2 +--R 882%i cosh(x) - 651cosh(x) - 336%i cosh(x) + 105 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 21cosh(x) - 63%i cosh(x) + 105cosh(x) + 147%i cosh(x) +--R + +--R 3 2 +--R - 147cosh(x) - 105%i cosh(x) + 63cosh(x) + 21%i +--R * +--R acoth(cosh(x)) +--R + +--R 9 +--R (- 3coth(x)csch(x) - 12%i coth(x))sinh(x) +--R + +--R (- 21cosh(x) - 15%i)coth(x)csch(x) + (- 84%i cosh(x) + 60)coth(x) +--R + +--R - 20%i cosh(x) + 42 +--R * +--R 8 +--R sinh(x) +--R + +--R 2 +--R (- 63cosh(x) - 96%i cosh(x) + 36)coth(x)csch(x) +--R + +--R 2 2 +--R (- 252%i cosh(x) + 384cosh(x) + 144%i)coth(x) - 140%i cosh(x) +--R + +--R 334cosh(x) + 210%i +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 +--R (- 105cosh(x) - 261%i cosh(x) + 204cosh(x) + 60%i)coth(x)csch(x) +--R + +--R 3 2 +--R (- 420%i cosh(x) + 1044cosh(x) + 816%i cosh(x) - 240)coth(x) +--R + +--R 3 2 +--R - 420%i cosh(x) + 1144cosh(x) + 1300%i cosh(x) - 490 +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 105cosh(x) - 390%i cosh(x) + 483cosh(x) + 288%i cosh(x) - 78) +--R * +--R coth(x)csch(x) +--R + +--R 4 3 2 +--R - 420%i cosh(x) + 1560cosh(x) + 1932%i cosh(x) - 1152cosh(x) +--R + +--R - 312%i +--R * +--R coth(x) +--R + +--R 4 3 2 +--R - 700%i cosh(x) + 2202cosh(x) + 3416%i cosh(x) - 2546cosh(x) - 770%i +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 63cosh(x) - 345%i cosh(x) + 615cosh(x) + 561%i cosh(x) +--R + +--R - 306cosh(x) - 78%i +--R * +--R coth(x)csch(x) +--R + +--R 5 4 3 2 +--R - 252%i cosh(x) + 1380cosh(x) + 2460%i cosh(x) - 2244cosh(x) +--R + +--R - 1224%i cosh(x) + 312 +--R * +--R coth(x) +--R + +--R 5 4 3 2 +--R - 700%i cosh(x) + 2600cosh(x) + 4930%i cosh(x) - 5436cosh(x) +--R + +--R - 3248%i cosh(x) + 894 +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R - 21cosh(x) - 180%i cosh(x) + 450cosh(x) + 564%i cosh(x) +--R + +--R 2 +--R - 465cosh(x) - 240%i cosh(x) + 60 +--R * +--R coth(x)csch(x) +--R + +--R 6 5 4 3 +--R - 84%i cosh(x) + 720cosh(x) + 1800%i cosh(x) - 2256cosh(x) +--R + +--R 2 +--R - 1860%i cosh(x) + 960cosh(x) + 240%i +--R * +--R coth(x) +--R + +--R 6 5 4 3 +--R - 420%i cosh(x) + 1922cosh(x) + 4210%i cosh(x) - 6084cosh(x) +--R + +--R 2 +--R - 5404%i cosh(x) + 2938cosh(x) + 790%i +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 3cosh(x) - 51%i cosh(x) + 186cosh(x) + 306%i cosh(x) +--R + +--R 3 2 +--R - 339cosh(x) - 267%i cosh(x) + 132cosh(x) + 36%i +--R * +--R coth(x)csch(x) +--R + +--R 7 6 5 4 +--R - 12%i cosh(x) + 204cosh(x) + 744%i cosh(x) - 1224cosh(x) +--R + +--R 3 2 +--R - 1356%i cosh(x) + 1068cosh(x) + 528%i cosh(x) - 144 +--R * +--R coth(x) +--R + +--R 7 6 5 4 +--R - 140%i cosh(x) + 864cosh(x) + 2120%i cosh(x) - 3746cosh(x) +--R + +--R 3 2 +--R - 4424%i cosh(x) + 3544cosh(x) + 1852%i cosh(x) - 558 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R - 6%i cosh(x) + 39cosh(x) + 84%i cosh(x) - 117cosh(x) +--R + +--R 3 2 +--R - 126%i cosh(x) + 93cosh(x) + 48%i cosh(x) - 15 +--R * +--R coth(x)csch(x) +--R + +--R 7 6 5 4 +--R 24cosh(x) + 156%i cosh(x) - 336cosh(x) - 468%i cosh(x) +--R + +--R 3 2 +--R 504cosh(x) + 372%i cosh(x) - 192cosh(x) - 60%i +--R * +--R coth(x) +--R + +--R 8 7 6 5 +--R - 20%i cosh(x) + 214cosh(x) + 580%i cosh(x) - 1194cosh(x) +--R + +--R 4 3 2 +--R - 1778%i cosh(x) + 1850cosh(x) + 1424%i cosh(x) - 774cosh(x) - 278%i +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 3cosh(x) + 9%i cosh(x) - 15cosh(x) - 21%i cosh(x) + 21cosh(x) +--R + +--R 2 +--R 15%i cosh(x) - 9cosh(x) - 3%i +--R * +--R coth(x)csch(x) +--R + +--R 7 6 5 4 +--R 12%i cosh(x) - 36cosh(x) - 60%i cosh(x) + 84cosh(x) +--R + +--R 3 2 +--R 84%i cosh(x) - 60cosh(x) - 36%i cosh(x) + 12 +--R * +--R coth(x) +--R + +--R 8 7 6 5 4 +--R 22cosh(x) + 66%i cosh(x) - 152cosh(x) - 280%i cosh(x) + 350cosh(x) +--R + +--R 3 2 +--R 362%i cosh(x) - 260cosh(x) - 172%i cosh(x) + 64 +--R / +--R 9 8 +--R 6sinh(x) + (42cosh(x) + 30%i)sinh(x) +--R + +--R 2 7 +--R (126cosh(x) + 192%i cosh(x) - 72)sinh(x) +--R + +--R 3 2 6 +--R (210cosh(x) + 522%i cosh(x) - 408cosh(x) - 120%i)sinh(x) +--R + +--R 4 3 2 +--R (210cosh(x) + 780%i cosh(x) - 966cosh(x) - 576%i cosh(x) + 156) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 126cosh(x) + 690%i cosh(x) - 1230cosh(x) - 1122%i cosh(x) +--R + +--R 612cosh(x) + 156%i +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 42cosh(x) + 360%i cosh(x) - 900cosh(x) - 1128%i cosh(x) +--R + +--R 2 +--R 930cosh(x) + 480%i cosh(x) - 120 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 6cosh(x) + 102%i cosh(x) - 372cosh(x) - 612%i cosh(x) +--R + +--R 3 2 +--R 678cosh(x) + 534%i cosh(x) - 264cosh(x) - 72%i +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 12%i cosh(x) - 78cosh(x) - 168%i cosh(x) + 234cosh(x) +--R + +--R 3 2 +--R 252%i cosh(x) - 186cosh(x) - 96%i cosh(x) + 30 +--R * +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 6cosh(x) - 18%i cosh(x) + 30cosh(x) + 42%i cosh(x) - 42cosh(x) +--R + +--R 2 +--R - 30%i cosh(x) + 18cosh(x) + 6%i +--R Type: Expression(Complex(Integer)) +--E 214 + +--S 215 of 552 +d0742:= D(m0742,x) +--R +--R +--R (207) +--R 14 +--R - 21sinh(x) +--R + +--R 2 2 2 +--R ((6cosh(x) - 6)coth(x) - 3cosh(x) + 3)csch(x) +--R + +--R 2 2 2 +--R (12%i cosh(x) - 12%i)coth(x) - 32%i cosh(x) - 210cosh(x) - 115%i +--R * +--R 13 +--R sinh(x) +--R + +--R 3 2 2 +--R (60cosh(x) + 42%i cosh(x) - 60cosh(x) - 42%i)coth(x) +--R + +--R 3 2 +--R - 30cosh(x) - 21%i cosh(x) + 30cosh(x) + 21%i +--R * +--R csch(x) +--R + +--R 3 2 2 +--R (120%i cosh(x) - 84cosh(x) - 120%i cosh(x) + 84)coth(x) +--R + +--R 3 2 +--R - 320%i cosh(x) - 739cosh(x) - 1066%i cosh(x) + 298 +--R * +--R 12 +--R sinh(x) +--R + +--R 4 3 2 +--R 270cosh(x) + 396%i cosh(x) - 414cosh(x) - 396%i cosh(x) +--R + +--R 144 +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 +--R - 135cosh(x) - 198%i cosh(x) + 207cosh(x) + 198%i cosh(x) - 72 +--R * +--R csch(x) +--R + +--R 4 3 2 +--R 540%i cosh(x) - 792cosh(x) - 828%i cosh(x) + 792cosh(x) +--R + +--R 288%i +--R * +--R 2 +--R coth(x) +--R + +--R 4 3 2 +--R - 1420%i cosh(x) - 588cosh(x) - 3781%i cosh(x) + 2478cosh(x) + 518%i +--R * +--R 11 +--R sinh(x) +--R + +--R 5 4 3 +--R 720cosh(x) + 1674%i cosh(x) - 1980cosh(x) +--R + +--R 2 +--R - 2010%i cosh(x) + 1260cosh(x) + 336%i +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 2 +--R - 360cosh(x) - 837%i cosh(x) + 990cosh(x) + 1005%i cosh(x) +--R + +--R - 630cosh(x) - 168%i +--R * +--R csch(x) +--R + +--R 5 4 3 2 +--R 1440%i cosh(x) - 3348cosh(x) - 3960%i cosh(x) + 4020cosh(x) +--R + +--R 2520%i cosh(x) - 672 +--R * +--R 2 +--R coth(x) +--R + +--R 5 4 3 2 +--R - 3640%i cosh(x) + 3604cosh(x) - 5284%i cosh(x) + 7727cosh(x) +--R + +--R 3674%i cosh(x) - 663 +--R * +--R 10 +--R sinh(x) +--R + +--R 6 5 4 +--R 1260cosh(x) + 4176%i cosh(x) - 6174cosh(x) +--R + +--R 3 2 +--R - 6852%i cosh(x) + 5520cosh(x) + 2676%i cosh(x) - 606 +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 +--R - 630cosh(x) - 2088%i cosh(x) + 3087cosh(x) + 3426%i cosh(x) +--R + +--R 2 +--R - 2760cosh(x) - 1338%i cosh(x) + 303 +--R * +--R csch(x) +--R + +--R 6 5 4 3 +--R 2520%i cosh(x) - 8352cosh(x) - 12348%i cosh(x) + 13704cosh(x) +--R + +--R 2 +--R 11040%i cosh(x) - 5352cosh(x) - 1212%i +--R * +--R 2 +--R coth(x) +--R + +--R 6 5 4 3 +--R - 5820%i cosh(x) + 13860cosh(x) + 3636%i cosh(x) + 8752cosh(x) +--R + +--R 2 +--R 8797%i cosh(x) - 3712cosh(x) - 565%i +--R * +--R 9 +--R sinh(x) +--R + +--R 7 6 5 +--R 1512cosh(x) + 6804%i cosh(x) - 12744cosh(x) +--R + +--R 4 3 2 +--R - 16218%i cosh(x) + 15552cosh(x) + 10296%i cosh(x) +--R + +--R - 4320cosh(x) - 882%i +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R - 756cosh(x) - 3402%i cosh(x) + 6372cosh(x) + 8109%i cosh(x) +--R + +--R 3 2 +--R - 7776cosh(x) - 5148%i cosh(x) + 2160cosh(x) + 441%i +--R * +--R csch(x) +--R + +--R 7 6 5 +--R 3024%i cosh(x) - 13608cosh(x) - 25488%i cosh(x) +--R + +--R 4 3 2 +--R 32436cosh(x) + 31104%i cosh(x) - 20592cosh(x) - 8640%i cosh(x) +--R + +--R 1764 +--R * +--R 2 +--R coth(x) +--R + +--R 7 6 5 4 +--R - 5664%i cosh(x) + 24138cosh(x) + 26196%i cosh(x) - 9100cosh(x) +--R + +--R 3 2 +--R 2640%i cosh(x) - 4522cosh(x) - 1836%i cosh(x) - 16 +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 6 +--R 1260cosh(x) + 7560%i cosh(x) - 17892cosh(x) +--R + +--R 5 4 3 +--R - 26760%i cosh(x) + 30060cosh(x) + 24744%i cosh(x) +--R + +--R 2 +--R - 14484cosh(x) - 5544%i cosh(x) + 1056 +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 +--R - 630cosh(x) - 3780%i cosh(x) + 8946cosh(x) + 13380%i cosh(x) +--R + +--R 4 3 2 +--R - 15030cosh(x) - 12372%i cosh(x) + 7242cosh(x) +--R + +--R 2772%i cosh(x) - 528 +--R * +--R csch(x) +--R + +--R 8 7 6 +--R 2520%i cosh(x) - 15120cosh(x) - 35784%i cosh(x) +--R + +--R 5 4 3 +--R 53520cosh(x) + 60120%i cosh(x) - 49488cosh(x) +--R + +--R 2 +--R - 28968%i cosh(x) + 11088cosh(x) + 2112%i +--R * +--R 2 +--R coth(x) +--R + +--R 8 7 6 5 +--R - 2520%i cosh(x) + 23664cosh(x) + 45390%i cosh(x) - 42164cosh(x) +--R + +--R 4 3 2 +--R - 27832%i cosh(x) + 13320cosh(x) + 4618%i cosh(x) - 2380cosh(x) +--R + +--R - 924%i +--R * +--R 7 +--R sinh(x) +--R + +--R 9 8 7 +--R 720cosh(x) + 5796%i cosh(x) - 17352cosh(x) +--R + +--R 6 5 4 +--R - 30828%i cosh(x) + 40440cosh(x) + 39972%i cosh(x) +--R + +--R 3 2 +--R - 29544cosh(x) - 15996%i cosh(x) + 5736cosh(x) + 1056%i +--R * +--R 2 +--R coth(x) +--R + +--R 9 8 7 6 +--R - 360cosh(x) - 2898%i cosh(x) + 8676cosh(x) + 15414%i cosh(x) +--R + +--R 5 4 3 +--R - 20220cosh(x) - 19986%i cosh(x) + 14772cosh(x) +--R + +--R 2 +--R 7998%i cosh(x) - 2868cosh(x) - 528%i +--R * +--R csch(x) +--R + +--R 9 8 7 +--R 1440%i cosh(x) - 11592cosh(x) - 34704%i cosh(x) +--R + +--R 6 5 4 +--R 61656cosh(x) + 80880%i cosh(x) - 79944cosh(x) +--R + +--R 3 2 +--R - 59088%i cosh(x) + 31992cosh(x) + 11472%i cosh(x) - 2112 +--R * +--R 2 +--R coth(x) +--R + +--R 9 8 7 6 +--R 1200%i cosh(x) + 11067cosh(x) + 40128%i cosh(x) - 58366cosh(x) +--R + +--R 5 4 3 2 +--R - 61756%i cosh(x) + 50404cosh(x) + 31128%i cosh(x) - 15566cosh(x) +--R + +--R - 7172%i cosh(x) + 1373 +--R * +--R 6 +--R sinh(x) +--R + +--R 10 9 8 +--R 270cosh(x) + 3024%i cosh(x) - 11610cosh(x) +--R + +--R 7 6 5 +--R - 24696%i cosh(x) + 37764cosh(x) + 44136%i cosh(x) +--R + +--R 4 3 2 +--R - 39492cosh(x) - 27288%i cosh(x) + 13950cosh(x) +--R + +--R 4824%i cosh(x) - 882 +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 +--R - 135cosh(x) - 1512%i cosh(x) + 5805cosh(x) +--R + +--R 7 6 5 +--R 12348%i cosh(x) - 18882cosh(x) - 22068%i cosh(x) +--R + +--R 4 3 2 +--R 19746cosh(x) + 13644%i cosh(x) - 6975cosh(x) - 2412%i cosh(x) +--R + +--R 441 +--R * +--R csch(x) +--R + +--R 10 9 8 7 +--R 540%i cosh(x) - 6048cosh(x) - 23220%i cosh(x) + 49392cosh(x) +--R + +--R 6 5 4 +--R 75528%i cosh(x) - 88272cosh(x) - 78984%i cosh(x) +--R + +--R 3 2 +--R 54576cosh(x) + 27900%i cosh(x) - 9648cosh(x) - 1764%i +--R * +--R 2 +--R coth(x) +--R + +--R 10 9 8 7 +--R 2760%i cosh(x) - 2370cosh(x) + 15405%i cosh(x) - 38720cosh(x) +--R + +--R 6 5 4 3 +--R - 60114%i cosh(x) + 69628cosh(x) + 61204%i cosh(x) - 40256cosh(x) +--R + +--R 2 +--R - 22778%i cosh(x) + 8358cosh(x) + 1171%i +--R * +--R 5 +--R sinh(x) +--R + +--R 11 10 9 +--R 60cosh(x) + 1026%i cosh(x) - 5244cosh(x) +--R + +--R 8 7 6 +--R - 13542%i cosh(x) + 24120cosh(x) + 33036%i cosh(x) +--R + +--R 5 4 3 +--R - 35064cosh(x) - 29484%i cosh(x) + 19404cosh(x) +--R + +--R 2 +--R 9570%i cosh(x) - 3276cosh(x) - 606%i +--R * +--R 2 +--R coth(x) +--R + +--R 11 10 9 8 +--R - 30cosh(x) - 513%i cosh(x) + 2622cosh(x) + 6771%i cosh(x) +--R + +--R 7 6 5 +--R - 12060cosh(x) - 16518%i cosh(x) + 17532cosh(x) +--R + +--R 4 3 2 +--R 14742%i cosh(x) - 9702cosh(x) - 4785%i cosh(x) + 1638cosh(x) +--R + +--R 303%i +--R * +--R csch(x) +--R + +--R 11 10 9 +--R 120%i cosh(x) - 2052cosh(x) - 10488%i cosh(x) +--R + +--R 8 7 6 +--R 27084cosh(x) + 48240%i cosh(x) - 66072cosh(x) +--R + +--R 5 4 3 +--R - 70128%i cosh(x) + 58968cosh(x) + 38808%i cosh(x) +--R + +--R 2 +--R - 19140cosh(x) - 6552%i cosh(x) + 1212 +--R * +--R 2 +--R coth(x) +--R + +--R 11 10 9 8 +--R 2080%i cosh(x) - 7119cosh(x) - 4474%i cosh(x) - 6538cosh(x) +--R + +--R 7 6 5 4 +--R - 25328%i cosh(x) + 46338cosh(x) + 57796%i cosh(x) - 51912cosh(x) +--R + +--R 3 2 +--R - 36480%i cosh(x) + 20077cosh(x) + 5734%i cosh(x) - 846 +--R * +--R 4 +--R sinh(x) +--R + +--R 12 11 10 +--R 6cosh(x) + 204%i cosh(x) - 1518cosh(x) +--R + +--R 9 8 7 +--R - 4908%i cosh(x) + 10212cosh(x) + 16296%i cosh(x) +--R + +--R 6 5 4 +--R - 20292cosh(x) - 20232%i cosh(x) + 16326cosh(x) +--R + +--R 3 2 +--R 10380%i cosh(x) - 5070cosh(x) - 1740%i cosh(x) + 336 +--R * +--R 2 +--R coth(x) +--R + +--R 12 11 10 9 +--R - 3cosh(x) - 102%i cosh(x) + 759cosh(x) + 2454%i cosh(x) +--R + +--R 8 7 6 +--R - 5106cosh(x) - 8148%i cosh(x) + 10146cosh(x) +--R + +--R 5 4 3 2 +--R 10116%i cosh(x) - 8163cosh(x) - 5190%i cosh(x) + 2535cosh(x) +--R + +--R 870%i cosh(x) - 168 +--R * +--R csch(x) +--R + +--R 12 11 10 9 +--R 12%i cosh(x) - 408cosh(x) - 3036%i cosh(x) + 9816cosh(x) +--R + +--R 8 7 6 +--R 20424%i cosh(x) - 32592cosh(x) - 40584%i cosh(x) +--R + +--R 5 4 3 +--R 40464cosh(x) + 32652%i cosh(x) - 20760cosh(x) +--R + +--R 2 +--R - 10140%i cosh(x) + 3480cosh(x) + 672%i +--R * +--R 2 +--R coth(x) +--R + +--R 12 11 10 9 +--R 868%i cosh(x) - 4852cosh(x) - 8329%i cosh(x) + 8630cosh(x) +--R + +--R 8 7 6 5 +--R 3130%i cosh(x) + 9968cosh(x) + 24718%i cosh(x) - 33812cosh(x) +--R + +--R 4 3 2 +--R - 30452%i cosh(x) + 23044cosh(x) + 10619%i cosh(x) - 2978cosh(x) +--R + +--R - 554%i +--R * +--R 3 +--R sinh(x) +--R + +--R 12 11 10 +--R 18%i cosh(x) - 252cosh(x) - 1098%i cosh(x) +--R + +--R 9 8 7 +--R 2700cosh(x) + 5004%i cosh(x) - 7272cosh(x) +--R + +--R 6 5 4 +--R - 8460%i cosh(x) + 8136cosh(x) + 6354%i cosh(x) +--R + +--R 3 2 +--R - 3996cosh(x) - 1962%i cosh(x) + 684cosh(x) + 144%i +--R * +--R 2 +--R coth(x) +--R + +--R 12 11 10 9 +--R - 9%i cosh(x) + 126cosh(x) + 549%i cosh(x) - 1350cosh(x) +--R + +--R 8 7 6 5 +--R - 2502%i cosh(x) + 3636cosh(x) + 4230%i cosh(x) - 4068cosh(x) +--R + +--R 4 3 2 +--R - 3177%i cosh(x) + 1998cosh(x) + 981%i cosh(x) - 342cosh(x) +--R + +--R - 72%i +--R * +--R csch(x) +--R + +--R 12 11 10 9 +--R - 36cosh(x) - 504%i cosh(x) + 2196cosh(x) + 5400%i cosh(x) +--R + +--R 8 7 6 +--R - 10008cosh(x) - 14544%i cosh(x) + 16920cosh(x) +--R + +--R 5 4 3 2 +--R 16272%i cosh(x) - 12708cosh(x) - 7992%i cosh(x) + 3924cosh(x) +--R + +--R 1368%i cosh(x) - 288 +--R * +--R 2 +--R coth(x) +--R + +--R 13 12 11 10 +--R 200%i cosh(x) - 1722cosh(x) - 4204%i cosh(x) + 6743cosh(x) +--R + +--R 9 8 7 6 +--R 8018%i cosh(x) - 5365cosh(x) + 544%i cosh(x) - 8566cosh(x) +--R + +--R 5 4 3 2 +--R - 11972%i cosh(x) + 12256cosh(x) + 8716%i cosh(x) - 3617cosh(x) +--R + +--R - 1302%i cosh(x) + 271 +--R * +--R 2 +--R sinh(x) +--R + +--R 12 11 10 +--R - 18cosh(x) - 132%i cosh(x) + 396cosh(x) +--R + +--R 9 8 7 +--R 852%i cosh(x) - 1446cosh(x) - 1944%i cosh(x) +--R + +--R 6 5 4 +--R 2184cosh(x) + 2040%i cosh(x) - 1566cosh(x) +--R + +--R 3 2 +--R - 996%i cosh(x) + 492cosh(x) + 180%i cosh(x) - 42 +--R * +--R 2 +--R coth(x) +--R + +--R 12 11 10 9 +--R 9cosh(x) + 66%i cosh(x) - 198cosh(x) - 426%i cosh(x) +--R + +--R 8 7 6 5 +--R 723cosh(x) + 972%i cosh(x) - 1092cosh(x) - 1020%i cosh(x) +--R + +--R 4 3 2 +--R 783cosh(x) + 498%i cosh(x) - 246cosh(x) - 90%i cosh(x) + 21 +--R * +--R csch(x) +--R + +--R 12 11 10 9 +--R - 36%i cosh(x) + 264cosh(x) + 792%i cosh(x) - 1704cosh(x) +--R + +--R 8 7 6 5 +--R - 2892%i cosh(x) + 3888cosh(x) + 4368%i cosh(x) - 4080cosh(x) +--R + +--R 4 3 2 +--R - 3132%i cosh(x) + 1992cosh(x) + 984%i cosh(x) - 360cosh(x) +--R + +--R - 84%i +--R * +--R 2 +--R coth(x) +--R + +--R 14 13 12 11 +--R 20%i cosh(x) - 320cosh(x) - 1006%i cosh(x) + 2016cosh(x) +--R + +--R 10 9 8 7 +--R 3181%i cosh(x) - 3636cosh(x) - 3063%i cosh(x) + 1072cosh(x) +--R + +--R 6 5 4 3 +--R - 1182%i cosh(x) + 2088cosh(x) + 2864%i cosh(x) - 1584cosh(x) +--R + +--R 2 +--R - 899%i cosh(x) + 364cosh(x) + 85%i +--R * +--R sinh(x) +--R + +--R 12 11 10 9 +--R - 6%i cosh(x) + 24cosh(x) + 60%i cosh(x) - 120cosh(x) +--R + +--R 8 7 6 5 +--R - 186%i cosh(x) + 240cosh(x) + 264%i cosh(x) - 240cosh(x) +--R + +--R 4 3 2 +--R - 186%i cosh(x) + 120cosh(x) + 60%i cosh(x) - 24cosh(x) - 6%i +--R * +--R 2 +--R coth(x) +--R + +--R 12 11 10 9 +--R 3%i cosh(x) - 12cosh(x) - 30%i cosh(x) + 60cosh(x) +--R + +--R 8 7 6 5 +--R 93%i cosh(x) - 120cosh(x) - 132%i cosh(x) + 120cosh(x) +--R + +--R 4 3 2 +--R 93%i cosh(x) - 60cosh(x) - 30%i cosh(x) + 12cosh(x) + 3%i +--R * +--R csch(x) +--R + +--R 12 11 10 9 +--R 12cosh(x) + 48%i cosh(x) - 120cosh(x) - 240%i cosh(x) +--R + +--R 8 7 6 5 +--R 372cosh(x) + 480%i cosh(x) - 528cosh(x) - 480%i cosh(x) +--R + +--R 4 3 2 +--R 372cosh(x) + 240%i cosh(x) - 120cosh(x) - 48%i cosh(x) + 12 +--R * +--R 2 +--R coth(x) +--R + +--R 14 13 12 11 +--R - 24cosh(x) - 96%i cosh(x) + 228cosh(x) + 432%i cosh(x) +--R + +--R 10 9 8 7 +--R - 624cosh(x) - 720%i cosh(x) + 684cosh(x) + 288%i cosh(x) +--R + +--R 6 5 4 3 +--R - 216cosh(x) + 192%i cosh(x) - 132cosh(x) - 144%i cosh(x) +--R + +--R 2 +--R 96cosh(x) + 48%i cosh(x) - 12 +--R / +--R 2 13 +--R (6cosh(x) - 6)sinh(x) +--R + +--R 3 2 12 +--R (60cosh(x) + 42%i cosh(x) - 60cosh(x) - 42%i)sinh(x) +--R + +--R 4 3 2 +--R (270cosh(x) + 396%i cosh(x) - 414cosh(x) - 396%i cosh(x) + 144) +--R * +--R 11 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 720cosh(x) + 1674%i cosh(x) - 1980cosh(x) - 2010%i cosh(x) +--R + +--R 1260cosh(x) + 336%i +--R * +--R 10 +--R sinh(x) +--R + +--R 6 5 4 3 +--R 1260cosh(x) + 4176%i cosh(x) - 6174cosh(x) - 6852%i cosh(x) +--R + +--R 2 +--R 5520cosh(x) + 2676%i cosh(x) - 606 +--R * +--R 9 +--R sinh(x) +--R + +--R 7 6 5 4 +--R 1512cosh(x) + 6804%i cosh(x) - 12744cosh(x) - 16218%i cosh(x) +--R + +--R 3 2 +--R 15552cosh(x) + 10296%i cosh(x) - 4320cosh(x) - 882%i +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 6 5 +--R 1260cosh(x) + 7560%i cosh(x) - 17892cosh(x) - 26760%i cosh(x) +--R + +--R 4 3 2 +--R 30060cosh(x) + 24744%i cosh(x) - 14484cosh(x) - 5544%i cosh(x) +--R + +--R 1056 +--R * +--R 7 +--R sinh(x) +--R + +--R 9 8 7 6 +--R 720cosh(x) + 5796%i cosh(x) - 17352cosh(x) - 30828%i cosh(x) +--R + +--R 5 4 3 2 +--R 40440cosh(x) + 39972%i cosh(x) - 29544cosh(x) - 15996%i cosh(x) +--R + +--R 5736cosh(x) + 1056%i +--R * +--R 6 +--R sinh(x) +--R + +--R 10 9 8 7 +--R 270cosh(x) + 3024%i cosh(x) - 11610cosh(x) - 24696%i cosh(x) +--R + +--R 6 5 4 3 +--R 37764cosh(x) + 44136%i cosh(x) - 39492cosh(x) - 27288%i cosh(x) +--R + +--R 2 +--R 13950cosh(x) + 4824%i cosh(x) - 882 +--R * +--R 5 +--R sinh(x) +--R + +--R 11 10 9 8 +--R 60cosh(x) + 1026%i cosh(x) - 5244cosh(x) - 13542%i cosh(x) +--R + +--R 7 6 5 4 +--R 24120cosh(x) + 33036%i cosh(x) - 35064cosh(x) - 29484%i cosh(x) +--R + +--R 3 2 +--R 19404cosh(x) + 9570%i cosh(x) - 3276cosh(x) - 606%i +--R * +--R 4 +--R sinh(x) +--R + +--R 12 11 10 9 +--R 6cosh(x) + 204%i cosh(x) - 1518cosh(x) - 4908%i cosh(x) +--R + +--R 8 7 6 5 +--R 10212cosh(x) + 16296%i cosh(x) - 20292cosh(x) - 20232%i cosh(x) +--R + +--R 4 3 2 +--R 16326cosh(x) + 10380%i cosh(x) - 5070cosh(x) - 1740%i cosh(x) + 336 +--R * +--R 3 +--R sinh(x) +--R + +--R 12 11 10 9 +--R 18%i cosh(x) - 252cosh(x) - 1098%i cosh(x) + 2700cosh(x) +--R + +--R 8 7 6 5 +--R 5004%i cosh(x) - 7272cosh(x) - 8460%i cosh(x) + 8136cosh(x) +--R + +--R 4 3 2 +--R 6354%i cosh(x) - 3996cosh(x) - 1962%i cosh(x) + 684cosh(x) + 144%i +--R * +--R 2 +--R sinh(x) +--R + +--R 12 11 10 9 +--R - 18cosh(x) - 132%i cosh(x) + 396cosh(x) + 852%i cosh(x) +--R + +--R 8 7 6 5 +--R - 1446cosh(x) - 1944%i cosh(x) + 2184cosh(x) + 2040%i cosh(x) +--R + +--R 4 3 2 +--R - 1566cosh(x) - 996%i cosh(x) + 492cosh(x) + 180%i cosh(x) - 42 +--R * +--R sinh(x) +--R + +--R 12 11 10 9 +--R - 6%i cosh(x) + 24cosh(x) + 60%i cosh(x) - 120cosh(x) +--R + +--R 8 7 6 5 +--R - 186%i cosh(x) + 240cosh(x) + 264%i cosh(x) - 240cosh(x) +--R + +--R 4 3 2 +--R - 186%i cosh(x) + 120cosh(x) + 60%i cosh(x) - 24cosh(x) - 6%i +--R Type: Expression(Complex(Integer)) +--E 215 + +--S 216 of 552 +t0743:= sinh(x)^2/(a+b*cosh(x))^2 +--R +--R +--R 2 +--R sinh(x) +--R (208) ------------------------------ +--R 2 2 2 +--R b cosh(x) + 2a b cosh(x) + a +--R Type: Expression(Integer) +--E 216 + +--S 217 of 552 +r0743:= x/b^2-2*a*atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/b^2/_ + (a^2-b^2)^(1/2)-sinh(x)/b/(a+b*cosh(x)) +--R +--R +--R (209) +--R x +--R (b - a)tanh(-) +--R 2 2 +--R (2a b cosh(x) + 2a )atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R (- b sinh(x) + b x cosh(x) + a x)\|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R (b cosh(x) + a b )\|- b + a +--R Type: Expression(Integer) +--E 217 + +--S 218 of 552 +a0743:= integrate(t0743,x) +--R +--R +--R (210) +--R [ +--R 2 2 2 +--R a b sinh(x) + (2a b cosh(x) + 2a )sinh(x) + a b cosh(x) +--R + +--R 2 +--R 2a cosh(x) + a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + (- 2b + 2a b)cosh(x) - 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 2 2 +--R b x sinh(x) + (2b x cosh(x) + 2a x + 2a)sinh(x) + b x cosh(x) +--R + +--R (2a x + 2a)cosh(x) + b x + 2b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 2 3 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b )sinh(x) + b cosh(x) + 2a b cosh(x) +--R + +--R 3 +--R b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 2 2 2 +--R - 2a b sinh(x) + (- 4a b cosh(x) - 4a )sinh(x) - 2a b cosh(x) +--R + +--R 2 +--R - 4a cosh(x) - 2a b +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 2 +--R b x sinh(x) + (2b x cosh(x) + 2a x + 2a)sinh(x) + b x cosh(x) +--R + +--R (2a x + 2a)cosh(x) + b x + 2b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 3 2 3 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b )sinh(x) + b cosh(x) + 2a b cosh(x) +--R + +--R 3 +--R b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 218 + +--S 219 of 552 +m0743a:= a0743.1-r0743 +--R +--R +--R (211) +--R 2 2 2 +--R (a b cosh(x) + a b)sinh(x) +--R + +--R 2 2 2 3 2 3 +--R (2a b cosh(x) + 4a b cosh(x) + 2a )sinh(x) + a b cosh(x) +--R + +--R 2 2 2 3 2 +--R 3a b cosh(x) + (a b + 2a )cosh(x) + a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + (- 2b + 2a b)cosh(x) - 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R 2 2 2 +--R (- 2a b cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 3 2 3 +--R (- 4a b cosh(x) - 8a b cosh(x) - 4a )sinh(x) - 2a b cosh(x) +--R + +--R 2 2 2 3 2 +--R - 6a b cosh(x) + (- 2a b - 4a )cosh(x) - 2a b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b cosh(x) + 4a b cosh(x) + b + 2a )sinh(x) + 2a b cosh(x) +--R + +--R 2 2 +--R (2b + 2a )cosh(x) + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 2 +--R (b cosh(x) + a b )sinh(x) +--R + +--R 4 2 3 2 2 4 3 +--R (2b cosh(x) + 4a b cosh(x) + 2a b )sinh(x) + b cosh(x) +--R + +--R 3 2 4 2 2 3 +--R 3a b cosh(x) + (b + 2a b )cosh(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 552 +d0743a:= D(m0743a,x) +--R +--R +--R (212) +--R 4 3 6 +--R (- b + a b )sinh(x) +--R + +--R 4 3 3 2 2 5 +--R ((- 4b + 4a b )cosh(x) - 4a b + 4a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R (- 5b + 4a b )cosh(x) + (- 11a b + 9a b )cosh(x) - 2b + 2a b +--R + +--R 2 2 3 +--R - 4a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 2 2 +--R - 4a b cosh(x) + (- 8a b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 2 2 3 +--R (- 4b + 4a b - 12a b )cosh(x) - 4a b + 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 +--R (5b - 11a b )cosh(x) + (2a b - 26a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 4b + 2a b - 16a b - 18a b)cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 +--R (- 10a b + 6a b - 16a b - 4a )cosh(x) - b + a b - 4a b +--R + +--R 3 4 +--R 2a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 5 3 2 2 4 +--R (4b - 8a b )cosh(x) + (4a b - 24a b )cosh(x) +--R + +--R 4 2 2 3 3 +--R (- 4b - 12a b - 24a b)cosh(x) +--R + +--R 3 3 4 2 2 2 4 3 +--R (- 12a b - 20a b - 8a )cosh(x) + (- 12a b - 8a )cosh(x) - 4a b +--R * +--R sinh(x) +--R + +--R 4 3 6 3 2 2 5 +--R (b - 2a b )cosh(x) + (a b - 7a b )cosh(x) +--R + +--R 4 2 2 3 4 +--R (- 2b - 4a b - 9a b)cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 6a b - 2a b - 8a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (b - 2a b - 8a b - 2a b - 4a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (a b - 3a b - 4a b)cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 6 4 3 3 2 2 5 +--R (- b - a b )sinh(x) + ((- 4b - 4a b )cosh(x) - 4a b - 4a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R (- 5b - 4a b )cosh(x) + (- 11a b - 9a b )cosh(x) - 2b - 2a b +--R + +--R 2 2 3 +--R - 4a b - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 2 2 +--R 4a b cosh(x) + (- 8a b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 2 2 3 +--R (- 4b - 4a b - 12a b )cosh(x) - 4a b - 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 +--R (5b + 11a b )cosh(x) + (2a b + 26a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 4b - 2a b - 16a b + 18a b)cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 +--R (- 10a b - 6a b - 16a b + 4a )cosh(x) - b - a b - 4a b - 2a b +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 5 3 2 2 4 +--R (4b + 8a b )cosh(x) + (4a b + 24a b )cosh(x) +--R + +--R 4 2 2 3 3 3 3 4 2 +--R (- 4b - 12a b + 24a b)cosh(x) + (- 12a b - 20a b + 8a )cosh(x) +--R + +--R 2 2 4 3 +--R (- 12a b - 8a )cosh(x) - 4a b +--R * +--R sinh(x) +--R + +--R 4 3 6 3 2 2 5 +--R (b + 2a b )cosh(x) + (a b + 7a b )cosh(x) +--R + +--R 4 2 2 3 4 3 2 2 3 4 3 +--R (- 2b - 4a b + 9a b)cosh(x) + (- 6a b + 2a b - 8a b + 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 3 2 2 3 +--R (b + 2a b - 8a b + 2a b - 4a )cosh(x) + (a b + 3a b - 4a b)cosh(x) +--R + +--R 3 +--R a b +--R / +--R 6 5 2 5 2 4 2 4 3 3 4 +--R ((b - a b )cosh(x) + (2a b - 2a b )cosh(x) + a b - a b )sinh(x) +--R + +--R 6 5 3 5 2 4 2 +--R (4b - 4a b )cosh(x) + (12a b - 12a b )cosh(x) +--R + +--R 2 4 3 3 3 3 4 2 +--R (12a b - 12a b )cosh(x) + 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 5 2 4 3 +--R (6b - 6a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 +--R (2b - 2a b + 34a b - 34a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 4 3 3 4 2 +--R (4a b - 4a b + 20a b - 20a b )cosh(x) + 2a b - 2a b + 4a b +--R + +--R 5 +--R - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 5 5 2 4 4 +--R (4b - 4a b )cosh(x) + (20a b - 20a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (4b - 4a b + 36a b - 36a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 +--R (12a b - 12a b + 28a b - 28a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 3 4 2 +--R (12a b - 12a b + 8a b - 8a b)cosh(x) + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 6 5 6 5 2 4 5 +--R (b - a b )cosh(x) + (6a b - 6a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (2b - 2a b + 13a b - 13a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (8a b - 8a b + 12a b - 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (b - a b + 10a b - 10a b + 4a b - 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 4 3 3 +--R (2a b - 2a b + 4a b - 4a b )cosh(x) + a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 5 2 5 2 4 2 4 3 3 4 +--R ((b + a b )cosh(x) + (2a b + 2a b )cosh(x) + a b + a b )sinh(x) +--R + +--R 6 5 3 5 2 4 2 +--R (4b + 4a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 2 4 3 3 3 3 4 2 +--R (12a b + 12a b )cosh(x) + 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 5 2 4 3 +--R (6b + 6a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 +--R (2b + 2a b + 34a b + 34a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 4 3 3 4 2 5 +--R (4a b + 4a b + 20a b + 20a b )cosh(x) + 2a b + 2a b + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 5 5 2 4 4 +--R (4b + 4a b )cosh(x) + (20a b + 20a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (4b + 4a b + 36a b + 36a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 +--R (12a b + 12a b + 28a b + 28a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 3 4 2 +--R (12a b + 12a b + 8a b + 8a b)cosh(x) + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 6 5 6 5 2 4 5 +--R (b + a b )cosh(x) + (6a b + 6a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (2b + 2a b + 13a b + 13a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (8a b + 8a b + 12a b + 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (b + a b + 10a b + 10a b + 4a b + 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 4 3 3 +--R (2a b + 2a b + 4a b + 4a b )cosh(x) + a b + a b +--R Type: Expression(Integer) +--E 220 + +--S 221 of 552 +m0743b:= a0743.2-r0743 +--R +--R +--R (213) +--R 2 2 2 +--R (- 2a b cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 3 2 3 +--R (- 4a b cosh(x) - 8a b cosh(x) - 4a )sinh(x) - 2a b cosh(x) +--R + +--R 2 2 2 3 2 +--R - 6a b cosh(x) + (- 2a b - 4a )cosh(x) - 2a b +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 +--R (- 2a b cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 2 3 2 3 +--R (- 4a b cosh(x) - 8a b cosh(x) - 4a )sinh(x) - 2a b cosh(x) +--R + +--R 2 2 2 3 2 +--R - 6a b cosh(x) + (- 2a b - 4a )cosh(x) - 2a b +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sinh(x) + b cosh(x) + a)\|b - a +--R \|- b + a atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b cosh(x) + 4a b cosh(x) + b + 2a )sinh(x) + 2a b cosh(x) +--R + +--R 2 2 +--R (2b + 2a )cosh(x) + 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 3 2 +--R (b cosh(x) + a b )sinh(x) +--R + +--R 4 2 3 2 2 4 3 +--R (2b cosh(x) + 4a b cosh(x) + 2a b )sinh(x) + b cosh(x) +--R + +--R 3 2 4 2 2 3 +--R 3a b cosh(x) + (b + 2a b )cosh(x) + a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 552 +d0743b:= D(m0743b,x) +--R +--R +--R (214) +--R 4 3 6 +--R (- b + a b )sinh(x) +--R + +--R 4 3 3 2 2 5 +--R ((- 4b + 4a b )cosh(x) - 4a b + 4a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R (- 5b + 4a b )cosh(x) + (- 11a b + 9a b )cosh(x) - 2b + 2a b +--R + +--R 2 2 3 +--R - 4a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 2 2 +--R - 4a b cosh(x) + (- 8a b - 4a b )cosh(x) +--R + +--R 4 3 2 2 3 2 2 3 +--R (- 4b + 4a b - 12a b )cosh(x) - 4a b + 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 +--R (5b - 11a b )cosh(x) + (2a b - 26a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 4b + 2a b - 16a b - 18a b)cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 +--R (- 10a b + 6a b - 16a b - 4a )cosh(x) - b + a b - 4a b +--R + +--R 3 4 +--R 2a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 5 3 2 2 4 +--R (4b - 8a b )cosh(x) + (4a b - 24a b )cosh(x) +--R + +--R 4 2 2 3 3 +--R (- 4b - 12a b - 24a b)cosh(x) +--R + +--R 3 3 4 2 2 2 4 3 +--R (- 12a b - 20a b - 8a )cosh(x) + (- 12a b - 8a )cosh(x) - 4a b +--R * +--R sinh(x) +--R + +--R 4 3 6 3 2 2 5 +--R (b - 2a b )cosh(x) + (a b - 7a b )cosh(x) +--R + +--R 4 2 2 3 4 +--R (- 2b - 4a b - 9a b)cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 6a b - 2a b - 8a b - 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (b - 2a b - 8a b - 2a b - 4a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (a b - 3a b - 4a b)cosh(x) - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 6 4 3 3 2 2 5 +--R (- b - a b )sinh(x) + ((- 4b - 4a b )cosh(x) - 4a b - 4a b )sinh(x) +--R + +--R 4 3 2 3 2 2 4 3 +--R (- 5b - 4a b )cosh(x) + (- 11a b - 9a b )cosh(x) - 2b - 2a b +--R + +--R 2 2 3 +--R - 4a b - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 2 2 +--R 4a b cosh(x) + (- 8a b + 4a b )cosh(x) +--R + +--R 4 3 2 2 3 2 2 3 +--R (- 4b - 4a b - 12a b )cosh(x) - 4a b - 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 4 3 2 2 3 +--R (5b + 11a b )cosh(x) + (2a b + 26a b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 4b - 2a b - 16a b + 18a b)cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 +--R (- 10a b - 6a b - 16a b + 4a )cosh(x) - b - a b - 4a b - 2a b +--R + +--R 4 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 5 3 2 2 4 +--R (4b + 8a b )cosh(x) + (4a b + 24a b )cosh(x) +--R + +--R 4 2 2 3 3 3 3 4 2 +--R (- 4b - 12a b + 24a b)cosh(x) + (- 12a b - 20a b + 8a )cosh(x) +--R + +--R 2 2 4 3 +--R (- 12a b - 8a )cosh(x) - 4a b +--R * +--R sinh(x) +--R + +--R 4 3 6 3 2 2 5 +--R (b + 2a b )cosh(x) + (a b + 7a b )cosh(x) +--R + +--R 4 2 2 3 4 3 2 2 3 4 3 +--R (- 2b - 4a b + 9a b)cosh(x) + (- 6a b + 2a b - 8a b + 4a )cosh(x) +--R + +--R 4 3 2 2 3 4 2 3 2 2 3 +--R (b + 2a b - 8a b + 2a b - 4a )cosh(x) + (a b + 3a b - 4a b)cosh(x) +--R + +--R 3 +--R a b +--R / +--R 6 5 2 5 2 4 2 4 3 3 4 +--R ((b - a b )cosh(x) + (2a b - 2a b )cosh(x) + a b - a b )sinh(x) +--R + +--R 6 5 3 5 2 4 2 +--R (4b - 4a b )cosh(x) + (12a b - 12a b )cosh(x) +--R + +--R 2 4 3 3 3 3 4 2 +--R (12a b - 12a b )cosh(x) + 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 5 2 4 3 +--R (6b - 6a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 +--R (2b - 2a b + 34a b - 34a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 4 3 3 4 2 +--R (4a b - 4a b + 20a b - 20a b )cosh(x) + 2a b - 2a b + 4a b +--R + +--R 5 +--R - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 5 5 2 4 4 +--R (4b - 4a b )cosh(x) + (20a b - 20a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (4b - 4a b + 36a b - 36a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 +--R (12a b - 12a b + 28a b - 28a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 3 4 2 +--R (12a b - 12a b + 8a b - 8a b)cosh(x) + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 6 5 6 5 2 4 5 +--R (b - a b )cosh(x) + (6a b - 6a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (2b - 2a b + 13a b - 13a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (8a b - 8a b + 12a b - 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (b - a b + 10a b - 10a b + 4a b - 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 4 3 3 +--R (2a b - 2a b + 4a b - 4a b )cosh(x) + a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 5 2 5 2 4 2 4 3 3 4 +--R ((b + a b )cosh(x) + (2a b + 2a b )cosh(x) + a b + a b )sinh(x) +--R + +--R 6 5 3 5 2 4 2 +--R (4b + 4a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 2 4 3 3 3 3 4 2 +--R (12a b + 12a b )cosh(x) + 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 5 2 4 3 +--R (6b + 6a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 +--R (2b + 2a b + 34a b + 34a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 4 3 3 4 2 5 +--R (4a b + 4a b + 20a b + 20a b )cosh(x) + 2a b + 2a b + 4a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 5 5 2 4 4 +--R (4b + 4a b )cosh(x) + (20a b + 20a b )cosh(x) +--R + +--R 6 5 2 4 3 3 3 +--R (4b + 4a b + 36a b + 36a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 +--R (12a b + 12a b + 28a b + 28a b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 3 3 4 2 +--R (12a b + 12a b + 8a b + 8a b)cosh(x) + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 6 5 6 5 2 4 5 +--R (b + a b )cosh(x) + (6a b + 6a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 +--R (2b + 2a b + 13a b + 13a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (8a b + 8a b + 12a b + 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (b + a b + 10a b + 10a b + 4a b + 4a b)cosh(x) +--R + +--R 5 2 4 3 3 4 2 2 4 3 3 +--R (2a b + 2a b + 4a b + 4a b )cosh(x) + a b + a b +--R Type: Expression(Integer) +--E 222 + +--S 223 of 552 +t0744:= sinh(x)^2/(1+cosh(x))^2 +--R +--R +--R 2 +--R sinh(x) +--R (215) ----------------------- +--R 2 +--R cosh(x) + 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 223 + +--S 224 of 552 +r0744:= x-2*tanh(1/2*x) +--R +--R +--R x +--R (216) - 2tanh(-) + x +--R 2 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 552 +a0744:= integrate(t0744,x) +--R +--R +--R x sinh(x) + x cosh(x) + x + 4 +--R (217) ----------------------------- +--R sinh(x) + cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 225 + +--S 226 of 552 +m0744:= a0744-r0744 +--R +--R +--R x +--R (2sinh(x) + 2cosh(x) + 2)tanh(-) + 4 +--R 2 +--R (218) ------------------------------------ +--R sinh(x) + cosh(x) + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 552 +d0744:= D(m0744,x) +--R +--R +--R (219) +--R 2 2 x 2 +--R (- sinh(x) + (- 2cosh(x) - 2)sinh(x) - cosh(x) - 2cosh(x) - 1)tanh(-) +--R 2 +--R + +--R 2 2 +--R sinh(x) + (2cosh(x) - 2)sinh(x) + cosh(x) - 2cosh(x) + 1 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2)sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 552 +t0745:= sinh(x)^2/(1-cosh(x))^2 +--R +--R +--R 2 +--R sinh(x) +--R (220) ----------------------- +--R 2 +--R cosh(x) - 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 228 + +--S 229 of 552 +r0745:= x-2*coth(1/2*x) +--R +--R +--R x +--R (221) - 2coth(-) + x +--R 2 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 552 +a0745:= integrate(t0745,x) +--R +--R +--R x sinh(x) + x cosh(x) - x - 4 +--R (222) ----------------------------- +--R sinh(x) + cosh(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 230 + +--S 231 of 552 +m0745:= a0745-r0745 +--R +--R +--R x x +--R 2coth(-)sinh(x) + (2cosh(x) - 2)coth(-) - 4 +--R 2 2 +--R (223) ------------------------------------------- +--R sinh(x) + cosh(x) - 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 552 +d0745:= D(m0745,x) +--R +--R +--R (224) +--R x 2 2 +--R (- coth(-) + 1)sinh(x) +--R 2 +--R + +--R x 2 +--R ((- 2cosh(x) + 2)coth(-) + 2cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R (- cosh(x) + 2cosh(x) - 1)coth(-) + cosh(x) + 2cosh(x) + 1 +--R 2 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2)sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 552 +t0746:= sinh(x)^3/(1+cosh(x))^2 +--R +--R +--R 3 +--R sinh(x) +--R (225) ----------------------- +--R 2 +--R cosh(x) + 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 233 + +--S 234 of 552 +r0746:= cosh(x)-2*log(1+cosh(x)) +--R +--R +--R (226) - 2log(cosh(x) + 1) + cosh(x) +--R Type: Expression(Integer) +--E 234 + +--S 235 of 552 +a0746:= integrate(t0746,x) +--R +--R +--R (227) +--R 2 +--R (- 8sinh(x) - 8cosh(x))log(sinh(x) + cosh(x) + 1) + sinh(x) +--R + +--R 2 +--R (2cosh(x) + 4x)sinh(x) + cosh(x) + 4x cosh(x) + 1 +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 235 + +--S 236 of 552 +m0746:= a0746-r0746 +--R +--R +--R (228) +--R (- 8sinh(x) - 8cosh(x))log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (4sinh(x) + 4cosh(x))log(cosh(x) + 1) + sinh(x) + 4x sinh(x) - cosh(x) +--R + +--R 4x cosh(x) + 1 +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 236 + +--S 237 of 552 +d0746:= D(m0746,x) +--R +--R +--R (229) +--R 3 2 2 +--R (- cosh(x) + 3)sinh(x) + (- cosh(x) + 2cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 3 +--R (cosh(x) - 3cosh(x) - cosh(x) + 3)sinh(x) + cosh(x) - 2cosh(x) +--R + +--R 2cosh(x) - 1 +--R / +--R 2 2 3 +--R (2cosh(x) + 2)sinh(x) + (4cosh(x) + 6cosh(x) + 2)sinh(x) + 2cosh(x) +--R + +--R 2 +--R 4cosh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 237 + +--S 238 of 552 +t0747:= sinh(x)^3/(1-cosh(x))^2 +--R +--R +--R 3 +--R sinh(x) +--R (230) ----------------------- +--R 2 +--R cosh(x) - 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 238 + +--S 239 of 552 +r0747:= cosh(x)+2*log(1-cosh(x)) +--R +--R +--R (231) 2log(- cosh(x) + 1) + cosh(x) +--R Type: Expression(Integer) +--E 239 + +--S 240 of 552 +a0747:= integrate(t0747,x) +--R +--R +--R (232) +--R 2 +--R (8sinh(x) + 8cosh(x))log(sinh(x) + cosh(x) - 1) + sinh(x) +--R + +--R 2 +--R (2cosh(x) - 4x)sinh(x) + cosh(x) - 4x cosh(x) + 1 +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 240 + +--S 241 of 552 +m0747:= a0747-r0747 +--R +--R +--R (233) +--R (8sinh(x) + 8cosh(x))log(sinh(x) + cosh(x) - 1) +--R + +--R 2 +--R (- 4sinh(x) - 4cosh(x))log(- cosh(x) + 1) + sinh(x) - 4x sinh(x) +--R + +--R 2 +--R - cosh(x) - 4x cosh(x) + 1 +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 241 + +--S 242 of 552 +d0747:= D(m0747,x) +--R +--R +--R (234) +--R 3 2 2 +--R (- cosh(x) - 3)sinh(x) + (- cosh(x) - 2cosh(x) - 1)sinh(x) +--R + +--R 3 2 4 3 +--R (cosh(x) + 3cosh(x) - cosh(x) - 3)sinh(x) + cosh(x) + 2cosh(x) +--R + +--R - 2cosh(x) - 1 +--R / +--R 2 2 3 +--R (2cosh(x) - 2)sinh(x) + (4cosh(x) - 6cosh(x) + 2)sinh(x) + 2cosh(x) +--R + +--R 2 +--R - 4cosh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 242 + +--S 243 of 552 +t0748:= cosh(x)^3/(1+%i*sinh(x))^3 +--R +--R +--R 3 +--R %i cosh(x) +--R (235) --------------------------------------- +--R 3 2 +--R sinh(x) - 3%i sinh(x) - 3sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 243 + +--S 244 of 552 +r0748:= %i*log(1+%i*sinh(x))+2*%i/(1+%i*sinh(x)) +--R +--R +--R (%i sinh(x) + 1)log(%i sinh(x) + 1) + 2 +--R (236) --------------------------------------- +--R sinh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 244 + +--S 245 of 552 +a0748:= integrate(t0748,x) +--R +--R +--R (237) +--R 2 2 +--R 2%i sinh(x) + (4%i cosh(x) + 4)sinh(x) + 2%i cosh(x) + 4cosh(x) +--R + +--R - 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 2 2 +--R - %i x sinh(x) + (- 2%i x cosh(x) - 2x + 4)sinh(x) - %i x cosh(x) +--R + +--R (- 2x + 4)cosh(x) + %i x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2%i)sinh(x) + cosh(x) - 2%i cosh(x) - 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 245 + +--S 246 of 552 +m0748:= a0748-r0748 +--R +--R +--R (238) +--R 3 2 +--R 2%i sinh(x) + (4%i cosh(x) + 6)sinh(x) +--R + +--R 2 2 +--R (2%i cosh(x) + 8cosh(x) - 6%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 3 2 +--R - %i sinh(x) + (- 2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (- %i cosh(x) - 4cosh(x) + 3%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R * +--R log(%i sinh(x) + 1) +--R + +--R 3 2 +--R - %i x sinh(x) + (- 2%i x cosh(x) - 3x + 2)sinh(x) +--R + +--R 2 2 +--R (- %i x cosh(x) - 4x cosh(x) + 3%i x)sinh(x) + (- x - 2)cosh(x) +--R + +--R 2%i x cosh(x) + x + 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) - 3%i)sinh(x) + (cosh(x) - 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2cosh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 246 + +--S 247 of 552 +d0748:= D(m0748,x) +--R +--R +--R (239) +--R 5 4 3 +--R %i sinh(x) + (2%i cosh(x) - 1)sinh(x) + (- 2cosh(x) + 2%i)sinh(x) +--R + +--R 3 2 +--R (- 2%i cosh(x) + 6%i cosh(x) - 2)sinh(x) +--R + +--R 4 3 4 +--R (- %i cosh(x) + 2cosh(x) - 2cosh(x) + %i)sinh(x) + cosh(x) +--R + +--R 3 +--R - 4%i cosh(x) + 4%i cosh(x) - 1 +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) - 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) - 9%i cosh(x) - 18cosh(x) + 10%i)sinh(x) +--R + +--R 3 2 3 +--R (- 2%i cosh(x) - 9cosh(x) + 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R 3%i cosh(x) + 3cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 247 + +--S 248 of 552 +t0749:= cosh(x)^3/(1-%i*sinh(x))^3 +--R +--R +--R 3 +--R %i cosh(x) +--R (240) - --------------------------------------- +--R 3 2 +--R sinh(x) + 3%i sinh(x) - 3sinh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 248 + +--S 249 of 552 +r0749:= -%i*log(1-%i*sinh(x))-2*%i/(1-%i*sinh(x)) +--R +--R +--R (- %i sinh(x) + 1)log(- %i sinh(x) + 1) + 2 +--R (241) ------------------------------------------- +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 249 + +--S 250 of 552 +a0749:= integrate(t0749,x) +--R +--R +--R (242) +--R 2 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) + 4)sinh(x) - 2%i cosh(x) + 4cosh(x) +--R + +--R 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 2 2 +--R %i x sinh(x) + (2%i x cosh(x) - 2x + 4)sinh(x) + %i x cosh(x) +--R + +--R (- 2x + 4)cosh(x) - %i x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2%i)sinh(x) + cosh(x) + 2%i cosh(x) - 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 250 + +--S 251 of 552 +m0749:= a0749-r0749 +--R +--R +--R (243) +--R 3 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) + 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) + 8cosh(x) + 6%i)sinh(x) + 2cosh(x) + 4%i cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 3 2 +--R %i sinh(x) + (2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (%i cosh(x) - 4cosh(x) - 3%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1 +--R * +--R log(- %i sinh(x) + 1) +--R + +--R 3 2 +--R %i x sinh(x) + (2%i x cosh(x) - 3x + 2)sinh(x) +--R + +--R 2 2 +--R (%i x cosh(x) - 4x cosh(x) - 3%i x)sinh(x) + (- x - 2)cosh(x) +--R + +--R - 2%i x cosh(x) + x + 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) + 3%i)sinh(x) + (cosh(x) + 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R %i cosh(x) - 2cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 251 + +--S 252 of 552 +d0749:= D(m0749,x) +--R +--R +--R (244) +--R 5 4 3 +--R - %i sinh(x) + (- 2%i cosh(x) - 1)sinh(x) + (- 2cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 +--R (2%i cosh(x) - 6%i cosh(x) - 2)sinh(x) +--R + +--R 4 3 4 +--R (%i cosh(x) + 2cosh(x) - 2cosh(x) - %i)sinh(x) + cosh(x) +--R + +--R 3 +--R 4%i cosh(x) - 4%i cosh(x) - 1 +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) + 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) + 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) + 9%i cosh(x) - 18cosh(x) - 10%i)sinh(x) +--R + +--R 3 2 3 +--R (2%i cosh(x) - 9cosh(x) - 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R - 3%i cosh(x) + 3cosh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 252 + +--S 253 of 552 +t0750:= sinh(x)^3/(1+cosh(x))^3 +--R +--R +--R 3 +--R sinh(x) +--R (245) ----------------------------------- +--R 3 2 +--R cosh(x) + 3cosh(x) + 3cosh(x) + 1 +--R Type: Expression(Integer) +--E 253 + +--S 254 of 552 +r0750:= 2/(1+cosh(x))+log(1+cosh(x)) +--R +--R +--R (cosh(x) + 1)log(cosh(x) + 1) + 2 +--R (246) --------------------------------- +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 552 +a0750:= integrate(t0750,x) +--R +--R +--R (247) +--R 2 2 +--R (2sinh(x) + (4cosh(x) + 4)sinh(x) + 2cosh(x) + 4cosh(x) + 2) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R - x sinh(x) + (- 2x cosh(x) - 2x + 4)sinh(x) - x cosh(x) +--R + +--R (- 2x + 4)cosh(x) - x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2)sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 255 + +--S 256 of 552 +m0750:= a0750-r0750 +--R +--R +--R (248) +--R 2 2 +--R (2cosh(x) + 2)sinh(x) + (4cosh(x) + 8cosh(x) + 4)sinh(x) +--R + +--R 3 2 +--R 2cosh(x) + 6cosh(x) + 6cosh(x) + 2 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- cosh(x) - 1)sinh(x) + (- 2cosh(x) - 4cosh(x) - 2)sinh(x) +--R + +--R 3 2 +--R - cosh(x) - 3cosh(x) - 3cosh(x) - 1 +--R * +--R log(cosh(x) + 1) +--R + +--R 2 2 +--R (- x cosh(x) - x - 2)sinh(x) + (- 2x cosh(x) - 4x cosh(x) - 2x)sinh(x) +--R + +--R 3 2 +--R - x cosh(x) + (- 3x + 2)cosh(x) - 3x cosh(x) - x - 2 +--R / +--R 2 2 3 +--R (cosh(x) + 1)sinh(x) + (2cosh(x) + 4cosh(x) + 2)sinh(x) + cosh(x) +--R + +--R 2 +--R 3cosh(x) + 3cosh(x) + 1 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 552 +d0750:= D(m0750,x) +--R +--R +--R (249) +--R 4 2 3 +--R (- cosh(x) + 1)sinh(x) + (- 2cosh(x) + 2cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 5 +--R (2cosh(x) - 2cosh(x) - 6cosh(x) + 2cosh(x) + 4)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R - cosh(x) - 2cosh(x) + 2cosh(x) + cosh(x) - 1 +--R / +--R 2 3 +--R (cosh(x) + 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 2 +--R (3cosh(x) + 9cosh(x) + 9cosh(x) + 3)sinh(x) +--R + +--R 4 3 2 5 +--R (3cosh(x) + 12cosh(x) + 18cosh(x) + 12cosh(x) + 3)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R 5cosh(x) + 10cosh(x) + 10cosh(x) + 5cosh(x) + 1 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 552 +t0751:= sinh(x)^3/(1-cosh(x))^3 +--R +--R +--R 3 +--R sinh(x) +--R (250) - ----------------------------------- +--R 3 2 +--R cosh(x) - 3cosh(x) + 3cosh(x) - 1 +--R Type: Expression(Integer) +--E 258 + +--S 259 of 552 +r0751:= -2/(1-cosh(x))-log(1-cosh(x)) +--R +--R +--R (- cosh(x) + 1)log(- cosh(x) + 1) + 2 +--R (251) ------------------------------------- +--R cosh(x) - 1 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 552 +a0751:= integrate(t0751,x) +--R +--R +--R (252) +--R 2 2 +--R (- 2sinh(x) + (- 4cosh(x) + 4)sinh(x) - 2cosh(x) + 4cosh(x) - 2) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R x sinh(x) + (2x cosh(x) - 2x + 4)sinh(x) + x cosh(x) +--R + +--R (- 2x + 4)cosh(x) + x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2)sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 260 + +--S 261 of 552 +m0751:= a0751-r0751 +--R +--R +--R (253) +--R 2 2 +--R (- 2cosh(x) + 2)sinh(x) + (- 4cosh(x) + 8cosh(x) - 4)sinh(x) +--R + +--R 3 2 +--R - 2cosh(x) + 6cosh(x) - 6cosh(x) + 2 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 3 +--R (cosh(x) - 1)sinh(x) + (2cosh(x) - 4cosh(x) + 2)sinh(x) + cosh(x) +--R + +--R 2 +--R - 3cosh(x) + 3cosh(x) - 1 +--R * +--R log(- cosh(x) + 1) +--R + +--R 2 2 +--R (x cosh(x) - x - 2)sinh(x) + (2x cosh(x) - 4x cosh(x) + 2x)sinh(x) +--R + +--R 3 2 +--R x cosh(x) + (- 3x + 2)cosh(x) + 3x cosh(x) - x - 2 +--R / +--R 2 2 3 +--R (cosh(x) - 1)sinh(x) + (2cosh(x) - 4cosh(x) + 2)sinh(x) + cosh(x) +--R + +--R 2 +--R - 3cosh(x) + 3cosh(x) - 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 552 +d0751:= D(m0751,x) +--R +--R +--R (254) +--R 4 2 3 +--R (cosh(x) + 1)sinh(x) + (2cosh(x) + 2cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 5 +--R (- 2cosh(x) - 2cosh(x) + 6cosh(x) + 2cosh(x) - 4)sinh(x) - cosh(x) +--R + +--R 4 3 2 +--R - cosh(x) + 2cosh(x) + 2cosh(x) - cosh(x) - 1 +--R / +--R 2 3 +--R (cosh(x) - 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 2 +--R (3cosh(x) - 9cosh(x) + 9cosh(x) - 3)sinh(x) +--R + +--R 4 3 2 5 +--R (3cosh(x) - 12cosh(x) + 18cosh(x) - 12cosh(x) + 3)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R - 5cosh(x) + 10cosh(x) - 10cosh(x) + 5cosh(x) - 1 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 552 +t0752:= sinh(x)^2/(a+b*sinh(x)^2) +--R +--R +--R 2 +--R sinh(x) +--R (255) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 263 + +--S 264 of 552 +r0752:= x/b-a^(1/2)*atan((-a+b)^(1/2)*tanh(x)/a^(1/2))/b/(-a+b)^(1/2) +--R +--R +--R +-----+ +--R +-+ tanh(x)\|b - a +-----+ +--R - \|a atan(---------------) + x\|b - a +--R +-+ +--R \|a +--R (256) --------------------------------------- +--R +-----+ +--R b\|b - a +--R Type: Expression(Integer) +--E 264 + +--S 265 of 552 +a0752:= integrate(t0752,x) +--R +--R +--R (257) +--R [ +--R +-------+ +--R | a +--R |- ----- +--R \| b - a +--R * +--R log +--R 2 2 2 +--R (- 4b + 4a b)sinh(x) + (- 8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 4b + 4a b)cosh(x) + 4b - 12a b + 8a +--R * +--R +-------+ +--R | a +--R |- ----- +--R \| b - a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2x +--R / +--R 2b +--R , +--R +-----+ +--R | a +--R +-----+ (2b - 2a) |----- +--R | a \|b - a +--R |----- atan(----------------------------------------------------) + x +--R \|b - a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R ----------------------------------------------------------------------] +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 265 + +--S 266 of 552 +m0752a:= a0752.1-r0752 +--R +--R +--R (258) +--R +-------+ +--R | a +-----+ +--R |- ----- \|b - a +--R \| b - a +--R * +--R log +--R 2 2 2 +--R (- 4b + 4a b)sinh(x) + (- 8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 4b + 4a b)cosh(x) + 4b - 12a b + 8a +--R * +--R +-------+ +--R | a +--R |- ----- +--R \| b - a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R +-----+ +--R +-+ tanh(x)\|b - a +--R 2\|a atan(---------------) +--R +-+ +--R \|a +--R / +--R +-----+ +--R 2b\|b - a +--R Type: Expression(Integer) +--E 266 + +--S 267 of 552 +d0752a:= D(m0752a,x) +--R +--R +--R (259) +--R 4 3 2 2 +--R - a sinh(x) - 4a cosh(x)sinh(x) + (- 6a cosh(x) - 2a)sinh(x) +--R + +--R 3 4 2 +--R (- 4a cosh(x) - 4a cosh(x))sinh(x) - a cosh(x) - 2a cosh(x) - a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) - 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) - 4a cosh(x))sinh(x) + a cosh(x) - 2a cosh(x) + a +--R / +--R 2 4 2 3 +--R (b - a b)sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a b)cosh(x) - 2b + 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b - 4a b)cosh(x) + (- 4b + 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b - a b)cosh(x) + (- 2b + 6a b - 4a )cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) - 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (- 4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (- 2a b + 4a )cosh(x) + a b +--R Type: Expression(Integer) +--E 267 + +--S 268 of 552 +m0752b:= a0752.2-r0752 +--R +--R +--R (260) +--R +-----+ +--R +-+ tanh(x)\|b - a +--R \|a atan(---------------) +--R +-+ +--R \|a +--R + +--R +-----+ +--R | a +--R +-----+ (2b - 2a) |----- +--R | a +-----+ \|b - a +--R |----- \|b - a atan(----------------------------------------------------) +--R \|b - a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R / +--R +-----+ +--R b\|b - a +--R Type: Expression(Integer) +--E 268 + +--S 269 of 552 +d0752b:= D(m0752b,x) +--R +--R +--R (261) +--R 4 3 2 2 +--R - a sinh(x) - 4a cosh(x)sinh(x) + (- 6a cosh(x) - 2a)sinh(x) +--R + +--R 3 4 2 +--R (- 4a cosh(x) - 4a cosh(x))sinh(x) - a cosh(x) - 2a cosh(x) - a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) - 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) - 4a cosh(x))sinh(x) + a cosh(x) - 2a cosh(x) + a +--R / +--R 2 4 2 3 +--R (b - a b)sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a b)cosh(x) - 2b + 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b - 4a b)cosh(x) + (- 4b + 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b - a b)cosh(x) + (- 2b + 6a b - 4a )cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) - 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (- 4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (- 2a b + 4a )cosh(x) + a b +--R Type: Expression(Integer) +--E 269 + +--S 270 of 552 +t0753:= sinh(x)^3/(a+b*sinh(x)^2) +--R +--R +--R 3 +--R sinh(x) +--R (262) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 270 + +--S 271 of 552 +r0753:= a*atanh((-b)^(1/2)*cosh(x)/(a-b)^(1/2))/(a-b)^(1/2)/(-b)^(3/2)+_ + cosh(x)/b +--R +--R +--R +---+ +--R cosh(x)\|- b +---+ +-------+ +--R - a atanh(-------------) + cosh(x)\|- b \|- b + a +--R +-------+ +--R \|- b + a +--R (263) -------------------------------------------------- +--R +---+ +-------+ +--R b\|- b \|- b + a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 552 +a0753:= integrate(t0753,x) +--R +--R +--R (264) +--R [ +--R (a sinh(x) + a cosh(x)) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (6b - 4a)cosh(x) + b +--R * +--R +--------+ +--R | 2 +--R \|b - a b +--R + +--R 2 3 2 2 +--R (4b - 4a b)sinh(x) + (12b - 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((12b - 12a b)cosh(x) + 4b - 4a b)sinh(x) +--R + +--R 2 3 2 +--R (4b - 4a b)cosh(x) + (4b - 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R +--------+ +--R 2 2 | 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|b - a b +--R / +--R +--------+ +--R | 2 +--R (2b sinh(x) + 2b cosh(x))\|b - a b +--R , +--R +--R +----------+ +--R | 2 +--R (sinh(x) + cosh(x))\|- b + a b +--R (2a sinh(x) + 2a cosh(x))atan(--------------------------------) +--R 2b - 2a +--R + +--R (2a sinh(x) + 2a cosh(x)) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) - 3b + 4a)sinh(x) + b cosh(x) + (- 3b + 4a)cosh(x) +--R / +--R +----------+ +--R | 2 +--R 2\|- b + a b +--R + +--R +----------+ +--R 2 2 | 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- b + a b +--R / +--R +----------+ +--R | 2 +--R (2b sinh(x) + 2b cosh(x))\|- b + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 272 + +--S 273 of 552 +m0753a:= a0753.1-r0753 +--R +--R +--R (265) +--R +---+ +-------+ +--R (a sinh(x) + a cosh(x))\|- b \|- b + a +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (6b - 4a)cosh(x) + b +--R * +--R +--------+ +--R | 2 +--R \|b - a b +--R + +--R 2 3 2 2 +--R (4b - 4a b)sinh(x) + (12b - 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((12b - 12a b)cosh(x) + 4b - 4a b)sinh(x) +--R + +--R 2 3 2 +--R (4b - 4a b)cosh(x) + (4b - 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R +--------+ +---+ +--R | 2 cosh(x)\|- b +--R (2a sinh(x) + 2a cosh(x))\|b - a b atanh(-------------) +--R +-------+ +--R \|- b + a +--R + +--R +--------+ +--R 2 2 +---+ +-------+ | 2 +--R (sinh(x) - cosh(x) + 1)\|- b \|- b + a \|b - a b +--R / +--R +--------+ +--R +---+ +-------+ | 2 +--R (2b sinh(x) + 2b cosh(x))\|- b \|- b + a \|b - a b +--R Type: Expression(Integer) +--E 273 + +--S 274 of 552 +d0753a:= D(m0753a,x) +--R +--R +--R (266) +--R 2 6 +--R (- b cosh(x) + b + a)sinh(x) +--R + +--R 3 5 +--R (- 4b cosh(x) + (4b + 6a)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 5b cosh(x) + (6b + 7a)cosh(x) - b + 5a)sinh(x) +--R + +--R 3 3 +--R (- 4a cosh(x) + 12a cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (5b cosh(x) + (- 11b - 9a)cosh(x) + (7b + 6a)cosh(x) - b + 3a)sinh(x) +--R + +--R 7 5 3 +--R 4b cosh(x) + (- 12b - 2a)cosh(x) + (12b - 4a)cosh(x) +--R + +--R (- 4b + 6a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) + (- 4b + a)cosh(x) + (6b - 3a)cosh(x) + (- 4b + 3a)cosh(x) +--R + +--R b - a +--R / +--R 2 2 2 5 +--R (2b cosh(x) - 2b + 2a b)sinh(x) +--R + +--R 2 3 2 4 +--R (10b cosh(x) + (- 10b + 10a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 3 +--R (20b cosh(x) + (- 24b + 28a b)cosh(x) + 4b - 12a b + 8a )sinh(x) +--R + +--R 2 5 2 3 +--R 20b cosh(x) + (- 32b + 44a b)cosh(x) +--R + +--R 2 2 +--R (12b - 36a b + 24a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 10b cosh(x) + (- 22b + 34a b)cosh(x) +--R + +--R 2 2 2 2 +--R (14b - 36a b + 24a )cosh(x) - 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 7 2 5 2 2 3 +--R 2b cosh(x) + (- 6b + 10a b)cosh(x) + (6b - 12a b + 8a )cosh(x) +--R + +--R 2 +--R (- 2b + 2a b)cosh(x) +--R Type: Expression(Integer) +--E 274 + +--S 275 of 552 +m0753b:= a0753.2-r0753 +--R +--R +--R (267) +--R +----------+ +---+ +--R | 2 cosh(x)\|- b +--R (2a sinh(x) + 2a cosh(x))\|- b + a b atanh(-------------) +--R +-------+ +--R \|- b + a +--R + +--R +---+ +-------+ +--R (2a sinh(x) + 2a cosh(x))\|- b \|- b + a +--R * +--R +----------+ +--R | 2 +--R (sinh(x) + cosh(x))\|- b + a b +--R atan(--------------------------------) +--R 2b - 2a +--R + +--R +---+ +-------+ +--R (2a sinh(x) + 2a cosh(x))\|- b \|- b + a +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) - 3b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (- 3b + 4a)cosh(x) +--R / +--R +----------+ +--R | 2 +--R 2\|- b + a b +--R + +--R +----------+ +--R 2 2 | 2 +---+ +-------+ +--R (sinh(x) - cosh(x) + 1)\|- b + a b \|- b \|- b + a +--R / +--R +----------+ +--R | 2 +---+ +-------+ +--R (2b sinh(x) + 2b cosh(x))\|- b + a b \|- b \|- b + a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 552 +d0753b:= D(m0753b,x) +--R +--R +--R (268) +--R 2 6 +--R (- b cosh(x) + b + a)sinh(x) +--R + +--R 3 5 +--R (- 4b cosh(x) + (4b + 6a)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 5b cosh(x) + (6b + 7a)cosh(x) - b + 5a)sinh(x) +--R + +--R 3 3 +--R (- 4a cosh(x) + 12a cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (5b cosh(x) + (- 11b - 9a)cosh(x) + (7b + 6a)cosh(x) - b + 3a)sinh(x) +--R + +--R 7 5 3 +--R 4b cosh(x) + (- 12b - 2a)cosh(x) + (12b - 4a)cosh(x) +--R + +--R (- 4b + 6a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) + (- 4b + a)cosh(x) + (6b - 3a)cosh(x) + (- 4b + 3a)cosh(x) +--R + +--R b - a +--R / +--R 2 2 2 5 +--R (2b cosh(x) - 2b + 2a b)sinh(x) +--R + +--R 2 3 2 4 +--R (10b cosh(x) + (- 10b + 10a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 3 +--R (20b cosh(x) + (- 24b + 28a b)cosh(x) + 4b - 12a b + 8a )sinh(x) +--R + +--R 2 5 2 3 +--R 20b cosh(x) + (- 32b + 44a b)cosh(x) +--R + +--R 2 2 +--R (12b - 36a b + 24a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 10b cosh(x) + (- 22b + 34a b)cosh(x) +--R + +--R 2 2 2 2 +--R (14b - 36a b + 24a )cosh(x) - 2b + 2a b +--R * +--R sinh(x) +--R + +--R 2 7 2 5 2 2 3 +--R 2b cosh(x) + (- 6b + 10a b)cosh(x) + (6b - 12a b + 8a )cosh(x) +--R + +--R 2 +--R (- 2b + 2a b)cosh(x) +--R Type: Expression(Integer) +--E 276 + +--S 277 of 552 +t0754:= sinh(x)^4/(a+b*sinh(x)^2) +--R +--R +--R 4 +--R sinh(x) +--R (269) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 552 +r0754:= -a*x/b^2-1/2*x/b+a^(3/2)*atan((-a+b)^(1/2)*_ + tanh(x)/a^(1/2))/b^2/(-a+b)^(1/2)+1/2*cosh(x)*sinh(x)/b +--R +--R +--R (270) +--R +-----+ +--R +-+ tanh(x)\|b - a +-----+ +--R 2a\|a atan(---------------) + (b cosh(x)sinh(x) + (- b - 2a)x)\|b - a +--R +-+ +--R \|a +--R ---------------------------------------------------------------------- +--R 2 +-----+ +--R 2b \|b - a +--R Type: Expression(Integer) +--E 278 + +--S 279 of 552 +a0754:= integrate(t0754,x) +--R +--R +--R (271) +--R [ +--R +-------+ +--R 2 2 | a +--R (4a sinh(x) + 8a cosh(x)sinh(x) + 4a cosh(x) ) |- ----- +--R \| b - a +--R * +--R log +--R 2 2 2 +--R (4b - 4a b)sinh(x) + (8b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4b - 4a b)cosh(x) - 4b + 12a b - 8a +--R * +--R +-------+ +--R | a +--R |- ----- +--R \| b - a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + (- 4b - 8a)x)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 8b - 16a)x cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 4b - 8a)x cosh(x) - b +--R / +--R 2 2 2 2 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R , +--R +--R +-----+ +--R 2 2 | a +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) ) |----- +--R \|b - a +--R * +--R +-----+ +--R | a +--R (2b - 2a) |----- +--R \|b - a +--R atan(----------------------------------------------------) +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + (- 4b - 8a)x)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 8b - 16a)x cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 4b - 8a)x cosh(x) - b +--R / +--R 2 2 2 2 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 279 + +--S 280 of 552 +m0754a:= a0754.1-r0754 +--R +--R +--R (272) +--R +-------+ +--R 2 2 | a +-----+ +--R (4a sinh(x) + 8a cosh(x)sinh(x) + 4a cosh(x) ) |- ----- \|b - a +--R \| b - a +--R * +--R log +--R 2 2 2 +--R (4b - 4a b)sinh(x) + (8b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4b - 4a b)cosh(x) - 4b + 12a b - 8a +--R * +--R +-------+ +--R | a +--R |- ----- +--R \| b - a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 2 +-+ +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) )\|a +--R * +--R +-----+ +--R tanh(x)\|b - a +--R atan(---------------) +--R +-+ +--R \|a +--R + +--R 4 2 2 4 +-----+ +--R (b sinh(x) - 2b cosh(x) sinh(x) + b cosh(x) - b)\|b - a +--R / +--R 2 2 2 2 2 +-----+ +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b - a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 552 +d0754a:= D(m0754a,x) +--R +--R +--R (273) +--R 2 8 2 7 +--R (- b + a b)sinh(x) + (- 4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((- 4b + 4a b)cosh(x) + 2b - 6a b + 8a )sinh(x) +--R + +--R 2 3 2 2 5 +--R ((4b - 4a b)cosh(x) + (4b - 12a b + 32a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R ((10b - 10a b)cosh(x) + (- 2b + 6a b + 56a )cosh(x) + 8a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (4b - 4a b)cosh(x) + (- 8b + 24a b + 64a )cosh(x) +--R + +--R 2 2 +--R (4b - 4a b + 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (- 4b + 4a b)cosh(x) + (- 2b + 6a b + 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (8b - 8a b + 48a )cosh(x) - 2b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R (- 4b + 4a b)cosh(x) + (4b - 12a b + 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (4b - 4a b + 32a )cosh(x) + (- 4b + 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 2 6 2 4 +--R (- b + a b)cosh(x) + (2b - 6a b + 8a )cosh(x) + 8a cosh(x) +--R + +--R 2 2 2 +--R (- 2b + 6a b)cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 6 +--R (- 4a b cosh(x) + 2a b - 8a )sinh(x) +--R + +--R 3 2 5 +--R (4a b cosh(x) + (4a b - 32a )cosh(x))sinh(x) +--R + +--R 4 2 2 2 4 +--R (10a b cosh(x) + (- 2a b - 56a )cosh(x) + 8a )sinh(x) +--R + +--R 5 2 3 2 3 +--R (4a b cosh(x) + (- 8a b - 64a )cosh(x) + (4a b + 32a )cosh(x))sinh(x) +--R + +--R 6 2 4 2 2 +--R - 4a b cosh(x) + (- 2a b - 56a )cosh(x) + (8a b + 48a )cosh(x) +--R + +--R - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 2 3 +--R - 4a b cosh(x) + (4a b - 32a )cosh(x) + (4a b + 32a )cosh(x) +--R + +--R - 4a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 2 6 2 4 2 +--R - a b cosh(x) + (2a b - 8a )cosh(x) + 8a cosh(x) - 2a b cosh(x) + a b +--R / +--R 3 2 6 3 2 5 +--R (4b - 4a b )sinh(x) + (24b - 24a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 4 +--R ((60b - 60a b )cosh(x) - 8b + 24a b - 16a b)sinh(x) +--R + +--R 3 2 3 3 2 2 3 +--R ((80b - 80a b )cosh(x) + (- 32b + 96a b - 64a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R (60b - 60a b )cosh(x) + (- 48b + 144a b - 96a b)cosh(x) +--R + +--R 3 2 +--R 4b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (24b - 24a b )cosh(x) + (- 32b + 96a b - 64a b)cosh(x) +--R + +--R 3 2 +--R (8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (4b - 4a b )cosh(x) + (- 8b + 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (4b - 4a b )cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 5 +--R 4a b sinh(x) + 24a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (60a b cosh(x) - 8a b + 16a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (80a b cosh(x) + (- 32a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 2 +--R (60a b cosh(x) + (- 48a b + 96a b)cosh(x) + 4a b )sinh(x) +--R + +--R 2 5 2 2 3 2 +--R (24a b cosh(x) + (- 32a b + 64a b)cosh(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 2 2 +--R 4a b cosh(x) + (- 8a b + 16a b)cosh(x) + 4a b cosh(x) +--R Type: Expression(Integer) +--E 281 + +--S 282 of 552 +m0754b:= a0754.2-r0754 +--R +--R +--R (274) +--R 2 2 +-+ +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) )\|a +--R * +--R +-----+ +--R tanh(x)\|b - a +--R atan(---------------) +--R +-+ +--R \|a +--R + +--R +-----+ +--R 2 2 | a +-----+ +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) ) |----- \|b - a +--R \|b - a +--R * +--R +-----+ +--R | a +--R (2b - 2a) |----- +--R \|b - a +--R atan(----------------------------------------------------) +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R 4 2 2 4 +-----+ +--R (b sinh(x) - 2b cosh(x) sinh(x) + b cosh(x) - b)\|b - a +--R / +--R 2 2 2 2 2 +-----+ +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b - a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 552 +d0754b:= D(m0754b,x) +--R +--R +--R (275) +--R 2 8 2 7 +--R (- b + a b)sinh(x) + (- 4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((- 4b + 4a b)cosh(x) + 2b - 6a b + 8a )sinh(x) +--R + +--R 2 3 2 2 5 +--R ((4b - 4a b)cosh(x) + (4b - 12a b + 32a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R ((10b - 10a b)cosh(x) + (- 2b + 6a b + 56a )cosh(x) + 8a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (4b - 4a b)cosh(x) + (- 8b + 24a b + 64a )cosh(x) +--R + +--R 2 2 +--R (4b - 4a b + 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (- 4b + 4a b)cosh(x) + (- 2b + 6a b + 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (8b - 8a b + 48a )cosh(x) - 2b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R (- 4b + 4a b)cosh(x) + (4b - 12a b + 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (4b - 4a b + 32a )cosh(x) + (- 4b + 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 2 6 2 4 +--R (- b + a b)cosh(x) + (2b - 6a b + 8a )cosh(x) + 8a cosh(x) +--R + +--R 2 2 2 +--R (- 2b + 6a b)cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 6 +--R (- 4a b cosh(x) + 2a b - 8a )sinh(x) +--R + +--R 3 2 5 +--R (4a b cosh(x) + (4a b - 32a )cosh(x))sinh(x) +--R + +--R 4 2 2 2 4 +--R (10a b cosh(x) + (- 2a b - 56a )cosh(x) + 8a )sinh(x) +--R + +--R 5 2 3 2 3 +--R (4a b cosh(x) + (- 8a b - 64a )cosh(x) + (4a b + 32a )cosh(x))sinh(x) +--R + +--R 6 2 4 2 2 +--R - 4a b cosh(x) + (- 2a b - 56a )cosh(x) + (8a b + 48a )cosh(x) +--R + +--R - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 2 3 +--R - 4a b cosh(x) + (4a b - 32a )cosh(x) + (4a b + 32a )cosh(x) +--R + +--R - 4a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 2 6 2 4 2 +--R - a b cosh(x) + (2a b - 8a )cosh(x) + 8a cosh(x) - 2a b cosh(x) + a b +--R / +--R 3 2 6 3 2 5 +--R (4b - 4a b )sinh(x) + (24b - 24a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 4 +--R ((60b - 60a b )cosh(x) - 8b + 24a b - 16a b)sinh(x) +--R + +--R 3 2 3 3 2 2 3 +--R ((80b - 80a b )cosh(x) + (- 32b + 96a b - 64a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R (60b - 60a b )cosh(x) + (- 48b + 144a b - 96a b)cosh(x) +--R + +--R 3 2 +--R 4b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (24b - 24a b )cosh(x) + (- 32b + 96a b - 64a b)cosh(x) +--R + +--R 3 2 +--R (8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (4b - 4a b )cosh(x) + (- 8b + 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (4b - 4a b )cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 5 +--R 4a b sinh(x) + 24a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (60a b cosh(x) - 8a b + 16a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (80a b cosh(x) + (- 32a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 2 +--R (60a b cosh(x) + (- 48a b + 96a b)cosh(x) + 4a b )sinh(x) +--R + +--R 2 5 2 2 3 2 +--R (24a b cosh(x) + (- 32a b + 64a b)cosh(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 2 2 +--R 4a b cosh(x) + (- 8a b + 16a b)cosh(x) + 4a b cosh(x) +--R Type: Expression(Integer) +--E 283 + +--S 284 of 552 +t0755:= sinh(x)^5/(a+b*sinh(x)^2) +--R +--R +--R 5 +--R sinh(x) +--R (276) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 552 +r0755:= a^2*atanh((-b)^(1/2)*cosh(x)/(a-b)^(1/2))/(a-b)^(1/2)/(-b)^(5/2)-_ + a*cosh(x)/b^2-cosh(x)/b+1/3*cosh(x)^3/b +--R +--R +--R (277) +--R +---+ +--R 2 cosh(x)\|- b 3 +---+ +-------+ +--R 3a atanh(-------------) + (b cosh(x) + (- 3b - 3a)cosh(x))\|- b \|- b + a +--R +-------+ +--R \|- b + a +--R --------------------------------------------------------------------------- +--R 2 +---+ +-------+ +--R 3b \|- b \|- b + a +--R Type: Expression(Integer) +--E 285 + +--S 286 of 552 +a0755:= integrate(t0755,x) +--R +--R +--R (278) +--R [ +--R 2 3 2 2 2 2 +--R 12a sinh(x) + 36a cosh(x)sinh(x) + 36a cosh(x) sinh(x) +--R + +--R 2 3 +--R 12a cosh(x) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (6b - 4a)cosh(x) + b +--R * +--R +--------+ +--R | 2 +--R \|b - a b +--R + +--R 2 3 2 2 +--R (- 4b + 4a b)sinh(x) + (- 12b + 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((- 12b + 12a b)cosh(x) - 4b + 4a b)sinh(x) +--R + +--R 2 3 2 +--R (- 4b + 4a b)cosh(x) + (- 4b + 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 6 5 2 4 +--R b sinh(x) + 6b cosh(x)sinh(x) + (15b cosh(x) - 9b - 12a)sinh(x) +--R + +--R 3 3 +--R (20b cosh(x) + (- 36b - 48a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) + (- 54b - 72a)cosh(x) - 9b - 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (- 36b - 48a)cosh(x) + (- 18b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (- 9b - 12a)cosh(x) + (- 9b - 12a)cosh(x) + b +--R * +--R +--------+ +--R | 2 +--R \|b - a b +--R / +--R 2 3 2 2 2 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 2 3 +--R 24b cosh(x) +--R * +--R +--------+ +--R | 2 +--R \|b - a b +--R , +--R +--R 2 3 2 2 2 2 +--R - 24a sinh(x) - 72a cosh(x)sinh(x) - 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R - 24a cosh(x) +--R * +--R +----------+ +--R | 2 +--R (sinh(x) + cosh(x))\|- b + a b +--R atan(--------------------------------) +--R 2b - 2a +--R + +--R 2 3 2 2 2 2 +--R - 24a sinh(x) - 72a cosh(x)sinh(x) - 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R - 24a cosh(x) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) - 3b + 4a)sinh(x) + b cosh(x) + (- 3b + 4a)cosh(x) +--R / +--R +----------+ +--R | 2 +--R 2\|- b + a b +--R + +--R 6 5 2 4 +--R b sinh(x) + 6b cosh(x)sinh(x) + (15b cosh(x) - 9b - 12a)sinh(x) +--R + +--R 3 3 +--R (20b cosh(x) + (- 36b - 48a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) + (- 54b - 72a)cosh(x) - 9b - 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (- 36b - 48a)cosh(x) + (- 18b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (- 9b - 12a)cosh(x) + (- 9b - 12a)cosh(x) + b +--R * +--R +----------+ +--R | 2 +--R \|- b + a b +--R / +--R 2 3 2 2 2 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 2 3 +--R 24b cosh(x) +--R * +--R +----------+ +--R | 2 +--R \|- b + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 286 + +--S 287 of 552 +m0755a:= a0755.1-r0755 +--R +--R +--R (279) +--R 2 3 2 2 2 2 +--R 12a sinh(x) + 36a cosh(x)sinh(x) + 36a cosh(x) sinh(x) +--R + +--R 2 3 +--R 12a cosh(x) +--R * +--R +---+ +-------+ +--R \|- b \|- b + a +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (6b - 4a)cosh(x) + b +--R * +--R +--------+ +--R | 2 +--R \|b - a b +--R + +--R 2 3 2 2 +--R (- 4b + 4a b)sinh(x) + (- 12b + 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((- 12b + 12a b)cosh(x) - 4b + 4a b)sinh(x) +--R + +--R 2 3 2 +--R (- 4b + 4a b)cosh(x) + (- 4b + 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 3 2 2 2 2 +--R - 24a sinh(x) - 72a cosh(x)sinh(x) - 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R - 24a cosh(x) +--R * +--R +--------+ +---+ +--R | 2 cosh(x)\|- b +--R \|b - a b atanh(-------------) +--R +-------+ +--R \|- b + a +--R + +--R 6 5 2 4 +--R b sinh(x) + 6b cosh(x)sinh(x) + (15b cosh(x) - 9b - 12a)sinh(x) +--R + +--R 3 3 +--R (12b cosh(x) + (- 12b - 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 9b cosh(x) + 18b cosh(x) - 9b - 12a)sinh(x) +--R + +--R 5 3 +--R (- 18b cosh(x) + (36b + 24a)cosh(x) + (- 18b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 7b cosh(x) + (15b + 12a)cosh(x) + (- 9b - 12a)cosh(x) + b +--R * +--R +--------+ +--R +---+ +-------+ | 2 +--R \|- b \|- b + a \|b - a b +--R / +--R 2 3 2 2 2 2 2 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +--------+ +--R +---+ +-------+ | 2 +--R \|- b \|- b + a \|b - a b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 552 +d0755a:= D(m0755a,x) +--R +--R +--R (280) +--R 2 10 +--R (b cosh(x) - b + a)sinh(x) +--R + +--R 3 9 +--R (10b cosh(x) + (- 10b + 10a)cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (37b cosh(x) + (- 34b + 45a)cosh(x) - 3b - 5a)sinh(x) +--R + +--R 5 3 7 +--R (64b cosh(x) + (- 48b + 120a)cosh(x) + (- 16b - 40a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (42b cosh(x) + (2b + 178a)cosh(x) + (- 50b - 76a)cosh(x) + 6b - 22a) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 5 3 +--R - 28b cosh(x) + (108b + 92a)cosh(x) + (- 100b + 40a)cosh(x) +--R + +--R (20b - 100a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 4 +--R - 70b cosh(x) + (160b - 110a)cosh(x) + (- 108b + 290a)cosh(x) +--R + +--R 2 +--R (16b - 170a)cosh(x) + 2b - 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 +--R - 48b cosh(x) + (96b - 200a)cosh(x) + (- 32b + 360a)cosh(x) +--R + +--R 3 +--R (- 32b - 120a)cosh(x) + (16b - 40a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 +--R - 11b cosh(x) + (7b - 115a)cosh(x) + (50b + 180a)cosh(x) +--R + +--R 4 2 +--R (- 82b - 10a)cosh(x) + (41b - 60a)cosh(x) - 5b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 +--R 2b cosh(x) + (- 18b - 22a)cosh(x) + (52b + 24a)cosh(x) +--R + +--R 5 3 +--R (- 68b + 28a)cosh(x) + (42b - 40a)cosh(x) + (- 10b + 10a)cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 +--R b cosh(x) + (- 6b + a)cosh(x) + (15b - 5a)cosh(x) +--R + +--R 6 4 2 +--R (- 20b + 10a)cosh(x) + (15b - 10a)cosh(x) + (- 6b + 5a)cosh(x) + b - a +--R / +--R 2 2 2 7 +--R (8b cosh(x) - 8b + 8a b)sinh(x) +--R + +--R 2 3 2 6 +--R (56b cosh(x) + (- 56b + 56a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (168b cosh(x) + (- 184b + 200a b)cosh(x) + 16b - 48a b + 32a ) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 280b cosh(x) + (- 360b + 440a b)cosh(x) +--R + +--R 2 2 +--R (80b - 240a b + 160a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 280b cosh(x) + (- 440b + 600a b)cosh(x) +--R + +--R 2 2 2 2 +--R (168b - 480a b + 320a )cosh(x) - 8b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 168b cosh(x) + (- 328b + 488a b)cosh(x) +--R + +--R 2 2 3 2 +--R (184b - 480a b + 320a )cosh(x) + (- 24b + 24a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 56b cosh(x) + (- 136b + 216a b)cosh(x) +--R + +--R 2 2 4 2 2 +--R (104b - 240a b + 160a )cosh(x) + (- 24b + 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 9 2 7 2 2 5 +--R 8b cosh(x) + (- 24b + 40a b)cosh(x) + (24b - 48a b + 32a )cosh(x) +--R + +--R 2 3 +--R (- 8b + 8a b)cosh(x) +--R Type: Expression(Integer) +--E 288 + +--S 289 of 552 +m0755b:= a0755.2-r0755 +--R +--R +--R (281) +--R 2 3 2 2 2 2 +--R - 24a sinh(x) - 72a cosh(x)sinh(x) - 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R - 24a cosh(x) +--R * +--R +----------+ +---+ +--R | 2 cosh(x)\|- b +--R \|- b + a b atanh(-------------) +--R +-------+ +--R \|- b + a +--R + +--R 2 3 2 2 2 2 +--R - 24a sinh(x) - 72a cosh(x)sinh(x) - 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R - 24a cosh(x) +--R * +--R +----------+ +--R | 2 +--R +---+ +-------+ (sinh(x) + cosh(x))\|- b + a b +--R \|- b \|- b + a atan(--------------------------------) +--R 2b - 2a +--R + +--R 2 3 2 2 2 2 +--R - 24a sinh(x) - 72a cosh(x)sinh(x) - 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R - 24a cosh(x) +--R * +--R +---+ +-------+ +--R \|- b \|- b + a +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) - 3b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (- 3b + 4a)cosh(x) +--R / +--R +----------+ +--R | 2 +--R 2\|- b + a b +--R + +--R 6 5 2 4 +--R b sinh(x) + 6b cosh(x)sinh(x) + (15b cosh(x) - 9b - 12a)sinh(x) +--R + +--R 3 3 +--R (12b cosh(x) + (- 12b - 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 9b cosh(x) + 18b cosh(x) - 9b - 12a)sinh(x) +--R + +--R 5 3 +--R (- 18b cosh(x) + (36b + 24a)cosh(x) + (- 18b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 7b cosh(x) + (15b + 12a)cosh(x) + (- 9b - 12a)cosh(x) + b +--R * +--R +----------+ +--R | 2 +---+ +-------+ +--R \|- b + a b \|- b \|- b + a +--R / +--R 2 3 2 2 2 2 2 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +----------+ +--R | 2 +---+ +-------+ +--R \|- b + a b \|- b \|- b + a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 552 +d0755b:= D(m0755b,x) +--R +--R +--R (282) +--R 2 10 +--R (b cosh(x) - b + a)sinh(x) +--R + +--R 3 9 +--R (10b cosh(x) + (- 10b + 10a)cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (37b cosh(x) + (- 34b + 45a)cosh(x) - 3b - 5a)sinh(x) +--R + +--R 5 3 7 +--R (64b cosh(x) + (- 48b + 120a)cosh(x) + (- 16b - 40a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (42b cosh(x) + (2b + 178a)cosh(x) + (- 50b - 76a)cosh(x) + 6b - 22a) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 5 3 +--R - 28b cosh(x) + (108b + 92a)cosh(x) + (- 100b + 40a)cosh(x) +--R + +--R (20b - 100a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 4 +--R - 70b cosh(x) + (160b - 110a)cosh(x) + (- 108b + 290a)cosh(x) +--R + +--R 2 +--R (16b - 170a)cosh(x) + 2b - 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 +--R - 48b cosh(x) + (96b - 200a)cosh(x) + (- 32b + 360a)cosh(x) +--R + +--R 3 +--R (- 32b - 120a)cosh(x) + (16b - 40a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 +--R - 11b cosh(x) + (7b - 115a)cosh(x) + (50b + 180a)cosh(x) +--R + +--R 4 2 +--R (- 82b - 10a)cosh(x) + (41b - 60a)cosh(x) - 5b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 +--R 2b cosh(x) + (- 18b - 22a)cosh(x) + (52b + 24a)cosh(x) +--R + +--R 5 3 +--R (- 68b + 28a)cosh(x) + (42b - 40a)cosh(x) + (- 10b + 10a)cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 +--R b cosh(x) + (- 6b + a)cosh(x) + (15b - 5a)cosh(x) +--R + +--R 6 4 2 +--R (- 20b + 10a)cosh(x) + (15b - 10a)cosh(x) + (- 6b + 5a)cosh(x) + b - a +--R / +--R 2 2 2 7 +--R (8b cosh(x) - 8b + 8a b)sinh(x) +--R + +--R 2 3 2 6 +--R (56b cosh(x) + (- 56b + 56a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (168b cosh(x) + (- 184b + 200a b)cosh(x) + 16b - 48a b + 32a ) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 280b cosh(x) + (- 360b + 440a b)cosh(x) +--R + +--R 2 2 +--R (80b - 240a b + 160a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 280b cosh(x) + (- 440b + 600a b)cosh(x) +--R + +--R 2 2 2 2 +--R (168b - 480a b + 320a )cosh(x) - 8b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 168b cosh(x) + (- 328b + 488a b)cosh(x) +--R + +--R 2 2 3 2 +--R (184b - 480a b + 320a )cosh(x) + (- 24b + 24a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 56b cosh(x) + (- 136b + 216a b)cosh(x) +--R + +--R 2 2 4 2 2 +--R (104b - 240a b + 160a )cosh(x) + (- 24b + 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 9 2 7 2 2 5 +--R 8b cosh(x) + (- 24b + 40a b)cosh(x) + (24b - 48a b + 32a )cosh(x) +--R + +--R 2 3 +--R (- 8b + 8a b)cosh(x) +--R Type: Expression(Integer) +--E 290 + +--S 291 of 552 +t0756:= sinh(x)^6/(a+b*sinh(x)^2) +--R +--R +--R 6 +--R sinh(x) +--R (283) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 552 +r0756:= a^2*x/b^3+1/2*a*x/b^2+3/8*x/b-a^(5/2)*atan((-a+b)^(1/2)*_ + tanh(x)/a^(1/2))/b^3/(-a+b)^(1/2)-1/2*a*cosh(x)*_ + sinh(x)/b^2-3/8*cosh(x)*sinh(x)/b+1/4*cosh(x)*sinh(x)^3/b +--R +--R +--R (284) +--R +-----+ +--R 2 +-+ tanh(x)\|b - a +--R - 8a \|a atan(---------------) +--R +-+ +--R \|a +--R + +--R 2 3 2 +--R 2b cosh(x)sinh(x) + (- 3b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 +--R (3b + 4a b + 8a )x +--R * +--R +-----+ +--R \|b - a +--R / +--R 3 +-----+ +--R 8b \|b - a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 552 +a0756:= integrate(t0756,x) +--R +--R +--R (285) +--R [ +--R 2 4 2 3 2 2 2 +--R 32a sinh(x) + 128a cosh(x)sinh(x) + 192a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R 128a cosh(x) sinh(x) + 32a cosh(x) +--R * +--R +-------+ +--R | a +--R |- ----- +--R \| b - a +--R * +--R log +--R 2 2 2 +--R (- 4b + 4a b)sinh(x) + (- 8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 4b + 4a b)cosh(x) + 4b - 12a b + 8a +--R * +--R +-------+ +--R | a +--R |- ----- +--R \| b - a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) - 8b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (56b cosh(x) + (- 48b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (70b cosh(x) + (- 120b - 120a b)cosh(x) + (24b + 32a b + 64a )x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 56b cosh(x) + (- 160b - 160a b)cosh(x) +--R + +--R 2 2 +--R (96b + 128a b + 256a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 28b cosh(x) + (- 120b - 120a b)cosh(x) +--R + +--R 2 2 2 2 +--R (144b + 192a b + 384a )x cosh(x) + 8b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (- 48b - 48a b)cosh(x) +--R + +--R 2 2 3 2 +--R (96b + 128a b + 256a )x cosh(x) + (16b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 4 +--R b cosh(x) + (- 8b - 8a b)cosh(x) + (24b + 32a b + 64a )x cosh(x) +--R + +--R 2 2 2 +--R (8b + 8a b)cosh(x) - b +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R , +--R +--R 2 4 2 3 2 2 2 +--R 64a sinh(x) + 256a cosh(x)sinh(x) + 384a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R 256a cosh(x) sinh(x) + 64a cosh(x) +--R * +--R +-----+ +--R | a +--R +-----+ (2b - 2a) |----- +--R | a \|b - a +--R |----- atan(----------------------------------------------------) +--R \|b - a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) - 8b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (56b cosh(x) + (- 48b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (70b cosh(x) + (- 120b - 120a b)cosh(x) + (24b + 32a b + 64a )x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 56b cosh(x) + (- 160b - 160a b)cosh(x) +--R + +--R 2 2 +--R (96b + 128a b + 256a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 28b cosh(x) + (- 120b - 120a b)cosh(x) +--R + +--R 2 2 2 2 +--R (144b + 192a b + 384a )x cosh(x) + 8b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (- 48b - 48a b)cosh(x) +--R + +--R 2 2 3 2 +--R (96b + 128a b + 256a )x cosh(x) + (16b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 4 +--R b cosh(x) + (- 8b - 8a b)cosh(x) + (24b + 32a b + 64a )x cosh(x) +--R + +--R 2 2 2 +--R (8b + 8a b)cosh(x) - b +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 293 + +--S 294 of 552 +m0756a:= a0756.1-r0756 +--R +--R +--R (286) +--R 2 4 2 3 2 2 2 +--R 32a sinh(x) + 128a cosh(x)sinh(x) + 192a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R 128a cosh(x) sinh(x) + 32a cosh(x) +--R * +--R +-------+ +--R | a +-----+ +--R |- ----- \|b - a +--R \| b - a +--R * +--R log +--R 2 2 2 +--R (- 4b + 4a b)sinh(x) + (- 8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 4b + 4a b)cosh(x) + 4b - 12a b + 8a +--R * +--R +-------+ +--R | a +--R |- ----- +--R \| b - a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 4 2 3 2 2 2 +--R 64a sinh(x) + 256a cosh(x)sinh(x) + 384a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R 256a cosh(x) sinh(x) + 64a cosh(x) +--R * +--R +-----+ +--R +-+ tanh(x)\|b - a +--R \|a atan(---------------) +--R +-+ +--R \|a +--R + +--R 2 8 2 7 +--R b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (- 36b cosh(x) - 8b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (- 40b cosh(x) + (- 24b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R (6b cosh(x) + (- 24b + 8a b)cosh(x) )sinh(x) +--R + +--R 2 5 2 3 3 +--R (40b cosh(x) + (- 16b + 32a b)cosh(x) )sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (28b cosh(x) + (- 24b + 8a b)cosh(x) + 8b + 8a b)sinh(x) +--R + +--R 2 7 2 5 2 +--R (8b cosh(x) + (- 24b - 16a b)cosh(x) + (16b + 16a b)cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 2 +--R b cosh(x) + (- 8b - 8a b)cosh(x) + (8b + 8a b)cosh(x) - b +--R * +--R +-----+ +--R \|b - a +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R +-----+ +--R \|b - a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 552 +d0756a:= D(m0756a,x) +--R +--R +--R (287) +--R 3 2 12 3 2 11 +--R (- 3b + 3a b )sinh(x) + (- 20b + 20a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 10 +--R ((- 58b + 58a b )cosh(x) + 8b - 16a b + 8a b)sinh(x) +--R + +--R 3 2 3 3 2 2 +--R ((- 100b + 100a b )cosh(x) + (36b - 68a b + 32a b)cosh(x)) +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R (- 121b + 121a b )cosh(x) + (48b - 104a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 +--R - 7b + 7a b + 16a b - 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (- 104b + 104a b )cosh(x) + (- 32b - 64a b + 96a b)cosh(x) +--R + +--R 3 2 3 +--R (- 16b + 80a b - 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 28b + 28a b )cosh(x) + (- 192b + 16a b + 176a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 3 +--R (24b - 120a b + 160a b - 512a )cosh(x) - 2b + 2a b - 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 7 3 2 2 5 +--R (88b - 88a b )cosh(x) + (- 312b + 152a b + 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (128b - 368a b + 176a b - 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b + 8a b + 16a b - 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 8 3 2 2 6 +--R (155b - 155a b )cosh(x) + (- 304b + 352a b - 48a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (194b - 514a b + 160a b - 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 78b + 14a b + 64a b - 480a )cosh(x) + 9b - 17a b - 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 9 3 2 2 7 +--R (124b - 124a b )cosh(x) + (- 192b + 416a b - 224a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (144b - 384a b + 176a b - 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b + 16a b + 96a b - 640a )cosh(x) +--R + +--R 3 2 2 +--R (36b - 68a b - 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 10 3 2 2 8 +--R (54b - 54a b )cosh(x) + (- 72b + 256a b - 184a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (48b - 144a b + 160a b - 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 78b + 14a b + 64a b - 480a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (54b - 102a b - 48a b)cosh(x) - 6b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 11 3 2 2 9 +--R (12b - 12a b )cosh(x) + (- 12b + 76a b - 64a b)cosh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 80a b - 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b + 8a b + 16a b - 192a )cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (36b - 68a b - 32a b)cosh(x) + (- 12b + 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 12 2 2 10 +--R (b - a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 3b + 3a b + 16a b - 32a )cosh(x) +--R + +--R 3 2 3 6 3 2 2 4 +--R (- 2b + 2a b - 32a )cosh(x) + (9b - 17a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 6b + 6a b )cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 12 2 11 +--R - 3a b sinh(x) - 20a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 10 +--R (- 58a b cosh(x) + 8a b - 8a b)sinh(x) +--R + +--R 2 3 2 2 9 +--R (- 100a b cosh(x) + (36a b - 32a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 3 8 +--R (- 121a b cosh(x) + (48a b - 56a b)cosh(x) - 7a b + 32a )sinh(x) +--R + +--R 2 5 2 2 3 +--R - 104a b cosh(x) + (- 32a b - 96a b)cosh(x) +--R + +--R 2 2 3 +--R (- 16a b - 16a b + 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R - 28a b cosh(x) + (- 192a b - 176a b)cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (24a b - 96a b + 512a )cosh(x) - 2a b - 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R 88a b cosh(x) + (- 312a b - 160a b)cosh(x) +--R + +--R 2 2 3 3 2 2 3 +--R (128a b - 240a b + 832a )cosh(x) + (- 24a b - 16a b - 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R 155a b cosh(x) + (- 304a b + 48a b)cosh(x) +--R + +--R 2 2 3 4 +--R (194a b - 320a b + 960a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 78a b - 64a b - 480a )cosh(x) + 9a b - 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 9 2 2 7 +--R 124a b cosh(x) + (- 192a b + 224a b)cosh(x) +--R + +--R 2 2 3 5 +--R (144a b - 240a b + 832a )cosh(x) +--R + +--R 2 2 3 3 2 2 +--R (- 112a b - 96a b - 640a )cosh(x) + (36a b - 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 2 2 8 +--R 54a b cosh(x) + (- 72a b + 184a b)cosh(x) +--R + +--R 2 2 3 6 2 2 3 4 +--R (48a b - 96a b + 512a )cosh(x) + (- 78a b - 64a b - 480a )cosh(x) +--R + +--R 2 2 2 2 +--R (54a b - 48a b)cosh(x) - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 2 9 +--R 12a b cosh(x) + (- 12a b + 64a b)cosh(x) +--R + +--R 2 3 7 2 2 3 5 +--R (- 16a b + 192a )cosh(x) + (- 24a b - 16a b - 192a )cosh(x) +--R + +--R 2 2 3 2 +--R (36a b - 32a b)cosh(x) - 12a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 12 2 10 2 3 8 +--R a b cosh(x) + 8a b cosh(x) + (- 3a b + 32a )cosh(x) +--R + +--R 2 3 6 2 2 4 2 2 2 +--R (- 2a b - 32a )cosh(x) + (9a b - 8a b)cosh(x) - 6a b cosh(x) + a b +--R / +--R 4 3 8 4 3 7 +--R (16b - 16a b )sinh(x) + (128b - 128a b )cosh(x)sinh(x) +--R + +--R 4 3 2 4 3 2 2 6 +--R ((448b - 448a b )cosh(x) - 32b + 96a b - 64a b )sinh(x) +--R + +--R 4 3 3 4 3 2 2 +--R ((896b - 896a b )cosh(x) + (- 192b + 576a b - 384a b )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 +--R (1120b - 1120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 480b + 1440a b - 960a b )cosh(x) + 16b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 +--R (896b - 896a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 640b + 1920a b - 1280a b )cosh(x) + (64b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 +--R (448b - 448a b )cosh(x) +--R + +--R 4 3 2 2 4 4 3 2 +--R (- 480b + 1440a b - 960a b )cosh(x) + (96b - 96a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 4 3 2 2 5 +--R (128b - 128a b )cosh(x) + (- 192b + 576a b - 384a b )cosh(x) +--R + +--R 4 3 3 +--R (64b - 64a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (16b - 16a b )cosh(x) + (- 32b + 96a b - 64a b )cosh(x) +--R + +--R 4 3 4 +--R (16b - 16a b )cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 8 3 7 +--R 16a b sinh(x) + 128a b cosh(x)sinh(x) +--R + +--R 3 2 3 2 2 6 +--R (448a b cosh(x) - 32a b + 64a b )sinh(x) +--R + +--R 3 3 3 2 2 5 +--R (896a b cosh(x) + (- 192a b + 384a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 2 3 4 +--R (1120a b cosh(x) + (- 480a b + 960a b )cosh(x) + 16a b )sinh(x) +--R + +--R 3 5 3 2 2 3 3 +--R (896a b cosh(x) + (- 640a b + 1280a b )cosh(x) + 64a b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 2 2 4 3 2 +--R (448a b cosh(x) + (- 480a b + 960a b )cosh(x) + 96a b cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 2 2 5 3 3 +--R (128a b cosh(x) + (- 192a b + 384a b )cosh(x) + 64a b cosh(x) )sinh(x) +--R + +--R 3 8 3 2 2 6 3 4 +--R 16a b cosh(x) + (- 32a b + 64a b )cosh(x) + 16a b cosh(x) +--R Type: Expression(Integer) +--E 295 + +--S 296 of 552 +m0756b:= a0756.2-r0756 +--R +--R +--R (288) +--R 2 4 2 3 2 2 2 +--R 64a sinh(x) + 256a cosh(x)sinh(x) + 384a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R 256a cosh(x) sinh(x) + 64a cosh(x) +--R * +--R +-----+ +--R +-+ tanh(x)\|b - a +--R \|a atan(---------------) +--R +-+ +--R \|a +--R + +--R 2 4 2 3 2 2 2 +--R 64a sinh(x) + 256a cosh(x)sinh(x) + 384a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R 256a cosh(x) sinh(x) + 64a cosh(x) +--R * +--R +-----+ +--R | a +-----+ +--R |----- \|b - a +--R \|b - a +--R * +--R +-----+ +--R | a +--R (2b - 2a) |----- +--R \|b - a +--R atan(----------------------------------------------------) +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R 2 8 2 7 +--R b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (- 36b cosh(x) - 8b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (- 40b cosh(x) + (- 24b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R (6b cosh(x) + (- 24b + 8a b)cosh(x) )sinh(x) +--R + +--R 2 5 2 3 3 +--R (40b cosh(x) + (- 16b + 32a b)cosh(x) )sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (28b cosh(x) + (- 24b + 8a b)cosh(x) + 8b + 8a b)sinh(x) +--R + +--R 2 7 2 5 2 +--R (8b cosh(x) + (- 24b - 16a b)cosh(x) + (16b + 16a b)cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 2 +--R b cosh(x) + (- 8b - 8a b)cosh(x) + (8b + 8a b)cosh(x) - b +--R * +--R +-----+ +--R \|b - a +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R +-----+ +--R \|b - a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 552 +d0756b:= D(m0756b,x) +--R +--R +--R (289) +--R 3 2 12 3 2 11 +--R (- 3b + 3a b )sinh(x) + (- 20b + 20a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 10 +--R ((- 58b + 58a b )cosh(x) + 8b - 16a b + 8a b)sinh(x) +--R + +--R 3 2 3 3 2 2 +--R ((- 100b + 100a b )cosh(x) + (36b - 68a b + 32a b)cosh(x)) +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R (- 121b + 121a b )cosh(x) + (48b - 104a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 +--R - 7b + 7a b + 16a b - 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (- 104b + 104a b )cosh(x) + (- 32b - 64a b + 96a b)cosh(x) +--R + +--R 3 2 3 +--R (- 16b + 80a b - 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 28b + 28a b )cosh(x) + (- 192b + 16a b + 176a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 3 +--R (24b - 120a b + 160a b - 512a )cosh(x) - 2b + 2a b - 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 7 3 2 2 5 +--R (88b - 88a b )cosh(x) + (- 312b + 152a b + 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (128b - 368a b + 176a b - 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b + 8a b + 16a b - 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 8 3 2 2 6 +--R (155b - 155a b )cosh(x) + (- 304b + 352a b - 48a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (194b - 514a b + 160a b - 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 78b + 14a b + 64a b - 480a )cosh(x) + 9b - 17a b - 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 9 3 2 2 7 +--R (124b - 124a b )cosh(x) + (- 192b + 416a b - 224a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (144b - 384a b + 176a b - 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b + 16a b + 96a b - 640a )cosh(x) +--R + +--R 3 2 2 +--R (36b - 68a b - 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 10 3 2 2 8 +--R (54b - 54a b )cosh(x) + (- 72b + 256a b - 184a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (48b - 144a b + 160a b - 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 78b + 14a b + 64a b - 480a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (54b - 102a b - 48a b)cosh(x) - 6b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 11 3 2 2 9 +--R (12b - 12a b )cosh(x) + (- 12b + 76a b - 64a b)cosh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 80a b - 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b + 8a b + 16a b - 192a )cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (36b - 68a b - 32a b)cosh(x) + (- 12b + 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 12 2 2 10 +--R (b - a b )cosh(x) + (8a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 3b + 3a b + 16a b - 32a )cosh(x) +--R + +--R 3 2 3 6 3 2 2 4 +--R (- 2b + 2a b - 32a )cosh(x) + (9b - 17a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 6b + 6a b )cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 12 2 11 +--R - 3a b sinh(x) - 20a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 10 +--R (- 58a b cosh(x) + 8a b - 8a b)sinh(x) +--R + +--R 2 3 2 2 9 +--R (- 100a b cosh(x) + (36a b - 32a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 3 8 +--R (- 121a b cosh(x) + (48a b - 56a b)cosh(x) - 7a b + 32a )sinh(x) +--R + +--R 2 5 2 2 3 +--R - 104a b cosh(x) + (- 32a b - 96a b)cosh(x) +--R + +--R 2 2 3 +--R (- 16a b - 16a b + 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R - 28a b cosh(x) + (- 192a b - 176a b)cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (24a b - 96a b + 512a )cosh(x) - 2a b - 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R 88a b cosh(x) + (- 312a b - 160a b)cosh(x) +--R + +--R 2 2 3 3 2 2 3 +--R (128a b - 240a b + 832a )cosh(x) + (- 24a b - 16a b - 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R 155a b cosh(x) + (- 304a b + 48a b)cosh(x) +--R + +--R 2 2 3 4 +--R (194a b - 320a b + 960a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (- 78a b - 64a b - 480a )cosh(x) + 9a b - 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 9 2 2 7 +--R 124a b cosh(x) + (- 192a b + 224a b)cosh(x) +--R + +--R 2 2 3 5 +--R (144a b - 240a b + 832a )cosh(x) +--R + +--R 2 2 3 3 2 2 +--R (- 112a b - 96a b - 640a )cosh(x) + (36a b - 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 2 2 8 +--R 54a b cosh(x) + (- 72a b + 184a b)cosh(x) +--R + +--R 2 2 3 6 2 2 3 4 +--R (48a b - 96a b + 512a )cosh(x) + (- 78a b - 64a b - 480a )cosh(x) +--R + +--R 2 2 2 2 +--R (54a b - 48a b)cosh(x) - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 2 9 +--R 12a b cosh(x) + (- 12a b + 64a b)cosh(x) +--R + +--R 2 3 7 2 2 3 5 +--R (- 16a b + 192a )cosh(x) + (- 24a b - 16a b - 192a )cosh(x) +--R + +--R 2 2 3 2 +--R (36a b - 32a b)cosh(x) - 12a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 12 2 10 2 3 8 +--R a b cosh(x) + 8a b cosh(x) + (- 3a b + 32a )cosh(x) +--R + +--R 2 3 6 2 2 4 2 2 2 +--R (- 2a b - 32a )cosh(x) + (9a b - 8a b)cosh(x) - 6a b cosh(x) + a b +--R / +--R 4 3 8 4 3 7 +--R (16b - 16a b )sinh(x) + (128b - 128a b )cosh(x)sinh(x) +--R + +--R 4 3 2 4 3 2 2 6 +--R ((448b - 448a b )cosh(x) - 32b + 96a b - 64a b )sinh(x) +--R + +--R 4 3 3 4 3 2 2 +--R ((896b - 896a b )cosh(x) + (- 192b + 576a b - 384a b )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 +--R (1120b - 1120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 480b + 1440a b - 960a b )cosh(x) + 16b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 +--R (896b - 896a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 640b + 1920a b - 1280a b )cosh(x) + (64b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 +--R (448b - 448a b )cosh(x) +--R + +--R 4 3 2 2 4 4 3 2 +--R (- 480b + 1440a b - 960a b )cosh(x) + (96b - 96a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 4 3 2 2 5 +--R (128b - 128a b )cosh(x) + (- 192b + 576a b - 384a b )cosh(x) +--R + +--R 4 3 3 +--R (64b - 64a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (16b - 16a b )cosh(x) + (- 32b + 96a b - 64a b )cosh(x) +--R + +--R 4 3 4 +--R (16b - 16a b )cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 8 3 7 +--R 16a b sinh(x) + 128a b cosh(x)sinh(x) +--R + +--R 3 2 3 2 2 6 +--R (448a b cosh(x) - 32a b + 64a b )sinh(x) +--R + +--R 3 3 3 2 2 5 +--R (896a b cosh(x) + (- 192a b + 384a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 2 3 4 +--R (1120a b cosh(x) + (- 480a b + 960a b )cosh(x) + 16a b )sinh(x) +--R + +--R 3 5 3 2 2 3 3 +--R (896a b cosh(x) + (- 640a b + 1280a b )cosh(x) + 64a b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 2 2 4 3 2 +--R (448a b cosh(x) + (- 480a b + 960a b )cosh(x) + 96a b cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 2 2 5 3 3 +--R (128a b cosh(x) + (- 192a b + 384a b )cosh(x) + 64a b cosh(x) )sinh(x) +--R + +--R 3 8 3 2 2 6 3 4 +--R 16a b cosh(x) + (- 32a b + 64a b )cosh(x) + 16a b cosh(x) +--R Type: Expression(Integer) +--E 297 + +--S 298 of 552 +t0757:= sinh(x)^7/(a+b*sinh(x)^2) +--R +--R +--R 7 +--R sinh(x) +--R (290) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 552 +r0757:= a^3*atanh((-b)^(1/2)*cosh(x)/(a-b)^(1/2))/(a-b)^(1/2)/(-b)^(7/2)+_ + a^2*cosh(x)/b^3+a*cosh(x)/b^2+cosh(x)/b-1/3*a*cosh(x)^3/b^2-_ + 2/3*cosh(x)^3/b+1/5*cosh(x)^5/b +--R +--R +--R (291) +--R +---+ +--R 3 cosh(x)\|- b +--R - 15a atanh(-------------) +--R +-------+ +--R \|- b + a +--R + +--R 2 5 2 3 2 2 +--R (3b cosh(x) + (- 10b - 5a b)cosh(x) + (15b + 15a b + 15a )cosh(x)) +--R * +--R +---+ +-------+ +--R \|- b \|- b + a +--R / +--R 3 +---+ +-------+ +--R 15b \|- b \|- b + a +--R Type: Expression(Integer) +--E 299 + +--S 300 of 552 +a0757:= integrate(t0757,x) +--R +--R +--R (292) +--R [ +--R 3 5 3 4 3 2 3 +--R 240a sinh(x) + 1200a cosh(x)sinh(x) + 2400a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 2400a cosh(x) sinh(x) + 1200a cosh(x) sinh(x) + 240a cosh(x) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (6b - 4a)cosh(x) + b +--R * +--R +--------+ +--R | 2 +--R \|b - a b +--R + +--R 2 3 2 2 +--R (4b - 4a b)sinh(x) + (12b - 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((12b - 12a b)cosh(x) + 4b - 4a b)sinh(x) +--R + +--R 2 3 2 +--R (4b - 4a b)cosh(x) + (4b - 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) - 25b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (- 200b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (- 700b - 560a b)cosh(x) + 150b + 180a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 756b cosh(x) + (- 1400b - 1120a b)cosh(x) +--R + +--R 2 2 +--R (900b + 1080a b + 1440a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (- 1750b - 1400a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (2250b + 2700a b + 3600a )cosh(x) + 150b + 180a b + 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (- 1400b - 1120a b)cosh(x) +--R + +--R 2 2 3 +--R (3000b + 3600a b + 4800a )cosh(x) +--R + +--R 2 2 +--R (600b + 720a b + 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (- 700b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (2250b + 2700a b + 3600a )cosh(x) +--R + +--R 2 2 2 2 +--R (900b + 1080a b + 1440a )cosh(x) - 25b - 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (- 200b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (900b + 1080a b + 1440a )cosh(x) +--R + +--R 2 2 3 2 +--R (600b + 720a b + 960a )cosh(x) + (- 50b - 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (- 25b - 20a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (150b + 180a b + 240a )cosh(x) + (150b + 180a b + 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 25b - 20a b)cosh(x) + 3b +--R * +--R +--------+ +--R | 2 +--R \|b - a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +--------+ +--R | 2 +--R \|b - a b +--R , +--R +--R 3 5 3 4 3 2 3 +--R 480a sinh(x) + 2400a cosh(x)sinh(x) + 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800a cosh(x) sinh(x) + 2400a cosh(x) sinh(x) + 480a cosh(x) +--R * +--R +----------+ +--R | 2 +--R (sinh(x) + cosh(x))\|- b + a b +--R atan(--------------------------------) +--R 2b - 2a +--R + +--R 3 5 3 4 3 2 3 +--R 480a sinh(x) + 2400a cosh(x)sinh(x) + 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800a cosh(x) sinh(x) + 2400a cosh(x) sinh(x) + 480a cosh(x) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) - 3b + 4a)sinh(x) + b cosh(x) + (- 3b + 4a)cosh(x) +--R / +--R +----------+ +--R | 2 +--R 2\|- b + a b +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) - 25b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (- 200b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (- 700b - 560a b)cosh(x) + 150b + 180a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 756b cosh(x) + (- 1400b - 1120a b)cosh(x) +--R + +--R 2 2 +--R (900b + 1080a b + 1440a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (- 1750b - 1400a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (2250b + 2700a b + 3600a )cosh(x) + 150b + 180a b + 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (- 1400b - 1120a b)cosh(x) +--R + +--R 2 2 3 +--R (3000b + 3600a b + 4800a )cosh(x) +--R + +--R 2 2 +--R (600b + 720a b + 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (- 700b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (2250b + 2700a b + 3600a )cosh(x) +--R + +--R 2 2 2 2 +--R (900b + 1080a b + 1440a )cosh(x) - 25b - 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (- 200b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (900b + 1080a b + 1440a )cosh(x) +--R + +--R 2 2 3 2 +--R (600b + 720a b + 960a )cosh(x) + (- 50b - 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (- 25b - 20a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (150b + 180a b + 240a )cosh(x) + (150b + 180a b + 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 25b - 20a b)cosh(x) + 3b +--R * +--R +----------+ +--R | 2 +--R \|- b + a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +----------+ +--R | 2 +--R \|- b + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 300 + +--S 301 of 552 +m0757a:= a0757.1-r0757 +--R +--R +--R (293) +--R 3 5 3 4 3 2 3 +--R 240a sinh(x) + 1200a cosh(x)sinh(x) + 2400a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 2400a cosh(x) sinh(x) + 1200a cosh(x) sinh(x) + 240a cosh(x) +--R * +--R +---+ +-------+ +--R \|- b \|- b + a +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (6b - 4a)cosh(x) + b +--R * +--R +--------+ +--R | 2 +--R \|b - a b +--R + +--R 2 3 2 2 +--R (4b - 4a b)sinh(x) + (12b - 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((12b - 12a b)cosh(x) + 4b - 4a b)sinh(x) +--R + +--R 2 3 2 +--R (4b - 4a b)cosh(x) + (4b - 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 3 5 3 4 3 2 3 +--R 480a sinh(x) + 2400a cosh(x)sinh(x) + 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800a cosh(x) sinh(x) + 2400a cosh(x) sinh(x) + 480a cosh(x) +--R * +--R +--------+ +---+ +--R | 2 cosh(x)\|- b +--R \|b - a b atanh(-------------) +--R +-------+ +--R \|- b + a +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) - 25b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (- 200b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (- 700b - 560a b)cosh(x) + 150b + 180a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 660b cosh(x) + (- 1080b - 960a b)cosh(x) +--R + +--R 2 2 +--R (420b + 600a b + 960a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 150b cosh(x) + (- 150b - 600a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 150b + 300a b + 1200a )cosh(x) + 150b + 180a b + 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R - 600b cosh(x) + (1800b + 480a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- 1800b - 1200a b)cosh(x) + (600b + 720a b + 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R - 825b cosh(x) + (2500b + 1040a b)cosh(x) +--R + +--R 2 2 4 +--R (- 2550b - 2100a b - 1200a )cosh(x) +--R + +--R 2 2 2 2 +--R (900b + 1080a b + 1440a )cosh(x) - 25b - 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R - 450b cosh(x) + (1400b + 640a b)cosh(x) +--R + +--R 2 2 5 +--R (- 1500b - 1320a b - 960a )cosh(x) +--R + +--R 2 2 3 2 +--R (600b + 720a b + 960a )cosh(x) + (- 50b - 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R - 93b cosh(x) + (295b + 140a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 330b - 300a b - 240a )cosh(x) + (150b + 180a b + 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 25b - 20a b)cosh(x) + 3b +--R * +--R +--------+ +--R +---+ +-------+ | 2 +--R \|- b \|- b + a \|b - a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +--------+ +--R +---+ +-------+ | 2 +--R \|- b \|- b + a \|b - a b +--R Type: Expression(Integer) +--E 301 + +--S 302 of 552 +d0757a:= D(m0757a,x) +--R +--R +--R (294) +--R 2 14 +--R (b cosh(x) - b + a)sinh(x) +--R + +--R 3 13 +--R (14b cosh(x) + (- 14b + 14a)cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (91b cosh(x) + (- 98b + 91a)cosh(x) + 7b - 7a)sinh(x) +--R + +--R 5 3 11 +--R (364b cosh(x) + (- 448b + 364a)cosh(x) + (84b - 84a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 969b cosh(x) + (- 1367b + 1001a)cosh(x) + (387b - 462a)cosh(x) +--R + +--R 11b + 21a +--R * +--R 10 +--R sinh(x) +--R + +--R 7 5 3 +--R 1714b cosh(x) + (- 2678b + 2002a)cosh(x) + (886b - 1540a)cosh(x) +--R + +--R (78b + 210a)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 6 4 +--R 1851b cosh(x) + (- 2948b + 2875a)cosh(x) + (762b - 3081a)cosh(x) +--R + +--R 2 +--R (364b + 561a)cosh(x) - 29b + 93a +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 +--R 744b cosh(x) + (- 464b + 2536a)cosh(x) + (- 1344b - 2856a)cosh(x) +--R + +--R 3 +--R (1232b - 168a)cosh(x) + (- 168b + 616a)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 +--R - 1029b cosh(x) + (3969b + 315a)cosh(x) +--R + +--R 6 4 +--R (- 5282b + 1596a)cosh(x) + (2770b - 3654a)cosh(x) +--R + +--R 2 +--R (- 425b + 1708a)cosh(x) - 3b + 35a +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 +--R - 2030b cosh(x) + (6790b - 2478a)cosh(x) +--R + +--R 7 5 +--R (- 8140b + 7896a)cosh(x) + (3980b - 8148a)cosh(x) +--R + +--R 3 +--R (- 550b + 2520a)cosh(x) + (- 50b + 210a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 +--R - 1687b cosh(x) + (5838b - 3479a)cosh(x) +--R + +--R 8 6 +--R (- 7229b + 9975a)cosh(x) + (3508b - 9030a)cosh(x) +--R + +--R 4 2 +--R (- 225b + 2030a)cosh(x) + (- 226b + 525a)cosh(x) + 21b - 21a +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 +--R - 788b cosh(x) + (2896b - 2324a)cosh(x) +--R + +--R 9 7 +--R (- 3748b + 6524a)cosh(x) + (1664b - 5544a)cosh(x) +--R + +--R 5 3 +--R (356b + 728a)cosh(x) + (- 464b + 700a)cosh(x) + (84b - 84a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 +--R - 197b cosh(x) + (759b - 805a)cosh(x) + (- 961b + 2226a)cosh(x) +--R + +--R 8 6 +--R (187b - 1743a)cosh(x) + (577b - 84a)cosh(x) +--R + +--R 4 2 +--R (- 491b + 525a)cosh(x) + (133b - 126a)cosh(x) - 7b + 7a +--R * +--R 2 +--R sinh(x) +--R + +--R 15 13 11 +--R - 18b cosh(x) + (62b - 114a)cosh(x) + (- 26b + 300a)cosh(x) +--R + +--R 9 7 +--R (- 170b - 174a)cosh(x) + (330b - 152a)cosh(x) +--R + +--R 5 3 +--R (- 262b + 210a)cosh(x) + (98b - 84a)cosh(x) + (- 14b + 14a)cosh(x) +--R * +--R sinh(x) +--R + +--R 16 14 12 +--R b cosh(x) + (- 8b + a)cosh(x) + (28b - 7a)cosh(x) +--R + +--R 10 8 6 +--R (- 56b + 21a)cosh(x) + (70b - 35a)cosh(x) + (- 56b + 35a)cosh(x) +--R + +--R 4 2 +--R (28b - 21a)cosh(x) + (- 8b + 7a)cosh(x) + b - a +--R / +--R 2 2 2 9 +--R (32b cosh(x) - 32b + 32a b)sinh(x) +--R + +--R 2 3 2 8 +--R (288b cosh(x) + (- 288b + 288a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (1152b cosh(x) + (- 1216b + 1280a b)cosh(x) + 64b - 192a b + 128a ) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 2688b cosh(x) + (- 3136b + 3584a b)cosh(x) +--R + +--R 2 2 +--R (448b - 1344a b + 896a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 4032b cosh(x) + (- 5376b + 6720a b)cosh(x) +--R + +--R 2 2 2 2 +--R (1376b - 4032a b + 2688a )cosh(x) - 32b + 32a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 4032b cosh(x) + (- 6272b + 8512a b)cosh(x) +--R + +--R 2 2 3 2 +--R (2400b - 6720a b + 4480a )cosh(x) + (- 160b + 160a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 2688b cosh(x) + (- 4928b + 7168a b)cosh(x) +--R + +--R 2 2 4 2 2 +--R (2560b - 6720a b + 4480a )cosh(x) + (- 320b + 320a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 1152b cosh(x) + (- 2496b + 3840a b)cosh(x) +--R + +--R 2 2 5 2 3 +--R (1664b - 4032a b + 2688a )cosh(x) + (- 320b + 320a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 10 2 8 +--R 288b cosh(x) + (- 736b + 1184a b)cosh(x) +--R + +--R 2 2 6 2 4 +--R (608b - 1344a b + 896a )cosh(x) + (- 160b + 160a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 11 2 9 +--R 32b cosh(x) + (- 96b + 160a b)cosh(x) +--R + +--R 2 2 7 2 5 +--R (96b - 192a b + 128a )cosh(x) + (- 32b + 32a b)cosh(x) +--R Type: Expression(Integer) +--E 302 + +--S 303 of 552 +m0757b:= a0757.2-r0757 +--R +--R +--R (295) +--R 3 5 3 4 3 2 3 +--R 480a sinh(x) + 2400a cosh(x)sinh(x) + 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800a cosh(x) sinh(x) + 2400a cosh(x) sinh(x) + 480a cosh(x) +--R * +--R +----------+ +---+ +--R | 2 cosh(x)\|- b +--R \|- b + a b atanh(-------------) +--R +-------+ +--R \|- b + a +--R + +--R 3 5 3 4 3 2 3 +--R 480a sinh(x) + 2400a cosh(x)sinh(x) + 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800a cosh(x) sinh(x) + 2400a cosh(x) sinh(x) + 480a cosh(x) +--R * +--R +----------+ +--R | 2 +--R +---+ +-------+ (sinh(x) + cosh(x))\|- b + a b +--R \|- b \|- b + a atan(--------------------------------) +--R 2b - 2a +--R + +--R 3 5 3 4 3 2 3 +--R 480a sinh(x) + 2400a cosh(x)sinh(x) + 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800a cosh(x) sinh(x) + 2400a cosh(x) sinh(x) + 480a cosh(x) +--R * +--R +---+ +-------+ +--R \|- b \|- b + a +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) - 3b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (- 3b + 4a)cosh(x) +--R / +--R +----------+ +--R | 2 +--R 2\|- b + a b +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) - 25b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (- 200b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (- 700b - 560a b)cosh(x) + 150b + 180a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 660b cosh(x) + (- 1080b - 960a b)cosh(x) +--R + +--R 2 2 +--R (420b + 600a b + 960a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 150b cosh(x) + (- 150b - 600a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 150b + 300a b + 1200a )cosh(x) + 150b + 180a b + 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R - 600b cosh(x) + (1800b + 480a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- 1800b - 1200a b)cosh(x) + (600b + 720a b + 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R - 825b cosh(x) + (2500b + 1040a b)cosh(x) +--R + +--R 2 2 4 +--R (- 2550b - 2100a b - 1200a )cosh(x) +--R + +--R 2 2 2 2 +--R (900b + 1080a b + 1440a )cosh(x) - 25b - 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R - 450b cosh(x) + (1400b + 640a b)cosh(x) +--R + +--R 2 2 5 +--R (- 1500b - 1320a b - 960a )cosh(x) +--R + +--R 2 2 3 2 +--R (600b + 720a b + 960a )cosh(x) + (- 50b - 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R - 93b cosh(x) + (295b + 140a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 330b - 300a b - 240a )cosh(x) + (150b + 180a b + 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 25b - 20a b)cosh(x) + 3b +--R * +--R +----------+ +--R | 2 +---+ +-------+ +--R \|- b + a b \|- b \|- b + a +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +----------+ +--R | 2 +---+ +-------+ +--R \|- b + a b \|- b \|- b + a +--R Type: Expression(Integer) +--E 303 + +--S 304 of 552 +d0757b:= D(m0757b,x) +--R +--R +--R (296) +--R 2 14 +--R (b cosh(x) - b + a)sinh(x) +--R + +--R 3 13 +--R (14b cosh(x) + (- 14b + 14a)cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (91b cosh(x) + (- 98b + 91a)cosh(x) + 7b - 7a)sinh(x) +--R + +--R 5 3 11 +--R (364b cosh(x) + (- 448b + 364a)cosh(x) + (84b - 84a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 969b cosh(x) + (- 1367b + 1001a)cosh(x) + (387b - 462a)cosh(x) +--R + +--R 11b + 21a +--R * +--R 10 +--R sinh(x) +--R + +--R 7 5 3 +--R 1714b cosh(x) + (- 2678b + 2002a)cosh(x) + (886b - 1540a)cosh(x) +--R + +--R (78b + 210a)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 6 4 +--R 1851b cosh(x) + (- 2948b + 2875a)cosh(x) + (762b - 3081a)cosh(x) +--R + +--R 2 +--R (364b + 561a)cosh(x) - 29b + 93a +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 +--R 744b cosh(x) + (- 464b + 2536a)cosh(x) + (- 1344b - 2856a)cosh(x) +--R + +--R 3 +--R (1232b - 168a)cosh(x) + (- 168b + 616a)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 +--R - 1029b cosh(x) + (3969b + 315a)cosh(x) +--R + +--R 6 4 +--R (- 5282b + 1596a)cosh(x) + (2770b - 3654a)cosh(x) +--R + +--R 2 +--R (- 425b + 1708a)cosh(x) - 3b + 35a +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 +--R - 2030b cosh(x) + (6790b - 2478a)cosh(x) +--R + +--R 7 5 +--R (- 8140b + 7896a)cosh(x) + (3980b - 8148a)cosh(x) +--R + +--R 3 +--R (- 550b + 2520a)cosh(x) + (- 50b + 210a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 +--R - 1687b cosh(x) + (5838b - 3479a)cosh(x) +--R + +--R 8 6 +--R (- 7229b + 9975a)cosh(x) + (3508b - 9030a)cosh(x) +--R + +--R 4 2 +--R (- 225b + 2030a)cosh(x) + (- 226b + 525a)cosh(x) + 21b - 21a +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 +--R - 788b cosh(x) + (2896b - 2324a)cosh(x) +--R + +--R 9 7 +--R (- 3748b + 6524a)cosh(x) + (1664b - 5544a)cosh(x) +--R + +--R 5 3 +--R (356b + 728a)cosh(x) + (- 464b + 700a)cosh(x) + (84b - 84a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 +--R - 197b cosh(x) + (759b - 805a)cosh(x) + (- 961b + 2226a)cosh(x) +--R + +--R 8 6 +--R (187b - 1743a)cosh(x) + (577b - 84a)cosh(x) +--R + +--R 4 2 +--R (- 491b + 525a)cosh(x) + (133b - 126a)cosh(x) - 7b + 7a +--R * +--R 2 +--R sinh(x) +--R + +--R 15 13 11 +--R - 18b cosh(x) + (62b - 114a)cosh(x) + (- 26b + 300a)cosh(x) +--R + +--R 9 7 +--R (- 170b - 174a)cosh(x) + (330b - 152a)cosh(x) +--R + +--R 5 3 +--R (- 262b + 210a)cosh(x) + (98b - 84a)cosh(x) + (- 14b + 14a)cosh(x) +--R * +--R sinh(x) +--R + +--R 16 14 12 +--R b cosh(x) + (- 8b + a)cosh(x) + (28b - 7a)cosh(x) +--R + +--R 10 8 6 +--R (- 56b + 21a)cosh(x) + (70b - 35a)cosh(x) + (- 56b + 35a)cosh(x) +--R + +--R 4 2 +--R (28b - 21a)cosh(x) + (- 8b + 7a)cosh(x) + b - a +--R / +--R 2 2 2 9 +--R (32b cosh(x) - 32b + 32a b)sinh(x) +--R + +--R 2 3 2 8 +--R (288b cosh(x) + (- 288b + 288a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (1152b cosh(x) + (- 1216b + 1280a b)cosh(x) + 64b - 192a b + 128a ) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 2688b cosh(x) + (- 3136b + 3584a b)cosh(x) +--R + +--R 2 2 +--R (448b - 1344a b + 896a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 4032b cosh(x) + (- 5376b + 6720a b)cosh(x) +--R + +--R 2 2 2 2 +--R (1376b - 4032a b + 2688a )cosh(x) - 32b + 32a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 4032b cosh(x) + (- 6272b + 8512a b)cosh(x) +--R + +--R 2 2 3 2 +--R (2400b - 6720a b + 4480a )cosh(x) + (- 160b + 160a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 2688b cosh(x) + (- 4928b + 7168a b)cosh(x) +--R + +--R 2 2 4 2 2 +--R (2560b - 6720a b + 4480a )cosh(x) + (- 320b + 320a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 1152b cosh(x) + (- 2496b + 3840a b)cosh(x) +--R + +--R 2 2 5 2 3 +--R (1664b - 4032a b + 2688a )cosh(x) + (- 320b + 320a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 10 2 8 +--R 288b cosh(x) + (- 736b + 1184a b)cosh(x) +--R + +--R 2 2 6 2 4 +--R (608b - 1344a b + 896a )cosh(x) + (- 160b + 160a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 11 2 9 +--R 32b cosh(x) + (- 96b + 160a b)cosh(x) +--R + +--R 2 2 7 2 5 +--R (96b - 192a b + 128a )cosh(x) + (- 32b + 32a b)cosh(x) +--R Type: Expression(Integer) +--E 304 + +--S 305 of 552 +t0758:= cosh(x)^2/(a+b*sinh(x)^2) +--R +--R +--R 2 +--R cosh(x) +--R (297) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 552 +r0758:= x/b+(-a+b)^(1/2)*atan((-a+b)^(1/2)*tanh(x)/a^(1/2))/a^(1/2)/b +--R +--R +--R +-----+ +--R +-----+ tanh(x)\|b - a +-+ +--R \|b - a atan(---------------) + x\|a +--R +-+ +--R \|a +--R (298) ------------------------------------- +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 552 +a0758:= integrate(t0758,x) +--R +--R +--R (299) +--R [ +--R +-------+ +--R |- b + a +--R |------- +--R \| a +--R * +--R log +--R 2 2 +--R 4a b sinh(x) + 8a b cosh(x)sinh(x) + 4a b cosh(x) - 4a b +--R + +--R 2 +--R 8a +--R * +--R +-------+ +--R |- b + a +--R |------- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2x +--R / +--R 2b +--R , +--R +-----+ +--R |b - a +--R +-----+ 2a |----- +--R |b - a \| a +--R - |----- atan(----------------------------------------------------) + x +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R ------------------------------------------------------------------------] +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 307 + +--S 308 of 552 +m0758a:= a0758.1-r0758 +--R +--R +--R (300) +--R +-------+ +--R |- b + a +-+ +--R |------- \|a +--R \| a +--R * +--R log +--R 2 2 +--R 4a b sinh(x) + 8a b cosh(x)sinh(x) + 4a b cosh(x) - 4a b +--R + +--R 2 +--R 8a +--R * +--R +-------+ +--R |- b + a +--R |------- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R +-----+ +--R +-----+ tanh(x)\|b - a +--R - 2\|b - a atan(---------------) +--R +-+ +--R \|a +--R / +--R +-+ +--R 2b\|a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 552 +d0758a:= D(m0758a,x) +--R +--R +--R (301) +--R 4 3 +--R (b - a)sinh(x) + (4b - 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((6b - 6a)cosh(x) + 2b - 2a)sinh(x) +--R + +--R 3 4 +--R ((4b - 4a)cosh(x) + (4b - 4a)cosh(x))sinh(x) + (b - a)cosh(x) +--R + +--R 2 +--R (2b - 2a)cosh(x) + b - a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R (- b + a)sinh(x) + (- 4b + 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((- 6b + 6a)cosh(x) + 2b - 2a)sinh(x) +--R + +--R 3 4 +--R ((- 4b + 4a)cosh(x) + (4b - 4a)cosh(x))sinh(x) + (- b + a)cosh(x) +--R + +--R 2 +--R (2b - 2a)cosh(x) - b + a +--R / +--R 2 4 2 3 +--R (b - a b)sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a b)cosh(x) - 2b + 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b - 4a b)cosh(x) + (- 4b + 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b - a b)cosh(x) + (- 2b + 6a b - 4a )cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) - 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (- 4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (- 2a b + 4a )cosh(x) + a b +--R Type: Expression(Integer) +--E 309 + +--S 310 of 552 +m0758b:= a0758.2-r0758 +--R +--R +--R (302) +--R +-----+ +--R +-----+ tanh(x)\|b - a +--R - \|b - a atan(---------------) +--R +-+ +--R \|a +--R + +--R +-----+ +--R |b - a +--R +-----+ 2a |----- +--R +-+ |b - a \| a +--R - \|a |----- atan(----------------------------------------------------) +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R / +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 552 +d0758b:= D(m0758b,x) +--R +--R +--R (303) +--R 4 3 +--R (b - a)sinh(x) + (4b - 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((6b - 6a)cosh(x) + 2b - 2a)sinh(x) +--R + +--R 3 4 +--R ((4b - 4a)cosh(x) + (4b - 4a)cosh(x))sinh(x) + (b - a)cosh(x) +--R + +--R 2 +--R (2b - 2a)cosh(x) + b - a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R (- b + a)sinh(x) + (- 4b + 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((- 6b + 6a)cosh(x) + 2b - 2a)sinh(x) +--R + +--R 3 4 +--R ((- 4b + 4a)cosh(x) + (4b - 4a)cosh(x))sinh(x) + (- b + a)cosh(x) +--R + +--R 2 +--R (2b - 2a)cosh(x) - b + a +--R / +--R 2 4 2 3 +--R (b - a b)sinh(x) + (4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((6b - 6a b)cosh(x) - 2b + 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b - 4a b)cosh(x) + (- 4b + 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b - a b)cosh(x) + (- 2b + 6a b - 4a )cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) - 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (- 4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (- 2a b + 4a )cosh(x) + a b +--R Type: Expression(Integer) +--E 311 + +--S 312 of 552 +t0759:= cosh(x)^3/(a+b*sinh(x)^2) +--R +--R +--R 3 +--R cosh(x) +--R (304) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 312 + +--S 313 of 552 +r0759:= -(a-b)*atan(b^(1/2)*sinh(x)/a^(1/2))/a^(1/2)/b^(3/2)+sinh(x)/b +--R +--R +--R +-+ +--R sinh(x)\|b +-+ +-+ +--R (b - a)atan(-----------) + sinh(x)\|a \|b +--R +-+ +--R \|a +--R (305) ------------------------------------------ +--R +-+ +-+ +--R b\|a \|b +--R Type: Expression(Integer) +--E 313 + +--S 314 of 552 +a0759:= integrate(t0759,x) +--R +--R +--R (306) +--R [ +--R ((b - a)sinh(x) + (b - a)cosh(x)) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R 4a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (12a b cosh(x) - 4a b)sinh(x) + 4a b cosh(x) - 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 2 +-----+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- a b +--R / +--R +-----+ +--R (2b sinh(x) + 2b cosh(x))\|- a b +--R , +--R +--R +---+ +--R (sinh(x) + cosh(x))\|a b +--R ((2b - 2a)sinh(x) + (2b - 2a)cosh(x))atan(-------------------------) +--R 2a +--R + +--R ((2b - 2a)sinh(x) + (2b - 2a)cosh(x)) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) - b + 4a)sinh(x) + b cosh(x) + (- b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|a b +--R / +--R +---+ +--R (2b sinh(x) + 2b cosh(x))\|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 314 + +--S 315 of 552 +m0759a:= a0759.1-r0759 +--R +--R +--R (307) +--R +-+ +-+ +--R ((b - a)sinh(x) + (b - a)cosh(x))\|a \|b +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R 4a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (12a b cosh(x) - 4a b)sinh(x) + 4a b cosh(x) - 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R +-+ +--R +-----+ sinh(x)\|b +--R ((- 2b + 2a)sinh(x) + (- 2b + 2a)cosh(x))\|- a b atan(-----------) +--R +-+ +--R \|a +--R + +--R 2 2 +-----+ +-+ +-+ +--R (- sinh(x) + cosh(x) - 1)\|- a b \|a \|b +--R / +--R +-----+ +-+ +-+ +--R (2b sinh(x) + 2b cosh(x))\|- a b \|a \|b +--R Type: Expression(Integer) +--E 315 + +--S 316 of 552 +d0759a:= D(m0759a,x) +--R +--R +--R (308) +--R 8 7 2 6 +--R b sinh(x) + 4b cosh(x)sinh(x) + (5b cosh(x) + 3b + a)sinh(x) +--R + +--R 5 +--R (14b - 2a)cosh(x)sinh(x) +--R + +--R 4 2 4 +--R (- 5b cosh(x) + (20b - 9a)cosh(x) + 3b + 3a)sinh(x) +--R + +--R 5 3 3 +--R (- 4b cosh(x) + (4b - 4a)cosh(x) + (8b + 4a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- b cosh(x) + (- 13b + 7a)cosh(x) + (13b - 6a)cosh(x) + b + 3a) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 +--R ((- 10b + 6a)cosh(x) + (12b - 12a)cosh(x) + (- 2b + 6a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 2b + a)cosh(x) + (4b - 5a)cosh(x) + (- 2b + 3a)cosh(x) + a +--R / +--R 2 7 2 6 2 2 2 5 +--R 2b sinh(x) + 10b cosh(x)sinh(x) + (20b cosh(x) - 4b + 10a b)sinh(x) +--R + +--R 2 3 2 4 +--R (20b cosh(x) + (- 12b + 34a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 3 +--R (10b cosh(x) + (- 12b + 44a b)cosh(x) + 2b - 4a b + 8a )sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (2b cosh(x) + (- 4b + 28a b)cosh(x) + (2b - 12a b + 24a )cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 5 +--R (10a b cosh(x) + (- 12a b + 24a )cosh(x) + 2a b)sinh(x) + 2a b cosh(x) +--R + +--R 2 3 +--R (- 4a b + 8a )cosh(x) + 2a b cosh(x) +--R Type: Expression(Integer) +--E 316 + +--S 317 of 552 +m0759b:= a0759.2-r0759 +--R +--R +--R (309) +--R +-+ +-+ +--R ((2b - 2a)sinh(x) + (2b - 2a)cosh(x))\|a \|b +--R * +--R +---+ +--R (sinh(x) + cosh(x))\|a b +--R atan(-------------------------) +--R 2a +--R + +--R +-+ +--R +---+ sinh(x)\|b +--R ((- 2b + 2a)sinh(x) + (- 2b + 2a)cosh(x))\|a b atan(-----------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R ((2b - 2a)sinh(x) + (2b - 2a)cosh(x))\|a \|b +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) - b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (- b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 2 2 +-+ +-+ +---+ +--R (- sinh(x) + cosh(x) - 1)\|a \|b \|a b +--R / +--R +-+ +-+ +---+ +--R (2b sinh(x) + 2b cosh(x))\|a \|b \|a b +--R Type: Expression(Integer) +--E 317 + +--S 318 of 552 +d0759b:= D(m0759b,x) +--R +--R +--R (310) +--R 8 7 2 6 +--R b sinh(x) + 4b cosh(x)sinh(x) + (5b cosh(x) + 3b + a)sinh(x) +--R + +--R 5 +--R (14b - 2a)cosh(x)sinh(x) +--R + +--R 4 2 4 +--R (- 5b cosh(x) + (20b - 9a)cosh(x) + 3b + 3a)sinh(x) +--R + +--R 5 3 3 +--R (- 4b cosh(x) + (4b - 4a)cosh(x) + (8b + 4a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- b cosh(x) + (- 13b + 7a)cosh(x) + (13b - 6a)cosh(x) + b + 3a) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 +--R ((- 10b + 6a)cosh(x) + (12b - 12a)cosh(x) + (- 2b + 6a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 2b + a)cosh(x) + (4b - 5a)cosh(x) + (- 2b + 3a)cosh(x) + a +--R / +--R 2 7 2 6 2 2 2 5 +--R 2b sinh(x) + 10b cosh(x)sinh(x) + (20b cosh(x) - 4b + 10a b)sinh(x) +--R + +--R 2 3 2 4 +--R (20b cosh(x) + (- 12b + 34a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 3 +--R (10b cosh(x) + (- 12b + 44a b)cosh(x) + 2b - 4a b + 8a )sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (2b cosh(x) + (- 4b + 28a b)cosh(x) + (2b - 12a b + 24a )cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 2 5 +--R (10a b cosh(x) + (- 12a b + 24a )cosh(x) + 2a b)sinh(x) + 2a b cosh(x) +--R + +--R 2 3 +--R (- 4a b + 8a )cosh(x) + 2a b cosh(x) +--R Type: Expression(Integer) +--E 318 + +--S 319 of 552 +t0760:= cosh(x)^4/(a+b*sinh(x)^2) +--R +--R +--R 4 +--R cosh(x) +--R (311) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 552 +r0760:= -a*x/b^2+3/2*x/b+(-a+b)^(3/2)*atan((-a+b)^(1/2)*_ + tanh(x)/a^(1/2))/a^(1/2)/b^2+1/2*cosh(x)*sinh(x)/b +--R +--R +--R (312) +--R +-----+ +--R +-----+ tanh(x)\|b - a +-+ +--R (2b - 2a)\|b - a atan(---------------) + (b cosh(x)sinh(x) + (3b - 2a)x)\|a +--R +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R 2 +-+ +--R 2b \|a +--R Type: Expression(Integer) +--E 320 + +--S 321 of 552 +a0760:= integrate(t0760,x) +--R +--R +--R (313) +--R [ +--R 2 2 +--R ((4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) ) +--R * +--R +-------+ +--R |- b + a +--R |------- +--R \| a +--R * +--R log +--R 2 2 +--R 4a b sinh(x) + 8a b cosh(x)sinh(x) + 4a b cosh(x) - 4a b +--R + +--R 2 +--R 8a +--R * +--R +-------+ +--R |- b + a +--R |------- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + (12b - 8a)x)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (24b - 16a)x cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (12b - 8a)x cosh(x) - b +--R / +--R 2 2 2 2 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R , +--R +--R 2 +--R (- 8b + 8a)sinh(x) + (- 16b + 16a)cosh(x)sinh(x) +--R + +--R 2 +--R (- 8b + 8a)cosh(x) +--R * +--R +-----+ +--R |b - a +--R +-----+ 2a |----- +--R |b - a \| a +--R |----- atan(----------------------------------------------------) +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + (12b - 8a)x)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (24b - 16a)x cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (12b - 8a)x cosh(x) - b +--R / +--R 2 2 2 2 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 321 + +--S 322 of 552 +m0760a:= a0760.1-r0760 +--R +--R +--R (314) +--R 2 2 +--R ((4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) ) +--R * +--R +-------+ +--R |- b + a +-+ +--R |------- \|a +--R \| a +--R * +--R log +--R 2 2 +--R 4a b sinh(x) + 8a b cosh(x)sinh(x) + 4a b cosh(x) - 4a b +--R + +--R 2 +--R 8a +--R * +--R +-------+ +--R |- b + a +--R |------- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 +--R (- 8b + 8a)sinh(x) + (- 16b + 16a)cosh(x)sinh(x) +--R + +--R 2 +--R (- 8b + 8a)cosh(x) +--R * +--R +-----+ +--R +-----+ tanh(x)\|b - a +--R \|b - a atan(---------------) +--R +-+ +--R \|a +--R + +--R 4 2 2 4 +-+ +--R (b sinh(x) - 2b cosh(x) sinh(x) + b cosh(x) - b)\|a +--R / +--R 2 2 2 2 2 +-+ +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 552 +d0760a:= D(m0760a,x) +--R +--R +--R (315) +--R 2 8 2 7 +--R (- b + a b)sinh(x) + (- 4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((- 4b + 4a b)cosh(x) + 6b - 14a b + 8a )sinh(x) +--R + +--R 2 3 2 2 5 +--R ((4b - 4a b)cosh(x) + (28b - 60a b + 32a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (10b - 10a b)cosh(x) + (58b - 114a b + 56a )cosh(x) + 8b +--R + +--R 2 +--R - 16a b + 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (4b - 4a b)cosh(x) + (72b - 136a b + 64a )cosh(x) +--R + +--R 2 2 +--R (36b - 68a b + 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (- 4b + 4a b)cosh(x) + (58b - 114a b + 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (56b - 104a b + 48a )cosh(x) + 2b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R (- 4b + 4a b)cosh(x) + (28b - 60a b + 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (36b - 68a b + 32a )cosh(x) + (4b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R (- b + a b)cosh(x) + (6b - 14a b + 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (8b - 16a b + 8a )cosh(x) + (2b - 2a b)cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (- 4a b cosh(x) - 4b + 10a b - 8a )sinh(x) +--R + +--R 3 2 2 5 +--R (4a b cosh(x) + (- 24b + 52a b - 32a )cosh(x))sinh(x) +--R + +--R 4 2 2 2 2 2 +--R (10a b cosh(x) + (- 60b + 118a b - 56a )cosh(x) + 8b - 16a b + 8a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 2 3 +--R 4a b cosh(x) + (- 80b + 152a b - 64a )cosh(x) +--R + +--R 2 2 +--R (32b - 60a b + 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 2 4 +--R - 4a b cosh(x) + (- 60b + 118a b - 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (48b - 88a b + 48a )cosh(x) - 4b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 2 5 +--R - 4a b cosh(x) + (- 24b + 52a b - 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (32b - 60a b + 32a )cosh(x) + (- 8b + 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 2 2 6 +--R - a b cosh(x) + (- 4b + 10a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 +--R (8b - 16a b + 8a )cosh(x) + (- 4b + 6a b)cosh(x) + a b +--R / +--R 3 2 6 3 2 5 +--R (4b - 4a b )sinh(x) + (24b - 24a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 4 +--R ((60b - 60a b )cosh(x) - 8b + 24a b - 16a b)sinh(x) +--R + +--R 3 2 3 3 2 2 3 +--R ((80b - 80a b )cosh(x) + (- 32b + 96a b - 64a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R (60b - 60a b )cosh(x) + (- 48b + 144a b - 96a b)cosh(x) +--R + +--R 3 2 +--R 4b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (24b - 24a b )cosh(x) + (- 32b + 96a b - 64a b)cosh(x) +--R + +--R 3 2 +--R (8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (4b - 4a b )cosh(x) + (- 8b + 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (4b - 4a b )cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 5 +--R 4a b sinh(x) + 24a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (60a b cosh(x) - 8a b + 16a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (80a b cosh(x) + (- 32a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 2 +--R (60a b cosh(x) + (- 48a b + 96a b)cosh(x) + 4a b )sinh(x) +--R + +--R 2 5 2 2 3 2 +--R (24a b cosh(x) + (- 32a b + 64a b)cosh(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 2 2 +--R 4a b cosh(x) + (- 8a b + 16a b)cosh(x) + 4a b cosh(x) +--R Type: Expression(Integer) +--E 323 + +--S 324 of 552 +m0760b:= a0760.2-r0760 +--R +--R +--R (316) +--R 2 +--R (- 8b + 8a)sinh(x) + (- 16b + 16a)cosh(x)sinh(x) +--R + +--R 2 +--R (- 8b + 8a)cosh(x) +--R * +--R +-----+ +--R +-----+ tanh(x)\|b - a +--R \|b - a atan(---------------) +--R +-+ +--R \|a +--R + +--R 2 +--R (- 8b + 8a)sinh(x) + (- 16b + 16a)cosh(x)sinh(x) +--R + +--R 2 +--R (- 8b + 8a)cosh(x) +--R * +--R +-----+ +--R |b - a +--R +-----+ 2a |----- +--R +-+ |b - a \| a +--R \|a |----- atan(----------------------------------------------------) +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R 4 2 2 4 +-+ +--R (b sinh(x) - 2b cosh(x) sinh(x) + b cosh(x) - b)\|a +--R / +--R 2 2 2 2 2 +-+ +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|a +--R Type: Expression(Integer) +--E 324 + +--S 325 of 552 +d0760b:= D(m0760b,x) +--R +--R +--R (317) +--R 2 8 2 7 +--R (- b + a b)sinh(x) + (- 4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((- 4b + 4a b)cosh(x) + 6b - 14a b + 8a )sinh(x) +--R + +--R 2 3 2 2 5 +--R ((4b - 4a b)cosh(x) + (28b - 60a b + 32a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (10b - 10a b)cosh(x) + (58b - 114a b + 56a )cosh(x) + 8b +--R + +--R 2 +--R - 16a b + 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (4b - 4a b)cosh(x) + (72b - 136a b + 64a )cosh(x) +--R + +--R 2 2 +--R (36b - 68a b + 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (- 4b + 4a b)cosh(x) + (58b - 114a b + 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (56b - 104a b + 48a )cosh(x) + 2b - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R (- 4b + 4a b)cosh(x) + (28b - 60a b + 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (36b - 68a b + 32a )cosh(x) + (4b - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R (- b + a b)cosh(x) + (6b - 14a b + 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (8b - 16a b + 8a )cosh(x) + (2b - 2a b)cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (- 4a b cosh(x) - 4b + 10a b - 8a )sinh(x) +--R + +--R 3 2 2 5 +--R (4a b cosh(x) + (- 24b + 52a b - 32a )cosh(x))sinh(x) +--R + +--R 4 2 2 2 2 2 +--R (10a b cosh(x) + (- 60b + 118a b - 56a )cosh(x) + 8b - 16a b + 8a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 2 3 +--R 4a b cosh(x) + (- 80b + 152a b - 64a )cosh(x) +--R + +--R 2 2 +--R (32b - 60a b + 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 2 4 +--R - 4a b cosh(x) + (- 60b + 118a b - 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (48b - 88a b + 48a )cosh(x) - 4b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 2 5 +--R - 4a b cosh(x) + (- 24b + 52a b - 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (32b - 60a b + 32a )cosh(x) + (- 8b + 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 2 2 6 +--R - a b cosh(x) + (- 4b + 10a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 +--R (8b - 16a b + 8a )cosh(x) + (- 4b + 6a b)cosh(x) + a b +--R / +--R 3 2 6 3 2 5 +--R (4b - 4a b )sinh(x) + (24b - 24a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 4 +--R ((60b - 60a b )cosh(x) - 8b + 24a b - 16a b)sinh(x) +--R + +--R 3 2 3 3 2 2 3 +--R ((80b - 80a b )cosh(x) + (- 32b + 96a b - 64a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R (60b - 60a b )cosh(x) + (- 48b + 144a b - 96a b)cosh(x) +--R + +--R 3 2 +--R 4b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (24b - 24a b )cosh(x) + (- 32b + 96a b - 64a b)cosh(x) +--R + +--R 3 2 +--R (8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (4b - 4a b )cosh(x) + (- 8b + 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (4b - 4a b )cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 6 2 5 +--R 4a b sinh(x) + 24a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (60a b cosh(x) - 8a b + 16a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (80a b cosh(x) + (- 32a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 2 +--R (60a b cosh(x) + (- 48a b + 96a b)cosh(x) + 4a b )sinh(x) +--R + +--R 2 5 2 2 3 2 +--R (24a b cosh(x) + (- 32a b + 64a b)cosh(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 2 2 +--R 4a b cosh(x) + (- 8a b + 16a b)cosh(x) + 4a b cosh(x) +--R Type: Expression(Integer) +--E 325 + +--S 326 of 552 +t0761:= cosh(x)^5/(a+b*sinh(x)^2) +--R +--R +--R 5 +--R cosh(x) +--R (318) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 552 +r0761:= (a-b)^2*atan(b^(1/2)*sinh(x)/a^(1/2))/a^(1/2)/b^(5/2)-_ + a*sinh(x)/b^2+2*sinh(x)/b+1/3*sinh(x)^3/b +--R +--R +--R (319) +--R +-+ +--R 2 2 sinh(x)\|b 3 +-+ +-+ +--R (3b - 6a b + 3a )atan(-----------) + (b sinh(x) + (6b - 3a)sinh(x))\|a \|b +--R +-+ +--R \|a +--R ----------------------------------------------------------------------------- +--R 2 +-+ +-+ +--R 3b \|a \|b +--R Type: Expression(Integer) +--E 327 + +--S 328 of 552 +a0761:= integrate(t0761,x) +--R +--R +--R (320) +--R [ +--R 2 2 3 +--R (12b - 24a b + 12a )sinh(x) +--R + +--R 2 2 2 +--R (36b - 72a b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (36b - 72a b + 36a )cosh(x) sinh(x) + (12b - 24a b + 12a )cosh(x) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R 4a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (12a b cosh(x) - 4a b)sinh(x) + 4a b cosh(x) - 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 6 5 +--R b sinh(x) + 6b cosh(x)sinh(x) +--R + +--R 2 4 +--R (15b cosh(x) + 21b - 12a)sinh(x) +--R + +--R 3 3 +--R (20b cosh(x) + (84b - 48a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) + (126b - 72a)cosh(x) - 21b + 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (84b - 48a)cosh(x) + (- 42b + 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (21b - 12a)cosh(x) + (- 21b + 12a)cosh(x) - b +--R * +--R +-----+ +--R \|- a b +--R / +--R 2 3 2 2 2 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 2 3 +--R 24b cosh(x) +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 2 2 3 +--R (24b - 48a b + 24a )sinh(x) +--R + +--R 2 2 2 +--R (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---+ +--R (sinh(x) + cosh(x))\|a b +--R atan(-------------------------) +--R 2a +--R + +--R 2 2 3 +--R (24b - 48a b + 24a )sinh(x) +--R + +--R 2 2 2 +--R (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) - b + 4a)sinh(x) + b cosh(x) + (- b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 6 5 +--R b sinh(x) + 6b cosh(x)sinh(x) +--R + +--R 2 4 +--R (15b cosh(x) + 21b - 12a)sinh(x) +--R + +--R 3 3 +--R (20b cosh(x) + (84b - 48a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) + (126b - 72a)cosh(x) - 21b + 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (84b - 48a)cosh(x) + (- 42b + 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (21b - 12a)cosh(x) + (- 21b + 12a)cosh(x) - b +--R * +--R +---+ +--R \|a b +--R / +--R 2 3 2 2 2 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 2 3 +--R 24b cosh(x) +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 328 + +--S 329 of 552 +m0761a:= a0761.1-r0761 +--R +--R +--R (321) +--R 2 2 3 2 2 2 +--R (12b - 24a b + 12a )sinh(x) + (36b - 72a b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (36b - 72a b + 36a )cosh(x) sinh(x) + (12b - 24a b + 12a )cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R 4a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (12a b cosh(x) - 4a b)sinh(x) + 4a b cosh(x) - 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 2 3 +--R (- 24b + 48a b - 24a )sinh(x) +--R + +--R 2 2 2 +--R (- 72b + 144a b - 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 72b + 144a b - 72a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 24b + 48a b - 24a )cosh(x) +--R * +--R +-+ +--R +-----+ sinh(x)\|b +--R \|- a b atan(-----------) +--R +-+ +--R \|a +--R + +--R 6 5 +--R - 7b sinh(x) - 18b cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 9b cosh(x) - 27b + 12a)sinh(x) +--R + +--R 3 3 +--R (12b cosh(x) + (- 60b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) - 18b cosh(x) - 21b + 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (36b - 24a)cosh(x) + (- 42b + 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (21b - 12a)cosh(x) + (- 21b + 12a)cosh(x) - b +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R / +--R 2 3 2 2 2 2 2 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 329 + +--S 330 of 552 +d0761a:= D(m0761a,x) +--R +--R +--R (322) +--R 12 11 2 10 +--R b sinh(x) + 2b cosh(x)sinh(x) + (- 11b cosh(x) + 5b + a)sinh(x) +--R + +--R 3 9 +--R (- 48b cosh(x) + (40b - 22a)cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 70b cosh(x) + (108b - 115a)cosh(x) + 10b + 5a)sinh(x) +--R + +--R 5 3 7 +--R (- 28b cosh(x) + (104b - 200a)cosh(x) + (76b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 42b cosh(x) + (- 50b - 110a)cosh(x) + (230b - 180a)cosh(x) + 10b +--R + +--R 10a +--R * +--R 6 +--R sinh(x) +--R + +--R 7 5 3 +--R 64b cosh(x) + (- 200b + 92a)cosh(x) + (328b - 360a)cosh(x) +--R + +--R (40b + 28a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 4 +--R 37b cosh(x) + (- 180b + 178a)cosh(x) + (182b - 290a)cosh(x) +--R + +--R 2 +--R (92b - 10a)cosh(x) + 5b + 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 +--R 10b cosh(x) + (- 72b + 120a)cosh(x) + (- 60b - 40a)cosh(x) +--R + +--R 3 +--R (152b - 120a)cosh(x) + (2b + 40a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 +--R b cosh(x) + (- 11b + 45a)cosh(x) + (- 126b + 76a)cosh(x) +--R + +--R 4 2 +--R (154b - 170a)cosh(x) + (- 19b + 60a)cosh(x) + b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 +--R 10a cosh(x) + (- 56b + 40a)cosh(x) + (80b - 100a)cosh(x) +--R + +--R 3 +--R (- 24b + 40a)cosh(x) + 10a cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 +--R a cosh(x) + (- 8b + 5a)cosh(x) + (16b - 22a)cosh(x) +--R + +--R 4 2 +--R (- 8b + 10a)cosh(x) + 5a cosh(x) + a +--R / +--R 2 9 2 8 +--R 8b sinh(x) + 56b cosh(x)sinh(x) +--R + +--R 2 2 2 7 +--R (168b cosh(x) - 16b + 40a b)sinh(x) +--R + +--R 2 3 2 6 +--R (280b cosh(x) + (- 80b + 216a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 5 +--R (280b cosh(x) + (- 160b + 488a b)cosh(x) + 8b - 16a b + 32a )sinh(x) +--R + +--R 2 5 2 3 +--R 168b cosh(x) + (- 160b + 600a b)cosh(x) +--R + +--R 2 2 +--R (24b - 80a b + 160a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 56b cosh(x) + (- 80b + 440a b)cosh(x) +--R + +--R 2 2 2 +--R (24b - 160a b + 320a )cosh(x) + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (- 16b + 200a b)cosh(x) +--R + +--R 2 2 3 +--R (8b - 160a b + 320a )cosh(x) + 24a b cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 2 +--R (56a b cosh(x) + (- 80a b + 160a )cosh(x) + 24a b cosh(x) )sinh(x) +--R + +--R 7 2 5 3 +--R 8a b cosh(x) + (- 16a b + 32a )cosh(x) + 8a b cosh(x) +--R Type: Expression(Integer) +--E 330 + +--S 331 of 552 +m0761b:= a0761.2-r0761 +--R +--R +--R (323) +--R 2 2 3 2 2 2 +--R (24b - 48a b + 24a )sinh(x) + (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +---+ +--R +-+ +-+ (sinh(x) + cosh(x))\|a b +--R \|a \|b atan(-------------------------) +--R 2a +--R + +--R 2 2 3 +--R (- 24b + 48a b - 24a )sinh(x) +--R + +--R 2 2 2 +--R (- 72b + 144a b - 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 72b + 144a b - 72a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 24b + 48a b - 24a )cosh(x) +--R * +--R +-+ +--R +---+ sinh(x)\|b +--R \|a b atan(-----------) +--R +-+ +--R \|a +--R + +--R 2 2 3 2 2 2 +--R (24b - 48a b + 24a )sinh(x) + (72b - 144a b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (72b - 144a b + 72a )cosh(x) sinh(x) + (24b - 48a b + 24a )cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) - b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (- b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 6 5 +--R - 7b sinh(x) - 18b cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 9b cosh(x) - 27b + 12a)sinh(x) +--R + +--R 3 3 +--R (12b cosh(x) + (- 60b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) - 18b cosh(x) - 21b + 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (36b - 24a)cosh(x) + (- 42b + 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (21b - 12a)cosh(x) + (- 21b + 12a)cosh(x) - b +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R / +--R 2 3 2 2 2 2 2 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 331 + +--S 332 of 552 +d0761b:= D(m0761b,x) +--R +--R +--R (324) +--R 12 11 2 10 +--R b sinh(x) + 2b cosh(x)sinh(x) + (- 11b cosh(x) + 5b + a)sinh(x) +--R + +--R 3 9 +--R (- 48b cosh(x) + (40b - 22a)cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 70b cosh(x) + (108b - 115a)cosh(x) + 10b + 5a)sinh(x) +--R + +--R 5 3 7 +--R (- 28b cosh(x) + (104b - 200a)cosh(x) + (76b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 42b cosh(x) + (- 50b - 110a)cosh(x) + (230b - 180a)cosh(x) + 10b +--R + +--R 10a +--R * +--R 6 +--R sinh(x) +--R + +--R 7 5 3 +--R 64b cosh(x) + (- 200b + 92a)cosh(x) + (328b - 360a)cosh(x) +--R + +--R (40b + 28a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 4 +--R 37b cosh(x) + (- 180b + 178a)cosh(x) + (182b - 290a)cosh(x) +--R + +--R 2 +--R (92b - 10a)cosh(x) + 5b + 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 +--R 10b cosh(x) + (- 72b + 120a)cosh(x) + (- 60b - 40a)cosh(x) +--R + +--R 3 +--R (152b - 120a)cosh(x) + (2b + 40a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 +--R b cosh(x) + (- 11b + 45a)cosh(x) + (- 126b + 76a)cosh(x) +--R + +--R 4 2 +--R (154b - 170a)cosh(x) + (- 19b + 60a)cosh(x) + b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 +--R 10a cosh(x) + (- 56b + 40a)cosh(x) + (80b - 100a)cosh(x) +--R + +--R 3 +--R (- 24b + 40a)cosh(x) + 10a cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 +--R a cosh(x) + (- 8b + 5a)cosh(x) + (16b - 22a)cosh(x) +--R + +--R 4 2 +--R (- 8b + 10a)cosh(x) + 5a cosh(x) + a +--R / +--R 2 9 2 8 +--R 8b sinh(x) + 56b cosh(x)sinh(x) +--R + +--R 2 2 2 7 +--R (168b cosh(x) - 16b + 40a b)sinh(x) +--R + +--R 2 3 2 6 +--R (280b cosh(x) + (- 80b + 216a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 5 +--R (280b cosh(x) + (- 160b + 488a b)cosh(x) + 8b - 16a b + 32a )sinh(x) +--R + +--R 2 5 2 3 +--R 168b cosh(x) + (- 160b + 600a b)cosh(x) +--R + +--R 2 2 +--R (24b - 80a b + 160a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 56b cosh(x) + (- 80b + 440a b)cosh(x) +--R + +--R 2 2 2 +--R (24b - 160a b + 320a )cosh(x) + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (- 16b + 200a b)cosh(x) +--R + +--R 2 2 3 +--R (8b - 160a b + 320a )cosh(x) + 24a b cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 2 +--R (56a b cosh(x) + (- 80a b + 160a )cosh(x) + 24a b cosh(x) )sinh(x) +--R + +--R 7 2 5 3 +--R 8a b cosh(x) + (- 16a b + 32a )cosh(x) + 8a b cosh(x) +--R Type: Expression(Integer) +--E 332 + +--S 333 of 552 +t0762:= cosh(x)^6/(a+b*sinh(x)^2) +--R +--R +--R 6 +--R cosh(x) +--R (325) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 552 +r0762:= (a-b)^2*x/b^3-1/2*a*x/b^2+7/8*x/b+(-a+b)^(5/2)*_ + atan((-a+b)^(1/2)*tanh(x)/a^(1/2))/a^(1/2)/b^3-_ + 1/2*a*cosh(x)*sinh(x)/b^2+7/8*cosh(x)*sinh(x)/b+_ + 1/4*cosh(x)^3*sinh(x)/b +--R +--R +--R (326) +--R +-----+ +--R 2 2 +-----+ tanh(x)\|b - a +--R (8b - 16a b + 8a )\|b - a atan(---------------) +--R +-+ +--R \|a +--R + +--R 2 3 2 2 2 +-+ +--R ((2b cosh(x) + (7b - 4a b)cosh(x))sinh(x) + (15b - 20a b + 8a )x)\|a +--R / +--R 3 +-+ +--R 8b \|a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 552 +a0762:= integrate(t0762,x) +--R +--R +--R (327) +--R [ +--R 2 2 4 +--R (32b - 64a b + 32a )sinh(x) +--R + +--R 2 2 3 +--R (128b - 256a b + 128a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (192b - 384a b + 192a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (128b - 256a b + 128a )cosh(x) sinh(x) +--R + +--R 2 2 4 +--R (32b - 64a b + 32a )cosh(x) +--R * +--R +-------+ +--R |- b + a +--R |------- +--R \| a +--R * +--R log +--R 2 2 +--R 4a b sinh(x) + 8a b cosh(x)sinh(x) + 4a b cosh(x) - 4a b +--R + +--R 2 +--R 8a +--R * +--R +-------+ +--R |- b + a +--R |------- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) + 16b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (56b cosh(x) + (96b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (70b cosh(x) + (240b - 120a b)cosh(x) + (120b - 160a b + 64a )x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 56b cosh(x) + (320b - 160a b)cosh(x) +--R + +--R 2 2 +--R (480b - 640a b + 256a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 28b cosh(x) + (240b - 120a b)cosh(x) +--R + +--R 2 2 2 2 +--R (720b - 960a b + 384a )x cosh(x) - 16b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (96b - 48a b)cosh(x) +--R + +--R 2 2 3 2 +--R (480b - 640a b + 256a )x cosh(x) + (- 32b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 4 +--R b cosh(x) + (16b - 8a b)cosh(x) + (120b - 160a b + 64a )x cosh(x) +--R + +--R 2 2 2 +--R (- 16b + 8a b)cosh(x) - b +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R , +--R +--R 2 2 4 +--R (- 64b + 128a b - 64a )sinh(x) +--R + +--R 2 2 3 +--R (- 256b + 512a b - 256a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 384b + 768a b - 384a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 256b + 512a b - 256a )cosh(x) sinh(x) +--R + +--R 2 2 4 +--R (- 64b + 128a b - 64a )cosh(x) +--R * +--R +-----+ +--R |b - a +--R +-----+ 2a |----- +--R |b - a \| a +--R |----- atan(----------------------------------------------------) +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) + 16b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (56b cosh(x) + (96b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (70b cosh(x) + (240b - 120a b)cosh(x) + (120b - 160a b + 64a )x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 56b cosh(x) + (320b - 160a b)cosh(x) +--R + +--R 2 2 +--R (480b - 640a b + 256a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 28b cosh(x) + (240b - 120a b)cosh(x) +--R + +--R 2 2 2 2 +--R (720b - 960a b + 384a )x cosh(x) - 16b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (96b - 48a b)cosh(x) +--R + +--R 2 2 3 2 +--R (480b - 640a b + 256a )x cosh(x) + (- 32b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 4 +--R b cosh(x) + (16b - 8a b)cosh(x) + (120b - 160a b + 64a )x cosh(x) +--R + +--R 2 2 2 +--R (- 16b + 8a b)cosh(x) - b +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 335 + +--S 336 of 552 +m0762a:= a0762.1-r0762 +--R +--R +--R (328) +--R 2 2 4 +--R (32b - 64a b + 32a )sinh(x) +--R + +--R 2 2 3 +--R (128b - 256a b + 128a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (192b - 384a b + 192a )cosh(x) sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (128b - 256a b + 128a )cosh(x) sinh(x) + (32b - 64a b + 32a )cosh(x) +--R * +--R +-------+ +--R |- b + a +-+ +--R |------- \|a +--R \| a +--R * +--R log +--R 2 2 +--R 4a b sinh(x) + 8a b cosh(x)sinh(x) + 4a b cosh(x) - 4a b +--R + +--R 2 +--R 8a +--R * +--R +-------+ +--R |- b + a +--R |------- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) - 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (- 4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (- 2b + 4a b)cosh(x) + b - 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 2 4 +--R (- 64b + 128a b - 64a )sinh(x) +--R + +--R 2 2 3 +--R (- 256b + 512a b - 256a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 384b + 768a b - 384a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 256b + 512a b - 256a )cosh(x) sinh(x) +--R + +--R 2 2 4 +--R (- 64b + 128a b - 64a )cosh(x) +--R * +--R +-----+ +--R +-----+ tanh(x)\|b - a +--R \|b - a atan(---------------) +--R +-+ +--R \|a +--R + +--R 2 8 2 7 +--R b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (28b cosh(x) + 16b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (40b cosh(x) + (40b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R (6b cosh(x) + (16b + 8a b)cosh(x) )sinh(x) +--R + +--R 2 5 2 3 3 +--R (- 40b cosh(x) + (- 16b + 32a b)cosh(x) )sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (- 36b cosh(x) + (16b + 8a b)cosh(x) - 16b + 8a b)sinh(x) +--R + +--R 2 7 2 5 2 +--R (- 8b cosh(x) + (40b - 16a b)cosh(x) + (- 32b + 16a b)cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 2 +--R b cosh(x) + (16b - 8a b)cosh(x) + (- 16b + 8a b)cosh(x) - b +--R * +--R +-+ +--R \|a +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 336 + +--S 337 of 552 +d0762a:= D(m0762a,x) +--R +--R +--R (329) +--R 3 2 12 3 2 11 +--R (b - a b )sinh(x) + (12b - 12a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 10 +--R ((54b - 54a b )cosh(x) - 8b + 16a b - 8a b)sinh(x) +--R + +--R 3 2 3 3 2 2 +--R ((124b - 124a b )cosh(x) + (- 52b + 116a b - 64a b)cosh(x)) +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R (155b - 155a b )cosh(x) + (- 112b + 296a b - 184a b)cosh(x) +--R + +--R 3 2 2 3 +--R 29b - 93a b + 96a b - 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (88b - 88a b )cosh(x) + (- 32b + 256a b - 224a b)cosh(x) +--R + +--R 3 2 2 3 +--R (176b - 544a b + 560a b - 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 28b + 28a b )cosh(x) + (256b - 208a b - 48a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (464b - 1392a b + 1440a b - 512a )cosh(x) + 34b - 98a b +--R + +--R 2 3 +--R 96a b - 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 7 3 2 2 5 +--R (- 104b + 104a b )cosh(x) + (472b - 632a b + 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (736b - 2160a b + 2256a b - 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (232b - 632a b + 592a b - 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 8 3 2 2 6 +--R (- 121b + 121a b )cosh(x) + (368b - 544a b + 176a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (834b - 2434a b + 2560a b - 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (622b - 1646a b + 1504a b - 480a )cosh(x) + b + 7a b - 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 9 3 2 2 7 +--R (- 100b + 100a b )cosh(x) + (128b - 224a b + 96a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (720b - 2144a b + 2256a b - 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (848b - 2224a b + 2016a b - 640a )cosh(x) +--R + +--R 3 2 2 +--R (4b + 28a b - 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 10 3 2 2 8 +--R (- 58b + 58a b )cosh(x) + (8b - 64a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (440b - 1368a b + 1440a b - 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (622b - 1646a b + 1504a b - 480a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (6b + 42a b - 48a b)cosh(x) + 6b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 11 3 2 2 9 +--R (- 20b + 20a b )cosh(x) + (- 4b - 28a b + 32a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (160b - 528a b + 560a b - 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (232b - 632a b + 592a b - 192a )cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (4b + 28a b - 32a b)cosh(x) + (12b - 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 12 2 2 10 +--R (- 3b + 3a b )cosh(x) + (- 8a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 8 +--R (25b - 89a b + 96a b - 32a )cosh(x) +--R + +--R 3 2 2 3 6 3 2 2 4 +--R (34b - 98a b + 96a b - 32a )cosh(x) + (b + 7a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b - 6a b )cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 12 2 11 +--R a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 10 +--R (54a b cosh(x) - 8a b + 8a b)sinh(x) +--R + +--R 2 3 2 2 9 +--R (124a b cosh(x) + (- 52a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 3 2 +--R 155a b cosh(x) + (- 112a b + 184a b)cosh(x) - 16b + 61a b +--R + +--R 2 3 +--R - 80a b + 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R 88a b cosh(x) + (- 32a b + 224a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 128b + 432a b - 496a b + 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R - 28a b cosh(x) + (256a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 448b + 1360a b - 1376a b + 512a )cosh(x) + 32b - 94a b +--R + +--R 2 3 +--R 96a b - 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R - 104a b cosh(x) + (472a b - 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 896b + 2528a b - 2320a b + 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (192b - 536a b + 560a b - 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R - 121a b cosh(x) + (368a b - 176a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 1120b + 3074a b - 2720a b + 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (480b - 1298a b + 1376a b - 480a )cosh(x) - 16b + 33a b - 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 9 2 2 7 +--R - 100a b cosh(x) + (128a b - 96a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 896b + 2512a b - 2320a b + 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (640b - 1712a b + 1824a b - 640a )cosh(x) +--R + +--R 3 2 2 +--R (- 64b + 132a b - 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 2 2 8 +--R - 58a b cosh(x) + (8a b - 56a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 448b + 1336a b - 1376a b + 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (480b - 1298a b + 1376a b - 480a )cosh(x) +--R + +--R 3 2 2 2 2 +--R (- 96b + 198a b - 48a b)cosh(x) + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 2 9 +--R - 20a b cosh(x) + (- 4a b - 32a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (- 128b + 416a b - 496a b + 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (192b - 536a b + 560a b - 192a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 64b + 132a b - 32a b)cosh(x) + 12a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 12 2 10 +--R - 3a b cosh(x) - 8a b cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 16b + 57a b - 80a b + 32a )cosh(x) +--R + +--R 3 2 2 3 6 3 2 2 4 +--R (32b - 94a b + 96a b - 32a )cosh(x) + (- 16b + 33a b - 8a b)cosh(x) +--R + +--R 2 2 2 +--R 6a b cosh(x) + a b +--R / +--R 4 3 8 4 3 7 +--R (16b - 16a b )sinh(x) + (128b - 128a b )cosh(x)sinh(x) +--R + +--R 4 3 2 4 3 2 2 6 +--R ((448b - 448a b )cosh(x) - 32b + 96a b - 64a b )sinh(x) +--R + +--R 4 3 3 4 3 2 2 +--R ((896b - 896a b )cosh(x) + (- 192b + 576a b - 384a b )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 +--R (1120b - 1120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 480b + 1440a b - 960a b )cosh(x) + 16b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 +--R (896b - 896a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 640b + 1920a b - 1280a b )cosh(x) + (64b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 +--R (448b - 448a b )cosh(x) +--R + +--R 4 3 2 2 4 4 3 2 +--R (- 480b + 1440a b - 960a b )cosh(x) + (96b - 96a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 4 3 2 2 5 +--R (128b - 128a b )cosh(x) + (- 192b + 576a b - 384a b )cosh(x) +--R + +--R 4 3 3 +--R (64b - 64a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (16b - 16a b )cosh(x) + (- 32b + 96a b - 64a b )cosh(x) +--R + +--R 4 3 4 +--R (16b - 16a b )cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 8 3 7 +--R 16a b sinh(x) + 128a b cosh(x)sinh(x) +--R + +--R 3 2 3 2 2 6 +--R (448a b cosh(x) - 32a b + 64a b )sinh(x) +--R + +--R 3 3 3 2 2 5 +--R (896a b cosh(x) + (- 192a b + 384a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 2 3 4 +--R (1120a b cosh(x) + (- 480a b + 960a b )cosh(x) + 16a b )sinh(x) +--R + +--R 3 5 3 2 2 3 3 +--R (896a b cosh(x) + (- 640a b + 1280a b )cosh(x) + 64a b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 2 2 4 3 2 +--R (448a b cosh(x) + (- 480a b + 960a b )cosh(x) + 96a b cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 2 2 5 3 3 +--R (128a b cosh(x) + (- 192a b + 384a b )cosh(x) + 64a b cosh(x) )sinh(x) +--R + +--R 3 8 3 2 2 6 3 4 +--R 16a b cosh(x) + (- 32a b + 64a b )cosh(x) + 16a b cosh(x) +--R Type: Expression(Integer) +--E 337 + +--S 338 of 552 +m0762b:= a0762.2-r0762 +--R +--R +--R (330) +--R 2 2 4 +--R (- 64b + 128a b - 64a )sinh(x) +--R + +--R 2 2 3 +--R (- 256b + 512a b - 256a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 384b + 768a b - 384a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 256b + 512a b - 256a )cosh(x) sinh(x) +--R + +--R 2 2 4 +--R (- 64b + 128a b - 64a )cosh(x) +--R * +--R +-----+ +--R +-----+ tanh(x)\|b - a +--R \|b - a atan(---------------) +--R +-+ +--R \|a +--R + +--R 2 2 4 +--R (- 64b + 128a b - 64a )sinh(x) +--R + +--R 2 2 3 +--R (- 256b + 512a b - 256a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 384b + 768a b - 384a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 256b + 512a b - 256a )cosh(x) sinh(x) +--R + +--R 2 2 4 +--R (- 64b + 128a b - 64a )cosh(x) +--R * +--R +-----+ +--R |b - a +--R +-----+ 2a |----- +--R +-+ |b - a \| a +--R \|a |----- atan(----------------------------------------------------) +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) - b + 2a +--R + +--R 2 8 2 7 +--R b sinh(x) + 8b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (28b cosh(x) + 16b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (40b cosh(x) + (40b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R (6b cosh(x) + (16b + 8a b)cosh(x) )sinh(x) +--R + +--R 2 5 2 3 3 +--R (- 40b cosh(x) + (- 16b + 32a b)cosh(x) )sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (- 36b cosh(x) + (16b + 8a b)cosh(x) - 16b + 8a b)sinh(x) +--R + +--R 2 7 2 5 2 +--R (- 8b cosh(x) + (40b - 16a b)cosh(x) + (- 32b + 16a b)cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 2 +--R b cosh(x) + (16b - 8a b)cosh(x) + (- 16b + 8a b)cosh(x) - b +--R * +--R +-+ +--R \|a +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 552 +d0762b:= D(m0762b,x) +--R +--R +--R (331) +--R 3 2 12 3 2 11 +--R (b - a b )sinh(x) + (12b - 12a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 10 +--R ((54b - 54a b )cosh(x) - 8b + 16a b - 8a b)sinh(x) +--R + +--R 3 2 3 3 2 2 +--R ((124b - 124a b )cosh(x) + (- 52b + 116a b - 64a b)cosh(x)) +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R (155b - 155a b )cosh(x) + (- 112b + 296a b - 184a b)cosh(x) +--R + +--R 3 2 2 3 +--R 29b - 93a b + 96a b - 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (88b - 88a b )cosh(x) + (- 32b + 256a b - 224a b)cosh(x) +--R + +--R 3 2 2 3 +--R (176b - 544a b + 560a b - 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 28b + 28a b )cosh(x) + (256b - 208a b - 48a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (464b - 1392a b + 1440a b - 512a )cosh(x) + 34b - 98a b +--R + +--R 2 3 +--R 96a b - 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 7 3 2 2 5 +--R (- 104b + 104a b )cosh(x) + (472b - 632a b + 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (736b - 2160a b + 2256a b - 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (232b - 632a b + 592a b - 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 8 3 2 2 6 +--R (- 121b + 121a b )cosh(x) + (368b - 544a b + 176a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (834b - 2434a b + 2560a b - 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (622b - 1646a b + 1504a b - 480a )cosh(x) + b + 7a b - 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 9 3 2 2 7 +--R (- 100b + 100a b )cosh(x) + (128b - 224a b + 96a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (720b - 2144a b + 2256a b - 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (848b - 2224a b + 2016a b - 640a )cosh(x) +--R + +--R 3 2 2 +--R (4b + 28a b - 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 10 3 2 2 8 +--R (- 58b + 58a b )cosh(x) + (8b - 64a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (440b - 1368a b + 1440a b - 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (622b - 1646a b + 1504a b - 480a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (6b + 42a b - 48a b)cosh(x) + 6b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 11 3 2 2 9 +--R (- 20b + 20a b )cosh(x) + (- 4b - 28a b + 32a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (160b - 528a b + 560a b - 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (232b - 632a b + 592a b - 192a )cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (4b + 28a b - 32a b)cosh(x) + (12b - 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 12 2 2 10 +--R (- 3b + 3a b )cosh(x) + (- 8a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 8 +--R (25b - 89a b + 96a b - 32a )cosh(x) +--R + +--R 3 2 2 3 6 3 2 2 4 +--R (34b - 98a b + 96a b - 32a )cosh(x) + (b + 7a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b - 6a b )cosh(x) + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 12 2 11 +--R a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 10 +--R (54a b cosh(x) - 8a b + 8a b)sinh(x) +--R + +--R 2 3 2 2 9 +--R (124a b cosh(x) + (- 52a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 3 2 +--R 155a b cosh(x) + (- 112a b + 184a b)cosh(x) - 16b + 61a b +--R + +--R 2 3 +--R - 80a b + 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R 88a b cosh(x) + (- 32a b + 224a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 128b + 432a b - 496a b + 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R - 28a b cosh(x) + (256a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 448b + 1360a b - 1376a b + 512a )cosh(x) + 32b - 94a b +--R + +--R 2 3 +--R 96a b - 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R - 104a b cosh(x) + (472a b - 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 896b + 2528a b - 2320a b + 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (192b - 536a b + 560a b - 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R - 121a b cosh(x) + (368a b - 176a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 1120b + 3074a b - 2720a b + 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (480b - 1298a b + 1376a b - 480a )cosh(x) - 16b + 33a b - 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 9 2 2 7 +--R - 100a b cosh(x) + (128a b - 96a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 896b + 2512a b - 2320a b + 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (640b - 1712a b + 1824a b - 640a )cosh(x) +--R + +--R 3 2 2 +--R (- 64b + 132a b - 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 2 2 8 +--R - 58a b cosh(x) + (8a b - 56a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 448b + 1336a b - 1376a b + 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (480b - 1298a b + 1376a b - 480a )cosh(x) +--R + +--R 3 2 2 2 2 +--R (- 96b + 198a b - 48a b)cosh(x) + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 2 9 +--R - 20a b cosh(x) + (- 4a b - 32a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (- 128b + 416a b - 496a b + 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (192b - 536a b + 560a b - 192a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 64b + 132a b - 32a b)cosh(x) + 12a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 12 2 10 +--R - 3a b cosh(x) - 8a b cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 16b + 57a b - 80a b + 32a )cosh(x) +--R + +--R 3 2 2 3 6 3 2 2 4 +--R (32b - 94a b + 96a b - 32a )cosh(x) + (- 16b + 33a b - 8a b)cosh(x) +--R + +--R 2 2 2 +--R 6a b cosh(x) + a b +--R / +--R 4 3 8 4 3 7 +--R (16b - 16a b )sinh(x) + (128b - 128a b )cosh(x)sinh(x) +--R + +--R 4 3 2 4 3 2 2 6 +--R ((448b - 448a b )cosh(x) - 32b + 96a b - 64a b )sinh(x) +--R + +--R 4 3 3 4 3 2 2 +--R ((896b - 896a b )cosh(x) + (- 192b + 576a b - 384a b )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 +--R (1120b - 1120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 480b + 1440a b - 960a b )cosh(x) + 16b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 +--R (896b - 896a b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 640b + 1920a b - 1280a b )cosh(x) + (64b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 +--R (448b - 448a b )cosh(x) +--R + +--R 4 3 2 2 4 4 3 2 +--R (- 480b + 1440a b - 960a b )cosh(x) + (96b - 96a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 4 3 2 2 5 +--R (128b - 128a b )cosh(x) + (- 192b + 576a b - 384a b )cosh(x) +--R + +--R 4 3 3 +--R (64b - 64a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (16b - 16a b )cosh(x) + (- 32b + 96a b - 64a b )cosh(x) +--R + +--R 4 3 4 +--R (16b - 16a b )cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 8 3 7 +--R 16a b sinh(x) + 128a b cosh(x)sinh(x) +--R + +--R 3 2 3 2 2 6 +--R (448a b cosh(x) - 32a b + 64a b )sinh(x) +--R + +--R 3 3 3 2 2 5 +--R (896a b cosh(x) + (- 192a b + 384a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 2 3 4 +--R (1120a b cosh(x) + (- 480a b + 960a b )cosh(x) + 16a b )sinh(x) +--R + +--R 3 5 3 2 2 3 3 +--R (896a b cosh(x) + (- 640a b + 1280a b )cosh(x) + 64a b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 2 2 4 3 2 +--R (448a b cosh(x) + (- 480a b + 960a b )cosh(x) + 96a b cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 2 2 5 3 3 +--R (128a b cosh(x) + (- 192a b + 384a b )cosh(x) + 64a b cosh(x) )sinh(x) +--R + +--R 3 8 3 2 2 6 3 4 +--R 16a b cosh(x) + (- 32a b + 64a b )cosh(x) + 16a b cosh(x) +--R Type: Expression(Integer) +--E 339 + +--S 340 of 552 +t0763:= cosh(x)^7/(a+b*sinh(x)^2) +--R +--R +--R 7 +--R cosh(x) +--R (332) -------------- +--R 2 +--R b sinh(x) + a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 552 +r0763:= -(a-b)^3*atan(b^(1/2)*sinh(x)/a^(1/2))/a^(1/2)/b^(7/2)+_ + (a-b)^2*sinh(x)/b^3-a*sinh(x)/b^2+2*sinh(x)/b-_ + 1/3*a*sinh(x)^3/b^2+sinh(x)^3/b+1/5*sinh(x)^5/b +--R +--R +--R (333) +--R +-+ +--R 3 2 2 3 sinh(x)\|b +--R (15b - 45a b + 45a b - 15a )atan(-----------) +--R +-+ +--R \|a +--R + +--R 2 5 2 3 2 2 +--R (3b sinh(x) + (15b - 5a b)sinh(x) + (45b - 45a b + 15a )sinh(x)) +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 3 +-+ +-+ +--R 15b \|a \|b +--R Type: Expression(Integer) +--E 341 + +--S 342 of 552 +a0763:= integrate(t0763,x) +--R +--R +--R (334) +--R [ +--R 3 2 2 3 5 +--R (240b - 720a b + 720a b - 240a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (1200b - 3600a b + 3600a b - 1200a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (1200b - 3600a b + 3600a b - 1200a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (240b - 720a b + 720a b - 240a )cosh(x) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R 4a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (12a b cosh(x) - 4a b)sinh(x) + 4a b cosh(x) - 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) + 45b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (360b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (1260b - 560a b)cosh(x) + 570b - 660a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 756b cosh(x) + (2520b - 1120a b)cosh(x) +--R + +--R 2 2 +--R (3420b - 3960a b + 1440a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (3150b - 1400a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (8550b - 9900a b + 3600a )cosh(x) - 570b + 660a b - 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (2520b - 1120a b)cosh(x) +--R + +--R 2 2 3 +--R (11400b - 13200a b + 4800a )cosh(x) +--R + +--R 2 2 +--R (- 2280b + 2640a b - 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (1260b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (8550b - 9900a b + 3600a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 3420b + 3960a b - 1440a )cosh(x) - 45b + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (360b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (3420b - 3960a b + 1440a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 2280b + 2640a b - 960a )cosh(x) + (- 90b + 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (45b - 20a b)cosh(x) +--R + +--R 2 2 6 +--R (570b - 660a b + 240a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 570b + 660a b - 240a )cosh(x) + (- 45b + 20a b)cosh(x) - 3b +--R * +--R +-----+ +--R \|- a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 3 2 2 3 5 +--R (480b - 1440a b + 1440a b - 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (4800b - 14400a b + 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (4800b - 14400a b + 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (480b - 1440a b + 1440a b - 480a )cosh(x) +--R * +--R +---+ +--R (sinh(x) + cosh(x))\|a b +--R atan(-------------------------) +--R 2a +--R + +--R 3 2 2 3 5 +--R (480b - 1440a b + 1440a b - 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (4800b - 14400a b + 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (4800b - 14400a b + 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (480b - 1440a b + 1440a b - 480a )cosh(x) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) - b + 4a)sinh(x) + b cosh(x) + (- b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) + 45b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (360b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (1260b - 560a b)cosh(x) + 570b - 660a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 756b cosh(x) + (2520b - 1120a b)cosh(x) +--R + +--R 2 2 +--R (3420b - 3960a b + 1440a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (3150b - 1400a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (8550b - 9900a b + 3600a )cosh(x) - 570b + 660a b - 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (2520b - 1120a b)cosh(x) +--R + +--R 2 2 3 +--R (11400b - 13200a b + 4800a )cosh(x) +--R + +--R 2 2 +--R (- 2280b + 2640a b - 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (1260b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (8550b - 9900a b + 3600a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 3420b + 3960a b - 1440a )cosh(x) - 45b + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (360b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (3420b - 3960a b + 1440a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 2280b + 2640a b - 960a )cosh(x) + (- 90b + 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (45b - 20a b)cosh(x) +--R + +--R 2 2 6 +--R (570b - 660a b + 240a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 570b + 660a b - 240a )cosh(x) + (- 45b + 20a b)cosh(x) - 3b +--R * +--R +---+ +--R \|a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 342 + +--S 343 of 552 +m0763a:= a0763.1-r0763 +--R +--R +--R (335) +--R 3 2 2 3 5 +--R (240b - 720a b + 720a b - 240a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (1200b - 3600a b + 3600a b - 1200a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (1200b - 3600a b + 3600a b - 1200a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (240b - 720a b + 720a b - 240a )cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R 4a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (12a b cosh(x) - 4a b)sinh(x) + 4a b cosh(x) - 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 2b + 4a)cosh(x) + b +--R + +--R 3 2 2 3 5 +--R (- 480b + 1440a b - 1440a b + 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 2400b + 7200a b - 7200a b + 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 4800b + 14400a b - 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 4800b + 14400a b - 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 2400b + 7200a b - 7200a b + 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 480b + 1440a b - 1440a b + 480a )cosh(x) +--R * +--R +-+ +--R +-----+ sinh(x)\|b +--R \|- a b atan(-----------) +--R +-+ +--R \|a +--R + +--R 2 10 2 9 +--R - 93b sinh(x) - 450b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (- 825b cosh(x) - 435b + 140a b)sinh(x) +--R + +--R 2 3 2 7 +--R (- 600b cosh(x) + (- 2040b + 640a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 150b cosh(x) + (- 3540b + 1040a b)cosh(x) - 870b + 780a b +--R + +--R 2 +--R - 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 660b cosh(x) + (- 2280b + 480a b)cosh(x) +--R + +--R 2 2 +--R (- 3780b + 3240a b - 960a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (750b - 600a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 5850b + 4500a b - 1200a )cosh(x) - 570b + 660a b - 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (2040b - 960a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- 3000b + 1200a b)cosh(x) + (- 2280b + 2640a b - 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (1260b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (1350b - 2700a b + 1200a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 3420b + 3960a b - 1440a )cosh(x) - 45b + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (360b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (1980b - 2520a b + 960a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 2280b + 2640a b - 960a )cosh(x) + (- 90b + 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (45b - 20a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (570b - 660a b + 240a )cosh(x) + (- 570b + 660a b - 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 45b + 20a b)cosh(x) - 3b +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 343 + +--S 344 of 552 +d0763a:= D(m0763a,x) +--R +--R +--R (336) +--R 16 15 2 14 +--R b sinh(x) - 18b cosh(x)sinh(x) + (- 197b cosh(x) + 7b + a)sinh(x) +--R + +--R 3 13 +--R (- 788b cosh(x) + (52b - 114a)cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (- 1687b cosh(x) + (46b - 805a)cosh(x) + 21b + 7a)sinh(x) +--R + +--R 5 3 +--R (- 2030b cosh(x) + (- 572b - 2324a)cosh(x) + (274b - 300a)cosh(x)) +--R * +--R 11 +--R sinh(x) +--R + +--R 6 4 +--R - 1029b cosh(x) + (- 2359b - 3479a)cosh(x) +--R + +--R 2 +--R (1265b - 2226a)cosh(x) + 35b + 21a +--R * +--R 10 +--R sinh(x) +--R + +--R 7 5 3 +--R 744b cosh(x) + (- 4312b - 2478a)cosh(x) + (2776b - 6524a)cosh(x) +--R + +--R (344b - 174a)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 6 4 +--R 1851b cosh(x) + (- 4284b + 315a)cosh(x) + (2746b - 9975a)cosh(x) +--R + +--R 2 +--R (1556b - 1743a)cosh(x) + 35b + 35a +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 +--R 1714b cosh(x) + (- 2072b + 2536a)cosh(x) + (- 244b - 7896a)cosh(x) +--R + +--R 3 +--R (3880b - 5544a)cosh(x) + (178b + 152a)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 6 +--R 969b cosh(x) + (73b + 2875a)cosh(x) + (- 3686b - 1596a)cosh(x) +--R + +--R 4 2 +--R (5522b - 9030a)cosh(x) + (493b + 84a)cosh(x) + 21b + 35a +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 +--R 364b cosh(x) + (676b + 2002a)cosh(x) + (- 4200b + 2856a)cosh(x) +--R + +--R 5 3 +--R (4168b - 8148a)cosh(x) + (1084b - 728a)cosh(x) + (52b + 210a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 +--R 91b cosh(x) + (366b + 1001a)cosh(x) + (- 2319b + 3081a)cosh(x) +--R + +--R 6 4 +--R (884b - 3654a)cosh(x) + (1805b - 2030a)cosh(x) +--R + +--R 2 +--R (- 34b + 525a)cosh(x) + 7b + 21a +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 +--R 14b cosh(x) + (84b + 364a)cosh(x) + (- 654b + 1540a)cosh(x) +--R + +--R 7 5 +--R (- 1064b - 168a)cosh(x) + (1970b - 2520a)cosh(x) +--R + +--R 3 +--R (- 236b + 700a)cosh(x) + (14b + 84a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 +--R b cosh(x) + (7b + 91a)cosh(x) + (- 75b + 462a)cosh(x) +--R + +--R 8 6 +--R (- 925b + 561a)cosh(x) + (1283b - 1708a)cosh(x) +--R + +--R 4 2 +--R (- 299b + 525a)cosh(x) + (7b + 126a)cosh(x) + b + 7a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R 14a cosh(x) + 84a cosh(x) + (- 288b + 210a)cosh(x) +--R + +--R 7 5 3 +--R (448b - 616a)cosh(x) + (- 160b + 210a)cosh(x) + 84a cosh(x) +--R + +--R 14a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R a cosh(x) + 7a cosh(x) + (- 32b + 21a)cosh(x) + (64b - 93a)cosh(x) +--R + +--R 6 4 2 +--R (- 32b + 35a)cosh(x) + 21a cosh(x) + 7a cosh(x) + a +--R / +--R 2 11 2 10 +--R 32b sinh(x) + 288b cosh(x)sinh(x) +--R + +--R 2 2 2 9 +--R (1152b cosh(x) - 64b + 160a b)sinh(x) +--R + +--R 2 3 2 8 +--R (2688b cosh(x) + (- 448b + 1184a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (4032b cosh(x) + (- 1344b + 3840a b)cosh(x) + 32b - 64a b + 128a ) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 4032b cosh(x) + (- 2240b + 7168a b)cosh(x) +--R + +--R 2 2 +--R (160b - 448a b + 896a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 2688b cosh(x) + (- 2240b + 8512a b)cosh(x) +--R + +--R 2 2 2 +--R (320b - 1344a b + 2688a )cosh(x) + 32a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 1152b cosh(x) + (- 1344b + 6720a b)cosh(x) +--R + +--R 2 2 3 +--R (320b - 2240a b + 4480a )cosh(x) + 160a b cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 288b cosh(x) + (- 448b + 3584a b)cosh(x) +--R + +--R 2 2 4 2 +--R (160b - 2240a b + 4480a )cosh(x) + 320a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 32b cosh(x) + (- 64b + 1280a b)cosh(x) +--R + +--R 2 2 5 3 +--R (32b - 1344a b + 2688a )cosh(x) + 320a b cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 2 6 4 +--R (288a b cosh(x) + (- 448a b + 896a )cosh(x) + 160a b cosh(x) )sinh(x) +--R + +--R 9 2 7 5 +--R 32a b cosh(x) + (- 64a b + 128a )cosh(x) + 32a b cosh(x) +--R Type: Expression(Integer) +--E 344 + +--S 345 of 552 +m0763b:= a0763.2-r0763 +--R +--R +--R (337) +--R 3 2 2 3 5 +--R (480b - 1440a b + 1440a b - 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (4800b - 14400a b + 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (4800b - 14400a b + 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (480b - 1440a b + 1440a b - 480a )cosh(x) +--R * +--R +---+ +--R +-+ +-+ (sinh(x) + cosh(x))\|a b +--R \|a \|b atan(-------------------------) +--R 2a +--R + +--R 3 2 2 3 5 +--R (- 480b + 1440a b - 1440a b + 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 2400b + 7200a b - 7200a b + 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 4800b + 14400a b - 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 4800b + 14400a b - 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 2400b + 7200a b - 7200a b + 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 480b + 1440a b - 1440a b + 480a )cosh(x) +--R * +--R +-+ +--R +---+ sinh(x)\|b +--R \|a b atan(-----------) +--R +-+ +--R \|a +--R + +--R 3 2 2 3 5 +--R (480b - 1440a b + 1440a b - 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (4800b - 14400a b + 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (4800b - 14400a b + 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b - 7200a b + 7200a b - 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (480b - 1440a b + 1440a b - 480a )cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) - b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (- b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 2 10 2 9 +--R - 93b sinh(x) - 450b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (- 825b cosh(x) - 435b + 140a b)sinh(x) +--R + +--R 2 3 2 7 +--R (- 600b cosh(x) + (- 2040b + 640a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 150b cosh(x) + (- 3540b + 1040a b)cosh(x) - 870b + 780a b +--R + +--R 2 +--R - 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 660b cosh(x) + (- 2280b + 480a b)cosh(x) +--R + +--R 2 2 +--R (- 3780b + 3240a b - 960a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (750b - 600a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 5850b + 4500a b - 1200a )cosh(x) - 570b + 660a b - 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (2040b - 960a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- 3000b + 1200a b)cosh(x) + (- 2280b + 2640a b - 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (1260b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (1350b - 2700a b + 1200a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 3420b + 3960a b - 1440a )cosh(x) - 45b + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (360b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (1980b - 2520a b + 960a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 2280b + 2640a b - 960a )cosh(x) + (- 90b + 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (45b - 20a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (570b - 660a b + 240a )cosh(x) + (- 570b + 660a b - 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 45b + 20a b)cosh(x) - 3b +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 345 + +--S 346 of 552 +d0763b:= D(m0763b,x) +--R +--R +--R (338) +--R 16 15 2 14 +--R b sinh(x) - 18b cosh(x)sinh(x) + (- 197b cosh(x) + 7b + a)sinh(x) +--R + +--R 3 13 +--R (- 788b cosh(x) + (52b - 114a)cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (- 1687b cosh(x) + (46b - 805a)cosh(x) + 21b + 7a)sinh(x) +--R + +--R 5 3 +--R (- 2030b cosh(x) + (- 572b - 2324a)cosh(x) + (274b - 300a)cosh(x)) +--R * +--R 11 +--R sinh(x) +--R + +--R 6 4 +--R - 1029b cosh(x) + (- 2359b - 3479a)cosh(x) +--R + +--R 2 +--R (1265b - 2226a)cosh(x) + 35b + 21a +--R * +--R 10 +--R sinh(x) +--R + +--R 7 5 3 +--R 744b cosh(x) + (- 4312b - 2478a)cosh(x) + (2776b - 6524a)cosh(x) +--R + +--R (344b - 174a)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 6 4 +--R 1851b cosh(x) + (- 4284b + 315a)cosh(x) + (2746b - 9975a)cosh(x) +--R + +--R 2 +--R (1556b - 1743a)cosh(x) + 35b + 35a +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 +--R 1714b cosh(x) + (- 2072b + 2536a)cosh(x) + (- 244b - 7896a)cosh(x) +--R + +--R 3 +--R (3880b - 5544a)cosh(x) + (178b + 152a)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 6 +--R 969b cosh(x) + (73b + 2875a)cosh(x) + (- 3686b - 1596a)cosh(x) +--R + +--R 4 2 +--R (5522b - 9030a)cosh(x) + (493b + 84a)cosh(x) + 21b + 35a +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 +--R 364b cosh(x) + (676b + 2002a)cosh(x) + (- 4200b + 2856a)cosh(x) +--R + +--R 5 3 +--R (4168b - 8148a)cosh(x) + (1084b - 728a)cosh(x) + (52b + 210a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 +--R 91b cosh(x) + (366b + 1001a)cosh(x) + (- 2319b + 3081a)cosh(x) +--R + +--R 6 4 +--R (884b - 3654a)cosh(x) + (1805b - 2030a)cosh(x) +--R + +--R 2 +--R (- 34b + 525a)cosh(x) + 7b + 21a +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 +--R 14b cosh(x) + (84b + 364a)cosh(x) + (- 654b + 1540a)cosh(x) +--R + +--R 7 5 +--R (- 1064b - 168a)cosh(x) + (1970b - 2520a)cosh(x) +--R + +--R 3 +--R (- 236b + 700a)cosh(x) + (14b + 84a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 +--R b cosh(x) + (7b + 91a)cosh(x) + (- 75b + 462a)cosh(x) +--R + +--R 8 6 +--R (- 925b + 561a)cosh(x) + (1283b - 1708a)cosh(x) +--R + +--R 4 2 +--R (- 299b + 525a)cosh(x) + (7b + 126a)cosh(x) + b + 7a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R 14a cosh(x) + 84a cosh(x) + (- 288b + 210a)cosh(x) +--R + +--R 7 5 3 +--R (448b - 616a)cosh(x) + (- 160b + 210a)cosh(x) + 84a cosh(x) +--R + +--R 14a cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 +--R a cosh(x) + 7a cosh(x) + (- 32b + 21a)cosh(x) + (64b - 93a)cosh(x) +--R + +--R 6 4 2 +--R (- 32b + 35a)cosh(x) + 21a cosh(x) + 7a cosh(x) + a +--R / +--R 2 11 2 10 +--R 32b sinh(x) + 288b cosh(x)sinh(x) +--R + +--R 2 2 2 9 +--R (1152b cosh(x) - 64b + 160a b)sinh(x) +--R + +--R 2 3 2 8 +--R (2688b cosh(x) + (- 448b + 1184a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (4032b cosh(x) + (- 1344b + 3840a b)cosh(x) + 32b - 64a b + 128a ) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 4032b cosh(x) + (- 2240b + 7168a b)cosh(x) +--R + +--R 2 2 +--R (160b - 448a b + 896a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 2688b cosh(x) + (- 2240b + 8512a b)cosh(x) +--R + +--R 2 2 2 +--R (320b - 1344a b + 2688a )cosh(x) + 32a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 1152b cosh(x) + (- 1344b + 6720a b)cosh(x) +--R + +--R 2 2 3 +--R (320b - 2240a b + 4480a )cosh(x) + 160a b cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 288b cosh(x) + (- 448b + 3584a b)cosh(x) +--R + +--R 2 2 4 2 +--R (160b - 2240a b + 4480a )cosh(x) + 320a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 32b cosh(x) + (- 64b + 1280a b)cosh(x) +--R + +--R 2 2 5 3 +--R (32b - 1344a b + 2688a )cosh(x) + 320a b cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 2 6 4 +--R (288a b cosh(x) + (- 448a b + 896a )cosh(x) + 160a b cosh(x) )sinh(x) +--R + +--R 9 2 7 5 +--R 32a b cosh(x) + (- 64a b + 128a )cosh(x) + 32a b cosh(x) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 552 +t0764:= cosh(x)^2/(a+a*sinh(x)^2) +--R +--R +--R 2 +--R cosh(x) +--R (339) -------------- +--R 2 +--R a sinh(x) + a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 552 +r0764:= x/a +--R +--R +--R x +--R (340) - +--R a +--R Type: Fraction(Polynomial(Integer)) +--E 348 + +--S 349 of 552 +a0764:= integrate(t0764,x) +--R +--R +--R x +--R (341) - +--R a +--R Type: Union(Expression(Integer),...) +--E 349 + +--S 350 of 552 +m0764:= a0764-r0764 +--R +--R +--R (342) 0 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 552 +d0764:= D(m0764,x) +--R +--R +--R (343) 0 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 552 +t0765:= cosh(x)^4/(a+a*sinh(x)^2) +--R +--R +--R 4 +--R cosh(x) +--R (344) -------------- +--R 2 +--R a sinh(x) + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 552 +r0765:= 1/2*(x+cosh(x)*sinh(x))/a +--R +--R +--R cosh(x)sinh(x) + x +--R (345) ------------------ +--R 2a +--R Type: Expression(Integer) +--E 353 + +--S 354 of 552 +a0765:= integrate(t0765,x) +--R +--R +--R cosh(x)sinh(x) + x +--R (346) ------------------ +--R 2a +--R Type: Union(Expression(Integer),...) +--E 354 + +--S 355 of 552 +m0765:= a0765-r0765 +--R +--R +--R (347) 0 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 552 +d0765:= D(m0765,x) +--R +--R +--R (348) 0 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 552 +t0766:= cosh(x)^2/(1-sinh(x)^2) +--R +--R +--R 2 +--R cosh(x) +--R (349) - ------------ +--R 2 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 552 +r0766:= -x+atanh(2^(1/2)*tanh(x))*2^(1/2) +--R +--R +--R +-+ +-+ +--R (350) \|2 atanh(\|2 tanh(x)) - x +--R Type: Expression(Integer) +--E 358 + +--S 359 of 552 +a0766:= integrate(t0766,x) +--R +--R +--R (351) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R - 2x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 359 + +--S 360 of 552 +m0766:= a0766-r0766 +--R +--R +--R (352) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ +-+ +--R - 2\|2 atanh(\|2 tanh(x)) +--R / +--R 2 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 552 +d0766:= D(m0766,x) +--R +--R +--R (353) +--R +-+ 4 +-+ 3 +--R (4\|2 - 6)sinh(x) + (24\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 56\|2 + 84)cosh(x) - 8\|2 + 12)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 - 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (- 8\|2 + 12)cosh(x) - 12\|2 + 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (4\|2 - 6)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((40\|2 - 60)cosh(x) - 16\|2 + 24)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (- 16\|2 + 24)cosh(x) + 12\|2 - 18 +--R / +--R +-+ 4 +-+ 3 +--R (12\|2 - 18)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((24\|2 - 36)cosh(x) - 40\|2 + 60)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (72\|2 - 96)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (12\|2 - 18)cosh(x) + (- 40\|2 + 60)cosh(x) + 12\|2 - 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 12\|2 + 18)cosh(x) + 20\|2 - 30)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((12\|2 - 16)cosh(x) + (- 36\|2 + 48)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + (20\|2 - 30)cosh(x) - 6\|2 + 9 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 552 +t0767:= cosh(x)^3/(1-sinh(x)^2) +--R +--R +--R 3 +--R cosh(x) +--R (354) - ------------ +--R 2 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 552 +r0767:= 2*atanh(sinh(x))-sinh(x) +--R +--R +--R (355) 2atanh(sinh(x)) - sinh(x) +--R Type: Expression(Integer) +--E 363 + +--S 364 of 552 +a0767:= integrate(t0767,x) +--R +--R +--R (356) +--R - 2sinh(x) + 2 +--R (- 2sinh(x) - 2cosh(x))log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2sinh(x) - 2 2 +--R (2sinh(x) + 2cosh(x))log(-----------------) - sinh(x) - 2cosh(x)sinh(x) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R - cosh(x) + 1 +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 364 + +--S 365 of 552 +m0767:= a0767-r0767 +--R +--R +--R (357) +--R - 2sinh(x) + 2 +--R (- 2sinh(x) - 2cosh(x))log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R - 2sinh(x) - 2 +--R (2sinh(x) + 2cosh(x))log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 4sinh(x) - 4cosh(x))atanh(sinh(x)) + sinh(x) - cosh(x) + 1 +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 365 + +--S 366 of 552 +d0767:= D(m0767,x) +--R +--R +--R 2 2 +--R - sinh(x) + cosh(x) - 1 +--R (358) ------------------------- +--R 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 366 + +--S 367 of 552 +t0768:= cosh(x)^4/(1-sinh(x)^2) +--R +--R +--R 4 +--R cosh(x) +--R (359) - ------------ +--R 2 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 552 +r0768:= -5/2*x+2*atanh(2^(1/2)*tanh(x))*2^(1/2)-1/2*cosh(x)*sinh(x) +--R +--R +--R +-+ +-+ +--R 4\|2 atanh(\|2 tanh(x)) - cosh(x)sinh(x) - 5x +--R (360) --------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 552 +a0768:= integrate(t0768,x) +--R +--R +--R (361) +--R +-+ 2 +-+ +-+ 2 +--R (8\|2 sinh(x) + 16\|2 cosh(x)sinh(x) + 8\|2 cosh(x) ) +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) - 20x)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) - 40x cosh(x))sinh(x) - cosh(x) - 20x cosh(x) + 1 +--R / +--R 2 2 +--R 8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) +--R Type: Union(Expression(Integer),...) +--E 369 + +--S 370 of 552 +m0768:= a0768-r0768 +--R +--R +--R (362) +--R +-+ 2 +-+ +-+ 2 +--R (8\|2 sinh(x) + 16\|2 cosh(x)sinh(x) + 8\|2 cosh(x) ) +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ 2 +-+ +-+ 2 +--R (- 16\|2 sinh(x) - 32\|2 cosh(x)sinh(x) - 16\|2 cosh(x) ) +--R * +--R +-+ +--R atanh(\|2 tanh(x)) +--R + +--R 4 2 2 4 +--R - sinh(x) + 2cosh(x) sinh(x) - cosh(x) + 1 +--R / +--R 2 2 +--R 8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) +--R Type: Expression(Integer) +--E 370 + +--S 371 of 552 +d0768:= D(m0768,x) +--R +--R +--R (363) +--R +-+ 8 +-+ 7 +--R (12\|2 - 18)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 6 +--R (- 8\|2 + 12)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((24\|2 - 32)cosh(x) + (328\|2 - 448)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 24\|2 + 36)cosh(x) + (8\|2 + 52)cosh(x) - 64\|2 + 96) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (24\|2 - 32)cosh(x) + (- 656\|2 + 1024)cosh(x) +--R + +--R +-+ +--R (88\|2 - 96)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((8\|2 + 52)cosh(x) + (208\|2 - 248)cosh(x) - 56\|2 + 84) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 24\|2 + 32)cosh(x) + (328\|2 - 448)cosh(x) +--R + +--R +-+ 3 +-+ +--R (88\|2 - 96)cosh(x) + (- 264\|2 + 384)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (12\|2 - 18)cosh(x) + (- 8\|2 + 12)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 64\|2 + 96)cosh(x) + (- 56\|2 + 84)cosh(x) - 12\|2 + 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 6 +--R (52\|2 - 78)sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R ((- 12\|2 + 16)cosh(x) + (- 164\|2 + 208)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R ((12\|2 - 18)cosh(x) + (- 52\|2 + 14)cosh(x) - 128\|2 + 192)sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 12\|2 + 16)cosh(x) + (328\|2 - 544)cosh(x) +--R + +--R +-+ +--R (- 76\|2 + 144)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 52\|2 + 14)cosh(x) + (152\|2 - 164)cosh(x) + 76\|2 - 114) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (12\|2 - 16)cosh(x) + (- 164\|2 + 208)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 76\|2 + 144)cosh(x) + (228\|2 - 336)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R (- 6\|2 + 9)cosh(x) + (52\|2 - 78)cosh(x) + (- 128\|2 + 192)cosh(x) +--R + +--R +-+ 2 +-+ +--R (76\|2 - 114)cosh(x) + 6\|2 - 9 +--R / +--R +-+ 6 5 +--R (48\|2 - 72)sinh(x) - 16cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R ((- 48\|2 + 40)cosh(x) - 160\|2 + 240)sinh(x) +--R + +--R 3 +-+ 3 +--R (- 32cosh(x) + (- 32\|2 + 96)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 48\|2 + 40)cosh(x) + (256\|2 - 288)cosh(x) + 48\|2 - 72) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 +-+ 3 +-+ +--R (- 16cosh(x) + (- 32\|2 + 96)cosh(x) + (96\|2 - 144)cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (48\|2 - 72)cosh(x) + (- 160\|2 + 240)cosh(x) +--R + +--R +-+ 2 +--R (48\|2 - 72)cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 6 5 +--R (- 24\|2 + 36)sinh(x) + 8cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R ((24\|2 - 20)cosh(x) + 80\|2 - 120)sinh(x) +--R + +--R 3 +-+ 3 +--R (16cosh(x) + (16\|2 - 48)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R ((24\|2 - 20)cosh(x) + (- 128\|2 + 144)cosh(x) - 24\|2 + 36)sinh(x) +--R + +--R 5 +-+ 3 +-+ +--R (8cosh(x) + (16\|2 - 48)cosh(x) + (- 48\|2 + 72)cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R (- 24\|2 + 36)cosh(x) + (80\|2 - 120)cosh(x) + (- 24\|2 + 36)cosh(x) +--R Type: Expression(Integer) +--E 371 + +--S 372 of 552 +t0769:= coth(x)/(1-sinh(x)^2) +--R +--R +--R coth(x) +--R (364) - ------------ +--R 2 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 552 +r0769:= atanh(-3+2*cosh(x)^2) +--R +--R +--R 2 +--R (365) atanh(2cosh(x) - 3) +--R Type: Expression(Integer) +--E 373 + +--S 374 of 552 +a0769:= integrate(t0769,x) +--R +--R +--R (366) +--R 2 2 +--R 2sinh(x) + 2cosh(x) - 6 2sinh(x) +--R - log(-------------------------------------) + 2log(- -----------------) +--R 2 2 sinh(x) - cosh(x) +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R ------------------------------------------------------------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 374 + +--S 375 of 552 +m0769:= a0769-r0769 +--R +--R +--R (367) +--R 2 2 +--R 2sinh(x) + 2cosh(x) - 6 2sinh(x) +--R - log(-------------------------------------) + 2log(- -----------------) +--R 2 2 sinh(x) - cosh(x) +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R - 2atanh(2cosh(x) - 3) +--R / +--R 2 +--R Type: Expression(Integer) +--E 375 + +--S 376 of 552 +d0769:= D(m0769,x) +--R +--R +--R (368) +--R 4 5 3 2 7 +--R cosh(x)sinh(x) + (- cosh(x) + 4cosh(x) - 5cosh(x))sinh(x) + cosh(x) +--R + +--R 5 3 +--R - 6cosh(x) + 11cosh(x) - 6cosh(x) +--R / +--R 4 2 3 +--R (cosh(x) - 3cosh(x) + 2)sinh(x) +--R + +--R 6 4 2 +--R (cosh(x) - 6cosh(x) + 11cosh(x) - 6)sinh(x) +--R Type: Expression(Integer) +--E 376 + +--S 377 of 552 +t0770:= cosh(x)^4/(1-sinh(x)^2)^2 +--R +--R +--R 4 +--R cosh(x) +--R (369) ------------------------ +--R 4 2 +--R sinh(x) - 2sinh(x) + 1 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 552 +r0770:= x-1/2*atanh(2^(1/2)*tanh(x))*2^(1/2)+tanh(x)/(1-2*tanh(x)^2) +--R +--R +--R (370) +--R +-+ 2 +-+ +-+ 2 +--R (- 2\|2 tanh(x) + \|2 )atanh(\|2 tanh(x)) + 4x tanh(x) - 2tanh(x) - 2x +--R ------------------------------------------------------------------------ +--R 2 +--R 4tanh(x) - 2 +--R Type: Expression(Integer) +--E 378 + +--S 379 of 552 +a0770:= integrate(t0770,x) +--R +--R +--R (371) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 6)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 12cosh(x))sinh(x) + cosh(x) - 6cosh(x) + 1 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 + 12)sinh(x) + (- 16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 + 12)cosh(x) - 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ 4 +-+ 3 +--R 2x\|2 sinh(x) + 8x\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12x\|2 cosh(x) + (- 12x - 12)\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8x\|2 cosh(x) + (- 24x - 24)\|2 cosh(x))sinh(x) + 2x\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 12x - 12)\|2 cosh(x) + (2x + 4)\|2 +--R / +--R +-+ 4 +-+ 3 +-+ 2 +-+ 2 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) + (12\|2 cosh(x) - 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (8\|2 cosh(x) - 24\|2 cosh(x))sinh(x) + 2\|2 cosh(x) - 12\|2 cosh(x) +--R + +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 379 + +--S 380 of 552 +m0770:= a0770-r0770 +--R +--R +--R (372) +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 12)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 24cosh(x))sinh(x) + 2cosh(x) - 12cosh(x) + 2 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 6)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 12cosh(x))sinh(x) - cosh(x) + 6cosh(x) - 1 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 + 12)sinh(x) + (- 16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 + 12)cosh(x) - 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 24)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 48cosh(x))sinh(x) + 4cosh(x) - 24cosh(x) + 4 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) + 12)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) + 24cosh(x))sinh(x) - 2cosh(x) + 12cosh(x) - 2 +--R * +--R +-+ +--R atanh(\|2 tanh(x)) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- 24\|2 sinh(x) - 48\|2 cosh(x)sinh(x) - 24\|2 cosh(x) + 8\|2 ) +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|2 cosh(x) - 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8\|2 cosh(x) - 24\|2 cosh(x))sinh(x) + 2\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 12\|2 cosh(x) + 2\|2 +--R * +--R tanh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R 12\|2 sinh(x) + 24\|2 cosh(x)sinh(x) + 12\|2 cosh(x) - 4\|2 +--R / +--R +-+ 4 +-+ 3 +--R 4\|2 sinh(x) + 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (24\|2 cosh(x) - 24\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (16\|2 cosh(x) - 48\|2 cosh(x))sinh(x) + 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 24\|2 cosh(x) + 4\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 2\|2 sinh(x) - 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 12\|2 cosh(x) + 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (- 8\|2 cosh(x) + 24\|2 cosh(x))sinh(x) - 2\|2 cosh(x) + 12\|2 cosh(x) +--R + +--R +-+ +--R - 2\|2 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 552 +d0770:= D(m0770,x) +--R +--R +--R (373) +--R +-+ 12 +-+ 11 +--R (12\|2 + 16)sinh(x) + (32\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 56\|2 - 160)cosh(x) + 240\|2 + 320)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 224\|2 - 608)cosh(x) + (1408\|2 + 1888)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (116\|2 - 528)cosh(x) + (2864\|2 + 3904)cosh(x) - 660\|2 +--R + +--R - 880 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (1216\|2 + 576)cosh(x) + (1024\|2 + 1664)cosh(x) +--R + +--R +-+ +--R (- 4608\|2 - 6208)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (1904\|2 + 1344)cosh(x) + (- 5152\|2 - 6272)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 6288\|2 - 8128)cosh(x) - 576\|2 - 768 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (1216\|2 + 576)cosh(x) + (- 8960\|2 - 11200)cosh(x) +--R + +--R +-+ 3 +-+ +--R (5760\|2 + 9280)cosh(x) + (- 1984\|2 - 2496)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (116\|2 - 528)cosh(x) + (- 5152\|2 - 6272)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (16200\|2 + 24160)cosh(x) + (- 2752\|2 - 3072)cosh(x) +--R + +--R +-+ +--R 228\|2 + 304 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 224\|2 - 608)cosh(x) + (1024\|2 + 1664)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (5760\|2 + 9280)cosh(x) + (- 2688\|2 - 2688)cosh(x) +--R + +--R +-+ +--R (4064\|2 + 5664)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 56\|2 - 160)cosh(x) + (2864\|2 + 3904)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 6288\|2 - 8128)cosh(x) + (- 2752\|2 - 3072)cosh(x) +--R + +--R +-+ 2 +-+ +--R (7944\|2 + 11104)cosh(x) - 48\|2 - 64 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (32\|2 + 32)cosh(x) + (1408\|2 + 1888)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 4608\|2 - 6208)cosh(x) + (- 1984\|2 - 2496)cosh(x) +--R + +--R +-+ 3 +-+ +--R (4064\|2 + 5664)cosh(x) + (64\|2 + 96)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (12\|2 + 16)cosh(x) + (240\|2 + 320)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 660\|2 - 880)cosh(x) + (- 576\|2 - 768)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (228\|2 + 304)cosh(x) + (- 48\|2 - 64)cosh(x) + 36\|2 + 48 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 12\|2 - 16)sinh(x) + (- 32\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((56\|2 + 160)cosh(x) - 240\|2 - 320)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((224\|2 + 608)cosh(x) + (- 1408\|2 - 1888)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 116\|2 + 528)cosh(x) + (- 2864\|2 - 3904)cosh(x) + 660\|2 +--R + +--R 880 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 1216\|2 - 576)cosh(x) + (- 1024\|2 - 1664)cosh(x) +--R + +--R +-+ +--R (4608\|2 + 6208)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 1904\|2 - 1344)cosh(x) + (5152\|2 + 6272)cosh(x) +--R + +--R +-+ 2 +-+ +--R (6288\|2 + 8128)cosh(x) + 576\|2 + 768 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 1216\|2 - 576)cosh(x) + (8960\|2 + 11200)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 5760\|2 - 9280)cosh(x) + (1984\|2 + 2496)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 116\|2 + 528)cosh(x) + (5152\|2 + 6272)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 16200\|2 - 24160)cosh(x) + (2752\|2 + 3072)cosh(x) +--R + +--R +-+ +--R - 228\|2 - 304 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (224\|2 + 608)cosh(x) + (- 1024\|2 - 1664)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 5760\|2 - 9280)cosh(x) + (2688\|2 + 2688)cosh(x) +--R + +--R +-+ +--R (- 4064\|2 - 5664)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (56\|2 + 160)cosh(x) + (- 2864\|2 - 3904)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (6288\|2 + 8128)cosh(x) + (2752\|2 + 3072)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 7944\|2 - 11104)cosh(x) + 48\|2 + 64 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 32\|2 - 32)cosh(x) + (- 1408\|2 - 1888)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (4608\|2 + 6208)cosh(x) + (1984\|2 + 2496)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 4064\|2 - 5664)cosh(x) + (- 64\|2 - 96)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 12\|2 - 16)cosh(x) + (- 240\|2 - 320)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (660\|2 + 880)cosh(x) + (576\|2 + 768)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 228\|2 - 304)cosh(x) + (48\|2 + 64)cosh(x) - 36\|2 - 48 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 6\|2 - 8)sinh(x) + (- 48\|2 - 64)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 156\|2 - 208)cosh(x) + 198\|2 + 264)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 240\|2 - 320)cosh(x) + (1000\|2 + 1296)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 90\|2 - 120)cosh(x) + (1886\|2 + 2280)cosh(x) - 876\|2 - 1168) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (288\|2 + 384)cosh(x) + (1216\|2 + 960)cosh(x) +--R + +--R +-+ +--R (- 3568\|2 - 4576)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (504\|2 + 672)cosh(x) + (- 1060\|2 - 2544)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 4432\|2 - 4864)cosh(x) + 1212\|2 + 1616 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (288\|2 + 384)cosh(x) + (- 2384\|2 - 4512)cosh(x) +--R + +--R +-+ 3 +-+ +--R (368\|2 + 3040)cosh(x) + (2912\|2 + 3584)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 90\|2 - 120)cosh(x) + (- 1060\|2 - 2544)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4216\|2 + 8992)cosh(x) + (1556\|2 + 944)cosh(x) - 654\|2 - 872 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 240\|2 - 320)cosh(x) + (1216\|2 + 960)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (368\|2 + 3040)cosh(x) + (- 288\|2 - 2048)cosh(x) +--R + +--R +-+ +--R (- 480\|2 - 480)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 156\|2 - 208)cosh(x) + (1886\|2 + 2280)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 4432\|2 - 4864)cosh(x) + (1556\|2 + 944)cosh(x) +--R + +--R +-+ 2 +-+ +--R (348\|2 + 784)cosh(x) + 126\|2 + 168 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 48\|2 - 64)cosh(x) + (1000\|2 + 1296)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 3568\|2 - 4576)cosh(x) + (2912\|2 + 3584)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 480\|2 - 480)cosh(x) + (184\|2 + 240)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 6\|2 - 8)cosh(x) + (198\|2 + 264)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 876\|2 - 1168)cosh(x) + (1212\|2 + 1616)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 654\|2 - 872)cosh(x) + (126\|2 + 168)cosh(x) +--R / +--R +-+ 12 +-+ 11 +--R (36\|2 + 48)sinh(x) + (224\|2 + 288)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((568\|2 + 672)cosh(x) - 552\|2 - 736)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((736\|2 + 672)cosh(x) + (- 2592\|2 - 3296)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (476\|2 - 48)cosh(x) + (- 4680\|2 - 5216)cosh(x) + 2844\|2 +--R + +--R 3792 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (64\|2 - 960)cosh(x) + (- 3840\|2 - 2176)cosh(x) +--R + +--R +-+ +--R (9664\|2 + 12096)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 112\|2 - 1344)cosh(x) + (- 912\|2 + 3904)cosh(x) +--R + +--R +-+ 2 +-+ +--R (11440\|2 + 11328)cosh(x) - 5424\|2 - 7232 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (64\|2 - 960)cosh(x) + (576\|2 + 6848)cosh(x) +--R + +--R +-+ 3 +-+ +--R (4288\|2 - 2880)cosh(x) + (- 13632\|2 - 16832)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (476\|2 - 48)cosh(x) + (- 912\|2 + 3904)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 664\|2 - 11808)cosh(x) + (- 8976\|2 - 6848)cosh(x) +--R + +--R +-+ +--R 2844\|2 + 3792 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (736\|2 + 672)cosh(x) + (- 3840\|2 - 2176)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (4288\|2 - 2880)cosh(x) + (- 1536\|2 + 5504)cosh(x) +--R + +--R +-+ +--R (5984\|2 + 7584)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (568\|2 + 672)cosh(x) + (- 4680\|2 - 5216)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (11440\|2 + 11328)cosh(x) + (- 8976\|2 - 6848)cosh(x) +--R + +--R +-+ 2 +-+ +--R (6552\|2 + 7968)cosh(x) - 552\|2 - 736 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (224\|2 + 288)cosh(x) + (- 2592\|2 - 3296)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (9664\|2 + 12096)cosh(x) + (- 13632\|2 - 16832)cosh(x) +--R + +--R +-+ 3 +-+ +--R (5984\|2 + 7584)cosh(x) + (- 672\|2 - 864)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (36\|2 + 48)cosh(x) + (- 552\|2 - 736)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (2844\|2 + 3792)cosh(x) + (- 5424\|2 - 7232)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (2844\|2 + 3792)cosh(x) + (- 552\|2 - 736)cosh(x) + 36\|2 + 48 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 36\|2 - 48)sinh(x) + (- 224\|2 - 288)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 568\|2 - 672)cosh(x) + 552\|2 + 736)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 736\|2 - 672)cosh(x) + (2592\|2 + 3296)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 476\|2 + 48)cosh(x) + (4680\|2 + 5216)cosh(x) - 2844\|2 +--R + +--R - 3792 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 64\|2 + 960)cosh(x) + (3840\|2 + 2176)cosh(x) +--R + +--R +-+ +--R (- 9664\|2 - 12096)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (112\|2 + 1344)cosh(x) + (912\|2 - 3904)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 11440\|2 - 11328)cosh(x) + 5424\|2 + 7232 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 64\|2 + 960)cosh(x) + (- 576\|2 - 6848)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 4288\|2 + 2880)cosh(x) + (13632\|2 + 16832)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 476\|2 + 48)cosh(x) + (912\|2 - 3904)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (664\|2 + 11808)cosh(x) + (8976\|2 + 6848)cosh(x) - 2844\|2 +--R + +--R - 3792 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 736\|2 - 672)cosh(x) + (3840\|2 + 2176)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 4288\|2 + 2880)cosh(x) + (1536\|2 - 5504)cosh(x) +--R + +--R +-+ +--R (- 5984\|2 - 7584)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 568\|2 - 672)cosh(x) + (4680\|2 + 5216)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 11440\|2 - 11328)cosh(x) + (8976\|2 + 6848)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 6552\|2 - 7968)cosh(x) + 552\|2 + 736 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 224\|2 - 288)cosh(x) + (2592\|2 + 3296)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 9664\|2 - 12096)cosh(x) + (13632\|2 + 16832)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 5984\|2 - 7584)cosh(x) + (672\|2 + 864)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 36\|2 - 48)cosh(x) + (552\|2 + 736)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 2844\|2 - 3792)cosh(x) + (5424\|2 + 7232)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 2844\|2 - 3792)cosh(x) + (552\|2 + 736)cosh(x) - 36\|2 - 48 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (9\|2 + 12)sinh(x) + (56\|2 + 72)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((142\|2 + 168)cosh(x) - 138\|2 - 184)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((184\|2 + 168)cosh(x) + (- 648\|2 - 824)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((119\|2 - 12)cosh(x) + (- 1170\|2 - 1304)cosh(x) + 711\|2 + 948) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (16\|2 - 240)cosh(x) + (- 960\|2 - 544)cosh(x) +--R + +--R +-+ +--R (2416\|2 + 3024)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 28\|2 - 336)cosh(x) + (- 228\|2 + 976)cosh(x) +--R + +--R +-+ 2 +-+ +--R (2860\|2 + 2832)cosh(x) - 1356\|2 - 1808 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (16\|2 - 240)cosh(x) + (144\|2 + 1712)cosh(x) +--R + +--R +-+ 3 +-+ +--R (1072\|2 - 720)cosh(x) + (- 3408\|2 - 4208)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (119\|2 - 12)cosh(x) + (- 228\|2 + 976)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 166\|2 - 2952)cosh(x) + (- 2244\|2 - 1712)cosh(x) + 711\|2 +--R + +--R 948 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (184\|2 + 168)cosh(x) + (- 960\|2 - 544)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (1072\|2 - 720)cosh(x) + (- 384\|2 + 1376)cosh(x) +--R + +--R +-+ +--R (1496\|2 + 1896)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (142\|2 + 168)cosh(x) + (- 1170\|2 - 1304)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (2860\|2 + 2832)cosh(x) + (- 2244\|2 - 1712)cosh(x) +--R + +--R +-+ 2 +-+ +--R (1638\|2 + 1992)cosh(x) - 138\|2 - 184 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (56\|2 + 72)cosh(x) + (- 648\|2 - 824)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (2416\|2 + 3024)cosh(x) + (- 3408\|2 - 4208)cosh(x) +--R + +--R +-+ 3 +-+ +--R (1496\|2 + 1896)cosh(x) + (- 168\|2 - 216)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (9\|2 + 12)cosh(x) + (- 138\|2 - 184)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (711\|2 + 948)cosh(x) + (- 1356\|2 - 1808)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (711\|2 + 948)cosh(x) + (- 138\|2 - 184)cosh(x) + 9\|2 + 12 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 552 +t0771:= sinh(x)^2/(a+b*cosh(x)^2) +--R +--R +--R 2 +--R sinh(x) +--R (374) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 382 + +--S 383 of 552 +r0771:= x/b-(a+b)^(1/2)*atanh(a^(1/2)*tanh(x)/(a+b)^(1/2))/a^(1/2)/b +--R +--R +--R +-+ +--R +-----+ tanh(x)\|a +-+ +--R - \|b + a atanh(-----------) + x\|a +--R +-----+ +--R \|b + a +--R (375) ------------------------------------ +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 383 + +--S 384 of 552 +a0771:= integrate(t0771,x) +--R +--R +--R (376) +--R [ +--R +-----+ +--R |b + a +--R |----- +--R \| a +--R * +--R log +--R 2 2 +--R 4a b sinh(x) + 8a b cosh(x)sinh(x) + 4a b cosh(x) + 4a b +--R + +--R 2 +--R 8a +--R * +--R +-----+ +--R |b + a +--R |----- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2x +--R / +--R 2b +--R , +--R +-------+ +--R |- b - a +--R +-------+ 2a |------- +--R |- b - a \| a +--R - |------- atan(----------------------------------------------------) + x +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R --------------------------------------------------------------------------] +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 384 + +--S 385 of 552 +m0771a:= a0771.1-r0771 +--R +--R +--R (377) +--R +-----+ +--R +-+ |b + a +--R \|a |----- +--R \| a +--R * +--R log +--R 2 2 +--R 4a b sinh(x) + 8a b cosh(x)sinh(x) + 4a b cosh(x) + 4a b +--R + +--R 2 +--R 8a +--R * +--R +-----+ +--R |b + a +--R |----- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R +-+ +--R +-----+ tanh(x)\|a +--R 2\|b + a atanh(-----------) +--R +-----+ +--R \|b + a +--R / +--R +-+ +--R 2b\|a +--R Type: Expression(Integer) +--E 385 + +--S 386 of 552 +d0771a:= D(m0771a,x) +--R +--R +--R (378) +--R 4 3 +--R (b + a)sinh(x) + (4b + 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((6b + 6a)cosh(x) + 2b + 2a)sinh(x) +--R + +--R 3 4 +--R ((4b + 4a)cosh(x) + (4b + 4a)cosh(x))sinh(x) + (b + a)cosh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x) + b + a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R (- b - a)sinh(x) + (- 4b - 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((- 6b - 6a)cosh(x) + 2b + 2a)sinh(x) +--R + +--R 3 4 +--R ((- 4b - 4a)cosh(x) + (4b + 4a)cosh(x))sinh(x) + (- b - a)cosh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x) - b - a +--R / +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) + 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (2a b + 4a )cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (- b - a b)sinh(x) + (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 6a b)cosh(x) - 2b - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4b - 4a b)cosh(x) + (- 4b - 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- b - a b)cosh(x) + (- 2b - 6a b - 4a )cosh(x) - b - a b +--R Type: Expression(Integer) +--E 386 + +--S 387 of 552 +m0771b:= a0771.2-r0771 +--R +--R +--R (379) +--R +-+ +--R +-----+ tanh(x)\|a +--R \|b + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +-------+ +--R |- b - a +--R +-------+ 2a |------- +--R |- b - a +-+ \| a +--R - |------- \|a atan(----------------------------------------------------) +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R / +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 387 + +--S 388 of 552 +d0771b:= D(m0771b,x) +--R +--R +--R (380) +--R 4 3 +--R (b + a)sinh(x) + (4b + 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((6b + 6a)cosh(x) + 2b + 2a)sinh(x) +--R + +--R 3 4 +--R ((4b + 4a)cosh(x) + (4b + 4a)cosh(x))sinh(x) + (b + a)cosh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x) + b + a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 +--R (- b - a)sinh(x) + (- 4b - 4a)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((- 6b - 6a)cosh(x) + 2b + 2a)sinh(x) +--R + +--R 3 4 +--R ((- 4b - 4a)cosh(x) + (4b + 4a)cosh(x))sinh(x) + (- b - a)cosh(x) +--R + +--R 2 +--R (2b + 2a)cosh(x) - b - a +--R / +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) + 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (2a b + 4a )cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (- b - a b)sinh(x) + (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 6a b)cosh(x) - 2b - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4b - 4a b)cosh(x) + (- 4b - 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- b - a b)cosh(x) + (- 2b - 6a b - 4a )cosh(x) - b - a b +--R Type: Expression(Integer) +--E 388 + +--S 389 of 552 +t0772:= sinh(x)^3/(a+b*cosh(x)^2) +--R +--R +--R 3 +--R sinh(x) +--R (381) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 389 + +--S 390 of 552 +r0772:= -(a+b)*atan(b^(1/2)*cosh(x)/a^(1/2))/a^(1/2)/b^(3/2)+cosh(x)/b +--R +--R +--R +-+ +--R cosh(x)\|b +-+ +-+ +--R (- b - a)atan(-----------) + cosh(x)\|a \|b +--R +-+ +--R \|a +--R (382) -------------------------------------------- +--R +-+ +-+ +--R b\|a \|b +--R Type: Expression(Integer) +--E 390 + +--S 391 of 552 +a0772:= integrate(t0772,x) +--R +--R +--R (383) +--R [ +--R ((b + a)sinh(x) + (b + a)cosh(x)) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R - 4a b sinh(x) - 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 12a b cosh(x) - 4a b)sinh(x) - 4a b cosh(x) - 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 2 +-----+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|- a b +--R / +--R +-----+ +--R (2b sinh(x) + 2b cosh(x))\|- a b +--R , +--R +--R ((- 2b - 2a)sinh(x) + (- 2b - 2a)cosh(x)) +--R * +--R +---+ +--R (sinh(x) + cosh(x))\|a b +--R atan(-------------------------) +--R 2a +--R + +--R ((2b + 2a)sinh(x) + (2b + 2a)cosh(x)) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) + b + 4a)sinh(x) + b cosh(x) + (b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 2 2 +---+ +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)\|a b +--R / +--R +---+ +--R (2b sinh(x) + 2b cosh(x))\|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 391 + +--S 392 of 552 +m0772a:= a0772.1-r0772 +--R +--R +--R (384) +--R +-+ +-+ +--R ((b + a)sinh(x) + (b + a)cosh(x))\|a \|b +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R - 4a b sinh(x) - 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 12a b cosh(x) - 4a b)sinh(x) - 4a b cosh(x) - 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R +-+ +--R +-----+ cosh(x)\|b +--R ((2b + 2a)sinh(x) + (2b + 2a)cosh(x))\|- a b atan(-----------) +--R +-+ +--R \|a +--R + +--R 2 2 +-----+ +-+ +-+ +--R (sinh(x) - cosh(x) + 1)\|- a b \|a \|b +--R / +--R +-----+ +-+ +-+ +--R (2b sinh(x) + 2b cosh(x))\|- a b \|a \|b +--R Type: Expression(Integer) +--E 392 + +--S 393 of 552 +d0772a:= D(m0772a,x) +--R +--R +--R (385) +--R 2 6 +--R (- b cosh(x) + 2b + a)sinh(x) +--R + +--R 3 5 +--R (- 4b cosh(x) + (10b + 6a)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 5b cosh(x) + (13b + 7a)cosh(x) + 4b + 5a)sinh(x) +--R + +--R 3 3 +--R ((- 4b - 4a)cosh(x) + (12b + 12a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (5b cosh(x) + (- 20b - 9a)cosh(x) + (13b + 6a)cosh(x) + 2b + 3a) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R 4b cosh(x) + (- 14b - 2a)cosh(x) + (8b - 4a)cosh(x) +--R + +--R (2b + 6a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) + (- 3b + a)cosh(x) + (3b - 3a)cosh(x) + (- b + 3a)cosh(x) +--R + +--R - a +--R / +--R 2 2 5 2 3 4 +--R (2b cosh(x) + 2a b)sinh(x) + (10b cosh(x) + 10a b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 3 +--R (20b cosh(x) + (4b + 28a b)cosh(x) + 4a b + 8a )sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (20b cosh(x) + (12b + 44a b)cosh(x) + (12a b + 24a )cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R 10b cosh(x) + (12b + 34a b)cosh(x) + (2b + 12a b + 24a )cosh(x) +--R + +--R 2a b +--R * +--R sinh(x) +--R + +--R 2 7 2 5 2 2 3 +--R 2b cosh(x) + (4b + 10a b)cosh(x) + (2b + 4a b + 8a )cosh(x) +--R + +--R 2a b cosh(x) +--R Type: Expression(Integer) +--E 393 + +--S 394 of 552 +m0772b:= a0772.2-r0772 +--R +--R +--R (386) +--R +-+ +-+ +--R ((- 2b - 2a)sinh(x) + (- 2b - 2a)cosh(x))\|a \|b +--R * +--R +---+ +--R (sinh(x) + cosh(x))\|a b +--R atan(-------------------------) +--R 2a +--R + +--R +-+ +--R +---+ cosh(x)\|b +--R ((2b + 2a)sinh(x) + (2b + 2a)cosh(x))\|a b atan(-----------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R ((2b + 2a)sinh(x) + (2b + 2a)cosh(x))\|a \|b +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) + b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 2 2 +-+ +-+ +---+ +--R (sinh(x) - cosh(x) + 1)\|a \|b \|a b +--R / +--R +-+ +-+ +---+ +--R (2b sinh(x) + 2b cosh(x))\|a \|b \|a b +--R Type: Expression(Integer) +--E 394 + +--S 395 of 552 +d0772b:= D(m0772b,x) +--R +--R +--R (387) +--R 2 6 +--R (- b cosh(x) + 2b + a)sinh(x) +--R + +--R 3 5 +--R (- 4b cosh(x) + (10b + 6a)cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 5b cosh(x) + (13b + 7a)cosh(x) + 4b + 5a)sinh(x) +--R + +--R 3 3 +--R ((- 4b - 4a)cosh(x) + (12b + 12a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (5b cosh(x) + (- 20b - 9a)cosh(x) + (13b + 6a)cosh(x) + 2b + 3a) +--R * +--R 2 +--R sinh(x) +--R + +--R 7 5 3 +--R 4b cosh(x) + (- 14b - 2a)cosh(x) + (8b - 4a)cosh(x) +--R + +--R (2b + 6a)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R b cosh(x) + (- 3b + a)cosh(x) + (3b - 3a)cosh(x) + (- b + 3a)cosh(x) +--R + +--R - a +--R / +--R 2 2 5 2 3 4 +--R (2b cosh(x) + 2a b)sinh(x) + (10b cosh(x) + 10a b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 3 +--R (20b cosh(x) + (4b + 28a b)cosh(x) + 4a b + 8a )sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (20b cosh(x) + (12b + 44a b)cosh(x) + (12a b + 24a )cosh(x))sinh(x) +--R + +--R 2 6 2 4 2 2 2 +--R 10b cosh(x) + (12b + 34a b)cosh(x) + (2b + 12a b + 24a )cosh(x) +--R + +--R 2a b +--R * +--R sinh(x) +--R + +--R 2 7 2 5 2 2 3 +--R 2b cosh(x) + (4b + 10a b)cosh(x) + (2b + 4a b + 8a )cosh(x) +--R + +--R 2a b cosh(x) +--R Type: Expression(Integer) +--E 395 + +--S 396 of 552 +t0773:= sinh(x)^4/(a+b*cosh(x)^2) +--R +--R +--R 4 +--R sinh(x) +--R (388) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 396 + +--S 397 of 552 +r0773:= -a*x/b^2-3/2*x/b+(a+b)^(3/2)*atanh(a^(1/2)*tanh(x)/_ + (a+b)^(1/2))/a^(1/2)/b^2+1/2*cosh(x)*sinh(x)/b +--R +--R +--R (389) +--R +-+ +--R +-----+ tanh(x)\|a +-+ +--R (2b + 2a)\|b + a atanh(-----------) + (b cosh(x)sinh(x) + (- 3b - 2a)x)\|a +--R +-----+ +--R \|b + a +--R --------------------------------------------------------------------------- +--R 2 +-+ +--R 2b \|a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 552 +a0773:= integrate(t0773,x) +--R +--R +--R (390) +--R [ +--R 2 2 +--R ((4b + 4a)sinh(x) + (8b + 8a)cosh(x)sinh(x) + (4b + 4a)cosh(x) ) +--R * +--R +-----+ +--R |b + a +--R |----- +--R \| a +--R * +--R log +--R 2 2 +--R - 4a b sinh(x) - 8a b cosh(x)sinh(x) - 4a b cosh(x) +--R + +--R 2 +--R - 4a b - 8a +--R * +--R +-----+ +--R |b + a +--R |----- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + (- 12b - 8a)x)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 24b - 16a)x cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 12b - 8a)x cosh(x) - b +--R / +--R 2 2 2 2 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R , +--R +--R 2 2 +--R ((8b + 8a)sinh(x) + (16b + 16a)cosh(x)sinh(x) + (8b + 8a)cosh(x) ) +--R * +--R +-------+ +--R |- b - a +--R +-------+ 2a |------- +--R |- b - a \| a +--R |------- atan(----------------------------------------------------) +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + (- 12b - 8a)x)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 24b - 16a)x cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 12b - 8a)x cosh(x) - b +--R / +--R 2 2 2 2 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 398 + +--S 399 of 552 +m0773a:= a0773.1-r0773 +--R +--R +--R (391) +--R 2 2 +-+ +--R ((4b + 4a)sinh(x) + (8b + 8a)cosh(x)sinh(x) + (4b + 4a)cosh(x) )\|a +--R * +--R +-----+ +--R |b + a +--R |----- +--R \| a +--R * +--R log +--R 2 2 +--R - 4a b sinh(x) - 8a b cosh(x)sinh(x) - 4a b cosh(x) - 4a b +--R + +--R 2 +--R - 8a +--R * +--R +-----+ +--R |b + a +--R |----- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 +--R (- 8b - 8a)sinh(x) + (- 16b - 16a)cosh(x)sinh(x) +--R + +--R 2 +--R (- 8b - 8a)cosh(x) +--R * +--R +-+ +--R +-----+ tanh(x)\|a +--R \|b + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 2 2 4 +-+ +--R (b sinh(x) - 2b cosh(x) sinh(x) + b cosh(x) - b)\|a +--R / +--R 2 2 2 2 2 +-+ +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|a +--R Type: Expression(Integer) +--E 399 + +--S 400 of 552 +d0773a:= D(m0773a,x) +--R +--R +--R (392) +--R 8 7 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (- 4a b cosh(x) - 4b - 10a b - 8a )sinh(x) +--R + +--R 3 2 2 5 +--R (4a b cosh(x) + (- 24b - 52a b - 32a )cosh(x))sinh(x) +--R + +--R 4 2 2 2 2 +--R 10a b cosh(x) + (- 60b - 118a b - 56a )cosh(x) - 8b - 16a b +--R + +--R 2 +--R - 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 2 3 +--R 4a b cosh(x) + (- 80b - 152a b - 64a )cosh(x) +--R + +--R 2 2 +--R (- 32b - 60a b - 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 2 4 +--R - 4a b cosh(x) + (- 60b - 118a b - 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 48b - 88a b - 48a )cosh(x) - 4b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 2 5 +--R - 4a b cosh(x) + (- 24b - 52a b - 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 32b - 60a b - 32a )cosh(x) + (- 8b - 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 2 2 6 +--R - a b cosh(x) + (- 4b - 10a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 +--R (- 8b - 16a b - 8a )cosh(x) + (- 4b - 6a b)cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 8 2 7 +--R (b + a b)sinh(x) + (4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((4b + 4a b)cosh(x) + 6b + 14a b + 8a )sinh(x) +--R + +--R 2 3 2 2 5 +--R ((- 4b - 4a b)cosh(x) + (28b + 60a b + 32a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 10b - 10a b)cosh(x) + (58b + 114a b + 56a )cosh(x) - 8b +--R + +--R 2 +--R - 16a b - 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (- 4b - 4a b)cosh(x) + (72b + 136a b + 64a )cosh(x) +--R + +--R 2 2 +--R (- 36b - 68a b - 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (4b + 4a b)cosh(x) + (58b + 114a b + 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 56b - 104a b - 48a )cosh(x) + 2b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R (4b + 4a b)cosh(x) + (28b + 60a b + 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 36b - 68a b - 32a )cosh(x) + (4b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R (b + a b)cosh(x) + (6b + 14a b + 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 8b - 16a b - 8a )cosh(x) + (2b + 2a b)cosh(x) - b - a b +--R / +--R 2 6 2 5 +--R 4a b sinh(x) + 24a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (60a b cosh(x) + 8a b + 16a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (80a b cosh(x) + (32a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 2 +--R (60a b cosh(x) + (48a b + 96a b)cosh(x) + 4a b )sinh(x) +--R + +--R 2 5 2 2 3 2 +--R (24a b cosh(x) + (32a b + 64a b)cosh(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 2 2 +--R 4a b cosh(x) + (8a b + 16a b)cosh(x) + 4a b cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 6 3 2 5 +--R (- 4b - 4a b )sinh(x) + (- 24b - 24a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 4 +--R ((- 60b - 60a b )cosh(x) - 8b - 24a b - 16a b)sinh(x) +--R + +--R 3 2 3 3 2 2 3 +--R ((- 80b - 80a b )cosh(x) + (- 32b - 96a b - 64a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 3 +--R (- 60b - 60a b )cosh(x) + (- 48b - 144a b - 96a b)cosh(x) - 4b +--R + +--R 2 +--R - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (- 24b - 24a b )cosh(x) + (- 32b - 96a b - 64a b)cosh(x) +--R + +--R 3 2 +--R (- 8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 4b - 4a b )cosh(x) + (- 8b - 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (- 4b - 4a b )cosh(x) +--R Type: Expression(Integer) +--E 400 + +--S 401 of 552 +m0773b:= a0773.2-r0773 +--R +--R +--R (393) +--R 2 +--R (- 8b - 8a)sinh(x) + (- 16b - 16a)cosh(x)sinh(x) +--R + +--R 2 +--R (- 8b - 8a)cosh(x) +--R * +--R +-+ +--R +-----+ tanh(x)\|a +--R \|b + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 2 +--R ((8b + 8a)sinh(x) + (16b + 16a)cosh(x)sinh(x) + (8b + 8a)cosh(x) ) +--R * +--R +-------+ +--R |- b - a +--R +-------+ 2a |------- +--R |- b - a +-+ \| a +--R |------- \|a atan(----------------------------------------------------) +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R 4 2 2 4 +-+ +--R (b sinh(x) - 2b cosh(x) sinh(x) + b cosh(x) - b)\|a +--R / +--R 2 2 2 2 2 +-+ +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 552 +d0773b:= D(m0773b,x) +--R +--R +--R (394) +--R 8 7 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (- 4a b cosh(x) - 4b - 10a b - 8a )sinh(x) +--R + +--R 3 2 2 5 +--R (4a b cosh(x) + (- 24b - 52a b - 32a )cosh(x))sinh(x) +--R + +--R 4 2 2 2 2 +--R 10a b cosh(x) + (- 60b - 118a b - 56a )cosh(x) - 8b - 16a b +--R + +--R 2 +--R - 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 2 3 +--R 4a b cosh(x) + (- 80b - 152a b - 64a )cosh(x) +--R + +--R 2 2 +--R (- 32b - 60a b - 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 2 4 +--R - 4a b cosh(x) + (- 60b - 118a b - 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 48b - 88a b - 48a )cosh(x) - 4b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 2 5 +--R - 4a b cosh(x) + (- 24b - 52a b - 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 32b - 60a b - 32a )cosh(x) + (- 8b - 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 8 2 2 6 +--R - a b cosh(x) + (- 4b - 10a b - 8a )cosh(x) +--R + +--R 2 2 4 2 2 +--R (- 8b - 16a b - 8a )cosh(x) + (- 4b - 6a b)cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 8 2 7 +--R (b + a b)sinh(x) + (4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((4b + 4a b)cosh(x) + 6b + 14a b + 8a )sinh(x) +--R + +--R 2 3 2 2 5 +--R ((- 4b - 4a b)cosh(x) + (28b + 60a b + 32a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- 10b - 10a b)cosh(x) + (58b + 114a b + 56a )cosh(x) - 8b +--R + +--R 2 +--R - 16a b - 8a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (- 4b - 4a b)cosh(x) + (72b + 136a b + 64a )cosh(x) +--R + +--R 2 2 +--R (- 36b - 68a b - 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (4b + 4a b)cosh(x) + (58b + 114a b + 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 56b - 104a b - 48a )cosh(x) + 2b + 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R (4b + 4a b)cosh(x) + (28b + 60a b + 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 36b - 68a b - 32a )cosh(x) + (4b + 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R (b + a b)cosh(x) + (6b + 14a b + 8a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 8b - 16a b - 8a )cosh(x) + (2b + 2a b)cosh(x) - b - a b +--R / +--R 2 6 2 5 +--R 4a b sinh(x) + 24a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (60a b cosh(x) + 8a b + 16a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (80a b cosh(x) + (32a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 2 +--R (60a b cosh(x) + (48a b + 96a b)cosh(x) + 4a b )sinh(x) +--R + +--R 2 5 2 2 3 2 +--R (24a b cosh(x) + (32a b + 64a b)cosh(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 2 2 +--R 4a b cosh(x) + (8a b + 16a b)cosh(x) + 4a b cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 6 3 2 5 +--R (- 4b - 4a b )sinh(x) + (- 24b - 24a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 4 +--R ((- 60b - 60a b )cosh(x) - 8b - 24a b - 16a b)sinh(x) +--R + +--R 3 2 3 3 2 2 3 +--R ((- 80b - 80a b )cosh(x) + (- 32b - 96a b - 64a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 3 +--R (- 60b - 60a b )cosh(x) + (- 48b - 144a b - 96a b)cosh(x) - 4b +--R + +--R 2 +--R - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (- 24b - 24a b )cosh(x) + (- 32b - 96a b - 64a b)cosh(x) +--R + +--R 3 2 +--R (- 8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 4b - 4a b )cosh(x) + (- 8b - 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (- 4b - 4a b )cosh(x) +--R Type: Expression(Integer) +--E 402 + +--S 403 of 552 +t0774:= sinh(x)^5/(a+b*cosh(x)^2) +--R +--R +--R 5 +--R sinh(x) +--R (395) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 552 +r0774:= (a+b)^2*atan(b^(1/2)*cosh(x)/a^(1/2))/a^(1/2)/b^(5/2)-_ + a*cosh(x)/b^2-2*cosh(x)/b+1/3*cosh(x)^3/b +--R +--R +--R (396) +--R +-+ +--R 2 2 cosh(x)\|b +--R (3b + 6a b + 3a )atan(-----------) +--R +-+ +--R \|a +--R + +--R 3 +-+ +-+ +--R (b cosh(x) + (- 6b - 3a)cosh(x))\|a \|b +--R / +--R 2 +-+ +-+ +--R 3b \|a \|b +--R Type: Expression(Integer) +--E 404 + +--S 405 of 552 +a0774:= integrate(t0774,x) +--R +--R +--R (397) +--R [ +--R 2 2 3 +--R (12b + 24a b + 12a )sinh(x) +--R + +--R 2 2 2 +--R (36b + 72a b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (36b + 72a b + 36a )cosh(x) sinh(x) + (12b + 24a b + 12a )cosh(x) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R 4a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (12a b cosh(x) + 4a b)sinh(x) + 4a b cosh(x) + 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 6 5 +--R b sinh(x) + 6b cosh(x)sinh(x) +--R + +--R 2 4 +--R (15b cosh(x) - 21b - 12a)sinh(x) +--R + +--R 3 3 +--R (20b cosh(x) + (- 84b - 48a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) + (- 126b - 72a)cosh(x) - 21b - 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (- 84b - 48a)cosh(x) + (- 42b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (- 21b - 12a)cosh(x) + (- 21b - 12a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R / +--R 2 3 2 2 2 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 2 3 +--R 24b cosh(x) +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 2 2 3 +--R (24b + 48a b + 24a )sinh(x) +--R + +--R 2 2 2 +--R (72b + 144a b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (72b + 144a b + 72a )cosh(x) sinh(x) + (24b + 48a b + 24a )cosh(x) +--R * +--R +---+ +--R (sinh(x) + cosh(x))\|a b +--R atan(-------------------------) +--R 2a +--R + +--R 2 2 3 +--R (- 24b - 48a b - 24a )sinh(x) +--R + +--R 2 2 2 +--R (- 72b - 144a b - 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 72b - 144a b - 72a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 24b - 48a b - 24a )cosh(x) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) + b + 4a)sinh(x) + b cosh(x) + (b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 6 5 +--R b sinh(x) + 6b cosh(x)sinh(x) +--R + +--R 2 4 +--R (15b cosh(x) - 21b - 12a)sinh(x) +--R + +--R 3 3 +--R (20b cosh(x) + (- 84b - 48a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) + (- 126b - 72a)cosh(x) - 21b - 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (- 84b - 48a)cosh(x) + (- 42b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (- 21b - 12a)cosh(x) + (- 21b - 12a)cosh(x) + b +--R * +--R +---+ +--R \|a b +--R / +--R 2 3 2 2 2 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 2 3 +--R 24b cosh(x) +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 405 + +--S 406 of 552 +m0774a:= a0774.1-r0774 +--R +--R +--R (398) +--R 2 2 3 2 2 2 +--R (12b + 24a b + 12a )sinh(x) + (36b + 72a b + 36a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (36b + 72a b + 36a )cosh(x) sinh(x) + (12b + 24a b + 12a )cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R 4a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (12a b cosh(x) + 4a b)sinh(x) + 4a b cosh(x) + 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 2 3 +--R (- 24b - 48a b - 24a )sinh(x) +--R + +--R 2 2 2 +--R (- 72b - 144a b - 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 72b - 144a b - 72a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 24b - 48a b - 24a )cosh(x) +--R * +--R +-+ +--R +-----+ cosh(x)\|b +--R \|- a b atan(-----------) +--R +-+ +--R \|a +--R + +--R 6 5 2 4 +--R b sinh(x) + 6b cosh(x)sinh(x) + (15b cosh(x) - 21b - 12a)sinh(x) +--R + +--R 3 3 +--R (12b cosh(x) + (- 36b - 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 9b cosh(x) + 18b cosh(x) - 21b - 12a)sinh(x) +--R + +--R 5 3 +--R (- 18b cosh(x) + (60b + 24a)cosh(x) + (- 42b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 7b cosh(x) + (27b + 12a)cosh(x) + (- 21b - 12a)cosh(x) + b +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R / +--R 2 3 2 2 2 2 2 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 406 + +--S 407 of 552 +d0774a:= D(m0774a,x) +--R +--R +--R (399) +--R 2 10 3 9 +--R (b cosh(x) + a)sinh(x) + (10b cosh(x) + 10a cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (37b cosh(x) + (11b + 45a)cosh(x) - 8b - 5a)sinh(x) +--R + +--R 5 3 7 +--R (64b cosh(x) + (72b + 120a)cosh(x) + (- 56b - 40a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 42b cosh(x) + (180b + 178a)cosh(x) + (- 126b - 76a)cosh(x) - 16b +--R + +--R - 22a +--R * +--R 6 +--R sinh(x) +--R + +--R 7 5 3 +--R - 28b cosh(x) + (200b + 92a)cosh(x) + (- 60b + 40a)cosh(x) +--R + +--R (- 80b - 100a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 4 +--R - 70b cosh(x) + (50b - 110a)cosh(x) + (182b + 290a)cosh(x) +--R + +--R 2 +--R (- 154b - 170a)cosh(x) - 8b - 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 +--R - 48b cosh(x) + (- 104b - 200a)cosh(x) + (328b + 360a)cosh(x) +--R + +--R 3 +--R (- 152b - 120a)cosh(x) + (- 24b - 40a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 +--R - 11b cosh(x) + (- 108b - 115a)cosh(x) + (230b + 180a)cosh(x) +--R + +--R 4 2 +--R (- 92b - 10a)cosh(x) + (- 19b - 60a)cosh(x) + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 +--R 2b cosh(x) + (- 40b - 22a)cosh(x) + (76b + 24a)cosh(x) +--R + +--R 5 3 +--R (- 40b + 28a)cosh(x) + (2b - 40a)cosh(x) + 10a cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 +--R b cosh(x) + (- 5b + a)cosh(x) + (10b - 5a)cosh(x) +--R + +--R 6 4 2 +--R (- 10b + 10a)cosh(x) + (5b - 10a)cosh(x) + (- b + 5a)cosh(x) - a +--R / +--R 2 2 7 2 3 6 +--R (8b cosh(x) + 8a b)sinh(x) + (56b cosh(x) + 56a b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 5 +--R (168b cosh(x) + (16b + 200a b)cosh(x) + 16a b + 32a )sinh(x) +--R + +--R 2 5 2 3 2 +--R (280b cosh(x) + (80b + 440a b)cosh(x) + (80a b + 160a )cosh(x)) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 280b cosh(x) + (160b + 600a b)cosh(x) +--R + +--R 2 2 2 +--R (8b + 160a b + 320a )cosh(x) + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 168b cosh(x) + (160b + 488a b)cosh(x) +--R + +--R 2 2 3 +--R (24b + 160a b + 320a )cosh(x) + 24a b cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 56b cosh(x) + (80b + 216a b)cosh(x) +--R + +--R 2 2 4 2 +--R (24b + 80a b + 160a )cosh(x) + 24a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 9 2 7 2 2 5 +--R 8b cosh(x) + (16b + 40a b)cosh(x) + (8b + 16a b + 32a )cosh(x) +--R + +--R 3 +--R 8a b cosh(x) +--R Type: Expression(Integer) +--E 407 + +--S 408 of 552 +m0774b:= a0774.2-r0774 +--R +--R +--R (400) +--R 2 2 3 2 2 2 +--R (24b + 48a b + 24a )sinh(x) + (72b + 144a b + 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (72b + 144a b + 72a )cosh(x) sinh(x) + (24b + 48a b + 24a )cosh(x) +--R * +--R +---+ +--R +-+ +-+ (sinh(x) + cosh(x))\|a b +--R \|a \|b atan(-------------------------) +--R 2a +--R + +--R 2 2 3 +--R (- 24b - 48a b - 24a )sinh(x) +--R + +--R 2 2 2 +--R (- 72b - 144a b - 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 72b - 144a b - 72a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 24b - 48a b - 24a )cosh(x) +--R * +--R +-+ +--R +---+ cosh(x)\|b +--R \|a b atan(-----------) +--R +-+ +--R \|a +--R + +--R 2 2 3 +--R (- 24b - 48a b - 24a )sinh(x) +--R + +--R 2 2 2 +--R (- 72b - 144a b - 72a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- 72b - 144a b - 72a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 24b - 48a b - 24a )cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) + b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 6 5 2 4 +--R b sinh(x) + 6b cosh(x)sinh(x) + (15b cosh(x) - 21b - 12a)sinh(x) +--R + +--R 3 3 +--R (12b cosh(x) + (- 36b - 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 9b cosh(x) + 18b cosh(x) - 21b - 12a)sinh(x) +--R + +--R 5 3 +--R (- 18b cosh(x) + (60b + 24a)cosh(x) + (- 42b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R - 7b cosh(x) + (27b + 12a)cosh(x) + (- 21b - 12a)cosh(x) + b +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R / +--R 2 3 2 2 2 2 2 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 408 + +--S 409 of 552 +d0774b:= D(m0774b,x) +--R +--R +--R (401) +--R 2 10 3 9 +--R (b cosh(x) + a)sinh(x) + (10b cosh(x) + 10a cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (37b cosh(x) + (11b + 45a)cosh(x) - 8b - 5a)sinh(x) +--R + +--R 5 3 7 +--R (64b cosh(x) + (72b + 120a)cosh(x) + (- 56b - 40a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 42b cosh(x) + (180b + 178a)cosh(x) + (- 126b - 76a)cosh(x) - 16b +--R + +--R - 22a +--R * +--R 6 +--R sinh(x) +--R + +--R 7 5 3 +--R - 28b cosh(x) + (200b + 92a)cosh(x) + (- 60b + 40a)cosh(x) +--R + +--R (- 80b - 100a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 4 +--R - 70b cosh(x) + (50b - 110a)cosh(x) + (182b + 290a)cosh(x) +--R + +--R 2 +--R (- 154b - 170a)cosh(x) - 8b - 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 +--R - 48b cosh(x) + (- 104b - 200a)cosh(x) + (328b + 360a)cosh(x) +--R + +--R 3 +--R (- 152b - 120a)cosh(x) + (- 24b - 40a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 +--R - 11b cosh(x) + (- 108b - 115a)cosh(x) + (230b + 180a)cosh(x) +--R + +--R 4 2 +--R (- 92b - 10a)cosh(x) + (- 19b - 60a)cosh(x) + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 +--R 2b cosh(x) + (- 40b - 22a)cosh(x) + (76b + 24a)cosh(x) +--R + +--R 5 3 +--R (- 40b + 28a)cosh(x) + (2b - 40a)cosh(x) + 10a cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 +--R b cosh(x) + (- 5b + a)cosh(x) + (10b - 5a)cosh(x) +--R + +--R 6 4 2 +--R (- 10b + 10a)cosh(x) + (5b - 10a)cosh(x) + (- b + 5a)cosh(x) - a +--R / +--R 2 2 7 2 3 6 +--R (8b cosh(x) + 8a b)sinh(x) + (56b cosh(x) + 56a b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 5 +--R (168b cosh(x) + (16b + 200a b)cosh(x) + 16a b + 32a )sinh(x) +--R + +--R 2 5 2 3 2 +--R (280b cosh(x) + (80b + 440a b)cosh(x) + (80a b + 160a )cosh(x)) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 280b cosh(x) + (160b + 600a b)cosh(x) +--R + +--R 2 2 2 +--R (8b + 160a b + 320a )cosh(x) + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 168b cosh(x) + (160b + 488a b)cosh(x) +--R + +--R 2 2 3 +--R (24b + 160a b + 320a )cosh(x) + 24a b cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 56b cosh(x) + (80b + 216a b)cosh(x) +--R + +--R 2 2 4 2 +--R (24b + 80a b + 160a )cosh(x) + 24a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 9 2 7 2 2 5 +--R 8b cosh(x) + (16b + 40a b)cosh(x) + (8b + 16a b + 32a )cosh(x) +--R + +--R 3 +--R 8a b cosh(x) +--R Type: Expression(Integer) +--E 409 + +--S 410 of 552 +t0775:= sinh(x)^6/(a+b*cosh(x)^2) +--R +--R +--R 6 +--R sinh(x) +--R (402) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 552 +r0775:= 1/2*a*x/b^2+7/8*x/b+(a+b)^2*x/b^3-(a+b)^(5/2)*_ + atanh(a^(1/2)*tanh(x)/(a+b)^(1/2))/a^(1/2)/b^3-_ + 1/2*a*cosh(x)*sinh(x)/b^2-7/8*cosh(x)*sinh(x)/b+_ + 1/4*cosh(x)*sinh(x)^3/b +--R +--R +--R (403) +--R +-+ +--R 2 2 +-----+ tanh(x)\|a +--R (- 8b - 16a b - 8a )\|b + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 +--R 2b cosh(x)sinh(x) + (- 7b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 +--R (15b + 20a b + 8a )x +--R * +--R +-+ +--R \|a +--R / +--R 3 +-+ +--R 8b \|a +--R Type: Expression(Integer) +--E 411 + +--S 412 of 552 +a0775:= integrate(t0775,x) +--R +--R +--R (404) +--R [ +--R 2 2 4 +--R (32b + 64a b + 32a )sinh(x) +--R + +--R 2 2 3 +--R (128b + 256a b + 128a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (192b + 384a b + 192a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (128b + 256a b + 128a )cosh(x) sinh(x) +--R + +--R 2 2 4 +--R (32b + 64a b + 32a )cosh(x) +--R * +--R +-----+ +--R |b + a +--R |----- +--R \| a +--R * +--R log +--R 2 2 +--R 4a b sinh(x) + 8a b cosh(x)sinh(x) + 4a b cosh(x) + 4a b +--R + +--R 2 +--R 8a +--R * +--R +-----+ +--R |b + a +--R |----- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) - 16b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (56b cosh(x) + (- 96b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R 70b cosh(x) + (- 240b - 120a b)cosh(x) +--R + +--R 2 2 +--R (120b + 160a b + 64a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 56b cosh(x) + (- 320b - 160a b)cosh(x) +--R + +--R 2 2 +--R (480b + 640a b + 256a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 28b cosh(x) + (- 240b - 120a b)cosh(x) +--R + +--R 2 2 2 2 +--R (720b + 960a b + 384a )x cosh(x) + 16b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (- 96b - 48a b)cosh(x) +--R + +--R 2 2 3 2 +--R (480b + 640a b + 256a )x cosh(x) + (32b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 +--R b cosh(x) + (- 16b - 8a b)cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (120b + 160a b + 64a )x cosh(x) + (16b + 8a b)cosh(x) - b +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R , +--R +--R 2 2 4 +--R (- 64b - 128a b - 64a )sinh(x) +--R + +--R 2 2 3 +--R (- 256b - 512a b - 256a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 384b - 768a b - 384a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 256b - 512a b - 256a )cosh(x) sinh(x) +--R + +--R 2 2 4 +--R (- 64b - 128a b - 64a )cosh(x) +--R * +--R +-------+ +--R |- b - a +--R +-------+ 2a |------- +--R |- b - a \| a +--R |------- atan(----------------------------------------------------) +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) - 16b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (56b cosh(x) + (- 96b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 +--R 70b cosh(x) + (- 240b - 120a b)cosh(x) +--R + +--R 2 2 +--R (120b + 160a b + 64a )x +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 56b cosh(x) + (- 320b - 160a b)cosh(x) +--R + +--R 2 2 +--R (480b + 640a b + 256a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 28b cosh(x) + (- 240b - 120a b)cosh(x) +--R + +--R 2 2 2 2 +--R (720b + 960a b + 384a )x cosh(x) + 16b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (- 96b - 48a b)cosh(x) +--R + +--R 2 2 3 2 +--R (480b + 640a b + 256a )x cosh(x) + (32b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 +--R b cosh(x) + (- 16b - 8a b)cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (120b + 160a b + 64a )x cosh(x) + (16b + 8a b)cosh(x) - b +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 412 + +--S 413 of 552 +m0775a:= a0775.1-r0775 +--R +--R +--R (405) +--R 2 2 4 +--R (32b + 64a b + 32a )sinh(x) +--R + +--R 2 2 3 +--R (128b + 256a b + 128a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (192b + 384a b + 192a )cosh(x) sinh(x) +--R + +--R 2 2 3 2 2 4 +--R (128b + 256a b + 128a )cosh(x) sinh(x) + (32b + 64a b + 32a )cosh(x) +--R * +--R +-----+ +--R +-+ |b + a +--R \|a |----- +--R \| a +--R * +--R log +--R 2 2 +--R 4a b sinh(x) + 8a b cosh(x)sinh(x) + 4a b cosh(x) + 4a b +--R + +--R 2 +--R 8a +--R * +--R +-----+ +--R |b + a +--R |----- +--R \| a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 2 4 +--R (64b + 128a b + 64a )sinh(x) +--R + +--R 2 2 3 +--R (256b + 512a b + 256a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (384b + 768a b + 384a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (256b + 512a b + 256a )cosh(x) sinh(x) +--R + +--R 2 2 4 +--R (64b + 128a b + 64a )cosh(x) +--R * +--R +-+ +--R +-----+ tanh(x)\|a +--R \|b + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 8 2 7 +--R b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (- 36b cosh(x) - 16b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (- 40b cosh(x) + (- 40b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R (6b cosh(x) + (- 16b + 8a b)cosh(x) )sinh(x) +--R + +--R 2 5 2 3 3 +--R (40b cosh(x) + (16b + 32a b)cosh(x) )sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (28b cosh(x) + (- 16b + 8a b)cosh(x) + 16b + 8a b)sinh(x) +--R + +--R 2 7 2 5 2 +--R (8b cosh(x) + (- 40b - 16a b)cosh(x) + (32b + 16a b)cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 2 +--R b cosh(x) + (- 16b - 8a b)cosh(x) + (16b + 8a b)cosh(x) - b +--R * +--R +-+ +--R \|a +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 552 +d0775a:= D(m0775a,x) +--R +--R +--R (406) +--R 2 12 2 11 +--R - 3a b sinh(x) - 20a b cosh(x)sinh(x) +--R + +--R 2 2 2 10 +--R (- 58a b cosh(x) - 8a b)sinh(x) +--R + +--R 2 3 2 2 9 +--R (- 100a b cosh(x) + (4a b - 32a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 3 2 +--R - 121a b cosh(x) + (- 8a b - 56a b)cosh(x) + 16b + 57a b +--R + +--R 2 3 +--R 80a b + 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R - 104a b cosh(x) + (- 128a b - 96a b)cosh(x) +--R + +--R 3 2 2 3 +--R (128b + 416a b + 496a b + 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R - 28a b cosh(x) + (- 368a b - 176a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (448b + 1336a b + 1376a b + 512a )cosh(x) + 32b + 94a b +--R + +--R 2 3 +--R 96a b + 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R 88a b cosh(x) + (- 472a b - 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (896b + 2512a b + 2320a b + 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (192b + 536a b + 560a b + 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R 155a b cosh(x) + (- 256a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (1120b + 3074a b + 2720a b + 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (480b + 1298a b + 1376a b + 480a )cosh(x) + 16b + 33a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 9 2 2 7 +--R 124a b cosh(x) + (32a b + 224a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (896b + 2528a b + 2320a b + 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (640b + 1712a b + 1824a b + 640a )cosh(x) +--R + +--R 3 2 2 +--R (64b + 132a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 2 2 8 +--R 54a b cosh(x) + (112a b + 184a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (448b + 1360a b + 1376a b + 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (480b + 1298a b + 1376a b + 480a )cosh(x) +--R + +--R 3 2 2 2 2 +--R (96b + 198a b + 48a b)cosh(x) - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 2 9 +--R 12a b cosh(x) + (52a b + 64a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (128b + 432a b + 496a b + 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (192b + 536a b + 560a b + 192a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (64b + 132a b + 32a b)cosh(x) - 12a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 12 2 2 10 +--R a b cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 8 +--R (16b + 61a b + 80a b + 32a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (32b + 94a b + 96a b + 32a )cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (16b + 33a b + 8a b)cosh(x) - 6a b cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 12 3 2 11 +--R (3b + 3a b )sinh(x) + (20b + 20a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 10 +--R ((58b + 58a b )cosh(x) + 8a b + 8a b)sinh(x) +--R + +--R 3 2 3 3 2 2 9 +--R ((100b + 100a b )cosh(x) + (- 4b + 28a b + 32a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 3 +--R (121b + 121a b )cosh(x) + (8b + 64a b + 56a b)cosh(x) - 25b +--R + +--R 2 2 3 +--R - 89a b - 96a b - 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (104b + 104a b )cosh(x) + (128b + 224a b + 96a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 160b - 528a b - 560a b - 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (28b + 28a b )cosh(x) + (368b + 544a b + 176a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 440b - 1368a b - 1440a b - 512a )cosh(x) + 34b + 98a b +--R + +--R 2 3 +--R 96a b + 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 7 3 2 2 5 +--R (- 88b - 88a b )cosh(x) + (472b + 632a b + 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 720b - 2144a b - 2256a b - 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (232b + 632a b + 592a b + 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 8 3 2 2 6 +--R (- 155b - 155a b )cosh(x) + (256b + 208a b - 48a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 834b - 2434a b - 2560a b - 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (622b + 1646a b + 1504a b + 480a )cosh(x) - b + 7a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 9 3 2 2 7 +--R (- 124b - 124a b )cosh(x) + (- 32b - 256a b - 224a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 736b - 2160a b - 2256a b - 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (848b + 2224a b + 2016a b + 640a )cosh(x) +--R + +--R 3 2 2 +--R (- 4b + 28a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 10 3 2 2 8 +--R (- 54b - 54a b )cosh(x) + (- 112b - 296a b - 184a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 464b - 1392a b - 1440a b - 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (622b + 1646a b + 1504a b + 480a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 6b + 42a b + 48a b)cosh(x) + 6b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 11 3 2 2 9 +--R (- 12b - 12a b )cosh(x) + (- 52b - 116a b - 64a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (- 176b - 544a b - 560a b - 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (232b + 632a b + 592a b + 192a )cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 4b + 28a b + 32a b)cosh(x) + (12b + 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 12 3 2 2 10 +--R (- b - a b )cosh(x) + (- 8b - 16a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 29b - 93a b - 96a b - 32a )cosh(x) +--R + +--R 3 2 2 3 6 3 2 2 4 +--R (34b + 98a b + 96a b + 32a )cosh(x) + (- b + 7a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b + 6a b )cosh(x) - b - a b +--R / +--R 3 8 3 7 +--R 16a b sinh(x) + 128a b cosh(x)sinh(x) +--R + +--R 3 2 3 2 2 6 +--R (448a b cosh(x) + 32a b + 64a b )sinh(x) +--R + +--R 3 3 3 2 2 5 +--R (896a b cosh(x) + (192a b + 384a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 2 3 4 +--R (1120a b cosh(x) + (480a b + 960a b )cosh(x) + 16a b )sinh(x) +--R + +--R 3 5 3 2 2 3 3 +--R (896a b cosh(x) + (640a b + 1280a b )cosh(x) + 64a b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 2 2 4 3 2 +--R (448a b cosh(x) + (480a b + 960a b )cosh(x) + 96a b cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 2 2 5 3 3 +--R (128a b cosh(x) + (192a b + 384a b )cosh(x) + 64a b cosh(x) ) +--R * +--R sinh(x) +--R + +--R 3 8 3 2 2 6 3 4 +--R 16a b cosh(x) + (32a b + 64a b )cosh(x) + 16a b cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 8 4 3 7 +--R (- 16b - 16a b )sinh(x) + (- 128b - 128a b )cosh(x)sinh(x) +--R + +--R 4 3 2 4 3 2 2 6 +--R ((- 448b - 448a b )cosh(x) - 32b - 96a b - 64a b )sinh(x) +--R + +--R 4 3 3 4 3 2 2 +--R ((- 896b - 896a b )cosh(x) + (- 192b - 576a b - 384a b )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 +--R (- 1120b - 1120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 480b - 1440a b - 960a b )cosh(x) - 16b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 4 3 2 2 3 +--R (- 896b - 896a b )cosh(x) + (- 640b - 1920a b - 1280a b )cosh(x) +--R + +--R 4 3 +--R (- 64b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 4 3 2 2 4 +--R (- 448b - 448a b )cosh(x) + (- 480b - 1440a b - 960a b )cosh(x) +--R + +--R 4 3 2 +--R (- 96b - 96a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 4 3 2 2 5 +--R (- 128b - 128a b )cosh(x) + (- 192b - 576a b - 384a b )cosh(x) +--R + +--R 4 3 3 +--R (- 64b - 64a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (- 16b - 16a b )cosh(x) + (- 32b - 96a b - 64a b )cosh(x) +--R + +--R 4 3 4 +--R (- 16b - 16a b )cosh(x) +--R Type: Expression(Integer) +--E 414 + +--S 415 of 552 +m0775b:= a0775.2-r0775 +--R +--R +--R (407) +--R 2 2 4 +--R (64b + 128a b + 64a )sinh(x) +--R + +--R 2 2 3 +--R (256b + 512a b + 256a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (384b + 768a b + 384a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (256b + 512a b + 256a )cosh(x) sinh(x) +--R + +--R 2 2 4 +--R (64b + 128a b + 64a )cosh(x) +--R * +--R +-+ +--R +-----+ tanh(x)\|a +--R \|b + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 2 4 +--R (- 64b - 128a b - 64a )sinh(x) +--R + +--R 2 2 3 +--R (- 256b - 512a b - 256a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 384b - 768a b - 384a )cosh(x) sinh(x) +--R + +--R 2 2 3 +--R (- 256b - 512a b - 256a )cosh(x) sinh(x) +--R + +--R 2 2 4 +--R (- 64b - 128a b - 64a )cosh(x) +--R * +--R +-------+ +--R |- b - a +--R +-------+ 2a |------- +--R |- b - a +-+ \| a +--R |------- \|a atan(----------------------------------------------------) +--R \| a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R 2 8 2 7 +--R b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 2 2 2 6 +--R (- 36b cosh(x) - 16b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (- 40b cosh(x) + (- 40b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R (6b cosh(x) + (- 16b + 8a b)cosh(x) )sinh(x) +--R + +--R 2 5 2 3 3 +--R (40b cosh(x) + (16b + 32a b)cosh(x) )sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (28b cosh(x) + (- 16b + 8a b)cosh(x) + 16b + 8a b)sinh(x) +--R + +--R 2 7 2 5 2 +--R (8b cosh(x) + (- 40b - 16a b)cosh(x) + (32b + 16a b)cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 2 +--R b cosh(x) + (- 16b - 8a b)cosh(x) + (16b + 8a b)cosh(x) - b +--R * +--R +-+ +--R \|a +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 415 + +--S 416 of 552 +d0775b:= D(m0775b,x) +--R +--R +--R (408) +--R 2 12 2 11 +--R - 3a b sinh(x) - 20a b cosh(x)sinh(x) +--R + +--R 2 2 2 10 +--R (- 58a b cosh(x) - 8a b)sinh(x) +--R + +--R 2 3 2 2 9 +--R (- 100a b cosh(x) + (4a b - 32a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 3 2 +--R - 121a b cosh(x) + (- 8a b - 56a b)cosh(x) + 16b + 57a b +--R + +--R 2 3 +--R 80a b + 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R - 104a b cosh(x) + (- 128a b - 96a b)cosh(x) +--R + +--R 3 2 2 3 +--R (128b + 416a b + 496a b + 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R - 28a b cosh(x) + (- 368a b - 176a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (448b + 1336a b + 1376a b + 512a )cosh(x) + 32b + 94a b +--R + +--R 2 3 +--R 96a b + 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R 88a b cosh(x) + (- 472a b - 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (896b + 2512a b + 2320a b + 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (192b + 536a b + 560a b + 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R 155a b cosh(x) + (- 256a b + 48a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (1120b + 3074a b + 2720a b + 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (480b + 1298a b + 1376a b + 480a )cosh(x) + 16b + 33a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 9 2 2 7 +--R 124a b cosh(x) + (32a b + 224a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (896b + 2528a b + 2320a b + 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (640b + 1712a b + 1824a b + 640a )cosh(x) +--R + +--R 3 2 2 +--R (64b + 132a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 2 2 8 +--R 54a b cosh(x) + (112a b + 184a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (448b + 1360a b + 1376a b + 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (480b + 1298a b + 1376a b + 480a )cosh(x) +--R + +--R 3 2 2 2 2 +--R (96b + 198a b + 48a b)cosh(x) - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 2 9 +--R 12a b cosh(x) + (52a b + 64a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (128b + 432a b + 496a b + 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (192b + 536a b + 560a b + 192a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (64b + 132a b + 32a b)cosh(x) - 12a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 12 2 2 10 +--R a b cosh(x) + (8a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 8 +--R (16b + 61a b + 80a b + 32a )cosh(x) +--R + +--R 3 2 2 3 6 +--R (32b + 94a b + 96a b + 32a )cosh(x) +--R + +--R 3 2 2 4 2 2 2 +--R (16b + 33a b + 8a b)cosh(x) - 6a b cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 12 3 2 11 +--R (3b + 3a b )sinh(x) + (20b + 20a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 10 +--R ((58b + 58a b )cosh(x) + 8a b + 8a b)sinh(x) +--R + +--R 3 2 3 3 2 2 9 +--R ((100b + 100a b )cosh(x) + (- 4b + 28a b + 32a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 3 +--R (121b + 121a b )cosh(x) + (8b + 64a b + 56a b)cosh(x) - 25b +--R + +--R 2 2 3 +--R - 89a b - 96a b - 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (104b + 104a b )cosh(x) + (128b + 224a b + 96a b)cosh(x) +--R + +--R 3 2 2 3 +--R (- 160b - 528a b - 560a b - 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (28b + 28a b )cosh(x) + (368b + 544a b + 176a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 440b - 1368a b - 1440a b - 512a )cosh(x) + 34b + 98a b +--R + +--R 2 3 +--R 96a b + 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 7 3 2 2 5 +--R (- 88b - 88a b )cosh(x) + (472b + 632a b + 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 720b - 2144a b - 2256a b - 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (232b + 632a b + 592a b + 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 8 3 2 2 6 +--R (- 155b - 155a b )cosh(x) + (256b + 208a b - 48a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 834b - 2434a b - 2560a b - 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (622b + 1646a b + 1504a b + 480a )cosh(x) - b + 7a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 9 3 2 2 7 +--R (- 124b - 124a b )cosh(x) + (- 32b - 256a b - 224a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 736b - 2160a b - 2256a b - 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (848b + 2224a b + 2016a b + 640a )cosh(x) +--R + +--R 3 2 2 +--R (- 4b + 28a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 10 3 2 2 8 +--R (- 54b - 54a b )cosh(x) + (- 112b - 296a b - 184a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 464b - 1392a b - 1440a b - 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (622b + 1646a b + 1504a b + 480a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 6b + 42a b + 48a b)cosh(x) + 6b + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 11 3 2 2 9 +--R (- 12b - 12a b )cosh(x) + (- 52b - 116a b - 64a b)cosh(x) +--R + +--R 3 2 2 3 7 +--R (- 176b - 544a b - 560a b - 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (232b + 632a b + 592a b + 192a )cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 4b + 28a b + 32a b)cosh(x) + (12b + 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 12 3 2 2 10 +--R (- b - a b )cosh(x) + (- 8b - 16a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 8 +--R (- 29b - 93a b - 96a b - 32a )cosh(x) +--R + +--R 3 2 2 3 6 3 2 2 4 +--R (34b + 98a b + 96a b + 32a )cosh(x) + (- b + 7a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b + 6a b )cosh(x) - b - a b +--R / +--R 3 8 3 7 +--R 16a b sinh(x) + 128a b cosh(x)sinh(x) +--R + +--R 3 2 3 2 2 6 +--R (448a b cosh(x) + 32a b + 64a b )sinh(x) +--R + +--R 3 3 3 2 2 5 +--R (896a b cosh(x) + (192a b + 384a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 2 3 4 +--R (1120a b cosh(x) + (480a b + 960a b )cosh(x) + 16a b )sinh(x) +--R + +--R 3 5 3 2 2 3 3 +--R (896a b cosh(x) + (640a b + 1280a b )cosh(x) + 64a b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 2 2 4 3 2 +--R (448a b cosh(x) + (480a b + 960a b )cosh(x) + 96a b cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 2 2 5 3 3 +--R (128a b cosh(x) + (192a b + 384a b )cosh(x) + 64a b cosh(x) ) +--R * +--R sinh(x) +--R + +--R 3 8 3 2 2 6 3 4 +--R 16a b cosh(x) + (32a b + 64a b )cosh(x) + 16a b cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 8 4 3 7 +--R (- 16b - 16a b )sinh(x) + (- 128b - 128a b )cosh(x)sinh(x) +--R + +--R 4 3 2 4 3 2 2 6 +--R ((- 448b - 448a b )cosh(x) - 32b - 96a b - 64a b )sinh(x) +--R + +--R 4 3 3 4 3 2 2 +--R ((- 896b - 896a b )cosh(x) + (- 192b - 576a b - 384a b )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 +--R (- 1120b - 1120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 480b - 1440a b - 960a b )cosh(x) - 16b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 4 3 2 2 3 +--R (- 896b - 896a b )cosh(x) + (- 640b - 1920a b - 1280a b )cosh(x) +--R + +--R 4 3 +--R (- 64b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 4 3 2 2 4 +--R (- 448b - 448a b )cosh(x) + (- 480b - 1440a b - 960a b )cosh(x) +--R + +--R 4 3 2 +--R (- 96b - 96a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 4 3 2 2 5 +--R (- 128b - 128a b )cosh(x) + (- 192b - 576a b - 384a b )cosh(x) +--R + +--R 4 3 3 +--R (- 64b - 64a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (- 16b - 16a b )cosh(x) + (- 32b - 96a b - 64a b )cosh(x) +--R + +--R 4 3 4 +--R (- 16b - 16a b )cosh(x) +--R Type: Expression(Integer) +--E 416 + +--S 417 of 552 +t0776:= sinh(x)^7/(a+b*cosh(x)^2) +--R +--R +--R 7 +--R sinh(x) +--R (409) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 417 + +--S 418 of 552 +r0776:= -(a+b)^3*atan(b^(1/2)*cosh(x)/a^(1/2))/a^(1/2)/b^(7/2)+_ + a*cosh(x)/b^2+2*cosh(x)/b+(a+b)^2*cosh(x)/b^3-_ + 1/3*a*cosh(x)^3/b^2-cosh(x)^3/b+1/5*cosh(x)^5/b +--R +--R +--R (410) +--R +-+ +--R 3 2 2 3 cosh(x)\|b +--R (- 15b - 45a b - 45a b - 15a )atan(-----------) +--R +-+ +--R \|a +--R + +--R 2 5 2 3 2 2 +--R (3b cosh(x) + (- 15b - 5a b)cosh(x) + (45b + 45a b + 15a )cosh(x)) +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 3 +-+ +-+ +--R 15b \|a \|b +--R Type: Expression(Integer) +--E 418 + +--S 419 of 552 +a0776:= integrate(t0776,x) +--R +--R +--R (411) +--R [ +--R 3 2 2 3 5 +--R (240b + 720a b + 720a b + 240a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (1200b + 3600a b + 3600a b + 1200a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (1200b + 3600a b + 3600a b + 1200a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (240b + 720a b + 720a b + 240a )cosh(x) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R - 4a b sinh(x) - 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 12a b cosh(x) - 4a b)sinh(x) - 4a b cosh(x) - 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) - 45b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (- 360b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (- 1260b - 560a b)cosh(x) + 570b + 660a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 756b cosh(x) + (- 2520b - 1120a b)cosh(x) +--R + +--R 2 2 +--R (3420b + 3960a b + 1440a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (- 3150b - 1400a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (8550b + 9900a b + 3600a )cosh(x) + 570b + 660a b + 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (- 2520b - 1120a b)cosh(x) +--R + +--R 2 2 3 +--R (11400b + 13200a b + 4800a )cosh(x) +--R + +--R 2 2 +--R (2280b + 2640a b + 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (- 1260b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (8550b + 9900a b + 3600a )cosh(x) +--R + +--R 2 2 2 2 +--R (3420b + 3960a b + 1440a )cosh(x) - 45b - 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (- 360b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (3420b + 3960a b + 1440a )cosh(x) +--R + +--R 2 2 3 2 +--R (2280b + 2640a b + 960a )cosh(x) + (- 90b - 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (- 45b - 20a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (570b + 660a b + 240a )cosh(x) + (570b + 660a b + 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 45b - 20a b)cosh(x) + 3b +--R * +--R +-----+ +--R \|- a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 3 2 2 3 5 +--R (- 480b - 1440a b - 1440a b - 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 2400b - 7200a b - 7200a b - 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 4800b - 14400a b - 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 4800b - 14400a b - 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 2400b - 7200a b - 7200a b - 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 480b - 1440a b - 1440a b - 480a )cosh(x) +--R * +--R +---+ +--R (sinh(x) + cosh(x))\|a b +--R atan(-------------------------) +--R 2a +--R + +--R 3 2 2 3 5 +--R (480b + 1440a b + 1440a b + 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (4800b + 14400a b + 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (4800b + 14400a b + 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (480b + 1440a b + 1440a b + 480a )cosh(x) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) + b + 4a)sinh(x) + b cosh(x) + (b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) - 45b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (- 360b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (- 1260b - 560a b)cosh(x) + 570b + 660a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 756b cosh(x) + (- 2520b - 1120a b)cosh(x) +--R + +--R 2 2 +--R (3420b + 3960a b + 1440a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (- 3150b - 1400a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (8550b + 9900a b + 3600a )cosh(x) + 570b + 660a b + 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (- 2520b - 1120a b)cosh(x) +--R + +--R 2 2 3 +--R (11400b + 13200a b + 4800a )cosh(x) +--R + +--R 2 2 +--R (2280b + 2640a b + 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (- 1260b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (8550b + 9900a b + 3600a )cosh(x) +--R + +--R 2 2 2 2 +--R (3420b + 3960a b + 1440a )cosh(x) - 45b - 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (- 360b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (3420b + 3960a b + 1440a )cosh(x) +--R + +--R 2 2 3 2 +--R (2280b + 2640a b + 960a )cosh(x) + (- 90b - 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (- 45b - 20a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (570b + 660a b + 240a )cosh(x) + (570b + 660a b + 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 45b - 20a b)cosh(x) + 3b +--R * +--R +---+ +--R \|a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 419 + +--S 420 of 552 +m0776a:= a0776.1-r0776 +--R +--R +--R (412) +--R 3 2 2 3 5 +--R (240b + 720a b + 720a b + 240a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (1200b + 3600a b + 3600a b + 1200a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (1200b + 3600a b + 3600a b + 1200a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (240b + 720a b + 720a b + 240a )cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b - 4a)cosh(x) + b +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 +--R - 4a b sinh(x) - 12a b cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 12a b cosh(x) - 4a b)sinh(x) - 4a b cosh(x) - 4a b cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 3 2 2 3 5 +--R (480b + 1440a b + 1440a b + 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (4800b + 14400a b + 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (4800b + 14400a b + 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (480b + 1440a b + 1440a b + 480a )cosh(x) +--R * +--R +-+ +--R +-----+ cosh(x)\|b +--R \|- a b atan(-----------) +--R +-+ +--R \|a +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) - 45b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (- 360b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (- 1260b - 560a b)cosh(x) + 570b + 660a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 660b cosh(x) + (- 2040b - 960a b)cosh(x) +--R + +--R 2 2 +--R (1980b + 2520a b + 960a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 150b cosh(x) + (- 750b - 600a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (1350b + 2700a b + 1200a )cosh(x) + 570b + 660a b + 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R - 600b cosh(x) + (2280b + 480a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- 3000b - 1200a b)cosh(x) + (2280b + 2640a b + 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R - 825b cosh(x) + (3540b + 1040a b)cosh(x) +--R + +--R 2 2 4 +--R (- 5850b - 4500a b - 1200a )cosh(x) +--R + +--R 2 2 2 2 +--R (3420b + 3960a b + 1440a )cosh(x) - 45b - 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R - 450b cosh(x) + (2040b + 640a b)cosh(x) +--R + +--R 2 2 5 +--R (- 3780b - 3240a b - 960a )cosh(x) +--R + +--R 2 2 3 2 +--R (2280b + 2640a b + 960a )cosh(x) + (- 90b - 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R - 93b cosh(x) + (435b + 140a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 870b - 780a b - 240a )cosh(x) + (570b + 660a b + 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 45b - 20a b)cosh(x) + 3b +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 420 + +--S 421 of 552 +d0776a:= D(m0776a,x) +--R +--R +--R (413) +--R 2 14 3 13 +--R (b cosh(x) + a)sinh(x) + (14b cosh(x) + 14a cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (91b cosh(x) + (- 7b + 91a)cosh(x) - 7a)sinh(x) +--R + +--R 5 3 11 +--R (364b cosh(x) + (- 84b + 364a)cosh(x) - 84a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 969b cosh(x) + (- 366b + 1001a)cosh(x) + (- 75b - 462a)cosh(x) +--R + +--R 32b + 21a +--R * +--R 10 +--R sinh(x) +--R + +--R 7 5 3 +--R 1714b cosh(x) + (- 676b + 2002a)cosh(x) + (- 654b - 1540a)cosh(x) +--R + +--R (288b + 210a)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 6 4 +--R 1851b cosh(x) + (- 73b + 2875a)cosh(x) + (- 2319b - 3081a)cosh(x) +--R + +--R 2 +--R (925b + 561a)cosh(x) + 64b + 93a +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 +--R 744b cosh(x) + (2072b + 2536a)cosh(x) + (- 4200b - 2856a)cosh(x) +--R + +--R 3 +--R (1064b - 168a)cosh(x) + (448b + 616a)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 +--R - 1029b cosh(x) + (4284b + 315a)cosh(x) +--R + +--R 6 4 +--R (- 3686b + 1596a)cosh(x) + (- 884b - 3654a)cosh(x) +--R + +--R 2 +--R (1283b + 1708a)cosh(x) + 32b + 35a +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 +--R - 2030b cosh(x) + (4312b - 2478a)cosh(x) +--R + +--R 7 5 +--R (- 244b + 7896a)cosh(x) + (- 4168b - 8148a)cosh(x) +--R + +--R 3 +--R (1970b + 2520a)cosh(x) + (160b + 210a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 +--R - 1687b cosh(x) + (2359b - 3479a)cosh(x) +--R + +--R 8 6 +--R (2746b + 9975a)cosh(x) + (- 5522b - 9030a)cosh(x) +--R + +--R 4 2 +--R (1805b + 2030a)cosh(x) + (299b + 525a)cosh(x) - 21a +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 +--R - 788b cosh(x) + (572b - 2324a)cosh(x) + (2776b + 6524a)cosh(x) +--R + +--R 7 5 +--R (- 3880b - 5544a)cosh(x) + (1084b + 728a)cosh(x) +--R + +--R 3 +--R (236b + 700a)cosh(x) - 84a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 +--R - 197b cosh(x) + (- 46b - 805a)cosh(x) + (1265b + 2226a)cosh(x) +--R + +--R 8 6 +--R (- 1556b - 1743a)cosh(x) + (493b - 84a)cosh(x) +--R + +--R 4 2 +--R (34b + 525a)cosh(x) + (7b - 126a)cosh(x) + 7a +--R * +--R 2 +--R sinh(x) +--R + +--R 15 13 11 +--R - 18b cosh(x) + (- 52b - 114a)cosh(x) + (274b + 300a)cosh(x) +--R + +--R 9 7 +--R (- 344b - 174a)cosh(x) + (178b - 152a)cosh(x) +--R + +--R 5 3 +--R (- 52b + 210a)cosh(x) + (14b - 84a)cosh(x) + 14a cosh(x) +--R * +--R sinh(x) +--R + +--R 16 14 12 +--R b cosh(x) + (- 7b + a)cosh(x) + (21b - 7a)cosh(x) +--R + +--R 10 8 6 +--R (- 35b + 21a)cosh(x) + (35b - 35a)cosh(x) + (- 21b + 35a)cosh(x) +--R + +--R 4 2 +--R (7b - 21a)cosh(x) + (- b + 7a)cosh(x) - a +--R / +--R 2 2 9 2 3 8 +--R (32b cosh(x) + 32a b)sinh(x) + (288b cosh(x) + 288a b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 7 +--R (1152b cosh(x) + (64b + 1280a b)cosh(x) + 64a b + 128a )sinh(x) +--R + +--R 2 5 2 3 2 +--R (2688b cosh(x) + (448b + 3584a b)cosh(x) + (448a b + 896a )cosh(x)) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 4032b cosh(x) + (1344b + 6720a b)cosh(x) +--R + +--R 2 2 2 +--R (32b + 1344a b + 2688a )cosh(x) + 32a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 4032b cosh(x) + (2240b + 8512a b)cosh(x) +--R + +--R 2 2 3 +--R (160b + 2240a b + 4480a )cosh(x) + 160a b cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 2688b cosh(x) + (2240b + 7168a b)cosh(x) +--R + +--R 2 2 4 2 +--R (320b + 2240a b + 4480a )cosh(x) + 320a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 1152b cosh(x) + (1344b + 3840a b)cosh(x) +--R + +--R 2 2 5 3 +--R (320b + 1344a b + 2688a )cosh(x) + 320a b cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 10 2 8 +--R 288b cosh(x) + (448b + 1184a b)cosh(x) +--R + +--R 2 2 6 4 +--R (160b + 448a b + 896a )cosh(x) + 160a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 11 2 9 2 2 7 +--R 32b cosh(x) + (64b + 160a b)cosh(x) + (32b + 64a b + 128a )cosh(x) +--R + +--R 5 +--R 32a b cosh(x) +--R Type: Expression(Integer) +--E 421 + +--S 422 of 552 +m0776b:= a0776.2-r0776 +--R +--R +--R (414) +--R 3 2 2 3 5 +--R (- 480b - 1440a b - 1440a b - 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 2400b - 7200a b - 7200a b - 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 4800b - 14400a b - 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 4800b - 14400a b - 14400a b - 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 2400b - 7200a b - 7200a b - 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 480b - 1440a b - 1440a b - 480a )cosh(x) +--R * +--R +---+ +--R +-+ +-+ (sinh(x) + cosh(x))\|a b +--R \|a \|b atan(-------------------------) +--R 2a +--R + +--R 3 2 2 3 5 +--R (480b + 1440a b + 1440a b + 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (4800b + 14400a b + 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (4800b + 14400a b + 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (480b + 1440a b + 1440a b + 480a )cosh(x) +--R * +--R +-+ +--R +---+ cosh(x)\|b +--R \|a b atan(-----------) +--R +-+ +--R \|a +--R + +--R 3 2 2 3 5 +--R (480b + 1440a b + 1440a b + 480a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 +--R (4800b + 14400a b + 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 3 2 +--R (4800b + 14400a b + 14400a b + 4800a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 4 +--R (2400b + 7200a b + 7200a b + 2400a )cosh(x) sinh(x) +--R + +--R 3 2 2 3 5 +--R (480b + 1440a b + 1440a b + 480a )cosh(x) +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) + b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (b + 4a)cosh(x) +--R / +--R +---+ +--R 2\|a b +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) - 45b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (- 360b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (- 1260b - 560a b)cosh(x) + 570b + 660a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 660b cosh(x) + (- 2040b - 960a b)cosh(x) +--R + +--R 2 2 +--R (1980b + 2520a b + 960a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 150b cosh(x) + (- 750b - 600a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (1350b + 2700a b + 1200a )cosh(x) + 570b + 660a b + 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R - 600b cosh(x) + (2280b + 480a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- 3000b - 1200a b)cosh(x) + (2280b + 2640a b + 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R - 825b cosh(x) + (3540b + 1040a b)cosh(x) +--R + +--R 2 2 4 +--R (- 5850b - 4500a b - 1200a )cosh(x) +--R + +--R 2 2 2 2 +--R (3420b + 3960a b + 1440a )cosh(x) - 45b - 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R - 450b cosh(x) + (2040b + 640a b)cosh(x) +--R + +--R 2 2 5 +--R (- 3780b - 3240a b - 960a )cosh(x) +--R + +--R 2 2 3 2 +--R (2280b + 2640a b + 960a )cosh(x) + (- 90b - 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R - 93b cosh(x) + (435b + 140a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (- 870b - 780a b - 240a )cosh(x) + (570b + 660a b + 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 45b - 20a b)cosh(x) + 3b +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 422 + +--S 423 of 552 +d0776b:= D(m0776b,x) +--R +--R +--R (415) +--R 2 14 3 13 +--R (b cosh(x) + a)sinh(x) + (14b cosh(x) + 14a cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (91b cosh(x) + (- 7b + 91a)cosh(x) - 7a)sinh(x) +--R + +--R 5 3 11 +--R (364b cosh(x) + (- 84b + 364a)cosh(x) - 84a cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 969b cosh(x) + (- 366b + 1001a)cosh(x) + (- 75b - 462a)cosh(x) +--R + +--R 32b + 21a +--R * +--R 10 +--R sinh(x) +--R + +--R 7 5 3 +--R 1714b cosh(x) + (- 676b + 2002a)cosh(x) + (- 654b - 1540a)cosh(x) +--R + +--R (288b + 210a)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 6 4 +--R 1851b cosh(x) + (- 73b + 2875a)cosh(x) + (- 2319b - 3081a)cosh(x) +--R + +--R 2 +--R (925b + 561a)cosh(x) + 64b + 93a +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 +--R 744b cosh(x) + (2072b + 2536a)cosh(x) + (- 4200b - 2856a)cosh(x) +--R + +--R 3 +--R (1064b - 168a)cosh(x) + (448b + 616a)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 +--R - 1029b cosh(x) + (4284b + 315a)cosh(x) +--R + +--R 6 4 +--R (- 3686b + 1596a)cosh(x) + (- 884b - 3654a)cosh(x) +--R + +--R 2 +--R (1283b + 1708a)cosh(x) + 32b + 35a +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 +--R - 2030b cosh(x) + (4312b - 2478a)cosh(x) +--R + +--R 7 5 +--R (- 244b + 7896a)cosh(x) + (- 4168b - 8148a)cosh(x) +--R + +--R 3 +--R (1970b + 2520a)cosh(x) + (160b + 210a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 +--R - 1687b cosh(x) + (2359b - 3479a)cosh(x) +--R + +--R 8 6 +--R (2746b + 9975a)cosh(x) + (- 5522b - 9030a)cosh(x) +--R + +--R 4 2 +--R (1805b + 2030a)cosh(x) + (299b + 525a)cosh(x) - 21a +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 +--R - 788b cosh(x) + (572b - 2324a)cosh(x) + (2776b + 6524a)cosh(x) +--R + +--R 7 5 +--R (- 3880b - 5544a)cosh(x) + (1084b + 728a)cosh(x) +--R + +--R 3 +--R (236b + 700a)cosh(x) - 84a cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 +--R - 197b cosh(x) + (- 46b - 805a)cosh(x) + (1265b + 2226a)cosh(x) +--R + +--R 8 6 +--R (- 1556b - 1743a)cosh(x) + (493b - 84a)cosh(x) +--R + +--R 4 2 +--R (34b + 525a)cosh(x) + (7b - 126a)cosh(x) + 7a +--R * +--R 2 +--R sinh(x) +--R + +--R 15 13 11 +--R - 18b cosh(x) + (- 52b - 114a)cosh(x) + (274b + 300a)cosh(x) +--R + +--R 9 7 +--R (- 344b - 174a)cosh(x) + (178b - 152a)cosh(x) +--R + +--R 5 3 +--R (- 52b + 210a)cosh(x) + (14b - 84a)cosh(x) + 14a cosh(x) +--R * +--R sinh(x) +--R + +--R 16 14 12 +--R b cosh(x) + (- 7b + a)cosh(x) + (21b - 7a)cosh(x) +--R + +--R 10 8 6 +--R (- 35b + 21a)cosh(x) + (35b - 35a)cosh(x) + (- 21b + 35a)cosh(x) +--R + +--R 4 2 +--R (7b - 21a)cosh(x) + (- b + 7a)cosh(x) - a +--R / +--R 2 2 9 2 3 8 +--R (32b cosh(x) + 32a b)sinh(x) + (288b cosh(x) + 288a b cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 7 +--R (1152b cosh(x) + (64b + 1280a b)cosh(x) + 64a b + 128a )sinh(x) +--R + +--R 2 5 2 3 2 +--R (2688b cosh(x) + (448b + 3584a b)cosh(x) + (448a b + 896a )cosh(x)) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 4032b cosh(x) + (1344b + 6720a b)cosh(x) +--R + +--R 2 2 2 +--R (32b + 1344a b + 2688a )cosh(x) + 32a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 4032b cosh(x) + (2240b + 8512a b)cosh(x) +--R + +--R 2 2 3 +--R (160b + 2240a b + 4480a )cosh(x) + 160a b cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 2688b cosh(x) + (2240b + 7168a b)cosh(x) +--R + +--R 2 2 4 2 +--R (320b + 2240a b + 4480a )cosh(x) + 320a b cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 1152b cosh(x) + (1344b + 3840a b)cosh(x) +--R + +--R 2 2 5 3 +--R (320b + 1344a b + 2688a )cosh(x) + 320a b cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 10 2 8 +--R 288b cosh(x) + (448b + 1184a b)cosh(x) +--R + +--R 2 2 6 4 +--R (160b + 448a b + 896a )cosh(x) + 160a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 11 2 9 2 2 7 +--R 32b cosh(x) + (64b + 160a b)cosh(x) + (32b + 64a b + 128a )cosh(x) +--R + +--R 5 +--R 32a b cosh(x) +--R Type: Expression(Integer) +--E 423 + +--S 424 of 552 +t0777:= cosh(x)/(a+b*cosh(x)^2) +--R +--R +--R cosh(x) +--R (416) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 552 +r0777:= atan(b^(1/2)*sinh(x)/(a+b)^(1/2))/b^(1/2)/(a+b)^(1/2) +--R +--R +--R +-+ +--R sinh(x)\|b +--R atan(-----------) +--R +-----+ +--R \|b + a +--R (417) ----------------- +--R +-+ +-----+ +--R \|b \|b + a +--R Type: Expression(Integer) +--E 425 + +--S 426 of 552 +a0777:= integrate(t0777,x) +--R +--R +--R (418) +--R [ +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 6b - 4a)cosh(x) + b +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R + +--R 2 3 2 2 +--R (4b + 4a b)sinh(x) + (12b + 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((12b + 12a b)cosh(x) - 4b - 4a b)sinh(x) +--R + +--R 2 3 2 +--R (4b + 4a b)cosh(x) + (- 4b - 4a b)cosh(x) +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R / +--R +----------+ +--R | 2 +--R 2\|- b - a b +--R , +--R +--R +--------+ +--R | 2 +--R (sinh(x) + cosh(x))\|b + a b +--R atan(------------------------------) +--R 2b + 2a +--R + +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) + 3b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (3b + 4a)cosh(x) +--R / +--R +--------+ +--R | 2 +--R 2\|b + a b +--R / +--R +--------+ +--R | 2 +--R \|b + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 426 + +--S 427 of 552 +m0777a:= a0777.1-r0777 +--R +--R +--R (419) +--R +-+ +-----+ +--R \|b \|b + a +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 6b - 4a)cosh(x) + b +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R + +--R 2 3 2 2 +--R (4b + 4a b)sinh(x) + (12b + 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((12b + 12a b)cosh(x) - 4b - 4a b)sinh(x) +--R + +--R 2 3 2 +--R (4b + 4a b)cosh(x) + (- 4b - 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R +----------+ +-+ +--R | 2 sinh(x)\|b +--R - 2\|- b - a b atan(-----------) +--R +-----+ +--R \|b + a +--R / +--R +----------+ +--R | 2 +-+ +-----+ +--R 2\|- b - a b \|b \|b + a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 552 +d0777a:= D(m0777a,x) +--R +--R +--R (420) +--R 5 4 2 3 +--R 2b sinh(x) + 5b cosh(x)sinh(x) + (2b cosh(x) + 4b + 2a)sinh(x) +--R + +--R 3 2 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) +--R + +--R 4 2 5 +--R (- 4b cosh(x) + (2b - 2a)cosh(x) + 2b + 2a)sinh(x) - b cosh(x) +--R + +--R 3 +--R - 2a cosh(x) + (b + 2a)cosh(x) +--R / +--R 2 6 2 5 2 2 2 4 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 3b + 5a b)sinh(x) +--R + +--R 2 3 2 3 +--R (4b cosh(x) + (8b + 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 2 +--R (b cosh(x) + (8b + 10a b)cosh(x) + 3b + 6a b + 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b + 4a b)cosh(x) + (4b + 12a b + 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b + a b)cosh(x) + (2b + 6a b + 4a )cosh(x) + b + a b +--R Type: Expression(Integer) +--E 428 + +--S 429 of 552 +m0777b:= a0777.2-r0777 +--R +--R +--R (421) +--R +--------+ +--R | 2 +--R +-+ +-----+ (sinh(x) + cosh(x))\|b + a b +--R \|b \|b + a atan(------------------------------) +--R 2b + 2a +--R + +--R +--------+ +-+ +--R | 2 sinh(x)\|b +--R - \|b + a b atan(-----------) +--R +-----+ +--R \|b + a +--R + +--R +-+ +-----+ +--R \|b \|b + a +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) + 3b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (3b + 4a)cosh(x) +--R / +--R +--------+ +--R | 2 +--R 2\|b + a b +--R / +--R +--------+ +--R +-+ +-----+ | 2 +--R \|b \|b + a \|b + a b +--R Type: Expression(Integer) +--E 429 + +--S 430 of 552 +d0777b:= D(m0777b,x) +--R +--R +--R (422) +--R 5 4 2 3 +--R 2b sinh(x) + 5b cosh(x)sinh(x) + (2b cosh(x) + 4b + 2a)sinh(x) +--R + +--R 3 2 +--R (- 4b cosh(x) + (6b + 2a)cosh(x))sinh(x) +--R + +--R 4 2 5 +--R (- 4b cosh(x) + (2b - 2a)cosh(x) + 2b + 2a)sinh(x) - b cosh(x) +--R + +--R 3 +--R - 2a cosh(x) + (b + 2a)cosh(x) +--R / +--R 2 6 2 5 2 2 2 4 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 3b + 5a b)sinh(x) +--R + +--R 2 3 2 3 +--R (4b cosh(x) + (8b + 12a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 2 +--R (b cosh(x) + (8b + 10a b)cosh(x) + 3b + 6a b + 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((4b + 4a b)cosh(x) + (4b + 12a b + 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (b + a b)cosh(x) + (2b + 6a b + 4a )cosh(x) + b + a b +--R Type: Expression(Integer) +--E 430 + +--S 431 of 552 +t0778:= cosh(x)^2/(a+b*cosh(x)^2) +--R +--R +--R 2 +--R cosh(x) +--R (423) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 552 +r0778:= x/b-a^(1/2)*atanh(a^(1/2)*tanh(x)/(a+b)^(1/2))/b/(a+b)^(1/2) +--R +--R +--R +-+ +--R +-+ tanh(x)\|a +-----+ +--R - \|a atanh(-----------) + x\|b + a +--R +-----+ +--R \|b + a +--R (424) ------------------------------------ +--R +-----+ +--R b\|b + a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 552 +a0778:= integrate(t0778,x) +--R +--R +--R (425) +--R [ +--R +-----+ +--R | a +--R |----- +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4b + 4a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4b + 4a b)cosh(x) + 4b + 12a b + 8a +--R * +--R +-----+ +--R | a +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2x +--R / +--R 2b +--R , +--R +-------+ +--R | a +--R +-------+ (2b + 2a) |- ----- +--R | a \| b + a +--R - |- ----- atan(----------------------------------------------------) + x +--R \| b + a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R --------------------------------------------------------------------------] +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 433 + +--S 434 of 552 +m0778a:= a0778.1-r0778 +--R +--R +--R (426) +--R +-----+ +--R | a +-----+ +--R |----- \|b + a +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4b + 4a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4b + 4a b)cosh(x) + 4b + 12a b + 8a +--R * +--R +-----+ +--R | a +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R +-+ +--R +-+ tanh(x)\|a +--R 2\|a atanh(-----------) +--R +-----+ +--R \|b + a +--R / +--R +-----+ +--R 2b\|b + a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 552 +d0778a:= D(m0778a,x) +--R +--R +--R (427) +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - a sinh(x) - 4a cosh(x)sinh(x) + (- 6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (- 4a cosh(x) + 4a cosh(x))sinh(x) - a cosh(x) + 2a cosh(x) - a +--R / +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) + 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (2a b + 4a )cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (- b - a b)sinh(x) + (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 6a b)cosh(x) - 2b - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4b - 4a b)cosh(x) + (- 4b - 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- b - a b)cosh(x) + (- 2b - 6a b - 4a )cosh(x) - b - a b +--R Type: Expression(Integer) +--E 435 + +--S 436 of 552 +m0778b:= a0778.2-r0778 +--R +--R +--R (428) +--R +-+ +--R +-+ tanh(x)\|a +--R \|a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R - +--R +-------+ +--R | a +-----+ +--R |- ----- \|b + a +--R \| b + a +--R * +--R +-------+ +--R | a +--R (2b + 2a) |- ----- +--R \| b + a +--R atan(----------------------------------------------------) +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R / +--R +-----+ +--R b\|b + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 552 +d0778b:= D(m0778b,x) +--R +--R +--R (429) +--R 4 3 2 2 +--R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4a cosh(x) + 4a cosh(x))sinh(x) + a cosh(x) + 2a cosh(x) + a +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - a sinh(x) - 4a cosh(x)sinh(x) + (- 6a cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (- 4a cosh(x) + 4a cosh(x))sinh(x) - a cosh(x) + 2a cosh(x) - a +--R / +--R 4 3 +--R a b sinh(x) + 4a b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6a b cosh(x) + 2a b + 4a )sinh(x) +--R + +--R 3 2 4 +--R (4a b cosh(x) + (4a b + 8a )cosh(x))sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R (2a b + 4a )cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 +--R (- b - a b)sinh(x) + (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b - 6a b)cosh(x) - 2b - 6a b - 4a )sinh(x) +--R + +--R 2 3 2 2 +--R ((- 4b - 4a b)cosh(x) + (- 4b - 12a b - 8a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (- b - a b)cosh(x) + (- 2b - 6a b - 4a )cosh(x) - b - a b +--R Type: Expression(Integer) +--E 437 + +--S 438 of 552 +t0779:= cosh(x)^3/(a+b*cosh(x)^2) +--R +--R +--R 3 +--R cosh(x) +--R (430) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 438 + +--S 439 of 552 +r0779:= -a*atan(b^(1/2)*sinh(x)/(a+b)^(1/2))/b^(3/2)/(a+b)^(1/2)+sinh(x)/b +--R +--R +--R +-+ +--R sinh(x)\|b +-+ +-----+ +--R - a atan(-----------) + sinh(x)\|b \|b + a +--R +-----+ +--R \|b + a +--R (431) ------------------------------------------- +--R +-+ +-----+ +--R b\|b \|b + a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 552 +a0779:= integrate(t0779,x) +--R +--R +--R (432) +--R [ +--R (a sinh(x) + a cosh(x)) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 6b - 4a)cosh(x) + b +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R + +--R 2 3 2 2 +--R (- 4b - 4a b)sinh(x) + (- 12b - 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((- 12b - 12a b)cosh(x) + 4b + 4a b)sinh(x) +--R + +--R 2 3 2 +--R (- 4b - 4a b)cosh(x) + (4b + 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R +----------+ +--R 2 2 | 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|- b - a b +--R / +--R +----------+ +--R | 2 +--R (2b sinh(x) + 2b cosh(x))\|- b - a b +--R , +--R +--R +--------+ +--R | 2 +--R (sinh(x) + cosh(x))\|b + a b +--R (- 2a sinh(x) - 2a cosh(x))atan(------------------------------) +--R 2b + 2a +--R + +--R (- 2a sinh(x) - 2a cosh(x)) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) + 3b + 4a)sinh(x) + b cosh(x) + (3b + 4a)cosh(x) +--R / +--R +--------+ +--R | 2 +--R 2\|b + a b +--R + +--R +--------+ +--R 2 2 | 2 +--R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1)\|b + a b +--R / +--R +--------+ +--R | 2 +--R (2b sinh(x) + 2b cosh(x))\|b + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 440 + +--S 441 of 552 +m0779a:= a0779.1-r0779 +--R +--R +--R (433) +--R +-+ +-----+ +--R (a sinh(x) + a cosh(x))\|b \|b + a +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 6b - 4a)cosh(x) + b +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R + +--R 2 3 2 2 +--R (- 4b - 4a b)sinh(x) + (- 12b - 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((- 12b - 12a b)cosh(x) + 4b + 4a b)sinh(x) +--R + +--R 2 3 2 +--R (- 4b - 4a b)cosh(x) + (4b + 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R +----------+ +-+ +--R | 2 sinh(x)\|b +--R (2a sinh(x) + 2a cosh(x))\|- b - a b atan(-----------) +--R +-----+ +--R \|b + a +--R + +--R +----------+ +--R 2 2 | 2 +-+ +-----+ +--R (- sinh(x) + cosh(x) - 1)\|- b - a b \|b \|b + a +--R / +--R +----------+ +--R | 2 +-+ +-----+ +--R (2b sinh(x) + 2b cosh(x))\|- b - a b \|b \|b + a +--R Type: Expression(Integer) +--E 441 + +--S 442 of 552 +d0779a:= D(m0779a,x) +--R +--R +--R (434) +--R 8 7 2 6 +--R b sinh(x) + 4b cosh(x)sinh(x) + (5b cosh(x) + 4b + a)sinh(x) +--R + +--R 5 +--R (12b - 2a)cosh(x)sinh(x) +--R + +--R 4 2 4 +--R (- 5b cosh(x) + (11b - 9a)cosh(x) + 6b + 3a)sinh(x) +--R + +--R 5 3 3 +--R (- 4b cosh(x) - 4a cosh(x) + (12b + 4a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- b cosh(x) + (- 6b + 7a)cosh(x) + (7b - 6a)cosh(x) + 4b + 3a) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 +--R ((- 4b + 6a)cosh(x) - 12a cosh(x) + (4b + 6a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- b + a)cosh(x) + (- b - 5a)cosh(x) + (b + 3a)cosh(x) + b + a +--R / +--R 2 7 2 6 2 2 2 5 +--R 2b sinh(x) + 10b cosh(x)sinh(x) + (20b cosh(x) + 6b + 10a b)sinh(x) +--R + +--R 2 3 2 4 +--R (20b cosh(x) + (22b + 34a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 3 +--R (10b cosh(x) + (32b + 44a b)cosh(x) + 6b + 12a b + 8a )sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (2b cosh(x) + (24b + 28a b)cosh(x) + (14b + 36a b + 24a )cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R ((10b + 10a b)cosh(x) + (12b + 36a b + 24a )cosh(x) + 2b + 2a b) +--R * +--R sinh(x) +--R + +--R 2 5 2 2 3 2 +--R (2b + 2a b)cosh(x) + (4b + 12a b + 8a )cosh(x) + (2b + 2a b)cosh(x) +--R Type: Expression(Integer) +--E 442 + +--S 443 of 552 +m0779b:= a0779.2-r0779 +--R +--R +--R (435) +--R +-+ +-----+ +--R (- 2a sinh(x) - 2a cosh(x))\|b \|b + a +--R * +--R +--------+ +--R | 2 +--R (sinh(x) + cosh(x))\|b + a b +--R atan(------------------------------) +--R 2b + 2a +--R + +--R +--------+ +-+ +--R | 2 sinh(x)\|b +--R (2a sinh(x) + 2a cosh(x))\|b + a b atan(-----------) +--R +-----+ +--R \|b + a +--R + +--R +-+ +-----+ +--R (- 2a sinh(x) - 2a cosh(x))\|b \|b + a +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) + 3b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (3b + 4a)cosh(x) +--R / +--R +--------+ +--R | 2 +--R 2\|b + a b +--R + +--R +--------+ +--R 2 2 +-+ +-----+ | 2 +--R (- sinh(x) + cosh(x) - 1)\|b \|b + a \|b + a b +--R / +--R +--------+ +--R +-+ +-----+ | 2 +--R (2b sinh(x) + 2b cosh(x))\|b \|b + a \|b + a b +--R Type: Expression(Integer) +--E 443 + +--S 444 of 552 +d0779b:= D(m0779b,x) +--R +--R +--R (436) +--R 8 7 2 6 +--R b sinh(x) + 4b cosh(x)sinh(x) + (5b cosh(x) + 4b + a)sinh(x) +--R + +--R 5 +--R (12b - 2a)cosh(x)sinh(x) +--R + +--R 4 2 4 +--R (- 5b cosh(x) + (11b - 9a)cosh(x) + 6b + 3a)sinh(x) +--R + +--R 5 3 3 +--R (- 4b cosh(x) - 4a cosh(x) + (12b + 4a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- b cosh(x) + (- 6b + 7a)cosh(x) + (7b - 6a)cosh(x) + 4b + 3a) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 +--R ((- 4b + 6a)cosh(x) - 12a cosh(x) + (4b + 6a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- b + a)cosh(x) + (- b - 5a)cosh(x) + (b + 3a)cosh(x) + b + a +--R / +--R 2 7 2 6 2 2 2 5 +--R 2b sinh(x) + 10b cosh(x)sinh(x) + (20b cosh(x) + 6b + 10a b)sinh(x) +--R + +--R 2 3 2 4 +--R (20b cosh(x) + (22b + 34a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 3 +--R (10b cosh(x) + (32b + 44a b)cosh(x) + 6b + 12a b + 8a )sinh(x) +--R + +--R 2 5 2 3 2 2 +--R (2b cosh(x) + (24b + 28a b)cosh(x) + (14b + 36a b + 24a )cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 2 2 2 +--R ((10b + 10a b)cosh(x) + (12b + 36a b + 24a )cosh(x) + 2b + 2a b) +--R * +--R sinh(x) +--R + +--R 2 5 2 2 3 2 +--R (2b + 2a b)cosh(x) + (4b + 12a b + 8a )cosh(x) + (2b + 2a b)cosh(x) +--R Type: Expression(Integer) +--E 444 + +--S 445 of 552 +t0780:= cosh(x)^4/(a+b*cosh(x)^2) +--R +--R +--R 4 +--R cosh(x) +--R (437) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 552 +r0780:= -a*x/b^2+1/2*x/b+a^(3/2)*atanh(a^(1/2)*_ + tanh(x)/(a+b)^(1/2))/b^2/(a+b)^(1/2)+1/2*cosh(x)*sinh(x)/b +--R +--R +--R +-+ +--R +-+ tanh(x)\|a +-----+ +--R 2a\|a atanh(-----------) + (b cosh(x)sinh(x) + (b - 2a)x)\|b + a +--R +-----+ +--R \|b + a +--R (438) ----------------------------------------------------------------- +--R 2 +-----+ +--R 2b \|b + a +--R Type: Expression(Integer) +--E 446 + +--S 447 of 552 +a0780:= integrate(t0780,x) +--R +--R +--R (439) +--R [ +--R +-----+ +--R 2 2 | a +--R (4a sinh(x) + 8a cosh(x)sinh(x) + 4a cosh(x) ) |----- +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (- 4b - 4a b)sinh(x) + (- 8b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 4b - 4a b)cosh(x) - 4b - 12a b - 8a +--R * +--R +-----+ +--R | a +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + (4b - 8a)x)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (8b - 16a)x cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (4b - 8a)x cosh(x) - b +--R / +--R 2 2 2 2 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R , +--R +--R +-------+ +--R 2 2 | a +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) ) |- ----- +--R \| b + a +--R * +--R +-------+ +--R | a +--R (2b + 2a) |- ----- +--R \| b + a +--R atan(----------------------------------------------------) +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + (4b - 8a)x)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (8b - 16a)x cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (4b - 8a)x cosh(x) - b +--R / +--R 2 2 2 2 2 +--R 8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 447 + +--S 448 of 552 +m0780a:= a0780.1-r0780 +--R +--R +--R (440) +--R +-----+ +--R 2 2 | a +-----+ +--R (4a sinh(x) + 8a cosh(x)sinh(x) + 4a cosh(x) ) |----- \|b + a +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (- 4b - 4a b)sinh(x) + (- 8b - 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 4b - 4a b)cosh(x) - 4b - 12a b - 8a +--R * +--R +-----+ +--R | a +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R +-+ +--R 2 2 +-+ tanh(x)\|a +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) )\|a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 2 2 4 +-----+ +--R (b sinh(x) - 2b cosh(x) sinh(x) + b cosh(x) - b)\|b + a +--R / +--R 2 2 2 2 2 +-----+ +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b + a +--R Type: Expression(Integer) +--E 448 + +--S 449 of 552 +d0780a:= D(m0780a,x) +--R +--R +--R (441) +--R 8 7 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 6 +--R (- 4a b cosh(x) - 2a b - 8a )sinh(x) +--R + +--R 3 2 5 +--R (4a b cosh(x) + (- 4a b - 32a )cosh(x))sinh(x) +--R + +--R 4 2 2 2 4 +--R (10a b cosh(x) + (2a b - 56a )cosh(x) - 8a )sinh(x) +--R + +--R 5 2 3 2 +--R (4a b cosh(x) + (8a b - 64a )cosh(x) + (4a b - 32a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 2 2 +--R - 4a b cosh(x) + (2a b - 56a )cosh(x) + (8a b - 48a )cosh(x) +--R + +--R 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 2 3 +--R - 4a b cosh(x) + (- 4a b - 32a )cosh(x) + (4a b - 32a )cosh(x) +--R + +--R 4a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 2 6 2 4 2 +--R - a b cosh(x) + (- 2a b - 8a )cosh(x) - 8a cosh(x) + 2a b cosh(x) +--R + +--R a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 8 2 7 +--R (b + a b)sinh(x) + (4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((4b + 4a b)cosh(x) + 2b + 6a b + 8a )sinh(x) +--R + +--R 2 3 2 2 5 +--R ((- 4b - 4a b)cosh(x) + (4b + 12a b + 32a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 4 +--R ((- 10b - 10a b)cosh(x) + (- 2b - 6a b + 56a )cosh(x) - 8a )sinh(x) +--R + +--R 2 5 2 2 3 +--R (- 4b - 4a b)cosh(x) + (- 8b - 24a b + 64a )cosh(x) +--R + +--R 2 2 +--R (- 4b - 4a b - 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (4b + 4a b)cosh(x) + (- 2b - 6a b + 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 8b - 8a b - 48a )cosh(x) - 2b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R (4b + 4a b)cosh(x) + (4b + 12a b + 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 4b - 4a b - 32a )cosh(x) + (- 4b - 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 2 6 2 4 +--R (b + a b)cosh(x) + (2b + 6a b + 8a )cosh(x) - 8a cosh(x) +--R + +--R 2 2 2 +--R (- 2b - 6a b)cosh(x) - b - a b +--R / +--R 2 6 2 5 +--R 4a b sinh(x) + 24a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (60a b cosh(x) + 8a b + 16a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (80a b cosh(x) + (32a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 2 +--R (60a b cosh(x) + (48a b + 96a b)cosh(x) + 4a b )sinh(x) +--R + +--R 2 5 2 2 3 2 +--R (24a b cosh(x) + (32a b + 64a b)cosh(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 2 2 +--R 4a b cosh(x) + (8a b + 16a b)cosh(x) + 4a b cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 6 3 2 5 +--R (- 4b - 4a b )sinh(x) + (- 24b - 24a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 4 +--R ((- 60b - 60a b )cosh(x) - 8b - 24a b - 16a b)sinh(x) +--R + +--R 3 2 3 3 2 2 3 +--R ((- 80b - 80a b )cosh(x) + (- 32b - 96a b - 64a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 3 +--R (- 60b - 60a b )cosh(x) + (- 48b - 144a b - 96a b)cosh(x) - 4b +--R + +--R 2 +--R - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (- 24b - 24a b )cosh(x) + (- 32b - 96a b - 64a b)cosh(x) +--R + +--R 3 2 +--R (- 8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 4b - 4a b )cosh(x) + (- 8b - 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (- 4b - 4a b )cosh(x) +--R Type: Expression(Integer) +--E 449 + +--S 450 of 552 +m0780b:= a0780.2-r0780 +--R +--R +--R (442) +--R +-+ +--R 2 2 +-+ tanh(x)\|a +--R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) )\|a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +-------+ +--R 2 2 | a +-----+ +--R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) ) |- ----- \|b + a +--R \| b + a +--R * +--R +-------+ +--R | a +--R (2b + 2a) |- ----- +--R \| b + a +--R atan(----------------------------------------------------) +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R 4 2 2 4 +-----+ +--R (b sinh(x) - 2b cosh(x) sinh(x) + b cosh(x) - b)\|b + a +--R / +--R 2 2 2 2 2 +-----+ +--R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) )\|b + a +--R Type: Expression(Integer) +--E 450 + +--S 451 of 552 +d0780b:= D(m0780b,x) +--R +--R +--R (443) +--R 8 7 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) +--R + +--R 2 2 6 +--R (- 4a b cosh(x) - 2a b - 8a )sinh(x) +--R + +--R 3 2 5 +--R (4a b cosh(x) + (- 4a b - 32a )cosh(x))sinh(x) +--R + +--R 4 2 2 2 4 +--R (10a b cosh(x) + (2a b - 56a )cosh(x) - 8a )sinh(x) +--R + +--R 5 2 3 2 +--R (4a b cosh(x) + (8a b - 64a )cosh(x) + (4a b - 32a )cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 4 2 2 +--R - 4a b cosh(x) + (2a b - 56a )cosh(x) + (8a b - 48a )cosh(x) +--R + +--R 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 2 3 +--R - 4a b cosh(x) + (- 4a b - 32a )cosh(x) + (4a b - 32a )cosh(x) +--R + +--R 4a b cosh(x) +--R * +--R sinh(x) +--R + +--R 8 2 6 2 4 2 +--R - a b cosh(x) + (- 2a b - 8a )cosh(x) - 8a cosh(x) + 2a b cosh(x) +--R + +--R a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 8 2 7 +--R (b + a b)sinh(x) + (4b + 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 6 +--R ((4b + 4a b)cosh(x) + 2b + 6a b + 8a )sinh(x) +--R + +--R 2 3 2 2 5 +--R ((- 4b - 4a b)cosh(x) + (4b + 12a b + 32a )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 4 +--R ((- 10b - 10a b)cosh(x) + (- 2b - 6a b + 56a )cosh(x) - 8a )sinh(x) +--R + +--R 2 5 2 2 3 +--R (- 4b - 4a b)cosh(x) + (- 8b - 24a b + 64a )cosh(x) +--R + +--R 2 2 +--R (- 4b - 4a b - 32a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (4b + 4a b)cosh(x) + (- 2b - 6a b + 56a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 8b - 8a b - 48a )cosh(x) - 2b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R (4b + 4a b)cosh(x) + (4b + 12a b + 32a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 4b - 4a b - 32a )cosh(x) + (- 4b - 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 2 6 2 4 +--R (b + a b)cosh(x) + (2b + 6a b + 8a )cosh(x) - 8a cosh(x) +--R + +--R 2 2 2 +--R (- 2b - 6a b)cosh(x) - b - a b +--R / +--R 2 6 2 5 +--R 4a b sinh(x) + 24a b cosh(x)sinh(x) +--R + +--R 2 2 2 2 4 +--R (60a b cosh(x) + 8a b + 16a b)sinh(x) +--R + +--R 2 3 2 2 3 +--R (80a b cosh(x) + (32a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 2 +--R (60a b cosh(x) + (48a b + 96a b)cosh(x) + 4a b )sinh(x) +--R + +--R 2 5 2 2 3 2 +--R (24a b cosh(x) + (32a b + 64a b)cosh(x) + 8a b cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 2 2 +--R 4a b cosh(x) + (8a b + 16a b)cosh(x) + 4a b cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 6 3 2 5 +--R (- 4b - 4a b )sinh(x) + (- 24b - 24a b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 4 +--R ((- 60b - 60a b )cosh(x) - 8b - 24a b - 16a b)sinh(x) +--R + +--R 3 2 3 3 2 2 3 +--R ((- 80b - 80a b )cosh(x) + (- 32b - 96a b - 64a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 3 +--R (- 60b - 60a b )cosh(x) + (- 48b - 144a b - 96a b)cosh(x) - 4b +--R + +--R 2 +--R - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (- 24b - 24a b )cosh(x) + (- 32b - 96a b - 64a b)cosh(x) +--R + +--R 3 2 +--R (- 8b - 8a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 4b - 4a b )cosh(x) + (- 8b - 24a b - 16a b)cosh(x) +--R + +--R 3 2 2 +--R (- 4b - 4a b )cosh(x) +--R Type: Expression(Integer) +--E 451 + +--S 452 of 552 +t0781:= cosh(x)^5/(a+b*cosh(x)^2) +--R +--R +--R 5 +--R cosh(x) +--R (444) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 552 +r0781:= a^2*atan(b^(1/2)*sinh(x)/(a+b)^(1/2))/b^(5/2)/(a+b)^(1/2)-_ + a*sinh(x)/b^2+sinh(x)/b+1/3*sinh(x)^3/b +--R +--R +--R +-+ +--R 2 sinh(x)\|b 3 +-+ +-----+ +--R 3a atan(-----------) + (b sinh(x) + (3b - 3a)sinh(x))\|b \|b + a +--R +-----+ +--R \|b + a +--R (445) ------------------------------------------------------------------ +--R 2 +-+ +-----+ +--R 3b \|b \|b + a +--R Type: Expression(Integer) +--E 453 + +--S 454 of 552 +a0781:= integrate(t0781,x) +--R +--R +--R (446) +--R [ +--R 2 3 2 2 2 2 +--R 12a sinh(x) + 36a cosh(x)sinh(x) + 36a cosh(x) sinh(x) +--R + +--R 2 3 +--R 12a cosh(x) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 6b - 4a)cosh(x) + b +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R + +--R 2 3 2 2 +--R (4b + 4a b)sinh(x) + (12b + 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((12b + 12a b)cosh(x) - 4b - 4a b)sinh(x) +--R + +--R 2 3 2 +--R (4b + 4a b)cosh(x) + (- 4b - 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 6 5 2 4 +--R b sinh(x) + 6b cosh(x)sinh(x) + (15b cosh(x) + 9b - 12a)sinh(x) +--R + +--R 3 3 +--R (20b cosh(x) + (36b - 48a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) + (54b - 72a)cosh(x) - 9b + 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (36b - 48a)cosh(x) + (- 18b + 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (9b - 12a)cosh(x) + (- 9b + 12a)cosh(x) - b +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R / +--R 2 3 2 2 2 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 2 3 +--R 24b cosh(x) +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R , +--R +--R 2 3 2 2 2 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R 24a cosh(x) +--R * +--R +--------+ +--R | 2 +--R (sinh(x) + cosh(x))\|b + a b +--R atan(------------------------------) +--R 2b + 2a +--R + +--R 2 3 2 2 2 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R 24a cosh(x) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) + 3b + 4a)sinh(x) + b cosh(x) + (3b + 4a)cosh(x) +--R / +--R +--------+ +--R | 2 +--R 2\|b + a b +--R + +--R 6 5 2 4 +--R b sinh(x) + 6b cosh(x)sinh(x) + (15b cosh(x) + 9b - 12a)sinh(x) +--R + +--R 3 3 +--R (20b cosh(x) + (36b - 48a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) + (54b - 72a)cosh(x) - 9b + 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (36b - 48a)cosh(x) + (- 18b + 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (9b - 12a)cosh(x) + (- 9b + 12a)cosh(x) - b +--R * +--R +--------+ +--R | 2 +--R \|b + a b +--R / +--R 2 3 2 2 2 2 +--R 24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) +--R + +--R 2 3 +--R 24b cosh(x) +--R * +--R +--------+ +--R | 2 +--R \|b + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 454 + +--S 455 of 552 +m0781a:= a0781.1-r0781 +--R +--R +--R (447) +--R 2 3 2 2 2 2 +--R 12a sinh(x) + 36a cosh(x)sinh(x) + 36a cosh(x) sinh(x) +--R + +--R 2 3 +--R 12a cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 6b - 4a)cosh(x) + b +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R + +--R 2 3 2 2 +--R (4b + 4a b)sinh(x) + (12b + 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((12b + 12a b)cosh(x) - 4b - 4a b)sinh(x) +--R + +--R 2 3 2 +--R (4b + 4a b)cosh(x) + (- 4b - 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 3 2 2 2 2 +--R - 24a sinh(x) - 72a cosh(x)sinh(x) - 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R - 24a cosh(x) +--R * +--R +----------+ +-+ +--R | 2 sinh(x)\|b +--R \|- b - a b atan(-----------) +--R +-----+ +--R \|b + a +--R + +--R 6 5 +--R - 7b sinh(x) - 18b cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 9b cosh(x) - 15b + 12a)sinh(x) +--R + +--R 3 3 +--R (12b cosh(x) + (- 36b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) - 18b cosh(x) - 9b + 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (12b - 24a)cosh(x) + (- 18b + 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (9b - 12a)cosh(x) + (- 9b + 12a)cosh(x) - b +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- b - a b \|b \|b + a +--R / +--R 2 3 2 2 2 2 2 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- b - a b \|b \|b + a +--R Type: Expression(Integer) +--E 455 + +--S 456 of 552 +d0781a:= D(m0781a,x) +--R +--R +--R (448) +--R 12 11 2 10 +--R b sinh(x) + 2b cosh(x)sinh(x) + (- 11b cosh(x) + 6b + a)sinh(x) +--R + +--R 3 9 +--R (- 48b cosh(x) + (18b - 22a)cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 70b cosh(x) + (- 7b - 115a)cosh(x) + 15b + 5a)sinh(x) +--R + +--R 5 3 7 +--R (- 28b cosh(x) + (- 96b - 200a)cosh(x) + (52b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 42b cosh(x) + (- 160b - 110a)cosh(x) + (50b - 180a)cosh(x) + 20b +--R + +--R 10a +--R * +--R 6 +--R sinh(x) +--R + +--R 7 5 3 +--R 64b cosh(x) + (- 108b + 92a)cosh(x) + (- 32b - 360a)cosh(x) +--R + +--R (68b + 28a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 4 +--R 37b cosh(x) + (- 2b + 178a)cosh(x) + (- 108b - 290a)cosh(x) +--R + +--R 2 +--R (82b - 10a)cosh(x) + 15b + 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 +--R 10b cosh(x) + (48b + 120a)cosh(x) + (- 100b - 40a)cosh(x) +--R + +--R 3 +--R (32b - 120a)cosh(x) + (42b + 40a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 +--R b cosh(x) + (34b + 45a)cosh(x) + (- 50b + 76a)cosh(x) +--R + +--R 4 2 +--R (- 16b - 170a)cosh(x) + (41b + 60a)cosh(x) + 6b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 +--R (10b + 10a)cosh(x) + (- 16b + 40a)cosh(x) + (- 20b - 100a)cosh(x) +--R + +--R 3 +--R (16b + 40a)cosh(x) + (10b + 10a)cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 +--R (b + a)cosh(x) + (- 3b + 5a)cosh(x) + (- 6b - 22a)cosh(x) +--R + +--R 4 2 +--R (2b + 10a)cosh(x) + (5b + 5a)cosh(x) + b + a +--R / +--R 2 9 2 8 +--R 8b sinh(x) + 56b cosh(x)sinh(x) +--R + +--R 2 2 2 7 +--R (168b cosh(x) + 24b + 40a b)sinh(x) +--R + +--R 2 3 2 6 +--R (280b cosh(x) + (136b + 216a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 5 +--R (280b cosh(x) + (328b + 488a b)cosh(x) + 24b + 48a b + 32a )sinh(x) +--R + +--R 2 5 2 3 +--R 168b cosh(x) + (440b + 600a b)cosh(x) +--R + +--R 2 2 +--R (104b + 240a b + 160a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 56b cosh(x) + (360b + 440a b)cosh(x) +--R + +--R 2 2 2 2 +--R (184b + 480a b + 320a )cosh(x) + 8b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (184b + 200a b)cosh(x) +--R + +--R 2 2 3 2 +--R (168b + 480a b + 320a )cosh(x) + (24b + 24a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (56b + 56a b)cosh(x) + (80b + 240a b + 160a )cosh(x) +--R + +--R 2 2 +--R (24b + 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 7 2 2 5 2 3 +--R (8b + 8a b)cosh(x) + (16b + 48a b + 32a )cosh(x) + (8b + 8a b)cosh(x) +--R Type: Expression(Integer) +--E 456 + +--S 457 of 552 +m0781b:= a0781.2-r0781 +--R +--R +--R (449) +--R 2 3 2 2 2 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R 24a cosh(x) +--R * +--R +--------+ +--R | 2 +--R +-+ +-----+ (sinh(x) + cosh(x))\|b + a b +--R \|b \|b + a atan(------------------------------) +--R 2b + 2a +--R + +--R 2 3 2 2 2 2 +--R - 24a sinh(x) - 72a cosh(x)sinh(x) - 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R - 24a cosh(x) +--R * +--R +--------+ +-+ +--R | 2 sinh(x)\|b +--R \|b + a b atan(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 2 2 2 +--R 24a sinh(x) + 72a cosh(x)sinh(x) + 72a cosh(x) sinh(x) +--R + +--R 2 3 +--R 24a cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) + 3b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (3b + 4a)cosh(x) +--R / +--R +--------+ +--R | 2 +--R 2\|b + a b +--R + +--R 6 5 +--R - 7b sinh(x) - 18b cosh(x)sinh(x) +--R + +--R 2 4 +--R (- 9b cosh(x) - 15b + 12a)sinh(x) +--R + +--R 3 3 +--R (12b cosh(x) + (- 36b + 24a)cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (15b cosh(x) - 18b cosh(x) - 9b + 12a)sinh(x) +--R + +--R 5 3 +--R (6b cosh(x) + (12b - 24a)cosh(x) + (- 18b + 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R b cosh(x) + (9b - 12a)cosh(x) + (- 9b + 12a)cosh(x) - b +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|b \|b + a \|b + a b +--R / +--R 2 3 2 2 2 2 2 3 +--R (24b sinh(x) + 72b cosh(x)sinh(x) + 72b cosh(x) sinh(x) + 24b cosh(x) ) +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|b \|b + a \|b + a b +--R Type: Expression(Integer) +--E 457 + +--S 458 of 552 +d0781b:= D(m0781b,x) +--R +--R +--R (450) +--R 12 11 2 10 +--R b sinh(x) + 2b cosh(x)sinh(x) + (- 11b cosh(x) + 6b + a)sinh(x) +--R + +--R 3 9 +--R (- 48b cosh(x) + (18b - 22a)cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 70b cosh(x) + (- 7b - 115a)cosh(x) + 15b + 5a)sinh(x) +--R + +--R 5 3 7 +--R (- 28b cosh(x) + (- 96b - 200a)cosh(x) + (52b - 24a)cosh(x))sinh(x) +--R + +--R 6 4 2 +--R 42b cosh(x) + (- 160b - 110a)cosh(x) + (50b - 180a)cosh(x) + 20b +--R + +--R 10a +--R * +--R 6 +--R sinh(x) +--R + +--R 7 5 3 +--R 64b cosh(x) + (- 108b + 92a)cosh(x) + (- 32b - 360a)cosh(x) +--R + +--R (68b + 28a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 4 +--R 37b cosh(x) + (- 2b + 178a)cosh(x) + (- 108b - 290a)cosh(x) +--R + +--R 2 +--R (82b - 10a)cosh(x) + 15b + 10a +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 +--R 10b cosh(x) + (48b + 120a)cosh(x) + (- 100b - 40a)cosh(x) +--R + +--R 3 +--R (32b - 120a)cosh(x) + (42b + 40a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 +--R b cosh(x) + (34b + 45a)cosh(x) + (- 50b + 76a)cosh(x) +--R + +--R 4 2 +--R (- 16b - 170a)cosh(x) + (41b + 60a)cosh(x) + 6b + 5a +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 +--R (10b + 10a)cosh(x) + (- 16b + 40a)cosh(x) + (- 20b - 100a)cosh(x) +--R + +--R 3 +--R (16b + 40a)cosh(x) + (10b + 10a)cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 +--R (b + a)cosh(x) + (- 3b + 5a)cosh(x) + (- 6b - 22a)cosh(x) +--R + +--R 4 2 +--R (2b + 10a)cosh(x) + (5b + 5a)cosh(x) + b + a +--R / +--R 2 9 2 8 +--R 8b sinh(x) + 56b cosh(x)sinh(x) +--R + +--R 2 2 2 7 +--R (168b cosh(x) + 24b + 40a b)sinh(x) +--R + +--R 2 3 2 6 +--R (280b cosh(x) + (136b + 216a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 5 +--R (280b cosh(x) + (328b + 488a b)cosh(x) + 24b + 48a b + 32a )sinh(x) +--R + +--R 2 5 2 3 +--R 168b cosh(x) + (440b + 600a b)cosh(x) +--R + +--R 2 2 +--R (104b + 240a b + 160a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 56b cosh(x) + (360b + 440a b)cosh(x) +--R + +--R 2 2 2 2 +--R (184b + 480a b + 320a )cosh(x) + 8b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (184b + 200a b)cosh(x) +--R + +--R 2 2 3 2 +--R (168b + 480a b + 320a )cosh(x) + (24b + 24a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (56b + 56a b)cosh(x) + (80b + 240a b + 160a )cosh(x) +--R + +--R 2 2 +--R (24b + 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 7 2 2 5 2 3 +--R (8b + 8a b)cosh(x) + (16b + 48a b + 32a )cosh(x) + (8b + 8a b)cosh(x) +--R Type: Expression(Integer) +--E 458 + +--S 459 of 552 +t0782:= cosh(x)^6/(a+b*cosh(x)^2) +--R +--R +--R 6 +--R cosh(x) +--R (451) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 459 + +--S 460 of 552 +r0782:= a^2*x/b^3-1/2*a*x/b^2+3/8*x/b-a^(5/2)*atanh(a^(1/2)*_ + tanh(x)/(a+b)^(1/2))/b^3/(a+b)^(1/2)-_ + 1/2*a*cosh(x)*sinh(x)/b^2+3/8*cosh(x)*sinh(x)/b+_ + 1/4*cosh(x)^3*sinh(x)/b +--R +--R +--R (452) +--R +-+ +--R 2 +-+ tanh(x)\|a +--R - 8a \|a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 2 2 +-----+ +--R ((2b cosh(x) + (3b - 4a b)cosh(x))sinh(x) + (3b - 4a b + 8a )x)\|b + a +--R / +--R 3 +-----+ +--R 8b \|b + a +--R Type: Expression(Integer) +--E 460 + +--S 461 of 552 +a0782:= integrate(t0782,x) +--R +--R +--R (453) +--R [ +--R 2 4 2 3 2 2 2 +--R 32a sinh(x) + 128a cosh(x)sinh(x) + 192a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R 128a cosh(x) sinh(x) + 32a cosh(x) +--R * +--R +-----+ +--R | a +--R |----- +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4b + 4a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4b + 4a b)cosh(x) + 4b + 12a b + 8a +--R * +--R +-----+ +--R | a +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) + 8b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (56b cosh(x) + (48b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (70b cosh(x) + (120b - 120a b)cosh(x) + (24b - 32a b + 64a )x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 56b cosh(x) + (160b - 160a b)cosh(x) +--R + +--R 2 2 +--R (96b - 128a b + 256a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 28b cosh(x) + (120b - 120a b)cosh(x) +--R + +--R 2 2 2 2 +--R (144b - 192a b + 384a )x cosh(x) - 8b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (48b - 48a b)cosh(x) +--R + +--R 2 2 3 2 +--R (96b - 128a b + 256a )x cosh(x) + (- 16b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 4 +--R b cosh(x) + (8b - 8a b)cosh(x) + (24b - 32a b + 64a )x cosh(x) +--R + +--R 2 2 2 +--R (- 8b + 8a b)cosh(x) - b +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R , +--R +--R 2 4 2 3 2 2 2 +--R - 64a sinh(x) - 256a cosh(x)sinh(x) - 384a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R - 256a cosh(x) sinh(x) - 64a cosh(x) +--R * +--R +-------+ +--R | a +--R +-------+ (2b + 2a) |- ----- +--R | a \| b + a +--R |- ----- atan(----------------------------------------------------) +--R \| b + a 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) + 8b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (56b cosh(x) + (48b - 48a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (70b cosh(x) + (120b - 120a b)cosh(x) + (24b - 32a b + 64a )x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 56b cosh(x) + (160b - 160a b)cosh(x) +--R + +--R 2 2 +--R (96b - 128a b + 256a )x cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 28b cosh(x) + (120b - 120a b)cosh(x) +--R + +--R 2 2 2 2 +--R (144b - 192a b + 384a )x cosh(x) - 8b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 8b cosh(x) + (48b - 48a b)cosh(x) +--R + +--R 2 2 3 2 +--R (96b - 128a b + 256a )x cosh(x) + (- 16b + 16a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 4 +--R b cosh(x) + (8b - 8a b)cosh(x) + (24b - 32a b + 64a )x cosh(x) +--R + +--R 2 2 2 +--R (- 8b + 8a b)cosh(x) - b +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 461 + +--S 462 of 552 +m0782a:= a0782.1-r0782 +--R +--R +--R (454) +--R 2 4 2 3 2 2 2 +--R 32a sinh(x) + 128a cosh(x)sinh(x) + 192a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R 128a cosh(x) sinh(x) + 32a cosh(x) +--R * +--R +-----+ +--R | a +-----+ +--R |----- \|b + a +--R \|b + a +--R * +--R log +--R 2 2 2 +--R (4b + 4a b)sinh(x) + (8b + 8a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (4b + 4a b)cosh(x) + 4b + 12a b + 8a +--R * +--R +-----+ +--R | a +--R |----- +--R \|b + a +--R + +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6b cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 2 3 2 2 4 +--R (4b cosh(x) + (4b + 8a b)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 2 +--R (2b + 4a b)cosh(x) + b + 8a b + 8a +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 4 2 3 2 2 2 +--R 64a sinh(x) + 256a cosh(x)sinh(x) + 384a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R 256a cosh(x) sinh(x) + 64a cosh(x) +--R * +--R +-+ +--R +-+ tanh(x)\|a +--R \|a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) + 8b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (40b cosh(x) + (24b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R (6b cosh(x) + (24b + 8a b)cosh(x) )sinh(x) +--R + +--R 2 5 2 3 3 +--R (- 40b cosh(x) + (16b + 32a b)cosh(x) )sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (- 36b cosh(x) + (24b + 8a b)cosh(x) - 8b + 8a b)sinh(x) +--R + +--R 2 7 2 5 2 +--R (- 8b cosh(x) + (24b - 16a b)cosh(x) + (- 16b + 16a b)cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 2 +--R b cosh(x) + (8b - 8a b)cosh(x) + (- 8b + 8a b)cosh(x) - b +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R +-----+ +--R \|b + a +--R Type: Expression(Integer) +--E 462 + +--S 463 of 552 +d0782a:= D(m0782a,x) +--R +--R +--R (455) +--R 2 12 2 11 +--R a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 2 2 10 +--R (54a b cosh(x) + 8a b)sinh(x) +--R + +--R 2 3 2 2 9 +--R (124a b cosh(x) + (12a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 3 8 +--R (155a b cosh(x) + (72a b + 184a b)cosh(x) - 3a b + 32a )sinh(x) +--R + +--R 2 5 2 2 3 +--R 88a b cosh(x) + (192a b + 224a b)cosh(x) +--R + +--R 2 3 +--R (16a b + 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R - 28a b cosh(x) + (304a b + 48a b)cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (48a b + 96a b + 512a )cosh(x) + 2a b + 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R - 104a b cosh(x) + (312a b - 160a b)cosh(x) +--R + +--R 2 2 3 3 +--R (144a b + 240a b + 832a )cosh(x) +--R + +--R 2 2 3 +--R (24a b - 16a b + 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R - 121a b cosh(x) + (192a b - 176a b)cosh(x) +--R + +--R 2 2 3 4 +--R (194a b + 320a b + 960a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (78a b - 64a b + 480a )cosh(x) + 9a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 9 2 2 7 +--R - 100a b cosh(x) + (32a b - 96a b)cosh(x) +--R + +--R 2 2 3 5 +--R (128a b + 240a b + 832a )cosh(x) +--R + +--R 2 2 3 3 2 2 +--R (112a b - 96a b + 640a )cosh(x) + (36a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 2 2 8 +--R - 58a b cosh(x) + (- 48a b - 56a b)cosh(x) +--R + +--R 2 2 3 6 +--R (24a b + 96a b + 512a )cosh(x) +--R + +--R 2 2 3 4 2 2 2 2 +--R (78a b - 64a b + 480a )cosh(x) + (54a b + 48a b)cosh(x) + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 2 9 +--R - 20a b cosh(x) + (- 36a b - 32a b)cosh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 16a b + 192a )cosh(x) +--R + +--R 2 2 3 5 2 2 3 +--R (24a b - 16a b + 192a )cosh(x) + (36a b + 32a b)cosh(x) +--R + +--R 2 +--R 12a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 12 2 2 10 +--R - 3a b cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 2 3 8 2 3 6 +--R (- 7a b + 32a )cosh(x) + (2a b + 32a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (9a b + 8a b)cosh(x) + 6a b cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 12 3 2 11 +--R (- b - a b )sinh(x) + (- 12b - 12a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 10 +--R ((- 54b - 54a b )cosh(x) - 8a b - 8a b)sinh(x) +--R + +--R 3 2 3 3 2 2 9 +--R ((- 124b - 124a b )cosh(x) + (- 12b - 76a b - 64a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R (- 155b - 155a b )cosh(x) + (- 72b - 256a b - 184a b)cosh(x) +--R + +--R 3 2 2 3 +--R 3b + 3a b - 16a b - 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (- 88b - 88a b )cosh(x) + (- 192b - 416a b - 224a b)cosh(x) +--R + +--R 2 2 3 +--R (- 16a b - 80a b - 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (28b + 28a b )cosh(x) + (- 304b - 352a b - 48a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 3 +--R (- 48b - 144a b - 160a b - 512a )cosh(x) - 2b - 2a b + 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 7 3 2 2 5 +--R (104b + 104a b )cosh(x) + (- 312b - 152a b + 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 144b - 384a b - 176a b - 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b - 8a b + 16a b + 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 8 3 2 2 6 +--R (121b + 121a b )cosh(x) + (- 192b - 16a b + 176a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 194b - 514a b - 160a b - 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 78b - 14a b + 64a b + 480a )cosh(x) - 9b - 17a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 9 3 2 2 7 +--R (100b + 100a b )cosh(x) + (- 32b + 64a b + 96a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 128b - 368a b - 176a b - 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 16a b + 96a b + 640a )cosh(x) +--R + +--R 3 2 2 +--R (- 36b - 68a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 10 3 2 2 8 +--R (58b + 58a b )cosh(x) + (48b + 104a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 24b - 120a b - 160a b - 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 78b - 14a b + 64a b + 480a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 54b - 102a b + 48a b)cosh(x) - 6b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 11 3 2 2 9 +--R (20b + 20a b )cosh(x) + (36b + 68a b + 32a b)cosh(x) +--R + +--R 3 2 3 7 +--R (16b - 80a b - 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b - 8a b + 16a b + 192a )cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 36b - 68a b + 32a b)cosh(x) + (- 12b - 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 12 3 2 2 10 +--R (3b + 3a b )cosh(x) + (8b + 16a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 8 3 2 3 6 +--R (7b + 7a b - 16a b - 32a )cosh(x) + (- 2b - 2a b + 32a )cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 2 +--R (- 9b - 17a b + 8a b)cosh(x) + (- 6b - 6a b )cosh(x) - b - a b +--R / +--R 3 8 3 7 +--R 16a b sinh(x) + 128a b cosh(x)sinh(x) +--R + +--R 3 2 3 2 2 6 +--R (448a b cosh(x) + 32a b + 64a b )sinh(x) +--R + +--R 3 3 3 2 2 5 +--R (896a b cosh(x) + (192a b + 384a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 2 3 4 +--R (1120a b cosh(x) + (480a b + 960a b )cosh(x) + 16a b )sinh(x) +--R + +--R 3 5 3 2 2 3 3 +--R (896a b cosh(x) + (640a b + 1280a b )cosh(x) + 64a b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 2 2 4 3 2 +--R (448a b cosh(x) + (480a b + 960a b )cosh(x) + 96a b cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 2 2 5 3 3 +--R (128a b cosh(x) + (192a b + 384a b )cosh(x) + 64a b cosh(x) ) +--R * +--R sinh(x) +--R + +--R 3 8 3 2 2 6 3 4 +--R 16a b cosh(x) + (32a b + 64a b )cosh(x) + 16a b cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 8 4 3 7 +--R (- 16b - 16a b )sinh(x) + (- 128b - 128a b )cosh(x)sinh(x) +--R + +--R 4 3 2 4 3 2 2 6 +--R ((- 448b - 448a b )cosh(x) - 32b - 96a b - 64a b )sinh(x) +--R + +--R 4 3 3 4 3 2 2 +--R ((- 896b - 896a b )cosh(x) + (- 192b - 576a b - 384a b )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 +--R (- 1120b - 1120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 480b - 1440a b - 960a b )cosh(x) - 16b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 4 3 2 2 3 +--R (- 896b - 896a b )cosh(x) + (- 640b - 1920a b - 1280a b )cosh(x) +--R + +--R 4 3 +--R (- 64b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 4 3 2 2 4 +--R (- 448b - 448a b )cosh(x) + (- 480b - 1440a b - 960a b )cosh(x) +--R + +--R 4 3 2 +--R (- 96b - 96a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 4 3 2 2 5 +--R (- 128b - 128a b )cosh(x) + (- 192b - 576a b - 384a b )cosh(x) +--R + +--R 4 3 3 +--R (- 64b - 64a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (- 16b - 16a b )cosh(x) + (- 32b - 96a b - 64a b )cosh(x) +--R + +--R 4 3 4 +--R (- 16b - 16a b )cosh(x) +--R Type: Expression(Integer) +--E 463 + +--S 464 of 552 +m0782b:= a0782.2-r0782 +--R +--R +--R (456) +--R 2 4 2 3 2 2 2 +--R 64a sinh(x) + 256a cosh(x)sinh(x) + 384a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R 256a cosh(x) sinh(x) + 64a cosh(x) +--R * +--R +-+ +--R +-+ tanh(x)\|a +--R \|a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 4 2 3 2 2 2 +--R - 64a sinh(x) - 256a cosh(x)sinh(x) - 384a cosh(x) sinh(x) +--R + +--R 2 3 2 4 +--R - 256a cosh(x) sinh(x) - 64a cosh(x) +--R * +--R +-------+ +--R | a +-----+ +--R |- ----- \|b + a +--R \| b + a +--R * +--R +-------+ +--R | a +--R (2b + 2a) |- ----- +--R \| b + a +--R atan(----------------------------------------------------) +--R 2 2 +--R b sinh(x) + 2b cosh(x)sinh(x) + b cosh(x) + b + 2a +--R + +--R 2 8 2 7 2 2 2 6 +--R b sinh(x) + 8b cosh(x)sinh(x) + (28b cosh(x) + 8b - 8a b)sinh(x) +--R + +--R 2 3 2 5 +--R (40b cosh(x) + (24b - 16a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 4 +--R (6b cosh(x) + (24b + 8a b)cosh(x) )sinh(x) +--R + +--R 2 5 2 3 3 +--R (- 40b cosh(x) + (16b + 32a b)cosh(x) )sinh(x) +--R + +--R 2 6 2 4 2 2 +--R (- 36b cosh(x) + (24b + 8a b)cosh(x) - 8b + 8a b)sinh(x) +--R + +--R 2 7 2 5 2 +--R (- 8b cosh(x) + (24b - 16a b)cosh(x) + (- 16b + 16a b)cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 8 2 6 2 2 2 +--R b cosh(x) + (8b - 8a b)cosh(x) + (- 8b + 8a b)cosh(x) - b +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 4 3 3 3 2 2 +--R 64b sinh(x) + 256b cosh(x)sinh(x) + 384b cosh(x) sinh(x) +--R + +--R 3 3 3 4 +--R 256b cosh(x) sinh(x) + 64b cosh(x) +--R * +--R +-----+ +--R \|b + a +--R Type: Expression(Integer) +--E 464 + +--S 465 of 552 +d0782b:= D(m0782b,x) +--R +--R +--R (457) +--R 2 12 2 11 +--R a b sinh(x) + 12a b cosh(x)sinh(x) +--R + +--R 2 2 2 10 +--R (54a b cosh(x) + 8a b)sinh(x) +--R + +--R 2 3 2 2 9 +--R (124a b cosh(x) + (12a b + 64a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 3 8 +--R (155a b cosh(x) + (72a b + 184a b)cosh(x) - 3a b + 32a )sinh(x) +--R + +--R 2 5 2 2 3 +--R 88a b cosh(x) + (192a b + 224a b)cosh(x) +--R + +--R 2 3 +--R (16a b + 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R - 28a b cosh(x) + (304a b + 48a b)cosh(x) +--R + +--R 2 2 3 2 2 3 +--R (48a b + 96a b + 512a )cosh(x) + 2a b + 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 7 2 2 5 +--R - 104a b cosh(x) + (312a b - 160a b)cosh(x) +--R + +--R 2 2 3 3 +--R (144a b + 240a b + 832a )cosh(x) +--R + +--R 2 2 3 +--R (24a b - 16a b + 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R - 121a b cosh(x) + (192a b - 176a b)cosh(x) +--R + +--R 2 2 3 4 +--R (194a b + 320a b + 960a )cosh(x) +--R + +--R 2 2 3 2 2 2 +--R (78a b - 64a b + 480a )cosh(x) + 9a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 9 2 2 7 +--R - 100a b cosh(x) + (32a b - 96a b)cosh(x) +--R + +--R 2 2 3 5 +--R (128a b + 240a b + 832a )cosh(x) +--R + +--R 2 2 3 3 2 2 +--R (112a b - 96a b + 640a )cosh(x) + (36a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 2 2 8 +--R - 58a b cosh(x) + (- 48a b - 56a b)cosh(x) +--R + +--R 2 2 3 6 +--R (24a b + 96a b + 512a )cosh(x) +--R + +--R 2 2 3 4 2 2 2 2 +--R (78a b - 64a b + 480a )cosh(x) + (54a b + 48a b)cosh(x) + 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 11 2 2 9 +--R - 20a b cosh(x) + (- 36a b - 32a b)cosh(x) +--R + +--R 2 2 3 7 +--R (- 16a b + 16a b + 192a )cosh(x) +--R + +--R 2 2 3 5 2 2 3 +--R (24a b - 16a b + 192a )cosh(x) + (36a b + 32a b)cosh(x) +--R + +--R 2 +--R 12a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 12 2 2 10 +--R - 3a b cosh(x) + (- 8a b - 8a b)cosh(x) +--R + +--R 2 3 8 2 3 6 +--R (- 7a b + 32a )cosh(x) + (2a b + 32a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (9a b + 8a b)cosh(x) + 6a b cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 12 3 2 11 +--R (- b - a b )sinh(x) + (- 12b - 12a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 10 +--R ((- 54b - 54a b )cosh(x) - 8a b - 8a b)sinh(x) +--R + +--R 3 2 3 3 2 2 9 +--R ((- 124b - 124a b )cosh(x) + (- 12b - 76a b - 64a b)cosh(x))sinh(x) +--R + +--R 3 2 4 3 2 2 2 +--R (- 155b - 155a b )cosh(x) + (- 72b - 256a b - 184a b)cosh(x) +--R + +--R 3 2 2 3 +--R 3b + 3a b - 16a b - 32a +--R * +--R 8 +--R sinh(x) +--R + +--R 3 2 5 3 2 2 3 +--R (- 88b - 88a b )cosh(x) + (- 192b - 416a b - 224a b)cosh(x) +--R + +--R 2 2 3 +--R (- 16a b - 80a b - 192a )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 6 3 2 2 4 +--R (28b + 28a b )cosh(x) + (- 304b - 352a b - 48a b)cosh(x) +--R + +--R 3 2 2 3 2 3 2 3 +--R (- 48b - 144a b - 160a b - 512a )cosh(x) - 2b - 2a b + 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 7 3 2 2 5 +--R (104b + 104a b )cosh(x) + (- 312b - 152a b + 160a b)cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 144b - 384a b - 176a b - 832a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24b - 8a b + 16a b + 192a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 8 3 2 2 6 +--R (121b + 121a b )cosh(x) + (- 192b - 16a b + 176a b)cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 194b - 514a b - 160a b - 960a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 78b - 14a b + 64a b + 480a )cosh(x) - 9b - 17a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 9 3 2 2 7 +--R (100b + 100a b )cosh(x) + (- 32b + 64a b + 96a b)cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 128b - 368a b - 176a b - 832a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 112b - 16a b + 96a b + 640a )cosh(x) +--R + +--R 3 2 2 +--R (- 36b - 68a b + 32a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 10 3 2 2 8 +--R (58b + 58a b )cosh(x) + (48b + 104a b + 56a b)cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 24b - 120a b - 160a b - 512a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 78b - 14a b + 64a b + 480a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 54b - 102a b + 48a b)cosh(x) - 6b - 6a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 11 3 2 2 9 +--R (20b + 20a b )cosh(x) + (36b + 68a b + 32a b)cosh(x) +--R + +--R 3 2 3 7 +--R (16b - 80a b - 192a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 24b - 8a b + 16a b + 192a )cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (- 36b - 68a b + 32a b)cosh(x) + (- 12b - 12a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 12 3 2 2 10 +--R (3b + 3a b )cosh(x) + (8b + 16a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 8 3 2 3 6 +--R (7b + 7a b - 16a b - 32a )cosh(x) + (- 2b - 2a b + 32a )cosh(x) +--R + +--R 3 2 2 4 3 2 2 3 2 +--R (- 9b - 17a b + 8a b)cosh(x) + (- 6b - 6a b )cosh(x) - b - a b +--R / +--R 3 8 3 7 +--R 16a b sinh(x) + 128a b cosh(x)sinh(x) +--R + +--R 3 2 3 2 2 6 +--R (448a b cosh(x) + 32a b + 64a b )sinh(x) +--R + +--R 3 3 3 2 2 5 +--R (896a b cosh(x) + (192a b + 384a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 2 3 4 +--R (1120a b cosh(x) + (480a b + 960a b )cosh(x) + 16a b )sinh(x) +--R + +--R 3 5 3 2 2 3 3 +--R (896a b cosh(x) + (640a b + 1280a b )cosh(x) + 64a b cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 3 2 2 4 3 2 +--R (448a b cosh(x) + (480a b + 960a b )cosh(x) + 96a b cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 3 2 2 5 3 3 +--R (128a b cosh(x) + (192a b + 384a b )cosh(x) + 64a b cosh(x) ) +--R * +--R sinh(x) +--R + +--R 3 8 3 2 2 6 3 4 +--R 16a b cosh(x) + (32a b + 64a b )cosh(x) + 16a b cosh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 8 4 3 7 +--R (- 16b - 16a b )sinh(x) + (- 128b - 128a b )cosh(x)sinh(x) +--R + +--R 4 3 2 4 3 2 2 6 +--R ((- 448b - 448a b )cosh(x) - 32b - 96a b - 64a b )sinh(x) +--R + +--R 4 3 3 4 3 2 2 +--R ((- 896b - 896a b )cosh(x) + (- 192b - 576a b - 384a b )cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 4 +--R (- 1120b - 1120a b )cosh(x) +--R + +--R 4 3 2 2 2 4 3 +--R (- 480b - 1440a b - 960a b )cosh(x) - 16b - 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 5 4 3 2 2 3 +--R (- 896b - 896a b )cosh(x) + (- 640b - 1920a b - 1280a b )cosh(x) +--R + +--R 4 3 +--R (- 64b - 64a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 6 4 3 2 2 4 +--R (- 448b - 448a b )cosh(x) + (- 480b - 1440a b - 960a b )cosh(x) +--R + +--R 4 3 2 +--R (- 96b - 96a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 7 4 3 2 2 5 +--R (- 128b - 128a b )cosh(x) + (- 192b - 576a b - 384a b )cosh(x) +--R + +--R 4 3 3 +--R (- 64b - 64a b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 8 4 3 2 2 6 +--R (- 16b - 16a b )cosh(x) + (- 32b - 96a b - 64a b )cosh(x) +--R + +--R 4 3 4 +--R (- 16b - 16a b )cosh(x) +--R Type: Expression(Integer) +--E 465 + +--S 466 of 552 +t0783:= cosh(x)^7/(a+b*cosh(x)^2) +--R +--R +--R 7 +--R cosh(x) +--R (458) -------------- +--R 2 +--R b cosh(x) + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 552 +r0783:= -a^3*atan(b^(1/2)*sinh(x)/(a+b)^(1/2))/b^(7/2)/(a+b)^(1/2)+_ + a^2*sinh(x)/b^3-a*sinh(x)/b^2+sinh(x)/b-1/3*a*sinh(x)^3/b^2+_ + 2/3*sinh(x)^3/b+1/5*sinh(x)^5/b +--R +--R +--R (459) +--R +-+ +--R 3 sinh(x)\|b +--R - 15a atan(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 5 2 3 2 2 +--R (3b sinh(x) + (10b - 5a b)sinh(x) + (15b - 15a b + 15a )sinh(x)) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R / +--R 3 +-+ +-----+ +--R 15b \|b \|b + a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 552 +a0783:= integrate(t0783,x) +--R +--R +--R (460) +--R [ +--R 3 5 3 4 3 2 3 +--R 240a sinh(x) + 1200a cosh(x)sinh(x) + 2400a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 2400a cosh(x) sinh(x) + 1200a cosh(x) sinh(x) + 240a cosh(x) +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 6b - 4a)cosh(x) + b +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R + +--R 2 3 2 2 +--R (- 4b - 4a b)sinh(x) + (- 12b - 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((- 12b - 12a b)cosh(x) + 4b + 4a b)sinh(x) +--R + +--R 2 3 2 +--R (- 4b - 4a b)cosh(x) + (4b + 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) + 25b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (200b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (700b - 560a b)cosh(x) + 150b - 180a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 756b cosh(x) + (1400b - 1120a b)cosh(x) +--R + +--R 2 2 +--R (900b - 1080a b + 1440a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (1750b - 1400a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (2250b - 2700a b + 3600a )cosh(x) - 150b + 180a b - 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (1400b - 1120a b)cosh(x) +--R + +--R 2 2 3 +--R (3000b - 3600a b + 4800a )cosh(x) +--R + +--R 2 2 +--R (- 600b + 720a b - 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (700b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (2250b - 2700a b + 3600a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 900b + 1080a b - 1440a )cosh(x) - 25b + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (200b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (900b - 1080a b + 1440a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 600b + 720a b - 960a )cosh(x) + (- 50b + 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (25b - 20a b)cosh(x) +--R + +--R 2 2 6 +--R (150b - 180a b + 240a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 150b + 180a b - 240a )cosh(x) + (- 25b + 20a b)cosh(x) - 3b +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R , +--R +--R 3 5 3 4 3 2 3 +--R - 480a sinh(x) - 2400a cosh(x)sinh(x) - 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R - 4800a cosh(x) sinh(x) - 2400a cosh(x) sinh(x) - 480a cosh(x) +--R * +--R +--------+ +--R | 2 +--R (sinh(x) + cosh(x))\|b + a b +--R atan(------------------------------) +--R 2b + 2a +--R + +--R 3 5 3 4 3 2 3 +--R - 480a sinh(x) - 2400a cosh(x)sinh(x) - 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R - 4800a cosh(x) sinh(x) - 2400a cosh(x) sinh(x) - 480a cosh(x) +--R * +--R atan +--R 3 2 +--R b sinh(x) + 3b cosh(x)sinh(x) +--R + +--R 2 3 +--R (3b cosh(x) + 3b + 4a)sinh(x) + b cosh(x) + (3b + 4a)cosh(x) +--R / +--R +--------+ +--R | 2 +--R 2\|b + a b +--R + +--R 2 10 2 9 +--R 3b sinh(x) + 30b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (135b cosh(x) + 25b - 20a b)sinh(x) +--R + +--R 2 3 2 7 +--R (360b cosh(x) + (200b - 160a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 630b cosh(x) + (700b - 560a b)cosh(x) + 150b - 180a b +--R + +--R 2 +--R 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 756b cosh(x) + (1400b - 1120a b)cosh(x) +--R + +--R 2 2 +--R (900b - 1080a b + 1440a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (1750b - 1400a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (2250b - 2700a b + 3600a )cosh(x) - 150b + 180a b - 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (1400b - 1120a b)cosh(x) +--R + +--R 2 2 3 +--R (3000b - 3600a b + 4800a )cosh(x) +--R + +--R 2 2 +--R (- 600b + 720a b - 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (700b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (2250b - 2700a b + 3600a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 900b + 1080a b - 1440a )cosh(x) - 25b + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (200b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (900b - 1080a b + 1440a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 600b + 720a b - 960a )cosh(x) + (- 50b + 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (25b - 20a b)cosh(x) +--R + +--R 2 2 6 +--R (150b - 180a b + 240a )cosh(x) +--R + +--R 2 2 4 2 2 2 +--R (- 150b + 180a b - 240a )cosh(x) + (- 25b + 20a b)cosh(x) - 3b +--R * +--R +--------+ +--R | 2 +--R \|b + a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +--------+ +--R | 2 +--R \|b + a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 468 + +--S 469 of 552 +m0783a:= a0783.1-r0783 +--R +--R +--R (461) +--R 3 5 3 4 3 2 3 +--R 240a sinh(x) + 1200a cosh(x)sinh(x) + 2400a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 2400a cosh(x) sinh(x) + 1200a cosh(x) sinh(x) + 240a cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R * +--R log +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) - 6b - 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (- 12b - 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (- 6b - 4a)cosh(x) + b +--R * +--R +----------+ +--R | 2 +--R \|- b - a b +--R + +--R 2 3 2 2 +--R (- 4b - 4a b)sinh(x) + (- 12b - 12a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R ((- 12b - 12a b)cosh(x) + 4b + 4a b)sinh(x) +--R + +--R 2 3 2 +--R (- 4b - 4a b)cosh(x) + (4b + 4a b)cosh(x) +--R / +--R 4 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 +--R (6b cosh(x) + 2b + 4a)sinh(x) +--R + +--R 3 4 +--R (4b cosh(x) + (4b + 8a)cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 +--R (2b + 4a)cosh(x) + b +--R + +--R 3 5 3 4 3 2 3 +--R 480a sinh(x) + 2400a cosh(x)sinh(x) + 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800a cosh(x) sinh(x) + 2400a cosh(x) sinh(x) + 480a cosh(x) +--R * +--R +----------+ +-+ +--R | 2 sinh(x)\|b +--R \|- b - a b atan(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 10 2 9 +--R - 93b sinh(x) - 450b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (- 825b cosh(x) - 295b + 140a b)sinh(x) +--R + +--R 2 3 2 7 +--R (- 600b cosh(x) + (- 1400b + 640a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 150b cosh(x) + (- 2500b + 1040a b)cosh(x) - 330b + 300a b +--R + +--R 2 +--R - 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 660b cosh(x) + (- 1800b + 480a b)cosh(x) +--R + +--R 2 2 +--R (- 1500b + 1320a b - 960a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (150b - 600a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2550b + 2100a b - 1200a )cosh(x) - 150b + 180a b - 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (1080b - 960a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- 1800b + 1200a b)cosh(x) + (- 600b + 720a b - 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (700b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (- 150b - 300a b + 1200a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 900b + 1080a b - 1440a )cosh(x) - 25b + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (200b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (420b - 600a b + 960a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 600b + 720a b - 960a )cosh(x) + (- 50b + 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (25b - 20a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (150b - 180a b + 240a )cosh(x) + (- 150b + 180a b - 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 25b + 20a b)cosh(x) - 3b +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- b - a b \|b \|b + a +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- b - a b \|b \|b + a +--R Type: Expression(Integer) +--E 469 + +--S 470 of 552 +d0783a:= D(m0783a,x) +--R +--R +--R (462) +--R 16 15 2 14 +--R b sinh(x) - 18b cosh(x)sinh(x) + (- 197b cosh(x) + 8b + a)sinh(x) +--R + +--R 3 13 +--R (- 788b cosh(x) + (- 62b - 114a)cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (- 1687b cosh(x) + (- 759b - 805a)cosh(x) + 28b + 7a)sinh(x) +--R + +--R 5 3 +--R (- 2030b cosh(x) + (- 2896b - 2324a)cosh(x) + (- 26b - 300a)cosh(x)) +--R * +--R 11 +--R sinh(x) +--R + +--R 6 4 +--R - 1029b cosh(x) + (- 5838b - 3479a)cosh(x) +--R + +--R 2 +--R (- 961b - 2226a)cosh(x) + 56b + 21a +--R * +--R 10 +--R sinh(x) +--R + +--R 7 5 3 +--R 744b cosh(x) + (- 6790b - 2478a)cosh(x) + (- 3748b - 6524a)cosh(x) +--R + +--R (170b - 174a)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 6 4 +--R 1851b cosh(x) + (- 3969b + 315a)cosh(x) + (- 7229b - 9975a)cosh(x) +--R + +--R 2 +--R (- 187b - 1743a)cosh(x) + 70b + 35a +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 +--R 1714b cosh(x) + (464b + 2536a)cosh(x) + (- 8140b - 7896a)cosh(x) +--R + +--R 3 +--R (- 1664b - 5544a)cosh(x) + (330b + 152a)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 6 +--R 969b cosh(x) + (2948b + 2875a)cosh(x) + (- 5282b - 1596a)cosh(x) +--R + +--R 4 2 +--R (- 3508b - 9030a)cosh(x) + (577b + 84a)cosh(x) + 56b + 35a +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 +--R 364b cosh(x) + (2678b + 2002a)cosh(x) + (- 1344b + 2856a)cosh(x) +--R + +--R 5 3 +--R (- 3980b - 8148a)cosh(x) + (356b - 728a)cosh(x) +--R + +--R (262b + 210a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 +--R 91b cosh(x) + (1367b + 1001a)cosh(x) + (762b + 3081a)cosh(x) +--R + +--R 6 4 +--R (- 2770b - 3654a)cosh(x) + (- 225b - 2030a)cosh(x) +--R + +--R 2 +--R (491b + 525a)cosh(x) + 28b + 21a +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 +--R 14b cosh(x) + (448b + 364a)cosh(x) + (886b + 1540a)cosh(x) +--R + +--R 7 5 +--R (- 1232b - 168a)cosh(x) + (- 550b - 2520a)cosh(x) +--R + +--R 3 +--R (464b + 700a)cosh(x) + (98b + 84a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 +--R b cosh(x) + (98b + 91a)cosh(x) + (387b + 462a)cosh(x) +--R + +--R 8 6 +--R (- 364b + 561a)cosh(x) + (- 425b - 1708a)cosh(x) +--R + +--R 4 2 +--R (226b + 525a)cosh(x) + (133b + 126a)cosh(x) + 8b + 7a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R (14b + 14a)cosh(x) + (84b + 84a)cosh(x) + (- 78b + 210a)cosh(x) +--R + +--R 7 5 3 +--R (- 168b - 616a)cosh(x) + (50b + 210a)cosh(x) + (84b + 84a)cosh(x) +--R + +--R (14b + 14a)cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 +--R (b + a)cosh(x) + (7b + 7a)cosh(x) + (- 11b + 21a)cosh(x) +--R + +--R 8 6 4 +--R (- 29b - 93a)cosh(x) + (3b + 35a)cosh(x) + (21b + 21a)cosh(x) +--R + +--R 2 +--R (7b + 7a)cosh(x) + b + a +--R / +--R 2 11 2 10 +--R 32b sinh(x) + 288b cosh(x)sinh(x) +--R + +--R 2 2 2 9 +--R (1152b cosh(x) + 96b + 160a b)sinh(x) +--R + +--R 2 3 2 8 +--R (2688b cosh(x) + (736b + 1184a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (4032b cosh(x) + (2496b + 3840a b)cosh(x) + 96b + 192a b + 128a ) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 4032b cosh(x) + (4928b + 7168a b)cosh(x) +--R + +--R 2 2 +--R (608b + 1344a b + 896a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 2688b cosh(x) + (6272b + 8512a b)cosh(x) +--R + +--R 2 2 2 2 +--R (1664b + 4032a b + 2688a )cosh(x) + 32b + 32a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 1152b cosh(x) + (5376b + 6720a b)cosh(x) +--R + +--R 2 2 3 2 +--R (2560b + 6720a b + 4480a )cosh(x) + (160b + 160a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 288b cosh(x) + (3136b + 3584a b)cosh(x) +--R + +--R 2 2 4 2 2 +--R (2400b + 6720a b + 4480a )cosh(x) + (320b + 320a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 32b cosh(x) + (1216b + 1280a b)cosh(x) +--R + +--R 2 2 5 2 3 +--R (1376b + 4032a b + 2688a )cosh(x) + (320b + 320a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R (288b + 288a b)cosh(x) + (448b + 1344a b + 896a )cosh(x) +--R + +--R 2 4 +--R (160b + 160a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 9 2 2 7 +--R (32b + 32a b)cosh(x) + (64b + 192a b + 128a )cosh(x) +--R + +--R 2 5 +--R (32b + 32a b)cosh(x) +--R Type: Expression(Integer) +--E 470 + +--S 471 of 552 +m0783b:= a0783.2-r0783 +--R +--R +--R (463) +--R 3 5 3 4 3 2 3 +--R - 480a sinh(x) - 2400a cosh(x)sinh(x) - 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R - 4800a cosh(x) sinh(x) - 2400a cosh(x) sinh(x) - 480a cosh(x) +--R * +--R +--------+ +--R | 2 +--R +-+ +-----+ (sinh(x) + cosh(x))\|b + a b +--R \|b \|b + a atan(------------------------------) +--R 2b + 2a +--R + +--R 3 5 3 4 3 2 3 +--R 480a sinh(x) + 2400a cosh(x)sinh(x) + 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800a cosh(x) sinh(x) + 2400a cosh(x) sinh(x) + 480a cosh(x) +--R * +--R +--------+ +-+ +--R | 2 sinh(x)\|b +--R \|b + a b atan(-----------) +--R +-----+ +--R \|b + a +--R + +--R 3 5 3 4 3 2 3 +--R - 480a sinh(x) - 2400a cosh(x)sinh(x) - 4800a cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R - 4800a cosh(x) sinh(x) - 2400a cosh(x) sinh(x) - 480a cosh(x) +--R * +--R +-+ +-----+ +--R \|b \|b + a +--R * +--R atan +--R 3 2 2 +--R b sinh(x) + 3b cosh(x)sinh(x) + (3b cosh(x) + 3b + 4a)sinh(x) +--R + +--R 3 +--R b cosh(x) + (3b + 4a)cosh(x) +--R / +--R +--------+ +--R | 2 +--R 2\|b + a b +--R + +--R 2 10 2 9 +--R - 93b sinh(x) - 450b cosh(x)sinh(x) +--R + +--R 2 2 2 8 +--R (- 825b cosh(x) - 295b + 140a b)sinh(x) +--R + +--R 2 3 2 7 +--R (- 600b cosh(x) + (- 1400b + 640a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R 150b cosh(x) + (- 2500b + 1040a b)cosh(x) - 330b + 300a b +--R + +--R 2 +--R - 240a +--R * +--R 6 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 660b cosh(x) + (- 1800b + 480a b)cosh(x) +--R + +--R 2 2 +--R (- 1500b + 1320a b - 960a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 630b cosh(x) + (150b - 600a b)cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2550b + 2100a b - 1200a )cosh(x) - 150b + 180a b - 240a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 360b cosh(x) + (1080b - 960a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- 1800b + 1200a b)cosh(x) + (- 600b + 720a b - 960a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 135b cosh(x) + (700b - 560a b)cosh(x) +--R + +--R 2 2 4 +--R (- 150b - 300a b + 1200a )cosh(x) +--R + +--R 2 2 2 2 +--R (- 900b + 1080a b - 1440a )cosh(x) - 25b + 20a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 30b cosh(x) + (200b - 160a b)cosh(x) +--R + +--R 2 2 5 +--R (420b - 600a b + 960a )cosh(x) +--R + +--R 2 2 3 2 +--R (- 600b + 720a b - 960a )cosh(x) + (- 50b + 40a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 10 2 8 +--R 3b cosh(x) + (25b - 20a b)cosh(x) +--R + +--R 2 2 6 2 2 4 +--R (150b - 180a b + 240a )cosh(x) + (- 150b + 180a b - 240a )cosh(x) +--R + +--R 2 2 2 +--R (- 25b + 20a b)cosh(x) - 3b +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|b \|b + a \|b + a b +--R / +--R 3 5 3 4 3 2 3 +--R 480b sinh(x) + 2400b cosh(x)sinh(x) + 4800b cosh(x) sinh(x) +--R + +--R 3 3 2 3 4 3 5 +--R 4800b cosh(x) sinh(x) + 2400b cosh(x) sinh(x) + 480b cosh(x) +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|b \|b + a \|b + a b +--R Type: Expression(Integer) +--E 471 + +--S 472 of 552 +d0783b:= D(m0783b,x) +--R +--R +--R (464) +--R 16 15 2 14 +--R b sinh(x) - 18b cosh(x)sinh(x) + (- 197b cosh(x) + 8b + a)sinh(x) +--R + +--R 3 13 +--R (- 788b cosh(x) + (- 62b - 114a)cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (- 1687b cosh(x) + (- 759b - 805a)cosh(x) + 28b + 7a)sinh(x) +--R + +--R 5 3 +--R (- 2030b cosh(x) + (- 2896b - 2324a)cosh(x) + (- 26b - 300a)cosh(x)) +--R * +--R 11 +--R sinh(x) +--R + +--R 6 4 +--R - 1029b cosh(x) + (- 5838b - 3479a)cosh(x) +--R + +--R 2 +--R (- 961b - 2226a)cosh(x) + 56b + 21a +--R * +--R 10 +--R sinh(x) +--R + +--R 7 5 3 +--R 744b cosh(x) + (- 6790b - 2478a)cosh(x) + (- 3748b - 6524a)cosh(x) +--R + +--R (170b - 174a)cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 6 4 +--R 1851b cosh(x) + (- 3969b + 315a)cosh(x) + (- 7229b - 9975a)cosh(x) +--R + +--R 2 +--R (- 187b - 1743a)cosh(x) + 70b + 35a +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 +--R 1714b cosh(x) + (464b + 2536a)cosh(x) + (- 8140b - 7896a)cosh(x) +--R + +--R 3 +--R (- 1664b - 5544a)cosh(x) + (330b + 152a)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 6 +--R 969b cosh(x) + (2948b + 2875a)cosh(x) + (- 5282b - 1596a)cosh(x) +--R + +--R 4 2 +--R (- 3508b - 9030a)cosh(x) + (577b + 84a)cosh(x) + 56b + 35a +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 +--R 364b cosh(x) + (2678b + 2002a)cosh(x) + (- 1344b + 2856a)cosh(x) +--R + +--R 5 3 +--R (- 3980b - 8148a)cosh(x) + (356b - 728a)cosh(x) +--R + +--R (262b + 210a)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 +--R 91b cosh(x) + (1367b + 1001a)cosh(x) + (762b + 3081a)cosh(x) +--R + +--R 6 4 +--R (- 2770b - 3654a)cosh(x) + (- 225b - 2030a)cosh(x) +--R + +--R 2 +--R (491b + 525a)cosh(x) + 28b + 21a +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 +--R 14b cosh(x) + (448b + 364a)cosh(x) + (886b + 1540a)cosh(x) +--R + +--R 7 5 +--R (- 1232b - 168a)cosh(x) + (- 550b - 2520a)cosh(x) +--R + +--R 3 +--R (464b + 700a)cosh(x) + (98b + 84a)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 +--R b cosh(x) + (98b + 91a)cosh(x) + (387b + 462a)cosh(x) +--R + +--R 8 6 +--R (- 364b + 561a)cosh(x) + (- 425b - 1708a)cosh(x) +--R + +--R 4 2 +--R (226b + 525a)cosh(x) + (133b + 126a)cosh(x) + 8b + 7a +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 +--R (14b + 14a)cosh(x) + (84b + 84a)cosh(x) + (- 78b + 210a)cosh(x) +--R + +--R 7 5 3 +--R (- 168b - 616a)cosh(x) + (50b + 210a)cosh(x) + (84b + 84a)cosh(x) +--R + +--R (14b + 14a)cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 +--R (b + a)cosh(x) + (7b + 7a)cosh(x) + (- 11b + 21a)cosh(x) +--R + +--R 8 6 4 +--R (- 29b - 93a)cosh(x) + (3b + 35a)cosh(x) + (21b + 21a)cosh(x) +--R + +--R 2 +--R (7b + 7a)cosh(x) + b + a +--R / +--R 2 11 2 10 +--R 32b sinh(x) + 288b cosh(x)sinh(x) +--R + +--R 2 2 2 9 +--R (1152b cosh(x) + 96b + 160a b)sinh(x) +--R + +--R 2 3 2 8 +--R (2688b cosh(x) + (736b + 1184a b)cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 2 +--R (4032b cosh(x) + (2496b + 3840a b)cosh(x) + 96b + 192a b + 128a ) +--R * +--R 7 +--R sinh(x) +--R + +--R 2 5 2 3 +--R 4032b cosh(x) + (4928b + 7168a b)cosh(x) +--R + +--R 2 2 +--R (608b + 1344a b + 896a )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 6 2 4 +--R 2688b cosh(x) + (6272b + 8512a b)cosh(x) +--R + +--R 2 2 2 2 +--R (1664b + 4032a b + 2688a )cosh(x) + 32b + 32a b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 7 2 5 +--R 1152b cosh(x) + (5376b + 6720a b)cosh(x) +--R + +--R 2 2 3 2 +--R (2560b + 6720a b + 4480a )cosh(x) + (160b + 160a b)cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 8 2 6 +--R 288b cosh(x) + (3136b + 3584a b)cosh(x) +--R + +--R 2 2 4 2 2 +--R (2400b + 6720a b + 4480a )cosh(x) + (320b + 320a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 9 2 7 +--R 32b cosh(x) + (1216b + 1280a b)cosh(x) +--R + +--R 2 2 5 2 3 +--R (1376b + 4032a b + 2688a )cosh(x) + (320b + 320a b)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 8 2 2 6 +--R (288b + 288a b)cosh(x) + (448b + 1344a b + 896a )cosh(x) +--R + +--R 2 4 +--R (160b + 160a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 9 2 2 7 +--R (32b + 32a b)cosh(x) + (64b + 192a b + 128a )cosh(x) +--R + +--R 2 5 +--R (32b + 32a b)cosh(x) +--R Type: Expression(Integer) +--E 472 + +--S 473 of 552 +t0784:= sinh(x)^2/(a-a*cosh(x)^2) +--R +--R +--R 2 +--R sinh(x) +--R (465) - -------------- +--R 2 +--R a cosh(x) - a +--R Type: Expression(Integer) +--E 473 + +--S 474 of 552 +r0784:= -x/a +--R +--R +--R x +--R (466) - - +--R a +--R Type: Fraction(Polynomial(Integer)) +--E 474 + +--S 475 of 552 +a0784:= integrate(t0784,x) +--R +--R +--R x +--R (467) - - +--R a +--R Type: Union(Expression(Integer),...) +--E 475 + +--S 476 of 552 +m0784:= a0784-r0784 +--R +--R +--R (468) 0 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 552 +d0784:= D(m0784,x) +--R +--R +--R (469) 0 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 552 +t0785:= sinh(x)^3/(a-a*cosh(x)^2) +--R +--R +--R 3 +--R sinh(x) +--R (470) - -------------- +--R 2 +--R a cosh(x) - a +--R Type: Expression(Integer) +--E 478 + +--S 479 of 552 +r0785:= -cosh(x)/a +--R +--R +--R cosh(x) +--R (471) - ------- +--R a +--R Type: Expression(Integer) +--E 479 + +--S 480 of 552 +a0785:= integrate(t0785,x) +--R +--R +--R cosh(x) +--R (472) - ------- +--R a +--R Type: Union(Expression(Integer),...) +--E 480 + +--S 481 of 552 +m0785:= a0785-r0785 +--R +--R +--R (473) 0 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 552 +d0785:= D(m0785,x) +--R +--R +--R (474) 0 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 552 +t0786:= sinh(x)^4/(a-a*cosh(x)^2) +--R +--R +--R 4 +--R sinh(x) +--R (475) - -------------- +--R 2 +--R a cosh(x) - a +--R Type: Expression(Integer) +--E 483 + +--S 484 of 552 +r0786:= -1/2*(-x+cosh(x)*sinh(x))/a +--R +--R +--R - cosh(x)sinh(x) + x +--R (476) -------------------- +--R 2a +--R Type: Expression(Integer) +--E 484 + +--S 485 of 552 +a0786:= integrate(t0786,x) +--R +--R +--R - cosh(x)sinh(x) + x +--R (477) -------------------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 552 +m0786:= a0786-r0786 +--R +--R +--R (478) 0 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 552 +d0786:= D(m0786,x) +--R +--R +--R (479) 0 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 552 +t0787:= tanh(x)/(1+cosh(x)^2) +--R +--R +--R tanh(x) +--R (480) ------------ +--R 2 +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 488 + +--S 489 of 552 +r0787:= -atanh(3+2*sinh(x)^2) +--R +--R +--R 2 +--R (481) - atanh(2sinh(x) + 3) +--R Type: Expression(Integer) +--E 489 + +--S 490 of 552 +a0787:= integrate(t0787,x) +--R +--R +--R (482) +--R 2 2 +--R 2sinh(x) + 2cosh(x) + 6 2cosh(x) +--R - log(-------------------------------------) + 2log(- -----------------) +--R 2 2 sinh(x) - cosh(x) +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R ------------------------------------------------------------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 490 + +--S 491 of 552 +m0787:= a0787-r0787 +--R +--R +--R (483) +--R 2 2 +--R 2sinh(x) + 2cosh(x) + 6 2cosh(x) +--R - log(-------------------------------------) + 2log(- -----------------) +--R 2 2 sinh(x) - cosh(x) +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 2atanh(2sinh(x) + 3) +--R / +--R 2 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 552 +d0787:= D(m0787,x) +--R +--R +--R (484) +--R 7 2 5 2 3 +--R sinh(x) + (- cosh(x) + 6)sinh(x) + (- 4cosh(x) + 11)sinh(x) +--R + +--R 4 2 +--R (- cosh(x) - 5cosh(x) + 6)sinh(x) +--R / +--R 6 3 4 +--R cosh(x)sinh(x) + (cosh(x) + 6cosh(x))sinh(x) +--R + +--R 3 2 3 +--R (3cosh(x) + 11cosh(x))sinh(x) + 2cosh(x) + 6cosh(x) +--R Type: Expression(Integer) +--E 492 + +--S 493 of 552 +t0788:= cosh(a+b*x)^3*sinh(a+b*x)^n +--R +--R +--R 3 n +--R (485) cosh(b x + a) sinh(b x + a) +--R Type: Expression(Integer) +--E 493 + +--S 494 of 552 +r0788:= sinh(a+b*x)^(1+n)/b/(1+n)+sinh(a+b*x)^(3+n)/b/(3+n) +--R +--R +--R n + 3 n + 1 +--R (n + 1)sinh(b x + a) + (n + 3)sinh(b x + a) +--R (486) ----------------------------------------------------- +--R 2 +--R b n + 4b n + 3b +--R Type: Expression(Integer) +--E 494 + +--S 495 of 552 +a0788:= integrate(t0788,x) +--R +--R +--R (487) +--R 3 2 +--R ((n + 1)sinh(b x + a) + ((3n + 3)cosh(b x + a) + n + 9)sinh(b x + a)) +--R * +--R sinh(n log(sinh(b x + a))) +--R + +--R 3 2 +--R ((n + 1)sinh(b x + a) + ((3n + 3)cosh(b x + a) + n + 9)sinh(b x + a)) +--R * +--R cosh(n log(sinh(b x + a))) +--R / +--R 2 4 +--R (4b n + 16b n + 12b)sinh(b x + a) +--R + +--R 2 2 2 +--R (- 8b n - 32b n - 24b)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 +--R (4b n + 16b n + 12b)cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 552 +m0788:= a0788-r0788 +--R +--R +--R (488) +--R 3 2 +--R ((n + 1)sinh(b x + a) + ((3n + 3)cosh(b x + a) + n + 9)sinh(b x + a)) +--R * +--R sinh(n log(sinh(b x + a))) +--R + +--R 3 2 +--R ((n + 1)sinh(b x + a) + ((3n + 3)cosh(b x + a) + n + 9)sinh(b x + a)) +--R * +--R cosh(n log(sinh(b x + a))) +--R + +--R 4 2 2 +--R (- 4n - 4)sinh(b x + a) + (8n + 8)cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R (- 4n - 4)cosh(b x + a) +--R * +--R n + 3 +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (- 4n - 12)sinh(b x + a) + (8n + 24)cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R (- 4n - 12)cosh(b x + a) +--R * +--R n + 1 +--R sinh(b x + a) +--R / +--R 2 4 +--R (4b n + 16b n + 12b)sinh(b x + a) +--R + +--R 2 2 2 +--R (- 8b n - 32b n - 24b)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 +--R (4b n + 16b n + 12b)cosh(b x + a) +--R Type: Expression(Integer) +--E 496 + +--S 497 of 552 +d0788:= D(m0788,x) +--R +--R +--R (489) +--R 2 3 +--R (n + 9)cosh(b x + a)sinh(b x + a) + (3n + 3)cosh(b x + a) +--R + +--R (n + 9)cosh(b x + a) +--R * +--R sinh(n log(sinh(b x + a))) +--R + +--R 2 3 +--R (n + 9)cosh(b x + a)sinh(b x + a) + (3n + 3)cosh(b x + a) +--R + +--R (n + 9)cosh(b x + a) +--R * +--R cosh(n log(sinh(b x + a))) +--R + +--R 4 +--R (- 4n - 12)cosh(b x + a)sinh(b x + a) +--R + +--R 3 2 5 +--R (8n + 24)cosh(b x + a) sinh(b x + a) + (- 4n - 12)cosh(b x + a) +--R * +--R n + 2 +--R sinh(b x + a) +--R + +--R 4 +--R (- 4n - 12)cosh(b x + a)sinh(b x + a) +--R + +--R 3 2 5 +--R (8n + 24)cosh(b x + a) sinh(b x + a) + (- 4n - 12)cosh(b x + a) +--R * +--R n +--R sinh(b x + a) +--R / +--R 4 2 2 +--R (4n + 12)sinh(b x + a) + (- 8n - 24)cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R (4n + 12)cosh(b x + a) +--R Type: Expression(Integer) +--E 497 + +--S 498 of 552 +t0789:= cosh(a+b*x)^5*sinh(a+b*x)^n +--R +--R +--R 5 n +--R (490) cosh(b x + a) sinh(b x + a) +--R Type: Expression(Integer) +--E 498 + +--S 499 of 552 +r0789:= sinh(a+b*x)^(1+n)/b/(1+n)+2*sinh(a+b*x)^(3+n)/b/(3+n)+_ + sinh(a+b*x)^(5+n)/b/(5+n) +--R +--R +--R (491) +--R 2 n + 5 2 n + 3 +--R (n + 4n + 3)sinh(b x + a) + (2n + 12n + 10)sinh(b x + a) +--R + +--R 2 n + 1 +--R (n + 8n + 15)sinh(b x + a) +--R / +--R 3 2 +--R b n + 9b n + 23b n + 15b +--R Type: Expression(Integer) +--E 499 + +--S 500 of 552 +a0789:= integrate(t0789,x) +--R +--R +--R (492) +--R 2 5 +--R (- n - 4n - 3)sinh(b x + a) +--R + +--R 2 2 2 3 +--R ((- 10n - 40n - 30)cosh(b x + a) - 3n - 28n - 25)sinh(b x + a) +--R + +--R 2 4 +--R (- 5n - 20n - 15)cosh(b x + a) +--R + +--R 2 2 2 +--R (- 9n - 84n - 75)cosh(b x + a) - 2n - 24n - 150 +--R * +--R sinh(b x + a) +--R * +--R sinh(n log(sinh(b x + a))) +--R + +--R 2 5 +--R (- n - 4n - 3)sinh(b x + a) +--R + +--R 2 2 2 3 +--R ((- 10n - 40n - 30)cosh(b x + a) - 3n - 28n - 25)sinh(b x + a) +--R + +--R 2 4 +--R (- 5n - 20n - 15)cosh(b x + a) +--R + +--R 2 2 2 +--R (- 9n - 84n - 75)cosh(b x + a) - 2n - 24n - 150 +--R * +--R sinh(b x + a) +--R * +--R cosh(n log(sinh(b x + a))) +--R / +--R 3 2 6 +--R (16b n + 144b n + 368b n + 240b)sinh(b x + a) +--R + +--R 3 2 2 4 +--R (- 48b n - 432b n - 1104b n - 720b)cosh(b x + a) sinh(b x + a) +--R + +--R 3 2 4 2 +--R (48b n + 432b n + 1104b n + 720b)cosh(b x + a) sinh(b x + a) +--R + +--R 3 2 6 +--R (- 16b n - 144b n - 368b n - 240b)cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 500 + +--S 501 of 552 +m0789:= a0789-r0789 +--R +--R +--R (493) +--R 2 5 +--R (- n - 4n - 3)sinh(b x + a) +--R + +--R 2 2 2 3 +--R ((- 10n - 40n - 30)cosh(b x + a) - 3n - 28n - 25)sinh(b x + a) +--R + +--R 2 4 +--R (- 5n - 20n - 15)cosh(b x + a) +--R + +--R 2 2 2 +--R (- 9n - 84n - 75)cosh(b x + a) - 2n - 24n - 150 +--R * +--R sinh(b x + a) +--R * +--R sinh(n log(sinh(b x + a))) +--R + +--R 2 5 +--R (- n - 4n - 3)sinh(b x + a) +--R + +--R 2 2 2 3 +--R ((- 10n - 40n - 30)cosh(b x + a) - 3n - 28n - 25)sinh(b x + a) +--R + +--R 2 4 +--R (- 5n - 20n - 15)cosh(b x + a) +--R + +--R 2 2 2 +--R (- 9n - 84n - 75)cosh(b x + a) - 2n - 24n - 150 +--R * +--R sinh(b x + a) +--R * +--R cosh(n log(sinh(b x + a))) +--R + +--R 2 6 +--R (- 16n - 64n - 48)sinh(b x + a) +--R + +--R 2 2 4 +--R (48n + 192n + 144)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 2 +--R (- 48n - 192n - 144)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (16n + 64n + 48)cosh(b x + a) +--R * +--R n + 5 +--R sinh(b x + a) +--R + +--R 2 6 +--R (- 32n - 192n - 160)sinh(b x + a) +--R + +--R 2 2 4 +--R (96n + 576n + 480)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 2 +--R (- 96n - 576n - 480)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (32n + 192n + 160)cosh(b x + a) +--R * +--R n + 3 +--R sinh(b x + a) +--R + +--R 2 6 +--R (- 16n - 128n - 240)sinh(b x + a) +--R + +--R 2 2 4 +--R (48n + 384n + 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 2 +--R (- 48n - 384n - 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (16n + 128n + 240)cosh(b x + a) +--R * +--R n + 1 +--R sinh(b x + a) +--R / +--R 3 2 6 +--R (16b n + 144b n + 368b n + 240b)sinh(b x + a) +--R + +--R 3 2 2 4 +--R (- 48b n - 432b n - 1104b n - 720b)cosh(b x + a) sinh(b x + a) +--R + +--R 3 2 4 2 +--R (48b n + 432b n + 1104b n + 720b)cosh(b x + a) sinh(b x + a) +--R + +--R 3 2 6 +--R (- 16b n - 144b n - 368b n - 240b)cosh(b x + a) +--R Type: Expression(Integer) +--E 501 + +--S 502 of 552 +d0789:= D(m0789,x) +--R +--R +--R (494) +--R 2 4 +--R (- n - 28n - 75)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R (- 10n - 80n - 150)cosh(b x + a) +--R + +--R 2 +--R (- 3n - 52n - 225)cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 5 2 3 +--R (- 5n - 20n - 15)cosh(b x + a) + (- 9n - 84n - 75)cosh(b x + a) +--R + +--R 2 +--R (- 2n - 24n - 150)cosh(b x + a) +--R * +--R sinh(n log(sinh(b x + a))) +--R + +--R 2 4 +--R (- n - 28n - 75)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R (- 10n - 80n - 150)cosh(b x + a) +--R + +--R 2 +--R (- 3n - 52n - 225)cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 5 2 3 +--R (- 5n - 20n - 15)cosh(b x + a) + (- 9n - 84n - 75)cosh(b x + a) +--R + +--R 2 +--R (- 2n - 24n - 150)cosh(b x + a) +--R * +--R cosh(n log(sinh(b x + a))) +--R + +--R 2 6 +--R (- 16n - 128n - 240)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 4 +--R (48n + 384n + 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 5 2 +--R (- 48n - 384n - 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 7 +--R (16n + 128n + 240)cosh(b x + a) +--R * +--R n + 4 +--R sinh(b x + a) +--R + +--R 2 6 +--R (- 32n - 256n - 480)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 4 +--R (96n + 768n + 1440)cosh(b x + a) sinh(b x + a) +--R + +--R 2 5 2 +--R (- 96n - 768n - 1440)cosh(b x + a) sinh(b x + a) +--R + +--R 2 7 +--R (32n + 256n + 480)cosh(b x + a) +--R * +--R n + 2 +--R sinh(b x + a) +--R + +--R 2 6 +--R (- 16n - 128n - 240)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 4 +--R (48n + 384n + 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 5 2 +--R (- 48n - 384n - 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 7 +--R (16n + 128n + 240)cosh(b x + a) +--R * +--R n +--R sinh(b x + a) +--R / +--R 2 6 +--R (16n + 128n + 240)sinh(b x + a) +--R + +--R 2 2 4 +--R (- 48n - 384n - 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 2 +--R (48n + 384n + 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (- 16n - 128n - 240)cosh(b x + a) +--R Type: Expression(Integer) +--E 502 + +--S 503 of 552 +t0790:= cosh(a+b*x)^m*sinh(a+b*x)^3 +--R +--R +--R 3 m +--R (495) sinh(b x + a) cosh(b x + a) +--R Type: Expression(Integer) +--E 503 + +--S 504 of 552 +r0790:= -cosh(a+b*x)^(1+m)/b/(1+m)+cosh(a+b*x)^(3+m)/b/(3+m) +--R +--R +--R m + 3 m + 1 +--R (m + 1)cosh(b x + a) + (- m - 3)cosh(b x + a) +--R (496) ------------------------------------------------------- +--R 2 +--R b m + 4b m + 3b +--R Type: Expression(Integer) +--E 504 + +--S 505 of 552 +a0790:= integrate(t0790,x) +--R +--R +--R (497) +--R 2 3 +--R (3m + 3)cosh(b x + a)sinh(b x + a) + (m + 1)cosh(b x + a) +--R + +--R (- m - 9)cosh(b x + a) +--R * +--R sinh(m log(cosh(b x + a))) +--R + +--R 2 3 +--R (3m + 3)cosh(b x + a)sinh(b x + a) + (m + 1)cosh(b x + a) +--R + +--R (- m - 9)cosh(b x + a) +--R * +--R cosh(m log(cosh(b x + a))) +--R / +--R 2 4 +--R (4b m + 16b m + 12b)sinh(b x + a) +--R + +--R 2 2 2 +--R (- 8b m - 32b m - 24b)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 +--R (4b m + 16b m + 12b)cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 552 +m0790:= a0790-r0790 +--R +--R +--R (498) +--R 2 3 +--R (3m + 3)cosh(b x + a)sinh(b x + a) + (m + 1)cosh(b x + a) +--R + +--R (- m - 9)cosh(b x + a) +--R * +--R sinh(m log(cosh(b x + a))) +--R + +--R 2 3 +--R (3m + 3)cosh(b x + a)sinh(b x + a) + (m + 1)cosh(b x + a) +--R + +--R (- m - 9)cosh(b x + a) +--R * +--R cosh(m log(cosh(b x + a))) +--R + +--R 4 2 2 +--R (- 4m - 4)sinh(b x + a) + (8m + 8)cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R (- 4m - 4)cosh(b x + a) +--R * +--R m + 3 +--R cosh(b x + a) +--R + +--R 4 2 2 +--R (4m + 12)sinh(b x + a) + (- 8m - 24)cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R (4m + 12)cosh(b x + a) +--R * +--R m + 1 +--R cosh(b x + a) +--R / +--R 2 4 +--R (4b m + 16b m + 12b)sinh(b x + a) +--R + +--R 2 2 2 +--R (- 8b m - 32b m - 24b)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 +--R (4b m + 16b m + 12b)cosh(b x + a) +--R Type: Expression(Integer) +--E 506 + +--S 507 of 552 +d0790:= D(m0790,x) +--R +--R +--R (499) +--R 3 2 +--R ((3m + 3)sinh(b x + a) + ((m + 9)cosh(b x + a) - m - 9)sinh(b x + a)) +--R * +--R sinh(m log(cosh(b x + a))) +--R + +--R 3 2 +--R ((3m + 3)sinh(b x + a) + ((m + 9)cosh(b x + a) - m - 9)sinh(b x + a)) +--R * +--R cosh(m log(cosh(b x + a))) +--R + +--R 5 2 3 +--R (- 4m - 12)sinh(b x + a) + (8m + 24)cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R (- 4m - 12)cosh(b x + a) sinh(b x + a) +--R * +--R m + 2 +--R cosh(b x + a) +--R + +--R 5 2 3 +--R (4m + 12)sinh(b x + a) + (- 8m - 24)cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R (4m + 12)cosh(b x + a) sinh(b x + a) +--R * +--R m +--R cosh(b x + a) +--R / +--R 4 2 2 +--R (4m + 12)sinh(b x + a) + (- 8m - 24)cosh(b x + a) sinh(b x + a) +--R + +--R 4 +--R (4m + 12)cosh(b x + a) +--R Type: Expression(Integer) +--E 507 + +--S 508 of 552 +t0791:= cosh(a+b*x)^m*sinh(a+b*x)^5 +--R +--R +--R 5 m +--R (500) sinh(b x + a) cosh(b x + a) +--R Type: Expression(Integer) +--E 508 + +--S 509 of 552 +r0791:= cosh(a+b*x)^(1+m)/b/(1+m)-2*cosh(a+b*x)^(3+m)/b/(3+m)+_ + cosh(a+b*x)^(5+m)/b/(5+m) +--R +--R +--R (501) +--R 2 m + 5 2 m + 3 +--R (m + 4m + 3)cosh(b x + a) + (- 2m - 12m - 10)cosh(b x + a) +--R + +--R 2 m + 1 +--R (m + 8m + 15)cosh(b x + a) +--R / +--R 3 2 +--R b m + 9b m + 23b m + 15b +--R Type: Expression(Integer) +--E 509 + +--S 510 of 552 +a0791:= integrate(t0791,x) +--R +--R +--R (502) +--R 2 4 +--R (- 5m - 20m - 15)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 2 +--R ((- 10m - 40m - 30)cosh(b x + a) + (9m + 84m + 75)cosh(b x + a)) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 5 2 3 +--R (- m - 4m - 3)cosh(b x + a) + (3m + 28m + 25)cosh(b x + a) +--R + +--R 2 +--R (- 2m - 24m - 150)cosh(b x + a) +--R * +--R sinh(m log(cosh(b x + a))) +--R + +--R 2 4 +--R (- 5m - 20m - 15)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 2 +--R ((- 10m - 40m - 30)cosh(b x + a) + (9m + 84m + 75)cosh(b x + a)) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 5 2 3 +--R (- m - 4m - 3)cosh(b x + a) + (3m + 28m + 25)cosh(b x + a) +--R + +--R 2 +--R (- 2m - 24m - 150)cosh(b x + a) +--R * +--R cosh(m log(cosh(b x + a))) +--R / +--R 3 2 6 +--R (16b m + 144b m + 368b m + 240b)sinh(b x + a) +--R + +--R 3 2 2 4 +--R (- 48b m - 432b m - 1104b m - 720b)cosh(b x + a) sinh(b x + a) +--R + +--R 3 2 4 2 +--R (48b m + 432b m + 1104b m + 720b)cosh(b x + a) sinh(b x + a) +--R + +--R 3 2 6 +--R (- 16b m - 144b m - 368b m - 240b)cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 510 + +--S 511 of 552 +m0791:= a0791-r0791 +--R +--R +--R (503) +--R 2 4 +--R (- 5m - 20m - 15)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 2 +--R ((- 10m - 40m - 30)cosh(b x + a) + (9m + 84m + 75)cosh(b x + a)) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 5 2 3 +--R (- m - 4m - 3)cosh(b x + a) + (3m + 28m + 25)cosh(b x + a) +--R + +--R 2 +--R (- 2m - 24m - 150)cosh(b x + a) +--R * +--R sinh(m log(cosh(b x + a))) +--R + +--R 2 4 +--R (- 5m - 20m - 15)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 2 +--R ((- 10m - 40m - 30)cosh(b x + a) + (9m + 84m + 75)cosh(b x + a)) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 5 2 3 +--R (- m - 4m - 3)cosh(b x + a) + (3m + 28m + 25)cosh(b x + a) +--R + +--R 2 +--R (- 2m - 24m - 150)cosh(b x + a) +--R * +--R cosh(m log(cosh(b x + a))) +--R + +--R 2 6 +--R (- 16m - 64m - 48)sinh(b x + a) +--R + +--R 2 2 4 +--R (48m + 192m + 144)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 2 +--R (- 48m - 192m - 144)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (16m + 64m + 48)cosh(b x + a) +--R * +--R m + 5 +--R cosh(b x + a) +--R + +--R 2 6 +--R (32m + 192m + 160)sinh(b x + a) +--R + +--R 2 2 4 +--R (- 96m - 576m - 480)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 2 +--R (96m + 576m + 480)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (- 32m - 192m - 160)cosh(b x + a) +--R * +--R m + 3 +--R cosh(b x + a) +--R + +--R 2 6 +--R (- 16m - 128m - 240)sinh(b x + a) +--R + +--R 2 2 4 +--R (48m + 384m + 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 2 +--R (- 48m - 384m - 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (16m + 128m + 240)cosh(b x + a) +--R * +--R m + 1 +--R cosh(b x + a) +--R / +--R 3 2 6 +--R (16b m + 144b m + 368b m + 240b)sinh(b x + a) +--R + +--R 3 2 2 4 +--R (- 48b m - 432b m - 1104b m - 720b)cosh(b x + a) sinh(b x + a) +--R + +--R 3 2 4 2 +--R (48b m + 432b m + 1104b m + 720b)cosh(b x + a) sinh(b x + a) +--R + +--R 3 2 6 +--R (- 16b m - 144b m - 368b m - 240b)cosh(b x + a) +--R Type: Expression(Integer) +--E 511 + +--S 512 of 552 +d0791:= D(m0791,x) +--R +--R +--R (504) +--R 2 5 +--R (- 5m - 20m - 15)sinh(b x + a) +--R + +--R 2 2 2 3 +--R ((- 10m - 80m - 150)cosh(b x + a) + 9m + 84m + 75)sinh(b x + a) +--R + +--R 2 4 2 2 +--R (- m - 28m - 75)cosh(b x + a) + (3m + 52m + 225)cosh(b x + a) +--R + +--R 2 +--R - 2m - 24m - 150 +--R * +--R sinh(b x + a) +--R * +--R sinh(m log(cosh(b x + a))) +--R + +--R 2 5 +--R (- 5m - 20m - 15)sinh(b x + a) +--R + +--R 2 2 2 3 +--R ((- 10m - 80m - 150)cosh(b x + a) + 9m + 84m + 75)sinh(b x + a) +--R + +--R 2 4 2 2 +--R (- m - 28m - 75)cosh(b x + a) + (3m + 52m + 225)cosh(b x + a) +--R + +--R 2 +--R - 2m - 24m - 150 +--R * +--R sinh(b x + a) +--R * +--R cosh(m log(cosh(b x + a))) +--R + +--R 2 7 +--R (- 16m - 128m - 240)sinh(b x + a) +--R + +--R 2 2 5 +--R (48m + 384m + 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 3 +--R (- 48m - 384m - 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (16m + 128m + 240)cosh(b x + a) sinh(b x + a) +--R * +--R m + 4 +--R cosh(b x + a) +--R + +--R 2 7 +--R (32m + 256m + 480)sinh(b x + a) +--R + +--R 2 2 5 +--R (- 96m - 768m - 1440)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 3 +--R (96m + 768m + 1440)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (- 32m - 256m - 480)cosh(b x + a) sinh(b x + a) +--R * +--R m + 2 +--R cosh(b x + a) +--R + +--R 2 7 +--R (- 16m - 128m - 240)sinh(b x + a) +--R + +--R 2 2 5 +--R (48m + 384m + 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 3 +--R (- 48m - 384m - 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (16m + 128m + 240)cosh(b x + a) sinh(b x + a) +--R * +--R m +--R cosh(b x + a) +--R / +--R 2 6 +--R (16m + 128m + 240)sinh(b x + a) +--R + +--R 2 2 4 +--R (- 48m - 384m - 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 2 +--R (48m + 384m + 720)cosh(b x + a) sinh(b x + a) +--R + +--R 2 6 +--R (- 16m - 128m - 240)cosh(b x + a) +--R Type: Expression(Integer) +--E 512 + +--S 513 of 552 +t0792:= sech(a+b*x)^2*tanh(a+b*x)^n +--R +--R +--R 2 n +--R (505) sech(b x + a) tanh(b x + a) +--R Type: Expression(Integer) +--E 513 + +--S 514 of 552 +r0792:= tanh(a+b*x)^(1+n)/b/(1+n) +--R +--R +--R n + 1 +--R tanh(b x + a) +--R (506) ------------------ +--R b n + b +--R Type: Expression(Integer) +--E 514 + +--S 515 of 552 +a0792:= integrate(t0792,x) +--R +--R +--R (507) +--R sinh(b x + a) +--R sinh(b x + a)sinh(n log(-------------)) +--R cosh(b x + a) +--R + +--R sinh(b x + a) +--R sinh(b x + a)cosh(n log(-------------)) +--R cosh(b x + a) +--R / +--R (b n + b)cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 515 + +--S 516 of 552 +m0792:= a0792-r0792 +--R +--R +--R (508) +--R sinh(b x + a) +--R sinh(b x + a)sinh(n log(-------------)) +--R cosh(b x + a) +--R + +--R sinh(b x + a) n + 1 +--R sinh(b x + a)cosh(n log(-------------)) - cosh(b x + a)tanh(b x + a) +--R cosh(b x + a) +--R / +--R (b n + b)cosh(b x + a) +--R Type: Expression(Integer) +--E 516 + +--S 517 of 552 +d0792:= D(m0792,x) +--R +--R +--R (509) +--R 2 2 sinh(b x + a) +--R (- sinh(b x + a) + cosh(b x + a) )sinh(n log(-------------)) +--R cosh(b x + a) +--R + +--R 2 2 sinh(b x + a) +--R (- sinh(b x + a) + cosh(b x + a) )cosh(n log(-------------)) +--R cosh(b x + a) +--R + +--R 2 2 2 n +--R (cosh(b x + a) tanh(b x + a) - cosh(b x + a) )tanh(b x + a) +--R / +--R 2 +--R cosh(b x + a) +--R Type: Expression(Integer) +--E 517 + +--S 518 of 552 +t0793:= sech(a+b*x)^n*tanh(a+b*x)^3 +--R +--R +--R 3 n +--R (510) tanh(b x + a) sech(b x + a) +--R Type: Expression(Integer) +--E 518 + +--S 519 of 552 +r0793:= -sech(a+b*x)^n/b/n+sech(a+b*x)^(2+n)/b/(2+n) +--R +--R +--R n + 2 n +--R n sech(b x + a) + (- n - 2)sech(b x + a) +--R (511) ---------------------------------------------- +--R 2 +--R b n + 2b n +--R Type: Expression(Integer) +--E 519 + +--S 520 of 552 +a0793:= integrate(t0793,x) +--R +--R +--R (512) +--R 2 2 +--R ((- n - 2)sinh(b x + a) + (- n - 2)cosh(b x + a) + n - 2) +--R * +--R sinh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) + 1 +--R + +--R 2 2 +--R ((- n - 2)sinh(b x + a) + (- n - 2)cosh(b x + a) + n - 2) +--R * +--R cosh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) + 1 +--R / +--R 2 2 2 2 2 +--R (b n + 2b n)sinh(b x + a) + (b n + 2b n)cosh(b x + a) + b n + 2b n +--R Type: Union(Expression(Integer),...) +--E 520 + +--S 521 of 552 +m0793:= a0793-r0793 +--R +--R +--R (513) +--R 2 2 +--R ((- n - 2)sinh(b x + a) + (- n - 2)cosh(b x + a) + n - 2) +--R * +--R sinh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) + 1 +--R + +--R 2 2 +--R ((- n - 2)sinh(b x + a) + (- n - 2)cosh(b x + a) + n - 2) +--R * +--R cosh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) + 1 +--R + +--R 2 2 n + 2 +--R (- n sinh(b x + a) - n cosh(b x + a) - n)sech(b x + a) +--R + +--R 2 2 n +--R ((n + 2)sinh(b x + a) + (n + 2)cosh(b x + a) + n + 2)sech(b x + a) +--R / +--R 2 2 2 2 2 +--R (b n + 2b n)sinh(b x + a) + (b n + 2b n)cosh(b x + a) + b n + 2b n +--R Type: Expression(Integer) +--E 521 + +--S 522 of 552 +d0793:= D(m0793,x) +--R +--R +--R (514) +--R 6 5 +--R (n + 2)sinh(b x + a) + (2n + 4)cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R ((3n + 6)cosh(b x + a) - n + 2)sinh(b x + a) +--R + +--R 3 3 +--R (4n + 8)cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 +--R ((3n + 6)cosh(b x + a) + (- 2n - 12)cosh(b x + a) - n - 2) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 +--R ((2n + 4)cosh(b x + a) + (- 2n - 4)cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 +--R (n + 2)cosh(b x + a) + (- n + 2)cosh(b x + a) +--R + +--R 2 +--R (- n - 2)cosh(b x + a) + n - 2 +--R * +--R sinh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) + 1 +--R + +--R 6 5 +--R (n + 2)sinh(b x + a) + (2n + 4)cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R ((3n + 6)cosh(b x + a) - n + 2)sinh(b x + a) +--R + +--R 3 3 +--R (4n + 8)cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 +--R ((3n + 6)cosh(b x + a) + (- 2n - 12)cosh(b x + a) - n - 2) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 +--R ((2n + 4)cosh(b x + a) + (- 2n - 4)cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 +--R (n + 2)cosh(b x + a) + (- n + 2)cosh(b x + a) +--R + +--R 2 +--R (- n - 2)cosh(b x + a) + n - 2 +--R * +--R cosh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) + 1 +--R + +--R 6 +--R (n + 2)sech(b x + a)sinh(b x + a) +--R + +--R 5 +--R (2n + 4)cosh(b x + a)sech(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R ((3n + 6)cosh(b x + a) + 3n + 6)sech(b x + a)sinh(b x + a) +--R + +--R 3 +--R ((4n + 8)cosh(b x + a) + (4n + 8)cosh(b x + a))sech(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R ((3n + 6)cosh(b x + a) + (6n + 12)cosh(b x + a) + 3n + 6) +--R * +--R 2 +--R sech(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (2n + 4)cosh(b x + a) + (4n + 8)cosh(b x + a) +--R + +--R (2n + 4)cosh(b x + a) +--R * +--R sech(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R (n + 2)cosh(b x + a) + (3n + 6)cosh(b x + a) +--R + +--R 2 +--R (3n + 6)cosh(b x + a) + n + 2 +--R * +--R sech(b x + a) +--R * +--R n + 1 +--R tanh(b x + a)sech(b x + a) +--R + +--R 6 +--R (- n - 2)sech(b x + a)sinh(b x + a) +--R + +--R 5 +--R (- 2n - 4)cosh(b x + a)sech(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R ((- 3n - 6)cosh(b x + a) - 3n - 6)sech(b x + a)sinh(b x + a) +--R + +--R 3 +--R ((- 4n - 8)cosh(b x + a) + (- 4n - 8)cosh(b x + a))sech(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R ((- 3n - 6)cosh(b x + a) + (- 6n - 12)cosh(b x + a) - 3n - 6) +--R * +--R 2 +--R sech(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (- 2n - 4)cosh(b x + a) + (- 4n - 8)cosh(b x + a) +--R + +--R (- 2n - 4)cosh(b x + a) +--R * +--R sech(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R (- n - 2)cosh(b x + a) + (- 3n - 6)cosh(b x + a) +--R + +--R 2 +--R (- 3n - 6)cosh(b x + a) - n - 2 +--R * +--R sech(b x + a) +--R * +--R n - 1 +--R tanh(b x + a)sech(b x + a) +--R / +--R 6 5 +--R (n + 2)sinh(b x + a) + (2n + 4)cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R ((3n + 6)cosh(b x + a) + 3n + 6)sinh(b x + a) +--R + +--R 3 3 +--R ((4n + 8)cosh(b x + a) + (4n + 8)cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R ((3n + 6)cosh(b x + a) + (6n + 12)cosh(b x + a) + 3n + 6)sinh(b x + a) +--R + +--R 5 3 +--R (2n + 4)cosh(b x + a) + (4n + 8)cosh(b x + a) +--R + +--R (2n + 4)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (n + 2)cosh(b x + a) + (3n + 6)cosh(b x + a) + (3n + 6)cosh(b x + a) +--R + +--R n + 2 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 552 +t0794:= sech(a+b*x)^4*tanh(a+b*x)^(1/2) +--R +--R +--R 4 +-------------+ +--R (515) sech(b x + a) \|tanh(b x + a) +--R Type: Expression(Integer) +--E 523 + +--S 524 of 552 +r0794:= -2/21*tanh(a+b*x)^(3/2)*(-7+3*tanh(a+b*x)^2)/b +--R +--R +--R 3 +-------------+ +--R (- 6tanh(b x + a) + 14tanh(b x + a))\|tanh(b x + a) +--R (516) ----------------------------------------------------- +--R 21b +--R Type: Expression(Integer) +--E 524 + +--S 525 of 552 +a0794:= integrate(t0794,x) +--R +--R +--R (517) +--R 10 9 +--R 672sinh(b x + a) + 6720cosh(b x + a)sinh(b x + a) +--R + +--R 2 8 +--R (30240cosh(b x + a) + 784)sinh(b x + a) +--R + +--R 3 7 +--R (80640cosh(b x + a) + 6272cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 6 +--R (141120cosh(b x + a) + 21952cosh(b x + a) - 168)sinh(b x + a) +--R + +--R 5 3 +--R (169344cosh(b x + a) + 43904cosh(b x + a) - 1008cosh(b x + a)) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 141120cosh(b x + a) + 54880cosh(b x + a) - 2520cosh(b x + a) +--R + +--R - 336 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 80640cosh(b x + a) + 43904cosh(b x + a) - 3360cosh(b x + a) +--R + +--R - 1344cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 30240cosh(b x + a) + 21952cosh(b x + a) - 2520cosh(b x + a) +--R + +--R 2 +--R - 2016cosh(b x + a) - 56 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 6720cosh(b x + a) + 6272cosh(b x + a) - 1008cosh(b x + a) +--R + +--R 3 +--R - 1344cosh(b x + a) - 112cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 672cosh(b x + a) + 784cosh(b x + a) - 168cosh(b x + a) +--R + +--R 4 2 +--R - 336cosh(b x + a) - 56cosh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 10 9 +--R - 672sinh(b x + a) - 6720cosh(b x + a)sinh(b x + a) +--R + +--R 2 8 +--R (- 30240cosh(b x + a) - 112)sinh(b x + a) +--R + +--R 3 7 +--R (- 80640cosh(b x + a) - 896cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 6 +--R (- 141120cosh(b x + a) - 3136cosh(b x + a) + 616)sinh(b x + a) +--R + +--R 5 3 +--R (- 169344cosh(b x + a) - 6272cosh(b x + a) + 3696cosh(b x + a)) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 141120cosh(b x + a) - 7840cosh(b x + a) + 9240cosh(b x + a) +--R + +--R 112 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 80640cosh(b x + a) - 6272cosh(b x + a) + 12320cosh(b x + a) +--R + +--R 448cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R - 30240cosh(b x + a) - 3136cosh(b x + a) + 9240cosh(b x + a) +--R + +--R 2 +--R 672cosh(b x + a) - 56 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R - 6720cosh(b x + a) - 896cosh(b x + a) + 3696cosh(b x + a) +--R + +--R 3 +--R 448cosh(b x + a) - 112cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 10 8 6 +--R - 672cosh(b x + a) - 112cosh(b x + a) + 616cosh(b x + a) +--R + +--R 4 2 +--R 112cosh(b x + a) - 56cosh(b x + a) - 16 +--R / +--R 14 13 +--R 168b sinh(b x + a) + 2352b cosh(b x + a)sinh(b x + a) +--R + +--R 2 12 +--R (15288b cosh(b x + a) + 756b)sinh(b x + a) +--R + +--R 3 11 +--R (61152b cosh(b x + a) + 9072b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R (168168b cosh(b x + a) + 49896b cosh(b x + a) + 1260b) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 5 3 +--R 336336b cosh(b x + a) + 166320b cosh(b x + a) +--R + +--R 12600b cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 6 4 +--R 504504b cosh(b x + a) + 374220b cosh(b x + a) +--R + +--R 2 +--R 56700b cosh(b x + a) + 819b +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 7 5 +--R 576576b cosh(b x + a) + 598752b cosh(b x + a) +--R + +--R 3 +--R 151200b cosh(b x + a) + 6552b cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 8 6 +--R 504504b cosh(b x + a) + 698544b cosh(b x + a) +--R + +--R 4 2 +--R 264600b cosh(b x + a) + 22932b cosh(b x + a) - 84b +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 9 7 +--R 336336b cosh(b x + a) + 598752b cosh(b x + a) +--R + +--R 5 3 +--R 317520b cosh(b x + a) + 45864b cosh(b x + a) - 504b cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 10 8 +--R 168168b cosh(b x + a) + 374220b cosh(b x + a) +--R + +--R 6 4 +--R 264600b cosh(b x + a) + 57330b cosh(b x + a) +--R + +--R 2 +--R - 1260b cosh(b x + a) - 378b +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 11 9 +--R 61152b cosh(b x + a) + 166320b cosh(b x + a) +--R + +--R 7 5 +--R 151200b cosh(b x + a) + 45864b cosh(b x + a) +--R + +--R 3 +--R - 1680b cosh(b x + a) - 1512b cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 12 10 +--R 15288b cosh(b x + a) + 49896b cosh(b x + a) +--R + +--R 8 6 +--R 56700b cosh(b x + a) + 22932b cosh(b x + a) +--R + +--R 4 2 +--R - 1260b cosh(b x + a) - 2268b cosh(b x + a) - 168b +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 13 11 +--R 2352b cosh(b x + a) + 9072b cosh(b x + a) +--R + +--R 9 7 +--R 12600b cosh(b x + a) + 6552b cosh(b x + a) +--R + +--R 5 3 +--R - 504b cosh(b x + a) - 1512b cosh(b x + a) - 336b cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 14 12 10 +--R 168b cosh(b x + a) + 756b cosh(b x + a) + 1260b cosh(b x + a) +--R + +--R 8 6 4 +--R 819b cosh(b x + a) - 84b cosh(b x + a) - 378b cosh(b x + a) +--R + +--R 2 +--R - 168b cosh(b x + a) - 21b +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 14 13 +--R - 168b sinh(b x + a) - 2352b cosh(b x + a)sinh(b x + a) +--R + +--R 2 12 +--R (- 15288b cosh(b x + a) - 588b)sinh(b x + a) +--R + +--R 3 11 +--R (- 61152b cosh(b x + a) - 7056b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 10 +--R (- 168168b cosh(b x + a) - 38808b cosh(b x + a) - 588b)sinh(b x + a) +--R + +--R 5 3 +--R - 336336b cosh(b x + a) - 129360b cosh(b x + a) +--R + +--R - 5880b cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 504504b cosh(b x + a) - 291060b cosh(b x + a) +--R + +--R 2 +--R - 26460b cosh(b x + a) + 147b +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 576576b cosh(b x + a) - 465696b cosh(b x + a) +--R + +--R 3 +--R - 70560b cosh(b x + a) + 1176b cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 504504b cosh(b x + a) - 543312b cosh(b x + a) +--R + +--R 4 2 +--R - 123480b cosh(b x + a) + 4116b cosh(b x + a) + 588b +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 336336b cosh(b x + a) - 465696b cosh(b x + a) +--R + +--R 5 3 +--R - 148176b cosh(b x + a) + 8232b cosh(b x + a) + 3528b cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 168168b cosh(b x + a) - 291060b cosh(b x + a) +--R + +--R 6 4 +--R - 123480b cosh(b x + a) + 10290b cosh(b x + a) +--R + +--R 2 +--R 8820b cosh(b x + a) + 294b +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 61152b cosh(b x + a) - 129360b cosh(b x + a) +--R + +--R 7 5 +--R - 70560b cosh(b x + a) + 8232b cosh(b x + a) +--R + +--R 3 +--R 11760b cosh(b x + a) + 1176b cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 15288b cosh(b x + a) - 38808b cosh(b x + a) +--R + +--R 8 6 4 +--R - 26460b cosh(b x + a) + 4116b cosh(b x + a) + 8820b cosh(b x + a) +--R + +--R 2 +--R 1764b cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 2352b cosh(b x + a) - 7056b cosh(b x + a) +--R + +--R 9 7 5 +--R - 5880b cosh(b x + a) + 1176b cosh(b x + a) + 3528b cosh(b x + a) +--R + +--R 3 +--R 1176b cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 14 12 10 +--R - 168b cosh(b x + a) - 588b cosh(b x + a) - 588b cosh(b x + a) +--R + +--R 8 6 4 +--R 147b cosh(b x + a) + 588b cosh(b x + a) + 294b cosh(b x + a) - 21b +--R Type: Union(Expression(Integer),...) +--E 525 + +--S 526 of 552 +m0794:= a0794-r0794 +--R +--R +--R (518) +--R 14 13 +--R 48sinh(b x + a) + 672cosh(b x + a)sinh(b x + a) +--R + +--R 2 12 +--R (4368cosh(b x + a) + 216)sinh(b x + a) +--R + +--R 3 11 +--R (17472cosh(b x + a) + 2592cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R (48048cosh(b x + a) + 14256cosh(b x + a) + 360) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 5 3 +--R 96096cosh(b x + a) + 47520cosh(b x + a) +--R + +--R 3600cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 6 4 +--R 144144cosh(b x + a) + 106920cosh(b x + a) +--R + +--R 2 +--R 16200cosh(b x + a) + 234 +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 7 5 +--R 164736cosh(b x + a) + 171072cosh(b x + a) +--R + +--R 3 +--R 43200cosh(b x + a) + 1872cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 8 6 +--R 144144cosh(b x + a) + 199584cosh(b x + a) +--R + +--R 4 2 +--R 75600cosh(b x + a) + 6552cosh(b x + a) - 24 +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 9 7 +--R 96096cosh(b x + a) + 171072cosh(b x + a) +--R + +--R 5 3 +--R 90720cosh(b x + a) + 13104cosh(b x + a) +--R + +--R - 144cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 10 8 +--R 48048cosh(b x + a) + 106920cosh(b x + a) +--R + +--R 6 4 +--R 75600cosh(b x + a) + 16380cosh(b x + a) +--R + +--R 2 +--R - 360cosh(b x + a) - 108 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 11 9 +--R 17472cosh(b x + a) + 47520cosh(b x + a) +--R + +--R 7 5 +--R 43200cosh(b x + a) + 13104cosh(b x + a) +--R + +--R 3 +--R - 480cosh(b x + a) - 432cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 12 10 +--R 4368cosh(b x + a) + 14256cosh(b x + a) +--R + +--R 8 6 +--R 16200cosh(b x + a) + 6552cosh(b x + a) +--R + +--R 4 2 +--R - 360cosh(b x + a) - 648cosh(b x + a) - 48 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 13 11 +--R 672cosh(b x + a) + 2592cosh(b x + a) +--R + +--R 9 7 +--R 3600cosh(b x + a) + 1872cosh(b x + a) +--R + +--R 5 3 +--R - 144cosh(b x + a) - 432cosh(b x + a) - 96cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 14 12 10 +--R 48cosh(b x + a) + 216cosh(b x + a) + 360cosh(b x + a) +--R + +--R 8 6 4 +--R 234cosh(b x + a) - 24cosh(b x + a) - 108cosh(b x + a) +--R + +--R 2 +--R - 48cosh(b x + a) - 6 +--R * +--R 3 +--R tanh(b x + a) +--R + +--R 14 13 +--R - 112sinh(b x + a) - 1568cosh(b x + a)sinh(b x + a) +--R + +--R 2 12 +--R (- 10192cosh(b x + a) - 504)sinh(b x + a) +--R + +--R 3 11 +--R (- 40768cosh(b x + a) - 6048cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R (- 112112cosh(b x + a) - 33264cosh(b x + a) - 840) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 5 3 +--R - 224224cosh(b x + a) - 110880cosh(b x + a) +--R + +--R - 8400cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 336336cosh(b x + a) - 249480cosh(b x + a) +--R + +--R 2 +--R - 37800cosh(b x + a) - 546 +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 384384cosh(b x + a) - 399168cosh(b x + a) +--R + +--R 3 +--R - 100800cosh(b x + a) - 4368cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 336336cosh(b x + a) - 465696cosh(b x + a) +--R + +--R 4 2 +--R - 176400cosh(b x + a) - 15288cosh(b x + a) + 56 +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 224224cosh(b x + a) - 399168cosh(b x + a) +--R + +--R 5 3 +--R - 211680cosh(b x + a) - 30576cosh(b x + a) +--R + +--R 336cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 112112cosh(b x + a) - 249480cosh(b x + a) +--R + +--R 6 4 +--R - 176400cosh(b x + a) - 38220cosh(b x + a) +--R + +--R 2 +--R 840cosh(b x + a) + 252 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 40768cosh(b x + a) - 110880cosh(b x + a) +--R + +--R 7 5 +--R - 100800cosh(b x + a) - 30576cosh(b x + a) +--R + +--R 3 +--R 1120cosh(b x + a) + 1008cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 10192cosh(b x + a) - 33264cosh(b x + a) +--R + +--R 8 6 +--R - 37800cosh(b x + a) - 15288cosh(b x + a) +--R + +--R 4 2 +--R 840cosh(b x + a) + 1512cosh(b x + a) + 112 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 1568cosh(b x + a) - 6048cosh(b x + a) +--R + +--R 9 7 +--R - 8400cosh(b x + a) - 4368cosh(b x + a) +--R + +--R 5 3 +--R 336cosh(b x + a) + 1008cosh(b x + a) + 224cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 14 12 +--R - 112cosh(b x + a) - 504cosh(b x + a) +--R + +--R 10 8 6 +--R - 840cosh(b x + a) - 546cosh(b x + a) + 56cosh(b x + a) +--R + +--R 4 2 +--R 252cosh(b x + a) + 112cosh(b x + a) + 14 +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 14 13 +--R - 48sinh(b x + a) - 672cosh(b x + a)sinh(b x + a) +--R + +--R 2 12 +--R (- 4368cosh(b x + a) - 168)sinh(b x + a) +--R + +--R 3 11 +--R (- 17472cosh(b x + a) - 2016cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R (- 48048cosh(b x + a) - 11088cosh(b x + a) - 168) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 5 3 +--R - 96096cosh(b x + a) - 36960cosh(b x + a) +--R + +--R - 1680cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 144144cosh(b x + a) - 83160cosh(b x + a) +--R + +--R 2 +--R - 7560cosh(b x + a) + 42 +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 164736cosh(b x + a) - 133056cosh(b x + a) +--R + +--R 3 +--R - 20160cosh(b x + a) + 336cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 144144cosh(b x + a) - 155232cosh(b x + a) +--R + +--R 4 2 +--R - 35280cosh(b x + a) + 1176cosh(b x + a) + 168 +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 96096cosh(b x + a) - 133056cosh(b x + a) +--R + +--R 5 3 +--R - 42336cosh(b x + a) + 2352cosh(b x + a) + 1008cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 48048cosh(b x + a) - 83160cosh(b x + a) +--R + +--R 6 4 +--R - 35280cosh(b x + a) + 2940cosh(b x + a) +--R + +--R 2 +--R 2520cosh(b x + a) + 84 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 17472cosh(b x + a) - 36960cosh(b x + a) +--R + +--R 7 5 +--R - 20160cosh(b x + a) + 2352cosh(b x + a) +--R + +--R 3 +--R 3360cosh(b x + a) + 336cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 4368cosh(b x + a) - 11088cosh(b x + a) +--R + +--R 8 6 +--R - 7560cosh(b x + a) + 1176cosh(b x + a) +--R + +--R 4 2 +--R 2520cosh(b x + a) + 504cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 672cosh(b x + a) - 2016cosh(b x + a) +--R + +--R 9 7 5 +--R - 1680cosh(b x + a) + 336cosh(b x + a) + 1008cosh(b x + a) +--R + +--R 3 +--R 336cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 14 12 10 +--R - 48cosh(b x + a) - 168cosh(b x + a) - 168cosh(b x + a) +--R + +--R 8 6 4 +--R 42cosh(b x + a) + 168cosh(b x + a) + 84cosh(b x + a) - 6 +--R * +--R 3 +--R tanh(b x + a) +--R + +--R 14 13 +--R 112sinh(b x + a) + 1568cosh(b x + a)sinh(b x + a) +--R + +--R 2 12 +--R (10192cosh(b x + a) + 392)sinh(b x + a) +--R + +--R 3 11 +--R (40768cosh(b x + a) + 4704cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 10 +--R (112112cosh(b x + a) + 25872cosh(b x + a) + 392)sinh(b x + a) +--R + +--R 5 3 +--R 224224cosh(b x + a) + 86240cosh(b x + a) +--R + +--R 3920cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 6 4 +--R 336336cosh(b x + a) + 194040cosh(b x + a) +--R + +--R 2 +--R 17640cosh(b x + a) - 98 +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 7 5 +--R 384384cosh(b x + a) + 310464cosh(b x + a) +--R + +--R 3 +--R 47040cosh(b x + a) - 784cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 8 6 +--R 336336cosh(b x + a) + 362208cosh(b x + a) +--R + +--R 4 2 +--R 82320cosh(b x + a) - 2744cosh(b x + a) - 392 +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 9 7 +--R 224224cosh(b x + a) + 310464cosh(b x + a) +--R + +--R 5 3 +--R 98784cosh(b x + a) - 5488cosh(b x + a) - 2352cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 10 8 +--R 112112cosh(b x + a) + 194040cosh(b x + a) +--R + +--R 6 4 2 +--R 82320cosh(b x + a) - 6860cosh(b x + a) - 5880cosh(b x + a) +--R + +--R - 196 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 11 9 +--R 40768cosh(b x + a) + 86240cosh(b x + a) +--R + +--R 7 5 3 +--R 47040cosh(b x + a) - 5488cosh(b x + a) - 7840cosh(b x + a) +--R + +--R - 784cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 12 10 +--R 10192cosh(b x + a) + 25872cosh(b x + a) +--R + +--R 8 6 4 +--R 17640cosh(b x + a) - 2744cosh(b x + a) - 5880cosh(b x + a) +--R + +--R 2 +--R - 1176cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 13 11 +--R 1568cosh(b x + a) + 4704cosh(b x + a) +--R + +--R 9 7 5 +--R 3920cosh(b x + a) - 784cosh(b x + a) - 2352cosh(b x + a) +--R + +--R 3 +--R - 784cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 14 12 10 +--R 112cosh(b x + a) + 392cosh(b x + a) + 392cosh(b x + a) +--R + +--R 8 6 4 +--R - 98cosh(b x + a) - 392cosh(b x + a) - 196cosh(b x + a) + 14 +--R * +--R tanh(b x + a) +--R * +--R +-------------+ +--R \|tanh(b x + a) +--R + +--R 10 9 +--R 672sinh(b x + a) + 6720cosh(b x + a)sinh(b x + a) +--R + +--R 2 8 +--R (30240cosh(b x + a) + 784)sinh(b x + a) +--R + +--R 3 7 +--R (80640cosh(b x + a) + 6272cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 6 +--R (141120cosh(b x + a) + 21952cosh(b x + a) - 168)sinh(b x + a) +--R + +--R 5 3 +--R (169344cosh(b x + a) + 43904cosh(b x + a) - 1008cosh(b x + a)) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 141120cosh(b x + a) + 54880cosh(b x + a) - 2520cosh(b x + a) +--R + +--R - 336 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 80640cosh(b x + a) + 43904cosh(b x + a) - 3360cosh(b x + a) +--R + +--R - 1344cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R 30240cosh(b x + a) + 21952cosh(b x + a) - 2520cosh(b x + a) +--R + +--R 2 +--R - 2016cosh(b x + a) - 56 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R 6720cosh(b x + a) + 6272cosh(b x + a) - 1008cosh(b x + a) +--R + +--R 3 +--R - 1344cosh(b x + a) - 112cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 10 8 6 +--R 672cosh(b x + a) + 784cosh(b x + a) - 168cosh(b x + a) +--R + +--R 4 2 +--R - 336cosh(b x + a) - 56cosh(b x + a) +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 10 9 +--R - 672sinh(b x + a) - 6720cosh(b x + a)sinh(b x + a) +--R + +--R 2 8 +--R (- 30240cosh(b x + a) - 112)sinh(b x + a) +--R + +--R 3 7 +--R (- 80640cosh(b x + a) - 896cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 6 +--R (- 141120cosh(b x + a) - 3136cosh(b x + a) + 616)sinh(b x + a) +--R + +--R 5 3 +--R (- 169344cosh(b x + a) - 6272cosh(b x + a) + 3696cosh(b x + a)) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - 141120cosh(b x + a) - 7840cosh(b x + a) + 9240cosh(b x + a) +--R + +--R 112 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 7 5 3 +--R - 80640cosh(b x + a) - 6272cosh(b x + a) + 12320cosh(b x + a) +--R + +--R 448cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 8 6 4 +--R - 30240cosh(b x + a) - 3136cosh(b x + a) + 9240cosh(b x + a) +--R + +--R 2 +--R 672cosh(b x + a) - 56 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 9 7 5 +--R - 6720cosh(b x + a) - 896cosh(b x + a) + 3696cosh(b x + a) +--R + +--R 3 +--R 448cosh(b x + a) - 112cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 10 8 6 +--R - 672cosh(b x + a) - 112cosh(b x + a) + 616cosh(b x + a) +--R + +--R 4 2 +--R 112cosh(b x + a) - 56cosh(b x + a) - 16 +--R / +--R 14 13 +--R 168b sinh(b x + a) + 2352b cosh(b x + a)sinh(b x + a) +--R + +--R 2 12 +--R (15288b cosh(b x + a) + 756b)sinh(b x + a) +--R + +--R 3 11 +--R (61152b cosh(b x + a) + 9072b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R (168168b cosh(b x + a) + 49896b cosh(b x + a) + 1260b) +--R * +--R 10 +--R sinh(b x + a) +--R + +--R 5 3 +--R 336336b cosh(b x + a) + 166320b cosh(b x + a) +--R + +--R 12600b cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 6 4 +--R 504504b cosh(b x + a) + 374220b cosh(b x + a) +--R + +--R 2 +--R 56700b cosh(b x + a) + 819b +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 7 5 +--R 576576b cosh(b x + a) + 598752b cosh(b x + a) +--R + +--R 3 +--R 151200b cosh(b x + a) + 6552b cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 8 6 +--R 504504b cosh(b x + a) + 698544b cosh(b x + a) +--R + +--R 4 2 +--R 264600b cosh(b x + a) + 22932b cosh(b x + a) - 84b +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 9 7 +--R 336336b cosh(b x + a) + 598752b cosh(b x + a) +--R + +--R 5 3 +--R 317520b cosh(b x + a) + 45864b cosh(b x + a) - 504b cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 10 8 +--R 168168b cosh(b x + a) + 374220b cosh(b x + a) +--R + +--R 6 4 +--R 264600b cosh(b x + a) + 57330b cosh(b x + a) +--R + +--R 2 +--R - 1260b cosh(b x + a) - 378b +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 11 9 +--R 61152b cosh(b x + a) + 166320b cosh(b x + a) +--R + +--R 7 5 +--R 151200b cosh(b x + a) + 45864b cosh(b x + a) +--R + +--R 3 +--R - 1680b cosh(b x + a) - 1512b cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 12 10 +--R 15288b cosh(b x + a) + 49896b cosh(b x + a) +--R + +--R 8 6 +--R 56700b cosh(b x + a) + 22932b cosh(b x + a) +--R + +--R 4 2 +--R - 1260b cosh(b x + a) - 2268b cosh(b x + a) - 168b +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 13 11 +--R 2352b cosh(b x + a) + 9072b cosh(b x + a) +--R + +--R 9 7 +--R 12600b cosh(b x + a) + 6552b cosh(b x + a) +--R + +--R 5 3 +--R - 504b cosh(b x + a) - 1512b cosh(b x + a) - 336b cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 14 12 10 +--R 168b cosh(b x + a) + 756b cosh(b x + a) + 1260b cosh(b x + a) +--R + +--R 8 6 4 +--R 819b cosh(b x + a) - 84b cosh(b x + a) - 378b cosh(b x + a) +--R + +--R 2 +--R - 168b cosh(b x + a) - 21b +--R * +--R +-------------+ +--R |sinh(b x + a) +--R |------------- +--R \|cosh(b x + a) +--R + +--R 14 13 +--R - 168b sinh(b x + a) - 2352b cosh(b x + a)sinh(b x + a) +--R + +--R 2 12 +--R (- 15288b cosh(b x + a) - 588b)sinh(b x + a) +--R + +--R 3 11 +--R (- 61152b cosh(b x + a) - 7056b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 10 +--R (- 168168b cosh(b x + a) - 38808b cosh(b x + a) - 588b)sinh(b x + a) +--R + +--R 5 3 +--R - 336336b cosh(b x + a) - 129360b cosh(b x + a) +--R + +--R - 5880b cosh(b x + a) +--R * +--R 9 +--R sinh(b x + a) +--R + +--R 6 4 +--R - 504504b cosh(b x + a) - 291060b cosh(b x + a) +--R + +--R 2 +--R - 26460b cosh(b x + a) + 147b +--R * +--R 8 +--R sinh(b x + a) +--R + +--R 7 5 +--R - 576576b cosh(b x + a) - 465696b cosh(b x + a) +--R + +--R 3 +--R - 70560b cosh(b x + a) + 1176b cosh(b x + a) +--R * +--R 7 +--R sinh(b x + a) +--R + +--R 8 6 +--R - 504504b cosh(b x + a) - 543312b cosh(b x + a) +--R + +--R 4 2 +--R - 123480b cosh(b x + a) + 4116b cosh(b x + a) + 588b +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 9 7 +--R - 336336b cosh(b x + a) - 465696b cosh(b x + a) +--R + +--R 5 3 +--R - 148176b cosh(b x + a) + 8232b cosh(b x + a) + 3528b cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 10 8 +--R - 168168b cosh(b x + a) - 291060b cosh(b x + a) +--R + +--R 6 4 +--R - 123480b cosh(b x + a) + 10290b cosh(b x + a) +--R + +--R 2 +--R 8820b cosh(b x + a) + 294b +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 11 9 +--R - 61152b cosh(b x + a) - 129360b cosh(b x + a) +--R + +--R 7 5 +--R - 70560b cosh(b x + a) + 8232b cosh(b x + a) +--R + +--R 3 +--R 11760b cosh(b x + a) + 1176b cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 12 10 +--R - 15288b cosh(b x + a) - 38808b cosh(b x + a) +--R + +--R 8 6 4 +--R - 26460b cosh(b x + a) + 4116b cosh(b x + a) + 8820b cosh(b x + a) +--R + +--R 2 +--R 1764b cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 13 11 +--R - 2352b cosh(b x + a) - 7056b cosh(b x + a) +--R + +--R 9 7 5 +--R - 5880b cosh(b x + a) + 1176b cosh(b x + a) + 3528b cosh(b x + a) +--R + +--R 3 +--R 1176b cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 14 12 10 +--R - 168b cosh(b x + a) - 588b cosh(b x + a) - 588b cosh(b x + a) +--R + +--R 8 6 4 +--R 147b cosh(b x + a) + 588b cosh(b x + a) + 294b cosh(b x + a) - 21b +--R Type: Expression(Integer) +--E 526 + +--S 527 of 552 +--d0794:= D(m0794,x) +--E 527 + +--S 528 of 552 +t0795:= sech(a+b*x)^4*tanh(a+b*x)^n +--R +--R +--R 4 n +--R (519) sech(b x + a) tanh(b x + a) +--R Type: Expression(Integer) +--E 528 + +--S 528 of 552 +r0795:= tanh(a+b*x)^(1+n)/b/(1+n)-tanh(a+b*x)^(3+n)/b/(3+n) +--R +--R +--R n + 3 n + 1 +--R (- n - 1)tanh(b x + a) + (n + 3)tanh(b x + a) +--R (520) ------------------------------------------------------- +--R 2 +--R b n + 4b n + 3b +--R Type: Expression(Integer) +--E 528 + +--S 530 of 552 +a0795:= integrate(t0795,x) +--R +--R +--R (521) +--R 3 2 +--R (2sinh(b x + a) + (6cosh(b x + a) + 4n + 6)sinh(b x + a)) +--R * +--R sinh(b x + a) +--R sinh(n log(-------------)) +--R cosh(b x + a) +--R + +--R 3 2 +--R (2sinh(b x + a) + (6cosh(b x + a) + 4n + 6)sinh(b x + a)) +--R * +--R sinh(b x + a) +--R cosh(n log(-------------)) +--R cosh(b x + a) +--R / +--R 2 2 +--R (3b n + 12b n + 9b)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 2 +--R (b n + 4b n + 3b)cosh(b x + a) + (3b n + 12b n + 9b)cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 530 + +--S 531 of 552 +m0795:= a0795-r0795 +--R +--R +--R (522) +--R 3 2 +--R (2sinh(b x + a) + (6cosh(b x + a) + 4n + 6)sinh(b x + a)) +--R * +--R sinh(b x + a) +--R sinh(n log(-------------)) +--R cosh(b x + a) +--R + +--R 3 2 +--R (2sinh(b x + a) + (6cosh(b x + a) + 4n + 6)sinh(b x + a)) +--R * +--R sinh(b x + a) +--R cosh(n log(-------------)) +--R cosh(b x + a) +--R + +--R 2 3 +--R (3n + 3)cosh(b x + a)sinh(b x + a) + (n + 1)cosh(b x + a) +--R + +--R (3n + 3)cosh(b x + a) +--R * +--R n + 3 +--R tanh(b x + a) +--R + +--R 2 3 +--R (- 3n - 9)cosh(b x + a)sinh(b x + a) + (- n - 3)cosh(b x + a) +--R + +--R (- 3n - 9)cosh(b x + a) +--R * +--R n + 1 +--R tanh(b x + a) +--R / +--R 2 2 +--R (3b n + 12b n + 9b)cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 2 +--R (b n + 4b n + 3b)cosh(b x + a) + (3b n + 12b n + 9b)cosh(b x + a) +--R Type: Expression(Integer) +--E 531 + +--S 532 of 552 +d0795:= D(m0795,x) +--R +--R +--R (523) +--R 6 +--R (- 6n - 6)sinh(b x + a) +--R + +--R 2 2 4 +--R ((- 14n + 18)cosh(b x + a) - 12n - 36n - 24)sinh(b x + a) +--R + +--R 4 2 2 2 +--R (14n - 18)cosh(b x + a) + (8n - 24n)cosh(b x + a) - 12n - 30n +--R + +--R - 18 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 6 2 4 +--R (6n + 6)cosh(b x + a) + (4n + 28n + 24)cosh(b x + a) +--R + +--R 2 2 +--R (12n + 30n + 18)cosh(b x + a) +--R * +--R sinh(b x + a) +--R sinh(n log(-------------)) +--R cosh(b x + a) +--R + +--R 6 +--R (- 6n - 6)sinh(b x + a) +--R + +--R 2 2 4 +--R ((- 14n + 18)cosh(b x + a) - 12n - 36n - 24)sinh(b x + a) +--R + +--R 4 2 2 2 +--R (14n - 18)cosh(b x + a) + (8n - 24n)cosh(b x + a) - 12n - 30n +--R + +--R - 18 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 6 2 4 +--R (6n + 6)cosh(b x + a) + (4n + 28n + 24)cosh(b x + a) +--R + +--R 2 2 +--R (12n + 30n + 18)cosh(b x + a) +--R * +--R sinh(b x + a) +--R cosh(n log(-------------)) +--R cosh(b x + a) +--R + +--R 2 2 4 +--R (- 9n - 36n - 27)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 +--R (- 6n - 24n - 18)cosh(b x + a) +--R + +--R 2 2 +--R (- 18n - 72n - 54)cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 6 2 4 +--R (- n - 4n - 3)cosh(b x + a) + (- 6n - 24n - 18)cosh(b x + a) +--R + +--R 2 2 +--R (- 9n - 36n - 27)cosh(b x + a) +--R * +--R 2 +--R tanh(b x + a) +--R + +--R 2 2 4 +--R (9n + 36n + 27)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 2 2 +--R ((6n + 24n + 18)cosh(b x + a) + (18n + 72n + 54)cosh(b x + a) ) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 6 2 4 +--R (n + 4n + 3)cosh(b x + a) + (6n + 24n + 18)cosh(b x + a) +--R + +--R 2 2 +--R (9n + 36n + 27)cosh(b x + a) +--R * +--R n + 2 +--R tanh(b x + a) +--R + +--R 2 2 4 +--R (9n + 36n + 27)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 +--R (6n + 24n + 18)cosh(b x + a) +--R + +--R 2 2 +--R (18n + 72n + 54)cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 6 2 4 +--R (n + 4n + 3)cosh(b x + a) + (6n + 24n + 18)cosh(b x + a) +--R + +--R 2 2 +--R (9n + 36n + 27)cosh(b x + a) +--R * +--R 2 +--R tanh(b x + a) +--R + +--R 2 2 4 +--R (- 9n - 36n - 27)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 +--R (- 6n - 24n - 18)cosh(b x + a) +--R + +--R 2 2 +--R (- 18n - 72n - 54)cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 6 2 4 +--R (- n - 4n - 3)cosh(b x + a) + (- 6n - 24n - 18)cosh(b x + a) +--R + +--R 2 2 +--R (- 9n - 36n - 27)cosh(b x + a) +--R * +--R n +--R tanh(b x + a) +--R / +--R 2 2 4 +--R (9n + 36n + 27)cosh(b x + a) sinh(b x + a) +--R + +--R 2 4 2 2 +--R ((6n + 24n + 18)cosh(b x + a) + (18n + 72n + 54)cosh(b x + a) ) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 6 2 4 +--R (n + 4n + 3)cosh(b x + a) + (6n + 24n + 18)cosh(b x + a) +--R + +--R 2 2 +--R (9n + 36n + 27)cosh(b x + a) +--R Type: Expression(Integer) +--E 532 + +--S 533 of 552 +t0796:= coth(a+b*x)^n*csch(a+b*x)^2 +--R +--R +--R 2 n +--R (524) csch(b x + a) coth(b x + a) +--R Type: Expression(Integer) +--E 533 + +--S 534 of 552 +r0796:= -coth(a+b*x)^(1+n)/b/(1+n) +--R +--R +--R n + 1 +--R coth(b x + a) +--R (525) - ------------------ +--R b n + b +--R Type: Expression(Integer) +--E 534 + +--S 535 of 552 +a0796:= integrate(t0796,x) +--R +--R +--R (526) +--R cosh(b x + a) +--R - cosh(b x + a)sinh(n log(-------------)) +--R sinh(b x + a) +--R + +--R cosh(b x + a) +--R - cosh(b x + a)cosh(n log(-------------)) +--R sinh(b x + a) +--R / +--R (b n + b)sinh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 535 + +--S 536 of 552 +m0796:= a0796-r0796 +--R +--R +--R (527) +--R cosh(b x + a) +--R - cosh(b x + a)sinh(n log(-------------)) +--R sinh(b x + a) +--R + +--R cosh(b x + a) n + 1 +--R - cosh(b x + a)cosh(n log(-------------)) + sinh(b x + a)coth(b x + a) +--R sinh(b x + a) +--R / +--R (b n + b)sinh(b x + a) +--R Type: Expression(Integer) +--E 536 + +--S 537 of 552 +d0796:= D(m0796,x) +--R +--R +--R (528) +--R 2 2 cosh(b x + a) +--R (- sinh(b x + a) + cosh(b x + a) )sinh(n log(-------------)) +--R sinh(b x + a) +--R + +--R 2 2 cosh(b x + a) +--R (- sinh(b x + a) + cosh(b x + a) )cosh(n log(-------------)) +--R sinh(b x + a) +--R + +--R 2 2 n +--R (- coth(b x + a) + 1)sinh(b x + a) coth(b x + a) +--R / +--R 2 +--R sinh(b x + a) +--R Type: Expression(Integer) +--E 537 + +--S 538 of 552 +t0797:= coth(a+b*x)^3*csch(a+b*x)^n +--R +--R +--R 3 n +--R (529) coth(b x + a) csch(b x + a) +--R Type: Expression(Integer) +--E 538 + +--S 539 of 552 +r0797:= -csch(a+b*x)^n/b/n-csch(a+b*x)^(2+n)/b/(2+n) +--R +--R +--R n + 2 n +--R - n csch(b x + a) + (- n - 2)csch(b x + a) +--R (530) ------------------------------------------------ +--R 2 +--R b n + 2b n +--R Type: Expression(Integer) +--E 539 + +--S 540 of 552 +a0797:= integrate(t0797,x) +--R +--R +--R (531) +--R 2 2 +--R ((- n - 2)sinh(b x + a) + (- n - 2)cosh(b x + a) - n + 2) +--R * +--R sinh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) - 1 +--R + +--R 2 2 +--R ((- n - 2)sinh(b x + a) + (- n - 2)cosh(b x + a) - n + 2) +--R * +--R cosh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) - 1 +--R / +--R 2 2 2 2 2 +--R (b n + 2b n)sinh(b x + a) + (b n + 2b n)cosh(b x + a) - b n - 2b n +--R Type: Union(Expression(Integer),...) +--E 540 + +--S 541 of 552 +m0797:= a0797-r0797 +--R +--R +--R (532) +--R 2 2 +--R ((- n - 2)sinh(b x + a) + (- n - 2)cosh(b x + a) - n + 2) +--R * +--R sinh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) - 1 +--R + +--R 2 2 +--R ((- n - 2)sinh(b x + a) + (- n - 2)cosh(b x + a) - n + 2) +--R * +--R cosh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) - 1 +--R + +--R 2 2 n + 2 +--R (n sinh(b x + a) + n cosh(b x + a) - n)csch(b x + a) +--R + +--R 2 2 n +--R ((n + 2)sinh(b x + a) + (n + 2)cosh(b x + a) - n - 2)csch(b x + a) +--R / +--R 2 2 2 2 2 +--R (b n + 2b n)sinh(b x + a) + (b n + 2b n)cosh(b x + a) - b n - 2b n +--R Type: Expression(Integer) +--E 541 + +--S 542 of 552 +d0797:= D(m0797,x) +--R +--R +--R (533) +--R 6 5 +--R (n + 2)sinh(b x + a) + (2n + 4)cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R ((3n + 6)cosh(b x + a) + n - 2)sinh(b x + a) +--R + +--R 3 3 +--R (4n + 8)cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 +--R ((3n + 6)cosh(b x + a) + (2n + 12)cosh(b x + a) - n - 2) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 +--R ((2n + 4)cosh(b x + a) + (- 2n - 4)cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 +--R (n + 2)cosh(b x + a) + (n - 2)cosh(b x + a) +--R + +--R 2 +--R (- n - 2)cosh(b x + a) - n + 2 +--R * +--R sinh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) - 1 +--R + +--R 6 5 +--R (n + 2)sinh(b x + a) + (2n + 4)cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R ((3n + 6)cosh(b x + a) + n - 2)sinh(b x + a) +--R + +--R 3 3 +--R (4n + 8)cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 +--R ((3n + 6)cosh(b x + a) + (2n + 12)cosh(b x + a) - n - 2) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 +--R ((2n + 4)cosh(b x + a) + (- 2n - 4)cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 +--R (n + 2)cosh(b x + a) + (n - 2)cosh(b x + a) +--R + +--R 2 +--R (- n - 2)cosh(b x + a) - n + 2 +--R * +--R cosh +--R n +--R * +--R log +--R 2sinh(b x + a) + 2cosh(b x + a) +--R / +--R 2 +--R sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) +--R + +--R 2 +--R cosh(b x + a) - 1 +--R + +--R 6 +--R (- n - 2)coth(b x + a)csch(b x + a)sinh(b x + a) +--R + +--R 5 +--R (- 2n - 4)cosh(b x + a)coth(b x + a)csch(b x + a)sinh(b x + a) +--R + +--R 2 +--R ((- 3n - 6)cosh(b x + a) + 3n + 6)coth(b x + a)csch(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 +--R ((- 4n - 8)cosh(b x + a) + (4n + 8)cosh(b x + a))coth(b x + a) +--R * +--R 3 +--R csch(b x + a)sinh(b x + a) +--R + +--R 4 2 +--R ((- 3n - 6)cosh(b x + a) + (6n + 12)cosh(b x + a) - 3n - 6) +--R * +--R 2 +--R coth(b x + a)csch(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (- 2n - 4)cosh(b x + a) + (4n + 8)cosh(b x + a) +--R + +--R (- 2n - 4)cosh(b x + a) +--R * +--R coth(b x + a)csch(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R (- n - 2)cosh(b x + a) + (3n + 6)cosh(b x + a) +--R + +--R 2 +--R (- 3n - 6)cosh(b x + a) + n + 2 +--R * +--R coth(b x + a)csch(b x + a) +--R * +--R n + 1 +--R csch(b x + a) +--R + +--R 6 +--R (- n - 2)coth(b x + a)csch(b x + a)sinh(b x + a) +--R + +--R 5 +--R (- 2n - 4)cosh(b x + a)coth(b x + a)csch(b x + a)sinh(b x + a) +--R + +--R 2 +--R ((- 3n - 6)cosh(b x + a) + 3n + 6)coth(b x + a)csch(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 +--R ((- 4n - 8)cosh(b x + a) + (4n + 8)cosh(b x + a))coth(b x + a) +--R * +--R 3 +--R csch(b x + a)sinh(b x + a) +--R + +--R 4 2 +--R ((- 3n - 6)cosh(b x + a) + (6n + 12)cosh(b x + a) - 3n - 6) +--R * +--R 2 +--R coth(b x + a)csch(b x + a)sinh(b x + a) +--R + +--R 5 3 +--R (- 2n - 4)cosh(b x + a) + (4n + 8)cosh(b x + a) +--R + +--R (- 2n - 4)cosh(b x + a) +--R * +--R coth(b x + a)csch(b x + a)sinh(b x + a) +--R + +--R 6 4 +--R (- n - 2)cosh(b x + a) + (3n + 6)cosh(b x + a) +--R + +--R 2 +--R (- 3n - 6)cosh(b x + a) + n + 2 +--R * +--R coth(b x + a)csch(b x + a) +--R * +--R n - 1 +--R csch(b x + a) +--R / +--R 6 5 +--R (n + 2)sinh(b x + a) + (2n + 4)cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R ((3n + 6)cosh(b x + a) - 3n - 6)sinh(b x + a) +--R + +--R 3 3 +--R ((4n + 8)cosh(b x + a) + (- 4n - 8)cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R ((3n + 6)cosh(b x + a) + (- 6n - 12)cosh(b x + a) + 3n + 6) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R (2n + 4)cosh(b x + a) + (- 4n - 8)cosh(b x + a) +--R + +--R (2n + 4)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (n + 2)cosh(b x + a) + (- 3n - 6)cosh(b x + a) + (3n + 6)cosh(b x + a) +--R + +--R - n - 2 +--R Type: Expression(Integer) +--E 542 + +--S 543 of 552 +t0798:= coth(x)^n*csch(x)^4 +--R +--R +--R 4 n +--R (534) csch(x) coth(x) +--R Type: Expression(Integer) +--E 543 + +--S 544 of 552 +r0798:= coth(x)^(1+n)/(1+n)-coth(x)^(3+n)/(3+n) +--R +--R +--R n + 3 n + 1 +--R (- n - 1)coth(x) + (n + 3)coth(x) +--R (535) ------------------------------------------- +--R 2 +--R n + 4n + 3 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 552 +a0798:= integrate(t0798,x) +--R +--R +--R (536) +--R 2 3 cosh(x) +--R (6cosh(x)sinh(x) + 2cosh(x) + (- 4n - 6)cosh(x))sinh(n log(-------)) +--R sinh(x) +--R + +--R 2 3 cosh(x) +--R (6cosh(x)sinh(x) + 2cosh(x) + (- 4n - 6)cosh(x))cosh(n log(-------)) +--R sinh(x) +--R / +--R 2 3 2 2 2 +--R (n + 4n + 3)sinh(x) + ((3n + 12n + 9)cosh(x) - 3n - 12n - 9)sinh(x) +--R Type: Union(Expression(Integer),...) +--E 545 + +--S 546 of 552 +m0798:= a0798-r0798 +--R +--R +--R (537) +--R 2 3 cosh(x) +--R (6cosh(x)sinh(x) + 2cosh(x) + (- 4n - 6)cosh(x))sinh(n log(-------)) +--R sinh(x) +--R + +--R 2 3 cosh(x) +--R (6cosh(x)sinh(x) + 2cosh(x) + (- 4n - 6)cosh(x))cosh(n log(-------)) +--R sinh(x) +--R + +--R 3 2 n + 3 +--R ((n + 1)sinh(x) + ((3n + 3)cosh(x) - 3n - 3)sinh(x))coth(x) +--R + +--R 3 2 n + 1 +--R ((- n - 3)sinh(x) + ((- 3n - 9)cosh(x) + 3n + 9)sinh(x))coth(x) +--R / +--R 2 3 2 2 2 +--R (n + 4n + 3)sinh(x) + ((3n + 12n + 9)cosh(x) - 3n - 12n - 9)sinh(x) +--R Type: Expression(Integer) +--E 546 + +--S 547 of 552 +d0798:= D(m0798,x) +--R +--R +--R (538) +--R 6 2 2 4 +--R (6n + 6)sinh(x) + ((14n - 18)cosh(x) - 4n - 28n - 24)sinh(x) +--R + +--R 4 2 2 2 +--R ((- 14n + 18)cosh(x) + (- 8n + 24n)cosh(x) + 12n + 30n + 18) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 +--R (- 6n - 6)cosh(x) + (12n + 36n + 24)cosh(x) +--R + +--R 2 2 +--R (- 12n - 30n - 18)cosh(x) +--R * +--R cosh(x) +--R sinh(n log(-------)) +--R sinh(x) +--R + +--R 6 2 2 4 +--R (6n + 6)sinh(x) + ((14n - 18)cosh(x) - 4n - 28n - 24)sinh(x) +--R + +--R 4 2 2 2 +--R ((- 14n + 18)cosh(x) + (- 8n + 24n)cosh(x) + 12n + 30n + 18) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 4 +--R (- 6n - 6)cosh(x) + (12n + 36n + 24)cosh(x) +--R + +--R 2 2 +--R (- 12n - 30n - 18)cosh(x) +--R * +--R cosh(x) +--R cosh(n log(-------)) +--R sinh(x) +--R + +--R 2 2 2 6 +--R ((- n - 4n - 3)coth(x) + n + 4n + 3)sinh(x) +--R + +--R 2 2 2 2 +--R ((- 6n - 24n - 18)cosh(x) + 6n + 24n + 18)coth(x) +--R + +--R 2 2 2 +--R (6n + 24n + 18)cosh(x) - 6n - 24n - 18 +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (- 9n - 36n - 27)cosh(x) + (18n + 72n + 54)cosh(x) - 9n +--R + +--R - 36n - 27 +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 2 2 2 +--R (9n + 36n + 27)cosh(x) + (- 18n - 72n - 54)cosh(x) + 9n +--R + +--R 36n + 27 +--R * +--R 2 +--R sinh(x) +--R * +--R n + 2 +--R coth(x) +--R + +--R 2 2 2 6 +--R ((n + 4n + 3)coth(x) - n - 4n - 3)sinh(x) +--R + +--R 2 2 2 2 +--R ((6n + 24n + 18)cosh(x) - 6n - 24n - 18)coth(x) +--R + +--R 2 2 2 +--R (- 6n - 24n - 18)cosh(x) + 6n + 24n + 18 +--R * +--R 4 +--R sinh(x) +--R + +--R 2 4 2 2 2 +--R (9n + 36n + 27)cosh(x) + (- 18n - 72n - 54)cosh(x) + 9n +--R + +--R 36n + 27 +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 2 2 2 +--R (- 9n - 36n - 27)cosh(x) + (18n + 72n + 54)cosh(x) - 9n +--R + +--R - 36n - 27 +--R * +--R 2 +--R sinh(x) +--R * +--R n +--R coth(x) +--R / +--R 2 6 +--R (n + 4n + 3)sinh(x) +--R + +--R 2 2 2 4 +--R ((6n + 24n + 18)cosh(x) - 6n - 24n - 18)sinh(x) +--R + +--R 2 4 2 2 2 +--R (9n + 36n + 27)cosh(x) + (- 18n - 72n - 54)cosh(x) + 9n + 36n +--R + +--R 27 +--R * +--R 2 +--R sinh(x) +--R Type: Expression(Integer) +--E 547 + +--S 548 of 552 +t0799:= coth(x)^4*csch(x)^3 +--R +--R +--R 4 3 +--R (539) coth(x) csch(x) +--R Type: Expression(Integer) +--E 548 + +--S 549 of 552 +r0799:= 1/16*acoth(cosh(x))+1/16*coth(x)*csch(x)+_ + 1/24*coth(x)^3*csch(x)-1/6*coth(x)^5*csch(x) +--R +--R +--R 5 3 +--R 3acoth(cosh(x)) + (- 8coth(x) + 2coth(x) + 3coth(x))csch(x) +--R (540) ------------------------------------------------------------- +--R 48 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 552 +a0799:= integrate(t0799,x) +--R +--R +--R (541) +--R 12 11 2 10 +--R 3sinh(x) + 36cosh(x)sinh(x) + (198cosh(x) - 18)sinh(x) +--R + +--R 3 9 +--R (660cosh(x) - 180cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (1485cosh(x) - 810cosh(x) + 45)sinh(x) +--R + +--R 5 3 7 +--R (2376cosh(x) - 2160cosh(x) + 360cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (2772cosh(x) - 3780cosh(x) + 1260cosh(x) - 60)sinh(x) +--R + +--R 7 5 3 5 +--R (2376cosh(x) - 4536cosh(x) + 2520cosh(x) - 360cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (1485cosh(x) - 3780cosh(x) + 3150cosh(x) - 900cosh(x) + 45) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 660cosh(x) - 2160cosh(x) + 2520cosh(x) - 1200cosh(x) +--R + +--R 180cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 198cosh(x) - 810cosh(x) + 1260cosh(x) - 900cosh(x) +--R + +--R 2 +--R 270cosh(x) - 18 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 36cosh(x) - 180cosh(x) + 360cosh(x) - 360cosh(x) +--R + +--R 3 +--R 180cosh(x) - 36cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 3cosh(x) - 18cosh(x) + 45cosh(x) - 60cosh(x) + 45cosh(x) +--R + +--R 2 +--R - 18cosh(x) + 3 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 12 11 2 10 +--R - 3sinh(x) - 36cosh(x)sinh(x) + (- 198cosh(x) + 18)sinh(x) +--R + +--R 3 9 +--R (- 660cosh(x) + 180cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 1485cosh(x) + 810cosh(x) - 45)sinh(x) +--R + +--R 5 3 7 +--R (- 2376cosh(x) + 2160cosh(x) - 360cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 2772cosh(x) + 3780cosh(x) - 1260cosh(x) + 60)sinh(x) +--R + +--R 7 5 3 5 +--R (- 2376cosh(x) + 4536cosh(x) - 2520cosh(x) + 360cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1485cosh(x) + 3780cosh(x) - 3150cosh(x) + 900cosh(x) - 45) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 660cosh(x) + 2160cosh(x) - 2520cosh(x) + 1200cosh(x) +--R + +--R - 180cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 198cosh(x) + 810cosh(x) - 1260cosh(x) + 900cosh(x) +--R + +--R 2 +--R - 270cosh(x) + 18 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 36cosh(x) + 180cosh(x) - 360cosh(x) + 360cosh(x) +--R + +--R 3 +--R - 180cosh(x) + 36cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 3cosh(x) + 18cosh(x) - 45cosh(x) + 60cosh(x) - 45cosh(x) +--R + +--R 2 +--R 18cosh(x) - 3 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 11 10 2 9 +--R - 6sinh(x) - 66cosh(x)sinh(x) + (- 330cosh(x) - 94)sinh(x) +--R + +--R 3 8 +--R (- 990cosh(x) - 846cosh(x))sinh(x) +--R + +--R 4 2 7 +--R (- 1980cosh(x) - 3384cosh(x) - 156)sinh(x) +--R + +--R 5 3 6 +--R (- 2772cosh(x) - 7896cosh(x) - 1092cosh(x))sinh(x) +--R + +--R 6 4 2 5 +--R (- 2772cosh(x) - 11844cosh(x) - 3276cosh(x) - 156)sinh(x) +--R + +--R 7 5 3 4 +--R (- 1980cosh(x) - 11844cosh(x) - 5460cosh(x) - 780cosh(x))sinh(x) +--R + +--R 8 6 4 2 3 +--R (- 990cosh(x) - 7896cosh(x) - 5460cosh(x) - 1560cosh(x) - 94)sinh(x) +--R + +--R 9 7 5 3 +--R - 330cosh(x) - 3384cosh(x) - 3276cosh(x) - 1560cosh(x) +--R + +--R - 282cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 66cosh(x) - 846cosh(x) - 1092cosh(x) - 780cosh(x) +--R + +--R 2 +--R - 282cosh(x) - 6 +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R - 6cosh(x) - 94cosh(x) - 156cosh(x) - 156cosh(x) - 94cosh(x) +--R + +--R - 6cosh(x) +--R / +--R 12 11 2 10 +--R 48sinh(x) + 576cosh(x)sinh(x) + (3168cosh(x) - 288)sinh(x) +--R + +--R 3 9 +--R (10560cosh(x) - 2880cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (23760cosh(x) - 12960cosh(x) + 720)sinh(x) +--R + +--R 5 3 7 +--R (38016cosh(x) - 34560cosh(x) + 5760cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (44352cosh(x) - 60480cosh(x) + 20160cosh(x) - 960)sinh(x) +--R + +--R 7 5 3 5 +--R (38016cosh(x) - 72576cosh(x) + 40320cosh(x) - 5760cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (23760cosh(x) - 60480cosh(x) + 50400cosh(x) - 14400cosh(x) + 720) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 10560cosh(x) - 34560cosh(x) + 40320cosh(x) - 19200cosh(x) +--R + +--R 2880cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 3168cosh(x) - 12960cosh(x) + 20160cosh(x) - 14400cosh(x) +--R + +--R 2 +--R 4320cosh(x) - 288 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 576cosh(x) - 2880cosh(x) + 5760cosh(x) - 5760cosh(x) +--R + +--R 3 +--R 2880cosh(x) - 576cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 48cosh(x) - 288cosh(x) + 720cosh(x) - 960cosh(x) + 720cosh(x) +--R + +--R 2 +--R - 288cosh(x) + 48 +--R Type: Union(Expression(Integer),...) +--E 550 + +--S 551 of 552 +m0799:= a0799-r0799 +--R +--R +--R (542) +--R 12 11 2 10 +--R 3sinh(x) + 36cosh(x)sinh(x) + (198cosh(x) - 18)sinh(x) +--R + +--R 3 9 +--R (660cosh(x) - 180cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (1485cosh(x) - 810cosh(x) + 45)sinh(x) +--R + +--R 5 3 7 +--R (2376cosh(x) - 2160cosh(x) + 360cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (2772cosh(x) - 3780cosh(x) + 1260cosh(x) - 60)sinh(x) +--R + +--R 7 5 3 5 +--R (2376cosh(x) - 4536cosh(x) + 2520cosh(x) - 360cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (1485cosh(x) - 3780cosh(x) + 3150cosh(x) - 900cosh(x) + 45) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 660cosh(x) - 2160cosh(x) + 2520cosh(x) - 1200cosh(x) +--R + +--R 180cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 198cosh(x) - 810cosh(x) + 1260cosh(x) - 900cosh(x) +--R + +--R 2 +--R 270cosh(x) - 18 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 36cosh(x) - 180cosh(x) + 360cosh(x) - 360cosh(x) +--R + +--R 3 +--R 180cosh(x) - 36cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 3cosh(x) - 18cosh(x) + 45cosh(x) - 60cosh(x) + 45cosh(x) +--R + +--R 2 +--R - 18cosh(x) + 3 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 12 11 2 10 +--R - 3sinh(x) - 36cosh(x)sinh(x) + (- 198cosh(x) + 18)sinh(x) +--R + +--R 3 9 +--R (- 660cosh(x) + 180cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 1485cosh(x) + 810cosh(x) - 45)sinh(x) +--R + +--R 5 3 7 +--R (- 2376cosh(x) + 2160cosh(x) - 360cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 2772cosh(x) + 3780cosh(x) - 1260cosh(x) + 60)sinh(x) +--R + +--R 7 5 3 5 +--R (- 2376cosh(x) + 4536cosh(x) - 2520cosh(x) + 360cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1485cosh(x) + 3780cosh(x) - 3150cosh(x) + 900cosh(x) - 45) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 660cosh(x) + 2160cosh(x) - 2520cosh(x) + 1200cosh(x) +--R + +--R - 180cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 198cosh(x) + 810cosh(x) - 1260cosh(x) + 900cosh(x) +--R + +--R 2 +--R - 270cosh(x) + 18 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 36cosh(x) + 180cosh(x) - 360cosh(x) + 360cosh(x) +--R + +--R 3 +--R - 180cosh(x) + 36cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 3cosh(x) + 18cosh(x) - 45cosh(x) + 60cosh(x) - 45cosh(x) +--R + +--R 2 +--R 18cosh(x) - 3 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 12 11 2 10 +--R - 3sinh(x) - 36cosh(x)sinh(x) + (- 198cosh(x) + 18)sinh(x) +--R + +--R 3 9 +--R (- 660cosh(x) + 180cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (- 1485cosh(x) + 810cosh(x) - 45)sinh(x) +--R + +--R 5 3 7 +--R (- 2376cosh(x) + 2160cosh(x) - 360cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 2772cosh(x) + 3780cosh(x) - 1260cosh(x) + 60)sinh(x) +--R + +--R 7 5 3 5 +--R (- 2376cosh(x) + 4536cosh(x) - 2520cosh(x) + 360cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 1485cosh(x) + 3780cosh(x) - 3150cosh(x) + 900cosh(x) - 45) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 660cosh(x) + 2160cosh(x) - 2520cosh(x) + 1200cosh(x) +--R + +--R - 180cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 198cosh(x) + 810cosh(x) - 1260cosh(x) + 900cosh(x) +--R + +--R 2 +--R - 270cosh(x) + 18 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 36cosh(x) + 180cosh(x) - 360cosh(x) + 360cosh(x) +--R + +--R 3 +--R - 180cosh(x) + 36cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R - 3cosh(x) + 18cosh(x) - 45cosh(x) + 60cosh(x) - 45cosh(x) +--R + +--R 2 +--R 18cosh(x) - 3 +--R * +--R acoth(cosh(x)) +--R + +--R 5 3 12 +--R (8coth(x) - 2coth(x) - 3coth(x))csch(x)sinh(x) +--R + +--R 5 3 +--R ((96cosh(x)coth(x) - 24cosh(x)coth(x) - 36cosh(x)coth(x))csch(x) - 6) +--R * +--R 11 +--R sinh(x) +--R + +--R 2 5 2 3 +--R (528cosh(x) - 48)coth(x) + (- 132cosh(x) + 12)coth(x) +--R + +--R 2 +--R (- 198cosh(x) + 18)coth(x) +--R * +--R csch(x) +--R + +--R - 66cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 3 5 +--R (1760cosh(x) - 480cosh(x))coth(x) +--R + +--R 3 3 +--R (- 440cosh(x) + 120cosh(x))coth(x) +--R + +--R 3 +--R (- 660cosh(x) + 180cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R 2 +--R - 330cosh(x) - 94 +--R * +--R 9 +--R sinh(x) +--R + +--R 4 2 5 +--R (3960cosh(x) - 2160cosh(x) + 120)coth(x) +--R + +--R 4 2 3 +--R (- 990cosh(x) + 540cosh(x) - 30)coth(x) +--R + +--R 4 2 +--R (- 1485cosh(x) + 810cosh(x) - 45)coth(x) +--R * +--R csch(x) +--R + +--R 3 +--R - 990cosh(x) - 846cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 5 3 5 +--R (6336cosh(x) - 5760cosh(x) + 960cosh(x))coth(x) +--R + +--R 5 3 3 +--R (- 1584cosh(x) + 1440cosh(x) - 240cosh(x))coth(x) +--R + +--R 5 3 +--R (- 2376cosh(x) + 2160cosh(x) - 360cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R 4 2 +--R - 1980cosh(x) - 3384cosh(x) - 156 +--R * +--R 7 +--R sinh(x) +--R + +--R 6 4 2 5 +--R (7392cosh(x) - 10080cosh(x) + 3360cosh(x) - 160)coth(x) +--R + +--R 6 4 2 3 +--R (- 1848cosh(x) + 2520cosh(x) - 840cosh(x) + 40)coth(x) +--R + +--R 6 4 2 +--R (- 2772cosh(x) + 3780cosh(x) - 1260cosh(x) + 60)coth(x) +--R * +--R csch(x) +--R + +--R 5 3 +--R - 2772cosh(x) - 7896cosh(x) - 1092cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 5 3 +--R (6336cosh(x) - 12096cosh(x) + 6720cosh(x) - 960cosh(x)) +--R * +--R 5 +--R coth(x) +--R + +--R 7 5 3 +--R (- 1584cosh(x) + 3024cosh(x) - 1680cosh(x) + 240cosh(x)) +--R * +--R 3 +--R coth(x) +--R + +--R 7 5 3 +--R (- 2376cosh(x) + 4536cosh(x) - 2520cosh(x) + 360cosh(x))coth(x) +--R * +--R csch(x) +--R + +--R 6 4 2 +--R - 2772cosh(x) - 11844cosh(x) - 3276cosh(x) - 156 +--R * +--R 5 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 3960cosh(x) - 10080cosh(x) + 8400cosh(x) - 2400cosh(x) +--R + +--R 120 +--R * +--R 5 +--R coth(x) +--R + +--R 8 6 4 2 +--R - 990cosh(x) + 2520cosh(x) - 2100cosh(x) + 600cosh(x) +--R + +--R - 30 +--R * +--R 3 +--R coth(x) +--R + +--R 8 6 4 2 +--R - 1485cosh(x) + 3780cosh(x) - 3150cosh(x) + 900cosh(x) +--R + +--R - 45 +--R * +--R coth(x) +--R * +--R csch(x) +--R + +--R 7 5 3 +--R - 1980cosh(x) - 11844cosh(x) - 5460cosh(x) - 780cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 1760cosh(x) - 5760cosh(x) + 6720cosh(x) - 3200cosh(x) +--R + +--R 480cosh(x) +--R * +--R 5 +--R coth(x) +--R + +--R 9 7 5 3 +--R - 440cosh(x) + 1440cosh(x) - 1680cosh(x) + 800cosh(x) +--R + +--R - 120cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 9 7 5 3 +--R - 660cosh(x) + 2160cosh(x) - 2520cosh(x) + 1200cosh(x) +--R + +--R - 180cosh(x) +--R * +--R coth(x) +--R * +--R csch(x) +--R + +--R 8 6 4 2 +--R - 990cosh(x) - 7896cosh(x) - 5460cosh(x) - 1560cosh(x) - 94 +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 528cosh(x) - 2160cosh(x) + 3360cosh(x) - 2400cosh(x) +--R + +--R 2 +--R 720cosh(x) - 48 +--R * +--R 5 +--R coth(x) +--R + +--R 10 8 6 4 +--R - 132cosh(x) + 540cosh(x) - 840cosh(x) + 600cosh(x) +--R + +--R 2 +--R - 180cosh(x) + 12 +--R * +--R 3 +--R coth(x) +--R + +--R 10 8 6 4 +--R - 198cosh(x) + 810cosh(x) - 1260cosh(x) + 900cosh(x) +--R + +--R 2 +--R - 270cosh(x) + 18 +--R * +--R coth(x) +--R * +--R csch(x) +--R + +--R 9 7 5 3 +--R - 330cosh(x) - 3384cosh(x) - 3276cosh(x) - 1560cosh(x) - 282cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 96cosh(x) - 480cosh(x) + 960cosh(x) - 960cosh(x) +--R + +--R 3 +--R 480cosh(x) - 96cosh(x) +--R * +--R 5 +--R coth(x) +--R + +--R 11 9 7 5 +--R - 24cosh(x) + 120cosh(x) - 240cosh(x) + 240cosh(x) +--R + +--R 3 +--R - 120cosh(x) + 24cosh(x) +--R * +--R 3 +--R coth(x) +--R + +--R 11 9 7 5 +--R - 36cosh(x) + 180cosh(x) - 360cosh(x) + 360cosh(x) +--R + +--R 3 +--R - 180cosh(x) + 36cosh(x) +--R * +--R coth(x) +--R * +--R csch(x) +--R + +--R 10 8 6 4 +--R - 66cosh(x) - 846cosh(x) - 1092cosh(x) - 780cosh(x) +--R + +--R 2 +--R - 282cosh(x) - 6 +--R * +--R sinh(x) +--R + +--R 12 10 8 6 +--R 8cosh(x) - 48cosh(x) + 120cosh(x) - 160cosh(x) +--R + +--R 4 2 +--R 120cosh(x) - 48cosh(x) + 8 +--R * +--R 5 +--R coth(x) +--R + +--R 12 10 8 6 4 +--R - 2cosh(x) + 12cosh(x) - 30cosh(x) + 40cosh(x) - 30cosh(x) +--R + +--R 2 +--R 12cosh(x) - 2 +--R * +--R 3 +--R coth(x) +--R + +--R 12 10 8 6 4 +--R - 3cosh(x) + 18cosh(x) - 45cosh(x) + 60cosh(x) - 45cosh(x) +--R + +--R 2 +--R 18cosh(x) - 3 +--R * +--R coth(x) +--R * +--R csch(x) +--R + +--R 11 9 7 5 3 +--R - 6cosh(x) - 94cosh(x) - 156cosh(x) - 156cosh(x) - 94cosh(x) +--R + +--R - 6cosh(x) +--R / +--R 12 11 2 10 +--R 48sinh(x) + 576cosh(x)sinh(x) + (3168cosh(x) - 288)sinh(x) +--R + +--R 3 9 +--R (10560cosh(x) - 2880cosh(x))sinh(x) +--R + +--R 4 2 8 +--R (23760cosh(x) - 12960cosh(x) + 720)sinh(x) +--R + +--R 5 3 7 +--R (38016cosh(x) - 34560cosh(x) + 5760cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (44352cosh(x) - 60480cosh(x) + 20160cosh(x) - 960)sinh(x) +--R + +--R 7 5 3 5 +--R (38016cosh(x) - 72576cosh(x) + 40320cosh(x) - 5760cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (23760cosh(x) - 60480cosh(x) + 50400cosh(x) - 14400cosh(x) + 720) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 10560cosh(x) - 34560cosh(x) + 40320cosh(x) - 19200cosh(x) +--R + +--R 2880cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 3168cosh(x) - 12960cosh(x) + 20160cosh(x) - 14400cosh(x) +--R + +--R 2 +--R 4320cosh(x) - 288 +--R * +--R 2 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 576cosh(x) - 2880cosh(x) + 5760cosh(x) - 5760cosh(x) +--R + +--R 3 +--R 2880cosh(x) - 576cosh(x) +--R * +--R sinh(x) +--R + +--R 12 10 8 6 4 +--R 48cosh(x) - 288cosh(x) + 720cosh(x) - 960cosh(x) + 720cosh(x) +--R + +--R 2 +--R - 288cosh(x) + 48 +--R Type: Expression(Integer) +--E 551 + +--S 552 of 552 +d0799:= D(m0799,x) +--R +--R +--R (543) +--R 15 +--R sinh(x) +--R + +--R 2 6 2 4 +--R (- 16cosh(x) + 16)coth(x) + (16cosh(x) - 16)coth(x) +--R + +--R 2 +--R - cosh(x) + 1 +--R * +--R csch(x) +--R + +--R 14cosh(x) +--R * +--R 14 +--R sinh(x) +--R + +--R 3 6 +--R (- 224cosh(x) + 224cosh(x))coth(x) +--R + +--R 3 4 3 +--R (224cosh(x) - 224cosh(x))coth(x) - 14cosh(x) + 14cosh(x) +--R * +--R csch(x) +--R + +--R 2 +--R 91cosh(x) - 7 +--R * +--R 13 +--R sinh(x) +--R + +--R 4 2 6 +--R (- 1456cosh(x) + 1568cosh(x) - 112)coth(x) +--R + +--R 4 2 4 4 +--R (1456cosh(x) - 1568cosh(x) + 112)coth(x) - 91cosh(x) +--R + +--R 2 +--R 98cosh(x) - 7 +--R * +--R csch(x) +--R + +--R 3 +--R 364cosh(x) - 84cosh(x) +--R * +--R 12 +--R sinh(x) +--R + +--R 5 3 6 +--R (- 5824cosh(x) + 7168cosh(x) - 1344cosh(x))coth(x) +--R + +--R 5 3 4 5 +--R (5824cosh(x) - 7168cosh(x) + 1344cosh(x))coth(x) - 364cosh(x) +--R + +--R 3 +--R 448cosh(x) - 84cosh(x) +--R * +--R csch(x) +--R + +--R 4 2 +--R 1001cosh(x) - 334cosh(x) - 107 +--R * +--R 11 +--R sinh(x) +--R + +--R 6 4 2 6 +--R (- 16016cosh(x) + 23408cosh(x) - 7728cosh(x) + 336)coth(x) +--R + +--R 6 4 2 4 +--R (16016cosh(x) - 23408cosh(x) + 7728cosh(x) - 336)coth(x) +--R + +--R 6 4 2 +--R - 1001cosh(x) + 1463cosh(x) - 483cosh(x) + 21 +--R * +--R csch(x) +--R + +--R 5 3 +--R 2002cosh(x) - 132cosh(x) - 1198cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 32032cosh(x) + 56672cosh(x) - 28000cosh(x) + 3360cosh(x)) +--R * +--R 6 +--R coth(x) +--R + +--R 7 5 3 +--R (32032cosh(x) - 56672cosh(x) + 28000cosh(x) - 3360cosh(x)) +--R * +--R 4 +--R coth(x) +--R + +--R 7 5 3 +--R - 2002cosh(x) + 3542cosh(x) - 1750cosh(x) + 210cosh(x) +--R * +--R csch(x) +--R + +--R 6 4 2 +--R 3003cosh(x) + 3575cosh(x) - 5583cosh(x) - 547 +--R * +--R 9 +--R sinh(x) +--R + +--R 8 6 4 +--R - 48048cosh(x) + 103488cosh(x) - 70560cosh(x) +--R + +--R 2 +--R 15680cosh(x) - 560 +--R * +--R 6 +--R coth(x) +--R + +--R 8 6 4 +--R 48048cosh(x) - 103488cosh(x) + 70560cosh(x) +--R + +--R 2 +--R - 15680cosh(x) + 560 +--R * +--R 4 +--R coth(x) +--R + +--R 8 6 4 2 +--R - 3003cosh(x) + 6468cosh(x) - 4410cosh(x) + 980cosh(x) - 35 +--R * +--R csch(x) +--R + +--R 7 5 3 +--R 3432cosh(x) + 15576cosh(x) - 13992cosh(x) - 4888cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 +--R - 54912cosh(x) + 143616cosh(x) - 129024cosh(x) +--R + +--R 3 +--R 44800cosh(x) - 4480cosh(x) +--R * +--R 6 +--R coth(x) +--R + +--R 9 7 5 +--R 54912cosh(x) - 143616cosh(x) + 129024cosh(x) +--R + +--R 3 +--R - 44800cosh(x) + 4480cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 9 7 5 3 +--R - 3432cosh(x) + 8976cosh(x) - 8064cosh(x) + 2800cosh(x) +--R + +--R - 280cosh(x) +--R * +--R csch(x) +--R + +--R 8 6 4 2 +--R 3003cosh(x) + 35772cosh(x) - 19398cosh(x) - 18644cosh(x) - 733 +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 6 +--R - 48048cosh(x) + 151536cosh(x) - 174048cosh(x) +--R + +--R 4 2 +--R 86240cosh(x) - 16240cosh(x) + 560 +--R * +--R 6 +--R coth(x) +--R + +--R 10 8 6 +--R 48048cosh(x) - 151536cosh(x) + 174048cosh(x) +--R + +--R 4 2 +--R - 86240cosh(x) + 16240cosh(x) - 560 +--R * +--R 4 +--R coth(x) +--R + +--R 10 8 6 4 +--R - 3003cosh(x) + 9471cosh(x) - 10878cosh(x) + 5390cosh(x) +--R + +--R 2 +--R - 1015cosh(x) + 35 +--R * +--R csch(x) +--R + +--R 9 7 5 3 +--R 2002cosh(x) + 53592cosh(x) - 10836cosh(x) - 39592cosh(x) +--R + +--R - 5166cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 +--R - 32032cosh(x) + 120736cosh(x) - 173376cosh(x) +--R + +--R 5 3 +--R 116032cosh(x) - 34720cosh(x) + 3360cosh(x) +--R * +--R 6 +--R coth(x) +--R + +--R 11 9 7 +--R 32032cosh(x) - 120736cosh(x) + 173376cosh(x) +--R + +--R 5 3 +--R - 116032cosh(x) + 34720cosh(x) - 3360cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 11 9 7 5 +--R - 2002cosh(x) + 7546cosh(x) - 10836cosh(x) + 7252cosh(x) +--R + +--R 3 +--R - 2170cosh(x) + 210cosh(x) +--R * +--R csch(x) +--R + +--R 10 8 6 4 +--R 1001cosh(x) + 55671cosh(x) + 9786cosh(x) - 50834cosh(x) +--R + +--R 2 +--R - 15091cosh(x) - 533 +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 +--R - 16016cosh(x) + 71456cosh(x) - 126000cosh(x) +--R + +--R 6 4 2 +--R 109760cosh(x) - 47600cosh(x) + 8736cosh(x) - 336 +--R * +--R 6 +--R coth(x) +--R + +--R 12 10 8 +--R 16016cosh(x) - 71456cosh(x) + 126000cosh(x) +--R + +--R 6 4 2 +--R - 109760cosh(x) + 47600cosh(x) - 8736cosh(x) + 336 +--R * +--R 4 +--R coth(x) +--R + +--R 12 10 8 6 +--R - 1001cosh(x) + 4466cosh(x) - 7875cosh(x) + 6860cosh(x) +--R + +--R 4 2 +--R - 2975cosh(x) + 546cosh(x) - 21 +--R * +--R csch(x) +--R + +--R 11 9 7 5 +--R 364cosh(x) + 40700cosh(x) + 24792cosh(x) - 39592cosh(x) +--R + +--R 3 +--R - 23620cosh(x) - 2644cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 +--R - 5824cosh(x) + 30464cosh(x) - 64960cosh(x) +--R + +--R 7 5 3 +--R 71680cosh(x) - 42560cosh(x) + 12544cosh(x) - 1344cosh(x) +--R * +--R 6 +--R coth(x) +--R + +--R 13 11 9 +--R 5824cosh(x) - 30464cosh(x) + 64960cosh(x) +--R + +--R 7 5 3 +--R - 71680cosh(x) + 42560cosh(x) - 12544cosh(x) + 1344cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 13 11 9 7 +--R - 364cosh(x) + 1904cosh(x) - 4060cosh(x) + 4480cosh(x) +--R + +--R 5 3 +--R - 2660cosh(x) + 784cosh(x) - 84cosh(x) +--R * +--R csch(x) +--R + +--R 12 10 8 6 +--R 91cosh(x) + 20658cosh(x) + 22833cosh(x) - 17108cosh(x) +--R + +--R 4 2 +--R - 21235cosh(x) - 5118cosh(x) - 121 +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 +--R - 1456cosh(x) + 8848cosh(x) - 22512cosh(x) +--R + +--R 8 6 4 2 +--R 30800cosh(x) - 24080cosh(x) + 10416cosh(x) - 2128cosh(x) +--R + +--R 112 +--R * +--R 6 +--R coth(x) +--R + +--R 14 12 10 +--R 1456cosh(x) - 8848cosh(x) + 22512cosh(x) +--R + +--R 8 6 4 +--R - 30800cosh(x) + 24080cosh(x) - 10416cosh(x) +--R + +--R 2 +--R 2128cosh(x) - 112 +--R * +--R 4 +--R coth(x) +--R + +--R 14 12 10 8 +--R - 91cosh(x) + 553cosh(x) - 1407cosh(x) + 1925cosh(x) +--R + +--R 6 4 2 +--R - 1505cosh(x) + 651cosh(x) - 133cosh(x) + 7 +--R * +--R csch(x) +--R + +--R 13 11 9 7 +--R 14cosh(x) + 6956cosh(x) + 11602cosh(x) - 2584cosh(x) +--R + +--R 5 3 +--R - 10798cosh(x) - 4820cosh(x) - 370cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 15 13 11 9 +--R - 224cosh(x) + 1568cosh(x) - 4704cosh(x) + 7840cosh(x) +--R + +--R 7 5 3 +--R - 7840cosh(x) + 4704cosh(x) - 1568cosh(x) + 224cosh(x) +--R * +--R 6 +--R coth(x) +--R + +--R 15 13 11 9 +--R 224cosh(x) - 1568cosh(x) + 4704cosh(x) - 7840cosh(x) +--R + +--R 7 5 3 +--R 7840cosh(x) - 4704cosh(x) + 1568cosh(x) - 224cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 15 13 11 9 +--R - 14cosh(x) + 98cosh(x) - 294cosh(x) + 490cosh(x) +--R + +--R 7 5 3 +--R - 490cosh(x) + 294cosh(x) - 98cosh(x) + 14cosh(x) +--R * +--R csch(x) +--R + +--R 14 12 10 8 +--R cosh(x) + 1401cosh(x) + 3221cosh(x) + 733cosh(x) +--R + +--R 6 4 2 +--R - 2781cosh(x) - 2197cosh(x) - 377cosh(x) - 1 +--R * +--R sinh(x) +--R + +--R 16 14 12 10 +--R - 16cosh(x) + 128cosh(x) - 448cosh(x) + 896cosh(x) +--R + +--R 8 6 4 2 +--R - 1120cosh(x) + 896cosh(x) - 448cosh(x) + 128cosh(x) - 16 +--R * +--R 6 +--R coth(x) +--R + +--R 16 14 12 10 +--R 16cosh(x) - 128cosh(x) + 448cosh(x) - 896cosh(x) +--R + +--R 8 6 4 2 +--R 1120cosh(x) - 896cosh(x) + 448cosh(x) - 128cosh(x) + 16 +--R * +--R 4 +--R coth(x) +--R + +--R 16 14 12 10 8 +--R - cosh(x) + 8cosh(x) - 28cosh(x) + 56cosh(x) - 70cosh(x) +--R + +--R 6 4 2 +--R 56cosh(x) - 28cosh(x) + 8cosh(x) - 1 +--R * +--R csch(x) +--R + +--R 13 11 9 7 5 +--R 128cosh(x) + 384cosh(x) + 256cosh(x) - 256cosh(x) - 384cosh(x) +--R + +--R 3 +--R - 128cosh(x) +--R / +--R 2 14 3 13 +--R (16cosh(x) - 16)sinh(x) + (224cosh(x) - 224cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (1456cosh(x) - 1568cosh(x) + 112)sinh(x) +--R + +--R 5 3 11 +--R (5824cosh(x) - 7168cosh(x) + 1344cosh(x))sinh(x) +--R + +--R 6 4 2 10 +--R (16016cosh(x) - 23408cosh(x) + 7728cosh(x) - 336)sinh(x) +--R + +--R 7 5 3 9 +--R (32032cosh(x) - 56672cosh(x) + 28000cosh(x) - 3360cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (48048cosh(x) - 103488cosh(x) + 70560cosh(x) - 15680cosh(x) + 560) +--R * +--R 8 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 54912cosh(x) - 143616cosh(x) + 129024cosh(x) - 44800cosh(x) +--R + +--R 4480cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 48048cosh(x) - 151536cosh(x) + 174048cosh(x) - 86240cosh(x) +--R + +--R 2 +--R 16240cosh(x) - 560 +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 32032cosh(x) - 120736cosh(x) + 173376cosh(x) - 116032cosh(x) +--R + +--R 3 +--R 34720cosh(x) - 3360cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 16016cosh(x) - 71456cosh(x) + 126000cosh(x) - 109760cosh(x) +--R + +--R 4 2 +--R 47600cosh(x) - 8736cosh(x) + 336 +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 5824cosh(x) - 30464cosh(x) + 64960cosh(x) - 71680cosh(x) +--R + +--R 5 3 +--R 42560cosh(x) - 12544cosh(x) + 1344cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 8 +--R 1456cosh(x) - 8848cosh(x) + 22512cosh(x) - 30800cosh(x) +--R + +--R 6 4 2 +--R 24080cosh(x) - 10416cosh(x) + 2128cosh(x) - 112 +--R * +--R 2 +--R sinh(x) +--R + +--R 15 13 11 9 +--R 224cosh(x) - 1568cosh(x) + 4704cosh(x) - 7840cosh(x) +--R + +--R 7 5 3 +--R 7840cosh(x) - 4704cosh(x) + 1568cosh(x) - 224cosh(x) +--R * +--R sinh(x) +--R + +--R 16 14 12 10 8 +--R 16cosh(x) - 128cosh(x) + 448cosh(x) - 896cosh(x) + 1120cosh(x) +--R + +--R 6 4 2 +--R - 896cosh(x) + 448cosh(x) - 128cosh(x) + 16 +--R Type: Expression(Integer) +--E 552 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper700-799.input.pdf b/src/axiom-website/CATS/richhyper700-799.input.pdf new file mode 100644 index 0000000..6426d6a Binary files /dev/null and b/src/axiom-website/CATS/richhyper700-799.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper800-899.input.pamphlet b/src/axiom-website/CATS/richhyper800-899.input.pamphlet new file mode 100644 index 0000000..55b52ae --- /dev/null +++ b/src/axiom-website/CATS/richhyper800-899.input.pamphlet @@ -0,0 +1,14553 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper800-899.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper800-899.output +)spool richhyper800-899.output +)set message auto off +)clear all + +--S 1 of 502 +t0800:= sinh(a+b*x)*cosh(a+b*x)/x^2 +--R +--R +--R cosh(b x + a)sinh(b x + a) +--R (1) -------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 502 +r0800:= b*cosh(2*a)*Chi(2*b*x)-1/2*sinh(2*a+2*b*x)/x+b*sinh(2*a)*Shi(2*b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 502 +a0800:= integrate(t0800,x) +--R +--R +--R x +--R ++ cosh(%I b + a)sinh(%I b + a) +--R (2) | ---------------------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 502 +--m0800:= a0800-r0800 +--E 4 + +--S 5 of 502 +--d0800:= D(m0800,x) +--E 5 + +--S 6 of 502 +t0801:= sinh(a+b*x)*cosh(a+b*x)/x^3 +--R +--R +--R cosh(b x + a)sinh(b x + a) +--R (3) -------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 502 +r0801:= -1/2*b*cosh(2*a+2*b*x)/x+b^2*Chi(2*b*x)*sinh(2*a)-_ + 1/4*sinh(2*a+2*b*x)/x^2+b^2*cosh(2*a)*Shi(2*b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 502 +a0801:= integrate(t0801,x) +--R +--R +--R x +--R ++ cosh(%I b + a)sinh(%I b + a) +--R (4) | ---------------------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 502 +--m0801:= a0801-r0801 +--E 9 + +--S 10 of 502 +--d0801:= D(m0801,x) +--E 10 + +--S 11 of 502 +t0802:= sinh(a+b*x)^2*cosh(a+b*x)/x^2 +--R +--R +--R 2 +--R cosh(b x + a)sinh(b x + a) +--R (5) --------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 502 +r0802:= 1/4*(cosh(a+b*x)-cosh(3*a+3*b*x)-b*Chi(b*x)*sinh(a)*x+_ + 3*b*Chi(3*b*x)*sinh(3*a)*x-b*cosh(a)*Shi(b*x)*x+_ + 3*b*cosh(3*a)*Shi(3*b*x)*x)/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 502 +a0802:= integrate(t0802,x) +--R +--R +--R x 2 +--R ++ cosh(%I b + a)sinh(%I b + a) +--R (6) | ----------------------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 502 +--m0802:= a0802-r0802 +--E 14 + +--S 15 of 502 +--d0802:= D(m0802,x) +--E 15 + +--S 16 of 502 +t0803:= sinh(a+b*x)^2*cosh(a+b*x)/x^3 +--R +--R +--R 2 +--R cosh(b x + a)sinh(b x + a) +--R (7) --------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 502 +r0803:= 1/8*(cosh(a+b*x)-cosh(3*a+3*b*x)-b^2*cosh(a)*Chi(b*x)*x^2+_ + 9*b^2*cosh(3*a)*Chi(3*b*x)*x^2+b*x*sinh(a+b*x)-_ + 3*b*x*sinh(3*a+3*b*x)-b^2*sinh(a)*Shi(b*x)*x^2+_ + 9*b^2*sinh(3*a)*Shi(3*b*x)*x^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 502 +a0803:= integrate(t0803,x) +--R +--R +--R x 2 +--R ++ cosh(%I b + a)sinh(%I b + a) +--R (8) | ----------------------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 502 +--m0803:= a0803-r0803 +--E 19 + +--S 20 of 502 +--d0803:= D(m0803,x) +--E 20 + +--S 21 of 502 +t0804:= sinh(a+b*x)*cosh(a+b*x)^2/x^2 +--R +--R +--R 2 +--R cosh(b x + a) sinh(b x + a) +--R (9) --------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 502 +r0804:= -1/4*(-b*cosh(a)*Chi(b*x)*x-3*b*cosh(3*a)*Chi(3*b*x)*x+_ + sinh(a+b*x)+sinh(3*a+3*b*x)-b*sinh(a)*Shi(b*x)*x-_ + 3*b*sinh(3*a)*Shi(3*b*x)*x)/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 502 +a0804:= integrate(t0804,x) +--R +--R +--R x 2 +--R ++ cosh(%I b + a) sinh(%I b + a) +--R (10) | ----------------------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 502 +--m0804:= a0804-r0804 +--E 24 + +--S 25 of 502 +--d0804:= D(m0804,x) +--E 25 + +--S 26 of 502 +t0805:= sinh(a+b*x)*cosh(a+b*x)^2/x^3 +--R +--R +--R 2 +--R cosh(b x + a) sinh(b x + a) +--R (11) --------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 502 +r0805:= -1/8*(b*cosh(a+b*x)*x+3*b*cosh(3*a+3*b*x)*x-_ + b^2*Chi(b*x)*sinh(a)*x^2-9*b^2*Chi(3*b*x)*sinh(3*a)*x^2+_ + sinh(a+b*x)+sinh(3*a+3*b*x)-b^2*cosh(a)*Shi(b*x)*x^2-_ + 9*b^2*cosh(3*a)*Shi(3*b*x)*x^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 502 +a0805:= integrate(t0805,x) +--R +--R +--R x 2 +--R ++ cosh(%I b + a) sinh(%I b + a) +--R (12) | ----------------------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 502 +--m0805:= a0805-r0805 +--E 29 + +--S 30 of 502 +--d0805:= D(m0805,x) +--E 30 + +--S 31 of 502 +t0806:= x*sinh(a+b*x)^2*cosh(a+b*x)^2 +--R +--R +--R 2 2 +--R (13) x cosh(b x + a) sinh(b x + a) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 502 +r0806:= -1/128*(8*b^2*x^2+cosh(4*a+4*b*x)-4*x*sinh(4*a+4*b*x)*b)/b^2 +--R +--R +--R 2 2 +--R 4b x sinh(4b x + 4a) - cosh(4b x + 4a) - 8b x +--R (14) ---------------------------------------------- +--R 2 +--R 128b +--R Type: Expression(Integer) +--E 32 + +--S 33 of 502 +a0806:= integrate(t0806,x) +--R +--R +--R (15) +--R 4 3 +--R - sinh(b x + a) + 16b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 3 +--R - 6cosh(b x + a) sinh(b x + a) + 16b x cosh(b x + a) sinh(b x + a) +--R + +--R 4 2 2 +--R - cosh(b x + a) - 8b x +--R / +--R 2 +--R 128b +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 502 +m0806:= a0806-r0806 +--R +--R +--R (16) +--R 4 +--R - 4b x sinh(4b x + 4a) - sinh(b x + a) +--R + +--R 3 2 2 +--R 16b x cosh(b x + a)sinh(b x + a) - 6cosh(b x + a) sinh(b x + a) +--R + +--R 3 4 +--R 16b x cosh(b x + a) sinh(b x + a) + cosh(4b x + 4a) - cosh(b x + a) +--R / +--R 2 +--R 128b +--R Type: Expression(Integer) +--E 34 + +--S 35 of 502 +d0806:= D(m0806,x) +--R +--R +--R (17) +--R 4 2 2 +--R x sinh(b x + a) + 6x cosh(b x + a) sinh(b x + a) - x cosh(4b x + 4a) +--R + +--R 4 +--R x cosh(b x + a) +--R / +--R 8 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 502 +t0807:= x^2*sinh(a+b*x)^2*cosh(a+b*x)^2 +--R +--R +--R 2 2 2 +--R (18) x cosh(b x + a) sinh(b x + a) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 502 +r0807:= -1/768*(32*b^3*x^3+12*b*x*cosh(4*a+4*b*x)-3*sinh(4*a+4*b*x)-_ + 24*x^2*sinh(4*a+4*b*x)*b^2)/b^3 +--R +--R +--R 2 2 3 3 +--R (24b x + 3)sinh(4b x + 4a) - 12b x cosh(4b x + 4a) - 32b x +--R (19) ------------------------------------------------------------ +--R 3 +--R 768b +--R Type: Expression(Integer) +--E 37 + +--S 38 of 502 +a0807:= integrate(t0807,x) +--R +--R +--R (20) +--R 4 2 2 3 +--R - 3b x sinh(b x + a) + (24b x + 3)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R - 18b x cosh(b x + a) sinh(b x + a) +--R + +--R 2 2 3 4 3 3 +--R (24b x + 3)cosh(b x + a) sinh(b x + a) - 3b x cosh(b x + a) - 8b x +--R / +--R 3 +--R 192b +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 502 +m0807:= a0807-r0807 +--R +--R +--R (21) +--R 2 2 4 +--R (- 8b x - 1)sinh(4b x + 4a) - 4b x sinh(b x + a) +--R + +--R 2 2 3 +--R (32b x + 4)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R - 24b x cosh(b x + a) sinh(b x + a) +--R + +--R 2 2 3 +--R (32b x + 4)cosh(b x + a) sinh(b x + a) + 4b x cosh(4b x + 4a) +--R + +--R 4 +--R - 4b x cosh(b x + a) +--R / +--R 3 +--R 256b +--R Type: Expression(Integer) +--E 39 + +--S 40 of 502 +d0807:= D(m0807,x) +--R +--R +--R (22) +--R 2 4 2 2 2 2 +--R x sinh(b x + a) + 6x cosh(b x + a) sinh(b x + a) - x cosh(4b x + 4a) +--R + +--R 2 4 +--R x cosh(b x + a) +--R / +--R 8 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 502 +t0808:= x^3*sinh(a+b*x)^2*cosh(a+b*x)^2 +--R +--R +--R 3 2 2 +--R (23) x cosh(b x + a) sinh(b x + a) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 502 +r0808:= -1/1024*(32*b^4*x^4+3*cosh(4*a+4*b*x)+24*b^2*x^2*cosh(4*a+4*b*x)-_ + 12*x*sinh(4*a+4*b*x)*b-32*x^3*sinh(4*a+4*b*x)*b^3)/b^4 +--R +--R +--R (24) +--R 3 3 2 2 4 4 +--R (32b x + 12b x)sinh(4b x + 4a) + (- 24b x - 3)cosh(4b x + 4a) - 32b x +--R ------------------------------------------------------------------------ +--R 4 +--R 1024b +--R Type: Expression(Integer) +--E 42 + +--S 43 of 502 +a0808:= integrate(t0808,x) +--R +--R +--R (25) +--R 2 2 4 +--R (- 24b x - 3)sinh(b x + a) +--R + +--R 3 3 3 +--R (128b x + 48b x)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 +--R (- 144b x - 18)cosh(b x + a) sinh(b x + a) +--R + +--R 3 3 3 +--R (128b x + 48b x)cosh(b x + a) sinh(b x + a) +--R + +--R 2 2 4 4 4 +--R (- 24b x - 3)cosh(b x + a) - 32b x +--R / +--R 4 +--R 1024b +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 502 +m0808:= a0808-r0808 +--R +--R +--R (26) +--R 3 3 2 2 4 +--R (- 32b x - 12b x)sinh(4b x + 4a) + (- 24b x - 3)sinh(b x + a) +--R + +--R 3 3 3 +--R (128b x + 48b x)cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 +--R (- 144b x - 18)cosh(b x + a) sinh(b x + a) +--R + +--R 3 3 3 +--R (128b x + 48b x)cosh(b x + a) sinh(b x + a) +--R + +--R 2 2 2 2 4 +--R (24b x + 3)cosh(4b x + 4a) + (- 24b x - 3)cosh(b x + a) +--R / +--R 4 +--R 1024b +--R Type: Expression(Integer) +--E 44 + +--S 45 of 502 +d0808:= D(m0808,x) +--R +--R +--R (27) +--R 3 4 3 2 2 3 +--R x sinh(b x + a) + 6x cosh(b x + a) sinh(b x + a) - x cosh(4b x + 4a) +--R + +--R 3 4 +--R x cosh(b x + a) +--R / +--R 8 +--R Type: Expression(Integer) +--E 45 + +--S 46 of 502 +t0809:= sinh(a+b*x)^2*cosh(a+b*x)^2/x^3 +--R +--R +--R 2 2 +--R cosh(b x + a) sinh(b x + a) +--R (28) ---------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 502 +r0809:= 1/16/x^2-1/16*cosh(4*a+4*b*x)/x^2+b^2*cosh(4*a)*Chi(4*b*x)-_ + 1/4*b*sinh(4*a+4*b*x)/x+b^2*sinh(4*a)*Shi(4*b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 47 + +--S 48 of 502 +a0809:= integrate(t0809,x) +--R +--R +--R x 2 2 +--R ++ cosh(%I b + a) sinh(%I b + a) +--R (29) | ------------------------------ d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 502 +--m0809:= a0809-r0809 +--E 49 + +--S 50 of 502 +--d0809:= D(m0809,x) +--E 50 + +--S 51 of 502 +t0810:= x*sech(a+b*x)*tanh(a+b*x) +--R +--R +--R (30) x sech(b x + a)tanh(b x + a) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 502 +r0810:= atan(sinh(a+b*x))/b^2-x*sech(a+b*x)/b +--R +--R +--R atan(sinh(b x + a)) - b x sech(b x + a) +--R (31) --------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 52 + +--S 53 of 502 +a0810:= integrate(t0810,x) +--R +--R +--R (32) +--R 2 2 +--R (2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) + 2) +--R * +--R atan(sinh(b x + a) + cosh(b x + a)) +--R + +--R - 2b x sinh(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) + b +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 502 +m0810:= a0810-r0810 +--R +--R +--R (33) +--R 2 2 +--R (2sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) + 2cosh(b x + a) + 2) +--R * +--R atan(sinh(b x + a) + cosh(b x + a)) +--R + +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) - 1) +--R * +--R atan(sinh(b x + a)) +--R + +--R 2 +--R b x sech(b x + a)sinh(b x + a) +--R + +--R (2b x cosh(b x + a)sech(b x + a) - 2b x)sinh(b x + a) +--R + +--R 2 +--R (b x cosh(b x + a) + b x)sech(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) + b +--R Type: Expression(Integer) +--E 54 + +--S 55 of 502 +d0810:= D(m0810,x) +--R +--R +--R (34) +--R 6 +--R - b x sech(b x + a)sinh(b x + a) +--R + +--R 5 +--R - 4b x cosh(b x + a)sech(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (- 6b x cosh(b x + a) - 3b x)sech(b x + a)sinh(b x + a) +--R + +--R 3 +--R (- 4b x cosh(b x + a) - 8b x cosh(b x + a))sech(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- b x cosh(b x + a) - 8b x cosh(b x + a) - 3b x)sech(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 3 +--R (- 4b x cosh(b x + a) - 4b x cosh(b x + a))sech(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 4 2 +--R (- b x cosh(b x + a) - 2b x cosh(b x + a) - b x)sech(b x + a) +--R * +--R tanh(b x + a) +--R + +--R 6 +--R sech(b x + a)sinh(b x + a) +--R + +--R 5 +--R (4cosh(b x + a)sech(b x + a) + 2b x)sinh(b x + a) +--R + +--R 2 +--R ((6cosh(b x + a) + 3)sech(b x + a) + (6b x - 1)cosh(b x + a)) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 +--R (4cosh(b x + a) + 8cosh(b x + a))sech(b x + a) +--R + +--R 2 +--R (6b x - 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (cosh(b x + a) + 8cosh(b x + a) + 3)sech(b x + a) +--R + +--R 3 +--R (2b x - 6)cosh(b x + a) + (4b x - 2)cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 3 4 +--R (4cosh(b x + a) + 4cosh(b x + a))sech(b x + a) - 4cosh(b x + a) +--R + +--R 2 +--R (6b x - 4)cosh(b x + a) - 2b x +--R * +--R sinh(b x + a) +--R + +--R 4 2 5 +--R (cosh(b x + a) + 2cosh(b x + a) + 1)sech(b x + a) - cosh(b x + a) +--R + +--R 3 +--R (2b x - 2)cosh(b x + a) + (- 2b x - 1)cosh(b x + a) +--R / +--R 6 5 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (6b cosh(b x + a) + 3b)sinh(b x + a) +--R + +--R 3 3 +--R (4b cosh(b x + a) + 8b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (b cosh(b x + a) + 8b cosh(b x + a) + 3b)sinh(b x + a) +--R + +--R 3 4 +--R (4b cosh(b x + a) + 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 2 +--R 2b cosh(b x + a) + b +--R Type: Expression(Integer) +--E 55 + +--S 56 of 502 +t0811:= x^2*sech(a+b*x)*tanh(a+b*x) +--R +--R +--R 2 +--R (35) x sech(b x + a)tanh(b x + a) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 502 +r0811:= 4*x*atan(exp(1)^(a+b*x))/b^2-2*%i*polylog(2,-%i*exp(1)^(a+b*x))/b^3+_ + 2*%i*polylog(2,%i*exp(1)^(a+b*x))/b^3-x^2*sech(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 502 +a0811:= integrate(t0811,x) +--R +--R +--R x +--R ++ 2 +--R (36) | %I sech(%I b + a)tanh(%I b + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 502 +--m0811:= a0811-r0811 +--E 59 + +--S 60 of 502 +--d0811:= D(m0811,x) +--E 60 + +--S 61 of 502 +t0812:= x^3*sech(a+b*x)*tanh(a+b*x) +--R +--R +--R 3 +--R (37) x sech(b x + a)tanh(b x + a) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 502 +r0812:= 6*x^2*atan(exp(1)^(a+b*x))/b^2-6*%i*x*_ + polylog(2,-%i*exp(1)^(a+b*x))/b^3+6*%i*x*_ + polylog(2,%i*exp(1)^(a+b*x))/b^3+6*%i*_ + polylog(3,-%i*exp(1)^(a+b*x))/b^4-6*%i*_ + polylog(3,%i*exp(1)^(a+b*x))/b^4-x^3*sech(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 502 +a0812:= integrate(t0812,x) +--R +--R +--R x +--R ++ 3 +--R (38) | %I sech(%I b + a)tanh(%I b + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 502 +--m0812:= a0812-r0812 +--E 64 + +--S 65 of 502 +--d0812:= D(m0812,x) +--E 65 + +--S 66 of 502 +t0813:= x*sech(a+b*x)^2*tanh(a+b*x) +--R +--R +--R 2 +--R (39) x sech(b x + a) tanh(b x + a) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 502 +r0813:= -1/2*x*sech(a+b*x)^2/b+1/2*tanh(a+b*x)/b^2 +--R +--R +--R 2 +--R tanh(b x + a) - b x sech(b x + a) +--R (40) ---------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 67 + +--S 68 of 502 +a0813:= integrate(t0813,x) +--R +--R +--R (41) +--R - 2b x sinh(b x + a) + (- 2b x - 2)cosh(b x + a) +--R / +--R 2 3 2 2 +--R b sinh(b x + a) + 3b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 3 2 +--R (3b cosh(b x + a) + b )sinh(b x + a) + b cosh(b x + a) + 3b cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 502 +m0813:= a0813-r0813 +--R +--R +--R (42) +--R 3 2 +--R - sinh(b x + a) - 3cosh(b x + a)sinh(b x + a) +--R + +--R 2 3 +--R (- 3cosh(b x + a) - 1)sinh(b x + a) - cosh(b x + a) - 3cosh(b x + a) +--R * +--R tanh(b x + a) +--R + +--R 2 3 +--R b x sech(b x + a) sinh(b x + a) +--R + +--R 2 2 +--R 3b x cosh(b x + a)sech(b x + a) sinh(b x + a) +--R + +--R 2 2 +--R ((3b x cosh(b x + a) + b x)sech(b x + a) - 4b x)sinh(b x + a) +--R + +--R 3 2 +--R (b x cosh(b x + a) + 3b x cosh(b x + a))sech(b x + a) +--R + +--R (- 4b x - 4)cosh(b x + a) +--R / +--R 2 3 2 2 +--R 2b sinh(b x + a) + 6b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 3 +--R (6b cosh(b x + a) + 2b )sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 2 +--R 6b cosh(b x + a) +--R Type: Expression(Integer) +--E 69 + +--S 70 of 502 +d0813:= D(m0813,x) +--R +--R +--R (43) +--R 6 5 +--R sinh(b x + a) + 6cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (15cosh(b x + a) + 2)sinh(b x + a) +--R + +--R 3 3 +--R (20cosh(b x + a) + 12cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (15cosh(b x + a) + 24cosh(b x + a) + 1)sinh(b x + a) +--R + +--R 5 3 +--R (6cosh(b x + a) + 20cosh(b x + a) + 6cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 +--R cosh(b x + a) + 6cosh(b x + a) + 9cosh(b x + a) +--R * +--R 2 +--R tanh(b x + a) +--R + +--R 2 6 +--R - 2b x sech(b x + a) sinh(b x + a) +--R + +--R 2 5 +--R - 12b x cosh(b x + a)sech(b x + a) sinh(b x + a) +--R + +--R 2 2 4 +--R (- 30b x cosh(b x + a) - 4b x)sech(b x + a) sinh(b x + a) +--R + +--R 3 2 +--R (- 40b x cosh(b x + a) - 24b x cosh(b x + a))sech(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 30b x cosh(b x + a) - 48b x cosh(b x + a) - 2b x) +--R * +--R 2 2 +--R sech(b x + a) sinh(b x + a) +--R + +--R 5 3 +--R - 12b x cosh(b x + a) - 40b x cosh(b x + a) +--R + +--R - 12b x cosh(b x + a) +--R * +--R 2 +--R sech(b x + a) sinh(b x + a) +--R + +--R 6 4 +--R - 2b x cosh(b x + a) - 12b x cosh(b x + a) +--R + +--R 2 +--R - 18b x cosh(b x + a) +--R * +--R 2 +--R sech(b x + a) +--R * +--R tanh(b x + a) +--R + +--R 2 6 +--R (sech(b x + a) - 1)sinh(b x + a) +--R + +--R 2 5 +--R (6cosh(b x + a)sech(b x + a) - 6cosh(b x + a))sinh(b x + a) +--R + +--R 2 2 2 +--R ((15cosh(b x + a) + 2)sech(b x + a) - 15cosh(b x + a) + 8b x - 10) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 2 3 +--R (20cosh(b x + a) + 12cosh(b x + a))sech(b x + a) - 20cosh(b x + a) +--R + +--R (32b x - 28)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (15cosh(b x + a) + 24cosh(b x + a) + 1)sech(b x + a) +--R + +--R 4 2 +--R - 15cosh(b x + a) + (48b x - 24)cosh(b x + a) + 8b x - 9 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 2 +--R (6cosh(b x + a) + 20cosh(b x + a) + 6cosh(b x + a))sech(b x + a) +--R + +--R 5 3 +--R - 6cosh(b x + a) + (32b x - 4)cosh(b x + a) - 22cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 2 +--R (cosh(b x + a) + 6cosh(b x + a) + 9cosh(b x + a) )sech(b x + a) +--R + +--R 6 4 2 +--R - cosh(b x + a) + (8b x + 2)cosh(b x + a) + (- 8b x - 17)cosh(b x + a) +--R / +--R 6 5 +--R 2b sinh(b x + a) + 12b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (30b cosh(b x + a) + 4b)sinh(b x + a) +--R + +--R 3 3 +--R (40b cosh(b x + a) + 24b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (30b cosh(b x + a) + 48b cosh(b x + a) + 2b)sinh(b x + a) +--R + +--R 5 3 +--R (12b cosh(b x + a) + 40b cosh(b x + a) + 12b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 2b cosh(b x + a) + 12b cosh(b x + a) + 18b cosh(b x + a) +--R Type: Expression(Integer) +--E 70 + +--S 71 of 502 +t0814:= x^2*sech(a+b*x)^2*tanh(a+b*x) +--R +--R +--R 2 2 +--R (44) x sech(b x + a) tanh(b x + a) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 502 +r0814:= -log(cosh(a+b*x))/b^3-1/2*x^2*sech(a+b*x)^2/b+x*tanh(a+b*x)/b^2 +--R +--R +--R 2 2 2 +--R - 2log(cosh(b x + a)) + 2b x tanh(b x + a) - b x sech(b x + a) +--R (45) --------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 72 + +--S 73 of 502 +a0814:= integrate(t0814,x) +--R +--R +--R (46) +--R 4 3 +--R - sinh(b x + a) - 4cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 6cosh(b x + a) - 2)sinh(b x + a) +--R + +--R 3 4 +--R (- 4cosh(b x + a) - 4cosh(b x + a))sinh(b x + a) - cosh(b x + a) +--R + +--R 2 +--R - 2cosh(b x + a) - 1 +--R * +--R 2cosh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R 2b x sinh(b x + a) + 8b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 +--R (12b x cosh(b x + a) - 2b x + 2b x)sinh(b x + a) +--R + +--R 3 2 2 +--R (8b x cosh(b x + a) + (- 4b x + 4b x)cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 2 +--R 2b x cosh(b x + a) + (- 2b x + 2b x)cosh(b x + a) +--R / +--R 3 4 3 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 3 2 3 2 +--R (6b cosh(b x + a) + 2b )sinh(b x + a) +--R + +--R 3 3 3 3 4 +--R (4b cosh(b x + a) + 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 3 2 3 +--R 2b cosh(b x + a) + b +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 502 +m0814:= a0814-r0814 +--R +--R +--R (47) +--R 4 3 +--R 2sinh(b x + a) + 8cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (12cosh(b x + a) + 4)sinh(b x + a) +--R + +--R 3 4 +--R (8cosh(b x + a) + 8cosh(b x + a))sinh(b x + a) + 2cosh(b x + a) +--R + +--R 2 +--R 4cosh(b x + a) + 2 +--R * +--R log(cosh(b x + a)) +--R + +--R 4 3 +--R - 2sinh(b x + a) - 8cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 12cosh(b x + a) - 4)sinh(b x + a) +--R + +--R 3 4 +--R (- 8cosh(b x + a) - 8cosh(b x + a))sinh(b x + a) - 2cosh(b x + a) +--R + +--R 2 +--R - 4cosh(b x + a) - 2 +--R * +--R 2cosh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R - 2b x sinh(b x + a) - 8b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 12b x cosh(b x + a) - 4b x)sinh(b x + a) +--R + +--R 3 +--R (- 8b x cosh(b x + a) - 8b x cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 +--R - 2b x cosh(b x + a) - 4b x cosh(b x + a) - 2b x +--R * +--R tanh(b x + a) +--R + +--R 2 2 2 4 +--R (b x sech(b x + a) + 4b x)sinh(b x + a) +--R + +--R 2 2 2 3 +--R (4b x cosh(b x + a)sech(b x + a) + 16b x cosh(b x + a))sinh(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R (6b x cosh(b x + a) + 2b x )sech(b x + a) + 24b x cosh(b x + a) +--R + +--R 2 2 +--R - 4b x + 4b x +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 2 3 2 2 2 +--R (4b x cosh(b x + a) + 4b x cosh(b x + a))sech(b x + a) +--R + +--R 3 2 2 +--R 16b x cosh(b x + a) + (- 8b x + 8b x)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 2 2 4 2 2 2 2 2 2 +--R (b x cosh(b x + a) + 2b x cosh(b x + a) + b x )sech(b x + a) +--R + +--R 4 2 2 2 +--R 4b x cosh(b x + a) + (- 4b x + 4b x)cosh(b x + a) +--R / +--R 3 4 3 3 +--R 2b sinh(b x + a) + 8b cosh(b x + a)sinh(b x + a) +--R + +--R 3 2 3 2 +--R (12b cosh(b x + a) + 4b )sinh(b x + a) +--R + +--R 3 3 3 3 4 +--R (8b cosh(b x + a) + 8b cosh(b x + a))sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 3 2 3 +--R 4b cosh(b x + a) + 2b +--R Type: Expression(Integer) +--E 74 + +--S 75 of 502 +d0814:= D(m0814,x) +--R +--R +--R (48) +--R 6 5 +--R b x sinh(b x + a) + 6b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (15b x cosh(b x + a) + 3b x)sinh(b x + a) +--R + +--R 3 3 +--R (20b x cosh(b x + a) + 12b x cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (15b x cosh(b x + a) + 18b x cosh(b x + a) + 3b x)sinh(b x + a) +--R + +--R 5 3 +--R (6b x cosh(b x + a) + 12b x cosh(b x + a) + 6b x cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R b x cosh(b x + a) + 3b x cosh(b x + a) + 3b x cosh(b x + a) + b x +--R * +--R 2 +--R tanh(b x + a) +--R + +--R 2 2 2 6 +--R (- b x sech(b x + a) - 1)sinh(b x + a) +--R + +--R 2 2 2 5 +--R (- 6b x cosh(b x + a)sech(b x + a) - 6cosh(b x + a))sinh(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R (- 15b x cosh(b x + a) - 3b x )sech(b x + a) - 15cosh(b x + a) +--R + +--R - 3 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 2 2 3 2 2 2 +--R (- 20b x cosh(b x + a) - 12b x cosh(b x + a))sech(b x + a) +--R + +--R 3 +--R - 20cosh(b x + a) - 12cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 15b x cosh(b x + a) - 18b x cosh(b x + a) - 3b x ) +--R * +--R 2 +--R sech(b x + a) +--R + +--R 4 2 +--R - 15cosh(b x + a) - 18cosh(b x + a) - 3 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 2 5 2 2 3 +--R - 6b x cosh(b x + a) - 12b x cosh(b x + a) +--R + +--R 2 2 +--R - 6b x cosh(b x + a) +--R * +--R 2 +--R sech(b x + a) +--R + +--R 5 3 +--R - 6cosh(b x + a) - 12cosh(b x + a) - 6cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 2 2 6 2 2 4 2 2 2 +--R - b x cosh(b x + a) - 3b x cosh(b x + a) - 3b x cosh(b x + a) +--R + +--R 2 2 +--R - b x +--R * +--R 2 +--R sech(b x + a) +--R + +--R 6 4 2 +--R - cosh(b x + a) - 3cosh(b x + a) - 3cosh(b x + a) - 1 +--R * +--R tanh(b x + a) +--R + +--R 2 6 +--R (b x sech(b x + a) - b x + 1)sinh(b x + a) +--R + +--R 2 +--R (6b x cosh(b x + a)sech(b x + a) + (- 6b x + 6)cosh(b x + a)) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 2 2 +--R (15b x cosh(b x + a) + 3b x)sech(b x + a) +--R + +--R 2 2 2 +--R (- 15b x + 15)cosh(b x + a) + 4b x - 3b x + 1 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 2 +--R (20b x cosh(b x + a) + 12b x cosh(b x + a))sech(b x + a) +--R + +--R 3 2 2 +--R (- 20b x + 20)cosh(b x + a) + (16b x - 12b x + 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (15b x cosh(b x + a) + 18b x cosh(b x + a) + 3b x)sech(b x + a) +--R + +--R 4 2 2 2 +--R (- 15b x + 15)cosh(b x + a) + (24b x - 18b x + 6)cosh(b x + a) +--R + +--R 2 2 +--R - 4b x - 3b x - 1 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R (6b x cosh(b x + a) + 12b x cosh(b x + a) + 6b x cosh(b x + a)) +--R * +--R 2 +--R sech(b x + a) +--R + +--R 5 2 2 3 +--R (- 6b x + 6)cosh(b x + a) + (16b x - 12b x + 4)cosh(b x + a) +--R + +--R 2 2 +--R (- 8b x - 6b x - 2)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (b x cosh(b x + a) + 3b x cosh(b x + a) + 3b x cosh(b x + a) + b x) +--R * +--R 2 +--R sech(b x + a) +--R + +--R 6 2 2 4 +--R (- b x + 1)cosh(b x + a) + (4b x - 3b x + 1)cosh(b x + a) +--R + +--R 2 2 2 +--R (- 4b x - 3b x - 1)cosh(b x + a) - b x - 1 +--R / +--R 2 6 2 5 +--R b sinh(b x + a) + 6b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 4 +--R (15b cosh(b x + a) + 3b )sinh(b x + a) +--R + +--R 2 3 2 3 +--R (20b cosh(b x + a) + 12b cosh(b x + a))sinh(b x + a) +--R + +--R 2 4 2 2 2 2 +--R (15b cosh(b x + a) + 18b cosh(b x + a) + 3b )sinh(b x + a) +--R + +--R 2 5 2 3 2 +--R (6b cosh(b x + a) + 12b cosh(b x + a) + 6b cosh(b x + a))sinh(b x + a) +--R + +--R 2 6 2 4 2 2 2 +--R b cosh(b x + a) + 3b cosh(b x + a) + 3b cosh(b x + a) + b +--R Type: Expression(Integer) +--E 75 + +--S 76 of 502 +t0815:= x^3*sech(a+b*x)^2*tanh(a+b*x) +--R +--R +--R 3 2 +--R (49) x sech(b x + a) tanh(b x + a) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 502 +r0815:= 3/2*x^2/b^2-3*x*log(1+exp(1)^(2*a+2*b*x))/b^3-_ + 3/2*polylog(2,-exp(1)^(2*a+2*b*x))/b^4-1/2*x^3*sech(a+b*x)^2/b+_ + 3/2*x^2*tanh(a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 502 +a0815:= integrate(t0815,x) +--R +--R +--R x +--R ++ 3 2 +--R (50) | %I sech(%I b + a) tanh(%I b + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 502 +--m0815:= a0815-r0815 +--E 79 + +--S 80 of 502 +--d0815:= D(m0815,x) +--E 80 + +--S 81 of 502 +t0816:= x*csch(a+b*x)*coth(a+b*x) +--R +--R +--R (51) x coth(b x + a)csch(b x + a) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 502 +r0816:= -acoth(cosh(a+b*x))/b^2-x*csch(a+b*x)/b +--R +--R +--R - acoth(cosh(b x + a)) - b x csch(b x + a) +--R (52) ------------------------------------------ +--R 2 +--R b +--R Type: Expression(Integer) +--E 82 + +--S 83 of 502 +a0816:= integrate(t0816,x) +--R +--R +--R (53) +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) + 1) +--R * +--R log(sinh(b x + a) + cosh(b x + a) + 1) +--R + +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R log(sinh(b x + a) + cosh(b x + a) - 1) +--R + +--R - 2b x sinh(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 502 +m0816:= a0816-r0816 +--R +--R +--R (54) +--R 2 2 +--R (- sinh(b x + a) - 2cosh(b x + a)sinh(b x + a) - cosh(b x + a) + 1) +--R * +--R log(sinh(b x + a) + cosh(b x + a) + 1) +--R + +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R log(sinh(b x + a) + cosh(b x + a) - 1) +--R + +--R 2 2 +--R (sinh(b x + a) + 2cosh(b x + a)sinh(b x + a) + cosh(b x + a) - 1) +--R * +--R acoth(cosh(b x + a)) +--R + +--R 2 +--R b x csch(b x + a)sinh(b x + a) +--R + +--R (2b x cosh(b x + a)csch(b x + a) - 2b x)sinh(b x + a) +--R + +--R 2 +--R (b x cosh(b x + a) - b x)csch(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 2 2 2 2 2 +--R b sinh(b x + a) + 2b cosh(b x + a)sinh(b x + a) + b cosh(b x + a) - b +--R Type: Expression(Integer) +--E 84 + +--S 85 of 502 +d0816:= D(m0816,x) +--R +--R +--R (55) +--R 5 +--R - sinh(b x + a) +--R + +--R 2 2 +--R ((- b x cosh(b x + a) + b x)coth(b x + a) + cosh(b x + a) - 1) +--R * +--R csch(b x + a) +--R + +--R - 4cosh(b x + a) +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 +--R (- 4b x cosh(b x + a) + 4b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R 4cosh(b x + a) - 4cosh(b x + a) +--R * +--R csch(b x + a) +--R + +--R 2 +--R (2b x - 6)cosh(b x + a) - 2b x + 2 +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 6b x cosh(b x + a) + 8b x cosh(b x + a) - 2b x)coth(b x + a) +--R + +--R 4 2 +--R 6cosh(b x + a) - 8cosh(b x + a) + 2 +--R * +--R csch(b x + a) +--R + +--R 3 +--R (6b x - 4)cosh(b x + a) + (- 6b x + 4)cosh(b x + a) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R - 4b x cosh(b x + a) + 8b x cosh(b x + a) +--R + +--R - 4b x cosh(b x + a) +--R * +--R coth(b x + a) +--R + +--R 5 3 +--R 4cosh(b x + a) - 8cosh(b x + a) + 4cosh(b x + a) +--R * +--R csch(b x + a) +--R + +--R 4 2 +--R (6b x - 1)cosh(b x + a) + (- 4b x + 2)cosh(b x + a) - 2b x - 1 +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R - b x cosh(b x + a) + 3b x cosh(b x + a) - 3b x cosh(b x + a) +--R + +--R b x +--R * +--R coth(b x + a) +--R + +--R 6 4 2 +--R cosh(b x + a) - 3cosh(b x + a) + 3cosh(b x + a) - 1 +--R * +--R csch(b x + a) +--R + +--R 5 +--R 2b x cosh(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 4 +--R (b cosh(b x + a) - b)sinh(b x + a) +--R + +--R 3 3 +--R (4b cosh(b x + a) - 4b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (6b cosh(b x + a) - 8b cosh(b x + a) + 2b)sinh(b x + a) +--R + +--R 5 3 +--R (4b cosh(b x + a) - 8b cosh(b x + a) + 4b cosh(b x + a))sinh(b x + a) +--R + +--R 6 4 2 +--R b cosh(b x + a) - 3b cosh(b x + a) + 3b cosh(b x + a) - b +--R Type: Expression(Integer) +--E 85 + +--S 86 of 502 +t0817:= x^2*csch(a+b*x)*coth(a+b*x) +--R +--R +--R 2 +--R (56) x coth(b x + a)csch(b x + a) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 502 +r0817:= -4*x*atanh(exp(1)^(a+b*x))/b^2-x^2*csch(a+b*x)/b-_ + 2*polylog(2,-exp(1)^(a+b*x))/b^3+2*polylog(2,exp(1)^(a+b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 502 +a0817:= integrate(t0817,x) +--R +--R +--R x +--R ++ 2 +--R (57) | %I coth(%I b + a)csch(%I b + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 502 +--m0817:= a0817-r0817 +--E 89 + +--S 90 of 502 +--d0817:= D(m0817,x) +--E 90 + +--S 91 of 502 +t0818:= x^3*csch(a+b*x)*coth(a+b*x) +--R +--R +--R 3 +--R (58) x coth(b x + a)csch(b x + a) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 502 +r0818:= -6*x^2*atanh(exp(1)^(a+b*x))/b^2-x^3*csch(a+b*x)/b-_ + 6*x*polylog(2,-exp(1)^(a+b*x))/b^3+_ + 6*x*polylog(2,exp(1)^(a+b*x))/b^3+_ + 6*polylog(3,-exp(1)^(a+b*x))/b^4-_ + 6*polylog(3,exp(1)^(a+b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 502 +a0818:= integrate(t0818,x) +--R +--R +--R x +--R ++ 3 +--R (59) | %I coth(%I b + a)csch(%I b + a)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 502 +--m0818:= a0818-r0818 +--E 94 + +--S 95 of 502 +--d0818:= D(m0818,x) +--E 95 + +--S 96 of 502 +t0819:= x*csch(a+b*x)^2*coth(a+b*x) +--R +--R +--R 2 +--R (60) x coth(b x + a)csch(b x + a) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 502 +r0819:= -1/2*coth(a+b*x)/b^2-1/2*x*csch(a+b*x)^2/b +--R +--R +--R 2 +--R - b x csch(b x + a) - coth(b x + a) +--R (61) ------------------------------------ +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 97 + +--S 98 of 502 +a0819:= integrate(t0819,x) +--R +--R +--R (62) +--R (- 2b x - 2)sinh(b x + a) - 2b x cosh(b x + a) +--R / +--R 2 3 2 2 +--R b sinh(b x + a) + 3b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 3 2 +--R (3b cosh(b x + a) - 3b )sinh(b x + a) + b cosh(b x + a) - b cosh(b x + a) +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 502 +m0819:= a0819-r0819 +--R +--R +--R (63) +--R 2 3 +--R (b x csch(b x + a) + coth(b x + a))sinh(b x + a) +--R + +--R 2 +--R (3b x cosh(b x + a)csch(b x + a) + 3cosh(b x + a)coth(b x + a)) +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 2 +--R (3b x cosh(b x + a) - 3b x)csch(b x + a) +--R + +--R 2 +--R (3cosh(b x + a) - 3)coth(b x + a) - 4b x - 4 +--R * +--R sinh(b x + a) +--R + +--R 3 2 +--R (b x cosh(b x + a) - b x cosh(b x + a))csch(b x + a) +--R + +--R 3 +--R (cosh(b x + a) - cosh(b x + a))coth(b x + a) - 4b x cosh(b x + a) +--R / +--R 2 3 2 2 +--R 2b sinh(b x + a) + 6b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 3 +--R (6b cosh(b x + a) - 6b )sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 2 +--R - 2b cosh(b x + a) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 502 +d0819:= D(m0819,x) +--R +--R +--R (64) +--R 2 2 +--R ((- 2b x coth(b x + a) + 1)csch(b x + a) - coth(b x + a) + 1) +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 2 +--R (- 12b x cosh(b x + a)coth(b x + a) + 6cosh(b x + a))csch(b x + a) +--R + +--R 2 +--R - 6cosh(b x + a)coth(b x + a) + 6cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 2 2 +--R (- 30b x cosh(b x + a) + 12b x)coth(b x + a) + 15cosh(b x + a) +--R + +--R - 6 +--R * +--R 2 +--R csch(b x + a) +--R + +--R 2 2 2 +--R (- 15cosh(b x + a) + 6)coth(b x + a) + 15cosh(b x + a) + 8b x + 2 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 3 +--R (- 40b x cosh(b x + a) + 40b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R 20cosh(b x + a) - 20cosh(b x + a) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 3 2 +--R (- 20cosh(b x + a) + 20cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R 20cosh(b x + a) + (32b x - 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 30b x cosh(b x + a) + 48b x cosh(b x + a) - 18b x) +--R * +--R coth(b x + a) +--R + +--R 4 2 +--R 15cosh(b x + a) - 24cosh(b x + a) + 9 +--R * +--R 2 +--R csch(b x + a) +--R + +--R 4 2 2 +--R (- 15cosh(b x + a) + 24cosh(b x + a) - 9)coth(b x + a) +--R + +--R 4 2 +--R 15cosh(b x + a) + (48b x - 24)cosh(b x + a) + 8b x + 17 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 5 3 +--R - 12b x cosh(b x + a) + 24b x cosh(b x + a) +--R + +--R - 12b x cosh(b x + a) +--R * +--R coth(b x + a) +--R + +--R 5 3 +--R 6cosh(b x + a) - 12cosh(b x + a) + 6cosh(b x + a) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 5 3 2 +--R (- 6cosh(b x + a) + 12cosh(b x + a) - 6cosh(b x + a))coth(b x + a) +--R + +--R 5 3 +--R 6cosh(b x + a) + (32b x - 28)cosh(b x + a) + 22cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- 2b x cosh(b x + a) + 4b x cosh(b x + a) - 2b x cosh(b x + a) ) +--R * +--R coth(b x + a) +--R + +--R 6 4 2 +--R cosh(b x + a) - 2cosh(b x + a) + cosh(b x + a) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 6 4 2 2 +--R (- cosh(b x + a) + 2cosh(b x + a) - cosh(b x + a) )coth(b x + a) +--R + +--R 6 4 2 +--R cosh(b x + a) + (8b x - 10)cosh(b x + a) + (- 8b x + 9)cosh(b x + a) +--R / +--R 6 5 +--R 2b sinh(b x + a) + 12b cosh(b x + a)sinh(b x + a) +--R + +--R 2 4 +--R (30b cosh(b x + a) - 12b)sinh(b x + a) +--R + +--R 3 3 +--R (40b cosh(b x + a) - 40b cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 +--R (30b cosh(b x + a) - 48b cosh(b x + a) + 18b)sinh(b x + a) +--R + +--R 5 3 +--R (12b cosh(b x + a) - 24b cosh(b x + a) + 12b cosh(b x + a)) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R 2b cosh(b x + a) - 4b cosh(b x + a) + 2b cosh(b x + a) +--R Type: Expression(Integer) +--E 100 + +--S 101 of 502 +t0820:= x^2*csch(a+b*x)^2*coth(a+b*x) +--R +--R +--R 2 2 +--R (65) x coth(b x + a)csch(b x + a) +--R Type: Expression(Integer) +--E 101 + +--S 102 of 502 +r0820:= -x*coth(a+b*x)/b^2-1/2*x^2*csch(a+b*x)^2/b+log(sinh(a+b*x))/b^3 +--R +--R +--R 2 2 2 +--R 2log(sinh(b x + a)) - b x csch(b x + a) - 2b x coth(b x + a) +--R (66) ------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 102 + +--S 103 of 502 +a0820:= integrate(t0820,x) +--R +--R +--R (67) +--R 4 3 +--R sinh(b x + a) + 4cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (6cosh(b x + a) - 2)sinh(b x + a) +--R + +--R 3 4 +--R (4cosh(b x + a) - 4cosh(b x + a))sinh(b x + a) + cosh(b x + a) +--R + +--R 2 +--R - 2cosh(b x + a) + 1 +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 4 3 +--R - 2b x sinh(b x + a) - 8b x cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 2 +--R (- 12b x cosh(b x + a) - 2b x + 2b x)sinh(b x + a) +--R + +--R 3 2 2 +--R (- 8b x cosh(b x + a) + (- 4b x + 4b x)cosh(b x + a))sinh(b x + a) +--R + +--R 4 2 2 2 +--R - 2b x cosh(b x + a) + (- 2b x + 2b x)cosh(b x + a) +--R / +--R 3 4 3 3 +--R b sinh(b x + a) + 4b cosh(b x + a)sinh(b x + a) +--R + +--R 3 2 3 2 +--R (6b cosh(b x + a) - 2b )sinh(b x + a) +--R + +--R 3 3 3 3 4 +--R (4b cosh(b x + a) - 4b cosh(b x + a))sinh(b x + a) + b cosh(b x + a) +--R + +--R 3 2 3 +--R - 2b cosh(b x + a) + b +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 502 +m0820:= a0820-r0820 +--R +--R +--R (68) +--R 4 3 +--R - 2sinh(b x + a) - 8cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (- 12cosh(b x + a) + 4)sinh(b x + a) +--R + +--R 3 4 +--R (- 8cosh(b x + a) + 8cosh(b x + a))sinh(b x + a) - 2cosh(b x + a) +--R + +--R 2 +--R 4cosh(b x + a) - 2 +--R * +--R log(sinh(b x + a)) +--R + +--R 4 3 +--R 2sinh(b x + a) + 8cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 +--R (12cosh(b x + a) - 4)sinh(b x + a) +--R + +--R 3 4 +--R (8cosh(b x + a) - 8cosh(b x + a))sinh(b x + a) + 2cosh(b x + a) +--R + +--R 2 +--R - 4cosh(b x + a) + 2 +--R * +--R 2sinh(b x + a) +--R log(- -----------------------------) +--R sinh(b x + a) - cosh(b x + a) +--R + +--R 2 2 2 4 +--R (b x csch(b x + a) + 2b x coth(b x + a) - 4b x)sinh(b x + a) +--R + +--R 2 2 2 +--R 4b x cosh(b x + a)csch(b x + a) + 8b x cosh(b x + a)coth(b x + a) +--R + +--R - 16b x cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 2 2 2 2 +--R (6b x cosh(b x + a) - 2b x )csch(b x + a) +--R + +--R 2 2 +--R (12b x cosh(b x + a) - 4b x)coth(b x + a) - 24b x cosh(b x + a) +--R + +--R 2 2 +--R - 4b x + 4b x +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 2 3 2 2 2 +--R (4b x cosh(b x + a) - 4b x cosh(b x + a))csch(b x + a) +--R + +--R 3 +--R (8b x cosh(b x + a) - 8b x cosh(b x + a))coth(b x + a) +--R + +--R 3 2 2 +--R - 16b x cosh(b x + a) + (- 8b x + 8b x)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 2 2 4 2 2 2 2 2 2 +--R (b x cosh(b x + a) - 2b x cosh(b x + a) + b x )csch(b x + a) +--R + +--R 4 2 +--R (2b x cosh(b x + a) - 4b x cosh(b x + a) + 2b x)coth(b x + a) +--R + +--R 4 2 2 2 +--R - 4b x cosh(b x + a) + (- 4b x + 4b x)cosh(b x + a) +--R / +--R 3 4 3 3 +--R 2b sinh(b x + a) + 8b cosh(b x + a)sinh(b x + a) +--R + +--R 3 2 3 2 +--R (12b cosh(b x + a) - 4b )sinh(b x + a) +--R + +--R 3 3 3 3 4 +--R (8b cosh(b x + a) - 8b cosh(b x + a))sinh(b x + a) + 2b cosh(b x + a) +--R + +--R 3 2 3 +--R - 4b cosh(b x + a) + 2b +--R Type: Expression(Integer) +--E 104 + +--S 105 of 502 +d0820:= D(m0820,x) +--R +--R +--R (69) +--R 2 2 2 2 +--R (- b x coth(b x + a) + b x)csch(b x + a) - b x coth(b x + a) +--R + +--R coth(b x + a) + b x - 1 +--R * +--R 6 +--R sinh(b x + a) +--R + +--R 2 2 +--R (- 6b x cosh(b x + a)coth(b x + a) + 6b x cosh(b x + a)) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 2 +--R - 6b x cosh(b x + a)coth(b x + a) + 6cosh(b x + a)coth(b x + a) +--R + +--R (6b x - 6)cosh(b x + a) +--R * +--R 5 +--R sinh(b x + a) +--R + +--R 2 2 2 2 2 +--R (- 15b x cosh(b x + a) + 3b x )coth(b x + a) +--R + +--R 2 +--R 15b x cosh(b x + a) - 3b x +--R * +--R 2 +--R csch(b x + a) +--R + +--R 2 2 +--R (- 15b x cosh(b x + a) + 3b x)coth(b x + a) +--R + +--R 2 2 +--R (15cosh(b x + a) - 3)coth(b x + a) + (15b x - 15)cosh(b x + a) +--R + +--R 2 2 +--R 4b x - 3b x + 1 +--R * +--R 4 +--R sinh(b x + a) +--R + +--R 2 2 3 2 2 +--R (- 20b x cosh(b x + a) + 12b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R 20b x cosh(b x + a) - 12b x cosh(b x + a) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 3 2 +--R (- 20b x cosh(b x + a) + 12b x cosh(b x + a))coth(b x + a) +--R + +--R 3 +--R (20cosh(b x + a) - 12cosh(b x + a))coth(b x + a) +--R + +--R 3 2 2 +--R (20b x - 20)cosh(b x + a) + (16b x - 12b x + 4)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + a) +--R + +--R 2 2 4 2 2 2 2 2 +--R (- 15b x cosh(b x + a) + 18b x cosh(b x + a) - 3b x ) +--R * +--R coth(b x + a) +--R + +--R 4 2 +--R 15b x cosh(b x + a) - 18b x cosh(b x + a) + 3b x +--R * +--R 2 +--R csch(b x + a) +--R + +--R 4 2 2 +--R (- 15b x cosh(b x + a) + 18b x cosh(b x + a) - 3b x)coth(b x + a) +--R + +--R 4 2 +--R (15cosh(b x + a) - 18cosh(b x + a) + 3)coth(b x + a) +--R + +--R 4 2 2 2 +--R (15b x - 15)cosh(b x + a) + (24b x - 18b x + 6)cosh(b x + a) +--R + +--R 2 2 +--R 4b x + 3b x + 1 +--R * +--R 2 +--R sinh(b x + a) +--R + +--R 2 2 5 2 2 3 +--R - 6b x cosh(b x + a) + 12b x cosh(b x + a) +--R + +--R 2 2 +--R - 6b x cosh(b x + a) +--R * +--R coth(b x + a) +--R + +--R 5 3 +--R 6b x cosh(b x + a) - 12b x cosh(b x + a) + 6b x cosh(b x + a) +--R * +--R 2 +--R csch(b x + a) +--R + +--R 5 3 +--R (- 6b x cosh(b x + a) + 12b x cosh(b x + a) - 6b x cosh(b x + a)) +--R * +--R 2 +--R coth(b x + a) +--R + +--R 5 3 +--R (6cosh(b x + a) - 12cosh(b x + a) + 6cosh(b x + a))coth(b x + a) +--R + +--R 5 2 2 3 +--R (6b x - 6)cosh(b x + a) + (16b x - 12b x + 4)cosh(b x + a) +--R + +--R 2 2 +--R (8b x + 6b x + 2)cosh(b x + a) +--R * +--R sinh(b x + a) +--R + +--R 2 2 6 2 2 4 2 2 2 +--R - b x cosh(b x + a) + 3b x cosh(b x + a) - 3b x cosh(b x + a) +--R + +--R 2 2 +--R b x +--R * +--R coth(b x + a) +--R + +--R 6 4 2 +--R b x cosh(b x + a) - 3b x cosh(b x + a) + 3b x cosh(b x + a) - b x +--R * +--R 2 +--R csch(b x + a) +--R + +--R 6 4 2 +--R - b x cosh(b x + a) + 3b x cosh(b x + a) - 3b x cosh(b x + a) +--R + +--R b x +--R * +--R 2 +--R coth(b x + a) +--R + +--R 6 4 2 +--R (cosh(b x + a) - 3cosh(b x + a) + 3cosh(b x + a) - 1)coth(b x + a) +--R + +--R 6 2 2 4 +--R (b x - 1)cosh(b x + a) + (4b x - 3b x + 1)cosh(b x + a) +--R + +--R 2 2 2 +--R (4b x + 3b x + 1)cosh(b x + a) - b x - 1 +--R / +--R 2 6 2 5 +--R b sinh(b x + a) + 6b cosh(b x + a)sinh(b x + a) +--R + +--R 2 2 2 4 +--R (15b cosh(b x + a) - 3b )sinh(b x + a) +--R + +--R 2 3 2 3 +--R (20b cosh(b x + a) - 12b cosh(b x + a))sinh(b x + a) +--R + +--R 2 4 2 2 2 2 +--R (15b cosh(b x + a) - 18b cosh(b x + a) + 3b )sinh(b x + a) +--R + +--R 2 5 2 3 2 +--R (6b cosh(b x + a) - 12b cosh(b x + a) + 6b cosh(b x + a))sinh(b x + a) +--R + +--R 2 6 2 4 2 2 2 +--R b cosh(b x + a) - 3b cosh(b x + a) + 3b cosh(b x + a) - b +--R Type: Expression(Integer) +--E 105 + +--S 106 of 502 +t0821:= x^3*csch(a+b*x)^2*coth(a+b*x) +--R +--R +--R 3 2 +--R (70) x coth(b x + a)csch(b x + a) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 502 +r0821:= -3/2*x^2/b^2-3/2*x^2*coth(a+b*x)/b^2-1/2*x^3*csch(a+b*x)^2/b+_ + 3*x*log(1-exp(1)^(2*a+2*b*x))/b^3+_ + 3/2*polylog(2,exp(1)^(2*a+2*b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 502 +a0821:= integrate(t0821,x) +--R +--R +--R x +--R ++ 3 2 +--R (71) | %I coth(%I b + a)csch(%I b + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 502 +--m0821:= a0821-r0821 +--E 109 + +--S 110 of 502 +--d0821:= D(m0821,x) +--E 110 + +--S 111 of 502 +t0822:= x*csch(x)*sech(x)^2 +--R +--R +--R 2 +--R (72) x csch(x)sech(x) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 502 +r0822:= -2*atan(tanh(1/2*x))+x*log(1-exp(1)^(-x))-_ + x*log(1+exp(1)^(-x))+polylog(2,-exp(1)^(-x))-_ + polylog(2,exp(1)^(-x))+x*sech(x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 112 + +--S 113 of 502 +a0822:= integrate(t0822,x) +--R +--R +--R x +--R ++ 2 +--R (73) | %I csch(%I)sech(%I) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 502 +--m0822:= a0822-r0822 +--E 114 + +--S 115 of 502 +--d0822:= D(m0822,x) +--E 115 + +--S 116 of 502 +t0823:= x*sinh(a+b*x)*cosh(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (74) x cosh(b x + a)sinh(b x + a)\|cosh(b x + a) +--R Type: Expression(Integer) +--E 116 + +--S 117 of 502 +r0823:= -2/25*(-5*x*cosh(a+b*x)^(5/2)*b-6*%i*EllipticE(1/2*%i*(a+b*x),2)+_ + 2*cosh(a+b*x)^(3/2)*sinh(a+b*x))/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 502 +a0823:= integrate(t0823,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 118 + +--S 119 of 502 +--m0823:= a0823-r0823 +--E 119 + +--S 120 of 502 +--d0823:= D(m0823,x) +--E 120 + +--S 121 of 502 +t0824:= x*sinh(a+b*x)*cosh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (75) x sinh(b x + a)\|cosh(b x + a) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 502 +r0824:= -2/9*(-3*x*cosh(a+b*x)^(3/2)*b-_ + 2*%i*EllipticF(1/2*%i*(a+b*x),2)+2*cosh(a+b*x)^(1/2)*sinh(a+b*x))/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 502 +a0824:= integrate(t0824,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 123 + +--S 124 of 502 +--m0824:= a0824-r0824 +--E 124 + +--S 125 of 502 +--d0824:= D(m0824,x) +--E 125 + +--S 126 of 502 +t0825:= x*sinh(a+b*x)/cosh(a+b*x)^(1/2) +--R +--R +--R x sinh(b x + a) +--R (76) ---------------- +--R +-------------+ +--R \|cosh(b x + a) +--R Type: Expression(Integer) +--E 126 + +--S 127 of 502 +r0825:= 2*(x*cosh(a+b*x)^(1/2)*b+2*%i*EllipticE(1/2*%i*(a+b*x),2))/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 502 +a0825:= integrate(t0825,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 128 + +--S 129 of 502 +--m0825:= a0825-r0825 +--E 129 + +--S 130 of 502 +--d0825:= D(m0825,x) +--E 130 + +--S 131 of 502 +t0826:= x*sinh(a+b*x)/cosh(a+b*x)^(3/2) +--R +--R +--R x sinh(b x + a) +--R (77) ----------------------------- +--R +-------------+ +--R cosh(b x + a)\|cosh(b x + a) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 502 +r0826:= -2*x/b/cosh(a+b*x)^(1/2)-4*%i*EllipticF(1/2*%i*(a+b*x),2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 502 +a0826:= integrate(t0826,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 133 + +--S 134 of 502 +--m0826:= a0826-r0826 +--E 134 + +--S 135 of 502 +--d0826:= D(m0826,x) +--E 135 + +--S 136 of 502 +t0827:= x*sinh(a+b*x)/cosh(a+b*x)^(5/2) +--R +--R +--R x sinh(b x + a) +--R (78) ------------------------------ +--R 2 +-------------+ +--R cosh(b x + a) \|cosh(b x + a) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 502 +r0827:= -2/3*x/b/cosh(a+b*x)^(3/2)+4/3*%i*EllipticE(1/2*%i*(a+b*x),2)/b^2+_ + 4/3*sinh(a+b*x)/b^2/cosh(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 137 + +--S 138 of 502 +a0827:= integrate(t0827,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 138 + +--S 139 of 502 +--m0827:= a0827-r0827 +--E 139 + +--S 140 of 502 +--d0827:= D(m0827,x) +--E 140 + +--S 141 of 502 +t0828:= x*cosh(a+b*x)*sinh(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (79) x cosh(b x + a)sinh(b x + a)\|sinh(b x + a) +--R Type: Expression(Integer) +--E 141 + +--S 142 of 502 +r0828:= -12/25*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + sinh(a+b*x)^(1/2)/b^2/(%i*sinh(a+b*x))^(1/2)-4/25*_ + cosh(a+b*x)*sinh(a+b*x)^(3/2)/b^2+2/5*x*sinh(a+b*x)^(5/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 142 + +--S 143 of 502 +a0828:= integrate(t0828,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 143 + +--S 144 of 502 +--m0828:= a0828-r0828 +--E 144 + +--S 145 of 502 +--d0828:= D(m0828,x) +--E 145 + +--S 146 of 502 +t0829:= x*cosh(a+b*x)*sinh(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (80) x cosh(b x + a)\|sinh(b x + a) +--R Type: Expression(Integer) +--E 146 + +--S 147 of 502 +r0829:= 2/9*(-2*%i*EllipticF(-1/4*%pi+1/2*%i*a+1/2*%i*b*x,2)*_ + (%i*sinh(a+b*x))^(1/2)-2*cosh(a+b*x)*sinh(a+b*x)+_ + 3*b*x*cosh(a+b*x)^2-3*b*x)/sinh(a+b*x)^(1/2)/b^2 +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Expression(Complex(Integer)) +--R Polynomial(Complex(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 502 +a0829:= integrate(t0829,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 148 + +--S 149 of 502 +--m0829:= a0829-r0829 +--E 149 + +--S 150 of 502 +--d0829:= D(m0829,x) +--E 150 + +--S 151 of 502 +t0830:= x*cosh(a+b*x)/sinh(a+b*x)^(1/2) +--R +--R +--R x cosh(b x + a) +--R (81) ---------------- +--R +-------------+ +--R \|sinh(b x + a) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 502 +r0830:= 2*x*sinh(a+b*x)^(1/2)/b+4*%i*EllipticE(-1/4*%pi+_ + 1/2*%i*(a+b*x),2)*sinh(a+b*x)^(1/2)/b^2/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 152 + +--S 153 of 502 +a0830:= integrate(t0830,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 153 + +--S 154 of 502 +--m0830:= a0830-r0830 +--E 154 + +--S 155 of 502 +--d0830:= D(m0830,x) +--E 155 + +--S 156 of 502 +t0831:= x*cosh(a+b*x)/sinh(a+b*x)^(3/2) +--R +--R +--R x cosh(b x + a) +--R (82) ----------------------------- +--R +-------------+ +--R sinh(b x + a)\|sinh(b x + a) +--R Type: Expression(Integer) +--E 156 + +--S 157 of 502 +r0831:= -2*(b*x+2*%i*EllipticF(-1/4*%pi+1/2*%i*a+1/2*%i*b*x,2)*_ + (%i*sinh(a+b*x))^(1/2))/sinh(a+b*x)^(1/2)/b^2 +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Expression(Complex(Integer)) +--R Polynomial(Complex(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 157 + +--S 158 of 502 +a0831:= integrate(t0831,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 158 + +--S 159 of 502 +--m0831:= a0831-r0831 +--E 159 + +--S 160 of 502 +--d0831:= D(m0831,x) +--E 160 + +--S 161 of 502 +t0832:= x*cosh(a+b*x)/sinh(a+b*x)^(5/2) +--R +--R +--R x cosh(b x + a) +--R (83) ------------------------------ +--R 2 +-------------+ +--R sinh(b x + a) \|sinh(b x + a) +--R Type: Expression(Integer) +--E 161 + +--S 162 of 502 +r0832:= -2/3*x/b/sinh(a+b*x)^(3/2)-4/3*cosh(a+b*x)/b^2/sinh(a+b*x)^(1/2)-_ + 4/3*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + sinh(a+b*x)^(1/2)/b^2/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 502 +a0832:= integrate(t0832,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 163 + +--S 164 of 502 +--m0832:= a0832-r0832 +--E 164 + +--S 165 of 502 +--d0832:= D(m0832,x) +--E 165 + +--S 166 of 502 +t0833:= x*sinh(a+b*x)*sech(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (84) x sech(b x + a) sinh(b x + a)\|sech(b x + a) +--R Type: Expression(Integer) +--E 166 + +--S 167 of 502 +r0833:= 2/3*(1/cosh(a+b*x))^(1/2)*(2*%i*cosh(a+b*x)^(3/2)*_ + EllipticE(1/2*%i*(a+b*x),2)-b*x+2*cosh(a+b*x)*_ + sinh(a+b*x))/cosh(a+b*x)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 167 + +--S 168 of 502 +a0833:= integrate(t0833,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 168 + +--S 169 of 502 +--m0833:= a0833-r0833 +--E 169 + +--S 170 of 502 +--d0833:= D(m0833,x) +--E 170 + +--S 171 of 502 +t0834:= x*sinh(a+b*x)*sech(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (85) x sech(b x + a)sinh(b x + a)\|sech(b x + a) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 502 +r0834:= -2*(1/cosh(a+b*x))^(1/2)*(b*x+2*%i*cosh(a+b*x)^(1/2)*_ + EllipticF(1/2*%i*(a+b*x),2))/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 172 + +--S 173 of 502 +a0834:= integrate(t0834,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 173 + +--S 174 of 502 +--m0834:= a0834-r0834 +--E 174 + +--S 175 of 502 +--d0834:= D(m0834,x) +--E 175 + +--S 176 of 502 +t0835:= x*sinh(a+b*x)*sech(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (86) x sinh(b x + a)\|sech(b x + a) +--R Type: Expression(Integer) +--E 176 + +--S 177 of 502 +r0835:= 2*x/b/sech(a+b*x)^(1/2)+4*%i*cosh(a+b*x)^(1/2)*_ + EllipticE(1/2*%i*(a+b*x),2)*sech(a+b*x)^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 177 + +--S 178 of 502 +a0835:= integrate(t0835,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 178 + +--S 179 of 502 +--m0835:= a0835-r0835 +--E 179 + +--S 180 of 502 +--d0835:= D(m0835,x) +--E 180 + +--S 181 of 502 +t0836:= x*sinh(a+b*x)/sech(a+b*x)^(1/2) +--R +--R +--R x sinh(b x + a) +--R (87) ---------------- +--R +-------------+ +--R \|sech(b x + a) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 502 +r0836:= -2/9*(-3*b*x*cosh(a+b*x)^(3/2)-2*%i*EllipticF(1/2*%i*(a+b*x),2)+_ + 2*sinh(a+b*x)*cosh(a+b*x)^(1/2))/cosh(a+b*x)^(1/2)/_ + (1/cosh(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 182 + +--S 183 of 502 +a0836:= integrate(t0836,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 183 + +--S 184 of 502 +--m0836:= a0836-r0836 +--E 184 + +--S 185 of 502 +--d0836:= D(m0836,x) +--E 185 + +--S 186 of 502 +t0837:= x*sinh(a+b*x)/sech(a+b*x)^(3/2) +--R +--R +--R x sinh(b x + a) +--R (88) ----------------------------- +--R +-------------+ +--R sech(b x + a)\|sech(b x + a) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 502 +r0837:= 2/25*(5*b*x*cosh(a+b*x)^(5/2)+6*%i*EllipticE(1/2*%i*(a+b*x),2)-_ + 2*sinh(a+b*x)*cosh(a+b*x)^(3/2))/cosh(a+b*x)^(1/2)/_ + (1/cosh(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 187 + +--S 188 of 502 +a0837:= integrate(t0837,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 188 + +--S 189 of 502 +--m0837:= a0837-r0837 +--E 189 + +--S 190 of 502 +--d0837:= D(m0837,x) +--E 190 + +--S 191 of 502 +t0838:= x*cosh(a+b*x)*csch(a+b*x)^(5/2) +--R +--R +--R 2 +-------------+ +--R (89) x cosh(b x + a)csch(b x + a) \|csch(b x + a) +--R Type: Expression(Integer) +--E 191 + +--S 192 of 502 +r0838:= -4/3*cosh(a+b*x)*csch(a+b*x)^(1/2)/b^2-2/3*x*csch(a+b*x)^(3/2)/b-_ + 4/3*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b^2/_ + csch(a+b*x)^(1/2)/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 192 + +--S 193 of 502 +a0838:= integrate(t0838,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 193 + +--S 194 of 502 +--m0838:= a0838-r0838 +--E 194 + +--S 195 of 502 +--d0838:= D(m0838,x) +--E 195 + +--S 196 of 502 +t0839:= x*cosh(a+b*x)*csch(a+b*x)^(3/2) +--R +--R +--R +-------------+ +--R (90) x cosh(b x + a)csch(b x + a)\|csch(b x + a) +--R Type: Expression(Integer) +--E 196 + +--S 197 of 502 +r0839:= -2*(1/sinh(a+b*x))^(1/2)*(b*x+2*%i*_ + EllipticF(-1/4*%pi+1/2*%i*a+1/2*%i*b*x,2)*(%i*sinh(a+b*x))^(1/2))/b^2 +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Expression(Complex(Integer)) +--R Polynomial(Complex(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 197 + +--S 198 of 502 +a0839:= integrate(t0839,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 198 + +--S 199 of 502 +--m0839:= a0839-r0839 +--E 199 + +--S 200 of 502 +--d0839:= D(m0839,x) +--E 200 + +--S 201 of 502 +t0840:= x*cosh(a+b*x)*csch(a+b*x)^(1/2) +--R +--R +--R +-------------+ +--R (91) x cosh(b x + a)\|csch(b x + a) +--R Type: Expression(Integer) +--E 201 + +--S 202 of 502 +r0840:= 2*x/b/csch(a+b*x)^(1/2)+4*%i*_ + EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b^2/csch(a+b*x)^(1/2)/_ + (%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 202 + +--S 203 of 502 +a0840:= integrate(t0840,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 203 + +--S 204 of 502 +--m0840:= a0840-r0840 +--E 204 + +--S 205 of 502 +--d0840:= D(m0840,x) +--E 205 + +--S 206 of 502 +t0841:= x*cosh(a+b*x)/csch(a+b*x)^(1/2) +--R +--R +--R x cosh(b x + a) +--R (92) ---------------- +--R +-------------+ +--R \|csch(b x + a) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 502 +r0841:= 2/3*x/b/csch(a+b*x)^(3/2)-4/9*cosh(a+b*x)/b^2/csch(a+b*x)^(1/2)-_ + 4/9*%i*csch(a+b*x)^(1/2)*EllipticF(-1/4*%pi+1/2*%i*(a+b*x),2)*_ + (%i*sinh(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 207 + +--S 208 of 502 +a0841:= integrate(t0841,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 208 + +--S 209 of 502 +--m0841:= a0841-r0841 +--E 209 + +--S 210 of 502 +--d0841:= D(m0841,x) +--E 210 + +--S 211 of 502 +t0842:= x*cosh(a+b*x)/csch(a+b*x)^(3/2) +--R +--R +--R x cosh(b x + a) +--R (93) ----------------------------- +--R +-------------+ +--R csch(b x + a)\|csch(b x + a) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 502 +r0842:= 2/5*x/b/csch(a+b*x)^(5/2)-4/25*cosh(a+b*x)/b^2/csch(a+b*x)^(3/2)-_ + 12/25*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*x),2)/b^2/_ + csch(a+b*x)^(1/2)/(%i*sinh(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 212 + +--S 213 of 502 +a0842:= integrate(t0842,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 213 + +--S 214 of 502 +--m0842:= a0842-r0842 +--E 214 + +--S 215 of 502 +--d0842:= D(m0842,x) +--E 215 + +--S 216 of 502 +t0843:= csch(x)^(1/2)*(x*cosh(x)-4*sech(x)*tanh(x)) +--R +--R +--R +-------+ +--R (94) (- 4sech(x)tanh(x) + x cosh(x))\|csch(x) +--R Type: Expression(Integer) +--E 216 + +--S 217 of 502 +r0843:= 2*x/csch(x)^(1/2)-4*sech(x)/csch(x)^(3/2) +--R +--R +--R - 4sech(x) + 2x csch(x) +--R (95) ----------------------- +--R +-------+ +--R csch(x)\|csch(x) +--R Type: Expression(Integer) +--E 217 + +--S 218 of 502 +a0843:= integrate(t0843,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 218 + +--S 219 of 502 +--m0843:= a0843-r0843 +--E 219 + +--S 220 of 502 +--d0843:= D(m0843,x) +--E 220 + +--S 221 of 502 +t0844:= 1/(a+b*sinh(x)*cosh(x)) +--R +--R +--R 1 +--R (96) -------------------- +--R b cosh(x)sinh(x) + a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 502 +r0844:= -2*atanh((b-2*a*tanh(x))/(4*a^2+b^2)^(1/2))/(4*a^2+b^2)^(1/2) +--R +--R +--R 2a tanh(x) - b +--R 2atanh(--------------) +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R (97) ---------------------- +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R Type: Expression(Integer) +--E 222 + +--S 223 of 502 +a0844:= integrate(t0844,x) +--R +--R +--R (98) +--R log +--R 2 4 2 3 2 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 4 2 +--R (4b cosh(x) + 8a b cosh(x))sinh(x) + b cosh(x) + 4a b cosh(x) +--R + +--R 2 2 +--R b + 8a +--R * +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R + +--R 3 2 2 3 2 +--R (- 2b - 8a b)sinh(x) + (- 4b - 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (- 2b - 8a b)cosh(x) - 4a b - 16a +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 4a)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 8a cosh(x))sinh(x) + b cosh(x) + 4a cosh(x) - b +--R / +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 502 +m0844:= a0844-r0844 +--R +--R +--R (99) +--R log +--R 2 4 2 3 2 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 4a b)sinh(x) +--R + +--R 2 3 2 4 +--R (4b cosh(x) + 8a b cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 +--R 4a b cosh(x) + b + 8a +--R * +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R + +--R 3 2 2 3 2 +--R (- 2b - 8a b)sinh(x) + (- 4b - 16a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (- 2b - 8a b)cosh(x) - 4a b - 16a +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 4a)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 8a cosh(x))sinh(x) + b cosh(x) + 4a cosh(x) - b +--R + +--R 2a tanh(x) - b +--R - 2atanh(--------------) +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R / +--R +--------+ +--R | 2 2 +--R \|b + 4a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 502 +d0844:= D(m0844,x) +--R +--R +--R (100) +--R 4 3 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) - 6b cosh(x) sinh(x) +--R + +--R 3 4 +--R - 4b cosh(x) sinh(x) - b cosh(x) + b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 +--R (- 4b sinh(x) - 8b cosh(x)sinh(x) - 4b cosh(x) )tanh(x) + b sinh(x) +--R + +--R 3 2 2 3 +--R 4b cosh(x)sinh(x) + 6b cosh(x) sinh(x) + 4b cosh(x) sinh(x) +--R + +--R 4 +--R b cosh(x) - b +--R / +--R 4 3 2 2 2 +--R a b sinh(x) + 4a b cosh(x)sinh(x) + (6a b cosh(x) + 4a )sinh(x) +--R + +--R 3 2 4 2 2 +--R (4a b cosh(x) + 8a cosh(x))sinh(x) + a b cosh(x) + 4a cosh(x) - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 3 2 2 2 +--R - b sinh(x) - 4b cosh(x)sinh(x) + (- 6b cosh(x) - 4a b)sinh(x) +--R + +--R 2 3 2 4 2 2 +--R (- 4b cosh(x) - 8a b cosh(x))sinh(x) - b cosh(x) - 4a b cosh(x) + b +--R * +--R tanh(x) +--R + +--R 4 3 2 2 2 +--R - a b sinh(x) - 4a b cosh(x)sinh(x) + (- 6a b cosh(x) - 4a )sinh(x) +--R + +--R 3 2 4 2 2 +--R (- 4a b cosh(x) - 8a cosh(x))sinh(x) - a b cosh(x) - 4a cosh(x) + a b +--R Type: Expression(Integer) +--E 225 + +--S 226 of 502 +t0845:= x/(a+b*sinh(x)*cosh(x)) +--R +--R +--R x +--R (101) -------------------- +--R b cosh(x)sinh(x) + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 502 +r0845:= 1/2*(2*x*log((-2*a+(4*a^2+b^2)^(1/2)-b*exp(2*x))/_ + (-2*a+(4*a^2+b^2)^(1/2)))-2*x*log((2*a+(4*a^2+b^2)^(1/2)+_ + b*exp(2*x))/(2*a+(4*a^2+b^2)^(1/2)))+polylog(2,b*exp(2*x)/_ + (-2*a+(4*a^2+b^2)^(1/2)))-_ + polylog(2,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x)))/(4*a^2+b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 502 +a0845:= integrate(t0845,x) +--R +--R +--R x +--R ++ %I +--R (102) | ---------------------- d%I +--R ++ b cosh(%I)sinh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 502 +--m0845:= a0845-r0845 +--E 229 + +--S 230 of 502 +--d0845:= D(m0845,x) +--E 230 + +--S 231 of 502 +t0846:= x^2/(a+b*sinh(x)*cosh(x)) +--R +--R +--R 2 +--R x +--R (103) -------------------- +--R b cosh(x)sinh(x) + a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 502 +r0846:= 1/2*(2*x^2*log((-2*a+(4*a^2+b^2)^(1/2)-b*exp(2*x))/_ + (-2*a+(4*a^2+b^2)^(1/2)))-2*x^2*log((2*a+(4*a^2+b^2)^(1/2)+_ + b*exp(2*x))/(2*a+(4*a^2+b^2)^(1/2)))+_ + 2*x*polylog(2,b*exp(2*x)/(-2*a+(4*a^2+b^2)^(1/2)))-_ + 2*x*polylog(2,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x))-_ + polylog(3,b*exp(2*x)/(-2*a+(4*a^2+b^2)^(1/2)))+_ + polylog(3,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x)))/(4*a^2+b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 232 + +--S 233 of 502 +a0846:= integrate(t0846,x) +--R +--R +--R x 2 +--R ++ %I +--R (104) | ---------------------- d%I +--R ++ b cosh(%I)sinh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 502 +--m0846:= a0846-r0846 +--E 234 + +--S 235 of 502 +--d0846:= D(m0846,x) +--E 235 + +--S 236 of 502 +t0847:= x^3/(a+b*sinh(x)*cosh(x)) +--R +--R +--R 3 +--R x +--R (105) -------------------- +--R b cosh(x)sinh(x) + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 502 +r0847:= 1/4*(4*x^3*log((-2*a+(4*a^2+b^2)^(1/2)-b*exp(2*x))/_ + (-2*a+(4*a^2+b^2)^(1/2)))-4*x^3*log((2*a+(4*a^2+b^2)^(1/2)+_ + b*exp(2*x))/(2*a+(4*a^2+b^2)^(1/2)))+_ + 6*x^2*polylog(2,b*exp(2*x)/(-2*a+(4*a^2+b^2)^(1/2)))-_ + 6*x^2*polylog(2,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x))-_ + 6*x*polylog(3,b*exp(2*x)/(-2*a+(4*a^2+b^2)^(1/2)))+_ + 6*x*polylog(3,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x))+_ + 3*polylog(4,b*exp(2*x)/(-2*a+(4*a^2+b^2)^(1/2)))-_ + 3*polylog(4,-1/(2*a+(4*a^2+b^2)^(1/2))*b*exp(2*x)))/(4*a^2+b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 502 +a0847:= integrate(t0847,x) +--R +--R +--R x 3 +--R ++ %I +--R (106) | ---------------------- d%I +--R ++ b cosh(%I)sinh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 502 +--m0847:= a0847-r0847 +--E 239 + +--S 240 of 502 +--d0847:= D(m0847,x) +--E 240 + +--S 241 of 502 +t0848:= (a-b*sinh(x))/(b+a*sinh(x))^2 +--R +--R +--R - b sinh(x) + a +--R (107) ------------------------------ +--R 2 2 2 +--R a sinh(x) + 2a b sinh(x) + b +--R Type: Expression(Integer) +--E 241 + +--S 242 of 502 +r0848:= -cosh(x)/(b+a*sinh(x)) +--R +--R +--R cosh(x) +--R (108) - ------------- +--R a sinh(x) + b +--R Type: Expression(Integer) +--E 242 + +--S 243 of 502 +a0848:= integrate(t0848,x) +--R +--R +--R (109) +--R 2b sinh(x) + 2b cosh(x) - 2a +--R ------------------------------------------------------------------------ +--R 2 2 2 2 2 2 +--R a sinh(x) + (2a cosh(x) + 2a b)sinh(x) + a cosh(x) + 2a b cosh(x) - a +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 502 +m0848:= a0848-r0848 +--R +--R +--R (110) +--R 2 2 +--R (a cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R (2a cosh(x) + 4a b cosh(x) + 2b - 2a )sinh(x) + a cosh(x) +--R + +--R 2 2 2 +--R 2a b cosh(x) + (2b - a )cosh(x) - 2a b +--R / +--R 3 3 3 2 2 +--R a sinh(x) + (2a cosh(x) + 3a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (a cosh(x) + 4a b cosh(x) + 2a b - a )sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - a b +--R Type: Expression(Integer) +--E 244 + +--S 245 of 502 +d0848:= D(m0848,x) +--R +--R +--R (111) +--R 3 6 3 2 5 +--R a sinh(x) + (4a cosh(x) + 3a b)sinh(x) +--R + +--R 3 2 2 2 3 4 +--R (5a cosh(x) + 10a b cosh(x) + 4a b + 2a )sinh(x) +--R + +--R 2 2 2 3 3 2 3 +--R (8a b cosh(x) + (8a b + 4a )cosh(x) + 2b + 4a b)sinh(x) +--R + +--R 3 4 2 3 3 2 3 2 +--R - 5a cosh(x) - 6a b cosh(x) + 4a cosh(x) + (2b + 10a b)cosh(x) +--R + +--R 2 3 +--R 4a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 4 2 3 3 +--R - 4a cosh(x) - 11a b cosh(x) + (- 8a b + 4a )cosh(x) +--R + +--R 3 2 2 2 3 2 +--R (- 2b + 10a b)cosh(x) + 8a b cosh(x) + 2b + a b +--R * +--R sinh(x) +--R + +--R 3 6 2 5 2 3 4 +--R - a cosh(x) - 4a b cosh(x) + (- 4a b + 2a )cosh(x) +--R + +--R 3 2 3 2 3 2 3 +--R (- 2b + 4a b)cosh(x) + (4a b - a )cosh(x) + 2b cosh(x) +--R / +--R 4 6 4 3 5 +--R a sinh(x) + (4a cosh(x) + 6a b)sinh(x) +--R + +--R 4 2 3 2 2 4 4 +--R (6a cosh(x) + 20a b cosh(x) + 13a b - 2a )sinh(x) +--R + +--R 4 3 3 2 2 2 4 3 3 +--R (4a cosh(x) + 24a b cosh(x) + (36a b - 4a )cosh(x) + 12a b - 8a b) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 3 3 2 2 4 2 +--R a cosh(x) + 12a b cosh(x) + (34a b - 2a )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (28a b - 12a b)cosh(x) + 4b - 10a b + a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R 2a b cosh(x) + 12a b cosh(x) + (20a b - 4a b)cosh(x) +--R + +--R 4 2 2 3 3 +--R (8b - 12a b )cosh(x) - 4a b + 2a b +--R * +--R sinh(x) +--R + +--R 2 2 4 3 3 4 2 2 2 3 2 2 +--R a b cosh(x) + 4a b cosh(x) + (4b - 2a b )cosh(x) - 4a b cosh(x) + a b +--R Type: Expression(Integer) +--E 245 + +--S 246 of 502 +t0849:= x*(b-a*sinh(x))/(a+b*sinh(x))^2 +--R +--R +--R - a x sinh(x) + b x +--R (112) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 246 + +--S 247 of 502 +r0849:= log(a+b*sinh(x))/b-x*cosh(x)/(a+b*sinh(x)) +--R +--R +--R (b sinh(x) + a)log(b sinh(x) + a) - b x cosh(x) +--R (113) ----------------------------------------------- +--R 2 +--R b sinh(x) + a b +--R Type: Expression(Integer) +--E 247 + +--S 248 of 502 +a0849:= integrate(t0849,x) +--R +--R +--R (114) +--R 2 2 +--R (b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) - b) +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R - 2b x sinh(x) + (- 4b x cosh(x) - 2a x)sinh(x) - 2b x cosh(x) +--R + +--R - 2a x cosh(x) +--R / +--R 2 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) - b +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 502 +m0849:= a0849-r0849 +--R +--R +--R (115) +--R 2 3 2 2 +--R - b sinh(x) + (- 2b cosh(x) - 3a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- b cosh(x) - 4a b cosh(x) + b - 2a )sinh(x) - a b cosh(x) +--R + +--R 2 +--R - 2a cosh(x) + a b +--R * +--R log(b sinh(x) + a) +--R + +--R 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 3a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b cosh(x) + 4a b cosh(x) - b + 2a )sinh(x) + a b cosh(x) +--R + +--R 2 +--R 2a cosh(x) - a b +--R * +--R - 2b sinh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 +--R - 2b x sinh(x) + (- 3b x cosh(x) - 4a b x)sinh(x) +--R + +--R 2 2 3 2 2 +--R (- 4a b x cosh(x) - 2a x)sinh(x) + b x cosh(x) + (- b - 2a )x cosh(x) +--R / +--R 3 3 3 2 2 +--R b sinh(x) + (2b cosh(x) + 3a b )sinh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (b cosh(x) + 4a b cosh(x) - b + 2a b)sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - a b +--R Type: Expression(Integer) +--E 249 + +--S 250 of 502 +d0849:= D(m0849,x) +--R +--R +--R (116) +--R 3 3 6 3 3 2 2 5 +--R (b x - b )sinh(x) + ((4b x - 3b )cosh(x) + 3a b x - 4a b )sinh(x) +--R + +--R 3 3 2 2 2 3 2 +--R (5b x - 2b )cosh(x) + (10a b x - 9a b )cosh(x) + (2b + 4a b)x +--R + +--R 2 +--R - 5a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 +--R 2b cosh(x) + (8a b x - 2a b )cosh(x) +--R + +--R 3 2 3 2 2 3 2 3 +--R ((4b + 8a b)x - 2b - 8a b)cosh(x) + (4a b + 2a )x - 2a b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 2 3 +--R (- 5b x + 3b )cosh(x) + (- 6a b x + 8a b )cosh(x) +--R + +--R 3 3 2 2 2 3 2 3 +--R (4b x - 4b + 2a b)cosh(x) + ((10a b + 2a )x - 8a b - 2a )cosh(x) +--R + +--R 3 2 3 2 +--R (b + 4a b)x + b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 2 4 +--R (- 4b x + b )cosh(x) + (- 11a b x + 6a b )cosh(x) +--R + +--R 3 2 3 2 3 +--R ((4b - 8a b)x - 2b + 8a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 2 +--R ((10a b - 2a )x - 8a b + 2a )cosh(x) + (8a b x + b - 8a b)cosh(x) +--R + +--R 2 3 2 3 +--R (a b + 2a )x + 2a b - 2a +--R * +--R sinh(x) +--R + +--R 3 6 2 2 5 +--R - b x cosh(x) + (- 4a b x + a b )cosh(x) +--R + +--R 3 2 2 4 2 3 2 3 3 +--R ((2b - 4a b)x + 3a b)cosh(x) + ((4a b - 2a )x - 2a b + 2a )cosh(x) +--R + +--R 3 2 2 2 3 2 3 2 +--R ((- b + 4a b)x - 4a b)cosh(x) + (2a x + a b - 2a )cosh(x) + a b +--R / +--R 4 6 4 3 5 +--R b sinh(x) + (4b cosh(x) + 6a b )sinh(x) +--R + +--R 4 2 3 4 2 2 4 +--R (6b cosh(x) + 20a b cosh(x) - 2b + 13a b )sinh(x) +--R + +--R 4 3 3 2 4 2 2 3 +--R 4b cosh(x) + 24a b cosh(x) + (- 4b + 36a b )cosh(x) - 8a b +--R + +--R 3 +--R 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 3 3 4 2 2 2 +--R b cosh(x) + 12a b cosh(x) + (- 2b + 34a b )cosh(x) +--R + +--R 3 3 4 2 2 4 +--R (- 12a b + 28a b)cosh(x) + b - 10a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 3 2 +--R 2a b cosh(x) + 12a b cosh(x) + (- 4a b + 20a b)cosh(x) +--R + +--R 2 2 4 3 3 +--R (- 12a b + 8a )cosh(x) + 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 2 2 4 3 3 2 2 4 2 3 +--R a b cosh(x) + 4a b cosh(x) + (- 2a b + 4a )cosh(x) - 4a b cosh(x) +--R + +--R 2 2 +--R a b +--R Type: Expression(Integer) +--E 250 + +--S 251 of 502 +t0850:= x*(b+a*cosh(x))/(a+b*cosh(x))^2 +--R +--R +--R a x cosh(x) + b x +--R (117) ------------------------------ +--R 2 2 2 +--R b cosh(x) + 2a b cosh(x) + a +--R Type: Expression(Integer) +--E 251 + +--S 252 of 502 +r0850:= -log(a+b*cosh(x))/b+x*sinh(x)/(a+b*cosh(x)) +--R +--R +--R (- b cosh(x) - a)log(b cosh(x) + a) + b x sinh(x) +--R (118) ------------------------------------------------- +--R 2 +--R b cosh(x) + a b +--R Type: Expression(Integer) +--E 252 + +--S 253 of 502 +a0850:= integrate(t0850,x) +--R +--R +--R (119) +--R 2 2 +--R - b sinh(x) + (- 2b cosh(x) - 2a)sinh(x) - b cosh(x) - 2a cosh(x) +--R + +--R - b +--R * +--R - 2b cosh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R 2b x sinh(x) + (4b x cosh(x) + 2a x)sinh(x) + 2b x cosh(x) + 2a x cosh(x) +--R / +--R 2 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) + b +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 502 +m0850:= a0850-r0850 +--R +--R +--R (120) +--R 2 2 2 2 2 +--R (b cosh(x) + a b)sinh(x) + (2b cosh(x) + 4a b cosh(x) + 2a )sinh(x) +--R + +--R 2 3 2 2 2 +--R b cosh(x) + 3a b cosh(x) + (b + 2a )cosh(x) + a b +--R * +--R log(b cosh(x) + a) +--R + +--R 2 2 +--R (- b cosh(x) - a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (- 2b cosh(x) - 4a b cosh(x) - 2a )sinh(x) - b cosh(x) +--R + +--R 2 2 2 +--R - 3a b cosh(x) + (- b - 2a )cosh(x) - a b +--R * +--R - 2b cosh(x) - 2a +--R log(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 2 3 2 2 2 2 +--R - b x sinh(x) + (3b x cosh(x) + 4a b x cosh(x) + (- b + 2a )x)sinh(x) +--R + +--R 2 3 2 2 +--R 2b x cosh(x) + 4a b x cosh(x) + 2a x cosh(x) +--R / +--R 3 2 2 3 2 2 2 +--R (b cosh(x) + a b )sinh(x) + (2b cosh(x) + 4a b cosh(x) + 2a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R b cosh(x) + 3a b cosh(x) + (b + 2a b)cosh(x) + a b +--R Type: Expression(Integer) +--E 254 + +--S 255 of 502 +d0850:= D(m0850,x) +--R +--R +--R (121) +--R 3 6 3 3 2 2 5 +--R b x sinh(x) + ((4b x - b )cosh(x) + 4a b x - a b )sinh(x) +--R + +--R 3 3 2 2 2 3 2 +--R (5b x - 3b )cosh(x) + (11a b x - 6a b )cosh(x) + (2b + 4a b)x +--R + +--R 2 +--R - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 +--R - 2b cosh(x) + (6a b x - 8a b )cosh(x) +--R + +--R 3 2 3 2 2 3 2 3 +--R ((4b + 8a b)x - 2b - 8a b)cosh(x) + (4a b + 2a )x - 2a b - 2a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 4 2 2 3 +--R (- 5b x + 2b )cosh(x) + (- 8a b x + 2a b )cosh(x) +--R + +--R 3 3 2 2 2 3 2 3 +--R (4b x - 4b - 2a b)cosh(x) + ((10a b + 2a )x - 8a b - 2a )cosh(x) +--R + +--R 3 2 2 +--R (b + 4a b)x - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 2 2 4 +--R (- 4b x + 3b )cosh(x) + (- 10a b x + 9a b )cosh(x) +--R + +--R 3 2 3 2 3 +--R ((4b - 8a b)x - 2b + 8a b)cosh(x) +--R + +--R 2 3 2 3 2 2 3 2 +--R ((10a b - 2a )x - 8a b + 2a )cosh(x) + (8a b x - b - 8a b)cosh(x) +--R + +--R 3 2 3 +--R 2a x - a b - 2a +--R * +--R sinh(x) +--R + +--R 3 3 6 2 2 5 +--R (- b x + b )cosh(x) + (- 3a b x + 4a b )cosh(x) +--R + +--R 3 2 2 4 2 3 2 3 3 +--R ((2b - 4a b)x + 5a b)cosh(x) + ((4a b - 2a )x - 2a b + 2a )cosh(x) +--R + +--R 3 2 3 2 2 +--R ((- b + 4a b)x - b - 4a b)cosh(x) +--R + +--R 2 3 2 3 2 +--R ((- a b + 2a )x - 2a b - 2a )cosh(x) - a b +--R / +--R 4 2 3 2 2 4 +--R (b cosh(x) + 2a b cosh(x) + a b )sinh(x) +--R + +--R 4 3 3 2 2 2 3 3 +--R (4b cosh(x) + 12a b cosh(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 4 4 3 3 4 2 2 2 +--R 6b cosh(x) + 24a b cosh(x) + (2b + 34a b )cosh(x) +--R + +--R 3 3 2 2 4 +--R (4a b + 20a b)cosh(x) + 2a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 3 4 4 2 2 3 +--R 4b cosh(x) + 20a b cosh(x) + (4b + 36a b )cosh(x) +--R + +--R 3 3 2 2 2 4 3 +--R (12a b + 28a b)cosh(x) + (12a b + 8a )cosh(x) + 4a b +--R * +--R sinh(x) +--R + +--R 4 6 3 5 4 2 2 4 +--R b cosh(x) + 6a b cosh(x) + (2b + 13a b )cosh(x) +--R + +--R 3 3 3 4 2 2 4 2 +--R (8a b + 12a b)cosh(x) + (b + 10a b + 4a )cosh(x) +--R + +--R 3 3 2 2 +--R (2a b + 4a b)cosh(x) + a b +--R Type: Expression(Integer) +--E 255 + +--S 256 of 502 +t0851:= sinh(x)/(a+%i*a*sinh(x))^(1/2) +--R +--R +--R sinh(x) +--R (122) ------------------- +--R +----------------+ +--R \|%i a sinh(x) + a +--R Type: Expression(Complex(Integer)) +--E 256 + +--S 257 of 502 +r0851:= 2*(cosh(x)+%i*atan(sinh(1/4*%i*%pi+1/2*x))*_ + cosh(1/4*%i*%pi+1/2*x))/(a*(1+%i*sinh(x)))^(1/2) +--R +--R +--R 2x + %i %pi 2x + %i %pi +--R 2%i cosh(-----------)atan(sinh(-----------)) + 2cosh(x) +--R 4 4 +--R (123) ------------------------------------------------------- +--R +----------------+ +--R \|%i a sinh(x) + a +--R Type: Expression(Complex(Integer)) +--E 257 + +--S 258 of 502 +a0851:= integrate(t0851,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 258 + +--S 259 of 502 +--m0851:= a0851-r0851 +--E 259 + +--S 260 of 502 +--d0851:= D(m0851,x) +--E 260 + +--S 261 of 502 +t0852:= sinh(x)/(a-%i*a*sinh(x))^(1/2) +--R +--R +--R sinh(x) +--R (124) --------------------- +--R +------------------+ +--R \|- %i a sinh(x) + a +--R Type: Expression(Complex(Integer)) +--E 261 + +--S 262 of 502 +r0852:= 2*(cosh(x)+%i*atanh(cosh(1/4*%i*%pi+1/2*x))*_ + sinh(1/4*%i*%pi+1/2*x))/(-a*(-1+%i*sinh(x)))^(1/2) +--R +--R +--R 2x + %i %pi 2x + %i %pi +--R 2%i sinh(-----------)atanh(cosh(-----------)) + 2cosh(x) +--R 4 4 +--R (125) -------------------------------------------------------- +--R +------------------+ +--R \|- %i a sinh(x) + a +--R Type: Expression(Complex(Integer)) +--E 262 + +--S 263 of 502 +a0852:= integrate(t0852,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 263 + +--S 264 of 502 +--m0852:= a0852-r0852 +--E 264 + +--S 265 of 502 +--d0852:= D(m0852,x) +--E 265 + +--S 266 of 502 +t0853:= sinh(x)/(a+b*sinh(x))^(1/2) +--R +--R +--R sinh(x) +--R (126) ---------------- +--R +-------------+ +--R \|b sinh(x) + a +--R Type: Expression(Integer) +--E 266 + +--S 267 of 502 +r0853:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*_ + (a+b*sinh(x))^(1/2)/b/((a+b*sinh(x))/(a-%i*b))^(1/2)+_ + 2*%i*a*EllipticF(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*_ + ((a+b*sinh(x))/(a-%i*b))^(1/2)/b/(a+b*sinh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 502 +a0853:= integrate(t0853,x) +--R +--R +--R x +--R ++ sinh(%I) +--R (127) | ----------------- d%I +--R ++ +--------------+ +--R \|b sinh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 502 +--m0853:= a0853-r0853 +--E 269 + +--S 270 of 502 +--d0853:= D(m0853,x) +--E 270 + +--S 271 of 502 +t0854:= (A+B*sinh(x))/(a+%i*a*sinh(x))^(1/2) +--R +--R +--R B sinh(x) + A +--R (128) ------------------- +--R +----------------+ +--R \|%i a sinh(x) + a +--R Type: Expression(Complex(Integer)) +--E 271 + +--S 272 of 502 +r0854:= 2*B*cosh(x)/(a+%i*a*sinh(x))^(1/2)-2*%i*(%i*A-B)*_ + atan(sinh(1/4*%i*%pi+1/2*x))*cosh(1/4*%i*%pi+1/2*x)/_ + (a+%i*a*sinh(x))^(1/2) +--R +--R +--R 2x + %i %pi 2x + %i %pi +--R (2%i B + 2A)cosh(-----------)atan(sinh(-----------)) + 2B cosh(x) +--R 4 4 +--R (129) ----------------------------------------------------------------- +--R +----------------+ +--R \|%i a sinh(x) + a +--R Type: Expression(Complex(Integer)) +--E 272 + +--S 273 of 502 +a0854:= integrate(t0854,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 273 + +--S 274 of 502 +--m0854:= a0854-r0854 +--E 274 + +--S 275 of 502 +--d0854:= D(m0854,x) +--E 275 + +--S 276 of 502 +t0855:= (A+B*sinh(x))/(a-%i*a*sinh(x))^(1/2) +--R +--R +--R B sinh(x) + A +--R (130) --------------------- +--R +------------------+ +--R \|- %i a sinh(x) + a +--R Type: Expression(Complex(Integer)) +--E 276 + +--S 277 of 502 +r0855:= 2*B*cosh(x)/(a-%i*a*sinh(x))^(1/2)+2*%i*(%i*A+B)*_ + atanh(cosh(1/4*%i*%pi+1/2*x))*sinh(1/4*%i*%pi+1/2*x)/_ + (a-%i*a*sinh(x))^(1/2) +--R +--R +--R 2x + %i %pi 2x + %i %pi +--R (2%i B - 2A)sinh(-----------)atanh(cosh(-----------)) + 2B cosh(x) +--R 4 4 +--R (131) ------------------------------------------------------------------ +--R +------------------+ +--R \|- %i a sinh(x) + a +--R Type: Expression(Complex(Integer)) +--E 277 + +--S 278 of 502 +a0855:= integrate(t0855,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 278 + +--S 279 of 502 +--m0855:= a0855-r0855 +--E 279 + +--S 280 of 502 +--d0855:= D(m0855,x) +--E 280 + +--S 281 of 502 +t0856:= (A+B*sinh(x))/(a+b*sinh(x))^(1/2) +--R +--R +--R B sinh(x) + A +--R (132) ---------------- +--R +-------------+ +--R \|b sinh(x) + a +--R Type: Expression(Integer) +--E 281 + +--S 282 of 502 +r0856:= -2*%i*B*EllipticE(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*_ + (a+b*sinh(x))^(1/2)/b/((a+b*sinh(x))/(a-%i*b))^(1/2)-_ + 2*%i*(A*b-a*B)*EllipticF(-1/4*%pi+1/2*%i*x,2*%i*b/(a-%i*b))*_ + ((a+b*sinh(x))/(a-%i*b))^(1/2)/b/(a+b*sinh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 502 +a0856:= integrate(t0856,x) +--R +--R +--R x +--R ++ B sinh(%I) + A +--R (133) | ----------------- d%I +--R ++ +--------------+ +--R \|b sinh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 502 +--m0856:= a0856-r0856 +--E 284 + +--S 285 of 502 +--d0856:= D(m0856,x) +--E 285 + +--S 286 of 502 +t0857:= cosh(x)/(a+a*cosh(x))^(1/2) +--R +--R +--R cosh(x) +--R (134) ---------------- +--R +-------------+ +--R \|a cosh(x) + a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 502 +r0857:= -2*(atan(sinh(1/2*x))*cosh(1/2*x)-sinh(x))/(a*(1+cosh(x)))^(1/2) +--R +--R +--R x x +--R - 2cosh(-)atan(sinh(-)) + 2sinh(x) +--R 2 2 +--R (135) ---------------------------------- +--R +-------------+ +--R \|a cosh(x) + a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 502 +a0857:= integrate(t0857,x) +--R +--R +--R (136) +--R +-+ +-------------------+ +--R |2 | a +--R (2sinh(x) + 2cosh(x)) |- |------------------- +--R \|a \|2sinh(x) + 2cosh(x) +--R * +--R +-------------------+ +--R | a +--R 2 |------------------- +--R \|2sinh(x) + 2cosh(x) +--R atan(-----------------------) +--R +-+ +--R |2 +--R a |- +--R \|a +--R + +--R sinh(x) + cosh(x) - 1 +--R / +--R +-------------------+ +--R | a +--R (sinh(x) + cosh(x)) |------------------- +--R \|2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 502 +m0857:= a0857-r0857 +--R +--R +--R (137) +--R +-+ +-------------------+ +--R |2 | a +-------------+ +--R (2sinh(x) + 2cosh(x)) |- |------------------- \|a cosh(x) + a +--R \|a \|2sinh(x) + 2cosh(x) +--R * +--R +-------------------+ +--R | a +--R 2 |------------------- +--R \|2sinh(x) + 2cosh(x) +--R atan(-----------------------) +--R +-+ +--R |2 +--R a |- +--R \|a +--R + +--R +-------------+ +--R (sinh(x) + cosh(x) - 1)\|a cosh(x) + a +--R + +--R x x x 2 +--R (2cosh(-)sinh(x) + 2cosh(-)cosh(x))atan(sinh(-)) - 2sinh(x) +--R 2 2 2 +--R + +--R - 2cosh(x)sinh(x) +--R * +--R +-------------------+ +--R | a +--R |------------------- +--R \|2sinh(x) + 2cosh(x) +--R / +--R +-------------------+ +--R | a +-------------+ +--R (sinh(x) + cosh(x)) |------------------- \|a cosh(x) + a +--R \|2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 289 + +--S 290 of 502 +d0857:= D(m0857,x) +--R +--R +--R (138) +--R x 2 2 +--R ((cosh(x) + 1)sinh(-) + cosh(x) + 1)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R ((2cosh(x) + 2cosh(x))sinh(-) + 2cosh(x) + 2cosh(x))sinh(x) +--R 2 +--R + +--R 3 2 x 2 3 2 +--R (cosh(x) + cosh(x) + cosh(x) + 1)sinh(-) + cosh(x) + cosh(x) +--R 2 +--R + +--R cosh(x) + 1 +--R * +--R +-------------+ +--R \|a cosh(x) + a +--R + +--R x x 2 x 3 +--R (- 2cosh(-)sinh(-) - 2cosh(-))sinh(x) +--R 2 2 2 +--R + +--R x 3 +--R (2cosh(x) + 2)sinh(-) +--R 2 +--R + +--R x x x 2 +--R (- 4cosh(-)cosh(x) - 2cosh(-))sinh(-) +--R 2 2 2 +--R + +--R x x x +--R (2cosh(x) + 2)sinh(-) - 4cosh(-)cosh(x) - 2cosh(-) +--R 2 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 2 x 3 +--R (4cosh(x) + 6cosh(x) + 2)sinh(-) +--R 2 +--R + +--R x 2 x x 2 +--R (- 2cosh(-)cosh(x) - 2cosh(-)cosh(x))sinh(-) +--R 2 2 2 +--R + +--R 2 x x 2 +--R (4cosh(x) + 6cosh(x) + 2)sinh(-) - 2cosh(-)cosh(x) +--R 2 2 +--R + +--R x +--R - 2cosh(-)cosh(x) +--R 2 +--R * +--R sinh(x) +--R + +--R 3 2 x 3 +--R (2cosh(x) + 4cosh(x) + 2cosh(x))sinh(-) +--R 2 +--R + +--R 3 2 x +--R (2cosh(x) + 4cosh(x) + 2cosh(x))sinh(-) +--R 2 +--R * +--R x +--R atan(sinh(-)) +--R 2 +--R + +--R x 2 4 +--R (2sinh(-) + 2)sinh(x) +--R 2 +--R + +--R x 2 3 +--R ((4cosh(x) + 2)sinh(-) + 4cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R (- 2cosh(x) - 2cosh(x))sinh(-) - 2cosh(x) +--R 2 +--R + +--R x 2 x 2 +--R (2cosh(-) - 2)cosh(x) + 2cosh(-) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 x 2 3 +--R (- 8cosh(x) - 12cosh(x) - 4cosh(x))sinh(-) - 8cosh(x) +--R 2 +--R + +--R x 2 2 x 2 x 2 +--R (4cosh(-) - 12)cosh(x) + (6cosh(-) - 4)cosh(x) + 2cosh(-) +--R 2 2 2 +--R * +--R sinh(x) +--R + +--R 4 3 2 x 2 4 +--R (- 4cosh(x) - 8cosh(x) - 4cosh(x) )sinh(-) - 4cosh(x) +--R 2 +--R + +--R x 2 3 x 2 2 x 2 +--R (2cosh(-) - 8)cosh(x) + (4cosh(-) - 4)cosh(x) + 2cosh(-) cosh(x) +--R 2 2 2 +--R * +--R +-------------------+ +--R | a +--R |------------------- +--R \|2sinh(x) + 2cosh(x) +--R / +--R x 2 2 +--R ((2cosh(x) + 2)sinh(-) + 2cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R ((4cosh(x) + 6cosh(x) + 2)sinh(-) + 4cosh(x) + 6cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 3 2 x 2 3 2 +--R (2cosh(x) + 4cosh(x) + 2cosh(x))sinh(-) + 2cosh(x) + 4cosh(x) +--R 2 +--R + +--R 2cosh(x) +--R * +--R +-------------------+ +--R | a +-------------+ +--R |------------------- \|a cosh(x) + a +--R \|2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 290 + +--S 291 of 502 +t0858:= cosh(x)/(a-a*cosh(x))^(1/2) +--R +--R +--R cosh(x) +--R (139) ------------------ +--R +---------------+ +--R \|- a cosh(x) + a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 502 +r0858:= -2*(atanh(cosh(1/2*x))*sinh(1/2*x)-sinh(x))/(-(cosh(x)-1)*a)^(1/2) +--R +--R +--R x x +--R - 2sinh(-)atanh(cosh(-)) + 2sinh(x) +--R 2 2 +--R (140) ----------------------------------- +--R +---------------+ +--R \|- a cosh(x) + a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 502 +a0858:= integrate(t0858,x) +--R +--R +--R (141) +--R +---+ +---------------------+ +--R | 2 | a +--R (sinh(x) + cosh(x)) |- - |- ------------------- +--R \| a \| 2sinh(x) + 2cosh(x) +--R * +--R log +--R +---+ +---------------------+ +--R | 2 | a +--R (2sinh(x) + 2cosh(x)) |- - |- ------------------- - sinh(x) +--R \| a \| 2sinh(x) + 2cosh(x) +--R + +--R - cosh(x) - 1 +--R / +--R sinh(x) + cosh(x) - 1 +--R + +--R sinh(x) + cosh(x) + 1 +--R / +--R +---------------------+ +--R | a +--R (sinh(x) + cosh(x)) |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 502 +m0858:= a0858-r0858 +--R +--R +--R (142) +--R +---+ +---------------------+ +--R | 2 +---------------+ | a +--R (sinh(x) + cosh(x)) |- - \|- a cosh(x) + a |- ------------------- +--R \| a \| 2sinh(x) + 2cosh(x) +--R * +--R log +--R +---+ +---------------------+ +--R | 2 | a +--R (2sinh(x) + 2cosh(x)) |- - |- ------------------- - sinh(x) +--R \| a \| 2sinh(x) + 2cosh(x) +--R + +--R - cosh(x) - 1 +--R / +--R sinh(x) + cosh(x) - 1 +--R + +--R x x x 2 +--R (2sinh(-)sinh(x) + 2cosh(x)sinh(-))atanh(cosh(-)) - 2sinh(x) +--R 2 2 2 +--R + +--R - 2cosh(x)sinh(x) +--R * +--R +---------------------+ +--R | a +--R |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R + +--R +---------------+ +--R (sinh(x) + cosh(x) + 1)\|- a cosh(x) + a +--R / +--R +---------------------+ +--R +---------------+ | a +--R (sinh(x) + cosh(x))\|- a cosh(x) + a |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 294 + +--S 295 of 502 +d0858:= D(m0858,x) +--R +--R +--R (143) +--R x 2 x 3 +--R (- 2cosh(-) + 2)sinh(-)sinh(x) +--R 2 2 +--R + +--R x 2 x 2 x +--R ((- 4cosh(-) + 4)cosh(x) + 2cosh(-) - 2)sinh(-) +--R 2 2 2 +--R + +--R x 3 x x 3 x +--R (2cosh(-) - 2cosh(-))cosh(x) - 2cosh(-) + 2cosh(-) +--R 2 2 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R x 2 2 x 2 x +--R ((- 2cosh(-) + 2)cosh(x) + (2cosh(-) - 2)cosh(x))sinh(-) +--R 2 2 2 +--R + +--R x 3 x 2 +--R (4cosh(-) - 4cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x x 3 x +--R (- 6cosh(-) + 6cosh(-))cosh(x) + 2cosh(-) - 2cosh(-) +--R 2 2 2 2 +--R * +--R sinh(x) +--R + +--R x 3 x 3 x 3 x 2 +--R (2cosh(-) - 2cosh(-))cosh(x) + (- 4cosh(-) + 4cosh(-))cosh(x) +--R 2 2 2 2 +--R + +--R x 3 x +--R (2cosh(-) - 2cosh(-))cosh(x) +--R 2 2 +--R * +--R x +--R atanh(cosh(-)) +--R 2 +--R + +--R x 2 4 +--R (2cosh(-) - 2)sinh(x) +--R 2 +--R + +--R x 2 x 2 3 +--R ((4cosh(-) - 4)cosh(x) - 2cosh(-) + 2)sinh(x) +--R 2 2 +--R + +--R x 2 x 2 2 +--R (- 2cosh(x) + 2)sinh(-) + (- 2cosh(-) + 2)cosh(x) +--R 2 2 +--R + +--R x 2 +--R (2cosh(-) - 2)cosh(x) +--R 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 2 x 2 x 2 3 +--R (- 4cosh(x) + 6cosh(x) - 2)sinh(-) + (- 8cosh(-) + 8)cosh(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (12cosh(-) - 12)cosh(x) + (- 4cosh(-) + 4)cosh(x) +--R 2 2 +--R * +--R sinh(x) +--R + +--R 3 2 x 2 +--R (- 2cosh(x) + 4cosh(x) - 2cosh(x))sinh(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (- 4cosh(-) + 4)cosh(x) + (8cosh(-) - 8)cosh(x) +--R 2 2 +--R + +--R x 2 2 +--R (- 4cosh(-) + 4)cosh(x) +--R 2 +--R * +--R +---------------------+ +--R | a +--R |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R + +--R x 2 x 2 2 +--R ((cosh(-) - 1)cosh(x) - cosh(-) + 1)sinh(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R ((2cosh(-) - 2)cosh(x) + (- 2cosh(-) + 2)cosh(x))sinh(x) +--R 2 2 +--R + +--R x 2 3 x 2 2 +--R (cosh(-) - 1)cosh(x) + (- cosh(-) + 1)cosh(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (cosh(-) - 1)cosh(x) - cosh(-) + 1 +--R 2 2 +--R * +--R +---------------+ +--R \|- a cosh(x) + a +--R / +--R x 2 x 2 2 +--R ((2cosh(-) - 2)cosh(x) - 2cosh(-) + 2)sinh(x) +--R 2 2 +--R + +--R x 2 2 x 2 x 2 +--R ((4cosh(-) - 4)cosh(x) + (- 6cosh(-) + 6)cosh(x) + 2cosh(-) - 2) +--R 2 2 2 +--R * +--R sinh(x) +--R + +--R x 2 3 x 2 2 +--R (2cosh(-) - 2)cosh(x) + (- 4cosh(-) + 4)cosh(x) +--R 2 2 +--R + +--R x 2 +--R (2cosh(-) - 2)cosh(x) +--R 2 +--R * +--R +---------------------+ +--R +---------------+ | a +--R \|- a cosh(x) + a |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 295 + +--S 296 of 502 +t0859:= cosh(x)/(a+b*cosh(x))^(1/2) +--R +--R +--R cosh(x) +--R (144) ---------------- +--R +-------------+ +--R \|b cosh(x) + a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 502 +r0859:= -2*%i*(a+b*cosh(x))^(1/2)*(EllipticE(1/2*%i*x,2*b/(a+b))*a+_ + EllipticE(1/2*%i*x,2*b/(a+b))*b-_ + a*EllipticF(1/2*%i*x,2*b/(a+b)))/(a+b)/b/((a+b*cosh(x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 297 + +--S 298 of 502 +a0859:= integrate(t0859,x) +--R +--R +--R x +--R ++ cosh(%I) +--R (145) | ----------------- d%I +--R ++ +--------------+ +--R \|b cosh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 502 +--m0859:= a0859-r0859 +--E 299 + +--S 300 of 502 +--d0859:= D(m0859,x) +--E 300 + +--S 301 of 502 +t0860:= (A+B*cosh(x))/(a+a*cosh(x))^(1/2) +--R +--R +--R B cosh(x) + A +--R (146) ---------------- +--R +-------------+ +--R \|a cosh(x) + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 502 +r0860:= 2*(A-B)*atan(sinh(1/2*x))*cosh(1/2*x)/(a+a*cosh(x))^(1/2)+_ + 2*B*sinh(x)/(a+a*cosh(x))^(1/2) +--R +--R +--R x x +--R (- 2B + 2A)cosh(-)atan(sinh(-)) + 2B sinh(x) +--R 2 2 +--R (147) -------------------------------------------- +--R +-------------+ +--R \|a cosh(x) + a +--R Type: Expression(Integer) +--E 302 + +--S 303 of 502 +a0860:= integrate(t0860,x) +--R +--R +--R (148) +--R +-+ +-------------------+ +--R |2 | a +--R ((2B - 2A)sinh(x) + (2B - 2A)cosh(x)) |- |------------------- +--R \|a \|2sinh(x) + 2cosh(x) +--R * +--R +-------------------+ +--R | a +--R 2 |------------------- +--R \|2sinh(x) + 2cosh(x) +--R atan(-----------------------) +--R +-+ +--R |2 +--R a |- +--R \|a +--R + +--R B sinh(x) + B cosh(x) - B +--R / +--R +-------------------+ +--R | a +--R (sinh(x) + cosh(x)) |------------------- +--R \|2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 502 +m0860:= a0860-r0860 +--R +--R +--R (149) +--R +-+ +-------------------+ +--R |2 | a +--R ((2B - 2A)sinh(x) + (2B - 2A)cosh(x)) |- |------------------- +--R \|a \|2sinh(x) + 2cosh(x) +--R * +--R +-------------------+ +--R | a +--R 2 |------------------- +--R +-------------+ \|2sinh(x) + 2cosh(x) +--R \|a cosh(x) + a atan(-----------------------) +--R +-+ +--R |2 +--R a |- +--R \|a +--R + +--R +-------------+ +--R (B sinh(x) + B cosh(x) - B)\|a cosh(x) + a +--R + +--R x x x +--R ((2B - 2A)cosh(-)sinh(x) + (2B - 2A)cosh(-)cosh(x))atan(sinh(-)) +--R 2 2 2 +--R + +--R 2 +--R - 2B sinh(x) - 2B cosh(x)sinh(x) +--R * +--R +-------------------+ +--R | a +--R |------------------- +--R \|2sinh(x) + 2cosh(x) +--R / +--R +-------------------+ +--R | a +-------------+ +--R (sinh(x) + cosh(x)) |------------------- \|a cosh(x) + a +--R \|2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 304 + +--S 305 of 502 +d0860:= D(m0860,x) +--R +--R +--R (150) +--R x 2 2 +--R ((B cosh(x) + B)sinh(-) + B cosh(x) + B)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R (2B cosh(x) + (2B + 2A)cosh(x) + 2A)sinh(-) + 2B cosh(x) +--R 2 +--R + +--R (2B + 2A)cosh(x) + 2A +--R * +--R sinh(x) +--R + +--R 3 2 x 2 +--R (B cosh(x) + (B + 2A)cosh(x) + (B + 2A)cosh(x) + B)sinh(-) +--R 2 +--R + +--R 3 2 +--R B cosh(x) + (B + 2A)cosh(x) + (B + 2A)cosh(x) + B +--R * +--R +-------------+ +--R \|a cosh(x) + a +--R + +--R x x 2 x 3 +--R ((- 2B + 2A)cosh(-)sinh(-) + (- 2B + 2A)cosh(-))sinh(x) +--R 2 2 2 +--R + +--R x 3 +--R ((2B - 2A)cosh(x) + 2B - 2A)sinh(-) +--R 2 +--R + +--R x x x 2 +--R ((- 4B + 4A)cosh(-)cosh(x) + (- 2B + 2A)cosh(-))sinh(-) +--R 2 2 2 +--R + +--R x +--R ((2B - 2A)cosh(x) + 2B - 2A)sinh(-) +--R 2 +--R + +--R x x +--R (- 4B + 4A)cosh(-)cosh(x) + (- 2B + 2A)cosh(-) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 2 x 3 +--R ((4B - 4A)cosh(x) + (6B - 6A)cosh(x) + 2B - 2A)sinh(-) +--R 2 +--R + +--R x 2 x +--R ((- 2B + 2A)cosh(-)cosh(x) + (- 2B + 2A)cosh(-)cosh(x)) +--R 2 2 +--R * +--R x 2 +--R sinh(-) +--R 2 +--R + +--R 2 x +--R ((4B - 4A)cosh(x) + (6B - 6A)cosh(x) + 2B - 2A)sinh(-) +--R 2 +--R + +--R x 2 x +--R (- 2B + 2A)cosh(-)cosh(x) + (- 2B + 2A)cosh(-)cosh(x) +--R 2 2 +--R * +--R sinh(x) +--R + +--R 3 2 +--R ((2B - 2A)cosh(x) + (4B - 4A)cosh(x) + (2B - 2A)cosh(x)) +--R * +--R x 3 +--R sinh(-) +--R 2 +--R + +--R 3 2 x +--R ((2B - 2A)cosh(x) + (4B - 4A)cosh(x) + (2B - 2A)cosh(x))sinh(-) +--R 2 +--R * +--R x +--R atan(sinh(-)) +--R 2 +--R + +--R x 2 4 +--R (2B sinh(-) + 2B)sinh(x) +--R 2 +--R + +--R x 2 3 +--R ((4B cosh(x) + 2B)sinh(-) + 4B cosh(x) + 2B)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R (- 2B cosh(x) - 2B cosh(x))sinh(-) - 2B cosh(x) +--R 2 +--R + +--R x 2 x 2 +--R ((2B - 2A)cosh(-) - 2B)cosh(x) + (2B - 2A)cosh(-) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 x 2 3 +--R (- 8B cosh(x) - 12B cosh(x) - 4B cosh(x))sinh(-) - 8B cosh(x) +--R 2 +--R + +--R x 2 2 +--R ((4B - 4A)cosh(-) - 12B)cosh(x) +--R 2 +--R + +--R x 2 x 2 +--R ((6B - 6A)cosh(-) - 4B)cosh(x) + (2B - 2A)cosh(-) +--R 2 2 +--R * +--R sinh(x) +--R + +--R 4 3 2 x 2 4 +--R (- 4B cosh(x) - 8B cosh(x) - 4B cosh(x) )sinh(-) - 4B cosh(x) +--R 2 +--R + +--R x 2 3 x 2 2 +--R ((2B - 2A)cosh(-) - 8B)cosh(x) + ((4B - 4A)cosh(-) - 4B)cosh(x) +--R 2 2 +--R + +--R x 2 +--R (2B - 2A)cosh(-) cosh(x) +--R 2 +--R * +--R +-------------------+ +--R | a +--R |------------------- +--R \|2sinh(x) + 2cosh(x) +--R / +--R x 2 2 +--R ((2cosh(x) + 2)sinh(-) + 2cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R ((4cosh(x) + 6cosh(x) + 2)sinh(-) + 4cosh(x) + 6cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 3 2 x 2 3 2 +--R (2cosh(x) + 4cosh(x) + 2cosh(x))sinh(-) + 2cosh(x) + 4cosh(x) +--R 2 +--R + +--R 2cosh(x) +--R * +--R +-------------------+ +--R | a +-------------+ +--R |------------------- \|a cosh(x) + a +--R \|2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 305 + +--S 306 of 502 +t0861:= (A+B*cosh(x))/(a-a*cosh(x))^(1/2) +--R +--R +--R B cosh(x) + A +--R (151) ------------------ +--R +---------------+ +--R \|- a cosh(x) + a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 502 +r0861:= -2*(A+B)*atanh(cosh(1/2*x))*sinh(1/2*x)/(a-a*cosh(x))^(1/2)+_ + 2*B*sinh(x)/(a-a*cosh(x))^(1/2) +--R +--R +--R x x +--R (- 2B - 2A)sinh(-)atanh(cosh(-)) + 2B sinh(x) +--R 2 2 +--R (152) --------------------------------------------- +--R +---------------+ +--R \|- a cosh(x) + a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 502 +a0861:= integrate(t0861,x) +--R +--R +--R (153) +--R +---+ +---------------------+ +--R | 2 | a +--R ((B + A)sinh(x) + (B + A)cosh(x)) |- - |- ------------------- +--R \| a \| 2sinh(x) + 2cosh(x) +--R * +--R log +--R +---+ +---------------------+ +--R | 2 | a +--R (2sinh(x) + 2cosh(x)) |- - |- ------------------- - sinh(x) +--R \| a \| 2sinh(x) + 2cosh(x) +--R + +--R - cosh(x) - 1 +--R / +--R sinh(x) + cosh(x) - 1 +--R + +--R B sinh(x) + B cosh(x) + B +--R / +--R +---------------------+ +--R | a +--R (sinh(x) + cosh(x)) |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 502 +m0861:= a0861-r0861 +--R +--R +--R (154) +--R +---+ +--R | 2 +---------------+ +--R ((B + A)sinh(x) + (B + A)cosh(x)) |- - \|- a cosh(x) + a +--R \| a +--R * +--R +---------------------+ +--R | a +--R |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R * +--R log +--R +---+ +---------------------+ +--R | 2 | a +--R (2sinh(x) + 2cosh(x)) |- - |- ------------------- - sinh(x) +--R \| a \| 2sinh(x) + 2cosh(x) +--R + +--R - cosh(x) - 1 +--R / +--R sinh(x) + cosh(x) - 1 +--R + +--R x x x +--R ((2B + 2A)sinh(-)sinh(x) + (2B + 2A)cosh(x)sinh(-))atanh(cosh(-)) +--R 2 2 2 +--R + +--R 2 +--R - 2B sinh(x) - 2B cosh(x)sinh(x) +--R * +--R +---------------------+ +--R | a +--R |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R + +--R +---------------+ +--R (B sinh(x) + B cosh(x) + B)\|- a cosh(x) + a +--R / +--R +---------------------+ +--R +---------------+ | a +--R (sinh(x) + cosh(x))\|- a cosh(x) + a |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 309 + +--S 310 of 502 +d0861:= D(m0861,x) +--R +--R +--R (155) +--R x 2 x 3 +--R ((- 2B - 2A)cosh(-) + 2B + 2A)sinh(-)sinh(x) +--R 2 2 +--R + +--R x 2 +--R ((- 4B - 4A)cosh(-) + 4B + 4A)cosh(x) +--R 2 +--R + +--R x 2 +--R (2B + 2A)cosh(-) - 2B - 2A +--R 2 +--R * +--R x +--R sinh(-) +--R 2 +--R + +--R x 3 x +--R ((2B + 2A)cosh(-) + (- 2B - 2A)cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x +--R (- 2B - 2A)cosh(-) + (2B + 2A)cosh(-) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R x 2 2 +--R ((- 2B - 2A)cosh(-) + 2B + 2A)cosh(x) +--R 2 +--R + +--R x 2 +--R ((2B + 2A)cosh(-) - 2B - 2A)cosh(x) +--R 2 +--R * +--R x +--R sinh(-) +--R 2 +--R + +--R x 3 x 2 +--R ((4B + 4A)cosh(-) + (- 4B - 4A)cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x +--R ((- 6B - 6A)cosh(-) + (6B + 6A)cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x +--R (2B + 2A)cosh(-) + (- 2B - 2A)cosh(-) +--R 2 2 +--R * +--R sinh(x) +--R + +--R x 3 x 3 +--R ((2B + 2A)cosh(-) + (- 2B - 2A)cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x 2 +--R ((- 4B - 4A)cosh(-) + (4B + 4A)cosh(-))cosh(x) +--R 2 2 +--R + +--R x 3 x +--R ((2B + 2A)cosh(-) + (- 2B - 2A)cosh(-))cosh(x) +--R 2 2 +--R * +--R x +--R atanh(cosh(-)) +--R 2 +--R + +--R x 2 4 +--R (2B cosh(-) - 2B)sinh(x) +--R 2 +--R + +--R x 2 x 2 3 +--R ((4B cosh(-) - 4B)cosh(x) - 2B cosh(-) + 2B)sinh(x) +--R 2 2 +--R + +--R x 2 +--R ((- 2B - 2A)cosh(x) + 2B + 2A)sinh(-) +--R 2 +--R + +--R x 2 2 x 2 +--R (- 2B cosh(-) + 2B)cosh(x) + (2B cosh(-) - 2B)cosh(x) +--R 2 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 2 x 2 +--R ((- 4B - 4A)cosh(x) + (6B + 6A)cosh(x) - 2B - 2A)sinh(-) +--R 2 +--R + +--R x 2 3 x 2 2 +--R (- 8B cosh(-) + 8B)cosh(x) + (12B cosh(-) - 12B)cosh(x) +--R 2 2 +--R + +--R x 2 +--R (- 4B cosh(-) + 4B)cosh(x) +--R 2 +--R * +--R sinh(x) +--R + +--R 3 2 +--R ((- 2B - 2A)cosh(x) + (4B + 4A)cosh(x) + (- 2B - 2A)cosh(x)) +--R * +--R x 2 +--R sinh(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (- 4B cosh(-) + 4B)cosh(x) + (8B cosh(-) - 8B)cosh(x) +--R 2 2 +--R + +--R x 2 2 +--R (- 4B cosh(-) + 4B)cosh(x) +--R 2 +--R * +--R +---------------------+ +--R | a +--R |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R + +--R x 2 x 2 2 +--R ((B cosh(-) - B)cosh(x) - B cosh(-) + B)sinh(x) +--R 2 2 +--R + +--R x 2 2 +--R (2B cosh(-) - 2B)cosh(x) +--R 2 +--R + +--R x 2 x 2 +--R ((- 2B + 2A)cosh(-) + 2B - 2A)cosh(x) - 2A cosh(-) + 2A +--R 2 2 +--R * +--R sinh(x) +--R + +--R x 2 3 x 2 2 +--R (B cosh(-) - B)cosh(x) + ((- B + 2A)cosh(-) + B - 2A)cosh(x) +--R 2 2 +--R + +--R x 2 x 2 +--R ((B - 2A)cosh(-) - B + 2A)cosh(x) - B cosh(-) + B +--R 2 2 +--R * +--R +---------------+ +--R \|- a cosh(x) + a +--R / +--R x 2 x 2 2 +--R ((2cosh(-) - 2)cosh(x) - 2cosh(-) + 2)sinh(x) +--R 2 2 +--R + +--R x 2 2 x 2 x 2 +--R ((4cosh(-) - 4)cosh(x) + (- 6cosh(-) + 6)cosh(x) + 2cosh(-) - 2) +--R 2 2 2 +--R * +--R sinh(x) +--R + +--R x 2 3 x 2 2 +--R (2cosh(-) - 2)cosh(x) + (- 4cosh(-) + 4)cosh(x) +--R 2 2 +--R + +--R x 2 +--R (2cosh(-) - 2)cosh(x) +--R 2 +--R * +--R +---------------------+ +--R +---------------+ | a +--R \|- a cosh(x) + a |- ------------------- +--R \| 2sinh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 310 + +--S 311 of 502 +t0862:= (A+B*cosh(x))/(a+b*cosh(x))^(1/2) +--R +--R +--R B cosh(x) + A +--R (156) ---------------- +--R +-------------+ +--R \|b cosh(x) + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 502 +r0862:= -2*%i*B*(a+b*cosh(x))^(1/2)*EllipticE(1/2*%i*x,2*b/(a+b))/b/_ + ((a+b*cosh(x))/(a+b))^(1/2)-2*%i*(A*b-a*B)*_ + ((a+b*cosh(x))/(a+b))^(1/2)*EllipticF(1/2*%i*x,2*b/(a+b))/_ + b/(a+b*cosh(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 312 + +--S 313 of 502 +a0862:= integrate(t0862,x) +--R +--R +--R x +--R ++ B cosh(%I) + A +--R (157) | ----------------- d%I +--R ++ +--------------+ +--R \|b cosh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 502 +--m0862:= a0862-r0862 +--E 314 + +--S 315 of 502 +--d0862:= D(m0862,x) +--E 315 + +--S 316 of 502 +t0863:= (1+sinh(x)^2)/(1-sinh(x)^2) +--R +--R +--R 2 +--R - sinh(x) - 1 +--R (158) -------------- +--R 2 +--R sinh(x) - 1 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 502 +r0863:= -x+atanh(2^(1/2)*tanh(x))*2^(1/2) +--R +--R +--R +-+ +-+ +--R (159) \|2 atanh(\|2 tanh(x)) - x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 502 +a0863:= integrate(t0863,x) +--R +--R +--R (160) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R - 2x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 502 +m0863:= a0863-r0863 +--R +--R +--R (161) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ +-+ +--R - 2\|2 atanh(\|2 tanh(x)) +--R / +--R 2 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 502 +d0863:= D(m0863,x) +--R +--R +--R (162) +--R +-+ 4 +-+ 3 +--R (4\|2 - 6)sinh(x) + (24\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 56\|2 + 84)cosh(x) - 8\|2 + 12)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 - 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (- 8\|2 + 12)cosh(x) - 12\|2 + 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (4\|2 - 6)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((40\|2 - 60)cosh(x) - 16\|2 + 24)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (- 16\|2 + 24)cosh(x) + 12\|2 - 18 +--R / +--R +-+ 4 +-+ 3 +--R (12\|2 - 18)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((24\|2 - 36)cosh(x) - 40\|2 + 60)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (72\|2 - 96)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (12\|2 - 18)cosh(x) + (- 40\|2 + 60)cosh(x) + 12\|2 - 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 12\|2 + 18)cosh(x) + 20\|2 - 30)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((12\|2 - 16)cosh(x) + (- 36\|2 + 48)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + (20\|2 - 30)cosh(x) - 6\|2 + 9 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 502 +t0864:= (1-sinh(x)^2)/(1+sinh(x)^2) +--R +--R +--R 2 +--R - sinh(x) + 1 +--R (163) -------------- +--R 2 +--R sinh(x) + 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 502 +r0864:= -x+2*tanh(x) +--R +--R +--R (164) 2tanh(x) - x +--R Type: Expression(Integer) +--E 322 + +--S 323 of 502 +a0864:= integrate(t0864,x) +--R +--R +--R 2sinh(x) + (- x - 2)cosh(x) +--R (165) --------------------------- +--R cosh(x) +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 502 +m0864:= a0864-r0864 +--R +--R +--R - 2cosh(x)tanh(x) + 2sinh(x) - 2cosh(x) +--R (166) --------------------------------------- +--R cosh(x) +--R Type: Expression(Integer) +--E 324 + +--S 325 of 502 +d0864:= D(m0864,x) +--R +--R +--R 2 2 2 +--R 2cosh(x) tanh(x) - 2sinh(x) +--R (167) ----------------------------- +--R 2 +--R cosh(x) +--R Type: Expression(Integer) +--E 325 + +--S 326 of 502 +t0865:= (1+cosh(x)^2)/(1-cosh(x)^2) +--R +--R +--R 2 +--R - cosh(x) - 1 +--R (168) -------------- +--R 2 +--R cosh(x) - 1 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 502 +r0865:= -x+2*coth(x) +--R +--R +--R (169) 2coth(x) - x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 502 +a0865:= integrate(t0865,x) +--R +--R +--R (- x - 2)sinh(x) + 2cosh(x) +--R (170) --------------------------- +--R sinh(x) +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 502 +m0865:= a0865-r0865 +--R +--R +--R (- 2coth(x) - 2)sinh(x) + 2cosh(x) +--R (171) ---------------------------------- +--R sinh(x) +--R Type: Expression(Integer) +--E 329 + +--S 330 of 502 +d0865:= D(m0865,x) +--R +--R +--R 2 2 2 +--R 2coth(x) sinh(x) - 2cosh(x) +--R (172) ----------------------------- +--R 2 +--R sinh(x) +--R Type: Expression(Integer) +--E 330 + +--S 331 of 502 +t0866:= (1-cosh(x)^2)/(1+cosh(x)^2) +--R +--R +--R 2 +--R - cosh(x) + 1 +--R (173) -------------- +--R 2 +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 502 +r0866:= -x+atanh(1/2*2^(1/2)*tanh(x))*2^(1/2) +--R +--R +--R +-+ +--R +-+ \|2 tanh(x) +--R (174) \|2 atanh(-----------) - x +--R 2 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 502 +a0866:= integrate(t0866,x) +--R +--R +--R (175) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) - 2\|2 + 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R - 2x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 502 +m0866:= a0866-r0866 +--R +--R +--R (176) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) - 2\|2 + 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ +--R +-+ \|2 tanh(x) +--R - 2\|2 atanh(-----------) +--R 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 502 +d0866:= D(m0866,x) +--R +--R +--R (177) +--R +-+ 4 +-+ 3 +--R (- 4\|2 + 6)sinh(x) + (24\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 40\|2 + 60)cosh(x) - 16\|2 + 24)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 - 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 4\|2 + 6)cosh(x) + (- 16\|2 + 24)cosh(x) - 12\|2 + 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 4\|2 + 6)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((56\|2 - 84)cosh(x) - 8\|2 + 12)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 4\|2 + 6)cosh(x) + (- 8\|2 + 12)cosh(x) + 12\|2 - 18 +--R / +--R +-+ 4 +-+ 3 +--R (6\|2 - 9)sinh(x) + (- 12\|2 + 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((12\|2 - 18)cosh(x) + 20\|2 - 30)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 12\|2 + 16)cosh(x) + (- 36\|2 + 48)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (6\|2 - 9)cosh(x) + (20\|2 - 30)cosh(x) + 6\|2 - 9 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 12\|2 + 18)sinh(x) + (24\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 24\|2 + 36)cosh(x) - 40\|2 + 60)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 - 32)cosh(x) + (72\|2 - 96)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 12\|2 + 18)cosh(x) + (- 40\|2 + 60)cosh(x) - 12\|2 + 18 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 502 +t0867:= (cosh(x)*coth(x))^(1/2) +--R +--R +--R +--------------+ +--R (178) \|cosh(x)coth(x) +--R Type: Expression(Integer) +--E 336 + +--S 337 of 502 +r0867:= 2*(cosh(x)*coth(x))^(1/2)*tanh(x) +--R +--R +--R +--------------+ +--R (179) 2tanh(x)\|cosh(x)coth(x) +--R Type: Expression(Integer) +--E 337 + +--S 338 of 502 +a0867:= integrate(t0867,x) +--R +--R +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R (180) ------------------------------------------------ +--R sinh(x) + cosh(x) +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 502 +m0867:= a0867-r0867 +--R +--R +--R (181) +--R +--------------+ +--R (- 2sinh(x) - 2cosh(x))tanh(x)\|cosh(x)coth(x) +--R + +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 339 + +--S 340 of 502 +d0867:= D(m0867,x) +--R +--R +--R (182) +--R 2 2 +--------------+ +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)\|cosh(x)coth(x) +--R + +--R 2 3 2 +--R (2cosh(x)coth(x)sinh(x) - 2cosh(x) coth(x))tanh(x) +--R + +--R 3 2 2 +--R - coth(x)sinh(x) + (cosh(x)coth(x) - cosh(x))sinh(x) +--R + +--R 2 3 2 3 +--R cosh(x) coth(x)sinh(x) - cosh(x) coth(x) + cosh(x) +--R * +--R tanh(x) +--R + +--R 2 3 +--R - 2cosh(x)coth(x)sinh(x) + 2cosh(x) coth(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R +---------------------------------------------+ +--R | 2 2 +--R 2 2 |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R (sinh(x) - cosh(x) ) |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R Type: Expression(Integer) +--E 340 + +--S 341 of 502 +t0868:= (cosh(x)*coth(x))^(3/2) +--R +--R +--R +--------------+ +--R (183) cosh(x)coth(x)\|cosh(x)coth(x) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 502 +r0868:= -2/3*(4-cosh(x)^2)*(cosh(x)*coth(x))^(1/2)*sech(x) +--R +--R +--R 2 +--------------+ +--R (2cosh(x) - 8)sech(x)\|cosh(x)coth(x) +--R (184) --------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 502 +a0868:= integrate(t0868,x) +--R +--R +--R (185) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 14)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 28cosh(x))sinh(x) + cosh(x) - 14cosh(x) + 1 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) - 6)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) - 12cosh(x))sinh(x) + 6cosh(x) - 6cosh(x) +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 502 +m0868:= a0868-r0868 +--R +--R +--R (186) +--R 2 4 +--R (- 4cosh(x) + 16)sech(x)sinh(x) +--R + +--R 3 3 +--R (- 16cosh(x) + 64cosh(x))sech(x)sinh(x) +--R + +--R 4 2 2 +--R (- 24cosh(x) + 100cosh(x) - 16)sech(x)sinh(x) +--R + +--R 5 3 +--R (- 16cosh(x) + 72cosh(x) - 32cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 +--R (- 4cosh(x) + 20cosh(x) - 16cosh(x) )sech(x) +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 14)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 28cosh(x))sinh(x) + cosh(x) - 14cosh(x) + 1 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) - 6)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) - 12cosh(x))sinh(x) + 6cosh(x) - 6cosh(x) +--R Type: Expression(Integer) +--E 344 + +--S 345 of 502 +d0868:= D(m0868,x) +--R +--R +--R (187) +--R 6 5 2 4 +--R - 3sinh(x) - 18cosh(x)sinh(x) + (- 45cosh(x) - 9)sinh(x) +--R + +--R 3 3 +--R (- 60cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) - 54cosh(x) - 9)sinh(x) +--R + +--R 5 3 6 +--R (- 18cosh(x) - 36cosh(x) - 18cosh(x))sinh(x) - 3cosh(x) +--R + +--R 4 2 +--R - 9cosh(x) - 9cosh(x) - 3 +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R + +--R 3 5 +--R (4cosh(x) - 16cosh(x))coth(x)sech(x)sinh(x) +--R + +--R 4 2 4 +--R (12cosh(x) - 48cosh(x) )coth(x)sech(x)sinh(x) +--R + +--R 5 3 3 +--R (8cosh(x) - 36cosh(x) + 16cosh(x))coth(x)sech(x)sinh(x) +--R + +--R 6 4 2 2 +--R (- 8cosh(x) + 28cosh(x) + 16cosh(x) )coth(x)sech(x)sinh(x) +--R + +--R 7 5 3 +--R (- 12cosh(x) + 52cosh(x) - 16cosh(x) )coth(x)sech(x)sinh(x) +--R + +--R 8 6 4 +--R (- 4cosh(x) + 20cosh(x) - 16cosh(x) )coth(x)sech(x) +--R * +--R tanh(x) +--R + +--R 2 6 +--R (- 10cosh(x) + 8)coth(x)sech(x)sinh(x) +--R + +--R 3 2 +--R (2cosh(x) - 8cosh(x))coth(x) +--R + +--R 3 3 +--R (- 30cosh(x) + 24cosh(x))coth(x) - 2cosh(x) + 8cosh(x) +--R * +--R 5 +--R sech(x)sinh(x) +--R + +--R 4 2 2 +--R (6cosh(x) - 24cosh(x) )coth(x) +--R + +--R 4 2 4 2 +--R (- 20cosh(x) + 26cosh(x) - 8)coth(x) - 6cosh(x) + 24cosh(x) +--R * +--R 4 +--R sech(x)sinh(x) +--R + +--R 5 3 2 +--R (4cosh(x) - 18cosh(x) + 8cosh(x))coth(x) +--R + +--R 5 3 5 +--R (20cosh(x) - 6cosh(x) - 8cosh(x))coth(x) - 4cosh(x) +--R + +--R 3 +--R 18cosh(x) - 8cosh(x) +--R * +--R 3 +--R sech(x)sinh(x) +--R + +--R 6 4 2 2 +--R (- 4cosh(x) + 14cosh(x) + 8cosh(x) )coth(x) +--R + +--R 6 4 2 6 +--R (30cosh(x) - 34cosh(x) + 8cosh(x) )coth(x) + 4cosh(x) +--R + +--R 4 2 +--R - 14cosh(x) - 8cosh(x) +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 7 5 3 2 +--R (- 6cosh(x) + 26cosh(x) - 8cosh(x) )coth(x) +--R + +--R 7 5 3 7 +--R (10cosh(x) - 18cosh(x) + 8cosh(x) )coth(x) + 6cosh(x) +--R + +--R 5 3 +--R - 26cosh(x) + 8cosh(x) +--R * +--R sech(x)sinh(x) +--R + +--R 8 6 4 2 8 +--R (- 2cosh(x) + 10cosh(x) - 8cosh(x) )coth(x) + 2cosh(x) +--R + +--R 6 4 +--R - 10cosh(x) + 8cosh(x) +--R * +--R sech(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 5 4 2 3 +--R 6sinh(x) + 18cosh(x)sinh(x) + (12cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 2 +--R (- 12cosh(x) - 6cosh(x))sinh(x) + (- 18cosh(x) + 6cosh(x) )sinh(x) +--R + +--R 5 3 +--R - 6cosh(x) + 6cosh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--------------+ +--R |--------------------------------------------- \|cosh(x)coth(x) +--R \| sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 345 + +--S 346 of 502 +t0869:= (cosh(x)*coth(x))^(5/2) +--R +--R +--R 2 2 +--------------+ +--R (188) cosh(x) coth(x) \|cosh(x)coth(x) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 502 +r0869:= 2/15*(cosh(x)*coth(x))^(1/2)*(32-(8-3*cosh(x)^2)*coth(x)^2)*tanh(x) +--R +--R +--R 2 2 +--------------+ +--R ((6cosh(x) - 16)coth(x) + 64)tanh(x)\|cosh(x)coth(x) +--R (189) ------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 502 +a0869:= integrate(t0869,x) +--R +--R +--R (190) +--R 8 7 2 6 +--R 3sinh(x) + 24cosh(x)sinh(x) + (84cosh(x) + 108)sinh(x) +--R + +--R 3 5 +--R (168cosh(x) + 648cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (210cosh(x) + 1620cosh(x) - 302)sinh(x) +--R + +--R 5 3 3 +--R (168cosh(x) + 2160cosh(x) - 1208cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (84cosh(x) + 1620cosh(x) - 1812cosh(x) + 108)sinh(x) +--R + +--R 7 5 3 +--R (24cosh(x) + 648cosh(x) - 1208cosh(x) + 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 3cosh(x) + 108cosh(x) - 302cosh(x) + 108cosh(x) + 3 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 7 6 2 5 +--R 60sinh(x) + 420cosh(x)sinh(x) + (1260cosh(x) - 120)sinh(x) +--R + +--R 3 4 +--R (2100cosh(x) - 600cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (2100cosh(x) - 1200cosh(x) + 60)sinh(x) +--R + +--R 5 3 2 +--R (1260cosh(x) - 1200cosh(x) + 180cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (420cosh(x) - 600cosh(x) + 180cosh(x) )sinh(x) + 60cosh(x) +--R + +--R 5 3 +--R - 120cosh(x) + 60cosh(x) +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 502 +m0869:= a0869-r0869 +--R +--R +--R (191) +--R 2 2 7 +--R ((- 24cosh(x) + 64)coth(x) - 256)sinh(x) +--R + +--R 3 2 6 +--R ((- 168cosh(x) + 448cosh(x))coth(x) - 1792cosh(x))sinh(x) +--R + +--R 4 2 2 2 +--R ((- 504cosh(x) + 1392cosh(x) - 128)coth(x) - 5376cosh(x) + 512) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 840cosh(x) + 2480cosh(x) - 640cosh(x))coth(x) +--R + +--R 3 +--R - 8960cosh(x) + 2560cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 840cosh(x) + 2720cosh(x) - 1304cosh(x) + 64)coth(x) +--R + +--R 4 2 +--R - 8960cosh(x) + 5120cosh(x) - 256 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 504cosh(x) + 1824cosh(x) - 1352cosh(x) + 192cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 5 3 +--R - 5376cosh(x) + 5120cosh(x) - 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 168cosh(x) + 688cosh(x) - 712cosh(x) + 192cosh(x) )coth(x) +--R + +--R 6 4 2 +--R - 1792cosh(x) + 2560cosh(x) - 768cosh(x) +--R * +--R sinh(x) +--R + +--R 9 7 5 3 2 +--R (- 24cosh(x) + 112cosh(x) - 152cosh(x) + 64cosh(x) )coth(x) +--R + +--R 7 5 3 +--R - 256cosh(x) + 512cosh(x) - 256cosh(x) +--R * +--R +--------------+ +--R tanh(x)\|cosh(x)coth(x) +--R + +--R 8 7 2 6 +--R 3sinh(x) + 24cosh(x)sinh(x) + (84cosh(x) + 108)sinh(x) +--R + +--R 3 5 +--R (168cosh(x) + 648cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (210cosh(x) + 1620cosh(x) - 302)sinh(x) +--R + +--R 5 3 3 +--R (168cosh(x) + 2160cosh(x) - 1208cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (84cosh(x) + 1620cosh(x) - 1812cosh(x) + 108)sinh(x) +--R + +--R 7 5 3 +--R (24cosh(x) + 648cosh(x) - 1208cosh(x) + 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 3cosh(x) + 108cosh(x) - 302cosh(x) + 108cosh(x) + 3 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 7 6 2 5 +--R 60sinh(x) + 420cosh(x)sinh(x) + (1260cosh(x) - 120)sinh(x) +--R + +--R 3 4 +--R (2100cosh(x) - 600cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (2100cosh(x) - 1200cosh(x) + 60)sinh(x) +--R + +--R 5 3 2 +--R (1260cosh(x) - 1200cosh(x) + 180cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (420cosh(x) - 600cosh(x) + 180cosh(x) )sinh(x) + 60cosh(x) +--R + +--R 5 3 +--R - 120cosh(x) + 60cosh(x) +--R Type: Expression(Integer) +--E 349 + +--S 350 of 502 +d0869:= D(m0869,x) +--R +--R +--R (192) +--R 10 9 2 8 +--R - 15sinh(x) - 150cosh(x)sinh(x) + (- 675cosh(x) - 75)sinh(x) +--R + +--R 3 7 +--R (- 1800cosh(x) - 600cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 3150cosh(x) - 2100cosh(x) - 150)sinh(x) +--R + +--R 5 3 5 +--R (- 3780cosh(x) - 4200cosh(x) - 900cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 3150cosh(x) - 5250cosh(x) - 2250cosh(x) - 150)sinh(x) +--R + +--R 7 5 3 3 +--R (- 1800cosh(x) - 4200cosh(x) - 3000cosh(x) - 600cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 675cosh(x) - 2100cosh(x) - 2250cosh(x) - 900cosh(x) - 75) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 150cosh(x) - 600cosh(x) - 900cosh(x) - 600cosh(x) +--R + +--R - 150cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 15cosh(x) - 75cosh(x) - 150cosh(x) - 150cosh(x) - 75cosh(x) +--R + +--R - 15 +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R + +--R 3 3 8 +--R ((24cosh(x) - 64cosh(x))coth(x) + 256cosh(x)coth(x))sinh(x) +--R + +--R 4 2 3 2 +--R ((144cosh(x) - 384cosh(x) )coth(x) + 1536cosh(x) coth(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 3 +--R (336cosh(x) - 944cosh(x) + 128cosh(x))coth(x) +--R + +--R 3 +--R (3584cosh(x) - 512cosh(x))coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (336cosh(x) - 1088cosh(x) + 512cosh(x) )coth(x) +--R + +--R 4 2 +--R (3584cosh(x) - 2048cosh(x) )coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 240cosh(x) + 664cosh(x) - 64cosh(x))coth(x) +--R + +--R 3 +--R (- 2560cosh(x) + 256cosh(x))coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 336cosh(x) + 896cosh(x) + 48cosh(x) - 128cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 6 2 +--R (- 3584cosh(x) + 512cosh(x) )coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (- 336cosh(x) + 1136cosh(x) - 640cosh(x) )coth(x) +--R + +--R 7 5 +--R (- 3584cosh(x) + 2560cosh(x) )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 +--R (- 144cosh(x) + 576cosh(x) - 560cosh(x) + 128cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 8 6 4 +--R (- 1536cosh(x) + 2048cosh(x) - 512cosh(x) )coth(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R (- 24cosh(x) + 112cosh(x) - 152cosh(x) + 64cosh(x) )coth(x) +--R + +--R 9 7 5 +--R (- 256cosh(x) + 512cosh(x) - 256cosh(x) )coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 9 +--R ((- 60cosh(x) + 32)coth(x) - 128coth(x))sinh(x) +--R + +--R 3 4 +--R (60cosh(x) - 160cosh(x))coth(x) +--R + +--R 3 3 +--R (- 360cosh(x) + 192cosh(x))coth(x) +--R + +--R 3 2 +--R (- 60cosh(x) + 288cosh(x))coth(x) - 768cosh(x)coth(x) +--R + +--R - 128cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 4 +--R (360cosh(x) - 960cosh(x) )coth(x) +--R + +--R 4 2 3 +--R (- 840cosh(x) + 568cosh(x) - 64)coth(x) +--R + +--R 4 2 2 +--R (- 360cosh(x) + 1728cosh(x) )coth(x) +--R + +--R 2 2 +--R (- 1792cosh(x) + 256)coth(x) - 768cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 4 +--R (840cosh(x) - 2360cosh(x) + 320cosh(x))coth(x) +--R + +--R 5 3 3 +--R (- 840cosh(x) + 928cosh(x) - 256cosh(x))coth(x) +--R + +--R 5 3 2 +--R (- 840cosh(x) + 4152cosh(x) - 576cosh(x))coth(x) +--R + +--R 3 3 +--R (- 1792cosh(x) + 1024cosh(x))coth(x) - 1792cosh(x) +--R + +--R 256cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 4 +--R (840cosh(x) - 2720cosh(x) + 1280cosh(x) )coth(x) +--R + +--R 4 2 3 +--R (600cosh(x) - 380cosh(x) + 32)coth(x) +--R + +--R 6 4 2 2 +--R (- 840cosh(x) + 4512cosh(x) - 2304cosh(x) )coth(x) +--R + +--R 2 4 2 +--R (1280cosh(x) - 128)coth(x) - 1792cosh(x) + 1024cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 4 +--R (- 600cosh(x) + 1660cosh(x) - 160cosh(x))coth(x) +--R + +--R 7 5 3 3 +--R (840cosh(x) - 448cosh(x) - 120cosh(x) + 64cosh(x))coth(x) +--R + +--R 5 3 2 +--R (600cosh(x) - 2940cosh(x) + 288cosh(x))coth(x) +--R + +--R 5 3 +--R (1792cosh(x) - 256cosh(x))coth(x) + 1280cosh(x) - 128cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 840cosh(x) + 2240cosh(x) + 120cosh(x) - 320cosh(x) ) +--R * +--R 4 +--R coth(x) +--R + +--R 8 6 4 3 +--R (840cosh(x) - 1048cosh(x) + 320cosh(x) )coth(x) +--R + +--R 8 6 4 2 +--R (840cosh(x) - 4032cosh(x) - 120cosh(x) + 576cosh(x) ) +--R * +--R 2 +--R coth(x) +--R + +--R 6 4 6 +--R (1792cosh(x) - 1280cosh(x) )coth(x) + 1792cosh(x) +--R + +--R 2 +--R - 256cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 4 +--R (- 840cosh(x) + 2840cosh(x) - 1600cosh(x) )coth(x) +--R + +--R 9 7 5 3 +--R (360cosh(x) - 672cosh(x) + 376cosh(x) - 64cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 9 7 5 2 +--R (840cosh(x) - 4632cosh(x) + 2880cosh(x) )coth(x) +--R + +--R 7 5 3 +--R (768cosh(x) - 1024cosh(x) + 256cosh(x) )coth(x) +--R + +--R 7 5 +--R 1792cosh(x) - 1280cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 +--R - 360cosh(x) + 1440cosh(x) - 1400cosh(x) +--R + +--R 4 +--R 320cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 10 8 6 4 +--R (60cosh(x) - 152cosh(x) + 124cosh(x) - 32cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 10 8 6 4 +--R (360cosh(x) - 2208cosh(x) + 2424cosh(x) - 576cosh(x) ) +--R * +--R 2 +--R coth(x) +--R + +--R 8 6 4 +--R (128cosh(x) - 256cosh(x) + 128cosh(x) )coth(x) +--R + +--R 8 6 4 +--R 768cosh(x) - 1024cosh(x) + 256cosh(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 4 +--R (- 60cosh(x) + 280cosh(x) - 380cosh(x) + 160cosh(x) )coth(x) +--R + +--R 11 9 7 5 2 +--R (60cosh(x) - 408cosh(x) + 636cosh(x) - 288cosh(x) )coth(x) +--R + +--R 9 7 5 +--R 128cosh(x) - 256cosh(x) + 128cosh(x) +--R * +--R tanh(x) +--R + +--R 3 3 8 +--R ((- 24cosh(x) + 64cosh(x))coth(x) - 256cosh(x)coth(x))sinh(x) +--R + +--R 4 2 3 2 7 +--R ((- 144cosh(x) + 384cosh(x) )coth(x) - 1536cosh(x) coth(x))sinh(x) +--R + +--R 5 3 3 +--R (- 336cosh(x) + 944cosh(x) - 128cosh(x))coth(x) +--R + +--R 3 +--R (- 3584cosh(x) + 512cosh(x))coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- 336cosh(x) + 1088cosh(x) - 512cosh(x) )coth(x) +--R + +--R 4 2 +--R (- 3584cosh(x) + 2048cosh(x) )coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 +--R (240cosh(x) - 664cosh(x) + 64cosh(x))coth(x) +--R + +--R 3 +--R (2560cosh(x) - 256cosh(x))coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (336cosh(x) - 896cosh(x) - 48cosh(x) + 128cosh(x) )coth(x) +--R + +--R 6 2 +--R (3584cosh(x) - 512cosh(x) )coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (336cosh(x) - 1136cosh(x) + 640cosh(x) )coth(x) +--R + +--R 7 5 +--R (3584cosh(x) - 2560cosh(x) )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 3 +--R (144cosh(x) - 576cosh(x) + 560cosh(x) - 128cosh(x) )coth(x) +--R + +--R 8 6 4 +--R (1536cosh(x) - 2048cosh(x) + 512cosh(x) )coth(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R (24cosh(x) - 112cosh(x) + 152cosh(x) - 64cosh(x) )coth(x) +--R + +--R 9 7 5 +--R (256cosh(x) - 512cosh(x) + 256cosh(x) )coth(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 8 7 2 6 +--R 60sinh(x) + 360cosh(x)sinh(x) + (840cosh(x) - 120)sinh(x) +--R + +--R 3 5 2 4 +--R (840cosh(x) - 480cosh(x))sinh(x) + (- 600cosh(x) + 60)sinh(x) +--R + +--R 5 3 +--R (- 840cosh(x) + 120cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 840cosh(x) + 600cosh(x) )sinh(x) +--R + +--R 7 5 3 8 +--R (- 360cosh(x) + 480cosh(x) - 120cosh(x) )sinh(x) - 60cosh(x) +--R + +--R 6 4 +--R 120cosh(x) - 60cosh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--------------+ +--R |--------------------------------------------- \|cosh(x)coth(x) +--R \| sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 350 + +--S 351 of 502 +t0870:= (sinh(x)*tanh(x))^(1/2) +--R +--R +--R +--------------+ +--R (193) \|sinh(x)tanh(x) +--R Type: Expression(Integer) +--E 351 + +--S 352 of 502 +r0870:= 2*coth(x)*(sinh(x)*tanh(x))^(1/2) +--R +--R +--R +--------------+ +--R (194) 2coth(x)\|sinh(x)tanh(x) +--R Type: Expression(Integer) +--E 352 + +--S 353 of 502 +a0870:= integrate(t0870,x) +--R +--R +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R (195) ------------------------------------------------ +--R sinh(x) + cosh(x) +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 502 +m0870:= a0870-r0870 +--R +--R +--R (196) +--R +--------------+ +--R (- 2coth(x)sinh(x) - 2cosh(x)coth(x))\|sinh(x)tanh(x) +--R + +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 354 + +--S 355 of 502 +d0870:= D(m0870,x) +--R +--R +--R (197) +--R 2 2 +--------------+ +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)\|sinh(x)tanh(x) +--R + +--R 3 2 2 +--R (coth(x)sinh(x) - cosh(x) coth(x)sinh(x))tanh(x) +--R + +--R 2 3 2 +--R (2coth(x) - 2)sinh(x) - cosh(x)coth(x)sinh(x) +--R + +--R 2 2 2 3 +--R (- 2cosh(x) coth(x) + 2cosh(x) )sinh(x) + cosh(x) coth(x) +--R * +--R tanh(x) +--R + +--R 3 2 +--R - coth(x)sinh(x) + cosh(x) coth(x)sinh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R +---------------------------------------------+ +--R | 2 2 +--R 2 2 |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R (sinh(x) - cosh(x) ) |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R * +--R +--------------+ +--R \|sinh(x)tanh(x) +--R Type: Expression(Integer) +--E 355 + +--S 356 of 502 +t0871:= (sinh(x)*tanh(x))^(3/2) +--R +--R +--R +--------------+ +--R (198) sinh(x)tanh(x)\|sinh(x)tanh(x) +--R Type: Expression(Integer) +--E 356 + +--S 357 of 502 +r0871:= 2/3*csch(x)*(4+sinh(x)^2)*(sinh(x)*tanh(x))^(1/2) +--R +--R +--R 2 +--------------+ +--R (2csch(x)sinh(x) + 8csch(x))\|sinh(x)tanh(x) +--R (199) ---------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 502 +a0871:= integrate(t0871,x) +--R +--R +--R (200) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 14)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 28cosh(x))sinh(x) + cosh(x) + 14cosh(x) + 1 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) + 6)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) + 12cosh(x))sinh(x) + 6cosh(x) + 6cosh(x) +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 502 +m0871:= a0871-r0871 +--R +--R +--R (201) +--R 6 5 +--R - 4csch(x)sinh(x) - 16cosh(x)csch(x)sinh(x) +--R + +--R 2 4 +--R (- 24cosh(x) - 20)csch(x)sinh(x) +--R + +--R 3 3 +--R (- 16cosh(x) - 72cosh(x))csch(x)sinh(x) +--R + +--R 4 2 2 +--R (- 4cosh(x) - 100cosh(x) - 16)csch(x)sinh(x) +--R + +--R 3 +--R (- 64cosh(x) - 32cosh(x))csch(x)sinh(x) +--R + +--R 4 2 +--R (- 16cosh(x) - 16cosh(x) )csch(x) +--R * +--R +--------------+ +--R \|sinh(x)tanh(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 14)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 28cosh(x))sinh(x) + cosh(x) + 14cosh(x) + 1 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) + 6)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) + 12cosh(x))sinh(x) + 6cosh(x) + 6cosh(x) +--R Type: Expression(Integer) +--E 359 + +--S 360 of 502 +d0871:= D(m0871,x) +--R +--R +--R (202) +--R 6 5 2 4 +--R - 3sinh(x) - 18cosh(x)sinh(x) + (- 45cosh(x) + 9)sinh(x) +--R + +--R 3 3 +--R (- 60cosh(x) + 36cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) + 54cosh(x) - 9)sinh(x) +--R + +--R 5 3 6 +--R (- 18cosh(x) + 36cosh(x) - 18cosh(x))sinh(x) - 3cosh(x) +--R + +--R 4 2 +--R 9cosh(x) - 9cosh(x) + 3 +--R * +--R +--------------+ +--R \|sinh(x)tanh(x) +--R + +--R 8 7 +--R 2csch(x)sinh(x) + 6cosh(x)csch(x)sinh(x) +--R + +--R 2 6 +--R (4cosh(x) + 10)csch(x)sinh(x) +--R + +--R 3 5 +--R (- 4cosh(x) + 26cosh(x))csch(x)sinh(x) +--R + +--R 4 2 4 +--R (- 6cosh(x) + 14cosh(x) + 8)csch(x)sinh(x) +--R + +--R 5 3 3 +--R (- 2cosh(x) - 18cosh(x) + 8cosh(x))csch(x)sinh(x) +--R + +--R 4 2 2 +--R (- 24cosh(x) - 8cosh(x) )csch(x)sinh(x) +--R + +--R 5 3 +--R (- 8cosh(x) - 8cosh(x) )csch(x)sinh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 8 +--R 4coth(x)csch(x)sinh(x) +--R + +--R 7 +--R (12cosh(x)coth(x) - 10cosh(x))csch(x)sinh(x) +--R + +--R 2 2 6 +--R ((8cosh(x) + 20)coth(x) - 30cosh(x) )csch(x)sinh(x) +--R + +--R 3 3 +--R ((- 8cosh(x) + 52cosh(x))coth(x) - 20cosh(x) - 18cosh(x)) +--R * +--R 5 +--R csch(x)sinh(x) +--R + +--R 4 2 4 +--R (- 12cosh(x) + 28cosh(x) + 16)coth(x) + 20cosh(x) +--R + +--R 2 +--R - 34cosh(x) +--R * +--R 4 +--R csch(x)sinh(x) +--R + +--R 5 3 5 +--R (- 4cosh(x) - 36cosh(x) + 16cosh(x))coth(x) + 30cosh(x) +--R + +--R 3 +--R - 6cosh(x) - 8cosh(x) +--R * +--R 3 +--R csch(x)sinh(x) +--R + +--R 4 2 6 4 +--R (- 48cosh(x) - 16cosh(x) )coth(x) + 10cosh(x) + 26cosh(x) +--R + +--R 2 +--R - 8cosh(x) +--R * +--R 2 +--R csch(x)sinh(x) +--R + +--R 5 3 5 3 +--R ((- 16cosh(x) - 16cosh(x) )coth(x) + 24cosh(x) + 8cosh(x) ) +--R * +--R csch(x)sinh(x) +--R + +--R 6 4 +--R (8cosh(x) + 8cosh(x) )csch(x) +--R * +--R tanh(x) +--R + +--R 8 7 +--R - 2csch(x)sinh(x) - 6cosh(x)csch(x)sinh(x) +--R + +--R 2 6 +--R (- 4cosh(x) - 10)csch(x)sinh(x) +--R + +--R 3 5 +--R (4cosh(x) - 26cosh(x))csch(x)sinh(x) +--R + +--R 4 2 4 +--R (6cosh(x) - 14cosh(x) - 8)csch(x)sinh(x) +--R + +--R 5 3 3 +--R (2cosh(x) + 18cosh(x) - 8cosh(x))csch(x)sinh(x) +--R + +--R 4 2 2 +--R (24cosh(x) + 8cosh(x) )csch(x)sinh(x) +--R + +--R 5 3 +--R (8cosh(x) + 8cosh(x) )csch(x)sinh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 5 4 2 3 +--R 6sinh(x) + 18cosh(x)sinh(x) + (12cosh(x) + 6)sinh(x) +--R + +--R 3 2 4 2 +--R (- 12cosh(x) + 6cosh(x))sinh(x) + (- 18cosh(x) - 6cosh(x) )sinh(x) +--R + +--R 5 3 +--R - 6cosh(x) - 6cosh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--------------+ +--R |--------------------------------------------- \|sinh(x)tanh(x) +--R \| sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 360 + +--S 361 of 502 +t0872:= (sinh(x)*tanh(x))^(5/2) +--R +--R +--R 2 2 +--------------+ +--R (203) sinh(x) tanh(x) \|sinh(x)tanh(x) +--R Type: Expression(Integer) +--E 361 + +--S 362 of 502 +r0872:= -2/15*coth(x)*(sinh(x)*tanh(x))^(1/2)*(32-(8+3*sinh(x)^2)*tanh(x)^2) +--R +--R +--R (204) +--R 2 2 +--------------+ +--R ((6coth(x)sinh(x) + 16coth(x))tanh(x) - 64coth(x))\|sinh(x)tanh(x) +--R --------------------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 502 +a0872:= integrate(t0872,x) +--R +--R +--R (205) +--R 8 7 2 6 +--R 3sinh(x) + 24cosh(x)sinh(x) + (84cosh(x) - 108)sinh(x) +--R + +--R 3 5 +--R (168cosh(x) - 648cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (210cosh(x) - 1620cosh(x) - 302)sinh(x) +--R + +--R 5 3 3 +--R (168cosh(x) - 2160cosh(x) - 1208cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (84cosh(x) - 1620cosh(x) - 1812cosh(x) - 108)sinh(x) +--R + +--R 7 5 3 +--R (24cosh(x) - 648cosh(x) - 1208cosh(x) - 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 3cosh(x) - 108cosh(x) - 302cosh(x) - 108cosh(x) + 3 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 7 6 2 5 +--R 60sinh(x) + 420cosh(x)sinh(x) + (1260cosh(x) + 120)sinh(x) +--R + +--R 3 4 +--R (2100cosh(x) + 600cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (2100cosh(x) + 1200cosh(x) + 60)sinh(x) +--R + +--R 5 3 2 +--R (1260cosh(x) + 1200cosh(x) + 180cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (420cosh(x) + 600cosh(x) + 180cosh(x) )sinh(x) + 60cosh(x) +--R + +--R 5 3 +--R 120cosh(x) + 60cosh(x) +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 502 +m0872:= a0872-r0872 +--R +--R +--R (206) +--R 9 8 +--R - 24coth(x)sinh(x) - 168cosh(x)coth(x)sinh(x) +--R + +--R 2 7 +--R (- 504cosh(x) - 112)coth(x)sinh(x) +--R + +--R 3 6 +--R (- 840cosh(x) - 688cosh(x))coth(x)sinh(x) +--R + +--R 4 2 5 +--R (- 840cosh(x) - 1824cosh(x) - 152)coth(x)sinh(x) +--R + +--R 5 3 4 +--R (- 504cosh(x) - 2720cosh(x) - 712cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 3 +--R (- 168cosh(x) - 2480cosh(x) - 1352cosh(x) - 64)coth(x)sinh(x) +--R + +--R 7 5 3 +--R (- 24cosh(x) - 1392cosh(x) - 1304cosh(x) - 192cosh(x)) +--R * +--R 2 +--R coth(x)sinh(x) +--R + +--R 6 4 2 +--R (- 448cosh(x) - 640cosh(x) - 192cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (- 64cosh(x) - 128cosh(x) - 64cosh(x) )coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 7 6 +--R 256coth(x)sinh(x) + 1792cosh(x)coth(x)sinh(x) +--R + +--R 2 5 +--R (5376cosh(x) + 512)coth(x)sinh(x) +--R + +--R 3 4 +--R (8960cosh(x) + 2560cosh(x))coth(x)sinh(x) +--R + +--R 4 2 3 +--R (8960cosh(x) + 5120cosh(x) + 256)coth(x)sinh(x) +--R + +--R 5 3 2 +--R (5376cosh(x) + 5120cosh(x) + 768cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 +--R (1792cosh(x) + 2560cosh(x) + 768cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 +--R (256cosh(x) + 512cosh(x) + 256cosh(x) )coth(x) +--R * +--R +--------------+ +--R \|sinh(x)tanh(x) +--R + +--R 8 7 2 6 +--R 3sinh(x) + 24cosh(x)sinh(x) + (84cosh(x) - 108)sinh(x) +--R + +--R 3 5 +--R (168cosh(x) - 648cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (210cosh(x) - 1620cosh(x) - 302)sinh(x) +--R + +--R 5 3 3 +--R (168cosh(x) - 2160cosh(x) - 1208cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (84cosh(x) - 1620cosh(x) - 1812cosh(x) - 108)sinh(x) +--R + +--R 7 5 3 +--R (24cosh(x) - 648cosh(x) - 1208cosh(x) - 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 3cosh(x) - 108cosh(x) - 302cosh(x) - 108cosh(x) + 3 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 7 6 2 5 +--R 60sinh(x) + 420cosh(x)sinh(x) + (1260cosh(x) + 120)sinh(x) +--R + +--R 3 4 +--R (2100cosh(x) + 600cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (2100cosh(x) + 1200cosh(x) + 60)sinh(x) +--R + +--R 5 3 2 +--R (1260cosh(x) + 1200cosh(x) + 180cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (420cosh(x) + 600cosh(x) + 180cosh(x) )sinh(x) + 60cosh(x) +--R + +--R 5 3 +--R 120cosh(x) + 60cosh(x) +--R Type: Expression(Integer) +--E 364 + +--S 365 of 502 +d0872:= D(m0872,x) +--R +--R +--R (207) +--R 10 9 2 8 +--R - 15sinh(x) - 150cosh(x)sinh(x) + (- 675cosh(x) + 75)sinh(x) +--R + +--R 3 7 +--R (- 1800cosh(x) + 600cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 3150cosh(x) + 2100cosh(x) - 150)sinh(x) +--R + +--R 5 3 5 +--R (- 3780cosh(x) + 4200cosh(x) - 900cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 3150cosh(x) + 5250cosh(x) - 2250cosh(x) + 150)sinh(x) +--R + +--R 7 5 3 3 +--R (- 1800cosh(x) + 4200cosh(x) - 3000cosh(x) + 600cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 675cosh(x) + 2100cosh(x) - 2250cosh(x) + 900cosh(x) - 75) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 150cosh(x) + 600cosh(x) - 900cosh(x) + 600cosh(x) +--R + +--R - 150cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 15cosh(x) + 75cosh(x) - 150cosh(x) + 150cosh(x) - 75cosh(x) +--R + +--R 15 +--R * +--R +--------------+ +--R \|sinh(x)tanh(x) +--R + +--R 11 10 +--R 60coth(x)sinh(x) + 360cosh(x)coth(x)sinh(x) +--R + +--R 2 9 +--R (840cosh(x) + 280)coth(x)sinh(x) +--R + +--R 3 8 +--R (840cosh(x) + 1440cosh(x))coth(x)sinh(x) +--R + +--R 2 7 +--R (2840cosh(x) + 380)coth(x)sinh(x) +--R + +--R 5 3 6 +--R (- 840cosh(x) + 2240cosh(x) + 1400cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 5 +--R (- 840cosh(x) - 600cosh(x) + 1600cosh(x) + 160)coth(x)sinh(x) +--R + +--R 7 5 3 +--R (- 360cosh(x) - 2720cosh(x) - 120cosh(x) + 320cosh(x)) +--R * +--R 4 +--R coth(x)sinh(x) +--R + +--R 8 6 4 3 +--R (- 60cosh(x) - 2360cosh(x) - 1660cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 2 +--R (- 960cosh(x) - 1280cosh(x) - 320cosh(x) )coth(x)sinh(x) +--R + +--R 8 6 4 +--R (- 160cosh(x) - 320cosh(x) - 160cosh(x) )coth(x)sinh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 2 11 +--R (24coth(x) - 24)sinh(x) +--R + +--R 2 10 +--R (144cosh(x)coth(x) - 60cosh(x)coth(x) - 144cosh(x))sinh(x) +--R + +--R 2 2 2 +--R (336cosh(x) + 112)coth(x) - 360cosh(x) coth(x) +--R + +--R 2 +--R - 336cosh(x) - 112 +--R * +--R 9 +--R sinh(x) +--R + +--R 3 2 +--R (336cosh(x) + 576cosh(x))coth(x) +--R + +--R 3 3 +--R (- 840cosh(x) - 152cosh(x))coth(x) - 336cosh(x) - 576cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 2 2 +--R (1136cosh(x) + 152)coth(x) +--R + +--R 4 2 2 +--R (- 840cosh(x) - 672cosh(x) )coth(x) - 1136cosh(x) - 152 +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 336cosh(x) + 896cosh(x) + 560cosh(x))coth(x) +--R + +--R 3 5 +--R (- 1048cosh(x) - 124cosh(x))coth(x) + 336cosh(x) +--R + +--R 3 +--R - 896cosh(x) - 560cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 336cosh(x) - 240cosh(x) + 640cosh(x) + 64)coth(x) +--R + +--R 6 4 2 +--R (840cosh(x) - 448cosh(x) - 376cosh(x) )coth(x) +--R + +--R 6 4 2 +--R 336cosh(x) + 240cosh(x) - 640cosh(x) - 64 +--R * +--R 5 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 144cosh(x) - 1088cosh(x) - 48cosh(x) + 128cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 7 5 3 +--R (840cosh(x) + 600cosh(x) - 320cosh(x) - 32cosh(x))coth(x) +--R + +--R 7 5 3 +--R 144cosh(x) + 1088cosh(x) + 48cosh(x) - 128cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 24cosh(x) - 944cosh(x) - 664cosh(x) )coth(x) +--R + +--R 8 6 4 2 +--R (360cosh(x) + 928cosh(x) + 120cosh(x) - 64cosh(x) )coth(x) +--R + +--R 8 6 4 +--R 24cosh(x) + 944cosh(x) + 664cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (- 384cosh(x) - 512cosh(x) - 128cosh(x) )coth(x) +--R + +--R 9 7 5 7 +--R (60cosh(x) + 568cosh(x) + 380cosh(x) )coth(x) + 384cosh(x) +--R + +--R 5 3 +--R 512cosh(x) + 128cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 64cosh(x) - 128cosh(x) - 64cosh(x) )coth(x) +--R + +--R 8 6 4 8 +--R (192cosh(x) + 256cosh(x) + 64cosh(x) )coth(x) + 64cosh(x) +--R + +--R 6 4 +--R 128cosh(x) + 64cosh(x) +--R * +--R sinh(x) +--R + +--R 9 7 5 +--R (32cosh(x) + 64cosh(x) + 32cosh(x) )coth(x) +--R * +--R 3 +--R tanh(x) +--R + +--R 11 10 +--R - 60coth(x)sinh(x) - 360cosh(x)coth(x)sinh(x) +--R + +--R 2 9 +--R (- 840cosh(x) - 408)coth(x)sinh(x) +--R + +--R 3 8 +--R (- 840cosh(x) - 2208cosh(x))coth(x)sinh(x) +--R + +--R 2 7 +--R (- 4632cosh(x) - 636)coth(x)sinh(x) +--R + +--R 5 3 6 +--R (840cosh(x) - 4032cosh(x) - 2424cosh(x))coth(x)sinh(x) +--R + +--R 6 4 2 5 +--R (840cosh(x) + 600cosh(x) - 2880cosh(x) - 288)coth(x)sinh(x) +--R + +--R 7 5 3 +--R (360cosh(x) + 4512cosh(x) + 120cosh(x) - 576cosh(x))coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 3 +--R (60cosh(x) + 4152cosh(x) + 2940cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 2 +--R (1728cosh(x) + 2304cosh(x) + 576cosh(x) )coth(x)sinh(x) +--R + +--R 8 6 4 +--R (288cosh(x) + 576cosh(x) + 288cosh(x) )coth(x)sinh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 9 +--R (- 256coth(x) + 256)sinh(x) +--R + +--R 2 8 +--R (- 1536cosh(x)coth(x) + 128cosh(x)coth(x) + 1536cosh(x))sinh(x) +--R + +--R 2 2 2 +--R (- 3584cosh(x) - 512)coth(x) + 768cosh(x) coth(x) +--R + +--R 2 +--R 3584cosh(x) + 512 +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 +--R (- 3584cosh(x) - 2048cosh(x))coth(x) +--R + +--R 3 3 +--R (1792cosh(x) + 256cosh(x))coth(x) + 3584cosh(x) + 2048cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 +--R (- 2560cosh(x) - 256)coth(x) +--R + +--R 4 2 2 +--R (1792cosh(x) + 1024cosh(x) )coth(x) + 2560cosh(x) + 256 +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 +--R (3584cosh(x) - 512cosh(x))coth(x) +--R + +--R 3 5 +--R (1280cosh(x) + 128cosh(x))coth(x) - 3584cosh(x) + 512cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 4 2 +--R (3584cosh(x) + 2560cosh(x) )coth(x) +--R + +--R 6 2 6 +--R (- 1792cosh(x) + 256cosh(x) )coth(x) - 3584cosh(x) +--R + +--R 4 +--R - 2560cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 7 5 3 2 +--R (1536cosh(x) + 2048cosh(x) + 512cosh(x) )coth(x) +--R + +--R 7 5 7 +--R (- 1792cosh(x) - 1280cosh(x) )coth(x) - 1536cosh(x) +--R + +--R 5 3 +--R - 2048cosh(x) - 512cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (256cosh(x) + 512cosh(x) + 256cosh(x) )coth(x) +--R + +--R 8 6 4 +--R (- 768cosh(x) - 1024cosh(x) - 256cosh(x) )coth(x) +--R + +--R 8 6 4 +--R - 256cosh(x) - 512cosh(x) - 256cosh(x) +--R * +--R sinh(x) +--R + +--R 9 7 5 +--R (- 128cosh(x) - 256cosh(x) - 128cosh(x) )coth(x) +--R * +--R tanh(x) +--R + +--R 9 8 +--R 128coth(x)sinh(x) + 768cosh(x)coth(x)sinh(x) +--R + +--R 2 7 +--R (1792cosh(x) + 256)coth(x)sinh(x) +--R + +--R 3 6 +--R (1792cosh(x) + 1024cosh(x))coth(x)sinh(x) +--R + +--R 2 5 +--R (1280cosh(x) + 128)coth(x)sinh(x) +--R + +--R 5 4 +--R (- 1792cosh(x) + 256cosh(x))coth(x)sinh(x) +--R + +--R 6 4 3 +--R (- 1792cosh(x) - 1280cosh(x) )coth(x)sinh(x) +--R + +--R 7 5 3 2 +--R (- 768cosh(x) - 1024cosh(x) - 256cosh(x) )coth(x)sinh(x) +--R + +--R 8 6 4 +--R (- 128cosh(x) - 256cosh(x) - 128cosh(x) )coth(x)sinh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 8 7 2 6 +--R 60sinh(x) + 360cosh(x)sinh(x) + (840cosh(x) + 120)sinh(x) +--R + +--R 3 5 2 4 +--R (840cosh(x) + 480cosh(x))sinh(x) + (600cosh(x) + 60)sinh(x) +--R + +--R 5 3 +--R (- 840cosh(x) + 120cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 840cosh(x) - 600cosh(x) )sinh(x) +--R + +--R 7 5 3 8 +--R (- 360cosh(x) - 480cosh(x) - 120cosh(x) )sinh(x) - 60cosh(x) +--R + +--R 6 4 +--R - 120cosh(x) - 60cosh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) - 2 +--------------+ +--R |--------------------------------------------- \|sinh(x)tanh(x) +--R \| sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 365 + +--S 366 of 502 +t0873:= (a+b*sinh(x)*cosh(x))^(1/2) +--R +--R +--R +--------------------+ +--R (208) \|b cosh(x)sinh(x) + a +--R Type: Expression(Integer) +--E 366 + +--S 367 of 502 +r0873:= -1/2*%i*EllipticE(-1/4*%pi+%i*x,2*%i*b/(2*a-%i*b))*_ + (2*a+b*sinh(2*x))^(1/2)*2^(1/2)/((2*a+b*sinh(2*x))/(2*a-%i*b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 367 + +--S 368 of 502 +a0873:= integrate(t0873,x) +--R +--R +--R x +--R ++ +----------------------+ +--R (209) | \|b cosh(%I)sinh(%I) + a d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 502 +--m0873:= a0873-r0873 +--E 369 + +--S 370 of 502 +--d0873:= D(m0873,x) +--E 370 + +--S 371 of 502 +t0874:= 1/(a+b*sinh(x)*cosh(x))^(1/2) +--R +--R +--R 1 +--R (210) ----------------------- +--R +--------------------+ +--R \|b cosh(x)sinh(x) + a +--R Type: Expression(Integer) +--E 371 + +--S 372 of 502 +r0874:= -%i*2^(1/2)*EllipticF(-1/4*%pi+%i*x,2*%i*b/(2*a-%i*b))*_ + ((2*a+b*sinh(2*x))/(2*a-%i*b))^(1/2)/(2*a+b*sinh(2*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 372 + +--S 373 of 502 +a0874:= integrate(t0874,x) +--R +--R +--R x +--R ++ 1 +--R (211) | ------------------------- d%I +--R ++ +----------------------+ +--R \|b cosh(%I)sinh(%I) + a +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 502 +--m0874:= a0874-r0874 +--E 374 + +--S 375 of 502 +--d0874:= D(m0874,x) +--E 375 + +--S 376 of 502 +t0875:= (a*cosh(x)+b*sinh(x))^4 +--R +--R +--R (212) +--R 4 4 3 3 2 2 2 2 +--R b sinh(x) + 4a b cosh(x)sinh(x) + 6a b cosh(x) sinh(x) +--R + +--R 3 3 4 4 +--R 4a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 376 + +--S 377 of 502 +r0875:= 3/8*(a^2-b^2)^2*x+3/8*(a^2-b^2)*(b*cosh(x)+a*sinh(x))*_ + (a*cosh(x)+b*sinh(x))+1/4*(b*cosh(x)+a*sinh(x))*(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R (213) +--R 3 4 4 2 2 3 +--R 2a b sinh(x) + (2b + 6a b )cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 2 +--R ((6a b + 6a b)cosh(x) - 3a b + 3a b)sinh(x) +--R + +--R 2 2 4 3 4 4 3 4 +--R ((6a b + 2a )cosh(x) + (- 3b + 3a )cosh(x))sinh(x) + 2a b cosh(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 3a b + 3a b)cosh(x) + (3b - 6a b + 3a )x +--R / +--R 8 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 502 +a0875:= integrate(t0875,x) +--R +--R +--R (214) +--R 3 3 4 4 2 2 4 3 +--R (a b + a b)sinh(x) + (b + 6a b + a )cosh(x)sinh(x) +--R + +--R 3 3 2 3 3 2 +--R ((6a b + 6a b)cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 4 2 2 4 3 4 4 +--R ((b + 6a b + a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 4 2 2 4 +--R (a b + a b)cosh(x) + (- 4a b + 4a b)cosh(x) + (3b - 6a b + 3a )x +--R / +--R 8 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 502 +m0875:= a0875-r0875 +--R +--R +--R (215) +--R 3 3 4 4 4 3 +--R (- a b + a b)sinh(x) + (- b + a )cosh(x)sinh(x) +--R + +--R 3 3 2 4 4 3 4 4 +--R (- a b + a b)sinh(x) + ((b - a )cosh(x) + (- b + a )cosh(x))sinh(x) +--R + +--R 3 3 4 3 3 2 +--R (a b - a b)cosh(x) + (- a b + a b)cosh(x) +--R / +--R 8 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 502 +d0875:= D(m0875,x) +--R +--R +--R (216) +--R 4 4 4 3 3 3 +--R (- b + a )sinh(x) + (- 4a b + 4a b)cosh(x)sinh(x) +--R + +--R 4 4 2 +--R (- b + a )sinh(x) +--R + +--R 3 3 3 3 3 +--R ((4a b - 4a b)cosh(x) + (- 4a b + 4a b)cosh(x))sinh(x) +--R + +--R 4 4 4 4 4 2 +--R (b - a )cosh(x) + (- b + a )cosh(x) +--R / +--R 8 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 502 +t0876:= 1/(a*cosh(x)+b*sinh(x))^3 +--R +--R +--R (217) +--R 1 +--R --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 381 + +--S 382 of 502 +r0876:= 1/2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ + 1/2*(b*cosh(x)+a*sinh(x))/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R (218) +--R 2 2 2 2 +--R (- b sinh(x) - 2a b cosh(x)sinh(x) - a cosh(x) ) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R (- a sinh(x) - b cosh(x))\|- b + a +--R / +--R 4 2 2 2 3 3 +--R (2b - 2a b )sinh(x) + (4a b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 4 2 +--R (2a b - 2a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 382 + +--S 383 of 502 +a0876:= integrate(t0876,x) +--R +--R +--R (219) +--R [ +--R 2 2 4 2 2 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a b + 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a b + 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (- 2b + 2a )cosh(x) + b - 2a b + a +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (2b - 2a )sinh(x) + (2b - 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 3 2 +--R (- 2b - 2a)sinh(x) + (- 6b - 6a)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((- 6b - 6a)cosh(x) - 2b + 2a)sinh(x) + (- 2b - 2a)cosh(x) +--R + +--R (- 2b + 2a)cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 3 3 4 4 +--R (2b + 4a b - 4a b - 2a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (8b + 16a b - 16a b - 8a )cosh(x)sinh(x) +--R + +--R 4 3 3 4 2 4 2 2 4 2 +--R ((12b + 24a b - 24a b - 12a )cosh(x) - 4b + 8a b - 4a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (8b + 16a b - 16a b - 8a )cosh(x) +--R + +--R 4 2 2 4 +--R (- 8b + 16a b - 8a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 3 4 4 4 2 2 4 2 +--R (2b + 4a b - 4a b - 2a )cosh(x) + (- 4b + 8a b - 4a )cosh(x) +--R + +--R 4 3 3 4 +--R 2b - 4a b + 4a b - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 2 2 4 2 2 3 +--R (b + 2a b + a )sinh(x) + (4b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a b + 6a )cosh(x) - 2b + 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b + 8a b + 4a )cosh(x) + (- 4b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (- 2b + 2a )cosh(x) + b - 2a b + a +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 2 +--R (- b - a)sinh(x) + (- 3b - 3a)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((- 3b - 3a)cosh(x) - b + a)sinh(x) + (- b - a)cosh(x) +--R + +--R (- b + a)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 3 4 4 +--R (b + 2a b - 2a b - a )sinh(x) +--R + +--R 4 3 3 4 3 +--R (4b + 8a b - 8a b - 4a )cosh(x)sinh(x) +--R + +--R 4 3 3 4 2 4 2 2 4 2 +--R ((6b + 12a b - 12a b - 6a )cosh(x) - 2b + 4a b - 2a )sinh(x) +--R + +--R 4 3 3 4 3 4 2 2 4 +--R ((4b + 8a b - 8a b - 4a )cosh(x) + (- 4b + 8a b - 4a )cosh(x)) +--R * +--R sinh(x) +--R + +--R 4 3 3 4 4 4 2 2 4 2 4 +--R (b + 2a b - 2a b - a )cosh(x) + (- 2b + 4a b - 2a )cosh(x) + b +--R + +--R 3 3 4 +--R - 2a b + 2a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 383 + +--S 384 of 502 +--m0876:= a0876-r0876 +--E 384 + +--S 385 of 502 +--d0876:= D(m0876,x) +--E 385 + +--S 386 of 502 +t0877:= 1/(a*cosh(x)+b*sinh(x))^4 +--R +--R +--R (220) +--R 1 +--R / +--R 4 4 3 3 2 2 2 2 +--R b sinh(x) + 4a b cosh(x)sinh(x) + 6a b cosh(x) sinh(x) +--R + +--R 3 3 4 4 +--R 4a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 386 + +--S 387 of 502 +r0877:= 1/3*(b*cosh(x)+a*sinh(x))/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^3+_ + 2/3*sinh(x)/a/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) +--R +--R +--R (221) +--R 2 3 2 2 2 2 +--R - 2b sinh(x) - 4a b cosh(x)sinh(x) + (- 2a cosh(x) - a )sinh(x) +--R + +--R - a b cosh(x) +--R / +--R 5 3 3 3 2 4 4 2 2 +--R (3a b - 3a b )sinh(x) + (9a b - 9a b )cosh(x)sinh(x) +--R + +--R 3 3 5 2 4 2 6 3 +--R (9a b - 9a b)cosh(x) sinh(x) + (3a b - 3a )cosh(x) +--R Type: Expression(Integer) +--E 387 + +--S 388 of 502 +a0877:= integrate(t0877,x) +--R +--R +--R (222) +--R (- 16b - 8a)sinh(x) + (- 8b - 16a)cosh(x) +--R / +--R 5 4 2 3 3 2 4 5 5 +--R (3b + 15a b + 30a b + 30a b + 15a b + 3a )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (15b + 75a b + 150a b + 150a b + 75a b + 15a )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (30b + 150a b + 300a b + 300a b + 150a b + 30a )cosh(x) - 9b +--R + +--R 4 2 3 3 2 4 5 +--R - 27a b - 18a b + 18a b + 27a b + 9a +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (30b + 150a b + 300a b + 300a b + 150a b + 30a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 27b - 81a b - 54a b + 54a b + 81a b + 27a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (15b + 75a b + 150a b + 150a b + 75a b + 15a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (- 27b - 81a b - 54a b + 54a b + 81a b + 27a )cosh(x) + 12b +--R + +--R 4 2 3 3 2 4 5 +--R 6a b - 24a b - 12a b + 12a b + 6a +--R * +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (3b + 15a b + 30a b + 30a b + 15a b + 3a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 9b - 27a b - 18a b + 18a b + 27a b + 9a )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (6b + 12a b - 12a b - 24a b + 6a b + 12a )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 502 +m0877:= a0877-r0877 +--R +--R +--R (223) +--R 6 5 2 4 3 3 4 2 8 +--R (2b + 8a b + 12a b + 8a b + 2a b )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (10b + 44a b + 76a b + 64a b + 26a b + 4a b)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (20b + 100a b + 202a b + 208a b + 112a b + 28a b + 2a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R - 6b - 12a b + a b + 16a b + 12a b + 4a b + a +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (20b + 120a b + 290a b + 360a b + 240a b + 80a b + 10a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 18b - 47a b - 15a b + 62a b + 76a b + 33a b + 5a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (10b + 80a b + 240a b + 360a b + 290a b + 120a b + 20a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 18b - 67a b - 48a b + 94a b + 170a b + 93a b + 16a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 8b - 20a b - 7a b + 6a b + 4a b + 6a b + 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (2b + 28a b + 112a b + 208a b + 202a b + 100a b + 20a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (- 6b - 38a b - 40a b + 76a b + 178a b + 122a b + 28a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4b + 9a b - 91a b - 6a b + 46a b + 29a b + 9a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (4a b + 26a b + 64a b + 76a b + 44a b + 10a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (- 2a b + 3a b + 44a b + 94a b + 78a b + 23a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 2 4 +--R (- a b - 35a b - 118a b + 70a b + 71a b + 13a )cosh(x) + 4a b +--R + +--R 3 3 4 2 5 6 +--R - 2a b - 6a b + 2a b + 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (2a b + 8a b + 12a b + 8a b + 2a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (5a b + 15a b + 22a b + 26a b + 21a b + 7a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 9a b - 17a b - 26a b - 34a b + 67a b + 19a )cosh(x) +--R + +--R 5 3 3 4 2 6 +--R (4a b - 4a b - 4a b + 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (a b + 4a b + 6a b + 4a b + a b)cosh(x) +--R + +--R 5 2 4 4 2 5 6 4 +--R (- 3a b - 6a b - 2a b - 5a b + 16a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (2a b + 2a b - 6a b - 2a b + 4a b)cosh(x) +--R / +--R 9 2 8 3 7 5 5 6 4 7 3 8 +--R (3a b + 12a b + 15a b - 15a b - 12a b - 3a b )sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 15a b + 69a b + 111a b + 45a b - 75a b - 105a b - 51a b +--R + +--R 8 2 +--R - 9a b +--R * +--R 7 +--R cosh(x)sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 30a b + 165a b + 339a b + 261a b - 105a b - 345a b +--R + +--R 7 3 8 2 9 +--R - 255a b - 81a b - 9a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 9a b - 18a b + 9a b + 36a b + 9a b - 18a b - 9a b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 30a b + 210a b + 555a b + 633a b + 87a b - 555a b - 615a b +--R + +--R 8 2 9 10 +--R - 285a b - 57a b - 3a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 27a b - 81a b - 27a b + 135a b + 135a b - 27a b - 81a b +--R + +--R 8 2 +--R - 27a b +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 15a b + 150a b + 525a b + 825a b + 435a b - 435a b +--R + +--R 7 3 8 2 9 10 +--R - 825a b - 525a b - 150a b - 15a +--R * +--R 4 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 27a b - 135a b - 162a b + 135a b + 378a b + 135a b +--R + +--R 7 3 8 2 9 +--R - 162a b - 135a b - 27a b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 12a b - 6a b - 30a b + 12a b + 24a b - 6a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 3a b + 57a b + 285a b + 615a b + 555a b - 87a b - 633a b +--R + +--R 8 2 9 10 +--R - 555a b - 210a b - 30a +--R * +--R 5 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 9a b - 99a b - 234a b - 54a b + 396a b + 396a b - 54a b +--R + +--R 8 2 9 10 +--R - 234a b - 99a b - 9a +--R * +--R 3 +--R cosh(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 6a b + 42a b - 42a b - 102a b + 66a b + 78a b - 30a b +--R + +--R 8 2 +--R - 18a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 9a b + 81a b + 255a b + 345a b + 105a b - 261a b - 339a b +--R + +--R 9 10 +--R - 165a b - 30a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 27a b - 135a b - 162a b + 135a b + 378a b + 135a b +--R + +--R 8 2 9 10 +--R - 162a b - 135a b - 27a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 18a b + 54a b - 90a b - 126a b + 126a b + 90a b - 54a b +--R + +--R 9 +--R - 18a b +--R * +--R 2 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 9a b + 51a b + 105a b + 75a b - 45a b - 111a b - 69a b +--R + +--R 10 +--R - 15a +--R * +--R 7 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R - 27a b - 81a b - 27a b + 135a b + 135a b - 27a b - 81a b +--R + +--R 10 +--R - 27a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 18a b + 30a b - 78a b - 66a b + 102a b + 42a b - 42a b +--R + +--R 10 +--R - 6a +--R * +--R 3 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 4 6 5 5 6 4 8 2 9 10 8 +--R (3a b + 12a b + 15a b - 15a b - 12a b - 3a )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 10 6 +--R (- 9a b - 18a b + 9a b + 36a b + 9a b - 18a b - 9a )cosh(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 10 4 +--R (6a b + 6a b - 24a b - 12a b + 30a b + 6a b - 12a )cosh(x) +--R Type: Expression(Integer) +--E 389 + +--S 390 of 502 +--d0877:= D(m0877,x) +--E 390 + +--S 391 of 502 +t0878:= 1/(a*cosh(x)+b*sinh(x))^5 +--R +--R +--R (224) +--R 1 +--R / +--R 5 5 4 4 2 3 2 3 +--R b sinh(x) + 5a b cosh(x)sinh(x) + 10a b cosh(x) sinh(x) +--R + +--R 3 2 3 2 4 4 5 5 +--R 10a b cosh(x) sinh(x) + 5a b cosh(x) sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 391 + +--S 392 of 502 +r0878:= 3/8*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+_ + 1/4*(b*cosh(x)+a*sinh(x))/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^4+_ + 3/8*(b*cosh(x)+a*sinh(x))/(a^2-b^2)^2/(a*cosh(x)+b*sinh(x))^2 +--R +--R +--R (225) +--R 4 4 3 3 2 2 2 2 +--R 3b sinh(x) + 12a b cosh(x)sinh(x) + 18a b cosh(x) sinh(x) +--R + +--R 3 3 4 4 +--R 12a b cosh(x) sinh(x) + 3a cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 2 +--R 3a b sinh(x) + (3b + 6a b)cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 3 +--R ((6a b + 3a )cosh(x) - 2a b + 2a )sinh(x) + 3a b cosh(x) +--R + +--R 3 2 +--R (- 2b + 2a b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 8 2 6 4 4 4 +--R (8b - 16a b + 8a b )sinh(x) +--R + +--R 7 3 5 5 3 3 +--R (32a b - 64a b + 32a b )cosh(x)sinh(x) +--R + +--R 2 6 4 4 6 2 2 2 +--R (48a b - 96a b + 48a b )cosh(x) sinh(x) +--R + +--R 3 5 5 3 7 3 4 4 6 2 8 4 +--R (32a b - 64a b + 32a b)cosh(x) sinh(x) + (8a b - 16a b + 8a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 392 + +--S 393 of 502 +a0878:= integrate(t0878,x) +--R +--R +--R (226) +--R [ +--R 4 3 2 2 3 4 8 +--R (3b + 12a b + 18a b + 12a b + 3a )sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (24b + 96a b + 144a b + 96a b + 24a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (84b + 336a b + 504a b + 336a b + 84a )cosh(x) - 12b +--R + +--R 3 3 4 +--R - 24a b + 24a b + 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (168b + 672a b + 1008a b + 672a b + 168a )cosh(x) +--R + +--R 4 3 3 4 +--R (- 72b - 144a b + 144a b + 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (210b + 840a b + 1260a b + 840a b + 210a )cosh(x) +--R + +--R 4 3 3 4 2 4 2 2 +--R (- 180b - 360a b + 360a b + 180a )cosh(x) + 18b - 36a b +--R + +--R 4 +--R 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (168b + 672a b + 1008a b + 672a b + 168a )cosh(x) +--R + +--R 4 3 3 4 3 +--R (- 240b - 480a b + 480a b + 240a )cosh(x) +--R + +--R 4 2 2 4 +--R (72b - 144a b + 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (84b + 336a b + 504a b + 336a b + 84a )cosh(x) +--R + +--R 4 3 3 4 4 +--R (- 180b - 360a b + 360a b + 180a )cosh(x) +--R + +--R 4 2 2 4 2 4 3 3 4 +--R (108b - 216a b + 108a )cosh(x) - 12b + 24a b - 24a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (24b + 96a b + 144a b + 96a b + 24a )cosh(x) +--R + +--R 4 3 3 4 5 +--R (- 72b - 144a b + 144a b + 72a )cosh(x) +--R + +--R 4 2 2 4 3 +--R (72b - 144a b + 72a )cosh(x) +--R + +--R 4 3 3 4 +--R (- 24b + 48a b - 48a b + 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 8 +--R (3b + 12a b + 18a b + 12a b + 3a )cosh(x) +--R + +--R 4 3 3 4 6 +--R (- 12b - 24a b + 24a b + 12a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (18b - 36a b + 18a )cosh(x) +--R + +--R 4 3 3 4 2 4 3 2 2 +--R (- 12b + 24a b - 24a b + 12a )cosh(x) + 3b - 12a b + 18a b +--R + +--R 3 4 +--R - 12a b + 3a +--R * +--R log +--R 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R - b + a +--R + +--R 3 2 2 3 7 +--R (6b + 18a b + 18a b + 6a )sinh(x) +--R + +--R 3 2 2 3 6 +--R (42b + 126a b + 126a b + 42a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (126b + 378a b + 378a b + 126a )cosh(x) - 22b - 22a b +--R + +--R 2 3 +--R 22a b + 22a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (210b + 630a b + 630a b + 210a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 110b - 110a b + 110a b + 110a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (210b + 630a b + 630a b + 210a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 220b - 220a b + 220a b + 220a )cosh(x) - 22b + 22a b +--R + +--R 2 3 +--R 22a b - 22a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (126b + 378a b + 378a b + 126a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 220b - 220a b + 220a b + 220a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 66b + 66a b + 66a b - 66a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (42b + 126a b + 126a b + 42a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 110b - 110a b + 110a b + 110a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 66b + 66a b + 66a b - 66a )cosh(x) + 6b - 18a b + 18a b +--R + +--R 3 +--R - 6a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (6b + 18a b + 18a b + 6a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 22b - 22a b + 22a b + 22a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 22b + 22a b + 22a b - 22a )cosh(x) +--R + +--R 3 2 2 3 +--R (6b - 18a b + 18a b - 6a )cosh(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 +--R 8b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b + 32a b +--R + +--R 8 +--R 8a +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 64b + 256a b + 256a b - 256a b - 640a b - 256a b + 256a b +--R + +--R 7 8 +--R 256a b + 64a +--R * +--R 7 +--R cosh(x)sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 224b + 896a b + 896a b - 896a b - 2240a b - 896a b +--R + +--R 6 2 7 8 +--R 896a b + 896a b + 224a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 32b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 8 +--R 32a +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 448b + 1792a b + 1792a b - 1792a b - 4480a b - 1792a b +--R + +--R 6 2 7 8 +--R 1792a b + 1792a b + 448a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 192b - 384a b + 384a b + 1152a b - 1152a b - 384a b +--R + +--R 7 8 +--R 384a b + 192a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 560b + 2240a b + 2240a b - 2240a b - 5600a b - 2240a b +--R + +--R 6 2 7 8 +--R 2240a b + 2240a b + 560a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 480b - 960a b + 960a b + 2880a b - 2880a b - 960a b +--R + +--R 7 8 +--R 960a b + 480a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R 48b - 192a b + 288a b - 192a b + 48a +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 448b + 1792a b + 1792a b - 1792a b - 4480a b - 1792a b +--R + +--R 6 2 7 8 +--R 1792a b + 1792a b + 448a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 +--R - 640b - 1280a b + 1280a b + 3840a b - 3840a b +--R + +--R 6 2 7 8 +--R - 1280a b + 1280a b + 640a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R (192b - 768a b + 1152a b - 768a b + 192a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 224b + 896a b + 896a b - 896a b - 2240a b - 896a b +--R + +--R 6 2 7 8 +--R 896a b + 896a b + 224a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 480b - 960a b + 960a b + 2880a b - 2880a b - 960a b +--R + +--R 7 8 +--R 960a b + 480a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 8 +--R (288b - 1152a b + 1728a b - 1152a b + 288a )cosh(x) - 32b +--R + +--R 7 2 6 3 5 5 3 6 2 7 8 +--R 64a b + 64a b - 192a b + 192a b - 64a b - 64a b + 32a +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 64b + 256a b + 256a b - 256a b - 640a b - 256a b +--R + +--R 6 2 7 8 +--R 256a b + 256a b + 64a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 192b - 384a b + 384a b + 1152a b - 1152a b - 384a b +--R + +--R 7 8 +--R 384a b + 192a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (192b - 768a b + 1152a b - 768a b + 192a )cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 64b + 128a b + 128a b - 384a b + 384a b - 128a b +--R + +--R 7 8 +--R - 128a b + 64a +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 +--R 8b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b + 32a b +--R + +--R 8 +--R 8a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 32b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 8 +--R 32a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (48b - 192a b + 288a b - 192a b + 48a )cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 32b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 8 +--R 32a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 8 +--R 8b - 32a b + 32a b + 32a b - 80a b + 32a b + 32a b - 32a b + 8a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 4 3 2 2 3 4 8 +--R (- 3b - 12a b - 18a b - 12a b - 3a )sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 24b - 96a b - 144a b - 96a b - 24a )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (- 84b - 336a b - 504a b - 336a b - 84a )cosh(x) + 12b +--R + +--R 3 3 4 +--R 24a b - 24a b - 12a +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 168b - 672a b - 1008a b - 672a b - 168a )cosh(x) +--R + +--R 4 3 3 4 +--R (72b + 144a b - 144a b - 72a )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 210b - 840a b - 1260a b - 840a b - 210a )cosh(x) +--R + +--R 4 3 3 4 2 4 2 2 4 +--R (180b + 360a b - 360a b - 180a )cosh(x) - 18b + 36a b - 18a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 168b - 672a b - 1008a b - 672a b - 168a )cosh(x) +--R + +--R 4 3 3 4 3 +--R (240b + 480a b - 480a b - 240a )cosh(x) +--R + +--R 4 2 2 4 +--R (- 72b + 144a b - 72a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 84b - 336a b - 504a b - 336a b - 84a )cosh(x) +--R + +--R 4 3 3 4 4 +--R (180b + 360a b - 360a b - 180a )cosh(x) +--R + +--R 4 2 2 4 2 4 3 3 +--R (- 108b + 216a b - 108a )cosh(x) + 12b - 24a b + 24a b +--R + +--R 4 +--R - 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 24b - 96a b - 144a b - 96a b - 24a )cosh(x) +--R + +--R 4 3 3 4 5 +--R (72b + 144a b - 144a b - 72a )cosh(x) +--R + +--R 4 2 2 4 3 +--R (- 72b + 144a b - 72a )cosh(x) +--R + +--R 4 3 3 4 +--R (24b - 48a b + 48a b - 24a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 3b - 12a b - 18a b - 12a b - 3a )cosh(x) +--R + +--R 4 3 3 4 6 +--R (12b + 24a b - 24a b - 12a )cosh(x) +--R + +--R 4 2 2 4 4 +--R (- 18b + 36a b - 18a )cosh(x) +--R + +--R 4 3 3 4 2 4 3 2 2 +--R (12b - 24a b + 24a b - 12a )cosh(x) - 3b + 12a b - 18a b +--R + +--R 3 4 +--R 12a b - 3a +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 3 2 2 3 7 +--R (3b + 9a b + 9a b + 3a )sinh(x) +--R + +--R 3 2 2 3 6 +--R (21b + 63a b + 63a b + 21a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (63b + 189a b + 189a b + 63a )cosh(x) - 11b - 11a b +--R + +--R 2 3 +--R 11a b + 11a +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (105b + 315a b + 315a b + 105a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 55b - 55a b + 55a b + 55a )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (105b + 315a b + 315a b + 105a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 110b - 110a b + 110a b + 110a )cosh(x) - 11b + 11a b +--R + +--R 2 3 +--R 11a b - 11a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (63b + 189a b + 189a b + 63a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 110b - 110a b + 110a b + 110a )cosh(x) +--R + +--R 3 2 2 3 +--R (- 33b + 33a b + 33a b - 33a )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (21b + 63a b + 63a b + 21a )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 55b - 55a b + 55a b + 55a )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 33b + 33a b + 33a b - 33a )cosh(x) + 3b - 9a b + 9a b +--R + +--R 3 +--R - 3a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 7 +--R (3b + 9a b + 9a b + 3a )cosh(x) +--R + +--R 3 2 2 3 5 +--R (- 11b - 11a b + 11a b + 11a )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 11b + 11a b + 11a b - 11a )cosh(x) +--R + +--R 3 2 2 3 +--R (3b - 9a b + 9a b - 3a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4b + 16a b + 16a b - 16a b - 40a b - 16a b + 16a b + 16a b +--R + +--R 8 +--R 4a +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 32b + 128a b + 128a b - 128a b - 320a b - 128a b + 128a b +--R + +--R 7 8 +--R 128a b + 32a +--R * +--R 7 +--R cosh(x)sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 112b + 448a b + 448a b - 448a b - 1120a b - 448a b +--R + +--R 6 2 7 8 +--R 448a b + 448a b + 112a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R - 16b - 32a b + 32a b + 96a b - 96a b - 32a b + 32a b + 16a +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 224b + 896a b + 896a b - 896a b - 2240a b - 896a b +--R + +--R 6 2 7 8 +--R 896a b + 896a b + 224a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 96b - 192a b + 192a b + 576a b - 576a b - 192a b +--R + +--R 7 8 +--R 192a b + 96a +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 280b + 1120a b + 1120a b - 1120a b - 2800a b - 1120a b +--R + +--R 6 2 7 8 +--R 1120a b + 1120a b + 280a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 240b - 480a b + 480a b + 1440a b - 1440a b - 480a b +--R + +--R 7 8 +--R 480a b + 240a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R 24b - 96a b + 144a b - 96a b + 24a +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 224b + 896a b + 896a b - 896a b - 2240a b - 896a b +--R + +--R 6 2 7 8 +--R 896a b + 896a b + 224a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 320b - 640a b + 640a b + 1920a b - 1920a b - 640a b +--R + +--R 7 8 +--R 640a b + 320a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R (96b - 384a b + 576a b - 384a b + 96a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 112b + 448a b + 448a b - 448a b - 1120a b - 448a b +--R + +--R 6 2 7 8 +--R 448a b + 448a b + 112a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 240b - 480a b + 480a b + 1440a b - 1440a b - 480a b +--R + +--R 7 8 +--R 480a b + 240a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 2 8 +--R (144b - 576a b + 864a b - 576a b + 144a )cosh(x) - 16b +--R + +--R 7 2 6 3 5 5 3 6 2 7 8 +--R 32a b + 32a b - 96a b + 96a b - 32a b - 32a b + 16a +--R * +--R 2 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 32b + 128a b + 128a b - 128a b - 320a b - 128a b +--R + +--R 6 2 7 8 +--R 128a b + 128a b + 32a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 96b - 192a b + 192a b + 576a b - 576a b - 192a b +--R + +--R 7 8 +--R 192a b + 96a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (96b - 384a b + 576a b - 384a b + 96a )cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 32b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 8 +--R 32a +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4b + 16a b + 16a b - 16a b - 40a b - 16a b + 16a b + 16a b +--R + +--R 8 +--R 4a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 16b - 32a b + 32a b + 96a b - 96a b - 32a b + 32a b +--R + +--R 8 +--R 16a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (24b - 96a b + 144a b - 96a b + 24a )cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R - 16b + 32a b + 32a b - 96a b + 96a b - 32a b - 32a b +--R + +--R 8 +--R 16a +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 8 +--R 4b - 16a b + 16a b + 16a b - 40a b + 16a b + 16a b - 16a b + 4a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 393 + +--S 394 of 502 +m0878a:= a0878.1-r0878 +--R +--R +--R (227) +--R 8 7 2 6 3 5 4 4 12 +--R (3b + 12a b + 18a b + 12a b + 3a b )sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (24b + 108a b + 192a b + 168a b + 72a b + 12a b )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 84b + 432a b + 906a b + 984a b + 576a b + 168a b +--R + +--R 6 2 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R - 12b - 24a b + 24a b + 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 168b + 1008a b + 2496a b + 3276a b + 2424a b + 984a b +--R + +--R 6 2 7 +--R 192a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 72b - 192a b - 96a b + 144a b + 168a b + 48a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 210b + 1512a b + 4452a b + 6984a b + 6309a b + 3276a b +--R + +--R 6 2 7 8 +--R 906a b + 108a b + 3a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 180b - 648a b - 648a b + 216a b + 756a b + 432a b +--R + +--R 6 2 +--R 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 +--R 18b - 36a b + 18a b +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 168b + 1512a b + 5376a b + 10080a b + 10944a b +--R + +--R 5 3 6 2 7 8 +--R 6984a b + 2496a b + 432a b + 24a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 240b - 1200a b - 1872a b - 432a b + 1584a b + 1584a b +--R + +--R 6 2 7 +--R 528a b + 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (72b + 72a b - 144a b - 144a b + 72a b + 72a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 84b + 1008a b + 4452a b + 10080a b + 13104a b +--R + +--R 5 3 6 2 7 8 +--R 10080a b + 4452a b + 1008a b + 84a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 180b - 1320a b - 3000a b - 2088a b + 1512a b +--R + +--R 5 3 6 2 7 8 +--R 3096a b + 1656a b + 312a b + 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 108b + 288a b - 108a b - 576a b - 108a b + 288a b +--R + +--R 6 2 +--R 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R - 12b + 24a b - 24a b + 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 24b + 432a b + 2496a b + 6984a b + 10944a b + 10080a b +--R + +--R 6 2 7 8 +--R 5376a b + 1512a b + 168a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 72b - 864a b - 2880a b - 3456a b + 3456a b + 2880a b +--R + +--R 7 8 +--R 864a b + 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 72b + 432a b + 288a b - 792a b - 792a b + 288a b +--R + +--R 6 2 7 +--R 432a b + 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 3 5 4 4 5 3 +--R (- 24b + 96a b - 48a b - 72a b + 48a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 3b + 108a b + 906a b + 3276a b + 6309a b + 6984a b +--R + +--R 6 2 7 8 +--R 4452a b + 1512a b + 210a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 12b - 312a b - 1656a b - 3096a b - 1512a b + 2088a b +--R + +--R 6 2 7 8 +--R 3000a b + 1320a b + 180a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 18b + 288a b + 612a b - 288a b - 1260a b - 288a b +--R + +--R 6 2 7 8 +--R 612a b + 288a b + 18a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 12b - 72a b + 120a b + 120a b - 180a b - 48a b +--R + +--R 6 2 +--R 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 3b - 12a b + 18a b - 12a b + 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 12a b + 192a b + 984a b + 2424a b + 3276a b + 2496a b +--R + +--R 7 8 +--R 1008a b + 168a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 48a b - 528a b - 1584a b - 1584a b + 432a b + 1872a b +--R + +--R 7 8 +--R 1200a b + 240a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 72a b + 432a b + 288a b - 792a b - 792a b + 288a b +--R + +--R 7 8 +--R 432a b + 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 2 6 3 5 5 3 6 2 7 3 +--R (- 48a b - 48a b + 240a b - 240a b + 48a b + 48a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (12a b - 48a b + 72a b - 48a b + 12a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 18a b + 168a b + 576a b + 984a b + 906a b + 432a b +--R + +--R 8 +--R 84a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 72a b - 432a b - 756a b - 216a b + 648a b + 648a b +--R + +--R 8 +--R 180a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 108a b + 288a b - 108a b - 576a b - 108a b + 288a b +--R + +--R 8 +--R 108a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 72a b + 48a b + 180a b - 120a b - 120a b + 72a b +--R + +--R 8 +--R 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (18a b - 72a b + 108a b - 72a b + 18a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 11 +--R (12a b + 72a b + 168a b + 192a b + 108a b + 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 9 +--R (- 48a b - 168a b - 144a b + 96a b + 192a b + 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 7 +--R (72a b + 72a b - 144a b - 144a b + 72a b + 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 5 +--R (- 48a b + 72a b + 48a b - 96a b + 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 +--R (12a b - 48a b + 72a b - 48a b + 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (3a b + 12a b + 18a b + 12a b + 3a )cosh(x) +--R + +--R 4 4 5 3 7 8 10 +--R (- 12a b - 24a b + 24a b + 12a )cosh(x) +--R + +--R 4 4 6 2 8 8 +--R (18a b - 36a b + 18a )cosh(x) +--R + +--R 4 4 5 3 7 8 6 +--R (- 12a b + 24a b - 24a b + 12a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (3a b - 12a b + 18a b - 12a b + 3a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) +--R + +--R b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 +--R (- 2b + 2a )sinh(x) + (- 2b + 2a )cosh(x) +--R / +--R 2 2 +--R (b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b +--R + +--R a +--R + +--R 8 7 2 6 3 5 4 4 12 +--R (- 3b - 12a b - 18a b - 12a b - 3a b )sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 24b - 108a b - 192a b - 168a b - 72a b - 12a b )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 84b - 432a b - 906a b - 984a b - 576a b - 168a b +--R + +--R 6 2 +--R - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 12b + 24a b - 24a b - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 168b - 1008a b - 2496a b - 3276a b - 2424a b - 984a b +--R + +--R 6 2 7 +--R - 192a b - 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (72b + 192a b + 96a b - 144a b - 168a b - 48a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 210b - 1512a b - 4452a b - 6984a b - 6309a b +--R + +--R 5 3 6 2 7 8 +--R - 3276a b - 906a b - 108a b - 3a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 180b + 648a b + 648a b - 216a b - 756a b - 432a b +--R + +--R 6 2 +--R - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 +--R - 18b + 36a b - 18a b +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 168b - 1512a b - 5376a b - 10080a b - 10944a b +--R + +--R 5 3 6 2 7 8 +--R - 6984a b - 2496a b - 432a b - 24a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 240b + 1200a b + 1872a b + 432a b - 1584a b - 1584a b +--R + +--R 6 2 7 +--R - 528a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 72b - 72a b + 144a b + 144a b - 72a b - 72a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 84b - 1008a b - 4452a b - 10080a b - 13104a b +--R + +--R 5 3 6 2 7 8 +--R - 10080a b - 4452a b - 1008a b - 84a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 180b + 1320a b + 3000a b + 2088a b - 1512a b - 3096a b +--R + +--R 6 2 7 8 +--R - 1656a b - 312a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 108b - 288a b + 108a b + 576a b + 108a b - 288a b +--R + +--R 6 2 +--R - 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 12b - 24a b + 24a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 24b - 432a b - 2496a b - 6984a b - 10944a b +--R + +--R 5 3 6 2 7 8 +--R - 10080a b - 5376a b - 1512a b - 168a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R 72b + 864a b + 2880a b + 3456a b - 3456a b - 2880a b +--R + +--R 7 8 +--R - 864a b - 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 72b - 432a b - 288a b + 792a b + 792a b - 288a b +--R + +--R 6 2 7 +--R - 432a b - 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 3 5 4 4 5 3 +--R (24b - 96a b + 48a b + 72a b - 48a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 3b - 108a b - 906a b - 3276a b - 6309a b - 6984a b +--R + +--R 6 2 7 8 +--R - 4452a b - 1512a b - 210a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 12b + 312a b + 1656a b + 3096a b + 1512a b - 2088a b +--R + +--R 6 2 7 8 +--R - 3000a b - 1320a b - 180a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 18b - 288a b - 612a b + 288a b + 1260a b + 288a b +--R + +--R 6 2 7 8 +--R - 612a b - 288a b - 18a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R (12b + 72a b - 120a b - 120a b + 180a b + 48a b - 72a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 3b + 12a b - 18a b + 12a b - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 12a b - 192a b - 984a b - 2424a b - 3276a b - 2496a b +--R + +--R 7 8 +--R - 1008a b - 168a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 48a b + 528a b + 1584a b + 1584a b - 432a b - 1872a b +--R + +--R 7 8 +--R - 1200a b - 240a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 72a b - 432a b - 288a b + 792a b + 792a b - 288a b +--R + +--R 7 8 +--R - 432a b - 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 2 6 3 5 5 3 6 2 7 3 +--R (48a b + 48a b - 240a b + 240a b - 48a b - 48a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (- 12a b + 48a b - 72a b + 48a b - 12a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 18a b - 168a b - 576a b - 984a b - 906a b - 432a b +--R + +--R 8 +--R - 84a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 72a b + 432a b + 756a b + 216a b - 648a b - 648a b +--R + +--R 8 +--R - 180a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 108a b - 288a b + 108a b + 576a b + 108a b - 288a b +--R + +--R 8 +--R - 108a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (72a b - 48a b - 180a b + 120a b + 120a b - 72a b - 12a ) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (- 18a b + 72a b - 108a b + 72a b - 18a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 11 +--R (- 12a b - 72a b - 168a b - 192a b - 108a b - 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 9 +--R (48a b + 168a b + 144a b - 96a b - 192a b - 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 7 +--R (- 72a b - 72a b + 144a b + 144a b - 72a b - 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 5 +--R (48a b - 72a b - 48a b + 96a b - 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 +--R (- 12a b + 48a b - 72a b + 48a b - 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (- 3a b - 12a b - 18a b - 12a b - 3a )cosh(x) +--R + +--R 4 4 5 3 7 8 10 +--R (12a b + 24a b - 24a b - 12a )cosh(x) +--R + +--R 4 4 6 2 8 8 +--R (- 18a b + 36a b - 18a )cosh(x) +--R + +--R 4 4 5 3 7 8 6 +--R (12a b - 24a b + 24a b - 12a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (- 3a b + 12a b - 18a b + 12a b - 3a )cosh(x) +--R * +--R +-------+ +--R | 2 2 a sinh(x) + b cosh(x) +--R \|b - a atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 7 6 2 5 3 4 4 3 5 2 11 +--R (6b + 15a b + 6a b - 12a b - 12a b - 3a b )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (39b + 114a b + 78a b - 66a b - 111a b - 48a b - 6a b)cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 102b + 360a b + 366a b - 93a b - 408a b - 264a b +--R + +--R 6 7 +--R - 60a b - 3a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R - 22b - 8a b + 54a b + 32a b - 24a b - 22a b - 8a b - 2a +--R * +--R 9 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 126b + 582a b + 855a b + 162a b - 738a b - 720a b +--R + +--R 6 7 +--R - 243a b - 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 96b - 78a b + 264a b + 302a b - 78a b - 208a b +--R + +--R 6 7 +--R - 90a b - 16a +--R * +--R cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 42b + 420a b + 1026a b + 702a b - 558a b - 1044a b +--R + +--R 6 7 +--R - 510a b - 78a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 132b - 192a b + 504a b + 964a b + 36a b - 704a b +--R + +--R 6 7 +--R - 408a b - 68a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R - 22b - 4a b + 6a b + 22a b + 32a b - 10a b - 16a b - 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 84b - 126a b + 378a b + 882a b + 252a b - 630a b +--R + +--R 6 7 +--R - 546a b - 126a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 16b - 20a b + 548a b + 1368a b + 368a b - 1164a b +--R + +--R 6 7 +--R - 932a b - 184a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 92b - 158a b + 66a b + 246a b + 166a b - 40a b +--R + +--R 6 7 +--R - 140a b - 48a +--R * +--R cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 126b - 546a b - 630a b + 252a b + 882a b + 378a b +--R + +--R 6 7 +--R - 126a b - 84a +--R * +--R 6 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 242b + 618a b + 662a b + 734a b + 218a b - 1054a b +--R + +--R 6 7 +--R - 1122a b - 298a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 186b - 558a b + 6a b + 912a b + 612a b - 216a b +--R + +--R 6 7 +--R - 432a b - 138a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 +--R 6b + 6a b - 6a b - 42a b + 24a b + 24a b - 12a +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 78b - 510a b - 1044a b - 558a b + 702a b + 1026a b +--R + +--R 6 7 +--R 420a b + 42a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 298b + 1122a b + 1054a b - 218a b - 734a b - 662a b +--R + +--R 6 7 +--R - 618a b - 242a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 250b - 858a b - 328a b + 1550a b + 1340a b - 460a b +--R + +--R 6 7 +--R - 762a b - 232a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 30b + 54a b - 114a b - 102a b + 48a b + 168a b - 36a b +--R + +--R 7 +--R - 48a +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 24b - 243a b - 720a b - 738a b + 162a b + 855a b +--R + +--R 6 7 +--R 582a b + 126a +--R * +--R 8 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 184b + 932a b + 1164a b - 368a b - 1368a b - 548a b +--R + +--R 6 7 +--R 20a b - 16a +--R * +--R 6 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 232b - 762a b - 460a b + 1340a b + 1550a b - 328a b +--R + +--R 6 7 +--R - 858a b - 250a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 72b + 84a b - 204a b - 288a b + 252a b + 240a b - 72a b +--R + +--R 7 +--R - 84a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R - 11a b + 28a b - 10a b - 20a b + 5a b + 16a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 3b - 60a b - 264a b - 408a b - 93a b + 366a b +--R + +--R 6 7 +--R 360a b + 102a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 68b + 408a b + 704a b - 36a b - 964a b - 504a b +--R + +--R 6 7 +--R 192a b + 132a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 138b - 432a b - 216a b + 612a b + 912a b + 6a b +--R + +--R 6 7 +--R - 558a b - 186a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 84b + 72a b - 240a b - 252a b + 288a b + 204a b - 84a b +--R + +--R 7 +--R - 72a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 11b + 12a b + 16a b + 20a b - 95a b + 56a b + 18a b +--R + +--R 7 +--R - 16a +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 6a b - 48a b - 111a b - 66a b + 78a b + 114a b + 39a ) +--R * +--R 10 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 16b + 90a b + 208a b + 78a b - 302a b - 264a b + 78a b +--R + +--R 7 +--R 96a +--R * +--R 8 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 48b - 140a b - 40a b + 166a b + 246a b + 66a b +--R + +--R 6 7 +--R - 158a b - 92a +--R * +--R 6 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 48b + 36a b - 168a b - 48a b + 102a b + 114a b - 54a b +--R + +--R 7 +--R - 30a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 16b + 18a b + 56a b - 95a b + 20a b + 16a b + 12a b +--R + +--R 7 +--R - 11a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 5 2 6 7 +--R 2a b - 8a b + 10a b - 10a b + 8a b - 2a +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 11 +--R (- 3a b - 12a b - 12a b + 6a b + 15a b + 6a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (2b + 8a b + 22a b + 24a b - 32a b - 54a b + 8a b + 22a ) +--R * +--R 9 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (- 8b - 16a b - 10a b + 32a b + 22a b + 6a b - 4a b - 22a ) +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (12b - 24a b - 24a b + 42a b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (- 8b + 16a b + 5a b - 20a b - 10a b + 28a b - 11a b)cosh(x) +--R + +--R 7 6 2 5 4 3 5 2 6 +--R (2b - 8a b + 10a b - 10a b + 8a b - 2a b)cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 8b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b +--R + +--R 7 5 8 4 +--R 32a b + 8a b +--R * +--R 12 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 64b + 288a b + 384a b - 128a b - 768a b - 576a b + 128a b +--R + +--R 7 5 8 4 9 3 +--R 384a b + 192a b + 32a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 224b + 1152a b + 1968a b + 320a b - 3072a b - 3648a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R - 608a b + 1728a b + 1440a b + 448a b + 48a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 5 7 6 6 7 5 +--R - 32b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 8 4 +--R 32a b +--R * +--R 10 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 448b + 2688a b + 5760a b + 3360a b - 6400a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 12160a b - 5760a b + 3520a b + 5440a b + 2560a b +--R + +--R 10 2 11 +--R 512a b + 32a b +--R * +--R 3 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R - 192b - 512a b + 128a b + 1408a b + 768a b - 1152a b +--R + +--R 6 6 7 5 8 4 9 3 +--R - 1152a b + 128a b + 448a b + 128a b +--R * +--R cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 560b + 4032a b + 10752a b + 10560a b - 6360a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 24480a b - 19360a b + 1440a b + 12000a b + 8160a b +--R + +--R 10 2 11 12 +--R 2400a b + 288a b + 8a +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 480b - 1728a b - 768a b + 4032a b + 4992a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 10 2 +--R - 1728a b - 5568a b - 1728a b + 1632a b + 1152a b + 192a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R 48b - 192a b + 288a b - 192a b + 48a b +--R * +--R 8 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 448b + 4032a b + 13440a b + 18816a b + 960a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 31104a b - 37376a b - 9216a b + 15936a b + 16320a b +--R + +--R 10 2 11 12 +--R 6528a b + 1152a b + 64a +--R * +--R 5 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 640b - 3200a b - 3712a b + 5248a b + 13568a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 3328a b - 12032a b - 9472a b + 1408a b + 3968a b +--R + +--R 10 2 11 +--R 1408a b + 128a b +--R * +--R 3 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 192b + 192a b - 768a b - 768a b + 1152a b + 1152a b +--R + +--R 6 6 7 5 8 4 9 3 +--R - 768a b - 768a b + 192a b + 192a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 224b + 2688a b + 11424a b + 21504a b + 11424a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 24192a b - 46144a b - 24192a b + 11424a b + 21504a b +--R + +--R 10 2 11 12 +--R 11424a b + 2688a b + 224a +--R * +--R 6 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 480b - 3520a b - 7040a b + 1472a b + 19552a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 15872a b - 11648a b - 21248a b - 4768a b + 6592a b +--R + +--R 10 2 11 12 +--R 4352a b + 832a b + 32a +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 288b + 768a b - 864a b - 3072a b + 576a b + 4608a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 576a b - 3072a b - 864a b + 768a b + 288a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 5 7 6 6 7 5 +--R - 32b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 8 4 +--R 32a b +--R * +--R 6 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 64b + 1152a b + 6528a b + 16320a b + 15936a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 9216a b - 37376a b - 31104a b + 960a b + 18816a b +--R + +--R 10 2 11 12 +--R 13440a b + 4032a b + 448a +--R * +--R 7 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 192b - 2304a b - 7296a b - 4608a b + 15168a b +--R + +--R 5 7 7 5 8 4 9 3 10 2 +--R 25344a b - 25344a b - 15168a b + 4608a b + 7296a b +--R + +--R 11 12 +--R 2304a b + 192a +--R * +--R 5 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 192b + 1152a b + 384a b - 4416a b - 3456a b + 6144a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 11 +--R 6144a b - 3456a b - 4416a b + 384a b + 1152a b + 192a b +--R * +--R 3 +--R cosh(x) +--R + +--R 12 2 10 3 9 4 8 5 7 6 6 +--R - 64b + 384a b - 128a b - 768a b + 384a b + 640a b +--R + +--R 7 5 8 4 9 3 +--R - 384a b - 192a b + 128a b +--R * +--R cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 8b + 288a b + 2400a b + 8160a b + 12000a b + 1440a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R - 19360a b - 24480a b - 6360a b + 10560a b + 10752a b +--R + +--R 11 12 +--R 4032a b + 560a +--R * +--R 8 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 32b - 832a b - 4352a b - 6592a b + 4768a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 21248a b + 11648a b - 15872a b - 19552a b - 1472a b +--R + +--R 10 2 11 12 +--R 7040a b + 3520a b + 480a +--R * +--R 6 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 48b + 768a b + 1536a b - 2304a b - 6576a b + 1536a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 11 +--R 9984a b + 1536a b - 6576a b - 2304a b + 1536a b + 768a b +--R + +--R 12 +--R 48a +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R - 32b - 192a b + 384a b + 704a b - 1152a b - 960a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 1472a b + 576a b - 864a b - 128a b + 192a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 8b - 32a b + 32a b + 32a b - 80a b + 32a b + 32a b +--R + +--R 7 5 8 4 +--R - 32a b + 8a b +--R * +--R 4 +--R sinh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 32a b + 512a b + 2560a b + 5440a b + 3520a b - 5760a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R - 12160a b - 6400a b + 3360a b + 5760a b + 2688a b + 448a +--R * +--R 9 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 +--R - 128a b - 1408a b - 3968a b - 1408a b + 9472a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 12032a b - 3328a b - 13568a b - 5248a b + 3712a b +--R + +--R 11 12 +--R 3200a b + 640a +--R * +--R 7 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 192a b + 1152a b + 384a b - 4416a b - 3456a b + 6144a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R 6144a b - 3456a b - 4416a b + 384a b + 1152a b + 192a +--R * +--R 5 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 7 5 +--R - 128a b - 128a b + 896a b + 256a b - 2048a b + 2048a b +--R + +--R 8 4 9 3 10 2 11 +--R - 256a b - 896a b + 128a b + 128a b +--R * +--R 3 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 32a b - 128a b + 128a b + 128a b - 320a b + 128a b +--R + +--R 7 5 8 4 9 3 +--R 128a b - 128a b + 32a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 48a b + 448a b + 1440a b + 1728a b - 608a b - 3648a b +--R + +--R 8 4 9 3 10 2 11 12 +--R - 3072a b + 320a b + 1968a b + 1152a b + 224a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 +--R - 192a b - 1152a b - 1632a b + 1728a b + 5568a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R 1728a b - 4992a b - 4032a b + 768a b + 1728a b + 480a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 288a b + 768a b - 864a b - 3072a b + 576a b + 4608a b +--R + +--R 8 4 9 3 10 2 11 12 +--R 576a b - 3072a b - 864a b + 768a b + 288a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R - 192a b + 128a b + 864a b - 576a b - 1472a b + 960a b +--R + +--R 8 4 9 3 10 2 11 12 +--R 1152a b - 704a b - 384a b + 192a b + 32a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 48a b - 192a b + 192a b + 192a b - 480a b + 192a b +--R + +--R 8 4 9 3 10 2 +--R 192a b - 192a b + 48a b +--R * +--R 2 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 32a b + 192a b + 384a b + 128a b - 576a b - 768a b +--R + +--R 9 3 10 2 11 12 +--R - 128a b + 384a b + 288a b + 64a +--R * +--R 11 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R - 128a b - 448a b - 128a b + 1152a b + 1152a b - 768a b +--R + +--R 9 3 10 2 11 12 +--R - 1408a b - 128a b + 512a b + 192a +--R * +--R 9 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 192a b + 192a b - 768a b - 768a b + 1152a b + 1152a b +--R + +--R 9 3 10 2 11 12 +--R - 768a b - 768a b + 192a b + 192a +--R * +--R 7 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R - 128a b + 192a b + 384a b - 640a b - 384a b + 768a b +--R + +--R 9 3 10 2 12 +--R 128a b - 384a b + 64a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 32a b - 128a b + 128a b + 128a b - 320a b + 128a b +--R + +--R 9 3 10 2 11 +--R 128a b - 128a b + 32a b +--R * +--R 3 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 8a b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b +--R + +--R 11 12 +--R 32a b + 8a +--R * +--R 12 +--R cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 9 3 10 2 11 +--R - 32a b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 12 +--R 32a +--R * +--R 10 +--R cosh(x) +--R + +--R 4 8 6 6 8 4 10 2 12 8 +--R (48a b - 192a b + 288a b - 192a b + 48a )cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 9 3 10 2 11 +--R - 32a b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 12 +--R 32a +--R * +--R 6 +--R cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 8a b - 32a b + 32a b + 32a b - 80a b + 32a b + 32a b +--R + +--R 11 12 +--R - 32a b + 8a +--R * +--R 4 +--R cosh(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 502 +--d0878a:= D(m0878a,x) +--E 395 + +--S 396 of 502 +m0878b:= a0878.2-r0878 +--R +--R +--R (228) +--R 8 7 2 6 3 5 4 4 12 +--R (- 6b - 24a b - 36a b - 24a b - 6a b )sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 48b - 216a b - 384a b - 336a b - 144a b - 24a b )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 168b - 864a b - 1812a b - 1968a b - 1152a b - 336a b +--R + +--R 6 2 +--R - 36a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 24b + 48a b - 48a b - 24a b +--R * +--R 10 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 336b - 2016a b - 4992a b - 6552a b - 4848a b +--R + +--R 5 3 6 2 7 +--R - 1968a b - 384a b - 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (144b + 384a b + 192a b - 288a b - 336a b - 96a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 420b - 3024a b - 8904a b - 13968a b - 12618a b +--R + +--R 5 3 6 2 7 8 +--R - 6552a b - 1812a b - 216a b - 6a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 360b + 1296a b + 1296a b - 432a b - 1512a b - 864a b +--R + +--R 6 2 +--R - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 +--R - 36b + 72a b - 36a b +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 336b - 3024a b - 10752a b - 20160a b - 21888a b +--R + +--R 5 3 6 2 7 8 +--R - 13968a b - 4992a b - 864a b - 48a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 480b + 2400a b + 3744a b + 864a b - 3168a b - 3168a b +--R + +--R 6 2 7 +--R - 1056a b - 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 144b - 144a b + 288a b + 288a b - 144a b - 144a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 168b - 2016a b - 8904a b - 20160a b - 26208a b +--R + +--R 5 3 6 2 7 8 +--R - 20160a b - 8904a b - 2016a b - 168a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 360b + 2640a b + 6000a b + 4176a b - 3024a b - 6192a b +--R + +--R 6 2 7 8 +--R - 3312a b - 624a b - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 216b - 576a b + 216a b + 1152a b + 216a b - 576a b +--R + +--R 6 2 +--R - 216a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 24b - 48a b + 48a b - 24a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 48b - 864a b - 4992a b - 13968a b - 21888a b +--R + +--R 5 3 6 2 7 8 +--R - 20160a b - 10752a b - 3024a b - 336a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R 144b + 1728a b + 5760a b + 6912a b - 6912a b - 5760a b +--R + +--R 7 8 +--R - 1728a b - 144a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 144b - 864a b - 576a b + 1584a b + 1584a b - 576a b +--R + +--R 6 2 7 +--R - 864a b - 144a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 3 5 4 4 5 3 +--R (48b - 192a b + 96a b + 144a b - 96a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 6b - 216a b - 1812a b - 6552a b - 12618a b - 13968a b +--R + +--R 6 2 7 8 +--R - 8904a b - 3024a b - 420a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 24b + 624a b + 3312a b + 6192a b + 3024a b - 4176a b +--R + +--R 6 2 7 8 +--R - 6000a b - 2640a b - 360a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 36b - 576a b - 1224a b + 576a b + 2520a b + 576a b +--R + +--R 6 2 7 8 +--R - 1224a b - 576a b - 36a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 24b + 144a b - 240a b - 240a b + 360a b + 96a b +--R + +--R 6 2 +--R - 144a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 6b + 24a b - 36a b + 24a b - 6a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 24a b - 384a b - 1968a b - 4848a b - 6552a b +--R + +--R 6 2 7 8 +--R - 4992a b - 2016a b - 336a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 96a b + 1056a b + 3168a b + 3168a b - 864a b - 3744a b +--R + +--R 7 8 +--R - 2400a b - 480a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 144a b - 864a b - 576a b + 1584a b + 1584a b - 576a b +--R + +--R 7 8 +--R - 864a b - 144a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 2 6 3 5 5 3 6 2 7 3 +--R (96a b + 96a b - 480a b + 480a b - 96a b - 96a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (- 24a b + 96a b - 144a b + 96a b - 24a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 36a b - 336a b - 1152a b - 1968a b - 1812a b - 864a b +--R + +--R 8 +--R - 168a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 144a b + 864a b + 1512a b + 432a b - 1296a b - 1296a b +--R + +--R 8 +--R - 360a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 216a b - 576a b + 216a b + 1152a b + 216a b - 576a b +--R + +--R 8 +--R - 216a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 144a b - 96a b - 360a b + 240a b + 240a b - 144a b +--R + +--R 8 +--R - 24a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (- 36a b + 144a b - 216a b + 144a b - 36a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 11 +--R (- 24a b - 144a b - 336a b - 384a b - 216a b - 48a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 9 +--R (96a b + 336a b + 288a b - 192a b - 384a b - 144a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (- 144a b - 144a b + 288a b + 288a b - 144a b - 144a ) +--R * +--R 7 +--R cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 5 +--R (96a b - 144a b - 96a b + 192a b - 48a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 +--R (- 24a b + 96a b - 144a b + 96a b - 24a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (- 6a b - 24a b - 36a b - 24a b - 6a )cosh(x) +--R + +--R 4 4 5 3 7 8 10 +--R (24a b + 48a b - 48a b - 24a )cosh(x) +--R + +--R 4 4 6 2 8 8 +--R (- 36a b + 72a b - 36a )cosh(x) +--R + +--R 4 4 5 3 7 8 6 +--R (24a b - 48a b + 48a b - 24a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (- 6a b + 24a b - 36a b + 24a b - 6a )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R (sinh(x) + cosh(x))\|- b + a +--R atan(-------------------------------) +--R b - a +--R + +--R 8 7 2 6 3 5 4 4 12 +--R (- 3b - 12a b - 18a b - 12a b - 3a b )sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 24b - 108a b - 192a b - 168a b - 72a b - 12a b )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 84b - 432a b - 906a b - 984a b - 576a b - 168a b +--R + +--R 6 2 +--R - 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 12b + 24a b - 24a b - 12a b +--R * +--R 10 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 168b - 1008a b - 2496a b - 3276a b - 2424a b - 984a b +--R + +--R 6 2 7 +--R - 192a b - 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (72b + 192a b + 96a b - 144a b - 168a b - 48a b )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 210b - 1512a b - 4452a b - 6984a b - 6309a b +--R + +--R 5 3 6 2 7 8 +--R - 3276a b - 906a b - 108a b - 3a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 180b + 648a b + 648a b - 216a b - 756a b - 432a b +--R + +--R 6 2 +--R - 72a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 6 4 4 +--R - 18b + 36a b - 18a b +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 168b - 1512a b - 5376a b - 10080a b - 10944a b +--R + +--R 5 3 6 2 7 8 +--R - 6984a b - 2496a b - 432a b - 24a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 240b + 1200a b + 1872a b + 432a b - 1584a b - 1584a b +--R + +--R 6 2 7 +--R - 528a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 72b - 72a b + 144a b + 144a b - 72a b - 72a b )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 84b - 1008a b - 4452a b - 10080a b - 13104a b +--R + +--R 5 3 6 2 7 8 +--R - 10080a b - 4452a b - 1008a b - 84a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 180b + 1320a b + 3000a b + 2088a b - 1512a b - 3096a b +--R + +--R 6 2 7 8 +--R - 1656a b - 312a b - 12a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 108b - 288a b + 108a b + 576a b + 108a b - 288a b +--R + +--R 6 2 +--R - 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 3 5 4 4 +--R 12b - 24a b + 24a b - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 24b - 432a b - 2496a b - 6984a b - 10944a b +--R + +--R 5 3 6 2 7 8 +--R - 10080a b - 5376a b - 1512a b - 168a +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R 72b + 864a b + 2880a b + 3456a b - 3456a b - 2880a b +--R + +--R 7 8 +--R - 864a b - 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 72b - 432a b - 288a b + 792a b + 792a b - 288a b +--R + +--R 6 2 7 +--R - 432a b - 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 6 3 5 4 4 5 3 +--R (24b - 96a b + 48a b + 72a b - 48a b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 3b - 108a b - 906a b - 3276a b - 6309a b - 6984a b +--R + +--R 6 2 7 8 +--R - 4452a b - 1512a b - 210a +--R * +--R 8 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 12b + 312a b + 1656a b + 3096a b + 1512a b - 2088a b +--R + +--R 6 2 7 8 +--R - 3000a b - 1320a b - 180a +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 18b - 288a b - 612a b + 288a b + 1260a b + 288a b +--R + +--R 6 2 7 8 +--R - 612a b - 288a b - 18a +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R (12b + 72a b - 120a b - 120a b + 180a b + 48a b - 72a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 3b + 12a b - 18a b + 12a b - 3a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 12a b - 192a b - 984a b - 2424a b - 3276a b - 2496a b +--R + +--R 7 8 +--R - 1008a b - 168a +--R * +--R 9 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 48a b + 528a b + 1584a b + 1584a b - 432a b - 1872a b +--R + +--R 7 8 +--R - 1200a b - 240a +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 72a b - 432a b - 288a b + 792a b + 792a b - 288a b +--R + +--R 7 8 +--R - 432a b - 72a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 2 6 3 5 5 3 6 2 7 3 +--R (48a b + 48a b - 240a b + 240a b - 48a b - 48a b)cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (- 12a b + 48a b - 72a b + 48a b - 12a b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 18a b - 168a b - 576a b - 984a b - 906a b - 432a b +--R + +--R 8 +--R - 84a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 72a b + 432a b + 756a b + 216a b - 648a b - 648a b +--R + +--R 8 +--R - 180a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 108a b - 288a b + 108a b + 576a b + 108a b - 288a b +--R + +--R 8 +--R - 108a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (72a b - 48a b - 180a b + 120a b + 120a b - 72a b - 12a ) +--R * +--R 4 +--R cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (- 18a b + 72a b - 108a b + 72a b - 18a b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 11 +--R (- 12a b - 72a b - 168a b - 192a b - 108a b - 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 9 +--R (48a b + 168a b + 144a b - 96a b - 192a b - 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 7 +--R (- 72a b - 72a b + 144a b + 144a b - 72a b - 72a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 8 5 +--R (48a b - 72a b - 48a b + 96a b - 24a )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 +--R (- 12a b + 48a b - 72a b + 48a b - 12a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (- 3a b - 12a b - 18a b - 12a b - 3a )cosh(x) +--R + +--R 4 4 5 3 7 8 10 +--R (12a b + 24a b - 24a b - 12a )cosh(x) +--R + +--R 4 4 6 2 8 8 +--R (- 18a b + 36a b - 18a )cosh(x) +--R + +--R 4 4 5 3 7 8 6 +--R (12a b - 24a b + 24a b - 12a )cosh(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (- 3a b + 12a b - 18a b + 12a b - 3a )cosh(x) +--R * +--R a sinh(x) + b cosh(x) +--R atan(---------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 7 6 2 5 3 4 4 3 5 2 11 +--R (6b + 15a b + 6a b - 12a b - 12a b - 3a b )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (39b + 114a b + 78a b - 66a b - 111a b - 48a b - 6a b)cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 102b + 360a b + 366a b - 93a b - 408a b - 264a b +--R + +--R 6 7 +--R - 60a b - 3a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R - 22b - 8a b + 54a b + 32a b - 24a b - 22a b - 8a b - 2a +--R * +--R 9 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 126b + 582a b + 855a b + 162a b - 738a b - 720a b +--R + +--R 6 7 +--R - 243a b - 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 96b - 78a b + 264a b + 302a b - 78a b - 208a b +--R + +--R 6 7 +--R - 90a b - 16a +--R * +--R cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 42b + 420a b + 1026a b + 702a b - 558a b - 1044a b +--R + +--R 6 7 +--R - 510a b - 78a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 132b - 192a b + 504a b + 964a b + 36a b - 704a b +--R + +--R 6 7 +--R - 408a b - 68a +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R - 22b - 4a b + 6a b + 22a b + 32a b - 10a b - 16a b - 8a +--R * +--R 7 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 84b - 126a b + 378a b + 882a b + 252a b - 630a b +--R + +--R 6 7 +--R - 546a b - 126a +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 16b - 20a b + 548a b + 1368a b + 368a b - 1164a b +--R + +--R 6 7 +--R - 932a b - 184a +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 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302a b - 264a b + 78a b +--R + +--R 7 +--R 96a +--R * +--R 8 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 48b - 140a b - 40a b + 166a b + 246a b + 66a b +--R + +--R 6 7 +--R - 158a b - 92a +--R * +--R 6 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 48b + 36a b - 168a b - 48a b + 102a b + 114a b - 54a b +--R + +--R 7 +--R - 30a +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 16b + 18a b + 56a b - 95a b + 20a b + 16a b + 12a b +--R + +--R 7 +--R - 11a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 5 2 6 7 +--R 2a b - 8a b + 10a b - 10a b + 8a b - 2a +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 11 +--R (- 3a b - 12a b - 12a b + 6a b + 15a b + 6a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (2b + 8a b + 22a b + 24a b - 32a b - 54a b + 8a b + 22a ) +--R * +--R 9 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (- 8b - 16a b - 10a b + 32a b + 22a b + 6a b - 4a b - 22a ) +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (12b - 24a b - 24a b + 42a b + 6a b - 6a b - 6a )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (- 8b + 16a b + 5a b - 20a b - 10a b + 28a b - 11a b)cosh(x) +--R + +--R 7 6 2 5 4 3 5 2 6 +--R (2b - 8a b + 10a b - 10a b + 8a b - 2a b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 8b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b +--R + +--R 7 5 8 4 +--R 32a b + 8a b +--R * +--R 12 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R 64b + 288a b + 384a b - 128a b - 768a b - 576a b + 128a b +--R + +--R 7 5 8 4 9 3 +--R 384a b + 192a b + 32a b +--R * +--R 11 +--R cosh(x)sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 224b + 1152a b + 1968a b + 320a b - 3072a b - 3648a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R - 608a b + 1728a b + 1440a b + 448a b + 48a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 5 7 6 6 7 5 +--R - 32b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 8 4 +--R 32a b +--R * +--R 10 +--R 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+--R 8 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 448b + 4032a b + 13440a b + 18816a b + 960a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 31104a b - 37376a b - 9216a b + 15936a b + 16320a b +--R + +--R 10 2 11 12 +--R 6528a b + 1152a b + 64a +--R * +--R 5 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 640b - 3200a b - 3712a b + 5248a b + 13568a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 3328a b - 12032a b - 9472a b + 1408a b + 3968a b +--R + +--R 10 2 11 +--R 1408a b + 128a b +--R * +--R 3 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 192b + 192a b - 768a b - 768a b + 1152a b + 1152a b +--R + +--R 6 6 7 5 8 4 9 3 +--R - 768a b - 768a b + 192a b + 192a b +--R * +--R cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 224b + 2688a b + 11424a b + 21504a b + 11424a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 24192a b - 46144a b - 24192a b + 11424a b + 21504a b +--R + +--R 10 2 11 12 +--R 11424a b + 2688a b + 224a +--R * +--R 6 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 480b - 3520a b - 7040a b + 1472a b + 19552a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 15872a b - 11648a b - 21248a b - 4768a b + 6592a b +--R + +--R 10 2 11 12 +--R 4352a b + 832a b + 32a +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 288b + 768a b - 864a b - 3072a b + 576a b + 4608a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 576a b - 3072a b - 864a b + 768a b + 288a b +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 5 7 6 6 7 5 +--R - 32b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 8 4 +--R 32a b +--R * +--R 6 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 64b + 1152a b + 6528a b + 16320a b + 15936a b +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 9216a b - 37376a b - 31104a b + 960a b + 18816a b +--R + +--R 10 2 11 12 +--R 13440a b + 4032a b + 448a +--R * +--R 7 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 192b - 2304a b - 7296a b - 4608a b + 15168a b +--R + +--R 5 7 7 5 8 4 9 3 10 2 +--R 25344a b - 25344a b - 15168a b + 4608a b + 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12 +--R 3200a b + 640a +--R * +--R 7 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 192a b + 1152a b + 384a b - 4416a b - 3456a b + 6144a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R 6144a b - 3456a b - 4416a b + 384a b + 1152a b + 192a +--R * +--R 5 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 7 5 +--R - 128a b - 128a b + 896a b + 256a b - 2048a b + 2048a b +--R + +--R 8 4 9 3 10 2 11 +--R - 256a b - 896a b + 128a b + 128a b +--R * +--R 3 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 32a b - 128a b + 128a b + 128a b - 320a b + 128a b +--R + +--R 7 5 8 4 9 3 +--R 128a b - 128a b + 32a b +--R * +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 48a b + 448a b + 1440a b + 1728a b - 608a b - 3648a b +--R + +--R 8 4 9 3 10 2 11 12 +--R - 3072a b + 320a b + 1968a b + 1152a b + 224a +--R * +--R 10 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 +--R - 192a b - 1152a b - 1632a b + 1728a b + 5568a b +--R + +--R 7 5 8 4 9 3 10 2 11 12 +--R 1728a b - 4992a b - 4032a b + 768a b + 1728a b + 480a +--R * +--R 8 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 288a b + 768a b - 864a b - 3072a b + 576a b + 4608a b +--R + +--R 8 4 9 3 10 2 11 12 +--R 576a b - 3072a b - 864a b + 768a b + 288a +--R * +--R 6 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R - 192a b + 128a b + 864a b - 576a b - 1472a b + 960a b +--R + +--R 8 4 9 3 10 2 11 12 +--R 1152a b - 704a b - 384a b + 192a b + 32a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 48a b - 192a b + 192a b + 192a b - 480a b + 192a b +--R + +--R 8 4 9 3 10 2 +--R 192a b - 192a b + 48a b +--R * +--R 2 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 32a b + 192a b + 384a b + 128a b - 576a b - 768a b +--R + +--R 9 3 10 2 11 12 +--R - 128a b + 384a b + 288a b + 64a +--R * +--R 11 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R - 128a b - 448a b - 128a b + 1152a b + 1152a b - 768a b +--R + +--R 9 3 10 2 11 12 +--R - 1408a b - 128a b + 512a b + 192a +--R * +--R 9 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 192a b + 192a b - 768a b - 768a b + 1152a b + 1152a b +--R + +--R 9 3 10 2 11 12 +--R - 768a b - 768a b + 192a b + 192a +--R * +--R 7 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R - 128a b + 192a b + 384a b - 640a b - 384a b + 768a b +--R + +--R 9 3 10 2 12 +--R 128a b - 384a b + 64a +--R * +--R 5 +--R cosh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 32a b - 128a b + 128a b + 128a b - 320a b + 128a b +--R + +--R 9 3 10 2 11 +--R 128a b - 128a b + 32a b +--R * +--R 3 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 8a b + 32a b + 32a b - 32a b - 80a b - 32a b + 32a b +--R + +--R 11 12 +--R 32a b + 8a +--R * +--R 12 +--R cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 9 3 10 2 11 +--R - 32a b - 64a b + 64a b + 192a b - 192a b - 64a b + 64a b +--R + +--R 12 +--R 32a +--R * +--R 10 +--R cosh(x) +--R + +--R 4 8 6 6 8 4 10 2 12 8 +--R (48a b - 192a b + 288a b - 192a b + 48a )cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 9 3 10 2 11 +--R - 32a b + 64a b + 64a b - 192a b + 192a b - 64a b - 64a b +--R + +--R 12 +--R 32a +--R * +--R 6 +--R cosh(x) +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 8a b - 32a b + 32a b + 32a b - 80a b + 32a b + 32a b +--R + +--R 11 12 +--R - 32a b + 8a +--R * +--R 4 +--R cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 396 + +--S 397 of 502 +--d0878b:= D(m0878b,x) +--E 397 + +--S 398 of 502 +t0879:= (a*cosh(x)+b*sinh(x))^(1/2) +--R +--R +--R +---------------------+ +--R (229) \|b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 398 + +--S 399 of 502 +r0879:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (a*cosh(x)+b*sinh(x))^(1/2)/(-(a*cosh(x)+b*sinh(x))/_ + (a^2-b^2)^(1/2))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial(Complex(Integer)) +--R Variable(a) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 399 + +--S 400 of 502 +a0879:= integrate(t0879,x) +--R +--R +--R x +--R ++ +-----------------------+ +--R (230) | \|b sinh(%I) + a cosh(%I) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 400 + +--S 401 of 502 +--m0879:= a0879-r0879 +--E 401 + +--S 402 of 502 +--d0879:= D(m0879,x) +--E 402 + +--S 403 of 502 +t0880:= (a*cosh(x)+b*sinh(x))^(3/2) +--R +--R +--R +---------------------+ +--R (231) (b sinh(x) + a cosh(x))\|b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 403 + +--S 404 of 502 +r0880:= 2/3*(b*cosh(x)+a*sinh(x))*(a*cosh(x)+b*sinh(x))^(1/2)-_ + 2/3*%i*(a^2-b^2)*EllipticF(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (-(a*cosh(x)+b*sinh(x))/(a^2-b^2)^(1/2))^(1/2)/(a*cosh(x)+_ + b*sinh(x))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial(Complex(Integer)) +--R Variable(a) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 404 + +--S 405 of 502 +a0880:= integrate(t0880,x) +--R +--R +--R x +--R ++ +-----------------------+ +--R (232) | (b sinh(%I) + a cosh(%I))\|b sinh(%I) + a cosh(%I) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 405 + +--S 406 of 502 +--m0880:= a0880-r0880 +--E 406 + +--S 407 of 502 +--d0880:= D(m0880,x) +--E 407 + +--S 408 of 502 +t0881:= (a*cosh(x)+b*sinh(x))^(5/2) +--R +--R +--R (233) +--R 2 2 2 2 +---------------------+ +--R (b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) )\|b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 408 + +--S 409 of 502 +r0881:= 2/5*(b*cosh(x)+a*sinh(x))*(a*cosh(x)+b*sinh(x))^(3/2)-_ + 6/5*%i*(a^2-b^2)*EllipticE(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (a*cosh(x)+b*sinh(x))^(1/2)/(-(a*cosh(x)+b*sinh(x))/_ + (a^2-b^2)^(1/2))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial(Complex(Integer)) +--R Variable(a) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 409 + +--S 410 of 502 +a0881:= integrate(t0881,x) +--R +--R +--R (234) +--R INTSIGN +--R , +--R x +--R , +--R 2 2 2 2 +--R (b sinh(%I) + 2a b cosh(%I)sinh(%I) + a cosh(%I) ) +--R * +--R +-----------------------+ +--R \|b sinh(%I) + a cosh(%I) d%I +--R Type: Union(Expression(Integer),...) +--E 410 + +--S 411 of 502 +--m0881:= a0881-r0881 +--E 411 + +--S 412 of 502 +--d0881:= D(m0881,x) +--E 412 + +--S 413 of 502 +t0882:= 1/(a*cosh(x)+b*sinh(x))^(1/2) +--R +--R +--R 1 +--R (235) ------------------------ +--R +---------------------+ +--R \|b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 413 + +--S 414 of 502 +r0882:= -2*%i*EllipticF(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (-(a*cosh(x)+b*sinh(x))/(a^2-b^2)^(1/2))^(1/2)/_ + (a*cosh(x)+b*sinh(x))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial(Complex(Integer)) +--R Variable(a) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 414 + +--S 415 of 502 +a0882:= integrate(t0882,x) +--R +--R +--R x +--R ++ 1 +--R (236) | -------------------------- d%I +--R ++ +-----------------------+ +--R \|b sinh(%I) + a cosh(%I) +--R Type: Union(Expression(Integer),...) +--E 415 + +--S 416 of 502 +--m0882:= a0882-r0882 +--E 416 + +--S 417 of 502 +--d0882:= D(m0882,x) +--E 417 + +--S 418 of 502 +t0883:= 1/(a*cosh(x)+b*sinh(x))^(3/2) +--R +--R +--R 1 +--R (237) ----------------------------------------------- +--R +---------------------+ +--R (b sinh(x) + a cosh(x))\|b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 418 + +--S 419 of 502 +r0883:= 2*(b*cosh(x)+a*sinh(x))/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^(1/2)+_ + 2*%i*EllipticE(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (a*cosh(x)+b*sinh(x))^(1/2)/(a^2-b^2)/_ + (-(a*cosh(x)+b*sinh(x))/(a^2-b^2)^(1/2))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial(Complex(Integer)) +--R Variable(a) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 419 + +--S 420 of 502 +a0883:= integrate(t0883,x) +--R +--R +--R x +--R ++ 1 +--R (238) | --------------------------------------------------- d%I +--R ++ +-----------------------+ +--R (b sinh(%I) + a cosh(%I))\|b sinh(%I) + a cosh(%I) +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 502 +--m0883:= a0883-r0883 +--E 421 + +--S 422 of 502 +--d0883:= D(m0883,x) +--E 422 + +--S 423 of 502 +t0884:= 1/(a*cosh(x)+b*sinh(x))^(5/2) +--R +--R +--R (239) +--R 1 +--R ----------------------------------------------------------------------- +--R 2 2 2 2 +---------------------+ +--R (b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) )\|b sinh(x) + a cosh(x) +--R Type: Expression(Integer) +--E 423 + +--S 424 of 502 +r0884:= 2/3*(b*cosh(x)+a*sinh(x))/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^(3/2)-_ + 2/3*%i*EllipticF(-1/4*%pi+1/2*%i*(x+%i*atan(%i*b,a)),2)*_ + (-(a*cosh(x)+b*sinh(x))/(a^2-b^2)^(1/2))^(1/2)/_ + (a^2-b^2)/(a*cosh(x)+b*sinh(x))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial(Complex(Integer)) +--R Variable(a) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 424 + +--S 425 of 502 +a0884:= integrate(t0884,x) +--R +--R +--R (240) +--R INTSIGN +--R , +--R x +--R , +--R 1 +--R / +--R 2 2 2 2 +--R (b sinh(%I) + 2a b cosh(%I)sinh(%I) + a cosh(%I) ) +--R * +--R +-----------------------+ +--R \|b sinh(%I) + a cosh(%I) +--R * +--R d%I +--R Type: Union(Expression(Integer),...) +--E 425 + +--S 426 of 502 +--m0884:= a0884-r0884 +--E 426 + +--S 427 of 502 +--d0884:= D(m0884,x) +--E 427 + +--S 428 of 502 +t0885:= (sech(x)+%i*tanh(x))^3 +--R +--R +--R 3 2 2 3 +--R (241) - %i tanh(x) - 3sech(x)tanh(x) + 3%i sech(x) tanh(x) + sech(x) +--R Type: Expression(Complex(Integer)) +--E 428 + +--S 429 of 502 +r0885:= -%i*log(1-%i*sinh(x))-2*%i/(1-%i*sinh(x)) +--R +--R +--R (- %i sinh(x) + 1)log(- %i sinh(x) + 1) + 2 +--R (242) ------------------------------------------- +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 429 + +--S 430 of 502 +a0885:= integrate(t0885,x) +--R +--R +--R (243) +--R 2 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) + 4)sinh(x) - 2%i cosh(x) + 4cosh(x) +--R + +--R 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 2 2 +--R %i x sinh(x) + (2%i x cosh(x) - 2x + 4)sinh(x) + %i x cosh(x) +--R + +--R (- 2x + 4)cosh(x) - %i x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2%i)sinh(x) + cosh(x) + 2%i cosh(x) - 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 430 + +--S 431 of 502 +m0885:= a0885-r0885 +--R +--R +--R (244) +--R 3 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) + 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) + 8cosh(x) + 6%i)sinh(x) + 2cosh(x) + 4%i cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 3 2 +--R %i sinh(x) + (2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (%i cosh(x) - 4cosh(x) - 3%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1 +--R * +--R log(- %i sinh(x) + 1) +--R + +--R 3 2 +--R %i x sinh(x) + (2%i x cosh(x) - 3x + 2)sinh(x) +--R + +--R 2 2 +--R (%i x cosh(x) - 4x cosh(x) - 3%i x)sinh(x) + (- x - 2)cosh(x) +--R + +--R - 2%i x cosh(x) + x + 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) + 3%i)sinh(x) + (cosh(x) + 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R %i cosh(x) - 2cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 431 + +--S 432 of 502 +d0885:= D(m0885,x) +--R +--R +--R (245) +--R 5 4 3 +--R - %i sinh(x) + (- 2%i cosh(x) - 1)sinh(x) + (- 2cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 +--R (2%i cosh(x) - 6%i cosh(x) - 2)sinh(x) +--R + +--R 4 3 4 +--R (%i cosh(x) + 2cosh(x) - 2cosh(x) - %i)sinh(x) + cosh(x) +--R + +--R 3 +--R 4%i cosh(x) - 4%i cosh(x) - 1 +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) + 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) + 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) + 9%i cosh(x) - 18cosh(x) - 10%i)sinh(x) +--R + +--R 3 2 3 +--R (2%i cosh(x) - 9cosh(x) - 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R - 3%i cosh(x) + 3cosh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 432 + +--S 433 of 502 +t0886:= (sech(x)+%i*tanh(x))^5 +--R +--R +--R (246) +--R 5 4 2 3 3 2 +--R %i tanh(x) + 5sech(x)tanh(x) - 10%i sech(x) tanh(x) - 10sech(x) tanh(x) +--R + +--R 4 5 +--R 5%i sech(x) tanh(x) + sech(x) +--R Type: Expression(Complex(Integer)) +--E 433 + +--S 434 of 502 +r0886:= %i*log(1-%i*sinh(x))-2*%i/(1-%i*sinh(x))^2+4*%i/(1-%i*sinh(x)) +--R +--R +--R 2 +--R (%i sinh(x) - 2sinh(x) - %i)log(- %i sinh(x) + 1) - 4sinh(x) - 2%i +--R (247) ------------------------------------------------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 434 + +--S 435 of 502 +a0886:= integrate(t0886,x) +--R +--R +--R (248) +--R 4 3 +--R 2%i sinh(x) + (8%i cosh(x) - 8)sinh(x) +--R + +--R 2 2 +--R (12%i cosh(x) - 24cosh(x) - 12%i)sinh(x) +--R + +--R 3 2 4 +--R (8%i cosh(x) - 24cosh(x) - 24%i cosh(x) + 8)sinh(x) + 2%i cosh(x) +--R + +--R 3 2 +--R - 8cosh(x) - 12%i cosh(x) + 8cosh(x) + 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 4 3 +--R - %i x sinh(x) + (- 4%i x cosh(x) + 4x - 8)sinh(x) +--R + +--R 2 2 +--R (- 6%i x cosh(x) + (12x - 24)cosh(x) + 6%i x - 8%i)sinh(x) +--R + +--R 3 2 +--R - 4%i x cosh(x) + (12x - 24)cosh(x) + (12%i x - 16%i)cosh(x) - 4x +--R + +--R 8 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R - %i x cosh(x) + (4x - 8)cosh(x) + (6%i x - 8%i)cosh(x) +--R + +--R (- 4x + 8)cosh(x) - %i x +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) + 4%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) + 12%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 12%i cosh(x) - 12cosh(x) - 4%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R 4%i cosh(x) - 6cosh(x) - 4%i cosh(x) + 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 435 + +--S 436 of 502 +m0886:= a0886-r0886 +--R +--R +--R (249) +--R 6 5 +--R 2%i sinh(x) + (8%i cosh(x) - 12)sinh(x) +--R + +--R 2 4 +--R (12%i cosh(x) - 40cosh(x) - 30%i)sinh(x) +--R + +--R 3 2 3 +--R (8%i cosh(x) - 48cosh(x) - 80%i cosh(x) + 40)sinh(x) +--R + +--R 4 3 2 +--R (2%i cosh(x) - 24cosh(x) - 72%i cosh(x) + 80cosh(x) + 30%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 4cosh(x) - 24%i cosh(x) + 48cosh(x) + 40%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R - 2%i cosh(x) + 8cosh(x) + 12%i cosh(x) - 8cosh(x) - 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 6 5 +--R - %i sinh(x) + (- 4%i cosh(x) + 6)sinh(x) +--R + +--R 2 4 +--R (- 6%i cosh(x) + 20cosh(x) + 15%i)sinh(x) +--R + +--R 3 2 3 +--R (- 4%i cosh(x) + 24cosh(x) + 40%i cosh(x) - 20)sinh(x) +--R + +--R 4 3 2 +--R (- %i cosh(x) + 12cosh(x) + 36%i cosh(x) - 40cosh(x) - 15%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2cosh(x) + 12%i cosh(x) - 24cosh(x) - 20%i cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 +--R %i cosh(x) - 4cosh(x) - 6%i cosh(x) + 4cosh(x) + %i +--R * +--R log(- %i sinh(x) + 1) +--R + +--R 6 5 +--R - %i x sinh(x) + (- 4%i x cosh(x) + 6x - 4)sinh(x) +--R + +--R 2 4 +--R (- 6%i x cosh(x) + (20x - 8)cosh(x) + 15%i x - 6%i)sinh(x) +--R + +--R 3 2 3 +--R (- 4%i x cosh(x) + 24x cosh(x) + (40%i x - 8%i)cosh(x) - 20x)sinh(x) +--R + +--R 4 3 2 +--R - %i x cosh(x) + (12x + 8)cosh(x) + (36%i x + 4%i)cosh(x) +--R + +--R (- 40x - 8)cosh(x) - 15%i x - 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2x + 4)cosh(x) + (12%i x + 8%i)cosh(x) + (- 24x - 8)cosh(x) +--R + +--R (- 20%i x - 8%i)cosh(x) + 6x + 4 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (%i x + 2%i)cosh(x) - 4x cosh(x) + (- 6%i x - 4%i)cosh(x) + 4x cosh(x) +--R + +--R %i x + 2%i +--R / +--R 6 5 +--R sinh(x) + (4cosh(x) + 6%i)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) + 20%i cosh(x) - 15)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) + 24%i cosh(x) - 40cosh(x) - 20%i)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) + 12%i cosh(x) - 36cosh(x) - 40%i cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 +--R (2%i cosh(x) - 12cosh(x) - 24%i cosh(x) + 20cosh(x) + 6%i)sinh(x) +--R + +--R 4 3 2 +--R - cosh(x) - 4%i cosh(x) + 6cosh(x) + 4%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 436 + +--S 437 of 502 +d0886:= D(m0886,x) +--R +--R +--R (250) +--R 8 7 +--R %i sinh(x) + (4%i cosh(x) + 2)sinh(x) +--R + +--R 2 6 +--R (5%i cosh(x) + 8cosh(x) + 2%i)sinh(x) +--R + +--R 2 5 +--R (10cosh(x) + 16%i cosh(x) + 6)sinh(x) +--R + +--R 4 2 4 +--R (- 5%i cosh(x) + 25%i cosh(x) + 20cosh(x))sinh(x) +--R + +--R 5 4 2 3 +--R (- 4%i cosh(x) - 10cosh(x) + 20cosh(x) + 20%i cosh(x) + 6)sinh(x) +--R + +--R 6 5 4 2 +--R - %i cosh(x) - 8cosh(x) - 20%i cosh(x) + 35%i cosh(x) + 16cosh(x) +--R + +--R - 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 2 +--R - 2cosh(x) - 8%i cosh(x) - 10cosh(x) + 10cosh(x) + 8%i cosh(x) +--R + +--R 2 +--R * +--R sinh(x) +--R + +--R 6 5 4 2 +--R %i cosh(x) - 4cosh(x) - 15%i cosh(x) + 15%i cosh(x) + 4cosh(x) - %i +--R / +--R 8 7 +--R sinh(x) + (5cosh(x) + 8%i)sinh(x) +--R + +--R 2 6 +--R (10cosh(x) + 35%i cosh(x) - 28)sinh(x) +--R + +--R 3 2 5 +--R (10cosh(x) + 60%i cosh(x) - 105cosh(x) - 56%i)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) + 50%i cosh(x) - 150cosh(x) - 175%i cosh(x) + 70)sinh(x) +--R + +--R 5 4 3 2 +--R cosh(x) + 20%i cosh(x) - 100cosh(x) - 200%i cosh(x) + 175cosh(x) +--R + +--R 56%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 3%i cosh(x) - 30cosh(x) - 100%i cosh(x) + 150cosh(x) +--R + +--R 105%i cosh(x) - 28 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) - 20%i cosh(x) + 50cosh(x) + 60%i cosh(x) - 35cosh(x) +--R + +--R - 8%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R - %i cosh(x) + 5cosh(x) + 10%i cosh(x) - 10cosh(x) - 5%i cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 437 + +--S 438 of 502 +t0887:= 1/(sech(x)+%i*tanh(x)) +--R +--R +--R %i +--R (251) - -------------------- +--R tanh(x) - %i sech(x) +--R Type: Expression(Complex(Integer)) +--E 438 + +--S 439 of 502 +r0887:= -%i*log(1+%i*sinh(x)) +--R +--R +--R (252) - %i log(%i sinh(x) + 1) +--R Type: Expression(Complex(Integer)) +--E 439 + +--S 440 of 502 +a0887:= integrate(t0887,x) +--R +--R +--R (253) - 2%i log(sinh(x) + cosh(x) - %i) + %i x +--R Type: Union(Expression(Complex(Integer)),...) +--E 440 + +--S 441 of 502 +m0887:= a0887-r0887 +--R +--R +--R (254) - 2%i log(sinh(x) + cosh(x) - %i) + %i log(%i sinh(x) + 1) + %i x +--R Type: Expression(Complex(Integer)) +--E 441 + +--S 442 of 502 +d0887:= D(m0887,x) +--R +--R +--R 2 2 +--R - %i sinh(x) + %i cosh(x) - %i +--R (255) -------------------------------------------------- +--R 2 +--R sinh(x) + (cosh(x) - 2%i)sinh(x) - %i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 442 + +--S 443 of 502 +t0888:= 1/(sech(x)+%i*tanh(x))^2 +--R +--R +--R 1 +--R (256) - ---------------------------------------- +--R 2 2 +--R tanh(x) - 2%i sech(x)tanh(x) - sech(x) +--R Type: Expression(Complex(Integer)) +--E 443 + +--S 444 of 502 +r0888:= -x+2*%i*sech(x)+2*tanh(x) +--R +--R +--R (257) 2tanh(x) + 2%i sech(x) - x +--R Type: Expression(Complex(Integer)) +--E 444 + +--S 445 of 502 +a0888:= integrate(t0888,x) +--R +--R +--R - x sinh(x) - x cosh(x) + %i x + 4%i +--R (258) ------------------------------------ +--R sinh(x) + cosh(x) - %i +--R Type: Union(Expression(Complex(Integer)),...) +--E 445 + +--S 446 of 502 +m0888:= a0888-r0888 +--R +--R +--R (259) +--R (- 2sinh(x) - 2cosh(x) + 2%i)tanh(x) - 2%i sech(x)sinh(x) +--R + +--R (- 2%i cosh(x) - 2)sech(x) + 4%i +--R / +--R sinh(x) + cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 446 + +--S 447 of 502 +d0888:= D(m0888,x) +--R +--R +--R (260) +--R 2 2 +--R (2sinh(x) + (4cosh(x) - 4%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 +--R 2%i sech(x)sinh(x) + (4%i cosh(x) + 4)sech(x)sinh(x) +--R + +--R 2 +--R (2%i cosh(x) + 4cosh(x) - 2%i)sech(x) +--R * +--R tanh(x) +--R + +--R 2 2 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2%i)sinh(x) + cosh(x) - 2%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 447 + +--S 448 of 502 +t0889:= 1/(sech(x)+%i*tanh(x))^3 +--R +--R +--R %i +--R (261) --------------------------------------------------------------- +--R 3 2 2 3 +--R tanh(x) - 3%i sech(x)tanh(x) - 3sech(x) tanh(x) + %i sech(x) +--R Type: Expression(Complex(Integer)) +--E 448 + +--S 449 of 502 +r0889:= %i*log(1+%i*sinh(x))+2*%i/(1+%i*sinh(x)) +--R +--R +--R (%i sinh(x) + 1)log(%i sinh(x) + 1) + 2 +--R (262) --------------------------------------- +--R sinh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 449 + +--S 450 of 502 +a0889:= integrate(t0889,x) +--R +--R +--R (263) +--R 2 2 +--R 2%i sinh(x) + (4%i cosh(x) + 4)sinh(x) + 2%i cosh(x) + 4cosh(x) +--R + +--R - 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 2 2 +--R - %i x sinh(x) + (- 2%i x cosh(x) - 2x + 4)sinh(x) - %i x cosh(x) +--R + +--R (- 2x + 4)cosh(x) + %i x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2%i)sinh(x) + cosh(x) - 2%i cosh(x) - 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 450 + +--S 451 of 502 +m0889:= a0889-r0889 +--R +--R +--R (264) +--R 3 2 +--R 2%i sinh(x) + (4%i cosh(x) + 6)sinh(x) +--R + +--R 2 2 +--R (2%i cosh(x) + 8cosh(x) - 6%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 3 2 +--R - %i sinh(x) + (- 2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (- %i cosh(x) - 4cosh(x) + 3%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R * +--R log(%i sinh(x) + 1) +--R + +--R 3 2 +--R - %i x sinh(x) + (- 2%i x cosh(x) - 3x + 2)sinh(x) +--R + +--R 2 2 +--R (- %i x cosh(x) - 4x cosh(x) + 3%i x)sinh(x) + (- x - 2)cosh(x) +--R + +--R 2%i x cosh(x) + x + 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) - 3%i)sinh(x) + (cosh(x) - 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2cosh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 451 + +--S 452 of 502 +d0889:= D(m0889,x) +--R +--R +--R (265) +--R 5 4 3 +--R %i sinh(x) + (2%i cosh(x) - 1)sinh(x) + (- 2cosh(x) + 2%i)sinh(x) +--R + +--R 3 2 +--R (- 2%i cosh(x) + 6%i cosh(x) - 2)sinh(x) +--R + +--R 4 3 4 +--R (- %i cosh(x) + 2cosh(x) - 2cosh(x) + %i)sinh(x) + cosh(x) +--R + +--R 3 +--R - 4%i cosh(x) + 4%i cosh(x) - 1 +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) - 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) - 9%i cosh(x) - 18cosh(x) + 10%i)sinh(x) +--R + +--R 3 2 3 +--R (- 2%i cosh(x) - 9cosh(x) + 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R 3%i cosh(x) + 3cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 452 + +--S 453 of 502 +t0890:= 1/(sech(x)+%i*tanh(x))^4 +--R +--R +--R (266) +--R 1 +--R / +--R 4 3 2 2 3 +--R tanh(x) - 4%i sech(x)tanh(x) - 6sech(x) tanh(x) + 4%i sech(x) tanh(x) +--R + +--R 4 +--R sech(x) +--R Type: Expression(Complex(Integer)) +--E 453 + +--S 454 of 502 +r0890:= x-4*%i*sech(x)+8/3*%i*sech(x)^3-8/3*tanh(x)^3 +--R +--R +--R 8 3 8 3 +--R (267) - - tanh(x) + - %i sech(x) - 4%i sech(x) + x +--R 3 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 454 + +--S 455 of 502 +a0890:= integrate(t0890,x) +--R +--R +--R (268) +--R 2 2 +--R 3x sinh(x) + (6x cosh(x) - 12%i x - 40%i)sinh(x) + 3x cosh(x) +--R + +--R (- 6%i x - 8%i)cosh(x) - 9x - 24 +--R / +--R 2 2 +--R 3sinh(x) + (6cosh(x) - 12%i)sinh(x) + 3cosh(x) - 6%i cosh(x) - 9 +--R Type: Union(Expression(Complex(Integer)),...) +--E 455 + +--S 456 of 502 +m0890:= a0890-r0890 +--R +--R +--R (269) +--R 8 2 16 32 8 2 16 +--R - sinh(x) + (-- cosh(x) - -- %i)sinh(x) + - cosh(x) - -- %i cosh(x) +--R 3 3 3 3 3 +--R + +--R - 8 +--R * +--R 3 +--R tanh(x) +--R + +--R 8 3 2 +--R (- - %i sech(x) + 4%i sech(x))sinh(x) +--R 3 +--R + +--R 16 32 3 40 +--R ((- -- %i cosh(x) - --)sech(x) + (8%i cosh(x) + 16)sech(x) - -- %i) +--R 3 3 3 +--R * +--R sinh(x) +--R + +--R 8 2 16 3 +--R (- - %i cosh(x) - -- cosh(x) + 8%i)sech(x) +--R 3 3 +--R + +--R 2 8 +--R (4%i cosh(x) + 8cosh(x) - 12%i)sech(x) - - %i cosh(x) - 8 +--R 3 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 4%i)sinh(x) + cosh(x) - 2%i cosh(x) - 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 456 + +--S 457 of 502 +d0890:= D(m0890,x) +--R +--R +--R (270) +--R 4 3 +--R - 8sinh(x) + (- 32cosh(x) + 64%i)sinh(x) +--R + +--R 2 2 +--R (- 48cosh(x) + 160%i cosh(x) + 176)sinh(x) +--R + +--R 3 2 +--R (- 32cosh(x) + 128%i cosh(x) + 224cosh(x) - 192%i)sinh(x) +--R + +--R 4 3 2 +--R - 8cosh(x) + 32%i cosh(x) + 80cosh(x) - 96%i cosh(x) - 72 +--R * +--R 4 +--R tanh(x) +--R + +--R 4 3 +--R 8sinh(x) + (32cosh(x) - 64%i)sinh(x) +--R + +--R 2 2 +--R (48cosh(x) - 160%i cosh(x) - 176)sinh(x) +--R + +--R 3 2 4 +--R (32cosh(x) - 128%i cosh(x) - 224cosh(x) + 192%i)sinh(x) + 8cosh(x) +--R + +--R 3 2 +--R - 32%i cosh(x) - 80cosh(x) + 96%i cosh(x) + 72 +--R * +--R 2 +--R tanh(x) +--R + +--R 3 4 +--R (8%i sech(x) - 4%i sech(x))sinh(x) +--R + +--R 3 3 +--R ((32%i cosh(x) + 64)sech(x) + (- 16%i cosh(x) - 32)sech(x))sinh(x) +--R + +--R 2 3 +--R (48%i cosh(x) + 160cosh(x) - 176%i)sech(x) +--R + +--R 2 +--R (- 24%i cosh(x) - 80cosh(x) + 88%i)sech(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3 +--R (32%i cosh(x) + 128cosh(x) - 224%i cosh(x) - 192)sech(x) +--R + +--R 3 2 +--R (- 16%i cosh(x) - 64cosh(x) + 112%i cosh(x) + 96)sech(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (8%i cosh(x) + 32cosh(x) - 80%i cosh(x) - 96cosh(x) + 72%i) +--R * +--R 3 +--R sech(x) +--R + +--R 4 3 2 +--R (- 4%i cosh(x) - 16cosh(x) + 40%i cosh(x) + 48cosh(x) - 36%i)sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 +--R 24%i sinh(x) + (40%i cosh(x) + 32)sinh(x) +--R + +--R 2 3 +--R (8%i cosh(x) + 32cosh(x) - 8%i)sinh(x) - 8%i cosh(x) + 8%i cosh(x) +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) - 8%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) - 20%i cosh(x) - 22)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 16%i cosh(x) - 28cosh(x) + 24%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R - 4%i cosh(x) - 10cosh(x) + 12%i cosh(x) + 9 +--R Type: Expression(Complex(Fraction(Integer))) +--E 457 + +--S 458 of 502 +t0891:= 1/(sech(x)+%i*tanh(x))^5 +--R +--R +--R (271) +--R - +--R %i +--R / +--R 5 4 2 3 +--R tanh(x) - 5%i sech(x)tanh(x) - 10sech(x) tanh(x) +--R + +--R 3 2 4 5 +--R 10%i sech(x) tanh(x) + 5sech(x) tanh(x) - %i sech(x) +--R Type: Expression(Complex(Integer)) +--E 458 + +--S 459 of 502 +r0891:= -%i*log(1+%i*sinh(x))+2*%i/(1+%i*sinh(x))^2-4*%i/(1+%i*sinh(x)) +--R +--R +--R 2 +--R (- %i sinh(x) - 2sinh(x) + %i)log(%i sinh(x) + 1) - 4sinh(x) + 2%i +--R (272) ------------------------------------------------------------------- +--R 2 +--R sinh(x) - 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 459 + +--S 460 of 502 +a0891:= integrate(t0891,x) +--R +--R +--R (273) +--R 4 3 +--R - 2%i sinh(x) + (- 8%i cosh(x) - 8)sinh(x) +--R + +--R 2 2 +--R (- 12%i cosh(x) - 24cosh(x) + 12%i)sinh(x) +--R + +--R 3 2 +--R (- 8%i cosh(x) - 24cosh(x) + 24%i cosh(x) + 8)sinh(x) +--R + +--R 4 3 2 +--R - 2%i cosh(x) - 8cosh(x) + 12%i cosh(x) + 8cosh(x) - 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 4 3 +--R %i x sinh(x) + (4%i x cosh(x) + 4x - 8)sinh(x) +--R + +--R 2 2 +--R (6%i x cosh(x) + (12x - 24)cosh(x) - 6%i x + 8%i)sinh(x) +--R + +--R 3 2 +--R 4%i x cosh(x) + (12x - 24)cosh(x) + (- 12%i x + 16%i)cosh(x) - 4x +--R + +--R 8 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R %i x cosh(x) + (4x - 8)cosh(x) + (- 6%i x + 8%i)cosh(x) +--R + +--R (- 4x + 8)cosh(x) + %i x +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) - 12%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 12%i cosh(x) - 12cosh(x) + 4%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R - 4%i cosh(x) - 6cosh(x) + 4%i cosh(x) + 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 460 + +--S 461 of 502 +m0891:= a0891-r0891 +--R +--R +--R (274) +--R 6 5 +--R - 2%i sinh(x) + (- 8%i cosh(x) - 12)sinh(x) +--R + +--R 2 4 +--R (- 12%i cosh(x) - 40cosh(x) + 30%i)sinh(x) +--R + +--R 3 2 3 +--R (- 8%i cosh(x) - 48cosh(x) + 80%i cosh(x) + 40)sinh(x) +--R + +--R 4 3 2 +--R (- 2%i cosh(x) - 24cosh(x) + 72%i cosh(x) + 80cosh(x) - 30%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 4cosh(x) + 24%i cosh(x) + 48cosh(x) - 40%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R 2%i cosh(x) + 8cosh(x) - 12%i cosh(x) - 8cosh(x) + 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 6 5 +--R %i sinh(x) + (4%i cosh(x) + 6)sinh(x) +--R + +--R 2 4 +--R (6%i cosh(x) + 20cosh(x) - 15%i)sinh(x) +--R + +--R 3 2 3 +--R (4%i cosh(x) + 24cosh(x) - 40%i cosh(x) - 20)sinh(x) +--R + +--R 4 3 2 2 +--R (%i cosh(x) + 12cosh(x) - 36%i cosh(x) - 40cosh(x) + 15%i)sinh(x) +--R + +--R 4 3 2 +--R (2cosh(x) - 12%i cosh(x) - 24cosh(x) + 20%i cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 +--R - %i cosh(x) - 4cosh(x) + 6%i cosh(x) + 4cosh(x) - %i +--R * +--R log(%i sinh(x) + 1) +--R + +--R 6 5 +--R %i x sinh(x) + (4%i x cosh(x) + 6x - 4)sinh(x) +--R + +--R 2 4 +--R (6%i x cosh(x) + (20x - 8)cosh(x) - 15%i x + 6%i)sinh(x) +--R + +--R 3 2 3 +--R (4%i x cosh(x) + 24x cosh(x) + (- 40%i x + 8%i)cosh(x) - 20x)sinh(x) +--R + +--R 4 3 2 +--R %i x cosh(x) + (12x + 8)cosh(x) + (- 36%i x - 4%i)cosh(x) +--R + +--R (- 40x - 8)cosh(x) + 15%i x + 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2x + 4)cosh(x) + (- 12%i x - 8%i)cosh(x) + (- 24x - 8)cosh(x) +--R + +--R (20%i x + 8%i)cosh(x) + 6x + 4 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (- %i x - 2%i)cosh(x) - 4x cosh(x) + (6%i x + 4%i)cosh(x) + 4x cosh(x) +--R + +--R - %i x - 2%i +--R / +--R 6 5 +--R sinh(x) + (4cosh(x) - 6%i)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) - 20%i cosh(x) - 15)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) - 24%i cosh(x) - 40cosh(x) + 20%i)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) - 12%i cosh(x) - 36cosh(x) + 40%i cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 +--R (- 2%i cosh(x) - 12cosh(x) + 24%i cosh(x) + 20cosh(x) - 6%i)sinh(x) +--R + +--R 4 3 2 +--R - cosh(x) + 4%i cosh(x) + 6cosh(x) - 4%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 461 + +--S 462 of 502 +d0891:= D(m0891,x) +--R +--R +--R (275) +--R 8 7 +--R - %i sinh(x) + (- 4%i cosh(x) + 2)sinh(x) +--R + +--R 2 6 +--R (- 5%i cosh(x) + 8cosh(x) - 2%i)sinh(x) +--R + +--R 2 5 +--R (10cosh(x) - 16%i cosh(x) + 6)sinh(x) +--R + +--R 4 2 4 +--R (5%i cosh(x) - 25%i cosh(x) + 20cosh(x))sinh(x) +--R + +--R 5 4 2 3 +--R (4%i cosh(x) - 10cosh(x) + 20cosh(x) - 20%i cosh(x) + 6)sinh(x) +--R + +--R 6 5 4 2 +--R %i cosh(x) - 8cosh(x) + 20%i cosh(x) - 35%i cosh(x) + 16cosh(x) +--R + +--R 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 2 +--R - 2cosh(x) + 8%i cosh(x) - 10cosh(x) + 10cosh(x) - 8%i cosh(x) +--R + +--R 2 +--R * +--R sinh(x) +--R + +--R 6 5 4 2 +--R - %i cosh(x) - 4cosh(x) + 15%i cosh(x) - 15%i cosh(x) + 4cosh(x) + %i +--R / +--R 8 7 +--R sinh(x) + (5cosh(x) - 8%i)sinh(x) +--R + +--R 2 6 +--R (10cosh(x) - 35%i cosh(x) - 28)sinh(x) +--R + +--R 3 2 5 +--R (10cosh(x) - 60%i cosh(x) - 105cosh(x) + 56%i)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) - 50%i cosh(x) - 150cosh(x) + 175%i cosh(x) + 70)sinh(x) +--R + +--R 5 4 3 2 +--R cosh(x) - 20%i cosh(x) - 100cosh(x) + 200%i cosh(x) + 175cosh(x) +--R + +--R - 56%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3%i cosh(x) - 30cosh(x) + 100%i cosh(x) + 150cosh(x) +--R + +--R - 105%i cosh(x) - 28 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) + 20%i cosh(x) + 50cosh(x) - 60%i cosh(x) - 35cosh(x) +--R + +--R 8%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R %i cosh(x) + 5cosh(x) - 10%i cosh(x) - 10cosh(x) + 5%i cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 462 + +--S 463 of 502 +t0892:= (sech(x)-%i*tanh(x))^3 +--R +--R +--R 3 2 2 3 +--R (276) %i tanh(x) - 3sech(x)tanh(x) - 3%i sech(x) tanh(x) + sech(x) +--R Type: Expression(Complex(Integer)) +--E 463 + +--S 464 of 502 +r0892:= %i*log(-%i+sinh(x))-2/(%i-sinh(x)) +--R +--R +--R (%i sinh(x) + 1)log(sinh(x) - %i) + 2 +--R (277) ------------------------------------- +--R sinh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 464 + +--S 465 of 502 +a0892:= integrate(t0892,x) +--R +--R +--R (278) +--R 2 2 +--R 2%i sinh(x) + (4%i cosh(x) + 4)sinh(x) + 2%i cosh(x) + 4cosh(x) +--R + +--R - 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 2 2 +--R - %i x sinh(x) + (- 2%i x cosh(x) - 2x + 4)sinh(x) - %i x cosh(x) +--R + +--R (- 2x + 4)cosh(x) + %i x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2%i)sinh(x) + cosh(x) - 2%i cosh(x) - 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 465 + +--S 466 of 502 +m0892:= a0892-r0892 +--R +--R +--R (279) +--R 3 2 +--R 2%i sinh(x) + (4%i cosh(x) + 6)sinh(x) +--R + +--R 2 2 +--R (2%i cosh(x) + 8cosh(x) - 6%i)sinh(x) + 2cosh(x) - 4%i cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 3 2 +--R - %i sinh(x) + (- 2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (- %i cosh(x) - 4cosh(x) + 3%i)sinh(x) - cosh(x) + 2%i cosh(x) + 1 +--R * +--R log(sinh(x) - %i) +--R + +--R 3 2 +--R - %i x sinh(x) + (- 2%i x cosh(x) - 3x + 2)sinh(x) +--R + +--R 2 2 +--R (- %i x cosh(x) - 4x cosh(x) + 3%i x)sinh(x) + (- x - 2)cosh(x) +--R + +--R 2%i x cosh(x) + x + 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) - 3%i)sinh(x) + (cosh(x) - 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R - %i cosh(x) - 2cosh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 466 + +--S 467 of 502 +d0892:= D(m0892,x) +--R +--R +--R (280) +--R 5 4 3 +--R %i sinh(x) + (2%i cosh(x) - 1)sinh(x) + (- 2cosh(x) + 2%i)sinh(x) +--R + +--R 3 2 +--R (- 2%i cosh(x) + 6%i cosh(x) - 2)sinh(x) +--R + +--R 4 3 4 +--R (- %i cosh(x) + 2cosh(x) - 2cosh(x) + %i)sinh(x) + cosh(x) +--R + +--R 3 +--R - 4%i cosh(x) + 4%i cosh(x) - 1 +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) - 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) - 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) - 9%i cosh(x) - 18cosh(x) + 10%i)sinh(x) +--R + +--R 3 2 3 +--R (- 2%i cosh(x) - 9cosh(x) + 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R 3%i cosh(x) + 3cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 467 + +--S 468 of 502 +t0893:= (sech(x)-%i*tanh(x))^5 +--R +--R +--R (281) +--R 5 4 2 3 +--R - %i tanh(x) + 5sech(x)tanh(x) + 10%i sech(x) tanh(x) +--R + +--R 3 2 4 5 +--R - 10sech(x) tanh(x) - 5%i sech(x) tanh(x) + sech(x) +--R Type: Expression(Complex(Integer)) +--E 468 + +--S 469 of 502 +r0893:= -%i*log(1+%i*sinh(x))+2*%i/(1+%i*sinh(x))^2-4*%i/(1+%i*sinh(x)) +--R +--R +--R 2 +--R (- %i sinh(x) - 2sinh(x) + %i)log(%i sinh(x) + 1) - 4sinh(x) + 2%i +--R (282) ------------------------------------------------------------------- +--R 2 +--R sinh(x) - 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 469 + +--S 470 of 502 +a0893:= integrate(t0893,x) +--R +--R +--R (283) +--R 4 3 +--R - 2%i sinh(x) + (- 8%i cosh(x) - 8)sinh(x) +--R + +--R 2 2 +--R (- 12%i cosh(x) - 24cosh(x) + 12%i)sinh(x) +--R + +--R 3 2 +--R (- 8%i cosh(x) - 24cosh(x) + 24%i cosh(x) + 8)sinh(x) +--R + +--R 4 3 2 +--R - 2%i cosh(x) - 8cosh(x) + 12%i cosh(x) + 8cosh(x) - 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 4 3 +--R %i x sinh(x) + (4%i x cosh(x) + 4x - 8)sinh(x) +--R + +--R 2 2 +--R (6%i x cosh(x) + (12x - 24)cosh(x) - 6%i x + 8%i)sinh(x) +--R + +--R 3 2 +--R 4%i x cosh(x) + (12x - 24)cosh(x) + (- 12%i x + 16%i)cosh(x) - 4x +--R + +--R 8 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R %i x cosh(x) + (4x - 8)cosh(x) + (- 6%i x + 8%i)cosh(x) +--R + +--R (- 4x + 8)cosh(x) + %i x +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) - 4%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) - 12%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) - 12%i cosh(x) - 12cosh(x) + 4%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R - 4%i cosh(x) - 6cosh(x) + 4%i cosh(x) + 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 470 + +--S 471 of 502 +m0893:= a0893-r0893 +--R +--R +--R (284) +--R 6 5 +--R - 2%i sinh(x) + (- 8%i cosh(x) - 12)sinh(x) +--R + +--R 2 4 +--R (- 12%i cosh(x) - 40cosh(x) + 30%i)sinh(x) +--R + +--R 3 2 3 +--R (- 8%i cosh(x) - 48cosh(x) + 80%i cosh(x) + 40)sinh(x) +--R + +--R 4 3 2 +--R (- 2%i cosh(x) - 24cosh(x) + 72%i cosh(x) + 80cosh(x) - 30%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 4cosh(x) + 24%i cosh(x) + 48cosh(x) - 40%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R 2%i cosh(x) + 8cosh(x) - 12%i cosh(x) - 8cosh(x) + 2%i +--R * +--R log(sinh(x) + cosh(x) - %i) +--R + +--R 6 5 +--R %i sinh(x) + (4%i cosh(x) + 6)sinh(x) +--R + +--R 2 4 +--R (6%i cosh(x) + 20cosh(x) - 15%i)sinh(x) +--R + +--R 3 2 3 +--R (4%i cosh(x) + 24cosh(x) - 40%i cosh(x) - 20)sinh(x) +--R + +--R 4 3 2 2 +--R (%i cosh(x) + 12cosh(x) - 36%i cosh(x) - 40cosh(x) + 15%i)sinh(x) +--R + +--R 4 3 2 +--R (2cosh(x) - 12%i cosh(x) - 24cosh(x) + 20%i cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 +--R - %i cosh(x) - 4cosh(x) + 6%i cosh(x) + 4cosh(x) - %i +--R * +--R log(%i sinh(x) + 1) +--R + +--R 6 5 +--R %i x sinh(x) + (4%i x cosh(x) + 6x - 4)sinh(x) +--R + +--R 2 4 +--R (6%i x cosh(x) + (20x - 8)cosh(x) - 15%i x + 6%i)sinh(x) +--R + +--R 3 2 3 +--R (4%i x cosh(x) + 24x cosh(x) + (- 40%i x + 8%i)cosh(x) - 20x)sinh(x) +--R + +--R 4 3 2 +--R %i x cosh(x) + (12x + 8)cosh(x) + (- 36%i x - 4%i)cosh(x) +--R + +--R (- 40x - 8)cosh(x) + 15%i x + 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2x + 4)cosh(x) + (- 12%i x - 8%i)cosh(x) + (- 24x - 8)cosh(x) +--R + +--R (20%i x + 8%i)cosh(x) + 6x + 4 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (- %i x - 2%i)cosh(x) - 4x cosh(x) + (6%i x + 4%i)cosh(x) + 4x cosh(x) +--R + +--R - %i x - 2%i +--R / +--R 6 5 +--R sinh(x) + (4cosh(x) - 6%i)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) - 20%i cosh(x) - 15)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) - 24%i cosh(x) - 40cosh(x) + 20%i)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) - 12%i cosh(x) - 36cosh(x) + 40%i cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 +--R (- 2%i cosh(x) - 12cosh(x) + 24%i cosh(x) + 20cosh(x) - 6%i)sinh(x) +--R + +--R 4 3 2 +--R - cosh(x) + 4%i cosh(x) + 6cosh(x) - 4%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 471 + +--S 472 of 502 +d0893:= D(m0893,x) +--R +--R +--R (285) +--R 8 7 +--R - %i sinh(x) + (- 4%i cosh(x) + 2)sinh(x) +--R + +--R 2 6 +--R (- 5%i cosh(x) + 8cosh(x) - 2%i)sinh(x) +--R + +--R 2 5 +--R (10cosh(x) - 16%i cosh(x) + 6)sinh(x) +--R + +--R 4 2 4 +--R (5%i cosh(x) - 25%i cosh(x) + 20cosh(x))sinh(x) +--R + +--R 5 4 2 3 +--R (4%i cosh(x) - 10cosh(x) + 20cosh(x) - 20%i cosh(x) + 6)sinh(x) +--R + +--R 6 5 4 2 +--R %i cosh(x) - 8cosh(x) + 20%i cosh(x) - 35%i cosh(x) + 16cosh(x) +--R + +--R 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 2 +--R - 2cosh(x) + 8%i cosh(x) - 10cosh(x) + 10cosh(x) - 8%i cosh(x) +--R + +--R 2 +--R * +--R sinh(x) +--R + +--R 6 5 4 2 +--R - %i cosh(x) - 4cosh(x) + 15%i cosh(x) - 15%i cosh(x) + 4cosh(x) + %i +--R / +--R 8 7 +--R sinh(x) + (5cosh(x) - 8%i)sinh(x) +--R + +--R 2 6 +--R (10cosh(x) - 35%i cosh(x) - 28)sinh(x) +--R + +--R 3 2 5 +--R (10cosh(x) - 60%i cosh(x) - 105cosh(x) + 56%i)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) - 50%i cosh(x) - 150cosh(x) + 175%i cosh(x) + 70)sinh(x) +--R + +--R 5 4 3 2 +--R cosh(x) - 20%i cosh(x) - 100cosh(x) + 200%i cosh(x) + 175cosh(x) +--R + +--R - 56%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3%i cosh(x) - 30cosh(x) + 100%i cosh(x) + 150cosh(x) +--R + +--R - 105%i cosh(x) - 28 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) + 20%i cosh(x) + 50cosh(x) - 60%i cosh(x) - 35cosh(x) +--R + +--R 8%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R %i cosh(x) + 5cosh(x) - 10%i cosh(x) - 10cosh(x) + 5%i cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 472 + +--S 473 of 502 +t0894:= 1/(sech(x)-%i*tanh(x)) +--R +--R +--R %i +--R (286) -------------------- +--R tanh(x) + %i sech(x) +--R Type: Expression(Complex(Integer)) +--E 473 + +--S 474 of 502 +r0894:= %i*log(1-%i*sinh(x)) +--R +--R +--R (287) %i log(- %i sinh(x) + 1) +--R Type: Expression(Complex(Integer)) +--E 474 + +--S 475 of 502 +a0894:= integrate(t0894,x) +--R +--R +--R (288) 2%i log(sinh(x) + cosh(x) + %i) - %i x +--R Type: Union(Expression(Complex(Integer)),...) +--E 475 + +--S 476 of 502 +m0894:= a0894-r0894 +--R +--R +--R (289) 2%i log(sinh(x) + cosh(x) + %i) - %i log(- %i sinh(x) + 1) - %i x +--R Type: Expression(Complex(Integer)) +--E 476 + +--S 477 of 502 +d0894:= D(m0894,x) +--R +--R +--R 2 2 +--R %i sinh(x) - %i cosh(x) + %i +--R (290) -------------------------------------------------- +--R 2 +--R sinh(x) + (cosh(x) + 2%i)sinh(x) + %i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 477 + +--S 478 of 502 +t0895:= 1/(sech(x)-%i*tanh(x))^2 +--R +--R +--R 1 +--R (291) - ---------------------------------------- +--R 2 2 +--R tanh(x) + 2%i sech(x)tanh(x) - sech(x) +--R Type: Expression(Complex(Integer)) +--E 478 + +--S 479 of 502 +r0895:= -x-2*%i*sech(x)+2*tanh(x) +--R +--R +--R (292) 2tanh(x) - 2%i sech(x) - x +--R Type: Expression(Complex(Integer)) +--E 479 + +--S 480 of 502 +a0895:= integrate(t0895,x) +--R +--R +--R - x sinh(x) - x cosh(x) - %i x - 4%i +--R (293) ------------------------------------ +--R sinh(x) + cosh(x) + %i +--R Type: Union(Expression(Complex(Integer)),...) +--E 480 + +--S 481 of 502 +m0895:= a0895-r0895 +--R +--R +--R (294) +--R (- 2sinh(x) - 2cosh(x) - 2%i)tanh(x) + 2%i sech(x)sinh(x) +--R + +--R (2%i cosh(x) - 2)sech(x) - 4%i +--R / +--R sinh(x) + cosh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 481 + +--S 482 of 502 +d0895:= D(m0895,x) +--R +--R +--R (295) +--R 2 2 +--R (2sinh(x) + (4cosh(x) + 4%i)sinh(x) + 2cosh(x) + 4%i cosh(x) - 2) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 +--R - 2%i sech(x)sinh(x) + (- 4%i cosh(x) + 4)sech(x)sinh(x) +--R + +--R 2 +--R (- 2%i cosh(x) + 4cosh(x) + 2%i)sech(x) +--R * +--R tanh(x) +--R + +--R 2 2 +--R - 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2%i)sinh(x) + cosh(x) + 2%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 482 + +--S 483 of 502 +t0896:= 1/(sech(x)-%i*tanh(x))^3 +--R +--R +--R %i +--R (296) - --------------------------------------------------------------- +--R 3 2 2 3 +--R tanh(x) + 3%i sech(x)tanh(x) - 3sech(x) tanh(x) - %i sech(x) +--R Type: Expression(Complex(Integer)) +--E 483 + +--S 484 of 502 +r0896:= -%i*log(1-%i*sinh(x))-2*%i/(1-%i*sinh(x)) +--R +--R +--R (- %i sinh(x) + 1)log(- %i sinh(x) + 1) + 2 +--R (297) ------------------------------------------- +--R sinh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 484 + +--S 485 of 502 +a0896:= integrate(t0896,x) +--R +--R +--R (298) +--R 2 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) + 4)sinh(x) - 2%i cosh(x) + 4cosh(x) +--R + +--R 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 2 2 +--R %i x sinh(x) + (2%i x cosh(x) - 2x + 4)sinh(x) + %i x cosh(x) +--R + +--R (- 2x + 4)cosh(x) - %i x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2%i)sinh(x) + cosh(x) + 2%i cosh(x) - 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 485 + +--S 486 of 502 +m0896:= a0896-r0896 +--R +--R +--R (299) +--R 3 2 +--R - 2%i sinh(x) + (- 4%i cosh(x) + 6)sinh(x) +--R + +--R 2 2 +--R (- 2%i cosh(x) + 8cosh(x) + 6%i)sinh(x) + 2cosh(x) + 4%i cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 3 2 +--R %i sinh(x) + (2%i cosh(x) - 3)sinh(x) +--R + +--R 2 2 +--R (%i cosh(x) - 4cosh(x) - 3%i)sinh(x) - cosh(x) - 2%i cosh(x) + 1 +--R * +--R log(- %i sinh(x) + 1) +--R + +--R 3 2 +--R %i x sinh(x) + (2%i x cosh(x) - 3x + 2)sinh(x) +--R + +--R 2 2 +--R (%i x cosh(x) - 4x cosh(x) - 3%i x)sinh(x) + (- x - 2)cosh(x) +--R + +--R - 2%i x cosh(x) + x + 2 +--R / +--R 3 2 2 +--R sinh(x) + (2cosh(x) + 3%i)sinh(x) + (cosh(x) + 4%i cosh(x) - 3)sinh(x) +--R + +--R 2 +--R %i cosh(x) - 2cosh(x) - %i +--R Type: Expression(Complex(Integer)) +--E 486 + +--S 487 of 502 +d0896:= D(m0896,x) +--R +--R +--R (300) +--R 5 4 3 +--R - %i sinh(x) + (- 2%i cosh(x) - 1)sinh(x) + (- 2cosh(x) - 2%i)sinh(x) +--R + +--R 3 2 +--R (2%i cosh(x) - 6%i cosh(x) - 2)sinh(x) +--R + +--R 4 3 4 +--R (%i cosh(x) + 2cosh(x) - 2cosh(x) - %i)sinh(x) + cosh(x) +--R + +--R 3 +--R 4%i cosh(x) - 4%i cosh(x) - 1 +--R / +--R 5 4 +--R sinh(x) + (3cosh(x) + 5%i)sinh(x) +--R + +--R 2 3 +--R (3cosh(x) + 12%i cosh(x) - 10)sinh(x) +--R + +--R 3 2 2 +--R (cosh(x) + 9%i cosh(x) - 18cosh(x) - 10%i)sinh(x) +--R + +--R 3 2 3 +--R (2%i cosh(x) - 9cosh(x) - 12%i cosh(x) + 5)sinh(x) - cosh(x) +--R + +--R 2 +--R - 3%i cosh(x) + 3cosh(x) + %i +--R Type: Expression(Complex(Integer)) +--E 487 + +--S 488 of 502 +t0897:= 1/(sech(x)-%i*tanh(x))^4 +--R +--R +--R (301) +--R 1 +--R / +--R 4 3 2 2 3 +--R tanh(x) + 4%i sech(x)tanh(x) - 6sech(x) tanh(x) - 4%i sech(x) tanh(x) +--R + +--R 4 +--R sech(x) +--R Type: Expression(Complex(Integer)) +--E 488 + +--S 489 of 502 +r0897:= x+4*%i*sech(x)-8/3*%i*sech(x)^3-8/3*tanh(x)^3 +--R +--R +--R 8 3 8 3 +--R (302) - - tanh(x) - - %i sech(x) + 4%i sech(x) + x +--R 3 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 489 + +--S 490 of 502 +a0897:= integrate(t0897,x) +--R +--R +--R (303) +--R 2 2 +--R 3x sinh(x) + (6x cosh(x) + 12%i x + 40%i)sinh(x) + 3x cosh(x) +--R + +--R (6%i x + 8%i)cosh(x) - 9x - 24 +--R / +--R 2 2 +--R 3sinh(x) + (6cosh(x) + 12%i)sinh(x) + 3cosh(x) + 6%i cosh(x) - 9 +--R Type: Union(Expression(Complex(Integer)),...) +--E 490 + +--S 491 of 502 +m0897:= a0897-r0897 +--R +--R +--R (304) +--R 8 2 16 32 8 2 16 +--R - sinh(x) + (-- cosh(x) + -- %i)sinh(x) + - cosh(x) + -- %i cosh(x) +--R 3 3 3 3 3 +--R + +--R - 8 +--R * +--R 3 +--R tanh(x) +--R + +--R 8 3 2 +--R (- %i sech(x) - 4%i sech(x))sinh(x) +--R 3 +--R + +--R 16 32 3 40 +--R ((-- %i cosh(x) - --)sech(x) + (- 8%i cosh(x) + 16)sech(x) + -- %i) +--R 3 3 3 +--R * +--R sinh(x) +--R + +--R 8 2 16 3 +--R (- %i cosh(x) - -- cosh(x) - 8%i)sech(x) +--R 3 3 +--R + +--R 2 8 +--R (- 4%i cosh(x) + 8cosh(x) + 12%i)sech(x) + - %i cosh(x) - 8 +--R 3 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 4%i)sinh(x) + cosh(x) + 2%i cosh(x) - 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 491 + +--S 492 of 502 +d0897:= D(m0897,x) +--R +--R +--R (305) +--R 4 3 +--R - 8sinh(x) + (- 32cosh(x) - 64%i)sinh(x) +--R + +--R 2 2 +--R (- 48cosh(x) - 160%i cosh(x) + 176)sinh(x) +--R + +--R 3 2 +--R (- 32cosh(x) - 128%i cosh(x) + 224cosh(x) + 192%i)sinh(x) +--R + +--R 4 3 2 +--R - 8cosh(x) - 32%i cosh(x) + 80cosh(x) + 96%i cosh(x) - 72 +--R * +--R 4 +--R tanh(x) +--R + +--R 4 3 +--R 8sinh(x) + (32cosh(x) + 64%i)sinh(x) +--R + +--R 2 2 +--R (48cosh(x) + 160%i cosh(x) - 176)sinh(x) +--R + +--R 3 2 4 +--R (32cosh(x) + 128%i cosh(x) - 224cosh(x) - 192%i)sinh(x) + 8cosh(x) +--R + +--R 3 2 +--R 32%i cosh(x) - 80cosh(x) - 96%i cosh(x) + 72 +--R * +--R 2 +--R tanh(x) +--R + +--R 3 4 +--R (- 8%i sech(x) + 4%i sech(x))sinh(x) +--R + +--R 3 3 +--R ((- 32%i cosh(x) + 64)sech(x) + (16%i cosh(x) - 32)sech(x))sinh(x) +--R + +--R 2 3 +--R (- 48%i cosh(x) + 160cosh(x) + 176%i)sech(x) +--R + +--R 2 +--R (24%i cosh(x) - 80cosh(x) - 88%i)sech(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 3 +--R (- 32%i cosh(x) + 128cosh(x) + 224%i cosh(x) - 192)sech(x) +--R + +--R 3 2 +--R (16%i cosh(x) - 64cosh(x) - 112%i cosh(x) + 96)sech(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (- 8%i cosh(x) + 32cosh(x) + 80%i cosh(x) - 96cosh(x) - 72%i) +--R * +--R 3 +--R sech(x) +--R + +--R 4 3 2 +--R (4%i cosh(x) - 16cosh(x) - 40%i cosh(x) + 48cosh(x) + 36%i)sech(x) +--R * +--R tanh(x) +--R + +--R 3 2 +--R - 24%i sinh(x) + (- 40%i cosh(x) + 32)sinh(x) +--R + +--R 2 3 +--R (- 8%i cosh(x) + 32cosh(x) + 8%i)sinh(x) + 8%i cosh(x) - 8%i cosh(x) +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) + 8%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) + 20%i cosh(x) - 22)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 16%i cosh(x) - 28cosh(x) - 24%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R 4%i cosh(x) - 10cosh(x) - 12%i cosh(x) + 9 +--R Type: Expression(Complex(Fraction(Integer))) +--E 492 + +--S 493 of 502 +t0898:= 1/(sech(x)-%i*tanh(x))^5 +--R +--R +--R (306) +--R %i +--R / +--R 5 4 2 3 +--R tanh(x) + 5%i sech(x)tanh(x) - 10sech(x) tanh(x) +--R + +--R 3 2 4 5 +--R - 10%i sech(x) tanh(x) + 5sech(x) tanh(x) + %i sech(x) +--R Type: Expression(Complex(Integer)) +--E 493 + +--S 494 of 502 +r0898:= %i*log(1-%i*sinh(x))-2*%i/(1-%i*sinh(x))^2+4*%i/(1-%i*sinh(x)) +--R +--R +--R 2 +--R (%i sinh(x) - 2sinh(x) - %i)log(- %i sinh(x) + 1) - 4sinh(x) - 2%i +--R (307) ------------------------------------------------------------------- +--R 2 +--R sinh(x) + 2%i sinh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 494 + +--S 495 of 502 +a0898:= integrate(t0898,x) +--R +--R +--R (308) +--R 4 3 +--R 2%i sinh(x) + (8%i cosh(x) - 8)sinh(x) +--R + +--R 2 2 +--R (12%i cosh(x) - 24cosh(x) - 12%i)sinh(x) +--R + +--R 3 2 4 +--R (8%i cosh(x) - 24cosh(x) - 24%i cosh(x) + 8)sinh(x) + 2%i cosh(x) +--R + +--R 3 2 +--R - 8cosh(x) - 12%i cosh(x) + 8cosh(x) + 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 4 3 +--R - %i x sinh(x) + (- 4%i x cosh(x) + 4x - 8)sinh(x) +--R + +--R 2 2 +--R (- 6%i x cosh(x) + (12x - 24)cosh(x) + 6%i x - 8%i)sinh(x) +--R + +--R 3 2 +--R - 4%i x cosh(x) + (12x - 24)cosh(x) + (12%i x - 16%i)cosh(x) - 4x +--R + +--R 8 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R - %i x cosh(x) + (4x - 8)cosh(x) + (6%i x - 8%i)cosh(x) +--R + +--R (- 4x + 8)cosh(x) - %i x +--R / +--R 4 3 +--R sinh(x) + (4cosh(x) + 4%i)sinh(x) +--R + +--R 2 2 +--R (6cosh(x) + 12%i cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 +--R (4cosh(x) + 12%i cosh(x) - 12cosh(x) - 4%i)sinh(x) + cosh(x) +--R + +--R 3 2 +--R 4%i cosh(x) - 6cosh(x) - 4%i cosh(x) + 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 495 + +--S 496 of 502 +m0898:= a0898-r0898 +--R +--R +--R (309) +--R 6 5 +--R 2%i sinh(x) + (8%i cosh(x) - 12)sinh(x) +--R + +--R 2 4 +--R (12%i cosh(x) - 40cosh(x) - 30%i)sinh(x) +--R + +--R 3 2 3 +--R (8%i cosh(x) - 48cosh(x) - 80%i cosh(x) + 40)sinh(x) +--R + +--R 4 3 2 +--R (2%i cosh(x) - 24cosh(x) - 72%i cosh(x) + 80cosh(x) + 30%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (- 4cosh(x) - 24%i cosh(x) + 48cosh(x) + 40%i cosh(x) - 12)sinh(x) +--R + +--R 4 3 2 +--R - 2%i cosh(x) + 8cosh(x) + 12%i cosh(x) - 8cosh(x) - 2%i +--R * +--R log(sinh(x) + cosh(x) + %i) +--R + +--R 6 5 +--R - %i sinh(x) + (- 4%i cosh(x) + 6)sinh(x) +--R + +--R 2 4 +--R (- 6%i cosh(x) + 20cosh(x) + 15%i)sinh(x) +--R + +--R 3 2 3 +--R (- 4%i cosh(x) + 24cosh(x) + 40%i cosh(x) - 20)sinh(x) +--R + +--R 4 3 2 +--R (- %i cosh(x) + 12cosh(x) + 36%i cosh(x) - 40cosh(x) - 15%i) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2cosh(x) + 12%i cosh(x) - 24cosh(x) - 20%i cosh(x) + 6)sinh(x) +--R + +--R 4 3 2 +--R %i cosh(x) - 4cosh(x) - 6%i cosh(x) + 4cosh(x) + %i +--R * +--R log(- %i sinh(x) + 1) +--R + +--R 6 5 +--R - %i x sinh(x) + (- 4%i x cosh(x) + 6x - 4)sinh(x) +--R + +--R 2 4 +--R (- 6%i x cosh(x) + (20x - 8)cosh(x) + 15%i x - 6%i)sinh(x) +--R + +--R 3 2 3 +--R (- 4%i x cosh(x) + 24x cosh(x) + (40%i x - 8%i)cosh(x) - 20x)sinh(x) +--R + +--R 4 3 2 +--R - %i x cosh(x) + (12x + 8)cosh(x) + (36%i x + 4%i)cosh(x) +--R + +--R (- 40x - 8)cosh(x) - 15%i x - 4%i +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 +--R (2x + 4)cosh(x) + (12%i x + 8%i)cosh(x) + (- 24x - 8)cosh(x) +--R + +--R (- 20%i x - 8%i)cosh(x) + 6x + 4 +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R (%i x + 2%i)cosh(x) - 4x cosh(x) + (- 6%i x - 4%i)cosh(x) + 4x cosh(x) +--R + +--R %i x + 2%i +--R / +--R 6 5 +--R sinh(x) + (4cosh(x) + 6%i)sinh(x) +--R + +--R 2 4 +--R (6cosh(x) + 20%i cosh(x) - 15)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) + 24%i cosh(x) - 40cosh(x) - 20%i)sinh(x) +--R + +--R 4 3 2 2 +--R (cosh(x) + 12%i cosh(x) - 36cosh(x) - 40%i cosh(x) + 15)sinh(x) +--R + +--R 4 3 2 +--R (2%i cosh(x) - 12cosh(x) - 24%i cosh(x) + 20cosh(x) + 6%i)sinh(x) +--R + +--R 4 3 2 +--R - cosh(x) - 4%i cosh(x) + 6cosh(x) + 4%i cosh(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 496 + +--S 497 of 502 +d0898:= D(m0898,x) +--R +--R +--R (310) +--R 8 7 +--R %i sinh(x) + (4%i cosh(x) + 2)sinh(x) +--R + +--R 2 6 +--R (5%i cosh(x) + 8cosh(x) + 2%i)sinh(x) +--R + +--R 2 5 +--R (10cosh(x) + 16%i cosh(x) + 6)sinh(x) +--R + +--R 4 2 4 +--R (- 5%i cosh(x) + 25%i cosh(x) + 20cosh(x))sinh(x) +--R + +--R 5 4 2 3 +--R (- 4%i cosh(x) - 10cosh(x) + 20cosh(x) + 20%i cosh(x) + 6)sinh(x) +--R + +--R 6 5 4 2 +--R - %i cosh(x) - 8cosh(x) - 20%i cosh(x) + 35%i cosh(x) + 16cosh(x) +--R + +--R - 2%i +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 4 2 +--R - 2cosh(x) - 8%i cosh(x) - 10cosh(x) + 10cosh(x) + 8%i cosh(x) +--R + +--R 2 +--R * +--R sinh(x) +--R + +--R 6 5 4 2 +--R %i cosh(x) - 4cosh(x) - 15%i cosh(x) + 15%i cosh(x) + 4cosh(x) - %i +--R / +--R 8 7 +--R sinh(x) + (5cosh(x) + 8%i)sinh(x) +--R + +--R 2 6 +--R (10cosh(x) + 35%i cosh(x) - 28)sinh(x) +--R + +--R 3 2 5 +--R (10cosh(x) + 60%i cosh(x) - 105cosh(x) - 56%i)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) + 50%i cosh(x) - 150cosh(x) - 175%i cosh(x) + 70)sinh(x) +--R + +--R 5 4 3 2 +--R cosh(x) + 20%i cosh(x) - 100cosh(x) - 200%i cosh(x) + 175cosh(x) +--R + +--R 56%i +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 +--R 3%i cosh(x) - 30cosh(x) - 100%i cosh(x) + 150cosh(x) +--R + +--R 105%i cosh(x) - 28 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 +--R - 3cosh(x) - 20%i cosh(x) + 50cosh(x) + 60%i cosh(x) - 35cosh(x) +--R + +--R - 8%i +--R * +--R sinh(x) +--R + +--R 5 4 3 2 +--R - %i cosh(x) + 5cosh(x) + 10%i cosh(x) - 10cosh(x) - 5%i cosh(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 497 + +--S 498 of 502 +t0899:= (coth(x)+csch(x))^3 +--R +--R +--R 3 2 2 3 +--R (311) csch(x) + 3coth(x)csch(x) + 3coth(x) csch(x) + coth(x) +--R Type: Expression(Integer) +--E 498 + +--S 499 of 502 +r0899:= 2/(1-cosh(x))+log(1-cosh(x)) +--R +--R +--R (cosh(x) - 1)log(- cosh(x) + 1) - 2 +--R (312) ----------------------------------- +--R cosh(x) - 1 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 502 +a0899:= integrate(t0899,x) +--R +--R +--R (313) +--R 2 2 +--R (2sinh(x) + (4cosh(x) - 4)sinh(x) + 2cosh(x) - 4cosh(x) + 2) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R - x sinh(x) + (- 2x cosh(x) + 2x - 4)sinh(x) - x cosh(x) +--R + +--R (2x - 4)cosh(x) - x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2)sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 500 + +--S 501 of 502 +m0899:= a0899-r0899 +--R +--R +--R (314) +--R 2 2 +--R (2cosh(x) - 2)sinh(x) + (4cosh(x) - 8cosh(x) + 4)sinh(x) +--R + +--R 3 2 +--R 2cosh(x) - 6cosh(x) + 6cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R (- cosh(x) + 1)sinh(x) + (- 2cosh(x) + 4cosh(x) - 2)sinh(x) +--R + +--R 3 2 +--R - cosh(x) + 3cosh(x) - 3cosh(x) + 1 +--R * +--R log(- cosh(x) + 1) +--R + +--R 2 2 +--R (- x cosh(x) + x + 2)sinh(x) + (- 2x cosh(x) + 4x cosh(x) - 2x)sinh(x) +--R + +--R 3 2 +--R - x cosh(x) + (3x - 2)cosh(x) - 3x cosh(x) + x + 2 +--R / +--R 2 2 3 +--R (cosh(x) - 1)sinh(x) + (2cosh(x) - 4cosh(x) + 2)sinh(x) + cosh(x) +--R + +--R 2 +--R - 3cosh(x) + 3cosh(x) - 1 +--R Type: Expression(Integer) +--E 501 + +--S 502 of 502 +d0899:= D(m0899,x) +--R +--R +--R (315) +--R 4 2 3 +--R (- cosh(x) - 1)sinh(x) + (- 2cosh(x) - 2cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 5 +--R (2cosh(x) + 2cosh(x) - 6cosh(x) - 2cosh(x) + 4)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R cosh(x) - 2cosh(x) - 2cosh(x) + cosh(x) + 1 +--R / +--R 2 3 +--R (cosh(x) - 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 2 +--R (3cosh(x) - 9cosh(x) + 9cosh(x) - 3)sinh(x) +--R + +--R 4 3 2 5 +--R (3cosh(x) - 12cosh(x) + 18cosh(x) - 12cosh(x) + 3)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R - 5cosh(x) + 10cosh(x) - 10cosh(x) + 5cosh(x) - 1 +--R Type: Expression(Integer) +--E 502 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper800-899.input.pdf b/src/axiom-website/CATS/richhyper800-899.input.pdf new file mode 100644 index 0000000..b93e914 Binary files /dev/null and b/src/axiom-website/CATS/richhyper800-899.input.pdf differ diff --git a/src/axiom-website/CATS/richhyper900-999.input.pamphlet b/src/axiom-website/CATS/richhyper900-999.input.pamphlet new file mode 100644 index 0000000..6e38a4c --- /dev/null +++ b/src/axiom-website/CATS/richhyper900-999.input.pamphlet @@ -0,0 +1,45740 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richhyper900-999.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richhyper900-999.output +)spool richhyper900-999.output +)set message auto off +)clear all + +--S 1 of 518 +t0900:= (coth(x)+csch(x))^5 +--R +--R +--R (1) +--R 5 4 2 3 3 2 +--R csch(x) + 5coth(x)csch(x) + 10coth(x) csch(x) + 10coth(x) csch(x) +--R + +--R 4 5 +--R 5coth(x) csch(x) + coth(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 518 +r0900:= -2/(1-cosh(x))^2+4/(1-cosh(x))+log(1-cosh(x)) +--R +--R +--R 2 +--R (cosh(x) - 2cosh(x) + 1)log(- cosh(x) + 1) - 4cosh(x) + 2 +--R (2) ---------------------------------------------------------- +--R 2 +--R cosh(x) - 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 518 +a0900:= integrate(t0900,x) +--R +--R +--R (3) +--R 4 3 +--R 2sinh(x) + (8cosh(x) - 8)sinh(x) +--R + +--R 2 2 +--R (12cosh(x) - 24cosh(x) + 12)sinh(x) +--R + +--R 3 2 4 +--R (8cosh(x) - 24cosh(x) + 24cosh(x) - 8)sinh(x) + 2cosh(x) +--R + +--R 3 2 +--R - 8cosh(x) + 12cosh(x) - 8cosh(x) + 2 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 3 +--R - x sinh(x) + (- 4x cosh(x) + 4x - 8)sinh(x) +--R + +--R 2 2 +--R (- 6x cosh(x) + (12x - 24)cosh(x) - 6x + 8)sinh(x) +--R + +--R 3 2 +--R (- 4x cosh(x) + (12x - 24)cosh(x) + (- 12x + 16)cosh(x) + 4x - 8) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R - x cosh(x) + (4x - 8)cosh(x) + (- 6x + 8)cosh(x) + (4x - 8)cosh(x) - x +--R / +--R 4 3 2 2 +--R sinh(x) + (4cosh(x) - 4)sinh(x) + (6cosh(x) - 12cosh(x) + 6)sinh(x) +--R + +--R 3 2 4 3 +--R (4cosh(x) - 12cosh(x) + 12cosh(x) - 4)sinh(x) + cosh(x) - 4cosh(x) +--R + +--R 2 +--R 6cosh(x) - 4cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 518 +m0900:= a0900-r0900 +--R +--R +--R (4) +--R 2 4 +--R (2cosh(x) - 4cosh(x) + 2)sinh(x) +--R + +--R 3 2 3 +--R (8cosh(x) - 24cosh(x) + 24cosh(x) - 8)sinh(x) +--R + +--R 4 3 2 2 +--R (12cosh(x) - 48cosh(x) + 72cosh(x) - 48cosh(x) + 12)sinh(x) +--R + +--R 5 4 3 2 +--R (8cosh(x) - 40cosh(x) + 80cosh(x) - 80cosh(x) + 40cosh(x) - 8) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 2cosh(x) - 12cosh(x) + 30cosh(x) - 40cosh(x) + 30cosh(x) +--R + +--R - 12cosh(x) + 2 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 4 +--R (- cosh(x) + 2cosh(x) - 1)sinh(x) +--R + +--R 3 2 3 +--R (- 4cosh(x) + 12cosh(x) - 12cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 2 +--R (- 6cosh(x) + 24cosh(x) - 36cosh(x) + 24cosh(x) - 6)sinh(x) +--R + +--R 5 4 3 2 +--R - 4cosh(x) + 20cosh(x) - 40cosh(x) + 40cosh(x) - 20cosh(x) +--R + +--R 4 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - cosh(x) + 6cosh(x) - 15cosh(x) + 20cosh(x) - 15cosh(x) +--R + +--R 6cosh(x) - 1 +--R * +--R log(- cosh(x) + 1) +--R + +--R 2 4 +--R (- x cosh(x) + (2x + 4)cosh(x) - x - 2)sinh(x) +--R + +--R 3 2 3 +--R (- 4x cosh(x) + (12x + 8)cosh(x) + (- 12x - 8)cosh(x) + 4x)sinh(x) +--R + +--R 4 3 2 +--R - 6x cosh(x) + 24x cosh(x) + (- 36x - 4)cosh(x) + (24x + 8)cosh(x) +--R + +--R - 6x - 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R - 4x cosh(x) + (20x - 8)cosh(x) + (- 40x + 8)cosh(x) +--R + +--R 2 +--R (40x + 8)cosh(x) + (- 20x - 8)cosh(x) + 4x +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - x cosh(x) + (6x - 4)cosh(x) + (- 15x + 6)cosh(x) + 20x cosh(x) +--R + +--R 2 +--R (- 15x - 4)cosh(x) + (6x + 4)cosh(x) - x - 2 +--R / +--R 2 4 +--R (cosh(x) - 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) - 12cosh(x) + 12cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 2 +--R (6cosh(x) - 24cosh(x) + 36cosh(x) - 24cosh(x) + 6)sinh(x) +--R + +--R 5 4 3 2 +--R (4cosh(x) - 20cosh(x) + 40cosh(x) - 40cosh(x) + 20cosh(x) - 4)sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) - 6cosh(x) + 15cosh(x) - 20cosh(x) + 15cosh(x) - 6cosh(x) + 1 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 518 +d0900:= D(m0900,x) +--R +--R +--R (5) +--R 2 6 +--R (- cosh(x) - 2cosh(x) - 1)sinh(x) +--R + +--R 3 2 5 +--R (- 4cosh(x) - 8cosh(x) + 8cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 4 +--R (- 5cosh(x) - 10cosh(x) + 20cosh(x) + 10cosh(x) - 15)sinh(x) +--R + +--R 6 5 4 3 2 +--R 5cosh(x) + 10cosh(x) - 25cosh(x) - 20cosh(x) + 35cosh(x) +--R + +--R 10cosh(x) - 15 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 4cosh(x) + 8cosh(x) - 16cosh(x) - 20cosh(x) + 20cosh(x) +--R + +--R 2 +--R 16cosh(x) - 8cosh(x) - 4 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 3 2 +--R cosh(x) + 2cosh(x) - 2cosh(x) - 6cosh(x) + 6cosh(x) + 2cosh(x) +--R + +--R - 2cosh(x) - 1 +--R / +--R 3 2 5 +--R (cosh(x) - 3cosh(x) + 3cosh(x) - 1)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) - 20cosh(x) + 30cosh(x) - 20cosh(x) + 5)sinh(x) +--R + +--R 5 4 3 2 +--R (10cosh(x) - 50cosh(x) + 100cosh(x) - 100cosh(x) + 50cosh(x) - 10) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 10cosh(x) - 60cosh(x) + 150cosh(x) - 200cosh(x) + 150cosh(x) +--R + +--R - 60cosh(x) + 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 5cosh(x) - 35cosh(x) + 105cosh(x) - 175cosh(x) + 175cosh(x) +--R + +--R 2 +--R - 105cosh(x) + 35cosh(x) - 5 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 3 +--R cosh(x) - 8cosh(x) + 28cosh(x) - 56cosh(x) + 70cosh(x) - 56cosh(x) +--R + +--R 2 +--R 28cosh(x) - 8cosh(x) + 1 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 518 +t0901:= 1/(coth(x)+csch(x)) +--R +--R +--R 1 +--R (6) ----------------- +--R csch(x) + coth(x) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 518 +r0901:= log(1+cosh(x)) +--R +--R +--R (7) log(cosh(x) + 1) +--R Type: Expression(Integer) +--E 7 + +--S 8 of 518 +a0901:= integrate(t0901,x) +--R +--R +--R (8) 2log(sinh(x) + cosh(x) + 1) - x +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 518 +m0901:= a0901-r0901 +--R +--R +--R (9) 2log(sinh(x) + cosh(x) + 1) - log(cosh(x) + 1) - x +--R Type: Expression(Integer) +--E 9 + +--S 10 of 518 +d0901:= D(m0901,x) +--R +--R +--R 2 2 +--R - sinh(x) + cosh(x) - 1 +--R (10) ---------------------------------------------- +--R 2 +--R (cosh(x) + 1)sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 518 +t0902:= 1/(coth(x)+csch(x))^2 +--R +--R +--R 1 +--R (11) ------------------------------------- +--R 2 2 +--R csch(x) + 2coth(x)csch(x) + coth(x) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 518 +r0902:= x-2*tanh(1/2*x) +--R +--R +--R x +--R (12) - 2tanh(-) + x +--R 2 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 518 +a0902:= integrate(t0902,x) +--R +--R +--R x sinh(x) + x cosh(x) + x + 4 +--R (13) ----------------------------- +--R sinh(x) + cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 518 +m0902:= a0902-r0902 +--R +--R +--R x +--R (2sinh(x) + 2cosh(x) + 2)tanh(-) + 4 +--R 2 +--R (14) ------------------------------------ +--R sinh(x) + cosh(x) + 1 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 518 +d0902:= D(m0902,x) +--R +--R +--R (15) +--R 2 2 x 2 +--R (- sinh(x) + (- 2cosh(x) - 2)sinh(x) - cosh(x) - 2cosh(x) - 1)tanh(-) +--R 2 +--R + +--R 2 2 +--R sinh(x) + (2cosh(x) - 2)sinh(x) + cosh(x) - 2cosh(x) + 1 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2)sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 15 + +--S 16 of 518 +t0903:= 1/(coth(x)+csch(x))^3 +--R +--R +--R 1 +--R (16) --------------------------------------------------------- +--R 3 2 2 3 +--R csch(x) + 3coth(x)csch(x) + 3coth(x) csch(x) + coth(x) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 518 +r0903:= 2/(1+cosh(x))+log(1+cosh(x)) +--R +--R +--R (cosh(x) + 1)log(cosh(x) + 1) + 2 +--R (17) --------------------------------- +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 518 +a0903:= integrate(t0903,x) +--R +--R +--R (18) +--R 2 2 +--R (2sinh(x) + (4cosh(x) + 4)sinh(x) + 2cosh(x) + 4cosh(x) + 2) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R - x sinh(x) + (- 2x cosh(x) - 2x + 4)sinh(x) - x cosh(x) +--R + +--R (- 2x + 4)cosh(x) - x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2)sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 518 +m0903:= a0903-r0903 +--R +--R +--R (19) +--R 2 2 +--R (2cosh(x) + 2)sinh(x) + (4cosh(x) + 8cosh(x) + 4)sinh(x) +--R + +--R 3 2 +--R 2cosh(x) + 6cosh(x) + 6cosh(x) + 2 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R (- cosh(x) - 1)sinh(x) + (- 2cosh(x) - 4cosh(x) - 2)sinh(x) +--R + +--R 3 2 +--R - cosh(x) - 3cosh(x) - 3cosh(x) - 1 +--R * +--R log(cosh(x) + 1) +--R + +--R 2 2 +--R (- x cosh(x) - x - 2)sinh(x) + (- 2x cosh(x) - 4x cosh(x) - 2x)sinh(x) +--R + +--R 3 2 +--R - x cosh(x) + (- 3x + 2)cosh(x) - 3x cosh(x) - x - 2 +--R / +--R 2 2 3 +--R (cosh(x) + 1)sinh(x) + (2cosh(x) + 4cosh(x) + 2)sinh(x) + cosh(x) +--R + +--R 2 +--R 3cosh(x) + 3cosh(x) + 1 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 518 +d0903:= D(m0903,x) +--R +--R +--R (20) +--R 4 2 3 +--R (- cosh(x) + 1)sinh(x) + (- 2cosh(x) + 2cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 5 +--R (2cosh(x) - 2cosh(x) - 6cosh(x) + 2cosh(x) + 4)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R - cosh(x) - 2cosh(x) + 2cosh(x) + cosh(x) - 1 +--R / +--R 2 3 +--R (cosh(x) + 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 2 +--R (3cosh(x) + 9cosh(x) + 9cosh(x) + 3)sinh(x) +--R + +--R 4 3 2 5 +--R (3cosh(x) + 12cosh(x) + 18cosh(x) + 12cosh(x) + 3)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R 5cosh(x) + 10cosh(x) + 10cosh(x) + 5cosh(x) + 1 +--R Type: Expression(Integer) +--E 20 + +--S 21 of 518 +t0904:= 1/(coth(x)+csch(x))^4 +--R +--R +--R (21) +--R 1 +--R ----------------------------------------------------------------------------- +--R 4 3 2 2 3 4 +--R csch(x) + 4coth(x)csch(x) + 6coth(x) csch(x) + 4coth(x) csch(x) + coth(x) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 518 +r0904:= x-2*tanh(1/2*x)-2/3*tanh(1/2*x)^3 +--R +--R +--R x 3 x +--R - 2tanh(-) - 6tanh(-) + 3x +--R 2 2 +--R (22) --------------------------- +--R 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 518 +a0904:= integrate(t0904,x) +--R +--R +--R (23) +--R 2 2 +--R 3x sinh(x) + (6x cosh(x) + 6x + 8)sinh(x) + 3x cosh(x) +--R + +--R (12x + 40)cosh(x) + 9x + 24 +--R / +--R 2 2 +--R 3sinh(x) + (6cosh(x) + 6)sinh(x) + 3cosh(x) + 12cosh(x) + 9 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 518 +m0904:= a0904-r0904 +--R +--R +--R (24) +--R 2 2 x 3 +--R (2sinh(x) + (4cosh(x) + 4)sinh(x) + 2cosh(x) + 8cosh(x) + 6)tanh(-) +--R 2 +--R + +--R 2 2 x +--R (6sinh(x) + (12cosh(x) + 12)sinh(x) + 6cosh(x) + 24cosh(x) + 18)tanh(-) +--R 2 +--R + +--R 8sinh(x) + 40cosh(x) + 24 +--R / +--R 2 2 +--R 3sinh(x) + (6cosh(x) + 6)sinh(x) + 3cosh(x) + 12cosh(x) + 9 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 518 +d0904:= D(m0904,x) +--R +--R +--R (25) +--R 4 3 +--R - sinh(x) + (- 4cosh(x) - 4)sinh(x) +--R + +--R 2 2 +--R (- 6cosh(x) - 16cosh(x) - 10)sinh(x) +--R + +--R 3 2 4 +--R (- 4cosh(x) - 20cosh(x) - 28cosh(x) - 12)sinh(x) - cosh(x) +--R + +--R 3 2 +--R - 8cosh(x) - 22cosh(x) - 24cosh(x) - 9 +--R * +--R x 4 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 +--R sinh(x) + (4cosh(x) + 12)sinh(x) + (6cosh(x) + 8cosh(x) + 10)sinh(x) +--R + +--R 3 2 4 3 +--R (4cosh(x) - 20cosh(x) - 4cosh(x) + 20)sinh(x) + cosh(x) - 16cosh(x) +--R + +--R 2 +--R - 10cosh(x) + 16cosh(x) + 9 +--R / +--R 4 3 2 2 +--R sinh(x) + (4cosh(x) + 4)sinh(x) + (6cosh(x) + 16cosh(x) + 10)sinh(x) +--R + +--R 3 2 4 3 +--R (4cosh(x) + 20cosh(x) + 28cosh(x) + 12)sinh(x) + cosh(x) + 8cosh(x) +--R + +--R 2 +--R 22cosh(x) + 24cosh(x) + 9 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 518 +t0905:= 1/(coth(x)+csch(x))^5 +--R +--R +--R (26) +--R 1 +--R / +--R 5 4 2 3 3 2 +--R csch(x) + 5coth(x)csch(x) + 10coth(x) csch(x) + 10coth(x) csch(x) +--R + +--R 4 5 +--R 5coth(x) csch(x) + coth(x) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 518 +r0905:= -2/(1+cosh(x))^2+4/(1+cosh(x))+log(1+cosh(x)) +--R +--R +--R 2 +--R (cosh(x) + 2cosh(x) + 1)log(cosh(x) + 1) + 4cosh(x) + 2 +--R (27) -------------------------------------------------------- +--R 2 +--R cosh(x) + 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 518 +a0905:= integrate(t0905,x) +--R +--R +--R (28) +--R 4 3 +--R 2sinh(x) + (8cosh(x) + 8)sinh(x) +--R + +--R 2 2 +--R (12cosh(x) + 24cosh(x) + 12)sinh(x) +--R + +--R 3 2 4 +--R (8cosh(x) + 24cosh(x) + 24cosh(x) + 8)sinh(x) + 2cosh(x) +--R + +--R 3 2 +--R 8cosh(x) + 12cosh(x) + 8cosh(x) + 2 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 +--R - x sinh(x) + (- 4x cosh(x) - 4x + 8)sinh(x) +--R + +--R 2 2 +--R (- 6x cosh(x) + (- 12x + 24)cosh(x) - 6x + 8)sinh(x) +--R + +--R 3 2 +--R (- 4x cosh(x) + (- 12x + 24)cosh(x) + (- 12x + 16)cosh(x) - 4x + 8) +--R * +--R sinh(x) +--R + +--R 4 3 2 +--R - x cosh(x) + (- 4x + 8)cosh(x) + (- 6x + 8)cosh(x) +--R + +--R (- 4x + 8)cosh(x) - x +--R / +--R 4 3 2 2 +--R sinh(x) + (4cosh(x) + 4)sinh(x) + (6cosh(x) + 12cosh(x) + 6)sinh(x) +--R + +--R 3 2 4 3 +--R (4cosh(x) + 12cosh(x) + 12cosh(x) + 4)sinh(x) + cosh(x) + 4cosh(x) +--R + +--R 2 +--R 6cosh(x) + 4cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 518 +m0905:= a0905-r0905 +--R +--R +--R (29) +--R 2 4 +--R (2cosh(x) + 4cosh(x) + 2)sinh(x) +--R + +--R 3 2 3 +--R (8cosh(x) + 24cosh(x) + 24cosh(x) + 8)sinh(x) +--R + +--R 4 3 2 2 +--R (12cosh(x) + 48cosh(x) + 72cosh(x) + 48cosh(x) + 12)sinh(x) +--R + +--R 5 4 3 2 +--R (8cosh(x) + 40cosh(x) + 80cosh(x) + 80cosh(x) + 40cosh(x) + 8) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 2cosh(x) + 12cosh(x) + 30cosh(x) + 40cosh(x) + 30cosh(x) +--R + +--R 12cosh(x) + 2 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 4 +--R (- cosh(x) - 2cosh(x) - 1)sinh(x) +--R + +--R 3 2 3 +--R (- 4cosh(x) - 12cosh(x) - 12cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 2 +--R (- 6cosh(x) - 24cosh(x) - 36cosh(x) - 24cosh(x) - 6)sinh(x) +--R + +--R 5 4 3 2 +--R - 4cosh(x) - 20cosh(x) - 40cosh(x) - 40cosh(x) - 20cosh(x) +--R + +--R - 4 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - cosh(x) - 6cosh(x) - 15cosh(x) - 20cosh(x) - 15cosh(x) +--R + +--R - 6cosh(x) - 1 +--R * +--R log(cosh(x) + 1) +--R + +--R 2 4 +--R (- x cosh(x) + (- 2x - 4)cosh(x) - x - 2)sinh(x) +--R + +--R 3 2 3 +--R (- 4x cosh(x) + (- 12x - 8)cosh(x) + (- 12x - 8)cosh(x) - 4x)sinh(x) +--R + +--R 4 3 2 +--R - 6x cosh(x) - 24x cosh(x) + (- 36x - 4)cosh(x) +--R + +--R (- 24x - 8)cosh(x) - 6x - 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R - 4x cosh(x) + (- 20x + 8)cosh(x) + (- 40x + 8)cosh(x) +--R + +--R 2 +--R (- 40x - 8)cosh(x) + (- 20x - 8)cosh(x) - 4x +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R - x cosh(x) + (- 6x + 4)cosh(x) + (- 15x + 6)cosh(x) - 20x cosh(x) +--R + +--R 2 +--R (- 15x - 4)cosh(x) + (- 6x - 4)cosh(x) - x - 2 +--R / +--R 2 4 +--R (cosh(x) + 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) + 12cosh(x) + 12cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 2 +--R (6cosh(x) + 24cosh(x) + 36cosh(x) + 24cosh(x) + 6)sinh(x) +--R + +--R 5 4 3 2 +--R (4cosh(x) + 20cosh(x) + 40cosh(x) + 40cosh(x) + 20cosh(x) + 4)sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) + 6cosh(x) + 15cosh(x) + 20cosh(x) + 15cosh(x) + 6cosh(x) + 1 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 518 +d0905:= D(m0905,x) +--R +--R +--R (30) +--R 2 6 +--R (- cosh(x) + 2cosh(x) - 1)sinh(x) +--R + +--R 3 2 5 +--R (- 4cosh(x) + 8cosh(x) + 8cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 4 +--R (- 5cosh(x) + 10cosh(x) + 20cosh(x) - 10cosh(x) - 15)sinh(x) +--R + +--R 6 5 4 3 2 +--R 5cosh(x) - 10cosh(x) - 25cosh(x) + 20cosh(x) + 35cosh(x) +--R + +--R - 10cosh(x) - 15 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 4cosh(x) - 8cosh(x) - 16cosh(x) + 20cosh(x) + 20cosh(x) +--R + +--R 2 +--R - 16cosh(x) - 8cosh(x) + 4 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 3 2 +--R cosh(x) - 2cosh(x) - 2cosh(x) + 6cosh(x) - 6cosh(x) + 2cosh(x) +--R + +--R 2cosh(x) - 1 +--R / +--R 3 2 5 +--R (cosh(x) + 3cosh(x) + 3cosh(x) + 1)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) + 20cosh(x) + 30cosh(x) + 20cosh(x) + 5)sinh(x) +--R + +--R 5 4 3 2 +--R (10cosh(x) + 50cosh(x) + 100cosh(x) + 100cosh(x) + 50cosh(x) + 10) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 10cosh(x) + 60cosh(x) + 150cosh(x) + 200cosh(x) + 150cosh(x) +--R + +--R 60cosh(x) + 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 5cosh(x) + 35cosh(x) + 105cosh(x) + 175cosh(x) + 175cosh(x) +--R + +--R 2 +--R 105cosh(x) + 35cosh(x) + 5 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 3 +--R cosh(x) + 8cosh(x) + 28cosh(x) + 56cosh(x) + 70cosh(x) + 56cosh(x) +--R + +--R 2 +--R 28cosh(x) + 8cosh(x) + 1 +--R Type: Expression(Integer) +--E 30 + +--S 31 of 518 +t0906:= -coth(x)+csch(x) +--R +--R +--R (31) csch(x) - coth(x) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 518 +r0906:= -2*log(cosh(1/2*x)) +--R +--R +--R x +--R (32) - 2log(cosh(-)) +--R 2 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 518 +a0906:= integrate(t0906,x) +--R +--R +--R (33) - 2log(sinh(x) + cosh(x) + 1) + x +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 518 +m0906:= a0906-r0906 +--R +--R +--R x +--R (34) - 2log(sinh(x) + cosh(x) + 1) + 2log(cosh(-)) + x +--R 2 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 518 +d0906:= D(m0906,x) +--R +--R +--R (35) +--R x x x x x +--R (sinh(-) - cosh(-))sinh(x) + (cosh(x) + 1)sinh(-) - cosh(-)cosh(x) + cosh(-) +--R 2 2 2 2 2 +--R ---------------------------------------------------------------------------- +--R x x x +--R cosh(-)sinh(x) + cosh(-)cosh(x) + cosh(-) +--R 2 2 2 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 518 +t0907:= (-coth(x)+csch(x))^3 +--R +--R +--R 3 2 2 3 +--R (36) csch(x) - 3coth(x)csch(x) + 3coth(x) csch(x) - coth(x) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 518 +r0907:= -2/(1+cosh(x))-log(1+cosh(x)) +--R +--R +--R (- cosh(x) - 1)log(cosh(x) + 1) - 2 +--R (37) ----------------------------------- +--R cosh(x) + 1 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 518 +a0907:= integrate(t0907,x) +--R +--R +--R (38) +--R 2 2 +--R (- 2sinh(x) + (- 4cosh(x) - 4)sinh(x) - 2cosh(x) - 4cosh(x) - 2) +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 +--R x sinh(x) + (2x cosh(x) + 2x - 4)sinh(x) + x cosh(x) + (2x - 4)cosh(x) +--R + +--R x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) + 2)sinh(x) + cosh(x) + 2cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 518 +m0907:= a0907-r0907 +--R +--R +--R (39) +--R 2 2 +--R (- 2cosh(x) - 2)sinh(x) + (- 4cosh(x) - 8cosh(x) - 4)sinh(x) +--R + +--R 3 2 +--R - 2cosh(x) - 6cosh(x) - 6cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 3 +--R (cosh(x) + 1)sinh(x) + (2cosh(x) + 4cosh(x) + 2)sinh(x) + cosh(x) +--R + +--R 2 +--R 3cosh(x) + 3cosh(x) + 1 +--R * +--R log(cosh(x) + 1) +--R + +--R 2 2 +--R (x cosh(x) + x + 2)sinh(x) + (2x cosh(x) + 4x cosh(x) + 2x)sinh(x) +--R + +--R 3 2 +--R x cosh(x) + (3x - 2)cosh(x) + 3x cosh(x) + x + 2 +--R / +--R 2 2 3 +--R (cosh(x) + 1)sinh(x) + (2cosh(x) + 4cosh(x) + 2)sinh(x) + cosh(x) +--R + +--R 2 +--R 3cosh(x) + 3cosh(x) + 1 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 518 +d0907:= D(m0907,x) +--R +--R +--R (40) +--R 4 2 3 +--R (cosh(x) - 1)sinh(x) + (2cosh(x) - 2cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 5 +--R (- 2cosh(x) + 2cosh(x) + 6cosh(x) - 2cosh(x) - 4)sinh(x) - cosh(x) +--R + +--R 4 3 2 +--R cosh(x) + 2cosh(x) - 2cosh(x) - cosh(x) + 1 +--R / +--R 2 3 +--R (cosh(x) + 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 2 +--R (3cosh(x) + 9cosh(x) + 9cosh(x) + 3)sinh(x) +--R + +--R 4 3 2 5 +--R (3cosh(x) + 12cosh(x) + 18cosh(x) + 12cosh(x) + 3)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R 5cosh(x) + 10cosh(x) + 10cosh(x) + 5cosh(x) + 1 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 518 +t0908:= (-coth(x)+csch(x))^5 +--R +--R +--R (41) +--R 5 4 2 3 3 2 +--R csch(x) - 5coth(x)csch(x) + 10coth(x) csch(x) - 10coth(x) csch(x) +--R + +--R 4 5 +--R 5coth(x) csch(x) - coth(x) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 518 +r0908:= 2/(1+cosh(x))^2-4/(1+cosh(x))-log(1+cosh(x)) +--R +--R +--R 2 +--R (- cosh(x) - 2cosh(x) - 1)log(cosh(x) + 1) - 4cosh(x) - 2 +--R (42) ---------------------------------------------------------- +--R 2 +--R cosh(x) + 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 518 +a0908:= integrate(t0908,x) +--R +--R +--R (43) +--R 4 3 +--R - 2sinh(x) + (- 8cosh(x) - 8)sinh(x) +--R + +--R 2 2 +--R (- 12cosh(x) - 24cosh(x) - 12)sinh(x) +--R + +--R 3 2 4 +--R (- 8cosh(x) - 24cosh(x) - 24cosh(x) - 8)sinh(x) - 2cosh(x) +--R + +--R 3 2 +--R - 8cosh(x) - 12cosh(x) - 8cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 +--R x sinh(x) + (4x cosh(x) + 4x - 8)sinh(x) +--R + +--R 2 2 +--R (6x cosh(x) + (12x - 24)cosh(x) + 6x - 8)sinh(x) +--R + +--R 3 2 +--R (4x cosh(x) + (12x - 24)cosh(x) + (12x - 16)cosh(x) + 4x - 8)sinh(x) +--R + +--R 4 3 2 +--R x cosh(x) + (4x - 8)cosh(x) + (6x - 8)cosh(x) + (4x - 8)cosh(x) + x +--R / +--R 4 3 2 2 +--R sinh(x) + (4cosh(x) + 4)sinh(x) + (6cosh(x) + 12cosh(x) + 6)sinh(x) +--R + +--R 3 2 4 3 +--R (4cosh(x) + 12cosh(x) + 12cosh(x) + 4)sinh(x) + cosh(x) + 4cosh(x) +--R + +--R 2 +--R 6cosh(x) + 4cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 518 +m0908:= a0908-r0908 +--R +--R +--R (44) +--R 2 4 +--R (- 2cosh(x) - 4cosh(x) - 2)sinh(x) +--R + +--R 3 2 3 +--R (- 8cosh(x) - 24cosh(x) - 24cosh(x) - 8)sinh(x) +--R + +--R 4 3 2 2 +--R (- 12cosh(x) - 48cosh(x) - 72cosh(x) - 48cosh(x) - 12)sinh(x) +--R + +--R 5 4 3 2 +--R - 8cosh(x) - 40cosh(x) - 80cosh(x) - 80cosh(x) - 40cosh(x) +--R + +--R - 8 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 2cosh(x) - 12cosh(x) - 30cosh(x) - 40cosh(x) - 30cosh(x) +--R + +--R - 12cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 4 +--R (cosh(x) + 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) + 12cosh(x) + 12cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 2 +--R (6cosh(x) + 24cosh(x) + 36cosh(x) + 24cosh(x) + 6)sinh(x) +--R + +--R 5 4 3 2 +--R (4cosh(x) + 20cosh(x) + 40cosh(x) + 40cosh(x) + 20cosh(x) + 4) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) + 6cosh(x) + 15cosh(x) + 20cosh(x) + 15cosh(x) +--R + +--R 6cosh(x) + 1 +--R * +--R log(cosh(x) + 1) +--R + +--R 2 4 +--R (x cosh(x) + (2x + 4)cosh(x) + x + 2)sinh(x) +--R + +--R 3 2 3 +--R (4x cosh(x) + (12x + 8)cosh(x) + (12x + 8)cosh(x) + 4x)sinh(x) +--R + +--R 4 3 2 +--R 6x cosh(x) + 24x cosh(x) + (36x + 4)cosh(x) + (24x + 8)cosh(x) +--R + +--R 6x + 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R 4x cosh(x) + (20x - 8)cosh(x) + (40x - 8)cosh(x) +--R + +--R 2 +--R (40x + 8)cosh(x) + (20x + 8)cosh(x) + 4x +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R x cosh(x) + (6x - 4)cosh(x) + (15x - 6)cosh(x) + 20x cosh(x) +--R + +--R 2 +--R (15x + 4)cosh(x) + (6x + 4)cosh(x) + x + 2 +--R / +--R 2 4 +--R (cosh(x) + 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) + 12cosh(x) + 12cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 2 +--R (6cosh(x) + 24cosh(x) + 36cosh(x) + 24cosh(x) + 6)sinh(x) +--R + +--R 5 4 3 2 +--R (4cosh(x) + 20cosh(x) + 40cosh(x) + 40cosh(x) + 20cosh(x) + 4)sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) + 6cosh(x) + 15cosh(x) + 20cosh(x) + 15cosh(x) + 6cosh(x) + 1 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 518 +d0908:= D(m0908,x) +--R +--R +--R (45) +--R 2 6 +--R (cosh(x) - 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 5 +--R (4cosh(x) - 8cosh(x) - 8cosh(x) + 4)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) - 10cosh(x) - 20cosh(x) + 10cosh(x) + 15)sinh(x) +--R + +--R 6 5 4 3 2 +--R - 5cosh(x) + 10cosh(x) + 25cosh(x) - 20cosh(x) - 35cosh(x) +--R + +--R 10cosh(x) + 15 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 4cosh(x) + 8cosh(x) + 16cosh(x) - 20cosh(x) - 20cosh(x) +--R + +--R 2 +--R 16cosh(x) + 8cosh(x) - 4 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 3 2 +--R - cosh(x) + 2cosh(x) + 2cosh(x) - 6cosh(x) + 6cosh(x) - 2cosh(x) +--R + +--R - 2cosh(x) + 1 +--R / +--R 3 2 5 +--R (cosh(x) + 3cosh(x) + 3cosh(x) + 1)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) + 20cosh(x) + 30cosh(x) + 20cosh(x) + 5)sinh(x) +--R + +--R 5 4 3 2 +--R (10cosh(x) + 50cosh(x) + 100cosh(x) + 100cosh(x) + 50cosh(x) + 10) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 10cosh(x) + 60cosh(x) + 150cosh(x) + 200cosh(x) + 150cosh(x) +--R + +--R 60cosh(x) + 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 5cosh(x) + 35cosh(x) + 105cosh(x) + 175cosh(x) + 175cosh(x) +--R + +--R 2 +--R 105cosh(x) + 35cosh(x) + 5 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 3 +--R cosh(x) + 8cosh(x) + 28cosh(x) + 56cosh(x) + 70cosh(x) + 56cosh(x) +--R + +--R 2 +--R 28cosh(x) + 8cosh(x) + 1 +--R Type: Expression(Integer) +--E 45 + +--S 46 of 518 +t0909:= 1/(-coth(x)+csch(x)) +--R +--R +--R 1 +--R (46) ----------------- +--R csch(x) - coth(x) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 518 +r0909:= -log(1-cosh(x)) +--R +--R +--R (47) - log(- cosh(x) + 1) +--R Type: Expression(Integer) +--E 47 + +--S 48 of 518 +a0909:= integrate(t0909,x) +--R +--R +--R (48) - 2log(sinh(x) + cosh(x) - 1) + x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 518 +m0909:= a0909-r0909 +--R +--R +--R (49) - 2log(sinh(x) + cosh(x) - 1) + log(- cosh(x) + 1) + x +--R Type: Expression(Integer) +--E 49 + +--S 50 of 518 +d0909:= D(m0909,x) +--R +--R +--R 2 2 +--R sinh(x) - cosh(x) + 1 +--R (50) ---------------------------------------------- +--R 2 +--R (cosh(x) - 1)sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 518 +t0910:= 1/(-coth(x)+csch(x))^2 +--R +--R +--R 1 +--R (51) ------------------------------------- +--R 2 2 +--R csch(x) - 2coth(x)csch(x) + coth(x) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 518 +r0910:= x-2*coth(1/2*x) +--R +--R +--R x +--R (52) - 2coth(-) + x +--R 2 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 518 +a0910:= integrate(t0910,x) +--R +--R +--R x sinh(x) + x cosh(x) - x - 4 +--R (53) ----------------------------- +--R sinh(x) + cosh(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 518 +m0910:= a0910-r0910 +--R +--R +--R x x +--R 2coth(-)sinh(x) + (2cosh(x) - 2)coth(-) - 4 +--R 2 2 +--R (54) ------------------------------------------- +--R sinh(x) + cosh(x) - 1 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 518 +d0910:= D(m0910,x) +--R +--R +--R (55) +--R x 2 2 +--R (- coth(-) + 1)sinh(x) +--R 2 +--R + +--R x 2 +--R ((- 2cosh(x) + 2)coth(-) + 2cosh(x) + 2)sinh(x) +--R 2 +--R + +--R 2 x 2 2 +--R (- cosh(x) + 2cosh(x) - 1)coth(-) + cosh(x) + 2cosh(x) + 1 +--R 2 +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2)sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 518 +t0911:= 1/(-coth(x)+csch(x))^3 +--R +--R +--R 1 +--R (56) --------------------------------------------------------- +--R 3 2 2 3 +--R csch(x) - 3coth(x)csch(x) + 3coth(x) csch(x) - coth(x) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 518 +r0911:= -2/(1-cosh(x))-log(1-cosh(x)) +--R +--R +--R (- cosh(x) + 1)log(- cosh(x) + 1) + 2 +--R (57) ------------------------------------- +--R cosh(x) - 1 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 518 +a0911:= integrate(t0911,x) +--R +--R +--R (58) +--R 2 2 +--R (- 2sinh(x) + (- 4cosh(x) + 4)sinh(x) - 2cosh(x) + 4cosh(x) - 2) +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 +--R x sinh(x) + (2x cosh(x) - 2x + 4)sinh(x) + x cosh(x) +--R + +--R (- 2x + 4)cosh(x) + x +--R / +--R 2 2 +--R sinh(x) + (2cosh(x) - 2)sinh(x) + cosh(x) - 2cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 518 +m0911:= a0911-r0911 +--R +--R +--R (59) +--R 2 2 +--R (- 2cosh(x) + 2)sinh(x) + (- 4cosh(x) + 8cosh(x) - 4)sinh(x) +--R + +--R 3 2 +--R - 2cosh(x) + 6cosh(x) - 6cosh(x) + 2 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 3 +--R (cosh(x) - 1)sinh(x) + (2cosh(x) - 4cosh(x) + 2)sinh(x) + cosh(x) +--R + +--R 2 +--R - 3cosh(x) + 3cosh(x) - 1 +--R * +--R log(- cosh(x) + 1) +--R + +--R 2 2 +--R (x cosh(x) - x - 2)sinh(x) + (2x cosh(x) - 4x cosh(x) + 2x)sinh(x) +--R + +--R 3 2 +--R x cosh(x) + (- 3x + 2)cosh(x) + 3x cosh(x) - x - 2 +--R / +--R 2 2 3 +--R (cosh(x) - 1)sinh(x) + (2cosh(x) - 4cosh(x) + 2)sinh(x) + cosh(x) +--R + +--R 2 +--R - 3cosh(x) + 3cosh(x) - 1 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 518 +d0911:= D(m0911,x) +--R +--R +--R (60) +--R 4 2 3 +--R (cosh(x) + 1)sinh(x) + (2cosh(x) + 2cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 5 +--R (- 2cosh(x) - 2cosh(x) + 6cosh(x) + 2cosh(x) - 4)sinh(x) - cosh(x) +--R + +--R 4 3 2 +--R - cosh(x) + 2cosh(x) + 2cosh(x) - cosh(x) - 1 +--R / +--R 2 3 +--R (cosh(x) - 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 2 +--R (3cosh(x) - 9cosh(x) + 9cosh(x) - 3)sinh(x) +--R + +--R 4 3 2 5 +--R (3cosh(x) - 12cosh(x) + 18cosh(x) - 12cosh(x) + 3)sinh(x) + cosh(x) +--R + +--R 4 3 2 +--R - 5cosh(x) + 10cosh(x) - 10cosh(x) + 5cosh(x) - 1 +--R Type: Expression(Integer) +--E 60 + +--S 61 of 518 +t0912:= 1/(-coth(x)+csch(x))^4 +--R +--R +--R (61) +--R 1 +--R ----------------------------------------------------------------------------- +--R 4 3 2 2 3 4 +--R csch(x) - 4coth(x)csch(x) + 6coth(x) csch(x) - 4coth(x) csch(x) + coth(x) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 518 +r0912:= x-2*coth(1/2*x)-2/3*coth(1/2*x)^3 +--R +--R +--R x 3 x +--R - 2coth(-) - 6coth(-) + 3x +--R 2 2 +--R (62) --------------------------- +--R 3 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 518 +a0912:= integrate(t0912,x) +--R +--R +--R (63) +--R 2 2 +--R 3x sinh(x) + (6x cosh(x) - 6x - 8)sinh(x) + 3x cosh(x) +--R + +--R (- 12x - 40)cosh(x) + 9x + 24 +--R / +--R 2 2 +--R 3sinh(x) + (6cosh(x) - 6)sinh(x) + 3cosh(x) - 12cosh(x) + 9 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 518 +m0912:= a0912-r0912 +--R +--R +--R (64) +--R x 3 x 2 +--R (2coth(-) + 6coth(-))sinh(x) +--R 2 2 +--R + +--R x 3 x +--R ((4cosh(x) - 4)coth(-) + (12cosh(x) - 12)coth(-) - 8)sinh(x) +--R 2 2 +--R + +--R 2 x 3 2 x +--R (2cosh(x) - 8cosh(x) + 6)coth(-) + (6cosh(x) - 24cosh(x) + 18)coth(-) +--R 2 2 +--R + +--R - 40cosh(x) + 24 +--R / +--R 2 2 +--R 3sinh(x) + (6cosh(x) - 6)sinh(x) + 3cosh(x) - 12cosh(x) + 9 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 518 +d0912:= D(m0912,x) +--R +--R +--R (65) +--R x 4 4 +--R (- coth(-) + 1)sinh(x) +--R 2 +--R + +--R x 4 3 +--R ((- 4cosh(x) + 4)coth(-) + 4cosh(x) - 12)sinh(x) +--R 2 +--R + +--R 2 x 4 2 +--R ((- 6cosh(x) + 16cosh(x) - 10)coth(-) + 6cosh(x) - 8cosh(x) + 10) +--R 2 +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 x 4 3 +--R (- 4cosh(x) + 20cosh(x) - 28cosh(x) + 12)coth(-) + 4cosh(x) +--R 2 +--R + +--R 2 +--R 20cosh(x) - 4cosh(x) - 20 +--R * +--R sinh(x) +--R + +--R 4 3 2 x 4 4 +--R (- cosh(x) + 8cosh(x) - 22cosh(x) + 24cosh(x) - 9)coth(-) + cosh(x) +--R 2 +--R + +--R 3 2 +--R 16cosh(x) - 10cosh(x) - 16cosh(x) + 9 +--R / +--R 4 3 2 2 +--R sinh(x) + (4cosh(x) - 4)sinh(x) + (6cosh(x) - 16cosh(x) + 10)sinh(x) +--R + +--R 3 2 4 3 +--R (4cosh(x) - 20cosh(x) + 28cosh(x) - 12)sinh(x) + cosh(x) - 8cosh(x) +--R + +--R 2 +--R 22cosh(x) - 24cosh(x) + 9 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 518 +t0913:= 1/(-coth(x)+csch(x))^5 +--R +--R +--R (66) +--R 1 +--R / +--R 5 4 2 3 3 2 +--R csch(x) - 5coth(x)csch(x) + 10coth(x) csch(x) - 10coth(x) csch(x) +--R + +--R 4 5 +--R 5coth(x) csch(x) - coth(x) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 518 +r0913:= 2/(1-cosh(x))^2-4/(1-cosh(x))-log(1-cosh(x)) +--R +--R +--R 2 +--R (- cosh(x) + 2cosh(x) - 1)log(- cosh(x) + 1) + 4cosh(x) - 2 +--R (67) ------------------------------------------------------------ +--R 2 +--R cosh(x) - 2cosh(x) + 1 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 518 +a0913:= integrate(t0913,x) +--R +--R +--R (68) +--R 4 3 +--R - 2sinh(x) + (- 8cosh(x) + 8)sinh(x) +--R + +--R 2 2 +--R (- 12cosh(x) + 24cosh(x) - 12)sinh(x) +--R + +--R 3 2 4 +--R (- 8cosh(x) + 24cosh(x) - 24cosh(x) + 8)sinh(x) - 2cosh(x) +--R + +--R 3 2 +--R 8cosh(x) - 12cosh(x) + 8cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 4 3 +--R x sinh(x) + (4x cosh(x) - 4x + 8)sinh(x) +--R + +--R 2 2 +--R (6x cosh(x) + (- 12x + 24)cosh(x) + 6x - 8)sinh(x) +--R + +--R 3 2 +--R (4x cosh(x) + (- 12x + 24)cosh(x) + (12x - 16)cosh(x) - 4x + 8)sinh(x) +--R + +--R 4 3 2 +--R x cosh(x) + (- 4x + 8)cosh(x) + (6x - 8)cosh(x) + (- 4x + 8)cosh(x) + x +--R / +--R 4 3 2 2 +--R sinh(x) + (4cosh(x) - 4)sinh(x) + (6cosh(x) - 12cosh(x) + 6)sinh(x) +--R + +--R 3 2 4 3 +--R (4cosh(x) - 12cosh(x) + 12cosh(x) - 4)sinh(x) + cosh(x) - 4cosh(x) +--R + +--R 2 +--R 6cosh(x) - 4cosh(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 518 +m0913:= a0913-r0913 +--R +--R +--R (69) +--R 2 4 +--R (- 2cosh(x) + 4cosh(x) - 2)sinh(x) +--R + +--R 3 2 3 +--R (- 8cosh(x) + 24cosh(x) - 24cosh(x) + 8)sinh(x) +--R + +--R 4 3 2 2 +--R (- 12cosh(x) + 48cosh(x) - 72cosh(x) + 48cosh(x) - 12)sinh(x) +--R + +--R 5 4 3 2 +--R - 8cosh(x) + 40cosh(x) - 80cosh(x) + 80cosh(x) - 40cosh(x) +--R + +--R 8 +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R - 2cosh(x) + 12cosh(x) - 30cosh(x) + 40cosh(x) - 30cosh(x) +--R + +--R 12cosh(x) - 2 +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 4 +--R (cosh(x) - 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) - 12cosh(x) + 12cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 2 +--R (6cosh(x) - 24cosh(x) + 36cosh(x) - 24cosh(x) + 6)sinh(x) +--R + +--R 5 4 3 2 +--R (4cosh(x) - 20cosh(x) + 40cosh(x) - 40cosh(x) + 20cosh(x) - 4) +--R * +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) - 6cosh(x) + 15cosh(x) - 20cosh(x) + 15cosh(x) +--R + +--R - 6cosh(x) + 1 +--R * +--R log(- cosh(x) + 1) +--R + +--R 2 4 +--R (x cosh(x) + (- 2x - 4)cosh(x) + x + 2)sinh(x) +--R + +--R 3 2 3 +--R (4x cosh(x) + (- 12x - 8)cosh(x) + (12x + 8)cosh(x) - 4x)sinh(x) +--R + +--R 4 3 2 +--R 6x cosh(x) - 24x cosh(x) + (36x + 4)cosh(x) + (- 24x - 8)cosh(x) +--R + +--R 6x + 4 +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 +--R 4x cosh(x) + (- 20x + 8)cosh(x) + (40x - 8)cosh(x) +--R + +--R 2 +--R (- 40x - 8)cosh(x) + (20x + 8)cosh(x) - 4x +--R * +--R sinh(x) +--R + +--R 6 5 4 3 +--R x cosh(x) + (- 6x + 4)cosh(x) + (15x - 6)cosh(x) - 20x cosh(x) +--R + +--R 2 +--R (15x + 4)cosh(x) + (- 6x - 4)cosh(x) + x + 2 +--R / +--R 2 4 +--R (cosh(x) - 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 3 +--R (4cosh(x) - 12cosh(x) + 12cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 2 +--R (6cosh(x) - 24cosh(x) + 36cosh(x) - 24cosh(x) + 6)sinh(x) +--R + +--R 5 4 3 2 +--R (4cosh(x) - 20cosh(x) + 40cosh(x) - 40cosh(x) + 20cosh(x) - 4)sinh(x) +--R + +--R 6 5 4 3 2 +--R cosh(x) - 6cosh(x) + 15cosh(x) - 20cosh(x) + 15cosh(x) - 6cosh(x) + 1 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 518 +d0913:= D(m0913,x) +--R +--R +--R (70) +--R 2 6 +--R (cosh(x) + 2cosh(x) + 1)sinh(x) +--R + +--R 3 2 5 +--R (4cosh(x) + 8cosh(x) - 8cosh(x) - 4)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) + 10cosh(x) - 20cosh(x) - 10cosh(x) + 15)sinh(x) +--R + +--R 6 5 4 3 2 +--R - 5cosh(x) - 10cosh(x) + 25cosh(x) + 20cosh(x) - 35cosh(x) +--R + +--R - 10cosh(x) + 15 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R - 4cosh(x) - 8cosh(x) + 16cosh(x) + 20cosh(x) - 20cosh(x) +--R + +--R 2 +--R - 16cosh(x) + 8cosh(x) + 4 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 3 2 +--R - cosh(x) - 2cosh(x) + 2cosh(x) + 6cosh(x) - 6cosh(x) - 2cosh(x) +--R + +--R 2cosh(x) + 1 +--R / +--R 3 2 5 +--R (cosh(x) - 3cosh(x) + 3cosh(x) - 1)sinh(x) +--R + +--R 4 3 2 4 +--R (5cosh(x) - 20cosh(x) + 30cosh(x) - 20cosh(x) + 5)sinh(x) +--R + +--R 5 4 3 2 +--R (10cosh(x) - 50cosh(x) + 100cosh(x) - 100cosh(x) + 50cosh(x) - 10) +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 4 3 2 +--R 10cosh(x) - 60cosh(x) + 150cosh(x) - 200cosh(x) + 150cosh(x) +--R + +--R - 60cosh(x) + 10 +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 5 4 3 +--R 5cosh(x) - 35cosh(x) + 105cosh(x) - 175cosh(x) + 175cosh(x) +--R + +--R 2 +--R - 105cosh(x) + 35cosh(x) - 5 +--R * +--R sinh(x) +--R + +--R 8 7 6 5 4 3 +--R cosh(x) - 8cosh(x) + 28cosh(x) - 56cosh(x) + 70cosh(x) - 56cosh(x) +--R + +--R 2 +--R 28cosh(x) - 8cosh(x) + 1 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 518 +t0914:= (csch(x)+sinh(x))^(1/2) +--R +--R +--R +-----------------+ +--R (71) \|sinh(x) + csch(x) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 518 +r0914:= 2*(cosh(x)*coth(x))^(1/2)*tanh(x) +--R +--R +--R +--------------+ +--R (72) 2tanh(x)\|cosh(x)coth(x) +--R Type: Expression(Integer) +--E 72 + +--S 73 of 518 +a0914:= integrate(t0914,x) +--R +--R +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R (73) ------------------------------------------------ +--R sinh(x) + cosh(x) +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 518 +m0914:= a0914-r0914 +--R +--R +--R (74) +--R +--------------+ +--R (- 2sinh(x) - 2cosh(x))tanh(x)\|cosh(x)coth(x) +--R + +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 74 + +--S 75 of 518 +d0914:= D(m0914,x) +--R +--R +--R (75) +--R 2 2 +--------------+ +--R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)\|cosh(x)coth(x) +--R + +--R 2 3 2 +--R (2cosh(x)coth(x)sinh(x) - 2cosh(x) coth(x))tanh(x) +--R + +--R 3 2 2 +--R - coth(x)sinh(x) + (cosh(x)coth(x) - cosh(x))sinh(x) +--R + +--R 2 3 2 3 +--R cosh(x) coth(x)sinh(x) - cosh(x) coth(x) + cosh(x) +--R * +--R tanh(x) +--R + +--R 2 3 +--R - 2cosh(x)coth(x)sinh(x) + 2cosh(x) coth(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R +---------------------------------------------+ +--R | 2 2 +--R 2 2 |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R (sinh(x) - cosh(x) ) |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R Type: Expression(Integer) +--E 75 + +--S 76 of 518 +t0915:= (csch(x)+sinh(x))^(3/2) +--R +--R +--R +-----------------+ +--R (76) (sinh(x) + csch(x))\|sinh(x) + csch(x) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 518 +r0915:= -2/3*(4-cosh(x)^2)*(cosh(x)*coth(x))^(1/2)*sech(x) +--R +--R +--R 2 +--------------+ +--R (2cosh(x) - 8)sech(x)\|cosh(x)coth(x) +--R (77) --------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 518 +a0915:= integrate(t0915,x) +--R +--R +--R (78) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 14)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 28cosh(x))sinh(x) + cosh(x) - 14cosh(x) + 1 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) - 6)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) - 12cosh(x))sinh(x) + 6cosh(x) - 6cosh(x) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 518 +m0915:= a0915-r0915 +--R +--R +--R (79) +--R 2 4 +--R (- 4cosh(x) + 16)sech(x)sinh(x) +--R + +--R 3 3 +--R (- 16cosh(x) + 64cosh(x))sech(x)sinh(x) +--R + +--R 4 2 2 +--R (- 24cosh(x) + 100cosh(x) - 16)sech(x)sinh(x) +--R + +--R 5 3 +--R (- 16cosh(x) + 72cosh(x) - 32cosh(x))sech(x)sinh(x) +--R + +--R 6 4 2 +--R (- 4cosh(x) + 20cosh(x) - 16cosh(x) )sech(x) +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R + +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 14)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 28cosh(x))sinh(x) + cosh(x) - 14cosh(x) + 1 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 4 3 2 2 +--R 6sinh(x) + 24cosh(x)sinh(x) + (36cosh(x) - 6)sinh(x) +--R + +--R 3 4 2 +--R (24cosh(x) - 12cosh(x))sinh(x) + 6cosh(x) - 6cosh(x) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 518 +d0915:= D(m0915,x) +--R +--R +--R (80) +--R 6 5 2 4 +--R - 3sinh(x) - 18cosh(x)sinh(x) + (- 45cosh(x) - 9)sinh(x) +--R + +--R 3 3 +--R (- 60cosh(x) - 36cosh(x))sinh(x) +--R + +--R 4 2 2 +--R (- 45cosh(x) - 54cosh(x) - 9)sinh(x) +--R + +--R 5 3 6 +--R (- 18cosh(x) - 36cosh(x) - 18cosh(x))sinh(x) - 3cosh(x) +--R + +--R 4 2 +--R - 9cosh(x) - 9cosh(x) - 3 +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R + +--R 3 5 +--R (4cosh(x) - 16cosh(x))coth(x)sech(x)sinh(x) +--R + +--R 4 2 4 +--R (12cosh(x) - 48cosh(x) )coth(x)sech(x)sinh(x) +--R + +--R 5 3 3 +--R (8cosh(x) - 36cosh(x) + 16cosh(x))coth(x)sech(x)sinh(x) +--R + +--R 6 4 2 2 +--R (- 8cosh(x) + 28cosh(x) + 16cosh(x) )coth(x)sech(x)sinh(x) +--R + +--R 7 5 3 +--R (- 12cosh(x) + 52cosh(x) - 16cosh(x) )coth(x)sech(x)sinh(x) +--R + +--R 8 6 4 +--R (- 4cosh(x) + 20cosh(x) - 16cosh(x) )coth(x)sech(x) +--R * +--R tanh(x) +--R + +--R 2 6 +--R (- 10cosh(x) + 8)coth(x)sech(x)sinh(x) +--R + +--R 3 2 +--R (2cosh(x) - 8cosh(x))coth(x) +--R + +--R 3 3 +--R (- 30cosh(x) + 24cosh(x))coth(x) - 2cosh(x) + 8cosh(x) +--R * +--R 5 +--R sech(x)sinh(x) +--R + +--R 4 2 2 +--R (6cosh(x) - 24cosh(x) )coth(x) +--R + +--R 4 2 4 2 +--R (- 20cosh(x) + 26cosh(x) - 8)coth(x) - 6cosh(x) + 24cosh(x) +--R * +--R 4 +--R sech(x)sinh(x) +--R + +--R 5 3 2 +--R (4cosh(x) - 18cosh(x) + 8cosh(x))coth(x) +--R + +--R 5 3 5 +--R (20cosh(x) - 6cosh(x) - 8cosh(x))coth(x) - 4cosh(x) +--R + +--R 3 +--R 18cosh(x) - 8cosh(x) +--R * +--R 3 +--R sech(x)sinh(x) +--R + +--R 6 4 2 2 +--R (- 4cosh(x) + 14cosh(x) + 8cosh(x) )coth(x) +--R + +--R 6 4 2 6 +--R (30cosh(x) - 34cosh(x) + 8cosh(x) )coth(x) + 4cosh(x) +--R + +--R 4 2 +--R - 14cosh(x) - 8cosh(x) +--R * +--R 2 +--R sech(x)sinh(x) +--R + +--R 7 5 3 2 +--R (- 6cosh(x) + 26cosh(x) - 8cosh(x) )coth(x) +--R + +--R 7 5 3 7 +--R (10cosh(x) - 18cosh(x) + 8cosh(x) )coth(x) + 6cosh(x) +--R + +--R 5 3 +--R - 26cosh(x) + 8cosh(x) +--R * +--R sech(x)sinh(x) +--R + +--R 8 6 4 2 8 +--R (- 2cosh(x) + 10cosh(x) - 8cosh(x) )coth(x) + 2cosh(x) +--R + +--R 6 4 +--R - 10cosh(x) + 8cosh(x) +--R * +--R sech(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 5 4 2 3 +--R 6sinh(x) + 18cosh(x)sinh(x) + (12cosh(x) - 6)sinh(x) +--R + +--R 3 2 4 2 +--R (- 12cosh(x) - 6cosh(x))sinh(x) + (- 18cosh(x) + 6cosh(x) )sinh(x) +--R + +--R 5 3 +--R - 6cosh(x) + 6cosh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--------------+ +--R |--------------------------------------------- \|cosh(x)coth(x) +--R \| sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 80 + +--S 81 of 518 +t0916:= (csch(x)+sinh(x))^(5/2) +--R +--R +--R 2 2 +-----------------+ +--R (81) (sinh(x) + 2csch(x)sinh(x) + csch(x) )\|sinh(x) + csch(x) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 518 +r0916:= 2/15*(cosh(x)*coth(x))^(1/2)*(32-(8-3*cosh(x)^2)*coth(x)^2)*tanh(x) +--R +--R +--R 2 2 +--------------+ +--R ((6cosh(x) - 16)coth(x) + 64)tanh(x)\|cosh(x)coth(x) +--R (82) ------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 518 +a0916:= integrate(t0916,x) +--R +--R +--R (83) +--R 8 7 2 6 +--R 3sinh(x) + 24cosh(x)sinh(x) + (84cosh(x) + 108)sinh(x) +--R + +--R 3 5 +--R (168cosh(x) + 648cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (210cosh(x) + 1620cosh(x) - 302)sinh(x) +--R + +--R 5 3 3 +--R (168cosh(x) + 2160cosh(x) - 1208cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (84cosh(x) + 1620cosh(x) - 1812cosh(x) + 108)sinh(x) +--R + +--R 7 5 3 +--R (24cosh(x) + 648cosh(x) - 1208cosh(x) + 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 3cosh(x) + 108cosh(x) - 302cosh(x) + 108cosh(x) + 3 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 7 6 2 5 +--R 60sinh(x) + 420cosh(x)sinh(x) + (1260cosh(x) - 120)sinh(x) +--R + +--R 3 4 +--R (2100cosh(x) - 600cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (2100cosh(x) - 1200cosh(x) + 60)sinh(x) +--R + +--R 5 3 2 +--R (1260cosh(x) - 1200cosh(x) + 180cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (420cosh(x) - 600cosh(x) + 180cosh(x) )sinh(x) + 60cosh(x) +--R + +--R 5 3 +--R - 120cosh(x) + 60cosh(x) +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 518 +m0916:= a0916-r0916 +--R +--R +--R (84) +--R 2 2 7 +--R ((- 24cosh(x) + 64)coth(x) - 256)sinh(x) +--R + +--R 3 2 6 +--R ((- 168cosh(x) + 448cosh(x))coth(x) - 1792cosh(x))sinh(x) +--R + +--R 4 2 2 2 +--R ((- 504cosh(x) + 1392cosh(x) - 128)coth(x) - 5376cosh(x) + 512) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 2 +--R (- 840cosh(x) + 2480cosh(x) - 640cosh(x))coth(x) +--R + +--R 3 +--R - 8960cosh(x) + 2560cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 6 4 2 2 +--R (- 840cosh(x) + 2720cosh(x) - 1304cosh(x) + 64)coth(x) +--R + +--R 4 2 +--R - 8960cosh(x) + 5120cosh(x) - 256 +--R * +--R 3 +--R sinh(x) +--R + +--R 7 5 3 +--R (- 504cosh(x) + 1824cosh(x) - 1352cosh(x) + 192cosh(x)) +--R * +--R 2 +--R coth(x) +--R + +--R 5 3 +--R - 5376cosh(x) + 5120cosh(x) - 768cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 168cosh(x) + 688cosh(x) - 712cosh(x) + 192cosh(x) )coth(x) +--R + +--R 6 4 2 +--R - 1792cosh(x) + 2560cosh(x) - 768cosh(x) +--R * +--R sinh(x) +--R + +--R 9 7 5 3 2 +--R (- 24cosh(x) + 112cosh(x) - 152cosh(x) + 64cosh(x) )coth(x) +--R + +--R 7 5 3 +--R - 256cosh(x) + 512cosh(x) - 256cosh(x) +--R * +--R +--------------+ +--R tanh(x)\|cosh(x)coth(x) +--R + +--R 8 7 2 6 +--R 3sinh(x) + 24cosh(x)sinh(x) + (84cosh(x) + 108)sinh(x) +--R + +--R 3 5 +--R (168cosh(x) + 648cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (210cosh(x) + 1620cosh(x) - 302)sinh(x) +--R + +--R 5 3 3 +--R (168cosh(x) + 2160cosh(x) - 1208cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (84cosh(x) + 1620cosh(x) - 1812cosh(x) + 108)sinh(x) +--R + +--R 7 5 3 +--R (24cosh(x) + 648cosh(x) - 1208cosh(x) + 216cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 3cosh(x) + 108cosh(x) - 302cosh(x) + 108cosh(x) + 3 +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 7 6 2 5 +--R 60sinh(x) + 420cosh(x)sinh(x) + (1260cosh(x) - 120)sinh(x) +--R + +--R 3 4 +--R (2100cosh(x) - 600cosh(x))sinh(x) +--R + +--R 4 2 3 +--R (2100cosh(x) - 1200cosh(x) + 60)sinh(x) +--R + +--R 5 3 2 +--R (1260cosh(x) - 1200cosh(x) + 180cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (420cosh(x) - 600cosh(x) + 180cosh(x) )sinh(x) + 60cosh(x) +--R + +--R 5 3 +--R - 120cosh(x) + 60cosh(x) +--R Type: Expression(Integer) +--E 84 + +--S 85 of 518 +d0916:= D(m0916,x) +--R +--R +--R (85) +--R 10 9 2 8 +--R - 15sinh(x) - 150cosh(x)sinh(x) + (- 675cosh(x) - 75)sinh(x) +--R + +--R 3 7 +--R (- 1800cosh(x) - 600cosh(x))sinh(x) +--R + +--R 4 2 6 +--R (- 3150cosh(x) - 2100cosh(x) - 150)sinh(x) +--R + +--R 5 3 5 +--R (- 3780cosh(x) - 4200cosh(x) - 900cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 3150cosh(x) - 5250cosh(x) - 2250cosh(x) - 150)sinh(x) +--R + +--R 7 5 3 3 +--R (- 1800cosh(x) - 4200cosh(x) - 3000cosh(x) - 600cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 675cosh(x) - 2100cosh(x) - 2250cosh(x) - 900cosh(x) - 75) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 150cosh(x) - 600cosh(x) - 900cosh(x) - 600cosh(x) +--R + +--R - 150cosh(x) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 15cosh(x) - 75cosh(x) - 150cosh(x) - 150cosh(x) - 75cosh(x) +--R + +--R - 15 +--R * +--R +--------------+ +--R \|cosh(x)coth(x) +--R + +--R 3 3 8 +--R ((24cosh(x) - 64cosh(x))coth(x) + 256cosh(x)coth(x))sinh(x) +--R + +--R 4 2 3 2 +--R ((144cosh(x) - 384cosh(x) )coth(x) + 1536cosh(x) coth(x)) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 3 +--R (336cosh(x) - 944cosh(x) + 128cosh(x))coth(x) +--R + +--R 3 +--R (3584cosh(x) - 512cosh(x))coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (336cosh(x) - 1088cosh(x) + 512cosh(x) )coth(x) +--R + +--R 4 2 +--R (3584cosh(x) - 2048cosh(x) )coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 +--R (- 240cosh(x) + 664cosh(x) - 64cosh(x))coth(x) +--R + +--R 3 +--R (- 2560cosh(x) + 256cosh(x))coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 336cosh(x) + 896cosh(x) + 48cosh(x) - 128cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 6 2 +--R (- 3584cosh(x) + 512cosh(x) )coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (- 336cosh(x) + 1136cosh(x) - 640cosh(x) )coth(x) +--R + +--R 7 5 +--R (- 3584cosh(x) + 2560cosh(x) )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 +--R (- 144cosh(x) + 576cosh(x) - 560cosh(x) + 128cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 8 6 4 +--R (- 1536cosh(x) + 2048cosh(x) - 512cosh(x) )coth(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R (- 24cosh(x) + 112cosh(x) - 152cosh(x) + 64cosh(x) )coth(x) +--R + +--R 9 7 5 +--R (- 256cosh(x) + 512cosh(x) - 256cosh(x) )coth(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 3 9 +--R ((- 60cosh(x) + 32)coth(x) - 128coth(x))sinh(x) +--R + +--R 3 4 +--R (60cosh(x) - 160cosh(x))coth(x) +--R + +--R 3 3 +--R (- 360cosh(x) + 192cosh(x))coth(x) +--R + +--R 3 2 +--R (- 60cosh(x) + 288cosh(x))coth(x) - 768cosh(x)coth(x) +--R + +--R - 128cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 4 2 4 +--R (360cosh(x) - 960cosh(x) )coth(x) +--R + +--R 4 2 3 +--R (- 840cosh(x) + 568cosh(x) - 64)coth(x) +--R + +--R 4 2 2 +--R (- 360cosh(x) + 1728cosh(x) )coth(x) +--R + +--R 2 2 +--R (- 1792cosh(x) + 256)coth(x) - 768cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 5 3 4 +--R (840cosh(x) - 2360cosh(x) + 320cosh(x))coth(x) +--R + +--R 5 3 3 +--R (- 840cosh(x) + 928cosh(x) - 256cosh(x))coth(x) +--R + +--R 5 3 2 +--R (- 840cosh(x) + 4152cosh(x) - 576cosh(x))coth(x) +--R + +--R 3 3 +--R (- 1792cosh(x) + 1024cosh(x))coth(x) - 1792cosh(x) +--R + +--R 256cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 4 +--R (840cosh(x) - 2720cosh(x) + 1280cosh(x) )coth(x) +--R + +--R 4 2 3 +--R (600cosh(x) - 380cosh(x) + 32)coth(x) +--R + +--R 6 4 2 2 +--R (- 840cosh(x) + 4512cosh(x) - 2304cosh(x) )coth(x) +--R + +--R 2 4 2 +--R (1280cosh(x) - 128)coth(x) - 1792cosh(x) + 1024cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 4 +--R (- 600cosh(x) + 1660cosh(x) - 160cosh(x))coth(x) +--R + +--R 7 5 3 3 +--R (840cosh(x) - 448cosh(x) - 120cosh(x) + 64cosh(x))coth(x) +--R + +--R 5 3 2 +--R (600cosh(x) - 2940cosh(x) + 288cosh(x))coth(x) +--R + +--R 5 3 +--R (1792cosh(x) - 256cosh(x))coth(x) + 1280cosh(x) - 128cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (- 840cosh(x) + 2240cosh(x) + 120cosh(x) - 320cosh(x) ) +--R * +--R 4 +--R coth(x) +--R + +--R 8 6 4 3 +--R (840cosh(x) - 1048cosh(x) + 320cosh(x) )coth(x) +--R + +--R 8 6 4 2 +--R (840cosh(x) - 4032cosh(x) - 120cosh(x) + 576cosh(x) ) +--R * +--R 2 +--R coth(x) +--R + +--R 6 4 6 +--R (1792cosh(x) - 1280cosh(x) )coth(x) + 1792cosh(x) +--R + +--R 2 +--R - 256cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 4 +--R (- 840cosh(x) + 2840cosh(x) - 1600cosh(x) )coth(x) +--R + +--R 9 7 5 3 +--R (360cosh(x) - 672cosh(x) + 376cosh(x) - 64cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 9 7 5 2 +--R (840cosh(x) - 4632cosh(x) + 2880cosh(x) )coth(x) +--R + +--R 7 5 3 +--R (768cosh(x) - 1024cosh(x) + 256cosh(x) )coth(x) +--R + +--R 7 5 +--R 1792cosh(x) - 1280cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 +--R - 360cosh(x) + 1440cosh(x) - 1400cosh(x) +--R + +--R 4 +--R 320cosh(x) +--R * +--R 4 +--R coth(x) +--R + +--R 10 8 6 4 +--R (60cosh(x) - 152cosh(x) + 124cosh(x) - 32cosh(x) ) +--R * +--R 3 +--R coth(x) +--R + +--R 10 8 6 4 +--R (360cosh(x) - 2208cosh(x) + 2424cosh(x) - 576cosh(x) ) +--R * +--R 2 +--R coth(x) +--R + +--R 8 6 4 +--R (128cosh(x) - 256cosh(x) + 128cosh(x) )coth(x) +--R + +--R 8 6 4 +--R 768cosh(x) - 1024cosh(x) + 256cosh(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 4 +--R (- 60cosh(x) + 280cosh(x) - 380cosh(x) + 160cosh(x) )coth(x) +--R + +--R 11 9 7 5 2 +--R (60cosh(x) - 408cosh(x) + 636cosh(x) - 288cosh(x) )coth(x) +--R + +--R 9 7 5 +--R 128cosh(x) - 256cosh(x) + 128cosh(x) +--R * +--R tanh(x) +--R + +--R 3 3 8 +--R ((- 24cosh(x) + 64cosh(x))coth(x) - 256cosh(x)coth(x))sinh(x) +--R + +--R 4 2 3 2 7 +--R ((- 144cosh(x) + 384cosh(x) )coth(x) - 1536cosh(x) coth(x))sinh(x) +--R + +--R 5 3 3 +--R (- 336cosh(x) + 944cosh(x) - 128cosh(x))coth(x) +--R + +--R 3 +--R (- 3584cosh(x) + 512cosh(x))coth(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 6 4 2 3 +--R (- 336cosh(x) + 1088cosh(x) - 512cosh(x) )coth(x) +--R + +--R 4 2 +--R (- 3584cosh(x) + 2048cosh(x) )coth(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 5 3 3 +--R (240cosh(x) - 664cosh(x) + 64cosh(x))coth(x) +--R + +--R 3 +--R (2560cosh(x) - 256cosh(x))coth(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (336cosh(x) - 896cosh(x) - 48cosh(x) + 128cosh(x) )coth(x) +--R + +--R 6 2 +--R (3584cosh(x) - 512cosh(x) )coth(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (336cosh(x) - 1136cosh(x) + 640cosh(x) )coth(x) +--R + +--R 7 5 +--R (3584cosh(x) - 2560cosh(x) )coth(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 10 8 6 4 3 +--R (144cosh(x) - 576cosh(x) + 560cosh(x) - 128cosh(x) )coth(x) +--R + +--R 8 6 4 +--R (1536cosh(x) - 2048cosh(x) + 512cosh(x) )coth(x) +--R * +--R sinh(x) +--R + +--R 11 9 7 5 3 +--R (24cosh(x) - 112cosh(x) + 152cosh(x) - 64cosh(x) )coth(x) +--R + +--R 9 7 5 +--R (256cosh(x) - 512cosh(x) + 256cosh(x) )coth(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--R |--------------------------------------------- +--R \| sinh(x) - cosh(x) +--R / +--R 8 7 2 6 +--R 60sinh(x) + 360cosh(x)sinh(x) + (840cosh(x) - 120)sinh(x) +--R + +--R 3 5 2 4 +--R (840cosh(x) - 480cosh(x))sinh(x) + (- 600cosh(x) + 60)sinh(x) +--R + +--R 5 3 +--R (- 840cosh(x) + 120cosh(x))sinh(x) +--R + +--R 6 4 2 +--R (- 840cosh(x) + 600cosh(x) )sinh(x) +--R + +--R 7 5 3 8 +--R (- 360cosh(x) + 480cosh(x) - 120cosh(x) )sinh(x) - 60cosh(x) +--R + +--R 6 4 +--R 120cosh(x) - 60cosh(x) +--R * +--R +---------------------------------------------+ +--R | 2 2 +--R |- 2sinh(x) - 4cosh(x)sinh(x) - 2cosh(x) + 2 +--------------+ +--R |--------------------------------------------- \|cosh(x)coth(x) +--R \| sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 85 + +--S 86 of 518 +t0917:= (sech(x)-cosh(x))^(1/2) +--R +--R +--R +-----------------+ +--R (86) \|sech(x) - cosh(x) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 518 +r0917:= -2*sinh(x)/(-sinh(x)*tanh(x))^(1/2) +--R +--R +--R 2sinh(x) +--R (87) - ------------------- +--R +----------------+ +--R \|- sinh(x)tanh(x) +--R Type: Expression(Integer) +--E 87 + +--S 88 of 518 +a0917:= integrate(t0917,x) +--R +--R +--R (88) 0 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 518 +m0917:= a0917-r0917 +--R +--R +--R 2sinh(x) +--R (89) ------------------- +--R +----------------+ +--R \|- sinh(x)tanh(x) +--R Type: Expression(Integer) +--E 89 + +--S 90 of 518 +d0917:= D(m0917,x) +--R +--R +--R 2 +--R sinh(x)tanh(x) + cosh(x)tanh(x) - sinh(x) +--R (90) ------------------------------------------ +--R +----------------+ +--R tanh(x)\|- sinh(x)tanh(x) +--R Type: Expression(Integer) +--E 90 + +--S 91 of 518 +t0918:= (sech(x)-cosh(x))^(3/2) +--R +--R +--R +-----------------+ +--R (91) (sech(x) - cosh(x))\|sech(x) - cosh(x) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 518 +r0918:= 2/3*coth(x)*csch(x)^2*(4+sinh(x)^2)*(-sinh(x)*tanh(x))^(3/2) +--R +--R +--R (92) +--R 2 3 2 +--R (- 2coth(x)csch(x) sinh(x) - 8coth(x)csch(x) sinh(x))tanh(x) +--R * +--R +----------------+ +--R \|- sinh(x)tanh(x) +--R / +--R 3 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 518 +a0918:= integrate(t0918,x) +--R +--R +--R (93) 0 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 518 +m0918:= a0918-r0918 +--R +--R +--R (94) +--R 2 3 2 +--R (2coth(x)csch(x) sinh(x) + 8coth(x)csch(x) sinh(x))tanh(x) +--R * +--R +----------------+ +--R \|- sinh(x)tanh(x) +--R / +--R 3 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 518 +d0918:= D(m0918,x) +--R +--R +--R (95) +--R 2 4 2 2 3 +--R (3coth(x)csch(x) sinh(x) + 12coth(x)csch(x) sinh(x) )tanh(x) +--R + +--R 2 2 4 2 3 +--R (6coth(x) - 2)csch(x) sinh(x) - 7cosh(x)coth(x)csch(x) sinh(x) +--R + +--R 2 2 2 2 +--R (24coth(x) - 8)csch(x) sinh(x) - 12cosh(x)coth(x)csch(x) sinh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 4 2 2 +--R (- 3coth(x)csch(x) sinh(x) - 12coth(x)csch(x) sinh(x) )tanh(x) +--R / +--R +----------------+ +--R 3\|- sinh(x)tanh(x) +--R Type: Expression(Integer) +--E 95 + +--S 96 of 518 +t0919:= (sech(x)-cosh(x))^(5/2) +--R +--R +--R 2 2 +-----------------+ +--R (96) (sech(x) - 2cosh(x)sech(x) + cosh(x) )\|sech(x) - cosh(x) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 518 +r0919:= 2/15*coth(x)^2*csch(x)*(-sinh(x)*tanh(x))^(3/2)*_ + (32-(8+3*sinh(x)^2)*tanh(x)^2) +--R +--R +--R (97) +--R 2 3 2 3 +--R (6coth(x) csch(x)sinh(x) + 16coth(x) csch(x)sinh(x))tanh(x) +--R + +--R 2 +--R - 64coth(x) csch(x)sinh(x)tanh(x) +--R * +--R +----------------+ +--R \|- sinh(x)tanh(x) +--R / +--R 15 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 518 +a0919:= integrate(t0919,x) +--R +--R +--R (98) 0 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 518 +m0919:= a0919-r0919 +--R +--R +--R (99) +--R 2 3 2 3 +--R (- 6coth(x) csch(x)sinh(x) - 16coth(x) csch(x)sinh(x))tanh(x) +--R + +--R 2 +--R 64coth(x) csch(x)sinh(x)tanh(x) +--R * +--R +----------------+ +--R \|- sinh(x)tanh(x) +--R / +--R 15 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 518 +d0919:= D(m0919,x) +--R +--R +--R (100) +--R 2 4 2 2 5 +--R (- 21coth(x) csch(x)sinh(x) - 56coth(x) csch(x)sinh(x) )tanh(x) +--R + +--R 3 4 +--R (- 18coth(x) + 12coth(x))csch(x)sinh(x) +--R + +--R 2 3 +--R 21cosh(x)coth(x) csch(x)sinh(x) +--R + +--R 3 2 +--R (- 48coth(x) + 32coth(x))csch(x)sinh(x) +--R + +--R 2 +--R 24cosh(x)coth(x) csch(x)sinh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R 2 4 2 2 3 +--R (21coth(x) csch(x)sinh(x) + 152coth(x) csch(x)sinh(x) )tanh(x) +--R + +--R 3 2 +--R (192coth(x) - 128coth(x))csch(x)sinh(x) +--R + +--R 2 +--R - 96cosh(x)coth(x) csch(x)sinh(x) +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 +--R - 96coth(x) csch(x)sinh(x) tanh(x) +--R / +--R +----------------+ +--R 15\|- sinh(x)tanh(x) +--R Type: Expression(Integer) +--E 100 + +--S 101 of 518 +t0920:= 1/(cosh(x)^2+sinh(x)^2) +--R +--R +--R 1 +--R (101) ------------------- +--R 2 2 +--R sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 101 + +--S 102 of 518 +r0920:= atan(tanh(x)) +--R +--R +--R (102) atan(tanh(x)) +--R Type: Expression(Integer) +--E 102 + +--S 103 of 518 +a0920:= integrate(t0920,x) +--R +--R +--R sinh(x) + cosh(x) +--R (103) - atan(-----------------) +--R sinh(x) - cosh(x) +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 518 +m0920:= a0920-r0920 +--R +--R +--R sinh(x) + cosh(x) +--R (104) - atan(tanh(x)) - atan(-----------------) +--R sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 104 + +--S 105 of 518 +d0920:= D(m0920,x) +--R +--R +--R 2 2 2 +--R 2cosh(x) tanh(x) - 2sinh(x) +--R (105) --------------------------------------------------- +--R 2 2 2 2 2 +--R (sinh(x) + cosh(x) )tanh(x) + sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 105 + +--S 106 of 518 +t0921:= 1/(cosh(x)^2+sinh(x)^2)^3 +--R +--R +--R 1 +--R (106) ----------------------------------------------------------- +--R 6 2 4 4 2 6 +--R sinh(x) + 3cosh(x) sinh(x) + 3cosh(x) sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 518 +r0921:= 1/4*atan(sinh(2*x))+1/4*sech(2*x)*tanh(2*x) +--R +--R +--R atan(sinh(2x)) + sech(2x)tanh(2x) +--R (107) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 518 +a0921:= integrate(t0921,x) +--R +--R +--R (108) +--R 8 7 2 6 +--R - sinh(x) - 8cosh(x)sinh(x) - 28cosh(x) sinh(x) +--R + +--R 3 5 4 4 +--R - 56cosh(x) sinh(x) + (- 70cosh(x) - 2)sinh(x) +--R + +--R 5 3 +--R (- 56cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 2 2 +--R (- 28cosh(x) - 12cosh(x) )sinh(x) +--R + +--R 7 3 8 4 +--R (- 8cosh(x) - 8cosh(x) )sinh(x) - cosh(x) - 2cosh(x) - 1 +--R * +--R sinh(x) + cosh(x) +--R atan(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 6 5 2 4 3 3 +--R sinh(x) + 6cosh(x)sinh(x) + 15cosh(x) sinh(x) + 20cosh(x) sinh(x) +--R + +--R 4 2 5 6 +--R (15cosh(x) - 1)sinh(x) + (6cosh(x) - 2cosh(x))sinh(x) + cosh(x) +--R + +--R 2 +--R - cosh(x) +--R / +--R 8 7 2 6 3 5 +--R 2sinh(x) + 16cosh(x)sinh(x) + 56cosh(x) sinh(x) + 112cosh(x) sinh(x) +--R + +--R 4 4 5 3 +--R (140cosh(x) + 4)sinh(x) + (112cosh(x) + 16cosh(x))sinh(x) +--R + +--R 6 2 2 7 3 +--R (56cosh(x) + 24cosh(x) )sinh(x) + (16cosh(x) + 16cosh(x) )sinh(x) +--R + +--R 8 4 +--R 2cosh(x) + 4cosh(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 518 +m0921:= a0921-r0921 +--R +--R +--R (109) +--R 8 7 2 6 +--R - sinh(x) - 8cosh(x)sinh(x) - 28cosh(x) sinh(x) +--R + +--R 3 5 4 4 +--R - 56cosh(x) sinh(x) + (- 70cosh(x) - 2)sinh(x) +--R + +--R 5 3 +--R (- 56cosh(x) - 8cosh(x))sinh(x) +--R + +--R 6 2 2 +--R (- 28cosh(x) - 12cosh(x) )sinh(x) +--R + +--R 7 3 8 4 +--R (- 8cosh(x) - 8cosh(x) )sinh(x) - cosh(x) - 2cosh(x) - 1 +--R * +--R atan(sinh(2x)) +--R + +--R 8 7 2 6 +--R - 2sinh(x) - 16cosh(x)sinh(x) - 56cosh(x) sinh(x) +--R + +--R 3 5 4 4 +--R - 112cosh(x) sinh(x) + (- 140cosh(x) - 4)sinh(x) +--R + +--R 5 3 +--R (- 112cosh(x) - 16cosh(x))sinh(x) +--R + +--R 6 2 2 +--R (- 56cosh(x) - 24cosh(x) )sinh(x) +--R + +--R 7 3 8 4 +--R (- 16cosh(x) - 16cosh(x) )sinh(x) - 2cosh(x) - 4cosh(x) - 2 +--R * +--R sinh(x) + cosh(x) +--R atan(-----------------) +--R sinh(x) - cosh(x) +--R + +--R 8 7 +--R - sech(2x)sinh(x) - 8cosh(x)sech(2x)sinh(x) +--R + +--R 2 6 3 5 +--R - 28cosh(x) sech(2x)sinh(x) - 56cosh(x) sech(2x)sinh(x) +--R + +--R 4 4 +--R (- 70cosh(x) - 2)sech(2x)sinh(x) +--R + +--R 5 3 +--R (- 56cosh(x) - 8cosh(x))sech(2x)sinh(x) +--R + +--R 6 2 2 +--R (- 28cosh(x) - 12cosh(x) )sech(2x)sinh(x) +--R + +--R 7 3 +--R (- 8cosh(x) - 8cosh(x) )sech(2x)sinh(x) +--R + +--R 8 4 +--R (- cosh(x) - 2cosh(x) - 1)sech(2x) +--R * +--R tanh(2x) +--R + +--R 6 5 2 4 3 3 +--R 2sinh(x) + 12cosh(x)sinh(x) + 30cosh(x) sinh(x) + 40cosh(x) sinh(x) +--R + +--R 4 2 5 6 +--R (30cosh(x) - 2)sinh(x) + (12cosh(x) - 4cosh(x))sinh(x) + 2cosh(x) +--R + +--R 2 +--R - 2cosh(x) +--R / +--R 8 7 2 6 3 5 +--R 4sinh(x) + 32cosh(x)sinh(x) + 112cosh(x) sinh(x) + 224cosh(x) sinh(x) +--R + +--R 4 4 5 3 +--R (280cosh(x) + 8)sinh(x) + (224cosh(x) + 32cosh(x))sinh(x) +--R + +--R 6 2 2 7 3 +--R (112cosh(x) + 48cosh(x) )sinh(x) + (32cosh(x) + 32cosh(x) )sinh(x) +--R + +--R 8 4 +--R 4cosh(x) + 8cosh(x) + 4 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 518 +d0921:= D(m0921,x) +--R +--R +--R (110) +--R 14 13 +--R 2sech(2x)sinh(x) + 24cosh(x)sech(2x)sinh(x) +--R + +--R 2 12 3 11 +--R 134cosh(x) sech(2x)sinh(x) + 464cosh(x) sech(2x)sinh(x) +--R + +--R 4 10 +--R (1122cosh(x) + 6)sech(2x)sinh(x) +--R + +--R 5 9 +--R (2024cosh(x) + 48cosh(x))sech(2x)sinh(x) +--R + +--R 6 2 8 +--R (2838cosh(x) + 174cosh(x) )sech(2x)sinh(x) +--R + +--R 7 3 7 +--R (3168cosh(x) + 384cosh(x) )sech(2x)sinh(x) +--R + +--R 8 4 6 +--R (2838cosh(x) + 588cosh(x) + 6)sech(2x)sinh(x) +--R + +--R 9 5 5 +--R (2024cosh(x) + 672cosh(x) + 24cosh(x))sech(2x)sinh(x) +--R + +--R 10 6 2 4 +--R (1122cosh(x) + 588cosh(x) + 42cosh(x) )sech(2x)sinh(x) +--R + +--R 11 7 3 3 +--R (464cosh(x) + 384cosh(x) + 48cosh(x) )sech(2x)sinh(x) +--R + +--R 12 8 4 2 +--R (134cosh(x) + 174cosh(x) + 42cosh(x) + 2)sech(2x)sinh(x) +--R + +--R 13 9 5 +--R (24cosh(x) + 48cosh(x) + 24cosh(x) )sech(2x)sinh(x) +--R + +--R 14 10 6 2 +--R (2cosh(x) + 6cosh(x) + 6cosh(x) + 2cosh(x) )sech(2x) +--R * +--R 2 +--R sinh(2x) +--R + +--R 14 13 +--R 2sech(2x)sinh(x) + 24cosh(x)sech(2x)sinh(x) +--R + +--R 2 12 3 11 +--R 134cosh(x) sech(2x)sinh(x) + 464cosh(x) sech(2x)sinh(x) +--R + +--R 4 10 +--R (1122cosh(x) + 6)sech(2x)sinh(x) +--R + +--R 5 9 +--R (2024cosh(x) + 48cosh(x))sech(2x)sinh(x) +--R + +--R 6 2 8 +--R (2838cosh(x) + 174cosh(x) )sech(2x)sinh(x) +--R + +--R 7 3 7 +--R (3168cosh(x) + 384cosh(x) )sech(2x)sinh(x) +--R + +--R 8 4 6 +--R (2838cosh(x) + 588cosh(x) + 6)sech(2x)sinh(x) +--R + +--R 9 5 5 +--R (2024cosh(x) + 672cosh(x) + 24cosh(x))sech(2x)sinh(x) +--R + +--R 10 6 2 4 +--R (1122cosh(x) + 588cosh(x) + 42cosh(x) )sech(2x)sinh(x) +--R + +--R 11 7 3 3 +--R (464cosh(x) + 384cosh(x) + 48cosh(x) )sech(2x)sinh(x) +--R + +--R 12 8 4 2 +--R (134cosh(x) + 174cosh(x) + 42cosh(x) + 2)sech(2x)sinh(x) +--R + +--R 13 9 5 +--R (24cosh(x) + 48cosh(x) + 24cosh(x) )sech(2x)sinh(x) +--R + +--R 14 10 6 2 +--R (2cosh(x) + 6cosh(x) + 6cosh(x) + 2cosh(x) )sech(2x) +--R * +--R 2 +--R tanh(2x) +--R + +--R 14 +--R (- sech(2x) - 1)sinh(x) +--R + +--R 13 +--R (- 12cosh(x)sech(2x) - 12cosh(x))sinh(x) +--R + +--R 2 2 12 +--R (- 67cosh(x) sech(2x) - 65cosh(x) - 2)sinh(x) +--R + +--R 3 3 11 +--R (- 232cosh(x) sech(2x) - 208cosh(x) - 20cosh(x))sinh(x) +--R + +--R 4 4 2 10 +--R ((- 561cosh(x) - 3)sech(2x) - 429cosh(x) - 92cosh(x) - 3)sinh(x) +--R + +--R 5 5 3 +--R (- 1012cosh(x) - 24cosh(x))sech(2x) - 572cosh(x) - 260cosh(x) +--R + +--R - 24cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 2 6 4 +--R (- 1419cosh(x) - 87cosh(x) )sech(2x) - 429cosh(x) - 510cosh(x) +--R + +--R 2 +--R - 81cosh(x) + 12 +--R * +--R 8 +--R sinh(x) +--R + +--R 7 3 5 +--R (- 1584cosh(x) - 192cosh(x) )sech(2x) - 744cosh(x) +--R + +--R 3 +--R - 144cosh(x) + 72cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 4 8 +--R (- 1419cosh(x) - 294cosh(x) - 3)sech(2x) + 429cosh(x) +--R + +--R 6 4 2 +--R - 840cosh(x) - 126cosh(x) + 192cosh(x) - 3 +--R * +--R 6 +--R sinh(x) +--R + +--R 9 5 9 +--R (- 1012cosh(x) - 336cosh(x) - 12cosh(x))sech(2x) + 572cosh(x) +--R + +--R 7 3 +--R - 744cosh(x) + 312cosh(x) - 12cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 2 +--R (- 561cosh(x) - 294cosh(x) - 21cosh(x) )sech(2x) +--R + +--R 10 8 6 4 +--R 429cosh(x) - 510cosh(x) + 126cosh(x) + 360cosh(x) +--R + +--R 2 +--R - 15cosh(x) - 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 3 +--R (- 232cosh(x) - 192cosh(x) - 24cosh(x) )sech(2x) +--R + +--R 11 9 7 5 +--R 208cosh(x) - 260cosh(x) + 144cosh(x) + 312cosh(x) - 4cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 4 +--R (- 67cosh(x) - 87cosh(x) - 21cosh(x) - 1)sech(2x) +--R + +--R 12 10 8 6 4 +--R 65cosh(x) - 92cosh(x) + 81cosh(x) + 192cosh(x) + 15cosh(x) +--R + +--R 2 +--R - 4cosh(x) - 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 5 13 +--R (- 12cosh(x) - 24cosh(x) - 12cosh(x) )sech(2x) + 12cosh(x) +--R + +--R 11 9 7 5 3 +--R - 20cosh(x) + 24cosh(x) + 72cosh(x) + 12cosh(x) - 4cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 6 2 14 +--R (- cosh(x) - 3cosh(x) - 3cosh(x) - cosh(x) )sech(2x) + cosh(x) +--R + +--R 12 10 8 6 4 +--R - 2cosh(x) + 3cosh(x) + 12cosh(x) + 3cosh(x) - 2cosh(x) +--R + +--R 2 +--R cosh(x) +--R * +--R 2 +--R sinh(2x) +--R + +--R 14 +--R (- sech(2x) - cosh(2x) - 1)sinh(x) +--R + +--R 13 +--R (- 12cosh(x)sech(2x) - 12cosh(x)cosh(2x) - 12cosh(x))sinh(x) +--R + +--R 2 2 2 12 +--R (- 67cosh(x) sech(2x) - 67cosh(x) cosh(2x) - 65cosh(x) - 2)sinh(x) +--R + +--R 3 3 3 +--R (- 232cosh(x) sech(2x) - 232cosh(x) cosh(2x) - 208cosh(x) - 20cosh(x)) +--R * +--R 11 +--R sinh(x) +--R + +--R 4 4 +--R (- 561cosh(x) - 3)sech(2x) + (- 561cosh(x) - 3)cosh(2x) +--R + +--R 4 2 +--R - 429cosh(x) - 92cosh(x) - 3 +--R * +--R 10 +--R sinh(x) +--R + +--R 5 +--R (- 1012cosh(x) - 24cosh(x))sech(2x) +--R + +--R 5 5 3 +--R (- 1012cosh(x) - 24cosh(x))cosh(2x) - 572cosh(x) - 260cosh(x) +--R + +--R - 24cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 6 2 +--R (- 1419cosh(x) - 87cosh(x) )sech(2x) +--R + +--R 6 2 6 4 +--R (- 1419cosh(x) - 87cosh(x) )cosh(2x) - 429cosh(x) - 510cosh(x) +--R + +--R 2 +--R - 81cosh(x) + 12 +--R * +--R 8 +--R sinh(x) +--R + +--R 7 3 +--R (- 1584cosh(x) - 192cosh(x) )sech(2x) +--R + +--R 7 3 5 3 +--R (- 1584cosh(x) - 192cosh(x) )cosh(2x) - 744cosh(x) - 144cosh(x) +--R + +--R 72cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 8 4 +--R (- 1419cosh(x) - 294cosh(x) - 3)sech(2x) +--R + +--R 8 4 8 +--R (- 1419cosh(x) - 294cosh(x) - 3)cosh(2x) + 429cosh(x) +--R + +--R 6 4 2 +--R - 840cosh(x) - 126cosh(x) + 192cosh(x) - 3 +--R * +--R 6 +--R sinh(x) +--R + +--R 9 5 +--R (- 1012cosh(x) - 336cosh(x) - 12cosh(x))sech(2x) +--R + +--R 9 5 9 +--R (- 1012cosh(x) - 336cosh(x) - 12cosh(x))cosh(2x) + 572cosh(x) +--R + +--R 7 3 +--R - 744cosh(x) + 312cosh(x) - 12cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 6 2 +--R (- 561cosh(x) - 294cosh(x) - 21cosh(x) )sech(2x) +--R + +--R 10 6 2 10 +--R (- 561cosh(x) - 294cosh(x) - 21cosh(x) )cosh(2x) + 429cosh(x) +--R + +--R 8 6 4 2 +--R - 510cosh(x) + 126cosh(x) + 360cosh(x) - 15cosh(x) - 2 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 7 3 +--R (- 232cosh(x) - 192cosh(x) - 24cosh(x) )sech(2x) +--R + +--R 11 7 3 11 +--R (- 232cosh(x) - 192cosh(x) - 24cosh(x) )cosh(2x) + 208cosh(x) +--R + +--R 9 7 5 +--R - 260cosh(x) + 144cosh(x) + 312cosh(x) - 4cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 12 8 4 +--R (- 67cosh(x) - 87cosh(x) - 21cosh(x) - 1)sech(2x) +--R + +--R 12 8 4 12 +--R (- 67cosh(x) - 87cosh(x) - 21cosh(x) - 1)cosh(2x) + 65cosh(x) +--R + +--R 10 8 6 4 2 +--R - 92cosh(x) + 81cosh(x) + 192cosh(x) + 15cosh(x) - 4cosh(x) - 1 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 9 5 +--R (- 12cosh(x) - 24cosh(x) - 12cosh(x) )sech(2x) +--R + +--R 13 9 5 13 +--R (- 12cosh(x) - 24cosh(x) - 12cosh(x) )cosh(2x) + 12cosh(x) +--R + +--R 11 9 7 5 3 +--R - 20cosh(x) + 24cosh(x) + 72cosh(x) + 12cosh(x) - 4cosh(x) +--R * +--R sinh(x) +--R + +--R 14 10 6 2 +--R (- cosh(x) - 3cosh(x) - 3cosh(x) - cosh(x) )sech(2x) +--R + +--R 14 10 6 2 14 +--R (- cosh(x) - 3cosh(x) - 3cosh(x) - cosh(x) )cosh(2x) + cosh(x) +--R + +--R 12 10 8 6 4 2 +--R - 2cosh(x) + 3cosh(x) + 12cosh(x) + 3cosh(x) - 2cosh(x) + cosh(x) +--R / +--R 14 13 2 12 +--R 2sinh(x) + 24cosh(x)sinh(x) + 134cosh(x) sinh(x) +--R + +--R 3 11 4 10 +--R 464cosh(x) sinh(x) + (1122cosh(x) + 6)sinh(x) +--R + +--R 5 9 +--R (2024cosh(x) + 48cosh(x))sinh(x) +--R + +--R 6 2 8 +--R (2838cosh(x) + 174cosh(x) )sinh(x) +--R + +--R 7 3 7 +--R (3168cosh(x) + 384cosh(x) )sinh(x) +--R + +--R 8 4 6 +--R (2838cosh(x) + 588cosh(x) + 6)sinh(x) +--R + +--R 9 5 5 +--R (2024cosh(x) + 672cosh(x) + 24cosh(x))sinh(x) +--R + +--R 10 6 2 4 +--R (1122cosh(x) + 588cosh(x) + 42cosh(x) )sinh(x) +--R + +--R 11 7 3 3 +--R (464cosh(x) + 384cosh(x) + 48cosh(x) )sinh(x) +--R + +--R 12 8 4 2 +--R (134cosh(x) + 174cosh(x) + 42cosh(x) + 2)sinh(x) +--R + +--R 13 9 5 14 +--R (24cosh(x) + 48cosh(x) + 24cosh(x) )sinh(x) + 2cosh(x) +--R + +--R 10 6 2 +--R 6cosh(x) + 6cosh(x) + 2cosh(x) +--R * +--R 2 +--R sinh(2x) +--R + +--R 14 13 2 12 +--R 2sinh(x) + 24cosh(x)sinh(x) + 134cosh(x) sinh(x) +--R + +--R 3 11 4 10 +--R 464cosh(x) sinh(x) + (1122cosh(x) + 6)sinh(x) +--R + +--R 5 9 6 2 8 +--R (2024cosh(x) + 48cosh(x))sinh(x) + (2838cosh(x) + 174cosh(x) )sinh(x) +--R + +--R 7 3 7 +--R (3168cosh(x) + 384cosh(x) )sinh(x) +--R + +--R 8 4 6 +--R (2838cosh(x) + 588cosh(x) + 6)sinh(x) +--R + +--R 9 5 5 +--R (2024cosh(x) + 672cosh(x) + 24cosh(x))sinh(x) +--R + +--R 10 6 2 4 +--R (1122cosh(x) + 588cosh(x) + 42cosh(x) )sinh(x) +--R + +--R 11 7 3 3 +--R (464cosh(x) + 384cosh(x) + 48cosh(x) )sinh(x) +--R + +--R 12 8 4 2 +--R (134cosh(x) + 174cosh(x) + 42cosh(x) + 2)sinh(x) +--R + +--R 13 9 5 14 10 +--R (24cosh(x) + 48cosh(x) + 24cosh(x) )sinh(x) + 2cosh(x) + 6cosh(x) +--R + +--R 6 2 +--R 6cosh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 110 + +--S 111 of 518 +t0922:= 1/(cosh(x)^2-sinh(x)^2) +--R +--R +--R 1 +--R (111) - ------------------- +--R 2 2 +--R sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 518 +r0922:= x +--R +--R +--R (112) x +--R Type: Variable(x) +--E 112 + +--S 113 of 518 +a0922:= integrate(t0922,x) +--R +--R +--R (113) x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 518 +m0922:= a0922-r0922 +--R +--R +--R (114) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 518 +d0922:= D(m0922,x) +--R +--R +--R (115) 0 +--R Type: Expression(Integer) +--E 115 + +--S 116 of 518 +t0923:= 1/(cosh(x)^2-sinh(x)^2)^2 +--R +--R +--R 1 +--R (116) --------------------------------------- +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) +--R Type: Expression(Integer) +--E 116 + +--S 117 of 518 +r0923:= x +--R +--R +--R (117) x +--R Type: Variable(x) +--E 117 + +--S 118 of 518 +a0923:= integrate(t0923,x) +--R +--R +--R (118) x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 518 +m0923:= a0923-r0923 +--R +--R +--R (119) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 518 +d0923:= D(m0923,x) +--R +--R +--R (120) 0 +--R Type: Expression(Integer) +--E 120 + +--S 121 of 518 +t0924:= 1/(cosh(x)^2-sinh(x)^2)^3 +--R +--R +--R 1 +--R (121) - ----------------------------------------------------------- +--R 6 2 4 4 2 6 +--R sinh(x) - 3cosh(x) sinh(x) + 3cosh(x) sinh(x) - cosh(x) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 518 +r0924:= x +--R +--R +--R (122) x +--R Type: Variable(x) +--E 122 + +--S 123 of 518 +a0924:= integrate(t0924,x) +--R +--R +--R (123) x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 518 +m0924:= a0924-r0924 +--R +--R +--R (124) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 518 +d0924:= D(m0924,x) +--R +--R +--R (125) 0 +--R Type: Expression(Integer) +--E 125 + +--S 126 of 518 +t0925:= 1/(sech(x)^2+tanh(x)^2) +--R +--R +--R 1 +--R (126) ------------------- +--R 2 2 +--R tanh(x) + sech(x) +--R Type: Expression(Integer) +--E 126 + +--S 127 of 518 +r0925:= x +--R +--R +--R (127) x +--R Type: Variable(x) +--E 127 + +--S 128 of 518 +a0925:= integrate(t0925,x) +--R +--R +--R (128) x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 518 +m0925:= a0925-r0925 +--R +--R +--R (129) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 518 +d0925:= D(m0925,x) +--R +--R +--R (130) 0 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 518 +t0926:= 1/(sech(x)^2+tanh(x)^2)^2 +--R +--R +--R 1 +--R (131) --------------------------------------- +--R 4 2 2 4 +--R tanh(x) + 2sech(x) tanh(x) + sech(x) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 518 +r0926:= x +--R +--R +--R (132) x +--R Type: Variable(x) +--E 132 + +--S 133 of 518 +a0926:= integrate(t0926,x) +--R +--R +--R (133) x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 518 +m0926:= a0926-r0926 +--R +--R +--R (134) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 518 +d0926:= D(m0926,x) +--R +--R +--R (135) 0 +--R Type: Expression(Integer) +--E 135 + +--S 136 of 518 +t0927:= 1/(sech(x)^2+tanh(x)^2)^3 +--R +--R +--R 1 +--R (136) ----------------------------------------------------------- +--R 6 2 4 4 2 6 +--R tanh(x) + 3sech(x) tanh(x) + 3sech(x) tanh(x) + sech(x) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 518 +r0927:= x +--R +--R +--R (137) x +--R Type: Variable(x) +--E 137 + +--S 138 of 518 +a0927:= integrate(t0927,x) +--R +--R +--R (138) x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 518 +m0927:= a0927-r0927 +--R +--R +--R (139) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 518 +d0927:= D(m0927,x) +--R +--R +--R (140) 0 +--R Type: Expression(Integer) +--E 140 + +--S 141 of 518 +t0928:= 1/(sech(x)^2-tanh(x)^2) +--R +--R +--R 1 +--R (141) - ------------------- +--R 2 2 +--R tanh(x) - sech(x) +--R Type: Expression(Integer) +--E 141 + +--S 142 of 518 +r0928:= -x+atanh(2^(1/2)*tanh(x))*2^(1/2) +--R +--R +--R +-+ +-+ +--R (142) \|2 atanh(\|2 tanh(x)) - x +--R Type: Expression(Integer) +--E 142 + +--S 143 of 518 +a0928:= integrate(t0928,x) +--R +--R +--R (143) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R - 2x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 518 +m0928:= a0928-r0928 +--R +--R +--R (144) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + 2\|2 - 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ +-+ +--R - 2\|2 atanh(\|2 tanh(x)) +--R / +--R 2 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 518 +d0928:= D(m0928,x) +--R +--R +--R (145) +--R +-+ 4 +-+ 3 +--R (4\|2 - 6)sinh(x) + (24\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 56\|2 + 84)cosh(x) - 8\|2 + 12)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 - 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (- 8\|2 + 12)cosh(x) - 12\|2 + 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (4\|2 - 6)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((40\|2 - 60)cosh(x) - 16\|2 + 24)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 - 6)cosh(x) + (- 16\|2 + 24)cosh(x) + 12\|2 - 18 +--R / +--R +-+ 4 +-+ 3 +--R (12\|2 - 18)sinh(x) + (- 24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((24\|2 - 36)cosh(x) - 40\|2 + 60)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 + 32)cosh(x) + (72\|2 - 96)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (12\|2 - 18)cosh(x) + (- 40\|2 + 60)cosh(x) + 12\|2 - 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 6\|2 + 9)sinh(x) + (12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 12\|2 + 18)cosh(x) + 20\|2 - 30)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((12\|2 - 16)cosh(x) + (- 36\|2 + 48)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 6\|2 + 9)cosh(x) + (20\|2 - 30)cosh(x) - 6\|2 + 9 +--R Type: Expression(Integer) +--E 145 + +--S 146 of 518 +t0929:= 1/(sech(x)^2-tanh(x)^2)^2 +--R +--R +--R 1 +--R (146) --------------------------------------- +--R 4 2 2 4 +--R tanh(x) - 2sech(x) tanh(x) + sech(x) +--R Type: Expression(Integer) +--E 146 + +--S 147 of 518 +r0929:= x-1/2*atanh(2^(1/2)*tanh(x))*2^(1/2)+tanh(x)/(1-2*tanh(x)^2) +--R +--R +--R (147) +--R +-+ 2 +-+ +-+ 2 +--R (- 2\|2 tanh(x) + \|2 )atanh(\|2 tanh(x)) + 4x tanh(x) - 2tanh(x) - 2x +--R ------------------------------------------------------------------------ +--R 2 +--R 4tanh(x) - 2 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 518 +a0929:= integrate(t0929,x) +--R +--R +--R (148) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) - 6)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) - 12cosh(x))sinh(x) + cosh(x) - 6cosh(x) + 1 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 + 12)sinh(x) + (- 16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 + 12)cosh(x) - 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ 4 +-+ 3 +--R 2x\|2 sinh(x) + 8x\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12x\|2 cosh(x) + (- 12x - 12)\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8x\|2 cosh(x) + (- 24x - 24)\|2 cosh(x))sinh(x) + 2x\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 12x - 12)\|2 cosh(x) + (2x + 4)\|2 +--R / +--R +-+ 4 +-+ 3 +-+ 2 +-+ 2 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) + (12\|2 cosh(x) - 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (8\|2 cosh(x) - 24\|2 cosh(x))sinh(x) + 2\|2 cosh(x) - 12\|2 cosh(x) +--R + +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 518 +m0929:= a0929-r0929 +--R +--R +--R (149) +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) - 12)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) - 24cosh(x))sinh(x) + 2cosh(x) - 12cosh(x) + 2 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - sinh(x) - 4cosh(x)sinh(x) + (- 6cosh(x) + 6)sinh(x) +--R + +--R 3 4 2 +--R (- 4cosh(x) + 12cosh(x))sinh(x) - cosh(x) + 6cosh(x) - 1 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 + 12)sinh(x) + (- 16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 + 12)cosh(x) - 3\|2 - 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R 4 3 2 2 +--R 4sinh(x) + 16cosh(x)sinh(x) + (24cosh(x) - 24)sinh(x) +--R + +--R 3 4 2 +--R (16cosh(x) - 48cosh(x))sinh(x) + 4cosh(x) - 24cosh(x) + 4 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) + 12)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) + 24cosh(x))sinh(x) - 2cosh(x) + 12cosh(x) - 2 +--R * +--R +-+ +--R atanh(\|2 tanh(x)) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- 24\|2 sinh(x) - 48\|2 cosh(x)sinh(x) - 24\|2 cosh(x) + 8\|2 ) +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|2 cosh(x) - 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8\|2 cosh(x) - 24\|2 cosh(x))sinh(x) + 2\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 12\|2 cosh(x) + 2\|2 +--R * +--R tanh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R 12\|2 sinh(x) + 24\|2 cosh(x)sinh(x) + 12\|2 cosh(x) - 4\|2 +--R / +--R +-+ 4 +-+ 3 +--R 4\|2 sinh(x) + 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (24\|2 cosh(x) - 24\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (16\|2 cosh(x) - 48\|2 cosh(x))sinh(x) + 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 24\|2 cosh(x) + 4\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 2\|2 sinh(x) - 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 12\|2 cosh(x) + 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (- 8\|2 cosh(x) + 24\|2 cosh(x))sinh(x) - 2\|2 cosh(x) + 12\|2 cosh(x) +--R + +--R +-+ +--R - 2\|2 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 518 +d0929:= D(m0929,x) +--R +--R +--R (150) +--R +-+ 12 +-+ 11 +--R (12\|2 + 16)sinh(x) + (32\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 56\|2 - 160)cosh(x) + 240\|2 + 320)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 224\|2 - 608)cosh(x) + (1408\|2 + 1888)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (116\|2 - 528)cosh(x) + (2864\|2 + 3904)cosh(x) - 660\|2 +--R + +--R - 880 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (1216\|2 + 576)cosh(x) + (1024\|2 + 1664)cosh(x) +--R + +--R +-+ +--R (- 4608\|2 - 6208)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (1904\|2 + 1344)cosh(x) + (- 5152\|2 - 6272)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 6288\|2 - 8128)cosh(x) - 576\|2 - 768 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (1216\|2 + 576)cosh(x) + (- 8960\|2 - 11200)cosh(x) +--R + +--R +-+ 3 +-+ +--R (5760\|2 + 9280)cosh(x) + (- 1984\|2 - 2496)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (116\|2 - 528)cosh(x) + (- 5152\|2 - 6272)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (16200\|2 + 24160)cosh(x) + (- 2752\|2 - 3072)cosh(x) +--R + +--R +-+ +--R 228\|2 + 304 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 224\|2 - 608)cosh(x) + (1024\|2 + 1664)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (5760\|2 + 9280)cosh(x) + (- 2688\|2 - 2688)cosh(x) +--R + +--R +-+ +--R (4064\|2 + 5664)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 56\|2 - 160)cosh(x) + (2864\|2 + 3904)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 6288\|2 - 8128)cosh(x) + (- 2752\|2 - 3072)cosh(x) +--R + +--R +-+ 2 +-+ +--R (7944\|2 + 11104)cosh(x) - 48\|2 - 64 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (32\|2 + 32)cosh(x) + (1408\|2 + 1888)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 4608\|2 - 6208)cosh(x) + (- 1984\|2 - 2496)cosh(x) +--R + +--R +-+ 3 +-+ +--R (4064\|2 + 5664)cosh(x) + (64\|2 + 96)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (12\|2 + 16)cosh(x) + (240\|2 + 320)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 660\|2 - 880)cosh(x) + (- 576\|2 - 768)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (228\|2 + 304)cosh(x) + (- 48\|2 - 64)cosh(x) + 36\|2 + 48 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 12\|2 - 16)sinh(x) + (- 32\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((56\|2 + 160)cosh(x) - 240\|2 - 320)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((224\|2 + 608)cosh(x) + (- 1408\|2 - 1888)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 116\|2 + 528)cosh(x) + (- 2864\|2 - 3904)cosh(x) + 660\|2 +--R + +--R 880 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 1216\|2 - 576)cosh(x) + (- 1024\|2 - 1664)cosh(x) +--R + +--R +-+ +--R (4608\|2 + 6208)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 1904\|2 - 1344)cosh(x) + (5152\|2 + 6272)cosh(x) +--R + +--R +-+ 2 +-+ +--R (6288\|2 + 8128)cosh(x) + 576\|2 + 768 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 1216\|2 - 576)cosh(x) + (8960\|2 + 11200)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 5760\|2 - 9280)cosh(x) + (1984\|2 + 2496)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 116\|2 + 528)cosh(x) + (5152\|2 + 6272)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 16200\|2 - 24160)cosh(x) + (2752\|2 + 3072)cosh(x) +--R + +--R +-+ +--R - 228\|2 - 304 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (224\|2 + 608)cosh(x) + (- 1024\|2 - 1664)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 5760\|2 - 9280)cosh(x) + (2688\|2 + 2688)cosh(x) +--R + +--R +-+ +--R (- 4064\|2 - 5664)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (56\|2 + 160)cosh(x) + (- 2864\|2 - 3904)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (6288\|2 + 8128)cosh(x) + (2752\|2 + 3072)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 7944\|2 - 11104)cosh(x) + 48\|2 + 64 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 32\|2 - 32)cosh(x) + (- 1408\|2 - 1888)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (4608\|2 + 6208)cosh(x) + (1984\|2 + 2496)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 4064\|2 - 5664)cosh(x) + (- 64\|2 - 96)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 12\|2 - 16)cosh(x) + (- 240\|2 - 320)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (660\|2 + 880)cosh(x) + (576\|2 + 768)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 228\|2 - 304)cosh(x) + (48\|2 + 64)cosh(x) - 36\|2 - 48 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 6\|2 - 8)sinh(x) + (- 48\|2 - 64)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 156\|2 - 208)cosh(x) + 198\|2 + 264)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 240\|2 - 320)cosh(x) + (1000\|2 + 1296)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((- 90\|2 - 120)cosh(x) + (1886\|2 + 2280)cosh(x) - 876\|2 - 1168) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (288\|2 + 384)cosh(x) + (1216\|2 + 960)cosh(x) +--R + +--R +-+ +--R (- 3568\|2 - 4576)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (504\|2 + 672)cosh(x) + (- 1060\|2 - 2544)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 4432\|2 - 4864)cosh(x) + 1212\|2 + 1616 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (288\|2 + 384)cosh(x) + (- 2384\|2 - 4512)cosh(x) +--R + +--R +-+ 3 +-+ +--R (368\|2 + 3040)cosh(x) + (2912\|2 + 3584)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 90\|2 - 120)cosh(x) + (- 1060\|2 - 2544)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4216\|2 + 8992)cosh(x) + (1556\|2 + 944)cosh(x) - 654\|2 - 872 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 240\|2 - 320)cosh(x) + (1216\|2 + 960)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (368\|2 + 3040)cosh(x) + (- 288\|2 - 2048)cosh(x) +--R + +--R +-+ +--R (- 480\|2 - 480)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 156\|2 - 208)cosh(x) + (1886\|2 + 2280)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 4432\|2 - 4864)cosh(x) + (1556\|2 + 944)cosh(x) +--R + +--R +-+ 2 +-+ +--R (348\|2 + 784)cosh(x) + 126\|2 + 168 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 48\|2 - 64)cosh(x) + (1000\|2 + 1296)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 3568\|2 - 4576)cosh(x) + (2912\|2 + 3584)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 480\|2 - 480)cosh(x) + (184\|2 + 240)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 6\|2 - 8)cosh(x) + (198\|2 + 264)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 876\|2 - 1168)cosh(x) + (1212\|2 + 1616)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 654\|2 - 872)cosh(x) + (126\|2 + 168)cosh(x) +--R / +--R +-+ 12 +-+ 11 +--R (36\|2 + 48)sinh(x) + (224\|2 + 288)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((568\|2 + 672)cosh(x) - 552\|2 - 736)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((736\|2 + 672)cosh(x) + (- 2592\|2 - 3296)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (476\|2 - 48)cosh(x) + (- 4680\|2 - 5216)cosh(x) + 2844\|2 +--R + +--R 3792 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (64\|2 - 960)cosh(x) + (- 3840\|2 - 2176)cosh(x) +--R + +--R +-+ +--R (9664\|2 + 12096)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 112\|2 - 1344)cosh(x) + (- 912\|2 + 3904)cosh(x) +--R + +--R +-+ 2 +-+ +--R (11440\|2 + 11328)cosh(x) - 5424\|2 - 7232 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (64\|2 - 960)cosh(x) + (576\|2 + 6848)cosh(x) +--R + +--R +-+ 3 +-+ +--R (4288\|2 - 2880)cosh(x) + (- 13632\|2 - 16832)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (476\|2 - 48)cosh(x) + (- 912\|2 + 3904)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 664\|2 - 11808)cosh(x) + (- 8976\|2 - 6848)cosh(x) +--R + +--R +-+ +--R 2844\|2 + 3792 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (736\|2 + 672)cosh(x) + (- 3840\|2 - 2176)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (4288\|2 - 2880)cosh(x) + (- 1536\|2 + 5504)cosh(x) +--R + +--R +-+ +--R (5984\|2 + 7584)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (568\|2 + 672)cosh(x) + (- 4680\|2 - 5216)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (11440\|2 + 11328)cosh(x) + (- 8976\|2 - 6848)cosh(x) +--R + +--R +-+ 2 +-+ +--R (6552\|2 + 7968)cosh(x) - 552\|2 - 736 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (224\|2 + 288)cosh(x) + (- 2592\|2 - 3296)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (9664\|2 + 12096)cosh(x) + (- 13632\|2 - 16832)cosh(x) +--R + +--R +-+ 3 +-+ +--R (5984\|2 + 7584)cosh(x) + (- 672\|2 - 864)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (36\|2 + 48)cosh(x) + (- 552\|2 - 736)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (2844\|2 + 3792)cosh(x) + (- 5424\|2 - 7232)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (2844\|2 + 3792)cosh(x) + (- 552\|2 - 736)cosh(x) + 36\|2 + 48 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 36\|2 - 48)sinh(x) + (- 224\|2 - 288)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 568\|2 - 672)cosh(x) + 552\|2 + 736)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 736\|2 - 672)cosh(x) + (2592\|2 + 3296)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 476\|2 + 48)cosh(x) + (4680\|2 + 5216)cosh(x) - 2844\|2 +--R + +--R - 3792 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 64\|2 + 960)cosh(x) + (3840\|2 + 2176)cosh(x) +--R + +--R +-+ +--R (- 9664\|2 - 12096)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (112\|2 + 1344)cosh(x) + (912\|2 - 3904)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 11440\|2 - 11328)cosh(x) + 5424\|2 + 7232 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 64\|2 + 960)cosh(x) + (- 576\|2 - 6848)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 4288\|2 + 2880)cosh(x) + (13632\|2 + 16832)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 476\|2 + 48)cosh(x) + (912\|2 - 3904)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (664\|2 + 11808)cosh(x) + (8976\|2 + 6848)cosh(x) - 2844\|2 +--R + +--R - 3792 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 736\|2 - 672)cosh(x) + (3840\|2 + 2176)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 4288\|2 + 2880)cosh(x) + (1536\|2 - 5504)cosh(x) +--R + +--R +-+ +--R (- 5984\|2 - 7584)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 568\|2 - 672)cosh(x) + (4680\|2 + 5216)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 11440\|2 - 11328)cosh(x) + (8976\|2 + 6848)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 6552\|2 - 7968)cosh(x) + 552\|2 + 736 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 224\|2 - 288)cosh(x) + (2592\|2 + 3296)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 9664\|2 - 12096)cosh(x) + (13632\|2 + 16832)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 5984\|2 - 7584)cosh(x) + (672\|2 + 864)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 36\|2 - 48)cosh(x) + (552\|2 + 736)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 2844\|2 - 3792)cosh(x) + (5424\|2 + 7232)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 2844\|2 - 3792)cosh(x) + (552\|2 + 736)cosh(x) - 36\|2 - 48 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (9\|2 + 12)sinh(x) + (56\|2 + 72)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((142\|2 + 168)cosh(x) - 138\|2 - 184)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((184\|2 + 168)cosh(x) + (- 648\|2 - 824)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((119\|2 - 12)cosh(x) + (- 1170\|2 - 1304)cosh(x) + 711\|2 + 948) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (16\|2 - 240)cosh(x) + (- 960\|2 - 544)cosh(x) +--R + +--R +-+ +--R (2416\|2 + 3024)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 28\|2 - 336)cosh(x) + (- 228\|2 + 976)cosh(x) +--R + +--R +-+ 2 +-+ +--R (2860\|2 + 2832)cosh(x) - 1356\|2 - 1808 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (16\|2 - 240)cosh(x) + (144\|2 + 1712)cosh(x) +--R + +--R +-+ 3 +-+ +--R (1072\|2 - 720)cosh(x) + (- 3408\|2 - 4208)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (119\|2 - 12)cosh(x) + (- 228\|2 + 976)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 166\|2 - 2952)cosh(x) + (- 2244\|2 - 1712)cosh(x) + 711\|2 +--R + +--R 948 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (184\|2 + 168)cosh(x) + (- 960\|2 - 544)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (1072\|2 - 720)cosh(x) + (- 384\|2 + 1376)cosh(x) +--R + +--R +-+ +--R (1496\|2 + 1896)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (142\|2 + 168)cosh(x) + (- 1170\|2 - 1304)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (2860\|2 + 2832)cosh(x) + (- 2244\|2 - 1712)cosh(x) +--R + +--R +-+ 2 +-+ +--R (1638\|2 + 1992)cosh(x) - 138\|2 - 184 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (56\|2 + 72)cosh(x) + (- 648\|2 - 824)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (2416\|2 + 3024)cosh(x) + (- 3408\|2 - 4208)cosh(x) +--R + +--R +-+ 3 +-+ +--R (1496\|2 + 1896)cosh(x) + (- 168\|2 - 216)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (9\|2 + 12)cosh(x) + (- 138\|2 - 184)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (711\|2 + 948)cosh(x) + (- 1356\|2 - 1808)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (711\|2 + 948)cosh(x) + (- 138\|2 - 184)cosh(x) + 9\|2 + 12 +--R Type: Expression(Integer) +--E 150 + +--S 151 of 518 +t0930:= 1/(sech(x)^2-tanh(x)^2)^3 +--R +--R +--R 1 +--R (151) - ----------------------------------------------------------- +--R 6 2 4 4 2 6 +--R tanh(x) - 3sech(x) tanh(x) + 3sech(x) tanh(x) - sech(x) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 518 +r0930:= -x+7/8*atanh(2^(1/2)*tanh(x))*2^(1/2)-3/2*tanh(x)/(1-2*tanh(x)^2)^2+_ + 4*tanh(x)^3/(1-2*tanh(x)^2)^2+7*tanh(x)/(4-8*tanh(x)^2) +--R +--R +--R (152) +--R +-+ 4 +-+ 2 +-+ +-+ +--R (28\|2 tanh(x) - 28\|2 tanh(x) + 7\|2 )atanh(\|2 tanh(x)) +--R + +--R 4 3 2 +--R - 32x tanh(x) + 4tanh(x) + 32x tanh(x) + 2tanh(x) - 8x +--R / +--R 4 2 +--R 32tanh(x) - 32tanh(x) + 8 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 518 +a0930:= integrate(t0930,x) +--R +--R +--R (153) +--R 8 7 2 6 +--R 7sinh(x) + 56cosh(x)sinh(x) + (196cosh(x) - 84)sinh(x) +--R + +--R 3 5 +--R (392cosh(x) - 504cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (490cosh(x) - 1260cosh(x) + 266)sinh(x) +--R + +--R 5 3 3 +--R (392cosh(x) - 1680cosh(x) + 1064cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (196cosh(x) - 1260cosh(x) + 1596cosh(x) - 84)sinh(x) +--R + +--R 7 5 3 +--R (56cosh(x) - 504cosh(x) + 1064cosh(x) - 168cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 7cosh(x) - 84cosh(x) + 266cosh(x) - 84cosh(x) + 7 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R +-+ 8 +-+ 7 +--R - 8x\|2 sinh(x) - 64x\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 224x\|2 cosh(x) + (96x + 68)\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 448x\|2 cosh(x) + (576x + 408)\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 560x\|2 cosh(x) + (1440x + 1020)\|2 cosh(x) + (- 304x - 228)\|2 ) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R - 448x\|2 cosh(x) + (1920x + 1360)\|2 cosh(x) +--R + +--R +-+ +--R (- 1216x - 912)\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R - 224x\|2 cosh(x) + (1440x + 1020)\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 1824x - 1368)\|2 cosh(x) + (96x + 76)\|2 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R - 64x\|2 cosh(x) + (576x + 408)\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 1216x - 912)\|2 cosh(x) + (192x + 152)\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 8x\|2 cosh(x) + (96x + 68)\|2 cosh(x) + (- 304x - 228)\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (96x + 76)\|2 cosh(x) + (- 8x - 12)\|2 +--R / +--R +-+ 8 +-+ 7 +--R 8\|2 sinh(x) + 64\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (224\|2 cosh(x) - 96\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (448\|2 cosh(x) - 576\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (560\|2 cosh(x) - 1440\|2 cosh(x) + 304\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (448\|2 cosh(x) - 1920\|2 cosh(x) + 1216\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (224\|2 cosh(x) - 1440\|2 cosh(x) + 1824\|2 cosh(x) - 96\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (64\|2 cosh(x) - 576\|2 cosh(x) + 1216\|2 cosh(x) - 192\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +-+ +--R 8\|2 cosh(x) - 96\|2 cosh(x) + 304\|2 cosh(x) - 96\|2 cosh(x) + 8\|2 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 518 +m0930:= a0930-r0930 +--R +--R +--R (154) +--R 8 7 2 6 +--R 28sinh(x) + 224cosh(x)sinh(x) + (784cosh(x) - 336)sinh(x) +--R + +--R 3 5 +--R (1568cosh(x) - 2016cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1960cosh(x) - 5040cosh(x) + 1064)sinh(x) +--R + +--R 5 3 3 +--R (1568cosh(x) - 6720cosh(x) + 4256cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (784cosh(x) - 5040cosh(x) + 6384cosh(x) - 336)sinh(x) +--R + +--R 7 5 3 +--R (224cosh(x) - 2016cosh(x) + 4256cosh(x) - 672cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 28cosh(x) - 336cosh(x) + 1064cosh(x) - 336cosh(x) + 28 +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 28sinh(x) - 224cosh(x)sinh(x) + (- 784cosh(x) + 336)sinh(x) +--R + +--R 3 5 +--R (- 1568cosh(x) + 2016cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1960cosh(x) + 5040cosh(x) - 1064)sinh(x) +--R + +--R 5 3 3 +--R (- 1568cosh(x) + 6720cosh(x) - 4256cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 784cosh(x) + 5040cosh(x) - 6384cosh(x) + 336)sinh(x) +--R + +--R 7 5 3 +--R (- 224cosh(x) + 2016cosh(x) - 4256cosh(x) + 672cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 28cosh(x) + 336cosh(x) - 1064cosh(x) + 336cosh(x) - 28 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 7sinh(x) + 56cosh(x)sinh(x) + (196cosh(x) - 84)sinh(x) +--R + +--R 3 5 +--R (392cosh(x) - 504cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (490cosh(x) - 1260cosh(x) + 266)sinh(x) +--R + +--R 5 3 3 +--R (392cosh(x) - 1680cosh(x) + 1064cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (196cosh(x) - 1260cosh(x) + 1596cosh(x) - 84)sinh(x) +--R + +--R 7 5 3 +--R (56cosh(x) - 504cosh(x) + 1064cosh(x) - 168cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 7cosh(x) - 84cosh(x) + 266cosh(x) - 84cosh(x) + 7 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 - 12)sinh(x) + (- 16\|2 + 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 - 12)cosh(x) - 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) - 3 +--R + +--R 8 7 +--R - 56sinh(x) - 448cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 1568cosh(x) + 672)sinh(x) +--R + +--R 3 5 +--R (- 3136cosh(x) + 4032cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 3920cosh(x) + 10080cosh(x) - 2128)sinh(x) +--R + +--R 5 3 3 +--R (- 3136cosh(x) + 13440cosh(x) - 8512cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 1568cosh(x) + 10080cosh(x) - 12768cosh(x) + 672)sinh(x) +--R + +--R 7 5 3 +--R (- 448cosh(x) + 4032cosh(x) - 8512cosh(x) + 1344cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - 56cosh(x) + 672cosh(x) - 2128cosh(x) + 672cosh(x) - 56 +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 56sinh(x) + 448cosh(x)sinh(x) + (1568cosh(x) - 672)sinh(x) +--R + +--R 3 5 +--R (3136cosh(x) - 4032cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (3920cosh(x) - 10080cosh(x) + 2128)sinh(x) +--R + +--R 5 3 3 +--R (3136cosh(x) - 13440cosh(x) + 8512cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (1568cosh(x) - 10080cosh(x) + 12768cosh(x) - 672)sinh(x) +--R + +--R 7 5 3 +--R (448cosh(x) - 4032cosh(x) + 8512cosh(x) - 1344cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 56cosh(x) - 672cosh(x) + 2128cosh(x) - 672cosh(x) + 56 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 14sinh(x) - 112cosh(x)sinh(x) + (- 392cosh(x) + 168)sinh(x) +--R + +--R 3 5 +--R (- 784cosh(x) + 1008cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 980cosh(x) + 2520cosh(x) - 532)sinh(x) +--R + +--R 5 3 3 +--R (- 784cosh(x) + 3360cosh(x) - 2128cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 392cosh(x) + 2520cosh(x) - 3192cosh(x) + 168)sinh(x) +--R + +--R 7 5 3 +--R (- 112cosh(x) + 1008cosh(x) - 2128cosh(x) + 336cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 14cosh(x) + 168cosh(x) - 532cosh(x) + 168cosh(x) - 14 +--R * +--R +-+ +--R atanh(\|2 tanh(x)) +--R + +--R +-+ 6 +-+ 5 +--R 272\|2 sinh(x) + 1632\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (4080\|2 cosh(x) - 912\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (5440\|2 cosh(x) - 3648\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (4080\|2 cosh(x) - 5472\|2 cosh(x) + 304\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (1632\|2 cosh(x) - 3648\|2 cosh(x) + 608\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 272\|2 cosh(x) - 912\|2 cosh(x) + 304\|2 cosh(x) - 48\|2 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 4\|2 sinh(x) - 32\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 112\|2 cosh(x) + 48\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 224\|2 cosh(x) + 288\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 280\|2 cosh(x) + 720\|2 cosh(x) - 152\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 224\|2 cosh(x) + 960\|2 cosh(x) - 608\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 112\|2 cosh(x) + 720\|2 cosh(x) - 912\|2 cosh(x) + 48\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 32\|2 cosh(x) + 288\|2 cosh(x) - 608\|2 cosh(x) +--R + +--R +-+ +--R 96\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 4\|2 cosh(x) + 48\|2 cosh(x) - 152\|2 cosh(x) + 48\|2 cosh(x) +--R + +--R +-+ +--R - 4\|2 +--R * +--R 3 +--R tanh(x) +--R + +--R +-+ 6 +-+ 5 +--R - 272\|2 sinh(x) - 1632\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (- 4080\|2 cosh(x) + 912\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (- 5440\|2 cosh(x) + 3648\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 4080\|2 cosh(x) + 5472\|2 cosh(x) - 304\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 1632\|2 cosh(x) + 3648\|2 cosh(x) - 608\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 272\|2 cosh(x) + 912\|2 cosh(x) - 304\|2 cosh(x) + 48\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 2\|2 sinh(x) - 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 56\|2 cosh(x) + 24\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 112\|2 cosh(x) + 144\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 140\|2 cosh(x) + 360\|2 cosh(x) - 76\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 112\|2 cosh(x) + 480\|2 cosh(x) - 304\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 56\|2 cosh(x) + 360\|2 cosh(x) - 456\|2 cosh(x) + 24\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 16\|2 cosh(x) + 144\|2 cosh(x) - 304\|2 cosh(x) +--R + +--R +-+ +--R 48\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 2\|2 cosh(x) + 24\|2 cosh(x) - 76\|2 cosh(x) + 24\|2 cosh(x) +--R + +--R +-+ +--R - 2\|2 +--R * +--R tanh(x) +--R + +--R +-+ 6 +-+ 5 +--R 68\|2 sinh(x) + 408\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (1020\|2 cosh(x) - 228\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (1360\|2 cosh(x) - 912\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (1020\|2 cosh(x) - 1368\|2 cosh(x) + 76\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (408\|2 cosh(x) - 912\|2 cosh(x) + 152\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 68\|2 cosh(x) - 228\|2 cosh(x) + 76\|2 cosh(x) - 12\|2 +--R / +--R +-+ 8 +-+ 7 +--R 32\|2 sinh(x) + 256\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (896\|2 cosh(x) - 384\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (1792\|2 cosh(x) - 2304\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (2240\|2 cosh(x) - 5760\|2 cosh(x) + 1216\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (1792\|2 cosh(x) - 7680\|2 cosh(x) + 4864\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (896\|2 cosh(x) - 5760\|2 cosh(x) + 7296\|2 cosh(x) - 384\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 256\|2 cosh(x) - 2304\|2 cosh(x) + 4864\|2 cosh(x) +--R + +--R +-+ +--R - 768\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 32\|2 cosh(x) - 384\|2 cosh(x) + 1216\|2 cosh(x) - 384\|2 cosh(x) +--R + +--R +-+ +--R 32\|2 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 32\|2 sinh(x) - 256\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 896\|2 cosh(x) + 384\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 1792\|2 cosh(x) + 2304\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 2240\|2 cosh(x) + 5760\|2 cosh(x) - 1216\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 1792\|2 cosh(x) + 7680\|2 cosh(x) - 4864\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 896\|2 cosh(x) + 5760\|2 cosh(x) - 7296\|2 cosh(x) + 384\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 256\|2 cosh(x) + 2304\|2 cosh(x) - 4864\|2 cosh(x) +--R + +--R +-+ +--R 768\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 32\|2 cosh(x) + 384\|2 cosh(x) - 1216\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 384\|2 cosh(x) - 32\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 8\|2 sinh(x) + 64\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (224\|2 cosh(x) - 96\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (448\|2 cosh(x) - 576\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (560\|2 cosh(x) - 1440\|2 cosh(x) + 304\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (448\|2 cosh(x) - 1920\|2 cosh(x) + 1216\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (224\|2 cosh(x) - 1440\|2 cosh(x) + 1824\|2 cosh(x) - 96\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (64\|2 cosh(x) - 576\|2 cosh(x) + 1216\|2 cosh(x) - 192\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +-+ +--R 8\|2 cosh(x) - 96\|2 cosh(x) + 304\|2 cosh(x) - 96\|2 cosh(x) + 8\|2 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 518 +--d0930:= D(m0930,x) +--E 155 + +--S 156 of 518 +t0931:= 1/(coth(x)^2+csch(x)^2) +--R +--R +--R 1 +--R (155) ------------------- +--R 2 2 +--R csch(x) + coth(x) +--R Type: Expression(Integer) +--E 156 + +--S 157 of 518 +r0931:= x-atanh(1/2*2^(1/2)*tanh(x))*2^(1/2) +--R +--R +--R +-+ +--R +-+ \|2 tanh(x) +--R (156) - \|2 atanh(-----------) + x +--R 2 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 518 +a0931:= integrate(t0931,x) +--R +--R +--R (157) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (6\|2 + 9)sinh(x) + (- 12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (6\|2 + 9)cosh(x) + 2\|2 + 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R 2x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 518 +m0931:= a0931-r0931 +--R +--R +--R (158) +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 2 +-+ +--R (6\|2 + 9)sinh(x) + (- 12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (6\|2 + 9)cosh(x) + 2\|2 + 3 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ +--R +-+ \|2 tanh(x) +--R 2\|2 atanh(-----------) +--R 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 518 +d0931:= D(m0931,x) +--R +--R +--R (159) +--R +-+ 4 +-+ 3 +--R (4\|2 + 6)sinh(x) + (- 24\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((40\|2 + 60)cosh(x) + 16\|2 + 24)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 24\|2 - 32)cosh(x) + (- 24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 + 6)cosh(x) + (16\|2 + 24)cosh(x) + 12\|2 + 18 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (4\|2 + 6)sinh(x) + (24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 56\|2 - 84)cosh(x) + 8\|2 + 12)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 + 32)cosh(x) + (- 24\|2 - 32)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4\|2 + 6)cosh(x) + (8\|2 + 12)cosh(x) - 12\|2 - 18 +--R / +--R +-+ 4 +-+ 3 +--R (6\|2 + 9)sinh(x) + (- 12\|2 - 16)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((12\|2 + 18)cosh(x) + 20\|2 + 30)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((- 12\|2 - 16)cosh(x) + (- 36\|2 - 48)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (6\|2 + 9)cosh(x) + (20\|2 + 30)cosh(x) + 6\|2 + 9 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 12\|2 - 18)sinh(x) + (24\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R ((- 24\|2 - 36)cosh(x) - 40\|2 - 60)sinh(x) +--R + +--R +-+ 3 +-+ +--R ((24\|2 + 32)cosh(x) + (72\|2 + 96)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 12\|2 - 18)cosh(x) + (- 40\|2 - 60)cosh(x) - 12\|2 - 18 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 518 +t0932:= 1/(coth(x)^2+csch(x)^2)^2 +--R +--R +--R 1 +--R (160) --------------------------------------- +--R 4 2 2 4 +--R csch(x) + 2coth(x) csch(x) + coth(x) +--R Type: Expression(Integer) +--E 161 + +--S 162 of 518 +r0932:= x-1/2*atanh(1/2*2^(1/2)*tanh(x))*2^(1/2)-tanh(x)/(2-tanh(x)^2) +--R +--R +--R (161) +--R +-+ +--R +-+ 2 +-+ \|2 tanh(x) 2 +--R (- \|2 tanh(x) + 2\|2 )atanh(-----------) + 2x tanh(x) + 2tanh(x) - 4x +--R 2 +--R ------------------------------------------------------------------------ +--R 2 +--R 2tanh(x) - 4 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 518 +a0932:= integrate(t0932,x) +--R +--R +--R (162) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 6)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 12cosh(x))sinh(x) + cosh(x) + 6cosh(x) + 1 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 + 12)sinh(x) + (- 16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 + 12)cosh(x) + 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ 4 +-+ 3 +--R 2x\|2 sinh(x) + 8x\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12x\|2 cosh(x) + (12x + 12)\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8x\|2 cosh(x) + (24x + 24)\|2 cosh(x))sinh(x) + 2x\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (12x + 12)\|2 cosh(x) + (2x + 4)\|2 +--R / +--R +-+ 4 +-+ 3 +-+ 2 +-+ 2 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) + (12\|2 cosh(x) + 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +-+ 2 +--R (8\|2 cosh(x) + 24\|2 cosh(x))sinh(x) + 2\|2 cosh(x) + 12\|2 cosh(x) +--R + +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 518 +m0932:= a0932-r0932 +--R +--R +--R (163) +--R 4 3 2 2 +--R sinh(x) + 4cosh(x)sinh(x) + (6cosh(x) + 6)sinh(x) +--R + +--R 3 4 2 +--R (4cosh(x) + 12cosh(x))sinh(x) + cosh(x) + 6cosh(x) + 1 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 2sinh(x) - 8cosh(x)sinh(x) + (- 12cosh(x) - 12)sinh(x) +--R + +--R 3 4 2 +--R (- 8cosh(x) - 24cosh(x))sinh(x) - 2cosh(x) - 12cosh(x) - 2 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 + 12)sinh(x) + (- 16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 + 12)cosh(x) + 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R 4 3 2 2 +--R 2sinh(x) + 8cosh(x)sinh(x) + (12cosh(x) + 12)sinh(x) +--R + +--R 3 4 2 +--R (8cosh(x) + 24cosh(x))sinh(x) + 2cosh(x) + 12cosh(x) + 2 +--R * +--R 2 +--R tanh(x) +--R + +--R 4 3 2 2 +--R - 4sinh(x) - 16cosh(x)sinh(x) + (- 24cosh(x) - 24)sinh(x) +--R + +--R 3 4 2 +--R (- 16cosh(x) - 48cosh(x))sinh(x) - 4cosh(x) - 24cosh(x) - 4 +--R * +--R +-+ +--R \|2 tanh(x) +--R atanh(-----------) +--R 2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ 2 +--R (12\|2 sinh(x) + 24\|2 cosh(x)sinh(x) + 12\|2 cosh(x) + 4\|2 )tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 2\|2 sinh(x) - 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 12\|2 cosh(x) - 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 8\|2 cosh(x) - 24\|2 cosh(x))sinh(x) - 2\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 12\|2 cosh(x) - 2\|2 +--R * +--R tanh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R - 24\|2 sinh(x) - 48\|2 cosh(x)sinh(x) - 24\|2 cosh(x) - 8\|2 +--R / +--R +-+ 4 +-+ 3 +--R 2\|2 sinh(x) + 8\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|2 cosh(x) + 12\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (8\|2 cosh(x) + 24\|2 cosh(x))sinh(x) + 2\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R 12\|2 cosh(x) + 2\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 4 +-+ 3 +--R - 4\|2 sinh(x) - 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 24\|2 cosh(x) - 24\|2 )sinh(x) +--R + +--R +-+ 3 +-+ +-+ 4 +--R (- 16\|2 cosh(x) - 48\|2 cosh(x))sinh(x) - 4\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 24\|2 cosh(x) - 4\|2 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 518 +d0932:= D(m0932,x) +--R +--R +--R (164) +--R +-+ 12 +-+ 11 +--R (- 6\|2 - 8)sinh(x) + (- 48\|2 - 64)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 156\|2 - 208)cosh(x) - 198\|2 - 264)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 240\|2 - 320)cosh(x) + (- 1000\|2 - 1296)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 90\|2 - 120)cosh(x) + (- 1886\|2 - 2280)cosh(x) - 876\|2 +--R + +--R - 1168 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (288\|2 + 384)cosh(x) + (- 1216\|2 - 960)cosh(x) +--R + +--R +-+ +--R (- 3568\|2 - 4576)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (504\|2 + 672)cosh(x) + (1060\|2 + 2544)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 4432\|2 - 4864)cosh(x) - 1212\|2 - 1616 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (288\|2 + 384)cosh(x) + (2384\|2 + 4512)cosh(x) +--R + +--R +-+ 3 +-+ +--R (368\|2 + 3040)cosh(x) + (- 2912\|2 - 3584)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 90\|2 - 120)cosh(x) + (1060\|2 + 2544)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (4216\|2 + 8992)cosh(x) + (- 1556\|2 - 944)cosh(x) - 654\|2 +--R + +--R - 872 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 240\|2 - 320)cosh(x) + (- 1216\|2 - 960)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (368\|2 + 3040)cosh(x) + (288\|2 + 2048)cosh(x) +--R + +--R +-+ +--R (- 480\|2 - 480)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 156\|2 - 208)cosh(x) + (- 1886\|2 - 2280)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 4432\|2 - 4864)cosh(x) + (- 1556\|2 - 944)cosh(x) +--R + +--R +-+ 2 +-+ +--R (348\|2 + 784)cosh(x) - 126\|2 - 168 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 48\|2 - 64)cosh(x) + (- 1000\|2 - 1296)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 3568\|2 - 4576)cosh(x) + (- 2912\|2 - 3584)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 480\|2 - 480)cosh(x) + (- 184\|2 - 240)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 6\|2 - 8)cosh(x) + (- 198\|2 - 264)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 876\|2 - 1168)cosh(x) + (- 1212\|2 - 1616)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 654\|2 - 872)cosh(x) + (- 126\|2 - 168)cosh(x) +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 12\|2 - 16)sinh(x) + (- 32\|2 - 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((56\|2 + 160)cosh(x) + 240\|2 + 320)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((224\|2 + 608)cosh(x) + (1408\|2 + 1888)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 116\|2 + 528)cosh(x) + (2864\|2 + 3904)cosh(x) + 660\|2 +--R + +--R 880 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 1216\|2 - 576)cosh(x) + (1024\|2 + 1664)cosh(x) +--R + +--R +-+ +--R (4608\|2 + 6208)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 1904\|2 - 1344)cosh(x) + (- 5152\|2 - 6272)cosh(x) +--R + +--R +-+ 2 +-+ +--R (6288\|2 + 8128)cosh(x) - 576\|2 - 768 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 1216\|2 - 576)cosh(x) + (- 8960\|2 - 11200)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 5760\|2 - 9280)cosh(x) + (- 1984\|2 - 2496)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 116\|2 + 528)cosh(x) + (- 5152\|2 - 6272)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (- 16200\|2 - 24160)cosh(x) + (- 2752\|2 - 3072)cosh(x) +--R + +--R +-+ +--R - 228\|2 - 304 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (224\|2 + 608)cosh(x) + (1024\|2 + 1664)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 5760\|2 - 9280)cosh(x) + (- 2688\|2 - 2688)cosh(x) +--R + +--R +-+ +--R (- 4064\|2 - 5664)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (56\|2 + 160)cosh(x) + (2864\|2 + 3904)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (6288\|2 + 8128)cosh(x) + (- 2752\|2 - 3072)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 7944\|2 - 11104)cosh(x) - 48\|2 - 64 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 32\|2 - 32)cosh(x) + (1408\|2 + 1888)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (4608\|2 + 6208)cosh(x) + (- 1984\|2 - 2496)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 4064\|2 - 5664)cosh(x) + (64\|2 + 96)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 12\|2 - 16)cosh(x) + (240\|2 + 320)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (660\|2 + 880)cosh(x) + (- 576\|2 - 768)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 228\|2 - 304)cosh(x) + (- 48\|2 - 64)cosh(x) - 36\|2 - 48 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (12\|2 + 16)sinh(x) + (32\|2 + 32)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 56\|2 - 160)cosh(x) - 240\|2 - 320)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 224\|2 - 608)cosh(x) + (- 1408\|2 - 1888)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((116\|2 - 528)cosh(x) + (- 2864\|2 - 3904)cosh(x) - 660\|2 - 880) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (1216\|2 + 576)cosh(x) + (- 1024\|2 - 1664)cosh(x) +--R + +--R +-+ +--R (- 4608\|2 - 6208)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (1904\|2 + 1344)cosh(x) + (5152\|2 + 6272)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 6288\|2 - 8128)cosh(x) + 576\|2 + 768 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (1216\|2 + 576)cosh(x) + (8960\|2 + 11200)cosh(x) +--R + +--R +-+ 3 +-+ +--R (5760\|2 + 9280)cosh(x) + (1984\|2 + 2496)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (116\|2 - 528)cosh(x) + (5152\|2 + 6272)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (16200\|2 + 24160)cosh(x) + (2752\|2 + 3072)cosh(x) + 228\|2 + 304 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 224\|2 - 608)cosh(x) + (- 1024\|2 - 1664)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (5760\|2 + 9280)cosh(x) + (2688\|2 + 2688)cosh(x) +--R + +--R +-+ +--R (4064\|2 + 5664)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 56\|2 - 160)cosh(x) + (- 2864\|2 - 3904)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 6288\|2 - 8128)cosh(x) + (2752\|2 + 3072)cosh(x) +--R + +--R +-+ 2 +-+ +--R (7944\|2 + 11104)cosh(x) + 48\|2 + 64 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (32\|2 + 32)cosh(x) + (- 1408\|2 - 1888)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 4608\|2 - 6208)cosh(x) + (1984\|2 + 2496)cosh(x) +--R + +--R +-+ 3 +-+ +--R (4064\|2 + 5664)cosh(x) + (- 64\|2 - 96)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (12\|2 + 16)cosh(x) + (- 240\|2 - 320)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 660\|2 - 880)cosh(x) + (576\|2 + 768)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (228\|2 + 304)cosh(x) + (48\|2 + 64)cosh(x) + 36\|2 + 48 +--R / +--R +-+ 12 +-+ 11 +--R (9\|2 + 12)sinh(x) + (56\|2 + 72)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((142\|2 + 168)cosh(x) + 138\|2 + 184)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((184\|2 + 168)cosh(x) + (648\|2 + 824)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (119\|2 - 12)cosh(x) + (1170\|2 + 1304)cosh(x) + 711\|2 +--R + +--R 948 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (16\|2 - 240)cosh(x) + (960\|2 + 544)cosh(x) +--R + +--R +-+ +--R (2416\|2 + 3024)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 28\|2 - 336)cosh(x) + (228\|2 - 976)cosh(x) +--R + +--R +-+ 2 +-+ +--R (2860\|2 + 2832)cosh(x) + 1356\|2 + 1808 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (16\|2 - 240)cosh(x) + (- 144\|2 - 1712)cosh(x) +--R + +--R +-+ 3 +-+ +--R (1072\|2 - 720)cosh(x) + (3408\|2 + 4208)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (119\|2 - 12)cosh(x) + (228\|2 - 976)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 166\|2 - 2952)cosh(x) + (2244\|2 + 1712)cosh(x) + 711\|2 +--R + +--R 948 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (184\|2 + 168)cosh(x) + (960\|2 + 544)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (1072\|2 - 720)cosh(x) + (384\|2 - 1376)cosh(x) +--R + +--R +-+ +--R (1496\|2 + 1896)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (142\|2 + 168)cosh(x) + (1170\|2 + 1304)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (2860\|2 + 2832)cosh(x) + (2244\|2 + 1712)cosh(x) +--R + +--R +-+ 2 +-+ +--R (1638\|2 + 1992)cosh(x) + 138\|2 + 184 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (56\|2 + 72)cosh(x) + (648\|2 + 824)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (2416\|2 + 3024)cosh(x) + (3408\|2 + 4208)cosh(x) +--R + +--R +-+ 3 +-+ +--R (1496\|2 + 1896)cosh(x) + (168\|2 + 216)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (9\|2 + 12)cosh(x) + (138\|2 + 184)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (711\|2 + 948)cosh(x) + (1356\|2 + 1808)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (711\|2 + 948)cosh(x) + (138\|2 + 184)cosh(x) + 9\|2 + 12 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (- 36\|2 - 48)sinh(x) + (- 224\|2 - 288)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((- 568\|2 - 672)cosh(x) - 552\|2 - 736)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((- 736\|2 - 672)cosh(x) + (- 2592\|2 - 3296)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 476\|2 + 48)cosh(x) + (- 4680\|2 - 5216)cosh(x) - 2844\|2 +--R + +--R - 3792 +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 64\|2 + 960)cosh(x) + (- 3840\|2 - 2176)cosh(x) +--R + +--R +-+ +--R (- 9664\|2 - 12096)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (112\|2 + 1344)cosh(x) + (- 912\|2 + 3904)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 11440\|2 - 11328)cosh(x) - 5424\|2 - 7232 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 64\|2 + 960)cosh(x) + (576\|2 + 6848)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 4288\|2 + 2880)cosh(x) + (- 13632\|2 - 16832)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 476\|2 + 48)cosh(x) + (- 912\|2 + 3904)cosh(x) +--R + +--R +-+ 4 +-+ 2 +--R (664\|2 + 11808)cosh(x) + (- 8976\|2 - 6848)cosh(x) +--R + +--R +-+ +--R - 2844\|2 - 3792 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (- 736\|2 - 672)cosh(x) + (- 3840\|2 - 2176)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (- 4288\|2 + 2880)cosh(x) + (- 1536\|2 + 5504)cosh(x) +--R + +--R +-+ +--R (- 5984\|2 - 7584)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (- 568\|2 - 672)cosh(x) + (- 4680\|2 - 5216)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 11440\|2 - 11328)cosh(x) + (- 8976\|2 - 6848)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 6552\|2 - 7968)cosh(x) - 552\|2 - 736 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (- 224\|2 - 288)cosh(x) + (- 2592\|2 - 3296)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (- 9664\|2 - 12096)cosh(x) + (- 13632\|2 - 16832)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 5984\|2 - 7584)cosh(x) + (- 672\|2 - 864)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (- 36\|2 - 48)cosh(x) + (- 552\|2 - 736)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (- 2844\|2 - 3792)cosh(x) + (- 5424\|2 - 7232)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 2844\|2 - 3792)cosh(x) + (- 552\|2 - 736)cosh(x) - 36\|2 - 48 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 12 +-+ 11 +--R (36\|2 + 48)sinh(x) + (224\|2 + 288)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 10 +--R ((568\|2 + 672)cosh(x) + 552\|2 + 736)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R ((736\|2 + 672)cosh(x) + (2592\|2 + 3296)cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R ((476\|2 - 48)cosh(x) + (4680\|2 + 5216)cosh(x) + 2844\|2 + 3792) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R (64\|2 - 960)cosh(x) + (3840\|2 + 2176)cosh(x) +--R + +--R +-+ +--R (9664\|2 + 12096)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R (- 112\|2 - 1344)cosh(x) + (912\|2 - 3904)cosh(x) +--R + +--R +-+ 2 +-+ +--R (11440\|2 + 11328)cosh(x) + 5424\|2 + 7232 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R (64\|2 - 960)cosh(x) + (- 576\|2 - 6848)cosh(x) +--R + +--R +-+ 3 +-+ +--R (4288\|2 - 2880)cosh(x) + (13632\|2 + 16832)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R (476\|2 - 48)cosh(x) + (912\|2 - 3904)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 664\|2 - 11808)cosh(x) + (8976\|2 + 6848)cosh(x) + 2844\|2 +--R + +--R 3792 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R (736\|2 + 672)cosh(x) + (3840\|2 + 2176)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (4288\|2 - 2880)cosh(x) + (1536\|2 - 5504)cosh(x) +--R + +--R +-+ +--R (5984\|2 + 7584)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ 8 +--R (568\|2 + 672)cosh(x) + (4680\|2 + 5216)cosh(x) +--R + +--R +-+ 6 +-+ 4 +--R (11440\|2 + 11328)cosh(x) + (8976\|2 + 6848)cosh(x) +--R + +--R +-+ 2 +-+ +--R (6552\|2 + 7968)cosh(x) + 552\|2 + 736 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 11 +-+ 9 +--R (224\|2 + 288)cosh(x) + (2592\|2 + 3296)cosh(x) +--R + +--R +-+ 7 +-+ 5 +--R (9664\|2 + 12096)cosh(x) + (13632\|2 + 16832)cosh(x) +--R + +--R +-+ 3 +-+ +--R (5984\|2 + 7584)cosh(x) + (672\|2 + 864)cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 12 +-+ 10 +--R (36\|2 + 48)cosh(x) + (552\|2 + 736)cosh(x) +--R + +--R +-+ 8 +-+ 6 +--R (2844\|2 + 3792)cosh(x) + (5424\|2 + 7232)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (2844\|2 + 3792)cosh(x) + (552\|2 + 736)cosh(x) + 36\|2 + 48 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 518 +t0933:= 1/(coth(x)^2+csch(x)^2)^3 +--R +--R +--R 1 +--R (165) ----------------------------------------------------------- +--R 6 2 4 4 2 6 +--R csch(x) + 3coth(x) csch(x) + 3coth(x) csch(x) + coth(x) +--R Type: Expression(Integer) +--E 166 + +--S 167 of 518 +r0933:= x-7/8*atanh(1/2*2^(1/2)*tanh(x))*2^(1/2)-tanh(x)/(2-tanh(x)^2)^2+_ + tanh(x)/(8-4*tanh(x)^2) +--R +--R +--R (166) +--R +-+ +--R +-+ 4 +-+ 2 +-+ \|2 tanh(x) +--R (- 7\|2 tanh(x) + 28\|2 tanh(x) - 28\|2 )atanh(-----------) +--R 2 +--R + +--R 4 3 2 +--R 8x tanh(x) - 2tanh(x) - 32x tanh(x) - 4tanh(x) + 32x +--R / +--R 4 2 +--R 8tanh(x) - 32tanh(x) + 32 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 518 +a0933:= integrate(t0933,x) +--R +--R +--R (167) +--R 8 7 2 6 +--R 7sinh(x) + 56cosh(x)sinh(x) + (196cosh(x) + 84)sinh(x) +--R + +--R 3 5 +--R (392cosh(x) + 504cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (490cosh(x) + 1260cosh(x) + 266)sinh(x) +--R + +--R 5 3 3 +--R (392cosh(x) + 1680cosh(x) + 1064cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (196cosh(x) + 1260cosh(x) + 1596cosh(x) + 84)sinh(x) +--R + +--R 7 5 3 +--R (56cosh(x) + 504cosh(x) + 1064cosh(x) + 168cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 7cosh(x) + 84cosh(x) + 266cosh(x) + 84cosh(x) + 7 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 + 12)sinh(x) + (- 16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 + 12)cosh(x) + 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R +-+ 8 +-+ 7 +--R 8x\|2 sinh(x) + 64x\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (224x\|2 cosh(x) + (96x + 68)\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (448x\|2 cosh(x) + (576x + 408)\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (560x\|2 cosh(x) + (1440x + 1020)\|2 cosh(x) + (304x + 228)\|2 ) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R 448x\|2 cosh(x) + (1920x + 1360)\|2 cosh(x) +--R + +--R +-+ +--R (1216x + 912)\|2 cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R 224x\|2 cosh(x) + (1440x + 1020)\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (1824x + 1368)\|2 cosh(x) + (96x + 76)\|2 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R 64x\|2 cosh(x) + (576x + 408)\|2 cosh(x) +--R + +--R +-+ 3 +-+ +--R (1216x + 912)\|2 cosh(x) + (192x + 152)\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 8x\|2 cosh(x) + (96x + 68)\|2 cosh(x) + (304x + 228)\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R (96x + 76)\|2 cosh(x) + (8x + 12)\|2 +--R / +--R +-+ 8 +-+ 7 +--R 8\|2 sinh(x) + 64\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (224\|2 cosh(x) + 96\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (448\|2 cosh(x) + 576\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (560\|2 cosh(x) + 1440\|2 cosh(x) + 304\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (448\|2 cosh(x) + 1920\|2 cosh(x) + 1216\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (224\|2 cosh(x) + 1440\|2 cosh(x) + 1824\|2 cosh(x) + 96\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (64\|2 cosh(x) + 576\|2 cosh(x) + 1216\|2 cosh(x) + 192\|2 cosh(x)) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +-+ +--R 8\|2 cosh(x) + 96\|2 cosh(x) + 304\|2 cosh(x) + 96\|2 cosh(x) + 8\|2 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 518 +m0933:= a0933-r0933 +--R +--R +--R (168) +--R 8 7 2 6 +--R 7sinh(x) + 56cosh(x)sinh(x) + (196cosh(x) + 84)sinh(x) +--R + +--R 3 5 +--R (392cosh(x) + 504cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (490cosh(x) + 1260cosh(x) + 266)sinh(x) +--R + +--R 5 3 3 +--R (392cosh(x) + 1680cosh(x) + 1064cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (196cosh(x) + 1260cosh(x) + 1596cosh(x) + 84)sinh(x) +--R + +--R 7 5 3 +--R (56cosh(x) + 504cosh(x) + 1064cosh(x) + 168cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 7cosh(x) + 84cosh(x) + 266cosh(x) + 84cosh(x) + 7 +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 2 6 +--R - 28sinh(x) - 224cosh(x)sinh(x) + (- 784cosh(x) - 336)sinh(x) +--R + +--R 3 5 +--R (- 1568cosh(x) - 2016cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 1960cosh(x) - 5040cosh(x) - 1064)sinh(x) +--R + +--R 5 3 3 +--R (- 1568cosh(x) - 6720cosh(x) - 4256cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 784cosh(x) - 5040cosh(x) - 6384cosh(x) - 336)sinh(x) +--R + +--R 7 5 3 +--R (- 224cosh(x) - 2016cosh(x) - 4256cosh(x) - 672cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R - 28cosh(x) - 336cosh(x) - 1064cosh(x) - 336cosh(x) - 28 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 28sinh(x) + 224cosh(x)sinh(x) + (784cosh(x) + 336)sinh(x) +--R + +--R 3 5 +--R (1568cosh(x) + 2016cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (1960cosh(x) + 5040cosh(x) + 1064)sinh(x) +--R + +--R 5 3 3 +--R (1568cosh(x) + 6720cosh(x) + 4256cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (784cosh(x) + 5040cosh(x) + 6384cosh(x) + 336)sinh(x) +--R + +--R 7 5 3 +--R (224cosh(x) + 2016cosh(x) + 4256cosh(x) + 672cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 28cosh(x) + 336cosh(x) + 1064cosh(x) + 336cosh(x) + 28 +--R * +--R log +--R +-+ 2 +-+ +--R (9\|2 + 12)sinh(x) + (- 16\|2 - 24)cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ +--R (9\|2 + 12)cosh(x) + 3\|2 + 4 +--R / +--R 2 2 +--R sinh(x) + cosh(x) + 3 +--R + +--R 8 7 2 6 +--R 14sinh(x) + 112cosh(x)sinh(x) + (392cosh(x) + 168)sinh(x) +--R + +--R 3 5 +--R (784cosh(x) + 1008cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (980cosh(x) + 2520cosh(x) + 532)sinh(x) +--R + +--R 5 3 3 +--R (784cosh(x) + 3360cosh(x) + 2128cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (392cosh(x) + 2520cosh(x) + 3192cosh(x) + 168)sinh(x) +--R + +--R 7 5 3 +--R (112cosh(x) + 1008cosh(x) + 2128cosh(x) + 336cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 14cosh(x) + 168cosh(x) + 532cosh(x) + 168cosh(x) + 14 +--R * +--R 4 +--R tanh(x) +--R + +--R 8 7 +--R - 56sinh(x) - 448cosh(x)sinh(x) +--R + +--R 2 6 +--R (- 1568cosh(x) - 672)sinh(x) +--R + +--R 3 5 +--R (- 3136cosh(x) - 4032cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (- 3920cosh(x) - 10080cosh(x) - 2128)sinh(x) +--R + +--R 5 3 3 +--R (- 3136cosh(x) - 13440cosh(x) - 8512cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (- 1568cosh(x) - 10080cosh(x) - 12768cosh(x) - 672)sinh(x) +--R + +--R 7 5 3 +--R (- 448cosh(x) - 4032cosh(x) - 8512cosh(x) - 1344cosh(x)) +--R * +--R sinh(x) +--R + +--R 8 6 4 2 +--R - 56cosh(x) - 672cosh(x) - 2128cosh(x) - 672cosh(x) - 56 +--R * +--R 2 +--R tanh(x) +--R + +--R 8 7 2 6 +--R 56sinh(x) + 448cosh(x)sinh(x) + (1568cosh(x) + 672)sinh(x) +--R + +--R 3 5 +--R (3136cosh(x) + 4032cosh(x))sinh(x) +--R + +--R 4 2 4 +--R (3920cosh(x) + 10080cosh(x) + 2128)sinh(x) +--R + +--R 5 3 3 +--R (3136cosh(x) + 13440cosh(x) + 8512cosh(x))sinh(x) +--R + +--R 6 4 2 2 +--R (1568cosh(x) + 10080cosh(x) + 12768cosh(x) + 672)sinh(x) +--R + +--R 7 5 3 +--R (448cosh(x) + 4032cosh(x) + 8512cosh(x) + 1344cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 56cosh(x) + 672cosh(x) + 2128cosh(x) + 672cosh(x) + 56 +--R * +--R +-+ +--R \|2 tanh(x) +--R atanh(-----------) +--R 2 +--R + +--R +-+ 6 +-+ 5 +--R 68\|2 sinh(x) + 408\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (1020\|2 cosh(x) + 228\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (1360\|2 cosh(x) + 912\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (1020\|2 cosh(x) + 1368\|2 cosh(x) + 76\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (408\|2 cosh(x) + 912\|2 cosh(x) + 152\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 68\|2 cosh(x) + 228\|2 cosh(x) + 76\|2 cosh(x) + 12\|2 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 2\|2 sinh(x) + 16\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (56\|2 cosh(x) + 24\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (112\|2 cosh(x) + 144\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (140\|2 cosh(x) + 360\|2 cosh(x) + 76\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (112\|2 cosh(x) + 480\|2 cosh(x) + 304\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (56\|2 cosh(x) + 360\|2 cosh(x) + 456\|2 cosh(x) + 24\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 16\|2 cosh(x) + 144\|2 cosh(x) + 304\|2 cosh(x) +--R + +--R +-+ +--R 48\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 2\|2 cosh(x) + 24\|2 cosh(x) + 76\|2 cosh(x) + 24\|2 cosh(x) +--R + +--R +-+ +--R 2\|2 +--R * +--R 3 +--R tanh(x) +--R + +--R +-+ 6 +-+ 5 +--R - 272\|2 sinh(x) - 1632\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (- 4080\|2 cosh(x) - 912\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (- 5440\|2 cosh(x) - 3648\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 4080\|2 cosh(x) - 5472\|2 cosh(x) - 304\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 1632\|2 cosh(x) - 3648\|2 cosh(x) - 608\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R - 272\|2 cosh(x) - 912\|2 cosh(x) - 304\|2 cosh(x) - 48\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 4\|2 sinh(x) + 32\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (112\|2 cosh(x) + 48\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (224\|2 cosh(x) + 288\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (280\|2 cosh(x) + 720\|2 cosh(x) + 152\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (224\|2 cosh(x) + 960\|2 cosh(x) + 608\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (112\|2 cosh(x) + 720\|2 cosh(x) + 912\|2 cosh(x) + 48\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 32\|2 cosh(x) + 288\|2 cosh(x) + 608\|2 cosh(x) +--R + +--R +-+ +--R 96\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 4\|2 cosh(x) + 48\|2 cosh(x) + 152\|2 cosh(x) + 48\|2 cosh(x) +--R + +--R +-+ +--R 4\|2 +--R * +--R tanh(x) +--R + +--R +-+ 6 +-+ 5 +--R 272\|2 sinh(x) + 1632\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 4 +--R (4080\|2 cosh(x) + 912\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 3 +--R (5440\|2 cosh(x) + 3648\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (4080\|2 cosh(x) + 5472\|2 cosh(x) + 304\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (1632\|2 cosh(x) + 3648\|2 cosh(x) + 608\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 272\|2 cosh(x) + 912\|2 cosh(x) + 304\|2 cosh(x) + 48\|2 +--R / +--R +-+ 8 +-+ 7 +--R 8\|2 sinh(x) + 64\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (224\|2 cosh(x) + 96\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (448\|2 cosh(x) + 576\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (560\|2 cosh(x) + 1440\|2 cosh(x) + 304\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (448\|2 cosh(x) + 1920\|2 cosh(x) + 1216\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (224\|2 cosh(x) + 1440\|2 cosh(x) + 1824\|2 cosh(x) + 96\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 64\|2 cosh(x) + 576\|2 cosh(x) + 1216\|2 cosh(x) +--R + +--R +-+ +--R 192\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 8\|2 cosh(x) + 96\|2 cosh(x) + 304\|2 cosh(x) + 96\|2 cosh(x) +--R + +--R +-+ +--R 8\|2 +--R * +--R 4 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R - 32\|2 sinh(x) - 256\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (- 896\|2 cosh(x) - 384\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (- 1792\|2 cosh(x) - 2304\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (- 2240\|2 cosh(x) - 5760\|2 cosh(x) - 1216\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (- 1792\|2 cosh(x) - 7680\|2 cosh(x) - 4864\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 896\|2 cosh(x) - 5760\|2 cosh(x) - 7296\|2 cosh(x) - 384\|2 ) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 256\|2 cosh(x) - 2304\|2 cosh(x) - 4864\|2 cosh(x) +--R + +--R +-+ +--R - 768\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 32\|2 cosh(x) - 384\|2 cosh(x) - 1216\|2 cosh(x) +--R + +--R +-+ 2 +-+ +--R - 384\|2 cosh(x) - 32\|2 +--R * +--R 2 +--R tanh(x) +--R + +--R +-+ 8 +-+ 7 +--R 32\|2 sinh(x) + 256\|2 cosh(x)sinh(x) +--R + +--R +-+ 2 +-+ 6 +--R (896\|2 cosh(x) + 384\|2 )sinh(x) +--R + +--R +-+ 3 +-+ 5 +--R (1792\|2 cosh(x) + 2304\|2 cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ 4 +--R (2240\|2 cosh(x) + 5760\|2 cosh(x) + 1216\|2 )sinh(x) +--R + +--R +-+ 5 +-+ 3 +-+ 3 +--R (1792\|2 cosh(x) + 7680\|2 cosh(x) + 4864\|2 cosh(x))sinh(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (896\|2 cosh(x) + 5760\|2 cosh(x) + 7296\|2 cosh(x) + 384\|2 )sinh(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 256\|2 cosh(x) + 2304\|2 cosh(x) + 4864\|2 cosh(x) +--R + +--R +-+ +--R 768\|2 cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R 32\|2 cosh(x) + 384\|2 cosh(x) + 1216\|2 cosh(x) + 384\|2 cosh(x) +--R + +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 518 +--d0933:= D(m0933,x) +--E 170 + +--S 171 of 518 +t0934:= 1/(coth(x)^2-csch(x)^2) +--R +--R +--R 1 +--R (169) - ------------------- +--R 2 2 +--R csch(x) - coth(x) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 518 +r0934:= x +--R +--R +--R (170) x +--R Type: Variable(x) +--E 172 + +--S 173 of 518 +a0934:= integrate(t0934,x) +--R +--R +--R (171) x +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 518 +m0934:= a0934-r0934 +--R +--R +--R (172) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 518 +d0934:= D(m0934,x) +--R +--R +--R (173) 0 +--R Type: Expression(Integer) +--E 175 + +--S 176 of 518 +t0935:= 1/(coth(x)^2-csch(x)^2)^2 +--R +--R +--R 1 +--R (174) --------------------------------------- +--R 4 2 2 4 +--R csch(x) - 2coth(x) csch(x) + coth(x) +--R Type: Expression(Integer) +--E 176 + +--S 177 of 518 +r0935:= x +--R +--R +--R (175) x +--R Type: Variable(x) +--E 177 + +--S 178 of 518 +a0935:= integrate(t0935,x) +--R +--R +--R (176) x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 518 +m0935:= a0935-r0935 +--R +--R +--R (177) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 518 +d0935:= D(m0935,x) +--R +--R +--R (178) 0 +--R Type: Expression(Integer) +--E 180 + +--S 181 of 518 +t0936:= 1/(coth(x)^2-csch(x)^2)^3 +--R +--R +--R 1 +--R (179) - ----------------------------------------------------------- +--R 6 2 4 4 2 6 +--R csch(x) - 3coth(x) csch(x) + 3coth(x) csch(x) - coth(x) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 518 +r0936:= x +--R +--R +--R (180) x +--R Type: Variable(x) +--E 182 + +--S 183 of 518 +a0936:= integrate(t0936,x) +--R +--R +--R (181) x +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 518 +m0936:= a0936-r0936 +--R +--R +--R (182) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 518 +d0936:= D(m0936,x) +--R +--R +--R (183) 0 +--R Type: Expression(Integer) +--E 185 + +--S 186 of 518 +t0937:= ((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^3 +--R +--R +--R (184) +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (3c sinh(x) + 6b c cosh(x)sinh(x) + 3b cosh(x) - c + b )\|- c + b +--R + +--R 3 3 2 2 2 2 3 2 +--R c sinh(x) + 3b c cosh(x)sinh(x) + (3b c cosh(x) - 3c + 3b c)sinh(x) +--R + +--R 3 3 2 3 +--R b cosh(x) + (- 3b c + 3b )cosh(x) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 518 +r0937:= 5/2*(b^2-c^2)^(3/2)*x+5/2*c*(b^2-c^2)*cosh(x)+_ + 5/2*b*(b^2-c^2)*sinh(x)+5/6*(b^2-c^2)^(1/2)*(c*cosh(x)+_ + b*sinh(x))*((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))+_ + 1/3*(c*cosh(x)+b*sinh(x))*((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^2 +--R +--R +--R (185) +--R 2 2 2 2 +--R 9b c sinh(x) + (9c + 9b )cosh(x)sinh(x) + 9b c cosh(x) +--R + +--R 2 2 +--R (- 15c + 15b )x +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 2 3 3 2 2 +--R 2b c sinh(x) + (2c + 4b c)cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 3 +--R ((4b c + 2b )cosh(x) - 22b c + 22b )sinh(x) + 2b c cosh(x) +--R + +--R 3 2 +--R (- 22c + 22b c)cosh(x) +--R / +--R 6 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 518 +a0937:= integrate(t0937,x) +--R +--R +--R (186) +--R 2 2 5 2 2 4 +--R (9c + 18b c + 9b )sinh(x) + (45c + 90b c + 45b )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R ((90c + 180b c + 90b )cosh(x) + (- 60c + 60b )x)sinh(x) +--R + +--R 2 2 3 2 2 2 +--R ((90c + 180b c + 90b )cosh(x) + (- 180c + 180b )x cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (45c + 90b c + 45b )cosh(x) + (- 180c + 180b )x cosh(x) - 9c +--R + +--R 2 +--R 18b c - 9b +--R * +--R sinh(x) +--R + +--R 2 2 5 2 2 3 +--R (9c + 18b c + 9b )cosh(x) + (- 60c + 60b )x cosh(x) +--R + +--R 2 2 +--R (- 9c + 18b c - 9b )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 3 2 2 3 6 +--R (c + 3b c + 3b c + b )sinh(x) +--R + +--R 3 2 2 3 5 +--R (6c + 18b c + 18b c + 6b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((15c + 45b c + 45b c + 15b )cosh(x) - 45c - 45b c + 45b c + 45b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (20c + 60b c + 60b c + 20b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 180c - 180b c + 180b c + 180b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (15c + 45b c + 45b c + 15b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 270c - 270b c + 270b c + 270b )cosh(x) - 45c + 45b c + 45b c +--R + +--R 3 +--R - 45b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6c + 18b c + 18b c + 6b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 180c - 180b c + 180b c + 180b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 90c + 90b c + 90b c - 90b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (c + 3b c + 3b c + b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 45c - 45b c + 45b c + 45b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 45c + 45b c + 45b c - 45b )cosh(x) + c - 3b c + 3b c - b +--R / +--R 3 2 2 3 +--R 24sinh(x) + 72cosh(x)sinh(x) + 72cosh(x) sinh(x) + 24cosh(x) +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 518 +m0937:= a0937-r0937 +--R +--R +--R (187) +--R 2 2 5 2 2 4 +--R (9c - 18b c + 9b )sinh(x) + (9c - 18b c + 9b )cosh(x)sinh(x) +--R + +--R 2 2 2 3 +--R (- 18c + 36b c - 18b )cosh(x) sinh(x) +--R + +--R 2 2 3 2 +--R (- 18c + 36b c - 18b )cosh(x) sinh(x) +--R + +--R 2 2 4 2 2 +--R ((9c - 18b c + 9b )cosh(x) - 9c + 18b c - 9b )sinh(x) +--R + +--R 2 2 5 2 2 +--R (9c - 18b c + 9b )cosh(x) + (- 9c + 18b c - 9b )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 3 2 2 3 6 +--R (c - 5b c + 3b c + b )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 2c - 6b c + 2b c + 6b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((- 9c + 5b c - 3b c + 7b )cosh(x) - 45c + 43b c + 45b c - 43b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 4c + 4b c + 4b c - 4b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 92c + 84b c + 92b c - 84b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (7c - 3b c + 5b c - 9b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 6c - 6b c + 6b c + 6b )cosh(x) - 45c + 45b c + 45b c - 45b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (6c + 2b c - 6b c - 2b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (84c - 92b c - 84b c + 92b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 90c + 90b c + 90b c - 90b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 3 2 2 3 4 +--R (c + 3b c - 5b c + b )cosh(x) + (43c - 45b c - 43b c + 45b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 45c + 45b c + 45b c - 45b )cosh(x) + c - 3b c + 3b c - b +--R / +--R 3 2 2 3 +--R 24sinh(x) + 72cosh(x)sinh(x) + 72cosh(x) sinh(x) + 24cosh(x) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 518 +d0937:= D(m0937,x) +--R +--R +--R (188) +--R 2 2 5 +--R (- 18c + 36b c - 18b )sinh(x) +--R + +--R 2 2 4 +--R (- 18c + 36b c - 18b )cosh(x)sinh(x) +--R + +--R 2 2 2 3 +--R (36c - 72b c + 36b )cosh(x) sinh(x) +--R + +--R 2 2 3 2 +--R (36c - 72b c + 36b )cosh(x) sinh(x) +--R + +--R 2 2 4 2 2 +--R ((- 18c + 36b c - 18b )cosh(x) + 18c - 36b c + 18b )sinh(x) +--R + +--R 2 2 5 2 2 +--R (- 18c + 36b c - 18b )cosh(x) + (18c - 36b c + 18b )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 3 2 2 3 6 +--R (- 5c + 9b c - 7b c + 3b )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 6c - 2b c + 6b c + 2b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((5c - 33b c + 31b c - 3b )cosh(x) + 43c - 45b c - 43b c + 45b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (4c - 4b c - 4b c + 4b )cosh(x) +--R + +--R 3 2 2 3 +--R (84c - 92b c - 84b c + 92b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 3c + 31b c - 33b c + 5b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 6c - 6b c + 6b c + 6b )cosh(x) + 45c - 45b c - 45b c + 45b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (2c + 6b c - 2b c - 6b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 92c + 84b c + 92b c - 84b )cosh(x) +--R + +--R 3 2 2 3 +--R (90c - 90b c - 90b c + 90b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (3c - 7b c + 9b c - 5b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 45c + 43b c + 45b c - 43b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (45c - 45b c - 45b c + 45b )cosh(x) - 3c + 9b c - 9b c + 3b +--R / +--R 3 2 2 3 +--R 24sinh(x) + 72cosh(x)sinh(x) + 72cosh(x) sinh(x) + 24cosh(x) +--R Type: Expression(Integer) +--E 190 + +--S 191 of 518 +t0938:= 1/((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x)) +--R +--R +--R 1 +--R (189) ------------------------------------ +--R +---------+ +--R | 2 2 +--R \|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 191 + +--S 192 of 518 +r0938:= -2/(c+(b-(b^2-c^2)^(1/2))*tanh(1/2*x)) +--R +--R +--R 2 +--R (190) ----------------------------------- +--R +---------+ +--R x | 2 2 x +--R tanh(-)\|- c + b - b tanh(-) - c +--R 2 2 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 518 +a0938:= integrate(t0938,x) +--R +--R +--R 2 +--R (191) - ---------------------------------------------- +--R +---------+ +--R | 2 2 +--R \|- c + b + (c + b)sinh(x) + (c + b)cosh(x) +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 518 +m0938:= a0938-r0938 +--R +--R +--R (192) +--R +---------+ +--R x | 2 2 x +--R (- 2tanh(-) - 2)\|- c + b + 2b tanh(-) + (- 2c - 2b)sinh(x) +--R 2 2 +--R + +--R (- 2c - 2b)cosh(x) + 2c +--R / +--R +---------+ +--R x | 2 2 +--R (((c + b)sinh(x) + (c + b)cosh(x) - b)tanh(-) - c)\|- c + b +--R 2 +--R + +--R 2 2 2 2 x +--R ((- b c - b )sinh(x) + (- b c - b )cosh(x) - c + b )tanh(-) +--R 2 +--R + +--R 2 2 +--R (- c - b c)sinh(x) + (- c - b c)cosh(x) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 518 +d0938:= D(m0938,x) +--R +--R +--R (193) +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2b)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2b cosh(x) - c + b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R x 2 +--R (4c sinh(x) + 4c cosh(x))tanh(-) + (- c - b)sinh(x) +--R 2 +--R + +--R 2 +--R ((- 2c - 2b)cosh(x) + 2b)sinh(x) + (- c - b)cosh(x) + 2b cosh(x) + c +--R + +--R - b +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 2 2 2 2 +--R (- b c - b )sinh(x) + ((- 2b c - 2b )cosh(x) - 2b )sinh(x) +--R + +--R 2 2 2 2 +--R (- b c - b )cosh(x) - 2b cosh(x) + b c - b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R x 2 2 +--R (- 4b c sinh(x) - 4b c cosh(x))tanh(-) + (b c + b )sinh(x) +--R 2 +--R + +--R 2 2 2 2 2 +--R ((2b c + 2b )cosh(x) - 2b )sinh(x) + (b c + b )cosh(x) - 2b cosh(x) +--R + +--R 2 +--R - b c + b +--R / +--R 2 2 2 2 2 +--R (2b c + 2b )sinh(x) + ((4b c + 4b )cosh(x) + 2c - 4b )sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b c + 2b )cosh(x) + (2c - 4b )cosh(x) - 2b c + 2b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 +--R (2c + 2b c)sinh(x) + ((4c + 4b c)cosh(x) - 4b c)sinh(x) +--R + +--R 2 2 2 +--R (2c + 2b c)cosh(x) - 4b c cosh(x) - 2c + 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 2 +--R - 2c sinh(x) - 2c cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 3 2 2 3 2 +--R (c + b c - 2b c - 2b )sinh(x) +--R + +--R 3 2 2 3 2 3 +--R ((2c + 2b c - 4b c - 4b )cosh(x) - 4b c + 4b )sinh(x) +--R + +--R 3 2 2 3 2 2 3 3 2 +--R (c + b c - 2b c - 2b )cosh(x) + (- 4b c + 4b )cosh(x) - c + b c +--R + +--R 2 3 +--R 2b c - 2b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 +--R (- 2b c - 2b c)sinh(x) +--R + +--R 2 2 3 2 +--R ((- 4b c - 4b c)cosh(x) - 4c + 4b c)sinh(x) +--R + +--R 2 2 2 3 2 2 2 +--R (- 2b c - 2b c)cosh(x) + (- 4c + 4b c)cosh(x) + 2b c - 2b c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 2 +--R (- c - b c )sinh(x) + (- 2c - 2b c )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 +--R (- c - b c )cosh(x) + c - b c +--R Type: Expression(Integer) +--E 195 + +--S 196 of 518 +t0939:= 1/((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^2 +--R +--R +--R (194) +--R 1 +--R / +--R +---------+ +--R | 2 2 2 2 +--R (2c sinh(x) + 2b cosh(x))\|- c + b + c sinh(x) + 2b c cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R b cosh(x) - c + b +--R Type: Expression(Integer) +--E 196 + +--S 197 of 518 +r0939:= 1/3*(c*cosh(x)+b*sinh(x))/(b^2-c^2)^(1/2)/((b^2-c^2)^(1/2)+_ + b*cosh(x)+c*sinh(x))^2-2/3/(b^2-c^2)^(1/2)/_ + (c+(b-(b^2-c^2)^(1/2))*tanh(1/2*x)) +--R +--R +--R (195) +--R 2 x 2 2 +--R (b sinh(x) + b c cosh(x))tanh(-) - 2c sinh(x) +--R 2 +--R + +--R 2 2 2 2 2 +--R (- 4b c cosh(x) + b c)sinh(x) - 2b cosh(x) + c cosh(x) + 2c - 2b +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 2 3 3 2 x 3 2 +--R ((b c - b )sinh(x) + (c - b c)cosh(x))tanh(-) + (4c - 4b c)sinh(x) +--R 2 +--R + +--R 2 3 +--R (4b c - 4b )cosh(x) +--R / +--R 4 2 2 2 +--R (3c - 3b c )sinh(x) +--R + +--R 3 3 3 3 +--R ((6b c - 6b c)cosh(x) - 6b c + 6b c)sinh(x) +--R + +--R 2 2 4 2 2 2 4 4 2 2 4 +--R (3b c - 3b )cosh(x) + (- 6b c + 6b )cosh(x) - 3c + 6b c - 3b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 2 3 3 +--R (- 6c + 6b c )sinh(x) + (- 6b c + 6b c)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 4 3 2 2 +--R (- 3b c + 3b c )sinh(x) +--R + +--R 2 3 4 5 2 3 4 +--R ((- 6b c + 6b c)cosh(x) - 6c + 12b c - 6b c)sinh(x) +--R + +--R 3 2 5 2 4 3 2 5 4 +--R (- 3b c + 3b )cosh(x) + (- 6b c + 12b c - 6b )cosh(x) + 3b c +--R + +--R 3 2 5 +--R - 6b c + 3b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 2 3 2 4 3 2 +--R (- 3c + 3b c )sinh(x) + (- 6b c + 6b c )cosh(x)sinh(x) +--R + +--R 2 3 4 2 5 2 3 4 +--R (- 3b c + 3b c)cosh(x) + 3c - 6b c + 3b c +--R Type: Expression(Integer) +--E 197 + +--S 198 of 518 +a0939:= integrate(t0939,x) +--R +--R +--R (196) +--R +---------+ +--R | 2 2 +--R - 2\|- c + b + (- 6c - 6b)sinh(x) + (- 6c - 6b)cosh(x) +--R / +--R 2 2 2 2 2 +--R (9c + 18b c + 9b )sinh(x) + (18c + 36b c + 18b )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (9c + 18b c + 9b )cosh(x) - 3c + 3b +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 3 2 2 3 3 +--R (3c + 9b c + 9b c + 3b )sinh(x) +--R + +--R 3 2 2 3 2 +--R (9c + 27b c + 27b c + 9b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((9c + 27b c + 27b c + 9b )cosh(x) - 9c - 9b c + 9b c + 9b )sinh(x) +--R + +--R 3 2 2 3 3 3 2 2 3 +--R (3c + 9b c + 9b c + 3b )cosh(x) + (- 9c - 9b c + 9b c + 9b )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 518 +m0939:= a0939-r0939 +--R +--R +--R (197) +--R 2 2 3 4 4 +--R (- b c - 2b c - b )sinh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 +--R (- b c - 5b c - 7b c - 3b )cosh(x) - 6c - 3b c + 3b c +--R + +--R 3 4 +--R 3b c + 3b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 2 +--R (- 3b c - 9b c - 9b c - 3b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 9c - 21b c + 3b c + 21b c + 6b )cosh(x) + 14b c + b c +--R + +--R 3 4 +--R - 12b c - 3b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 3b c - 7b c - 5b c - b )cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 6c - 21b c - 3b c + 21b c + 9b )cosh(x) +--R + +--R 3 2 2 3 4 4 3 +--R (15b c + 19b c - 19b c - 15b )cosh(x) + 10c - 3b c +--R + +--R 2 2 3 4 +--R - 17b c + 3b c + 7b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- b c - 2b c - b c)cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 3c - 3b c - 3b c + 3b c + 6b )cosh(x) +--R + +--R 3 2 2 3 4 2 +--R (3b c + 12b c - b c - 14b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (7c + 3b c - 17b c - 3b c + 10b )cosh(x) - 2b c + 2b c +--R + +--R 3 4 +--R 2b c - 2b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 5 +--R (2c + 4b c + 2b c )sinh(x) +--R + +--R 4 3 2 2 3 3 2 2 3 4 +--R ((6c + 16b c + 14b c + 4b c)cosh(x) - b c - 2b c - b c)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (6c + 24b c + 32b c + 16b c + 2b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- c - 5b c - 7b c - 3b c)cosh(x) - 20c - 16b c + 18b c +--R + +--R 3 4 +--R 16b c + 2b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2c + 16b c + 32b c + 24b c + 6b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (- 3c - 9b c - 9b c - 3b c)cosh(x) +--R + +--R 4 3 2 2 3 4 4 3 +--R (- 36c - 60b c + 18b c + 60b c + 18b )cosh(x) + 14c + b c +--R + +--R 2 2 3 +--R - 12b c - 3b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 4 +--R (4b c + 14b c + 16b c + 6b )cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 3c - 7b c - 5b c - b c)cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 18c - 60b c - 18b c + 60b c + 36b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (15c + 19b c - 19b c - 15b c)cosh(x) + 10c - 4b c - 16b c +--R + +--R 3 4 +--R 4b c + 6b +--R * +--R sinh(x) +--R + +--R 2 2 3 4 5 4 3 2 2 4 +--R (2b c + 4b c + 2b )cosh(x) + (- c - 2b c - b c )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2c - 16b c - 18b c + 16b c + 20b )cosh(x) +--R + +--R 4 3 2 2 3 2 +--R (3c + 12b c - b c - 14b c)cosh(x) +--R + +--R 4 3 2 2 3 4 4 3 2 2 +--R (6c + 4b c - 16b c - 4b c + 10b )cosh(x) - 2c + 2b c + 2b c +--R + +--R 3 +--R - 2b c +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 4 2 3 4 5 4 +--R (- b c - 2b c + 2b c + b )sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- c - 5b c - 6b c + 2b c + 7b c + 3b )cosh(x) + 6b c +--R + +--R 2 3 3 2 4 5 +--R 3b c - 3b c - 3b c - 3b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 3c - 9b c - 6b c + 6b c + 9b c + 3b )cosh(x) +--R + +--R 4 2 3 3 2 4 5 5 4 +--R (9b c + 21b c - 3b c - 21b c - 6b )cosh(x) + 14c + b c +--R + +--R 2 3 3 2 4 5 +--R - 26b c - 4b c + 12b c + 3b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 3c - 7b c - 2b c + 6b c + 5b c + b )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (6b c + 21b c + 3b c - 21b c - 9b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (15c + 19b c - 34b c - 34b c + 19b c + 15b )cosh(x) - 10b c +--R + +--R 2 3 3 2 4 5 +--R 3b c + 17b c - 3b c - 7b +--R * +--R sinh(x) +--R + +--R 5 4 3 2 4 4 +--R (- c - 2b c + 2b c + b c)cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (3b c + 3b c + 3b c - 3b c - 6b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (3c + 12b c - 4b c - 26b c + b c + 14b )cosh(x) +--R + +--R 4 2 3 3 2 4 5 5 4 2 3 +--R (- 7b c - 3b c + 17b c + 3b c - 10b )cosh(x) - 2c + 2b c + 4b c +--R + +--R 3 2 4 5 +--R - 4b c - 2b c + 2b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 10c - 14b c + 6b c + 14b c + 4b c)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 4 +--R (- 24c - 52b c - 8b c + 48b c + 32b c + 4b )cosh(x) + 6c + 3b c +--R + +--R 2 3 3 2 4 +--R - 3b c - 3b c - 3b c +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 18c - 66b c - 48b c + 48b c + 66b c + 18b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 +--R (9c + 21b c - 3b c - 21b c - 6b c)cosh(x) + 20c + 4b c - 38b c +--R + +--R 3 2 4 5 +--R - 10b c + 18b c + 6b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 4c - 32b c - 48b c + 8b c + 52b c + 24b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (6c + 21b c + 3b c - 21b c - 9b c)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (24c + 28b c - 52b c - 52b c + 28b c + 24b )cosh(x) - 10c +--R + +--R 4 2 3 3 2 4 +--R 3b c + 17b c - 3b c - 7b c +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 4b c - 14b c - 6b c + 14b c + 10b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (3c + 3b c + 3b c - 3b c - 6b c)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (6c + 18b c - 10b c - 38b c + 4b c + 20b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 +--R (- 7c - 3b c + 17b c + 3b c - 10b c)cosh(x) - 2c + 2b c + 4b c +--R + +--R 3 2 4 5 +--R - 4b c - 2b c + 2b +--R / +--R 6 5 3 3 4 2 5 +--R (3c + 6b c - 6b c - 3b c )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (9c + 24b c + 12b c - 18b c - 21b c - 6b c)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 15b c - 21b c + 9b c + 21b c + 6b c +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (9c + 36b c + 39b c - 12b c - 45b c - 24b c - 3b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 36b c - 78b c - 12b c + 72b c + 48b c + 6b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R - 30c - 24b c + 57b c + 48b c - 24b c - 24b c - 3b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (3c + 24b c + 45b c + 12b c - 39b c - 36b c - 9b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (- 27b c - 99b c - 72b c + 72b c + 99b c + 27b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 6 +--R (- 54c - 90b c + 81b c + 180b c - 90b c - 27b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 30b c + 6b c - 57b c - 15b c + 27b c + 9b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (6b c + 21b c + 18b c - 12b c - 24b c - 9b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 6b c - 48b c - 72b c + 12b c + 78b c + 36b )cosh(x) +--R + +--R 6 5 3 3 4 2 5 6 2 +--R (- 27c - 90b c + 180b c + 81b c - 90b c - 54b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (36b c + 42b c - 78b c - 78b c + 42b c + 36b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 15c - 6b c - 39b c + 12b c + 33b c - 6b c - 9b +--R * +--R sinh(x) +--R + +--R 2 4 3 3 5 6 5 +--R (3b c + 6b c - 6b c - 3b )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 6b c - 21b c - 9b c + 21b c + 15b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 3c - 24b c - 24b c + 48b c + 57b c - 24b c - 30b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (9b c + 27b c - 15b c - 57b c + 6b c + 30b )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (9c + 6b c - 33b c - 12b c + 39b c + 6b c - 15b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 3b c + 3b c + 6b c - 6b c - 3b c + 3b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 15c - 21b c + 9b c + 21b c + 6b c )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (- 36c - 78b c - 12b c + 72b c + 48b c + 6b c)cosh(x)sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 27c - 99b c - 72b c + 72b c + 99b c + 27b c)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 30c + 6b c - 57b c - 15b c + 27b c + 9b c +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (- 6c - 48b c - 72b c + 12b c + 78b c + 36b c)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (36c + 42b c - 78b c - 78b c + 42b c + 36b c)cosh(x) +--R * +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 6b c - 21b c - 9b c + 21b c + 15b c)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 6 +--R (9c + 27b c - 15b c - 57b c + 6b c + 30b c)cosh(x) - 3c +--R + +--R 5 2 4 3 3 4 2 5 +--R 3b c + 6b c - 6b c - 3b c + 3b c +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 6 2 5 4 3 5 2 5 +--R (- 3b c - 6b c + 6b c + 3b c )sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 9b c - 24b c - 12b c + 18b c + 21b c + 6b c)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 15c - 21b c + 24b c + 42b c - 3b c - 21b c - 6b c +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 9b c - 36b c - 39b c + 12b c + 45b c + 24b c + 3b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 36c - 78b c + 24b c + 150b c + 60b c - 66b c - 48b c +--R + +--R 7 +--R - 6b +--R * +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R 30b c + 24b c - 57b c - 48b c + 24b c + 24b c + 3b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 3b c - 24b c - 45b c - 12b c + 39b c + 36b c + 9b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 27c - 99b c - 45b c + 171b c + 171b c - 45b c - 99b c +--R + +--R 7 +--R - 27b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 6 7 7 +--R (54b c + 90b c - 81b c - 180b c + 90b c + 27b )cosh(x) + 30c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R 6b c - 87b c - 21b c + 84b c + 24b c - 27b c - 9b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 4 +--R (- 6b c - 21b c - 18b c + 12b c + 24b c + 9b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 6c - 48b c - 66b c + 60b c + 150b c + 24b c - 78b c +--R + +--R 7 +--R - 36b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 2 5 4 3 5 2 6 7 2 +--R (27b c + 90b c - 180b c - 81b c + 90b c + 54b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 36c + 42b c - 114b c - 120b c + 120b c + 114b c - 42b c +--R + +--R 7 +--R - 36b +--R * +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R - 15b c + 6b c + 39b c - 12b c - 33b c + 6b c + 9b +--R * +--R sinh(x) +--R + +--R 3 4 4 3 6 7 5 +--R (- 3b c - 6b c + 6b c + 3b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 4 +--R (- 6b c - 21b c - 3b c + 42b c + 24b c - 21b c - 15b )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (3b c + 24b c + 24b c - 48b c - 57b c + 24b c + 30b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (9c + 27b c - 24b c - 84b c + 21b c + 87b c - 6b c - 30b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 9b c - 6b c + 33b c + 12b c - 39b c - 6b c + 15b )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R - 3c + 3b c + 9b c - 9b c - 9b c + 9b c + 3b c - 3b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 7 6 3 4 4 3 5 +--R (- 3c - 6b c + 6b c + 3b c )sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (- 9c - 24b c - 12b c + 18b c + 21b c + 6b c )cosh(x)sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 2 +--R (- 9c - 36b c - 39b c + 12b c + 45b c + 24b c + 3b c)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 30c + 24b c - 57b c - 48b c + 24b c + 24b c + 3b c +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (- 3c - 24b c - 45b c - 12b c + 39b c + 36b c + 9b c)cosh(x) +--R + +--R 7 6 2 5 3 4 5 2 6 +--R (54c + 90b c - 81b c - 180b c + 90b c + 27b c)cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 4 +--R (- 6b c - 21b c - 18b c + 12b c + 24b c + 9b c)cosh(x) +--R + +--R 7 6 3 4 4 3 5 2 6 2 7 +--R (27c + 90b c - 180b c - 81b c + 90b c + 54b c)cosh(x) - 15c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 6b c + 39b c - 12b c - 33b c + 6b c + 9b c +--R * +--R sinh(x) +--R + +--R 2 5 3 4 5 2 6 5 +--R (- 3b c - 6b c + 6b c + 3b c)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (3c + 24b c + 24b c - 48b c - 57b c + 24b c + 30b c)cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (- 9c - 6b c + 33b c + 12b c - 39b c - 6b c + 15b c)cosh(x) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 518 +--d0939:= D(m0939,x) +--E 200 + +--S 201 of 518 +t0940:= 1/((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^3 +--R +--R +--R (198) +--R 1 +--R / +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (3c sinh(x) + 6b c cosh(x)sinh(x) + 3b cosh(x) - c + b )\|- c + b +--R + +--R 3 3 2 2 2 2 3 2 +--R c sinh(x) + 3b c cosh(x)sinh(x) + (3b c cosh(x) - 3c + 3b c)sinh(x) +--R + +--R 3 3 2 3 +--R b cosh(x) + (- 3b c + 3b )cosh(x) +--R Type: Expression(Integer) +--E 201 + +--S 202 of 518 +r0940:= 1/5*(c*cosh(x)+b*sinh(x))/(b^2-c^2)^(1/2)/((b^2-c^2)^(1/2)+_ + b*cosh(x)+c*sinh(x))^3+2/15*(c*cosh(x)+_ + b*sinh(x))/(b^2-c^2)/((b^2-c^2)^(1/2)+b*cosh(x)+_ + c*sinh(x))^2-4/15/(b^2-c^2)/(c+(b-(b^2-c^2)^(1/2))*tanh(1/2*x)) +--R +--R +--R (199) +--R 2 3 4 +--R - 2b c sinh(x) +--R + +--R 4 3 2 4 3 2 3 +--R ((- 2b c - 6b c )cosh(x) - 9b c + 9b c )sinh(x) +--R + +--R 2 3 4 2 5 2 3 4 +--R (- 6b c - 6b c)cosh(x) + (- 9c - 9b c + 18b c)cosh(x) +--R + +--R 2 3 4 +--R 12b c - 12b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (- 6b c - 2b )cosh(x) + (- 18b c + 9b c + 9b )cosh(x) +--R + +--R 4 5 4 3 2 5 +--R (12b c - 12b )cosh(x) + 5b c - 10b c + 5b +--R * +--R sinh(x) +--R + +--R 4 4 2 3 4 3 +--R - 2b c cosh(x) + (- 9b c + 9b c)cosh(x) +--R + +--R 2 3 4 2 5 2 3 4 +--R (12b c - 12b c)cosh(x) + (5c - 10b c + 5b c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 5 4 4 4 +--R 4c sinh(x) + (20b c cosh(x) - 2b c )sinh(x) +--R + +--R 2 3 2 5 2 3 5 2 3 3 +--R (40b c cosh(x) + (- 2c - 6b c )cosh(x) - 40c + 40b c )sinh(x) +--R + +--R 3 2 3 4 3 2 2 +--R 40b c cosh(x) + (- 6b c - 6b c )cosh(x) +--R + +--R 4 3 2 4 3 2 +--R (- 120b c + 120b c )cosh(x) + 12b c - 12b c +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 2 3 4 3 +--R 20b c cosh(x) + (- 6b c - 2b c)cosh(x) +--R + +--R 2 3 4 2 5 4 5 +--R (- 120b c + 120b c)cosh(x) + (12c - 12b c)cosh(x) + 20c +--R + +--R 2 3 4 +--R - 40b c + 20b c +--R * +--R sinh(x) +--R + +--R 5 5 3 2 4 3 2 5 3 +--R 4b cosh(x) - 2b c cosh(x) + (- 40b c + 40b )cosh(x) +--R + +--R 4 3 2 2 4 3 2 5 +--R (12b c - 12b c )cosh(x) + (20b c - 40b c + 20b )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 5 3 3 4 +--R (- 2b c + 2b c )sinh(x) +--R + +--R 6 2 4 4 2 2 4 4 2 3 +--R ((- 2c - 4b c + 6b c )cosh(x) + 9b c - 9b c )sinh(x) +--R + +--R 5 5 2 5 3 3 5 +--R (- 6b c + 6b c)cosh(x) + (9b c + 9b c - 18b c)cosh(x) +--R + +--R 5 3 3 5 +--R 12b c - 24b c + 12b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (- 6b c + 4b c + 2b )cosh(x) + (18b c - 9b c - 9b )cosh(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 6 +--R (12c - 12b c - 12b c + 12b )cosh(x) - 5b c + 10b c - 5b +--R * +--R sinh(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (- 2b c + 2b c)cosh(x) + (9b c - 9b c)cosh(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (12b c - 24b c + 12b c)cosh(x) + (- 5b c + 10b c - 5b c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 6 2 4 4 +--R (- 20c + 20b c )sinh(x) +--R + +--R 5 3 3 5 3 3 3 +--R ((- 80b c + 80b c )cosh(x) + 9b c - 9b c )sinh(x) +--R + +--R 2 4 4 2 2 6 2 4 4 2 6 +--R (- 120b c + 120b c )cosh(x) + (9c + 9b c - 18b c )cosh(x) + 40c +--R + +--R 2 4 4 2 +--R - 80b c + 40b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 5 3 5 3 3 5 2 +--R (- 80b c + 80b c)cosh(x) + (18b c - 9b c - 9b c)cosh(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (80b c - 160b c + 80b c)cosh(x) - 5b c + 10b c - 5b c +--R * +--R sinh(x) +--R + +--R 4 2 6 4 2 4 4 2 3 +--R (- 20b c + 20b )cosh(x) + (9b c - 9b c )cosh(x) +--R + +--R 2 4 4 2 6 2 6 2 4 4 2 6 +--R (40b c - 80b c + 40b )cosh(x) + (- 5c + 10b c - 5b c )cosh(x) - 4c +--R + +--R 2 4 4 2 6 +--R 12b c - 12b c + 4b +--R / +--R 7 3 5 5 +--R (15b c - 15b c )sinh(x) +--R + +--R 2 6 4 4 8 2 6 4 4 4 +--R ((75b c - 75b c )cosh(x) + 75c - 150b c + 75b c )sinh(x) +--R + +--R 3 5 5 3 2 +--R (150b c - 150b c )cosh(x) +--R + +--R 7 3 5 5 3 7 3 5 +--R (300b c - 600b c + 300b c )cosh(x) - 150b c + 300b c +--R + +--R 5 3 +--R - 150b c +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 6 2 3 +--R (150b c - 150b c )cosh(x) +--R + +--R 2 6 4 4 6 2 2 +--R (450b c - 900b c + 450b c )cosh(x) +--R + +--R 2 6 4 4 6 2 8 2 6 +--R (- 450b c + 900b c - 450b c )cosh(x) - 150c + 450b c +--R + +--R 4 4 6 2 +--R - 450b c + 150b c +--R * +--R 2 +--R sinh(x) +--R + +--R 5 3 7 4 +--R (75b c - 75b c)cosh(x) +--R + +--R 3 5 5 3 7 3 +--R (300b c - 600b c + 300b c)cosh(x) +--R + +--R 3 5 5 3 7 2 +--R (- 450b c + 900b c - 450b c)cosh(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 300b c + 900b c - 900b c + 300b c)cosh(x) + 75b c +--R + +--R 3 5 5 3 7 +--R - 225b c + 225b c - 75b c +--R * +--R sinh(x) +--R + +--R 6 2 8 5 4 4 6 2 8 4 +--R (15b c - 15b )cosh(x) + (75b c - 150b c + 75b )cosh(x) +--R + +--R 4 4 6 2 8 3 +--R (- 150b c + 300b c - 150b )cosh(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 150b c + 450b c - 450b c + 150b )cosh(x) +--R + +--R 2 6 4 4 6 2 8 8 2 6 +--R (75b c - 225b c + 225b c - 75b )cosh(x) + 15c - 60b c +--R + +--R 4 4 6 2 8 +--R 90b c - 60b c + 15b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 8 2 6 5 7 3 5 4 +--R (15c - 15b c )sinh(x) + (75b c - 75b c )cosh(x)sinh(x) +--R + +--R 2 6 4 4 2 8 2 6 4 4 3 +--R ((150b c - 150b c )cosh(x) - 150c + 300b c - 150b c )sinh(x) +--R + +--R 3 5 5 3 3 +--R (150b c - 150b c )cosh(x) +--R + +--R 7 3 5 5 3 +--R (- 450b c + 900b c - 450b c )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 6 2 4 +--R (75b c - 75b c )cosh(x) +--R + +--R 2 6 4 4 6 2 2 8 2 6 +--R (- 450b c + 900b c - 450b c )cosh(x) + 75c - 225b c +--R + +--R 4 4 6 2 +--R 225b c - 75b c +--R * +--R sinh(x) +--R + +--R 5 3 7 5 3 5 5 3 7 3 +--R (15b c - 15b c)cosh(x) + (- 150b c + 300b c - 150b c)cosh(x) +--R + +--R 7 3 5 5 3 7 +--R (75b c - 225b c + 225b c - 75b c)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 9 2 7 4 5 5 +--R (15c - 30b c + 15b c )sinh(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 +--R ((75b c - 150b c + 75b c )cosh(x) - 75b c + 150b c - 75b c ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 7 4 5 6 3 2 +--R (150b c - 300b c + 150b c )cosh(x) +--R + +--R 2 7 4 5 6 3 9 2 7 +--R (- 300b c + 600b c - 300b c )cosh(x) - 150c + 450b c +--R + +--R 4 5 6 3 +--R - 450b c + 150b c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (150b c - 300b c + 150b c )cosh(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 450b c + 900b c - 450b c )cosh(x) +--R + +--R 8 3 6 5 4 7 2 8 +--R (- 450b c + 1350b c - 1350b c + 450b c )cosh(x) + 150b c +--R + +--R 3 6 5 4 7 2 +--R - 450b c + 450b c - 150b c +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (75b c - 150b c + 75b c)cosh(x) +--R + +--R 4 5 6 3 8 3 +--R (- 300b c + 600b c - 300b c)cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 450b c + 1350b c - 1350b c + 450b c)cosh(x) +--R + +--R 2 7 4 5 6 3 8 9 2 7 +--R (300b c - 900b c + 900b c - 300b c)cosh(x) + 75c - 300b c +--R + +--R 4 5 6 3 8 +--R 450b c - 300b c + 75b c +--R * +--R sinh(x) +--R + +--R 5 4 7 2 9 5 +--R (15b c - 30b c + 15b )cosh(x) +--R + +--R 5 4 7 2 9 4 +--R (- 75b c + 150b c - 75b )cosh(x) +--R + +--R 3 6 5 4 7 2 9 3 +--R (- 150b c + 450b c - 450b c + 150b )cosh(x) +--R + +--R 3 6 5 4 7 2 9 2 +--R (150b c - 450b c + 450b c - 150b )cosh(x) +--R + +--R 8 3 6 5 4 7 2 9 8 +--R (75b c - 300b c + 450b c - 300b c + 75b )cosh(x) - 15b c +--R + +--R 3 6 5 4 7 2 9 +--R 60b c - 90b c + 60b c - 15b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 9 2 7 4 5 4 +--R (- 75c + 150b c - 75b c )sinh(x) +--R + +--R 8 3 6 5 4 3 +--R (- 300b c + 600b c - 300b c )cosh(x)sinh(x) +--R + +--R 2 7 4 5 6 3 2 9 2 7 4 5 +--R (- 450b c + 900b c - 450b c )cosh(x) + 150c - 450b c + 450b c +--R + +--R 6 3 +--R - 150b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 300b c + 600b c - 300b c )cosh(x) +--R + +--R 8 3 6 5 4 7 2 +--R (300b c - 900b c + 900b c - 300b c )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 5 6 3 8 4 +--R (- 75b c + 150b c - 75b c)cosh(x) +--R + +--R 2 7 4 5 6 3 8 2 9 2 7 4 5 +--R (150b c - 450b c + 450b c - 150b c)cosh(x) - 15c + 60b c - 90b c +--R + +--R 6 3 8 +--R 60b c - 15b c +--R Type: Expression(Integer) +--E 202 + +--S 203 of 518 +a0940:= integrate(t0940,x) +--R +--R +--R (200) +--R +---------+ +--R | 2 2 2 +--R (- 20sinh(x) - 20cosh(x))\|- c + b + (- 40c - 40b)sinh(x) +--R + +--R 2 +--R (- 80c - 80b)cosh(x)sinh(x) + (- 40c - 40b)cosh(x) + 4c - 4b +--R / +--R 3 2 2 3 4 +--R (75c + 225b c + 225b c + 75b )sinh(x) +--R + +--R 3 2 2 3 3 +--R (300c + 900b c + 900b c + 300b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (450c + 1350b c + 1350b c + 450b )cosh(x) - 150c - 150b c +--R + +--R 2 3 +--R 150b c + 150b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (300c + 900b c + 900b c + 300b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 300c - 300b c + 300b c + 300b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (75c + 225b c + 225b c + 75b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 150c - 150b c + 150b c + 150b )cosh(x) + 15c - 15b c - 15b c +--R + +--R 3 +--R 15b +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 4 3 2 2 3 4 5 +--R (15c + 60b c + 90b c + 60b c + 15b )sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (75c + 300b c + 450b c + 300b c + 75b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (150c + 600b c + 900b c + 600b c + 150b )cosh(x) - 150c +--R + +--R 3 3 4 +--R - 300b c + 300b c + 150b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (150c + 600b c + 900b c + 600b c + 150b )cosh(x) +--R + +--R 4 3 3 4 +--R (- 450c - 900b c + 900b c + 450b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (75c + 300b c + 450b c + 300b c + 75b )cosh(x) +--R + +--R 4 3 3 4 2 4 2 2 4 +--R (- 450c - 900b c + 900b c + 450b )cosh(x) + 75c - 150b c + 75b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (15c + 60b c + 90b c + 60b c + 15b )cosh(x) +--R + +--R 4 3 3 4 3 +--R (- 150c - 300b c + 300b c + 150b )cosh(x) +--R + +--R 4 2 2 4 +--R (75c - 150b c + 75b )cosh(x) +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 518 +m0940:= a0940-r0940 +--R +--R +--R (201) +--R 2 6 3 5 4 4 5 3 9 +--R (2b c + 6b c + 6b c + 2b c )sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (2b c + 16b c + 42b c + 50b c + 28b c + 6b c )cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 19b c + 47b c + 18b c - 38b c - 37b c - 9b c +--R * +--R 8 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 10b c + 56b c + 138b c + 184b c + 134b c + 48b c +--R + +--R 7 +--R 6b c +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 19c + 132b c + 281b c + 166b c - 171b c - 280b c +--R + +--R 6 2 7 +--R - 129b c - 18b c +--R * +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R - 40b c - 77b c - 106b c - 4b c + 134b c + 81b c + 12b c +--R * +--R 7 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 20b c + 110b c + 276b c + 398b c + 340b c + 162b c +--R + +--R 7 8 +--R 36b c + 2b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 85c + 413b c + 804b c + 595b c - 304b c - 861b c +--R + +--R 6 2 7 8 +--R - 576b c - 147b c - 9b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 157b c - 646b c - 686b c - 2b c + 657b c + 636b c +--R + +--R 7 8 +--R 186b c + 12b +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 220c - 155b c + 195b c + 255b c + 245b c - 25b c +--R + +--R 6 2 7 8 +--R - 215b c - 75b c - 5b +--R * +--R 6 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 20b c + 130b c + 360b c + 562b c + 536b c + 306b c +--R + +--R 7 8 +--R 92b c + 10b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 150c + 730b c + 1439b c + 1212b c - 247b c +--R + +--R 5 3 6 2 7 8 +--R - 1478b c - 1287b c - 464b c - 55b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 340b c - 1612b c - 2256b c - 389b c + 1774b c +--R + +--R 6 2 7 8 +--R 1896b c + 822b c + 105b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 595c - 1680b c + 70b c + 2660b c + 1640b c +--R + +--R 5 3 6 2 7 8 +--R - 360b c - 1030b c - 620b c - 85b +--R * +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 504b c + 137b c - 736b c - 355b c + 70b c + 185b c +--R + +--R 7 8 +--R 170b c + 25b +--R * +--R 5 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 10b c + 92b c + 306b c + 536b c + 562b c + 360b c +--R + +--R 7 8 +--R 130b c + 20b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 +--R 130c + 765b c + 1700b c + 1625b c - 1625b c +--R + +--R 6 2 7 8 +--R - 1700b c - 765b c - 130b +--R * +--R 4 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 450b c - 2080b c - 3745b c - 1650b c + 2510b c +--R + +--R 6 2 7 8 +--R 3410b c + 1685b c + 320b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 775c - 3525b c - 2405b c + 5385b c + 6655b c +--R + +--R 5 3 6 2 7 8 +--R - 95b c - 3095b c - 1765b c - 380b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 1145b c + 2330b c - 1715b c - 4110b c - 355b c +--R + +--R 6 2 7 8 +--R 1600b c + 885b c + 220b +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 620c - 23b c - 1599b c - 160b c + 1324b c + 353b c +--R + +--R 6 2 7 8 +--R - 295b c - 170b c - 50b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 2b c + 36b c + 162b c + 340b c + 398b c + 276b c +--R + +--R 7 8 +--R 110b c + 20b +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 55c + 464b c + 1287b c + 1478b c + 247b c - 1212b c +--R + +--R 6 2 7 8 +--R - 1439b c - 730b c - 150b +--R * +--R 5 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 320b c - 1685b c - 3410b c - 2510b c + 1650b c +--R + +--R 6 2 7 8 +--R 3745b c + 2080b c + 450b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 700c - 3220b c - 4560b c + 3220b c + 10520b c +--R + +--R 5 3 6 2 7 8 +--R 3220b c - 4560b c - 3220b c - 700b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 1050b c + 4280b c + 950b c - 8220b c - 4750b c +--R + +--R 6 2 7 8 +--R 3260b c + 2830b c + 600b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 1217c + 1716b c - 3839b c - 4618b c + 3613b c +--R + +--R 5 3 6 2 7 8 +--R 4232b c - 721b c - 1330b c - 270b +--R * +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 440b c + 161b c + 1078b c - 210b c - 898b c - b c +--R + +--R 7 8 +--R 260b c + 50b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 6b c + 48b c + 134b c + 184b c + 138b c + 56b c +--R + +--R 8 +--R 10b +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 9c + 147b c + 576b c + 861b c + 304b c - 595b c +--R + +--R 6 2 7 8 +--R - 804b c - 413b c - 85b +--R * +--R 6 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 105b c - 822b c - 1896b c - 1774b c + 389b c +--R + +--R 6 2 7 8 +--R 2256b c + 1612b c + 340b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 380c - 1765b c - 3095b c - 95b c + 6655b c +--R + +--R 5 3 6 2 7 8 +--R 5385b c - 2405b c - 3525b c - 775b +--R * +--R 4 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 600b c + 2830b c + 3260b c - 4750b c - 8220b c +--R + +--R 6 2 7 8 +--R 950b c + 4280b c + 1050b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 +--R 835c + 2791b c - 1562b c - 8589b c + 8589b c +--R + +--R 6 2 7 8 +--R 1562b c - 2791b c - 835b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 719b c - 602b c + 2492b c + 1378b c - 2641b c +--R + +--R 6 2 7 8 +--R - 1136b c + 868b c + 360b +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 180c + 143b c + 549b c - 373b c - 623b c + 317b c +--R + +--R 6 2 7 8 +--R 319b c - 87b c - 65b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 8 +--R (6b c + 28b c + 50b c + 42b c + 16b c + 2b )cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 18b c + 129b c + 280b c + 171b c - 166b c - 281b c +--R + +--R 7 8 +--R - 132b c - 19b +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 12b c - 186b c - 636b c - 657b c + 2b c + 686b c +--R + +--R 7 8 +--R 646b c + 157b +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 85c - 620b c - 1030b c - 360b c + 1640b c +--R + +--R 5 3 6 2 7 8 +--R 2660b c + 70b c - 1680b c - 595b +--R * +--R 5 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 220b c + 885b c + 1600b c - 355b c - 4110b c +--R + +--R 6 2 7 8 +--R - 1715b c + 2330b c + 1145b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 270c + 1330b c + 721b c - 4232b c - 3613b c +--R + +--R 5 3 6 2 7 8 +--R 4618b c + 3839b c - 1716b c - 1217b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 360b c - 868b c + 1136b c + 2641b c - 1378b c +--R + +--R 6 2 7 8 +--R - 2492b c + 602b c + 719b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 217c - 56b c + 980b c + 56b c - 1526b c + 56b c +--R + +--R 6 2 7 8 +--R 980b c - 56b c - 217b +--R * +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 40b c - 55b c - 90b c + 135b c + 60b c - 105b c - 10b c +--R + +--R 8 +--R 25b +--R * +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 9 +--R (2b c + 6b c + 6b c + 2b c)cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (9b c + 37b c + 38b c - 18b c - 47b c - 19b c)cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (- 12b c - 81b c - 134b c + 4b c + 106b c + 77b c + 40b ) +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 5c - 75b c - 215b c - 25b c + 245b c + 255b c +--R + +--R 6 2 7 8 +--R 195b c - 155b c - 220b +--R * +--R 6 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 25b c + 170b c + 185b c + 70b c - 355b c - 736b c +--R + +--R 7 8 +--R 137b c + 504b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 50c + 170b c + 295b c - 353b c - 1324b c + 160b c +--R + +--R 6 2 7 8 +--R 1599b c + 23b c - 620b +--R * +--R 4 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 50b c - 260b c + b c + 898b c + 210b c - 1078b c +--R + +--R 7 8 +--R - 161b c + 440b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 65c - 87b c + 319b c + 317b c - 623b c - 373b c +--R + +--R 6 2 7 8 +--R 549b c + 143b c - 180b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 25b c - 10b c - 105b c + 60b c + 135b c - 90b c - 55b c +--R + +--R 8 +--R 40b +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R 4c - 8b c - 8b c + 24b c - 24b c + 8b c + 8b c - 4b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 8 7 2 6 3 5 10 +--R (- 4c - 12b c - 12b c - 4b c )sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 7 +--R (- 20c - 80b c - 120b c - 80b c - 20b c )cosh(x) + 2b c +--R + +--R 2 6 3 5 4 4 +--R 6b c + 6b c + 2b c +--R * +--R 9 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 2 +--R (- 40c - 220b c - 460b c - 460b c - 220b c - 40b c )cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 8 +--R (2c + 16b c + 42b c + 50b c + 28b c + 6b c )cosh(x) + 180c +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 360b c + 40b c - 320b c - 220b c - 40b c +--R * +--R 8 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 40c - 320b c - 920b c - 1280b c - 920b c - 320b c +--R + +--R 6 2 +--R - 40b c +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R (10c + 56b c + 138b c + 184b c + 134b c + 48b c + 6b c ) +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 720c + 2240b c + 1640b c - 1280b c - 2240b c - 960b c +--R + +--R 6 2 +--R - 120b c +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 40c - 77b c - 106b c - 4b c + 134b c + 81b c + 12b c +--R * +--R 7 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 20c - 260b c - 1060b c - 2020b c - 2020b c - 1060b c +--R + +--R 6 2 7 +--R - 260b c - 20b c +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 20c + 110b c + 276b c + 398b c + 340b c + 162b c +--R + +--R 6 2 7 +--R 36b c + 2b c +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 1120c + 5320b c + 7400b c + 440b c - 6960b c - 5640b c +--R + +--R 6 2 7 +--R - 1560b c - 120b c +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 157c - 646b c - 686b c - 2b c + 657b c + 636b c +--R + +--R 6 2 7 +--R 186b c + 12b c +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 840c - 840b c + 1400b c + 1680b c - 300b c - 820b c +--R + +--R 6 2 7 +--R - 260b c - 20b c +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 4c - 112b c - 712b c - 1904b c - 2600b c - 1904b c +--R + +--R 6 2 7 8 +--R - 712b c - 112b c - 4b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 20c + 130b c + 360b c + 562b c + 536b c + 306b c +--R + +--R 6 2 7 +--R 92b c + 10b c +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 840c + 6240b c + 13960b c + 8800b c - 8080b c +--R + +--R 5 3 6 2 7 8 +--R - 13920b c - 6680b c - 1120b c - 40b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 340c - 1612b c - 2256b c - 389b c + 1774b c + 1896b c +--R + +--R 6 2 7 +--R 822b c + 105b c +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 2520c - 5600b c + 1960b c + 10560b c + 3700b c +--R + +--R 5 3 6 2 7 8 +--R - 4400b c - 3120b c - 560b c - 20b +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 504c + 137b c - 736b c - 355b c + 70b c + 185b c + 170b c +--R + +--R 7 +--R 25b c +--R * +--R 5 +--R sinh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 20b c - 260b c - 1060b c - 2020b c - 2020b c +--R + +--R 6 2 7 8 +--R - 1060b c - 260b c - 20b +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 10c + 92b c + 306b c + 536b c + 562b c + 360b c +--R + +--R 6 2 7 +--R 130b c + 20b c +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 +--R 300c + 3800b c + 13400b c + 16600b c - 16600b c +--R + +--R 6 2 7 8 +--R - 13400b c - 3800b c - 300b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 450c - 2080b c - 3745b c - 1650b c + 2510b c +--R + +--R 5 3 6 2 7 +--R 3410b c + 1685b c + 320b c +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 2800c - 11200b c - 6000b c + 18800b c + 20000b c +--R + +--R 5 3 6 2 7 8 +--R - 3900b c - 10900b c - 3700b c - 300b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 1145c + 2330b c - 1715b c - 4110b c - 355b c + 1600b c +--R + +--R 6 2 7 +--R 885b c + 220b c +--R * +--R cosh(x) +--R + +--R 8 2 6 3 5 4 4 5 3 6 2 +--R 840c - 2240b c - 280b c + 1980b c + 520b c - 560b c +--R + +--R 7 8 +--R - 240b c - 20b +--R * +--R 4 +--R sinh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 40b c - 320b c - 920b c - 1280b c - 920b c - 320b c +--R + +--R 8 +--R - 40b +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 2c + 36b c + 162b c + 340b c + 398b c + 276b c +--R + +--R 6 2 7 +--R 110b c + 20b c +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 40c + 1120b c + 6680b c + 13920b c + 8080b c - 8800b c +--R + +--R 6 2 7 8 +--R - 13960b c - 6240b c - 840b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 320c - 1685b c - 3410b c - 2510b c + 1650b c +--R + +--R 5 3 6 2 7 +--R 3745b c + 2080b c + 450b c +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 1400c - 9600b c - 14600b c + 9600b c + 32000b c +--R + +--R 5 3 6 2 7 8 +--R 9600b c - 14600b c - 9600b c - 1400b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 1050c + 4280b c + 950b c - 8220b c - 4750b c + 3260b c +--R + +--R 6 2 7 +--R 2830b c + 600b c +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 1680c + 2240b c - 5320b c - 6080b c + 5160b c + 5600b c +--R + +--R 6 2 7 8 +--R - 1240b c - 1760b c - 280b +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 440c + 161b c + 1078b c - 210b c - 898b c - b c + 260b c +--R + +--R 7 +--R 50b c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 8 +--R (- 40b c - 220b c - 460b c - 460b c - 220b c - 40b )cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R (6b c + 48b c + 134b c + 184b c + 138b c + 56b c + 10b c) +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 120b c + 1560b c + 5640b c + 6960b c - 440b c - 7400b c +--R + +--R 7 8 +--R - 5320b c - 1120b +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 105c - 822b c - 1896b c - 1774b c + 389b c + 2256b c +--R + +--R 6 2 7 +--R 1612b c + 340b c +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 300c - 3700b c - 10900b c - 3900b c + 20000b c +--R + +--R 5 3 6 2 7 8 +--R 18800b c - 6000b c - 11200b c - 2800b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 600c + 2830b c + 3260b c - 4750b c - 8220b c + 950b c +--R + +--R 6 2 7 +--R 4280b c + 1050b c +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 +--R 1120c + 3640b c - 2120b c - 11160b c + 11160b c +--R + +--R 6 2 7 8 +--R 2120b c - 3640b c - 1120b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 719c - 602b c + 2492b c + 1378b c - 2641b c - 1136b c +--R + +--R 6 2 7 +--R 868b c + 360b c +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 180c + 180b c + 500b c - 460b c - 500b c + 380b c +--R + +--R 6 2 7 8 +--R 220b c - 100b c - 40b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 5 3 6 2 7 8 9 +--R (- 20b c - 80b c - 120b c - 80b c - 20b )cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (6b c + 28b c + 50b c + 42b c + 16b c + 2b c)cosh(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 120b c + 960b c + 2240b c + 1280b c - 1640b c - 2240b c +--R + +--R 8 +--R - 720b +--R * +--R 7 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 12c - 186b c - 636b c - 657b c + 2b c + 686b c +--R + +--R 6 2 7 +--R 646b c + 157b c +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 20c - 560b c - 3120b c - 4400b c + 3700b c + 10560b c +--R + +--R 6 2 7 8 +--R 1960b c - 5600b c - 2520b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 220c + 885b c + 1600b c - 355b c - 4110b c - 1715b c +--R + +--R 6 2 7 +--R 2330b c + 1145b c +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 280c + 1760b c + 1240b c - 5600b c - 5160b c + 6080b c +--R + +--R 6 2 7 8 +--R 5320b c - 2240b c - 1680b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 360c - 868b c + 1136b c + 2641b c - 1378b c - 2492b c +--R + +--R 6 2 7 +--R 602b c + 719b c +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 180c - 80b c + 880b c + 80b c - 1400b c + 80b c +--R + +--R 6 2 7 8 +--R 880b c - 80b c - 180b +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 40c - 55b c - 90b c + 135b c + 60b c - 105b c - 10b c +--R + +--R 7 +--R 25b c +--R * +--R sinh(x) +--R + +--R 5 3 6 2 7 8 10 +--R (- 4b c - 12b c - 12b c - 4b )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 9 +--R (2b c + 6b c + 6b c + 2b c )cosh(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 8 +--R (40b c + 220b c + 320b c - 40b c - 360b c - 180b )cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R (- 12b c - 81b c - 134b c + 4b c + 106b c + 77b c + 40b c) +--R * +--R 7 +--R cosh(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 20b c - 260b c - 820b c - 300b c + 1680b c + 1400b c +--R + +--R 7 8 +--R - 840b c - 840b +--R * +--R 6 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 25c + 170b c + 185b c + 70b c - 355b c - 736b c + 137b c +--R + +--R 7 +--R 504b c +--R * +--R 5 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 20c + 240b c + 560b c - 520b c - 1980b c + 280b c +--R + +--R 6 2 8 +--R 2240b c - 840b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 50c - 260b c + b c + 898b c + 210b c - 1078b c - 161b c +--R + +--R 7 +--R 440b c +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 40c - 100b c + 220b c + 380b c - 500b c - 460b c +--R + +--R 6 2 7 8 +--R 500b c + 180b c - 180b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 25c - 10b c - 105b c + 60b c + 135b c - 90b c - 55b c +--R + +--R 7 +--R 40b c +--R * +--R cosh(x) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R 4c - 8b c - 8b c + 24b c - 24b c + 8b c + 8b c - 4b +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 9 +--R (2b c + 6b c + 4b c - 4b c - 6b c - 2b c )sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 2c + 16b c + 40b c + 34b c - 14b c - 44b c - 28b c +--R + +--R 7 2 +--R - 6b c +--R * +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 19b c - 47b c - 18b c + 38b c + 37b c + 9b c +--R * +--R 8 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 10c + 56b c + 128b c + 128b c - 4b c - 136b c - 128b c +--R + +--R 7 2 8 +--R - 48b c - 6b c +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 19b c - 132b c - 281b c - 166b c + 171b c + 280b c +--R + +--R 7 2 8 +--R 129b c + 18b c +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 40c - 77b c - 66b c + 73b c + 240b c + 85b c - 122b c +--R + +--R 7 2 8 +--R - 81b c - 12b c +--R * +--R 7 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 20c + 110b c + 256b c + 288b c + 64b c - 236b c +--R + +--R 6 3 7 2 8 9 +--R - 304b c - 160b c - 36b c - 2b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 85b c - 413b c - 804b c - 595b c + 304b c + 861b c +--R + +--R 7 2 8 9 +--R 576b c + 147b c + 9b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 157c - 646b c - 529b c + 644b c + 1343b c + 638b c +--R + +--R 6 3 7 2 8 9 +--R - 471b c - 624b c - 186b c - 12b +--R * +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 220b c + 155b c - 195b c - 255b c - 245b c + 25b c +--R + +--R 7 2 8 9 +--R 215b c + 75b c + 5b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 20c + 130b c + 340b c + 432b c + 176b c - 256b c +--R + +--R 6 3 7 2 8 9 +--R - 444b c - 296b c - 92b c - 10b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 150b c - 730b c - 1439b c - 1212b c + 247b c +--R + +--R 6 3 7 2 8 9 +--R 1478b c + 1287b c + 464b c + 55b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 340c - 1612b c - 1916b c + 1223b c + 4030b c +--R + +--R 5 4 6 3 7 2 8 9 +--R 2285b c - 952b c - 1791b c - 822b c - 105b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 595b c + 1680b c - 70b c - 2660b c - 1640b c + 360b c +--R + +--R 7 2 8 9 +--R 1030b c + 620b c + 85b +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 504c + 137b c - 1240b c - 492b c + 806b c + 540b c +--R + +--R 6 3 7 2 8 9 +--R 100b c - 160b c - 170b c - 25b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 10c + 92b c + 296b c + 444b c + 256b c - 176b c +--R + +--R 6 3 7 2 8 9 +--R - 432b c - 340b c - 130b c - 20b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 6 3 +--R - 130b c - 765b c - 1700b c - 1625b c + 1625b c +--R + +--R 7 2 8 9 +--R 1700b c + 765b c + 130b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 450c - 2080b c - 3295b c + 430b c + 6255b c + 5060b c +--R + +--R 6 3 7 2 8 9 +--R - 825b c - 3090b c - 1685b c - 320b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 775b c + 3525b c + 2405b c - 5385b c - 6655b c + 95b c +--R + +--R 7 2 8 9 +--R 3095b c + 1765b c + 380b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 1145c + 2330b c - 2860b c - 6440b c + 1360b c + 5710b c +--R + +--R 6 3 7 2 8 9 +--R 1240b c - 1380b c - 885b c - 220b +--R * +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 620b c + 23b c + 1599b c + 160b c - 1324b c - 353b c +--R + +--R 7 2 8 9 +--R 295b c + 170b c + 50b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 2c + 36b c + 160b c + 304b c + 236b c - 64b c - 288b c +--R + +--R 7 2 8 9 +--R - 256b c - 110b c - 20b +--R * +--R 6 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 55b c - 464b c - 1287b c - 1478b c - 247b c + 1212b c +--R + +--R 7 2 8 9 +--R 1439b c + 730b c + 150b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 320c - 1685b c - 3090b c - 825b c + 5060b c + 6255b c +--R + +--R 6 3 7 2 8 9 +--R 430b c - 3295b c - 2080b c - 450b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 700b c + 3220b c + 4560b c - 3220b c - 10520b c +--R + +--R 6 3 7 2 8 9 +--R - 3220b c + 4560b c + 3220b c + 700b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 1050c + 4280b c - 100b c - 12500b c - 5700b c +--R + +--R 5 4 6 3 7 2 8 9 +--R 11480b c + 7580b c - 2660b c - 2830b c - 600b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 1217b c - 1716b c + 3839b c + 4618b c - 3613b c +--R + +--R 6 3 7 2 8 9 +--R - 4232b c + 721b c + 1330b c + 270b +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 440c + 161b c + 1518b c - 371b c - 1976b c + 209b c +--R + +--R 6 3 7 2 8 9 +--R 1158b c + 51b c - 260b c - 50b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 6b c + 48b c + 128b c + 136b c + 4b c - 128b c +--R + +--R 7 2 8 9 +--R - 128b c - 56b c - 10b +--R * +--R 7 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 9b c - 147b c - 576b c - 861b c - 304b c + 595b c +--R + +--R 7 2 8 9 +--R 804b c + 413b c + 85b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 105c - 822b c - 1791b c - 952b c + 2285b c + 4030b c +--R + +--R 6 3 7 2 8 9 +--R 1223b c - 1916b c - 1612b c - 340b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 380b c + 1765b c + 3095b c + 95b c - 6655b c - 5385b c +--R + +--R 7 2 8 9 +--R 2405b c + 3525b c + 775b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 600c + 2830b c + 2660b c - 7580b c - 11480b c + 5700b c +--R + +--R 6 3 7 2 8 9 +--R 12500b c + 100b c - 4280b c - 1050b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 6 3 +--R - 835b c - 2791b c + 1562b c + 8589b c - 8589b c +--R + +--R 7 2 8 9 +--R - 1562b c + 2791b c + 835b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 719c - 602b c + 3211b c + 1980b c - 5133b c - 2514b c +--R + +--R 6 3 7 2 8 9 +--R 3509b c + 1496b c - 868b c - 360b +--R * +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 180b c - 143b c - 549b c + 373b c + 623b c - 317b c +--R + +--R 7 2 8 9 +--R - 319b c + 87b c + 65b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R 6b c + 28b c + 44b c + 14b c - 34b c - 40b c - 16b c +--R + +--R 9 +--R - 2b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 18b c - 129b c - 280b c - 171b c + 166b c + 281b c +--R + +--R 8 9 +--R 132b c + 19b +--R * +--R 7 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 12c - 186b c - 624b c - 471b c + 638b c + 1343b c +--R + +--R 6 3 7 2 8 9 +--R 644b c - 529b c - 646b c - 157b +--R * +--R 6 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 85b c + 620b c + 1030b c + 360b c - 1640b c - 2660b c +--R + +--R 7 2 8 9 +--R - 70b c + 1680b c + 595b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 220c + 885b c + 1380b c - 1240b c - 5710b c - 1360b c +--R + +--R 6 3 7 2 8 9 +--R 6440b c + 2860b c - 2330b c - 1145b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 270b c - 1330b c - 721b c + 4232b c + 3613b c +--R + +--R 6 3 7 2 8 9 +--R - 4618b c - 3839b c + 1716b c + 1217b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 360c - 868b c + 1496b c + 3509b c - 2514b c - 5133b c +--R + +--R 6 3 7 2 8 9 +--R 1980b c + 3211b c - 602b c - 719b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 217b c + 56b c - 980b c - 56b c + 1526b c - 56b c +--R + +--R 7 2 8 9 +--R - 980b c + 56b c + 217b +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 40c - 55b c - 130b c + 190b c + 150b c - 240b c - 70b c +--R + +--R 7 2 8 9 +--R 130b c + 10b c - 25b +--R * +--R sinh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (2b c + 6b c + 4b c - 4b c - 6b c - 2b c)cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 8 +--R (- 9b c - 37b c - 38b c + 18b c + 47b c + 19b c)cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 12b c - 81b c - 122b c + 85b c + 240b c + 73b c - 66b c +--R + +--R 8 9 +--R - 77b c - 40b +--R * +--R 7 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 5b c + 75b c + 215b c + 25b c - 245b c - 255b c - 195b c +--R + +--R 8 9 +--R 155b c + 220b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 25c + 170b c + 160b c - 100b c - 540b c - 806b c + 492b c +--R + +--R 7 2 8 9 +--R 1240b c - 137b c - 504b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 50b c - 170b c - 295b c + 353b c + 1324b c - 160b c +--R + +--R 7 2 8 9 +--R - 1599b c - 23b c + 620b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 50c - 260b c + 51b c + 1158b c + 209b c - 1976b c +--R + +--R 6 3 7 2 8 9 +--R - 371b c + 1518b c + 161b c - 440b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 65b c + 87b c - 319b c - 317b c + 623b c + 373b c - 549b c +--R + +--R 8 9 +--R - 143b c + 180b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 25c - 10b c - 130b c + 70b c + 240b c - 150b c - 190b c +--R + +--R 7 2 8 9 +--R 130b c + 55b c - 40b +--R * +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 6 3 7 2 8 9 +--R - 4b c + 8b c + 8b c - 24b c + 24b c - 8b c - 8b c + 4b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 9 8 2 7 3 6 4 5 5 4 9 +--R (40c + 100b c + 40b c - 80b c - 80b c - 20b c )sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (180c + 640b c + 640b c - 200b c - 740b c - 440b c - 80b c ) +--R * +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 19b c - 47b c - 18b c + 38b c + 37b c + 9b c +--R * +--R 8 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 320c + 1640b c + 2720b c + 920b c - 2080b c - 2440b c +--R + +--R 6 3 7 2 +--R - 960b c - 120b c +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 19c - 132b c - 281b c - 166b c + 171b c + 280b c +--R + +--R 6 3 7 2 +--R 129b c + 18b c +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 480c - 720b c + 640b c + 1400b c + 160b c - 640b c - 320b c +--R + +--R 7 2 +--R - 40b c +--R * +--R 7 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 280c + 2160b c + 5400b c + 4720b c - 1640b c - 5840b c +--R + +--R 6 3 7 2 8 +--R - 3960b c - 1040b c - 80b c +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 85c - 413b c - 804b c - 595b c + 304b c + 861b c +--R + +--R 6 3 7 2 8 +--R 576b c + 147b c + 9b c +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 1680c - 4480b c - 280b c + 7920b c + 5520b c - 2400b c +--R + +--R 6 3 7 2 8 +--R - 3480b c - 1040b c - 80b c +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 220c + 155b c - 195b c - 255b c - 245b c + 25b c + 215b c +--R + +--R 7 2 8 +--R 75b c + 5b c +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 120c + 1540b c + 5800b c + 8560b c + 2600b c - 6640b c +--R + +--R 6 3 7 2 8 9 +--R - 7960b c - 3440b c - 560b c - 20b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 150c - 730b c - 1439b c - 1212b c + 247b c + 1478b c +--R + +--R 6 3 7 2 8 +--R 1287b c + 464b c + 55b c +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 2240c - 9800b c - 8560b c + 13080b c + 22720b c + 3200b c +--R + +--R 6 3 7 2 8 9 +--R - 10800b c - 6440b c - 1120b c - 40b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 595c + 1680b c - 70b c - 2660b c - 1640b c + 360b c +--R + +--R 6 3 7 2 8 +--R 1030b c + 620b c + 85b c +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 1008c + 504b c - 2800b c - 1624b c + 2472b c + 1724b c +--R + +--R 6 3 7 2 8 9 +--R - 568b c - 600b c - 112b c - 4b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 20c + 560b c + 3440b c + 7960b c + 6640b c - 2600b c +--R + +--R 6 3 7 2 8 9 +--R - 8560b c - 5800b c - 1540b c - 120b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 5 4 6 3 +--R - 130c - 765b c - 1700b c - 1625b c + 1625b c + 1700b c +--R + +--R 7 2 8 +--R 765b c + 130b c +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 1400c - 10000b c - 18200b c + 3200b c + 35600b c +--R + +--R 5 4 6 3 7 2 8 9 +--R 23200b c - 11000b c - 16000b c - 5000b c - 400b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 775c + 3525b c + 2405b c - 5385b c - 6655b c + 95b c +--R + +--R 6 3 7 2 8 +--R 3095b c + 1765b c + 380b c +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 2520c + 4480b c - 6440b c - 12960b c + 3820b c + 12400b c +--R + +--R 6 3 7 2 8 9 +--R 1560b c - 3800b c - 1460b c - 120b +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 620c + 23b c + 1599b c + 160b c - 1324b c - 353b c + 295b c +--R + +--R 7 2 8 +--R 170b c + 50b c +--R * +--R 4 +--R sinh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 80b c + 1040b c + 3960b c + 5840b c + 1640b c - 4720b c +--R + +--R 7 2 8 9 +--R - 5400b c - 2160b c - 280b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 55c - 464b c - 1287b c - 1478b c - 247b c + 1212b c +--R + +--R 6 3 7 2 8 +--R 1439b c + 730b c + 150b c +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 400c - 5000b c - 16000b c - 11000b c + 23200b c +--R + +--R 5 4 6 3 7 2 8 9 +--R 35600b c + 3200b c - 18200b c - 10000b c - 1400b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 700c + 3220b c + 4560b c - 3220b c - 10520b c - 3220b c +--R + +--R 6 3 7 2 8 +--R 4560b c + 3220b c + 700b c +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 2240c + 8120b c - 960b c - 23800b c - 10240b c + 22320b c +--R + +--R 6 3 7 2 8 9 +--R 14480b c - 5800b c - 5520b c - 840b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 1217c - 1716b c + 3839b c + 4618b c - 3613b c - 4232b c +--R + +--R 6 3 7 2 8 +--R 721b c + 1330b c + 270b c +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 480c + 240b c + 1600b c - 600b c - 2000b c + 440b c +--R + +--R 6 3 7 2 8 9 +--R 1120b c - 40b c - 240b c - 40b +--R * +--R 3 +--R sinh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R 120b c + 960b c + 2440b c + 2080b c - 920b c - 2720b c +--R + +--R 8 9 +--R - 1640b c - 320b +--R * +--R 7 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 9c - 147b c - 576b c - 861b c - 304b c + 595b c + 804b c +--R + +--R 7 2 8 +--R 413b c + 85b c +--R * +--R 6 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 40c - 1120b c - 6440b c - 10800b c + 3200b c + 22720b c +--R + +--R 6 3 7 2 8 9 +--R 13080b c - 8560b c - 9800b c - 2240b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 380c + 1765b c + 3095b c + 95b c - 6655b c - 5385b c +--R + +--R 6 3 7 2 8 +--R 2405b c + 3525b c + 775b c +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 840c + 5520b c + 5800b c - 14480b c - 22320b c + 10240b c +--R + +--R 6 3 7 2 8 9 +--R 23800b c + 960b c - 8120b c - 2240b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 5 4 6 3 +--R - 835c - 2791b c + 1562b c + 8589b c - 8589b c - 1562b c +--R + +--R 7 2 8 +--R 2791b c + 835b c +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 720c - 640b c + 3320b c + 2000b c - 5400b c - 2400b c +--R + +--R 6 3 7 2 8 9 +--R 3720b c + 1360b c - 920b c - 320b +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 180c - 143b c - 549b c + 373b c + 623b c - 317b c - 319b c +--R + +--R 7 2 8 +--R 87b c + 65b c +--R * +--R 2 +--R sinh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (80b c + 440b c + 740b c + 200b c - 640b c - 640b c - 180b ) +--R * +--R 8 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 18b c - 129b c - 280b c - 171b c + 166b c + 281b c +--R + +--R 7 2 8 +--R 132b c + 19b c +--R * +--R 7 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 80b c - 1040b c - 3480b c - 2400b c + 5520b c + 7920b c +--R + +--R 7 2 8 9 +--R - 280b c - 4480b c - 1680b +--R * +--R 6 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 85c + 620b c + 1030b c + 360b c - 1640b c - 2660b c +--R + +--R 6 3 7 2 8 +--R - 70b c + 1680b c + 595b c +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 120c + 1460b c + 3800b c - 1560b c - 12400b c - 3820b c +--R + +--R 6 3 7 2 8 9 +--R 12960b c + 6440b c - 4480b c - 2520b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 270c - 1330b c - 721b c + 4232b c + 3613b c - 4618b c +--R + +--R 6 3 7 2 8 +--R - 3839b c + 1716b c + 1217b c +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 320c - 920b c + 1360b c + 3720b c - 2400b c - 5400b c +--R + +--R 6 3 7 2 8 9 +--R 2000b c + 3320b c - 640b c - 720b +--R * +--R 2 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 217c + 56b c - 980b c - 56b c + 1526b c - 56b c - 980b c +--R + +--R 7 2 8 +--R 56b c + 217b c +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 40c - 60b c - 120b c + 200b c + 120b c - 240b c - 40b c +--R + +--R 7 2 9 +--R 120b c - 20b +--R * +--R sinh(x) +--R + +--R 4 5 5 4 6 3 7 2 8 9 9 +--R (20b c + 80b c + 80b c - 40b c - 100b c - 40b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (- 9b c - 37b c - 38b c + 18b c + 47b c + 19b c )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R - 40b c - 320b c - 640b c + 160b c + 1400b c + 640b c - 720b c +--R + +--R 9 +--R - 480b +--R * +--R 7 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 5c + 75b c + 215b c + 25b c - 245b c - 255b c - 195b c +--R + +--R 7 2 8 +--R 155b c + 220b c +--R * +--R 6 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 4c + 112b c + 600b c + 568b c - 1724b c - 2472b c + 1624b c +--R + +--R 7 2 8 9 +--R 2800b c - 504b c - 1008b +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 50c - 170b c - 295b c + 353b c + 1324b c - 160b c - 1599b c +--R + +--R 7 2 8 +--R - 23b c + 620b c +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 40c - 240b c - 40b c + 1120b c + 440b c - 2000b c - 600b c +--R + +--R 7 2 8 9 +--R 1600b c + 240b c - 480b +--R * +--R 3 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 65c + 87b c - 319b c - 317b c + 623b c + 373b c - 549b c +--R + +--R 7 2 8 +--R - 143b c + 180b c +--R * +--R 2 +--R cosh(x) +--R + +--R 9 2 7 3 6 4 5 5 4 6 3 7 2 +--R 20c - 120b c + 40b c + 240b c - 120b c - 200b c + 120b c +--R + +--R 8 9 +--R 60b c - 40b +--R * +--R cosh(x) +--R + +--R 9 8 2 7 3 6 5 4 6 3 7 2 8 +--R - 4c + 8b c + 8b c - 24b c + 24b c - 8b c - 8b c + 4b c +--R / +--R 10 2 9 3 8 4 7 5 6 6 5 10 +--R (15b c + 45b c + 30b c - 30b c - 45b c - 15b c )sinh(x) +--R + +--R 10 2 9 3 8 5 6 6 5 7 4 +--R (75b c + 300b c + 375b c - 375b c - 300b c - 75b c ) +--R * +--R cosh(x) +--R + +--R 11 10 3 8 4 7 5 6 6 5 +--R 150c + 375b c - 675b c - 450b c + 225b c + 300b c +--R + +--R 7 4 +--R 75b c +--R * +--R 9 +--R sinh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 150b c + 825b c + 1575b c + 900b c - 900b c +--R + +--R 6 5 7 4 8 3 +--R - 1575b c - 825b c - 150b c +--R * +--R 2 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 675c + 2400b c + 1725b c - 3150b c - 5175b c +--R + +--R 5 6 6 5 7 4 8 3 +--R - 900b c + 2475b c + 1650b c + 300b c +--R * +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 675b c - 1350b c + 525b c + 2550b c + 975b c +--R + +--R 6 5 7 4 8 3 +--R - 1050b c - 825b c - 150b c +--R * +--R 8 +--R sinh(x) +--R + +--R 10 2 9 3 8 4 7 6 5 +--R 150b c + 1200b c + 3300b c + 3600b c - 3600b c +--R + +--R 7 4 8 3 9 2 +--R - 3300b c - 1200b c - 150b c +--R * +--R 3 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 1200c + 6150b c + 9000b c - 2700b c - 18000b c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R - 12600b c + 4200b c + 8700b c + 3600b c + 450b c +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 2700b c - 8400b c - 3450b c + 13200b c + 14550b c +--R + +--R 6 5 7 4 8 3 9 2 +--R - 1200b c - 7950b c - 3600b c - 450b c +--R * +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 1800c - 2700b c + 4200b c + 7950b c - 1800b c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R - 7650b c - 1800b c + 2250b c + 1200b c + 150b c +--R * +--R 7 +--R sinh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 75b c + 975b c + 3900b c + 6600b c + 3600b c +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 3600b c - 6600b c - 3900b c - 975b c - 75b c +--R * +--R 4 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 1050c + 8100b c + 19200b c + 9600b c - 26400b c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R - 39600b c - 8700b c + 18000b c + 14550b c + 3900b c +--R + +--R 10 +--R 300b c +--R * +--R 3 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 +--R - 4200b c - 19950b c - 23550b c + 18300b c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R 53850b c + 22800b c - 20250b c - 20700b c - 5850b c +--R + +--R 10 +--R - 450b c +--R * +--R 2 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 6300c - 16800b c + 5250b c + 46500b c + 21750b c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R - 38700b c - 33750b c + 5100b c + 12750b c + 3900b c +--R + +--R 10 +--R 300b c +--R * +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 3150b c + 3150b c - 8400b c - 9450b c + 6375b c +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 9375b c - 150b c - 3000b c - 975b c - 75b c +--R * +--R 6 +--R sinh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 15b c + 420b c + 2655b c + 6720b c + 7080b c +--R + +--R 7 4 8 3 9 2 10 11 +--R - 7080b c - 6720b c - 2655b c - 420b c - 15b +--R * +--R 5 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 450c + 5775b c + 21300b c + 26325b c - 12000b c +--R + +--R 5 6 6 5 7 4 8 3 +--R - 57000b c - 39600b c + 12000b c + 27750b c +--R + +--R 9 2 10 11 +--R 12825b c + 2100b c + 75b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 +--R - 3150b c - 23400b c - 49200b c - 9600b c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R 82650b c + 85200b c - 5250b c - 48000b c - 24900b c +--R + +--R 10 11 +--R - 4200b c - 150b +--R * +--R 3 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 +--R - 8400c - 36750b c - 23700b c + 85800b c +--R + +--R 4 7 5 6 6 5 7 4 +--R 117300b c - 37050b c - 125700b c - 36150b c +--R + +--R 8 3 9 2 10 11 +--R 36300b c + 24000b c + 4200b c + 150b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 9450b c + 21000b c - 16800b c - 60600b c - 6525b c +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 56100b c + 25575b c - 14400b c - 11625b c - 2100b c +--R + +--R 11 +--R - 75b +--R * +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 3780c + 1890b c - 14280b c - 7980b c + 19770b c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R 12555b c - 11400b c - 8715b c + 1710b c + 2235b c +--R + +--R 10 11 +--R 420b c + 15b +--R * +--R 5 +--R sinh(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R 75b c + 975b c + 3900b c + 6600b c + 3600b c +--R + +--R 7 4 8 3 9 2 10 11 +--R - 3600b c - 6600b c - 3900b c - 975b c - 75b +--R * +--R 6 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 75c + 2100b c + 12825b c + 27750b c + 12000b c +--R + +--R 5 6 6 5 7 4 8 3 +--R - 39600b c - 57000b c - 12000b c + 26325b c +--R + +--R 9 2 10 11 +--R 21300b c + 5775b c + 450b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 +--R - 1125b c - 14250b c - 49125b c - 48000b c +--R + +--R 5 6 6 5 7 4 8 3 +--R 50250b c + 124500b c + 50250b c - 48000b c +--R + +--R 9 2 10 11 +--R - 49125b c - 14250b c - 1125b +--R * +--R 4 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 +--R - 5250c - 37500b c - 63000b c + 49500b c +--R + +--R 4 7 5 6 6 5 7 4 +--R 201750b c + 75000b c - 174750b c - 147000b c +--R + +--R 8 3 9 2 10 11 +--R 22500b c + 58500b c + 18750b c + 1500b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 +--R 10500b c + 42000b c + 12000b c - 112500b c +--R + +--R 5 6 6 5 7 4 8 3 +--R - 97500b c + 85125b c + 115875b c - 750b c +--R + +--R 9 2 10 11 +--R - 39750b c - 13875b c - 1125b +--R * +--R 2 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 9450c + 16800b c - 33600b c - 65400b c + 38475b c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R 95100b c - 8475b c - 60750b c - 11325b c + 13800b c +--R + +--R 10 11 +--R 5475b c + 450b +--R * +--R cosh(x) +--R + +--R 10 3 8 4 7 5 6 6 5 +--R - 3150b c + 11550b c + 1050b c - 15825b c - 3000b c +--R + +--R 7 4 8 3 9 2 10 11 +--R 9525b c + 2850b c - 2025b c - 900b c - 75b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 8 4 7 5 6 6 5 8 3 +--R 150b c + 1200b c + 3300b c + 3600b c - 3600b c +--R + +--R 9 2 10 11 +--R - 3300b c - 1200b c - 150b +--R * +--R 7 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 300b c + 3900b c + 14550b c + 18000b c - 8700b c +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 39600b c - 26400b c + 9600b c + 19200b c + 8100b c +--R + +--R 11 +--R 1050b +--R * +--R 6 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 150b c - 4200b c - 24900b c - 48000b c - 5250b c +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 85200b c + 82650b c - 9600b c - 49200b c - 23400b c +--R + +--R 11 +--R - 3150b +--R * +--R 5 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 +--R - 1500c - 18750b c - 58500b c - 22500b c +--R + +--R 4 7 5 6 6 5 7 4 +--R 147000b c + 174750b c - 75000b c - 201750b c +--R + +--R 8 3 9 2 10 11 +--R - 49500b c + 63000b c + 37500b c + 5250b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 +--R 5250b c + 36000b c + 49500b c - 72000b c +--R + +--R 5 6 7 4 8 3 9 2 +--R - 174750b c + 174750b c + 72000b c - 49500b c +--R + +--R 10 11 +--R - 36000b c - 5250b +--R * +--R 3 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 8400c + 30450b c - 12000b c - 119700b c - 34800b c +--R + +--R 5 6 6 5 7 4 8 3 +--R 172950b c + 92700b c - 105450b c - 75000b c +--R + +--R 9 2 10 11 +--R 18600b c + 20700b c + 3150b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 +--R - 6300b c - 8400b c + 26250b c + 31200b c +--R + +--R 5 6 6 5 7 4 8 3 +--R - 39300b c - 43800b c + 24000b c + 27600b c +--R + +--R 9 2 10 11 +--R - 3600b c - 6600b c - 1050b +--R * +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 1800c + 900b c + 7800b c - 3150b c - 13500b c +--R + +--R 5 6 6 5 7 4 8 3 10 11 +--R 3900b c + 11700b c - 1800b c - 5100b c + 900b c + 150b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 7 5 6 6 5 7 4 8 3 +--R 150b c + 825b c + 1575b c + 900b c - 900b c +--R + +--R 9 2 10 11 +--R - 1575b c - 825b c - 150b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R 450b c + 3600b c + 8700b c + 4200b c - 12600b c +--R + +--R 7 4 8 3 9 2 10 11 +--R - 18000b c - 2700b c + 9000b c + 6150b c + 1200b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R - 450b c - 5850b c - 20700b c - 20250b c + 22800b c +--R + +--R 7 4 8 3 9 2 10 11 +--R 53850b c + 18300b c - 23550b c - 19950b c - 4200b +--R * +--R 6 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 150c - 4200b c - 24000b c - 36300b c + 36150b c +--R + +--R 5 6 6 5 7 4 8 3 +--R 125700b c + 37050b c - 117300b c - 85800b c +--R + +--R 9 2 10 11 +--R 23700b c + 36750b c + 8400b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 1125b c + 13875b c + 39750b c + 750b c - 115875b c +--R + +--R 6 5 7 4 8 3 9 2 +--R - 85125b c + 97500b c + 112500b c - 12000b c +--R + +--R 10 11 +--R - 42000b c - 10500b +--R * +--R 4 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 3150c + 20700b c + 18600b c - 75000b c - 105450b c +--R + +--R 5 6 6 5 7 4 8 3 +--R 92700b c + 172950b c - 34800b c - 119700b c +--R + +--R 9 2 10 11 +--R - 12000b c + 30450b c + 8400b +--R * +--R 3 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 +--R - 4200b c - 13650b c + 12150b c + 55500b c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R - 7950b c - 83700b c - 7950b c + 55500b c + 12150b c +--R + +--R 10 11 +--R - 13650b c - 4200b +--R * +--R 2 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 2700c - 2400b c + 15150b c + 9900b c - 32700b c +--R + +--R 5 6 6 5 7 4 8 3 +--R - 16500b c + 34200b c + 14100b c - 17400b c +--R + +--R 9 2 10 11 +--R - 6300b c + 3450b c + 1200b +--R * +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 675b c - 675b c - 2550b c + 2400b c + 3750b c +--R + +--R 6 5 7 4 8 3 9 2 10 11 +--R - 3150b c - 2700b c + 1800b c + 975b c - 375b c - 150b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 6 6 5 7 4 9 2 10 11 +--R (75b c + 300b c + 375b c - 375b c - 300b c - 75b ) +--R * +--R 9 +--R cosh(x) +--R + +--R 3 8 4 7 5 6 6 5 7 4 +--R 300b c + 1650b c + 2475b c - 900b c - 5175b c +--R + +--R 8 3 9 2 10 11 +--R - 3150b c + 1725b c + 2400b c + 675b +--R * +--R 8 +--R cosh(x) +--R + +--R 3 8 4 7 5 6 6 5 7 4 +--R - 450b c - 3600b c - 7950b c - 1200b c + 14550b c +--R + +--R 8 3 9 2 10 11 +--R 13200b c - 3450b c - 8400b c - 2700b +--R * +--R 7 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 300b c - 3900b c - 12750b c - 5100b c + 33750b c +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 38700b c - 21750b c - 46500b c - 5250b c + 16800b c +--R + +--R 11 +--R 6300b +--R * +--R 6 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 75b c + 2100b c + 11625b c + 14400b c - 25575b c +--R + +--R 6 5 7 4 8 3 9 2 +--R - 56100b c + 6525b c + 60600b c + 16800b c +--R + +--R 10 11 +--R - 21000b c - 9450b +--R * +--R 5 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 450c + 5475b c + 13800b c - 11325b c - 60750b c +--R + +--R 5 6 6 5 7 4 8 3 +--R - 8475b c + 95100b c + 38475b c - 65400b c +--R + +--R 9 2 10 11 +--R - 33600b c + 16800b c + 9450b +--R * +--R 4 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 1050b c - 6600b c - 3600b c + 27600b c + 24000b c +--R + +--R 6 5 7 4 8 3 9 2 +--R - 43800b c - 39300b c + 31200b c + 26250b c +--R + +--R 10 11 +--R - 8400b c - 6300b +--R * +--R 3 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 1200c - 3450b c + 6300b c + 17400b c - 14100b c +--R + +--R 5 6 6 5 7 4 8 3 +--R - 34200b c + 16500b c + 32700b c - 9900b c +--R + +--R 9 2 10 11 +--R - 15150b c + 2400b c + 2700b +--R * +--R 2 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 675b c + 300b c - 3975b c - 600b c + 8550b c +--R + +--R 7 4 8 3 9 2 10 11 +--R - 8550b c + 600b c + 3975b c - 300b c - 675b +--R * +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 150c - 225b c - 600b c + 975b c + 900b c - 1650b c +--R + +--R 6 5 7 4 8 3 9 2 11 +--R - 600b c + 1350b c + 150b c - 525b c + 75b +--R * +--R sinh(x) +--R + +--R 6 5 7 4 8 3 9 2 10 11 10 +--R (15b c + 45b c + 30b c - 30b c - 45b c - 15b )cosh(x) +--R + +--R 4 7 5 6 6 5 7 4 8 3 10 +--R 75b c + 300b c + 225b c - 450b c - 675b c + 375b c +--R + +--R 11 +--R 150b +--R * +--R 9 +--R cosh(x) +--R + +--R 4 7 5 6 6 5 7 4 8 3 9 2 +--R - 150b c - 825b c - 1050b c + 975b c + 2550b c + 525b c +--R + +--R 10 11 +--R - 1350b c - 675b +--R * +--R 8 +--R cosh(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R - 150b c - 1200b c - 2250b c + 1800b c + 7650b c +--R + +--R 7 4 8 3 9 2 10 11 +--R 1800b c - 7950b c - 4200b c + 2700b c + 1800b +--R * +--R 7 +--R cosh(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 +--R 75b c + 975b c + 3000b c + 150b c - 9375b c - 6375b c +--R + +--R 8 3 9 2 10 11 +--R 9450b c + 8400b c - 3150b c - 3150b +--R * +--R 6 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 15c + 420b c + 2235b c + 1710b c - 8715b c - 11400b c +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 12555b c + 19770b c - 7980b c - 14280b c + 1890b c +--R + +--R 11 +--R 3780b +--R * +--R 5 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 75b c - 900b c - 2025b c + 2850b c + 9525b c +--R + +--R 6 5 7 4 8 3 9 2 11 +--R - 3000b c - 15825b c + 1050b c + 11550b c - 3150b +--R * +--R 4 +--R cosh(x) +--R + +--R 11 10 3 8 4 7 5 6 +--R - 150c - 900b c + 5100b c + 1800b c - 11700b c +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 3900b c + 13500b c + 3150b c - 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43800b c - 39300b c + 31200b c + 26250b c - 8400b c +--R + +--R 10 +--R - 6300b c +--R * +--R 3 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 6 5 +--R 675c + 300b c - 3975b c - 600b c + 8550b c - 8550b c +--R + +--R 7 4 8 3 9 2 10 +--R 600b c + 3975b c - 300b c - 675b c +--R * +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 5 6 6 5 7 4 8 3 9 2 10 10 +--R (15b c + 45b c + 30b c - 30b c - 45b c - 15b c)cosh(x) +--R + +--R 3 8 4 7 5 6 6 5 7 4 8 3 +--R - 150b c - 825b c - 1050b c + 975b c + 2550b c + 525b c +--R + +--R 9 2 10 +--R - 1350b c - 675b c +--R * +--R 8 +--R cosh(x) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 75b c + 975b c + 3000b c + 150b c - 9375b c - 6375b c +--R + +--R 7 4 8 3 9 2 10 +--R 9450b c + 8400b c - 3150b c - 3150b c +--R * +--R 6 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 75c - 900b c - 2025b c + 2850b c + 9525b c - 3000b c +--R + +--R 6 5 7 4 8 3 10 +--R - 15825b c + 1050b c + 11550b c - 3150b c +--R * +--R 4 +--R cosh(x) +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 150c + 375b c - 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4200b c - 7950b c + 1800b c + 7650b c +--R + +--R 7 5 8 4 9 3 10 2 +--R 1800b c - 2250b c - 1200b c - 150b c +--R * +--R 7 +--R sinh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 75c + 975b c + 3825b c + 5625b c - 300b c - 10200b c +--R + +--R 6 6 7 5 8 4 9 3 10 2 11 +--R - 10200b c - 300b c + 5625b c + 3825b c + 975b c + 75b c +--R * +--R 4 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 +--R - 1050b c - 8100b c - 19200b c - 9600b c + 26400b c +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 39600b c + 8700b c - 18000b c - 14550b c - 3900b c +--R + +--R 11 +--R - 300b c +--R * +--R 3 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 4200c - 19950b c - 19350b c + 38250b c + 77400b c +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 4500b c - 74100b c - 43500b c + 14400b c + 20250b c +--R + +--R 10 2 11 +--R 5850b c + 450b c +--R * +--R 2 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 +--R 6300b c + 16800b c - 5250b c - 46500b c - 21750b c +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R 38700b c + 33750b c - 5100b c - 12750b c - 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11700b c + 1800b c + 5100b c - 900b c - 150b c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 +--R - 450b c - 3600b c - 8700b c - 4200b c + 12600b c +--R + +--R 7 5 8 4 9 3 10 2 11 +--R 18000b c + 2700b c - 9000b c - 6150b c - 1200b c +--R * +--R 7 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 150c + 4200b c + 24000b c + 36300b c - 36150b c +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 125700b c - 37050b c + 117300b c + 85800b c - 23700b c +--R + +--R 10 2 11 +--R - 36750b c - 8400b c +--R * +--R 5 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 3150c - 20700b c - 18600b c + 75000b c + 105450b c +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R - 92700b c - 172950b c + 34800b c + 119700b c + 12000b c +--R + +--R 10 2 11 +--R - 30450b c - 8400b c +--R * +--R 3 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 2700c + 2400b c - 15150b c - 9900b c + 32700b c +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 16500b c - 34200b c - 14100b c + 17400b c + 6300b c +--R + +--R 10 2 11 +--R - 3450b c - 1200b c +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R - 300b c - 1650b c - 2475b c + 900b c + 5175b c + 3150b c +--R + +--R 9 3 10 2 11 +--R - 1725b c - 2400b c - 675b c +--R * +--R 8 +--R cosh(x) +--R + +--R 11 2 10 3 9 4 8 5 7 +--R 300b c + 3900b c + 12750b c + 5100b c - 33750b c +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R - 38700b c + 21750b c + 46500b c + 5250b c - 16800b c +--R + +--R 11 +--R - 6300b c +--R * +--R 6 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R - 450c - 5475b c - 13800b c + 11325b c + 60750b c +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 8475b c - 95100b c - 38475b c + 65400b c + 33600b c +--R + +--R 10 2 11 +--R - 16800b c - 9450b c +--R * +--R 4 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 +--R 1200c + 3450b c - 6300b c - 17400b c + 14100b c +--R + +--R 5 7 6 6 7 5 8 4 9 3 +--R 34200b c - 16500b c - 32700b c + 9900b c + 15150b c +--R + +--R 10 2 11 +--R - 2400b c - 2700b c +--R * +--R 2 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R - 150c + 225b c + 600b c - 975b c - 900b c + 1650b c +--R + +--R 6 6 7 5 8 4 9 3 11 +--R 600b c - 1350b c - 150b c + 525b c - 75b c +--R * +--R sinh(x) +--R + +--R 4 8 5 7 6 6 7 5 8 4 10 2 11 +--R (- 75b c - 300b c - 225b c + 450b c + 675b c - 375b c - 150b c) +--R * +--R 9 +--R cosh(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 150b c + 1200b c + 2250b c - 1800b c - 7650b c - 1800b c +--R + +--R 8 4 9 3 10 2 11 +--R 7950b c + 4200b c - 2700b c - 1800b c +--R * +--R 7 +--R cosh(x) +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R - 15c - 420b c - 2235b c - 1710b c + 8715b c + 11400b c +--R + +--R 6 6 7 5 8 4 9 3 10 2 11 +--R - 12555b c - 19770b c + 7980b c + 14280b c - 1890b c - 3780b c +--R * +--R 5 +--R cosh(x) +--R + +--R 12 11 3 9 4 8 5 7 6 6 +--R 150c + 900b c - 5100b c - 1800b c + 11700b c + 3900b c +--R + +--R 7 5 8 4 9 3 10 2 11 +--R - 13500b c - 3150b c + 7800b c + 900b c - 1800b c +--R * +--R 3 +--R cosh(x) +--R + +--R 12 2 10 3 9 4 8 5 7 6 6 +--R - 75c + 525b c - 150b c - 1350b c + 600b c + 1650b c +--R + +--R 7 5 8 4 9 3 10 2 11 +--R - 900b c - 975b c + 600b c + 225b c - 150b c +--R * +--R cosh(x) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 518 +--d0940:= D(m0940,x) +--E 205 + +--S 206 of 518 +t0941:= ((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^(1/2) +--R +--R +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R (202) \|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 518 +r0941:= 2*(c*cosh(x)+b*sinh(x))/((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^(1/2) +--R +--R +--R 2b sinh(x) + 2c cosh(x) +--R (203) --------------------------------------- +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 207 + +--S 208 of 518 +a0941:= integrate(t0941,x) +--R +--R +--R (204) +--R 2 2 +--R (c + b)sinh(x) + (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) + c - b +--R / +--R (sinh(x) + cosh(x)) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 518 +m0941:= a0941-r0941 +--R +--R +--R (205) +--R 2 2 +--R ((c + b)sinh(x) + (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) + c - b) +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R + +--R 2 2 +--R (- 2b sinh(x) + (- 2c - 2b)cosh(x)sinh(x) - 2c cosh(x) ) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R / +--R (sinh(x) + cosh(x)) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 209 + +--S 210 of 518 +d0941:= D(m0941,x) +--R +--R +--R (206) +--R 2 2 4 2 2 3 +--R (5c + 6b c + b )sinh(x) + (16c + 24b c + 8b )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((18c + 36b c + 18b )cosh(x) - 10c + 4b c + 6b )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((8c + 24b c + 16b )cosh(x) + (- 16c + 16b )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 +--R (c + 6b c + 5b )cosh(x) + (- 6c - 4b c + 10b )cosh(x) + c +--R + +--R 2 +--R - 2b c + b +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 3 2 2 5 3 2 2 3 4 +--R (c + 2b c + b c)sinh(x) + (4c + 9b c + 6b c + b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R ((6c + 16b c + 14b c + 4b )cosh(x) - 10c - 4b c + 10b c + 4b ) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (4c + 14b c + 16b c + 6b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 24c - 18b c + 24b c + 18b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (c + 6b c + 9b c + 4b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 18c - 24b c + 18b c + 24b )cosh(x) + 5c - 6b c - 3b c + 4b +--R * +--R sinh(x) +--R + +--R 2 2 3 5 3 2 2 3 3 +--R (b c + 2b c + b )cosh(x) + (- 4c - 10b c + 4b c + 10b )cosh(x) +--R + +--R 3 2 2 3 +--R (4c - 3b c - 6b c + 5b )cosh(x) +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R + +--R 2 2 4 +--R (- 12c - 4b c + 4b )sinh(x) +--R + +--R 2 2 3 +--R (- 28c - 24b c + 4b )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 16c - 40b c - 16b )cosh(x) + 4c - 4b c)sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4c - 24b c - 28b )cosh(x) + (4c - 4b )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 +--R (4c - 4b c - 12b )cosh(x) + (4b c - 4b )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 3 2 2 3 5 +--R (- 4c - 4b c + 2b c + 2b )sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 12c - 16b c + 2b c + 6b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 10c - 22b c - 10b c + 2b )cosh(x) + 12c - 4b c - 10b c +--R + +--R 3 +--R 2b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (2c - 10b c - 22b c - 10b )cosh(x) +--R + +--R 3 2 2 3 +--R (20c + 8b c - 22b c - 6b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (6c + 2b c - 16b c - 12b )cosh(x) +--R + +--R 3 2 2 3 2 +--R (6c + 22b c - 8b c - 20b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (2c + 2b c - 4b c - 4b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 2c + 10b c + 4b c - 12b )cosh(x) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R / +--R 3 2 +--R (6c + 2b)sinh(x) + (14c + 10b)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((10c + 14b)cosh(x) - 2c + 2b)sinh(x) + (2c + 6b)cosh(x) +--R + +--R (- 2c + 2b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 2 4 2 2 3 +--R (2c + 2b c)sinh(x) + (6c + 8b c + 2b )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6c + 12b c + 6b )cosh(x) - 6c + 2b c + 4b )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((2c + 8b c + 6b )cosh(x) + (- 10c + 10b )cosh(x))sinh(x) +--R + +--R 2 4 2 2 2 +--R (2b c + 2b )cosh(x) + (- 4c - 2b c + 6b )cosh(x) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 210 + +--S 211 of 518 +t0942:= ((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^(3/2) +--R +--R +--R (207) +--R +------------------------------------+ +--R +---------+ | +---------+ +--R | 2 2 | | 2 2 +--R (\|- c + b + c sinh(x) + b cosh(x))\|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 518 +r0942:= 8/3*(b^2-c^2)^(1/2)*(c*cosh(x)+b*sinh(x))/((b^2-c^2)^(1/2)+_ + b*cosh(x)+c*sinh(x))^(1/2)+2/3*(c*cosh(x)+_ + b*sinh(x))*((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^(1/2) +--R +--R +--R (208) +--R +---------+ +--R | 2 2 2 +--R (10b sinh(x) + 10c cosh(x))\|- c + b + 2b c sinh(x) +--R + +--R 2 2 2 +--R (2c + 2b )cosh(x)sinh(x) + 2b c cosh(x) +--R / +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R 3\|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 212 + +--S 213 of 518 +a0942:= integrate(t0942,x) +--R +--R +--R (209) +--R 3 2 +--R (10c + 10b)sinh(x) + (30c + 30b)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((30c + 30b)cosh(x) + 10c - 10b)sinh(x) + (10c + 10b)cosh(x) +--R + +--R (10c - 10b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 2 2 4 2 2 3 +--R (c + 2b c + b )sinh(x) + (4c + 8b c + 4b )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 3 +--R (6c + 12b c + 6b )cosh(x) sinh(x) + (4c + 8b c + 4b )cosh(x) sinh(x) +--R + +--R 2 2 4 2 2 +--R (c + 2b c + b )cosh(x) - c + 2b c - b +--R / +--R 2 2 +--R (6sinh(x) + 12cosh(x)sinh(x) + 6cosh(x) ) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 518 +m0942:= a0942-r0942 +--R +--R +--R (210) +--R 3 2 +--R (10c + 10b)sinh(x) + (30c + 30b)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((30c + 30b)cosh(x) + 10c - 10b)sinh(x) + (10c + 10b)cosh(x) +--R + +--R (10c - 10b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 2 2 4 2 2 3 +--R (c + 2b c + b )sinh(x) + (4c + 8b c + 4b )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (6c + 12b c + 6b )cosh(x) sinh(x) +--R + +--R 2 2 3 2 2 4 2 +--R (4c + 8b c + 4b )cosh(x) sinh(x) + (c + 2b c + b )cosh(x) - c +--R + +--R 2 +--R 2b c - b +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R + +--R 3 2 +--R - 20b sinh(x) + (- 20c - 40b)cosh(x)sinh(x) +--R + +--R 2 3 +--R (- 40c - 20b)cosh(x) sinh(x) - 20c cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 4 2 2 3 +--R - 4b c sinh(x) + (- 4c - 8b c - 4b )cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 8c - 8b c - 8b )cosh(x) sinh(x) +--R + +--R 2 2 3 4 +--R (- 4c - 8b c - 4b )cosh(x) sinh(x) - 4b c cosh(x) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R / +--R 2 2 +--R (6sinh(x) + 12cosh(x)sinh(x) + 6cosh(x) ) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 214 + +--S 215 of 518 +d0942:= D(m0942,x) +--R +--R +--R (211) +--R 3 2 2 3 6 +--R (21c + 45b c + 27b c + 3b )sinh(x) +--R + +--R 3 2 2 3 5 +--R (108c + 252b c + 180b c + 36b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (225c + 585b c + 495b c + 135b )cosh(x) - 105c - 45b c +--R + +--R 2 3 +--R 105b c + 45b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (240c + 720b c + 720b c + 240b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 360c - 240b c + 360b c + 240b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (135c + 495b c + 585b c + 225b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 450c - 450b c + 450b c + 450b )cosh(x) + 63c - 81b c +--R + +--R 2 3 +--R - 27b c + 45b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (36c + 180b c + 252b c + 108b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 240c - 360b c + 240b c + 360b )cosh(x) +--R + +--R 3 2 2 3 +--R (108c - 108b c - 108b c + 108b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (3c + 27b c + 45b c + 21b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 45c - 105b c + 45b c + 105b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (45c - 27b c - 81b c + 63b )cosh(x) - 3c + 9b c - 9b c + 3b +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 4 3 2 2 3 7 +--R (3c + 9b c + 9b c + 3b c)sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (18c + 57b c + 63b c + 27b c + 3b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 3 +--R (45c + 153b c + 189b c + 99b c + 18b )cosh(x) - 63c - 81b c +--R + +--R 2 2 3 4 +--R 45b c + 81b c + 18b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (60c + 225b c + 315b c + 195b c + 45b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 270c - 405b c + 135b c + 405b c + 135b )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (45c + 195b c + 315b c + 225b c + 60b )cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (- 450c - 810b c + 90b c + 810b c + 360b )cosh(x) + 105c +--R + +--R 3 2 2 3 4 +--R - 45b c - 165b c + 45b c + 60b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (18c + 99b c + 189b c + 153b c + 45b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 360c - 810b c - 90b c + 810b c + 450b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (270c - 45b c - 495b c + 45b c + 225b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (3c + 27b c + 63b c + 57b c + 18b )cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 135c - 405b c - 135b c + 405b c + 270b )cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (225c + 45b c - 495b c - 45b c + 270b )cosh(x) - 21c +--R + +--R 3 2 2 3 4 +--R 45b c - 9b c - 33b c + 18b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 7 +--R (3b c + 9b c + 9b c + 3b )cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 18c - 81b c - 45b c + 81b c + 63b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (60c + 45b c - 165b c - 45b c + 105b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 18c + 33b c + 9b c - 45b c + 21b )cosh(x) +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R + +--R 3 2 2 3 6 +--R (- 64c - 48b c + 4b c + 12b )sinh(x) +--R + +--R 3 2 2 3 5 +--R (- 240c - 328b c - 48b c + 40b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 332c - 756b c - 352b c)cosh(x) + 128c - 48b c - 92b c +--R + +--R 3 +--R 12b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 184c - 776b c - 776b c - 184b )cosh(x) +--R + +--R 3 2 2 3 +--R (336c + 56b c - 336b c - 56b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 4 +--R (- 352b c - 756b c - 332b )cosh(x) +--R + +--R 3 2 2 3 2 +--R (276c + 348b c - 348b c - 276b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (40c - 48b c - 328b c - 240b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (56c + 336b c - 56b c - 336b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (12c + 4b c - 48b c - 64b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 12c + 92b c + 48b c - 128b )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 4 3 2 2 3 7 +--R (- 8c - 8b c - 4b c - 4b c)sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 32c - 64b c - 48b c - 20b c - 4b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (- 52c - 180b c - 184b c - 72b c - 16b )cosh(x) + 144c +--R + +--R 3 2 2 3 4 +--R 32b c - 156b c - 44b c + 24b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 48c - 244b c - 340b c - 176b c - 32b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (464c + 360b c - 504b c - 348b c + 28b )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 32c - 176b c - 340b c - 244b c - 48b )cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (516c + 884b c - 348b c - 860b c - 192b )cosh(x) - 40c +--R + +--R 3 2 2 3 +--R 40b c + 40b c - 40b c +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 16c - 72b c - 184b c - 180b c - 52b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (192c + 860b c + 348b c - 884b c - 516b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 80c + 40b c + 120b c - 40b c - 40b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4c - 20b c - 48b c - 64b c - 32b )cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 28c + 348b c + 504b c - 360b c - 464b )cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 40c - 40b c + 120b c + 40b c - 80b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 7 +--R (- 4b c - 4b c - 8b c - 8b )cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 24c + 44b c + 156b c - 32b c - 144b )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 40b c + 40b c + 40b c - 40b )cosh(x) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R / +--R 4 3 +--R (36c + 12b)sinh(x) + (120c + 72b)cosh(x)sinh(x) +--R + +--R 2 2 +--R ((144c + 144b)cosh(x) - 12c + 12b)sinh(x) +--R + +--R 3 +--R ((72c + 120b)cosh(x) + (- 24c + 24b)cosh(x))sinh(x) +--R + +--R 4 2 +--R (12c + 36b)cosh(x) + (- 12c + 12b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 2 5 2 2 4 +--R (12c + 12b c)sinh(x) + (48c + 60b c + 12b )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 3 +--R ((72c + 120b c + 48b )cosh(x) - 36c + 12b c + 24b )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((48c + 120b c + 72b )cosh(x) + (- 96c + 12b c + 84b )cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R ((12c + 60b c + 48b )cosh(x) + (- 84c - 12b c + 96b )cosh(x) ) +--R * +--R sinh(x) +--R + +--R 2 5 2 2 3 +--R (12b c + 12b )cosh(x) + (- 24c - 12b c + 36b )cosh(x) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 215 + +--S 216 of 518 +t0943:= ((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^(5/2) +--R +--R +--R (212) +--R +---------+ +--R | 2 2 2 2 +--R (2c sinh(x) + 2b cosh(x))\|- c + b + c sinh(x) + 2b c cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R b cosh(x) - c + b +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 216 + +--S 217 of 518 +r0943:= 64/15*(b^2-c^2)*(c*cosh(x)+b*sinh(x))/((b^2-c^2)^(1/2)+_ + b*cosh(x)+c*sinh(x))^(1/2)+16/15*(b^2-c^2)^(1/2)*(c*cosh(x)+_ + b*sinh(x))*((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^(1/2)+_ + 2/5*(c*cosh(x)+b*sinh(x))*((b^2-c^2)^(1/2)+b*cosh(x)+c*sinh(x))^(3/2) +--R +--R +--R (213) +--R 2 2 2 2 +--R (28b c sinh(x) + (28c + 28b )cosh(x)sinh(x) + 28b c cosh(x) ) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 2 3 3 2 2 +--R 6b c sinh(x) + (6c + 12b c)cosh(x)sinh(x) +--R + +--R 2 3 2 2 3 2 3 +--R ((12b c + 6b )cosh(x) - 86b c + 86b )sinh(x) + 6b c cosh(x) +--R + +--R 3 2 +--R (- 86c + 86b c)cosh(x) +--R / +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R 15\|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 217 + +--S 218 of 518 +a0943:= integrate(t0943,x) +--R +--R +--R (214) +--R 2 2 5 +--R (28c + 56b c + 28b )sinh(x) +--R + +--R 2 2 4 +--R (140c + 280b c + 140b )cosh(x)sinh(x) +--R + +--R 2 2 2 3 +--R (280c + 560b c + 280b )cosh(x) sinh(x) +--R + +--R 2 2 3 2 +--R (280c + 560b c + 280b )cosh(x) sinh(x) +--R + +--R 2 2 4 2 2 +--R ((140c + 280b c + 140b )cosh(x) - 28c + 56b c - 28b )sinh(x) +--R + +--R 2 2 5 2 2 +--R (28c + 56b c + 28b )cosh(x) + (- 28c + 56b c - 28b )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 3 2 2 3 6 +--R (3c + 9b c + 9b c + 3b )sinh(x) +--R + +--R 3 2 2 3 5 +--R (18c + 54b c + 54b c + 18b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (45c + 135b c + 135b c + 45b )cosh(x) - 175c - 175b c + 175b c +--R + +--R 3 +--R 175b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (60c + 180b c + 180b c + 60b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 700c - 700b c + 700b c + 700b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (45c + 135b c + 135b c + 45b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 1050c - 1050b c + 1050b c + 1050b )cosh(x) - 175c + 175b c +--R + +--R 2 3 +--R 175b c - 175b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (18c + 54b c + 54b c + 18b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 700c - 700b c + 700b c + 700b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 350c + 350b c + 350b c - 350b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (3c + 9b c + 9b c + 3b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 175c - 175b c + 175b c + 175b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 175c + 175b c + 175b c - 175b )cosh(x) + 3c - 9b c + 9b c - 3b +--R / +--R 3 2 2 3 +--R (60sinh(x) + 180cosh(x)sinh(x) + 180cosh(x) sinh(x) + 60cosh(x) ) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 518 +m0943:= a0943-r0943 +--R +--R +--R (215) +--R 2 2 5 +--R (28c + 56b c + 28b )sinh(x) +--R + +--R 2 2 4 +--R (140c + 280b c + 140b )cosh(x)sinh(x) +--R + +--R 2 2 2 3 +--R (280c + 560b c + 280b )cosh(x) sinh(x) +--R + +--R 2 2 3 2 +--R (280c + 560b c + 280b )cosh(x) sinh(x) +--R + +--R 2 2 4 2 2 +--R ((140c + 280b c + 140b )cosh(x) - 28c + 56b c - 28b )sinh(x) +--R + +--R 2 2 5 2 2 +--R (28c + 56b c + 28b )cosh(x) + (- 28c + 56b c - 28b )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 3 2 2 3 6 +--R (3c + 9b c + 9b c + 3b )sinh(x) +--R + +--R 3 2 2 3 5 +--R (18c + 54b c + 54b c + 18b )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 +--R (45c + 135b c + 135b c + 45b )cosh(x) - 175c - 175b c +--R + +--R 2 3 +--R 175b c + 175b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (60c + 180b c + 180b c + 60b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 700c - 700b c + 700b c + 700b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (45c + 135b c + 135b c + 45b )cosh(x) +--R + +--R 3 2 2 3 2 3 +--R (- 1050c - 1050b c + 1050b c + 1050b )cosh(x) - 175c +--R + +--R 2 2 3 +--R 175b c + 175b c - 175b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 3 5 +--R (18c + 54b c + 54b c + 18b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (- 700c - 700b c + 700b c + 700b )cosh(x) +--R + +--R 3 2 2 3 +--R (- 350c + 350b c + 350b c - 350b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (3c + 9b c + 9b c + 3b )cosh(x) +--R + +--R 3 2 2 3 4 +--R (- 175c - 175b c + 175b c + 175b )cosh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 175c + 175b c + 175b c - 175b )cosh(x) + 3c - 9b c + 9b c - 3b +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R + +--R 5 2 2 4 +--R - 112b c sinh(x) + (- 112c - 336b c - 112b )cosh(x)sinh(x) +--R + +--R 2 2 2 3 +--R (- 336c - 448b c - 336b )cosh(x) sinh(x) +--R + +--R 2 2 3 2 +--R (- 336c - 448b c - 336b )cosh(x) sinh(x) +--R + +--R 2 2 4 5 +--R (- 112c - 336b c - 112b )cosh(x) sinh(x) - 112b c cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 2 6 3 2 2 5 +--R - 24b c sinh(x) + (- 24c - 72b c - 48b c)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 2 3 +--R ((- 72c - 120b c - 144b c - 24b )cosh(x) + 344b c - 344b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 3 3 +--R (- 72c - 168b c - 168b c - 72b )cosh(x) +--R + +--R 3 2 2 3 +--R (344c + 1032b c - 344b c - 1032b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 3 4 +--R (- 24c - 144b c - 120b c - 72b )cosh(x) +--R + +--R 3 2 2 3 2 +--R (1032c + 1032b c - 1032b c - 1032b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 +--R (- 48b c - 72b c - 24b )cosh(x) +--R + +--R 3 2 2 3 3 +--R (1032c + 344b c - 1032b c - 344b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 3 2 4 +--R - 24b c cosh(x) + (344c - 344b c)cosh(x) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R / +--R 3 2 2 3 +--R (60sinh(x) + 180cosh(x)sinh(x) + 180cosh(x) sinh(x) + 60cosh(x) ) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 219 + +--S 220 of 518 +d0943:= D(m0943,x) +--R +--R +--R (216) +--R 4 3 2 2 3 4 8 +--R (135c + 420b c + 450b c + 180b c + 15b )sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (960c + 3120b c + 3600b c + 1680b c + 240b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2940c + 10080b c + 12600b c + 6720b c + 1260b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R - 1260c - 1680b c + 840b c + 1680b c + 420b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (5040c + 18480b c + 25200b c + 15120b c + 3360b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 6720c - 10080b c + 3360b c + 10080b c + 3360b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (5250c + 21000b c + 31500b c + 21000b c + 5250b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 14700c - 25200b c + 4200b c + 25200b c + 10500b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 2 3 4 +--R 1890c - 840b c - 2940b c + 840b c + 1050b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (3360c + 15120b c + 25200b c + 18480b c + 5040b )cosh(x) +--R + +--R 4 3 3 4 3 +--R (- 16800c - 33600b c + 33600b c + 16800b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (6720c - 1680b c - 11760b c + 1680b c + 5040b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (1260c + 6720b c + 12600b c + 10080b c + 2940b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 10500c - 25200b c - 4200b c + 25200b c + 14700b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 4 2 2 4 2 4 3 +--R (8820c - 17640b c + 8820b )cosh(x) - 540c + 1200b c +--R + +--R 2 2 3 4 +--R - 360b c - 720b c + 420b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (240c + 1680b c + 3600b c + 3120b c + 960b )cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 3360c - 10080b c - 3360b c + 10080b c + 6720b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (5040c + 1680b c - 11760b c - 1680b c + 6720b )cosh(x) +--R + +--R 4 3 3 4 +--R (- 960c + 1920b c - 1920b c + 960b )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 8 +--R (15c + 180b c + 450b c + 420b c + 135b )cosh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 420c - 1680b c - 840b c + 1680b c + 1260b )cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (1050c + 840b c - 2940b c - 840b c + 1890b )cosh(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (- 420c + 720b c + 360b c - 1200b c + 540b )cosh(x) + 15c +--R + +--R 3 2 2 3 4 +--R - 60b c + 90b c - 60b c + 15b +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 5 4 2 3 3 2 4 9 +--R (15c + 60b c + 90b c + 60b c + 15b c)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (120c + 495b c + 780b c + 570b c + 180b c + 15b )cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (420c + 1800b c + 3000b c + 2400b c + 900b c + 120b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R - 540c - 1200b c - 240b c + 1080b c + 780b c + 120b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (840c + 3780b c + 6720b c + 5880b c + 2520b c + 420b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 3360c - 7980b c - 2520b c + 6720b c + 5880b c + 1260b ) +--R * +--R cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (1050c + 5040b c + 9660b c + 9240b c + 4410b c + 840b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 8820c - 22680b c - 10080b c + 17640b c + 18900b c +--R + +--R 5 +--R 5040b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R 1890c + 840b c - 3780b c - 1680b c + 1890b c + 840b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (840c + 4410b c + 9240b c + 9660b c + 5040b c + 1050b ) +--R * +--R 5 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 12600c - 35700b c - 21000b c + 25200b c + 33600b c +--R + +--R 5 +--R 10500b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (8400c + 5250b c - 16800b c - 10500b c + 8400b c + 5250b ) +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (420c + 2520b c + 5880b c + 6720b c + 3780b c + 840b ) +--R * +--R 6 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 10500c - 33600b c - 25200b c + 21000b c + 35700b c +--R + +--R 5 +--R 12600b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 14700c + 12600b c - 29400b c - 25200b c + 14700b c +--R + +--R 5 +--R 12600b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R - 1260c + 1680b c + 1680b c - 2520b c - 420b c + 840b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (120c + 900b c + 2400b c + 3000b c + 1800b c + 420b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 5040c - 18900b c - 17640b c + 10080b c + 22680b c +--R + +--R 5 +--R 8820b +--R * +--R 5 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 12600c + 14700b c - 25200b c - 29400b c + 12600b c +--R + +--R 5 +--R 14700b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 3360c + 3780b c + 5880b c - 6720b c - 2520b c + 2940b ) +--R * +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (15c + 180b c + 570b c + 780b c + 495b c + 120b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 1260c - 5880b c - 6720b c + 2520b c + 7980b c + 3360b ) +--R * +--R 6 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (5250c + 8400b c - 10500b c - 16800b c + 5250b c + 8400b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 2940c + 2520b c + 6720b c - 5880b c - 3780b c + 3360b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R 135c - 420b c + 330b c + 180b c - 345b c + 120b +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 9 +--R (15b c + 60b c + 90b c + 60b c + 15b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 120c - 780b c - 1080b c + 240b c + 1200b c + 540b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (840c + 1890b c - 1680b c - 3780b c + 840b c + 1890b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 840c + 420b c + 2520b c - 1680b c - 1680b c + 1260b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (120c - 345b c + 180b c + 330b c - 420b c + 135b )cosh(x) +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R + +--R 4 3 2 2 3 8 +--R (- 368c - 272b c - 352b c - 208b c)sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 1744c - 3264b c - 2848b c - 1536b c - 208b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 3648c - 11776b c - 11488b c - 5504b c - 1184b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R 2784c + 416b c - 2544b c - 896b c + 240b +--R * +--R 6 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 4720c - 20608b c - 25952b c - 12992b c - 2928b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (11552c + 7712b c - 11616b c - 7712b c + 64b )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 4400c - 20640b c - 33920b c - 20640b c - 4400b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (18608c + 25664b c - 15600b c - 24224b c - 4448b )cosh(x) +--R + +--R 4 3 2 2 3 +--R - 688c + 688b c + 688b c - 688b c +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2928c - 12992b c - 25952b c - 20608b c - 4720b ) +--R * +--R 5 +--R cosh(x) +--R + +--R 4 3 3 4 3 +--R (14112c + 35776b c - 35776b c - 14112b )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2064c + 1376b c + 2752b c - 1376b c - 688b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 1184c - 5504b c - 11488b c - 11776b c - 3648b )cosh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (4448c + 24224b c + 15600b c - 25664b c - 18608b )cosh(x) +--R + +--R 4 2 2 4 2 +--R (- 2064c + 4128b c - 2064b )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 208c - 1536b c - 2848b c - 3264b c - 1744b )cosh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 64c + 7712b c + 11616b c - 7712b c - 11552b )cosh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 688c - 1376b c + 2752b c + 1376b c - 2064b )cosh(x) +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 8 +--R (- 208b c - 352b c - 272b c - 368b )cosh(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 240c + 896b c + 2544b c - 416b c - 2784b )cosh(x) +--R + +--R 3 2 2 3 4 4 +--R (- 688b c + 688b c + 688b c - 688b )cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 5 4 2 3 3 2 9 +--R (- 48c - 48b c - 72b c - 72b c )sinh(x) +--R + +--R 5 4 2 3 3 2 4 8 +--R (- 240c - 576b c - 696b c - 504b c - 144b c)cosh(x)sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 552c - 2232b c - 2976b c - 2016b c - 792b c - 72b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R 1504c + 864b c - 1088b c - 1104b c - 296b c + 120b +--R * +--R 7 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 840c - 4344b c - 7104b c - 5376b c - 2136b c - 360b ) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (6880c + 8800b c - 4208b c - 8864b c - 2792b c + 184b )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 960c - 5040b c - 10272b c - 9312b c - 3888b c - 768b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (12896c + 27568b c - 304b c - 25760b c - 12952b c - 1448b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R - 2288c + 912b c + 3784b c - 1032b c - 1496b c + 120b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 768c - 3888b c - 9312b c - 10272b c - 5040b c - 960b ) +--R * +--R 5 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 12624c + 40448b c + 19008b c - 34192b c - 31272b c +--R + +--R 5 +--R - 6616b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 8240c - 224b c + 15688b c + 1240b c - 7448b c - 1016b ) +--R * +--R cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 360c - 2136b c - 5376b c - 7104b c - 4344b c - 840b ) +--R * +--R 6 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R 6616c + 31272b c + 34192b c - 19008b c - 40448b c +--R + +--R 5 +--R - 12624b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 10872c - 7640b c + 23328b c + 13696b c - 12456b c +--R + +--R 5 +--R - 6056b +--R * +--R 2 +--R cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 72c - 792b c - 2016b c - 2976b c - 2232b c - 552b ) +--R * +--R 7 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (1448c + 12952b c + 25760b c + 304b c - 27568b c - 12896b ) +--R * +--R 5 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R - 6056c - 12456b c + 13696b c + 23328b c - 7640b c +--R + +--R 5 +--R - 10872b +--R * +--R 3 +--R cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (- 144b c - 504b c - 696b c - 576b c - 240b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 184c + 2792b c + 8864b c + 4208b c - 8800b c - 6880b ) +--R * +--R 6 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 1016c - 7448b c + 1240b c + 15688b c - 224b c - 8240b ) +--R * +--R 4 +--R cosh(x) +--R * +--R sinh(x) +--R + +--R 2 3 3 2 4 5 9 +--R (- 72b c - 72b c - 48b c - 48b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 120c + 296b c + 1104b c + 1088b c - 864b c - 1504b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (120c - 1496b c - 1032b c + 3784b c + 912b c - 2288b )cosh(x) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R / +--R 5 4 +--R (360c + 120b)sinh(x) + (1560c + 840b)cosh(x)sinh(x) +--R + +--R 2 3 +--R ((2640c + 2160b)cosh(x) - 120c + 120b)sinh(x) +--R + +--R 3 2 +--R ((2160c + 2640b)cosh(x) + (- 360c + 360b)cosh(x))sinh(x) +--R + +--R 4 2 +--R ((840c + 1560b)cosh(x) + (- 360c + 360b)cosh(x) )sinh(x) +--R + +--R 5 3 +--R (120c + 360b)cosh(x) + (- 120c + 120b)cosh(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- c + b +--R + +--R 2 6 2 2 5 +--R (120c + 120b c)sinh(x) + (600c + 720b c + 120b )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 4 +--R ((1200c + 1800b c + 600b )cosh(x) - 360c + 120b c + 240b )sinh(x) +--R + +--R 2 2 3 +--R (1200c + 2400b c + 1200b )cosh(x) +--R + +--R 2 2 +--R (- 1320c + 240b c + 1080b )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 2 2 +--R ((600c + 1800b c + 1200b )cosh(x) + (- 1800c + 1800b )cosh(x) ) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 +--R (120c + 720b c + 600b )cosh(x) +--R + +--R 2 2 3 +--R (- 1080c - 240b c + 1320b )cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 +--R (120b c + 120b )cosh(x) + (- 240c - 120b c + 360b )cosh(x) +--R * +--R ROOT +--R +---------+ +--R | 2 2 2 +--R (2sinh(x) + 2cosh(x))\|- c + b + (c + b)sinh(x) +--R + +--R 2 +--R (2c + 2b)cosh(x)sinh(x) + (c + b)cosh(x) - c + b +--R / +--R 2sinh(x) + 2cosh(x) +--R * +--R +------------------------------------+ +--R | +---------+ +--R | | 2 2 +--R \|\|- c + b + c sinh(x) + b cosh(x) +--R Type: Expression(Integer) +--E 220 + +--S 221 of 518 +t0944:= 1/(a+b*cosh(x)+c*sinh(x))^2 +--R +--R +--R (217) +--R 1 +--R -------------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sinh(x) + (2b c cosh(x) + 2a c)sinh(x) + b cosh(x) + 2a b cosh(x) + a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 518 +r0944:= -2*a*atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ + (a^2-b^2+c^2)^(3/2)-(c*cosh(x)+b*sinh(x))/_ + (a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x)) +--R +--R +--R (218) +--R x +--R (b - a)tanh(-) + c +--R 2 2 +--R (- 2a c sinh(x) - 2a b cosh(x) - 2a )atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R +------------+ +--R | 2 2 2 +--R (- b sinh(x) - c cosh(x))\|c - b + a +--R / +--R 3 2 2 2 3 2 2 2 +--R (c + (- b + a )c)sinh(x) + (b c - b + a b)cosh(x) + a c - a b +--R + +--R 3 +--R a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 222 + +--S 223 of 518 +a0944:= integrate(t0944,x) +--R +--R +--R (219) +--R [ +--R 2 2 +--R (a c + a b)sinh(x) + ((2a c + 2a b)cosh(x) + 2a )sinh(x) +--R + +--R 2 2 +--R (a c + a b)cosh(x) + 2a cosh(x) - a c + a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R +------------+ +--R | 2 2 2 +--R (2a sinh(x) + 2a cosh(x) - 2c + 2b)\|c - b + a +--R / +--R 3 2 2 2 3 2 2 +--R (c + b c + (- b + a )c - b + a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (c + b c + (- b + a )c - b + a b)cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 2 +--R (2a c - 2a b + 2a )cosh(x) - c + b c + (b - a )c - b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R , +--R +--R 2 2 +--R (- 2a c - 2a b)sinh(x) + ((- 4a c - 4a b)cosh(x) - 4a )sinh(x) +--R + +--R 2 2 +--R (- 2a c - 2a b)cosh(x) - 4a cosh(x) + 2a c - 2a b +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (2a sinh(x) + 2a cosh(x) - 2c + 2b)\|- c + b - a +--R / +--R 3 2 2 2 3 2 2 +--R (c + b c + (- b + a )c - b + a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (c + b c + (- b + a )c - b + a b)cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 2 +--R (2a c - 2a b + 2a )cosh(x) - c + b c + (b - a )c - b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 223 + +--S 224 of 518 +m0944a:= a0944.1-r0944 +--R +--R +--R (220) +--R 2 3 +--R (a c + a b c)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((2a c + 3a b c + a b )cosh(x) + 3a c + a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (a c + 3a b c + 2a b )cosh(x) + (4a c + 4a b)cosh(x) - a c +--R + +--R 3 +--R a b c + 2a +--R * +--R sinh(x) +--R + +--R 2 3 2 2 2 +--R (a b c + a b )cosh(x) + (a c + 3a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- a b c + a b + 2a )cosh(x) - a c + a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c - 2b c + (2b - 2a )c + 2b - 2a b)cosh(x) - 2a c +--R + +--R 2 3 +--R 2a b - 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 2 3 +--R (2a c + 2a b c)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((4a c + 6a b c + 2a b )cosh(x) + 6a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (2a c + 6a b c + 4a b )cosh(x) + (8a c + 8a b)cosh(x) - 2a c +--R + +--R 3 +--R 2a b c + 4a +--R * +--R sinh(x) +--R + +--R 2 3 2 2 2 +--R (2a b c + 2a b )cosh(x) + (2a c + 6a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- 2a b c + 2a b + 4a )cosh(x) - 2a c + 2a b +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 3 2 2 2 +--R (b c + b )sinh(x) + ((c + 3b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (2c + 3b c + b )cosh(x) + (4a c + 4a b)cosh(x) - 2c + b c + b +--R + +--R 2 +--R 2a +--R * +--R sinh(x) +--R + +--R 2 3 2 +--R (c + b c)cosh(x) + (2a c + 2a b)cosh(x) +--R + +--R 2 2 2 +--R (- c - b c + 2b + 2a )cosh(x) - 2a c + 2a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 4 3 2 2 2 3 2 3 +--R (c + b c + (- b + a )c + (- b + a b)c)sinh(x) +--R + +--R 4 3 2 2 2 3 2 4 2 2 +--R (2c + 3b c + (- b + 2a )c + (- 3b + 3a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 3a c + a b c + (- 3a b + 3a )c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 2 3 2 4 2 2 2 +--R (c + 3b c + (b + a )c + (- 3b + 3a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (4a c + 4a b c + (- 4a b + 4a )c - 4a b + 4a b)cosh(x) - c +--R + +--R 3 2 2 2 3 2 2 2 4 +--R b c + (b + a )c + (- b + a b)c - 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 2 2 3 +--R (b c + b c + (- b + a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 2 +--R (a c + 3a b c + (- a b + a )c - 3a b + 3a b)cosh(x) +--R + +--R 3 2 2 2 3 2 4 2 2 4 3 +--R (- b c + (b + 2a )c + (b - a b)c - b - a b + 2a )cosh(x) - a c +--R + +--R 2 2 3 3 3 +--R a b c + (a b - a )c - a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 518 +d0944a:= D(m0944a,x) +--R +--R +--R (221) +--R 4 2 3 2 2 4 3 5 4 6 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )sinh(x) +--R + +--R 4 2 3 2 2 4 3 5 +--R 4b c + (8b + 2a b)c + 8a b c + (- 8b + 10a b )c - 4b +--R + +--R 4 +--R 4a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 4 +--R (5a b + a )c + (6a b + 2a b)c + (- 3a b + 5a b )c - 4a b +--R + +--R 2 3 +--R 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 2 2 4 3 +--R (5b + a)c + (10b + 10a b)c + 23a b c + (- 10b + 20a b )c +--R + +--R 5 4 +--R - 5b + 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 +--R (16a b + 4a )c + (21a b + 17a b)c + (- 6a b + 26a b )c +--R + +--R 4 2 3 +--R - 11a b + 13a b +--R * +--R cosh(x) +--R + +--R 4 2 2 3 2 2 2 3 5 +--R (2b - 4a)c + (2a b + 12a b + a )c + (4a b + 6a b)c - 2b +--R + +--R 4 2 3 3 2 +--R 2a b - 4a b + 5a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (4a c + 20a b c + 32a b c + 20a b c + 4a b )cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 +--R (14a b + 10a )c + (24a b + 44a b)c + (6a b + 50a b )c +--R + +--R 4 2 3 +--R - 4a b + 16a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 2 2 3 2 +--R (4b - 8a)c + (8b - 12a b)c + (4a b + 28a b + 8a )c +--R + +--R 4 3 2 2 3 5 4 2 3 +--R (- 8b + 12a b + 24a b + 24a b)c - 4b + 4a b - 4a b +--R + +--R 3 2 +--R 16a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 3 2 2 3 4 +--R (2a b - 10a )c + 4a b c + (- 2a b + 6a b + 12a b)c - 4a b +--R + +--R 2 3 4 +--R 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 2 2 +--R (- 5b + 6a)c + (- 10b + 20a b)c + 23a b c +--R + +--R 4 3 5 4 +--R (10b + 10a b )c + 5b + a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 4a b + 16a )c + (6a b + 50a b)c + (24a b + 44a b )c +--R + +--R 4 2 3 +--R 14a b + 10a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R (4b - 6a)c + (16b - 24a b)c + (16a b + 18a )c +--R + +--R 4 3 2 2 3 5 4 2 3 +--R (- 16b + 24a b + 40a b + 36a b)c - 4b + 6a b + 16a b +--R + +--R 3 2 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 2 2 +--R (8a b - 20a )c + (10a b - 18a b)c +--R + +--R 3 2 2 3 4 4 2 3 3 2 +--R (- 8a b + 24a b + 24a b + 4a )c - 10a b + 14a b + 12a b +--R + +--R 4 +--R 8a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 3 2 4 3 2 2 3 +--R b c - 2b c + (a b - 10a )c + (2b - 2a b + 4a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 +--R - b + a b - 4a b + 6a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 2 2 4 3 +--R (- 4b + 4a)c + (- 8b + 10a b)c + 8a b c + (8b + 2a b )c +--R + +--R 5 +--R 4b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 11a b + 13a )c + (- 6a b + 26a b)c + (21a b + 17a b )c +--R + +--R 4 2 3 +--R 16a b + 4a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 2 3 2 2 3 2 +--R (4b - 4a)c + (8b - 12a b)c + (- 4a b - 4a b + 16a )c +--R + +--R 4 3 2 2 3 5 4 2 3 +--R (- 8b + 12a b + 24a b + 24a b)c - 4b + 8a b + 28a b +--R + +--R 3 2 +--R 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 2 2 2 +--R (10a b - 14a )c + (8a b - 24a b)c +--R + +--R 3 2 2 3 4 4 2 3 3 2 +--R (- 10a b + 18a b + 12a b + 8a )c - 8a b + 20a b + 24a b +--R + +--R 4 +--R 4a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 3 2 3 2 3 3 2 +--R 2a b c + (- 4a b + 4a b - 16a )c + 2a b c - 4a b + 16a b +--R + +--R 4 +--R 8a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 4 4 +--R (a b + a )c + (- 2a b - 2a b)c + (a b + a b - 4a )c + 4a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 5 6 +--R ((- b + a)c + (- 2b + 2a b)c + a b c + 2b c + b )cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 4 +--R (- 4a b + 4a )c + (- 3a b + 5a b)c + (6a b + 2a b )c + 5a b +--R + +--R 2 3 +--R a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 2 2 3 2 2 2 3 5 +--R (2b - 2a)c + (- 2a b - 4a b + 5a )c + (4a b + 6a b)c - 2b +--R + +--R 4 2 3 3 2 +--R 4a b + 12a b + a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 2 2 2 3 4 4 +--R (4a b - 4a )c + (2a b - 6a b)c + (- 4a b + 4a )c - 2a b +--R + +--R 2 3 3 2 +--R 10a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 2 3 2 2 3 2 +--R (- b + a)c + (2b - 2a b)c + (a b + 4a b - 6a )c +--R + +--R 4 2 2 3 5 3 2 4 +--R (- 2b - 4a b - 4a b)c + b + 10a b + 4a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 2 2 4 4 2 3 4 +--R ((a b + a b)c + (- 2a b - 2a b - 4a )c + a b + a b + 4a b) +--R * +--R cosh(x) +--R + +--R 3 2 3 3 2 +--R a c - 2a b c + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 4 3 2 4 6 +--R (2c + 4b c - 4b c - 2b c)sinh(x) +--R + +--R 5 4 3 2 4 4 3 +--R (8c + 16b c - 16b c - 8b c)cosh(x) + 10a c + 12a b c +--R + +--R 2 2 3 +--R - 6a b c - 8a b c +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 4 2 +--R (10c + 20b c - 20b c - 10b c)cosh(x) +--R + +--R 4 3 2 2 3 5 2 3 +--R (32a c + 42a b c - 12a b c - 22a b c)cosh(x) + 4c + 24a c +--R + +--R 2 2 4 2 2 +--R 8a b c + (- 4b - 8a b )c +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 2 +--R (28a c + 48a b c + 12a b c - 8a b c)cosh(x) +--R + +--R 5 4 2 3 3 2 2 4 2 2 +--R (8c + 16b c + 56a c + (- 16b + 48a b)c + (- 8b - 8a b )c) +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 +--R 4a c + 8a b c + (- 4a b + 24a )c - 8a b c +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 4 4 +--R (- 10c - 20b c + 20b c + 10b c)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 8a c + 12a b c + 48a b c + 28a b c)cosh(x) +--R + +--R 5 4 2 3 3 2 2 +--R 8c + 32b c + 32a c + (- 32b + 80a b)c +--R + +--R 4 2 2 +--R (- 8b + 32a b )c +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 +--R (16a c + 20a b c + (- 16a b + 48a )c + (- 20a b + 24a b)c) +--R * +--R cosh(x) +--R + +--R 5 4 3 2 2 4 2 2 4 +--R 2c - 4b c + (4b + 8a b)c + (- 2b - 8a b + 8a )c +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 4 5 +--R (- 8c - 16b c + 16b c + 8b c)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 22a c - 12a b c + 42a b c + 32a b c)cosh(x) +--R + +--R 5 4 2 3 3 2 2 4 2 2 +--R (8c + 16b c - 8a c + (- 16b + 48a b)c + (- 8b + 56a b )c) +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 +--R (20a c + 16a b c + (- 20a b + 24a )c + (- 16a b + 48a b)c) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 2 4 4 3 2 2 +--R (8a c + (- 8a b + 16a )c)cosh(x) + 2a c - 4a b c + 2a b c +--R * +--R sinh(x) +--R + +--R 5 4 3 2 4 6 +--R (- 2c - 4b c + 4b c + 2b c)cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 8a c - 6a b c + 12a b c + 10a b c)cosh(x) +--R + +--R 5 2 3 2 2 4 2 2 4 +--R (4c - 8a c + 8a b c + (- 4b + 24a b )c)cosh(x) +--R + +--R 4 3 2 2 3 3 3 +--R (8a c + 4a b c - 8a b c + (- 4a b + 24a b)c)cosh(x) +--R + +--R 5 4 2 3 3 2 2 4 4 2 +--R (- 2c + 4b c + 8a c + (- 4b - 8a b)c + (2b + 8a )c)cosh(x) +--R + +--R 3 2 2 3 +--R (2a b c - 4a b c + 2a b c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 3 2 2 4 3 5 4 6 +--R (b c + 2b c - a b c + (- 2b - 2a b )c - b - a b )sinh(x) +--R + +--R 4 2 3 2 2 4 3 5 +--R 4b c + (8b - 2a b)c - 8a b c + (- 8b - 10a b )c - 4b +--R + +--R 4 +--R - 4a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 4 2 3 +--R (5a b - a )c + (6a b - 2a b)c + (- 3a b - 5a b )c - 4a b - 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 2 2 4 3 +--R (5b - a)c + (10b - 10a b)c - 23a b c + (- 10b - 20a b )c +--R + +--R 5 4 +--R - 5b - 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 +--R (16a b - 4a )c + (21a b - 17a b)c + (- 6a b - 26a b )c +--R + +--R 4 2 3 +--R - 11a b - 13a b +--R * +--R cosh(x) +--R + +--R 4 2 2 3 2 2 2 3 5 +--R (2b + 4a)c + (- 2a b + 12a b - a )c + (4a b - 6a b)c - 2b +--R + +--R 4 2 3 3 2 +--R - 2a b - 4a b - 5a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 4a c - 20a b c - 32a b c - 20a b c - 4a b )cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 4 +--R (14a b - 10a )c + (24a b - 44a b)c + (6a b - 50a b )c - 4a b +--R + +--R 2 3 +--R - 16a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 2 2 3 2 +--R (4b + 8a)c + (8b + 12a b)c + (- 4a b + 28a b - 8a )c +--R + +--R 4 3 2 2 3 5 4 2 3 3 2 +--R (- 8b - 12a b + 24a b - 24a b)c - 4b - 4a b - 4a b - 16a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 3 2 2 3 4 +--R (2a b + 10a )c + 4a b c + (- 2a b - 6a b + 12a b)c - 4a b +--R + +--R 2 3 4 +--R - 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 2 2 4 3 +--R (- 5b - 6a)c + (- 10b - 20a b)c - 23a b c + (10b - 10a b )c +--R + +--R 5 4 +--R 5b - a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 4a b - 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32a b + 56a b + 56a b)c +--R + +--R 5 2 4 3 3 4 2 6 2 5 3 4 +--R (- 68a b - 68a b + 68a b + 68a b )c - 24a b - 24a b + 24a b +--R + +--R 4 3 +--R 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 2 5 3 2 2 3 4 +--R (- 2b - 2a)c + (- 8b - 8a b)c + (2b + 2a b + 32a b + 32a )c +--R + +--R 4 3 2 2 3 3 +--R (16b + 16a b + 68a b + 68a b)c +--R + +--R 5 4 4 5 2 +--R (2b + 2a b + 34a b + 34a )c +--R + +--R 6 5 2 4 3 3 4 2 5 7 6 +--R (- 8b - 8a b - 68a b - 68a b + 76a b + 76a b)c - 2b - 2a b +--R + +--R 2 5 3 4 4 3 5 2 +--R - 32a b - 32a b + 34a b + 34a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 5 2 2 4 +--R (- 12a b - 12a )c + (- 8a b - 8a b)c +--R + +--R 3 2 2 3 4 3 +--R (28a b + 28a b + 16a b + 16a )c +--R + +--R 4 2 3 3 2 4 2 +--R (12a b + 12a b + 12a b + 12a b)c +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 16a b - 16a b - 12a b - 12a b + 28a b + 28a )c - 4a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 4a b - 16a b - 16a b + 20a b + 20a b +--R * +--R cosh(x) +--R + +--R 6 2 5 2 3 4 +--R (b + a)c + (- 2b - 2a b)c + (- 9a b - 9a )c +--R + +--R 4 3 2 2 3 3 +--R (2b + 2a b + 6a b + 6a b)c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- b - a b + 13a b + 13a b - 6a b - 6a )c +--R + +--R 2 4 3 3 4 2 5 2 5 3 4 4 3 5 2 +--R (- 8a b - 8a b + 8a b + 8a b)c - 2a b - 2a b - 2a b - 2a b +--R + +--R 6 7 +--R 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 2 4 4 3 2 2 3 3 +--R (2b + 2a b)c + (8b + 8a b )c + (8b + 8a b + 2a b + 2a b)c +--R + +--R 5 4 2 3 3 2 2 +--R (- 4b - 4a b + 8a b + 8a b )c +--R + +--R 6 5 2 4 3 3 7 6 2 5 3 4 +--R (- 10b - 10a b + 10a b + 10a b )c - 4b - 4a b + 4a b + 4a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 5 2 2 4 +--R (2a b + 2a )c + (20a b + 20a b)c +--R + +--R 3 2 2 3 4 3 3 2 4 2 +--R (36a b + 36a b + 2a b + 2a )c + (20a b + 20a b)c +--R + +--R 5 2 4 3 3 4 2 6 2 5 3 4 +--R (- 38a b - 38a b + 38a b + 38a b )c - 20a b - 20a b + 20a b +--R + +--R 4 3 +--R 20a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 5 3 2 2 3 4 +--R (- 4b - 4a b)c + (- 4b - 4a b + 12a b + 12a )c +--R + +--R 4 3 2 2 3 3 +--R (8b + 8a b + 44a b + 44a b)c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (8b + 8a b + 20a b + 20a b + 12a b + 12a )c +--R + +--R 6 5 2 4 3 3 4 2 5 7 6 +--R (- 4b - 4a b - 44a b - 44a b + 48a b + 48a b)c - 4b - 4a b +--R + +--R 2 5 3 4 4 3 5 2 +--R - 32a b - 32a b + 36a b + 36a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 5 2 2 4 +--R (- 4a b - 4a )c + (- 16a b - 16a b)c +--R + +--R 3 2 2 3 4 3 +--R (12a b + 12a b + 16a b + 16a )c +--R + +--R 4 2 3 3 2 4 2 +--R (28a b + 28a b + 12a b + 12a b)c +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 8a b - 8a b - 12a b - 12a b + 20a b + 20a )c - 12a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 12a b - 16a b - 16a b + 28a b + 28a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 5 3 2 2 3 4 +--R (2b + 2a b)c + (- 4b - 4a b - 12a b - 12a )c +--R + +--R 2 2 3 3 5 4 2 3 3 2 4 5 2 +--R (2a b + 2a b)c + (4b + 4a b + 20a b + 20a b - 4a b - 4a )c +--R + +--R 6 5 2 4 3 3 2 5 3 4 4 3 +--R (- 2b - 2a b + 2a b + 2a b )c - 12a b - 12a b + 4a b +--R + +--R 5 2 6 7 +--R 4a b + 8a b + 8a +--R * +--R cosh(x) +--R + +--R 2 5 2 2 4 3 4 3 +--R (2a b + 2a )c + (- 4a b - 4a b)c + (- 2a b - 2a )c +--R + +--R 4 2 3 2 5 2 4 3 3 4 2 5 6 +--R (4a b + 4a b )c + (- 2a b - 2a b + 6a b + 6a b - 4a b - 4a )c +--R + +--R 3 4 4 3 5 2 6 +--R - 4a b - 4a b + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 3 2 4 4 3 3 2 3 3 2 2 +--R (b + a b )c + (2b + 2a b )c + (a b + a b )c +--R + +--R 6 5 2 4 3 3 7 6 2 5 3 4 +--R (- 2b - 2a b + 2a b + 2a b )c - b - a b + a b + a b +--R * +--R 6 +--R cosh(x) +--R + +--R 2 2 4 3 2 2 3 +--R (2a b + 2a b)c + (8a b + 8a b )c +--R + +--R 4 2 3 3 2 4 2 5 2 4 3 3 4 2 +--R (4a b + 4a b + 2a b + 2a b)c + (- 8a b - 8a b + 8a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 +--R - 6a b - 6a b + 6a b + 6a b +--R * +--R 5 +--R cosh(x) +--R + +--R 3 2 2 3 4 2 2 3 3 +--R (- 2b - 2a b + a b + a )c + (10a b + 10a b)c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (4b + 4a b + 10a b + 10a b + a b + a )c +--R + +--R 2 4 3 3 4 2 5 7 6 2 5 3 4 +--R (- 10a b - 10a b + 10a b + 10a b)c - 2b - 2a b - 11a b - 11a b +--R + +--R 4 3 5 2 +--R 13a b + 13a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 2 4 3 2 2 3 4 3 +--R (- 4a b - 4a b)c + (- 4a b - 4a b + 4a b + 4a )c +--R + +--R 4 2 3 3 2 4 2 +--R (12a b + 12a b + 8a b + 8a b)c +--R + +--R 5 2 4 3 3 4 2 5 6 6 2 5 3 4 +--R (4a b + 4a b - 8a b - 8a b + 4a b + 4a )c - 8a b - 8a b - 4a b +--R + +--R 4 3 5 2 6 +--R - 4a b + 12a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 3 +--R (b + a b - 2a b - 2a )c + (- 2b - 2a b - 8a b - 8a b)c +--R + +--R 2 3 3 2 4 5 2 +--R (13a b + 13a b + 2a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 7 6 2 5 +--R (2b + 2a b + 6a b + 6a b - 8a b - 8a b)c - b - a b - 9a b +--R + +--R 3 4 4 3 5 2 6 7 +--R - 9a b + 6a b + 6a b + 4a b + 4a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3 2 2 3 4 3 +--R (2a b + 2a b)c + (- 4a b - 4a b - 4a b - 4a )c +--R + +--R 3 2 4 2 5 2 4 5 6 6 2 5 +--R (6a b + 6a b)c + (4a b + 4a b - 4a b - 4a )c - 2a b - 2a b +--R + +--R 3 4 4 3 5 2 6 +--R - 2a b - 2a b + 4a b + 4a b +--R * +--R cosh(x) +--R + +--R 2 3 4 2 2 3 3 4 5 2 +--R (a b + a )c + (- 2a b - 2a b)c + (a b + a )c +--R + +--R 2 4 3 3 4 2 5 2 5 3 4 4 3 5 2 +--R (2a b + 2a b - 2a b - 2a b)c - a b - a b + a b + a b +--R Type: Expression(Integer) +--E 225 + +--S 226 of 518 +m0944b:= a0944.2-r0944 +--R +--R +--R (222) +--R 2 3 +--R (2a c + 2a b c)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((4a c + 6a b c + 2a b )cosh(x) + 6a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (2a c + 6a b c + 4a b )cosh(x) + (8a c + 8a b)cosh(x) - 2a c +--R + +--R 3 +--R 2a b c + 4a +--R * +--R sinh(x) +--R + +--R 2 3 2 2 2 +--R (2a b c + 2a b )cosh(x) + (2a c + 6a b)cosh(x) +--R + +--R 2 3 2 2 +--R (- 2a b c + 2a b + 4a )cosh(x) - 2a c + 2a b +--R * +--R x +--R +--------------+ (b - a)tanh(-) + c +--R | 2 2 2 2 +--R \|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 3 +--R (- 2a c - 2a b c)sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- 4a c - 6a b c - 2a b )cosh(x) - 6a c - 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 2a c - 6a b c - 4a b )cosh(x) + (- 8a c - 8a b)cosh(x) +--R + +--R 2 3 +--R 2a c - 2a b c - 4a +--R * +--R sinh(x) +--R + +--R 2 3 2 2 2 +--R (- 2a b c - 2a b )cosh(x) + (- 2a c - 6a b)cosh(x) +--R + +--R 2 3 2 2 +--R (2a b c - 2a b - 4a )cosh(x) + 2a c - 2a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 2 3 2 2 2 +--R (b c + b )sinh(x) + ((c + 3b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (2c + 3b c + b )cosh(x) + (4a c + 4a b)cosh(x) - 2c + b c + b +--R + +--R 2 +--R 2a +--R * +--R sinh(x) +--R + +--R 2 3 2 +--R (c + b c)cosh(x) + (2a c + 2a b)cosh(x) +--R + +--R 2 2 2 +--R (- c - b c + 2b + 2a )cosh(x) - 2a c + 2a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R / +--R 4 3 2 2 2 3 2 3 +--R (c + b c + (- b + a )c + (- b + a b)c)sinh(x) +--R + +--R 4 3 2 2 2 3 2 4 2 2 +--R (2c + 3b c + (- b + 2a )c + (- 3b + 3a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 3a c + a b c + (- 3a b + 3a )c - a b + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 2 3 2 4 2 2 2 +--R (c + 3b c + (b + a )c + (- 3b + 3a b)c - 2b + 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (4a c + 4a b c + (- 4a b + 4a )c - 4a b + 4a b)cosh(x) - c +--R + +--R 3 2 2 2 3 2 2 2 4 +--R b c + (b + a )c + (- b + a b)c - 2a b + 2a +--R * +--R sinh(x) +--R + +--R 3 2 2 3 2 4 2 2 3 +--R (b c + b c + (- b + a b)c - b + a b )cosh(x) +--R + +--R 3 2 2 3 3 3 2 +--R (a c + 3a b c + (- a b + a )c - 3a b + 3a b)cosh(x) +--R + +--R 3 2 2 2 3 2 4 2 2 4 3 +--R (- b c + (b + 2a )c + (b - a b)c - b - a b + 2a )cosh(x) - a c +--R + +--R 2 2 3 3 3 +--R a b c + (a b - a )c - a b + a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 518 +d0944b:= D(m0944b,x) +--R +--R +--R (223) +--R 4 2 3 2 2 4 3 5 4 6 +--R (b c + 2b c + a b c + (- 2b + 2a b )c - b + a b )sinh(x) +--R + +--R 4 2 3 2 2 4 3 5 +--R 4b c + (8b + 2a b)c + 8a b c + (- 8b + 10a b )c - 4b +--R + +--R 4 +--R 4a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 4 +--R (5a b + a )c + (6a b + 2a b)c + (- 3a b + 5a b )c - 4a b +--R + +--R 2 3 +--R 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 2 2 4 3 +--R (5b + a)c + (10b + 10a b)c + 23a b c + (- 10b + 20a b )c +--R + +--R 5 4 +--R - 5b + 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 +--R (16a b + 4a )c + (21a b + 17a b)c + (- 6a b + 26a b )c +--R + +--R 4 2 3 +--R - 11a b + 13a b +--R * +--R cosh(x) +--R + +--R 4 2 2 3 2 2 2 3 5 +--R (2b - 4a)c + (2a b + 12a b + a )c + (4a b + 6a b)c - 2b +--R + +--R 4 2 3 3 2 +--R 2a b - 4a b + 5a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (4a c + 20a b c + 32a b c + 20a b c + 4a b )cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 +--R (14a b + 10a )c + (24a b + 44a b)c + (6a b + 50a b )c +--R + +--R 4 2 3 +--R - 4a b + 16a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 2 2 3 2 +--R (4b - 8a)c + (8b - 12a b)c + (4a b + 28a b + 8a )c +--R + +--R 4 3 2 2 3 5 4 2 3 +--R (- 8b + 12a b + 24a b + 24a b)c - 4b + 4a b - 4a b +--R + +--R 3 2 +--R 16a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 3 2 2 3 4 +--R (2a b - 10a )c + 4a b c + (- 2a b + 6a b + 12a b)c - 4a b +--R + +--R 2 3 4 +--R 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 2 2 +--R (- 5b + 6a)c + (- 10b + 20a b)c + 23a b c +--R + +--R 4 3 5 4 +--R (10b + 10a b )c + 5b + a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 4a b + 16a )c + (6a b + 50a b)c + (24a b + 44a b )c +--R + +--R 4 2 3 +--R 14a b + 10a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 2 3 2 3 2 +--R (4b - 6a)c + (16b - 24a b)c + (16a b + 18a )c +--R + +--R 4 3 2 2 3 5 4 2 3 +--R (- 16b + 24a b + 40a b + 36a b)c - 4b + 6a b + 16a b +--R + +--R 3 2 +--R 18a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 2 2 +--R (8a b - 20a )c + (10a b - 18a b)c +--R + +--R 3 2 2 3 4 4 2 3 3 2 +--R (- 8a b + 24a b + 24a b + 4a )c - 10a b + 14a b + 12a b +--R + +--R 4 +--R 8a b +--R * +--R cosh(x) +--R + +--R 4 2 3 2 3 2 4 3 2 2 3 +--R b c - 2b c + (a b - 10a )c + (2b - 2a b + 4a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 +--R - b + a b - 4a b + 6a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 2 2 4 3 +--R (- 4b + 4a)c + (- 8b + 10a b)c + 8a b c + (8b + 2a b )c +--R + +--R 5 +--R 4b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 +--R (- 11a b + 13a )c + (- 6a b + 26a b)c + (21a b + 17a b )c +--R + +--R 4 2 3 +--R 16a b + 4a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 2 3 2 2 3 2 +--R (4b - 4a)c + (8b - 12a b)c + (- 4a b - 4a b + 16a )c +--R + +--R 4 3 2 2 3 5 4 2 3 +--R (- 8b + 12a b + 24a b + 24a b)c - 4b + 8a b + 28a b +--R + +--R 3 2 +--R 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 3 2 2 2 +--R (10a b - 14a )c + (8a b - 24a b)c +--R + +--R 3 2 2 3 4 4 2 3 3 2 +--R (- 10a b + 18a b + 12a b + 8a )c - 8a b + 20a b + 24a b +--R + +--R 4 +--R 4a b +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 3 2 3 2 3 3 2 +--R 2a b c + (- 4a b + 4a b - 16a )c + 2a b c - 4a b + 16a b +--R + +--R 4 +--R 8a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 4 4 +--R (a b + a )c + (- 2a b - 2a b)c + (a b + a b - 4a )c + 4a b +--R * +--R sinh(x) +--R + +--R 4 2 3 2 2 4 5 6 +--R ((- b + a)c + (- 2b + 2a b)c + a b c + 2b c + b )cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 4 +--R (- 4a b + 4a )c + (- 3a b + 5a b)c + (6a b + 2a b )c + 5a b +--R + +--R 2 3 +--R a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 2 2 3 2 2 2 3 5 +--R (2b - 2a)c + (- 2a b - 4a b + 5a )c + (4a b + 6a b)c - 2b +--R + +--R 4 2 3 3 2 +--R 4a b + 12a b + a b +--R * +--R 4 +--R cosh(x) +--R + +--R 2 3 2 2 2 3 4 4 +--R (4a b - 4a )c + (2a b - 6a b)c + (- 4a b + 4a )c - 2a b +--R + +--R 2 3 3 2 +--R 10a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 2 3 2 2 3 2 +--R (- b + a)c + (2b - 2a b)c + (a b + 4a b - 6a )c +--R + +--R 4 2 2 3 5 3 2 4 +--R (- 2b - 4a b - 4a b)c + b + 10a b + 4a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 3 2 2 4 4 2 3 4 +--R ((a b + a b)c + (- 2a b - 2a b - 4a )c + a b + a b + 4a b) +--R * +--R cosh(x) +--R + +--R 3 2 3 3 2 +--R a c - 2a b c + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 4 3 2 4 6 +--R (2c + 4b c - 4b c - 2b c)sinh(x) +--R + +--R 5 4 3 2 4 4 3 +--R (8c + 16b c - 16b c - 8b c)cosh(x) + 10a c + 12a b c +--R + +--R 2 2 3 +--R - 6a b c - 8a b c +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 4 2 +--R (10c + 20b c - 20b c - 10b c)cosh(x) +--R + +--R 4 3 2 2 3 5 2 3 +--R (32a c + 42a b c - 12a b c - 22a b c)cosh(x) + 4c + 24a c +--R + +--R 2 2 4 2 2 +--R 8a b c + (- 4b - 8a b )c +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 2 +--R (28a c + 48a b c + 12a b c - 8a b c)cosh(x) +--R + +--R 5 4 2 3 3 2 2 4 2 2 +--R (8c + 16b c + 56a c + (- 16b + 48a b)c + (- 8b - 8a b )c) +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 +--R 4a c + 8a b c + (- 4a b + 24a )c - 8a b c +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 4 4 +--R (- 10c - 20b c + 20b c + 10b c)cosh(x) +--R + +--R 4 3 2 2 3 3 +--R (- 8a c + 12a b c + 48a b c + 28a b c)cosh(x) +--R + +--R 5 4 2 3 3 2 2 +--R 8c + 32b c + 32a c + (- 32b + 80a b)c +--R + +--R 4 2 2 +--R (- 8b + 32a b )c +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 +--R (16a c + 20a b c + (- 16a b + 48a )c + (- 20a b + 24a b)c) +--R * +--R cosh(x) +--R + +--R 5 4 3 2 2 4 2 2 4 +--R 2c - 4b c + (4b + 8a b)c + (- 2b - 8a b + 8a )c +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 4 5 +--R (- 8c - 16b c + 16b c + 8b c)cosh(x) +--R + +--R 4 3 2 2 3 4 +--R (- 22a c - 12a b c + 42a b c + 32a b c)cosh(x) +--R + +--R 5 4 2 3 3 2 2 4 2 2 +--R (8c + 16b c - 8a c + (- 16b + 48a b)c + (- 8b + 56a b )c) +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 +--R (20a c + 16a b c + (- 20a b + 24a )c + (- 16a b + 48a b)c) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 3 2 2 4 4 3 2 2 +--R (8a c + (- 8a b + 16a )c)cosh(x) + 2a c - 4a b c + 2a b c +--R * +--R sinh(x) +--R + +--R 5 4 3 2 4 6 +--R (- 2c - 4b c + 4b c + 2b c)cosh(x) +--R + +--R 4 3 2 2 3 5 +--R (- 8a c - 6a b c + 12a b c + 10a b c)cosh(x) +--R + +--R 5 2 3 2 2 4 2 2 4 +--R (4c - 8a c + 8a b c + (- 4b + 24a b )c)cosh(x) +--R + +--R 4 3 2 2 3 3 3 +--R (8a c + 4a b c - 8a b c + (- 4a b + 24a b)c)cosh(x) +--R + +--R 5 4 2 3 3 2 2 4 4 2 +--R (- 2c + 4b c + 8a c + (- 4b - 8a b)c + (2b + 8a )c)cosh(x) +--R + +--R 3 2 2 3 +--R (2a b c - 4a b c + 2a b c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 3 2 2 4 3 5 4 6 +--R (b c + 2b c - a b c + (- 2b - 2a b )c - b - a b )sinh(x) +--R + +--R 4 2 3 2 2 4 3 5 +--R 4b c + (8b - 2a b)c - 8a b c + (- 8b - 10a b )c - 4b +--R + +--R 4 +--R - 4a b +--R * +--R cosh(x) +--R + +--R 2 3 2 2 2 3 2 2 4 2 3 +--R (5a b - a )c + (6a b - 2a b)c + (- 3a b - 5a b )c - 4a b - 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 2 2 4 3 +--R (5b - a)c + (10b - 10a b)c - 23a b c + (- 10b - 20a b )c +--R + +--R 5 4 +--R - 5b - 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8a b - 8a b + 4a b + 4a )c - 8a b - 8a b - 4a b +--R + +--R 4 3 5 2 6 +--R - 4a b + 12a b + 12a b +--R * +--R 3 +--R cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 3 +--R (b + a b - 2a b - 2a )c + (- 2b - 2a b - 8a b - 8a b)c +--R + +--R 2 3 3 2 4 5 2 +--R (13a b + 13a b + 2a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 7 6 2 5 +--R (2b + 2a b + 6a b + 6a b - 8a b - 8a b)c - b - a b - 9a b +--R + +--R 3 4 4 3 5 2 6 7 +--R - 9a b + 6a b + 6a b + 4a b + 4a +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 4 3 2 2 3 4 3 +--R (2a b + 2a b)c + (- 4a b - 4a b - 4a b - 4a )c +--R + +--R 3 2 4 2 5 2 4 5 6 6 2 5 +--R (6a b + 6a b)c + (4a b + 4a b - 4a b - 4a )c - 2a b - 2a b +--R + +--R 3 4 4 3 5 2 6 +--R - 2a b - 2a b + 4a b + 4a b +--R * +--R cosh(x) +--R + +--R 2 3 4 2 2 3 3 4 5 2 +--R (a b + a )c + (- 2a b - 2a b)c + (a b + a )c +--R + +--R 2 4 3 3 4 2 5 2 5 3 4 4 3 5 2 +--R (2a b + 2a b - 2a b - 2a b)c - a b - a b + a b + a b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 518 +t0945:= 1/(a+b*cosh(x)+c*sinh(x))^3 +--R +--R +--R (224) +--R 1 +--R / +--R 3 3 2 2 2 +--R c sinh(x) + (3b c cosh(x) + 3a c )sinh(x) +--R + +--R 2 2 2 3 3 +--R (3b c cosh(x) + 6a b c cosh(x) + 3a c)sinh(x) + b cosh(x) +--R + +--R 2 2 2 3 +--R 3a b cosh(x) + 3a b cosh(x) + a +--R Type: Expression(Integer) +--E 228 + +--S 229 of 518 +r0945:= -1/2*(c*cosh(x)+b*sinh(x))/(a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x))^2-_ + 1/2*(2*(2*a^2+b^2-c^2)*atanh((c-(a-b)*tanh(1/2*x))/_ + (a^2-b^2+c^2)^(1/2))+3*a*(a^2-b^2+c^2)^(1/2)*_ + (c*cosh(x)+b*sinh(x))/(a+b*cosh(x)+c*sinh(x)))/(a^2-b^2+c^2)^(5/2) +--R +--R +--R (225) +--R 4 2 2 2 2 +--R (2c + (- 2b - 4a )c )sinh(x) +--R + +--R 3 3 2 3 2 3 +--R ((4b c + (- 4b - 8a b)c)cosh(x) + 4a c + (- 4a b - 8a )c)sinh(x) +--R + +--R 2 2 4 2 2 2 2 3 3 +--R (2b c - 2b - 4a b )cosh(x) + (4a b c - 4a b - 8a b)cosh(x) +--R + +--R 2 2 2 2 4 +--R 2a c - 2a b - 4a +--R * +--R x +--R (b - a)tanh(-) + c +--R 2 +--R atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 +--R - 3a b c sinh(x) +--R + +--R 2 2 2 3 2 +--R ((- 3a c - 3a b )cosh(x) - b c + b - 4a b)sinh(x) +--R + +--R 2 3 2 2 +--R - 3a b c cosh(x) + (- c + (b - 4a )c)cosh(x) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (- 4b + 4a )c + (2b - 4a b + 2a )c )sinh(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (- 8b + 8a b)c + (4b - 8a b + 4a b)c)cosh(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (- 8a b + 8a )c + (4a b - 8a b + 4a )c +--R * +--R sinh(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (- 4b + 4a b )c + 2b - 4a b + 2a b )cosh(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (- 8a b + 8a b)c + 4a b - 8a b + 4a b)cosh(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (- 4a b + 4a )c + 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 518 +a0945:= integrate(t0945,x) +--R +--R +--R (226) +--R [ +--R 4 3 2 2 3 2 4 2 2 4 +--R (c + 2b c - 2a c + (- 2b - 4a b)c - b - 2a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (4c + 8b c - 8a c + (- 8b - 16a b)c - 4b - 8a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 4a c + 4a b c + (- 4a b - 8a )c - 4a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (6c + 12b c - 12a c + (- 12b - 24a b)c - 6b - 12a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 3 3 3 +--R (12a c + 12a b c + (- 12a b - 24a )c - 12a b - 24a b) +--R * +--R cosh(x) +--R + +--R 4 2 2 2 4 2 2 4 +--R - 2c + (4b + 8a )c - 2b - 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 +--R (4c + 8b c - 8a c + (- 8b - 16a b)c - 4b - 8a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R (12a c + 12a b c + (- 12a b - 24a )c - 12a b - 24a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 2 2 4 2 2 4 3 +--R (- 4c + (8b + 16a )c - 4b - 16a b - 16a )cosh(x) - 4a c +--R + +--R 2 2 3 3 3 +--R 4a b c + (4a b + 8a )c - 4a b - 8a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 +--R (c + 2b c - 2a c + (- 2b - 4a b)c - b - 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 3 +--R (4a c + 4a b c + (- 4a b - 8a )c - 4a b - 8a b)cosh(x) +--R + +--R 4 2 2 2 4 2 2 4 2 +--R (- 2c + (4b + 8a )c - 2b - 8a b - 8a )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (- 4a c + 4a b c + (4a b + 8a )c - 4a b - 8a b)cosh(x) + c +--R + +--R 3 2 2 3 2 4 2 2 +--R - 2b c - 2a c + (2b + 4a b)c - b - 2a b +--R * +--R log +--R 2 2 2 +--R (c + 2b c + b )sinh(x) +--R + +--R 2 2 +--R ((2c + 4b c + 2b )cosh(x) + 2a c + 2a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (c + 2b c + b )cosh(x) + (2a c + 2a b)cosh(x) + c - b +--R + +--R 2 +--R 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 3 2 2 2 3 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2c + 2b c + (- 2b + 2a )c - 2b + 2a b)cosh(x) + 2a c +--R + +--R 2 3 +--R - 2a b + 2a +--R / +--R 2 +--R (c + b)sinh(x) + ((2c + 2b)cosh(x) + 2a)sinh(x) +--R + +--R 2 +--R (c + b)cosh(x) + 2a cosh(x) - c + b +--R + +--R 3 2 2 2 3 2 3 +--R (- 2c - 2b c + (2b + 4a )c + 2b + 4a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 6c - 6b c + (6b + 12a )c + 6b + 12a b)cosh(x) - 6a c +--R + +--R 2 3 +--R 6a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 6c - 6b c + (6b + 12a )c + 6b + 12a b)cosh(x) +--R + +--R 2 2 3 3 2 2 2 +--R (- 12a c + 12a b + 24a )cosh(x) - 2c + 2b c + (2b - 20a )c +--R + +--R 3 2 +--R - 2b + 20a b +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 2 3 +--R (- 2c - 2b c + (2b + 4a )c + 2b + 4a b)cosh(x) +--R + +--R 2 2 3 2 +--R (- 6a c + 6a b + 12a )cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 2c + 2b c + (2b - 20a )c - 2b + 20a b)cosh(x) + 6a c +--R + +--R 2 +--R - 12a b c + 6a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R / +--R 6 5 2 2 4 3 2 3 +--R 2c + 4b c + (- 2b + 4a )c + (- 8b + 8a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 4 2 +--R (- 2b + 2a )c + (4b - 8a b + 4a b)c + 2b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 8c + 16b c + (- 8b + 16a )c + (- 32b + 32a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 +--R (- 8b + 8a )c + (16b - 32a b + 16a b)c + 8b - 16a b +--R + +--R 4 2 +--R 8a b +--R * +--R cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R 8a c + 8a b c + (- 16a b + 16a )c + (- 16a b + 16a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (8a b - 16a b + 8a )c + 8a b - 16a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 12c + 24b c + (- 12b + 24a )c + (- 48b + 48a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 +--R (- 12b + 12a )c + (24b - 48a b + 24a b)c + 12b - 24a b +--R + +--R 4 2 +--R 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 +--R 24a c + 24a b c + (- 48a b + 48a )c +--R + +--R 3 3 2 4 3 2 5 5 +--R (- 48a b + 48a b)c + (24a b - 48a b + 24a )c + 24a b +--R + +--R 3 3 5 +--R - 48a b + 24a b +--R * +--R cosh(x) +--R + +--R 6 2 4 4 4 2 6 4 2 6 +--R - 4c + 12b c + (- 12b + 12a )c + 4b - 12a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 8c + 16b c + (- 8b + 16a )c + (- 32b + 32a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 +--R (- 8b + 8a )c + (16b - 32a b + 16a b)c + 8b - 16a b +--R + +--R 4 2 +--R 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 +--R 24a c + 24a b c + (- 48a b + 48a )c +--R + +--R 3 3 2 4 3 2 5 5 +--R (- 48a b + 48a b)c + (24a b - 48a b + 24a )c + 24a b +--R + +--R 3 3 5 +--R - 48a b + 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 4 4 4 2 6 4 2 6 +--R (- 8c + 24b c + (- 24b + 24a )c + 8b - 24a b + 16a )cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 8a c + 8a b c + (16a b - 16a )c + (- 16a b + 16a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (- 8a b + 16a b - 8a )c + 8a b - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 2c + 4b c + (- 2b + 4a )c + (- 8b + 8a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 4 2 +--R (- 2b + 2a )c + (4b - 8a b + 4a b)c + 2b - 4a b + 2a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R 8a c + 8a b c + (- 16a b + 16a )c + (- 16a b + 16a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (8a b - 16a b + 8a )c + 8a b - 16a b + 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 2 4 4 4 2 6 4 2 6 2 +--R (- 4c + 12b c + (- 12b + 12a )c + 4b - 12a b + 8a )cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 8a c + 8a b c + (16a b - 16a )c + (- 16a b + 16a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (- 8a b + 16a b - 8a )c + 8a b - 16a b + 8a b +--R * +--R cosh(x) +--R + +--R 6 5 2 2 4 3 2 3 4 4 2 +--R 2c - 4b c + (- 2b + 4a )c + (8b - 8a b)c + (- 2b + 2a )c +--R + +--R 5 2 3 4 6 2 4 4 2 +--R (- 4b + 8a b - 4a b)c + 2b - 4a b + 2a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R , +--R +--R 4 3 2 2 3 2 4 2 2 4 +--R (c + 2b c - 2a c + (- 2b - 4a b)c - b - 2a b )sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (4c + 8b c - 8a c + (- 8b - 16a b)c - 4b - 8a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R 4a c + 4a b c + (- 4a b - 8a )c - 4a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (6c + 12b c - 12a c + (- 12b - 24a b)c - 6b - 12a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 2 2 3 3 3 +--R (12a c + 12a b c + (- 12a b - 24a )c - 12a b - 24a b) +--R * +--R cosh(x) +--R + +--R 4 2 2 2 4 2 2 4 +--R - 2c + (4b + 8a )c - 2b - 8a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 +--R (4c + 8b c - 8a c + (- 8b - 16a b)c - 4b - 8a b )cosh(x) +--R + +--R 3 2 2 3 3 3 +--R (12a c + 12a b c + (- 12a b - 24a )c - 12a b - 24a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 2 2 4 2 2 4 3 +--R (- 4c + (8b + 16a )c - 4b - 16a b - 16a )cosh(x) - 4a c +--R + +--R 2 2 3 3 3 +--R 4a b c + (4a b + 8a )c - 4a b - 8a b +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 2 2 4 +--R (c + 2b c - 2a c + (- 2b - 4a b)c - b - 2a b )cosh(x) +--R + +--R 3 2 2 3 3 3 3 +--R (4a c + 4a b c + (- 4a b - 8a )c - 4a b - 8a b)cosh(x) +--R + +--R 4 2 2 2 4 2 2 4 2 +--R (- 2c + (4b + 8a )c - 2b - 8a b - 8a )cosh(x) +--R + +--R 3 2 2 3 3 3 4 +--R (- 4a c + 4a b c + (4a b + 8a )c - 4a b - 8a b)cosh(x) + c +--R + +--R 3 2 2 3 2 4 2 2 +--R - 2b c - 2a c + (2b + 4a b)c - b - 2a b +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 3 2 2 2 3 2 3 +--R (- c - b c + (b + 2a )c + b + 2a b)sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 3c - 3b c + (3b + 6a )c + 3b + 6a b)cosh(x) - 3a c +--R + +--R 2 3 +--R 3a b + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 3c - 3b c + (3b + 6a )c + 3b + 6a b)cosh(x) +--R + +--R 2 2 3 3 2 2 2 3 +--R (- 6a c + 6a b + 12a )cosh(x) - c + b c + (b - 10a )c - b +--R + +--R 2 +--R 10a b +--R * +--R sinh(x) +--R + +--R 3 2 2 2 3 2 3 +--R (- c - b c + (b + 2a )c + b + 2a b)cosh(x) +--R + +--R 2 2 3 2 +--R (- 3a c + 3a b + 6a )cosh(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- c + b c + (b - 10a )c - b + 10a b)cosh(x) + 3a c - 6a b c +--R + +--R 2 +--R 3a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R 6 5 2 2 4 3 2 3 4 4 2 +--R c + 2b c + (- b + 2a )c + (- 4b + 4a b)c + (- b + a )c +--R + +--R 5 2 3 4 6 2 4 4 2 +--R (2b - 4a b + 2a b)c + b - 2a b + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 4c + 8b c + (- 4b + 8a )c + (- 16b + 16a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 4 2 +--R (- 4b + 4a )c + (8b - 16a b + 8a b)c + 4b - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R 4a c + 4a b c + (- 8a b + 8a )c + (- 8a b + 8a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (4a b - 8a b + 4a )c + 4a b - 8a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 6c + 12b c + (- 6b + 12a )c + (- 24b + 24a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 +--R (- 6b + 6a )c + (12b - 24a b + 12a b)c + 6b - 12a b +--R + +--R 4 2 +--R 6a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 +--R 12a c + 12a b c + (- 24a b + 24a )c +--R + +--R 3 3 2 4 3 2 5 5 +--R (- 24a b + 24a b)c + (12a b - 24a b + 12a )c + 12a b +--R + +--R 3 3 5 +--R - 24a b + 12a b +--R * +--R cosh(x) +--R + +--R 6 2 4 4 4 2 6 4 2 6 +--R - 2c + 6b c + (- 6b + 6a )c + 2b - 6a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 4c + 8b c + (- 4b + 8a )c + (- 16b + 16a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 4 2 +--R (- 4b + 4a )c + (8b - 16a b + 8a b)c + 4b - 8a b + 4a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 +--R 12a c + 12a b c + (- 24a b + 24a )c +--R + +--R 3 3 2 4 3 2 5 5 +--R (- 24a b + 24a b)c + (12a b - 24a b + 12a )c + 12a b +--R + +--R 3 3 5 +--R - 24a b + 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 4 4 4 2 6 4 2 6 +--R (- 4c + 12b c + (- 12b + 12a )c + 4b - 12a b + 8a )cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 4a c + 4a b c + (8a b - 8a )c + (- 8a b + 8a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (- 4a b + 8a b - 4a )c + 4a b - 8a b + 4a b +--R * +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 4 4 2 +--R c + 2b c + (- b + 2a )c + (- 4b + 4a b)c + (- b + a )c +--R + +--R 5 2 3 4 6 2 4 4 2 +--R (2b - 4a b + 2a b)c + b - 2a b + a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R 4a c + 4a b c + (- 8a b + 8a )c + (- 8a b + 8a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (4a b - 8a b + 4a )c + 4a b - 8a b + 4a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 2 4 4 4 2 6 4 2 6 2 +--R (- 2c + 6b c + (- 6b + 6a )c + 2b - 6a b + 4a )cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 4a c + 4a b c + (8a b - 8a )c + (- 8a b + 8a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (- 4a b + 8a b - 4a )c + 4a b - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 6 5 2 2 4 3 2 3 4 4 2 +--R c - 2b c + (- b + 2a )c + (4b - 4a b)c + (- b + a )c +--R + +--R 5 2 3 4 6 2 4 4 2 +--R (- 2b + 4a b - 2a b)c + b - 2a b + a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 230 + +--S 231 of 518 +m0945a:= a0945.1-r0945 +--R +--R +--R (227) +--R 6 5 2 4 3 2 3 4 2 2 2 6 +--R (c + 2b c - 2a c + (- 2b - 4a b)c + (- b - 2a b )c )sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 4c + 10b c + (4b - 8a )c + (- 8b - 20a b)c +--R + +--R 4 2 2 2 5 2 3 +--R (- 8b - 16a b )c + (- 2b - 4a b )c +--R * +--R cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R 6a c + 8a b c + (- 4a b - 12a )c + (- 8a b - 16a b)c +--R + +--R 4 3 2 +--R (- 2a b - 4a b )c +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 6c + 20b c + (17b - 12a )c + (- 10b - 40a b)c +--R + +--R 4 2 2 2 5 2 3 6 2 4 +--R (- 22b - 46a b )c + (- 10b - 20a b )c - b - 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 3 3 3 3 2 +--R 20a c + 38a b c - 40a c + (- 36a b - 76a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 20a b - 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4a b c + (- 2a b + 4a )c + (8a b - 8a b)c +--R + +--R 2 4 6 2 2 5 4 3 6 2 6 4 4 6 2 +--R (- 2a b + 2a )c + (- 4a b + 8a b - 4a b)c + 2a b - 4a b + 2a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 518 +--d0945a:= D(m0945a,x) +--E 232 + +--S 233 of 518 +m0945b:= a0945.2-r0945 +--R +--R +--R (228) +--R 6 5 2 4 3 2 3 4 2 2 2 6 +--R (- 2c - 4b c + 4a c + (4b + 8a b)c + (2b + 4a b )c )sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R - 8c - 20b c + (- 8b + 16a )c + (16b + 40a b)c +--R + +--R 4 2 2 2 5 2 3 +--R (16b + 32a b )c + (4b + 8a b )c +--R * +--R cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 12a c - 16a b c + (8a b + 24a )c + (16a b + 32a b)c +--R + +--R 4 3 2 +--R (4a b + 8a b )c +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R - 12c - 40b c + (- 34b + 24a )c + (20b + 80a b)c +--R + +--R 4 2 2 2 5 2 3 6 2 4 +--R (44b + 92a b )c + (20b + 40a b )c + 2b + 4a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 3 3 3 3 2 +--R - 40a c - 76a b c + 80a c + (72a b + 152a b)c +--R + +--R 4 3 2 5 3 3 +--R (40a b + 80a b )c + 4a b + 8a b +--R * +--R cosh(x) +--R + +--R 6 2 2 4 2 3 4 2 2 4 2 +--R 4c + (- 8b - 34a )c - 20a b c + (4b + 32a b + 52a )c +--R + +--R 2 3 4 2 4 4 2 +--R (20a b + 40a b)c + 2a b + 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 2 4 2 3 +--R - 8c - 40b c + (- 56b + 16a )c + 80a b c +--R + +--R 4 2 2 2 5 2 3 6 2 4 +--R (56b + 128a b )c + (40b + 80a b )c + 8b + 16a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 +--R - 48a c - 136a b c + (- 64a b + 96a )c +--R + +--R 3 3 2 4 3 2 5 3 3 +--R (112a b + 272a b)c + (112a b + 224a b )c + 24a b + 48a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 8c + 8b c + (- 16b - 88a )c + (- 16b - 112a b)c +--R + +--R 4 2 2 4 2 5 2 3 4 2 4 +--R (8b + 64a b + 144a )c + (8b + 112a b + 192a b)c + 24a b +--R + +--R 4 2 +--R 48a b +--R * +--R cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R 16a c - 8a b c + (- 24a b - 56a )c + (8a b + 8a b)c +--R + +--R 4 3 2 5 3 3 5 +--R (8a b + 40a b + 48a )c + 8a b + 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R - 2c - 20b c + (- 44b + 4a )c + (- 20b + 40a b)c +--R + +--R 4 2 2 2 5 2 3 6 2 4 +--R (34b + 92a b )c + (40b + 80a b )c + 12b + 24a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 4 2 3 3 +--R - 24a c - 112a b c + (- 112a b + 48a )c +--R + +--R 3 3 2 4 3 2 5 3 3 +--R (64a b + 224a b)c + (136a b + 272a b )c + 48a b + 96a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 4c + 16b c + (- 4b - 76a )c + (- 32b - 184a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 +--R (- 4b + 136a )c + (16b + 184a b + 304a b)c + 4b + 76a b +--R + +--R 4 2 +--R 136a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 +--R 24a c + 16a b c + (- 56a b - 104a )c +--R + +--R 3 3 2 4 3 2 5 5 +--R (- 24a b - 72a b)c + (32a b + 120a b + 112a )c + 8a b +--R + +--R 3 3 5 +--R 56a b + 80a b +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 2 3 +--R - 2c + 4b c + 24a c + (- 4b - 24a b)c +--R + +--R 4 2 2 4 2 2 3 4 2 4 4 2 6 +--R (2b - 20a b - 48a )c + (16a b + 32a b)c + 4a b + 16a b + 16a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 2 3 4 2 2 2 +--R - 4b c - 16b c + (- 16b + 8a b)c + (8b + 32a b )c +--R + +--R 5 2 3 6 2 4 +--R (20b + 40a b )c + 8b + 16a b +--R * +--R 5 +--R cosh(x) +--R + +--R 5 4 2 3 3 3 2 +--R - 4a c - 40a b c + (- 72a b + 8a )c + 80a b c +--R + +--R 4 3 2 5 3 3 +--R (76a b + 152a b )c + 40a b + 80a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 2 4 3 2 3 +--R 8b c + (8b - 24a )c + (- 16b - 112a b)c +--R + +--R 4 2 2 4 2 5 2 3 4 6 +--R (- 16b - 64a b + 48a )c + (8b + 112a b + 192a b)c + 8b +--R + +--R 2 4 4 2 +--R 88a b + 144a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 +--R 8a c + 32a b c + (- 24a b - 56a )c +--R + +--R 3 3 2 4 3 2 5 5 +--R (- 56a b - 120a b)c + (16a b + 72a b + 80a )c + 24a b +--R + +--R 3 3 5 +--R 104a b + 112a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 2 4 2 3 +--R - 4b c + (8b + 24a )c + 8a b c +--R + +--R 4 2 2 4 2 5 2 3 2 4 4 2 +--R (- 8b - 64a b - 64a )c + (4b + 8a b )c + 24a b + 64a b +--R + +--R 6 +--R 32a +--R * +--R cosh(x) +--R + +--R 5 4 3 3 3 3 2 +--R - 4a c + 8a b c + 16a c + (- 8a b - 24a b)c +--R + +--R 4 5 3 3 5 +--R (4a b - 16a )c + 8a b + 16a b +--R * +--R sinh(x) +--R + +--R 2 4 3 3 2 2 2 5 2 3 6 2 4 6 +--R (- 2b c - 4b c + 4a b c + (4b + 8a b )c + 2b + 4a b )cosh(x) +--R + +--R 4 2 3 3 3 2 4 3 2 +--R - 4a b c - 16a b c + (- 8a b + 8a b)c + (16a b + 32a b )c +--R + +--R 5 3 3 +--R 12a b + 24a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 4 2 3 4 2 2 4 2 +--R (4b - 2a )c - 20a b c + (- 8b - 32a b + 4a )c +--R + +--R 2 3 4 6 2 4 4 2 +--R (20a b + 40a b)c + 4b + 34a b + 52a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 2 3 3 3 3 2 +--R 8a b c + (8a b - 8a )c + (- 24a b - 40a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (- 8a b - 8a b + 16a )c + 16a b + 56a b + 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3 2 3 2 2 4 2 +--R (- 2b + 4a )c + (4b + 16a b)c + (- 20a b - 16a )c +--R + +--R 5 2 3 4 6 2 4 4 2 6 +--R (- 4b - 24a b - 32a b)c + 2b + 24a b + 48a b + 16a +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 4 3 2 5 5 +--R - 4a b c + (8a b + 8a )c + (- 8a b - 24a b - 16a )c + 4a b +--R + +--R 3 3 5 +--R 16a b + 16a b +--R * +--R cosh(x) +--R + +--R 2 4 2 3 4 2 2 3 4 2 4 4 2 +--R - 2a c + 4a b c + 4a c + (- 4a b - 8a b)c + 2a b + 4a b +--R * +--R x +--R +--------------+ (b - a)tanh(-) + c +--R | 2 2 2 2 +--R \|- c + b - a atanh(------------------) +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 6 5 2 4 3 2 3 4 2 2 2 6 +--R (2c + 4b c - 4a c + (- 4b - 8a b)c + (- 2b - 4a b )c )sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 8c + 20b c + (8b - 16a )c + (- 16b - 40a b)c +--R + +--R 4 2 2 2 5 2 3 +--R (- 16b - 32a b )c + (- 4b - 8a b )c +--R * +--R cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R 12a c + 16a b c + (- 8a b - 24a )c + (- 16a b - 32a b)c +--R + +--R 4 3 2 +--R (- 4a b - 8a b )c +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 12c + 40b c + (34b - 24a )c + (- 20b - 80a b)c +--R + +--R 4 2 2 2 5 2 3 6 2 4 +--R (- 44b - 92a b )c + (- 20b - 40a b )c - 2b - 4a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 3 3 3 3 2 +--R 40a c + 76a b c - 80a c + (- 72a b - 152a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 40a b - 80a b )c - 4a b - 8a b +--R * +--R cosh(x) +--R + +--R 6 2 2 4 2 3 4 2 2 4 2 +--R - 4c + (8b + 34a )c + 20a b c + (- 4b - 32a b - 52a )c +--R + +--R 2 3 4 2 4 4 2 +--R (- 20a b - 40a b)c - 2a b - 4a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 2 4 2 3 +--R 8c + 40b c + (56b - 16a )c - 80a b c +--R + +--R 4 2 2 2 5 2 3 6 2 4 +--R (- 56b - 128a b )c + (- 40b - 80a b )c - 8b - 16a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 +--R 48a c + 136a b c + (64a b - 96a )c +--R + +--R 3 3 2 4 3 2 5 +--R (- 112a b - 272a b)c + (- 112a b - 224a b )c - 24a b +--R + +--R 3 3 +--R - 48a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R - 8c - 8b c + (16b + 88a )c + (16b + 112a b)c +--R + +--R 4 2 2 4 2 5 2 3 4 +--R (- 8b - 64a b - 144a )c + (- 8b - 112a b - 192a b)c +--R + +--R 2 4 4 2 +--R - 24a b - 48a b +--R * +--R cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 16a c + 8a b c + (24a b + 56a )c + (- 8a b - 8a b)c +--R + +--R 4 3 2 5 3 3 5 +--R (- 8a b - 40a b - 48a )c - 8a b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R 2c + 20b c + (44b - 4a )c + (20b - 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8a b)c + (- 8b - 32a b )c +--R + +--R 5 2 3 6 2 4 +--R (- 20b - 40a b )c - 8b - 16a b +--R * +--R 5 +--R cosh(x) +--R + +--R 5 4 2 3 3 3 2 +--R 4a c + 40a b c + (72a b - 8a )c - 80a b c +--R + +--R 4 3 2 5 3 3 +--R (- 76a b - 152a b )c - 40a b - 80a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 2 4 3 2 3 +--R - 8b c + (- 8b + 24a )c + (16b + 112a b)c +--R + +--R 4 2 2 4 2 5 2 3 4 6 +--R (16b + 64a b - 48a )c + (- 8b - 112a b - 192a b)c - 8b +--R + +--R 2 4 4 2 +--R - 88a b - 144a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 8a c - 32a b c + (24a b + 56a )c + (56a b + 120a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (- 16a b - 72a b - 80a )c - 24a b - 104a b - 112a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 2 4 2 3 4 2 2 4 2 +--R 4b c + (- 8b - 24a )c - 8a b c + (8b + 64a b + 64a )c +--R + +--R 5 2 3 2 4 4 2 6 +--R (- 4b - 8a b )c - 24a b - 64a b - 32a +--R * +--R cosh(x) +--R + +--R 5 4 3 3 3 3 2 4 5 +--R 4a c - 8a b c - 16a c + (8a b + 24a b)c + (- 4a b + 16a )c +--R + +--R 3 3 5 +--R - 8a b - 16a b +--R * +--R sinh(x) +--R + +--R 2 4 3 3 2 2 2 5 2 3 6 2 4 6 +--R (2b c + 4b c - 4a b c + (- 4b - 8a b )c - 2b - 4a b )cosh(x) +--R + +--R 4 2 3 3 3 2 4 3 2 +--R 4a b c + 16a b c + (8a b - 8a b)c + (- 16a b - 32a b )c +--R + +--R 5 3 3 +--R - 12a b - 24a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 4 2 3 4 2 2 4 2 +--R (- 4b + 2a )c + 20a b c + (8b + 32a b - 4a )c +--R + +--R 2 3 4 6 2 4 4 2 +--R (- 20a b - 40a b)c - 4b - 34a b - 52a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 2 3 3 3 3 2 +--R - 8a b c + (- 8a b + 8a )c + (24a b + 40a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (8a b + 8a b - 16a )c - 16a b - 56a b - 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 4 3 2 3 2 2 4 2 +--R (2b - 4a )c + (- 4b - 16a b)c + (20a b + 16a )c +--R + +--R 5 2 3 4 6 2 4 4 2 6 +--R (4b + 24a b + 32a b)c - 2b - 24a b - 48a b - 16a +--R * +--R 2 +--R cosh(x) +--R + +--R 4 2 3 3 4 3 2 5 5 +--R 4a b c + (- 8a b - 8a )c + (8a b + 24a b + 16a )c - 4a b +--R + +--R 3 3 5 +--R - 16a b - 16a b +--R * +--R cosh(x) +--R + +--R 2 4 2 3 4 2 2 3 4 2 4 4 2 +--R 2a c - 4a b c - 4a c + (4a b + 8a b)c - 2a b - 4a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((c + b)sinh(x) + (c + b)cosh(x) + a)\|- c + b - a +--R atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R 3 2 2 3 6 +--R (3a b c + 6a b c + 3a b c)sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (3a c + 18a b c + 30a b c + 18a b c + 3a b )cosh(x) - 2c +--R + +--R 4 2 2 3 3 2 2 4 2 2 5 +--R - b c + (4b + 4a )c + (2b + 20a b)c + (- 2b + 20a b )c - b +--R + +--R 2 3 +--R 4a b +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (12a c + 45a b c + 66a b c + 45a b c + 12a b )cosh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 5c - 4b c + (10b + 28a )c + (8b + 92a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 5b + 92a b )c - 4b + 28a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 10a c - 6a b c + (14a b + 20a )c + (6a b + 36a b)c - 4a b +--R + +--R 3 2 +--R 16a b +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (18a c + 60a b c + 84a b c + 60a b c + 18a b )cosh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c - 4b c + (4b + 64a )c + (8b + 176a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 2b + 176a b )c - 4b + 64a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 +--R - 26a c - 24a b c + (28a b + 76a )c + (24a b + 144a b)c +--R + +--R 4 3 2 +--R - 2a b + 68a b +--R * +--R cosh(x) +--R + +--R 5 2 2 3 3 2 2 2 2 4 5 +--R - 2c + (2b - 34a )c + (2b + 2a b)c + (26a b + 28a )c - 2b +--R + +--R 2 3 4 +--R 6a b + 20a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (12a c + 45a b c + 66a b c + 45a b c + 12a b )cosh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 4c + 2b c + (- 8b + 64a )c + (- 4b + 176a b)c +--R + +--R 4 2 2 5 2 3 +--R (4b + 176a b )c + 2b + 64a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 3 2 3 3 4 +--R - 18a c - 36a b c + 108a c + (36a b + 216a b)c + 18a b +--R + +--R 3 2 +--R 108a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 4c - 6b c + (10b - 66a )c + (10b - 46a b)c +--R + +--R 4 2 2 4 5 2 3 4 +--R (- 6b + 74a b + 76a )c - 4b + 38a b + 68a b +--R * +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R 2a c - 9a b c + (8a b - 46a )c + (3a b + 24a b)c - 4a b +--R + +--R 3 2 5 +--R 22a b + 12a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 5 +--R (3a c + 18a b c + 30a b c + 18a b c + 3a b )cosh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 4c + 5b c + (- 8b + 28a )c + (- 10b + 92a b)c +--R + +--R 4 2 2 5 2 3 +--R (4b + 92a b )c + 5b + 28a b +--R * +--R 4 +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 +--R 2a c - 24a b c + (- 28a b + 68a )c + (24a b + 144a b)c +--R + +--R 4 3 2 +--R 26a b + 76a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 4c - 6b c + (10b - 38a )c + (10b - 74a b)c +--R + +--R 4 2 2 4 5 2 3 4 +--R (- 6b + 46a b + 68a )c - 4b + 66a b + 76a b +--R * +--R 2 +--R cosh(x) +--R + +--R 4 3 2 3 2 3 4 +--R - 5a c + 6a b c + (- 2a b - 68a )c + 6a b c - 5a b +--R + +--R 3 2 5 +--R 68a b + 24a +--R * +--R cosh(x) +--R + +--R 4 2 2 3 2 2 4 2 2 4 5 +--R b c + (- 2b + 10a )c - 18a b c + (2b + 6a b - 20a )c - b +--R + +--R 2 3 4 +--R 2a b + 20a b +--R * +--R sinh(x) +--R + +--R 3 2 2 3 6 +--R (3a b c + 6a b c + 3a b c)cosh(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 +--R c + 2b c + (- 2b + 4a )c + (- 4b + 20a b)c + (b + 20a b )c +--R + +--R 5 2 3 +--R 2b + 4a b +--R * +--R 5 +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R 4a c - 6a b c + (- 14a b + 16a )c + (6a b + 36a b)c + 10a b +--R + +--R 3 2 +--R 20a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 2 3 3 2 2 2 2 4 5 +--R - 2c + (2b - 6a )c + (2b - 26a b)c + (- 2a b + 20a )c - 2b +--R + +--R 2 3 4 +--R 34a b + 28a b +--R * +--R 3 +--R cosh(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 4a c + 3a b c + (8a b - 22a )c + (- 9a b - 24a b)c + 2a b +--R + +--R 3 2 5 +--R 46a b + 12a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 4 2 3 3 2 2 4 2 2 4 +--R c - 2b c + 2a c + (2b + 6a b)c + (- b - 18a b - 20a )c +--R + +--R 2 3 4 +--R 10a b + 20a b +--R * +--R cosh(x) +--R + +--R 3 2 3 3 2 +--R 6a c - 12a b c + 6a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R / +--R 8 7 2 2 6 3 2 5 4 4 4 +--R 2c + 4b c + (- 2b + 4a )c + (- 8b + 8a b)c + (- 2b + 2a )c +--R + +--R 5 2 3 4 3 6 2 4 4 2 2 +--R (4b - 8a b + 4a b)c + (2b - 4a b + 2a b )c +--R * +--R 6 +--R sinh(x) +--R + +--R 8 7 2 6 3 2 5 +--R 8c + 20b c + 16a c + (- 36b + 40a b)c +--R + +--R 4 2 2 4 4 5 2 3 4 3 +--R (- 24b + 16a b + 8a )c + (12b - 32a b + 20a b)c +--R + +--R 6 2 4 4 2 2 7 2 5 4 3 +--R (16b - 32a b + 16a b )c + (4b - 8a b + 4a b )c +--R * +--R cosh(x) +--R + +--R 7 6 2 3 5 3 3 4 +--R 12a c + 16a b c + (- 20a b + 24a )c + (- 32a b + 32a b)c +--R + +--R 4 3 2 5 3 5 3 3 5 2 +--R (4a b - 16a b + 12a )c + (16a b - 32a b + 16a b)c +--R + +--R 6 3 4 5 2 +--R (4a b - 8a b + 4a b )c +--R * +--R 5 +--R sinh(x) +--R + +--R 8 7 2 2 6 3 2 5 +--R 12c + 40b c + (22b + 24a )c + (- 60b + 80a b)c +--R + +--R 4 2 2 4 4 2 3 4 3 +--R (- 78b + 68a b + 12a )c + (- 40a b + 40a b)c +--R + +--R 6 2 4 4 2 2 7 2 5 4 3 8 +--R (42b - 88a b + 46a b )c + (20b - 40a b + 20a b )c + 2b +--R + +--R 2 6 4 4 +--R - 4a b + 2a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 3 5 +--R 40a c + 76a b c + (- 40a b + 80a )c +--R + +--R 3 3 4 4 5 3 +--R (- 148a b + 152a b)c + (- 40a b + 40a )c +--R + +--R 5 3 3 5 2 6 3 4 5 2 +--R (68a b - 144a b + 76a b)c + (40a b - 80a b + 40a b )c +--R + +--R 7 3 5 5 3 +--R 4a b - 8a b + 4a b +--R * +--R cosh(x) +--R + +--R 8 2 2 6 2 5 4 2 2 4 4 +--R - 4c + (12b + 18a )c + 20a b c + (- 12b - 34a b + 48a )c +--R + +--R 2 3 4 3 6 2 4 4 2 6 2 +--R (- 40a b + 40a b)c + (4b + 14a b - 44a b + 26a )c +--R + +--R 2 5 4 3 6 2 6 4 4 6 2 +--R (20a b - 40a b + 20a b)c + 2a b - 4a b + 2a b +--R * +--R 4 +--R sinh(x) +--R + +--R 8 7 2 2 6 3 2 5 +--R 8c + 40b c + (48b + 16a )c + (- 40b + 80a b)c +--R + +--R 4 2 2 4 4 5 4 3 +--R (- 112b + 112a b + 8a )c + (- 40b + 40a b)c +--R + +--R 6 2 4 4 2 2 7 2 5 4 3 8 +--R (48b - 112a b + 64a b )c + (40b - 80a b + 40a b )c + 8b +--R + +--R 2 6 4 4 +--R - 16a b + 8a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 3 5 3 3 4 +--R 48a c + 136a b c + (16a b + 96a )c + (- 248a b + 272a b)c +--R + +--R 4 3 2 5 3 5 3 3 5 2 +--R (- 176a b + 128a b + 48a )c + (88a b - 224a b + 136a b)c +--R + +--R 6 3 4 5 2 7 3 5 5 3 +--R (112a b - 224a b + 112a b )c + 24a b - 48a b + 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 8 7 2 2 6 3 2 5 +--R - 8c - 8b c + (24b + 56a )c + (24b + 80a b)c +--R + +--R 4 2 2 4 4 5 2 3 4 3 +--R (- 24b - 88a b + 136a )c + (- 24b - 160a b + 184a b)c +--R + +--R 6 2 4 4 2 6 2 +--R (8b + 8a b - 88a b + 72a )c +--R + +--R 7 2 5 4 3 6 2 6 4 4 6 2 +--R (8b + 80a b - 184a b + 96a b)c + 24a b - 48a b + 24a b +--R * +--R cosh(x) +--R + +--R 7 6 2 3 5 3 3 4 +--R - 16a c + 8a b c + (40a b - 8a )c + (- 16a b + 24a b)c +--R + +--R 4 5 3 5 3 3 5 2 +--R (- 32a b + 32a )c + (8a b - 32a b + 24a b)c +--R + +--R 6 3 4 5 2 7 3 5 5 3 7 +--R (8a b + 8a b - 40a b + 24a )c + 8a b - 16a b + 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 8 7 2 2 6 2 5 +--R 2c + 20b c + (42b + 4a )c + 40a b c +--R + +--R 4 2 2 4 4 5 2 3 4 3 +--R (- 78b + 88a b + 2a )c + (- 60b + 40a b + 20a b)c +--R + +--R 6 2 4 4 2 2 7 2 5 4 3 8 +--R (22b - 68a b + 46a b )c + (40b - 80a b + 40a b )c + 12b +--R + +--R 2 6 4 4 +--R - 24a b + 12a b +--R * +--R 4 +--R cosh(x) +--R + +--R 7 6 2 3 5 3 3 4 +--R 24a c + 112a b c + (88a b + 48a )c + (- 176a b + 224a b)c +--R + +--R 4 3 2 5 3 5 3 3 5 2 +--R (- 248a b + 224a b + 24a )c + (16a b - 128a b + 112a b)c +--R + +--R 6 3 4 5 2 7 3 5 5 3 +--R (136a b - 272a b + 136a b )c + 48a b - 96a b + 48a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 7 2 2 6 3 2 5 +--R - 4c - 16b c + (8b + 60a )c + (48b + 120a b)c +--R + +--R 2 2 4 4 5 2 3 4 3 +--R (- 60a b + 132a )c + (- 48b - 240a b + 288a b)c +--R + +--R 6 2 4 6 2 +--R (- 8b - 60a b + 68a )c +--R + +--R 7 2 5 4 3 6 8 2 6 4 4 +--R (16b + 120a b - 288a b + 152a b)c + 4b + 60a b - 132a b +--R + +--R 6 2 +--R 68a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 6 2 3 5 3 3 4 +--R - 24a c - 16a b c + (80a b + 8a )c + (40a b + 8a b)c +--R + +--R 4 5 3 5 3 3 5 2 +--R (- 88a b + 88a )c + (- 32a b - 32a b + 64a b)c +--R + +--R 6 3 4 5 2 7 7 3 5 5 3 +--R (32a b - 8a b - 80a b + 56a )c + 8a b + 24a b - 72a b +--R + +--R 7 +--R 40a b +--R * +--R cosh(x) +--R + +--R 8 7 2 2 6 3 2 5 +--R 2c - 4b c + (- 2b - 16a )c + (8b + 8a b)c +--R + +--R 4 2 2 4 4 5 2 3 4 3 +--R (- 2b + 44a b - 30a )c + (- 4b - 24a b + 28a b)c +--R + +--R 6 2 4 4 2 6 2 2 5 4 3 6 +--R (2b - 32a b + 34a b - 4a )c + (16a b - 32a b + 16a b)c +--R + +--R 2 6 6 2 8 +--R 4a b - 12a b + 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 6 3 2 5 4 2 2 4 +--R 4b c + 16b c + (12b + 8a b)c + (- 24b + 32a b )c +--R + +--R 5 2 3 4 3 2 4 4 2 2 +--R (- 36b + 32a b + 4a b)c + (- 16a b + 16a b )c +--R + +--R 7 2 5 4 3 8 2 6 4 4 +--R (20b - 40a b + 20a b )c + 8b - 16a b + 8a b +--R * +--R 5 +--R cosh(x) +--R + +--R 7 6 2 3 5 3 3 4 +--R 4a c + 40a b c + (68a b + 8a )c + (- 40a b + 80a b)c +--R + +--R 4 3 2 5 3 5 5 2 +--R (- 148a b + 144a b + 4a )c + (- 40a b + 40a b)c +--R + +--R 6 3 4 5 2 7 3 5 5 3 +--R (76a b - 152a b + 76a b )c + 40a b - 80a b + 40a b +--R * +--R 4 +--R cosh(x) +--R + +--R 7 2 2 6 3 2 5 +--R - 8b c + (- 8b + 24a )c + (24b + 80a b)c +--R + +--R 4 2 2 4 4 5 2 3 4 3 +--R (24b + 8a b + 48a )c + (- 24b - 160a b + 184a b)c +--R + +--R 6 2 4 4 2 6 2 +--R (- 24b - 88a b + 88a b + 24a )c +--R + +--R 7 2 5 4 3 6 8 2 6 4 4 +--R (8b + 80a b - 184a b + 96a b)c + 8b + 56a b - 136a b +--R + +--R 6 2 +--R 72a b +--R * +--R 3 +--R cosh(x) +--R + +--R 7 6 2 3 5 3 3 4 +--R - 8a c - 32a b c + (32a b + 24a )c + (88a b - 8a b)c +--R + +--R 4 3 2 5 3 5 5 2 +--R (- 40a b - 32a b + 72a )c + (- 80a b + 80a b)c +--R + +--R 6 3 4 5 2 7 7 3 5 5 3 +--R (16a b + 8a b - 64a b + 40a )c + 24a b + 8a b - 88a b +--R + +--R 7 +--R 56a b +--R * +--R 2 +--R cosh(x) +--R + +--R 7 2 2 6 3 2 5 +--R 4b c + (- 8b - 24a )c + (- 4b + 8a b)c +--R + +--R 4 2 2 4 4 5 4 3 +--R (16b + 56a b - 32a )c + (- 4b + 4a b)c +--R + +--R 6 2 4 4 2 6 2 7 2 5 4 3 +--R (- 8b - 56a b + 56a b + 8a )c + (4b - 8a b + 4a b )c +--R + +--R 2 6 4 4 6 2 8 +--R 24a b - 32a b - 8a b + 16a +--R * +--R cosh(x) +--R + +--R 7 6 2 5 3 3 4 +--R 4a c - 8a b c - 4a b c + (16a b - 8a b)c +--R + +--R 4 3 2 5 3 5 5 2 +--R (- 4a b + 16a b - 12a )c + (- 8a b + 8a b)c +--R + +--R 6 3 4 5 2 7 3 5 5 3 7 +--R (4a b - 16a b + 20a b - 8a )c + 8a b - 16a b + 8a b +--R * +--R sinh(x) +--R + +--R 2 6 3 5 4 2 2 4 5 2 3 3 +--R 2b c + 4b c + (- 2b + 4a b )c + (- 8b + 8a b )c +--R + +--R 6 4 2 2 7 2 5 4 3 8 2 6 4 4 +--R (- 2b + 2a b )c + (4b - 8a b + 4a b )c + 2b - 4a b + 2a b +--R * +--R 6 +--R cosh(x) +--R + +--R 6 2 5 3 3 4 4 3 2 3 +--R 4a b c + 16a b c + (4a b + 8a b)c + (- 32a b + 32a b )c +--R + +--R 5 3 3 5 2 6 3 4 5 2 7 +--R (- 20a b + 16a b + 4a b)c + (16a b - 32a b + 16a b )c + 12a b +--R + +--R 3 5 5 3 +--R - 24a b + 12a b +--R * +--R 5 +--R cosh(x) +--R + +--R 2 2 6 2 5 4 2 2 4 4 +--R (- 4b + 2a )c + 20a b c + (12b + 14a b + 4a )c +--R + +--R 2 3 4 3 6 2 4 4 2 6 2 +--R (- 40a b + 40a b)c + (- 12b - 34a b + 44a b + 2a )c +--R + +--R 2 5 4 3 6 8 2 6 4 4 6 2 +--R (20a b - 40a b + 20a b)c + 4b + 18a b - 48a b + 26a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 2 3 5 3 3 4 +--R - 8a b c + (- 8a b + 8a )c + (32a b + 8a b)c +--R + +--R 4 3 2 5 3 5 5 2 +--R (16a b - 32a b + 16a )c + (- 40a b + 40a b)c +--R + +--R 6 3 4 5 2 7 7 3 5 5 3 7 +--R (- 8a b + 24a b - 24a b + 8a )c + 16a b - 8a b - 32a b + 24a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 2 6 3 2 5 4 2 2 4 +--R (2b - 4a )c + (- 4b - 16a b)c + (- 2b + 32a b )c +--R + +--R 5 2 3 4 3 6 2 4 4 2 6 2 +--R (8b + 24a b - 32a b)c + (- 2b - 44a b + 34a b + 12a )c +--R + +--R 7 2 5 4 3 6 8 2 6 4 4 6 2 +--R (- 4b - 8a b + 28a b - 16a b)c + 2b + 16a b - 30a b + 4a b +--R + +--R 8 +--R 8a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 2 3 5 3 3 4 +--R 4a b c + (- 8a b - 8a )c + (- 4a b + 16a b)c +--R + +--R 4 5 3 5 3 3 5 2 +--R (16a b - 16a )c + (- 4a b - 16a b + 20a b)c +--R + +--R 6 3 4 5 2 7 7 5 3 7 +--R (- 8a b + 8a b + 8a b - 8a )c + 4a b - 12a b + 8a b +--R * +--R cosh(x) +--R + +--R 2 6 2 5 2 2 4 4 2 3 4 3 +--R 2a c - 4a b c + (- 2a b + 4a )c + (8a b - 8a b)c +--R + +--R 2 4 6 2 2 5 4 3 6 2 6 4 4 6 2 +--R (- 2a b + 2a )c + (- 4a b + 8a b - 4a b)c + 2a b - 4a b + 2a b +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c + b - a \|c - b + a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 518 +--d0945b:= D(m0945b,x) +--E 234 + +--S 235 of 518 +t0946:= 1/(a+a*cosh(x)+c*sinh(x))^2 +--R +--R +--R (229) +--R 1 +--R ------------------------------------------------------------------------ +--R 2 2 2 2 2 2 +--R c sinh(x) + (2a c cosh(x) + 2a c)sinh(x) + a cosh(x) + 2a cosh(x) + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 518 +r0946:= a*log(a+c*tanh(1/2*x))/c^3-(c*cosh(x)+a*sinh(x))/c^2/_ + (a+a*cosh(x)+c*sinh(x)) +--R +--R +--R (230) +--R 2 2 x 2 +--R (a c sinh(x) + a cosh(x) + a )log(c tanh(-) + a) - a c sinh(x) - c cosh(x) +--R 2 +--R -------------------------------------------------------------------------- +--R 4 3 3 +--R c sinh(x) + a c cosh(x) + a c +--R Type: Expression(Integer) +--E 236 + +--S 237 of 518 +a0946:= integrate(t0946,x) +--R +--R +--R (231) +--R 2 2 2 2 +--R (a c + a )sinh(x) + ((2a c + 2a )cosh(x) + 2a )sinh(x) +--R + +--R 2 2 2 2 +--R (a c + a )cosh(x) + 2a cosh(x) - a c + a +--R * +--R log((c + a)sinh(x) + (c + a)cosh(x) - c + a) +--R + +--R 2 2 2 2 +--R (- a c - a )sinh(x) + ((- 2a c - 2a )cosh(x) - 2a )sinh(x) +--R + +--R 2 2 2 2 +--R (- a c - a )cosh(x) - 2a cosh(x) + a c - a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 +--R 2a c sinh(x) + 2a c cosh(x) - 2c + 2a c +--R / +--R 4 3 2 4 3 3 +--R (c + a c )sinh(x) + ((2c + 2a c )cosh(x) + 2a c )sinh(x) +--R + +--R 4 3 2 3 4 3 +--R (c + a c )cosh(x) + 2a c cosh(x) - c + a c +--R Type: Union(Expression(Integer),...) +--E 237 + +--S 238 of 518 +m0946:= a0946-r0946 +--R +--R +--R (232) +--R 2 2 3 +--R (- a c - a c)sinh(x) +--R + +--R 2 2 3 2 3 2 +--R ((- 2a c - 3a c - a )cosh(x) - 3a c - a )sinh(x) +--R + +--R 2 2 3 2 2 3 2 +--R (- a c - 3a c - 2a )cosh(x) + (- 4a c - 4a )cosh(x) + a c +--R + +--R 2 3 +--R - a c - 2a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 3 2 2 3 +--R (- a c - a )cosh(x) + (- a c - 3a )cosh(x) + (a c - 3a )cosh(x) +--R + +--R 2 3 +--R a c - a +--R * +--R x +--R log(c tanh(-) + a) +--R 2 +--R + +--R 2 2 3 +--R (a c + a c)sinh(x) +--R + +--R 2 2 3 2 3 2 +--R ((2a c + 3a c + a )cosh(x) + 3a c + a )sinh(x) +--R + +--R 2 2 3 2 2 3 2 2 +--R (a c + 3a c + 2a )cosh(x) + (4a c + 4a )cosh(x) - a c + a c +--R + +--R 3 +--R 2a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 3 2 2 3 2 +--R (a c + a )cosh(x) + (a c + 3a )cosh(x) + (- a c + 3a )cosh(x) - a c +--R + +--R 3 +--R a +--R * +--R log((c + a)sinh(x) + (c + a)cosh(x) - c + a) +--R + +--R 2 2 3 +--R (- a c - a c)sinh(x) +--R + +--R 2 2 3 2 3 2 +--R ((- 2a c - 3a c - a )cosh(x) - 3a c - a )sinh(x) +--R + +--R 2 2 3 2 2 3 2 +--R (- a c - 3a c - 2a )cosh(x) + (- 4a c - 4a )cosh(x) + a c +--R + +--R 2 3 +--R - a c - 2a +--R * +--R sinh(x) +--R + +--R 2 3 3 2 3 2 2 3 +--R (- a c - a )cosh(x) + (- a c - 3a )cosh(x) + (a c - 3a )cosh(x) +--R + +--R 2 3 +--R a c - a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 2 3 +--R (a c + a c)sinh(x) +--R + +--R 3 2 2 2 2 2 +--R ((c + 3a c + 2a c)cosh(x) + 2a c + 2a c)sinh(x) +--R + +--R 3 2 2 2 2 2 3 2 +--R (2c + 3a c + a c)cosh(x) + (4a c + 4a c)cosh(x) - 2c + a c +--R + +--R 2 +--R 3a c +--R * +--R sinh(x) +--R + +--R 3 2 3 2 2 2 +--R (c + a c )cosh(x) + (2a c + 2a c)cosh(x) +--R + +--R 3 2 2 2 2 +--R (- c - a c + 4a c)cosh(x) - 2a c + 2a c +--R / +--R 5 4 3 +--R (c + a c )sinh(x) +--R + +--R 5 4 2 3 4 2 3 2 +--R ((2c + 3a c + a c )cosh(x) + 3a c + a c )sinh(x) +--R + +--R 5 4 2 3 2 4 2 3 5 4 +--R (c + 3a c + 2a c )cosh(x) + (4a c + 4a c )cosh(x) - c + a c +--R + +--R 2 3 +--R 2a c +--R * +--R sinh(x) +--R + +--R 4 2 3 3 4 2 3 2 4 2 3 +--R (a c + a c )cosh(x) + (a c + 3a c )cosh(x) + (- a c + 3a c )cosh(x) +--R + +--R 4 2 3 +--R - a c + a c +--R Type: Expression(Integer) +--E 238 + +--S 239 of 518 +d0946:= D(m0946,x) +--R +--R +--R (233) +--R 4 2 3 3 2 6 +--R (a c + 2a c + a c )sinh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 +--R ((4a c + 10a c + 8a c + 2a c)cosh(x) + 6a c + 8a c + 2a c) +--R * +--R 5 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (6a c + 20a c + 23a c + 10a c + a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 3 2 4 +--R (20a c + 38a c + 20a c + 2a )cosh(x) - 2a c + 15a c + 10a c +--R + +--R 5 +--R a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (4a c + 20a c + 32a c + 20a c + 4a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (24a c + 68a c + 56a c + 12a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 +--R (- 4a c - 4a c + 40a c + 52a c + 12a )cosh(x) - 8a c + 4a c +--R + +--R 4 5 +--R 16a c + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (a c + 10a c + 23a c + 20a c + 6a )cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (12a c + 56a c + 68a c + 24a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 2a c - 8a c + 34a c + 84a c + 36a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 +--R (- 12a c - 8a c + 44a c + 24a )cosh(x) + a c - 2a c - 9a c +--R + +--R 4 5 +--R 8a c + 6a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (2a c + 8a c + 10a c + 4a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (2a c + 20a c + 38a c + 20a )cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 4a c + 8a c + 52a c + 40a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (- 4a c - 16a c + 28a c + 40a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 3 3 2 4 5 +--R (2a c - 16a c + 2a c + 20a )cosh(x) + 2a c - 4a c - 2a c + 4a +--R * +--R sinh(x) +--R + +--R 3 2 4 5 6 3 2 4 5 5 +--R (a c + 2a c + a )cosh(x) + (2a c + 8a c + 6a )cosh(x) +--R + +--R 3 2 4 5 4 3 2 5 3 +--R (- a c + 10a c + 15a )cosh(x) + (- 4a c + 20a )cosh(x) +--R + +--R 3 2 4 5 2 3 2 4 5 3 2 +--R (- a c - 10a c + 15a )cosh(x) + (2a c - 8a c + 6a )cosh(x) + a c +--R + +--R 4 5 +--R - 2a c + a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 4 3 2 4 6 +--R (2c + 4a c - 4a c - 2a c)sinh(x) +--R + +--R 5 4 3 2 4 4 2 3 3 2 +--R (8c + 16a c - 16a c - 8a c)cosh(x) + 10a c + 12a c - 6a c +--R + +--R 4 +--R - 8a c +--R * +--R 5 +--R sinh(x) +--R + +--R 5 4 3 2 4 2 +--R (10c + 20a c - 20a c - 10a c)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 +--R (32a c + 42a c - 12a c - 22a c)cosh(x) + 4c + 24a c + 8a c +--R + +--R 4 +--R - 12a c +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (28a c + 48a c + 12a c - 8a c)cosh(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 +--R (8c + 16a c + 56a c + 32a c - 16a c)cosh(x) + 4a c + 8a c +--R + +--R 3 2 4 +--R 20a c - 8a c +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 3 2 4 4 +--R (- 10c - 20a c + 20a c + 10a c)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a c + 12a c + 48a c + 28a c)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (8c + 32a c + 32a c + 48a c + 24a c)cosh(x) +--R + +--R 4 2 3 3 2 4 5 4 3 2 +--R (16a c + 20a c + 32a c + 4a c)cosh(x) + 2c - 4a c + 12a c +--R + +--R 4 +--R - 2a c +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 3 2 4 5 +--R (- 8c - 16a c + 16a c + 8a c)cosh(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 22a c - 12a c + 42a c + 32a c)cosh(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (8c + 16a c - 8a c + 32a c + 48a c)cosh(x) +--R + +--R 4 2 3 3 2 4 2 2 3 4 +--R (20a c + 16a c + 4a c + 32a c)cosh(x) + (8a c + 8a c)cosh(x) +--R + +--R 4 2 3 3 2 +--R 2a c - 4a c + 2a c +--R * +--R sinh(x) +--R + +--R 5 4 3 2 4 6 +--R (- 2c - 4a c + 4a c + 2a c)cosh(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 8a c - 6a c + 12a c + 10a c)cosh(x) +--R + +--R 5 2 3 3 2 4 4 +--R (4c - 8a c + 8a c + 20a c)cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (8a c + 4a c - 8a c + 20a c)cosh(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 2c + 4a c + 8a c - 12a c + 10a c)cosh(x) +--R + +--R 2 3 3 2 4 +--R (2a c - 4a c + 2a c)cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 2 3 3 2 4 5 6 +--R (a c + 2a c - a c - 4a c - 2a )sinh(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 +--R (4a c + 6a c - 8a c - 18a c - 8a )cosh(x) + 4a c + 4a c - 8a c +--R + +--R 5 +--R - 8a +--R * +--R 5 +--R sinh(x) +--R + +--R 4 3 2 4 5 2 +--R (4a c - 23a c - 30a c - 11a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 3 2 4 5 +--R (12a c + 4a c - 32a c - 24a )cosh(x) + 6a c + 9a c - 2a c - 13a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 4a c - 20a c - 32a c - 20a c - 4a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (4a c - 20a c - 44a c - 20a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 +--R (12a c + 20a c + 16a c - 20a c - 28a )cosh(x) + 12a c + 4a c +--R + +--R 4 5 +--R 4a c - 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 2 3 3 2 5 4 +--R (- 11a c - 30a c - 23a c + 4a )cosh(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 20a c - 44a c - 20a c + 4a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (10a c + 40a c - 2a c - 36a c - 12a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R (28a c + 28a c - 12a c - 20a )cosh(x) + a c - 2a c + 9a c + 4a c +--R + +--R 5 +--R - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 8a c - 18a c - 8a c + 6a c + 4a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 24a c - 32a c + 4a c + 12a )cosh(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (8a c + 20a c - 16a c - 20a c + 8a )cosh(x) +--R + +--R 2 3 3 2 4 5 2 +--R (24a c + 32a c - 24a c - 8a )cosh(x) +--R + +--R 2 3 3 2 4 5 4 5 +--R (- 2a c + 24a c - 2a c - 12a )cosh(x) + 4a c - 4a +--R * +--R sinh(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (- 2a c - 4a c - a c + 2a c + a )cosh(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 8a c - 8a c + 4a c + 4a )cosh(x) +--R + +--R 4 3 2 4 5 4 2 3 3 2 4 3 +--R (4a c - 7a c - 2a c + 5a )cosh(x) + (8a c + 8a c - 8a c)cosh(x) +--R + +--R 4 2 3 3 2 4 5 2 4 5 +--R (- 2a c + 4a c + 9a c - 2a c - 5a )cosh(x) + (4a c - 4a )cosh(x) +--R + +--R 3 2 4 5 +--R - a c + 2a c - a +--R / +--R 7 6 2 5 6 +--R (2c + 4a c + 2a c )sinh(x) +--R + +--R 7 6 2 5 3 4 6 2 5 3 4 +--R ((8c + 20a c + 16a c + 4a c )cosh(x) + 12a c + 16a c + 4a c ) +--R * +--R 5 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 +--R (12c + 40a c + 46a c + 20a c + 2a c )cosh(x) +--R + +--R 6 2 5 3 4 4 3 7 2 5 3 4 +--R (40a c + 76a c + 40a c + 4a c )cosh(x) - 4c + 30a c + 20a c +--R + +--R 4 3 +--R 2a c +--R * +--R 4 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (8c + 40a c + 64a c + 40a c + 8a c )cosh(x) +--R + +--R 6 2 5 3 4 4 3 2 +--R (48a c + 136a c + 112a c + 24a c )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 6 +--R (- 8c - 8a c + 80a c + 104a c + 24a c )cosh(x) - 16a c +--R + +--R 2 5 3 4 4 3 +--R 8a c + 32a c + 8a c +--R * +--R 3 +--R sinh(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (2c + 20a c + 46a c + 40a c + 12a c )cosh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (24a c + 112a c + 136a c + 48a c )cosh(x) +--R + +--R 7 6 2 5 3 4 4 3 2 +--R (- 4c - 16a c + 68a c + 168a c + 72a c )cosh(x) +--R + +--R 6 2 5 3 4 4 3 7 6 +--R (- 24a c - 16a c + 88a c + 48a c )cosh(x) + 2c - 4a c +--R + +--R 2 5 3 4 4 3 +--R - 18a c + 16a c + 12a c +--R * +--R 2 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 +--R (4a c + 16a c + 20a c + 8a c )cosh(x) +--R + +--R 6 2 5 3 4 4 3 4 +--R (4a c + 40a c + 76a c + 40a c )cosh(x) +--R + +--R 6 2 5 3 4 4 3 3 +--R (- 8a c + 16a c + 104a c + 80a c )cosh(x) +--R + +--R 6 2 5 3 4 4 3 2 +--R (- 8a c - 32a c + 56a c + 80a c )cosh(x) +--R + +--R 6 2 5 3 4 4 3 6 2 5 3 4 +--R (4a c - 32a c + 4a c + 40a c )cosh(x) + 4a c - 8a c - 4a c +--R + +--R 4 3 +--R 8a c +--R * +--R sinh(x) +--R + +--R 2 5 3 4 4 3 6 2 5 3 4 4 3 5 +--R (2a c + 4a c + 2a c )cosh(x) + (4a c + 16a c + 12a c )cosh(x) +--R + +--R 2 5 3 4 4 3 4 2 5 4 3 3 +--R (- 2a c + 20a c + 30a c )cosh(x) + (- 8a c + 40a c )cosh(x) +--R + +--R 2 5 3 4 4 3 2 +--R (- 2a c - 20a c + 30a c )cosh(x) +--R + +--R 2 5 3 4 4 3 2 5 3 4 4 3 +--R (4a c - 16a c + 12a c )cosh(x) + 2a c - 4a c + 2a c +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 6 2 5 3 4 6 +--R (2a c + 4a c + 2a c )sinh(x) +--R + +--R 6 2 5 3 4 4 3 2 5 3 4 4 3 +--R ((8a c + 20a c + 16a c + 4a c )cosh(x) + 12a c + 16a c + 4a c ) +--R * +--R 5 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 +--R (12a c + 40a c + 46a c + 20a c + 2a c )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 4 4 3 +--R (40a c + 76a c + 40a c + 4a c )cosh(x) - 4a c + 30a c + 20a c +--R + +--R 5 2 +--R 2a c +--R * +--R 4 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (8a c + 40a c + 64a c + 40a c + 8a c )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 +--R (48a c + 136a c + 112a c + 24a c )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 5 3 4 +--R (- 8a c - 8a c + 80a c + 104a c + 24a c )cosh(x) - 16a c + 8a c +--R + +--R 4 3 5 2 +--R 32a c + 8a c +--R * +--R 3 +--R sinh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 4 +--R (2a c + 20a c + 46a c + 40a c + 12a c )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (24a c + 112a c + 136a c + 48a c )cosh(x) +--R + +--R 6 2 5 3 4 4 3 5 2 2 +--R (- 4a c - 16a c + 68a c + 168a c + 72a c )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 3 4 +--R (- 24a c - 16a c + 88a c + 48a c )cosh(x) + 2a c - 4a c - 18a c +--R + +--R 4 3 5 2 +--R 16a c + 12a c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 4 3 5 2 5 +--R (4a c + 16a c + 20a c + 8a c )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 4 +--R (4a c + 40a c + 76a c + 40a c )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (- 8a c + 16a c + 104a c + 80a c )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 +--R (- 8a c - 32a c + 56a c + 80a c )cosh(x) +--R + +--R 2 5 3 4 4 3 5 2 2 5 3 4 4 3 +--R (4a c - 32a c + 4a c + 40a c )cosh(x) + 4a c - 8a c - 4a c +--R + +--R 5 2 +--R 8a c +--R * +--R sinh(x) +--R + +--R 3 4 4 3 5 2 6 3 4 4 3 5 2 5 +--R (2a c + 4a c + 2a c )cosh(x) + (4a c + 16a c + 12a c )cosh(x) +--R + +--R 3 4 4 3 5 2 4 3 4 5 2 3 +--R (- 2a c + 20a c + 30a c )cosh(x) + (- 8a c + 40a c )cosh(x) +--R + +--R 3 4 4 3 5 2 2 3 4 4 3 5 2 +--R (- 2a c - 20a c + 30a c )cosh(x) + (4a c - 16a c + 12a c )cosh(x) +--R + +--R 3 4 4 3 5 2 +--R 2a c - 4a c + 2a c +--R Type: Expression(Integer) +--E 239 + +--S 240 of 518 +t0947:= 1/(a+a*cosh(x)+c*sinh(x))^3 +--R +--R +--R (234) +--R 1 +--R / +--R 3 3 2 2 2 +--R c sinh(x) + (3a c cosh(x) + 3a c )sinh(x) +--R + +--R 2 2 2 2 3 3 3 2 +--R (3a c cosh(x) + 6a c cosh(x) + 3a c)sinh(x) + a cosh(x) + 3a cosh(x) +--R + +--R 3 3 +--R 3a cosh(x) + a +--R Type: Expression(Integer) +--E 240 + +--S 241 of 518 +r0947:= -1/2*(c*cosh(x)+a*sinh(x))/c^2/(a+a*cosh(x)+c*sinh(x))^2+_ + 1/2*((3*a^2-c^2)*log(a+c*tanh(1/2*x))-_ + 3*a*c*(c*cosh(x)+a*sinh(x))/(a+a*cosh(x)+c*sinh(x)))/c^5 +--R +--R +--R (235) +--R 4 2 2 2 +--R (- c + 3a c )sinh(x) +--R + +--R 3 3 3 3 +--R ((- 2a c + 6a c)cosh(x) - 2a c + 6a c)sinh(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (- a c + 3a )cosh(x) + (- 2a c + 6a )cosh(x) - a c + 3a +--R * +--R x +--R log(c tanh(-) + a) +--R 2 +--R + +--R 2 2 2 3 3 3 3 +--R - 3a c sinh(x) + ((- 3a c - 3a c)cosh(x) - a c - 3a c)sinh(x) +--R + +--R 2 2 2 4 2 2 +--R - 3a c cosh(x) + (- c - 3a c )cosh(x) +--R / +--R 7 2 6 6 2 5 2 +--R 2c sinh(x) + (4a c cosh(x) + 4a c )sinh(x) + 2a c cosh(x) +--R + +--R 2 5 2 5 +--R 4a c cosh(x) + 2a c +--R Type: Expression(Integer) +--E 241 + +--S 242 of 518 +a0947:= integrate(t0947,x) +--R +--R +--R (236) +--R 4 3 2 2 3 4 4 +--R (- c - 2a c + 2a c + 6a c + 3a )sinh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 4c - 8a c + 8a c + 24a c + 12a )cosh(x) - 4a c - 4a c +--R + +--R 3 4 +--R 12a c + 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 6c - 12a c + 12a c + 36a c + 18a )cosh(x) +--R + +--R 3 2 2 3 4 4 2 2 4 +--R (- 12a c - 12a c + 36a c + 36a )cosh(x) + 2c - 12a c + 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 4c - 8a c + 8a c + 24a c + 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 +--R (- 12a c - 12a c + 36a c + 36a )cosh(x) +--R + +--R 4 2 2 4 3 2 2 3 4 +--R (4c - 24a c + 36a )cosh(x) + 4a c - 4a c - 12a c + 12a +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- c - 2a c + 2a c + 6a c + 3a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (- 4a c - 4a c + 12a c + 12a )cosh(x) +--R + +--R 4 2 2 4 2 3 2 2 3 4 +--R (2c - 12a c + 18a )cosh(x) + (4a c - 4a c - 12a c + 12a )cosh(x) +--R + +--R 4 3 2 2 3 4 +--R - c + 2a c + 2a c - 6a c + 3a +--R * +--R log((c + a)sinh(x) + (c + a)cosh(x) - c + a) +--R + +--R 4 3 2 2 3 4 4 +--R (c + 2a c - 2a c - 6a c - 3a )sinh(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (4c + 8a c - 8a c - 24a c - 12a )cosh(x) + 4a c + 4a c +--R + +--R 3 4 +--R - 12a c - 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 2 +--R (6c + 12a c - 12a c - 36a c - 18a )cosh(x) +--R + +--R 3 2 2 3 4 4 2 2 4 +--R (12a c + 12a c - 36a c - 36a )cosh(x) - 2c + 12a c - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 3 +--R (4c + 8a c - 8a c - 24a c - 12a )cosh(x) +--R + +--R 3 2 2 3 4 2 +--R (12a c + 12a c - 36a c - 36a )cosh(x) +--R + +--R 4 2 2 4 3 2 2 3 4 +--R (- 4c + 24a c - 36a )cosh(x) - 4a c + 4a c + 12a c - 12a +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 4 4 +--R (c + 2a c - 2a c - 6a c - 3a )cosh(x) +--R + +--R 3 2 2 3 4 3 +--R (4a c + 4a c - 12a c - 12a )cosh(x) +--R + +--R 4 2 2 4 2 +--R (- 2c + 12a c - 18a )cosh(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 +--R (- 4a c + 4a c + 12a c - 12a )cosh(x) + c - 2a c - 2a c + 6a c +--R + +--R 4 +--R - 3a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 4 3 2 2 3 3 +--R (- 2c - 2a c + 6a c + 6a c)sinh(x) +--R + +--R 4 3 2 2 3 3 3 2 +--R ((- 6c - 6a c + 18a c + 18a c)cosh(x) - 6a c + 18a c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 3 +--R (- 6c - 6a c + 18a c + 18a c)cosh(x) + (- 12a c + 36a c)cosh(x) +--R + +--R 4 3 2 2 3 +--R - 2c + 2a c - 18a c + 18a c +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 3 3 3 2 +--R (- 2c - 2a c + 6a c + 6a c)cosh(x) + (- 6a c + 18a c)cosh(x) +--R + +--R 4 3 2 2 3 3 2 2 3 +--R (- 2c + 2a c - 18a c + 18a c)cosh(x) + 6a c - 12a c + 6a c +--R / +--R 7 6 2 5 4 +--R (2c + 4a c + 2a c )sinh(x) +--R + +--R 7 6 2 5 6 2 5 3 +--R ((8c + 16a c + 8a c )cosh(x) + 8a c + 8a c )sinh(x) +--R + +--R 7 6 2 5 2 6 2 5 7 +--R (12c + 24a c + 12a c )cosh(x) + (24a c + 24a c )cosh(x) - 4c +--R + +--R 2 5 +--R 12a c +--R * +--R 2 +--R sinh(x) +--R + +--R 7 6 2 5 3 6 2 5 2 +--R (8c + 16a c + 8a c )cosh(x) + (24a c + 24a c )cosh(x) +--R + +--R 7 2 5 6 2 5 +--R (- 8c + 24a c )cosh(x) - 8a c + 8a c +--R * +--R sinh(x) +--R + +--R 7 6 2 5 4 6 2 5 3 +--R (2c + 4a c + 2a c )cosh(x) + (8a c + 8a c )cosh(x) +--R + +--R 7 2 5 2 6 2 5 7 6 2 5 +--R (- 4c + 12a c )cosh(x) + (- 8a c + 8a c )cosh(x) + 2c - 4a c + 2a c +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 518 +m0947:= a0947-r0947 +--R +--R +--R (237) +--R 6 5 2 4 3 3 4 2 6 +--R (c + 2a c - 2a c - 6a c - 3a c )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (4c + 10a c - 4a c - 28a c - 24a c - 6a c)cosh(x) + 6a c +--R + +--R 2 4 3 3 4 2 5 +--R 8a c - 16a c - 24a c - 6a c +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (6c + 20a c + 5a c - 50a c - 68a c - 30a c - 3a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (20a c + 38a c - 40a c - 112a c - 60a c - 6a )cosh(x) - 2c +--R + +--R 2 4 3 3 4 2 5 6 +--R 21a c + 10a c - 44a c - 30a c - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4c + 20a c + 20a c - 40a c - 92a c - 60a c - 12a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (24a c + 68a c - 16a c - 192a c - 168a c - 36a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 4c - 4a c + 52a c + 64a c - 108a c - 156a c - 36a ) +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 8a c + 4a c + 40a c - 8a c - 48a c - 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (c + 10a c + 20a c - 10a c - 63a c - 60a c - 18a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (12a c + 56a c + 32a c - 144a c - 204a c - 72a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 2c - 8a c + 40a c + 108a c - 66a c - 252a c - 108a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 12a c - 8a c + 80a c + 48a c - 132a c - 72a )cosh(x) + c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 2a c - 12a c + 14a c + 33a c - 24a c - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (2a c + 8a c + 4a c - 20a c - 30a c - 12a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (2a c + 20a c + 32a c - 40a c - 114a c - 60a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 4a c + 8a c + 64a c + 16a c - 156a c - 120a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (- 4a c - 16a c + 40a c + 88a c - 84a c - 120a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (2a c - 16a c - 4a c + 68a c - 6a c - 60a )cosh(x) + 2a c +--R + +--R 2 4 3 3 4 2 5 6 +--R - 4a c - 8a c + 16a c + 6a c - 12a +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (a c + 2a c - 2a c - 6a c - 3a )cosh(x) +--R + +--R 2 4 3 3 5 6 5 +--R (2a c + 8a c - 24a c - 18a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- a c + 10a c + 18a c - 30a c - 45a )cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (- 4a c + 32a c - 60a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (- a c - 10a c + 18a c + 30a c - 45a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 4 3 3 4 2 5 +--R (2a c - 8a c + 24a c - 18a )cosh(x) + a c - 2a c - 2a c + 6a c +--R + +--R 6 +--R - 3a +--R * +--R x +--R log(c tanh(-) + a) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- c - 2a c + 2a c + 6a c + 3a c )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (- 4c - 10a c + 4a c + 28a c + 24a c + 6a c)cosh(x) - 6a c +--R + +--R 2 4 3 3 4 2 5 +--R - 8a c + 16a c + 24a c + 6a c +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (- 6c - 20a c - 5a c + 50a c + 68a c + 30a c + 3a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 20a c - 38a c + 40a c + 112a c + 60a c + 6a )cosh(x) + 2c +--R + +--R 2 4 3 3 4 2 5 6 +--R - 21a c - 10a c + 44a c + 30a c + 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 4c - 20a c - 20a c + 40a c + 92a c + 60a c + 12a ) +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (- 24a c - 68a c + 16a c + 192a c + 168a c + 36a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (4c + 4a c - 52a c - 64a c + 108a c + 156a c + 36a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 8a c - 4a c - 40a c + 8a c + 48a c + 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- c - 10a c - 20a c + 10a c + 63a c + 60a c + 18a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 12a c - 56a c - 32a c + 144a c + 204a c + 72a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (2c + 8a c - 40a c - 108a c + 66a c + 252a c + 108a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (12a c + 8a c - 80a c - 48a c + 132a c + 72a )cosh(x) - c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 2a c + 12a c - 14a c - 33a c + 24a c + 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 2a c - 8a c - 4a c + 20a c + 30a c + 12a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (- 2a c - 20a c - 32a c + 40a c + 114a c + 60a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (4a c - 8a c - 64a c - 16a c + 156a c + 120a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (4a c + 16a c - 40a c - 88a c + 84a c + 120a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 2a c + 16a c + 4a c - 68a c + 6a c + 60a )cosh(x) - 2a c +--R + +--R 2 4 3 3 4 2 5 6 +--R 4a c + 8a c - 16a c - 6a c + 12a +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- a c - 2a c + 2a c + 6a c + 3a )cosh(x) +--R + +--R 2 4 3 3 5 6 5 +--R (- 2a c - 8a c + 24a c + 18a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (a c - 10a c - 18a c + 30a c + 45a )cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (4a c - 32a c + 60a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (a c + 10a c - 18a c - 30a c + 45a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 4 3 3 4 2 5 +--R (- 2a c + 8a c - 24a c + 18a )cosh(x) - a c + 2a c + 2a c - 6a c +--R + +--R 6 +--R 3a +--R * +--R log((c + a)sinh(x) + (c + a)cosh(x) - c + a) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (c + 2a c - 2a c - 6a c - 3a c )sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (4c + 10a c - 4a c - 28a c - 24a c - 6a c)cosh(x) + 6a c +--R + +--R 2 4 3 3 4 2 5 +--R 8a c - 16a c - 24a c - 6a c +--R * +--R 5 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 +--R (6c + 20a c + 5a c - 50a c - 68a c - 30a c - 3a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (20a c + 38a c - 40a c - 112a c - 60a c - 6a )cosh(x) - 2c +--R + +--R 2 4 3 3 4 2 5 6 +--R 21a c + 10a c - 44a c - 30a c - 3a +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 3 +--R (4c + 20a c + 20a c - 40a c - 92a c - 60a c - 12a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (24a c + 68a c - 16a c - 192a c - 168a c - 36a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 4c - 4a c + 52a c + 64a c - 108a c - 156a c - 36a ) +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 8a c + 4a c + 40a c - 8a c - 48a c - 12a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (c + 10a c + 20a c - 10a c - 63a c - 60a c - 18a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (12a c + 56a c + 32a c - 144a c - 204a c - 72a )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 2c - 8a c + 40a c + 108a c - 66a c - 252a c - 108a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 12a c - 8a c + 80a c + 48a c - 132a c - 72a )cosh(x) + c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 2a c - 12a c + 14a c + 33a c - 24a c - 18a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (2a c + 8a c + 4a c - 20a c - 30a c - 12a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (2a c + 20a c + 32a c - 40a c - 114a c - 60a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 4a c + 8a c + 64a c + 16a c - 156a c - 120a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (- 4a c - 16a c + 40a c + 88a c - 84a c - 120a )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (2a c - 16a c - 4a c + 68a c - 6a c - 60a )cosh(x) + 2a c +--R + +--R 2 4 3 3 4 2 5 6 +--R - 4a c - 8a c + 16a c + 6a c - 12a +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (a c + 2a c - 2a c - 6a c - 3a )cosh(x) +--R + +--R 2 4 3 3 5 6 5 +--R (2a c + 8a c - 24a c - 18a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- a c + 10a c + 18a c - 30a c - 45a )cosh(x) +--R + +--R 2 4 4 2 6 3 +--R (- 4a c + 32a c - 60a )cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (- a c - 10a c + 18a c + 30a c - 45a )cosh(x) +--R + +--R 2 4 3 3 5 6 2 4 3 3 4 2 5 +--R (2a c - 8a c + 24a c - 18a )cosh(x) + a c - 2a c - 2a c + 6a c +--R + +--R 6 +--R - 3a +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R 2 4 3 3 4 2 6 +--R (3a c + 6a c + 3a c )sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 2 4 +--R (3a c + 18a c + 30a c + 18a c + 3a c)cosh(x) - 2c - a c + 8a c +--R + +--R 3 3 4 2 5 +--R 22a c + 18a c + 3a c +--R * +--R 5 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (12a c + 45a c + 66a c + 45a c + 12a c)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (- 5c - 4a c + 38a c + 100a c + 87a c + 24a c)cosh(x) - 10a c +--R + +--R 2 4 3 3 4 2 5 +--R - 6a c + 34a c + 42a c + 12a c +--R * +--R 4 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (18a c + 60a c + 84a c + 60a c + 18a c)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2c - 4a c + 68a c + 184a c + 174a c + 60a c)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 4 +--R (- 26a c - 24a c + 104a c + 168a c + 66a c)cosh(x) - 2c - 32a c +--R + +--R 3 3 4 2 5 +--R 4a c + 54a c + 24a c +--R * +--R 3 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (12a c + 45a c + 66a c + 45a c + 12a c)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (4c + 2a c + 56a c + 172a c + 180a c + 66a c)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 18a c - 36a c + 108a c + 252a c + 126a c)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (- 4c - 6a c - 56a c - 36a c + 144a c + 102a c)cosh(x) + 2a c +--R + +--R 2 4 3 3 4 2 5 +--R - 9a c - 38a c + 27a c + 30a c +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (3a c + 18a c + 30a c + 18a c + 3a c)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (4c + 5a c + 20a c + 82a c + 96a c + 33a c)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (2a c - 24a c + 40a c + 168a c + 102a c)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 4c - 6a c - 28a c - 64a c + 108a c + 138a c)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 5 2 4 +--R (- 5a c + 6a c - 70a c + 6a c + 87a c)cosh(x) + a c + 8a c +--R + +--R 3 3 4 2 5 +--R - 18a c - 12a c + 21a c +--R * +--R sinh(x) +--R + +--R 2 4 3 3 4 2 6 +--R (3a c + 6a c + 3a c )cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (c + 2a c + 2a c + 16a c + 21a c + 6a c)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (4a c - 6a c + 2a c + 42a c + 30a c)cosh(x) +--R + +--R 6 2 4 3 3 4 2 5 3 +--R (- 2c - 4a c - 24a c + 18a c + 60a c)cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 4a c + 3a c - 14a c - 33a c + 60a c)cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 3 4 2 +--R (c - 2a c + 2a c + 8a c - 39a c + 30a c)cosh(x) + 6a c - 12a c +--R + +--R 5 +--R 6a c +--R / +--R 9 8 2 7 6 +--R (2c + 4a c + 2a c )sinh(x) +--R + +--R 9 8 2 7 3 6 8 2 7 3 6 +--R ((8c + 20a c + 16a c + 4a c )cosh(x) + 12a c + 16a c + 4a c ) +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (12c + 40a c + 46a c + 20a c + 2a c )cosh(x) +--R + +--R 8 2 7 3 6 4 5 9 2 7 3 6 +--R (40a c + 76a c + 40a c + 4a c )cosh(x) - 4c + 30a c + 20a c +--R + +--R 4 5 +--R 2a c +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (8c + 40a c + 64a c + 40a c + 8a c )cosh(x) +--R + +--R 8 2 7 3 6 4 5 2 +--R (48a c + 136a c + 112a c + 24a c )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 8 2 7 +--R (- 8c - 8a c + 80a c + 104a c + 24a c )cosh(x) - 16a c + 8a c +--R + +--R 3 6 4 5 +--R 32a c + 8a c +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (2c + 20a c + 46a c + 40a c + 12a c )cosh(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (24a c + 112a c + 136a c + 48a c )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (- 4c - 16a c + 68a c + 168a c + 72a c )cosh(x) +--R + +--R 8 2 7 3 6 4 5 9 8 2 7 +--R (- 24a c - 16a c + 88a c + 48a c )cosh(x) + 2c - 4a c - 18a c +--R + +--R 3 6 4 5 +--R 16a c + 12a c +--R * +--R 2 +--R sinh(x) +--R + +--R 8 2 7 3 6 4 5 5 +--R (4a c + 16a c + 20a c + 8a c )cosh(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (4a c + 40a c + 76a c + 40a c )cosh(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (- 8a c + 16a c + 104a c + 80a c )cosh(x) +--R + +--R 8 2 7 3 6 4 5 2 +--R (- 8a c - 32a c + 56a c + 80a c )cosh(x) +--R + +--R 8 2 7 3 6 4 5 8 2 7 3 6 +--R (4a c - 32a c + 4a c + 40a c )cosh(x) + 4a c - 8a c - 4a c +--R + +--R 4 5 +--R 8a c +--R * +--R sinh(x) +--R + +--R 2 7 3 6 4 5 6 2 7 3 6 4 5 5 +--R (2a c + 4a c + 2a c )cosh(x) + (4a c + 16a c + 12a c )cosh(x) +--R + +--R 2 7 3 6 4 5 4 2 7 4 5 3 +--R (- 2a c + 20a c + 30a c )cosh(x) + (- 8a c + 40a c )cosh(x) +--R + +--R 2 7 3 6 4 5 2 2 7 3 6 4 5 +--R (- 2a c - 20a c + 30a c )cosh(x) + (4a c - 16a c + 12a c )cosh(x) +--R + +--R 2 7 3 6 4 5 +--R 2a c - 4a c + 2a c +--R Type: Expression(Integer) +--E 243 + +--S 244 of 518 +--d0947:= D(m0947,x) +--E 244 + +--S 245 of 518 +t0948:= (a+b*cosh(x)+c*sinh(x))^(1/2) +--R +--R +--R +-------------------------+ +--R (238) \|c sinh(x) + b cosh(x) + a +--R Type: Expression(Integer) +--E 245 + +--S 246 of 518 +r0948:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(x+%i*atan(%i*c,b)),2/_ + (1-a/(b^2-c^2)^(1/2)))*(a+b*cosh(x)+c*sinh(x))^(1/2)/_ + ((a+b*cosh(x)+c*sinh(x))/(a-(b^2-c^2)^(1/2)))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Polynomial(Complex(Integer)) +--R Variable(b) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 246 + +--S 247 of 518 +a0948:= integrate(t0948,x) +--R +--R +--R x +--R ++ +-----------------------------+ +--I (239) | \|c sinh(%BA) + b cosh(%BA) + a d%BA +--R ++ +--R Type: Union(Expression(Integer),...) +--E 247 + +--S 248 of 518 +m0948a:= a0948.1-r0948 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 248 + +--S 249 of 518 +d0948a:= D(m0948a,x) +--R +--R +--R (240) 0 +--R Type: Polynomial(Integer) +--E 249 + +--S 250 of 518 +m0948b:= a0948.2-r0948 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 250 + +--S 251 of 518 +d0948b:= D(m0948b,x) +--R +--R +--R (241) 0 +--R Type: Polynomial(Integer) +--E 251 + +--S 252 of 518 +t0949:= 1/(a+b*tanh(x)+c*sech(x)) +--R +--R +--R 1 +--R (242) ------------------------- +--R b tanh(x) + c sech(x) + a +--R Type: Expression(Integer) +--E 252 + +--S 253 of 518 +r0949:= a*x/(a^2-b^2)-2*a*c*atan((b+(a-c)*tanh(1/2*x))/_ + (a^2-b^2-c^2)^(1/2))/(a^2-b^2)/(a^2-b^2-c^2)^(1/2)-_ + b*log(c+a*cosh(x)+b*sinh(x))/(a^2-b^2) +--R +--R +--R (243) +--R +--------------+ +--R | 2 2 2 +--R b\|- c - b + a log(b sinh(x) + a cosh(x) + c) +--R + +--R x +--R (c - a)tanh(-) - b +--------------+ +--R 2 | 2 2 2 +--R - 2a c atan(------------------) - a x\|- c - b + a +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b - a )\|- c - b + a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 518 +a0949:= integrate(t0949,x) +--R +--R +--R (244) +--R [ +--R a c +--R * +--R log +--R 2 2 2 +--R (b + 2a b + a )sinh(x) +--R + +--R 2 2 +--R ((2b + 4a b + 2a )cosh(x) + (2b + 2a)c)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (2b + 2a)c cosh(x) + 2c + b +--R + +--R 2 +--R - a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- 2b - 2a)c - 2b - 2a b + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 3 3 +--R ((- 2b - 2a)c - 2b - 2a b + 2a b + 2a )cosh(x) - 2c +--R + +--R 2 2 +--R (- 2b + 2a )c +--R / +--R 2 +--R (b + a)sinh(x) + ((2b + 2a)cosh(x) + 2c)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + 2c cosh(x) - b + a +--R + +--R +------------+ +--R | 2 2 2 - 2b sinh(x) - 2a cosh(x) - 2c +--R b\|c + b - a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +------------+ +--R | 2 2 2 +--R (- b - a)x\|c + b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (b - a )\|c + b - a +--R , +--R +--R +--------------+ +--R | 2 2 2 - 2b sinh(x) - 2a cosh(x) - 2c +--R b\|- c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +--------------+ +--R | 2 2 2 +--R ((b + a)sinh(x) + (b + a)cosh(x) + c)\|- c - b + a +--R - 2a c atan(------------------------------------------------------) +--R 2 2 2 +--R c + b - a +--R + +--R +--------------+ +--R | 2 2 2 +--R (- b - a)x\|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b - a )\|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 254 + +--S 255 of 518 +m0949a:= a0949.1-r0949 +--R +--R +--R (245) +--R +--------------+ +--R | 2 2 2 +--R a c\|- c - b + a +--R * +--R log +--R 2 2 2 +--R (b + 2a b + a )sinh(x) +--R + +--R 2 2 +--R ((2b + 4a b + 2a )cosh(x) + (2b + 2a)c)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (2b + 2a)c cosh(x) + 2c + b - a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- 2b - 2a)c - 2b - 2a b + 2a b + 2a )sinh(x) +--R + +--R 2 3 2 2 3 3 +--R ((- 2b - 2a)c - 2b - 2a b + 2a b + 2a )cosh(x) - 2c +--R + +--R 2 2 +--R (- 2b + 2a )c +--R / +--R 2 +--R (b + a)sinh(x) + ((2b + 2a)cosh(x) + 2c)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + 2c cosh(x) - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - b\|- c - b + a \|c + b - a log(b sinh(x) + a cosh(x) + c) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 - 2b sinh(x) - 2a cosh(x) - 2c +--R b\|- c - b + a \|c + b - a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R +------------+ (c - a)tanh(-) - b +--R | 2 2 2 2 +--R 2a c\|c + b - a atan(------------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - b x\|- c - b + a \|c + b - a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (b - a )\|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 255 + +--S 256 of 518 +d0949a:= D(m0949a,x) +--R +--R +--R (246) +--R 2 2 2 2 +--R (- a b - a )c sinh(x) + ((- 2a b - 2a )c cosh(x) - 2a c)sinh(x) +--R + +--R 2 2 2 2 +--R (- a b - a )c cosh(x) - 2a c cosh(x) + (a b - a )c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R x 2 2 +--R (- 4a b c sinh(x) - 4a b c cosh(x))tanh(-) + (a b + a )c sinh(x) +--R 2 +--R + +--R 2 2 2 2 +--R ((2a b + 2a )c cosh(x) - 2a c)sinh(x) + (a b + a )c cosh(x) +--R + +--R 2 2 +--R - 2a c cosh(x) + (- a b + a )c +--R / +--R 3 2 2 3 3 2 2 3 4 2 +--R ((b + a b - a b - a )c - a b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 4 +--R ((2b + 2a b - 2a b - 2a )c - 2a b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 2 2 2 2 3 +--R (2b - 2a )c + (- 2a b + 2a )c +--R * +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 4 2 +--R ((b + a b - a b - a )c - a b - a b + a b + a )cosh(x) +--R + +--R 2 2 2 2 3 3 2 2 3 +--R ((2b - 2a )c + (- 2a b + 2a )c)cosh(x) + (- b + a b + a b - a )c +--R + +--R 3 2 2 3 4 +--R a b - a b - a b + a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (- 2b - 2a b + 2a b + 2a b)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((- 4b - 4a b + 4a b + 4a b)cosh(x) + (- 4b + 4a b)c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 +--R (- 2b - 2a b + 2a b + 2a b)cosh(x) + (- 4b + 4a b)c cosh(x) +--R + +--R 4 3 2 2 3 +--R 2b - 2a b - 2a b + 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 3 2 2 3 4 2 +--R ((- b - a b + a b + a )c - a b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 4 +--R ((- 2b - 2a b + 2a b + 2a )c - 2a b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 2 2 2 2 3 +--R (- 2b + 2a )c + (- 2a b + 2a )c +--R * +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 4 2 +--R ((- b - a b + a b + a )c - a b - a b + a b + a )cosh(x) +--R + +--R 2 2 2 2 3 3 2 2 3 +--R ((- 2b + 2a )c + (- 2a b + 2a )c)cosh(x) + (b - a b - a b + a )c +--R + +--R 3 2 2 3 4 +--R a b - a b - a b + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 518 +m0949b:= a0949.2-r0949 +--R +--R +--R (247) +--R +--------------+ +--R | 2 2 2 +--R - b\|- c - b + a log(b sinh(x) + a cosh(x) + c) +--R + +--R +--------------+ +--R | 2 2 2 - 2b sinh(x) - 2a cosh(x) - 2c +--R b\|- c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +--------------+ +--R | 2 2 2 +--R ((b + a)sinh(x) + (b + a)cosh(x) + c)\|- c - b + a +--R - 2a c atan(------------------------------------------------------) +--R 2 2 2 +--R c + b - a +--R + +--R x +--R (c - a)tanh(-) - b +--------------+ +--R 2 | 2 2 2 +--R 2a c atan(------------------) - b x\|- c - b + a +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b - a )\|- c - b + a +--R Type: Expression(Integer) +--E 257 + +--S 258 of 518 +d0949b:= D(m0949b,x) +--R +--R +--R (248) +--R 2 2 2 2 +--R (- a b - a )c sinh(x) + ((- 2a b - 2a )c cosh(x) - 2a c)sinh(x) +--R + +--R 2 2 2 2 +--R (- a b - a )c cosh(x) - 2a c cosh(x) + (a b - a )c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R x 2 2 +--R (- 4a b c sinh(x) - 4a b c cosh(x))tanh(-) + (a b + a )c sinh(x) +--R 2 +--R + +--R 2 2 2 2 +--R ((2a b + 2a )c cosh(x) - 2a c)sinh(x) + (a b + a )c cosh(x) +--R + +--R 2 2 +--R - 2a c cosh(x) + (- a b + a )c +--R / +--R 3 2 2 3 3 2 2 3 4 2 +--R ((b + a b - a b - a )c - a b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 4 +--R ((2b + 2a b - 2a b - 2a )c - 2a b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 2 2 2 2 3 +--R (2b - 2a )c + (- 2a b + 2a )c +--R * +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 4 2 +--R ((b + a b - a b - a )c - a b - a b + a b + a )cosh(x) +--R + +--R 2 2 2 2 3 3 2 2 3 +--R ((2b - 2a )c + (- 2a b + 2a )c)cosh(x) + (- b + a b + a b - a )c +--R + +--R 3 2 2 3 4 +--R a b - a b - a b + a +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (- 2b - 2a b + 2a b + 2a b)sinh(x) +--R + +--R 4 3 2 2 3 3 2 +--R ((- 4b - 4a b + 4a b + 4a b)cosh(x) + (- 4b + 4a b)c)sinh(x) +--R + +--R 4 3 2 2 3 2 3 2 +--R (- 2b - 2a b + 2a b + 2a b)cosh(x) + (- 4b + 4a b)c cosh(x) +--R + +--R 4 3 2 2 3 +--R 2b - 2a b - 2a b + 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 3 2 2 3 4 2 +--R ((- b - a b + a b + a )c - a b - a b + a b + a )sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 4 +--R ((- 2b - 2a b + 2a b + 2a )c - 2a b - 2a b + 2a b + 2a )cosh(x) +--R + +--R 2 2 2 2 3 +--R (- 2b + 2a )c + (- 2a b + 2a )c +--R * +--R sinh(x) +--R + +--R 3 2 2 3 3 2 2 3 4 2 +--R ((- b - a b + a b + a )c - a b - a b + a b + a )cosh(x) +--R + +--R 2 2 2 2 3 3 2 2 3 +--R ((- 2b + 2a )c + (- 2a b + 2a )c)cosh(x) + (b - a b - a b + a )c +--R + +--R 3 2 2 3 4 +--R a b - a b - a b + a +--R Type: Expression(Integer) +--E 258 + +--S 259 of 518 +t0950:= 1/(a+b*coth(x)+c*csch(x)) +--R +--R +--R 1 +--R (249) ------------------------- +--R c csch(x) + b coth(x) + a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 518 +r0950:= a*x/(a^2-b^2)-2*a*c*atan((a+(b-c)*tanh(1/2*x))/_ + (-a^2+b^2-c^2)^(1/2))/(a^2-b^2)/(-a^2+b^2-c^2)^(1/2)-_ + b*log(c+b*cosh(x)+a*sinh(x))/(a^2-b^2) +--R +--R +--R (250) +--R +--------------+ +--R | 2 2 2 +--R b\|- c + b - a log(a sinh(x) + b cosh(x) + c) +--R + +--R x +--R (c - b)tanh(-) - a +--------------+ +--R 2 | 2 2 2 +--R - 2a c atan(------------------) - a x\|- c + b - a +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b - a )\|- c + b - a +--R Type: Expression(Integer) +--E 260 + +--S 261 of 518 +a0950:= integrate(t0950,x) +--R +--R +--R (251) +--R [ +--R a c +--R * +--R log +--R 2 2 2 +--R (b + 2a b + a )sinh(x) +--R + +--R 2 2 +--R ((2b + 4a b + 2a )cosh(x) + (2b + 2a)c)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (2b + 2a)c cosh(x) + 2c - b +--R + +--R 2 +--R a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 3 2 2 3 +--R ((- 2b - 2a)c + 2b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 2 3 2 2 3 3 +--R ((- 2b - 2a)c + 2b + 2a b - 2a b - 2a )cosh(x) - 2c +--R + +--R 2 2 +--R (2b - 2a )c +--R / +--R 2 +--R (b + a)sinh(x) + ((2b + 2a)cosh(x) + 2c)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + 2c cosh(x) + b - a +--R + +--R +------------+ +--R | 2 2 2 - 2a sinh(x) - 2b cosh(x) - 2c +--R b\|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +------------+ +--R | 2 2 2 +--R (- b - a)x\|c - b + a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (b - a )\|c - b + a +--R , +--R +--R +--------------+ +--R | 2 2 2 - 2a sinh(x) - 2b cosh(x) - 2c +--R b\|- c + b - a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +--------------+ +--R | 2 2 2 +--R ((b + a)sinh(x) + (b + a)cosh(x) + c)\|- c + b - a +--R - 2a c atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (- b - a)x\|- c + b - a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b - a )\|- c + b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 261 + +--S 262 of 518 +m0950a:= a0950.1-r0950 +--R +--R +--R (252) +--R +--------------+ +--R | 2 2 2 +--R a c\|- c + b - a +--R * +--R log +--R 2 2 2 +--R (b + 2a b + a )sinh(x) +--R + +--R 2 2 +--R ((2b + 4a b + 2a )cosh(x) + (2b + 2a)c)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (b + 2a b + a )cosh(x) + (2b + 2a)c cosh(x) + 2c - b + a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c - b + a +--R + +--R 2 3 2 2 3 +--R ((- 2b - 2a)c + 2b + 2a b - 2a b - 2a )sinh(x) +--R + +--R 2 3 2 2 3 3 +--R ((- 2b - 2a)c + 2b + 2a b - 2a b - 2a )cosh(x) - 2c +--R + +--R 2 2 +--R (2b - 2a )c +--R / +--R 2 +--R (b + a)sinh(x) + ((2b + 2a)cosh(x) + 2c)sinh(x) +--R + +--R 2 +--R (b + a)cosh(x) + 2c cosh(x) + b - a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - b\|- c + b - a \|c - b + a log(a sinh(x) + b cosh(x) + c) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 - 2a sinh(x) - 2b cosh(x) - 2c +--R b\|- c + b - a \|c - b + a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R x +--R +------------+ (c - b)tanh(-) - a +--R | 2 2 2 2 +--R 2a c\|c - b + a atan(------------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - b x\|- c + b - a \|c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (b - a )\|- c + b - a \|c - b + a +--R Type: Expression(Integer) +--E 262 + +--S 263 of 518 +d0950a:= D(m0950a,x) +--R +--R +--R (253) +--R 2 2 2 +--R (- a b - a )c sinh(x) + ((- 2a b - 2a )c cosh(x) - 2a b c)sinh(x) +--R + +--R 2 2 2 +--R (- a b - a )c cosh(x) - 2a b c cosh(x) + (- a b + a )c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 x 2 2 +--R (- 4a c sinh(x) - 4a c cosh(x))tanh(-) + (a b + a )c sinh(x) +--R 2 +--R + +--R 2 2 2 +--R ((2a b + 2a )c cosh(x) - 2a b c)sinh(x) + (a b + a )c cosh(x) +--R + +--R 2 +--R - 2a b c cosh(x) + (a b - a )c +--R / +--R 3 2 2 3 4 3 2 2 3 2 +--R ((b + a b - a b - a )c - b - a b + a b + a b)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R ((2b + 2a b - 2a b - 2a )c - 2b - 2a b + 2a b + 2a b)cosh(x) +--R + +--R 2 2 2 3 2 +--R (2b - 2a )c + (- 2b + 2a b)c +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R ((b + a b - a b - a )c - b - a b + a b + a b)cosh(x) +--R + +--R 2 2 2 3 2 3 2 2 3 +--R ((2b - 2a )c + (- 2b + 2a b)c)cosh(x) + (b - a b - a b + a )c +--R + +--R 4 3 2 2 3 +--R - b + a b + a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 4 2 +--R (- 2a b - 2a b + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 3 4 2 3 +--R ((- 4a b - 4a b + 4a b + 4a )cosh(x) + (- 4a b + 4a )c)sinh(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- 2a b - 2a b + 2a b + 2a )cosh(x) + (- 4a b + 4a )c cosh(x) +--R + +--R 3 2 2 3 4 +--R - 2a b + 2a b + 2a b - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R ((- b - a b + a b + a )c - b - a b + a b + a b)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R ((- 2b - 2a b + 2a b + 2a )c - 2b - 2a b + 2a b + 2a b)cosh(x) +--R + +--R 2 2 2 3 2 +--R (- 2b + 2a )c + (- 2b + 2a b)c +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R ((- b - a b + a b + a )c - b - a b + a b + a b)cosh(x) +--R + +--R 2 2 2 3 2 3 2 2 3 +--R ((- 2b + 2a )c + (- 2b + 2a b)c)cosh(x) + (- b + a b + a b - a )c +--R + +--R 4 3 2 2 3 +--R - b + a b + a b - a b +--R Type: Expression(Integer) +--E 263 + +--S 264 of 518 +m0950b:= a0950.2-r0950 +--R +--R +--R (254) +--R +--------------+ +--R | 2 2 2 +--R - b\|- c + b - a log(a sinh(x) + b cosh(x) + c) +--R + +--R +--------------+ +--R | 2 2 2 - 2a sinh(x) - 2b cosh(x) - 2c +--R b\|- c + b - a log(------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +--------------+ +--R | 2 2 2 +--R ((b + a)sinh(x) + (b + a)cosh(x) + c)\|- c + b - a +--R - 2a c atan(------------------------------------------------------) +--R 2 2 2 +--R c - b + a +--R + +--R x +--R (c - b)tanh(-) - a +--------------+ +--R 2 | 2 2 2 +--R 2a c atan(------------------) - b x\|- c + b - a +--R +--------------+ +--R | 2 2 2 +--R \|- c + b - a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b - a )\|- c + b - a +--R Type: Expression(Integer) +--E 264 + +--S 265 of 518 +d0950b:= D(m0950b,x) +--R +--R +--R (255) +--R 2 2 2 +--R (- a b - a )c sinh(x) + ((- 2a b - 2a )c cosh(x) - 2a b c)sinh(x) +--R + +--R 2 2 2 +--R (- a b - a )c cosh(x) - 2a b c cosh(x) + (- a b + a )c +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 x 2 2 +--R (- 4a c sinh(x) - 4a c cosh(x))tanh(-) + (a b + a )c sinh(x) +--R 2 +--R + +--R 2 2 2 +--R ((2a b + 2a )c cosh(x) - 2a b c)sinh(x) + (a b + a )c cosh(x) +--R + +--R 2 +--R - 2a b c cosh(x) + (a b - a )c +--R / +--R 3 2 2 3 4 3 2 2 3 2 +--R ((b + a b - a b - a )c - b - a b + a b + a b)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R ((2b + 2a b - 2a b - 2a )c - 2b - 2a b + 2a b + 2a b)cosh(x) +--R + +--R 2 2 2 3 2 +--R (2b - 2a )c + (- 2b + 2a b)c +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R ((b + a b - a b - a )c - b - a b + a b + a b)cosh(x) +--R + +--R 2 2 2 3 2 3 2 2 3 +--R ((2b - 2a )c + (- 2b + 2a b)c)cosh(x) + (b - a b - a b + a )c +--R + +--R 4 3 2 2 3 +--R - b + a b + a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 4 2 +--R (- 2a b - 2a b + 2a b + 2a )sinh(x) +--R + +--R 3 2 2 3 4 2 3 +--R ((- 4a b - 4a b + 4a b + 4a )cosh(x) + (- 4a b + 4a )c)sinh(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- 2a b - 2a b + 2a b + 2a )cosh(x) + (- 4a b + 4a )c cosh(x) +--R + +--R 3 2 2 3 4 +--R - 2a b + 2a b + 2a b - 2a +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R ((- b - a b + a b + a )c - b - a b + a b + a b)sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R ((- 2b - 2a b + 2a b + 2a )c - 2b - 2a b + 2a b + 2a b)cosh(x) +--R + +--R 2 2 2 3 2 +--R (- 2b + 2a )c + (- 2b + 2a b)c +--R * +--R sinh(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R ((- b - a b + a b + a )c - b - a b + a b + a b)cosh(x) +--R + +--R 2 2 2 3 2 3 2 2 3 +--R ((- 2b + 2a )c + (- 2b + 2a b)c)cosh(x) + (- b + a b + a b - a )c +--R + +--R 4 3 2 2 3 +--R - b + a b + a b - a b +--R Type: Expression(Integer) +--E 265 + +--S 266 of 518 +t0951:= x*cosh(x)/(a+b*sinh(x))^2 +--R +--R +--R x cosh(x) +--R (256) ------------------------------ +--R 2 2 2 +--R b sinh(x) + 2a b sinh(x) + a +--R Type: Expression(Integer) +--E 266 + +--S 267 of 518 +r0951:= -2*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/b/(a^2+b^2)^(1/2)-_ + x/b/(a+b*sinh(x)) +--R +--R +--R x +--R a tanh(-) - b +-------+ +--R 2 | 2 2 +--R (2b sinh(x) + 2a)atanh(-------------) - x\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (257) --------------------------------------------------- +--R +-------+ +--R 2 | 2 2 +--R (b sinh(x) + a b)\|b + a +--R Type: Expression(Integer) +--E 267 + +--S 268 of 518 +a0951:= integrate(t0951,x) +--R +--R +--R (258) +--R 2 2 +--R (b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) - b) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R +-------+ +--R | 2 2 +--R (- 2x sinh(x) - 2x cosh(x))\|b + a +--R / +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) +--R + +--R 2 +--R - b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 518 +m0951:= a0951-r0951 +--R +--R +--R (259) +--R 2 3 2 2 +--R b sinh(x) + (2b cosh(x) + 3a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b cosh(x) + 4a b cosh(x) - b + 2a )sinh(x) + a b cosh(x) +--R + +--R 2 +--R 2a cosh(x) - a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 2 3 2 2 +--R - 2b sinh(x) + (- 4b cosh(x) - 6a b)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b cosh(x) - 8a b cosh(x) + 2b - 4a )sinh(x) - 2a b cosh(x) +--R + +--R 2 +--R - 4a cosh(x) + 2a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- b x sinh(x) + b x cosh(x) - b x)\|b + a +--R / +--R 3 3 3 2 2 +--R b sinh(x) + (2b cosh(x) + 3a b )sinh(x) +--R + +--R 3 2 2 3 2 2 2 +--R (b cosh(x) + 4a b cosh(x) - b + 2a b)sinh(x) + a b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 518 +d0951:= D(m0951,x) +--R +--R +--R (260) +--R 3 6 3 2 2 5 +--R - b sinh(x) + (- 4b cosh(x) + 2a b x - 5a b )sinh(x) +--R + +--R 3 2 2 2 2 3 2 +--R (- 6b cosh(x) + (5a b x - 16a b )cosh(x) + 4a b x + 2b - 8a b) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 2 2 2 +--R - 4b cosh(x) + (2a b x - 18a b )cosh(x) +--R + +--R 2 3 2 2 3 2 3 +--R (8a b x + 4b - 20a b)cosh(x) + (2a b + 2a )x + 6a b - 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 2 2 +--R - b cosh(x) + (- 4a b x - 8a b )cosh(x) + (2b - 16a b)cosh(x) +--R + +--R 2 3 2 3 2 3 2 +--R ((4a b + 2a )x + 8a b - 8a )cosh(x) + 4a b x - b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 2 2 3 +--R (- 4a b x - a b )cosh(x) + (- 8a b x - 4a b)cosh(x) +--R + +--R 2 3 2 3 2 2 2 +--R ((4a b - 2a )x + 2a b - 4a )cosh(x) + (8a b x + 4a b)cosh(x) +--R + +--R 3 2 +--R 2a x - a b +--R * +--R sinh(x) +--R + +--R 2 5 2 4 2 3 3 +--R - a b x cosh(x) - 4a b x cosh(x) + (2a b - 2a )x cosh(x) +--R + +--R 2 2 2 3 +--R 4a b x cosh(x) + (- a b + 2a )x cosh(x) +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 3 5 +--R (- 4b x - 2b )sinh(x) +--R + +--R 3 3 2 2 4 +--R ((- 10b x - 8b )cosh(x) - 8a b x - 10a b )sinh(x) +--R + +--R 3 3 2 2 2 +--R (- 4b x - 12b )cosh(x) + (- 16a b x - 32a b )cosh(x) +--R + +--R 3 2 3 2 +--R (- 4b - 4a b)x + 4b - 16a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 3 3 2 2 +--R (8b x - 8b )cosh(x) - 36a b cosh(x) +--R + +--R 3 2 3 2 2 2 3 +--R ((- 8b - 4a b)x + 8b - 40a b)cosh(x) - 8a b x + 12a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 3 4 2 2 3 +--R (8b x - 2b )cosh(x) + (16a b x - 16a b )cosh(x) +--R + +--R 3 2 3 2 2 +--R ((- 8b + 4a b)x + 4b - 32a b)cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (- 16a b x + 16a b - 16a )cosh(x) - 4a b x - 2b + 8a b +--R * +--R sinh(x) +--R + +--R 3 5 2 2 4 +--R 2b x cosh(x) + (8a b x - 2a b )cosh(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R ((- 4b + 4a b)x - 8a b)cosh(x) + (- 8a b x + 4a b - 8a )cosh(x) +--R + +--R 3 2 2 2 +--R ((2b - 4a b)x + 8a b)cosh(x) - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 6 3 2 2 5 +--R b sinh(x) + (4b cosh(x) - 2a b x + 5a b )sinh(x) +--R + +--R 3 2 2 2 2 3 2 4 +--R (6b cosh(x) + (- 5a b x + 16a b )cosh(x) - 4a b x - 2b + 8a b)sinh(x) +--R + +--R 3 3 2 2 2 +--R 4b cosh(x) + (- 2a b x + 18a b )cosh(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 8a b x - 4b + 20a b)cosh(x) + (- 2a b - 2a )x - 6a b + 4a +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 2 3 3 2 2 +--R b cosh(x) + (4a b x + 8a b )cosh(x) + (- 2b + 16a b)cosh(x) +--R + +--R 2 3 2 3 2 3 2 +--R ((- 4a b - 2a )x - 8a b + 8a )cosh(x) - 4a b x + b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 4 2 2 3 +--R (4a b x + a b )cosh(x) + (8a b x + 4a b)cosh(x) +--R + +--R 2 3 2 3 2 2 2 +--R ((- 4a b + 2a )x - 2a b + 4a )cosh(x) + (- 8a b x - 4a b)cosh(x) +--R + +--R 3 2 +--R - 2a x + a b +--R * +--R sinh(x) +--R + +--R 2 5 2 4 2 3 3 +--R a b x cosh(x) + 4a b x cosh(x) + (- 2a b + 2a )x cosh(x) +--R + +--R 2 2 2 3 +--R - 4a b x cosh(x) + (a b - 2a )x cosh(x) +--R / +--R 4 6 4 2 3 5 +--R a b sinh(x) + (4a b cosh(x) + 6a b )sinh(x) +--R + +--R 4 2 2 3 4 3 2 4 +--R (6a b cosh(x) + 20a b cosh(x) - 2a b + 13a b )sinh(x) +--R + +--R 4 3 2 3 2 4 3 2 +--R 4a b cosh(x) + 24a b cosh(x) + (- 4a b + 36a b )cosh(x) +--R + +--R 2 3 4 +--R - 8a b + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R a b cosh(x) + 12a b cosh(x) + (- 2a b + 34a b )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 12a b + 28a b)cosh(x) + a b - 10a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 2 3 4 2 +--R 2a b cosh(x) + 12a b cosh(x) + (- 4a b + 20a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 12a b + 8a )cosh(x) + 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 2 4 4 3 3 2 5 2 4 +--R a b cosh(x) + 4a b cosh(x) + (- 2a b + 4a )cosh(x) - 4a b cosh(x) +--R + +--R 3 2 +--R a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 6 5 4 5 +--R - 2b sinh(x) + (- 8b cosh(x) - 12a b )sinh(x) +--R + +--R 5 2 4 5 2 3 4 +--R (- 12b cosh(x) - 40a b cosh(x) + 4b - 26a b )sinh(x) +--R + +--R 5 3 4 2 5 2 3 4 +--R - 8b cosh(x) - 48a b cosh(x) + (8b - 72a b )cosh(x) + 16a b +--R + +--R 3 2 +--R - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 4 3 5 2 3 2 +--R - 2b cosh(x) - 24a b cosh(x) + (4b - 68a b )cosh(x) +--R + +--R 4 3 2 5 2 3 4 +--R (24a b - 56a b )cosh(x) - 2b + 20a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R - 4a b cosh(x) - 24a b cosh(x) + (8a b - 40a b )cosh(x) +--R + +--R 2 3 4 4 3 2 +--R (24a b - 16a b)cosh(x) - 4a b + 8a b +--R * +--R sinh(x) +--R + +--R 2 3 4 3 2 3 2 3 4 2 +--R - 2a b cosh(x) - 8a b cosh(x) + (4a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 +--R 8a b cosh(x) - 2a b +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 4 6 4 2 3 5 +--R - a b sinh(x) + (- 4a b cosh(x) - 6a b )sinh(x) +--R + +--R 4 2 2 3 4 3 2 4 +--R (- 6a b cosh(x) - 20a b cosh(x) + 2a b - 13a b )sinh(x) +--R + +--R 4 3 2 3 2 4 3 2 2 3 +--R - 4a b cosh(x) - 24a b cosh(x) + (4a b - 36a b )cosh(x) + 8a b +--R + +--R 4 +--R - 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R - a b cosh(x) - 12a b cosh(x) + (2a b - 34a b )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (12a b - 28a b)cosh(x) - a b + 10a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 2 3 4 2 +--R - 2a b cosh(x) - 12a b cosh(x) + (4a b - 20a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (12a b - 8a )cosh(x) - 2a b + 4a b +--R * +--R sinh(x) +--R + +--R 3 2 4 4 3 3 2 5 2 4 +--R - a b cosh(x) - 4a b cosh(x) + (2a b - 4a )cosh(x) + 4a b cosh(x) +--R + +--R 3 2 +--R - a b +--R Type: Expression(Integer) +--E 270 + +--S 271 of 518 +t0952:= x*cosh(x)/(a+b*sinh(x))^3 +--R +--R +--R x cosh(x) +--R (261) ---------------------------------------------- +--R 3 3 2 2 2 3 +--R b sinh(x) + 3a b sinh(x) + 3a b sinh(x) + a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 518 +r0952:= -a*atanh((b-a*tanh(1/2*x))/(a^2+b^2)^(1/2))/b/(a^2+b^2)^(3/2)-_ + 1/2*x/b/(a+b*sinh(x))^2-1/2*cosh(x)/(a^2+b^2)/(a+b*sinh(x)) +--R +--R +--R (262) +--R x +--R a tanh(-) - b +--R 2 2 2 3 2 +--R (2a b sinh(x) + 4a b sinh(x) + 2a )atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (- b cosh(x)sinh(x) - a b cosh(x) + (- b - a )x)\|b + a +--R / +--R +-------+ +--R 5 2 3 2 4 3 2 2 3 4 | 2 2 +--R ((2b + 2a b )sinh(x) + (4a b + 4a b )sinh(x) + 2a b + 2a b)\|b + a +--R Type: Expression(Integer) +--E 272 + +--S 273 of 518 +a0952:= integrate(t0952,x) +--R +--R +--R (263) +--R 2 4 2 2 3 +--R a b sinh(x) + (4a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (6a b cosh(x) + 12a b cosh(x) - 2a b + 4a )sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R (4a b cosh(x) + 12a b cosh(x) + (- 4a b + 8a )cosh(x) - 4a b) +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 3 2 2 +--R a b cosh(x) + 4a b cosh(x) + (- 2a b + 4a )cosh(x) - 4a b cosh(x) +--R + +--R 2 +--R a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 3 2 2 2 2 2 +--R 2a b sinh(x) + (6a b cosh(x) + (- 4b - 4a )x - 2b + 4a )sinh(x) +--R + +--R 2 2 2 2 2 +--R (6a b cosh(x) + ((- 8b - 8a )x - 4b + 8a )cosh(x) - 6a b)sinh(x) +--R + +--R 3 2 2 2 2 2 +--R 2a b cosh(x) + ((- 4b - 4a )x - 2b + 4a )cosh(x) - 6a b cosh(x) +--R + +--R 2 +--R 2b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 2 3 4 5 2 3 4 3 2 3 +--R (2b + 2a b )sinh(x) + ((8b + 8a b )cosh(x) + 8a b + 8a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 2 3 +--R (12b + 12a b )cosh(x) + (24a b + 24a b )cosh(x) - 4b + 4a b +--R + +--R 4 +--R 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (8b + 8a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (- 8b + 8a b + 16a b)cosh(x) - 8a b - 8a b +--R * +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (2b + 2a b )cosh(x) + (8a b + 8a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 2 3 +--R (- 4b + 4a b + 8a b)cosh(x) + (- 8a b - 8a b )cosh(x) + 2b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 518 +m0952:= a0952-r0952 +--R +--R +--R (264) +--R 4 6 4 2 3 5 +--R a b sinh(x) + (4a b cosh(x) + 6a b )sinh(x) +--R + +--R 4 2 2 3 4 3 2 4 +--R (6a b cosh(x) + 20a b cosh(x) - 2a b + 13a b )sinh(x) +--R + +--R 4 3 2 3 2 4 3 2 +--R 4a b cosh(x) + 24a b cosh(x) + (- 4a b + 36a b )cosh(x) +--R + +--R 2 3 4 +--R - 8a b + 12a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R a b cosh(x) + 12a b cosh(x) + (- 2a b + 34a b )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (- 12a b + 28a b)cosh(x) + a b - 10a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 2 3 4 2 +--R 2a b cosh(x) + 12a b cosh(x) + (- 4a b + 20a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 12a b + 8a )cosh(x) + 2a b - 4a b +--R * +--R sinh(x) +--R + +--R 3 2 4 4 3 3 2 5 2 4 +--R a b cosh(x) + 4a b cosh(x) + (- 2a b + 4a )cosh(x) - 4a b cosh(x) +--R + +--R 3 2 +--R a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b - 2a b)sinh(x) + (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R - b +--R + +--R 4 6 4 2 3 5 +--R - 2a b sinh(x) + (- 8a b cosh(x) - 12a b )sinh(x) +--R + +--R 4 2 2 3 4 3 2 4 +--R (- 12a b cosh(x) - 40a b cosh(x) + 4a b - 26a b )sinh(x) +--R + +--R 4 3 2 3 2 4 3 2 +--R - 8a b cosh(x) - 48a b cosh(x) + (8a b - 72a b )cosh(x) +--R + +--R 2 3 4 +--R 16a b - 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R - 2a b cosh(x) - 24a b cosh(x) + (4a b - 68a b )cosh(x) +--R + +--R 2 3 4 4 3 2 5 +--R (24a b - 56a b)cosh(x) - 2a b + 20a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 2 3 4 3 2 3 2 3 4 2 +--R - 4a b cosh(x) - 24a b cosh(x) + (8a b - 40a b)cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (24a b - 16a )cosh(x) - 4a b + 8a b +--R * +--R sinh(x) +--R + +--R 3 2 4 4 3 3 2 5 2 +--R - 2a b cosh(x) - 8a b cosh(x) + (4a b - 8a )cosh(x) +--R + +--R 4 3 2 +--R 8a b cosh(x) - 2a b +--R * +--R x +--R a tanh(-) - b +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 3 5 +--R (b cosh(x) + 2a b )sinh(x) +--R + +--R 4 2 3 4 2 2 4 2 2 +--R (4b cosh(x) + 11a b cosh(x) + (- 3b - 3a b )x - 2b + 8a b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 3 2 +--R 6b cosh(x) + 22a b cosh(x) +--R + +--R 4 2 2 4 2 2 3 3 +--R ((- 4b - 4a b )x - 6b + 28a b )cosh(x) + (- 4a b - 4a b)x +--R + +--R 3 3 +--R - 10a b + 10a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 3 3 +--R 4b cosh(x) + 20a b cosh(x) +--R + +--R 4 2 2 4 2 2 2 +--R ((2b + 2a b )x - 6b + 36a b )cosh(x) +--R + +--R 3 3 3 3 4 2 2 +--R ((- 4a b - 4a b)x - 20a b + 26a b)cosh(x) + (- 2b - 2a b )x +--R + +--R 4 2 2 4 +--R 2b - 14a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 3 4 +--R b cosh(x) + 8a b cosh(x) +--R + +--R 4 2 2 4 2 2 3 +--R ((4b + 4a b )x - 2b + 20a b )cosh(x) +--R + +--R 3 3 3 3 2 +--R ((4a b + 4a b)x - 12a b + 22a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((- 4b - 4a b )x + b - 20a b + 8a )cosh(x) + (- 4a b - 4a b)x +--R + +--R 3 3 +--R 4a b - 6a b +--R * +--R sinh(x) +--R + +--R 3 5 4 2 2 2 2 4 +--R a b cosh(x) + ((b + a b )x + 4a b )cosh(x) +--R + +--R 3 3 3 3 3 +--R ((4a b + 4a b)x - 2a b + 6a b)cosh(x) +--R + +--R 4 2 2 2 2 4 2 +--R ((- 2b - 2a b )x - 6a b + 4a )cosh(x) +--R + +--R 3 3 3 3 4 2 2 2 2 +--R ((- 4a b - 4a b)x + a b - 6a b)cosh(x) + (b + a b )x + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 7 2 5 6 +--R (2b + 2a b )sinh(x) +--R + +--R 7 2 5 6 3 4 5 +--R ((8b + 8a b )cosh(x) + 12a b + 12a b )sinh(x) +--R + +--R 7 2 5 2 6 3 4 7 2 5 +--R (12b + 12a b )cosh(x) + (40a b + 40a b )cosh(x) - 4b + 22a b +--R + +--R 4 3 +--R 26a b +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 5 3 6 3 4 2 +--R (8b + 8a b )cosh(x) + (48a b + 48a b )cosh(x) +--R + +--R 7 2 5 4 3 6 3 4 5 2 +--R (- 8b + 64a b + 72a b )cosh(x) - 16a b + 8a b + 24a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 5 4 6 3 4 3 +--R (2b + 2a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 7 2 5 4 3 2 +--R (- 4b + 64a b + 68a b )cosh(x) +--R + +--R 6 3 4 5 2 7 2 5 4 3 6 +--R (- 24a b + 32a b + 56a b )cosh(x) + 2b - 18a b - 12a b + 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 3 4 4 2 5 4 3 3 +--R (4a b + 4a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (- 8a b + 32a b + 40a b )cosh(x) +--R + +--R 2 5 4 3 6 6 3 4 5 2 +--R (- 24a b - 8a b + 16a b)cosh(x) + 4a b - 4a b - 8a b +--R * +--R sinh(x) +--R + +--R 2 5 4 3 4 3 4 5 2 3 +--R (2a b + 2a b )cosh(x) + (8a b + 8a b )cosh(x) +--R + +--R 2 5 4 3 6 2 3 4 5 2 2 5 +--R (- 4a b + 4a b + 8a b)cosh(x) + (- 8a b - 8a b )cosh(x) + 2a b +--R + +--R 4 3 +--R 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 274 + +--S 275 of 518 +--d0952:= D(m0952,x) +--E 275 + +--S 276 of 518 +t0953:= x*sinh(x)/(a+b*cosh(x))^2 +--R +--R +--R x sinh(x) +--R (265) ------------------------------ +--R 2 2 2 +--R b cosh(x) + 2a b cosh(x) + a +--R Type: Expression(Integer) +--E 276 + +--S 277 of 518 +r0953:= 2*atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/b/(a^2-b^2)^(1/2)-_ + x/b/(a+b*cosh(x)) +--R +--R +--R x +--R (b - a)tanh(-) +---------+ +--R 2 | 2 2 +--R (- 2b cosh(x) - 2a)atanh(--------------) - x\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (266) -------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R (b cosh(x) + a b)\|- b + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 518 +a0953:= integrate(t0953,x) +--R +--R +--R (267) +--R [ +--R 2 2 +--R (b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) + b) +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)sinh(x) + (2b - 2a b)cosh(x) + 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R +---------+ +--R | 2 2 +--R (- 2x sinh(x) - 2x cosh(x))\|- b + a +--R / +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) +--R + +--R 2 +--R b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 2 2 +--R 2b sinh(x) + (4b cosh(x) + 4a)sinh(x) + 2b cosh(x) + 4a cosh(x) +--R + +--R 2b +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R +-------+ +--R | 2 2 +--R (- 2x sinh(x) - 2x cosh(x))\|b - a +--R / +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) + 2a b cosh(x) +--R + +--R 2 +--R b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 278 + +--S 279 of 518 +m0953a:= a0953.1-r0953 +--R +--R +--R (268) +--R 2 2 2 2 2 +--R (b cosh(x) + a b)sinh(x) + (2b cosh(x) + 4a b cosh(x) + 2a )sinh(x) +--R + +--R 2 3 2 2 2 +--R b cosh(x) + 3a b cosh(x) + (b + 2a )cosh(x) + a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)sinh(x) + (2b - 2a b)cosh(x) + 2a b - 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R 2 2 +--R (2b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (4b cosh(x) + 8a b cosh(x) + 4a )sinh(x) + 2b cosh(x) +--R + +--R 2 2 2 +--R 6a b cosh(x) + (2b + 4a )cosh(x) + 2a b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (b x sinh(x) - b x cosh(x) + b x)\|- b + a +--R / +--R 3 2 2 3 2 2 2 +--R (b cosh(x) + a b )sinh(x) + (2b cosh(x) + 4a b cosh(x) + 2a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R b cosh(x) + 3a b cosh(x) + (b + 2a b)cosh(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 279 + +--S 280 of 518 +d0953a:= D(m0953a,x) +--R +--R +--R (269) +--R 3 2 5 +--R (- b + a b )x sinh(x) +--R + +--R 3 2 3 2 3 2 +--R b cosh(x) + ((- 4b + 4a b )x + b + a b )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b + 4a b)x + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 3 2 2 +--R 4b cosh(x) + ((- 4b + 4a b )x + 4b + 8a b )cosh(x) +--R + +--R 2 2 2 2 +--R ((- 8a b + 8a b)x + 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 2b + 2a b - 2a b + 2a )x + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 3 2 3 2 3 +--R 6b cosh(x) + ((2b - 2a b )x + 6b + 18a b )cosh(x) +--R + +--R 3 2 2 2 +--R (2b + 18a b + 16a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((- 4b + 4a b - 2a b + 2a )x + 2b + 2a b + 16a b + 4a ) +--R * +--R cosh(x) +--R + +--R 2 2 2 3 +--R (- 4a b + 4a b)x + 2a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 3 2 3 2 4 +--R 4b cosh(x) + ((5b - 5a b )x + 4b + 16a b )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R ((8a b - 8a b)x + 4b + 16a b + 20a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((- 4b + 4a b + 2a b - 2a )x + 4b + 8a b + 20a b + 8a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R ((- 8a b + 8a b)x + 8a b + 4a b + 8a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- b + a b - 2a b + 2a )x + 4a b +--R * +--R sinh(x) +--R + +--R 3 6 3 2 3 2 5 +--R b cosh(x) + ((2b - 2a b )x + b + 5a b )cosh(x) +--R + +--R 2 2 3 2 2 4 +--R ((4a b - 4a b)x + 2b + 5a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 3 +--R ((- 2b + 2a b + 2a b - 2a )x + 2b + 6a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 2 2 3 2 +--R ((- 4a b + 4a b)x + b + 6a b + 4a b + 4a )cosh(x) +--R + +--R 2 3 3 2 2 2 +--R ((- 2a b + 2a )x + b + a b + 4a b)cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 5 +--R (- b - a b )x sinh(x) +--R + +--R 3 2 3 2 3 2 +--R - b cosh(x) + ((- 4b - 4a b )x + b - a b )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 4a b)x + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 3 2 2 +--R - 4b cosh(x) + ((- 4b - 4a b )x + 4b - 8a b )cosh(x) +--R + +--R 2 2 2 2 +--R ((- 8a b - 8a b)x + 8a b - 4a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 2b - 2a b - 2a b - 2a )x + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 3 2 3 2 3 +--R - 6b cosh(x) + ((2b + 2a b )x + 6b - 18a b )cosh(x) +--R + +--R 3 2 2 2 +--R (- 2b + 18a b - 16a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((- 4b - 4a b - 2a b - 2a )x + 2b - 2a b + 16a b - 4a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 4a b - 4a b)x + 2a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 3 2 3 2 4 +--R - 4b cosh(x) + ((5b + 5a b )x + 4b - 16a b )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R ((8a b + 8a b)x - 4b + 16a b - 20a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 +--R ((- 4b - 4a b + 2a b + 2a )x + 4b - 8a b + 20a b - 8a )cosh(x) +--R + +--R 2 2 2 2 3 +--R ((- 8a b - 8a b)x + 8a b - 4a b + 8a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- b - a b - 2a b - 2a )x + 4a b +--R * +--R sinh(x) +--R + +--R 3 6 3 2 3 2 5 +--R - b cosh(x) + ((2b + 2a b )x + b - 5a b )cosh(x) +--R + +--R 2 2 3 2 2 4 +--R ((4a b + 4a b)x - 2b + 5a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 3 +--R ((- 2b - 2a b + 2a b + 2a )x + 2b - 6a b + 8a b - 4a )cosh(x) +--R + +--R 2 2 3 2 2 3 2 +--R ((- 4a b - 4a b)x - b + 6a b - 4a b + 4a )cosh(x) +--R + +--R 2 3 3 2 2 2 +--R ((- 2a b - 2a )x + b - a b + 4a b)cosh(x) + a b +--R / +--R 5 4 2 4 2 3 2 3 3 2 4 +--R ((b - a b )cosh(x) + (2a b - 2a b )cosh(x) + a b - a b )sinh(x) +--R + +--R 5 4 3 4 2 3 2 +--R (4b - 4a b )cosh(x) + (12a b - 12a b )cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (12a b - 12a b )cosh(x) + 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 4 4 2 3 3 +--R (6b - 6a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 +--R (2b - 2a b + 34a b - 34a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 +--R (4a b - 4a b + 20a b - 20a b)cosh(x) + 2a b - 2a b + 4a b +--R + +--R 5 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 4 2 3 4 +--R (4b - 4a b )cosh(x) + (20a b - 20a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (4b - 4a b + 36a b - 36a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (12a b - 12a b + 28a b - 28a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 2 4 +--R (12a b - 12a b + 8a b - 8a )cosh(x) + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 5 4 6 4 2 3 5 +--R (b - a b )cosh(x) + (6a b - 6a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (2b - 2a b + 13a b - 13a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (8a b - 8a b + 12a b - 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (b - a b + 10a b - 10a b + 4a b - 4a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (2a b - 2a b + 4a b - 4a b)cosh(x) + a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 4 2 3 2 3 3 2 4 +--R ((b + a b )cosh(x) + (2a b + 2a b )cosh(x) + a b + a b )sinh(x) +--R + +--R 5 4 3 4 2 3 2 +--R (4b + 4a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (12a b + 12a b )cosh(x) + 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 4 4 2 3 3 +--R (6b + 6a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 +--R (2b + 2a b + 34a b + 34a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 +--R (4a b + 4a b + 20a b + 20a b)cosh(x) + 2a b + 2a b + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 4 2 3 4 +--R (4b + 4a b )cosh(x) + (20a b + 20a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (4b + 4a b + 36a b + 36a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (12a b + 12a b + 28a b + 28a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 2 4 +--R (12a b + 12a b + 8a b + 8a )cosh(x) + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 4 6 4 2 3 5 +--R (b + a b )cosh(x) + (6a b + 6a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (2b + 2a b + 13a b + 13a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (8a b + 8a b + 12a b + 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (b + a b + 10a b + 10a b + 4a b + 4a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (2a b + 2a b + 4a b + 4a b)cosh(x) + a b + a b +--R Type: Expression(Integer) +--E 280 + +--S 281 of 518 +m0953b:= a0953.2-r0953 +--R +--R +--R (270) +--R 2 2 +--R (2b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (4b cosh(x) + 8a b cosh(x) + 4a )sinh(x) + 2b cosh(x) +--R + +--R 2 2 2 +--R 6a b cosh(x) + (2b + 4a )cosh(x) + 2a b +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 +--R (2b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 2 2 3 +--R (4b cosh(x) + 8a b cosh(x) + 4a )sinh(x) + 2b cosh(x) +--R + +--R 2 2 2 +--R 6a b cosh(x) + (2b + 4a )cosh(x) + 2a b +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sinh(x) + b cosh(x) + a)\|b - a +--R \|- b + a atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (b x sinh(x) - b x cosh(x) + b x)\|- b + a \|b - a +--R / +--R 3 2 2 3 2 2 2 +--R (b cosh(x) + a b )sinh(x) + (2b cosh(x) + 4a b cosh(x) + 2a b)sinh(x) +--R + +--R 3 3 2 2 3 2 2 +--R b cosh(x) + 3a b cosh(x) + (b + 2a b)cosh(x) + a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 281 + +--S 282 of 518 +d0953b:= D(m0953b,x) +--R +--R +--R (271) +--R 3 2 5 +--R (- b + a b )x sinh(x) +--R + +--R 3 2 3 2 3 2 +--R b cosh(x) + ((- 4b + 4a b )x + b + a b )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b + 4a b)x + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 3 2 2 +--R 4b cosh(x) + ((- 4b + 4a b )x + 4b + 8a b )cosh(x) +--R + +--R 2 2 2 2 +--R ((- 8a b + 8a b)x + 8a b + 4a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 2b + 2a b - 2a b + 2a )x + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 3 2 3 2 3 +--R 6b cosh(x) + ((2b - 2a b )x + 6b + 18a b )cosh(x) +--R + +--R 3 2 2 2 +--R (2b + 18a b + 16a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((- 4b + 4a b - 2a b + 2a )x + 2b + 2a b + 16a b + 4a ) +--R * +--R cosh(x) +--R + +--R 2 2 2 3 +--R (- 4a b + 4a b)x + 2a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 3 2 3 2 4 +--R 4b cosh(x) + ((5b - 5a b )x + 4b + 16a b )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R ((8a b - 8a b)x + 4b + 16a b + 20a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((- 4b + 4a b + 2a b - 2a )x + 4b + 8a b + 20a b + 8a ) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 2 2 2 3 +--R ((- 8a b + 8a b)x + 8a b + 4a b + 8a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- b + a b - 2a b + 2a )x + 4a b +--R * +--R sinh(x) +--R + +--R 3 6 3 2 3 2 5 +--R b cosh(x) + ((2b - 2a b )x + b + 5a b )cosh(x) +--R + +--R 2 2 3 2 2 4 +--R ((4a b - 4a b)x + 2b + 5a b + 8a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 3 +--R ((- 2b + 2a b + 2a b - 2a )x + 2b + 6a b + 8a b + 4a )cosh(x) +--R + +--R 2 2 3 2 2 3 2 +--R ((- 4a b + 4a b)x + b + 6a b + 4a b + 4a )cosh(x) +--R + +--R 2 3 3 2 2 2 +--R ((- 2a b + 2a )x + b + a b + 4a b)cosh(x) + a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 5 +--R (- b - a b )x sinh(x) +--R + +--R 3 2 3 2 3 2 +--R - b cosh(x) + ((- 4b - 4a b )x + b - a b )cosh(x) +--R + +--R 2 2 2 +--R (- 4a b - 4a b)x + a b +--R * +--R 4 +--R sinh(x) +--R + +--R 3 3 3 2 3 2 2 +--R - 4b cosh(x) + ((- 4b - 4a b )x + 4b - 8a b )cosh(x) +--R + +--R 2 2 2 2 +--R ((- 8a b - 8a b)x + 8a b - 4a b)cosh(x) +--R + +--R 3 2 2 3 2 +--R (- 2b - 2a b - 2a b - 2a )x + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 3 2 3 2 3 +--R - 6b cosh(x) + ((2b + 2a b )x + 6b - 18a b )cosh(x) +--R + +--R 3 2 2 2 +--R (- 2b + 18a b - 16a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R ((- 4b - 4a b - 2a b - 2a )x + 2b - 2a b + 16a b - 4a )cosh(x) +--R + +--R 2 2 2 3 +--R (- 4a b - 4a b)x + 2a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 3 2 3 2 4 +--R - 4b cosh(x) + ((5b + 5a b )x + 4b - 16a b )cosh(x) +--R + +--R 2 2 3 2 2 3 +--R ((8a b + 8a b)x - 4b + 16a b - 20a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 2 +--R ((- 4b - 4a b + 2a b + 2a )x + 4b - 8a b + 20a b - 8a )cosh(x) +--R + +--R 2 2 2 2 3 +--R ((- 8a b - 8a b)x + 8a b - 4a b + 8a )cosh(x) +--R + +--R 3 2 2 3 2 +--R (- b - a b - 2a b - 2a )x + 4a b +--R * +--R sinh(x) +--R + +--R 3 6 3 2 3 2 5 +--R - b cosh(x) + ((2b + 2a b )x + b - 5a b )cosh(x) +--R + +--R 2 2 3 2 2 4 +--R ((4a b + 4a b)x - 2b + 5a b - 8a b)cosh(x) +--R + +--R 3 2 2 3 3 2 2 3 3 +--R ((- 2b - 2a b + 2a b + 2a )x + 2b - 6a b + 8a b - 4a )cosh(x) +--R + +--R 2 2 3 2 2 3 2 +--R ((- 4a b - 4a b)x - b + 6a b - 4a b + 4a )cosh(x) +--R + +--R 2 3 3 2 2 2 +--R ((- 2a b - 2a )x + b - a b + 4a b)cosh(x) + a b +--R / +--R 5 4 2 4 2 3 2 3 3 2 4 +--R ((b - a b )cosh(x) + (2a b - 2a b )cosh(x) + a b - a b )sinh(x) +--R + +--R 5 4 3 4 2 3 2 +--R (4b - 4a b )cosh(x) + (12a b - 12a b )cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (12a b - 12a b )cosh(x) + 4a b - 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 4 4 2 3 3 +--R (6b - 6a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 +--R (2b - 2a b + 34a b - 34a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 +--R (4a b - 4a b + 20a b - 20a b)cosh(x) + 2a b - 2a b + 4a b +--R + +--R 5 +--R - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 4 2 3 4 +--R (4b - 4a b )cosh(x) + (20a b - 20a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (4b - 4a b + 36a b - 36a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (12a b - 12a b + 28a b - 28a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 2 4 +--R (12a b - 12a b + 8a b - 8a )cosh(x) + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 5 4 6 4 2 3 5 +--R (b - a b )cosh(x) + (6a b - 6a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (2b - 2a b + 13a b - 13a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (8a b - 8a b + 12a b - 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (b - a b + 10a b - 10a b + 4a b - 4a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (2a b - 2a b + 4a b - 4a b)cosh(x) + a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 5 4 2 4 2 3 2 3 3 2 4 +--R ((b + a b )cosh(x) + (2a b + 2a b )cosh(x) + a b + a b )sinh(x) +--R + +--R 5 4 3 4 2 3 2 +--R (4b + 4a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 2 3 3 2 3 2 4 +--R (12a b + 12a b )cosh(x) + 4a b + 4a b +--R * +--R 3 +--R sinh(x) +--R + +--R 5 4 4 4 2 3 3 +--R (6b + 6a b )cosh(x) + (24a b + 24a b )cosh(x) +--R + +--R 5 4 2 3 3 2 2 +--R (2b + 2a b + 34a b + 34a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 +--R (4a b + 4a b + 20a b + 20a b)cosh(x) + 2a b + 2a b + 4a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 5 4 5 4 2 3 4 +--R (4b + 4a b )cosh(x) + (20a b + 20a b )cosh(x) +--R + +--R 5 4 2 3 3 2 3 +--R (4b + 4a b + 36a b + 36a b )cosh(x) +--R + +--R 4 2 3 3 2 4 2 +--R (12a b + 12a b + 28a b + 28a b)cosh(x) +--R + +--R 2 3 3 2 4 5 3 2 4 +--R (12a b + 12a b + 8a b + 8a )cosh(x) + 4a b + 4a b +--R * +--R sinh(x) +--R + +--R 5 4 6 4 2 3 5 +--R (b + a b )cosh(x) + (6a b + 6a b )cosh(x) +--R + +--R 5 4 2 3 3 2 4 +--R (2b + 2a b + 13a b + 13a b )cosh(x) +--R + +--R 4 2 3 3 2 4 3 +--R (8a b + 8a b + 12a b + 12a b)cosh(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (b + a b + 10a b + 10a b + 4a b + 4a )cosh(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (2a b + 2a b + 4a b + 4a b)cosh(x) + a b + a b +--R Type: Expression(Integer) +--E 282 + +--S 283 of 518 +t0954:= x*sinh(x)/(a+b*cosh(x))^3 +--R +--R +--R x sinh(x) +--R (272) ---------------------------------------------- +--R 3 3 2 2 2 3 +--R b cosh(x) + 3a b cosh(x) + 3a b cosh(x) + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 518 +r0954:= a*atanh((a-b)*tanh(1/2*x)/(a^2-b^2)^(1/2))/b/(a^2-b^2)^(3/2)-_ + 1/2*x/b/(a+b*cosh(x))^2-1/2*sinh(x)/(a^2-b^2)/(a+b*cosh(x)) +--R +--R +--R (273) +--R x +--R (b - a)tanh(-) +--R 2 2 2 3 2 +--R (2a b cosh(x) + 4a b cosh(x) + 2a )atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R ((b cosh(x) + a b)sinh(x) + (- b + a )x)\|- b + a +--R / +--R +---------+ +--R 5 2 3 2 4 3 2 2 3 4 | 2 2 +--R ((2b - 2a b )cosh(x) + (4a b - 4a b )cosh(x) + 2a b - 2a b)\|- b + a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 518 +a0954:= integrate(t0954,x) +--R +--R +--R (274) +--R [ +--R 2 4 2 2 3 +--R a b sinh(x) + (4a b cosh(x) + 4a b)sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (6a b cosh(x) + 12a b cosh(x) + 2a b + 4a )sinh(x) +--R + +--R 2 3 2 2 2 3 2 +--R (4a b cosh(x) + 12a b cosh(x) + (4a b + 8a )cosh(x) + 4a b) +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 3 2 2 +--R a b cosh(x) + 4a b cosh(x) + (2a b + 4a )cosh(x) + 4a b cosh(x) +--R + +--R 2 +--R a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + (- 2b + 2a b)cosh(x) - 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) +--R + +--R 2a cosh(x) + b +--R + +--R 3 +--R - 2a b sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 6a b cosh(x) + (- 4b + 4a )x - 2b - 4a )sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 6a b cosh(x) + ((- 8b + 8a )x - 4b - 8a )cosh(x) - 6a b) +--R * +--R sinh(x) +--R + +--R 3 2 2 2 2 2 +--R - 2a b cosh(x) + ((- 4b + 4a )x - 2b - 4a )cosh(x) +--R + +--R 2 +--R - 6a b cosh(x) - 2b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 2 3 4 +--R (2b - 2a b )sinh(x) +--R + +--R 5 2 3 4 3 2 3 +--R ((8b - 8a b )cosh(x) + 8a b - 8a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 2 3 +--R (12b - 12a b )cosh(x) + (24a b - 24a b )cosh(x) + 4b + 4a b +--R + +--R 4 +--R - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (8b - 8a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (8b + 8a b - 16a b)cosh(x) + 8a b - 8a b +--R * +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (2b - 2a b )cosh(x) + (8a b - 8a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 2 3 +--R (4b + 4a b - 8a b)cosh(x) + (8a b - 8a b )cosh(x) + 2b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 2 4 2 2 3 +--R - a b sinh(x) + (- 4a b cosh(x) - 4a b)sinh(x) +--R + +--R 2 2 2 2 3 2 +--R (- 6a b cosh(x) - 12a b cosh(x) - 2a b - 4a )sinh(x) +--R + +--R 2 3 2 2 2 3 +--R - 4a b cosh(x) - 12a b cosh(x) + (- 4a b - 8a )cosh(x) +--R + +--R 2 +--R - 4a b +--R * +--R sinh(x) +--R + +--R 2 4 2 3 2 3 2 +--R - a b cosh(x) - 4a b cosh(x) + (- 2a b - 4a )cosh(x) +--R + +--R 2 2 +--R - 4a b cosh(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R (b sinh(x) + b cosh(x) + a)\|b - a +--R atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 3 +--R - a b sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 3a b cosh(x) + (- 2b + 2a )x - b - 2a )sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 3a b cosh(x) + ((- 4b + 4a )x - 2b - 4a )cosh(x) - 3a b) +--R * +--R sinh(x) +--R + +--R 3 2 2 2 2 2 +--R - a b cosh(x) + ((- 2b + 2a )x - b - 2a )cosh(x) - 3a b cosh(x) +--R + +--R 2 +--R - b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 5 2 3 4 5 2 3 4 3 2 3 +--R (b - a b )sinh(x) + ((4b - 4a b )cosh(x) + 4a b - 4a b )sinh(x) +--R + +--R 5 2 3 2 4 3 2 5 2 3 +--R (6b - 6a b )cosh(x) + (12a b - 12a b )cosh(x) + 2b + 2a b +--R + +--R 4 +--R - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 5 2 3 3 4 3 2 2 +--R (4b - 4a b )cosh(x) + (12a b - 12a b )cosh(x) +--R + +--R 5 2 3 4 4 3 2 +--R (4b + 4a b - 8a b)cosh(x) + 4a b - 4a b +--R * +--R sinh(x) +--R + +--R 5 2 3 4 4 3 2 3 +--R (b - a b )cosh(x) + (4a b - 4a b )cosh(x) +--R + +--R 5 2 3 4 2 4 3 2 5 2 3 +--R (2b + 2a b - 4a b)cosh(x) + (4a b - 4a b )cosh(x) + b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 285 + +--S 286 of 518 +m0954a:= a0954.1-r0954 +--R +--R +--R (275) +--R 4 2 2 3 3 2 4 +--R (a b cosh(x) + 2a b cosh(x) + a b )sinh(x) +--R + +--R 4 3 2 3 2 3 2 4 3 +--R (4a b cosh(x) + 12a b cosh(x) + 12a b cosh(x) + 4a b)sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R 6a b cosh(x) + 24a b cosh(x) + (2a b + 34a b )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (4a b + 20a b)cosh(x) + 2a b + 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 2 3 4 4 3 2 3 +--R 4a b cosh(x) + 20a b cosh(x) + (4a b + 36a b )cosh(x) +--R + +--R 2 3 4 2 3 2 5 4 +--R (12a b + 28a b)cosh(x) + (12a b + 8a )cosh(x) + 4a b +--R * +--R sinh(x) +--R + +--R 4 6 2 3 5 4 3 2 4 +--R a b cosh(x) + 6a b cosh(x) + (2a b + 13a b )cosh(x) +--R + +--R 2 3 4 3 4 3 2 5 2 +--R (8a b + 12a b)cosh(x) + (a b + 10a b + 4a )cosh(x) +--R + +--R 2 3 4 3 2 +--R (2a b + 4a b)cosh(x) + a b +--R * +--R log +--R 2 2 2 2 2 +--R b sinh(x) + (2b cosh(x) + 2a b)sinh(x) + b cosh(x) +--R + +--R 2 2 +--R 2a b cosh(x) - b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 2 3 +--R (- 2b + 2a b)sinh(x) + (- 2b + 2a b)cosh(x) - 2a b + 2a +--R / +--R 2 2 +--R b sinh(x) + (2b cosh(x) + 2a)sinh(x) + b cosh(x) + 2a cosh(x) +--R + +--R b +--R + +--R 4 2 2 3 3 2 4 +--R (- 2a b cosh(x) - 4a b cosh(x) - 2a b )sinh(x) +--R + +--R 4 3 2 3 2 3 2 4 3 +--R (- 8a b cosh(x) - 24a b cosh(x) - 24a b cosh(x) - 8a b)sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R - 12a b cosh(x) - 48a b cosh(x) + (- 4a b - 68a b )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 8a b - 40a b)cosh(x) - 4a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 2 3 4 4 3 2 3 +--R - 8a b cosh(x) - 40a b cosh(x) + (- 8a b - 72a b )cosh(x) +--R + +--R 2 3 4 2 3 2 5 4 +--R (- 24a b - 56a b)cosh(x) + (- 24a b - 16a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 6 2 3 5 4 3 2 4 +--R - 2a b cosh(x) - 12a b cosh(x) + (- 4a b - 26a b )cosh(x) +--R + +--R 2 3 4 3 4 3 2 5 2 +--R (- 16a b - 24a b)cosh(x) + (- 2a b - 20a b - 8a )cosh(x) +--R + +--R 2 3 4 3 2 +--R (- 4a b - 8a b)cosh(x) - 2a b +--R * +--R x +--R (b - a)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 5 +--R (- b cosh(x) - a b )sinh(x) +--R + +--R 4 2 3 4 2 2 2 2 4 +--R (- 4b cosh(x) - 8a b cosh(x) + (b - a b )x - 4a b )sinh(x) +--R + +--R 4 3 3 2 +--R - 6b cosh(x) - 20a b cosh(x) +--R + +--R 4 2 2 4 2 2 3 3 3 +--R ((4b - 4a b )x - 2b - 20a b )cosh(x) + (4a b - 4a b)x - 2a b +--R + +--R 3 +--R - 6a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 3 3 +--R - 4b cosh(x) - 22a b cosh(x) +--R + +--R 4 2 2 4 2 2 2 +--R ((2b - 2a b )x - 6b - 36a b )cosh(x) +--R + +--R 3 3 3 3 4 2 2 +--R ((4a b - 4a b)x - 12a b - 22a b)cosh(x) + (2b - 2a b )x +--R + +--R 2 2 4 +--R - 6a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 3 4 +--R - b cosh(x) - 11a b cosh(x) +--R + +--R 4 2 2 4 2 2 3 +--R ((- 4b + 4a b )x - 6b - 28a b )cosh(x) +--R + +--R 3 3 3 3 2 +--R ((- 4a b + 4a b)x - 20a b - 26a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((4b - 4a b )x - b - 20a b - 8a )cosh(x) + (4a b - 4a b)x +--R + +--R 3 3 +--R - a b - 6a b +--R * +--R sinh(x) +--R + +--R 3 5 4 2 2 4 2 2 4 +--R - 2a b cosh(x) + ((- 3b + 3a b )x - 2b - 8a b )cosh(x) +--R + +--R 3 3 3 3 3 +--R ((- 4a b + 4a b)x - 10a b - 10a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 +--R ((2b - 2a b )x - 2b - 14a b - 4a )cosh(x) +--R + +--R 3 3 3 3 4 2 2 2 2 +--R ((4a b - 4a b)x - 4a b - 6a b)cosh(x) + (b - a b )x - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 7 2 5 2 6 3 4 2 5 4 3 +--R ((2b - 2a b )cosh(x) + (4a b - 4a b )cosh(x) + 2a b - 2a b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 5 3 6 3 4 2 +--R (8b - 8a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 2 5 4 3 3 4 5 2 +--R (24a b - 24a b )cosh(x) + 8a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 5 4 6 3 4 3 +--R (12b - 12a b )cosh(x) + (48a b - 48a b )cosh(x) +--R + +--R 7 2 5 4 3 2 6 3 4 5 2 +--R (4b + 64a b - 68a b )cosh(x) + (8a b + 32a b - 40a b )cosh(x) +--R + +--R 2 5 4 3 6 +--R 4a b + 4a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 5 6 3 4 4 +--R (8b - 8a b )cosh(x) + (40a b - 40a b )cosh(x) +--R + +--R 7 2 5 4 3 3 +--R (8b + 64a b - 72a b )cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (24a b + 32a b - 56a b )cosh(x) +--R + +--R 2 5 4 3 6 3 4 5 2 +--R (24a b - 8a b - 16a b)cosh(x) + 8a b - 8a b +--R * +--R sinh(x) +--R + +--R 7 2 5 6 6 3 4 5 +--R (2b - 2a b )cosh(x) + (12a b - 12a b )cosh(x) +--R + +--R 7 2 5 4 3 4 6 3 4 5 2 3 +--R (4b + 22a b - 26a b )cosh(x) + (16a b + 8a b - 24a b )cosh(x) +--R + +--R 7 2 5 4 3 6 2 6 3 4 5 2 +--R (2b + 18a b - 12a b - 8a b)cosh(x) + (4a b + 4a b - 8a b )cosh(x) +--R + +--R 2 5 4 3 +--R 2a b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 518 +d0954a:= D(m0954a,x) +--R +--R +--R (276) +--R 6 5 5 2 4 8 +--R ((b - a b )cosh(x) + a b - a b )sinh(x) +--R + +--R 6 5 2 5 2 4 +--R (6b - 6a b )cosh(x) + (12a b - 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 4 3 3 +--R (- 2b + 2a b + 2a b - 2a b )x + 6a b - 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 3 5 2 4 2 +--R (14b - 15a b )cosh(x) + (43a b - 46a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 12b + 12a b + 12a b - 12a b )x + 4b - 4a b + 40a b +--R + +--R 3 3 +--R - 43a b +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 12a b + 12a b + 12a b - 12a b )x + 4a b - 4a b + 11a b +--R + +--R 4 2 +--R - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 4 5 2 4 3 +--R (14b - 20a b )cosh(x) + (62a b - 86a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 30b + 30a b + 30a b - 30a b )x + 18b - 18a b + 84a b +--R + +--R 3 3 +--R - 120a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (- 60a b + 60a b + 60a b - 60a b )x + 36a b - 36a b +--R + +--R 3 3 4 2 +--R 38a b - 62a b +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 +--R (- 6b + 6a b - 18a b + 18a b + 24a b - 24a b)x + 18a b +--R + +--R 3 3 4 2 5 +--R - 18a b + 2a b - 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 5 2 4 4 +--R - 15a b cosh(x) + (15a b - 90a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 32b + 32a b + 32a b - 32a b )x + 30b - 33a b + 30a b +--R + +--R 3 3 +--R - 177a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (- 96a b + 96a b + 96a b - 96a b )x + 93a b - 102a b +--R + +--R 3 3 4 2 +--R - 3a b - 138a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 24b + 24a b - 48a b + 48a b + 72a b - 72a b)x + 6b +--R + +--R 5 2 4 3 3 4 2 5 +--R - 6a b + 84a b - 93a b - 30a b - 36a b +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 24a b + 24a b + 16a b - 16a b + 8a b - 8a )x + 6a b +--R + +--R 2 4 3 3 4 2 5 +--R - 6a b + 21a b - 24a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 6 5 2 4 5 +--R (- 14b - 6a b )cosh(x) + (- 64a b - 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (2b - 2a b - 2a b + 2a b )x + 20b - 32a b - 130a b +--R + +--R 3 3 +--R - 158a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (- 24a b + 24a b + 24a b - 24a b )x + 92a b - 140a b +--R + +--R 3 3 4 2 +--R - 172a b - 180a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 36b + 36a b - 12a b + 12a b + 48a b - 48a b)x + 18b +--R + +--R 5 2 4 3 3 4 2 5 +--R - 18a b + 120a b - 192a b - 148a b - 80a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 72a b + 72a b + 56a b - 56a b + 16a b - 16a )x +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 36a b - 36a b + 44a b - 92a b - 64a b - 8a +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 +--R (- 6b + 6a b - 18a b + 18a b + 24a b - 24a b)x + 18a b +--R + +--R 3 3 4 2 5 6 +--R - 18a b - 4a b - 8a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 7 5 2 4 6 +--R (- 14b - a b )cosh(x) + (- 83a b - 22a b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 2 4 +--R (36b - 36a b - 36a b + 36a b )x - 18a b - 204a b +--R + +--R 3 3 +--R - 93a b +--R * +--R 5 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (84a b - 84a b - 84a b + 84a b )x + 18a b - 108a b +--R + +--R 3 3 4 2 +--R - 283a b - 152a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 32b + 32a b + 80a b - 80a b - 48a b + 48a b)x + 18b +--R + +--R 5 2 4 3 3 4 2 5 +--R - 21a b + 36a b - 210a b - 244a b - 104a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (- 96a b + 96a b + 96a b - 96a b )x + 57a b - 66a b +--R + +--R 3 3 4 2 5 6 +--R - 6a b - 156a b - 120a b - 24a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b + 12a b - 60a b + 60a b + 72a b - 72a b)x + 4b +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 4a b + 48a b - 57a b - 36a b - 36a b - 24a +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 2 4 +--R (- 12a b + 12a b + 4a b - 4a b + 8a b - 8a )x + 4a b - 4a b +--R + +--R 3 3 4 2 5 +--R 9a b - 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 8 5 2 4 7 +--R - 6b cosh(x) + (- 42a b - 6a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (30b - 30a b - 30a b + 30a b )x - 6b - 6a b - 120a b +--R + +--R 3 3 +--R - 36a b +--R * +--R 6 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (84a b - 84a b - 84a b + 84a b )x - 24a b - 48a b +--R + +--R 3 3 4 2 +--R - 186a b - 78a b +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 22b + 22a b + 94a b - 94a b - 72a b + 72a b)x + 6b +--R + +--R 5 2 4 3 3 4 2 5 +--R - 12a b - 42a b - 126a b - 174a b - 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 72a b + 72a b + 88a b - 88a b - 16a b + 16a )x +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 30a b - 54a b - 60a b - 132a b - 96a b - 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 6b + 6a b - 66a b + 66a b + 72a b - 72a b)x + 6b +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 6a b + 36a b - 72a b - 60a b - 48a b - 24a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 12a b + 12a b - 4a b + 4a b + 16a b - 16a )x + 12a b +--R + +--R 2 4 3 3 4 2 5 +--R - 12a b + 6a b - 30a b - 24a b +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 2 4 3 3 4 2 +--R (- 2b + 2a b + 2a b - 2a b )x + 6a b - 6a b - 6a b +--R * +--R sinh(x) +--R + +--R 6 9 5 2 4 8 +--R - b cosh(x) + (- 8a b - a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 3 3 +--R ((8b - 8a b - 8a b + 8a b )x - 2b - a b - 26a b - 7a b ) +--R * +--R 7 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (24a b - 24a b - 24a b + 24a b )x - 11a b - 10a b - 45a b +--R + +--R 4 2 +--R - 18a b +--R * +--R 6 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (- 8b + 8a b + 32a b - 32a b - 24a b + 24a b)x - 3a b +--R + +--R 2 4 3 3 4 2 5 +--R - 24a b - 33a b - 46a b - 20a b +--R * +--R 5 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 24a b + 24a b + 32a b - 32a b - 8a b + 8a )x + 3a b +--R + +--R 2 4 3 3 4 2 5 6 +--R - 18a b - 31a b - 44a b - 28a b - 8a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 5 2 4 +--R (- 24a b + 24a b + 24a b - 24a b)x + 2b - 3a b + 6a b +--R + +--R 3 3 4 2 5 6 +--R - 33a b - 28a b - 20a b - 8a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 4 2 5 6 5 2 4 3 3 4 2 +--R (- 8a b + 8a b + 8a b - 8a )x + 7a b - 10a b - 3a b - 18a b +--R + +--R 5 +--R - 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 3 3 +--R (b - a b + 4a b - 7a b - 6a b )cosh(x) + a b - a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 5 5 2 4 8 +--R ((b + a b )cosh(x) + a b + a b )sinh(x) +--R + +--R 6 5 2 5 2 4 +--R (6b + 6a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 4 3 3 +--R (- 2b - 2a b + 2a b + 2a b )x + 6a b + 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 3 5 2 4 2 +--R (14b + 15a b )cosh(x) + (43a b + 46a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 12b - 12a b + 12a b + 12a b )x + 4b + 4a b + 40a b +--R + +--R 3 3 +--R 43a b +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 12a b - 12a b + 12a b + 12a b )x + 4a b + 4a b + 11a b +--R + +--R 4 2 +--R 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 4 5 2 4 3 +--R (14b + 20a b )cosh(x) + (62a b + 86a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 30b - 30a b + 30a b + 30a b )x + 18b + 18a b + 84a b +--R + +--R 3 3 +--R 120a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 60a b - 60a b + 60a b + 60a b )x + 36a b + 36a b + 38a b +--R + +--R 4 2 +--R 62a b +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 6b - 6a b - 18a b - 18a b + 24a b + 24a b)x + 18a b + 18a b +--R + +--R 4 2 5 +--R 2a b + 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 5 2 4 4 +--R 15a b cosh(x) + (15a b + 90a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 32b - 32a b + 32a b + 32a b )x + 30b + 33a b + 30a b +--R + +--R 3 3 +--R 177a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 96a b - 96a b + 96a b + 96a b )x + 93a b + 102a b - 3a b +--R + +--R 4 2 +--R 138a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 24b - 24a b - 48a b - 48a b + 72a b + 72a b)x + 6b +--R + +--R 5 2 4 3 3 4 2 5 +--R 6a b + 84a b + 93a b - 30a b + 36a b +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 2 4 +--R (- 24a b - 24a b + 16a b + 16a b + 8a b + 8a )x + 6a b + 6a b +--R + +--R 3 3 4 2 5 +--R 21a b + 24a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 6 5 2 4 5 +--R (- 14b + 6a b )cosh(x) + (- 64a b + 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (2b + 2a b - 2a b - 2a b )x + 20b + 32a b - 130a b +--R + +--R 3 3 +--R 158a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (- 24a b - 24a b + 24a b + 24a b )x + 92a b + 140a b +--R + +--R 3 3 4 2 +--R - 172a b + 180a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 36b - 36a b - 12a b - 12a b + 48a b + 48a b)x + 18b +--R + +--R 5 2 4 3 3 4 2 5 +--R 18a b + 120a b + 192a b - 148a b + 80a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 72a b - 72a b + 56a b + 56a b + 16a b + 16a )x + 36a b +--R + +--R 2 4 3 3 4 2 5 6 +--R 36a b + 44a b + 92a b - 64a b + 8a +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 6b - 6a b - 18a b - 18a b + 24a b + 24a b)x + 18a b + 18a b +--R + +--R 4 2 5 6 +--R - 4a b + 8a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 7 5 2 4 6 +--R (- 14b + a b )cosh(x) + (- 83a b + 22a b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 2 4 3 3 +--R ((36b + 36a b - 36a b - 36a b )x + 18a b - 204a b + 93a b ) +--R * +--R 5 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (84a b + 84a b - 84a b - 84a b )x + 18a b + 108a b - 283a b +--R + +--R 4 2 +--R 152a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 32b - 32a b + 80a b + 80a b - 48a b - 48a b)x + 18b +--R + +--R 5 2 4 3 3 4 2 5 +--R 21a b + 36a b + 210a b - 244a b + 104a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 96a b - 96a b + 96a b + 96a b )x + 57a b + 66a b - 6a b +--R + +--R 4 2 5 6 +--R 156a b - 120a b + 24a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b - 12a b - 60a b - 60a b + 72a b + 72a b)x + 4b +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 4a b + 48a b + 57a b - 36a b + 36a b - 24a +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 2 4 +--R (- 12a b - 12a b + 4a b + 4a b + 8a b + 8a )x + 4a b + 4a b +--R + +--R 3 3 4 2 5 +--R 9a b + 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 8 5 2 4 7 +--R - 6b cosh(x) + (- 42a b + 6a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (30b + 30a b - 30a b - 30a b )x - 6b + 6a b - 120a b +--R + +--R 3 3 +--R 36a b +--R * +--R 6 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (84a b + 84a b - 84a b - 84a b )x - 24a b + 48a b - 186a b +--R + +--R 4 2 +--R 78a b +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 22b - 22a b + 94a b + 94a b - 72a b - 72a b)x + 6b +--R + +--R 5 2 4 3 3 4 2 5 +--R 12a b - 42a b + 126a b - 174a b + 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 72a b - 72a b + 88a b + 88a b - 16a b - 16a )x + 30a b +--R + +--R 2 4 3 3 4 2 5 6 +--R 54a b - 60a b + 132a b - 96a b + 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 6b - 6a b - 66a b - 66a b + 72a b + 72a b)x + 6b + 6a b +--R + +--R 2 4 3 3 4 2 5 6 +--R 36a b + 72a b - 60a b + 48a b - 24a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 12a b - 12a b - 4a b - 4a b + 16a b + 16a )x + 12a b +--R + +--R 2 4 3 3 4 2 5 +--R 12a b + 6a b + 30a b - 24a b +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 2 4 3 3 4 2 +--R (- 2b - 2a b + 2a b + 2a b )x + 6a b + 6a b - 6a b +--R * +--R sinh(x) +--R + +--R 6 9 5 2 4 8 +--R - b cosh(x) + (- 8a b + a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 3 3 7 +--R ((8b + 8a b - 8a b - 8a b )x - 2b + a b - 26a b + 7a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (24a b + 24a b - 24a b - 24a b )x - 11a b + 10a b - 45a b +--R + +--R 4 2 +--R 18a b +--R * +--R 6 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 2 4 +--R (- 8b - 8a b + 32a b + 32a b - 24a b - 24a b)x + 3a b - 24a b +--R + +--R 3 3 4 2 5 +--R 33a b - 46a b + 20a b +--R * +--R 5 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 2 4 +--R (- 24a b - 24a b + 32a b + 32a b - 8a b - 8a )x + 3a b + 18a b +--R + +--R 3 3 4 2 5 6 +--R - 31a b + 44a b - 28a b + 8a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 5 2 4 3 3 +--R (- 24a b - 24a b + 24a b + 24a b)x + 2b + 3a b + 6a b + 33a b +--R + +--R 4 2 5 6 +--R - 28a b + 20a b - 8a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 4 2 5 6 5 2 4 3 3 4 2 +--R (- 8a b - 8a b + 8a b + 8a )x + 7a b + 10a b - 3a b + 18a b +--R + +--R 5 +--R - 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 3 3 +--R (b + a b + 4a b + 7a b - 6a b )cosh(x) + a b + a b - a b +--R / +--R 9 8 2 7 3 6 3 +--R (2b - 2a b - 2a b + 2a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 2 +--R (6a b - 6a b - 6a b + 6a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 3 6 4 5 5 4 +--R (6a b - 6a b - 6a b + 6a b )cosh(x) + 2a b - 2a b - 2a b +--R + +--R 6 3 +--R 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 +--R (12b - 12a b - 12a b + 12a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (48a b - 48a b - 48a b + 48a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 2 +--R (72a b - 72a b - 72a b + 72a b )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 4 5 5 4 +--R (48a b - 48a b - 48a b + 48a b )cosh(x) + 12a b - 12a b +--R + +--R 6 3 7 2 +--R - 12a b + 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 5 +--R (30b - 30a b - 30a b + 30a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (150a b - 150a b - 150a b + 150a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 3 +--R (6b - 6a b + 288a b - 288a b - 294a b + 294a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 2 +--R (18a b - 18a b + 264a b - 264a b - 282a b + 282a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R (18a b - 18a b + 114a b - 114a b - 132a b + 132a b )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 6a b - 6a b + 18a b - 18a b - 24a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 6 +--R (40b - 40a b - 40a b + 40a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 +--R (240a b - 240a b - 240a b + 240a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 4 +--R (24b - 24a b + 552a b - 552a b - 576a b + 576a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 3 +--R (96a b - 96a b + 608a b - 608a b - 704a b + 704a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R (144a b - 144a b + 312a b - 312a b - 456a b + 456a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R (96a b - 96a b + 48a b - 48a b - 144a b + 144a b)cosh(x) +--R + +--R 4 5 5 4 6 3 7 2 8 9 +--R 24a b - 24a b - 8a b + 8a b - 16a b + 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 7 +--R (30b - 30a b - 30a b + 30a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 6 +--R (210a b - 210a b - 210a b + 210a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 5 +--R (36b - 36a b + 558a b - 558a b - 594a b + 594a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R (180a b - 180a b + 690a b - 690a b - 870a b + 870a b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b - 6a b + 342a b - 342a b + 348a b - 348a b - 696a b +--R + +--R 7 2 +--R 696a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 18a b - 18a b + 306a b - 306a b - 36a b + 36a b +--R + +--R 7 2 8 +--R - 288a b + 288a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R 18a b - 18a b + 126a b - 126a b - 96a b + 96a b - 48a b +--R + +--R 9 +--R 48a +--R * +--R cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 6a b - 6a b + 18a b - 18a b - 24a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 8 +--R (12b - 12a b - 12a b + 12a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 7 +--R (96a b - 96a b - 96a b + 96a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 +--R (24b - 24a b + 288a b - 288a b - 312a b + 312a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R (144a b - 144a b + 384a b - 384a b - 528a b + 528a b ) +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 12b - 12a b + 324a b - 324a b + 156a b - 156a b +--R + +--R 6 3 7 2 +--R - 492a b + 492a b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 48a b - 48a b + 336a b - 336a b - 144a b + 144a b +--R + +--R 7 2 8 +--R - 240a b + 240a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R 72a b - 72a b + 144a b - 144a b - 168a b + 168a b +--R + +--R 8 9 +--R - 48a b + 48a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 6 4 5 7 2 8 4 5 5 4 +--R (48a b - 48a b - 48a b + 48a b)cosh(x) + 12a b - 12a b +--R + +--R 6 3 7 2 +--R - 12a b + 12a b +--R * +--R sinh(x) +--R + +--R 9 8 2 7 3 6 9 +--R (2b - 2a b - 2a b + 2a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 8 +--R (18a b - 18a b - 18a b + 18a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 7 +--R (6b - 6a b + 60a b - 60a b - 66a b + 66a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 6 +--R (42a b - 42a b + 84a b - 84a b - 126a b + 126a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b - 6a b + 108a b - 108a b + 18a b - 18a b - 132a b +--R + +--R 7 2 +--R 132a b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 30a b - 30a b + 120a b - 120a b - 78a b + 78a b - 72a b +--R + +--R 8 +--R 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 2b - 2a b + 52a b - 52a b + 42a b - 42a b - 80a b + 80a b +--R + +--R 8 9 +--R - 16a b + 16a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 6a b - 6a b + 36a b - 36a b - 18a b + 18a b - 24a b +--R + +--R 8 +--R 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 3 6 +--R (6a b - 6a b + 6a b - 6a b - 12a b + 12a b )cosh(x) + 2a b +--R + +--R 4 5 5 4 6 3 +--R - 2a b - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 9 8 2 7 3 6 3 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 2 +--R (6a b + 6a b - 6a b - 6a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 3 6 4 5 5 4 6 3 +--R (6a b + 6a b - 6a b - 6a b )cosh(x) + 2a b + 2a b - 2a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 +--R (12b + 12a b - 12a b - 12a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (48a b + 48a b - 48a b - 48a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 2 +--R (72a b + 72a b - 72a b - 72a b )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 4 5 5 4 6 3 +--R (48a b + 48a b - 48a b - 48a b )cosh(x) + 12a b + 12a b - 12a b +--R + +--R 7 2 +--R - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 5 +--R (30b + 30a b - 30a b - 30a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (150a b + 150a b - 150a b - 150a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 3 +--R (6b + 6a b + 288a b + 288a b - 294a b - 294a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 2 +--R (18a b + 18a b + 264a b + 264a b - 282a b - 282a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R (18a b + 18a b + 114a b + 114a b - 132a b - 132a b )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 6a b + 6a b + 18a b + 18a b - 24a b - 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 6 +--R (40b + 40a b - 40a b - 40a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 +--R (240a b + 240a b - 240a b - 240a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 4 +--R (24b + 24a b + 552a b + 552a b - 576a b - 576a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 3 +--R (96a b + 96a b + 608a b + 608a b - 704a b - 704a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 2 +--R (144a b + 144a b + 312a b + 312a b - 456a b - 456a b )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R (96a b + 96a b + 48a b + 48a b - 144a b - 144a b)cosh(x) +--R + +--R 4 5 5 4 6 3 7 2 8 9 +--R 24a b + 24a b - 8a b - 8a b - 16a b - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 7 +--R (30b + 30a b - 30a b - 30a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 6 +--R (210a b + 210a b - 210a b - 210a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 5 +--R (36b + 36a b + 558a b + 558a b - 594a b - 594a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 4 +--R (180a b + 180a b + 690a b + 690a b - 870a b - 870a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b + 6a b + 342a b + 342a b + 348a b + 348a b - 696a b +--R + +--R 7 2 +--R - 696a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 18a b + 18a b + 306a b + 306a b - 36a b - 36a b - 288a b +--R + +--R 8 +--R - 288a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R 18a b + 18a b + 126a b + 126a b - 96a b - 96a b - 48a b +--R + +--R 9 +--R - 48a +--R * +--R cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 6a b + 6a b + 18a b + 18a b - 24a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 8 +--R (12b + 12a b - 12a b - 12a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 7 +--R (96a b + 96a b - 96a b - 96a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 +--R (24b + 24a b + 288a b + 288a b - 312a b - 312a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 5 +--R (144a b + 144a b + 384a b + 384a b - 528a b - 528a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 12b + 12a b + 324a b + 324a b + 156a b + 156a b - 492a b +--R + +--R 7 2 +--R - 492a b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 48a b + 48a b + 336a b + 336a b - 144a b - 144a b - 240a b +--R + +--R 8 +--R - 240a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R 72a b + 72a b + 144a b + 144a b - 168a b - 168a b - 48a b +--R + +--R 9 +--R - 48a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 6 4 5 7 2 8 4 5 5 4 6 3 +--R (48a b + 48a b - 48a b - 48a b)cosh(x) + 12a b + 12a b - 12a b +--R + +--R 7 2 +--R - 12a b +--R * +--R sinh(x) +--R + +--R 9 8 2 7 3 6 9 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 8 +--R (18a b + 18a b - 18a b - 18a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 7 +--R (6b + 6a b + 60a b + 60a b - 66a b - 66a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 6 +--R (42a b + 42a b + 84a b + 84a b - 126a b - 126a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (6b + 6a b + 108a b + 108a b + 18a b + 18a b - 132a b - 132a b ) +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 30a b + 30a b + 120a b + 120a b - 78a b - 78a b - 72a b +--R + +--R 8 +--R - 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 2b + 2a b + 52a b + 52a b + 42a b + 42a b - 80a b - 80a b +--R + +--R 8 9 +--R - 16a b - 16a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (6a b + 6a b + 36a b + 36a b - 18a b - 18a b - 24a b - 24a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 3 6 4 5 +--R (6a b + 6a b + 6a b + 6a b - 12a b - 12a b )cosh(x) + 2a b + 2a b +--R + +--R 5 4 6 3 +--R - 2a b - 2a b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 518 +m0954b:= a0954.2-r0954 +--R +--R +--R (277) +--R 4 2 2 3 3 2 4 +--R (- 2a b cosh(x) - 4a b cosh(x) - 2a b )sinh(x) +--R + +--R 4 3 2 3 2 3 2 4 3 +--R (- 8a b cosh(x) - 24a b cosh(x) - 24a b cosh(x) - 8a b)sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R - 12a b cosh(x) - 48a b cosh(x) + (- 4a b - 68a b )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 8a b - 40a b)cosh(x) - 4a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 2 3 4 4 3 2 3 +--R - 8a b cosh(x) - 40a b cosh(x) + (- 8a b - 72a b )cosh(x) +--R + +--R 2 3 4 2 3 2 5 4 +--R (- 24a b - 56a b)cosh(x) + (- 24a b - 16a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 6 2 3 5 4 3 2 4 +--R - 2a b cosh(x) - 12a b cosh(x) + (- 4a b - 26a b )cosh(x) +--R + +--R 2 3 4 3 4 3 2 5 2 +--R (- 16a b - 24a b)cosh(x) + (- 2a b - 20a b - 8a )cosh(x) +--R + +--R 2 3 4 3 2 +--R (- 4a b - 8a b)cosh(x) - 2a b +--R * +--R x +--R +-------+ (b - a)tanh(-) +--R | 2 2 2 +--R \|b - a atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 3 3 2 4 +--R (- 2a b cosh(x) - 4a b cosh(x) - 2a b )sinh(x) +--R + +--R 4 3 2 3 2 3 2 4 3 +--R (- 8a b cosh(x) - 24a b cosh(x) - 24a b cosh(x) - 8a b)sinh(x) +--R + +--R 4 4 2 3 3 4 3 2 2 +--R - 12a b cosh(x) - 48a b cosh(x) + (- 4a b - 68a b )cosh(x) +--R + +--R 2 3 4 3 2 5 +--R (- 8a b - 40a b)cosh(x) - 4a b - 8a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 2 3 4 4 3 2 3 +--R - 8a b cosh(x) - 40a b cosh(x) + (- 8a b - 72a b )cosh(x) +--R + +--R 2 3 4 2 3 2 5 4 +--R (- 24a b - 56a b)cosh(x) + (- 24a b - 16a )cosh(x) - 8a b +--R * +--R sinh(x) +--R + +--R 4 6 2 3 5 4 3 2 4 +--R - 2a b cosh(x) - 12a b cosh(x) + (- 4a b - 26a b )cosh(x) +--R + +--R 2 3 4 3 4 3 2 5 2 +--R (- 16a b - 24a b)cosh(x) + (- 2a b - 20a b - 8a )cosh(x) +--R + +--R 2 3 4 3 2 +--R (- 4a b - 8a b)cosh(x) - 2a b +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sinh(x) + b cosh(x) + a)\|b - a +--R \|- b + a atan(-------------------------------------) +--R 2 2 +--R b - a +--R + +--R 4 3 5 +--R (- b cosh(x) - a b )sinh(x) +--R + +--R 4 2 3 4 2 2 2 2 4 +--R (- 4b cosh(x) - 8a b cosh(x) + (b - a b )x - 4a b )sinh(x) +--R + +--R 4 3 3 2 +--R - 6b cosh(x) - 20a b cosh(x) +--R + +--R 4 2 2 4 2 2 3 3 3 +--R ((4b - 4a b )x - 2b - 20a b )cosh(x) + (4a b - 4a b)x - 2a b +--R + +--R 3 +--R - 6a b +--R * +--R 3 +--R sinh(x) +--R + +--R 4 4 3 3 +--R - 4b cosh(x) - 22a b cosh(x) +--R + +--R 4 2 2 4 2 2 2 +--R ((2b - 2a b )x - 6b - 36a b )cosh(x) +--R + +--R 3 3 3 3 4 2 2 +--R ((4a b - 4a b)x - 12a b - 22a b)cosh(x) + (2b - 2a b )x +--R + +--R 2 2 4 +--R - 6a b - 4a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 5 3 4 +--R - b cosh(x) - 11a b cosh(x) +--R + +--R 4 2 2 4 2 2 3 +--R ((- 4b + 4a b )x - 6b - 28a b )cosh(x) +--R + +--R 3 3 3 3 2 +--R ((- 4a b + 4a b)x - 20a b - 26a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 3 3 +--R ((4b - 4a b )x - b - 20a b - 8a )cosh(x) + (4a b - 4a b)x +--R + +--R 3 3 +--R - a b - 6a b +--R * +--R sinh(x) +--R + +--R 3 5 4 2 2 4 2 2 4 +--R - 2a b cosh(x) + ((- 3b + 3a b )x - 2b - 8a b )cosh(x) +--R + +--R 3 3 3 3 3 +--R ((- 4a b + 4a b)x - 10a b - 10a b)cosh(x) +--R + +--R 4 2 2 4 2 2 4 2 +--R ((2b - 2a b )x - 2b - 14a b - 4a )cosh(x) +--R + +--R 3 3 3 3 4 2 2 2 2 +--R ((4a b - 4a b)x - 4a b - 6a b)cosh(x) + (b - a b )x - 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 7 2 5 2 6 3 4 2 5 4 3 +--R ((2b - 2a b )cosh(x) + (4a b - 4a b )cosh(x) + 2a b - 2a b ) +--R * +--R 4 +--R sinh(x) +--R + +--R 7 2 5 3 6 3 4 2 +--R (8b - 8a b )cosh(x) + (24a b - 24a b )cosh(x) +--R + +--R 2 5 4 3 3 4 5 2 +--R (24a b - 24a b )cosh(x) + 8a b - 8a b +--R * +--R 3 +--R sinh(x) +--R + +--R 7 2 5 4 6 3 4 3 +--R (12b - 12a b )cosh(x) + (48a b - 48a b )cosh(x) +--R + +--R 7 2 5 4 3 2 6 3 4 5 2 +--R (4b + 64a b - 68a b )cosh(x) + (8a b + 32a b - 40a b )cosh(x) +--R + +--R 2 5 4 3 6 +--R 4a b + 4a b - 8a b +--R * +--R 2 +--R sinh(x) +--R + +--R 7 2 5 5 6 3 4 4 +--R (8b - 8a b )cosh(x) + (40a b - 40a b )cosh(x) +--R + +--R 7 2 5 4 3 3 +--R (8b + 64a b - 72a b )cosh(x) +--R + +--R 6 3 4 5 2 2 +--R (24a b + 32a b - 56a b )cosh(x) +--R + +--R 2 5 4 3 6 3 4 5 2 +--R (24a b - 8a b - 16a b)cosh(x) + 8a b - 8a b +--R * +--R sinh(x) +--R + +--R 7 2 5 6 6 3 4 5 +--R (2b - 2a b )cosh(x) + (12a b - 12a b )cosh(x) +--R + +--R 7 2 5 4 3 4 6 3 4 5 2 3 +--R (4b + 22a b - 26a b )cosh(x) + (16a b + 8a b - 24a b )cosh(x) +--R + +--R 7 2 5 4 3 6 2 6 3 4 5 2 +--R (2b + 18a b - 12a b - 8a b)cosh(x) + (4a b + 4a b - 8a b )cosh(x) +--R + +--R 2 5 4 3 +--R 2a b - 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 288 + +--S 289 of 518 +d0954b:= D(m0954b,x) +--R +--R +--R (278) +--R 6 5 5 2 4 8 +--R ((b - a b )cosh(x) + a b - a b )sinh(x) +--R + +--R 6 5 2 5 2 4 +--R (6b - 6a b )cosh(x) + (12a b - 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 4 3 3 +--R (- 2b + 2a b + 2a b - 2a b )x + 6a b - 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 3 5 2 4 2 +--R (14b - 15a b )cosh(x) + (43a b - 46a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 12b + 12a b + 12a b - 12a b )x + 4b - 4a b + 40a b +--R + +--R 3 3 +--R - 43a b +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 12a b + 12a b + 12a b - 12a b )x + 4a b - 4a b + 11a b +--R + +--R 4 2 +--R - 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 4 5 2 4 3 +--R (14b - 20a b )cosh(x) + (62a b - 86a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 30b + 30a b + 30a b - 30a b )x + 18b - 18a b + 84a b +--R + +--R 3 3 +--R - 120a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (- 60a b + 60a b + 60a b - 60a b )x + 36a b - 36a b +--R + +--R 3 3 4 2 +--R 38a b - 62a b +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 +--R (- 6b + 6a b - 18a b + 18a b + 24a b - 24a b)x + 18a b +--R + +--R 3 3 4 2 5 +--R - 18a b + 2a b - 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 5 2 4 4 +--R - 15a b cosh(x) + (15a b - 90a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 32b + 32a b + 32a b - 32a b )x + 30b - 33a b + 30a b +--R + +--R 3 3 +--R - 177a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (- 96a b + 96a b + 96a b - 96a b )x + 93a b - 102a b +--R + +--R 3 3 4 2 +--R - 3a b - 138a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 24b + 24a b - 48a b + 48a b + 72a b - 72a b)x + 6b +--R + +--R 5 2 4 3 3 4 2 5 +--R - 6a b + 84a b - 93a b - 30a b - 36a b +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 24a b + 24a b + 16a b - 16a b + 8a b - 8a )x + 6a b +--R + +--R 2 4 3 3 4 2 5 +--R - 6a b + 21a b - 24a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 6 5 2 4 5 +--R (- 14b - 6a b )cosh(x) + (- 64a b - 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (2b - 2a b - 2a b + 2a b )x + 20b - 32a b - 130a b +--R + +--R 3 3 +--R - 158a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (- 24a b + 24a b + 24a b - 24a b )x + 92a b - 140a b +--R + +--R 3 3 4 2 +--R - 172a b - 180a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 36b + 36a b - 12a b + 12a b + 48a b - 48a b)x + 18b +--R + +--R 5 2 4 3 3 4 2 5 +--R - 18a b + 120a b - 192a b - 148a b - 80a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 72a b + 72a b + 56a b - 56a b + 16a b - 16a )x +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 36a b - 36a b + 44a b - 92a b - 64a b - 8a +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 +--R (- 6b + 6a b - 18a b + 18a b + 24a b - 24a b)x + 18a b +--R + +--R 3 3 4 2 5 6 +--R - 18a b - 4a b - 8a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 7 5 2 4 6 +--R (- 14b - a b )cosh(x) + (- 83a b - 22a b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 2 4 +--R (36b - 36a b - 36a b + 36a b )x - 18a b - 204a b +--R + +--R 3 3 +--R - 93a b +--R * +--R 5 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (84a b - 84a b - 84a b + 84a b )x + 18a b - 108a b +--R + +--R 3 3 4 2 +--R - 283a b - 152a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 32b + 32a b + 80a b - 80a b - 48a b + 48a b)x + 18b +--R + +--R 5 2 4 3 3 4 2 5 +--R - 21a b + 36a b - 210a b - 244a b - 104a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (- 96a b + 96a b + 96a b - 96a b )x + 57a b - 66a b +--R + +--R 3 3 4 2 5 6 +--R - 6a b - 156a b - 120a b - 24a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b + 12a b - 60a b + 60a b + 72a b - 72a b)x + 4b +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 4a b + 48a b - 57a b - 36a b - 36a b - 24a +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 2 4 +--R (- 12a b + 12a b + 4a b - 4a b + 8a b - 8a )x + 4a b - 4a b +--R + +--R 3 3 4 2 5 +--R 9a b - 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 8 5 2 4 7 +--R - 6b cosh(x) + (- 42a b - 6a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (30b - 30a b - 30a b + 30a b )x - 6b - 6a b - 120a b +--R + +--R 3 3 +--R - 36a b +--R * +--R 6 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (84a b - 84a b - 84a b + 84a b )x - 24a b - 48a b +--R + +--R 3 3 4 2 +--R - 186a b - 78a b +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 22b + 22a b + 94a b - 94a b - 72a b + 72a b)x + 6b +--R + +--R 5 2 4 3 3 4 2 5 +--R - 12a b - 42a b - 126a b - 174a b - 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 72a b + 72a b + 88a b - 88a b - 16a b + 16a )x +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 30a b - 54a b - 60a b - 132a b - 96a b - 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 6b + 6a b - 66a b + 66a b + 72a b - 72a b)x + 6b +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 6a b + 36a b - 72a b - 60a b - 48a b - 24a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 12a b + 12a b - 4a b + 4a b + 16a b - 16a )x + 12a b +--R + +--R 2 4 3 3 4 2 5 +--R - 12a b + 6a b - 30a b - 24a b +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 2 4 3 3 4 2 +--R (- 2b + 2a b + 2a b - 2a b )x + 6a b - 6a b - 6a b +--R * +--R sinh(x) +--R + +--R 6 9 5 2 4 8 +--R - b cosh(x) + (- 8a b - a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 3 3 +--R ((8b - 8a b - 8a b + 8a b )x - 2b - a b - 26a b - 7a b ) +--R * +--R 7 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (24a b - 24a b - 24a b + 24a b )x - 11a b - 10a b - 45a b +--R + +--R 4 2 +--R - 18a b +--R * +--R 6 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (- 8b + 8a b + 32a b - 32a b - 24a b + 24a b)x - 3a b +--R + +--R 2 4 3 3 4 2 5 +--R - 24a b - 33a b - 46a b - 20a b +--R * +--R 5 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 24a b + 24a b + 32a b - 32a b - 8a b + 8a )x + 3a b +--R + +--R 2 4 3 3 4 2 5 6 +--R - 18a b - 31a b - 44a b - 28a b - 8a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 5 2 4 +--R (- 24a b + 24a b + 24a b - 24a b)x + 2b - 3a b + 6a b +--R + +--R 3 3 4 2 5 6 +--R - 33a b - 28a b - 20a b - 8a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 4 2 5 6 5 2 4 3 3 4 2 +--R (- 8a b + 8a b + 8a b - 8a )x + 7a b - 10a b - 3a b - 18a b +--R + +--R 5 +--R - 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 3 3 +--R (b - a b + 4a b - 7a b - 6a b )cosh(x) + a b - a b - a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 6 5 5 2 4 8 +--R ((b + a b )cosh(x) + a b + a b )sinh(x) +--R + +--R 6 5 2 5 2 4 +--R (6b + 6a b )cosh(x) + (12a b + 12a b )cosh(x) +--R + +--R 6 5 2 4 3 3 2 4 3 3 +--R (- 2b - 2a b + 2a b + 2a b )x + 6a b + 6a b +--R * +--R 7 +--R sinh(x) +--R + +--R 6 5 3 5 2 4 2 +--R (14b + 15a b )cosh(x) + (43a b + 46a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 12b - 12a b + 12a b + 12a b )x + 4b + 4a b + 40a b +--R + +--R 3 3 +--R 43a b +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 12a b - 12a b + 12a b + 12a b )x + 4a b + 4a b + 11a b +--R + +--R 4 2 +--R 12a b +--R * +--R 6 +--R sinh(x) +--R + +--R 6 5 4 5 2 4 3 +--R (14b + 20a b )cosh(x) + (62a b + 86a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 30b - 30a b + 30a b + 30a b )x + 18b + 18a b + 84a b +--R + +--R 3 3 +--R 120a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 60a b - 60a b + 60a b + 60a b )x + 36a b + 36a b + 38a b +--R + +--R 4 2 +--R 62a b +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 6b - 6a b - 18a b - 18a b + 24a b + 24a b)x + 18a b + 18a b +--R + +--R 4 2 5 +--R 2a b + 8a b +--R * +--R 5 +--R sinh(x) +--R + +--R 5 5 5 2 4 4 +--R 15a b cosh(x) + (15a b + 90a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (- 32b - 32a b + 32a b + 32a b )x + 30b + 33a b + 30a b +--R + +--R 3 3 +--R 177a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 96a b - 96a b + 96a b + 96a b )x + 93a b + 102a b - 3a b +--R + +--R 4 2 +--R 138a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 24b - 24a b - 48a b - 48a b + 72a b + 72a b)x + 6b +--R + +--R 5 2 4 3 3 4 2 5 +--R 6a b + 84a b + 93a b - 30a b + 36a b +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 2 4 +--R (- 24a b - 24a b + 16a b + 16a b + 8a b + 8a )x + 6a b + 6a b +--R + +--R 3 3 4 2 5 +--R 21a b + 24a b - 12a b +--R * +--R 4 +--R sinh(x) +--R + +--R 6 5 6 5 2 4 5 +--R (- 14b + 6a b )cosh(x) + (- 64a b + 56a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (2b + 2a b - 2a b - 2a b )x + 20b + 32a b - 130a b +--R + +--R 3 3 +--R 158a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 +--R (- 24a b - 24a b + 24a b + 24a b )x + 92a b + 140a b +--R + +--R 3 3 4 2 +--R - 172a b + 180a b +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 36b - 36a b - 12a b - 12a b + 48a b + 48a b)x + 18b +--R + +--R 5 2 4 3 3 4 2 5 +--R 18a b + 120a b + 192a b - 148a b + 80a b +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 72a b - 72a b + 56a b + 56a b + 16a b + 16a )x + 36a b +--R + +--R 2 4 3 3 4 2 5 6 +--R 36a b + 44a b + 92a b - 64a b + 8a +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 6b - 6a b - 18a b - 18a b + 24a b + 24a b)x + 18a b + 18a b +--R + +--R 4 2 5 6 +--R - 4a b + 8a b - 8a +--R * +--R 3 +--R sinh(x) +--R + +--R 6 5 7 5 2 4 6 +--R (- 14b + a b )cosh(x) + (- 83a b + 22a b )cosh(x) +--R + +--R 6 5 2 4 3 3 5 2 4 3 3 +--R ((36b + 36a b - 36a b - 36a b )x + 18a b - 204a b + 93a b ) +--R * +--R 5 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (84a b + 84a b - 84a b - 84a b )x + 18a b + 108a b - 283a b +--R + +--R 4 2 +--R 152a b +--R * +--R 4 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 32b - 32a b + 80a b + 80a b - 48a b - 48a b)x + 18b +--R + +--R 5 2 4 3 3 4 2 5 +--R 21a b + 36a b + 210a b - 244a b + 104a b +--R * +--R 3 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (- 96a b - 96a b + 96a b + 96a b )x + 57a b + 66a b - 6a b +--R + +--R 4 2 5 6 +--R 156a b - 120a b + 24a +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b - 12a b - 60a b - 60a b + 72a b + 72a b)x + 4b +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 4a b + 48a b + 57a b - 36a b + 36a b - 24a +--R * +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 2 4 +--R (- 12a b - 12a b + 4a b + 4a b + 8a b + 8a )x + 4a b + 4a b +--R + +--R 3 3 4 2 5 +--R 9a b + 12a b - 12a b +--R * +--R 2 +--R sinh(x) +--R + +--R 6 8 5 2 4 7 +--R - 6b cosh(x) + (- 42a b + 6a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (30b + 30a b - 30a b - 30a b )x - 6b + 6a b - 120a b +--R + +--R 3 3 +--R 36a b +--R * +--R 6 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (84a b + 84a b - 84a b - 84a b )x - 24a b + 48a b - 186a b +--R + +--R 4 2 +--R 78a b +--R * +--R 5 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 22b - 22a b + 94a b + 94a b - 72a b - 72a b)x + 6b +--R + +--R 5 2 4 3 3 4 2 5 +--R 12a b - 42a b + 126a b - 174a b + 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 72a b - 72a b + 88a b + 88a b - 16a b - 16a )x + 30a b +--R + +--R 2 4 3 3 4 2 5 6 +--R 54a b - 60a b + 132a b - 96a b + 24a +--R * +--R 3 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 6b - 6a b - 66a b - 66a b + 72a b + 72a b)x + 6b + 6a b +--R + +--R 2 4 3 3 4 2 5 6 +--R 36a b + 72a b - 60a b + 48a b - 24a +--R * +--R 2 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 12a b - 12a b - 4a b - 4a b + 16a b + 16a )x + 12a b +--R + +--R 2 4 3 3 4 2 5 +--R 12a b + 6a b + 30a b - 24a b +--R * +--R cosh(x) +--R + +--R 6 5 2 4 3 3 2 4 3 3 4 2 +--R (- 2b - 2a b + 2a b + 2a b )x + 6a b + 6a b - 6a b +--R * +--R sinh(x) +--R + +--R 6 9 5 2 4 8 +--R - b cosh(x) + (- 8a b + a b )cosh(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 3 3 7 +--R ((8b + 8a b - 8a b - 8a b )x - 2b + a b - 26a b + 7a b )cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 +--R (24a b + 24a b - 24a b - 24a b )x - 11a b + 10a b - 45a b +--R + +--R 4 2 +--R 18a b +--R * +--R 6 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 2 4 +--R (- 8b - 8a b + 32a b + 32a b - 24a b - 24a b)x + 3a b - 24a b +--R + +--R 3 3 4 2 5 +--R 33a b - 46a b + 20a b +--R * +--R 5 +--R cosh(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 2 4 +--R (- 24a b - 24a b + 32a b + 32a b - 8a b - 8a )x + 3a b + 18a b +--R + +--R 3 3 4 2 5 6 +--R - 31a b + 44a b - 28a b + 8a +--R * +--R 4 +--R cosh(x) +--R + +--R 2 4 3 3 4 2 5 6 5 2 4 3 3 +--R (- 24a b - 24a b + 24a b + 24a b)x + 2b + 3a b + 6a b + 33a b +--R + +--R 4 2 5 6 +--R - 28a b + 20a b - 8a +--R * +--R 3 +--R cosh(x) +--R + +--R 3 3 4 2 5 6 5 2 4 3 3 4 2 +--R (- 8a b - 8a b + 8a b + 8a )x + 7a b + 10a b - 3a b + 18a b +--R + +--R 5 +--R - 12a b +--R * +--R 2 +--R cosh(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 4 3 3 +--R (b + a b + 4a b + 7a b - 6a b )cosh(x) + a b + a b - a b +--R / +--R 9 8 2 7 3 6 3 +--R (2b - 2a b - 2a b + 2a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 2 +--R (6a b - 6a b - 6a b + 6a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 3 6 4 5 5 4 +--R (6a b - 6a b - 6a b + 6a b )cosh(x) + 2a b - 2a b - 2a b +--R + +--R 6 3 +--R 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 +--R (12b - 12a b - 12a b + 12a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (48a b - 48a b - 48a b + 48a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 2 +--R (72a b - 72a b - 72a b + 72a b )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 4 5 5 4 +--R (48a b - 48a b - 48a b + 48a b )cosh(x) + 12a b - 12a b +--R + +--R 6 3 7 2 +--R - 12a b + 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 5 +--R (30b - 30a b - 30a b + 30a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (150a b - 150a b - 150a b + 150a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 3 +--R (6b - 6a b + 288a b - 288a b - 294a b + 294a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 2 +--R (18a b - 18a b + 264a b - 264a b - 282a b + 282a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R (18a b - 18a b + 114a b - 114a b - 132a b + 132a b )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 6a b - 6a b + 18a b - 18a b - 24a b + 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 6 +--R (40b - 40a b - 40a b + 40a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 +--R (240a b - 240a b - 240a b + 240a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 4 +--R (24b - 24a b + 552a b - 552a b - 576a b + 576a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 3 +--R (96a b - 96a b + 608a b - 608a b - 704a b + 704a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R (144a b - 144a b + 312a b - 312a b - 456a b + 456a b ) +--R * +--R 2 +--R cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R (96a b - 96a b + 48a b - 48a b - 144a b + 144a b)cosh(x) +--R + +--R 4 5 5 4 6 3 7 2 8 9 +--R 24a b - 24a b - 8a b + 8a b - 16a b + 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 7 +--R (30b - 30a b - 30a b + 30a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 6 +--R (210a b - 210a b - 210a b + 210a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 5 +--R (36b - 36a b + 558a b - 558a b - 594a b + 594a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R (180a b - 180a b + 690a b - 690a b - 870a b + 870a b ) +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b - 6a b + 342a b - 342a b + 348a b - 348a b - 696a b +--R + +--R 7 2 +--R 696a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 18a b - 18a b + 306a b - 306a b - 36a b + 36a b +--R + +--R 7 2 8 +--R - 288a b + 288a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R 18a b - 18a b + 126a b - 126a b - 96a b + 96a b - 48a b +--R + +--R 9 +--R 48a +--R * +--R cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 6a b - 6a b + 18a b - 18a b - 24a b + 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 8 +--R (12b - 12a b - 12a b + 12a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 7 +--R (96a b - 96a b - 96a b + 96a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 +--R (24b - 24a b + 288a b - 288a b - 312a b + 312a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R (144a b - 144a b + 384a b - 384a b - 528a b + 528a b ) +--R * +--R 5 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 12b - 12a b + 324a b - 324a b + 156a b - 156a b +--R + +--R 6 3 7 2 +--R - 492a b + 492a b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 48a b - 48a b + 336a b - 336a b - 144a b + 144a b +--R + +--R 7 2 8 +--R - 240a b + 240a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R 72a b - 72a b + 144a b - 144a b - 168a b + 168a b +--R + +--R 8 9 +--R - 48a b + 48a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 6 4 5 7 2 8 4 5 5 4 +--R (48a b - 48a b - 48a b + 48a b)cosh(x) + 12a b - 12a b +--R + +--R 6 3 7 2 +--R - 12a b + 12a b +--R * +--R sinh(x) +--R + +--R 9 8 2 7 3 6 9 +--R (2b - 2a b - 2a b + 2a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 8 +--R (18a b - 18a b - 18a b + 18a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 7 +--R (6b - 6a b + 60a b - 60a b - 66a b + 66a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 6 +--R (42a b - 42a b + 84a b - 84a b - 126a b + 126a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b - 6a b + 108a b - 108a b + 18a b - 18a b - 132a b +--R + +--R 7 2 +--R 132a b +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 30a b - 30a b + 120a b - 120a b - 78a b + 78a b - 72a b +--R + +--R 8 +--R 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 2b - 2a b + 52a b - 52a b + 42a b - 42a b - 80a b + 80a b +--R + +--R 8 9 +--R - 16a b + 16a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 6a b - 6a b + 36a b - 36a b - 18a b + 18a b - 24a b +--R + +--R 8 +--R 24a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 3 6 +--R (6a b - 6a b + 6a b - 6a b - 12a b + 12a b )cosh(x) + 2a b +--R + +--R 4 5 5 4 6 3 +--R - 2a b - 2a b + 2a b +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 9 8 2 7 3 6 3 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 2 +--R (6a b + 6a b - 6a b - 6a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 3 6 4 5 5 4 6 3 +--R (6a b + 6a b - 6a b - 6a b )cosh(x) + 2a b + 2a b - 2a b - 2a b +--R * +--R 6 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 4 +--R (12b + 12a b - 12a b - 12a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (48a b + 48a b - 48a b - 48a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 2 +--R (72a b + 72a b - 72a b - 72a b )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 4 5 5 4 6 3 +--R (48a b + 48a b - 48a b - 48a b )cosh(x) + 12a b + 12a b - 12a b +--R + +--R 7 2 +--R - 12a b +--R * +--R 5 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 5 +--R (30b + 30a b - 30a b - 30a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (150a b + 150a b - 150a b - 150a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 3 +--R (6b + 6a b + 288a b + 288a b - 294a b - 294a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 2 +--R (18a b + 18a b + 264a b + 264a b - 282a b - 282a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R (18a b + 18a b + 114a b + 114a b - 132a b - 132a b )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 6a b + 6a b + 18a b + 18a b - 24a b - 24a b +--R * +--R 4 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 6 +--R (40b + 40a b - 40a b - 40a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 +--R (240a b + 240a b - 240a b - 240a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 4 +--R (24b + 24a b + 552a b + 552a b - 576a b - 576a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 3 +--R (96a b + 96a b + 608a b + 608a b - 704a b - 704a b )cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 2 +--R (144a b + 144a b + 312a b + 312a b - 456a b - 456a b )cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R (96a b + 96a b + 48a b + 48a b - 144a b - 144a b)cosh(x) +--R + +--R 4 5 5 4 6 3 7 2 8 9 +--R 24a b + 24a b - 8a b - 8a b - 16a b - 16a +--R * +--R 3 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 7 +--R (30b + 30a b - 30a b - 30a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 6 +--R (210a b + 210a b - 210a b - 210a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 5 +--R (36b + 36a b + 558a b + 558a b - 594a b - 594a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 4 +--R (180a b + 180a b + 690a b + 690a b - 870a b - 870a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b + 6a b + 342a b + 342a b + 348a b + 348a b - 696a b +--R + +--R 7 2 +--R - 696a b +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 18a b + 18a b + 306a b + 306a b - 36a b - 36a b - 288a b +--R + +--R 8 +--R - 288a b +--R * +--R 2 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R 18a b + 18a b + 126a b + 126a b - 96a b - 96a b - 48a b +--R + +--R 9 +--R - 48a +--R * +--R cosh(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 6a b + 6a b + 18a b + 18a b - 24a b - 24a b +--R * +--R 2 +--R sinh(x) +--R + +--R 9 8 2 7 3 6 8 +--R (12b + 12a b - 12a b - 12a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 7 +--R (96a b + 96a b - 96a b - 96a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 +--R (24b + 24a b + 288a b + 288a b - 312a b - 312a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 5 +--R (144a b + 144a b + 384a b + 384a b - 528a b - 528a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 12b + 12a b + 324a b + 324a b + 156a b + 156a b - 492a b +--R + +--R 7 2 +--R - 492a b +--R * +--R 4 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 48a b + 48a b + 336a b + 336a b - 144a b - 144a b - 240a b +--R + +--R 8 +--R - 240a b +--R * +--R 3 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R 72a b + 72a b + 144a b + 144a b - 168a b - 168a b - 48a b +--R + +--R 9 +--R - 48a +--R * +--R 2 +--R cosh(x) +--R + +--R 3 6 4 5 7 2 8 4 5 5 4 6 3 +--R (48a b + 48a b - 48a b - 48a b)cosh(x) + 12a b + 12a b - 12a b +--R + +--R 7 2 +--R - 12a b +--R * +--R sinh(x) +--R + +--R 9 8 2 7 3 6 9 +--R (2b + 2a b - 2a b - 2a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 8 +--R (18a b + 18a b - 18a b - 18a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 7 +--R (6b + 6a b + 60a b + 60a b - 66a b - 66a b )cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 6 +--R (42a b + 42a b + 84a b + 84a b - 126a b - 126a b )cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (6b + 6a b + 108a b + 108a b + 18a b + 18a b - 132a b - 132a b ) +--R * +--R 5 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 30a b + 30a b + 120a b + 120a b - 78a b - 78a b - 72a b +--R + +--R 8 +--R - 72a b +--R * +--R 4 +--R cosh(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 2b + 2a b + 52a b + 52a b + 42a b + 42a b - 80a b - 80a b +--R + +--R 8 9 +--R - 16a b - 16a +--R * +--R 3 +--R cosh(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (6a b + 6a b + 36a b + 36a b - 18a b - 18a b - 24a b - 24a b) +--R * +--R 2 +--R cosh(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 3 6 4 5 +--R (6a b + 6a b + 6a b + 6a b - 12a b - 12a b )cosh(x) + 2a b + 2a b +--R + +--R 5 4 6 3 +--R - 2a b - 2a b +--R Type: Expression(Integer) +--E 289 + +--S 290 of 518 +t0955:= x*sech(x)^2/(a+b*tanh(x))^2 +--R +--R +--R 2 +--R x sech(x) +--R (279) ------------------------------ +--R 2 2 2 +--R b tanh(x) + 2a b tanh(x) + a +--R Type: Expression(Integer) +--E 290 + +--S 291 of 518 +r0955:= a*x/b/(a^2-b^2)-log(a*cosh(x)+b*sinh(x))/(a^2-b^2)-x/b/(a+b*tanh(x)) +--R +--R +--R (b tanh(x) + a)log(b sinh(x) + a cosh(x)) - a x tanh(x) - b x +--R (280) ------------------------------------------------------------- +--R 3 2 2 3 +--R (b - a b)tanh(x) + a b - a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 518 +a0955:= integrate(t0955,x) +--R +--R +--R (281) +--R 2 2 +--R ((b + a)sinh(x) + (2b + 2a)cosh(x)sinh(x) + (b + a)cosh(x) - b + a) +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (- 2b - 2a)x sinh(x) + (- 4b - 4a)x cosh(x)sinh(x) + (- 2b - 2a)x cosh(x) +--R / +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )sinh(x) + (2b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )cosh(x) - b + a b + a b - a +--R Type: Union(Expression(Integer),...) +--E 292 + +--S 293 of 518 +m0955:= a0955-r0955 +--R +--R +--R (282) +--R 2 2 2 +--R (- b - a b)sinh(x) + (- 2b - 2a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- b - a b)cosh(x) + b - a b +--R * +--R tanh(x) +--R + +--R 2 2 2 +--R (- a b - a )sinh(x) + (- 2a b - 2a )cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (- a b - a )cosh(x) + a b - a +--R * +--R log(b sinh(x) + a cosh(x)) +--R + +--R 2 2 2 +--R (b + a b)sinh(x) + (2b + 2a b)cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (b + a b)cosh(x) - b + a b +--R * +--R tanh(x) +--R + +--R 2 2 2 2 2 +--R (a b + a )sinh(x) + (2a b + 2a )cosh(x)sinh(x) + (a b + a )cosh(x) +--R + +--R 2 +--R - a b + a +--R * +--R - 2b sinh(x) - 2a cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b - a b + a )x sinh(x) + (- 4b - 2a b + 2a )x cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (- 2b - a b + a )x cosh(x) + (- a b + a )x +--R * +--R tanh(x) +--R + +--R 2 2 2 2 2 +--R (b - a b - 2a )x sinh(x) + (2b - 2a b - 4a )x cosh(x)sinh(x) +--R + +--R 2 2 2 2 +--R (b - a b - 2a )x cosh(x) + (- b + a b)x +--R / +--R 4 3 2 2 3 2 +--R (b + a b - a b - a b)sinh(x) +--R + +--R 4 3 2 2 3 +--R (2b + 2a b - 2a b - 2a b)cosh(x)sinh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (b + a b - a b - a b)cosh(x) - b + a b + a b - a b +--R * +--R tanh(x) +--R + +--R 3 2 2 3 4 2 +--R (a b + a b - a b - a )sinh(x) +--R + +--R 3 2 2 3 4 +--R (2a b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (a b + a b - a b - a )cosh(x) - a b + a b + a b - a +--R Type: Expression(Integer) +--E 293 + +--S 294 of 518 +d0955:= D(m0955,x) +--R +--R +--R (283) +--R 2 2 2 4 +--R ((b + 2a b + a )x - b - a b)sinh(x) +--R + +--R 2 2 2 3 +--R ((4b + 8a b + 4a )x - 4b - 4a b)cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (((6b + 12a b + 6a )x - 6b - 6a b)cosh(x) + (2b + 2a )x - 2a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 3 +--R ((4b + 8a b + 4a )x - 4b - 4a b)cosh(x) +--R + +--R 2 2 +--R ((4b + 4a )x - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 4 +--R ((b + 2a b + a )x - b - a b)cosh(x) +--R + +--R 2 2 2 2 2 2 +--R ((2b + 2a )x - 2a b)cosh(x) + (b - 2a b + a )x + b - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 2 2 4 2 2 3 +--R (b - a )sinh(x) + (4b - 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b - 6a )cosh(x) + 8a b x - 2b - 2a )sinh(x) +--R + +--R 2 2 3 2 2 +--R ((4b - 4a )cosh(x) + (16a b x - 4b - 4a )cosh(x))sinh(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R (b - a )cosh(x) + (8a b x - 2b - 2a )cosh(x) + b - a +--R * +--R tanh(x) +--R + +--R 2 2 2 4 +--R ((- b - 2a b - a )x + a b + a )sinh(x) +--R + +--R 2 2 2 3 +--R ((- 4b - 8a b - 4a )x + 4a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (((- 6b - 12a b - 6a )x + 6a b + 6a )cosh(x) + (2b + 2a )x - 2a b) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 3 +--R ((- 4b - 8a b - 4a )x + 4a b + 4a )cosh(x) +--R + +--R 2 2 +--R ((4b + 4a )x - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 4 2 2 2 +--R ((- b - 2a b - a )x + a b + a )cosh(x) + ((2b + 2a )x - 2a b)cosh(x) +--R + +--R 2 2 2 +--R (- b + 2a b - a )x + a b - a +--R / +--R 4 3 2 2 4 4 3 2 2 3 +--R (b + 2a b + a b )sinh(x) + (4b + 8a b + 4a b )cosh(x)sinh(x) +--R + +--R 4 3 2 2 2 4 2 2 2 +--R ((6b + 12a b + 6a b )cosh(x) - 2b + 2a b )sinh(x) +--R + +--R 4 3 2 2 3 4 2 2 +--R ((4b + 8a b + 4a b )cosh(x) + (- 4b + 4a b )cosh(x))sinh(x) +--R + +--R 4 3 2 2 4 4 2 2 2 4 3 +--R (b + 2a b + a b )cosh(x) + (- 2b + 2a b )cosh(x) + b - 2a b +--R + +--R 2 2 +--R a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 2 3 4 +--R (2a b + 4a b + 2a b)sinh(x) +--R + +--R 3 2 2 3 3 +--R (8a b + 16a b + 8a b)cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 3 2 +--R ((12a b + 24a b + 12a b)cosh(x) - 4a b + 4a b)sinh(x) +--R + +--R 3 2 2 3 3 3 3 +--R ((8a b + 16a b + 8a b)cosh(x) + (- 8a b + 8a b)cosh(x))sinh(x) +--R + +--R 3 2 2 3 4 3 3 2 3 +--R (2a b + 4a b + 2a b)cosh(x) + (- 4a b + 4a b)cosh(x) + 2a b +--R + +--R 2 2 3 +--R - 4a b + 2a b +--R * +--R tanh(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (a b + 2a b + a )sinh(x) + (4a b + 8a b + 4a )cosh(x)sinh(x) +--R + +--R 2 2 3 4 2 2 2 4 2 +--R ((6a b + 12a b + 6a )cosh(x) - 2a b + 2a )sinh(x) +--R + +--R 2 2 3 4 3 2 2 4 +--R ((4a b + 8a b + 4a )cosh(x) + (- 4a b + 4a )cosh(x))sinh(x) +--R + +--R 2 2 3 4 4 2 2 4 2 2 2 3 4 +--R (a b + 2a b + a )cosh(x) + (- 2a b + 2a )cosh(x) + a b - 2a b + a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 518 +t0956:= x*csch(x)^2/(a+b*coth(x))^2 +--R +--R +--R 2 +--R x csch(x) +--R (284) ------------------------------ +--R 2 2 2 +--R b coth(x) + 2a b coth(x) + a +--R Type: Expression(Integer) +--E 295 + +--S 296 of 518 +r0956:= -a*x/b/(a^2-b^2)+x/b/(a+b*coth(x))+log(b*cosh(x)+a*sinh(x))/(a^2-b^2) +--R +--R +--R (- b coth(x) - a)log(a sinh(x) + b cosh(x)) + a x coth(x) + b x +--R (285) --------------------------------------------------------------- +--R 3 2 2 3 +--R (b - a b)coth(x) + a b - a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 518 +a0956:= integrate(t0956,x) +--R +--R +--R (286) +--R 2 2 +--R (- b - a)sinh(x) + (- 2b - 2a)cosh(x)sinh(x) + (- b - a)cosh(x) - b +--R + +--R a +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 +--R (2b + 2a)x sinh(x) + (4b + 4a)x cosh(x)sinh(x) + (2b + 2a)x cosh(x) +--R / +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )sinh(x) + (2b + 2a b - 2a b - 2a )cosh(x)sinh(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + a b - a b - a )cosh(x) + b - a b - a b + a +--R Type: Union(Expression(Integer),...) +--E 297 + +--S 298 of 518 +m0956:= a0956-r0956 +--R +--R +--R (287) +--R 2 2 2 +--R ((b + a b)coth(x) + a b + a )sinh(x) +--R + +--R 2 2 +--R ((2b + 2a b)cosh(x)coth(x) + (2a b + 2a )cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((b + a b)cosh(x) + b - a b)coth(x) + (a b + a )cosh(x) + a b - a +--R * +--R log(a sinh(x) + b cosh(x)) +--R + +--R 2 2 2 +--R ((- b - a b)coth(x) - a b - a )sinh(x) +--R + +--R 2 2 +--R ((- 2b - 2a b)cosh(x)coth(x) + (- 2a b - 2a )cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 +--R ((- b - a b)cosh(x) - b + a b)coth(x) + (- a b - a )cosh(x) - a b +--R + +--R 2 +--R a +--R * +--R - 2a sinh(x) - 2b cosh(x) +--R log(-------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 2 2 2 2 +--R ((2b + a b - a )x coth(x) + (- b + a b + 2a )x)sinh(x) +--R + +--R 2 2 2 2 +--R ((4b + 2a b - 2a )x cosh(x)coth(x) + (- 2b + 2a b + 4a )x cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 2 2 2 +--R ((2b + a b - a )x cosh(x) + (- a b + a )x)coth(x) +--R + +--R 2 2 2 2 +--R (- b + a b + 2a )x cosh(x) + (- b + a b)x +--R / +--R 4 3 2 2 3 3 2 2 3 4 2 +--R ((b + a b - a b - a b)coth(x) + a b + a b - a b - a )sinh(x) +--R + +--R 4 3 2 2 3 +--R (2b + 2a b - 2a b - 2a b)cosh(x)coth(x) +--R + +--R 3 2 2 3 4 +--R (2a b + 2a b - 2a b - 2a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R ((b + a b - a b - a b)cosh(x) + b - a b - a b + a b)coth(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (a b + a b - a b - a )cosh(x) + a b - a b - a b + a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 518 +d0956:= D(m0956,x) +--R +--R +--R (288) +--R 2 2 2 2 2 2 +--R ((- b - 2a b - a )x + b + a b)coth(x) + (- b + a )coth(x) +--R + +--R 2 2 2 +--R (b + 2a b + a )x - a b - a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 2 2 +--R ((- 4b - 8a b - 4a )x + 4b + 4a b)cosh(x)coth(x) +--R + +--R 2 2 2 2 2 +--R (- 4b + 4a )cosh(x)coth(x) + ((4b + 8a b + 4a )x - 4a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 6b - 12a b - 6a )x + 6b + 6a b)cosh(x) + (2b + 2a )x +--R + +--R - 2a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 2 2 2 +--R ((- 6b + 6a )cosh(x) + 8a b x - 2b - 2a )coth(x) +--R + +--R 2 2 2 2 2 2 +--R ((6b + 12a b + 6a )x - 6a b - 6a )cosh(x) + (2b + 2a )x - 2a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 2 3 +--R ((- 4b - 8a b - 4a )x + 4b + 4a b)cosh(x) +--R + +--R 2 2 +--R ((4b + 4a )x - 4a b)cosh(x) +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 3 2 2 +--R ((- 4b + 4a )cosh(x) + (16a b x - 4b - 4a )cosh(x))coth(x) +--R + +--R 2 2 2 3 +--R ((4b + 8a b + 4a )x - 4a b - 4a )cosh(x) +--R + +--R 2 2 +--R ((4b + 4a )x - 4a b)cosh(x) +--R * +--R sinh(x) +--R + +--R 2 2 2 4 +--R ((- b - 2a b - a )x + b + a b)cosh(x) +--R + +--R 2 2 2 2 2 2 +--R ((2b + 2a )x - 2a b)cosh(x) + (- b + 2a b - a )x - b + a b +--R * +--R 2 +--R coth(x) +--R + +--R 2 2 4 2 2 2 2 2 +--R ((- b + a )cosh(x) + (8a b x - 2b - 2a )cosh(x) - b + a )coth(x) +--R + +--R 2 2 2 4 2 2 2 +--R ((b + 2a b + a )x - a b - a )cosh(x) + ((2b + 2a )x - 2a b)cosh(x) +--R + +--R 2 2 2 +--R (b - 2a b + a )x - a b + a +--R / +--R 4 3 2 2 2 3 2 2 3 2 2 +--R (b + 2a b + a b )coth(x) + (2a b + 4a b + 2a b)coth(x) + a b +--R + +--R 3 4 +--R 2a b + a +--R * +--R 4 +--R sinh(x) +--R + +--R 4 3 2 2 2 +--R (4b + 8a b + 4a b )cosh(x)coth(x) +--R + +--R 3 2 2 3 2 2 3 4 +--R (8a b + 16a b + 8a b)cosh(x)coth(x) + (4a b + 8a b + 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 4 3 2 2 2 4 2 2 2 +--R ((6b + 12a b + 6a b )cosh(x) + 2b - 2a b )coth(x) +--R + +--R 3 2 2 3 2 3 3 +--R ((12a b + 24a b + 12a b)cosh(x) + 4a b - 4a b)coth(x) +--R + +--R 2 2 3 4 2 2 2 4 +--R (6a b + 12a b + 6a )cosh(x) + 2a b - 2a +--R * +--R 2 +--R sinh(x) +--R + +--R 4 3 2 2 3 4 2 2 2 +--R ((4b + 8a b + 4a b )cosh(x) + (4b - 4a b )cosh(x))coth(x) +--R + +--R 3 2 2 3 3 3 3 +--R ((8a b + 16a b + 8a b)cosh(x) + (8a b - 8a b)cosh(x))coth(x) +--R + +--R 2 2 3 4 3 2 2 4 +--R (4a b + 8a b + 4a )cosh(x) + (4a b - 4a )cosh(x) +--R * +--R sinh(x) +--R + +--R 4 3 2 2 4 4 2 2 2 4 3 +--R (b + 2a b + a b )cosh(x) + (2b - 2a b )cosh(x) + b - 2a b +--R + +--R 2 2 +--R a b +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 2 3 4 3 3 2 3 +--R (2a b + 4a b + 2a b)cosh(x) + (4a b - 4a b)cosh(x) + 2a b +--R + +--R 2 2 3 +--R - 4a b + 2a b +--R * +--R coth(x) +--R + +--R 2 2 3 4 4 2 2 4 2 2 2 3 4 +--R (a b + 2a b + a )cosh(x) + (2a b - 2a )cosh(x) + a b - 2a b + a +--R Type: Expression(Integer) +--E 299 + +--S 300 of 518 +t0957:= (a+b*sech(x))/(c+d*cosh(x)) +--R +--R +--R b sech(x) + a +--R (289) ------------- +--R d cosh(x) + c +--R Type: Expression(Integer) +--E 300 + +--S 301 of 518 +r0957:= b*atan(sinh(x))/c+2*(a*c-b*d)*atanh((c-d)*tanh(1/2*x)/_ + (c^2-d^2)^(1/2))/c/(c^2-d^2)^(1/2) +--R +--R +--R x +--R (d - c)tanh(-) +---------+ +--R 2 | 2 2 +--R (2b d - 2a c)atanh(--------------) + b\|- d + c atan(sinh(x)) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R (290) --------------------------------------------------------------- +--R +---------+ +--R | 2 2 +--R c\|- d + c +--R Type: Expression(Integer) +--E 301 + +--S 302 of 518 +a0957:= integrate(t0957,x) +--R +--R +--R (291) +--R [ +--R (b d - a c) +--R * +--R log +--R 2 2 2 2 2 +--R d sinh(x) + (2d cosh(x) + 2c d)sinh(x) + d cosh(x) +--R + +--R 2 2 +--R 2c d cosh(x) - d + 2c +--R * +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R 3 2 3 2 2 3 +--R (- 2d + 2c d)sinh(x) + (- 2d + 2c d)cosh(x) - 2c d + 2c +--R / +--R 2 2 +--R d sinh(x) + (2d cosh(x) + 2c)sinh(x) + d cosh(x) +--R + +--R 2c cosh(x) + d +--R + +--R +---------+ +--R | 2 2 +--R 2b\|- d + c atan(sinh(x) + cosh(x)) +--R / +--R +---------+ +--R | 2 2 +--R c\|- d + c +--R , +--R +--R +-------+ +--R | 2 2 +--R (d sinh(x) + d cosh(x) + c)\|d - c +--R (- 2b d + 2a c)atan(-------------------------------------) +--R 2 2 +--R d - c +--R + +--R +-------+ +--R | 2 2 +--R 2b\|d - c atan(sinh(x) + cosh(x)) +--R / +--R +-------+ +--R | 2 2 +--R c\|d - c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 302 + +--S 303 of 518 +m0957a:= a0957.1-r0957 +--R +--R +--R (292) +--R (b d - a c) +--R * +--R log +--R 2 2 2 2 2 +--R d sinh(x) + (2d cosh(x) + 2c d)sinh(x) + d cosh(x) +--R + +--R 2 2 +--R 2c d cosh(x) - d + 2c +--R * +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R 3 2 3 2 2 3 +--R (- 2d + 2c d)sinh(x) + (- 2d + 2c d)cosh(x) - 2c d + 2c +--R / +--R 2 2 +--R d sinh(x) + (2d cosh(x) + 2c)sinh(x) + d cosh(x) + 2c cosh(x) +--R + +--R d +--R + +--R x +--R (d - c)tanh(-) +--R 2 +--R (- 2b d + 2a c)atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +---------+ +---------+ +--R | 2 2 | 2 2 +--R 2b\|- d + c atan(sinh(x) + cosh(x)) - b\|- d + c atan(sinh(x)) +--R / +--R +---------+ +--R | 2 2 +--R c\|- d + c +--R Type: Expression(Integer) +--E 303 + +--S 304 of 518 +d0957a:= D(m0957a,x) +--R +--R +--R (293) +--R 2 6 +--R (- b d + a c d)sinh(x) +--R + +--R 2 5 +--R ((- 4b d + 4a c d)cosh(x) + (- 2b + 2a)c d)sinh(x) +--R + +--R 2 2 2 +--R (- 6b d + 6a c d)cosh(x) + (- b d + (- 5b + 6a)c d)cosh(x) +--R + +--R 2 2 +--R - 3b d + (4b + 3a)c d - 4b c +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 4b d + 4a c d)cosh(x) + (- 4b d + (- 2b + 6a)c d)cosh(x) +--R + +--R 2 2 +--R (- 8b d + (6b + 8a)c d - 6b c )cosh(x) + (- 4b + 4a)c d +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 +--R (- b d + a c d)cosh(x) + (- 6b d + (4b + 2a)c d)cosh(x) +--R + +--R 2 2 2 +--R (- 8b d + (- 2b + 8a)c d + 2b c )cosh(x) +--R + +--R 2 2 2 +--R (- 2b d + (- 6b + 8a)c d)cosh(x) - 3b d + (4b + 3a)c d - 4b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 +--R (- 4b d + 4b c d)cosh(x) +--R + +--R 2 2 3 +--R (- 4b d + (- 6b + 4a)c d + 6b c )cosh(x) +--R + +--R 2 2 +--R (- 4b d + (- 2b + 6a)c d)cosh(x) +--R + +--R 2 2 +--R (- 4b d + (6b + 4a)c d - 6b c )cosh(x) + (- 2b + 2a)c d +--R * +--R sinh(x) +--R + +--R 2 5 2 2 4 +--R (- b d + b c d)cosh(x) + (- b d + (- 2b + a)c d + 2b c )cosh(x) +--R + +--R 2 3 2 2 2 +--R (- 2b d + 2a c d)cosh(x) + (- 2b d + (2b + 2a)c d - 2b c )cosh(x) +--R + +--R 2 2 +--R (- b d + (- b + 2a)c d)cosh(x) - b d + a c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 5 +--R (b d - a c d)sinh(x) + ((4b d - 4a c d)cosh(x) + (2b + 2a)c d)sinh(x) +--R + +--R 2 2 2 2 +--R (6b d - 6a c d)cosh(x) + (- b d + (5b + 6a)c d)cosh(x) + 3b d +--R + +--R 2 +--R (4b - 3a)c d + 4b c +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4b d - 4a c d)cosh(x) + (- 4b d + (2b + 6a)c d)cosh(x) +--R + +--R 2 2 +--R (8b d + (6b - 8a)c d + 6b c )cosh(x) + (4b + 4a)c d +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 +--R (b d - a c d)cosh(x) + (- 6b d + (- 4b + 2a)c d)cosh(x) +--R + +--R 2 2 2 +--R (8b d + (- 2b - 8a)c d - 2b c )cosh(x) +--R + +--R 2 2 2 +--R (- 2b d + (6b + 8a)c d)cosh(x) + 3b d + (4b - 3a)c d + 4b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 2 3 +--R (- 4b d - 4b c d)cosh(x) + (4b d + (- 6b - 4a)c d - 6b c )cosh(x) +--R + +--R 2 2 +--R (- 4b d + (2b + 6a)c d)cosh(x) +--R + +--R 2 2 +--R (4b d + (6b - 4a)c d + 6b c )cosh(x) + (2b + 2a)c d +--R * +--R sinh(x) +--R + +--R 2 5 2 2 4 +--R (- b d - b c d)cosh(x) + (b d + (- 2b - a)c d - 2b c )cosh(x) +--R + +--R 2 3 2 2 2 +--R (- 2b d + 2a c d)cosh(x) + (2b d + (2b - 2a)c d + 2b c )cosh(x) +--R + +--R 2 2 +--R (- b d + (b + 2a)c d)cosh(x) + b d - a c d +--R / +--R 2 2 6 2 2 2 3 5 +--R (c d - c d)sinh(x) + ((4c d - 4c d)cosh(x) + 2c d - 2c )sinh(x) +--R + +--R 2 2 2 2 3 2 2 4 +--R ((6c d - 6c d)cosh(x) + (6c d - 6c )cosh(x) + 3c d - 3c d)sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (4c d - 4c d)cosh(x) + (6c d - 6c )cosh(x) +--R + +--R 2 2 2 3 +--R (8c d - 8c d)cosh(x) + 4c d - 4c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (c d - c d)cosh(x) + (2c d - 2c )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (8c d - 8c d)cosh(x) + (8c d - 8c )cosh(x) + 3c d - 3c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (4c d - 4c d)cosh(x) + (6c d - 6c )cosh(x) +--R + +--R 2 2 2 3 +--R (4c d - 4c d)cosh(x) + 2c d - 2c +--R * +--R sinh(x) +--R + +--R 2 2 4 2 3 3 2 2 2 +--R (c d - c d)cosh(x) + (2c d - 2c )cosh(x) + (2c d - 2c d)cosh(x) +--R + +--R 2 3 2 2 +--R (2c d - 2c )cosh(x) + c d - c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 6 2 2 2 3 5 +--R (c d + c d)sinh(x) + ((4c d + 4c d)cosh(x) + 2c d + 2c )sinh(x) +--R + +--R 2 2 2 2 3 2 2 4 +--R ((6c d + 6c d)cosh(x) + (6c d + 6c )cosh(x) + 3c d + 3c d)sinh(x) +--R + +--R 2 2 3 2 3 2 2 2 +--R (4c d + 4c d)cosh(x) + (6c d + 6c )cosh(x) + (8c d + 8c d)cosh(x) +--R + +--R 2 3 +--R 4c d + 4c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 2 2 2 +--R (c d + c d)cosh(x) + (2c d + 2c )cosh(x) + (8c d + 8c d)cosh(x) +--R + +--R 2 3 2 2 +--R (8c d + 8c )cosh(x) + 3c d + 3c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 2 2 +--R (4c d + 4c d)cosh(x) + (6c d + 6c )cosh(x) + (4c d + 4c d)cosh(x) +--R + +--R 2 3 +--R 2c d + 2c +--R * +--R sinh(x) +--R + +--R 2 2 4 2 3 3 2 2 2 +--R (c d + c d)cosh(x) + (2c d + 2c )cosh(x) + (2c d + 2c d)cosh(x) +--R + +--R 2 3 2 2 +--R (2c d + 2c )cosh(x) + c d + c d +--R Type: Expression(Integer) +--E 304 + +--S 305 of 518 +m0957b:= a0957.2-r0957 +--R +--R +--R (294) +--R x +--R +-------+ (d - c)tanh(-) +--R | 2 2 2 +--R (- 2b d + 2a c)\|d - c atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (d sinh(x) + d cosh(x) + c)\|d - c +--R (- 2b d + 2a c)\|- d + c atan(-------------------------------------) +--R 2 2 +--R d - c +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R 2b\|- d + c \|d - c atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R - b\|- d + c \|d - c atan(sinh(x)) +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R c\|- d + c \|d - c +--R Type: Expression(Integer) +--E 305 + +--S 306 of 518 +d0957b:= D(m0957b,x) +--R +--R +--R (295) +--R 2 6 +--R (- b d + a c d)sinh(x) +--R + +--R 2 5 +--R ((- 4b d + 4a c d)cosh(x) + (- 2b + 2a)c d)sinh(x) +--R + +--R 2 2 2 +--R (- 6b d + 6a c d)cosh(x) + (- b d + (- 5b + 6a)c d)cosh(x) +--R + +--R 2 2 +--R - 3b d + (4b + 3a)c d - 4b c +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (- 4b d + 4a c d)cosh(x) + (- 4b d + (- 2b + 6a)c d)cosh(x) +--R + +--R 2 2 +--R (- 8b d + (6b + 8a)c d - 6b c )cosh(x) + (- 4b + 4a)c d +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 +--R (- b d + a c d)cosh(x) + (- 6b d + (4b + 2a)c d)cosh(x) +--R + +--R 2 2 2 +--R (- 8b d + (- 2b + 8a)c d + 2b c )cosh(x) +--R + +--R 2 2 2 +--R (- 2b d + (- 6b + 8a)c d)cosh(x) - 3b d + (4b + 3a)c d - 4b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 +--R (- 4b d + 4b c d)cosh(x) +--R + +--R 2 2 3 +--R (- 4b d + (- 6b + 4a)c d + 6b c )cosh(x) +--R + +--R 2 2 +--R (- 4b d + (- 2b + 6a)c d)cosh(x) +--R + +--R 2 2 +--R (- 4b d + (6b + 4a)c d - 6b c )cosh(x) + (- 2b + 2a)c d +--R * +--R sinh(x) +--R + +--R 2 5 2 2 4 +--R (- b d + b c d)cosh(x) + (- b d + (- 2b + a)c d + 2b c )cosh(x) +--R + +--R 2 3 2 2 2 +--R (- 2b d + 2a c d)cosh(x) + (- 2b d + (2b + 2a)c d - 2b c )cosh(x) +--R + +--R 2 2 +--R (- b d + (- b + 2a)c d)cosh(x) - b d + a c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 6 2 5 +--R (b d - a c d)sinh(x) + ((4b d - 4a c d)cosh(x) + (2b + 2a)c d)sinh(x) +--R + +--R 2 2 2 2 +--R (6b d - 6a c d)cosh(x) + (- b d + (5b + 6a)c d)cosh(x) + 3b d +--R + +--R 2 +--R (4b - 3a)c d + 4b c +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 +--R (4b d - 4a c d)cosh(x) + (- 4b d + (2b + 6a)c d)cosh(x) +--R + +--R 2 2 +--R (8b d + (6b - 8a)c d + 6b c )cosh(x) + (4b + 4a)c d +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 3 +--R (b d - a c d)cosh(x) + (- 6b d + (- 4b + 2a)c d)cosh(x) +--R + +--R 2 2 2 +--R (8b d + (- 2b - 8a)c d - 2b c )cosh(x) +--R + +--R 2 2 2 +--R (- 2b d + (6b + 8a)c d)cosh(x) + 3b d + (4b - 3a)c d + 4b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 2 2 3 +--R (- 4b d - 4b c d)cosh(x) + (4b d + (- 6b - 4a)c d - 6b c )cosh(x) +--R + +--R 2 2 +--R (- 4b d + (2b + 6a)c d)cosh(x) +--R + +--R 2 2 +--R (4b d + (6b - 4a)c d + 6b c )cosh(x) + (2b + 2a)c d +--R * +--R sinh(x) +--R + +--R 2 5 2 2 4 +--R (- b d - b c d)cosh(x) + (b d + (- 2b - a)c d - 2b c )cosh(x) +--R + +--R 2 3 2 2 2 +--R (- 2b d + 2a c d)cosh(x) + (2b d + (2b - 2a)c d + 2b c )cosh(x) +--R + +--R 2 2 +--R (- b d + (b + 2a)c d)cosh(x) + b d - a c d +--R / +--R 2 2 6 2 2 2 3 5 +--R (c d - c d)sinh(x) + ((4c d - 4c d)cosh(x) + 2c d - 2c )sinh(x) +--R + +--R 2 2 2 2 3 2 2 4 +--R ((6c d - 6c d)cosh(x) + (6c d - 6c )cosh(x) + 3c d - 3c d)sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (4c d - 4c d)cosh(x) + (6c d - 6c )cosh(x) +--R + +--R 2 2 2 3 +--R (8c d - 8c d)cosh(x) + 4c d - 4c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (c d - c d)cosh(x) + (2c d - 2c )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (8c d - 8c d)cosh(x) + (8c d - 8c )cosh(x) + 3c d - 3c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (4c d - 4c d)cosh(x) + (6c d - 6c )cosh(x) +--R + +--R 2 2 2 3 +--R (4c d - 4c d)cosh(x) + 2c d - 2c +--R * +--R sinh(x) +--R + +--R 2 2 4 2 3 3 2 2 2 +--R (c d - c d)cosh(x) + (2c d - 2c )cosh(x) + (2c d - 2c d)cosh(x) +--R + +--R 2 3 2 2 +--R (2c d - 2c )cosh(x) + c d - c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 6 2 2 2 3 5 +--R (c d + c d)sinh(x) + ((4c d + 4c d)cosh(x) + 2c d + 2c )sinh(x) +--R + +--R 2 2 2 2 3 2 2 4 +--R ((6c d + 6c d)cosh(x) + (6c d + 6c )cosh(x) + 3c d + 3c d)sinh(x) +--R + +--R 2 2 3 2 3 2 2 2 +--R (4c d + 4c d)cosh(x) + (6c d + 6c )cosh(x) + (8c d + 8c d)cosh(x) +--R + +--R 2 3 +--R 4c d + 4c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 2 2 2 +--R (c d + c d)cosh(x) + (2c d + 2c )cosh(x) + (8c d + 8c d)cosh(x) +--R + +--R 2 3 2 2 +--R (8c d + 8c )cosh(x) + 3c d + 3c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 2 2 +--R (4c d + 4c d)cosh(x) + (6c d + 6c )cosh(x) + (4c d + 4c d)cosh(x) +--R + +--R 2 3 +--R 2c d + 2c +--R * +--R sinh(x) +--R + +--R 2 2 4 2 3 3 2 2 2 +--R (c d + c d)cosh(x) + (2c d + 2c )cosh(x) + (2c d + 2c d)cosh(x) +--R + +--R 2 3 2 2 +--R (2c d + 2c )cosh(x) + c d + c d +--R Type: Expression(Integer) +--E 306 + +--S 307 of 518 +t0958:= (a+b*csch(x))/(c+d*sinh(x)) +--R +--R +--R b csch(x) + a +--R (296) ------------- +--R d sinh(x) + c +--R Type: Expression(Integer) +--E 307 + +--S 308 of 518 +r0958:= -b*acoth(cosh(x))/c-2*(a*c-b*d)*atanh((d-c*tanh(1/2*x))/_ + (d^2+c^2)^(1/2))/c/(d^2+c^2)^(1/2) +--R +--R +--R x +--R c tanh(-) - d +-------+ +--R 2 | 2 2 +--R (- 2b d + 2a c)atanh(-------------) - b\|d + c acoth(cosh(x)) +--R +-------+ +--R | 2 2 +--R \|d + c +--R (297) --------------------------------------------------------------- +--R +-------+ +--R | 2 2 +--R c\|d + c +--R Type: Expression(Integer) +--E 308 + +--S 309 of 518 +a0958:= integrate(t0958,x) +--R +--R +--R (298) +--R (b d - a c) +--R * +--R log +--R 2 2 2 2 2 +--R d sinh(x) + (2d cosh(x) + 2c d)sinh(x) + d cosh(x) +--R + +--R 2 2 +--R 2c d cosh(x) + d + 2c +--R * +--R +-------+ +--R | 2 2 +--R \|d + c +--R + +--R 3 2 3 2 2 3 +--R (2d + 2c d)sinh(x) + (2d + 2c d)cosh(x) + 2c d + 2c +--R / +--R 2 2 +--R d sinh(x) + (2d cosh(x) + 2c)sinh(x) + d cosh(x) + 2c cosh(x) +--R + +--R - d +--R + +--R +-------+ +--R | 2 2 +--R - b\|d + c log(sinh(x) + cosh(x) + 1) +--R + +--R +-------+ +--R | 2 2 +--R b\|d + c log(sinh(x) + cosh(x) - 1) +--R / +--R +-------+ +--R | 2 2 +--R c\|d + c +--R Type: Union(Expression(Integer),...) +--E 309 + +--S 310 of 518 +m0958:= a0958-r0958 +--R +--R +--R (299) +--R (b d - a c) +--R * +--R log +--R 2 2 2 2 2 +--R d sinh(x) + (2d cosh(x) + 2c d)sinh(x) + d cosh(x) +--R + +--R 2 2 +--R 2c d cosh(x) + d + 2c +--R * +--R +-------+ +--R | 2 2 +--R \|d + c +--R + +--R 3 2 3 2 2 3 +--R (2d + 2c d)sinh(x) + (2d + 2c d)cosh(x) + 2c d + 2c +--R / +--R 2 2 +--R d sinh(x) + (2d cosh(x) + 2c)sinh(x) + d cosh(x) + 2c cosh(x) +--R + +--R - d +--R + +--R +-------+ +--R | 2 2 +--R - b\|d + c log(sinh(x) + cosh(x) + 1) +--R + +--R x +--R +-------+ c tanh(-) - d +--R | 2 2 2 +--R b\|d + c log(sinh(x) + cosh(x) - 1) + (2b d - 2a c)atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|d + c +--R + +--R +-------+ +--R | 2 2 +--R b\|d + c acoth(cosh(x)) +--R / +--R +-------+ +--R | 2 2 +--R c\|d + c +--R Type: Expression(Integer) +--E 310 + +--S 311 of 518 +d0958:= D(m0958,x) +--R +--R +--R (300) +--R 5 +--R - b c d sinh(x) +--R + +--R 2 2 2 2 +--R ((b d - a c d)cosh(x) - 4b c d cosh(x) - b d + a c d - 2b c ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 +--R (4b d - 4a c d)cosh(x) - 4b c d cosh(x) +--R + +--R 2 2 +--R (- 4b d + 4a c d - 6b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 +--R (6b d - 6a c d)cosh(x) + 2b c d cosh(x) +--R + +--R 2 2 2 2 +--R (- 8b d + 8a c d - 2b c )cosh(x) - 2b c d cosh(x) + 2b d +--R + +--R 2 +--R - 2a c d - 2b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 +--R (4b d - 4a c d)cosh(x) + 5b c d cosh(x) +--R + +--R 2 2 3 2 +--R (- 8b d + 8a c d + 6b c )cosh(x) - 6b c d cosh(x) +--R + +--R 2 2 +--R (4b d - 4a c d - 6b c )cosh(x) + b c d +--R * +--R sinh(x) +--R + +--R 2 6 5 +--R (b d - a c d)cosh(x) + 2b c d cosh(x) +--R + +--R 2 2 4 3 +--R (- 3b d + 3a c d + 4b c )cosh(x) - 4b c d cosh(x) +--R + +--R 2 2 2 2 +--R (3b d - 3a c d - 4b c )cosh(x) + 2b c d cosh(x) - b d + a c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 5 2 4 +--R 2b d sinh(x) + (8b d cosh(x) + 4b c d)sinh(x) +--R + +--R 2 2 2 +--R ((12b d - 4a c d)cosh(x) + 12b c d cosh(x) - 4b d + 4a c d) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 3 2 +--R (8b d - 12a c d)cosh(x) + 4b c d cosh(x) +--R + +--R 2 +--R (- 8b d + 12a c d)cosh(x) + 4b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 4 3 +--R (2b d - 12a c d)cosh(x) - 12b c d cosh(x) +--R + +--R 2 2 2 +--R (- 4b d + 16a c d)cosh(x) + 12b c d cosh(x) + 2b d - 4a c d +--R * +--R sinh(x) +--R + +--R 5 4 3 +--R - 4a c d cosh(x) - 8b c d cosh(x) + 8a c d cosh(x) +--R + +--R 2 +--R 8b c d cosh(x) - 4a c d cosh(x) +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 5 +--R b c d sinh(x) +--R + +--R 2 2 2 2 +--R ((- b d + a c d)cosh(x) + 4b c d cosh(x) + b d - a c d + 2b c ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 +--R (- 4b d + 4a c d)cosh(x) + 4b c d cosh(x) +--R + +--R 2 2 +--R (4b d - 4a c d + 6b c )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 3 +--R (- 6b d + 6a c d)cosh(x) - 2b c d cosh(x) +--R + +--R 2 2 2 2 +--R (8b d - 8a c d + 2b c )cosh(x) + 2b c d cosh(x) - 2b d + 2a c d +--R + +--R 2 +--R 2b c +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 4 +--R (- 4b d + 4a c d)cosh(x) - 5b c d cosh(x) +--R + +--R 2 2 3 2 +--R (8b d - 8a c d - 6b c )cosh(x) + 6b c d cosh(x) +--R + +--R 2 2 +--R (- 4b d + 4a c d + 6b c )cosh(x) - b c d +--R * +--R sinh(x) +--R + +--R 2 6 5 +--R (- b d + a c d)cosh(x) - 2b c d cosh(x) +--R + +--R 2 2 4 3 +--R (3b d - 3a c d - 4b c )cosh(x) + 4b c d cosh(x) +--R + +--R 2 2 2 2 +--R (- 3b d + 3a c d + 4b c )cosh(x) - 2b c d cosh(x) + b d - a c d +--R / +--R 2 2 2 4 +--R (c d cosh(x) - c d)sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (4c d cosh(x) + 2c cosh(x) - 4c d cosh(x) - 2c )sinh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R (6c d cosh(x) + 6c cosh(x) - 8c d cosh(x) - 6c cosh(x) + 2c d) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R 4c d cosh(x) + 6c cosh(x) - 8c d cosh(x) - 8c cosh(x) +--R + +--R 2 3 +--R 4c d cosh(x) + 2c +--R * +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R c d cosh(x) + 2c cosh(x) - 3c d cosh(x) - 4c cosh(x) +--R + +--R 2 2 3 2 +--R 3c d cosh(x) + 2c cosh(x) - c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 4 +--R (- 2c d cosh(x) + 2c d )sinh(x) +--R + +--R 2 3 2 2 2 2 3 +--R (- 8c d cosh(x) - 4c d cosh(x) + 8c d cosh(x) + 4c d)sinh(x) +--R + +--R 2 4 2 3 2 2 +--R - 12c d cosh(x) - 12c d cosh(x) + 16c d cosh(x) +--R + +--R 2 2 +--R 12c d cosh(x) - 4c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R - 8c d cosh(x) - 12c d cosh(x) + 16c d cosh(x) +--R + +--R 2 2 2 2 +--R 16c d cosh(x) - 8c d cosh(x) - 4c d +--R * +--R sinh(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 2c d cosh(x) - 4c d cosh(x) + 6c d cosh(x) + 8c d cosh(x) +--R + +--R 2 2 2 2 +--R - 6c d cosh(x) - 4c d cosh(x) + 2c d +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 2 2 4 +--R (- c d cosh(x) + c d)sinh(x) +--R + +--R 2 3 3 2 2 3 3 +--R (- 4c d cosh(x) - 2c cosh(x) + 4c d cosh(x) + 2c )sinh(x) +--R + +--R 2 4 3 3 2 2 3 2 +--R (- 6c d cosh(x) - 6c cosh(x) + 8c d cosh(x) + 6c cosh(x) - 2c d) +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 3 2 +--R - 4c d cosh(x) - 6c cosh(x) + 8c d cosh(x) + 8c cosh(x) +--R + +--R 2 3 +--R - 4c d cosh(x) - 2c +--R * +--R sinh(x) +--R + +--R 2 6 3 5 2 4 3 3 +--R - c d cosh(x) - 2c cosh(x) + 3c d cosh(x) + 4c cosh(x) +--R + +--R 2 2 3 2 +--R - 3c d cosh(x) - 2c cosh(x) + c d +--R Type: Expression(Integer) +--E 311 + +--S 312 of 518 +t0959:= (a+b*sech(x)^2)/(c+d*cosh(x)) +--R +--R +--R 2 +--R b sech(x) + a +--R (301) -------------- +--R d cosh(x) + c +--R Type: Expression(Integer) +--E 312 + +--S 313 of 518 +r0959:= -b*d*atan(sinh(x))/c^2+2*(a*c^2+b*d^2)*atanh((c-d)*tanh(1/2*x)/_ + (c^2-d^2)^(1/2))/c^2/(c^2-d^2)^(1/2)+b*tanh(x)/c +--R +--R +--R (302) +--R x +--R (d - c)tanh(-) +---------+ +--R 2 2 2 | 2 2 +--R (- 2b d - 2a c )atanh(--------------) - b d\|- d + c atan(sinh(x)) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +---------+ +--R | 2 2 +--R b c tanh(x)\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R c \|- d + c +--R Type: Expression(Integer) +--E 313 + +--S 314 of 518 +a0959:= integrate(t0959,x) +--R +--R +--R (303) +--R [ +--R 2 2 2 2 2 +--R (b d + a c )sinh(x) + (2b d + 2a c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b d + a c )cosh(x) + b d + a c +--R * +--R log +--R 2 2 2 2 2 +--R d sinh(x) + (2d cosh(x) + 2c d)sinh(x) + d cosh(x) +--R + +--R 2 2 +--R 2c d cosh(x) - d + 2c +--R * +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R 3 2 3 2 2 3 +--R (2d - 2c d)sinh(x) + (2d - 2c d)cosh(x) + 2c d - 2c +--R / +--R 2 2 +--R d sinh(x) + (2d cosh(x) + 2c)sinh(x) + d cosh(x) +--R + +--R 2c cosh(x) + d +--R + +--R 2 2 +--R (- 2b d sinh(x) - 4b d cosh(x)sinh(x) - 2b d cosh(x) - 2b d) +--R * +--R +---------+ +--R | 2 2 +--R \|- d + c atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +--R | 2 2 +--R - 2b c\|- d + c +--R / +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (c sinh(x) + 2c cosh(x)sinh(x) + c cosh(x) + c )\|- d + c +--R , +--R +--R 2 2 2 2 2 +--R (2b d + 2a c )sinh(x) + (4b d + 4a c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b d + 2a c )cosh(x) + 2b d + 2a c +--R * +--R +-------+ +--R | 2 2 +--R (d sinh(x) + d cosh(x) + c)\|d - c +--R atan(-------------------------------------) +--R 2 2 +--R d - c +--R + +--R 2 2 +--R (- 2b d sinh(x) - 4b d cosh(x)sinh(x) - 2b d cosh(x) - 2b d) +--R * +--R +-------+ +--R | 2 2 +--R \|d - c atan(sinh(x) + cosh(x)) +--R + +--R +-------+ +--R | 2 2 +--R - 2b c\|d - c +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (c sinh(x) + 2c cosh(x)sinh(x) + c cosh(x) + c )\|d - c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 314 + +--S 315 of 518 +m0959a:= a0959.1-r0959 +--R +--R +--R (304) +--R 2 2 2 2 2 +--R (b d + a c )sinh(x) + (2b d + 2a c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b d + a c )cosh(x) + b d + a c +--R * +--R log +--R 2 2 2 2 2 +--R d sinh(x) + (2d cosh(x) + 2c d)sinh(x) + d cosh(x) +--R + +--R 2 2 +--R 2c d cosh(x) - d + 2c +--R * +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R 3 2 3 2 2 3 +--R (2d - 2c d)sinh(x) + (2d - 2c d)cosh(x) + 2c d - 2c +--R / +--R 2 2 +--R d sinh(x) + (2d cosh(x) + 2c)sinh(x) + d cosh(x) + 2c cosh(x) +--R + +--R d +--R + +--R 2 2 2 2 2 +--R (2b d + 2a c )sinh(x) + (4b d + 4a c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b d + 2a c )cosh(x) + 2b d + 2a c +--R * +--R x +--R (d - c)tanh(-) +--R 2 +--R atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R 2 2 +--R (- 2b d sinh(x) - 4b d cosh(x)sinh(x) - 2b d cosh(x) - 2b d) +--R * +--R +---------+ +--R | 2 2 +--R \|- d + c atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (b d sinh(x) + 2b d cosh(x)sinh(x) + b d cosh(x) + b d)\|- d + c +--R * +--R atan(sinh(x)) +--R + +--R 2 2 +--R (- b c sinh(x) - 2b c cosh(x)sinh(x) - b c cosh(x) - b c)tanh(x) +--R + +--R - 2b c +--R * +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +--R 2 2 2 2 2 2 | 2 2 +--R (c sinh(x) + 2c cosh(x)sinh(x) + c cosh(x) + c )\|- d + c +--R Type: Expression(Integer) +--E 315 + +--S 316 of 518 +d0959a:= D(m0959a,x) +--R +--R +--R (305) +--R 2 2 8 +--R (b c d - b c d)sinh(x) +--R + +--R 2 2 2 3 7 +--R ((6b c d - 6b c d)cosh(x) + 2b c d - 2b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (15b c d - 15b c d)cosh(x) + (10b c d - 10b c )cosh(x) +--R + +--R 2 2 +--R 4b c d - 4b c d +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (20b c d - 20b c d)cosh(x) + (20b c d - 20b c )cosh(x) +--R + +--R 2 2 2 3 +--R (18b c d - 18b c d)cosh(x) + 6b c d - 6b c +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (15b c d - 15b c d)cosh(x) + (20b c d - 20b c )cosh(x) +--R + +--R 2 2 2 2 3 +--R (33b c d - 33b c d)cosh(x) + (22b c d - 22b c )cosh(x) +--R + +--R 2 2 +--R 6b c d - 6b c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6b c d - 6b c d)cosh(x) + (10b c d - 10b c )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (32b c d - 32b c d)cosh(x) + (32b c d - 32b c )cosh(x) +--R + +--R 2 2 2 3 +--R (18b c d - 18b c d)cosh(x) + 6b c d - 6b c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (b c d - b c d)cosh(x) + (2b c d - 2b c )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (18b c d - 18b c d)cosh(x) + (24b c d - 24b c )cosh(x) +--R + +--R 2 2 2 2 3 +--R (21b c d - 21b c d)cosh(x) + (14b c d - 14b c )cosh(x) +--R + +--R 2 2 +--R 4b c d - 4b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6b c d - 6b c d)cosh(x) + (10b c d - 10b c )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (12b c d - 12b c d)cosh(x) + (12b c d - 12b c )cosh(x) +--R + +--R 2 2 2 3 +--R (6b c d - 6b c d)cosh(x) + 2b c d - 2b c +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (b c d - b c d)cosh(x) + (2b c d - 2b c )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (3b c d - 3b c d)cosh(x) + (4b c d - 4b c )cosh(x) +--R + +--R 2 2 2 2 3 2 +--R (3b c d - 3b c d)cosh(x) + (2b c d - 2b c )cosh(x) + b c d +--R + +--R 2 +--R - b c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 8 +--R (b c d + b c d)sinh(x) +--R + +--R 2 2 2 3 7 +--R ((6b c d + 6b c d)cosh(x) + 2b c d + 2b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (15b c d + 15b c d)cosh(x) + (10b c d + 10b c )cosh(x) +--R + +--R 2 2 +--R 4b c d + 4b c d +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (20b c d + 20b c d)cosh(x) + (20b c d + 20b c )cosh(x) +--R + +--R 2 2 2 3 +--R (18b c d + 18b c d)cosh(x) + 6b c d + 6b c +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (15b c d + 15b c d)cosh(x) + (20b c d + 20b c )cosh(x) +--R + +--R 2 2 2 2 3 +--R (33b c d + 33b c d)cosh(x) + (22b c d + 22b c )cosh(x) +--R + +--R 2 2 +--R 6b c d + 6b c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6b c d + 6b c d)cosh(x) + (10b c d + 10b c )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (32b c d + 32b c d)cosh(x) + (32b c d + 32b c )cosh(x) +--R + +--R 2 2 2 3 +--R (18b c d + 18b c d)cosh(x) + 6b c d + 6b c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (b c d + b c d)cosh(x) + (2b c d + 2b c )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (18b c d + 18b c d)cosh(x) + (24b c d + 24b c )cosh(x) +--R + +--R 2 2 2 2 3 +--R (21b c d + 21b c d)cosh(x) + (14b c d + 14b c )cosh(x) +--R + +--R 2 2 +--R 4b c d + 4b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6b c d + 6b c d)cosh(x) + (10b c d + 10b c )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (12b c d + 12b c d)cosh(x) + (12b c d + 12b c )cosh(x) +--R + +--R 2 2 2 3 +--R (6b c d + 6b c d)cosh(x) + 2b c d + 2b c +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (b c d + b c d)cosh(x) + (2b c d + 2b c )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (3b c d + 3b c d)cosh(x) + (4b c d + 4b c )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (3b c d + 3b c d)cosh(x) + (2b c d + 2b c )cosh(x) + b c d + b c d +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 2 8 +--R (b d - b c d + (b + a)c d)sinh(x) +--R + +--R 3 2 2 2 +--R (6b d - 6b c d + (6b + 6a)c d)cosh(x) + 2b c d +--R + +--R 2 3 +--R (- 2b + 2a)c d + 2b c +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 2 +--R (15b d - 15b c d + (15b + 15a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (b d + 9b c d + (- 10b + 10a)c d + 10b c )cosh(x) + 4b d +--R + +--R 2 2 +--R - 4b c d + (4b + 4a)c d +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (20b d - 20b c d + (20b + 20a)c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b d + 14b c d + (- 20b + 20a)c d + 20b c )cosh(x) +--R + +--R 3 2 2 2 +--R (18b d - 16b c d + (16b + 18a)c d)cosh(x) + 6b c d +--R + +--R 2 3 +--R (2b + 6a)c d - 2b c +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (15b d - 15b c d + (15b + 15a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (15b d + 5b c d + (- 20b + 20a)c d + 20b c )cosh(x) +--R + +--R 3 2 2 2 +--R (33b d - 23b c d + (23b + 33a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (3b d + 19b c d + (2b + 22a)c d - 2b c )cosh(x) + 6b d +--R + +--R 2 2 +--R - 6b c d + (6b + 6a)c d +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (6b d - 6b c d + (6b + 6a)c d)cosh(x) +--R + +--R 3 2 2 3 4 +--R (20b d - 10b c d + (- 10b + 10a)c d + 10b c )cosh(x) +--R + +--R 3 2 2 3 +--R (32b d - 12b c d + (12b + 32a)c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (12b d + 20b c d + (- 8b + 32a)c d + 8b c )cosh(x) +--R + +--R 3 2 2 2 +--R (18b d - 14b c d + (14b + 18a)c d)cosh(x) + 6b c d +--R + +--R 2 3 +--R (2b + 6a)c d - 2b c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (b d - b c d + (b + a)c d)cosh(x) +--R + +--R 3 2 2 3 5 +--R (15b d - 13b c d + (- 2b + 2a)c d + 2b c )cosh(x) +--R + +--R 3 2 2 4 +--R (18b d + 2b c d + (- 2b + 18a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (18b d + 6b c d + (- 16b + 24a)c d + 16b c )cosh(x) +--R + +--R 3 2 2 2 +--R (21b d - 9b c d + (9b + 21a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (3b d + 11b c d + (10b + 14a)c d - 10b c )cosh(x) + 4b d +--R + +--R 2 2 +--R - 4b c d + (4b + 4a)c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 +--R (6b d - 6b c d )cosh(x) +--R + +--R 3 2 2 5 +--R (6b d + 4b c d + (- 4b + 6a)c d)cosh(x) +--R + +--R 3 2 2 3 4 +--R (12b d - 2b c d + (- 10b + 10a)c d + 10b c )cosh(x) +--R + +--R 3 2 3 +--R (12b d + 12a c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b d + 6b c d + (12b + 12a)c d - 12b c )cosh(x) +--R + +--R 3 2 2 2 +--R (6b d - 4b c d + (4b + 6a)c d)cosh(x) + 2b c d +--R + +--R 2 3 +--R (- 2b + 2a)c d + 2b c +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (b d - b c d )cosh(x) + (b d + b c d + (- b + a)c d)cosh(x) +--R + +--R 3 2 2 3 5 +--R (3b d - b c d + (- 2b + 2a)c d + 2b c )cosh(x) +--R + +--R 3 2 2 4 +--R (3b d + b c d + (- b + 3a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (3b d + b c d + (4b + 4a)c d - 4b c )cosh(x) +--R + +--R 3 2 2 2 +--R (3b d - b c d + (b + 3a)c d)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (b d + b c d + (- 2b + 2a)c d + 2b c )cosh(x) + b d - b c d +--R + +--R 2 +--R (b + a)c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 8 +--R (- b d - b c d + (- b - a)c d)sinh(x) +--R + +--R 3 2 2 2 +--R (- 6b d - 6b c d + (- 6b - 6a)c d)cosh(x) - 2b c d +--R + +--R 2 3 +--R (- 2b + 2a)c d - 2b c +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 2 +--R (- 15b d - 15b c d + (- 15b - 15a)c d)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (b d - 9b c d + (- 10b + 10a)c d - 10b c )cosh(x) - 4b d - 4b c d +--R + +--R 2 +--R (- 4b - 4a)c d +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 20b d - 20b c d + (- 20b - 20a)c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b d - 14b c d + (- 20b + 20a)c d - 20b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 18b d - 16b c d + (- 16b - 18a)c d)cosh(x) - 6b c d +--R + +--R 2 3 +--R (2b + 6a)c d + 2b c +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 15b d - 15b c d + (- 15b - 15a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (15b d - 5b c d + (- 20b + 20a)c d - 20b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 33b d - 23b c d + (- 23b - 33a)c d)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (3b d - 19b c d + (2b + 22a)c d + 2b c )cosh(x) - 6b d - 6b c d +--R + +--R 2 +--R (- 6b - 6a)c d +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 6b d - 6b c d + (- 6b - 6a)c d)cosh(x) +--R + +--R 3 2 2 3 4 +--R (20b d + 10b c d + (- 10b + 10a)c d - 10b c )cosh(x) +--R + +--R 3 2 2 3 +--R (- 32b d - 12b c d + (- 12b - 32a)c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (12b d - 20b c d + (- 8b + 32a)c d - 8b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 18b d - 14b c d + (- 14b - 18a)c d)cosh(x) - 6b c d +--R + +--R 2 3 +--R (2b + 6a)c d + 2b c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (- b d - b c d + (- b - a)c d)cosh(x) +--R + +--R 3 2 2 3 5 +--R (15b d + 13b c d + (- 2b + 2a)c d - 2b c )cosh(x) +--R + +--R 3 2 2 4 +--R (- 18b d + 2b c d + (2b - 18a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (18b d - 6b c d + (- 16b + 24a)c d - 16b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 21b d - 9b c d + (- 9b - 21a)c d)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (3b d - 11b c d + (10b + 14a)c d + 10b c )cosh(x) - 4b d - 4b c d +--R + +--R 2 +--R (- 4b - 4a)c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 +--R (6b d + 6b c d )cosh(x) +--R + +--R 3 2 2 5 +--R (- 6b d + 4b c d + (4b - 6a)c d)cosh(x) +--R + +--R 3 2 2 3 4 +--R (12b d + 2b c d + (- 10b + 10a)c d - 10b c )cosh(x) +--R + +--R 3 2 3 +--R (- 12b d - 12a c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b d - 6b c d + (12b + 12a)c d + 12b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 6b d - 4b c d + (- 4b - 6a)c d)cosh(x) - 2b c d +--R + +--R 2 3 +--R (- 2b + 2a)c d - 2b c +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (b d + b c d )cosh(x) + (- b d + b c d + (b - a)c d)cosh(x) +--R + +--R 3 2 2 3 5 +--R (3b d + b c d + (- 2b + 2a)c d - 2b c )cosh(x) +--R + +--R 3 2 2 4 +--R (- 3b d + b c d + (b - 3a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (3b d - b c d + (4b + 4a)c d + 4b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 3b d - b c d + (- b - 3a)c d)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (b d - b c d + (- 2b + 2a)c d - 2b c )cosh(x) - b d - b c d +--R + +--R 2 +--R (- b - a)c d +--R / +--R 2 2 3 8 2 2 3 3 4 7 +--R (c d - c d)sinh(x) + ((6c d - 6c d)cosh(x) + 2c d - 2c )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R ((15c d - 15c d)cosh(x) + (10c d - 10c )cosh(x) + 4c d - 4c d) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20c d - 20c d)cosh(x) + (20c d - 20c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18c d - 18c d)cosh(x) + 6c d - 6c +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15c d - 15c d)cosh(x) + (20c d - 20c )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33c d - 33c d)cosh(x) + (22c d - 22c )cosh(x) + 6c d - 6c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6c d - 6c d)cosh(x) + (10c d - 10c )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32c d - 32c d)cosh(x) + (32c d - 32c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18c d - 18c d)cosh(x) + 6c d - 6c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (c d - c d)cosh(x) + (2c d - 2c )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18c d - 18c d)cosh(x) + (24c d - 24c )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21c d - 21c d)cosh(x) + (14c d - 14c )cosh(x) + 4c d - 4c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6c d - 6c d)cosh(x) + (10c d - 10c )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12c d - 12c d)cosh(x) + (12c d - 12c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6c d - 6c d)cosh(x) + 2c d - 2c +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (c d - c d)cosh(x) + (2c d - 2c )cosh(x) + (3c d - 3c d)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4c d - 4c )cosh(x) + (3c d - 3c d)cosh(x) + (2c d - 2c )cosh(x) +--R + +--R 2 2 3 +--R c d - c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 8 2 2 3 3 4 7 +--R (c d + c d)sinh(x) + ((6c d + 6c d)cosh(x) + 2c d + 2c )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 6 +--R ((15c d + 15c d)cosh(x) + (10c d + 10c )cosh(x) + 4c d + 4c d)sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20c d + 20c d)cosh(x) + (20c d + 20c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18c d + 18c d)cosh(x) + 6c d + 6c +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15c d + 15c d)cosh(x) + (20c d + 20c )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33c d + 33c d)cosh(x) + (22c d + 22c )cosh(x) + 6c d + 6c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6c d + 6c d)cosh(x) + (10c d + 10c )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32c d + 32c d)cosh(x) + (32c d + 32c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18c d + 18c d)cosh(x) + 6c d + 6c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (c d + c d)cosh(x) + (2c d + 2c )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18c d + 18c d)cosh(x) + (24c d + 24c )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21c d + 21c d)cosh(x) + (14c d + 14c )cosh(x) + 4c d + 4c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6c d + 6c d)cosh(x) + (10c d + 10c )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12c d + 12c d)cosh(x) + (12c d + 12c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6c d + 6c d)cosh(x) + 2c d + 2c +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (c d + c d)cosh(x) + (2c d + 2c )cosh(x) + (3c d + 3c d)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4c d + 4c )cosh(x) + (3c d + 3c d)cosh(x) + (2c d + 2c )cosh(x) +--R + +--R 2 2 3 +--R c d + c d +--R Type: Expression(Integer) +--E 316 + +--S 317 of 518 +m0959b:= a0959.2-r0959 +--R +--R +--R (306) +--R 2 2 2 2 2 +--R (2b d + 2a c )sinh(x) + (4b d + 4a c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b d + 2a c )cosh(x) + 2b d + 2a c +--R * +--R x +--R +-------+ (d - c)tanh(-) +--R | 2 2 2 +--R \|d - c atanh(--------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R 2 2 2 2 2 +--R (2b d + 2a c )sinh(x) + (4b d + 4a c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (2b d + 2a c )cosh(x) + 2b d + 2a c +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (d sinh(x) + d cosh(x) + c)\|d - c +--R \|- d + c atan(-------------------------------------) +--R 2 2 +--R d - c +--R + +--R 2 2 +--R (- 2b d sinh(x) - 4b d cosh(x)sinh(x) - 2b d cosh(x) - 2b d) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- d + c \|d - c atan(sinh(x) + cosh(x)) +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (b d sinh(x) + 2b d cosh(x)sinh(x) + b d cosh(x) + b d)\|- d + c +--R * +--R +-------+ +--R | 2 2 +--R \|d - c atan(sinh(x)) +--R + +--R 2 2 +--R (- b c sinh(x) - 2b c cosh(x)sinh(x) - b c cosh(x) - b c)tanh(x) +--R + +--R - 2b c +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- d + c \|d - c +--R / +--R +---------+ +-------+ +--R 2 2 2 2 2 2 | 2 2 | 2 2 +--R (c sinh(x) + 2c cosh(x)sinh(x) + c cosh(x) + c )\|- d + c \|d - c +--R Type: Expression(Integer) +--E 317 + +--S 318 of 518 +d0959b:= D(m0959b,x) +--R +--R +--R (307) +--R 2 2 8 +--R (b c d - b c d)sinh(x) +--R + +--R 2 2 2 3 7 +--R ((6b c d - 6b c d)cosh(x) + 2b c d - 2b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (15b c d - 15b c d)cosh(x) + (10b c d - 10b c )cosh(x) +--R + +--R 2 2 +--R 4b c d - 4b c d +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (20b c d - 20b c d)cosh(x) + (20b c d - 20b c )cosh(x) +--R + +--R 2 2 2 3 +--R (18b c d - 18b c d)cosh(x) + 6b c d - 6b c +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (15b c d - 15b c d)cosh(x) + (20b c d - 20b c )cosh(x) +--R + +--R 2 2 2 2 3 +--R (33b c d - 33b c d)cosh(x) + (22b c d - 22b c )cosh(x) +--R + +--R 2 2 +--R 6b c d - 6b c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6b c d - 6b c d)cosh(x) + (10b c d - 10b c )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (32b c d - 32b c d)cosh(x) + (32b c d - 32b c )cosh(x) +--R + +--R 2 2 2 3 +--R (18b c d - 18b c d)cosh(x) + 6b c d - 6b c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (b c d - b c d)cosh(x) + (2b c d - 2b c )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (18b c d - 18b c d)cosh(x) + (24b c d - 24b c )cosh(x) +--R + +--R 2 2 2 2 3 +--R (21b c d - 21b c d)cosh(x) + (14b c d - 14b c )cosh(x) +--R + +--R 2 2 +--R 4b c d - 4b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6b c d - 6b c d)cosh(x) + (10b c d - 10b c )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (12b c d - 12b c d)cosh(x) + (12b c d - 12b c )cosh(x) +--R + +--R 2 2 2 3 +--R (6b c d - 6b c d)cosh(x) + 2b c d - 2b c +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (b c d - b c d)cosh(x) + (2b c d - 2b c )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (3b c d - 3b c d)cosh(x) + (4b c d - 4b c )cosh(x) +--R + +--R 2 2 2 2 3 2 +--R (3b c d - 3b c d)cosh(x) + (2b c d - 2b c )cosh(x) + b c d +--R + +--R 2 +--R - b c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 8 +--R (b c d + b c d)sinh(x) +--R + +--R 2 2 2 3 7 +--R ((6b c d + 6b c d)cosh(x) + 2b c d + 2b c )sinh(x) +--R + +--R 2 2 2 2 3 +--R (15b c d + 15b c d)cosh(x) + (10b c d + 10b c )cosh(x) +--R + +--R 2 2 +--R 4b c d + 4b c d +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 2 3 2 +--R (20b c d + 20b c d)cosh(x) + (20b c d + 20b c )cosh(x) +--R + +--R 2 2 2 3 +--R (18b c d + 18b c d)cosh(x) + 6b c d + 6b c +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 4 2 3 3 +--R (15b c d + 15b c d)cosh(x) + (20b c d + 20b c )cosh(x) +--R + +--R 2 2 2 2 3 +--R (33b c d + 33b c d)cosh(x) + (22b c d + 22b c )cosh(x) +--R + +--R 2 2 +--R 6b c d + 6b c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6b c d + 6b c d)cosh(x) + (10b c d + 10b c )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (32b c d + 32b c d)cosh(x) + (32b c d + 32b c )cosh(x) +--R + +--R 2 2 2 3 +--R (18b c d + 18b c d)cosh(x) + 6b c d + 6b c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (b c d + b c d)cosh(x) + (2b c d + 2b c )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (18b c d + 18b c d)cosh(x) + (24b c d + 24b c )cosh(x) +--R + +--R 2 2 2 2 3 +--R (21b c d + 21b c d)cosh(x) + (14b c d + 14b c )cosh(x) +--R + +--R 2 2 +--R 4b c d + 4b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 5 2 3 4 +--R (6b c d + 6b c d)cosh(x) + (10b c d + 10b c )cosh(x) +--R + +--R 2 2 3 2 3 2 +--R (12b c d + 12b c d)cosh(x) + (12b c d + 12b c )cosh(x) +--R + +--R 2 2 2 3 +--R (6b c d + 6b c d)cosh(x) + 2b c d + 2b c +--R * +--R sinh(x) +--R + +--R 2 2 6 2 3 5 +--R (b c d + b c d)cosh(x) + (2b c d + 2b c )cosh(x) +--R + +--R 2 2 4 2 3 3 +--R (3b c d + 3b c d)cosh(x) + (4b c d + 4b c )cosh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (3b c d + 3b c d)cosh(x) + (2b c d + 2b c )cosh(x) + b c d + b c d +--R * +--R 2 +--R tanh(x) +--R + +--R 3 2 2 8 +--R (b d - b c d + (b + a)c d)sinh(x) +--R + +--R 3 2 2 2 +--R (6b d - 6b c d + (6b + 6a)c d)cosh(x) + 2b c d +--R + +--R 2 3 +--R (- 2b + 2a)c d + 2b c +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 2 +--R (15b d - 15b c d + (15b + 15a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (b d + 9b c d + (- 10b + 10a)c d + 10b c )cosh(x) + 4b d +--R + +--R 2 2 +--R - 4b c d + (4b + 4a)c d +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (20b d - 20b c d + (20b + 20a)c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b d + 14b c d + (- 20b + 20a)c d + 20b c )cosh(x) +--R + +--R 3 2 2 2 +--R (18b d - 16b c d + (16b + 18a)c d)cosh(x) + 6b c d +--R + +--R 2 3 +--R (2b + 6a)c d - 2b c +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (15b d - 15b c d + (15b + 15a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (15b d + 5b c d + (- 20b + 20a)c d + 20b c )cosh(x) +--R + +--R 3 2 2 2 +--R (33b d - 23b c d + (23b + 33a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (3b d + 19b c d + (2b + 22a)c d - 2b c )cosh(x) + 6b d +--R + +--R 2 2 +--R - 6b c d + (6b + 6a)c d +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (6b d - 6b c d + (6b + 6a)c d)cosh(x) +--R + +--R 3 2 2 3 4 +--R (20b d - 10b c d + (- 10b + 10a)c d + 10b c )cosh(x) +--R + +--R 3 2 2 3 +--R (32b d - 12b c d + (12b + 32a)c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (12b d + 20b c d + (- 8b + 32a)c d + 8b c )cosh(x) +--R + +--R 3 2 2 2 +--R (18b d - 14b c d + (14b + 18a)c d)cosh(x) + 6b c d +--R + +--R 2 3 +--R (2b + 6a)c d - 2b c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (b d - b c d + (b + a)c d)cosh(x) +--R + +--R 3 2 2 3 5 +--R (15b d - 13b c d + (- 2b + 2a)c d + 2b c )cosh(x) +--R + +--R 3 2 2 4 +--R (18b d + 2b c d + (- 2b + 18a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (18b d + 6b c d + (- 16b + 24a)c d + 16b c )cosh(x) +--R + +--R 3 2 2 2 +--R (21b d - 9b c d + (9b + 21a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (3b d + 11b c d + (10b + 14a)c d - 10b c )cosh(x) + 4b d +--R + +--R 2 2 +--R - 4b c d + (4b + 4a)c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 +--R (6b d - 6b c d )cosh(x) +--R + +--R 3 2 2 5 +--R (6b d + 4b c d + (- 4b + 6a)c d)cosh(x) +--R + +--R 3 2 2 3 4 +--R (12b d - 2b c d + (- 10b + 10a)c d + 10b c )cosh(x) +--R + +--R 3 2 3 +--R (12b d + 12a c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b d + 6b c d + (12b + 12a)c d - 12b c )cosh(x) +--R + +--R 3 2 2 2 +--R (6b d - 4b c d + (4b + 6a)c d)cosh(x) + 2b c d +--R + +--R 2 3 +--R (- 2b + 2a)c d + 2b c +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (b d - b c d )cosh(x) + (b d + b c d + (- b + a)c d)cosh(x) +--R + +--R 3 2 2 3 5 +--R (3b d - b c d + (- 2b + 2a)c d + 2b c )cosh(x) +--R + +--R 3 2 2 4 +--R (3b d + b c d + (- b + 3a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (3b d + b c d + (4b + 4a)c d - 4b c )cosh(x) +--R + +--R 3 2 2 2 +--R (3b d - b c d + (b + 3a)c d)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (b d + b c d + (- 2b + 2a)c d + 2b c )cosh(x) + b d - b c d +--R + +--R 2 +--R (b + a)c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 2 2 8 +--R (- b d - b c d + (- b - a)c d)sinh(x) +--R + +--R 3 2 2 2 +--R (- 6b d - 6b c d + (- 6b - 6a)c d)cosh(x) - 2b c d +--R + +--R 2 3 +--R (- 2b + 2a)c d - 2b c +--R * +--R 7 +--R sinh(x) +--R + +--R 3 2 2 2 +--R (- 15b d - 15b c d + (- 15b - 15a)c d)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (b d - 9b c d + (- 10b + 10a)c d - 10b c )cosh(x) - 4b d - 4b c d +--R + +--R 2 +--R (- 4b - 4a)c d +--R * +--R 6 +--R sinh(x) +--R + +--R 3 2 2 3 +--R (- 20b d - 20b c d + (- 20b - 20a)c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b d - 14b c d + (- 20b + 20a)c d - 20b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 18b d - 16b c d + (- 16b - 18a)c d)cosh(x) - 6b c d +--R + +--R 2 3 +--R (2b + 6a)c d + 2b c +--R * +--R 5 +--R sinh(x) +--R + +--R 3 2 2 4 +--R (- 15b d - 15b c d + (- 15b - 15a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (15b d - 5b c d + (- 20b + 20a)c d - 20b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 33b d - 23b c d + (- 23b - 33a)c d)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (3b d - 19b c d + (2b + 22a)c d + 2b c )cosh(x) - 6b d - 6b c d +--R + +--R 2 +--R (- 6b - 6a)c d +--R * +--R 4 +--R sinh(x) +--R + +--R 3 2 2 5 +--R (- 6b d - 6b c d + (- 6b - 6a)c d)cosh(x) +--R + +--R 3 2 2 3 4 +--R (20b d + 10b c d + (- 10b + 10a)c d - 10b c )cosh(x) +--R + +--R 3 2 2 3 +--R (- 32b d - 12b c d + (- 12b - 32a)c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (12b d - 20b c d + (- 8b + 32a)c d - 8b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 18b d - 14b c d + (- 14b - 18a)c d)cosh(x) - 6b c d +--R + +--R 2 3 +--R (2b + 6a)c d + 2b c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 2 2 6 +--R (- b d - b c d + (- b - a)c d)cosh(x) +--R + +--R 3 2 2 3 5 +--R (15b d + 13b c d + (- 2b + 2a)c d - 2b c )cosh(x) +--R + +--R 3 2 2 4 +--R (- 18b d + 2b c d + (2b - 18a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (18b d - 6b c d + (- 16b + 24a)c d - 16b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 21b d - 9b c d + (- 9b - 21a)c d)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (3b d - 11b c d + (10b + 14a)c d + 10b c )cosh(x) - 4b d - 4b c d +--R + +--R 2 +--R (- 4b - 4a)c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 6 +--R (6b d + 6b c d )cosh(x) +--R + +--R 3 2 2 5 +--R (- 6b d + 4b c d + (4b - 6a)c d)cosh(x) +--R + +--R 3 2 2 3 4 +--R (12b d + 2b c d + (- 10b + 10a)c d - 10b c )cosh(x) +--R + +--R 3 2 3 +--R (- 12b d - 12a c d)cosh(x) +--R + +--R 3 2 2 3 2 +--R (6b d - 6b c d + (12b + 12a)c d + 12b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 6b d - 4b c d + (- 4b - 6a)c d)cosh(x) - 2b c d +--R + +--R 2 3 +--R (- 2b + 2a)c d - 2b c +--R * +--R sinh(x) +--R + +--R 3 2 7 3 2 2 6 +--R (b d + b c d )cosh(x) + (- b d + b c d + (b - a)c d)cosh(x) +--R + +--R 3 2 2 3 5 +--R (3b d + b c d + (- 2b + 2a)c d - 2b c )cosh(x) +--R + +--R 3 2 2 4 +--R (- 3b d + b c d + (b - 3a)c d)cosh(x) +--R + +--R 3 2 2 3 3 +--R (3b d - b c d + (4b + 4a)c d + 4b c )cosh(x) +--R + +--R 3 2 2 2 +--R (- 3b d - b c d + (- b - 3a)c d)cosh(x) +--R + +--R 3 2 2 3 3 2 +--R (b d - b c d + (- 2b + 2a)c d - 2b c )cosh(x) - b d - b c d +--R + +--R 2 +--R (- b - a)c d +--R / +--R 2 2 3 8 2 2 3 3 4 7 +--R (c d - c d)sinh(x) + ((6c d - 6c d)cosh(x) + 2c d - 2c )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R ((15c d - 15c d)cosh(x) + (10c d - 10c )cosh(x) + 4c d - 4c d) +--R * +--R 6 +--R sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20c d - 20c d)cosh(x) + (20c d - 20c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18c d - 18c d)cosh(x) + 6c d - 6c +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15c d - 15c d)cosh(x) + (20c d - 20c )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33c d - 33c d)cosh(x) + (22c d - 22c )cosh(x) + 6c d - 6c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6c d - 6c d)cosh(x) + (10c d - 10c )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32c d - 32c d)cosh(x) + (32c d - 32c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18c d - 18c d)cosh(x) + 6c d - 6c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (c d - c d)cosh(x) + (2c d - 2c )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18c d - 18c d)cosh(x) + (24c d - 24c )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21c d - 21c d)cosh(x) + (14c d - 14c )cosh(x) + 4c d - 4c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6c d - 6c d)cosh(x) + (10c d - 10c )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12c d - 12c d)cosh(x) + (12c d - 12c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6c d - 6c d)cosh(x) + 2c d - 2c +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (c d - c d)cosh(x) + (2c d - 2c )cosh(x) + (3c d - 3c d)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4c d - 4c )cosh(x) + (3c d - 3c d)cosh(x) + (2c d - 2c )cosh(x) +--R + +--R 2 2 3 +--R c d - c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 3 8 2 2 3 3 4 7 +--R (c d + c d)sinh(x) + ((6c d + 6c d)cosh(x) + 2c d + 2c )sinh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 6 +--R ((15c d + 15c d)cosh(x) + (10c d + 10c )cosh(x) + 4c d + 4c d)sinh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (20c d + 20c d)cosh(x) + (20c d + 20c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18c d + 18c d)cosh(x) + 6c d + 6c +--R * +--R 5 +--R sinh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (15c d + 15c d)cosh(x) + (20c d + 20c )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (33c d + 33c d)cosh(x) + (22c d + 22c )cosh(x) + 6c d + 6c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6c d + 6c d)cosh(x) + (10c d + 10c )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (32c d + 32c d)cosh(x) + (32c d + 32c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (18c d + 18c d)cosh(x) + 6c d + 6c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 +--R (c d + c d)cosh(x) + (2c d + 2c )cosh(x) +--R + +--R 2 2 3 4 3 4 3 +--R (18c d + 18c d)cosh(x) + (24c d + 24c )cosh(x) +--R + +--R 2 2 3 2 3 4 2 2 3 +--R (21c d + 21c d)cosh(x) + (14c d + 14c )cosh(x) + 4c d + 4c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 3 5 3 4 4 +--R (6c d + 6c d)cosh(x) + (10c d + 10c )cosh(x) +--R + +--R 2 2 3 3 3 4 2 +--R (12c d + 12c d)cosh(x) + (12c d + 12c )cosh(x) +--R + +--R 2 2 3 3 4 +--R (6c d + 6c d)cosh(x) + 2c d + 2c +--R * +--R sinh(x) +--R + +--R 2 2 3 6 3 4 5 2 2 3 4 +--R (c d + c d)cosh(x) + (2c d + 2c )cosh(x) + (3c d + 3c d)cosh(x) +--R + +--R 3 4 3 2 2 3 2 3 4 +--R (4c d + 4c )cosh(x) + (3c d + 3c d)cosh(x) + (2c d + 2c )cosh(x) +--R + +--R 2 2 3 +--R c d + c d +--R Type: Expression(Integer) +--E 318 + +--S 319 of 518 +t0960:= (a+b*csch(x)^2)/(c+d*sinh(x)) +--R +--R +--R 2 +--R b csch(x) + a +--R (308) -------------- +--R d sinh(x) + c +--R Type: Expression(Integer) +--E 319 + +--S 320 of 518 +r0960:= b*d*acoth(cosh(x))/c^2-2*(a*c^2+b*d^2)*_ + atanh((d-c*tanh(1/2*x))/(d^2+c^2)^(1/2))/c^2/(d^2+c^2)^(1/2)-_ + b*coth(x)/c +--R +--R +--R (309) +--R x +--R c tanh(-) - d +-------+ +--R 2 2 2 | 2 2 +--R (2b d + 2a c )atanh(-------------) + b d\|d + c acoth(cosh(x)) +--R +-------+ +--R | 2 2 +--R \|d + c +--R + +--R +-------+ +--R | 2 2 +--R - b c coth(x)\|d + c +--R / +--R +-------+ +--R 2 | 2 2 +--R c \|d + c +--R Type: Expression(Integer) +--E 320 + +--S 321 of 518 +a0960:= integrate(t0960,x) +--R +--R +--R (310) +--R 2 2 2 2 2 +--R (b d + a c )sinh(x) + (2b d + 2a c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b d + a c )cosh(x) - b d - a c +--R * +--R log +--R 2 2 2 2 2 +--R d sinh(x) + (2d cosh(x) + 2c d)sinh(x) + d cosh(x) +--R + +--R 2 2 +--R 2c d cosh(x) + d + 2c +--R * +--R +-------+ +--R | 2 2 +--R \|d + c +--R + +--R 3 2 3 2 2 3 +--R (- 2d - 2c d)sinh(x) + (- 2d - 2c d)cosh(x) - 2c d - 2c +--R / +--R 2 2 +--R d sinh(x) + (2d cosh(x) + 2c)sinh(x) + d cosh(x) + 2c cosh(x) +--R + +--R - d +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (b d sinh(x) + 2b d cosh(x)sinh(x) + b d cosh(x) - b d)\|d + c +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- b d sinh(x) - 2b d cosh(x)sinh(x) - b d cosh(x) + b d)\|d + c +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R +-------+ +--R | 2 2 +--R - 2b c\|d + c +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (c sinh(x) + 2c cosh(x)sinh(x) + c cosh(x) - c )\|d + c +--R Type: Union(Expression(Integer),...) +--E 321 + +--S 322 of 518 +m0960:= a0960-r0960 +--R +--R +--R (311) +--R 2 2 2 2 2 +--R (b d + a c )sinh(x) + (2b d + 2a c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (b d + a c )cosh(x) - b d - a c +--R * +--R log +--R 2 2 2 2 2 +--R d sinh(x) + (2d cosh(x) + 2c d)sinh(x) + d cosh(x) +--R + +--R 2 2 +--R 2c d cosh(x) + d + 2c +--R * +--R +-------+ +--R | 2 2 +--R \|d + c +--R + +--R 3 2 3 2 2 3 +--R (- 2d - 2c d)sinh(x) + (- 2d - 2c d)cosh(x) - 2c d - 2c +--R / +--R 2 2 +--R d sinh(x) + (2d cosh(x) + 2c)sinh(x) + d cosh(x) + 2c cosh(x) +--R + +--R - d +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (b d sinh(x) + 2b d cosh(x)sinh(x) + b d cosh(x) - b d)\|d + c +--R * +--R log(sinh(x) + cosh(x) + 1) +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- b d sinh(x) - 2b d cosh(x)sinh(x) - b d cosh(x) + b d)\|d + c +--R * +--R log(sinh(x) + cosh(x) - 1) +--R + +--R 2 2 2 2 2 +--R (- 2b d - 2a c )sinh(x) + (- 4b d - 4a c )cosh(x)sinh(x) +--R + +--R 2 2 2 2 2 +--R (- 2b d - 2a c )cosh(x) + 2b d + 2a c +--R * +--R x +--R c tanh(-) - d +--R 2 +--R atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|d + c +--R + +--R +-------+ +--R 2 2 | 2 2 +--R (- b d sinh(x) - 2b d cosh(x)sinh(x) - b d cosh(x) + b d)\|d + c +--R * +--R acoth(cosh(x)) +--R + +--R 2 +--R b c coth(x)sinh(x) + 2b c cosh(x)coth(x)sinh(x) +--R + +--R 2 +--R (b c cosh(x) - b c)coth(x) - 2b c +--R * +--R +-------+ +--R | 2 2 +--R \|d + c +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (c sinh(x) + 2c cosh(x)sinh(x) + c cosh(x) - c )\|d + c +--R Type: Expression(Integer) +--E 322 + +--S 323 of 518 +d0960:= D(m0960,x) +--R +--R +--R (312) +--R 2 7 +--R b c d sinh(x) +--R + +--R 2 2 2 2 +--R (- b c d cosh(x) + b c d)coth(x) +--R + +--R 3 2 2 2 3 2 +--R (- b d + (b - a)c d)cosh(x) + 6b c d cosh(x) + b d + (b + a)c d +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 +--R (- 6b c d cosh(x) - 2b c cosh(x) + 6b c d cosh(x) + 2b c ) +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 3 2 3 2 +--R (- 6b d + (6b - 6a)c d)cosh(x) + (13b c d + 2b c )cosh(x) +--R + +--R 3 2 2 3 +--R (6b d + (4b + 6a)c d)cosh(x) - b c d - 2b c +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 +--R - 15b c d cosh(x) - 10b c cosh(x) + 18b c d cosh(x) +--R + +--R 3 2 +--R 10b c cosh(x) - 3b c d +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 4 2 3 3 +--R (- 15b d + (15b - 15a)c d)cosh(x) + (10b c d + 10b c )cosh(x) +--R + +--R 3 2 2 2 3 +--R (18b d + (2b + 18a)c d)cosh(x) + (- 2b c d - 10b c )cosh(x) +--R + +--R 3 2 +--R - 3b d + (- b - 3a)c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 +--R - 20b c d cosh(x) - 20b c cosh(x) + 32b c d cosh(x) +--R + +--R 3 2 2 3 +--R 24b c cosh(x) - 12b c d cosh(x) - 4b c +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 5 +--R (- 20b d + (20b - 20a)c d)cosh(x) +--R + +--R 2 3 4 +--R (- 5b c d + 20b c )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (32b d + (- 12b + 32a)c d)cosh(x) + (6b c d - 16b c )cosh(x) +--R + +--R 3 2 2 3 +--R (- 12b d - 12a c d)cosh(x) - b c d - 4b c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 2 4 +--R - 15b c d cosh(x) - 20b c cosh(x) + 33b c d cosh(x) +--R + +--R 3 3 2 2 3 2 +--R 32b c cosh(x) - 21b c d cosh(x) - 12b c cosh(x) + 3b c d +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 6 +--R (- 15b d + (15b - 15a)c d)cosh(x) +--R + +--R 2 3 5 +--R (- 14b c d + 20b c )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (33b d + (- 23b + 33a)c d)cosh(x) + (20b c d - 8b c )cosh(x) +--R + +--R 3 2 2 2 3 +--R (- 21b d + (9b - 21a)c d)cosh(x) + (- 6b c d - 12b c )cosh(x) +--R + +--R 3 2 +--R 3b d + (- b + 3a)c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 2 5 +--R - 6b c d cosh(x) - 10b c cosh(x) + 18b c d cosh(x) +--R + +--R 3 4 2 3 3 2 +--R 22b c cosh(x) - 18b c d cosh(x) - 14b c cosh(x) +--R + +--R 2 3 +--R 6b c d cosh(x) + 2b c +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 7 2 3 6 +--R (- 6b d + (6b - 6a)c d)cosh(x) + (- 9b c d + 10b c )cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (18b d + (- 16b + 18a)c d)cosh(x) + (19b c d + 2b c )cosh(x) +--R + +--R 3 2 3 +--R (- 18b d + (14b - 18a)c d)cosh(x) +--R + +--R 2 3 2 3 2 +--R (- 11b c d - 10b c )cosh(x) + (6b d + (- 4b + 6a)c d)cosh(x) +--R + +--R 2 3 +--R b c d - 2b c +--R * +--R sinh(x) +--R + +--R 2 8 3 7 2 6 +--R - b c d cosh(x) - 2b c cosh(x) + 4b c d cosh(x) +--R + +--R 3 5 2 4 3 3 2 2 +--R 6b c cosh(x) - 6b c d cosh(x) - 6b c cosh(x) + 4b c d cosh(x) +--R + +--R 3 2 +--R 2b c cosh(x) - b c d +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 8 2 3 7 +--R (- b d + (b - a)c d)cosh(x) + (- 2b c d + 2b c )cosh(x) +--R + +--R 3 2 6 2 3 5 +--R (4b d + (- 4b + 4a)c d)cosh(x) + (6b c d + 2b c )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 6b d + (6b - 6a)c d)cosh(x) + (- 6b c d - 2b c )cosh(x) +--R + +--R 3 2 2 2 3 3 +--R (4b d + (- 4b + 4a)c d)cosh(x) + (2b c d - 2b c )cosh(x) - b d +--R + +--R 2 +--R (b - a)c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 3 7 +--R - 2b d sinh(x) +--R + +--R 2 2 2 2 2 2 +--R (2b c d cosh(x) - 2b c d )coth(x) - 2b c d cosh(x) +--R + +--R 3 2 +--R - 12b d cosh(x) - 2b c d +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 2 2 2 2 +--R (12b c d cosh(x) + 4b c d cosh(x) - 12b c d cosh(x) - 4b c d) +--R * +--R 2 +--R coth(x) +--R + +--R 2 3 3 2 2 +--R - 12b c d cosh(x) + (- 30b d + (- 4b - 4a)c d)cosh(x) +--R + +--R 2 3 2 +--R - 8b c d cosh(x) + 6b d + (4b + 4a)c d +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 2 3 2 2 +--R 30b c d cosh(x) + 20b c d cosh(x) - 36b c d cosh(x) +--R + +--R 2 2 +--R - 20b c d cosh(x) + 6b c d +--R * +--R 2 +--R coth(x) +--R + +--R 2 4 3 2 3 +--R - 30b c d cosh(x) + (- 40b d + (- 20b - 20a)c d)cosh(x) +--R + +--R 2 2 3 2 2 +--R - 4b c d cosh(x) + (24b d + (20b + 20a)c d)cosh(x) + 2b c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 2 4 2 3 +--R 40b c d cosh(x) + 40b c d cosh(x) - 64b c d cosh(x) +--R + +--R 2 2 2 2 +--R - 48b c d cosh(x) + 24b c d cosh(x) + 8b c d +--R * +--R 2 +--R coth(x) +--R + +--R 2 5 3 2 4 +--R - 40b c d cosh(x) + (- 30b d + (- 40b - 40a)c d)cosh(x) +--R + +--R 2 3 3 2 2 3 +--R 24b c d cosh(x) + (36b d + (32b + 48a)c d)cosh(x) - 6b d +--R + +--R 2 +--R (8b - 8a)c d +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 2 5 2 4 +--R 30b c d cosh(x) + 40b c d cosh(x) - 66b c d cosh(x) +--R + +--R 2 3 2 2 2 +--R - 64b c d cosh(x) + 42b c d cosh(x) + 24b c d cosh(x) +--R + +--R 2 +--R - 6b c d +--R * +--R 2 +--R coth(x) +--R + +--R 2 6 3 2 5 +--R - 30b c d cosh(x) + (- 12b d + (- 40b - 40a)c d)cosh(x) +--R + +--R 2 4 3 2 3 +--R 46b c d cosh(x) + (24b d + (16b + 64a)c d)cosh(x) +--R + +--R 2 2 3 2 2 +--R - 18b c d cosh(x) + (- 12b d + (24b - 24a)c d)cosh(x) + 2b c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 2 6 2 5 +--R 12b c d cosh(x) + 20b c d cosh(x) - 36b c d cosh(x) +--R + +--R 2 4 2 3 2 2 +--R - 44b c d cosh(x) + 36b c d cosh(x) + 28b c d cosh(x) +--R + +--R 2 2 +--R - 12b c d cosh(x) - 4b c d +--R * +--R 2 +--R coth(x) +--R + +--R 2 7 3 2 6 +--R - 12b c d cosh(x) + (- 2b d + (- 20b - 20a)c d)cosh(x) +--R + +--R 2 5 3 2 4 +--R 32b c d cosh(x) + (6b d + (- 4b + 44a)c d)cosh(x) +--R + +--R 2 3 3 2 2 +--R - 28b c d cosh(x) + (- 6b d + (20b - 28a)c d)cosh(x) +--R + +--R 2 3 2 +--R 8b c d cosh(x) + 2b d + (4b + 4a)c d +--R * +--R sinh(x) +--R + +--R 2 8 2 7 2 6 +--R 2b c d cosh(x) + 4b c d cosh(x) - 8b c d cosh(x) +--R + +--R 2 5 2 4 2 3 +--R - 12b c d cosh(x) + 12b c d cosh(x) + 12b c d cosh(x) +--R + +--R 2 2 2 2 +--R - 8b c d cosh(x) - 4b c d cosh(x) + 2b c d +--R * +--R 2 +--R coth(x) +--R + +--R 2 8 2 7 2 6 +--R - 2b c d cosh(x) + (- 4b - 4a)c d cosh(x) + 8b c d cosh(x) +--R + +--R 2 5 2 4 2 3 +--R (- 4b + 12a)c d cosh(x) - 12b c d cosh(x) + (4b - 12a)c d cosh(x) +--R + +--R 2 2 2 2 +--R 8b c d cosh(x) + (4b + 4a)c d cosh(x) - 2b c d +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 2 7 +--R - b c d sinh(x) +--R + +--R 2 2 2 2 3 2 2 +--R (b c d cosh(x) - b c d)coth(x) + (b d + (- b + a)c d)cosh(x) +--R + +--R 2 3 2 +--R - 6b c d cosh(x) - b d + (- b - a)c d +--R * +--R 6 +--R sinh(x) +--R + +--R 2 3 3 2 2 3 2 +--R (6b c d cosh(x) + 2b c cosh(x) - 6b c d cosh(x) - 2b c )coth(x) +--R + +--R 3 2 3 2 3 2 +--R (6b d + (- 6b + 6a)c d)cosh(x) + (- 13b c d - 2b c )cosh(x) +--R + +--R 3 2 2 3 +--R (- 6b d + (- 4b - 6a)c d)cosh(x) + b c d + 2b c +--R * +--R 5 +--R sinh(x) +--R + +--R 2 4 3 3 2 2 +--R 15b c d cosh(x) + 10b c cosh(x) - 18b c d cosh(x) +--R + +--R 3 2 +--R - 10b c cosh(x) + 3b c d +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 4 2 3 3 +--R (15b d + (- 15b + 15a)c d)cosh(x) + (- 10b c d - 10b c )cosh(x) +--R + +--R 3 2 2 2 3 +--R (- 18b d + (- 2b - 18a)c d)cosh(x) + (2b c d + 10b c )cosh(x) +--R + +--R 3 2 +--R 3b d + (b + 3a)c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 5 3 4 2 3 +--R 20b c d cosh(x) + 20b c cosh(x) - 32b c d cosh(x) +--R + +--R 3 2 2 3 +--R - 24b c cosh(x) + 12b c d cosh(x) + 4b c +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 5 2 3 4 +--R (20b d + (- 20b + 20a)c d)cosh(x) + (5b c d - 20b c )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (- 32b d + (12b - 32a)c d)cosh(x) + (- 6b c d + 16b c )cosh(x) +--R + +--R 3 2 2 3 +--R (12b d + 12a c d)cosh(x) + b c d + 4b c +--R * +--R 3 +--R sinh(x) +--R + +--R 2 6 3 5 2 4 +--R 15b c d cosh(x) + 20b c cosh(x) - 33b c d cosh(x) +--R + +--R 3 3 2 2 3 2 +--R - 32b c cosh(x) + 21b c d cosh(x) + 12b c cosh(x) - 3b c d +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 6 2 3 5 +--R (15b d + (- 15b + 15a)c d)cosh(x) + (14b c d - 20b c )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (- 33b d + (23b - 33a)c d)cosh(x) + (- 20b c d + 8b c )cosh(x) +--R + +--R 3 2 2 2 3 +--R (21b d + (- 9b + 21a)c d)cosh(x) + (6b c d + 12b c )cosh(x) +--R + +--R 3 2 +--R - 3b d + (b - 3a)c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 7 3 6 2 5 +--R 6b c d cosh(x) + 10b c cosh(x) - 18b c d cosh(x) +--R + +--R 3 4 2 3 3 2 +--R - 22b c cosh(x) + 18b c d cosh(x) + 14b c cosh(x) +--R + +--R 2 3 +--R - 6b c d cosh(x) - 2b c +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 7 2 3 6 +--R (6b d + (- 6b + 6a)c d)cosh(x) + (9b c d - 10b c )cosh(x) +--R + +--R 3 2 5 2 3 4 +--R (- 18b d + (16b - 18a)c d)cosh(x) + (- 19b c d - 2b c )cosh(x) +--R + +--R 3 2 3 2 3 2 +--R (18b d + (- 14b + 18a)c d)cosh(x) + (11b c d + 10b c )cosh(x) +--R + +--R 3 2 2 3 +--R (- 6b d + (4b - 6a)c d)cosh(x) - b c d + 2b c +--R * +--R sinh(x) +--R + +--R 2 8 3 7 2 6 3 5 +--R b c d cosh(x) + 2b c cosh(x) - 4b c d cosh(x) - 6b c cosh(x) +--R + +--R 2 4 3 3 2 2 3 +--R 6b c d cosh(x) + 6b c cosh(x) - 4b c d cosh(x) - 2b c cosh(x) +--R + +--R 2 +--R b c d +--R * +--R 2 +--R coth(x) +--R + +--R 3 2 8 2 3 7 +--R (b d + (- b + a)c d)cosh(x) + (2b c d - 2b c )cosh(x) +--R + +--R 3 2 6 2 3 5 +--R (- 4b d + (4b - 4a)c d)cosh(x) + (- 6b c d - 2b c )cosh(x) +--R + +--R 3 2 4 2 3 3 +--R (6b d + (- 6b + 6a)c d)cosh(x) + (6b c d + 2b c )cosh(x) +--R + +--R 3 2 2 2 3 3 +--R (- 4b d + (4b - 4a)c d)cosh(x) + (- 2b c d + 2b c )cosh(x) + b d +--R + +--R 2 +--R (- b + a)c d +--R / +--R 3 2 3 6 +--R (c d cosh(x) - c d)sinh(x) +--R + +--R 3 3 4 2 3 4 5 +--R (6c d cosh(x) + 2c cosh(x) - 6c d cosh(x) - 2c )sinh(x) +--R + +--R 3 4 4 3 3 2 4 +--R 15c d cosh(x) + 10c cosh(x) - 18c d cosh(x) - 10c cosh(x) +--R + +--R 3 +--R 3c d +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R 20c d cosh(x) + 20c cosh(x) - 32c d cosh(x) - 24c cosh(x) +--R + +--R 3 4 +--R 12c d cosh(x) + 4c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R 15c d cosh(x) + 20c cosh(x) - 33c d cosh(x) - 32c cosh(x) +--R + +--R 3 2 4 3 +--R 21c d cosh(x) + 12c cosh(x) - 3c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 4 4 +--R 6c d cosh(x) + 10c cosh(x) - 18c d cosh(x) - 22c cosh(x) +--R + +--R 3 3 4 2 3 4 +--R 18c d cosh(x) + 14c cosh(x) - 6c d cosh(x) - 2c +--R * +--R sinh(x) +--R + +--R 3 8 4 7 3 6 4 5 +--R c d cosh(x) + 2c cosh(x) - 4c d cosh(x) - 6c cosh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R 6c d cosh(x) + 6c cosh(x) - 4c d cosh(x) - 2c cosh(x) + c d +--R * +--R x 2 +--R tanh(-) +--R 2 +--R + +--R 2 2 2 2 2 6 +--R (- 2c d cosh(x) + 2c d )sinh(x) +--R + +--R 2 2 3 3 2 2 2 3 5 +--R (- 12c d cosh(x) - 4c d cosh(x) + 12c d cosh(x) + 4c d)sinh(x) +--R + +--R 2 2 4 3 3 2 2 2 +--R - 30c d cosh(x) - 20c d cosh(x) + 36c d cosh(x) +--R + +--R 3 2 2 +--R 20c d cosh(x) - 6c d +--R * +--R 4 +--R sinh(x) +--R + +--R 2 2 5 3 4 2 2 3 +--R - 40c d cosh(x) - 40c d cosh(x) + 64c d cosh(x) +--R + +--R 3 2 2 2 3 +--R 48c d cosh(x) - 24c d cosh(x) - 8c d +--R * +--R 3 +--R sinh(x) +--R + +--R 2 2 6 3 5 2 2 4 +--R - 30c d cosh(x) - 40c d cosh(x) + 66c d cosh(x) +--R + +--R 3 3 2 2 2 3 2 2 +--R 64c d cosh(x) - 42c d cosh(x) - 24c d cosh(x) + 6c d +--R * +--R 2 +--R sinh(x) +--R + +--R 2 2 7 3 6 2 2 5 +--R - 12c d cosh(x) - 20c d cosh(x) + 36c d cosh(x) +--R + +--R 3 4 2 2 3 3 2 2 2 +--R 44c d cosh(x) - 36c d cosh(x) - 28c d cosh(x) + 12c d cosh(x) +--R + +--R 3 +--R 4c d +--R * +--R sinh(x) +--R + +--R 2 2 8 3 7 2 2 6 3 5 +--R - 2c d cosh(x) - 4c d cosh(x) + 8c d cosh(x) + 12c d cosh(x) +--R + +--R 2 2 4 3 3 2 2 2 3 +--R - 12c d cosh(x) - 12c d cosh(x) + 8c d cosh(x) + 4c d cosh(x) +--R + +--R 2 2 +--R - 2c d +--R * +--R x +--R tanh(-) +--R 2 +--R + +--R 3 2 3 6 +--R (- c d cosh(x) + c d)sinh(x) +--R + +--R 3 3 4 2 3 4 5 +--R (- 6c d cosh(x) - 2c cosh(x) + 6c d cosh(x) + 2c )sinh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R (- 15c d cosh(x) - 10c cosh(x) + 18c d cosh(x) + 10c cosh(x) - 3c d) +--R * +--R 4 +--R sinh(x) +--R + +--R 3 5 4 4 3 3 4 2 +--R - 20c d cosh(x) - 20c cosh(x) + 32c d cosh(x) + 24c cosh(x) +--R + +--R 3 4 +--R - 12c d cosh(x) - 4c +--R * +--R 3 +--R sinh(x) +--R + +--R 3 6 4 5 3 4 4 3 +--R - 15c d cosh(x) - 20c cosh(x) + 33c d cosh(x) + 32c cosh(x) +--R + +--R 3 2 4 3 +--R - 21c d cosh(x) - 12c cosh(x) + 3c d +--R * +--R 2 +--R sinh(x) +--R + +--R 3 7 4 6 3 5 4 4 +--R - 6c d cosh(x) - 10c cosh(x) + 18c d cosh(x) + 22c cosh(x) +--R + +--R 3 3 4 2 3 4 +--R - 18c d cosh(x) - 14c cosh(x) + 6c d cosh(x) + 2c +--R * +--R sinh(x) +--R + +--R 3 8 4 7 3 6 4 5 +--R - c d cosh(x) - 2c cosh(x) + 4c d cosh(x) + 6c cosh(x) +--R + +--R 3 4 4 3 3 2 4 3 +--R - 6c d cosh(x) - 6c cosh(x) + 4c d cosh(x) + 2c cosh(x) - c d +--R Type: Expression(Integer) +--E 323 + +--S 324 of 518 +t0961:= sinh(a+b*x)*tanh(c+b*x) +--R +--R +--R (313) sinh(b x + a)tanh(b x + c) +--R Type: Expression(Integer) +--E 324 + +--S 325 of 518 +r0961:= (-atan(sinh(c+b*x))*cosh(a-c)+sinh(a+b*x))/b +--R +--R +--R - cosh(c - a)atan(sinh(b x + c)) + sinh(b x + a) +--R (314) ------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 325 + +--S 326 of 518 +a0961:= integrate(t0961,x) +--R +--R +--R (315) +--R 2 2 +--R (2sinh(c - a) - 4cosh(c - a)sinh(c - a) + 2cosh(c - a) + 2) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) + 2)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) + 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 2cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 2 +--R - cosh(b x + c) sinh(c - a) + 2cosh(c - a)cosh(b x + c) sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) + 1 +--R / +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 326 + +--S 327 of 518 +m0961:= a0961-r0961 +--R +--R +--R (316) +--R 2 2 +--R (2sinh(c - a) - 4cosh(c - a)sinh(c - a) + 2cosh(c - a) + 2) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) + 2)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 +--R (2cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R 2cosh(c - a)cosh(b x + c)sinh(c - a) - 2cosh(c - a) cosh(b x + c) +--R * +--R atan(sinh(b x + c)) +--R + +--R 2 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R (- 2sinh(c - a) + 2cosh(c - a))sinh(b x + a) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) + 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 2cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R (- 2cosh(b x + c)sinh(c - a) + 2cosh(c - a)cosh(b x + c))sinh(b x + a) +--R + +--R 2 2 2 +--R - cosh(b x + c) sinh(c - a) + 2cosh(c - a)cosh(b x + c) sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) + 1 +--R / +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 327 + +--S 328 of 518 +d0961:= D(m0961,x) +--R +--R +--R (317) +--R 2 2 6 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 4cosh(b x + c)sinh(c - a) +--R + +--R (8cosh(c - a)cosh(b x + c) - 2cosh(b x + a))sinh(c - a) +--R + +--R 2 +--R - 4cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R - 6cosh(b x + c) sinh(c - a) +--R + +--R 2 +--R (12cosh(c - a)cosh(b x + c) - 6cosh(b x + a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 2 +--R - 6cosh(c - a) cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + a)cosh(b x + c) + 1 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 4cosh(b x + c) - 2cosh(b x + c))sinh(c - a) +--R + +--R 3 2 +--R 8cosh(c - a)cosh(b x + c) - 6cosh(b x + a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) - 4cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R - 4cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (- 4cosh(c - a) + 2)cosh(b x + c) + 4cosh(c - a)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- cosh(b x + c) - 5cosh(b x + c) + 1)sinh(c - a) +--R + +--R 4 3 +--R 2cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R 16cosh(c - a)cosh(b x + c) - 8cosh(b x + a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R - cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 2cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (- 11cosh(c - a) + 1)cosh(b x + c) +--R + +--R 2 +--R 8cosh(c - a)cosh(b x + a)cosh(b x + c) + cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 4cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 3 2 +--R 14cosh(c - a)cosh(b x + c) - 6cosh(b x + a)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) - 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R - 10cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a)cosh(b x + a)cosh(b x + c) + 2cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + a) +--R * +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- cosh(b x + c) + cosh(b x + c) )sinh(c - a) +--R + +--R 4 3 +--R 4cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R - 2cosh(b x + a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 4 3 +--R - 3cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (- cosh(c - a) + 1)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + a)cosh(b x + c) - 1 +--R / +--R 5 +--R (2sinh(c - a) - 2cosh(c - a))sinh(b x + c) +--R + +--R 4 +--R (6cosh(b x + c)sinh(c - a) - 6cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 4)sinh(c - a) - 6cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (2cosh(b x + c) + 8cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 2)sinh(c - a) - 6cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 328 + +--S 329 of 518 +t0962:= sinh(a+b*x)*tanh(c+b*x)^2 +--R +--R +--R 2 +--R (318) sinh(b x + a)tanh(b x + c) +--R Type: Expression(Integer) +--E 329 + +--S 330 of 518 +r0962:= cosh(a+b*x)/b+cosh(a-c)*sech(c+b*x)/b-atan(sinh(c+b*x))*sinh(a-c)/b +--R +--R +--R (319) +--R sinh(c - a)atan(sinh(b x + c)) + cosh(c - a)sech(b x + c) + cosh(b x + a) +--R ------------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 330 + +--S 331 of 518 +a0962:= integrate(t0962,x) +--R +--R +--R (320) +--R 2 2 +--R (2sinh(c - a) - 4cosh(c - a)sinh(c - a) + 2cosh(c - a) - 2) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R 6cosh(b x + c)sinh(c - a) +--R + +--R - 12cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a) - 6)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 2)sinh(c - a) +--R + +--R 2 +--R (- 12cosh(c - a)cosh(b x + c) - 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (6cosh(c - a) - 6)cosh(b x + c) + 2cosh(c - a) - 2 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (2cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 4cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (2cosh(c - a) - 2)cosh(b x + c) + (2cosh(c - a) - 2)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 2 4 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 4cosh(b x + c)sinh(c - a) + 8cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 4cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) - 3)sinh(c - a) +--R + +--R 2 +--R (12cosh(c - a)cosh(b x + c) + 6cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 6cosh(c - a) cosh(b x + c) - 3cosh(c - a) - 3 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 4cosh(b x + c) - 6cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (8cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 4cosh(c - a) cosh(b x + c) + (- 6cosh(c - a) - 6)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- cosh(b x + c) - 3cosh(b x + c) )sinh(c - a) +--R + +--R 4 2 +--R (2cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) )sinh(c - a) +--R + +--R 2 4 2 2 +--R - cosh(c - a) cosh(b x + c) + (- 3cosh(c - a) - 3)cosh(b x + c) - 1 +--R / +--R 3 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c) + 2b)sinh(c - a) - 6b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2b cosh(b x + c) + 2b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2b cosh(c - a)cosh(b x + c) - 2b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 331 + +--S 332 of 518 +m0962:= a0962-r0962 +--R +--R +--R (321) +--R 2 2 +--R (2sinh(c - a) - 4cosh(c - a)sinh(c - a) + 2cosh(c - a) - 2) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R 6cosh(b x + c)sinh(c - a) +--R + +--R - 12cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a) - 6)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 2)sinh(c - a) +--R + +--R 2 +--R (- 12cosh(c - a)cosh(b x + c) - 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (6cosh(c - a) - 6)cosh(b x + c) + 2cosh(c - a) - 2 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (2cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 4cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (2cosh(c - a) - 2)cosh(b x + c) + (2cosh(c - a) - 2)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 3 +--R (- 2sinh(c - a) + 2cosh(c - a)sinh(c - a))sinh(b x + c) +--R + +--R 2 +--R - 6cosh(b x + c)sinh(c - a) +--R + +--R 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) - 2)sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 2cosh(b x + c) - 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R * +--R atan(sinh(b x + c)) +--R + +--R 2 2 4 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 4cosh(b x + c)sinh(c - a) +--R + +--R - 2cosh(c - a)sech(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 2 +--R 2cosh(c - a) sech(b x + c) - 4cosh(c - a) cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) - 3)sinh(c - a) +--R + +--R - 6cosh(c - a)cosh(b x + c)sech(b x + c) +--R + +--R 2 +--R 12cosh(c - a)cosh(b x + c) - 6cosh(b x + a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R 6cosh(c - a) cosh(b x + c)sech(b x + c) - 6cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a)cosh(b x + a)cosh(b x + c) - 3cosh(c - a) - 3 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 4cosh(b x + c) - 6cosh(b x + c))sinh(c - a) +--R + +--R 2 +--R (- 6cosh(c - a)cosh(b x + c) - 2cosh(c - a))sech(b x + c) +--R + +--R 3 2 +--R 8cosh(c - a)cosh(b x + c) - 6cosh(b x + a)cosh(b x + c) +--R + +--R 12cosh(c - a)cosh(b x + c) - 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (6cosh(c - a) cosh(b x + c) + 2cosh(c - a) )sech(b x + c) +--R + +--R 2 3 +--R - 4cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (- 6cosh(c - a) - 6)cosh(b x + c) + 2cosh(c - a)cosh(b x + a) +--R * +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- cosh(b x + c) - 3cosh(b x + c) )sinh(c - a) +--R + +--R 3 +--R (- 2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c) +--R + +--R 4 3 +--R 2cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R (2cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c))sech(b x + c) +--R + +--R 2 4 3 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (- 3cosh(c - a) - 3)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + a)cosh(b x + c) - 1 +--R / +--R 3 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c) + 2b)sinh(c - a) - 6b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2b cosh(b x + c) + 2b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2b cosh(c - a)cosh(b x + c) - 2b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 332 + +--S 333 of 518 +d0962:= D(m0962,x) +--R +--R +--R (322) +--R 2 +--R (2cosh(c - a)sech(b x + c)sinh(c - a) - 2cosh(c - a) sech(b x + c)) +--R * +--R 7 +--R sinh(b x + c) +--R + +--R 10cosh(c - a)cosh(b x + c)sech(b x + c)sinh(c - a) +--R + +--R 2 +--R - 10cosh(c - a) cosh(b x + c)sech(b x + c) +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 2 +--R (20cosh(c - a)cosh(b x + c) + 6cosh(c - a))sech(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (- 20cosh(c - a) cosh(b x + c) - 6cosh(c - a) )sech(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 3 +--R (20cosh(c - a)cosh(b x + c) + 22cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 3 2 +--R (- 20cosh(c - a) cosh(b x + c) - 22cosh(c - a) cosh(b x + c)) +--R * +--R sech(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 4 2 +--R 10cosh(c - a)cosh(b x + c) + 32cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 4 2 2 +--R - 10cosh(c - a) cosh(b x + c) - 32cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a) +--R * +--R sech(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 5 3 +--R 2cosh(c - a)cosh(b x + c) + 24cosh(c - a)cosh(b x + c) +--R + +--R 14cosh(c - a)cosh(b x + c) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 5 2 3 +--R - 2cosh(c - a) cosh(b x + c) - 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 14cosh(c - a) cosh(b x + c) +--R * +--R sech(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R 10cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 4 2 2 +--R - 10cosh(c - a) cosh(b x + c) - 12cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 2cosh(c - a) +--R * +--R sech(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R 2cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + c) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 5 2 3 +--R - 2cosh(c - a) cosh(b x + c) - 4cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 2cosh(c - a) cosh(b x + c) +--R * +--R sech(b x + c) +--R * +--R tanh(b x + c) +--R + +--R 2 2 8 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R (- 2sinh(c - a) + 2cosh(c - a))sinh(b x + a) +--R + +--R 2 +--R - 6cosh(b x + c)sinh(c - a) + 12cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R 7 +--R sinh(b x + c) +--R + +--R (- 10cosh(b x + c)sinh(c - a) + 10cosh(c - a)cosh(b x + c)) +--R * +--R sinh(b x + a) +--R + +--R 2 2 +--R (- 15cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (30cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 15cosh(c - a) cosh(b x + c) + cosh(c - a) + 1 +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 20cosh(b x + c) - 6)sinh(c - a) + 20cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 3 2 +--R - 20cosh(b x + c) sinh(c - a) +--R + +--R 3 +--R (40cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 20cosh(c - a) cosh(b x + c) + (2cosh(c - a) + 4)cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 3 +--R (- 20cosh(b x + c) - 22cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R 20cosh(c - a)cosh(b x + c) + 22cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) - 13cosh(b x + c) + 1)sinh(c - a) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) + 16cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 15cosh(c - a) cosh(b x + c) + (- 3cosh(c - a) + 6)cosh(b x + c) +--R + +--R 2 +--R cosh(c - a) - 1 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 4 2 +--R (- 10cosh(b x + c) - 32cosh(b x + c) - 6)sinh(c - a) +--R + +--R 4 2 +--R 10cosh(c - a)cosh(b x + c) + 32cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 5 3 2 +--R (- 6cosh(b x + c) - 32cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 12cosh(c - a)cosh(b x + c) + 44cosh(c - a)cosh(b x + c) +--R + +--R - 8cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) + (- 12cosh(c - a) + 4)cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 5 3 +--R (- 2cosh(b x + c) - 24cosh(b x + c) - 14cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 5 3 +--R 2cosh(c - a)cosh(b x + c) + 24cosh(c - a)cosh(b x + c) +--R + +--R 14cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (- cosh(b x + c) - 33cosh(b x + c) - cosh(b x + c) - 1) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 6 4 +--R 2cosh(c - a)cosh(b x + c) + 46cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 10cosh(c - a)cosh(b x + c) + 2cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) + (- 13cosh(c - a) + 1)cosh(b x + c) +--R + +--R 2 2 2 +--R (11cosh(c - a) + 4)cosh(b x + c) - cosh(c - a) - 1 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (- 10cosh(b x + c) - 12cosh(b x + c) - 2)sinh(c - a) +--R + +--R 4 2 +--R 10cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 5 3 2 +--R (- 16cosh(b x + c) - 4cosh(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 22cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) + (8cosh(c - a) + 4)cosh(b x + c) +--R + +--R 2 +--R (- 2cosh(c - a) - 4)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (- 2cosh(b x + c) - 4cosh(b x + c) - 2cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 2cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 2 +--R (- 3cosh(b x + c) - 2cosh(b x + c) - 3cosh(b x + c) )sinh(c - a) +--R + +--R 6 2 +--R (4cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) )sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) + (2cosh(c - a) + 1)cosh(b x + c) +--R + +--R 2 2 +--R (- cosh(c - a) - 2)cosh(b x + c) + 1 +--R / +--R 7 +--R (2sinh(c - a) - 2cosh(c - a))sinh(b x + c) +--R + +--R 6 +--R (10cosh(b x + c)sinh(c - a) - 10cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (20cosh(b x + c) + 6)sinh(c - a) - 20cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 3 +--R (20cosh(b x + c) + 22cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 20cosh(c - a)cosh(b x + c) - 22cosh(c - a)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 4 2 +--R (10cosh(b x + c) + 32cosh(b x + c) + 6)sinh(c - a) +--R + +--R 4 2 +--R - 10cosh(c - a)cosh(b x + c) - 32cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 5 3 +--R (2cosh(b x + c) + 24cosh(b x + c) + 14cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 2cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R + +--R - 14cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (10cosh(b x + c) + 12cosh(b x + c) + 2)sinh(c - a) +--R + +--R 4 2 +--R - 10cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (2cosh(b x + c) + 4cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 2cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 333 + +--S 334 of 518 +t0963:= sinh(a+b*x)*tanh(c+b*x)^3 +--R +--R +--R 3 +--R (323) sinh(b x + a)tanh(b x + c) +--R Type: Expression(Integer) +--E 334 + +--S 335 of 518 +r0963:= -3/2*atan(sinh(c+b*x))*cosh(a-c)/b+sech(c+b*x)*sinh(a-c)/b+_ + sinh(a+b*x)/b+1/2*cosh(a-c)*sech(c+b*x)*tanh(c+b*x)/b +--R +--R +--R (324) +--R - 3cosh(c - a)atan(sinh(b x + c)) + cosh(c - a)sech(b x + c)tanh(b x + c) +--R + +--R 2sinh(b x + a) - 2sech(b x + c)sinh(c - a) +--R / +--R 2b +--R Type: Expression(Integer) +--E 335 + +--S 336 of 518 +a0963:= integrate(t0963,x) +--R +--R +--R (325) +--R 2 2 +--R (3sinh(c - a) - 6cosh(c - a)sinh(c - a) + 3cosh(c - a) + 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R 15cosh(b x + c)sinh(c - a) +--R + +--R - 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (15cosh(c - a) + 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (30cosh(b x + c) + 6)sinh(c - a) +--R + +--R 2 +--R (- 60cosh(c - a)cosh(b x + c) - 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (30cosh(c - a) + 30)cosh(b x + c) + 6cosh(c - a) + 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (30cosh(b x + c) + 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 60cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (30cosh(c - a) + 30)cosh(b x + c) +--R + +--R 2 +--R (18cosh(c - a) + 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) + 18cosh(b x + c) + 3)sinh(c - a) +--R + +--R 4 2 +--R - 30cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (15cosh(c - a) + 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (18cosh(c - a) + 18)cosh(b x + c) + 3cosh(c - a) + 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (3cosh(b x + c) + 6cosh(b x + c) + 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R (3cosh(c - a) + 3)cosh(b x + c) + (6cosh(c - a) + 6)cosh(b x + c) +--R + +--R 2 +--R (3cosh(c - a) + 3)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 2 6 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 6cosh(b x + c)sinh(c - a) + 12cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 15cosh(b x + c) - 5)sinh(c - a) +--R + +--R 2 +--R (30cosh(c - a)cosh(b x + c) + 10cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 15cosh(c - a) cosh(b x + c) - 5cosh(c - a) + 2 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 20cosh(b x + c) - 20cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (40cosh(c - a)cosh(b x + c) + 40cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 20cosh(c - a) cosh(b x + c) + (- 20cosh(c - a) + 8)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) - 30cosh(b x + c) - 2)sinh(c - a) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) + 60cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 2 2 2 +--R (- 30cosh(c - a) + 12)cosh(b x + c) - 2cosh(c - a) + 5 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 6cosh(b x + c) - 20cosh(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 12cosh(c - a)cosh(b x + c) + 40cosh(c - a)cosh(b x + c) +--R + +--R 8cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) + (- 20cosh(c - a) + 8)cosh(b x + c) +--R + +--R 2 +--R (- 4cosh(c - a) + 10)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (- cosh(b x + c) - 5cosh(b x + c) - 2cosh(b x + c) )sinh(c - a) +--R + +--R 6 4 +--R 2cosh(c - a)cosh(b x + c) + 10cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) + (- 5cosh(c - a) + 2)cosh(b x + c) +--R + +--R 2 2 +--R (- 2cosh(c - a) + 5)cosh(b x + c) + 1 +--R / +--R 5 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R (10b cosh(b x + c)sinh(c - a) - 10b cosh(c - a)cosh(b x + c)) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (20b cosh(b x + c) + 4b)sinh(c - a) - 20b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (20b cosh(b x + c) + 12b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 20b cosh(c - a)cosh(b x + c) - 12b cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (10b cosh(b x + c) + 12b cosh(b x + c) + 2b)sinh(c - a) +--R + +--R 4 2 +--R - 10b cosh(c - a)cosh(b x + c) - 12b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (2b cosh(b x + c) + 4b cosh(b x + c) + 2b cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 2b cosh(c - a)cosh(b x + c) - 4b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 336 + +--S 337 of 518 +m0963:= a0963-r0963 +--R +--R +--R (326) +--R 2 2 +--R (3sinh(c - a) - 6cosh(c - a)sinh(c - a) + 3cosh(c - a) + 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R 15cosh(b x + c)sinh(c - a) +--R + +--R - 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (15cosh(c - a) + 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (30cosh(b x + c) + 6)sinh(c - a) +--R + +--R 2 +--R (- 60cosh(c - a)cosh(b x + c) - 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (30cosh(c - a) + 30)cosh(b x + c) + 6cosh(c - a) + 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (30cosh(b x + c) + 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 60cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (30cosh(c - a) + 30)cosh(b x + c) +--R + +--R 2 +--R (18cosh(c - a) + 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) + 18cosh(b x + c) + 3)sinh(c - a) +--R + +--R 4 2 +--R - 30cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (15cosh(c - a) + 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (18cosh(c - a) + 18)cosh(b x + c) + 3cosh(c - a) + 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (3cosh(b x + c) + 6cosh(b x + c) + 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R (3cosh(c - a) + 3)cosh(b x + c) + (6cosh(c - a) + 6)cosh(b x + c) +--R + +--R 2 +--R (3cosh(c - a) + 3)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 5 +--R (3cosh(c - a)sinh(c - a) - 3cosh(c - a) )sinh(b x + c) +--R + +--R 15cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 15cosh(c - a) cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 +--R (30cosh(c - a)cosh(b x + c) + 6cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 30cosh(c - a) cosh(b x + c) - 6cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (30cosh(c - a)cosh(b x + c) + 18cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R - 30cosh(c - a) cosh(b x + c) - 18cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R 15cosh(c - a)cosh(b x + c) + 18cosh(c - a)cosh(b x + c) +--R + +--R 3cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 15cosh(c - a) cosh(b x + c) - 18cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 3cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R 3cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) +--R + +--R 3cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 3cosh(c - a) cosh(b x + c) - 6cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 3cosh(c - a) cosh(b x + c) +--R * +--R atan(sinh(b x + c)) +--R + +--R 2 +--R (- cosh(c - a)sech(b x + c)sinh(c - a) + cosh(c - a) sech(b x + c)) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R - 5cosh(c - a)cosh(b x + c)sech(b x + c)sinh(c - a) +--R + +--R 2 +--R 5cosh(c - a) cosh(b x + c)sech(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 +--R (- 10cosh(c - a)cosh(b x + c) - 2cosh(c - a))sech(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (10cosh(c - a) cosh(b x + c) + 2cosh(c - a) )sech(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (- 10cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 3 2 +--R (10cosh(c - a) cosh(b x + c) + 6cosh(c - a) cosh(b x + c)) +--R * +--R sech(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R - 5cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 4 2 2 +--R 5cosh(c - a) cosh(b x + c) + 6cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R cosh(c - a) +--R * +--R sech(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R - cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a)cosh(b x + c) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 5 2 3 +--R cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R cosh(c - a) cosh(b x + c) +--R * +--R sech(b x + c) +--R * +--R tanh(b x + c) +--R + +--R 2 2 6 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R (- 2sinh(c - a) + 2cosh(c - a))sinh(b x + a) +--R + +--R 2 +--R (2sech(b x + c) - 6cosh(b x + c))sinh(c - a) +--R + +--R (- 2cosh(c - a)sech(b x + c) + 12cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R (- 10cosh(b x + c)sinh(c - a) + 10cosh(c - a)cosh(b x + c)) +--R * +--R sinh(b x + a) +--R + +--R 2 2 +--R (10cosh(b x + c)sech(b x + c) - 15cosh(b x + c) - 5)sinh(c - a) +--R + +--R - 10cosh(c - a)cosh(b x + c)sech(b x + c) +--R + +--R 2 +--R 30cosh(c - a)cosh(b x + c) + 10cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R - 15cosh(c - a) cosh(b x + c) - 5cosh(c - a) + 2 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 20cosh(b x + c) - 4)sinh(c - a) + 20cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 2 3 +--R (20cosh(b x + c) + 4)sech(b x + c) - 20cosh(b x + c) +--R + +--R - 20cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 +--R (- 20cosh(c - a)cosh(b x + c) - 4cosh(c - a))sech(b x + c) +--R + +--R 3 +--R 40cosh(c - a)cosh(b x + c) + 40cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R - 20cosh(c - a) cosh(b x + c) + (- 20cosh(c - a) + 8)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (- 20cosh(b x + c) - 12cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R 20cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 3 +--R (20cosh(b x + c) + 12cosh(b x + c))sech(b x + c) +--R + +--R 4 2 +--R - 15cosh(b x + c) - 30cosh(b x + c) - 2 +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 +--R (- 20cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) + 60cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 2 2 2 +--R (- 30cosh(c - a) + 12)cosh(b x + c) - 2cosh(c - a) + 5 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (- 10cosh(b x + c) - 12cosh(b x + c) - 2)sinh(c - a) +--R + +--R 4 2 +--R 10cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 4 2 +--R (10cosh(b x + c) + 12cosh(b x + c) + 2)sech(b x + c) +--R + +--R 5 3 +--R - 6cosh(b x + c) - 20cosh(b x + c) - 4cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 4 2 +--R - 10cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sech(b x + c) +--R + +--R 5 3 +--R 12cosh(c - a)cosh(b x + c) + 40cosh(c - a)cosh(b x + c) +--R + +--R 8cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) + (- 20cosh(c - a) + 8)cosh(b x + c) +--R + +--R 2 +--R (- 4cosh(c - a) + 10)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (- 2cosh(b x + c) - 4cosh(b x + c) - 2cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 2cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 5 3 +--R (2cosh(b x + c) + 4cosh(b x + c) + 2cosh(b x + c))sech(b x + c) +--R + +--R 6 4 2 +--R - cosh(b x + c) - 5cosh(b x + c) - 2cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 5 3 +--R - 2cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) +--R * +--R sech(b x + c) +--R + +--R 6 4 +--R 2cosh(c - a)cosh(b x + c) + 10cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) + (- 5cosh(c - a) + 2)cosh(b x + c) +--R + +--R 2 2 +--R (- 2cosh(c - a) + 5)cosh(b x + c) + 1 +--R / +--R 5 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R (10b cosh(b x + c)sinh(c - a) - 10b cosh(c - a)cosh(b x + c)) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (20b cosh(b x + c) + 4b)sinh(c - a) - 20b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (20b cosh(b x + c) + 12b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 20b cosh(c - a)cosh(b x + c) - 12b cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (10b cosh(b x + c) + 12b cosh(b x + c) + 2b)sinh(c - a) +--R + +--R 4 2 +--R - 10b cosh(c - a)cosh(b x + c) - 12b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (2b cosh(b x + c) + 4b cosh(b x + c) + 2b cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 2b cosh(c - a)cosh(b x + c) - 4b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 337 + +--S 338 of 518 +--d0963:= D(m0963,x) +--E 338 + +--S 339 of 518 +t0964:= sinh(a+b*x)*coth(c+b*x) +--R +--R +--R (327) coth(b x + c)sinh(b x + a) +--R Type: Expression(Integer) +--E 339 + +--S 340 of 518 +r0964:= (-acoth(cosh(c+b*x))*sinh(a-c)+sinh(a+b*x))/b +--R +--R +--R sinh(c - a)acoth(cosh(b x + c)) + sinh(b x + a) +--R (328) ----------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 340 + +--S 341 of 518 +a0964:= integrate(t0964,x) +--R +--R +--R (329) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) - 1) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R cosh(b x + c)sinh(c - a) - 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (cosh(c - a) - 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R - cosh(b x + c)sinh(c - a) + 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- cosh(c - a) + 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) + 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 2cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 2 +--R - cosh(b x + c) sinh(c - a) + 2cosh(c - a)cosh(b x + c) sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) + 1 +--R / +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 341 + +--S 342 of 518 +m0964:= a0964-r0964 +--R +--R +--R (330) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) - 1) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R cosh(b x + c)sinh(c - a) - 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (cosh(c - a) - 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R - cosh(b x + c)sinh(c - a) + 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- cosh(c - a) + 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 +--R (- 2sinh(c - a) + 2cosh(c - a)sinh(c - a))sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) + 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R * +--R acoth(cosh(b x + c)) +--R + +--R 2 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R (- 2sinh(c - a) + 2cosh(c - a))sinh(b x + a) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) + 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 2cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R (- 2cosh(b x + c)sinh(c - a) + 2cosh(c - a)cosh(b x + c))sinh(b x + a) +--R + +--R 2 2 2 +--R - cosh(b x + c) sinh(c - a) + 2cosh(c - a)cosh(b x + c) sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) + 1 +--R / +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 342 + +--S 343 of 518 +d0964:= D(m0964,x) +--R +--R +--R (331) +--R 2 2 +--R (- cosh(b x + c) + 3)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - cosh(c - a) cosh(b x + c) + cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 4cosh(b x + c) + 10cosh(b x + c))sinh(c - a) +--R + +--R 3 2 +--R 8cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R - 14cosh(c - a)cosh(b x + c) + 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R - 4cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R 2cosh(c - a)cosh(b x + a)cosh(b x + c) + 4cosh(c - a) cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 6cosh(b x + c) + 11cosh(b x + c) - 1)sinh(c - a) +--R + +--R 4 3 +--R 12cosh(c - a)cosh(b x + c) - 6cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R - 16cosh(c - a)cosh(b x + c) + 6cosh(b x + a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R - 6cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 6cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (5cosh(c - a) + 1)cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a)cosh(b x + a)cosh(b x + c) + cosh(c - a) - 1 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 4cosh(b x + c) + 4cosh(b x + c) )sinh(c - a) +--R + +--R 5 4 +--R 8cosh(c - a)cosh(b x + c) - 6cosh(b x + a)cosh(b x + c) +--R + +--R 3 2 +--R - 6cosh(c - a)cosh(b x + c) + 8cosh(b x + a)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) - 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R - 4cosh(c - a) cosh(b x + c) +--R + +--R 4 +--R 6cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 3 +--R (2cosh(c - a) + 2)cosh(b x + c) +--R + +--R 2 +--R - 8cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (2cosh(c - a) - 2)cosh(b x + c) + 2cosh(c - a)cosh(b x + a) +--R * +--R sinh(b x + c) +--R + +--R 6 2 2 +--R (- cosh(b x + c) + cosh(b x + c) )sinh(c - a) +--R + +--R 6 5 +--R 2cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R 3 2 +--R 4cosh(b x + a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(b x + a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 6 5 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 4 3 +--R cosh(b x + c) - 4cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a)cosh(b x + c) - 1 +--R / +--R 2 2 +--R (2cosh(b x + c) - 2)sinh(c - a) - 2cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (6cosh(b x + c) - 6cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 6cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (6cosh(b x + c) - 8cosh(b x + c) + 2)sinh(c - a) +--R + +--R 4 2 +--R - 6cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (2cosh(b x + c) - 4cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 2cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 343 + +--S 344 of 518 +t0965:= sinh(a+b*x)*coth(c+b*x)^2 +--R +--R +--R 2 +--R (332) coth(b x + c) sinh(b x + a) +--R Type: Expression(Integer) +--E 344 + +--S 345 of 518 +r0965:= -acoth(cosh(c+b*x))*cosh(a-c)/b+cosh(a+b*x)/b-csch(c+b*x)*sinh(a-c)/b +--R +--R +--R (333) +--R - cosh(c - a)acoth(cosh(b x + c)) + csch(b x + c)sinh(c - a) + cosh(b x + a) +--R ---------------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 345 + +--S 346 of 518 +a0965:= integrate(t0965,x) +--R +--R +--R (334) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) + 1) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R 3cosh(b x + c)sinh(c - a) - 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (3cosh(c - a) + 3)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (3cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (- 6cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (3cosh(c - a) + 3)cosh(b x + c) - cosh(c - a) - 1 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (cosh(b x + c) - cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 2cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (cosh(c - a) + 1)cosh(b x + c) + (- cosh(c - a) - 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R - 3cosh(b x + c)sinh(c - a) +--R + +--R 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 3cosh(c - a) - 3)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 3cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- 3cosh(c - a) - 3)cosh(b x + c) + cosh(c - a) + 1 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (- cosh(b x + c) + cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (- cosh(c - a) - 1)cosh(b x + c) + (cosh(c - a) + 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 2 4 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 4cosh(b x + c)sinh(c - a) + 8cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 4cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) + 3)sinh(c - a) +--R + +--R 2 +--R (12cosh(c - a)cosh(b x + c) - 6cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 6cosh(c - a) cosh(b x + c) + 3cosh(c - a) - 3 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 4cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (8cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 4cosh(c - a) cosh(b x + c) + (6cosh(c - a) - 6)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- cosh(b x + c) + 3cosh(b x + c) )sinh(c - a) +--R + +--R 4 2 +--R (2cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) )sinh(c - a) +--R + +--R 2 4 2 2 +--R - cosh(c - a) cosh(b x + c) + (3cosh(c - a) - 3)cosh(b x + c) + 1 +--R / +--R 3 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c) - 2b)sinh(c - a) - 6b cosh(c - a)cosh(b x + c) +--R + +--R 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2b cosh(b x + c) - 2b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2b cosh(c - a)cosh(b x + c) + 2b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 346 + +--S 347 of 518 +m0965:= a0965-r0965 +--R +--R +--R (335) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) + 1) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R 3cosh(b x + c)sinh(c - a) - 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (3cosh(c - a) + 3)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (3cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (- 6cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (3cosh(c - a) + 3)cosh(b x + c) - cosh(c - a) - 1 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (cosh(b x + c) - cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 2cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (cosh(c - a) + 1)cosh(b x + c) + (- cosh(c - a) - 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R - 3cosh(b x + c)sinh(c - a) +--R + +--R 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 3cosh(c - a) - 3)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 3cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- 3cosh(c - a) - 3)cosh(b x + c) + cosh(c - a) + 1 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (- cosh(b x + c) + cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (- cosh(c - a) - 1)cosh(b x + c) + (cosh(c - a) + 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 3 +--R (2cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c)sinh(c - a) - 6cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 6cosh(c - a) cosh(b x + c) + 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 2cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c) +--R * +--R acoth(cosh(b x + c)) +--R + +--R 2 2 4 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R (- 2csch(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 2cosh(c - a)csch(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 +--R - 4cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c)csch(b x + c) - 6cosh(b x + c) + 3)sinh(c - a) +--R + +--R 6cosh(c - a)cosh(b x + c)csch(b x + c) +--R + +--R 2 +--R 12cosh(c - a)cosh(b x + c) - 6cosh(b x + a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 2 +--R - 6cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a)cosh(b x + a)cosh(b x + c) + 3cosh(c - a) - 3 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 3 +--R (- 6cosh(b x + c) + 2)csch(b x + c) - 4cosh(b x + c) +--R + +--R 6cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c) - 2cosh(c - a))csch(b x + c) +--R + +--R 3 2 +--R 8cosh(c - a)cosh(b x + c) - 6cosh(b x + a)cosh(b x + c) +--R + +--R - 12cosh(c - a)cosh(b x + c) + 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R - 4cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (6cosh(c - a) - 6)cosh(b x + c) - 2cosh(c - a)cosh(b x + a) +--R * +--R sinh(b x + c) +--R + +--R 3 4 +--R (- 2cosh(b x + c) + 2cosh(b x + c))csch(b x + c) - cosh(b x + c) +--R + +--R 2 +--R 3cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))csch(b x + c) +--R + +--R 4 3 +--R 2cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a)cosh(b x + c) + 2cosh(b x + a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 4 3 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (3cosh(c - a) - 3)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + a)cosh(b x + c) + 1 +--R / +--R 3 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c) - 2b)sinh(c - a) - 6b cosh(c - a)cosh(b x + c) +--R + +--R 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2b cosh(b x + c) - 2b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2b cosh(c - a)cosh(b x + c) + 2b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 347 + +--S 348 of 518 +d0965:= D(m0965,x) +--R +--R +--R (336) +--R 2 2 +--R (- cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - cosh(c - a) cosh(b x + c) + 3cosh(c - a) +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 2cosh(b x + c) + 2)sinh(c - a) + 2cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 2 3 +--R (2cosh(b x + c) - 2)coth(b x + c)csch(b x + c) - 6cosh(b x + c) +--R + +--R 6cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a)cosh(b x + c) + 2cosh(c - a))coth(b x + c) +--R * +--R csch(b x + c) +--R + +--R 3 +--R 12cosh(c - a)cosh(b x + c) - 22cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R - 6cosh(c - a) cosh(b x + c) + 16cosh(c - a) cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 3 +--R (- 10cosh(b x + c) + 10cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R 10cosh(c - a)cosh(b x + c) - 10cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 3 +--R (10cosh(b x + c) - 10cosh(b x + c))coth(b x + c)csch(b x + c) +--R + +--R 4 2 +--R - 15cosh(b x + c) + 13cosh(b x + c) + 2 +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 +--R (- 10cosh(c - a)cosh(b x + c) + 10cosh(c - a)cosh(b x + c)) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) - 46cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 15cosh(c - a) cosh(b x + c) + (33cosh(c - a) + 1)cosh(b x + c) +--R + +--R 2 +--R - 2cosh(c - a) - 1 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 4 2 +--R (- 20cosh(b x + c) + 24cosh(b x + c) - 4)sinh(c - a) +--R + +--R 4 2 +--R 20cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 4 2 +--R (20cosh(b x + c) - 24cosh(b x + c) + 4)coth(b x + c) +--R * +--R csch(b x + c) +--R + +--R 5 3 +--R - 20cosh(b x + c) + 12cosh(b x + c) + 8cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 4 2 +--R - 20cosh(c - a)cosh(b x + c) + 24cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 5 3 +--R 40cosh(c - a)cosh(b x + c) - 44cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 20cosh(c - a) cosh(b x + c) + (32cosh(c - a) + 4)cosh(b x + c) +--R + +--R 2 +--R (- 4cosh(c - a) - 4)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 5 3 +--R (- 20cosh(b x + c) + 32cosh(b x + c) - 12cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 5 3 +--R 20cosh(c - a)cosh(b x + c) - 32cosh(c - a)cosh(b x + c) +--R + +--R 12cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 5 3 +--R (20cosh(b x + c) - 32cosh(b x + c) + 12cosh(b x + c)) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 6 4 2 +--R - 15cosh(b x + c) + 3cosh(b x + c) + 11cosh(b x + c) + 1 +--R * +--R 2 +--R sinh(c - a) +--R + +--R 5 3 +--R - 20cosh(c - a)cosh(b x + c) + 32cosh(c - a)cosh(b x + c) +--R + +--R - 12cosh(c - a)cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 6 4 +--R 30cosh(c - a)cosh(b x + c) - 16cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 10cosh(c - a)cosh(b x + c) - 4cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R - 15cosh(c - a) cosh(b x + c) + (13cosh(c - a) + 6)cosh(b x + c) +--R + +--R 2 2 2 +--R (- cosh(c - a) - 4)cosh(b x + c) + 3cosh(c - a) - 2 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 6 4 2 +--R (- 10cosh(b x + c) + 22cosh(b x + c) - 14cosh(b x + c) + 2) +--R * +--R sinh(c - a) +--R + +--R 6 4 +--R 10cosh(c - a)cosh(b x + c) - 22cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R 14cosh(c - a)cosh(b x + c) - 2cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 6 4 2 +--R (10cosh(b x + c) - 22cosh(b x + c) + 14cosh(b x + c) - 2) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 7 5 3 +--R - 6cosh(b x + c) - 2cosh(b x + c) + 6cosh(b x + c) +--R + +--R 2cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 6 4 +--R - 10cosh(c - a)cosh(b x + c) + 22cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 14cosh(c - a)cosh(b x + c) + 2cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 7 5 +--R 12cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R + +--R 3 +--R - 8cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 7 5 +--R - 6cosh(c - a) cosh(b x + c) + 4cosh(b x + c) +--R + +--R 2 3 2 +--R 2cosh(c - a) cosh(b x + c) + (4cosh(c - a) - 4)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 7 5 3 +--R - 2cosh(b x + c) + 6cosh(b x + c) - 6cosh(b x + c) +--R + +--R 2cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 7 5 +--R 2cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) +--R + +--R 3 +--R 6cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 7 5 3 +--R 2cosh(b x + c) - 6cosh(b x + c) + 6cosh(b x + c) +--R + +--R - 2cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 8 6 4 2 +--R - cosh(b x + c) - cosh(b x + c) + cosh(b x + c) + cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 7 5 +--R - 2cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) +--R + +--R 3 +--R - 6cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 8 6 +--R 2cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R + +--R 4 2 +--R - 2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 8 2 6 +--R - cosh(c - a) cosh(b x + c) + (- cosh(c - a) + 1)cosh(b x + c) +--R + +--R 2 4 2 2 +--R (cosh(c - a) + 1)cosh(b x + c) + (cosh(c - a) - 1)cosh(b x + c) - 1 +--R / +--R 2 2 +--R (2cosh(b x + c) - 2)sinh(c - a) - 2cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 3 +--R (10cosh(b x + c) - 10cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 10cosh(c - a)cosh(b x + c) + 10cosh(c - a)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 4 2 +--R (20cosh(b x + c) - 24cosh(b x + c) + 4)sinh(c - a) +--R + +--R 4 2 +--R - 20cosh(c - a)cosh(b x + c) + 24cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 5 3 +--R (20cosh(b x + c) - 32cosh(b x + c) + 12cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 20cosh(c - a)cosh(b x + c) + 32cosh(c - a)cosh(b x + c) +--R + +--R - 12cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 6 4 2 +--R (10cosh(b x + c) - 22cosh(b x + c) + 14cosh(b x + c) - 2) +--R * +--R sinh(c - a) +--R + +--R 6 4 +--R - 10cosh(c - a)cosh(b x + c) + 22cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 14cosh(c - a)cosh(b x + c) + 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 7 5 3 +--R (2cosh(b x + c) - 6cosh(b x + c) + 6cosh(b x + c) - 2cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 7 5 +--R - 2cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) +--R + +--R 3 +--R - 6cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 348 + +--S 349 of 518 +t0966:= sinh(a+b*x)*coth(c+b*x)^3 +--R +--R +--R 3 +--R (337) coth(b x + c) sinh(b x + a) +--R Type: Expression(Integer) +--E 349 + +--S 350 of 518 +r0966:= -cosh(a-c)*csch(c+b*x)/b-3/2*acoth(cosh(c+b*x))*sinh(a-c)/b-_ + 1/2*coth(c+b*x)*csch(c+b*x)*sinh(a-c)/b+sinh(a+b*x)/b +--R +--R +--R (338) +--R 3sinh(c - a)acoth(cosh(b x + c)) + 2sinh(b x + a) +--R + +--R coth(b x + c)csch(b x + c)sinh(c - a) - 2cosh(c - a)csch(b x + c) +--R / +--R 2b +--R Type: Expression(Integer) +--E 350 + +--S 351 of 518 +a0966:= integrate(t0966,x) +--R +--R +--R (339) +--R 2 2 +--R (3sinh(c - a) - 6cosh(c - a)sinh(c - a) + 3cosh(c - a) - 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R 15cosh(b x + c)sinh(c - a) +--R + +--R - 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (15cosh(c - a) - 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (30cosh(b x + c) - 6)sinh(c - a) +--R + +--R 2 +--R (- 60cosh(c - a)cosh(b x + c) + 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (30cosh(c - a) - 30)cosh(b x + c) - 6cosh(c - a) + 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (30cosh(b x + c) - 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 60cosh(c - a)cosh(b x + c) + 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (30cosh(c - a) - 30)cosh(b x + c) +--R + +--R 2 +--R (- 18cosh(c - a) + 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) - 18cosh(b x + c) + 3)sinh(c - a) +--R + +--R 4 2 +--R - 30cosh(c - a)cosh(b x + c) + 36cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (15cosh(c - a) - 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (- 18cosh(c - a) + 18)cosh(b x + c) + 3cosh(c - a) - 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (3cosh(b x + c) - 6cosh(b x + c) + 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R (3cosh(c - a) - 3)cosh(b x + c) +--R + +--R 2 3 2 +--R (- 6cosh(c - a) + 6)cosh(b x + c) + (3cosh(c - a) - 3)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- 3sinh(c - a) + 6cosh(c - a)sinh(c - a) - 3cosh(c - a) + 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R - 15cosh(b x + c)sinh(c - a) +--R + +--R 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 15cosh(c - a) + 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 30cosh(b x + c) + 6)sinh(c - a) +--R + +--R 2 +--R (60cosh(c - a)cosh(b x + c) - 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- 30cosh(c - a) + 30)cosh(b x + c) + 6cosh(c - a) - 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 30cosh(b x + c) + 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (60cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (- 30cosh(c - a) + 30)cosh(b x + c) +--R + +--R 2 +--R (18cosh(c - a) - 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) + 18cosh(b x + c) - 3)sinh(c - a) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (- 15cosh(c - a) + 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (18cosh(c - a) - 18)cosh(b x + c) - 3cosh(c - a) + 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 3cosh(b x + c) + 6cosh(b x + c) - 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R (- 3cosh(c - a) + 3)cosh(b x + c) +--R + +--R 2 3 2 +--R (6cosh(c - a) - 6)cosh(b x + c) + (- 3cosh(c - a) + 3)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 2 6 +--R (- 2sinh(c - a) + 4cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 12cosh(b x + c)sinh(c - a) + 24cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 12cosh(c - a) cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 30cosh(b x + c) + 10)sinh(c - a) +--R + +--R 2 +--R (60cosh(c - a)cosh(b x + c) - 20cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 30cosh(c - a) cosh(b x + c) + 10cosh(c - a) + 4 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 40cosh(b x + c) + 40cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (80cosh(c - a)cosh(b x + c) - 80cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 40cosh(c - a) cosh(b x + c) + (40cosh(c - a) + 16)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 30cosh(b x + c) + 60cosh(b x + c) - 4)sinh(c - a) +--R + +--R 4 2 +--R 60cosh(c - a)cosh(b x + c) - 120cosh(c - a)cosh(b x + c) +--R + +--R 8cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 30cosh(c - a) cosh(b x + c) + (60cosh(c - a) + 24)cosh(b x + c) +--R + +--R 2 +--R - 4cosh(c - a) - 10 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 12cosh(b x + c) + 40cosh(b x + c) - 8cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 24cosh(c - a)cosh(b x + c) - 80cosh(c - a)cosh(b x + c) +--R + +--R 16cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 12cosh(c - a) cosh(b x + c) + (40cosh(c - a) + 16)cosh(b x + c) +--R + +--R 2 +--R (- 8cosh(c - a) - 20)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (- 2cosh(b x + c) + 10cosh(b x + c) - 4cosh(b x + c) )sinh(c - a) +--R + +--R 6 4 +--R 4cosh(c - a)cosh(b x + c) - 20cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R 8cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R - 2cosh(c - a) cosh(b x + c) + (10cosh(c - a) + 4)cosh(b x + c) +--R + +--R 2 2 +--R (- 4cosh(c - a) - 10)cosh(b x + c) + 2 +--R / +--R 5 +--R (4b sinh(c - a) - 4b cosh(c - a))sinh(b x + c) +--R + +--R (20b cosh(b x + c)sinh(c - a) - 20b cosh(c - a)cosh(b x + c)) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (40b cosh(b x + c) - 8b)sinh(c - a) - 40b cosh(c - a)cosh(b x + c) +--R + +--R 8b cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (40b cosh(b x + c) - 24b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 40b cosh(c - a)cosh(b x + c) + 24b cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (20b cosh(b x + c) - 24b cosh(b x + c) + 4b)sinh(c - a) +--R + +--R 4 2 +--R - 20b cosh(c - a)cosh(b x + c) + 24b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (4b cosh(b x + c) - 8b cosh(b x + c) + 4b cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 4b cosh(c - a)cosh(b x + c) + 8b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 351 + +--S 352 of 518 +m0966:= a0966-r0966 +--R +--R +--R (340) +--R 2 2 +--R (3sinh(c - a) - 6cosh(c - a)sinh(c - a) + 3cosh(c - a) - 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R 15cosh(b x + c)sinh(c - a) +--R + +--R - 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (15cosh(c - a) - 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (30cosh(b x + c) - 6)sinh(c - a) +--R + +--R 2 +--R (- 60cosh(c - a)cosh(b x + c) + 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (30cosh(c - a) - 30)cosh(b x + c) - 6cosh(c - a) + 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (30cosh(b x + c) - 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 60cosh(c - a)cosh(b x + c) + 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (30cosh(c - a) - 30)cosh(b x + c) +--R + +--R 2 +--R (- 18cosh(c - a) + 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) - 18cosh(b x + c) + 3)sinh(c - a) +--R + +--R 4 2 +--R - 30cosh(c - a)cosh(b x + c) + 36cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (15cosh(c - a) - 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (- 18cosh(c - a) + 18)cosh(b x + c) + 3cosh(c - a) - 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (3cosh(b x + c) - 6cosh(b x + c) + 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R (3cosh(c - a) - 3)cosh(b x + c) +--R + +--R 2 3 2 +--R (- 6cosh(c - a) + 6)cosh(b x + c) + (3cosh(c - a) - 3)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- 3sinh(c - a) + 6cosh(c - a)sinh(c - a) - 3cosh(c - a) + 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R - 15cosh(b x + c)sinh(c - a) +--R + +--R 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 15cosh(c - a) + 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 30cosh(b x + c) + 6)sinh(c - a) +--R + +--R 2 +--R (60cosh(c - a)cosh(b x + c) - 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- 30cosh(c - a) + 30)cosh(b x + c) + 6cosh(c - a) - 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 30cosh(b x + c) + 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (60cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (- 30cosh(c - a) + 30)cosh(b x + c) +--R + +--R 2 +--R (18cosh(c - a) - 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) + 18cosh(b x + c) - 3)sinh(c - a) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (- 15cosh(c - a) + 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (18cosh(c - a) - 18)cosh(b x + c) - 3cosh(c - a) + 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 3cosh(b x + c) + 6cosh(b x + c) - 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R (- 3cosh(c - a) + 3)cosh(b x + c) +--R + +--R 2 3 2 +--R (6cosh(c - a) - 6)cosh(b x + c) + (- 3cosh(c - a) + 3)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 5 +--R (- 6sinh(c - a) + 6cosh(c - a)sinh(c - a))sinh(b x + c) +--R + +--R 2 +--R - 30cosh(b x + c)sinh(c - a) +--R + +--R 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 60cosh(b x + c) + 12)sinh(c - a) +--R + +--R 2 +--R (60cosh(c - a)cosh(b x + c) - 12cosh(c - a))sinh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 60cosh(b x + c) + 36cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (60cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 30cosh(b x + c) + 36cosh(b x + c) - 6)sinh(c - a) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 6cosh(b x + c) + 12cosh(b x + c) - 6cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R * +--R acoth(cosh(b x + c)) +--R + +--R 2 2 6 +--R (- 2sinh(c - a) + 4cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R (- 4sinh(c - a) + 4cosh(c - a))sinh(b x + a) +--R + +--R 2 +--R (- 2coth(b x + c)csch(b x + c) - 12cosh(b x + c))sinh(c - a) +--R + +--R (2cosh(c - a)coth(b x + c) + 4cosh(c - a))csch(b x + c) +--R + +--R 24cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 2 +--R - 4cosh(c - a) csch(b x + c) - 12cosh(c - a) cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R (- 20cosh(b x + c)sinh(c - a) + 20cosh(c - a)cosh(b x + c)) +--R * +--R sinh(b x + a) +--R + +--R 2 +--R - 10cosh(b x + c)coth(b x + c)csch(b x + c) - 30cosh(b x + c) +--R + +--R 10 +--R * +--R 2 +--R sinh(c - a) +--R + +--R 10cosh(c - a)cosh(b x + c)coth(b x + c) +--R + +--R 20cosh(c - a)cosh(b x + c) +--R * +--R csch(b x + c) +--R + +--R 2 +--R 60cosh(c - a)cosh(b x + c) - 20cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 +--R - 20cosh(c - a) cosh(b x + c)csch(b x + c) +--R + +--R 2 2 2 +--R - 30cosh(c - a) cosh(b x + c) + 10cosh(c - a) + 4 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 40cosh(b x + c) + 8)sinh(c - a) + 40cosh(c - a)cosh(b x + c) +--R + +--R - 8cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 2 +--R (- 20cosh(b x + c) + 4)coth(b x + c)csch(b x + c) +--R + +--R 3 +--R - 40cosh(b x + c) + 40cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 +--R (20cosh(c - a)cosh(b x + c) - 4cosh(c - a))coth(b x + c) +--R + +--R 2 +--R 40cosh(c - a)cosh(b x + c) - 8cosh(c - a) +--R * +--R csch(b x + c) +--R + +--R 3 +--R 80cosh(c - a)cosh(b x + c) - 80cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (- 40cosh(c - a) cosh(b x + c) + 8cosh(c - a) )csch(b x + c) +--R + +--R 2 3 2 +--R - 40cosh(c - a) cosh(b x + c) + (40cosh(c - a) + 16)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (- 40cosh(b x + c) + 24cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R 40cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 3 +--R (- 20cosh(b x + c) + 12cosh(b x + c))coth(b x + c)csch(b x + c) +--R + +--R 4 2 +--R - 30cosh(b x + c) + 60cosh(b x + c) - 4 +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 +--R (20cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c)) +--R * +--R coth(b x + c) +--R + +--R 3 +--R 40cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R * +--R csch(b x + c) +--R + +--R 4 2 +--R 60cosh(c - a)cosh(b x + c) - 120cosh(c - a)cosh(b x + c) +--R + +--R 8cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R (- 40cosh(c - a) cosh(b x + c) + 24cosh(c - a) cosh(b x + c)) +--R * +--R csch(b x + c) +--R + +--R 2 4 2 2 +--R - 30cosh(c - a) cosh(b x + c) + (60cosh(c - a) + 24)cosh(b x + c) +--R + +--R 2 +--R - 4cosh(c - a) - 10 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (- 20cosh(b x + c) + 24cosh(b x + c) - 4)sinh(c - a) +--R + +--R 4 2 +--R 20cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 4 2 +--R (- 10cosh(b x + c) + 12cosh(b x + c) - 2)coth(b x + c) +--R * +--R csch(b x + c) +--R + +--R 5 3 +--R - 12cosh(b x + c) + 40cosh(b x + c) - 8cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 4 2 +--R 10cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R coth(b x + c) +--R + +--R 4 2 +--R 20cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R csch(b x + c) +--R + +--R 5 3 +--R 24cosh(c - a)cosh(b x + c) - 80cosh(c - a)cosh(b x + c) +--R + +--R 16cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 20cosh(c - a) cosh(b x + c) + 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 4cosh(c - a) +--R * +--R csch(b x + c) +--R + +--R 2 5 2 3 +--R - 12cosh(c - a) cosh(b x + c) + (40cosh(c - a) + 16)cosh(b x + c) +--R + +--R 2 +--R (- 8cosh(c - a) - 20)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (- 4cosh(b x + c) + 8cosh(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 4cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 5 3 +--R (- 2cosh(b x + c) + 4cosh(b x + c) - 2cosh(b x + c))coth(b x + c) +--R * +--R csch(b x + c) +--R + +--R 6 4 2 +--R - 2cosh(b x + c) + 10cosh(b x + c) - 4cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 5 3 +--R 2cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + c) +--R * +--R coth(b x + c) +--R + +--R 5 3 +--R 4cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a)cosh(b x + c) +--R * +--R csch(b x + c) +--R + +--R 6 4 +--R 4cosh(c - a)cosh(b x + c) - 20cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R 8cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 4cosh(c - a) cosh(b x + c) + 8cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 4cosh(c - a) cosh(b x + c) +--R * +--R csch(b x + c) +--R + +--R 2 6 2 4 +--R - 2cosh(c - a) cosh(b x + c) + (10cosh(c - a) + 4)cosh(b x + c) +--R + +--R 2 2 +--R (- 4cosh(c - a) - 10)cosh(b x + c) + 2 +--R / +--R 5 +--R (4b sinh(c - a) - 4b cosh(c - a))sinh(b x + c) +--R + +--R (20b cosh(b x + c)sinh(c - a) - 20b cosh(c - a)cosh(b x + c)) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (40b cosh(b x + c) - 8b)sinh(c - a) - 40b cosh(c - a)cosh(b x + c) +--R + +--R 8b cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (40b cosh(b x + c) - 24b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 40b cosh(c - a)cosh(b x + c) + 24b cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (20b cosh(b x + c) - 24b cosh(b x + c) + 4b)sinh(c - a) +--R + +--R 4 2 +--R - 20b cosh(c - a)cosh(b x + c) + 24b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (4b cosh(b x + c) - 8b cosh(b x + c) + 4b cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 4b cosh(c - a)cosh(b x + c) + 8b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 352 + +--S 353 of 518 +--d0966:= D(m0966,x) +--E 353 + +--S 354 of 518 +t0967:= sinh(a+b*x)*sech(c+b*x) +--R +--R +--R (341) sech(b x + c)sinh(b x + a) +--R Type: Expression(Integer) +--E 354 + +--S 355 of 518 +r0967:= cosh(a-c)*log(cosh(c+b*x))/b+x*sinh(a-c) +--R +--R +--R cosh(c - a)log(cosh(b x + c)) - b x sinh(c - a) +--R (342) ----------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 355 + +--S 356 of 518 +a0967:= integrate(t0967,x) +--R +--R +--R (343) +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R 2cosh(b x + c) +--R log(- -----------------------------) +--R sinh(b x + c) - cosh(b x + c) +--R + +--R 2b x +--R / +--R 2b sinh(c - a) - 2b cosh(c - a) +--R Type: Union(Expression(Integer),...) +--E 356 + +--S 357 of 518 +m0967:= a0967-r0967 +--R +--R +--R (344) +--R 2 +--R (- 2cosh(c - a)sinh(c - a) + 2cosh(c - a) )log(cosh(b x + c)) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R 2cosh(b x + c) +--R log(- -----------------------------) +--R sinh(b x + c) - cosh(b x + c) +--R + +--R 2 +--R 2b x sinh(c - a) - 2b x cosh(c - a)sinh(c - a) + 2b x +--R / +--R 2b sinh(c - a) - 2b cosh(c - a) +--R Type: Expression(Integer) +--E 357 + +--S 358 of 518 +d0967:= D(m0967,x) +--R +--R +--R (345) +--R 2 2 +--R (- sinh(c - a) + cosh(c - a) - 1)sinh(b x + c) +--R + +--R 2 2 +--R cosh(b x + c)sinh(c - a) + (- cosh(c - a) + 1)cosh(b x + c) +--R / +--R 2cosh(b x + c)sinh(c - a) - 2cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 358 + +--S 359 of 518 +t0968:= sinh(a+b*x)*sech(c+b*x)^2 +--R +--R +--R 2 +--R (346) sech(b x + c) sinh(b x + a) +--R Type: Expression(Integer) +--E 359 + +--S 360 of 518 +r0968:= -cosh(a-c)*sech(c+b*x)/b+atan(sinh(c+b*x))*sinh(a-c)/b +--R +--R +--R - sinh(c - a)atan(sinh(b x + c)) - cosh(c - a)sech(b x + c) +--R (347) ----------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 360 + +--S 361 of 518 +a0968:= integrate(t0968,x) +--R +--R +--R (348) +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) +--R + +--R 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a) + 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (- cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- cosh(c - a) + 1)cosh(b x + c) - cosh(c - a) + 1 +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) + 1)sinh(b x + c) +--R + +--R 2 +--R cosh(b x + c)sinh(c - a) - 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (cosh(c - a) + 1)cosh(b x + c) +--R / +--R 2 +--R (b sinh(c - a) - b cosh(c - a))sinh(b x + c) +--R + +--R (2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (b cosh(b x + c) + b)sinh(c - a) - b cosh(c - a)cosh(b x + c) +--R + +--R - b cosh(c - a) +--R Type: Union(Expression(Integer),...) +--E 361 + +--S 362 of 518 +m0968:= a0968-r0968 +--R +--R +--R (349) +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) +--R + +--R 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a) + 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (- cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- cosh(c - a) + 1)cosh(b x + c) - cosh(c - a) + 1 +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 2 +--R (sinh(c - a) - cosh(c - a)sinh(c - a))sinh(b x + c) +--R + +--R 2 +--R (2cosh(b x + c)sinh(c - a) - 2cosh(c - a)cosh(b x + c)sinh(c - a)) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (- cosh(c - a)cosh(b x + c) - cosh(c - a))sinh(c - a) +--R * +--R atan(sinh(b x + c)) +--R + +--R 2 +--R (cosh(c - a)sech(b x + c)sinh(c - a) - cosh(c - a) sech(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R sinh(c - a) +--R + +--R (2cosh(c - a)cosh(b x + c)sech(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 +--R - 2cosh(c - a) cosh(b x + c)sech(b x + c) + cosh(c - a) + 1 +--R * +--R sinh(b x + c) +--R + +--R 2 +--R cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (cosh(c - a)cosh(b x + c) + cosh(c - a))sech(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (- cosh(c - a) cosh(b x + c) - cosh(c - a) )sech(b x + c) +--R + +--R 2 +--R (cosh(c - a) + 1)cosh(b x + c) +--R / +--R 2 +--R (b sinh(c - a) - b cosh(c - a))sinh(b x + c) +--R + +--R (2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (b cosh(b x + c) + b)sinh(c - a) - b cosh(c - a)cosh(b x + c) +--R + +--R - b cosh(c - a) +--R Type: Expression(Integer) +--E 362 + +--S 363 of 518 +d0968:= D(m0968,x) +--R +--R +--R (350) +--R 2 +--R (- cosh(c - a)sech(b x + c)sinh(c - a) + cosh(c - a) sech(b x + c)) +--R * +--R 6 +--R sinh(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c)sech(b x + c)sinh(c - a) +--R + +--R 2 +--R 4cosh(c - a) cosh(b x + c)sech(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R (- 6cosh(c - a)cosh(b x + c) - 3cosh(c - a))sech(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (6cosh(c - a) cosh(b x + c) + 3cosh(c - a) )sech(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 +--R (- 4cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 3 2 +--R (4cosh(c - a) cosh(b x + c) + 8cosh(c - a) cosh(b x + c)) +--R * +--R sech(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 +--R - cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R + +--R - 3cosh(c - a) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 4 2 2 +--R cosh(c - a) cosh(b x + c) + 8cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 3cosh(c - a) +--R * +--R sech(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 3 +--R (- 4cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 3 2 +--R (4cosh(c - a) cosh(b x + c) + 4cosh(c - a) cosh(b x + c)) +--R * +--R sech(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 4 2 +--R - cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a) +--R * +--R sech(b x + c)sinh(c - a) +--R + +--R 2 4 2 2 +--R cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R cosh(c - a) +--R * +--R sech(b x + c) +--R * +--R tanh(b x + c) +--R + +--R 2 2 5 +--R (- 2sinh(c - a) + 4cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 5cosh(b x + c)sinh(c - a) + 11cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 2cosh(b x + c) - 2)sinh(c - a) +--R + +--R 2 +--R (8cosh(c - a)cosh(b x + c) + 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 6cosh(c - a) cosh(b x + c) - 2cosh(c - a) + 2 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (4cosh(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 2cosh(c - a)cosh(b x + c) + 10cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R - 2cosh(c - a) cosh(b x + c) + (- 6cosh(c - a) + 2)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (4cosh(b x + c) - 2cosh(b x + c) )sinh(c - a) +--R + +--R 4 2 +--R (- 4cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) ) +--R * +--R sinh(c - a) +--R + +--R 2 2 +--R - 6cosh(c - a) cosh(b x + c) + 2 +--R * +--R sinh(b x + c) +--R + +--R 5 2 +--R (cosh(b x + c) + cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R - 2cosh(c - a) cosh(b x + c) + 2cosh(b x + c) +--R / +--R 6 +--R (sinh(c - a) - cosh(c - a))sinh(b x + c) +--R + +--R 5 +--R (4cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 3)sinh(c - a) - 6cosh(c - a)cosh(b x + c) +--R + +--R - 3cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 +--R (4cosh(b x + c) + 8cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 4cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 +--R (cosh(b x + c) + 8cosh(b x + c) + 3)sinh(c - a) +--R + +--R 4 2 +--R - cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) - 3cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 3 +--R (4cosh(b x + c) + 4cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 4cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 4 2 +--R (cosh(b x + c) + 2cosh(b x + c) + 1)sinh(c - a) +--R + +--R 4 2 +--R - cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) - cosh(c - a) +--R Type: Expression(Integer) +--E 363 + +--S 364 of 518 +t0969:= sinh(a+b*x)*sech(c+b*x)^3 +--R +--R +--R 3 +--R (351) sech(b x + c) sinh(b x + a) +--R Type: Expression(Integer) +--E 364 + +--S 365 of 518 +r0969:= -1/2*cosh(a-c)*sech(c+b*x)^2/b+sinh(a-c)*tanh(c+b*x)/b +--R +--R +--R 2 +--R - 2sinh(c - a)tanh(b x + c) - cosh(c - a)sech(b x + c) +--R (352) ------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 365 + +--S 366 of 518 +a0969:= integrate(t0969,x) +--R +--R +--R (353) +--R 2cosh(c - a)sinh(b x + c) - 4cosh(b x + c)sinh(c - a) +--R + +--R 2cosh(c - a)cosh(b x + c) +--R / +--R 2 2 3 +--R (b sinh(c - a) - b cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 +--R (3b cosh(b x + c)sinh(c - a) - 3b cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 2 2 +--R (3b cosh(b x + c) + b)sinh(c - a) - 3b cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (b cosh(b x + c) + 3b cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - b cosh(c - a) cosh(b x + c) - 3b cosh(c - a) cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 366 + +--S 367 of 518 +m0969:= a0969-r0969 +--R +--R +--R (354) +--R 3 2 3 +--R (2sinh(c - a) - 2cosh(c - a) sinh(c - a))sinh(b x + c) +--R + +--R 3 +--R 6cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c)sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 3 +--R (6cosh(b x + c) + 2)sinh(c - a) +--R + +--R 2 2 2 +--R (- 6cosh(c - a) cosh(b x + c) - 2cosh(c - a) )sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 3 +--R (2cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (- 2cosh(c - a) cosh(b x + c) - 6cosh(c - a) cosh(b x + c))sinh(c - a) +--R * +--R tanh(b x + c) +--R + +--R 2 2 3 2 +--R (cosh(c - a)sech(b x + c) sinh(c - a) - cosh(c - a) sech(b x + c) ) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 2 +--R 3cosh(c - a)cosh(b x + c)sech(b x + c) sinh(c - a) +--R + +--R 3 2 +--R - 3cosh(c - a) cosh(b x + c)sech(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 2 +--R (3cosh(c - a)cosh(b x + c) + cosh(c - a))sech(b x + c) sinh(c - a) +--R + +--R 3 2 3 2 +--R (- 3cosh(c - a) cosh(b x + c) - cosh(c - a) )sech(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (cosh(c - a)cosh(b x + c) + 3cosh(c - a)cosh(b x + c))sech(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R - 8cosh(b x + c)sinh(c - a) +--R + +--R 3 3 3 2 +--R (- cosh(c - a) cosh(b x + c) - 3cosh(c - a) cosh(b x + c))sech(b x + c) +--R + +--R 4cosh(c - a)cosh(b x + c) +--R / +--R 2 2 3 +--R (2b sinh(c - a) - 2b cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 2 2 +--R (6b cosh(b x + c) + 2b)sinh(c - a) - 6b cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (2b cosh(b x + c) + 6b cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 2b cosh(c - a) cosh(b x + c) - 6b cosh(c - a) cosh(b x + c) +--R Type: Expression(Integer) +--E 367 + +--S 368 of 518 +d0969:= D(m0969,x) +--R +--R +--R (355) +--R 3 2 6 +--R (- sinh(c - a) + cosh(c - a) sinh(c - a))sinh(b x + c) +--R + +--R 3 +--R - 6cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R 6cosh(c - a) cosh(b x + c)sinh(c - a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 3 +--R (- 15cosh(b x + c) - 2)sinh(c - a) +--R + +--R 2 2 2 +--R (15cosh(c - a) cosh(b x + c) + 2cosh(c - a) )sinh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 3 +--R (- 20cosh(b x + c) - 12cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (20cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c)) +--R * +--R sinh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 3 +--R (- 15cosh(b x + c) - 24cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 4 2 2 +--R 15cosh(c - a) cosh(b x + c) + 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R cosh(c - a) +--R * +--R sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 +--R (- 6cosh(b x + c) - 20cosh(b x + c) - 6cosh(b x + c)) +--R * +--R 3 +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R 6cosh(c - a) cosh(b x + c) + 20cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 3 +--R (- cosh(b x + c) - 6cosh(b x + c) - 9cosh(b x + c) )sinh(c - a) +--R + +--R 2 6 2 4 +--R cosh(c - a) cosh(b x + c) + 6cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R 9cosh(c - a) cosh(b x + c) +--R * +--R sinh(c - a) +--R * +--R 2 +--R tanh(b x + c) +--R + +--R 2 2 +--R - cosh(c - a)sech(b x + c) sinh(c - a) +--R + +--R 3 2 +--R cosh(c - a) sech(b x + c) +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 2 2 +--R - 6cosh(c - a)cosh(b x + c)sech(b x + c) sinh(c - a) +--R + +--R 3 2 +--R 6cosh(c - a) cosh(b x + c)sech(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 15cosh(c - a)cosh(b x + c) - 2cosh(c - a))sech(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 2 3 2 +--R (15cosh(c - a) cosh(b x + c) + 2cosh(c - a) )sech(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 +--R (- 20cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c)) +--R * +--R 2 2 +--R sech(b x + c) sinh(c - a) +--R + +--R 3 3 3 +--R (20cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sech(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 +--R - 15cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a) +--R * +--R 2 2 +--R sech(b x + c) sinh(c - a) +--R + +--R 3 4 3 2 +--R 15cosh(c - a) cosh(b x + c) + 24cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R cosh(c - a) +--R * +--R 2 +--R sech(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) - 20cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R 2 2 +--R sech(b x + c) sinh(c - a) +--R + +--R 3 5 3 3 +--R 6cosh(c - a) cosh(b x + c) + 20cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 6cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R sech(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 +--R - cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 9cosh(c - a)cosh(b x + c) +--R * +--R 2 2 +--R sech(b x + c) sinh(c - a) +--R + +--R 3 6 3 4 +--R cosh(c - a) cosh(b x + c) + 6cosh(c - a) cosh(b x + c) +--R + +--R 3 2 +--R 9cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R sech(b x + c) +--R * +--R tanh(b x + c) +--R + +--R 3 2 6 +--R (sinh(c - a) - cosh(c - a) sinh(c - a))sinh(b x + c) +--R + +--R 3 2 +--R (6cosh(b x + c)sinh(c - a) - 6cosh(c - a) cosh(b x + c)sinh(c - a)) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 3 +--R (15cosh(b x + c) + 2)sinh(c - a) +--R + +--R 2 2 2 +--R (- 15cosh(c - a) cosh(b x + c) - 2cosh(c - a) - 4)sinh(c - a) +--R + +--R - 4cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 3 +--R (20cosh(b x + c) + 12cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (- 20cosh(c - a) cosh(b x + c) - 12cosh(c - a) cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R - 16cosh(c - a)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 3 +--R (15cosh(b x + c) + 24cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 4 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 2 2 2 +--R (- 24cosh(c - a) + 24)cosh(b x + c) - cosh(c - a) - 4 +--R * +--R sinh(c - a) +--R + +--R 2 +--R - 24cosh(c - a)cosh(b x + c) - 4cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 3 +--R (6cosh(b x + c) + 20cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 2 5 +--R - 6cosh(c - a) cosh(b x + c) +--R + +--R 2 3 2 +--R (- 20cosh(c - a) + 32)cosh(b x + c) - 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 3 +--R - 16cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 3 +--R (cosh(b x + c) + 6cosh(b x + c) + 9cosh(b x + c) )sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) + (- 6cosh(c - a) + 12)cosh(b x + c) +--R + +--R 2 2 +--R (- 9cosh(c - a) + 4)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 4 2 +--R - 4cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R / +--R 2 2 6 +--R (sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 5 +--R (6cosh(b x + c)sinh(c - a) - 6cosh(c - a) cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 2 2 +--R (15cosh(b x + c) + 2)sinh(c - a) - 15cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 2cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (20cosh(b x + c) + 12cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 20cosh(c - a) cosh(b x + c) - 12cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) + 24cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 4 2 2 +--R - 15cosh(c - a) cosh(b x + c) - 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (6cosh(b x + c) + 20cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) - 20cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (cosh(b x + c) + 6cosh(b x + c) + 9cosh(b x + c) )sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) - 6cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R - 9cosh(c - a) cosh(b x + c) +--R Type: Expression(Integer) +--E 368 + +--S 369 of 518 +t0970:= sinh(a+b*x)*csch(c+b*x) +--R +--R +--R (356) csch(b x + c)sinh(b x + a) +--R Type: Expression(Integer) +--E 369 + +--S 370 of 518 +r0970:= x*cosh(a-c)+log(sinh(c+b*x))*sinh(a-c)/b +--R +--R +--R - sinh(c - a)log(sinh(b x + c)) + b x cosh(c - a) +--R (357) ------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 370 + +--S 371 of 518 +a0970:= integrate(t0970,x) +--R +--R +--R (358) +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R 2sinh(b x + c) +--R log(- -----------------------------) +--R sinh(b x + c) - cosh(b x + c) +--R + +--R - 2b x +--R / +--R 2b sinh(c - a) - 2b cosh(c - a) +--R Type: Union(Expression(Integer),...) +--E 371 + +--S 372 of 518 +m0970:= a0970-r0970 +--R +--R +--R (359) +--R 2 +--R (2sinh(c - a) - 2cosh(c - a)sinh(c - a))log(sinh(b x + c)) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R 2sinh(b x + c) +--R log(- -----------------------------) +--R sinh(b x + c) - cosh(b x + c) +--R + +--R 2 +--R - 2b x cosh(c - a)sinh(c - a) + 2b x cosh(c - a) - 2b x +--R / +--R 2b sinh(c - a) - 2b cosh(c - a) +--R Type: Expression(Integer) +--E 372 + +--S 373 of 518 +d0970:= D(m0970,x) +--R +--R +--R (360) +--R 2 2 +--R (- sinh(c - a) + cosh(c - a) - 1)sinh(b x + c) +--R + +--R 2 2 +--R cosh(b x + c)sinh(c - a) + (- cosh(c - a) + 1)cosh(b x + c) +--R / +--R (2sinh(c - a) - 2cosh(c - a))sinh(b x + c) +--R Type: Expression(Integer) +--E 373 + +--S 374 of 518 +t0971:= sinh(a+b*x)*csch(c+b*x)^2 +--R +--R +--R 2 +--R (361) csch(b x + c) sinh(b x + a) +--R Type: Expression(Integer) +--E 374 + +--S 375 of 518 +r0971:= -acoth(cosh(c+b*x))*cosh(a-c)/b-csch(c+b*x)*sinh(a-c)/b +--R +--R +--R - cosh(c - a)acoth(cosh(b x + c)) + csch(b x + c)sinh(c - a) +--R (362) ------------------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 375 + +--S 376 of 518 +a0971:= integrate(t0971,x) +--R +--R +--R (363) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) + 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) + 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (cosh(c - a) + 1)cosh(b x + c) - cosh(c - a) - 1 +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) +--R + +--R 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a) - 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (- cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- cosh(c - a) - 1)cosh(b x + c) + cosh(c - a) + 1 +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 2 +--R (2sinh(c - a) - 4cosh(c - a)sinh(c - a) + 2cosh(c - a) - 2) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) - 2)cosh(b x + c) +--R / +--R 2 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R (4b cosh(b x + c)sinh(c - a) - 4b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (2b cosh(b x + c) - 2b)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R + +--R 2b cosh(c - a) +--R Type: Union(Expression(Integer),...) +--E 376 + +--S 377 of 518 +m0971:= a0971-r0971 +--R +--R +--R (364) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) + 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) + 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (cosh(c - a) + 1)cosh(b x + c) - cosh(c - a) - 1 +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) +--R + +--R 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a) - 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (- cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- cosh(c - a) - 1)cosh(b x + c) + cosh(c - a) + 1 +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 2 +--R (2cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R (4cosh(c - a)cosh(b x + c)sinh(c - a) - 4cosh(c - a) cosh(b x + c)) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 2cosh(c - a) cosh(b x + c) + 2cosh(c - a) +--R * +--R acoth(cosh(b x + c)) +--R + +--R 2 +--R (- 2csch(b x + c)sinh(c - a) + 2cosh(c - a)csch(b x + c)sinh(c - a)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R (- 4cosh(b x + c)csch(b x + c) + 2)sinh(c - a) +--R + +--R (4cosh(c - a)cosh(b x + c)csch(b x + c) - 4cosh(c - a))sinh(c - a) +--R + +--R 2 +--R 2cosh(c - a) - 2 +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R ((- 2cosh(b x + c) + 2)csch(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a))csch(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) - 2)cosh(b x + c) +--R / +--R 2 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R (4b cosh(b x + c)sinh(c - a) - 4b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (2b cosh(b x + c) - 2b)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R + +--R 2b cosh(c - a) +--R Type: Expression(Integer) +--E 377 + +--S 378 of 518 +d0971:= D(m0971,x) +--R +--R +--R (365) +--R 2 5 +--R (- cosh(c - a)sinh(c - a) + cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 +--R (cosh(b x + c) - 1)coth(b x + c)csch(b x + c)sinh(c - a) +--R + +--R 2 +--R (- cosh(c - a)cosh(b x + c) + cosh(c - a))coth(b x + c) +--R * +--R csch(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 +--R 4cosh(c - a) cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 +--R (4cosh(b x + c) - 4cosh(b x + c))coth(b x + c)csch(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c) + 2 +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 +--R (- 4cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c)) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 +--R - 2cosh(c - a)cosh(b x + c) - 2cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 2 +--R 4cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 +--R (6cosh(b x + c) - 8cosh(b x + c) + 2)coth(b x + c)csch(b x + c) +--R + +--R 3 +--R - 6cosh(b x + c) + 6cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 4 2 +--R - 6cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 3 +--R 8cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R - 2cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 +--R (4cosh(b x + c) - 8cosh(b x + c) + 4cosh(b x + c)) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 4 2 +--R - 6cosh(b x + c) + 6cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 5 3 +--R - 4cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 4 2 +--R 11cosh(c - a)cosh(b x + c) - 10cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 5cosh(c - a) cosh(b x + c) + (4cosh(c - a) + 2)cosh(b x + c) +--R + +--R 2 +--R cosh(c - a) - 2 +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 +--R (cosh(b x + c) - 3cosh(b x + c) + 3cosh(b x + c) - 1) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 5 3 +--R - 2cosh(b x + c) + 2cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 6 4 +--R - cosh(c - a)cosh(b x + c) + 3cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 3cosh(c - a)cosh(b x + c) + cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 5 3 +--R 4cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 2cosh(c - a) cosh(b x + c) + (2cosh(c - a) + 2)cosh(b x + c) +--R + +--R - 2cosh(b x + c) +--R / +--R 2 2 +--R (cosh(b x + c) - 1)sinh(c - a) - cosh(c - a)cosh(b x + c) +--R + +--R cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 +--R (4cosh(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 4cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 +--R (6cosh(b x + c) - 8cosh(b x + c) + 2)sinh(c - a) +--R + +--R 4 2 +--R - 6cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 +--R (4cosh(b x + c) - 8cosh(b x + c) + 4cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 4cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 +--R (cosh(b x + c) - 3cosh(b x + c) + 3cosh(b x + c) - 1)sinh(c - a) +--R + +--R 6 4 +--R - cosh(c - a)cosh(b x + c) + 3cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 3cosh(c - a)cosh(b x + c) + cosh(c - a) +--R Type: Expression(Integer) +--E 378 + +--S 379 of 518 +t0972:= sinh(a+b*x)*csch(c+b*x)^3 +--R +--R +--R 3 +--R (366) csch(b x + c) sinh(b x + a) +--R Type: Expression(Integer) +--E 379 + +--S 380 of 518 +r0972:= -cosh(a-c)*coth(c+b*x)/b-1/2*csch(c+b*x)^2*sinh(a-c)/b +--R +--R +--R 2 +--R csch(b x + c) sinh(c - a) - 2cosh(c - a)coth(b x + c) +--R (367) ----------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 380 + +--S 381 of 518 +a0972:= integrate(t0972,x) +--R +--R +--R (368) +--R (- 2sinh(c - a) + 4cosh(c - a))sinh(b x + c) - 2cosh(b x + c)sinh(c - a) +--R / +--R 2 2 3 +--R (b sinh(c - a) - b cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 +--R (3b cosh(b x + c)sinh(c - a) - 3b cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 2 2 +--R (3b cosh(b x + c) - 3b)sinh(c - a) - 3b cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 3b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (b cosh(b x + c) - b cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - b cosh(c - a) cosh(b x + c) + b cosh(c - a) cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 518 +m0972:= a0972-r0972 +--R +--R +--R (369) +--R 2 3 2 +--R - csch(b x + c) sinh(c - a) + 2cosh(c - a)coth(b x + c)sinh(c - a) +--R + +--R 2 2 3 +--R cosh(c - a) csch(b x + c) sinh(c - a) - 2cosh(c - a) coth(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 3 +--R - 3cosh(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 +--R 6cosh(c - a)cosh(b x + c)coth(b x + c)sinh(c - a) +--R + +--R 2 2 +--R 3cosh(c - a) cosh(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 3 +--R - 6cosh(c - a) cosh(b x + c)coth(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 3 +--R (- 3cosh(b x + c) + 3)csch(b x + c) sinh(c - a) +--R + +--R 2 2 +--R (6cosh(c - a)cosh(b x + c) - 6cosh(c - a))coth(b x + c)sinh(c - a) +--R + +--R 2 2 2 2 +--R ((3cosh(c - a) cosh(b x + c) - 3cosh(c - a) )csch(b x + c) - 4) +--R * +--R sinh(c - a) +--R + +--R 3 2 3 +--R (- 6cosh(c - a) cosh(b x + c) + 6cosh(c - a) )coth(b x + c) +--R + +--R 8cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 3 +--R (- cosh(b x + c) + cosh(b x + c))csch(b x + c) sinh(c - a) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))coth(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 3 2 +--R (cosh(c - a) cosh(b x + c) - cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R csch(b x + c) +--R + +--R - 4cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 3 3 3 +--R (- 2cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c))coth(b x + c) +--R / +--R 2 2 3 +--R (2b sinh(c - a) - 2b cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 2 2 +--R (6b cosh(b x + c) - 6b)sinh(c - a) - 6b cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (2b cosh(b x + c) - 2b cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 2b cosh(c - a) cosh(b x + c) + 2b cosh(c - a) cosh(b x + c) +--R Type: Expression(Integer) +--E 382 + +--S 383 of 518 +d0972:= D(m0972,x) +--R +--R +--R (370) +--R 2 3 +--R coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 2 +--R (- cosh(c - a)coth(b x + c) + cosh(c - a))sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a) coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 3 2 3 +--R cosh(c - a) coth(b x + c) - cosh(c - a) +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 2 3 +--R 6cosh(b x + c)coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 +--R - 6cosh(c - a)cosh(b x + c)coth(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 2 +--R - 6cosh(c - a) cosh(b x + c)coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 3 2 3 +--R 6cosh(c - a) cosh(b x + c)coth(b x + c) - 6cosh(c - a) cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 3 +--R (15cosh(b x + c) - 6)coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 2 +--R (- 15cosh(c - a)cosh(b x + c) + 6cosh(c - a))coth(b x + c) +--R + +--R 2 +--R 15cosh(c - a)cosh(b x + c) - 6cosh(c - a) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 2 2 +--R (- 15cosh(c - a) cosh(b x + c) + 6cosh(c - a) )coth(b x + c) +--R * +--R 2 +--R csch(b x + c) +--R + +--R 4 +--R * +--R sinh(c - a) +--R + +--R 3 2 3 2 +--R (15cosh(c - a) cosh(b x + c) - 6cosh(c - a) )coth(b x + c) +--R + +--R 3 2 3 +--R - 15cosh(c - a) cosh(b x + c) + 6cosh(c - a) - 12cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (20cosh(b x + c) - 20cosh(b x + c))coth(b x + c)csch(b x + c) +--R * +--R 3 +--R sinh(c - a) +--R + +--R 3 +--R (- 20cosh(c - a)cosh(b x + c) + 20cosh(c - a)cosh(b x + c)) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 3 +--R 20cosh(c - a)cosh(b x + c) - 20cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 3 2 +--R (- 20cosh(c - a) cosh(b x + c) + 20cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R coth(b x + c)csch(b x + c) +--R + +--R 16cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 3 3 3 +--R (20cosh(c - a) cosh(b x + c) - 20cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 3 3 +--R - 20cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R (20cosh(c - a) - 32cosh(c - a))cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 +--R (15cosh(b x + c) - 24cosh(b x + c) + 9)coth(b x + c) +--R * +--R 2 3 +--R csch(b x + c) sinh(c - a) +--R + +--R 4 2 +--R - 15cosh(c - a)cosh(b x + c) + 24cosh(c - a)cosh(b x + c) +--R + +--R - 9cosh(c - a) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 4 2 +--R 15cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R + +--R 9cosh(c - a) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 15cosh(c - a) cosh(b x + c) + 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 9cosh(c - a) +--R * +--R 2 +--R coth(b x + c)csch(b x + c) +--R + +--R 2 +--R 24cosh(b x + c) + 4 +--R * +--R sinh(c - a) +--R + +--R 3 4 3 2 +--R 15cosh(c - a) cosh(b x + c) - 24cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 9cosh(c - a) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 3 4 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 3 2 3 +--R (24cosh(c - a) - 24cosh(c - a))cosh(b x + c) - 9cosh(c - a) +--R + +--R 4cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 +--R (6cosh(b x + c) - 12cosh(b x + c) + 6cosh(b x + c))coth(b x + c) +--R * +--R 2 3 +--R csch(b x + c) sinh(c - a) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 5 3 +--R 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R coth(b x + c)csch(b x + c) +--R + +--R 3 +--R 16cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 3 5 3 3 +--R 6cosh(c - a) cosh(b x + c) - 12cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 6cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 3 5 3 3 +--R - 6cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 +--R (cosh(b x + c) - 2cosh(b x + c) + cosh(b x + c) )coth(b x + c) +--R * +--R 2 3 +--R csch(b x + c) sinh(c - a) +--R + +--R 6 4 +--R - cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 6 4 +--R cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R coth(b x + c)csch(b x + c) +--R + +--R 4 2 +--R 4cosh(b x + c) - 4cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 3 6 3 4 +--R cosh(c - a) cosh(b x + c) - 2cosh(c - a) cosh(b x + c) +--R + +--R 3 2 +--R cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 3 6 +--R - cosh(c - a) cosh(b x + c) +--R + +--R 3 4 +--R (2cosh(c - a) + 4cosh(c - a))cosh(b x + c) +--R + +--R 3 2 +--R (- cosh(c - a) - 4cosh(c - a))cosh(b x + c) +--R / +--R 2 2 6 +--R (sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 5 +--R (6cosh(b x + c)sinh(c - a) - 6cosh(c - a) cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 2 2 +--R (15cosh(b x + c) - 6)sinh(c - a) - 15cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (20cosh(b x + c) - 20cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 20cosh(c - a) cosh(b x + c) + 20cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) - 24cosh(b x + c) + 9)sinh(c - a) +--R + +--R 2 4 2 2 +--R - 15cosh(c - a) cosh(b x + c) + 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 9cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (6cosh(b x + c) - 12cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (cosh(b x + c) - 2cosh(b x + c) + cosh(b x + c) )sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) +--R Type: Expression(Integer) +--E 383 + +--S 384 of 518 +t0973:= cosh(a+b*x)*tanh(c+b*x) +--R +--R +--R (371) cosh(b x + a)tanh(b x + c) +--R Type: Expression(Integer) +--E 384 + +--S 385 of 518 +r0973:= (cosh(a+b*x)-atan(sinh(c+b*x))*sinh(a-c))/b +--R +--R +--R sinh(c - a)atan(sinh(b x + c)) + cosh(b x + a) +--R (372) ---------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 385 + +--S 386 of 518 +a0973:= integrate(t0973,x) +--R +--R +--R (373) +--R 2 2 +--R (2sinh(c - a) - 4cosh(c - a)sinh(c - a) + 2cosh(c - a) - 2) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) - 2)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) + 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 2cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 2 +--R - cosh(b x + c) sinh(c - a) + 2cosh(c - a)cosh(b x + c) sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) - 1 +--R / +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 518 +m0973:= a0973-r0973 +--R +--R +--R (374) +--R 2 2 +--R (2sinh(c - a) - 4cosh(c - a)sinh(c - a) + 2cosh(c - a) - 2) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) - 2)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 +--R (- 2sinh(c - a) + 2cosh(c - a)sinh(c - a))sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) + 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R * +--R atan(sinh(b x + c)) +--R + +--R 2 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) +--R + +--R (4cosh(c - a)cosh(b x + c) - 2cosh(b x + a))sinh(c - a) +--R + +--R 2 +--R - 2cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R - cosh(b x + c) sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c))sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a)cosh(b x + c) - 1 +--R / +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 387 + +--S 388 of 518 +d0973:= D(m0973,x) +--R +--R +--R (375) +--R 2 2 6 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R (- 2sinh(c - a) + 2cosh(c - a))sinh(b x + a) +--R + +--R 2 +--R - 4cosh(b x + c)sinh(c - a) + 8cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 4cosh(c - a) cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R (- 6cosh(b x + c)sinh(c - a) + 6cosh(c - a)cosh(b x + c)) +--R * +--R sinh(b x + a) +--R + +--R 2 2 +--R - 6cosh(b x + c) sinh(c - a) +--R + +--R 2 2 2 +--R 12cosh(c - a)cosh(b x + c) sinh(c - a) - 6cosh(c - a) cosh(b x + c) +--R + +--R - 1 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) - 4)sinh(c - a) + 6cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 3 2 +--R (- 4cosh(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (8cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 4cosh(c - a) cosh(b x + c) + (- 2cosh(c - a) - 2)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (- 2cosh(b x + c) - 8cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R 2cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (- cosh(b x + c) - 11cosh(b x + c) + 1)sinh(c - a) +--R + +--R 4 2 +--R 2cosh(c - a)cosh(b x + c) + 16cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - cosh(c - a) cosh(b x + c) + (- 5cosh(c - a) - 1)cosh(b x + c) +--R + +--R 2 +--R cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) - 2)sinh(c - a) + 6cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 3 2 +--R - 10cosh(b x + c) sinh(c - a) +--R + +--R 3 +--R (14cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 4cosh(c - a) cosh(b x + c) + (2cosh(c - a) - 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (- 2cosh(b x + c) - 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R 2cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (- 3cosh(b x + c) - cosh(b x + c) )sinh(c - a) +--R + +--R 4 2 4 +--R 4cosh(c - a)cosh(b x + c) sinh(c - a) - cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R (cosh(c - a) - 1)cosh(b x + c) + 1 +--R / +--R 5 +--R (2sinh(c - a) - 2cosh(c - a))sinh(b x + c) +--R + +--R 4 +--R (6cosh(b x + c)sinh(c - a) - 6cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 4)sinh(c - a) - 6cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (2cosh(b x + c) + 8cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 2)sinh(c - a) - 6cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 388 + +--S 389 of 518 +t0974:= cosh(a+b*x)*tanh(c+b*x)^2 +--R +--R +--R 2 +--R (376) cosh(b x + a)tanh(b x + c) +--R Type: Expression(Integer) +--E 389 + +--S 390 of 518 +r0974:= -atan(sinh(c+b*x))*cosh(a-c)/b+sech(c+b*x)*sinh(a-c)/b+sinh(a+b*x)/b +--R +--R +--R (377) +--R - cosh(c - a)atan(sinh(b x + c)) + sinh(b x + a) - sech(b x + c)sinh(c - a) +--R --------------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 390 + +--S 391 of 518 +a0974:= integrate(t0974,x) +--R +--R +--R (378) +--R 2 2 +--R (2sinh(c - a) - 4cosh(c - a)sinh(c - a) + 2cosh(c - a) + 2) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R 6cosh(b x + c)sinh(c - a) +--R + +--R - 12cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a) + 6)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 2)sinh(c - a) +--R + +--R 2 +--R (- 12cosh(c - a)cosh(b x + c) - 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (6cosh(c - a) + 6)cosh(b x + c) + 2cosh(c - a) + 2 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (2cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 4cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (2cosh(c - a) + 2)cosh(b x + c) + (2cosh(c - a) + 2)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 2 4 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 4cosh(b x + c)sinh(c - a) + 8cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 4cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) - 3)sinh(c - a) +--R + +--R 2 +--R (12cosh(c - a)cosh(b x + c) + 6cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 6cosh(c - a) cosh(b x + c) - 3cosh(c - a) + 3 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 4cosh(b x + c) - 6cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (8cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 4cosh(c - a) cosh(b x + c) + (- 6cosh(c - a) + 6)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- cosh(b x + c) - 3cosh(b x + c) )sinh(c - a) +--R + +--R 4 2 +--R (2cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) )sinh(c - a) +--R + +--R 2 4 2 2 +--R - cosh(c - a) cosh(b x + c) + (- 3cosh(c - a) + 3)cosh(b x + c) + 1 +--R / +--R 3 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c) + 2b)sinh(c - a) - 6b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2b cosh(b x + c) + 2b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2b cosh(c - a)cosh(b x + c) - 2b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 518 +m0974:= a0974-r0974 +--R +--R +--R (379) +--R 2 2 +--R (2sinh(c - a) - 4cosh(c - a)sinh(c - a) + 2cosh(c - a) + 2) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R 6cosh(b x + c)sinh(c - a) +--R + +--R - 12cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a) + 6)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 2)sinh(c - a) +--R + +--R 2 +--R (- 12cosh(c - a)cosh(b x + c) - 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (6cosh(c - a) + 6)cosh(b x + c) + 2cosh(c - a) + 2 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (2cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 4cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (2cosh(c - a) + 2)cosh(b x + c) + (2cosh(c - a) + 2)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 3 +--R (2cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c)sinh(c - a) - 6cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 6cosh(c - a) cosh(b x + c) - 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 2cosh(c - a) cosh(b x + c) - 2cosh(c - a) cosh(b x + c) +--R * +--R atan(sinh(b x + c)) +--R + +--R 2 2 4 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R (- 2sinh(c - a) + 2cosh(c - a))sinh(b x + a) +--R + +--R 2 +--R (2sech(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R (- 2cosh(c - a)sech(b x + c) + 8cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 +--R - 4cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R (- 6cosh(b x + c)sinh(c - a) + 6cosh(c - a)cosh(b x + c)) +--R * +--R sinh(b x + a) +--R + +--R 2 2 +--R (6cosh(b x + c)sech(b x + c) - 6cosh(b x + c) - 3)sinh(c - a) +--R + +--R - 6cosh(c - a)cosh(b x + c)sech(b x + c) +--R + +--R 2 +--R 12cosh(c - a)cosh(b x + c) + 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R - 6cosh(c - a) cosh(b x + c) - 3cosh(c - a) + 3 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) - 2)sinh(c - a) + 6cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 2 3 +--R (6cosh(b x + c) + 2)sech(b x + c) - 4cosh(b x + c) +--R + +--R - 6cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 +--R (- 6cosh(c - a)cosh(b x + c) - 2cosh(c - a))sech(b x + c) +--R + +--R 3 +--R 8cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R - 4cosh(c - a) cosh(b x + c) + (- 6cosh(c - a) + 6)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (- 2cosh(b x + c) - 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R 2cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 3 4 +--R (2cosh(b x + c) + 2cosh(b x + c))sech(b x + c) - cosh(b x + c) +--R + +--R 2 +--R - 3cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 +--R (- 2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c) +--R + +--R 4 2 +--R 2cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - cosh(c - a) cosh(b x + c) + (- 3cosh(c - a) + 3)cosh(b x + c) + 1 +--R / +--R 3 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c) + 2b)sinh(c - a) - 6b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2b cosh(b x + c) + 2b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2b cosh(c - a)cosh(b x + c) - 2b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 392 + +--S 393 of 518 +d0974:= D(m0974,x) +--R +--R +--R (380) +--R 2 +--R - 2sech(b x + c)sinh(c - a) +--R + +--R 2cosh(c - a)sech(b x + c)sinh(c - a) +--R * +--R 7 +--R sinh(b x + c) +--R + +--R 2 +--R - 10cosh(b x + c)sech(b x + c)sinh(c - a) +--R + +--R 10cosh(c - a)cosh(b x + c)sech(b x + c)sinh(c - a) +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 20cosh(b x + c) - 6)sech(b x + c)sinh(c - a) +--R + +--R 2 +--R (20cosh(c - a)cosh(b x + c) + 6cosh(c - a))sech(b x + c) +--R * +--R sinh(c - a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 20cosh(b x + c) - 22cosh(b x + c))sech(b x + c)sinh(c - a) +--R + +--R 3 +--R (20cosh(c - a)cosh(b x + c) + 22cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 4 2 +--R (- 10cosh(b x + c) - 32cosh(b x + c) - 6)sech(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 4 2 +--R 10cosh(c - a)cosh(b x + c) + 32cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 5 3 +--R (- 2cosh(b x + c) - 24cosh(b x + c) - 14cosh(b x + c)) +--R * +--R 2 +--R sech(b x + c)sinh(c - a) +--R + +--R 5 3 +--R 2cosh(c - a)cosh(b x + c) + 24cosh(c - a)cosh(b x + c) +--R + +--R 14cosh(c - a)cosh(b x + c) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (- 10cosh(b x + c) - 12cosh(b x + c) - 2)sech(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 4 2 +--R 10cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (- 2cosh(b x + c) - 4cosh(b x + c) - 2cosh(b x + c))sech(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 5 3 +--R 2cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + c) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R tanh(b x + c) +--R + +--R 2 2 8 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 6cosh(b x + c)sinh(c - a) +--R + +--R (12cosh(c - a)cosh(b x + c) - 2cosh(b x + a))sinh(c - a) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a) +--R * +--R 7 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 15cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R 30cosh(c - a)cosh(b x + c) - 10cosh(b x + a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 2 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 10cosh(c - a)cosh(b x + a)cosh(b x + c) + cosh(c - a) - 1 +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 20cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 3 2 +--R 40cosh(c - a)cosh(b x + c) - 20cosh(b x + a)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) - 6cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R - 20cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 20cosh(c - a)cosh(b x + a)cosh(b x + c) - 4cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) - 3cosh(b x + c) + 1)sinh(c - a) +--R + +--R 4 3 +--R 30cosh(c - a)cosh(b x + c) - 20cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R 16cosh(c - a)cosh(b x + c) - 22cosh(b x + a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 20cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (- 13cosh(c - a) - 6)cosh(b x + c) +--R + +--R 2 +--R 22cosh(c - a)cosh(b x + a)cosh(b x + c) + cosh(c - a) + 1 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 6cosh(b x + c) - 12cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 5 4 +--R 12cosh(c - a)cosh(b x + c) - 10cosh(b x + a)cosh(b x + c) +--R + +--R 3 2 +--R 44cosh(c - a)cosh(b x + c) - 32cosh(b x + a)cosh(b x + c) +--R + +--R - 8cosh(c - a)cosh(b x + c) - 6cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R - 6cosh(c - a) cosh(b x + c) +--R + +--R 4 +--R 10cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 3 +--R (- 32cosh(c - a) - 4)cosh(b x + c) +--R + +--R 2 2 +--R 32cosh(c - a)cosh(b x + a)cosh(b x + c) + 2cosh(c - a) cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 6 4 2 +--R (- cosh(b x + c) - 13cosh(b x + c) + 11cosh(b x + c) - 1) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 6 5 +--R 2cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R 4 3 +--R 46cosh(c - a)cosh(b x + c) - 24cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R - 10cosh(c - a)cosh(b x + c) - 14cosh(b x + a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 6 +--R - cosh(c - a) cosh(b x + c) +--R + +--R 5 +--R 2cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 4 +--R (- 33cosh(c - a) - 1)cosh(b x + c) +--R + +--R 3 +--R 24cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (- cosh(c - a) - 4)cosh(b x + c) +--R + +--R 2 +--R 14cosh(c - a)cosh(b x + a)cosh(b x + c) - cosh(c - a) + 1 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 6cosh(b x + c) + 8cosh(b x + c) - 2cosh(b x + c))sinh(c - a) +--R + +--R 5 4 +--R 22cosh(c - a)cosh(b x + c) - 10cosh(b x + a)cosh(b x + c) +--R + +--R 3 2 +--R - 4cosh(c - a)cosh(b x + c) - 12cosh(b x + a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) - 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R - 16cosh(c - a) cosh(b x + c) +--R + +--R 4 +--R 10cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 3 +--R (- 4cosh(c - a) - 4)cosh(b x + c) +--R + +--R 2 +--R 12cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (- 4cosh(c - a) + 4)cosh(b x + c) + 2cosh(c - a)cosh(b x + a) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (- cosh(b x + c) + 2cosh(b x + c) - cosh(b x + c) )sinh(c - a) +--R + +--R 6 5 +--R 4cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R 3 2 +--R - 4cosh(b x + a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(b x + a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 6 5 +--R - 3cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 4 +--R (- 2cosh(c - a) - 1)cosh(b x + c) +--R + +--R 3 +--R 4cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (- 3cosh(c - a) + 2)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + a)cosh(b x + c) - 1 +--R / +--R 7 +--R (2sinh(c - a) - 2cosh(c - a))sinh(b x + c) +--R + +--R 6 +--R (10cosh(b x + c)sinh(c - a) - 10cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (20cosh(b x + c) + 6)sinh(c - a) - 20cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 3 +--R (20cosh(b x + c) + 22cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 20cosh(c - a)cosh(b x + c) - 22cosh(c - a)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 4 2 +--R (10cosh(b x + c) + 32cosh(b x + c) + 6)sinh(c - a) +--R + +--R 4 2 +--R - 10cosh(c - a)cosh(b x + c) - 32cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 5 3 +--R (2cosh(b x + c) + 24cosh(b x + c) + 14cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 2cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R + +--R - 14cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (10cosh(b x + c) + 12cosh(b x + c) + 2)sinh(c - a) +--R + +--R 4 2 +--R - 10cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (2cosh(b x + c) + 4cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 2cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 393 + +--S 394 of 518 +t0975:= cosh(a+b*x)*tanh(c+b*x)^3 +--R +--R +--R 3 +--R (381) cosh(b x + a)tanh(b x + c) +--R Type: Expression(Integer) +--E 394 + +--S 395 of 518 +r0975:= cosh(a+b*x)/b+cosh(a-c)*sech(c+b*x)/b-_ + 3/2*atan(sinh(c+b*x))*sinh(a-c)/b+1/2*sech(c+b*x)*_ + sinh(a-c)*tanh(c+b*x)/b +--R +--R +--R (382) +--R 3sinh(c - a)atan(sinh(b x + c)) - sech(b x + c)sinh(c - a)tanh(b x + c) +--R + +--R 2cosh(c - a)sech(b x + c) + 2cosh(b x + a) +--R / +--R 2b +--R Type: Expression(Integer) +--E 395 + +--S 396 of 518 +a0975:= integrate(t0975,x) +--R +--R +--R (383) +--R 2 2 +--R (3sinh(c - a) - 6cosh(c - a)sinh(c - a) + 3cosh(c - a) - 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R 15cosh(b x + c)sinh(c - a) +--R + +--R - 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (15cosh(c - a) - 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (30cosh(b x + c) + 6)sinh(c - a) +--R + +--R 2 +--R (- 60cosh(c - a)cosh(b x + c) - 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (30cosh(c - a) - 30)cosh(b x + c) + 6cosh(c - a) - 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (30cosh(b x + c) + 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 60cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (30cosh(c - a) - 30)cosh(b x + c) +--R + +--R 2 +--R (18cosh(c - a) - 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) + 18cosh(b x + c) + 3)sinh(c - a) +--R + +--R 4 2 +--R - 30cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (15cosh(c - a) - 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (18cosh(c - a) - 18)cosh(b x + c) + 3cosh(c - a) - 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (3cosh(b x + c) + 6cosh(b x + c) + 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R (3cosh(c - a) - 3)cosh(b x + c) + (6cosh(c - a) - 6)cosh(b x + c) +--R + +--R 2 +--R (3cosh(c - a) - 3)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 2 6 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 6cosh(b x + c)sinh(c - a) + 12cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 15cosh(b x + c) - 5)sinh(c - a) +--R + +--R 2 +--R (30cosh(c - a)cosh(b x + c) + 10cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 15cosh(c - a) cosh(b x + c) - 5cosh(c - a) - 2 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 20cosh(b x + c) - 20cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (40cosh(c - a)cosh(b x + c) + 40cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 20cosh(c - a) cosh(b x + c) + (- 20cosh(c - a) - 8)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) - 30cosh(b x + c) - 2)sinh(c - a) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) + 60cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 2 2 2 +--R (- 30cosh(c - a) - 12)cosh(b x + c) - 2cosh(c - a) - 5 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 6cosh(b x + c) - 20cosh(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 12cosh(c - a)cosh(b x + c) + 40cosh(c - a)cosh(b x + c) +--R + +--R 8cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) + (- 20cosh(c - a) - 8)cosh(b x + c) +--R + +--R 2 +--R (- 4cosh(c - a) - 10)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (- cosh(b x + c) - 5cosh(b x + c) - 2cosh(b x + c) )sinh(c - a) +--R + +--R 6 4 +--R 2cosh(c - a)cosh(b x + c) + 10cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) + (- 5cosh(c - a) - 2)cosh(b x + c) +--R + +--R 2 2 +--R (- 2cosh(c - a) - 5)cosh(b x + c) - 1 +--R / +--R 5 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R (10b cosh(b x + c)sinh(c - a) - 10b cosh(c - a)cosh(b x + c)) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (20b cosh(b x + c) + 4b)sinh(c - a) - 20b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (20b cosh(b x + c) + 12b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 20b cosh(c - a)cosh(b x + c) - 12b cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (10b cosh(b x + c) + 12b cosh(b x + c) + 2b)sinh(c - a) +--R + +--R 4 2 +--R - 10b cosh(c - a)cosh(b x + c) - 12b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (2b cosh(b x + c) + 4b cosh(b x + c) + 2b cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 2b cosh(c - a)cosh(b x + c) - 4b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 518 +m0975:= a0975-r0975 +--R +--R +--R (384) +--R 2 2 +--R (3sinh(c - a) - 6cosh(c - a)sinh(c - a) + 3cosh(c - a) - 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R 15cosh(b x + c)sinh(c - a) +--R + +--R - 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (15cosh(c - a) - 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (30cosh(b x + c) + 6)sinh(c - a) +--R + +--R 2 +--R (- 60cosh(c - a)cosh(b x + c) - 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (30cosh(c - a) - 30)cosh(b x + c) + 6cosh(c - a) - 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (30cosh(b x + c) + 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 60cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (30cosh(c - a) - 30)cosh(b x + c) +--R + +--R 2 +--R (18cosh(c - a) - 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) + 18cosh(b x + c) + 3)sinh(c - a) +--R + +--R 4 2 +--R - 30cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (15cosh(c - a) - 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (18cosh(c - a) - 18)cosh(b x + c) + 3cosh(c - a) - 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (3cosh(b x + c) + 6cosh(b x + c) + 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R (3cosh(c - a) - 3)cosh(b x + c) + (6cosh(c - a) - 6)cosh(b x + c) +--R + +--R 2 +--R (3cosh(c - a) - 3)cosh(b x + c) +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 5 +--R (- 3sinh(c - a) + 3cosh(c - a)sinh(c - a))sinh(b x + c) +--R + +--R 2 +--R - 15cosh(b x + c)sinh(c - a) +--R + +--R 15cosh(c - a)cosh(b x + c)sinh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 30cosh(b x + c) - 6)sinh(c - a) +--R + +--R 2 +--R (30cosh(c - a)cosh(b x + c) + 6cosh(c - a))sinh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 30cosh(b x + c) - 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (30cosh(c - a)cosh(b x + c) + 18cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) - 18cosh(b x + c) - 3)sinh(c - a) +--R + +--R 4 2 +--R 15cosh(c - a)cosh(b x + c) + 18cosh(c - a)cosh(b x + c) +--R + +--R 3cosh(c - a) +--R * +--R sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 3cosh(b x + c) - 6cosh(b x + c) - 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 3cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) +--R + +--R 3cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R * +--R atan(sinh(b x + c)) +--R + +--R 2 +--R (sech(b x + c)sinh(c - a) - cosh(c - a)sech(b x + c)sinh(c - a)) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R 5cosh(b x + c)sech(b x + c)sinh(c - a) +--R + +--R - 5cosh(c - a)cosh(b x + c)sech(b x + c)sinh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (10cosh(b x + c) + 2)sech(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 10cosh(c - a)cosh(b x + c) - 2cosh(c - a))sech(b x + c) +--R * +--R sinh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (10cosh(b x + c) + 6cosh(b x + c))sech(b x + c)sinh(c - a) +--R + +--R 3 +--R (- 10cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (5cosh(b x + c) + 6cosh(b x + c) + 1)sech(b x + c)sinh(c - a) +--R + +--R 4 2 +--R - 5cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (cosh(b x + c) + 2cosh(b x + c) + cosh(b x + c))sech(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 5 3 +--R - cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a)cosh(b x + c) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R tanh(b x + c) +--R + +--R 2 2 6 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 6cosh(b x + c)sinh(c - a) +--R + +--R - 2cosh(c - a)sech(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 2 +--R 2cosh(c - a) sech(b x + c) - 6cosh(c - a) cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 15cosh(b x + c) - 5)sinh(c - a) +--R + +--R - 10cosh(c - a)cosh(b x + c)sech(b x + c) +--R + +--R 2 +--R 30cosh(c - a)cosh(b x + c) - 10cosh(b x + a)cosh(b x + c) +--R + +--R 10cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 +--R 10cosh(c - a) cosh(b x + c)sech(b x + c) +--R + +--R 2 2 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 10cosh(c - a)cosh(b x + a)cosh(b x + c) - 5cosh(c - a) - 2 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 20cosh(b x + c) - 20cosh(b x + c))sinh(c - a) +--R + +--R 2 +--R (- 20cosh(c - a)cosh(b x + c) - 4cosh(c - a))sech(b x + c) +--R + +--R 3 2 +--R 40cosh(c - a)cosh(b x + c) - 20cosh(b x + a)cosh(b x + c) +--R + +--R 40cosh(c - a)cosh(b x + c) - 4cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (20cosh(c - a) cosh(b x + c) + 4cosh(c - a) )sech(b x + c) +--R + +--R 2 3 +--R - 20cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 20cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (- 20cosh(c - a) - 8)cosh(b x + c) + 4cosh(c - a)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) - 30cosh(b x + c) - 2)sinh(c - a) +--R + +--R 3 +--R (- 20cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c) +--R + +--R 4 3 +--R 30cosh(c - a)cosh(b x + c) - 20cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R 60cosh(c - a)cosh(b x + c) - 12cosh(b x + a)cosh(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R (20cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c)) +--R * +--R sech(b x + c) +--R + +--R 2 4 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 20cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (- 30cosh(c - a) - 12)cosh(b x + c) +--R + +--R 2 +--R 12cosh(c - a)cosh(b x + a)cosh(b x + c) - 2cosh(c - a) - 5 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 6cosh(b x + c) - 20cosh(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 4 2 +--R - 10cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sech(b x + c) +--R + +--R 5 4 +--R 12cosh(c - a)cosh(b x + c) - 10cosh(b x + a)cosh(b x + c) +--R + +--R 3 2 +--R 40cosh(c - a)cosh(b x + c) - 12cosh(b x + a)cosh(b x + c) +--R + +--R 8cosh(c - a)cosh(b x + c) - 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R 10cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 2cosh(c - a) +--R * +--R sech(b x + c) +--R + +--R 2 5 +--R - 6cosh(c - a) cosh(b x + c) +--R + +--R 4 +--R 10cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 3 +--R (- 20cosh(c - a) - 8)cosh(b x + c) +--R + +--R 2 +--R 12cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (- 4cosh(c - a) - 10)cosh(b x + c) + 2cosh(c - a)cosh(b x + a) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (- cosh(b x + c) - 5cosh(b x + c) - 2cosh(b x + c) )sinh(c - a) +--R + +--R 5 3 +--R - 2cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) +--R * +--R sech(b x + c) +--R + +--R 6 5 +--R 2cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R 4 3 +--R 10cosh(c - a)cosh(b x + c) - 4cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R 4cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R 2cosh(c - a) cosh(b x + c) + 4cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 2cosh(c - a) cosh(b x + c) +--R * +--R sech(b x + c) +--R + +--R 2 6 5 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 4 +--R (- 5cosh(c - a) - 2)cosh(b x + c) +--R + +--R 3 +--R 4cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (- 2cosh(c - a) - 5)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + a)cosh(b x + c) - 1 +--R / +--R 5 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R (10b cosh(b x + c)sinh(c - a) - 10b cosh(c - a)cosh(b x + c)) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (20b cosh(b x + c) + 4b)sinh(c - a) - 20b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (20b cosh(b x + c) + 12b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 20b cosh(c - a)cosh(b x + c) - 12b cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (10b cosh(b x + c) + 12b cosh(b x + c) + 2b)sinh(c - a) +--R + +--R 4 2 +--R - 10b cosh(c - a)cosh(b x + c) - 12b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (2b cosh(b x + c) + 4b cosh(b x + c) + 2b cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 2b cosh(c - a)cosh(b x + c) - 4b cosh(c - a)cosh(b x + c) +--R + +--R - 2b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 397 + +--S 398 of 518 +--d0975:= D(m0975,x) +--E 398 + +--S 399 of 518 +t0976:= cosh(a+b*x)*coth(c+b*x) +--R +--R +--R (385) cosh(b x + a)coth(b x + c) +--R Type: Expression(Integer) +--E 399 + +--S 400 of 518 +r0976:= -(acoth(cosh(c+b*x))*cosh(a-c)-cosh(a+b*x))/b +--R +--R +--R - cosh(c - a)acoth(cosh(b x + c)) + cosh(b x + a) +--R (386) ------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 400 + +--S 401 of 518 +a0976:= integrate(t0976,x) +--R +--R +--R (387) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) + 1) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R cosh(b x + c)sinh(c - a) - 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (cosh(c - a) + 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R - cosh(b x + c)sinh(c - a) + 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- cosh(c - a) - 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) + 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 2cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 2 +--R - cosh(b x + c) sinh(c - a) + 2cosh(c - a)cosh(b x + c) sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) - 1 +--R / +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 518 +m0976:= a0976-r0976 +--R +--R +--R (388) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) + 1) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R cosh(b x + c)sinh(c - a) - 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (cosh(c - a) + 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R - cosh(b x + c)sinh(c - a) + 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- cosh(c - a) - 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 +--R (2cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R 2cosh(c - a)cosh(b x + c)sinh(c - a) - 2cosh(c - a) cosh(b x + c) +--R * +--R acoth(cosh(b x + c)) +--R + +--R 2 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) +--R + +--R (4cosh(c - a)cosh(b x + c) - 2cosh(b x + a))sinh(c - a) +--R + +--R 2 +--R - 2cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R - cosh(b x + c) sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c))sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a)cosh(b x + c) - 1 +--R / +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 402 + +--S 403 of 518 +d0976:= D(m0976,x) +--R +--R +--R (389) +--R 2 2 +--R (- cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - cosh(c - a) cosh(b x + c) + 3cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 2cosh(b x + c) + 2)sinh(c - a) + 2cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 3 2 +--R (- 4cosh(b x + c) + 4cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (8cosh(c - a)cosh(b x + c) - 14cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 4cosh(c - a) cosh(b x + c) + 10cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (- 6cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R 6cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (- 6cosh(b x + c) + 5cosh(b x + c) + 1)sinh(c - a) +--R + +--R 4 2 +--R (12cosh(c - a)cosh(b x + c) - 16cosh(c - a)cosh(b x + c) ) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 6cosh(c - a) cosh(b x + c) + (11cosh(c - a) - 1)cosh(b x + c) +--R + +--R 2 +--R - cosh(c - a) + 1 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (- 6cosh(b x + c) + 8cosh(b x + c) - 2)sinh(c - a) +--R + +--R 4 2 +--R 6cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 5 3 2 +--R (- 4cosh(b x + c) + 2cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 8cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 4cosh(c - a) cosh(b x + c) + (4cosh(c - a) - 2)cosh(b x + c) +--R + +--R 2cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (- 2cosh(b x + c) + 4cosh(b x + c) - 2cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 2cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 6 2 2 +--R (- cosh(b x + c) + cosh(b x + c) )sinh(c - a) +--R + +--R 6 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) )sinh(c - a) +--R + +--R 2 6 4 +--R - cosh(c - a) cosh(b x + c) - cosh(b x + c) +--R + +--R 2 2 +--R cosh(c - a) cosh(b x + c) + 1 +--R / +--R 2 2 +--R (2cosh(b x + c) - 2)sinh(c - a) - 2cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (6cosh(b x + c) - 6cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 6cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (6cosh(b x + c) - 8cosh(b x + c) + 2)sinh(c - a) +--R + +--R 4 2 +--R - 6cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (2cosh(b x + c) - 4cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 2cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 403 + +--S 404 of 518 +t0977:= cosh(a+b*x)*coth(c+b*x)^2 +--R +--R +--R 2 +--R (390) cosh(b x + a)coth(b x + c) +--R Type: Expression(Integer) +--E 404 + +--S 405 of 518 +r0977:= -cosh(a-c)*csch(c+b*x)/b-acoth(cosh(c+b*x))*sinh(a-c)/b+sinh(a+b*x)/b +--R +--R +--R (391) +--R sinh(c - a)acoth(cosh(b x + c)) + sinh(b x + a) - cosh(c - a)csch(b x + c) +--R -------------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 405 + +--S 406 of 518 +a0977:= integrate(t0977,x) +--R +--R +--R (392) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) - 1) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R 3cosh(b x + c)sinh(c - a) - 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (3cosh(c - a) - 3)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (3cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (- 6cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (3cosh(c - a) - 3)cosh(b x + c) - cosh(c - a) + 1 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (cosh(b x + c) - cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 2cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (cosh(c - a) - 1)cosh(b x + c) + (- cosh(c - a) + 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R - 3cosh(b x + c)sinh(c - a) +--R + +--R 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 3cosh(c - a) + 3)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 3cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- 3cosh(c - a) + 3)cosh(b x + c) + cosh(c - a) - 1 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (- cosh(b x + c) + cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (- cosh(c - a) + 1)cosh(b x + c) + (cosh(c - a) - 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 2 4 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 4cosh(b x + c)sinh(c - a) + 8cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 4cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) + 3)sinh(c - a) +--R + +--R 2 +--R (12cosh(c - a)cosh(b x + c) - 6cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 6cosh(c - a) cosh(b x + c) + 3cosh(c - a) + 3 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 4cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (8cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 4cosh(c - a) cosh(b x + c) + (6cosh(c - a) + 6)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- cosh(b x + c) + 3cosh(b x + c) )sinh(c - a) +--R + +--R 4 2 +--R (2cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) )sinh(c - a) +--R + +--R 2 4 2 2 +--R - cosh(c - a) cosh(b x + c) + (3cosh(c - a) + 3)cosh(b x + c) - 1 +--R / +--R 3 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c) - 2b)sinh(c - a) - 6b cosh(c - a)cosh(b x + c) +--R + +--R 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2b cosh(b x + c) - 2b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2b cosh(c - a)cosh(b x + c) + 2b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 518 +m0977:= a0977-r0977 +--R +--R +--R (393) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) - 1) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R 3cosh(b x + c)sinh(c - a) - 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (3cosh(c - a) - 3)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (3cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (- 6cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (3cosh(c - a) - 3)cosh(b x + c) - cosh(c - a) + 1 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (cosh(b x + c) - cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 2cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (cosh(c - a) - 1)cosh(b x + c) + (- cosh(c - a) + 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 +--R - 3cosh(b x + c)sinh(c - a) +--R + +--R 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 3cosh(c - a) + 3)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 3cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- 3cosh(c - a) + 3)cosh(b x + c) + cosh(c - a) - 1 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (- cosh(b x + c) + cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R (- cosh(c - a) + 1)cosh(b x + c) + (cosh(c - a) - 1)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 3 +--R (- 2sinh(c - a) + 2cosh(c - a)sinh(c - a))sinh(b x + c) +--R + +--R 2 +--R - 6cosh(b x + c)sinh(c - a) +--R + +--R 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) + 2)sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 2cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))sinh(c - a) +--R * +--R acoth(cosh(b x + c)) +--R + +--R 2 2 4 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R (- 2sinh(c - a) + 2cosh(c - a))sinh(b x + a) +--R + +--R 2 +--R - 4cosh(b x + c)sinh(c - a) +--R + +--R (2cosh(c - a)csch(b x + c) + 8cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 2 +--R - 2cosh(c - a) csch(b x + c) - 4cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R (- 6cosh(b x + c)sinh(c - a) + 6cosh(c - a)cosh(b x + c)) +--R * +--R sinh(b x + a) +--R + +--R 2 2 +--R (- 6cosh(b x + c) + 3)sinh(c - a) +--R + +--R 6cosh(c - a)cosh(b x + c)csch(b x + c) +--R + +--R 2 +--R 12cosh(c - a)cosh(b x + c) - 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c)csch(b x + c) +--R + +--R 2 2 2 +--R - 6cosh(c - a) cosh(b x + c) + 3cosh(c - a) + 3 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) + 2)sinh(c - a) + 6cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R sinh(b x + a) +--R + +--R 3 2 +--R (- 4cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 2 +--R (6cosh(c - a)cosh(b x + c) - 2cosh(c - a))csch(b x + c) +--R + +--R 3 +--R 8cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (- 6cosh(c - a) cosh(b x + c) + 2cosh(c - a) )csch(b x + c) +--R + +--R 2 3 2 +--R - 4cosh(c - a) cosh(b x + c) + (6cosh(c - a) + 6)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (- 2cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R 2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + a) +--R + +--R 4 2 2 +--R (- cosh(b x + c) + 3cosh(b x + c) )sinh(c - a) +--R + +--R 3 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c))csch(b x + c) +--R + +--R 4 2 +--R 2cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R (- 2cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c))csch(b x + c) +--R + +--R 2 4 2 2 +--R - cosh(c - a) cosh(b x + c) + (3cosh(c - a) + 3)cosh(b x + c) - 1 +--R / +--R 3 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c) - 2b)sinh(c - a) - 6b cosh(c - a)cosh(b x + c) +--R + +--R 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (2b cosh(b x + c) - 2b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 2b cosh(c - a)cosh(b x + c) + 2b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 407 + +--S 408 of 518 +d0977:= D(m0977,x) +--R +--R +--R (394) +--R 2 2 +--R (- cosh(b x + c) + 3)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - cosh(c - a) cosh(b x + c) + cosh(c - a) +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 6cosh(b x + c) + 16cosh(b x + c))sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a)cosh(b x + c) + 2cosh(c - a))coth(b x + c) +--R * +--R csch(b x + c) +--R + +--R 3 2 +--R 12cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R - 22cosh(c - a)cosh(b x + c) + 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (2cosh(c - a) cosh(b x + c) - 2cosh(c - a) )coth(b x + c) +--R * +--R csch(b x + c) +--R + +--R 2 3 +--R - 6cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R 2cosh(c - a)cosh(b x + a)cosh(b x + c) + 6cosh(c - a) cosh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) + 33cosh(b x + c) - 2)sinh(c - a) +--R + +--R 3 +--R (- 10cosh(c - a)cosh(b x + c) + 10cosh(c - a)cosh(b x + c)) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 4 3 +--R 30cosh(c - a)cosh(b x + c) - 10cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R - 46cosh(c - a)cosh(b x + c) + 10cosh(b x + a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R (10cosh(c - a) cosh(b x + c) - 10cosh(c - a) cosh(b x + c)) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 4 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 10cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (13cosh(c - a) - 1)cosh(b x + c) +--R + +--R 2 +--R - 10cosh(c - a)cosh(b x + a)cosh(b x + c) + 2cosh(c - a) + 1 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 20cosh(b x + c) + 32cosh(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 4 2 +--R - 20cosh(c - a)cosh(b x + c) + 24cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 5 4 +--R 40cosh(c - a)cosh(b x + c) - 20cosh(b x + a)cosh(b x + c) +--R + +--R 3 2 +--R - 44cosh(c - a)cosh(b x + c) + 24cosh(b x + a)cosh(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c) - 4cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R 20cosh(c - a) cosh(b x + c) - 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 4cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 5 +--R - 20cosh(c - a) cosh(b x + c) +--R + +--R 4 +--R 20cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 3 +--R (12cosh(c - a) - 4)cosh(b x + c) +--R + +--R 2 +--R - 24cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (8cosh(c - a) + 4)cosh(b x + c) + 4cosh(c - a)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 6 4 2 +--R (- 15cosh(b x + c) + 13cosh(b x + c) - cosh(b x + c) + 3) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 5 3 +--R - 20cosh(c - a)cosh(b x + c) + 32cosh(c - a)cosh(b x + c) +--R + +--R - 12cosh(c - a)cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 6 5 +--R 30cosh(c - a)cosh(b x + c) - 20cosh(b x + a)cosh(b x + c) +--R + +--R 4 3 +--R - 16cosh(c - a)cosh(b x + c) + 32cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R - 10cosh(c - a)cosh(b x + c) - 12cosh(b x + a)cosh(b x + c) +--R + +--R - 4cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R 20cosh(c - a) cosh(b x + c) - 32cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 12cosh(c - a) cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 6 +--R - 15cosh(c - a) cosh(b x + c) +--R + +--R 5 +--R 20cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 4 +--R (3cosh(c - a) - 6)cosh(b x + c) +--R + +--R 3 +--R - 32cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (11cosh(c - a) + 4)cosh(b x + c) +--R + +--R 2 +--R 12cosh(c - a)cosh(b x + a)cosh(b x + c) + cosh(c - a) + 2 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 7 3 2 +--R (- 6cosh(b x + c) + 2cosh(b x + c) + 4cosh(b x + c))sinh(c - a) +--R + +--R 6 4 +--R - 10cosh(c - a)cosh(b x + c) + 22cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 14cosh(c - a)cosh(b x + c) + 2cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 7 6 +--R 12cosh(c - a)cosh(b x + c) - 10cosh(b x + a)cosh(b x + c) +--R + +--R 5 4 +--R 2cosh(c - a)cosh(b x + c) + 22cosh(b x + a)cosh(b x + c) +--R + +--R 3 2 +--R - 8cosh(c - a)cosh(b x + c) - 14cosh(b x + a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) + 2cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R 10cosh(c - a) cosh(b x + c) - 22cosh(c - a) cosh(b x + c) +--R + +--R 2 2 2 +--R 14cosh(c - a) cosh(b x + c) - 2cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 7 +--R - 6cosh(c - a) cosh(b x + c) +--R + +--R 6 +--R 10cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 5 +--R (- 2cosh(c - a) - 4)cosh(b x + c) +--R + +--R 4 +--R - 22cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 3 +--R 6cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 14cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (2cosh(c - a) + 4)cosh(b x + c) - 2cosh(c - a)cosh(b x + a) +--R * +--R sinh(b x + c) +--R + +--R 8 6 4 2 +--R (- cosh(b x + c) - cosh(b x + c) + cosh(b x + c) + cosh(b x + c) ) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 7 5 +--R - 2cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) +--R + +--R 3 +--R - 6cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 8 7 +--R 2cosh(c - a)cosh(b x + c) - 2cosh(b x + a)cosh(b x + c) +--R + +--R 6 5 +--R 2cosh(c - a)cosh(b x + c) + 6cosh(b x + a)cosh(b x + c) +--R + +--R 4 3 +--R - 2cosh(c - a)cosh(b x + c) - 6cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R - 2cosh(c - a)cosh(b x + c) + 2cosh(b x + a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 7 2 5 +--R 2cosh(c - a) cosh(b x + c) - 6cosh(c - a) cosh(b x + c) +--R + +--R 2 3 2 +--R 6cosh(c - a) cosh(b x + c) - 2cosh(c - a) cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 8 7 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 6 +--R (- cosh(c - a) - 1)cosh(b x + c) +--R + +--R 5 +--R - 6cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 4 +--R (cosh(c - a) - 1)cosh(b x + c) +--R + +--R 3 +--R 6cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (cosh(c - a) + 1)cosh(b x + c) - 2cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 1 +--R / +--R 2 2 +--R (2cosh(b x + c) - 2)sinh(c - a) - 2cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 3 +--R (10cosh(b x + c) - 10cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 10cosh(c - a)cosh(b x + c) + 10cosh(c - a)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 4 2 +--R (20cosh(b x + c) - 24cosh(b x + c) + 4)sinh(c - a) +--R + +--R 4 2 +--R - 20cosh(c - a)cosh(b x + c) + 24cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 5 3 +--R (20cosh(b x + c) - 32cosh(b x + c) + 12cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 20cosh(c - a)cosh(b x + c) + 32cosh(c - a)cosh(b x + c) +--R + +--R - 12cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 6 4 2 +--R (10cosh(b x + c) - 22cosh(b x + c) + 14cosh(b x + c) - 2) +--R * +--R sinh(c - a) +--R + +--R 6 4 +--R - 10cosh(c - a)cosh(b x + c) + 22cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 14cosh(c - a)cosh(b x + c) + 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 7 5 3 +--R (2cosh(b x + c) - 6cosh(b x + c) + 6cosh(b x + c) - 2cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 7 5 +--R - 2cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) +--R + +--R 3 +--R - 6cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 408 + +--S 409 of 518 +t0978:= cosh(a+b*x)*coth(c+b*x)^3 +--R +--R +--R 3 +--R (395) cosh(b x + a)coth(b x + c) +--R Type: Expression(Integer) +--E 409 + +--S 410 of 518 +r0978:= -3/2*acoth(cosh(c+b*x))*cosh(a-c)/b+cosh(a+b*x)/b-_ + 1/2*cosh(a-c)*coth(c+b*x)*csch(c+b*x)/b-csch(c+b*x)*sinh(a-c)/b +--R +--R +--R (396) +--R - 3cosh(c - a)acoth(cosh(b x + c)) + 2csch(b x + c)sinh(c - a) +--R + +--R - cosh(c - a)coth(b x + c)csch(b x + c) + 2cosh(b x + a) +--R / +--R 2b +--R Type: Expression(Integer) +--E 410 + +--S 411 of 518 +a0978:= integrate(t0978,x) +--R +--R +--R (397) +--R 2 2 +--R (3sinh(c - a) - 6cosh(c - a)sinh(c - a) + 3cosh(c - a) + 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R 15cosh(b x + c)sinh(c - a) +--R + +--R - 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (15cosh(c - a) + 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (30cosh(b x + c) - 6)sinh(c - a) +--R + +--R 2 +--R (- 60cosh(c - a)cosh(b x + c) + 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (30cosh(c - a) + 30)cosh(b x + c) - 6cosh(c - a) - 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (30cosh(b x + c) - 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 60cosh(c - a)cosh(b x + c) + 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (30cosh(c - a) + 30)cosh(b x + c) +--R + +--R 2 +--R (- 18cosh(c - a) - 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) - 18cosh(b x + c) + 3)sinh(c - a) +--R + +--R 4 2 +--R - 30cosh(c - a)cosh(b x + c) + 36cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (15cosh(c - a) + 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (- 18cosh(c - a) - 18)cosh(b x + c) + 3cosh(c - a) + 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (3cosh(b x + c) - 6cosh(b x + c) + 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R (3cosh(c - a) + 3)cosh(b x + c) +--R + +--R 2 3 2 +--R (- 6cosh(c - a) - 6)cosh(b x + c) + (3cosh(c - a) + 3)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- 3sinh(c - a) + 6cosh(c - a)sinh(c - a) - 3cosh(c - a) - 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R - 15cosh(b x + c)sinh(c - a) +--R + +--R 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 15cosh(c - a) - 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 30cosh(b x + c) + 6)sinh(c - a) +--R + +--R 2 +--R (60cosh(c - a)cosh(b x + c) - 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- 30cosh(c - a) - 30)cosh(b x + c) + 6cosh(c - a) + 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 30cosh(b x + c) + 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (60cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (- 30cosh(c - a) - 30)cosh(b x + c) +--R + +--R 2 +--R (18cosh(c - a) + 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) + 18cosh(b x + c) - 3)sinh(c - a) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (- 15cosh(c - a) - 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (18cosh(c - a) + 18)cosh(b x + c) - 3cosh(c - a) - 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 3cosh(b x + c) + 6cosh(b x + c) - 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R (- 3cosh(c - a) - 3)cosh(b x + c) +--R + +--R 2 3 2 +--R (6cosh(c - a) + 6)cosh(b x + c) + (- 3cosh(c - a) - 3)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 2 6 +--R (- 2sinh(c - a) + 4cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 12cosh(b x + c)sinh(c - a) + 24cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 12cosh(c - a) cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 30cosh(b x + c) + 10)sinh(c - a) +--R + +--R 2 +--R (60cosh(c - a)cosh(b x + c) - 20cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 30cosh(c - a) cosh(b x + c) + 10cosh(c - a) - 4 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 40cosh(b x + c) + 40cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (80cosh(c - a)cosh(b x + c) - 80cosh(c - a)cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 40cosh(c - a) cosh(b x + c) + (40cosh(c - a) - 16)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 30cosh(b x + c) + 60cosh(b x + c) - 4)sinh(c - a) +--R + +--R 4 2 +--R 60cosh(c - a)cosh(b x + c) - 120cosh(c - a)cosh(b x + c) +--R + +--R 8cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 30cosh(c - a) cosh(b x + c) + (60cosh(c - a) - 24)cosh(b x + c) +--R + +--R 2 +--R - 4cosh(c - a) + 10 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 12cosh(b x + c) + 40cosh(b x + c) - 8cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 24cosh(c - a)cosh(b x + c) - 80cosh(c - a)cosh(b x + c) +--R + +--R 16cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 12cosh(c - a) cosh(b x + c) + (40cosh(c - a) - 16)cosh(b x + c) +--R + +--R 2 +--R (- 8cosh(c - a) + 20)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (- 2cosh(b x + c) + 10cosh(b x + c) - 4cosh(b x + c) )sinh(c - a) +--R + +--R 6 4 +--R 4cosh(c - a)cosh(b x + c) - 20cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R 8cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R - 2cosh(c - a) cosh(b x + c) + (10cosh(c - a) - 4)cosh(b x + c) +--R + +--R 2 2 +--R (- 4cosh(c - a) + 10)cosh(b x + c) - 2 +--R / +--R 5 +--R (4b sinh(c - a) - 4b cosh(c - a))sinh(b x + c) +--R + +--R (20b cosh(b x + c)sinh(c - a) - 20b cosh(c - a)cosh(b x + c)) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (40b cosh(b x + c) - 8b)sinh(c - a) - 40b cosh(c - a)cosh(b x + c) +--R + +--R 8b cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (40b cosh(b x + c) - 24b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 40b cosh(c - a)cosh(b x + c) + 24b cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (20b cosh(b x + c) - 24b cosh(b x + c) + 4b)sinh(c - a) +--R + +--R 4 2 +--R - 20b cosh(c - a)cosh(b x + c) + 24b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (4b cosh(b x + c) - 8b cosh(b x + c) + 4b cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 4b cosh(c - a)cosh(b x + c) + 8b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a)cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 518 +m0978:= a0978-r0978 +--R +--R +--R (398) +--R 2 2 +--R (3sinh(c - a) - 6cosh(c - a)sinh(c - a) + 3cosh(c - a) + 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R 15cosh(b x + c)sinh(c - a) +--R + +--R - 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (15cosh(c - a) + 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (30cosh(b x + c) - 6)sinh(c - a) +--R + +--R 2 +--R (- 60cosh(c - a)cosh(b x + c) + 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (30cosh(c - a) + 30)cosh(b x + c) - 6cosh(c - a) - 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (30cosh(b x + c) - 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 60cosh(c - a)cosh(b x + c) + 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (30cosh(c - a) + 30)cosh(b x + c) +--R + +--R 2 +--R (- 18cosh(c - a) - 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) - 18cosh(b x + c) + 3)sinh(c - a) +--R + +--R 4 2 +--R - 30cosh(c - a)cosh(b x + c) + 36cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (15cosh(c - a) + 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (- 18cosh(c - a) - 18)cosh(b x + c) + 3cosh(c - a) + 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (3cosh(b x + c) - 6cosh(b x + c) + 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R (3cosh(c - a) + 3)cosh(b x + c) +--R + +--R 2 3 2 +--R (- 6cosh(c - a) - 6)cosh(b x + c) + (3cosh(c - a) + 3)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- 3sinh(c - a) + 6cosh(c - a)sinh(c - a) - 3cosh(c - a) - 3) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 +--R - 15cosh(b x + c)sinh(c - a) +--R + +--R 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 15cosh(c - a) - 15)cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 30cosh(b x + c) + 6)sinh(c - a) +--R + +--R 2 +--R (60cosh(c - a)cosh(b x + c) - 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- 30cosh(c - a) - 30)cosh(b x + c) + 6cosh(c - a) + 6 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 30cosh(b x + c) + 18cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (60cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 +--R (- 30cosh(c - a) - 30)cosh(b x + c) +--R + +--R 2 +--R (18cosh(c - a) + 18)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 15cosh(b x + c) + 18cosh(b x + c) - 3)sinh(c - a) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 +--R (- 15cosh(c - a) - 15)cosh(b x + c) +--R + +--R 2 2 2 +--R (18cosh(c - a) + 18)cosh(b x + c) - 3cosh(c - a) - 3 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 3cosh(b x + c) + 6cosh(b x + c) - 3cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 +--R (- 3cosh(c - a) - 3)cosh(b x + c) +--R + +--R 2 3 2 +--R (6cosh(c - a) + 6)cosh(b x + c) + (- 3cosh(c - a) - 3)cosh(b x + c) +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 5 +--R (6cosh(c - a)sinh(c - a) - 6cosh(c - a) )sinh(b x + c) +--R + +--R 30cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 30cosh(c - a) cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 +--R (60cosh(c - a)cosh(b x + c) - 12cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 60cosh(c - a) cosh(b x + c) + 12cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (60cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R - 60cosh(c - a) cosh(b x + c) + 36cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R 30cosh(c - a)cosh(b x + c) - 36cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 30cosh(c - a) cosh(b x + c) + 36cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R 6cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R acoth(cosh(b x + c)) +--R + +--R 2 2 6 +--R (- 2sinh(c - a) + 4cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R (- 4csch(b x + c) - 12cosh(b x + c))sinh(c - a) +--R + +--R (2cosh(c - a)coth(b x + c) + 4cosh(c - a))csch(b x + c) +--R + +--R 24cosh(c - a)cosh(b x + c) - 4cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 +--R - 2cosh(c - a) coth(b x + c)csch(b x + c) +--R + +--R 2 +--R - 12cosh(c - a) cosh(b x + c) + 4cosh(c - a)cosh(b x + a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 20cosh(b x + c)csch(b x + c) - 30cosh(b x + c) + 10)sinh(c - a) +--R + +--R 10cosh(c - a)cosh(b x + c)coth(b x + c) +--R + +--R 20cosh(c - a)cosh(b x + c) +--R * +--R csch(b x + c) +--R + +--R 2 +--R 60cosh(c - a)cosh(b x + c) - 20cosh(b x + a)cosh(b x + c) +--R + +--R - 20cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 +--R - 10cosh(c - a) cosh(b x + c)coth(b x + c)csch(b x + c) +--R + +--R 2 2 +--R - 30cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 20cosh(c - a)cosh(b x + a)cosh(b x + c) + 10cosh(c - a) - 4 +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 3 +--R (- 40cosh(b x + c) + 8)csch(b x + c) - 40cosh(b x + c) +--R + +--R 40cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 +--R (20cosh(c - a)cosh(b x + c) - 4cosh(c - a))coth(b x + c) +--R + +--R 2 +--R 40cosh(c - a)cosh(b x + c) - 8cosh(c - a) +--R * +--R csch(b x + c) +--R + +--R 3 2 +--R 80cosh(c - a)cosh(b x + c) - 40cosh(b x + a)cosh(b x + c) +--R + +--R - 80cosh(c - a)cosh(b x + c) + 8cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (- 20cosh(c - a) cosh(b x + c) + 4cosh(c - a) )coth(b x + c) +--R * +--R csch(b x + c) +--R + +--R 2 3 +--R - 40cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 40cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (40cosh(c - a) - 16)cosh(b x + c) - 8cosh(c - a)cosh(b x + a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (- 40cosh(b x + c) + 24cosh(b x + c))csch(b x + c) +--R + +--R 4 2 +--R - 30cosh(b x + c) + 60cosh(b x + c) - 4 +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 +--R (20cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c)) +--R * +--R coth(b x + c) +--R + +--R 3 +--R 40cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R * +--R csch(b x + c) +--R + +--R 4 3 +--R 60cosh(c - a)cosh(b x + c) - 40cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R - 120cosh(c - a)cosh(b x + c) + 24cosh(b x + a)cosh(b x + c) +--R + +--R 8cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R (- 20cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c)) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 4 +--R - 30cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 40cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (60cosh(c - a) - 24)cosh(b x + c) +--R + +--R 2 +--R - 24cosh(c - a)cosh(b x + a)cosh(b x + c) - 4cosh(c - a) + 10 +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (- 20cosh(b x + c) + 24cosh(b x + c) - 4)csch(b x + c) +--R + +--R 5 3 +--R - 12cosh(b x + c) + 40cosh(b x + c) - 8cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 4 2 +--R 10cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a) +--R * +--R coth(b x + c) +--R + +--R 4 2 +--R 20cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R csch(b x + c) +--R + +--R 5 4 +--R 24cosh(c - a)cosh(b x + c) - 20cosh(b x + a)cosh(b x + c) +--R + +--R 3 2 +--R - 80cosh(c - a)cosh(b x + c) + 24cosh(b x + a)cosh(b x + c) +--R + +--R 16cosh(c - a)cosh(b x + c) - 4cosh(b x + a) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 10cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 2cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 5 +--R - 12cosh(c - a) cosh(b x + c) +--R + +--R 4 +--R 20cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 3 +--R (40cosh(c - a) - 16)cosh(b x + c) +--R + +--R 2 +--R - 24cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R (- 8cosh(c - a) + 20)cosh(b x + c) + 4cosh(c - a)cosh(b x + a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (- 4cosh(b x + c) + 8cosh(b x + c) - 4cosh(b x + c))csch(b x + c) +--R + +--R 6 4 2 +--R - 2cosh(b x + c) + 10cosh(b x + c) - 4cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 5 3 +--R 2cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R + +--R 2cosh(c - a)cosh(b x + c) +--R * +--R coth(b x + c) +--R + +--R 5 3 +--R 4cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R + +--R 4cosh(c - a)cosh(b x + c) +--R * +--R csch(b x + c) +--R + +--R 6 5 +--R 4cosh(c - a)cosh(b x + c) - 4cosh(b x + a)cosh(b x + c) +--R + +--R 4 3 +--R - 20cosh(c - a)cosh(b x + c) + 8cosh(b x + a)cosh(b x + c) +--R + +--R 2 +--R 8cosh(c - a)cosh(b x + c) - 4cosh(b x + a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R - 2cosh(c - a) cosh(b x + c) + 4cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 2cosh(c - a) cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 6 5 +--R - 2cosh(c - a) cosh(b x + c) + 4cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 4 +--R (10cosh(c - a) - 4)cosh(b x + c) +--R + +--R 3 +--R - 8cosh(c - a)cosh(b x + a)cosh(b x + c) +--R + +--R 2 2 +--R (- 4cosh(c - a) + 10)cosh(b x + c) +--R + +--R 4cosh(c - a)cosh(b x + a)cosh(b x + c) - 2 +--R / +--R 5 +--R (4b sinh(c - a) - 4b cosh(c - a))sinh(b x + c) +--R + +--R (20b cosh(b x + c)sinh(c - a) - 20b cosh(c - a)cosh(b x + c)) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (40b cosh(b x + c) - 8b)sinh(c - a) - 40b cosh(c - a)cosh(b x + c) +--R + +--R 8b cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R (40b cosh(b x + c) - 24b cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 40b cosh(c - a)cosh(b x + c) + 24b cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 +--R (20b cosh(b x + c) - 24b cosh(b x + c) + 4b)sinh(c - a) +--R + +--R 4 2 +--R - 20b cosh(c - a)cosh(b x + c) + 24b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 5 3 +--R (4b cosh(b x + c) - 8b cosh(b x + c) + 4b cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 4b cosh(c - a)cosh(b x + c) + 8b cosh(c - a)cosh(b x + c) +--R + +--R - 4b cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 412 + +--S 413 of 518 +--d0978:= D(m0978,x) +--E 413 + +--S 414 of 518 +t0979:= cosh(a+b*x)*sech(c+b*x) +--R +--R +--R (399) cosh(b x + a)sech(b x + c) +--R Type: Expression(Integer) +--E 414 + +--S 415 of 518 +r0979:= x*cosh(a-c)+log(cosh(c+b*x))*sinh(a-c)/b +--R +--R +--R - sinh(c - a)log(cosh(b x + c)) + b x cosh(c - a) +--R (400) ------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 415 + +--S 416 of 518 +a0979:= integrate(t0979,x) +--R +--R +--R (401) +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R 2cosh(b x + c) +--R log(- -----------------------------) +--R sinh(b x + c) - cosh(b x + c) +--R + +--R - 2b x +--R / +--R 2b sinh(c - a) - 2b cosh(c - a) +--R Type: Union(Expression(Integer),...) +--E 416 + +--S 417 of 518 +m0979:= a0979-r0979 +--R +--R +--R (402) +--R 2 +--R (2sinh(c - a) - 2cosh(c - a)sinh(c - a))log(cosh(b x + c)) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R 2cosh(b x + c) +--R log(- -----------------------------) +--R sinh(b x + c) - cosh(b x + c) +--R + +--R 2 +--R - 2b x cosh(c - a)sinh(c - a) + 2b x cosh(c - a) - 2b x +--R / +--R 2b sinh(c - a) - 2b cosh(c - a) +--R Type: Expression(Integer) +--E 417 + +--S 418 of 518 +d0979:= D(m0979,x) +--R +--R +--R (403) +--R 2 2 +--R (sinh(c - a) - cosh(c - a) + 1)sinh(b x + c) +--R + +--R 2 2 +--R - cosh(b x + c)sinh(c - a) + (cosh(c - a) - 1)cosh(b x + c) +--R / +--R 2cosh(b x + c)sinh(c - a) - 2cosh(c - a)cosh(b x + c) +--R Type: Expression(Integer) +--E 418 + +--S 419 of 518 +t0980:= cosh(a+b*x)*sech(c+b*x)^2 +--R +--R +--R 2 +--R (404) cosh(b x + a)sech(b x + c) +--R Type: Expression(Integer) +--E 419 + +--S 420 of 518 +r0980:= atan(sinh(c+b*x))*cosh(a-c)/b-sech(c+b*x)*sinh(a-c)/b +--R +--R +--R cosh(c - a)atan(sinh(b x + c)) + sech(b x + c)sinh(c - a) +--R (405) --------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 420 + +--S 421 of 518 +a0980:= integrate(t0980,x) +--R +--R +--R (406) +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) +--R + +--R 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a) - 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (- cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- cosh(c - a) - 1)cosh(b x + c) - cosh(c - a) - 1 +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) - 1)sinh(b x + c) +--R + +--R 2 +--R cosh(b x + c)sinh(c - a) - 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (cosh(c - a) - 1)cosh(b x + c) +--R / +--R 2 +--R (b sinh(c - a) - b cosh(c - a))sinh(b x + c) +--R + +--R (2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (b cosh(b x + c) + b)sinh(c - a) - b cosh(c - a)cosh(b x + c) +--R + +--R - b cosh(c - a) +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 518 +m0980:= a0980-r0980 +--R +--R +--R (407) +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) +--R + +--R 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a) - 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (- cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- cosh(c - a) - 1)cosh(b x + c) - cosh(c - a) - 1 +--R * +--R atan(sinh(b x + c) + cosh(b x + c)) +--R + +--R 2 2 +--R (- cosh(c - a)sinh(c - a) + cosh(c - a) )sinh(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R 2cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R (- cosh(c - a)cosh(b x + c) - cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R cosh(c - a) cosh(b x + c) + cosh(c - a) +--R * +--R atan(sinh(b x + c)) +--R + +--R 2 +--R (- sech(b x + c)sinh(c - a) + cosh(c - a)sech(b x + c)sinh(c - a)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R (- 2cosh(b x + c)sech(b x + c) + 1)sinh(c - a) +--R + +--R (2cosh(c - a)cosh(b x + c)sech(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 +--R cosh(c - a) - 1 +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R ((- cosh(b x + c) - 1)sech(b x + c) + cosh(b x + c))sinh(c - a) +--R + +--R 2 +--R (cosh(c - a)cosh(b x + c) + cosh(c - a))sech(b x + c) +--R + +--R - 2cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 +--R (cosh(c - a) - 1)cosh(b x + c) +--R / +--R 2 +--R (b sinh(c - a) - b cosh(c - a))sinh(b x + c) +--R + +--R (2b cosh(b x + c)sinh(c - a) - 2b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (b cosh(b x + c) + b)sinh(c - a) - b cosh(c - a)cosh(b x + c) +--R + +--R - b cosh(c - a) +--R Type: Expression(Integer) +--E 422 + +--S 423 of 518 +d0980:= D(m0980,x) +--R +--R +--R (408) +--R 2 +--R (sech(b x + c)sinh(c - a) - cosh(c - a)sech(b x + c)sinh(c - a)) +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 2 +--R 4cosh(b x + c)sech(b x + c)sinh(c - a) +--R + +--R - 4cosh(c - a)cosh(b x + c)sech(b x + c)sinh(c - a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 3)sech(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 6cosh(c - a)cosh(b x + c) - 3cosh(c - a))sech(b x + c) +--R * +--R sinh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (4cosh(b x + c) + 8cosh(b x + c))sech(b x + c)sinh(c - a) +--R + +--R 3 +--R (- 4cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (cosh(b x + c) + 8cosh(b x + c) + 3)sech(b x + c)sinh(c - a) +--R + +--R 4 2 +--R - cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R + +--R - 3cosh(c - a) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 3 2 +--R (4cosh(b x + c) + 4cosh(b x + c))sech(b x + c)sinh(c - a) +--R + +--R 3 +--R (- 4cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c)) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (cosh(b x + c) + 2cosh(b x + c) + 1)sech(b x + c)sinh(c - a) +--R + +--R 4 2 +--R - cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a) +--R * +--R sech(b x + c)sinh(c - a) +--R * +--R tanh(b x + c) +--R + +--R 2 2 5 +--R (- 2sinh(c - a) + 4cosh(c - a)sinh(c - a) - 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 6cosh(b x + c)sinh(c - a) + 11cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R - 5cosh(c - a) cosh(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(b x + c) - 2)sinh(c - a) +--R + +--R 2 +--R (8cosh(c - a)cosh(b x + c) + 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R - 2cosh(c - a) cosh(b x + c) - 2cosh(c - a) - 2 +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 2cosh(b x + c) - 6cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R (- 2cosh(c - a)cosh(b x + c) + 10cosh(c - a)cosh(b x + c)) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R 4cosh(c - a) cosh(b x + c) + (- 4cosh(c - a) - 2)cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R - 6cosh(b x + c) sinh(c - a) +--R + +--R 4 2 +--R (- 4cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) ) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R 4cosh(c - a) cosh(b x + c) - 2cosh(c - a) cosh(b x + c) - 2 +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R - 2cosh(b x + c) sinh(c - a) +--R + +--R 5 3 +--R - cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 +--R cosh(c - a) cosh(b x + c) + (cosh(c - a) - 2)cosh(b x + c) +--R / +--R 6 +--R (sinh(c - a) - cosh(c - a))sinh(b x + c) +--R + +--R 5 +--R (4cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (6cosh(b x + c) + 3)sinh(c - a) - 6cosh(c - a)cosh(b x + c) +--R + +--R - 3cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 +--R (4cosh(b x + c) + 8cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 4cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 +--R (cosh(b x + c) + 8cosh(b x + c) + 3)sinh(c - a) +--R + +--R 4 2 +--R - cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) - 3cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 3 +--R (4cosh(b x + c) + 4cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 4cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 4 2 +--R (cosh(b x + c) + 2cosh(b x + c) + 1)sinh(c - a) +--R + +--R 4 2 +--R - cosh(c - a)cosh(b x + c) - 2cosh(c - a)cosh(b x + c) - cosh(c - a) +--R Type: Expression(Integer) +--E 423 + +--S 424 of 518 +t0981:= cosh(a+b*x)*sech(c+b*x)^3 +--R +--R +--R 3 +--R (409) cosh(b x + a)sech(b x + c) +--R Type: Expression(Integer) +--E 424 + +--S 425 of 518 +r0981:= -1/2*sech(c+b*x)^2*sinh(a-c)/b+cosh(a-c)*tanh(c+b*x)/b +--R +--R +--R 2 +--R 2cosh(c - a)tanh(b x + c) + sech(b x + c) sinh(c - a) +--R (410) ----------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 425 + +--S 426 of 518 +a0981:= integrate(t0981,x) +--R +--R +--R (411) +--R - 2sinh(c - a)sinh(b x + c) - 2cosh(b x + c)sinh(c - a) +--R + +--R 4cosh(c - a)cosh(b x + c) +--R / +--R 2 2 3 +--R (b sinh(c - a) - b cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 +--R (3b cosh(b x + c)sinh(c - a) - 3b cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 2 2 +--R (3b cosh(b x + c) + b)sinh(c - a) - 3b cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (b cosh(b x + c) + 3b cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - b cosh(c - a) cosh(b x + c) - 3b cosh(c - a) cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 426 + +--S 427 of 518 +m0981:= a0981-r0981 +--R +--R +--R (412) +--R 2 3 3 +--R (- 2cosh(c - a)sinh(c - a) + 2cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 3 +--R 6cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 6cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 3 2 3 +--R 6cosh(c - a) cosh(b x + c) + 2cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 +--R (- 2cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c)) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 3 3 +--R 2cosh(c - a) cosh(b x + c) + 6cosh(c - a) cosh(b x + c) +--R * +--R tanh(b x + c) +--R + +--R 2 3 2 2 +--R (- sech(b x + c) sinh(c - a) + cosh(c - a) sech(b x + c) sinh(c - a)) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 2 3 +--R - 3cosh(b x + c)sech(b x + c) sinh(c - a) +--R + +--R 2 2 +--R 3cosh(c - a) cosh(b x + c)sech(b x + c) sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 3 +--R (- 3cosh(b x + c) - 1)sech(b x + c) sinh(c - a) +--R + +--R 2 2 2 2 +--R ((3cosh(c - a) cosh(b x + c) + cosh(c - a) )sech(b x + c) - 4) +--R * +--R sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 3 +--R (- cosh(b x + c) - 3cosh(b x + c))sech(b x + c) sinh(c - a) +--R + +--R 2 3 2 +--R (cosh(c - a) cosh(b x + c) + 3cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sech(b x + c) +--R + +--R - 4cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 8cosh(c - a)cosh(b x + c) +--R / +--R 2 2 3 +--R (2b sinh(c - a) - 2b cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 2 2 +--R (6b cosh(b x + c) + 2b)sinh(c - a) - 6b cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 2b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (2b cosh(b x + c) + 6b cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 2b cosh(c - a) cosh(b x + c) - 6b cosh(c - a) cosh(b x + c) +--R Type: Expression(Integer) +--E 427 + +--S 428 of 518 +d0981:= D(m0981,x) +--R +--R +--R (413) +--R 2 3 6 +--R (cosh(c - a)sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 +--R 6cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 3 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R (15cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 3 2 3 +--R - 15cosh(c - a) cosh(b x + c) - 2cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 +--R (20cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c)) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 3 3 +--R - 20cosh(c - a) cosh(b x + c) - 12cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 +--R 15cosh(c - a)cosh(b x + c) + 24cosh(c - a)cosh(b x + c) +--R + +--R cosh(c - a) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 4 3 2 +--R - 15cosh(c - a) cosh(b x + c) - 24cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R - cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 +--R 6cosh(c - a)cosh(b x + c) + 20cosh(c - a)cosh(b x + c) +--R + +--R 6cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 5 3 3 +--R - 6cosh(c - a) cosh(b x + c) - 20cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 +--R cosh(c - a)cosh(b x + c) + 6cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R 9cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 6 3 4 +--R - cosh(c - a) cosh(b x + c) - 6cosh(c - a) cosh(b x + c) +--R + +--R 3 2 +--R - 9cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R tanh(b x + c) +--R + +--R 2 3 +--R sech(b x + c) sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a) sech(b x + c) sinh(c - a) +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 2 3 +--R 6cosh(b x + c)sech(b x + c) sinh(c - a) +--R + +--R 2 2 +--R - 6cosh(c - a) cosh(b x + c)sech(b x + c) sinh(c - a) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 3 +--R (15cosh(b x + c) + 2)sech(b x + c) sinh(c - a) +--R + +--R 2 2 2 2 +--R (- 15cosh(c - a) cosh(b x + c) - 2cosh(c - a) )sech(b x + c) +--R * +--R sinh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 3 +--R (20cosh(b x + c) + 12cosh(b x + c))sech(b x + c) sinh(c - a) +--R + +--R 2 3 2 +--R (- 20cosh(c - a) cosh(b x + c) - 12cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sech(b x + c) sinh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) + 24cosh(b x + c) + 1)sech(b x + c) +--R * +--R 3 +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R - 15cosh(c - a) cosh(b x + c) - 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - cosh(c - a) +--R * +--R 2 +--R sech(b x + c) sinh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 +--R (6cosh(b x + c) + 20cosh(b x + c) + 6cosh(b x + c)) +--R * +--R 2 3 +--R sech(b x + c) sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) - 20cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R sech(b x + c) sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (cosh(b x + c) + 6cosh(b x + c) + 9cosh(b x + c) )sech(b x + c) +--R * +--R 3 +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) - 6cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R - 9cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R sech(b x + c) sinh(c - a) +--R * +--R tanh(b x + c) +--R + +--R 2 3 6 +--R (- cosh(c - a)sinh(c - a) + cosh(c - a) )sinh(b x + c) +--R + +--R 2 3 +--R (- 6cosh(c - a)cosh(b x + c)sinh(c - a) + 6cosh(c - a) cosh(b x + c)) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 15cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 3 2 3 +--R 4sinh(c - a) + 15cosh(c - a) cosh(b x + c) + 2cosh(c - a) +--R + +--R 4cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 +--R (- 20cosh(c - a)cosh(b x + c) - 12cosh(c - a)cosh(b x + c)) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 3 +--R 16cosh(b x + c)sinh(c - a) + 20cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 12cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 +--R - 15cosh(c - a)cosh(b x + c) - 24cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 3 4 +--R (24cosh(b x + c) + 4)sinh(c - a) + 15cosh(c - a) cosh(b x + c) +--R + +--R 3 2 3 +--R (24cosh(c - a) - 24cosh(c - a))cosh(b x + c) + cosh(c - a) +--R + +--R 4cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) - 20cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 3 3 5 +--R 16cosh(b x + c) sinh(c - a) + 6cosh(c - a) cosh(b x + c) +--R + +--R 3 3 +--R (20cosh(c - a) - 32cosh(c - a))cosh(b x + c) +--R + +--R 3 +--R 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 +--R - cosh(c - a)cosh(b x + c) - 6cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 9cosh(c - a)cosh(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 4 2 +--R (4cosh(b x + c) - 4cosh(b x + c) )sinh(c - a) +--R + +--R 3 6 +--R cosh(c - a) cosh(b x + c) +--R + +--R 3 4 +--R (6cosh(c - a) - 12cosh(c - a))cosh(b x + c) +--R + +--R 3 2 +--R (9cosh(c - a) - 4cosh(c - a))cosh(b x + c) +--R / +--R 2 2 6 +--R (sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 5 +--R (6cosh(b x + c)sinh(c - a) - 6cosh(c - a) cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 2 2 +--R (15cosh(b x + c) + 2)sinh(c - a) - 15cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 2cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (20cosh(b x + c) + 12cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 20cosh(c - a) cosh(b x + c) - 12cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) + 24cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 4 2 2 +--R - 15cosh(c - a) cosh(b x + c) - 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (6cosh(b x + c) + 20cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) - 20cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (cosh(b x + c) + 6cosh(b x + c) + 9cosh(b x + c) )sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) - 6cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R - 9cosh(c - a) cosh(b x + c) +--R Type: Expression(Integer) +--E 428 + +--S 429 of 518 +t0982:= cosh(a+b*x)*csch(c+b*x) +--R +--R +--R (414) cosh(b x + a)csch(b x + c) +--R Type: Expression(Integer) +--E 429 + +--S 430 of 518 +r0982:= cosh(a-c)*log(sinh(c+b*x))/b+x*sinh(a-c) +--R +--R +--R cosh(c - a)log(sinh(b x + c)) - b x sinh(c - a) +--R (415) ----------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 430 + +--S 431 of 518 +a0982:= integrate(t0982,x) +--R +--R +--R (416) +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R 2sinh(b x + c) +--R log(- -----------------------------) +--R sinh(b x + c) - cosh(b x + c) +--R + +--R 2b x +--R / +--R 2b sinh(c - a) - 2b cosh(c - a) +--R Type: Union(Expression(Integer),...) +--E 431 + +--S 432 of 518 +m0982:= a0982-r0982 +--R +--R +--R (417) +--R 2 +--R (- 2cosh(c - a)sinh(c - a) + 2cosh(c - a) )log(sinh(b x + c)) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) - 1) +--R * +--R 2sinh(b x + c) +--R log(- -----------------------------) +--R sinh(b x + c) - cosh(b x + c) +--R + +--R 2 +--R 2b x sinh(c - a) - 2b x cosh(c - a)sinh(c - a) + 2b x +--R / +--R 2b sinh(c - a) - 2b cosh(c - a) +--R Type: Expression(Integer) +--E 432 + +--S 433 of 518 +d0982:= D(m0982,x) +--R +--R +--R (418) +--R 2 2 +--R (sinh(c - a) - cosh(c - a) + 1)sinh(b x + c) +--R + +--R 2 2 +--R - cosh(b x + c)sinh(c - a) + (cosh(c - a) - 1)cosh(b x + c) +--R / +--R (2sinh(c - a) - 2cosh(c - a))sinh(b x + c) +--R Type: Expression(Integer) +--E 433 + +--S 434 of 518 +t0983:= cosh(a+b*x)*csch(c+b*x)^2 +--R +--R +--R 2 +--R (419) cosh(b x + a)csch(b x + c) +--R Type: Expression(Integer) +--E 434 + +--S 435 of 518 +r0983:= -cosh(a-c)*csch(c+b*x)/b-acoth(cosh(c+b*x))*sinh(a-c)/b +--R +--R +--R sinh(c - a)acoth(cosh(b x + c)) - cosh(c - a)csch(b x + c) +--R (420) ---------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 435 + +--S 436 of 518 +a0983:= integrate(t0983,x) +--R +--R +--R (421) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) - 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) - 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (cosh(c - a) - 1)cosh(b x + c) - cosh(c - a) + 1 +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) +--R + +--R 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a) + 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (- cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- cosh(c - a) + 1)cosh(b x + c) + cosh(c - a) - 1 +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 2 +--R (2sinh(c - a) - 4cosh(c - a)sinh(c - a) + 2cosh(c - a) + 2) +--R * +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) + 2)cosh(b x + c) +--R / +--R 2 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R (4b cosh(b x + c)sinh(c - a) - 4b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (2b cosh(b x + c) - 2b)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R + +--R 2b cosh(c - a) +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 518 +m0983:= a0983-r0983 +--R +--R +--R (422) +--R 2 2 +--R (sinh(c - a) - 2cosh(c - a)sinh(c - a) + cosh(c - a) - 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) - 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a) - 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (cosh(b x + c) - 1)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a)cosh(b x + c) + 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (cosh(c - a) - 1)cosh(b x + c) - cosh(c - a) + 1 +--R * +--R log(sinh(b x + c) + cosh(b x + c) + 1) +--R + +--R 2 2 +--R (- sinh(c - a) + 2cosh(c - a)sinh(c - a) - cosh(c - a) + 1) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R - 2cosh(b x + c)sinh(c - a) +--R + +--R 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- 2cosh(c - a) + 2)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (- cosh(b x + c) + 1)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R + +--R 2 2 2 +--R (- cosh(c - a) + 1)cosh(b x + c) + cosh(c - a) - 1 +--R * +--R log(sinh(b x + c) + cosh(b x + c) - 1) +--R + +--R 2 2 +--R (- 2sinh(c - a) + 2cosh(c - a)sinh(c - a))sinh(b x + c) +--R + +--R 2 +--R - 4cosh(b x + c)sinh(c - a) +--R + +--R 4cosh(c - a)cosh(b x + c)sinh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 2 2 +--R (- 2cosh(b x + c) + 2)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a))sinh(c - a) +--R * +--R acoth(cosh(b x + c)) +--R + +--R 2 +--R (2cosh(c - a)csch(b x + c)sinh(c - a) - 2cosh(c - a) csch(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 +--R 2sinh(c - a) +--R + +--R (4cosh(c - a)cosh(b x + c)csch(b x + c) - 4cosh(c - a))sinh(c - a) +--R + +--R 2 2 +--R - 4cosh(c - a) cosh(b x + c)csch(b x + c) + 2cosh(c - a) + 2 +--R * +--R sinh(b x + c) +--R + +--R 2 +--R 2cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (2cosh(c - a)cosh(b x + c) - 2cosh(c - a))csch(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (- 2cosh(c - a) cosh(b x + c) + 2cosh(c - a) )csch(b x + c) +--R + +--R 2 +--R (2cosh(c - a) + 2)cosh(b x + c) +--R / +--R 2 +--R (2b sinh(c - a) - 2b cosh(c - a))sinh(b x + c) +--R + +--R (4b cosh(b x + c)sinh(c - a) - 4b cosh(c - a)cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 +--R (2b cosh(b x + c) - 2b)sinh(c - a) - 2b cosh(c - a)cosh(b x + c) +--R + +--R 2b cosh(c - a) +--R Type: Expression(Integer) +--E 437 + +--S 438 of 518 +d0983:= D(m0983,x) +--R +--R +--R (423) +--R 2 5 +--R (sinh(c - a) - cosh(c - a)sinh(c - a))sinh(b x + c) +--R + +--R 2 +--R 4cosh(b x + c)sinh(c - a) +--R + +--R 2 +--R (- cosh(c - a)cosh(b x + c) + cosh(c - a))coth(b x + c) +--R * +--R csch(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 2 2 +--R (cosh(c - a) cosh(b x + c) - cosh(c - a) )coth(b x + c)csch(b x + c) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 2 2 +--R 4cosh(b x + c) sinh(c - a) +--R + +--R 3 +--R (- 4cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c)) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 +--R - 2cosh(c - a)cosh(b x + c) - 2cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 3 2 +--R (4cosh(c - a) cosh(b x + c) - 4cosh(c - a) cosh(b x + c)) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 2 2 +--R - 2cosh(c - a) cosh(b x + c) + 2cosh(c - a) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 2 +--R (- 2cosh(b x + c) + 2cosh(b x + c))sinh(c - a) +--R + +--R 4 2 +--R - 6cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 3 +--R 8cosh(c - a)cosh(b x + c) - 8cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 4 2 2 +--R 6cosh(c - a) cosh(b x + c) - 8cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 2cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 3 2 +--R - 6cosh(c - a) cosh(b x + c) + 6cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (- 5cosh(b x + c) + 4cosh(b x + c) + 1)sinh(c - a) +--R + +--R 5 3 +--R - 4cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 4 2 +--R 11cosh(c - a)cosh(b x + c) - 10cosh(c - a)cosh(b x + c) +--R + +--R - cosh(c - a) +--R * +--R sinh(c - a) +--R + +--R 2 5 2 3 +--R 4cosh(c - a) cosh(b x + c) - 8cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 4cosh(c - a) cosh(b x + c) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 4 2 2 +--R - 6cosh(c - a) cosh(b x + c) + (6cosh(c - a) - 2)cosh(b x + c) + 2 +--R * +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (- 2cosh(b x + c) + 2cosh(b x + c) )sinh(c - a) +--R + +--R 6 4 +--R - cosh(c - a)cosh(b x + c) + 3cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 3cosh(c - a)cosh(b x + c) + cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 5 3 +--R 4cosh(c - a)cosh(b x + c) - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 2 6 2 4 +--R cosh(c - a) cosh(b x + c) - 3cosh(c - a) cosh(b x + c) +--R + +--R 2 2 2 +--R 3cosh(c - a) cosh(b x + c) - cosh(c - a) +--R * +--R coth(b x + c)csch(b x + c) +--R + +--R 2 5 2 3 +--R - 2cosh(c - a) cosh(b x + c) + (2cosh(c - a) - 2)cosh(b x + c) +--R + +--R 2cosh(b x + c) +--R / +--R 2 2 +--R (cosh(b x + c) - 1)sinh(c - a) - cosh(c - a)cosh(b x + c) +--R + +--R cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 +--R (4cosh(b x + c) - 4cosh(b x + c))sinh(c - a) +--R + +--R 3 +--R - 4cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 +--R (6cosh(b x + c) - 8cosh(b x + c) + 2)sinh(c - a) +--R + +--R 4 2 +--R - 6cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 2cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 +--R (4cosh(b x + c) - 8cosh(b x + c) + 4cosh(b x + c))sinh(c - a) +--R + +--R 5 3 +--R - 4cosh(c - a)cosh(b x + c) + 8cosh(c - a)cosh(b x + c) +--R + +--R - 4cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 +--R (cosh(b x + c) - 3cosh(b x + c) + 3cosh(b x + c) - 1)sinh(c - a) +--R + +--R 6 4 +--R - cosh(c - a)cosh(b x + c) + 3cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - 3cosh(c - a)cosh(b x + c) + cosh(c - a) +--R Type: Expression(Integer) +--E 438 + +--S 439 of 518 +t0984:= cosh(a+b*x)*csch(c+b*x)^3 +--R +--R +--R 3 +--R (424) cosh(b x + a)csch(b x + c) +--R Type: Expression(Integer) +--E 439 + +--S 440 of 518 +r0984:= -1/2*cosh(a-c)*csch(c+b*x)^2/b-coth(c+b*x)*sinh(a-c)/b +--R +--R +--R 2 +--R 2coth(b x + c)sinh(c - a) - cosh(c - a)csch(b x + c) +--R (425) ----------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 440 + +--S 441 of 518 +a0984:= integrate(t0984,x) +--R +--R +--R (426) +--R (- 4sinh(c - a) + 2cosh(c - a))sinh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R / +--R 2 2 3 +--R (b sinh(c - a) - b cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 +--R (3b cosh(b x + c)sinh(c - a) - 3b cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 2 2 +--R (3b cosh(b x + c) - 3b)sinh(c - a) - 3b cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 3b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (b cosh(b x + c) - b cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - b cosh(c - a) cosh(b x + c) + b cosh(c - a) cosh(b x + c) +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 518 +m0984:= a0984-r0984 +--R +--R +--R (427) +--R 3 2 2 +--R - 2coth(b x + c)sinh(c - a) + cosh(c - a)csch(b x + c) sinh(c - a) +--R + +--R 2 3 2 +--R 2cosh(c - a) coth(b x + c)sinh(c - a) - cosh(c - a) csch(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 3 +--R - 6cosh(b x + c)coth(b x + c)sinh(c - a) +--R + +--R 2 2 +--R 3cosh(c - a)cosh(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 +--R 6cosh(c - a) cosh(b x + c)coth(b x + c)sinh(c - a) +--R + +--R 3 2 +--R - 3cosh(c - a) cosh(b x + c)csch(b x + c) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 3 +--R (- 6cosh(b x + c) + 6)coth(b x + c)sinh(c - a) +--R + +--R 2 2 2 +--R (3cosh(c - a)cosh(b x + c) - 3cosh(c - a))csch(b x + c) sinh(c - a) +--R + +--R 2 2 2 +--R ((6cosh(c - a) cosh(b x + c) - 6cosh(c - a) )coth(b x + c) - 8) +--R * +--R sinh(c - a) +--R + +--R 3 2 3 2 +--R (- 3cosh(c - a) cosh(b x + c) + 3cosh(c - a) )csch(b x + c) +--R + +--R 4cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 3 +--R (- 2cosh(b x + c) + 2cosh(b x + c))coth(b x + c)sinh(c - a) +--R + +--R 3 2 +--R (cosh(c - a)cosh(b x + c) - cosh(c - a)cosh(b x + c))csch(b x + c) +--R * +--R 2 +--R sinh(c - a) +--R + +--R 2 3 2 +--R (2cosh(c - a) cosh(b x + c) - 2cosh(c - a) cosh(b x + c))coth(b x + c) +--R * +--R sinh(c - a) +--R + +--R 3 3 3 2 +--R (- cosh(c - a) cosh(b x + c) + cosh(c - a) cosh(b x + c))csch(b x + c) +--R + +--R 4cosh(c - a)cosh(b x + c) +--R / +--R 2 2 3 +--R (2b sinh(c - a) - 2b cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 +--R (6b cosh(b x + c)sinh(c - a) - 6b cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 2 2 2 2 +--R (6b cosh(b x + c) - 6b)sinh(c - a) - 6b cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6b cosh(c - a) +--R * +--R sinh(b x + c) +--R + +--R 3 2 +--R (2b cosh(b x + c) - 2b cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 2b cosh(c - a) cosh(b x + c) + 2b cosh(c - a) cosh(b x + c) +--R Type: Expression(Integer) +--E 442 + +--S 443 of 518 +d0984:= D(m0984,x) +--R +--R +--R (428) +--R 2 3 +--R (coth(b x + c) - 1)sinh(c - a) +--R + +--R 2 2 +--R - cosh(c - a)coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 2 2 +--R (- cosh(c - a) coth(b x + c) + cosh(c - a) )sinh(c - a) +--R + +--R 3 2 +--R cosh(c - a) coth(b x + c)csch(b x + c) +--R * +--R 6 +--R sinh(b x + c) +--R + +--R 2 3 +--R (6cosh(b x + c)coth(b x + c) - 6cosh(b x + c))sinh(c - a) +--R + +--R 2 2 +--R - 6cosh(c - a)cosh(b x + c)coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 2 +--R - 6cosh(c - a) cosh(b x + c)coth(b x + c) +--R + +--R 2 +--R 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 3 2 +--R 6cosh(c - a) cosh(b x + c)coth(b x + c)csch(b x + c) +--R * +--R 5 +--R sinh(b x + c) +--R + +--R 2 2 2 +--R ((15cosh(b x + c) - 6)coth(b x + c) - 15cosh(b x + c) + 6) +--R * +--R 3 +--R sinh(c - a) +--R + +--R 2 +--R (- 15cosh(c - a)cosh(b x + c) + 6cosh(c - a))coth(b x + c) +--R * +--R 2 2 +--R csch(b x + c) sinh(c - a) +--R + +--R 2 2 2 2 +--R (- 15cosh(c - a) cosh(b x + c) + 6cosh(c - a) )coth(b x + c) +--R + +--R 2 2 2 +--R 15cosh(c - a) cosh(b x + c) - 6cosh(c - a) + 12 +--R * +--R sinh(c - a) +--R + +--R 3 2 3 +--R (15cosh(c - a) cosh(b x + c) - 6cosh(c - a) )coth(b x + c) +--R * +--R 2 +--R csch(b x + c) +--R + +--R - 4cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (20cosh(b x + c) - 20cosh(b x + c))coth(b x + c) +--R + +--R 3 +--R - 20cosh(b x + c) + 20cosh(b x + c) +--R * +--R 3 +--R sinh(c - a) +--R + +--R 3 +--R (- 20cosh(c - a)cosh(b x + c) + 20cosh(c - a)cosh(b x + c)) +--R * +--R 2 2 +--R coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 3 2 +--R (- 20cosh(c - a) cosh(b x + c) + 20cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 2 3 2 +--R 20cosh(c - a) cosh(b x + c) + (- 20cosh(c - a) + 32)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 3 3 3 +--R (20cosh(c - a) cosh(b x + c) - 20cosh(c - a) cosh(b x + c)) +--R * +--R 2 +--R coth(b x + c)csch(b x + c) +--R + +--R - 16cosh(c - a)cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) - 24cosh(b x + c) + 9)coth(b x + c) +--R + +--R 4 2 +--R - 15cosh(b x + c) + 24cosh(b x + c) - 9 +--R * +--R 3 +--R sinh(c - a) +--R + +--R 4 2 +--R - 15cosh(c - a)cosh(b x + c) + 24cosh(c - a)cosh(b x + c) +--R + +--R - 9cosh(c - a) +--R * +--R 2 2 +--R coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 4 2 2 +--R - 15cosh(c - a) cosh(b x + c) + 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 9cosh(c - a) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 2 4 +--R 15cosh(c - a) cosh(b x + c) +--R + +--R 2 2 2 +--R (- 24cosh(c - a) + 24)cosh(b x + c) + 9cosh(c - a) - 4 +--R * +--R sinh(c - a) +--R + +--R 3 4 3 2 +--R 15cosh(c - a) cosh(b x + c) - 24cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 9cosh(c - a) +--R * +--R 2 +--R coth(b x + c)csch(b x + c) +--R + +--R 2 +--R - 24cosh(c - a)cosh(b x + c) - 4cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 +--R (6cosh(b x + c) - 12cosh(b x + c) + 6cosh(b x + c)) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 5 3 +--R - 6cosh(b x + c) + 12cosh(b x + c) - 6cosh(b x + c) +--R * +--R 3 +--R sinh(c - a) +--R + +--R 5 3 +--R - 6cosh(c - a)cosh(b x + c) + 12cosh(c - a)cosh(b x + c) +--R + +--R - 6cosh(c - a)cosh(b x + c) +--R * +--R 2 2 +--R coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 2 5 2 3 +--R 6cosh(c - a) cosh(b x + c) - 12cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 3 5 3 3 +--R 6cosh(c - a) cosh(b x + c) - 12cosh(c - a) cosh(b x + c) +--R + +--R 3 +--R 6cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R coth(b x + c)csch(b x + c) +--R + +--R 3 +--R - 16cosh(c - a)cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (cosh(b x + c) - 2cosh(b x + c) + cosh(b x + c) )coth(b x + c) +--R + +--R 6 4 2 +--R - cosh(b x + c) + 2cosh(b x + c) - cosh(b x + c) +--R * +--R 3 +--R sinh(c - a) +--R + +--R 6 4 +--R - cosh(c - a)cosh(b x + c) + 2cosh(c - a)cosh(b x + c) +--R + +--R 2 +--R - cosh(c - a)cosh(b x + c) +--R * +--R 2 2 +--R coth(b x + c)csch(b x + c) sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R coth(b x + c) +--R + +--R 2 6 2 4 +--R cosh(c - a) cosh(b x + c) + (- 2cosh(c - a) - 4)cosh(b x + c) +--R + +--R 2 2 +--R (cosh(c - a) + 4)cosh(b x + c) +--R * +--R sinh(c - a) +--R + +--R 3 6 3 4 +--R cosh(c - a) cosh(b x + c) - 2cosh(c - a) cosh(b x + c) +--R + +--R 3 2 +--R cosh(c - a) cosh(b x + c) +--R * +--R 2 +--R coth(b x + c)csch(b x + c) +--R + +--R 4 2 +--R - 4cosh(c - a)cosh(b x + c) + 4cosh(c - a)cosh(b x + c) +--R / +--R 2 2 6 +--R (sinh(c - a) - cosh(c - a) )sinh(b x + c) +--R + +--R 2 2 5 +--R (6cosh(b x + c)sinh(c - a) - 6cosh(c - a) cosh(b x + c))sinh(b x + c) +--R + +--R 2 2 2 2 +--R (15cosh(b x + c) - 6)sinh(c - a) - 15cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R 6cosh(c - a) +--R * +--R 4 +--R sinh(b x + c) +--R + +--R 3 2 +--R (20cosh(b x + c) - 20cosh(b x + c))sinh(c - a) +--R + +--R 2 3 2 +--R - 20cosh(c - a) cosh(b x + c) + 20cosh(c - a) cosh(b x + c) +--R * +--R 3 +--R sinh(b x + c) +--R + +--R 4 2 2 +--R (15cosh(b x + c) - 24cosh(b x + c) + 9)sinh(c - a) +--R + +--R 2 4 2 2 +--R - 15cosh(c - a) cosh(b x + c) + 24cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 9cosh(c - a) +--R * +--R 2 +--R sinh(b x + c) +--R + +--R 5 3 2 +--R (6cosh(b x + c) - 12cosh(b x + c) + 6cosh(b x + c))sinh(c - a) +--R + +--R 2 5 2 3 +--R - 6cosh(c - a) cosh(b x + c) + 12cosh(c - a) cosh(b x + c) +--R + +--R 2 +--R - 6cosh(c - a) cosh(b x + c) +--R * +--R sinh(b x + c) +--R + +--R 6 4 2 2 +--R (cosh(b x + c) - 2cosh(b x + c) + cosh(b x + c) )sinh(c - a) +--R + +--R 2 6 2 4 +--R - cosh(c - a) cosh(b x + c) + 2cosh(c - a) cosh(b x + c) +--R + +--R 2 2 +--R - cosh(c - a) cosh(b x + c) +--R Type: Expression(Integer) +--E 443 + +--S 444 of 518 +t0985:= sinh(x)^2/(a+b*sinh(2*x)) +--R +--R +--R 2 +--R sinh(x) +--R (429) -------------- +--R b sinh(2x) + a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 518 +r0985:= 1/2*atanh((b-a*tanh(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2)+_ + 1/4*log(a+b*sinh(2*x))/b +--R +--R +--R +-------+ +--R | 2 2 a tanh(x) - b +--R \|b + a log(b sinh(2x) + a) - 2b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R (430) ------------------------------------------------------- +--R +-------+ +--R | 2 2 +--R 4b\|b + a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 518 +a0985:= integrate(t0985,x) +--R +--R +--R (431) +--R b +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6b cosh(x) + 2a b)sinh(x) +--R + +--R 2 3 2 4 +--R (4b cosh(x) + 4a b cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 2 3 2 +--R (2b + 2a b)sinh(x) + (4b + 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4a cosh(x))sinh(x) + b cosh(x) + 2a cosh(x) - b +--R + +--R +-------+ +-------+ +--R | 2 2 4b cosh(x)sinh(x) + 2a | 2 2 +--R \|b + a log(-------------------------------------) - 2x\|b + a +--R 2 2 +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R +-------+ +--R | 2 2 +--R 4b\|b + a +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 518 +m0985:= a0985-r0985 +--R +--R +--R (432) +--R b +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6b cosh(x) + 2a b)sinh(x) +--R + +--R 2 3 2 4 +--R (4b cosh(x) + 4a b cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 2 3 2 +--R (2b + 2a b)sinh(x) + (4b + 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (2b + 2a b)cosh(x) + 2a b + 2a +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4a cosh(x))sinh(x) + b cosh(x) + 2a cosh(x) - b +--R + +--R +-------+ +--R | 2 2 +--R - \|b + a log(b sinh(2x) + a) +--R + +--R +-------+ +--R | 2 2 4b cosh(x)sinh(x) + 2a +--R \|b + a log(-------------------------------------) +--R 2 2 +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-------+ +--R a tanh(x) - b | 2 2 +--R 2b atanh(-------------) - 2x\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R | 2 2 +--R 4b\|b + a +--R Type: Expression(Integer) +--E 447 + +--S 448 of 518 +d0985:= D(m0985,x) +--R +--R +--R (433) +--R 2 6 3 2 5 +--R a b sinh(x) + (2b + 4a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 4 +--R ((8b + 7a b )cosh(x) + a b + 2a b)sinh(x) +--R + +--R 3 2 3 2 2 3 +--R ((12b + 8a b )cosh(x) + (4a b + 4a b)cosh(x))sinh(x) +--R + +--R 3 2 4 2 2 2 2 2 +--R ((8b + 7a b )cosh(x) + (6a b + 4a b)cosh(x) - a b )sinh(x) +--R + +--R 3 2 5 2 2 3 3 +--R ((2b + 4a b )cosh(x) + (4a b + 4a b)cosh(x) - 2b cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 2 2 2 +--R a b cosh(x) + (a b + 2a b)cosh(x) - a b cosh(x) - a b +--R * +--R sinh(2x) +--R + +--R 2 6 +--R a b sinh(x) +--R + +--R 2 2 2 5 +--R (- 2a b cosh(x)cosh(2x) + (2a b + 4a b)cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 8a b cosh(x) - a b)cosh(2x) + (8a b + 7a b)cosh(x) + a b +--R + +--R 3 +--R 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 +--R (- 12a b cosh(x) - 8a b cosh(x))cosh(2x) +--R + +--R 2 2 3 2 3 +--R (12a b + 8a b)cosh(x) + (4a b + 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 3 +--R (- 8a b cosh(x) - 14a b cosh(x) - 2a )cosh(2x) +--R + +--R 2 2 4 2 3 2 2 +--R (8a b + 7a b)cosh(x) + (6a b + 4a )cosh(x) - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (- 2a b cosh(x) - 8a b cosh(x) + (2a b - 4a )cosh(x))cosh(2x) +--R + +--R 2 2 5 2 3 3 2 +--R (2a b + 4a b)cosh(x) + (4a b + 4a )cosh(x) - 2a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 6 +--R (- a b cosh(x) - 2a cosh(x) + a b)cosh(2x) + a b cosh(x) +--R + +--R 2 3 4 2 2 2 +--R (a b + 2a )cosh(x) - a b cosh(x) - a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 6 3 5 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 3 2 2 4 +--R (- 14b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 3 2 3 +--R (- 16b cosh(x) + (8b - 8a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 3 2 2 +--R (- 14b cosh(x) + (16b - 8a b )cosh(x) + 2b + 4a b )sinh(x) +--R + +--R 3 5 3 2 3 2 +--R (- 8b cosh(x) + (8b - 8a b )cosh(x) + 8a b cosh(x))sinh(x) +--R + +--R 3 6 2 4 3 2 2 +--R - 2b cosh(x) - 4a b cosh(x) + (2b + 4a b )cosh(x) +--R * +--R sinh(2x) +--R + +--R 2 6 3 2 5 +--R - 2a b sinh(x) + (4b cosh(x)cosh(2x) - 8a b cosh(x))sinh(x) +--R + +--R 3 2 2 2 2 2 4 +--R ((16b cosh(x) + 2a b )cosh(2x) - 14a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 3 2 2 3 +--R (24b cosh(x) + 16a b cosh(x))cosh(2x) - 16a b cosh(x) +--R + +--R 2 2 +--R (8a b - 8a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 2 2 2 4 +--R (16b cosh(x) + 28a b cosh(x) + 4a b)cosh(2x) - 14a b cosh(x) +--R + +--R 2 2 2 2 2 +--R (16a b - 8a b)cosh(x) + 2a b + 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 3 3 2 +--R (4b cosh(x) + 16a b cosh(x) + (- 4b + 8a b)cosh(x))cosh(2x) +--R + +--R 2 5 2 2 3 2 +--R - 8a b cosh(x) + (8a b - 8a b)cosh(x) + 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 6 +--R (2a b cosh(x) + 4a b cosh(x) - 2a b )cosh(2x) - 2a b cosh(x) +--R + +--R 2 4 2 2 2 +--R - 4a b cosh(x) + (2a b + 4a b)cosh(x) +--R * +--R tanh(x) +--R + +--R 2 6 3 2 5 +--R - a b sinh(x) + (- 2b - 4a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 4 +--R ((- 8b - 7a b )cosh(x) - a b - 2a b)sinh(x) +--R + +--R 3 2 3 2 2 3 +--R ((- 12b - 8a b )cosh(x) + (- 4a b - 4a b)cosh(x))sinh(x) +--R + +--R 3 2 4 2 2 2 2 2 +--R ((- 8b - 7a b )cosh(x) + (- 6a b - 4a b)cosh(x) + a b )sinh(x) +--R + +--R 3 2 5 2 2 3 3 +--R ((- 2b - 4a b )cosh(x) + (- 4a b - 4a b)cosh(x) + 2b cosh(x)) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 2 2 2 +--R - a b cosh(x) + (- a b - 2a b)cosh(x) + a b cosh(x) + a b +--R * +--R sinh(2x) +--R + +--R 2 6 2 2 2 5 +--R - a b sinh(x) + (2a b cosh(x)cosh(2x) + (- 2a b - 4a b)cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 2 3 +--R ((8a b cosh(x) + a b)cosh(2x) + (- 8a b - 7a b)cosh(x) - a b - 2a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 2 3 +--R (12a b cosh(x) + 8a b cosh(x))cosh(2x) + (- 12a b - 8a b)cosh(x) +--R + +--R 2 3 +--R (- 4a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 3 +--R (8a b cosh(x) + 14a b cosh(x) + 2a )cosh(2x) +--R + +--R 2 2 4 2 3 2 2 +--R (- 8a b - 7a b)cosh(x) + (- 6a b - 4a )cosh(x) + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (2a b cosh(x) + 8a b cosh(x) + (- 2a b + 4a )cosh(x))cosh(2x) +--R + +--R 2 2 5 2 3 3 2 +--R (- 2a b - 4a b)cosh(x) + (- 4a b - 4a )cosh(x) + 2a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 6 +--R (a b cosh(x) + 2a cosh(x) - a b)cosh(2x) - a b cosh(x) +--R + +--R 2 3 4 2 2 2 +--R (- a b - 2a )cosh(x) + a b cosh(x) + a b +--R / +--R 3 5 3 2 2 2 4 +--R 4a b cosh(x)sinh(x) + (16a b cosh(x) + 2a b )sinh(x) +--R + +--R 3 3 2 2 3 +--R (24a b cosh(x) + 16a b cosh(x))sinh(x) +--R + +--R 3 4 2 2 2 3 2 +--R (16a b cosh(x) + 28a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 5 2 2 3 3 3 +--R (4a b cosh(x) + 16a b cosh(x) + (- 4a b + 8a b)cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R 2a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R sinh(2x) +--R + +--R 2 2 5 2 2 2 3 4 +--R 4a b cosh(x)sinh(x) + (16a b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 3 3 3 +--R (24a b cosh(x) + 16a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 4 2 +--R (16a b cosh(x) + 28a b cosh(x) + 4a )sinh(x) +--R + +--R 2 2 5 3 3 2 2 4 +--R (4a b cosh(x) + 16a b cosh(x) + (- 4a b + 8a )cosh(x))sinh(x) +--R + +--R 3 4 4 2 3 +--R 2a b cosh(x) + 4a cosh(x) - 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 5 4 2 3 4 +--R - 8b cosh(x)sinh(x) + (- 32b cosh(x) - 4a b )sinh(x) +--R + +--R 4 3 3 3 +--R (- 48b cosh(x) - 32a b cosh(x))sinh(x) +--R + +--R 4 4 3 2 2 2 2 +--R (- 32b cosh(x) - 56a b cosh(x) - 8a b )sinh(x) +--R + +--R 4 5 3 3 4 2 2 +--R (- 8b cosh(x) - 32a b cosh(x) + (8b - 16a b )cosh(x))sinh(x) +--R + +--R 3 4 2 2 2 3 +--R - 4a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R sinh(2x) +--R + +--R 3 5 3 2 2 2 4 +--R - 8a b cosh(x)sinh(x) + (- 32a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 2 2 3 +--R (- 48a b cosh(x) - 32a b cosh(x))sinh(x) +--R + +--R 3 4 2 2 2 3 2 +--R (- 32a b cosh(x) - 56a b cosh(x) - 8a b)sinh(x) +--R + +--R 3 5 2 2 3 3 3 +--R (- 8a b cosh(x) - 32a b cosh(x) + (8a b - 16a b)cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R - 4a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R tanh(x) +--R + +--R 3 5 3 2 2 2 4 +--R - 4a b cosh(x)sinh(x) + (- 16a b cosh(x) - 2a b )sinh(x) +--R + +--R 3 3 2 2 3 +--R (- 24a b cosh(x) - 16a b cosh(x))sinh(x) +--R + +--R 3 4 2 2 2 3 2 +--R (- 16a b cosh(x) - 28a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 5 2 2 3 3 3 +--R (- 4a b cosh(x) - 16a b cosh(x) + (4a b - 8a b)cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R - 2a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R sinh(2x) +--R + +--R 2 2 5 2 2 2 3 4 +--R - 4a b cosh(x)sinh(x) + (- 16a b cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 3 3 3 +--R (- 24a b cosh(x) - 16a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 4 2 +--R (- 16a b cosh(x) - 28a b cosh(x) - 4a )sinh(x) +--R + +--R 2 2 5 3 3 2 2 4 +--R (- 4a b cosh(x) - 16a b cosh(x) + (4a b - 8a )cosh(x))sinh(x) +--R + +--R 3 4 4 2 3 +--R - 2a b cosh(x) - 4a cosh(x) + 2a b +--R Type: Expression(Integer) +--E 448 + +--S 449 of 518 +t0986:= cosh(x)^2/(a+b*sinh(2*x)) +--R +--R +--R 2 +--R cosh(x) +--R (434) -------------- +--R b sinh(2x) + a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 518 +r0986:= -1/2*atanh((b-a*tanh(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(1/2)+_ + 1/4*log(a+b*sinh(2*x))/b +--R +--R +--R +-------+ +--R | 2 2 a tanh(x) - b +--R \|b + a log(b sinh(2x) + a) + 2b atanh(-------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R (435) ------------------------------------------------------- +--R +-------+ +--R | 2 2 +--R 4b\|b + a +--R Type: Expression(Integer) +--E 450 + +--S 451 of 518 +a0986:= integrate(t0986,x) +--R +--R +--R (436) +--R b +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6b cosh(x) + 2a b)sinh(x) +--R + +--R 2 3 2 4 +--R (4b cosh(x) + 4a b cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 2 3 2 +--R (- 2b - 2a b)sinh(x) + (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4a cosh(x))sinh(x) + b cosh(x) + 2a cosh(x) - b +--R + +--R +-------+ +-------+ +--R | 2 2 4b cosh(x)sinh(x) + 2a | 2 2 +--R \|b + a log(-------------------------------------) - 2x\|b + a +--R 2 2 +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R / +--R +-------+ +--R | 2 2 +--R 4b\|b + a +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 518 +m0986:= a0986-r0986 +--R +--R +--R (437) +--R b +--R * +--R log +--R 2 4 2 3 +--R b sinh(x) + 4b cosh(x)sinh(x) +--R + +--R 2 2 2 +--R (6b cosh(x) + 2a b)sinh(x) +--R + +--R 2 3 2 4 +--R (4b cosh(x) + 4a b cosh(x))sinh(x) + b cosh(x) +--R + +--R 2 2 2 +--R 2a b cosh(x) + b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 2 3 2 +--R (- 2b - 2a b)sinh(x) + (- 4b - 4a b)cosh(x)sinh(x) +--R + +--R 3 2 2 2 3 +--R (- 2b - 2a b)cosh(x) - 2a b - 2a +--R / +--R 4 3 2 2 +--R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2a)sinh(x) +--R + +--R 3 4 2 +--R (4b cosh(x) + 4a cosh(x))sinh(x) + b cosh(x) + 2a cosh(x) - b +--R + +--R +-------+ +--R | 2 2 +--R - \|b + a log(b sinh(2x) + a) +--R + +--R +-------+ +--R | 2 2 4b cosh(x)sinh(x) + 2a +--R \|b + a log(-------------------------------------) +--R 2 2 +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R +-------+ +--R a tanh(x) - b | 2 2 +--R - 2b atanh(-------------) - 2x\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R | 2 2 +--R 4b\|b + a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 518 +d0986:= D(m0986,x) +--R +--R +--R (438) +--R 2 6 3 2 5 +--R a b sinh(x) + (- 2b + 4a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 4 +--R ((- 8b + 7a b )cosh(x) - a b + 2a b)sinh(x) +--R + +--R 3 2 3 2 2 3 +--R ((- 12b + 8a b )cosh(x) + (- 4a b + 4a b)cosh(x))sinh(x) +--R + +--R 3 2 4 2 2 2 2 +--R ((- 8b + 7a b )cosh(x) + (- 6a b + 4a b)cosh(x) - a b ) +--R * +--R 2 +--R sinh(x) +--R + +--R 3 2 5 2 2 3 +--R (- 2b + 4a b )cosh(x) + (- 4a b + 4a b)cosh(x) +--R + +--R 3 +--R 2b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 6 2 2 4 2 2 2 +--R a b cosh(x) + (- a b + 2a b)cosh(x) - a b cosh(x) + a b +--R * +--R sinh(2x) +--R + +--R 2 6 +--R a b sinh(x) +--R + +--R 2 2 2 5 +--R (- 2a b cosh(x)cosh(2x) + (- 2a b + 4a b)cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 8a b cosh(x) - a b)cosh(2x) + (- 8a b + 7a b)cosh(x) - a b +--R + +--R 3 +--R 2a +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 +--R (- 12a b cosh(x) - 8a b cosh(x))cosh(2x) +--R + +--R 2 2 3 2 3 +--R (- 12a b + 8a b)cosh(x) + (- 4a b + 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 3 +--R (- 8a b cosh(x) - 14a b cosh(x) - 2a )cosh(2x) +--R + +--R 2 2 4 2 3 2 2 +--R (- 8a b + 7a b)cosh(x) + (- 6a b + 4a )cosh(x) - a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (- 2a b cosh(x) - 8a b cosh(x) + (2a b - 4a )cosh(x))cosh(2x) +--R + +--R 2 2 5 2 3 3 2 +--R (- 2a b + 4a b)cosh(x) + (- 4a b + 4a )cosh(x) + 2a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 6 +--R (- a b cosh(x) - 2a cosh(x) + a b)cosh(2x) + a b cosh(x) +--R + +--R 2 3 4 2 2 2 +--R (- a b + 2a )cosh(x) - a b cosh(x) + a b +--R * +--R 2 +--R tanh(x) +--R + +--R 3 6 3 5 +--R - 2b sinh(x) - 8b cosh(x)sinh(x) +--R + +--R 3 2 2 4 +--R (- 14b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 3 2 3 +--R (- 16b cosh(x) + (- 8b - 8a b )cosh(x))sinh(x) +--R + +--R 3 4 3 2 2 3 2 2 +--R (- 14b cosh(x) + (- 16b - 8a b )cosh(x) + 2b - 4a b )sinh(x) +--R + +--R 3 5 3 2 3 2 +--R (- 8b cosh(x) + (- 8b - 8a b )cosh(x) - 8a b cosh(x))sinh(x) +--R + +--R 3 6 2 4 3 2 2 +--R - 2b cosh(x) - 4a b cosh(x) + (2b - 4a b )cosh(x) +--R * +--R sinh(2x) +--R + +--R 2 6 3 2 5 +--R - 2a b sinh(x) + (4b cosh(x)cosh(2x) - 8a b cosh(x))sinh(x) +--R + +--R 3 2 2 2 2 2 4 +--R ((16b cosh(x) + 2a b )cosh(2x) - 14a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 3 2 2 3 +--R (24b cosh(x) + 16a b cosh(x))cosh(2x) - 16a b cosh(x) +--R + +--R 2 2 +--R (- 8a b - 8a b)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 3 4 2 2 2 2 4 +--R (16b cosh(x) + 28a b cosh(x) + 4a b)cosh(2x) - 14a b cosh(x) +--R + +--R 2 2 2 2 2 +--R (- 16a b - 8a b)cosh(x) + 2a b - 4a b +--R * +--R 2 +--R sinh(x) +--R + +--R 3 5 2 3 3 2 +--R (4b cosh(x) + 16a b cosh(x) + (- 4b + 8a b)cosh(x))cosh(2x) +--R + +--R 2 5 2 2 3 2 +--R - 8a b cosh(x) + (- 8a b - 8a b)cosh(x) - 8a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 2 2 2 2 6 +--R (2a b cosh(x) + 4a b cosh(x) - 2a b )cosh(2x) - 2a b cosh(x) +--R + +--R 2 4 2 2 2 +--R - 4a b cosh(x) + (2a b - 4a b)cosh(x) +--R * +--R tanh(x) +--R + +--R 2 6 3 2 5 +--R - a b sinh(x) + (2b - 4a b )cosh(x)sinh(x) +--R + +--R 3 2 2 2 2 4 +--R ((8b - 7a b )cosh(x) + a b - 2a b)sinh(x) +--R + +--R 3 2 3 2 2 3 +--R ((12b - 8a b )cosh(x) + (4a b - 4a b)cosh(x))sinh(x) +--R + +--R 3 2 4 2 2 2 2 2 +--R ((8b - 7a b )cosh(x) + (6a b - 4a b)cosh(x) + a b )sinh(x) +--R + +--R 3 2 5 2 2 3 3 +--R ((2b - 4a b )cosh(x) + (4a b - 4a b)cosh(x) - 2b cosh(x))sinh(x) +--R + +--R 2 6 2 2 4 2 2 2 +--R - a b cosh(x) + (a b - 2a b)cosh(x) + a b cosh(x) - a b +--R * +--R sinh(2x) +--R + +--R 2 6 2 2 2 5 +--R - a b sinh(x) + (2a b cosh(x)cosh(2x) + (2a b - 4a b)cosh(x))sinh(x) +--R + +--R 2 2 2 2 2 2 2 3 +--R ((8a b cosh(x) + a b)cosh(2x) + (8a b - 7a b)cosh(x) + a b - 2a ) +--R * +--R 4 +--R sinh(x) +--R + +--R 2 3 2 2 2 3 +--R (12a b cosh(x) + 8a b cosh(x))cosh(2x) + (12a b - 8a b)cosh(x) +--R + +--R 2 3 +--R (4a b - 4a )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 2 4 2 2 3 +--R (8a b cosh(x) + 14a b cosh(x) + 2a )cosh(2x) +--R + +--R 2 2 4 2 3 2 2 +--R (8a b - 7a b)cosh(x) + (6a b - 4a )cosh(x) + a b +--R * +--R 2 +--R sinh(x) +--R + +--R 2 5 2 3 2 3 +--R (2a b cosh(x) + 8a b cosh(x) + (- 2a b + 4a )cosh(x))cosh(2x) +--R + +--R 2 2 5 2 3 3 2 +--R (2a b - 4a b)cosh(x) + (4a b - 4a )cosh(x) - 2a b cosh(x) +--R * +--R sinh(x) +--R + +--R 2 4 3 2 2 2 6 +--R (a b cosh(x) + 2a cosh(x) - a b)cosh(2x) - a b cosh(x) +--R + +--R 2 3 4 2 2 2 +--R (a b - 2a )cosh(x) + a b cosh(x) - a b +--R / +--R 3 5 3 2 2 2 4 +--R 4a b cosh(x)sinh(x) + (16a b cosh(x) + 2a b )sinh(x) +--R + +--R 3 3 2 2 3 +--R (24a b cosh(x) + 16a b cosh(x))sinh(x) +--R + +--R 3 4 2 2 2 3 2 +--R (16a b cosh(x) + 28a b cosh(x) + 4a b)sinh(x) +--R + +--R 3 5 2 2 3 3 3 +--R (4a b cosh(x) + 16a b cosh(x) + (- 4a b + 8a b)cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R 2a b cosh(x) + 4a b cosh(x) - 2a b +--R * +--R sinh(2x) +--R + +--R 2 2 5 2 2 2 3 4 +--R 4a b cosh(x)sinh(x) + (16a b cosh(x) + 2a b)sinh(x) +--R + +--R 2 2 3 3 3 +--R (24a b cosh(x) + 16a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 4 2 +--R (16a b cosh(x) + 28a b cosh(x) + 4a )sinh(x) +--R + +--R 2 2 5 3 3 2 2 4 +--R (4a b cosh(x) + 16a b cosh(x) + (- 4a b + 8a )cosh(x))sinh(x) +--R + +--R 3 4 4 2 3 +--R 2a b cosh(x) + 4a cosh(x) - 2a b +--R * +--R 2 +--R tanh(x) +--R + +--R 4 5 4 2 3 4 +--R - 8b cosh(x)sinh(x) + (- 32b cosh(x) - 4a b )sinh(x) +--R + +--R 4 3 3 3 +--R (- 48b cosh(x) - 32a b cosh(x))sinh(x) +--R + +--R 4 4 3 2 2 2 2 +--R (- 32b cosh(x) - 56a b cosh(x) - 8a b )sinh(x) +--R + +--R 4 5 3 3 4 2 2 +--R (- 8b cosh(x) - 32a b cosh(x) + (8b - 16a b )cosh(x))sinh(x) +--R + +--R 3 4 2 2 2 3 +--R - 4a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R sinh(2x) +--R + +--R 3 5 3 2 2 2 4 +--R - 8a b cosh(x)sinh(x) + (- 32a b cosh(x) - 4a b )sinh(x) +--R + +--R 3 3 2 2 3 +--R (- 48a b cosh(x) - 32a b cosh(x))sinh(x) +--R + +--R 3 4 2 2 2 3 2 +--R (- 32a b cosh(x) - 56a b cosh(x) - 8a b)sinh(x) +--R + +--R 3 5 2 2 3 3 3 +--R (- 8a b cosh(x) - 32a b cosh(x) + (8a b - 16a b)cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R - 4a b cosh(x) - 8a b cosh(x) + 4a b +--R * +--R tanh(x) +--R + +--R 3 5 3 2 2 2 4 +--R - 4a b cosh(x)sinh(x) + (- 16a b cosh(x) - 2a b )sinh(x) +--R + +--R 3 3 2 2 3 +--R (- 24a b cosh(x) - 16a b cosh(x))sinh(x) +--R + +--R 3 4 2 2 2 3 2 +--R (- 16a b cosh(x) - 28a b cosh(x) - 4a b)sinh(x) +--R + +--R 3 5 2 2 3 3 3 +--R (- 4a b cosh(x) - 16a b cosh(x) + (4a b - 8a b)cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 2 2 +--R - 2a b cosh(x) - 4a b cosh(x) + 2a b +--R * +--R sinh(2x) +--R + +--R 2 2 5 2 2 2 3 4 +--R - 4a b cosh(x)sinh(x) + (- 16a b cosh(x) - 2a b)sinh(x) +--R + +--R 2 2 3 3 3 +--R (- 24a b cosh(x) - 16a b cosh(x))sinh(x) +--R + +--R 2 2 4 3 2 4 2 +--R (- 16a b cosh(x) - 28a b cosh(x) - 4a )sinh(x) +--R + +--R 2 2 5 3 3 2 2 4 +--R (- 4a b cosh(x) - 16a b cosh(x) + (4a b - 8a )cosh(x))sinh(x) +--R + +--R 3 4 4 2 3 +--R - 2a b cosh(x) - 4a cosh(x) + 2a b +--R Type: Expression(Integer) +--E 453 + +--S 454 of 518 +t0987:= tanh(2*x)*sinh(x) +--R +--R +--R (439) sinh(x)tanh(2x) +--R Type: Expression(Integer) +--E 454 + +--S 455 of 518 +r0987:= -1/2*atan(2^(1/2)*sinh(x))*2^(1/2)+sinh(x) +--R +--R +--R +-+ +-+ +--R - \|2 atan(\|2 sinh(x)) + 2sinh(x) +--R (440) ---------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 518 +a0987:= integrate(t0987,x) +--R +--R +--R (441) +--R +-+ +-+ +--R \|2 sinh(x) + \|2 cosh(x) +--R (- 2sinh(x) - 2cosh(x))atan(-------------------------) +--R 2 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R (2sinh(x) + 2cosh(x))atan(-----------------------------------------) +--R +-+ +-+ +--R \|2 sinh(x) - \|2 cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) - \|2 +--R / +--R +-+ +-+ +--R 2\|2 sinh(x) + 2\|2 cosh(x) +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 518 +m0987:= a0987-r0987 +--R +--R +--R (442) +--R +-+ +--R (2sinh(x) + 2cosh(x))atan(\|2 sinh(x)) +--R + +--R +-+ +-+ +--R \|2 sinh(x) + \|2 cosh(x) +--R (- 2sinh(x) - 2cosh(x))atan(-------------------------) +--R 2 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R (2sinh(x) + 2cosh(x))atan(-----------------------------------------) +--R +-+ +-+ +--R \|2 sinh(x) - \|2 cosh(x) +--R + +--R +-+ 2 +-+ 2 +-+ +--R - \|2 sinh(x) + \|2 cosh(x) - \|2 +--R / +--R +-+ +-+ +--R 2\|2 sinh(x) + 2\|2 cosh(x) +--R Type: Expression(Integer) +--E 457 + +--S 458 of 518 +d0987:= D(m0987,x) +--R +--R +--R (443) +--R 10 9 2 8 +--R 2sinh(x) + 12cosh(x)sinh(x) + (28cosh(x) + 23)sinh(x) +--R + +--R 3 7 2 6 +--R (28cosh(x) + 76cosh(x))sinh(x) + (86cosh(x) + 53)sinh(x) +--R + +--R 5 3 5 +--R (- 28cosh(x) + 16cosh(x) + 106cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 28cosh(x) - 48cosh(x) + 81cosh(x) + 47)sinh(x) +--R + +--R 7 5 3 3 +--R (- 12cosh(x) - 36cosh(x) - 8cosh(x) + 44cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 2cosh(x) + 2cosh(x) - 37cosh(x) + 28cosh(x) + 17)sinh(x) +--R + +--R 7 5 3 8 +--R (8cosh(x) - 2cosh(x) - 8cosh(x) + 2cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R - cosh(x) - 7cosh(x) + 5cosh(x) + 2 +--R / +--R 9 8 2 7 +--R 4sinh(x) + 28cosh(x)sinh(x) + (84cosh(x) + 26)sinh(x) +--R + +--R 3 6 +--R (140cosh(x) + 102cosh(x))sinh(x) +--R + +--R 4 2 5 +--R (140cosh(x) + 186cosh(x) + 48)sinh(x) +--R + +--R 5 3 4 +--R (84cosh(x) + 214cosh(x) + 88cosh(x))sinh(x) +--R + +--R 6 4 2 3 +--R (28cosh(x) + 158cosh(x) + 116cosh(x) + 26)sinh(x) +--R + +--R 7 5 3 2 +--R (4cosh(x) + 66cosh(x) + 108cosh(x) + 30cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (14cosh(x) + 44cosh(x) + 22cosh(x) + 4)sinh(x) + 2cosh(x) +--R + +--R 5 3 +--R 12cosh(x) + 18cosh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 458 + +--S 459 of 518 +t0988:= tanh(3*x)*sinh(x) +--R +--R +--R (444) sinh(x)tanh(3x) +--R Type: Expression(Integer) +--E 459 + +--S 460 of 518 +r0988:= -1/3*atan(3*sinh(x)/(1-2*sinh(x)^2))+sinh(x) +--R +--R +--R 3sinh(x) +--R atan(-------------) + 3sinh(x) +--R 2 +--R 2sinh(x) - 1 +--R (445) ------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 518 +a0988:= integrate(t0988,x) +--R +--R +--R (446) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R (2sinh(x) + 2cosh(x))atan(-------------------------------------) +--R sinh(x) - cosh(x) +--R + +--R 2 +--R (- 6sinh(x) - 6cosh(x))atan(sinh(x) + cosh(x)) + 3sinh(x) +--R + +--R 2 +--R 6cosh(x)sinh(x) + 3cosh(x) - 3 +--R / +--R 6sinh(x) + 6cosh(x) +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 518 +m0988:= a0988-r0988 +--R +--R +--R (447) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R (2sinh(x) + 2cosh(x))atan(-------------------------------------) +--R sinh(x) - cosh(x) +--R + +--R (- 6sinh(x) - 6cosh(x))atan(sinh(x) + cosh(x)) +--R + +--R 3sinh(x) 2 2 +--R (- 2sinh(x) - 2cosh(x))atan(-------------) - 3sinh(x) + 3cosh(x) - 3 +--R 2 +--R 2sinh(x) - 1 +--R / +--R 6sinh(x) + 6cosh(x) +--R Type: Expression(Integer) +--E 462 + +--S 463 of 518 +d0988:= D(m0988,x) +--R +--R +--R (448) +--R 12 11 2 10 +--R 4sinh(x) + 24cosh(x)sinh(x) + (56cosh(x) + 17)sinh(x) +--R + +--R 3 9 2 8 +--R (56cosh(x) + 58cosh(x))sinh(x) + (86cosh(x) + 28)sinh(x) +--R + +--R 5 3 7 +--R (- 56cosh(x) + 74cosh(x) + 70cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (- 56cosh(x) + 32cosh(x) + 69cosh(x) + 22)sinh(x) +--R + +--R 7 5 3 5 +--R (- 24cosh(x) - 2cosh(x) - 4cosh(x) + 36cosh(x))sinh(x) +--R + +--R 8 6 4 2 4 +--R (- 4cosh(x) - 6cosh(x) - 45cosh(x) + 49cosh(x) + 8)sinh(x) +--R + +--R 7 5 3 3 +--R (- 2cosh(x) - 10cosh(x) + 2cosh(x) - 2cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- cosh(x) + 11cosh(x) - 22cosh(x) + 11cosh(x) + 1)sinh(x) +--R + +--R 7 5 8 6 +--R (8cosh(x) - 6cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R 4 2 +--R - cosh(x) + cosh(x) +--R / +--R 11 10 2 9 +--R 8sinh(x) + 56cosh(x)sinh(x) + (168cosh(x) + 26)sinh(x) +--R + +--R 3 8 +--R (280cosh(x) + 118cosh(x))sinh(x) +--R + +--R 4 2 7 +--R (280cosh(x) + 274cosh(x) + 30)sinh(x) +--R + +--R 5 3 6 +--R (168cosh(x) + 414cosh(x) + 66cosh(x))sinh(x) +--R + +--R 6 4 2 5 +--R (56cosh(x) + 398cosh(x) + 114cosh(x) + 14)sinh(x) +--R + +--R 7 5 3 4 +--R (8cosh(x) + 226cosh(x) + 158cosh(x) + 2cosh(x))sinh(x) +--R + +--R 6 4 2 3 +--R (70cosh(x) + 130cosh(x) + 6cosh(x) + 2)sinh(x) +--R + +--R 7 5 3 2 +--R (10cosh(x) + 62cosh(x) + 26cosh(x) - 2cosh(x))sinh(x) +--R + +--R 6 4 2 7 5 +--R (14cosh(x) + 12cosh(x) - 2cosh(x) )sinh(x) + 2cosh(x) + 4cosh(x) +--R + +--R 3 +--R 2cosh(x) +--R Type: Expression(Integer) +--E 463 + +--S 464 of 518 +t0989:= tanh(4*x)*sinh(x) +--R +--R +--R (449) sinh(x)tanh(4x) +--R Type: Expression(Integer) +--E 464 + +--S 465 of 518 +r0989:= -1/4*(2-2^(1/2))^(1/2)*atan(2*sinh(x)/(2-2^(1/2))^(1/2))-_ + 1/4*(2+2^(1/2))^(1/2)*atan(2*sinh(x)/(2+2^(1/2))^(1/2))+sinh(x) +--R +--R +--R (450) +--R +----------+ +--------+ +--R | +-+ 2sinh(x) | +-+ 2sinh(x) +--R - \|- \|2 + 2 atan(-------------) - \|\|2 + 2 atan(-----------) + 4sinh(x) +--R +----------+ +--------+ +--R | +-+ | +-+ +--R \|- \|2 + 2 \|\|2 + 2 +--R ---------------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 465 + +--S 466 of 518 +a0989:= integrate(t0989,x) +--R +--R +--R (451) +--R +--------+ +--R | +-+ +--R |\|2 + 1 +--R (2sinh(x) + 2cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R +--------+ +--R | +-+ +--R |\|2 + 1 +--R (4sinh(x) + 4cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +--------+ +--R | +-+ +--R |\|2 - 1 +--R (2sinh(x) + 2cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R +--------+ +--R | +-+ +--R |\|2 - 1 +--R (4sinh(x) + 4cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 518 +m0989:= a0989-r0989 +--R +--R +--R (452) +--R +--------+ +--R | +-+ +--R |\|2 + 1 +--R (4sinh(x) + 4cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R +--------+ +--R | +-+ +--R |\|2 + 1 +--R (4sinh(x) + 4cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +--------+ +--R | +-+ +--R |\|2 - 1 +--R (4sinh(x) + 4cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R +--------+ +--R | +-+ +--R |\|2 - 1 +--R (4sinh(x) + 4cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +----------+ +--R | +-+ 2sinh(x) +--R (sinh(x) + cosh(x))\|- \|2 + 2 atan(-------------) +--R +----------+ +--R | +-+ +--R \|- \|2 + 2 +--R + +--R +--------+ +--R | +-+ 2sinh(x) 2 2 +--R (sinh(x) + cosh(x))\|\|2 + 2 atan(-----------) - 2sinh(x) + 2cosh(x) - 2 +--R +--------+ +--R | +-+ +--R \|\|2 + 2 +--R / +--R 4sinh(x) + 4cosh(x) +--R Type: Expression(Integer) +--E 467 + +--S 468 of 518 +d0989:= D(m0989,x) +--R +--R +--R (453) +--R 14 13 2 12 +--R 8sinh(x) + 64cosh(x)sinh(x) + 216cosh(x) sinh(x) +--R + +--R 3 11 +--R (384cosh(x) + 8cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (336cosh(x) + 64cosh(x) - 7)sinh(x) +--R + +--R 3 9 +--R (224cosh(x) - 54cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 336cosh(x) + 448cosh(x) - 179cosh(x) - 1)sinh(x) +--R + +--R 7 5 3 7 +--R (- 384cosh(x) + 560cosh(x) - 328cosh(x) - 8cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (- 216cosh(x) + 448cosh(x) - 350cosh(x) - 28cosh(x) - 8)sinh(x) +--R + +--R 9 7 5 3 +--R (- 64cosh(x) + 224cosh(x) - 196cosh(x) - 56cosh(x) - 32cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R (- 8cosh(x) + 64cosh(x) - 14cosh(x) - 70cosh(x) - 24cosh(x) ) +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (8cosh(x) + 56cosh(x) - 56cosh(x) - 24cosh(x))sinh(x) +--R + +--R 8 6 2 2 +--R (37cosh(x) - 28cosh(x) - 16cosh(x) + 7)sinh(x) +--R + +--R 9 7 10 8 +--R (10cosh(x) - 8cosh(x) - 2cosh(x))sinh(x) + cosh(x) - cosh(x) +--R + +--R 2 +--R - cosh(x) + 1 +--R / +--R 13 12 2 11 +--R 16sinh(x) + 144cosh(x)sinh(x) + (576cosh(x) + 16)sinh(x) +--R + +--R 3 10 +--R (1344cosh(x) + 144cosh(x))sinh(x) +--R + +--R 4 2 9 +--R (2016cosh(x) + 576cosh(x) + 2)sinh(x) +--R + +--R 5 3 8 +--R (2016cosh(x) + 1344cosh(x) + 18cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (1344cosh(x) + 2016cosh(x) + 72cosh(x) )sinh(x) +--R + +--R 7 5 3 6 +--R (576cosh(x) + 2016cosh(x) + 168cosh(x) )sinh(x) +--R + +--R 8 6 4 5 +--R (144cosh(x) + 1344cosh(x) + 252cosh(x) + 16)sinh(x) +--R + +--R 9 7 5 4 +--R (16cosh(x) + 576cosh(x) + 252cosh(x) + 16cosh(x))sinh(x) +--R + +--R 8 6 3 +--R (144cosh(x) + 168cosh(x) + 16)sinh(x) +--R + +--R 9 7 2 8 +--R (16cosh(x) + 72cosh(x) + 16cosh(x))sinh(x) + (18cosh(x) + 2)sinh(x) +--R + +--R 9 +--R 2cosh(x) + 2cosh(x) +--R Type: Expression(Integer) +--E 468 + +--S 469 of 518 +t0990:= tanh(5*x)*sinh(x) +--R +--R +--R (454) sinh(x)tanh(5x) +--R Type: Expression(Integer) +--E 469 + +--S 470 of 518 +r0990:= -1/5*atan(sinh(x))-1/5*(1/2*5^(1/2)-1/2)*_ + atan(2*2^(1/2)/(-5^(1/2)+3)^(1/2)*sinh(x))-1/5*(1/2+1/2*5^(1/2))*_ + atan(2*2^(1/2)/(5^(1/2)+3)^(1/2)*sinh(x))+sinh(x) +--R +--R +--R (455) +--R +--------+ +--R +-+ +-+ +-+ | +-+ +--R +-+ (\|2 \|5 - 3\|2 )sinh(x)\|\|5 + 3 +--R (\|5 + 1)atan(------------------------------------) +--R 2 +--R + +--R +----------+ +--R +-+ +-+ +-+ | +-+ +--R +-+ (\|2 \|5 + 3\|2 )sinh(x)\|- \|5 + 3 +--R (- \|5 + 1)atan(--------------------------------------) - 2atan(sinh(x)) +--R 2 +--R + +--R 10sinh(x) +--R / +--R 10 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 518 +a0990:= integrate(t0990,x) +--R +--R +--R (456) +--R +---------+ +--R | +-+ +--R |3\|5 + 5 +--R (10sinh(x) + 10cosh(x)) |--------- +--R | +-+ +--R \| 50\|5 +--R * +--R +---------+ +--R | +-+ +--R |3\|5 + 5 +--R (5sinh(x) + 5cosh(x)) |--------- +--R | +-+ +--R \| 50\|5 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +---------+ +--R | +-+ +--R |3\|5 - 5 +--R (10sinh(x) + 10cosh(x)) |--------- +--R | +-+ +--R \| 50\|5 +--R * +--R +---------+ +--R | +-+ +--R |3\|5 - 5 +--R (5sinh(x) + 5cosh(x)) |--------- +--R | +-+ +--R \| 50\|5 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2sinh(x) + 2cosh(x) +--R (2sinh(x) + 2cosh(x))atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 2 +--R 5sinh(x) + 10cosh(x)sinh(x) + 5cosh(x) - 5 +--R / +--R 10sinh(x) + 10cosh(x) +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 518 +m0990:= a0990-r0990 +--R +--R +--R (457) +--R +-+ +-+ +--R ((- \|5 - 1)sinh(x) + (- \|5 - 1)cosh(x)) +--R * +--R +--------+ +--R +-+ +-+ +-+ | +-+ +--R (\|2 \|5 - 3\|2 )sinh(x)\|\|5 + 3 +--R atan(------------------------------------) +--R 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|5 + 5 +--R (10sinh(x) + 10cosh(x)) |--------- +--R | +-+ +--R \| 50\|5 +--R * +--R +---------+ +--R | +-+ +--R |3\|5 + 5 +--R (5sinh(x) + 5cosh(x)) |--------- +--R | +-+ +--R \| 50\|5 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +---------+ +--R | +-+ +--R |3\|5 - 5 +--R (10sinh(x) + 10cosh(x)) |--------- +--R | +-+ +--R \| 50\|5 +--R * +--R +---------+ +--R | +-+ +--R |3\|5 - 5 +--R (5sinh(x) + 5cosh(x)) |--------- +--R | +-+ +--R \| 50\|5 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R ((\|5 - 1)sinh(x) + (\|5 - 1)cosh(x)) +--R * +--R +----------+ +--R +-+ +-+ +-+ | +-+ +--R (\|2 \|5 + 3\|2 )sinh(x)\|- \|5 + 3 +--R atan(--------------------------------------) +--R 2 +--R + +--R (2sinh(x) + 2cosh(x))atan(sinh(x)) +--R + +--R 2sinh(x) + 2cosh(x) +--R (2sinh(x) + 2cosh(x))atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 2 +--R - 5sinh(x) + 5cosh(x) - 5 +--R / +--R 10sinh(x) + 10cosh(x) +--R Type: Expression(Integer) +--E 472 + +--S 473 of 518 +d0990:= D(m0990,x) +--R +--R +--R (458) +--R +-+ +-+ +-+ 15 +--R (4\|2 \|5 + 4\|2 )cosh(x)sinh(x) +--R + +--R +-+ +-+ +-+ 2 14 +--R (44\|2 \|5 + 44\|2 )cosh(x) sinh(x) +--R + +--R +-+ +-+ +-+ 3 +-+ +-+ +-+ +--R ((220\|2 \|5 + 220\|2 )cosh(x) + (5\|2 \|5 + 3\|2 )cosh(x)) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 4 +-+ +-+ +-+ 2 +--R ((660\|2 \|5 + 660\|2 )cosh(x) + (55\|2 \|5 + 33\|2 )cosh(x) ) +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 5 +--R (1320\|2 \|5 + 1320\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 3 +-+ +-+ +-+ +--R (275\|2 \|5 + 165\|2 )cosh(x) + (\|2 \|5 - \|2 )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 6 +--R (1848\|2 \|5 + 1848\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 4 +-+ +-+ +-+ 2 +--R (825\|2 \|5 + 495\|2 )cosh(x) + (11\|2 \|5 - 11\|2 )cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 7 +--R (1848\|2 \|5 + 1848\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 5 +-+ +-+ +-+ 3 +--R (1650\|2 \|5 + 990\|2 )cosh(x) + (55\|2 \|5 - 55\|2 )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 8 +--R (1320\|2 \|5 + 1320\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 6 +-+ +-+ +-+ 4 +--R (2310\|2 \|5 + 1386\|2 )cosh(x) + (165\|2 \|5 - 165\|2 )cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 9 +--R (660\|2 \|5 + 660\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 7 +-+ +-+ +-+ 5 +--R (2310\|2 \|5 + 1386\|2 )cosh(x) + (330\|2 \|5 - 330\|2 )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 10 +--R (220\|2 \|5 + 220\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 8 +-+ +-+ +-+ 6 +--R (1650\|2 \|5 + 990\|2 )cosh(x) + (462\|2 \|5 - 462\|2 )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 11 +-+ +-+ +-+ 9 +--R (44\|2 \|5 + 44\|2 )cosh(x) + (825\|2 \|5 + 495\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 7 +-+ +-+ +-+ +--R (462\|2 \|5 - 462\|2 )cosh(x) + (4\|2 \|5 + 4\|2 )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 12 +-+ +-+ +-+ 10 +--R (4\|2 \|5 + 4\|2 )cosh(x) + (275\|2 \|5 + 165\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 8 +-+ +-+ +-+ 2 +--R (330\|2 \|5 - 330\|2 )cosh(x) + (4\|2 \|5 + 4\|2 )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 11 +-+ +-+ +-+ 9 +--R (55\|2 \|5 + 33\|2 )cosh(x) + (165\|2 \|5 - 165\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ +--R (5\|2 \|5 + 3\|2 )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 12 +-+ +-+ +-+ 10 +--R (5\|2 \|5 + 3\|2 )cosh(x) + (55\|2 \|5 - 55\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 2 +--R (5\|2 \|5 + 3\|2 )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 11 +-+ +-+ +-+ +--R ((11\|2 \|5 - 11\|2 )cosh(x) + (\|2 \|5 - \|2 )cosh(x))sinh(x) +--R + +--R +-+ +-+ +-+ 12 +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )cosh(x) + (\|2 \|5 - \|2 )cosh(x) +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 3 +--R + +--R +-+ +-+ +-+ 15 +--R (4\|2 \|5 - 4\|2 )cosh(x)sinh(x) +--R + +--R +-+ +-+ +-+ 2 14 +--R (44\|2 \|5 - 44\|2 )cosh(x) sinh(x) +--R + +--R +-+ +-+ +-+ 3 +-+ +-+ +-+ +--R ((220\|2 \|5 - 220\|2 )cosh(x) + (5\|2 \|5 - 3\|2 )cosh(x)) +--R * +--R 13 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 4 +-+ +-+ +-+ 2 +--R ((660\|2 \|5 - 660\|2 )cosh(x) + (55\|2 \|5 - 33\|2 )cosh(x) ) +--R * +--R 12 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 5 +--R (1320\|2 \|5 - 1320\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 3 +-+ +-+ +-+ +--R (275\|2 \|5 - 165\|2 )cosh(x) + (\|2 \|5 + \|2 )cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 6 +--R (1848\|2 \|5 - 1848\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 4 +-+ +-+ +-+ 2 +--R (825\|2 \|5 - 495\|2 )cosh(x) + (11\|2 \|5 + 11\|2 )cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 7 +--R (1848\|2 \|5 - 1848\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 5 +-+ +-+ +-+ 3 +--R (1650\|2 \|5 - 990\|2 )cosh(x) + (55\|2 \|5 + 55\|2 )cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 8 +--R (1320\|2 \|5 - 1320\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 6 +-+ +-+ +-+ 4 +--R (2310\|2 \|5 - 1386\|2 )cosh(x) + (165\|2 \|5 + 165\|2 )cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 9 +--R (660\|2 \|5 - 660\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 7 +-+ +-+ +-+ 5 +--R (2310\|2 \|5 - 1386\|2 )cosh(x) + (330\|2 \|5 + 330\|2 )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 10 +--R (220\|2 \|5 - 220\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 8 +-+ +-+ +-+ 6 +--R (1650\|2 \|5 - 990\|2 )cosh(x) + (462\|2 \|5 + 462\|2 )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 11 +-+ +-+ +-+ 9 +--R (44\|2 \|5 - 44\|2 )cosh(x) + (825\|2 \|5 - 495\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 7 +-+ +-+ +-+ +--R (462\|2 \|5 + 462\|2 )cosh(x) + (4\|2 \|5 - 4\|2 )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 12 +-+ +-+ +-+ 10 +--R (4\|2 \|5 - 4\|2 )cosh(x) + (275\|2 \|5 - 165\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 8 +-+ +-+ +-+ 2 +--R (330\|2 \|5 + 330\|2 )cosh(x) + (4\|2 \|5 - 4\|2 )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 11 +-+ +-+ +-+ 9 +--R (55\|2 \|5 - 33\|2 )cosh(x) + (165\|2 \|5 + 165\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ +--R (5\|2 \|5 - 3\|2 )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 12 +-+ +-+ +-+ 10 +--R (5\|2 \|5 - 3\|2 )cosh(x) + (55\|2 \|5 + 55\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 2 +--R (5\|2 \|5 - 3\|2 )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 11 +-+ +-+ +-+ +--R ((11\|2 \|5 + 11\|2 )cosh(x) + (\|2 \|5 + \|2 )cosh(x))sinh(x) +--R + +--R +-+ +-+ +-+ 12 +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )cosh(x) + (\|2 \|5 + \|2 )cosh(x) +--R * +--R +----------+ +--R | +-+ +--R \|- \|5 + 3 +--R + +--R 18 17 2 16 +--R 80sinh(x) + 800cosh(x)sinh(x) + (3520cosh(x) + 60)sinh(x) +--R + +--R 3 15 +--R (8800cosh(x) + 632cosh(x))sinh(x) +--R + +--R 4 2 14 +--R (13200cosh(x) + 2912cosh(x) - 75)sinh(x) +--R + +--R 5 3 13 +--R (10560cosh(x) + 7560cosh(x) - 726cosh(x))sinh(x) +--R + +--R 4 2 12 +--R (11580cosh(x) - 3176cosh(x) - 60)sinh(x) +--R + +--R 7 5 3 11 +--R (- 10560cosh(x) + 8880cosh(x) - 8330cosh(x) - 598cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 13200cosh(x) - 2016cosh(x) - 14715cosh(x) - 2683cosh(x) - 5) +--R * +--R 10 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 8800cosh(x) - 13296cosh(x) - 18780cosh(x) - 7140cosh(x) +--R + +--R - 50cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 3520cosh(x) - 16140cosh(x) - 18312cosh(x) - 12495cosh(x) +--R + +--R 2 +--R - 225cosh(x) - 80 +--R * +--R 8 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 800cosh(x) - 10920cosh(x) - 14292cosh(x) - 15060cosh(x) +--R + +--R 3 +--R - 600cosh(x) - 320cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 80cosh(x) - 4480cosh(x) - 9105cosh(x) - 12726cosh(x) +--R + +--R 4 2 +--R - 1050cosh(x) - 240cosh(x) - 60 +--R * +--R 6 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 1048cosh(x) - 4590cosh(x) - 7536cosh(x) - 1260cosh(x) +--R + +--R - 528cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 108cosh(x) - 1680cosh(x) - 3090cosh(x) - 1050cosh(x) +--R + +--R 2 +--R - 388cosh(x) + 75 +--R * +--R 4 +--R sinh(x) +--R + +--R 11 9 7 3 +--R (- 386cosh(x) - 870cosh(x) - 600cosh(x) - 236cosh(x))sinh(x) +--R + +--R 12 10 8 2 2 +--R (- 41cosh(x) - 175cosh(x) - 225cosh(x) - 171cosh(x) + 60)sinh(x) +--R + +--R 11 9 12 10 +--R (- 28cosh(x) - 50cosh(x) - 18cosh(x))sinh(x) - 3cosh(x) - 5cosh(x) +--R + +--R 2 +--R - 13cosh(x) + 5 +--R / +--R 17 16 2 15 +--R 160sinh(x) + 1760cosh(x)sinh(x) + (8800cosh(x) + 280)sinh(x) +--R + +--R 3 14 +--R (26400cosh(x) + 3080cosh(x))sinh(x) +--R + +--R 4 2 13 +--R (52800cosh(x) + 15400cosh(x) + 130)sinh(x) +--R + +--R 5 3 12 +--R (73920cosh(x) + 46200cosh(x) + 1430cosh(x))sinh(x) +--R + +--R 6 4 2 11 +--R (73920cosh(x) + 92400cosh(x) + 7150cosh(x) + 10)sinh(x) +--R + +--R 7 5 3 10 +--R (52800cosh(x) + 129360cosh(x) + 21450cosh(x) + 110cosh(x))sinh(x) +--R + +--R 8 6 4 2 9 +--R (26400cosh(x) + 129360cosh(x) + 42900cosh(x) + 550cosh(x) )sinh(x) +--R + +--R 9 7 5 3 8 +--R (8800cosh(x) + 92400cosh(x) + 60060cosh(x) + 1650cosh(x) )sinh(x) +--R + +--R 10 8 6 4 +--R (1760cosh(x) + 46200cosh(x) + 60060cosh(x) + 3300cosh(x) + 160) +--R * +--R 7 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 160cosh(x) + 15400cosh(x) + 42900cosh(x) + 4620cosh(x) +--R + +--R 160cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 10 8 6 5 +--R (3080cosh(x) + 21450cosh(x) + 4620cosh(x) + 280)sinh(x) +--R + +--R 11 9 7 4 +--R (280cosh(x) + 7150cosh(x) + 3300cosh(x) + 280cosh(x))sinh(x) +--R + +--R 10 8 3 +--R (1430cosh(x) + 1650cosh(x) + 130)sinh(x) +--R + +--R 11 9 2 +--R (130cosh(x) + 550cosh(x) + 130cosh(x))sinh(x) +--R + +--R 10 11 +--R (110cosh(x) + 10)sinh(x) + 10cosh(x) + 10cosh(x) +--R Type: Expression(Integer) +--E 473 + +--S 474 of 518 +t0991:= tanh(6*x)*sinh(x) +--R +--R +--R (459) sinh(x)tanh(6x) +--R Type: Expression(Integer) +--E 474 + +--S 475 of 518 +r0991:= -1/6*atan(2^(1/2)*sinh(x))*2^(1/2)-1/6*(1/2*6^(1/2)-1/2*2^(1/2))*_ + atan(2*sinh(x)/(1/2*6^(1/2)-1/2*2^(1/2)))-_ + 1/6*(1/2*6^(1/2)+1/2*2^(1/2))*_ + atan(2*sinh(x)/(1/2*6^(1/2)+1/2*2^(1/2)))+sinh(x) +--R +--R +--R (460) +--R +-+ +-+ +-+ +-+ 4sinh(x) +--R - 2\|2 atan(\|2 sinh(x)) + (- \|6 + \|2 )atan(-----------) +--R +-+ +-+ +--R \|6 - \|2 +--R + +--R +-+ +-+ 4sinh(x) +--R (- \|6 - \|2 )atan(-----------) + 12sinh(x) +--R +-+ +-+ +--R \|6 + \|2 +--R / +--R 12 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 518 +a0991:= integrate(t0991,x) +--R +--R +--R (461) +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 + 3 +--R (6\|2 sinh(x) + 6\|2 cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R +---------+ +--R | +-+ +--R |2\|3 + 3 +--R (6sinh(x) + 6cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 - 3 +--R (6\|2 sinh(x) + 6\|2 cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R +---------+ +--R | +-+ +--R |2\|3 - 3 +--R (6sinh(x) + 6cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +-+ +--R 2\|2 sinh(x) + 2\|2 cosh(x) +--R (sinh(x) + cosh(x))atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 2 +--R + +--R (sinh(x) + cosh(x)) +--R * +--R atan +--R +-+ 2 +-+ +-+ 2 +-+ +--R 2\|2 sinh(x) + 4\|2 cosh(x)sinh(x) + 2\|2 cosh(x) + 2\|2 +--R / +--R 5 4 2 3 +--R sinh(x) + 5cosh(x)sinh(x) + (10cosh(x) + 2)sinh(x) +--R + +--R 3 2 +--R (10cosh(x) + 6cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (5cosh(x) + 6cosh(x) + 3)sinh(x) + cosh(x) + 2cosh(x) +--R + +--R - cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R 3\|2 sinh(x) + 6\|2 cosh(x)sinh(x) + 3\|2 cosh(x) - 3\|2 +--R / +--R +-+ +-+ +--R 6\|2 sinh(x) + 6\|2 cosh(x) +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 518 +m0991:= a0991-r0991 +--R +--R +--R (462) +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 + 3 +--R (12\|2 sinh(x) + 12\|2 cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R +---------+ +--R | +-+ +--R |2\|3 + 3 +--R (6sinh(x) + 6cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +---------+ +--R | +-+ +--R +-+ +-+ |2\|3 - 3 +--R (12\|2 sinh(x) + 12\|2 cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R * +--R +---------+ +--R | +-+ +--R |2\|3 - 3 +--R (6sinh(x) + 6cosh(x)) |--------- +--R | +-+ +--R \| 36\|3 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +-+ +--R (4sinh(x) + 4cosh(x))atan(\|2 sinh(x)) +--R + +--R +-+ +-+ +-+ +-+ 4sinh(x) +--R ((\|2 \|6 - 2)sinh(x) + (\|2 \|6 - 2)cosh(x))atan(-----------) +--R +-+ +-+ +--R \|6 - \|2 +--R + +--R +-+ +-+ +-+ +-+ 4sinh(x) +--R ((\|2 \|6 + 2)sinh(x) + (\|2 \|6 + 2)cosh(x))atan(-----------) +--R +-+ +-+ +--R \|6 + \|2 +--R + +--R +-+ +-+ +--R 2\|2 sinh(x) + 2\|2 cosh(x) +--R (2sinh(x) + 2cosh(x))atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 2 +--R + +--R (2sinh(x) + 2cosh(x)) +--R * +--R atan +--R +-+ 2 +-+ +-+ 2 +-+ +--R 2\|2 sinh(x) + 4\|2 cosh(x)sinh(x) + 2\|2 cosh(x) + 2\|2 +--R / +--R 5 4 2 3 +--R sinh(x) + 5cosh(x)sinh(x) + (10cosh(x) + 2)sinh(x) +--R + +--R 3 2 +--R (10cosh(x) + 6cosh(x))sinh(x) +--R + +--R 4 2 5 3 +--R (5cosh(x) + 6cosh(x) + 3)sinh(x) + cosh(x) + 2cosh(x) +--R + +--R - cosh(x) +--R + +--R +-+ 2 +-+ 2 +-+ +--R - 6\|2 sinh(x) + 6\|2 cosh(x) - 6\|2 +--R / +--R +-+ +-+ +--R 12\|2 sinh(x) + 12\|2 cosh(x) +--R Type: Expression(Integer) +--E 477 + +--S 478 of 518 +d0991:= D(m0991,x) +--R +--R +--R (463) +--R 28 27 2 26 +--R 96sinh(x) + 1920cosh(x)sinh(x) + (18144cosh(x) + 624)sinh(x) +--R + +--R 3 25 +--R (107520cosh(x) + 11424cosh(x))sinh(x) +--R + +--R 4 2 24 +--R (446880cosh(x) + 98544cosh(x) + 1830)sinh(x) +--R + +--R 5 3 23 +--R (1378944cosh(x) + 531648cosh(x) + 29376cosh(x))sinh(x) +--R + +--R 6 4 2 22 +--R (3255840cosh(x) + 2007312cosh(x) + 221190cosh(x) + 3489)sinh(x) +--R + +--R 7 5 3 +--R (5953536cosh(x) + 5619744cosh(x) + 1037328cosh(x) + 46626cosh(x)) +--R * +--R 21 +--R sinh(x) +--R + +--R 8 6 4 2 +--R 8372160cosh(x) + 12046608cosh(x) + 3393162cosh(x) + 286209cosh(x) +--R + +--R 5553 +--R * +--R 20 +--R sinh(x) +--R + +--R 9 7 5 +--R 8682240cosh(x) + 20093184cosh(x) + 8216112cosh(x) +--R + +--R 3 +--R 1064604cosh(x) + 61020cosh(x) +--R * +--R 19 +--R sinh(x) +--R + +--R 10 8 6 +--R 5643456cosh(x) + 26139744cosh(x) + 15257370cosh(x) +--R + +--R 4 2 +--R 2660055cosh(x) + 294576cosh(x) + 6231 +--R * +--R 18 +--R sinh(x) +--R + +--R 9 7 5 +--R 26108736cosh(x) + 22229568cosh(x) + 4658970cosh(x) +--R + +--R 3 +--R 789132cosh(x) + 61698cosh(x) +--R * +--R 17 +--R sinh(x) +--R + +--R 12 10 8 +--R - 5643456cosh(x) + 18945888cosh(x) + 25827324cosh(x) +--R + +--R 6 4 2 +--R 5748783cosh(x) + 1127019cosh(x) + 265641cosh(x) + 1359 +--R * +--R 16 +--R sinh(x) +--R + +--R 13 11 9 +--R - 8682240cosh(x) + 8062080cosh(x) + 24292416cosh(x) +--R + +--R 7 5 3 +--R 4813776cosh(x) + 158064cosh(x) + 616824cosh(x) + 21888cosh(x) +--R * +--R 15 +--R sinh(x) +--R + +--R 14 12 10 +--R - 8372160cosh(x) - 1209312cosh(x) + 18901116cosh(x) +--R + +--R 8 6 4 2 +--R 2438346cosh(x) - 3048144cosh(x) + 676692cosh(x) + 122964cosh(x) +--R + +--R - 6722 +--R * +--R 14 +--R sinh(x) +--R + +--R 15 13 11 +--R - 5953536cosh(x) - 5643456cosh(x) + 12670944cosh(x) +--R + +--R 9 7 5 3 +--R 671076cosh(x) - 7596816cosh(x) - 364608cosh(x) + 351864cosh(x) +--R + +--R - 39812cosh(x) +--R * +--R 13 +--R sinh(x) +--R + +--R 16 14 12 +--R - 3255840cosh(x) - 5674464cosh(x) + 7852884cosh(x) +--R + +--R 10 8 6 4 +--R 913770cosh(x) - 10799478cosh(x) - 2756820cosh(x) + 553752cosh(x) +--R + +--R 2 +--R - 90542cosh(x) - 9734 +--R * +--R 12 +--R sinh(x) +--R + +--R 17 15 13 +--R - 1378944cosh(x) - 3720960cosh(x) + 4853664cosh(x) +--R + +--R 11 9 7 +--R 2516904cosh(x) - 10550712cosh(x) - 5380296cosh(x) +--R + +--R 5 3 +--R 372912cosh(x) - 74296cosh(x) - 70904cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 18 16 14 +--R - 446880cosh(x) - 1813968cosh(x) + 3023796cosh(x) +--R + +--R 12 10 8 +--R 3744078cosh(x) - 7353456cosh(x) - 6522294cosh(x) +--R + +--R 6 4 2 +--R - 306588cosh(x) + 65150cosh(x) - 203818cosh(x) - 3401 +--R * +--R 10 +--R sinh(x) +--R + +--R 19 17 15 +--R - 107520cosh(x) - 684000cosh(x) + 1770816cosh(x) +--R + +--R 13 11 9 +--R 3625380cosh(x) - 3541848cosh(x) - 5579340cosh(x) +--R + +--R 7 5 3 +--R - 1047672cosh(x) + 207092cosh(x) - 302520cosh(x) - 50094cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 20 18 16 +--R - 18144cosh(x) - 201552cosh(x) + 896382cosh(x) +--R + +--R 14 12 10 +--R 2524062cosh(x) - 970890cosh(x) - 3505290cosh(x) +--R + +--R 8 6 4 2 +--R - 1291506cosh(x) + 188290cosh(x) - 239780cosh(x) - 151223cosh(x) +--R + +--R 6927 +--R * +--R 8 +--R sinh(x) +--R + +--R 21 19 17 15 +--R - 1920cosh(x) - 45888cosh(x) + 369024cosh(x) + 1315536cosh(x) +--R + +--R 13 11 9 7 +--R 74928cosh(x) - 1627608cosh(x) - 981216cosh(x) + 49456cosh(x) +--R + +--R 5 3 +--R - 76048cosh(x) - 214752cosh(x) - 11296cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 22 20 18 16 +--R - 96cosh(x) - 7728cosh(x) + 117918cosh(x) + 519813cosh(x) +--R + +--R 14 12 10 8 +--R 240144cosh(x) - 543276cosh(x) - 504516cosh(x) - 47318cosh(x) +--R + +--R 6 4 2 +--R 27404cosh(x) - 165890cosh(x) - 48782cosh(x) + 9857 +--R * +--R 6 +--R sinh(x) +--R + +--R 21 19 17 15 +--R - 864cosh(x) + 27792cosh(x) + 155514cosh(x) + 144048cosh(x) +--R + +--R 13 11 9 7 +--R - 116784cosh(x) - 181752cosh(x) - 51804cosh(x) + 33840cosh(x) +--R + +--R 5 3 +--R - 67692cosh(x) - 64784cosh(x) + 4010cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 22 20 18 16 +--R - 48cosh(x) + 4482cosh(x) + 35013cosh(x) + 54741cosh(x) +--R + +--R 14 12 10 8 +--R - 8532cosh(x) - 48096cosh(x) - 22746cosh(x) + 12978cosh(x) +--R + +--R 6 4 2 +--R - 10422cosh(x) - 42056cosh(x) - 3539cosh(x) + 5009 +--R * +--R 4 +--R sinh(x) +--R + +--R 21 19 17 15 +--R 432cosh(x) + 5916cosh(x) + 14652cosh(x) + 3624cosh(x) +--R + +--R 13 11 9 7 +--R - 10320cosh(x) - 4728cosh(x) + 3720cosh(x) + 2352cosh(x) +--R + +--R 5 3 +--R - 13616cosh(x) - 7236cosh(x) + 1980cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 22 20 18 16 +--R 18cosh(x) + 747cosh(x) + 2688cosh(x) + 1335cosh(x) +--R + +--R 14 12 10 8 +--R - 1908cosh(x) - 102cosh(x) + 1278cosh(x) + 699cosh(x) +--R + +--R 6 4 2 +--R - 2866cosh(x) - 3781cosh(x) + 962cosh(x) + 1010 +--R * +--R 2 +--R sinh(x) +--R + +--R 21 19 17 15 +--R 66cosh(x) + 300cosh(x) + 186cosh(x) - 264cosh(x) +--R + +--R 13 11 9 7 5 +--R 108cosh(x) + 264cosh(x) - 54cosh(x) - 160cosh(x) - 470cosh(x) +--R + +--R 3 +--R - 108cosh(x) + 132cosh(x) +--R * +--R sinh(x) +--R + +--R 22 20 18 16 14 +--R 3cosh(x) + 15cosh(x) + 9cosh(x) - 21cosh(x) + 6cosh(x) +--R + +--R 12 10 8 6 4 +--R 24cosh(x) - 3cosh(x) - 7cosh(x) - 89cosh(x) - 67cosh(x) +--R + +--R 2 +--R 82cosh(x) + 48 +--R / +--R 27 26 2 25 +--R 192sinh(x) + 4032cosh(x)sinh(x) + (40320cosh(x) + 1440)sinh(x) +--R + +--R 3 24 +--R (255360cosh(x) + 27936cosh(x))sinh(x) +--R + +--R 4 2 23 +--R (1149120cosh(x) + 257472cosh(x) + 5100)sinh(x) +--R + +--R 5 3 22 +--R (3907008cosh(x) + 1499328cosh(x) + 89052cosh(x))sinh(x) +--R + +--R 6 4 2 21 +--R (10418688cosh(x) + 6188832cosh(x) + 737496cosh(x) + 12078)sinh(x) +--R + +--R 7 5 3 +--R (22325760cosh(x) + 19255968cosh(x) + 3853272cosh(x) + 185142cosh(x)) +--R * +--R 20 +--R sinh(x) +--R + +--R 8 6 4 +--R 39070080cosh(x) + 46884096cosh(x) + 14252268cosh(x) +--R + +--R 2 +--R 1340484cosh(x) + 20880 +--R * +--R 19 +--R sinh(x) +--R + +--R 9 7 5 +--R 56434560cosh(x) + 91535616cosh(x) + 39692988cosh(x) +--R + +--R 3 +--R 6099828cosh(x) + 279288cosh(x) +--R * +--R 18 +--R sinh(x) +--R + +--R 10 8 6 +--R 67721472cosh(x) + 145675584cosh(x) + 86430624cosh(x) +--R + +--R 4 2 +--R 19584102cosh(x) + 1752492cosh(x) + 22206 +--R * +--R 17 +--R sinh(x) +--R + +--R 11 9 7 +--R 67721472cosh(x) + 191071296cosh(x) + 150806688cosh(x) +--R + +--R 5 3 +--R 47213646cosh(x) + 6857700cosh(x) + 266814cosh(x) +--R * +--R 16 +--R sinh(x) +--R + +--R 12 10 8 +--R 56434560cosh(x) + 208001664cosh(x) + 214358616cosh(x) +--R + +--R 6 4 2 +--R 88808496cosh(x) + 18767712cosh(x) + 1496136cosh(x) + 6348 +--R * +--R 15 +--R sinh(x) +--R + +--R 13 11 9 +--R 39070080cosh(x) + 188652672cosh(x) + 250953144cosh(x) +--R + +--R 7 5 3 +--R 133673328cosh(x) + 38193408cosh(x) + 5189208cosh(x) + 92148cosh(x) +--R * +--R 14 +--R sinh(x) +--R + +--R 14 12 10 +--R 22325760cosh(x) + 142698816cosh(x) + 243628944cosh(x) +--R + +--R 8 6 4 +--R 163783548cosh(x) + 60013008cosh(x) + 12439680cosh(x) +--R + +--R 2 +--R 562284cosh(x) - 9504 +--R * +--R 13 +--R sinh(x) +--R + +--R 15 13 11 +--R 10418688cosh(x) + 89861184cosh(x) + 196794000cosh(x) +--R + +--R 9 7 5 +--R 165216012cosh(x) + 74655792cosh(x) + 21820176cosh(x) +--R + +--R 3 +--R 1987476cosh(x) - 57408cosh(x) +--R * +--R 12 +--R sinh(x) +--R + +--R 16 14 12 +--R 3907008cosh(x) + 46884096cosh(x) + 132303288cosh(x) +--R + +--R 10 8 6 +--R 138140184cosh(x) + 74833344cosh(x) + 28935048cosh(x) +--R + +--R 4 2 +--R 4631100cosh(x) - 127872cosh(x) + 1020 +--R * +--R 11 +--R sinh(x) +--R + +--R 17 15 13 +--R 1149120cosh(x) + 20093184cosh(x) + 73833816cosh(x) +--R + +--R 11 9 7 +--R 95996472cosh(x) + 61213680cosh(x) + 29577432cosh(x) +--R + +--R 5 3 +--R 7598724cosh(x) - 55296cosh(x) - 18852cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 18 16 14 +--R 255360cosh(x) + 6976800cosh(x) + 34010784cosh(x) +--R + +--R 12 10 8 +--R 55381404cosh(x) + 41218056cosh(x) + 23578380cosh(x) +--R + +--R 6 4 2 +--R 9098844cosh(x) + 351744cosh(x) - 109920cosh(x) + 23118 +--R * +--R 9 +--R sinh(x) +--R + +--R 19 17 15 +--R 40320cosh(x) + 1920672cosh(x) + 12817824cosh(x) +--R + +--R 13 11 9 +--R 26388012cosh(x) + 22944792cosh(x) + 14760156cosh(x) +--R + +--R 7 5 3 +--R 8093988cosh(x) + 962400cosh(x) - 246624cosh(x) + 65358cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 20 18 16 +--R 4032cosh(x) + 404928cosh(x) + 3903036cosh(x) +--R + +--R 14 12 10 +--R 10283568cosh(x) + 10544928cosh(x) + 7290648cosh(x) +--R + +--R 8 6 4 2 +--R 5378532cosh(x) + 1321728cosh(x) - 293112cosh(x) + 63936cosh(x) +--R + +--R 24960 +--R * +--R 7 +--R sinh(x) +--R + +--R 21 19 17 15 +--R 192cosh(x) + 61632cosh(x) + 943596cosh(x) + 3226992cosh(x) +--R + +--R 13 11 9 +--R 3966528cosh(x) + 2857800cosh(x) + 2659932cosh(x) +--R + +--R 7 5 3 +--R 1162752cosh(x) - 187128cosh(x) - 1392cosh(x) + 59112cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 20 18 16 14 +--R 6048cosh(x) + 176472cosh(x) + 796374cosh(x) + 1201104cosh(x) +--R + +--R 12 10 8 6 +--R 898800cosh(x) + 968388cosh(x) + 695520cosh(x) - 39600cosh(x) +--R + +--R 4 2 +--R - 57492cosh(x) + 60252cosh(x) + 11166 +--R * +--R 5 +--R sinh(x) +--R + +--R 21 19 17 15 +--R 288cosh(x) + 24408cosh(x) + 149310cosh(x) + 286128cosh(x) +--R + +--R 13 11 9 7 +--R 231072cosh(x) + 255036cosh(x) + 284544cosh(x) + 30096cosh(x) +--R + +--R 5 3 +--R - 53508cosh(x) + 30612cosh(x) + 19350cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 20 18 16 14 +--R 2268cosh(x) + 20292cosh(x) + 52272cosh(x) + 49176cosh(x) +--R + +--R 12 10 8 6 +--R 47124cosh(x) + 77184cosh(x) + 27612cosh(x) - 23376cosh(x) +--R + +--R 4 2 +--R 3672cosh(x) + 13572cosh(x) + 2076 +--R * +--R 3 +--R sinh(x) +--R + +--R 21 19 17 15 +--R 108cosh(x) + 1908cosh(x) + 7128cosh(x) + 8328cosh(x) +--R + +--R 13 11 9 7 +--R 5676cosh(x) + 13056cosh(x) + 10620cosh(x) - 4320cosh(x) +--R + +--R 5 3 +--R - 1776cosh(x) + 5748cosh(x) + 2484cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 20 18 16 14 +--R 126cosh(x) + 684cosh(x) + 966cosh(x) + 372cosh(x) +--R + +--R 12 10 8 6 +--R 1344cosh(x) + 2352cosh(x) - 42cosh(x) - 1140cosh(x) +--R + +--R 4 2 +--R 414cosh(x) + 660cosh(x) + 96 +--R * +--R sinh(x) +--R + +--R 21 19 17 15 13 +--R 6cosh(x) + 36cosh(x) + 54cosh(x) + 12cosh(x) + 96cosh(x) +--R + +--R 11 9 7 5 3 +--R 240cosh(x) + 6cosh(x) - 204cosh(x) + 54cosh(x) + 252cosh(x) +--R + +--R 96cosh(x) +--R Type: Expression(Integer) +--E 478 + +--S 479 of 518 +t0992:= coth(3*x)*sinh(x) +--R +--R +--R (464) coth(3x)sinh(x) +--R Type: Expression(Integer) +--E 479 + +--S 480 of 518 +r0992:= -1/3*atan(2/3*sinh(x)*3^(1/2))*3^(1/2)+sinh(x) +--R +--R +--R +-+ +--R +-+ 2\|3 sinh(x) +--R - \|3 atan(------------) + 3sinh(x) +--R 3 +--R (465) ----------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 480 + +--S 481 of 518 +a0992:= integrate(t0992,x) +--R +--R +--R (466) +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R (- 2sinh(x) - 2cosh(x))atan(-------------------------) +--R 3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 2 +--R (2sinh(x) + 2cosh(x))atan(-----------------------------------------) +--R +-+ +-+ +--R \|3 sinh(x) - \|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|3 sinh(x) + 2\|3 cosh(x)sinh(x) + \|3 cosh(x) - \|3 +--R / +--R +-+ +-+ +--R 2\|3 sinh(x) + 2\|3 cosh(x) +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 518 +m0992:= a0992-r0992 +--R +--R +--R (467) +--R +-+ +--R 2\|3 sinh(x) +--R (2sinh(x) + 2cosh(x))atan(------------) +--R 3 +--R + +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R (- 2sinh(x) - 2cosh(x))atan(-------------------------) +--R 3 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 2 +--R (2sinh(x) + 2cosh(x))atan(-----------------------------------------) +--R +-+ +-+ +--R \|3 sinh(x) - \|3 cosh(x) +--R + +--R +-+ 2 +-+ 2 +-+ +--R - \|3 sinh(x) + \|3 cosh(x) - \|3 +--R / +--R +-+ +-+ +--R 2\|3 sinh(x) + 2\|3 cosh(x) +--R Type: Expression(Integer) +--E 482 + +--S 483 of 518 +d0992:= D(m0992,x) +--R +--R +--R (468) +--R 10 9 2 8 +--R 4sinh(x) + 24cosh(x)sinh(x) + (56cosh(x) + 63)sinh(x) +--R + +--R 3 7 2 6 +--R (56cosh(x) + 206cosh(x))sinh(x) + (234cosh(x) + 217)sinh(x) +--R + +--R 5 3 5 +--R (- 56cosh(x) + 46cosh(x) + 394cosh(x))sinh(x) +--R + +--R 6 4 2 4 +--R (- 56cosh(x) - 144cosh(x) + 275cosh(x) + 293)sinh(x) +--R + +--R 7 5 3 3 +--R (- 24cosh(x) - 134cosh(x) - 52cosh(x) + 254cosh(x))sinh(x) +--R + +--R 8 6 4 2 2 +--R (- 4cosh(x) - 26cosh(x) - 161cosh(x) + 128cosh(x) + 171)sinh(x) +--R + +--R 7 5 3 8 +--R (10cosh(x) - 22cosh(x) - 30cosh(x) + 42cosh(x))sinh(x) + cosh(x) +--R + +--R 6 4 2 +--R - 11cosh(x) - 53cosh(x) + 27cosh(x) + 36 +--R / +--R 9 8 2 7 +--R 8sinh(x) + 56cosh(x)sinh(x) + (168cosh(x) + 86)sinh(x) +--R + +--R 3 6 +--R (280cosh(x) + 346cosh(x))sinh(x) +--R + +--R 4 2 5 +--R (280cosh(x) + 638cosh(x) + 260)sinh(x) +--R + +--R 5 3 4 +--R (168cosh(x) + 722cosh(x) + 540cosh(x))sinh(x) +--R + +--R 6 4 2 3 +--R (56cosh(x) + 514cosh(x) + 696cosh(x) + 246)sinh(x) +--R + +--R 7 5 3 2 +--R (8cosh(x) + 206cosh(x) + 584cosh(x) + 330cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (42cosh(x) + 228cosh(x) + 234cosh(x) + 72)sinh(x) + 6cosh(x) +--R + +--R 5 3 +--R 60cosh(x) + 150cosh(x) + 72cosh(x) +--R Type: Expression(Integer) +--E 483 + +--S 484 of 518 +t0993:= coth(4*x)*sinh(x) +--R +--R +--R (469) coth(4x)sinh(x) +--R Type: Expression(Integer) +--E 484 + +--S 485 of 518 +r0993:= -1/4*atan(sinh(x))-1/4*atan(2^(1/2)*sinh(x))*2^(1/2)+sinh(x) +--R +--R +--R +-+ +-+ +--R - \|2 atan(\|2 sinh(x)) - atan(sinh(x)) + 4sinh(x) +--R (470) -------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 485 + +--S 486 of 518 +a0993:= integrate(t0993,x) +--R +--R +--R (471) +--R +-+ +-+ +--R \|2 sinh(x) + \|2 cosh(x) +--R (- sinh(x) - cosh(x))atan(-------------------------) +--R 2 +--R + +--R +-+ +-+ +--R (- \|2 sinh(x) - \|2 cosh(x))atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R (sinh(x) + cosh(x))atan(-----------------------------------------) +--R +-+ +-+ +--R \|2 sinh(x) - \|2 cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) - \|2 +--R / +--R +-+ +-+ +--R 2\|2 sinh(x) + 2\|2 cosh(x) +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 518 +m0993:= a0993-r0993 +--R +--R +--R (472) +--R +-+ +--R (2sinh(x) + 2cosh(x))atan(\|2 sinh(x)) +--R + +--R +-+ +-+ +--R \|2 sinh(x) + \|2 cosh(x) +--R (- 2sinh(x) - 2cosh(x))atan(-------------------------) +--R 2 +--R + +--R +-+ +-+ +--R (- 2\|2 sinh(x) - 2\|2 cosh(x))atan(sinh(x) + cosh(x)) +--R + +--R +-+ +-+ +--R (\|2 sinh(x) + \|2 cosh(x))atan(sinh(x)) +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1 +--R (2sinh(x) + 2cosh(x))atan(-----------------------------------------) +--R +-+ +-+ +--R \|2 sinh(x) - \|2 cosh(x) +--R + +--R +-+ 2 +-+ 2 +-+ +--R - 2\|2 sinh(x) + 2\|2 cosh(x) - 2\|2 +--R / +--R +-+ +-+ +--R 4\|2 sinh(x) + 4\|2 cosh(x) +--R Type: Expression(Integer) +--E 487 + +--S 488 of 518 +d0993:= D(m0993,x) +--R +--R +--R (473) +--R 14 13 2 12 +--R 4sinh(x) + 32cosh(x)sinh(x) + (108cosh(x) + 42)sinh(x) +--R + +--R 3 11 +--R (192cosh(x) + 228cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (168cosh(x) + 518cosh(x) + 140)sinh(x) +--R + +--R 3 9 +--R (608cosh(x) + 551cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 168cosh(x) + 308cosh(x) + 921cosh(x) + 228)sinh(x) +--R + +--R 7 5 3 7 +--R (- 192cosh(x) - 120cosh(x) + 768cosh(x) + 641cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (- 108cosh(x) - 292cosh(x) + 156cosh(x) + 805cosh(x) + 216)sinh(x) +--R + +--R 9 7 5 3 +--R (- 32cosh(x) - 192cosh(x) - 266cosh(x) + 449cosh(x) + 377cosh(x)) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 4cosh(x) - 62cosh(x) - 210cosh(x) - 39cosh(x) + 371cosh(x) +--R + +--R 122 +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (- 12cosh(x) - 40cosh(x) - 165cosh(x) + 118cosh(x) + 97cosh(x)) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R (- 2cosh(x) + 16cosh(x) - 65cosh(x) - 46cosh(x) + 95cosh(x) + 36) +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (11cosh(x) + 3cosh(x) - 31cosh(x) + 11cosh(x) + 6cosh(x))sinh(x) +--R + +--R 10 8 6 4 2 +--R cosh(x) - cosh(x) - 13cosh(x) - 5cosh(x) + 14cosh(x) + 4 +--R / +--R 13 12 2 11 +--R 8sinh(x) + 72cosh(x)sinh(x) + (288cosh(x) + 68)sinh(x) +--R + +--R 3 10 +--R (672cosh(x) + 436cosh(x))sinh(x) +--R + +--R 4 2 9 +--R (1008cosh(x) + 1288cosh(x) + 208)sinh(x) +--R + +--R 5 3 8 +--R (1008cosh(x) + 2328cosh(x) + 936cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (672cosh(x) + 2832cosh(x) + 2052cosh(x) + 296)sinh(x) +--R + +--R 7 5 3 6 +--R (288cosh(x) + 2368cosh(x) + 2940cosh(x) + 912cosh(x))sinh(x) +--R + +--R 8 6 4 2 5 +--R (72cosh(x) + 1336cosh(x) + 2892cosh(x) + 1500cosh(x) + 208)sinh(x) +--R + +--R 9 7 5 3 +--R (8cosh(x) + 488cosh(x) + 1908cosh(x) + 1684cosh(x) + 424cosh(x)) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 3 +--R (108cosh(x) + 828cosh(x) + 1272cosh(x) + 516cosh(x) + 68)sinh(x) +--R + +--R 9 7 5 3 +--R (12cosh(x) + 228cosh(x) + 608cosh(x) + 444cosh(x) + 92cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (36cosh(x) + 164cosh(x) + 204cosh(x) + 68cosh(x) + 8)sinh(x) +--R + +--R 9 7 5 3 +--R 4cosh(x) + 28cosh(x) + 60cosh(x) + 44cosh(x) + 8cosh(x) +--R Type: Expression(Integer) +--E 488 + +--S 489 of 518 +t0994:= coth(5*x)*sinh(x) +--R +--R +--R (474) coth(5x)sinh(x) +--R Type: Expression(Integer) +--E 489 + +--S 490 of 518 +r0994:= -(1-1/5*5^(1/2))*atan(2*2^(1/2)/(5-5^(1/2))^(1/2)*sinh(x))/_ + (10-2*5^(1/2))^(1/2)-_ + (1+1/5*5^(1/2))*atan(2*2^(1/2)/(5+5^(1/2))^(1/2)*sinh(x))/_ + (10+2*5^(1/2))^(1/2)+sinh(x) +--R +--R +--R (475) +--R +--------+ +--R +------------+ +-+ +-+ +-+ | +-+ +--R +-+ | +-+ (\|2 \|5 - 5\|2 )sinh(x)\|\|5 + 5 +--R (\|5 + 5)\|- 2\|5 + 10 atan(------------------------------------) +--R 10 +--R + +--R +----------+ +--R +----------+ +-+ +-+ +-+ | +-+ +--R +-+ | +-+ (\|2 \|5 + 5\|2 )sinh(x)\|- \|5 + 5 +--R (\|5 - 5)\|2\|5 + 10 atan(--------------------------------------) +--R 10 +--R + +--R +------------+ +----------+ +--R | +-+ | +-+ +--R 5sinh(x)\|- 2\|5 + 10 \|2\|5 + 10 +--R / +--R +------------+ +----------+ +--R | +-+ | +-+ +--R 5\|- 2\|5 + 10 \|2\|5 + 10 +--R Type: Expression(Integer) +--E 490 + +--S 491 of 518 +a0994:= integrate(t0994,x) +--R +--R +--R (476) +--R +--------+ +--R | +-+ +--R |\|5 + 1 +--R (2sinh(x) + 2cosh(x)) |-------- +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 1 +--R (5sinh(x) + 5cosh(x)) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +--------+ +--R | +-+ +--R |\|5 - 1 +--R (2sinh(x) + 2cosh(x)) |-------- +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 1 +--R (5sinh(x) + 5cosh(x)) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R / +--R 2sinh(x) + 2cosh(x) +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 518 +m0994:= a0994-r0994 +--R +--R +--R (477) +--R +------------+ +--R +-+ +-+ | +-+ +--R ((- 2\|5 - 10)sinh(x) + (- 2\|5 - 10)cosh(x))\|- 2\|5 + 10 +--R * +--R +--------+ +--R +-+ +-+ +-+ | +-+ +--R (\|2 \|5 - 5\|2 )sinh(x)\|\|5 + 5 +--R atan(------------------------------------) +--R 10 +--R + +--R +--------+ +--R +------------+ | +-+ +----------+ +--R | +-+ |\|5 + 1 | +-+ +--R (10sinh(x) + 10cosh(x))\|- 2\|5 + 10 |-------- \|2\|5 + 10 +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 + 1 +--R (5sinh(x) + 5cosh(x)) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +--------+ +--R +------------+ | +-+ +----------+ +--R | +-+ |\|5 - 1 | +-+ +--R (10sinh(x) + 10cosh(x))\|- 2\|5 + 10 |-------- \|2\|5 + 10 +--R | +-+ +--R \| 10\|5 +--R * +--R +--------+ +--R | +-+ +--R |\|5 - 1 +--R (5sinh(x) + 5cosh(x)) |-------- +--R | +-+ +--R \| 10\|5 +--R atan(-----------------------------------------) +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) - 1 +--R + +--R +----------+ +--R +-+ +-+ | +-+ +--R ((- 2\|5 + 10)sinh(x) + (- 2\|5 + 10)cosh(x))\|2\|5 + 10 +--R * +--R +----------+ +--R +-+ +-+ +-+ | +-+ +--R (\|2 \|5 + 5\|2 )sinh(x)\|- \|5 + 5 +--R atan(--------------------------------------) +--R 10 +--R + +--R +------------+ +----------+ +--R 2 2 | +-+ | +-+ +--R (- 5sinh(x) + 5cosh(x) - 5)\|- 2\|5 + 10 \|2\|5 + 10 +--R / +--R +------------+ +----------+ +--R | +-+ | +-+ +--R (10sinh(x) + 10cosh(x))\|- 2\|5 + 10 \|2\|5 + 10 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 518 +d0994:= D(m0994,x) +--R +--R +--R (478) +--R +-+ 11 +-+ 2 10 +--R 8\|2 cosh(x)sinh(x) + 72\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 +-+ +-+ +-+ 9 +--R (288\|2 cosh(x) + (- \|2 \|5 + 13\|2 )cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ +-+ +-+ 2 8 +--R (672\|2 cosh(x) + (- 9\|2 \|5 + 101\|2 )cosh(x) )sinh(x) +--R + +--R +-+ 5 +-+ +-+ +-+ 3 +--R 1008\|2 cosh(x) + (- 36\|2 \|5 + 348\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ +--R (- \|2 \|5 + 13\|2 )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ +-+ +-+ 4 +--R 1008\|2 cosh(x) + (- 84\|2 \|5 + 700\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 2 +--R (- 7\|2 \|5 + 75\|2 )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ +-+ +-+ 5 +--R 672\|2 cosh(x) + (- 126\|2 \|5 + 910\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 3 +-+ +-+ +-+ +--R (- 21\|2 \|5 + 185\|2 )cosh(x) + (- \|2 \|5 + 13\|2 )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ +-+ +-+ 6 +--R 288\|2 cosh(x) + (- 126\|2 \|5 + 798\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 4 +-+ +-+ +-+ 2 +--R (- 35\|2 \|5 + 255\|2 )cosh(x) + (- 5\|2 \|5 + 49\|2 )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ +-+ +-+ 7 +--R 72\|2 cosh(x) + (- 84\|2 \|5 + 476\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 5 +--R (- 35\|2 \|5 + 215\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 3 +-+ +-+ +-+ +--R (- 10\|2 \|5 + 74\|2 )cosh(x) + (- \|2 \|5 + 13\|2 )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ +-+ +-+ 8 +--R 8\|2 cosh(x) + (- 36\|2 \|5 + 188\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 6 +--R (- 21\|2 \|5 + 113\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 4 +-+ +-+ +-+ 2 +--R (- 10\|2 \|5 + 58\|2 )cosh(x) + (- 3\|2 \|5 + 23\|2 )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 9 +-+ +-+ +-+ 7 +--R (- 9\|2 \|5 + 45\|2 )cosh(x) + (- 7\|2 \|5 + 35\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 5 +-+ +-+ +-+ 3 +--R (- 5\|2 \|5 + 25\|2 )cosh(x) + (- 3\|2 \|5 + 15\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ +--R (- \|2 \|5 + 5\|2 )cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ +-+ +-+ 10 +-+ +-+ +-+ 8 +--R (- \|2 \|5 + 5\|2 )cosh(x) + (- \|2 \|5 + 5\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 6 +-+ +-+ +-+ 4 +--R (- \|2 \|5 + 5\|2 )cosh(x) + (- \|2 \|5 + 5\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 2 +--R (- \|2 \|5 + 5\|2 )cosh(x) +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R +-+ 11 +-+ 2 10 +--R 8\|2 cosh(x)sinh(x) + 72\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 +-+ +-+ +-+ 9 +--R (288\|2 cosh(x) + (\|2 \|5 + 13\|2 )cosh(x))sinh(x) +--R + +--R +-+ 4 +-+ +-+ +-+ 2 8 +--R (672\|2 cosh(x) + (9\|2 \|5 + 101\|2 )cosh(x) )sinh(x) +--R + +--R +-+ 5 +-+ +-+ +-+ 3 +--R 1008\|2 cosh(x) + (36\|2 \|5 + 348\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ +--R (\|2 \|5 + 13\|2 )cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 6 +-+ +-+ +-+ 4 +--R 1008\|2 cosh(x) + (84\|2 \|5 + 700\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 2 +--R (7\|2 \|5 + 75\|2 )cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 7 +-+ +-+ +-+ 5 +--R 672\|2 cosh(x) + (126\|2 \|5 + 910\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 3 +-+ +-+ +-+ +--R (21\|2 \|5 + 185\|2 )cosh(x) + (\|2 \|5 + 13\|2 )cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 8 +-+ +-+ +-+ 6 +--R 288\|2 cosh(x) + (126\|2 \|5 + 798\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 4 +-+ +-+ +-+ 2 +--R (35\|2 \|5 + 255\|2 )cosh(x) + (5\|2 \|5 + 49\|2 )cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 9 +-+ +-+ +-+ 7 +--R 72\|2 cosh(x) + (84\|2 \|5 + 476\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 5 +-+ +-+ +-+ 3 +--R (35\|2 \|5 + 215\|2 )cosh(x) + (10\|2 \|5 + 74\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ +--R (\|2 \|5 + 13\|2 )cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 10 +-+ +-+ +-+ 8 +--R 8\|2 cosh(x) + (36\|2 \|5 + 188\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 6 +-+ +-+ +-+ 4 +--R (21\|2 \|5 + 113\|2 )cosh(x) + (10\|2 \|5 + 58\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 2 +--R (3\|2 \|5 + 23\|2 )cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ +-+ +-+ 9 +-+ +-+ +-+ 7 +--R (9\|2 \|5 + 45\|2 )cosh(x) + (7\|2 \|5 + 35\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 5 +-+ +-+ +-+ 3 +--R (5\|2 \|5 + 25\|2 )cosh(x) + (3\|2 \|5 + 15\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ +--R (\|2 \|5 + 5\|2 )cosh(x) +--R * +--R sinh(x) +--R + +--R +-+ +-+ +-+ 10 +-+ +-+ +-+ 8 +--R (\|2 \|5 + 5\|2 )cosh(x) + (\|2 \|5 + 5\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 6 +-+ +-+ +-+ 4 +--R (\|2 \|5 + 5\|2 )cosh(x) + (\|2 \|5 + 5\|2 )cosh(x) +--R + +--R +-+ +-+ +-+ 2 +--R (\|2 \|5 + 5\|2 )cosh(x) +--R * +--R +------------+ +----------+ +--R | +-+ | +-+ +--R \|- 2\|5 + 10 \|- \|5 + 5 +--R + +--R 14 13 2 12 +--R 160sinh(x) + 1280cosh(x)sinh(x) + (4320cosh(x) + 200)sinh(x) +--R + +--R 3 11 +--R (7680cosh(x) + 1280cosh(x))sinh(x) +--R + +--R 4 2 10 +--R (6720cosh(x) + 3160cosh(x) + 50)sinh(x) +--R + +--R 3 9 +--R (2880cosh(x) - 320cosh(x))sinh(x) +--R + +--R 6 4 2 8 +--R (- 6720cosh(x) - 2800cosh(x) - 3050cosh(x) )sinh(x) +--R + +--R 7 5 3 7 +--R (- 7680cosh(x) - 11200cosh(x) - 9200cosh(x) - 820cosh(x))sinh(x) +--R + +--R 8 6 4 2 6 +--R (- 4320cosh(x) - 15120cosh(x) - 15100cosh(x) - 3660cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R - 1280cosh(x) - 11840cosh(x) - 15600cosh(x) - 7060cosh(x) +--R + +--R - 820cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 160cosh(x) - 5720cosh(x) - 10820cosh(x) - 7820cosh(x) +--R + +--R 2 +--R - 2020cosh(x) + 160 +--R * +--R 4 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 1600cosh(x) - 5200cosh(x) - 5500cosh(x) - 2200cosh(x) +--R + +--R - 500cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 200cosh(x) - 1750cosh(x) - 2500cosh(x) - 1400cosh(x) +--R + +--R 2 +--R - 700cosh(x) + 200 +--R * +--R 2 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (- 400cosh(x) - 700cosh(x) - 500cosh(x) - 300cosh(x) - 100cosh(x)) +--R * +--R sinh(x) +--R + +--R 10 8 6 4 2 +--R - 50cosh(x) - 100cosh(x) - 100cosh(x) - 100cosh(x) - 100cosh(x) + 50 +--R / +--R 13 12 2 11 +--R 320sinh(x) + 2880cosh(x)sinh(x) + (11520cosh(x) + 720)sinh(x) +--R + +--R 3 10 +--R (26880cosh(x) + 5840cosh(x))sinh(x) +--R + +--R 4 2 9 +--R (40320cosh(x) + 21120cosh(x) + 820)sinh(x) +--R + +--R 5 3 8 +--R (40320cosh(x) + 44800cosh(x) + 5300cosh(x))sinh(x) +--R + +--R 6 4 2 7 +--R (26880cosh(x) + 61600cosh(x) + 15200cosh(x) + 820)sinh(x) +--R + +--R 7 5 3 6 +--R (11520cosh(x) + 57120cosh(x) + 25600cosh(x) + 3660cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (2880cosh(x) + 35840cosh(x) + 28200cosh(x) + 7060cosh(x) + 820) +--R * +--R 5 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 320cosh(x) + 14720cosh(x) + 21320cosh(x) + 7820cosh(x) +--R + +--R 2020cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (3600cosh(x) + 11200cosh(x) + 5500cosh(x) + 2200cosh(x) + 500) +--R * +--R 3 +--R sinh(x) +--R + +--R 9 7 5 3 +--R (400cosh(x) + 4000cosh(x) + 2500cosh(x) + 1400cosh(x) + 700cosh(x)) +--R * +--R 2 +--R sinh(x) +--R + +--R 8 6 4 2 +--R (900cosh(x) + 700cosh(x) + 500cosh(x) + 300cosh(x) + 100)sinh(x) +--R + +--R 9 7 5 3 +--R 100cosh(x) + 100cosh(x) + 100cosh(x) + 100cosh(x) + 100cosh(x) +--R Type: Expression(Integer) +--E 493 + +--S 494 of 518 +t0995:= coth(6*x)*sinh(x) +--R +--R +--R (479) coth(6x)sinh(x) +--R Type: Expression(Integer) +--E 494 + +--S 495 of 518 +r0995:= -1/6*atan(sinh(x))-1/6*atan(2*sinh(x))-_ + 1/6*atan(2/3*sinh(x)*3^(1/2))*3^(1/2)+sinh(x) +--R +--R +--R +-+ +--R +-+ 2\|3 sinh(x) +--R - \|3 atan(------------) - atan(2sinh(x)) - atan(sinh(x)) + 6sinh(x) +--R 3 +--R (480) -------------------------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 495 + +--S 496 of 518 +a0995:= integrate(t0995,x) +--R +--R +--R (481) +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R (- 3sinh(x) - 3cosh(x))atan(-------------------------) +--R 3 +--R + +--R 2 2 +--R +-+ +-+ sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R (\|3 sinh(x) + \|3 cosh(x))atan(-------------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +-+ +-+ +--R (- 3\|3 sinh(x) - 3\|3 cosh(x))atan(sinh(x) + cosh(x)) +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 2 +--R (3sinh(x) + 3cosh(x))atan(-----------------------------------------) +--R +-+ +-+ +--R \|3 sinh(x) - \|3 cosh(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R 3\|3 sinh(x) + 6\|3 cosh(x)sinh(x) + 3\|3 cosh(x) - 3\|3 +--R / +--R +-+ +-+ +--R 6\|3 sinh(x) + 6\|3 cosh(x) +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 518 +m0995:= a0995-r0995 +--R +--R +--R (482) +--R +-+ +--R 2\|3 sinh(x) +--R (3sinh(x) + 3cosh(x))atan(------------) +--R 3 +--R + +--R +-+ +-+ +--R \|3 sinh(x) + \|3 cosh(x) +--R (- 3sinh(x) - 3cosh(x))atan(-------------------------) +--R 3 +--R + +--R +-+ +-+ +--R (\|3 sinh(x) + \|3 cosh(x))atan(2sinh(x)) +--R + +--R 2 2 +--R +-+ +-+ sinh(x) + 2cosh(x)sinh(x) + cosh(x) +--R (\|3 sinh(x) + \|3 cosh(x))atan(-------------------------------------) +--R sinh(x) - cosh(x) +--R + +--R +-+ +-+ +--R (- 3\|3 sinh(x) - 3\|3 cosh(x))atan(sinh(x) + cosh(x)) +--R + +--R +-+ +-+ +--R (\|3 sinh(x) + \|3 cosh(x))atan(sinh(x)) +--R + +--R 2 2 +--R sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 2 +--R (3sinh(x) + 3cosh(x))atan(-----------------------------------------) +--R +-+ +-+ +--R \|3 sinh(x) - \|3 cosh(x) +--R + +--R +-+ 2 +-+ 2 +-+ +--R - 3\|3 sinh(x) + 3\|3 cosh(x) - 3\|3 +--R / +--R +-+ +-+ +--R 6\|3 sinh(x) + 6\|3 cosh(x) +--R Type: Expression(Integer) +--E 497 + +--S 498 of 518 +d0995:= D(m0995,x) +--R +--R +--R (483) +--R 20 19 2 18 +--R 16sinh(x) + 192cosh(x)sinh(x) + (1040cosh(x) + 272)sinh(x) +--R + +--R 3 17 +--R (3328cosh(x) + 2512cosh(x))sinh(x) +--R + +--R 4 2 16 +--R (6864cosh(x) + 10448cosh(x) + 1555)sinh(x) +--R + +--R 5 3 15 +--R (9152cosh(x) + 25632cosh(x) + 11064cosh(x))sinh(x) +--R + +--R 6 4 2 14 +--R (6864cosh(x) + 40336cosh(x) + 36407cosh(x) + 4480)sinh(x) +--R + +--R 5 3 13 +--R (40112cosh(x) + 72264cosh(x) + 23941cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R (- 6864cosh(x) + 19536cosh(x) + 92751cosh(x) + 63182cosh(x) + 7523) +--R * +--R 12 +--R sinh(x) +--R + +--R 9 7 5 3 +--R - 9152cosh(x) - 8256cosh(x) + 73424cosh(x) + 104258cosh(x) +--R + +--R 29136cosh(x) +--R * +--R 11 +--R sinh(x) +--R + +--R 10 8 6 4 +--R - 6864cosh(x) - 24144cosh(x) + 23331cosh(x) + 111616cosh(x) +--R + +--R 2 +--R 62184cosh(x) + 7804 +--R * +--R 10 +--R sinh(x) +--R + +--R 11 9 7 5 +--R - 3328cosh(x) - 22480cosh(x) - 20080cosh(x) + 71971cosh(x) +--R + +--R 3 +--R 85808cosh(x) + 20250cosh(x) +--R * +--R 9 +--R sinh(x) +--R + +--R 12 10 8 6 +--R - 1040cosh(x) - 12560cosh(x) - 31879cosh(x) + 14518cosh(x) +--R + +--R 4 2 +--R 77323cosh(x) + 36836cosh(x) + 5049 +--R * +--R 8 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 192cosh(x) - 4576cosh(x) - 20648cosh(x) - 19780cosh(x) +--R + +--R 5 3 +--R 40544cosh(x) + 41316cosh(x) + 7060cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 16cosh(x) - 1104cosh(x) - 7451cosh(x) - 20400cosh(x) +--R + +--R 6 4 2 +--R 4040cosh(x) + 31372cosh(x) + 13639cosh(x) + 1968 +--R * +--R 6 +--R sinh(x) +--R + +--R 13 11 9 7 +--R - 176cosh(x) - 1368cosh(x) - 8549cosh(x) - 9760cosh(x) +--R + +--R 5 3 +--R 13064cosh(x) + 10996cosh(x) + 425cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R 14 12 10 8 +--R - 16cosh(x) - 27cosh(x) - 1478cosh(x) - 6711cosh(x) +--R + +--R 6 4 2 +--R - 260cosh(x) + 7185cosh(x) + 3242cosh(x) + 417 +--R * +--R 4 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 32cosh(x) + 162cosh(x) - 1456cosh(x) - 2148cosh(x) +--R + +--R 5 3 +--R 2212cosh(x) + 1250cosh(x) - 396cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R cosh(x) + 112cosh(x) + 16cosh(x) - 984cosh(x) - 323cosh(x) +--R + +--R 4 2 +--R 884cosh(x) + 474cosh(x) + 36 +--R * +--R 2 +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R 29cosh(x) + 112cosh(x) - 34cosh(x) - 172cosh(x) + 125cosh(x) +--R + +--R 3 +--R 12cosh(x) - 72cosh(x) +--R * +--R sinh(x) +--R + +--R 14 12 10 8 6 +--R 2cosh(x) + 9cosh(x) - 16cosh(x) - 78cosh(x) - 22cosh(x) +--R + +--R 4 2 +--R 69cosh(x) + 36cosh(x) +--R / +--R 19 18 2 17 +--R 32sinh(x) + 416cosh(x)sinh(x) + (2496cosh(x) + 448)sinh(x) +--R + +--R 3 16 +--R (9152cosh(x) + 4544cosh(x))sinh(x) +--R + +--R 4 2 15 +--R (22880cosh(x) + 21504cosh(x) + 2278)sinh(x) +--R + +--R 5 3 14 +--R (41184cosh(x) + 63232cosh(x) + 17838cosh(x))sinh(x) +--R + +--R 6 4 2 13 +--R (54912cosh(x) + 129472cosh(x) + 67220cosh(x) + 5710)sinh(x) +--R + +--R 7 5 3 12 +--R (54912cosh(x) + 195264cosh(x) + 162164cosh(x) + 33286cosh(x))sinh(x) +--R + +--R 8 6 4 2 +--R 41184cosh(x) + 222720cosh(x) + 278946cosh(x) + 101228cosh(x) +--R + +--R 7996 +--R * +--R 11 +--R sinh(x) +--R + +--R 9 7 5 3 +--R 22880cosh(x) + 193536cosh(x) + 359050cosh(x) + 205340cosh(x) +--R + +--R 32348cosh(x) +--R * +--R 10 +--R sinh(x) +--R + +--R 10 8 6 4 +--R 9152cosh(x) + 127296cosh(x) + 352440cosh(x) + 299794cosh(x) +--R + +--R 2 +--R 80184cosh(x) + 6532 +--R * +--R 9 +--R sinh(x) +--R + +--R 11 9 7 5 +--R 2496cosh(x) + 62272cosh(x) + 263864cosh(x) + 329178cosh(x) +--R + +--R 3 +--R 138792cosh(x) + 16020cosh(x) +--R * +--R 8 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 416cosh(x) + 22016cosh(x) + 148682cosh(x) + 276200cosh(x) +--R + +--R 4 2 +--R 172600cosh(x) + 32912cosh(x) + 3062 +--R * +--R 7 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 32cosh(x) + 5376cosh(x) + 61666cosh(x) + 174472cosh(x) +--R + +--R 5 3 +--R 160280cosh(x) + 49680cosh(x) + 3230cosh(x) +--R * +--R 6 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 832cosh(x) + 18292cosh(x) + 80914cosh(x) + 112048cosh(x) +--R + +--R 4 2 +--R 52248cosh(x) + 5852cosh(x) + 750 +--R * +--R 5 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 64cosh(x) + 3732cosh(x) + 26842cosh(x) + 57392cosh(x) +--R + +--R 5 3 +--R 41144cosh(x) + 9020cosh(x) - 90cosh(x) +--R * +--R 4 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 494cosh(x) + 6124cosh(x) + 20204cosh(x) + 22160cosh(x) +--R + +--R 4 2 +--R 7454cosh(x) + 36cosh(x) + 72 +--R * +--R 3 +--R sinh(x) +--R + +--R 13 11 9 7 +--R 38cosh(x) + 924cosh(x) + 4844cosh(x) + 8592cosh(x) +--R + +--R 5 3 +--R 5366cosh(x) + 948cosh(x) - 72cosh(x) +--R * +--R 2 +--R sinh(x) +--R + +--R 12 10 8 6 +--R 78cosh(x) + 696cosh(x) + 1860cosh(x) + 1680cosh(x) +--R + +--R 4 2 +--R 366cosh(x) - 72cosh(x) +--R * +--R sinh(x) +--R + +--R 13 11 9 7 5 +--R 6cosh(x) + 72cosh(x) + 276cosh(x) + 432cosh(x) + 294cosh(x) +--R + +--R 3 +--R 72cosh(x) +--R Type: Expression(Integer) +--E 498 + +--S 499 of 518 +t0996:= sech(2*x)*sinh(x) +--R +--R +--R (484) sech(2x)sinh(x) +--R Type: Expression(Integer) +--E 499 + +--S 500 of 518 +r0996:= -1/2*atanh(2^(1/2)*cosh(x))*2^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 atanh(\|2 cosh(x)) +--R (485) - ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 500 + +--S 501 of 518 +a0996:= integrate(t0996,x) +--R +--R +--R +-+ 2 +-+ 2 +-+ +--R \|2 sinh(x) + \|2 cosh(x) - 4cosh(x) + 2\|2 +--R log(----------------------------------------------) +--R 2 2 +--R sinh(x) + cosh(x) +--R (486) --------------------------------------------------- +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 518 +m0996:= a0996-r0996 +--R +--R +--R (487) +--R +-+ 2 +-+ 2 +-+ +--R \|2 sinh(x) + \|2 cosh(x) - 4cosh(x) + 2\|2 +-+ +--R log(----------------------------------------------) + 2atanh(\|2 cosh(x)) +--R 2 2 +--R sinh(x) + cosh(x) +--R ------------------------------------------------------------------------- +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 518 +d0996:= D(m0996,x) +--R +--R +--R (488) +--R +-+ 5 +-+ 2 +-+ 3 +--R - \|2 sinh(x) + (- 4\|2 cosh(x) + 4cosh(x) - \|2 )sinh(x) +--R + +--R +-+ 4 3 +-+ 2 +--R (5\|2 cosh(x) - 4cosh(x) - 5\|2 cosh(x) + 4cosh(x))sinh(x) +--R / +--R +-+ 2 +-+ 4 +--R (2\|2 cosh(x) - \|2 )sinh(x) +--R + +--R +-+ 4 3 +-+ 2 +-+ 2 +--R (4\|2 cosh(x) - 8cosh(x) + 2\|2 cosh(x) + 4cosh(x) - 2\|2 )sinh(x) +--R + +--R +-+ 6 5 +-+ 4 3 +-+ 2 +--R 2\|2 cosh(x) - 8cosh(x) + 3\|2 cosh(x) + 4cosh(x) - 2\|2 cosh(x) +--R Type: Expression(Integer) +--E 503 + +--S 504 of 518 +t0997:= sech(3*x)*sinh(x) +--R +--R +--R (489) sech(3x)sinh(x) +--R Type: Expression(Integer) +--E 504 + +--S 505 of 518 +r0997:= -1/3*atanh(-1+8/3*cosh(x)^2) +--R +--R +--R 2 +--R 8cosh(x) - 3 +--R atanh(-------------) +--R 3 +--R (490) - -------------------- +--R 3 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 518 +a0997:= integrate(t0997,x) +--R +--R +--R (491) +--R 2 2 +--R 2sinh(x) + 2cosh(x) - 1 2cosh(x) +--R log(-------------------------------------) - 2log(- -----------------) +--R 2 2 sinh(x) - cosh(x) +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R ---------------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 518 +m0997:= a0997-r0997 +--R +--R +--R (492) +--R 2 2 +--R 2sinh(x) + 2cosh(x) - 1 2cosh(x) +--R log(-------------------------------------) - 2log(- -----------------) +--R 2 2 sinh(x) - cosh(x) +--R sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R + +--R 2 +--R 8cosh(x) - 3 +--R 2atanh(-------------) +--R 3 +--R / +--R 6 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 518 +d0997:= D(m0997,x) +--R +--R +--R 3 3 +--R - 8cosh(x)sinh(x) + (8cosh(x) - 8cosh(x))sinh(x) +--R (493) ------------------------------------------------------- +--R 2 2 4 2 +--R (24cosh(x) - 18)sinh(x) + 24cosh(x) - 30cosh(x) + 9 +--R Type: Expression(Integer) +--E 508 + +--S 509 of 518 +t0998:= sech(4*x)*sinh(x) +--R +--R +--R (494) sech(4x)sinh(x) +--R Type: Expression(Integer) +--E 509 + +--S 510 of 518 +r0998:= 1/4*atanh(2*cosh(x)/(2-2^(1/2))^(1/2))*(2+2^(1/2))^(1/2)-_ + 1/4*atanh(2*cosh(x)/(2+2^(1/2))^(1/2))*(2-2^(1/2))^(1/2) +--R +--R +--R +--------+ +----------+ +--R | +-+ 2cosh(x) | +-+ 2cosh(x) +--R \|\|2 + 2 atanh(-------------) - \|- \|2 + 2 atanh(-----------) +--R +----------+ +--------+ +--R | +-+ | +-+ +--R \|- \|2 + 2 \|\|2 + 2 +--R (495) ----------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 518 +a0998:= integrate(t0998,x) +--R +--R +--R (496) +--R - +--R +--------+ +--R | +-+ +--R |\|2 + 1 +--R |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R log +--R +--------+ +--R | +-+ +--R +-+ +-+ |\|2 + 1 +--R ((4\|2 - 8)sinh(x) + (4\|2 - 8)cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|2 - 1 +--R |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R log +--R +--------+ +--R | +-+ +--R +-+ +-+ |\|2 - 1 +--R ((4\|2 + 8)sinh(x) + (4\|2 + 8)cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 +--R + +--R +--------+ +--R | +-+ +--R |\|2 - 1 +--R |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R log +--R +--------+ +--R | +-+ +--R +-+ +-+ |\|2 - 1 +--R ((- 4\|2 - 8)sinh(x) + (- 4\|2 - 8)cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 +--R + +--R +--------+ +--R | +-+ +--R |\|2 + 1 +--R |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R log +--R +--------+ +--R | +-+ +--R +-+ +-+ |\|2 + 1 +--R ((- 4\|2 + 8)sinh(x) + (- 4\|2 + 8)cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 511 + +--S 512 of 518 +m0998:= a0998-r0998 +--R +--R +--R (497) +--R - +--R +--------+ +--R | +-+ +--R |\|2 + 1 +--R 2 |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R log +--R +--------+ +--R | +-+ +--R +-+ +-+ |\|2 + 1 +--R ((4\|2 - 8)sinh(x) + (4\|2 - 8)cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 +--R + +--R - +--R +--------+ +--R | +-+ +--R |\|2 - 1 +--R 2 |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R log +--R +--------+ +--R | +-+ +--R +-+ +-+ |\|2 - 1 +--R ((4\|2 + 8)sinh(x) + (4\|2 + 8)cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 +--R + +--R +--------+ +--R | +-+ +--R |\|2 - 1 +--R 2 |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R log +--R +--------+ +--R | +-+ +--R +-+ +-+ |\|2 - 1 +--R ((- 4\|2 - 8)sinh(x) + (- 4\|2 - 8)cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 +--R + +--R +--------+ +--R | +-+ +--R |\|2 + 1 +--R 2 |-------- +--R | +-+ +--R \| 8\|2 +--R * +--R log +--R +--------+ +--R | +-+ +--R +-+ +-+ |\|2 + 1 +--R ((- 4\|2 + 8)sinh(x) + (- 4\|2 + 8)cosh(x)) |-------- +--R | +-+ +--R \| 8\|2 +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +--R \|2 sinh(x) + 2\|2 cosh(x)sinh(x) + \|2 cosh(x) + \|2 +--R + +--R +--------+ +----------+ +--R | +-+ 2cosh(x) | +-+ 2cosh(x) +--R - \|\|2 + 2 atanh(-------------) + \|- \|2 + 2 atanh(-----------) +--R +----------+ +--------+ +--R | +-+ | +-+ +--R \|- \|2 + 2 \|\|2 + 2 +--R / +--R 4 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 518 +d0998:= D(m0998,x) +--R +--R +--R (498) +--R +-+ 9 +-+ 8 +-+ 2 7 +--R - \|2 sinh(x) - 8\|2 cosh(x)sinh(x) - 28\|2 cosh(x) sinh(x) +--R + +--R +-+ 3 6 +-+ 4 5 +--R - 56\|2 cosh(x) sinh(x) - 70\|2 cosh(x) sinh(x) +--R + +--R +-+ 5 4 +-+ 6 3 +--R - 56\|2 cosh(x) sinh(x) - 28\|2 cosh(x) sinh(x) +--R + +--R +-+ 7 2 +-+ 8 +-+ +--R - 8\|2 cosh(x) sinh(x) + (- \|2 cosh(x) - \|2 )sinh(x) +--R * +--R +----------+ +--------+ +--R | +-+ | +-+ +--R \|- \|2 + 2 \|\|2 + 2 +--R + +--R 4 2 5 +--R (16cosh(x) - 16cosh(x) + 2)sinh(x) +--R + +--R 5 3 4 +--R (80cosh(x) - 80cosh(x) + 10cosh(x))sinh(x) +--R + +--R 6 4 2 3 +--R (160cosh(x) - 176cosh(x) + 36cosh(x) - 2)sinh(x) +--R + +--R 7 5 3 2 +--R (160cosh(x) - 208cosh(x) + 68cosh(x) - 6cosh(x))sinh(x) +--R + +--R 8 6 4 2 9 +--R (80cosh(x) - 128cosh(x) + 58cosh(x) - 6cosh(x) )sinh(x) + 16cosh(x) +--R + +--R 7 5 3 +--R - 32cosh(x) + 18cosh(x) - 2cosh(x) +--R / +--R 4 2 8 +--R (16cosh(x) - 16cosh(x) + 2)sinh(x) +--R + +--R 5 3 7 +--R (128cosh(x) - 128cosh(x) + 16cosh(x))sinh(x) +--R + +--R 6 4 2 6 +--R (448cosh(x) - 448cosh(x) + 56cosh(x) )sinh(x) +--R + +--R 7 5 3 5 +--R (896cosh(x) - 896cosh(x) + 112cosh(x) )sinh(x) +--R + +--R 8 6 4 4 +--R (1120cosh(x) - 1120cosh(x) + 140cosh(x) )sinh(x) +--R + +--R 9 7 5 3 +--R (896cosh(x) - 896cosh(x) + 112cosh(x) )sinh(x) +--R + +--R 10 8 6 2 +--R (448cosh(x) - 448cosh(x) + 56cosh(x) )sinh(x) +--R + +--R 11 9 7 12 +--R (128cosh(x) - 128cosh(x) + 16cosh(x) )sinh(x) + 16cosh(x) +--R + +--R 10 8 4 2 +--R - 16cosh(x) + 2cosh(x) + 16cosh(x) - 16cosh(x) + 2 +--R Type: Expression(Integer) +--E 513 + +--S 514 of 518 +t0999:= sech(5*x)*sinh(x) +--R +--R +--R (499) sech(5x)sinh(x) +--R Type: Expression(Integer) +--E 514 + +--S 515 of 518 +r0999:= -1/10*atanh(1/5*(3+8*sinh(x)^2)*5^(1/2))*5^(1/2)+1/10*log(cosh(x)^2)-_ + 1/20*log(1+12*sinh(x)^2+16*sinh(x)^4) +--R +--R +--R (500) +--R 4 2 2 +--R - log(16sinh(x) + 12sinh(x) + 1) + 2log(cosh(x) ) +--R + +--R +-+ 2 +-+ +--R +-+ 8\|5 sinh(x) + 3\|5 +--R - 2\|5 atanh(---------------------) +--R 5 +--R / +--R 20 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 518 +a0999:= integrate(t0999,x) +--R +--R +--R (501) +--R 5 +--R * +--R log +--R +-+ 4 +-+ 2 +-+ 2 +--R 4\|5 sinh(x) + (24\|5 cosh(x) - 4\|5 - 20)sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 4\|5 cosh(x) + (- 4\|5 - 20)cosh(x) + 7\|5 + 5 +--R / +--R 4 2 2 4 2 +--R 2sinh(x) + (12cosh(x) - 2)sinh(x) + 2cosh(x) - 2cosh(x) + 1 +--R + +--R - +--R +-+ +--R \|5 +--R * +--R log +--R 4 2 2 4 2 +--R 2sinh(x) + (12cosh(x) - 2)sinh(x) + 2cosh(x) - 2cosh(x) +--R + +--R 1 +--R / +--R 4 3 2 2 +--R sinh(x) - 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R - 4cosh(x) sinh(x) + cosh(x) +--R + +--R +-+ 2cosh(x) +--R 4\|5 log(- -----------------) +--R sinh(x) - cosh(x) +--R / +--R +-+ +--R 20\|5 +--R Type: Union(Expression(Integer),...) +--E 516 + +--S 517 of 518 +m0999:= a0999-r0999 +--R +--R +--R (502) +--R +-+ 4 2 +-+ 2 +--R \|5 log(16sinh(x) + 12sinh(x) + 1) - 2\|5 log(cosh(x) ) +--R + +--R 5 +--R * +--R log +--R +-+ 4 +-+ 2 +-+ 2 +--R 4\|5 sinh(x) + (24\|5 cosh(x) - 4\|5 - 20)sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 4\|5 cosh(x) + (- 4\|5 - 20)cosh(x) + 7\|5 + 5 +--R / +--R 4 2 2 4 2 +--R 2sinh(x) + (12cosh(x) - 2)sinh(x) + 2cosh(x) - 2cosh(x) + 1 +--R + +--R - +--R +-+ +--R \|5 +--R * +--R log +--R 4 2 2 4 2 +--R 2sinh(x) + (12cosh(x) - 2)sinh(x) + 2cosh(x) - 2cosh(x) +--R + +--R 1 +--R / +--R 4 3 2 2 +--R sinh(x) - 4cosh(x)sinh(x) + 6cosh(x) sinh(x) +--R + +--R 3 4 +--R - 4cosh(x) sinh(x) + cosh(x) +--R + +--R +-+ 2 +-+ +--R +-+ 2cosh(x) 8\|5 sinh(x) + 3\|5 +--R 4\|5 log(- -----------------) + 10atanh(---------------------) +--R sinh(x) - cosh(x) 5 +--R / +--R +-+ +--R 20\|5 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 518 +d0999:= D(m0999,x) +--R +--R +--R (503) +--R +-+ 11 +--R - 384\|5 cosh(x)sinh(x) +--R + +--R +-+ 3 +-+ 9 +--R (- 2048\|5 cosh(x) + (1888\|5 + 1920)cosh(x))sinh(x) +--R + +--R +-+ 5 +-+ 3 +--R 1280\|5 cosh(x) + (- 1792\|5 + 640)cosh(x) +--R + +--R +-+ +--R (704\|5 - 1600)cosh(x) +--R * +--R 7 +--R sinh(x) +--R + +--R +-+ 7 +-+ 5 +--R 1024\|5 cosh(x) + (- 3136\|5 - 1920)cosh(x) +--R + +--R +-+ 3 +-+ +--R (2848\|5 + 2720)cosh(x) + (- 1416\|5 - 2920)cosh(x) +--R * +--R 5 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +--R 128\|5 cosh(x) + (- 1024\|5 - 640)cosh(x) +--R + +--R +-+ 5 +-+ 3 +--R (2560\|5 + 3840)cosh(x) + (- 1840\|5 - 4080)cosh(x) +--R + +--R +-+ +--R (128\|5 + 640)cosh(x) +--R * +--R 3 +--R sinh(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 32\|5 cosh(x) + (32\|5 + 160)cosh(x) + (56\|5 - 40)cosh(x) +--R + +--R +-+ 3 +-+ +--R (- 32\|5 - 160)cosh(x) + (- 24\|5 + 40)cosh(x) +--R * +--R sinh(x) +--R / +--R +-+ 12 +-+ 2 +-+ 10 +--R 640\|5 sinh(x) + (7680\|5 cosh(x) - 800\|5 - 3200)sinh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (24320\|5 cosh(x) + (- 3200\|5 - 22400)cosh(x) + 1160\|5 + 1600) +--R * +--R 8 +--R sinh(x) +--R + +--R +-+ 6 +-+ 4 +--R 7680\|5 cosh(x) + (9280\|5 - 22400)cosh(x) +--R + +--R +-+ 2 +-+ +--R (3680\|5 - 5600)cosh(x) + 40\|5 + 400 +--R * +--R 6 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R 640\|5 cosh(x) + (4480\|5 - 3200)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (- 3120\|5 - 12800)cosh(x) + (5440\|5 + 4600)cosh(x) - 390\|5 +--R + +--R - 1150 +--R * +--R 4 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +--R 480\|5 cosh(x) + (- 480\|5 - 2400)cosh(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R (1000\|5 + 1600)cosh(x) + (- 460\|5 - 1100)cosh(x) + 330\|5 + 150 +--R * +--R 2 +--R sinh(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 40\|5 cosh(x) + (- 80\|5 - 200)cosh(x) + (130\|5 + 250)cosh(x) +--R + +--R +-+ 2 +-+ +--R (- 90\|5 - 150)cosh(x) + 35\|5 + 25 +--R Type: Expression(Integer) +--E 518 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richhyper900-999.input.pdf b/src/axiom-website/CATS/richhyper900-999.input.pdf new file mode 100644 index 0000000..3e10e7a Binary files /dev/null and b/src/axiom-website/CATS/richhyper900-999.input.pdf differ diff --git a/src/axiom-website/CATS/richintfunc000-032.input.pamphlet b/src/axiom-website/CATS/richintfunc000-032.input.pamphlet new file mode 100644 index 0000000..06e44ff --- /dev/null +++ b/src/axiom-website/CATS/richintfunc000-032.input.pamphlet @@ -0,0 +1,1788 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richintfunc000-032.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richintfunc000-032.output +)spool richintfunc000-032.output +)set message auto off +)clear all + +--S 1 of 165 +t0000:= x^m*Ei(b*x) +--R +--R +--R m +--R (1) Ei(b x)x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 165 +r0000:= -1/b/(1+m)*(-x^(1+m)*Ei(b*x)*b+x^m*(-b*x)^(-m)*Gamma(1+m,-b*x)) +--R +--R +--R - m m _ m + 1 +--R - (- b x) x | (m + 1,- b x) + b Ei(b x)x +--R (2) ----------------------------------------------- +--R b m + b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 165 +--a0000:= integrate(t0000,x) +--E 3 + +--S 4 of 165 +--m0000:= a0000-r0000 +--E 4 + +--S 5 of 165 +--d0000:= D(m0000,x) +--E 5 + +--S 6 of 165 +t0001:= exp(1)^(b*x)*Ei(b*x)/x^3 +--R +--R +--R b x +--R Ei(b x)%e +--R (3) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 165 +r0001:= -1/4*(exp(2*b*x)+4*exp(2*b*x)*b*x+2*Ei(b*x)*exp(b*x)+_ + 2*Ei(b*x)*exp(b*x)*b*x-x^2*Ei(b*x)^2*b^2-8*b^2*Ei(2*b*x)*x^2)/x^2 +--R +--R +--R (4) +--R 2b x b x 2 2 2 2 2 +--R (- 4b x - 1)%e + (- 2b x - 2)Ei(b x)%e + 8b x Ei(2b x) + b x Ei(b x) +--R ---------------------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 7 + +--S 8 of 165 +--a0001:= integrate(t0001,x) +--E 8 + +--S 9 of 165 +--m0001:= a0001-r0001 +--E 9 + +--S 10 of 165 +--d0001:= D(m0001,x) +--E 10 + +--S 11 of 165 +t0002:= exp(1)^(b*x)*Ei(b*x)/x^2 +--R +--R +--R b x +--R Ei(b x)%e +--R (5) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 165 +r0002:= -1/2*(2*exp(2*b*x)+2*Ei(b*x)*exp(b*x)-x*Ei(b*x)^2*b-4*b*Ei(2*b*x)*x)/x +--R +--R +--R 2b x b x 2 +--R - 2%e - 2Ei(b x)%e + 4b x Ei(2b x) + b x Ei(b x) +--R (6) -------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 12 + +--S 13 of 165 +--a0002:= integrate(t0002,x) +--E 13 + +--S 14 of 165 +--m0002:= a0002-r0002 +--E 14 + +--S 15 of 165 +--d0002:= D(m0002,x) +--E 15 + +--S 16 of 165 +t0003:= x*exp(1)^(a+b*x)*Ei(c+d*x) +--R +--R +--R b x + a +--R (7) x Ei(d x + c)%e +--R Type: Expression(Integer) +--E 16 + +--S 17 of 165 +r0003:= -exp(1)^(a+c+(b+d)*x)/b/(b+d)-exp(1)^(a+b*x)*(1-b*x)*Ei(c+d*x)/b^2+_ + (b*c+d)*exp(1)^(a-b*c/d)*Ei((b+d)*(c+d*x)/d)/b^2/d +--R +--R +--R (8) +--R (d + b)x + c + a 2 2 2 b x + a +--R - b d %e + ((b d + b d)x - d - b d)Ei(d x + c)%e +--R + +--R a d - b c +--R 2 --------- +--R 2 2 (d + b d)x + c d + b c d +--R (d + (b c + b)d + b c)Ei(-----------------------)%e +--R d +--R / +--R 2 2 3 +--R b d + b d +--R Type: Expression(Integer) +--E 17 + +--S 18 of 165 +--a0003:= integrate(t0003,x) +--E 18 + +--S 19 of 165 +--m0003:= a0003-r0003 +--E 19 + +--S 20 of 165 +--d0003:= D(m0003,x) +--E 20 + +--S 21 of 165 +t0004:= x^2*exp(1)^(a+b*x)*Ei(c+d*x) +--R +--R +--R 2 b x + a +--R (9) x Ei(d x + c)%e +--R Type: Expression(Integer) +--E 21 + +--S 22 of 165 +r0004:= exp(1)^(a+c+(b+d)*x)/b/(b+d)^2+2*exp(1)^(a+c+(b+d)*x)/b^2/(b+d)+_ + c*exp(1)^(a+c+(b+d)*x)/b/d/(b+d)-exp(1)^(a+c+(b+d)*x)*_ + x/b/(b+d)+exp(1)^(a+b*x)*(2-2*b*x+b^2*x^2)*Ei(c+d*x)/b^3-_ + (b^2*c^2+2*b*c*d+2*d^2)*exp(1)^(a-b*c/d)*Ei((b+d)*(c+d*x)/d)/b^3/d^2 +--R +--R +--R (10) +--R 2 3 3 2 3 2 2 2 3 (d + b)x + c + a +--R ((- b d - b d )x + 2b d + (b c + 3b )d + b c d)%e +--R + +--R 2 4 3 3 4 2 2 4 2 3 3 2 4 3 +--R (b d + 2b d + b d )x + (- 2b d - 4b d - 2b d )x + 2d + 4b d +--R + +--R 2 2 +--R 2b d +--R * +--R b x + a +--R Ei(d x + c)%e +--R + +--R 4 3 2 2 2 2 2 3 2 3 +--R - 2d + (- 2b c - 4b)d + (- b c - 4b c - 2b )d + (- 2b c - 2b c)d +--R + +--R 4 2 +--R - b c +--R * +--R a d - b c +--R 2 --------- +--R (d + b d)x + c d + b c d +--R Ei(-----------------------)%e +--R d +--R / +--R 3 4 4 3 5 2 +--R b d + 2b d + b d +--R Type: Expression(Integer) +--E 22 + +--S 23 of 165 +--a0004:= integrate(t0004,x) +--E 23 + +--S 24 of 165 +--m0004:= a0004-r0004 +--E 24 + +--S 25 of 165 +--d0004:= D(m0004,x) +--E 25 + +--S 26 of 165 +t0005:= x^m*Si(b*x) +--R +--R +--R m +--R (11) Si(b x)x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 165 +r0005:= 1/2*(x^m*(-%i*b*x)^(-m)*Gamma(1+m,-%i*b*x)+x^m*(%i*b*x)^(-m)*_ + Gamma(1+m,%i*b*x)+2*x^(1+m)*Si(b*x)*b)/b/(1+m) +--R +--R +--R (12) +--R m - m _ - m m _ +--R x (%i b x) | (m + 1,%i b x) + (- %i b x) x | (m + 1,- %i b x) +--R + +--R m + 1 +--R 2b Si(b x)x +--R / +--R 2b m + 2b +--R Type: Expression(Complex(Integer)) +--E 27 + +--S 28 of 165 +--a0005:= integrate(t0005,x) +--E 28 + +--S 29 of 165 +--m0005:= a0005-r0005 +--E 29 + +--S 30 of 165 +--d0005:= D(m0005,x) +--E 30 + +--S 31 of 165 +t0006:= sin(b*x)*Si(b*x)/x^3 +--R +--R +--R Si(b x)sin(b x) +--R (13) --------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 165 +r0006:= -1/4*(-4*b^2*Ci(2*b*x)*x^2+2*x*cos(b*x)*sin(b*x)*b+1-_ + cos(b*x)^2+x*b*sin(2*b*x)+2*x*cos(b*x)*Si(b*x)*b+2*sin(b*x)*Si(b*x)+_ + x^2*Si(b*x)^2*b^2)/x^2 +--R +--R +--R (14) +--R 2 +--R - b x sin(2b x) + (- 2b x cos(b x) - 2Si(b x))sin(b x) + cos(b x) +--R + +--R 2 2 2 2 2 +--R - 2b x Si(b x)cos(b x) - b x Si(b x) + 4b x Ci(2b x) - 1 +--R / +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 32 + +--S 33 of 165 +a0006:= integrate(t0006,x) +--R +--R +--R x +--R ++ Si(%A b)sin(%A b) +--R (15) | ----------------- d%A +--R ++ 3 +--R %A +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 165 +--m0006:= a0006-r0006 +--E 34 + +--S 35 of 165 +--d0006:= D(m0006,x) +--E 35 + +--S 36 of 165 +t0007:= x*sin(a+b*x)*Si(c+d*x) +--R +--R +--R (16) x Si(d x + c)sin(b x + a) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 165 +r0007:= 1/2*cos(a-c+(b-d)*x)/b/(b-d)-1/2*cos(a+c+(b+d)*x)/b/(b+d)-_ + 1/2*cos(a-b*c/d)*Ci((b-d)*(c+d*x)/d)/b^2+_ + 1/2*cos(a-b*c/d)*Ci((b+d)*(c+d*x)/d)/b^2+_ + 1/2*c*Ci((b-d)*(c+d*x)/d)*sin(a-b*c/d)/b/d-_ + 1/2*c*Ci((b+d)*(c+d*x)/d)*sin(a-b*c/d)/b/d-x*cos(a+b*x)*Si(c+d*x)/b+_ + sin(a+b*x)*Si(c+d*x)/b^2+1/2*c*cos(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b/d+_ + 1/2*sin(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b^2-_ + 1/2*c*cos(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b/d-_ + 1/2*sin(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b^2 +--R +--R +--R (17) +--R 3 2 +--R (2d - 2b d)Si(d x + c)sin(b x + a) +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d - b d)x + c d - b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (- b c d + b c)Ci(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (- d + b d)x - c d + b c +--R (b c d - b c)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R sin(---------) +--R d +--R + +--R 2 2 2 2 +--R (- b d + b d)cos((d + b)x + c + a) + (- b d - b d)cos((d - b)x + c - a) +--R + +--R 3 3 +--R (- 2b d + 2b d)x Si(d x + c)cos(b x + a) +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (- b c d + b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d - b d)x + c d - b c +--R (- b c d + b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (d - b d)Ci(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (- d + b d)x - c d + b c +--R (- d + b d)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R cos(---------) +--R d +--R / +--R 2 3 4 +--R 2b d - 2b d +--R Type: Expression(Integer) +--E 37 + +--S 38 of 165 +a0007:= integrate(t0007,x) +--R +--R +--R x +--R ++ +--R (18) | %A Si(%A d + c)sin(%A b + a)d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 165 +--m0007:= a0007-r0007 +--E 39 + +--S 40 of 165 +--d0007:= D(m0007,x) +--E 40 + +--S 41 of 165 +t0008:= cos(b*x)*Si(b*x)/x^2 +--R +--R +--R Si(b x)cos(b x) +--R (19) --------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 165 +r0008:= -1/2*(-2*b*Ci(2*b*x)*x+sin(2*b*x)+2*cos(b*x)*Si(b*x)+x*Si(b*x)^2*b)/x +--R +--R +--R 2 +--R - sin(2b x) - 2Si(b x)cos(b x) - b x Si(b x) + 2b x Ci(2b x) +--R (20) ------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 165 +a0008:= integrate(t0008,x) +--R +--R +--R x +--R ++ Si(%A b)cos(%A b) +--R (21) | ----------------- d%A +--R ++ 2 +--R %A +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 165 +--m0008:= a0008-r0008 +--E 44 + +--S 45 of 165 +--d0008:= D(m0008,x) +--E 45 + +--S 46 of 165 +t0009:= x*cos(a+b*x)*Si(c+d*x) +--R +--R +--R (22) x Si(d x + c)cos(b x + a) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 165 +r0009:= 1/2*c*cos(a-b*c/d)*Ci((b-d)*(c+d*x)/d)/b/d-_ + 1/2*c*cos(a-b*c/d)*Ci((b+d)*(c+d*x)/d)/b/d+_ + 1/2*Ci((b-d)*(c+d*x)/d)*sin(a-b*c/d)/b^2-_ + 1/2*Ci((b+d)*(c+d*x)/d)*sin(a-b*c/d)/b^2-_ + 1/2*sin(a-c+(b-d)*x)/b/(b-d)+1/2*sin(a+c+(b+d)*x)/b/_ + (b+d)+cos(a+b*x)*Si(c+d*x)/b^2+x*sin(a+b*x)*Si(c+d*x)/b+_ + 1/2*cos(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b^2-_ + 1/2*c*sin(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b/d-_ + 1/2*cos(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b^2+_ + 1/2*c*sin(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b/d +--R +--R +--R (23) +--R 2 2 2 2 +--R (b d - b d)sin((d + b)x + c + a) + (- b d - b d)sin((d - b)x + c - a) +--R + +--R 3 3 +--R (2b d - 2b d)x Si(d x + c)sin(b x + a) +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (b c d - b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d - b d)x + c d - b c +--R (b c d - b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Ci(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (- d + b d)x - c d + b c +--R (d - b d)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R sin(---------) +--R d +--R + +--R 3 2 +--R (2d - 2b d)Si(d x + c)cos(b x + a) +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d - b d)x + c d - b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (- b c d + b c)Ci(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (- d + b d)x - c d + b c +--R (b c d - b c)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R cos(---------) +--R d +--R / +--R 2 3 4 +--R 2b d - 2b d +--R Type: Expression(Integer) +--E 47 + +--S 48 of 165 +a0009:= integrate(t0009,x) +--R +--R +--R x +--R ++ +--R (24) | %A Si(%A d + c)cos(%A b + a)d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 165 +--m0009:= a0009-r0009 +--E 49 + +--S 50 of 165 +--d0009:= D(m0009,x) +--E 50 + +--S 51 of 165 +t0010:= x^m*Ci(b*x) +--R +--R +--R m +--R (25) Ci(b x)x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 165 +r0010:= 1/2*(%i*x^m*(-%i*b*x)^(-m)*Gamma(1+m,-%i*b*x)-%i*x^m*(%i*b*x)^(-m)*_ + Gamma(1+m,%i*b*x)+2*x^(1+m)*Ci(b*x)*b)/b/(1+m) +--R +--R +--R (26) +--R m - m _ - m m _ +--R - %i x (%i b x) | (m + 1,%i b x) + %i (- %i b x) x | (m + 1,- %i b x) +--R + +--R m + 1 +--R 2b Ci(b x)x +--R / +--R 2b m + 2b +--R Type: Expression(Complex(Integer)) +--E 52 + +--S 53 of 165 +a0010:= integrate(t0010,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 53 + +--S 54 of 165 +--m0010:= a0010-r0010 +--E 54 + +--S 55 of 165 +--d0010:= D(m0010,x) +--E 55 + +--S 56 of 165 +t0011:= Ci(b*x)*sin(b*x)/x^2 +--R +--R +--R Ci(b x)sin(b x) +--R (27) --------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 165 +r0011:= -1/2*(-x*Ci(b*x)^2*b-2*b*Ci(2*b*x)*x+2*sin(b*x)*Ci(b*x)+sin(2*b*x))/x +--R +--R +--R 2 +--R - sin(2b x) - 2Ci(b x)sin(b x) + 2b x Ci(2b x) + b x Ci(b x) +--R (28) ------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 165 +a0011:= integrate(t0011,x) +--R +--R +--R x +--R ++ Ci(%A b)sin(%A b) +--R (29) | ----------------- d%A +--R ++ 2 +--R %A +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 165 +--m0011:= a0011-r0011 +--E 59 + +--S 60 of 165 +--d0011:= D(m0011,x) +--E 60 + +--S 61 of 165 +t0012:= x*sin(a+b*x)*Ci(c+d*x) +--R +--R +--R (30) x Ci(d x + c)sin(b x + a) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 165 +r0012:= -x*cos(a+b*x)*Ci(c+d*x)/b-1/2*c*cos(a-b*c/d)*Ci((b-d)*(c+d*x)/d)/b/d-_ + 1/2*c*cos(a-b*c/d)*Ci((b+d)*(c+d*x)/d)/b/d-1/2*Ci((b-d)*(c+d*x)/d)*_ + sin(a-b*c/d)/b^2-1/2*Ci((b+d)*(c+d*x)/d)*sin(a-b*c/d)/b^2+Ci(c+d*x)*_ + sin(a+b*x)/b^2+1/2*sin(a-c+(b-d)*x)/b/(b-d)+1/2*sin(a+c+(b+d)*x)/_ + b/(b+d)-1/2*cos(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b^2+1/2*c*sin(a-b*c/d)*_ + Si((b-d)*(c+d*x)/d)/b/d-1/2*cos(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b^2+_ + 1/2*c*sin(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b/d +--R +--R +--R (31) +--R 2 2 2 2 +--R (b d - b d)sin((d + b)x + c + a) + (b d + b d)sin((d - b)x + c - a) +--R + +--R 3 2 +--R (2d - 2b d)Ci(d x + c)sin(b x + a) +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (b c d - b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d - b d)x + c d - b c +--R (- b c d + b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Ci(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (- d + b d)x - c d + b c +--R (- d + b d)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R sin(---------) +--R d +--R + +--R 3 3 +--R (- 2b d + 2b d)x Ci(d x + c)cos(b x + a) +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d - b d)x + c d - b c +--R (d - b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (- b c d + b c)Ci(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (- d + b d)x - c d + b c +--R (- b c d + b c)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R cos(---------) +--R d +--R / +--R 2 3 4 +--R 2b d - 2b d +--R Type: Expression(Integer) +--E 62 + +--S 63 of 165 +a0012:= integrate(t0012,x) +--R +--R +--R x +--R ++ +--R (32) | %A Ci(%A d + c)sin(%A b + a)d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 165 +--m0012:= a0012-r0012 +--E 64 + +--S 65 of 165 +--d0012:= D(m0012,x) +--E 65 + +--S 66 of 165 +t0013:= cos(b*x)*Ci(b*x)/x^3 +--R +--R +--R Ci(b x)cos(b x) +--R (33) --------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 165 +r0013:= 1/4*(-cos(b*x)^2-2*cos(b*x)*Ci(b*x)-x^2*Ci(b*x)^2*b^2-_ + 4*b^2*Ci(2*b*x)*x^2+2*x*cos(b*x)*sin(b*x)*b+_ + 2*x*Ci(b*x)*sin(b*x)*b+x*b*sin(2*b*x))/x^2 +--R +--R +--R (34) +--R 2 +--R b x sin(2b x) + (2b x cos(b x) + 2b x Ci(b x))sin(b x) - cos(b x) +--R + +--R 2 2 2 2 2 +--R - 2Ci(b x)cos(b x) - 4b x Ci(2b x) - b x Ci(b x) +--R / +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 67 + +--S 68 of 165 +a0013:= integrate(t0013,x) +--R +--R +--R x +--R ++ Ci(%A b)cos(%A b) +--R (35) | ----------------- d%A +--R ++ 3 +--R %A +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 165 +--m0013:= a0013-r0013 +--E 69 + +--S 70 of 165 +--d0013:= D(m0013,x) +--E 70 + +--S 71 of 165 +t0014:= x*cos(a+b*x)*Ci(c+d*x) +--R +--R +--R (36) x Ci(d x + c)cos(b x + a) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 165 +r0014:= 1/2*cos(a-c+(b-d)*x)/b/(b-d)+1/2*cos(a+c+(b+d)*x)/b/(b+d)+_ + cos(a+b*x)*Ci(c+d*x)/b^2-1/2*cos(a-b*c/d)*Ci((b-d)*(c+d*x)/d)/b^2-_ + 1/2*cos(a-b*c/d)*Ci((b+d)*(c+d*x)/d)/b^2+_ + 1/2*c*Ci((b-d)*(c+d*x)/d)*sin(a-b*c/d)/b/d+_ + 1/2*c*Ci((b+d)*(c+d*x)/d)*sin(a-b*c/d)/b/d+_ + x*Ci(c+d*x)*sin(a+b*x)/b+1/2*c*cos(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b/d+_ + 1/2*sin(a-b*c/d)*Si((b-d)*(c+d*x)/d)/b^2+_ + 1/2*c*cos(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b/d+_ + 1/2*sin(a-b*c/d)*Si((b+d)*(c+d*x)/d)/b^2 +--R +--R +--R (37) +--R 3 3 +--R (2b d - 2b d)x Ci(d x + c)sin(b x + a) +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (d - b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d - b d)x + c d - b c +--R (- d + b d)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (b c d - b c)Ci(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (- d + b d)x - c d + b c +--R (b c d - b c)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R sin(---------) +--R d +--R + +--R 2 2 2 2 +--R (b d - b d)cos((d + b)x + c + a) + (- b d - b d)cos((d - b)x + c - a) +--R + +--R 3 2 +--R (2d - 2b d)Ci(d x + c)cos(b x + a) +--R + +--R 2 +--R 2 3 (d + b d)x + c d + b c +--R (b c d - b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 2 3 (d - b d)x + c d - b c +--R (- b c d + b c)Si(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (d + b d)x + c d + b c +--R (- d + b d)Ci(-----------------------) +--R d +--R + +--R 2 +--R 3 2 (- d + b d)x - c d + b c +--R (- d + b d)Ci(-------------------------) +--R d +--R * +--R a d - b c +--R cos(---------) +--R d +--R / +--R 2 3 4 +--R 2b d - 2b d +--R Type: Expression(Integer) +--E 72 + +--S 73 of 165 +a0014:= integrate(t0014,x) +--R +--R +--R x +--R ++ +--R (38) | %A Ci(%A d + c)cos(%A b + a)d%A +--R ++ +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 165 +--m0014:= a0014-r0014 +--E 74 + +--S 75 of 165 +--d0014:= D(m0014,x) +--E 75 + +--S 76 of 165 +t0015:= x^m*Shi(b*x) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 76 + +--S 77 of 165 +r0015:= -1/2/b/(1+m)*(x^m*(b*x)^(-m)*Gamma(1+m,b*x)+x^m*(-b*x)^(-m)*_ + Gamma(1+m,-b*x)-2*x^(1+m)*Shi(b*x)*b) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 165 +--a0015:= integrate(t0015,x) +--E 78 + +--S 79 of 165 +--m0015:= a0015-r0015 +--E 79 + +--S 80 of 165 +--d0015:= D(m0015,x) +--E 80 + +--S 81 of 165 +t0016:= Shi(a+b*x)/x^3 +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 81 + +--S 82 of 165 +r0016:= 1/2*(b^2*cosh(a)*Chi(b*x)*a*x^2-b^2*Chi(b*x)*sinh(a)*x^2-_ + b*sinh(a+b*x)*a*x-b^2*cosh(a)*Shi(b*x)*x^2+b^2*sinh(a)*_ + Shi(b*x)*a*x^2+b^2*Shi(a+b*x)*x^2-Shi(a+b*x)*a^2)/a^2/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 165 +--a0016:= integrate(t0016,x) +--E 83 + +--S 84 of 165 +--m0016:= a0016-r0016 +--E 84 + +--S 85 of 165 +--d0016:= D(m0016,x) +--E 85 + +--S 86 of 165 +t0017:= Shi(a+b*x)/x^2 +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 86 + +--S 87 of 165 +r0017:= (b*Chi(b*x)*sinh(a)*x+b*cosh(a)*Shi(b*x)*x-Shi(a+b*x)*b*x-_ + Shi(a+b*x)*a)/a/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 165 +--a0017:= integrate(t0017,x) +--E 88 + +--S 89 of 165 +--m0017:= a0017-r0017 +--E 89 + +--S 90 of 165 +--d0017:= D(m0017,x) +--E 90 + +--S 91 of 165 +t0018:= sinh(b*x)*Shi(b*x)/x^3 +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 91 + +--S 92 of 165 +r0018:= -1/4*(-4*b^2*Chi(2*b*x)*x^2+2*x*cosh(b*x)*sinh(b*x)*b+cosh(b*x)^2-_ + 1+x*b*sinh(2*b*x)+2*x*cosh(b*x)*Shi(b*x)*b+2*sinh(b*x)*Shi(b*x)-_ + x^2*Shi(b*x)^2*b^2)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 165 +--a0018:= integrate(t0018,x) +--E 93 + +--S 94 of 165 +--m0018:= a0018-r0018 +--E 94 + +--S 95 of 165 +--d0018:= D(m0018,x) +--E 95 + +--S 96 of 165 +t0019:= sinh(a+b*x)*Shi(c+d*x) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 96 + +--S 97 of 165 +r0019:= 1/2*(Chi((b-d)*(c+d*x)/d)*sinh((-b*c+a*d)/d)-_ + Chi((b+d)*(c+d*x)/d)*sinh((-b*c+a*d)/d)+2*cosh(a+b*x)*Shi(c+d*x)+_ + cosh((-b*c+a*d)/d)*Shi((b-d)*(c+d*x)/d)-_ + cosh((-b*c+a*d)/d)*Shi((b+d)*(c+d*x)/d))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 165 +--a0019:= integrate(t0019,x) +--E 98 + +--S 99 of 165 +--m0019:= a0019-r0019 +--E 99 + +--S 100 of 165 +--d0019:= D(m0019,x) +--E 100 + +--S 101 of 165 +t0020:= x*sinh(a+b*x)*Shi(c+d*x) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 101 + +--S 102 of 165 +r0020:= 1/2*cosh(a-c+(b-d)*x)/b/(b-d)-1/2*cosh(a+c+(b+d)*x)/b/(b+d)-_ + 1/2*cosh(a-b*c/d)*Chi((b-d)*(c+d*x)/d)/b^2+_ + 1/2*cosh(a-b*c/d)*Chi((b+d)*(c+d*x)/d)/b^2-_ + 1/2*c*Chi((b-d)*(c+d*x)/d)*sinh(a-b*c/d)/b/d+_ + 1/2*c*Chi((b+d)*(c+d*x)/d)*sinh(a-b*c/d)/b/d+x*cosh(a+b*x)*_ + Shi(c+d*x)/b-sinh(a+b*x)*Shi(c+d*x)/b^2-1/2*c*cosh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b/d-1/2*sinh(a-b*c/d)*Shi((b-d)*(c+d*x)/d)/b^2+_ + 1/2*c*cosh(a-b*c/d)*Shi((b+d)*(c+d*x)/d)/b/d+_ + 1/2*sinh(a-b*c/d)*Shi((b+d)*(c+d*x)/d)/b^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 165 +--a0020:= integrate(t0020,x) +--E 103 + +--S 104 of 165 +--m0020:= a0020-r0020 +--E 104 + +--S 105 of 165 +--d0020:= D(m0020,x) +--E 105 + +--S 106 of 165 +t0021:= cosh(b*x)*Shi(b*x)/x^2 +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 106 + +--S 107 of 165 +r0021:= 1/2*(2*b*Chi(2*b*x)*x-sinh(2*b*x)-_ + 2*cosh(b*x)*Shi(b*x)+x*Shi(b*x)^2*b)/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 165 +--a0021:= integrate(t0021,x) +--E 108 + +--S 109 of 165 +--m0021:= a0021-r0021 +--E 109 + +--S 110 of 165 +--d0021:= D(m0021,x) +--E 110 + +--S 111 of 165 +t0022:= cosh(a+b*x)*Shi(c+d*x) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 111 + +--S 112 of 165 +r0022:= -1/2*(-cosh((-b*c+a*d)/d)*Chi((b-d)*(c+d*x)/d)+_ + cosh((-b*c+a*d)/d)*Chi((b+d)*(c+d*x)/d)-_ + 2*sinh(a+b*x)*Shi(c+d*x)-sinh((-b*c+a*d)/d)*Shi((b-d)*(c+d*x)/d)+_ + sinh((-b*c+a*d)/d)*Shi((b+d)*(c+d*x)/d))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 112 + +--S 113 of 165 +--a0022:= integrate(t0022,x) +--E 113 + +--S 114 of 165 +--m0022:= a0022-r0022 +--E 114 + +--S 115 of 165 +--d0022:= D(m0022,x) +--E 115 + +--S 116 of 165 +t0023:= x*cosh(a+b*x)*Shi(c+d*x) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 116 + +--S 117 of 165 +r0023:= -1/2*c*cosh(a-b*c/d)*Chi((b-d)*(c+d*x)/d)/b/d+_ + 1/2*c*cosh(a-b*c/d)*Chi((b+d)*(c+d*x)/d)/b/d-_ + 1/2*Chi((b-d)*(c+d*x)/d)*sinh(a-b*c/d)/b^2+_ + 1/2*Chi((b+d)*(c+d*x)/d)*sinh(a-b*c/d)/b^2+_ + 1/2*sinh(a-c+(b-d)*x)/b/(b-d)-_ + 1/2*sinh(a+c+(b+d)*x)/b/(b+d)-cosh(a+b*x)*Shi(c+d*x)/b^2+_ + x*sinh(a+b*x)*Shi(c+d*x)/b-1/2*cosh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b^2-1/2*c*sinh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b/d+1/2*cosh(a-b*c/d)*_ + Shi((b+d)*(c+d*x)/d)/b^2+1/2*c*sinh(a-b*c/d)*Shi((b+d)*(c+d*x)/d)/b/d +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 165 +--a0023:= integrate(t0023,x) +--E 118 + +--S 119 of 165 +--m0023:= a0023-r0023 +--E 119 + +--S 120 of 165 +--d0023:= D(m0023,x) +--E 120 + +--S 121 of 165 +t0024:= x^m*Chi(b*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 121 + +--S 122 of 165 +r0024:= 1/2/b/(1+m)*(x^m*(b*x)^(-m)*Gamma(1+m,b*x)-x^m*(-b*x)^(-m)*_ + Gamma(1+m,-b*x)+2*x^(1+m)*Chi(b*x)*b) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 165 +--a0024:= integrate(t0024,x) +--E 123 + +--S 124 of 165 +--m0024:= a0024-r0024 +--E 124 + +--S 125 of 165 +--d0024:= D(m0024,x) +--E 125 + +--S 126 of 165 +t0025:= Chi(a+b*x)/x^3 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 126 + +--S 127 of 165 +r0025:= -1/2*(b*cosh(a+b*x)*a*x+b^2*cosh(a)*Chi(b*x)*x^2-_ + b^2*Chi(a+b*x)*x^2+Chi(a+b*x)*a^2-b^2*Chi(b*x)*sinh(a)*a*x^2-_ + b^2*cosh(a)*Shi(b*x)*a*x^2+b^2*sinh(a)*Shi(b*x)*x^2)/a^2/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 165 +--a0025:= integrate(t0025,x) +--E 128 + +--S 129 of 165 +--m0025:= a0025-r0025 +--E 129 + +--S 130 of 165 +--d0025:= D(m0025,x) +--E 130 + +--S 131 of 165 +t0026:= Chi(a+b*x)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 131 + +--S 132 of 165 +r0026:= (b*cosh(a)*Chi(b*x)*x-Chi(a+b*x)*b*x-Chi(a+b*x)*a+_ + b*sinh(a)*Shi(b*x)*x)/a/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 165 +--a0026:= integrate(t0026,x) +--E 133 + +--S 134 of 165 +--m0026:= a0026-r0026 +--E 134 + +--S 135 of 165 +--d0026:= D(m0026,x) +--E 135 + +--S 136 of 165 +t0027:= Chi(b*x)*sinh(b*x)/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 136 + +--S 137 of 165 +r0027:= 1/2*(x*Chi(b*x)^2*b+2*b*Chi(2*b*x)*x-2*sinh(b*x)*Chi(b*x)-_ + sinh(2*b*x))/x +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 137 + +--S 138 of 165 +--a0027:= integrate(t0027,x) +--E 138 + +--S 139 of 165 +--m0027:= a0027-r0027 +--E 139 + +--S 140 of 165 +--d0027:= D(m0027,x) +--E 140 + +--S 141 of 165 +t0028:= sinh(a+b*x)*Chi(c+d*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 141 + +--S 142 of 165 +r0028:= -1/2*(-2*cosh(a+b*x)*Chi(c+d*x)+cosh((-b*c+a*d)/d)*_ + Chi((b-d)*(c+d*x)/d)+cosh((-b*c+a*d)/d)*Chi((b+d)*(c+d*x)/d)+_ + sinh((-b*c+a*d)/d)*Shi((b-d)*(c+d*x)/d)+sinh((-b*c+a*d)/d)*_ + Shi((b+d)*(c+d*x)/d))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 142 + +--S 143 of 165 +--a0028:= integrate(t0028,x) +--E 143 + +--S 144 of 165 +--m0028:= a0028-r0028 +--E 144 + +--S 145 of 165 +--d0028:= D(m0028,x) +--E 145 + +--S 146 of 165 +t0029:= x*sinh(a+b*x)*Chi(c+d*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 146 + +--S 147 of 165 +r0029:= x*cosh(a+b*x)*Chi(c+d*x)/b+1/2*c*cosh(a-b*c/d)*_ + Chi((b-d)*(c+d*x)/d)/b/d+1/2*c*cosh(a-b*c/d)*_ + Chi((b+d)*(c+d*x)/d)/b/d+1/2*Chi((b-d)*(c+d*x)/d)*_ + sinh(a-b*c/d)/b^2+1/2*Chi((b+d)*(c+d*x)/d)*sinh(a-b*c/d)/b^2-_ + Chi(c+d*x)*sinh(a+b*x)/b^2-1/2*sinh(a-c+(b-d)*x)/b/(b-d)-_ + 1/2*sinh(a+c+(b+d)*x)/b/(b+d)+1/2*cosh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b^2+1/2*c*sinh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b/d+1/2*cosh(a-b*c/d)*_ + Shi((b+d)*(c+d*x)/d)/b^2+1/2*c*sinh(a-b*c/d)*Shi((b+d)*(c+d*x)/d)/b/d +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 165 +--a0029:= integrate(t0029,x) +--E 148 + +--S 149 of 165 +--m0029:= a0029-r0029 +--E 149 + +--S 150 of 165 +--d0029:= D(m0029,x) +--E 150 + +--S 151 of 165 +t0030:= cosh(b*x)*Chi(b*x)/x^3 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 151 + +--S 152 of 165 +r0030:= 1/4*(-cosh(b*x)^2-2*cosh(b*x)*Chi(b*x)+x^2*Chi(b*x)^2*b^2+_ + 4*b^2*Chi(2*b*x)*x^2-2*x*cosh(b*x)*sinh(b*x)*b-_ + 2*x*Chi(b*x)*sinh(b*x)*b-x*b*sinh(2*b*x))/x^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 152 + +--S 153 of 165 +--a0030:= integrate(t0030,x) +--E 153 + +--S 154 of 165 +--m0030:= a0030-r0030 +--E 154 + +--S 155 of 165 +--d0030:= D(m0030,x) +--E 155 + +--S 156 of 165 +t0031:= cosh(a+b*x)*Chi(c+d*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 156 + +--S 157 of 165 +r0031:= -1/2*(Chi((b-d)*(c+d*x)/d)*sinh((-b*c+a*d)/d)+_ + Chi((b+d)*(c+d*x)/d)*sinh((-b*c+a*d)/d)-2*sinh(a+b*x)*_ + Chi(c+d*x)+cosh((-b*c+a*d)/d)*Shi((b-d)*(c+d*x)/d)+_ + cosh((-b*c+a*d)/d)*Shi((b+d)*(c+d*x)/d))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 157 + +--S 158 of 165 +--a0031:= integrate(t0031,x) +--E 158 + +--S 159 of 165 +--m0031:= a0031-r0031 +--E 159 + +--S 160 of 165 +--d0031:= D(m0031,x) +--E 160 + +--S 161 of 165 +t0032:= x*cosh(a+b*x)*Chi(c+d*x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 161 + +--S 162 of 165 +r0032:= -1/2*cosh(a-c+(b-d)*x)/b/(b-d)-1/2*cosh(a+c+(b+d)*x)/b/(b+d)-_ + cosh(a+b*x)*Chi(c+d*x)/b^2+1/2*cosh(a-b*c/d)*_ + Chi((b-d)*(c+d*x)/d)/b^2+1/2*cosh(a-b*c/d)*Chi((b+d)*(c+d*x)/d)/b^2+_ + 1/2*c*Chi((b-d)*(c+d*x)/d)*sinh(a-b*c/d)/b/d+_ + 1/2*c*Chi((b+d)*(c+d*x)/d)*sinh(a-b*c/d)/b/d+x*_ + Chi(c+d*x)*sinh(a+b*x)/b+1/2*c*cosh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b/d+1/2*sinh(a-b*c/d)*_ + Shi((b-d)*(c+d*x)/d)/b^2+1/2*c*cosh(a-b*c/d)*_ + Shi((b+d)*(c+d*x)/d)/b/d+1/2*sinh(a-b*c/d)*Shi((b+d)*(c+d*x)/d)/b^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 165 +--a0032:= integrate(t0032,x) +--E 163 + +--S 164 of 165 +--m0032:= a0032-r0032 +--E 164 + +--S 165 of 165 +--d0032:= D(m0032,x) +--E 165 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richintfunc000-032.input.pdf b/src/axiom-website/CATS/richintfunc000-032.input.pdf new file mode 100644 index 0000000..5e2a850 Binary files /dev/null and b/src/axiom-website/CATS/richintfunc000-032.input.pdf differ diff --git a/src/axiom-website/CATS/richinvhyper000-099.input.pamphlet b/src/axiom-website/CATS/richinvhyper000-099.input.pamphlet new file mode 100644 index 0000000..a7eab02 --- /dev/null +++ b/src/axiom-website/CATS/richinvhyper000-099.input.pamphlet @@ -0,0 +1,9696 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richinvhyper000-099.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richinvhyper000-099.output +)spool richinvhyper000-099.output +)set message auto off +)clear all + + +--S 1 of 510 +t0000:= asinh(x)^2 +--R +--R +--R 2 +--R (1) asinh(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 510 +r0000:= 2*x-2*(1+x^2)^(1/2)*asinh(x)+x*asinh(x)^2 +--R +--R +--R +------+ +--R | 2 2 +--R (2) - 2asinh(x)\|x + 1 + x asinh(x) + 2x +--R Type: Expression(Integer) +--E 2 + +--S 3 of 510 +a0000:= integrate(t0000,x) +--R +--R +--R (3) +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (2x\|x + 1 - 2x - 2)log(\|x + 1 + x) + 2x\|x + 1 - 2x +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 510 +m0000:= a0000-r0000 +--R +--R +--R (4) +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x + 1 - 2x - 2)log(\|x + 1 + x) +--R + +--R +------+ +--R 2 | 2 2 2 2 +--R (- x asinh(x) - 2x asinh(x))\|x + 1 + x asinh(x) + (2x + 2)asinh(x) +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Expression(Integer) +--E 4 + +--S 5 of 510 +d0000:= D(m0000,x) +--R +--R +--R +------+ 2 +--R | 2 2 +--R (5) log(\|x + 1 + x) - asinh(x) +--R Type: Expression(Integer) +--E 5 + +)clear all + + +--S 6 of 510 +t0001:= asinh(x)^3 +--R +--R +--R 3 +--R (1) asinh(x) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 510 +r0001:= -6*(1+x^2)^(1/2)+6*x*asinh(x)-3*(1+x^2)^(1/2)*asinh(x)^2+x*asinh(x)^3 +--R +--R +--R +------+ +--R 2 | 2 3 +--R (2) (- 3asinh(x) - 6)\|x + 1 + x asinh(x) + 6x asinh(x) +--R Type: Expression(Integer) +--E 7 + +--S 8 of 510 +a0001:= integrate(t0001,x) +--R +--R +--R (3) +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (3x\|x + 1 - 3x - 3)log(\|x + 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (6x\|x + 1 - 6x )log(\|x + 1 + x) + 6x\|x + 1 - 6x - 6 +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 510 +m0001:= a0001-r0001 +--R +--R +--R (4) +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (3x\|x + 1 - 3x - 3)log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (6x\|x + 1 - 6x )log(\|x + 1 + x) +--R + +--R +------+ +--R 3 2 | 2 2 3 +--R (- x asinh(x) - 3x asinh(x) - 6x asinh(x))\|x + 1 + x asinh(x) +--R + +--R 2 2 2 +--R (3x + 3)asinh(x) + 6x asinh(x) +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Expression(Integer) +--E 9 + +--S 10 of 510 +d0001:= D(m0001,x) +--R +--R +--R +------+ 3 +--R | 2 3 +--R (5) log(\|x + 1 + x) - asinh(x) +--R Type: Expression(Integer) +--E 10 + +)clear all + + +--S 11 of 510 +t0002:= asinh(x)^4 +--R +--R +--R 4 +--R (1) asinh(x) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 510 +r0002:= 24*x-24*(1+x^2)^(1/2)*asinh(x)+12*x*asinh(x)^2-_ + 4*(1+x^2)^(1/2)*asinh(x)^3+x*asinh(x)^4 +--R +--R +--R (2) +--R +------+ +--R 3 | 2 4 2 +--R (- 4asinh(x) - 24asinh(x))\|x + 1 + x asinh(x) + 12x asinh(x) + 24x +--R Type: Expression(Integer) +--E 12 + +--S 13 of 510 +a0002:= integrate(t0002,x) +--R +--R +--R (3) +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (4x\|x + 1 - 4x - 4)log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (12x\|x + 1 - 12x )log(\|x + 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (24x\|x + 1 - 24x - 24)log(\|x + 1 + x) + 24x\|x + 1 - 24x +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 510 +m0002:= a0002-r0002 +--R +--R +--R (4) +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (4x\|x + 1 - 4x - 4)log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (12x\|x + 1 - 12x )log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (24x\|x + 1 - 24x - 24)log(\|x + 1 + x) +--R + +--R +------+ +--R 4 3 2 | 2 +--R (- x asinh(x) - 4x asinh(x) - 12x asinh(x) - 24x asinh(x))\|x + 1 +--R + +--R 2 4 2 3 2 2 2 +--R x asinh(x) + (4x + 4)asinh(x) + 12x asinh(x) + (24x + 24)asinh(x) +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Expression(Integer) +--E 14 + +--S 15 of 510 +d0002:= D(m0002,x) +--R +--R +--R +------+ 4 +--R | 2 4 +--R (5) log(\|x + 1 + x) - asinh(x) +--R Type: Expression(Integer) +--E 15 + +)clear all + + +--S 16 of 510 +t0003:= asinh(x)^5 +--R +--R +--R 5 +--R (1) asinh(x) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 510 +r0003:= -120*(1+x^2)^(1/2)+120*x*asinh(x)-60*(1+x^2)^(1/2)*asinh(x)^2+_ + 20*x*asinh(x)^3-5*(1+x^2)^(1/2)*asinh(x)^4+x*asinh(x)^5 +--R +--R +--R (2) +--R +------+ +--R 4 2 | 2 5 3 +--R (- 5asinh(x) - 60asinh(x) - 120)\|x + 1 + x asinh(x) + 20x asinh(x) +--R + +--R 120x asinh(x) +--R Type: Expression(Integer) +--E 17 + +--S 18 of 510 +a0003:= integrate(t0003,x) +--R +--R +--R (3) +--R +------+ +------+ 5 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (5x\|x + 1 - 5x - 5)log(\|x + 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (20x\|x + 1 - 20x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (60x\|x + 1 - 60x - 60)log(\|x + 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (120x\|x + 1 - 120x )log(\|x + 1 + x) + 120x\|x + 1 - 120x - 120 +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 510 +m0003:= a0003-r0003 +--R +--R +--R (4) +--R +------+ +------+ 5 +--R | 2 2 | 2 +--R (x\|x + 1 - x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (5x\|x + 1 - 5x - 5)log(\|x + 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (20x\|x + 1 - 20x )log(\|x + 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (60x\|x + 1 - 60x - 60)log(\|x + 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (120x\|x + 1 - 120x )log(\|x + 1 + x) +--R + +--R 5 4 3 2 +--R - x asinh(x) - 5x asinh(x) - 20x asinh(x) - 60x asinh(x) +--R + +--R - 120x asinh(x) +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R 2 5 2 4 2 3 2 2 +--R x asinh(x) + (5x + 5)asinh(x) + 20x asinh(x) + (60x + 60)asinh(x) +--R + +--R 2 +--R 120x asinh(x) +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Expression(Integer) +--E 19 + +--S 20 of 510 +d0003:= D(m0003,x) +--R +--R +--R +------+ 5 +--R | 2 5 +--R (5) log(\|x + 1 + x) - asinh(x) +--R Type: Expression(Integer) +--E 20 + +)clear all + + +--S 21 of 510 +t0004:= 1/asinh(x) +--R +--R +--R 1 +--R (1) -------- +--R asinh(x) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 510 +r0004:= Chi(asinh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 510 +a0004:= integrate(t0004,x) +--R +--R +--R x +--R ++ 1 +--I (2) | --------- d%T +--I ++ asinh(%T) +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 510 +--m0004:= a0004-r0004 +--E 24 + +--S 25 of 510 +--d0004:= D(m0004,x) +--E 25 + +)clear all + + +--S 26 of 510 +t0005:= 1/asinh(x)^2 +--R +--R +--R 1 +--R (1) --------- +--R 2 +--R asinh(x) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 510 +r0005:= -(1+x^2)^(1/2)/asinh(x)+Shi(asinh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 510 +a0005:= integrate(t0005,x) +--R +--R +--R x +--R ++ 1 +--I (2) | ---------- d%T +--I ++ 2 +--R asinh(%T) +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 510 +--m0005:= a0005-r0005 +--E 29 + +--S 30 of 510 +--d0005:= D(m0005,x) +--E 30 + +)clear all + + +--S 31 of 510 +t0006:= 1/asinh(x)^3 +--R +--R +--R 1 +--R (1) --------- +--R 3 +--R asinh(x) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 510 +r0006:= 1/2*(-(1+x^2)^(1/2)-x*asinh(x)+Chi(asinh(x))*asinh(x)^2)/asinh(x)^2 +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 510 +a0006:= integrate(t0006,x) +--R +--R +--R x +--R ++ 1 +--I (2) | ---------- d%T +--R ++ 3 +--I asinh(%T) +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 510 +--m0006:= a0006-r0006 +--E 34 + +--S 35 of 510 +--d0006:= D(m0006,x) +--E 35 + +)clear all + + +--S 36 of 510 +t0007:= asinh(a*x)/x +--R +--R +--R asinh(a x) +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 510 +r0007:= 1/2*asinh(a*x)^2+asinh(a*x)*log(1-exp(1)^(-2*asinh(a*x)))-_ + 1/2*polylog(2,exp(1)^(-2*asinh(a*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 510 +a0007:= integrate(t0007,x) +--R +--R +--R x +--I ++ asinh(%T a) +--I (2) | ----------- d%T +--I ++ %T +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 510 +--m0007:= a0007-r0007 +--E 39 + +--S 40 of 510 +--d0007:= D(m0007,x) +--E 40 + +)clear all + + +--S 41 of 510 +t0008:= 1/(a+b*asinh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (1) ----------------------- +--R +--------------------+ +--R \|b asinh(d x + c) + a +--R Type: Expression(Integer) +--E 41 + +--S 42 of 510 +r0I08:= -1/2*%pi^(1/2)*(-exp(2*a/b)*erf((a+b*asinh(c+d*x))^(1/2)/b^(1/2))+_ + %i*erf(%i*(a+b*asinh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d +--R +--R +--R (2) +--R a 2a +--R - - -- +--------------------+ +--R b b +---+ \|b asinh(d x + c) + a +--R %e %e \|%pi erf(-----------------------) +--R +-+ +--R \|b +--R + +--R a +--R - - +--------------------+ +--R b +---+ %i\|b asinh(d x + c) + a +--R - %i %e \|%pi erf(-------------------------) +--R +-+ +--R \|b +--R / +--R +-+ +--R 2d\|b +--R Type: Expression(Complex(Integer)) +--E 42 + +--S 43 of 510 +a0008:= integrate(t0008,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 43 + +--S 44 of 510 +--m0008:= a0008-r0008 +--E 44 + +--S 45 of 510 +--d0008:= D(m0008,x) +--E 45 + +)clear all + + +--S 46 of 510 +t0009:= 1/(a-b*asinh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (1) ------------------------- +--R +----------------------+ +--R \|- b asinh(d x + c) + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 510 +r0009:= -1/2*%pi^(1/2)*(exp(2*a/b)*erf((a-b*asinh(c+d*x))^(1/2)/b^(1/2))-_ + %i*erf(%i*(a-b*asinh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d +--R +--R +--R (2) +--R a 2a +--R - - -- +----------------------+ +--R b b +---+ \|- b asinh(d x + c) + a +--R - %e %e \|%pi erf(-------------------------) +--R +-+ +--R \|b +--R + +--R a +--R - - +----------------------+ +--R b +---+ %i\|- b asinh(d x + c) + a +--R %i %e \|%pi erf(---------------------------) +--R +-+ +--R \|b +--R / +--R +-+ +--R 2d\|b +--R Type: Expression(Complex(Integer)) +--E 47 + +--S 48 of 510 +a0009:= integrate(t0009,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 48 + +--S 49 of 510 +--m0009:= a0009-r0009 +--E 49 + +--S 50 of 510 +--d0009:= D(m0009,x) +--E 50 + +)clear all + + +--S 51 of 510 +t0010:= asinh(x^(1/2))/x +--R +--R +--R +-+ +--R asinh(\|x ) +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 510 +r0010:= asinh(x^(1/2))^2+2*asinh(x^(1/2))*log(1-exp(1)^(-2*asinh(x^(1/2))))-_ + polylog(2,exp(1)^(-2*asinh(x^(1/2)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 510 +a0010:= integrate(t0010,x) +--R +--R +--R x +--+ +--I ++ asinh(\|%T ) +--I (2) | ------------ d%T +--I ++ %T +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 510 +--m0010:= a0010-r0010 +--E 54 + +--S 55 of 510 +--d0010:= D(m0010,x) +--E 55 + +)clear all + + +--S 56 of 510 +t0011:= acosh(x)^2 +--R +--R +--R 2 +--R (1) acosh(x) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 510 +r0011:= 2*x-2*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)+x*acosh(x)^2 +--R +--R +--R +-----+ +-----+ 2 +--R (2) - 2acosh(x)\|x - 1 \|x + 1 + x acosh(x) + 2x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 510 +a0011:= integrate(t0011,x) +--R +--R +--R (3) +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (2x\|x - 1 - 2x + 2)log(\|x - 1 + x) + 2x\|x - 1 - 2x +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 510 +m0011:= a0011-r0011 +--R +--R +--R (4) +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x - 1 - 2x + 2)log(\|x - 1 + x) +--R + +--R +------+ +--R +-----+ +-----+ 2 | 2 +--R (2acosh(x)\|x - 1 \|x + 1 - x acosh(x) )\|x - 1 +--R + +--R +-----+ +-----+ 2 2 +--R - 2x acosh(x)\|x - 1 \|x + 1 + x acosh(x) +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Expression(Integer) +--E 59 + +--S 60 of 510 +d0011:= D(m0011,x) +--R +--R +--R (5) +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) +--R * +--R +------+ 2 +--R | 2 +--R log(\|x - 1 + x) +--R + +--R 2 2 2 2 +-----+ +-----+ +--R ((- 2x + 1)acosh(x) + 4x acosh(x) - 4x + 2)\|x - 1 \|x + 1 +--R + +--R 3 3 +--R (4x - 2x)acosh(x) - 4x + 4x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 3 2 3 3 +-----+ +-----+ +--R ((2x - 2x)acosh(x) + (- 4x + 2x)acosh(x) + 4x - 4x)\|x - 1 \|x + 1 +--R + +--R 4 2 4 2 +--R (- 4x + 4x )acosh(x) + 4x - 6x + 2 +--R / +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R (2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 60 + +)clear all + + +--S 61 of 510 +t0012:= acosh(x)^3 +--R +--R +--R 3 +--R (1) acosh(x) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 510 +r0012:= -6*(-1+x)^(1/2)*(1+x)^(1/2)+6*x*acosh(x)-_ + 3*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)^2+x*acosh(x)^3 +--R +--R +--R 2 +-----+ +-----+ 3 +--R (2) (- 3acosh(x) - 6)\|x - 1 \|x + 1 + x acosh(x) + 6x acosh(x) +--R Type: Expression(Integer) +--E 62 + +--S 63 of 510 +a0012:= integrate(t0012,x) +--R +--R +--R (3) +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (3x\|x - 1 - 3x + 3)log(\|x - 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (6x\|x - 1 - 6x )log(\|x - 1 + x) + 6x\|x - 1 - 6x + 6 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 510 +m0012:= a0012-r0012 +--R +--R +--R (4) +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (3x\|x - 1 - 3x + 3)log(\|x - 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (6x\|x - 1 - 6x )log(\|x - 1 + x) +--R + +--R 2 +-----+ +-----+ 3 +--R ((3acosh(x) + 6)\|x - 1 \|x + 1 - x acosh(x) - 6x acosh(x) + 6x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 2 +-----+ +-----+ 2 3 2 2 +--R (- 3x acosh(x) - 6x)\|x - 1 \|x + 1 + x acosh(x) + 6x acosh(x) - 6x + 6 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Expression(Integer) +--E 64 + +--S 65 of 510 +d0012:= D(m0012,x) +--R +--R +--R (5) +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) +--R * +--R +------+ 3 +--R | 2 +--R log(\|x - 1 + x) +--R + +--R 2 3 2 2 2 2 +--R ((- 2x + 1)acosh(x) + 6x acosh(x) + (- 12x + 6)acosh(x) + 12x ) +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 3 2 3 3 +--R (6x - 3x)acosh(x) + (- 12x + 12x)acosh(x) + 12x - 6x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 3 3 3 2 3 +--R (2x - 2x)acosh(x) + (- 6x + 3x)acosh(x) + (12x - 12x)acosh(x) +--R + +--R 3 +--R - 12x + 6x +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 4 2 2 4 2 4 2 +--R (- 6x + 6x )acosh(x) + (12x - 18x + 6)acosh(x) - 12x + 12x +--R / +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R (2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 65 + +)clear all + + +--S 66 of 510 +t0013:= acosh(x)^4 +--R +--R +--R 4 +--R (1) acosh(x) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 510 +r0013:= 24*x-24*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)+12*x*acosh(x)^2-_ + 4*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)^3+x*acosh(x)^4 +--R +--R +--R (2) +--R 3 +-----+ +-----+ 4 2 +--R (- 4acosh(x) - 24acosh(x))\|x - 1 \|x + 1 + x acosh(x) + 12x acosh(x) +--R + +--R 24x +--R Type: Expression(Integer) +--E 67 + +--S 68 of 510 +a0013:= integrate(t0013,x) +--R +--R +--R (3) +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (4x\|x - 1 - 4x + 4)log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (12x\|x - 1 - 12x )log(\|x - 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (24x\|x - 1 - 24x + 24)log(\|x - 1 + x) + 24x\|x - 1 - 24x +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 510 +m0013:= a0013-r0013 +--R +--R +--R (4) +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (4x\|x - 1 - 4x + 4)log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (12x\|x - 1 - 12x )log(\|x - 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (24x\|x - 1 - 24x + 24)log(\|x - 1 + x) +--R + +--R 3 +-----+ +-----+ 4 +--R (4acosh(x) + 24acosh(x))\|x - 1 \|x + 1 - x acosh(x) +--R + +--R 2 +--R - 12x acosh(x) +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 3 +-----+ +-----+ 2 4 +--R (- 4x acosh(x) - 24x acosh(x))\|x - 1 \|x + 1 + x acosh(x) +--R + +--R 2 2 +--R 12x acosh(x) +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Expression(Integer) +--E 69 + +--S 70 of 510 +d0013:= D(m0013,x) +--R +--R +--R (5) +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) +--R * +--R +------+ 4 +--R | 2 +--R log(\|x - 1 + x) +--R + +--R 2 4 2 3 2 2 +--R (- 2x + 1)acosh(x) + 8x acosh(x) + (- 24x + 12)acosh(x) +--R + +--R 2 2 +--R 48x acosh(x) - 48x + 24 +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 3 3 3 2 3 +--R (8x - 4x)acosh(x) + (- 24x + 24x)acosh(x) + (48x - 24x)acosh(x) +--R + +--R 3 +--R - 48x + 48x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 3 4 3 3 3 2 +--R (2x - 2x)acosh(x) + (- 8x + 4x)acosh(x) + (24x - 24x)acosh(x) +--R + +--R 3 3 +--R (- 48x + 24x)acosh(x) + 48x - 48x +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 4 2 3 4 2 2 +--R (- 8x + 8x )acosh(x) + (24x - 36x + 12)acosh(x) +--R + +--R 4 2 4 2 +--R (- 48x + 48x )acosh(x) + 48x - 72x + 24 +--R / +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R (2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 70 + +)clear all + + +--S 71 of 510 +t0014:= acosh(x)^5 +--R +--R +--R 5 +--R (1) acosh(x) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 510 +r0014:= -120*(-1+x)^(1/2)*(1+x)^(1/2)+120*x*acosh(x)-60*(-1+x)^(1/2)*_ + (1+x)^(1/2)*acosh(x)^2+20*x*acosh(x)^3-_ + 5*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)^4+x*acosh(x)^5 +--R +--R +--R (2) +--R 4 2 +-----+ +-----+ 5 +--R (- 5acosh(x) - 60acosh(x) - 120)\|x - 1 \|x + 1 + x acosh(x) +--R + +--R 3 +--R 20x acosh(x) + 120x acosh(x) +--R Type: Expression(Integer) +--E 72 + +--S 73 of 510 +a0014:= integrate(t0014,x) +--R +--R +--R (3) +--R +------+ +------+ 5 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (5x\|x - 1 - 5x + 5)log(\|x - 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (20x\|x - 1 - 20x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (60x\|x - 1 - 60x + 60)log(\|x - 1 + x) +--R + +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (120x\|x - 1 - 120x )log(\|x - 1 + x) + 120x\|x - 1 - 120x + 120 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 510 +m0014:= a0014-r0014 +--R +--R +--R (4) +--R +------+ +------+ 5 +--R | 2 2 | 2 +--R (x\|x - 1 - x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 4 +--R | 2 2 | 2 +--R (5x\|x - 1 - 5x + 5)log(\|x - 1 + x) +--R + +--R +------+ +------+ 3 +--R | 2 2 | 2 +--R (20x\|x - 1 - 20x )log(\|x - 1 + x) +--R + +--R +------+ +------+ 2 +--R | 2 2 | 2 +--R (60x\|x - 1 - 60x + 60)log(\|x - 1 + x) +--R + +--R +------+ +------+ +--R | 2 2 | 2 +--R (120x\|x - 1 - 120x )log(\|x - 1 + x) +--R + +--R 4 2 +-----+ +-----+ 5 +--R (5acosh(x) + 60acosh(x) + 120)\|x - 1 \|x + 1 - x acosh(x) +--R + +--R 3 +--R - 20x acosh(x) - 120x acosh(x) + 120x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 4 2 +-----+ +-----+ 2 5 +--R (- 5x acosh(x) - 60x acosh(x) - 120x)\|x - 1 \|x + 1 + x acosh(x) +--R + +--R 2 3 2 2 +--R 20x acosh(x) + 120x acosh(x) - 120x + 120 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Expression(Integer) +--E 74 + +--S 75 of 510 +d0014:= D(m0014,x) +--R +--R +--R (5) +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) +--R * +--R +------+ 5 +--R | 2 +--R log(\|x - 1 + x) +--R + +--R 2 5 2 4 2 3 +--R (- 2x + 1)acosh(x) + 10x acosh(x) + (- 40x + 20)acosh(x) +--R + +--R 2 2 2 2 +--R 120x acosh(x) + (- 240x + 120)acosh(x) + 240x +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 3 4 3 3 +--R (10x - 5x)acosh(x) + (- 40x + 40x)acosh(x) +--R + +--R 3 2 3 3 +--R (120x - 60x)acosh(x) + (- 240x + 240x)acosh(x) + 240x - 120x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 3 5 3 4 3 3 +--R (2x - 2x)acosh(x) + (- 10x + 5x)acosh(x) + (40x - 40x)acosh(x) +--R + +--R 3 2 3 3 +--R (- 120x + 60x)acosh(x) + (240x - 240x)acosh(x) - 240x + 120x +--R * +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R + +--R 4 2 4 4 2 3 +--R (- 10x + 10x )acosh(x) + (40x - 60x + 20)acosh(x) +--R + +--R 4 2 2 4 2 4 2 +--R (- 120x + 120x )acosh(x) + (240x - 360x + 120)acosh(x) - 240x + 240x +--R / +--R +------+ +--R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ +--R (2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 75 + +)clear all + + +--S 76 of 510 +t0015:= 1/acosh(x) +--R +--R +--R 1 +--R (1) -------- +--R acosh(x) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 510 +r0015:= Shi(acosh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 510 +a0015:= integrate(t0015,x) +--R +--R +--R x +--R ++ 1 +--I (2) | --------- d%T +--I ++ acosh(%T) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 510 +--m0015:= a0015-r0015 +--E 79 + +--S 80 of 510 +--d0015:= D(m0015,x) +--E 80 + +)clear all + + +--S 81 of 510 +t0016:= 1/acosh(x)^2 +--R +--R +--R 1 +--R (1) --------- +--R 2 +--R acosh(x) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 510 +r0016:= -(-1+x)^(1/2)*(1+x)^(1/2)/acosh(x)+Chi(acosh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 510 +a0016:= integrate(t0016,x) +--R +--R +--R x +--R ++ 1 +--I (2) | ---------- d%T +--R ++ 2 +--I acosh(%T) +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 510 +--m0016:= a0016-r0016 +--E 84 + +--S 85 of 510 +--d0016:= D(m0016,x) +--E 85 + +)clear all + + +--S 86 of 510 +t0017:= 1/acosh(x)^3 +--R +--R +--R 1 +--R (1) --------- +--R 3 +--R acosh(x) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 510 +r0017:= -1/2*((-1+x)^(1/2)*(1+x)^(1/2)+x*acosh(x)-_ + Shi(acosh(x))*acosh(x)^2)/acosh(x)^2 +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 510 +a0017:= integrate(t0017,x) +--R +--R +--R x +--R ++ 1 +--I (2) | ---------- d%T +--R ++ 3 +--I acosh(%T) +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 510 +--m0017:= a0017-r0017 +--E 89 + +--S 90 of 510 +--d0017:= D(m0017,x) +--E 90 + +)clear all + + +--S 91 of 510 +t0018:= x*acosh(a*x) +--R +--R +--R (1) x acosh(a x) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 510 +r0018:= -1/4*(x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a+acosh(a*x)-_ + 2*x^2*acosh(a*x)*a^2)/a^2 +--R +--R +--R +-------+ +-------+ 2 2 +--R - a x\|a x - 1 \|a x + 1 + (2a x - 1)acosh(a x) +--R (2) ------------------------------------------------- +--R 2 +--R 4a +--R Type: Expression(Integer) +--E 92 + +--S 93 of 510 +a0018:= integrate(t0018,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R 3 3 | 2 2 4 4 2 2 | 2 2 +--R ((4a x - 2a x)\|a x - 1 - 4a x + 4a x - 1)log(\|a x - 1 + a x) +--R + +--R +--------+ +--R 3 3 | 2 2 4 4 2 2 +--R (2a x - a x)\|a x - 1 - 2a x + 2a x +--R / +--R +--------+ +--R 3 | 2 2 4 2 2 +--R 8a x\|a x - 1 - 8a x + 4a +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 510 +m0018:= a0018-r0018 +--R +--R +--R (4) +--R +--------+ +--------+ +--R 3 3 | 2 2 4 4 2 2 | 2 2 +--R ((4a x - 2a x)\|a x - 1 - 4a x + 4a x - 1)log(\|a x - 1 + a x) +--R + +--R 2 2 +-------+ +-------+ 3 3 3 3 +--R (2a x \|a x - 1 \|a x + 1 + (- 4a x + 2a x)acosh(a x) + 2a x - a x) +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 3 3 +-------+ +-------+ 4 4 2 2 +--R (- 2a x + a x)\|a x - 1 \|a x + 1 + (4a x - 4a x + 1)acosh(a x) +--R + +--R 4 4 2 2 +--R - 2a x + 2a x +--R / +--R +--------+ +--R 3 | 2 2 4 2 2 +--R 8a x\|a x - 1 - 8a x + 4a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 510 +d0018:= D(m0018,x) +--R +--R +--R (5) +--R +--------+ +--R 5 5 3 3 +-------+ +-------+ | 2 2 +--R (32a x - 32a x + 4a x)\|a x - 1 \|a x + 1 \|a x - 1 +--R + +--R 6 6 4 4 2 2 +-------+ +-------+ +--R (- 32a x + 48a x - 16a x )\|a x - 1 \|a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R log(\|a x - 1 + a x) +--R + +--R 5 5 3 3 5 5 3 3 +--R ((- 32a x + 32a x - 4a x)acosh(a x) + 16a x - 16a x + 4a x) +--R * +--R +-------+ +-------+ +--R \|a x - 1 \|a x + 1 +--R + +--R 6 6 4 4 2 2 +--R 16a x - 24a x + 10a x - 1 +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 6 6 4 4 2 2 6 6 4 4 2 2 +--R ((32a x - 48a x + 16a x )acosh(a x) - 16a x + 24a x - 10a x + 1) +--R * +--R +-------+ +-------+ +--R \|a x - 1 \|a x + 1 +--R + +--R 7 7 5 5 3 3 +--R - 16a x + 32a x - 20a x + 4a x +--R / +--R +--------+ +--R 5 4 3 2 +-------+ +-------+ | 2 2 +--R (32a x - 32a x + 4a)\|a x - 1 \|a x + 1 \|a x - 1 +--R + +--R 6 5 4 3 2 +-------+ +-------+ +--R (- 32a x + 48a x - 16a x)\|a x - 1 \|a x + 1 +--R Type: Expression(Integer) +--E 95 + +)clear all + + +--S 96 of 510 +t0019:= x^3*acosh(a*x) +--R +--R +--R 3 +--R (1) x acosh(a x) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 510 +r0019:= -1/32*(3*x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a+_ + 2*x^3*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a^3+3*acosh(a*x)-_ + 8*x^4*acosh(a*x)*a^4)/a^4 +--R +--R +--R 3 3 +-------+ +-------+ 4 4 +--R (- 2a x - 3a x)\|a x - 1 \|a x + 1 + (8a x - 3)acosh(a x) +--R (2) ------------------------------------------------------------ +--R 4 +--R 32a +--R Type: Expression(Integer) +--E 97 + +--S 98 of 510 +a0019:= integrate(t0019,x) +--R +--R +--R (3) +--R +--------+ +--R 7 7 5 5 3 3 | 2 2 8 8 6 6 +--R (64a x - 32a x - 24a x + 12a x)\|a x - 1 - 64a x + 64a x +--R + +--R 4 4 2 2 +--R 16a x - 24a x + 3 +--R * +--R +--------+ +--R | 2 2 +--R log(\|a x - 1 + a x) +--R + +--R +--------+ +--R 7 7 5 5 3 3 | 2 2 8 8 4 4 2 2 +--R (16a x + 8a x - 22a x + 3a x)\|a x - 1 - 16a x + 28a x - 12a x +--R / +--R +--------+ +--R 7 3 5 | 2 2 8 4 6 2 4 +--R (256a x - 128a x)\|a x - 1 - 256a x + 256a x - 32a +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 510 +m0019:= a0019-r0019 +--R +--R +--R (4) +--R +--------+ +--R 7 7 5 5 3 3 | 2 2 8 8 6 6 +--R (64a x - 32a x - 24a x + 12a x)\|a x - 1 - 64a x + 64a x +--R + +--R 4 4 2 2 +--R 16a x - 24a x + 3 +--R * +--R +--------+ +--R | 2 2 +--R log(\|a x - 1 + a x) +--R + +--R 6 6 4 4 2 2 +-------+ +-------+ +--R (16a x + 16a x - 12a x )\|a x - 1 \|a x + 1 +--R + +--R 7 7 5 5 3 3 7 7 5 5 +--R (- 64a x + 32a x + 24a x - 12a x)acosh(a x) + 16a x + 8a x +--R + +--R 3 3 +--R - 22a x + 3a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 7 7 5 5 3 3 +-------+ +-------+ +--R (- 16a x - 8a x + 22a x - 3a x)\|a x - 1 \|a x + 1 +--R + +--R 8 8 6 6 4 4 2 2 8 8 4 4 +--R (64a x - 64a x - 16a x + 24a x - 3)acosh(a x) - 16a x + 28a x +--R + +--R 2 2 +--R - 12a x +--R / +--R +--------+ +--R 7 3 5 | 2 2 8 4 6 2 4 +--R (256a x - 128a x)\|a x - 1 - 256a x + 256a x - 32a +--R Type: Expression(Integer) +--E 99 + +--S 100 of 510 +d0019:= D(m0019,x) +--R +--R +--R (5) +--R 11 11 9 9 7 7 5 5 3 3 +-------+ +--R (4096a x - 8192a x + 5120a x - 1024a x + 32a x )\|a x - 1 +--R * +--R +--------+ +--R +-------+ | 2 2 +--R \|a x + 1 \|a x - 1 +--R + +--R 12 12 10 10 8 8 6 6 4 4 +--R (- 4096a x + 10240a x - 8704a x + 2816a x - 256a x ) +--R * +--R +-------+ +-------+ +--R \|a x - 1 \|a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R log(\|a x - 1 + a x) +--R + +--R 11 11 9 9 7 7 5 5 3 3 +--R (- 4096a x + 8192a x - 5120a x + 1024a x - 32a x ) +--R * +--R acosh(a x) +--R + +--R 11 11 9 9 7 7 5 5 3 3 +--R 1024a x - 1536a x + 256a x + 512a x - 240a x + 24a x +--R * +--R +-------+ +-------+ +--R \|a x - 1 \|a x + 1 +--R + +--R 12 12 10 10 8 8 6 6 4 4 2 2 +--R 1024a x - 2048a x + 896a x + 512a x - 472a x + 96a x - 3 +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 12 12 10 10 8 8 6 6 4 4 +--R (4096a x - 10240a x + 8704a x - 2816a x + 256a x )acosh(a x) +--R + +--R 12 12 10 10 8 8 6 6 4 4 2 2 +--R - 1024a x + 2048a x - 896a x - 512a x + 472a x - 96a x + 3 +--R * +--R +-------+ +-------+ +--R \|a x - 1 \|a x + 1 +--R + +--R 13 13 11 11 9 9 7 7 5 5 3 3 +--R - 1024a x + 2560a x - 1792a x - 256a x + 752a x - 264a x + 24a x +--R / +--R 11 8 9 6 7 4 5 2 3 +-------+ +-------+ +--R (4096a x - 8192a x + 5120a x - 1024a x + 32a )\|a x - 1 \|a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 12 9 10 7 8 5 6 3 4 +-------+ +--R (- 4096a x + 10240a x - 8704a x + 2816a x - 256a x)\|a x - 1 +--R * +--R +-------+ +--R \|a x + 1 +--R Type: Expression(Integer) +--E 100 + +)clear all + + +--S 101 of 510 +t0020:= acosh(a*x)/x +--R +--R +--R acosh(a x) +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 510 +r0020:= 1/2*acosh(a*x)^2+acosh(a*x)*log(1+exp(1)^(-2*acosh(a*x)))-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(a*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 510 +a0020:= integrate(t0020,x) +--R +--R +--R x +--I ++ acosh(%T a) +--I (2) | ----------- d%T +--I ++ %T +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 510 +--m0020:= a0020-r0020 +--E 104 + +--S 105 of 510 +--d0020:= D(m0020,x) +--E 105 + +)clear all + + +--S 106 of 510 +t0021:= acosh(a*x)/x^2 +--R +--R +--R acosh(a x) +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 510 +r0021:= -acosh(a*x)/x+2*a*atan((-1+a*x)^(1/2)/(1+a*x)^(1/2)) +--R +--R +--R +-------+ +--R \|a x - 1 +--R 2a x atan(----------) - acosh(a x) +--R +-------+ +--R \|a x + 1 +--R (2) ---------------------------------- +--R x +--R Type: Expression(Integer) +--E 107 + +--S 108 of 510 +a0021:= integrate(t0021,x) +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R - log(\|a x - 1 + a x) + 2a x atan(\|a x - 1 - a x) +--R (3) ------------------------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 510 +m0021:= a0021-r0021 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R - log(\|a x - 1 + a x) + 2a x atan(\|a x - 1 - a x) +--R + +--R +-------+ +--R \|a x - 1 +--R - 2a x atan(----------) + acosh(a x) +--R +-------+ +--R \|a x + 1 +--R / +--R x +--R Type: Expression(Integer) +--E 109 + +--S 110 of 510 +d0021:= D(m0021,x) +--R +--R +--R (5) +--R +--------+ +--------+ +--R +-------+ +-------+ | 2 2 | 2 2 +--R \|a x - 1 \|a x + 1 \|a x - 1 log(\|a x - 1 + a x) +--R + +--R +--------+ +--R +-------+ +-------+ | 2 2 +--R (- acosh(a x)\|a x - 1 \|a x + 1 - a x)\|a x - 1 +--R + +--R +-------+ +-------+ +--R a x\|a x - 1 \|a x + 1 +--R / +--R +--------+ +--R 2 +-------+ +-------+ | 2 2 +--R x \|a x - 1 \|a x + 1 \|a x - 1 +--R Type: Expression(Integer) +--E 110 + +)clear all + + +--S 111 of 510 +t0022:= acosh(a*x)/x^4 +--R +--R +--R acosh(a x) +--R (1) ---------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 510 +r0022:= 1/6*(x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a-2*acosh(a*x)+_ + 2*a^3*atan((-1+a*x)^(1/2)/(1+a*x)^(1/2))*x^3)/x^3 +--R +--R +--R +-------+ +--R 3 3 \|a x - 1 +-------+ +-------+ +--R 2a x atan(----------) + a x\|a x - 1 \|a x + 1 - 2acosh(a x) +--R +-------+ +--R \|a x + 1 +--R (2) ------------------------------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 112 + +--S 113 of 510 +a0022:= integrate(t0022,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R | 2 2 2 2 | 2 2 +--R (- 4a x\|a x - 1 + 4a x - 2)log(\|a x - 1 + a x) +--R + +--R +--------+ +--------+ +--R 4 4 | 2 2 5 5 3 3 | 2 2 +--R (4a x \|a x - 1 - 4a x + 2a x )atan(\|a x - 1 - a x) +--R + +--R +--------+ +--R 3 3 | 2 2 4 4 2 2 +--R (- 2a x + a x)\|a x - 1 + 2a x - 2a x +--R / +--R +--------+ +--R 4 | 2 2 2 5 3 +--R 12a x \|a x - 1 - 12a x + 6x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 510 +m0022:= a0022-r0022 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 2 2 2 2 | 2 2 +--R (- 4a x\|a x - 1 + 4a x - 2)log(\|a x - 1 + a x) +--R + +--R +--------+ +--------+ +--R 4 4 | 2 2 5 5 3 3 | 2 2 +--R (4a x \|a x - 1 - 4a x + 2a x )atan(\|a x - 1 - a x) +--R + +--R +--------+ +-------+ +--R 4 4 | 2 2 5 5 3 3 \|a x - 1 +--R (- 4a x \|a x - 1 + 4a x - 2a x )atan(----------) +--R +-------+ +--R \|a x + 1 +--R + +--R +--------+ +--R 2 2 +-------+ +-------+ 3 3 | 2 2 +--R (- 2a x \|a x - 1 \|a x + 1 + 4a x acosh(a x) - 2a x + a x)\|a x - 1 +--R + +--R 3 3 +-------+ +-------+ 2 2 4 4 2 2 +--R (2a x - a x)\|a x - 1 \|a x + 1 + (- 4a x + 2)acosh(a x) + 2a x - 2a x +--R / +--R +--------+ +--R 4 | 2 2 2 5 3 +--R 12a x \|a x - 1 - 12a x + 6x +--R Type: Expression(Integer) +--E 114 + +--S 115 of 510 +d0022:= D(m0022,x) +--R +--R +--R (5) +--R +--------+ +--R 4 4 2 2 +-------+ +-------+ | 2 2 +--R (24a x - 24a x + 3)\|a x - 1 \|a x + 1 \|a x - 1 +--R + +--R 5 5 3 3 +-------+ +-------+ +--R (- 24a x + 36a x - 12a x)\|a x - 1 \|a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R log(\|a x - 1 + a x) +--R + +--R 4 4 2 2 4 4 2 2 +-------+ +--R ((- 24a x + 24a x - 3)acosh(a x) - 8a x + 4a x )\|a x - 1 +--R * +--R +-------+ +--R \|a x + 1 +--R + +--R 5 5 3 3 +--R - 8a x + 8a x - a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x - 1 +--R + +--R 5 5 3 3 5 5 3 3 +-------+ +--R ((24a x - 36a x + 12a x)acosh(a x) + 8a x - 8a x + a x)\|a x - 1 +--R * +--R +-------+ +--R \|a x + 1 +--R + +--R 6 6 4 4 2 2 +--R 8a x - 12a x + 4a x +--R / +--R +--------+ +--R 4 8 2 6 4 +-------+ +-------+ | 2 2 +--R (24a x - 24a x + 3x )\|a x - 1 \|a x + 1 \|a x - 1 +--R + +--R 5 9 3 7 5 +-------+ +-------+ +--R (- 24a x + 36a x - 12a x )\|a x - 1 \|a x + 1 +--R Type: Expression(Integer) +--E 115 + +)clear all + + +--S 116 of 510 +t0023:= x^2*acosh(a+b*x) +--R +--R +--R 2 +--R (1) x acosh(b x + a) +--R Type: Expression(Integer) +--E 116 + +--S 117 of 510 +r0023:= -1/18*(4*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)+_ + 11*a^2*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)-_ + 5*a*x*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b+_ + 2*x^2*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b^2-_ + 6*x^3*acosh(a+b*x)*b^3-18*a*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2))-_ + 12*a^3*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2)))/b^3 +--R +--R +--R (2) +--R +-+ +-----------+ +--R 3 \|2 \|b x + a - 1 +--R (12a + 18a)asinh(------------------) +--R 2 +--R + +--R 2 2 2 +-----------+ +-----------+ +--R (- 2b x + 5a b x - 11a - 4)\|b x + a - 1 \|b x + a + 1 +--R + +--R 3 3 +--R 6b x acosh(b x + a) +--R / +--R 3 +--R 18b +--R Type: Expression(Integer) +--E 117 + +--S 118 of 510 +a0023:= integrate(t0023,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 +--R 96b x + 192a b x + (96a - 24)b x + (96a + 144a)b x +--R + +--R 4 2 5 3 +--R (192a + 288a )b x + 96a + 120a - 36a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R - 96b x - 288a b x + (- 288a + 72)b x + (- 192a - 72a)b x +--R + +--R 4 2 2 2 5 3 6 4 +--R (- 288a - 432a )b x + (- 288a - 360a + 108a)b x - 96a - 72a +--R + +--R 2 +--R 108a +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 32b x + 16a b x + (32a + 40)b x + (208a + 192a)b x +--R + +--R 4 2 5 3 +--R (224a + 48a - 48)b x + 64a - 76a - 39a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R - 32b x - 48a b x + (- 48a - 24)b x + (- 240a - 240a)b x +--R + +--R 4 2 2 2 5 3 6 4 +--R (- 432a - 216a + 72)b x + (- 288a + 108a + 153a)b x - 64a + 108a +--R + +--R 2 +--R 9a - 16 +--R / +--R +----------------------+ +--R 5 2 4 2 3 | 2 2 2 6 3 +--R (288b x + 576a b x + (288a - 72)b )\|b x + 2a b x + a - 1 - 288b x +--R + +--R 5 2 2 4 3 3 +--R - 864a b x + (- 864a + 216)b x + (- 288a + 216a)b +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 510 +m0023:= a0023-r0023 +--R +--R +--R (4) +--R 5 5 4 4 2 3 3 3 2 2 +--R 96b x + 192a b x + (96a - 24)b x + (96a + 144a)b x +--R + +--R 4 2 5 3 +--R (192a + 288a )b x + 96a + 120a - 36a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R - 96b x - 288a b x + (- 288a + 72)b x + (- 192a - 72a)b x +--R + +--R 4 2 2 2 5 3 6 4 +--R (- 288a - 432a )b x + (- 288a - 360a + 108a)b x - 96a - 72a +--R + +--R 2 +--R 108a +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 3 2 2 4 2 5 3 +--R ((- 192a - 288a)b x + (- 384a - 576a )b x - 192a - 240a + 72a) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 3 3 3 4 2 2 2 5 3 +--R (192a + 288a)b x + (576a + 864a )b x + (576a + 720a - 216a)b x +--R + +--R 6 4 2 +--R 192a + 144a - 216a +--R * +--R +-+ +-----------+ +--R \|2 \|b x + a - 1 +--R asinh(------------------) +--R 2 +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 32b x - 16a b x + (48a + 56)b x + (272a + 148a)b x + 176a +--R + +--R 2 +--R 20a - 16 +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 5 5 4 4 2 3 3 5 5 +--R (- 96b x - 192a b x + (- 96a + 24)b x )acosh(b x + a) + 32b x +--R + +--R 4 4 2 3 3 3 2 2 +--R 16a b x + (32a + 40)b x + (208a + 192a)b x +--R + +--R 4 2 5 3 +--R (224a + 48a - 48)b x + 64a - 76a - 39a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 32b x - 16a b x + (- 32a - 40)b x + (- 320a - 228a)b x +--R + +--R 4 2 5 3 +--R (- 448a - 120a + 48)b x - 176a + 68a + 48a +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R (96b x + 288a b x + (288a - 72)b x + (96a - 72a)b x )acosh(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R - 32b x - 48a b x + (- 48a - 24)b x + (- 240a - 240a)b x +--R + +--R 4 2 2 2 5 3 6 4 +--R (- 432a - 216a + 72)b x + (- 288a + 108a + 153a)b x - 64a + 108a +--R + +--R 2 +--R 9a - 16 +--R / +--R +----------------------+ +--R 5 2 4 2 3 | 2 2 2 6 3 +--R (288b x + 576a b x + (288a - 72)b )\|b x + 2a b x + a - 1 - 288b x +--R + +--R 5 2 2 4 3 3 +--R - 864a b x + (- 864a + 216)b x + (- 288a + 216a)b +--R Type: Expression(Integer) +--E 119 + +--S 120 of 510 +d0023:= D(m0023,x) +--R +--R +--R (5) +--R 6 8 5 7 2 4 6 3 3 5 +--R 96b x + 576a b x + (1440a - 144)b x + (1920a - 576a)b x +--R + +--R 4 2 2 4 5 3 3 +--R (1440a - 864a + 54)b x + (576a - 576a + 108a)b x +--R + +--R 6 4 2 2 +--R (96a - 144a + 54a - 3)x +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 7 9 6 8 2 5 7 +--R - 96b x - 672a b x + (- 2016a + 192)b x +--R + +--R 3 4 6 4 2 3 5 +--R (- 3360a + 960a)b x + (- 3360a + 1920a - 114)b x +--R + +--R 5 3 2 4 +--R (- 2016a + 1920a - 342a)b x +--R + +--R 6 4 2 3 +--R (- 672a + 960a - 342a + 18)b x +--R + +--R 7 5 3 2 +--R (- 96a + 192a - 114a + 18a)x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 6 8 5 7 2 4 6 +--R - 96b x - 576a b x + (- 1440a + 144)b x +--R + +--R 3 3 5 4 2 2 4 +--R (- 1920a + 576a)b x + (- 1440a + 864a - 54)b x +--R + +--R 5 3 3 6 4 2 2 +--R (- 576a + 576a - 108a)b x + (- 96a + 144a - 54a + 3)x +--R * +--R acosh(b x + a) +--R + +--R 6 8 5 7 2 4 6 3 3 5 +--R 32b x + 160a b x + (320a - 32)b x + (320a - 96a)b x +--R + +--R 4 2 2 4 5 3 3 +--R (160a - 96a + 6)b x + (32a - 32a + 6a)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 7 9 6 8 2 5 7 3 4 6 +--R 32b x + 192a b x + (480a - 48)b x + (640a - 192a)b x +--R + +--R 4 2 3 5 5 3 2 4 +--R (480a - 288a + 18)b x + (192a - 192a + 36a)b x +--R + +--R 6 4 2 3 +--R (32a - 48a + 18a - 1)b x +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 7 9 6 8 2 5 7 3 4 6 +--R 96b x + 672a b x + (2016a - 192)b x + (3360a - 960a)b x +--R + +--R 4 2 3 5 5 3 2 4 +--R (3360a - 1920a + 114)b x + (2016a - 1920a + 342a)b x +--R + +--R 6 4 2 3 7 5 3 2 +--R (672a - 960a + 342a - 18)b x + (96a - 192a + 114a - 18a)x +--R * +--R acosh(b x + a) +--R + +--R 7 9 6 8 2 5 7 3 4 6 +--R - 32b x - 192a b x + (- 480a + 48)b x + (- 640a + 192a)b x +--R + +--R 4 2 3 5 5 3 2 4 +--R (- 480a + 288a - 18)b x + (- 192a + 192a - 36a)b x +--R + +--R 6 4 2 3 +--R (- 32a + 48a - 18a + 1)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 8 10 7 9 2 6 8 3 5 7 +--R - 32b x - 224a b x + (- 672a + 64)b x + (- 1120a + 320a)b x +--R + +--R 4 2 4 6 5 3 3 5 +--R (- 1120a + 640a - 38)b x + (- 672a + 640a - 114a)b x +--R + +--R 6 4 2 2 4 7 5 3 3 +--R (- 224a + 320a - 114a + 6)b x + (- 32a + 64a - 38a + 6a)b x +--R / +--R 6 6 5 5 2 4 4 3 3 3 +--R 96b x + 576a b x + (1440a - 144)b x + (1920a - 576a)b x +--R + +--R 4 2 2 2 5 3 6 4 +--R (1440a - 864a + 54)b x + (576a - 576a + 108a)b x + 96a - 144a +--R + +--R 2 +--R 54a - 3 +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R - 96b x - 672a b x + (- 2016a + 192)b x + (- 3360a + 960a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 3360a + 1920a - 114)b x + (- 2016a + 1920a - 342a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 672a + 960a - 342a + 18)b x - 96a + 192a - 114a + 18a +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R Type: Expression(Integer) +--E 120 + +)clear all + + +--S 121 of 510 +t0024:= x^3*acosh(a+b*x) +--R +--R +--R 3 +--R (1) x acosh(b x + a) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 510 +r0024:= 1/96*(55*a*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)+_ + 50*a^3*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)-_ + 9*x*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b-_ + 26*a^2*x*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b+_ + 14*a*x^2*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b^2-_ + 6*x^3*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)*b^3+_ + 24*x^4*acosh(a+b*x)*b^4-144*a^2*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2))-_ + 48*a^4*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2))-_ + 18*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2)))/b^4 +--R +--R +--R (2) +--R +-+ +-----------+ +--R 4 2 \|2 \|b x + a - 1 +--R (- 48a - 144a - 18)asinh(------------------) +--R 2 +--R + +--R 3 3 2 2 2 3 +-----------+ +--R (- 6b x + 14a b x + (- 26a - 9)b x + 50a + 55a)\|b x + a - 1 +--R * +--R +-----------+ +--R \|b x + a + 1 +--R + +--R 4 4 +--R 24b x acosh(b x + a) +--R / +--R 4 +--R 96b +--R Type: Expression(Integer) +--E 122 + +--S 123 of 510 +a0024:= integrate(t0024,x) +--R +--R +--R (3) +--R 7 7 6 6 2 5 5 3 4 4 +--R 1536b x + 4608a b x + (4608a - 768)b x + (1536a - 768a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 1536a - 4608a - 576)b x + (- 4608a - 13824a - 1728a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 4608a - 13056a + 576a + 288)b x - 1536a - 3840a + 1728a +--R + +--R 288a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 8 8 7 7 2 6 6 +--R - 1536b x - 6144a b x + (- 9216a + 1536)b x +--R + +--R 3 5 5 2 4 4 +--R (- 6144a + 3072a)b x + (6144a + 384)b x +--R + +--R 5 3 3 3 +--R (6144a + 18432a + 2304a)b x +--R + +--R 6 4 2 2 2 +--R (9216a + 26112a - 1152a - 576)b x +--R + +--R 7 5 3 8 6 4 +--R (6144a + 15360a - 6912a - 1152a)b x + 1536a + 3072a - 3840a + 72 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R 384b x + 640a b x + (384a + 192)b x + (- 384a - 1088a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 3864a - 8768a - 528)b x + (- 6984a - 11712a + 2256a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 4680a - 3508a + 5616a + 72)b x - 1048a + 716a + 2064a - 440a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 8 8 7 7 2 6 6 5 5 +--R - 384b x - 1024a b x - 1024a b x + 1024a b x +--R + +--R 4 2 4 4 5 3 3 3 +--R (4248a + 9920a + 672)b x + (10848a + 20224a - 2432a)b x +--R + +--R 6 4 2 2 2 +--R (11664a + 13544a - 11520a - 288)b x +--R + +--R 7 5 3 8 6 4 2 +--R (5728a + 976a - 9984a + 1472a)b x + 1048a - 1240a - 1837a + 1496a +--R / +--R 7 3 6 2 2 5 3 4 +--R (6144b x + 18432a b x + (18432a - 3072)b x + (6144a - 3072a)b ) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 8 4 7 3 2 6 2 +--R - 6144b x - 24576a b x + (- 36864a + 6144)b x +--R + +--R 3 5 4 2 4 +--R (- 24576a + 12288a)b x + (- 6144a + 6144a - 768)b +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 510 +m0024:= a0024-r0024 +--R +--R +--R (4) +--R 7 7 6 6 2 5 5 3 4 4 +--R 1536b x + 4608a b x + (4608a - 768)b x + (1536a - 768a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 1536a - 4608a - 576)b x + (- 4608a - 13824a - 1728a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 4608a - 13056a + 576a + 288)b x - 1536a - 3840a + 1728a +--R + +--R 288a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 8 8 7 7 2 6 6 +--R - 1536b x - 6144a b x + (- 9216a + 1536)b x +--R + +--R 3 5 5 2 4 4 +--R (- 6144a + 3072a)b x + (6144a + 384)b x +--R + +--R 5 3 3 3 +--R (6144a + 18432a + 2304a)b x +--R + +--R 6 4 2 2 2 +--R (9216a + 26112a - 1152a - 576)b x +--R + +--R 7 5 3 8 6 4 +--R (6144a + 15360a - 6912a - 1152a)b x + 1536a + 3072a - 3840a + 72 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 4 2 3 3 5 3 2 2 +--R (3072a + 9216a + 1152)b x + (9216a + 27648a + 3456a)b x +--R + +--R 6 4 2 7 5 3 +--R (9216a + 26112a - 1152a - 576)b x + 3072a + 7680a - 3456a +--R + +--R - 576a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 4 2 4 4 5 3 3 3 +--R (- 3072a - 9216a - 1152)b x + (- 12288a - 36864a - 4608a)b x +--R + +--R 6 4 2 2 2 +--R (- 18432a - 52224a + 2304a + 1152)b x +--R + +--R 7 5 3 8 6 4 +--R (- 12288a - 30720a + 13824a + 2304a)b x - 3072a - 6144a + 7680a +--R + +--R - 144 +--R * +--R +-+ +-----------+ +--R \|2 \|b x + a - 1 +--R asinh(------------------) +--R 2 +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R 384b x + 256a b x + (128a + 384)b x + (- 512a - 1536a)b x +--R + +--R 4 2 2 2 5 3 +--R (- 5504a - 9216a - 288)b x + (- 7936a - 9216a + 1472a)b x +--R + +--R 6 4 2 +--R - 3200a - 1920a + 1760a +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 7 7 6 6 2 5 5 +--R - 1536b x - 4608a b x + (- 4608a + 768)b x +--R + +--R 3 4 4 +--R (- 1536a + 768a)b x +--R * +--R acosh(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R 384b x + 640a b x + (384a + 192)b x + (- 384a - 1088a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 3864a - 8768a - 528)b x + (- 6984a - 11712a + 2256a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 4680a - 3508a + 5616a + 72)b x - 1048a + 716a + 2064a - 440a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R - 384b x - 640a b x + (- 384a - 192)b x + (384a + 1088a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (6016a + 10880a + 528)b x + (13440a + 18048a - 2256a)b x +--R + +--R 6 4 2 7 5 3 +--R (11136a + 8768a - 6672a - 72)b x + 3200a + 320a - 3120a + 440a +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 8 8 7 7 2 6 6 3 5 5 +--R 1536b x + 6144a b x + (9216a - 1536)b x + (6144a - 3072a)b x +--R + +--R 4 2 4 4 +--R (1536a - 1536a + 192)b x +--R * +--R acosh(b x + a) +--R + +--R 8 8 7 7 2 6 6 5 5 +--R - 384b x - 1024a b x - 1024a b x + 1024a b x +--R + +--R 4 2 4 4 5 3 3 3 +--R (4248a + 9920a + 672)b x + (10848a + 20224a - 2432a)b x +--R + +--R 6 4 2 2 2 +--R (11664a + 13544a - 11520a - 288)b x +--R + +--R 7 5 3 8 6 4 2 +--R (5728a + 976a - 9984a + 1472a)b x + 1048a - 1240a - 1837a + 1496a +--R / +--R 7 3 6 2 2 5 3 4 +--R (6144b x + 18432a b x + (18432a - 3072)b x + (6144a - 3072a)b ) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 8 4 7 3 2 6 2 +--R - 6144b x - 24576a b x + (- 36864a + 6144)b x +--R + +--R 3 5 4 2 4 +--R (- 24576a + 12288a)b x + (- 6144a + 6144a - 768)b +--R Type: Expression(Integer) +--E 124 + +--S 125 of 510 +d0024:= D(m0024,x) +--R +--R +--R (5) +--R 8 11 7 10 2 6 9 +--R 512b x + 4096a b x + (14336a - 1024)b x +--R + +--R 3 5 8 4 2 4 7 +--R (28672a - 6144a)b x + (35840a - 15360a + 640)b x +--R + +--R 5 3 3 6 +--R (28672a - 20480a + 2560a)b x +--R + +--R 6 4 2 2 5 +--R (14336a - 15360a + 3840a - 128)b x +--R + +--R 7 5 3 4 +--R (4096a - 6144a + 2560a - 256a)b x +--R + +--R 8 6 4 2 3 +--R (512a - 1024a + 640a - 128a + 4)x +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 9 12 8 11 2 7 10 +--R - 512b x - 4608a b x + (- 18432a + 1280)b x +--R + +--R 3 6 9 4 2 5 8 +--R (- 43008a + 8960a)b x + (- 64512a + 26880a - 1088)b x +--R + +--R 5 3 4 7 +--R (- 64512a + 44800a - 5440a)b x +--R + +--R 6 4 2 3 6 +--R (- 43008a + 44800a - 10880a + 352)b x +--R + +--R 7 5 3 2 5 +--R (- 18432a + 26880a - 10880a + 1056a)b x +--R + +--R 8 6 4 2 4 +--R (- 4608a + 8960a - 5440a + 1056a - 32)b x +--R + +--R 9 7 5 3 3 +--R (- 512a + 1280a - 1088a + 352a - 32a)x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 8 11 7 10 2 6 9 +--R - 512b x - 4096a b x + (- 14336a + 1024)b x +--R + +--R 3 5 8 4 2 4 7 +--R (- 28672a + 6144a)b x + (- 35840a + 15360a - 640)b x +--R + +--R 5 3 3 6 +--R (- 28672a + 20480a - 2560a)b x +--R + +--R 6 4 2 2 5 +--R (- 14336a + 15360a - 3840a + 128)b x +--R + +--R 7 5 3 4 +--R (- 4096a + 6144a - 2560a + 256a)b x +--R + +--R 8 6 4 2 3 +--R (- 512a + 1024a - 640a + 128a - 4)x +--R * +--R acosh(b x + a) +--R + +--R 8 11 7 10 2 6 9 3 5 8 +--R 128b x + 896a b x + (2688a - 192)b x + (4480a - 960a)b x +--R + +--R 4 2 4 7 5 3 3 6 +--R (4480a - 1920a + 80)b x + (2688a - 1920a + 240a)b x +--R + +--R 6 4 2 2 5 7 5 3 4 +--R (896a - 960a + 240a - 8)b x + (128a - 192a + 80a - 8a)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 9 12 8 11 2 7 10 3 6 9 +--R 128b x + 1024a b x + (3584a - 256)b x + (7168a - 1536a)b x +--R + +--R 4 2 5 8 5 3 4 7 +--R (8960a - 3840a + 160)b x + (7168a - 5120a + 640a)b x +--R + +--R 6 4 2 3 6 +--R (3584a - 3840a + 960a - 32)b x +--R + +--R 7 5 3 2 5 +--R (1024a - 1536a + 640a - 64a)b x +--R + +--R 8 6 4 2 4 +--R (128a - 256a + 160a - 32a + 1)b x +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 9 12 8 11 2 7 10 +--R 512b x + 4608a b x + (18432a - 1280)b x +--R + +--R 3 6 9 4 2 5 8 +--R (43008a - 8960a)b x + (64512a - 26880a + 1088)b x +--R + +--R 5 3 4 7 +--R (64512a - 44800a + 5440a)b x +--R + +--R 6 4 2 3 6 +--R (43008a - 44800a + 10880a - 352)b x +--R + +--R 7 5 3 2 5 +--R (18432a - 26880a + 10880a - 1056a)b x +--R + +--R 8 6 4 2 4 +--R (4608a - 8960a + 5440a - 1056a + 32)b x +--R + +--R 9 7 5 3 3 +--R (512a - 1280a + 1088a - 352a + 32a)x +--R * +--R acosh(b x + a) +--R + +--R 9 12 8 11 2 7 10 +--R - 128b x - 1024a b x + (- 3584a + 256)b x +--R + +--R 3 6 9 4 2 5 8 +--R (- 7168a + 1536a)b x + (- 8960a + 3840a - 160)b x +--R + +--R 5 3 4 7 6 4 2 3 6 +--R (- 7168a + 5120a - 640a)b x + (- 3584a + 3840a - 960a + 32)b x +--R + +--R 7 5 3 2 5 +--R (- 1024a + 1536a - 640a + 64a)b x +--R + +--R 8 6 4 2 4 +--R (- 128a + 256a - 160a + 32a - 1)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 10 13 9 12 2 8 11 +--R - 128b x - 1152a b x + (- 4608a + 320)b x +--R + +--R 3 7 10 4 2 6 9 +--R (- 10752a + 2240a)b x + (- 16128a + 6720a - 272)b x +--R + +--R 5 3 5 8 +--R (- 16128a + 11200a - 1360a)b x +--R + +--R 6 4 2 4 7 +--R (- 10752a + 11200a - 2720a + 88)b x +--R + +--R 7 5 3 3 6 +--R (- 4608a + 6720a - 2720a + 264a)b x +--R + +--R 8 6 4 2 2 5 +--R (- 1152a + 2240a - 1360a + 264a - 8)b x +--R + +--R 9 7 5 3 4 +--R (- 128a + 320a - 272a + 88a - 8a)b x +--R / +--R 8 8 7 7 2 6 6 3 5 5 +--R 512b x + 4096a b x + (14336a - 1024)b x + (28672a - 6144a)b x +--R + +--R 4 2 4 4 5 3 3 3 +--R (35840a - 15360a + 640)b x + (28672a - 20480a + 2560a)b x +--R + +--R 6 4 2 2 2 +--R (14336a - 15360a + 3840a - 128)b x +--R + +--R 7 5 3 8 6 4 2 +--R (4096a - 6144a + 2560a - 256a)b x + 512a - 1024a + 640a - 128a +--R + +--R 4 +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 9 9 8 8 2 7 7 +--R - 512b x - 4608a b x + (- 18432a + 1280)b x +--R + +--R 3 6 6 4 2 5 5 +--R (- 43008a + 8960a)b x + (- 64512a + 26880a - 1088)b x +--R + +--R 5 3 4 4 +--R (- 64512a + 44800a - 5440a)b x +--R + +--R 6 4 2 3 3 +--R (- 43008a + 44800a - 10880a + 352)b x +--R + +--R 7 5 3 2 2 +--R (- 18432a + 26880a - 10880a + 1056a)b x +--R + +--R 8 6 4 2 9 7 +--R (- 4608a + 8960a - 5440a + 1056a - 32)b x - 512a + 1280a +--R + +--R 5 3 +--R - 1088a + 352a - 32a +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R Type: Expression(Integer) +--E 125 + +)clear all + + +--S 126 of 510 +t0025:= acosh(a+b*x)/x^2 +--R +--R +--R acosh(b x + a) +--R (1) -------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 510 +r0025:= -acosh(a+b*x)/x-2*b*atan((-1-a)^(1/2)*_ + (a+b*x-1)^(1/2)/(-1+a)^(1/2)/(a+1+b*x)^(1/2))/(-1-a)^(1/2)/(-1+a)^(1/2) +--R +--R +--R (2) +--R +-------+ +-----------+ +--R \|- a - 1 \|b x + a - 1 +-------+ +-----+ +--R - 2b x atan(------------------------) - acosh(b x + a)\|- a - 1 \|a - 1 +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R ------------------------------------------------------------------------ +--R +-------+ +-----+ +--R x\|- a - 1 \|a - 1 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 510 +a0025:= integrate(t0025,x) +--R +--R +--R (3) +--R [ +--R +------+ +----------------------+ +--R | 2 | 2 2 2 +--R - \|a - 1 log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R b x +--R * +--R log +--R +------+ +----------------------+ +--R | 2 2 | 2 2 2 +--R (b x\|a - 1 + a - 1)\|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 2 | 2 2 +--R (- b x - a b x - a + 1)\|a - 1 + (- a + 1)b x +--R / +--R +----------------------+ +--R | 2 2 2 2 +--R x\|b x + 2a b x + a - 1 - b x - a x +--R / +--R +------+ +--R | 2 +--R x\|a - 1 +--R , +--R +--R +--------+ +----------------------+ +--R | 2 | 2 2 2 +--R - \|- a + 1 log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +--------+ +----------------------+ +--------+ +--R | 2 | 2 2 2 | 2 +--R \|- a + 1 \|b x + 2a b x + a - 1 - b x\|- a + 1 +--R - 2b x atan(-----------------------------------------------------) +--R 2 +--R a - 1 +--R / +--R +--------+ +--R | 2 +--R x\|- a + 1 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 128 + +--S 129 of 510 +m0025a:= a0025.1-r0025 +--R +--R +--R (4) +--R +------+ +----------------------+ +--R +-------+ +-----+ | 2 | 2 2 2 +--R - \|- a - 1 \|a - 1 \|a - 1 log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +-------+ +-----+ +--R b x\|- a - 1 \|a - 1 +--R * +--R log +--R +------+ +----------------------+ +--R | 2 2 | 2 2 2 +--R (b x\|a - 1 + a - 1)\|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 2 | 2 2 +--R (- b x - a b x - a + 1)\|a - 1 + (- a + 1)b x +--R / +--R +----------------------+ +--R | 2 2 2 2 +--R x\|b x + 2a b x + a - 1 - b x - a x +--R + +--R +------+ +-------+ +-----------+ +--R | 2 \|- a - 1 \|b x + a - 1 +--R 2b x\|a - 1 atan(------------------------) +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R + +--R +------+ +--R +-------+ +-----+ | 2 +--R acosh(b x + a)\|- a - 1 \|a - 1 \|a - 1 +--R / +--R +------+ +--R +-------+ +-----+ | 2 +--R x\|- a - 1 \|a - 1 \|a - 1 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 510 +d0025a:= D(m0025a,x) +--R +--R +--R (5) +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +-----------+ +-----------+ +--R (- acosh(b x + a)\|b x + a - 1 \|b x + a + 1 - b x) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +-----------+ +-----------+ +--R b x\|b x + a - 1 \|b x + a + 1 +--R / +--R +----------------------+ +--R 2 +-----------+ +-----------+ | 2 2 2 +--R x \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 510 +m0025b:= a0025.2-r0025 +--R +--R +--R (6) +--R +--------+ +----------------------+ +--R | 2 +-------+ +-----+ | 2 2 2 +--R - \|- a + 1 \|- a - 1 \|a - 1 log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R - +--R +-------+ +-----+ +--R 2b x\|- a - 1 \|a - 1 +--R * +--R +--------+ +----------------------+ +--------+ +--R | 2 | 2 2 2 | 2 +--R \|- a + 1 \|b x + 2a b x + a - 1 - b x\|- a + 1 +--R atan(-----------------------------------------------------) +--R 2 +--R a - 1 +--R + +--R +--------+ +-------+ +-----------+ +--R | 2 \|- a - 1 \|b x + a - 1 +--R 2b x\|- a + 1 atan(------------------------) +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R + +--R +--------+ +--R | 2 +-------+ +-----+ +--R acosh(b x + a)\|- a + 1 \|- a - 1 \|a - 1 +--R / +--R +--------+ +--R | 2 +-------+ +-----+ +--R x\|- a + 1 \|- a - 1 \|a - 1 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 510 +d0025b:= D(m0025b,x) +--R +--R +--R (7) +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +-----------+ +-----------+ +--R (- acosh(b x + a)\|b x + a - 1 \|b x + a + 1 - b x) +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +-----------+ +-----------+ +--R b x\|b x + a - 1 \|b x + a + 1 +--R / +--R +----------------------+ +--R 2 +-----------+ +-----------+ | 2 2 2 +--R x \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R Type: Expression(Integer) +--E 132 + +)clear all + + +--S 133 of 510 +t0026:= acosh(a+b*x)/x^3 +--R +--R +--R acosh(b x + a) +--R (1) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 133 + +--S 134 of 510 +r0026:= 1/2*b*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)/(1-a^2)/x-_ + 1/2*acosh(a+b*x)/x^2-a*b^2*atan((-1-a)^(1/2)*_ + (a+b*x-1)^(1/2)/(-1+a)^(1/2)/(a+1+b*x)^(1/2))/(-1-a)^(3/2)/(-1+a)^(3/2) +--R +--R +--R (2) +--R +-------+ +-----------+ +--R 2 2 \|- a - 1 \|b x + a - 1 +--R 2a b x atan(------------------------) +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R + +--R +-------+ +-----+ +-----------+ +-----------+ +--R - b x\|- a - 1 \|a - 1 \|b x + a - 1 \|b x + a + 1 +--R + +--R 2 +-------+ +-----+ +--R (- a + 1)acosh(b x + a)\|- a - 1 \|a - 1 +--R / +--R 2 2 +-------+ +-----+ +--R (2a - 2)x \|- a - 1 \|a - 1 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 510 +a0026:= integrate(t0026,x) +--R +--R +--R (3) +--R [ +--R +------+ +----------------------+ +--R 2 | 2 | 2 2 2 +--R (- a + 1)\|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 3 | 2 +--R ((a - 1)b x + a - a)\|a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +----------------------+ +--R 2 2 | 2 2 2 3 3 2 2 2 +--R (a b x \|b x + 2a b x + a - 1 - a b x - a b x ) +--R * +--R log +--R +------+ +----------------------+ +--R | 2 2 | 2 2 2 +--R (b x\|a - 1 - a + 1)\|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 2 | 2 2 +--R (- b x - a b x - a + 1)\|a - 1 + (a - 1)b x +--R / +--R +----------------------+ +--R | 2 2 2 2 +--R x\|b x + 2a b x + a - 1 - b x - a x +--R + +--R +------+ +----------------------+ +--R | 2 | 2 2 2 +--R a b x\|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 2 | 2 +--R (- a b x + (- a + 1)b x)\|a - 1 +--R / +--R +------+ +----------------------+ +--R 2 2 | 2 | 2 2 2 +--R (2a - 2)x \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 3 3 2 | 2 +--R ((- 2a + 2)b x + (- 2a + 2a)x )\|a - 1 +--R , +--R +--R +--------+ +----------------------+ +--R 2 | 2 | 2 2 2 +--R (- a + 1)\|- a + 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 3 | 2 +--R ((a - 1)b x + a - a)\|- a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +----------------------+ +--R 2 2 | 2 2 2 3 3 2 2 2 +--R (2a b x \|b x + 2a b x + a - 1 - 2a b x - 2a b x ) +--R * +--R +--------+ +----------------------+ +--------+ +--R | 2 | 2 2 2 | 2 +--R \|- a + 1 \|b x + 2a b x + a - 1 - b x\|- a + 1 +--R atan(-----------------------------------------------------) +--R 2 +--R a - 1 +--R + +--R +--------+ +----------------------+ +--R | 2 | 2 2 2 +--R a b x\|- a + 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 2 2 | 2 +--R (- a b x + (- a + 1)b x)\|- a + 1 +--R / +--R +--------+ +----------------------+ +--R 2 2 | 2 | 2 2 2 +--R (2a - 2)x \|- a + 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 3 3 2 | 2 +--R ((- 2a + 2)b x + (- 2a + 2a)x )\|- a + 1 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 135 + +--S 136 of 510 +m0026a:= a0026.1-r0026 +--R +--R +--R (4) +--R +------+ +----------------------+ +--R 2 +-------+ +-----+ | 2 | 2 2 2 +--R (- a + 1)\|- a - 1 \|a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 3 +-------+ +-----+ | 2 +--R ((a - 1)b x + a - a)\|- a - 1 \|a - 1 \|a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +----------------------+ +--R 2 2 +-------+ +-----+ | 2 2 2 +--R a b x \|- a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R 3 3 2 2 2 +-------+ +-----+ +--R (- a b x - a b x )\|- a - 1 \|a - 1 +--R * +--R log +--R +------+ +----------------------+ +--R | 2 2 | 2 2 2 +--R (b x\|a - 1 - a + 1)\|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 2 | 2 2 +--R (- b x - a b x - a + 1)\|a - 1 + (a - 1)b x +--R / +--R +----------------------+ +--R | 2 2 2 2 +--R x\|b x + 2a b x + a - 1 - b x - a x +--R + +--R +------+ +----------------------+ +--R 2 2 | 2 | 2 2 2 +--R - 2a b x \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 3 3 2 2 2 | 2 +--R (2a b x + 2a b x )\|a - 1 +--R * +--R +-------+ +-----------+ +--R \|- a - 1 \|b x + a - 1 +--R atan(------------------------) +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R + +--R +------+ +--R +-------+ +-----+ | 2 +-----------+ +-----------+ +--R b x\|- a - 1 \|a - 1 \|a - 1 \|b x + a - 1 \|b x + a + 1 +--R + +--R +------+ +--R 2 +-------+ +-----+ | 2 +--R ((a - 1)acosh(b x + a) + a b x)\|- a - 1 \|a - 1 \|a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 2 +-------+ +-----+ | 2 +-----------+ +-----------+ +--R (- b x - a b x)\|- a - 1 \|a - 1 \|a - 1 \|b x + a - 1 \|b x + a + 1 +--R + +--R 2 3 2 2 2 +--R (((- a + 1)b x - a + a)acosh(b x + a) - a b x + (- a + 1)b x) +--R * +--R +------+ +--R +-------+ +-----+ | 2 +--R \|- a - 1 \|a - 1 \|a - 1 +--R / +--R +------+ +----------------------+ +--R 2 2 +-------+ +-----+ | 2 | 2 2 2 +--R (2a - 2)x \|- a - 1 \|a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +------+ +--R 2 3 3 2 +-------+ +-----+ | 2 +--R ((- 2a + 2)b x + (- 2a + 2a)x )\|- a - 1 \|a - 1 \|a - 1 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 510 +d0026a:= D(m0026a,x) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 +--R 32b x + 160a b x + (336a - 56)b x + (384a - 184a)b x +--R + +--R 4 2 2 2 5 3 6 +--R (256a - 232a + 26)b x + (96a - 136a + 42a)b x + 16a +--R + +--R 4 2 +--R - 32a + 18a - 2 +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 5 5 3 4 4 +--R (- 32a + 32)b x + (- 144a + 144a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 256a + 296a - 40)b x + (- 224a + 328a - 104a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 96a + 184a - 98a + 10)b x - 16a + 40a - 32a + 8a +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 7 7 6 6 2 5 5 +--R - 32b x - 192a b x + (- 496a + 72)b x +--R + +--R 3 4 4 4 2 3 3 +--R (- 720a + 304a)b x + (- 640a + 520a - 50)b x +--R + +--R 5 3 2 2 +--R (- 352a + 456a - 124a)b x +--R + +--R 6 4 2 7 5 3 +--R (- 112a + 208a - 106a + 10)b x - 16a + 40a - 32a + 8a +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 6 6 3 5 5 4 2 4 4 +--R (32a - 32)b x + (176a - 176a)b x + (400a - 456a + 56)b x +--R + +--R 5 3 3 3 6 4 2 2 2 +--R (480a - 680a + 200a)b x + (320a - 584a + 290a - 26)b x +--R + +--R 7 5 3 8 6 4 2 +--R (112a - 264a + 196a - 44a)b x + 16a - 48a + 50a - 20a + 2 +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 6 6 5 5 2 4 4 +--R - 32b x - 160a b x + (- 336a + 56)b x +--R + +--R 3 3 3 4 2 2 2 +--R (- 384a + 184a)b x + (- 256a + 232a - 26)b x +--R + +--R 5 3 6 4 2 +--R (- 96a + 136a - 42a)b x - 16a + 32a - 18a + 2 +--R * +--R acosh(b x + a) +--R + +--R 6 6 5 5 2 4 4 3 3 3 +--R - 16b x - 64a b x + (- 104a + 20)b x + (- 88a + 48a)b x +--R + +--R 4 2 2 2 5 3 +--R (- 40a + 40a - 5)b x + (- 8a + 12a - 4a)b x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 5 5 3 4 4 +--R (32a - 32)b x + (144a - 144a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (256a - 296a + 40)b x + (224a - 328a + 104a)b x +--R + +--R 6 4 2 7 5 3 +--R (96a - 184a + 98a - 10)b x + 16a - 40a + 32a - 8a +--R * +--R acosh(b x + a) +--R + +--R 2 5 5 3 4 4 4 2 3 3 +--R (16a - 16)b x + (56a - 56a)b x + (72a - 84a + 12)b x +--R + +--R 5 3 2 2 6 4 2 +--R (40a - 60a + 20a)b x + (8a - 16a + 9a - 1)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R - 16b x - 80a b x + (- 168a + 28)b x + (- 192a + 92a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (- 128a + 116a - 13)b x + (- 48a + 68a - 21a)b x +--R + +--R 6 4 2 +--R (- 8a + 16a - 9a + 1)b x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 6 6 3 5 5 4 2 4 4 +--R (16a - 16)b x + (72a - 72a)b x + (128a - 148a + 20)b x +--R + +--R 5 3 3 3 6 4 2 2 2 +--R (112a - 164a + 52a)b x + (48a - 92a + 49a - 5)b x +--R + +--R 7 5 3 +--R (8a - 20a + 16a - 4a)b x +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R 32b x + 192a b x + (496a - 72)b x + (720a - 304a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (640a - 520a + 50)b x + (352a - 456a + 124a)b x +--R + +--R 6 4 2 7 5 3 +--R (112a - 208a + 106a - 10)b x + 16a - 40a + 32a - 8a +--R * +--R acosh(b x + a) +--R + +--R 7 7 6 6 2 5 5 3 4 4 +--R 16b x + 80a b x + (168a - 28)b x + (192a - 92a)b x +--R + +--R 4 2 3 3 5 3 2 2 +--R (128a - 116a + 13)b x + (48a - 68a + 21a)b x +--R + +--R 6 4 2 +--R (8a - 16a + 9a - 1)b x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 6 6 3 5 5 +--R (- 32a + 32)b x + (- 176a + 176a)b x +--R + +--R 4 2 4 4 5 3 3 3 +--R (- 400a + 456a - 56)b x + (- 480a + 680a - 200a)b x +--R + +--R 6 4 2 2 2 +--R (- 320a + 584a - 290a + 26)b x +--R + +--R 7 5 3 8 6 4 2 +--R (- 112a + 264a - 196a + 44a)b x - 16a + 48a - 50a + 20a - 2 +--R * +--R acosh(b x + a) +--R + +--R 2 6 6 3 5 5 4 2 4 4 +--R (- 16a + 16)b x + (- 72a + 72a)b x + (- 128a + 148a - 20)b x +--R + +--R 5 3 3 3 6 4 2 2 2 +--R (- 112a + 164a - 52a)b x + (- 48a + 92a - 49a + 5)b x +--R + +--R 7 5 3 +--R (- 8a + 20a - 16a + 4a)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 8 8 7 7 2 6 6 3 5 5 +--R 16b x + 96a b x + (248a - 36)b x + (360a - 152a)b x +--R + +--R 4 2 4 4 5 3 3 3 +--R (320a - 260a + 25)b x + (176a - 228a + 62a)b x +--R + +--R 6 4 2 2 2 7 5 3 +--R (56a - 104a + 53a - 5)b x + (8a - 20a + 16a - 4a)b x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 7 7 3 6 6 4 2 5 5 +--R (- 16a + 16)b x + (- 88a + 88a)b x + (- 200a + 228a - 28)b x +--R + +--R 5 3 4 4 6 4 2 3 3 +--R (- 240a + 340a - 100a)b x + (- 160a + 292a - 145a + 13)b x +--R + +--R 7 5 3 2 2 8 6 4 2 +--R (- 56a + 132a - 98a + 22a)b x + (- 8a + 24a - 25a + 10a - 1)b x +--R / +--R 6 9 5 8 2 4 7 3 3 6 +--R 32b x + 160a b x + (336a - 56)b x + (384a - 184a)b x +--R + +--R 4 2 2 5 5 3 4 +--R (256a - 232a + 26)b x + (96a - 136a + 42a)b x +--R + +--R 6 4 2 3 +--R (16a - 32a + 18a - 2)x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 5 8 3 4 7 4 2 3 6 +--R (- 32a + 32)b x + (- 144a + 144a)b x + (- 256a + 296a - 40)b x +--R + +--R 5 3 2 5 6 4 2 4 +--R (- 224a + 328a - 104a)b x + (- 96a + 184a - 98a + 10)b x +--R + +--R 7 5 3 3 +--R (- 16a + 40a - 32a + 8a)x +--R * +--R +----------------------+ +--R +-----------+ +-----------+ | 2 2 2 +--R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 +--R + +--R 7 10 6 9 2 5 8 3 4 7 +--R - 32b x - 192a b x + (- 496a + 72)b x + (- 720a + 304a)b x +--R + +--R 4 2 3 6 5 3 2 5 +--R (- 640a + 520a - 50)b x + (- 352a + 456a - 124a)b x +--R + +--R 6 4 2 4 7 5 3 3 +--R (- 112a + 208a - 106a + 10)b x + (- 16a + 40a - 32a + 8a)x +--R * +--R +------+ +--R | 2 +--R \|a - 1 +--R + +--R 2 6 9 3 5 8 4 2 4 7 +--R (32a - 32)b x + (176a - 176a)b x + (400a - 456a + 56)b x +--R + +--R 5 3 3 6 6 4 2 2 5 +--R (480a - 680a + 200a)b x + (320a - 584a + 290a - 26)b x +--R + +--R 7 5 3 4 8 6 4 2 3 +--R (112a - 264a + 196a - 44a)b x + (16a - 48a + 50a - 20a + 2)x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 510 +m0026b:= a0026.2-r0026 +--R +--R +--R (6) +--R +--------+ +----------------------+ +--R 2 | 2 +-------+ +-----+ | 2 2 2 +--R (- a + 1)\|- a + 1 \|- a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 3 | 2 +-------+ +-----+ +--R ((a - 1)b x + a - a)\|- a + 1 \|- a - 1 \|a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R +----------------------+ +--R 2 2 +-------+ +-----+ | 2 2 2 +--R 2a b x \|- a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R 3 3 2 2 2 +-------+ +-----+ +--R (- 2a b x - 2a b x )\|- a - 1 \|a - 1 +--R * +--R +--------+ +----------------------+ +--------+ +--R | 2 | 2 2 2 | 2 +--R \|- a + 1 \|b x + 2a b x + a - 1 - b x\|- a + 1 +--R atan(-----------------------------------------------------) +--R 2 +--R a - 1 +--R + +--R +--------+ +----------------------+ +--R 2 2 | 2 | 2 2 2 +--R - 2a b x \|- a + 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 3 3 2 2 2 | 2 +--R (2a b x + 2a b x )\|- a + 1 +--R * +--R +-------+ +-----------+ +--R \|- a - 1 \|b x + a - 1 +--R atan(------------------------) +--R +-----+ +-----------+ +--R \|a - 1 \|b x + a + 1 +--R + +--R +--------+ +--R | 2 +-------+ +-----+ +-----------+ +-----------+ +--R b x\|- a + 1 \|- a - 1 \|a - 1 \|b x + a - 1 \|b x + a + 1 +--R + +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R ((a - 1)acosh(b x + a) + a b x)\|- a + 1 \|- a - 1 \|a - 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 2 | 2 +-------+ +-----+ +-----------+ +-----------+ +--R (- b x - a b x)\|- a + 1 \|- a - 1 \|a - 1 \|b x + a - 1 \|b x + a + 1 +--R + +--R 2 3 2 2 2 +--R (((- a + 1)b x - a + a)acosh(b x + a) - a b x + (- a + 1)b x) +--R * +--R +--------+ +--R | 2 +-------+ +-----+ +--R \|- a + 1 \|- a - 1 \|a - 1 +--R / +--R +--------+ +----------------------+ +--R 2 2 | 2 +-------+ +-----+ | 2 2 2 +--R (2a - 2)x \|- a + 1 \|- a - 1 \|a - 1 \|b x + 2a b x + a - 1 +--R + +--R +--------+ +--R 2 3 3 2 | 2 +-------+ +-----+ +--R ((- 2a + 2)b x + (- 2a + 2a)x )\|- a + 1 \|- a - 1 \|a - 1 +--R Type: Expression(Integer) +--E 138 + +--S 139 of 510 +d0026b:= D(m0026b,x) +--R +--R +--R (7) +--R 2 2 2 +-----------+ +-----------+ +--R (4b x + 8a b x + 4a - 2)\|b x + a - 1 \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 3 3 2 2 2 3 +-----------+ +--R (- 4b x - 12a b x + (- 12a + 4)b x - 4a + 4a)\|b x + a - 1 +--R * +--R +-----------+ +--R \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a - 1 + b x + a) +--R + +--R 2 2 2 2 2 +--R ((- 4b x - 8a b x - 4a + 2)acosh(b x + a) - 2b x - 2a b x) +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 3 3 2 2 2 +--R - 2b x - 4a b x + (- 2a + 1)b x +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 3 3 2 2 2 3 3 3 +--R (4b x + 12a b x + (12a - 4)b x + 4a - 4a)acosh(b x + a) + 2b x +--R + +--R 2 2 2 +--R 4a b x + (2a - 1)b x +--R * +--R +-----------+ +-----------+ +--R \|b x + a - 1 \|b x + a + 1 +--R + +--R 4 4 3 3 2 2 2 3 +--R 2b x + 6a b x + (6a - 2)b x + (2a - 2a)b x +--R / +--R 2 5 4 2 3 +-----------+ +-----------+ +--R (4b x + 8a b x + (4a - 2)x )\|b x + a - 1 \|b x + a + 1 +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R 3 6 2 5 2 4 3 3 +-----------+ +--R (- 4b x - 12a b x + (- 12a + 4)b x + (- 4a + 4a)x )\|b x + a - 1 +--R * +--R +-----------+ +--R \|b x + a + 1 +--R Type: Expression(Integer) +--E 139 + +)clear all + + +--S 140 of 510 +t0027:= 1/(a+b*acosh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (1) ----------------------- +--R +--------------------+ +--R \|b acosh(d x + c) + a +--R Type: Expression(Integer) +--E 140 + +--S 141 of 510 +r0027:= -1/2*%pi^(1/2)*(exp(2*a/b)*erf((a+b*acosh(c+d*x))^(1/2)/b^(1/2))+_ + %i*erf(%i*(a+b*acosh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d +--R +--R +--R (2) +--R a 2a +--R - - -- +--------------------+ +--R b b +---+ \|b acosh(d x + c) + a +--R - %e %e \|%pi erf(-----------------------) +--R +-+ +--R \|b +--R + +--R a +--R - - +--------------------+ +--R b +---+ %i\|b acosh(d x + c) + a +--R - %i %e \|%pi erf(-------------------------) +--R +-+ +--R \|b +--R / +--R +-+ +--R 2d\|b +--R Type: Expression(Complex(Integer)) +--E 141 + +--S 142 of 510 +a0027:= integrate(t0027,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 142 + +--S 143 of 510 +--m0027:= a0027-r0027 +--E 143 + +--S 144 of 510 +--d0027:= D(m0027,x) +--E 144 + +)clear all + + +--S 145 of 510 +t0028:= 1/(a-b*acosh(c+d*x))^(1/2) +--R +--R +--R 1 +--R (1) ------------------------- +--R +----------------------+ +--R \|- b acosh(d x + c) + a +--R Type: Expression(Integer) +--E 145 + +--S 146 of 510 +r0028:= -1/2*%pi^(1/2)*(exp(2*a/b)*erf((a-b*acosh(c+d*x))^(1/2)/b^(1/2))+_ + %i*erf(%i*(a-b*acosh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d +--R +--R +--R (2) +--R a 2a +--R - - -- +----------------------+ +--R b b +---+ \|- b acosh(d x + c) + a +--R - %e %e \|%pi erf(-------------------------) +--R +-+ +--R \|b +--R + +--R a +--R - - +----------------------+ +--R b +---+ %i\|- b acosh(d x + c) + a +--R - %i %e \|%pi erf(---------------------------) +--R +-+ +--R \|b +--R / +--R +-+ +--R 2d\|b +--R Type: Expression(Complex(Integer)) +--E 146 + +--S 147 of 510 +a0028:= integrate(t0028,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 147 + +--S 148 of 510 +--m0028:= a0028-r0028 +--E 148 + +--S 149 of 510 +--d0028:= D(m0028,x) +--E 149 + +)clear all + + +--S 150 of 510 +t0029:= acosh(x^(1/2)) +--R +--R +--R +-+ +--R (1) acosh(\|x ) +--R Type: Expression(Integer) +--E 150 + +--S 151 of 510 +r0029:= -1/2*(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)*x^(1/2)-_ + 1/2*acosh(x^(1/2))+x*acosh(x^(1/2)) +--R +--R +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ +-+ +--R - \|x \|\|x - 1 \|\|x + 1 + (2x - 1)acosh(\|x ) +--R (2) -------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 151 + +-- sometimes this seems to come out with a different sign +-- +-- +-- (113) +-- +-----+ +-+ 2 +-+ +-----+ +-- ((4x - 2)\|x - 1 \|x + 4x - 4x + 1)log(\|x + \|x - 1 ) +-- + +-- +-----+ +-+ 2 +-- (- 2x + 1)\|x - 1 \|x - 2x + 2x +-- / +-- +-----+ +-+ +-- 4\|x - 1 \|x + 4x - 2 +-- Type: Union(Expression(Integer),...) + +--S 152 of 510 ok if failed. sometimes has different sign (see above) +a0029:= integrate(t0029,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 152 + +-- sometimes this seems sometimes have different sign +-- +-- +-- (114) +-- +--------+ +--------+ +-- +-+ +-----+ | +-+ | +-+ +-- ((2x - 1)\|x + 2x\|x - 1 )\|\|x - 1 \|\|x + 1 +-- + +-- +-----+ +-+ 2 +-+ +-----+ +-- ((4x - 2)\|x - 1 \|x + 4x - 4x + 1)log(\|x + \|x - 1 ) +-- + +-- +-----+ +-+ 2 +-+ +-- ((- 4x + 2)\|x - 1 \|x - 4x + 4x - 1)acosh(\|x ) +-- + +-- +-----+ +-+ 2 +-- (- 2x + 1)\|x - 1 \|x - 2x + 2x +-- / +-- +-----+ +-+ +-- 4\|x - 1 \|x + 4x - 2 +-- Type: Expression(Integer) +--S 153 of 510 ok if failed. sometimes has different sign (see above) +m0029:= a0029-r0029 +--R +--R +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ +-+ +--R \|x \|\|x - 1 \|\|x + 1 + (- 2x + 1)acosh(\|x ) + 2a0029 +--R (3) ----------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 153 + +-- sometimes this seems sometimes have different sign +-- +-- +-- (115) +-- 2 +-----+ +-+ 3 2 +-- ((32x - 32x + 4)\|x - 1 \|x + 32x - 48x + 16x) +-- * +-- +-+ +-----+ +-- log(\|x + \|x - 1 ) +-- + +-- 2 +-----+ +-+ 3 2 +-+ +-- ((- 32x + 32x - 4)\|x - 1 \|x - 32x + 48x - 16x)acosh(\|x ) +-- + +-- 2 +-----+ +-+ 3 2 +-- (- 16x + 16x - 4)\|x - 1 \|x - 16x + 24x - 10x + 1 +-- * +-- +--------+ +--------+ +-- | +-+ | +-+ +-- \|\|x - 1 \|\|x + 1 +-- + +-- 3 2 +-+ 3 2 +-----+ +-- (16x - 32x + 20x - 4)\|x + (16x - 24x + 10x - 1)\|x - 1 +-- / +-- +--------+ +--------+ +-- 2 +-----+ +-+ 3 2 | +-+ | +-+ +-- ((32x - 32x + 4)\|x - 1 \|x + 32x - 48x + 16x)\|\|x - 1 \|\|x + 1 +-- Type: Expression(Integer) + +--S 154 of 510 ok if failed. sometimes has different sign (see above) +d0029:= D(m0029,x) +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-----+ +-+ +-+ | +-+ | +-+ +--R (- 4\|x - 1 \|x acosh(\|x ) - 2x + 1)\|\|x - 1 \|\|x + 1 +--R + +--R +-----+ +--R (2x - 1)\|x - 1 +--R / +--R +--------+ +--------+ +--R +-----+ +-+ | +-+ | +-+ +--R 4\|x - 1 \|x \|\|x - 1 \|\|x + 1 +--R Type: Expression(Integer) +--E 154 + +)clear all + + +--S 155 of 510 +t0030:= acosh(x^(1/2))/x +--R +--R +--R +-+ +--R acosh(\|x ) +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 155 + +--S 156 of 510 +r0030:= acosh(x^(1/2))^2+2*acosh(x^(1/2))*log(1+exp(1)^(-2*acosh(x^(1/2))))-_ + polylog(2,-exp(1)^(-2*acosh(x^(1/2)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 156 + +--S 157 of 510 +a0030:= integrate(t0030,x) +--R +--R +--R x +--+ +--I ++ acosh(\|%T ) +--I (2) | ------------ d%T +--I ++ %T +--R Type: Union(Expression(Integer),...) +--E 157 + +--S 158 of 510 +--m0030:= a0030-r0030 +--E 158 + +--S 159 of 510 +--d0030:= D(m0030,x) +--E 159 + +)clear all + + +--S 160 of 510 +t0031:= x*atanh(a*x) +--R +--R +--R (1) x atanh(a x) +--R Type: Expression(Integer) +--E 160 + +--S 161 of 510 +r0031:= 1/2*(a*x-atanh(a*x)+x^2*atanh(a*x)*a^2)/a^2 +--R +--R +--R 2 2 +--R (a x - 1)atanh(a x) + a x +--R (2) -------------------------- +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 510 +a0031:= integrate(t0031,x) +--R +--R +--R 2 2 - a x - 1 +--R (a x - 1)log(---------) + 2a x +--R a x - 1 +--R (3) ------------------------------- +--R 2 +--R 4a +--R Type: Union(Expression(Integer),...) +--E 162 + +--S 163 of 510 +m0031:= a0031-r0031 +--R +--R +--R 2 2 - a x - 1 2 2 +--R (a x - 1)log(---------) + (- 2a x + 2)atanh(a x) +--R a x - 1 +--R (4) -------------------------------------------------- +--R 2 +--R 4a +--R Type: Expression(Integer) +--E 163 + +--S 164 of 510 +d0031:= D(m0031,x) +--R +--R +--R - a x - 1 +--R x log(---------) - 2x atanh(a x) +--R a x - 1 +--R (5) -------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 164 + +)clear all + + +--S 165 of 510 +t0032:= atanh(a*x)/x +--R +--R +--R atanh(a x) +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 165 + +--S 166 of 510 +r0032:= -1/2*polylog(2,-a*x)+1/2*polylog(2,a*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 166 + +--S 167 of 510 +a0032:= integrate(t0032,x) +--R +--R +--R x +--I ++ atanh(%T a) +--I (2) | ----------- d%T +--I ++ %T +--R Type: Union(Expression(Integer),...) +--E 167 + +--S 168 of 510 +--m0032:= a0032-r0032 +--E 168 + +--S 169 of 510 +--d0032:= D(m0032,x) +--E 169 + +)clear all + + +--S 170 of 510 +t0033:= atanh(a*x)/x^3 +--R +--R +--R atanh(a x) +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 170 + +--S 171 of 510 +r0033:= 1/2*(-atanh(a*x)+x^2*atanh(a*x)*a^2-a*x)/x^2 +--R +--R +--R 2 2 +--R (a x - 1)atanh(a x) - a x +--R (2) -------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 510 +a0033:= integrate(t0033,x) +--R +--R +--R 2 2 - a x - 1 +--R (a x - 1)log(---------) - 2a x +--R a x - 1 +--R (3) ------------------------------- +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 172 + +--S 173 of 510 +m0033:= a0033-r0033 +--R +--R +--R 2 2 - a x - 1 2 2 +--R (a x - 1)log(---------) + (- 2a x + 2)atanh(a x) +--R a x - 1 +--R (4) -------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 173 + +--S 174 of 510 +d0033:= D(m0033,x) +--R +--R +--R - a x - 1 +--R log(---------) - 2atanh(a x) +--R a x - 1 +--R (5) ---------------------------- +--R 3 +--R 2x +--R Type: Expression(Integer) +--E 174 + +)clear all + + +--S 175 of 510 +t0034:= (a+b*x)*atanh(a+b*x) +--R +--R +--R (1) (b x + a)atanh(b x + a) +--R Type: Expression(Integer) +--E 175 + +--S 176 of 510 +r0034:= 1/2/b*(a+b*x)-1/2*atanh(a+b*x)/b+1/2*(a+b*x)^2*atanh(a+b*x)/b +--R +--R +--R 2 2 2 +--R (b x + 2a b x + a - 1)atanh(b x + a) + b x + a +--R (2) ------------------------------------------------ +--R 2b +--R Type: Expression(Integer) +--E 176 + +--S 177 of 510 +a0034:= integrate(t0034,x) +--R +--R +--R 2 2 2 - b x - a - 1 +--R (b x + 2a b x + a - 1)log(-------------) + 2b x +--R b x + a - 1 +--R (3) ------------------------------------------------- +--R 4b +--R Type: Union(Expression(Integer),...) +--E 177 + +--S 178 of 510 +m0034:= a0034-r0034 +--R +--R +--R (4) +--R 2 2 2 - b x - a - 1 +--R (b x + 2a b x + a - 1)log(-------------) +--R b x + a - 1 +--R + +--R 2 2 2 +--R (- 2b x - 4a b x - 2a + 2)atanh(b x + a) - 2a +--R / +--R 4b +--R Type: Expression(Integer) +--E 178 + +--S 179 of 510 +d0034:= D(m0034,x) +--R +--R +--R - b x - a - 1 +--R (b x + a)log(-------------) + (- 2b x - 2a)atanh(b x + a) +--R b x + a - 1 +--R (5) --------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 179 + +)clear all + + +--S 180 of 510 +t0035:= (a+b*x)^2*atanh(a+b*x) +--R +--R +--R 2 2 2 +--R (1) (b x + 2a b x + a )atanh(b x + a) +--R Type: Expression(Integer) +--E 180 + +--S 181 of 510 +r0035:= 1/6*(a+b*x)^2/b+1/3*(a+b*x)^3*atanh(a+b*x)/b+1/6*log(1-(a+b*x)^2)/b +--R +--R +--R (2) +--R 2 2 2 +--R log(- b x - 2a b x - a + 1) +--R + +--R 3 3 2 2 2 3 2 2 2 +--R (2b x + 6a b x + 6a b x + 2a )atanh(b x + a) + b x + 2a b x + a +--R / +--R 6b +--R Type: Expression(Integer) +--E 181 + +--S 182 of 510 +a0035:= integrate(t0035,x) +--R +--R +--R (3) +--R 3 3 +--R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) +--R + +--R 3 3 2 2 2 - b x - a - 1 2 2 +--R (b x + 3a b x + 3a b x)log(-------------) + b x + 2a b x +--R b x + a - 1 +--R / +--R 6b +--R Type: Union(Expression(Integer),...) +--E 182 + +--S 183 of 510 +m0035:= a0035-r0035 +--R +--R +--R (4) +--R 3 3 +--R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) +--R + +--R 3 3 2 2 2 - b x - a - 1 +--R (b x + 3a b x + 3a b x)log(-------------) +--R b x + a - 1 +--R + +--R 2 2 2 +--R - log(- b x - 2a b x - a + 1) +--R + +--R 3 3 2 2 2 3 2 +--R (- 2b x - 6a b x - 6a b x - 2a )atanh(b x + a) - a +--R / +--R 6b +--R Type: Expression(Integer) +--E 183 + +--S 184 of 510 +d0035:= D(m0035,x) +--R +--R +--R (5) +--R 2 2 2 - b x - a - 1 +--R (b x + 2a b x + a )log(-------------) +--R b x + a - 1 +--R + +--R 2 2 2 +--R (- 2b x - 4a b x - 2a )atanh(b x + a) +--R / +--R 2 +--R Type: Expression(Integer) +--E 184 + +)clear all + + +--S 185 of 510 +t0036:= atanh(1+x)/(2+2*x) +--R +--R +--R atanh(x + 1) +--R (1) ------------ +--R 2x + 2 +--R Type: Expression(Integer) +--E 185 + +--S 186 of 510 +r0036:= -1/4*polylog(2,-1-x)+1/4*polylog(2,1+x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 186 + +--S 187 of 510 +a0036:= integrate(t0036,x) +--R +--R +--R x +--I ++ atanh(%T + 1) +--I (2) | ------------- d%T +--I ++ 2%T + 2 +--R Type: Union(Expression(Integer),...) +--E 187 + +--S 188 of 510 +--m0036:= a0036-r0036 +--E 188 + +--S 189 of 510 +--d0036:= D(m0036,x) +--E 189 + +)clear all + + +--S 190 of 510 +t0037:= atanh(a+b*x)/(a+b*x) +--R +--R +--R atanh(b x + a) +--R (1) -------------- +--R b x + a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 510 +r0037:= -1/2*(polylog(2,-a-b*x)-polylog(2,a+b*x))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 191 + +--S 192 of 510 +a0037:= integrate(t0037,x) +--R +--R +--R x +--I ++ atanh(%T b + a) +--I (2) | --------------- d%T +--I ++ %T b + a +--R Type: Union(Expression(Integer),...) +--E 192 + +--S 193 of 510 +--m0037:= a0037-r0037 +--E 193 + +--S 194 of 510 +--d0037:= D(m0037,x) +--E 194 + +)clear all + + +--S 195 of 510 +t0038:= atanh(x)/(1-x^2)^2 +--R +--R +--R atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 195 + +--S 196 of 510 +r0038:= 1/4*(1-2*x*atanh(x)-atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) +--R +--R +--R 2 2 +--R (x - 1)atanh(x) - 2x atanh(x) + 1 +--R (2) ----------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 510 +a0038:= integrate(t0038,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R (x - 1)log(-------) - 4x log(-------) + 4 +--R x - 1 x - 1 +--R (3) ------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression(Integer),...) +--E 197 + +--S 198 of 510 +m0038:= a0038-r0038 +--R +--R +--R (4) +--R 2 - x - 1 2 - x - 1 2 2 +--R (x - 1)log(-------) - 4x log(-------) + (- 4x + 4)atanh(x) + 8x atanh(x) +--R x - 1 x - 1 +--R ---------------------------------------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Expression(Integer) +--E 198 + +--S 199 of 510 +d0038:= D(m0038,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) ------------------------ +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression(Integer) +--E 199 + +)clear all + + +--S 200 of 510 +t0039:= atanh(x)^2/(1-x^2)^2 +--R +--R +--R 2 +--R atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 510 +r0039:= 1/12*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2-2*atanh(x)^3+_ + 2*x^2*atanh(x)^3)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (2x - 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x +--R (2) ---------------------------------------------------------- +--R 2 +--R 12x - 12 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 510 +a0039:= integrate(t0039,x) +--R +--R +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x +--R x - 1 x - 1 x - 1 +--R (3) ---------------------------------------------------------------------- +--R 2 +--R 48x - 48 +--R Type: Union(Expression(Integer),...) +--E 202 + +--S 203 of 510 +m0039:= a0039-r0039 +--R +--R +--R (4) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (- 8x + 8)atanh(x) + 24x atanh(x) + (- 12x - 12)atanh(x) +--R / +--R 2 +--R 48x - 48 +--R Type: Expression(Integer) +--E 203 + +--S 204 of 510 +d0039:= D(m0039,x) +--R +--R +--R - x - 1 2 2 +--R log(-------) - 4atanh(x) +--R x - 1 +--R (5) -------------------------- +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression(Integer) +--E 204 + +)clear all + + +--S 205 of 510 +t0040:= 1/(a-a*x^2)/(b-2*b*atanh(x)) +--R +--R +--R 1 +--R (1) --------------------------------------- +--R 2 2 +--R (2a b x - 2a b)atanh(x) - a b x + a b +--R Type: Expression(Integer) +--E 205 + +--S 206 of 510 +r0040:= -1/2*log(1-2*atanh(x))/a/b +--R +--R +--R log(- 2atanh(x) + 1) +--R (2) - -------------------- +--R 2a b +--R Type: Expression(Integer) +--E 206 + +--S 207 of 510 +a0040:= integrate(t0040,x) +--R +--R +--R - x - 1 +--R log(log(-------) - 1) +--R x - 1 +--R (3) - --------------------- +--R 2a b +--R Type: Union(Expression(Integer),...) +--E 207 + +--S 208 of 510 +m0040:= a0040-r0040 +--R +--R +--R - x - 1 +--R - log(log(-------) - 1) + log(- 2atanh(x) + 1) +--R x - 1 +--R (4) ---------------------------------------------- +--R 2a b +--R Type: Expression(Integer) +--E 208 + +--S 209 of 510 +d0040:= D(m0040,x) +--R +--R +--R (5) +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R / +--R 2 2 - x - 1 +--R ((2a b x - 2a b)atanh(x) - a b x + a b)log(-------) +--R x - 1 +--R + +--R 2 2 +--R (- 2a b x + 2a b)atanh(x) + a b x - a b +--R Type: Expression(Integer) +--E 209 + +)clear all + + +--S 210 of 510 +t0041:= x*atanh(x)/(1-x^2) +--R +--R +--R x atanh(x) +--R (1) - ---------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 210 + +--S 211 of 510 +r0041:= -1/2*atanh(x)^2+atanh(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 510 +a0041:= integrate(t0041,x) +--R +--R +--R x +--I ++ %T atanh(%T) +--I (2) | - ------------ d%T +--R ++ 2 +--I %T - 1 +--R Type: Union(Expression(Integer),...) +--E 212 + +--S 213 of 510 +--m0041:= a0041-r0041 +--E 213 + +--S 214 of 510 +--d0041:= D(m0041,x) +--E 214 + +)clear all + + +--S 215 of 510 +t0042:= x*atanh(x)/(1-x^2)^2 +--R +--R +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 215 + +--S 216 of 510 +r0042:= -1/4*(-x+atanh(x)+x^2*atanh(x))/(-1+x^2) +--R +--R +--R 2 +--R (- x - 1)atanh(x) + x +--R (2) ---------------------- +--R 2 +--R 4x - 4 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 510 +a0042:= integrate(t0042,x) +--R +--R +--R 2 - x - 1 +--R (- x - 1)log(-------) + 2x +--R x - 1 +--R (3) --------------------------- +--R 2 +--R 8x - 8 +--R Type: Union(Expression(Integer),...) +--E 217 + +--S 218 of 510 +m0042:= a0042-r0042 +--R +--R +--R 2 - x - 1 2 +--R (- x - 1)log(-------) + (2x + 2)atanh(x) +--R x - 1 +--R (4) ------------------------------------------ +--R 2 +--R 8x - 8 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 510 +d0042:= D(m0042,x) +--R +--R +--R - x - 1 +--R x log(-------) - 2x atanh(x) +--R x - 1 +--R (5) ---------------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression(Integer) +--E 219 + +)clear all + + +--S 220 of 510 +t0043:= x*atanh(x)/(1-x^2)^3 +--R +--R +--R x atanh(x) +--R (1) - ------------------ +--R 6 4 2 +--R x - 3x + 3x - 1 +--R Type: Expression(Integer) +--E 220 + +--S 221 of 510 +r0043:= -1/32*(5*x-3*x^3-5*atanh(x)-6*x^2*atanh(x)+3*atanh(x)*x^4)/(-1+x^2)^2 +--R +--R +--R 4 2 3 +--R (- 3x + 6x + 5)atanh(x) + 3x - 5x +--R (2) ------------------------------------ +--R 4 2 +--R 32x - 64x + 32 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 510 +a0043:= integrate(t0043,x) +--R +--R +--R 4 2 - x - 1 3 +--R (- 3x + 6x + 5)log(-------) + 6x - 10x +--R x - 1 +--R (3) ----------------------------------------- +--R 4 2 +--R 64x - 128x + 64 +--R Type: Union(Expression(Integer),...) +--E 222 + +--S 223 of 510 +m0043:= a0043-r0043 +--R +--R +--R 4 2 - x - 1 4 2 +--R (- 3x + 6x + 5)log(-------) + (6x - 12x - 10)atanh(x) +--R x - 1 +--R (4) --------------------------------------------------------- +--R 4 2 +--R 64x - 128x + 64 +--R Type: Expression(Integer) +--E 223 + +--S 224 of 510 +d0043:= D(m0043,x) +--R +--R +--R - x - 1 +--R - x log(-------) + 2x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 6 4 2 +--R 2x - 6x + 6x - 2 +--R Type: Expression(Integer) +--E 224 + +)clear all + + +--S 225 of 510 +t0044:= x^3*atanh(x)/(1-x^2) +--R +--R +--R 3 +--R x atanh(x) +--R (1) - ---------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 225 + +--S 226 of 510 +r0044:= -1/2*x+1/2*atanh(x)-1/2*x^2*atanh(x)-1/2*atanh(x)^2+_ + atanh(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 226 + +--S 227 of 510 +a0044:= integrate(t0044,x) +--R +--R +--R x 3 +--I ++ %T atanh(%T) +--I (2) | - ------------ d%T +--R ++ 2 +--I %T - 1 +--R Type: Union(Expression(Integer),...) +--E 227 + +--S 228 of 510 +--m0044:= a0044-r0044 +--E 228 + +--S 229 of 510 +--d0044:= D(m0044,x) +--E 229 + +)clear all + + +--S 230 of 510 +t0045:= x^2*atanh(x)/(1-x^2) +--R +--R +--R 2 +--R x atanh(x) +--R (1) - ---------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 230 + +--S 231 of 510 +r0045:= -x*atanh(x)+1/2*atanh(x)^2-1/2*log(1-x^2) +--R +--R +--R 2 2 +--R - log(- x + 1) + atanh(x) - 2x atanh(x) +--R (2) ----------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 510 +a0045:= integrate(t0045,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R - 4log(x - 1) + log(-------) - 4x log(-------) +--R x - 1 x - 1 +--R (3) ------------------------------------------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 232 + +--S 233 of 510 +m0045:= a0045-r0045 +--R +--R +--R (4) +--R 2 - x - 1 2 - x - 1 2 +--R - 4log(x - 1) + log(-------) - 4x log(-------) + 4log(- x + 1) +--R x - 1 x - 1 +--R + +--R 2 +--R - 4atanh(x) + 8x atanh(x) +--R / +--R 8 +--R Type: Expression(Integer) +--E 233 + +--S 234 of 510 +d0045:= D(m0045,x) +--R +--R +--R 2 - x - 1 2 +--R - x log(-------) + 2x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 2 +--R 2x - 2 +--R Type: Expression(Integer) +--E 234 + +)clear all + + +--S 235 of 510 +t0046:= x*atanh(x)/(1-x^2) +--R +--R +--R x atanh(x) +--R (1) - ---------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 235 + +--S 236 of 510 +r0046:= -1/2*atanh(x)^2+atanh(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 236 + +--S 237 of 510 +a0046:= integrate(t0046,x) +--R +--R +--R x +--I ++ %T atanh(%T) +--I (2) | - ------------ d%T +--R ++ 2 +--I %T - 1 +--R Type: Union(Expression(Integer),...) +--E 237 + +--S 238 of 510 +--m0046:= a0046-r0046 +--E 238 + +--S 239 of 510 +--d0046:= D(m0046,x) +--E 239 + +)clear all + + +--S 240 of 510 +t0047:= atanh(x)/x/(1-x^2) +--R +--R +--R atanh(x) +--R (1) - -------- +--R 3 +--R x - x +--R Type: Expression(Integer) +--E 240 + +--S 241 of 510 +r0047:= -1/2*atanh(x)^2+atanh(x)*log(-2*x/(1-x))+1/2*polylog(2,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 241 + +--S 242 of 510 +a0047:= integrate(t0047,x) +--R +--R +--R x +--I ++ atanh(%T) +--I (2) | - --------- d%T +--R ++ 3 +--I %T - %T +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 510 +--m0047:= a0047-r0047 +--E 243 + +--S 244 of 510 +--d0047:= D(m0047,x) +--E 244 + +)clear all + + +--S 245 of 510 +t0048:= atanh(x)/x^2/(1-x^2) +--R +--R +--R atanh(x) +--R (1) - -------- +--R 4 2 +--R x - x +--R Type: Expression(Integer) +--E 245 + +--S 246 of 510 +r0048:= -atanh(x)/x+1/2*atanh(x)^2+log(x/(1-x^2)^(1/2)) +--R +--R +--R x 2 +--R 2x log(-----------) + x atanh(x) - 2atanh(x) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R (2) --------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 246 + +--S 247 of 510 +a0048:= integrate(t0048,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R - 4x log(x - 1) + 8x log(x) + x log(-------) - 4log(-------) +--R x - 1 x - 1 +--R (3) -------------------------------------------------------------- +--R 8x +--R Type: Union(Expression(Integer),...) +--E 247 + +--S 248 of 510 +m0048:= a0048-r0048 +--R +--R +--R (4) +--R x 2 - x - 1 2 +--R - 8x log(-----------) - 4x log(x - 1) + 8x log(x) + x log(-------) +--R +--------+ x - 1 +--R | 2 +--R \|- x + 1 +--R + +--R - x - 1 2 +--R - 4log(-------) - 4x atanh(x) + 8atanh(x) +--R x - 1 +--R / +--R 8x +--R Type: Expression(Integer) +--E 248 + +--S 249 of 510 +d0048:= D(m0048,x) +--R +--R +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R (5) -------------------------- +--R 4 2 +--R 2x - 2x +--R Type: Expression(Integer) +--E 249 + +)clear all + + +--S 250 of 510 +t0049:= atanh(x)/x^3/(1-x^2) +--R +--R +--R atanh(x) +--R (1) - -------- +--R 5 3 +--R x - x +--R Type: Expression(Integer) +--E 250 + +--S 251 of 510 +r0049:= -1/2/x+1/2*atanh(x)-1/2*atanh(x)/x^2-1/2*atanh(x)^2+_ + atanh(x)*log(-2*x/(1-x))+1/2*polylog(2,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 251 + +--S 252 of 510 +a0049:= integrate(t0049,x) +--R +--R +--R x +--I ++ atanh(%T) +--I (2) | - --------- d%T +--R ++ 5 3 +--I %T - %T +--R Type: Union(Expression(Integer),...) +--E 252 + +--S 253 of 510 +--m0049:= a0049-r0049 +--E 253 + +--S 254 of 510 +--d0049:= D(m0049,x) +--E 254 + +)clear all + + +--S 255 of 510 +t0050:= x^3*atanh(x)^2/(1-x^2) +--R +--R +--R 3 2 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 255 + +--S 256 of 510 +r0050:= -x*atanh(x)+1/2*atanh(x)^2-1/2*x^2*atanh(x)^2-_ + 1/3*atanh(x)^3+atanh(x)^2*log(2/(1-x))-_ + 1/2*log(1-x^2)+atanh(x)*polylog(2,1-2/(1-x))-_ + 1/2*polylog(3,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 256 + +--S 257 of 510 +a0050:= integrate(t0050,x) +--R +--R +--R x 3 2 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 +--R Type: Union(Expression(Integer),...) +--E 257 + +--S 258 of 510 +--m0050:= a0050-r0050 +--E 258 + +--S 259 of 510 +--d0050:= D(m0050,x) +--E 259 + +)clear all + + +--S 260 of 510 +t0051:= x^2*atanh(x)^2/(1-x^2) +--R +--R +--R 2 2 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 510 +r0051:= -atanh(x)^2-x*atanh(x)^2+1/3*atanh(x)^3+_ + 2*atanh(x)*log(2/(1-x))+polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 261 + +--S 262 of 510 +a0051:= integrate(t0051,x) +--R +--R +--R x 2 2 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 +--R Type: Union(Expression(Integer),...) +--E 262 + +--S 263 of 510 +--m0051:= a0051-r0051 +--E 263 + +--S 264 of 510 +--d0051:= D(m0051,x) +--E 264 + +)clear all + + +--S 265 of 510 +t0052:= x*atanh(x)^2/(1-x^2) +--R +--R +--R 2 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 510 +r0052:= -1/3*atanh(x)^3+atanh(x)^2*log(2/(1-x))+_ + atanh(x)*polylog(2,1-2/(1-x))-1/2*polylog(3,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 266 + +--S 267 of 510 +a0052:= integrate(t0052,x) +--R +--R +--R x 2 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 +--R Type: Union(Expression(Integer),...) +--E 267 + +--S 268 of 510 +--m0052:= a0052-r0052 +--E 268 + +--S 269 of 510 +--d0052:= D(m0052,x) +--E 269 + +)clear all + + +--S 270 of 510 +t0053:= atanh(x)^2/x/(1-x^2) +--R +--R +--R 2 +--R atanh(x) +--R (1) - --------- +--R 3 +--R x - x +--R Type: Expression(Integer) +--E 270 + +--S 271 of 510 +r0053:= -1/3*atanh(x)^3+atanh(x)^2*log(-2*x/(1-x))+_ + atanh(x)*polylog(2,-1+2/(1-x))-1/2*polylog(3,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 271 + +--S 272 of 510 +a0053:= integrate(t0053,x) +--R +--R +--R x 2 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 3 +--I %T - %T +--R Type: Union(Expression(Integer),...) +--E 272 + +--S 273 of 510 +--m0053:= a0053-r0053 +--E 273 + +--S 274 of 510 +--d0053:= D(m0053,x) +--E 274 + +)clear all + + +--S 275 of 510 +t0054:= atanh(x)^2/x^2/(1-x^2) +--R +--R +--R 2 +--R atanh(x) +--R (1) - --------- +--R 4 2 +--R x - x +--R Type: Expression(Integer) +--E 275 + +--S 276 of 510 +r0054:= -atanh(x)^2-atanh(x)^2/x+1/3*atanh(x)^3+_ + 2*atanh(x)*log(-2*x/(1-x))+polylog(2,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 276 + +--S 277 of 510 +a0054:= integrate(t0054,x) +--R +--R +--R x 2 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 4 2 +--I %T - %T +--R Type: Union(Expression(Integer),...) +--E 277 + +--S 278 of 510 +--m0054:= a0054-r0054 +--E 278 + +--S 279 of 510 +--d0054:= D(m0054,x) +--E 279 + +)clear all + + +--S 280 of 510 +t0055:= atanh(x)^2/x^3/(1-x^2) +--R +--R +--R 2 +--R atanh(x) +--R (1) - --------- +--R 5 3 +--R x - x +--R Type: Expression(Integer) +--E 280 + +--S 281 of 510 +r0055:= -atanh(x)/x+1/2*atanh(x)^2-1/2*atanh(x)^2/x^2-_ + 1/3*atanh(x)^3+atanh(x)^2*log(-2*x/(1-x))+_ + log(x/(1-x^2)^(1/2))+atanh(x)*polylog(2,-1+2/(1-x))-_ + 1/2*polylog(3,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 281 + +--S 282 of 510 +a0055:= integrate(t0055,x) +--R +--R +--R x 2 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 5 3 +--I %T - %T +--R Type: Union(Expression(Integer),...) +--E 282 + +--S 283 of 510 +--m0055:= a0055-r0055 +--E 283 + +--S 284 of 510 +--d0055:= D(m0055,x) +--E 284 + +)clear all + + +--S 285 of 510 +t0056:= x^3*atanh(x)^3/(1-x^2) +--R +--R +--R 3 3 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 285 + +--S 286 of 510 +r0056:= -3/2*atanh(x)^2-3/2*x*atanh(x)^2+1/2*atanh(x)^3-_ + 1/2*x^2*atanh(x)^3-1/4*atanh(x)^4+_ + 3*atanh(x)*log(2/(1-x))+atanh(x)^3*log(2/(1-x))+_ + 3/2*(1+atanh(x)^2)*polylog(2,1-2/(1-x))-_ + 3/2*atanh(x)*polylog(3,1-2/(1-x))+3/4*polylog(4,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 286 + +--S 287 of 510 +a0056:= integrate(t0056,x) +--R +--R +--R x 3 3 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 +--R Type: Union(Expression(Integer),...) +--E 287 + +--S 288 of 510 +--m0056:= a0056-r0056 +--E 288 + +--S 289 of 510 +--d0056:= D(m0056,x) +--E 289 + +)clear all + + +--S 290 of 510 +t0057:= x^2*atanh(x)^3/(1-x^2) +--R +--R +--R 2 3 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 510 +r0057:= -atanh(x)^3-x*atanh(x)^3+1/4*atanh(x)^4+_ + 3*atanh(x)^2*log(2/(1-x))+3*atanh(x)*polylog(2,1-2/(1-x))-_ + 3/2*polylog(3,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 291 + +--S 292 of 510 +a0057:= integrate(t0057,x) +--R +--R +--R x 2 3 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 +--R Type: Union(Expression(Integer),...) +--E 292 + +--S 293 of 510 +--m0057:= a0057-r0057 +--E 293 + +--S 294 of 510 +--d0057:= D(m0057,x) +--E 294 + +)clear all + + +--S 295 of 510 +t0058:= x*atanh(x)^3/(1-x^2) +--R +--R +--R 3 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 295 + +--S 296 of 510 +r0058:= -1/4*atanh(x)^4+atanh(x)^3*log(2)+atanh(x)^3*log(-1/(-1+x))+_ + 3/2*polylog(2,(1+x)/(-1+x))*atanh(x)^2-_ + 3/2*atanh(x)*polylog(3,(1+x)/(-1+x))+3/4*polylog(4,(1+x)/(-1+x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 296 + +--S 297 of 510 +a0058:= integrate(t0058,x) +--R +--R +--R x 3 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 +--R Type: Union(Expression(Integer),...) +--E 297 + +--S 298 of 510 +--m0058:= a0058-r0058 +--E 298 + +--S 299 of 510 +--d0058:= D(m0058,x) +--E 299 + +)clear all + + +--S 300 of 510 +t0059:= atanh(x)^3/x/(1-x^2) +--R +--R +--R 3 +--R atanh(x) +--R (1) - --------- +--R 3 +--R x - x +--R Type: Expression(Integer) +--E 300 + +--S 301 of 510 +r0059:= -1/4*atanh(x)^4+atanh(x)^3*log(-2*x/(1-x))+_ + 3/2*atanh(x)^2*polylog(2,-1+2/(1-x))-_ + 3/2*atanh(x)*polylog(3,-1+2/(1-x))+3/4*polylog(4,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 301 + +--S 302 of 510 +a0059:= integrate(t0059,x) +--R +--R +--R x 3 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 3 +--I %T - %T +--R Type: Union(Expression(Integer),...) +--E 302 + +--S 303 of 510 +--m0059:= a0059-r0059 +--E 303 + +--S 304 of 510 +--d0059:= D(m0059,x) +--E 304 + +)clear all + + +--S 305 of 510 +t0060:= atanh(x)^3/x^2/(1-x^2) +--R +--R +--R 3 +--R atanh(x) +--R (1) - --------- +--R 4 2 +--R x - x +--R Type: Expression(Integer) +--E 305 + +--S 306 of 510 +r0060:= -atanh(x)^3-atanh(x)^3/x+1/4*atanh(x)^4+_ + 3*atanh(x)^2*log(-2*x/(1-x))+_ + 3*atanh(x)*polylog(2,-1+2/(1-x))-3/2*polylog(3,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 306 + +--S 307 of 510 +a0060:= integrate(t0060,x) +--R +--R +--R x 3 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 4 2 +--I %T - %T +--R Type: Union(Expression(Integer),...) +--E 307 + +--S 308 of 510 +--m0060:= a0060-r0060 +--E 308 + +--S 309 of 510 +--d0060:= D(m0060,x) +--E 309 + +)clear all + + +--S 310 of 510 +t0061:= atanh(x)^3/x^3/(1-x^2) +--R +--R +--R 3 +--R atanh(x) +--R (1) - --------- +--R 5 3 +--R x - x +--R Type: Expression(Integer) +--E 310 + +--S 311 of 510 +r0061:= -3/2*atanh(x)^2-3/2*atanh(x)^2/x+1/2*atanh(x)^3-_ + 1/2*atanh(x)^3/x^2-1/4*atanh(x)^4+3*atanh(x)*log(-2*x/(1-x))+_ + atanh(x)^3*log(-2*x/(1-x))+_ + 3/2*(1+atanh(x)^2)*polylog(2,-1+2/(1-x))-_ + 3/2*atanh(x)*polylog(3,-1+2/(1-x))+3/4*polylog(4,-1+2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 311 + +--S 312 of 510 +a0061:= integrate(t0061,x) +--R +--R +--R x 3 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 5 3 +--I %T - %T +--R Type: Union(Expression(Integer),...) +--E 312 + +--S 313 of 510 +--m0061:= a0061-r0061 +--E 313 + +--S 314 of 510 +--d0061:= D(m0061,x) +--E 314 + +)clear all + + +--S 315 of 510 +t0062:= x^3*atanh(x)/(1-x^2)^2 +--R +--R +--R 3 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 510 +r0062:= 1/2*atanh(x)^2+1/4*atanh(x)*cosh(2*atanh(x))-_ + atanh(x)*log(2/(1-x))-1/2*polylog(2,1-2/(1-x))-1/8*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 316 + +--S 317 of 510 +a0062:= integrate(t0062,x) +--R +--R +--R x 3 +--I ++ %T atanh(%T) +--I (2) | -------------- d%T +--R ++ 4 2 +--I %T - 2%T + 1 +--R Type: Union(Expression(Integer),...) +--E 317 + +--S 318 of 510 +--m0062:= a0062-r0062 +--E 318 + +--S 319 of 510 +--d0062:= D(m0062,x) +--E 319 + +)clear all + + +--S 320 of 510 +t0063:= x^2*atanh(x)/(1-x^2)^2 +--R +--R +--R 2 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 510 +r0063:= -x^2/(4-4*x^2)+x*atanh(x)/(2-2*x^2)-1/4*atanh(x)^2 +--R +--R +--R 2 2 2 +--R (- x + 1)atanh(x) - 2x atanh(x) + x +--R (2) -------------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 510 +a0063:= integrate(t0063,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R (- x + 1)log(-------) - 4x log(-------) + 4 +--R x - 1 x - 1 +--R (3) --------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression(Integer),...) +--E 322 + +--S 323 of 510 +m0063:= a0063-r0063 +--R +--R +--R (4) +--R 2 - x - 1 2 - x - 1 2 2 +--R (- x + 1)log(-------) - 4x log(-------) + (4x - 4)atanh(x) +--R x - 1 x - 1 +--R + +--R 2 +--R 8x atanh(x) - 4x + 4 +--R / +--R 2 +--R 16x - 16 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 510 +d0063:= D(m0063,x) +--R +--R +--R 2 - x - 1 2 +--R x log(-------) - 2x atanh(x) +--R x - 1 +--R (5) ---------------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression(Integer) +--E 324 + +)clear all + + +--S 325 of 510 +t0064:= x*atanh(x)/(1-x^2)^2 +--R +--R +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 510 +r0064:= -1/4*(-x+atanh(x)+x^2*atanh(x))/(-1+x^2) +--R +--R +--R 2 +--R (- x - 1)atanh(x) + x +--R (2) ---------------------- +--R 2 +--R 4x - 4 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 510 +a0064:= integrate(t0064,x) +--R +--R +--R 2 - x - 1 +--R (- x - 1)log(-------) + 2x +--R x - 1 +--R (3) --------------------------- +--R 2 +--R 8x - 8 +--R Type: Union(Expression(Integer),...) +--E 327 + +--S 328 of 510 +m0064:= a0064-r0064 +--R +--R +--R 2 - x - 1 2 +--R (- x - 1)log(-------) + (2x + 2)atanh(x) +--R x - 1 +--R (4) ------------------------------------------ +--R 2 +--R 8x - 8 +--R Type: Expression(Integer) +--E 328 + +--S 329 of 510 +d0064:= D(m0064,x) +--R +--R +--R - x - 1 +--R x log(-------) - 2x atanh(x) +--R x - 1 +--R (5) ---------------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression(Integer) +--E 329 + +)clear all + + +--S 330 of 510 +t0065:= atanh(x)/(1-x^2)^2 +--R +--R +--R atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 330 + +--S 331 of 510 +r0065:= 1/4*(1-2*x*atanh(x)-atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) +--R +--R +--R 2 2 +--R (x - 1)atanh(x) - 2x atanh(x) + 1 +--R (2) ----------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 510 +a0065:= integrate(t0065,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R (x - 1)log(-------) - 4x log(-------) + 4 +--R x - 1 x - 1 +--R (3) ------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression(Integer),...) +--E 332 + +--S 333 of 510 +m0065:= a0065-r0065 +--R +--R +--R (4) +--R 2 - x - 1 2 - x - 1 2 2 +--R (x - 1)log(-------) - 4x log(-------) + (- 4x + 4)atanh(x) + 8x atanh(x) +--R x - 1 x - 1 +--R ---------------------------------------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Expression(Integer) +--E 333 + +--S 334 of 510 +d0065:= D(m0065,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) ------------------------ +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression(Integer) +--E 334 + +)clear all + + +--S 335 of 510 +t0066:= atanh(x)/x/(1-x^2)^2 +--R +--R +--R atanh(x) +--R (1) ------------ +--R 5 3 +--R x - 2x + x +--R Type: Expression(Integer) +--E 335 + +--S 336 of 510 +r0066:= -1/2*atanh(x)^2+1/4*atanh(x)*cosh(2*atanh(x))+_ + atanh(x)*log(-2*x/(1-x))+1/2*polylog(2,-1+2/(1-x))-1/8*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 336 + +--S 337 of 510 +a0066:= integrate(t0066,x) +--R +--R +--R x +--I ++ atanh(%T) +--I (2) | --------------- d%T +--R ++ 5 3 +--I %T - 2%T + %T +--R Type: Union(Expression(Integer),...) +--E 337 + +--S 338 of 510 +--m0066:= a0066-r0066 +--E 338 + +--S 339 of 510 +--d0066:= D(m0066,x) +--E 339 + +)clear all + + +--S 340 of 510 +t0067:= atanh(x)/x^2/(1-x^2)^2 +--R +--R +--R atanh(x) +--R (1) ------------- +--R 6 4 2 +--R x - 2x + x +--R Type: Expression(Integer) +--E 340 + +--S 341 of 510 +r0067:= -atanh(x)/x+3/4*atanh(x)^2-1/8*cosh(2*atanh(x))+_ + log(x/(1-x^2)^(1/2))+1/4*atanh(x)*sinh(2*atanh(x)) +--R +--R +--R (2) +--R x +--R 2x atanh(x)sinh(2atanh(x)) + 8x log(-----------) - x cosh(2atanh(x)) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 2 +--R 6x atanh(x) - 8atanh(x) +--R / +--R 8x +--R Type: Expression(Integer) +--E 341 + +--S 342 of 510 +a0067:= integrate(t0067,x) +--R +--R +--R (3) +--R 3 2 3 3 - x - 1 2 +--R (- 8x + 8x)log(x - 1) + (16x - 16x)log(x) + (3x - 3x)log(-------) +--R x - 1 +--R + +--R 2 - x - 1 +--R (- 12x + 8)log(-------) + 4x +--R x - 1 +--R / +--R 3 +--R 16x - 16x +--R Type: Union(Expression(Integer),...) +--E 342 + +--S 343 of 510 +m0067:= a0067-r0067 +--R +--R +--R (4) +--R 3 3 x +--R (- 4x + 4x)atanh(x)sinh(2atanh(x)) + (- 16x + 16x)log(-----------) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R + +--R 3 3 2 3 +--R (2x - 2x)cosh(2atanh(x)) + (- 8x + 8x)log(x - 1) + (16x - 16x)log(x) +--R + +--R 3 - x - 1 2 2 - x - 1 +--R (3x - 3x)log(-------) + (- 12x + 8)log(-------) +--R x - 1 x - 1 +--R + +--R 3 2 2 +--R (- 12x + 12x)atanh(x) + (16x - 16)atanh(x) + 4x +--R / +--R 3 +--R 16x - 16x +--R Type: Expression(Integer) +--E 343 + +--S 344 of 510 +d0067:= D(m0067,x) +--R +--R +--R (5) +--R 4 2 - x - 1 4 2 +--R (x - x )atanh(x)cosh(2atanh(x)) + log(-------) + (x + x - 2)atanh(x) +--R x - 1 +--R ----------------------------------------------------------------------- +--R 6 4 2 +--R 2x - 4x + 2x +--R Type: Expression(Integer) +--E 344 + +)clear all + + +--S 345 of 510 +t0068:= atanh(x)/x^3/(1-x^2)^2 +--R +--R +--R atanh(x) +--R (1) ------------- +--R 7 5 3 +--R x - 2x + x +--R Type: Expression(Integer) +--E 345 + +--S 346 of 510 +r0068:= -1/2/x-1/2*(1-x^2)*atanh(x)/x^2-atanh(x)^2+_ + 1/4*atanh(x)*cosh(2*atanh(x))+2*atanh(x)*log(-2*x/(1-x))+_ + polylog(2,-1+2/(1-x))-1/8*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 346 + +--S 347 of 510 +a0068:= integrate(t0068,x) +--R +--R +--R x +--I ++ atanh(%T) +--I (2) | ---------------- d%T +--R ++ 7 5 3 +--I %T - 2%T + %T +--R Type: Union(Expression(Integer),...) +--E 347 + +--S 348 of 510 +--m0068:= a0068-r0068 +--E 348 + +--S 349 of 510 +--d0068:= D(m0068,x) +--E 349 + +)clear all + + +--S 350 of 510 +t0069:= x^3*atanh(x)^2/(1-x^2)^2 +--R +--R +--R 3 2 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 510 +r0069:= 1/3*atanh(x)^3+1/8*cosh(2*atanh(x))+_ + 1/4*atanh(x)^2*cosh(2*atanh(x))-atanh(x)^2*log(2/(1-x))-_ + atanh(x)*polylog(2,1-2/(1-x))+1/2*polylog(3,1-2/(1-x))-_ + 1/4*atanh(x)*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 351 + +--S 352 of 510 +a0069:= integrate(t0069,x) +--R +--R +--R x 3 2 +--I ++ %T atanh(%T) +--I (2) | -------------- d%T +--R ++ 4 2 +--I %T - 2%T + 1 +--R Type: Union(Expression(Integer),...) +--E 352 + +--S 353 of 510 +--m0069:= a0069-r0069 +--E 353 + +--S 354 of 510 +--d0069:= D(m0069,x) +--E 354 + +)clear all + + +--S 355 of 510 +t0070:= x^2*atanh(x)^2/(1-x^2)^2 +--R +--R +--R 2 2 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 510 +r0070:= -1/12*(3*x-3*atanh(x)-3*x^2*atanh(x)+6*x*atanh(x)^2-_ + 2*atanh(x)^3+2*x^2*atanh(x)^3)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (- 2x + 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x +--R (2) ------------------------------------------------------------ +--R 2 +--R 12x - 12 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 510 +a0070:= integrate(t0070,x) +--R +--R +--R (3) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (- x + 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x +--R x - 1 x - 1 x - 1 +--R ------------------------------------------------------------------------ +--R 2 +--R 48x - 48 +--R Type: Union(Expression(Integer),...) +--E 357 + +--S 358 of 510 +m0070:= a0070-r0070 +--R +--R +--R (4) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (- x + 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (8x - 8)atanh(x) + 24x atanh(x) + (- 12x - 12)atanh(x) +--R / +--R 2 +--R 48x - 48 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 510 +d0070:= D(m0070,x) +--R +--R +--R 2 - x - 1 2 2 2 +--R x log(-------) - 4x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression(Integer) +--E 359 + +)clear all + + +--S 360 of 510 +t0071:= x*atanh(x)^2/(1-x^2)^2 +--R +--R +--R 2 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 510 +r0071:= -1/4*(1-2*x*atanh(x)+atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) +--R +--R +--R 2 2 +--R (- x - 1)atanh(x) + 2x atanh(x) - 1 +--R (2) ------------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 510 +a0071:= integrate(t0071,x) +--R +--R +--R 2 - x - 1 2 - x - 1 +--R (- x - 1)log(-------) + 4x log(-------) - 4 +--R x - 1 x - 1 +--R (3) --------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression(Integer),...) +--E 362 + +--S 363 of 510 +m0071:= a0071-r0071 +--R +--R +--R (4) +--R 2 - x - 1 2 - x - 1 2 2 +--R (- x - 1)log(-------) + 4x log(-------) + (4x + 4)atanh(x) - 8x atanh(x) +--R x - 1 x - 1 +--R ---------------------------------------------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 510 +d0071:= D(m0071,x) +--R +--R +--R - x - 1 2 2 +--R x log(-------) - 4x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression(Integer) +--E 364 + +)clear all + + +--S 365 of 510 +t0072:= atanh(x)^2/(1-x^2)^2 +--R +--R +--R 2 +--R atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 510 +r0072:= 1/12*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2-_ + 2*atanh(x)^3+2*x^2*atanh(x)^3)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (2x - 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x +--R (2) ---------------------------------------------------------- +--R 2 +--R 12x - 12 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 510 +a0072:= integrate(t0072,x) +--R +--R +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x +--R x - 1 x - 1 x - 1 +--R (3) ---------------------------------------------------------------------- +--R 2 +--R 48x - 48 +--R Type: Union(Expression(Integer),...) +--E 367 + +--S 368 of 510 +m0072:= a0072-r0072 +--R +--R +--R (4) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (- 8x + 8)atanh(x) + 24x atanh(x) + (- 12x - 12)atanh(x) +--R / +--R 2 +--R 48x - 48 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 510 +d0072:= D(m0072,x) +--R +--R +--R - x - 1 2 2 +--R log(-------) - 4atanh(x) +--R x - 1 +--R (5) -------------------------- +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression(Integer) +--E 369 + +)clear all + + +--S 370 of 510 +t0073:= atanh(x)^2/x/(1-x^2)^2 +--R +--R +--R 2 +--R atanh(x) +--R (1) ------------ +--R 5 3 +--R x - 2x + x +--R Type: Expression(Integer) +--E 370 + +--S 371 of 510 +r0073:= -1/3*atanh(x)^3+1/8*cosh(2*atanh(x))+_ + 1/4*atanh(x)^2*cosh(2*atanh(x))+atanh(x)^2*log(-2*x/(1-x))+_ + atanh(x)*polylog(2,-1+2/(1-x))-1/2*polylog(3,-1+2/(1-x))-_ + 1/4*atanh(x)*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 371 + +--S 372 of 510 +a0073:= integrate(t0073,x) +--R +--R +--R x 2 +--I ++ atanh(%T) +--I (2) | --------------- d%T +--R ++ 5 3 +--I %T - 2%T + %T +--R Type: Union(Expression(Integer),...) +--E 372 + +--S 373 of 510 +--m0073:= a0073-r0073 +--E 373 + +--S 374 of 510 +--d0073:= D(m0073,x) +--E 374 + +)clear all + + +--S 375 of 510 +t0074:= atanh(x)^2/x^2/(1-x^2)^2 +--R +--R +--R 2 +--R atanh(x) +--R (1) ------------- +--R 6 4 2 +--R x - 2x + x +--R Type: Expression(Integer) +--E 375 + +--S 376 of 510 +r0074:= -atanh(x)^2-atanh(x)^2/x+1/2*atanh(x)^3-_ + 1/4*atanh(x)*cosh(2*atanh(x))+2*atanh(x)*log(-2*x/(1-x))+_ + polylog(2,-1+2/(1-x))+1/8*sinh(2*atanh(x))+_ + 1/4*atanh(x)^2*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 376 + +--S 377 of 510 +a0074:= integrate(t0074,x) +--R +--R +--R x 2 +--I ++ atanh(%T) +--I (2) | ---------------- d%T +--R ++ 6 4 2 +--I %T - 2%T + %T +--R Type: Union(Expression(Integer),...) +--E 377 + +--S 378 of 510 +--m0074:= a0074-r0074 +--E 378 + +--S 379 of 510 +--d0074:= D(m0074,x) +--E 379 + +)clear all + + +--S 380 of 510 +t0075:= atanh(x)^2/x^3/(1-x^2)^2 +--R +--R +--R 2 +--R atanh(x) +--R (1) ------------- +--R 7 5 3 +--R x - 2x + x +--R Type: Expression(Integer) +--E 380 + +--S 381 of 510 +r0075:= -atanh(x)/x-1/2*(1-x^2)*atanh(x)^2/x^2-2/3*atanh(x)^3+_ + 1/8*cosh(2*atanh(x))+1/4*atanh(x)^2*cosh(2*atanh(x))+_ + 2*atanh(x)^2*log(-2*x/(1-x))+log(x/(1-x^2)^(1/2))+_ + 2*atanh(x)*polylog(2,-1+2/(1-x))-polylog(3,-1+2/(1-x))-_ + 1/4*atanh(x)*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 381 + +--S 382 of 510 +a0075:= integrate(t0075,x) +--R +--R +--R x 2 +--I ++ atanh(%T) +--I (2) | ---------------- d%T +--R ++ 7 5 3 +--I %T - 2%T + %T +--R Type: Union(Expression(Integer),...) +--E 382 + +--S 383 of 510 +--m0075:= a0075-r0075 +--E 383 + +--S 384 of 510 +--d0075:= D(m0075,x) +--E 384 + +)clear all + + +--S 385 of 510 +t0076:= x^3*atanh(x)^3/(1-x^2)^2 +--R +--R +--R 3 3 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 385 + +--S 386 of 510 +r0076:= 1/4*atanh(x)^4+3/8*atanh(x)*cosh(2*atanh(x))+_ + 1/4*atanh(x)^3*cosh(2*atanh(x))-atanh(x)^3*log(2/(1-x))-_ + 3/2*atanh(x)^2*polylog(2,1-2/(1-x))+_ + 3/2*atanh(x)*polylog(3,1-2/(1-x))-_ + 3/4*polylog(4,1-2/(1-x))-3/16*sinh(2*atanh(x))-_ + 3/8*atanh(x)^2*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 386 + +--S 387 of 510 +a0076:= integrate(t0076,x) +--R +--R +--R x 3 3 +--I ++ %T atanh(%T) +--I (2) | -------------- d%T +--R ++ 4 2 +--I %T - 2%T + 1 +--R Type: Union(Expression(Integer),...) +--E 387 + +--S 388 of 510 +--m0076:= a0076-r0076 +--E 388 + +--S 389 of 510 +--d0076:= D(m0076,x) +--E 389 + +)clear all + + +--S 390 of 510 +t0077:= x^2*atanh(x)^3/(1-x^2)^2 +--R +--R +--R 2 3 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 510 +r0077:= -1/8*(-3*x^2+6*x*atanh(x)-3*atanh(x)^2-3*x^2*atanh(x)^2+_ + 4*x*atanh(x)^3-atanh(x)^4+atanh(x)^4*x^2)/(-1+x^2) +--R +--R +--R (2) +--R 2 4 3 2 2 2 +--R (- x + 1)atanh(x) - 4x atanh(x) + (3x + 3)atanh(x) - 6x atanh(x) + 3x +--R --------------------------------------------------------------------------- +--R 2 +--R 8x - 8 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 510 +a0077:= integrate(t0077,x) +--R +--R +--R (3) +--R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 +--R (- x + 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R - x - 1 +--R - 48x log(-------) + 48 +--R x - 1 +--R / +--R 2 +--R 128x - 128 +--R Type: Union(Expression(Integer),...) +--E 392 + +--S 393 of 510 +m0077:= a0077-r0077 +--R +--R +--R (4) +--R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 +--R (- x + 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R - x - 1 2 4 3 +--R - 48x log(-------) + (16x - 16)atanh(x) + 64x atanh(x) +--R x - 1 +--R + +--R 2 2 2 +--R (- 48x - 48)atanh(x) + 96x atanh(x) - 48x + 48 +--R / +--R 2 +--R 128x - 128 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 510 +d0077:= D(m0077,x) +--R +--R +--R 2 - x - 1 3 2 3 +--R x log(-------) - 8x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 4 2 +--R 8x - 16x + 8 +--R Type: Expression(Integer) +--E 394 + +)clear all + + +--S 395 of 510 +t0078:= x*atanh(x)^3/(1-x^2)^2 +--R +--R +--R 3 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 510 +r0078:= -1/8*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2+2*atanh(x)^3+_ + 2*x^2*atanh(x)^3)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (- 2x - 2)atanh(x) + 6x atanh(x) + (- 3x - 3)atanh(x) + 3x +--R (2) -------------------------------------------------------------- +--R 2 +--R 8x - 8 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 510 +a0078:= integrate(t0078,x) +--R +--R +--R (3) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (- x - 1)log(-------) + 6x log(-------) + (- 6x - 6)log(-------) + 12x +--R x - 1 x - 1 x - 1 +--R -------------------------------------------------------------------------- +--R 2 +--R 32x - 32 +--R Type: Union(Expression(Integer),...) +--E 397 + +--S 398 of 510 +m0078:= a0078-r0078 +--R +--R +--R (4) +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (- x - 1)log(-------) + 6x log(-------) + (- 6x - 6)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (8x + 8)atanh(x) - 24x atanh(x) + (12x + 12)atanh(x) +--R / +--R 2 +--R 32x - 32 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 510 +d0078:= D(m0078,x) +--R +--R +--R - x - 1 3 3 +--R x log(-------) - 8x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 4 2 +--R 8x - 16x + 8 +--R Type: Expression(Integer) +--E 399 + +)clear all + + +--S 400 of 510 +t0079:= atanh(x)^3/(1-x^2)^2 +--R +--R +--R 3 +--R atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 510 +r0079:= 1/8*(3-6*x*atanh(x)+3*atanh(x)^2+3*x^2*atanh(x)^2-_ + 4*x*atanh(x)^3-atanh(x)^4+atanh(x)^4*x^2)/(-1+x^2) +--R +--R +--R (2) +--R 2 4 3 2 2 +--R (x - 1)atanh(x) - 4x atanh(x) + (3x + 3)atanh(x) - 6x atanh(x) + 3 +--R ----------------------------------------------------------------------- +--R 2 +--R 8x - 8 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 510 +a0079:= integrate(t0079,x) +--R +--R +--R (3) +--R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 +--R (x - 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R - x - 1 +--R - 48x log(-------) + 48 +--R x - 1 +--R / +--R 2 +--R 128x - 128 +--R Type: Union(Expression(Integer),...) +--E 402 + +--S 403 of 510 +m0079:= a0079-r0079 +--R +--R +--R (4) +--R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 +--R (x - 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) +--R x - 1 x - 1 x - 1 +--R + +--R - x - 1 2 4 3 +--R - 48x log(-------) + (- 16x + 16)atanh(x) + 64x atanh(x) +--R x - 1 +--R + +--R 2 2 +--R (- 48x - 48)atanh(x) + 96x atanh(x) +--R / +--R 2 +--R 128x - 128 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 510 +d0079:= D(m0079,x) +--R +--R +--R - x - 1 3 3 +--R log(-------) - 8atanh(x) +--R x - 1 +--R (5) -------------------------- +--R 4 2 +--R 8x - 16x + 8 +--R Type: Expression(Integer) +--E 404 + +)clear all + + +--S 405 of 510 +t0080:= atanh(x)^3/x/(1-x^2)^2 +--R +--R +--R 3 +--R atanh(x) +--R (1) ------------ +--R 5 3 +--R x - 2x + x +--R Type: Expression(Integer) +--E 405 + +--S 406 of 510 +r0080:= -1/4*atanh(x)^4+3/8*atanh(x)*cosh(2*atanh(x))+_ + 1/4*atanh(x)^3*cosh(2*atanh(x))+atanh(x)^3*log(-2*x/(1-x))+_ + 3/2*atanh(x)^2*polylog(2,-1+2/(1-x))-_ + 3/2*atanh(x)*polylog(3,-1+2/(1-x))+3/4*polylog(4,-1+2/(1-x))-_ + 3/16*sinh(2*atanh(x))-3/8*atanh(x)^2*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 406 + +--S 407 of 510 +a0080:= integrate(t0080,x) +--R +--R +--R x 3 +--I ++ atanh(%T) +--I (2) | --------------- d%T +--R ++ 5 3 +--I %T - 2%T + %T +--R Type: Union(Expression(Integer),...) +--E 407 + +--S 408 of 510 +--m0080:= a0080-r0080 +--E 408 + +--S 409 of 510 +--d0080:= D(m0080,x) +--E 409 + +)clear all + + +--S 410 of 510 +t0081:= atanh(x)^3/x^2/(1-x^2)^2 +--R +--R +--R 3 +--R atanh(x) +--R (1) ------------- +--R 6 4 2 +--R x - 2x + x +--R Type: Expression(Integer) +--E 410 + +--S 411 of 510 +r0081:= -atanh(x)^3-atanh(x)^3/x+3/8*atanh(x)^4-_ + 3/16*cosh(2*atanh(x))-3/8*atanh(x)^2*cosh(2*atanh(x))+_ + 3*atanh(x)^2*log(-2*x/(1-x))+3*atanh(x)*polylog(2,-1+2/(1-x))-_ + 3/2*polylog(3,-1+2/(1-x))+_ + 3/8*atanh(x)*sinh(2*atanh(x))+1/4*atanh(x)^3*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 411 + +--S 412 of 510 +a0081:= integrate(t0081,x) +--R +--R +--R x 3 +--I ++ atanh(%T) +--I (2) | ---------------- d%T +--R ++ 6 4 2 +--I %T - 2%T + %T +--R Type: Union(Expression(Integer),...) +--E 412 + +--S 413 of 510 +--m0081:= a0081-r0081 +--E 413 + +--S 414 of 510 +--d0081:= D(m0081,x) +--E 414 + +)clear all + + +--S 415 of 510 +t0082:= atanh(x)^3/x^3/(1-x^2)^2 +--R +--R +--R 3 +--R atanh(x) +--R (1) ------------- +--R 7 5 3 +--R x - 2x + x +--R Type: Expression(Integer) +--E 415 + +--S 416 of 510 +r0082:= -3/2*atanh(x)^2-3/2*atanh(x)^2/x-1/2*(1-x^2)*atanh(x)^3/x^2-_ + 1/2*atanh(x)^4+3/8*atanh(x)*cosh(2*atanh(x))+_ + 1/4*atanh(x)^3*cosh(2*atanh(x))+3*atanh(x)*log(-2*x/(1-x))+_ + 2*atanh(x)^3*log(-2*x/(1-x))+_ + 3/2*(1+2*atanh(x)^2)*polylog(2,-1+2/(1-x))-_ + 3*atanh(x)*polylog(3,-1+2/(1-x))+_ + 3/2*polylog(4,-1+2/(1-x))-3/16*sinh(2*atanh(x))-_ + 3/8*atanh(x)^2*sinh(2*atanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 416 + +--S 417 of 510 +a0082:= integrate(t0082,x) +--R +--R +--R x 3 +--I ++ atanh(%T) +--I (2) | ---------------- d%T +--R ++ 7 5 3 +--I %T - 2%T + %T +--R Type: Union(Expression(Integer),...) +--E 417 + +--S 418 of 510 +--m0082:= a0082-r0082 +--E 418 + +--S 419 of 510 +--d0082:= D(m0082,x) +--E 419 + +)clear all + + +--S 420 of 510 +t0083:= x^2/(1-x^2)^2/atanh(x) +--R +--R +--R 2 +--R x +--R (1) ---------------------- +--R 4 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression(Integer) +--E 420 + +--S 421 of 510 +r0083:= 1/2*Chi(2*atanh(x))-1/2*log(atanh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 421 + +--S 422 of 510 +a0083:= integrate(t0083,x) +--R +--R +--R x 2 +--I ++ %T +--I (2) | ------------------------- d%T +--R ++ 4 2 +--I (%T - 2%T + 1)atanh(%T) +--R Type: Union(Expression(Integer),...) +--E 422 + +--S 423 of 510 +--m0083:= a0083-r0083 +--E 423 + +--S 424 of 510 +--d0083:= D(m0083,x) +--E 424 + +)clear all + + +--S 425 of 510 +t0084:= x/(1-x^2)^2/atanh(x) +--R +--R +--R x +--R (1) ---------------------- +--R 4 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression(Integer) +--E 425 + +--S 426 of 510 +r0084:= 1/2*Shi(2*atanh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 426 + +--S 427 of 510 +a0084:= integrate(t0084,x) +--R +--R +--R x +--I ++ %T +--I (2) | ------------------------- d%T +--R ++ 4 2 +--I (%T - 2%T + 1)atanh(%T) +--R Type: Union(Expression(Integer),...) +--E 427 + +--S 428 of 510 +--m0084:= a0084-r0084 +--E 428 + +--S 429 of 510 +--d0084:= D(m0084,x) +--E 429 + +)clear all + + +--S 430 of 510 +t0085:= 1/(1-x^2)^2/atanh(x) +--R +--R +--R 1 +--R (1) ---------------------- +--R 4 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression(Integer) +--E 430 + +--S 431 of 510 +r0085:= 1/2*Chi(2*atanh(x))+1/2*log(atanh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 431 + +--S 432 of 510 +a0085:= integrate(t0085,x) +--R +--R +--R x +--R ++ 1 +--I (2) | ------------------------- d%T +--R ++ 4 2 +--I (%T - 2%T + 1)atanh(%T) +--R Type: Union(Expression(Integer),...) +--E 432 + +--S 433 of 510 +--m0085:= a0085-r0085 +--E 433 + +--S 434 of 510 +--d0085:= D(m0085,x) +--E 434 + +)clear all + + +--S 435 of 510 +t0086:= x^2/(1-x^2)^2/atanh(x)^2 +--R +--R +--R 2 +--R x +--R (1) ----------------------- +--R 4 2 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression(Integer) +--E 435 + +--S 436 of 510 +r0086:= -x^2/(1-x^2)/atanh(x)+Shi(2*atanh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 436 + +--S 437 of 510 +a0086:= integrate(t0086,x) +--R +--R +--R x 2 +--I ++ %T +--I (2) | -------------------------- d%T +--R ++ 4 2 2 +--I (%T - 2%T + 1)atanh(%T) +--R Type: Union(Expression(Integer),...) +--E 437 + +--S 438 of 510 +--m0086:= a0086-r0086 +--E 438 + +--S 439 of 510 +--d0086:= D(m0086,x) +--E 439 + +)clear all + + +--S 440 of 510 +t0087:= x/(1-x^2)^2/atanh(x)^2 +--R +--R +--R x +--R (1) ----------------------- +--R 4 2 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression(Integer) +--E 440 + +--S 441 of 510 +r0087:= Chi(2*atanh(x))-1/2*sinh(2*atanh(x))/atanh(x) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 441 + +--S 442 of 510 +a0087:= integrate(t0087,x) +--R +--R +--R x +--I ++ %T +--I (2) | -------------------------- d%T +--R ++ 4 2 2 +--I (%T - 2%T + 1)atanh(%T) +--R Type: Union(Expression(Integer),...) +--E 442 + +--S 443 of 510 +--m0087:= a0087-r0087 +--E 443 + +--S 444 of 510 +--d0087:= D(m0087,x) +--E 444 + +)clear all + + +--S 445 of 510 +t0088:= 1/(1-x^2)^2/atanh(x)^2 +--R +--R +--R 1 +--R (1) ----------------------- +--R 4 2 2 +--R (x - 2x + 1)atanh(x) +--R Type: Expression(Integer) +--E 445 + +--S 446 of 510 +r0088:= -1/(1-x^2)/atanh(x)+Shi(2*atanh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 446 + +--S 447 of 510 +a0088:= integrate(t0088,x) +--R +--R +--R x +--R ++ 1 +--I (2) | -------------------------- d%T +--R ++ 4 2 2 +--I (%T - 2%T + 1)atanh(%T) +--R Type: Union(Expression(Integer),...) +--E 447 + +--S 448 of 510 +--m0088:= a0088-r0088 +--E 448 + +--S 449 of 510 +--d0088:= D(m0088,x) +--E 449 + +)clear all + + +--S 450 of 510 +t0089:= x^2/(1-x^2)^2/atanh(x)^3 +--R +--R +--R 2 +--R x +--R (1) ----------------------- +--R 4 2 3 +--R (x - 2x + 1)atanh(x) +--R Type: Expression(Integer) +--E 450 + +--S 451 of 510 +r0089:= -1/2*x^2/(1-x^2)/atanh(x)^2-x/(1-x^2)/atanh(x)+Chi(2*atanh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 451 + +--S 452 of 510 +a0089:= integrate(t0089,x) +--R +--R +--R x 2 +--I ++ %T +--I (2) | -------------------------- d%T +--R ++ 4 2 3 +--I (%T - 2%T + 1)atanh(%T) +--R Type: Union(Expression(Integer),...) +--E 452 + +--S 453 of 510 +--m0089:= a0089-r0089 +--E 453 + +--S 454 of 510 +--d0089:= D(m0089,x) +--E 454 + +)clear all + + +--S 455 of 510 +t0090:= x/(1-x^2)^2/atanh(x)^3 +--R +--R +--R x +--R (1) ----------------------- +--R 4 2 3 +--R (x - 2x + 1)atanh(x) +--R Type: Expression(Integer) +--E 455 + +--S 456 of 510 +r0090:= -1/2*cosh(2*atanh(x))/atanh(x)-_ + 1/4*sinh(2*atanh(x))/atanh(x)^2+Shi(2*atanh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 456 + +--S 457 of 510 +a0090:= integrate(t0090,x) +--R +--R +--R x +--I ++ %T +--I (2) | -------------------------- d%T +--R ++ 4 2 3 +--I (%T - 2%T + 1)atanh(%T) +--R Type: Union(Expression(Integer),...) +--E 457 + +--S 458 of 510 +--m0090:= a0090-r0090 +--E 458 + +--S 459 of 510 +--d0090:= D(m0090,x) +--E 459 + +)clear all + + +--S 460 of 510 +t0091:= 1/(1-x^2)^2/atanh(x)^3 +--R +--R +--R 1 +--R (1) ----------------------- +--R 4 2 3 +--R (x - 2x + 1)atanh(x) +--R Type: Expression(Integer) +--E 460 + +--S 461 of 510 +r0091:= -1/2/(1-x^2)/atanh(x)^2-x/(1-x^2)/atanh(x)+Chi(2*atanh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 461 + +--S 462 of 510 +a0091:= integrate(t0091,x) +--R +--R +--R x +--R ++ 1 +--I (2) | -------------------------- d%T +--R ++ 4 2 3 +--I (%T - 2%T + 1)atanh(%T) +--R Type: Union(Expression(Integer),...) +--E 462 + +--S 463 of 510 +--m0091:= a0091-r0091 +--E 463 + +--S 464 of 510 +--d0091:= D(m0091,x) +--E 464 + +)clear all + + +--S 465 of 510 +t0092:= atanh(x)/(a+b*x^2)^(3/2) +--R +--R +--R atanh(x) +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 465 + +--S 466 of 510 +r0092:= x*atanh(x)/a/(a+b*x^2)^(1/2)-_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a/(a+b)^(1/2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-----+ +--R - \|b x + a atanh(-----------) + x atanh(x)\|b + a +--R +-----+ +--R \|b + a +--R (2) ---------------------------------------------------- +--R +--------+ +--R +-----+ | 2 +--R a\|b + a \|b x + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 510 +a0092:= integrate(t0092,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R +--------+ +--R - x - 1 +-----+ | 2 - x - 1 +-+ +-----+ +--R - x log(-------)\|b + a \|b x + a + x log(-------)\|a \|b + a +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-+ +-----+ | 2 2 2 +-----+ +--R 2a\|a \|b + a \|b x + a + (- 2a b x - 2a )\|b + a +--R , +--R +--R +--------+ +--R +-+ | 2 2 +--R (- 2\|a \|b x + a + 2b x + 2a) +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R +--------+ +--R - x - 1 +-------+ | 2 - x - 1 +-------+ +-+ +--R - x log(-------)\|- b - a \|b x + a + x log(-------)\|- b - a \|a +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-------+ +-+ | 2 2 2 +-------+ +--R 2a\|- b - a \|a \|b x + a + (- 2a b x - 2a )\|- b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 467 + +--S 468 of 510 +m0092a:= a0092.1-r0092 +--R +--R +--R (4) +--R +--------+ +--R 2 | 2 2 +-+ +--R ((b x + a)\|b x + a + (- b x - a)\|a ) +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((2b x + 2a)\|b x + a + (- 2b x - 2a)\|a )atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +--------+ +--R - x - 1 +-+ +-----+ | 2 +--R (- x log(-------) + 2x atanh(x))\|a \|b + a \|b x + a +--R x - 1 +--R + +--R 3 - x - 1 3 +-----+ +--R ((b x + a x)log(-------) + (- 2b x - 2a x)atanh(x))\|b + a +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-----+ | 2 2 2 +-+ +-----+ +--R (2a b x + 2a )\|b + a \|b x + a + (- 2a b x - 2a )\|a \|b + a +--R Type: Expression(Integer) +--E 468 + +--S 469 of 510 +d0092a:= D(m0092a,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) ------------------------ +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 469 + +--S 470 of 510 +m0092b:= a0092.2-r0092 +--R +--R +--R (6) +--R +--------+ +--R 2 +-------+ | 2 2 +-------+ +-+ +--R ((2b x + 2a)\|- b - a \|b x + a + (- 2b x - 2a)\|- b - a \|a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +--------+ +--R 2 +-----+ | 2 2 +-+ +-----+ +--R ((- 2b x - 2a)\|b + a \|b x + a + (2b x + 2a)\|a \|b + a ) +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R +--------+ +--R - x - 1 +-------+ +-+ +-----+ | 2 +--R (- x log(-------) + 2x atanh(x))\|- b - a \|a \|b + a \|b x + a +--R x - 1 +--R + +--R 3 - x - 1 3 +-------+ +-----+ +--R ((b x + a x)log(-------) + (- 2b x - 2a x)atanh(x))\|- b - a \|b + a +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ +-----+ | 2 +--R (2a b x + 2a )\|- b - a \|b + a \|b x + a +--R + +--R 2 2 +-------+ +-+ +-----+ +--R (- 2a b x - 2a )\|- b - a \|a \|b + a +--R Type: Expression(Integer) +--E 470 + +--S 471 of 510 +d0092b:= D(m0092b,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (7) ------------------------ +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 471 + +)clear all + + +--S 472 of 510 +t0093:= atanh(x)/(a+b*x^2)^(5/2) +--R +--R +--R atanh(x) +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 510 +r0093:= 1/3/a/(a+b)/(a+b*x^2)^(1/2)+_ + 1/3*x*(3*a+2*b*x^2)*atanh(x)/a^2/(a+b*x^2)^(3/2)-_ + 1/3*(3*a+2*b)*atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^2/(a+b)^(3/2) +--R +--R +--R (2) +--R +--------+ +--R +--------+ | 2 +--R 2 2 2 | 2 \|b x + a +--R ((- 2b - 3a b)x - 2a b - 3a )\|b x + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 2 2 +-----+ +--R (((2b + 2a b)x + (3a b + 3a )x)atanh(x) + a b x + a )\|b + a +--R / +--R +--------+ +--R 2 2 3 2 3 4 +-----+ | 2 +--R ((3a b + 3a b)x + 3a b + 3a )\|b + a \|b x + a +--R Type: Expression(Integer) +--E 473 + +--S 474 of 510 +a0093:= integrate(t0093,x) +--R +--R +--R (3) +--R [ +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b + 12a b )x + (32a b + 48a b )x + (40a b + 60a b)x +--R + +--R 3 4 +--R 16a b + 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b - 3a b )x + (- 20a b - 30a b )x + (- 50a b - 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b - 72a b)x - 16a b - 24a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b - 2a b )x + (- 19a b - 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b - 40a b)x + (- 24a b - 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b + 8a b )x + (36a b + 36a b )x + (52a b + 52a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b + 24a b )x + (96a b + 96a b )x + (120a b + 120a b)x +--R + +--R 5 6 +--R 48a b + 48a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b - 6a b )x + (- 60a b - 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b - 150a b )x + (- 144a b - 144a b)x - 48a b - 48a +--R * +--R +-----+ +--R \|b + a +--R , +--R +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (4b + 6a b )x + (40a b + 60a b )x + (100a b + 150a b )x +--R + +--R 3 2 4 2 4 5 +--R (96a b + 144a b)x + 32a b + 48a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b - 2a b )x + (- 19a b - 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b - 40a b)x + (- 24a b - 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b + 8a b )x + (36a b + 36a b )x + (52a b + 52a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b + 24a b )x + (96a b + 96a b )x + (120a b + 120a b)x +--R + +--R 5 6 +--R 48a b + 48a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b - a \|a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b - 6a b )x + (- 60a b - 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b - 150a b )x + (- 144a b - 144a b)x - 48a b - 48a +--R * +--R +-------+ +--R \|- b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 474 + +--S 475 of 510 +m0093a:= a0093.1-r0093 +--R +--R +--R (4) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b + 3a b )x + (18a b + 27a b )x + (32a b + 48a b)x +--R + +--R 3 4 +--R 16a b + 24a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b - 12a b )x + (- 32a b - 48a b )x + (- 40a b - 60a b)x +--R + +--R 3 4 +--R - 16a b - 24a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b - 8a b )x + (- 28a b - 28a b)x + (- 24a b - 24a )x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b + 16a b )x + (56a b + 56a b)x + (48a b + 48a )x)atanh(x) +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b + 2a b )x + (19a b + 19a b )x + (40a b + 40a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b - 4a b )x + (- 38a b - 38a b )x + (- 80a b - 80a b)x +--R + +--R 3 4 +--R (- 48a b - 48a )x +--R * +--R atanh(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-----+ +--R \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b + 6a b )x + (54a b + 54a b )x + (96a b + 96a b)x + 48a b +--R + +--R 6 +--R 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b - 24a b )x + (- 96a b - 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b - 120a b)x - 48a b - 48a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression(Integer) +--E 475 + +--S 476 of 510 +d0093a:= D(m0093a,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 476 + +--S 477 of 510 +m0093b:= a0093.2-r0093 +--R +--R +--R (6) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 4b - 6a b )x + (- 36a b - 54a b )x + (- 64a b - 96a b)x +--R + +--R 3 4 +--R - 32a b - 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (16b + 24a b )x + (64a b + 96a b )x + (80a b + 120a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b - 8a b )x + (- 28a b - 28a b)x + (- 24a b - 24a )x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b + 16a b )x + (56a b + 56a b)x + (48a b + 48a )x)atanh(x) +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b - a \|a \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b + 2a b )x + (19a b + 19a b )x + (40a b + 40a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b - 4a b )x + (- 38a b - 38a b )x + (- 80a b - 80a b)x +--R + +--R 3 4 +--R (- 48a b - 48a )x +--R * +--R atanh(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-------+ +-----+ +--R \|- b - a \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b + 6a b )x + (54a b + 54a b )x + (96a b + 96a b)x + 48a b +--R + +--R 6 +--R 48a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b - a \|b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b - 24a b )x + (- 96a b - 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b - 120a b)x - 48a b - 48a +--R * +--R +-------+ +-+ +-----+ +--R \|- b - a \|a \|b + a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 510 +d0093b:= D(m0093b,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (7) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 478 + +)clear all + + +--S 479 of 510 +t0094:= atanh(x)/(a+b*x^2)^(7/2) +--R +--R +--R atanh(x) +--R (1) ------------------------------------------ +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 479 + +--S 480 of 510 +r0094:= 1/15/a/(a+b)/(a+b*x^2)^(3/2)+_ + 1/15*(7*a+4*b)/a^2/(a+b)^2/(a+b*x^2)^(1/2)+_ + 1/15*x*(8*(a+b*x^2)^2+a*(7*a+4*b*x^2))*_ + atanh(x)/a^3/(a+b*x^2)^(5/2)-1/15*(15*a^2+20*a*b+8*b^2)*_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^3/(a+b)^(5/2) +--R +--R +--R (2) +--R 4 3 2 2 4 3 2 2 3 2 2 2 +--R (- 8b - 20a b - 15a b )x + (- 16a b - 40a b - 30a b)x - 8a b +--R + +--R 3 4 +--R - 20a b - 15a +--R * +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +--R \|b x + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 3 2 2 5 3 2 2 3 3 +--R (8b + 16a b + 8a b )x + (20a b + 40a b + 20a b)x +--R + +--R 2 2 3 4 +--R (15a b + 30a b + 15a )x +--R * +--R atanh(x) +--R + +--R 3 2 2 4 2 2 3 2 3 4 +--R (4a b + 7a b )x + (9a b + 15a b)x + 5a b + 8a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 5 2 +--R (15a b + 30a b + 15a b )x + (30a b + 60a b + 30a b)x + 15a b +--R + +--R 6 7 +--R 30a b + 15a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R Type: Expression(Integer) +--E 480 + +--S 481 of 510 +a0094:= integrate(t0094,x) +--R +--R +--R (3) +--R [ +--R 8 7 2 6 12 +--R (64b + 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b + 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b + 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b + 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b + 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b + 11520a b + 8640a b)x + 1024a b + 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b - 20a b - 15a b )x + (- 280a b - 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b - 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b - 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b - 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b - 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b - 12800a b - 9600a b)x - 1024a b - 2560a b - 1920a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 8 7 2 6 13 +--R (- 8b - 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b - 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b - 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b - 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b - 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b - 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b + 114a b )x + (766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b + 4080a b )x + (4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b + 4608a b )x + (896a b + 1280a b)x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b + 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b + 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b + 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b + 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b + 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b + 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b + 3840a b + 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b - 16a b )x + (- 286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b - 2672a b )x + (- 4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b - 8480a b )x + (- 3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b - 1280a b)x +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b + 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b + 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b + 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b + 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b + 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b + 34560a b + 17280a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b - 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b - 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b - 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b - 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b - 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b - 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b - 38400a b - 19200a b)x - 3840a b - 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-----+ +--R \|b + a +--R , +--R +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b +--R + +--R 8 +--R - 3840a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (16b + 40a b + 30a b )x + (560a b + 1400a b + 1050a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (4144a b + 10360a b + 7770a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (13328a b + 33320a b + 24990a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (22528a b + 56320a b + 42240a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (20992a b + 52480a b + 39360a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (10240a b + 25600a b + 19200a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 8 7 2 6 13 +--R (- 8b - 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b - 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b - 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b - 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b - 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b - 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b + 114a b )x + (766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b + 4080a b )x + (4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b + 4608a b )x + (896a b + 1280a b)x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b + 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b + 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b + 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b + 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b + 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b + 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b + 3840a b + 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b - 16a b )x + (- 286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b - 2672a b )x + (- 4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b - 8480a b )x + (- 3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b - 1280a b)x +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b + 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b + 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b + 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b + 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b + 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b + 34560a b + 17280a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b - a \|a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b - 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b - 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b - 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b - 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b - 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b - 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b - 38400a b - 19200a b)x - 3840a b - 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-------+ +--R \|- b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 481 + +--S 482 of 510 +m0094a:= a0094.1-r0094 +--R +--R +--R (4) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b + 20a b + 15a b )x + (272a b + 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b + 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b + 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b + 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b + 10240a b + 7680a b)x + 1024a b + 2560a b + 1920a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b - 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b - 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b - 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b - 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b - 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b - 11520a b - 8640a b)x - 1024a b - 2560a b - 1920a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b + 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b + 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b + 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b + 20480a b + 15360a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b - 3840a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 7 6 2 5 11 +--R (- 64b - 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b - 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b - 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b - 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b - 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b + 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b + 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b + 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b + 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b + 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b + 7680a b + 3840a )x +--R * +--R atanh(x) +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b + 16a b )x + (340a b + 544a b )x + (2250a b + 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b + 9728a b )x + (8000a b + 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b + 8192a b)x + 1280a b + 2048a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b + 16a b + 8a b )x + (276a b + 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b + 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b + 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b + 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b + 12800a b + 6400a b)x + (1920a b + 3840a b + 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b - 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b - 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b - 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b - 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b - 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b - 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b - 7680a b - 3840a )x +--R * +--R atanh(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b - 128a b )x + (- 1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b - 7296a b )x + (- 9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b - 16640a b )x + (- 5760a b - 9216a b)x - 1280a b +--R + +--R 8 +--R - 2048a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b + 60a b + 30a b )x + (1020a b + 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b + 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b + 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b + 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b + 30720a b + 15360a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b - 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b - 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b - 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b - 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b - 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b - 34560a b - 17280a b)x - 3840a b - 7680a b - 3840a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 510 +d0094a:= D(m0094a,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 483 + +--S 484 of 510 +m0094b:= a0094.2-r0094 +--R +--R +--R (6) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b + 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b + 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b + 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b + 20480a b + 15360a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b - 3840a +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 8 7 2 6 12 +--R (- 16b - 40a b - 30a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 544a b - 1360a b - 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3600a b - 9000a b - 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 9728a b - 24320a b - 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 12800a b - 32000a b - 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 8192a b - 20480a b - 15360a b)x - 2048a b - 5120a b - 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 8 7 2 6 12 +--R (128b + 320a b + 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (1664a b + 4160a b + 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (7296a b + 18240a b + 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (15232a b + 38080a b + 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (16640a b + 41600a b + 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (9216a b + 23040a b + 17280a b)x + 2048a b + 5120a b + 3840a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 7 6 2 5 11 +--R (- 64b - 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b - 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b - 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b - 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b - 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b + 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b + 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b + 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b + 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b + 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b + 7680a b + 3840a )x +--R * +--R atanh(x) +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b + 16a b )x + (340a b + 544a b )x + (2250a b + 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b + 9728a b )x + (8000a b + 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b + 8192a b)x + 1280a b + 2048a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b - a \|a \|b + a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b + 16a b + 8a b )x + (276a b + 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b + 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b + 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b + 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b + 12800a b + 6400a b)x + (1920a b + 3840a b + 1920a )x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b - 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b - 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b - 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b - 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b - 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b - 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b - 7680a b - 3840a )x +--R * +--R atanh(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b - 128a b )x + (- 1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b - 7296a b )x + (- 9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b - 16640a b )x + (- 5760a b - 9216a b)x - 1280a b +--R + +--R 8 +--R - 2048a +--R * +--R +-------+ +-----+ +--R \|- b - a \|b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b + 60a b + 30a b )x + (1020a b + 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b + 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b + 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b + 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b + 30720a b + 15360a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b - a \|b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b - 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b - 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b - 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b - 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b - 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b - 34560a b - 17280a b)x - 3840a b - 7680a b - 3840a +--R * +--R +-------+ +-+ +-----+ +--R \|- b - a \|a \|b + a +--R Type: Expression(Integer) +--E 484 + +--S 485 of 510 +d0094b:= D(m0094b,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (7) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 485 + +)clear all + + +--S 486 of 510 +t0095:= atanh(x)*(a-a*x^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (1) atanh(x)\|- a x + a +--R Type: Expression(Integer) +--E 486 + +--S 487 of 510 +r0095:= 1/2/(1-x^2)^(1/2)*(a*(1-x^2))^(1/2)*((1-x^2)^(1/2)+_ + x*(1-x^2)^(1/2)*atanh(x)+2*atan(exp(1)^atanh(x))*atanh(x)-_ + %i*polylog(2,-%i*exp(1)^atanh(x))+%i*polylog(2,%i*exp(1)^atanh(x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 487 + +--S 488 of 510 +a0095:= integrate(t0095,x) +--R +--R +--R x +------------+ +--R ++ | 2 +--I (2) | atanh(%T)\|(- %T + 1)a d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 510 +--m0095:= a0095-r0095 +--E 489 + +--S 490 of 510 +--d0095:= D(m0095,x) +--E 490 + +)clear all + + +--S 491 of 510 +t0096:= atanh(x)/(a-a*x^2)^(1/2) +--R +--R +--R atanh(x) +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- a x + a +--R Type: Expression(Integer) +--E 491 + +--S 492 of 510 +r0096:= (1-x^2)^(1/2)*(2*atan(exp(1)^atanh(x))*atanh(x)-_ + %i*polylog(2,-%i*exp(1)^atanh(x))+_ + %i*polylog(2,%i*exp(1)^atanh(x)))/(a*(1-x^2))^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 492 + +--S 493 of 510 +a0096:= integrate(t0096,x) +--R +--R +--R x +--I ++ atanh(%T) +--I (2) | --------------- d%T +--R ++ +------------+ +--R | 2 +--I \|(- %T + 1)a +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 510 +--m0096:= a0096-r0096 +--E 494 + +--S 495 of 510 +--d0096:= D(m0096,x) +--E 495 + +)clear all + + +--S 496 of 510 +t0097:= atanh(x)/(a-a*x^2)^(3/2) +--R +--R +--R atanh(x) +--R (1) - ----------------------- +--R +----------+ +--R 2 | 2 +--R (a x - a)\|- a x + a +--R Type: Expression(Integer) +--E 496 + +--S 497 of 510 +r0097:= (x*atanh(x)-1)/(-a*(-1+x^2))^(1/2)/a +--R +--R +--R x atanh(x) - 1 +--R (2) -------------- +--R +----------+ +--R | 2 +--R a\|- a x + a +--R Type: Expression(Integer) +--E 497 + +--S 498 of 510 +a0097:= integrate(t0097,x) +--R +--R +--R +----------+ +--R - x - 1 2 +-+ - x - 1 | 2 +--R (x log(-------) - 2x )\|a - x log(-------)\|- a x + a +--R x - 1 x - 1 +--R (3) -------------------------------------------------------- +--R +----------+ +--R | 2 +-+ 2 2 2 +--R 2a\|- a x + a \|a + 2a x - 2a +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 510 +m0097:= a0097-r0097 +--R +--R +--R (4) +--R +----------+ +--R - x - 1 2 | 2 +-+ +--R (- x log(-------) + 2x atanh(x) + 2x - 2)\|- a x + a \|a +--R x - 1 +--R + +--R 3 - x - 1 3 2 +--R (- a x + a x)log(-------) + (2a x - 2a x)atanh(x) - 2a x + 2a +--R x - 1 +--R / +--R +----------+ +--R 2 2 2 +-+ 2 2 2 | 2 +--R (2a x - 2a )\|a + (- 2a x + 2a )\|- a x + a +--R Type: Expression(Integer) +--E 499 + +--S 500 of 510 +d0097:= D(m0097,x) +--R +--R +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R (5) -------------------------- +--R +----------+ +--R 2 | 2 +--R (2a x - 2a)\|- a x + a +--R Type: Expression(Integer) +--E 500 + +)clear all + + +--S 501 of 510 +t0098:= atanh(x)/(a-a*x^2)^(5/2) +--R +--R +--R atanh(x) +--R (1) -------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (a x - 2a x + a )\|- a x + a +--R Type: Expression(Integer) +--E 501 + +--S 502 of 510 +r0098:= 1/9*(7-6*x^2-9*x*atanh(x)+_ + 6*atanh(x)*x^3)/(-1+x^2)/(-a*(-1+x^2))^(1/2)/a^2 +--R +--R +--R 3 2 +--R (6x - 9x)atanh(x) - 6x + 7 +--R (2) ---------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (9a x - 9a )\|- a x + a +--R Type: Expression(Integer) +--E 502 + +--S 503 of 510 +a0098:= integrate(t0098,x) +--R +--R +--R (3) +--R 5 3 - x - 1 6 4 2 +-+ +--R ((18x - 51x + 36x)log(-------) - 14x + 48x - 36x )\|a +--R x - 1 +--R + +--R +----------+ +--R 5 3 - x - 1 4 2 | 2 +--R ((- 6x + 33x - 36x)log(-------) - 30x + 36x )\|- a x + a +--R x - 1 +--R / +--R +----------+ +--R 2 4 2 2 2 | 2 +-+ 3 6 3 4 3 2 +--R (54a x - 126a x + 72a )\|- a x + a \|a + 18a x - 108a x + 162a x +--R + +--R 3 +--R - 72a +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 510 +m0098:= a0098-r0098 +--R +--R +--R (4) +--R 5 3 - x - 1 5 3 +--R (- 18x + 51x - 36x)log(-------) + (36x - 102x + 72x)atanh(x) +--R x - 1 +--R + +--R 6 4 2 +--R 14x - 84x + 126x - 56 +--R * +--R +----------+ +--R | 2 +-+ +--R \|- a x + a \|a +--R + +--R 7 5 3 - x - 1 +--R (- 6a x + 39a x - 69a x + 36a x)log(-------) +--R x - 1 +--R + +--R 7 5 3 6 4 2 +--R (12a x - 78a x + 138a x - 72a x)atanh(x) - 42a x + 140a x - 154a x +--R + +--R 56a +--R / +--R 3 6 3 4 3 2 3 +-+ +--R (54a x - 180a x + 198a x - 72a )\|a +--R + +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (- 18a x + 108a x - 162a x + 72a )\|- a x + a +--R Type: Expression(Integer) +--E 504 + +--S 505 of 510 +d0098:= D(m0098,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) ---------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (2a x - 4a x + 2a )\|- a x + a +--R Type: Expression(Integer) +--E 505 + +)clear all + + +--S 506 of 510 +t0099:= atanh(x)/(a-a*x^2)^(7/2) +--R +--R +--R atanh(x) +--R (1) - ---------------------------------------- +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x - 3a x + 3a x - a )\|- a x + a +--R Type: Expression(Integer) +--E 506 + +--S 507 of 510 +r0099:= 1/225*(-149-120*x^4+260*x^2+225*x*atanh(x)+120*x^5*atanh(x)-_ + 300*atanh(x)*x^3)/(-1+x^2)^2/(-a*(-1+x^2))^(1/2)/a^3 +--R +--R +--R 5 3 4 2 +--R (120x - 300x + 225x)atanh(x) - 120x + 260x - 149 +--R (2) ---------------------------------------------------- +--R +----------+ +--R 3 4 3 2 3 | 2 +--R (225a x - 450a x + 225a )\|- a x + a +--R Type: Expression(Integer) +--E 507 + +--S 508 of 510 +a0099:= integrate(t0099,x) +--R +--R +--R (3) +--R 9 7 5 3 - x - 1 10 +--R (600x - 3900x + 9045x - 9300x + 3600x)log(-------) - 298x +--R x - 1 +--R + +--R 8 6 4 2 +--R 3270x - 8990x + 9600x - 3600x +--R * +--R +-+ +--R \|a +--R + +--R 9 7 5 3 - x - 1 8 +--R (- 120x + 1740x - 5745x + 7500x - 3600x)log(-------) - 1250x +--R x - 1 +--R + +--R 6 4 2 +--R 5540x - 7800x + 3600x +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R / +--R +----------+ +--R 3 8 3 6 3 4 3 2 3 | 2 +-+ +--R (2250a x - 13500a x + 27450a x - 23400a x + 7200a )\|- a x + a \|a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R 450a x - 6750a x + 24750a x - 38250a x + 27000a x - 7200a +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 510 +m0099:= a0099-r0099 +--R +--R +--R (4) +--R 9 7 5 3 - x - 1 +--R (- 600x + 3900x - 9045x + 9300x - 3600x)log(-------) +--R x - 1 +--R + +--R 9 7 5 3 10 +--R (1200x - 7800x + 18090x - 18600x + 7200x)atanh(x) + 298x +--R + +--R 8 6 4 2 +--R - 4470x + 16390x - 25330x + 17880x - 4768 +--R * +--R +----------+ +--R | 2 +-+ +--R \|- a x + a \|a +--R + +--R 11 9 7 5 3 +--R (- 120a x + 1860a x - 7485a x + 13245a x - 11100a x + 3600a x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R + +--R 11 9 7 5 3 +--R (240a x - 3720a x + 14970a x - 26490a x + 22200a x - 7200a x) +--R * +--R atanh(x) +--R + +--R 10 8 6 4 2 +--R - 1490a x + 10430a x - 27118a x + 33674a x - 20264a x + 4768a +--R / +--R 4 10 4 8 4 6 4 4 4 2 4 +-+ +--R (2250a x - 15750a x + 40950a x - 50850a x + 30600a x - 7200a )\|a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R (- 450a x + 6750a x - 24750a x + 38250a x - 27000a x + 7200a ) +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R Type: Expression(Integer) +--E 509 + +--S 510 of 510 +d0099:= D(m0099,x) +--R +--R +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R (5) ------------------------------------------ +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (2a x - 6a x + 6a x - 2a )\|- a x + a +--R Type: Expression(Integer) +--E 510 + +)spool + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richinvhyper000-099.input.pdf b/src/axiom-website/CATS/richinvhyper000-099.input.pdf new file mode 100644 index 0000000..cc5abe1 Binary files /dev/null and b/src/axiom-website/CATS/richinvhyper000-099.input.pdf differ diff --git a/src/axiom-website/CATS/richinvhyper100-199.input.pamphlet b/src/axiom-website/CATS/richinvhyper100-199.input.pamphlet new file mode 100644 index 0000000..41c0df4 --- /dev/null +++ b/src/axiom-website/CATS/richinvhyper100-199.input.pamphlet @@ -0,0 +1,7873 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richinvhyper100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richinvhyper100-199.output +)spool richinvhyper100-199.output +)set message auto off +)clear all + +--S 1 of 506 +t0100:= atanh(x^(1/2)) +--R +--R +--R +-+ +--R (1) atanh(\|x ) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 506 +r0100:= x^(1/2)-atanh(x^(1/2))+x*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (2) (x - 1)atanh(\|x ) + \|x +--R Type: Expression(Integer) +--E 2 + +--S 3 of 506 +a0100:= integrate(t0100,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R (x - 1)log(----------) + 2\|x +--R +-+ +--R \|x - 1 +--R (3) ------------------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 506 +m0100:= a0100-r0100 +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (4) ---------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 506 +d0100:= D(m0100,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (5) ------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 506 +t0101:= x*atanh(x^(1/2)) +--R +--R +--R +-+ +--R (6) x atanh(\|x ) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 506 +r0101:= 1/2*x^(1/2)+1/6*x^(3/2)-1/2*atanh(x^(1/2))+1/2*x^2*atanh(x^(1/2)) +--R +--R +--R 2 +-+ +-+ +--R (3x - 3)atanh(\|x ) + (x + 3)\|x +--R (7) ---------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 506 +a0101:= integrate(t0101,x) +--R +--R +--R +-+ +--R 2 - \|x - 1 +-+ +--R (3x - 3)log(----------) + (2x + 6)\|x +--R +-+ +--R \|x - 1 +--R (8) --------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 506 +m0101:= a0101-r0101 +--R +--R +--R +-+ +--R 2 - \|x - 1 2 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (9) ------------------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 506 +d0101:= D(m0101,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R x log(----------) - 2x atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (10) ---------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 506 +t0102:= atanh(x^(1/2))/x^2 +--R +--R +--R +-+ +--R atanh(\|x ) +--R (11) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 506 +r0102:= -1/x^(1/2)+atanh(x^(1/2))-atanh(x^(1/2))/x +--R +--R +--R +-+ +-+ +--R (x - 1)\|x atanh(\|x ) - x +--R (12) -------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 12 + +--S 13 of 506 +a0102:= integrate(t0102,x) +--R +--R +--R +-+ +--R +-+ - \|x - 1 +--R (x - 1)\|x log(----------) - 2x +--R +-+ +--R \|x - 1 +--R (13) ------------------------------- +--R +-+ +--R 2x\|x +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 506 +m0102:= a0102-r0102 +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (14) ---------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 14 + +--S 15 of 506 +d0102:= D(m0102,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (15) ------------------------------ +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 15 + +--S 16 of 506 +t0103:= atanh(x^(1/2))/x^3 +--R +--R +--R +-+ +--R atanh(\|x ) +--R (16) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 506 +r0103:= -1/6/x^(3/2)-1/2/x^(1/2)+1/2*atanh(x^(1/2))-1/2*atanh(x^(1/2))/x^2 +--R +--R +--R 2 +-+ +-+ 2 +--R (3x - 3)\|x atanh(\|x ) - 3x - x +--R (17) ---------------------------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression(Integer) +--E 17 + +--S 18 of 506 +a0103:= integrate(t0103,x) +--R +--R +--R +-+ +--R 2 +-+ - \|x - 1 2 +--R (3x - 3)\|x log(----------) - 6x - 2x +--R +-+ +--R \|x - 1 +--R (18) --------------------------------------- +--R 2 +-+ +--R 12x \|x +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 506 +m0103:= a0103-r0103 +--R +--R +--R +-+ +--R 2 - \|x - 1 2 +-+ +--R (x - 1)log(----------) + (- 2x + 2)atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (19) ------------------------------------------------ +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 19 + +--S 20 of 506 +d0103:= D(m0103,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (20) ------------------------------ +--R 3 +--R 2x +--R Type: Expression(Integer) +--E 20 + +--S 21 of 506 +t0104:= x^(1/2)*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (21) \|x atanh(\|x ) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 506 +r0104:= 1/3*x+2/3*x^(3/2)*atanh(x^(1/2))+1/3*log(1-x) +--R +--R +--R +-+ +-+ +--R 2x\|x atanh(\|x ) + log(- x + 1) + x +--R (22) ------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 506 +a0104:= integrate(t0104,x) +--R +--R +--R +-+ +--R +-+ - \|x - 1 +--R x\|x log(----------) + log(x - 1) + x +--R +-+ +--R \|x - 1 +--R (23) ------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 506 +m0104:= a0104-r0104 +--R +--R +--R +-+ +--R +-+ - \|x - 1 +-+ +-+ +--R x\|x log(----------) - 2x\|x atanh(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R (24) -------------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 506 +d0104:= D(m0104,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R x log(----------) - 2x atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (25) ---------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 25 + +--S 26 of 506 +t0105:= x^(3/2)*atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (26) x\|x atanh(\|x ) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 506 +r0105:= 1/5*x+1/10*x^2+2/5*x^(5/2)*atanh(x^(1/2))+1/5*log(1-x) +--R +--R +--R 2 +-+ +-+ 2 +--R 4x \|x atanh(\|x ) + 2log(- x + 1) + x + 2x +--R (27) -------------------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 506 +a0105:= integrate(t0105,x) +--R +--R +--R +-+ +--R 2 +-+ - \|x - 1 2 +--R 2x \|x log(----------) + 2log(x - 1) + x + 2x +--R +-+ +--R \|x - 1 +--R (28) ---------------------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 506 +m0105:= a0105-r0105 +--R +--R +--R (29) +--R +-+ +--R 2 +-+ - \|x - 1 2 +-+ +-+ +--R x \|x log(----------) - 2x \|x atanh(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R ---------------------------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 506 +d0105:= D(m0105,x) +--R +--R +--R +-+ +--R 2 - \|x - 1 2 +-+ +--R x log(----------) - 2x atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (30) ---------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 30 + +--S 31 of 506 +t0106:= atanh(x^(1/2))/x^(3/2) +--R +--R +--R +-+ +--R atanh(\|x ) +--R (31) ----------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 506 +r0106:= 2*atanh(-1+2*x)-2*atanh(x^(1/2))/x^(1/2) +--R +--R +--R +-+ +-+ +--R - 2atanh(\|x ) + 2atanh(2x - 1)\|x +--R (32) ----------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 32 + +--S 33 of 506 +a0106:= integrate(t0106,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R - log(----------) + (log(x) - log(x - 1))\|x +--R +-+ +--R \|x - 1 +--R (33) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 506 +m0106:= a0106-r0106 +--R +--R +--R (34) +--R +-+ +--R - \|x - 1 +-+ +-+ +--R - log(----------) + 2atanh(\|x ) + (log(x) - log(x - 1) - 2atanh(2x - 1))\|x +--R +-+ +--R \|x - 1 +--R ----------------------------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 34 + +--S 35 of 506 +d0106:= D(m0106,x) +--R +--R +--R +-+ +--R - \|x - 1 +-+ +--R log(----------) - 2atanh(\|x ) +--R +-+ +--R \|x - 1 +--R (35) ------------------------------ +--R +-+ +--R 2x\|x +--R Type: Expression(Integer) +--E 35 + +--S 36 of 506 +t0107:= x*acoth(a*x) +--R +--R +--R (36) x acoth(a x) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 506 +r0107:= 1/2*(a*x+x^2*acoth(a*x)*a^2-atanh(a*x))/a^2 +--R +--R +--R 2 2 +--R - atanh(a x) + a x acoth(a x) + a x +--R (37) ----------------------------------- +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 506 +a0107:= integrate(t0107,x) +--R +--R +--R 2 2 a x + 1 +--R (a x - 1)log(-------) + 2a x +--R a x - 1 +--R (38) ----------------------------- +--R 2 +--R 4a +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 506 +m0107:= a0107-r0107 +--R +--R +--R 2 2 a x + 1 2 2 +--R (a x - 1)log(-------) + 2atanh(a x) - 2a x acoth(a x) +--R a x - 1 +--R (39) ------------------------------------------------------ +--R 2 +--R 4a +--R Type: Expression(Integer) +--E 39 + +--S 40 of 506 +d0107:= D(m0107,x) +--R +--R +--R a x + 1 +--R x log(-------) - 2x acoth(a x) +--R a x - 1 +--R (40) ------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 506 +t0108:= acoth(a*x)/x +--R +--R +--R acoth(a x) +--R (41) ---------- +--R x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 506 +r0108:= 1/2*polylog(2,-1/a/x)-1/2*polylog(2,1/a/x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 of 506 +a0108:= integrate(t0108,x) +--R +--R +--R x +--I ++ acoth(%Q a) +--I (42) | ----------- d%Q +--I ++ %Q +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 506 +--m0108:= a0108-r0108 +--E 44 + +--S 45 of 506 +--d0108:= D(m0108,x) +--E 45 + +--S 46 of 506 +t0109:= acoth(a*x)/x^3 +--R +--R +--R acoth(a x) +--R (43) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 506 +r0109:= -1/2*(a*x+acoth(a*x)-a^2*atanh(a*x)*x^2)/x^2 +--R +--R +--R 2 2 +--R a x atanh(a x) - acoth(a x) - a x +--R (44) --------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 47 + +--S 48 of 506 +a0109:= integrate(t0109,x) +--R +--R +--R 2 2 a x + 1 +--R (a x - 1)log(-------) - 2a x +--R a x - 1 +--R (45) ----------------------------- +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 506 +m0109:= a0109-r0109 +--R +--R +--R 2 2 a x + 1 2 2 +--R (a x - 1)log(-------) - 2a x atanh(a x) + 2acoth(a x) +--R a x - 1 +--R (46) ------------------------------------------------------ +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 49 + +--S 50 of 506 +d0109:= D(m0109,x) +--R +--R +--R a x + 1 +--R log(-------) - 2acoth(a x) +--R a x - 1 +--R (47) -------------------------- +--R 3 +--R 2x +--R Type: Expression(Integer) +--E 50 + +--S 51 of 506 +t0110:= (a+b*x)*acoth(a+b*x) +--R +--R +--R (48) (b x + a)acoth(b x + a) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 506 +r0110:= 1/2/b*(a+b*x)+1/2*(a+b*x)^2*acoth(a+b*x)/b-1/2*atanh(a+b*x)/b +--R +--R +--R 2 2 2 +--R - atanh(b x + a) + (b x + 2a b x + a )acoth(b x + a) + b x + a +--R (49) --------------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 52 + +--S 53 of 506 +a0110:= integrate(t0110,x) +--R +--R +--R 2 2 2 b x + a + 1 +--R (b x + 2a b x + a - 1)log(-----------) + 2b x +--R b x + a - 1 +--R (50) ----------------------------------------------- +--R 4b +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 506 +m0110:= a0110-r0110 +--R +--R +--R (51) +--R 2 2 2 b x + a + 1 +--R (b x + 2a b x + a - 1)log(-----------) + 2atanh(b x + a) +--R b x + a - 1 +--R + +--R 2 2 2 +--R (- 2b x - 4a b x - 2a )acoth(b x + a) - 2a +--R / +--R 4b +--R Type: Expression(Integer) +--E 54 + +--S 55 of 506 +d0110:= D(m0110,x) +--R +--R +--R b x + a + 1 +--R (b x + a)log(-----------) + (- 2b x - 2a)acoth(b x + a) +--R b x + a - 1 +--R (52) ------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 506 +t0111:= (a+b*x)^2*acoth(a+b*x) +--R +--R +--R 2 2 2 +--R (53) (b x + 2a b x + a )acoth(b x + a) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 506 +r0111:= 1/6*(a+b*x)^2/b+1/3*(a+b*x)^3*acoth(a+b*x)/b+1/6*log(1-(a+b*x)^2)/b +--R +--R +--R (54) +--R 2 2 2 +--R log(- b x - 2a b x - a + 1) +--R + +--R 3 3 2 2 2 3 2 2 2 +--R (2b x + 6a b x + 6a b x + 2a )acoth(b x + a) + b x + 2a b x + a +--R / +--R 6b +--R Type: Expression(Integer) +--E 57 + +--S 58 of 506 +a0111:= integrate(t0111,x) +--R +--R +--R (55) +--R 3 3 +--R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) +--R + +--R 3 3 2 2 2 b x + a + 1 2 2 +--R (b x + 3a b x + 3a b x)log(-----------) + b x + 2a b x +--R b x + a - 1 +--R / +--R 6b +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 506 +m0111:= a0111-r0111 +--R +--R +--R (56) +--R 3 3 +--R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) +--R + +--R 3 3 2 2 2 b x + a + 1 2 2 2 +--R (b x + 3a b x + 3a b x)log(-----------) - log(- b x - 2a b x - a + 1) +--R b x + a - 1 +--R + +--R 3 3 2 2 2 3 2 +--R (- 2b x - 6a b x - 6a b x - 2a )acoth(b x + a) - a +--R / +--R 6b +--R Type: Expression(Integer) +--E 59 + +--S 60 of 506 +d0111:= D(m0111,x) +--R +--R +--R (57) +--R 2 2 2 b x + a + 1 2 2 2 +--R (b x + 2a b x + a )log(-----------) + (- 2b x - 4a b x - 2a )acoth(b x + a) +--R b x + a - 1 +--R ----------------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 60 + +--S 61 of 506 +t0112:= acoth(1+x)/(2+2*x) +--R +--R +--R acoth(x + 1) +--R (58) ------------ +--R 2x + 2 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 506 +r0112:= 1/4*polylog(2,-1/(1+x))-1/4*polylog(2,1/(1+x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 506 +a0112:= integrate(t0112,x) +--R +--R +--R x +--I ++ acoth(%Q + 1) +--I (59) | ------------- d%Q +--I ++ 2%Q + 2 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 506 +--m0112:= a0112-r0112 +--E 64 + +--S 65 of 506 +--d0112:= D(m0112,x) +--E 65 + +--S 66 of 506 +t0113:= acoth(a+b*x)/(a+b*x) +--R +--R +--R acoth(b x + a) +--R (60) -------------- +--R b x + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 506 +r0113:= 1/2*(polylog(2,-1/(a+b*x))-polylog(2,1/(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 of 506 +a0113:= integrate(t0113,x) +--R +--R +--R x +--I ++ acoth(%Q b + a) +--I (61) | --------------- d%Q +--I ++ %Q b + a +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 506 +--m0113:= a0113-r0113 +--E 69 + +--S 70 of 506 +--d0113:= D(m0113,x) +--E 70 + +--S 71 of 506 +t0114:= 1/(1-x^2)/acoth(x) +--R +--R +--R 1 +--R (62) - ---------------- +--R 2 +--R (x - 1)acoth(x) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 506 +r0114:= log(acoth(x)) +--R +--R +--R (63) log(acoth(x)) +--R Type: Expression(Integer) +--E 72 + +--S 73 of 506 +a0114:= integrate(t0114,x) +--R +--R +--R x + 1 +--R (64) log(log(-----)) +--R x - 1 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 506 +m0114:= a0114-r0114 +--R +--R +--R x + 1 +--R (65) log(log(-----)) - log(acoth(x)) +--R x - 1 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 506 +d0114:= D(m0114,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (66) -------------------------- +--R 2 x + 1 +--R (x - 1)acoth(x)log(-----) +--R x - 1 +--R Type: Expression(Integer) +--E 75 + +--S 76 of 506 +t0115:= acoth(x)^n/(1-x^2) +--R +--R +--R n +--R acoth(x) +--R (67) - --------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 506 +r0115:= acoth(x)^(1+n)/(1+n) +--R +--R +--R n + 1 +--R acoth(x) +--R (68) ------------- +--R n + 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 506 +a0115:= integrate(t0115,x) +--R +--R +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x + 1 x - 1 x + 1 x - 1 +--R log(-----)sinh(n log(----------)) + log(-----)cosh(n log(----------)) +--R x - 1 2 x - 1 2 +--R (69) --------------------------------------------------------------------- +--R 2n + 2 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 506 +m0115:= a0115-r0115 +--R +--R +--R (70) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x + 1 x - 1 x + 1 x - 1 +--R log(-----)sinh(n log(----------)) + log(-----)cosh(n log(----------)) +--R x - 1 2 x - 1 2 +--R + +--R n + 1 +--R - 2acoth(x) +--R / +--R 2n + 2 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 506 +d0115:= D(m0115,x) +--R +--R +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 n +--R - sinh(n log(----------)) - cosh(n log(----------)) + acoth(x) +--R 2 2 +--R (71) --------------------------------------------------------------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 80 + +--S 81 of 506 +t0116:= acoth(x)/(1-x^2)^2 +--R +--R +--R acoth(x) +--R (72) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 506 +r0116:= 1/(-4+4*x^2)-x*acoth(x)/(-2+2*x^2)+1/4*acoth(x)^2 +--R +--R +--R 2 2 +--R (x - 1)acoth(x) - 2x acoth(x) + 1 +--R (73) ----------------------------------- +--R 2 +--R 4x - 4 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 506 +a0116:= integrate(t0116,x) +--R +--R +--R 2 x + 1 2 x + 1 +--R (x - 1)log(-----) - 4x log(-----) + 4 +--R x - 1 x - 1 +--R (74) --------------------------------------- +--R 2 +--R 16x - 16 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 506 +m0116:= a0116-r0116 +--R +--R +--R (75) +--R 2 x + 1 2 x + 1 2 2 +--R (x - 1)log(-----) - 4x log(-----) + (- 4x + 4)acoth(x) + 8x acoth(x) +--R x - 1 x - 1 +--R ------------------------------------------------------------------------ +--R 2 +--R 16x - 16 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 506 +d0116:= D(m0116,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (76) ---------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression(Integer) +--E 85 + +--S 86 of 506 +t0117:= acoth(x)^2/(1-x^2)^2 +--R +--R +--R 2 +--R acoth(x) +--R (77) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 506 +r0117:= 1/12*(-3*x+3*acoth(x)+3*x^2*acoth(x)-6*x*acoth(x)^2-_ + 2*acoth(x)^3+2*acoth(x)^3*x^2)/(-1+x^2) +--R +--R +--R 2 3 2 2 +--R (2x - 2)acoth(x) - 6x acoth(x) + (3x + 3)acoth(x) - 3x +--R (78) ---------------------------------------------------------- +--R 2 +--R 12x - 12 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 506 +a0117:= integrate(t0117,x) +--R +--R +--R 2 x + 1 3 x + 1 2 2 x + 1 +--R (x - 1)log(-----) - 6x log(-----) + (6x + 6)log(-----) - 12x +--R x - 1 x - 1 x - 1 +--R (79) ---------------------------------------------------------------- +--R 2 +--R 48x - 48 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 506 +m0117:= a0117-r0117 +--R +--R +--R (80) +--R 2 x + 1 3 x + 1 2 2 x + 1 +--R (x - 1)log(-----) - 6x log(-----) + (6x + 6)log(-----) +--R x - 1 x - 1 x - 1 +--R + +--R 2 3 2 2 +--R (- 8x + 8)acoth(x) + 24x acoth(x) + (- 12x - 12)acoth(x) +--R / +--R 2 +--R 48x - 48 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 506 +d0117:= D(m0117,x) +--R +--R +--R x + 1 2 2 +--R log(-----) - 4acoth(x) +--R x - 1 +--R (81) ------------------------ +--R 4 2 +--R 4x - 8x + 4 +--R Type: Expression(Integer) +--E 90 + +--S 91 of 506 +t0118:= 1/(a-a*x^2)/(b-2*b*acoth(x)) +--R +--R +--R 1 +--R (82) --------------------------------------- +--R 2 2 +--R (2a b x - 2a b)acoth(x) - a b x + a b +--R Type: Expression(Integer) +--E 91 + +--S 92 of 506 +r0118:= -1/2*log(1-2*acoth(x))/a/b +--R +--R +--R log(- 2acoth(x) + 1) +--R (83) - -------------------- +--R 2a b +--R Type: Expression(Integer) +--E 92 + +--S 93 of 506 +a0118:= integrate(t0118,x) +--R +--R +--R x + 1 +--R log(log(-----) - 1) +--R x - 1 +--R (84) - ------------------- +--R 2a b +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 506 +m0118:= a0118-r0118 +--R +--R +--R x + 1 +--R - log(log(-----) - 1) + log(- 2acoth(x) + 1) +--R x - 1 +--R (85) -------------------------------------------- +--R 2a b +--R Type: Expression(Integer) +--E 94 + +--S 95 of 506 +d0118:= D(m0118,x) +--R +--R +--R (86) +--R x + 1 +--R - log(-----) + 2acoth(x) +--R x - 1 +--R / +--R 2 2 x + 1 +--R ((2a b x - 2a b)acoth(x) - a b x + a b)log(-----) +--R x - 1 +--R + +--R 2 2 +--R (- 2a b x + 2a b)acoth(x) + a b x - a b +--R Type: Expression(Integer) +--E 95 + +--S 96 of 506 +t0119:= x*acoth(x)/(1-x^2) +--R +--R +--R x acoth(x) +--R (87) - ---------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 506 +r0119:= -1/2*acoth(x)^2+acoth(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 506 +a0119:= integrate(t0119,x) +--R +--R +--R x +--I ++ %Q acoth(%Q) +--I (88) | - ------------ d%Q +--R ++ 2 +--I %Q - 1 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 506 +--m0119:= a0119-r0119 +--E 99 + +--S 100 of 506 +--d0119:= D(m0119,x) +--E 100 + +--S 101 of 506 +t0120:= x*acoth(x)/(1-x^2)^2 +--R +--R +--R x acoth(x) +--R (89) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 506 +r0120:= -1/4*(-x+acoth(x)+x^2*acoth(x))/(-1+x^2) +--R +--R +--R 2 +--R (- x - 1)acoth(x) + x +--R (90) ---------------------- +--R 2 +--R 4x - 4 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 506 +a0120:= integrate(t0120,x) +--R +--R +--R 2 x + 1 +--R (- x - 1)log(-----) + 2x +--R x - 1 +--R (91) ------------------------- +--R 2 +--R 8x - 8 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 506 +m0120:= a0120-r0120 +--R +--R +--R 2 x + 1 2 +--R (- x - 1)log(-----) + (2x + 2)acoth(x) +--R x - 1 +--R (92) ---------------------------------------- +--R 2 +--R 8x - 8 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 506 +d0120:= D(m0120,x) +--R +--R +--R x + 1 +--R x log(-----) - 2x acoth(x) +--R x - 1 +--R (93) -------------------------- +--R 4 2 +--R 2x - 4x + 2 +--R Type: Expression(Integer) +--E 105 + +--S 106 of 506 +t0121:= x*acoth(x)/(1-x^2)^3 +--R +--R +--R x acoth(x) +--R (94) - ------------------ +--R 6 4 2 +--R x - 3x + 3x - 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 506 +r0121:= -1/32*(5*x-3*x^3-5*acoth(x)+3*acoth(x)*x^4-6*x^2*acoth(x))/(-1+x^2)^2 +--R +--R +--R 4 2 3 +--R (- 3x + 6x + 5)acoth(x) + 3x - 5x +--R (95) ------------------------------------ +--R 4 2 +--R 32x - 64x + 32 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 506 +a0121:= integrate(t0121,x) +--R +--R +--R 4 2 x + 1 3 +--R (- 3x + 6x + 5)log(-----) + 6x - 10x +--R x - 1 +--R (96) --------------------------------------- +--R 4 2 +--R 64x - 128x + 64 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 506 +m0121:= a0121-r0121 +--R +--R +--R 4 2 x + 1 4 2 +--R (- 3x + 6x + 5)log(-----) + (6x - 12x - 10)acoth(x) +--R x - 1 +--R (97) ------------------------------------------------------- +--R 4 2 +--R 64x - 128x + 64 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 506 +d0121:= D(m0121,x) +--R +--R +--R x + 1 +--R - x log(-----) + 2x acoth(x) +--R x - 1 +--R (98) ---------------------------- +--R 6 4 2 +--R 2x - 6x + 6x - 2 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 506 +t0122:= acoth(x)/(a+b*x^2)^(3/2) +--R +--R +--R acoth(x) +--R (99) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 111 + +--S 112 of 506 +r0122:= x*acoth(x)/a/(a+b*x^2)^(1/2)-_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a/(a+b)^(1/2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-----+ +--R - \|b x + a atanh(-----------) + x acoth(x)\|b + a +--R +-----+ +--R \|b + a +--R (100) ---------------------------------------------------- +--R +--------+ +--R +-----+ | 2 +--R a\|b + a \|b x + a +--R Type: Expression(Integer) +--E 112 + +--S 113 of 506 +a0122:= integrate(t0122,x) +--R +--R +--R (101) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R +--------+ +--R x + 1 +-----+ | 2 x + 1 +-+ +-----+ +--R - x log(-----)\|b + a \|b x + a + x log(-----)\|a \|b + a +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-+ +-----+ | 2 2 2 +-----+ +--R 2a\|a \|b + a \|b x + a + (- 2a b x - 2a )\|b + a +--R , +--R +--R +--------+ +--R +-+ | 2 2 +--R (- 2\|a \|b x + a + 2b x + 2a) +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R +--------+ +--R x + 1 +-------+ | 2 x + 1 +-------+ +-+ +--R - x log(-----)\|- b - a \|b x + a + x log(-----)\|- b - a \|a +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-------+ +-+ | 2 2 2 +-------+ +--R 2a\|- b - a \|a \|b x + a + (- 2a b x - 2a )\|- b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 113 + +--S 114 of 506 +m0122a:= a0122.1-r0122 +--R +--R +--R (102) +--R +--------+ +--R 2 | 2 2 +-+ +--R ((b x + a)\|b x + a + (- b x - a)\|a ) +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((2b x + 2a)\|b x + a + (- 2b x - 2a)\|a )atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +--------+ +--R x + 1 +-+ +-----+ | 2 +--R (- x log(-----) + 2x acoth(x))\|a \|b + a \|b x + a +--R x - 1 +--R + +--R 3 x + 1 3 +-----+ +--R ((b x + a x)log(-----) + (- 2b x - 2a x)acoth(x))\|b + a +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-----+ | 2 2 2 +-+ +-----+ +--R (2a b x + 2a )\|b + a \|b x + a + (- 2a b x - 2a )\|a \|b + a +--R Type: Expression(Integer) +--E 114 + +--S 115 of 506 +d0122a:= D(m0122a,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (103) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 115 + +--S 116 of 506 +m0122b:= a0122.2-r0122 +--R +--R +--R (104) +--R +--------+ +--R 2 +-------+ | 2 2 +-------+ +-+ +--R ((2b x + 2a)\|- b - a \|b x + a + (- 2b x - 2a)\|- b - a \|a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R +--------+ +--R 2 +-----+ | 2 2 +-+ +-----+ +--R ((- 2b x - 2a)\|b + a \|b x + a + (2b x + 2a)\|a \|b + a ) +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R +--------+ +--R x + 1 +-------+ +-+ +-----+ | 2 +--R (- x log(-----) + 2x acoth(x))\|- b - a \|a \|b + a \|b x + a +--R x - 1 +--R + +--R 3 x + 1 3 +-------+ +-----+ +--R ((b x + a x)log(-----) + (- 2b x - 2a x)acoth(x))\|- b - a \|b + a +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ +-----+ | 2 +--R (2a b x + 2a )\|- b - a \|b + a \|b x + a +--R + +--R 2 2 +-------+ +-+ +-----+ +--R (- 2a b x - 2a )\|- b - a \|a \|b + a +--R Type: Expression(Integer) +--E 116 + +--S 117 of 506 +d0122b:= D(m0122b,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (105) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 117 + +--S 118 of 506 +t0123:= acoth(x)/(a+b*x^2)^(5/2) +--R +--R +--R acoth(x) +--R (106) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 118 + +--S 119 of 506 +r0123:= 1/3/a/(a+b)/(a+b*x^2)^(1/2)+1/3*x*(3*a+2*b*x^2)*_ + acoth(x)/a^2/(a+b*x^2)^(3/2)-1/3*(3*a+2*b)*_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^2/(a+b)^(3/2) +--R +--R +--R (107) +--R +--------+ +--R +--------+ | 2 +--R 2 2 2 | 2 \|b x + a +--R ((- 2b - 3a b)x - 2a b - 3a )\|b x + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 2 2 +-----+ +--R (((2b + 2a b)x + (3a b + 3a )x)acoth(x) + a b x + a )\|b + a +--R / +--R +--------+ +--R 2 2 3 2 3 4 +-----+ | 2 +--R ((3a b + 3a b)x + 3a b + 3a )\|b + a \|b x + a +--R Type: Expression(Integer) +--E 119 + +--S 120 of 506 +a0123:= integrate(t0123,x) +--R +--R +--R (108) +--R [ +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b + 12a b )x + (32a b + 48a b )x + (40a b + 60a b)x +--R + +--R 3 4 +--R 16a b + 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b - 3a b )x + (- 20a b - 30a b )x + (- 50a b - 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b - 72a b)x - 16a b - 24a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b - 2a b )x + (- 19a b - 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b - 40a b)x + (- 24a b - 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b + 8a b )x + (36a b + 36a b )x + (52a b + 52a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b + 24a b )x + (96a b + 96a b )x + (120a b + 120a b)x +--R + +--R 5 6 +--R 48a b + 48a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b - 6a b )x + (- 60a b - 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b - 150a b )x + (- 144a b - 144a b)x - 48a b - 48a +--R * +--R +-----+ +--R \|b + a +--R , +--R +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (4b + 6a b )x + (40a b + 60a b )x + (100a b + 150a b )x +--R + +--R 3 2 4 2 4 5 +--R (96a b + 144a b)x + 32a b + 48a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b - 2a b )x + (- 19a b - 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b - 40a b)x + (- 24a b - 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b + 8a b )x + (36a b + 36a b )x + (52a b + 52a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b + 24a b )x + (96a b + 96a b )x + (120a b + 120a b)x +--R + +--R 5 6 +--R 48a b + 48a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b - a \|a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b - 6a b )x + (- 60a b - 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b - 150a b )x + (- 144a b - 144a b)x - 48a b - 48a +--R * +--R +-------+ +--R \|- b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 120 + +--S 121 of 506 +m0123a:= a0123.1-r0123 +--R +--R +--R (109) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b + 3a b )x + (18a b + 27a b )x + (32a b + 48a b)x +--R + +--R 3 4 +--R 16a b + 24a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b - 12a b )x + (- 32a b - 48a b )x + (- 40a b - 60a b)x +--R + +--R 3 4 +--R - 16a b - 24a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b - 8a b )x + (- 28a b - 28a b)x + (- 24a b - 24a )x) +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b + 16a b )x + (56a b + 56a b)x + (48a b + 48a )x)acoth(x) +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b + 2a b )x + (19a b + 19a b )x + (40a b + 40a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b - 4a b )x + (- 38a b - 38a b )x + (- 80a b - 80a b)x +--R + +--R 3 4 +--R (- 48a b - 48a )x +--R * +--R acoth(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-----+ +--R \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b + 6a b )x + (54a b + 54a b )x + (96a b + 96a b)x + 48a b +--R + +--R 6 +--R 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b - 24a b )x + (- 96a b - 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b - 120a b)x - 48a b - 48a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 506 +d0123a:= D(m0123a,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (110) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 122 + +--S 123 of 506 +m0123b:= a0123.2-r0123 +--R +--R +--R (111) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b - 24a b )x + (- 64a b - 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b - 120a b)x - 32a b - 48a +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 4b - 6a b )x + (- 36a b - 54a b )x + (- 64a b - 96a b)x +--R + +--R 3 4 +--R - 32a b - 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (16b + 24a b )x + (64a b + 96a b )x + (80a b + 120a b)x +--R + +--R 3 4 +--R 32a b + 48a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b - 8a b )x + (- 28a b - 28a b)x + (- 24a b - 24a )x) +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b + 16a b )x + (56a b + 56a b)x + (48a b + 48a )x)acoth(x) +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b - a \|a \|b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b + 2a b )x + (19a b + 19a b )x + (40a b + 40a b)x +--R + +--R 3 4 +--R (24a b + 24a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b - 4a b )x + (- 38a b - 38a b )x + (- 80a b - 80a b)x +--R + +--R 3 4 +--R (- 48a b - 48a )x +--R * +--R acoth(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-------+ +-----+ +--R \|- b - a \|b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b + 6a b )x + (54a b + 54a b )x + (96a b + 96a b)x + 48a b +--R + +--R 6 +--R 48a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b - a \|b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b - 24a b )x + (- 96a b - 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b - 120a b)x - 48a b - 48a +--R * +--R +-------+ +-+ +-----+ +--R \|- b - a \|a \|b + a +--R Type: Expression(Integer) +--E 123 + +--S 124 of 506 +d0123b:= D(m0123b,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (112) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 124 + +--S 125 of 506 +t0124:= acoth(x)/(a+b*x^2)^(7/2) +--R +--R +--R acoth(x) +--R (113) ------------------------------------------ +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 125 + +--S 126 of 506 +r0124:= 1/15/a/(a+b)/(a+b*x^2)^(3/2)+_ + 1/15*(7*a+4*b)/a^2/(a+b)^2/(a+b*x^2)^(1/2)+_ + 1/15*x*(8*(a+b*x^2)^2+a*(7*a+4*b*x^2))*_ + acoth(x)/a^3/(a+b*x^2)^(5/2)-1/15*(15*a^2+20*a*b+8*b^2)*_ + atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^3/(a+b)^(5/2) +--R +--R +--R (114) +--R 4 3 2 2 4 3 2 2 3 2 2 2 +--R (- 8b - 20a b - 15a b )x + (- 16a b - 40a b - 30a b)x - 8a b +--R + +--R 3 4 +--R - 20a b - 15a +--R * +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +--R \|b x + a atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 4 3 2 2 5 3 2 2 3 3 +--R (8b + 16a b + 8a b )x + (20a b + 40a b + 20a b)x +--R + +--R 2 2 3 4 +--R (15a b + 30a b + 15a )x +--R * +--R acoth(x) +--R + +--R 3 2 2 4 2 2 3 2 3 4 +--R (4a b + 7a b )x + (9a b + 15a b)x + 5a b + 8a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 5 2 +--R (15a b + 30a b + 15a b )x + (30a b + 60a b + 30a b)x + 15a b +--R + +--R 6 7 +--R 30a b + 15a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 506 +a0124:= integrate(t0124,x) +--R +--R +--R (115) +--R [ +--R 8 7 2 6 12 +--R (64b + 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b + 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b + 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b + 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b + 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b + 11520a b + 8640a b)x + 1024a b + 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b - 20a b - 15a b )x + (- 280a b - 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b - 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b - 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b - 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b - 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b - 12800a b - 9600a b)x - 1024a b - 2560a b - 1920a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 8 7 2 6 13 +--R (- 8b - 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b - 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b - 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b - 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b - 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b - 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b + 114a b )x + (766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b + 4080a b )x + (4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b + 4608a b )x + (896a b + 1280a b)x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b + 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b + 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b + 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b + 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b + 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b + 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b - 16a b )x + (- 286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b - 2672a b )x + (- 4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b - 8480a b )x + (- 3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b - 1280a b)x +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b + 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b + 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b + 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b + 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b + 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b + 34560a b + 17280a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b - 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b - 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b - 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b - 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b - 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b - 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b - 38400a b - 19200a b)x - 3840a b - 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-----+ +--R \|b + a +--R , +--R +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b +--R + +--R 8 +--R - 3840a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (16b + 40a b + 30a b )x + (560a b + 1400a b + 1050a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (4144a b + 10360a b + 7770a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (13328a b + 33320a b + 24990a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (22528a b + 56320a b + 42240a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (20992a b + 52480a b + 39360a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (10240a b + 25600a b + 19200a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 8 7 2 6 13 +--R (- 8b - 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b - 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b - 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b - 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b - 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b - 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b + 114a b )x + (766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b + 4080a b )x + (4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b + 4608a b )x + (896a b + 1280a b)x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b + 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b + 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b + 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b + 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b + 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b + 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b - 16a b )x + (- 286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b - 2672a b )x + (- 4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b - 8480a b )x + (- 3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b - 1280a b)x +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b + 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b + 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b + 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b + 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b + 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b + 34560a b + 17280a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b - a \|a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b - 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b - 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b - 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b - 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b - 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b - 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b - 38400a b - 19200a b)x - 3840a b - 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-------+ +--R \|- b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 127 + +--S 128 of 506 +m0124a:= a0124.1-r0124 +--R +--R +--R (116) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b + 20a b + 15a b )x + (272a b + 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b + 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b + 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b + 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b + 10240a b + 7680a b)x + 1024a b + 2560a b + 1920a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b - 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b - 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b - 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b - 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b - 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b - 11520a b - 8640a b)x - 1024a b - 2560a b - 1920a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 4 2 2 2 +-----+ +--R (- 4a x + (- 4a b + 8a )x - 8a )\|b + a +--R + +--R 2 2 4 2 2 +-+ +--R ((- 2b + 2a b + 4a )x + (- 8a b - 8a )x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 2 +--R ((b + 2a b)x + (b - 4a b + 4a )x + (8a b - 8a )x + 8a ) +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b - 2a b)x + (6a b + 2a b - 4a )x + (8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (- 4a b + 8a )x - 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (b - 8a b)x + (8a b - 8a )x + 8a )\|a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b + 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b + 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b + 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b + 20480a b + 15360a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b - 3840a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 7 6 2 5 11 +--R (- 64b - 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b - 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b - 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b - 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b - 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b + 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b + 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b + 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b + 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b + 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b + 7680a b + 3840a )x +--R * +--R acoth(x) +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b + 16a b )x + (340a b + 544a b )x + (2250a b + 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b + 9728a b )x + (8000a b + 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b + 8192a b)x + 1280a b + 2048a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b + 16a b + 8a b )x + (276a b + 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b + 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b + 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b + 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b + 12800a b + 6400a b)x + (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b - 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b - 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b - 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b - 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b - 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b - 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b - 7680a b - 3840a )x +--R * +--R acoth(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b - 128a b )x + (- 1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b - 7296a b )x + (- 9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b - 16640a b )x + (- 5760a b - 9216a b)x - 1280a b +--R + +--R 8 +--R - 2048a +--R * +--R +-----+ +--R \|b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b + 60a b + 30a b )x + (1020a b + 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b + 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b + 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b + 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b + 30720a b + 15360a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b - 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b - 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b - 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b - 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b - 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b - 34560a b - 17280a b)x - 3840a b - 7680a b - 3840a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R Type: Expression(Integer) +--E 128 + +--S 129 of 506 +d0124a:= D(m0124a,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (117) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 129 + +--S 130 of 506 +m0124b:= a0124.2-r0124 +--R +--R +--R (118) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b + 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b + 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b + 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b + 20480a b + 15360a b)x + 2048a b + 5120a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b - a \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b - 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b - 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b - 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b - 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b - 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b - 23040a b - 17280a b)x - 2048a b - 5120a b - 3840a +--R * +--R +-------+ +-+ +--R \|- b - a \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-----+ +--R \|b + a +--R + +--R 8 7 2 6 12 +--R (- 16b - 40a b - 30a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 544a b - 1360a b - 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3600a b - 9000a b - 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 9728a b - 24320a b - 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 12800a b - 32000a b - 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 8192a b - 20480a b - 15360a b)x - 2048a b - 5120a b - 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b + a \|b x + a +--R + +--R 8 7 2 6 12 +--R (128b + 320a b + 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (1664a b + 4160a b + 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (7296a b + 18240a b + 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (15232a b + 38080a b + 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (16640a b + 41600a b + 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (9216a b + 23040a b + 17280a b)x + 2048a b + 5120a b + 3840a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +--------+ +--R +-------+ | 2 2 +-------+ +-+ +--R \|- b - a \|b x + a + (x - 1)\|- b - a \|a +--R atan(----------------------------------------------) +--R 2 +--R (b + a)x +--R + +--R 7 6 2 5 11 +--R (- 64b - 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b - 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b - 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b - 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b - 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b - 3840a b - 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b + 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b + 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b + 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b + 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b + 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b + 7680a b + 3840a )x +--R * +--R acoth(x) +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b + 16a b )x + (340a b + 544a b )x + (2250a b + 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b + 9728a b )x + (8000a b + 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b + 8192a b)x + 1280a b + 2048a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b - a \|a \|b + a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b + 16a b + 8a b )x + (276a b + 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b + 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b + 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b + 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b + 12800a b + 6400a b)x + (1920a b + 3840a b + 1920a )x +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b - 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b - 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b - 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b - 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b - 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b - 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b - 7680a b - 3840a )x +--R * +--R acoth(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b - 128a b )x + (- 1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b - 7296a b )x + (- 9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b - 16640a b )x + (- 5760a b - 9216a b)x - 1280a b +--R + +--R 8 +--R - 2048a +--R * +--R +-------+ +-----+ +--R \|- b - a \|b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b + 60a b + 30a b )x + (1020a b + 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b + 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b + 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b + 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b + 30720a b + 15360a b)x + 3840a b + 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b - a \|b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b - 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b - 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b - 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b - 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b - 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b - 34560a b - 17280a b)x - 3840a b - 7680a b - 3840a +--R * +--R +-------+ +-+ +-----+ +--R \|- b - a \|a \|b + a +--R Type: Expression(Integer) +--E 130 + +--S 131 of 506 +d0124b:= D(m0124b,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (119) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 131 + +--S 132 of 506 +t0125:= acoth(x)*(a-a*x^2)^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R (120) acoth(x)\|- a x + a +--R Type: Expression(Integer) +--E 132 + +--S 133 of 506 +r0125:= 1/2/(1-1/x^2)^(1/2)/x*(a*(1-x^2))^(1/2)*((1-1/x^2)^(1/2)*x+_ + (1-1/x^2)^(1/2)*x^2*acoth(x)-2*acoth(x)*_ + atanh(exp(1)^acoth(x))-polylog(2,-exp(1)^acoth(x))+_ + polylog(2,exp(1)^acoth(x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 133 + +--S 134 of 506 +a0125:= integrate(t0125,x) +--R +--R +--R x +------------+ +--R ++ | 2 +--I (121) | acoth(%Q)\|(- %Q + 1)a d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 134 + +--S 135 of 506 +--m0125:= a0125-r0125 +--E 135 + +--S 136 of 506 +--d0125:= D(m0125,x) +--E 136 + +--S 137 of 506 +t0126:= acoth(x)/(a-a*x^2)^(1/2) +--R +--R +--R acoth(x) +--R (122) ------------- +--R +----------+ +--R | 2 +--R \|- a x + a +--R Type: Expression(Integer) +--E 137 + +--S 138 of 506 +r0126:= (1-1/x^2)^(1/2)*x*(2*acoth(x)*atanh(exp(1)^acoth(x))+_ + polylog(2,-exp(1)^acoth(x))-_ + polylog(2,exp(1)^acoth(x)))/(a*(1-x^2))^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 138 + +--S 139 of 506 +a0126:= integrate(t0126,x) +--R +--R +--R x +--I ++ acoth(%Q) +--I (123) | --------------- d%Q +--R ++ +------------+ +--R | 2 +--I \|(- %Q + 1)a +--R Type: Union(Expression(Integer),...) +--E 139 + +--S 140 of 506 +--m0126:= a0126-r0126 +--E 140 + +--S 141 of 506 +--d0126:= D(m0126,x) +--E 141 + +--S 142 of 506 +t0127:= acoth(x)/(a-a*x^2)^(3/2) +--R +--R +--R acoth(x) +--R (124) - ----------------------- +--R +----------+ +--R 2 | 2 +--R (a x - a)\|- a x + a +--R Type: Expression(Integer) +--E 142 + +--S 143 of 506 +r0127:= (x*acoth(x)-1)/a/(-a*(-1+x^2))^(1/2) +--R +--R +--R x acoth(x) - 1 +--R (125) -------------- +--R +----------+ +--R | 2 +--R a\|- a x + a +--R Type: Expression(Integer) +--E 143 + +--S 144 of 506 +a0127:= integrate(t0127,x) +--R +--R +--R +----------+ +--R x + 1 2 +-+ x + 1 | 2 +--R (x log(-----) - 2x )\|a - x log(-----)\|- a x + a +--R x - 1 x - 1 +--R (126) ---------------------------------------------------- +--R +----------+ +--R | 2 +-+ 2 2 2 +--R 2a\|- a x + a \|a + 2a x - 2a +--R Type: Union(Expression(Integer),...) +--E 144 + +--S 145 of 506 +m0127:= a0127-r0127 +--R +--R +--R (127) +--R +----------+ +--R x + 1 2 | 2 +-+ +--R (- x log(-----) + 2x acoth(x) + 2x - 2)\|- a x + a \|a +--R x - 1 +--R + +--R 3 x + 1 3 2 +--R (- a x + a x)log(-----) + (2a x - 2a x)acoth(x) - 2a x + 2a +--R x - 1 +--R / +--R +----------+ +--R 2 2 2 +-+ 2 2 2 | 2 +--R (2a x - 2a )\|a + (- 2a x + 2a )\|- a x + a +--R Type: Expression(Integer) +--E 145 + +--S 146 of 506 +d0127:= D(m0127,x) +--R +--R +--R x + 1 +--R - log(-----) + 2acoth(x) +--R x - 1 +--R (128) ------------------------- +--R +----------+ +--R 2 | 2 +--R (2a x - 2a)\|- a x + a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 506 +t0128:= acoth(x)/(a-a*x^2)^(5/2) +--R +--R +--R acoth(x) +--R (129) -------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (a x - 2a x + a )\|- a x + a +--R Type: Expression(Integer) +--E 147 + +--S 148 of 506 +r0128:= 1/9*(6*acoth(x)*x^3-6*x^2-9*x*acoth(x)+7)/a^2/_ + (-1+x^2)/(-a*(-1+x^2))^(1/2) +--R +--R +--R 3 2 +--R (6x - 9x)acoth(x) - 6x + 7 +--R (130) ---------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (9a x - 9a )\|- a x + a +--R Type: Expression(Integer) +--E 148 + +--S 149 of 506 +a0128:= integrate(t0128,x) +--R +--R +--R (131) +--R 5 3 x + 1 6 4 2 +-+ +--R ((18x - 51x + 36x)log(-----) - 14x + 48x - 36x )\|a +--R x - 1 +--R + +--R +----------+ +--R 5 3 x + 1 4 2 | 2 +--R ((- 6x + 33x - 36x)log(-----) - 30x + 36x )\|- a x + a +--R x - 1 +--R / +--R +----------+ +--R 2 4 2 2 2 | 2 +-+ 3 6 3 4 3 2 +--R (54a x - 126a x + 72a )\|- a x + a \|a + 18a x - 108a x + 162a x +--R + +--R 3 +--R - 72a +--R Type: Union(Expression(Integer),...) +--E 149 + +--S 150 of 506 +m0128:= a0128-r0128 +--R +--R +--R (132) +--R 5 3 x + 1 5 3 6 +--R (- 18x + 51x - 36x)log(-----) + (36x - 102x + 72x)acoth(x) + 14x +--R x - 1 +--R + +--R 4 2 +--R - 84x + 126x - 56 +--R * +--R +----------+ +--R | 2 +-+ +--R \|- a x + a \|a +--R + +--R 7 5 3 x + 1 +--R (- 6a x + 39a x - 69a x + 36a x)log(-----) +--R x - 1 +--R + +--R 7 5 3 6 4 2 +--R (12a x - 78a x + 138a x - 72a x)acoth(x) - 42a x + 140a x - 154a x +--R + +--R 56a +--R / +--R 3 6 3 4 3 2 3 +-+ +--R (54a x - 180a x + 198a x - 72a )\|a +--R + +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (- 18a x + 108a x - 162a x + 72a )\|- a x + a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 506 +d0128:= D(m0128,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (133) ---------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (2a x - 4a x + 2a )\|- a x + a +--R Type: Expression(Integer) +--E 151 + +--S 152 of 506 +t0129:= acoth(x)/(a-a*x^2)^(7/2) +--R +--R +--R acoth(x) +--R (134) - ---------------------------------------- +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x - 3a x + 3a x - a )\|- a x + a +--R Type: Expression(Integer) +--E 152 + +--S 153 of 506 +r0129:= 1/225*(120*acoth(x)*x^5-120*x^4-300*acoth(x)*x^3+260*x^2+_ + 225*x*acoth(x)-149)/a^3/(-1+x^2)^2/(-a*(-1+x^2))^(1/2) +--R +--R +--R 5 3 4 2 +--R (120x - 300x + 225x)acoth(x) - 120x + 260x - 149 +--R (135) ---------------------------------------------------- +--R +----------+ +--R 3 4 3 2 3 | 2 +--R (225a x - 450a x + 225a )\|- a x + a +--R Type: Expression(Integer) +--E 153 + +--S 154 of 506 +a0129:= integrate(t0129,x) +--R +--R +--R (136) +--R 9 7 5 3 x + 1 10 +--R (600x - 3900x + 9045x - 9300x + 3600x)log(-----) - 298x +--R x - 1 +--R + +--R 8 6 4 2 +--R 3270x - 8990x + 9600x - 3600x +--R * +--R +-+ +--R \|a +--R + +--R 9 7 5 3 x + 1 8 +--R (- 120x + 1740x - 5745x + 7500x - 3600x)log(-----) - 1250x +--R x - 1 +--R + +--R 6 4 2 +--R 5540x - 7800x + 3600x +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R / +--R +----------+ +--R 3 8 3 6 3 4 3 2 3 | 2 +-+ +--R (2250a x - 13500a x + 27450a x - 23400a x + 7200a )\|- a x + a \|a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R 450a x - 6750a x + 24750a x - 38250a x + 27000a x - 7200a +--R Type: Union(Expression(Integer),...) +--E 154 + +--S 155 of 506 +m0129:= a0129-r0129 +--R +--R +--R (137) +--R 9 7 5 3 x + 1 +--R (- 600x + 3900x - 9045x + 9300x - 3600x)log(-----) +--R x - 1 +--R + +--R 9 7 5 3 10 +--R (1200x - 7800x + 18090x - 18600x + 7200x)acoth(x) + 298x +--R + +--R 8 6 4 2 +--R - 4470x + 16390x - 25330x + 17880x - 4768 +--R * +--R +----------+ +--R | 2 +-+ +--R \|- a x + a \|a +--R + +--R 11 9 7 5 3 +--R (- 120a x + 1860a x - 7485a x + 13245a x - 11100a x + 3600a x) +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R + +--R 11 9 7 5 3 +--R (240a x - 3720a x + 14970a x - 26490a x + 22200a x - 7200a x) +--R * +--R acoth(x) +--R + +--R 10 8 6 4 2 +--R - 1490a x + 10430a x - 27118a x + 33674a x - 20264a x + 4768a +--R / +--R 4 10 4 8 4 6 4 4 4 2 4 +-+ +--R (2250a x - 15750a x + 40950a x - 50850a x + 30600a x - 7200a )\|a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R (- 450a x + 6750a x - 24750a x + 38250a x - 27000a x + 7200a ) +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R Type: Expression(Integer) +--E 155 + +--S 156 of 506 +d0129:= D(m0129,x) +--R +--R +--R x + 1 +--R - log(-----) + 2acoth(x) +--R x - 1 +--R (138) ------------------------------------------ +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (2a x - 6a x + 6a x - 2a )\|- a x + a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 506 +t0130:= acoth(x^(1/2)) +--R +--R +--R +-+ +--R (139) acoth(\|x ) +--R Type: Expression(Integer) +--E 157 + +--S 158 of 506 +r0130:= x^(1/2)+x*acoth(x^(1/2))-atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R (140) - atanh(\|x ) + x acoth(\|x ) + \|x +--R Type: Expression(Integer) +--E 158 + +--S 159 of 506 +a0130:= integrate(t0130,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R (x - 1)log(--------) + 2\|x +--R +-+ +--R \|x - 1 +--R (141) ---------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 159 + +--S 160 of 506 +m0130:= a0130-r0130 +--R +--R +--R +-+ +--R \|x + 1 +-+ +-+ +--R (x - 1)log(--------) + 2atanh(\|x ) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (142) ---------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 506 +d0130:= D(m0130,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (143) ---------------------------- +--R 2 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 506 +t0131:= x*acoth(x^(1/2)) +--R +--R +--R +-+ +--R (144) x acoth(\|x ) +--R Type: Expression(Integer) +--E 162 + +--S 163 of 506 +r0131:= 1/2*x^(1/2)+1/6*x^(3/2)+1/2*x^2*acoth(x^(1/2))-1/2*atanh(x^(1/2)) +--R +--R +--R +-+ 2 +-+ +-+ +--R - 3atanh(\|x ) + 3x acoth(\|x ) + (x + 3)\|x +--R (145) --------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 163 + +--S 164 of 506 +a0131:= integrate(t0131,x) +--R +--R +--R +-+ +--R 2 \|x + 1 +-+ +--R (3x - 3)log(--------) + (2x + 6)\|x +--R +-+ +--R \|x - 1 +--R (146) ------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 164 + +--S 165 of 506 +m0131:= a0131-r0131 +--R +--R +--R +-+ +--R 2 \|x + 1 +-+ 2 +-+ +--R (x - 1)log(--------) + 2atanh(\|x ) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (147) ----------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 506 +d0131:= D(m0131,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R x log(--------) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (148) -------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 506 +t0132:= acoth(x^(1/2))/x +--R +--R +--R +-+ +--R acoth(\|x ) +--R (149) ----------- +--R x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 506 +r0132:= polylog(2,-1/x^(1/2))-polylog(2,1/x^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 168 + +--S 169 of 506 +a0132:= integrate(t0132,x) +--R +--R +--R x +--+ +--I ++ acoth(\|%Q ) +--I (150) | ------------ d%Q +--I ++ %Q +--R Type: Union(Expression(Integer),...) +--E 169 + +--S 170 of 506 +--m0132:= a0132-r0132 +--E 170 + +--S 171 of 506 +--d0132:= D(m0132,x) +--E 171 + +--S 172 of 506 +t0133:= acoth(x^(1/2))/x^2 +--R +--R +--R +-+ +--R acoth(\|x ) +--R (151) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 172 + +--S 173 of 506 +r0133:= -1/x^(1/2)-acoth(x^(1/2))/x+atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +-+ +-+ +--R x\|x atanh(\|x ) - \|x acoth(\|x ) - x +--R (152) -------------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 173 + +--S 174 of 506 +a0133:= integrate(t0133,x) +--R +--R +--R +-+ +--R +-+ \|x + 1 +--R (x - 1)\|x log(--------) - 2x +--R +-+ +--R \|x - 1 +--R (153) ----------------------------- +--R +-+ +--R 2x\|x +--R Type: Union(Expression(Integer),...) +--E 174 + +--S 175 of 506 +m0133:= a0133-r0133 +--R +--R +--R +-+ +--R \|x + 1 +-+ +-+ +--R (x - 1)log(--------) - 2x atanh(\|x ) + 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (154) ---------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 175 + +--S 176 of 506 +d0133:= D(m0133,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (155) ---------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 506 +t0134:= acoth(x^(1/2))/x^3 +--R +--R +--R +-+ +--R acoth(\|x ) +--R (156) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 506 +r0134:= -1/6/x^(3/2)-1/2/x^(1/2)-1/2*acoth(x^(1/2))/x^2+1/2*atanh(x^(1/2)) +--R +--R +--R 2 +-+ +-+ +-+ +-+ 2 +--R 3x \|x atanh(\|x ) - 3\|x acoth(\|x ) - 3x - x +--R (157) ----------------------------------------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression(Integer) +--E 178 + +--S 179 of 506 +a0134:= integrate(t0134,x) +--R +--R +--R +-+ +--R 2 +-+ \|x + 1 2 +--R (3x - 3)\|x log(--------) - 6x - 2x +--R +-+ +--R \|x - 1 +--R (158) ------------------------------------- +--R 2 +-+ +--R 12x \|x +--R Type: Union(Expression(Integer),...) +--E 179 + +--S 180 of 506 +m0134:= a0134-r0134 +--R +--R +--R +-+ +--R 2 \|x + 1 2 +-+ +-+ +--R (x - 1)log(--------) - 2x atanh(\|x ) + 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (159) ----------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 180 + +--S 181 of 506 +d0134:= D(m0134,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (160) ---------------------------- +--R 3 +--R 2x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 506 +t0135:= x^(1/2)*acoth(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (161) \|x acoth(\|x ) +--R Type: Expression(Integer) +--E 182 + +--S 183 of 506 +r0135:= 1/3*x+2/3*x^(3/2)*acoth(x^(1/2))+1/3*log(1-x) +--R +--R +--R +-+ +-+ +--R 2x\|x acoth(\|x ) + log(- x + 1) + x +--R (162) ------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 183 + +--S 184 of 506 +a0135:= integrate(t0135,x) +--R +--R +--R +-+ +--R +-+ \|x + 1 +--R x\|x log(--------) + log(x - 1) + x +--R +-+ +--R \|x - 1 +--R (163) ----------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 184 + +--S 185 of 506 +m0135:= a0135-r0135 +--R +--R +--R +-+ +--R +-+ \|x + 1 +-+ +-+ +--R x\|x log(--------) - 2x\|x acoth(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R (164) ------------------------------------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 185 + +--S 186 of 506 +d0135:= D(m0135,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R x log(--------) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (165) -------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 186 + +--S 187 of 506 +t0136:= x^(3/2)*acoth(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (166) x\|x acoth(\|x ) +--R Type: Expression(Integer) +--E 187 + +--S 188 of 506 +r0136:= 1/5*x+1/10*x^2+2/5*x^(5/2)*acoth(x^(1/2))+1/5*log(1-x) +--R +--R +--R 2 +-+ +-+ 2 +--R 4x \|x acoth(\|x ) + 2log(- x + 1) + x + 2x +--R (167) -------------------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 188 + +--S 189 of 506 +a0136:= integrate(t0136,x) +--R +--R +--R +-+ +--R 2 +-+ \|x + 1 2 +--R 2x \|x log(--------) + 2log(x - 1) + x + 2x +--R +-+ +--R \|x - 1 +--R (168) -------------------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 189 + +--S 190 of 506 +m0136:= a0136-r0136 +--R +--R +--R +-+ +--R 2 +-+ \|x + 1 2 +-+ +-+ +--R x \|x log(--------) - 2x \|x acoth(\|x ) + log(x - 1) - log(- x + 1) +--R +-+ +--R \|x - 1 +--R (169) -------------------------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 190 + +--S 191 of 506 +d0136:= D(m0136,x) +--R +--R +--R +-+ +--R 2 \|x + 1 2 +-+ +--R x log(--------) - 2x acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (170) -------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 191 + +--S 192 of 506 +t0137:= acoth(x^(1/2))/x^(3/2) +--R +--R +--R +-+ +--R acoth(\|x ) +--R (171) ----------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 506 +r0137:= -2*acoth(x^(1/2))/x^(1/2)+2*atanh(-1+2*x) +--R +--R +--R +-+ +-+ +--R - 2acoth(\|x ) + 2atanh(2x - 1)\|x +--R (172) ----------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 193 + +--S 194 of 506 +a0137:= integrate(t0137,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R - log(--------) + (log(x) - log(x - 1))\|x +--R +-+ +--R \|x - 1 +--R (173) ------------------------------------------- +--R +-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 194 + +--S 195 of 506 +m0137:= a0137-r0137 +--R +--R +--R (174) +--R +-+ +--R \|x + 1 +-+ +-+ +--R - log(--------) + 2acoth(\|x ) + (log(x) - log(x - 1) - 2atanh(2x - 1))\|x +--R +-+ +--R \|x - 1 +--R --------------------------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 195 + +--S 196 of 506 +d0137:= D(m0137,x) +--R +--R +--R +-+ +--R \|x + 1 +-+ +--R log(--------) - 2acoth(\|x ) +--R +-+ +--R \|x - 1 +--R (175) ---------------------------- +--R +-+ +--R 2x\|x +--R Type: Expression(Integer) +--E 196 + +--S 197 of 506 +t0138:= x^3*asech(a*x) +--R +--R +--R 3 +--R (176) x asech(a x) +--R Type: Expression(Integer) +--E 197 + +--S 198 of 506 +r0138:= -1/16*((1-a*x)/(1+a*x))^(1/2)*(1+a*x)^3/a^4-_ + 1/24*((1-a*x)/(1+a*x))^(3/2)*(1+a*x)^3/a^4-_ + 1/16*((1-a*x)/(1+a*x))^(5/2)*(1+a*x)^3/a^4+1/4*x^4*asech(a*x) +--R +--R +--R +---------+ +--R 3 3 2 2 |- a x + 1 4 4 +--R (- a x - a x - 2a x - 2) |--------- + 3a x asech(a x) +--R \| a x + 1 +--R (177) -------------------------------------------------------- +--R 4 +--R 12a +--R Type: Expression(Integer) +--E 198 + +--S 199 of 506 +a0138:= integrate(t0138,x) +--R +--R +--R (178) +--R +----------+ +--R +----------+ | 2 2 +--R 2 6 4 | 2 2 2 6 4 \|- a x + 1 + 1 +--R ((3a x - 12x )\|- a x + 1 - 9a x + 12x )log(-----------------) +--R a x +--R + +--R +----------+ +--R 4 | 2 2 2 6 4 +--R 3x \|- a x + 1 + a x - 3x +--R / +--R +----------+ +--R 2 2 | 2 2 2 2 +--R (12a x - 48)\|- a x + 1 - 36a x + 48 +--R Type: Union(Expression(Integer),...) +--E 199 + +--S 200 of 506 +m0138:= a0138-r0138 +--R +--R +--R (179) +--R +----------+ +--R +----------+ | 2 2 +--R 6 6 4 4 | 2 2 6 6 4 4 \|- a x + 1 + 1 +--R ((3a x - 12a x )\|- a x + 1 - 9a x + 12a x )log(-----------------) +--R a x +--R + +--R +----------+ +--R 5 5 4 4 3 3 2 2 | 2 2 5 5 4 4 +--R (a x + a x - 2a x - 2a x - 8a x - 8)\|- a x + 1 - 3a x - 3a x +--R + +--R 3 3 2 2 +--R - 2a x - 2a x + 8a x + 8 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 6 6 4 4 4 4 | 2 2 +--R ((- 3a x + 12a x )asech(a x) + 3a x )\|- a x + 1 +--R + +--R 6 6 4 4 6 6 4 4 +--R (9a x - 12a x )asech(a x) + a x - 3a x +--R / +--R +----------+ +--R 6 2 4 | 2 2 6 2 4 +--R (12a x - 48a )\|- a x + 1 - 36a x + 48a +--R Type: Expression(Integer) +--E 200 + +--S 201 of 506 +d0138:= D(m0138,x) +--R +--R +--R (180) +--R 7 10 6 9 5 8 4 7 3 6 2 5 4 +--R 4a x + 4a x - 72a x - 72a x + 192a x + 192a x - 128a x +--R + +--R 3 +--R - 128x +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 4 +--R - 24a x - 24a x + 152a x + 152a x - 256a x - 256a x + 128a x +--R + +--R 3 +--R 128x +--R * +--R +----------+ +--R +---------+ | 2 2 +--R |- a x + 1 \|- a x + 1 + 1 +--R |--------- log(-----------------) +--R \| a x + 1 a x +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 +--R - 4a x - 4a x + 72a x + 72a x - 192a x - 192a x +--R + +--R 4 3 +--R 128a x + 128x +--R * +--R asech(a x) +--R + +--R 5 8 4 7 3 6 2 5 4 3 +--R 6a x + 6a x - 32a x - 32a x + 32a x + 32x +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 +--R 24a x + 24a x - 152a x - 152a x + 256a x + 256a x +--R + +--R 4 3 +--R - 128a x - 128x +--R * +--R asech(a x) +--R + +--R 7 10 6 9 5 8 4 7 3 6 2 5 4 3 +--R a x + a x - 18a x - 18a x + 48a x + 48a x - 32a x - 32x +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 6 9 4 7 2 5 3 | 2 2 6 9 4 7 2 5 +--R (- a x + 18a x - 48a x + 32x )\|- a x + 1 + 6a x - 38a x + 64a x +--R + +--R 3 +--R - 32x +--R / +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R (4a x + 4a x - 72a x - 72a x + 192a x + 192a x - 128a x - 128) +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - 24a x - 24a x + 152a x + 152a x - 256a x - 256a x + 128a x + 128 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 506 +t0139:= asech(a*x)/x +--R +--R +--R asech(a x) +--R (181) ---------- +--R x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 506 +r0139:= -1/2*asech(a*x)^2-asech(a*x)*_ + log(1+exp(1)^(-2*asech(a*x)))+1/2*polylog(2,-exp(1)^(-2*asech(a*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 203 + +--S 204 of 506 +a0139:= integrate(t0139,x) +--R +--R +--R x +--I ++ asech(%Q a) +--I (182) | ----------- d%Q +--I ++ %Q +--R Type: Union(Expression(Integer),...) +--E 204 + +--S 205 of 506 +--m0139:= a0139-r0139 +--E 205 + +--S 206 of 506 +--d0139:= D(m0139,x) +--E 206 + +--S 207 of 506 +t0140:= asech(a*x)/x^3 +--R +--R +--R asech(a x) +--R (183) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 207 + +--S 208 of 506 +r0140:= 1/4*((-(-1+a*x)/(1+a*x))^(1/2)*a*x+(-(-1+a*x)/(1+a*x))^(1/2)-_ + 2*asech(a*x)+2*a^2*atanh((-(-1+a*x)/(1+a*x))^(1/2))*x^2)/x^2 +--R +--R +--R +---------+ +---------+ +--R 2 2 |- a x + 1 |- a x + 1 +--R 2a x atanh( |--------- ) + (a x + 1) |--------- - 2asech(a x) +--R \| a x + 1 \| a x + 1 +--R (184) -------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 208 + +--S 209 of 506 +a0140:= integrate(t0140,x) +--R +--R +--R (185) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 4 4 2 2 \|- a x + 1 + 1 +--R ((2a x - 4)\|- a x + 1 + a x - 4a x + 4)log(-----------------) +--R a x +--R + +--R +----------+ +--R 2 2 | 2 2 2 2 +--R (a x - 2)\|- a x + 1 - 2a x + 2 +--R / +--R +----------+ +--R 2 | 2 2 2 4 2 +--R 8x \|- a x + 1 + 4a x - 8x +--R Type: Union(Expression(Integer),...) +--E 209 + +--S 210 of 506 +m0140:= a0140-r0140 +--R +--R +--R (186) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 4 4 2 2 \|- a x + 1 + 1 +--R ((2a x - 4)\|- a x + 1 + a x - 4a x + 4)log(-----------------) +--R a x +--R + +--R +----------+ +---------+ +--R 2 2 | 2 2 4 4 2 2 |- a x + 1 +--R (- 4a x \|- a x + 1 - 2a x + 4a x )atanh( |--------- ) +--R \| a x + 1 +--R + +--R +----------+ +---------+ +--R | 2 2 3 3 2 2 |- a x + 1 +--R ((- 2a x - 2)\|- a x + 1 - a x - a x + 2a x + 2) |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 2 2 | 2 2 2 2 2 2 +--R (4asech(a x) + a x - 2)\|- a x + 1 + (2a x - 4)asech(a x) - 2a x + 2 +--R / +--R +----------+ +--R 2 | 2 2 2 4 2 +--R 8x \|- a x + 1 + 4a x - 8x +--R Type: Expression(Integer) +--E 210 + +--S 211 of 506 +d0140:= D(m0140,x) +--R +--R +--R (187) +--R +----------+ +--R 5 5 4 4 3 3 2 2 | 2 2 5 5 +--R (2a x + 2a x - 16a x - 16a x + 16a x + 16)\|- a x + 1 - 8a x +--R + +--R 4 4 3 3 2 2 +--R - 8a x + 24a x + 24a x - 16a x - 16 +--R * +--R +----------+ +--R +---------+ | 2 2 +--R |- a x + 1 \|- a x + 1 + 1 +--R |--------- log(-----------------) +--R \| a x + 1 a x +--R + +--R 5 5 4 4 3 3 2 2 +--R (- 2a x - 2a x + 16a x + 16a x - 16a x - 16)asech(a x) +--R + +--R 3 3 2 2 +--R - 4a x - 4a x + 8a x + 8 +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 5 5 4 4 3 3 2 2 5 5 +--R (8a x + 8a x - 24a x - 24a x + 16a x + 16)asech(a x) - a x +--R + +--R 4 4 3 3 2 2 +--R - a x + 8a x + 8a x - 8a x - 8 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 4 4 2 2 | 2 2 4 4 2 2 +--R (a x - 8a x + 8)\|- a x + 1 - 4a x + 12a x - 8 +--R / +--R +----------+ +--R 5 8 4 7 3 6 2 5 4 3 | 2 2 5 8 +--R (2a x + 2a x - 16a x - 16a x + 16a x + 16x )\|- a x + 1 - 8a x +--R + +--R 4 7 3 6 2 5 4 3 +--R - 8a x + 24a x + 24a x - 16a x - 16x +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 506 +t0141:= asech(a*x)/x^4 +--R +--R +--R asech(a x) +--R (188) ---------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 506 +r0141:= 1/12*((1-a*x)/(1+a*x))^(1/2)*(1+a*x)^3/x^3-_ + 1/18*((1-a*x)/(1+a*x))^(3/2)*(1+a*x)^3/x^3+_ + 1/12*((1-a*x)/(1+a*x))^(5/2)*(1+a*x)^3/x^3-1/3*asech(a*x)/x^3 +--R +--R +--R +---------+ +--R 3 3 2 2 |- a x + 1 +--R (2a x + 2a x + a x + 1) |--------- - 3asech(a x) +--R \| a x + 1 +--R (189) --------------------------------------------------- +--R 3 +--R 9x +--R Type: Expression(Integer) +--E 213 + +--S 214 of 506 +a0141:= integrate(t0141,x) +--R +--R +--R (190) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 2 2 \|- a x + 1 + 1 +--R ((- 3a x + 12)\|- a x + 1 + 9a x - 12)log(-----------------) +--R a x +--R + +--R +----------+ +--R 4 4 2 2 | 2 2 6 6 4 4 2 2 +--R (- 6a x + 5a x + 4)\|- a x + 1 - 2a x + 9a x - 3a x - 4 +--R / +--R +----------+ +--R 2 5 3 | 2 2 2 5 3 +--R (9a x - 36x )\|- a x + 1 - 27a x + 36x +--R Type: Union(Expression(Integer),...) +--E 214 + +--S 215 of 506 +m0141:= a0141-r0141 +--R +--R +--R (191) +--R +----------+ +--R +----------+ | 2 2 +--R 2 2 | 2 2 2 2 \|- a x + 1 + 1 +--R ((- 3a x + 12)\|- a x + 1 + 9a x - 12)log(-----------------) +--R a x +--R + +--R +----------+ +--R 5 5 4 4 3 3 2 2 | 2 2 5 5 +--R (- 2a x - 2a x + 7a x + 7a x + 4a x + 4)\|- a x + 1 + 6a x +--R + +--R 4 4 3 3 2 2 +--R 6a x - 5a x - 5a x - 4a x - 4 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 2 2 4 4 2 2 | 2 2 +--R ((3a x - 12)asech(a x) - 6a x + 5a x + 4)\|- a x + 1 +--R + +--R 2 2 6 6 4 4 2 2 +--R (- 9a x + 12)asech(a x) - 2a x + 9a x - 3a x - 4 +--R / +--R +----------+ +--R 2 5 3 | 2 2 2 5 3 +--R (9a x - 36x )\|- a x + 1 - 27a x + 36x +--R Type: Expression(Integer) +--E 215 + +--S 216 of 506 +d0141:= D(m0141,x) +--R +--R +--R (192) +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R (3a x + 3a x - 54a x - 54a x + 144a x + 144a x - 96a x - 96) +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - 18a x - 18a x + 114a x + 114a x - 192a x - 192a x + 96a x + 96 +--R * +--R +----------+ +--R +---------+ | 2 2 +--R |- a x + 1 \|- a x + 1 + 1 +--R |--------- log(-----------------) +--R \| a x + 1 a x +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - 3a x - 3a x + 54a x + 54a x - 144a x - 144a x + 96a x +--R + +--R 96 +--R * +--R asech(a x) +--R + +--R 5 5 4 4 3 3 2 2 +--R - 6a x - 6a x + 32a x + 32a x - 32a x - 32 +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R 18a x + 18a x - 114a x - 114a x + 192a x + 192a x - 96a x +--R + +--R - 96 +--R * +--R asech(a x) +--R + +--R 7 7 6 6 5 5 4 4 3 3 2 2 +--R - a x - a x + 18a x + 18a x - 48a x - 48a x + 32a x + 32 +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R + +--R +----------+ +--R 6 6 4 4 2 2 | 2 2 6 6 4 4 2 2 +--R (a x - 18a x + 48a x - 32)\|- a x + 1 - 6a x + 38a x - 64a x + 32 +--R / +--R 7 11 6 10 5 9 4 8 3 7 2 6 5 +--R 3a x + 3a x - 54a x - 54a x + 144a x + 144a x - 96a x +--R + +--R 4 +--R - 96x +--R * +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R + +--R 7 11 6 10 5 9 4 8 3 7 2 6 5 +--R - 18a x - 18a x + 114a x + 114a x - 192a x - 192a x + 96a x +--R + +--R 4 +--R 96x +--R * +--R +---------+ +--R |- a x + 1 +--R |--------- +--R \| a x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 506 +t0142:= x*asech(x^(1/2)) +--R +--R +--R +-+ +--R (193) x asech(\|x ) +--R Type: Expression(Integer) +--E 217 + +--S 218 of 506 +r0142:= -1/8*((1-x^(1/2))/(1+x^(1/2)))^(1/2)*(1+x^(1/2))^3-_ + 1/12*((1-x^(1/2))/(1+x^(1/2)))^(3/2)*(1+x^(1/2))^3-_ + 1/8*((1-x^(1/2))/(1+x^(1/2)))^(5/2)*(1+x^(1/2))^3+_ + 1/2*x^2*asech(x^(1/2)) +--R +--R +--R (194) +--R +----------+ +--R | +-+ +--R 2 +-+ 3 2 |- \|x + 1 +--R ((- 4x - 12x - 8)\|x - x - 8x - 13x - 2) |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R 3 2 +-+ 3 2 +-+ +--R ((3x + 9x )\|x + 9x + 3x )asech(\|x ) +--R / +--R +-+ +--R (6x + 18)\|x + 18x + 6 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 506 +a0142:= integrate(t0142,x) +--R +--R +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +-------+ +--R 2 \| x |- x + 1 +-+ +--R 3x log(------------------) + (- x - 2) |------- \|x +--R +-+ \| x +--R \|x +--R (195) ---------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 219 + +--S 220 of 506 +m0142:= a0142-r0142 +--R +--R +--R (196) +--R +----------+ +--R | +-+ +--R 2 +-+ 3 2 |- \|x + 1 +--R ((4x + 12x + 8)\|x + x + 8x + 13x + 2) |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R 3 2 +-+ 3 2 \| x +--R ((3x + 9x )\|x + 9x + 3x )log(------------------) +--R +-+ +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+ +--R ((- 3x - 9x )\|x - 9x - 3x )asech(\|x ) +--R + +--R +-------+ +-------+ +--R 2 |- x + 1 +-+ 3 2 |- x + 1 +--R (- 3x - 7x - 2) |------- \|x + (- x - 5x - 6x) |------- +--R \| x \| x +--R / +--R +-+ +--R (6x + 18)\|x + 18x + 6 +--R Type: Expression(Integer) +--E 220 + +--S 221 of 506 +d0142:= D(m0142,x) +--R +--R +--R (197) +--R 7 6 5 4 3 2 +-------+ +--R (4x + 220x + 1320x + 1848x + 660x + 44x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (44x + 660x + 1848x + 1320x + 220x + 4x)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (44x + 660x + 1848x + 1320x + 220x + 4x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (4x + 220x + 1320x + 1848x + 660x + 44x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R \| x +--R log(------------------) +--R +-+ +--R \|x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (- 4x - 220x - 1320x - 1848x - 660x - 44x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (- 44x - 660x - 1848x - 1320x - 220x - 4x)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (- 44x - 660x - 1848x - 1320x - 220x - 4x )\|- x + 1 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x +--R + +--R 7 6 5 4 3 2 +-------+ +--R (- 4x - 220x - 1320x - 1848x - 660x - 44x )\|- x + 1 +--R * +--R +-+ +--R asech(\|x ) +--R + +--R +-------+ +--R 7 6 5 4 3 2 |- x + 1 6 +--R (x + 55x + 330x + 462x + 165x + 11x ) |------- + 11x +--R \| x +--R + +--R 5 4 3 2 +--R 165x + 462x + 330x + 55x + x +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 7 6 5 4 3 2 |- x + 1 7 6 +--R (11x + 165x + 462x + 330x + 55x + x ) |------- + x + 55x +--R \| x +--R + +--R 5 4 3 2 +--R 330x + 462x + 165x + 11x +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R 6 5 4 3 2 +-------+ |- x + 1 +--R (- 10x - 120x - 252x - 120x - 10x )\|- x + 1 |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (- x - 45x - 210x - 210x - 45x - x)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 7 6 5 4 3 2 +-------+ |- x + 1 +--R (- x - 45x - 210x - 210x - 45x - x )\|- x + 1 |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (- 10x - 120x - 252x - 120x - 10x )\|- x + 1 +--R / +--R +-------+ +--R 6 5 4 3 2 +-------+ |- x + 1 +--R (4x + 220x + 1320x + 1848x + 660x + 44x)\|- x + 1 |------- +--R \| x +--R + +--R 5 4 3 2 +-------+ +--R (44x + 660x + 1848x + 1320x + 220x + 4)\|- x + 1 +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 6 5 4 3 2 +-------+ |- x + 1 +--R (44x + 660x + 1848x + 1320x + 220x + 4x)\|- x + 1 |------- +--R \| x +--R + +--R 6 5 4 3 2 +-------+ +--R (4x + 220x + 1320x + 1848x + 660x + 44x)\|- x + 1 +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 506 +t0143:= x^2*asech(x^(1/2)) +--R +--R +--R 2 +-+ +--R (198) x asech(\|x ) +--R Type: Expression(Integer) +--E 222 + +--S 223 of 506 +r0143:= -8/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)+1/3*x^3*asech(x^(1/2))-_ + 8/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(1/2)-_ + 4/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x-_ + 4/45*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(3/2)-_ + 1/15*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^2-_ + 1/15*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(5/2) +--R +--R +--R +----------+ +--R | +-+ +--R 2 +-+ 2 |- \|x + 1 3 +-+ +--R ((- 3x - 4x - 8)\|x - 3x - 4x - 8) |---------- + 15x asech(\|x ) +--R | +-+ +--R \| \|x + 1 +--R (199) -------------------------------------------------------------------- +--R 45 +--R Type: Expression(Integer) +--E 223 + +--S 224 of 506 +a0143:= integrate(t0143,x) +--R +--R +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +-------+ +--R 3 \| x 2 |- x + 1 +-+ +--R 15x log(------------------) + (- 3x - 4x - 8) |------- \|x +--R +-+ \| x +--R \|x +--R (200) ------------------------------------------------------------ +--R 45 +--R Type: Union(Expression(Integer),...) +--E 224 + +--S 225 of 506 +m0143:= a0143-r0143 +--R +--R +--R (201) +--R +----------+ +--R | +-+ +--R 2 +-+ 2 |- \|x + 1 +--R ((3x + 4x + 8)\|x + 3x + 4x + 8) |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R 3 \| x 3 +-+ +--R 15x log(------------------) - 15x asech(\|x ) +--R +-+ +--R \|x +--R + +--R +-------+ +--R 2 |- x + 1 +-+ +--R (- 3x - 4x - 8) |------- \|x +--R \| x +--R / +--R 45 +--R Type: Expression(Integer) +--E 225 + +--S 226 of 506 +d0143:= D(m0143,x) +--R +--R +--R (202) +--R +-------+ +--R 3 2 +-------+ |- x + 1 3 2 +-------+ +-+ +--R ((18x + 6x )\|- x + 1 |------- + (6x + 18x )\|- x + 1 )\|x +--R \| x +--R + +--R +-------+ +--R 4 3 +-------+ |- x + 1 3 2 +-------+ +--R (6x + 18x )\|- x + 1 |------- + (18x + 6x )\|- x + 1 +--R \| x +--R * +--R +-------+ +--R |- x + 1 +-+ +--R |------- \|x + 1 +--R \| x +--R log(------------------) +--R +-+ +--R \|x +--R + +--R +-------+ +--R 3 2 +-------+ |- x + 1 3 2 +-------+ +--R ((- 18x - 6x )\|- x + 1 |------- + (- 6x - 18x )\|- x + 1 ) +--R \| x +--R * +--R +-+ +--R \|x +--R + +--R +-------+ +--R 4 3 +-------+ |- x + 1 3 2 +-------+ +--R (- 6x - 18x )\|- x + 1 |------- + (- 18x - 6x )\|- x + 1 +--R \| x +--R * +--R +-+ +--R asech(\|x ) +--R + +--R +-------+ +-------+ +--R 3 2 |- x + 1 3 2 +-+ 4 3 |- x + 1 3 2 +--R ((3x + x ) |------- + x + 3x )\|x + (x + 3x ) |------- + 3x + x +--R \| x \| x +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R + +--R +-------+ +--R 3 2 +-------+ |- x + 1 2 +-------+ +-+ +--R ((- x - x )\|- x + 1 |------- - 2x \|- x + 1 )\|x +--R \| x +--R + +--R +-------+ +--R 3 +-------+ |- x + 1 3 2 +-------+ +--R - 2x \|- x + 1 |------- + (- x - x )\|- x + 1 +--R \| x +--R / +--R +-------+ +--R +-------+ |- x + 1 +-------+ +-+ +--R ((18x + 6)\|- x + 1 |------- + (6x + 18)\|- x + 1 )\|x +--R \| x +--R + +--R +-------+ +--R 2 +-------+ |- x + 1 +-------+ +--R (6x + 18x)\|- x + 1 |------- + (18x + 6)\|- x + 1 +--R \| x +--R * +--R +----------+ +--R | +-+ +--R |- \|x + 1 +--R |---------- +--R | +-+ +--R \| \|x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 506 +t0144:= asech(x^(1/2))/x +--R +--R +--R +-+ +--R asech(\|x ) +--R (203) ----------- +--R x +--R Type: Expression(Integer) +--E 227 + +--S 228 of 506 +r0144:= -asech(x^(1/2))^2-2*asech(x^(1/2))*_ + log(1+exp(1)^(-2*asech(x^(1/2))))+_ + polylog(2,-exp(1)^(-2*asech(x^(1/2)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 228 + +--S 229 of 506 +a0144:= integrate(t0144,x) +--R +--R +--R x +--+ +--I ++ asech(\|%Q ) +--I (204) | ------------ d%Q +--I ++ %Q +--R Type: Union(Expression(Integer),...) +--E 229 + +--S 230 of 506 +--m0144:= a0144-r0144 +--E 230 + +--S 231 of 506 +--d0144:= D(m0144,x) +--E 231 + +--S 232 of 506 +t0145:= asech(x^(1/2))/x^3 +--R +--R +--R +-+ +--R asech(\|x ) +--R (205) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 232 + +--S 233 of 506 +r0145:= 1/16*(2*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x+_ + 3*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^2+_ + 3*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(3/2)+_ + 2*(-(-1+x^(1/2))/(1+x^(1/2)))^(1/2)*x^(1/2)+_ + 6*atanh((-(-1+x^(1/2))/(1+x^(1/2)))^(1/2))*x^(5/2)-_ + 8*asech(x^(1/2))*x^(1/2))/x^(5/2) +--R +--R +--R (206) +--R +----------+ +----------+ +--R | +-+ | +-+ +--R 2 +-+ |- \|x + 1 +-+ 2 |- \|x + 1 +--R 6x \|x atanh( |---------- ) + ((3x + 2)\|x + 3x + 2x) |---------- +--R | +-+ | +-+ +--R \| \|x + 1 \| \|x + 1 +--R + +--R +-+ +-+ +--R - 8\|x asech(\|x ) +--R / +--R 2 +-+ +--R 16x \|x +--R Type: Expression(Integer) +--E 233 + +--S 234 of 506 +a0145:= integrate(t0145,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 234 + +--S 235 of 506 +--m0145:= a0145-r0145 +--E 235 + +--S 236 of 506 +--d0145:= D(m0145,x) +--E 236 + +--S 237 of 506 +t0146:= x^2*acsch(a*x) +--R +--R +--R 2 +--R (207) x acsch(a x) +--R Type: Expression(Integer) +--E 237 + +--S 238 of 506 +r0146:= 1/6*(1+1/a^2/x^2)^(1/2)*x^2/a+1/3*x^3*acsch(a*x)-_ + 1/6*atanh((1+1/a^2/x^2)^(1/2))/a^3 +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x + 1 2 2 |a x + 1 3 3 +--R - atanh( |-------- ) + a x |-------- + 2a x acsch(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R (208) -------------------------------------------------------- +--R 3 +--R 6a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 506 +a0146:= integrate(t0146,x) +--R +--R +--R (209) +--R +--------+ +--------+ +--R | 2 2 2 2 | 2 2 +--R (2a x\|a x + 1 - 2a x - 1)log(\|a x + 1 - a x) +--R + +--R +--------+ +--R +--------+ | 2 2 +--R 4 4 | 2 2 5 5 3 3 \|a x + 1 + 1 +--R (4a x \|a x + 1 - 4a x - 2a x )log(---------------) +--R a x +--R + +--R +--------+ +--R 3 3 | 2 2 4 4 2 2 +--R (- 2a x - a x)\|a x + 1 + 2a x + 2a x +--R / +--R +--------+ +--R 4 | 2 2 5 2 3 +--R 12a x\|a x + 1 - 12a x - 6a +--R Type: Union(Expression(Integer),...) +--E 239 + +--S 240 of 506 +m0146:= a0146-r0146 +--R +--R +--R (210) +--R +--------+ +--------+ +--R | 2 2 2 2 | 2 2 +--R (2a x\|a x + 1 - 2a x - 1)log(\|a x + 1 - a x) +--R + +--R +--------+ +--R +--------+ | 2 2 +--R 4 4 | 2 2 5 5 3 3 \|a x + 1 + 1 +--R (4a x \|a x + 1 - 4a x - 2a x )log(---------------) +--R a x +--R + +--R +--------+ +--R +--------+ | 2 2 +--R | 2 2 2 2 |a x + 1 +--R (2a x\|a x + 1 - 2a x - 1)atanh( |-------- ) +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--------+ +--R 3 3 |a x + 1 4 4 3 3 | 2 2 +--R (- 2a x |-------- - 4a x acsch(a x) - 2a x - a x)\|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 4 4 2 2 |a x + 1 5 5 3 3 4 4 2 2 +--R (2a x + a x ) |-------- + (4a x + 2a x )acsch(a x) + 2a x + 2a x +--R | 2 2 +--R \| a x +--R / +--R +--------+ +--R 4 | 2 2 5 2 3 +--R 12a x\|a x + 1 - 12a x - 6a +--R Type: Expression(Integer) +--E 240 + +--S 241 of 506 +d0146:= D(m0146,x) +--R +--R +--R (211) +--R +--------+ +--R | 2 2 +--------+ +--R 5 6 3 4 2 |a x + 1 | 2 2 +--R (24a x + 24a x + 3a x ) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 7 4 5 2 3 |a x + 1 +--R (- 24a x - 36a x - 12a x ) |-------- +--R | 2 2 +--R \| a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 + 1 +--R log(---------------) +--R a x +--R + +--R +--------+ +--R | 2 2 +--R 5 6 3 4 2 4 5 2 3 |a x + 1 +--R ((- 24a x - 24a x - 3a x )acsch(a x) - 8a x - 4a x ) |-------- +--R | 2 2 +--R \| a x +--R + +--R 4 5 2 3 +--R - 8a x - 8a x - x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 +--R + +--R +--------+ +--R | 2 2 +--R 6 7 4 5 2 3 5 6 3 4 2 |a x + 1 +--R ((24a x + 36a x + 12a x )acsch(a x) + 8a x + 8a x + a x ) |-------- +--R | 2 2 +--R \| a x +--R + +--R 5 6 3 4 2 +--R 8a x + 12a x + 4a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R 5 4 3 2 |a x + 1 | 2 2 +--R (24a x + 24a x + 3a) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 5 4 3 2 |a x + 1 +--R (- 24a x - 36a x - 12a x) |-------- +--R | 2 2 +--R \| a x +--R Type: Expression(Integer) +--E 241 + +--S 242 of 506 +t0147:= acsch(a*x)/x +--R +--R +--R acsch(a x) +--R (212) ---------- +--R x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 506 +r0147:= -1/2*acsch(a*x)^2-acsch(a*x)*log(1-exp(1)^(-2*acsch(a*x)))+_ + 1/2*polylog(2,exp(1)^(-2*acsch(a*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 243 + +--S 244 of 506 +a0147:= integrate(t0147,x) +--R +--R +--R x +--I ++ acsch(%Q a) +--I (213) | ----------- d%Q +--I ++ %Q +--R Type: Union(Expression(Integer),...) +--E 244 + +--S 245 of 506 +--m0147:= a0147-r0147 +--E 245 + +--S 246 of 506 +--d0147:= D(m0147,x) +--E 246 + +--S 247 of 506 +t0148:= acsch(a*x)/x^3 +--R +--R +--R acsch(a x) +--R (214) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 506 +r0148:= 1/4*a*(1+1/a^2/x^2)^(1/2)/x-1/2*acsch(a*x)/x^2-1/4*a^2*asinh(1/a/x) +--R +--R +--R +--------+ +--R | 2 2 +--R |a x + 1 2 2 1 +--R a x |-------- - a x asinh(---) - 2acsch(a x) +--R | 2 2 a x +--R \| a x +--R (215) --------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 248 + +--S 249 of 506 +a0148:= integrate(t0148,x) +--R +--R +--R (216) +--R +--------+ +--R +--------+ | 2 2 +--R 3 3 | 2 2 4 4 2 2 \|a x + 1 + 1 +--R ((- 2a x - 4a x)\|a x + 1 + 2a x + 5a x + 2)log(---------------) +--R a x +--R + +--R +--------+ +--R 2 2 | 2 2 3 3 +--R (- 2a x - 1)\|a x + 1 + 2a x + 2a x +--R / +--R +--------+ +--R 3 | 2 2 2 4 2 +--R 8a x \|a x + 1 - 8a x - 4x +--R Type: Union(Expression(Integer),...) +--E 249 + +--S 250 of 506 +m0148:= a0148-r0148 +--R +--R +--R (217) +--R +--------+ +--R +--------+ | 2 2 +--R 3 3 | 2 2 4 4 2 2 \|a x + 1 + 1 +--R ((- 2a x - 4a x)\|a x + 1 + 2a x + 5a x + 2)log(---------------) +--R a x +--R + +--R +--------+ +--R | 2 2 +--R 2 2 |a x + 1 3 3 1 2 2 +--R (- 2a x |-------- + 2a x asinh(---) + 4a x acsch(a x) - 2a x - 1) +--R | 2 2 a x +--R \| a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 +--R + +--R +--------+ +--R | 2 2 +--R 3 3 |a x + 1 4 4 2 2 1 +--R (2a x + a x) |-------- + (- 2a x - a x )asinh(---) +--R | 2 2 a x +--R \| a x +--R + +--R 2 2 3 3 +--R (- 4a x - 2)acsch(a x) + 2a x + 2a x +--R / +--R +--------+ +--R 3 | 2 2 2 4 2 +--R 8a x \|a x + 1 - 8a x - 4x +--R Type: Expression(Integer) +--E 250 + +--S 251 of 506 +d0148:= D(m0148,x) +--R +--R +--R (218) +--R +--------+ +--R | 2 2 +--------+ +--R 5 5 3 3 |a x + 1 | 2 2 +--R (16a x + 16a x + 2a x) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 6 4 4 2 2 |a x + 1 +--R (- 16a x - 24a x - 8a x ) |-------- +--R | 2 2 +--R \| a x +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 + 1 +--R log(---------------) +--R a x +--R + +--R +--------+ +--R | 2 2 +--R 5 5 3 3 4 4 2 2 |a x + 1 +--R ((- 16a x - 16a x - 2a x)acsch(a x) + 8a x + 4a x ) |-------- +--R | 2 2 +--R \| a x +--R + +--R 4 4 2 2 +--R 8a x + 8a x + 1 +--R * +--R +--------+ +--R | 2 2 +--R \|a x + 1 +--R + +--R +--------+ +--R | 2 2 +--R 6 6 4 4 2 2 5 5 3 3 |a x + 1 +--R ((16a x + 24a x + 8a x )acsch(a x) - 8a x - 8a x - a x) |-------- +--R | 2 2 +--R \| a x +--R + +--R 5 5 3 3 +--R - 8a x - 12a x - 4a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R 5 8 3 6 4 |a x + 1 | 2 2 +--R (16a x + 16a x + 2a x ) |-------- \|a x + 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 6 9 4 7 2 5 |a x + 1 +--R (- 16a x - 24a x - 8a x ) |-------- +--R | 2 2 +--R \| a x +--R Type: Expression(Integer) +--E 251 + +--S 252 of 506 +t0149:= acsch(x^(1/2))/x +--R +--R +--R +-+ +--R acsch(\|x ) +--R (219) ----------- +--R x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 506 +r0149:= -acsch(x^(1/2))^2-2*acsch(x^(1/2))*_ + log(1-exp(1)^(-2*acsch(x^(1/2))))+polylog(2,exp(1)^(-2*acsch(x^(1/2)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 253 + +--S 254 of 506 +a0149:= integrate(t0149,x) +--R +--R +--R x +--+ +--I ++ acsch(\|%Q ) +--I (220) | ------------ d%Q +--I ++ %Q +--R Type: Union(Expression(Integer),...) +--E 254 + +--S 255 of 506 +--m0149:= a0149-r0149 +--E 255 + +--S 256 of 506 +--d0149:= D(m0149,x) +--E 256 + +--S 257 of 506 +t0150:= acsch(x^(1/2))/x^2 +--R +--R +--R +-+ +--R acsch(\|x ) +--R (221) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 506 +r0150:= 1/2*(1/x+1)^(1/2)/x^(1/2)-1/2*acsch(x^(1/2))-acsch(x^(1/2))/x +--R +--R +--R +-----+ +--R +-+ +-+ |x + 1 +--R (- x - 2)\|x acsch(\|x ) + x |----- +--R \| x +--R (222) ------------------------------------ +--R +-+ +--R 2x\|x +--R Type: Expression(Integer) +--E 258 + +--S 259 of 506 +a0150:= integrate(t0150,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 259 + +--S 260 of 506 +--m0150:= a0150-r0150 +--E 260 + +--S 261 of 506 +--d0150:= D(m0150,x) +--E 261 + +--S 262 of 506 +t0151:= acosh(1/x) +--R +--R +--R 1 +--R (223) acosh(-) +--R x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 506 +r0151:= x*asech(x)-2*atan((-(-1+x)/(1+x))^(1/2)) +--R +--R +--R +-------+ +--R |- x + 1 +--R (224) - 2atan( |------- ) + x asech(x) +--R \| x + 1 +--R Type: Expression(Integer) +--E 263 + +--S 264 of 506 +a0151:= integrate(t0151,x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R \|- x + 1 + 1 \|- x + 1 - 1 +--R (225) x log(---------------) - 2atan(---------------) +--R x x +--R Type: Union(Expression(Integer),...) +--E 264 + +--S 265 of 506 +m0151:= a0151-r0151 +--R +--R +--R (226) +--R +--------+ +--------+ +--R | 2 +-------+ | 2 +--R \|- x + 1 + 1 |- x + 1 \|- x + 1 - 1 +--R x log(---------------) + 2atan( |------- ) - 2atan(---------------) +--R x \| x + 1 x +--R + +--R - x asech(x) +--R Type: Expression(Integer) +--E 265 + +--S 266 of 506 +d0151:= D(m0151,x) +--R +--R +--R (227) +--R +--------+ +--R +--------+ +-------+ | 2 +--R | 2 |- x + 1 \|- x + 1 + 1 +--R (x + 1)\|- x + 1 |------- log(---------------) +--R \| x + 1 x +--R + +--R +--------+ +-------+ +--------+ +--R | 2 |- x + 1 | 2 +--R ((- x - 1)asech(x)\|- x + 1 + x + 1) |------- - \|- x + 1 +--R \| x + 1 +--R / +--R +--------+ +-------+ +--R | 2 |- x + 1 +--R (x + 1)\|- x + 1 |------- +--R \| x + 1 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 506 +t0152:= atanh(1/x) +--R +--R +--R 1 +--R (228) atanh(-) +--R x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 506 +r0152:= x*acoth(x)+1/2*log(1-x^2) +--R +--R +--R 2 +--R log(- x + 1) + 2x acoth(x) +--R (229) --------------------------- +--R 2 +--R Type: Expression(Integer) +--E 268 + +--S 269 of 506 +a0152:= integrate(t0152,x) +--R +--R +--R 2 x + 1 +--R log(x - 1) + x log(-----) +--R x - 1 +--R (230) -------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 269 + +--S 270 of 506 +m0152:= a0152-r0152 +--R +--R +--R 2 x + 1 2 +--R log(x - 1) + x log(-----) - log(- x + 1) - 2x acoth(x) +--R x - 1 +--R (231) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 270 + +--S 271 of 506 +d0152:= D(m0152,x) +--R +--R +--R x + 1 +--R log(-----) - 2acoth(x) +--R x - 1 +--R (232) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 506 +t0153:= acoth(1/x) +--R +--R +--R 1 +--R (233) acoth(-) +--R x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 506 +r0153:= x*atanh(x)+1/2*log(1-x^2) +--R +--R +--R 2 +--R log(- x + 1) + 2x atanh(x) +--R (234) --------------------------- +--R 2 +--R Type: Expression(Integer) +--E 273 + +--S 274 of 506 +a0153:= integrate(t0153,x) +--R +--R +--R 2 - x - 1 +--R log(x - 1) + x log(-------) +--R x - 1 +--R (235) ---------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 274 + +--S 275 of 506 +m0153:= a0153-r0153 +--R +--R +--R 2 - x - 1 2 +--R log(x - 1) + x log(-------) - log(- x + 1) - 2x atanh(x) +--R x - 1 +--R (236) ---------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 506 +d0153:= D(m0153,x) +--R +--R +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (237) ------------------------ +--R 2 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 506 +t0154:= atanh(a+b*x)/x +--R +--R +--R atanh(b x + a) +--R (238) -------------- +--R x +--R Type: Expression(Integer) +--E 277 + +--S 278 of 506 +r0154:= -1/2*log(b*x/(1-a))*log(1-a-b*x)+1/2*log(-b*x/(1+a))*log(a+1+b*x)-_ + 1/2*polylog(2,1-b*x/(1-a))+1/2*polylog(2,1+b*x/(1+a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 278 + +--S 279 of 506 +a0154:= integrate(t0154,x) +--R +--R +--R x +--I ++ atanh(%Q b + a) +--I (239) | --------------- d%Q +--I ++ %Q +--R Type: Union(Expression(Integer),...) +--E 279 + +--S 280 of 506 +--m0154:= a0154-r0154 +--E 280 + +--S 281 of 506 +--d0154:= D(m0154,x) +--E 281 + +--S 282 of 506 +t0155:= acoth(a+b*x)/x +--R +--R +--R acoth(b x + a) +--R (240) -------------- +--R x +--R Type: Expression(Integer) +--E 282 + +--S 283 of 506 +r0155:= 1/2*log(x)*log((a+b*x-1)/(-1+a))-1/2*log(x)*log((a+1+b*x)/(1+a))-_ + 1/2*log(x)*log((a+b*x-1)/(a+b*x))+_ + 1/2*log(x)*log((a+1+b*x)/(a+b*x))+_ + 1/2*polylog(2,-b*x/(-1+a))-1/2*polylog(2,-b*x/(1+a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 283 + +--S 284 of 506 +a0155:= integrate(t0155,x) +--R +--R +--R x +--I ++ acoth(%Q b + a) +--I (241) | --------------- d%Q +--I ++ %Q +--R Type: Union(Expression(Integer),...) +--E 284 + +--S 285 of 506 +--m0155:= a0155-r0155 +--E 285 + +--S 286 of 506 +--d0155:= D(m0155,x) +--E 286 + +--S 287 of 506 +t0156:= asinh(a+b*x)/(a*d/b+d*x) +--R +--R +--R b asinh(b x + a) +--R (242) ---------------- +--R b d x + a d +--R Type: Expression(Integer) +--E 287 + +--S 288 of 506 +r0156:= 1/2*asinh(a+b*x)^2/d+asinh(a+b*x)*log(1-exp(1)^(-2*asinh(a+b*x)))/d-_ + 1/2*polylog(2,exp(1)^(-2*asinh(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 288 + +--S 289 of 506 +a0156:= integrate(t0156,x) +--R +--R +--R x +--I ++ b asinh(%Q b + a) +--I (243) | ----------------- d%Q +--I ++ (%Q b + a)d +--R Type: Union(Expression(Integer),...) +--E 289 + +--S 290 of 506 +--m0156:= a0156-r0156 +--E 290 + +--S 291 of 506 +--d0156:= D(m0156,x) +--E 291 + +--S 292 of 506 +t0157:= acosh(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acosh(b x + a) +--R (244) ---------------- +--R b d x + a d +--R Type: Expression(Integer) +--E 292 + +--S 293 of 506 +r0157:= 1/2*acosh(a+b*x)^2/d+acosh(a+b*x)*log(1+exp(1)^(-2*acosh(a+b*x)))/d-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 293 + +--S 294 of 506 +a0157:= integrate(t0157,x) +--R +--R +--R x +--I ++ b acosh(%Q b + a) +--I (245) | ----------------- d%Q +--I ++ (%Q b + a)d +--R Type: Union(Expression(Integer),...) +--E 294 + +--S 295 of 506 +--m0157:= a0157-r0157 +--E 295 + +--S 296 of 506 +--d0157:= D(m0157,x) +--E 296 + +--S 297 of 506 +t0158:= atanh(a+b*x)/(a*d/b+d*x) +--R +--R +--R b atanh(b x + a) +--R (246) ---------------- +--R b d x + a d +--R Type: Expression(Integer) +--E 297 + +--S 298 of 506 +r0158:= -1/2*(polylog(2,-a-b*x)-polylog(2,a+b*x))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 298 + +--S 299 of 506 +a0158:= integrate(t0158,x) +--R +--R +--R x +--I ++ b atanh(%Q b + a) +--I (247) | ----------------- d%Q +--I ++ (%Q b + a)d +--R Type: Union(Expression(Integer),...) +--E 299 + +--S 300 of 506 +--m0158:= a0158-r0158 +--E 300 + +--S 301 of 506 +--d0158:= D(m0158,x) +--E 301 + +--S 302 of 506 +t0159:= acoth(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acoth(b x + a) +--R (248) ---------------- +--R b d x + a d +--R Type: Expression(Integer) +--E 302 + +--S 303 of 506 +r0159:= 1/2*(polylog(2,-1/(a+b*x))-polylog(2,1/(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 303 + +--S 304 of 506 +a0159:= integrate(t0159,x) +--R +--R +--R x +--I ++ b acoth(%Q b + a) +--I (249) | ----------------- d%Q +--I ++ (%Q b + a)d +--R Type: Union(Expression(Integer),...) +--E 304 + +--S 305 of 506 +--m0159:= a0159-r0159 +--E 305 + +--S 306 of 506 +--d0159:= D(m0159,x) +--E 306 + +--S 307 of 506 +t0160:= asech(a+b*x)/(a*d/b+d*x) +--R +--R +--R b asech(b x + a) +--R (250) ---------------- +--R b d x + a d +--R Type: Expression(Integer) +--E 307 + +--S 308 of 506 +r0160:= -1/2*asech(a+b*x)^2/d-asech(a+b*x)*_ + log(1+exp(1)^(-2*asech(a+b*x)))/d+_ + 1/2*polylog(2,-exp(1)^(-2*asech(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 308 + +--S 309 of 506 +a0160:= integrate(t0160,x) +--R +--R +--R x +--I ++ b asech(%Q b + a) +--I (251) | ----------------- d%Q +--I ++ (%Q b + a)d +--R Type: Union(Expression(Integer),...) +--E 309 + +--S 310 of 506 +--m0160:= a0160-r0160 +--E 310 + +--S 311 of 506 +--d0160:= D(m0160,x) +--E 311 + +--S 312 of 506 +t0161:= acsch(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acsch(b x + a) +--R (252) ---------------- +--R b d x + a d +--R Type: Expression(Integer) +--E 312 + +--S 313 of 506 +r0161:= -1/2*acsch(a+b*x)^2/d-acsch(a+b*x)*_ + log(1-exp(1)^(-2*acsch(a+b*x)))/d+_ + 1/2*polylog(2,exp(1)^(-2*acsch(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 313 + +--S 314 of 506 +a0161:= integrate(t0161,x) +--R +--R +--R x +--I ++ b acsch(%Q b + a) +--I (253) | ----------------- d%Q +--I ++ (%Q b + a)d +--R Type: Union(Expression(Integer),...) +--E 314 + +--S 315 of 506 +--m0161:= a0161-r0161 +--E 315 + +--S 316 of 506 +--d0161:= D(m0161,x) +--E 316 + +--S 317 of 506 +t0162:= x/(1+x^2)^(1/2)/asinh(x) +--R +--R +--R x +--R (254) ----------------- +--R +------+ +--R | 2 +--R asinh(x)\|x + 1 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 506 +r0162:= Shi(asinh(x)) +--R +--R There are no library operations named Shi +--R Use HyperDoc Browse or issue +--R )what op Shi +--R to learn if there is any operation containing " Shi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Shi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 318 + +--S 319 of 506 +a0162:= integrate(t0162,x) +--R +--R +--R x +--I ++ %Q +--I (255) | ------------------- d%Q +--R ++ +-------+ +--R | 2 +--I asinh(%Q)\|%Q + 1 +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 506 +--m0162:= a0162-r0162 +--E 320 + +--S 321 of 506 +--d0162:= D(m0162,x) +--E 321 + +--S 322 of 506 +t0163:= x/(-1+x)^(1/2)/(1+x)^(1/2)/acosh(x) +--R +--R +--R x +--R (256) ------------------------ +--R +-----+ +-----+ +--R acosh(x)\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 506 +r0163:= Chi(acosh(x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 323 + +--S 324 of 506 +a0163:= integrate(t0163,x) +--R +--R +--R x +--I ++ %Q +--I (257) | --------------------------- d%Q +--R ++ +------+ +------+ +--I acosh(%Q)\|%Q - 1 \|%Q + 1 +--R Type: Union(Expression(Integer),...) +--E 324 + +--S 325 of 506 +--m0163:= a0163-r0163 +--E 325 + +--S 326 of 506 +--d0163:= D(m0163,x) +--E 326 + +--S 327 of 506 +t0164:= asinh(a*x^n)/x +--R +--R +--R n +--R asinh(a x ) +--R (258) ----------- +--R x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 506 +r0164:= 1/2*asinh(a*x^n)^2/n+asinh(a*x^n)*_ + log(1-exp(1)^(-2*asinh(a*x^n)))/n-_ + 1/2*polylog(2,exp(1)^(-2*asinh(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 328 + +--S 329 of 506 +a0164:= integrate(t0164,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 329 + +--S 330 of 506 +--m0164:= a0164-r0164 +--E 330 + +--S 331 of 506 +--d0164:= D(m0164,x) +--E 331 + +--S 332 of 506 +t0165:= acosh(a*x^n)/x +--R +--R +--R n +--R acosh(a x ) +--R (259) ----------- +--R x +--R Type: Expression(Integer) +--E 332 + +--S 333 of 506 +r0165:= 1/2*acosh(a*x^n)^2/n+acosh(a*x^n)*_ + log(1+exp(1)^(-2*acosh(a*x^n)))/n-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 333 + +--S 334 of 506 +a0165:= integrate(t0165,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 334 + +--S 335 of 506 +--m0165:= a0165-r0165 +--E 335 + +--S 336 of 506 +--d0165:= D(m0165,x) +--E 336 + +--S 337 of 506 +t0166:= atanh(a*x^n)/x +--R +--R +--R n +--R atanh(a x ) +--R (260) ----------- +--R x +--R Type: Expression(Integer) +--E 337 + +--S 338 of 506 +r0166:= -1/2/n*(polylog(2,-a*x^n)-polylog(2,a*x^n)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 338 + +--S 339 of 506 +a0166:= integrate(t0166,x) +--R +--R +--R x n +--I ++ atanh(a %Q ) +--I (261) | ------------ d%Q +--I ++ %Q +--R Type: Union(Expression(Integer),...) +--E 339 + +--S 340 of 506 +--m0166:= a0166-r0166 +--E 340 + +--S 341 of 506 +--d0166:= D(m0166,x) +--E 341 + +--S 342 of 506 +t0167:= acoth(a*x^n)/x +--R +--R +--R n +--R acoth(a x ) +--R (262) ----------- +--R x +--R Type: Expression(Integer) +--E 342 + +--S 343 of 506 +r0167:= 1/2/n*(polylog(2,-1/a*x^(-n))-polylog(2,1/a*x^(-n))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 343 + +--S 344 of 506 +a0167:= integrate(t0167,x) +--R +--R +--R x n +--I ++ acoth(a %Q ) +--I (263) | ------------ d%Q +--I ++ %Q +--R Type: Union(Expression(Integer),...) +--E 344 + +--S 345 of 506 +--m0167:= a0167-r0167 +--E 345 + +--S 346 of 506 +--d0167:= D(m0167,x) +--E 346 + +--S 347 of 506 +t0168:= asech(a*x^n)/x +--R +--R +--R n +--R asech(a x ) +--R (264) ----------- +--R x +--R Type: Expression(Integer) +--E 347 + +--S 348 of 506 +r0168:= -1/2*asech(a*x^n)^2/n-asech(a*x^n)*_ + log(1+exp(1)^(-2*asech(a*x^n)))/n+_ + 1/2*polylog(2,-exp(1)^(-2*asech(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 348 + +--S 349 of 506 +a0168:= integrate(t0168,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 349 + +--S 350 of 506 +--m0168:= a0168-r0168 +--E 350 + +--S 351 of 506 +--d0168:= D(m0168,x) +--E 351 + +--S 352 of 506 +t0169:= acsch(a*x^n)/x +--R +--R +--R n +--R acsch(a x ) +--R (265) ----------- +--R x +--R Type: Expression(Integer) +--E 352 + +--S 353 of 506 +r0169:= -1/2*acsch(a*x^n)^2/n-acsch(a*x^n)*_ + log(1-exp(1)^(-2*acsch(a*x^n)))/n+_ + 1/2*polylog(2,exp(1)^(-2*acsch(a*x^n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 353 + +--S 354 of 506 +a0169:= integrate(t0169,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 354 + +--S 355 of 506 +--m0169:= a0169-r0169 +--E 355 + +--S 356 of 506 +--d0169:= D(m0169,x) +--E 356 + +--S 357 of 506 +t0170:= x^3*acsch(a+b*x^4) +--R +--R +--R 3 4 +--R (266) x acsch(b x + a) +--R Type: Expression(Integer) +--E 357 + +--S 358 of 506 +r0170:= 1/4*(a+b*x^4)*acsch(a+b*x^4)/b+1/4*atanh((1+1/(a+b*x^4)^2)^(1/2))/b +--R +--R +--R +-----------------------+ +--R | 2 8 4 2 +--R |b x + 2a b x + a + 1 4 4 +--R atanh( |----------------------- ) + (b x + a)acsch(b x + a) +--R | 2 8 4 2 +--R \| b x + 2a b x + a +--R (267) ------------------------------------------------------------- +--R 4b +--R Type: Expression(Integer) +--E 358 + +--S 359 of 506 +a0170:= integrate(t0170,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 359 + +--S 360 of 506 +--m0170:= a0170-r0170 +--E 360 + +--S 361 of 506 +--d0170:= D(m0170,x) +--E 361 + +--S 362 of 506 +t0171:= x^(-1+n)*asinh(a+b*x^n) +--R +--R +--R n - 1 n +--R (268) x asinh(b x + a) +--R Type: Expression(Integer) +--E 362 + +--S 363 of 506 +r0171:= -(1+(a+b*x^n)^2)^(1/2)/b/n+(a+b*x^n)*asinh(a+b*x^n)/b/n +--R +--R +--R +--------------------------+ +--R | 2 n 2 n 2 n n +--R - \|b (x ) + 2a b x + a + 1 + (b x + a)asinh(b x + a) +--R (269) ----------------------------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 363 + +--S 364 of 506 +a0171:= integrate(t0171,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 364 + +--S 365 of 506 +--m0171:= a0171-r0171 +--E 365 + +--S 366 of 506 +--d0171:= D(m0171,x) +--E 366 + +--S 367 of 506 +t0172:= x^(-1+n)*acosh(a+b*x^n) +--R +--R +--R n - 1 n +--R (270) x acosh(b x + a) +--R Type: Expression(Integer) +--E 367 + +--S 368 of 506 +r0172:= -(-1+a+b*x^n)^(1/2)*(1+a+b*x^n)^(1/2)/b/n+(a+b*x^n)*acosh(a+b*x^n)/b/n +--R +--R +--R +------------+ +------------+ +--R | n | n n n +--R - \|b x + a - 1 \|b x + a + 1 + (b x + a)acosh(b x + a) +--R (271) ------------------------------------------------------------ +--R b n +--R Type: Expression(Integer) +--E 368 + +--S 369 of 506 +a0172:= integrate(t0172,x) +--R +--R +--R >> Error detected within library code: +--R Sorry - cannot handle that integrand yet +--R +--R Continuing to read the file... +--R +--E 369 + +--S 370 of 506 +--m0172:= a0172-r0172 +--E 370 + +--S 371 of 506 +--d0172:= D(m0172,x) +--E 371 + +--S 372 of 506 +t0173:= x^(-1+n)*atanh(a+b*x^n) +--R +--R +--R n - 1 n +--R (272) x atanh(b x + a) +--R Type: Expression(Integer) +--E 372 + +--S 373 of 506 +r0173:= (a+b*x^n)*atanh(a+b*x^n)/b/n+1/2*log(1-(a+b*x^n)^2)/b/n +--R +--R +--R 2 n 2 n 2 n n +--R log(- b (x ) - 2a b x - a + 1) + (2b x + 2a)atanh(b x + a) +--R (273) --------------------------------------------------------------- +--R 2b n +--R Type: Expression(Integer) +--E 373 + +--S 374 of 506 +a0173:= integrate(t0173,x) +--R +--R +--R (274) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R - b sinh(n log(x)) - b cosh(n log(x)) - a - 1 +--R log(---------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R / +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 374 + +--S 375 of 506 +m0173:= a0173-r0173 +--R +--R +--R (275) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R - b sinh(n log(x)) - b cosh(n log(x)) - a - 1 +--R log(---------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R 2 n 2 n 2 n n +--R - log(- b (x ) - 2a b x - a + 1) + (- 2b x - 2a)atanh(b x + a) +--R / +--R 2b n +--R Type: Expression(Integer) +--E 375 + +--S 376 of 506 +d0173:= D(m0173,x) +--R +--R +--R (276) +--R (sinh(n log(x)) + cosh(n log(x))) +--R * +--R - b sinh(n log(x)) - b cosh(n log(x)) - a - 1 +--R log(---------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R n - 1 n +--R - 2x x atanh(b x + a) +--R / +--R 2x +--R Type: Expression(Integer) +--E 376 + +--S 377 of 506 +t0174:= x^(-1+n)*acoth(a+b*x^n) +--R +--R +--R n - 1 n +--R (277) x acoth(b x + a) +--R Type: Expression(Integer) +--E 377 + +--S 378 of 506 +r0174:= (a+b*x^n)*acoth(a+b*x^n)/b/n+1/2*log(1-(a+b*x^n)^2)/b/n +--R +--R +--R 2 n 2 n 2 n n +--R log(- b (x ) - 2a b x - a + 1) + (2b x + 2a)acoth(b x + a) +--R (278) --------------------------------------------------------------- +--R 2b n +--R Type: Expression(Integer) +--E 378 + +--S 379 of 506 +a0174:= integrate(t0174,x) +--R +--R +--R (279) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R b sinh(n log(x)) + b cosh(n log(x)) + a + 1 +--R log(-------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R / +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 379 + +--S 380 of 506 +m0174:= a0174-r0174 +--R +--R +--R (280) +--R (a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a + 1) +--R + +--R (- a + 1)log(b sinh(n log(x)) + b cosh(n log(x)) + a - 1) +--R + +--R (b sinh(n log(x)) + b cosh(n log(x))) +--R * +--R b sinh(n log(x)) + b cosh(n log(x)) + a + 1 +--R log(-------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R 2 n 2 n 2 n n +--R - log(- b (x ) - 2a b x - a + 1) + (- 2b x - 2a)acoth(b x + a) +--R / +--R 2b n +--R Type: Expression(Integer) +--E 380 + +--S 381 of 506 +d0174:= D(m0174,x) +--R +--R +--R (281) +--R (sinh(n log(x)) + cosh(n log(x))) +--R * +--R b sinh(n log(x)) + b cosh(n log(x)) + a + 1 +--R log(-------------------------------------------) +--R b sinh(n log(x)) + b cosh(n log(x)) + a - 1 +--R + +--R n - 1 n +--R - 2x x acoth(b x + a) +--R / +--R 2x +--R Type: Expression(Integer) +--E 381 + +--S 382 of 506 +t0175:= x^(-1+n)*asech(a+b*x^n) +--R +--R +--R n - 1 n +--R (282) x asech(b x + a) +--R Type: Expression(Integer) +--E 382 + +--S 383 of 506 +r0175:= (a+b*x^n)*asech(a+b*x^n)/b/n-_ + 2*atan(((1-a-b*x^n)/(1+a+b*x^n))^(1/2))/b/n +--R +--R +--R +--------------+ +--R | n +--R |- b x - a + 1 n n +--R - 2atan( |-------------- ) + (b x + a)asech(b x + a) +--R | n +--R \| b x + a + 1 +--R (283) ------------------------------------------------------ +--R b n +--R Type: Expression(Integer) +--E 383 + +--S 384 of 506 +a0175:= integrate(t0175,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 384 + +--S 385 of 506 +--m0175:= a0175-r0175 +--E 385 + +--S 386 of 506 +--d0175:= D(m0175,x) +--E 386 + +--S 387 of 506 +t0176:= x^(-1+n)*acsch(a+b*x^n) +--R +--R +--R n - 1 n +--R (284) x acsch(b x + a) +--R Type: Expression(Integer) +--E 387 + +--S 388 of 506 +r0176:= (a+b*x^n)*acsch(a+b*x^n)/b/n+atanh((1+1/(a+b*x^n)^2)^(1/2))/b/n +--R +--R +--R +--------------------------+ +--R | 2 n 2 n 2 +--R |b (x ) + 2a b x + a + 1 n n +--R atanh( |-------------------------- ) + (b x + a)acsch(b x + a) +--R | 2 n 2 n 2 +--R \| b (x ) + 2a b x + a +--R (285) ---------------------------------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 388 + +--S 389 of 506 +a0176:= integrate(t0176,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 389 + +--S 390 of 506 +--m0176:= a0176-r0176 +--E 390 + +--S 391 of 506 +--d0176:= D(m0176,x) +--E 391 + +--S 392 of 506 +t0177:= asinh(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (286) asinh(c %e ) +--R Type: Expression(Integer) +--E 392 + +--S 393 of 506 +r0177:= 1/2*asinh(c*exp(1)^(a+b*x))^2/b+asinh(c*exp(1)^(a+b*x))*_ + log(1-exp(1)^(-2*asinh(c*exp(1)^(a+b*x))))/b-_ + 1/2*polylog(2,exp(1)^(-2*asinh(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 393 + +--S 394 of 506 +a0177:= integrate(t0177,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 394 + +--S 395 of 506 +--m0177:= a0177-r0177 +--E 395 + +--S 396 of 506 +--d0177:= D(m0177,x) +--E 396 + +--S 397 of 506 +t0178:= acosh(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (287) acosh(c %e ) +--R Type: Expression(Integer) +--E 397 + +--S 398 of 506 +r0178:= 1/2*acosh(c*exp(1)^(a+b*x))^2/b+acosh(c*exp(1)^(a+b*x))*_ + log(1+exp(1)^(-2*acosh(c*exp(1)^(a+b*x))))/b-_ + 1/2*polylog(2,-exp(1)^(-2*acosh(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 398 + +--S 399 of 506 +a0178:= integrate(t0178,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 399 + +--S 400 of 506 +--m0178:= a0178-r0178 +--E 400 + +--S 401 of 506 +--d0178:= D(m0178,x) +--E 401 + +--S 402 of 506 +t0179:= asech(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (288) asech(c %e ) +--R Type: Expression(Integer) +--E 402 + +--S 403 of 506 +r0179:= -1/2*asech(c*exp(1)^(a+b*x))^2/b-asech(c*exp(1)^(a+b*x))*_ + log(1+exp(1)^(-2*asech(c*exp(1)^(a+b*x))))/b+_ + 1/2*polylog(2,-exp(1)^(-2*asech(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 403 + +--S 404 of 506 +a0179:= integrate(t0179,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 404 + +--S 405 of 506 +--m0179:= a0179-r0179 +--E 405 + +--S 406 of 506 +--d0179:= D(m0179,x) +--E 406 + +--S 407 of 506 +t0180:= acsch(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (289) acsch(c %e ) +--R Type: Expression(Integer) +--E 407 + +--S 408 of 506 +r0180:= -1/2*acsch(c*exp(1)^(a+b*x))^2/b-acsch(c*exp(1)^(a+b*x))*_ + log(1-exp(1)^(-2*acsch(c*exp(1)^(a+b*x))))/b+_ + 1/2*polylog(2,exp(1)^(-2*acsch(c*exp(1)^(a+b*x))))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 408 + +--S 409 of 506 +a0180:= integrate(t0180,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 409 + +--S 410 of 506 +--m0180:= a0180-r0180 +--E 410 + +--S 411 of 506 +--d0180:= D(m0180,x) +--E 411 + +--S 412 of 506 +t0181:= atanh(exp(x)) +--R +--R +--R x +--R (290) atanh(%e ) +--R Type: Expression(Integer) +--E 412 + +--S 413 of 506 +r0181:= -1/2*polylog(2,-exp(x))+1/2*polylog(2,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 413 + +--S 414 of 506 +a0181:= integrate(t0181,x) +--R +--R +--R x +--I ++ %Q +--I (291) | atanh(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 414 + +--S 415 of 506 +--m0181:= a0181-r0181 +--E 415 + +--S 416 of 506 +--d0181:= D(m0181,x) +--E 416 + +--S 417 of 506 +t0182:= x*atanh(exp(x)) +--R +--R +--R x +--R (292) x atanh(%e ) +--R Type: Expression(Integer) +--E 417 + +--S 418 of 506 +r0182:= -1/2*x*polylog(2,-exp(x))+1/2*x*polylog(2,exp(x))+_ + 1/2*polylog(3,-exp(x))-1/2*polylog(3,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 418 + +--S 419 of 506 +a0182:= integrate(t0182,x) +--R +--R +--R x +--I ++ %Q +--I (293) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 419 + +--S 420 of 506 +--m0182:= a0182-r0182 +--E 420 + +--S 421 of 506 +--d0182:= D(m0182,x) +--E 421 + +--S 422 of 506 +t0183:= x^2*atanh(exp(x)) +--R +--R +--R 2 x +--R (294) x atanh(%e ) +--R Type: Expression(Integer) +--E 422 + +--S 423 of 506 +r0183:= -1/2*x^2*polylog(2,-exp(x))+1/2*x^2*polylog(2,exp(x))+_ + x*polylog(3,-exp(x))-x*polylog(3,exp(x))-_ + polylog(4,-exp(x))+polylog(4,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 423 + +--S 424 of 506 +a0183:= integrate(t0183,x) +--R +--R +--R x +--I ++ 2 %Q +--I (295) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 424 + +--S 425 of 506 +--m0183:= a0183-r0183 +--E 425 + +--S 426 of 506 +--d0183:= D(m0183,x) +--E 426 + +--S 427 of 506 +t0184:= atanh(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (296) atanh(%e ) +--R Type: Expression(Integer) +--E 427 + +--S 428 of 506 +r0184:= -1/2*(polylog(2,-exp(a+b*x))-polylog(2,exp(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 428 + +--S 429 of 506 +a0184:= integrate(t0184,x) +--R +--R +--R x +--I ++ %Q b + a +--I (297) | atanh(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 429 + +--S 430 of 506 +--m0184:= a0184-r0184 +--E 430 + +--S 431 of 506 +--d0184:= D(m0184,x) +--E 431 + +--S 432 of 506 +t0185:= x*atanh(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (298) x atanh(%e ) +--R Type: Expression(Integer) +--E 432 + +--S 433 of 506 +r0185:= 1/2*(-x*polylog(2,-exp(a+b*x))*b+x*polylog(2,exp(a+b*x))*b+_ + polylog(3,-exp(a+b*x))-polylog(3,exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 433 + +--S 434 of 506 +a0185:= integrate(t0185,x) +--R +--R +--R x +--I ++ %Q b + a +--I (299) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 434 + +--S 435 of 506 +--m0185:= a0185-r0185 +--E 435 + +--S 436 of 506 +--d0185:= D(m0185,x) +--E 436 + +--S 437 of 506 +t0186:= x^2*atanh(exp(1)^(a+b*x)) +--R +--R +--R 2 b x + a +--R (300) x atanh(%e ) +--R Type: Expression(Integer) +--E 437 + +--S 438 of 506 +r0186:= 1/2*(-x^2*polylog(2,-exp(a+b*x))*b^2+_ + x^2*polylog(2,exp(a+b*x))*b^2+2*x*polylog(3,-exp(a+b*x))*b-_ + 2*x*polylog(3,exp(a+b*x))*b-2*polylog(4,-exp(a+b*x))+_ + 2*polylog(4,exp(a+b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 438 + +--S 439 of 506 +a0186:= integrate(t0186,x) +--R +--R +--R x +--I ++ 2 %Q b + a +--I (301) | %Q atanh(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 439 + +--S 440 of 506 +--m0186:= a0186-r0186 +--E 440 + +--S 441 of 506 +--d0186:= D(m0186,x) +--E 441 + +--S 442 of 506 +t0187:= atanh(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (302) atanh(b f + a) +--R Type: Expression(Integer) +--E 442 + +--S 443 of 506 +r0187:= 1/2/d/log(f)*(2*x*atanh(a+b*f^(c+d*x))*d*log(f)+_ + x*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d*log(f)-_ + x*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d*log(f)+_ + polylog(2,-b*f^(c+d*x)/(-1+a))-polylog(2,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 443 + +--S 444 of 506 +a0187:= integrate(t0187,x) +--R +--R +--R x +--I ++ %Q d + c +--I (303) | atanh(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 444 + +--S 445 of 506 +--m0187:= a0187-r0187 +--E 445 + +--S 446 of 506 +--d0187:= D(m0187,x) +--E 446 + +--S 447 of 506 +t0188:= x*atanh(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (304) x atanh(b f + a) +--R Type: Expression(Integer) +--E 447 + +--S 448 of 506 +r0188:= 1/4/d^2/log(f)^2*(2*x^2*atanh(a+b*f^(c+d*x))*d^2*log(f)^2+_ + x^2*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^2*log(f)^2-_ + x^2*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^2*log(f)^2+_ + 2*x*polylog(2,-b*f^(c+d*x)/(-1+a))*d*log(f)-_ + 2*x*polylog(2,-b*f^(c+d*x)/(1+a))*d*log(f)-_ + 2*polylog(3,-b*f^(c+d*x)/(-1+a))+2*polylog(3,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 448 + +--S 449 of 506 +a0188:= integrate(t0188,x) +--R +--R +--R x +--I ++ %Q d + c +--I (305) | %Q atanh(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 449 + +--S 450 of 506 +--m0188:= a0188-r0188 +--E 450 + +--S 451 of 506 +--d0188:= D(m0188,x) +--E 451 + +--S 452 of 506 +t0189:= x^2*atanh(a+b*f^(c+d*x)) +--R +--R +--R 2 d x + c +--R (306) x atanh(b f + a) +--R Type: Expression(Integer) +--E 452 + +--S 453 of 506 +r0189:= 1/6/d^3/log(f)^3*(2*x^3*atanh(a+b*f^(c+d*x))*d^3*log(f)^3+_ + x^3*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^3*log(f)^3-_ + x^3*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^3*log(f)^3+_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(-1+a))*d^2*log(f)^2-_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(1+a))*d^2*log(f)^2-_ + 6*x*polylog(3,-b*f^(c+d*x)/(-1+a))*d*log(f)+_ + 6*x*polylog(3,-b*f^(c+d*x)/(1+a))*d*log(f)+_ + 6*polylog(4,-b*f^(c+d*x)/(-1+a))-6*polylog(4,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 453 + +--S 454 of 506 +a0189:= integrate(t0189,x) +--R +--R +--R x +--I ++ 2 %Q d + c +--I (307) | %Q atanh(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 454 + +--S 455 of 506 +--m0189:= a0189-r0189 +--E 455 + +--S 456 of 506 +--d0189:= D(m0189,x) +--E 456 + +--S 457 of 506 +t0190:= acoth(exp(x)) +--R +--R +--R x +--R (308) acoth(%e ) +--R Type: Expression(Integer) +--E 457 + +--S 458 of 506 +r0190:= 1/2*polylog(2,-exp(-x))-1/2*polylog(2,exp(-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 458 + +--S 459 of 506 +a0190:= integrate(t0190,x) +--R +--R +--R x +--I ++ %Q +--I (309) | acoth(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 459 + +--S 460 of 506 +--m0190:= a0190-r0190 +--E 460 + +--S 461 of 506 +--d0190:= D(m0190,x) +--E 461 + +--S 462 of 506 +t0191:= x*acoth(exp(x)) +--R +--R +--R x +--R (310) x acoth(%e ) +--R Type: Expression(Integer) +--E 462 + +--S 463 of 506 +r0191:= 1/2*x*polylog(2,-exp(-x))-1/2*x*polylog(2,exp(-x))+_ + 1/2*polylog(3,-exp(-x))-1/2*polylog(3,exp(-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 463 + +--S 464 of 506 +a0191:= integrate(t0191,x) +--R +--R +--R x +--I ++ %Q +--I (311) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 464 + +--S 465 of 506 +--m0191:= a0191-r0191 +--E 465 + +--S 466 of 506 +--d0191:= D(m0191,x) +--E 466 + +--S 467 of 506 +t0192:= x^2*acoth(exp(x)) +--R +--R +--R 2 x +--R (312) x acoth(%e ) +--R Type: Expression(Integer) +--E 467 + +--S 468 of 506 +r0192:= 1/2*x^2*polylog(2,-exp(-x))-1/2*x^2*polylog(2,exp(-x))+_ + x*polylog(3,-exp(-x))-x*polylog(3,exp(-x))+_ + polylog(4,-exp(-x))-polylog(4,exp(-x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 468 + +--S 469 of 506 +a0192:= integrate(t0192,x) +--R +--R +--R x +--I ++ 2 %Q +--I (313) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 469 + +--S 470 of 506 +--m0192:= a0192-r0192 +--E 470 + +--S 471 of 506 +--d0192:= D(m0192,x) +--E 471 + +--S 472 of 506 +t0193:= acoth(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (314) acoth(%e ) +--R Type: Expression(Integer) +--E 472 + +--S 473 of 506 +r0193:= 1/2*(polylog(2,-exp(-a-b*x))-polylog(2,exp(-a-b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 473 + +--S 474 of 506 +a0193:= integrate(t0193,x) +--R +--R +--R x +--I ++ %Q b + a +--I (315) | acoth(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 474 + +--S 475 of 506 +--m0193:= a0193-r0193 +--E 475 + +--S 476 of 506 +--d0193:= D(m0193,x) +--E 476 + +--S 477 of 506 +t0194:= x*acoth(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (316) x acoth(%e ) +--R Type: Expression(Integer) +--E 477 + +--S 478 of 506 +r0194:= 1/2*(x*polylog(2,-exp(-a-b*x))*b-x*polylog(2,exp(-a-b*x))*b+_ + polylog(3,-exp(-a-b*x))-polylog(3,exp(-a-b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 478 + +--S 479 of 506 +a0194:= integrate(t0194,x) +--R +--R +--R x +--I ++ %Q b + a +--I (317) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 479 + +--S 480 of 506 +--m0194:= a0194-r0194 +--E 480 + +--S 481 of 506 +--d0194:= D(m0194,x) +--E 481 + +--S 482 of 506 +t0195:= x^2*acoth(exp(1)^(a+b*x)) +--R +--R +--R 2 b x + a +--R (318) x acoth(%e ) +--R Type: Expression(Integer) +--E 482 + +--S 483 of 506 +r0195:= 1/2*(x^2*polylog(2,-exp(-a-b*x))*b^2-x^2*polylog(2,exp(-a-b*x))*b^2+_ + 2*x*polylog(3,-exp(-a-b*x))*b-2*x*polylog(3,exp(-a-b*x))*b+_ + 2*polylog(4,-exp(-a-b*x))-2*polylog(4,exp(-a-b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 483 + +--S 484 of 506 +a0195:= integrate(t0195,x) +--R +--R +--R x +--I ++ 2 %Q b + a +--I (319) | %Q acoth(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 484 + +--S 485 of 506 +--m0195:= a0195-r0195 +--E 485 + +--S 486 of 506 +--d0195:= D(m0195,x) +--E 486 + +--S 487 of 506 +t0196:= acoth(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (320) acoth(b f + a) +--R Type: Expression(Integer) +--E 487 + +--S 488 of 506 +r0196:= 1/2/d/log(f)*(2*x*acoth(a+b*f^(c+d*x))*d*log(f)+_ + x*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d*log(f)-_ + x*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d*log(f)+_ + polylog(2,-b*f^(c+d*x)/(-1+a))-polylog(2,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 488 + +--S 489 of 506 +a0196:= integrate(t0196,x) +--R +--R +--R x +--I ++ %Q d + c +--I (321) | acoth(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 489 + +--S 490 of 506 +--m0196:= a0196-r0196 +--E 490 + +--S 491 of 506 +--d0196:= D(m0196,x) +--E 491 + +--S 492 of 506 +t0197:= x*acoth(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (322) x acoth(b f + a) +--R Type: Expression(Integer) +--E 492 + +--S 493 of 506 +r0197:= 1/4/d^2/log(f)^2*(2*x^2*acoth(a+b*f^(c+d*x))*d^2*log(f)^2+_ + x^2*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^2*log(f)^2-_ + x^2*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^2*log(f)^2+_ + 2*x*polylog(2,-b*f^(c+d*x)/(-1+a))*d*log(f)-_ + 2*x*polylog(2,-b*f^(c+d*x)/(1+a))*d*log(f)-_ + 2*polylog(3,-b*f^(c+d*x)/(-1+a))+2*polylog(3,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 493 + +--S 494 of 506 +a0197:= integrate(t0197,x) +--R +--R +--R x +--I ++ %Q d + c +--I (323) | %Q acoth(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 494 + +--S 495 of 506 +--m0197:= a0197-r0197 +--E 495 + +--S 496 of 506 +--d0197:= D(m0197,x) +--E 496 + +--S 497 of 506 +t0198:= x^2*acoth(a+b*f^(c+d*x)) +--R +--R +--R 2 d x + c +--R (324) x acoth(b f + a) +--R Type: Expression(Integer) +--E 497 + +--S 498 of 506 +r0198:= 1/6/d^3/log(f)^3*(2*x^3*acoth(a+b*f^(c+d*x))*d^3*log(f)^3+_ + x^3*log(1/(-1+a)*(-1+a+b*f^(c+d*x)))*d^3*log(f)^3-_ + x^3*log(1/(1+a)*(1+a+b*f^(c+d*x)))*d^3*log(f)^3+_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(-1+a))*d^2*log(f)^2-_ + 3*x^2*polylog(2,-b*f^(c+d*x)/(1+a))*d^2*log(f)^2-_ + 6*x*polylog(3,-b*f^(c+d*x)/(-1+a))*d*log(f)+_ + 6*x*polylog(3,-b*f^(c+d*x)/(1+a))*d*log(f)+_ + 6*polylog(4,-b*f^(c+d*x)/(-1+a))-6*polylog(4,-b*f^(c+d*x)/(1+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 498 + +--S 499 of 506 +a0198:= integrate(t0198,x) +--R +--R +--R x +--I ++ 2 %Q d + c +--I (325) | %Q acoth(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 499 + +--S 500 of 506 +--m0198:= a0198-r0198 +--E 500 + +--S 501 of 506 +--d0198:= D(m0198,x) +--E 501 + +--S 502 of 506 +t0199:= atanh(cosh(x)) +--R +--R +--R (326) atanh(cosh(x)) +--R Type: Expression(Integer) +--E 502 + +--S 503 of 506 +r0199:= -2*x*atanh(exp(x))+x*atanh(cosh(x))-_ + polylog(2,-exp(x))+polylog(2,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 503 + +--S 504 of 506 +a0199:= integrate(t0199,x) +--R +--R +--R x +--R ++ +--I (327) | atanh(cosh(%Q))d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 504 + +--S 505 of 506 +--m0199:= a0199-r0199 +--E 505 + +--S 506 of 506 +--d0199:= D(m0199,x) +--E 506 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richinvhyper100-199.input.pdf b/src/axiom-website/CATS/richinvhyper100-199.input.pdf new file mode 100644 index 0000000..31d5333 Binary files /dev/null and b/src/axiom-website/CATS/richinvhyper100-199.input.pdf differ diff --git a/src/axiom-website/CATS/richinvhyper200-296.input.pamphlet b/src/axiom-website/CATS/richinvhyper200-296.input.pamphlet new file mode 100644 index 0000000..b2beef5 --- /dev/null +++ b/src/axiom-website/CATS/richinvhyper200-296.input.pamphlet @@ -0,0 +1,13573 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richinvhyper200-296.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richinvhyper200-296.output +)spool richinvhyper200-296.output +)set message auto off +)clear all + +--S 1 of 489 +t0200:= x*atanh(cosh(x)) +--R +--R +--R (1) x atanh(cosh(x)) +--R Type: Expression Integer +--E 1 + +--S 2 of 489 +r0200:= -x^2*atanh(exp(x))+1/2*x^2*atanh(cosh(x))-x*polylog(2,-exp(x))+_ + x*polylog(2,exp(x))+polylog(3,-exp(x))-polylog(3,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 489 +a0200:= integrate(t0200,x) +--R +--R +--R x +--R ++ +--R (2) | %I atanh(cosh(%I))d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 3 + +--S 4 of 489 +--m0200:= a0200-r0200 +--E 4 + +--S 5 of 489 +--d0200:= D(m0200,x) +--E 5 + +--S 6 of 489 +t0201:= x^2*atanh(cosh(x)) +--R +--R +--R 2 +--R (3) x atanh(cosh(x)) +--R Type: Expression Integer +--E 6 + +--S 7 of 489 +r0201:= -2/3*x^3*atanh(exp(x))+1/3*x^3*atanh(cosh(x))-_ + x^2*polylog(2,-exp(x))+x^2*polylog(2,exp(x))+_ + 2*x*polylog(3,-exp(x))-2*x*polylog(3,exp(x))-_ + 2*polylog(4,-exp(x))+2*polylog(4,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 489 +a0201:= integrate(t0201,x) +--R +--R +--R x +--R ++ 2 +--R (4) | %I atanh(cosh(%I))d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 8 + +--S 9 of 489 +--m0201:= a0201-r0201 +--E 9 + +--S 10 of 489 +--d0201:= D(m0201,x) +--E 10 + +--S 11 of 489 +t0202:= acoth(cosh(x)) +--R +--R +--R (5) acoth(cosh(x)) +--R Type: Expression Integer +--E 11 + +--S 12 of 489 +r0202:= x*acoth(cosh(x))-2*x*atanh(exp(x))-polylog(2,-exp(x))+polylog(2,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 489 +a0202:= integrate(t0202,x) +--R +--R +--R x +--R ++ +--R (6) | acoth(cosh(%I))d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 13 + +--S 14 of 489 +--m0202:= a0202-r0202 +--E 14 + +--S 15 of 489 +--d0202:= D(m0202,x) +--E 15 + +--S 16 of 489 +t0203:= x*acoth(cosh(x)) +--R +--R +--R (7) x acoth(cosh(x)) +--R Type: Expression Integer +--E 16 + +--S 17 of 489 +r0203:= 1/2*x^2*acoth(cosh(x))-x^2*atanh(exp(x))-x*polylog(2,-exp(x))+_ + x*polylog(2,exp(x))+polylog(3,-exp(x))-polylog(3,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 489 +a0203:= integrate(t0203,x) +--R +--R +--R x +--R ++ +--R (8) | %I acoth(cosh(%I))d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 18 + +--S 19 of 489 +--m0203:= a0203-r0203 +--E 19 + +--S 20 of 489 +--d0203:= D(m0203,x) +--E 20 + +--S 21 of 489 +t0204:= x^2*acoth(cosh(x)) +--R +--R +--R 2 +--R (9) x acoth(cosh(x)) +--R Type: Expression Integer +--E 21 + +--S 22 of 489 +r0204:= 1/3*x^3*acoth(cosh(x))-2/3*x^3*atanh(exp(x))-x^2*polylog(2,-exp(x))+_ + x^2*polylog(2,exp(x))+2*x*polylog(3,-exp(x))-_ + 2*x*polylog(3,exp(x))-2*polylog(4,-exp(x))+2*polylog(4,exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 489 +a0204:= integrate(t0204,x) +--R +--R +--R x +--R ++ 2 +--R (10) | %I acoth(cosh(%I))d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 23 + +--S 24 of 489 +--m0204:= a0204-r0204 +--E 24 + +--S 25 of 489 +--d0204:= D(m0204,x) +--E 25 + +--S 26 of 489 +t0205:= x^2*exp(1)^acosh(x) +--R +--R +--R 2 acosh(x) +--R (11) x %e +--R Type: Expression Integer +--E 26 + +--S 27 of 489 +r0205:= 1/4*x^4-1/8*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/4*(-1+x)^(1/2)*_ + (1+x)^(1/2)*x^3-1/8*acosh(x) +--R +--R +--R 3 +-----+ +-----+ 4 +--R (2x - x)\|x - 1 \|x + 1 - acosh(x) + 2x +--R (12) ------------------------------------------ +--R 8 +--R Type: Expression Integer +--E 27 + +--S 28 of 489 +a0205:= integrate(t0205,x) +--R +--R +--R (13) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((8x - 4x)\|x - 1 - 8x + 8x - 1)log(\|x - 1 - x) +--R + +--R +------+ +--R 5 3 | 2 6 4 2 +--R (16x - 10x + x)\|x - 1 - 16x + 18x - 4x +--R / +--R +------+ +--R 3 | 2 4 2 +--R (64x - 32x)\|x - 1 - 64x + 64x - 8 +--R Type: Union(Expression Integer,...) +--E 28 + +--S 29 of 489 +m0205:= a0205-r0205 +--R +--R +--R (14) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((8x - 4x)\|x - 1 - 8x + 8x - 1)log(\|x - 1 - x) +--R + +--R 6 4 2 +-----+ +-----+ 3 7 +--R (- 16x + 16x - 4x )\|x - 1 \|x + 1 + (8x - 4x)acosh(x) - 16x +--R + +--R 5 3 +--R 24x - 10x + x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 7 5 3 +-----+ +-----+ 4 2 +--R (16x - 24x + 10x - x)\|x - 1 \|x + 1 + (- 8x + 8x - 1)acosh(x) +--R + +--R 8 6 4 2 +--R 16x - 32x + 20x - 4x +--R / +--R +------+ +--R 3 | 2 4 2 +--R (64x - 32x)\|x - 1 - 64x + 64x - 8 +--R Type: Expression Integer +--E 29 + +--S 30 of 489 +d0205:= D(m0205,x) +--R +--R +--R (15) +--R 11 9 7 5 3 +-----+ +-----+ +--R (- 1024x + 2560x - 2304x + 896x - 144x + 8x)\|x - 1 \|x + 1 +--R + +--R 12 10 8 6 4 2 +--R - 1024x + 3072x - 3456x + 1792x - 424x + 40x - 1 +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R 12 10 8 6 4 2 +-----+ +-----+ +--R (1024x - 3072x + 3456x - 1792x + 424x - 40x + 1)\|x - 1 \|x + 1 +--R + +--R 13 11 9 7 5 3 +--R 1024x - 3584x + 4864x - 3200x + 1040x - 152x + 8x +--R / +--R +------+ +--R 8 6 4 2 +-----+ +-----+ | 2 +--R (1024x - 2048x + 1280x - 256x + 8)\|x - 1 \|x + 1 \|x - 1 +--R + +--R 9 7 5 3 +-----+ +-----+ +--R (- 1024x + 2560x - 2176x + 704x - 64x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 30 + +--S 31 of 489 +t0206:= exp(1)^acosh(x) +--R +--R +--R acosh(x) +--R (16) %e +--R Type: Expression Integer +--E 31 + +--S 32 of 489 +r0206:= 1/2*x^2+1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)-1/2*acosh(x) +--R +--R +--R +-----+ +-----+ 2 +--R x\|x - 1 \|x + 1 - acosh(x) + x +--R (17) --------------------------------- +--R 2 +--R Type: Expression Integer +--E 32 + +--S 33 of 489 +a0206:= integrate(t0206,x) +--R +--R +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (2x\|x - 1 - 2x + 1)log(\|x - 1 - x) + x\|x - 1 - x +--R (18) ----------------------------------------------------------- +--R +------+ +--R | 2 2 +--R 4x\|x - 1 - 4x + 2 +--R Type: Union(Expression Integer,...) +--E 33 + +--S 34 of 489 +m0206:= a0206-r0206 +--R +--R +--R (19) +--R +------+ +------+ +--R | 2 2 | 2 +--R (2x\|x - 1 - 2x + 1)log(\|x - 1 - x) +--R + +--R +------+ +--R 2 +-----+ +-----+ 3 | 2 +--R (- 2x \|x - 1 \|x + 1 + 2x acosh(x) - 2x + x)\|x - 1 +--R + +--R 3 +-----+ +-----+ 2 4 2 +--R (2x - x)\|x - 1 \|x + 1 + (- 2x + 1)acosh(x) + 2x - 2x +--R / +--R +------+ +--R | 2 2 +--R 4x\|x - 1 - 4x + 2 +--R Type: Expression Integer +--E 34 + +--S 35 of 489 +d0206:= D(m0206,x) +--R +--R +--R (20) +--R +------+ +--R 5 3 +-----+ +-----+ 6 4 2 | 2 +--R ((- 16x + 16x - 4x)\|x - 1 \|x + 1 - 16x + 24x - 10x + 1)\|x - 1 +--R + +--R 6 4 2 +-----+ +-----+ 7 5 3 +--R (16x - 24x + 10x - 1)\|x - 1 \|x + 1 + 16x - 32x + 20x - 4x +--R / +--R +------+ +--R 4 2 +-----+ +-----+ | 2 +--R (16x - 16x + 2)\|x - 1 \|x + 1 \|x - 1 +--R + +--R 5 3 +-----+ +-----+ +--R (- 16x + 24x - 8x)\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 35 + +--S 36 of 489 +t0207:= exp(1)^acosh(x)/x +--R +--R +--R acosh(x) +--R %e +--R (21) ---------- +--R x +--R Type: Expression Integer +--E 36 + +--S 37 of 489 +r0207:= x+(-1+x)^(1/2)*(1+x)^(1/2)-2*atan((-1+x)^(1/2)/(1+x)^(1/2)) +--R +--R +--R +-----+ +--R \|x - 1 +-----+ +-----+ +--R (22) - 2atan(--------) + \|x - 1 \|x + 1 + x +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 37 + +--S 38 of 489 +a0207:= integrate(t0207,x) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (- 2\|x - 1 + 2x)atan(\|x - 1 - x) - 1 +--R (23) ------------------------------------------ +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression Integer,...) +--E 38 + +--S 39 of 489 +m0207:= a0207-r0207 +--R +--R +--R (24) +--R +------+ +------+ +------+ +-----+ +--R | 2 | 2 | 2 \|x - 1 +--R (- 2\|x - 1 + 2x)atan(\|x - 1 - x) + (2\|x - 1 - 2x)atan(--------) +--R +-----+ +--R \|x + 1 +--R + +--R +------+ +--R +-----+ +-----+ | 2 +-----+ +-----+ 2 +--R (- \|x - 1 \|x + 1 - x)\|x - 1 + x\|x - 1 \|x + 1 + x - 1 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Expression Integer +--E 39 + +--S 40 of 489 +d0207:= D(m0207,x) +--R +--R +--R (25) +--R +------+ +--R 3 +-----+ +-----+ 4 2 | 2 +--R ((- 2x + 2x)\|x - 1 \|x + 1 - 2x + 3x - 1)\|x - 1 +--R + +--R 4 2 +-----+ +-----+ 5 3 +--R (2x - 3x + 1)\|x - 1 \|x + 1 + 2x - 4x + 2x +--R / +--R +------+ +--R 3 +-----+ +-----+ | 2 4 2 +-----+ +-----+ +--R (2x - x)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x )\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 40 + +--S 41 of 489 +t0208:= exp(1)^acosh(x)/x^2 +--R +--R +--R acosh(x) +--R %e +--R (26) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 41 + +--S 42 of 489 +r0208:= -(-1+x)^(1/2)*(1+x)^(1/2)/x+acosh(x)+log(x) +--R +--R +--R +-----+ +-----+ +--R - \|x - 1 \|x + 1 + x log(x) + x acosh(x) +--R (27) ------------------------------------------ +--R x +--R Type: Expression Integer +--E 42 + +--S 43 of 489 +a0208:= integrate(t0208,x) +--R +--R +--R (28) +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 2 +--R (- x\|x - 1 + x )log(\|x - 1 - x) + x log(x)\|x - 1 - x log(x) + 1 +--R ------------------------------------------------------------------------ +--R +------+ +--R | 2 2 +--R x\|x - 1 - x +--R Type: Union(Expression Integer,...) +--E 43 + +--S 44 of 489 +m0208:= a0208-r0208 +--R +--R +--R (29) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- x\|x - 1 + x )log(\|x - 1 - x) +--R + +--R +------+ +--R +-----+ +-----+ | 2 +-----+ +-----+ 2 +--R (\|x - 1 \|x + 1 - x acosh(x))\|x - 1 - x\|x - 1 \|x + 1 + x acosh(x) +--R + +--R 1 +--R / +--R +------+ +--R | 2 2 +--R x\|x - 1 - x +--R Type: Expression Integer +--E 44 + +--S 45 of 489 +d0208:= D(m0208,x) +--R +--R +--R (30) +--R +------+ +--R +-----+ +-----+ 2 | 2 2 +-----+ +-----+ +--R (2x\|x - 1 \|x + 1 + 2x - 1)\|x - 1 + (- 2x + 1)\|x - 1 \|x + 1 +--R + +--R 3 +--R - 2x + 2x +--R / +--R +------+ +--R 4 2 +-----+ +-----+ | 2 5 3 +-----+ +-----+ +--R (2x - x )\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x )\|x - 1 \|x + 1 +--R Type: Expression Integer +--E 45 + +--S 46 of 489 +t0209:= exp(1)^(3*atanh(x)) +--R +--R +--R 3atanh(x) +--R (31) %e +--R Type: Expression Integer +--E 46 + +--S 47 of 489 +r0209:= -(-5+x)*(1+x)^(1/2)/(1-x)^(1/2)-3*asin(x) +--R +--R +--R +-----+ +-------+ +--R (- x + 5)\|x + 1 - 3asin(x)\|- x + 1 +--R (32) -------------------------------------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 47 + +--S 48 of 489 +a0209:= integrate(t0209,x) +--R +--R +--R +-------+ +-------+ +--R |- x - 1 |- x - 1 +--R (33) - 6atan( |------- ) + (- x + 5) |------- +--R \| x - 1 \| x - 1 +--R Type: Union(Expression Integer,...) +--E 48 + +--S 49 of 489 +m0209:= a0209-r0209 +--R +--R +--R (34) +--R +-------+ +--R +-------+ |- x - 1 +-----+ +--R - 6\|- x + 1 atan( |------- ) + (x - 5)\|x + 1 +--R \| x - 1 +--R + +--R +-------+ +--R +-------+ |- x - 1 +-------+ +--R (- x + 5)\|- x + 1 |------- + 3asin(x)\|- x + 1 +--R \| x - 1 +--R / +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 49 + +--S 50 of 489 +d0209:= D(m0209,x) +--R +--R +--R (35) +--R +-------+ +--R 2 +-------+ |- x - 1 +--R (3x - 6x + 3)\|- x + 1 |------- +--R \| x - 1 +--R + +--R +--------+ +--R 2 | 2 +-------+ +--R (x + 2x + 1)\|- x + 1 \|- x + 1 +--R * +--R +-----+ +--R \|x + 1 +--R + +--R +--------+ +-------+ +--R 3 2 | 2 |- x - 1 +--R (x - 2x + 5x - 4)\|- x + 1 |------- +--R \| x - 1 +--R / +--R +--------+ +-------+ +--R 2 | 2 +-------+ |- x - 1 +-----+ +--R (x - 2x + 1)\|- x + 1 \|- x + 1 |------- \|x + 1 +--R \| x - 1 +--R Type: Expression Integer +--E 50 + +--S 51 of 489 +t0210:= x^2*exp(1)^(1/2*atanh(x)) +--R +--R +--R atanh(x) +--R -------- +--R 2 2 +--R (36) x %e +--R Type: Expression Integer +--E 51 + +--S 52 of 489 +r0210:= -29/24*exp(1)^(1/2*atanh(x))*(1-x)+13/12*exp(1)^(1/2*atanh(x))*_ + (1-x)^2-1/3*exp(1)^(1/2*atanh(x))*(1-x)^3+3/16*atan(-1+2^(1/2)*_ + exp(1)^(1/2*atanh(x)))*2^(1/2)+3/16*atan(1+2^(1/2)*exp(1)^(1/2*_ + atanh(x)))*2^(1/2)-3/32*log(1-2^(1/2)*exp(1)^(1/2*atanh(x))+_ + exp(1)^atanh(x))*2^(1/2)+3/32*log(1+2^(1/2)*exp(1)^(1/2*atanh(x))+_ + exp(1)^atanh(x))*2^(1/2) +--R +--R +--R (37) +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R 9\|2 log(%e + \|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R - 9\|2 log(%e - \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ +-+ 2 +-+ +-+ 2 +--R 18\|2 atan(\|2 %e + 1) + 18\|2 atan(\|2 %e - 1) +--R + +--R atanh(x) +--R -------- +--R 3 2 2 +--R (32x + 8x + 4x - 44)%e +--R / +--R 96 +--R Type: Expression Integer +--E 52 + +--S 53 of 489 +a0210:= integrate(t0210,x) +--R +--R +--R (38) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R 9\|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - 9\|2 log((%e ) - \|2 %e + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 18\|2 atan(----------------------) - 18\|2 atan(----------------------) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 2 4 +--R (32x + 8x + 4x - 44)%e +--R / +--R 96 +--R Type: Union(Expression Integer,...) +--E 53 + +--S 54 of 489 +m0210:= a0210-r0210 +--R +--R +--R (39) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R 9\|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - 9\|2 log((%e ) - \|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R - 9\|2 log(%e + \|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R 9\|2 log(%e - \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ +-+ 2 +-+ +-+ 2 +--R - 18\|2 atan(\|2 %e + 1) - 18\|2 atan(\|2 %e - 1) +--R + +--R +-+ 1 +-+ 1 +--R - 18\|2 atan(----------------------) - 18\|2 atan(----------------------) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 atanh(x) +--R ------------ -------- +--R 3 2 4 3 2 2 +--R (32x + 8x + 4x - 44)%e + (- 32x - 8x - 4x + 44)%e +--R / +--R 96 +--R Type: Expression Integer +--E 54 + +--S 55 of 489 +d0210:= D(m0210,x) +--R +--R +--R (40) +--R atanh(x) 4 +--R -------- +--R 4 2 2 4 2 +--R ((16x - 16x - 3x + 3)(%e ) + 16x - 16x - 3x + 3) +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 4 2 2 4 2 +--R ((32x - 32x - 6x + 6)(%e ) + 32x - 32x - 6x + 6) +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 +--R -------- +--R 4 2 2 +--R (- 32x + 32x + 6x - 6)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 4 2 2 +--R (16x - 16x - 3x + 3)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 32x + 32x + 6x - 6)(%e ) + 16x - 16x - 3x + 3 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 4 2 2 2 +--R (- 16x + 16x + 3x - 3)(%e ) + 3(%e ) +--R + +--R atanh(x) +--R -------- +--R 4 2 2 +--R (- 16x + 16x + 3x)%e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 4 2 2 2 +--R (- 32x + 32x + 6x - 9)(%e ) + 6(%e ) +--R + +--R atanh(x) +--R -------- +--R 4 2 2 +--R (- 32x + 32x + 6x - 3)%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 +--R -------- +--R 4 2 2 +--R (32x - 32x - 6x + 6)(%e ) +--R + +--R atanh(x) 5 +--R -------- +--R 4 2 2 +--R (- 16x + 16x + 3x - 6)(%e ) +--R + +--R atanh(x) 3 +--R -------- +--R 4 2 2 +--R (32x - 32x - 6x + 3)(%e ) +--R + +--R atanh(x) +--R -------- +--R 4 2 2 +--R (- 16x + 16x + 3x + 3)%e +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 4 2 2 4 2 +--R ((16x - 16x - 3x - 3)(%e ) + 16x - 16x - 3x - 3) +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 4 2 2 4 2 +--R ((32x - 32x - 6x - 6)(%e ) + 32x - 32x - 6x - 6) +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 +--R -------- +--R 4 2 2 +--R (- 32x + 32x + 6x + 6)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 4 2 2 +--R (16x - 16x - 3x - 3)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 32x + 32x + 6x + 6)(%e ) + 16x - 16x - 3x - 3 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 4 2 2 2 +--R (- 16x + 16x + 3x - 3)(%e ) + 3(%e ) +--R + +--R atanh(x) +--R -------- +--R 4 2 2 +--R (- 16x + 16x + 3x)%e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 4 2 2 2 +--R (- 32x + 32x + 6x - 9)(%e ) + 6(%e ) +--R + +--R atanh(x) +--R -------- +--R 4 2 2 +--R (- 32x + 32x + 6x - 3)%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 +--R -------- +--R 4 2 2 +--R (32x - 32x - 6x + 6)(%e ) +--R + +--R atanh(x) 5 +--R -------- +--R 4 2 2 +--R (- 16x + 16x + 3x - 6)(%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 4 2 2 4 2 2 +--R (32x - 32x - 6x + 3)(%e ) + (- 16x + 16x + 3x + 3)%e +--R / +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((16x - 16)(%e ) + 16x - 16)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) +--R ((32x - 32)(%e ) + 32x - 32)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 32x + 32)(%e ) + (16x - 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- 32x + 32)(%e ) + 16x - 16 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((16x - 16)(%e ) + 16x - 16)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) +--R ((32x - 32)(%e ) + 32x - 32)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 32x + 32)(%e ) + (16x - 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- 32x + 32)(%e ) + 16x - 16 +--R Type: Expression Integer +--E 55 + +--S 56 of 489 +t0211:= x*exp(1)^(1/2*atanh(x)) +--R +--R +--R atanh(x) +--R -------- +--R 2 +--R (41) x %e +--R Type: Expression Integer +--E 56 + +--S 57 of 489 +r0211:= -5/4*exp(1)^(1/2*atanh(x))*(1-x)+1/2*exp(1)^(1/2*atanh(x))*(1-x)^2+_ + 1/8*atan(-1+2^(1/2)*exp(1)^(1/2*atanh(x)))*2^(1/2)+_ + 1/8*atan(1+2^(1/2)*exp(1)^(1/2*atanh(x)))*2^(1/2)-_ + 1/16*log(1-2^(1/2)*exp(1)^(1/2*atanh(x))+exp(1)^atanh(x))*2^(1/2)+_ + 1/16*log(1+2^(1/2)*exp(1)^(1/2*atanh(x))+exp(1)^atanh(x))*2^(1/2) +--R +--R +--R (42) +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R \|2 log(%e + \|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R - \|2 log(%e - \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ +-+ 2 +-+ +-+ 2 +--R 2\|2 atan(\|2 %e + 1) + 2\|2 atan(\|2 %e - 1) +--R + +--R atanh(x) +--R -------- +--R 2 2 +--R (8x + 4x - 12)%e +--R / +--R 16 +--R Type: Expression Integer +--E 57 + +--S 58 of 489 +a0211:= integrate(t0211,x) +--R +--R +--R (43) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log((%e ) - \|2 %e + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(----------------------) - 2\|2 atan(----------------------) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 2 4 +--R (8x + 4x - 12)%e +--R / +--R 16 +--R Type: Union(Expression Integer,...) +--E 58 + +--S 59 of 489 +m0211:= a0211-r0211 +--R +--R +--R (44) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log((%e ) - \|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R - \|2 log(%e + \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ atanh(x) +-+ 2 +-+ +-+ 2 +--R \|2 log(%e - \|2 %e + 1) - 2\|2 atan(\|2 %e + 1) +--R + +--R atanh(x) +--R -------- +--R +-+ +-+ 2 +-+ 1 +--R - 2\|2 atan(\|2 %e - 1) - 2\|2 atan(----------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 4 +--R \|2 %e - 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 1 2 4 +--R - 2\|2 atan(----------------------) + (8x + 4x - 12)%e +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 4 +--R \|2 %e + 1 +--R + +--R atanh(x) +--R -------- +--R 2 2 +--R (- 8x - 4x + 12)%e +--R / +--R 16 +--R Type: Expression Integer +--E 59 + +--S 60 of 489 +d0211:= D(m0211,x) +--R +--R +--R (45) +--R atanh(x) 4 +--R -------- +--R 3 2 3 atanh(x) 2 +--R ((8x - 9x + 1)(%e ) + 8x - 9x + 1)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 3 2 3 atanh(x) +--R ((16x - 18x + 2)(%e ) + 16x - 18x + 2)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 3 2 3 2 +--R (- 16x + 18x - 2)(%e ) + (8x - 9x + 1)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 3 +--R (- 16x + 18x - 2)(%e ) + 8x - 9x + 1 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 3 2 2 +--R (- 8x + 9x - 1)(%e ) + (%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R (- 8x + 9x)%e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 3 2 2 +--R (- 16x + 18x - 3)(%e ) + 2(%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R (- 16x + 18x - 1)%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 atanh(x) 5 +--R -------- -------- +--R 3 2 3 2 +--R (16x - 18x + 2)(%e ) + (- 8x + 9x - 2)(%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R (16x - 18x + 1)(%e ) + (- 8x + 9x + 1)%e +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 3 2 3 atanh(x) 2 +--R ((8x - 9x - 1)(%e ) + 8x - 9x - 1)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 3 2 3 atanh(x) +--R ((16x - 18x - 2)(%e ) + 16x - 18x - 2)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 3 2 3 2 +--R (- 16x + 18x + 2)(%e ) + (8x - 9x - 1)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 3 +--R (- 16x + 18x + 2)(%e ) + 8x - 9x - 1 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 3 2 2 +--R (- 8x + 9x - 1)(%e ) + (%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R (- 8x + 9x)%e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 +--R -------- -------- +--R 3 2 2 +--R (- 16x + 18x - 3)(%e ) + 2(%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R (- 16x + 18x - 1)%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 atanh(x) 5 +--R -------- -------- +--R 3 2 3 2 +--R (16x - 18x + 2)(%e ) + (- 8x + 9x - 2)(%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R (16x - 18x + 1)(%e ) + (- 8x + 9x + 1)%e +--R / +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((8x - 8)(%e ) + 8x - 8)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) +--R ((16x - 16)(%e ) + 16x - 16)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 16x + 16)(%e ) + (8x - 8)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- 16x + 16)(%e ) + 8x - 8 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((8x - 8)(%e ) + 8x - 8)(%e ) +--R + +--R atanh(x) 4 +--R -------- +--R 2 2 2 atanh(x) +--R ((16x - 16)(%e ) + 16x - 16)%e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 16x + 16)(%e ) + (8x - 8)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- 16x + 16)(%e ) + 8x - 8 +--R Type: Expression Integer +--E 60 + +--S 61 of 489 +t0212:= exp(1)^(1/2*atanh(x)) +--R +--R +--R atanh(x) +--R -------- +--R 2 +--R (46) %e +--R Type: Expression Integer +--E 61 + +--S 62 of 489 +r0212:= -(1-x)^(3/4)*(1+x)^(1/4)-1/2*atan(-1+2^(1/2)*(1-x)^(1/4)/_ + (1+x)^(1/4))*2^(1/2)-1/2*atan(1+2^(1/2)*(1-x)^(1/4)/(1+x)^(1/4))*_ + 2^(1/2)-1/4*log(1+(1-x)^(1/2)/(1+x)^(1/2)-2^(1/2)*(1-x)^(1/4)/_ + (1+x)^(1/4))*2^(1/2)+1/4*log(1+(1-x)^(1/2)/(1+x)^(1/2)+2^(1/2)*_ + (1-x)^(1/4)/(1+x)^(1/4))*2^(1/2) +--R +--R +--R (47) +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R - \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ \|x + 1 + \|2 \|- x + 1 +--R - 2\|2 atan(-------------------------) +--R 4+-----+ +--R \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ \|x + 1 - \|2 \|- x + 1 4+-------+3 4+-----+ +--R 2\|2 atan(-------------------------) - 4\|- x + 1 \|x + 1 +--R 4+-----+ +--R \|x + 1 +--R / +--R 4 +--R Type: Expression Integer +--E 62 + +--S 63 of 489 +a0212:= integrate(t0212,x) +--R +--R +--R (48) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log((%e ) - \|2 %e + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(----------------------) - 2\|2 atan(----------------------) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (4x - 4)%e +--R / +--R 4 +--R Type: Union(Expression Integer,...) +--E 63 + +--S 64 of 489 +m0212:= a0212-r0212 +--R +--R +--R (49) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log((%e ) - \|2 %e + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(----------------------) - 2\|2 atan(----------------------) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R - \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ 4+-----+ +-+4+-------+ +--R 4 +-+ \|x + 1 + \|2 \|- x + 1 +--R (4x - 4)%e + 2\|2 atan(-------------------------) +--R 4+-----+ +--R \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ \|x + 1 - \|2 \|- x + 1 4+-------+3 4+-----+ +--R - 2\|2 atan(-------------------------) + 4\|- x + 1 \|x + 1 +--R 4+-----+ +--R \|x + 1 +--R / +--R 4 +--R Type: Expression Integer +--E 64 + +--S 65 of 489 +d0212:= D(m0212,x) +--R +--R +--R (50) +--R 2 4+-------+3 4+-----+3 +--R (4x - 2x - 2)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ +--R (- 4x + 2x + 2)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 4+-------+ +--R (- 4x + 2x + 2)\|- x + 1 +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R 2 +-------+ +-----+ 2 4+-----+2 +--R ((4x - x - 3)\|- x + 1 \|x + 1 + 3x - x - 2)\|x + 1 +--R + +--R +-------+4+-------+2 +-----+ +--R (- x - 2)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 4+-------+2 +--R (- 4x - 3x + 4x + 3)\|- x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R 2 4+-------+3 4+-----+3 +--R (4x - 2x - 6)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ +--R (- 4x + 2x + 6)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 4+-------+ +--R (- 4x + 2x + 6)\|- x + 1 +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R 2 +-------+ +-----+ 2 4+-----+2 +--R ((4x - x - 3)\|- x + 1 \|x + 1 + 3x - x - 2)\|x + 1 +--R + +--R +-------+4+-------+2 +-----+ 3 2 4+-------+2 +--R (- x - 2)\|- x + 1 \|- x + 1 \|x + 1 + (- 4x - 3x + 4x + 3)\|- x + 1 +--R / +--R 2 4+-------+3 4+-----+3 +--R (4x - 4)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ 2 4+-------+ +--R ((- 4x + 4)\|- x + 1 \|- x + 1 \|x + 1 + (- 4x + 4)\|- x + 1 ) +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R 2 4+-------+3 4+-----+3 +--R (4x - 4)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ 2 4+-------+ 4+-----+ +--R ((- 4x + 4)\|- x + 1 \|- x + 1 \|x + 1 + (- 4x + 4)\|- x + 1 )\|x + 1 +--R Type: Expression Integer +--E 65 + +--S 66 of 489 +t0213:= exp(1)^(1/2*atanh(x))/x +--R +--R +--R atanh(x) +--R -------- +--R 2 +--R %e +--R (51) ---------- +--R x +--R Type: Expression Integer +--E 66 + +--S 67 of 489 +r0213:= -2*atan(exp(1)^(1/2*atanh(x)))+atan(-1+2^(1/2)*_ + exp(1)^(1/2*atanh(x)))*2^(1/2)+atan(1+2^(1/2)*_ + exp(1)^(1/2*atanh(x)))*2^(1/2)+log(-1+exp(1)^(1/2*atanh(x)))-_ + log(1+exp(1)^(1/2*atanh(x)))-1/2*log(1-2^(1/2)*_ + exp(1)^(1/2*atanh(x))+exp(1)^atanh(x))*2^(1/2)+_ + 1/2*log(1+2^(1/2)*exp(1)^(1/2*atanh(x))+exp(1)^atanh(x))*2^(1/2) +--R +--R +--R (52) +--R atanh(x) +--R -------- +--R +-+ atanh(x) +-+ 2 +--R \|2 log(%e + \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ atanh(x) +-+ 2 2 +--R - \|2 log(%e - \|2 %e + 1) - 2log(%e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R 2 +-+ +-+ 2 +--R 2log(%e - 1) + 2\|2 atan(\|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ +-+ 2 2 +--R 2\|2 atan(\|2 %e - 1) - 4atan(%e ) +--R / +--R 2 +--R Type: Expression Integer +--E 67 + +--S 68 of 489 +a0213:= integrate(t0213,x) +--R +--R +--R (53) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R - log((%e ) - \|2 %e + 1) +--R + +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log(%e + 1) + \|2 log(%e - 1) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R +-+ 2%e 1 +--R \|2 atan(---------------------) - 2atan(----------------------) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R (%e ) - 1 \|2 %e - 1 +--R + +--R 1 +--R - 2atan(----------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 4 +--R \|2 %e + 1 +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression Integer,...) +--E 68 + +--S 69 of 489 +m0213:= a0213-r0213 +--R +--R +--R (54) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R log((%e ) + \|2 %e + 1) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R - log((%e ) - \|2 %e + 1) +--R + +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 4 +-+ 4 +--R - \|2 log(%e + 1) + \|2 log(%e - 1) +--R + +--R atanh(x) +--R -------- +--R atanh(x) +-+ 2 +--R - log(%e + \|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R atanh(x) +-+ 2 +-+ 2 +--R log(%e - \|2 %e + 1) + \|2 log(%e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ 2 +-+ 2 +--R - \|2 log(%e - 1) - 2atan(\|2 %e + 1) +--R + +--R atanh(x) atanh(x) +--R -------- -------- +--R +-+ 2 +-+ 2 +--R - 2atan(\|2 %e - 1) + 2\|2 atan(%e ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R +-+ 2%e 1 +--R \|2 atan(---------------------) - 2atan(----------------------) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 +-+ 4 +--R (%e ) - 1 \|2 %e - 1 +--R + +--R 1 +--R - 2atan(----------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 4 +--R \|2 %e + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 69 + +--S 70 of 489 +d0213:= D(m0213,x) +--R +--R +--R (55) +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R ((%e ) + 3(%e ) - (%e ) + %e ) +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 2 2 2 +--R - (%e ) + 2(%e ) + 6(%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 2 2 +--R - 2(%e ) + 3%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R - (%e ) - 5(%e ) + 5(%e ) - 3(%e ) +--R * +--R - x - 1 8 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 8 +--R -------- +--R 2 atanh(x) 2 +--R (- 4(%e ) + 4)(%e ) +--R + +--R atanh(x) 8 atanh(x) 10 atanh(x) 8 +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R (- 8(%e ) + 8)%e + 8(%e ) - 4(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 +--R - 8(%e ) + 4 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (- (%e ) - 3(%e ) + (%e ) - %e ) +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (%e ) - 2(%e ) - 6(%e ) + 2(%e ) +--R + +--R atanh(x) +--R -------- +--R 2 +--R - 3%e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (%e ) + 5(%e ) - 5(%e ) + 3(%e ) +--R / +--R atanh(x) 8 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((x - 1)(%e ) - x + 1)(%e ) +--R + +--R atanh(x) 8 +--R -------- +--R 2 2 2 atanh(x) +--R ((2x - 2)(%e ) - 2x + 2)%e +--R + +--R atanh(x) 10 atanh(x) 8 +--R -------- -------- +--R 2 2 2 2 +--R (- 2x + 2)(%e ) + (x - 1)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (2x - 2)(%e ) - x + 1 +--R * +--R - x - 1 8 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 8 +--R -------- +--R 2 2 2 atanh(x) 2 +--R ((- x + 1)(%e ) + x - 1)(%e ) +--R + +--R atanh(x) 8 atanh(x) 10 +--R -------- -------- +--R 2 2 2 atanh(x) 2 2 +--R ((- 2x + 2)(%e ) + 2x - 2)%e + (2x - 2)(%e ) +--R + +--R atanh(x) 8 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R (- x + 1)(%e ) + (- 2x + 2)(%e ) + x - 1 +--R Type: Expression Integer +--E 70 + +--S 71 of 489 +t0214:= exp(1)^(1/2*atanh(x))/x^2 +--R +--R +--R atanh(x) +--R -------- +--R 2 +--R %e +--R (56) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 71 + +--S 72 of 489 +r0214:= 1/(2-2*exp(1)^(1/2*atanh(x)))-1/(2+2*exp(1)^(1/2*atanh(x)))+_ + exp(1)^(1/2*atanh(x))/(1+exp(1)^atanh(x))-_ + atan(exp(1)^(1/2*atanh(x)))+1/2*log(-1+exp(1)^(1/2*atanh(x)))-_ + 1/2*log(1+exp(1)^(1/2*atanh(x))) +--R +--R +--R (57) +--R atanh(x) 2 atanh(x) 2 atanh(x) +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R ((- (%e ) + 1)%e - (%e ) + 1)log(%e + 1) +--R + +--R atanh(x) 2 atanh(x) 2 atanh(x) +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R (((%e ) - 1)%e + (%e ) - 1)log(%e - 1) +--R + +--R atanh(x) 2 atanh(x) 2 atanh(x) +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R ((- 2(%e ) + 2)%e - 2(%e ) + 2)atan(%e ) +--R + +--R atanh(x) atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R - 2%e %e + 2(%e ) - 4%e +--R / +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R (2(%e ) - 2)%e + 2(%e ) - 2 +--R Type: Expression Integer +--E 72 + +--S 73 of 489 +a0214:= integrate(t0214,x) +--R +--R +--R (58) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 4 +--R - x log(%e + 1) + x log(%e - 1) +--R + +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 4 4 +--R - 2x atan(%e ) + (2x - 2)%e +--R / +--R 2x +--R Type: Union(Expression Integer,...) +--E 73 + +--S 74 of 489 +m0214:= a0214-r0214 +--R +--R +--R (59) +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((- x (%e ) + x)%e - x (%e ) + x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R log(%e + 1) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((x (%e ) - x)%e + x (%e ) - x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R log(%e - 1) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((x (%e ) - x)%e + x (%e ) - x) +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e + 1) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((- x (%e ) + x)%e - x (%e ) + x) +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e - 1) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((- 2x (%e ) + 2x)%e - 2x (%e ) + 2x) +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R atan(%e ) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((2x (%e ) - 2x)%e + 2x (%e ) - 2x) +--R * +--R atanh(x) +--R -------- +--R 2 +--R atan(%e ) +--R + +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R ((2x - 2)(%e ) - 2x + 2)%e + (2x - 2)(%e ) +--R + +--R - 2x + 2 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 atanh(x) 2 2 +--R 2x %e %e - 2x (%e ) + 4x %e +--R / +--R atanh(x) 2 atanh(x) 2 +--R -------- -------- +--R 2 atanh(x) 2 +--R (2x (%e ) - 2x)%e + 2x (%e ) - 2x +--R Type: Expression Integer +--E 74 + +--S 75 of 489 +d0214:= D(m0214,x) +--R +--R +--R (60) +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (x + x - 2)(%e ) + (- x - x + 2)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- x - x + 2)(%e ) + x + x - 2 +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (2x + 2x - 4)(%e ) + (- 2x - 2x + 4)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- 2x - 2x + 4)(%e ) + 2x + 2x - 4 +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (x + x - 2)(%e ) + (- x - x + 2)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (- x - x + 2)(%e ) + x + x - 2 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 2 2 2 atanh(x) 2 +--R (x (%e ) + 4x (%e ) - x %e )(%e ) +--R + +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- +--R 2 2 2 2 2 2 +--R - x (%e ) + 3x (%e ) + 9x (%e ) +--R + +--R atanh(x) +--R -------- +--R 2 2 +--R - 3x %e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 atanh(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R x (%e ) + 3x (%e ) +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 3x - x + 2)(%e ) + (3x + x - 2)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (3x + x - 2)(%e ) - 3x - x + 2 +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 6x - 2x + 4)(%e ) + (6x + 2x - 4)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (6x + 2x - 4)(%e ) - 6x - 2x + 4 +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 3x - x + 2)(%e ) + (3x + x - 2)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 2 2 +--R (3x + x - 2)(%e ) - 3x - x + 2 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 2 2 2 atanh(x) 2 +--R (- x (%e ) - 4x (%e ) + x %e )(%e ) +--R + +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 2 2 2 2 +--R (x (%e ) - 3x (%e ) - 9x (%e ) + 3x %e ) +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 7 atanh(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R - x (%e ) - 3x (%e ) +--R / +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (2x - 2x )(%e ) + (- 2x + 2x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 2x + 2x )(%e ) + 2x - 2x +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (4x - 4x )(%e ) + (- 4x + 4x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 4x + 4x )(%e ) + 4x - 4x +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (2x - 2x )(%e ) + (- 2x + 2x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 2x + 2x )(%e ) + 2x - 2x +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (- 2x + 2x )(%e ) + (2x - 2x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (2x - 2x )(%e ) - 2x + 2x +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (- 4x + 4x )(%e ) + (4x - 4x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (4x - 4x )(%e ) - 4x + 4x +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 6 atanh(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (- 2x + 2x )(%e ) + (2x - 2x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (2x - 2x )(%e ) - 2x + 2x +--R Type: Expression Integer +--E 75 + +--S 76 of 489 +t0215:= exp(1)^(1/2*atanh(x))/x^3 +--R +--R +--R atanh(x) +--R -------- +--R 2 +--R %e +--R (61) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 76 + +--S 77 of 489 +r0215:= -1/8/(1-exp(1)^(1/2*atanh(x)))^2+3/(8-8*exp(1)^(1/2*atanh(x)))+_ + 1/8/(1+exp(1)^(1/2*atanh(x)))^2-3/(8+8*exp(1)^(1/2*atanh(x)))-_ + 1/2*exp(1)^(1/2*atanh(x))/(1+exp(1)^atanh(x))^2+_ + 3*exp(1)^(1/2*atanh(x))/(4+4*exp(1)^atanh(x))-_ + 1/4*atan(exp(1)^(1/2*atanh(x)))+1/8*log(-1+exp(1)^(1/2*atanh(x)))-_ + 1/8*log(1+exp(1)^(1/2*atanh(x))) +--R +--R +--R (62) +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 atanh(x) 2 +--R (- (%e ) + 2(%e ) - 1)(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 atanh(x) 4 +--R -------- -------- -------- +--R 2 2 atanh(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)%e - (%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 +--R 2(%e ) - 1 +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e + 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 atanh(x) 2 +--R ((%e ) - 2(%e ) + 1)(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 atanh(x) 4 +--R -------- -------- -------- +--R 2 2 atanh(x) 2 +--R (2(%e ) - 4(%e ) + 2)%e + (%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 +--R - 2(%e ) + 1 +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e - 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 atanh(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 atanh(x) 4 +--R -------- -------- -------- +--R 2 2 atanh(x) 2 +--R (- 4(%e ) + 8(%e ) - 4)%e - 2(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 +--R 4(%e ) - 2 +--R * +--R atanh(x) +--R -------- +--R 2 +--R atan(%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 2 2 atanh(x) 2 +--R (- 6(%e ) + 2%e )(%e ) +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 atanh(x) +--R (6(%e ) - 24(%e ) + 10%e )%e +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 +--R 2(%e ) - 10(%e ) + 4%e +--R / +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 atanh(x) 2 +--R (8(%e ) - 16(%e ) + 8)(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 atanh(x) 4 +--R -------- -------- -------- +--R 2 2 atanh(x) 2 +--R (16(%e ) - 32(%e ) + 16)%e + 8(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 2 +--R - 16(%e ) + 8 +--R Type: Expression Integer +--E 77 + +--S 78 of 489 +a0215:= integrate(t0215,x) +--R +--R +--R (63) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 2 4 2 4 +--R - x log(%e + 1) + x log(%e - 1) +--R + +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 2 4 2 4 +--R - 2x atan(%e ) + (6x - 2x - 4)%e +--R / +--R 2 +--R 8x +--R Type: Union(Expression Integer,...) +--E 78 + +--S 79 of 489 +m0215:= a0215-r0215 +--R +--R +--R (64) +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (- x (%e ) + 2x (%e ) - x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (- 2x (%e ) + 4x (%e ) - 2x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R - x (%e ) + 2x (%e ) - x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R log(%e + 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (x (%e ) - 2x (%e ) + x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (2x (%e ) - 4x (%e ) + 2x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R x (%e ) - 2x (%e ) + x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R log(%e - 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (x (%e ) - 2x (%e ) + x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (2x (%e ) - 4x (%e ) + 2x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R x (%e ) - 2x (%e ) + x +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e + 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (- x (%e ) + 2x (%e ) - x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (- 2x (%e ) + 4x (%e ) - 2x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R - x (%e ) + 2x (%e ) - x +--R * +--R atanh(x) +--R -------- +--R 2 +--R log(%e - 1) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (- 2x (%e ) + 4x (%e ) - 2x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (- 4x (%e ) + 8x (%e ) - 4x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R - 2x (%e ) + 4x (%e ) - 2x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R atan(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (2x (%e ) - 4x (%e ) + 2x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (4x (%e ) - 8x (%e ) + 4x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R 2x (%e ) - 4x (%e ) + 2x +--R * +--R atanh(x) +--R -------- +--R 2 +--R atan(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 +--R (6x - 2x - 4)(%e ) + (- 12x + 4x + 8)(%e ) +--R + +--R 2 +--R 6x - 2x - 4 +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 +--R (12x - 4x - 8)(%e ) + (- 24x + 8x + 16)(%e ) +--R + +--R 2 +--R 12x - 4x - 8 +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R (6x - 2x - 4)(%e ) + (- 12x + 4x + 8)(%e ) + 6x +--R + +--R - 2x - 4 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 2 2 2 2 atanh(x) 2 +--R (6x (%e ) - 2x %e )(%e ) +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 2 2 2 atanh(x) +--R (- 6x (%e ) + 24x (%e ) - 10x %e )%e +--R + +--R atanh(x) 5 atanh(x) 3 atanh(x) +--R -------- -------- -------- +--R 2 2 2 2 2 2 +--R - 2x (%e ) + 10x (%e ) - 4x %e +--R / +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) 2 +--R (8x (%e ) - 16x (%e ) + 8x )(%e ) +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 atanh(x) +--R (16x (%e ) - 32x (%e ) + 16x )%e +--R + +--R atanh(x) 4 atanh(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R 8x (%e ) - 16x (%e ) + 8x +--R Type: Expression Integer +--E 79 + +--S 80 of 489 +d0215:= D(m0215,x) +--R +--R +--R (65) +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x + 9x - 8)(%e ) + (2x - 18x + 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 2x + 18x - 16)(%e ) + x - 9x + 8 +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 3x + 27x - 24)(%e ) + (6x - 54x + 48)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 6x + 54x - 48)(%e ) + 3x - 27x + 24 +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 3x + 27x - 24)(%e ) + (6x - 54x + 48)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 6x + 54x - 48)(%e ) + 3x - 27x + 24 +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x + 9x - 8)(%e ) + (2x - 18x + 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 2x + 18x - 16)(%e ) + x - 9x + 8 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R 3x (%e ) + 11x (%e ) + x (%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R x %e +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R - 3x (%e ) + 15x (%e ) + 33x (%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R - 3x (%e ) + 6x %e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R 6x (%e ) - 3x (%e ) + 33x (%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R 15x (%e ) - 3x %e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R x (%e ) + x (%e ) + 11x (%e ) +--R + +--R atanh(x) 3 +--R -------- +--R 3 2 +--R 3x (%e ) +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x - 9x + 8)(%e ) + (2x + 18x - 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 2x - 18x + 16)(%e ) + x + 9x - 8 +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 3x - 27x + 24)(%e ) + (6x + 54x - 48)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 6x - 54x + 48)(%e ) + 3x + 27x - 24 +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 3x - 27x + 24)(%e ) + (6x + 54x - 48)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 6x - 54x + 48)(%e ) + 3x + 27x - 24 +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x - 9x + 8)(%e ) + (2x + 18x - 16)(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 2x - 18x + 16)(%e ) + x + 9x - 8 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R %e +--R + +--R atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R - 3x (%e ) - 11x (%e ) - x (%e ) +--R + +--R atanh(x) +--R -------- +--R 3 2 +--R - x %e +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R 3x (%e ) - 15x (%e ) - 33x (%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R 3x (%e ) - 6x %e +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 +--R -------- -------- -------- +--R 3 2 3 2 3 2 +--R - 6x (%e ) + 3x (%e ) - 33x (%e ) +--R + +--R atanh(x) 3 atanh(x) +--R -------- -------- +--R 3 2 3 2 +--R - 15x (%e ) + 3x %e +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 9 atanh(x) 7 atanh(x) 5 atanh(x) 3 +--R -------- -------- -------- -------- +--R 3 2 3 2 3 2 3 2 +--R - x (%e ) - x (%e ) - 11x (%e ) - 3x (%e ) +--R / +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (8x - 8x )(%e ) + (- 16x + 16x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (16x - 16x )(%e ) - 8x + 8x +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (24x - 24x )(%e ) + (- 48x + 48x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (48x - 48x )(%e ) - 24x + 24x +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (24x - 24x )(%e ) + (- 48x + 48x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (48x - 48x )(%e ) - 24x + 24x +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (8x - 8x )(%e ) + (- 16x + 16x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (16x - 16x )(%e ) - 8x + 8x +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 8x + 8x )(%e ) + (16x - 16x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 16x + 16x )(%e ) + 8x - 8x +--R * +--R atanh(x) 3 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 24x + 24x )(%e ) + (48x - 48x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 48x + 48x )(%e ) + 24x - 24x +--R * +--R atanh(x) 2 +--R (%e ) +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 24x + 24x )(%e ) + (48x - 48x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 48x + 48x )(%e ) + 24x - 24x +--R * +--R atanh(x) +--R %e +--R + +--R atanh(x) 8 atanh(x) 6 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 8x + 8x )(%e ) + (16x - 16x )(%e ) +--R + +--R atanh(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 16x + 16x )(%e ) + 8x - 8x +--R Type: Expression Integer +--E 80 + +--S 81 of 489 +t0216:= exp(1)^(1/3*atanh(x)) +--R +--R +--R atanh(x) +--R -------- +--R 3 +--R (66) %e +--R Type: Expression Integer +--E 81 + +--S 82 of 489 +r0216:= -(1-x)^(5/6)*(1+x)^(1/6)-2/3*atan((1-x)^(1/6)/(1+x)^(1/6))-_ + 1/3*atan(-3^(1/2)+2*(1-x)^(1/6)/(1+x)^(1/6))-_ + 1/3*atan(3^(1/2)+2*(1-x)^(1/6)/(1+x)^(1/6))-_ + 1/6*log(1+(1-x)^(1/3)/(1+x)^(1/3)-_ + 3^(1/2)*(1-x)^(1/6)/(1+x)^(1/6))*3^(1/2)+_ + 1/6*log(1+(1-x)^(1/3)/(1+x)^(1/3)+_ + 3^(1/2)*(1-x)^(1/6)/(1+x)^(1/6))*3^(1/2) +--R +--R +--R (67) +--R 3+-----+ 3+-------+ 6+-----+ +-+6+-------+3+-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|3 \|- x + 1 \|x + 1 +--R \|3 log(--------------------------------------------------------) +--R 3+-----+6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 3+-----+ 3+-------+ 6+-----+ +-+6+-------+3+-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|3 \|- x + 1 \|x + 1 +--R - \|3 log(--------------------------------------------------------) +--R 3+-----+6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-+6+-----+ 6+-------+ +-+6+-----+ 6+-------+ +--R \|3 \|x + 1 + 2\|- x + 1 \|3 \|x + 1 - 2\|- x + 1 +--R - 2atan(--------------------------) + 2atan(--------------------------) +--R 6+-----+ 6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 6+-------+ +--R \|- x + 1 6+-------+5 6+-----+ +--R - 4atan(----------) - 6\|- x + 1 \|x + 1 +--R 6+-----+ +--R \|x + 1 +--R / +--R 6 +--R Type: Expression Integer +--E 82 + +--S 83 of 489 +a0216:= integrate(t0216,x) +--R +--R +--R (68) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R log +--R - x - 1 2 +--R 3 2 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R sin(----------) + (%e ) +--R 2 +--R + +--R - x - 1 +--R 3 log(-------) 3 2 +--R atan(----) x - 1 atan(----) +--R +-+ ------------ +-+ +--R \|3 6 \|3 +--R 2cos(----------)%e + cos(----------) +--R 2 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R log +--R - x - 1 2 +--R 3 2 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R sin(----------) + (%e ) +--R 2 +--R + +--R - x - 1 +--R 3 log(-------) 3 2 +--R atan(----) x - 1 atan(----) +--R +-+ ------------ +-+ +--R \|3 6 \|3 +--R - 2cos(----------)%e + cos(----------) +--R 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R - 2sin(----------)atan(--------------------------------) +--R 2 - x - 1 +--R log(-------) 3 +--R x - 1 atan(----) +--R ------------ +-+ +--R 6 \|3 +--R %e - cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R - 2sin(----------)atan(--------------------------------) +--R 2 - x - 1 +--R log(-------) 3 +--R x - 1 atan(----) +--R ------------ +-+ +--R 6 \|3 +--R %e + cos(----------) +--R 2 +--R + +--R - x - 1 +--R log(-------) - x - 1 +--R x - 1 log(-------) +--R ------------ x - 1 +--R 6 ------------ +--R 2%e 6 +--R - atan(---------------------) + (3x - 3)%e +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) - 1 +--R / +--R 3 +--R Type: Union(Expression Integer,...) +--E 83 + +--S 84 of 489 +m0216:= a0216-r0216 +--R +--R +--R (69) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) +--R 2 +--R * +--R log +--R - x - 1 2 +--R 3 2 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R sin(----------) + (%e ) +--R 2 +--R + +--R - x - 1 +--R 3 log(-------) 3 2 +--R atan(----) x - 1 atan(----) +--R +-+ ------------ +-+ +--R \|3 6 \|3 +--R 2cos(----------)%e + cos(----------) +--R 2 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R 2cos(----------) +--R 2 +--R * +--R log +--R - x - 1 2 +--R 3 2 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R sin(----------) + (%e ) +--R 2 +--R + +--R - x - 1 +--R 3 log(-------) 3 2 +--R atan(----) x - 1 atan(----) +--R +-+ ------------ +-+ +--R \|3 6 \|3 +--R - 2cos(----------)%e + cos(----------) +--R 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R - 4sin(----------)atan(--------------------------------) +--R 2 - x - 1 +--R log(-------) 3 +--R x - 1 atan(----) +--R ------------ +-+ +--R 6 \|3 +--R %e - cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R - 4sin(----------)atan(--------------------------------) +--R 2 - x - 1 +--R log(-------) 3 +--R x - 1 atan(----) +--R ------------ +-+ +--R 6 \|3 +--R %e + cos(----------) +--R 2 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R 2%e +--R - 2atan(---------------------) +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) - 1 +--R + +--R 3+-----+ 3+-------+ 6+-----+ +-+6+-------+3+-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|3 \|- x + 1 \|x + 1 +--R - \|3 log(--------------------------------------------------------) +--R 3+-----+6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 3+-----+ 3+-------+ 6+-----+ +-+6+-------+3+-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|3 \|- x + 1 \|x + 1 +--R \|3 log(--------------------------------------------------------) +--R 3+-----+6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +-+6+-----+ 6+-------+ +--R 6 \|3 \|x + 1 + 2\|- x + 1 +--R (6x - 6)%e + 2atan(--------------------------) +--R 6+-----+ +--R \|x + 1 +--R + +--R +-+6+-----+ 6+-------+ 6+-------+ +--R \|3 \|x + 1 - 2\|- x + 1 \|- x + 1 +--R - 2atan(--------------------------) + 4atan(----------) +--R 6+-----+ 6+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 6+-------+5 6+-----+ +--R 6\|- x + 1 \|x + 1 +--R / +--R 6 +--R Type: Expression Integer +--E 84 + +--S 85 of 489 +d0216:= D(m0216,x) +--R +--R +--R (70) +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 60)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 26x + 20)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 52x + 40)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 38x + 6x + 20)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x +--R + +--R 2 +--R 33x - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 72)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 30x + 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 60x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 42x + 6x + 24)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R %e +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x + 33x +--R + +--R - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 36x - 96)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 24x + 44x + 32)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 48x + 88x + 64)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (36x - 12x - 68x + 12x + 32)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (18x + 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (72x + 60x - 72x - 60)\|- x + 1 \|x + 1 - 36x + 6x +--R + +--R 2 +--R 66x - 6x - 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 108x - 96x + 108x + 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 12x - 36x - 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (6x + 6x - 6x - 6)\|- x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 36x - 120)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 24x + 52x + 40)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 48x + 104x + 80)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (36x - 12x - 76x + 12x + 40)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 36x - 120)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 24x + 52x + 40)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 48x + 104x + 80)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (36x - 12x - 76x + 12x + 40)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (18x + 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (72x + 60x - 72x - 60)\|- x + 1 \|x + 1 - 36x + 6x +--R + +--R 2 +--R 66x - 6x - 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 108x - 96x + 108x + 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 12x - 36x - 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (6x + 6x - 6x - 6)\|- x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (18x + 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (72x + 60x - 72x - 60)\|- x + 1 \|x + 1 - 36x + 6x +--R + +--R 2 +--R 66x - 6x - 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 108x - 96x + 108x + 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 12x - 36x - 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (6x + 6x - 6x - 6)\|- x + 1 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 36x - 144)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 24x + 60x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 48x + 120x + 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (36x - 12x - 84x + 12x + 48)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 +--R 3 2 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R cos(----------) %e +--R 2 +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (18x + 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (72x + 60x - 72x - 60)\|- x + 1 \|x + 1 - 36x + 6x +--R + +--R 2 +--R 66x - 6x - 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 108x - 96x + 108x + 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 12x - 36x - 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (6x + 6x - 6x - 6)\|- x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 36)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 18x + 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 36x + 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 30x + 6x + 12)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 7 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x + 33x +--R + +--R - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R - x - 1 6 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (- 108x + 36x + 96)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (36x + 24x - 44x - 32)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (72x + 48x - 88x - 64)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (- 36x + 12x + 68x - 12x - 32)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 48)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 22x + 16)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 44x + 32)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 34x + 6x + 16)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 5 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (- 18x - 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (- 36x - 30x + 36x + 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (- 72x - 60x + 72x + 60)\|- x + 1 \|x + 1 + 36x - 6x +--R + +--R 2 +--R - 66x + 6x + 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (108x + 96x - 108x - 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (12x + 36x + 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (- 6x - 6x + 6x + 6)\|- x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x + 33x +--R + +--R - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 60)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 26x + 20)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 52x + 40)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 38x + 6x + 20)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (- 108x + 36x + 120)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (36x + 24x - 52x - 40)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (72x + 48x - 104x - 80)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (- 36x + 12x + 76x - 12x - 40)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x +--R + +--R 2 +--R 33x - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (- 18x - 18)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (- 36x - 30x + 36x + 30)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 +--R (- 72x - 60x + 72x + 60)\|- x + 1 \|x + 1 + 36x - 6x +--R + +--R 2 +--R - 66x + 6x + 30 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (108x + 96x - 108x - 96)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (12x + 36x + 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (- 6x - 6x + 6x + 6)\|- x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 18x - 72)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 12x + 30x + 24)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 24x + 60x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 3 2 6+-------+ +--R (18x - 6x - 42x + 6x + 24)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 +--R 3 4 log(-------) +--R atan(----) x - 1 +--R +-+ ------------ +--R \|3 6 +--R cos(----------) %e +--R 2 +--R + +--R 3+-------+6+-------+4 3+-----+2 6+-----+4 +--R (9x + 9)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+3+-----+2 +--R (18x + 15x - 18x - 15)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 3+-----+ 4 3 2 +--R (36x + 30x - 36x - 30)\|- x + 1 \|x + 1 - 18x + 3x + 33x +--R + +--R - 3x - 15 +--R * +--R 6+-----+2 +--R \|x + 1 +--R + +--R 3 2 3+-------+6+-------+2 3+-----+2 +--R (- 54x - 48x + 54x + 48)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 3+-------+2 6+-------+2 3+-----+ +--R (- 6x - 18x - 12)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 6+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R / +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 72x + 72x + 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (36x - 72x + 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 72x + 72x + 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (36x - 72x + 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 72x + 72x + 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (36x - 72x + 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (108x - 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 72x - 72x + 72x + 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (36x - 72x + 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 6 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (- 108x + 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (36x + 36x - 36x - 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (72x + 72x - 72x - 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (- 36x + 72x - 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (- 108x + 108)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (36x + 36x - 36x - 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (72x + 72x - 72x - 72)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (- 36x + 72x - 36)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 6 +--R (%e ) +--R + +--R 2 3+-------+6+-------+3 3+-----+2 6+-----+5 +--R (54x - 54)\|- x + 1 \|- x + 1 \|x + 1 \|x + 1 +--R + +--R 3 2 3+-------+6+-------+3+-----+2 +--R (- 18x - 18x + 18x + 18)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 6+-------+3+-----+ +--R (- 36x - 36x + 36x + 36)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 4 2 6+-------+ +--R (18x - 36x + 18)\|- x + 1 +--R * +--R 6+-----+ +--R \|x + 1 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R Type: Expression Integer +--E 85 + +--S 86 of 489 +t0217:= exp(1)^(2/3*atanh(x)) +--R +--R +--R 2atanh(x) +--R --------- +--R 3 +--R (71) %e +--R Type: Expression Integer +--E 86 + +--S 87 of 489 +r0217:= -(1-x)^(2/3)*(1+x)^(1/3)+_ + 2/3*atan(1/3*(1-2*(1-x)^(1/3)/(1+x)^(1/3))*3^(1/2))*3^(1/2)-_ + 1/3*log(1+(1-x)^(2/3)/(1+x)^(2/3)-(1-x)^(1/3)/(1+x)^(1/3))+_ + 2/3*log(1+(1-x)^(1/3)/(1+x)^(1/3)) +--R +--R +--R (72) +--R 3+-----+ 3+-------+ +--R \|x + 1 + \|- x + 1 +--R 2log(---------------------) +--R 3+-----+ +--R \|x + 1 +--R + +--R 3+-----+2 3+-------+3+-----+ 3+-------+2 +--R \|x + 1 - \|- x + 1 \|x + 1 + \|- x + 1 +--R - log(--------------------------------------------) +--R 3+-----+2 +--R \|x + 1 +--R + +--R +-+3+-----+ +-+3+-------+ +--R +-+ \|3 \|x + 1 - 2\|3 \|- x + 1 3+-------+2 3+-----+ +--R 2\|3 atan(------------------------------) - 3\|- x + 1 \|x + 1 +--R 3+-----+ +--R 3\|x + 1 +--R / +--R 3 +--R Type: Expression Integer +--E 87 + +--S 88 of 489 +a0217:= integrate(t0217,x) +--R +--R +--R (73) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 3 3 +--R - \|3 log((%e ) - %e + 1) +--R + +--R - x - 1 +--R - x - 1 log(-------) +--R log(-------) x - 1 +--R x - 1 ------------ +--R ------------ +-+ 3 +-+ +--R +-+ 3 2\|3 %e - \|3 +--R 2\|3 log(%e + 1) + 6atan(--------------------------) +--R 3 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 3 +--R (3x - 3)\|3 %e +--R / +--R +-+ +--R 3\|3 +--R Type: Union(Expression Integer,...) +--E 88 + +--S 89 of 489 +m0217:= a0217-r0217 +--R +--R +--R (74) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-+ 3 3 +--R - \|3 log((%e ) - %e + 1) +--R + +--R - x - 1 +--R - x - 1 log(-------) +--R log(-------) x - 1 +--R x - 1 ------------ +--R ------------ +-+ 3 +-+ +--R +-+ 3 2\|3 %e - \|3 +--R 2\|3 log(%e + 1) + 6atan(--------------------------) +--R 3 +--R + +--R 3+-----+ 3+-------+ +--R +-+ \|x + 1 + \|- x + 1 +--R - 2\|3 log(---------------------) +--R 3+-----+ +--R \|x + 1 +--R + +--R 3+-----+2 3+-------+3+-----+ 3+-------+2 +--R +-+ \|x + 1 - \|- x + 1 \|x + 1 + \|- x + 1 +--R \|3 log(--------------------------------------------) +--R 3+-----+2 +--R \|x + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +-+3+-----+ +-+3+-------+ +--R +-+ 3 \|3 \|x + 1 - 2\|3 \|- x + 1 +--R (3x - 3)\|3 %e - 6atan(------------------------------) +--R 3+-----+ +--R 3\|x + 1 +--R + +--R +-+3+-------+2 3+-----+ +--R 3\|3 \|- x + 1 \|x + 1 +--R / +--R +-+ +--R 3\|3 +--R Type: Expression Integer +--E 89 + +--S 90 of 489 +d0217:= D(m0217,x) +--R +--R +--R (75) +--R 3 2 3+-----+2 +--R (3x - 5x + x + 1)\|x + 1 +--R + +--R 3 2 3+-------+3+-----+ +--R (- 3x - x + 3x + 1)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + x - 3x - 1)\|- x + 1 +--R * +--R - x - 1 4 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 +--R (%e ) +--R + +--R 3 2 3+-----+2 +--R (3x + 3x - 3x - 3)\|x + 1 +--R + +--R 3 2 3+-------+3+-----+ +--R (- 3x - 3x + 3x + 3)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 +--R (%e ) +--R + +--R 3 2 3+-----+2 +--R (3x - 5x - 3x + 5)\|x + 1 +--R + +--R 3 2 3+-------+3+-----+ +--R (- 3x - x + 7x + 5)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + x - 7x - 5)\|- x + 1 +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 +--R %e +--R + +--R 3 2 3+-----+2 3 2 3+-------+3+-----+ +--R (3x + 3x - 3x - 3)\|x + 1 + (- 3x - 3x + 3x + 3)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R / +--R 3 2 3+-----+2 +--R (3x - 3x - 3x + 3)\|x + 1 +--R + +--R 3 2 3+-------+3+-----+ +--R (- 3x - 3x + 3x + 3)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R * +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 +--R (%e ) +--R + +--R 3 2 3+-----+2 3 2 3+-------+3+-----+ +--R (3x - 3x - 3x + 3)\|x + 1 + (- 3x - 3x + 3x + 3)\|- x + 1 \|x + 1 +--R + +--R 3 2 3+-------+2 +--R (3x + 3x - 3x - 3)\|- x + 1 +--R Type: Expression Integer +--E 90 + +--S 91 of 489 +t0218:= exp(1)^(1/4*atanh(x)) +--R +--R +--R atanh(x) +--R -------- +--R 4 +--R (76) %e +--R Type: Expression Integer +--E 91 + +--S 92 of 489 +r0218:= -(1-x)^(7/8)*(1+x)^(1/8)-_ + 1/2*atan(sec(1/8*%pi)*((1-x)^(1/8)/(1+x)^(1/8)-sin(1/8*%pi)))*_ + cos(1/8*%pi)-1/2*atan(sec(1/8*%pi)*((1-x)^(1/8)/(1+x)^(1/8)+_ + sin(1/8*%pi)))*cos(1/8*%pi)-1/4*cos(1/8*%pi)*_ + log(1+(1-x)^(1/4)/(1+x)^(1/4)-2*(1-x)^(1/8)*_ + cos(1/8*%pi)/(1+x)^(1/8))+1/4*cos(1/8*%pi)*_ + log(1+(1-x)^(1/4)/(1+x)^(1/4)+2*(1-x)^(1/8)*_ + cos(1/8*%pi)/(1+x)^(1/8))-1/2*atan(((1-x)^(1/8)/(1+x)^(1/8)-_ + cos(1/8*%pi))*csc(1/8*%pi))*sin(1/8*%pi)-_ + 1/2*atan(((1-x)^(1/8)/(1+x)^(1/8)+cos(1/8*%pi))*csc(1/8*%pi))*_ + sin(1/8*%pi)-1/4*log(1+(1-x)^(1/4)/(1+x)^(1/4)-2*(1-x)^(1/8)*_ + sin(1/8*%pi)/(1+x)^(1/8))*sin(1/8*%pi)+_ + 1/4*log(1+(1-x)^(1/4)/(1+x)^(1/4)+2*(1-x)^(1/8)*_ + sin(1/8*%pi)/(1+x)^(1/8))*sin(1/8*%pi) +--R +--R +--R (77) +--R %pi +--R sin(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + 2sin(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R %pi +--R cos(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + 2cos(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - +--R %pi +--R cos(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - 2cos(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - +--R %pi +--R sin(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - 2sin(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R sec(---)sin(---)\|x + 1 + sec(---)\|- x + 1 +--R %pi 8 8 8 +--R - 2cos(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R sec(---)sin(---)\|x + 1 - sec(---)\|- x + 1 +--R %pi 8 8 8 +--R 2cos(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R cos(---)csc(---)\|x + 1 + csc(---)\|- x + 1 +--R %pi 8 8 8 +--R - 2sin(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R cos(---)csc(---)\|x + 1 - csc(---)\|- x + 1 +--R %pi 8 8 8 +--R 2sin(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R 8+-------+7 8+-----+ +--R - 4\|- x + 1 \|x + 1 +--R / +--R 4 +--R Type: Expression Integer +--E 92 + +--S 93 of 489 +a0218:= integrate(t0218,x) +--R +--R +--R (78) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 8+---+ 8 8+---+ +-+ 8 8+---+2 +--R \|- 1 log((%e ) + \|- 1 \|2 %e + \|- 1 ) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 8+---+ 8 8+---+ +-+ 8 8+---+2 +--R - \|- 1 log((%e ) - \|- 1 \|2 %e + \|- 1 ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8+---+ +-+ 8 8+---+ +--R \|- 1 \|2 log(%e + \|- 1 ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8+---+ +-+ 8 8+---+ +--R - \|- 1 \|2 log(%e - \|- 1 ) +--R + +--R 8+---+ +--R 8+---+ +-+ \|- 1 +--R - 2\|- 1 \|2 atan(--------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8 +--R %e +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 8 8+---+ +--R \|2 %e - \|- 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R 8+---+ ------------ +--R 8+---+ \|- 1 +-+ 8 +--R - 2\|- 1 atan(---------------------------) + (4x - 4)\|2 %e +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 8 8+---+ +--R \|2 %e + \|- 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression Integer,...) +--E 93 + +--S 94 of 489 +m0218:= a0218-r0218 +--R +--R +--R (79) +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 8+---+ 8 8+---+ +-+ 8 8+---+2 +--R \|- 1 log((%e ) + \|- 1 \|2 %e + \|- 1 ) +--R + +--R - x - 1 2 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 8+---+ 8 8+---+ +-+ 8 8+---+2 +--R - \|- 1 log((%e ) - \|- 1 \|2 %e + \|- 1 ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8+---+ +-+ 8 8+---+ +--R \|- 1 \|2 log(%e + \|- 1 ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8+---+ +-+ 8 8+---+ +--R - \|- 1 \|2 log(%e - \|- 1 ) +--R + +--R 8+---+ +--R 8+---+ +-+ \|- 1 +--R - 2\|- 1 \|2 atan(--------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 8 +--R %e +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 8 8+---+ +--R \|2 %e - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------------------) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 8 8+---+ +--R \|2 %e + \|- 1 +--R + +--R - +--R +-+ %pi +--R \|2 sin(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + 2sin(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - +--R +-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 + 2cos(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - 2cos(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-+ %pi +--R \|2 sin(---) +--R 8 +--R * +--R 4+-----+ 4+-------+ 8+-----+ %pi 8+-------+4+-----+ +--R (\|x + 1 + \|- x + 1 )\|x + 1 - 2sin(---)\|- x + 1 \|x + 1 +--R 8 +--R log(-------------------------------------------------------------) +--R 4+-----+8+-----+ +--R \|x + 1 \|x + 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-+ 8 +--R (4x - 4)\|2 %e +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R sec(---)sin(---)\|x + 1 + sec(---)\|- x + 1 +--R +-+ %pi 8 8 8 +--R 2\|2 cos(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R sec(---)sin(---)\|x + 1 - sec(---)\|- x + 1 +--R +-+ %pi 8 8 8 +--R - 2\|2 cos(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R cos(---)csc(---)\|x + 1 + csc(---)\|- x + 1 +--R +-+ %pi 8 8 8 +--R 2\|2 sin(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R %pi %pi 8+-----+ %pi 8+-------+ +--R cos(---)csc(---)\|x + 1 - csc(---)\|- x + 1 +--R +-+ %pi 8 8 8 +--R - 2\|2 sin(---)atan(---------------------------------------------) +--R 8 8+-----+ +--R \|x + 1 +--R + +--R +-+8+-------+7 8+-----+ +--R 4\|2 \|- x + 1 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression Integer +--E 94 + +--S 95 of 489 +--d0218:= D(m0218,x) +--E 95 + +--S 96 of 489 +t0219:= x^2*exp(1)^atanh(a+b*x)/(1-a^2-2*a*b*x-b^2*x^2) +--R +--R +--R 2 atanh(b x + a) +--R x %e +--R (80) - ---------------------- +--R 2 2 2 +--R b x + 2a b x + a - 1 +--R Type: Expression Integer +--E 96 + +--S 97 of 489 +r0219:= 2*exp(1)^atanh(a+b*x)/b^3-3*a*exp(1)^atanh(a+b*x)/b^3+_ + a^2*exp(1)^atanh(a+b*x)/b^3-exp(1)^atanh(a+b*x)*x/b^2-_ + asin(a+b*x)/b^3+2*a*asin(a+b*x)/b^3 +--R +--R +--R 2 atanh(b x + a) +--R (- b x + a - 3a + 2)%e + (2a - 1)asin(b x + a) +--R (81) ------------------------------------------------------------- +--R 3 +--R b +--R Type: Expression Integer +--E 97 + +--S 98 of 489 +a0219:= integrate(t0219,x) +--R +--R +--R (82) +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (4a - 2)atan(%e ) +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 2 +--R (- b x + a - 3a + 2)%e +--R / +--R 3 +--R b +--R Type: Union(Expression Integer,...) +--E 98 + +--S 99 of 489 +m0219:= a0219-r0219 +--R +--R +--R (83) +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (4a - 2)atan(%e ) +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 2 +--R (- b x + a - 3a + 2)%e +--R + +--R 2 atanh(b x + a) +--R (b x - a + 3a - 2)%e + (- 2a + 1)asin(b x + a) +--R / +--R 3 +--R b +--R Type: Expression Integer +--E 99 + +--S 100 of 489 +d0219:= D(m0219,x) +--R +--R +--R (84) +--R +------------------------+ +--R 2 2 2 | 2 2 2 +--R (- b x + (- 2a + 1)b x - 2a + 3a - 1)\|- b x - 2a b x - a + 1 +--R * +--R - b x - a - 1 3 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R +------------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + (2a - 1)b x + 2a - 3a + 1)\|- b x - 2a b x - a + 1 +--R * +--R atanh(b x + a) +--R %e +--R + +--R 2 2 2 3 2 +--R (- 2a + 1)b x + (- 4a + 2a)b x - 2a + a + 2a - 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R +------------------------+ +--R 2 2 2 | 2 2 2 +--R (- b x + (- 2a + 1)b x - 2a - a + 1)\|- b x - 2a b x - a + 1 +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R +------------------------+ +--R 2 2 2 | 2 2 2 +--R (b x + (2a - 1)b x + 2a - 3a + 1)\|- b x - 2a b x - a + 1 +--R * +--R atanh(b x + a) +--R %e +--R + +--R 2 2 2 3 2 +--R (- 2a + 1)b x + (- 4a + 2a)b x - 2a + a + 2a - 1 +--R / +--R +------------------------+ +--R 4 2 3 2 2 | 2 2 2 +--R (b x + 2a b x + (a - 1)b )\|- b x - 2a b x - a + 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R +------------------------+ +--R 4 2 3 2 2 | 2 2 2 +--R (b x + 2a b x + (a - 1)b )\|- b x - 2a b x - a + 1 +--R Type: Expression Integer +--E 100 + +--S 101 of 489 +t0220:= x*exp(1)^atanh(a+b*x)/(1-a^2-2*a*b*x-b^2*x^2) +--R +--R +--R atanh(b x + a) +--R x %e +--R (85) - ---------------------- +--R 2 2 2 +--R b x + 2a b x + a - 1 +--R Type: Expression Integer +--E 101 + +--S 102 of 489 +r0220:= exp(1)^atanh(a+b*x)/b^2-a*exp(1)^atanh(a+b*x)/b^2-asin(a+b*x)/b^2 +--R +--R +--R atanh(b x + a) +--R (- a + 1)%e - asin(b x + a) +--R (86) ----------------------------------------- +--R 2 +--R b +--R Type: Expression Integer +--E 102 + +--S 103 of 489 +a0220:= integrate(t0220,x) +--R +--R +--R - b x - a - 1 - b x - a - 1 +--R log(-------------) log(-------------) +--R b x + a - 1 b x + a - 1 +--R ------------------ ------------------ +--R 2 2 +--R - 2atan(%e ) + (- a + 1)%e +--R (87) ------------------------------------------------------------- +--R 2 +--R b +--R Type: Union(Expression Integer,...) +--E 103 + +--S 104 of 489 +m0220:= a0220-r0220 +--R +--R +--R (88) +--R - b x - a - 1 - b x - a - 1 +--R log(-------------) log(-------------) +--R b x + a - 1 b x + a - 1 +--R ------------------ ------------------ +--R 2 2 +--R - 2atan(%e ) + (- a + 1)%e +--R + +--R atanh(b x + a) +--R (a - 1)%e + asin(b x + a) +--R / +--R 2 +--R b +--R Type: Expression Integer +--E 104 + +--S 105 of 489 +d0220:= D(m0220,x) +--R +--R +--R (89) +--R - b x - a - 1 3 +--R log(-------------) +--R b x + a - 1 +--R +------------------------+ ------------------ +--R | 2 2 2 2 +--R (a - 1)\|- b x - 2a b x - a + 1 (%e ) +--R + +--R +------------------------+ +--R | 2 2 2 atanh(b x + a) 2 2 +--R (- a + 1)\|- b x - 2a b x - a + 1 %e + b x + 2a b x +--R + +--R 2 +--R a - 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------------------------+ ------------------ +--R | 2 2 2 2 +--R (a + 1)\|- b x - 2a b x - a + 1 %e +--R + +--R +------------------------+ +--R | 2 2 2 atanh(b x + a) 2 2 2 +--R (- a + 1)\|- b x - 2a b x - a + 1 %e + b x + 2a b x + a +--R + +--R - 1 +--R / +--R +------------------------+ +--R 3 2 2 2 | 2 2 2 +--R (b x + 2a b x + (a - 1)b)\|- b x - 2a b x - a + 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R +------------------------+ +--R 3 2 2 2 | 2 2 2 +--R (b x + 2a b x + (a - 1)b)\|- b x - 2a b x - a + 1 +--R Type: Expression Integer +--E 105 + +--S 106 of 489 +t0221:= exp(1)^atanh(a+b*x)/x/(1-a^2-2*a*b*x-b^2*x^2) +--R +--R +--R atanh(b x + a) +--R %e +--R (90) - -------------------------- +--R 2 3 2 2 +--R b x + 2a b x + (a - 1)x +--R Type: Expression Integer +--E 106 + +--S 107 of 489 +r0221:= exp(1)^atanh(a+b*x)/(1-a)-2*atanh((-1+a)^(1/2)*_ + exp(1)^atanh(a+b*x)/(-1-a)^(1/2))/(-1-a)^(1/2)/(-1+a)^(3/2) +--R +--R +--R (91) +--R +-----+ atanh(b x + a) +--R \|a - 1 %e +-------+ +-----+ atanh(b x + a) +--R - 2atanh(------------------------) - \|- a - 1 \|a - 1 %e +--R +-------+ +--R \|- a - 1 +--R ----------------------------------------------------------------------- +--R +-------+ +-----+ +--R (a - 1)\|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 107 + +--S 108 of 489 +a0221:= integrate(t0221,x) +--R +--R +--R (92) +--R [ +--R log +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 3 2 2 +--R ((a - 1)b x + a - a - a + 1)%e +--R + +--R +--------+ +--R 2 | 2 +--R (- a b x - a + 1)\|- a + 1 +--R / +--R x +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +--------+ ------------------ +--R | 2 2 +--R - \|- a + 1 %e +--R / +--R +--------+ +--R | 2 +--R (a - 1)\|- a + 1 +--R , +--R - b x - a - 1 +--R log(-------------) - b x - a - 1 +--R b x + a - 1 log(-------------) +--R +------+ ------------------ b x + a - 1 +--R | 2 2 +------+ ------------------ +--R \|a - 1 %e | 2 2 +--R 2atan(-----------------------------) - \|a - 1 %e +--R a + 1 +--R --------------------------------------------------------------------] +--R +------+ +--R | 2 +--R (a - 1)\|a - 1 +--R Type: Union(List Expression Integer,...) +--E 108 + +--S 109 of 489 +m0221a:= a0221.1-r0221 +--R +--R +--R (93) +--R +-------+ +-----+ +--R \|- a - 1 \|a - 1 +--R * +--R log +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 3 2 2 +--R ((a - 1)b x + a - a - a + 1)%e +--R + +--R +--------+ +--R 2 | 2 +--R (- a b x - a + 1)\|- a + 1 +--R / +--R x +--R + +--R +--------+ +-----+ atanh(b x + a) +--R | 2 \|a - 1 %e +--R 2\|- a + 1 atanh(------------------------) +--R +-------+ +--R \|- a - 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +--------+ ------------------ +--R | 2 +-------+ +-----+ 2 +--R - \|- a + 1 \|- a - 1 \|a - 1 %e +--R + +--R +--------+ +--R | 2 +-------+ +-----+ atanh(b x + a) +--R \|- a + 1 \|- a - 1 \|a - 1 %e +--R / +--R +--------+ +--R | 2 +-------+ +-----+ +--R (a - 1)\|- a + 1 \|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 109 + +--S 110 of 489 +d0221a:= D(m0221a,x) +--R +--R +--R (94) +--R 2 2 2 3 2 atanh(b x + a) 2 +--R ((a - 1)b x + (a - a - a + 1)b x)(%e ) +--R + +--R 2 2 2 3 2 +--R (a + 2a + 1)b x + (a + a - a - 1)b x +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 2 2 2 3 2 atanh(b x + a) 3 +--R ((- a + 1)b x + (- a + a + a - 1)b x)(%e ) +--R + +--R +--------+ +--R 2 3 2 | 2 atanh(b x + a) 2 +--R ((a - a)b x + a - a - a + 1)\|- a + 1 (%e ) +--R + +--R 2 2 2 3 2 atanh(b x + a) +--R ((- a + 1)b x + (- a + a + a - 1)b x)%e +--R + +--R +--------+ +--R 2 3 2 | 2 +--R ((a + a)b x + a + a - a - 1)\|- a + 1 +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R +--------+ +--R 2 2 2 | 2 atanh(b x + a) 3 +--R (a b x + (a - 1)b x)\|- a + 1 (%e ) +--R + +--R 2 2 2 3 4 2 atanh(b x + a) 2 +--R ((a - 1)b x + (2a - 2a)b x + a - 2a + 1)(%e ) +--R + +--R +--------+ +--R 2 2 2 | 2 atanh(b x + a) 2 2 2 +--R (a b x + (a - 1)b x)\|- a + 1 %e + (a + 2a + 1)b x +--R + +--R 3 2 4 3 +--R (2a + 4a + 2a)b x + a + 2a - 2a - 1 +--R / +--R 3 2 3 4 4 3 2 2 3 +--R (a - a - a + 1)b x + (3a - 4a - 2a + 4a - 1)b x +--R + +--R 5 4 3 2 2 +--R (3a - 5a - 2a + 6a - a - 1)b x +--R + +--R 6 5 4 3 2 +--R (a - 2a - a + 4a - a - 2a + 1)x +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 3 2 3 4 4 3 2 2 3 +--R (a + a - a - 1)b x + (3a + 2a - 4a - 2a + 1)b x +--R + +--R 5 4 3 2 2 6 4 2 +--R (3a + a - 6a - 2a + 3a + 1)b x + (a - 3a + 3a - 1)x +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R 2 3 4 3 2 2 3 +--R (- a + a)b x + (- 3a + 3a + a - 1)b x +--R + +--R 4 3 2 2 5 4 3 2 +--R (- 3a + 3a + 3a - 3a)b x + (- a + a + 2a - 2a - a + 1)x +--R * +--R +--------+ +--R | 2 atanh(b x + a) 2 +--R \|- a + 1 (%e ) +--R + +--R 2 3 4 3 2 2 3 +--R (- a - a)b x + (- 3a - 3a + a + 1)b x +--R + +--R 4 3 2 2 5 4 3 2 +--R (- 3a - 3a + 3a + 3a)b x + (- a - a + 2a + 2a - a - 1)x +--R * +--R +--------+ +--R | 2 +--R \|- a + 1 +--R Type: Expression Integer +--E 110 + +--S 111 of 489 +m0221b:= a0221.2-r0221 +--R +--R +--R (95) +--R +------+ +-----+ atanh(b x + a) +--R | 2 \|a - 1 %e +--R 2\|a - 1 atanh(------------------------) +--R +-------+ +--R \|- a - 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R | 2 2 +--R +-------+ +-----+ \|a - 1 %e +--R 2\|- a - 1 \|a - 1 atan(-----------------------------) +--R a + 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R +-------+ +-----+ | 2 2 +--R - \|- a - 1 \|a - 1 \|a - 1 %e +--R + +--R +------+ +--R +-------+ +-----+ | 2 atanh(b x + a) +--R \|- a - 1 \|a - 1 \|a - 1 %e +--R / +--R +------+ +--R +-------+ +-----+ | 2 +--R (a - 1)\|- a - 1 \|a - 1 \|a - 1 +--R Type: Expression Integer +--E 111 + +--S 112 of 489 +d0221b:= D(m0221b,x) +--R +--R +--R (96) +--R - b x - a - 1 3 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R atanh(b x + a) 2 2 +--R ((a - 1)b (%e ) + (a + 1)b)(%e ) +--R + +--R atanh(b x + a) 3 atanh(b x + a) +--R ((- a + 1)b (%e ) + (- a + 1)b %e ) +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R atanh(b x + a) 2 2 +--R ((a - 1)b (%e ) + (a + 1)b)%e +--R + +--R atanh(b x + a) 3 atanh(b x + a) +--R (- a - 1)b (%e ) + (- a - 1)b %e +--R / +--R 2 2 2 3 2 4 3 +--R ((a - 2a + 1)b x + (2a - 4a + 2a)b x + a - 2a + 2a - 1) +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 2 2 2 3 4 2 +--R (a - 1)b x + (2a - 2a)b x + a - 2a + 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 2 2 2 3 4 2 atanh(b x + a) 2 +--R ((a - 1)b x + (2a - 2a)b x + a - 2a + 1)(%e ) +--R + +--R 2 2 2 3 2 4 3 +--R (a + 2a + 1)b x + (2a + 4a + 2a)b x + a + 2a - 2a - 1 +--R Type: Expression Integer +--E 112 + +--S 113 of 489 +t0222:= exp(1)^atanh(a+b*x)/x^2/(1-a^2-2*a*b*x-b^2*x^2) +--R +--R +--R atanh(b x + a) +--R %e +--R (97) - --------------------------- +--R 2 4 3 2 2 +--R b x + 2a b x + (a - 1)x +--R Type: Expression Integer +--E 113 + +--S 114 of 489 +r0222:= b*exp(1)^atanh(a+b*x)/(1-a)^2+_ + 2*b*exp(1)^atanh(a+b*x)/(1-a)^2/(1+a)/(1+a+(-1+a)*(-1+2/(1-a-b*x)))+_ + 2*b*atanh((-1+a)^(1/2)*exp(1)^atanh(a+b*x)/_ + (-1-a)^(1/2))/(-1-a)^(3/2)/(-1+a)^(5/2)+_ + 4*b*atanh((-1+a)^(1/2)*exp(1)^atanh(a+b*x)/(-1-a)^(1/2))/_ + (-1-a)^(1/2)/(-1+a)^(5/2) +--R +--R +--R (98) +--R +-----+ atanh(b x + a) +--R \|a - 1 %e +--R (4a + 2)b x atanh(------------------------) +--R +-------+ +--R \|- a - 1 +--R + +--R +-------+ +-----+ atanh(b x + a) +--R ((a + 2)b x + a - 1)\|- a - 1 \|a - 1 %e +--R / +--R 3 2 +-------+ +-----+ +--R (a - a - a + 1)x\|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 114 + +--S 115 of 489 +a0222:= integrate(t0222,x) +--R +--R +--R (99) +--R [ +--R (2a + 1)b x +--R * +--R log +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 3 2 2 +--R ((- a + 1)b x - a + a + a - 1)%e +--R + +--R +--------+ +--R 2 | 2 +--R (- a b x - a + 1)\|- a + 1 +--R / +--R x +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +--------+ ------------------ +--R | 2 2 +--R ((a + 2)b x + a - 1)\|- a + 1 %e +--R / +--R +--------+ +--R 3 2 | 2 +--R (a - a - a + 1)x\|- a + 1 +--R , +--R +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R | 2 2 +--R \|a - 1 %e +--R (- 4a - 2)b x atan(-----------------------------) +--R a + 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R | 2 2 +--R ((a + 2)b x + a - 1)\|a - 1 %e +--R / +--R +------+ +--R 3 2 | 2 +--R (a - a - a + 1)x\|a - 1 +--R ] +--R Type: Union(List Expression Integer,...) +--E 115 + +--S 116 of 489 +m0222a:= a0222.1-r0222 +--R +--R +--R (100) +--R +-------+ +-----+ +--R (2a + 1)b x\|- a - 1 \|a - 1 +--R * +--R log +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 3 2 2 +--R ((- a + 1)b x - a + a + a - 1)%e +--R + +--R +--------+ +--R 2 | 2 +--R (- a b x - a + 1)\|- a + 1 +--R / +--R x +--R + +--R +--------+ +-----+ atanh(b x + a) +--R | 2 \|a - 1 %e +--R (- 4a - 2)b x\|- a + 1 atanh(------------------------) +--R +-------+ +--R \|- a - 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +--------+ ------------------ +--R | 2 +-------+ +-----+ 2 +--R ((a + 2)b x + a - 1)\|- a + 1 \|- a - 1 \|a - 1 %e +--R + +--R +--------+ +--R | 2 +-------+ +-----+ atanh(b x + a) +--R ((- a - 2)b x - a + 1)\|- a + 1 \|- a - 1 \|a - 1 %e +--R / +--R +--------+ +--R 3 2 | 2 +-------+ +-----+ +--R (a - a - a + 1)x\|- a + 1 \|- a - 1 \|a - 1 +--R Type: Expression Integer +--E 116 + +--S 117 of 489 +d0222a:= D(m0222a,x) +--R +--R +--R (101) +--R 3 2 3 3 4 3 2 2 2 +--R (- 2a - a + 2a + 1)b x + (- 4a + 2a + 6a - 2a - 2)b x +--R + +--R 5 4 3 2 6 5 4 3 2 +--R (- 3a + 4a + 4a - 6a - a + 2)b x - a + 2a + a - 4a + a +--R + +--R 2a - 1 +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 3 2 3 3 4 3 2 2 2 +--R (- 2a - 5a - 4a - 1)b x + (- 4a - 6a + 2a + 6a + 2)b x +--R + +--R 5 4 3 2 6 4 2 +--R (- 3a - 2a + 6a + 4a - 3a - 2)b x - a + 3a - 3a + 1 +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 3 2 3 3 4 3 2 2 2 +--R (2a + a - 2a - 1)b x + (4a - 2a - 6a + 2a + 2)b x +--R + +--R 5 4 3 2 6 5 4 3 2 +--R (3a - 4a - 4a + 6a + a - 2)b x + a - 2a - a + 4a - a +--R + +--R - 2a + 1 +--R * +--R atanh(b x + a) 3 +--R (%e ) +--R + +--R +--------+ +--R 4 3 2 5 4 3 2 | 2 +--R ((- a + a + a - a)b x - a + a + 2a - 2a - a + 1)\|- a + 1 +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 3 2 3 3 4 3 2 2 2 +--R (2a + a - 2a - 1)b x + (4a + 2a - 4a - 2a)b x +--R + +--R 5 4 3 2 6 4 2 +--R (3a + 2a - 6a - 4a + 3a + 2)b x + a - 3a + 3a - 1 +--R * +--R atanh(b x + a) +--R %e +--R + +--R +--------+ +--R 4 3 2 5 4 3 2 | 2 +--R ((- a - a + a + a)b x - a - a + 2a + 2a - a - 1)\|- a + 1 +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R 2 3 3 3 2 2 4 3 2 +--R (2a + a)b x + (4a - 3a - 1)b x + (3a - 2a - 4a + 2a + 1)b x +--R + +--R 5 4 3 2 +--R a - a - 2a + 2a + a - 1 +--R * +--R +--------+ +--R | 2 atanh(b x + a) 3 +--R \|- a + 1 (%e ) +--R + +--R 3 2 3 3 4 3 2 2 2 +--R (- 2a - a + 2a + 1)b x + (- 4a - 2a + 4a + 2a)b x +--R + +--R 5 4 3 2 +--R (- 2a - a + 4a + 2a - 2a - 1)b x +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 2 3 3 3 2 2 2 +--R (2a + a)b x + (4a + 4a - a - 1)b x +--R + +--R 4 3 2 5 4 3 2 +--R (3a + 4a - 2a - 4a - 1)b x + a + a - 2a - 2a + a + 1 +--R * +--R +--------+ +--R | 2 atanh(b x + a) +--R \|- a + 1 %e +--R + +--R 3 2 3 3 4 3 2 2 2 +--R (- 2a - 5a - 4a - 1)b x + (- 4a - 10a - 8a - 2a)b x +--R + +--R 5 4 3 2 +--R (- 2a - 5a - 2a + 4a + 4a + 1)b x +--R / +--R 5 4 3 2 3 5 +--R (a - a - 2a + 2a + a - 1)b x +--R + +--R 6 5 4 3 2 2 4 +--R (3a - 4a - 5a + 8a + a - 4a + 1)b x +--R + +--R 7 6 5 4 3 2 3 +--R (3a - 5a - 5a + 11a + a - 7a + a + 1)b x +--R + +--R 8 7 6 5 3 2 2 +--R (a - 2a - 2a + 6a - 6a + 2a + 2a - 1)x +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 5 4 3 2 3 5 +--R (a + a - 2a - 2a + a + 1)b x +--R + +--R 6 5 4 3 2 2 4 +--R (3a + 2a - 7a - 4a + 5a + 2a - 1)b x +--R + +--R 7 6 5 4 3 2 3 +--R (3a + a - 9a - 3a + 9a + 3a - 3a - 1)b x +--R + +--R 8 6 4 2 2 +--R (a - 4a + 6a - 4a + 1)x +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R 4 3 2 3 5 5 4 3 2 2 4 +--R (a - a - a + a)b x + (3a - 3a - 4a + 4a + a - 1)b x +--R + +--R 6 5 4 3 2 3 +--R (3a - 3a - 6a + 6a + 3a - 3a)b x +--R + +--R 7 6 5 4 3 2 2 +--R (a - a - 3a + 3a + 3a - 3a - a + 1)x +--R * +--R +--------+ +--R | 2 atanh(b x + a) 2 +--R \|- a + 1 (%e ) +--R + +--R 4 3 2 3 5 5 4 3 2 2 4 +--R (a + a - a - a)b x + (3a + 3a - 4a - 4a + a + 1)b x +--R + +--R 6 5 4 3 2 3 +--R (3a + 3a - 6a - 6a + 3a + 3a)b x +--R + +--R 7 6 5 4 3 2 2 +--R (a + a - 3a - 3a + 3a + 3a - a - 1)x +--R * +--R +--------+ +--R | 2 +--R \|- a + 1 +--R Type: Expression Integer +--E 117 + +--S 118 of 489 +m0222b:= a0222.2-r0222 +--R +--R +--R (102) +--R +------+ +-----+ atanh(b x + a) +--R | 2 \|a - 1 %e +--R (- 4a - 2)b x\|a - 1 atanh(------------------------) +--R +-------+ +--R \|- a - 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R | 2 2 +--R +-------+ +-----+ \|a - 1 %e +--R (- 4a - 2)b x\|- a - 1 \|a - 1 atan(-----------------------------) +--R a + 1 +--R + +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R +------+ ------------------ +--R +-------+ +-----+ | 2 2 +--R ((a + 2)b x + a - 1)\|- a - 1 \|a - 1 \|a - 1 %e +--R + +--R +------+ +--R +-------+ +-----+ | 2 atanh(b x + a) +--R ((- a - 2)b x - a + 1)\|- a - 1 \|a - 1 \|a - 1 %e +--R / +--R +------+ +--R 3 2 +-------+ +-----+ | 2 +--R (a - a - a + 1)x\|- a - 1 \|a - 1 \|a - 1 +--R Type: Expression Integer +--E 118 + +--S 119 of 489 +d0222b:= D(m0222b,x) +--R +--R +--R (103) +--R 2 2 2 3 2 4 3 +--R ((- 2a + a + 1)b x + (- 2a + 3a - 1)b x - a + 2a - 2a + 1) +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 2 2 2 3 2 4 2 +--R (- 2a - 3a - 1)b x + (- 2a - a + 2a + 1)b x - a + 2a - 1 +--R * +--R - b x - a - 1 3 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 2 2 2 3 2 4 3 +--R ((2a - a - 1)b x + (2a - 3a + 1)b x + a - 2a + 2a - 1) +--R * +--R atanh(b x + a) 3 +--R (%e ) +--R + +--R 2 2 2 3 2 4 2 +--R ((2a - a - 1)b x + (2a + a - 2a - 1)b x + a - 2a + 1) +--R * +--R atanh(b x + a) +--R %e +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 2 2 2 3 2 4 2 +--R ((- 2a + a + 1)b x + (- 2a - a + 2a + 1)b x - a + 2a - 1) +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 2 2 2 3 2 4 3 +--R (- 2a - 3a - 1)b x + (- 2a - 5a - 4a - 1)b x - a - 2a + 2a + 1 +--R * +--R - b x - a - 1 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R %e +--R + +--R 2 2 2 3 2 4 2 +--R ((2a + 3a + 1)b x + (2a + a - 2a - 1)b x + a - 2a + 1) +--R * +--R atanh(b x + a) 3 +--R (%e ) +--R + +--R 2 2 2 3 2 4 3 +--R ((2a + 3a + 1)b x + (2a + 5a + 4a + 1)b x + a + 2a - 2a - 1) +--R * +--R atanh(b x + a) +--R %e +--R / +--R 4 3 2 4 5 4 2 3 +--R (a - 2a + 2a - 1)b x + (2a - 4a + 4a - 2a)b x +--R + +--R 6 5 4 3 2 2 +--R (a - 2a - a + 4a - a - 2a + 1)x +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 4 2 2 4 5 3 3 6 4 2 2 +--R (a - 2a + 1)b x + (2a - 4a + 2a)b x + (a - 3a + 3a - 1)x +--R * +--R - b x - a - 1 2 +--R log(-------------) +--R b x + a - 1 +--R ------------------ +--R 2 +--R (%e ) +--R + +--R 4 2 2 4 5 3 3 6 4 2 2 +--R ((a - 2a + 1)b x + (2a - 4a + 2a)b x + (a - 3a + 3a - 1)x ) +--R * +--R atanh(b x + a) 2 +--R (%e ) +--R + +--R 4 3 2 4 5 4 2 3 +--R (a + 2a - 2a - 1)b x + (2a + 4a - 4a - 2a)b x +--R + +--R 6 5 4 3 2 2 +--R (a + 2a - a - 4a - a + 2a + 1)x +--R Type: Expression Integer +--E 119 + +--S 120 of 489 +t0223:= exp(1)^atanh(x)*(1-x)^(1/2) +--R +--R +--R +-------+ atanh(x) +--R (104) \|- x + 1 %e +--R Type: Expression Integer +--E 120 + +--S 121 of 489 +r0223:= 2/3*(1+x)^(3/2) +--R +--R +--R +-----+ +--R (2x + 2)\|x + 1 +--R (105) ---------------- +--R 3 +--R Type: Expression Integer +--E 121 + +--S 122 of 489 +a0223:= integrate(t0223,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-------+ 2 +--R (2x + 2)\|- x + 1 %e +--R (106) -------------------------------- +--R 3 +--R Type: Union(Expression Integer,...) +--E 122 + +--S 123 of 489 +m0223:= a0223-r0223 +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-------+ 2 +-----+ +--R (2x + 2)\|- x + 1 %e + (- 2x - 2)\|x + 1 +--R (107) ----------------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 123 + +--S 124 of 489 +d0223:= D(m0223,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-----+ 2 +-------+ +--R (- x + 1)\|x + 1 %e + (- x - 1)\|- x + 1 +--R (108) ----------------------------------------------------- +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 124 + +--S 125 of 489 +t0224:= exp(1)^atanh(x)/(1-x)^(1/2) +--R +--R +--R atanh(x) +--R %e +--R (109) ---------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 125 + +--S 126 of 489 +r0224:= -2*(1+x)^(1/2)+2*2^(1/2)*atanh(1/2*(1+x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-----+ +--R +-+ \|2 \|x + 1 +-----+ +--R (110) 2\|2 atanh(------------) - 2\|x + 1 +--R 2 +--R Type: Expression Integer +--E 126 + +--S 127 of 489 +--a0224:= integrate(t0224,x) +--E 127 + +--S 128 of 489 +--m0224:= a0224-r0224 +--E 128 + +--S 129 of 489 +--d0224:= D(m0224,x) +--E 129 + +--S 130 of 489 +t0225:= exp(1)^atanh(x)/(1-x)^(3/2) +--R +--R +--R atanh(x) +--R %e +--R (111) - ----------------- +--R +-------+ +--R (x - 1)\|- x + 1 +--R Type: Expression Integer +--E 130 + +--S 131 of 489 +r0225:= (1+x)^(1/2)/(1-x)-1/2*2^(1/2)*atanh(1/2*(1+x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-----+ +--R +-+ \|2 \|x + 1 +-----+ +--R (- x + 1)\|2 atanh(------------) - 2\|x + 1 +--R 2 +--R (112) -------------------------------------------- +--R 2x - 2 +--R Type: Expression Integer +--E 131 + +--S 132 of 489 +--a0225:= integrate(t0225,x) +--E 132 + +--S 133 of 489 +--m0225:= a0225-r0225 +--E 133 + +--S 134 of 489 +--d0225:= D(m0225,x) +--E 134 + +--S 135 of 489 +t0226:= exp(1)^atanh(x)*(1+x)^(3/2) +--R +--R +--R +-----+ atanh(x) +--R (113) (x + 1)\|x + 1 %e +--R Type: Expression Integer +--E 135 + +--S 136 of 489 +r0226:= -86/15*(1-x)^(1/2)-28/15*(1-x)^(1/2)*x-2/5*(1-x)^(1/2)*x^2 +--R +--R +--R 2 +-------+ +--R (- 6x - 28x - 86)\|- x + 1 +--R (114) ---------------------------- +--R 15 +--R Type: Expression Integer +--E 136 + +--S 137 of 489 +a0226:= integrate(t0226,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 2 +-----+ 2 +--R (18x + 66x + 174x - 258)\|x + 1 %e + 430x + 430 +--R (115) ------------------------------------------------------------- +--R 45x + 45 +--R Type: Union(Expression Integer,...) +--E 137 + +--S 138 of 489 +m0226:= a0226-r0226 +--R +--R +--R (116) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 2 +-----+ 2 +--R (18x + 66x + 174x - 258)\|x + 1 %e +--R + +--R 3 2 +-------+ +--R (18x + 102x + 342x + 258)\|- x + 1 + 430x + 430 +--R / +--R 45x + 45 +--R Type: Expression Integer +--E 138 + +--S 139 of 489 +d0226:= D(m0226,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 2 +-------+ 2 2 +-----+ +--R (x + 2x + 1)\|- x + 1 %e + (- x - 2x - 1)\|x + 1 +--R (117) --------------------------------------------------------------- +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 139 + +--S 140 of 489 +t0227:= exp(1)^atanh(x)/(1+x)^(1/2) +--R +--R +--R atanh(x) +--R %e +--R (118) ---------- +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 140 + +--S 141 of 489 +r0227:= -2*(1-x)^(1/2) +--R +--R +--R +-------+ +--R (119) - 2\|- x + 1 +--R Type: Expression Integer +--E 141 + +--S 142 of 489 +a0227:= integrate(t0227,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-----+ 2 +--R (6x - 6)\|x + 1 %e - 10x - 10 +--R (120) ----------------------------------------- +--R 3x + 3 +--R Type: Union(Expression Integer,...) +--E 142 + +--S 143 of 489 +m0227:= a0227-r0227 +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-----+ 2 +-------+ +--R (6x - 6)\|x + 1 %e + (6x + 6)\|- x + 1 - 10x - 10 +--R (121) -------------------------------------------------------------- +--R 3x + 3 +--R Type: Expression Integer +--E 143 + +--S 144 of 489 +d0227:= D(m0227,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R +-------+ 2 +-----+ +--R \|- x + 1 %e - \|x + 1 +--R (122) ----------------------------------- +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 144 + +--S 145 of 489 +t0228:= exp(1)^atanh(x)/(1+x)^(3/2) +--R +--R +--R atanh(x) +--R %e +--R (123) --------------- +--R +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression Integer +--E 145 + +--S 146 of 489 +r0228:= -2^(1/2)*atanh(1/2*(1-x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-------+ +--R +-+ \|2 \|- x + 1 +--R (124) - \|2 atanh(--------------) +--R 2 +--R Type: Expression Integer +--E 146 + +--S 147 of 489 +--a0228:= integrate(t0228,x) +--E 147 + +--S 148 of 489 +--m0228:= a0228-r0228 +--E 148 + +--S 149 of 489 +--d0228:= D(m0228,x) +--E 149 + +--S 150 of 489 +t0229:= x*exp(1)^atanh(x)/(1-x) +--R +--R +--R atanh(x) +--R x %e +--R (125) - ------------ +--R x - 1 +--R Type: Expression Integer +--E 150 + +--S 151 of 489 +r0229:= -(-3+x)*(1+x)^(1/2)/(1-x)^(1/2)-2*asin(x) +--R +--R +--R +-----+ +-------+ +--R (- x + 3)\|x + 1 - 2asin(x)\|- x + 1 +--R (126) -------------------------------------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 151 + +--S 152 of 489 +a0229:= integrate(t0229,x) +--R +--R +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R 2 2 +--R (127) - 4atan(%e ) + (- x + 3)%e +--R Type: Union(Expression Integer,...) +--E 152 + +--S 153 of 489 +m0229:= a0229-r0229 +--R +--R +--R (128) +--R - x - 1 - x - 1 +--R log(-------) log(-------) +--R x - 1 x - 1 +--R ------------ ------------ +--R +-------+ 2 +-------+ 2 +--R - 4\|- x + 1 atan(%e ) + (- x + 3)\|- x + 1 %e +--R + +--R +-----+ +-------+ +--R (x - 3)\|x + 1 + 2asin(x)\|- x + 1 +--R / +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 153 + +--S 154 of 489 +d0229:= D(m0229,x) +--R +--R +--R (129) +--R - x - 1 3 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 | 2 +-------+ +-----+ 2 +--R (- x + x - 2)\|- x + 1 \|- x + 1 \|x + 1 (%e ) +--R + +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 +-------+ +-----+ 3 | 2 2 +--R ((2x - 2)\|- x + 1 \|x + 1 + (x + x + 2)\|- x + 1 )(%e ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 | 2 +-------+ +-----+ 2 +--R (- x + x + 2)\|- x + 1 \|- x + 1 \|x + 1 %e +--R + +--R +--------+ +--R 2 +-------+ +-----+ 3 | 2 +--R (2x - 2)\|- x + 1 \|x + 1 + (x + x + 2)\|- x + 1 +--R / +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 | 2 +-------+ +-----+ 2 +--R (x - 1)\|- x + 1 \|- x + 1 \|x + 1 (%e ) +--R + +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 154 + +--S 155 of 489 +t0230:= x*exp(1)^atanh(x)/(1-x)^(1/2) +--R +--R +--R atanh(x) +--R x %e +--R (130) ------------ +--R +-------+ +--R \|- x + 1 +--R Type: Expression Integer +--E 155 + +--S 156 of 489 +r0230:= -2*(1+x)^(1/2)-2/3*(1+x)^(3/2)+2*2^(1/2)*atanh(1/2*(1+x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-----+ +--R +-+ \|2 \|x + 1 +-----+ +--R 6\|2 atanh(------------) + (- 2x - 8)\|x + 1 +--R 2 +--R (131) --------------------------------------------- +--R 3 +--R Type: Expression Integer +--E 156 + +--S 157 of 489 +--a0230:= integrate(t0230,x) +--E 157 + +--S 158 of 489 +--m0230:= a0230-r0230 +--E 158 + +--S 159 of 489 +--d0230:= D(m0230,x) +--E 159 + +--S 160 of 489 +t0231:= x*exp(1)^atanh(x)/(1-x)^(3/2) +--R +--R +--R atanh(x) +--R x %e +--R (132) - ----------------- +--R +-------+ +--R (x - 1)\|- x + 1 +--R Type: Expression Integer +--E 160 + +--S 161 of 489 +r0231:= 2*(1+x)^(1/2)+(1+x)^(1/2)/(1-x)-_ + 5/2*2^(1/2)*atanh(1/2*(1+x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-----+ +--R +-+ \|2 \|x + 1 +-----+ +--R (- 5x + 5)\|2 atanh(------------) + (4x - 6)\|x + 1 +--R 2 +--R (133) ---------------------------------------------------- +--R 2x - 2 +--R Type: Expression Integer +--E 161 + +--S 162 of 489 +--a0231:= integrate(t0231,x) +--E 162 + +--S 163 of 489 +--m0231:= a0231-r0231 +--E 163 + +--S 164 of 489 +--d0231:= D(m0231,x) +--E 164 + +--S 165 of 489 +t0232:= x*exp(1)^atanh(x)*(1+x)^(3/2) +--R +--R +--R 2 +-----+ atanh(x) +--R (134) (x + x)\|x + 1 %e +--R Type: Expression Integer +--E 165 + +--S 166 of 489 +r0232:= -8*(1-x)^(1/2)+16/3*(1-x)^(3/2)-2*(1-x)^(5/2)+2/7*(1-x)^(7/2) +--R +--R +--R 3 2 +-------+ +--R (- 6x - 24x - 46x - 92)\|- x + 1 +--R (135) ----------------------------------- +--R 21 +--R Type: Expression Integer +--E 166 + +--S 167 of 489 +a0232:= integrate(t0232,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 3 2 +-----+ 2 +--R (6x + 18x + 22x + 46x - 92)\|x + 1 %e +--R (136) ---------------------------------------------------- +--R 21x + 21 +--R Type: Union(Expression Integer,...) +--E 167 + +--S 168 of 489 +m0232:= a0232-r0232 +--R +--R +--R (137) +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 4 3 2 +-----+ 2 +--R (6x + 18x + 22x + 46x - 92)\|x + 1 %e +--R + +--R 4 3 2 +-------+ +--R (6x + 30x + 70x + 138x + 92)\|- x + 1 +--R / +--R 21x + 21 +--R Type: Expression Integer +--E 168 + +--S 169 of 489 +d0232:= D(m0232,x) +--R +--R +--R - x - 1 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 2 +-------+ 2 3 2 +-----+ +--R (x + 2x + x)\|- x + 1 %e + (- x - 2x - x)\|x + 1 +--R (138) ----------------------------------------------------------------- +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression Integer +--E 169 + +--S 170 of 489 +t0233:= x*exp(1)^atanh(x)/(1+x)^(3/2) +--R +--R +--R atanh(x) +--R x %e +--R (139) --------------- +--R +-----+ +--R (x + 1)\|x + 1 +--R Type: Expression Integer +--E 170 + +--S 171 of 489 +r0233:= -2*(1-x)^(1/2)+2^(1/2)*atanh(1/2*(1-x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-------+ +--R +-+ \|2 \|- x + 1 +-------+ +--R (140) \|2 atanh(--------------) - 2\|- x + 1 +--R 2 +--R Type: Expression Integer +--E 171 + +--S 172 of 489 +--a0233:= integrate(t0233,x) +--E 172 + +--S 173 of 489 +--m0233:= a0233-r0233 +--E 173 + +--S 174 of 489 +--d0233:= D(m0233,x) +--E 174 + +--S 175 of 489 +t0234:= sin(x)*exp(1)^atanh(x)*(1-x)^(1/2) +--R +--R +--R +-------+ atanh(x) +--R (141) sin(x)\|- x + 1 %e +--R Type: Expression Integer +--E 175 + +--S 176 of 489 +r0234:= -(1+x)^(1/2)*cos(x)+1/2*2^(1/2)*%pi^(1/2)*cos(1)*_ + FresnelC(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))+1/2*2^(1/2)*_ + %pi^(1/2)*FresnelS(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*sin(1) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 176 + +--S 177 of 489 +a0234:= integrate(t0234,x) +--R +--R +--R x +--R ++ +--------+ atanh(%I) +--R (142) | sin(%I)\|- %I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 177 + +--S 178 of 489 +--m0234:= a0234-r0234 +--E 178 + +--S 179 of 489 +--d0234:= D(m0234,x) +--E 179 + +--S 180 of 489 +t0235:= sin(x)*exp(1)^atanh(x)*(1-x)^(3/2) +--R +--R +--R +-------+ atanh(x) +--R (143) (- x + 1)sin(x)\|- x + 1 %e +--R Type: Expression Integer +--E 180 + +--S 181 of 489 +r0235:= -2*(1+x)^(1/2)*cos(x)+(1+x)^(3/2)*cos(x)+1/4*2^(1/2)*_ + %pi^(1/2)*FresnelC(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*(4*cos(1)-_ + 3*sin(1))+1/4*2^(1/2)*%pi^(1/2)*_ + FresnelS(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*(3*cos(1)+4*sin(1))-_ + 3/2*(1+x)^(1/2)*sin(x) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 181 + +--S 182 of 489 +a0235:= integrate(t0235,x) +--R +--R +--R x +--R ++ +--------+ atanh(%I) +--R (144) | (- %I + 1)sin(%I)\|- %I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 182 + +--S 183 of 489 +--m0235:= a0235-r0235 +--E 183 + +--S 184 of 489 +--d0235:= D(m0235,x) +--E 184 + +--S 185 of 489 +t0236:= sin(x)*exp(1)^atanh(x)*(1+x)^(1/2) +--R +--R +--R +-----+ atanh(x) +--R (145) sin(x)\|x + 1 %e +--R Type: Expression Integer +--E 185 + +--S 186 of 489 +r0236:= (1-x)^(1/2)*cos(x)+1/2*2^(1/2)*%pi^(1/2)*_ + FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*_ + (4*cos(1)-sin(1))-1/2*2^(1/2)*%pi^(1/2)*_ + FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*(cos(1)+4*sin(1)) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 186 + +--S 187 of 489 +a0236:= integrate(t0236,x) +--R +--R +--R x +--R ++ +------+ atanh(%I) +--R (146) | sin(%I)\|%I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 187 + +--S 188 of 489 +--m0236:= a0236-r0236 +--E 188 + +--S 189 of 489 +--d0236:= D(m0236,x) +--E 189 + +--S 190 of 489 +t0237:= sin(x)*exp(1)^atanh(x)*(1+x)^(3/2) +--R +--R +--R +-----+ atanh(x) +--R (147) (x + 1)sin(x)\|x + 1 %e +--R Type: Expression Integer +--E 190 + +--S 191 of 489 +r0237:= 4*(1-x)^(1/2)*cos(x)-(1-x)^(3/2)*cos(x)+1/4*2^(1/2)*%pi^(1/2)*_ + FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*(13*cos(1)-8*sin(1))-_ + 1/4*2^(1/2)*%pi^(1/2)*FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*_ + (8*cos(1)+13*sin(1))-3/2*(1-x)^(1/2)*sin(x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 191 + +--S 192 of 489 +a0237:= integrate(t0237,x) +--R +--R +--R x +--R ++ +------+ atanh(%I) +--R (148) | (%I + 1)sin(%I)\|%I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 192 + +--S 193 of 489 +--m0237:= a0237-r0237 +--E 193 + +--S 194 of 489 +--d0237:= D(m0237,x) +--E 194 + +--S 195 of 489 +t0238:= sin(x)*exp(1)^atanh(x)/(1+x)^(1/2) +--R +--R +--R atanh(x) +--R sin(x)%e +--R (149) ---------------- +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 195 + +--S 196 of 489 +r0238:= 2^(1/2)*%pi^(1/2)*(FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*cos(1)-_ + FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*sin(1)) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 196 + +--S 197 of 489 +a0238:= integrate(t0238,x) +--R +--R +--R x atanh(%I) +--R ++ sin(%I)%e +--R (150) | ------------------ d%I +--R ++ +------+ +--R \|%I + 1 +--R Type: Union(Expression Integer,...) +--E 197 + +--S 198 of 489 +--m0238:= a0238-r0238 +--E 198 + +--S 199 of 489 +--d0238:= D(m0238,x) +--E 199 + +--S 200 of 489 +t0239:= x*sin(x)*exp(1)^atanh(x)*(1-x)^(1/2) +--R +--R +--R +-------+ atanh(x) +--R (151) x sin(x)\|- x + 1 %e +--R Type: Expression Integer +--E 200 + +--S 201 of 489 +r0239:= (1+x)^(1/2)*cos(x)-(1+x)^(3/2)*cos(x)-1/4*2^(1/2)*%pi^(1/2)*_ + FresnelC(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*(2*cos(1)-3*sin(1))-_ + 1/4*2^(1/2)*%pi^(1/2)*FresnelS(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*_ + (3*cos(1)+2*sin(1))+3/2*(1+x)^(1/2)*sin(x) +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 201 + +--S 202 of 489 +a0239:= integrate(t0239,x) +--R +--R +--R x +--R ++ +--------+ atanh(%I) +--R (152) | %I sin(%I)\|- %I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 202 + +--S 203 of 489 +--m0239:= a0239-r0239 +--E 203 + +--S 204 of 489 +--d0239:= D(m0239,x) +--E 204 + +--S 205 of 489 +t0240:= x*sin(x)*exp(1)^atanh(x)*(1-x)^(3/2) +--R +--R +--R 2 +-------+ atanh(x) +--R (153) (- x + x)sin(x)\|- x + 1 %e +--R Type: Expression Integer +--E 205 + +--S 206 of 489 +r0240:= -7/4*(1+x)^(1/2)*cos(x)-3*(1+x)^(3/2)*cos(x)+(1+x)^(5/2)*cos(x)-_ + 1/8*2^(1/2)*%pi^(1/2)*FresnelS(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*_ + (18*cos(1)-7*sin(1))+1/8*2^(1/2)*%pi^(1/2)*_ + FresnelC(2^(1/2)/%pi^(1/2)*(1+x)^(1/2))*(7*cos(1)+18*sin(1))+_ + 9/2*(1+x)^(1/2)*sin(x)-5/2*(1+x)^(3/2)*sin(x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 206 + +--S 207 of 489 +a0240:= integrate(t0240,x) +--R +--R +--R x +--R ++ 2 +--------+ atanh(%I) +--R (154) | (- %I + %I)sin(%I)\|- %I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 207 + +--S 208 of 489 +--m0240:= a0240-r0240 +--E 208 + +--S 209 of 489 +--d0240:= D(m0240,x) +--E 209 + +--S 210 of 489 +t0241:= x*sin(x)*exp(1)^atanh(x)*(1+x)^(1/2) +--R +--R +--R +-----+ atanh(x) +--R (155) x sin(x)\|x + 1 %e +--R Type: Expression Integer +--E 210 + +--S 211 of 489 +r0241:= 3*(1-x)^(1/2)*cos(x)-(1-x)^(3/2)*cos(x)+1/4*2^(1/2)*%pi^(1/2)*_ + FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*(5*cos(1)-6*sin(1))-_ + 1/4*2^(1/2)*%pi^(1/2)*FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*_ + (6*cos(1)+5*sin(1))-3/2*(1-x)^(1/2)*sin(x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 489 +a0241:= integrate(t0241,x) +--R +--R +--R x +--R ++ +------+ atanh(%I) +--R (156) | %I sin(%I)\|%I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 212 + +--S 213 of 489 +--m0241:= a0241-r0241 +--E 213 + +--S 214 of 489 +--d0241:= D(m0241,x) +--E 214 + +--S 215 of 489 +t0242:= x*sin(x)*exp(1)^atanh(x)*(1+x)^(3/2) +--R +--R +--R 2 +-----+ atanh(x) +--R (157) (x + x)sin(x)\|x + 1 %e +--R Type: Expression Integer +--E 215 + +--S 216 of 489 +r0242:= 17/4*(1-x)^(1/2)*cos(x)-5*(1-x)^(3/2)*cos(x)+(1-x)^(5/2)*cos(x)+_ + 1/8*2^(1/2)*%pi^(1/2)*FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*_ + (2*cos(1)-17*sin(1))-1/8*2^(1/2)*%pi^(1/2)*_ + FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*(17*cos(1)+2*sin(1))-_ + 15/2*(1-x)^(1/2)*sin(x)+5/2*(1-x)^(3/2)*sin(x) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 216 + +--S 217 of 489 +a0242:= integrate(t0242,x) +--R +--R +--R x +--R ++ 2 +------+ atanh(%I) +--R (158) | (%I + %I)sin(%I)\|%I + 1 %e d%I +--R ++ +--R Type: Union(Expression Integer,...) +--E 217 + +--S 218 of 489 +--m0242:= a0242-r0242 +--E 218 + +--S 219 of 489 +--d0242:= D(m0242,x) +--E 219 + +--S 220 of 489 +t0243:= x*sin(x)*exp(1)^atanh(x)/(1+x)^(1/2) +--R +--R +--R atanh(x) +--R x sin(x)%e +--R (159) ------------------ +--R +-----+ +--R \|x + 1 +--R Type: Expression Integer +--E 220 + +--S 221 of 489 +r0243:= (1-x)^(1/2)*cos(x)+1/2*2^(1/2)*%pi^(1/2)*_ + FresnelS(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*(2*cos(1)-sin(1))-_ + 1/2*2^(1/2)*%pi^(1/2)*FresnelC(2^(1/2)/%pi^(1/2)*(1-x)^(1/2))*_ + (cos(1)+2*sin(1)) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression Integer +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 221 + +--S 222 of 489 +a0243:= integrate(t0243,x) +--R +--R +--R x atanh(%I) +--R ++ %I sin(%I)%e +--R (160) | --------------------- d%I +--R ++ +------+ +--R \|%I + 1 +--R Type: Union(Expression Integer,...) +--E 222 + +--S 223 of 489 +--m0243:= a0243-r0243 +--E 223 + +--S 224 of 489 +--d0243:= D(m0243,x) +--E 224 + +--S 225 of 489 +t0244:= exp(1)^atanh(x)/(1-x^2)^(3/2) +--R +--R +--R atanh(x) +--R %e +--R (161) - ------------------- +--R +--------+ +--R 2 | 2 +--R (x - 1)\|- x + 1 +--R Type: Expression Integer +--E 225 + +--S 226 of 489 +r0244:= 1/(2-2*x)+1/2*atanh(x) +--R +--R +--R (x - 1)atanh(x) - 1 +--R (162) ------------------- +--R 2x - 2 +--R Type: Expression Integer +--E 226 + +--S 227 of 489 +a0244:= integrate(t0244,x) +--R +--R +--R (163) +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 | 2 2 2 +--R 2 (x + 1)\|- x + 1 %e - 2x - 2x +--R (- x + 1)log(--------------------------------------------) +--R 3 2 +--R x + x - x - 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R | 2 2 +--R - 2x\|- x + 1 %e +--R / +--R 2 +--R 4x - 4 +--R Type: Union(Expression Integer,...) +--E 227 + +--S 228 of 489 +m0244:= a0244-r0244 +--R +--R +--R (164) +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 2 | 2 2 2 +--R 2 (x + 1)\|- x + 1 %e - 2x - 2x +--R (- x + 1)log(--------------------------------------------) +--R 3 2 +--R x + x - x - 1 +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R | 2 2 2 +--R - 2x\|- x + 1 %e + (- 2x + 2)atanh(x) + 2x + 2 +--R / +--R 2 +--R 4x - 4 +--R Type: Expression Integer +--E 228 + +--S 229 of 489 +d0244:= D(m0244,x) +--R +--R +--R (165) +--R - x - 1 2 +--R log(-------) +--R x - 1 +--R ------------ +--R 3 2 2 +--R (- x + x - x + 1)(%e ) +--R + +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R | 2 2 3 2 +--R (- 2x - 2)\|- x + 1 %e - x + x + 3x + 1 +--R / +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 4 3 2 | 2 2 4 3 2 +--R (2x - 4x + 4x - 4x + 2)\|- x + 1 %e - 4x + 4x + 4x - 4x +--R Type: Expression Integer +--E 229 + +--S 230 of 489 +t0245:= exp(1)^atanh(x)*(a-a*x^2)^(7/2) +--R +--R +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 atanh(x) +--R (166) (- a x + 3a x - 3a x + a )\|- a x + a %e +--R Type: Expression Integer +--E 230 + +--S 231 of 489 +r0245:= -1/280*(-a*(-1+x^2))^(1/2)*(1+x)^5*_ + a^3*(-93+185*x-135*x^2+35*x^3)/(1-x^2)^(1/2) +--R +--R +--R (167) +--R 3 8 3 7 3 6 3 5 3 4 3 3 3 2 +--R - 35a x - 40a x + 140a x + 168a x - 210a x - 280a x + 140a x +--R + +--R 3 3 +--R 280a x + 93a +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R / +--R +--------+ +--R | 2 +--R 280\|- x + 1 +--R Type: Expression Integer +--E 231 + +--S 232 of 489 +a0245:= integrate(t0245,x) +--R +--R +--R (168) +--R 3 8 3 7 3 6 3 5 3 4 3 3 3 2 +--R - 35a x - 40a x + 140a x + 168a x - 210a x - 280a x + 140a x +--R + +--R 3 +--R 280a x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R +----------+ ------------ +--R | 2 2 +--R \|- a x + a %e +--R / +--R 280x + 280 +--R Type: Union(Expression Integer,...) +--E 232 + +--S 233 of 489 +m0245:= a0245-r0245 +--R +--R +--R (169) +--R 3 8 3 7 3 6 3 5 3 4 3 3 3 2 +--R - 35a x - 40a x + 140a x + 168a x - 210a x - 280a x + 140a x +--R + +--R 3 +--R 280a x +--R * +--R - x - 1 +--R log(-------) +--R x - 1 +--R +----------+ +--------+ ------------ +--R | 2 | 2 2 +--R \|- a x + a \|- x + 1 %e +--R + +--R 3 9 3 8 3 7 3 6 3 5 3 4 3 3 +--R 35a x + 75a x - 100a x - 308a x + 42a x + 490a x + 140a x +--R + +--R 3 2 3 3 +--R - 420a x - 373a x - 93a +--R * +--R +----------+ +--R | 2 +--R \|- a x + a +--R / +--R +--------+ +--R | 2 +--R (280x + 280)\|- x + 1 +--R Type: Expression Integer +--E 233 + +--S 234 of 489 +d0245:= D(m0245,x) +--R +--R +--R (170) +--R - x - 1 +--R log(-------) +--R x - 1 +--R +--------+ ------------ +--R 4 8 4 6 4 4 4 2 4 | 2 2 4 9 +--R (a x - 4a x + 6a x - 4a x + a )\|- x + 1 %e - a x +--R + +--R 4 8 4 7 4 6 4 5 4 4 4 3 4 2 4 4 +--R - a x + 4a x + 4a x - 6a x - 6a x + 4a x + 4a x - a x - a +--R / +--R +----------+ +--------+ +--R | 2 | 2 +--R \|- a x + a \|- x + 1 +--R Type: Expression Integer +--E 234 + +--S 235 of 489 +t0246:= exp(1)^atanh(x)/(a-a*x^2)^(3/2) +--R +--R +--R atanh(x) +--R %e +--R (171) - ----------------------- +--R +----------+ +--R 2 | 2 +--R (a x - a)\|- a x + a +--R Type: Expression Integer +--E 235 + +--S 236 of 489 +r0246:= 1/2*(1-x^2)^(3/2)*(1/(1-x)+atanh(x))/(a-a*x^2)^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R ((x - 1)atanh(x) - 1)\|- x + 1 +--R (172) -------------------------------- +--R +----------+ +--R | 2 +--R (2a x - 2a)\|- a x + a +--R Type: Expression Integer +--E 236 + +--S 237 of 489 +--a0246:= integrate(t0246,x) +--E 237 + +--S 238 of 489 +--m0246:= a0246-r0246 +--E 238 + +--S 239 of 489 +--d0246:= D(m0246,x) +--E 239 + +--S 240 of 489 +t0247:= exp(1)^atanh(x)/(a-a*x^2)^(5/2) +--R +--R +--R atanh(x) +--R %e +--R (173) -------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (a x - 2a x + a )\|- a x + a +--R Type: Expression Integer +--E 240 + +--S 241 of 489 +r0247:= 1/8*(1-x^2)^(5/2)*(1/(1-x)^2+2/(1-x)-_ + 1/(1+x)+3*atanh(x))/(a-a*x^2)^(5/2) +--R +--R +--R +--------+ +--R 3 2 2 | 2 +--R ((3x - 3x - 3x + 3)atanh(x) - 3x + 3x + 2)\|- x + 1 +--R (174) -------------------------------------------------------- +--R +----------+ +--R 2 3 2 2 2 2 | 2 +--R (8a x - 8a x - 8a x + 8a )\|- a x + a +--R Type: Expression Integer +--E 241 + +--S 242 of 489 +--a0247:= integrate(t0247,x) +--E 242 + +--S 243 of 489 +--m0247:= a0247-r0247 +--E 243 + +--S 244 of 489 +--d0247:= D(m0247,x) +--E 244 + +--S 245 of 489 +t0248:= exp(1)^atanh(x)/(a-a*x^2)^(7/2) +--R +--R +--R atanh(x) +--R %e +--R (175) - ---------------------------------------- +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x - 3a x + 3a x - a )\|- a x + a +--R Type: Expression Integer +--E 245 + +--S 246 of 489 +r0248:= 1/96*(1-x^2)^(7/2)*(4/(1-x)^3+9/(1-x)^2+_ + 18/(1-x)-3/(1+x)^2-12/(1+x)+30*atanh(x))/(a-a*x^2)^(7/2) +--R +--R +--R (176) +--R 5 4 3 2 4 3 2 +--R (15x - 15x - 30x + 30x + 15x - 15)atanh(x) - 15x + 15x + 25x +--R + +--R - 25x - 8 +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R / +--R +----------+ +--R 3 5 3 4 3 3 3 2 3 3 | 2 +--R (48a x - 48a x - 96a x + 96a x + 48a x - 48a )\|- a x + a +--R Type: Expression Integer +--E 246 + +--S 247 of 489 +--a0248:= integrate(t0248,x) +--E 247 + +--S 248 of 489 +--m0248:= a0248-r0248 +--E 248 + +--S 249 of 489 +--d0248:= D(m0248,x) +--E 249 + +--S 250 of 489 +t0249:= exp(1)^atanh(x)/(1-1/x^2)^(5/2) +--R +--R +--R 4 atanh(x) +--R x %e +--R (177) ----------------------- +--R +------+ +--R | 2 +--R 4 2 |x - 1 +--R (x - 2x + 1) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 250 + +--S 251 of 489 +r0249:= 1/16*(1-x^2)^(5/2)*(2/(1-x)^2-16/(1-x)-_ + 16*x+2/(1+x)-23*log(1-x)+7*log(1+x))/(1-1/x^2)^(5/2)/x^5 +--R +--R +--R (178) +--R 3 2 3 2 +--R (7x - 7x - 7x + 7)log(x + 1) + (- 23x + 23x + 23x - 23)log(- x + 1) +--R + +--R 4 3 2 +--R - 16x + 16x + 34x - 18x - 12 +--R * +--R +--------+ +--R | 2 +--R \|- x + 1 +--R / +--R +------+ +--R | 2 +--R 4 3 2 |x - 1 +--R (16x - 16x - 16x + 16x) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 251 + +--S 252 of 489 +--a0249:= integrate(t0249,x) +--E 252 + +--S 253 of 489 +--m0249:= a0249-r0249 +--E 253 + +--S 254 of 489 +--d0249:= D(m0249,x) +--E 254 + +--S 255 of 489 +t0250:= x*exp(1)^acoth(x) +--R +--R +--R acoth(x) +--R (179) x %e +--R Type: Expression Integer +--E 255 + +--S 256 of 489 +r0250:= (1-1/x^2)^(1/2)*x+1/2*(1-1/x^2)^(1/2)*x^2+1/2*atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 2 |x - 1 +--R atanh( |------ ) + (x + 2x) |------ +--R | 2 | 2 +--R \| x \| x +--R (180) ------------------------------------- +--R 2 +--R Type: Expression Integer +--E 256 + +--S 257 of 489 +a0250:= integrate(t0250,x) +--R +--R +--R (181) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 2 +--R log(%e + 1) - log(%e - 1) + (x + x - 2)%e +--R ------------------------------------------------------------------------ +--R 2 +--R Type: Union(Expression Integer,...) +--E 257 + +--S 258 of 489 +m0250:= a0250-r0250 +--R +--R +--R (182) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 2 +--R log(%e + 1) - log(%e - 1) + (x + x - 2)%e +--R + +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 2 |x - 1 +--R - atanh( |------ ) + (- x - 2x) |------ +--R | 2 | 2 +--R \| x \| x +--R / +--R 2 +--R Type: Expression Integer +--E 258 + +--S 259 of 489 +d0250:= D(m0250,x) +--R +--R +--R (183) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 3 |x - 1 2 +--R (2x - 3x + 1) |------ (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 3 2 2 +--R (- 2x - 2x + 2x + 2)(%e ) +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 3 |x - 1 2 3 2 +--R (- 2x + 3x + 1) |------ %e + 2x + 2x - 2x - 2 +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 2 |x - 1 2 2 |x - 1 +--R (2x - 2) |------ (%e ) + (- 2x + 2) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 259 + +--S 260 of 489 +t0251:= exp(1)^acoth(x) +--R +--R +--R acoth(x) +--R (184) %e +--R Type: Expression Integer +--E 260 + +--S 261 of 489 +r0251:= (1-1/x^2)^(1/2)*x+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R (185) atanh( |------ ) + x |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 261 + +--S 262 of 489 +a0251:= integrate(t0251,x) +--R +--R +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R (186) log(%e + 1) - log(%e - 1) + (x - 1)%e +--R Type: Union(Expression Integer,...) +--E 262 + +--S 263 of 489 +m0251:= a0251-r0251 +--R +--R +--R (187) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R log(%e + 1) - log(%e - 1) + (x - 1)%e +--R + +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R - atanh( |------ ) - x |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 263 + +--S 264 of 489 +d0251:= D(m0251,x) +--R +--R +--R (188) +--R x + 1 3 x + 1 2 +--R log(-----) log(-----) +--R +------+ x - 1 x - 1 +--R | 2 ---------- ---------- +--R 3 2 |x - 1 2 3 2 2 +--R (x - x ) |------ (%e ) + (- x - x + x + 1)(%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 3 2 |x - 1 2 3 2 +--R (- x + x + 2x) |------ %e + x + x - x - 1 +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 3 |x - 1 2 3 |x - 1 +--R (x - x) |------ (%e ) + (- x + x) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 264 + +--S 265 of 489 +t0252:= exp(1)^acoth(x)/x +--R +--R +--R acoth(x) +--R %e +--R (189) ---------- +--R x +--R Type: Expression Integer +--E 265 + +--S 266 of 489 +r0252:= -acsc(x)+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 +--R (190) atanh( |------ ) - acsc(x) +--R | 2 +--R \| x +--R Type: Expression Integer +--E 266 + +--S 267 of 489 +a0252:= integrate(t0252,x) +--R +--R +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R (191) log(%e + 1) - log(%e - 1) - 2atan(%e ) +--R Type: Union(Expression Integer,...) +--E 267 + +--S 268 of 489 +m0252:= a0252-r0252 +--R +--R +--R (192) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R log(%e + 1) - log(%e - 1) - 2atan(%e ) +--R + +--R +------+ +--R | 2 +--R |x - 1 +--R - atanh( |------ ) + acsc(x) +--R | 2 +--R \| x +--R Type: Expression Integer +--E 268 + +--S 269 of 489 +d0252:= D(m0252,x) +--R +--R +--R (193) +--R x + 1 4 +--R log(-----) +--R +------+ x - 1 +--R +------+ | 2 ---------- +--R 2 | 2 2 |x - 1 2 +--R ((- x + 1)\|x - 1 + (- x + 1) |------ )(%e ) +--R | 2 +--R \| x +--R + +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 +------+ ---------- +------+ | 2 +--R |x - 1 | 2 2 2 | 2 2 |x - 1 +--R 4x |------ \|x - 1 (%e ) + (x - 1)\|x - 1 + (x - 1) |------ +--R | 2 | 2 +--R \| x \| x +--R / +--R x + 1 4 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 +------+ ---------- | 2 +------+ +--R 3 |x - 1 | 2 2 3 |x - 1 | 2 +--R (x - x) |------ \|x - 1 (%e ) + (- x + x) |------ \|x - 1 +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 269 + +--S 270 of 489 +t0253:= exp(1)^acoth(x)/x^2 +--R +--R +--R acoth(x) +--R %e +--R (194) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 270 + +--S 271 of 489 +r0253:= (1-1/x^2)^(1/2)-acsc(x) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 +--R (195) |------ - acsc(x) +--R | 2 +--R \| x +--R Type: Expression Integer +--E 271 + +--S 272 of 489 +a0253:= integrate(t0253,x) +--R +--R +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 +--R - 2x atan(%e ) + (x - 1)%e +--R (196) --------------------------------------------- +--R x +--R Type: Union(Expression Integer,...) +--E 272 + +--S 273 of 489 +m0253:= a0253-r0253 +--R +--R +--R (197) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +------+ +--R ---------- ---------- | 2 +--R 2 2 |x - 1 +--R - 2x atan(%e ) + (x - 1)%e - x |------ + x acsc(x) +--R | 2 +--R \| x +--R ---------------------------------------------------------------------- +--R x +--R Type: Expression Integer +--E 273 + +--S 274 of 489 +d0253:= D(m0253,x) +--R +--R +--R (198) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 2 |x - 1 | 2 2 +--R (x - x) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +--R +------+ | 2 ---------- +--R 2 | 2 4 2 |x - 1 2 +--R ((- x + 1)\|x - 1 + (- x + x ) |------ )(%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +------+ +--R 3 2 |x - 1 | 2 2 2 | 2 +--R (2x + x - x) |------ \|x - 1 %e + (- x + 1)\|x - 1 +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 4 2 |x - 1 +--R (- x + x ) |------ +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 +------+ ---------- | 2 +------+ +--R 5 3 |x - 1 | 2 2 5 3 |x - 1 | 2 +--R (x - x ) |------ \|x - 1 (%e ) + (x - x ) |------ \|x - 1 +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 274 + +--S 275 of 489 +t0254:= exp(1)^acoth(x)/x^3 +--R +--R +--R acoth(x) +--R %e +--R (199) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 275 + +--S 276 of 489 +r0254:= (1-1/x^2)^(1/2)+1/2*(1-1/x^2)^(1/2)/x-1/2*acsc(x) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 +--R (2x + 1) |------ - x acsc(x) +--R | 2 +--R \| x +--R (200) ----------------------------- +--R 2x +--R Type: Expression Integer +--E 276 + +--S 277 of 489 +a0254:= integrate(t0254,x) +--R +--R +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 2 2 +--R - 2x atan(%e ) + (2x - x - 1)%e +--R (201) --------------------------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression Integer,...) +--E 277 + +--S 278 of 489 +m0254:= a0254-r0254 +--R +--R +--R (202) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 2 2 +--R - 2x atan(%e ) + (2x - x - 1)%e +--R + +--R +------+ +--R | 2 +--R 2 |x - 1 2 +--R (- 2x - x) |------ + x acsc(x) +--R | 2 +--R \| x +--R / +--R 2 +--R 2x +--R Type: Expression Integer +--E 278 + +--S 279 of 489 +d0254:= D(m0254,x) +--R +--R +--R (203) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 4 3 |x - 1 | 2 2 +--R (- x + 3x - 2x) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R +------+ +--R +------+ | 2 +--R 4 3 2 | 2 5 3 |x - 1 +--R ((x - 2x - 3x + 2x + 2)\|x - 1 + (- x + x ) |------ ) +--R | 2 +--R \| x +--R * +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 +--R (%e ) +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 4 3 |x - 1 | 2 2 +--R (x + 3x - 2x) |------ \|x - 1 %e +--R | 2 +--R \| x +--R + +--R +------+ +--R +------+ | 2 +--R 4 3 2 | 2 5 3 |x - 1 +--R (x - 2x - 3x + 2x + 2)\|x - 1 + (- x + x ) |------ +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 6 4 |x - 1 | 2 2 +--R (2x - 2x ) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +------+ +--R 6 4 |x - 1 | 2 +--R (2x - 2x ) |------ \|x - 1 +--R | 2 +--R \| x +--R Type: Expression Integer +--E 279 + +--S 280 of 489 +t0255:= x^2*exp(1)^(3*acoth(x)) +--R +--R +--R 2 3acoth(x) +--R (204) x %e +--R Type: Expression Integer +--E 280 + +--S 281 of 489 +r0255:= 1/6*(-33*x+26*x^2-52+9*x^3+2*x^4+33*_ + atanh(((-1+x^2)/x^2)^(1/2))*((-1+x^2)/x^2)^(1/2)*x)/_ + x/((-1+x^2)/x^2)^(1/2) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 4 3 2 +--R 33x |------ atanh( |------ ) + 2x + 9x + 26x - 33x - 52 +--R | 2 | 2 +--R \| x \| x +--R (205) ---------------------------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R 6x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 281 + +--S 282 of 489 +a0255:= integrate(t0255,x) +--R +--R +--R (206) +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 3 2 |x + 1 +--R 33log( |----- + 1) - 33log( |----- - 1) + (2x + 7x + 19x - 52) |----- +--R \|x - 1 \|x - 1 \|x - 1 +--R -------------------------------------------------------------------------- +--R 6 +--R Type: Union(Expression Integer,...) +--E 282 + +--S 283 of 489 +m0255:= a0255-r0255 +--R +--R +--R (207) +--R +------+ +------+ +--R | 2 +-----+ | 2 +-----+ +--R |x - 1 |x + 1 |x - 1 |x + 1 +--R 33x |------ log( |----- + 1) - 33x |------ log( |----- - 1) +--R | 2 \|x - 1 | 2 \|x - 1 +--R \| x \| x +--R + +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R - 33x |------ atanh( |------ ) +--R | 2 | 2 +--R \| x \| x +--R + +--R +------+ +--R | 2 +-----+ +--R 4 3 2 |x - 1 |x + 1 4 3 2 +--R (2x + 7x + 19x - 52x) |------ |----- - 2x - 9x - 26x + 33x + 52 +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +--R |x - 1 +--R 6x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 283 + +--S 284 of 489 +d0255:= D(m0255,x) +--R +--R +--R +------+ +--R +-----+ | 2 +--R 4 3 2 |x + 1 4 3 2 |x - 1 +--R (- x - x + x + x) |----- + (x + 2x + x ) |------ +--R \|x - 1 | 2 +--R \| x +--R (208) ------------------------------------------------------- +--R +------+ +--R | 2 +-----+ +--R 2 |x - 1 |x + 1 +--R (x - 2x + 1) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 284 + +--S 285 of 489 +t0256:= x*exp(1)^(3*acoth(x)) +--R +--R +--R 3acoth(x) +--R (209) x %e +--R Type: Expression Integer +--E 285 + +--S 286 of 489 +r0256:= 1/2*(-9*x-14+6*x^2+x^3+9*_ + atanh(((-1+x^2)/x^2)^(1/2))*((-1+x^2)/x^2)^(1/2)*x)/_ + ((-1+x^2)/x^2)^(1/2)/x +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 3 2 +--R 9x |------ atanh( |------ ) + x + 6x - 9x - 14 +--R | 2 | 2 +--R \| x \| x +--R (210) ------------------------------------------------ +--R +------+ +--R | 2 +--R |x - 1 +--R 2x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 286 + +--S 287 of 489 +a0256:= integrate(t0256,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 2 |x + 1 +--R 9log( |----- + 1) - 9log( |----- - 1) + (x + 5x - 14) |----- +--R \|x - 1 \|x - 1 \|x - 1 +--R (211) ---------------------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 287 + +--S 288 of 489 +m0256:= a0256-r0256 +--R +--R +--R (212) +--R +------+ +------+ +--R | 2 +-----+ | 2 +-----+ +--R |x - 1 |x + 1 |x - 1 |x + 1 +--R 9x |------ log( |----- + 1) - 9x |------ log( |----- - 1) +--R | 2 \|x - 1 | 2 \|x - 1 +--R \| x \| x +--R + +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +-----+ +--R |x - 1 |x - 1 3 2 |x - 1 |x + 1 3 +--R - 9x |------ atanh( |------ ) + (x + 5x - 14x) |------ |----- - x +--R | 2 | 2 | 2 \|x - 1 +--R \| x \| x \| x +--R + +--R 2 +--R - 6x + 9x + 14 +--R / +--R +------+ +--R | 2 +--R |x - 1 +--R 2x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 288 + +--S 289 of 489 +d0256:= D(m0256,x) +--R +--R +--R +------+ +--R +-----+ | 2 +--R 3 2 |x + 1 3 2 |x - 1 +--R (- x - x + x + 1) |----- + (x + 2x + x) |------ +--R \|x - 1 | 2 +--R \| x +--R (213) ----------------------------------------------------- +--R +------+ +--R | 2 +-----+ +--R 2 |x - 1 |x + 1 +--R (x - 2x + 1) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 289 + +--S 290 of 489 +t0257:= exp(1)^(3*acoth(x)) +--R +--R +--R 3acoth(x) +--R (214) %e +--R Type: Expression Integer +--E 290 + +--S 291 of 489 +r0257:= (-4*x-5+x^2+3*atanh(((-1+x^2)/x^2)^(1/2))*((-1+x^2)/x^2)^(1/2)*x)/_ + ((-1+x^2)/x^2)^(1/2)/x +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 2 +--R 3x |------ atanh( |------ ) + x - 4x - 5 +--R | 2 | 2 +--R \| x \| x +--R (215) ----------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 291 + +--S 292 of 489 +a0257:= integrate(t0257,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R (216) 3log( |----- + 1) - 3log( |----- - 1) + (x - 5) |----- +--R \|x - 1 \|x - 1 \|x - 1 +--R Type: Union(Expression Integer,...) +--E 292 + +--S 293 of 489 +m0257:= a0257-r0257 +--R +--R +--R (217) +--R +------+ +------+ +--R | 2 +-----+ | 2 +-----+ +--R |x - 1 |x + 1 |x - 1 |x + 1 +--R 3x |------ log( |----- + 1) - 3x |------ log( |----- - 1) +--R | 2 \|x - 1 | 2 \|x - 1 +--R \| x \| x +--R + +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +-----+ +--R |x - 1 |x - 1 2 |x - 1 |x + 1 2 +--R - 3x |------ atanh( |------ ) + (x - 5x) |------ |----- - x + 4x + 5 +--R | 2 | 2 | 2 \|x - 1 +--R \| x \| x \| x +--R / +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 293 + +--S 294 of 489 +d0257:= D(m0257,x) +--R +--R +--R +------+ +--R +-----+ | 2 +--R 3 2 |x + 1 3 2 |x - 1 +--R (- x - x + x + 1) |----- + (x + 2x + x) |------ +--R \|x - 1 | 2 +--R \| x +--R (218) ----------------------------------------------------- +--R +------+ +--R | 2 +-----+ +--R 3 2 |x - 1 |x + 1 +--R (x - 2x + x) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 294 + +--S 295 of 489 +t0258:= exp(1)^(3*acoth(x))/x +--R +--R +--R 3acoth(x) +--R %e +--R (219) ----------- +--R x +--R Type: Expression Integer +--E 295 + +--S 296 of 489 +r0258:= -4/(1-1/x^2)^(1/2)-4/(1-1/x^2)^(1/2)/x+acsc(x)+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R |x - 1 |x - 1 |x - 1 +--R x |------ atanh( |------ ) + x acsc(x) |------ - 4x - 4 +--R | 2 | 2 | 2 +--R \| x \| x \| x +--R (220) -------------------------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 296 + +--S 297 of 489 +a0258:= integrate(t0258,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 |x + 1 +--R (221) log( |----- + 1) - log( |----- - 1) + 2atan( |----- ) - 4 |----- +--R \|x - 1 \|x - 1 \|x - 1 \|x - 1 +--R Type: Union(Expression Integer,...) +--E 297 + +--S 298 of 489 +m0258:= a0258-r0258 +--R +--R +--R (222) +--R +------+ +------+ +--R | 2 +-----+ | 2 +-----+ +--R |x - 1 |x + 1 |x - 1 |x + 1 +--R x |------ log( |----- + 1) - x |------ log( |----- - 1) +--R | 2 \|x - 1 | 2 \|x - 1 +--R \| x \| x +--R + +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +-----+ +--R |x - 1 |x - 1 |x - 1 |x + 1 +--R - x |------ atanh( |------ ) + 2x |------ atan( |----- ) +--R | 2 | 2 | 2 \|x - 1 +--R \| x \| x \| x +--R + +--R +------+ +------+ +--R | 2 +-----+ | 2 +--R |x - 1 |x + 1 |x - 1 +--R - 4x |------ |----- - x acsc(x) |------ + 4x + 4 +--R | 2 \|x - 1 | 2 +--R \| x \| x +--R / +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 298 + +--S 299 of 489 +d0258:= D(m0258,x) +--R +--R +--R (223) +--R +------+ +--R +-----+ | 2 +------+ +--R 2 |x + 1 2 |x - 1 | 2 +--R ((- x - 2x + 3) |----- + (x + 2x + 1) |------ )\|x - 1 +--R \|x - 1 | 2 +--R \| x +--R + +--R +------+ +--R | 2 +-----+ +--R 2 |x - 1 |x + 1 +--R (x - 2x + 1) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +-----+ +------+ +--R 3 2 |x - 1 |x + 1 | 2 +--R (x - 2x + x) |------ |----- \|x - 1 +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 299 + +--S 300 of 489 +t0259:= exp(1)^(3*acoth(x))/x^2 +--R +--R +--R 3acoth(x) +--R %e +--R (224) ----------- +--R 2 +--R x +--R Type: Expression Integer +--E 300 + +--S 301 of 489 +r0259:= (-5*x^2+1-4*x+3*acsc(x)*_ + ((-1+x^2)/x^2)^(1/2)*x^2)/((-1+x^2)/x^2)^(1/2)/x^2 +--R +--R +--R +------+ +--R | 2 +--R 2 |x - 1 2 +--R 3x acsc(x) |------ - 5x - 4x + 1 +--R | 2 +--R \| x +--R (225) ---------------------------------- +--R +------+ +--R | 2 +--R 2 |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 301 + +--S 302 of 489 +a0259:= integrate(t0259,x) +--R +--R +--R +-----+ +-----+ +--R |x + 1 |x + 1 +--R 6x atan( |----- ) + (- 5x + 1) |----- +--R \|x - 1 \|x - 1 +--R (226) -------------------------------------- +--R x +--R Type: Union(Expression Integer,...) +--E 302 + +--S 303 of 489 +m0259:= a0259-r0259 +--R +--R +--R (227) +--R +------+ +------+ +--R | 2 +-----+ | 2 +-----+ +--R 2 |x - 1 |x + 1 2 |x - 1 |x + 1 +--R 6x |------ atan( |----- ) + (- 5x + x) |------ |----- +--R | 2 \|x - 1 | 2 \|x - 1 +--R \| x \| x +--R + +--R +------+ +--R | 2 +--R 2 |x - 1 2 +--R - 3x acsc(x) |------ + 5x + 4x - 1 +--R | 2 +--R \| x +--R / +--R +------+ +--R | 2 +--R 2 |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 303 + +--S 304 of 489 +d0259:= D(m0259,x) +--R +--R +--R (228) +--R +------+ +--R +-----+ | 2 +------+ +--R 3 2 |x + 1 3 2 |x - 1 | 2 +--R ((- 4x + 5x - 2x + 1) |----- + (x + 2x + x) |------ )\|x - 1 +--R \|x - 1 | 2 +--R \| x +--R + +--R +------+ +--R | 2 +-----+ +--R 4 3 2 |x - 1 |x + 1 +--R (3x - 6x + 3x ) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +-----+ +------+ +--R 5 4 3 |x - 1 |x + 1 | 2 +--R (x - 2x + x ) |------ |----- \|x - 1 +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 304 + +--S 305 of 489 +t0260:= exp(1)^(3*acoth(x))/x^3 +--R +--R +--R 3acoth(x) +--R %e +--R (229) ----------- +--R 3 +--R x +--R Type: Expression Integer +--E 305 + +--S 306 of 489 +r0260:= -7*((-1+x^2)/x^2)^(1/2)-_ + 4*((-1+x^2)/x^2)^(1/2)/(-1+x)-1/2*((-1+x^2)/x^2)^(1/2)/x+9/2*acsc(x) +--R +--R +--R +------+ +--R | 2 +--R 2 |x - 1 2 +--R (- 14x + 5x + 1) |------ + (9x - 9x)acsc(x) +--R | 2 +--R \| x +--R (230) ---------------------------------------------- +--R 2 +--R 2x - 2x +--R Type: Expression Integer +--E 306 + +--S 307 of 489 +a0260:= integrate(t0260,x) +--R +--R +--R +-----+ +-----+ +--R 2 |x + 1 2 |x + 1 +--R 18x atan( |----- ) + (- 14x + 5x + 1) |----- +--R \|x - 1 \|x - 1 +--R (231) ---------------------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression Integer,...) +--E 307 + +--S 308 of 489 +m0260:= a0260-r0260 +--R +--R +--R (232) +--R +-----+ +-----+ +--R 3 2 |x + 1 3 2 |x + 1 +--R (18x - 18x )atan( |----- ) + (- 14x + 19x - 4x - 1) |----- +--R \|x - 1 \|x - 1 +--R + +--R +------+ +--R | 2 +--R 3 2 |x - 1 3 2 +--R (14x - 5x - x) |------ + (- 9x + 9x )acsc(x) +--R | 2 +--R \| x +--R / +--R 3 2 +--R 2x - 2x +--R Type: Expression Integer +--E 308 + +--S 309 of 489 +d0260:= D(m0260,x) +--R +--R +--R (233) +--R +------+ +--R +-----+ | 2 +--R 4 3 2 |x + 1 3 2 |x - 1 +--R ((- 9x + 16x - 11x + 2x + 2) |----- + (2x + 4x + 2x) |------ ) +--R \|x - 1 | 2 +--R \| x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R +------+ +--R | 2 +-----+ +--R 5 4 3 |x - 1 |x + 1 +--R (9x - 18x + 9x ) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +-----+ +------+ +--R 6 5 4 |x - 1 |x + 1 | 2 +--R (2x - 4x + 2x ) |------ |----- \|x - 1 +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 309 + +--S 310 of 489 +t0261:= x^2*exp(1)^(1/2*acoth(x)) +--R +--R +--R acoth(x) +--R -------- +--R 2 2 +--R (234) x %e +--R Type: Expression Integer +--E 310 + +--S 311 of 489 +r0261:= -1/6*(16*x^3+4*x^2+2*x-22+18*atan(1/((-1+x)/(1+x))^(1/4))*_ + ((-1+x)/(1+x))^(1/4)+9*log((((-1+x)/(1+x))^(1/4)+1)/_ + ((-1+x)/(1+x))^(1/4))*((-1+x)/(1+x))^(1/4)-_ + 9*log(-(((-1+x)/(1+x))^(1/4)-1)/((-1+x)/(1+x))^(1/4))*_ + ((-1+x)/(1+x))^(1/4))*((-1+x)/(1+x))^(3/4)/_ + (((-1+x)/(1+x))^(1/2)+1)^3/(((-1+x)/(1+x))^(1/4)+1)^3/_ + (((-1+x)/(1+x))^(1/4)-1)^3/(-1+x)/(1+x)^2 +--R +--R +--R (235) +--R +-----+ +-----+ +--R |x - 1 |x - 1 +--R 4|----- + 1 - 4|----- + 1 +--R \|x + 1 \|x + 1 1 +--R - 9log(------------) + 9log(--------------) - 18atan(--------) +--R +-----+ +-----+ +-----+ +--R |x - 1 |x - 1 |x - 1 +--R 4|----- 4|----- 4|----- +--R \|x + 1 \|x + 1 \|x + 1 +--R + +--R +-----+3 +--R 3 2 |x - 1 +--R (- 16x - 36x - 42x - 22) 4|----- +--R \|x + 1 +--R / +--R +-----+ +-----+2 +--R 3 2 |x - 1 3 2 |x - 1 +--R ((96x + 192x + 120x + 24) |----- + 96x + 96x - 24x - 24) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 3 2 |x - 1 3 +--R (- 96x - 96x + 24x + 24) |----- - 96x + 72x - 24 +--R \|x + 1 +--R Type: Expression Integer +--E 311 + +--S 312 of 489 +a0261:= integrate(t0261,x) +--R +--R +--R (236) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 4 4 +--R 9log(%e + 1) - 9log(%e - 1) + 18atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 3 2 4 +--R (16x + 4x + 2x - 22)%e +--R / +--R 48 +--R Type: Union(Expression Integer,...) +--E 312 + +--S 313 of 489 +m0261:= a0261-r0261 +--R +--R +--R (237) +--R +-----+ +-----+2 +--R 3 2 |x - 1 3 2 |x - 1 +--R ((36x + 72x + 45x + 9) |----- + 36x + 36x - 9x - 9) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 3 2 |x - 1 3 +--R (- 36x - 36x + 9x + 9) |----- - 36x + 27x - 9 +--R \|x + 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R log(%e + 1) +--R + +--R +-----+ +-----+2 +--R 3 2 |x - 1 3 2 |x - 1 +--R ((- 36x - 72x - 45x - 9) |----- - 36x - 36x + 9x + 9) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 3 2 |x - 1 3 +--R (36x + 36x - 9x - 9) |----- + 36x - 27x + 9 +--R \|x + 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R log(%e - 1) +--R + +--R +-----+ +-----+2 +--R 3 2 |x - 1 3 2 |x - 1 +--R ((72x + 144x + 90x + 18) |----- + 72x + 72x - 18x - 18) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 3 2 |x - 1 3 +--R (- 72x - 72x + 18x + 18) |----- - 72x + 54x - 18 +--R \|x + 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R atan(%e ) +--R + +--R +-----+ +-----+ +--R |x - 1 |x - 1 +--R 4|----- + 1 - 4|----- + 1 +--R \|x + 1 \|x + 1 +--R 18log(------------) - 18log(--------------) +--R +-----+ +-----+ +--R |x - 1 |x - 1 +--R 4|----- 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 +--R (64x + 144x + 120x - 36x - 162x - 108x - 22) |----- + 64x +--R \|x + 1 +--R + +--R 5 4 3 2 +--R 80x + 8x - 100x - 94x + 20x + 22 +--R * +--R +-----+2 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 5 +--R (- 64x - 80x - 8x + 100x + 94x - 20x - 22) |----- - 64x - 16x +--R \|x + 1 +--R + +--R 4 3 2 +--R 40x + 84x + 2x - 68x + 22 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R +-----+3 +--R 1 3 2 |x - 1 +--R 36atan(--------) + (32x + 72x + 84x + 44) 4|----- +--R +-----+ \|x + 1 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R / +--R +-----+ +-----+2 +--R 3 2 |x - 1 3 2 |x - 1 +--R ((192x + 384x + 240x + 48) |----- + 192x + 192x - 48x - 48) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 3 2 |x - 1 3 +--R (- 192x - 192x + 48x + 48) |----- - 192x + 144x - 48 +--R \|x + 1 +--R Type: Expression Integer +--E 313 + +--S 314 of 489 +d0261:= D(m0261,x) +--R +--R +--R (238) +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((36x - 45x + 9) |----- + 36x - 36x - 27x + 27x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (- 36x + 36x + 27x - 27x) |----- - 36x + 72x - 27x - 18x + 9 +--R \|x + 1 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((- 36x + 45x - 9) |----- - 36x + 36x + 27x - 27x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (36x - 36x - 27x + 27x) |----- + 36x - 72x + 27x + 18x - 9 +--R \|x + 1 +--R * +--R +-----+ +--R |x - 1 +--R 4|----- + 1 +--R \|x + 1 +--R log(------------) +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((- 36x + 45x - 9) |----- - 36x + 36x + 27x - 27x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (36x - 36x - 27x + 27x) |----- + 36x - 72x + 27x + 18x - 9 +--R \|x + 1 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((36x - 45x + 9) |----- + 36x - 36x - 27x + 27x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (- 36x + 36x + 27x - 27x) |----- - 36x + 72x - 27x - 18x + 9 +--R \|x + 1 +--R * +--R +-----+ +--R |x - 1 +--R - 4|----- + 1 +--R \|x + 1 +--R log(--------------) +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R 10 8 7 6 5 4 3 2 +--R (512x - 1280x - 96x + 1152x + 144x - 432x - 54x + 54x ) +--R * +--R +-----+ +--R |x - 1 +--R |----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R 512x - 512x - 1024x + 928x + 800x - 608x - 288x + 174x +--R + +--R 2 +--R 36x - 18x +--R * +--R +-----+2 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 512x + 512x + 1024x - 928x - 800x + 608x + 288x - 174x +--R + +--R 2 +--R - 36x + 18x +--R * +--R +-----+ +--R |x - 1 +--R |----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 512x + 1024x + 256x - 1440x + 192x + 816x - 208x - 202x +--R + +--R 2 +--R 62x + 18x - 6 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((72x - 90x + 18) |----- + 72x - 72x - 54x + 54x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (- 72x + 72x + 54x - 54x) |----- - 72x + 144x - 54x - 36x +--R \|x + 1 +--R + +--R 18 +--R * +--R 1 +--R atan(--------) +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 5 +--R (- 16x - 56x + 60x + 122x - 44x - 66x) |----- - 16x - 40x +--R \|x + 1 +--R + +--R 4 3 2 +--R 92x + 42x - 98x - 2x + 22 +--R * +--R +-----+3 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 +--R (16x + 40x - 124x - 42x + 130x + 2x - 22) |----- + 16x +--R \|x + 1 +--R + +--R 5 4 3 2 +--R 24x - 140x + 78x + 88x - 66x +--R * +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R 10 8 7 6 5 4 3 +--R - 512x + 1280x + 96x - 960x - 144x + 144x + 54x +--R + +--R 2 +--R 54x +--R * +--R +-----+ +--R |x - 1 +--R |----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R - 512x + 512x + 1024x - 928x - 608x + 416x + 96x + 18x +--R + +--R - 18x +--R * +--R +-----+2 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R 512x - 512x - 1024x + 928x + 608x - 416x - 96x - 18x +--R + +--R 18x +--R * +--R +-----+ +--R |x - 1 +--R |----- +--R \|x + 1 +--R + +--R 10 9 8 7 6 5 4 3 +--R 512x - 1024x - 256x + 1440x - 384x - 432x + 112x + 10x +--R + +--R 2 +--R 22x + 6x - 6 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R +-----+ +-----+2 +--R 4 2 |x - 1 4 3 2 |x - 1 +--R ((- 72x + 90x - 18) |----- - 72x + 72x + 54x - 54x) 4|----- +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +--R 4 3 2 |x - 1 4 3 2 +--R (72x - 72x - 54x + 54x) |----- + 72x - 144x + 54x + 36x - 18 +--R \|x + 1 +--R * +--R 1 +--R atan(--------) +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 5 +--R (16x + 56x - 60x - 122x + 44x + 66x) |----- + 16x + 40x +--R \|x + 1 +--R + +--R 4 3 2 +--R - 92x - 42x + 98x + 2x - 22 +--R * +--R +-----+3 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 6 5 4 3 2 |x - 1 6 +--R (- 16x - 40x + 124x + 42x - 130x - 2x + 22) |----- - 16x +--R \|x + 1 +--R + +--R 5 4 3 2 +--R - 24x + 140x - 78x - 88x + 66x +--R * +--R +-----+ +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R / +--R +-----+ +--R 8 6 4 2 |x - 1 8 7 +--R (512x - 1280x + 1056x - 288x ) |----- + 512x - 512x +--R \|x + 1 +--R + +--R 6 5 4 3 2 +--R - 1024x + 1024x + 608x - 608x - 96x + 96x +--R * +--R +-----+2 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R 8 7 6 5 4 3 2 +--R (- 512x + 512x + 1024x - 1024x - 608x + 608x + 96x - 96x) +--R * +--R +-----+ +--R |x - 1 +--R |----- +--R \|x + 1 +--R + +--R 8 7 6 5 4 3 2 +--R - 512x + 1024x + 256x - 1536x + 480x + 576x - 256x - 64x + 32 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R +-----+ +--R 8 6 4 2 |x - 1 8 7 6 +--R (- 512x + 1280x - 1056x + 288x ) |----- - 512x + 512x + 1024x +--R \|x + 1 +--R + +--R 5 4 3 2 +--R - 1024x - 608x + 608x + 96x - 96x +--R * +--R +-----+2 +--R |x - 1 +--R 4|----- +--R \|x + 1 +--R + +--R +-----+ +--R 8 7 6 5 4 3 2 |x - 1 +--R (512x - 512x - 1024x + 1024x + 608x - 608x - 96x + 96x) |----- +--R \|x + 1 +--R + +--R 8 7 6 5 4 3 2 +--R 512x - 1024x - 256x + 1536x - 480x - 576x + 256x + 64x - 32 +--R Type: Expression Integer +--E 314 + +--S 315 of 489 +t0262:= x*exp(1)^(1/2*acoth(x)) +--R +--R +--R acoth(x) +--R -------- +--R 2 +--R (239) x %e +--R Type: Expression Integer +--E 315 + +--S 316 of 489 +r0262:= 1/8/(1-exp(1)^(1/2*acoth(x)))^2-3/(8-8*exp(1)^(1/2*acoth(x)))-_ + 1/8/(1+exp(1)^(1/2*acoth(x)))^2+3/(8+8*exp(1)^(1/2*acoth(x)))+_ + 1/2*exp(1)^(1/2*acoth(x))/(1+exp(1)^acoth(x))^2-_ + 3*exp(1)^(1/2*acoth(x))/(4+4*exp(1)^acoth(x))+_ + 1/4*atan(exp(1)^(1/2*acoth(x)))-1/8*log(-1+exp(1)^(1/2*acoth(x)))+_ + 1/8*log(1+exp(1)^(1/2*acoth(x))) +--R +--R +--R (240) +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R ((%e ) - 2(%e ) + 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (2(%e ) - 4(%e ) + 2)%e + (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 2(%e ) + 1 +--R * +--R acoth(x) +--R -------- +--R 2 +--R log(%e + 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (- (%e ) + 2(%e ) - 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)%e - (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R 2(%e ) - 1 +--R * +--R acoth(x) +--R -------- +--R 2 +--R log(%e - 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (2(%e ) - 4(%e ) + 2)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (4(%e ) - 8(%e ) + 4)%e + 2(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 4(%e ) + 2 +--R * +--R acoth(x) +--R -------- +--R 2 +--R atan(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (6(%e ) - 2%e )(%e ) +--R + +--R acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- +--R 2 2 2 acoth(x) +--R (- 6(%e ) + 24(%e ) - 10%e )%e +--R + +--R acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- +--R 2 2 2 +--R - 2(%e ) + 10(%e ) - 4%e +--R / +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (8(%e ) - 16(%e ) + 8)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (16(%e ) - 32(%e ) + 16)%e + 8(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 16(%e ) + 8 +--R Type: Expression Integer +--E 316 + +--S 317 of 489 +a0262:= integrate(t0262,x) +--R +--R +--R (241) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 4 4 +--R log(%e + 1) - log(%e - 1) + 2atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 4 +--R (4x + 2x - 6)%e +--R / +--R 8 +--R Type: Union(Expression Integer,...) +--E 317 + +--S 318 of 489 +m0262:= a0262-r0262 +--R +--R +--R (242) +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R ((%e ) - 2(%e ) + 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (2(%e ) - 4(%e ) + 2)%e + (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 2(%e ) + 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R log(%e + 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (- (%e ) + 2(%e ) - 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)%e - (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R 2(%e ) - 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R log(%e - 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (- (%e ) + 2(%e ) - 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)%e - (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R 2(%e ) - 1 +--R * +--R acoth(x) +--R -------- +--R 2 +--R log(%e + 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R ((%e ) - 2(%e ) + 1)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (2(%e ) - 4(%e ) + 2)%e + (%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 2(%e ) + 1 +--R * +--R acoth(x) +--R -------- +--R 2 +--R log(%e - 1) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (2(%e ) - 4(%e ) + 2)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (4(%e ) - 8(%e ) + 4)%e + 2(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 4(%e ) + 2 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R atan(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (- 2(%e ) + 4(%e ) - 2)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (- 4(%e ) + 8(%e ) - 4)%e - 2(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R 4(%e ) - 2 +--R * +--R acoth(x) +--R -------- +--R 2 +--R atan(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 2 2 +--R (4x + 2x - 6)(%e ) + (- 8x - 4x + 12)(%e ) +--R + +--R 2 +--R 4x + 2x - 6 +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 2 2 +--R (8x + 4x - 12)(%e ) + (- 16x - 8x + 24)(%e ) +--R + +--R 2 +--R 8x + 4x - 12 +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R (4x + 2x - 6)(%e ) + (- 8x - 4x + 12)(%e ) + 4x +--R + +--R 2x - 6 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (- 6(%e ) + 2%e )(%e ) +--R + +--R acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- +--R 2 2 2 acoth(x) +--R (6(%e ) - 24(%e ) + 10%e )%e +--R + +--R acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- +--R 2 2 2 +--R 2(%e ) - 10(%e ) + 4%e +--R / +--R acoth(x) 4 acoth(x) 2 +--R -------- -------- +--R 2 2 acoth(x) 2 +--R (8(%e ) - 16(%e ) + 8)(%e ) +--R + +--R acoth(x) 4 acoth(x) 2 acoth(x) 4 +--R -------- -------- -------- +--R 2 2 acoth(x) 2 +--R (16(%e ) - 32(%e ) + 16)%e + 8(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 +--R - 16(%e ) + 8 +--R Type: Expression Integer +--E 318 + +--S 319 of 489 +d0262:= D(m0262,x) +--R +--R +--R (243) +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (8x - 9x + 1)(%e ) + (- 16x + 18x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (16x - 18x + 2)(%e ) - 8x + 9x - 1 +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (24x - 27x + 3)(%e ) + (- 48x + 54x - 6)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (48x - 54x + 6)(%e ) - 24x + 27x - 3 +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (24x - 27x + 3)(%e ) + (- 48x + 54x - 6)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (48x - 54x + 6)(%e ) - 24x + 27x - 3 +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (8x - 9x + 1)(%e ) + (- 16x + 18x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (16x - 18x + 2)(%e ) - 8x + 9x - 1 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 7 acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (- 3(%e ) - 11(%e ) - (%e ) - %e ) +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 +--R -------- -------- -------- +--R 2 2 2 +--R 3(%e ) - 15(%e ) - 33(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 +--R 3(%e ) - 6%e +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 +--R -------- -------- -------- +--R 2 2 2 +--R - 6(%e ) + 3(%e ) - 33(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 +--R - 15(%e ) + 3%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R - (%e ) - (%e ) - 11(%e ) - 3(%e ) +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (- 8x + 9x + 1)(%e ) + (16x - 18x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (- 16x + 18x + 2)(%e ) + 8x - 9x - 1 +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (- 24x + 27x + 3)(%e ) + (48x - 54x - 6)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (- 48x + 54x + 6)(%e ) + 24x - 27x - 3 +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (- 24x + 27x + 3)(%e ) + (48x - 54x - 6)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (- 48x + 54x + 6)(%e ) + 24x - 27x - 3 +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 3 2 3 2 +--R (- 8x + 9x + 1)(%e ) + (16x - 18x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 3 +--R (- 16x + 18x + 2)(%e ) + 8x - 9x - 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R acoth(x) 7 acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (3(%e ) + 11(%e ) + (%e ) + %e ) +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R - 3(%e ) + 15(%e ) + 33(%e ) - 3(%e ) +--R + +--R acoth(x) +--R -------- +--R 2 +--R 6%e +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R 6(%e ) - 3(%e ) + 33(%e ) + 15(%e ) +--R + +--R acoth(x) +--R -------- +--R 2 +--R - 3%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (%e ) + (%e ) + 11(%e ) + 3(%e ) +--R / +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (8x - 8)(%e ) + (- 16x + 16)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (16x - 16)(%e ) - 8x + 8 +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (24x - 24)(%e ) + (- 48x + 48)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (48x - 48)(%e ) - 24x + 24 +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (24x - 24)(%e ) + (- 48x + 48)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (48x - 48)(%e ) - 24x + 24 +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (8x - 8)(%e ) + (- 16x + 16)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (16x - 16)(%e ) - 8x + 8 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (- 8x + 8)(%e ) + (16x - 16)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 16x + 16)(%e ) + 8x - 8 +--R * +--R acoth(x) 3 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (- 24x + 24)(%e ) + (48x - 48)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 48x + 48)(%e ) + 24x - 24 +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (- 24x + 24)(%e ) + (48x - 48)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 48x + 48)(%e ) + 24x - 24 +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 8 acoth(x) 6 +--R -------- -------- +--R 2 2 2 2 +--R (- 8x + 8)(%e ) + (16x - 16)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 16x + 16)(%e ) + 8x - 8 +--R Type: Expression Integer +--E 319 + +--S 320 of 489 +t0263:= exp(1)^(1/2*acoth(x)) +--R +--R +--R acoth(x) +--R -------- +--R 2 +--R (244) %e +--R Type: Expression Integer +--E 320 + +--S 321 of 489 +r0263:= -(1-x)^(3/4)*(1+x)^(1/4)+1/4*2^(1/2)*(2*%pi-_ + 2*acot(-1+2^(1/2)*(1-x)^(1/4)/(1+x)^(1/4))-_ + 2*acot(1+2^(1/2)*(1-x)^(1/4)/(1+x)^(1/4))-_ + log(1+(1-x)^(1/2)/(1+x)^(1/2)-2^(1/2)*_ + (1-x)^(1/4)/(1+x)^(1/4))+log(1+(1-x)^(1/2)/(1+x)^(1/2)+_ + 2^(1/2)*(1-x)^(1/4)/(1+x)^(1/4))) +--R +--R +--R (245) +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R - \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ \|x + 1 + \|2 \|- x + 1 +--R - 2\|2 acot(-------------------------) +--R 4+-----+ +--R \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ - \|x + 1 + \|2 \|- x + 1 4+-------+3 4+-----+ +-+ +--R - 2\|2 acot(---------------------------) - 4\|- x + 1 \|x + 1 + 2%pi\|2 +--R 4+-----+ +--R \|x + 1 +--R / +--R 4 +--R Type: Expression Integer +--E 321 + +--S 322 of 489 +a0263:= integrate(t0263,x) +--R +--R +--R (246) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 4 4 +--R log(%e + 1) - log(%e - 1) + 2atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (2x - 2)%e +--R / +--R 2 +--R Type: Union(Expression Integer,...) +--E 322 + +--S 323 of 489 +m0263:= a0263-r0263 +--R +--R +--R (247) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 4 4 +--R 2log(%e + 1) - 2log(%e - 1) + 4atan(%e ) +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 + \|2 \|- x + 1 \|x + 1 +--R - \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R +-----+ +-------+ 4+-----+ +-+4+-------+ +-----+ +--R +-+ (\|x + 1 + \|- x + 1 )\|x + 1 - \|2 \|- x + 1 \|x + 1 +--R \|2 log(--------------------------------------------------------) +--R +-----+4+-----+ +--R \|x + 1 \|x + 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- 4+-----+ +-+4+-------+ +--R 4 +-+ \|x + 1 + \|2 \|- x + 1 +--R (4x - 4)%e + 2\|2 acot(-------------------------) +--R 4+-----+ +--R \|x + 1 +--R + +--R 4+-----+ +-+4+-------+ +--R +-+ - \|x + 1 + \|2 \|- x + 1 4+-------+3 4+-----+ +-+ +--R 2\|2 acot(---------------------------) + 4\|- x + 1 \|x + 1 - 2%pi\|2 +--R 4+-----+ +--R \|x + 1 +--R / +--R 4 +--R Type: Expression Integer +--E 323 + +--S 324 of 489 +d0263:= D(m0263,x) +--R +--R +--R (248) +--R 2 4+-------+3 4+-----+3 +--R (4x - 2x - 2)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ +--R (- 4x + 2x + 2)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 4+-------+ +--R (- 4x + 2x + 2)\|- x + 1 +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R 2 +-------+ +-----+ 2 4+-----+2 +--R ((4x - 3x - 1)\|- x + 1 \|x + 1 + 5x - 3x - 2)\|x + 1 +--R + +--R +-------+4+-------+2 +-----+ 3 2 4+-------+2 +--R x\|- x + 1 \|- x + 1 \|x + 1 + (- 4x - x + 6x + 3)\|- x + 1 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R 2 4+-------+3 4+-----+3 +--R (- 4x + 2x + 6)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ +--R (4x - 2x - 6)\|- x + 1 \|- x + 1 \|x + 1 +--R + +--R 2 4+-------+ +--R (4x - 2x - 6)\|- x + 1 +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R 2 +-------+ +-----+ 2 4+-----+2 +--R ((- 4x + 3x + 1)\|- x + 1 \|x + 1 - 5x + 3x + 2)\|x + 1 +--R + +--R +-------+4+-------+2 +-----+ 3 2 4+-------+2 +--R - x\|- x + 1 \|- x + 1 \|x + 1 + (4x + x - 6x - 3)\|- x + 1 +--R / +--R 2 4+-------+3 4+-----+3 +--R (4x - 4)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ 2 4+-------+ +--R ((- 4x + 4)\|- x + 1 \|- x + 1 \|x + 1 + (- 4x + 4)\|- x + 1 ) +--R * +--R 4+-----+ +--R \|x + 1 +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R 2 4+-------+3 4+-----+3 +--R (- 4x + 4)\|- x + 1 \|x + 1 +--R + +--R 2 +-------+4+-------+ +-----+ 2 4+-------+ 4+-----+ +--R ((4x - 4)\|- x + 1 \|- x + 1 \|x + 1 + (4x - 4)\|- x + 1 )\|x + 1 +--R Type: Expression Integer +--E 324 + +--S 325 of 489 +t0264:= exp(1)^(1/2*acoth(x))/x +--R +--R +--R acoth(x) +--R -------- +--R 2 +--R %e +--R (249) ---------- +--R x +--R Type: Expression Integer +--E 325 + +--S 326 of 489 +r0264:= 2*atan(exp(1)^(1/2*acoth(x)))-2^(1/2)*_ + atan(-1+2^(1/2)*exp(1)^(1/2*acoth(x)))-2^(1/2)*_ + atan(1+2^(1/2)*exp(1)^(1/2*acoth(x)))-log(-1+exp(1)^(1/2*acoth(x)))+_ + log(1+exp(1)^(1/2*acoth(x)))+1/2*log(1-2^(1/2)*_ + exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2)-_ + 1/2*log(1+2^(1/2)*exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2) +--R +--R +--R (250) +--R acoth(x) +--R -------- +--R +-+ acoth(x) +-+ 2 +--R - \|2 log(%e + \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ acoth(x) +-+ 2 2 +--R \|2 log(%e - \|2 %e + 1) + 2log(%e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R 2 +-+ +-+ 2 +--R - 2log(%e - 1) - 2\|2 atan(\|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ +-+ 2 2 +--R - 2\|2 atan(\|2 %e - 1) + 4atan(%e ) +--R / +--R 2 +--R Type: Expression Integer +--E 326 + +--S 327 of 489 +a0264:= integrate(t0264,x) +--R +--R +--R (251) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 4 +-+ 4 +--R - log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 +-+ 4 +-+ 4 +--R log((%e ) - \|2 %e + 1) + \|2 log(%e + 1) +--R + +--R x + 1 +--R x + 1 log(-----) +--R log(-----) x - 1 +--R x - 1 ---------- +--R ---------- 4 +--R +-+ 4 +-+ 2%e +--R - \|2 log(%e - 1) - \|2 atan(-------------------) +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) - 1 +--R + +--R 1 1 +--R 2atan(--------------------) + 2atan(--------------------) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression Integer,...) +--E 327 + +--S 328 of 489 +m0264:= a0264-r0264 +--R +--R +--R (252) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 4 +-+ 4 +--R - log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 4 +-+ 4 +-+ 4 +--R log((%e ) - \|2 %e + 1) + \|2 log(%e + 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 acoth(x) +--R ---------- -------- +--R +-+ 4 acoth(x) +-+ 2 +--R - \|2 log(%e - 1) + log(%e + \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R acoth(x) +-+ 2 +-+ 2 +--R - log(%e - \|2 %e + 1) - \|2 log(%e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ 2 +-+ 2 +--R \|2 log(%e - 1) + 2atan(\|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ 2 +-+ 2 +--R 2atan(\|2 %e - 1) - 2\|2 atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R +-+ 2%e 1 +--R - \|2 atan(-------------------) + 2atan(--------------------) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 4 +-+ 4 +--R (%e ) - 1 \|2 %e - 1 +--R + +--R 1 +--R 2atan(--------------------) +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R +-+ 4 +--R \|2 %e + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression Integer +--E 328 + +--S 329 of 489 +d0264:= D(m0264,x) +--R +--R +--R (253) +--R acoth(x) 7 acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (- (%e ) - 3(%e ) + (%e ) - %e ) +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (%e ) - 2(%e ) - 6(%e ) + 2(%e ) +--R + +--R acoth(x) +--R -------- +--R 2 +--R - 3%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R (%e ) + 5(%e ) - 5(%e ) + 3(%e ) +--R * +--R x + 1 8 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 8 acoth(x) 8 +--R -------- -------- +--R 2 acoth(x) 2 2 acoth(x) +--R (4(%e ) - 4)(%e ) + (8(%e ) - 8)%e +--R + +--R acoth(x) 10 acoth(x) 8 acoth(x) 2 +--R -------- -------- -------- +--R 2 2 2 +--R - 8(%e ) + 4(%e ) + 8(%e ) - 4 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 7 acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R ((%e ) + 3(%e ) - (%e ) + %e ) +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R - (%e ) + 2(%e ) + 6(%e ) - 2(%e ) +--R + +--R acoth(x) +--R -------- +--R 2 +--R 3%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 9 acoth(x) 7 acoth(x) 5 acoth(x) 3 +--R -------- -------- -------- -------- +--R 2 2 2 2 +--R - (%e ) - 5(%e ) + 5(%e ) - 3(%e ) +--R / +--R acoth(x) 8 +--R -------- +--R 2 2 2 acoth(x) 2 +--R ((x - 1)(%e ) - x + 1)(%e ) +--R + +--R acoth(x) 8 +--R -------- +--R 2 2 2 acoth(x) +--R ((2x - 2)(%e ) - 2x + 2)%e +--R + +--R acoth(x) 10 acoth(x) 8 +--R -------- -------- +--R 2 2 2 2 +--R (- 2x + 2)(%e ) + (x - 1)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (2x - 2)(%e ) - x + 1 +--R * +--R x + 1 8 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 8 +--R -------- +--R 2 2 2 acoth(x) 2 +--R ((- x + 1)(%e ) + x - 1)(%e ) +--R + +--R acoth(x) 8 acoth(x) 10 +--R -------- -------- +--R 2 2 2 acoth(x) 2 2 +--R ((- 2x + 2)(%e ) + 2x - 2)%e + (2x - 2)(%e ) +--R + +--R acoth(x) 8 acoth(x) 2 +--R -------- -------- +--R 2 2 2 2 2 +--R (- x + 1)(%e ) + (- 2x + 2)(%e ) + x - 1 +--R Type: Expression Integer +--E 329 + +--S 330 of 489 +t0265:= exp(1)^(1/2*acoth(x))/x^2 +--R +--R +--R acoth(x) +--R -------- +--R 2 +--R %e +--R (254) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 330 + +--S 331 of 489 +r0265:= -exp(1)^(1/2*acoth(x))*(1-x)/x-1/2*2^(1/2)*atan(-1+2^(1/2)*_ + exp(1)^(1/2*acoth(x)))-1/2*2^(1/2)*atan(1+2^(1/2)*_ + exp(1)^(1/2*acoth(x)))+1/4*log(1-2^(1/2)*_ + exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2)-_ + 1/4*log(1+2^(1/2)*exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2) +--R +--R +--R (255) +--R acoth(x) +--R -------- +--R +-+ acoth(x) +-+ 2 +--R - x\|2 log(%e + \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R +-+ acoth(x) +-+ 2 +--R x\|2 log(%e - \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ +-+ 2 +-+ +-+ 2 +--R - 2x\|2 atan(\|2 %e + 1) - 2x\|2 atan(\|2 %e - 1) +--R + +--R acoth(x) +--R -------- +--R 2 +--R (4x - 4)%e +--R / +--R 4x +--R Type: Expression Integer +--E 331 + +--S 332 of 489 +a0265:= integrate(t0265,x) +--R +--R +--R (256) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R - x\|2 log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R x\|2 log((%e ) - \|2 %e + 1) +--R + +--R +-+ 1 +-+ 1 +--R 2x\|2 atan(--------------------) + 2x\|2 atan(--------------------) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (4x - 4)%e +--R / +--R 4x +--R Type: Union(Expression Integer,...) +--E 332 + +--S 333 of 489 +m0265:= a0265-r0265 +--R +--R +--R (257) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R - x\|2 log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R x\|2 log((%e ) - \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R +-+ acoth(x) +-+ 2 +--R x\|2 log(%e + \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R +-+ acoth(x) +-+ 2 +--R - x\|2 log(%e - \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R +-+ +-+ 2 +-+ +-+ 2 +--R 2x\|2 atan(\|2 %e + 1) + 2x\|2 atan(\|2 %e - 1) +--R + +--R +-+ 1 +-+ 1 +--R 2x\|2 atan(--------------------) + 2x\|2 atan(--------------------) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 acoth(x) +--R ---------- -------- +--R 4 2 +--R (4x - 4)%e + (- 4x + 4)%e +--R / +--R 4x +--R Type: Expression Integer +--E 333 + +--S 334 of 489 +d0265:= D(m0265,x) +--R +--R +--R (258) +--R acoth(x) 4 +--R -------- +--R 2 2 2 acoth(x) 2 +--R ((x + x - 2)(%e ) + x + x - 2)(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 2 2 2 acoth(x) +--R ((2x + 2x - 4)(%e ) + 2x + 2x - 4)%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 2x - 2x + 4)(%e ) + (x + x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 2x - 2x + 4)(%e ) + x + x - 2 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R (- x - x + 2)(%e ) - x (%e ) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (- 2x - x + 2)%e +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R (- x - 2x + 4)(%e ) - 2x (%e ) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (- 3x - 2x + 4)%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 7 acoth(x) 5 +--R -------- -------- +--R 2 2 2 +--R (2x + 2x - 4)(%e ) + (- x + 2)(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 2 2 +--R (3x + 2x - 4)(%e ) + (- 3x - x + 2)%e +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 2 2 2 acoth(x) 2 +--R ((3x + x - 2)(%e ) + 3x + x - 2)(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 2 2 2 acoth(x) +--R ((6x + 2x - 4)(%e ) + 6x + 2x - 4)%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 2 2 2 2 +--R (- 6x - 2x + 4)(%e ) + (3x + x - 2)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 2 2 2 +--R (- 6x - 2x + 4)(%e ) + 3x + x - 2 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R (- x - x + 2)(%e ) - x (%e ) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (- 2x - x + 2)%e +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 2 2 2 2 +--R (- x - 2x + 4)(%e ) - 2x (%e ) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (- 3x - 2x + 4)%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 7 acoth(x) 5 +--R -------- -------- +--R 2 2 2 +--R (2x + 2x - 4)(%e ) + (- x + 2)(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 2 2 2 2 +--R (3x + 2x - 4)(%e ) + (- 3x - x + 2)%e +--R / +--R acoth(x) 4 +--R -------- +--R 4 2 2 4 2 acoth(x) 2 +--R ((2x - 2x )(%e ) + 2x - 2x )(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 4 2 2 4 2 acoth(x) +--R ((4x - 4x )(%e ) + 4x - 4x )%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (- 4x + 4x )(%e ) + (2x - 2x )(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 4x + 4x )(%e ) + 2x - 2x +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 4 2 2 4 2 acoth(x) 2 +--R ((2x - 2x )(%e ) + 2x - 2x )(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 4 2 2 4 2 acoth(x) +--R ((4x - 4x )(%e ) + 4x - 4x )%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 4 2 2 4 2 2 +--R (- 4x + 4x )(%e ) + (2x - 2x )(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 4 2 2 4 2 +--R (- 4x + 4x )(%e ) + 2x - 2x +--R Type: Expression Integer +--E 334 + +--S 335 of 489 +t0266:= exp(1)^(1/2*acoth(x))/x^3 +--R +--R +--R acoth(x) +--R -------- +--R 2 +--R %e +--R (259) ---------- +--R 3 +--R x +--R Type: Expression Integer +--E 335 + +--S 336 of 489 +r0266:= -1/2*exp(1)^(1/2*acoth(x))*(1-x)^2/x^2-_ + 5/4*exp(1)^(1/2*acoth(x))*(1-x)/x-_ + 1/8*2^(1/2)*atan(-1+2^(1/2)*exp(1)^(1/2*acoth(x)))-_ + 1/8*2^(1/2)*atan(1+2^(1/2)*exp(1)^(1/2*acoth(x)))+_ + 1/16*log(1-2^(1/2)*exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2)-_ + 1/16*log(1+2^(1/2)*exp(1)^(1/2*acoth(x))+exp(1)^acoth(x))*2^(1/2) +--R +--R +--R (260) +--R acoth(x) +--R -------- +--R 2 +-+ acoth(x) +-+ 2 +--R - x \|2 log(%e + \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R 2 +-+ acoth(x) +-+ 2 +--R x \|2 log(%e - \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R 2 +-+ +-+ 2 2 +-+ +-+ 2 +--R - 2x \|2 atan(\|2 %e + 1) - 2x \|2 atan(\|2 %e - 1) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (12x - 4x - 8)%e +--R / +--R 2 +--R 16x +--R Type: Expression Integer +--E 336 + +--S 337 of 489 +a0266:= integrate(t0266,x) +--R +--R +--R (261) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 +-+ 4 +-+ 4 +--R - x \|2 log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 +-+ 4 +-+ 4 +--R x \|2 log((%e ) - \|2 %e + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R 2x \|2 atan(--------------------) + 2x \|2 atan(--------------------) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 4 +--R (12x - 4x - 8)%e +--R / +--R 2 +--R 16x +--R Type: Union(Expression Integer,...) +--E 337 + +--S 338 of 489 +m0266:= a0266-r0266 +--R +--R +--R (262) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 +-+ 4 +-+ 4 +--R - x \|2 log((%e ) + \|2 %e + 1) +--R + +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 +-+ 4 +-+ 4 +--R x \|2 log((%e ) - \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R 2 +-+ acoth(x) +-+ 2 +--R x \|2 log(%e + \|2 %e + 1) +--R + +--R acoth(x) +--R -------- +--R 2 +-+ acoth(x) +-+ 2 +--R - x \|2 log(%e - \|2 %e + 1) +--R + +--R acoth(x) acoth(x) +--R -------- -------- +--R 2 +-+ +-+ 2 2 +-+ +-+ 2 +--R 2x \|2 atan(\|2 %e + 1) + 2x \|2 atan(\|2 %e - 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R 2x \|2 atan(--------------------) + 2x \|2 atan(--------------------) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R +-+ 4 +-+ 4 +--R \|2 %e - 1 \|2 %e + 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 acoth(x) +--R ---------- -------- +--R 2 4 2 2 +--R (12x - 4x - 8)%e + (- 12x + 4x + 8)%e +--R / +--R 2 +--R 16x +--R Type: Expression Integer +--E 338 + +--S 339 of 489 +d0266:= D(m0266,x) +--R +--R +--R (263) +--R acoth(x) 4 +--R -------- +--R 3 2 2 3 2 acoth(x) 2 +--R ((- x + 9x - 8)(%e ) - x + 9x - 8)(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 3 2 2 3 2 acoth(x) +--R ((- 2x + 18x - 16)(%e ) - 2x + 18x - 16)%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (2x - 18x + 16)(%e ) + (- x + 9x - 8)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (2x - 18x + 16)(%e ) - x + 9x - 8 +--R * +--R x + 1 5 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 3 2 2 3 2 +--R (x - 9x + 8)(%e ) - x (%e ) +--R + +--R acoth(x) +--R -------- +--R 2 2 +--R (- 9x + 8)%e +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 3 2 2 3 2 +--R (3x - 18x + 16)(%e ) - 2x (%e ) +--R + +--R acoth(x) +--R -------- +--R 3 2 2 +--R (x - 18x + 16)%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 7 acoth(x) 5 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 2x + 18x - 16)(%e ) + (2x - 9x + 8)(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x + 18x - 16)(%e ) + (- x - 9x + 8)%e +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 3 2 2 3 2 acoth(x) 2 +--R ((x + 9x - 8)(%e ) + x + 9x - 8)(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 3 2 2 3 2 acoth(x) +--R ((2x + 18x - 16)(%e ) + 2x + 18x - 16)%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 2x - 18x + 16)(%e ) + (x + 9x - 8)(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 3 2 2 3 2 +--R (- 2x - 18x + 16)(%e ) + x + 9x - 8 +--R * +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R %e +--R + +--R acoth(x) 5 acoth(x) 3 acoth(x) +--R -------- -------- -------- +--R 3 2 2 3 2 2 2 +--R ((x - 9x + 8)(%e ) - x (%e ) + (- 9x + 8)%e ) +--R * +--R acoth(x) 2 +--R (%e ) +--R + +--R acoth(x) 5 acoth(x) 3 +--R -------- -------- +--R 3 2 2 3 2 +--R (3x - 18x + 16)(%e ) - 2x (%e ) +--R + +--R acoth(x) +--R -------- +--R 3 2 2 +--R (x - 18x + 16)%e +--R * +--R acoth(x) +--R %e +--R + +--R acoth(x) 7 acoth(x) 5 +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- 2x + 18x - 16)(%e ) + (2x - 9x + 8)(%e ) +--R + +--R acoth(x) 3 acoth(x) +--R -------- -------- +--R 3 2 2 3 2 2 +--R (- x + 18x - 16)(%e ) + (- x - 9x + 8)%e +--R / +--R acoth(x) 4 +--R -------- +--R 5 3 2 5 3 acoth(x) 2 +--R ((8x - 8x )(%e ) + 8x - 8x )(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 5 3 2 5 3 acoth(x) +--R ((16x - 16x )(%e ) + 16x - 16x )%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 16x + 16x )(%e ) + (8x - 8x )(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 16x + 16x )(%e ) + 8x - 8x +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 +--R (%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 5 3 2 5 3 acoth(x) 2 +--R ((8x - 8x )(%e ) + 8x - 8x )(%e ) +--R + +--R acoth(x) 4 +--R -------- +--R 5 3 2 5 3 acoth(x) +--R ((16x - 16x )(%e ) + 16x - 16x )%e +--R + +--R acoth(x) 6 acoth(x) 4 +--R -------- -------- +--R 5 3 2 5 3 2 +--R (- 16x + 16x )(%e ) + (8x - 8x )(%e ) +--R + +--R acoth(x) 2 +--R -------- +--R 5 3 2 5 3 +--R (- 16x + 16x )(%e ) + 8x - 8x +--R Type: Expression Integer +--E 339 + +--S 340 of 489 +t0267:= exp(1)^acoth(x)*(1-x) +--R +--R +--R acoth(x) +--R (264) (- x + 1)%e +--R Type: Expression Integer +--E 340 + +--S 341 of 489 +r0267:= -1/2*(1-1/x^2)^(1/2)*x^2+1/2*atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 2 |x - 1 +--R atanh( |------ ) - x |------ +--R | 2 | 2 +--R \| x \| x +--R (265) ------------------------------ +--R 2 +--R Type: Expression Integer +--E 341 + +--S 342 of 489 +a0267:= integrate(t0267,x) +--R +--R +--R (266) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 2 +--R log(%e + 1) - log(%e - 1) + (- x + x)%e +--R ---------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression Integer,...) +--E 342 + +--S 343 of 489 +m0267:= a0267-r0267 +--R +--R +--R (267) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 2 +--R log(%e + 1) - log(%e - 1) + (- x + x)%e +--R + +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 2 |x - 1 +--R - atanh( |------ ) + x |------ +--R | 2 | 2 +--R \| x \| x +--R / +--R 2 +--R Type: Expression Integer +--E 343 + +--S 344 of 489 +d0267:= D(m0267,x) +--R +--R +--R (268) +--R x + 1 3 x + 1 2 +--R log(-----) log(-----) +--R x - 1 +------+ x - 1 +--R ---------- | 2 ---------- +--R 3 2 2 3 |x - 1 2 +--R (- 2x + 2x + x - 1)(%e ) + (2x - 2x) |------ (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +------+ +--R ---------- | 2 +--R 3 2 2 3 |x - 1 +--R (2x - 2x - x + 3)%e + (- 2x + 2x) |------ +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 2 2 +--R (2x - 2)(%e ) - 2x + 2 +--R Type: Expression Integer +--E 344 + +--S 345 of 489 +t0268:= exp(1)^acoth(x)/(1-x) +--R +--R +--R acoth(x) +--R %e +--R (269) - ---------- +--R x - 1 +--R Type: Expression Integer +--E 345 + +--S 346 of 489 +r0268:= -2*x*(-(1-x^2)/x^2)^(1/2)/(1-x)-atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R (- x + 1)atanh( |------ ) + 2x |------ +--R | 2 | 2 +--R \| x \| x +--R (270) --------------------------------------- +--R x - 1 +--R Type: Expression Integer +--E 346 + +--S 347 of 489 +a0268:= integrate(t0268,x) +--R +--R +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R (271) - log(%e + 1) + log(%e - 1) + 2%e +--R Type: Union(Expression Integer,...) +--E 347 + +--S 348 of 489 +m0268:= a0268-r0268 +--R +--R +--R (272) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 +--R (- x + 1)log(%e + 1) + (x - 1)log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +------+ +------+ +--R ---------- | 2 | 2 +--R 2 |x - 1 |x - 1 +--R (2x - 2)%e + (x - 1)atanh( |------ ) - 2x |------ +--R | 2 | 2 +--R \| x \| x +--R / +--R x - 1 +--R Type: Expression Integer +--E 348 + +--S 349 of 489 +d0268:= D(m0268,x) +--R +--R +--R (273) +--R x + 1 3 x + 1 2 +--R log(-----) log(-----) +--R +------+ x - 1 x - 1 +--R | 2 ---------- ---------- +--R |x - 1 2 2 2 2 +--R - 2x |------ (%e ) + (x + 2x + 1)(%e ) - x - 2x - 1 +--R | 2 +--R \| x +--R ------------------------------------------------------------------------- +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 3 |x - 1 2 3 |x - 1 +--R (x - x) |------ (%e ) + (- x + x) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 349 + +--S 350 of 489 +t0269:= exp(1)^acoth(x)/(-1+x) +--R +--R +--R acoth(x) +--R %e +--R (274) ---------- +--R x - 1 +--R Type: Expression Integer +--E 350 + +--S 351 of 489 +r0269:= 2*x*(-(1-x^2)/x^2)^(1/2)/(1-x)+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R (x - 1)atanh( |------ ) - 2x |------ +--R | 2 | 2 +--R \| x \| x +--R (275) ------------------------------------- +--R x - 1 +--R Type: Expression Integer +--E 351 + +--S 352 of 489 +a0269:= integrate(t0269,x) +--R +--R +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R (276) log(%e + 1) - log(%e - 1) - 2%e +--R Type: Union(Expression Integer,...) +--E 352 + +--S 353 of 489 +m0269:= a0269-r0269 +--R +--R +--R (277) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 +--R (x - 1)log(%e + 1) + (- x + 1)log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +------+ +------+ +--R ---------- | 2 | 2 +--R 2 |x - 1 |x - 1 +--R (- 2x + 2)%e + (- x + 1)atanh( |------ ) + 2x |------ +--R | 2 | 2 +--R \| x \| x +--R / +--R x - 1 +--R Type: Expression Integer +--E 353 + +--S 354 of 489 +d0269:= D(m0269,x) +--R +--R +--R (278) +--R x + 1 3 x + 1 2 +--R log(-----) log(-----) +--R +------+ x - 1 x - 1 +--R | 2 ---------- ---------- +--R |x - 1 2 2 2 2 +--R 2x |------ (%e ) + (- x - 2x - 1)(%e ) + x + 2x + 1 +--R | 2 +--R \| x +--R ------------------------------------------------------------------------- +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 3 |x - 1 2 3 |x - 1 +--R (x - x) |------ (%e ) + (- x + x) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 354 + +--S 355 of 489 +t0270:= exp(1)^acoth(x)*(1-x^2) +--R +--R +--R 2 acoth(x) +--R (279) (- x + 1)%e +--R Type: Expression Integer +--E 355 + +--S 356 of 489 +r0270:= -1/2*(1-1/x^2)^(1/2)*x^2-1/3*(1-1/x^2)^(3/2)*x^3+_ + 1/2*atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 3 2 |x - 1 +--R 3atanh( |------ ) + (- 2x - 3x + 2x) |------ +--R | 2 | 2 +--R \| x \| x +--R (280) ----------------------------------------------- +--R 6 +--R Type: Expression Integer +--E 356 + +--S 357 of 489 +a0270:= integrate(t0270,x) +--R +--R +--R (281) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 +--R 3log(%e + 1) - 3log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 3 2 2 +--R (- 2x - x + 5x - 2)%e +--R / +--R 6 +--R Type: Union(Expression Integer,...) +--E 357 + +--S 358 of 489 +m0270:= a0270-r0270 +--R +--R +--R (282) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 +--R 3log(%e + 1) - 3log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +------+ +--R ---------- | 2 +--R 3 2 2 |x - 1 +--R (- 2x - x + 5x - 2)%e - 3atanh( |------ ) +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 3 2 |x - 1 +--R (2x + 3x - 2x) |------ +--R | 2 +--R \| x +--R / +--R 6 +--R Type: Expression Integer +--E 358 + +--S 359 of 489 +d0270:= D(m0270,x) +--R +--R +--R (283) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 5 3 2 |x - 1 2 +--R (- 2x + 4x - x - x) |------ (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 5 4 3 2 2 +--R (2x + 2x - 4x - 4x + 2x + 2)(%e ) +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 5 3 2 |x - 1 2 5 4 3 2 +--R (2x - 4x + x + 3x) |------ %e - 2x - 2x + 4x + 4x - 2x - 2 +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 3 |x - 1 2 3 |x - 1 +--R (2x - 2x) |------ (%e ) + (- 2x + 2x) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 359 + +--S 360 of 489 +t0271:= exp(1)^acoth(x)/(1-x^2)^(3/2) +--R +--R +--R acoth(x) +--R %e +--R (284) - ------------------- +--R +--------+ +--R 2 | 2 +--R (x - 1)\|- x + 1 +--R Type: Expression Integer +--E 360 + +--S 361 of 489 +r0271:= -1/2*(1-1/x^2)^(1/2)*x*(1/(1-x)+atanh(x))/(1-x^2)^(1/2) +--R +--R +--R +------+ +--R | 2 +--R 2 |x - 1 +--R ((- x + x)atanh(x) + x) |------ +--R | 2 +--R \| x +--R (285) --------------------------------- +--R +--------+ +--R | 2 +--R (2x - 2)\|- x + 1 +--R Type: Expression Integer +--E 361 + +--S 362 of 489 +--a0271:= integrate(t0271,x) +--E 362 + +--S 363 of 489 +--m0271:= a0271-r0271 +--E 363 + +--S 364 of 489 +--d0271:= D(m0271,x) +--E 364 + +--S 365 of 489 +t0272:= exp(1)^acoth(x)/(1-x^2)^(5/2) +--R +--R +--R acoth(x) +--R %e +--R (286) ------------------------- +--R +--------+ +--R 4 2 | 2 +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression Integer +--E 365 + +--S 366 of 489 +r0272:= -1/8*(1-1/x^2)^(1/2)*x*(1/(1-x)^2+_ + 2/(1-x)-1/(1+x)+3*atanh(x))/(1-x^2)^(1/2) +--R +--R +--R +------+ +--R | 2 +--R 4 3 2 3 2 |x - 1 +--R ((- 3x + 3x + 3x - 3x)atanh(x) + 3x - 3x - 2x) |------ +--R | 2 +--R \| x +--R (287) ------------------------------------------------------------ +--R +--------+ +--R 3 2 | 2 +--R (8x - 8x - 8x + 8)\|- x + 1 +--R Type: Expression Integer +--E 366 + +--S 367 of 489 +--a0272:= integrate(t0272,x) +--E 367 + +--S 368 of 489 +--m0272:= a0272-r0272 +--E 368 + +--S 369 of 489 +--d0272:= D(m0272,x) +--E 369 + +--S 370 of 489 +t0273:= exp(1)^acoth(x)/(a-a*x^2)^(3/2) +--R +--R +--R acoth(x) +--R %e +--R (288) - ----------------------- +--R +----------+ +--R 2 | 2 +--R (a x - a)\|- a x + a +--R Type: Expression Integer +--E 370 + +--S 371 of 489 +r0273:= 1/2*(1-1/x^2)^(3/2)*x^3*(1/(1-x)+atanh(x))/(a-a*x^2)^(3/2) +--R +--R +--R +------+ +--R | 2 +--R 2 |x - 1 +--R ((- x + x)atanh(x) + x) |------ +--R | 2 +--R \| x +--R (289) --------------------------------- +--R +----------+ +--R | 2 +--R (2a x - 2a)\|- a x + a +--R Type: Expression Integer +--E 371 + +--S 372 of 489 +--a0273:= integrate(t0273,x) +--E 372 + +--S 373 of 489 +--m0273:= a0273-r0273 +--E 373 + +--S 374 of 489 +--d0273:= D(m0273,x) +--E 374 + +--S 375 of 489 +t0274:= exp(1)^acoth(x)/(a-a*x^2)^(5/2) +--R +--R +--R acoth(x) +--R %e +--R (290) -------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (a x - 2a x + a )\|- a x + a +--R Type: Expression Integer +--E 375 + +--S 376 of 489 +r0274:= -1/8*(1-1/x^2)^(5/2)*x^5*(1/(1-x)^2+2/(1-x)-1/(1+x)+_ + 3*atanh(x))/(a-a*x^2)^(5/2) +--R +--R +--R +------+ +--R | 2 +--R 4 3 2 3 2 |x - 1 +--R ((- 3x + 3x + 3x - 3x)atanh(x) + 3x - 3x - 2x) |------ +--R | 2 +--R \| x +--R (291) ------------------------------------------------------------ +--R +----------+ +--R 2 3 2 2 2 2 | 2 +--R (8a x - 8a x - 8a x + 8a )\|- a x + a +--R Type: Expression Integer +--E 376 + +--S 377 of 489 +--a0274:= integrate(t0274,x) +--E 377 + +--S 378 of 489 +--m0274:= a0274-r0274 +--E 378 + +--S 379 of 489 +--d0274:= D(m0274,x) +--E 379 + +--S 380 of 489 +t0275:= exp(1)^acoth(x)*(1-1/x^2) +--R +--R +--R 2 acoth(x) +--R (x - 1)%e +--R (292) ------------------ +--R 2 +--R x +--R Type: Expression Integer +--E 380 + +--S 381 of 489 +r0275:= -(1-1/x^2)^(1/2)+(1-1/x^2)^(1/2)*x+acsc(x)+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R (293) atanh( |------ ) + (x - 1) |------ + acsc(x) +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 381 + +--S 382 of 489 +a0275:= integrate(t0275,x) +--R +--R +--R (294) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R x log(%e + 1) - x log(%e - 1) + 2x atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 2 +--R (x - 2x + 1)%e +--R / +--R x +--R Type: Union(Expression Integer,...) +--E 382 + +--S 383 of 489 +m0275:= a0275-r0275 +--R +--R +--R (295) +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R x log(%e + 1) - x log(%e - 1) + 2x atan(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +------+ +------+ +--R ---------- | 2 | 2 +--R 2 2 |x - 1 2 |x - 1 +--R (x - 2x + 1)%e - x atanh( |------ ) + (- x + x) |------ +--R | 2 | 2 +--R \| x \| x +--R + +--R - x acsc(x) +--R / +--R x +--R Type: Expression Integer +--E 383 + +--S 384 of 489 +d0275:= D(m0275,x) +--R +--R +--R (296) +--R x + 1 5 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 5 4 2 |x - 1 | 2 2 +--R (x - x - x + x) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 4 +--R log(-----) +--R +------+ x - 1 +--R +------+ | 2 ---------- +--R 5 4 3 2 | 2 4 2 |x - 1 2 +--R ((- x - x + x + 2x - 1)\|x - 1 + (x - x ) |------ )(%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 5 4 3 2 |x - 1 | 2 2 +--R (- x + x + 4x + x - x) |------ \|x - 1 %e +--R | 2 +--R \| x +--R + +--R +------+ +--R +------+ | 2 +--R 5 4 3 2 | 2 4 2 |x - 1 +--R (x + x - x - 2x + 1)\|x - 1 + (- x + x ) |------ +--R | 2 +--R \| x +--R / +--R x + 1 4 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 +------+ ---------- | 2 +------+ +--R 5 3 |x - 1 | 2 2 5 3 |x - 1 | 2 +--R (x - x ) |------ \|x - 1 (%e ) + (- x + x ) |------ \|x - 1 +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 384 + +--S 385 of 489 +t0276:= exp(1)^acoth(x)*(1-1/x^2)^2 +--R +--R +--R 4 2 acoth(x) +--R (x - 2x + 1)%e +--R (297) ------------------------ +--R 4 +--R x +--R Type: Expression Integer +--E 385 + +--S 386 of 489 +r0276:= -(1-1/x^2)^(1/2)-1/3*(1-1/x^2)^(3/2)+_ + 1/2*(1-1/x^2)^(1/2)/x+(1-1/x^2)^(1/2)*x+3/2*acsc(x)+_ + atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R 2 |x - 1 3 2 |x - 1 2 +--R 6x atanh( |------ ) + (6x - 8x + 3x + 2) |------ + 9x acsc(x) +--R | 2 | 2 +--R \| x \| x +--R (298) ---------------------------------------------------------------- +--R 2 +--R 6x +--R Type: Expression Integer +--E 386 + +--S 387 of 489 +a0276:= integrate(t0276,x) +--R +--R +--R (299) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 3 2 3 2 +--R 6x log(%e + 1) - 6x log(%e - 1) +--R + +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 3 2 4 3 2 2 +--R 18x atan(%e ) + (6x - 14x + 11x - x - 2)%e +--R / +--R 3 +--R 6x +--R Type: Union(Expression Integer,...) +--E 387 + +--S 388 of 489 +m0276:= a0276-r0276 +--R +--R +--R (300) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 3 2 3 2 +--R 6x log(%e + 1) - 6x log(%e - 1) +--R + +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 3 2 4 3 2 2 +--R 18x atan(%e ) + (6x - 14x + 11x - x - 2)%e +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 3 |x - 1 4 3 2 |x - 1 3 +--R - 6x atanh( |------ ) + (- 6x + 8x - 3x - 2x) |------ - 9x acsc(x) +--R | 2 | 2 +--R \| x \| x +--R / +--R 3 +--R 6x +--R Type: Expression Integer +--E 388 + +--S 389 of 489 +d0276:= D(m0276,x) +--R +--R +--R (301) +--R x + 1 5 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 7 6 5 4 3 |x - 1 | 2 2 +--R (2x - 2x - x - 3x + 6x - 2x) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R +------+ +--R 7 6 5 4 3 2 | 2 +--R (- 2x - 2x + 3x + 6x - 3x - 6x + 2x + 2)\|x - 1 +--R + +--R +------+ +--R | 2 +--R 6 4 |x - 1 +--R (3x - 3x ) |------ +--R | 2 +--R \| x +--R * +--R x + 1 4 +--R log(-----) +--R x - 1 +--R ---------- +--R 2 +--R (%e ) +--R + +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 5 |x - 1 | 2 2 +--R - 2x |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 7 6 5 4 3 |x - 1 | 2 2 +--R (- 2x + 2x + 11x + 3x - 6x + 2x) |------ \|x - 1 %e +--R | 2 +--R \| x +--R + +--R +------+ +--R 7 6 5 4 3 2 | 2 +--R (2x + 2x - 3x - 6x + 3x + 6x - 2x - 2)\|x - 1 +--R + +--R +------+ +--R | 2 +--R 6 4 |x - 1 +--R (- 3x + 3x ) |------ +--R | 2 +--R \| x +--R / +--R x + 1 4 +--R log(-----) +--R +------+ x - 1 +--R | 2 +------+ ---------- +--R 7 5 |x - 1 | 2 2 +--R (2x - 2x ) |------ \|x - 1 (%e ) +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +------+ +--R 7 5 |x - 1 | 2 +--R (- 2x + 2x ) |------ \|x - 1 +--R | 2 +--R \| x +--R Type: Expression Integer +--E 389 + +--S 390 of 489 +t0277:= exp(1)^acoth(x)/(1-1/x^2) +--R +--R +--R 2 acoth(x) +--R x %e +--R (302) ------------ +--R 2 +--R x - 1 +--R Type: Expression Integer +--E 390 + +--S 391 of 489 +r0277:= -1/(1-1/x^2)^(1/2)-x/(1-1/x^2)^(1/2)+_ + 2*(1-1/x^2)^(1/2)*x+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 2 +--R x |------ atanh( |------ ) + x - x - 2 +--R | 2 | 2 +--R \| x \| x +--R (303) --------------------------------------- +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 391 + +--S 392 of 489 +a0277:= integrate(t0277,x) +--R +--R +--R x + 1 x + 1 x + 1 +--R log(-----) log(-----) log(-----) +--R x - 1 x - 1 x - 1 +--R ---------- ---------- ---------- +--R 2 2 2 +--R (304) log(%e + 1) - log(%e - 1) + (x - 2)%e +--R Type: Union(Expression Integer,...) +--E 392 + +--S 393 of 489 +m0277:= a0277-r0277 +--R +--R +--R (305) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R +------+ x - 1 +------+ x - 1 +--R | 2 ---------- | 2 ---------- +--R |x - 1 2 |x - 1 2 +--R x |------ log(%e + 1) - x |------ log(%e - 1) +--R | 2 | 2 +--R \| x \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +------+ +------+ +--R | 2 ---------- | 2 | 2 +--R 2 |x - 1 2 |x - 1 |x - 1 2 +--R (x - 2x) |------ %e - x |------ atanh( |------ ) - x + x + 2 +--R | 2 | 2 | 2 +--R \| x \| x \| x +--R / +--R +------+ +--R | 2 +--R |x - 1 +--R x |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 393 + +--S 394 of 489 +d0277:= D(m0277,x) +--R +--R +--R (306) +--R x + 1 3 x + 1 2 +--R log(-----) log(-----) +--R +------+ x - 1 x - 1 +--R | 2 ---------- ---------- +--R 2 |x - 1 2 2 2 +--R (x - x + 1) |------ (%e ) + (- x - x)(%e ) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 2 |x - 1 2 2 +--R (- x + x + 1) |------ %e + x + x +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 2 |x - 1 2 2 |x - 1 +--R (x - 1) |------ (%e ) + (- x + 1) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 394 + +--S 395 of 489 +t0278:= exp(1)^acoth(x)/(1-1/x^2)^2 +--R +--R +--R 4 acoth(x) +--R x %e +--R (307) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Expression Integer +--E 395 + +--S 396 of 489 +r0278:= -1/3/(1-1/x^2)^(3/2)-1/(1-1/x^2)^(1/2)-_ + 1/3*x/(1-1/x^2)^(3/2)-4/3*x/(1-1/x^2)^(1/2)+_ + 8/3*(1-1/x^2)^(1/2)*x+atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R 2 |x - 1 |x - 1 3 2 +--R (3x - 3x) |------ atanh( |------ ) + 3x - 7x - 5x + 8 +--R | 2 | 2 +--R \| x \| x +--R (308) -------------------------------------------------------- +--R +------+ +--R | 2 +--R 2 |x - 1 +--R (3x - 3x) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 396 + +--S 397 of 489 +a0278:= integrate(t0278,x) +--R +--R +--R (309) +--R x + 1 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- ---------- +--R 2 2 2 2 +--R (3x - 3)log(%e + 1) + (- 3x + 3)log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 3 2 2 +--R (3x - 7x - 5x + 8)%e +--R / +--R 2 +--R 3x - 3 +--R Type: Union(Expression Integer,...) +--E 397 + +--S 398 of 489 +m0278:= a0278-r0278 +--R +--R +--R (310) +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 3 |x - 1 2 +--R (3x - 3x) |------ log(%e + 1) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 3 |x - 1 2 +--R (- 3x + 3x) |------ log(%e - 1) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 4 3 2 |x - 1 2 +--R (3x - 7x - 5x + 8x) |------ %e +--R | 2 +--R \| x +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 3 |x - 1 |x - 1 4 3 2 +--R (- 3x + 3x) |------ atanh( |------ ) - 3x + 4x + 12x - 3x - 8 +--R | 2 | 2 +--R \| x \| x +--R / +--R +------+ +--R | 2 +--R 3 |x - 1 +--R (3x - 3x) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 398 + +--S 399 of 489 +d0278:= D(m0278,x) +--R +--R +--R (311) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 4 3 2 |x - 1 2 +--R (x - x + x + x - 1) |------ (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 3 2 +--R (- x - x )(%e ) +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 4 3 2 |x - 1 2 4 3 +--R (- x + x + x - x - 1) |------ %e + x + x +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +------+ +--R | 2 ---------- | 2 +--R 4 2 |x - 1 2 4 2 |x - 1 +--R (x - 2x + 1) |------ (%e ) + (- x + 2x - 1) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 399 + +--S 400 of 489 +t0279:= exp(1)^acoth(x)/(1-1/x^2)^3 +--R +--R +--R 6 acoth(x) +--R x %e +--R (312) ------------------ +--R 6 4 2 +--R x - 3x + 3x - 1 +--R Type: Expression Integer +--E 400 + +--S 401 of 489 +r0279:= -1/5/(1-1/x^2)^(5/2)-1/3/(1-1/x^2)^(3/2)-1/(1-1/x^2)^(1/2)-_ + 1/5*x/(1-1/x^2)^(5/2)-2/5*x/(1-1/x^2)^(3/2)-_ + 8/5*x/(1-1/x^2)^(1/2)+16/5*(1-1/x^2)^(1/2)*x+atanh((1-1/x^2)^(1/2)) +--R +--R +--R (313) +--R +------+ +------+ +--R | 2 | 2 +--R 4 3 2 |x - 1 |x - 1 5 4 3 +--R (15x - 15x - 15x + 15x) |------ atanh( |------ ) + 15x - 38x - 52x +--R | 2 | 2 +--R \| x \| x +--R + +--R 2 +--R 87x + 33x - 48 +--R / +--R +------+ +--R | 2 +--R 4 3 2 |x - 1 +--R (15x - 15x - 15x + 15x) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 401 + +--S 402 of 489 +a0279:= integrate(t0279,x) +--R +--R +--R (314) +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 2 2 +--R (15x - 30x + 15)log(%e + 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 4 2 2 +--R (- 15x + 30x - 15)log(%e - 1) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R ---------- +--R 5 4 3 2 2 +--R (15x - 38x - 52x + 87x + 33x - 48)%e +--R / +--R 4 2 +--R 15x - 30x + 15 +--R Type: Union(Expression Integer,...) +--E 402 + +--S 403 of 489 +m0279:= a0279-r0279 +--R +--R +--R (315) +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 5 3 |x - 1 2 +--R (15x - 30x + 15x) |------ log(%e + 1) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 5 3 |x - 1 2 +--R (- 15x + 30x - 15x) |------ log(%e - 1) +--R | 2 +--R \| x +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 6 5 4 3 2 |x - 1 2 +--R (15x - 38x - 52x + 87x + 33x - 48x) |------ %e +--R | 2 +--R \| x +--R + +--R +------+ +------+ +--R | 2 | 2 +--R 5 3 |x - 1 |x - 1 6 5 4 +--R (- 15x + 30x - 15x) |------ atanh( |------ ) - 15x + 23x + 90x +--R | 2 | 2 +--R \| x \| x +--R + +--R 3 2 +--R - 35x - 120x + 15x + 48 +--R / +--R +------+ +--R | 2 +--R 5 3 |x - 1 +--R (15x - 30x + 15x) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 403 + +--S 404 of 489 +d0279:= D(m0279,x) +--R +--R +--R (316) +--R x + 1 3 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 6 5 4 3 2 |x - 1 2 +--R (x - x + x + 2x - 2x - x + 1) |------ (%e ) +--R | 2 +--R \| x +--R + +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 6 5 2 +--R (- x - x )(%e ) +--R + +--R x + 1 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 6 5 4 3 2 |x - 1 2 6 5 +--R (- x + x + x - 2x - 2x + x + 1) |------ %e + x + x +--R | 2 +--R \| x +--R / +--R x + 1 2 +--R log(-----) +--R +------+ x - 1 +--R | 2 ---------- +--R 6 4 2 |x - 1 2 +--R (x - 3x + 3x - 1) |------ (%e ) +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 6 4 2 |x - 1 +--R (- x + 3x - 3x + 1) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 404 + +--S 405 of 489 +t0280:= exp(1)^(3*acoth(x))*(1-1/x^2) +--R +--R +--R 2 3acoth(x) +--R (x - 1)%e +--R (317) ------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 405 + +--S 406 of 489 +r0280:= (1-1/x^2)^(1/2)+(1-1/x^2)^(1/2)*x-3*acsc(x)+3*atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x - 1 |x - 1 +--R (318) 3atanh( |------ ) + (x + 1) |------ - 3acsc(x) +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 406 + +--S 407 of 489 +a0280:= integrate(t0280,x) +--R +--R +--R (319) +--R +-----+ +-----+ +-----+ +--R |x + 1 |x + 1 |x + 1 +--R 3x log( |----- + 1) - 3x log( |----- - 1) - 6x atan( |----- ) +--R \|x - 1 \|x - 1 \|x - 1 +--R + +--R +-----+ +--R 2 |x + 1 +--R (x - 1) |----- +--R \|x - 1 +--R / +--R x +--R Type: Union(Expression Integer,...) +--E 407 + +--S 408 of 489 +m0280:= a0280-r0280 +--R +--R +--R (320) +--R +------+ +--R +-----+ +-----+ | 2 +--R |x + 1 |x + 1 |x - 1 +--R 3x log( |----- + 1) - 3x log( |----- - 1) - 3x atanh( |------ ) +--R \|x - 1 \|x - 1 | 2 +--R \| x +--R + +--R +------+ +--R +-----+ +-----+ | 2 +--R |x + 1 2 |x + 1 2 |x - 1 +--R - 6x atan( |----- ) + (x - 1) |----- + (- x - x) |------ + 3x acsc(x) +--R \|x - 1 \|x - 1 | 2 +--R \| x +--R / +--R x +--R Type: Expression Integer +--E 408 + +--S 409 of 489 +d0280:= D(m0280,x) +--R +--R +--R (321) +--R +------+ +--R +-----+ | 2 +--R 4 3 2 |x + 1 4 3 2 |x - 1 +--R ((- x - 2x + 3x - x + 1) |----- + (x + 3x + 3x + x) |------ ) +--R \|x - 1 | 2 +--R \| x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R +------+ +--R | 2 +-----+ +--R 3 2 |x - 1 |x + 1 +--R (- 3x + 3x ) |------ |----- +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +-----+ +------+ +--R 4 3 |x - 1 |x + 1 | 2 +--R (x - x ) |------ |----- \|x - 1 +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 409 + +--S 410 of 489 +t0281:= exp(1)^(3*acoth(x))*(1-1/x^2)^2 +--R +--R +--R 4 2 3acoth(x) +--R (x - 2x + 1)%e +--R (322) ------------------------- +--R 4 +--R x +--R Type: Expression Integer +--E 410 + +--S 411 of 489 +r0281:= -3*(1-1/x^2)^(1/2)+1/3*(1-1/x^2)^(3/2)-_ + 3/2*(1-1/x^2)^(1/2)/x+(1-1/x^2)^(1/2)*x-1/2*acsc(x)+_ + 3*atanh((1-1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R 2 |x - 1 3 2 |x - 1 2 +--R 18x atanh( |------ ) + (6x - 16x - 9x - 2) |------ - 3x acsc(x) +--R | 2 | 2 +--R \| x \| x +--R (323) ------------------------------------------------------------------ +--R 2 +--R 6x +--R Type: Expression Integer +--E 411 + +--S 412 of 489 +a0281:= integrate(t0281,x) +--R +--R +--R (324) +--R +-----+ +-----+ +-----+ +--R 3 |x + 1 3 |x + 1 3 |x + 1 +--R 18x log( |----- + 1) - 18x log( |----- - 1) - 6x atan( |----- ) +--R \|x - 1 \|x - 1 \|x - 1 +--R + +--R +-----+ +--R 4 3 2 |x + 1 +--R (6x - 22x + 7x + 7x + 2) |----- +--R \|x - 1 +--R / +--R 3 +--R 6x +--R Type: Union(Expression Integer,...) +--E 412 + +--S 413 of 489 +m0281:= a0281-r0281 +--R +--R +--R (325) +--R +------+ +--R +-----+ +-----+ | 2 +--R 3 |x + 1 3 |x + 1 3 |x - 1 +--R 18x log( |----- + 1) - 18x log( |----- - 1) - 18x atanh( |------ ) +--R \|x - 1 \|x - 1 | 2 +--R \| x +--R + +--R +-----+ +-----+ +--R 3 |x + 1 4 3 2 |x + 1 +--R - 6x atan( |----- ) + (6x - 22x + 7x + 7x + 2) |----- +--R \|x - 1 \|x - 1 +--R + +--R +------+ +--R | 2 +--R 4 3 2 |x - 1 3 +--R (- 6x + 16x + 9x + 2x) |------ + 3x acsc(x) +--R | 2 +--R \| x +--R / +--R 3 +--R 6x +--R Type: Expression Integer +--E 413 + +--S 414 of 489 +d0281:= D(m0281,x) +--R +--R +--R (326) +--R +-----+ +--R 5 4 3 2 |x + 1 +--R (- 2x - 6x - 3x + 4x + 6x + 2) |----- +--R \|x - 1 +--R + +--R +------+ +--R | 2 +--R 5 4 3 2 |x - 1 +--R (2x + 8x + 12x + 8x + 2x) |------ +--R | 2 +--R \| x +--R * +--R +------+ +--R | 2 +--R \|x - 1 +--R + +--R +------+ +--R | 2 +-----+ +--R 4 |x - 1 |x + 1 +--R - x |------ |----- +--R | 2 \|x - 1 +--R \| x +--R / +--R +------+ +--R | 2 +-----+ +------+ +--R 5 |x - 1 |x + 1 | 2 +--R 2x |------ |----- \|x - 1 +--R | 2 \|x - 1 +--R \| x +--R Type: Expression Integer +--E 414 + +--S 415 of 489 +t0282:= exp(1)^acoth(x)*(1-1/x^2)^(1/2) +--R +--R +--R +------+ +--R | 2 +--R |x - 1 acoth(x) +--R (327) |------ %e +--R | 2 +--R \| x +--R Type: Expression Integer +--E 415 + +--S 416 of 489 +r0282:= x+log(x) +--R +--R +--R (328) log(x) + x +--R Type: Expression Integer +--E 416 + +--S 417 of 489 +a0282:= integrate(t0282,x) +--R +--R +--R (329) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (- x + 4)\|x - 1 %e + x + x + 4x + 4 +--R (- x - 1)log(--------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R | 2 2 +--R (x - 2)\|x - 1 %e +--R / +--R x + 1 +--R Type: Union(Expression Integer,...) +--E 417 + +--S 418 of 489 +m0282:= a0282-r0282 +--R +--R +--R (330) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (- x + 4)\|x - 1 %e + x + x + 4x + 4 +--R (- x - 1)log(--------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R | 2 2 2 +--R (x - 2)\|x - 1 %e + (- x - 1)log(x) - x - x +--R / +--R x + 1 +--R Type: Expression Integer +--E 418 + +--S 419 of 489 +d0282:= D(m0282,x) +--R +--R +--R (331) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- +------+ ---------- +--R 3 2 2 2 | 2 2 +--R (x - x - 4x + 4)(%e ) + (- 2x - 2x)\|x - 1 %e +--R + +--R 3 2 +--R x + 3x + 6x + 4 +--R / +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (x - 4)\|x - 1 %e - x - x - 4x - 4 +--R Type: Expression Integer +--E 419 + +--S 420 of 489 +t0283:= exp(1)^acoth(x)*(1-1/x^2)^(3/2) +--R +--R +--R +------+ +--R | 2 +--R 2 |x - 1 acoth(x) +--R (x - 1) |------ %e +--R | 2 +--R \| x +--R (332) --------------------------- +--R 2 +--R x +--R Type: Expression Integer +--E 420 + +--S 421 of 489 +r0283:= 1/2/x^2+1/x+x+log(x) +--R +--R +--R 2 3 +--R 2x log(x) + 2x + 2x + 1 +--R (333) ------------------------ +--R 2 +--R 2x +--R Type: Expression Integer +--E 421 + +--S 422 of 489 +a0283:= integrate(t0283,x) +--R +--R +--R (334) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R 3 2 (- x + 4)\|x - 1 %e + x + x + 4x + 4 +--R (- 8x - 8x )log(--------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 3 2 | 2 2 +--R (8x - 21x + 8x + 4)\|x - 1 %e +--R / +--R 3 2 +--R 8x + 8x +--R Type: Union(Expression Integer,...) +--E 422 + +--S 423 of 489 +m0283:= a0283-r0283 +--R +--R +--R (335) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R 3 2 (- x + 4)\|x - 1 %e + x + x + 4x + 4 +--R (- 8x - 8x )log(--------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 3 2 | 2 2 3 2 4 +--R (8x - 21x + 8x + 4)\|x - 1 %e + (- 8x - 8x )log(x) - 8x +--R + +--R 3 2 +--R - 8x - 8x - 12x - 4 +--R / +--R 3 2 +--R 8x + 8x +--R Type: Expression Integer +--E 423 + +--S 424 of 489 +d0283:= D(m0283,x) +--R +--R +--R (336) +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 6 5 4 3 2 2 +--R (x - x - 5x + 4x + 5x - 4)(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 5 4 3 2 | 2 2 6 5 4 3 +--R (- 2x - 2x + 2x + 2x )\|x - 1 %e + x + 3x + 5x + 2x +--R + +--R 2 +--R - 5x - 8x - 4 +--R / +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 5 3 | 2 2 6 5 4 3 +--R (x - 4x )\|x - 1 %e - x - x - 4x - 4x +--R Type: Expression Integer +--E 424 + +--S 425 of 489 +t0284:= exp(1)^acoth(x)*(1-1/x^2)^(5/2) +--R +--R +--R +------+ +--R | 2 +--R 4 2 |x - 1 acoth(x) +--R (x - 2x + 1) |------ %e +--R | 2 +--R \| x +--R (337) --------------------------------- +--R 4 +--R x +--R Type: Expression Integer +--E 425 + +--S 426 of 489 +r0284:= -1/4/x^4-1/3/x^3+1/x^2+2/x+x+log(x) +--R +--R +--R 4 5 3 2 +--R 12x log(x) + 12x + 24x + 12x - 4x - 3 +--R (338) ---------------------------------------- +--R 4 +--R 12x +--R Type: Expression Integer +--E 426 + +--S 427 of 489 +a0284:= integrate(t0284,x) +--R +--R +--R (339) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R 5 4 (x - 4)\|x - 1 %e - x - x - 4x - 4 +--R (- 192x - 192x )log(------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 5 4 3 2 | 2 2 +--R (192x + 523x + 384x + 192x - 64x - 48)\|x - 1 %e +--R / +--R 5 4 +--R 192x + 192x +--R Type: Union(Expression Integer,...) +--E 427 + +--S 428 of 489 +m0284:= a0284-r0284 +--R +--R +--R (340) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R 5 4 (x - 4)\|x - 1 %e - x - x - 4x - 4 +--R (- 192x - 192x )log(------------------------------------------------) +--R 2 +--R x + x +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 5 4 3 2 | 2 2 +--R (192x + 523x + 384x + 192x - 64x - 48)\|x - 1 %e +--R + +--R 5 4 6 5 4 3 2 +--R (- 192x - 192x )log(x) - 192x - 192x - 384x - 576x - 128x + 112x + 48 +--R / +--R 5 4 +--R 192x + 192x +--R Type: Expression Integer +--E 428 + +--S 429 of 489 +d0284:= D(m0284,x) +--R +--R +--R (341) +--R x + 1 2 +--R log(-----) +--R x - 1 +--R ---------- +--R 8 7 6 5 4 2 2 +--R (x - x - 6x + 4x + 11x - 13x + 4)(%e ) +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 7 6 5 4 3 2 | 2 2 8 7 +--R (- 2x - 2x + 4x + 4x - 2x - 2x )\|x - 1 %e + x + 3x +--R + +--R 6 4 3 2 +--R 4x - 9x - 14x - 3x + 8x + 4 +--R / +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 7 5 | 2 2 8 7 6 5 +--R (x - 4x )\|x - 1 %e - x - x - 4x - 4x +--R Type: Expression Integer +--E 429 + +--S 430 of 489 +t0285:= exp(1)^acoth(x)/(1-1/x^2)^(1/2) +--R +--R +--R acoth(x) +--R %e +--R (342) ---------- +--R +------+ +--R | 2 +--R |x - 1 +--R |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 430 + +--S 431 of 489 +r0285:= x+log(1-x) +--R +--R +--R (343) log(- x + 1) + x +--R Type: Expression Integer +--E 431 + +--S 432 of 489 +a0285:= integrate(t0285,x) +--R +--R +--R (344) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (- x + 2x)\|x - 1 %e + x - x + 2 +--R (- x - 1)log(----------------------------------------------) +--R 2 +--R x - 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R | 2 2 +--R x\|x - 1 %e +--R / +--R x + 1 +--R Type: Union(Expression Integer,...) +--E 432 + +--S 433 of 489 +m0285:= a0285-r0285 +--R +--R +--R (345) +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (- x + 2x)\|x - 1 %e + x - x + 2 +--R (- x - 1)log(----------------------------------------------) +--R 2 +--R x - 1 +--R + +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R | 2 2 2 +--R x\|x - 1 %e + (- x - 1)log(- x + 1) - x - x +--R / +--R x + 1 +--R Type: Expression Integer +--E 433 + +--S 434 of 489 +d0285:= D(m0285,x) +--R +--R +--R (346) +--R x + 1 2 x + 1 +--R log(-----) log(-----) +--R x - 1 x - 1 +--R ---------- +------+ ---------- +--R 3 2 2 2 | 2 2 3 2 +--R (x - 3x + 2x)(%e ) + (- 2x + 2x)\|x - 1 %e + x + x +--R ---------------------------------------------------------------------------- +--R x + 1 +--R log(-----) +--R x - 1 +--R +------+ ---------- +--R 2 | 2 2 3 2 +--R (x - 2x)\|x - 1 %e - x + x - 2 +--R Type: Expression Integer +--E 434 + +--S 435 of 489 +t0286:= exp(1)^acoth(x)/(1-1/x^2)^(3/2) +--R +--R +--R 2 acoth(x) +--R x %e +--R (347) ----------------- +--R +------+ +--R | 2 +--R 2 |x - 1 +--R (x - 1) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 435 + +--S 436 of 489 +r0286:= 1/(2-2*x)+x+5/4*log(1-x)-1/4*log(1+x) +--R +--R +--R 2 +--R (- x + 1)log(x + 1) + (5x - 5)log(- x + 1) + 4x - 4x - 2 +--R (348) --------------------------------------------------------- +--R 4x - 4 +--R Type: Expression Integer +--E 436 + +--S 437 of 489 +--a0286:= integrate(t0286,x) +--E 437 + +--S 438 of 489 +--m0286:= a0286-r0286 +--E 438 + +--S 439 of 489 +--d0286:= D(m0286,x) +--E 439 + +--S 440 of 489 +t0287:= exp(1)^acoth(x)/(1-1/x^2)^(5/2) +--R +--R +--R 4 acoth(x) +--R x %e +--R (349) ----------------------- +--R +------+ +--R | 2 +--R 4 2 |x - 1 +--R (x - 2x + 1) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 440 + +--S 441 of 489 +r0287:= -1/8/(1-x)^2+1/(1-x)+x-1/(8+8*x)+23/16*log(1-x)-7/16*log(1+x) +--R +--R +--R (350) +--R 3 2 3 2 +--R (- 7x + 7x + 7x - 7)log(x + 1) + (23x - 23x - 23x + 23)log(- x + 1) +--R + +--R 4 3 2 +--R 16x - 16x - 34x + 18x + 12 +--R / +--R 3 2 +--R 16x - 16x - 16x + 16 +--R Type: Expression Integer +--E 441 + +--S 442 of 489 +--a0287:= integrate(t0287,x) +--E 442 + +--S 443 of 489 +--m0287:= a0287-r0287 +--E 443 + +--S 444 of 489 +--d0287:= D(m0287,x) +--E 444 + +--S 445 of 489 +t0288:= x^2*exp(1)^asech(x) +--R +--R +--R 2 asech(x) +--R (351) x %e +--R Type: Expression Integer +--E 445 + +--S 446 of 489 +r0288:= 1/2*x^2-1/3*(-(-1+x)/(1+x))^(1/2)-_ + 1/3*x*(-(-1+x)/(1+x))^(1/2)+_ + 1/3*x^2*(-(-1+x)/(1+x))^(1/2)+1/3*x^3*(-(-1+x)/(1+x))^(1/2) +--R +--R +--R +-------+ +--R 3 2 |- x + 1 2 +--R (2x + 2x - 2x - 2) |------- + 3x +--R \| x + 1 +--R (352) ------------------------------------ +--R 6 +--R Type: Expression Integer +--E 446 + +--S 447 of 489 +a0288:= integrate(t0288,x) +--R +--R +--R +--------+ +--R 4 | 2 6 4 +--R - 3x \|- x + 1 - 2x + 3x +--R (353) --------------------------------- +--R +--------+ +--R 2 | 2 2 +--R (6x - 24)\|- x + 1 - 18x + 24 +--R Type: Union(Expression Integer,...) +--E 447 + +--S 448 of 489 +m0288:= a0288-r0288 +--R +--R +--R (354) +--R +--------+ +--R 5 4 3 2 | 2 5 4 3 2 +--R (- x - x + 5x + 5x - 4x - 4)\|- x + 1 + 3x + 3x - 7x - 7x +--R + +--R 4x + 4 +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x + 1 +--R + +--R +--------+ +--R 4 2 | 2 6 4 2 +--R (- 3x + 6x )\|- x + 1 - x + 6x - 6x +--R / +--R +--------+ +--R 2 | 2 2 +--R (3x - 12)\|- x + 1 - 9x + 12 +--R Type: Expression Integer +--E 448 + +--S 449 of 489 +d0288:= D(m0288,x) +--R +--R +--R (355) +--R +--------+ +--R 7 5 3 | 2 9 7 5 3 +--R (- 6x + 38x - 64x + 32x)\|- x + 1 - x + 19x - 66x + 80x +--R + +--R - 32x +--R * +--R +-------+ +--R |- x + 1 +--R |------- +--R \| x + 1 +--R + +--R +--------+ +--R 8 7 6 5 4 3 2 | 2 8 7 +--R (x - x - 18x + 18x + 48x - 48x - 32x + 32x)\|- x + 1 - 6x + 6x +--R + +--R 6 5 4 3 2 +--R 38x - 38x - 64x + 64x + 32x - 32x +--R / +--R +--------+ +-------+ +--R 6 4 2 | 2 6 4 2 |- x + 1 +--R ((x - 18x + 48x - 32)\|- x + 1 - 6x + 38x - 64x + 32) |------- +--R \| x + 1 +--R Type: Expression Integer +--E 449 + +--S 450 of 489 +t0289:= exp(1)^asech(x) +--R +--R +--R asech(x) +--R (356) %e +--R Type: Expression Integer +--E 450 + +--S 451 of 489 +r0289:= ((1-x)/(1+x))^(1/2)*(1+x)-2*atanh(((1-x)/(1+x))^(1/2))+log(x) +--R +--R +--R +-------+ +-------+ +--R |- x + 1 |- x + 1 +--R (357) - 2atanh( |------- ) + (x + 1) |------- + log(x) +--R \| x + 1 \| x + 1 +--R Type: Expression Integer +--E 451 + +--S 452 of 489 +a0289:= integrate(t0289,x) +--R +--R +--R (358) +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 \|- x + 1 - 1 | 2 2 +--R (\|- x + 1 - 1)log(---------------) + log(x)\|- x + 1 - log(x) - x +--R x +--R ----------------------------------------------------------------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R Type: Union(Expression Integer,...) +--E 452 + +--S 453 of 489 +m0289:= a0289-r0289 +--R +--R +--R (359) +--R +--------+ +--R +--------+ | 2 +--R | 2 \|- x + 1 - 1 +--R (\|- x + 1 - 1)log(---------------) +--R x +--R + +--R +--------+ +-------+ +--R | 2 |- x + 1 +--R (2\|- x + 1 - 2)atanh( |------- ) +--R \| x + 1 +--R + +--R +--------+ +-------+ +--R | 2 |- x + 1 2 +--R ((- x - 1)\|- x + 1 + x + 1) |------- - x +--R \| x + 1 +--R / +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 +--R Type: Expression Integer +--E 453 + +--S 454 of 489 +d0289:= D(m0289,x) +--R +--R +--R (360) +--R +--------+ +-------+ +--R 2 | 2 4 2 |- x + 1 +--R ((- 2x + 2)\|- x + 1 - x + 3x - 2) |------- +--R \| x + 1 +--R + +--R +--------+ +--R 3 2 | 2 3 2 +--R (x - x - 2x + 2)\|- x + 1 - 2x + 2x + 2x - 2 +--R / +--R +--------+ +-------+ +--R 3 | 2 3 |- x + 1 +--R ((x - 2x)\|- x + 1 - 2x + 2x) |------- +--R \| x + 1 +--R Type: Expression Integer +--E 454 + +--S 455 of 489 +t0290:= exp(1)^asech(x)/x^2 +--R +--R +--R asech(x) +--R %e +--R (361) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 455 + +--S 456 of 489 +r0290:= -1/2*(1+x*(-(-1+x)/(1+x))^(1/2)+(-(-1+x)/(1+x))^(1/2)-_ + 2*atanh((-(-1+x)/(1+x))^(1/2))*x^2)/x^2 +--R +--R +--R +-------+ +-------+ +--R 2 |- x + 1 |- x + 1 +--R 2x atanh( |------- ) + (- x - 1) |------- - 1 +--R \| x + 1 \| x + 1 +--R (362) ---------------------------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 456 + +--S 457 of 489 +a0290:= integrate(t0290,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 2 \|- x + 1 - 1 | 2 +--R (- 2\|- x + 1 - x + 2)log(---------------) - \|- x + 1 + 1 +--R x +--R (363) --------------------------------------------------------------- +--R +--------+ +--R | 2 2 +--R 4\|- x + 1 + 2x - 4 +--R Type: Union(Expression Integer,...) +--E 457 + +--S 458 of 489 +m0290:= a0290-r0290 +--R +--R +--R (364) +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 4 2 \|- x + 1 - 1 +--R (- 2x \|- x + 1 - x + 2x )log(---------------) +--R x +--R + +--R +--------+ +-------+ +--R 2 | 2 4 2 |- x + 1 +--R (- 4x \|- x + 1 - 2x + 4x )atanh( |------- ) +--R \| x + 1 +--R + +--R +--------+ +-------+ +--R | 2 3 2 |- x + 1 +--R ((2x + 2)\|- x + 1 + x + x - 2x - 2) |------- +--R \| x + 1 +--R + +--R +--------+ +--R 2 | 2 2 +--R (- x + 2)\|- x + 1 + 2x - 2 +--R / +--R +--------+ +--R 2 | 2 4 2 +--R 4x \|- x + 1 + 2x - 4x +--R Type: Expression Integer +--E 458 + +--S 459 of 489 +d0290:= D(m0290,x) +--R +--R +--R (365) +--R +--------+ +-------+ +--R 4 2 | 2 6 4 2 |- x + 1 +--R ((- 4x + 12x - 8)\|- x + 1 - x + 9x - 16x + 8) |------- +--R \| x + 1 +--R + +--R +--------+ +--R 5 4 3 2 | 2 5 4 3 2 +--R (x - x - 8x + 8x + 8x - 8)\|- x + 1 - 4x + 4x + 12x - 12x - 8x +--R + +--R 8 +--R / +--R +--------+ +-------+ +--R 7 5 3 | 2 7 5 3 |- x + 1 +--R ((x - 8x + 8x )\|- x + 1 - 4x + 12x - 8x ) |------- +--R \| x + 1 +--R Type: Expression Integer +--E 459 + +--S 460 of 489 +t0291:= x*exp(1)^acsch(x) +--R +--R +--R acsch(x) +--R (366) x %e +--R Type: Expression Integer +--E 460 + +--S 461 of 489 +r0291:= x+1/2*(1+1/x^2)^(1/2)*x^2+1/2*atanh((1+1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x + 1 2 |x + 1 +--R atanh( |------ ) + x |------ + 2x +--R | 2 | 2 +--R \| x \| x +--R (367) ----------------------------------- +--R 2 +--R Type: Expression Integer +--E 461 + +--S 462 of 489 +a0291:= integrate(t0291,x) +--R +--R +--R (368) +--R +------+ +------+ +------+ +--R | 2 2 | 2 3 2 | 2 +--R (- 2x\|x + 1 + 2x + 1)log(\|x + 1 - x) + (- 2x + 4x - x)\|x + 1 +--R + +--R 4 3 2 +--R 2x - 4x + 2x - 2x +--R / +--R +------+ +--R | 2 2 +--R 4x\|x + 1 - 4x - 2 +--R Type: Union(Expression Integer,...) +--E 462 + +--S 463 of 489 +m0291:= a0291-r0291 +--R +--R +--R (369) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- 2x\|x + 1 + 2x + 1)log(\|x + 1 - x) +--R + +--R +------+ +--R +------+ | 2 +--R | 2 2 |x + 1 +--R (- 2x\|x + 1 + 2x + 1)atanh( |------ ) +--R | 2 +--R \| x +--R + +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 3 |x + 1 3 | 2 4 2 |x + 1 4 2 +--R (- 2x |------ - 2x - x)\|x + 1 + (2x + x ) |------ + 2x + 2x +--R | 2 | 2 +--R \| x \| x +--R / +--R +------+ +--R | 2 2 +--R 4x\|x + 1 - 4x - 2 +--R Type: Expression Integer +--E 463 + +--S 464 of 489 +d0291:= D(m0291,x) +--R +--R +--R (370) +--R +------+ +--R | 2 +------+ +--R 6 4 2 |x + 1 6 4 2 | 2 +--R ((- 8x - 12x - 4x ) |------ - 8x - 16x - 9x - 1)\|x + 1 +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 7 5 3 |x + 1 7 5 3 +--R (8x + 16x + 9x + x) |------ + 8x + 20x + 16x + 4x +--R | 2 +--R \| x +--R / +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 5 3 |x + 1 | 2 6 4 2 |x + 1 +--R (8x + 8x + x) |------ \|x + 1 + (- 8x - 12x - 4x ) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 464 + +--S 465 of 489 +t0292:= exp(1)^acsch(x) +--R +--R +--R acsch(x) +--R (371) %e +--R Type: Expression Integer +--E 465 + +--S 466 of 489 +r0292:= (1+1/x^2)^(1/2)*x-acsch(x)+log(x) +--R +--R +--R +------+ +--R | 2 +--R |x + 1 +--R (372) x |------ + log(x) - acsch(x) +--R | 2 +--R \| x +--R Type: Expression Integer +--E 466 + +--S 467 of 489 +a0292:= integrate(t0292,x) +--R +--R +--R (373) +--R +------+ +------+ +--R | 2 | 2 +--R (- \|x + 1 + x)log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R (\|x + 1 - x)log(\|x + 1 - x - 1) + (log(x) - x)\|x + 1 - x log(x) +--R + +--R 2 +--R x + 1 +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Union(Expression Integer,...) +--E 467 + +--S 468 of 489 +m0292:= a0292-r0292 +--R +--R +--R (374) +--R +------+ +------+ +--R | 2 | 2 +--R (- \|x + 1 + x)log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R | 2 | 2 +--R (\|x + 1 - x)log(\|x + 1 - x - 1) +--R + +--R +------+ +------+ +--R | 2 +------+ | 2 +--R |x + 1 | 2 2 |x + 1 2 +--R (- x |------ + acsch(x) - x)\|x + 1 + x |------ - x acsch(x) + x + 1 +--R | 2 | 2 +--R \| x \| x +--R / +--R +------+ +--R | 2 +--R \|x + 1 - x +--R Type: Expression Integer +--E 468 + +--S 469 of 489 +d0292:= D(m0292,x) +--R +--R +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 2 |x + 1 2 | 2 3 |x + 1 3 +--R (- 2x |------ - 2x - 1)\|x + 1 + (2x + x) |------ + 2x + 2x +--R | 2 | 2 +--R \| x \| x +--R (375) ------------------------------------------------------------------- +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 2 |x + 1 | 2 3 |x + 1 +--R (2x + 1) |------ \|x + 1 + (- 2x - 2x) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 469 + +--S 470 of 489 +t0293:= exp(1)^acsch(x)/x +--R +--R +--R acsch(x) +--R %e +--R (376) ---------- +--R x +--R Type: Expression Integer +--E 470 + +--S 471 of 489 +r0293:= -(1+1/x^2)^(1/2)-1/x+atanh((1+1/x^2)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R |x + 1 |x + 1 +--R x atanh( |------ ) - x |------ - 1 +--R | 2 | 2 +--R \| x \| x +--R (377) ----------------------------------- +--R x +--R Type: Expression Integer +--E 471 + +--S 472 of 489 +a0293:= integrate(t0293,x) +--R +--R +--R +------+ +------+ +------+ +--R | 2 2 | 2 | 2 +--R (- x\|x + 1 + x )log(\|x + 1 - x) - \|x + 1 + x - 1 +--R (378) --------------------------------------------------------- +--R +------+ +--R | 2 2 +--R x\|x + 1 - x +--R Type: Union(Expression Integer,...) +--E 472 + +--S 473 of 489 +m0293:= a0293-r0293 +--R +--R +--R (379) +--R +------+ +------+ +--R | 2 2 | 2 +--R (- x\|x + 1 + x )log(\|x + 1 - x) +--R + +--R +------+ +------+ +------+ +--R +------+ | 2 | 2 +------+ | 2 +--R | 2 2 |x + 1 |x + 1 | 2 2 |x + 1 +--R (- x\|x + 1 + x )atanh( |------ ) + x |------ \|x + 1 - x |------ - 1 +--R | 2 | 2 | 2 +--R \| x \| x \| x +--R / +--R +------+ +--R | 2 2 +--R x\|x + 1 - x +--R Type: Expression Integer +--E 473 + +--S 474 of 489 +d0293:= D(m0293,x) +--R +--R +--R (380) +--R +------+ +--R | 2 +------+ +--R 4 2 |x + 1 4 2 | 2 +--R ((- 2x - 2x ) |------ - 2x - 3x - 1)\|x + 1 +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 5 3 |x + 1 5 3 +--R (2x + 3x + x) |------ + 2x + 4x + 2x +--R | 2 +--R \| x +--R / +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 5 3 |x + 1 | 2 6 4 |x + 1 +--R (2x + x ) |------ \|x + 1 + (- 2x - 2x ) |------ +--R | 2 | 2 +--R \| x \| x +--R Type: Expression Integer +--E 474 + +--S 475 of 489 +t0294:= exp(1)^acsch(x)/x^2 +--R +--R +--R acsch(x) +--R %e +--R (381) ---------- +--R 2 +--R x +--R Type: Expression Integer +--E 475 + +--S 476 of 489 +r0294:= -1/2/x^2-1/2*(1+1/x^2)^(1/2)/x-1/2*acsch(x) +--R +--R +--R +------+ +--R | 2 +--R |x + 1 2 +--R - x |------ - x acsch(x) - 1 +--R | 2 +--R \| x +--R (382) ----------------------------- +--R 2 +--R 2x +--R Type: Expression Integer +--E 476 + +--S 477 of 489 +a0294:= integrate(t0294,x) +--R +--R +--R (383) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R (- 2x \|x + 1 + 2x + x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +------+ +--R 3 | 2 4 2 | 2 2 | 2 +--R (2x \|x + 1 - 2x - x )log(\|x + 1 - x - 1) + (2x - 2x + 1)\|x + 1 +--R + +--R 3 2 +--R - 2x + 2x - 2x + 1 +--R / +--R +------+ +--R 3 | 2 4 2 +--R 4x \|x + 1 - 4x - 2x +--R Type: Union(Expression Integer,...) +--E 477 + +--S 478 of 489 +m0294:= a0294-r0294 +--R +--R +--R (384) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R (- 2x \|x + 1 + 2x + x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R (2x \|x + 1 - 2x - x )log(\|x + 1 - x - 1) +--R + +--R +------+ +------+ +--R | 2 +------+ | 2 +--R 2 |x + 1 3 2 | 2 3 |x + 1 +--R (2x |------ + 2x acsch(x) + 2x + 1)\|x + 1 + (- 2x - x) |------ +--R | 2 | 2 +--R \| x \| x +--R + +--R 4 2 3 +--R (- 2x - x )acsch(x) - 2x - 2x +--R / +--R +------+ +--R 3 | 2 4 2 +--R 4x \|x + 1 - 4x - 2x +--R Type: Expression Integer +--E 478 + +--S 479 of 489 +d0294:= D(m0294,x) +--R +--R +--R (385) +--R +------+ +--R | 2 +--R 7 5 3 |x + 1 7 5 3 +--R ((- 16x - 44x - 25x - 2x) |------ - 16x - 52x - 45x - 10x) +--R | 2 +--R \| x +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R +------+ +--R | 2 +--R 8 6 4 2 |x + 1 8 6 4 2 +--R (16x + 52x + 45x + 10x ) |------ + 16x + 60x + 69x + 27x + 2 +--R | 2 +--R \| x +--R / +--R +------+ +--R | 2 +------+ +--R 9 7 5 |x + 1 | 2 +--R (32x + 40x + 10x ) |------ \|x + 1 +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 10 8 6 4 |x + 1 +--R (- 32x - 56x - 26x - 2x ) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 479 + +--S 480 of 489 +t0295:= exp(1)^acsch(x)/x^4 +--R +--R +--R acsch(x) +--R %e +--R (386) ---------- +--R 4 +--R x +--R Type: Expression Integer +--E 480 + +--S 481 of 489 +r0295:= -1/4/x^4-1/4*(1+1/x^2)^(1/2)/x^3-1/8*(1+1/x^2)^(1/2)/x+1/8*acsch(x) +--R +--R +--R +------+ +--R | 2 +--R 3 |x + 1 4 +--R (- x - 2x) |------ + x acsch(x) - 2 +--R | 2 +--R \| x +--R (387) ------------------------------------- +--R 4 +--R 8x +--R Type: Expression Integer +--E 481 + +--S 482 of 489 +a0295:= integrate(t0295,x) +--R +--R +--R (388) +--R +------+ +------+ +--R 7 5 | 2 8 6 4 | 2 +--R ((8x + 4x )\|x + 1 - 8x - 8x - x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 7 5 | 2 8 6 4 | 2 +--R ((- 8x - 4x )\|x + 1 + 8x + 8x + x )log(\|x + 1 - x - 1) +--R + +--R +------+ +--R 6 4 3 2 | 2 7 5 4 3 +--R (8x + 24x - 16x + 17x - 8x + 2)\|x + 1 - 8x - 28x + 16x - 28x +--R + +--R 2 +--R 16x - 8x + 2 +--R / +--R +------+ +--R 7 5 | 2 8 6 4 +--R (64x + 32x )\|x + 1 - 64x - 64x - 8x +--R Type: Union(Expression Integer,...) +--E 482 + +--S 483 of 489 +m0295:= a0295-r0295 +--R +--R +--R (389) +--R +------+ +------+ +--R 7 5 | 2 8 6 4 | 2 +--R ((8x + 4x )\|x + 1 - 8x - 8x - x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 7 5 | 2 8 6 4 | 2 +--R ((- 8x - 4x )\|x + 1 + 8x + 8x + x )log(\|x + 1 - x - 1) +--R + +--R +------+ +--R | 2 +--R 6 4 2 |x + 1 7 5 6 4 +--R (8x + 20x + 8x ) |------ + (- 8x - 4x )acsch(x) + 8x + 24x +--R | 2 +--R \| x +--R + +--R 2 +--R 17x + 2 +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R +------+ +--R | 2 +--R 7 5 3 |x + 1 8 6 4 7 +--R (- 8x - 24x - 17x - 2x) |------ + (8x + 8x + x )acsch(x) - 8x +--R | 2 +--R \| x +--R + +--R 5 3 +--R - 28x - 28x - 8x +--R / +--R +------+ +--R 7 5 | 2 8 6 4 +--R (64x + 32x )\|x + 1 - 64x - 64x - 8x +--R Type: Expression Integer +--E 483 + +--S 484 of 489 +d0295:= D(m0295,x) +--R +--R +--R (390) +--R +------+ +--R | 2 +--R 13 11 9 7 5 3 |x + 1 +--R (- 256x - 2496x - 5872x - 5544x - 2241x - 328x - 8x) |------ +--R | 2 +--R \| x +--R + +--R 13 11 9 7 5 3 +--R - 256x - 2624x - 7088x - 8184x - 4425x - 1032x - 72x +--R * +--R +------+ +--R | 2 +--R \|x + 1 +--R + +--R +------+ +--R | 2 +--R 14 12 10 8 6 4 2 |x + 1 +--R (256x + 2624x + 7088x + 8184x + 4425x + 1032x + 72x ) |------ +--R | 2 +--R \| x +--R + +--R 14 12 10 8 6 4 2 +--R 256x + 2752x + 8368x + 11416x + 7785x + 2569x + 336x + 8 +--R / +--R +------+ +--R | 2 +------+ +--R 15 13 11 9 7 |x + 1 | 2 +--R (2048x + 4608x + 3456x + 960x + 72x ) |------ \|x + 1 +--R | 2 +--R \| x +--R + +--R +------+ +--R | 2 +--R 16 14 12 10 8 6 |x + 1 +--R (- 2048x - 5632x - 5504x - 2240x - 328x - 8x ) |------ +--R | 2 +--R \| x +--R Type: Expression Integer +--E 484 + +--S 485 of 489 +t0296:= acosh(c/(a+b*x)) +--R +--R +--R c +--R (391) acosh(-------) +--R b x + a +--R Type: Expression Integer +--E 485 + +--S 486 of 489 +r0296:= -(-asech((a+b*x)/c)*a-_ + asech((a+b*x)/c)*b*x+2*c*atan((-(-c+a+b*x)/(c+a+b*x))^(1/2)))/b +--R +--R +--R +-------------+ +--R |- b x + c - a b x + a +--R - 2c atan( |------------- ) + (b x + a)asech(-------) +--R \| b x + c + a c +--R (392) ----------------------------------------------------- +--R b +--R Type: Expression Integer +--E 486 + +--S 487 of 489 +a0296:= integrate(t0296,x) +--R +--R +--R (393) +--R +-------------------------+ +--R | 2 2 2 2 +--R \|- b x - 2a b x + c - a + c +--R b x log(--------------------------------) +--R b x + a +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R (- b x - a)\|c - a + a\|- b x - 2a b x + c - a + b c x +--R - a log(-------------------------------------------------------------) +--R x +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R (- b x - a)\|c - a + a\|- b x - 2a b x + c - a - b c x +--R a log(-------------------------------------------------------------) +--R x +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R \|c - a - \|- b x - 2a b x + c - a +--R 2c atan(-----------------------------------------) +--R b x +--R / +--R b +--R Type: Union(Expression Integer,...) +--E 487 + +--S 488 of 489 +m0296:= a0296-r0296 +--R +--R +--R (394) +--R +-------------------------+ +--R | 2 2 2 2 +--R \|- b x - 2a b x + c - a + c +--R b x log(--------------------------------) +--R b x + a +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R (- b x - a)\|c - a + a\|- b x - 2a b x + c - a + b c x +--R - a log(-------------------------------------------------------------) +--R x +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R (- b x - a)\|c - a + a\|- b x - 2a b x + c - a - b c x +--R a log(-------------------------------------------------------------) +--R x +--R + +--R +-------+ +-------------------------+ +--R | 2 2 | 2 2 2 2 +--R \|c - a - \|- b x - 2a b x + c - a +--R 2c atan(-----------------------------------------) +--R b x +--R + +--R +-------------+ +--R |- b x + c - a b x + a +--R 2c atan( |------------- ) + (- b x - a)asech(-------) +--R \| b x + c + a c +--R / +--R b +--R Type: Expression Integer +--E 488 + +--S 489 of 489 +d0296:= D(m0296,x) +--R +--R +--R (395) +--R +-------------------------+ +--R | 2 2 2 2 +-------------+ +--R |- b x - 2a b x + c - a |- b x + c - a +--R (b x + c + a) |------------------------- |------------- +--R | 2 \| b x + c + a +--R \| c +--R * +--R +-------------------------+ +--R | 2 2 2 2 +--R \|- b x - 2a b x + c - a + c +--R log(--------------------------------) +--R b x + a +--R + +--R +-------------------------+ +--R | 2 2 2 2 +--R b x + a |- b x - 2a b x + c - a +--R (- b x - c - a)asech(-------) |------------------------- + b x + c +--R c | 2 +--R \| c +--R + +--R a +--R * +--R +-------------+ +--R |- b x + c - a +--R |------------- +--R \| b x + c + a +--R + +--R +-------------------------+ +--R | 2 2 2 2 +--R |- b x - 2a b x + c - a +--R - c |------------------------- +--R | 2 +--R \| c +--R / +--R +-------------------------+ +--R | 2 2 2 2 +-------------+ +--R |- b x - 2a b x + c - a |- b x + c - a +--R (b x + c + a) |------------------------- |------------- +--R | 2 \| b x + c + a +--R \| c +--R Type: Expression Integer +--E 489 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richinvhyper200-296.input.pdf b/src/axiom-website/CATS/richinvhyper200-296.input.pdf new file mode 100644 index 0000000..6321d8f Binary files /dev/null and b/src/axiom-website/CATS/richinvhyper200-296.input.pdf differ diff --git a/src/axiom-website/CATS/richinvtrig000-092.input.pamphlet b/src/axiom-website/CATS/richinvtrig000-092.input.pamphlet new file mode 100644 index 0000000..f23cbd4 --- /dev/null +++ b/src/axiom-website/CATS/richinvtrig000-092.input.pamphlet @@ -0,0 +1,11670 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richinvtrig000-092.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richinvtrig000-092.output +)spool richinvtrig000-092.output +)set message auto off +)clear all + +--S 1 of 477 +t0000:= asin(a*x)/x +--R +--R +--R asin(a x) +--R (1) --------- +--R x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 477 +r0000:= -1/2*%i*asin(a*x)^2+asin(a*x)*log(-2*%i*_ + (%i*a*x+(1-a^2*x^2)^(1/2))*a*x)-_ + 1/2*%i*polylog(2,(%i*a*x+(1-a^2*x^2)^(1/2))^2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 477 +a0000:= integrate(t0000,x) +--R +--R +--R x +--R ++ asin(%Q a) +--R (2) | ---------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 477 +--m0000:= a0000-r0000 +--E 4 + +--S 5 of 477 +--d0000:= D(m0000,x) +--E 5 + +--S 6 of 477 +t0001:= asin(x^(1/2))/x +--R +--R +--R +-+ +--R asin(\|x ) +--R (3) ---------- +--R x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 477 +r0001:= -%i*asin(x^(1/2))^2+2*asin(x^(1/2))*_ + log(-2*%i*(%i*x+(1-x)^(1/2)*x^(1/2)))-_ + %i*polylog(2,((1-x)^(1/2)+%i*x^(1/2))^2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 477 +a0001:= integrate(t0001,x) +--R +--R +--R x +--+ +--R ++ asin(\|%Q ) +--R (4) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 477 +--m0001:= a0001-r0001 +--E 9 + +--S 10 of 477 +--d0001:= D(m0001,x) +--E 10 + +--S 11 of 477 +t0002:= atan(a*x)/x +--R +--R +--R atan(a x) +--R (5) --------- +--R x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 477 +r0002:= 1/2*%i*polylog(2,-%i*a*x)-1/2*%i*polylog(2,%i*a*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 477 +a0002:= integrate(t0002,x) +--R +--R +--R x +--R ++ atan(%Q a) +--R (6) | ---------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 477 +--m0002:= a0002-r0002 +--E 14 + +--S 15 of 477 +--d0002:= D(m0002,x) +--E 15 + +--S 16 of 477 +t0003:= atan(1+x)/(2+2*x) +--R +--R +--R atan(x + 1) +--R (7) ----------- +--R 2x + 2 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 477 +r0003:= 1/4*%i*polylog(2,-%i*(1+x))-1/4*%i*polylog(2,%i*(1+x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 477 +a0003:= integrate(t0003,x) +--R +--R +--R x +--R ++ atan(%Q + 1) +--R (8) | ------------ d%Q +--R ++ 2%Q + 2 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 477 +--m0003:= a0003-r0003 +--E 19 + +--S 20 of 477 +--d0003:= D(m0003,x) +--E 20 + +--S 21 of 477 +t0004:= atan(a+b*x)/(a+b*x) +--R +--R +--R atan(b x + a) +--R (9) ------------- +--R b x + a +--R Type: Expression(Integer) +--E 21 + +--S 22 of 477 +r0004:= 1/2*%i*(polylog(2,-%i*(a+b*x))-polylog(2,%i*(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 477 +a0004:= integrate(t0004,x) +--R +--R +--R x +--R ++ atan(%Q b + a) +--R (10) | -------------- d%Q +--R ++ %Q b + a +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 477 +--m0004:= a0004-r0004 +--E 24 + +--S 25 of 477 +--d0004:= D(m0004,x) +--E 25 + +--S 26 of 477 +t0005:= atan(x)/(a+b*x^2)^(3/2) +--R +--R +--R atan(x) +--R (11) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 477 +r0005:= x*atan(x)/a/(a+b*x^2)^(1/2)+atanh((a+b*x^2)^(1/2)/_ + (a-b)^(1/2))/a/(a-b)^(1/2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-------+ +--R \|b x + a atanh(-----------) + x atan(x)\|- b + a +--R +-------+ +--R \|- b + a +--R (12) --------------------------------------------------- +--R +--------+ +--R +-------+ | 2 +--R a\|- b + a \|b x + a +--R Type: Expression(Integer) +--E 27 + +--S 28 of 477 +a0005:= integrate(t0005,x) +--R +--R +--R (13) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R +--------+ +--R 2x +-------+ | 2 2x +-------+ +-+ +--R x atan(------)\|- b + a \|b x + a - x atan(------)\|- b + a \|a +--R 2 2 +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-------+ +-+ | 2 2 2 +-------+ +--R 2a\|- b + a \|a \|b x + a + (- 2a b x - 2a )\|- b + a +--R , +--R +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R +--------+ +--R 2x +-----+ | 2 2x +-+ +-----+ +--R x atan(------)\|b - a \|b x + a - x atan(------)\|a \|b - a +--R 2 2 +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-+ +-----+ | 2 2 2 +-----+ +--R 2a\|a \|b - a \|b x + a + (- 2a b x - 2a )\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 28 + +--S 29 of 477 +m0005a:= a0005.1-r0005 +--R +--R +--R (14) +--R +--------+ +--R 2 | 2 2 +-+ +--R ((b x + a)\|b x + a + (- b x - a)\|a ) +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((- 2b x - 2a)\|b x + a + (2b x + 2a)\|a )atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R +--------+ +--R 2x +-------+ +-+ | 2 +--R (2x atan(x) + x atan(------))\|- b + a \|a \|b x + a +--R 2 +--R x - 1 +--R + +--R 3 3 2x +-------+ +--R ((- 2b x - 2a x)atan(x) + (- b x - a x)atan(------))\|- b + a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ | 2 2 2 +-------+ +-+ +--R (2a b x + 2a )\|- b + a \|b x + a + (- 2a b x - 2a )\|- b + a \|a +--R Type: Expression(Integer) +--E 29 + +--S 30 of 477 +d0005a:= D(m0005a,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (15) ------------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 30 + +--S 31 of 477 +m0005b:= a0005.2-r0005 +--R +--R +--R (16) +--R +--------+ +--R 2 +-----+ | 2 2 +-+ +-----+ +--R ((- 2b x - 2a)\|b - a \|b x + a + (2b x + 2a)\|a \|b - a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R +--------+ +--R 2 +-------+ | 2 2 +-------+ +-+ +--R ((b x + a)\|- b + a \|b x + a + (- b x - a)\|- b + a \|a ) +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R +--------+ +--R 2x +-------+ +-+ +-----+ | 2 +--R (2x atan(x) + x atan(------))\|- b + a \|a \|b - a \|b x + a +--R 2 +--R x - 1 +--R + +--R 3 3 2x +-------+ +-----+ +--R ((- 2b x - 2a x)atan(x) + (- b x - a x)atan(------))\|- b + a \|b - a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ +-----+ | 2 +--R (2a b x + 2a )\|- b + a \|b - a \|b x + a +--R + +--R 2 2 +-------+ +-+ +-----+ +--R (- 2a b x - 2a )\|- b + a \|a \|b - a +--R Type: Expression(Integer) +--E 31 + +--S 32 of 477 +d0005b:= D(m0005b,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (17) ------------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 32 + +--S 33 of 477 +t0006:= atan(x)/(a+b*x^2)^(5/2) +--R +--R +--R atan(x) +--R (18) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 33 + +--S 34 of 477 +r0006:= -1/3/a/(a-b)/(a+b*x^2)^(1/2)+1/3*x*(3*a+2*b*x^2)*_ + atan(x)/a^2/(a+b*x^2)^(3/2)+1/3*(3*a-2*b)*_ + atanh((a+b*x^2)^(1/2)/(a-b)^(1/2))/a^2/(a-b)^(3/2) +--R +--R +--R (19) +--R +--------+ +--R +--------+ | 2 +--R 2 2 2 | 2 \|b x + a +--R ((2b - 3a b)x + 2a b - 3a )\|b x + a atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 2 3 2 2 2 +-------+ +--R (((2b - 2a b)x + (3a b - 3a )x)atan(x) + a b x + a )\|- b + a +--R / +--R +--------+ +--R 2 2 3 2 3 4 +-------+ | 2 +--R ((3a b - 3a b)x + 3a b - 3a )\|- b + a \|b x + a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 477 +a0006:= integrate(t0006,x) +--R +--R +--R (20) +--R [ +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b - 12a b )x + (32a b - 48a b )x + (40a b - 60a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b + 3a b )x + (- 20a b + 30a b )x + (- 50a b + 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b + 72a b)x - 16a b + 24a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b - 2a b )x + (19a b - 19a b )x + (40a b - 40a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 +--R (- 8b + 8a b )x + (- 36a b + 36a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 52a b + 52a b)x + (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b - 24a b )x + (96a b - 96a b )x + (120a b - 120a b)x +--R + +--R 5 6 +--R 48a b - 48a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b + 6a b )x + (- 60a b + 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b + 150a b )x + (- 144a b + 144a b)x - 48a b + 48a +--R * +--R +-------+ +--R \|- b + a +--R , +--R +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b - 12a b )x + (32a b - 48a b )x + (40a b - 60a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b + 3a b )x + (- 20a b + 30a b )x + (- 50a b + 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b + 72a b)x - 16a b + 24a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b - 2a b )x + (19a b - 19a b )x + (40a b - 40a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R 6a b x + 14a b x + 8a b x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 +--R (- 8b + 8a b )x + (- 36a b + 36a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 52a b + 52a b)x + (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R - 2b x - 12a b x - 18a b x - 8a b x +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b - 24a b )x + (96a b - 96a b )x + (120a b - 120a b)x +--R + +--R 5 6 +--R 48a b - 48a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b + 6a b )x + (- 60a b + 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b + 150a b )x + (- 144a b + 144a b)x - 48a b + 48a +--R * +--R +-----+ +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 35 + +--S 36 of 477 +m0006a:= a0006.1-r0006 +--R +--R +--R (21) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b - 3a b )x + (18a b - 27a b )x + (32a b - 48a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b + 12a b )x + (- 32a b + 48a b )x + (- 40a b + 60a b)x +--R + +--R 3 4 +--R - 16a b + 24a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 4b + 6a b )x + (- 36a b + 54a b )x + (- 64a b + 96a b)x +--R + +--R 3 4 +--R - 32a b + 48a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (16b - 24a b )x + (64a b - 96a b )x + (80a b - 120a b)x +--R + +--R 3 4 +--R 32a b - 48a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b - 16a b )x + (56a b - 56a b)x + (48a b - 48a )x)atan(x) +--R + +--R 3 2 5 2 2 3 2 3 2x +--R ((8b - 8a b )x + (28a b - 28a b)x + (24a b - 24a )x)atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b + 4a b )x + (- 38a b + 38a b )x + (- 80a b + 80a b)x +--R + +--R 3 4 +--R (- 48a b + 48a )x +--R * +--R atan(x) +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 2b + 2a b )x + (- 19a b + 19a b )x + (- 40a b + 40a b)x +--R + +--R 3 4 +--R (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b - 6a b )x + (54a b - 54a b )x + (96a b - 96a b)x + 48a b +--R + +--R 6 +--R - 48a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b + 24a b )x + (- 96a b + 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b + 120a b)x - 48a b + 48a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R Type: Expression(Integer) +--E 36 + +--S 37 of 477 +d0006a:= D(m0006a,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (22) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 477 +m0006b:= a0006.2-r0006 +--R +--R +--R (23) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 4b + 6a b )x + (- 36a b + 54a b )x + (- 64a b + 96a b)x +--R + +--R 3 4 +--R - 32a b + 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (16b - 24a b )x + (64a b - 96a b )x + (80a b - 120a b)x +--R + +--R 3 4 +--R 32a b - 48a +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b - 3a b )x + (18a b - 27a b )x + (32a b - 48a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b + 12a b )x + (- 32a b + 48a b )x + (- 40a b + 60a b)x +--R + +--R 3 4 +--R - 16a b + 24a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b - 16a b )x + (56a b - 56a b)x + (48a b - 48a )x)atan(x) +--R + +--R 3 2 5 2 2 3 2 3 2x +--R ((8b - 8a b )x + (28a b - 28a b)x + (24a b - 24a )x)atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 4 2 2 3 +--R 2b x + 18a b x + 32a b x + 16a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b + a \|a \|b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b + 4a b )x + (- 38a b + 38a b )x + (- 80a b + 80a b)x +--R + +--R 3 4 +--R (- 48a b + 48a )x +--R * +--R atan(x) +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 2b + 2a b )x + (- 19a b + 19a b )x + (- 40a b + 40a b)x +--R + +--R 3 4 +--R (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 4 +--R - 8a b x - 32a b x - 40a b x - 16a +--R * +--R +-------+ +-----+ +--R \|- b + a \|b - a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b - 6a b )x + (54a b - 54a b )x + (96a b - 96a b)x + 48a b +--R + +--R 6 +--R - 48a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b + a \|b - a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b + 24a b )x + (- 96a b + 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b + 120a b)x - 48a b + 48a +--R * +--R +-------+ +-+ +-----+ +--R \|- b + a \|a \|b - a +--R Type: Expression(Integer) +--E 38 + +--S 39 of 477 +d0006b:= D(m0006b,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (24) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 39 + +--S 40 of 477 +t0007:= atan(x)/(a+b*x^2)^(7/2) +--R +--R +--R atan(x) +--R (25) ------------------------------------------ +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 477 +r0007:= -1/15/a/(a-b)/(a+b*x^2)^(3/2)-1/15*(7*a-4*b)/a^2/(a-b)^2/_ + (a+b*x^2)^(1/2)+1/15*x*(8*(a+b*x^2)^2+a*(7*a+4*b*x^2))*_ + atan(x)/a^3/(a+b*x^2)^(5/2)+1/15*(15*a^2-20*a*b+8*b^2)*_ + atanh((a+b*x^2)^(1/2)/(a-b)^(1/2))/a^3/(a-b)^(5/2) +--R +--R +--R (26) +--R 4 3 2 2 4 3 2 2 3 2 2 2 +--R (8b - 20a b + 15a b )x + (16a b - 40a b + 30a b)x + 8a b +--R + +--R 3 4 +--R - 20a b + 15a +--R * +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +--R \|b x + a atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 4 3 2 2 5 3 2 2 3 3 +--R (8b - 16a b + 8a b )x + (20a b - 40a b + 20a b)x +--R + +--R 2 2 3 4 +--R (15a b - 30a b + 15a )x +--R * +--R atan(x) +--R + +--R 3 2 2 4 2 2 3 2 3 4 +--R (4a b - 7a b )x + (9a b - 15a b)x + 5a b - 8a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 5 2 +--R (15a b - 30a b + 15a b )x + (30a b - 60a b + 30a b)x + 15a b +--R + +--R 6 7 +--R - 30a b + 15a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R Type: Expression(Integer) +--E 41 + +--S 42 of 477 +a0007:= integrate(t0007,x) +--R +--R +--R (27) +--R [ +--R 8 7 2 6 12 +--R (64b - 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b - 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b - 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b - 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b - 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b - 11520a b + 8640a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b + 20a b - 15a b )x + (- 280a b + 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b + 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b + 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b + 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b + 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b + 12800a b - 9600a b)x - 1024a b + 2560a b - 1920a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b - 16a b + 8a b )x + (276a b - 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b - 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b - 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b - 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (6400a b - 12800a b + 6400a b)x +--R + +--R 6 2 7 8 +--R (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b - 114a b )x + (766a b - 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b - 4080a b )x + (4272a b - 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b - 4608a b )x + (896a b - 1280a b)x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 8 7 2 6 13 +--R (- 64b + 128a b - 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 864a b + 1728a b - 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 4056a b + 8112a b - 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 9320a b + 18640a b - 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 11504a b + 23008a b - 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 7360a b + 14720a b - 7360a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b + 16a b )x + (- 286a b + 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b + 2672a b )x + (- 4490a b + 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b + 8480a b )x + (- 3616a b + 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b + 1280a b)x +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b - 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b - 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b - 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b - 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b - 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b - 34560a b + 17280a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b + 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b + 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b + 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b + 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b + 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b + 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b + 38400a b - 19200a b)x - 3840a b + 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-------+ +--R \|- b + a +--R , +--R +--R 8 7 2 6 12 +--R (64b - 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b - 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b - 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b - 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b - 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b - 11520a b + 8640a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b + 20a b - 15a b )x + (- 280a b + 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b + 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b + 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b + 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b + 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b + 12800a b - 9600a b)x - 1024a b + 2560a b - 1920a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b - 16a b + 8a b )x + (276a b - 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b - 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b - 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b - 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (6400a b - 12800a b + 6400a b)x +--R + +--R 6 2 7 8 +--R (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (72a b - 114a b )x + (766a b - 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (2694a b - 4080a b )x + (4272a b - 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (3168a b - 4608a b )x + (896a b - 1280a b)x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 8 7 2 6 13 +--R (- 64b + 128a b - 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 864a b + 1728a b - 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 4056a b + 8112a b - 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 9320a b + 18640a b - 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 11504a b + 23008a b - 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 7360a b + 14720a b - 7360a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (- 10b + 16a b )x + (- 286a b + 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (- 1742a b + 2672a b )x + (- 4490a b + 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (- 5744a b + 8480a b )x + (- 3616a b + 5248a b )x +--R + +--R 6 2 7 2 +--R (- 896a b + 1280a b)x +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b - 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b - 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b - 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b - 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b - 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b - 34560a b + 17280a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b + 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b + 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b + 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b + 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b + 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b + 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b + 38400a b - 19200a b)x - 3840a b + 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-----+ +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 42 + +--S 43 of 477 +m0007a:= a0007.1-r0007 +--R +--R +--R (28) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b - 20a b + 15a b )x + (272a b - 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b - 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b - 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b - 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b - 10240a b + 7680a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b + 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b + 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b + 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b + 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b + 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b + 11520a b - 8640a b)x - 1024a b + 2560a b - 1920a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((- 2b - 2a b + 4a )x + (- 8a b + 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (2a b - 2a b)x + (6a b - 2a b - 4a )x + (8a b - 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 8 7 2 6 12 +--R (- 16b + 40a b - 30a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 544a b + 1360a b - 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3600a b + 9000a b - 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 9728a b + 24320a b - 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 12800a b + 32000a b - 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 8192a b + 20480a b - 15360a b)x - 2048a b + 5120a b - 3840a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (128b - 320a b + 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (1664a b - 4160a b + 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (7296a b - 18240a b + 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (15232a b - 38080a b + 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (16640a b - 41600a b + 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (9216a b - 23040a b + 17280a b)x + 2048a b - 5120a b + 3840a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 7 6 2 5 11 +--R (128b - 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b - 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b - 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b - 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b - 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b - 7680a b + 3840a )x +--R * +--R atan(x) +--R + +--R 7 6 2 5 11 6 2 5 3 4 9 +--R (64b - 128a b + 64a b )x + (800a b - 1600a b + 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (3256a b - 6512a b + 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (6064a b - 12128a b + 6064a b )x +--R + +--R 4 3 5 2 6 3 5 2 6 7 +--R (5440a b - 10880a b + 5440a b)x + (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b - 16a b )x + (340a b - 544a b )x + (2250a b - 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b - 9728a b )x + (8000a b - 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b - 8192a b)x + 1280a b - 2048a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 8 7 2 6 13 +--R (- 16b + 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b + 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b + 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b + 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b + 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b + 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b + 7680a b - 3840a )x +--R * +--R atan(x) +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (- 8b + 16a b - 8a b )x + (- 276a b + 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b + 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b + 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b + 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b + 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b + 128a b )x + (- 1040a b + 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b + 7296a b )x + (- 9520a b + 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b + 16640a b )x + (- 5760a b + 9216a b)x - 1280a b +--R + +--R 8 +--R 2048a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b - 60a b + 30a b )x + (1020a b - 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b - 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b - 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b - 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b - 30720a b + 15360a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b + 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b + 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b + 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b + 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b + 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b + 34560a b - 17280a b)x - 3840a b + 7680a b - 3840a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R Type: Expression(Integer) +--E 43 + +--S 44 of 477 +d0007a:= D(m0007a,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (29) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 44 + +--S 45 of 477 +m0007b:= a0007.2-r0007 +--R +--R +--R (30) +--R 8 7 2 6 12 +--R (- 16b + 40a b - 30a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 544a b + 1360a b - 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3600a b + 9000a b - 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 9728a b + 24320a b - 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 12800a b + 32000a b - 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 8192a b + 20480a b - 15360a b)x - 2048a b + 5120a b - 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 8 7 2 6 12 +--R (128b - 320a b + 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (1664a b - 4160a b + 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (7296a b - 18240a b + 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (15232a b - 38080a b + 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (16640a b - 41600a b + 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (9216a b - 23040a b + 17280a b)x + 2048a b - 5120a b + 3840a +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b - 20a b + 15a b )x + (272a b - 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b - 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b - 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b - 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b - 10240a b + 7680a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b + 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b + 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b + 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b + 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b + 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b + 11520a b - 8640a b)x - 1024a b + 2560a b - 1920a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 7 6 2 5 11 +--R (128b - 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b - 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b - 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b - 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b - 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b - 7680a b + 3840a )x +--R * +--R atan(x) +--R + +--R 7 6 2 5 11 6 2 5 3 4 9 +--R (64b - 128a b + 64a b )x + (800a b - 1600a b + 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (3256a b - 6512a b + 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (6064a b - 12128a b + 6064a b )x +--R + +--R 4 3 5 2 6 3 5 2 6 7 +--R (5440a b - 10880a b + 5440a b)x + (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 6 12 6 2 5 10 2 5 3 4 8 +--R (10b - 16a b )x + (340a b - 544a b )x + (2250a b - 3600a b )x +--R + +--R 3 4 4 3 6 4 3 5 2 4 +--R (6080a b - 9728a b )x + (8000a b - 12800a b )x +--R + +--R 5 2 6 2 6 7 +--R (5120a b - 8192a b)x + 1280a b - 2048a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b + a \|a \|b - a \|b x + a +--R + +--R 8 7 2 6 13 +--R (- 16b + 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b + 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b + 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b + 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b + 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b + 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b + 7680a b - 3840a )x +--R * +--R atan(x) +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (- 8b + 16a b - 8a b )x + (- 276a b + 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b + 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b + 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b + 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b + 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 80a b + 128a b )x + (- 1040a b + 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 4560a b + 7296a b )x + (- 9520a b + 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 +--R (- 10400a b + 16640a b )x + (- 5760a b + 9216a b)x - 1280a b +--R + +--R 8 +--R 2048a +--R * +--R +-------+ +-----+ +--R \|- b + a \|b - a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b - 60a b + 30a b )x + (1020a b - 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b - 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b - 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b - 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b - 30720a b + 15360a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b + a \|b - a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b + 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b + 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b + 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b + 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b + 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b + 34560a b - 17280a b)x - 3840a b + 7680a b - 3840a +--R * +--R +-------+ +-+ +-----+ +--R \|- b + a \|a \|b - a +--R Type: Expression(Integer) +--E 45 + +--S 46 of 477 +d0007b:= D(m0007b,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (31) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 46 + +--S 47 of 477 +t0008:= atan(x)*(a+a*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R (32) atan(x)\|a x + a +--R Type: Expression(Integer) +--E 47 + +--S 48 of 477 +r0008:= -1/2/(1+x^2)^(1/2)*(a*(1+x^2))^(1/2)*((1+x^2)^(1/2)-_ + x*(1+x^2)^(1/2)*atan(x)+2*%i*atan(exp(1)^(%i*atan(x)))*_ + atan(x)-%i*polylog(2,-%i*exp(1)^(%i*atan(x)))+_ + %i*polylog(2,%i*exp(1)^(%i*atan(x)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 48 + +--S 49 of 477 +a0008:= integrate(t0008,x) +--R +--R +--R x +----------+ +--R ++ | 2 +--R (33) | atan(%Q)\|(%Q + 1)a d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 49 + +--S 50 of 477 +--m0008:= a0008-r0008 +--E 50 + +--S 51 of 477 +--d0008:= D(m0008,x) +--E 51 + +--S 52 of 477 +t0009:= atan(x)/(a+a*x^2)^(1/2) +--R +--R +--R atan(x) +--R (34) ----------- +--R +--------+ +--R | 2 +--R \|a x + a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 477 +r0009:= -%i*(1+x^2)^(1/2)*(2*atan(exp(1)^(%i*atan(x)))*atan(x)-_ + polylog(2,-%i*exp(1)^(%i*atan(x)))+_ + polylog(2,%i*exp(1)^(%i*atan(x))))/(a*(1+x^2))^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 53 + +--S 54 of 477 +a0009:= integrate(t0009,x) +--R +--R +--R x +--R ++ atan(%Q) +--R (35) | ------------- d%Q +--R ++ +----------+ +--R | 2 +--R \|(%Q + 1)a +--R Type: Union(Expression(Integer),...) +--E 54 + +--S 55 of 477 +--m0009:= a0009-r0009 +--E 55 + +--S 56 of 477 +--d0009:= D(m0009,x) +--E 56 + +--S 57 of 477 +t0010:= atan(x)/(a+a*x^2)^(3/2) +--R +--R +--R atan(x) +--R (36) --------------------- +--R +--------+ +--R 2 | 2 +--R (a x + a)\|a x + a +--R Type: Expression(Integer) +--E 57 + +--S 58 of 477 +r0010:= (1+atan(x)*x)/a/(a*(1+x^2))^(1/2) +--R +--R +--R x atan(x) + 1 +--R (37) ------------- +--R +--------+ +--R | 2 +--R a\|a x + a +--R Type: Expression(Integer) +--E 58 + +--S 59 of 477 +a0010:= integrate(t0010,x) +--R +--R +--R +--------+ +--R 2x | 2 2x 2 +-+ +--R x atan(------)\|a x + a + (- x atan(------) - 2x )\|a +--R 2 2 +--R x - 1 x - 1 +--R (38) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 2 2 2 +--R 2a\|a \|a x + a - 2a x - 2a +--R Type: Union(Expression(Integer),...) +--E 59 + +--S 60 of 477 +m0010:= a0010-r0010 +--R +--R +--R (39) +--R +--------+ +--R 2x 2 +-+ | 2 +--R (2x atan(x) + x atan(------) + 2x + 2)\|a \|a x + a +--R 2 +--R x - 1 +--R + +--R 3 3 2x 2 +--R (- 2a x - 2a x)atan(x) + (- a x - a x)atan(------) - 2a x - 2a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 2 | 2 2 2 2 +-+ +--R (2a x + 2a )\|a x + a + (- 2a x - 2a )\|a +--R Type: Expression(Integer) +--E 60 + +--S 61 of 477 +d0010:= D(m0010,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (40) ------------------------- +--R +--------+ +--R 2 | 2 +--R (2a x + 2a)\|a x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 477 +t0011:= atan(x)/(a+a*x^2)^(5/2) +--R +--R +--R atan(x) +--R (41) ------------------------------ +--R +--------+ +--R 2 4 2 2 2 | 2 +--R (a x + 2a x + a )\|a x + a +--R Type: Expression(Integer) +--E 62 + +--S 63 of 477 +r0011:= 1/9*(6+1/(1+x^2)+6*atan(x)*x+3*x*atan(x)/(1+x^2))/a^2/(a*(1+x^2))^(1/2) +--R +--R +--R 3 2 +--R (6x + 9x)atan(x) + 6x + 7 +--R (42) --------------------------- +--R +--------+ +--R 2 2 2 | 2 +--R (9a x + 9a )\|a x + a +--R Type: Expression(Integer) +--E 63 + +--S 64 of 477 +a0011:= integrate(t0011,x) +--R +--R +--R (43) +--R +--------+ +--R 5 3 2x 4 2 | 2 +--R ((6x + 33x + 36x)atan(------) + 30x + 36x )\|a x + a +--R 2 +--R x - 1 +--R + +--R 5 3 2x 6 4 2 +-+ +--R ((- 18x - 51x - 36x)atan(------) - 14x - 48x - 36x )\|a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 4 2 2 2 +-+ | 2 3 6 3 4 3 2 +--R (54a x + 126a x + 72a )\|a \|a x + a - 18a x - 108a x - 162a x +--R + +--R 3 +--R - 72a +--R Type: Union(Expression(Integer),...) +--E 64 + +--S 65 of 477 +m0011:= a0011-r0011 +--R +--R +--R (44) +--R 5 3 5 3 2x 6 +--R (36x + 102x + 72x)atan(x) + (18x + 51x + 36x)atan(------) + 14x +--R 2 +--R x - 1 +--R + +--R 4 2 +--R 84x + 126x + 56 +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|a x + a +--R + +--R 7 5 3 +--R (- 12a x - 78a x - 138a x - 72a x)atan(x) +--R + +--R 7 5 3 2x 6 4 +--R (- 6a x - 39a x - 69a x - 36a x)atan(------) - 42a x - 140a x +--R 2 +--R x - 1 +--R + +--R 2 +--R - 154a x - 56a +--R / +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (18a x + 108a x + 162a x + 72a )\|a x + a +--R + +--R 3 6 3 4 3 2 3 +-+ +--R (- 54a x - 180a x - 198a x - 72a )\|a +--R Type: Expression(Integer) +--E 65 + +--S 66 of 477 +d0011:= D(m0011,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (45) -------------------------------- +--R +--------+ +--R 2 4 2 2 2 | 2 +--R (2a x + 4a x + 2a )\|a x + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 477 +t0012:= atan(x)/(a+a*x^2)^(7/2) +--R +--R +--R atan(x) +--R (46) -------------------------------------- +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x + 3a x + 3a x + a )\|a x + a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 477 +r0012:= 1/225*(149+120*x^4+260*x^2+225*atan(x)*x+120*atan(x)*x^5+_ + 300*atan(x)*x^3)/(1+x^2)^2/a^3/(a*(1+x^2))^(1/2) +--R +--R +--R 5 3 4 2 +--R (120x + 300x + 225x)atan(x) + 120x + 260x + 149 +--R (47) --------------------------------------------------- +--R +--------+ +--R 3 4 3 2 3 | 2 +--R (225a x + 450a x + 225a )\|a x + a +--R Type: Expression(Integer) +--E 68 + +--S 69 of 477 +a0012:= integrate(t0012,x) +--R +--R +--R (48) +--R 9 7 5 3 2x 8 +--R (120x + 1740x + 5745x + 7500x + 3600x)atan(------) + 1250x +--R 2 +--R x - 1 +--R + +--R 6 4 2 +--R 5540x + 7800x + 3600x +--R * +--R +--------+ +--R | 2 +--R \|a x + a +--R + +--R 9 7 5 3 2x 10 +--R (- 600x - 3900x - 9045x - 9300x - 3600x)atan(------) - 298x +--R 2 +--R x - 1 +--R + +--R 8 6 4 2 +--R - 3270x - 8990x - 9600x - 3600x +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 3 8 3 6 3 4 3 2 3 +-+ | 2 +--R (2250a x + 13500a x + 27450a x + 23400a x + 7200a )\|a \|a x + a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R - 450a x - 6750a x - 24750a x - 38250a x - 27000a x - 7200a +--R Type: Union(Expression(Integer),...) +--E 69 + +--S 70 of 477 +m0012:= a0012-r0012 +--R +--R +--R (49) +--R 9 7 5 3 +--R (1200x + 7800x + 18090x + 18600x + 7200x)atan(x) +--R + +--R 9 7 5 3 2x 10 +--R (600x + 3900x + 9045x + 9300x + 3600x)atan(------) + 298x +--R 2 +--R x - 1 +--R + +--R 8 6 4 2 +--R 4470x + 16390x + 25330x + 17880x + 4768 +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|a x + a +--R + +--R 11 9 7 5 3 +--R (- 240a x - 3720a x - 14970a x - 26490a x - 22200a x - 7200a x) +--R * +--R atan(x) +--R + +--R 11 9 7 5 3 +--R (- 120a x - 1860a x - 7485a x - 13245a x - 11100a x - 3600a x) +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 10 8 6 4 2 +--R - 1490a x - 10430a x - 27118a x - 33674a x - 20264a x - 4768a +--R / +--R 4 10 4 8 4 6 4 4 4 2 4 +--R (450a x + 6750a x + 24750a x + 38250a x + 27000a x + 7200a ) +--R * +--R +--------+ +--R | 2 +--R \|a x + a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +-+ +--R (- 2250a x - 15750a x - 40950a x - 50850a x - 30600a x - 7200a )\|a +--R Type: Expression(Integer) +--E 70 + +--S 71 of 477 +d0012:= D(m0012,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (50) ---------------------------------------- +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (2a x + 6a x + 6a x + 2a )\|a x + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 477 +t0013:= atan(x^(1/2))/x +--R +--R +--R +-+ +--R atan(\|x ) +--R (51) ---------- +--R x +--R Type: Expression(Integer) +--E 72 + +--S 73 of 477 +r0013:= %i*polylog(2,-%i*x^(1/2))-%i*polylog(2,%i*x^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 73 + +--S 74 of 477 +a0013:= integrate(t0013,x) +--R +--R +--R x +--+ +--R ++ atan(\|%Q ) +--R (52) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 74 + +--S 75 of 477 +--m0013:= a0013-r0013 +--E 75 + +--S 76 of 477 +--d0013:= D(m0013,x) +--E 76 + +--S 77 of 477 +t0014:= acot(a*x)/x +--R +--R +--R acot(a x) +--R (53) --------- +--R x +--R Type: Expression(Integer) +--E 77 + +--S 78 of 477 +r0014:= -1/2*%i*polylog(2,-%i/a/x)+1/2*%i*polylog(2,%i/a/x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 78 + +--S 79 of 477 +a0014:= integrate(t0014,x) +--R +--R +--R x +--R ++ acot(%Q a) +--R (54) | ---------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 79 + +--S 80 of 477 +--m0014:= a0014-r0014 +--E 80 + +--S 81 of 477 +--d0014:= D(m0014,x) +--E 81 + +--S 82 of 477 +t0015:= acot(1+x)/(2+2*x) +--R +--R +--R acot(x + 1) +--R (55) ----------- +--R 2x + 2 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 477 +r0015:= -1/4*%i*polylog(2,-%i/(1+x))+1/4*%i*polylog(2,%i/(1+x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 83 + +--S 84 of 477 +a0015:= integrate(t0015,x) +--R +--R +--R x +--R ++ acot(%Q + 1) +--R (56) | ------------ d%Q +--R ++ 2%Q + 2 +--R Type: Union(Expression(Integer),...) +--E 84 + +--S 85 of 477 +--m0015:= a0015-r0015 +--E 85 + +--S 86 of 477 +--d0015:= D(m0015,x) +--E 86 + +--S 87 of 477 +t0016:= acot(a+b*x)/(a+b*x) +--R +--R +--R acot(b x + a) +--R (57) ------------- +--R b x + a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 477 +r0016:= -1/2*%i*(polylog(2,-%i/(a+b*x))-polylog(2,%i/(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 88 + +--S 89 of 477 +a0016:= integrate(t0016,x) +--R +--R +--R x +--R ++ acot(%Q b + a) +--R (58) | -------------- d%Q +--R ++ %Q b + a +--R Type: Union(Expression(Integer),...) +--E 89 + +--S 90 of 477 +--m0016:= a0016-r0016 +--E 90 + +--S 91 of 477 +--d0016:= D(m0016,x) +--E 91 + +--S 92 of 477 +t0017:= acot(x)/(1+x^2)^2 +--R +--R +--R acot(x) +--R (59) ------------ +--R 4 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 477 +r0017:= -1/(4+4*x^2)+x*acot(x)/(2+2*x^2)-1/4*acot(x)^2 +--R +--R +--R 2 2 +--R (- x - 1)acot(x) + 2x acot(x) - 1 +--R (60) ----------------------------------- +--R 2 +--R 4x + 4 +--R Type: Expression(Integer) +--E 93 + +--S 94 of 477 +a0017:= integrate(t0017,x) +--R +--R +--R 2 2x 2 2x +--R (- x - 1)atan(------) + 4x atan(------) - 4 +--R 2 2 +--R x - 1 x - 1 +--R (61) --------------------------------------------- +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 94 + +--S 95 of 477 +m0017:= a0017-r0017 +--R +--R +--R (62) +--R 2 2x 2 2x 2 2 +--R (- x - 1)atan(------) + 4x atan(------) + (4x + 4)acot(x) - 8x acot(x) +--R 2 2 +--R x - 1 x - 1 +--R -------------------------------------------------------------------------- +--R 2 +--R 16x + 16 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 477 +d0017:= D(m0017,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (63) ----------------------- +--R 4 2 +--R 2x + 4x + 2 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 477 +t0018:= x*acot(x)/(1+x^2) +--R +--R +--R x acot(x) +--R (64) --------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 477 +r0018:= 1/2*%i*acot(x)^2-acot(x)*log(1-exp(1)^(2*%i*acot(x)))+_ + 1/2*%i*polylog(2,exp(1)^(2*%i*acot(x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 98 + +--S 99 of 477 +a0018:= integrate(t0018,x) +--R +--R +--R x +--R ++ %Q acot(%Q) +--R (65) | ----------- d%Q +--R ++ 2 +--R %Q + 1 +--R Type: Union(Expression(Integer),...) +--E 99 + +--S 100 of 477 +--m0018:= a0018-r0018 +--E 100 + +--S 101 of 477 +--d0018:= D(m0018,x) +--E 101 + +--S 102 of 477 +t0019:= acot(x)/(a+b*x^2)^(3/2) +--R +--R +--R acot(x) +--R (66) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 102 + +--S 103 of 477 +r0019:= x*acot(x)/a/(a+b*x^2)^(1/2)-atanh((a+b*x^2)^(1/2)/(a-b)^(1/2))/_ + a/(a-b)^(1/2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-------+ +--R - \|b x + a atanh(-----------) + x acot(x)\|- b + a +--R +-------+ +--R \|- b + a +--R (67) ----------------------------------------------------- +--R +--------+ +--R +-------+ | 2 +--R a\|- b + a \|b x + a +--R Type: Expression(Integer) +--E 103 + +--S 104 of 477 +a0019:= integrate(t0019,x) +--R +--R +--R (68) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R +--------+ +--R 2x +-------+ | 2 2x +-------+ +-+ +--R - x atan(------)\|- b + a \|b x + a + x atan(------)\|- b + a \|a +--R 2 2 +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-------+ +-+ | 2 2 2 +-------+ +--R 2a\|- b + a \|a \|b x + a + (- 2a b x - 2a )\|- b + a +--R , +--R +--R +--------+ +--R +-+ | 2 2 +--R (- \|a \|b x + a + b x + a) +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R +--------+ +--R 2x +-----+ | 2 2x +-+ +-----+ +--R - x atan(------)\|b - a \|b x + a + x atan(------)\|a \|b - a +--R 2 2 +--R x - 1 x - 1 +--R / +--R +--------+ +--R +-+ +-----+ | 2 2 2 +-----+ +--R 2a\|a \|b - a \|b x + a + (- 2a b x - 2a )\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 104 + +--S 105 of 477 +m0019a:= a0019.1-r0019 +--R +--R +--R (69) +--R +--------+ +--R 2 | 2 2 +-+ +--R ((b x + a)\|b x + a + (- b x - a)\|a ) +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((2b x + 2a)\|b x + a + (- 2b x - 2a)\|a )atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R +--------+ +--R 2x +-------+ +-+ | 2 +--R (- x atan(------) + 2x acot(x))\|- b + a \|a \|b x + a +--R 2 +--R x - 1 +--R + +--R 3 2x 3 +-------+ +--R ((b x + a x)atan(------) + (- 2b x - 2a x)acot(x))\|- b + a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ | 2 2 2 +-------+ +-+ +--R (2a b x + 2a )\|- b + a \|b x + a + (- 2a b x - 2a )\|- b + a \|a +--R Type: Expression(Integer) +--E 105 + +--S 106 of 477 +d0019a:= D(m0019a,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (70) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 106 + +--S 107 of 477 +m0019b:= a0019.2-r0019 +--R +--R +--R (71) +--R +--------+ +--R 2 +-----+ | 2 2 +-+ +-----+ +--R ((2b x + 2a)\|b - a \|b x + a + (- 2b x - 2a)\|a \|b - a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R +--------+ +--R 2 +-------+ | 2 2 +-------+ +-+ +--R ((- b x - a)\|- b + a \|b x + a + (b x + a)\|- b + a \|a ) +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R +--------+ +--R 2x +-------+ +-+ +-----+ | 2 +--R (- x atan(------) + 2x acot(x))\|- b + a \|a \|b - a \|b x + a +--R 2 +--R x - 1 +--R + +--R 3 2x 3 +-------+ +-----+ +--R ((b x + a x)atan(------) + (- 2b x - 2a x)acot(x))\|- b + a \|b - a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 +-------+ +-----+ | 2 +--R (2a b x + 2a )\|- b + a \|b - a \|b x + a +--R + +--R 2 2 +-------+ +-+ +-----+ +--R (- 2a b x - 2a )\|- b + a \|a \|b - a +--R Type: Expression(Integer) +--E 107 + +--S 108 of 477 +d0019b:= D(m0019b,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (72) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 108 + +--S 109 of 477 +t0020:= acot(x)/(a+b*x^2)^(5/2) +--R +--R +--R acot(x) +--R (73) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 109 + +--S 110 of 477 +r0020:= 1/3/a/(a-b)/(a+b*x^2)^(1/2)+1/3*x*(3*a+2*b*x^2)*_ + acot(x)/a^2/(a+b*x^2)^(3/2)-1/3*(3*a-2*b)*_ + atanh((a+b*x^2)^(1/2)/(a-b)^(1/2))/a^2/(a-b)^(3/2) +--R +--R +--R (74) +--R +--------+ +--R +--------+ | 2 +--R 2 2 2 | 2 \|b x + a +--R ((- 2b + 3a b)x - 2a b + 3a )\|b x + a atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 2 3 2 2 2 +-------+ +--R (((2b - 2a b)x + (3a b - 3a )x)acot(x) - a b x - a )\|- b + a +--R / +--R +--------+ +--R 2 2 3 2 3 4 +-------+ | 2 +--R ((3a b - 3a b)x + 3a b - 3a )\|- b + a \|b x + a +--R Type: Expression(Integer) +--E 110 + +--S 111 of 477 +a0020:= integrate(t0020,x) +--R +--R +--R (75) +--R [ +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b - 12a b )x + (32a b - 48a b )x + (40a b - 60a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (- 2b + 3a b )x + (- 20a b + 30a b )x + (- 50a b + 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (- 48a b + 72a b)x - 16a b + 24a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b + 2a b )x + (- 19a b + 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b + 40a b)x + (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R - 6a b x - 14a b x - 8a b x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b - 8a b )x + (36a b - 36a b )x + (52a b - 52a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R 2b x + 12a b x + 18a b x + 8a b x +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b - 24a b )x + (96a b - 96a b )x + (120a b - 120a b)x +--R + +--R 5 6 +--R 48a b - 48a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b + 6a b )x + (- 60a b + 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b + 150a b )x + (- 144a b + 144a b)x - 48a b + 48a +--R * +--R +-------+ +--R \|- b + a +--R , +--R +--R 4 3 6 3 2 2 4 +--R (- 8b + 12a b )x + (- 32a b + 48a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 40a b + 60a b)x - 16a b + 24a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 4 8 4 2 3 6 2 3 3 2 4 +--R (2b - 3a b )x + (20a b - 30a b )x + (50a b - 75a b )x +--R + +--R 3 2 4 2 4 5 +--R (48a b - 72a b)x + 16a b - 24a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 4 3 7 3 2 2 5 +--R (- 2b + 2a b )x + (- 19a b + 19a b )x +--R + +--R 2 2 3 3 3 4 +--R (- 40a b + 40a b)x + (- 24a b + 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 6 2 2 4 3 2 +--R - 6a b x - 14a b x - 8a b x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (8b - 8a b )x + (36a b - 36a b )x + (52a b - 52a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 8 3 6 2 2 4 3 2 +--R 2b x + 12a b x + 18a b x + 8a b x +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 +--R (24a b - 24a b )x + (96a b - 96a b )x + (120a b - 120a b)x +--R + +--R 5 6 +--R 48a b - 48a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|b x + a +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 6a b + 6a b )x + (- 60a b + 60a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 7 +--R (- 150a b + 150a b )x + (- 144a b + 144a b)x - 48a b + 48a +--R * +--R +-----+ +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 111 + +--S 112 of 477 +m0020a:= a0020.1-r0020 +--R +--R +--R (76) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (2b - 3a b )x + (18a b - 27a b )x + (32a b - 48a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 8b + 12a b )x + (- 32a b + 48a b )x + (- 40a b + 60a b)x +--R + +--R 3 4 +--R - 16a b + 24a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b - 6a b )x + (36a b - 54a b )x + (64a b - 96a b)x +--R + +--R 3 4 +--R 32a b - 48a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b + 24a b )x + (- 64a b + 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b + 120a b)x - 32a b + 48a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b + 8a b )x + (- 28a b + 28a b)x + (- 24a b + 24a )x) +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b - 16a b )x + (56a b - 56a b)x + (48a b - 48a )x)acot(x) +--R + +--R 3 6 2 4 2 2 3 +--R - 2b x - 18a b x - 32a b x - 16a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b - 2a b )x + (19a b - 19a b )x + (40a b - 40a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b + 4a b )x + (- 38a b + 38a b )x + (- 80a b + 80a b)x +--R + +--R 3 4 +--R (- 48a b + 48a )x +--R * +--R acot(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R 8a b x + 32a b x + 40a b x + 16a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b - 6a b )x + (54a b - 54a b )x + (96a b - 96a b)x + 48a b +--R + +--R 6 +--R - 48a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b + 24a b )x + (- 96a b + 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b + 120a b)x - 48a b + 48a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R Type: Expression(Integer) +--E 112 + +--S 113 of 477 +d0020a:= D(m0020a,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (77) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 113 + +--S 114 of 477 +m0020b:= a0020.2-r0020 +--R +--R +--R (78) +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (4b - 6a b )x + (36a b - 54a b )x + (64a b - 96a b)x +--R + +--R 3 4 +--R 32a b - 48a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 4 3 6 3 2 2 4 +--R (- 16b + 24a b )x + (- 64a b + 96a b )x +--R + +--R 2 2 3 2 3 4 +--R (- 80a b + 120a b)x - 32a b + 48a +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (- 2b + 3a b )x + (- 18a b + 27a b )x + (- 32a b + 48a b)x +--R + +--R 3 4 +--R - 16a b + 24a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 4 3 6 3 2 2 4 2 2 3 2 +--R (8b - 12a b )x + (32a b - 48a b )x + (40a b - 60a b)x +--R + +--R 3 4 +--R 16a b - 24a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 3 2 5 2 2 3 2 3 +--R ((- 8b + 8a b )x + (- 28a b + 28a b)x + (- 24a b + 24a )x) +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 3 2 5 2 2 3 2 3 +--R ((16b - 16a b )x + (56a b - 56a b)x + (48a b - 48a )x)acot(x) +--R + +--R 3 6 2 4 2 2 3 +--R - 2b x - 18a b x - 32a b x - 16a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b + a \|a \|b - a \|b x + a +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (2b - 2a b )x + (19a b - 19a b )x + (40a b - 40a b)x +--R + +--R 3 4 +--R (24a b - 24a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 4 3 7 3 2 2 5 2 2 3 3 +--R (- 4b + 4a b )x + (- 38a b + 38a b )x + (- 80a b + 80a b)x +--R + +--R 3 4 +--R (- 48a b + 48a )x +--R * +--R acot(x) +--R + +--R 3 6 2 2 4 3 2 4 +--R 8a b x + 32a b x + 40a b x + 16a +--R * +--R +-------+ +-----+ +--R \|- b + a \|b - a +--R / +--R 2 4 3 3 6 3 3 4 2 4 4 2 5 2 5 +--R (6a b - 6a b )x + (54a b - 54a b )x + (96a b - 96a b)x + 48a b +--R + +--R 6 +--R - 48a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b + a \|b - a \|b x + a +--R + +--R 2 4 3 3 6 3 3 4 2 4 +--R (- 24a b + 24a b )x + (- 96a b + 96a b )x +--R + +--R 4 2 5 2 5 6 +--R (- 120a b + 120a b)x - 48a b + 48a +--R * +--R +-------+ +-+ +-----+ +--R \|- b + a \|a \|b - a +--R Type: Expression(Integer) +--E 114 + +--S 115 of 477 +d0020b:= D(m0020b,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (79) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 115 + +--S 116 of 477 +t0021:= acot(x)/(a+b*x^2)^(7/2) +--R +--R +--R acot(x) +--R (80) ------------------------------------------ +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 116 + +--S 117 of 477 +r0021:= 1/15/a/(a-b)/(a+b*x^2)^(3/2)+1/15*(7*a-4*b)/a^2/(a-b)^2/_ + (a+b*x^2)^(1/2)+1/15*x*(8*(a+b*x^2)^2+a*(7*a+4*b*x^2))*_ + acot(x)/a^3/(a+b*x^2)^(5/2)-1/15*(15*a^2-20*a*b+8*b^2)*_ + atanh((a+b*x^2)^(1/2)/(a-b)^(1/2))/a^3/(a-b)^(5/2) +--R +--R +--R (81) +--R 4 3 2 2 4 3 2 2 3 2 2 2 +--R (- 8b + 20a b - 15a b )x + (- 16a b + 40a b - 30a b)x - 8a b +--R + +--R 3 4 +--R 20a b - 15a +--R * +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +--R \|b x + a atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 4 3 2 2 5 3 2 2 3 3 +--R (8b - 16a b + 8a b )x + (20a b - 40a b + 20a b)x +--R + +--R 2 2 3 4 +--R (15a b - 30a b + 15a )x +--R * +--R acot(x) +--R + +--R 3 2 2 4 2 2 3 2 3 4 +--R (- 4a b + 7a b )x + (- 9a b + 15a b)x - 5a b + 8a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 3 4 4 3 5 2 4 4 3 5 2 6 2 5 2 +--R (15a b - 30a b + 15a b )x + (30a b - 60a b + 30a b)x + 15a b +--R + +--R 6 7 +--R - 30a b + 15a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R Type: Expression(Integer) +--E 117 + +--S 118 of 477 +a0021:= integrate(t0021,x) +--R +--R +--R (82) +--R [ +--R 8 7 2 6 12 +--R (64b - 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b - 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b - 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b - 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b - 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b - 11520a b + 8640a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (- 8b + 20a b - 15a b )x + (- 280a b + 700a b - 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (- 2072a b + 5180a b - 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (- 6664a b + 16660a b - 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (- 11264a b + 28160a b - 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (- 10496a b + 26240a b - 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (- 5120a b + 12800a b - 9600a b)x - 1024a b + 2560a b - 1920a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 8 7 2 6 13 +--R (- 8b + 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b + 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b + 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b + 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b + 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b + 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 72a b + 114a b )x + (- 766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 2694a b + 4080a b )x + (- 4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (- 3168a b + 4608a b )x + (- 896a b + 1280a b)x +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b - 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b - 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b - 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b - 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b - 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b - 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (10b - 16a b )x + (286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (1742a b - 2672a b )x + (4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (5744a b - 8480a b )x + (3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (896a b - 1280a b)x +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b - 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b - 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b - 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b - 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b - 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b - 34560a b + 17280a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b + 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b + 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b + 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b + 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b + 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b + 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b + 38400a b - 19200a b)x - 3840a b + 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-------+ +--R \|- b + a +--R , +--R +--R 8 7 2 6 12 +--R (- 64b + 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b + 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b + 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b + 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b + 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 +--R (- 4608a b + 11520a b - 8640a b)x - 1024a b + 2560a b +--R + +--R 8 +--R - 1920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 8 2 7 14 8 2 7 3 6 12 +--R (8b - 20a b + 15a b )x + (280a b - 700a b + 525a b )x +--R + +--R 2 7 3 6 4 5 10 +--R (2072a b - 5180a b + 3885a b )x +--R + +--R 3 6 4 5 5 4 8 +--R (6664a b - 16660a b + 12495a b )x +--R + +--R 4 5 5 4 6 3 6 +--R (11264a b - 28160a b + 21120a b )x +--R + +--R 5 4 6 3 7 2 4 +--R (10496a b - 26240a b + 19680a b )x +--R + +--R 6 3 7 2 8 2 7 2 8 9 +--R (5120a b - 12800a b + 9600a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 8 7 2 6 13 +--R (- 8b + 16a b - 8a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 276a b + 552a b - 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 1935a b + 3870a b - 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 5728a b + 11456a b - 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 8544a b + 17088a b - 8544a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 6400a b + 12800a b - 6400a b)x +--R + +--R 6 2 7 8 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (- 72a b + 114a b )x + (- 766a b + 1186a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (- 2694a b + 4080a b )x + (- 4272a b + 6336a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 +--R (- 3168a b + 4608a b )x + (- 896a b + 1280a b)x +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 8 7 2 6 13 +--R (64b - 128a b + 64a b )x +--R + +--R 7 2 6 3 5 11 +--R (864a b - 1728a b + 864a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (4056a b - 8112a b + 4056a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (9320a b - 18640a b + 9320a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (11504a b - 23008a b + 11504a b )x +--R + +--R 5 3 6 2 7 3 +--R (7360a b - 14720a b + 7360a b)x +--R + +--R 6 2 7 8 +--R (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 14 7 2 6 12 +--R (10b - 16a b )x + (286a b - 448a b )x +--R + +--R 2 6 3 5 10 3 5 4 4 8 +--R (1742a b - 2672a b )x + (4490a b - 6752a b )x +--R + +--R 4 4 5 3 6 5 3 6 2 4 +--R (5744a b - 8480a b )x + (3616a b - 5248a b )x +--R + +--R 6 2 7 2 +--R (896a b - 1280a b)x +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R / +--R 3 8 4 7 5 6 12 +--R (240a b - 480a b + 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (3120a b - 6240a b + 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (13680a b - 27360a b + 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (28560a b - 57120a b + 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (31200a b - 62400a b + 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (17280a b - 34560a b + 17280a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b - a \|b x + a +--R + +--R 3 9 4 8 5 7 14 +--R (- 30a b + 60a b - 30a b )x +--R + +--R 4 8 5 7 6 6 12 +--R (- 1050a b + 2100a b - 1050a b )x +--R + +--R 5 7 6 6 7 5 10 +--R (- 7770a b + 15540a b - 7770a b )x +--R + +--R 6 6 7 5 8 4 8 +--R (- 24990a b + 49980a b - 24990a b )x +--R + +--R 7 5 8 4 9 3 6 +--R (- 42240a b + 84480a b - 42240a b )x +--R + +--R 8 4 9 3 10 2 4 +--R (- 39360a b + 78720a b - 39360a b )x +--R + +--R 9 3 10 2 11 2 10 2 11 +--R (- 19200a b + 38400a b - 19200a b)x - 3840a b + 7680a b +--R + +--R 12 +--R - 3840a +--R * +--R +-----+ +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 118 + +--S 119 of 477 +m0021a:= a0021.1-r0021 +--R +--R +--R (83) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (8b - 20a b + 15a b )x + (272a b - 680a b + 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (1800a b - 4500a b + 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (4864a b - 12160a b + 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (6400a b - 16000a b + 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4096a b - 10240a b + 7680a b)x + 1024a b - 2560a b + 1920a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 64b + 160a b - 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 832a b + 2080a b - 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 3648a b + 9120a b - 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 7616a b + 19040a b - 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 8320a b + 20800a b - 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4608a b + 11520a b - 8640a b)x - 1024a b + 2560a b - 1920a +--R * +--R +-+ +--R \|a +--R * +--R log +--R 2 2 4 2 2 +-+ +--R ((2b + 2a b - 4a )x + (8a b - 8a )x )\|a +--R + +--R 2 4 2 2 2 +-------+ +--R (4a x + (4a b + 8a )x + 8a )\|- b + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 6 2 2 4 2 2 +--R (b - 2a b)x + (- b - 4a b - 4a )x + (- 8a b - 8a )x +--R + +--R 2 +--R - 8a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R + +--R 2 2 6 2 2 3 4 2 3 2 +--R (- 2a b + 2a b)x + (- 6a b + 2a b + 4a )x + (- 8a b + 8a )x +--R / +--R +--------+ +--R 4 2 2 2 | 2 +--R (4a b x + (4a b + 8a )x + 8a )\|b x + a +--R + +--R 2 6 2 4 2 2 2 +-+ +--R (- b x + (- b - 8a b)x + (- 8a b - 8a )x - 8a )\|a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b - 40a b + 30a b )x + (544a b - 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b - 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b - 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b - 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b - 20480a b + 15360a b)x + 2048a b - 5120a b + 3840a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b + 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b + 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b + 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b + 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b + 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b + 23040a b - 17280a b)x - 2048a b + 5120a b - 3840a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 7 6 2 5 11 +--R (- 64b + 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b + 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b + 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b + 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b + 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b - 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b - 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b - 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b - 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b - 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b - 7680a b + 3840a )x +--R * +--R acot(x) +--R + +--R 7 6 12 6 2 5 10 +--R (- 10b + 16a b )x + (- 340a b + 544a b )x +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 2250a b + 3600a b )x + (- 6080a b + 9728a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 +--R (- 8000a b + 12800a b )x + (- 5120a b + 8192a b)x - 1280a b +--R + +--R 7 +--R 2048a +--R * +--R +--------+ +--R +-------+ +-+ | 2 +--R \|- b + a \|a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b - 16a b + 8a b )x + (276a b - 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b - 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b - 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b - 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b - 12800a b + 6400a b)x + (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b + 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b + 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b + 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b + 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b + 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b + 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b + 7680a b - 3840a )x +--R * +--R acot(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (80a b - 128a b )x + (1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (4560a b - 7296a b )x + (9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 8 +--R (10400a b - 16640a b )x + (5760a b - 9216a b)x + 1280a b - 2048a +--R * +--R +-------+ +--R \|- b + a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b - 60a b + 30a b )x + (1020a b - 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b - 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b - 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b - 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b - 30720a b + 15360a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b + 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b + 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b + 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b + 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b + 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b + 34560a b - 17280a b)x - 3840a b + 7680a b - 3840a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R Type: Expression(Integer) +--E 119 + +--S 120 of 477 +d0021a:= D(m0021a,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (84) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 120 + +--S 121 of 477 +m0021b:= a0021.2-r0021 +--R +--R +--R (85) +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (16b - 40a b + 30a b )x + (544a b - 1360a b + 1020a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3600a b - 9000a b + 6750a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (9728a b - 24320a b + 18240a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (12800a b - 32000a b + 24000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (8192a b - 20480a b + 15360a b)x + 2048a b - 5120a b + 3840a +--R * +--R +--------+ +--R +-----+ | 2 +--R \|b - a \|b x + a +--R + +--R 8 7 2 6 12 +--R (- 128b + 320a b - 240a b )x +--R + +--R 7 2 6 3 5 10 +--R (- 1664a b + 4160a b - 3120a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 7296a b + 18240a b - 13680a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 15232a b + 38080a b - 28560a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 16640a b + 41600a b - 31200a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 9216a b + 23040a b - 17280a b)x - 2048a b + 5120a b - 3840a +--R * +--R +-+ +-----+ +--R \|a \|b - a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-------+ +--R \|- b + a +--R + +--R 8 7 2 6 12 7 2 6 3 5 10 +--R (- 8b + 20a b - 15a b )x + (- 272a b + 680a b - 510a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (- 1800a b + 4500a b - 3375a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (- 4864a b + 12160a b - 9120a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (- 6400a b + 16000a b - 12000a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (- 4096a b + 10240a b - 7680a b)x - 1024a b + 2560a b - 1920a +--R * +--R +--------+ +--R +-------+ | 2 +--R \|- b + a \|b x + a +--R + +--R 8 7 2 6 12 +--R (64b - 160a b + 120a b )x +--R + +--R 7 2 6 3 5 10 +--R (832a b - 2080a b + 1560a b )x +--R + +--R 2 6 3 5 4 4 8 +--R (3648a b - 9120a b + 6840a b )x +--R + +--R 3 5 4 4 5 3 6 +--R (7616a b - 19040a b + 14280a b )x +--R + +--R 4 4 5 3 6 2 4 +--R (8320a b - 20800a b + 15600a b )x +--R + +--R 5 3 6 2 7 2 6 2 7 8 +--R (4608a b - 11520a b + 8640a b)x + 1024a b - 2560a b + 1920a +--R * +--R +-------+ +-+ +--R \|- b + a \|a +--R * +--R +--------+ +--R 2 +-----+ | 2 4 2 +-+ +-----+ +--R 2x \|b - a \|b x + a + (- 2x - 2x )\|a \|b - a +--R atan(---------------------------------------------------------) +--R +--------+ +--R 2 +-+ | 2 4 2 +--R (2x + 2)\|a \|b x + a + (b - 2a)x + (- b - 2a)x - 2a +--R + +--R 7 6 2 5 11 +--R (- 64b + 128a b - 64a b )x +--R + +--R 6 2 5 3 4 9 +--R (- 800a b + 1600a b - 800a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (- 3256a b + 6512a b - 3256a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (- 6064a b + 12128a b - 6064a b )x +--R + +--R 4 3 5 2 6 3 +--R (- 5440a b + 10880a b - 5440a b)x +--R + +--R 5 2 6 7 +--R (- 1920a b + 3840a b - 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 7 6 2 5 11 +--R (128b - 256a b + 128a b )x +--R + +--R 6 2 5 3 4 9 +--R (1600a b - 3200a b + 1600a b )x +--R + +--R 2 5 3 4 4 3 7 +--R (6512a b - 13024a b + 6512a b )x +--R + +--R 3 4 4 3 5 2 5 +--R (12128a b - 24256a b + 12128a b )x +--R + +--R 4 3 5 2 6 3 +--R (10880a b - 21760a b + 10880a b)x +--R + +--R 5 2 6 7 +--R (3840a b - 7680a b + 3840a )x +--R * +--R acot(x) +--R + +--R 7 6 12 6 2 5 10 +--R (- 10b + 16a b )x + (- 340a b + 544a b )x +--R + +--R 2 5 3 4 8 3 4 4 3 6 +--R (- 2250a b + 3600a b )x + (- 6080a b + 9728a b )x +--R + +--R 4 3 5 2 4 5 2 6 2 6 +--R (- 8000a b + 12800a b )x + (- 5120a b + 8192a b)x - 1280a b +--R + +--R 7 +--R 2048a +--R * +--R +--------+ +--R +-------+ +-+ +-----+ | 2 +--R \|- b + a \|a \|b - a \|b x + a +--R + +--R 8 7 2 6 13 7 2 6 3 5 11 +--R (8b - 16a b + 8a b )x + (276a b - 552a b + 276a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (1935a b - 3870a b + 1935a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (5728a b - 11456a b + 5728a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (8544a b - 17088a b + 8544a b )x +--R + +--R 5 3 6 2 7 3 6 2 7 8 +--R (6400a b - 12800a b + 6400a b)x + (1920a b - 3840a b + 1920a )x +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 8 7 2 6 13 +--R (- 16b + 32a b - 16a b )x +--R + +--R 7 2 6 3 5 11 +--R (- 552a b + 1104a b - 552a b )x +--R + +--R 2 6 3 5 4 4 9 +--R (- 3870a b + 7740a b - 3870a b )x +--R + +--R 3 5 4 4 5 3 7 +--R (- 11456a b + 22912a b - 11456a b )x +--R + +--R 4 4 5 3 6 2 5 +--R (- 17088a b + 34176a b - 17088a b )x +--R + +--R 5 3 6 2 7 3 +--R (- 12800a b + 25600a b - 12800a b)x +--R + +--R 6 2 7 8 +--R (- 3840a b + 7680a b - 3840a )x +--R * +--R acot(x) +--R + +--R 7 2 6 12 2 6 3 5 10 +--R (80a b - 128a b )x + (1040a b - 1664a b )x +--R + +--R 3 5 4 4 8 4 4 5 3 6 +--R (4560a b - 7296a b )x + (9520a b - 15232a b )x +--R + +--R 5 3 6 2 4 6 2 7 2 7 8 +--R (10400a b - 16640a b )x + (5760a b - 9216a b)x + 1280a b - 2048a +--R * +--R +-------+ +-----+ +--R \|- b + a \|b - a +--R / +--R 3 8 4 7 5 6 12 4 7 5 6 6 5 10 +--R (30a b - 60a b + 30a b )x + (1020a b - 2040a b + 1020a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (6750a b - 13500a b + 6750a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (18240a b - 36480a b + 18240a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (24000a b - 48000a b + 24000a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (15360a b - 30720a b + 15360a b)x + 3840a b - 7680a b + 3840a +--R * +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- b + a \|b - a \|b x + a +--R + +--R 3 8 4 7 5 6 12 +--R (- 240a b + 480a b - 240a b )x +--R + +--R 4 7 5 6 6 5 10 +--R (- 3120a b + 6240a b - 3120a b )x +--R + +--R 5 6 6 5 7 4 8 +--R (- 13680a b + 27360a b - 13680a b )x +--R + +--R 6 5 7 4 8 3 6 +--R (- 28560a b + 57120a b - 28560a b )x +--R + +--R 7 4 8 3 9 2 4 +--R (- 31200a b + 62400a b - 31200a b )x +--R + +--R 8 3 9 2 10 2 9 2 10 11 +--R (- 17280a b + 34560a b - 17280a b)x - 3840a b + 7680a b - 3840a +--R * +--R +-------+ +-+ +-----+ +--R \|- b + a \|a \|b - a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 477 +d0021b:= D(m0021b,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (86) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R Type: Expression(Integer) +--E 122 + +--S 123 of 477 +t0022:= acot(x)*(a+a*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R (87) acot(x)\|a x + a +--R Type: Expression(Integer) +--E 123 + +--S 124 of 477 +r0022:= 1/2/(1+1/x^2)^(1/2)/x*(a*(1+x^2))^(1/2)*((1+1/x^2)^(1/2)*x+_ + (1+1/x^2)^(1/2)*x^2*acot(x)+2*acot(x)*atanh(exp(1)^(%i*acot(x)))-_ + %i*polylog(2,-exp(1)^(%i*acot(x)))+%i*polylog(2,exp(1)^(%i*acot(x)))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 124 + +--S 125 of 477 +a0022:= integrate(t0022,x) +--R +--R +--R x +----------+ +--R ++ | 2 +--R (88) | acot(%Q)\|(%Q + 1)a d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 125 + +--S 126 of 477 +--m0022:= a0022-r0022 +--E 126 + +--S 127 of 477 +--d0022:= D(m0022,x) +--E 127 + +--S 128 of 477 +t0023:= acot(x)/(a+a*x^2)^(1/2) +--R +--R +--R acot(x) +--R (89) ----------- +--R +--------+ +--R | 2 +--R \|a x + a +--R Type: Expression(Integer) +--E 128 + +--S 129 of 477 +r0023:= (1+1/x^2)^(1/2)*x*(2*acot(x)*atanh(exp(1)^(%i*acot(x)))-_ + %i*polylog(2,-exp(1)^(%i*acot(x)))+_ + %i*polylog(2,exp(1)^(%i*acot(x))))/(a*(1+x^2))^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 129 + +--S 130 of 477 +a0023:= integrate(t0023,x) +--R +--R +--R x +--R ++ acot(%Q) +--R (90) | ------------- d%Q +--R ++ +----------+ +--R | 2 +--R \|(%Q + 1)a +--R Type: Union(Expression(Integer),...) +--E 130 + +--S 131 of 477 +--m0023:= a0023-r0023 +--E 131 + +--S 132 of 477 +--d0023:= D(m0023,x) +--E 132 + +--S 133 of 477 +t0024:= acot(x)/(a+a*x^2)^(3/2) +--R +--R +--R acot(x) +--R (91) --------------------- +--R +--------+ +--R 2 | 2 +--R (a x + a)\|a x + a +--R Type: Expression(Integer) +--E 133 + +--S 134 of 477 +r0024:= -(1-x*acot(x))/a/(a*(1+x^2))^(1/2) +--R +--R +--R x acot(x) - 1 +--R (92) ------------- +--R +--------+ +--R | 2 +--R a\|a x + a +--R Type: Expression(Integer) +--E 134 + +--S 135 of 477 +a0024:= integrate(t0024,x) +--R +--R +--R +--------+ +--R 2x | 2 2x 2 +-+ +--R - x atan(------)\|a x + a + (x atan(------) + 2x )\|a +--R 2 2 +--R x - 1 x - 1 +--R (93) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 2 2 2 +--R 2a\|a \|a x + a - 2a x - 2a +--R Type: Union(Expression(Integer),...) +--E 135 + +--S 136 of 477 +m0024:= a0024-r0024 +--R +--R +--R (94) +--R +--------+ +--R 2x 2 +-+ | 2 +--R (- x atan(------) + 2x acot(x) - 2x - 2)\|a \|a x + a +--R 2 +--R x - 1 +--R + +--R 3 2x 3 2 +--R (a x + a x)atan(------) + (- 2a x - 2a x)acot(x) + 2a x + 2a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 2 2 | 2 2 2 2 +-+ +--R (2a x + 2a )\|a x + a + (- 2a x - 2a )\|a +--R Type: Expression(Integer) +--E 136 + +--S 137 of 477 +d0024:= D(m0024,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (95) ----------------------- +--R +--------+ +--R 2 | 2 +--R (2a x + 2a)\|a x + a +--R Type: Expression(Integer) +--E 137 + +--S 138 of 477 +t0025:= acot(x)/(a+a*x^2)^(5/2) +--R +--R +--R acot(x) +--R (96) ------------------------------ +--R +--------+ +--R 2 4 2 2 2 | 2 +--R (a x + 2a x + a )\|a x + a +--R Type: Expression(Integer) +--E 138 + +--S 139 of 477 +r0025:= -1/9*(6+1/(1+x^2)-3*x*(2+1/(1+x^2))*acot(x))/a^2/(a*(1+x^2))^(1/2) +--R +--R +--R 3 2 +--R (6x + 9x)acot(x) - 6x - 7 +--R (97) --------------------------- +--R +--------+ +--R 2 2 2 | 2 +--R (9a x + 9a )\|a x + a +--R Type: Expression(Integer) +--E 139 + +--S 140 of 477 +a0025:= integrate(t0025,x) +--R +--R +--R (98) +--R +--------+ +--R 5 3 2x 4 2 | 2 +--R ((- 6x - 33x - 36x)atan(------) - 30x - 36x )\|a x + a +--R 2 +--R x - 1 +--R + +--R 5 3 2x 6 4 2 +-+ +--R ((18x + 51x + 36x)atan(------) + 14x + 48x + 36x )\|a +--R 2 +--R x - 1 +--R / +--R +--------+ +--R 2 4 2 2 2 +-+ | 2 3 6 3 4 3 2 +--R (54a x + 126a x + 72a )\|a \|a x + a - 18a x - 108a x - 162a x +--R + +--R 3 +--R - 72a +--R Type: Union(Expression(Integer),...) +--E 140 + +--S 141 of 477 +m0025:= a0025-r0025 +--R +--R +--R (99) +--R 5 3 2x 5 3 +--R (- 18x - 51x - 36x)atan(------) + (36x + 102x + 72x)acot(x) +--R 2 +--R x - 1 +--R + +--R 6 4 2 +--R - 14x - 84x - 126x - 56 +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|a x + a +--R + +--R 7 5 3 2x +--R (6a x + 39a x + 69a x + 36a x)atan(------) +--R 2 +--R x - 1 +--R + +--R 7 5 3 6 4 2 +--R (- 12a x - 78a x - 138a x - 72a x)acot(x) + 42a x + 140a x + 154a x +--R + +--R 56a +--R / +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (18a x + 108a x + 162a x + 72a )\|a x + a +--R + +--R 3 6 3 4 3 2 3 +-+ +--R (- 54a x - 180a x - 198a x - 72a )\|a +--R Type: Expression(Integer) +--E 141 + +--S 142 of 477 +d0025:= D(m0025,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (100) -------------------------------- +--R +--------+ +--R 2 4 2 2 2 | 2 +--R (2a x + 4a x + 2a )\|a x + a +--R Type: Expression(Integer) +--E 142 + +--S 143 of 477 +t0026:= acot(x)/(a+a*x^2)^(7/2) +--R +--R +--R acot(x) +--R (101) -------------------------------------- +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x + 3a x + 3a x + a )\|a x + a +--R Type: Expression(Integer) +--E 143 + +--S 144 of 477 +r0026:= -1/225*(120+9/(1+x^2)^2+20/(1+x^2)-15*x*(8+3/(1+x^2)^2+_ + 4/(1+x^2))*acot(x))/a^3/(a*(1+x^2))^(1/2) +--R +--R +--R 5 3 4 2 +--R (120x + 300x + 225x)acot(x) - 120x - 260x - 149 +--R (102) --------------------------------------------------- +--R +--------+ +--R 3 4 3 2 3 | 2 +--R (225a x + 450a x + 225a )\|a x + a +--R Type: Expression(Integer) +--E 144 + +--S 145 of 477 +a0026:= integrate(t0026,x) +--R +--R +--R (103) +--R 9 7 5 3 2x 8 +--R (- 120x - 1740x - 5745x - 7500x - 3600x)atan(------) - 1250x +--R 2 +--R x - 1 +--R + +--R 6 4 2 +--R - 5540x - 7800x - 3600x +--R * +--R +--------+ +--R | 2 +--R \|a x + a +--R + +--R 9 7 5 3 2x 10 +--R (600x + 3900x + 9045x + 9300x + 3600x)atan(------) + 298x +--R 2 +--R x - 1 +--R + +--R 8 6 4 2 +--R 3270x + 8990x + 9600x + 3600x +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 3 8 3 6 3 4 3 2 3 +-+ | 2 +--R (2250a x + 13500a x + 27450a x + 23400a x + 7200a )\|a \|a x + a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +--R - 450a x - 6750a x - 24750a x - 38250a x - 27000a x - 7200a +--R Type: Union(Expression(Integer),...) +--E 145 + +--S 146 of 477 +m0026:= a0026-r0026 +--R +--R +--R (104) +--R 9 7 5 3 2x +--R (- 600x - 3900x - 9045x - 9300x - 3600x)atan(------) +--R 2 +--R x - 1 +--R + +--R 9 7 5 3 10 +--R (1200x + 7800x + 18090x + 18600x + 7200x)acot(x) - 298x +--R + +--R 8 6 4 2 +--R - 4470x - 16390x - 25330x - 17880x - 4768 +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|a x + a +--R + +--R 11 9 7 5 3 +--R (120a x + 1860a x + 7485a x + 13245a x + 11100a x + 3600a x) +--R * +--R 2x +--R atan(------) +--R 2 +--R x - 1 +--R + +--R 11 9 7 5 3 +--R (- 240a x - 3720a x - 14970a x - 26490a x - 22200a x - 7200a x) +--R * +--R acot(x) +--R + +--R 10 8 6 4 2 +--R 1490a x + 10430a x + 27118a x + 33674a x + 20264a x + 4768a +--R / +--R 4 10 4 8 4 6 4 4 4 2 4 +--R (450a x + 6750a x + 24750a x + 38250a x + 27000a x + 7200a ) +--R * +--R +--------+ +--R | 2 +--R \|a x + a +--R + +--R 4 10 4 8 4 6 4 4 4 2 4 +-+ +--R (- 2250a x - 15750a x - 40950a x - 50850a x - 30600a x - 7200a )\|a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 477 +d0026:= D(m0026,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (105) ---------------------------------------- +--R +--------+ +--R 3 6 3 4 3 2 3 | 2 +--R (2a x + 6a x + 6a x + 2a )\|a x + a +--R Type: Expression(Integer) +--E 147 + +--S 148 of 477 +t0027:= acot(x^(1/2))/x +--R +--R +--R +-+ +--R acot(\|x ) +--R (106) ---------- +--R x +--R Type: Expression(Integer) +--E 148 + +--S 149 of 477 +r0027:= -%i*polylog(2,-%i/x^(1/2))+%i*polylog(2,%i/x^(1/2)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 149 + +--S 150 of 477 +a0027:= integrate(t0027,x) +--R +--R +--R x +--+ +--R ++ acot(\|%Q ) +--R (107) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 150 + +--S 151 of 477 +--m0027:= a0027-r0027 +--E 151 + +--S 152 of 477 +--d0027:= D(m0027,x) +--E 152 + +--S 153 of 477 +t0028:= x^2*asec(a*x) +--R +--R +--R 2 +--R (108) x asec(a x) +--R Type: Expression(Integer) +--E 153 + +--S 154 of 477 +r0028:= -1/6*(1-1/a^2/x^2)^(1/2)*x^2/a+1/3*x^3*asec(a*x)-_ + 1/6*atanh((1-1/a^2/x^2)^(1/2))/a^3 +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x - 1 2 2 |a x - 1 3 3 +--R - atanh( |-------- ) - a x |-------- + 2a x asec(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R (109) ------------------------------------------------------- +--R 3 +--R 6a +--R Type: Expression(Integer) +--E 154 + +--S 155 of 477 +a0028:= integrate(t0028,x) +--R +--R +--R (110) +--R +----------+ +----------+ +--R +-+ | 2 2 | 2 2 +--R +-+ 2a x\|2 \|- a x + 1 3 3 2\|- a x + 1 +--R - 2\|2 atan(---------------------) + a x atan(--------------) +--R 2 2 2 2 +--R 3a x - 2 a x +--R + +--R +----------+ +--R a x | 2 2 +--R - 5atan(-------------) + a x\|- a x + 1 +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R / +--R 3 +--R 6a +--R Type: Union(Expression(Integer),...) +--E 155 + +--S 156 of 477 +m0028:= a0028-r0028 +--R +--R +--R (111) +--R +--------+ +----------+ +--R | 2 2 +-+ | 2 2 +--R |a x - 1 +-+ 2a x\|2 \|- a x + 1 +--R atanh( |-------- ) - 2\|2 atan(---------------------) +--R | 2 2 2 2 +--R \| a x 3a x - 2 +--R + +--R +----------+ +--------+ +--R | 2 2 | 2 2 +--R 3 3 2\|- a x + 1 a x 2 2 |a x - 1 +--R a x atan(--------------) - 5atan(-------------) + a x |-------- +--R 2 2 +----------+ | 2 2 +--R a x | 2 2 \| a x +--R \|- a x + 1 +--R + +--R +----------+ +--R | 2 2 3 3 +--R a x\|- a x + 1 - 2a x asec(a x) +--R / +--R 3 +--R 6a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 477 +d0028:= D(m0028,x) +--R +--R +--R (112) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R 2 |a x - 1 | 2 2 2\|- a x + 1 +--R 3a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--------+ +--R | 2 2 +--------+ | 2 2 +--R 2 |a x - 1 | 2 2 2 |a x - 1 +--R (- 6a x asec(a x) |-------- + 2x)\|a x - 1 - 2a x |-------- +--R | 2 2 | 2 2 +--R \| a x \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 | 2 2 +--R 6a |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression(Integer) +--E 157 + +--S 158 of 477 +t0029:= x^4*asec(a*x) +--R +--R +--R 4 +--R (113) x asec(a x) +--R Type: Expression(Integer) +--E 158 + +--S 159 of 477 +r0029:= -3/40*(1-1/a^2/x^2)^(1/2)*x^2/a^3-1/20*(1-1/a^2/x^2)^(1/2)*x^4/a+_ + 1/5*x^5*asec(a*x)-3/40*atanh((1-1/a^2/x^2)^(1/2))/a^5 +--R +--R +--R (114) +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x - 1 4 4 2 2 |a x - 1 5 5 +--R - 3atanh( |-------- ) + (- 2a x - 3a x ) |-------- + 8a x asec(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R --------------------------------------------------------------------- +--R 5 +--R 40a +--R Type: Expression(Integer) +--E 159 + +--S 160 of 477 +a0029:= integrate(t0029,x) +--R +--R +--R (115) +--R +----------+ +----------+ +--R +-+ | 2 2 | 2 2 +--R +-+ 2a x\|2 \|- a x + 1 5 5 2\|- a x + 1 +--R - 16\|2 atan(---------------------) + 4a x atan(--------------) +--R 2 2 2 2 +--R 3a x - 2 a x +--R + +--R +----------+ +--R a x 3 3 | 2 2 +--R - 43atan(-------------) + (2a x + 11a x)\|- a x + 1 +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R / +--R 5 +--R 40a +--R Type: Union(Expression(Integer),...) +--E 160 + +--S 161 of 477 +m0029:= a0029-r0029 +--R +--R +--R (116) +--R +--------+ +----------+ +--R | 2 2 +-+ | 2 2 +--R |a x - 1 +-+ 2a x\|2 \|- a x + 1 +--R 3atanh( |-------- ) - 16\|2 atan(---------------------) +--R | 2 2 2 2 +--R \| a x 3a x - 2 +--R + +--R +----------+ +--R | 2 2 +--R 5 5 2\|- a x + 1 a x +--R 4a x atan(--------------) - 43atan(-------------) +--R 2 2 +----------+ +--R a x | 2 2 +--R \|- a x + 1 +--R + +--R +--------+ +--R | 2 2 +----------+ +--R 4 4 2 2 |a x - 1 3 3 | 2 2 5 5 +--R (2a x + 3a x ) |-------- + (2a x + 11a x)\|- a x + 1 - 8a x asec(a x) +--R | 2 2 +--R \| a x +--R / +--R 5 +--R 40a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 477 +d0029:= D(m0029,x) +--R +--R +--R (117) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R 4 |a x - 1 | 2 2 2\|- a x + 1 +--R 5a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--------+ +--R | 2 2 +--------+ | 2 2 +--R 4 |a x - 1 3 | 2 2 4 |a x - 1 +--R (- 10a x asec(a x) |-------- + 2x )\|a x - 1 - 2a x |-------- +--R | 2 2 | 2 2 +--R \| a x \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 | 2 2 +--R 10a |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression(Integer) +--E 162 + +--S 163 of 477 +t0030:= asec(a*x)/x^3 +--R +--R +--R asec(a x) +--R (118) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 163 + +--S 164 of 477 +r0030:= 1/4*a*(1-1/a^2/x^2)^(1/2)/x-1/4*a^2*acsc(a*x)-1/2*asec(a*x)/x^2 +--R +--R +--R +--------+ +--R | 2 2 +--R |a x - 1 2 2 +--R a x |-------- - 2asec(a x) - a x acsc(a x) +--R | 2 2 +--R \| a x +--R (119) ------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 164 + +--S 165 of 477 +a0030:= integrate(t0030,x) +--R +--R +--R (120) +--R +----------+ +----------+ +--R 2 2 | 2 2 2 2 | 2 2 +--R a x log(\|- a x + 1 + 1) - a x log(\|- a x + 1 - 1) +--R + +--R +----------+ +--R | 2 2 +--R 2 2 2\|- a x + 1 +--R (a x - 2)atan(--------------) +--R 2 2 +--R a x +--R / +--R 2 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 165 + +--S 166 of 477 +m0030:= a0030-r0030 +--R +--R +--R (121) +--R +----------+ +----------+ +--R 2 2 | 2 2 2 2 | 2 2 +--R a x log(\|- a x + 1 + 1) - a x log(\|- a x + 1 - 1) +--R + +--R +----------+ +--------+ +--R | 2 2 | 2 2 +--R 2 2 2\|- a x + 1 |a x - 1 +--R (a x - 2)atan(--------------) - 2a x |-------- + 4asec(a x) +--R 2 2 | 2 2 +--R a x \| a x +--R + +--R 2 2 +--R 2a x acsc(a x) +--R / +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 166 + +--S 167 of 477 +d0030:= D(m0030,x) +--R +--R +--R (122) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R |a x - 1 | 2 2 2\|- a x + 1 +--R 2a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 2 2 | 2 2 +--R (- 4a x asec(a x) |-------- + a x - 2)\|a x - 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 3 3 |a x - 1 +--R (- a x + 2a x) |-------- +--R | 2 2 +--R \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R 4 |a x - 1 | 2 2 +--R 4a x |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 477 +t0031:= x*asec(a+b*x) +--R +--R +--R (123) x asec(b x + a) +--R Type: Expression(Integer) +--E 168 + +--S 169 of 477 +r0031:= -1/2*(a+b*x)*(1-1/(a+b*x)^2)^(1/2)/b^2-a*(a+b*x)*asec(a+b*x)/b^2+_ + 1/2*(a+b*x)^2*asec(a+b*x)/b^2+a*atanh((1-1/(a+b*x)^2)^(1/2))/b^2 +--R +--R +--R (124) +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R 2a atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 2 2 2 +--R (- b x - a) |---------------------- + (b x - a )asec(b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 169 + +--S 170 of 477 +a0031:= integrate(t0031,x) +--R +--R +--R (125) +--R - +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R - +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2 2 2\|- b x - 2a b x - a + 1 +--R b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +------------------------+ +--R b x + a | 2 2 2 +--R 4a atan(---------------------------) + 2\|- b x - 2a b x - a + 1 +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 2 +--R 4b +--R Type: Union(Expression(Integer),...) +--E 170 + +--S 171 of 477 +m0031:= a0031-r0031 +--R +--R +--R (126) +--R - +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R - +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R - 4a atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2 2 2\|- b x - 2a b x - a + 1 +--R b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R 4a atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +----------------------+ +--R | 2 2 2 +------------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (2b x + 2a) |---------------------- + 2\|- b x - 2a b x - a + 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R 2 2 2 +--R (- 2b x + 2a )asec(b x + a) +--R / +--R 2 +--R 4b +--R Type: Expression(Integer) +--E 171 + +--S 172 of 477 +d0031:= D(m0031,x) +--R +--R +--R (127) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 2 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (b x + a b x) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 |b x + 2a b x + a - 1 +--R ((- 2b x - 2a b x)asec(b x + a) |---------------------- + b x - a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 +--R (- b x + a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (2b x + 2a b) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 477 +t0032:= x^2*asec(a+b*x) +--R +--R +--R 2 +--R (128) x asec(b x + a) +--R Type: Expression(Integer) +--E 173 + +--S 174 of 477 +r0032:= a*(a+b*x)*(1-1/(a+b*x)^2)^(1/2)/b^3-1/6*(a+b*x)^2*_ + (1-1/(a+b*x)^2)^(1/2)/b^3+a^2*(a+b*x)*asec(a+b*x)/b^3-_ + a*(a+b*x)^2*asec(a+b*x)/b^3+1/3*(a+b*x)^3*asec(a+b*x)/b^3-_ + 1/6*atanh((1-1/(a+b*x)^2)^(1/2))/b^3-_ + a^2*atanh((1-1/(a+b*x)^2)^(1/2))/b^3 +--R +--R +--R (129) +--R +----------------------+ +--R | 2 2 2 +--R 2 |b x + 2a b x + a - 1 +--R (- 6a - 1)atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 +--R (- b x + 4a b x + 5a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R 3 3 3 +--R (2b x + 2a )asec(b x + a) +--R / +--R 3 +--R 6b +--R Type: Expression(Integer) +--E 174 + +--S 175 of 477 +a0032:= integrate(t0032,x) +--R +--R +--R (130) +--R 3 +--R 3b +--R * +--R +-------------------------------------------------------------------+ +--R | +-------------------------------------+ +--R | | 10 8 6 4 2 +--R | 6 |18a + 240a + 944a + 960a + 288a 6 4 2 +--R |18b |------------------------------------- - a - 30a - 60a - 8 +--R | | 12 +--R | \| 81b +--R |------------------------------------------------------------------- +--R | 6 +--R \| 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 3 3 2\|- b x - 2a b x - a + 1 +--R 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R 2 b x + a +--R (- 12a - 10)atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +------------------------+ +--R | 2 2 2 +--R (2b x - 10a)\|- b x - 2a b x - a + 1 +--R / +--R 3 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 175 + +--S 176 of 477 +m0032:= a0032-r0032 +--R +--R +--R (131) +--R 3 +--R 3b +--R * +--R +-------------------------------------------------------------------+ +--R | +-------------------------------------+ +--R | | 10 8 6 4 2 +--R | 6 |18a + 240a + 944a + 960a + 288a 6 4 2 +--R |18b |------------------------------------- - a - 30a - 60a - 8 +--R | | 12 +--R | \| 81b +--R |------------------------------------------------------------------- +--R | 6 +--R \| 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 |b x + 2a b x + a - 1 +--R (12a + 2)atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 3 3 2\|- b x - 2a b x - a + 1 +--R 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R 2 b x + a +--R (- 12a - 10)atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 +--R (2b x - 8a b x - 10a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 3 3 3 +--R (2b x - 10a)\|- b x - 2a b x - a + 1 + (- 4b x - 4a )asec(b x + a) +--R / +--R 3 +--R 12b +--R Type: Expression(Integer) +--E 176 + +--S 177 of 477 +d0032:= D(m0032,x) +--R +--R +--R (132) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 3 3 2 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (3b x + 3a b x ) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 3 3 2 2 |b x + 2a b x + a - 1 2 2 +--R (- 6b x - 6a b x )asec(b x + a) |---------------------- + 2b x +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R 2 +--R - 2a b x + 2a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 3 3 3 |b x + 2a b x + a - 1 +--R (- 2b x - 2a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 3 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (6b x + 6a b ) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression(Integer) +--E 177 + +--S 178 of 477 +t0033:= asec(x^(1/2)) +--R +--R +--R +-+ +--R (133) asec(\|x ) +--R Type: Expression(Integer) +--E 178 + +--S 179 of 477 +r0033:= -(-1+x)^(1/2)+x*asec(x^(1/2)) +--R +--R +--R +-+ +-----+ +--R (134) x asec(\|x ) - \|x - 1 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 477 +a0033:= integrate(t0033,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-------+ +--R (x - 2)atan(-----------) + 2\|- x + 1 +--R x +--R (135) -------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 180 + +--S 181 of 477 +m0033:= a0033-r0033 +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +-----+ +-------+ +--R (x - 2)atan(-----------) - 2x asec(\|x ) + 2\|x - 1 + 2\|- x + 1 +--R x +--R (136) ------------------------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 477 +d0033:= D(m0033,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R atan(-----------) - 2asec(\|x ) +--R x +--R (137) ------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 477 +t0034:= asec(x^(1/2))/x^2 +--R +--R +--R +-+ +--R asec(\|x ) +--R (138) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 183 + +--S 184 of 477 +r0034:= -1/2*(-(-1+x)^(1/2)+x*acsc(x^(1/2))+2*asec(x^(1/2)))/x +--R +--R +--R +-+ +-+ +-----+ +--R - 2asec(\|x ) - x acsc(\|x ) + \|x - 1 +--R (139) --------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 184 + +--S 185 of 477 +a0034:= integrate(t0034,x) +--R +--R +--R (140) +--R +-------+ +--R +-------+ +-------+ 2\|- x + 1 +--R x log(\|- x + 1 + 1) - x log(\|- x + 1 - 1) + (x - 2)atan(-----------) +--R x +--R ------------------------------------------------------------------------ +--R 4x +--R Type: Union(Expression(Integer),...) +--E 185 + +--S 186 of 477 +m0034:= a0034-r0034 +--R +--R +--R (141) +--R +-------+ +--R +-------+ +-------+ 2\|- x + 1 +--R x log(\|- x + 1 + 1) - x log(\|- x + 1 - 1) + (x - 2)atan(-----------) +--R x +--R + +--R +-+ +-+ +-----+ +--R 4asec(\|x ) + 2x acsc(\|x ) - 2\|x - 1 +--R / +--R 4x +--R Type: Expression(Integer) +--E 186 + +--S 187 of 477 +d0034:= D(m0034,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R atan(-----------) - 2asec(\|x ) +--R x +--R (142) ------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 477 +t0035:= asec(x^(1/2))/x^3 +--R +--R +--R +-+ +--R asec(\|x ) +--R (143) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 188 + +--S 189 of 477 +r0035:= -1/16*(-2*(-1+x)^(1/2)-3*(-1+x)^(1/2)*x+_ + 3*x^2*acsc(x^(1/2))+8*asec(x^(1/2)))/x^2 +--R +--R +--R +-+ 2 +-+ +-----+ +--R - 8asec(\|x ) - 3x acsc(\|x ) + (3x + 2)\|x - 1 +--R (144) ------------------------------------------------ +--R 2 +--R 16x +--R Type: Expression(Integer) +--E 189 + +--S 190 of 477 +a0035:= integrate(t0035,x) +--R +--R +--R (145) +--R 2 +-------+ 2 +-------+ +--R 2x log(\|- x + 1 + 1) - 2x log(\|- x + 1 - 1) +--R + +--R +-------+ +--R 2 2\|- x + 1 +-------+ +--R (x - 4)atan(-----------) + 2x\|- x + 1 +--R x +--R / +--R 2 +--R 16x +--R Type: Union(Expression(Integer),...) +--E 190 + +--S 191 of 477 +m0035:= a0035-r0035 +--R +--R +--R (146) +--R 2 +-------+ 2 +-------+ +--R 2x log(\|- x + 1 + 1) - 2x log(\|- x + 1 - 1) +--R + +--R +-------+ +--R 2 2\|- x + 1 +-+ 2 +-+ +--R (x - 4)atan(-----------) + 8asec(\|x ) + 3x acsc(\|x ) +--R x +--R + +--R +-----+ +-------+ +--R (- 3x - 2)\|x - 1 + 2x\|- x + 1 +--R / +--R 2 +--R 16x +--R Type: Expression(Integer) +--E 191 + +--S 192 of 477 +d0035:= D(m0035,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R atan(-----------) - 2asec(\|x ) +--R x +--R (147) ------------------------------- +--R 3 +--R 2x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 477 +t0036:= x^2*acsc(a*x) +--R +--R +--R 2 +--R (148) x acsc(a x) +--R Type: Expression(Integer) +--E 193 + +--S 194 of 477 +r0036:= 1/6*(1-1/a^2/x^2)^(1/2)*x^2/a+1/3*x^3*acsc(a*x)+_ + 1/6*atanh((1-1/a^2/x^2)^(1/2))/a^3 +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x - 1 2 2 |a x - 1 3 3 +--R atanh( |-------- ) + a x |-------- + 2a x acsc(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R (149) ----------------------------------------------------- +--R 3 +--R 6a +--R Type: Expression(Integer) +--E 194 + +--S 195 of 477 +a0036:= integrate(t0036,x) +--R +--R +--R (150) +--R +----------+ +----------+ +--R +-+ | 2 2 | 2 2 +--R +-+ 2a x\|2 \|- a x + 1 3 3 2\|- a x + 1 +--R 2\|2 atan(---------------------) - a x atan(--------------) +--R 2 2 2 2 +--R 3a x - 2 a x +--R + +--R +----------+ +--R a x | 2 2 +--R 5atan(-------------) - a x\|- a x + 1 +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R / +--R 3 +--R 6a +--R Type: Union(Expression(Integer),...) +--E 195 + +--S 196 of 477 +m0036:= a0036-r0036 +--R +--R +--R (151) +--R +--------+ +----------+ +--R | 2 2 +-+ | 2 2 +--R |a x - 1 +-+ 2a x\|2 \|- a x + 1 +--R - atanh( |-------- ) + 2\|2 atan(---------------------) +--R | 2 2 2 2 +--R \| a x 3a x - 2 +--R + +--R +----------+ +--------+ +--R | 2 2 | 2 2 +--R 3 3 2\|- a x + 1 a x 2 2 |a x - 1 +--R - a x atan(--------------) + 5atan(-------------) - a x |-------- +--R 2 2 +----------+ | 2 2 +--R a x | 2 2 \| a x +--R \|- a x + 1 +--R + +--R +----------+ +--R | 2 2 3 3 +--R - a x\|- a x + 1 - 2a x acsc(a x) +--R / +--R 3 +--R 6a +--R Type: Expression(Integer) +--E 196 + +--S 197 of 477 +d0036:= D(m0036,x) +--R +--R +--R (152) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R 2 |a x - 1 | 2 2 2\|- a x + 1 +--R - 3a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--------+ +--R | 2 2 +--------+ | 2 2 +--R 2 |a x - 1 | 2 2 2 |a x - 1 +--R (- 6a x acsc(a x) |-------- - 2x)\|a x - 1 + 2a x |-------- +--R | 2 2 | 2 2 +--R \| a x \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 | 2 2 +--R 6a |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 477 +t0037:= x^4*acsc(a*x) +--R +--R +--R 4 +--R (153) x acsc(a x) +--R Type: Expression(Integer) +--E 198 + +--S 199 of 477 +r0037:= 3/40*(1-1/a^2/x^2)^(1/2)*x^2/a^3+1/20*(1-1/a^2/x^2)^(1/2)*x^4/a+_ + 1/5*x^5*acsc(a*x)+3/40*atanh((1-1/a^2/x^2)^(1/2))/a^5 +--R +--R +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R |a x - 1 4 4 2 2 |a x - 1 5 5 +--R 3atanh( |-------- ) + (2a x + 3a x ) |-------- + 8a x acsc(a x) +--R | 2 2 | 2 2 +--R \| a x \| a x +--R (154) ----------------------------------------------------------------- +--R 5 +--R 40a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 477 +a0037:= integrate(t0037,x) +--R +--R +--R (155) +--R +----------+ +----------+ +--R +-+ | 2 2 | 2 2 +--R +-+ 2a x\|2 \|- a x + 1 5 5 2\|- a x + 1 +--R 16\|2 atan(---------------------) - 4a x atan(--------------) +--R 2 2 2 2 +--R 3a x - 2 a x +--R + +--R +----------+ +--R a x 3 3 | 2 2 +--R 43atan(-------------) + (- 2a x - 11a x)\|- a x + 1 +--R +----------+ +--R | 2 2 +--R \|- a x + 1 +--R / +--R 5 +--R 40a +--R Type: Union(Expression(Integer),...) +--E 200 + +--S 201 of 477 +m0037:= a0037-r0037 +--R +--R +--R (156) +--R +--------+ +----------+ +--R | 2 2 +-+ | 2 2 +--R |a x - 1 +-+ 2a x\|2 \|- a x + 1 +--R - 3atanh( |-------- ) + 16\|2 atan(---------------------) +--R | 2 2 2 2 +--R \| a x 3a x - 2 +--R + +--R +----------+ +--R | 2 2 +--R 5 5 2\|- a x + 1 a x +--R - 4a x atan(--------------) + 43atan(-------------) +--R 2 2 +----------+ +--R a x | 2 2 +--R \|- a x + 1 +--R + +--R +--------+ +--R | 2 2 +----------+ +--R 4 4 2 2 |a x - 1 3 3 | 2 2 +--R (- 2a x - 3a x ) |-------- + (- 2a x - 11a x)\|- a x + 1 +--R | 2 2 +--R \| a x +--R + +--R 5 5 +--R - 8a x acsc(a x) +--R / +--R 5 +--R 40a +--R Type: Expression(Integer) +--E 201 + +--S 202 of 477 +d0037:= D(m0037,x) +--R +--R +--R (157) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R 4 |a x - 1 | 2 2 2\|- a x + 1 +--R - 5a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--------+ +--R | 2 2 +--------+ | 2 2 +--R 4 |a x - 1 3 | 2 2 4 |a x - 1 +--R (- 10a x acsc(a x) |-------- - 2x )\|a x - 1 + 2a x |-------- +--R | 2 2 | 2 2 +--R \| a x \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 | 2 2 +--R 10a |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 477 +t0038:= acsc(a*x)/x +--R +--R +--R acsc(a x) +--R (158) --------- +--R x +--R Type: Expression(Integer) +--E 203 + +--S 204 of 477 +r0038:= 1/2*%i*acsc(a*x)^2-acsc(a*x)*log(1-((1-1/a^2/x^2)^(1/2)+%i/a/x)^2)+_ + 1/2*%i*polylog(2,((1-1/a^2/x^2)^(1/2)+%i/a/x)^2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 204 + +--S 205 of 477 +a0038:= integrate(t0038,x) +--R +--R +--R x +--R ++ acsc(%Q a) +--R (159) | ---------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 205 + +--S 206 of 477 +--m0038:= a0038-r0038 +--E 206 + +--S 207 of 477 +--d0038:= D(m0038,x) +--E 207 + +--S 208 of 477 +t0039:= acsc(a*x)/x^3 +--R +--R +--R acsc(a x) +--R (160) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 208 + +--S 209 of 477 +r0039:= -1/4*a*(1-1/a^2/x^2)^(1/2)/x+1/4*a^2*acsc(a*x)-1/2*acsc(a*x)/x^2 +--R +--R +--R +--------+ +--R | 2 2 +--R |a x - 1 2 2 +--R - a x |-------- + (a x - 2)acsc(a x) +--R | 2 2 +--R \| a x +--R (161) -------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 209 + +--S 210 of 477 +a0039:= integrate(t0039,x) +--R +--R +--R (162) +--R +----------+ +----------+ +--R 2 2 | 2 2 2 2 | 2 2 +--R - a x log(\|- a x + 1 + 1) + a x log(\|- a x + 1 - 1) +--R + +--R +----------+ +--R | 2 2 +--R 2 2 2\|- a x + 1 +--R (- a x + 2)atan(--------------) +--R 2 2 +--R a x +--R / +--R 2 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 210 + +--S 211 of 477 +m0039:= a0039-r0039 +--R +--R +--R (163) +--R +----------+ +----------+ +--R 2 2 | 2 2 2 2 | 2 2 +--R - a x log(\|- a x + 1 + 1) + a x log(\|- a x + 1 - 1) +--R + +--R +----------+ +--------+ +--R | 2 2 | 2 2 +--R 2 2 2\|- a x + 1 |a x - 1 2 2 +--R (- a x + 2)atan(--------------) + 2a x |-------- + (- 2a x + 4)acsc(a x) +--R 2 2 | 2 2 +--R a x \| a x +--R / +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 477 +d0039:= D(m0039,x) +--R +--R +--R (164) +--R +--------+ +----------+ +--R | 2 2 +--------+ | 2 2 +--R |a x - 1 | 2 2 2\|- a x + 1 +--R - 2a x |-------- \|a x - 1 atan(--------------) +--R | 2 2 2 2 +--R \| a x a x +--R + +--R +--------+ +--R | 2 2 +--------+ +--R |a x - 1 2 2 | 2 2 +--R (- 4a x acsc(a x) |-------- - a x + 2)\|a x - 1 +--R | 2 2 +--R \| a x +--R + +--R +--------+ +--R | 2 2 +--R 3 3 |a x - 1 +--R (a x - 2a x) |-------- +--R | 2 2 +--R \| a x +--R / +--R +--------+ +--R | 2 2 +--------+ +--R 4 |a x - 1 | 2 2 +--R 4a x |-------- \|a x - 1 +--R | 2 2 +--R \| a x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 477 +t0040:= x*acsc(a+b*x) +--R +--R +--R (165) x acsc(b x + a) +--R Type: Expression(Integer) +--E 213 + +--S 214 of 477 +r0040:= 1/2*(a+b*x)*(1-1/(a+b*x)^2)^(1/2)/b^2-a*(a+b*x)*acsc(a+b*x)/b^2+_ + 1/2*(a+b*x)^2*acsc(a+b*x)/b^2-a*atanh((1-1/(a+b*x)^2)^(1/2))/b^2 +--R +--R +--R (166) +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R - 2a atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 2 2 2 +--R (b x + a) |---------------------- + (b x - a )acsc(b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 214 + +--S 215 of 477 +a0040:= integrate(t0040,x) +--R +--R +--R (167) +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R - +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R - +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2 2 2\|- b x - 2a b x - a + 1 +--R - b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +------------------------+ +--R b x + a | 2 2 2 +--R - 4a atan(---------------------------) - 2\|- b x - 2a b x - a + 1 +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 2 +--R 4b +--R Type: Union(Expression(Integer),...) +--E 215 + +--S 216 of 477 +m0040:= a0040-r0040 +--R +--R +--R (168) +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R - +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |-------------------------------------- +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (2a + 8a + 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +--------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |- 8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |-------------------------------------- +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a 7 +--R ((2a - 8a + 8)b x + (2a - 8a + 8a)b ) |-------------- + a +--R | 8 +--R \| 2b +--R + +--R 5 3 +--R - 2a - 4a + 8a +--R + +--R - +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R 2 | \| 2b +--R b |------------------------------------ +--R | 4 +--R \| 4b +--R * +--R log +--R +--------------+ +--R +------------------------+ | 6 4 2 +--R 6 | 2 2 2 |a + 4a + 4a +--R - 8a b \|- b x - 2a b x - a + 1 |-------------- +--R | 8 +--R \| 2b +--R + +--R +------------------------+ +--R 5 3 2 | 2 2 2 +--R (- 2a - 8a - 8a)b \|- b x - 2a b x - a + 1 +--R * +--R +------------------------------------+ +--R | +--------------+ +--R | | 6 4 2 +--R | 4 |a + 4a + 4a 4 2 +--R |8b |-------------- - a - 12a - 4 +--R | | 8 +--R | \| 2b +--R |------------------------------------ +--R | 4 +--R \| 4b +--R + +--R +--------------+ +--R | 6 4 2 +--R 4 2 5 5 3 4 |a + 4a + 4a +--R ((- 2a + 8a - 8)b x + (- 2a + 8a - 8a)b ) |-------------- +--R | 8 +--R \| 2b +--R + +--R 7 5 3 +--R a - 2a - 4a + 8a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R 4a atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2 2 2\|- b x - 2a b x - a + 1 +--R - b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R - 4a atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +----------------------+ +--R | 2 2 2 +------------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (- 2b x - 2a) |---------------------- - 2\|- b x - 2a b x - a + 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R 2 2 2 +--R (- 2b x + 2a )acsc(b x + a) +--R / +--R 2 +--R 4b +--R Type: Expression(Integer) +--E 216 + +--S 217 of 477 +d0040:= D(m0040,x) +--R +--R +--R (169) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 2 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (- b x - a b x) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 |b x + 2a b x + a - 1 +--R ((- 2b x - 2a b x)acsc(b x + a) |---------------------- - b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 +--R (b x - a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (2b x + 2a b) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression(Integer) +--E 217 + +--S 218 of 477 +t0041:= x^2*acsc(a+b*x) +--R +--R +--R 2 +--R (170) x acsc(b x + a) +--R Type: Expression(Integer) +--E 218 + +--S 219 of 477 +r0041:= -a*(a+b*x)*(1-1/(a+b*x)^2)^(1/2)/b^3+1/6*(a+b*x)^2*_ + (1-1/(a+b*x)^2)^(1/2)/b^3+a^2*(a+b*x)*acsc(a+b*x)/b^3-_ + a*(a+b*x)^2*acsc(a+b*x)/b^3+1/3*(a+b*x)^3*acsc(a+b*x)/b^3+_ + 1/6*atanh((1-1/(a+b*x)^2)^(1/2))/b^3+_ + a^2*atanh((1-1/(a+b*x)^2)^(1/2))/b^3 +--R +--R +--R (171) +--R +----------------------+ +--R | 2 2 2 +--R 2 |b x + 2a b x + a - 1 +--R (6a + 1)atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 3 3 3 +--R (b x - 4a b x - 5a ) |---------------------- + (2b x + 2a )acsc(b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R 3 +--R 6b +--R Type: Expression(Integer) +--E 219 + +--S 220 of 477 +a0041:= integrate(t0041,x) +--R +--R +--R (172) +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R +-------------------------------------------------------------------+ +--R | +-------------------------------------+ +--R | | 10 8 6 4 2 +--R | 6 |18a + 240a + 944a + 960a + 288a 6 4 2 +--R |18b |------------------------------------- - a - 30a - 60a - 8 +--R | | 12 +--R | \| 81b +--R |------------------------------------------------------------------- +--R | 6 +--R \| 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 3 3 2\|- b x - 2a b x - a + 1 +--R - 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R 2 b x + a +--R (12a + 10)atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +------------------------+ +--R | 2 2 2 +--R (- 2b x + 10a)\|- b x - 2a b x - a + 1 +--R / +--R 3 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 220 + +--S 221 of 477 +m0041:= a0041-r0041 +--R +--R +--R (173) +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (81a + 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R - +--R 3 +--R 3b +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R - 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (9a + 114a + 396a + 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 +--R - 18b |------------------------------------- - a +--R | 12 +--R \| 81b +--R + +--R 4 2 +--R - 30a - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 7 5 3 6 +--R ((9a - 54a + 108a - 72)b x + (9a - 54a + 108a - 72a)b ) +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R 3 +--R 3b +--R * +--R +-------------------------------------------------------------------+ +--R | +-------------------------------------+ +--R | | 10 8 6 4 2 +--R | 6 |18a + 240a + 944a + 960a + 288a 6 4 2 +--R |18b |------------------------------------- - a - 30a - 60a - 8 +--R | | 12 +--R | \| 81b +--R |------------------------------------------------------------------- +--R | 6 +--R \| 9b +--R * +--R log +--R +------------------------+ +--R 2 9 | 2 2 2 +--R (- 81a - 54)b \|- b x - 2a b x - a + 1 +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R +------------------------+ +--R 8 6 4 2 3 | 2 2 2 +--R (- 9a - 114a - 396a - 216a )b \|- b x - 2a b x - a + 1 +--R * +--R ROOT +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R 6 |18a + 240a + 944a + 960a + 288a 6 4 +--R 18b |------------------------------------- - a - 30a +--R | 12 +--R \| 81b +--R + +--R 2 +--R - 60a - 8 +--R / +--R 6 +--R 9b +--R + +--R 6 4 2 7 +--R (- 9a + 54a - 108a + 72)b x +--R + +--R 7 5 3 6 +--R (- 9a + 54a - 108a + 72a)b +--R * +--R +-------------------------------------+ +--R | 10 8 6 4 2 +--R |18a + 240a + 944a + 960a + 288a +--R |------------------------------------- +--R | 12 +--R \| 81b +--R + +--R 11 9 7 5 3 +--R 3a + 2a - 72a + 144a - 16a - 96a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 |b x + 2a b x + a - 1 +--R (- 12a - 2)atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 3 3 2\|- b x - 2a b x - a + 1 +--R - 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R 2 b x + a +--R (12a + 10)atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 2 2 2 |b x + 2a b x + a - 1 +--R (- 2b x + 8a b x + 10a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 3 3 3 +--R (- 2b x + 10a)\|- b x - 2a b x - a + 1 + (- 4b x - 4a )acsc(b x + a) +--R / +--R 3 +--R 12b +--R Type: Expression(Integer) +--E 221 + +--S 222 of 477 +d0041:= D(m0041,x) +--R +--R +--R (174) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 3 3 2 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (- 3b x - 3a b x ) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R 3 3 2 2 |b x + 2a b x + a - 1 2 2 +--R (- 6b x - 6a b x )acsc(b x + a) |---------------------- - 2b x +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R 2 +--R 2a b x - 2a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R 3 3 3 |b x + 2a b x + a - 1 +--R (2b x + 2a ) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R 3 2 |b x + 2a b x + a - 1 | 2 2 2 +--R (6b x + 6a b ) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression(Integer) +--E 222 + +--S 223 of 477 +t0042:= acsc(x^(1/2)) +--R +--R +--R +-+ +--R (175) acsc(\|x ) +--R Type: Expression(Integer) +--E 223 + +--S 224 of 477 +r0042:= (-1+x)^(1/2)+x*acsc(x^(1/2)) +--R +--R +--R +-+ +-----+ +--R (176) x acsc(\|x ) + \|x - 1 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 477 +a0042:= integrate(t0042,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-------+ +--R (- x + 2)atan(-----------) - 2\|- x + 1 +--R x +--R (177) ---------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 225 + +--S 226 of 477 +m0042:= a0042-r0042 +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +-----+ +-------+ +--R (- x + 2)atan(-----------) - 2x acsc(\|x ) - 2\|x - 1 - 2\|- x + 1 +--R x +--R (178) -------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 477 +d0042:= D(m0042,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R - atan(-----------) - 2acsc(\|x ) +--R x +--R (179) --------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 477 +t0043:= acsc(x^(1/2))/x +--R +--R +--R +-+ +--R acsc(\|x ) +--R (180) ---------- +--R x +--R Type: Expression(Integer) +--E 228 + +--S 229 of 477 +r0043:= %i*acsc(x^(1/2))^2-2*acsc(x^(1/2))*log(1-((1-1/x)^(1/2)+_ + %i/x^(1/2))^2)+%i*polylog(2,((1-1/x)^(1/2)+%i/x^(1/2))^2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 229 + +--S 230 of 477 +a0043:= integrate(t0043,x) +--R +--R +--R x +--+ +--R ++ acsc(\|%Q ) +--R (181) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 230 + +--S 231 of 477 +--m0043:= a0043-r0043 +--E 231 + +--S 232 of 477 +--d0043:= D(m0043,x) +--E 232 + +--S 233 of 477 +t0044:= acsc(x^(1/2))/x^2 +--R +--R +--R +-+ +--R acsc(\|x ) +--R (182) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 233 + +--S 234 of 477 +r0044:= -1/2*((-1+x)^(1/2)-x*acsc(x^(1/2))+2*acsc(x^(1/2)))/x +--R +--R +--R +-+ +-----+ +--R (x - 2)acsc(\|x ) - \|x - 1 +--R (183) ---------------------------- +--R 2x +--R Type: Expression(Integer) +--E 234 + +--S 235 of 477 +a0044:= integrate(t0044,x) +--R +--R +--R (184) +--R +-------+ +--R +-------+ +-------+ 2\|- x + 1 +--R - x log(\|- x + 1 + 1) + x log(\|- x + 1 - 1) + (- x + 2)atan(-----------) +--R x +--R ---------------------------------------------------------------------------- +--R 4x +--R Type: Union(Expression(Integer),...) +--E 235 + +--S 236 of 477 +m0044:= a0044-r0044 +--R +--R +--R (185) +--R +-------+ +-------+ +--R - x log(\|- x + 1 + 1) + x log(\|- x + 1 - 1) +--R + +--R +-------+ +--R 2\|- x + 1 +-+ +-----+ +--R (- x + 2)atan(-----------) + (- 2x + 4)acsc(\|x ) + 2\|x - 1 +--R x +--R / +--R 4x +--R Type: Expression(Integer) +--E 236 + +--S 237 of 477 +d0044:= D(m0044,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R - atan(-----------) - 2acsc(\|x ) +--R x +--R (186) --------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 237 + +--S 238 of 477 +t0045:= acsc(x^(1/2))/x^3 +--R +--R +--R +-+ +--R acsc(\|x ) +--R (187) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 238 + +--S 239 of 477 +r0045:= -1/16*(2*(-1+x)^(1/2)+3*(-1+x)^(1/2)*x-3*x^2*acsc(x^(1/2))+_ + 8*acsc(x^(1/2)))/x^2 +--R +--R +--R 2 +-+ +-----+ +--R (3x - 8)acsc(\|x ) + (- 3x - 2)\|x - 1 +--R (188) ---------------------------------------- +--R 2 +--R 16x +--R Type: Expression(Integer) +--E 239 + +--S 240 of 477 +a0045:= integrate(t0045,x) +--R +--R +--R (189) +--R 2 +-------+ 2 +-------+ +--R - 2x log(\|- x + 1 + 1) + 2x log(\|- x + 1 - 1) +--R + +--R +-------+ +--R 2 2\|- x + 1 +-------+ +--R (- x + 4)atan(-----------) - 2x\|- x + 1 +--R x +--R / +--R 2 +--R 16x +--R Type: Union(Expression(Integer),...) +--E 240 + +--S 241 of 477 +m0045:= a0045-r0045 +--R +--R +--R (190) +--R 2 +-------+ 2 +-------+ +--R - 2x log(\|- x + 1 + 1) + 2x log(\|- x + 1 - 1) +--R + +--R +-------+ +--R 2 2\|- x + 1 2 +-+ +-----+ +--R (- x + 4)atan(-----------) + (- 3x + 8)acsc(\|x ) + (3x + 2)\|x - 1 +--R x +--R + +--R +-------+ +--R - 2x\|- x + 1 +--R / +--R 2 +--R 16x +--R Type: Expression(Integer) +--E 241 + +--S 242 of 477 +d0045:= D(m0045,x) +--R +--R +--R +-------+ +--R 2\|- x + 1 +-+ +--R - atan(-----------) - 2acsc(\|x ) +--R x +--R (191) --------------------------------- +--R 3 +--R 2x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 477 +t0046:= asec(a+b*x) +--R +--R +--R (192) asec(b x + a) +--R Type: Expression(Integer) +--E 243 + +--S 244 of 477 +r0046:= (a+b*x)*asec(a+b*x)/b-atanh((1-1/(a+b*x)^2)^(1/2))/b +--R +--R +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R - atanh( |---------------------- ) + (b x + a)asec(b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R (193) ----------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 244 + +--S 245 of 477 +a0046:= integrate(t0046,x) +--R +--R +--R (194) +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R - 4atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 4b +--R Type: Union(Expression(Integer),...) +--E 245 + +--S 246 of 477 +m0046:= a0046-r0046 +--R +--R +--R (195) +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R 4atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R - 4atan(---------------------------) + (- 4b x - 4a)asec(b x + a) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 4b +--R Type: Expression(Integer) +--E 246 + +--S 247 of 477 +d0046:= D(m0046,x) +--R +--R +--R (196) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (b x + a) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R ((- 2b x - 2a)asec(b x + a) |---------------------- + 2) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R (- 2b x - 2a) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (2b x + 2a) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 477 +t0047:= acsc(a+b*x) +--R +--R +--R (197) acsc(b x + a) +--R Type: Expression(Integer) +--E 248 + +--S 249 of 477 +r0047:= (a+b*x)*acsc(a+b*x)/b+atanh((1-1/(a+b*x)^2)^(1/2))/b +--R +--R +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R atanh( |---------------------- ) + (b x + a)acsc(b x + a) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R (198) --------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 249 + +--S 250 of 477 +a0047:= integrate(t0047,x) +--R +--R +--R (199) +--R - +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R - 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R 4atan(---------------------------) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 4b +--R Type: Union(Expression(Integer),...) +--E 250 + +--S 251 of 477 +m0047:= a0047-r0047 +--R +--R +--R (200) +--R - +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R - +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |-------------------- +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R a b\|- b x - 2a b x - a + 1 +--R * +--R +--------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |- 2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |-------------------- +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((a - 2)b x + (a - 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R b |------------------ +--R | 2 +--R \| b +--R * +--R log +--R +---+ +--R +------------------------+ | 2 +--R 3 | 2 2 2 |2a +--R - b \|- b x - 2a b x - a + 1 |--- +--R | 4 +--R \| b +--R + +--R +------------------------+ +--R 2 | 2 2 2 +--R - a b\|- b x - 2a b x - a + 1 +--R * +--R +------------------+ +--R | +---+ +--R | | 2 +--R | 2 |2a 2 +--R |2b |--- - a - 2 +--R | | 4 +--R | \| b +--R |------------------ +--R | 2 +--R \| b +--R + +--R +---+ +--R | 2 +--R 2 3 3 2 |2a 3 +--R ((- a + 2)b x + (- a + 2a)b ) |--- + a - 2a +--R | 4 +--R \| b +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R - 4atanh( |---------------------- ) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R + +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R - 2b x atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R b x + a +--R 4atan(---------------------------) + (- 4b x - 4a)acsc(b x + a) +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R 4b +--R Type: Expression(Integer) +--E 251 + +--S 252 of 477 +d0047:= D(m0047,x) +--R +--R +--R (201) +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (- b x - a) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +------------------------+ +--R | 2 2 2 +--R 2\|- b x - 2a b x - a + 1 +--R atan(----------------------------) +--R 2 2 2 +--R b x + 2a b x + a +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R ((- 2b x - 2a)acsc(b x + a) |---------------------- - 2) +--R | 2 2 2 +--R \| b x + 2a b x + a +--R * +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a - 1 +--R + +--R +----------------------+ +--R | 2 2 2 +--R |b x + 2a b x + a - 1 +--R (2b x + 2a) |---------------------- +--R | 2 2 2 +--R \| b x + 2a b x + a +--R / +--R +----------------------+ +--R | 2 2 2 +----------------------+ +--R |b x + 2a b x + a - 1 | 2 2 2 +--R (2b x + 2a) |---------------------- \|b x + 2a b x + a - 1 +--R | 2 2 2 +--R \| b x + 2a b x + a +--R Type: Expression(Integer) +--E 252 + +--S 253 of 477 +t0048:= atan(1/x) +--R +--R +--R 1 +--R (202) atan(-) +--R x +--R Type: Expression(Integer) +--E 253 + +--S 254 of 477 +r0048:= x*acot(x)+1/2*log(1+x^2) +--R +--R +--R 2 +--R log(x + 1) + 2x acot(x) +--R (203) ------------------------ +--R 2 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 477 +a0048:= integrate(t0048,x) +--R +--R +--R 2 2x +--R log(x + 1) + x atan(------) +--R 2 +--R x - 1 +--R (204) ---------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 255 + +--S 256 of 477 +m0048:= a0048-r0048 +--R +--R +--R 2x +--R x atan(------) - 2x acot(x) +--R 2 +--R x - 1 +--R (205) --------------------------- +--R 2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 477 +d0048:= D(m0048,x) +--R +--R +--R 2x +--R atan(------) - 2acot(x) +--R 2 +--R x - 1 +--R (206) ----------------------- +--R 2 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 477 +t0049:= acot(1/x) +--R +--R +--R 1 +--R (207) acot(-) +--R x +--R Type: Expression(Integer) +--E 258 + +--S 259 of 477 +r0049:= atan(x)*x-1/2*log(1+x^2) +--R +--R +--R 2 +--R - log(x + 1) + 2x atan(x) +--R (208) -------------------------- +--R 2 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 477 +a0049:= integrate(t0049,x) +--R +--R +--R 2 2x +--R - log(x + 1) - x atan(------) +--R 2 +--R x - 1 +--R (209) ------------------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 260 + +--S 261 of 477 +m0049:= a0049-r0049 +--R +--R +--R 2x +--R - 2x atan(x) - x atan(------) +--R 2 +--R x - 1 +--R (210) ----------------------------- +--R 2 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 477 +d0049:= D(m0049,x) +--R +--R +--R 2x +--R - 2atan(x) - atan(------) +--R 2 +--R x - 1 +--R (211) ------------------------- +--R 2 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 477 +t0050:= asec(1/x) +--R +--R +--R 1 +--R (212) asec(-) +--R x +--R Type: Expression(Integer) +--E 263 + +--S 264 of 477 +r0050:= -(1-x^2)^(1/2)+x*acos(x) +--R +--R +--R +--------+ +--R | 2 +--R (213) - \|- x + 1 + x acos(x) +--R Type: Expression(Integer) +--E 264 + +--S 265 of 477 +a0050:= integrate(t0050,x) +--R +--R +--R (214) +--R +------+ +--R +------+ 2 +-+ | 2 3 +-+ +--R +-+ | 2 (4x + 2)\|2 \|x - 1 + (- 4x + 2x)\|2 +--R x\|2 atan(2x\|x - 1 ) - atan(-----------------------------------------) +--R +------+ +--R 5 | 2 6 4 2 +--R (8x - 2x)\|x - 1 - 8x + 4x + 2x + 3 +--R + +--R +-+ +--R 2x\|2 +--R - atan(-------) +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 265 + +--S 266 of 477 +m0050:= a0050-r0050 +--R +--R +--R (215) +--R +------+ +--R +------+ 2 +-+ | 2 3 +-+ +--R +-+ | 2 (4x + 2)\|2 \|x - 1 + (- 4x + 2x)\|2 +--R x\|2 atan(2x\|x - 1 ) - atan(-----------------------------------------) +--R +------+ +--R 5 | 2 6 4 2 +--R (8x - 2x)\|x - 1 - 8x + 4x + 2x + 3 +--R + +--R +--------+ +-+ +--R +-+ | 2 2x\|2 +-+ +--R 2\|2 \|- x + 1 - atan(-------) - 2x\|2 acos(x) +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 477 +d0050:= D(m0050,x) +--R +--R +--R +------+ +--R | 2 +--R atan(2x\|x - 1 ) - 2acos(x) +--R (216) ---------------------------- +--R 2 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 477 +t0051:= acsc(1/x) +--R +--R +--R 1 +--R (217) acsc(-) +--R x +--R Type: Expression(Integer) +--E 268 + +--S 269 of 477 +r0051:= (1-x^2)^(1/2)+x*asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (218) \|- x + 1 + x asin(x) +--R Type: Expression(Integer) +--E 269 + +--S 270 of 477 +a0051:= integrate(t0051,x) +--R +--R +--R (219) +--R +------+ +--R +-+ | 2 +--R - x\|2 atan(2x\|x - 1 ) +--R + +--R +------+ +--R 2 +-+ | 2 3 +-+ +-+ +--R (4x + 2)\|2 \|x - 1 + (- 4x + 2x)\|2 2x\|2 +--R atan(-----------------------------------------) + atan(-------) +--R +------+ 2 +--R 5 | 2 6 4 2 2x - 1 +--R (8x - 2x)\|x - 1 - 8x + 4x + 2x + 3 +--R / +--R +-+ +--R 2\|2 +--R Type: Union(Expression(Integer),...) +--E 270 + +--S 271 of 477 +m0051:= a0051-r0051 +--R +--R +--R (220) +--R +------+ +--R +-+ | 2 +--R - x\|2 atan(2x\|x - 1 ) +--R + +--R +------+ +--R 2 +-+ | 2 3 +-+ +--------+ +--R (4x + 2)\|2 \|x - 1 + (- 4x + 2x)\|2 +-+ | 2 +--R atan(-----------------------------------------) - 2\|2 \|- x + 1 +--R +------+ +--R 5 | 2 6 4 2 +--R (8x - 2x)\|x - 1 - 8x + 4x + 2x + 3 +--R + +--R +-+ +--R 2x\|2 +-+ +--R atan(-------) - 2x\|2 asin(x) +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 477 +d0051:= D(m0051,x) +--R +--R +--R +------+ +--R | 2 +--R - atan(2x\|x - 1 ) - 2asin(x) +--R (221) ------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 477 +t0052:= atan(a+b*x)/x +--R +--R +--R atan(b x + a) +--R (222) ------------- +--R x +--R Type: Expression(Integer) +--E 273 + +--S 274 of 477 +r0052:= 1/2*%i*log(%i*b*x/(1-%i*a))*log(1-%i*a-%i*b*x)-_ + 1/2*%i*log(-%i*b*x/(1+%i*a))*log(1+%i*a+%i*b*x)+_ + 1/2*%i*polylog(2,1-%i*b*x/(1-%i*a))-_ + 1/2*%i*polylog(2,1+%i*b*x/(1+%i*a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 274 + +--S 275 of 477 +a0052:= integrate(t0052,x) +--R +--R +--R x +--R ++ atan(%Q b + a) +--R (223) | -------------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 275 + +--S 276 of 477 +--m0052:= a0052-r0052 +--E 276 + +--S 277 of 477 +--d0052:= D(m0052,x) +--E 277 + +--S 278 of 477 +t0053:= acot(a+b*x)/x +--R +--R +--R acot(b x + a) +--R (224) ------------- +--R x +--R Type: Expression(Integer) +--E 278 + +--S 279 of 477 +r0053:= 1/2*%i*(-log(x)*log((%i-a-b*x)/(%i-a))+_ + log(x)*log((%i+a+b*x)/(%i+a))+_ + log(x)*log(-(%i-a-b*x)/(a+b*x))-_ + log(x)*log((%i+a+b*x)/(a+b*x))-_ + polylog(2,b*x/(%i-a))+polylog(2,-b*x/(%i+a))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 279 + +--S 280 of 477 +a0053:= integrate(t0053,x) +--R +--R +--R x +--R ++ acot(%Q b + a) +--R (225) | -------------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 280 + +--S 281 of 477 +--m0053:= a0053-r0053 +--E 281 + +--S 282 of 477 +--d0053:= D(m0053,x) +--E 282 + +--S 283 of 477 +t0054:= asin(a+b*x)/(a*d/b+d*x) +--R +--R +--R b asin(b x + a) +--R (226) --------------- +--R b d x + a d +--R Type: Expression(Integer) +--E 283 + +--S 284 of 477 +r0054:= -1/2*%i*asin(a+b*x)^2/d+asin(a+b*x)*log(1-(%i*(a+b*x)+_ + (1-a^2-2*a*b*x-b^2*x^2)^(1/2))^2)/d-_ + 1/2*%i*polylog(2,(%i*(a+b*x)+(1-a^2-2*a*b*x-b^2*x^2)^(1/2))^2)/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 284 + +--S 285 of 477 +a0054:= integrate(t0054,x) +--R +--R +--R x +--R ++ b asin(%Q b + a) +--R (227) | ---------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression(Integer),...) +--E 285 + +--S 286 of 477 +--m0054:= a0054-r0054 +--E 286 + +--S 287 of 477 +--d0054:= D(m0054,x) +--E 287 + +--S 288 of 477 +t0055:= atan(a+b*x)/(a*d/b+d*x) +--R +--R +--R b atan(b x + a) +--R (228) --------------- +--R b d x + a d +--R Type: Expression(Integer) +--E 288 + +--S 289 of 477 +r0055:= 1/2*%i*(polylog(2,-%i*(a+b*x))-polylog(2,%i*(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 289 + +--S 290 of 477 +a0055:= integrate(t0055,x) +--R +--R +--R x +--R ++ b atan(%Q b + a) +--R (229) | ---------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression(Integer),...) +--E 290 + +--S 291 of 477 +--m0055:= a0055-r0055 +--E 291 + +--S 292 of 477 +--d0055:= D(m0055,x) +--E 292 + +--S 293 of 477 +t0056:= acot(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acot(b x + a) +--R (230) --------------- +--R b d x + a d +--R Type: Expression(Integer) +--E 293 + +--S 294 of 477 +r0056:= -1/2*%i*(polylog(2,-%i/(a+b*x))-polylog(2,%i/(a+b*x)))/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Complex(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 294 + +--S 295 of 477 +a0056:= integrate(t0056,x) +--R +--R +--R x +--R ++ b acot(%Q b + a) +--R (231) | ---------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression(Integer),...) +--E 295 + +--S 296 of 477 +--m0056:= a0056-r0056 +--E 296 + +--S 297 of 477 +--d0056:= D(m0056,x) +--E 297 + +--S 298 of 477 +t0057:= acsc(a+b*x)/(a*d/b+d*x) +--R +--R +--R b acsc(b x + a) +--R (232) --------------- +--R b d x + a d +--R Type: Expression(Integer) +--E 298 + +--S 299 of 477 +r0057:= 1/2*%i*acsc(a+b*x)^2/d-acsc(a+b*x)*log(1-(%i/(a+b*x)+_ + (1-1/(a+b*x)^2)^(1/2))^2)/d+1/2*%i*_ + polylog(2,(%i/(a+b*x)+(1-1/(a+b*x)^2)^(1/2))^2)/d +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 299 + +--S 300 of 477 +a0057:= integrate(t0057,x) +--R +--R +--R x +--R ++ b acsc(%Q b + a) +--R (233) | ---------------- d%Q +--R ++ (%Q b + a)d +--R Type: Union(Expression(Integer),...) +--E 300 + +--S 301 of 477 +--m0057:= a0057-r0057 +--E 301 + +--S 302 of 477 +--d0057:= D(m0057,x) +--E 302 + +--S 303 of 477 +t0058:= asin(a*x^n)/x +--R +--R +--R n +--R asin(a x ) +--R (234) ---------- +--R x +--R Type: Expression(Integer) +--E 303 + +--S 304 of 477 +r0058:= -1/2*%i*asin(a*x^n)^2/n+asin(a*x^n)*_ + log(1-(%i*a*x^n+(1-a^2*x^(2*n))^(1/2))^2)/n-_ + 1/2*%i*polylog(2,(%i*a*x^n+(1-a^2*x^(2*n))^(1/2))^2)/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 304 + +--S 305 of 477 +a0058:= integrate(t0058,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 305 + +--S 306 of 477 +--m0058:= a0058-r0058 +--E 306 + +--S 307 of 477 +--d0058:= D(m0058,x) +--E 307 + +--S 308 of 477 +t0059:= atan(a*x^n)/x +--R +--R +--R n +--R atan(a x ) +--R (235) ---------- +--R x +--R Type: Expression(Integer) +--E 308 + +--S 309 of 477 +r0059:= 1/2*%i*(polylog(2,-%i*a*x^n)-polylog(2,%i*a*x^n))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 309 + +--S 310 of 477 +a0059:= integrate(t0059,x) +--R +--R +--R x n +--R ++ atan(a %Q ) +--R (236) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 310 + +--S 311 of 477 +--m0059:= a0059-r0059 +--E 311 + +--S 312 of 477 +--d0059:= D(m0059,x) +--E 312 + +--S 313 of 477 +t0060:= acot(a*x^n)/x +--R +--R +--R n +--R acot(a x ) +--R (237) ---------- +--R x +--R Type: Expression(Integer) +--E 313 + +--S 314 of 477 +r0060:= -1/2*%i*(polylog(2,-%i/a*x^(-n))-polylog(2,%i/a*x^(-n)))/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 314 + +--S 315 of 477 +a0060:= integrate(t0060,x) +--R +--R +--R x n +--R ++ acot(a %Q ) +--R (238) | ----------- d%Q +--R ++ %Q +--R Type: Union(Expression(Integer),...) +--E 315 + +--S 316 of 477 +--m0060:= a0060-r0060 +--E 316 + +--S 317 of 477 +--d0060:= D(m0060,x) +--E 317 + +--S 318 of 477 +t0061:= acsc(a*x^n)/x +--R +--R +--R n +--R acsc(a x ) +--R (239) ---------- +--R x +--R Type: Expression(Integer) +--E 318 + +--S 319 of 477 +r0061:= 1/2*%i*acsc(a*x^n)^2/n-acsc(a*x^n)*log(1-(%i/a/(x^n)+_ + (1-1/a^2/(x^(2*n)))^(1/2))^2)/n+1/2*%i*_ + polylog(2,(%i/a/(x^n)+(1-1/a^2/(x^(2*n)))^(1/2))^2)/n +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 319 + +--S 320 of 477 +a0061:= integrate(t0061,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 320 + +--S 321 of 477 +--m0061:= a0061-r0061 +--E 321 + +--S 322 of 477 +--d0061:= D(m0061,x) +--E 322 + +--S 323 of 477 +t0062:= x^3*asec(a+b*x^4) +--R +--R +--R 3 4 +--R (240) x asec(b x + a) +--R Type: Expression(Integer) +--E 323 + +--S 324 of 477 +r0062:= 1/4*(a+b*x^4)*asec(a+b*x^4)/b-1/4*atanh((1-1/(a+b*x^4)^2)^(1/2))/b +--R +--R +--R +-----------------------+ +--R | 2 8 4 2 +--R |b x + 2a b x + a - 1 4 4 +--R - atanh( |----------------------- ) + (b x + a)asec(b x + a) +--R | 2 8 4 2 +--R \| b x + 2a b x + a +--R (241) -------------------------------------------------------------- +--R 4b +--R Type: Expression(Integer) +--E 324 + +--S 325 of 477 +a0062:= integrate(t0062,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 325 + +--S 326 of 477 +--m0062:= a0062-r0062 +--E 326 + +--S 327 of 477 +--d0062:= D(m0062,x) +--E 327 + +--S 328 of 477 +t0063:= x^3*acsc(a+b*x^4) +--R +--R +--R 3 4 +--R (242) x acsc(b x + a) +--R Type: Expression(Integer) +--E 328 + +--S 329 of 477 +r0063:= 1/4*(a+b*x^4)*acsc(a+b*x^4)/b+1/4*atanh((1-1/(a+b*x^4)^2)^(1/2))/b +--R +--R +--R +-----------------------+ +--R | 2 8 4 2 +--R |b x + 2a b x + a - 1 4 4 +--R atanh( |----------------------- ) + (b x + a)acsc(b x + a) +--R | 2 8 4 2 +--R \| b x + 2a b x + a +--R (243) ------------------------------------------------------------ +--R 4b +--R Type: Expression(Integer) +--E 329 + +--S 330 of 477 +a0063:= integrate(t0063,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 330 + +--S 331 of 477 +--m0063:= a0063-r0063 +--E 331 + +--S 332 of 477 +--d0063:= D(m0063,x) +--E 332 + +--S 333 of 477 +t0064:= x^(-1+n)*asin(a+b*x^n) +--R +--R +--R n - 1 n +--R (244) x asin(b x + a) +--R Type: Expression(Integer) +--E 333 + +--S 334 of 477 +r0064:= (1-(a+b*x^n)^2)^(1/2)/b/n+(a+b*x^n)*asin(a+b*x^n)/b/n +--R +--R +--R +----------------------------+ +--R | 2 n 2 n 2 n n +--R \|- b (x ) - 2a b x - a + 1 + (b x + a)asin(b x + a) +--R (245) ---------------------------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 334 + +--S 335 of 477 +a0064:= integrate(t0064,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 335 + +--S 336 of 477 +--m0064:= a0064-r0064 +--E 336 + +--S 337 of 477 +--d0064:= D(m0064,x) +--E 337 + +--S 338 of 477 +t0065:= x^(-1+n)*acos(a+b*x^n) +--R +--R +--R n - 1 n +--R (246) x acos(b x + a) +--R Type: Expression(Integer) +--E 338 + +--S 339 of 477 +r0065:= -(1-(a+b*x^n)^2)^(1/2)/b/n+(a+b*x^n)*acos(a+b*x^n)/b/n +--R +--R +--R +----------------------------+ +--R | 2 n 2 n 2 n n +--R - \|- b (x ) - 2a b x - a + 1 + (b x + a)acos(b x + a) +--R (247) ------------------------------------------------------------ +--R b n +--R Type: Expression(Integer) +--E 339 + +--S 340 of 477 +a0065:= integrate(t0065,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 340 + +--S 341 of 477 +--m0065:= a0065-r0065 +--E 341 + +--S 342 of 477 +--d0065:= D(m0065,x) +--E 342 + +--S 343 of 477 +t0066:= x^(-1+n)*atan(a+b*x^n) +--R +--R +--R n - 1 n +--R (248) x atan(b x + a) +--R Type: Expression(Integer) +--E 343 + +--S 344 of 477 +r0066:= (a+b*x^n)*atan(a+b*x^n)/b/n-1/2*log(1+(a+b*x^n)^2)/b/n +--R +--R +--R 2 n 2 n 2 n n +--R - log(b (x ) + 2a b x + a + 1) + (2b x + 2a)atan(b x + a) +--R (249) -------------------------------------------------------------- +--R 2b n +--R Type: Expression(Integer) +--E 344 + +--S 345 of 477 +a0066:= integrate(t0066,x) +--R +--R +--R (250) +--R 2 n log(x) 2 n log(x) 2 +--R - log(b (%e ) + 2a b %e + a + 1) +--R + +--R n log(x) +--R n log(x) 2b %e + 2a +--R (- b %e - a)atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R / +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 345 + +--S 346 of 477 +m0066:= a0066-r0066 +--R +--R +--R (251) +--R 2 n log(x) 2 n log(x) 2 +--R - log(b (%e ) + 2a b %e + a + 1) +--R + +--R n log(x) +--R n log(x) 2b %e + 2a +--R (- b %e - a)atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R + +--R 2 n 2 n 2 n n +--R log(b (x ) + 2a b x + a + 1) + (- 2b x - 2a)atan(b x + a) +--R / +--R 2b n +--R Type: Expression(Integer) +--E 346 + +--S 347 of 477 +d0066:= D(m0066,x) +--R +--R +--R (252) +--R n log(x) +--R n log(x) 2b %e + 2a +--R - %e atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R + +--R n - 1 n +--R - 2x x atan(b x + a) +--R / +--R 2x +--R Type: Expression(Integer) +--E 347 + +--S 348 of 477 +t0067:= x^(-1+n)*acot(a+b*x^n) +--R +--R +--R n - 1 n +--R (253) x acot(b x + a) +--R Type: Expression(Integer) +--E 348 + +--S 349 of 477 +r0067:= (a+b*x^n)*acot(a+b*x^n)/b/n+1/2*log(1+(a+b*x^n)^2)/b/n +--R +--R +--R 2 n 2 n 2 n n +--R log(b (x ) + 2a b x + a + 1) + (2b x + 2a)acot(b x + a) +--R (254) ------------------------------------------------------------ +--R 2b n +--R Type: Expression(Integer) +--E 349 + +--S 350 of 477 +a0067:= integrate(t0067,x) +--R +--R +--R (255) +--R 2 n log(x) 2 n log(x) 2 +--R log(b (%e ) + 2a b %e + a + 1) +--R + +--R n log(x) +--R n log(x) 2b %e + 2a +--R (b %e + a)atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R / +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 350 + +--S 351 of 477 +m0067:= a0067-r0067 +--R +--R +--R (256) +--R 2 n log(x) 2 n log(x) 2 +--R log(b (%e ) + 2a b %e + a + 1) +--R + +--R n log(x) +--R n log(x) 2b %e + 2a +--R (b %e + a)atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R + +--R 2 n 2 n 2 n n +--R - log(b (x ) + 2a b x + a + 1) + (- 2b x - 2a)acot(b x + a) +--R / +--R 2b n +--R Type: Expression(Integer) +--E 351 + +--S 352 of 477 +d0067:= D(m0067,x) +--R +--R +--R (257) +--R n log(x) +--R n log(x) 2b %e + 2a +--R %e atan(------------------------------------------) +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b %e + a - 1 +--R + +--R n - 1 n +--R - 2x x acot(b x + a) +--R / +--R 2x +--R Type: Expression(Integer) +--E 352 + +--S 353 of 477 +t0068:= x^(-1+n)*asec(a+b*x^n) +--R +--R +--R n - 1 n +--R (258) x asec(b x + a) +--R Type: Expression(Integer) +--E 353 + +--S 354 of 477 +r0068:= (a+b*x^n)*asec(a+b*x^n)/b/n-atanh((1-1/(a+b*x^n)^2)^(1/2))/b/n +--R +--R +--R +--------------------------+ +--R | 2 n 2 n 2 +--R |b (x ) + 2a b x + a - 1 n n +--R - atanh( |-------------------------- ) + (b x + a)asec(b x + a) +--R | 2 n 2 n 2 +--R \| b (x ) + 2a b x + a +--R (259) ----------------------------------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 354 + +--S 355 of 477 +a0068:= integrate(t0068,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 355 + +--S 356 of 477 +--m0068:= a0068-r0068 +--E 356 + +--S 357 of 477 +--d0068:= D(m0068,x) +--E 357 + +--S 358 of 477 +t0069:= x^(-1+n)*acsc(a+b*x^n) +--R +--R +--R n - 1 n +--R (260) x acsc(b x + a) +--R Type: Expression(Integer) +--E 358 + +--S 359 of 477 +r0069:= (a+b*x^n)*acsc(a+b*x^n)/b/n+atanh((1-1/(a+b*x^n)^2)^(1/2))/b/n +--R +--R +--R +--------------------------+ +--R | 2 n 2 n 2 +--R |b (x ) + 2a b x + a - 1 n n +--R atanh( |-------------------------- ) + (b x + a)acsc(b x + a) +--R | 2 n 2 n 2 +--R \| b (x ) + 2a b x + a +--R (261) --------------------------------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 359 + +--S 360 of 477 +a0069:= integrate(t0069,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 360 + +--S 361 of 477 +--m0069:= a0069-r0069 +--E 361 + +--S 362 of 477 +--d0069:= D(m0069,x) +--E 362 + +--S 363 of 477 +t0070:= asin(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (262) asin(%e ) +--R Type: Expression(Integer) +--E 363 + +--S 364 of 477 +r0070:= -1/2*(%i*asin(exp(a+b*x))^2-2*asin(exp(a+b*x))*_ + log(-2*%i*exp(a+b*x)*(%i*exp(a+b*x)+(1-exp(2*a+2*b*x))^(1/2)))+_ + %i*polylog(2,(%i*exp(a+b*x)+(1-exp(2*a+2*b*x))^(1/2))^2))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 364 + +--S 365 of 477 +a0070:= integrate(t0070,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 365 + +--S 366 of 477 +--m0070:= a0070-r0070 +--E 366 + +--S 367 of 477 +--d0070:= D(m0070,x) +--E 367 + +--S 368 of 477 +t0071:= acsc(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (263) acsc(%e ) +--R Type: Expression(Integer) +--E 368 + +--S 369 of 477 +r0071:= 1/2*%i*acsc(exp(1)^(a+b*x))^2/b-acsc(exp(1)^(a+b*x))*_ + log(1-(%i*exp(1)^(-a-b*x)+(1-exp(1)^(-2*a-2*b*x))^(1/2))^2)/b+_ + 1/2*%i*polylog(2,(%i*exp(1)^(-a-b*x)+_ + (1-exp(1)^(-2*a-2*b*x))^(1/2))^2)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 369 + +--S 370 of 477 +a0071:= integrate(t0071,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 370 + +--S 371 of 477 +--m0071:= a0071-r0071 +--E 371 + +--S 372 of 477 +--d0071:= D(m0071,x) +--E 372 + +--S 373 of 477 +t0072:= acsc(c*exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (264) acsc(c %e ) +--R Type: Expression(Integer) +--E 373 + +--S 374 of 477 +r0072:= 1/2*%i*acsc(c*exp(1)^(a+b*x))^2/b-acsc(c*exp(1)^(a+b*x))*_ + log(1-(%i*exp(1)^(-a-b*x)/c+(1-exp(1)^(-2*a-2*b*x)/c^2)^(1/2))^2)/b+_ + 1/2*%i*polylog(2,(%i*exp(1)^(-a-b*x)/c+_ + (1-exp(1)^(-2*a-2*b*x)/c^2)^(1/2))^2)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 374 + +--S 375 of 477 +a0072:= integrate(t0072,x) +--R +--R +--R >> Error detected within library code: +--R failed - cannot handle that integrand +--R +--R Continuing to read the file... +--R +--E 375 + +--S 376 of 477 +--m0072:= a0072-r0072 +--E 376 + +--S 377 of 477 +--d0072:= D(m0072,x) +--E 377 + +--S 378 of 477 +t0073:= atan(exp(x)) +--R +--R +--R x +--R (265) atan(%e ) +--R Type: Expression(Integer) +--E 378 + +--S 379 of 477 +r0073:= 1/2*%i*polylog(2,-%i*exp(x))-_ + 1/2*%i*polylog(2,%i*exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 379 + +--S 380 of 477 +a0073:= integrate(t0073,x) +--R +--R +--R x +--R ++ %Q +--R (266) | atan(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 380 + +--S 381 of 477 +--m0073:= a0073-r0073 +--E 381 + +--S 382 of 477 +--d0073:= D(m0073,x) +--E 382 + +--S 383 of 477 +t0074:= atan(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (267) atan(%e ) +--R Type: Expression(Integer) +--E 383 + +--S 384 of 477 +r0074:= 1/2*%i*(polylog(2,-%i*exp(a+b*x))-polylog(2,%i*exp(a+b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 384 + +--S 385 of 477 +a0074:= integrate(t0074,x) +--R +--R +--R x +--R ++ %Q b + a +--R (268) | atan(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 385 + +--S 386 of 477 +--m0074:= a0074-r0074 +--E 386 + +--S 387 of 477 +--d0074:= D(m0074,x) +--E 387 + +--S 388 of 477 +t0075:= x*atan(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (269) x atan(%e ) +--R Type: Expression(Integer) +--E 388 + +--S 389 of 477 +r0075:= 1/2*%i*(x*polylog(2,-%i*exp(a+b*x))*b-_ + x*polylog(2,%i*exp(a+b*x))*b-_ + polylog(3,-%i*exp(a+b*x))+_ + polylog(3,%i*exp(a+b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 389 + +--S 390 of 477 +a0075:= integrate(t0075,x) +--R +--R +--R x +--R ++ %Q b + a +--R (270) | %Q atan(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 390 + +--S 391 of 477 +--m0075:= a0075-r0075 +--E 391 + +--S 392 of 477 +--d0075:= D(m0075,x) +--E 392 + +--S 393 of 477 +t0076:= x^2*atan(exp(1)^(a+b*x)) +--R +--R +--R 2 b x + a +--R (271) x atan(%e ) +--R Type: Expression(Integer) +--E 393 + +--S 394 of 477 +r0076:= 1/2*%i*(x^2*polylog(2,-%i*exp(a+b*x))*b^2-_ + x^2*polylog(2,%i*exp(a+b*x))*b^2-_ + 2*x*polylog(3,-%i*exp(a+b*x))*b+_ + 2*x*polylog(3,%i*exp(a+b*x))*b+_ + 2*polylog(4,-%i*exp(a+b*x))-_ + 2*polylog(4,%i*exp(a+b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 394 + +--S 395 of 477 +a0076:= integrate(t0076,x) +--R +--R +--R x +--R ++ 2 %Q b + a +--R (272) | %Q atan(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 395 + +--S 396 of 477 +--m0076:= a0076-r0076 +--E 396 + +--S 397 of 477 +--d0076:= D(m0076,x) +--E 397 + +--S 398 of 477 +t0077:= atan(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (273) atan(b f + a) +--R Type: Expression(Integer) +--E 398 + +--S 399 of 477 +r0077:= 1/2*%i*(log(-b*f^(c+d*x)/(%i+a))*log(-%i*(%i+a+b*f^(c+d*x)))-_ + log(b*f^(c+d*x)/(%i-a))*log(%i*(-%i+a+b*f^(c+d*x)))+_ + polylog(2,(-1+%i*a+%i*b*f^(c+d*x))/(-1+%i*a))-_ + polylog(2,(1+%i*a+%i*b*f^(c+d*x))/(1+%i*a)))/d/log(f) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 399 + +--S 400 of 477 +a0077:= integrate(t0077,x) +--R +--R +--R x +--R ++ %Q d + c +--R (274) | atan(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 400 + +--S 401 of 477 +--m0077:= a0077-r0077 +--E 401 + +--S 402 of 477 +--d0077:= D(m0077,x) +--E 402 + +--S 403 of 477 +t0078:= x*atan(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (275) x atan(b f + a) +--R Type: Expression(Integer) +--E 403 + +--S 404 of 477 +r0078:= 1/4*%i*x^2*log(1-%i*a-%i*b*f^(c+d*x))-_ + 1/4*%i*x^2*log(1+%i*a+%i*b*f^(c+d*x))-_ + 1/4*%i*x^2*log(1-%i*b*f^(c+d*x)/(1-%i*a))+_ + 1/4*%i*x^2*log(1+%i*b*f^(c+d*x)/(1+%i*a))-_ + 1/2*%i*x*polylog(2,%i*b*f^(c+d*x)/(1-%i*a))/d/log(f)+_ + 1/2*%i*x*polylog(2,-%i*b*f^(c+d*x)/(1+%i*a))/d/log(f)+_ + 1/2*%i*polylog(3,%i*b*f^(c+d*x)/(1-%i*a))/d^2/log(f)^2-_ + 1/2*%i*polylog(3,-%i*b*f^(c+d*x)/(1+%i*a))/d^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 404 + +--S 405 of 477 +a0078:= integrate(t0078,x) +--R +--R +--R x +--R ++ %Q d + c +--R (276) | %Q atan(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 405 + +--S 406 of 477 +--m0078:= a0078-r0078 +--E 406 + +--S 407 of 477 +--d0078:= D(m0078,x) +--E 407 + +--S 408 of 477 +t0079:= x^2*atan(a+b*f^(c+d*x)) +--R +--R +--R 2 d x + c +--R (277) x atan(b f + a) +--R Type: Expression(Integer) +--E 408 + +--S 409 of 477 +r0079:= 1/6*%i*x^3*log(1-%i*a-%i*b*f^(c+d*x))-_ + 1/6*%i*x^3*log(1+%i*a+%i*b*f^(c+d*x))-_ + 1/6*%i*x^3*log(1-%i*b*f^(c+d*x)/(1-%i*a))+_ + 1/6*%i*x^3*log(1+%i*b*f^(c+d*x)/(1+%i*a))-_ + 1/2*%i*x^2*polylog(2,%i*b*f^(c+d*x)/(1-%i*a))/d/log(f)+_ + 1/2*%i*x^2*polylog(2,-%i*b*f^(c+d*x)/(1+%i*a))/d/log(f)+_ + %i*x*polylog(3,%i*b*f^(c+d*x)/(1-%i*a))/d^2/log(f)^2-_ + %i*x*polylog(3,-%i*b*f^(c+d*x)/(1+%i*a))/d^2/log(f)^2-_ + %i*polylog(4,%i*b*f^(c+d*x)/(1-%i*a))/d^3/log(f)^3+_ + %i*polylog(4,-%i*b*f^(c+d*x)/(1+%i*a))/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 409 + +--S 410 of 477 +a0079:= integrate(t0079,x) +--R +--R +--R x +--R ++ 2 %Q d + c +--R (278) | %Q atan(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 410 + +--S 411 of 477 +--m0079:= a0079-r0079 +--E 411 + +--S 412 of 477 +--d0079:= D(m0079,x) +--E 412 + +--S 413 of 477 +t0080:= acot(exp(x)) +--R +--R +--R x +--R (279) acot(%e ) +--R Type: Expression(Integer) +--E 413 + +--S 414 of 477 +r0080:= -1/2*%i*polylog(2,-%i/exp(x))+1/2*%i*polylog(2,%i/exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 414 + +--S 415 of 477 +a0080:= integrate(t0080,x) +--R +--R +--R x +--R ++ %Q +--R (280) | acot(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 415 + +--S 416 of 477 +--m0080:= a0080-r0080 +--E 416 + +--S 417 of 477 +--d0080:= D(m0080,x) +--E 417 + +--S 418 of 477 +t0081:= x*acot(exp(x)) +--R +--R +--R x +--R (281) x acot(%e ) +--R Type: Expression(Integer) +--E 418 + +--S 419 of 477 +r0081:= 1/2*%i*(-x*polylog(2,-%i*exp(-x))+x*_ + polylog(2,%i*exp(-x))-_ + polylog(3,-%i*exp(-x))+_ + polylog(3,%i*exp(-x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 419 + +--S 420 of 477 +a0081:= integrate(t0081,x) +--R +--R +--R x +--R ++ %Q +--R (282) | %Q acot(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 477 +--m0081:= a0081-r0081 +--E 421 + +--S 422 of 477 +--d0081:= D(m0081,x) +--E 422 + +--S 423 of 477 +t0082:= x^2*acot(exp(x)) +--R +--R +--R 2 x +--R (283) x acot(%e ) +--R Type: Expression(Integer) +--E 423 + +--S 424 of 477 +r0082:= -1/2*%i*x^2*polylog(2,-%i/exp(x))+_ + 1/2*%i*x^2*polylog(2,%i/exp(x))-_ + %i*x*polylog(3,-%i/exp(x))+_ + %i*x*polylog(3,%i/exp(x))-_ + %i*polylog(4,-%i/exp(x))+_ + %i*polylog(4,%i/exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 424 + +--S 425 of 477 +a0082:= integrate(t0082,x) +--R +--R +--R x +--R ++ 2 %Q +--R (284) | %Q acot(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 425 + +--S 426 of 477 +--m0082:= a0082-r0082 +--E 426 + +--S 427 of 477 +--d0082:= D(m0082,x) +--E 427 + +--S 428 of 477 +t0083:= acot(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (285) acot(%e ) +--R Type: Expression(Integer) +--E 428 + +--S 429 of 477 +r0083:= -1/2*%i*(polylog(2,-%i*exp(-a-b*x))-polylog(2,%i*exp(-a-b*x)))/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 429 + +--S 430 of 477 +a0083:= integrate(t0083,x) +--R +--R +--R x +--R ++ %Q b + a +--R (286) | acot(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 430 + +--S 431 of 477 +--m0083:= a0083-r0083 +--E 431 + +--S 432 of 477 +--d0083:= D(m0083,x) +--E 432 + +--S 433 of 477 +t0084:= x*acot(exp(1)^(a+b*x)) +--R +--R +--R b x + a +--R (287) x acot(%e ) +--R Type: Expression(Integer) +--E 433 + +--S 434 of 477 +r0084:= -1/2*%i*(x*polylog(2,-%i*exp(-a-b*x))*b-_ + x*polylog(2,%i*exp(-a-b*x))*b+_ + polylog(3,-%i*exp(-a-b*x))-_ + polylog(3,%i*exp(-a-b*x)))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 434 + +--S 435 of 477 +a0084:= integrate(t0084,x) +--R +--R +--R x +--R ++ %Q b + a +--R (288) | %Q acot(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 435 + +--S 436 of 477 +--m0084:= a0084-r0084 +--E 436 + +--S 437 of 477 +--d0084:= D(m0084,x) +--E 437 + +--S 438 of 477 +t0085:= x^2*acot(exp(1)^(a+b*x)) +--R +--R +--R 2 b x + a +--R (289) x acot(%e ) +--R Type: Expression(Integer) +--E 438 + +--S 439 of 477 +r0085:= -1/2*%i*(x^2*polylog(2,-%i*exp(-a-b*x))*b^2-_ + x^2*polylog(2,%i*exp(-a-b*x))*b^2+_ + 2*x*polylog(3,-%i*exp(-a-b*x))*b-_ + 2*x*polylog(3,%i*exp(-a-b*x))*b+_ + 2*polylog(4,-%i*exp(-a-b*x))-_ + 2*polylog(4,%i*exp(-a-b*x)))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 439 + +--S 440 of 477 +a0085:= integrate(t0085,x) +--R +--R +--R x +--R ++ 2 %Q b + a +--R (290) | %Q acot(%e )d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 477 +--m0085:= a0085-r0085 +--E 441 + +--S 442 of 477 +--d0085:= D(m0085,x) +--E 442 + +--S 443 of 477 +t0086:= acot(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (291) acot(b f + a) +--R Type: Expression(Integer) +--E 443 + +--S 444 of 477 +r0086:= -1/2*%i*(log(f^(c+d*x))*_ + log(-(-%i+a+b*f^(c+d*x))/(%i-a))-_ + log(f^(c+d*x))*_ + log((%i+a+b*f^(c+d*x))/(%i+a))-_ + log(f^(c+d*x))*_ + log((-%i+a+b*f^(c+d*x))/(a+b*f^(c+d*x)))+_ + log(f^(c+d*x))*_ + log((%i+a+b*f^(c+d*x))/(a+b*f^(c+d*x)))+_ + polylog(2,b*f^(c+d*x)/(%i-a))-_ + polylog(2,-b*f^(c+d*x)/(%i+a)))/d/log(f) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 444 + +--S 445 of 477 +a0086:= integrate(t0086,x) +--R +--R +--R x +--R ++ %Q d + c +--R (292) | acot(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 445 + +--S 446 of 477 +--m0086:= a0086-r0086 +--E 446 + +--S 447 of 477 +--d0086:= D(m0086,x) +--E 447 + +--S 448 of 477 +t0087:= x*acot(a+b*f^(c+d*x)) +--R +--R +--R d x + c +--R (293) x acot(b f + a) +--R Type: Expression(Integer) +--E 448 + +--S 449 of 477 +r0087:= -1/4*%i*x^2*log(1-b*f^(c+d*x)/(%i-a))+_ + 1/4*%i*x^2*log(1+b*f^(c+d*x)/(%i+a))+_ + 1/4*%i*x^2*log(1-%i/(a+b*f^(c+d*x)))-_ + 1/4*%i*x^2*log(1+%i/(a+b*f^(c+d*x)))-_ + 1/2*%i*x*polylog(2,b*f^(c+d*x)/(%i-a))/d/log(f)+_ + 1/2*%i*x*polylog(2,-b*f^(c+d*x)/(%i+a))/d/log(f)+_ + 1/2*%i*polylog(3,b*f^(c+d*x)/(%i-a))/d^2/log(f)^2-_ + 1/2*%i*polylog(3,-b*f^(c+d*x)/(%i+a))/d^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 449 + +--S 450 of 477 +a0087:= integrate(t0087,x) +--R +--R +--R x +--R ++ %Q d + c +--R (294) | %Q acot(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 450 + +--S 451 of 477 +--m0087:= a0087-r0087 +--E 451 + +--S 452 of 477 +--d0087:= D(m0087,x) +--E 452 + +--S 453 of 477 +t0088:= x^2*acot(a+b*f^(c+d*x)) +--R +--R +--R 2 d x + c +--R (295) x acot(b f + a) +--R Type: Expression(Integer) +--E 453 + +--S 454 of 477 +r0088:= -1/6*%i*x^3*log(1-b*f^(c+d*x)/(%i-a))+_ + 1/6*%i*x^3*log(1+b*f^(c+d*x)/(%i+a))+_ + 1/6*%i*x^3*log(1-%i/(a+b*f^(c+d*x)))-_ + 1/6*%i*x^3*log(1+%i/(a+b*f^(c+d*x)))-_ + 1/2*%i*x^2*polylog(2,b*f^(c+d*x)/(%i-a))/d/log(f)+_ + 1/2*%i*x^2*polylog(2,-b*f^(c+d*x)/(%i+a))/d/log(f)+_ + %i*x*polylog(3,b*f^(c+d*x)/(%i-a))/d^2/log(f)^2-_ + %i*x*polylog(3,-b*f^(c+d*x)/(%i+a))/d^2/log(f)^2-_ + %i*polylog(4,b*f^(c+d*x)/(%i-a))/d^3/log(f)^3+_ + %i*polylog(4,-b*f^(c+d*x)/(%i+a))/d^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 454 + +--S 455 of 477 +a0088:= integrate(t0088,x) +--R +--R +--R x +--R ++ 2 %Q d + c +--R (296) | %Q acot(b f + a)d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 455 + +--S 456 of 477 +--m0088:= a0088-r0088 +--E 456 + +--S 457 of 477 +--d0088:= D(m0088,x) +--E 457 + +--S 458 of 477 +t0089:= atan(sinh(x)) +--R +--R +--R (297) atan(sinh(x)) +--R Type: Expression(Integer) +--E 458 + +--S 459 of 477 +r0089:= -2*x*atan(exp(x))+x*atan(sinh(x))+_ + %i*polylog(2,-%i*exp(x))-_ + %i*polylog(2,%i*exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 459 + +--S 460 of 477 +a0089:= integrate(t0089,x) +--R +--R +--R x +--R ++ +--R (298) | atan(sinh(%Q))d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 460 + +--S 461 of 477 +--m0089:= a0089-r0089 +--E 461 + +--S 462 of 477 +--d0089:= D(m0089,x) +--E 462 + +--S 463 of 477 +t0090:= x*atan(sinh(x)) +--R +--R +--R (299) x atan(sinh(x)) +--R Type: Expression(Integer) +--E 463 + +--S 464 of 477 +r0090:= -x^2*atan(exp(x))+1/2*x^2*atan(sinh(x))+_ + %i*x*polylog(2,-%i*exp(x))-_ + %i*x*polylog(2,%i*exp(x))-_ + %i*polylog(3,-%i*exp(x))+_ + %i*polylog(3,%i*exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 464 + +--S 465 of 477 +a0090:= integrate(t0090,x) +--R +--R +--R x +--R ++ +--R (300) | %Q atan(sinh(%Q))d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 465 + +--S 466 of 477 +--m0090:= a0090-r0090 +--E 466 + +--S 467 of 477 +--d0090:= D(m0090,x) +--E 467 + +--S 468 of 477 +t0091:= x^2*atan(sinh(x)) +--R +--R +--R 2 +--R (301) x atan(sinh(x)) +--R Type: Expression(Integer) +--E 468 + +--S 469 of 477 +r0091:= -2/3*x^3*atan(exp(x))+1/3*x^3*atan(sinh(x))+_ + %i*x^2*polylog(2,-%i*exp(x))-_ + %i*x^2*polylog(2,%i*exp(x))-_ + 2*%i*x*polylog(3,-%i*exp(x))+_ + 2*%i*x*polylog(3,%i*exp(x))+_ + 2*%i*polylog(4,-%i*exp(x))-_ + 2*%i*polylog(4,%i*exp(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 469 + +--S 470 of 477 +a0091:= integrate(t0091,x) +--R +--R +--R x +--R ++ 2 +--R (302) | %Q atan(sinh(%Q))d%Q +--R ++ +--R Type: Union(Expression(Integer),...) +--E 470 + +--S 471 of 477 +--m0091:= a0091-r0091 +--E 471 + +--S 472 of 477 +--d0091:= D(m0091,x) +--E 472 + +--S 473 of 477 +t0092:= (1-x^2)^(1/2)*acos(x) +--R +--R +--R +--------+ +--R | 2 +--R (303) acos(x)\|- x + 1 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 477 +r0092:= 1/4*x^2+1/2*x*(1-x^2)^(1/2)*acos(x)-1/4*acos(x)^2 +--R +--R +--R +--------+ +--R | 2 2 2 +--R 2x acos(x)\|- x + 1 - acos(x) + x +--R (304) ------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 477 +a0092:= integrate(t0092,x) +--R +--R +--R +--------+ 2 +--------+ +--R | 2 +--------+ | 2 +--R 2x\|- x + 1 | 2 2x\|- x + 1 2 +--R - atan(-------------) + 4x\|- x + 1 atan(-------------) + 4x +--R 2 2 +--R 2x - 1 2x - 1 +--R (305) --------------------------------------------------------------- +--R 16 +--R Type: Union(Expression(Integer),...) +--E 475 + +--S 476 of 477 +m0092:= a0092-r0092 +--R +--R +--R (306) +--R +--------+ 2 +--------+ +--R | 2 +--------+ | 2 +--R 2x\|- x + 1 | 2 2x\|- x + 1 +--R - atan(-------------) + 4x\|- x + 1 atan(-------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R +--------+ +--R | 2 2 +--R - 8x acos(x)\|- x + 1 + 4acos(x) +--R / +--R 16 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 477 +d0092:= D(m0092,x) +--R +--R +--R +--------+ +--R | 2 +--R 2 2x\|- x + 1 2 +--R (- x + 1)atan(-------------) + (2x - 2)acos(x) +--R 2 +--R 2x - 1 +--R (307) ------------------------------------------------ +--R +--------+ +--R | 2 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 477 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richinvtrig000-092.input.pdf b/src/axiom-website/CATS/richinvtrig000-092.input.pdf new file mode 100644 index 0000000..609adec Binary files /dev/null and b/src/axiom-website/CATS/richinvtrig000-092.input.pdf differ diff --git a/src/axiom-website/CATS/richlog000-099.input.pamphlet b/src/axiom-website/CATS/richlog000-099.input.pamphlet new file mode 100644 index 0000000..d1ee19b --- /dev/null +++ b/src/axiom-website/CATS/richlog000-099.input.pamphlet @@ -0,0 +1,5433 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richlog000-099.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richlog000-099.output +)spool richlog000-099.output +)set message auto off +)clear all + +--S 1 of 500 +t0000:= x^2*log(a*x^n) +--R +--R +--R 2 n +--R (1) x log(a x ) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0000:= 1/9*x^3*(-n+3*log(a*x^n)) +--R +--R +--R 3 n 3 +--R 3x log(a x ) - n x +--R (2) ------------------- +--R 9 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0000:= integrate(t0000,x) +--R +--R +--R 3 3 3 +--R 3n x log(x) + 3x log(a) - n x +--R (3) ------------------------------ +--R 9 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0000:= a0000-r0000 +--R +--R +--R 3 n 3 3 +--R - x log(a x ) + n x log(x) + x log(a) +--R (4) ------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0000:= D(m0000,x) +--R +--R +--R 2 n n 2 2 2 n 3 n - 1 +--R - 3x x log(a x ) + (3n x log(x) + 3x log(a) + n x )x - n x x +--R (5) ------------------------------------------------------------------ +--R n +--R 3x +--R Type: Expression(Integer) +--E 5 + +--S 6 of 500 +t0001:= x^3*log(a*x^n) +--R +--R +--R 3 n +--R (6) x log(a x ) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0001:= 1/16*x^4*(-n+4*log(a*x^n)) +--R +--R +--R 4 n 4 +--R 4x log(a x ) - n x +--R (7) ------------------- +--R 16 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0001:= integrate(t0001,x) +--R +--R +--R 4 4 4 +--R 4n x log(x) + 4x log(a) - n x +--R (8) ------------------------------ +--R 16 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0001:= a0001-r0001 +--R +--R +--R 4 n 4 4 +--R - x log(a x ) + n x log(x) + x log(a) +--R (9) ------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0001:= D(m0001,x) +--R +--R +--R 3 n n 3 3 3 n 4 n - 1 +--R - 4x x log(a x ) + (4n x log(x) + 4x log(a) + n x )x - n x x +--R (10) ------------------------------------------------------------------ +--R n +--R 4x +--R Type: Expression(Integer) +--E 10 + +--S 11 of 500 +t0002:= log(a*x^n)/x^2 +--R +--R +--R n +--R log(a x ) +--R (11) --------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0002:= -1/x*(log(a*x^n)+n) +--R +--R +--R n +--R - log(a x ) - n +--R (12) --------------- +--R x +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0002:= integrate(t0002,x) +--R +--R +--R - n log(x) - log(a) - n +--R (13) ----------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0002:= a0002-r0002 +--R +--R +--R n +--R log(a x ) - n log(x) - log(a) +--R (14) ----------------------------- +--R x +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0002:= D(m0002,x) +--R +--R +--R n n n n - 1 +--R - x log(a x ) + (n log(x) + log(a) - n)x + n x x +--R (15) ------------------------------------------------------ +--R 2 n +--R x x +--R Type: Expression(Integer) +--E 15 + +--S 16 of 500 +t0003:= log(a*x^n)/x^3 +--R +--R +--R n +--R log(a x ) +--R (16) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0003:= -1/4/x^2*(2*log(a*x^n)+n) +--R +--R +--R n +--R - 2log(a x ) - n +--R (17) ---------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0003:= integrate(t0003,x) +--R +--R +--R - 2n log(x) - 2log(a) - n +--R (18) ------------------------- +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0003:= a0003-r0003 +--R +--R +--R n +--R log(a x ) - n log(x) - log(a) +--R (19) ----------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0003:= D(m0003,x) +--R +--R +--R n n n n - 1 +--R - 2x log(a x ) + (2n log(x) + 2log(a) - n)x + n x x +--R (20) --------------------------------------------------------- +--R 3 n +--R 2x x +--R Type: Expression(Integer) +--E 20 + +--S 21 of 500 +t0004:= x^m*log(a*x^n) +--R +--R +--R m n +--R (21) x log(a x ) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0004:= 1/(1+m)^2*x^(1+m)*(-n+log(a*x^n)+log(a*x^n)*m) +--R +--R +--R m + 1 n m + 1 +--R (m + 1)x log(a x ) - n x +--R (22) --------------------------------- +--R 2 +--R m + 2m + 1 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0004:= integrate(t0004,x) +--R +--R +--R m log(x) +--R ((m + 1)n x log(x) + (m + 1)x log(a) - n x)%e +--R (23) ----------------------------------------------------- +--R 2 +--R m + 2m + 1 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0004:= a0004-r0004 +--R +--R +--R (24) +--R m + 1 n +--R (- m - 1)x log(a x ) +--R + +--R m log(x) m + 1 +--R ((m + 1)n x log(x) + (m + 1)x log(a) - n x)%e + n x +--R / +--R 2 +--R m + 2m + 1 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0004:= D(m0004,x) +--R +--R +--R (25) +--R m n n n m log(x) +--R (- m - 1)x x log(a x ) + ((m + 1)n log(x) + (m + 1)log(a))x %e +--R + +--R m n m + 1 n - 1 +--R n x x - n x x +--R / +--R n +--R (m + 1)x +--R Type: Expression(Integer) +--E 25 + +--S 26 of 500 +t0005:= x^3*log(c*(a*x^n)^p) +--R +--R +--R 3 n p +--R (26) x log(c (a x ) ) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0005:= 1/16*x^4*(-n*p+4*log(c*(a*x^n)^p)) +--R +--R +--R 4 n p 4 +--R 4x log(c (a x ) ) - n p x +--R (27) -------------------------- +--R 16 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0005:= integrate(t0005,x) +--R +--R +--R 4 4 4 4 +--R 4n p x log(x) + 4x log(c) + 4p x log(a) - n p x +--R (28) ------------------------------------------------ +--R 16 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0005:= a0005-r0005 +--R +--R +--R 4 n p 4 4 4 +--R - x log(c (a x ) ) + n p x log(x) + x log(c) + p x log(a) +--R (29) --------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0005:= D(m0005,x) +--R +--R +--R (30) +--R 3 n p n p +--R - 4x (a x ) log(c (a x ) ) +--R + +--R 3 3 3 3 n p +--R (4n p x log(x) + 4x log(c) + 4p x log(a) + n p x )(a x ) +--R + +--R 4 n - 1 n p - 1 +--R - a n p x x (a x ) +--R / +--R n p +--R 4(a x ) +--R Type: Expression(Integer) +--E 30 + +--S 31 of 500 +t0006:= x^m*log(c*(a*x^n)^p) +--R +--R +--R m n p +--R (31) x log(c (a x ) ) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0006:= -n*p*x^(1+m)/(1+m)^2+x^(1+m)*log(c*(a*x^n)^p)/(1+m) +--R +--R +--R m + 1 n p m + 1 +--R (m + 1)x log(c (a x ) ) - n p x +--R (32) ---------------------------------------- +--R 2 +--R m + 2m + 1 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0006:= integrate(t0006,x) +--R +--R +--R (33) +--R m log(x) +--R ((m + 1)n p x log(x) + (m + 1)x log(c) + (m + 1)p x log(a) - n p x)%e +--R ----------------------------------------------------------------------------- +--R 2 +--R m + 2m + 1 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0006:= a0006-r0006 +--R +--R +--R (34) +--R m + 1 n p +--R (- m - 1)x log(c (a x ) ) +--R + +--R ((m + 1)n p x log(x) + (m + 1)x log(c) + (m + 1)p x log(a) - n p x) +--R * +--R m log(x) +--R %e +--R + +--R m + 1 +--R n p x +--R / +--R 2 +--R m + 2m + 1 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0006:= D(m0006,x) +--R +--R +--R (35) +--R m n p n p +--R (- m - 1)x (a x ) log(c (a x ) ) +--R + +--R m log(x) +--R ((m + 1)n p log(x) + (m + 1)log(c) + (m + 1)p log(a))%e +--R + +--R m +--R n p x +--R * +--R n p +--R (a x ) +--R + +--R m + 1 n - 1 n p - 1 +--R - a n p x x (a x ) +--R / +--R n p +--R (m + 1)(a x ) +--R Type: Expression(Integer) +--E 35 + +--S 36 of 500 +t0007:= x*log(a*x^n)^2 +--R +--R +--R n 2 +--R (36) x log(a x ) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0007:= 1/4*x^2*(n^2-2*n*log(a*x^n)+2*log(a*x^n)^2) +--R +--R +--R 2 n 2 2 n 2 2 +--R 2x log(a x ) - 2n x log(a x ) + n x +--R (37) ------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0007:= integrate(t0007,x) +--R +--R +--R (38) +--R 2 2 2 2 2 2 2 2 2 2 2 +--R 2n x log(x) + (4n x log(a) - 2n x )log(x) + 2x log(a) - 2n x log(a) + n x +--R ---------------------------------------------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0007:= a0007-r0007 +--R +--R +--R (39) +--R 2 n 2 2 n 2 2 2 2 2 2 +--R - x log(a x ) + n x log(a x ) + n x log(x) + (2n x log(a) - n x )log(x) +--R + +--R 2 2 2 +--R x log(a) - n x log(a) +--R / +--R 2 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0007:= D(m0007,x) +--R +--R +--R (40) +--R n n 2 n 2 n - 1 n +--R - 2x x log(a x ) + (2n x x - 2n x x )log(a x ) +--R + +--R 2 2 2 2 n 2 2 n - 1 +--R (2n x log(x) + 4n x log(a)log(x) + 2x log(a) - n x)x + n x x +--R / +--R n +--R 2x +--R Type: Expression(Integer) +--E 40 + +--S 41 of 500 +t0008:= x^2*log(a*x^n)^2 +--R +--R +--R 2 n 2 +--R (41) x log(a x ) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0008:= 1/27*x^3*(2*n^2-6*n*log(a*x^n)+9*log(a*x^n)^2) +--R +--R +--R 3 n 2 3 n 2 3 +--R 9x log(a x ) - 6n x log(a x ) + 2n x +--R (42) -------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0008:= integrate(t0008,x) +--R +--R +--R (43) +--R 2 3 2 3 2 3 3 2 3 +--R 9n x log(x) + (18n x log(a) - 6n x )log(x) + 9x log(a) - 6n x log(a) +--R + +--R 2 3 +--R 2n x +--R / +--R 27 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0008:= a0008-r0008 +--R +--R +--R (44) +--R 3 n 2 3 n 2 3 2 +--R - 3x log(a x ) + 2n x log(a x ) + 3n x log(x) +--R + +--R 3 2 3 3 2 3 +--R (6n x log(a) - 2n x )log(x) + 3x log(a) - 2n x log(a) +--R / +--R 9 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0008:= D(m0008,x) +--R +--R +--R (45) +--R 2 n n 2 2 n 3 n - 1 n +--R - 9x x log(a x ) + (6n x x - 6n x x )log(a x ) +--R + +--R 2 2 2 2 2 2 2 2 n 2 3 n - 1 +--R (9n x log(x) + 18n x log(a)log(x) + 9x log(a) - 2n x )x + 2n x x +--R / +--R n +--R 9x +--R Type: Expression(Integer) +--E 45 + +--S 46 of 500 +t0009:= x^3*log(a*x^n)^2 +--R +--R +--R 3 n 2 +--R (46) x log(a x ) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0009:= 1/32*x^4*(n^2-4*n*log(a*x^n)+8*log(a*x^n)^2) +--R +--R +--R 4 n 2 4 n 2 4 +--R 8x log(a x ) - 4n x log(a x ) + n x +--R (47) ------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0009:= integrate(t0009,x) +--R +--R +--R (48) +--R 2 4 2 4 2 4 4 2 4 2 4 +--R 8n x log(x) + (16n x log(a) - 4n x )log(x) + 8x log(a) - 4n x log(a) + n x +--R ----------------------------------------------------------------------------- +--R 32 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0009:= a0009-r0009 +--R +--R +--R (49) +--R 4 n 2 4 n 2 4 2 +--R - 2x log(a x ) + n x log(a x ) + 2n x log(x) +--R + +--R 4 2 4 4 2 4 +--R (4n x log(a) - n x )log(x) + 2x log(a) - n x log(a) +--R / +--R 8 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0009:= D(m0009,x) +--R +--R +--R (50) +--R 3 n n 2 3 n 4 n - 1 n +--R - 8x x log(a x ) + (4n x x - 4n x x )log(a x ) +--R + +--R 2 3 2 3 3 2 2 3 n 2 4 n - 1 +--R (8n x log(x) + 16n x log(a)log(x) + 8x log(a) - n x )x + n x x +--R / +--R n +--R 8x +--R Type: Expression(Integer) +--E 50 + +--S 51 of 500 +t0000:= log(a*x^n)^2/x^2 +--R +--R +--R n 2 +--R log(a x ) +--R (51) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0000:= -1/x*(2*n^2+2*n*log(a*x^n)+log(a*x^n)^2) +--R +--R +--R n 2 n 2 +--R - log(a x ) - 2n log(a x ) - 2n +--R (52) --------------------------------- +--R x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0000:= integrate(t0000,x) +--R +--R +--R 2 2 2 2 2 +--R - n log(x) + (- 2n log(a) - 2n )log(x) - log(a) - 2n log(a) - 2n +--R (53) ------------------------------------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0000:= a0000-r0000 +--R +--R +--R (54) +--R n 2 n 2 2 2 +--R log(a x ) + 2n log(a x ) - n log(x) + (- 2n log(a) - 2n )log(x) +--R + +--R 2 +--R - log(a) - 2n log(a) +--R / +--R x +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0000:= D(m0000,x) +--R +--R +--R (55) +--R n n 2 n n - 1 n +--R - x log(a x ) + (- 2n x + 2n x x )log(a x ) +--R + +--R 2 2 2 2 n 2 n - 1 +--R (n log(x) + 2n log(a)log(x) + log(a) - 2n )x + 2n x x +--R / +--R 2 n +--R x x +--R Type: Expression(Integer) +--E 55 + +--S 56 of 500 +t0011:= log(a*x^n)^2/x^3 +--R +--R +--R n 2 +--R log(a x ) +--R (56) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0011:= -1/4/x^2*(n^2+2*n*log(a*x^n)+2*log(a*x^n)^2) +--R +--R +--R n 2 n 2 +--R - 2log(a x ) - 2n log(a x ) - n +--R (57) --------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0011:= integrate(t0011,x) +--R +--R +--R 2 2 2 2 2 +--R - 2n log(x) + (- 4n log(a) - 2n )log(x) - 2log(a) - 2n log(a) - n +--R (58) -------------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0011:= a0011-r0011 +--R +--R +--R (59) +--R n 2 n 2 2 2 2 +--R log(a x ) + n log(a x ) - n log(x) + (- 2n log(a) - n )log(x) - log(a) +--R + +--R - n log(a) +--R / +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0011:= D(m0011,x) +--R +--R +--R (60) +--R n n 2 n n - 1 n +--R - 2x log(a x ) + (- 2n x + 2n x x )log(a x ) +--R + +--R 2 2 2 2 n 2 n - 1 +--R (2n log(x) + 4n log(a)log(x) + 2log(a) - n )x + n x x +--R / +--R 3 n +--R 2x x +--R Type: Expression(Integer) +--E 60 + +--S 61 of 500 +t0012:= x^m*log(a*x^n)^2 +--R +--R +--R m n 2 +--R (61) x log(a x ) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0012:= 2*n^2*x^(1+m)/(1+m)^3-2*n*x^(1+m)*log(a*x^n)/(1+m)^2+_ + x^(1+m)*log(a*x^n)^2/(1+m) +--R +--R +--R (62) +--R 2 m + 1 n 2 m + 1 n 2 m + 1 +--R (m + 2m + 1)x log(a x ) + (- 2m - 2)n x log(a x ) + 2n x +--R ----------------------------------------------------------------------- +--R 3 2 +--R m + 3m + 3m + 1 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0012:= integrate(t0012,x) +--R +--R +--R (63) +--R 2 2 2 +--R (m + 2m + 1)n x log(x) +--R + +--R 2 2 +--R ((2m + 4m + 2)n x log(a) + (- 2m - 2)n x)log(x) +--R + +--R 2 2 2 +--R (m + 2m + 1)x log(a) + (- 2m - 2)n x log(a) + 2n x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 3m + 3m + 1 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0012:= a0012-r0012 +--R +--R +--R (64) +--R 2 m + 1 n 2 m + 1 n +--R (- m - 2m - 1)x log(a x ) + (2m + 2)n x log(a x ) +--R + +--R 2 2 2 +--R (m + 2m + 1)n x log(x) +--R + +--R 2 2 +--R ((2m + 4m + 2)n x log(a) + (- 2m - 2)n x)log(x) +--R + +--R 2 2 2 +--R (m + 2m + 1)x log(a) + (- 2m - 2)n x log(a) + 2n x +--R * +--R m log(x) +--R %e +--R + +--R 2 m + 1 +--R - 2n x +--R / +--R 3 2 +--R m + 3m + 3m + 1 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0012:= D(m0012,x) +--R +--R +--R (65) +--R 2 m n n 2 +--R (- m - 2m - 1)x x log(a x ) +--R + +--R m n m + 1 n - 1 n +--R ((2m + 2)n x x + (- 2m - 2)n x x )log(a x ) +--R + +--R 2 2 2 2 +--R (m + 2m + 1)n log(x) + (2m + 4m + 2)n log(a)log(x) +--R + +--R 2 2 +--R (m + 2m + 1)log(a) +--R * +--R n m log(x) +--R x %e +--R + +--R 2 m n 2 m + 1 n - 1 +--R - 2n x x + 2n x x +--R / +--R 2 n +--R (m + 2m + 1)x +--R Type: Expression(Integer) +--E 65 + +--S 66 of 500 +t0013:= x^m*log(a*x)^3 +--R +--R +--R 3 m +--R (66) log(a x) x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0013:= -6*x^(1+m)/(1+m)^4+6*x^(1+m)*log(a*x)/(1+m)^3-_ + 3*x^(1+m)*log(a*x)^2/(1+m)^2+x^(1+m)*log(a*x)^3/(1+m) +--R +--R +--R (67) +--R 3 2 3 2 2 +--R (m + 3m + 3m + 1)log(a x) + (- 3m - 6m - 3)log(a x) +--R + +--R (6m + 6)log(a x) - 6 +--R * +--R m + 1 +--R x +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0013:= integrate(t0013,x) +--R +--R +--R (68) +--R 3 2 3 +--R (m + 3m + 3m + 1)x log(x) +--R + +--R 3 2 2 2 +--R ((3m + 9m + 9m + 3)x log(a) + (- 3m - 6m - 3)x)log(x) +--R + +--R 3 2 2 2 +--R (3m + 9m + 9m + 3)x log(a) + (- 6m - 12m - 6)x log(a) +--R + +--R (6m + 6)x +--R * +--R log(x) +--R + +--R 3 2 3 2 2 +--R (m + 3m + 3m + 1)x log(a) + (- 3m - 6m - 3)x log(a) +--R + +--R (6m + 6)x log(a) - 6x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0013:= a0013-r0013 +--R +--R +--R (69) +--R 3 2 3 +--R (m + 3m + 3m + 1)x log(x) +--R + +--R 3 2 2 2 +--R ((3m + 9m + 9m + 3)x log(a) + (- 3m - 6m - 3)x)log(x) +--R + +--R 3 2 2 2 +--R (3m + 9m + 9m + 3)x log(a) + (- 6m - 12m - 6)x log(a) +--R + +--R (6m + 6)x +--R * +--R log(x) +--R + +--R 3 2 3 2 2 +--R (m + 3m + 3m + 1)x log(a) + (- 3m - 6m - 3)x log(a) +--R + +--R (6m + 6)x log(a) - 6x +--R * +--R m log(x) +--R %e +--R + +--R 3 2 3 2 2 +--R (- m - 3m - 3m - 1)log(a x) + (3m + 6m + 3)log(a x) +--R + +--R (- 6m - 6)log(a x) + 6 +--R * +--R m + 1 +--R x +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0013:= D(m0013,x) +--R +--R +--R (70) +--R 3 2 3 3 2 2 +--R (m + 3m + 3m + 1)x log(x) + (3m + 9m + 9m + 3)x log(a)log(x) +--R + +--R 3 2 2 3 2 3 +--R (3m + 9m + 9m + 3)x log(a) log(x) + (m + 3m + 3m + 1)x log(a) +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m + 1 +--R ((- 3m - 6m - 3)log(a x) + (6m + 6)log(a x) - 6)x +--R + +--R 3 2 3 2 2 +--R (- m - 3m - 3m - 1)x log(a x) + (3m + 6m + 3)x log(a x) +--R + +--R (- 6m - 6)x log(a x) + 6x +--R * +--R m +--R x +--R / +--R 3 2 +--R (m + 3m + 3m + 1)x +--R Type: Expression(Integer) +--E 70 + +--S 71 of 500 +t0014:= log(a*x^n)^3 +--R +--R +--R n 3 +--R (71) log(a x ) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0014:= x*(-6*n^3+6*n^2*log(a*x^n)-3*n*log(a*x^n)^2+log(a*x^n)^3) +--R +--R +--R n 3 n 2 2 n 3 +--R (72) x log(a x ) - 3n x log(a x ) + 6n x log(a x ) - 6n x +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0014:= integrate(t0014,x) +--R +--R +--R (73) +--R 3 3 2 3 2 +--R n x log(x) + (3n x log(a) - 3n x)log(x) +--R + +--R 2 2 3 3 2 +--R (3n x log(a) - 6n x log(a) + 6n x)log(x) + x log(a) - 3n x log(a) +--R + +--R 2 3 +--R 6n x log(a) - 6n x +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0014:= a0014-r0014 +--R +--R +--R (74) +--R n 3 n 2 2 n 3 3 +--R - x log(a x ) + 3n x log(a x ) - 6n x log(a x ) + n x log(x) +--R + +--R 2 3 2 2 2 3 +--R (3n x log(a) - 3n x)log(x) + (3n x log(a) - 6n x log(a) + 6n x)log(x) +--R + +--R 3 2 2 +--R x log(a) - 3n x log(a) + 6n x log(a) +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0014:= D(m0014,x) +--R +--R +--R (75) +--R n n 3 n n - 1 n 2 +--R - x log(a x ) + (3n x - 3n x x )log(a x ) +--R + +--R 2 n 2 n - 1 n +--R (- 6n x + 6n x x )log(a x ) +--R + +--R 3 3 2 2 2 3 3 n +--R (n log(x) + 3n log(a)log(x) + 3n log(a) log(x) + log(a) + 6n )x +--R + +--R 3 n - 1 +--R - 6n x x +--R / +--R n +--R x +--R Type: Expression(Integer) +--E 75 + +--S 76 of 500 +t0015:= x*log(a*x^n)^3 +--R +--R +--R n 3 +--R (76) x log(a x ) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0015:= 1/8*x^2*(-3*n^3+6*n^2*log(a*x^n)-6*n*log(a*x^n)^2+4*log(a*x^n)^3) +--R +--R +--R 2 n 3 2 n 2 2 2 n 3 2 +--R 4x log(a x ) - 6n x log(a x ) + 6n x log(a x ) - 3n x +--R (77) -------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0015:= integrate(t0015,x) +--R +--R +--R (78) +--R 3 2 3 2 2 3 2 2 +--R 4n x log(x) + (12n x log(a) - 6n x )log(x) +--R + +--R 2 2 2 2 3 2 2 3 2 2 +--R (12n x log(a) - 12n x log(a) + 6n x )log(x) + 4x log(a) - 6n x log(a) +--R + +--R 2 2 3 2 +--R 6n x log(a) - 3n x +--R / +--R 8 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0015:= a0015-r0015 +--R +--R +--R (79) +--R 2 n 3 2 n 2 2 2 n 3 2 3 +--R - 2x log(a x ) + 3n x log(a x ) - 3n x log(a x ) + 2n x log(x) +--R + +--R 2 2 3 2 2 2 2 2 2 3 2 +--R (6n x log(a) - 3n x )log(x) + (6n x log(a) - 6n x log(a) + 3n x )log(x) +--R + +--R 2 3 2 2 2 2 +--R 2x log(a) - 3n x log(a) + 3n x log(a) +--R / +--R 4 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0015:= D(m0015,x) +--R +--R +--R (80) +--R n n 3 n 2 n - 1 n 2 +--R - 4x x log(a x ) + (6n x x - 6n x x )log(a x ) +--R + +--R 2 n 2 2 n - 1 n +--R (- 6n x x + 6n x x )log(a x ) +--R + +--R 3 3 2 2 2 3 +--R 4n x log(x) + 12n x log(a)log(x) + 12n x log(a) log(x) + 4x log(a) +--R + +--R 3 +--R 3n x +--R * +--R n +--R x +--R + +--R 3 2 n - 1 +--R - 3n x x +--R / +--R n +--R 4x +--R Type: Expression(Integer) +--E 80 + +--S 81 of 500 +t0016:= x^2*log(a*x^n)^3 +--R +--R +--R 2 n 3 +--R (81) x log(a x ) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0016:= 1/27*x^3*(-2*n^3+6*n^2*log(a*x^n)-9*n*log(a*x^n)^2+9*log(a*x^n)^3) +--R +--R +--R 3 n 3 3 n 2 2 3 n 3 3 +--R 9x log(a x ) - 9n x log(a x ) + 6n x log(a x ) - 2n x +--R (82) -------------------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0016:= integrate(t0016,x) +--R +--R +--R (83) +--R 3 3 3 2 3 3 3 2 +--R 9n x log(x) + (27n x log(a) - 9n x )log(x) +--R + +--R 3 2 2 3 3 3 3 3 3 2 +--R (27n x log(a) - 18n x log(a) + 6n x )log(x) + 9x log(a) - 9n x log(a) +--R + +--R 2 3 3 3 +--R 6n x log(a) - 2n x +--R / +--R 27 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0016:= a0016-r0016 +--R +--R +--R (84) +--R 3 n 3 3 n 2 2 3 n 3 3 3 +--R - 3x log(a x ) + 3n x log(a x ) - 2n x log(a x ) + 3n x log(x) +--R + +--R 2 3 3 3 2 3 2 2 3 3 3 +--R (9n x log(a) - 3n x )log(x) + (9n x log(a) - 6n x log(a) + 2n x )log(x) +--R + +--R 3 3 3 2 2 3 +--R 3x log(a) - 3n x log(a) + 2n x log(a) +--R / +--R 9 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0016:= D(m0016,x) +--R +--R +--R (85) +--R 2 n n 3 2 n 3 n - 1 n 2 +--R - 9x x log(a x ) + (9n x x - 9n x x )log(a x ) +--R + +--R 2 2 n 2 3 n - 1 n +--R (- 6n x x + 6n x x )log(a x ) +--R + +--R 3 2 3 2 2 2 2 2 2 3 +--R 9n x log(x) + 27n x log(a)log(x) + 27n x log(a) log(x) + 9x log(a) +--R + +--R 3 2 +--R 2n x +--R * +--R n +--R x +--R + +--R 3 3 n - 1 +--R - 2n x x +--R / +--R n +--R 9x +--R Type: Expression(Integer) +--E 85 + +--S 86 of 500 +t0017:= x^3*log(a*x^n)^3 +--R +--R +--R 3 n 3 +--R (86) x log(a x ) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0017:= 1/128*x^4*(-3*n^3+12*n^2*log(a*x^n)-24*n*log(a*x^n)^2+32*log(a*x^n)^3) +--R +--R +--R 4 n 3 4 n 2 2 4 n 3 4 +--R 32x log(a x ) - 24n x log(a x ) + 12n x log(a x ) - 3n x +--R (87) ----------------------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0017:= integrate(t0017,x) +--R +--R +--R (88) +--R 3 4 3 2 4 3 4 2 +--R 32n x log(x) + (96n x log(a) - 24n x )log(x) +--R + +--R 4 2 2 4 3 4 4 3 +--R (96n x log(a) - 48n x log(a) + 12n x )log(x) + 32x log(a) +--R + +--R 4 2 2 4 3 4 +--R - 24n x log(a) + 12n x log(a) - 3n x +--R / +--R 128 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0017:= a0017-r0017 +--R +--R +--R (89) +--R 4 n 3 4 n 2 2 4 n 3 4 3 +--R - 8x log(a x ) + 6n x log(a x ) - 3n x log(a x ) + 8n x log(x) +--R + +--R 2 4 3 4 2 +--R (24n x log(a) - 6n x )log(x) +--R + +--R 4 2 2 4 3 4 4 3 4 2 +--R (24n x log(a) - 12n x log(a) + 3n x )log(x) + 8x log(a) - 6n x log(a) +--R + +--R 2 4 +--R 3n x log(a) +--R / +--R 32 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0017:= D(m0017,x) +--R +--R +--R (90) +--R 3 n n 3 3 n 4 n - 1 n 2 +--R - 32x x log(a x ) + (24n x x - 24n x x )log(a x ) +--R + +--R 2 3 n 2 4 n - 1 n +--R (- 12n x x + 12n x x )log(a x ) +--R + +--R 3 3 3 2 3 2 3 2 +--R 32n x log(x) + 96n x log(a)log(x) + 96n x log(a) log(x) +--R + +--R 3 3 3 3 +--R 32x log(a) + 3n x +--R * +--R n +--R x +--R + +--R 3 4 n - 1 +--R - 3n x x +--R / +--R n +--R 32x +--R Type: Expression(Integer) +--E 90 + +--S 91 of 500 +t0018:= log(a*x^n)^3/x^2 +--R +--R +--R n 3 +--R log(a x ) +--R (91) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0018:= -1/x*(6*n^3+6*n^2*log(a*x^n)+3*n*log(a*x^n)^2+log(a*x^n)^3) +--R +--R +--R n 3 n 2 2 n 3 +--R - log(a x ) - 3n log(a x ) - 6n log(a x ) - 6n +--R (92) ------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0018:= integrate(t0018,x) +--R +--R +--R (93) +--R 3 3 2 3 2 +--R - n log(x) + (- 3n log(a) - 3n )log(x) +--R + +--R 2 2 3 3 2 2 +--R (- 3n log(a) - 6n log(a) - 6n )log(x) - log(a) - 3n log(a) - 6n log(a) +--R + +--R 3 +--R - 6n +--R / +--R x +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0018:= a0018-r0018 +--R +--R +--R (94) +--R n 3 n 2 2 n 3 3 +--R log(a x ) + 3n log(a x ) + 6n log(a x ) - n log(x) +--R + +--R 2 3 2 2 2 3 +--R (- 3n log(a) - 3n )log(x) + (- 3n log(a) - 6n log(a) - 6n )log(x) +--R + +--R 3 2 2 +--R - log(a) - 3n log(a) - 6n log(a) +--R / +--R x +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0018:= D(m0018,x) +--R +--R +--R (95) +--R n n 3 n n - 1 n 2 +--R - x log(a x ) + (- 3n x + 3n x x )log(a x ) +--R + +--R 2 n 2 n - 1 n +--R (- 6n x + 6n x x )log(a x ) +--R + +--R 3 3 2 2 2 3 3 n +--R (n log(x) + 3n log(a)log(x) + 3n log(a) log(x) + log(a) - 6n )x +--R + +--R 3 n - 1 +--R 6n x x +--R / +--R 2 n +--R x x +--R Type: Expression(Integer) +--E 95 + +--S 96 of 500 +t0019:= log(a*x^n)^3/x^3 +--R +--R +--R n 3 +--R log(a x ) +--R (96) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0019:= -1/8/x^2*(3*n^3+6*n^2*log(a*x^n)+6*n*log(a*x^n)^2+4*log(a*x^n)^3) +--R +--R +--R n 3 n 2 2 n 3 +--R - 4log(a x ) - 6n log(a x ) - 6n log(a x ) - 3n +--R (97) -------------------------------------------------- +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0019:= integrate(t0019,x) +--R +--R +--R (98) +--R 3 3 2 3 2 +--R - 4n log(x) + (- 12n log(a) - 6n )log(x) +--R + +--R 2 2 3 3 2 +--R (- 12n log(a) - 12n log(a) - 6n )log(x) - 4log(a) - 6n log(a) +--R + +--R 2 3 +--R - 6n log(a) - 3n +--R / +--R 2 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0019:= a0019-r0019 +--R +--R +--R (99) +--R n 3 n 2 2 n 3 3 +--R 2log(a x ) + 3n log(a x ) + 3n log(a x ) - 2n log(x) +--R + +--R 2 3 2 2 2 3 +--R (- 6n log(a) - 3n )log(x) + (- 6n log(a) - 6n log(a) - 3n )log(x) +--R + +--R 3 2 2 +--R - 2log(a) - 3n log(a) - 3n log(a) +--R / +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0019:= D(m0019,x) +--R +--R +--R (100) +--R n n 3 n n - 1 n 2 +--R - 4x log(a x ) + (- 6n x + 6n x x )log(a x ) +--R + +--R 2 n 2 n - 1 n +--R (- 6n x + 6n x x )log(a x ) +--R + +--R 3 3 2 2 2 3 3 n +--R (4n log(x) + 12n log(a)log(x) + 12n log(a) log(x) + 4log(a) - 3n )x +--R + +--R 3 n - 1 +--R 3n x x +--R / +--R 3 n +--R 4x x +--R Type: Expression(Integer) +--E 100 + +--S 101 of 500 +t0020:= x^m*log(a*x^n)^3 +--R +--R +--R m n 3 +--R (101) x log(a x ) +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0020:= -6*n^3*x^(1+m)/(1+m)^4+6*n^2*x^(1+m)*log(a*x^n)/(1+m)^3-_ + 3*n*x^(1+m)*log(a*x^n)^2/(1+m)^2+x^(1+m)*log(a*x^n)^3/(1+m) +--R +--R +--R (102) +--R 3 2 m + 1 n 3 2 m + 1 n 2 +--R (m + 3m + 3m + 1)x log(a x ) + (- 3m - 6m - 3)n x log(a x ) +--R + +--R 2 m + 1 n 3 m + 1 +--R (6m + 6)n x log(a x ) - 6n x +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0020:= integrate(t0020,x) +--R +--R +--R (103) +--R 3 2 3 3 +--R (m + 3m + 3m + 1)n x log(x) +--R + +--R 3 2 2 2 3 2 +--R ((3m + 9m + 9m + 3)n x log(a) + (- 3m - 6m - 3)n x)log(x) +--R + +--R 3 2 2 2 2 +--R (3m + 9m + 9m + 3)n x log(a) + (- 6m - 12m - 6)n x log(a) +--R + +--R 3 +--R (6m + 6)n x +--R * +--R log(x) +--R + +--R 3 2 3 2 2 +--R (m + 3m + 3m + 1)x log(a) + (- 3m - 6m - 3)n x log(a) +--R + +--R 2 3 +--R (6m + 6)n x log(a) - 6n x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0020:= a0020-r0020 +--R +--R +--R (104) +--R 3 2 m + 1 n 3 2 m + 1 n 2 +--R (- m - 3m - 3m - 1)x log(a x ) + (3m + 6m + 3)n x log(a x ) +--R + +--R 2 m + 1 n +--R (- 6m - 6)n x log(a x ) +--R + +--R 3 2 3 3 +--R (m + 3m + 3m + 1)n x log(x) +--R + +--R 3 2 2 2 3 2 +--R ((3m + 9m + 9m + 3)n x log(a) + (- 3m - 6m - 3)n x)log(x) +--R + +--R 3 2 2 2 2 +--R (3m + 9m + 9m + 3)n x log(a) + (- 6m - 12m - 6)n x log(a) +--R + +--R 3 +--R (6m + 6)n x +--R * +--R log(x) +--R + +--R 3 2 3 2 2 +--R (m + 3m + 3m + 1)x log(a) + (- 3m - 6m - 3)n x log(a) +--R + +--R 2 3 +--R (6m + 6)n x log(a) - 6n x +--R * +--R m log(x) +--R %e +--R + +--R 3 m + 1 +--R 6n x +--R / +--R 4 3 2 +--R m + 4m + 6m + 4m + 1 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0020:= D(m0020,x) +--R +--R +--R (105) +--R 3 2 m n n 3 +--R (- m - 3m - 3m - 1)x x log(a x ) +--R + +--R 2 m n 2 m + 1 n - 1 n 2 +--R ((3m + 6m + 3)n x x + (- 3m - 6m - 3)n x x )log(a x ) +--R + +--R 2 m n 2 m + 1 n - 1 n +--R ((- 6m - 6)n x x + (6m + 6)n x x )log(a x ) +--R + +--R 3 2 3 3 3 2 2 2 +--R (m + 3m + 3m + 1)n log(x) + (3m + 9m + 9m + 3)n log(a)log(x) +--R + +--R 3 2 2 3 2 3 +--R (3m + 9m + 9m + 3)n log(a) log(x) + (m + 3m + 3m + 1)log(a) +--R * +--R n m log(x) +--R x %e +--R + +--R 3 m n 3 m + 1 n - 1 +--R 6n x x - 6n x x +--R / +--R 3 2 n +--R (m + 3m + 3m + 1)x +--R Type: Expression(Integer) +--E 105 + +--S 106 of 500 +t0021:= 1/log(a*x) +--R +--R +--R 1 +--R (106) -------- +--R log(a x) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0021:= li(a*x)/a +--R +--R +--R li(a x) +--R (107) ------- +--R a +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0021:= integrate(t0021,x) +--R +--R +--R li(a x) +--R (108) ------- +--R a +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0021:= a0021-r0021 +--R +--R +--R (109) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0021:= D(m0021,x) +--R +--R +--R (110) 0 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 500 +t0022:= x^m/log(a*x) +--R +--R +--R m +--R x +--R (111) -------- +--R log(a x) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0022:= x^m/a*(a*x)^(-m)*Ei((1+m)*log(a*x)) +--R +--R +--R m - m +--R x (a x) Ei((m + 1)log(a x)) +--R (112) ----------------------------- +--R a +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0022:= integrate(t0022,x) +--R +--R +--R x m +--R ++ %D +--R (113) | --------- d%D +--R ++ log(%D a) +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +--m0022:= a0022-r0022 +--E 114 + +--S 115 of 500 +--d0022:= D(m0022,x) +--E 115 + +--S 116 of 500 +t0023:= 1/log(a*x^n) +--R +--R +--R 1 +--R (114) --------- +--R n +--R log(a x ) +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0023:= x*Ei(log(a*x^n)/n)/n/((a*x^n)^(1/n)) +--R +--R +--R n +--R log(a x ) +--R x Ei(---------) +--R n +--R (115) --------------- +--R 1 +--R - +--R n n +--R n (a x ) +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0023:= integrate(t0023,x) +--R +--R +--R x +--R ++ 1 +--R (116) | ---------- d%D +--R ++ n +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +--m0023:= a0023-r0023 +--E 119 + +--S 120 of 500 +--d0023:= D(m0023,x) +--E 120 + +--S 121 of 500 +t0024:= x/log(a*x^n) +--R +--R +--R x +--R (117) --------- +--R n +--R log(a x ) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0024:= x^2*Ei(2*log(a*x^n)/n)/n*(a*x^n)^(-2/n) +--R +--R +--R 2 +--R - - n +--R 2 n n 2log(a x ) +--R x (a x ) Ei(----------) +--R n +--R (118) ------------------------- +--R n +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +--a0024:= integrate(t0024,x) +--E 123 + +--S 124 of 500 +--m0024:= a0024-r0024 +--E 124 + +--S 125 of 500 +d0024:= D(m0024,x) +--R +--R +--R (119) 0 +--R Type: Polynomial(Integer) +--E 125 + +--S 126 of 500 +t0025:= x^2/log(a*x^n) +--R +--R +--R 2 +--R x +--R (120) --------- +--R n +--R log(a x ) +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0025:= x^3*Ei(3*log(a*x^n)/n)/n*(a*x^n)^(-3/n) +--R +--R +--R 3 +--R - - n +--R 3 n n 3log(a x ) +--R x (a x ) Ei(----------) +--R n +--R (121) ------------------------- +--R n +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0025:= integrate(t0025,x) +--R +--R +--R x 2 +--R ++ %D +--R (122) | ---------- d%D +--R ++ n +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +--m0025:= a0025-r0025 +--E 129 + +--S 130 of 500 +--d0025:= D(m0025,x) +--E 130 + +--S 131 of 500 +t0026:= x^3/log(a*x^n) +--R +--R +--R 3 +--R x +--R (123) --------- +--R n +--R log(a x ) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0026:= x^4*Ei(4*log(a*x^n)/n)/n*(a*x^n)^(-4/n) +--R +--R +--R 4 +--R - - n +--R 4 n n 4log(a x ) +--R x (a x ) Ei(----------) +--R n +--R (124) ------------------------- +--R n +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0026:= integrate(t0026,x) +--R +--R +--R x 3 +--R ++ %D +--R (125) | ---------- d%D +--R ++ n +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +--m0026:= a0026-r0026 +--E 134 + +--S 135 of 500 +--d0026:= D(m0026,x) +--E 135 + +--S 136 of 500 +t0027:= 1/x^2/log(a*x^n) +--R +--R +--R 1 +--R (126) ----------- +--R 2 n +--R x log(a x ) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0027:= (a*x^n)^(1/n)*Ei(-log(a*x^n)/n)/n/x +--R +--R +--R 1 +--R - n +--R n n log(a x ) +--R (a x ) Ei(- ---------) +--R n +--R (127) ---------------------- +--R n x +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0027:= integrate(t0027,x) +--R +--R +--R x +--R ++ 1 +--R (128) | ------------- d%D +--R ++ 2 n +--R %D log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +--m0027:= a0027-r0027 +--E 139 + +--S 140 of 500 +--d0027:= D(m0027,x) +--E 140 + +--S 141 of 500 +t0028:= 1/x^3/log(a*x^n) +--R +--R +--R 1 +--R (129) ----------- +--R 3 n +--R x log(a x ) +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0028:= (a*x^n)^(2/n)*Ei(-2*log(a*x^n)/n)/n/x^2 +--R +--R +--R 2 +--R - n +--R n n 2log(a x ) +--R (a x ) Ei(- ----------) +--R n +--R (130) ----------------------- +--R 2 +--R n x +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0028:= integrate(t0028,x) +--R +--R +--R x +--R ++ 1 +--R (131) | ------------- d%D +--R ++ 3 n +--R %D log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +--m0028:= a0028-r0028 +--E 144 + +--S 145 of 500 +--d0028:= D(m0028,x) +--E 145 + +--S 146 of 500 +t0029:= x^m/log(a*x^n) +--R +--R +--R m +--R x +--R (132) --------- +--R n +--R log(a x ) +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0029:= x^(1+m)*Ei((1+m)*log(a*x^n)/n)/n*(a*x^n)^(-(1+m)/n) +--R +--R +--R - m - 1 +--R ------- n +--R m + 1 n n (m + 1)log(a x ) +--R x (a x ) Ei(----------------) +--R n +--R (133) --------------------------------------- +--R n +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0029:= integrate(t0029,x) +--R +--R +--R x m +--R ++ %D +--R (134) | ---------- d%D +--R ++ n +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +--m0029:= a0029-r0029 +--E 149 + +--S 150 of 500 +--d0029:= D(m0029,x) +--E 150 + +--S 151 of 500 +t0030:= x^m/log(c*(a*x^n)^p) +--R +--R +--R m +--R x +--R (135) -------------- +--R n p +--R log(c (a x ) ) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0030:= x^(1+m)*Ei((1+m)*log(c*(a*x^n)^p)/n/p)*(c*(a*x^n)^p)^(-(1+m)/n/p)/n/p +--R +--R +--R - m - 1 +--R ------- n p +--R m + 1 n p n p (m + 1)log(c (a x ) ) +--R x (c (a x ) ) Ei(---------------------) +--R n p +--R (136) ------------------------------------------------- +--R n p +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0030:= integrate(t0030,x) +--R +--R +--R x m +--R ++ %D +--R (137) | --------------- d%D +--R ++ n p +--R log(c (a %D ) ) +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +--m0030:= a0030-r0030 +--E 154 + +--S 155 of 500 +--d0030:= D(m0030,x) +--E 155 + +--S 156 of 500 +t0031:= x^m/log(a*x)^2 +--R +--R +--R m +--R x +--R (138) --------- +--R 2 +--R log(a x) +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0031:= (1+m)*x^(1+m)*(a*x)^(-1-m)*Ei((1+m)*log(a*x))-x^(1+m)/log(a*x) +--R +--R +--R m + 1 - m - 1 m + 1 +--R (m + 1)log(a x)x (a x) Ei((m + 1)log(a x)) - x +--R (139) ------------------------------------------------------------- +--R log(a x) +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0031:= integrate(t0031,x) +--R +--R +--R x m +--R ++ %D +--R (140) | ---------- d%D +--R ++ 2 +--R log(%D a) +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +--m0031:= a0031-r0031 +--E 159 + +--S 160 of 500 +--d0031:= D(m0031,x) +--E 160 + +--S 161 of 500 +t0032:= 1/log(a*x^n)^2 +--R +--R +--R 1 +--R (141) ---------- +--R n 2 +--R log(a x ) +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0032:= x*Ei(log(a*x^n)/n)/((a*x^n)^(1/n))/n^2-x/n/log(a*x^n) +--R +--R +--R 1 +--R n - +--R n log(a x ) n n +--R x log(a x )Ei(---------) - n x (a x ) +--R n +--R (142) -------------------------------------- +--R 1 +--R - +--R 2 n n n +--R n log(a x )(a x ) +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0032:= integrate(t0032,x) +--R +--R +--R x +--R ++ 1 +--R (143) | ----------- d%D +--R ++ n 2 +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +--m0032:= a0032-r0032 +--E 164 + +--S 165 of 500 +--d0032:= D(m0032,x) +--E 165 + +--S 166 of 500 +t0033:= x/log(a*x^n)^2 +--R +--R +--R x +--R (144) ---------- +--R n 2 +--R log(a x ) +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0033:= 2*x^2*Ei(2*log(a*x^n)/n)/((a*x^n)^(2/n))/n^2-x^2/n/log(a*x^n) +--R +--R +--R 2 +--R n - +--R 2 n 2log(a x ) 2 n n +--R 2x log(a x )Ei(----------) - n x (a x ) +--R n +--R (145) ---------------------------------------- +--R 2 +--R - +--R 2 n n n +--R n log(a x )(a x ) +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0033:= integrate(t0033,x) +--R +--R +--R x +--R ++ %D +--R (146) | ----------- d%D +--R ++ n 2 +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +--m0033:= a0033-r0033 +--E 169 + +--S 170 of 500 +--d0033:= D(m0033,x) +--E 170 + +--S 171 of 500 +t0034:= x^2/log(a*x^n)^2 +--R +--R +--R 2 +--R x +--R (147) ---------- +--R n 2 +--R log(a x ) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0034:= 3*x^3*Ei(3*log(a*x^n)/n)/((a*x^n)^(3/n))/n^2-x^3/n/log(a*x^n) +--R +--R +--R 3 +--R n - +--R 3 n 3log(a x ) 3 n n +--R 3x log(a x )Ei(----------) - n x (a x ) +--R n +--R (148) ---------------------------------------- +--R 3 +--R - +--R 2 n n n +--R n log(a x )(a x ) +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0034:= integrate(t0034,x) +--R +--R +--R x 2 +--R ++ %D +--R (149) | ----------- d%D +--R ++ n 2 +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +--m0034:= a0034-r0034 +--E 174 + +--S 175 of 500 +--d0034:= D(m0034,x) +--E 175 + +--S 176 of 500 +t0035:= x^3/log(a*x^n)^2 +--R +--R +--R 3 +--R x +--R (150) ---------- +--R n 2 +--R log(a x ) +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0035:= 4*x^4*Ei(4*log(a*x^n)/n)/((a*x^n)^(4/n))/n^2-x^4/n/log(a*x^n) +--R +--R +--R 4 +--R n - +--R 4 n 4log(a x ) 4 n n +--R 4x log(a x )Ei(----------) - n x (a x ) +--R n +--R (151) ---------------------------------------- +--R 4 +--R - +--R 2 n n n +--R n log(a x )(a x ) +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0035:= integrate(t0035,x) +--R +--R +--R x 3 +--R ++ %D +--R (152) | ----------- d%D +--R ++ n 2 +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +--m0035:= a0035-r0035 +--E 179 + +--S 180 of 500 +--d0035:= D(m0035,x) +--E 180 + +--S 181 of 500 +t0036:= 1/x^2/log(a*x^n)^2 +--R +--R +--R 1 +--R (153) ------------ +--R 2 n 2 +--R x log(a x ) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0036:= -(a*x^n)^(1/n)*Ei(-log(a*x^n)/n)/n^2/x-1/n/x/log(a*x^n) +--R +--R +--R 1 +--R - n +--R n n n log(a x ) +--R - log(a x )(a x ) Ei(- ---------) - n +--R n +--R (154) ------------------------------------- +--R 2 n +--R n x log(a x ) +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0036:= integrate(t0036,x) +--R +--R +--R x +--R ++ 1 +--R (155) | -------------- d%D +--R ++ 2 n 2 +--R %D log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +--m0036:= a0036-r0036 +--E 184 + +--S 185 of 500 +--d0036:= D(m0036,x) +--E 185 + +--S 186 of 500 +t0037:= 1/x^3/log(a*x^n)^2 +--R +--R +--R 1 +--R (156) ------------ +--R 3 n 2 +--R x log(a x ) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0037:= -2*(a*x^n)^(2/n)*Ei(-2*log(a*x^n)/n)/n^2/x^2-1/n/x^2/log(a*x^n) +--R +--R +--R 2 +--R - n +--R n n n 2log(a x ) +--R - 2log(a x )(a x ) Ei(- ----------) - n +--R n +--R (157) --------------------------------------- +--R 2 2 n +--R n x log(a x ) +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0037:= integrate(t0037,x) +--R +--R +--R x +--R ++ 1 +--R (158) | -------------- d%D +--R ++ 3 n 2 +--R %D log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +--m0037:= a0037-r0037 +--E 189 + +--S 190 of 500 +--d0037:= D(m0037,x) +--E 190 + +--S 191 of 500 +t0038:= x^m/log(a*x^n)^2 +--R +--R +--R m +--R x +--R (159) ---------- +--R n 2 +--R log(a x ) +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0038:= (1+m)*x^(1+m)*Ei((1+m)*log(a*x^n)/n)/((a*x^n)^((1+m)/n))/n^2-_ + x^(1+m)/n/log(a*x^n) +--R +--R +--R m + 1 +--R n ----- +--R m + 1 n (m + 1)log(a x ) m + 1 n n +--R (m + 1)x log(a x )Ei(----------------) - n x (a x ) +--R n +--R (160) ---------------------------------------------------------------- +--R m + 1 +--R ----- +--R 2 n n n +--R n log(a x )(a x ) +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0038:= integrate(t0038,x) +--R +--R +--R x m +--R ++ %D +--R (161) | ----------- d%D +--R ++ n 2 +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +--m0038:= a0038-r0038 +--E 194 + +--S 195 of 500 +--d0038:= D(m0038,x) +--E 195 + +--S 196 of 500 +t0039:= x^m/log(a*x)^3 +--R +--R +--R m +--R x +--R (162) --------- +--R 3 +--R log(a x) +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0039:= 1/2*(1+m)^2*x^(1+m)*(a*x)^(-1-m)*Ei((1+m)*log(a*x))-_ + 1/2*x^(1+m)/log(a*x)^2-1/2*(1+m)*x^(1+m)/log(a*x) +--R +--R +--R (163) +--R 2 2 m + 1 - m - 1 +--R (m + 2m + 1)log(a x) x (a x) Ei((m + 1)log(a x)) +--R + +--R m + 1 +--R ((- m - 1)log(a x) - 1)x +--R / +--R 2 +--R 2log(a x) +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0039:= integrate(t0039,x) +--R +--R +--R x m +--R ++ %D +--R (164) | ---------- d%D +--R ++ 3 +--R log(%D a) +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +--m0039:= a0039-r0039 +--E 199 + +--S 200 of 500 +--d0039:= D(m0039,x) +--E 200 + +--S 201 of 500 +t0040:= 1/log(a*x^n)^3 +--R +--R +--R 1 +--R (165) ---------- +--R n 3 +--R log(a x ) +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0040:= 1/2/n^3/log(a*x^n)^2*x*(Ei(log(a*x^n)/n)*_ + (a*x^n)^(-1/n)*log(a*x^n)^2-n^2-n*log(a*x^n)) +--R +--R +--R 1 +--R - - n +--R n 2 n n log(a x ) n 2 +--R x log(a x ) (a x ) Ei(---------) - n x log(a x ) - n x +--R n +--R (166) -------------------------------------------------------- +--R 3 n 2 +--R 2n log(a x ) +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0040:= integrate(t0040,x) +--R +--R +--R x +--R ++ 1 +--R (167) | ----------- d%D +--R ++ n 3 +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +--m0040:= a0040-r0040 +--E 204 + +--S 205 of 500 +--d0040:= D(m0040,x) +--E 205 + +--S 206 of 500 +t0041:= x/log(a*x^n)^3 +--R +--R +--R x +--R (168) ---------- +--R n 3 +--R log(a x ) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0041:= 1/2/n^3/log(a*x^n)^2*x^2*(4*Ei(2*log(a*x^n)/n)*(a*x^n)^(-2/n)*_ + log(a*x^n)^2-n^2-2*n*log(a*x^n)) +--R +--R +--R 2 +--R - - n +--R 2 n 2 n n 2log(a x ) 2 n 2 2 +--R 4x log(a x ) (a x ) Ei(----------) - 2n x log(a x ) - n x +--R n +--R (169) ------------------------------------------------------------ +--R 3 n 2 +--R 2n log(a x ) +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0041:= integrate(t0041,x) +--R +--R +--R x +--R ++ %D +--R (170) | ----------- d%D +--R ++ n 3 +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +--m0041:= a0041-r0041 +--E 209 + +--S 210 of 500 +--d0041:= D(m0041,x) +--E 210 + +--S 211 of 500 +t0042:= x^2/log(a*x^n)^3 +--R +--R +--R 2 +--R x +--R (171) ---------- +--R n 3 +--R log(a x ) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0042:= 1/2/n^3/log(a*x^n)^2*x^3*(9*Ei(3*log(a*x^n)/n)*(a*x^n)^(-3/n)*_ + log(a*x^n)^2-n^2-3*n*log(a*x^n)) +--R +--R +--R 3 +--R - - n +--R 3 n 2 n n 3log(a x ) 3 n 2 3 +--R 9x log(a x ) (a x ) Ei(----------) - 3n x log(a x ) - n x +--R n +--R (172) ------------------------------------------------------------ +--R 3 n 2 +--R 2n log(a x ) +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0042:= integrate(t0042,x) +--R +--R +--R x 2 +--R ++ %D +--R (173) | ----------- d%D +--R ++ n 3 +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +--m0042:= a0042-r0042 +--E 214 + +--S 215 of 500 +--d0042:= D(m0042,x) +--E 215 + +--S 216 of 500 +t0043:= x^3/log(a*x^n)^3 +--R +--R +--R 3 +--R x +--R (174) ---------- +--R n 3 +--R log(a x ) +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0043:= 1/2/n^3/log(a*x^n)^2*x^4*(16*Ei(4*log(a*x^n)/n)*(a*x^n)^(-4/n)*_ + log(a*x^n)^2-n^2-4*n*log(a*x^n)) +--R +--R +--R 4 +--R - - n +--R 4 n 2 n n 4log(a x ) 4 n 2 4 +--R 16x log(a x ) (a x ) Ei(----------) - 4n x log(a x ) - n x +--R n +--R (175) ------------------------------------------------------------- +--R 3 n 2 +--R 2n log(a x ) +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0043:= integrate(t0043,x) +--R +--R +--R x 3 +--R ++ %D +--R (176) | ----------- d%D +--R ++ n 3 +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +--m0043:= a0043-r0043 +--E 219 + +--S 220 of 500 +--d0043:= D(m0043,x) +--E 220 + +--S 221 of 500 +t0044:= 1/x^2/log(a*x^n)^3 +--R +--R +--R 1 +--R (177) ------------ +--R 2 n 3 +--R x log(a x ) +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0044:= 1/2/n^3/x/log(a*x^n)^2*((a*x^n)^(1/n)*Ei(-log(a*x^n)/n)*_ + log(a*x^n)^2-n^2+n*log(a*x^n)) +--R +--R +--R 1 +--R - n +--R n 2 n n log(a x ) n 2 +--R log(a x ) (a x ) Ei(- ---------) + n log(a x ) - n +--R n +--R (178) --------------------------------------------------- +--R 3 n 2 +--R 2n x log(a x ) +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0044:= integrate(t0044,x) +--R +--R +--R x +--R ++ 1 +--R (179) | -------------- d%D +--R ++ 2 n 3 +--R %D log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +--m0044:= a0044-r0044 +--E 224 + +--S 225 of 500 +--d0044:= D(m0044,x) +--E 225 + +--S 226 of 500 +t0045:= 1/x^3/log(a*x^n)^3 +--R +--R +--R 1 +--R (180) ------------ +--R 3 n 3 +--R x log(a x ) +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0045:= 2*(a*x^n)^(2/n)*Ei(-2*log(a*x^n)/n)/n^3/x^2-_ + 1/2/n/x^2/log(a*x^n)^2+1/n^2/x^2/log(a*x^n) +--R +--R +--R 2 +--R - n +--R n 2 n n 2log(a x ) n 2 +--R 4log(a x ) (a x ) Ei(- ----------) + 2n log(a x ) - n +--R n +--R (181) ------------------------------------------------------ +--R 3 2 n 2 +--R 2n x log(a x ) +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0045:= integrate(t0045,x) +--R +--R +--R x +--R ++ 1 +--R (182) | -------------- d%D +--R ++ 3 n 3 +--R %D log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +--m0045:= a0045-r0045 +--E 229 + +--S 230 of 500 +--d0045:= D(m0045,x) +--E 230 + +--S 231 of 500 +t0046:= x^m/log(a*x^n)^3 +--R +--R +--R m +--R x +--R (183) ---------- +--R n 3 +--R log(a x ) +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0046:= 1/2*(1+m)^2*x^(1+m)*Ei((1+m)*log(a*x^n)/n)/((a*x^n)^((1+m)/n))/n^3-_ + 1/2*x^(1+m)/n/log(a*x^n)^2-1/2*(1+m)*x^(1+m)/n^2/log(a*x^n) +--R +--R +--R (184) +--R n +--R 2 m + 1 n 2 (m + 1)log(a x ) +--R (m + 2m + 1)x log(a x ) Ei(----------------) +--R n +--R + +--R m + 1 +--R ----- +--R m + 1 n 2 m + 1 n n +--R ((- m - 1)n x log(a x ) - n x )(a x ) +--R / +--R m + 1 +--R ----- +--R 3 n 2 n n +--R 2n log(a x ) (a x ) +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0046:= integrate(t0046,x) +--R +--R +--R x m +--R ++ %D +--R (185) | ----------- d%D +--R ++ n 3 +--R log(a %D ) +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +--m0046:= a0046-r0046 +--E 234 + +--S 235 of 500 +--d0046:= D(m0046,x) +--E 235 + +--S 236 of 500 +t0047:= log(a*x^n)^(3/2) +--R +--R +--R +---------+ +--R n | n +--R (186) log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0047:= 1/4*x*(3*(a*x^n)^(-1/n)*n^(3/2)*%pi^(1/2)*_ + erfi(log(a*x^n)^(1/2)/n^(1/2))-6*n*log(a*x^n)^(1/2)+_ + 4*log(a*x^n)^(3/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 500 +a0047:= integrate(t0047,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 238 + +--S 239 of 500 +--m0047:= a0047-r0047 +--E 239 + +--S 240 of 500 +--d0047:= D(m0047,x) +--E 240 + +--S 241 of 500 +t0048:= x*log(a*x^n)^(3/2) +--R +--R +--R +---------+ +--R n | n +--R (187) x log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0048:= 1/32*x^2*(3*(a*x^n)^(-2/n)*n^(3/2)*2^(1/2)*%pi^(1/2)*_ + erfi(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))-12*n*log(a*x^n)^(1/2)+_ + 16*log(a*x^n)^(3/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 242 + +--S 243 of 500 +a0048:= integrate(t0048,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 243 + +--S 244 of 500 +--m0048:= a0048-r0048 +--E 244 + +--S 245 of 500 +--d0048:= D(m0048,x) +--E 245 + +--S 246 of 500 +t0049:= x^2*log(a*x^n)^(3/2) +--R +--R +--R +---------+ +--R 2 n | n +--R (188) x log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0049:= 1/36*x^3*((a*x^n)^(-3/n)*n^(3/2)*3^(1/2)*%pi^(1/2)*_ + erfi(3^(1/2)*log(a*x^n)^(1/2)/n^(1/2))-6*n*log(a*x^n)^(1/2)+_ + 12*log(a*x^n)^(3/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 247 + +--S 248 of 500 +a0049:= integrate(t0049,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 248 + +--S 249 of 500 +--m0049:= a0049-r0049 +--E 249 + +--S 250 of 500 +--d0049:= D(m0049,x) +--E 250 + +--S 251 of 500 +t0050:= x^3*log(a*x^n)^(3/2) +--R +--R +--R +---------+ +--R 3 n | n +--R (189) x log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0050:= 1/128*x^4*(3*(a*x^n)^(-4/n)*n^(3/2)*%pi^(1/2)*_ + erfi(2*log(a*x^n)^(1/2)/n^(1/2))-12*n*log(a*x^n)^(1/2)+_ + 32*log(a*x^n)^(3/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 252 + +--S 253 of 500 +a0050:= integrate(t0050,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 253 + +--S 254 of 500 +--m0050:= a0050-r0050 +--E 254 + +--S 255 of 500 +--d0050:= D(m0050,x) +--E 255 + +--S 256 of 500 +t0051:= log(a*x^n)^(3/2)/x^2 +--R +--R +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R (190) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0051:= -1/4*(-3*n^(3/2)*%pi^(1/2)*(a*x^n)^(1/n)*_ + erf(log(a*x^n)^(1/2)/n^(1/2))+6*n*log(a*x^n)^(1/2)+_ + 4*log(a*x^n)^(3/2))/x +--R +--R +--R (191) +--R 1 +---------+ +--R - | n +---------+ +--R +-+ +---+ n n \|log(a x ) n | n +--R 3n\|n \|%pi (a x ) erf(------------) + (- 4log(a x ) - 6n)\|log(a x ) +--R +-+ +--R \|n +--R ---------------------------------------------------------------------- +--R 4x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0051:= integrate(t0051,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 258 + +--S 259 of 500 +--m0051:= a0051-r0051 +--E 259 + +--S 260 of 500 +--d0051:= D(m0051,x) +--E 260 + +--S 261 of 500 +t0052:= log(a*x^n)^(3/2)/x^3 +--R +--R +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R (192) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0052:= -1/32*(-3*n^(3/2)*2^(1/2)*%pi^(1/2)*(a*x^n)^(2/n)*_ + erf(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))+12*n*log(a*x^n)^(1/2)+_ + 16*log(a*x^n)^(3/2))/x^2 +--R +--R +--R (193) +--R 2 +---------+ +--R - +-+ | n +--R +-+ +-+ +---+ n n \|2 \|log(a x ) +--R 3n\|2 \|n \|%pi (a x ) erf(----------------) +--R +-+ +--R \|n +--R + +--R +---------+ +--R n | n +--R (- 16log(a x ) - 12n)\|log(a x ) +--R / +--R 2 +--R 32x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0052:= integrate(t0052,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 263 + +--S 264 of 500 +--m0052:= a0052-r0052 +--E 264 + +--S 265 of 500 +--d0052:= D(m0052,x) +--E 265 + +--S 266 of 500 +t0053:= x^m*log(a*x^n)^(3/2) +--R +--R +--R +---------+ +--R m n | n +--R (194) x log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0053:= 3/4*n^(3/2)*%pi^(1/2)*x^(1+m)*erfi((1+m)^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^((1+m)/n))/(1+m)^(5/2)-_ + 3/2*n*x^(1+m)*log(a*x^n)^(1/2)/(1+m)^2+x^(1+m)*log(a*x^n)^(3/2)/(1+m) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 500 +a0053:= integrate(t0053,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 268 + +--S 269 of 500 +--m0053:= a0053-r0053 +--E 269 + +--S 270 of 500 +--d0053:= D(m0053,x) +--E 270 + +--S 271 of 500 +t0054:= log(a*x^n)^(1/2) +--R +--R +--R +---------+ +--R | n +--R (195) \|log(a x ) +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0054:= -1/2*n^(1/2)*%pi^(1/2)*x*erfi(log(a*x^n)^(1/2)/n^(1/2))/_ + ((a*x^n)^(1/n))+x*log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 272 + +--S 273 of 500 +a0054:= integrate(t0054,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 273 + +--S 274 of 500 +--m0054:= a0054-r0054 +--E 274 + +--S 275 of 500 +--d0054:= D(m0054,x) +--E 275 + +--S 276 of 500 +t0055:= x*log(a*x^n)^(1/2) +--R +--R +--R +---------+ +--R | n +--R (196) x\|log(a x ) +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0055:= 1/8*x^2*(-(a*x^n)^(-2/n)*n^(1/2)*2^(1/2)*%pi^(1/2)*_ + erfi(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))+4*log(a*x^n)^(1/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 277 + +--S 278 of 500 +a0055:= integrate(t0055,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 278 + +--S 279 of 500 +--m0055:= a0055-r0055 +--E 279 + +--S 280 of 500 +--d0055:= D(m0055,x) +--E 280 + +--S 281 of 500 +t0056:= x^2*log(a*x^n)^(1/2) +--R +--R +--R +---------+ +--R 2 | n +--R (197) x \|log(a x ) +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0056:= 1/18*x^3*(-(a*x^n)^(-3/n)*n^(1/2)*3^(1/2)*%pi^(1/2)*erfi(3^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))+6*log(a*x^n)^(1/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 500 +a0056:= integrate(t0056,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 283 + +--S 284 of 500 +--m0056:= a0056-r0056 +--E 284 + +--S 285 of 500 +--d0056:= D(m0056,x) +--E 285 + +--S 286 of 500 +t0057:= x^3*log(a*x^n)^(1/2) +--R +--R +--R +---------+ +--R 3 | n +--R (198) x \|log(a x ) +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0057:= 1/16*x^4*(-(a*x^n)^(-4/n)*n^(1/2)*%pi^(1/2)*_ + erfi(2*log(a*x^n)^(1/2)/n^(1/2))+4*log(a*x^n)^(1/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 287 + +--S 288 of 500 +a0057:= integrate(t0057,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 288 + +--S 289 of 500 +--m0057:= a0057-r0057 +--E 289 + +--S 290 of 500 +--d0057:= D(m0057,x) +--E 290 + +--S 291 of 500 +t0058:= log(a*x^n)^(1/2)/x^2 +--R +--R +--R +---------+ +--R | n +--R \|log(a x ) +--R (199) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0058:= -1/2*(-n^(1/2)*%pi^(1/2)*(a*x^n)^(1/n)*_ + erf(log(a*x^n)^(1/2)/n^(1/2))+2*log(a*x^n)^(1/2))/x +--R +--R +--R 1 +---------+ +--R - | n +---------+ +--R +-+ +---+ n n \|log(a x ) | n +--R \|n \|%pi (a x ) erf(------------) - 2\|log(a x ) +--R +-+ +--R \|n +--R (200) -------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0058:= integrate(t0058,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 293 + +--S 294 of 500 +--m0058:= a0058-r0058 +--E 294 + +--S 295 of 500 +--d0058:= D(m0058,x) +--E 295 + +--S 296 of 500 +t0059:= log(a*x^n)^(1/2)/x^3 +--R +--R +--R +---------+ +--R | n +--R \|log(a x ) +--R (201) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0059:= -1/8*(-n^(1/2)*2^(1/2)*%pi^(1/2)*(a*x^n)^(2/n)*_ + erf(2^(1/2)*log(a*x^n)^(1/2)/n^(1/2))+4*log(a*x^n)^(1/2))/x^2 +--R +--R +--R 2 +---------+ +--R - +-+ | n +---------+ +--R +-+ +-+ +---+ n n \|2 \|log(a x ) | n +--R \|2 \|n \|%pi (a x ) erf(----------------) - 4\|log(a x ) +--R +-+ +--R \|n +--R (202) ---------------------------------------------------------- +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0059:= integrate(t0059,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 298 + +--S 299 of 500 +--m0059:= a0059-r0059 +--E 299 + +--S 300 of 500 +--d0059:= D(m0059,x) +--E 300 + +--S 301 of 500 +t0060:= x^m*log(a*x^n)^(1/2) +--R +--R +--R +---------+ +--R m | n +--R (203) x \|log(a x ) +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0060:= 1/2*x*x^m*(-(a*x^n)^(-(1+m)/n)*n^(1/2)*%pi^(1/2)*_ + erfi((1+m)^(1/2)*log(a*x^n)^(1/2)/n^(1/2))+2*(1+m)^(1/2)*_ + log(a*x^n)^(1/2))/(1+m)^(3/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 302 + +--S 303 of 500 +a0060:= integrate(t0060,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 303 + +--S 304 of 500 +--m0060:= a0060-r0060 +--E 304 + +--S 305 of 500 +--d0060:= D(m0060,x) +--E 305 + +--S 306 of 500 +t0061:= 1/log(a*x^n)^(1/2) +--R +--R +--R 1 +--R (204) ------------ +--R +---------+ +--R | n +--R \|log(a x ) +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0061:= %pi^(1/2)*x*erfi(log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)/((a*x^n)^(1/n)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 307 + +--S 308 of 500 +a0061:= integrate(t0061,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 308 + +--S 309 of 500 +--m0061:= a0061-r0061 +--E 309 + +--S 310 of 500 +--d0061:= D(m0061,x) +--E 310 + +--S 311 of 500 +t0062:= x/log(a*x^n)^(1/2) +--R +--R +--R x +--R (205) ------------ +--R +---------+ +--R | n +--R \|log(a x ) +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0062:= 1/2*2^(1/2)*%pi^(1/2)*x^2*erfi(2^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)*(a*x^n)^(-2/n) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 312 + +--S 313 of 500 +a0062:= integrate(t0062,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 313 + +--S 314 of 500 +--m0062:= a0062-r0062 +--E 314 + +--S 315 of 500 +--d0062:= D(m0062,x) +--E 315 + +--S 316 of 500 +t0063:= x^2/log(a*x^n)^(1/2) +--R +--R +--R 2 +--R x +--R (206) ------------ +--R +---------+ +--R | n +--R \|log(a x ) +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0063:= 1/3*3^(1/2)*%pi^(1/2)*x^3*erfi(3^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)*(a*x^n)^(-3/n) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 317 + +--S 318 of 500 +a0063:= integrate(t0063,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 318 + +--S 319 of 500 +--m0063:= a0063-r0063 +--E 319 + +--S 320 of 500 +--d0063:= D(m0063,x) +--E 320 + +--S 321 of 500 +t0064:= x^3/log(a*x^n)^(1/2) +--R +--R +--R 3 +--R x +--R (207) ------------ +--R +---------+ +--R | n +--R \|log(a x ) +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0064:= 1/2*%pi^(1/2)*x^4*erfi(2*log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)*_ + (a*x^n)^(-4/n) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 322 + +--S 323 of 500 +a0064:= integrate(t0064,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 323 + +--S 324 of 500 +--m0064:= a0064-r0064 +--E 324 + +--S 325 of 500 +--d0064:= D(m0064,x) +--E 325 + +--S 326 of 500 +t0065:= 1/x^2/log(a*x^n)^(1/2) +--R +--R +--R 1 +--R (208) -------------- +--R +---------+ +--R 2 | n +--R x \|log(a x ) +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0065:= %pi^(1/2)*(a*x^n)^(1/n)*erf(log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)/x +--R +--R +--R 1 +---------+ +--R - | n +--R +---+ n n \|log(a x ) +--R \|%pi (a x ) erf(------------) +--R +-+ +--R \|n +--R (209) ------------------------------ +--R +-+ +--R x\|n +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0065:= integrate(t0065,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 328 + +--S 329 of 500 +--m0065:= a0065-r0065 +--E 329 + +--S 330 of 500 +--d0065:= D(m0065,x) +--E 330 + +--S 331 of 500 +t0066:= 1/x^3/log(a*x^n)^(1/2) +--R +--R +--R 1 +--R (210) -------------- +--R +---------+ +--R 3 | n +--R x \|log(a x ) +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0066:= 1/2*2^(1/2)*%pi^(1/2)*(a*x^n)^(2/n)*erf(2^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/n^(1/2)/x^2 +--R +--R +--R 2 +---------+ +--R - +-+ | n +--R +-+ +---+ n n \|2 \|log(a x ) +--R \|2 \|%pi (a x ) erf(----------------) +--R +-+ +--R \|n +--R (211) -------------------------------------- +--R 2 +-+ +--R 2x \|n +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0066:= integrate(t0066,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 333 + +--S 334 of 500 +--m0066:= a0066-r0066 +--E 334 + +--S 335 of 500 +--d0066:= D(m0066,x) +--E 335 + +--S 336 of 500 +t0067:= x^m/log(a*x^n)^(1/2) +--R +--R +--R m +--R x +--R (212) ------------ +--R +---------+ +--R | n +--R \|log(a x ) +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0067:= %pi^(1/2)*x^(1+m)*erfi((1+m)^(1/2)*log(a*x^n)^(1/2)/n^(1/2))*_ + (a*x^n)^(-(1+m)/n)/(1+m)^(1/2)/n^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 337 + +--S 338 of 500 +a0067:= integrate(t0067,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 338 + +--S 339 of 500 +--m0067:= a0067-r0067 +--E 339 + +--S 340 of 500 +--d0067:= D(m0067,x) +--E 340 + +--S 341 of 500 +t0068:= 1/log(a*x^n)^(3/2) +--R +--R +--R 1 +--R (213) --------------------- +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0068:= 2*%pi^(1/2)*x*erfi(log(a*x^n)^(1/2)/n^(1/2))/n^(3/2)/_ + ((a*x^n)^(1/n))-2*x/n/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 342 + +--S 343 of 500 +a0068:= integrate(t0068,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 343 + +--S 344 of 500 +--m0068:= a0068-r0068 +--E 344 + +--S 345 of 500 +--d0068:= D(m0068,x) +--E 345 + +--S 346 of 500 +t0069:= x/log(a*x^n)^(3/2) +--R +--R +--R x +--R (214) --------------------- +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0069:= 2*2^(1/2)*%pi^(1/2)*x^2*erfi(2^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(2/n))/n^(3/2)-_ + 2*x^2/n/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 347 + +--S 348 of 500 +a0069:= integrate(t0069,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 348 + +--S 349 of 500 +--m0069:= a0069-r0069 +--E 349 + +--S 350 of 500 +--d0069:= D(m0069,x) +--E 350 + +--S 351 of 500 +t0070:= x^2/log(a*x^n)^(3/2) +--R +--R +--R 2 +--R x +--R (215) --------------------- +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0070:= 2*3^(1/2)*%pi^(1/2)*x^3*erfi(3^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(3/n))/n^(3/2)-_ + 2*x^3/n/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 352 + +--S 353 of 500 +a0070:= integrate(t0070,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 353 + +--S 354 of 500 +--m0070:= a0070-r0070 +--E 354 + +--S 355 of 500 +--d0070:= D(m0070,x) +--E 355 + +--S 356 of 500 +t0071:= x^3/log(a*x^n)^(3/2) +--R +--R +--R 3 +--R x +--R (216) --------------------- +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0071:= 4*%pi^(1/2)*x^4*erfi(2*log(a*x^n)^(1/2)/n^(1/2))/_ + n^(3/2)/((a*x^n)^(4/n))-2*x^4/n/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 357 + +--S 358 of 500 +a0071:= integrate(t0071,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 358 + +--S 359 of 500 +--m0071:= a0071-r0071 +--E 359 + +--S 360 of 500 +--d0071:= D(m0071,x) +--E 360 + +--S 361 of 500 +t0072:= 1/x^2/log(a*x^n)^(3/2) +--R +--R +--R 1 +--R (217) ----------------------- +--R +---------+ +--R 2 n | n +--R x log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0072:= -2*%pi^(1/2)*(a*x^n)^(1/n)*erf(log(a*x^n)^(1/2)/n^(1/2))/n^(3/2)/x-_ + 2/n/x/log(a*x^n)^(1/2) +--R +--R +--R 1 +---------+ +--R - +---------+ | n +--R +---+ n n | n \|log(a x ) +-+ +--R - 2\|%pi (a x ) \|log(a x ) erf(------------) - 2\|n +--R +-+ +--R \|n +--R (218) ----------------------------------------------------- +--R +---------+ +--R +-+ | n +--R n x\|n \|log(a x ) +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0072:= integrate(t0072,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 363 + +--S 364 of 500 +--m0072:= a0072-r0072 +--E 364 + +--S 365 of 500 +--d0072:= D(m0072,x) +--E 365 + +--S 366 of 500 +t0073:= 1/x^3/log(a*x^n)^(3/2) +--R +--R +--R 1 +--R (219) ----------------------- +--R +---------+ +--R 3 n | n +--R x log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0073:= -2*2^(1/2)*%pi^(1/2)*(a*x^n)^(2/n)*erf(2^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/n^(3/2)/x^2-2/n/x^2/log(a*x^n)^(1/2) +--R +--R +--R 2 +---------+ +--R - +---------+ +-+ | n +--R +-+ +---+ n n | n \|2 \|log(a x ) +-+ +--R - 2\|2 \|%pi (a x ) \|log(a x ) erf(----------------) - 2\|n +--R +-+ +--R \|n +--R (220) ------------------------------------------------------------- +--R +---------+ +--R 2 +-+ | n +--R n x \|n \|log(a x ) +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0073:= integrate(t0073,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 368 + +--S 369 of 500 +--m0073:= a0073-r0073 +--E 369 + +--S 370 of 500 +--d0073:= D(m0073,x) +--E 370 + +--S 371 of 500 +t0074:= x^m/log(a*x^n)^(3/2) +--R +--R +--R m +--R x +--R (221) --------------------- +--R +---------+ +--R n | n +--R log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0074:= 2*(1+m)^(1/2)*%pi^(1/2)*x^(1+m)*erfi((1+m)^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^((1+m)/n))/n^(3/2)-_ + 2*x^(1+m)/n/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 372 + +--S 373 of 500 +a0074:= integrate(t0074,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 373 + +--S 374 of 500 +--m0074:= a0074-r0074 +--E 374 + +--S 375 of 500 +--d0074:= D(m0074,x) +--E 375 + +--S 376 of 500 +t0075:= 1/log(a*x^n)^(5/2) +--R +--R +--R 1 +--R (222) ---------------------- +--R +---------+ +--R n 2 | n +--R log(a x ) \|log(a x ) +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0075:= 4/3*%pi^(1/2)*x*erfi(log(a*x^n)^(1/2)/n^(1/2))/_ + ((a*x^n)^(1/n))/n^(5/2)-2/3*x/n/log(a*x^n)^(3/2)-_ + 4/3*x/n^2/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 377 + +--S 378 of 500 +a0075:= integrate(t0075,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 378 + +--S 379 of 500 +--m0075:= a0075-r0075 +--E 379 + +--S 380 of 500 +--d0075:= D(m0075,x) +--E 380 + +--S 381 of 500 +t0076:= x/log(a*x^n)^(5/2) +--R +--R +--R x +--R (223) ---------------------- +--R +---------+ +--R n 2 | n +--R log(a x ) \|log(a x ) +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0076:= 8/3*2^(1/2)*%pi^(1/2)*x^2*erfi(2^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(2/n))/n^(5/2)-_ + 2/3*x^2/n/log(a*x^n)^(3/2)-8/3*x^2/n^2/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 382 + +--S 383 of 500 +a0076:= integrate(t0076,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 383 + +--S 384 of 500 +--m0076:= a0076-r0076 +--E 384 + +--S 385 of 500 +--d0076:= D(m0076,x) +--E 385 + +--S 386 of 500 +t0077:= x^2/log(a*x^n)^(5/2) +--R +--R +--R 2 +--R x +--R (224) ---------------------- +--R +---------+ +--R n 2 | n +--R log(a x ) \|log(a x ) +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0077:= 4*3^(1/2)*%pi^(1/2)*x^3*erfi(3^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^(3/n))/n^(5/2)-_ + 2/3*x^3/n/log(a*x^n)^(3/2)-4*x^3/n^2/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 387 + +--S 388 of 500 +a0077:= integrate(t0077,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 388 + +--S 389 of 500 +--m0077:= a0077-r0077 +--E 389 + +--S 390 of 500 +--d0077:= D(m0077,x) +--E 390 + +--S 391 of 500 +t0078:= x^3/log(a*x^n)^(5/2) +--R +--R +--R 3 +--R x +--R (225) ---------------------- +--R +---------+ +--R n 2 | n +--R log(a x ) \|log(a x ) +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0078:= 32/3*%pi^(1/2)*x^4*erfi(2*log(a*x^n)^(1/2)/n^(1/2))/_ + ((a*x^n)^(4/n))/n^(5/2)-2/3*x^4/n/log(a*x^n)^(3/2)-_ + 16/3*x^4/n^2/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 392 + +--S 393 of 500 +a0078:= integrate(t0078,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 393 + +--S 394 of 500 +--m0078:= a0078-r0078 +--E 394 + +--S 395 of 500 +--d0078:= D(m0078,x) +--E 395 + +--S 396 of 500 +t0079:= 1/x^2/log(a*x^n)^(5/2) +--R +--R +--R 1 +--R (226) ------------------------ +--R +---------+ +--R 2 n 2 | n +--R x log(a x ) \|log(a x ) +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0079:= 4/3*%pi^(1/2)*(a*x^n)^(1/n)*erf(log(a*x^n)^(1/2)/n^(1/2))/n^(5/2)/x-_ + 2/3/n/x/log(a*x^n)^(3/2)+4/3/n^2/x/log(a*x^n)^(1/2) +--R +--R +--R (227) +--R 1 +---------+ +--R - +---------+ | n +--R +---+ n n n | n \|log(a x ) +-+ n +--R 4\|%pi log(a x )(a x ) \|log(a x ) erf(------------) + 4\|n log(a x ) +--R +-+ +--R \|n +--R + +--R +-+ +--R - 2n\|n +--R / +--R +---------+ +--R 2 +-+ n | n +--R 3n x\|n log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0079:= integrate(t0079,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 398 + +--S 399 of 500 +--m0079:= a0079-r0079 +--E 399 + +--S 400 of 500 +--d0079:= D(m0079,x) +--E 400 + +--S 401 of 500 +t0080:= 1/x^3/log(a*x^n)^(5/2) +--R +--R +--R 1 +--R (228) ------------------------ +--R +---------+ +--R 3 n 2 | n +--R x log(a x ) \|log(a x ) +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0080:= 8/3*2^(1/2)*%pi^(1/2)*(a*x^n)^(2/n)*erf(2^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/n^(5/2)/x^2-2/3/n/x^2/log(a*x^n)^(3/2)+_ + 8/3/n^2/x^2/log(a*x^n)^(1/2) +--R +--R +--R (229) +--R 2 +---------+ +--R - +---------+ +-+ | n +--R +-+ +---+ n n n | n \|2 \|log(a x ) +--R 8\|2 \|%pi log(a x )(a x ) \|log(a x ) erf(----------------) +--R +-+ +--R \|n +--R + +--R +-+ n +-+ +--R 8\|n log(a x ) - 2n\|n +--R / +--R +---------+ +--R 2 2 +-+ n | n +--R 3n x \|n log(a x )\|log(a x ) +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0080:= integrate(t0080,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 403 + +--S 404 of 500 +--m0080:= a0080-r0080 +--E 404 + +--S 405 of 500 +--d0080:= D(m0080,x) +--E 405 + +--S 406 of 500 +t0081:= x^m/log(a*x^n)^(5/2) +--R +--R +--R m +--R x +--R (230) ---------------------- +--R +---------+ +--R n 2 | n +--R log(a x ) \|log(a x ) +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0081:= 4/3*(1+m)^(3/2)*%pi^(1/2)*x^(1+m)*erfi((1+m)^(1/2)*_ + log(a*x^n)^(1/2)/n^(1/2))/((a*x^n)^((1+m)/n))/n^(5/2)-_ + 2/3*x^(1+m)/n/log(a*x^n)^(3/2)-4/3*(1+m)*x^(1+m)/n^2/log(a*x^n)^(1/2) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 407 + +--S 408 of 500 +a0081:= integrate(t0081,x) +--R +--R +--R >> Error detected within library code: +--R Function not supported by Risch d.e. +--R +--R Continuing to read the file... +--R +--E 408 + +--S 409 of 500 +--m0081:= a0081-r0081 +--E 409 + +--S 410 of 500 +--d0081:= D(m0081,x) +--E 410 + +--S 411 of 500 +t0082:= log(a*x)^p +--R +--R +--R p +--R (231) log(a x) +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0082:= Gamma(p+1,-log(a*x))*log(a*x)^p/((-log(a*x))^p)/a +--R +--R +--R p _ +--R log(a x) | (p + 1,- log(a x)) +--R (232) ----------------------------- +--R p +--R a (- log(a x)) +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0082:= integrate(t0082,x) +--R +--R +--R x +--R ++ p +--R (233) | log(%D a) d%D +--R ++ +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +--m0082:= a0082-r0082 +--E 414 + +--S 415 of 500 +--d0082:= D(m0082,x) +--E 415 + +--S 416 of 500 +t0083:= x*log(a*x)^p +--R +--R +--R p +--R (234) x log(a x) +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0083:= 2^(-1-p)*Gamma(p+1,-2*log(a*x))*log(a*x)^p/((-log(a*x))^p)/a^2 +--R +--R +--R - p - 1 p _ +--R 2 log(a x) | (p + 1,- 2log(a x)) +--R (235) -------------------------------------- +--R 2 p +--R a (- log(a x)) +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0083:= integrate(t0083,x) +--R +--R +--R x +--R ++ p +--R (236) | %D log(%D a) d%D +--R ++ +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +--m0083:= a0083-r0083 +--E 419 + +--S 420 of 500 +--d0083:= D(m0083,x) +--E 420 + +--S 421 of 500 +t0084:= x^2*log(a*x)^p +--R +--R +--R 2 p +--R (237) x log(a x) +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0084:= 3^(-1-p)*Gamma(p+1,-3*log(a*x))*log(a*x)^p/((-log(a*x))^p)/a^3 +--R +--R +--R - p - 1 p _ +--R 3 log(a x) | (p + 1,- 3log(a x)) +--R (238) -------------------------------------- +--R 3 p +--R a (- log(a x)) +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0084:= integrate(t0084,x) +--R +--R +--R x +--R ++ 2 p +--R (239) | %D log(%D a) d%D +--R ++ +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +--m0084:= a0084-r0084 +--E 424 + +--S 425 of 500 +--d0084:= D(m0084,x) +--E 425 + +--S 426 of 500 +t0085:= x^3*log(a*x)^p +--R +--R +--R 3 p +--R (240) x log(a x) +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0085:= 4^(-1-p)*Gamma(p+1,-4*log(a*x))*log(a*x)^p/((-log(a*x))^p)/a^4 +--R +--R +--R - p - 1 p _ +--R 4 log(a x) | (p + 1,- 4log(a x)) +--R (241) -------------------------------------- +--R 4 p +--R a (- log(a x)) +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0085:= integrate(t0085,x) +--R +--R +--R x +--R ++ 3 p +--R (242) | %D log(%D a) d%D +--R ++ +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +--m0085:= a0085-r0085 +--E 429 + +--S 430 of 500 +--d0085:= D(m0085,x) +--E 430 + +--S 431 of 500 +t0086:= log(a*x)^p/x^2 +--R +--R +--R p +--R log(a x) +--R (243) --------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0086:= -a*Gamma(p+1,log(a*x)) +--R +--R +--R _ +--R (244) - a| (p + 1,log(a x)) +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0086:= integrate(t0086,x) +--R +--R +--R x p +--R ++ log(%D a) +--R (245) | ---------- d%D +--R ++ 2 +--R %D +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +--m0086:= a0086-r0086 +--E 434 + +--S 435 of 500 +--d0086:= D(m0086,x) +--E 435 + +--S 436 of 500 +t0087:= log(a*x)^p/x^3 +--R +--R +--R p +--R log(a x) +--R (246) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0087:= -2^(-1-p)*a^2*Gamma(p+1,2*log(a*x)) +--R +--R +--R 2 - p - 1 _ +--R (247) - a 2 | (p + 1,2log(a x)) +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0087:= integrate(t0087,x) +--R +--R +--R x p +--R ++ log(%D a) +--R (248) | ---------- d%D +--R ++ 3 +--R %D +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +--m0087:= a0087-r0087 +--E 439 + +--S 440 of 500 +--d0087:= D(m0087,x) +--E 440 + +--S 441 of 500 +t0088:= x^m*log(a*x)^p +--R +--R +--R m p +--R (249) x log(a x) +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0088:= x^m/a*(a*x)^(-m)*Gamma(p+1,-(1+m)*log(a*x))*_ + log(a*x)^p*(-(1+m)*log(a*x))^(-p)/(1+m) +--R +--R +--R m - m - p p _ +--R x (a x) ((- m - 1)log(a x)) log(a x) | (p + 1,(- m - 1)log(a x)) +--R (250) -------------------------------------------------------------------- +--R a m + a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0088:= integrate(t0088,x) +--R +--R +--R x +--R ++ m p +--R (251) | %D log(%D a) d%D +--R ++ +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +--m0088:= a0088-r0088 +--E 444 + +--S 445 of 500 +--d0088:= D(m0088,x) +--E 445 + +--S 446 of 500 +t0089:= log(a*x^n)^p +--R +--R +--R n p +--R (252) log(a x ) +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0089:= x*Gamma(p+1,-log(a*x^n)/n)*log(a*x^n)^p/((a*x^n)^(1/n))/_ + ((-log(a*x^n)/n)^p) +--R +--R +--R n +--R n p _ log(a x ) +--R x log(a x ) | (p + 1,- ---------) +--R n +--R (253) --------------------------------- +--R 1 +--R - n p +--R n n log(a x ) +--R (a x ) (- ---------) +--R n +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0089:= integrate(t0089,x) +--R +--R +--R x +--R ++ n p +--R (254) | log(a %D ) d%D +--R ++ +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +--m0089:= a0089-r0089 +--E 449 + +--S 450 of 500 +--d0089:= D(m0089,x) +--E 450 + +--S 451 of 500 +t0090:= x*log(a*x^n)^p +--R +--R +--R n p +--R (255) x log(a x ) +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0090:= 2^(-1-p)*x^2*Gamma(p+1,-2*log(a*x^n)/n)*_ + log(a*x^n)^p*(a*x^n)^(-2/n)*(-log(a*x^n)/n)^(-p) +--R +--R +--R 2 +--R - - n - p n +--R 2 - p - 1 n n log(a x ) n p _ 2log(a x ) +--R (256) x 2 (a x ) (- ---------) log(a x ) | (p + 1,- ----------) +--R n n +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0090:= integrate(t0090,x) +--R +--R +--R x +--R ++ n p +--R (257) | %D log(a %D ) d%D +--R ++ +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +--m0090:= a0090-r0090 +--E 454 + +--S 455 of 500 +--d0090:= D(m0090,x) +--E 455 + +--S 456 of 500 +t0091:= x^2*log(a*x^n)^p +--R +--R +--R 2 n p +--R (258) x log(a x ) +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0091:= 3^(-1-p)*x^3*Gamma(p+1,-3*log(a*x^n)/n)*_ + log(a*x^n)^p*(a*x^n)^(-3/n)*(-log(a*x^n)/n)^(-p) +--R +--R +--R 3 +--R - - n - p n +--R 3 - p - 1 n n log(a x ) n p _ 3log(a x ) +--R (259) x 3 (a x ) (- ---------) log(a x ) | (p + 1,- ----------) +--R n n +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0091:= integrate(t0091,x) +--R +--R +--R x +--R ++ 2 n p +--R (260) | %D log(a %D ) d%D +--R ++ +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +--m0091:= a0091-r0091 +--E 459 + +--S 460 of 500 +--d0091:= D(m0091,x) +--E 460 + +--S 461 of 500 +t0092:= x^3*log(a*x^n)^p +--R +--R +--R 3 n p +--R (261) x log(a x ) +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0092:= 2^(-2*p-2)*x^4*Gamma(p+1,-4*log(a*x^n)/n)*_ + log(a*x^n)^p*(a*x^n)^(-4/n)*(-log(a*x^n)/n)^(-p) +--R +--R +--R 4 +--R - - n - p n +--R 4 - 2p - 2 n n log(a x ) n p _ 4log(a x ) +--R (262) x 2 (a x ) (- ---------) log(a x ) | (p + 1,- ----------) +--R n n +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0092:= integrate(t0092,x) +--R +--R +--R x +--R ++ 3 n p +--R (263) | %D log(a %D ) d%D +--R ++ +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +--m0092:= a0092-r0092 +--E 464 + +--S 465 of 500 +--d0092:= D(m0092,x) +--E 465 + +--S 466 of 500 +t0093:= log(a*x^n)^p/x^2 +--R +--R +--R n p +--R log(a x ) +--R (264) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0093:= -(a*x^n)^(1/n)*Gamma(p+1,log(a*x^n)/n)*_ + log(a*x^n)^p/((log(a*x^n)/n)^p)/x +--R +--R +--R 1 +--R - n +--R n n n p _ log(a x ) +--R (a x ) log(a x ) | (p + 1,---------) +--R n +--R (265) - ------------------------------------ +--R n p +--R log(a x ) +--R x (---------) +--R n +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0093:= integrate(t0093,x) +--R +--R +--R x n p +--R ++ log(a %D ) +--R (266) | ----------- d%D +--R ++ 2 +--R %D +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +--m0093:= a0093-r0093 +--E 469 + +--S 470 of 500 +--d0093:= D(m0093,x) +--E 470 + +--S 471 of 500 +t0094:= log(a*x^n)^p/x^3 +--R +--R +--R n p +--R log(a x ) +--R (267) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0094:= -2^(-1-p)*(a*x^n)^(2/n)*Gamma(p+1,2*log(a*x^n)/n)*_ + log(a*x^n)^p/((log(a*x^n)/n)^p)/x^2 +--R +--R +--R 2 +--R - n +--R - p - 1 n n n p _ 2log(a x ) +--R 2 (a x ) log(a x ) | (p + 1,----------) +--R n +--R (268) - --------------------------------------------- +--R n p +--R 2 log(a x ) +--R x (---------) +--R n +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0094:= integrate(t0094,x) +--R +--R +--R x n p +--R ++ log(a %D ) +--R (269) | ----------- d%D +--R ++ 3 +--R %D +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +--m0094:= a0094-r0094 +--E 474 + +--S 475 of 500 +--d0094:= D(m0094,x) +--E 475 + +--S 476 of 500 +t0095:= x^m*log(a*x^n)^p +--R +--R +--R m n p +--R (270) x log(a x ) +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0095:= x^(1+m)*Gamma(p+1,-(1+m)*log(a*x^n)/n)*log(a*x^n)^p*_ + (a*x^n)^(-(1+m)/n)*(-(1+m)*log(a*x^n)/n)^(-p)/(1+m) +--R +--R +--R (271) +--R - m - 1 +--R ------- n - p +--R m + 1 n n (- m - 1)log(a x ) n p +--R x (a x ) (------------------) log(a x ) +--R n +--R * +--R n +--R _ (- m - 1)log(a x ) +--R | (p + 1,------------------) +--R n +--R / +--R m + 1 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0095:= integrate(t0095,x) +--R +--R +--R x +--R ++ m n p +--R (272) | %D log(a %D ) d%D +--R ++ +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +--m0095:= a0095-r0095 +--E 479 + +--S 480 of 500 +--d0095:= D(m0095,x) +--E 480 + +--S 481 of 500 +t0096:= (a+b*log(c*x^n))^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R (273) b log(c x ) + 3a b log(c x ) + 3a b log(c x ) + a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0096:= 6*a*b^2*n^2*x-6*b^3*n^3*x+6*b^3*n^2*x*log(c*x^n)-_ + 3*b*n*x*(a+b*log(c*x^n))^2+x*(a+b*log(c*x^n))^3 +--R +--R +--R (274) +--R 3 n 3 3 2 n 2 +--R b x log(c x ) + (- 3b n + 3a b )x log(c x ) +--R + +--R 3 2 2 2 n 3 3 2 2 2 3 +--R (6b n - 6a b n + 3a b)x log(c x ) + (- 6b n + 6a b n - 3a b n + a )x +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0096:= integrate(t0096,x) +--R +--R +--R (275) +--R 3 3 3 3 2 3 3 2 2 2 +--R b n x log(x) + (3b n x log(c) + (- 3b n + 3a b n )x)log(x) +--R + +--R 3 2 3 2 2 +--R 3b n x log(c) + (- 6b n + 6a b n)x log(c) +--R + +--R 3 3 2 2 2 +--R (6b n - 6a b n + 3a b n)x +--R * +--R log(x) +--R + +--R 3 3 3 2 2 3 2 2 2 +--R b x log(c) + (- 3b n + 3a b )x log(c) + (6b n - 6a b n + 3a b)x log(c) +--R + +--R 3 3 2 2 2 3 +--R (- 6b n + 6a b n - 3a b n + a )x +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0096:= a0096-r0096 +--R +--R +--R (276) +--R 3 n 3 3 2 n 2 +--R - b x log(c x ) + (3b n - 3a b )x log(c x ) +--R + +--R 3 2 2 2 n 3 3 3 +--R (- 6b n + 6a b n - 3a b)x log(c x ) + b n x log(x) +--R + +--R 3 2 3 3 2 2 2 +--R (3b n x log(c) + (- 3b n + 3a b n )x)log(x) +--R + +--R 3 2 3 2 2 +--R 3b n x log(c) + (- 6b n + 6a b n)x log(c) +--R + +--R 3 3 2 2 2 +--R (6b n - 6a b n + 3a b n)x +--R * +--R log(x) +--R + +--R 3 3 3 2 2 3 2 2 2 +--R b x log(c) + (- 3b n + 3a b )x log(c) + (6b n - 6a b n + 3a b)x log(c) +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0096:= D(m0096,x) +--R +--R +--R (277) +--R 3 n n 3 3 2 n 3 n - 1 n 2 +--R - b x log(c x ) + ((3b n - 3a b )x - 3b n x x )log(c x ) +--R + +--R 3 2 2 2 n 3 2 2 n - 1 n +--R ((- 6b n + 6a b n - 3a b)x + (6b n - 6a b n)x x )log(c x ) +--R + +--R 3 3 3 3 2 2 2 2 +--R b n log(x) + (3b n log(c) + 3a b n )log(x) +--R + +--R 3 2 2 2 3 3 +--R (3b n log(c) + 6a b n log(c) + 3a b n)log(x) + b log(c) +--R + +--R 2 2 2 3 3 2 2 2 +--R 3a b log(c) + 3a b log(c) + 6b n - 6a b n + 3a b n +--R * +--R n +--R x +--R + +--R 3 3 2 2 2 n - 1 +--R (- 6b n + 6a b n - 3a b n)x x +--R / +--R n +--R x +--R Type: Expression(Integer) +--E 485 + +--S 486 of 500 +t0097:= 1/(a+b*log(c*x^n)) +--R +--R +--R 1 +--R (278) --------------- +--R n +--R b log(c x ) + a +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0097:= x*Ei((a+b*log(c*x^n))/b/n)/b*exp(-a/b/n)/n*(c*x^n)^(-1/n) +--R +--R +--R a 1 +--R - --- - - n +--R b n n n b log(c x ) + a +--R x %e (c x ) Ei(---------------) +--R b n +--R (279) ------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0097:= integrate(t0097,x) +--R +--R +--R x +--R ++ 1 +--R (280) | ---------------- d%D +--R ++ n +--R b log(c %D ) + a +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +--m0097:= a0097-r0097 +--E 489 + +--S 490 of 500 +--d0097:= D(m0097,x) +--E 490 + +--S 491 of 500 +t0098:= 1/(a+b*log(c*x^n))^2 +--R +--R +--R 1 +--R (281) ---------------------------------- +--R 2 n 2 n 2 +--R b log(c x ) + 2a b log(c x ) + a +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0098:= x*Ei((a+b*log(c*x^n))/b/n)/(exp(1)^(a/b/n))/_ + ((c*x^n)^(1/n))/b^2/n^2-x/b/n/(a+b*log(c*x^n)) +--R +--R +--R a 1 +--R n --- - +--R n b log(c x ) + a b n n n +--R (b x log(c x ) + a x)Ei(---------------) - b n x %e (c x ) +--R b n +--R (282) ------------------------------------------------------------- +--R a a 1 +--R --- --- - +--R 3 2 b n n 2 2 b n n n +--R (b n %e log(c x ) + a b n %e )(c x ) +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0098:= integrate(t0098,x) +--R +--R +--R x +--R ++ 1 +--R (283) | ------------------------------------ d%D +--R ++ 2 n 2 n 2 +--R b log(c %D ) + 2a b log(c %D ) + a +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +--m0098:= a0098-r0098 +--E 494 + +--S 495 of 500 +--d0098:= D(m0098,x) +--E 495 + +--S 496 of 500 +t0099:= 1/(a+b*log(c*x^n))^3 +--R +--R +--R 1 +--R (284) ---------------------------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b log(c x ) + 3a b log(c x ) + 3a b log(c x ) + a +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0099:= 1/2*x*Ei((a+b*log(c*x^n))/b/n)/(exp(1)^(a/b/n))/_ + ((c*x^n)^(1/n))/b^3/n^3-1/2*x/b/n/(a+b*log(c*x^n))^2-_ + 1/2*x/b^2/n^2/(a+b*log(c*x^n)) +--R +--R +--R (285) +--R n +--R 2 n 2 n 2 b log(c x ) + a +--R (b x log(c x ) + 2a b x log(c x ) + a x)Ei(---------------) +--R b n +--R + +--R a a 1 +--R --- --- - +--R 2 b n n 2 2 b n n n +--R (- b n x %e log(c x ) + (- b n - a b n)x %e )(c x ) +--R / +--R a a a 1 +--R --- --- --- - +--R 5 3 b n n 2 4 3 b n n 2 3 3 b n n n +--R (2b n %e log(c x ) + 4a b n %e log(c x ) + 2a b n %e )(c x ) +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0099:= integrate(t0099,x) +--R +--R +--R x +--R ++ 1 +--R (286) | ------------------------------------------------------- d%D +--R ++ 3 n 3 2 n 2 2 n 3 +--R b log(c %D ) + 3a b log(c %D ) + 3a b log(c %D ) + a +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +--m0099:= a0099-r0099 +--E 499 + +--S 500 of 500 +--d0099:= D(m0099,x) +--E 500 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richlog000-099.input.pdf b/src/axiom-website/CATS/richlog000-099.input.pdf new file mode 100644 index 0000000..c2038a4 Binary files /dev/null and b/src/axiom-website/CATS/richlog000-099.input.pdf differ diff --git a/src/axiom-website/CATS/richlog100-199.input.pamphlet b/src/axiom-website/CATS/richlog100-199.input.pamphlet new file mode 100644 index 0000000..b3f1493 --- /dev/null +++ b/src/axiom-website/CATS/richlog100-199.input.pamphlet @@ -0,0 +1,7846 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richlog100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richlog100-199.output +)spool richlog100-199.output +)set message auto off +)clear all + +--S 1 of 518 +t0100:= (a+b*log(c*x^n))^m +--R +--R +--R n m +--R (1) (b log(c x ) + a) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 518 +r0100:= x*Gamma(1+m,-(a+b*log(c*x^n))/b/n)*(a+b*log(c*x^n))^m*_ + exp(-a/b/n)*(c*x^n)^(-1/n)*(-(a+b*log(c*x^n))/b/n)^(-m) +--R +--R +--R (2) +--R a 1 +--R - --- - - n - m +--R b n n n - b log(c x ) - a n m +--R x %e (c x ) (-----------------) (b log(c x ) + a) +--R b n +--R * +--R n +--R _ - b log(c x ) - a +--R | (m + 1,-----------------) +--R b n +--R Type: Expression(Integer) +--E 2 + +--S 3 of 518 +a0100:= integrate(t0100,x) +--R +--R +--R x +--R ++ n m +--R (3) | (b log(c %L ) + a) d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 518 +m0100:= a0100-r0100 +--R +--R +--R (4) +--R x +--R ++ n m +--R | (b log(c %L ) + a) d%L +--R ++ +--R + +--R - +--R a 1 +--R - --- - - n - m +--R b n n n - b log(c x ) - a n m +--R x %e (c x ) (-----------------) (b log(c x ) + a) +--R b n +--R * +--R n +--R _ - b log(c x ) - a +--R | (m + 1,-----------------) +--R b n +--R Type: Expression(Integer) +--E 4 + +--S 5 of 518 +d0100:= D(m0100,x) +--R +--R +--R (5) +--R a 1 a - n - 1 +--R - --- - - - --- ------- +--R b n n n n b n n - 1 n n n +--R (- %e x (c x ) + c x %e x x (c x ) ) +--R * +--R n - m +--R - b log(c x ) - a +--R (-----------------) +--R b n +--R + +--R a 1 +--R - --- - - n - m - 1 +--R b n n - 1 n n - b log(c x ) - a +--R - m x %e x (c x ) (-----------------) +--R b n +--R * +--R n m +--R (b log(c x ) + a) +--R + +--R - +--R a 1 +--R - --- - - n - m +--R b n n - 1 n n - b log(c x ) - a +--R b m n x %e x (c x ) (-----------------) +--R b n +--R * +--R n m - 1 +--R (b log(c x ) + a) +--R * +--R n +--R _ - b log(c x ) - a +--R | (m + 1,-----------------) +--R b n +--R + +--R - +--R n +--R a 1 b log(c x ) + a +--R - --- - - --------------- n - m +--R b n n - 1 n n b n - b log(c x ) - a +--R x %e x (c x ) %e (-----------------) +--R b n +--R * +--R n m +--R - b log(c x ) - a +--R (-----------------) +--R b n +--R + +--R n +--R x +--R * +--R n m +--R (b log(c x ) + a) +--R / +--R n +--R x +--R Type: Expression(Integer) +--E 5 + +--S 6 of 518 +t0101:= x^m/(a+b*log(c*x^n)) +--R +--R +--R m +--R x +--R (6) --------------- +--R n +--R b log(c x ) + a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 518 +r0101:= x^(1+m)*Ei((1+m)*(a+b*log(c*x^n))/b/n)*exp(-a*(1+m)/b/n)*_ + (c*x^n)^(-(1+m)/n)/b/n +--R +--R +--R - a m - a - m - 1 +--R --------- ------- n +--R b n m + 1 n n (b m + b)log(c x ) + a m + a +--R %e x (c x ) Ei(----------------------------) +--R b n +--R (7) -------------------------------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 7 + +--S 8 of 518 +a0101:= integrate(t0101,x) +--R +--R +--R x m +--R ++ %L +--R (8) | ---------------- d%L +--R ++ n +--R b log(c %L ) + a +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 518 +--m0101:= a0101-r0101 +--E 9 + +--S 10 of 518 +--d0101:= D(m0101,x) +--E 10 + +--S 11 of 518 +t0102:= x^m/(a+b*log(c*x^n))^2 +--R +--R +--R m +--R x +--R (9) ---------------------------------- +--R 2 n 2 n 2 +--R b log(c x ) + 2a b log(c x ) + a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 518 +r0102:= (1+m)*x^(1+m)*Ei((1+m)*(a+b*log(c*x^n))/b/n)/_ + (exp(1)^(a*(1+m)/b/n))/((c*x^n)^((1+m)/n))/b^2/n^2-x^(1+m)/_ + b/n/(a+b*log(c*x^n)) +--R +--R +--R (10) +--R m + 1 n m + 1 +--R ((b m + b)x log(c x ) + (a m + a)x ) +--R * +--R n +--R (b m + b)log(c x ) + a m + a +--R Ei(----------------------------) +--R b n +--R + +--R a m + a m + 1 +--R ------- ----- +--R b n m + 1 n n +--R - b n %e x (c x ) +--R / +--R a m + a a m + a m + 1 +--R ------- ------- ----- +--R 3 2 b n n 2 2 b n n n +--R (b n %e log(c x ) + a b n %e )(c x ) +--R Type: Expression(Integer) +--E 12 + +--S 13 of 518 +a0102:= integrate(t0102,x) +--R +--R +--R x m +--R ++ %L +--R (11) | ------------------------------------ d%L +--R ++ 2 n 2 n 2 +--R b log(c %L ) + 2a b log(c %L ) + a +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 518 +--m0102:= a0102-r0102 +--E 14 + +--S 15 of 518 +--d0102:= D(m0102,x) +--E 15 + +--S 16 of 518 +t0103:= x^m*(a+b*log(c*x^n))^p +--R +--R +--R m n p +--R (12) x (b log(c x ) + a) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 518 +r0103:= x^(1+m)*Gamma(p+1,-(1+m)*(a+b*log(c*x^n))/b/n)*_ + (a+b*log(c*x^n))^p*exp(-a*(1+m)/b/n)*(c*x^n)^(-(1+m)/n)*_ + (-(1+m)*(a+b*log(c*x^n))/b/n)^(-p)/(1+m) +--R +--R +--R (13) +--R - a m - a - m - 1 +--R --------- ------- n - p +--R b n m + 1 n n (- b m - b)log(c x ) - a m - a +--R %e x (c x ) (------------------------------) +--R b n +--R * +--R n +--R n p _ (- b m - b)log(c x ) - a m - a +--R (b log(c x ) + a) | (p + 1,------------------------------) +--R b n +--R / +--R m + 1 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 518 +a0103:= integrate(t0103,x) +--R +--R +--R x +--R ++ m n p +--R (14) | %L (b log(c %L ) + a) d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 518 +--m0103:= a0103-r0103 +--E 19 + +--S 20 of 518 +--d0103:= D(m0103,x) +--E 20 + +--S 21 of 518 +t0104:= x^4*log(c*(a+b*x)^n) +--R +--R +--R 4 n +--R (15) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 518 +r0104:= 1/300/b^5*(-60*a^4*n*x*b+30*a^3*n*x^2*b^2-20*a^2*n*x^3*b^3+_ + 15*a*n*x^4*b^4-12*n*x^5*b^5+60*a^5*n*log(a+b*x)+_ + 60*x^5*log(c*(a+b*x)^n)*b^5) +--R +--R +--R (16) +--R 5 5 n 5 5 5 4 4 +--R 60b x log(c (b x + a) ) + 60a n log(b x + a) - 12b n x + 15a b n x +--R + +--R 2 3 3 3 2 2 4 +--R - 20a b n x + 30a b n x - 60a b n x +--R / +--R 5 +--R 300b +--R Type: Expression(Integer) +--E 22 + +--S 23 of 518 +a0104:= integrate(t0104,x) +--R +--R +--R (17) +--R 5 5 5 5 5 5 5 4 4 +--R (60b n x + 60a n)log(b x + a) + 60b x log(c) - 12b n x + 15a b n x +--R + +--R 2 3 3 3 2 2 4 +--R - 20a b n x + 30a b n x - 60a b n x +--R / +--R 5 +--R 300b +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 518 +m0104:= a0104-r0104 +--R +--R +--R 5 n 5 5 +--R - x log(c (b x + a) ) + n x log(b x + a) + x log(c) +--R (18) --------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 518 +d0104:= D(m0104,x) +--R +--R +--R (19) +--R 5 4 n n +--R (- 5b x - 5a x )(b x + a) log(c (b x + a) ) +--R + +--R 5 4 5 4 5 +--R ((5b n x + 5a n x )log(b x + a) + (5b x + 5a x )log(c) + b n x ) +--R * +--R n +--R (b x + a) +--R + +--R 2 6 5 n - 1 +--R (- b n x - a b n x )(b x + a) +--R / +--R n +--R (5b x + 5a)(b x + a) +--R Type: Expression(Integer) +--E 25 + +--S 26 of 518 +t0105:= x^3*log(c*(a+b*x)^n) +--R +--R +--R 3 n +--R (20) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 518 +r0105:= -1/48/b^4*(-12*x*a^3*n*b+6*a^2*b^2*n*x^2-4*a*b^3*n*x^3+_ + 3*b^4*n*x^4+12*a^4*n*log(a+b*x)-12*x^4*log(c*(a+b*x)^n)*b^4) +--R +--R +--R (21) +--R 4 4 n 4 4 4 3 3 +--R 12b x log(c (b x + a) ) - 12a n log(b x + a) - 3b n x + 4a b n x +--R + +--R 2 2 2 3 +--R - 6a b n x + 12a b n x +--R / +--R 4 +--R 48b +--R Type: Expression(Integer) +--E 27 + +--S 28 of 518 +a0105:= integrate(t0105,x) +--R +--R +--R (22) +--R 4 4 4 4 4 4 4 3 3 +--R (12b n x - 12a n)log(b x + a) + 12b x log(c) - 3b n x + 4a b n x +--R + +--R 2 2 2 3 +--R - 6a b n x + 12a b n x +--R / +--R 4 +--R 48b +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 518 +m0105:= a0105-r0105 +--R +--R +--R 4 n 4 4 +--R - x log(c (b x + a) ) + n x log(b x + a) + x log(c) +--R (23) --------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 518 +d0105:= D(m0105,x) +--R +--R +--R (24) +--R 4 3 n n +--R (- 4b x - 4a x )(b x + a) log(c (b x + a) ) +--R + +--R 4 3 4 3 4 +--R ((4b n x + 4a n x )log(b x + a) + (4b x + 4a x )log(c) + b n x ) +--R * +--R n +--R (b x + a) +--R + +--R 2 5 4 n - 1 +--R (- b n x - a b n x )(b x + a) +--R / +--R n +--R (4b x + 4a)(b x + a) +--R Type: Expression(Integer) +--E 30 + +--S 31 of 518 +t0106:= x^2*log(c*(a+b*x)^n) +--R +--R +--R 2 n +--R (25) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 518 +r0106:= 1/18/b^3*(-6*n*b*x*a^2+3*a*b^2*n*x^2-2*b^3*n*x^3+_ + 6*a^3*n*log(a+b*x)+6*x^3*log(c*(a+b*x)^n)*b^3) +--R +--R +--R (26) +--R 3 3 n 3 3 3 2 2 2 +--R 6b x log(c (b x + a) ) + 6a n log(b x + a) - 2b n x + 3a b n x - 6a b n x +--R --------------------------------------------------------------------------- +--R 3 +--R 18b +--R Type: Expression(Integer) +--E 32 + +--S 33 of 518 +a0106:= integrate(t0106,x) +--R +--R +--R (27) +--R 3 3 3 3 3 3 3 2 2 2 +--R (6b n x + 6a n)log(b x + a) + 6b x log(c) - 2b n x + 3a b n x - 6a b n x +--R --------------------------------------------------------------------------- +--R 3 +--R 18b +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 518 +m0106:= a0106-r0106 +--R +--R +--R 3 n 3 3 +--R - x log(c (b x + a) ) + n x log(b x + a) + x log(c) +--R (28) --------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 518 +d0106:= D(m0106,x) +--R +--R +--R (29) +--R 3 2 n n +--R (- 3b x - 3a x )(b x + a) log(c (b x + a) ) +--R + +--R 3 2 3 2 3 +--R ((3b n x + 3a n x )log(b x + a) + (3b x + 3a x )log(c) + b n x ) +--R * +--R n +--R (b x + a) +--R + +--R 2 4 3 n - 1 +--R (- b n x - a b n x )(b x + a) +--R / +--R n +--R (3b x + 3a)(b x + a) +--R Type: Expression(Integer) +--E 35 + +--S 36 of 518 +t0107:= log(c*(a+b*x)^n)/x +--R +--R +--R n +--R log(c (b x + a) ) +--R (30) ----------------- +--R x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 518 +r0107:= log(-b*x/a)*log(c*(a+b*x)^n)+n*polylog(2,1+b*x/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 518 +a0107:= integrate(t0107,x) +--R +--R +--R x n +--R ++ log(c (%L b + a) ) +--R (31) | ------------------ d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 518 +--m0107:= a0107-r0107 +--E 39 + +--S 40 of 518 +--d0107:= D(m0107,x) +--E 40 + +--S 41 of 518 +t0108:= log(c*(a+b*x)^n)/x^2 +--R +--R +--R n +--R log(c (b x + a) ) +--R (32) ----------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 518 +r0108:= b*n*log(x)/a-b*n*log(a+b*x)/a-log(c*(a+b*x)^n)/x +--R +--R +--R n +--R - a log(c (b x + a) ) - b n x log(b x + a) + b n x log(x) +--R (33) --------------------------------------------------------- +--R a x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 518 +a0108:= integrate(t0108,x) +--R +--R +--R (- b n x - a n)log(b x + a) + b n x log(x) - a log(c) +--R (34) ----------------------------------------------------- +--R a x +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 518 +m0108:= a0108-r0108 +--R +--R +--R n +--R log(c (b x + a) ) - n log(b x + a) - log(c) +--R (35) ------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 44 + +--S 45 of 518 +d0108:= D(m0108,x) +--R +--R +--R (36) +--R n n +--R (- b x - a)(b x + a) log(c (b x + a) ) +--R + +--R n +--R ((b n x + a n)log(b x + a) + (b x + a)log(c) - b n x)(b x + a) +--R + +--R 2 2 n - 1 +--R (b n x + a b n x)(b x + a) +--R / +--R 3 2 n +--R (b x + a x )(b x + a) +--R Type: Expression(Integer) +--E 45 + +--S 46 of 518 +t0109:= log(c*(a+b*x)^n)/x^3 +--R +--R +--R n +--R log(c (b x + a) ) +--R (37) ----------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 518 +r0109:= -1/2/a^2/x^2*(a*b*n*x+b^2*n*log(x)*x^2-b^2*n*log(a+b*x)*x^2+_ + log(c*(a+b*x)^n)*a^2) +--R +--R +--R 2 n 2 2 2 2 +--R - a log(c (b x + a) ) + b n x log(b x + a) - b n x log(x) - a b n x +--R (38) ------------------------------------------------------------------- +--R 2 2 +--R 2a x +--R Type: Expression(Integer) +--E 47 + +--S 48 of 518 +a0109:= integrate(t0109,x) +--R +--R +--R 2 2 2 2 2 2 +--R (b n x - a n)log(b x + a) - b n x log(x) - a log(c) - a b n x +--R (39) -------------------------------------------------------------- +--R 2 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 518 +m0109:= a0109-r0109 +--R +--R +--R n +--R log(c (b x + a) ) - n log(b x + a) - log(c) +--R (40) ------------------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 49 + +--S 50 of 518 +d0109:= D(m0109,x) +--R +--R +--R (41) +--R n n +--R (- 2b x - 2a)(b x + a) log(c (b x + a) ) +--R + +--R n +--R ((2b n x + 2a n)log(b x + a) + (2b x + 2a)log(c) - b n x)(b x + a) +--R + +--R 2 2 n - 1 +--R (b n x + a b n x)(b x + a) +--R / +--R 4 3 n +--R (2b x + 2a x )(b x + a) +--R Type: Expression(Integer) +--E 50 + +--S 51 of 518 +t0110:= log(c*(a+b*x)^n)/x^4 +--R +--R +--R n +--R log(c (b x + a) ) +--R (42) ----------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 518 +r0110:= 1/6/a^3/x^3*(-n*b*x*a^2+2*a*b^2*n*x^2+2*b^3*n*log(x)*x^3-_ + 2*b^3*n*log(a+b*x)*x^3-2*log(c*(a+b*x)^n)*a^3) +--R +--R +--R (43) +--R 3 n 3 3 3 3 2 2 +--R - 2a log(c (b x + a) ) - 2b n x log(b x + a) + 2b n x log(x) + 2a b n x +--R + +--R 2 +--R - a b n x +--R / +--R 3 3 +--R 6a x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 518 +a0110:= integrate(t0110,x) +--R +--R +--R (44) +--R 3 3 3 3 3 3 2 2 +--R (- 2b n x - 2a n)log(b x + a) + 2b n x log(x) - 2a log(c) + 2a b n x +--R + +--R 2 +--R - a b n x +--R / +--R 3 3 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 518 +m0110:= a0110-r0110 +--R +--R +--R n +--R log(c (b x + a) ) - n log(b x + a) - log(c) +--R (45) ------------------------------------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 54 + +--S 55 of 518 +d0110:= D(m0110,x) +--R +--R +--R (46) +--R n n +--R (- 3b x - 3a)(b x + a) log(c (b x + a) ) +--R + +--R n +--R ((3b n x + 3a n)log(b x + a) + (3b x + 3a)log(c) - b n x)(b x + a) +--R + +--R 2 2 n - 1 +--R (b n x + a b n x)(b x + a) +--R / +--R 5 4 n +--R (3b x + 3a x )(b x + a) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 518 +t0111:= x^4*log(c*(a+b*x^2)^n) +--R +--R +--R 4 2 n +--R (47) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 518 +r0111:= -2/5*a^2*n*x/b^2+2/15*a*n*x^3/b-2/25*n*x^5+_ + 2/5*a^(5/2)*n*atan(b^(1/2)*x/a^(1/2))/b^(5/2)+_ + 1/5*x^5*log(c*(a+b*x^2)^n) +--R +--R +--R (48) +--R +-+ +--R 2 5 +-+ 2 n 2 +-+ x\|b +--R 15b x \|b log(c (b x + a) ) + 30a n\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 2 5 3 2 +-+ +--R (- 6b n x + 10a b n x - 30a n x)\|b +--R / +--R 2 +-+ +--R 75b \|b +--R Type: Expression(Integer) +--E 57 + +--S 58 of 518 +a0111:= integrate(t0111,x) +--R +--R +--R (49) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 2 | a \| b 2 5 2 +--R 15a n |- - log(---------------------) + 15b n x log(b x + a) +--R \| b 2 +--R b x + a +--R + +--R 2 5 2 5 3 2 +--R 15b x log(c) - 6b n x + 10a b n x - 30a n x +--R / +--R 2 +--R 75b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 2 |a \|b 2 5 2 2 5 2 5 +--R - 30a n |- atan(----) + 15b n x log(b x + a) + 15b x log(c) - 6b n x +--R \|b x +--R + +--R 3 2 +--R 10a b n x - 30a n x +--R / +--R 2 +--R 75b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 58 + +--S 59 of 518 +m0111a:= a0111.1-r0111 +--R +--R +--R (50) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 2 | a +-+ \| b 2 5 +-+ 2 n +--R a n |- - \|b log(---------------------) - b x \|b log(c (b x + a) ) +--R \| b 2 +--R b x + a +--R + +--R +-+ +--R 2 +-+ x\|b 2 5 2 2 5 +-+ +--R - 2a n\|a atan(-----) + (b n x log(b x + a) + b x log(c))\|b +--R +-+ +--R \|a +--R / +--R 2 +-+ +--R 5b \|b +--R Type: Expression(Integer) +--E 59 + +--S 60 of 518 +d0111a:= D(m0111a,x) +--R +--R +--R (51) +--R 6 4 2 n 2 n +--R (- 5b x - 5a x )(b x + a) log(c (b x + a) ) +--R + +--R 6 4 2 6 4 6 +--R ((5b n x + 5a n x )log(b x + a) + (5b x + 5a x )log(c) + 2b n x ) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 8 6 2 n - 1 +--R (- 2b n x - 2a b n x )(b x + a) +--R / +--R 2 2 n +--R (5b x + 5a)(b x + a) +--R Type: Expression(Integer) +--E 60 + +--S 61 of 518 +m0111b:= a0111.2-r0111 +--R +--R +--R (52) +--R +-+ +--R 2 5 +-+ 2 n 2 +-+ x\|b +--R - b x \|b log(c (b x + a) ) - 2a n\|a atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R |a +--R +-+ |- +--R 2 |a +-+ \|b 2 5 2 2 5 +-+ +--R - 2a n |- \|b atan(----) + (b n x log(b x + a) + b x log(c))\|b +--R \|b x +--R / +--R 2 +-+ +--R 5b \|b +--R Type: Expression(Integer) +--E 61 + +--S 62 of 518 +d0111b:= D(m0111b,x) +--R +--R +--R (53) +--R 6 4 2 n 2 n +--R (- 5b x - 5a x )(b x + a) log(c (b x + a) ) +--R + +--R 6 4 2 6 4 6 +--R ((5b n x + 5a n x )log(b x + a) + (5b x + 5a x )log(c) + 2b n x ) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 8 6 2 n - 1 +--R (- 2b n x - 2a b n x )(b x + a) +--R / +--R 2 2 n +--R (5b x + 5a)(b x + a) +--R Type: Expression(Integer) +--E 62 + +--S 63 of 518 +t0112:= x^3*log(c*(a+b*x^2)^n) +--R +--R +--R 3 2 n +--R (54) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 63 + +--S 64 of 518 +r0112:= 1/4*a*n*x^2/b-1/8*n*x^4-1/4*a^2*n*log(a+b*x^2)/b^2+_ + 1/4*x^4*log(c*(a+b*x^2)^n) +--R +--R +--R 2 4 2 n 2 2 2 4 2 +--R 2b x log(c (b x + a) ) - 2a n log(b x + a) - b n x + 2a b n x +--R (55) ----------------------------------------------------------------- +--R 2 +--R 8b +--R Type: Expression(Integer) +--E 64 + +--S 65 of 518 +a0112:= integrate(t0112,x) +--R +--R +--R 2 4 2 2 2 4 2 4 2 +--R (2b n x - 2a n)log(b x + a) + 2b x log(c) - b n x + 2a b n x +--R (56) ---------------------------------------------------------------- +--R 2 +--R 8b +--R Type: Union(Expression(Integer),...) +--E 65 + +--S 66 of 518 +m0112:= a0112-r0112 +--R +--R +--R 4 2 n 4 2 4 +--R - x log(c (b x + a) ) + n x log(b x + a) + x log(c) +--R (57) ----------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 518 +d0112:= D(m0112,x) +--R +--R +--R (58) +--R 5 3 2 n 2 n +--R (- 2b x - 2a x )(b x + a) log(c (b x + a) ) +--R + +--R 5 3 2 5 3 5 +--R ((2b n x + 2a n x )log(b x + a) + (2b x + 2a x )log(c) + b n x ) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 7 5 2 n - 1 +--R (- b n x - a b n x )(b x + a) +--R / +--R 2 2 n +--R (2b x + 2a)(b x + a) +--R Type: Expression(Integer) +--E 67 + +--S 68 of 518 +t0113:= x^2*log(c*(a+b*x^2)^n) +--R +--R +--R 2 2 n +--R (59) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 68 + +--S 69 of 518 +r0113:= 2/3*a*n*x/b-2/9*n*x^3-2/3*a^(3/2)*n*atan(b^(1/2)*x/a^(1/2))/b^(3/2)+_ + 1/3*x^3*log(c*(a+b*x^2)^n) +--R +--R +--R (60) +--R +-+ +--R 3 +-+ 2 n +-+ x\|b 3 +-+ +--R 3b x \|b log(c (b x + a) ) - 6a n\|a atan(-----) + (- 2b n x + 6a n x)\|b +--R +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +--R 9b\|b +--R Type: Expression(Integer) +--E 69 + +--S 70 of 518 +a0113:= integrate(t0113,x) +--R +--R +--R (61) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R | a \| b 3 2 +--R 3a n |- - log(-----------------------) + 3b n x log(b x + a) +--R \| b 2 +--R b x + a +--R + +--R 3 3 +--R 3b x log(c) - 2b n x + 6a n x +--R / +--R 9b +--R , +--R +-+ +--R |a +--R +-+ |- +--R |a \|b 3 2 3 3 +--R 6a n |- atan(----) + 3b n x log(b x + a) + 3b x log(c) - 2b n x + 6a n x +--R \|b x +--R --------------------------------------------------------------------------] +--R 9b +--R Type: Union(List(Expression(Integer)),...) +--E 70 + +--S 71 of 518 +m0113a:= a0113.1-r0113 +--R +--R +--R (62) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 3 +-+ 2 n | a +-+ \| b +--R - b x \|b log(c (b x + a) ) + a n |- - \|b log(-----------------------) +--R \| b 2 +--R b x + a +--R + +--R +-+ +--R +-+ x\|b 3 2 3 +-+ +--R 2a n\|a atan(-----) + (b n x log(b x + a) + b x log(c))\|b +--R +-+ +--R \|a +--R / +--R +-+ +--R 3b\|b +--R Type: Expression(Integer) +--E 71 + +--S 72 of 518 +d0113a:= D(m0113a,x) +--R +--R +--R (63) +--R 4 2 2 n 2 n +--R (- 3b x - 3a x )(b x + a) log(c (b x + a) ) +--R + +--R 4 2 2 4 2 4 +--R ((3b n x + 3a n x )log(b x + a) + (3b x + 3a x )log(c) + 2b n x ) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 6 4 2 n - 1 +--R (- 2b n x - 2a b n x )(b x + a) +--R / +--R 2 2 n +--R (3b x + 3a)(b x + a) +--R Type: Expression(Integer) +--E 72 + +--S 73 of 518 +m0113b:= a0113.2-r0113 +--R +--R +--R (64) +--R +-+ +--R 3 +-+ 2 n +-+ x\|b +--R - b x \|b log(c (b x + a) ) + 2a n\|a atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R |a +--R +-+ |- +--R |a +-+ \|b 3 2 3 +-+ +--R 2a n |- \|b atan(----) + (b n x log(b x + a) + b x log(c))\|b +--R \|b x +--R / +--R +-+ +--R 3b\|b +--R Type: Expression(Integer) +--E 73 + +--S 74 of 518 +d0113b:= D(m0113b,x) +--R +--R +--R (65) +--R 4 2 2 n 2 n +--R (- 3b x - 3a x )(b x + a) log(c (b x + a) ) +--R + +--R 4 2 2 4 2 4 +--R ((3b n x + 3a n x )log(b x + a) + (3b x + 3a x )log(c) + 2b n x ) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 6 4 2 n - 1 +--R (- 2b n x - 2a b n x )(b x + a) +--R / +--R 2 2 n +--R (3b x + 3a)(b x + a) +--R Type: Expression(Integer) +--E 74 + +--S 75 of 518 +t0114:= x*log(c*(a+b*x^2)^n) +--R +--R +--R 2 n +--R (66) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 75 + +--S 76 of 518 +r0114:= -1/2*n*x^2+1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)/b +--R +--R +--R 2 2 n 2 +--R (b x + a)log(c (b x + a) ) - b n x +--R (67) ------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 76 + +--S 77 of 518 +a0114:= integrate(t0114,x) +--R +--R +--R 2 2 2 2 +--R (b n x + a n)log(b x + a) + b x log(c) - b n x +--R (68) ------------------------------------------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 77 + +--S 78 of 518 +m0114:= a0114-r0114 +--R +--R +--R (69) +--R 2 2 n 2 2 2 +--R (- b x - a)log(c (b x + a) ) + (b n x + a n)log(b x + a) + b x log(c) +--R ------------------------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 78 + +--S 79 of 518 +d0114:= D(m0114,x) +--R +--R +--R (70) +--R 2 n 2 n +--R - x (b x + a) log(c (b x + a) ) +--R + +--R 2 2 n +--R (n x log(b x + a) + x log(c) + n x)(b x + a) +--R + +--R 3 2 n - 1 +--R (- b n x - a n x)(b x + a) +--R / +--R 2 n +--R (b x + a) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 518 +t0115:= log(c*(a+b*x^2)^n)/x +--R +--R +--R 2 n +--R log(c (b x + a) ) +--R (71) ------------------ +--R x +--R Type: Expression(Integer) +--E 80 + +--S 81 of 518 +r0115:= 1/2*log(-b*x^2/a)*log(c*(a+b*x^2)^n)+1/2*n*polylog(2,1+b*x^2/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 81 + +--S 82 of 518 +a0115:= integrate(t0115,x) +--R +--R +--R x 2 n +--R ++ log(c (%L b + a) ) +--R (72) | ------------------ d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 82 + +--S 83 of 518 +m0115a:= a0115.1-r0115 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 83 + +--S 84 of 518 +d0115a:= D(m0115a,x) +--R +--R +--R (73) 0 +--R Type: Polynomial(Integer) +--E 84 + +--S 85 of 518 +m0115b:= a0115.2-r0115 +--R +--R There are 33 exposed and 3 unexposed library operations named elt +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op elt +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named elt +--R with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 85 + +--S 86 of 518 +d0115b:= D(m0115b,x) +--R +--R +--R (74) 0 +--R Type: Polynomial(Integer) +--E 86 + +--S 87 of 518 +t0116:= log(c*(a+b*x^2)^n)/x^2 +--R +--R +--R 2 n +--R log(c (b x + a) ) +--R (75) ------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 87 + +--S 88 of 518 +r0116:= 2*b^(1/2)*n*atan(b^(1/2)*x/a^(1/2))/a^(1/2)-log(c*(a+b*x^2)^n)/x +--R +--R +--R +-+ +--R +-+ 2 n +-+ x\|b +--R - \|a log(c (b x + a) ) + 2n x\|b atan(-----) +--R +-+ +--R \|a +--R (76) ---------------------------------------------- +--R +-+ +--R x\|a +--R Type: Expression(Integer) +--E 88 + +--S 89 of 518 +a0116:= integrate(t0116,x) +--R +--R +--R (77) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R | b \| a 2 +--R n x |- - log(---------------------) - n log(b x + a) - log(c) +--R \| a 2 +--R b x + a +--R [--------------------------------------------------------------, +--R x +--R +-+ +--R |b +--R +-+ a |- +--R |b \|a 2 +--R - 2n x |- atan(-----) - n log(b x + a) - log(c) +--R \|a b x +--R ------------------------------------------------] +--R x +--R Type: Union(List(Expression(Integer)),...) +--E 89 + +--S 90 of 518 +m0116a:= a0116.1-r0116 +--R +--R +--R (78) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R | b +-+ \| a +-+ 2 n +--R n x |- - \|a log(---------------------) + \|a log(c (b x + a) ) +--R \| a 2 +--R b x + a +--R + +--R +-+ +--R +-+ x\|b 2 +-+ +--R - 2n x\|b atan(-----) + (- n log(b x + a) - log(c))\|a +--R +-+ +--R \|a +--R / +--R +-+ +--R x\|a +--R Type: Expression(Integer) +--E 90 + +--S 91 of 518 +d0116a:= D(m0116a,x) +--R +--R +--R (79) +--R 2 2 n 2 n +--R (- b x - a)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 2 2 n +--R ((b n x + a n)log(b x + a) + (b x + a)log(c) - 2b n x )(b x + a) +--R + +--R 2 4 2 2 n - 1 +--R (2b n x + 2a b n x )(b x + a) +--R / +--R 4 2 2 n +--R (b x + a x )(b x + a) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 518 +m0116b:= a0116.2-r0116 +--R +--R +--R (80) +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ 2 n +-+ x\|b +-+ |b \|a +--R \|a log(c (b x + a) ) - 2n x\|b atan(-----) - 2n x\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R + +--R 2 +-+ +--R (- n log(b x + a) - log(c))\|a +--R / +--R +-+ +--R x\|a +--R Type: Expression(Integer) +--E 92 + +--S 93 of 518 +d0116b:= D(m0116b,x) +--R +--R +--R (81) +--R 2 2 n 2 n +--R (- b x - a)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 2 2 n +--R ((b n x + a n)log(b x + a) + (b x + a)log(c) - 2b n x )(b x + a) +--R + +--R 2 4 2 2 n - 1 +--R (2b n x + 2a b n x )(b x + a) +--R / +--R 4 2 2 n +--R (b x + a x )(b x + a) +--R Type: Expression(Integer) +--E 93 + +--S 94 of 518 +t0117:= log(c*(a+b*x^2)^n)/x^3 +--R +--R +--R 2 n +--R log(c (b x + a) ) +--R (82) ------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 94 + +--S 95 of 518 +r0117:= b*n*log(x)/a-1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)/a/x^2 +--R +--R +--R 2 2 n 2 +--R (- b x - a)log(c (b x + a) ) + 2b n x log(x) +--R (83) ---------------------------------------------- +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 95 + +--S 96 of 518 +a0117:= integrate(t0117,x) +--R +--R +--R 2 2 2 +--R (- b n x - a n)log(b x + a) + 2b n x log(x) - a log(c) +--R (84) -------------------------------------------------------- +--R 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 96 + +--S 97 of 518 +m0117:= a0117-r0117 +--R +--R +--R (85) +--R 2 2 n 2 2 +--R (b x + a)log(c (b x + a) ) + (- b n x - a n)log(b x + a) - a log(c) +--R ----------------------------------------------------------------------- +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 518 +d0117:= D(m0117,x) +--R +--R +--R (86) +--R 2 n 2 n +--R - a (b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 n +--R (a n log(b x + a) + a log(c) - b n x )(b x + a) +--R + +--R 2 4 2 2 n - 1 +--R (b n x + a b n x )(b x + a) +--R / +--R 3 2 n +--R a x (b x + a) +--R Type: Expression(Integer) +--E 98 + +--S 99 of 518 +t0118:= log(c*(a+b*x^2)^n)/x^4 +--R +--R +--R 2 n +--R log(c (b x + a) ) +--R (87) ------------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 99 + +--S 100 of 518 +r0118:= -2/3*b*n/a/x-2/3*b^(3/2)*n*atan(b^(1/2)*x/a^(1/2))/a^(3/2)-_ + 1/3*log(c*(a+b*x^2)^n)/x^3 +--R +--R +--R +-+ +--R +-+ 2 n 3 +-+ x\|b 2 +-+ +--R - a\|a log(c (b x + a) ) - 2b n x \|b atan(-----) - 2b n x \|a +--R +-+ +--R \|a +--R (88) ---------------------------------------------------------------- +--R 3 +-+ +--R 3a x \|a +--R Type: Expression(Integer) +--E 100 + +--S 101 of 518 +a0118:= integrate(t0118,x) +--R +--R +--R (89) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 3 | b \| a 2 +--R b n x |- - log(-----------------------) - a n log(b x + a) - a log(c) +--R \| a 2 +--R b x + a +--R + +--R 2 +--R - 2b n x +--R / +--R 3 +--R 3a x +--R , +--R +-+ +--R |b +--R +-+ a |- +--R 3 |b \|a 2 2 +--R 2b n x |- atan(-----) - a n log(b x + a) - a log(c) - 2b n x +--R \|a b x +--R ---------------------------------------------------------------] +--R 3 +--R 3a x +--R Type: Union(List(Expression(Integer)),...) +--E 101 + +--S 102 of 518 +m0118a:= a0118.1-r0118 +--R +--R +--R (90) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R +-+ 2 n 3 | b +-+ \| a +--R a\|a log(c (b x + a) ) + b n x |- - \|a log(-----------------------) +--R \| a 2 +--R b x + a +--R + +--R +-+ +--R 3 +-+ x\|b 2 +-+ +--R 2b n x \|b atan(-----) + (- a n log(b x + a) - a log(c))\|a +--R +-+ +--R \|a +--R / +--R 3 +-+ +--R 3a x \|a +--R Type: Expression(Integer) +--E 102 + +--S 103 of 518 +d0118a:= D(m0118a,x) +--R +--R +--R (91) +--R 2 2 n 2 n +--R (- 3b x - 3a)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 2 2 n +--R ((3b n x + 3a n)log(b x + a) + (3b x + 3a)log(c) - 2b n x )(b x + a) +--R + +--R 2 4 2 2 n - 1 +--R (2b n x + 2a b n x )(b x + a) +--R / +--R 6 4 2 n +--R (3b x + 3a x )(b x + a) +--R Type: Expression(Integer) +--E 103 + +--S 104 of 518 +m0118b:= a0118.2-r0118 +--R +--R +--R (92) +--R +-+ +--R +-+ 2 n 3 +-+ x\|b +--R a\|a log(c (b x + a) ) + 2b n x \|b atan(-----) +--R +-+ +--R \|a +--R + +--R +-+ +--R |b +--R +-+ a |- +--R 3 +-+ |b \|a 2 +-+ +--R 2b n x \|a |- atan(-----) + (- a n log(b x + a) - a log(c))\|a +--R \|a b x +--R / +--R 3 +-+ +--R 3a x \|a +--R Type: Expression(Integer) +--E 104 + +--S 105 of 518 +d0118b:= D(m0118b,x) +--R +--R +--R (93) +--R 2 2 n 2 n +--R (- 3b x - 3a)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 2 2 n +--R ((3b n x + 3a n)log(b x + a) + (3b x + 3a)log(c) - 2b n x )(b x + a) +--R + +--R 2 4 2 2 n - 1 +--R (2b n x + 2a b n x )(b x + a) +--R / +--R 6 4 2 n +--R (3b x + 3a x )(b x + a) +--R Type: Expression(Integer) +--E 105 + +--S 106 of 518 +t0119:= x^4*log(c*(a+b*x^3)^n) +--R +--R +--R 4 3 n +--R (94) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 518 +r0119:= 3/10*a*n*x^2/b-3/25*n*x^5-1/5*3^(1/2)*a^(5/3)*n*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*x*3^(1/2)/a^(1/3))/b^(5/3)+_ + 1/5*a^(5/3)*n*log(a^(1/3)/b^(1/3)+x)/b^(5/3)-_ + 1/10*a^(5/3)*n*log(a^(2/3)/b^(2/3)-a^(1/3)*x/b^(1/3)+x^2)/b^(5/3)+_ + 1/5*x^5*log(c*(a+b*x^3)^n) +--R +--R +--R (95) +--R 5 3+-+2 3 n +--R 10b x \|b log(c (b x + a) ) +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+2 x \|b - x\|a \|b + \|a +--R - 5a n \|a log(---------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R 3+-+2 x\|b + \|a +-+3+-+2 2x\|3 \|b - \|3 \|a +--R 10a n \|a log(------------) - 10a n\|3 \|a atan(---------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R + +--R 5 2 3+-+2 +--R (- 6b n x + 15a n x )\|b +--R / +--R 3+-+2 +--R 50b \|b +--R Type: Expression(Integer) +--E 107 + +--S 108 of 518 +a0119:= integrate(t0119,x) +--R +--R +--R (96) +--R +--+ +--+2 +--R | 2 | 2 +--R |a |a +--R 10a n |-- log(b |-- + a x) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R |a |a |a 2 +--R - 5a n |-- log(- b x |-- + a |-- + a x ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +--R +--+ b\|3 |-- +--R | 2 3| 2 +--R +-+ |a \|b 5 3 +--R - 10a n\|3 |-- atan(--------------- + 10b n x log(b x + a) +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R b |-- - 2a x +--R 3| 2 +--R \|b +--R + +--R 5 5 2 +--R 10b x log(c) - 6b n x + 15a n x +--R / +--R 50b +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 518 +m0119:= a0119-r0119 +--R +--R +--R (97) +--R +--+ +--+2 +--R | 2 | 2 +--R |a 3+-+2 |a 5 3+-+2 3 n +--R 2a n |-- \|b log(b |-- + a x - 2b x \|b log(c (b x + a) ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 3+-+ 3+-+ +--R 3+-+2 x \|b - x\|a \|b + \|a 3+-+2 x\|b + \|a +--R a n \|a log(---------------------------) - 2a n \|a log(------------) +--R 3+-+2 3+-+ +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R |a 3+-+2 |a |a 2 +--R - a n |-- \|b log(- b x |-- + a |-- + a x ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+2 2x\|3 \|b - \|3 \|a +--R 2a n\|3 \|a atan(---------------------) +--R 3+-+ +--R 3\|a +--R + +--R +--+2 +--R | 2 +--R +-+ |a +--R +--+ b\|3 |-- +--R | 2 3| 2 +--R +-+ |a 3+-+2 \|b +--R - 2a n\|3 |-- \|b atan(---------------) +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R b |-- - 2a x +--R 3| 2 +--R \|b +--R + +--R 5 3 5 3+-+2 +--R (2b n x log(b x + a) + 2b x log(c))\|b +--R / +--R 3+-+2 +--R 10b \|b +--R Type: Expression(Integer) +--E 109 + +--S 110 of 518 +d0119:= D(m0119,x) +--R +--R +--R (98) +--R 7 4 3 n 3 n +--R (- 5b x - 5a x )(b x + a) log(c (b x + a) ) +--R + +--R 7 4 3 7 4 7 +--R ((5b n x + 5a n x )log(b x + a) + (5b x + 5a x )log(c) + 3b n x ) +--R * +--R 3 n +--R (b x + a) +--R + +--R 2 10 7 3 n - 1 +--R (- 3b n x - 3a b n x )(b x + a) +--R / +--R 3 3 n +--R (5b x + 5a)(b x + a) +--R Type: Expression(Integer) +--E 110 + +--S 111 of 518 +t0120:= x^3*log(c*(a+b*x^3)^n) +--R +--R +--R 3 3 n +--R (99) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 518 +r0120:= 3/4*a*n*x/b-3/16*n*x^4-1/4*3^(1/2)*a^(4/3)*n*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*x*3^(1/2)/a^(1/3))/b^(4/3)-_ + 1/4*a^(4/3)*n*log(a^(1/3)/b^(1/3)+x)/b^(4/3)+_ + 1/8*a^(4/3)*n*log(a^(2/3)/b^(2/3)-a^(1/3)*x/b^(1/3)+x^2)/b^(4/3)+_ + 1/4*x^4*log(c*(a+b*x^3)^n) +--R +--R +--R (100) +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 4 3+-+ 3 n 3+-+ x \|b - x\|a \|b + \|a +--R 4b x \|b log(c (b x + a) + 2a n\|a log(---------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R 3+-+ x\|b + \|a +-+3+-+ 2x\|3 \|b - \|3 \|a +--R - 4a n\|a log(------------) - 4a n\|3 \|a atan(---------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R + +--R 4 3+-+ +--R (- 3b n x + 12a n x)\|b +--R / +--R 3+-+ +--R 16b\|b +--R Type: Expression(Integer) +--E 112 + +--S 113 of 518 +a0120:= integrate(t0120,x) +--R +--R +--R (101) +--R +---+ +---+2 +---+ +---+ +---+ +--R | a | a | a 2 | a | a +--R - 2a n 3|- - log(3|- - + x 3|- - + x + 4a n 3|- - log(- 3|- - + x) +--R \| b \| b \| b \| b \| b +--R + +--R +---+ +--R +-+ | a +--R +---+ \|3 3|- - +--R +-+ | a \| b 4 3 4 +--R 4a n\|3 3|- - atan(----------- + 4b n x log(b x + a) + 4b x log(c) +--R \| b +---+ +--R | a +--R 3|- - + 2x +--R \| b +--R + +--R 4 +--R - 3b n x + 12a n x +--R / +--R 16b +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 518 +m0120:= a0120-r0120 +--R +--R +--R (102) +--R +---+ +---+2 +---+ +--R | a 3+-+ | a | a 2 4 3+-+ 3 n +--R - a n 3|- - \|b log(3|- - + x 3|- - + x - 2b x \|b log(c (b x + a) ) +--R \| b \| b \| b +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 3+-+ 3+-+ +--R 3+-+ x \|b - x\|a \|b + \|a 3+-+ x\|b + \|a +--R - a n\|a log(---------------------------) + 2a n\|a log(------------) +--R 3+-+2 3+-+ +--R \|b \|b +--R + +--R +---+ +---+ +-+3+-+ +-+3+-+ +--R | a 3+-+ | a +-+3+-+ 2x\|3 \|b - \|3 \|a +--R 2a n 3|- - \|b log(- 3|- - + x + 2a n\|3 \|a atan(---------------------) +--R \| b \| b 3+-+ +--R 3\|a +--R + +--R +---+ +--R +-+ | a +--R +---+ \|3 3|- - +--R +-+ | a 3+-+ \| b +--R 2a n\|3 3|- - \|b atan(-----------) +--R \| b +---+ +--R | a +--R 3|- - + 2x +--R \| b +--R + +--R 4 3 4 3+-+ +--R (2b n x log(b x + a) + 2b x log(c))\|b +--R / +--R 3+-+ +--R 8b\|b +--R Type: Expression(Integer) +--E 114 + +--S 115 of 518 +d0120:= D(m0120,x) +--R +--R +--R (103) +--R 6 3 3 n 3 n +--R (- 4b x - 4a x )(b x + a) log(c (b x + a) ) +--R + +--R 6 3 3 6 3 6 +--R ((4b n x + 4a n x )log(b x + a) + (4b x + 4a x )log(c) + 3b n x ) +--R * +--R 3 n +--R (b x + a) +--R + +--R 2 9 6 3 n - 1 +--R (- 3b n x - 3a b n x )(b x + a) +--R / +--R 3 3 n +--R (4b x + 4a)(b x + a) +--R Type: Expression(Integer) +--E 115 + +--S 116 of 518 +t0121:= x^2*log(c*(a+b*x^3)^n) +--R +--R +--R 2 3 n +--R (104) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 116 + +--S 117 of 518 +r0121:= -1/3*n*x^3+1/3*(a+b*x^3)*log(c*(a+b*x^3)^n)/b +--R +--R +--R 3 3 n 3 +--R (b x + a)log(c (b x + a) ) - b n x +--R (105) ------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 117 + +--S 118 of 518 +a0121:= integrate(t0121,x) +--R +--R +--R 3 3 3 3 +--R (b n x + a n)log(b x + a) + b x log(c) - b n x +--R (106) ------------------------------------------------- +--R 3b +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 518 +m0121:= a0121-r0121 +--R +--R +--R (107) +--R 3 3 n 3 3 3 +--R (- b x - a)log(c (b x + a) ) + (b n x + a n)log(b x + a) + b x log(c) +--R ------------------------------------------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 119 + +--S 120 of 518 +d0121:= D(m0121,x) +--R +--R +--R (108) +--R 2 3 n 3 n +--R - x (b x + a) log(c (b x + a) ) +--R + +--R 2 3 2 2 3 n +--R (n x log(b x + a) + x log(c) + n x )(b x + a) +--R + +--R 5 2 3 n - 1 +--R (- b n x - a n x )(b x + a) +--R / +--R 3 n +--R (b x + a) +--R Type: Expression(Integer) +--E 120 + +--S 121 of 518 +t0122:= x*log(c*(a+b*x^3)^n) +--R +--R +--R 3 n +--R (109) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 518 +r0122:= -3/4*n*x^2+1/2*3^(1/2)*a^(2/3)*n*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*x*3^(1/2)/a^(1/3))/b^(2/3)-_ + 1/2*a^(2/3)*n*log(a^(1/3)/b^(1/3)+x)/b^(2/3)+_ + 1/4*a^(2/3)*n*log(a^(2/3)/b^(2/3)-a^(1/3)*x/b^(1/3)+x^2)/b^(2/3)+_ + 1/2*x^2*log(c*(a+b*x^3)^n) +--R +--R +--R (110) +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 2 3+-+2 3 n 3+-+2 x \|b - x\|a \|b + \|a +--R 2x \|b log(c (b x + a) + n \|a log(---------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R 3+-+2 x\|b + \|a +-+3+-+2 2x\|3 \|b - \|3 \|a +--R - 2n \|a log(------------) + 2n\|3 \|a atan(---------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R + +--R 2 3+-+2 +--R - 3n x \|b +--R / +--R 3+-+2 +--R 4\|b +--R Type: Expression(Integer) +--E 122 + +--S 123 of 518 +a0122:= integrate(t0122,x) +--R +--R +--R (111) +--R +----+ +----+2 +--R | 2 | 2 +--R | a | a +--R 2n |- -- log(b |- -- + a x) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R | a | a | a 2 +--R - n |- -- log(- b x |- -- - a |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+2 +--R | 2 +--R +-+ | a +--R +----+ b\|3 |- -- +--R | 2 3| 2 +--R +-+ | a \| b 2 3 2 +--R - 2n\|3 |- -- atan(----------------- + 2n x log(b x + a) + 2x log(c) +--R 3| 2 +----+2 +--R \| b | 2 +--R | a +--R b |- -- - 2a x +--R 3| 2 +--R \| b +--R + +--R 2 +--R - 3n x +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 518 +m0122:= a0122-r0122 +--R +--R +--R (112) +--R +----+ +----+2 +--R | 2 | 2 +--R | a 3+-+2 | a 2 3+-+2 3 n +--R 2n |- -- \|b log(b |- -- + a x - 2x \|b log(c (b x + a) ) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 3+-+ 3+-+ +--R 3+-+2 x \|b - x\|a \|b + \|a 3+-+2 x\|b + \|a +--R - n \|a log(---------------------------) + 2n \|a log(------------) +--R 3+-+2 3+-+ +--R \|b \|b +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R | a 3+-+2 | a | a 2 +--R - n |- -- \|b log(- b x |- -- - a |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+2 2x\|3 \|b - \|3 \|a +--R - 2n\|3 \|a atan(---------------------) +--R 3+-+ +--R 3\|a +--R + +--R +----+2 +--R | 2 +--R +-+ | a +--R +----+ b\|3 |- -- +--R | 2 3| 2 +--R +-+ | a 3+-+2 \| b +--R - 2n\|3 |- -- \|b atan(-----------------) +--R 3| 2 +----+2 +--R \| b | 2 +--R | a +--R b |- -- - 2a x +--R 3| 2 +--R \| b +--R + +--R 2 3 2 3+-+2 +--R (2n x log(b x + a) + 2x log(c))\|b +--R / +--R 3+-+2 +--R 4\|b +--R Type: Expression(Integer) +--E 124 + +--S 125 of 518 +d0122:= D(m0122,x) +--R +--R +--R (113) +--R 4 3 n 3 n +--R (- 2b x - 2a x)(b x + a) log(c (b x + a) ) +--R + +--R 4 3 4 4 +--R ((2b n x + 2a n x)log(b x + a) + (2b x + 2a x)log(c) + 3b n x ) +--R * +--R 3 n +--R (b x + a) +--R + +--R 2 7 4 3 n - 1 +--R (- 3b n x - 3a b n x )(b x + a) +--R / +--R 3 3 n +--R (2b x + 2a)(b x + a) +--R Type: Expression(Integer) +--E 125 + +--S 126 of 518 +t0123:= log(c*(a+b*x^3)^n)/x +--R +--R +--R 3 n +--R log(c (b x + a) ) +--R (114) ------------------ +--R x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 518 +r0123:= 1/3*log(-b*x^3/a)*log(c*(a+b*x^3)^n)+1/3*n*polylog(2,1+b*x^3/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 518 +a0123:= integrate(t0123,x) +--R +--R +--R x 3 n +--R ++ log(c (%L b + a) ) +--R (115) | ------------------ d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 518 +--m0123:= a0123-r0123 +--E 129 + +--S 130 of 518 +--d0123:= D(m0123,x) +--E 130 + +--S 131 of 518 +t0124:= log(c*(a+b*x^3)^n)/x^2 +--R +--R +--R 3 n +--R log(c (b x + a) ) +--R (116) ------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 518 +r0124:= 3^(1/2)*b^(1/3)*n*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*x*3^(1/2)/a^(1/3))/a^(1/3)-_ + b^(1/3)*n*log(a^(1/3)/b^(1/3)+x)/a^(1/3)+_ + 1/2*b^(1/3)*n*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*x/b^(1/3)+x^2)/a^(1/3)-log(c*(a+b*x^3)^n)/x +--R +--R +--R (117) +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ 3 n 3+-+ x \|b - x\|a \|b + \|a +--R - 2\|a log(c (b x + a) ) + n x\|b log(---------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R 3+-+ x\|b + \|a +-+3+-+ 2x\|3 \|b - \|3 \|a +--R - 2n x\|b log(------------) + 2n x\|3 \|b atan(---------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R / +--R 3+-+ +--R 2x\|a +--R Type: Expression(Integer) +--E 132 + +--S 133 of 518 +a0124:= integrate(t0124,x) +--R +--R +--R (118) +--R +---+ +---+2 +--R | b | b +--R 2n x 3|- - log(a 3|- - + b x) +--R \| a \| a +--R + +--R +---+ +---+2 +---+ +--R | b | b | b 2 +--R - n x 3|- - log(- a x 3|- - - a 3|- - + b x ) +--R \| a \| a \| a +--R + +--R +---+2 +--R +-+ | b +--R +---+ a\|3 3|- - +--R +-+ | b \| a 3 +--R - 2n x\|3 3|- - atan(---------------- - 2n log(b x + a) - 2log(c) +--R \| a +---+2 +--R | b +--R a 3|- - - 2b x +--R \| a +--R / +--R 2x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 518 +m0124:= a0124-r0124 +--R +--R +--R (119) +--R +---+ +---+2 +--R | b 3+-+ | b 3+-+ 3 n +--R 2n x 3|- - \|a log(a 3|- - + b x + 2\|a log(c (b x + a) ) +--R \| a \| a +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 3+-+ 3+-+ +--R 3+-+ x \|b - x\|a \|b + \|a 3+-+ x\|b + \|a +--R - n x\|b log(---------------------------) + 2n x\|b log(------------) +--R 3+-+2 3+-+ +--R \|b \|b +--R + +--R +---+ +---+2 +---+ +--R | b 3+-+ | b | b 2 +--R - n x 3|- - \|a log(- a x 3|- - - a 3|- - + b x ) +--R \| a \| a \| a +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ 2x\|3 \|b - \|3 \|a +--R - 2n x\|3 \|b atan(---------------------) +--R 3+-+ +--R 3\|a +--R + +--R +---+2 +--R +-+ | b +--R +---+ a\|3 3|- - +--R +-+ | b 3+-+ \| a +--R - 2n x\|3 3|- - \|a atan(----------------) +--R \| a +---+2 +--R | b +--R a 3|- - - 2b x +--R \| a +--R + +--R 3 3+-+ +--R (- 2n log(b x + a) - 2log(c))\|a +--R / +--R 3+-+ +--R 2x\|a +--R Type: Expression(Integer) +--E 134 + +--S 135 of 518 +d0124:= D(m0124,x) +--R +--R +--R (120) +--R 3 3 n 3 n +--R (- b x - a)(b x + a) log(c (b x + a) ) +--R + +--R 3 3 3 3 3 n +--R ((b n x + a n)log(b x + a) + (b x + a)log(c) - 3b n x )(b x + a) +--R + +--R 2 6 3 3 n - 1 +--R (3b n x + 3a b n x )(b x + a) +--R / +--R 5 2 3 n +--R (b x + a x )(b x + a) +--R Type: Expression(Integer) +--E 135 + +--S 136 of 518 +t0125:= log(c*(a+b*x^3)^n)/x^3 +--R +--R +--R 3 n +--R log(c (b x + a) ) +--R (121) ------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 518 +r0125:= 1/2*3^(1/2)*b^(2/3)*n*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*x*3^(1/2)/a^(1/3))/a^(2/3)+_ + 1/2*b^(2/3)*n*log(a^(1/3)/b^(1/3)+x)/a^(2/3)-_ + 1/4*b^(2/3)*n*log(a^(2/3)/b^(2/3)-a^(1/3)*x/b^(1/3)+x^2)/a^(2/3)-_ + 1/2*log(c*(a+b*x^3)^n)/x^2 +--R +--R +--R (122) +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+2 3 n 2 3+-+2 x \|b - x\|a \|b + \|a +--R - 2\|a log(c (b x + a) ) - n x \|b log(---------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R 2 3+-+2 x\|b + \|a 2 +-+3+-+2 2x\|3 \|b - \|3 \|a +--R 2n x \|b log(------------ + 2n x \|3 \|b atan(---------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R / +--R 2 3+-+2 +--R 4x \|a +--R Type: Expression(Integer) +--E 137 + +--S 138 of 518 +a0125:= integrate(t0125,x) +--R +--R +--R (123) +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R 2 |b 2 |b |b 2 2 +--R - n x |-- log(a |-- - a b x |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+ +--R | 2 +--R +-+ |b +--R +--+ +--+ +--+ a\|3 |-- +--R | 2 | 2 | 2 3| 2 +--R 2 |b |b 2 +-+ |b \|a +--R 2n x |-- log(a |-- + b x + 2n x \|3 |-- atan(-------------) +--R 3| 2 3| 2 3| 2 +--+ +--R \|a \|a \|a | 2 +--R |b +--R a |-- - 2b x +--R 3| 2 +--R \|a +--R + +--R 3 +--R - 2n log(b x + a) - 2log(c) +--R / +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 518 +m0125:= a0125-r0125 +--R +--R +--R (124) +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R 2 3+-+2 |b 2 |b |b 2 2 +--R - n x \|a |-- log(a |-- - a b x |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+ +--+ +--R | 2 | 2 +--R 2 3+-+2 |b |b 3+-+2 3 n +--R 2n x \|a |-- log(a |-- + b + 2\|a log(c (b x + a) ) +--R 3| 2 3| 2 +--R \|a \|a +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 3+-+ 3+-+ +--R 2 3+-+2 x \|b - x\|a \|b + \|a 2 3+-+2 x\|b + \|a +--R n x \|b log(--------------------------- - 2n x \|b log(------------) +--R 3+-+2 3+-+ +--R \|b \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 2 +-+3+-+2 2x\|3 \|b - \|3 \|a +--R - 2n x \|3 \|b atan(---------------------) +--R 3+-+ +--R 3\|a +--R + +--R +--+ +--R | 2 +--R +-+ |b +--R +--+ a\|3 |-- +--R | 2 3| 2 +--R 2 +-+3+-+2 |b \|a +--R 2n x \|3 \|a |-- atan(-------------) +--R 3| 2 +--+ +--R \|a | 2 +--R |b +--R a |-- - 2b x +--R 3| 2 +--R \|a +--R + +--R 3 3+-+2 +--R (- 2n log(b x + a) - 2log(c))\|a +--R / +--R 2 3+-+2 +--R 4x \|a +--R Type: Expression(Integer) +--E 139 + +--S 140 of 518 +d0125:= D(m0125,x) +--R +--R +--R (125) +--R 3 3 n 3 n +--R (- 2b x - 2a)(b x + a) log(c (b x + a) ) +--R + +--R 3 3 3 3 3 n +--R ((2b n x + 2a n)log(b x + a) + (2b x + 2a)log(c) - 3b n x )(b x + a) +--R + +--R 2 6 3 3 n - 1 +--R (3b n x + 3a b n x )(b x + a) +--R / +--R 6 3 3 n +--R (2b x + 2a x )(b x + a) +--R Type: Expression(Integer) +--E 140 + +--S 141 of 518 +t0126:= log(c*(a+b*x^3)^n)/x^4 +--R +--R +--R 3 n +--R log(c (b x + a) ) +--R (126) ------------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 518 +r0126:= b*n*log(x)/a-1/3*b*n*log(a+b*x^3)/a-1/3*log(c*(a+b*x^3)^n)/x^3 +--R +--R +--R 3 n 3 3 3 +--R - a log(c (b x + a) ) - b n x log(b x + a) + 3b n x log(x) +--R (127) ------------------------------------------------------------ +--R 3 +--R 3a x +--R Type: Expression(Integer) +--E 142 + +--S 143 of 518 +a0126:= integrate(t0126,x) +--R +--R +--R 3 3 3 +--R (- b n x - a n)log(b x + a) + 3b n x log(x) - a log(c) +--R (128) -------------------------------------------------------- +--R 3 +--R 3a x +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 518 +m0126:= a0126-r0126 +--R +--R +--R 3 n 3 +--R log(c (b x + a) ) - n log(b x + a) - log(c) +--R (129) --------------------------------------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 144 + +--S 145 of 518 +d0126:= D(m0126,x) +--R +--R +--R (130) +--R 3 3 n 3 n +--R (- b x - a)(b x + a) log(c (b x + a) ) +--R + +--R 3 3 3 3 3 n +--R ((b n x + a n)log(b x + a) + (b x + a)log(c) - b n x )(b x + a) +--R + +--R 2 6 3 3 n - 1 +--R (b n x + a b n x )(b x + a) +--R / +--R 7 4 3 n +--R (b x + a x )(b x + a) +--R Type: Expression(Integer) +--E 145 + +--S 146 of 518 +t0127:= x^4*log(c*(a+b/x)^n) +--R +--R +--R 4 a x + b n +--R (131) x log(c (-------) ) +--R x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 518 +r0127:= 1/60/a^5*(-12*b^4*n*x*a+6*b^3*n*x^2*a^2-4*b^2*n*x^3*a^3+_ + 3*b*n*x^4*a^4+12*x^5*log(c*((a*x+b)/x)^n)*a^5+12*b^5*n*log(a*x+b)) +--R +--R +--R (132) +--R 5 5 a x + b n 5 4 4 3 2 3 +--R 12a x log(c (-------) ) + 12b n log(a x + b) + 3a b n x - 4a b n x +--R x +--R + +--R 2 3 2 4 +--R 6a b n x - 12a b n x +--R / +--R 5 +--R 60a +--R Type: Expression(Integer) +--E 147 + +--S 148 of 518 +a0127:= integrate(t0127,x) +--R +--R +--R (133) +--R 5 5 5 5 5 a x + b 4 4 +--R 12b n log(a x + b) + 12a x log(c) + 12a n x log(-------) + 3a b n x +--R x +--R + +--R 3 2 3 2 3 2 4 +--R - 4a b n x + 6a b n x - 12a b n x +--R / +--R 5 +--R 60a +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 518 +m0127:= a0127-r0127 +--R +--R +--R 5 a x + b n 5 5 a x + b +--R - x log(c (-------) ) + x log(c) + n x log(-------) +--R x x +--R (134) --------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 518 +d0127:= D(m0127,x) +--R +--R +--R (135) +--R 5 4 a x + b n a x + b n +--R (- 5a x - 5b x )(-------) log(c (-------) ) +--R x x +--R + +--R 5 4 5 4 a x + b 4 +--R ((5a x + 5b x )log(c) + (5a n x + 5b n x )log(-------) - b n x ) +--R x +--R * +--R a x + b n +--R (-------) +--R x +--R + +--R 4 2 3 a x + b n - 1 +--R (a b n x + b n x )(-------) +--R x +--R / +--R a x + b n +--R (5a x + 5b)(-------) +--R x +--R Type: Expression(Integer) +--E 150 + +--S 151 of 518 +t0128:= x^3*log(c*(a+b/x)^n) +--R +--R +--R 3 a x + b n +--R (136) x log(c (-------) ) +--R x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 518 +r0128:= 1/24/a^4*(6*b^3*n*x*a-3*a^2*b^2*n*x^2+2*x^3*n*b*a^3+_ + 6*x^4*log(c*((a*x+b)/x)^n)*a^4-6*b^4*n*log(a*x+b)) +--R +--R +--R (137) +--R 4 4 a x + b n 4 3 3 2 2 2 3 +--R 6a x log(c (-------) ) - 6b n log(a x + b) + 2a b n x - 3a b n x + 6a b n x +--R x +--R ----------------------------------------------------------------------------- +--R 4 +--R 24a +--R Type: Expression(Integer) +--E 152 + +--S 153 of 518 +a0128:= integrate(t0128,x) +--R +--R +--R (138) +--R 4 4 4 4 4 a x + b 3 3 +--R - 6b n log(a x + b) + 6a x log(c) + 6a n x log(-------) + 2a b n x +--R x +--R + +--R 2 2 2 3 +--R - 3a b n x + 6a b n x +--R / +--R 4 +--R 24a +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 518 +m0128:= a0128-r0128 +--R +--R +--R 4 a x + b n 4 4 a x + b +--R - x log(c (-------) ) + x log(c) + n x log(-------) +--R x x +--R (139) --------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 518 +d0128:= D(m0128,x) +--R +--R +--R (140) +--R 4 3 a x + b n a x + b n +--R (- 4a x - 4b x )(-------) log(c (-------) ) +--R x x +--R + +--R 4 3 4 3 a x + b 3 +--R ((4a x + 4b x )log(c) + (4a n x + 4b n x )log(-------) - b n x ) +--R x +--R * +--R a x + b n +--R (-------) +--R x +--R + +--R 3 2 2 a x + b n - 1 +--R (a b n x + b n x )(-------) +--R x +--R / +--R a x + b n +--R (4a x + 4b)(-------) +--R x +--R Type: Expression(Integer) +--E 155 + +--S 156 of 518 +t0129:= x^2*log(c*(a+b/x)^n) +--R +--R +--R 2 a x + b n +--R (141) x log(c (-------) ) +--R x +--R Type: Expression(Integer) +--E 156 + +--S 157 of 518 +r0129:= 1/6/a^3*(-2*b^2*n*x*a+x^2*n*b*a^2+2*x^3*log(c*((a*x+b)/x)^n)*a^3+_ + 2*b^3*n*log(a*x+b)) +--R +--R +--R 3 3 a x + b n 3 2 2 2 +--R 2a x log(c (-------) ) + 2b n log(a x + b) + a b n x - 2a b n x +--R x +--R (142) ---------------------------------------------------------------- +--R 3 +--R 6a +--R Type: Expression(Integer) +--E 157 + +--S 158 of 518 +a0129:= integrate(t0129,x) +--R +--R +--R (143) +--R 3 3 3 3 3 a x + b 2 2 2 +--R 2b n log(a x + b) + 2a x log(c) + 2a n x log(-------) + a b n x - 2a b n x +--R x +--R --------------------------------------------------------------------------- +--R 3 +--R 6a +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 518 +m0129:= a0129-r0129 +--R +--R +--R 3 a x + b n 3 3 a x + b +--R - x log(c (-------) ) + x log(c) + n x log(-------) +--R x x +--R (144) --------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 518 +d0129:= D(m0129,x) +--R +--R +--R (145) +--R 3 2 a x + b n a x + b n +--R (- 3a x - 3b x )(-------) log(c (-------) ) +--R x x +--R + +--R 3 2 3 2 a x + b 2 +--R ((3a x + 3b x )log(c) + (3a n x + 3b n x )log(-------) - b n x ) +--R x +--R * +--R a x + b n +--R (-------) +--R x +--R + +--R 2 2 a x + b n - 1 +--R (a b n x + b n x)(-------) +--R x +--R / +--R a x + b n +--R (3a x + 3b)(-------) +--R x +--R Type: Expression(Integer) +--E 160 + +--S 161 of 518 +t0130:= x*log(c*(a+b/x)^n) +--R +--R +--R a x + b n +--R (146) x log(c (-------) ) +--R x +--R Type: Expression(Integer) +--E 161 + +--S 162 of 518 +r0130:= 1/2/a^2*(a*b*n*x+x^2*log(c*((a*x+b)/x)^n)*a^2-b^2*n*log(a*x+b)) +--R +--R +--R 2 2 a x + b n 2 +--R a x log(c (-------) ) - b n log(a x + b) + a b n x +--R x +--R (147) -------------------------------------------------- +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 518 +a0130:= integrate(t0130,x) +--R +--R +--R 2 2 2 2 2 a x + b +--R - b n log(a x + b) + a x log(c) + a n x log(-------) + a b n x +--R x +--R (148) -------------------------------------------------------------- +--R 2 +--R 2a +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 518 +m0130:= a0130-r0130 +--R +--R +--R 2 a x + b n 2 2 a x + b +--R - x log(c (-------) ) + x log(c) + n x log(-------) +--R x x +--R (149) --------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 518 +d0130:= D(m0130,x) +--R +--R +--R (150) +--R 2 a x + b n a x + b n +--R (- 2a x - 2b x)(-------) log(c (-------) ) +--R x x +--R + +--R 2 2 a x + b a x + b n +--R ((2a x + 2b x)log(c) + (2a n x + 2b n x)log(-------) - b n x)(-------) +--R x x +--R + +--R 2 a x + b n - 1 +--R (a b n x + b n)(-------) +--R x +--R / +--R a x + b n +--R (2a x + 2b)(-------) +--R x +--R Type: Expression(Integer) +--E 165 + +--S 166 of 518 +t0131:= log(c*(a+b/x)^n)/x +--R +--R +--R a x + b n +--R log(c (-------) ) +--R x +--R (151) ----------------- +--R x +--R Type: Expression(Integer) +--E 166 + +--S 167 of 518 +r0131:= -log(c*(a+b/x)^n)*log(-b/a/x)-n*polylog(2,1+b/a/x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 167 + +--S 168 of 518 +a0131:= integrate(t0131,x) +--R +--R +--R b + %L a n +--R x log(c (--------) ) +--R ++ %L +--R (152) | ------------------ d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 518 +--m0131:= a0131-r0131 +--E 169 + +--S 170 of 518 +--d0131:= D(m0131,x) +--E 170 + +--S 171 of 518 +t0132:= log(c*(a+b/x)^n)/x^2 +--R +--R +--R a x + b n +--R log(c (-------) ) +--R x +--R (153) ----------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 518 +r0132:= n/x-(a+b/x)*log(c*(a+b/x)^n)/b +--R +--R +--R a x + b n +--R (- a x - b)log(c (-------) ) + b n +--R x +--R (154) ---------------------------------- +--R b x +--R Type: Expression(Integer) +--E 172 + +--S 173 of 518 +a0132:= integrate(t0132,x) +--R +--R +--R a x + b +--R - b log(c) + (- a n x - b n)log(-------) + b n +--R x +--R (155) ---------------------------------------------- +--R b x +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 518 +m0132:= a0132-r0132 +--R +--R +--R a x + b n a x + b +--R (a x + b)log(c (-------) ) - b log(c) + (- a n x - b n)log(-------) +--R x x +--R (156) ------------------------------------------------------------------- +--R b x +--R Type: Expression(Integer) +--E 174 + +--S 175 of 518 +d0132:= D(m0132,x) +--R +--R +--R (157) +--R a x + b n a x + b n +--R - x (-------) log(c (-------) ) +--R x x +--R + +--R a x + b a x + b n +--R (x log(c) + n x log(-------) + n x)(-------) +--R x x +--R + +--R a x + b n - 1 +--R (- a n x - b n)(-------) +--R x +--R / +--R 3 a x + b n +--R x (-------) +--R x +--R Type: Expression(Integer) +--E 175 + +--S 176 of 518 +t0133:= log(c*(a+b/x)^n)/x^3 +--R +--R +--R a x + b n +--R log(c (-------) ) +--R x +--R (158) ----------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 518 +r0133:= -1/4/b^2/x^2*(-b^2*n+2*a*b*n*x+2*log(c*((a*x+b)/x)^n)*b^2+_ + 2*a^2*n*log(x)*x^2-2*a^2*n*log(a*x+b)*x^2) +--R +--R +--R (159) +--R 2 a x + b n 2 2 2 2 2 +--R - 2b log(c (-------) ) + 2a n x log(a x + b) - 2a n x log(x) - 2a b n x + b n +--R x +--R ----------------------------------------------------------------------------- +--R 2 2 +--R 4b x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 518 +a0133:= integrate(t0133,x) +--R +--R +--R 2 2 2 2 a x + b 2 +--R - 2b log(c) + (2a n x - 2b n)log(-------) - 2a b n x + b n +--R x +--R (160) ----------------------------------------------------------- +--R 2 2 +--R 4b x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 518 +m0133:= a0133-r0133 +--R +--R +--R (161) +--R 2 a x + b n 2 2 2 2 2 +--R b log(c (-------) ) - a n x log(a x + b) + a n x log(x) - b log(c) +--R x +--R + +--R 2 2 2 a x + b +--R (a n x - b n)log(-------) +--R x +--R / +--R 2 2 +--R 2b x +--R Type: Expression(Integer) +--E 179 + +--S 180 of 518 +d0133:= D(m0133,x) +--R +--R +--R (162) +--R 2 a x + b n a x + b n +--R (- 2a x - 2b x)(-------) log(c (-------) ) +--R x x +--R + +--R 2 2 a x + b a x + b n +--R ((2a x + 2b x)log(c) + (2a n x + 2b n x)log(-------) + b n x)(-------) +--R x x +--R + +--R 2 a x + b n - 1 +--R (- a b n x - b n)(-------) +--R x +--R / +--R 5 4 a x + b n +--R (2a x + 2b x )(-------) +--R x +--R Type: Expression(Integer) +--E 180 + +--S 181 of 518 +t0134:= log(c*(a+b/x)^n)/x^4 +--R +--R +--R a x + b n +--R log(c (-------) ) +--R x +--R (163) ----------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 518 +r0134:= -1/18/b^3/x^3*(-2*b^3*n+3*b^2*n*x*a-6*x^2*n*b*a^2+_ + 6*log(c*((a*x+b)/x)^n)*b^3-6*a^3*n*log(x)*x^3+6*a^3*n*log(a*x+b)*x^3) +--R +--R +--R (164) +--R 3 a x + b n 3 3 3 3 2 2 +--R - 6b log(c (-------) ) - 6a n x log(a x + b) + 6a n x log(x) + 6a b n x +--R x +--R + +--R 2 3 +--R - 3a b n x + 2b n +--R / +--R 3 3 +--R 18b x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 518 +a0134:= integrate(t0134,x) +--R +--R +--R (165) +--R 3 3 3 3 a x + b 2 2 2 3 +--R - 6b log(c) + (- 6a n x - 6b n)log(-------) + 6a b n x - 3a b n x + 2b n +--R x +--R -------------------------------------------------------------------------- +--R 3 3 +--R 18b x +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 518 +m0134:= a0134-r0134 +--R +--R +--R (166) +--R 3 a x + b n 3 3 3 3 3 +--R b log(c (-------) ) + a n x log(a x + b) - a n x log(x) - b log(c) +--R x +--R + +--R 3 3 3 a x + b +--R (- a n x - b n)log(-------) +--R x +--R / +--R 3 3 +--R 3b x +--R Type: Expression(Integer) +--E 184 + +--S 185 of 518 +d0134:= D(m0134,x) +--R +--R +--R (167) +--R 2 a x + b n a x + b n +--R (- 3a x - 3b x)(-------) log(c (-------) ) +--R x x +--R + +--R 2 2 a x + b a x + b n +--R ((3a x + 3b x)log(c) + (3a n x + 3b n x)log(-------) + b n x)(-------) +--R x x +--R + +--R 2 a x + b n - 1 +--R (- a b n x - b n)(-------) +--R x +--R / +--R 6 5 a x + b n +--R (3a x + 3b x )(-------) +--R x +--R Type: Expression(Integer) +--E 185 + +--S 186 of 518 +t0135:= x^4*log(c*(a+b/x^2)^n) +--R +--R +--R 2 n +--R 4 a x + b +--R (168) x log(c (--------) ) +--R 2 +--R x +--R Type: Expression(Integer) +--E 186 + +--S 187 of 518 +r0135:= -2/5*b^2*n*x/a^2+2/15*b*n*x^3/a+_ + 2/5*b^(5/2)*n*atan(a^(1/2)*x/b^(1/2))/a^(5/2)+_ + 1/5*x^5*log(c*(a+b/x^2)^n) +--R +--R +--R (169) +--R 2 n +-+ +--R 2 5 +-+ a x + b 2 +-+ x\|a 3 2 +-+ +--R 3a x \|a log(c (--------) ) + 6b n\|b atan(-----) + (2a b n x - 6b n x)\|a +--R 2 +-+ +--R x \|b +--R ---------------------------------------------------------------------------- +--R 2 +-+ +--R 15a \|a +--R Type: Expression(Integer) +--E 187 + +--S 188 of 518 +a0135:= integrate(t0135,x) +--R +--R +--R (170) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R 2 | b \| a 2 5 +--R 3b n |- - log(---------------------) + 3a x log(c) +--R \| a 2 +--R a x + b +--R + +--R 2 +--R 2 5 a x + b 3 2 +--R 3a n x log(--------) + 2a b n x - 6b n x +--R 2 +--R x +--R / +--R 2 +--R 15a +--R , +--R +--R +-+ +--R |b +--R +-+ |- 2 +--R 2 |b \|a 2 5 2 5 a x + b 3 +--R - 6b n |- atan(----) + 3a x log(c) + 3a n x log(--------) + 2a b n x +--R \|a x 2 +--R x +--R + +--R 2 +--R - 6b n x +--R / +--R 2 +--R 15a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 188 + +--S 189 of 518 +m0135a:= a0135.1-r0135 +--R +--R +--R (171) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b 2 n +--R 2 | b +-+ \| a 2 5 +-+ a x + b +--R b n |- - \|a log(---------------------) - a x \|a log(c (--------) ) +--R \| a 2 2 +--R a x + b x +--R + +--R +-+ 2 +--R 2 +-+ x\|a 2 5 2 5 a x + b +-+ +--R - 2b n\|b atan(-----) + (a x log(c) + a n x log(--------))\|a +--R +-+ 2 +--R \|b x +--R / +--R 2 +-+ +--R 5a \|a +--R Type: Expression(Integer) +--E 189 + +--S 190 of 518 +d0135a:= D(m0135a,x) +--R +--R +--R (172) +--R 2 n 2 n +--R 6 4 a x + b a x + b +--R (- 5a x - 5b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 6 4 6 4 a x + b 4 +--R ((5a x + 5b x )log(c) + (5a n x + 5b n x )log(--------) - 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 4 2 2 a x + b +--R (2a b n x + 2b n x )(--------) +--R 2 +--R x +--R / +--R 2 n +--R 2 a x + b +--R (5a x + 5b)(--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 190 + +--S 191 of 518 +m0135b:= a0135.2-r0135 +--R +--R +--R (173) +--R +-+ +--R |b +--R 2 n +-+ |- +--R 2 5 +-+ a x + b 2 +-+ |b \|a +--R - a x \|a log(c (--------) ) - 2b n\|a |- atan(----) +--R 2 \|a x +--R x +--R + +--R +-+ 2 +--R 2 +-+ x\|a 2 5 2 5 a x + b +-+ +--R - 2b n\|b atan(-----) + (a x log(c) + a n x log(--------))\|a +--R +-+ 2 +--R \|b x +--R / +--R 2 +-+ +--R 5a \|a +--R Type: Expression(Integer) +--E 191 + +--S 192 of 518 +d0135b:= D(m0135b,x) +--R +--R +--R (174) +--R 2 n 2 n +--R 6 4 a x + b a x + b +--R (- 5a x - 5b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 6 4 6 4 a x + b 4 +--R ((5a x + 5b x )log(c) + (5a n x + 5b n x )log(--------) - 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 4 2 2 a x + b +--R (2a b n x + 2b n x )(--------) +--R 2 +--R x +--R / +--R 2 n +--R 2 a x + b +--R (5a x + 5b)(--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 518 +t0136:= x^3*log(c*(a+b/x^2)^n) +--R +--R +--R 2 n +--R 3 a x + b +--R (175) x log(c (--------) ) +--R 2 +--R x +--R Type: Expression(Integer) +--E 193 + +--S 194 of 518 +r0136:= 1/4*b*n*x^2/a+1/4*x^4*log(c*(a+b/x^2)^n)-1/4*b^2*n*log(a*x^2+b)/a^2 +--R +--R +--R 2 n +--R 2 4 a x + b 2 2 2 +--R a x log(c (--------) ) - b n log(a x + b) + a b n x +--R 2 +--R x +--R (176) ----------------------------------------------------- +--R 2 +--R 4a +--R Type: Expression(Integer) +--E 194 + +--S 195 of 518 +a0136:= integrate(t0136,x) +--R +--R +--R 2 +--R 2 2 2 4 2 4 a x + b 2 +--R - b n log(a x + b) + a x log(c) + a n x log(--------) + a b n x +--R 2 +--R x +--R (177) ----------------------------------------------------------------- +--R 2 +--R 4a +--R Type: Union(Expression(Integer),...) +--E 195 + +--S 196 of 518 +m0136:= a0136-r0136 +--R +--R +--R 2 n 2 +--R 4 a x + b 4 4 a x + b +--R - x log(c (--------) ) + x log(c) + n x log(--------) +--R 2 2 +--R x x +--R (178) ----------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 518 +d0136:= D(m0136,x) +--R +--R +--R (179) +--R 2 n 2 n +--R 5 3 a x + b a x + b +--R (- 2a x - 2b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 5 3 5 3 a x + b 3 +--R ((2a x + 2b x )log(c) + (2a n x + 2b n x )log(--------) - b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 3 2 a x + b +--R (a b n x + b n x)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 2 a x + b +--R (2a x + 2b)(--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 518 +t0137:= x^2*log(c*(a+b/x^2)^n) +--R +--R +--R 2 n +--R 2 a x + b +--R (180) x log(c (--------) ) +--R 2 +--R x +--R Type: Expression(Integer) +--E 198 + +--S 199 of 518 +r0137:= 2/3*b*n*x/a-2/3*b^(3/2)*n*atan(a^(1/2)*x/b^(1/2))/a^(3/2)+_ + 1/3*x^3*log(c*(a+b/x^2)^n) +--R +--R +--R 2 n +-+ +--R 3 +-+ a x + b +-+ x\|a +-+ +--R a x \|a log(c (--------) ) - 2b n\|b atan(-----) + 2b n x\|a +--R 2 +-+ +--R x \|b +--R (181) ------------------------------------------------------------- +--R +-+ +--R 3a\|a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 518 +a0137:= integrate(t0137,x) +--R +--R +--R (182) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R | b \| a 3 +--R b n |- - log(-----------------------) + a x log(c) +--R \| a 2 +--R a x + b +--R + +--R 2 +--R 3 a x + b +--R a n x log(--------) + 2b n x +--R 2 +--R x +--R / +--R 3a +--R , +--R +-+ +--R |b +--R +-+ |- 2 +--R |b \|a 3 3 a x + b +--R 2b n |- atan(----) + a x log(c) + a n x log(--------) + 2b n x +--R \|a x 2 +--R x +--R --------------------------------------------------------------] +--R 3a +--R Type: Union(List(Expression(Integer)),...) +--E 200 + +--S 201 of 518 +m0137a:= a0137.1-r0137 +--R +--R +--R (183) +--R +---+ +--R | b 2 +--R 2 n +---+ - 2a x |- - + a x - b +--R 3 +-+ a x + b | b +-+ \| a +--R - a x \|a log(c (--------) ) + b n |- - \|a log(-----------------------) +--R 2 \| a 2 +--R x a x + b +--R + +--R +-+ 2 +--R +-+ x\|a 3 3 a x + b +-+ +--R 2b n\|b atan(-----) + (a x log(c) + a n x log(--------))\|a +--R +-+ 2 +--R \|b x +--R / +--R +-+ +--R 3a\|a +--R Type: Expression(Integer) +--E 201 + +--S 202 of 518 +d0137a:= D(m0137a,x) +--R +--R +--R (184) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- 3a x - 3b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((3a x + 3b x )log(c) + (3a n x + 3b n x )log(--------) - 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (2a b n x + 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 2 a x + b +--R (3a x + 3b)(--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 518 +m0137b:= a0137.2-r0137 +--R +--R +--R (185) +--R +-+ +--R |b +--R 2 n +-+ |- +--R 3 +-+ a x + b +-+ |b \|a +--R - a x \|a log(c (--------) ) + 2b n\|a |- atan(----) +--R 2 \|a x +--R x +--R + +--R +-+ 2 +--R +-+ x\|a 3 3 a x + b +-+ +--R 2b n\|b atan(-----) + (a x log(c) + a n x log(--------))\|a +--R +-+ 2 +--R \|b x +--R / +--R +-+ +--R 3a\|a +--R Type: Expression(Integer) +--E 203 + +--S 204 of 518 +d0137b:= D(m0137b,x) +--R +--R +--R (186) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- 3a x - 3b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((3a x + 3b x )log(c) + (3a n x + 3b n x )log(--------) - 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (2a b n x + 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 2 a x + b +--R (3a x + 3b)(--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 204 + +--S 205 of 518 +t0138:= x*log(c*(a+b/x^2)^n) +--R +--R +--R 2 n +--R a x + b +--R (187) x log(c (--------) ) +--R 2 +--R x +--R Type: Expression(Integer) +--E 205 + +--S 206 of 518 +r0138:= 1/2*x^2*log(c*(a+b/x^2)^n)+1/2*b*n*log(a*x^2+b)/a +--R +--R +--R 2 n +--R 2 a x + b 2 +--R a x log(c (--------) ) + b n log(a x + b) +--R 2 +--R x +--R (188) ------------------------------------------ +--R 2a +--R Type: Expression(Integer) +--E 206 + +--S 207 of 518 +a0138:= integrate(t0138,x) +--R +--R +--R 2 +--R 2 2 2 a x + b +--R b n log(a x + b) + a x log(c) + a n x log(--------) +--R 2 +--R x +--R (189) ---------------------------------------------------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 207 + +--S 208 of 518 +m0138:= a0138-r0138 +--R +--R +--R 2 n 2 +--R 2 a x + b 2 2 a x + b +--R - x log(c (--------) ) + x log(c) + n x log(--------) +--R 2 2 +--R x x +--R (190) ----------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 208 + +--S 209 of 518 +d0138:= D(m0138,x) +--R +--R +--R (191) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- a x - b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((a x + b x )log(c) + (a n x + b n x )log(--------) - b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (a b n x + b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 3 a x + b +--R (a x + b x)(--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 209 + +--S 210 of 518 +t0139:= log(c*(a+b/x^2)^n)/x +--R +--R +--R 2 n +--R a x + b +--R log(c (--------) ) +--R 2 +--R x +--R (192) ------------------ +--R x +--R Type: Expression(Integer) +--E 210 + +--S 211 of 518 +r0139:= -1/2*log(c*(a+b/x^2)^n)*log(-b/a/x^2)-1/2*n*polylog(2,1+b/a/x^2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 518 +a0139:= integrate(t0139,x) +--R +--R +--R 2 n +--R b + %L a +--R log(c (--------) ) +--R x 2 +--R ++ %L +--R (193) | ------------------ d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 212 + +--S 213 of 518 +--m0139:= a0139-r0139 +--E 213 + +--S 214 of 518 +--d0139:= D(m0139,x) +--E 214 + +--S 215 of 518 +t0140:= log(c*(a+b/x^2)^n)/x^2 +--R +--R +--R 2 n +--R a x + b +--R log(c (--------) ) +--R 2 +--R x +--R (194) ------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 215 + +--S 216 of 518 +r0140:= 2*n/x+2*a^(1/2)*n*atan(a^(1/2)*x/b^(1/2))/b^(1/2)-log(c*(a+b/x^2)^n)/x +--R +--R +--R 2 n +-+ +--R +-+ a x + b +-+ x\|a +-+ +--R - \|b log(c (--------) ) + 2n x\|a atan(-----) + 2n\|b +--R 2 +-+ +--R x \|b +--R (195) ------------------------------------------------------- +--R +-+ +--R x\|b +--R Type: Expression(Integer) +--E 216 + +--S 217 of 518 +a0140:= integrate(t0140,x) +--R +--R +--R (196) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b 2 +--R | a \| b a x + b +--R n x |- - log(---------------------) - log(c) - n log(--------) + 2n +--R \| b 2 2 +--R a x + b x +--R [-------------------------------------------------------------------, +--R x +--R +-+ +--R |a +--R +-+ b |- 2 +--R |a \|b a x + b +--R - 2n x |- atan(-----) - log(c) - n log(--------) + 2n +--R \|b a x 2 +--R x +--R -----------------------------------------------------] +--R x +--R Type: Union(List(Expression(Integer)),...) +--E 217 + +--S 218 of 518 +m0140a:= a0140.1-r0140 +--R +--R +--R (197) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b 2 n +--R | a +-+ \| b +-+ a x + b +--R n x |- - \|b log(---------------------) + \|b log(c (--------) ) +--R \| b 2 2 +--R a x + b x +--R + +--R +-+ 2 +--R +-+ x\|a a x + b +-+ +--R - 2n x\|a atan(-----) + (- log(c) - n log(--------))\|b +--R +-+ 2 +--R \|b x +--R / +--R +-+ +--R x\|b +--R Type: Expression(Integer) +--E 218 + +--S 219 of 518 +d0140a:= D(m0140a,x) +--R +--R +--R (198) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- a x - b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((a x + b x )log(c) + (a n x + b n x )log(--------) + 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (- 2a b n x - 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 6 4 a x + b +--R (a x + b x )(--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 219 + +--S 220 of 518 +m0140b:= a0140.2-r0140 +--R +--R +--R (199) +--R +-+ +--R |a +--R 2 n +-+ b |- +-+ +--R +-+ a x + b |a +-+ \|b +-+ x\|a +--R \|b log(c (--------) ) - 2n x |- \|b atan(-----) - 2n x\|a atan(-----) +--R 2 \|b a x +-+ +--R x \|b +--R + +--R 2 +--R a x + b +-+ +--R (- log(c) - n log(--------))\|b +--R 2 +--R x +--R / +--R +-+ +--R x\|b +--R Type: Expression(Integer) +--E 220 + +--S 221 of 518 +d0140b:= D(m0140b,x) +--R +--R +--R (200) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- a x - b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((a x + b x )log(c) + (a n x + b n x )log(--------) + 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (- 2a b n x - 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 6 4 a x + b +--R (a x + b x )(--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 221 + +--S 222 of 518 +t0141:= log(c*(a+b/x^2)^n)/x^3 +--R +--R +--R 2 n +--R a x + b +--R log(c (--------) ) +--R 2 +--R x +--R (201) ------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 518 +r0141:= 1/2*n/x^2-1/2*(a+b/x^2)*log(c*(a+b/x^2)^n)/b +--R +--R +--R 2 n +--R 2 a x + b +--R (- a x - b)log(c (--------) ) + b n +--R 2 +--R x +--R (202) ------------------------------------ +--R 2 +--R 2b x +--R Type: Expression(Integer) +--E 223 + +--S 224 of 518 +a0141:= integrate(t0141,x) +--R +--R +--R 2 +--R 2 a x + b +--R - b log(c) + (- a n x - b n)log(--------) + b n +--R 2 +--R x +--R (203) ------------------------------------------------ +--R 2 +--R 2b x +--R Type: Union(Expression(Integer),...) +--E 224 + +--S 225 of 518 +m0141:= a0141-r0141 +--R +--R +--R (204) +--R 2 n 2 +--R 2 a x + b 2 a x + b +--R (a x + b)log(c (--------) ) - b log(c) + (- a n x - b n)log(--------) +--R 2 2 +--R x x +--R ----------------------------------------------------------------------- +--R 2 +--R 2b x +--R Type: Expression(Integer) +--E 225 + +--S 226 of 518 +d0141:= D(m0141,x) +--R +--R +--R (205) +--R 2 n 2 n +--R 2 a x + b a x + b +--R - x (--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 2 n +--R 2 2 a x + b 2 a x + b +--R (x log(c) + n x log(--------) + n x )(--------) +--R 2 2 +--R x x +--R + +--R 2 n - 1 +--R 2 a x + b +--R (- a n x - b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 5 a x + b +--R x (--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 226 + +--S 227 of 518 +t0142:= log(c*(a+b/x^2)^n)/x^4 +--R +--R +--R 2 n +--R a x + b +--R log(c (--------) ) +--R 2 +--R x +--R (206) ------------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 227 + +--S 228 of 518 +r0142:= 2/9*n/x^3-2/3*a*n/b/x-2/3*a^(3/2)*n*_ + atan(a^(1/2)*x/b^(1/2))/b^(3/2)-1/3*log(c*(a+b/x^2)^n)/x^3 +--R +--R +--R (207) +--R 2 n +-+ +--R +-+ a x + b 3 +-+ x\|a 2 +-+ +--R - 3b\|b log(c (--------) ) - 6a n x \|a atan(-----) + (- 6a n x + 2b n)\|b +--R 2 +-+ +--R x \|b +--R ---------------------------------------------------------------------------- +--R 3 +-+ +--R 9b x \|b +--R Type: Expression(Integer) +--E 228 + +--S 229 of 518 +a0142:= integrate(t0142,x) +--R +--R +--R (208) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +--R 3 | a \| b +--R 3a n x |- - log(-----------------------) - 3b log(c) +--R \| b 2 +--R a x + b +--R + +--R 2 +--R a x + b 2 +--R - 3b n log(--------) - 6a n x + 2b n +--R 2 +--R x +--R / +--R 3 +--R 9b x +--R , +--R +-+ +--R |a +--R +-+ b |- 2 +--R 3 |a \|b a x + b 2 +--R 6a n x |- atan(-----) - 3b log(c) - 3b n log(--------) - 6a n x + 2b n +--R \|b a x 2 +--R x +--R ------------------------------------------------------------------------] +--R 3 +--R 9b x +--R Type: Union(List(Expression(Integer)),...) +--E 229 + +--S 230 of 518 +m0142a:= a0142.1-r0142 +--R +--R +--R (209) +--R +---+ +--R | a 2 +--R 2 n +---+ - 2b x |- - + a x - b +--R +-+ a x + b 3 | a +-+ \| b +--R b\|b log(c (--------) ) + a n x |- - \|b log(-----------------------) +--R 2 \| b 2 +--R x a x + b +--R + +--R +-+ 2 +--R 3 +-+ x\|a a x + b +-+ +--R 2a n x \|a atan(-----) + (- b log(c) - b n log(--------))\|b +--R +-+ 2 +--R \|b x +--R / +--R 3 +-+ +--R 3b x \|b +--R Type: Expression(Integer) +--E 230 + +--S 231 of 518 +d0142a:= D(m0142a,x) +--R +--R +--R (210) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- 3a x - 3b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((3a x + 3b x )log(c) + (3a n x + 3b n x )log(--------) + 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (- 2a b n x - 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 8 6 a x + b +--R (3a x + 3b x )(--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 231 + +--S 232 of 518 +m0142b:= a0142.2-r0142 +--R +--R +--R (211) +--R +-+ +--R |a +--R 2 n +-+ b |- +--R +-+ a x + b 3 |a +-+ \|b +--R b\|b log(c (--------) ) + 2a n x |- \|b atan(-----) +--R 2 \|b a x +--R x +--R + +--R +-+ 2 +--R 3 +-+ x\|a a x + b +-+ +--R 2a n x \|a atan(-----) + (- b log(c) - b n log(--------))\|b +--R +-+ 2 +--R \|b x +--R / +--R 3 +-+ +--R 3b x \|b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 518 +d0142b:= D(m0142b,x) +--R +--R +--R (212) +--R 2 n 2 n +--R 4 2 a x + b a x + b +--R (- 3a x - 3b x )(--------) log(c (--------) ) +--R 2 2 +--R x x +--R + +--R 2 +--R 4 2 4 2 a x + b 2 +--R ((3a x + 3b x )log(c) + (3a n x + 3b n x )log(--------) + 2b n x ) +--R 2 +--R x +--R * +--R 2 n +--R a x + b +--R (--------) +--R 2 +--R x +--R + +--R 2 n - 1 +--R 2 2 a x + b +--R (- 2a b n x - 2b n)(--------) +--R 2 +--R x +--R / +--R 2 n +--R 8 6 a x + b +--R (3a x + 3b x )(--------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 233 + +--S 234 of 518 +t0143:= x^4*log(c*(a+b*x^(1/2))^n) +--R +--R +--R 4 +-+ n +--R (213) x log(c (b\|x + a) ) +--R Type: Expression(Integer) +--E 234 + +--S 235 of 518 +r0143:= 1/12600*(2520*a^9*n*x^(1/2)*b-1260*a^8*n*x*b^2+840*a^7*n*_ + x^(3/2)*b^3-630*a^6*n*x^2*b^4+504*a^5*n*x^(5/2)*b^5-420*a^4*n*_ + x^3*b^6+360*a^3*n*x^(7/2)*b^7-315*a^2*n*x^4*b^8+_ + 280*a*n*x^(9/2)*b^9-252*n*x^5*b^10-2520*a^10*n*log(a+b*x^(1/2))+_ + 2520*x^5*log(c*(a+b*x^(1/2))^n)*b^10)/b^10 +--R +--R +--R (214) +--R 10 5 +-+ n 10 +-+ +--R 2520b x log(c (b\|x + a) ) - 2520a n log(b\|x + a) +--R + +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ +--R (280a b n x + 360a b n x + 504a b n x + 840a b n x + 2520a b n)\|x +--R + +--R 10 5 2 8 4 4 6 3 6 4 2 8 2 +--R - 252b n x - 315a b n x - 420a b n x - 630a b n x - 1260a b n x +--R / +--R 10 +--R 12600b +--R Type: Expression(Integer) +--E 235 + +--S 236 of 518 +a0143:= integrate(t0143,x) +--R +--R +--R (215) +--R 10 5 10 +-+ +--R (2520b n x - 2520a n)log(b\|x + a) +--R + +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ +--R (280a b n x + 360a b n x + 504a b n x + 840a b n x + 2520a b n)\|x +--R + +--R 10 5 10 5 2 8 4 4 6 3 6 4 2 +--R 2520b x log(c) - 252b n x - 315a b n x - 420a b n x - 630a b n x +--R + +--R 8 2 +--R - 1260a b n x +--R / +--R 10 +--R 12600b +--R Type: Union(Expression(Integer),...) +--E 236 + +--S 237 of 518 +m0143:= a0143-r0143 +--R +--R +--R 5 +-+ n 5 +-+ 5 +--R - x log(c (b\|x + a) ) + n x log(b\|x + a) + x log(c) +--R (216) ------------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 518 +d0143:= D(m0143,x) +--R +--R +--R (217) +--R 4 +-+ 4 +-+ n +-+ n +--R (- 10b x \|x - 10a x )(b\|x + a) log(c (b\|x + a) ) +--R + +--R 4 +-+ 4 +-+ 4 4 +-+ +--R (10b n x \|x + 10a n x )log(b\|x + a) + (10b x log(c) + b n x )\|x +--R + +--R 4 +--R 10a x log(c) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R 4 +-+ 2 5 +-+ n - 1 +--R (- a b n x \|x - b n x )(b\|x + a) +--R / +--R +-+ +-+ n +--R (10b\|x + 10a)(b\|x + a) +--R Type: Expression(Integer) +--E 238 + +--S 239 of 518 +t0144:= x^3*log(c*(a+b*x^(1/2))^n) +--R +--R +--R 3 +-+ n +--R (218) x log(c (b\|x + a) ) +--R Type: Expression(Integer) +--E 239 + +--S 240 of 518 +r0144:= 1/3360*(840*a^7*n*x^(1/2)*b-420*a^6*n*x*b^2+280*a^5*n*x^(3/2)*b^3-_ + 210*a^4*n*x^2*b^4+168*a^3*n*x^(5/2)*b^5-140*a^2*n*x^3*b^6+_ + 120*a*n*x^(7/2)*b^7-105*n*x^4*b^8-840*a^8*n*log(a+b*x^(1/2))+_ + 840*x^4*log(c*(a+b*x^(1/2))^n)*b^8)/b^8 +--R +--R +--R (219) +--R 8 4 +-+ n 8 +-+ +--R 840b x log(c (b\|x + a) ) - 840a n log(b\|x + a) +--R + +--R 7 3 3 5 2 5 3 7 +-+ 8 4 +--R (120a b n x + 168a b n x + 280a b n x + 840a b n)\|x - 105b n x +--R + +--R 2 6 3 4 4 2 6 2 +--R - 140a b n x - 210a b n x - 420a b n x +--R / +--R 8 +--R 3360b +--R Type: Expression(Integer) +--E 240 + +--S 241 of 518 +a0144:= integrate(t0144,x) +--R +--R +--R (220) +--R 8 4 8 +-+ +--R (840b n x - 840a n)log(b\|x + a) +--R + +--R 7 3 3 5 2 5 3 7 +-+ 8 4 +--R (120a b n x + 168a b n x + 280a b n x + 840a b n)\|x + 840b x log(c) +--R + +--R 8 4 2 6 3 4 4 2 6 2 +--R - 105b n x - 140a b n x - 210a b n x - 420a b n x +--R / +--R 8 +--R 3360b +--R Type: Union(Expression(Integer),...) +--E 241 + +--S 242 of 518 +m0144:= a0144-r0144 +--R +--R +--R 4 +-+ n 4 +-+ 4 +--R - x log(c (b\|x + a) ) + n x log(b\|x + a) + x log(c) +--R (221) ------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 518 +d0144:= D(m0144,x) +--R +--R +--R (222) +--R 3 +-+ 3 +-+ n +-+ n +--R (- 8b x \|x - 8a x )(b\|x + a) log(c (b\|x + a) ) +--R + +--R 3 +-+ 3 +-+ 3 3 +-+ +--R (8b n x \|x + 8a n x )log(b\|x + a) + (8b x log(c) + b n x )\|x +--R + +--R 3 +--R 8a x log(c) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R 3 +-+ 2 4 +-+ n - 1 +--R (- a b n x \|x - b n x )(b\|x + a) +--R / +--R +-+ +-+ n +--R (8b\|x + 8a)(b\|x + a) +--R Type: Expression(Integer) +--E 243 + +--S 244 of 518 +t0145:= x^2*log(c*(a+b*x^(1/2))^n) +--R +--R +--R 2 +-+ n +--R (223) x log(c (b\|x + a) ) +--R Type: Expression(Integer) +--E 244 + +--S 245 of 518 +r0145:= 1/180*(60*a^5*n*x^(1/2)*b-30*a^4*n*x*b^2+20*a^3*n*x^(3/2)*b^3-_ + 15*a^2*n*x^2*b^4+12*a*n*x^(5/2)*b^5-10*n*x^3*b^6-_ + 60*a^6*n*log(a+b*x^(1/2))+60*x^3*log(c*(a+b*x^(1/2))^n)*b^6)/b^6 +--R +--R +--R (224) +--R 6 3 +-+ n 6 +-+ +--R 60b x log(c (b\|x + a) ) - 60a n log(b\|x + a) +--R + +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 +--R (12a b n x + 20a b n x + 60a b n)\|x - 10b n x - 15a b n x - 30a b n x +--R / +--R 6 +--R 180b +--R Type: Expression(Integer) +--E 245 + +--S 246 of 518 +a0145:= integrate(t0145,x) +--R +--R +--R (225) +--R 6 3 6 +-+ 5 2 3 3 5 +-+ +--R (60b n x - 60a n)log(b\|x + a) + (12a b n x + 20a b n x + 60a b n)\|x +--R + +--R 6 3 6 3 2 4 2 4 2 +--R 60b x log(c) - 10b n x - 15a b n x - 30a b n x +--R / +--R 6 +--R 180b +--R Type: Union(Expression(Integer),...) +--E 246 + +--S 247 of 518 +m0145:= a0145-r0145 +--R +--R +--R 3 +-+ n 3 +-+ 3 +--R - x log(c (b\|x + a) ) + n x log(b\|x + a) + x log(c) +--R (226) ------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 518 +d0145:= D(m0145,x) +--R +--R +--R (227) +--R 2 +-+ 2 +-+ n +-+ n +--R (- 6b x \|x - 6a x )(b\|x + a) log(c (b\|x + a) ) +--R + +--R 2 +-+ 2 +-+ 2 2 +-+ +--R (6b n x \|x + 6a n x )log(b\|x + a) + (6b x log(c) + b n x )\|x +--R + +--R 2 +--R 6a x log(c) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R 2 +-+ 2 3 +-+ n - 1 +--R (- a b n x \|x - b n x )(b\|x + a) +--R / +--R +-+ +-+ n +--R (6b\|x + 6a)(b\|x + a) +--R Type: Expression(Integer) +--E 248 + +--S 249 of 518 +t0146:= x*log(c*(a+b*x^(1/2))^n) +--R +--R +--R +-+ n +--R (228) x log(c (b\|x + a) ) +--R Type: Expression(Integer) +--E 249 + +--S 250 of 518 +r0146:= 1/24*(12*a^3*n*x^(1/2)*b-6*b^2*n*x*a^2+4*a*n*x^(3/2)*b^3-_ + 3*n*x^2*b^4-12*a^4*n*log(a+b*x^(1/2))+_ + 12*x^2*log(c*(a+b*x^(1/2))^n)*b^4)/b^4 +--R +--R +--R (229) +--R 4 2 +-+ n 4 +-+ +--R 12b x log(c (b\|x + a) ) - 12a n log(b\|x + a) +--R + +--R 3 3 +-+ 4 2 2 2 +--R (4a b n x + 12a b n)\|x - 3b n x - 6a b n x +--R / +--R 4 +--R 24b +--R Type: Expression(Integer) +--E 250 + +--S 251 of 518 +a0146:= integrate(t0146,x) +--R +--R +--R (230) +--R 4 2 4 +-+ 3 3 +-+ +--R (12b n x - 12a n)log(b\|x + a) + (4a b n x + 12a b n)\|x +--R + +--R 4 2 4 2 2 2 +--R 12b x log(c) - 3b n x - 6a b n x +--R / +--R 4 +--R 24b +--R Type: Union(Expression(Integer),...) +--E 251 + +--S 252 of 518 +m0146:= a0146-r0146 +--R +--R +--R 2 +-+ n 2 +-+ 2 +--R - x log(c (b\|x + a) ) + n x log(b\|x + a) + x log(c) +--R (231) ------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 518 +d0146:= D(m0146,x) +--R +--R +--R (232) +--R +-+ +-+ n +-+ n +--R (- 4b x\|x - 4a x)(b\|x + a) log(c (b\|x + a) ) +--R + +--R +-+ +-+ +-+ +--R (4b n x\|x + 4a n x)log(b\|x + a) + (4b x log(c) + b n x)\|x +--R + +--R 4a x log(c) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R +-+ 2 2 +-+ n - 1 +--R (- a b n x\|x - b n x )(b\|x + a) +--R / +--R +-+ +-+ n +--R (4b\|x + 4a)(b\|x + a) +--R Type: Expression(Integer) +--E 253 + +--S 254 of 518 +t0147:= log(c*(a+b*x^(1/2))^n) +--R +--R +--R +-+ n +--R (233) log(c (b\|x + a) ) +--R Type: Expression(Integer) +--E 254 + +--S 255 of 518 +r0147:= a*n*x^(1/2)/b-1/2*n*x-a^2*n*log(a+b*x^(1/2))/b^2+_ + x*log(c*(a+b*x^(1/2))^n) +--R +--R +--R 2 +-+ n 2 +-+ +-+ 2 +--R 2b x log(c (b\|x + a) ) - 2a n log(b\|x + a) + 2a b n\|x - b n x +--R (234) ------------------------------------------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 255 + +--S 256 of 518 +a0147:= integrate(t0147,x) +--R +--R +--R 2 2 +-+ +-+ 2 2 +--R (2b n x - 2a n)log(b\|x + a) + 2a b n\|x + 2b x log(c) - b n x +--R (235) ---------------------------------------------------------------- +--R 2 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 256 + +--S 257 of 518 +m0147:= a0147-r0147 +--R +--R +--R +-+ n +-+ +--R (236) - x log(c (b\|x + a) ) + n x log(b\|x + a) + x log(c) +--R Type: Expression(Integer) +--E 257 + +--S 258 of 518 +d0147:= D(m0147,x) +--R +--R +--R (237) +--R +-+ +-+ n +-+ n +--R (- 2b\|x - 2a)(b\|x + a) log(c (b\|x + a) ) +--R + +--R +-+ +-+ +-+ +--R ((2b n\|x + 2a n)log(b\|x + a) + (2b log(c) + b n)\|x + 2a log(c)) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R +-+ 2 +-+ n - 1 +--R (- a b n\|x - b n x)(b\|x + a) +--R / +--R +-+ +-+ n +--R (2b\|x + 2a)(b\|x + a) +--R Type: Expression(Integer) +--E 258 + +--S 259 of 518 +t0148:= log(c*(a+b*x^(1/2))^n)/x +--R +--R +--R +-+ n +--R log(c (b\|x + a) ) +--R (238) ------------------- +--R x +--R Type: Expression(Integer) +--E 259 + +--S 260 of 518 +r0148:= 2*log(c*(a+b*x^(1/2))^n)*log(-b*x^(1/2)/a)+2*n*polylog(2,1+b*x^(1/2)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 260 + +--S 261 of 518 +a0148:= integrate(t0148,x) +--R +--R +--R x +--+ n +--R ++ log(c (b\|%L + a) ) +--R (239) | -------------------- d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 261 + +--S 262 of 518 +--m0148:= a0148-r0148 +--E 262 + +--S 263 of 518 +--d0148:= D(m0148,x) +--E 263 + +--S 264 of 518 +t0149:= log(c*(a+b*x^(1/2))^n)/x^2 +--R +--R +--R +-+ n +--R log(c (b\|x + a) ) +--R (240) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 518 +r0149:= -b*n/a/x^(1/2)+b^2*n*log(a+b*x^(1/2))/a^2-_ + log(c*(a+b*x^(1/2))^n)/x-1/2*b^2*n*log(x)/a^2 +--R +--R +--R (241) +--R 2 +-+ +-+ n 2 +-+ +-+ +--R - 2a \|x log(c (b\|x + a) ) + 2b n x\|x log(b\|x + a) +--R + +--R 2 +-+ +--R - b n x log(x)\|x - 2a b n x +--R / +--R 2 +-+ +--R 2a x\|x +--R Type: Expression(Integer) +--E 265 + +--S 266 of 518 +a0149:= integrate(t0149,x) +--R +--R +--R 2 2 +-+ 2 +-+ +-+ 2 +--R (b n x - a n)log(b\|x + a) - b n x log(\|x ) - a b n\|x - a log(c) +--R (242) -------------------------------------------------------------------- +--R 2 +--R a x +--R Type: Union(Expression(Integer),...) +--E 266 + +--S 267 of 518 +m0149:= a0149-r0149 +--R +--R +--R (243) +--R 2 +-+ n 2 +-+ 2 +-+ +--R 2a log(c (b\|x + a) ) - 2a n log(b\|x + a) - 2b n x log(\|x ) +--R + +--R 2 2 +--R b n x log(x) - 2a log(c) +--R / +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 518 +d0149:= D(m0149,x) +--R +--R +--R (244) +--R +-+ +-+ n +-+ n +--R (- 2b\|x - 2a)(b\|x + a) log(c (b\|x + a) ) +--R + +--R +-+ +-+ +-+ +--R ((2b n\|x + 2a n)log(b\|x + a) + (2b log(c) - b n)\|x + 2a log(c)) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R +-+ 2 +-+ n - 1 +--R (a b n\|x + b n x)(b\|x + a) +--R / +--R 2 +-+ 2 +-+ n +--R (2b x \|x + 2a x )(b\|x + a) +--R Type: Expression(Integer) +--E 268 + +--S 269 of 518 +t0150:= log(c*(a+b*x^(1/2))^n)/x^3 +--R +--R +--R +-+ n +--R log(c (b\|x + a) ) +--R (245) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 269 + +--S 270 of 518 +r0150:= -1/6*b*n/a/x^(3/2)+1/4*b^2*n/a^2/x-1/2*b^3*n/a^3/x^(1/2)+_ + 1/2*b^4*n*log(a+b*x^(1/2))/a^4-_ + 1/2*log(c*(a+b*x^(1/2))^n)/x^2-1/4*b^4*n*log(x)/a^4 +--R +--R +--R (246) +--R 4 +-+ +-+ n 4 2 +-+ +-+ +--R - 6a \|x log(c (b\|x + a) ) + 6b n x \|x log(b\|x + a) +--R + +--R 4 2 2 2 +-+ 3 2 3 +--R (- 3b n x log(x) + 3a b n x)\|x - 6a b n x - 2a b n x +--R / +--R 4 2 +-+ +--R 12a x \|x +--R Type: Expression(Integer) +--E 270 + +--S 271 of 518 +a0150:= integrate(t0150,x) +--R +--R +--R (247) +--R 4 2 4 +-+ 4 2 +-+ +--R (6b n x - 6a n)log(b\|x + a) - 6b n x log(\|x ) +--R + +--R 3 3 +-+ 4 2 2 +--R (- 6a b n x - 2a b n)\|x - 6a log(c) + 3a b n x +--R / +--R 4 2 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 271 + +--S 272 of 518 +m0150:= a0150-r0150 +--R +--R +--R (248) +--R 4 +-+ n 4 +-+ 4 2 +-+ +--R 2a log(c (b\|x + a) ) - 2a n log(b\|x + a) - 2b n x log(\|x ) +--R + +--R 4 2 4 +--R b n x log(x) - 2a log(c) +--R / +--R 4 2 +--R 4a x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 518 +d0150:= D(m0150,x) +--R +--R +--R (249) +--R +-+ +-+ n +-+ n +--R (- 4b\|x - 4a)(b\|x + a) log(c (b\|x + a) ) +--R + +--R +-+ +-+ +-+ +--R ((4b n\|x + 4a n)log(b\|x + a) + (4b log(c) - b n)\|x + 4a log(c)) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R +-+ 2 +-+ n - 1 +--R (a b n\|x + b n x)(b\|x + a) +--R / +--R 3 +-+ 3 +-+ n +--R (4b x \|x + 4a x )(b\|x + a) +--R Type: Expression(Integer) +--E 273 + +--S 274 of 518 +t0151:= log(c*(a+b*x^(1/2))^n)/x^4 +--R +--R +--R +-+ n +--R log(c (b\|x + a) ) +--R (250) ------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 274 + +--S 275 of 518 +r0151:= -1/180*(12*b*n*a^5*x-15*b^2*n*x^(3/2)*a^4+20*b^3*n*x^2*a^3-_ + 30*b^4*n*x^(5/2)*a^2+60*b^5*n*x^3*a-_ + 60*b^6*n*log(a+b*x^(1/2))*x^(7/2)+_ + 60*log(c*(a+b*x^(1/2))^n)*x^(1/2)*a^6+_ + 30*b^6*n*log(x)*x^(7/2))/x^(7/2)/a^6 +--R +--R +--R (251) +--R 6 +-+ +-+ n 6 3 +-+ +-+ +--R - 60a \|x log(c (b\|x + a) ) + 60b n x \|x log(b\|x + a) +--R + +--R 6 3 2 4 2 4 2 +-+ 5 3 3 3 2 +--R (- 30b n x log(x) + 30a b n x + 15a b n x)\|x - 60a b n x - 20a b n x +--R + +--R 5 +--R - 12a b n x +--R / +--R 6 3 +-+ +--R 180a x \|x +--R Type: Expression(Integer) +--E 275 + +--S 276 of 518 +a0151:= integrate(t0151,x) +--R +--R +--R (252) +--R 6 3 6 +-+ 6 3 +-+ +--R (60b n x - 60a n)log(b\|x + a) - 60b n x log(\|x ) +--R + +--R 5 2 3 3 5 +-+ 6 2 4 2 +--R (- 60a b n x - 20a b n x - 12a b n)\|x - 60a log(c) + 30a b n x +--R + +--R 4 2 +--R 15a b n x +--R / +--R 6 3 +--R 180a x +--R Type: Union(Expression(Integer),...) +--E 276 + +--S 277 of 518 +m0151:= a0151-r0151 +--R +--R +--R (253) +--R 6 +-+ n 6 +-+ 6 3 +-+ +--R 2a log(c (b\|x + a) ) - 2a n log(b\|x + a) - 2b n x log(\|x ) +--R + +--R 6 3 6 +--R b n x log(x) - 2a log(c) +--R / +--R 6 3 +--R 6a x +--R Type: Expression(Integer) +--E 277 + +--S 278 of 518 +d0151:= D(m0151,x) +--R +--R +--R (254) +--R +-+ +-+ n +-+ n +--R (- 6b\|x - 6a)(b\|x + a) log(c (b\|x + a) ) +--R + +--R +-+ +-+ +-+ +--R ((6b n\|x + 6a n)log(b\|x + a) + (6b log(c) - b n)\|x + 6a log(c)) +--R * +--R +-+ n +--R (b\|x + a) +--R + +--R +-+ 2 +-+ n - 1 +--R (a b n\|x + b n x)(b\|x + a) +--R / +--R 4 +-+ 4 +-+ n +--R (6b x \|x + 6a x )(b\|x + a) +--R Type: Expression(Integer) +--E 278 + +--S 279 of 518 +t0152:= 1/log(a+b*x) +--R +--R +--R 1 +--R (255) ------------ +--R log(b x + a) +--R Type: Expression(Integer) +--E 279 + +--S 280 of 518 +r0152:= li(a+b*x)/b +--R +--R +--R li(b x + a) +--R (256) ----------- +--R b +--R Type: Expression(Integer) +--E 280 + +--S 281 of 518 +a0152:= integrate(t0152,x) +--R +--R +--R li(b x + a) +--R (257) ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 281 + +--S 282 of 518 +m0152:= a0152-r0152 +--R +--R +--R (258) 0 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 518 +d0152:= D(m0152,x) +--R +--R +--R (259) 0 +--R Type: Expression(Integer) +--E 283 + +--S 284 of 518 +t0153:= log(a+b*x^2)^2 +--R +--R +--R 2 2 +--R (260) log(b x + a) +--R Type: Expression(Integer) +--E 284 + +--S 285 of 518 +r0153:= 8*x-4*x*log(a+b*x^2)+x*log(a+b*x^2)^2-1/(-b)^(1/2)*a^(1/2)*_ + (log(-a^(1/2)/(-b)^(1/2)+x)^2-log(a^(1/2)/(-b)^(1/2)+x)^2+_ + 4*atanh((-b)^(1/2)*x/a^(1/2))*(log(-a^(1/2)/(-b)^(1/2)+x)+_ + log(a^(1/2)/(-b)^(1/2)+x))-4*log(-(a^(1/2)-(-b)^(1/2)*x)/_ + (a^(1/2)+(-b)^(1/2)*x))+2*log(a^(1/2)/(-b)^(1/2)+x)*_ + log(1/2-1/2*(-b)^(1/2)*x/a^(1/2))-2*log(-a^(1/2)/(-b)^(1/2)+x)*_ + log(1/2+1/2*(-b)^(1/2)*x/a^(1/2))-4*atanh((-b)^(1/2)*x/a^(1/2))*_ + log(a+b*x^2)-2*polylog(2,1/2-1/2*(-b)^(1/2)*x/a^(1/2))+2*_ + polylog(2,1/2+1/2*(-b)^(1/2)*x/a^(1/2))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 285 + +--S 286 of 518 +a0153:= integrate(t0153,x) +--R +--R +--R x +--R ++ 2 2 +--R (261) | log(%L b + a) d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 286 + +--S 287 of 518 +--m0153:= a0153-r0153 +--E 287 + +--S 288 of 518 +--d0153:= D(m0153,x) +--E 288 + +--S 289 of 518 +t0154:= x*log(a+b*x^2)^2 +--R +--R +--R 2 2 +--R (262) x log(b x + a) +--R Type: Expression(Integer) +--E 289 + +--S 290 of 518 +r0154:= x^2-(a+b*x^2)*log(a+b*x^2)/b+1/2*(a+b*x^2)*log(a+b*x^2)^2/b +--R +--R +--R 2 2 2 2 2 2 +--R (b x + a)log(b x + a) + (- 2b x - 2a)log(b x + a) + 2b x +--R (263) -------------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 290 + +--S 291 of 518 +a0154:= integrate(t0154,x) +--R +--R +--R 2 2 2 2 2 2 +--R (b x + a)log(b x + a) + (- 2b x - 2a)log(b x + a) + 2b x +--R (264) -------------------------------------------------------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 291 + +--S 292 of 518 +m0154:= a0154-r0154 +--R +--R +--R (265) 0 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 518 +d0154:= D(m0154,x) +--R +--R +--R (266) 0 +--R Type: Expression(Integer) +--E 293 + +--S 294 of 518 +t0155:= log(a+b*x^2)^2/x +--R +--R +--R 2 2 +--R log(b x + a) +--R (267) -------------- +--R x +--R Type: Expression(Integer) +--E 294 + +--S 295 of 518 +r0155:= 1/2*log(-b*x^2/a)*log(a+b*x^2)^2+_ + log(a+b*x^2)*polylog(2,1+b*x^2/a)-polylog(3,(a+b*x^2)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 295 + +--S 296 of 518 +a0155:= integrate(t0155,x) +--R +--R +--R x 2 2 +--R ++ log(%L b + a) +--R (268) | -------------- d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 296 + +--S 297 of 518 +--m0155:= a0155-r0155 +--E 297 + +--S 298 of 518 +--d0155:= D(m0155,x) +--E 298 + +--S 299 of 518 +t0156:= log(a+b*x^2)^2/x^3 +--R +--R +--R 2 2 +--R log(b x + a) +--R (269) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 299 + +--S 300 of 518 +r0156:= b*log(-b*x^2/a)*log(a+b*x^2)/a-_ + 1/2*(a+b*x^2)*log(a+b*x^2)^2/a/x^2+b*polylog(2,1+b*x^2/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 300 + +--S 301 of 518 +a0156:= integrate(t0156,x) +--R +--R +--R x 2 2 +--R ++ log(%L b + a) +--R (270) | -------------- d%L +--R ++ 3 +--R %L +--R Type: Union(Expression(Integer),...) +--E 301 + +--S 302 of 518 +--m0156:= a0156-r0156 +--E 302 + +--S 303 of 518 +--d0156:= D(m0156,x) +--E 303 + +--S 304 of 518 +t0157:= x*log(a+b*x^2)^3 +--R +--R +--R 2 3 +--R (271) x log(b x + a) +--R Type: Expression(Integer) +--E 304 + +--S 305 of 518 +r0157:= -3*x^2+3*(a+b*x^2)*log(a+b*x^2)/b-_ + 3/2*(a+b*x^2)*log(a+b*x^2)^2/b+1/2*(a+b*x^2)*log(a+b*x^2)^3/b +--R +--R +--R (272) +--R 2 2 3 2 2 2 +--R (b x + a)log(b x + a) + (- 3b x - 3a)log(b x + a) +--R + +--R 2 2 2 +--R (6b x + 6a)log(b x + a) - 6b x +--R / +--R 2b +--R Type: Expression(Integer) +--E 305 + +--S 306 of 518 +a0157:= integrate(t0157,x) +--R +--R +--R (273) +--R 2 2 3 2 2 2 +--R (b x + a)log(b x + a) + (- 3b x - 3a)log(b x + a) +--R + +--R 2 2 2 +--R (6b x + 6a)log(b x + a) - 6b x +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 306 + +--S 307 of 518 +m0157:= a0157-r0157 +--R +--R +--R (274) 0 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 518 +d0157:= D(m0157,x) +--R +--R +--R (275) 0 +--R Type: Expression(Integer) +--E 308 + +--S 309 of 518 +t0158:= log(a+b*x^2)^3/x +--R +--R +--R 2 3 +--R log(b x + a) +--R (276) -------------- +--R x +--R Type: Expression(Integer) +--E 309 + +--S 310 of 518 +r0158:= 1/2*log(-b*x^2/a)*log(a+b*x^2)^3+_ + 3/2*log(a+b*x^2)^2*polylog(2,1+b*x^2/a)-_ + 3*log(a+b*x^2)*polylog(3,1+b*x^2/a)+3*polylog(4,(a+b*x^2)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 310 + +--S 311 of 518 +a0158:= integrate(t0158,x) +--R +--R +--R x 2 3 +--R ++ log(%L b + a) +--R (277) | -------------- d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 311 + +--S 312 of 518 +--m0158:= a0158-r0158 +--E 312 + +--S 313 of 518 +--d0158:= D(m0158,x) +--E 313 + +--S 314 of 518 +t0159:= log(a+b*x^2)^3/x^3 +--R +--R +--R 2 3 +--R log(b x + a) +--R (278) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 314 + +--S 315 of 518 +r0159:= 3/2*b*log(-b*x^2/a)*log(a+b*x^2)^2/a-_ + 1/2*(a+b*x^2)*log(a+b*x^2)^3/a/x^2+_ + 3*b*log(a+b*x^2)*polylog(2,1+b*x^2/a)/a-3*b*polylog(3,(a+b*x^2)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 315 + +--S 316 of 518 +a0159:= integrate(t0159,x) +--R +--R +--R x 2 3 +--R ++ log(%L b + a) +--R (279) | -------------- d%L +--R ++ 3 +--R %L +--R Type: Union(Expression(Integer),...) +--E 316 + +--S 317 of 518 +--m0159:= a0159-r0159 +--E 317 + +--S 318 of 518 +--d0159:= D(m0159,x) +--E 318 + +--S 319 of 518 +t0160:= x^3/log(a+b*x^2) +--R +--R +--R 3 +--R x +--R (280) ------------- +--R 2 +--R log(b x + a) +--R Type: Expression(Integer) +--E 319 + +--S 320 of 518 +r0160:= -1/2*(-Ei(2*log(a+b*x^2))+a*li(a+b*x^2))/b^2 +--R +--R +--R 2 2 +--R Ei(2log(b x + a)) - a li(b x + a) +--R (281) ----------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 320 + +--S 321 of 518 +a0160:= integrate(t0160,x) +--R +--R +--R x 3 +--R ++ %L +--R (282) | ------------- d%L +--R ++ 2 +--R log(%L b + a) +--R Type: Union(Expression(Integer),...) +--E 321 + +--S 322 of 518 +--m0160:= a0160-r0160 +--E 322 + +--S 323 of 518 +--d0160:= D(m0160,x) +--E 323 + +--S 324 of 518 +t0161:= x^3/log(a+b*x^2)^2 +--R +--R +--R 3 +--R x +--R (283) -------------- +--R 2 2 +--R log(b x + a) +--R Type: Expression(Integer) +--E 324 + +--S 325 of 518 +r0161:= -1/2*(-2*Ei(2*log(a+b*x^2))*log(a+b*x^2)+a*b*x^2+b^2*x^4+_ + a*li(a+b*x^2)*log(a+b*x^2))/b^2/log(a+b*x^2) +--R +--R +--R (284) +--R 2 2 2 2 2 4 +--R 2log(b x + a)Ei(2log(b x + a)) - a li(b x + a)log(b x + a) - b x +--R + +--R 2 +--R - a b x +--R / +--R 2 2 +--R 2b log(b x + a) +--R Type: Expression(Integer) +--E 325 + +--S 326 of 518 +a0161:= integrate(t0161,x) +--R +--R +--R x 3 +--R ++ %L +--R (285) | -------------- d%L +--R ++ 2 2 +--R log(%L b + a) +--R Type: Union(Expression(Integer),...) +--E 326 + +--S 327 of 518 +m0161:= a0161-r0161 +--R +--R +--R (286) +--R x 3 +--R 2 2 ++ %L +--R 2b log(b x + a) | -------------- d%L +--R ++ 2 2 +--R log(%L b + a) +--R + +--R 2 2 2 2 2 4 +--R - 2log(b x + a)Ei(2log(b x + a)) + a li(b x + a)log(b x + a) + b x +--R + +--R 2 +--R a b x +--R / +--R 2 2 +--R 2b log(b x + a) +--R Type: Expression(Integer) +--E 327 + +--S 328 of 518 +d0161:= D(m0161,x) +--R +--R +--R 2 +--R 2log(b x + a) 2 5 3 2 +--R - 2x %e + 2b x + 4a b x + 2a x +--R (287) ---------------------------------------------- +--R 2 2 2 +--R (b x + a b)log(b x + a) +--R Type: Expression(Integer) +--E 328 + +--S 329 of 518 +t0162:= x^3/log(a+b*x^2)^3 +--R +--R +--R 3 +--R x +--R (288) -------------- +--R 2 3 +--R log(b x + a) +--R Type: Expression(Integer) +--E 329 + +--S 330 of 518 +r0162:= -1/4*(-4*Ei(2*log(a+b*x^2))*log(a+b*x^2)^2+a*b*x^2+b^2*x^4+_ + log(a+b*x^2)*a^2+3*log(a+b*x^2)*a*b*x^2+2*log(a+b*x^2)*b^2*x^4+_ + a*li(a+b*x^2)*log(a+b*x^2)^2)/b^2/log(a+b*x^2)^2 +--R +--R +--R (289) +--R 2 2 2 2 2 2 +--R 4log(b x + a) Ei(2log(b x + a)) - a li(b x + a)log(b x + a) +--R + +--R 2 4 2 2 2 2 4 2 +--R (- 2b x - 3a b x - a )log(b x + a) - b x - a b x +--R / +--R 2 2 2 +--R 4b log(b x + a) +--R Type: Expression(Integer) +--E 330 + +--S 331 of 518 +a0162:= integrate(t0162,x) +--R +--R +--R x 3 +--R ++ %L +--R (290) | -------------- d%L +--R ++ 2 3 +--R log(%L b + a) +--R Type: Union(Expression(Integer),...) +--E 331 + +--S 332 of 518 +--m0162:= a0162-r0162 +--E 332 + +--S 333 of 518 +--d0162:= D(m0162,x) +--E 333 + +--S 334 of 518 +t0163:= log(c*(a+b*x^2)^n)^2 +--R +--R +--R 2 n 2 +--R (291) log(c (b x + a) ) +--R Type: Expression(Integer) +--E 334 + +--S 335 of 518 +r0163:= 8*n^2*x-4*n*x*log(c*(a+b*x^2)^n)+x*log(c*(a+b*x^2)^n)^2-_ + 1/(-b)^(1/2)*a^(1/2)*n*(n*log(-a^(1/2)/(-b)^(1/2)+x)^2-_ + n*log(a^(1/2)/(-b)^(1/2)+x)^2+4*n*atanh((-b)^(1/2)*x/a^(1/2))*_ + (log(-a^(1/2)/(-b)^(1/2)+x)+log(a^(1/2)/(-b)^(1/2)+x))-_ + 4*n*log(-(a^(1/2)-(-b)^(1/2)*x)/(a^(1/2)+(-b)^(1/2)*x))+_ + 2*n*log(a^(1/2)/(-b)^(1/2)+x)*log(1/2-1/2*(-b)^(1/2)*x/a^(1/2))-_ + 2*n*log(-a^(1/2)/(-b)^(1/2)+x)*log(1/2+1/2*(-b)^(1/2)*x/a^(1/2))-_ + 4*atanh((-b)^(1/2)*x/a^(1/2))*log(c*(a+b*x^2)^n)-_ + 2*n*polylog(2,1/2-1/2*(-b)^(1/2)*x/a^(1/2))+_ + 2*n*polylog(2,1/2+1/2*(-b)^(1/2)*x/a^(1/2))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 335 + +--S 336 of 518 +a0163:= integrate(t0163,x) +--R +--R +--R x +--R ++ 2 n 2 +--R (292) | log(c (%L b + a) ) d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 336 + +--S 337 of 518 +--m0163:= a0163-r0163 +--E 337 + +--S 338 of 518 +--d0163:= D(m0163,x) +--E 338 + +--S 339 of 518 +t0164:= x*log(c*(a+b*x^2)^n)^2 +--R +--R +--R 2 n 2 +--R (293) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 339 + +--S 340 of 518 +r0164:= n^2*x^2-n*(a+b*x^2)*log(c*(a+b*x^2)^n)/b+_ + 1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)^2/b +--R +--R +--R (294) +--R 2 2 n 2 2 2 n +--R (b x + a)log(c (b x + a) ) + (- 2b n x - 2a n)log(c (b x + a) ) +--R + +--R 2 2 +--R 2b n x +--R / +--R 2b +--R Type: Expression(Integer) +--E 340 + +--S 341 of 518 +a0164:= integrate(t0164,x) +--R +--R +--R (295) +--R 2 2 2 2 2 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R ((2b n x + 2a n)log(c) - 2b n x - 2a n )log(b x + a) + b x log(c) +--R + +--R 2 2 2 +--R - 2b n x log(c) + 2b n x +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 341 + +--S 342 of 518 +m0164:= a0164-r0164 +--R +--R +--R (296) +--R 2 2 n 2 2 2 n +--R (- b x - a)log(c (b x + a) ) + (2b n x + 2a n)log(c (b x + a) ) +--R + +--R 2 2 2 2 2 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 +--R ((2b n x + 2a n)log(c) - 2b n x - 2a n )log(b x + a) + b x log(c) +--R + +--R 2 +--R - 2b n x log(c) +--R / +--R 2b +--R Type: Expression(Integer) +--E 342 + +--S 343 of 518 +d0164:= D(m0164,x) +--R +--R +--R (297) +--R 2 n 2 n 2 +--R - x (b x + a) log(c (b x + a) ) +--R + +--R 2 n 3 2 n - 1 +--R (2n x (b x + a) + (- 2b n x - 2a n x)(b x + a) ) +--R * +--R 2 n +--R log(c (b x + a) ) +--R + +--R 2 2 2 2 2 2 +--R (n x log(b x + a) + 2n x log(c)log(b x + a) + x log(c) - 2n x) +--R * +--R 2 n +--R (b x + a) +--R + +--R 2 3 2 2 n - 1 +--R (2b n x + 2a n x)(b x + a) +--R / +--R 2 n +--R (b x + a) +--R Type: Expression(Integer) +--E 343 + +--S 344 of 518 +t0165:= x^3*log(c*(a+b*x^2)^n)^2 +--R +--R +--R 3 2 n 2 +--R (298) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 344 + +--S 345 of 518 +r0165:= -3/4*a*n^2*x^2/b+1/8*n^2*x^4+1/4*a^2*n^2*log(a+b*x^2)/b^2-_ + 1/4*n*x^4*log(c*(a+b*x^2)^n)+1/2*a*n*(a+b*x^2)*_ + log(c*(a+b*x^2)^n)/b^2-1/4*a^2*log(c*(a+b*x^2)^n)^2/b^2+_ + 1/4*x^4*log(c*(a+b*x^2)^n)^2 +--R +--R +--R (299) +--R 2 4 2 2 n 2 +--R (2b x - 2a )log(c (b x + a) ) +--R + +--R 2 4 2 2 2 n 2 2 2 +--R (- 2b n x + 4a b n x + 4a n)log(c (b x + a) ) + 2a n log(b x + a) +--R + +--R 2 2 4 2 2 +--R b n x - 6a b n x +--R / +--R 2 +--R 8b +--R Type: Expression(Integer) +--E 345 + +--S 346 of 518 +a0165:= integrate(t0165,x) +--R +--R +--R (300) +--R 2 2 4 2 2 2 2 +--R (2b n x - 2a n )log(b x + a) +--R + +--R 2 4 2 2 2 4 2 2 2 2 2 +--R ((4b n x - 4a n)log(c) - 2b n x + 4a b n x + 6a n )log(b x + a) +--R + +--R 2 4 2 2 4 2 2 2 4 2 2 +--R 2b x log(c) + (- 2b n x + 4a b n x )log(c) + b n x - 6a b n x +--R / +--R 2 +--R 8b +--R Type: Union(Expression(Integer),...) +--E 346 + +--S 347 of 518 +m0165:= a0165-r0165 +--R +--R +--R (301) +--R 2 4 2 2 n 2 +--R (- b x + a )log(c (b x + a) ) +--R + +--R 2 4 2 2 2 n +--R (b n x - 2a b n x - 2a n)log(c (b x + a) ) +--R + +--R 2 2 4 2 2 2 2 +--R (b n x - a n )log(b x + a) +--R + +--R 2 4 2 2 2 4 2 2 2 2 2 +--R ((2b n x - 2a n)log(c) - b n x + 2a b n x + 2a n )log(b x + a) +--R + +--R 2 4 2 2 4 2 +--R b x log(c) + (- b n x + 2a b n x )log(c) +--R / +--R 2 +--R 4b +--R Type: Expression(Integer) +--E 347 + +--S 348 of 518 +d0165:= D(m0165,x) +--R +--R +--R (302) +--R 2 5 3 2 n 2 n 2 +--R (- 2b x - 2a b x )(b x + a) log(c (b x + a) ) +--R + +--R 2 5 2 2 n +--R (2b n x - 2a n x)(b x + a) +--R + +--R 3 7 2 5 2 3 3 2 n - 1 +--R (- 2b n x - 2a b n x + 2a b n x + 2a n x)(b x + a) +--R * +--R 2 n +--R log(c (b x + a) ) +--R + +--R 2 2 5 2 3 2 2 +--R (2b n x + 2a b n x )log(b x + a) +--R + +--R 2 5 3 2 2 5 3 2 +--R (4b n x + 4a b n x )log(c)log(b x + a) + (2b x + 2a b x )log(c) +--R + +--R 2 2 5 2 3 2 2 +--R - b n x + 2a b n x + 2a n x +--R * +--R 2 n +--R (b x + a) +--R + +--R 3 2 7 2 2 5 2 2 3 3 2 2 n - 1 +--R (b n x - a b n x - 4a b n x - 2a n x)(b x + a) +--R / +--R 2 2 2 n +--R (2b x + 2a b)(b x + a) +--R Type: Expression(Integer) +--E 348 + +--S 349 of 518 +t0166:= log(c*(a+b*x^2)^n)^2/x +--R +--R +--R 2 n 2 +--R log(c (b x + a) ) +--R (303) ------------------- +--R x +--R Type: Expression(Integer) +--E 349 + +--S 350 of 518 +r0166:= 1/2*log(-b*x^2/a)*log(c*(a+b*x^2)^n)^2+_ + n*log(c*(a+b*x^2)^n)*polylog(2,1+b*x^2/a)-n^2*polylog(3,(a+b*x^2)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 350 + +--S 351 of 518 +a0166:= integrate(t0166,x) +--R +--R +--R x 2 n 2 +--R ++ log(c (%L b + a) ) +--R (304) | ------------------- d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 351 + +--S 352 of 518 +--m0166:= a0166-r0166 +--E 352 + +--S 353 of 518 +--d0166:= D(m0166,x) +--E 353 + +--S 354 of 518 +t0167:= log(c*(a+b*x^2)^n)^2/x^3 +--R +--R +--R 2 n 2 +--R log(c (b x + a) ) +--R (305) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 354 + +--S 355 of 518 +r0167:= b*n*log(-b*x^2/a)*log(c*(a+b*x^2)^n)/a-_ + 1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)^2/a/x^2+b*n^2*polylog(2,1+b*x^2/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 355 + +--S 356 of 518 +a0167:= integrate(t0167,x) +--R +--R +--R x 2 n 2 +--R ++ log(c (%L b + a) ) +--R (306) | ------------------- d%L +--R ++ 3 +--R %L +--R Type: Union(Expression(Integer),...) +--E 356 + +--S 357 of 518 +--m0167:= a0167-r0167 +--E 357 + +--S 358 of 518 +--d0167:= D(m0167,x) +--E 358 + +--S 359 of 518 +t0168:= x*log(c*(a+b*x^2)^n)^3 +--R +--R +--R 2 n 3 +--R (307) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 359 + +--S 360 of 518 +r0168:= -3*n^3*x^2+3*n^2*(a+b*x^2)*log(c*(a+b*x^2)^n)/b-_ + 3/2*n*(a+b*x^2)*log(c*(a+b*x^2)^n)^2/b+_ + 1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)^3/b +--R +--R +--R (308) +--R 2 2 n 3 2 2 n 2 +--R (b x + a)log(c (b x + a) ) + (- 3b n x - 3a n)log(c (b x + a) ) +--R + +--R 2 2 2 2 n 3 2 +--R (6b n x + 6a n )log(c (b x + a) ) - 6b n x +--R / +--R 2b +--R Type: Expression(Integer) +--E 360 + +--S 361 of 518 +a0168:= integrate(t0168,x) +--R +--R +--R (309) +--R 3 2 3 2 3 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 2 3 2 3 2 2 +--R ((3b n x + 3a n )log(c) - 3b n x - 3a n )log(b x + a) +--R + +--R 2 2 2 2 2 3 2 3 +--R ((3b n x + 3a n)log(c) + (- 6b n x - 6a n )log(c) + 6b n x + 6a n ) +--R * +--R 2 +--R log(b x + a) +--R + +--R 2 3 2 2 2 2 3 2 +--R b x log(c) - 3b n x log(c) + 6b n x log(c) - 6b n x +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 361 + +--S 362 of 518 +m0168:= a0168-r0168 +--R +--R +--R (310) +--R 2 2 n 3 2 2 n 2 +--R (- b x - a)log(c (b x + a) ) + (3b n x + 3a n)log(c (b x + a) ) +--R + +--R 2 2 2 2 n 3 2 3 2 3 +--R (- 6b n x - 6a n )log(c (b x + a) ) + (b n x + a n )log(b x + a) +--R + +--R 2 2 2 3 2 3 2 2 +--R ((3b n x + 3a n )log(c) - 3b n x - 3a n )log(b x + a) +--R + +--R 2 2 2 2 2 3 2 3 +--R ((3b n x + 3a n)log(c) + (- 6b n x - 6a n )log(c) + 6b n x + 6a n ) +--R * +--R 2 +--R log(b x + a) +--R + +--R 2 3 2 2 2 2 +--R b x log(c) - 3b n x log(c) + 6b n x log(c) +--R / +--R 2b +--R Type: Expression(Integer) +--E 362 + +--S 363 of 518 +d0168:= D(m0168,x) +--R +--R +--R (311) +--R 2 n 2 n 3 +--R - x (b x + a) log(c (b x + a) ) +--R + +--R 2 n 3 2 n - 1 +--R (3n x (b x + a) + (- 3b n x - 3a n x)(b x + a) ) +--R * +--R 2 n 2 +--R log(c (b x + a) ) +--R + +--R 2 2 n 2 3 2 2 n - 1 +--R (- 6n x (b x + a) + (6b n x + 6a n x)(b x + a) ) +--R * +--R 2 n +--R log(c (b x + a) ) +--R + +--R 3 2 3 2 2 2 +--R n x log(b x + a) + 3n x log(c)log(b x + a) +--R + +--R 2 2 3 3 +--R 3n x log(c) log(b x + a) + x log(c) + 6n x +--R * +--R 2 n +--R (b x + a) +--R + +--R 3 3 3 2 n - 1 +--R (- 6b n x - 6a n x)(b x + a) +--R / +--R 2 n +--R (b x + a) +--R Type: Expression(Integer) +--E 363 + +--S 364 of 518 +t0169:= x^3*log(c*(a+b*x^2)^n)^3 +--R +--R +--R 3 2 n 3 +--R (312) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 364 + +--S 365 of 518 +r0169:= 21/8*a*n^3*x^2/b-3/16*n^3*x^4-3/8*a^2*n^3*log(a+b*x^2)/b^2+_ + 3/8*n^2*x^4*log(c*(a+b*x^2)^n)-9/4*a*n^2*(a+b*x^2)*_ + log(c*(a+b*x^2)^n)/b^2-3/8*n*x^4*log(c*(a+b*x^2)^n)^2+_ + 9/8*a*n*(a+2/3*b*x^2)*log(c*(a+b*x^2)^n)^2/b^2-_ + 1/4*a^2*log(c*(a+b*x^2)^n)^3/b^2+1/4*x^4*log(c*(a+b*x^2)^n)^3 +--R +--R +--R (313) +--R 2 4 2 2 n 3 +--R (4b x - 4a )log(c (b x + a) ) +--R + +--R 2 4 2 2 2 n 2 +--R (- 6b n x + 12a b n x + 18a n)log(c (b x + a) ) +--R + +--R 2 2 4 2 2 2 2 2 n 2 3 2 +--R (6b n x - 36a b n x - 36a n )log(c (b x + a) ) - 6a n log(b x + a) +--R + +--R 2 3 4 3 2 +--R - 3b n x + 42a b n x +--R / +--R 2 +--R 16b +--R Type: Expression(Integer) +--E 365 + +--S 366 of 518 +a0169:= integrate(t0169,x) +--R +--R +--R (314) +--R 2 3 4 2 3 2 3 +--R (4b n x - 4a n )log(b x + a) +--R + +--R 2 2 4 2 2 2 3 4 3 2 2 3 2 2 +--R ((12b n x - 12a n )log(c) - 6b n x + 12a b n x + 18a n )log(b x + a) +--R + +--R 2 4 2 2 2 2 4 2 2 2 2 +--R (12b n x - 12a n)log(c) + (- 12b n x + 24a b n x + 36a n )log(c) +--R + +--R 2 3 4 3 2 2 3 +--R 6b n x - 36a b n x - 42a n +--R * +--R 2 +--R log(b x + a) +--R + +--R 2 4 3 2 4 2 2 +--R 4b x log(c) + (- 6b n x + 12a b n x )log(c) +--R + +--R 2 2 4 2 2 2 3 4 3 2 +--R (6b n x - 36a b n x )log(c) - 3b n x + 42a b n x +--R / +--R 2 +--R 16b +--R Type: Union(Expression(Integer),...) +--E 366 + +--S 367 of 518 +m0169:= a0169-r0169 +--R +--R +--R (315) +--R 2 4 2 2 n 3 +--R (- 2b x + 2a )log(c (b x + a) ) +--R + +--R 2 4 2 2 2 n 2 +--R (3b n x - 6a b n x - 9a n)log(c (b x + a) ) +--R + +--R 2 2 4 2 2 2 2 2 n +--R (- 3b n x + 18a b n x + 18a n )log(c (b x + a) ) +--R + +--R 2 3 4 2 3 2 3 +--R (2b n x - 2a n )log(b x + a) +--R + +--R 2 2 4 2 2 2 3 4 3 2 2 3 2 2 +--R ((6b n x - 6a n )log(c) - 3b n x + 6a b n x + 9a n )log(b x + a) +--R + +--R 2 4 2 2 2 2 4 2 2 2 2 +--R (6b n x - 6a n)log(c) + (- 6b n x + 12a b n x + 18a n )log(c) +--R + +--R 2 3 4 3 2 2 3 +--R 3b n x - 18a b n x - 18a n +--R * +--R 2 +--R log(b x + a) +--R + +--R 2 4 3 2 4 2 2 +--R 2b x log(c) + (- 3b n x + 6a b n x )log(c) +--R + +--R 2 2 4 2 2 +--R (3b n x - 18a b n x )log(c) +--R / +--R 2 +--R 8b +--R Type: Expression(Integer) +--E 367 + +--S 368 of 518 +d0169:= D(m0169,x) +--R +--R +--R (316) +--R 2 5 3 2 n 2 n 3 +--R (- 4b x - 4a b x )(b x + a) log(c (b x + a) ) +--R + +--R 2 5 2 2 n +--R (6b n x - 6a n x)(b x + a) +--R + +--R 3 7 2 5 2 3 3 2 n - 1 +--R (- 6b n x - 6a b n x + 6a b n x + 6a n x)(b x + a) +--R * +--R 2 n 2 +--R log(c (b x + a) ) +--R + +--R 2 2 5 2 3 2 2 2 n +--R (- 6b n x + 12a b n x + 18a n x)(b x + a) +--R + +--R 3 2 7 2 2 5 2 2 3 3 2 2 n - 1 +--R (6b n x - 6a b n x - 30a b n x - 18a n x)(b x + a) +--R * +--R 2 n +--R log(c (b x + a) ) +--R + +--R 2 3 5 3 3 2 3 +--R (4b n x + 4a b n x )log(b x + a) +--R + +--R 2 2 5 2 3 2 2 +--R (12b n x + 12a b n x )log(c)log(b x + a) +--R + +--R 2 5 3 2 2 +--R (12b n x + 12a b n x )log(c) log(b x + a) +--R + +--R 2 5 3 3 2 3 5 3 3 2 3 +--R (4b x + 4a b x )log(c) + 3b n x - 18a b n x - 18a n x +--R * +--R 2 n +--R (b x + a) +--R + +--R 3 3 7 2 3 5 2 3 3 3 3 2 n - 1 +--R (- 3b n x + 15a b n x + 36a b n x + 18a n x)(b x + a) +--R / +--R 2 2 2 n +--R (4b x + 4a b)(b x + a) +--R Type: Expression(Integer) +--E 368 + +--S 369 of 518 +t0170:= log(c*(a+b*x^2)^n)^3/x +--R +--R +--R 2 n 3 +--R log(c (b x + a) ) +--R (317) ------------------- +--R x +--R Type: Expression(Integer) +--E 369 + +--S 370 of 518 +r0170:= 1/2*log(-b*x^2/a)*log(c*(a+b*x^2)^n)^3+_ + 3/2*n*log(c*(a+b*x^2)^n)^2*polylog(2,1+b*x^2/a)-_ + 3*n^2*log(c*(a+b*x^2)^n)*polylog(3,1+b*x^2/a)+_ + 3*n^3*polylog(4,(a+b*x^2)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 370 + +--S 371 of 518 +a0170:= integrate(t0170,x) +--R +--R +--R x 2 n 3 +--R ++ log(c (%L b + a) ) +--R (318) | ------------------- d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 371 + +--S 372 of 518 +--m0170:= a0170-r0170 +--E 372 + +--S 373 of 518 +--d0170:= D(m0170,x) +--E 373 + +--S 374 of 518 +t0171:= log(c*(a+b*x^2)^n)^3/x^3 +--R +--R +--R 2 n 3 +--R log(c (b x + a) ) +--R (319) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 374 + +--S 375 of 518 +r0171:= 3/2*b*n*log(-b*x^2/a)*log(c*(a+b*x^2)^n)^2/a-_ + 1/2*(a+b*x^2)*log(c*(a+b*x^2)^n)^3/a/x^2+_ + 3*b*n^2*log(c*(a+b*x^2)^n)*polylog(2,1+b*x^2/a)/a-_ + 3*b*n^3*polylog(3,(a+b*x^2)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 375 + +--S 376 of 518 +a0171:= integrate(t0171,x) +--R +--R +--R x 2 n 3 +--R ++ log(c (%L b + a) ) +--R (320) | ------------------- d%L +--R ++ 3 +--R %L +--R Type: Union(Expression(Integer),...) +--E 376 + +--S 377 of 518 +--m0171:= a0171-r0171 +--E 377 + +--S 378 of 518 +--d0171:= D(m0171,x) +--E 378 + +--S 379 of 518 +t0172:= x/log(c*(a+b*x^2)^n) +--R +--R +--R x +--R (321) ------------------ +--R 2 n +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 379 + +--S 380 of 518 +r0172:= 1/2*(a+b*x^2)*Ei(log(c*(a+b*x^2)^n)/n)/b/n/((c*(a+b*x^2)^n)^(1/n)) +--R +--R +--R 2 n +--R 2 log(c (b x + a) ) +--R (b x + a)Ei(------------------) +--R n +--R (322) -------------------------------- +--R 1 +--R - +--R 2 n n +--R 2b n (c (b x + a) ) +--R Type: Expression(Integer) +--E 380 + +--S 381 of 518 +a0172:= integrate(t0172,x) +--R +--R +--R x +--R ++ %L +--R (323) | ------------------ d%L +--R ++ 2 n +--R log(c (%L b + a) ) +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 518 +--m0172:= a0172-r0172 +--E 382 + +--S 383 of 518 +--d0172:= D(m0172,x) +--E 383 + +--S 384 of 518 +t0173:= x^3/log(c*(a+b*x^2)^n) +--R +--R +--R 3 +--R x +--R (324) ------------------ +--R 2 n +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 384 + +--S 385 of 518 +r0173:= -1/2*a*(a+b*x^2)*Ei(log(c*(a+b*x^2)^n)/n)/_ + ((c*(a+b*x^2)^n)^(1/n))/b^2/n+1/2*(a+b*x^2)^2*_ + Ei(2*log(c*(a+b*x^2)^n)/n)/((c*(a+b*x^2)^n)^(2/n))/b^2/n +--R +--R +--R (325) +--R 1 +--R - 2 n +--R 2 4 2 2 2 n n 2log(c (b x + a) ) +--R (b x + 2a b x + a )(c (b x + a) ) Ei(-------------------) +--R n +--R + +--R 2 +--R - 2 n +--R 2 2 2 n n log(c (b x + a) ) +--R (- a b x - a )(c (b x + a) ) Ei(------------------) +--R n +--R / +--R 1 2 +--R - - +--R 2 2 n n 2 n n +--R 2b n (c (b x + a) ) (c (b x + a) ) +--R Type: Expression(Integer) +--E 385 + +--S 386 of 518 +a0173:= integrate(t0173,x) +--R +--R +--R x 3 +--R ++ %L +--R (326) | ------------------ d%L +--R ++ 2 n +--R log(c (%L b + a) ) +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 518 +--m0173:= a0173-r0173 +--E 387 + +--S 388 of 518 +--d0173:= D(m0173,x) +--E 388 + +--S 389 of 518 +t0174:= x/log(c*(a+b*x^2)^n)^2 +--R +--R +--R x +--R (327) ------------------- +--R 2 n 2 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 389 + +--S 390 of 518 +r0174:= 1/2*(a+b*x^2)*(Ei(log(c*(a+b*x^2)^n)/n)*_ + (c*(a+b*x^2)^n)^(-1/n)*log(c*(a+b*x^2)^n)-n)/n^2/b/log(c*(a+b*x^2)^n) +--R +--R +--R (328) +--R 1 +--R - - 2 n +--R 2 2 n 2 n n log(c (b x + a) ) +--R (b x + a)log(c (b x + a) )(c (b x + a) ) Ei(------------------) +--R n +--R + +--R 2 +--R - b n x - a n +--R / +--R 2 2 n +--R 2b n log(c (b x + a) ) +--R Type: Expression(Integer) +--E 390 + +--S 391 of 518 +a0174:= integrate(t0174,x) +--R +--R +--R x +--R ++ %L +--R (329) | ------------------- d%L +--R ++ 2 n 2 +--R log(c (%L b + a) ) +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 518 +--m0174:= a0174-r0174 +--E 392 + +--S 393 of 518 +--d0174:= D(m0174,x) +--E 393 + +--S 394 of 518 +t0175:= x^3/log(c*(a+b*x^2)^n)^2 +--R +--R +--R 3 +--R x +--R (330) ------------------- +--R 2 n 2 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 394 + +--S 395 of 518 +r0175:= -1/2*a*(a+b*x^2)*Ei(log(c*(a+b*x^2)^n)/n)/_ + ((c*(a+b*x^2)^n)^(1/n))/b^2/n^2+(a+b*x^2)^2*_ + Ei(2*log(c*(a+b*x^2)^n)/n)/((c*(a+b*x^2)^n)^(2/n))/b^2/n^2+_ + 1/2*a*(a+b*x^2)/b^2/n/log(c*(a+b*x^2)^n)-_ + 1/2*(a+b*x^2)^2/b^2/n/log(c*(a+b*x^2)^n) +--R +--R +--R (331) +--R 1 +--R - +--R 2 4 2 2 2 n 2 n n +--R (2b x + 4a b x + 2a )log(c (b x + a) )(c (b x + a) ) +--R * +--R 2 n +--R 2log(c (b x + a) ) +--R Ei(-------------------) +--R n +--R + +--R 2 +--R - 2 n +--R 2 2 2 n 2 n n log(c (b x + a) ) +--R (- a b x - a )log(c (b x + a) )(c (b x + a) ) Ei(------------------) +--R n +--R + +--R 1 2 +--R - - +--R 2 4 2 2 n n 2 n n +--R (- b n x - a b n x )(c (b x + a) ) (c (b x + a) ) +--R / +--R 1 2 +--R - - +--R 2 2 2 n 2 n n 2 n n +--R 2b n log(c (b x + a) )(c (b x + a) ) (c (b x + a) ) +--R Type: Expression(Integer) +--E 395 + +--S 396 of 518 +a0175:= integrate(t0175,x) +--R +--R +--R x 3 +--R ++ %L +--R (332) | ------------------- d%L +--R ++ 2 n 2 +--R log(c (%L b + a) ) +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 518 +--m0175:= a0175-r0175 +--E 397 + +--S 398 of 518 +--d0175:= D(m0175,x) +--E 398 + +--S 399 of 518 +t0176:= x/log(c*(a+b*x^2)^n)^3 +--R +--R +--R x +--R (333) ------------------- +--R 2 n 3 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 399 + +--S 400 of 518 +r0176:= 1/4*(a+b*x^2)*(Ei(log(c*(a+b*x^2)^n)/n)*_ + (c*(a+b*x^2)^n)^(-1/n)*log(c*(a+b*x^2)^n)^2-_ + n^2-n*log(c*(a+b*x^2)^n))/n^3/b/log(c*(a+b*x^2)^n)^2 +--R +--R +--R (334) +--R 1 +--R - - 2 n +--R 2 2 n 2 2 n n log(c (b x + a) ) +--R (b x + a)log(c (b x + a) ) (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 2 2 n 2 2 2 +--R (- b n x - a n)log(c (b x + a) ) - b n x - a n +--R / +--R 3 2 n 2 +--R 4b n log(c (b x + a) ) +--R Type: Expression(Integer) +--E 400 + +--S 401 of 518 +a0176:= integrate(t0176,x) +--R +--R +--R x +--R ++ %L +--R (335) | ------------------- d%L +--R ++ 2 n 3 +--R log(c (%L b + a) ) +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 518 +--m0176:= a0176-r0176 +--E 402 + +--S 403 of 518 +--d0176:= D(m0176,x) +--E 403 + +--S 404 of 518 +t0177:= x^3/log(c*(a+b*x^2)^n)^3 +--R +--R +--R 3 +--R x +--R (336) ------------------- +--R 2 n 3 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 404 + +--S 405 of 518 +r0177:= 1/4*(a+b*x^2)*(-Ei(log(c*(a+b*x^2)^n)/n)*(c*(a+b*x^2)^n)^(-1/n)*_ + log(c*(a+b*x^2)^n)^2*a+4*Ei(2*log(c*(a+b*x^2)^n)/n)*_ + (c*(a+b*x^2)^n)^(-2/n)*log(c*(a+b*x^2)^n)^2*a+_ + 4*Ei(2*log(c*(a+b*x^2)^n)/n)*(c*(a+b*x^2)^n)^(-2/n)*_ + log(c*(a+b*x^2)^n)^2*b*x^2-n^2*x^2*b-n*log(c*(a+b*x^2)^n)*a-_ + 2*n*log(c*(a+b*x^2)^n)*b*x^2)/n^3/b^2/log(c*(a+b*x^2)^n)^2 +--R +--R +--R (337) +--R 2 +--R - - +--R 2 4 2 2 2 n 2 2 n n +--R (4b x + 8a b x + 4a )log(c (b x + a) ) (c (b x + a) ) +--R * +--R 2 n +--R 2log(c (b x + a) ) +--R Ei(-------------------) +--R n +--R + +--R 1 +--R - - +--R 2 2 2 n 2 2 n n +--R (- a b x - a )log(c (b x + a) ) (c (b x + a) ) +--R * +--R 2 n +--R log(c (b x + a) ) +--R Ei(------------------) +--R n +--R + +--R 2 4 2 2 2 n 2 2 4 2 2 +--R (- 2b n x - 3a b n x - a n)log(c (b x + a) ) - b n x - a b n x +--R / +--R 2 3 2 n 2 +--R 4b n log(c (b x + a) ) +--R Type: Expression(Integer) +--E 405 + +--S 406 of 518 +a0177:= integrate(t0177,x) +--R +--R +--R x 3 +--R ++ %L +--R (338) | ------------------- d%L +--R ++ 2 n 3 +--R log(c (%L b + a) ) +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 518 +--m0177:= a0177-r0177 +--E 407 + +--S 408 of 518 +--d0177:= D(m0177,x) +--E 408 + +--S 409 of 518 +t0178:= log(c*(a*x+b)/x) +--R +--R +--R a c x + b c +--R (339) log(-----------) +--R x +--R Type: Expression(Integer) +--E 409 + +--S 410 of 518 +r0178:= b*log(a*x+b)/a+x*log(c*(a*x+b)/x) +--R +--R +--R a c x + b c +--R b log(a x + b) + a x log(-----------) +--R x +--R (340) ------------------------------------- +--R a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 518 +a0178:= integrate(t0178,x) +--R +--R +--R a c x + b c +--R b log(a x + b) + a x log(-----------) +--R x +--R (341) ------------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 518 +m0178:= a0178-r0178 +--R +--R +--R (342) 0 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 518 +d0178:= D(m0178,x) +--R +--R +--R (343) 0 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 518 +t0179:= log(c*(a*x+b)/x)^2 +--R +--R +--R a c x + b c 2 +--R (344) log(-----------) +--R x +--R Type: Expression(Integer) +--E 414 + +--S 415 of 518 +r0179:= (a*x+b)*log(a*c+b*c/x)^2/a-2*b*log(a*c+b*c/x)*log(-b/a/x)/a-_ + 2*b*polylog(2,1+b/a/x)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 415 + +--S 416 of 518 +a0179:= integrate(t0179,x) +--R +--R +--R x +--R ++ (b + %L a)c 2 +--R (345) | log(-----------) d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 416 + +--S 417 of 518 +--m0179:= a0179-r0179 +--E 417 + +--S 418 of 518 +--d0179:= D(m0179,x) +--E 418 + +--S 419 of 518 +t0180:= log(c*(a*x+b)/x)^3 +--R +--R +--R a c x + b c 3 +--R (346) log(-----------) +--R x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 518 +r0180:= (a*x+b)*log(a*c+b*c/x)^3/a-3*b*log(a*c+b*c/x)^2*log(-b/a/x)/a-_ + 6*b*log(a*c+b*c/x)*polylog(2,1+b/a/x)/a+6*b*polylog(3,(a+b/x)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 420 + +--S 421 of 518 +a0180:= integrate(t0180,x) +--R +--R +--R x +--R ++ (b + %L a)c 3 +--R (347) | log(-----------) d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 518 +--m0180:= a0180-r0180 +--E 422 + +--S 423 of 518 +--d0180:= D(m0180,x) +--E 423 + +--S 424 of 518 +t0181:= log(c*x/(a*x+b))^2 +--R +--R +--R c x 2 +--R (348) log(-------) +--R a x + b +--R Type: Expression(Integer) +--E 424 + +--S 425 of 518 +r0181:= (2*b*log(b/(a*x+b))*log(c*x/(a*x+b))+x*log(c*x/(a*x+b))^2*a+_ + 2*b*polylog(2,a*x/(a*x+b)))/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 425 + +--S 426 of 518 +a0181:= integrate(t0181,x) +--R +--R +--R x +--R ++ %L c 2 +--R (349) | log(--------) d%L +--R ++ b + %L a +--R Type: Union(Expression(Integer),...) +--E 426 + +--S 427 of 518 +--m0181:= a0181-r0181 +--E 427 + +--S 428 of 518 +--d0181:= D(m0181,x) +--E 428 + +--S 429 of 518 +t0182:= log(c*x/(a*x+b))^3 +--R +--R +--R c x 3 +--R (350) log(-------) +--R a x + b +--R Type: Expression(Integer) +--E 429 + +--S 430 of 518 +r0182:= (3*b*log(b/(a*x+b))*log(c*x/(a*x+b))^2+x*log(c*x/(a*x+b))^3*a+_ + 6*b*log(c*x/(a*x+b))*polylog(2,a*x/(a*x+b))-_ + 6*b*polylog(3,a*x/(a*x+b)))/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 430 + +--S 431 of 518 +a0182:= integrate(t0182,x) +--R +--R +--R x +--R ++ %L c 3 +--R (351) | log(--------) d%L +--R ++ b + %L a +--R Type: Union(Expression(Integer),...) +--E 431 + +--S 432 of 518 +--m0182:= a0182-r0182 +--E 432 + +--S 433 of 518 +--d0182:= D(m0182,x) +--E 433 + +--S 434 of 518 +t0183:= log(c*(a*x+b)^2/x^2) +--R +--R +--R 2 2 2 +--R a c x + 2a b c x + b c +--R (352) log(-----------------------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 434 + +--S 435 of 518 +r0183:= 2*b*log(a*x+b)/a+x*log(c*(a*x+b)^2/x^2) +--R +--R +--R 2 2 2 +--R a c x + 2a b c x + b c +--R 2b log(a x + b) + a x log(-----------------------) +--R 2 +--R x +--R (353) -------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 435 + +--S 436 of 518 +a0183:= integrate(t0183,x) +--R +--R +--R 2 2 2 +--R a c x + 2a b c x + b c +--R 2b log(a x + b) + a x log(-----------------------) +--R 2 +--R x +--R (354) -------------------------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 518 +m0183:= a0183-r0183 +--R +--R +--R (355) 0 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 518 +d0183:= D(m0183,x) +--R +--R +--R (356) 0 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 518 +t0184:= log(c*(a*x+b)^2/x^2)^2 +--R +--R +--R 2 2 2 2 +--R a c x + 2a b c x + b c +--R (357) log(-----------------------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 518 +r0184:= (a*x+b)*log(c*(a+b/x)^2)^2/a-4*b*log(c*(a+b/x)^2)*log(-b/a/x)/a-_ + 8*b*polylog(2,1+b/a/x)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 440 + +--S 441 of 518 +a0184:= integrate(t0184,x) +--R +--R +--R x 2 2 2 2 +--R ++ (b + 2%L a b + %L a )c +--R (358) | log(-----------------------) d%L +--R ++ 2 +--R %L +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 518 +--m0184:= a0184-r0184 +--E 442 + +--S 443 of 518 +--d0184:= D(m0184,x) +--E 443 + +--S 444 of 518 +t0185:= log(c*(a*x+b)^2/x^2)^3 +--R +--R +--R 2 2 2 3 +--R a c x + 2a b c x + b c +--R (359) log(-----------------------) +--R 2 +--R x +--R Type: Expression(Integer) +--E 444 + +--S 445 of 518 +r0185:= (a*x+b)*log(c*(a+b/x)^2)^3/a-6*b*log(c*(a+b/x)^2)^2*log(-b/a/x)/a-_ + 24*b*log(c*(a+b/x)^2)*polylog(2,1+b/a/x)/a+48*b*polylog(3,(a+b/x)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 445 + +--S 446 of 518 +a0185:= integrate(t0185,x) +--R +--R +--R x 2 2 2 3 +--R ++ (b + 2%L a b + %L a )c +--R (360) | log(-----------------------) d%L +--R ++ 2 +--R %L +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 518 +--m0185:= a0185-r0185 +--E 447 + +--S 448 of 518 +--d0185:= D(m0185,x) +--E 448 + +--S 449 of 518 +t0186:= log(c*x^2/(a*x+b)^2) +--R +--R +--R 2 +--R c x +--R (361) log(------------------) +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 449 + +--S 450 of 518 +r0186:= x*log(c*x^2/(a*x+b)^2)-2*b*log(a*x+b)/a +--R +--R +--R 2 +--R c x +--R - 2b log(a x + b) + a x log(------------------) +--R 2 2 2 +--R a x + 2a b x + b +--R (362) ----------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 450 + +--S 451 of 518 +a0186:= integrate(t0186,x) +--R +--R +--R 2 +--R c x +--R - 2b log(a x + b) + a x log(------------------) +--R 2 2 2 +--R a x + 2a b x + b +--R (363) ----------------------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 518 +m0186:= a0186-r0186 +--R +--R +--R (364) 0 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 518 +d0186:= D(m0186,x) +--R +--R +--R (365) 0 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 518 +t0187:= log(c*x^2/(a*x+b)^2)^2 +--R +--R +--R 2 2 +--R c x +--R (366) log(------------------) +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 454 + +--S 455 of 518 +r0187:= (a*x+b)*log(c/(a+b/x)^2)^2/a+4*b*log(c/(a+b/x)^2)*log(-b/a/x)/a-_ + 8*b*polylog(2,1+b/a/x)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 455 + +--S 456 of 518 +a0187:= integrate(t0187,x) +--R +--R +--R x 2 2 +--R ++ %L c +--R (367) | log(--------------------) d%L +--R ++ 2 2 2 +--R b + 2%L a b + %L a +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 518 +--m0187:= a0187-r0187 +--E 457 + +--S 458 of 518 +--d0187:= D(m0187,x) +--E 458 + +--S 459 of 518 +t0188:= log(c*x^2/(a*x+b)^2)^3 +--R +--R +--R 2 3 +--R c x +--R (368) log(------------------) +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 459 + +--S 460 of 518 +r0188:= (a*x+b)*log(c/(a+b/x)^2)^3/a+6*b*log(c/(a+b/x)^2)^2*log(-b/a/x)/a-_ + 24*b*log(c/(a+b/x)^2)*polylog(2,1+b/a/x)/a-48*b*polylog(3,(a+b/x)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 460 + +--S 461 of 518 +a0188:= integrate(t0188,x) +--R +--R +--R x 2 3 +--R ++ %L c +--R (369) | log(--------------------) d%L +--R ++ 2 2 2 +--R b + 2%L a b + %L a +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 518 +--m0188:= a0188-r0188 +--E 462 + +--S 463 of 518 +--d0188:= D(m0188,x) +--E 463 + +--S 464 of 518 +t0189:= log(c*(a+b/x)^n)^2 +--R +--R +--R a x + b n 2 +--R (370) log(c (-------) ) +--R x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 518 +r0189:= (a*x+b)*log(c*(a+b/x)^n)^2/a-2*b*n*log(c*(a+b/x)^n)*log(-b/a/x)/a-_ + 2*b*n^2*polylog(2,1+b/a/x)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 465 + +--S 466 of 518 +a0189:= integrate(t0189,x) +--R +--R +--R x +--R ++ b + %L a n 2 +--R (371) | log(c (--------) ) d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 518 +--m0189:= a0189-r0189 +--E 467 + +--S 468 of 518 +--d0189:= D(m0189,x) +--E 468 + +--S 469 of 518 +t0190:= log(c*(a+b/x)^n)^3 +--R +--R +--R a x + b n 3 +--R (372) log(c (-------) ) +--R x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 518 +r0190:= (a*x+b)*log(c*(a+b/x)^n)^3/a-3*b*n*log(c*(a+b/x)^n)^2*log(-b/a/x)/a-_ + 6*b*n^2*log(c*(a+b/x)^n)*polylog(2,1+b/a/x)/a+_ + 6*b*n^3*polylog(3,(a+b/x)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 470 + +--S 471 of 518 +a0190:= integrate(t0190,x) +--R +--R +--R x +--R ++ b + %L a n 3 +--R (373) | log(c (--------) ) d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 518 +--m0190:= a0190-r0190 +--E 472 + +--S 473 of 518 +--d0190:= D(m0190,x) +--E 473 + +--S 474 of 518 +t0191:= log(a+b*x^(1/2))/x^(1/2) +--R +--R +--R +-+ +--R log(b\|x + a) +--R (374) -------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 474 + +--S 475 of 518 +r0191:= -2*x^(1/2)+2*(a+b*x^(1/2))*log(a+b*x^(1/2))/b +--R +--R +--R +-+ +-+ +-+ +--R (2b\|x + 2a)log(b\|x + a) - 2b\|x +--R (375) ------------------------------------ +--R b +--R Type: Expression(Integer) +--E 475 + +--S 476 of 518 +a0191:= integrate(t0191,x) +--R +--R +--R +-+ +-+ +-+ +--R (2b\|x + 2a)log(b\|x + a) - 2b\|x +--R (376) ------------------------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 518 +m0191:= a0191-r0191 +--R +--R +--R (377) 0 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 518 +d0191:= D(m0191,x) +--R +--R +--R (378) 0 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 518 +t0192:= log(2+b*x^m)/x +--R +--R +--R m +--R log(b x + 2) +--R (379) ------------- +--R x +--R Type: Expression(Integer) +--E 479 + +--S 480 of 518 +r0192:= 1/m*(log(2)*log(x^m)-polylog(2,-1/2*b*x^m)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 480 + +--S 481 of 518 +a0192:= integrate(t0192,x) +--R +--R +--R x m +--R ++ log(b %L + 2) +--R (380) | -------------- d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 518 +--m0192:= a0192-r0192 +--E 482 + +--S 483 of 518 +--d0192:= D(m0192,x) +--E 483 + +--S 484 of 518 +t0193:= log(c*(a+b*x^m)^n)/x +--R +--R +--R m n +--R log(c (b x + a) ) +--R (381) ------------------ +--R x +--R Type: Expression(Integer) +--E 484 + +--S 485 of 518 +r0193:= 1/m*(log(-b*x^m/a)*log(c*(a+b*x^m)^n)+n*polylog(2,(a+b*x^m)/a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 485 + +--S 486 of 518 +a0193:= integrate(t0193,x) +--R +--R +--R x m n +--R ++ log(c (b %L + a) ) +--R (382) | ------------------- d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 518 +--m0193:= a0193-r0193 +--E 487 + +--S 488 of 518 +--d0193:= D(m0193,x) +--E 488 + +--S 489 of 518 +t0194:= log(c*(a+b*x^m)^n)^2/x +--R +--R +--R m n 2 +--R log(c (b x + a) ) +--R (383) ------------------- +--R x +--R Type: Expression(Integer) +--E 489 + +--S 490 of 518 +r0194:= -1/m*(-log(-b*x^m/a)*log(c*(a+b*x^m)^n)^2-_ + 2*n*log(c*(a+b*x^m)^n)*polylog(2,(a+b*x^m)/a)+_ + 2*n^2*polylog(3,(a+b*x^m)/a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 490 + +--S 491 of 518 +a0194:= integrate(t0194,x) +--R +--R +--R x m n 2 +--R ++ log(c (b %L + a) ) +--R (384) | -------------------- d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 518 +--m0194:= a0194-r0194 +--E 492 + +--S 493 of 518 +--d0194:= D(m0194,x) +--E 493 + +--S 494 of 518 +t0195:= log(c*(a+b*x^m)^n)^3/x +--R +--R +--R m n 3 +--R log(c (b x + a) ) +--R (385) ------------------- +--R x +--R Type: Expression(Integer) +--E 494 + +--S 495 of 518 +r0195:= 1/m*(log(-b*x^m/a)*log(c*(a+b*x^m)^n)^3+_ + 3*n*log(c*(a+b*x^m)^n)^2*polylog(2,(a+b*x^m)/a)-_ + 6*n^2*log(c*(a+b*x^m)^n)*polylog(3,(a+b*x^m)/a)+_ + 6*n^3*polylog(4,(a+b*x^m)/a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 495 + +--S 496 of 518 +a0195:= integrate(t0195,x) +--R +--R +--R x m n 3 +--R ++ log(c (b %L + a) ) +--R (386) | -------------------- d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 518 +--m0195:= a0195-r0195 +--E 497 + +--S 498 of 518 +--d0195:= D(m0195,x) +--E 498 + +--S 499 of 518 +t0196:= x^2*log(c*(a+b*x)^n)^2 +--R +--R +--R 2 n 2 +--R (387) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 499 + +--S 500 of 518 +r0196:= 11/9*a^2*n^2*x/b^2-5/18*a*n^2*x^2/b+2/27*n^2*x^3-_ + 5/9*a^3*n^2*log(a+b*x)/b^3+1/3*a*n*x^2*log(c*(a+b*x)^n)/b-_ + 2/9*n*x^3*log(c*(a+b*x)^n)-2/3*a^2*n*(a+b*x)*log(c*(a+b*x)^n)/b^3+_ + 1/3*a^3*log(c*(a+b*x)^n)^2/b^3+1/3*x^3*log(c*(a+b*x)^n)^2 +--R +--R +--R (388) +--R 3 3 3 n 2 +--R (18b x + 18a )log(c (b x + a) ) +--R + +--R 3 3 2 2 2 3 n +--R (- 12b n x + 18a b n x - 36a b n x - 36a n)log(c (b x + a) ) +--R + +--R 3 2 3 2 3 2 2 2 2 2 +--R - 30a n log(b x + a) + 4b n x - 15a b n x + 66a b n x +--R / +--R 3 +--R 54b +--R Type: Expression(Integer) +--E 500 + +--S 501 of 518 +a0196:= integrate(t0196,x) +--R +--R +--R (389) +--R 3 2 3 3 2 2 +--R (18b n x + 18a n )log(b x + a) +--R + +--R 3 3 3 3 2 3 2 2 2 2 2 3 2 +--R ((36b n x + 36a n)log(c) - 12b n x + 18a b n x - 36a b n x - 66a n ) +--R * +--R log(b x + a) +--R + +--R 3 3 2 3 3 2 2 2 3 2 3 +--R 18b x log(c) + (- 12b n x + 18a b n x - 36a b n x)log(c) + 4b n x +--R + +--R 2 2 2 2 2 +--R - 15a b n x + 66a b n x +--R / +--R 3 +--R 54b +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 518 +m0196:= a0196-r0196 +--R +--R +--R (390) +--R 3 3 3 n 2 +--R (- 3b x - 3a )log(c (b x + a) ) +--R + +--R 3 3 2 2 2 3 n +--R (2b n x - 3a b n x + 6a b n x + 6a n)log(c (b x + a) ) +--R + +--R 3 2 3 3 2 2 +--R (3b n x + 3a n )log(b x + a) +--R + +--R 3 3 3 3 2 3 2 2 2 2 2 3 2 +--R ((6b n x + 6a n)log(c) - 2b n x + 3a b n x - 6a b n x - 6a n ) +--R * +--R log(b x + a) +--R + +--R 3 3 2 3 3 2 2 2 +--R 3b x log(c) + (- 2b n x + 3a b n x - 6a b n x)log(c) +--R / +--R 3 +--R 9b +--R Type: Expression(Integer) +--E 502 + +--S 503 of 518 +d0196:= D(m0196,x) +--R +--R +--R (391) +--R 3 3 2 2 n n 2 +--R (- 9b x - 9a b x )(b x + a) log(c (b x + a) ) +--R + +--R 3 3 3 n +--R (6b n x + 6a n)(b x + a) +--R + +--R 4 4 3 3 3 4 n - 1 +--R (- 6b n x - 6a b n x - 6a b n x - 6a n)(b x + a) +--R * +--R n +--R log(c (b x + a) ) +--R + +--R 3 2 3 2 2 2 2 +--R (9b n x + 9a b n x )log(b x + a) +--R + +--R 3 3 2 2 3 3 2 2 2 +--R (18b n x + 18a b n x )log(c)log(b x + a) + (9b x + 9a b x )log(c) +--R + +--R 3 2 3 2 2 2 2 2 3 2 +--R - 2b n x + 3a b n x - 6a b n x - 6a n +--R * +--R n +--R (b x + a) +--R + +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 n - 1 +--R (2b n x - a b n x + 3a b n x + 12a b n x + 6a n )(b x + a) +--R / +--R 3 2 n +--R (9b x + 9a b )(b x + a) +--R Type: Expression(Integer) +--E 503 + +--S 504 of 518 +t0197:= x*log(c*(a+b*x)^n)^2 +--R +--R +--R n 2 +--R (392) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 504 + +--S 505 of 518 +r0197:= -3/2*a*n^2*x/b+1/4*n^2*x^2+1/2*a^2*n^2*log(a+b*x)/b^2-1/2*n*x^2*_ + log(c*(a+b*x)^n)+a*n*(a+b*x)*log(c*(a+b*x)^n)/b^2-_ + 1/2*a^2*log(c*(a+b*x)^n)^2/b^2+1/2*x^2*log(c*(a+b*x)^n)^2 +--R +--R +--R (393) +--R 2 2 2 n 2 +--R (2b x - 2a )log(c (b x + a) ) +--R + +--R 2 2 2 n 2 2 +--R (- 2b n x + 4a b n x + 4a n)log(c (b x + a) ) + 2a n log(b x + a) +--R + +--R 2 2 2 2 +--R b n x - 6a b n x +--R / +--R 2 +--R 4b +--R Type: Expression(Integer) +--E 505 + +--S 506 of 518 +a0197:= integrate(t0197,x) +--R +--R +--R (394) +--R 2 2 2 2 2 2 +--R (2b n x - 2a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((4b n x - 4a n)log(c) - 2b n x + 4a b n x + 6a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R 2b x log(c) + (- 2b n x + 4a b n x)log(c) + b n x - 6a b n x +--R / +--R 2 +--R 4b +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 518 +m0197:= a0197-r0197 +--R +--R +--R (395) +--R 2 2 2 n 2 +--R (- b x + a )log(c (b x + a) ) +--R + +--R 2 2 2 n +--R (b n x - 2a b n x - 2a n)log(c (b x + a) ) +--R + +--R 2 2 2 2 2 2 +--R (b n x - a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((2b n x - 2a n)log(c) - b n x + 2a b n x + 2a n )log(b x + a) +--R + +--R 2 2 2 2 2 +--R b x log(c) + (- b n x + 2a b n x)log(c) +--R / +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 507 + +--S 508 of 518 +d0197:= D(m0197,x) +--R +--R +--R (396) +--R 2 2 n n 2 +--R (- 2b x - 2a b x)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 n +--R (2b n x - 2a n)(b x + a) +--R + +--R 3 3 2 2 2 3 n - 1 +--R (- 2b n x - 2a b n x + 2a b n x + 2a n)(b x + a) +--R * +--R n +--R log(c (b x + a) ) +--R + +--R 2 2 2 2 2 +--R (2b n x + 2a b n x)log(b x + a) +--R + +--R 2 2 2 2 2 +--R (4b n x + 4a b n x)log(c)log(b x + a) + (2b x + 2a b x)log(c) +--R + +--R 2 2 2 2 2 2 +--R - b n x + 2a b n x + 2a n +--R * +--R n +--R (b x + a) +--R + +--R 3 2 3 2 2 2 2 2 3 2 n - 1 +--R (b n x - a b n x - 4a b n x - 2a n )(b x + a) +--R / +--R 2 n +--R (2b x + 2a b)(b x + a) +--R Type: Expression(Integer) +--E 508 + +--S 509 of 518 +t0198:= log(c*(a+b*x)^n)^2 +--R +--R +--R n 2 +--R (397) log(c (b x + a) ) +--R Type: Expression(Integer) +--E 509 + +--S 510 of 518 +r0198:= 2*n^2*x-2*n*(a+b*x)*log(c*(a+b*x)^n)/b+(a+b*x)*log(c*(a+b*x)^n)^2/b +--R +--R +--R (398) +--R n 2 n 2 +--R (b x + a)log(c (b x + a) ) + (- 2b n x - 2a n)log(c (b x + a) ) + 2b n x +--R ------------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 510 + +--S 511 of 518 +a0198:= integrate(t0198,x) +--R +--R +--R (399) +--R 2 2 2 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 2 +--R ((2b n x + 2a n)log(c) - 2b n x - 2a n )log(b x + a) + b x log(c) +--R + +--R 2 +--R - 2b n x log(c) + 2b n x +--R / +--R b +--R Type: Union(Expression(Integer),...) +--E 511 + +--S 512 of 518 +m0198:= a0198-r0198 +--R +--R +--R (400) +--R n 2 n +--R (- b x - a)log(c (b x + a) ) + (2b n x + 2a n)log(c (b x + a) ) +--R + +--R 2 2 2 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 2 +--R ((2b n x + 2a n)log(c) - 2b n x - 2a n )log(b x + a) + b x log(c) +--R + +--R - 2b n x log(c) +--R / +--R b +--R Type: Expression(Integer) +--E 512 + +--S 513 of 518 +d0198:= D(m0198,x) +--R +--R +--R (401) +--R n n 2 +--R - (b x + a) log(c (b x + a) ) +--R + +--R n n - 1 n +--R (2n (b x + a) + (- 2b n x - 2a n)(b x + a) )log(c (b x + a) ) +--R + +--R 2 2 2 2 n +--R (n log(b x + a) + 2n log(c)log(b x + a) + log(c) - 2n )(b x + a) +--R + +--R 2 2 n - 1 +--R (2b n x + 2a n )(b x + a) +--R / +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 513 + +--S 514 of 518 +t0199:= log(c*(a+b*x)^n)^2/x +--R +--R +--R n 2 +--R log(c (b x + a) ) +--R (402) ------------------ +--R x +--R Type: Expression(Integer) +--E 514 + +--S 515 of 518 +r0199:= log(-b*x/a)*log(c*(a+b*x)^n)^2+2*n*log(c*(a+b*x)^n)*_ + polylog(2,1+b*x/a)-2*n^2*polylog(3,(a+b*x)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 515 + +--S 516 of 518 +a0199:= integrate(t0199,x) +--R +--R +--R x n 2 +--R ++ log(c (%L b + a) ) +--R (403) | ------------------- d%L +--R ++ %L +--R Type: Union(Expression(Integer),...) +--E 516 + +--S 517 of 518 +--m0199:= a0199-r0199 +--E 517 + +--S 518 of 518 +--d0199:= D(m0199,x) +--E 518 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richlog100-199.input.pdf b/src/axiom-website/CATS/richlog100-199.input.pdf new file mode 100644 index 0000000..8c33281 Binary files /dev/null and b/src/axiom-website/CATS/richlog100-199.input.pdf differ diff --git a/src/axiom-website/CATS/richlog200-299.input.pamphlet b/src/axiom-website/CATS/richlog200-299.input.pamphlet new file mode 100644 index 0000000..77b939c --- /dev/null +++ b/src/axiom-website/CATS/richlog200-299.input.pamphlet @@ -0,0 +1,6139 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richlog200-299.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richlog200-299.output +)spool richlog200-299.output +)set message auto off +)clear all + +--S 1 of 514 +t0200:= log(c*(a+b*x)^n)^2/x^2 +--R +--R +--R n 2 +--R log(c (b x + a) ) +--R (1) ------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 514 +r0200:= 2*b*n*log(-b*x/a)*log(c*(a+b*x)^n)/a-(a+b*x)*log(c*(a+b*x)^n)^2/a/x+_ + 2*b*n^2*polylog(2,1+b*x/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 514 +a0200:= integrate(t0200,x) +--R +--R +--R x n 2 +--R ++ log(c (%I b + a) ) +--R (2) | ------------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 514 +--m0200:= a0200-r0200 +--E 4 + +--S 5 of 514 +--d0200:= D(m0200,x) +--E 5 + +--S 6 of 514 +t0201:= log(c*(a+b*x)^n)^2/x^3 +--R +--R +--R n 2 +--R log(c (b x + a) ) +--R (3) ------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 514 +r0201:= b^2*n^2*log(x)/a^2-b^2*n^2*log(a+b*x)/a^2-b*n*log(c*(a+b*x)^n)/a/x-_ + b^2*n*log(-b*x/a)*log(c*(a+b*x)^n)/a^2+1/2*b^2*_ + log(c*(a+b*x)^n)^2/a^2-1/2*log(c*(a+b*x)^n)^2/x^2-_ + b^2*n^2*polylog(2,1+b*x/a)/a^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 514 +a0201:= integrate(t0201,x) +--R +--R +--R x n 2 +--R ++ log(c (%I b + a) ) +--R (4) | ------------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 514 +--m0201:= a0201-r0201 +--E 9 + +--S 10 of 514 +--d0201:= D(m0201,x) +--E 10 + +--S 11 of 514 +t0202:= x*log(c*(a+b*x)^n)^3 +--R +--R +--R n 3 +--R (5) x log(c (b x + a) ) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 514 +r0202:= 21/4*a*n^3*x/b-3/8*n^3*x^2-3/4*a^2*n^3*log(a+b*x)/b^2+_ + 3/4*n^2*x^2*log(c*(a+b*x)^n)-9/2*a*n^2*(a+b*x)*log(c*(a+b*x)^n)/b^2-_ + 3/4*n*x^2*log(c*(a+b*x)^n)^2+9/4*a*n*(a+2/3*b*x)*_ + log(c*(a+b*x)^n)^2/b^2-1/2*a^2*log(c*(a+b*x)^n)^3/b^2+_ + 1/2*x^2*log(c*(a+b*x)^n)^3 +--R +--R +--R (6) +--R 2 2 2 n 3 +--R (4b x - 4a )log(c (b x + a) ) +--R + +--R 2 2 2 n 2 +--R (- 6b n x + 12a b n x + 18a n)log(c (b x + a) ) +--R + +--R 2 2 2 2 2 2 n 2 3 +--R (6b n x - 36a b n x - 36a n )log(c (b x + a) ) - 6a n log(b x + a) +--R + +--R 2 3 2 3 +--R - 3b n x + 42a b n x +--R / +--R 2 +--R 8b +--R Type: Expression(Integer) +--E 12 + +--S 13 of 514 +a0202:= integrate(t0202,x) +--R +--R +--R (7) +--R 2 3 2 2 3 3 +--R (4b n x - 4a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 3 2 3 2 3 2 +--R ((12b n x - 12a n )log(c) - 6b n x + 12a b n x + 18a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (12b n x - 12a n)log(c) + (- 12b n x + 24a b n x + 36a n )log(c) +--R + +--R 2 3 2 3 2 3 +--R 6b n x - 36a b n x - 42a n +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 2 2 +--R 4b x log(c) + (- 6b n x + 12a b n x)log(c) +--R + +--R 2 2 2 2 2 3 2 3 +--R (6b n x - 36a b n x)log(c) - 3b n x + 42a b n x +--R / +--R 2 +--R 8b +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 514 +m0202:= a0202-r0202 +--R +--R +--R (8) +--R 2 2 2 n 3 +--R (- 2b x + 2a )log(c (b x + a) ) +--R + +--R 2 2 2 n 2 +--R (3b n x - 6a b n x - 9a n)log(c (b x + a) ) +--R + +--R 2 2 2 2 2 2 n +--R (- 3b n x + 18a b n x + 18a n )log(c (b x + a) ) +--R + +--R 2 3 2 2 3 3 +--R (2b n x - 2a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 3 2 3 2 3 2 +--R ((6b n x - 6a n )log(c) - 3b n x + 6a b n x + 9a n )log(b x + a) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (6b n x - 6a n)log(c) + (- 6b n x + 12a b n x + 18a n )log(c) +--R + +--R 2 3 2 3 2 3 +--R 3b n x - 18a b n x - 18a n +--R * +--R log(b x + a) +--R + +--R 2 2 3 2 2 2 2 2 2 2 +--R 2b x log(c) + (- 3b n x + 6a b n x)log(c) + (3b n x - 18a b n x)log(c) +--R / +--R 2 +--R 4b +--R Type: Expression(Integer) +--E 14 + +--S 15 of 514 +d0202:= D(m0202,x) +--R +--R +--R (9) +--R 2 2 n n 3 +--R (- 4b x - 4a b x)(b x + a) log(c (b x + a) ) +--R + +--R 2 2 2 n +--R (6b n x - 6a n)(b x + a) +--R + +--R 3 3 2 2 2 3 n - 1 +--R (- 6b n x - 6a b n x + 6a b n x + 6a n)(b x + a) +--R * +--R n 2 +--R log(c (b x + a) ) +--R + +--R 2 2 2 2 2 2 n +--R (- 6b n x + 12a b n x + 18a n )(b x + a) +--R + +--R 3 2 3 2 2 2 2 2 3 2 n - 1 +--R (6b n x - 6a b n x - 30a b n x - 18a n )(b x + a) +--R * +--R n +--R log(c (b x + a) ) +--R + +--R 2 3 2 3 3 +--R (4b n x + 4a b n x)log(b x + a) +--R + +--R 2 2 2 2 2 +--R (12b n x + 12a b n x)log(c)log(b x + a) +--R + +--R 2 2 2 2 2 3 +--R (12b n x + 12a b n x)log(c) log(b x + a) + (4b x + 4a b x)log(c) +--R + +--R 2 3 2 3 2 3 +--R 3b n x - 18a b n x - 18a n +--R * +--R n +--R (b x + a) +--R + +--R 3 3 3 2 3 2 2 3 3 3 n - 1 +--R (- 3b n x + 15a b n x + 36a b n x + 18a n )(b x + a) +--R / +--R 2 n +--R (4b x + 4a b)(b x + a) +--R Type: Expression(Integer) +--E 15 + +--S 16 of 514 +t0203:= log(c*(a+b*x)^n)^3 +--R +--R +--R n 3 +--R (10) log(c (b x + a) ) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 514 +r0203:= -6*n^3*x+6*n^2*(a+b*x)*log(c*(a+b*x)^n)/b-_ + 3*n*(a+b*x)*log(c*(a+b*x)^n)^2/b+(a+b*x)*log(c*(a+b*x)^n)^3/b +--R +--R +--R (11) +--R n 3 n 2 +--R (b x + a)log(c (b x + a) ) + (- 3b n x - 3a n)log(c (b x + a) ) +--R + +--R 2 2 n 3 +--R (6b n x + 6a n )log(c (b x + a) ) - 6b n x +--R / +--R b +--R Type: Expression(Integer) +--E 17 + +--S 18 of 514 +a0203:= integrate(t0203,x) +--R +--R +--R (12) +--R 3 3 3 +--R (b n x + a n )log(b x + a) +--R + +--R 2 2 3 3 2 +--R ((3b n x + 3a n )log(c) - 3b n x - 3a n )log(b x + a) +--R + +--R 2 2 2 3 3 +--R ((3b n x + 3a n)log(c) + (- 6b n x - 6a n )log(c) + 6b n x + 6a n ) +--R * +--R log(b x + a) +--R + +--R 3 2 2 3 +--R b x log(c) - 3b n x log(c) + 6b n x log(c) - 6b n x +--R / +--R b +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 514 +m0203:= a0203-r0203 +--R +--R +--R (13) +--R n 3 n 2 +--R (- b x - a)log(c (b x + a) ) + (3b n x + 3a n)log(c (b x + a) ) +--R + +--R 2 2 n 3 3 3 +--R (- 6b n x - 6a n )log(c (b x + a) ) + (b n x + a n )log(b x + a) +--R + +--R 2 2 3 3 2 +--R ((3b n x + 3a n )log(c) - 3b n x - 3a n )log(b x + a) +--R + +--R 2 2 2 3 3 +--R ((3b n x + 3a n)log(c) + (- 6b n x - 6a n )log(c) + 6b n x + 6a n ) +--R * +--R log(b x + a) +--R + +--R 3 2 2 +--R b x log(c) - 3b n x log(c) + 6b n x log(c) +--R / +--R b +--R Type: Expression(Integer) +--E 19 + +--S 20 of 514 +d0203:= D(m0203,x) +--R +--R +--R (14) +--R n n 3 +--R - (b x + a) log(c (b x + a) ) +--R + +--R n n - 1 n 2 +--R (3n (b x + a) + (- 3b n x - 3a n)(b x + a) )log(c (b x + a) ) +--R + +--R 2 n 2 2 n - 1 n +--R (- 6n (b x + a) + (6b n x + 6a n )(b x + a) )log(c (b x + a) ) +--R + +--R 3 3 2 2 2 +--R n log(b x + a) + 3n log(c)log(b x + a) + 3n log(c) log(b x + a) +--R + +--R 3 3 +--R log(c) + 6n +--R * +--R n +--R (b x + a) +--R + +--R 3 3 n - 1 +--R (- 6b n x - 6a n )(b x + a) +--R / +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 20 + +--S 21 of 514 +t0204:= log(c*(a+b*x)^n)^3/x +--R +--R +--R n 3 +--R log(c (b x + a) ) +--R (15) ------------------ +--R x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 514 +r0204:= log(-b*x/a)*log(c*(a+b*x)^n)^3+3*n*log(c*(a+b*x)^n)^2*_ + polylog(2,1+b*x/a)-6*n^2*log(c*(a+b*x)^n)*_ + polylog(3,1+b*x/a)+6*n^3*polylog(4,(a+b*x)/a) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 514 +a0204:= integrate(t0204,x) +--R +--R +--R x n 3 +--R ++ log(c (%I b + a) ) +--R (16) | ------------------- d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 514 +--m0204:= a0204-r0204 +--E 24 + +--S 25 of 514 +--d0204:= D(m0204,x) +--E 25 + +--S 26 of 514 +t0205:= log(c*(a+b*x)^n)^3/x^2 +--R +--R +--R n 3 +--R log(c (b x + a) ) +--R (17) ------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 514 +r0205:= 3*b*n*log(-b*x/a)*log(c*(a+b*x)^n)^2/a-_ + (a+b*x)*log(c*(a+b*x)^n)^3/a/x+6*b*n^2*log(c*(a+b*x)^n)*_ + polylog(2,1+b*x/a)/a-6*b*n^3*polylog(3,(a+b*x)/a)/a +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 514 +a0205:= integrate(t0205,x) +--R +--R +--R x n 3 +--R ++ log(c (%I b + a) ) +--R (18) | ------------------- d%I +--R ++ 2 +--R %I +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 514 +--m0205:= a0205-r0205 +--E 29 + +--S 30 of 514 +--d0205:= D(m0205,x) +--E 30 + +--S 31 of 514 +t0206:= log(c*(a+b*x)^n)^3/x^3 +--R +--R +--R n 3 +--R log(c (b x + a) ) +--R (19) ------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 514 +r0206:= 3*b^2*n^2*log(-b*x/a)*log(c*(a+b*x)^n)/a^2-3/2*b*n*(a+b*x)*_ + log(c*(a+b*x)^n)^2/a^2/x-3/2*b^2*n*log(-b*x/a)*_ + log(c*(a+b*x)^n)^2/a^2+1/2*b^2*log(c*(a+b*x)^n)^3/a^2-1/2*_ + log(c*(a+b*x)^n)^3/x^2+3*b^2*n^2*(n-log(c*(a+b*x)^n))*_ + polylog(2,1+b*x/a)/a^2+3*b^2*n^3*polylog(3,(a+b*x)/a)/a^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 514 +a0206:= integrate(t0206,x) +--R +--R +--R x n 3 +--R ++ log(c (%I b + a) ) +--R (20) | ------------------- d%I +--R ++ 3 +--R %I +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 514 +--m0206:= a0206-r0206 +--E 34 + +--S 35 of 514 +--d0206:= D(m0206,x) +--E 35 + +--S 36 of 514 +t0207:= x^3/log(c*(a+b*x)^n) +--R +--R +--R 3 +--R x +--R (21) ----------------- +--R n +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 514 +r0207:= -a^3*(a+b*x)*Ei(log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(1/n))/b^4/n+_ + 3*a^2*(a+b*x)^2*Ei(2*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(2/n))/b^4/n-_ + 3*a*(a+b*x)^3*Ei(3*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(3/n))/b^4/n+_ + (a+b*x)^4*Ei(4*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(4/n))/b^4/n +--R +--R +--R (22) +--R 1 2 +--R - - +--R 4 4 3 3 2 2 2 3 4 n n n n +--R (b x + 4a b x + 6a b x + 4a b x + a )(c (b x + a) ) (c (b x + a) ) +--R * +--R 3 +--R - n +--R n n 4log(c (b x + a) ) +--R (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 1 2 +--R - - +--R 3 3 2 2 2 3 4 n n n n +--R (- 3a b x - 9a b x - 9a b x - 3a )(c (b x + a) ) (c (b x + a) ) +--R * +--R 4 +--R - n +--R n n 3log(c (b x + a) ) +--R (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 1 3 4 +--R - - - +--R 2 2 2 3 4 n n n n n n +--R (3a b x + 6a b x + 3a )(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R * +--R n +--R 2log(c (b x + a) ) +--R Ei(------------------) +--R n +--R + +--R 2 3 4 +--R - - - +--R 3 4 n n n n n n +--R (- a b x - a )(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R * +--R n +--R log(c (b x + a) ) +--R Ei(-----------------) +--R n +--R / +--R 1 2 3 4 +--R - - - - +--R 4 n n n n n n n n +--R b n (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R Type: Expression(Integer) +--E 37 + +--S 38 of 514 +a0207:= integrate(t0207,x) +--R +--R +--R x 3 +--R ++ %I +--R (23) | ------------------ d%I +--R ++ n +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 514 +--m0207:= a0207-r0207 +--E 39 + +--S 40 of 514 +--d0207:= D(m0207,x) +--E 40 + +--S 41 of 514 +t0208:= x^2/log(c*(a+b*x)^n) +--R +--R +--R 2 +--R x +--R (24) ----------------- +--R n +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 514 +r0208:= a^2*(a+b*x)*Ei(log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(1/n))/b^3/n-_ + 2*a*(a+b*x)^2*Ei(2*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(2/n))/b^3/n+_ + (a+b*x)^3*Ei(3*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(3/n))/b^3/n +--R +--R +--R (25) +--R 1 2 +--R - - +--R 3 3 2 2 2 3 n n n n +--R (b x + 3a b x + 3a b x + a )(c (b x + a) ) (c (b x + a) ) +--R * +--R n +--R 3log(c (b x + a) ) +--R Ei(------------------) +--R n +--R + +--R 1 3 +--R - - +--R 2 2 2 3 n n n n +--R (- 2a b x - 4a b x - 2a )(c (b x + a) ) (c (b x + a) ) +--R * +--R n +--R 2log(c (b x + a) ) +--R Ei(------------------) +--R n +--R + +--R 2 3 +--R - - n +--R 2 3 n n n n log(c (b x + a) ) +--R (a b x + a )(c (b x + a) ) (c (b x + a) ) Ei(-----------------) +--R n +--R / +--R 1 2 3 +--R - - - +--R 3 n n n n n n +--R b n (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R Type: Expression(Integer) +--E 42 + +--S 43 of 514 +a0208:= integrate(t0208,x) +--R +--R +--R x 2 +--R ++ %I +--R (26) | ------------------ d%I +--R ++ n +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 514 +--m0208:= a0208-r0208 +--E 44 + +--S 45 of 514 +--d0208:= D(m0208,x) +--E 45 + +--S 46 of 514 +t0209:= x/log(c*(a+b*x)^n) +--R +--R +--R x +--R (27) ----------------- +--R n +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 514 +r0209:= -a*(a+b*x)*Ei(log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(1/n))/b^2/n+_ + (a+b*x)^2*Ei(2*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(2/n))/b^2/n +--R +--R +--R (28) +--R 1 +--R - n +--R 2 2 2 n n 2log(c (b x + a) ) +--R (b x + 2a b x + a )(c (b x + a) ) Ei(------------------) +--R n +--R + +--R 2 +--R - n +--R 2 n n log(c (b x + a) ) +--R (- a b x - a )(c (b x + a) ) Ei(-----------------) +--R n +--R / +--R 1 2 +--R - - +--R 2 n n n n +--R b n (c (b x + a) ) (c (b x + a) ) +--R Type: Expression(Integer) +--E 47 + +--S 48 of 514 +a0209:= integrate(t0209,x) +--R +--R +--R x +--R ++ %I +--R (29) | ------------------ d%I +--R ++ n +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 514 +--m0209:= a0209-r0209 +--E 49 + +--S 50 of 514 +--d0209:= D(m0209,x) +--E 50 + +--S 51 of 514 +t0210:= 1/log(c*(a+b*x)^n) +--R +--R +--R 1 +--R (30) ----------------- +--R n +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 514 +r0210:= (a+b*x)*Ei(log(c*(a+b*x)^n)/n)/b/n/((c*(a+b*x)^n)^(1/n)) +--R +--R +--R n +--R log(c (b x + a) ) +--R (b x + a)Ei(-----------------) +--R n +--R (31) ------------------------------ +--R 1 +--R - +--R n n +--R b n (c (b x + a) ) +--R Type: Expression(Integer) +--E 52 + +--S 53 of 514 +a0210:= integrate(t0210,x) +--R +--R +--R x +--R ++ 1 +--R (32) | ------------------ d%I +--R ++ n +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 514 +--m0210:= a0210-r0210 +--E 54 + +--S 55 of 514 +--d0210:= D(m0210,x) +--E 55 + +--S 56 of 514 +t0211:= x^3/log(c*(a+b*x)^n)^2 +--R +--R +--R 3 +--R x +--R (33) ------------------ +--R n 2 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 514 +r0211:= -a^3*(a+b*x)*Ei(log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(1/n))/b^4/n^2+_ + 6*a^2*(a+b*x)^2*Ei(2*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(2/n))/_ + b^4/n^2-9*a*(a+b*x)^3*Ei(3*log(c*(a+b*x)^n)/n)/_ + ((c*(a+b*x)^n)^(3/n))/b^4/n^2+4*(a+b*x)^4*Ei(4*log(c*(a+b*x)^n)/n)/_ + ((c*(a+b*x)^n)^(4/n))/b^4/n^2+a^3*(a+b*x)/b^4/n/log(c*(a+b*x)^n)-_ + 3*a^2*(a+b*x)^2/b^4/n/log(c*(a+b*x)^n)+3*a*(a+b*x)^3/b^4/n/_ + log(c*(a+b*x)^n)-(a+b*x)^4/b^4/n/log(c*(a+b*x)^n) +--R +--R +--R (34) +--R 4 4 3 3 2 2 2 3 4 n +--R (4b x + 16a b x + 24a b x + 16a b x + 4a )log(c (b x + a) ) +--R * +--R 1 2 3 +--R - - - n +--R n n n n n n 4log(c (b x + a) ) +--R (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 1 +--R - +--R 3 3 2 2 2 3 4 n n n +--R (- 9a b x - 27a b x - 27a b x - 9a )log(c (b x + a) )(c (b x + a) ) +--R * +--R 2 4 +--R - - n +--R n n n n 3log(c (b x + a) ) +--R (c (b x + a) ) (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 1 +--R - +--R 2 2 2 3 4 n n n +--R (6a b x + 12a b x + 6a )log(c (b x + a) )(c (b x + a) ) +--R * +--R 3 4 +--R - - n +--R n n n n 2log(c (b x + a) ) +--R (c (b x + a) ) (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 2 3 +--R - - +--R 3 4 n n n n n +--R (- a b x - a )log(c (b x + a) )(c (b x + a) ) (c (b x + a) ) +--R * +--R 4 +--R - n +--R n n log(c (b x + a) ) +--R (c (b x + a) ) Ei(-----------------) +--R n +--R + +--R 1 2 3 +--R - - - +--R 4 4 3 3 n n n n n n +--R (- b n x - a b n x )(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R * +--R 4 +--R - +--R n n +--R (c (b x + a) ) +--R / +--R 1 2 3 +--R - - - +--R 4 2 n n n n n n n +--R b n log(c (b x + a) )(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R * +--R 4 +--R - +--R n n +--R (c (b x + a) ) +--R Type: Expression(Integer) +--E 57 + +--S 58 of 514 +a0211:= integrate(t0211,x) +--R +--R +--R x 3 +--R ++ %I +--R (35) | ------------------- d%I +--R ++ n 2 +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 514 +--m0211:= a0211-r0211 +--E 59 + +--S 60 of 514 +--d0211:= D(m0211,x) +--E 60 + +--S 61 of 514 +t0212:= x^2/log(c*(a+b*x)^n)^2 +--R +--R +--R 2 +--R x +--R (36) ------------------ +--R n 2 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 514 +r0212:= a^2*(a+b*x)*Ei(log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(1/n))/b^3/n^2-_ + 4*a*(a+b*x)^2*Ei(2*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(2/n))/b^3/n^2+_ + 3*(a+b*x)^3*Ei(3*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(3/n))/b^3/n^2-_ + a^2*(a+b*x)/b^3/n/log(c*(a+b*x)^n)+2*a*(a+b*x)^2/b^3/n/_ + log(c*(a+b*x)^n)-(a+b*x)^3/b^3/n/log(c*(a+b*x)^n) +--R +--R +--R (37) +--R 1 +--R - +--R 3 3 2 2 2 3 n n n +--R (3b x + 9a b x + 9a b x + 3a )log(c (b x + a) )(c (b x + a) ) +--R * +--R 2 +--R - n +--R n n 3log(c (b x + a) ) +--R (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 1 +--R - +--R 2 2 2 3 n n n +--R (- 4a b x - 8a b x - 4a )log(c (b x + a) )(c (b x + a) ) +--R * +--R 3 +--R - n +--R n n 2log(c (b x + a) ) +--R (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 2 3 +--R - - +--R 2 3 n n n n n +--R (a b x + a )log(c (b x + a) )(c (b x + a) ) (c (b x + a) ) +--R * +--R n +--R log(c (b x + a) ) +--R Ei(-----------------) +--R n +--R + +--R 1 2 3 +--R - - - +--R 3 3 2 2 n n n n n n +--R (- b n x - a b n x )(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R / +--R 1 2 3 +--R - - - +--R 3 2 n n n n n n n +--R b n log(c (b x + a) )(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R Type: Expression(Integer) +--E 62 + +--S 63 of 514 +a0212:= integrate(t0212,x) +--R +--R +--R x 2 +--R ++ %I +--R (38) | ------------------- d%I +--R ++ n 2 +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 514 +--m0212:= a0212-r0212 +--E 64 + +--S 65 of 514 +--d0212:= D(m0212,x) +--E 65 + +--S 66 of 514 +t0213:= x/log(c*(a+b*x)^n)^2 +--R +--R +--R x +--R (39) ------------------ +--R n 2 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 514 +r0213:= -a*(a+b*x)*Ei(log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(1/n))/b^2/n^2+_ + 2*(a+b*x)^2*Ei(2*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(2/n))/b^2/n^2+_ + a*(a+b*x)/b^2/n/log(c*(a+b*x)^n)-(a+b*x)^2/b^2/n/log(c*(a+b*x)^n) +--R +--R +--R (40) +--R 1 +--R - +--R 2 2 2 n n n +--R (2b x + 4a b x + 2a )log(c (b x + a) )(c (b x + a) ) +--R * +--R n +--R 2log(c (b x + a) ) +--R Ei(------------------) +--R n +--R + +--R 2 +--R - n +--R 2 n n n log(c (b x + a) ) +--R (- a b x - a )log(c (b x + a) )(c (b x + a) ) Ei(-----------------) +--R n +--R + +--R 1 2 +--R - - +--R 2 2 n n n n +--R (- b n x - a b n x)(c (b x + a) ) (c (b x + a) ) +--R / +--R 1 2 +--R - - +--R 2 2 n n n n n +--R b n log(c (b x + a) )(c (b x + a) ) (c (b x + a) ) +--R Type: Expression(Integer) +--E 67 + +--S 68 of 514 +a0213:= integrate(t0213,x) +--R +--R +--R x +--R ++ %I +--R (41) | ------------------- d%I +--R ++ n 2 +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 514 +--m0213:= a0213-r0213 +--E 69 + +--S 70 of 514 +--d0213:= D(m0213,x) +--E 70 + +--S 71 of 514 +t0214:= 1/log(c*(a+b*x)^n)^2 +--R +--R +--R 1 +--R (42) ------------------ +--R n 2 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 514 +r0214:= (a+b*x)*Ei(log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(1/n))/b/n^2-_ + (a+b*x)/b/n/log(c*(a+b*x)^n) +--R +--R +--R (43) +--R n +--R n log(c (b x + a) ) +--R (b x + a)log(c (b x + a) )Ei(-----------------) +--R n +--R + +--R 1 +--R - +--R n n +--R (- b n x - a n)(c (b x + a) ) +--R / +--R 1 +--R - +--R 2 n n n +--R b n log(c (b x + a) )(c (b x + a) ) +--R Type: Expression(Integer) +--E 72 + +--S 73 of 514 +a0214:= integrate(t0214,x) +--R +--R +--R x +--R ++ 1 +--R (44) | ------------------- d%I +--R ++ n 2 +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 514 +--m0214:= a0214-r0214 +--E 74 + +--S 75 of 514 +--d0214:= D(m0214,x) +--E 75 + +--S 76 of 514 +t0215:= x^3/log(c*(a+b*x)^n)^3 +--R +--R +--R 3 +--R x +--R (45) ------------------ +--R n 3 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 514 +r0215:= -1/2*a^3*(a+b*x)*Ei(log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(1/n))/_ + b^4/n^3+6*a^2*(a+b*x)^2*Ei(2*log(c*(a+b*x)^n)/n)/_ + ((c*(a+b*x)^n)^(2/n))/b^4/n^3-27/2*a*(a+b*x)^3*_ + Ei(3*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(3/n))/b^4/n^3+8*(a+b*x)^4*_ + Ei(4*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(4/n))/b^4/n^3-_ + 1/2*x^3*(a+b*x)/b/n/log(c*(a+b*x)^n)^2-_ + 1/2*x^2*(a+b*x)*(3*a+4*b*x)/b^2/n^2/log(c*(a+b*x)^n) +--R +--R +--R (46) +--R 4 4 3 3 2 2 2 3 4 n 2 +--R (16b x + 64a b x + 96a b x + 64a b x + 16a )log(c (b x + a) ) +--R * +--R 1 2 3 +--R - - - n +--R n n n n n n 4log(c (b x + a) ) +--R (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 3 3 2 2 2 3 4 n 2 +--R (- 27a b x - 81a b x - 81a b x - 27a )log(c (b x + a) ) +--R * +--R 1 2 4 +--R - - - n +--R n n n n n n 3log(c (b x + a) ) +--R (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 1 +--R - +--R 2 2 2 3 4 n 2 n n +--R (12a b x + 24a b x + 12a )log(c (b x + a) ) (c (b x + a) ) +--R * +--R 3 4 +--R - - n +--R n n n n 2log(c (b x + a) ) +--R (c (b x + a) ) (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 2 3 +--R - - +--R 3 4 n 2 n n n n +--R (- a b x - a )log(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R * +--R 4 +--R - n +--R n n log(c (b x + a) ) +--R (c (b x + a) ) Ei(-----------------) +--R n +--R + +--R 4 4 3 3 2 2 2 n 4 2 4 +--R (- 4b n x - 7a b n x - 3a b n x )log(c (b x + a) ) - b n x +--R + +--R 3 2 3 +--R - a b n x +--R * +--R 1 2 3 4 +--R - - - - +--R n n n n n n n n +--R (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R / +--R 1 2 3 +--R - - - +--R 4 3 n 2 n n n n n n +--R 2b n log(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R * +--R 4 +--R - +--R n n +--R (c (b x + a) ) +--R Type: Expression(Integer) +--E 77 + +--S 78 of 514 +a0215:= integrate(t0215,x) +--R +--R +--R x 3 +--R ++ %I +--R (47) | ------------------- d%I +--R ++ n 3 +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 514 +--m0215:= a0215-r0215 +--E 79 + +--S 80 of 514 +--d0215:= D(m0215,x) +--E 80 + +--S 81 of 514 +t0216:= x^2/log(c*(a+b*x)^n)^3 +--R +--R +--R 2 +--R x +--R (48) ------------------ +--R n 3 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 514 +r0216:= 1/2*a^2*(a+b*x)*Ei(log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(1/n))/b^3/n^3-_ + 4*a*(a+b*x)^2*Ei(2*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(2/n))/b^3/n^3+_ + 9/2*(a+b*x)^3*Ei(3*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(3/n))/b^3/n^3-_ + 1/2*x^2*(a+b*x)/b/n/log(c*(a+b*x)^n)^2-1/2*x*(a+b*x)*_ + (2*a+3*b*x)/b^2/n^2/log(c*(a+b*x)^n) +--R +--R +--R (49) +--R 1 +--R - +--R 3 3 2 2 2 3 n 2 n n +--R (9b x + 27a b x + 27a b x + 9a )log(c (b x + a) ) (c (b x + a) ) +--R * +--R 2 +--R - n +--R n n 3log(c (b x + a) ) +--R (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 1 +--R - +--R 2 2 2 3 n 2 n n +--R (- 8a b x - 16a b x - 8a )log(c (b x + a) ) (c (b x + a) ) +--R * +--R 3 +--R - n +--R n n 2log(c (b x + a) ) +--R (c (b x + a) ) Ei(------------------) +--R n +--R + +--R 2 3 +--R - - +--R 2 3 n 2 n n n n +--R (a b x + a )log(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R * +--R n +--R log(c (b x + a) ) +--R Ei(-----------------) +--R n +--R + +--R 3 3 2 2 2 n 3 2 3 +--R (- 3b n x - 5a b n x - 2a b n x)log(c (b x + a) ) - b n x +--R + +--R 2 2 2 +--R - a b n x +--R * +--R 1 2 3 +--R - - - +--R n n n n n n +--R (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R / +--R 1 2 3 +--R - - - +--R 3 3 n 2 n n n n n n +--R 2b n log(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R Type: Expression(Integer) +--E 82 + +--S 83 of 514 +a0216:= integrate(t0216,x) +--R +--R +--R x 2 +--R ++ %I +--R (50) | ------------------- d%I +--R ++ n 3 +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 514 +--m0216:= a0216-r0216 +--E 84 + +--S 85 of 514 +--d0216:= D(m0216,x) +--E 85 + +--S 86 of 514 +t0217:= x/log(c*(a+b*x)^n)^3 +--R +--R +--R x +--R (51) ------------------ +--R n 3 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 514 +r0217:= -1/2*a*(a+b*x)*Ei(log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(1/n))/b^2/n^3+_ + 2*(a+b*x)^2*Ei(2*log(c*(a+b*x)^n)/n)/((c*(a+b*x)^n)^(2/n))/b^2/n^3-_ + 1/2*x*(a+b*x)/b/n/log(c*(a+b*x)^n)^2-1/2*(a+b*x)*(a+2*b*x)/_ + b^2/n^2/log(c*(a+b*x)^n) +--R +--R +--R (52) +--R 1 +--R - +--R 2 2 2 n 2 n n +--R (4b x + 8a b x + 4a )log(c (b x + a) ) (c (b x + a) ) +--R * +--R n +--R 2log(c (b x + a) ) +--R Ei(------------------) +--R n +--R + +--R 2 +--R - n +--R 2 n 2 n n log(c (b x + a) ) +--R (- a b x - a )log(c (b x + a) ) (c (b x + a) ) Ei(-----------------) +--R n +--R + +--R 2 2 2 n 2 2 2 2 +--R ((- 2b n x - 3a b n x - a n)log(c (b x + a) ) - b n x - a b n x) +--R * +--R 1 2 +--R - - +--R n n n n +--R (c (b x + a) ) (c (b x + a) ) +--R / +--R 1 2 +--R - - +--R 2 3 n 2 n n n n +--R 2b n log(c (b x + a) ) (c (b x + a) ) (c (b x + a) ) +--R Type: Expression(Integer) +--E 87 + +--S 88 of 514 +a0217:= integrate(t0217,x) +--R +--R +--R x +--R ++ %I +--R (53) | ------------------- d%I +--R ++ n 3 +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 514 +--m0217:= a0217-r0217 +--E 89 + +--S 90 of 514 +--d0217:= D(m0217,x) +--E 90 + +--S 91 of 514 +t0218:= 1/log(c*(a+b*x)^n)^3 +--R +--R +--R 1 +--R (54) ------------------ +--R n 3 +--R log(c (b x + a) ) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 514 +r0218:= 1/2*(a+b*x)*(Ei(log(c*(a+b*x)^n)/n)*(c*(a+b*x)^n)^(-1/n)*_ + log(c*(a+b*x)^n)^2-n^2-n*log(c*(a+b*x)^n))/n^3/b/log(c*(a+b*x)^n)^2 +--R +--R +--R (55) +--R 1 +--R - - n +--R n 2 n n log(c (b x + a) ) +--R (b x + a)log(c (b x + a) ) (c (b x + a) ) Ei(-----------------) +--R n +--R + +--R n 2 2 +--R (- b n x - a n)log(c (b x + a) ) - b n x - a n +--R / +--R 3 n 2 +--R 2b n log(c (b x + a) ) +--R Type: Expression(Integer) +--E 92 + +--S 93 of 514 +a0218:= integrate(t0218,x) +--R +--R +--R x +--R ++ 1 +--R (56) | ------------------- d%I +--R ++ n 3 +--R log(c (%I b + a) ) +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 514 +--m0218:= a0218-r0218 +--E 94 + +--S 95 of 514 +--d0218:= D(m0218,x) +--E 95 + +--S 96 of 514 +t0219:= log(c+d*x)/(a+b*x)^3 +--R +--R +--R log(d x + c) +--R (57) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 96 + +--S 97 of 514 +r0219:= -1/2*d/b/(b*c-a*d)/(a+b*x)-1/2*d^2*log(a+b*x)/b/(b*c-a*d)^2+_ + 1/2*d^2*log(c+d*x)/b/(b*c-a*d)^2-1/2*log(c+d*x)/b/(a+b*x)^2 +--R +--R +--R (58) +--R 2 2 2 2 2 2 +--R (b d x + 2a b d x + 2a b c d - b c )log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- b d x - 2a b d x - a d )log(b x + a) + (a b d - b c d)x + a d +--R + +--R - a b c d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (2a b d - 4a b c d + 2b c )x + (4a b d - 8a b c d + 4a b c )x +--R + +--R 4 2 3 2 2 3 2 +--R 2a b d - 4a b c d + 2a b c +--R Type: Expression(Integer) +--E 97 + +--S 98 of 514 +a0219:= integrate(t0219,x) +--R +--R +--R (59) +--R 2 2 2 2 2 2 +--R (b d x + 2a b d x + 2a b c d - b c )log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (- b d x - 2a b d x - a d )log(b x + a) + (a b d - b c d)x + a d +--R + +--R - a b c d +--R / +--R 2 3 2 4 5 2 2 3 2 2 2 3 4 2 +--R (2a b d - 4a b c d + 2b c )x + (4a b d - 8a b c d + 4a b c )x +--R + +--R 4 2 3 2 2 3 2 +--R 2a b d - 4a b c d + 2a b c +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 514 +m0219:= a0219-r0219 +--R +--R +--R (60) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 514 +d0219:= D(m0219,x) +--R +--R +--R (61) 0 +--R Type: Expression(Integer) +--E 100 + +--S 101 of 514 +t0220:= log(c+d*x)^2/(a+b*x)^2 +--R +--R +--R 2 +--R log(d x + c) +--R (62) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 101 + +--S 102 of 514 +r0220:= 2*d*log(-d*(a+b*x)/(b*c-a*d))*log(c+d*x)/b/(b*c-a*d)-_ + d*log(c+d*x)^2/b/(b*c-a*d)-log(c+d*x)^2/b/(a+b*x)+_ + 2*d*polylog(2,b*(c+d*x)/(b*c-a*d))/b/(b*c-a*d) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 514 +a0220:= integrate(t0220,x) +--R +--R +--R x 2 +--R ++ log(%I d + c) +--R (63) | -------------------- d%I +--R ++ 2 2 2 +--R %I b + 2%I a b + a +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 514 +--m0220:= a0220-r0220 +--E 104 + +--S 105 of 514 +--d0220:= D(m0220,x) +--E 105 + +--S 106 of 514 +t0221:= log(c+d*x)^2/(a+b*x)^3 +--R +--R +--R 2 +--R log(d x + c) +--R (64) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 106 + +--S 107 of 514 +r0221:= d^2*log(a+b*x)/b/(b*c-a*d)^2-d^2*log(c+d*x)/b/(b*c-a*d)^2-_ + d*log(c+d*x)/b/(b*c-a*d)/(a+b*x)-d^2*log(-d*(a+b*x)/(b*c-a*d))*_ + log(c+d*x)/b/(b*c-a*d)^2+1/2*d^2*log(c+d*x)^2/b/(b*c-a*d)^2-_ + 1/2*log(c+d*x)^2/b/(a+b*x)^2-d^2*polylog(2,b*(c+d*x)/_ + (b*c-a*d))/b/(b*c-a*d)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 514 +a0221:= integrate(t0221,x) +--R +--R +--R x 2 +--R ++ log(%I d + c) +--R (65) | ------------------------------- d%I +--R ++ 3 3 2 2 2 3 +--R %I b + 3%I a b + 3%I a b + a +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 514 +--m0221:= a0221-r0221 +--E 109 + +--S 110 of 514 +--d0221:= D(m0221,x) +--E 110 + +--S 111 of 514 +t0222:= log(c+d*x)^3/(a+b*x)^2 +--R +--R +--R 3 +--R log(d x + c) +--R (66) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 111 + +--S 112 of 514 +r0222:= 3*d*log(-d*(a+b*x)/(b*c-a*d))*log(c+d*x)^2/b/(b*c-a*d)-_ + d*log(c+d*x)^3/b/(b*c-a*d)-log(c+d*x)^3/b/(a+b*x)+_ + 6*d*log(c+d*x)*polylog(2,b*(c+d*x)/(b*c-a*d))/b/(b*c-a*d)-_ + 6*d*polylog(3,b*(c+d*x)/(b*c-a*d))/b/(b*c-a*d) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 112 + +--S 113 of 514 +a0222:= integrate(t0222,x) +--R +--R +--R x 3 +--R ++ log(%I d + c) +--R (67) | -------------------- d%I +--R ++ 2 2 2 +--R %I b + 2%I a b + a +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 514 +--m0222:= a0222-r0222 +--E 114 + +--S 115 of 514 +--d0222:= D(m0222,x) +--E 115 + +--S 116 of 514 +t0223:= log(c+d*x)^3/(a+b*x)^3 +--R +--R +--R 3 +--R log(d x + c) +--R (68) ---------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 116 + +--S 117 of 514 +r0223:= 3*d^2*log(-d*(a+b*x)/(b*c-a*d))*log(c+d*x)/b/(b*c-a*d)^2-_ + 3/2*d^2*log(c+d*x)^2/b/(b*c-a*d)^2-3/2*d*log(c+d*x)^2/b/_ + (b*c-a*d)/(a+b*x)-3/2*d^2*log(-d*(a+b*x)/(b*c-a*d))*log(c+d*x)^2/_ + b/(b*c-a*d)^2+1/2*d^2*log(c+d*x)^3/b/(b*c-a*d)^2-1/2*log(c+d*x)^3/_ + b/(a+b*x)^2+3*d^2*(1-log(c+d*x))*polylog(2,b*(c+d*x)/(b*c-a*d))/_ + b/(b*c-a*d)^2+3*d^2*polylog(3,b*(c+d*x)/(b*c-a*d))/b/(b*c-a*d)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 514 +a0223:= integrate(t0223,x) +--R +--R +--R x 3 +--R ++ log(%I d + c) +--R (69) | ------------------------------- d%I +--R ++ 3 3 2 2 2 3 +--R %I b + 3%I a b + 3%I a b + a +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 514 +--m0223:= a0223-r0223 +--E 119 + +--S 120 of 514 +--d0223:= D(m0223,x) +--E 120 + +--S 121 of 514 +t0224:= log(c*(a+b*x)^n)/(d+e*x^2) +--R +--R +--R n +--R log(c (b x + a) ) +--R (70) ----------------- +--R 2 +--R e x + d +--R Type: Expression(Integer) +--E 121 + +--S 122 of 514 +r0224:= -1/2*(log(c*(a+b*x)^n)*log(-b*(-e)^(1/2)*(-d^(1/2)+(-e)^(1/2)*x)/_ + (b*d^(1/2)*(-e)^(1/2)-a*e))-log(c*(a+b*x)^n)*log(b*(-e)^(1/2)*_ + (d^(1/2)+(-e)^(1/2)*x)/(b*d^(1/2)*(-e)^(1/2)+a*e))+_ + n*polylog(2,-e*(a+b*x)/(b*d^(1/2)*(-e)^(1/2)-a*e))-_ + n*polylog(2,e*(a+b*x)/(b*d^(1/2)*(-e)^(1/2)+a*e)))/d^(1/2)/(-e)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 514 +a0224:= integrate(t0224,x) +--R +--R +--R x n +--R ++ log(c (%I b + a) ) +--R (71) | ------------------ d%I +--R ++ 2 +--R %I e + d +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 514 +--m0224:= a0224-r0224 +--E 124 + +--S 125 of 514 +--d0224:= D(m0224,x) +--E 125 + +--S 126 of 514 +t0225:= log(c*(a+b*x)^n)^2/(d+e*x^2) +--R +--R +--R n 2 +--R log(c (b x + a) ) +--R (72) ------------------ +--R 2 +--R e x + d +--R Type: Expression(Integer) +--E 126 + +--S 127 of 514 +r0225:= -1/2*(log(c*(a+b*x)^n)^2*log(-b*(-e)^(1/2)*(-d^(1/2)+(-e)^(1/2)*x)/_ + (b*d^(1/2)*(-e)^(1/2)-a*e))-log(c*(a+b*x)^n)^2*log(b*(-e)^(1/2)*_ + (d^(1/2)+(-e)^(1/2)*x)/(b*d^(1/2)*(-e)^(1/2)+a*e))+_ + 2*n*log(c*(a+b*x)^n)*polylog(2,-e*(a+b*x)/(b*d^(1/2)*_ + (-e)^(1/2)-a*e))-2*n*log(c*(a+b*x)^n)*polylog(2,e*(a+b*x)/_ + (b*d^(1/2)*(-e)^(1/2)+a*e))-2*n^2*polylog(3,-e*(a+b*x)/_ + (b*d^(1/2)*(-e)^(1/2)-a*e))+2*n^2*polylog(3,e*(a+b*x)/_ + (b*d^(1/2)*(-e)^(1/2)+a*e)))/d^(1/2)/(-e)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 514 +a0225:= integrate(t0225,x) +--R +--R +--R x n 2 +--R ++ log(c (%I b + a) ) +--R (73) | ------------------- d%I +--R ++ 2 +--R %I e + d +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 514 +--m0225:= a0225-r0225 +--E 129 + +--S 130 of 514 +--d0225:= D(m0225,x) +--E 130 + +--S 131 of 514 +t0226:= log(c*(a+b*x)^n)^3/(d+e*x^2) +--R +--R +--R n 3 +--R log(c (b x + a) ) +--R (74) ------------------ +--R 2 +--R e x + d +--R Type: Expression(Integer) +--E 131 + +--S 132 of 514 +r0226:= -1/2*(log(c*(a+b*x)^n)^3*log(-b*(-e)^(1/2)*_ + (-d^(1/2)+(-e)^(1/2)*x)/(b*d^(1/2)*(-e)^(1/2)-a*e))-_ + log(c*(a+b*x)^n)^3*log(b*(-e)^(1/2)*(d^(1/2)+(-e)^(1/2)*x)/_ + (b*d^(1/2)*(-e)^(1/2)+a*e))+3*n*log(c*(a+b*x)^n)^2*_ + polylog(2,-e*(a+b*x)/(b*d^(1/2)*(-e)^(1/2)-a*e))-_ + 3*n*log(c*(a+b*x)^n)^2*polylog(2,e*(a+b*x)/(b*d^(1/2)*(-e)^(1/2)+_ + a*e))-6*n^2*log(c*(a+b*x)^n)*polylog(3,-e*(a+b*x)/(b*d^(1/2)*_ + (-e)^(1/2)-a*e))+6*n^2*log(c*(a+b*x)^n)*polylog(3,e*(a+b*x)/_ + (b*d^(1/2)*(-e)^(1/2)+a*e))+6*n^3*polylog(4,-e*(a+b*x)/_ + (b*d^(1/2)*(-e)^(1/2)-a*e))-6*n^3*polylog(4,e*(a+b*x)/_ + (b*d^(1/2)*(-e)^(1/2)+a*e)))/d^(1/2)/(-e)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 514 +a0226:= integrate(t0226,x) +--R +--R +--R x n 3 +--R ++ log(c (%I b + a) ) +--R (75) | ------------------- d%I +--R ++ 2 +--R %I e + d +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 514 +--m0226:= a0226-r0226 +--E 134 + +--S 135 of 514 +--d0226:= D(m0226,x) +--E 135 + +--S 136 of 514 +t0227:= log(c*(a+b*x)^n)/(d*x+e*x^2) +--R +--R +--R n +--R log(c (b x + a) ) +--R (76) ----------------- +--R 2 +--R e x + d x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 514 +r0227:= -1/d*(-log(-b*x/a)*log(c*(a+b*x)^n)+_ + log(c*(a+b*x)^n)*log(-b*(d+e*x)/(a*e-b*d))+_ + n*polylog(2,e*(a+b*x)/(a*e-b*d))-n*polylog(2,(a+b*x)/a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 137 + +--S 138 of 514 +a0227:= integrate(t0227,x) +--R +--R +--R x n +--R ++ log(c (%I b + a) ) +--R (77) | ------------------ d%I +--R ++ 2 +--R %I e + %I d +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 514 +--m0227:= a0227-r0227 +--E 139 + +--S 140 of 514 +--d0227:= D(m0227,x) +--E 140 + +--S 141 of 514 +t0228:= log(c*(a+b*x)^n)^2/(d*x+e*x^2) +--R +--R +--R n 2 +--R log(c (b x + a) ) +--R (78) ------------------ +--R 2 +--R e x + d x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 514 +r0228:= -1/d*(-log(-b*x/a)*log(c*(a+b*x)^n)^2+log(c*(a+b*x)^n)^2*_ + log(-b*(d+e*x)/(a*e-b*d))+2*n*log(c*(a+b*x)^n)*_ + polylog(2,e*(a+b*x)/(a*e-b*d))-2*n*log(c*(a+b*x)^n)*_ + polylog(2,(a+b*x)/a)+2*n^2*polylog(3,(a+b*x)/a)-2*_ + n^2*polylog(3,e*(a+b*x)/(a*e-b*d))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 142 + +--S 143 of 514 +a0228:= integrate(t0228,x) +--R +--R +--R x n 2 +--R ++ log(c (%I b + a) ) +--R (79) | ------------------- d%I +--R ++ 2 +--R %I e + %I d +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 514 +--m0228:= a0228-r0228 +--E 144 + +--S 145 of 514 +--d0228:= D(m0228,x) +--E 145 + +--S 146 of 514 +t0229:= log(c*(a+b*x)^n)^3/(d*x+e*x^2) +--R +--R +--R n 3 +--R log(c (b x + a) ) +--R (80) ------------------ +--R 2 +--R e x + d x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 514 +r0229:= -1/d*(-log(-b*x/a)*log(c*(a+b*x)^n)^3+log(c*(a+b*x)^n)^3*_ + log(-b*(d+e*x)/(a*e-b*d))+3*n*log(c*(a+b*x)^n)^2*_ + polylog(2,e*(a+b*x)/(a*e-b*d))-3*n*log(c*(a+b*x)^n)^2*_ + polylog(2,(a+b*x)/a)-6*n^2*log(c*(a+b*x)^n)*_ + polylog(3,e*(a+b*x)/(a*e-b*d))+6*n^2*log(c*(a+b*x)^n)*_ + polylog(3,(a+b*x)/a)-6*n^3*polylog(4,(a+b*x)/a)+6*n^3*_ + polylog(4,e*(a+b*x)/(a*e-b*d))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 514 +a0229:= integrate(t0229,x) +--R +--R +--R x n 3 +--R ++ log(c (%I b + a) ) +--R (81) | ------------------- d%I +--R ++ 2 +--R %I e + %I d +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 514 +--m0229:= a0229-r0229 +--E 149 + +--S 150 of 514 +--d0229:= D(m0229,x) +--E 150 + +--S 151 of 514 +t0230:= log(a+b*x)/(c+d*x+e*x^2) +--R +--R +--R log(b x + a) +--R (82) -------------- +--R 2 +--R e x + d x + c +--R Type: Expression(Integer) +--E 151 + +--S 152 of 514 +r0230:= (log(a+b*x)*log(b*(-d+(d^2-4*c*e)^(1/2)-2*e*x)/_ + (b*(d^2-4*c*e)^(1/2)-b*d+2*a*e))-log(a+b*x)*_ + log(b*(d+(d^2-4*c*e)^(1/2)+2*e*x)/(b*(d^2-4*c*e)^(1/2)+_ + b*d-2*a*e))+polylog(2,2*e*(a+b*x)/(b*(d^2-4*c*e)^(1/2)-_ + b*d+2*a*e))-polylog(2,-2*e*(a+b*x)/(b*(d^2-4*c*e)^(1/2)+_ + b*d-2*a*e)))/(d^2-4*c*e)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 152 + +--S 153 of 514 +a0230:= integrate(t0230,x) +--R +--R +--R x +--R ++ log(%I b + a) +--R (83) | --------------- d%I +--R ++ 2 +--R %I e + %I d + c +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 514 +--m0230:= a0230-r0230 +--E 154 + +--S 155 of 514 +--d0230:= D(m0230,x) +--E 155 + +--S 156 of 514 +t0231:= log(c*(a+b*x)^n)/(d+e*x+f*x^2) +--R +--R +--R n +--R log(c (b x + a) ) +--R (84) ----------------- +--R 2 +--R f x + e x + d +--R Type: Expression(Integer) +--E 156 + +--S 157 of 514 +r0231:= (log(c*(a+b*x)^n)*log(b*(-e+(e^2-4*d*f)^(1/2)-2*f*x)/_ + (-b*e+2*a*f+b*(e^2-4*d*f)^(1/2)))-log(c*(a+b*x)^n)*_ + log(b*(e+(e^2-4*d*f)^(1/2)+2*f*x)/(b*e-2*a*f+b*(e^2-4*d*f)^(1/2)))+_ + n*polylog(2,2*f*(a+b*x)/(-b*e+2*a*f+b*(e^2-4*d*f)^(1/2)))-_ + n*polylog(2,-2*f*(a+b*x)/(b*e-2*a*f+b*(e^2-4*d*f)^(1/2))))/_ + (e^2-4*d*f)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 157 + +--S 158 of 514 +a0231:= integrate(t0231,x) +--R +--R +--R x n +--R ++ log(c (%I b + a) ) +--R (85) | ------------------ d%I +--R ++ 2 +--R %I f + %I e + d +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 514 +--m0231:= a0231-r0231 +--E 159 + +--S 160 of 514 +--d0231:= D(m0231,x) +--E 160 + +--S 161 of 514 +t0232:= log(c*(a+b*x)^n)^2/(d+e*x+f*x^2) +--R +--R +--R n 2 +--R log(c (b x + a) ) +--R (86) ------------------ +--R 2 +--R f x + e x + d +--R Type: Expression(Integer) +--E 161 + +--S 162 of 514 +r0232:= (log(c*(a+b*x)^n)^2*log(b*(-e+(e^2-4*d*f)^(1/2)-2*f*x)/_ + (-b*e+2*a*f+b*(e^2-4*d*f)^(1/2)))-log(c*(a+b*x)^n)^2*_ + log(b*(e+(e^2-4*d*f)^(1/2)+2*f*x)/(b*e-2*a*f+b*(e^2-4*d*f)^(1/2)))+_ + 2*n*log(c*(a+b*x)^n)*polylog(2,2*f*(a+b*x)/(-b*e+2*a*f+_ + b*(e^2-4*d*f)^(1/2)))-2*n*log(c*(a+b*x)^n)*polylog(2,-2*f*(a+b*x)/_ + (b*e-2*a*f+b*(e^2-4*d*f)^(1/2)))-2*n^2*polylog(3,2*f*(a+b*x)/_ + (-b*e+2*a*f+b*(e^2-4*d*f)^(1/2)))+2*n^2*_ + polylog(3,-2*f*(a+b*x)/(b*e-2*a*f+b*(e^2-4*d*f)^(1/2))))/_ + (e^2-4*d*f)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 514 +a0232:= integrate(t0232,x) +--R +--R +--R x n 2 +--R ++ log(c (%I b + a) ) +--R (87) | ------------------- d%I +--R ++ 2 +--R %I f + %I e + d +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 514 +--m0232:= a0232-r0232 +--E 164 + +--S 165 of 514 +--d0232:= D(m0232,x) +--E 165 + +--S 166 of 514 +t0233:= log(c*(a+b*x)^n)^3/(d+e*x+f*x^2) +--R +--R +--R n 3 +--R log(c (b x + a) ) +--R (88) ------------------ +--R 2 +--R f x + e x + d +--R Type: Expression(Integer) +--E 166 + +--S 167 of 514 +r0233:= (log(c*(a+b*x)^n)^3*log(b*(-e+(e^2-4*d*f)^(1/2)-2*f*x)/_ + (-b*e+2*a*f+b*(e^2-4*d*f)^(1/2)))-log(c*(a+b*x)^n)^3*_ + log(b*(e+(e^2-4*d*f)^(1/2)+2*f*x)/(b*e-2*a*f+b*(e^2-4*d*f)^(1/2)))+_ + 3*n*log(c*(a+b*x)^n)^2*polylog(2,2*f*(a+b*x)/_ + (-b*e+2*a*f+b*(e^2-4*d*f)^(1/2)))-3*n*log(c*(a+b*x)^n)^2*_ + polylog(2,-2*f*(a+b*x)/(b*e-2*a*f+b*(e^2-4*d*f)^(1/2)))-_ + 6*n^2*log(c*(a+b*x)^n)*polylog(3,2*f*(a+b*x)/_ + (-b*e+2*a*f+b*(e^2-4*d*f)^(1/2)))+6*n^2*log(c*(a+b*x)^n)*_ + polylog(3,-2*f*(a+b*x)/(b*e-2*a*f+b*(e^2-4*d*f)^(1/2)))+_ + 6*n^3*polylog(4,2*f*(a+b*x)/(-b*e+2*a*f+b*(e^2-4*d*f)^(1/2)))-_ + 6*n^3*polylog(4,-2*f*(a+b*x)/(b*e-2*a*f+b*(e^2-4*d*f)^(1/2))))/_ + (e^2-4*d*f)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 167 + +--S 168 of 514 +a0233:= integrate(t0233,x) +--R +--R +--R x n 3 +--R ++ log(c (%I b + a) ) +--R (89) | ------------------- d%I +--R ++ 2 +--R %I f + %I e + d +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 514 +--m0233:= a0233-r0233 +--E 169 + +--S 170 of 514 +--d0233:= D(m0233,x) +--E 170 + +--S 171 of 514 +t0234:= log(d*(b*x+c*x^2)^n)^2 +--R +--R +--R 2 n 2 +--R (90) log(d (c x + b x) ) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 514 +r0234:= -1/c*(-8*n^2*x*c+4*b*n^2*log(b+c*x)+2*b*n^2*log(-c*x/b)*_ + log(b+c*x)+b*n^2*log(b+c*x)^2+4*n*x*log(d*(x*(b+c*x))^n)*c-_ + x*log(d*(x*(b+c*x))^n)^2*c-2*b*n*log(b+c*x)*log(d*(x*(b+c*x))^n)+_ + 2*b*n^2*polylog(2,(b+c*x)/b)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 172 + +--S 173 of 514 +a0234:= integrate(t0234,x) +--R +--R +--R x +--R ++ 2 n 2 +--R (91) | log(d (%I c + %I b) ) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 514 +--m0234:= a0234-r0234 +--E 174 + +--S 175 of 514 +--d0234:= D(m0234,x) +--E 175 + +--S 176 of 514 +t0235:= log(d*(b*x+c*x^2)^n)/x +--R +--R +--R 2 n +--R log(d (c x + b x) ) +--R (92) -------------------- +--R x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 514 +r0235:= -1/2*n*log(x)^2-n*log(x)*log((b+c*x)/b)+log(x)*_ + log(d*(x*(b+c*x))^n)-n*polylog(2,-c*x/b) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 177 + +--S 178 of 514 +a0235:= integrate(t0235,x) +--R +--R +--R x 2 n +--R ++ log(d (%I c + %I b) ) +--R (93) | --------------------- d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 514 +--m0235:= a0235-r0235 +--E 179 + +--S 180 of 514 +--d0235:= D(m0235,x) +--E 180 + +--S 181 of 514 +t0236:= log(d*(a+b*x+c*x^2)^n) +--R +--R +--R 2 n +--R (94) log(d (c x + b x + a) ) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 514 +r0236:= -2*n*x+(b^2-4*a*c)^(1/2)*n*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/c+_ + 1/2*b*n*log(a+b*x+c*x^2)/c+x*log(d*(a+b*x+c*x^2)^n) +--R +--R +--R (95) +--R +-----------+ +--R 2 n | 2 2c x + b +--R 2c x log(d (c x + b x + a) ) + 2n\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R b n log(c x + b x + a) - 4c n x +--R / +--R 2c +--R Type: Expression(Integer) +--E 182 + +--S 183 of 514 +a0236:= integrate(t0236,x) +--R +--R +--R (96) +--R [ +--R +-----------+ +--R | 2 +--R n\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 +--R (2c n x + b n)log(c x + b x + a) + 2c x log(d) - 4c n x +--R / +--R 2c +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b 2 +--R - 2n\|4a c - b atan(------------) + (2c n x + b n)log(c x + b x + a) +--R 2c x + b +--R + +--R 2c x log(d) - 4c n x +--R / +--R 2c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 183 + +--S 184 of 514 +m0236a:= a0236.1-r0236 +--R +--R +--R (97) +--R +-----------+ +--R +-----------+ | 2 2 2 2 +--R | 2 (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R n\|- 4a c + b log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 n | 2 2c x + b +--R - 2c x log(d (c x + b x + a) ) - 2n\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R 2c n x log(c x + b x + a) + 2c x log(d) +--R / +--R 2c +--R Type: Expression(Integer) +--E 184 + +--S 185 of 514 +d0236a:= D(m0236a,x) +--R +--R +--R (98) +--R 2 2 n 2 n +--R (- c x - b x - a)(c x + b x + a) log(d (c x + b x + a) ) +--R + +--R 2 2 2 +--R (c n x + b n x + a n)log(c x + b x + a) + (c x + b x + a)log(d) +--R + +--R 2 +--R 2c n x + b n x +--R * +--R 2 n +--R (c x + b x + a) +--R + +--R 2 4 3 2 2 2 n - 1 +--R (- 2c n x - 3b c n x + (- 2a c - b )n x - a b n x)(c x + b x + a) +--R / +--R 2 2 n +--R (c x + b x + a)(c x + b x + a) +--R Type: Expression(Integer) +--E 185 + +--S 186 of 514 +m0236b:= a0236.2-r0236 +--R +--R +--R (99) +--R +-----------+ +--R 2 n | 2 2c x + b +--R - c x log(d (c x + b x + a) ) - n\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b 2 +--R - n\|4a c - b atan(------------) + c n x log(c x + b x + a) + c x log(d) +--R 2c x + b +--R / +--R c +--R Type: Expression(Integer) +--E 186 + +--S 187 of 514 +d0236b:= D(m0236b,x) +--R +--R +--R (100) +--R 2 2 n 2 n +--R (- c x - b x - a)(c x + b x + a) log(d (c x + b x + a) ) +--R + +--R 2 2 2 +--R (c n x + b n x + a n)log(c x + b x + a) + (c x + b x + a)log(d) +--R + +--R 2 +--R 2c n x + b n x +--R * +--R 2 n +--R (c x + b x + a) +--R + +--R 2 4 3 2 2 2 n - 1 +--R (- 2c n x - 3b c n x + (- 2a c - b )n x - a b n x)(c x + b x + a) +--R / +--R 2 2 n +--R (c x + b x + a)(c x + b x + a) +--R Type: Expression(Integer) +--E 187 + +--S 188 of 514 +t0237:= log(d*(a+b*x+c*x^2)^n)/x +--R +--R +--R 2 n +--R log(d (c x + b x + a) ) +--R (101) ------------------------ +--R x +--R Type: Expression(Integer) +--E 188 + +--S 189 of 514 +r0237:= -n*log(x)*log((-b+(b^2-4*a*c)^(1/2)-2*c*x)/(-b+(b^2-4*a*c)^(1/2)))-_ + n*log(x)*log((b+(b^2-4*a*c)^(1/2)+2*c*x)/(b+(b^2-4*a*c)^(1/2)))+_ + log(x)*log(d*(a+b*x+c*x^2)^n)-_ + n*polylog(2,2*c*x/(-b+(b^2-4*a*c)^(1/2)))-_ + n*polylog(2,-2*c*x/(b+(b^2-4*a*c)^(1/2))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 189 + +--S 190 of 514 +a0237:= integrate(t0237,x) +--R +--R +--R x 2 n +--R ++ log(d (%I c + %I b + a) ) +--R (102) | ------------------------- d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 190 + +--S 191 of 514 +--m0237:= a0237-r0237 +--E 191 + +--S 192 of 514 +--d0237:= D(m0237,x) +--E 192 + +--S 193 of 514 +t0238:= log(a+b*x+c*x^2) +--R +--R +--R 2 +--R (103) log(c x + b x + a) +--R Type: Expression(Integer) +--E 193 + +--S 194 of 514 +r0238:= -2*x+(b^2-4*a*c)^(1/2)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/c+_ + 1/2*b*log(a+b*x+c*x^2)/c+x*log(a+b*x+c*x^2) +--R +--R +--R (104) +--R +-----------+ +--R | 2 2c x + b 2 +--R 2\|- 4a c + b atanh(--------------) + (2c x + b)log(c x + b x + a) - 4c x +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R --------------------------------------------------------------------------- +--R 2c +--R Type: Expression(Integer) +--E 194 + +--S 195 of 514 +a0238:= integrate(t0238,x) +--R +--R +--R (105) +--R [ +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 +--R (2c x + b)log(c x + b x + a) - 4c x +--R / +--R 2c +--R , +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b 2 +--R - 2\|4a c - b atan(------------) + (2c x + b)log(c x + b x + a) - 4c x +--R 2c x + b +--R ------------------------------------------------------------------------] +--R 2c +--R Type: Union(List(Expression(Integer)),...) +--E 195 + +--S 196 of 514 +m0238a:= a0238.1-r0238 +--R +--R +--R (106) +--R +-----------+ +--R +-----------+ | 2 2 2 2 +--R | 2 (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R \|- 4a c + b log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R | 2 2c x + b +--R - 2\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2c +--R Type: Expression(Integer) +--E 196 + +--S 197 of 514 +d0238a:= D(m0238a,x) +--R +--R +--R (107) 0 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 514 +m0238b:= a0238.2-r0238 +--R +--R +--R (108) +--R +---------+ +--R +-----------+ +---------+ | 2 +--R | 2 2c x + b | 2 \|4a c - b +--R - \|- 4a c + b atanh(--------------) - \|4a c - b atan(------------) +--R +-----------+ 2c x + b +--R | 2 +--R \|- 4a c + b +--R ---------------------------------------------------------------------- +--R c +--R Type: Expression(Integer) +--E 198 + +--S 199 of 514 +d0238b:= D(m0238b,x) +--R +--R +--R (109) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 514 +t0239:= x*log(a+b*x+c*x^2) +--R +--R +--R 2 +--R (110) x log(c x + b x + a) +--R Type: Expression(Integer) +--E 200 + +--S 201 of 514 +r0239:= 1/2*b*x/c-1/2*x^2-1/2*b*(b^2-4*a*c)^(1/2)*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/c^2-1/4*(b^2-2*a*c)*_ + log(a+b*x+c*x^2)/c^2+1/2*x^2*log(a+b*x+c*x^2) +--R +--R +--R (111) +--R +-----------+ +--R | 2 2c x + b +--R - 2b\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 +--R (2c x + 2a c - b )log(c x + b x + a) - 2c x + 2b c x +--R / +--R 2 +--R 4c +--R Type: Expression(Integer) +--E 201 + +--S 202 of 514 +a0239:= integrate(t0239,x) +--R +--R +--R (112) +--R [ +--R +-----------+ +--R | 2 +--R b\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 2 +--R (2c x + 2a c - b )log(c x + b x + a) - 2c x + 2b c x +--R / +--R 2 +--R 4c +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b +--R 2b\|4a c - b atan(------------) +--R 2c x + b +--R + +--R 2 2 2 2 2 2 +--R (2c x + 2a c - b )log(c x + b x + a) - 2c x + 2b c x +--R / +--R 2 +--R 4c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 202 + +--S 203 of 514 +m0239a:= a0239.1-r0239 +--R +--R +--R (113) +--R +-----------+ +--R | 2 +--R b\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R | 2 2c x + b +--R 2b\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 +--R 4c +--R Type: Expression(Integer) +--E 203 + +--S 204 of 514 +d0239a:= D(m0239a,x) +--R +--R +--R (114) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 514 +m0239b:= a0239.2-r0239 +--R +--R +--R (115) +--R +---------+ +--R +-----------+ +---------+ | 2 +--R | 2 2c x + b | 2 \|4a c - b +--R b\|- 4a c + b atanh(--------------) + b\|4a c - b atan(------------) +--R +-----------+ 2c x + b +--R | 2 +--R \|- 4a c + b +--R ---------------------------------------------------------------------- +--R 2 +--R 2c +--R Type: Expression(Integer) +--E 205 + +--S 206 of 514 +d0239b:= D(m0239b,x) +--R +--R +--R (116) 0 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 514 +t0240:= x^2*log(a+b*x+c*x^2) +--R +--R +--R 2 2 +--R (117) x log(c x + b x + a) +--R Type: Expression(Integer) +--E 207 + +--S 208 of 514 +r0240:= -1/3*(b^2-2*a*c)*x/c^2+1/6*b*x^2/c-2/9*x^3+_ + 1/3*(b^4-a*c*(5*b^2-4*a*c))*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ + c^3/(b^2-4*a*c)^(1/2)+1/6*b*(b^2-3*a*c)*log(a+b*x+c*x^2)/c^3+_ + 1/3*x^3*log(a+b*x+c*x^2) +--R +--R +--R (118) +--R 2 2 2 4 2c x + b +--R (24a c - 30a b c + 6b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 3 2 3 3 2 2 +--R (6c x - 9a b c + 3b )log(c x + b x + a) - 4c x + 3b c x +--R + +--R 2 2 +--R (12a c - 6b c)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 18c \|- 4a c + b +--R Type: Expression(Integer) +--E 208 + +--S 209 of 514 +a0240:= integrate(t0240,x) +--R +--R +--R (119) +--R [ +--R +-----------+ +--R 2 | 2 +--R (3a c - 3b )\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 3 3 3 2 3 3 2 2 +--R (6c x - 9a b c + 3b )log(c x + b x + a) - 4c x + 3b c x +--R + +--R 2 2 +--R (12a c - 6b c)x +--R / +--R 3 +--R 18c +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 \|4a c - b +--R (6a c - 6b )\|4a c - b atan(------------) +--R 2c x + b +--R + +--R 3 3 3 2 3 3 2 2 +--R (6c x - 9a b c + 3b )log(c x + b x + a) - 4c x + 3b c x +--R + +--R 2 2 +--R (12a c - 6b c)x +--R / +--R 3 +--R 18c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 209 + +--S 210 of 514 +m0240a:= a0240.1-r0240 +--R +--R +--R (120) +--R 2 2 2 4 +--R (- 4a c + 5a b c - b ) +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 4 2c x + b +--R (- 8a c + 10a b c - 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 6c \|- 4a c + b +--R Type: Expression(Integer) +--E 210 + +--S 211 of 514 +d0240a:= D(m0240a,x) +--R +--R +--R (121) 0 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 514 +m0240b:= a0240.2-r0240 +--R +--R +--R (122) +--R 2 2 2 4 2c x + b +--R (- 4a c + 5a b c - b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ +---------+ | 2 +--R 2 | 2 | 2 \|4a c - b +--R (a c - b )\|- 4a c + b \|4a c - b atan(------------) +--R 2c x + b +--R / +--R +-----------+ +--R 3 | 2 +--R 3c \|- 4a c + b +--R Type: Expression(Integer) +--E 212 + +--S 213 of 514 +d0240b:= D(m0240b,x) +--R +--R +--R (123) 0 +--R Type: Expression(Integer) +--E 213 + +--S 214 of 514 +t0241:= x^3*log(a+b*x+c*x^2) +--R +--R +--R 3 2 +--R (124) x log(c x + b x + a) +--R Type: Expression(Integer) +--E 214 + +--S 215 of 514 +r0241:= 1/4*b*(b^2-3*a*c)*x/c^3-1/8*(b^2-2*a*c)*x^2/c^2+1/12*b*x^3/c-_ + 1/8*x^4-1/4*b*(b^4-2*a*c*(3*b^2-4*a*c))*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/c^4/(b^2-4*a*c)^(1/2)-_ + 1/8*(b^4-4*b^2*a*c+2*a^2*c^2)*log(a+b*x+c*x^2)/c^4+_ + 1/4*x^4*log(a+b*x+c*x^2) +--R +--R +--R (125) +--R 2 2 3 5 2c x + b +--R (- 48a b c + 36a b c - 6b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 4 4 2 2 2 4 2 4 4 3 3 +--R (6c x - 6a c + 12a b c - 3b )log(c x + b x + a) - 3c x + 2b c x +--R + +--R 3 2 2 2 2 3 +--R (6a c - 3b c )x + (- 18a b c + 6b c)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 | 2 +--R 24c \|- 4a c + b +--R Type: Expression(Integer) +--E 215 + +--S 216 of 514 +a0241:= integrate(t0241,x) +--R +--R +--R (126) +--R [ +--R +-----------+ +--R 3 | 2 +--R (6a b c - 3b )\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 4 4 2 2 2 4 2 4 4 3 3 +--R (6c x - 6a c + 12a b c - 3b )log(c x + b x + a) - 3c x + 2b c x +--R + +--R 3 2 2 2 2 3 +--R (6a c - 3b c )x + (- 18a b c + 6b c)x +--R / +--R 4 +--R 24c +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R 3 | 2 \|4a c - b +--R (- 12a b c + 6b )\|4a c - b atan(------------) +--R 2c x + b +--R + +--R 4 4 2 2 2 4 2 4 4 3 3 +--R (6c x - 6a c + 12a b c - 3b )log(c x + b x + a) - 3c x + 2b c x +--R + +--R 3 2 2 2 2 3 +--R (6a c - 3b c )x + (- 18a b c + 6b c)x +--R / +--R 4 +--R 24c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 216 + +--S 217 of 514 +m0241a:= a0241.1-r0241 +--R +--R +--R (127) +--R 2 2 3 5 +--R (- 8a b c + 6a b c - b ) +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 5 2c x + b +--R (16a b c - 12a b c + 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 | 2 +--R 8c \|- 4a c + b +--R Type: Expression(Integer) +--E 217 + +--S 218 of 514 +d0241a:= D(m0241a,x) +--R +--R +--R (128) 0 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 514 +m0241b:= a0241.2-r0241 +--R +--R +--R (129) +--R 2 2 3 5 2c x + b +--R (8a b c - 6a b c + b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ +---------+ | 2 +--R 3 | 2 | 2 \|4a c - b +--R (- 2a b c + b )\|- 4a c + b \|4a c - b atan(------------) +--R 2c x + b +--R / +--R +-----------+ +--R 4 | 2 +--R 4c \|- 4a c + b +--R Type: Expression(Integer) +--E 219 + +--S 220 of 514 +d0241b:= D(m0241b,x) +--R +--R +--R (130) 0 +--R Type: Expression(Integer) +--E 220 + +--S 221 of 514 +t0242:= log(a+b*x+c*x^2)/x +--R +--R +--R 2 +--R log(c x + b x + a) +--R (131) ------------------- +--R x +--R Type: Expression(Integer) +--E 221 + +--S 222 of 514 +r0242:= -log(x)*(log(1+2*c*x/(b-(b^2-4*a*c)^(1/2)))+_ + log(1+2*c*x/(b+(b^2-4*a*c)^(1/2)))-log(a+b*x+c*x^2))-_ + polylog(2,-2*c*x/(b-(b^2-4*a*c)^(1/2)))-_ + polylog(2,-2*c*x/(b+(b^2-4*a*c)^(1/2))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 222 + +--S 223 of 514 +a0242:= integrate(t0242,x) +--R +--R +--R x 2 +--R ++ log(%I c + %I b + a) +--R (132) | -------------------- d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 514 +--m0242:= a0242-r0242 +--E 224 + +--S 225 of 514 +--d0242:= D(m0242,x) +--E 225 + +--S 226 of 514 +t0243:= log(a+b*x+c*x^2)/x^2 +--R +--R +--R 2 +--R log(c x + b x + a) +--R (133) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 226 + +--S 227 of 514 +r0243:= (b^2-4*a*c)^(1/2)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a+_ + b*log(x)/a-1/2*b*log(a+b*x+c*x^2)/a-log(a+b*x+c*x^2)/x +--R +--R +--R (134) +--R +-----------+ +--R | 2 2c x + b 2 +--R 2x\|- 4a c + b atanh(--------------) + (- b x - 2a)log(c x + b x + a) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2b x log(x) +--R / +--R 2a x +--R Type: Expression(Integer) +--E 227 + +--S 228 of 514 +a0243:= integrate(t0243,x) +--R +--R +--R (135) +--R [ +--R +-----------+ +--R | 2 +--R x\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 +--R (- b x - 2a)log(c x + b x + a) + 2b x log(x) +--R / +--R 2a x +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R | 2 \|4a c - b 2 +--R - 2x\|4a c - b atan(------------) + (- b x - 2a)log(c x + b x + a) +--R 2c x + b +--R + +--R 2b x log(x) +--R / +--R 2a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 228 + +--S 229 of 514 +m0243a:= a0243.1-r0243 +--R +--R +--R (136) +--R +-----------+ +--R +-----------+ | 2 2 2 2 +--R | 2 (2c x + b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R \|- 4a c + b log(-----------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R | 2 2c x + b +--R - 2\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 514 +d0243a:= D(m0243a,x) +--R +--R +--R (137) 0 +--R Type: Expression(Integer) +--E 230 + +--S 231 of 514 +m0243b:= a0243.2-r0243 +--R +--R +--R (138) +--R +---------+ +--R +-----------+ +---------+ | 2 +--R | 2 2c x + b | 2 \|4a c - b +--R - \|- 4a c + b atanh(--------------) - \|4a c - b atan(------------) +--R +-----------+ 2c x + b +--R | 2 +--R \|- 4a c + b +--R ---------------------------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 514 +d0243b:= D(m0243b,x) +--R +--R +--R (139) 0 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 514 +t0244:= log(a+b*x+c*x^2)/x^3 +--R +--R +--R 2 +--R log(c x + b x + a) +--R (140) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 233 + +--S 234 of 514 +r0244:= -1/2*b/a/x-1/2*b*(b^2-4*a*c)^(1/2)*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/a^2-1/2*(b^2-2*a*c)*log(x)/a^2+_ + 1/4*(b^2-2*a*c)*log(a+b*x+c*x^2)/a^2-1/2*log(a+b*x+c*x^2)/x^2 +--R +--R +--R (141) +--R +-----------+ +--R 2 | 2 2c x + b +--R - 2b x \|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 +--R ((- 2a c + b )x - 2a )log(c x + b x + a) + (4a c - 2b )x log(x) - 2a b x +--R / +--R 2 2 +--R 4a x +--R Type: Expression(Integer) +--E 234 + +--S 235 of 514 +a0244:= integrate(t0244,x) +--R +--R +--R (142) +--R [ +--R +-----------+ +--R 2 | 2 +--R b x \|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 2 +--R ((- 2a c + b )x - 2a )log(c x + b x + a) + (4a c - 2b )x log(x) +--R + +--R - 2a b x +--R / +--R 2 2 +--R 4a x +--R , +--R +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 \|4a c - b +--R 2b x \|4a c - b atan(------------) +--R 2c x + b +--R + +--R 2 2 2 2 2 2 +--R ((- 2a c + b )x - 2a )log(c x + b x + a) + (4a c - 2b )x log(x) +--R + +--R - 2a b x +--R / +--R 2 2 +--R 4a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 235 + +--S 236 of 514 +m0244a:= a0244.1-r0244 +--R +--R +--R (143) +--R +-----------+ +--R | 2 +--R b\|- 4a c + b +--R * +--R +-----------+ +--R | 2 2 2 2 +--R (- 2c x - b)\|- 4a c + b + 2c x + 2b c x - 2a c + b +--R log(-------------------------------------------------------) +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R | 2 2c x + b +--R 2b\|- 4a c + b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 +--R 4a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 514 +d0244a:= D(m0244a,x) +--R +--R +--R (144) 0 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 514 +m0244b:= a0244.2-r0244 +--R +--R +--R (145) +--R +---------+ +--R +-----------+ +---------+ | 2 +--R | 2 2c x + b | 2 \|4a c - b +--R b\|- 4a c + b atanh(--------------) + b\|4a c - b atan(------------) +--R +-----------+ 2c x + b +--R | 2 +--R \|- 4a c + b +--R ---------------------------------------------------------------------- +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 514 +d0244b:= D(m0244b,x) +--R +--R +--R (146) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 514 +t0245:= x*log(1+c*f^(a+b*x)) +--R +--R +--R b x + a +--R (147) x log(c f + 1) +--R Type: Expression(Integer) +--E 240 + +--S 241 of 514 +r0245:= -1/b^2/log(f)^2*(x*polylog(2,-c*f^(a+b*x))*b*log(f)-_ + polylog(3,-c*f^(a+b*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 241 + +--S 242 of 514 +a0245:= integrate(t0245,x) +--R +--R +--R x +--R ++ %I b + a +--R (148) | %I log(c f + 1)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 514 +--m0245:= a0245-r0245 +--E 243 + +--S 244 of 514 +--d0245:= D(m0245,x) +--E 244 + +--S 245 of 514 +t0246:= x^2*log(1+c*f^(a+b*x)) +--R +--R +--R 2 b x + a +--R (149) x log(c f + 1) +--R Type: Expression(Integer) +--E 245 + +--S 246 of 514 +r0246:= -1/b^3/log(f)^3*(x^2*polylog(2,-c*f^(a+b*x))*b^2*log(f)^2-_ + 2*x*polylog(3,-c*f^(a+b*x))*b*log(f)+2*polylog(4,-c*f^(a+b*x))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 246 + +--S 247 of 514 +a0246:= integrate(t0246,x) +--R +--R +--R x +--R ++ 2 %I b + a +--R (150) | %I log(c f + 1)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 247 + +--S 248 of 514 +--m0246:= a0246-r0246 +--E 248 + +--S 249 of 514 +--d0246:= D(m0246,x) +--E 249 + +--S 250 of 514 +t0247:= x*log(c+d*f^(a+b*x)) +--R +--R +--R b x + a +--R (151) x log(d f + c) +--R Type: Expression(Integer) +--E 250 + +--S 251 of 514 +r0247:= 1/2*x^2*log(c+d*f^(a+b*x))-1/2*x^2*log(1+d*f^(a+b*x)/c)-_ + x*polylog(2,-d*f^(a+b*x)/c)/b/log(f)+_ + polylog(3,-d*f^(a+b*x)/c)/b^2/log(f)^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 251 + +--S 252 of 514 +a0247:= integrate(t0247,x) +--R +--R +--R x +--R ++ %I b + a +--R (152) | %I log(d f + c)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 252 + +--S 253 of 514 +--m0247:= a0247-r0247 +--E 253 + +--S 254 of 514 +--d0247:= D(m0247,x) +--E 254 + +--S 255 of 514 +t0248:= x^2*log(c+d*f^(a+b*x)) +--R +--R +--R 2 b x + a +--R (153) x log(d f + c) +--R Type: Expression(Integer) +--E 255 + +--S 256 of 514 +r0248:= 1/3*x^3*log(c+d*f^(a+b*x))-1/3*x^3*log(1+d*f^(a+b*x)/c)-_ + x^2*polylog(2,-d*f^(a+b*x)/c)/b/log(f)+_ + 2*x*polylog(3,-d*f^(a+b*x)/c)/b^2/log(f)^2-_ + 2*polylog(4,-d*f^(a+b*x)/c)/b^3/log(f)^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 256 + +--S 257 of 514 +a0248:= integrate(t0248,x) +--R +--R +--R x +--R ++ 2 %I b + a +--R (154) | %I log(d f + c)d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 257 + +--S 258 of 514 +--m0248:= a0248-r0248 +--E 258 + +--S 259 of 514 +--d0248:= D(m0248,x) +--E 259 + +--S 260 of 514 +t0249:= exp(x)*log(a+b*exp(x)) +--R +--R +--R x x +--R (155) %e log(b %e + a) +--R Type: Expression(Integer) +--E 260 + +--S 261 of 514 +r0249:= -exp(x)+(a+b*exp(x))*log(a+b*exp(x))/b +--R +--R +--R x x x +--R (b %e + a)log(b %e + a) - b %e +--R (156) --------------------------------- +--R b +--R Type: Expression(Integer) +--E 261 + +--S 262 of 514 +a0249:= integrate(t0249,x) +--R +--R +--R x x x +--R (b %e + a)log(b %e + a) - b %e +--R (157) --------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 262 + +--S 263 of 514 +m0249:= a0249-r0249 +--R +--R +--R (158) 0 +--R Type: Expression(Integer) +--E 263 + +--S 264 of 514 +d0249:= D(m0249,x) +--R +--R +--R (159) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 514 +t0250:= 1/x/log(exp(x)) +--R +--R +--R 1 +--R (160) -- +--R 2 +--R x +--R Type: Expression(Integer) +--E 265 + +--S 266 of 514 +r0250:= (-log(x)+log(log(exp(x))))/(x-log(exp(x))) +--R +--R +--R >> Error detected within library code: +--R catdef: division by zero +--R +--R Continuing to read the file... +--R +--E 266 + +--S 267 of 514 +a0250:= integrate(t0250,x) +--R +--R +--R 1 +--R (161) - - +--R x +--R Type: Union(Expression(Integer),...) +--E 267 + +--S 268 of 514 +--m0250:= a0250-r0250 +--E 268 + +--S 269 of 514 +--d0250:= D(m0250,x) +--E 269 + +--S 270 of 514 +t0251:= log(sin(x)^2) +--R +--R +--R 2 +--R (162) log(sin(x) ) +--R Type: Expression(Integer) +--E 270 + +--S 271 of 514 +r0251:= %i*x^2-2*x*log(1-exp(2*%i*x))+x*log(sin(x)^2)+%i*polylog(2,exp(2*%i*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 271 + +--S 272 of 514 +a0251:= integrate(t0251,x) +--R +--R +--R x +--R ++ 2 +--R (163) | log(sin(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 272 + +--S 273 of 514 +--m0251:= a0251-r0251 +--E 273 + +--S 274 of 514 +--d0251:= D(m0251,x) +--E 274 + +--S 275 of 514 +t0252:= log(sin(x)^n) +--R +--R +--R n +--R (164) log(sin(x) ) +--R Type: Expression(Integer) +--E 275 + +--S 276 of 514 +r0252:= 1/2*%i*n*x^2-n*x*log(1-exp(2*%i*x))+x*log(sin(x)^n)+_ + 1/2*%i*n*polylog(2,exp(2*%i*x)) +--R +--R There are 12 exposed and 3 unexposed library operations named - +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op - +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named - +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 276 + +--S 277 of 514 +a0252:= integrate(t0252,x) +--R +--R +--R x +--R ++ n +--R (165) | log(sin(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 277 + +--S 278 of 514 +--m0252:= a0252-r0252 +--E 278 + +--S 279 of 514 +--d0252:= D(m0252,x) +--E 279 + +--S 280 of 514 +t0253:= log(cos(x)^2) +--R +--R +--R 2 +--R (166) log(cos(x) ) +--R Type: Expression(Integer) +--E 280 + +--S 281 of 514 +r0253:= %i*x^2-2*x*log(1+exp(2*%i*x))+x*log(cos(x)^2)+_ + %i*polylog(2,-exp(2*%i*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 281 + +--S 282 of 514 +a0253:= integrate(t0253,x) +--R +--R +--R x +--R ++ 2 +--R (167) | log(cos(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 282 + +--S 283 of 514 +--m0253:= a0253-r0253 +--E 283 + +--S 284 of 514 +--d0253:= D(m0253,x) +--E 284 + +--S 285 of 514 +t0254:= log(cos(x)^n) +--R +--R +--R n +--R (168) log(cos(x) ) +--R Type: Expression(Integer) +--E 285 + +--S 286 of 514 +r0254:= 1/2*%i*n*x^2-n*x*log(1+exp(2*%i*x))+x*log(cos(x)^n)+_ + 1/2*%i*n*polylog(2,-exp(2*%i*x)) +--R +--R There are 12 exposed and 3 unexposed library operations named - +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op - +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named - +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 286 + +--S 287 of 514 +a0254:= integrate(t0254,x) +--R +--R +--R x +--R ++ n +--R (169) | log(cos(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 287 + +--S 288 of 514 +--m0254:= a0254-r0254 +--E 288 + +--S 289 of 514 +--d0254:= D(m0254,x) +--E 289 + +--S 290 of 514 +t0255:= log(tan(x)^2) +--R +--R +--R 2 +--R (170) log(tan(x) ) +--R Type: Expression(Integer) +--E 290 + +--S 291 of 514 +r0255:= 1/2*%i*log(1-%i*tan(x))*log(tan(x)^2)-1/2*%i*log(1+%i*tan(x))*_ + log(tan(x)^2)-%i*polylog(2,-%i*tan(x))+%i*polylog(2,%i*tan(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 291 + +--S 292 of 514 +a0255:= integrate(t0255,x) +--R +--R +--R x +--R ++ 2 +--R (171) | log(tan(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 292 + +--S 293 of 514 +--m0255:= a0255-r0255 +--E 293 + +--S 294 of 514 +--d0255:= D(m0255,x) +--E 294 + +--S 295 of 514 +t0256:= log(tan(x)^n) +--R +--R +--R n +--R (172) log(tan(x) ) +--R Type: Expression(Integer) +--E 295 + +--S 296 of 514 +r0256:= 1/2*%i*log(1-%i*tan(x))*log(tan(x)^n)-1/2*%i*log(1+%i*tan(x))*_ + log(tan(x)^n)-1/2*%i*n*polylog(2,-%i*tan(x))+_ + 1/2*%i*n*polylog(2,%i*tan(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 296 + +--S 297 of 514 +a0256:= integrate(t0256,x) +--R +--R +--R x +--R ++ n +--R (173) | log(tan(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 297 + +--S 298 of 514 +--m0256:= a0256-r0256 +--E 298 + +--S 299 of 514 +--d0256:= D(m0256,x) +--E 299 + +--S 300 of 514 +t0257:= log(cot(x)^2) +--R +--R +--R 2 +--R (174) log(cot(x) ) +--R Type: Expression(Integer) +--E 300 + +--S 301 of 514 +r0257:= -1/2*%i*log(1-%i*cot(x))*log(cot(x)^2)+1/2*%i*log(1+%i*cot(x))*_ + log(cot(x)^2)+%i*polylog(2,-%i*cot(x))-%i*polylog(2,%i*cot(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 301 + +--S 302 of 514 +a0257:= integrate(t0257,x) +--R +--R +--R x +--R ++ 2 +--R (175) | log(cot(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 302 + +--S 303 of 514 +--m0257:= a0257-r0257 +--E 303 + +--S 304 of 514 +--d0257:= D(m0257,x) +--E 304 + +--S 305 of 514 +t0258:= log(cot(x)^n) +--R +--R +--R n +--R (176) log(cot(x) ) +--R Type: Expression(Integer) +--E 305 + +--S 306 of 514 +r0258:= -1/2*%i*log(1-%i*cot(x))*log(cot(x)^n)+1/2*%i*log(1+%i*cot(x))*_ + log(cot(x)^n)+1/2*%i*n*polylog(2,-%i*cot(x))-_ + 1/2*%i*n*polylog(2,%i*cot(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 306 + +--S 307 of 514 +a0258:= integrate(t0258,x) +--R +--R +--R x +--R ++ n +--R (177) | log(cot(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 307 + +--S 308 of 514 +--m0258:= a0258-r0258 +--E 308 + +--S 309 of 514 +--d0258:= D(m0258,x) +--E 309 + +--S 310 of 514 +t0259:= log(sec(x)) +--R +--R +--R (178) log(sec(x)) +--R Type: Expression(Integer) +--E 310 + +--S 311 of 514 +r0259:= -1/2*%i*x^2+x*log(1+exp(2*%i*x))+x*log(1/cos(x))-_ + 1/2*%i*polylog(2,-exp(2*%i*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 311 + +--S 312 of 514 +a0259:= integrate(t0259,x) +--R +--R +--R x +--R ++ +--R (179) | log(sec(%I))d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 312 + +--S 313 of 514 +--m0259:= a0259-r0259 +--E 313 + +--S 314 of 514 +--d0259:= D(m0259,x) +--E 314 + +--S 315 of 514 +t0260:= log(sec(x)^2) +--R +--R +--R 2 +--R (180) log(sec(x) ) +--R Type: Expression(Integer) +--E 315 + +--S 316 of 514 +r0260:= -%i*x^2+2*x*log(1+exp(2*%i*x))+x*log(1/cos(x)^2)-_ + %i*polylog(2,-exp(2*%i*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 316 + +--S 317 of 514 +a0260:= integrate(t0260,x) +--R +--R +--R x +--R ++ 2 +--R (181) | log(sec(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 317 + +--S 318 of 514 +--m0260:= a0260-r0260 +--E 318 + +--S 319 of 514 +--d0260:= D(m0260,x) +--E 319 + +--S 320 of 514 +t0261:= log(sec(x)^n) +--R +--R +--R n +--R (182) log(sec(x) ) +--R Type: Expression(Integer) +--E 320 + +--S 321 of 514 +r0261:= -1/2*%i*n*x^2+n*x*log(1+exp(2*%i*x))+x*log((1/cos(x))^n)-_ + 1/2*%i*n*polylog(2,-exp(2*%i*x)) +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 321 + +--S 322 of 514 +a0261:= integrate(t0261,x) +--R +--R +--R x +--R ++ n +--R (183) | log(sec(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 322 + +--S 323 of 514 +--m0261:= a0261-r0261 +--E 323 + +--S 324 of 514 +--d0261:= D(m0261,x) +--E 324 + +--S 325 of 514 +t0262:= log(csc(x)) +--R +--R +--R (184) log(csc(x)) +--R Type: Expression(Integer) +--E 325 + +--S 326 of 514 +r0262:= -1/2*%i*x^2+x*log(1-exp(2*%i*x))+x*log(1/sin(x))-_ + 1/2*%i*polylog(2,exp(2*%i*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 326 + +--S 327 of 514 +a0262:= integrate(t0262,x) +--R +--R +--R x +--R ++ +--R (185) | log(csc(%I))d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 327 + +--S 328 of 514 +--m0262:= a0262-r0262 +--E 328 + +--S 329 of 514 +--d0262:= D(m0262,x) +--E 329 + +--S 330 of 514 +t0263:= log(csc(x)^2) +--R +--R +--R 2 +--R (186) log(csc(x) ) +--R Type: Expression(Integer) +--E 330 + +--S 331 of 514 +r0263:= -%i*x^2+2*x*log(1-exp(2*%i*x))+x*log(1/sin(x)^2)-_ + %i*polylog(2,exp(2*%i*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 331 + +--S 332 of 514 +a0263:= integrate(t0263,x) +--R +--R +--R x +--R ++ 2 +--R (187) | log(csc(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 332 + +--S 333 of 514 +--m0263:= a0263-r0263 +--E 333 + +--S 334 of 514 +--d0263:= D(m0263,x) +--E 334 + +--S 335 of 514 +t0264:= log(csc(x)^n) +--R +--R +--R n +--R (188) log(csc(x) ) +--R Type: Expression(Integer) +--E 335 + +--S 336 of 514 +r0264:= -1/2*%i*n*x^2+n*x*log(1-exp(2*%i*x))+x*log((1/sin(x))^n)-_ + 1/2*%i*n*polylog(2,exp(2*%i*x)) +--R +--R There are 15 exposed and 5 unexposed library operations named + +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op + +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named + +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 336 + +--S 337 of 514 +a0264:= integrate(t0264,x) +--R +--R +--R x +--R ++ n +--R (189) | log(csc(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 337 + +--S 338 of 514 +--m0264:= a0264-r0264 +--E 338 + +--S 339 of 514 +--d0264:= D(m0264,x) +--E 339 + +--S 340 of 514 +t0265:= cos(x)*log(1/2-1/2*cos(2*x)) +--R +--R +--R - cos(2x) + 1 +--R (190) cos(x)log(-------------) +--R 2 +--R Type: Expression(Integer) +--E 340 + +--S 341 of 514 +r0265:= sin(x)*(-2+log(sin(x)^2)) +--R +--R +--R 2 +--R (191) sin(x)log(sin(x) ) - 2sin(x) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 514 +a0265:= integrate(t0265,x) +--R +--R +--R 2 +--R (192) sin(x)log(- cos(x) + 1) - 2sin(x) +--R Type: Union(Expression(Integer),...) +--E 342 + +--S 343 of 514 +m0265:= a0265-r0265 +--R +--R +--R 2 2 +--R (193) - sin(x)log(sin(x) ) + sin(x)log(- cos(x) + 1) +--R Type: Expression(Integer) +--E 343 + +--S 344 of 514 +d0265:= D(m0265,x) +--R +--R +--R (194) +--R 3 2 3 2 +--R (- cos(x) + cos(x))log(sin(x) ) + (cos(x) - cos(x))log(- cos(x) + 1) +--R + +--R 2 3 +--R - 2cos(x)sin(x) - 2cos(x) + 2cos(x) +--R / +--R 2 +--R cos(x) - 1 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 514 +t0266:= cot(x)/log(exp(1)*sin(x)) +--R +--R +--R cot(x) +--R (195) -------------- +--R log(%e sin(x)) +--R Type: Expression(Integer) +--E 345 + +--S 346 of 514 +r0266:= log(1+log(sin(x))) +--R +--R +--R (196) log(log(sin(x)) + 1) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 514 +a0266:= integrate(t0266,x) +--R +--R +--R (197) log(log(%e sin(x))) +--R Type: Union(Expression(Integer),...) +--E 347 + +--S 348 of 514 +m0266:= a0266-r0266 +--R +--R +--R (198) log(log(%e sin(x))) - log(log(sin(x)) + 1) +--R Type: Expression(Integer) +--E 348 + +--S 349 of 514 +d0266:= D(m0266,x) +--R +--R +--R - cos(x)log(%e sin(x)) + cos(x)log(sin(x)) + cos(x) +--R (199) --------------------------------------------------- +--R (sin(x)log(sin(x)) + sin(x))log(%e sin(x)) +--R Type: Expression(Integer) +--E 349 + +--S 350 of 514 +t0267:= cot(x)/log(exp(1)^sin(x)) +--R +--R +--R cot(x) +--R (200) ------ +--R sin(x) +--R Type: Expression(Integer) +--E 350 + +--S 351 of 514 +r0267:= (-log(log(exp(sin(x))))+log(sin(x)))/(log(exp(sin(x)))-sin(x)) +--R +--R +--R >> Error detected within library code: +--R catdef: division by zero +--R +--R Continuing to read the file... +--R +--E 351 + +--S 352 of 514 +a0267:= integrate(t0267,x) +--R +--R +--R 1 +--R (201) - ------ +--R sin(x) +--R Type: Union(Expression(Integer),...) +--E 352 + +--S 353 of 514 +--m0267:= a0267-r0267 +--E 353 + +--S 354 of 514 +--d0267:= D(m0267,x) +--E 354 + +--S 355 of 514 +t0268:= log(cos(x))*sec(x)^2 +--R +--R +--R 2 +--R (202) sec(x) log(cos(x)) +--R Type: Expression(Integer) +--E 355 + +--S 356 of 514 +r0268:= -x+tan(x)+log(cos(x))*tan(x) +--R +--R +--R (203) tan(x)log(cos(x)) + tan(x) - x +--R Type: Expression(Integer) +--E 356 + +--S 357 of 514 +a0268:= integrate(t0268,x) +--R +--R +--R sin(x)log(cos(x)) + sin(x) - x cos(x) +--R (204) ------------------------------------- +--R cos(x) +--R Type: Union(Expression(Integer),...) +--E 357 + +--S 358 of 514 +m0268:= a0268-r0268 +--R +--R +--R (- cos(x)tan(x) + sin(x))log(cos(x)) - cos(x)tan(x) + sin(x) +--R (205) ------------------------------------------------------------ +--R cos(x) +--R Type: Expression(Integer) +--E 358 + +--S 359 of 514 +d0268:= D(m0268,x) +--R +--R +--R (206) +--R 2 2 2 2 2 +--R (- cos(x) tan(x) + sin(x) )log(cos(x)) - cos(x) tan(x) + cos(x)sin(x)tan(x) +--R ----------------------------------------------------------------------------- +--R 2 +--R cos(x) +--R Type: Expression(Integer) +--E 359 + +--S 360 of 514 +t0269:= cot(x)*log(sin(x)) +--R +--R +--R (207) cot(x)log(sin(x)) +--R Type: Expression(Integer) +--E 360 + +--S 361 of 514 +r0269:= 1/2*log(sin(x))^2 +--R +--R +--R 2 +--R log(sin(x)) +--R (208) ------------ +--R 2 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 514 +a0269:= integrate(t0269,x) +--R +--R +--R 2 +--R log(sin(x)) +--R (209) ------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 362 + +--S 363 of 514 +m0269:= a0269-r0269 +--R +--R +--R (210) 0 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 514 +d0269:= D(m0269,x) +--R +--R +--R (211) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 514 +t0270:= tan(x)/log(cos(x)) +--R +--R +--R tan(x) +--R (212) ----------- +--R log(cos(x)) +--R Type: Expression(Integer) +--E 365 + +--S 366 of 514 +r0270:= -log(log(cos(x))) +--R +--R +--R (213) - log(log(cos(x))) +--R Type: Expression(Integer) +--E 366 + +--S 367 of 514 +a0270:= integrate(t0270,x) +--R +--R +--R (214) - log(log(cos(x))) +--R Type: Union(Expression(Integer),...) +--E 367 + +--S 368 of 514 +m0270:= a0270-r0270 +--R +--R +--R (215) 0 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 514 +d0270:= D(m0270,x) +--R +--R +--R (216) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 514 +t0271:= csc(x)*log(tan(x))*sec(x) +--R +--R +--R (217) csc(x)sec(x)log(tan(x)) +--R Type: Expression(Integer) +--E 370 + +--S 371 of 514 +r0271:= 1/2*log(tan(x))^2 +--R +--R +--R 2 +--R log(tan(x)) +--R (218) ------------ +--R 2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 514 +a0271:= integrate(t0271,x) +--R +--R +--R sin(x) 2 +--R log(------) +--R cos(x) +--R (219) ------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 372 + +--S 373 of 514 +m0271:= a0271-r0271 +--R +--R +--R 2 sin(x) 2 +--R - log(tan(x)) + log(------) +--R cos(x) +--R (220) ----------------------------- +--R 2 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 514 +d0271:= D(m0271,x) +--R +--R +--R (221) +--R 2 +--R (- cos(x)sin(x)tan(x) - cos(x)sin(x))log(tan(x)) +--R + +--R 2 2 sin(x) +--R (sin(x) + cos(x) )tan(x)log(------) +--R cos(x) +--R / +--R cos(x)sin(x)tan(x) +--R Type: Expression(Integer) +--E 374 + +--S 375 of 514 +t0272:= csc(2*x)*log(tan(x)) +--R +--R +--R (222) csc(2x)log(tan(x)) +--R Type: Expression(Integer) +--E 375 + +--S 376 of 514 +r0272:= 1/4*log(tan(x))^2 +--R +--R +--R 2 +--R log(tan(x)) +--R (223) ------------ +--R 4 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 514 +a0272:= integrate(t0272,x) +--R +--R +--R sin(x) 2 +--R log(------) +--R cos(x) +--R (224) ------------ +--R 4 +--R Type: Union(Expression(Integer),...) +--E 377 + +--S 378 of 514 +m0272:= a0272-r0272 +--R +--R +--R 2 sin(x) 2 +--R - log(tan(x)) + log(------) +--R cos(x) +--R (225) ----------------------------- +--R 4 +--R Type: Expression(Integer) +--E 378 + +--S 379 of 514 +d0272:= D(m0272,x) +--R +--R +--R (226) +--R 2 +--R (- cos(x)sin(x)tan(x) - cos(x)sin(x))log(tan(x)) +--R + +--R 2 2 sin(x) +--R (sin(x) + cos(x) )tan(x)log(------) +--R cos(x) +--R / +--R 2cos(x)sin(x)tan(x) +--R Type: Expression(Integer) +--E 379 + +--S 380 of 514 +t0273:= log(sinh(x)) +--R +--R +--R (227) log(sinh(x)) +--R Type: Expression(Integer) +--E 380 + +--S 381 of 514 +r0273:= 1/2*x^2-x*log(1-exp(2*x))+x*log(sinh(x))-1/2*polylog(2,exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 381 + +--S 382 of 514 +a0273:= integrate(t0273,x) +--R +--R +--R x +--R ++ +--R (228) | log(sinh(%I))d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 382 + +--S 383 of 514 +--m0273:= a0273-r0273 +--E 383 + +--S 384 of 514 +--d0273:= D(m0273,x) +--E 384 + +--S 385 of 514 +t0274:= log(sinh(x)^2) +--R +--R +--R 2 +--R (229) log(sinh(x) ) +--R Type: Expression(Integer) +--E 385 + +--S 386 of 514 +r0274:= x^2-2*x*log(1-exp(2*x))+x*log(sinh(x)^2)-polylog(2,exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 386 + +--S 387 of 514 +a0274:= integrate(t0274,x) +--R +--R +--R x +--R ++ 2 +--R (230) | log(sinh(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 387 + +--S 388 of 514 +--m0274:= a0274-r0274 +--E 388 + +--S 389 of 514 +--d0274:= D(m0274,x) +--E 389 + +--S 390 of 514 +t0275:= log(sinh(x)^n) +--R +--R +--R n +--R (231) log(sinh(x) ) +--R Type: Expression(Integer) +--E 390 + +--S 391 of 514 +r0275:= 1/2*n*x^2-n*x*log(1-exp(2*x))+x*log(sinh(x)^n)-_ + 1/2*n*polylog(2,exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 391 + +--S 392 of 514 +a0275:= integrate(t0275,x) +--R +--R +--R x +--R ++ n +--R (232) | log(sinh(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 392 + +--S 393 of 514 +--m0275:= a0275-r0275 +--E 393 + +--S 394 of 514 +--d0275:= D(m0275,x) +--E 394 + +--S 395 of 514 +t0276:= log(cosh(x)) +--R +--R +--R (233) log(cosh(x)) +--R Type: Expression(Integer) +--E 395 + +--S 396 of 514 +r0276:= 1/2*x^2-x*log(1+exp(2*x))+x*log(cosh(x))-1/2*polylog(2,-exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 396 + +--S 397 of 514 +a0276:= integrate(t0276,x) +--R +--R +--R x +--R ++ +--R (234) | log(cosh(%I))d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 397 + +--S 398 of 514 +--m0276:= a0276-r0276 +--E 398 + +--S 399 of 514 +--d0276:= D(m0276,x) +--E 399 + +--S 400 of 514 +t0277:= log(cosh(x)^2) +--R +--R +--R 2 +--R (235) log(cosh(x) ) +--R Type: Expression(Integer) +--E 400 + +--S 401 of 514 +r0277:= x^2-2*x*log(1+exp(2*x))+x*log(cosh(x)^2)-polylog(2,-exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 401 + +--S 402 of 514 +a0277:= integrate(t0277,x) +--R +--R +--R x +--R ++ 2 +--R (236) | log(cosh(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 402 + +--S 403 of 514 +--m0277:= a0277-r0277 +--E 403 + +--S 404 of 514 +--d0277:= D(m0277,x) +--E 404 + +--S 405 of 514 +t0278:= log(cosh(x)^n) +--R +--R +--R n +--R (237) log(cosh(x) ) +--R Type: Expression(Integer) +--E 405 + +--S 406 of 514 +r0278:= 1/2*n*x^2-n*x*log(1+exp(2*x))+x*log(cosh(x)^n)-_ + 1/2*n*polylog(2,-exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 406 + +--S 407 of 514 +a0278:= integrate(t0278,x) +--R +--R +--R x +--R ++ n +--R (238) | log(cosh(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 407 + +--S 408 of 514 +--m0278:= a0278-r0278 +--E 408 + +--S 409 of 514 +--d0278:= D(m0278,x) +--E 409 + +--S 410 of 514 +t0279:= log(tanh(x)^n) +--R +--R +--R n +--R (239) log(tanh(x) ) +--R Type: Expression(Integer) +--E 410 + +--S 411 of 514 +r0279:= -1/2*log(1-tanh(x))*log(tanh(x)^n)+1/2*log(tanh(x)^n)*_ + log(1+tanh(x))+1/2*n*polylog(2,-tanh(x))-1/2*n*polylog(2,tanh(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 411 + +--S 412 of 514 +a0279:= integrate(t0279,x) +--R +--R +--R x +--R ++ n +--R (240) | log(tanh(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 412 + +--S 413 of 514 +--m0279:= a0279-r0279 +--E 413 + +--S 414 of 514 +--d0279:= D(m0279,x) +--E 414 + +--S 415 of 514 +t0280:= log(coth(x)^n) +--R +--R +--R n +--R (241) log(coth(x) ) +--R Type: Expression(Integer) +--E 415 + +--S 416 of 514 +r0280:= -1/2*log(1-coth(x))*log(coth(x)^n)+1/2*log(coth(x)^n)*_ + log(1+coth(x))+1/2*n*polylog(2,-coth(x))-1/2*n*polylog(2,coth(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 416 + +--S 417 of 514 +a0280:= integrate(t0280,x) +--R +--R +--R x +--R ++ n +--R (242) | log(coth(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 417 + +--S 418 of 514 +--m0280:= a0280-r0280 +--E 418 + +--S 419 of 514 +--d0280:= D(m0280,x) +--E 419 + +--S 420 of 514 +t0281:= log(sech(x)) +--R +--R +--R (243) log(sech(x)) +--R Type: Expression(Integer) +--E 420 + +--S 421 of 514 +r0281:= -1/2*x^2+x*log(1+exp(2*x))+x*log(1/cosh(x))+1/2*polylog(2,-exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 421 + +--S 422 of 514 +a0281:= integrate(t0281,x) +--R +--R +--R x +--R ++ +--R (244) | log(sech(%I))d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 422 + +--S 423 of 514 +--m0281:= a0281-r0281 +--E 423 + +--S 424 of 514 +--d0281:= D(m0281,x) +--E 424 + +--S 425 of 514 +t0282:= log(sech(x)^2) +--R +--R +--R 2 +--R (245) log(sech(x) ) +--R Type: Expression(Integer) +--E 425 + +--S 426 of 514 +r0282:= -x^2+2*x*log(1+exp(2*x))+x*log(1/cosh(x)^2)+polylog(2,-exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 426 + +--S 427 of 514 +a0282:= integrate(t0282,x) +--R +--R +--R x +--R ++ 2 +--R (246) | log(sech(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 427 + +--S 428 of 514 +--m0282:= a0282-r0282 +--E 428 + +--S 429 of 514 +--d0282:= D(m0282,x) +--E 429 + +--S 430 of 514 +t0283:= log(sech(x)^n) +--R +--R +--R n +--R (247) log(sech(x) ) +--R Type: Expression(Integer) +--E 430 + +--S 431 of 514 +r0283:= -1/2*n*x^2+n*x*log(1+exp(2*x))+x*log((1/cosh(x))^n)+_ + 1/2*n*polylog(2,-exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 431 + +--S 432 of 514 +a0283:= integrate(t0283,x) +--R +--R +--R x +--R ++ n +--R (248) | log(sech(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 432 + +--S 433 of 514 +--m0283:= a0283-r0283 +--E 433 + +--S 434 of 514 +--d0283:= D(m0283,x) +--E 434 + +--S 435 of 514 +t0284:= log(csch(x)) +--R +--R +--R (249) log(csch(x)) +--R Type: Expression(Integer) +--E 435 + +--S 436 of 514 +r0284:= -1/2*x^2+x*log(1-exp(2*x))+x*log(1/sinh(x))+1/2*polylog(2,exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 436 + +--S 437 of 514 +a0284:= integrate(t0284,x) +--R +--R +--R x +--R ++ +--R (250) | log(csch(%I))d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 437 + +--S 438 of 514 +--m0284:= a0284-r0284 +--E 438 + +--S 439 of 514 +--d0284:= D(m0284,x) +--E 439 + +--S 440 of 514 +t0285:= log(csch(x)^2) +--R +--R +--R 2 +--R (251) log(csch(x) ) +--R Type: Expression(Integer) +--E 440 + +--S 441 of 514 +r0285:= -x^2+2*x*log(1-exp(2*x))+x*log(1/sinh(x)^2)+polylog(2,exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 441 + +--S 442 of 514 +a0285:= integrate(t0285,x) +--R +--R +--R x +--R ++ 2 +--R (252) | log(csch(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 442 + +--S 443 of 514 +--m0285:= a0285-r0285 +--E 443 + +--S 444 of 514 +--d0285:= D(m0285,x) +--E 444 + +--S 445 of 514 +t0286:= log(csch(x)^n) +--R +--R +--R n +--R (253) log(csch(x) ) +--R Type: Expression(Integer) +--E 445 + +--S 446 of 514 +r0286:= -1/2*n*x^2+n*x*log(1-exp(2*x))+x*log((1/sinh(x))^n)+_ + 1/2*n*polylog(2,exp(2*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 446 + +--S 447 of 514 +a0286:= integrate(t0286,x) +--R +--R +--R x +--R ++ n +--R (254) | log(csch(%I) )d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 447 + +--S 448 of 514 +--m0286:= a0286-r0286 +--E 448 + +--S 449 of 514 +--d0286:= D(m0286,x) +--E 449 + +--S 450 of 514 +t0287:= sec(a+b*log(c*x^n))/x +--R +--R +--R n +--R sec(b log(c x ) + a) +--R (255) -------------------- +--R x +--R Type: Expression(Integer) +--E 450 + +--S 451 of 514 +r0287:= atanh(sin(a+b*log(c*x^n)))/b/n +--R +--R +--R n +--R atanh(sin(b log(c x ) + a)) +--R (256) --------------------------- +--R b n +--R Type: Expression(Integer) +--E 451 + +--S 452 of 514 +a0287:= integrate(t0287,x) +--R +--R +--R (257) +--R log(sin(b n log(x) + b log(c) + a) + 1) +--R + +--R - log(sin(b n log(x) + b log(c) + a) - 1) +--R / +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 452 + +--S 453 of 514 +m0287:= a0287-r0287 +--R +--R +--R (258) +--R n +--R - 2atanh(sin(b log(c x ) + a)) + log(sin(b n log(x) + b log(c) + a) + 1) +--R + +--R - log(sin(b n log(x) + b log(c) + a) - 1) +--R / +--R 2b n +--R Type: Expression(Integer) +--E 453 + +--S 454 of 514 +d0287:= D(m0287,x) +--R +--R +--R (259) +--R n n 2 +--R - x cos(b n log(x) + b log(c) + a)sin(b log(c x ) + a) +--R + +--R n - 1 2 n - 1 n +--R (x x sin(b n log(x) + b log(c) + a) - x x )cos(b log(c x ) + a) +--R + +--R n +--R x cos(b n log(x) + b log(c) + a) +--R / +--R n 2 n n 2 +--R (x x sin(b n log(x) + b log(c) + a) - x x )sin(b log(c x ) + a) +--R + +--R n 2 n +--R - x x sin(b n log(x) + b log(c) + a) + x x +--R Type: Expression(Integer) +--E 454 + +--S 455 of 514 +t0288:= csc(a+b*log(c*x^n))/x +--R +--R +--R n +--R csc(b log(c x ) + a) +--R (260) -------------------- +--R x +--R Type: Expression(Integer) +--E 455 + +--S 456 of 514 +r0288:= -atanh(cos(a+b*log(c*x^n)))/b/n +--R +--R +--R n +--R atanh(cos(b log(c x ) + a)) +--R (261) - --------------------------- +--R b n +--R Type: Expression(Integer) +--E 456 + +--S 457 of 514 +a0288:= integrate(t0288,x) +--R +--R +--R (262) +--R - log(cos(b n log(x) + b log(c) + a) + 1) +--R + +--R log(cos(b n log(x) + b log(c) + a) - 1) +--R / +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 457 + +--S 458 of 514 +m0288:= a0288-r0288 +--R +--R +--R (263) +--R n +--R 2atanh(cos(b log(c x ) + a)) - log(cos(b n log(x) + b log(c) + a) + 1) +--R + +--R log(cos(b n log(x) + b log(c) + a) - 1) +--R / +--R 2b n +--R Type: Expression(Integer) +--E 458 + +--S 459 of 514 +d0288:= D(m0288,x) +--R +--R +--R (264) +--R n - 1 2 n - 1 n +--R (x x cos(b n log(x) + b log(c) + a) - x x )sin(b log(c x ) + a) +--R + +--R n n 2 +--R - x sin(b n log(x) + b log(c) + a)cos(b log(c x ) + a) +--R + +--R n +--R x sin(b n log(x) + b log(c) + a) +--R / +--R n 2 n n 2 +--R (x x cos(b n log(x) + b log(c) + a) - x x )cos(b log(c x ) + a) +--R + +--R n 2 n +--R - x x cos(b n log(x) + b log(c) + a) + x x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 514 +t0289:= sin(a+b*log(c*x^n))^(1/2)/x +--R +--R +--R +--------------------+ +--R | n +--R \|sin(b log(c x ) + a) +--R (265) ----------------------- +--R x +--R Type: Expression(Integer) +--E 460 + +--S 461 of 514 +r0289:= 2*EllipticE(1/2*a-1/4*%pi+1/2*b*log(c*x^n),2)/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 461 + +--S 462 of 514 +a0289:= integrate(t0289,x) +--R +--R +--R +---------------------+ +--R x | n +--R ++ \|sin(b log(c %I ) + a) +--R (266) | ------------------------ d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 462 + +--S 463 of 514 +--m0289:= a0289-r0289 +--E 463 + +--S 464 of 514 +--d0289:= D(m0289,x) +--E 464 + +--S 465 of 514 +t0290:= sin(a+b*log(c*x^n))^(3/2)/x +--R +--R +--R +--------------------+ +--R n | n +--R sin(b log(c x ) + a)\|sin(b log(c x ) + a) +--R (267) ------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 465 + +--S 466 of 514 +r0290:= 2/3/b/n*(EllipticF(1/2*a-1/4*%pi+1/2*b*log(c*x^n),2)-_ + cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^(1/2)) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 466 + +--S 467 of 514 +a0290:= integrate(t0290,x) +--R +--R +--R +---------------------+ +--R x n | n +--R ++ sin(b log(c %I ) + a)\|sin(b log(c %I ) + a) +--R (268) | --------------------------------------------- d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 467 + +--S 468 of 514 +--m0290:= a0290-r0290 +--E 468 + +--S 469 of 514 +--d0290:= D(m0290,x) +--E 469 + +--S 470 of 514 +t0291:= sin(a+b*log(c*x^n))^(5/2)/x +--R +--R +--R +--------------------+ +--R n 2 | n +--R sin(b log(c x ) + a) \|sin(b log(c x ) + a) +--R (269) -------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 470 + +--S 471 of 514 +r0291:= -2/5/b/n*(-3*EllipticE(1/2*a-1/4*%pi+1/2*b*log(c*x^n),2)+_ + cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^(3/2)) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 471 + +--S 472 of 514 +a0291:= integrate(t0291,x) +--R +--R +--R +---------------------+ +--R x n 2 | n +--R ++ sin(b log(c %I ) + a) \|sin(b log(c %I ) + a) +--R (270) | ---------------------------------------------- d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 472 + +--S 473 of 514 +--m0291:= a0291-r0291 +--E 473 + +--S 474 of 514 +--d0291:= D(m0291,x) +--E 474 + +--S 475 of 514 +t0292:= 1/x/sin(a+b*log(c*x^n))^(1/2) +--R +--R +--R 1 +--R (271) ------------------------ +--R +--------------------+ +--R | n +--R x\|sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 475 + +--S 476 of 514 +r0292:= 2*EllipticF(1/2*a-1/4*%pi+1/2*b*log(c*x^n),2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 476 + +--S 477 of 514 +a0292:= integrate(t0292,x) +--R +--R +--R x +--R ++ 1 +--R (272) | -------------------------- d%I +--R ++ +---------------------+ +--R | n +--R %I\|sin(b log(c %I ) + a) +--R Type: Union(Expression(Integer),...) +--E 477 + +--S 478 of 514 +--m0292:= a0292-r0292 +--E 478 + +--S 479 of 514 +--d0292:= D(m0292,x) +--E 479 + +--S 480 of 514 +t0293:= 1/x/sin(a+b*log(c*x^n))^(3/2) +--R +--R +--R 1 +--R (273) --------------------------------------------- +--R +--------------------+ +--R n | n +--R x sin(b log(c x ) + a)\|sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 480 + +--S 481 of 514 +r0293:= -2*EllipticE(1/2*a-1/4*%pi+1/2*b*log(c*x^n),2)/b/n-_ + 2*cos(a+b*log(c*x^n))/b/n/sin(a+b*log(c*x^n))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 481 + +--S 482 of 514 +a0293:= integrate(t0293,x) +--R +--R +--R x +--R ++ 1 +--R (274) | ------------------------------------------------ d%I +--R ++ +---------------------+ +--R n | n +--R %I sin(b log(c %I ) + a)\|sin(b log(c %I ) + a) +--R Type: Union(Expression(Integer),...) +--E 482 + +--S 483 of 514 +--m0293:= a0293-r0293 +--E 483 + +--S 484 of 514 +--d0293:= D(m0293,x) +--E 484 + +--S 485 of 514 +t0294:= 1/x/sin(a+b*log(c*x^n))^(5/2) +--R +--R +--R 1 +--R (275) ---------------------------------------------- +--R +--------------------+ +--R n 2 | n +--R x sin(b log(c x ) + a) \|sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 485 + +--S 486 of 514 +r0294:= 2/3*EllipticF(1/2*a-1/4*%pi+1/2*b*log(c*x^n),2)/b/n-_ + 2/3*cos(a+b*log(c*x^n))/b/n/sin(a+b*log(c*x^n))^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 486 + +--S 487 of 514 +a0294:= integrate(t0294,x) +--R +--R +--R x +--R ++ 1 +--R (276) | ------------------------------------------------- d%I +--R ++ +---------------------+ +--R n 2 | n +--R %I sin(b log(c %I ) + a) \|sin(b log(c %I ) + a) +--R Type: Union(Expression(Integer),...) +--E 487 + +--S 488 of 514 +--m0294:= a0294-r0294 +--E 488 + +--S 489 of 514 +--d0294:= D(m0294,x) +--E 489 + +--S 490 of 514 +t0295:= cos(a+b*log(c*x^n))^(1/2)/x +--R +--R +--R +--------------------+ +--R | n +--R \|cos(b log(c x ) + a) +--R (277) ----------------------- +--R x +--R Type: Expression(Integer) +--E 490 + +--S 491 of 514 +r0295:= 2*EllipticE(1/2*a+1/2*b*log(c*x^n),2)/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 491 + +--S 492 of 514 +a0295:= integrate(t0295,x) +--R +--R +--R +---------------------+ +--R x | n +--R ++ \|cos(b log(c %I ) + a) +--R (278) | ------------------------ d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 492 + +--S 493 of 514 +--m0295:= a0295-r0295 +--E 493 + +--S 494 of 514 +--d0295:= D(m0295,x) +--E 494 + +--S 495 of 514 +t0296:= cos(a+b*log(c*x^n))^(3/2)/x +--R +--R +--R +--------------------+ +--R n | n +--R cos(b log(c x ) + a)\|cos(b log(c x ) + a) +--R (279) ------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 495 + +--S 496 of 514 +r0296:= 2/3/b/n*(EllipticF(1/2*a+1/2*b*log(c*x^n),2)+_ + cos(a+b*log(c*x^n))^(1/2)*sin(a+b*log(c*x^n))) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 496 + +--S 497 of 514 +a0296:= integrate(t0296,x) +--R +--R +--R +---------------------+ +--R x n | n +--R ++ cos(b log(c %I ) + a)\|cos(b log(c %I ) + a) +--R (280) | --------------------------------------------- d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 497 + +--S 498 of 514 +--m0296:= a0296-r0296 +--E 498 + +--S 499 of 514 +--d0296:= D(m0296,x) +--E 499 + +--S 500 of 514 +t0297:= cos(a+b*log(c*x^n))^(5/2)/x +--R +--R +--R +--------------------+ +--R n 2 | n +--R cos(b log(c x ) + a) \|cos(b log(c x ) + a) +--R (281) -------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 500 + +--S 501 of 514 +r0297:= 2/5/b/n*(3*EllipticE(1/2*a+1/2*b*log(c*x^n),2)+_ + cos(a+b*log(c*x^n))^(3/2)*sin(a+b*log(c*x^n))) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 501 + +--S 502 of 514 +a0297:= integrate(t0297,x) +--R +--R +--R +---------------------+ +--R x n 2 | n +--R ++ cos(b log(c %I ) + a) \|cos(b log(c %I ) + a) +--R (282) | ---------------------------------------------- d%I +--R ++ %I +--R Type: Union(Expression(Integer),...) +--E 502 + +--S 503 of 514 +--m0297:= a0297-r0297 +--E 503 + +--S 504 of 514 +--d0297:= D(m0297,x) +--E 504 + +--S 505 of 514 +t0298:= 1/x/cos(a+b*log(c*x^n))^(1/2) +--R +--R +--R 1 +--R (283) ------------------------ +--R +--------------------+ +--R | n +--R x\|cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 505 + +--S 506 of 514 +r0298:= 2*EllipticF(1/2*a+1/2*b*log(c*x^n),2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 506 + +--S 507 of 514 +a0298:= integrate(t0298,x) +--R +--R +--R x +--R ++ 1 +--R (284) | -------------------------- d%I +--R ++ +---------------------+ +--R | n +--R %I\|cos(b log(c %I ) + a) +--R Type: Union(Expression(Integer),...) +--E 507 + +--S 508 of 514 +--m0298:= a0298-r0298 +--E 508 + +--S 509 of 514 +--d0298:= D(m0298,x) +--E 509 + +--S 510 of 514 +t0299:= 1/x/cos(a+b*log(c*x^n))^(3/2) +--R +--R +--R 1 +--R (285) --------------------------------------------- +--R +--------------------+ +--R n | n +--R x cos(b log(c x ) + a)\|cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 510 + +--S 511 of 514 +r0299:= -2*EllipticE(1/2*a+1/2*b*log(c*x^n),2)/b/n+_ + 2*sin(a+b*log(c*x^n))/b/n/cos(a+b*log(c*x^n))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 511 + +--S 512 of 514 +a0299:= integrate(t0299,x) +--R +--R +--R x +--R ++ 1 +--R (286) | ------------------------------------------------ d%I +--R ++ +---------------------+ +--R n | n +--R %I cos(b log(c %I ) + a)\|cos(b log(c %I ) + a) +--R Type: Union(Expression(Integer),...) +--E 512 + +--S 513 of 514 +--m0299:= a0299-r0299 +--E 513 + +--S 514 of 514 +--d0299:= D(m0299,x) +--E 514 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richlog200-299.input.pdf b/src/axiom-website/CATS/richlog200-299.input.pdf new file mode 100644 index 0000000..7453df0 Binary files /dev/null and b/src/axiom-website/CATS/richlog200-299.input.pdf differ diff --git a/src/axiom-website/CATS/richlog300-391.input.pamphlet b/src/axiom-website/CATS/richlog300-391.input.pamphlet new file mode 100644 index 0000000..3b4aeb4 --- /dev/null +++ b/src/axiom-website/CATS/richlog300-391.input.pamphlet @@ -0,0 +1,5022 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richlog300-391.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richlog300-391.output +)spool richlog300-391.output +)set message test on +)set message auto off +)clear all + +--S 1 of 460 +t0300:= 1/x/cos(a+b*log(c*x^n))^(5/2) +--R +--R +--R 1 +--R (1) ---------------------------------------------- +--R +--------------------+ +--R n 2 | n +--R x cos(b log(c x ) + a) \|cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 460 +r0300:= 2/3*EllipticF(1/2*a+1/2*b*log(c*x^n),2)/b/n+_ + 2/3*sin(a+b*log(c*x^n))/b/n/cos(a+b*log(c*x^n))^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 460 +a0300:= integrate(t0300,x) +--R +--R +--R x +--R ++ 1 +--R (2) | ------------------------------------------------- d%R +--R ++ +---------------------+ +--R n 2 | n +--R %R cos(b log(c %R ) + a) \|cos(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 460 +--m0300:= a0300-r0300 +--E 4 + +--S 5 of 460 +--d0300:= D(m0300,x) +--E 5 + +)clear all + +--S 6 of 460 +t0301:= sec(a+b*log(c*x^n))^(1/2)/x +--R +--R +--R +--------------------+ +--R | n +--R \|sec(b log(c x ) + a) +--R (1) ----------------------- +--R x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 460 +r0301:= 2*cos(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a+1/2*b*log(c*x^n),2)*_ + sec(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 460 +a0301:= integrate(t0301,x) +--R +--R +--R +---------------------+ +--R x | n +--R ++ \|sec(b log(c %R ) + a) +--R (2) | ------------------------ d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 460 +--m0301:= a0301-r0301 +--E 9 + +--S 10 of 460 +--d0301:= D(m0301,x) +--E 10 + +)clear all + +--S 11 of 460 +t0302:= sec(a+b*log(c*x^n))^(3/2)/x +--R +--R +--R +--------------------+ +--R n | n +--R sec(b log(c x ) + a)\|sec(b log(c x ) + a) +--R (1) ------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 460 +r0302:= -2*cos(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a+1/2*b*log(c*x^n),2)*_ + sec(a+b*log(c*x^n))^(1/2)/b/n+2*sec(a+b*log(c*x^n))^(1/2)*_ + sin(a+b*log(c*x^n))/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 460 +a0302:= integrate(t0302,x) +--R +--R +--R +---------------------+ +--R x n | n +--R ++ sec(b log(c %R ) + a)\|sec(b log(c %R ) + a) +--R (2) | --------------------------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 460 +--m0302:= a0302-r0302 +--E 14 + +--S 15 of 460 +--d0302:= D(m0302,x) +--E 15 + +)clear all + +--S 16 of 460 +t0303:= sec(a+b*log(c*x^n))^(5/2)/x +--R +--R +--R +--------------------+ +--R n 2 | n +--R sec(b log(c x ) + a) \|sec(b log(c x ) + a) +--R (1) -------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 460 +r0303:= 2/3*cos(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a+1/2*b*log(c*x^n),2)*_ + sec(a+b*log(c*x^n))^(1/2)/b/n+2/3*sec(a+b*log(c*x^n))^(3/2)*_ + sin(a+b*log(c*x^n))/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 460 +a0303:= integrate(t0303,x) +--R +--R +--R +---------------------+ +--R x n 2 | n +--R ++ sec(b log(c %R ) + a) \|sec(b log(c %R ) + a) +--R (2) | ---------------------------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 460 +--m0303:= a0303-r0303 +--E 19 + +--S 20 of 460 +--d0303:= D(m0303,x) +--E 20 + +)clear all + +--S 21 of 460 +t0304:= 1/x/sec(a+b*log(c*x^n))^(1/2) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------------------+ +--R | n +--R x\|sec(b log(c x ) + a) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 460 +r0304:= 2*cos(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a+1/2*b*log(c*x^n),2)*_ + sec(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 460 +a0304:= integrate(t0304,x) +--R +--R +--R x +--R ++ 1 +--R (2) | -------------------------- d%R +--R ++ +---------------------+ +--R | n +--R %R\|sec(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 460 +--m0304:= a0304-r0304 +--E 24 + +--S 25 of 460 +--d0304:= D(m0304,x) +--E 25 + +)clear all + +--S 26 of 460 +t0305:= 1/x/sec(a+b*log(c*x^n))^(3/2) +--R +--R +--R 1 +--R (1) --------------------------------------------- +--R +--------------------+ +--R n | n +--R x sec(b log(c x ) + a)\|sec(b log(c x ) + a) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 460 +r0305:= 2/3*cos(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a+_ + 1/2*b*log(c*x^n),2)*sec(a+b*log(c*x^n))^(1/2)/b/n+_ + 2/3*sin(a+b*log(c*x^n))/b/n/sec(a+b*log(c*x^n))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 460 +a0305:= integrate(t0305,x) +--R +--R +--R x +--R ++ 1 +--R (2) | ------------------------------------------------ d%R +--R ++ +---------------------+ +--R n | n +--R %R sec(b log(c %R ) + a)\|sec(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 460 +--m0305:= a0305-r0305 +--E 29 + +--S 30 of 460 +--d0305:= D(m0305,x) +--E 30 + +)clear all + +--S 31 of 460 +t0306:= 1/x/sec(a+b*log(c*x^n))^(5/2) +--R +--R +--R 1 +--R (1) ---------------------------------------------- +--R +--------------------+ +--R n 2 | n +--R x sec(b log(c x ) + a) \|sec(b log(c x ) + a) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 460 +r0306:= 6/5*cos(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a+_ + 1/2*b*log(c*x^n),2)*sec(a+b*log(c*x^n))^(1/2)/b/n+_ + 2/5*sin(a+b*log(c*x^n))/b/n/sec(a+b*log(c*x^n))^(3/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 460 +a0306:= integrate(t0306,x) +--R +--R +--R x +--R ++ 1 +--R (2) | ------------------------------------------------- d%R +--R ++ +---------------------+ +--R n 2 | n +--R %R sec(b log(c %R ) + a) \|sec(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 460 +--m0306:= a0306-r0306 +--E 34 + +--S 35 of 460 +--d0306:= D(m0306,x) +--E 35 + +)clear all + +--S 36 of 460 +t0307:= csc(a+b*log(c*x^n))^(1/2)/x +--R +--R +--R +--------------------+ +--R | n +--R \|csc(b log(c x ) + a) +--R (1) ----------------------- +--R x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 460 +r0307:= 2*csc(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a-1/4*%pi+_ + 1/2*b*log(c*x^n),2)*sin(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 460 +a0307:= integrate(t0307,x) +--R +--R +--R +---------------------+ +--R x | n +--R ++ \|csc(b log(c %R ) + a) +--R (2) | ------------------------ d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 460 +--m0307:= a0307-r0307 +--E 39 + +--S 40 of 460 +--d0307:= D(m0307,x) +--E 40 + +)clear all + +--S 41 of 460 +t0308:= csc(a+b*log(c*x^n))^(3/2)/x +--R +--R +--R +--------------------+ +--R n | n +--R csc(b log(c x ) + a)\|csc(b log(c x ) + a) +--R (1) ------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 460 +r0308:= -2*cos(a+b*log(c*x^n))*csc(a+b*log(c*x^n))^(1/2)/b/n-_ + 2*csc(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a-1/4*%pi+_ + 1/2*b*log(c*x^n),2)*sin(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 of 460 +a0308:= integrate(t0308,x) +--R +--R +--R +---------------------+ +--R x n | n +--R ++ csc(b log(c %R ) + a)\|csc(b log(c %R ) + a) +--R (2) | --------------------------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 460 +--m0308:= a0308-r0308 +--E 44 + +--S 45 of 460 +--d0308:= D(m0308,x) +--E 45 + +)clear all + +--S 46 of 460 +t0309:= csc(a+b*log(c*x^n))^(5/2)/x +--R +--R +--R +--------------------+ +--R n 2 | n +--R csc(b log(c x ) + a) \|csc(b log(c x ) + a) +--R (1) -------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 460 +r0309:= -2/3*cos(a+b*log(c*x^n))*csc(a+b*log(c*x^n))^(3/2)/b/n+_ + 2/3*csc(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a-1/4*%pi+_ + 1/2*b*log(c*x^n),2)*sin(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 47 + +--S 48 of 460 +a0309:= integrate(t0309,x) +--R +--R +--R +---------------------+ +--R x n 2 | n +--R ++ csc(b log(c %R ) + a) \|csc(b log(c %R ) + a) +--R (2) | ---------------------------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 460 +--m0309:= a0309-r0309 +--E 49 + +--S 50 of 460 +--d0309:= D(m0309,x) +--E 50 + +)clear all + +--S 51 of 460 +t0310:= 1/x/csc(a+b*log(c*x^n))^(1/2) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------------------+ +--R | n +--R x\|csc(b log(c x ) + a) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 460 +r0310:= 2*csc(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a-1/4*%pi+_ + 1/2*b*log(c*x^n),2)*sin(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 460 +a0310:= integrate(t0310,x) +--R +--R +--R x +--R ++ 1 +--R (2) | -------------------------- d%R +--R ++ +---------------------+ +--R | n +--R %R\|csc(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 460 +--m0310:= a0310-r0310 +--E 54 + +--S 55 of 460 +--d0310:= D(m0310,x) +--E 55 + +)clear all + +--S 56 of 460 +t0311:= 1/x/csc(a+b*log(c*x^n))^(3/2) +--R +--R +--R 1 +--R (1) --------------------------------------------- +--R +--------------------+ +--R n | n +--R x csc(b log(c x ) + a)\|csc(b log(c x ) + a) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 460 +r0311:= -2/3*cos(a+b*log(c*x^n))/b/n/csc(a+b*log(c*x^n))^(1/2)+_ + 2/3*csc(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a-1/4*%pi+_ + 1/2*b*log(c*x^n),2)*sin(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 460 +a0311:= integrate(t0311,x) +--R +--R +--R x +--R ++ 1 +--R (2) | ------------------------------------------------ d%R +--R ++ +---------------------+ +--R n | n +--R %R csc(b log(c %R ) + a)\|csc(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 460 +--m0311:= a0311-r0311 +--E 59 + +--S 60 of 460 +--d0311:= D(m0311,x) +--E 60 + +)clear all + +--S 61 of 460 +t0312:= 1/x/csc(a+b*log(c*x^n))^(5/2) +--R +--R +--R 1 +--R (1) ---------------------------------------------- +--R +--------------------+ +--R n 2 | n +--R x csc(b log(c x ) + a) \|csc(b log(c x ) + a) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 460 +r0312:= -2/5*cos(a+b*log(c*x^n))/b/n/csc(a+b*log(c*x^n))^(3/2)+_ + 6/5*csc(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a-1/4*%pi+_ + 1/2*b*log(c*x^n),2)*sin(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 460 +a0312:= integrate(t0312,x) +--R +--R +--R x +--R ++ 1 +--R (2) | ------------------------------------------------- d%R +--R ++ +---------------------+ +--R n 2 | n +--R %R csc(b log(c %R ) + a) \|csc(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 460 +--m0312:= a0312-r0312 +--E 64 + +--S 65 of 460 +--d0312:= D(m0312,x) +--E 65 + +)clear all + +--S 66 of 460 +t0313:= sin(log(a+b*x)) +--R +--R +--R (1) sin(log(b x + a)) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 460 +r0313:= -1/2*(a+b*x)*(cos(log(a+b*x))-sin(log(a+b*x)))/b +--R +--R +--R (b x + a)sin(log(b x + a)) + (- b x - a)cos(log(b x + a)) +--R (2) --------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 67 + +--S 68 of 460 +a0313:= integrate(t0313,x) +--R +--R +--R (b x + a)sin(log(b x + a)) + (- b x - a)cos(log(b x + a)) +--R (3) --------------------------------------------------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 460 +m0313:= a0313-r0313 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 460 +d0313:= D(m0313,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 460 +t0314:= tanh(a+b*log(c*x^n))^2/x +--R +--R +--R n 2 +--R tanh(b log(c x ) + a) +--R (1) ---------------------- +--R x +--R Type: Expression(Integer) +--E 71 + +--S 72 of 460 +r0314:= 1/b/n*(b*log(c*x^n)-tanh(a+b*log(c*x^n))) +--R +--R +--R n n +--R - tanh(b log(c x ) + a) + b log(c x ) +--R (2) ------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 72 + +--S 73 of 460 +a0314:= integrate(t0314,x) +--R +--R +--R (3) +--R - sinh(b n log(x) + b log(c) + a) +--R + +--R (b n log(x) + 1)cosh(b n log(x) + b log(c) + a) +--R / +--R b n cosh(b n log(x) + b log(c) + a) +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 460 +m0314:= a0314-r0314 +--R +--R +--R (4) +--R n +--R cosh(b n log(x) + b log(c) + a)tanh(b log(c x ) + a) +--R + +--R - sinh(b n log(x) + b log(c) + a) +--R + +--R n +--R - b cosh(b n log(x) + b log(c) + a)log(c x ) +--R + +--R (b n log(x) + 1)cosh(b n log(x) + b log(c) + a) +--R / +--R b n cosh(b n log(x) + b log(c) + a) +--R Type: Expression(Integer) +--E 74 + +--S 75 of 460 +d0314:= D(m0314,x) +--R +--R +--R (5) +--R n - 1 2 n 2 +--R - x x cosh(b n log(x) + b log(c) + a) tanh(b log(c x ) + a) +--R + +--R n 2 +--R x sinh(b n log(x) + b log(c) + a) +--R / +--R n 2 +--R x x cosh(b n log(x) + b log(c) + a) +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 460 +t0315:= coth(a+b*log(c*x^n))^2/x +--R +--R +--R n 2 +--R coth(b log(c x ) + a) +--R (1) ---------------------- +--R x +--R Type: Expression(Integer) +--E 76 + +--S 77 of 460 +r0315:= -1/b/n*(coth(a+b*log(c*x^n))-b*log(c*x^n)) +--R +--R +--R n n +--R - coth(b log(c x ) + a) + b log(c x ) +--R (2) ------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 77 + +--S 78 of 460 +a0315:= integrate(t0315,x) +--R +--R +--R (3) +--R (b n log(x) + 1)sinh(b n log(x) + b log(c) + a) +--R + +--R - cosh(b n log(x) + b log(c) + a) +--R / +--R b n sinh(b n log(x) + b log(c) + a) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 460 +m0315:= a0315-r0315 +--R +--R +--R (4) +--R n +--R sinh(b n log(x) + b log(c) + a)coth(b log(c x ) + a) +--R + +--R n +--R (- b log(c x ) + b n log(x) + 1)sinh(b n log(x) + b log(c) + a) +--R + +--R - cosh(b n log(x) + b log(c) + a) +--R / +--R b n sinh(b n log(x) + b log(c) + a) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 460 +d0315:= D(m0315,x) +--R +--R +--R (5) +--R n - 1 2 n 2 +--R - x x sinh(b n log(x) + b log(c) + a) coth(b log(c x ) + a) +--R + +--R n 2 +--R x cosh(b n log(x) + b log(c) + a) +--R / +--R n 2 +--R x x sinh(b n log(x) + b log(c) + a) +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 460 +t0316:= sinh(a+b*log(c*x^n))^(1/2)/x +--R +--R +--R +---------------------+ +--R | n +--R \|sinh(b log(c x ) + a) +--R (1) ------------------------ +--R x +--R Type: Expression(Integer) +--E 81 + +--S 82 of 460 +r0316:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ + sinh(a+b*log(c*x^n))^(1/2)/b/n/(%i*sinh(a+b*log(c*x^n)))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 460 +a0316:= integrate(t0316,x) +--R +--R +--R +----------------------+ +--R x | n +--R ++ \|sinh(b log(c %R ) + a) +--R (2) | ------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 460 +--m0316:= a0316-r0316 +--E 84 + +--S 85 of 460 +--d0316:= D(m0316,x) +--E 85 + +)clear all + +--S 86 of 460 +t0317:= sinh(a+b*log(c*x^n))^(3/2)/x +--R +--R +--R +---------------------+ +--R n | n +--R sinh(b log(c x ) + a)\|sinh(b log(c x ) + a) +--R (1) --------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 86 + +--S 87 of 460 +r0317:= 2/3*%i*EllipticF(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ + (%i*sinh(a+b*log(c*x^n)))^(1/2)/b/n/sinh(a+b*log(c*x^n))^(1/2)+_ + 2/3*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 460 +a0317:= integrate(t0317,x) +--R +--R +--R +----------------------+ +--R x n | n +--R ++ sinh(b log(c %R ) + a)\|sinh(b log(c %R ) + a) +--R (2) | ----------------------------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 460 +--m0317:= a0317-r0317 +--E 89 + +--S 90 of 460 +--d0317:= D(m0317,x) +--E 90 + +)clear all + +--S 91 of 460 +t0318:= sinh(a+b*log(c*x^n))^(5/2)/x +--R +--R +--R +---------------------+ +--R n 2 | n +--R sinh(b log(c x ) + a) \|sinh(b log(c x ) + a) +--R (1) ---------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 460 +r0318:= 6/5*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ + sinh(a+b*log(c*x^n))^(1/2)/b/n/(%i*sinh(a+b*log(c*x^n)))^(1/2)+_ + 2/5*cosh(a+b*log(c*x^n))*sinh(a+b*log(c*x^n))^(3/2)/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 460 +a0318:= integrate(t0318,x) +--R +--R +--R +----------------------+ +--R x n 2 | n +--R ++ sinh(b log(c %R ) + a) \|sinh(b log(c %R ) + a) +--R (2) | ------------------------------------------------ d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 460 +--m0318:= a0318-r0318 +--E 94 + +--S 95 of 460 +--d0318:= D(m0318,x) +--E 95 + +)clear all + +--S 96 of 460 +t0319:= 1/x/sinh(a+b*log(c*x^n))^(1/2) +--R +--R +--R 1 +--R (1) ------------------------- +--R +---------------------+ +--R | n +--R x\|sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 460 +r0319:= -2*%i*EllipticF(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ + (%i*sinh(a+b*log(c*x^n)))^(1/2)/b/n/sinh(a+b*log(c*x^n))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 460 +a0319:= integrate(t0319,x) +--R +--R +--R x +--R ++ 1 +--R (2) | --------------------------- d%R +--R ++ +----------------------+ +--R | n +--R %R\|sinh(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 460 +--m0319:= a0319-r0319 +--E 99 + +--S 100 of 460 +--d0319:= D(m0319,x) +--E 100 + +)clear all + +--S 101 of 460 +t0320:= 1/x/sinh(a+b*log(c*x^n))^(3/2) +--R +--R +--R 1 +--R (1) ----------------------------------------------- +--R +---------------------+ +--R n | n +--R x sinh(b log(c x ) + a)\|sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 101 + +--S 102 of 460 +r0320:= -2*cosh(a+b*log(c*x^n))/b/n/sinh(a+b*log(c*x^n))^(1/2)-_ + 2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ + sinh(a+b*log(c*x^n))^(1/2)/b/n/(%i*sinh(a+b*log(c*x^n)))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 460 +a0320:= integrate(t0320,x) +--R +--R +--R x +--R ++ 1 +--R (2) | -------------------------------------------------- d%R +--R ++ +----------------------+ +--R n | n +--R %R sinh(b log(c %R ) + a)\|sinh(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 460 +--m0320:= a0320-r0320 +--E 104 + +--S 105 of 460 +--d0320:= D(m0320,x) +--E 105 + +)clear all + +--S 106 of 460 +t0321:= 1/x/sinh(a+b*log(c*x^n))^(5/2) +--R +--R +--R 1 +--R (1) ------------------------------------------------ +--R +---------------------+ +--R n 2 | n +--R x sinh(b log(c x ) + a) \|sinh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 460 +r0321:= -2/3*cosh(a+b*log(c*x^n))/b/n/sinh(a+b*log(c*x^n))^(3/2)+_ + 2/3*%i*EllipticF(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ + (%i*sinh(a+b*log(c*x^n)))^(1/2)/b/n/sinh(a+b*log(c*x^n))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 460 +a0321:= integrate(t0321,x) +--R +--R +--R x +--R ++ 1 +--R (2) | --------------------------------------------------- d%R +--R ++ +----------------------+ +--R n 2 | n +--R %R sinh(b log(c %R ) + a) \|sinh(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 460 +--m0321:= a0321-r0321 +--E 109 + +--S 110 of 460 +--d0321:= D(m0321,x) +--E 110 + +)clear all + +--S 111 of 460 +t0322:= cosh(a+b*log(c*x^n))^(1/2)/x +--R +--R +--R +---------------------+ +--R | n +--R \|cosh(b log(c x ) + a) +--R (1) ------------------------ +--R x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 460 +r0322:= -2*%i*EllipticE(1/2*%i*(a+b*log(c*x^n)),2)/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 112 + +--S 113 of 460 +a0322:= integrate(t0322,x) +--R +--R +--R +----------------------+ +--R x | n +--R ++ \|cosh(b log(c %R ) + a) +--R (2) | ------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 460 +--m0322:= a0322-r0322 +--E 114 + +--S 115 of 460 +--d0322:= D(m0322,x) +--E 115 + +)clear all + +--S 116 of 460 +t0323:= cosh(a+b*log(c*x^n))^(3/2)/x +--R +--R +--R +---------------------+ +--R n | n +--R cosh(b log(c x ) + a)\|cosh(b log(c x ) + a) +--R (1) --------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 460 +r0323:= -2/3/b/n*(%i*EllipticF(1/2*%i*(a+b*log(c*x^n)),2)-_ + cosh(a+b*log(c*x^n))^(1/2)*sinh(a+b*log(c*x^n))) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 460 +a0323:= integrate(t0323,x) +--R +--R +--R +----------------------+ +--R x n | n +--R ++ cosh(b log(c %R ) + a)\|cosh(b log(c %R ) + a) +--R (2) | ----------------------------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 460 +--m0323:= a0323-r0323 +--E 119 + +--S 120 of 460 +--d0323:= D(m0323,x) +--E 120 + +)clear all + +--S 121 of 460 +t0324:= cosh(a+b*log(c*x^n))^(5/2)/x +--R +--R +--R +---------------------+ +--R n 2 | n +--R cosh(b log(c x ) + a) \|cosh(b log(c x ) + a) +--R (1) ---------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 460 +r0324:= 2/5/b/n*(-3*%i*EllipticE(1/2*%i*(a+b*log(c*x^n)),2)+_ + cosh(a+b*log(c*x^n))^(3/2)*sinh(a+b*log(c*x^n))) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 460 +a0324:= integrate(t0324,x) +--R +--R +--R +----------------------+ +--R x n 2 | n +--R ++ cosh(b log(c %R ) + a) \|cosh(b log(c %R ) + a) +--R (2) | ------------------------------------------------ d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 460 +--m0324:= a0324-r0324 +--E 124 + +--S 125 of 460 +--d0324:= D(m0324,x) +--E 125 + +)clear all + +--S 126 of 460 +t0325:= 1/x/cosh(a+b*log(c*x^n))^(1/2) +--R +--R +--R 1 +--R (1) ------------------------- +--R +---------------------+ +--R | n +--R x\|cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 126 + +--S 127 of 460 +r0325:= -2*%i*EllipticF(1/2*%i*(a+b*log(c*x^n)),2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 127 + +--S 128 of 460 +a0325:= integrate(t0325,x) +--R +--R +--R x +--R ++ 1 +--R (2) | --------------------------- d%R +--R ++ +----------------------+ +--R | n +--R %R\|cosh(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 460 +--m0325:= a0325-r0325 +--E 129 + +--S 130 of 460 +--d0325:= D(m0325,x) +--E 130 + +)clear all + +--S 131 of 460 +t0326:= 1/x/cosh(a+b*log(c*x^n))^(3/2) +--R +--R +--R 1 +--R (1) ----------------------------------------------- +--R +---------------------+ +--R n | n +--R x cosh(b log(c x ) + a)\|cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 460 +r0326:= 2*%i*EllipticE(1/2*%i*(a+b*log(c*x^n)),2)/b/n+_ + 2*sinh(a+b*log(c*x^n))/b/n/cosh(a+b*log(c*x^n))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 460 +a0326:= integrate(t0326,x) +--R +--R +--R x +--R ++ 1 +--R (2) | -------------------------------------------------- d%R +--R ++ +----------------------+ +--R n | n +--R %R cosh(b log(c %R ) + a)\|cosh(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 460 +--m0326:= a0326-r0326 +--E 134 + +--S 135 of 460 +--d0326:= D(m0326,x) +--E 135 + +)clear all + +--S 136 of 460 +t0327:= 1/x/cosh(a+b*log(c*x^n))^(5/2) +--R +--R +--R 1 +--R (1) ------------------------------------------------ +--R +---------------------+ +--R n 2 | n +--R x cosh(b log(c x ) + a) \|cosh(b log(c x ) + a) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 460 +r0327:= -2/3*%i*EllipticF(1/2*%i*(a+b*log(c*x^n)),2)/b/n+_ + 2/3*sinh(a+b*log(c*x^n))/b/n/cosh(a+b*log(c*x^n))^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 137 + +--S 138 of 460 +a0327:= integrate(t0327,x) +--R +--R +--R x +--R ++ 1 +--R (2) | --------------------------------------------------- d%R +--R ++ +----------------------+ +--R n 2 | n +--R %R cosh(b log(c %R ) + a) \|cosh(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 460 +--m0327:= a0327-r0327 +--E 139 + +--S 140 of 460 +--d0327:= D(m0327,x) +--E 140 + +)clear all + +--S 141 of 460 +t0328:= sech(a+b*log(c*x^n))^(1/2)/x +--R +--R +--R +---------------------+ +--R | n +--R \|sech(b log(c x ) + a) +--R (1) ------------------------ +--R x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 460 +r0328:= -2*%i*cosh(a+b*log(c*x^n))^(1/2)*_ + EllipticF(1/2*%i*(a+b*log(c*x^n)),2)*sech(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 142 + +--S 143 of 460 +a0328:= integrate(t0328,x) +--R +--R +--R +----------------------+ +--R x | n +--R ++ \|sech(b log(c %R ) + a) +--R (2) | ------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 460 +--m0328:= a0328-r0328 +--E 144 + +--S 145 of 460 +--d0328:= D(m0328,x) +--E 145 + +)clear all + +--S 146 of 460 +t0329:= sech(a+b*log(c*x^n))^(3/2)/x +--R +--R +--R +---------------------+ +--R n | n +--R sech(b log(c x ) + a)\|sech(b log(c x ) + a) +--R (1) --------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 460 +r0329:= 2*%i*cosh(a+b*log(c*x^n))^(1/2)*_ + EllipticE(1/2*%i*(a+b*log(c*x^n)),2)*sech(a+b*log(c*x^n))^(1/2)/b/n+_ + 2*sech(a+b*log(c*x^n))^(1/2)*sinh(a+b*log(c*x^n))/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 147 + +--S 148 of 460 +a0329:= integrate(t0329,x) +--R +--R +--R +----------------------+ +--R x n | n +--R ++ sech(b log(c %R ) + a)\|sech(b log(c %R ) + a) +--R (2) | ----------------------------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 460 +--m0329:= a0329-r0329 +--E 149 + +--S 150 of 460 +--d0329:= D(m0329,x) +--E 150 + +)clear all + +--S 151 of 460 +t0330:= sech(a+b*log(c*x^n))^(5/2)/x +--R +--R +--R +---------------------+ +--R n 2 | n +--R sech(b log(c x ) + a) \|sech(b log(c x ) + a) +--R (1) ---------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 460 +r0330:= -2/3*%i*cosh(a+b*log(c*x^n))^(1/2)*_ + EllipticF(1/2*%i*(a+b*log(c*x^n)),2)*sech(a+b*log(c*x^n))^(1/2)/b/n+_ + 2/3*sech(a+b*log(c*x^n))^(3/2)*sinh(a+b*log(c*x^n))/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 152 + +--S 153 of 460 +a0330:= integrate(t0330,x) +--R +--R +--R +----------------------+ +--R x n 2 | n +--R ++ sech(b log(c %R ) + a) \|sech(b log(c %R ) + a) +--R (2) | ------------------------------------------------ d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 460 +--m0330:= a0330-r0330 +--E 154 + +--S 155 of 460 +--d0330:= D(m0330,x) +--E 155 + +)clear all + +--S 156 of 460 +t0331:= 1/x/sech(a+b*log(c*x^n))^(1/2) +--R +--R +--R 1 +--R (1) ------------------------- +--R +---------------------+ +--R | n +--R x\|sech(b log(c x ) + a) +--R Type: Expression(Integer) +--E 156 + +--S 157 of 460 +r0331:= -2*%i*cosh(a+b*log(c*x^n))^(1/2)*_ + EllipticE(1/2*%i*(a+b*log(c*x^n)),2)*sech(a+b*log(c*x^n))^(1/2)/b/n +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 157 + +--S 158 of 460 +a0331:= integrate(t0331,x) +--R +--R +--R x +--R ++ 1 +--R (2) | --------------------------- d%R +--R ++ +----------------------+ +--R | n +--R %R\|sech(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 460 +--m0331:= a0331-r0331 +--E 159 + +--S 160 of 460 +--d0331:= D(m0331,x) +--E 160 + +)clear all + +--S 161 of 460 +t0332:= 1/x/sech(a+b*log(c*x^n))^(3/2) +--R +--R +--R 1 +--R (1) ----------------------------------------------- +--R +---------------------+ +--R n | n +--R x sech(b log(c x ) + a)\|sech(b log(c x ) + a) +--R Type: Expression(Integer) +--E 161 + +--S 162 of 460 +r0332:= -2/3*%i*cosh(a+b*log(c*x^n))^(1/2)*_ + EllipticF(1/2*%i*(a+b*log(c*x^n)),2)*sech(a+b*log(c*x^n))^(1/2)/b/n+_ + 2/3*sinh(a+b*log(c*x^n))/b/n/sech(a+b*log(c*x^n))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 460 +a0332:= integrate(t0332,x) +--R +--R +--R x +--R ++ 1 +--R (2) | -------------------------------------------------- d%R +--R ++ +----------------------+ +--R n | n +--R %R sech(b log(c %R ) + a)\|sech(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 460 +--m0332:= a0332-r0332 +--E 164 + +--S 165 of 460 +--d0332:= D(m0332,x) +--E 165 + +)clear all + +--S 166 of 460 +t0333:= 1/x/sech(a+b*log(c*x^n))^(5/2) +--R +--R +--R 1 +--R (1) ------------------------------------------------ +--R +---------------------+ +--R n 2 | n +--R x sech(b log(c x ) + a) \|sech(b log(c x ) + a) +--R Type: Expression(Integer) +--E 166 + +--S 167 of 460 +r0333:= -6/5*%i*cosh(a+b*log(c*x^n))^(1/2)*_ + EllipticE(1/2*%i*(a+b*log(c*x^n)),2)*sech(a+b*log(c*x^n))^(1/2)/b/n+_ + 2/5*sinh(a+b*log(c*x^n))/b/n/sech(a+b*log(c*x^n))^(3/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 167 + +--S 168 of 460 +a0333:= integrate(t0333,x) +--R +--R +--R x +--R ++ 1 +--R (2) | --------------------------------------------------- d%R +--R ++ +----------------------+ +--R n 2 | n +--R %R sech(b log(c %R ) + a) \|sech(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 460 +--m0333:= a0333-r0333 +--E 169 + +--S 170 of 460 +--d0333:= D(m0333,x) +--E 170 + +)clear all + +--S 171 of 460 +t0334:= csch(a+b*log(c*x^n))^(1/2)/x +--R +--R +--R +---------------------+ +--R | n +--R \|csch(b log(c x ) + a) +--R (1) ------------------------ +--R x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 460 +r0334:= -2*%i*csch(a+b*log(c*x^n))^(1/2)*_ + EllipticF(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ + (%i*sinh(a+b*log(c*x^n)))^(1/2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 172 + +--S 173 of 460 +a0334:= integrate(t0334,x) +--R +--R +--R +----------------------+ +--R x | n +--R ++ \|csch(b log(c %R ) + a) +--R (2) | ------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 460 +--m0334:= a0334-r0334 +--E 174 + +--S 175 of 460 +--d0334:= D(m0334,x) +--E 175 + +)clear all + +--S 176 of 460 +t0335:= csch(a+b*log(c*x^n))^(3/2)/x +--R +--R +--R +---------------------+ +--R n | n +--R csch(b log(c x ) + a)\|csch(b log(c x ) + a) +--R (1) --------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 460 +r0335:= -2*cosh(a+b*log(c*x^n))*csch(a+b*log(c*x^n))^(1/2)/b/n-_ + 2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)/b/n/_ + csch(a+b*log(c*x^n))^(1/2)/(%i*sinh(a+b*log(c*x^n)))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 177 + +--S 178 of 460 +a0335:= integrate(t0335,x) +--R +--R +--R +----------------------+ +--R x n | n +--R ++ csch(b log(c %R ) + a)\|csch(b log(c %R ) + a) +--R (2) | ----------------------------------------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 460 +--m0335:= a0335-r0335 +--E 179 + +--S 180 of 460 +--d0335:= D(m0335,x) +--E 180 + +)clear all + +--S 181 of 460 +t0336:= csch(a+b*log(c*x^n))^(5/2)/x +--R +--R +--R +---------------------+ +--R n 2 | n +--R csch(b log(c x ) + a) \|csch(b log(c x ) + a) +--R (1) ---------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 460 +r0336:= -2/3*cosh(a+b*log(c*x^n))*csch(a+b*log(c*x^n))^(3/2)/b/n+_ + 2/3*%i*csch(a+b*log(c*x^n))^(1/2)*EllipticF(-1/4*%pi+_ + 1/2*%i*(a+b*log(c*x^n)),2)*(%i*sinh(a+b*log(c*x^n)))^(1/2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 182 + +--S 183 of 460 +a0336:= integrate(t0336,x) +--R +--R +--R +----------------------+ +--R x n 2 | n +--R ++ csch(b log(c %R ) + a) \|csch(b log(c %R ) + a) +--R (2) | ------------------------------------------------ d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 460 +--m0336:= a0336-r0336 +--E 184 + +--S 185 of 460 +--d0336:= D(m0336,x) +--E 185 + +)clear all + +--S 186 of 460 +t0337:= 1/x/csch(a+b*log(c*x^n))^(1/2) +--R +--R +--R 1 +--R (1) ------------------------- +--R +---------------------+ +--R | n +--R x\|csch(b log(c x ) + a) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 460 +r0337:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)/b/n/_ + csch(a+b*log(c*x^n))^(1/2)/(%i*sinh(a+b*log(c*x^n)))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 187 + +--S 188 of 460 +a0337:= integrate(t0337,x) +--R +--R +--R x +--R ++ 1 +--R (2) | --------------------------- d%R +--R ++ +----------------------+ +--R | n +--R %R\|csch(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 460 +--m0337:= a0337-r0337 +--E 189 + +--S 190 of 460 +--d0337:= D(m0337,x) +--E 190 + +)clear all + +--S 191 of 460 +t0338:= 1/x/csch(a+b*log(c*x^n))^(3/2) +--R +--R +--R 1 +--R (1) ----------------------------------------------- +--R +---------------------+ +--R n | n +--R x csch(b log(c x ) + a)\|csch(b log(c x ) + a) +--R Type: Expression(Integer) +--E 191 + +--S 192 of 460 +r0338:= 2/3*cosh(a+b*log(c*x^n))/b/n/csch(a+b*log(c*x^n))^(1/2)+_ + 2/3*%i*csch(a+b*log(c*x^n))^(1/2)*EllipticF(-1/4*%pi+_ + 1/2*%i*(a+b*log(c*x^n)),2)*(%i*sinh(a+b*log(c*x^n)))^(1/2)/b/n +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 192 + +--S 193 of 460 +a0338:= integrate(t0338,x) +--R +--R +--R x +--R ++ 1 +--R (2) | -------------------------------------------------- d%R +--R ++ +----------------------+ +--R n | n +--R %R csch(b log(c %R ) + a)\|csch(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 460 +--m0338:= a0338-r0338 +--E 194 + +--S 195 of 460 +--d0338:= D(m0338,x) +--E 195 + +)clear all + +--S 196 of 460 +t0339:= 1/x/csch(a+b*log(c*x^n))^(5/2) +--R +--R +--R 1 +--R (1) ------------------------------------------------ +--R +---------------------+ +--R n 2 | n +--R x csch(b log(c x ) + a) \|csch(b log(c x ) + a) +--R Type: Expression(Integer) +--E 196 + +--S 197 of 460 +r0339:= 2/5*cosh(a+b*log(c*x^n))/b/n/csch(a+b*log(c*x^n))^(3/2)+_ + 6/5*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)/b/n/_ + csch(a+b*log(c*x^n))^(1/2)/(%i*sinh(a+b*log(c*x^n)))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Complex(Fraction(Integer))) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 197 + +--S 198 of 460 +a0339:= integrate(t0339,x) +--R +--R +--R x +--R ++ 1 +--R (2) | --------------------------------------------------- d%R +--R ++ +----------------------+ +--R n 2 | n +--R %R csch(b log(c %R ) + a) \|csch(b log(c %R ) + a) +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 460 +--m0339:= a0339-r0339 +--E 199 + +--S 200 of 460 +--d0339:= D(m0339,x) +--E 200 + +)clear all + +--S 201 of 460 +t0340:= 1/2*log(a+b*x) +--R +--R +--R log(b x + a) +--R (1) ------------ +--R 2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 460 +r0340:= -1/2*x+1/2*(a+b*x)*log(a+b*x)/b +--R +--R +--R (b x + a)log(b x + a) - b x +--R (2) --------------------------- +--R 2b +--R Type: Expression(Integer) +--E 202 + +--S 203 of 460 +a0340:= integrate(t0340,x) +--R +--R +--R (b x + a)log(b x + a) - b x +--R (3) --------------------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 460 +m0340:= a0340-r0340 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 460 +d0340:= D(m0340,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 460 +t0341:= log(x^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-----+ +-+ +--R (1) log(\|x + 1 + \|x ) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 460 +r0341:= -1/2*(x/(1+x))^(1/2)*(1+x)+1/2*atanh((x/(1+x))^(1/2))+_ + x*log(x^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R +-----+ +-+ | x | x +--R 2x log(\|x + 1 + \|x ) + atanh( |----- ) + (- x - 1) |----- +--R \|x + 1 \|x + 1 +--R (2) ------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 460 random value, ok to fail +a0341:= integrate(t0341,x) +--R +--R +--R (3) +--R +-+ +-----+ 2 +-----+ +-+ +--R ((4x + 2)\|x \|x + 1 + 4x + 4x + 1)log(\|x + 1 + \|x ) +--R + +--R +-+ +-----+ 2 +--R (- 2x - 1)\|x \|x + 1 - 2x - 2x +--R / +--R +-+ +-----+ +--R 4\|x \|x + 1 + 4x + 2 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 460 random value, ok to fail +m0341:= a0341-r0341 +--R +--R +--R +-----+ +-----+ +--R +-----+ +-+ | x | x +--R - 2x log(\|x + 1 + \|x ) - atanh( |----- ) + (x + 1) |----- + 2a0341 +--R \|x + 1 \|x + 1 +--R (4) ---------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 460 random value, ok to fail +d0341:= D(m0341,x) +--R +--R +--R +-----+ +--R +-+ +-----+ +-----+ +-+ | x +-+ +-----+ +--R - 2\|x \|x + 1 log(\|x + 1 + \|x ) + |----- \|x \|x + 1 - x +--R \|x + 1 +--R (5) -------------------------------------------------------------- +--R +-+ +-----+ +--R 2\|x \|x + 1 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 460 +t0342:= log(abs(a^2-x^2)) +--R +--R +--R 2 2 +--R (1) log(abs(x - a )) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 460 +r0342:= -2*x+2*a*atanh(x/a)+1/2*x*log((a^2-x^2)^2) +--R +--R +--R 4 2 2 4 x +--R x log(x - 2a x + a ) + 4a atanh(-) - 4x +--R a +--R (2) ----------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 460 +a0342:= integrate(t0342,x) +--R +--R +--R 2 2 +--R (3) x log(abs(x - a )) + a log(x + a) - a log(x - a) - 2x +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 460 +m0342:= a0342-r0342 +--R +--R +--R (4) +--R 2 2 4 2 2 4 +--R 2x log(abs(x - a )) - x log(x - 2a x + a ) + 2a log(x + a) +--R + +--R x +--R - 2a log(x - a) - 4a atanh(-) +--R a +--R / +--R 2 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 460 +d0342:= D(m0342,x) +--R +--R +--R 2 2 4 2 2 4 +--R 2log(abs(x - a )) - log(x - 2a x + a ) +--R (5) ----------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 460 +t0343:= log((-11+5*x)/(5+76*x)) +--R +--R +--R 5x - 11 +--R (1) log(-------) +--R 76x + 5 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 460 +r0343:= -11/5*log(11-5*x)+x*log((-11+5*x)/(5+76*x))-5/76*log(5+76*x) +--R +--R +--R 5x - 11 +--R - 25log(76x + 5) + 380x log(-------) - 836log(- 5x + 11) +--R 76x + 5 +--R (2) -------------------------------------------------------- +--R 380 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 460 +a0343:= integrate(t0343,x) +--R +--R +--R 5x - 11 +--R - 25log(76x + 5) - 836log(5x - 11) + 380x log(-------) +--R 76x + 5 +--R (3) ------------------------------------------------------ +--R 380 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 460 +m0343:= a0343-r0343 +--R +--R +--R - 11log(5x - 11) + 11log(- 5x + 11) +--R (4) ----------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 460 +d0343:= D(m0343,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 460 +t0344:= log((1+x)/(-1+x))/x^2 +--R +--R +--R x + 1 +--R log(-----) +--R x - 1 +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 221 + +--S 222 of 460 +r0344:= 2*log(x)-log(-(1+x)/(1-x))/x-log(1-x^2) +--R +--R +--R x + 1 2 +--R 2x log(x) - log(-----) - x log(- x + 1) +--R x - 1 +--R (2) ---------------------------------------- +--R x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 460 +a0344:= integrate(t0344,x) +--R +--R +--R 2 x + 1 +--R - x log(x - 1) + 2x log(x) - log(-----) +--R x - 1 +--R (3) ---------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 460 +m0344:= a0344-r0344 +--R +--R +--R 2 2 +--R (4) - log(x - 1) + log(- x + 1) +--R Type: Expression(Integer) +--E 224 + +--S 225 of 460 +d0344:= D(m0344,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 460 +t0345:= x*log((1+x)/x^2) +--R +--R +--R x + 1 +--R (1) x log(-----) +--R 2 +--R x +--R Type: Expression(Integer) +--E 226 + +--S 227 of 460 +r0345:= 1/2*x+1/4*x^2-1/2*log(1+x)+1/2*x^2*log((1+x)/x^2) +--R +--R +--R 2 x + 1 2 +--R - 2log(x + 1) + 2x log(-----) + x + 2x +--R 2 +--R x +--R (2) --------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 460 +a0345:= integrate(t0345,x) +--R +--R +--R 2 x + 1 2 +--R - 2log(x + 1) + 2x log(-----) + x + 2x +--R 2 +--R x +--R (3) --------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 460 +m0345:= a0345-r0345 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 460 +d0345:= D(m0345,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 460 +t0346:= (a+b*x)^n*log(a+b*x) +--R +--R +--R n +--R (1) log(b x + a)(b x + a) +--R Type: Expression(Integer) +--E 231 + +--S 232 of 460 +r0346:= 1/b/(1+n)^2*(a+b*x)^(1+n)*(-1+log(a+b*x)+n*log(a+b*x)) +--R +--R +--R n + 1 +--R ((n + 1)log(b x + a) - 1)(b x + a) +--R (2) --------------------------------------- +--R 2 +--R b n + 2b n + b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 460 +a0346:= integrate(t0346,x) +--R +--R +--R n log(b x + a) +--R (((b n + b)x + a n + a)log(b x + a) - b x - a)%e +--R (3) -------------------------------------------------------------- +--R 2 +--R b n + 2b n + b +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 460 +m0346:= a0346-r0346 +--R +--R +--R (4) +--R n log(b x + a) +--R (((b n + b)x + a n + a)log(b x + a) - b x - a)%e +--R + +--R n + 1 +--R ((- n - 1)log(b x + a) + 1)(b x + a) +--R / +--R 2 +--R b n + 2b n + b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 460 +d0346:= D(m0346,x) +--R +--R +--R (5) +--R n log(b x + a) n + 1 +--R ((b n + b)x + a n + a)log(b x + a)%e - (b x + a) +--R + +--R n +--R (((- b n - b)x - a n - a)log(b x + a) + b x + a)(b x + a) +--R / +--R (b n + b)x + a n + a +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 460 +t0347:= log((a+b*x)/(c+d*x))/x +--R +--R +--R b x + a +--R log(-------) +--R d x + c +--R (1) ------------ +--R x +--R Type: Expression(Integer) +--E 236 + +--S 237 of 460 +r0347:= -log((b*c-a*d)/b/(c+d*x))*log((a+b*x)/(c+d*x))+_ + log(-(b*c-a*d)*x/a/(c+d*x))*log((a+b*x)/(c+d*x))-_ + polylog(2,d*(x+a/b)/(c+d*x))+polylog(2,c*(1+b*x/a)/(c+d*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 460 +a0347:= integrate(t0347,x) +--R +--R +--R %R b + a +--R x log(--------) +--R ++ %R d + c +--R (2) | ------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 460 +--m0347:= a0347-r0347 +--E 239 + +--S 240 of 460 +--d0347:= D(m0347,x) +--E 240 + +)clear all + +--S 241 of 460 +t0348:= log((a+b*x)/(c+d*x))^2/x +--R +--R +--R b x + a 2 +--R log(-------) +--R d x + c +--R (1) ------------- +--R x +--R Type: Expression(Integer) +--E 241 + +--S 242 of 460 +r0348:= -log((b*c-a*d)/b/(c+d*x))*log((a+b*x)/(c+d*x))^2+_ + log(-(b*c-a*d)*x/a/(c+d*x))*log((a+b*x)/(c+d*x))^2-_ + 2*log((a+b*x)/(c+d*x))*polylog(2,d*(x+a/b)/(c+d*x))+_ + 2*log((a+b*x)/(c+d*x))*polylog(2,c*(1+b*x/a)/(c+d*x))-_ + 2*polylog(3,c*(a+b*x)/a/(c+d*x))+2*polylog(3,d*(a+b*x)/b/(c+d*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 242 + +--S 243 of 460 +a0348:= integrate(t0348,x) +--R +--R +--R %R b + a 2 +--R x log(--------) +--R ++ %R d + c +--R (2) | -------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 460 +--m0348:= a0348-r0348 +--E 244 + +--S 245 of 460 +--d0348:= D(m0348,x) +--E 245 + +)clear all + +--S 246 of 460 +t0349:= log(a*log(b*x^n)^p) +--R +--R +--R n p +--R (1) log(a log(b x ) ) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 460 +r0349:= -p*x*Ei(1/n*log(b*x^n))/((b*x^n)^(1/n))+x*log(a*log(b*x^n)^p) +--R +--R +--R 1 +--R - n +--R n n n p log(b x ) +--R x (b x ) log(a log(b x ) ) - p x Ei(---------) +--R n +--R (2) ---------------------------------------------- +--R 1 +--R - +--R n n +--R (b x ) +--R Type: Expression(Integer) +--E 247 + +--S 248 of 460 +a0349:= integrate(t0349,x) +--R +--R +--R x +--R ++ n p +--R (3) | log(a log(b %R ) )d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 460 +--m0349:= a0349-r0349 +--E 249 + +--S 250 of 460 +--d0349:= D(m0349,x) +--E 250 + +)clear all + +--S 251 of 460 +t0350:= x^m*log(a*log(b*x)^p) +--R +--R +--R m p +--R (1) x log(a log(b x) ) +--R Type: Expression(Integer) +--E 251 + +--S 252 of 460 +r0350:= -1/b/(1+m)*(p*x^m*(b*x)^(-m)*Ei((1+m)*log(b*x))-_ + x^(1+m)*log(a*log(b*x)^p)*b) +--R +--R +--R m + 1 p m - m +--R b x log(a log(b x) ) - p x (b x) Ei((m + 1)log(b x)) +--R (2) ---------------------------------------------------------- +--R b m + b +--R Type: Expression(Integer) +--E 252 + +--S 253 of 460 +a0350:= integrate(t0350,x) +--R +--R +--R x +--R ++ m p +--R (3) | %R log(a log(%R b) )d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 460 +--m0350:= a0350-r0350 +--E 254 + +--S 255 of 460 +--d0350:= D(m0350,x) +--E 255 + +)clear all + +--S 256 of 460 +t0351:= x^m*log(a*log(b*x^n)^p) +--R +--R +--R m n p +--R (1) x log(a log(b x ) ) +--R Type: Expression(Integer) +--E 256 + +--S 257 of 460 +r0351:= 1/(1+m)*x^(1+m)*(-p*Ei((1+m)/n*log(b*x^n))*(b*x^n)^(-(1+m)/n)+_ + log(a*log(b*x^n)^p)) +--R +--R +--R - m - 1 +--R ------- n +--R m + 1 n p m + 1 n n (m + 1)log(b x ) +--R x log(a log(b x ) ) - p x (b x ) Ei(----------------) +--R n +--R (2) ------------------------------------------------------------------- +--R m + 1 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 460 +a0351:= integrate(t0351,x) +--R +--R +--R x +--R ++ m n p +--R (3) | %R log(a log(b %R ) )d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 460 +--m0351:= a0351-r0351 +--E 259 + +--S 260 of 460 +--d0351:= D(m0351,x) +--E 260 + +)clear all + +--S 261 of 460 +t0352:= log(x)/(a+b*log(x))^(1/2) +--R +--R +--R log(x) +--R (1) --------------- +--R +------------+ +--R \|b log(x) + a +--R Type: Expression(Integer) +--E 261 + +--S 262 of 460 +r0352:= -1/2*(2*a+b)*%pi^(1/2)*erfi((a+b*log(x))^(1/2)/b^(1/2))/_ + (exp(1)^(a/b))/b^(3/2)+x*(a+b*log(x))^(1/2)/b +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 262 + +--S 263 of 460 +a0352:= integrate(t0352,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 263 + +--S 264 of 460 +--m0352:= a0352-r0352 +--E 264 + +--S 265 of 460 +--d0352:= D(m0352,x) +--E 265 + +)clear all + +--S 266 of 460 +t0353:= log(x)/(a-b*log(x))^(1/2) +--R +--R +--R log(x) +--R (1) ----------------- +--R +--------------+ +--R \|- b log(x) + a +--R Type: Expression(Integer) +--E 266 + +--S 267 of 460 +r0353:= -1/2*(2*a-b)*exp(1)^(a/b)*%pi^(1/2)*erf((a-b*log(x))^(1/2)/_ + b^(1/2))/b^(3/2)-x*(a-b*log(x))^(1/2)/b +--R +--R +--R a +--R - +--------------+ +--R b +---+ \|- b log(x) + a +-+ +--------------+ +--R (b - 2a)%e \|%pi erf(-----------------) - 2x\|b \|- b log(x) + a +--R +-+ +--R \|b +--R (2) ----------------------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 267 + +--S 268 of 460 +a0353:= integrate(t0353,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 268 + +--S 269 of 460 +--m0353:= a0353-r0353 +--E 269 + +--S 270 of 460 +--d0353:= D(m0353,x) +--E 270 + +)clear all + +--S 271 of 460 +t0354:= (A+B*log(x))/(a+b*log(x))^(1/2) +--R +--R +--R B log(x) + A +--R (1) --------------- +--R +------------+ +--R \|b log(x) + a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 460 +r0354:= 1/2*(2*A*b-(2*a+b)*B)*%pi^(1/2)*erfi((a+b*log(x))^(1/2)/b^(1/2))/_ + (exp(1)^(a/b))/b^(3/2)+B*x*(a+b*log(x))^(1/2)/b +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 272 + +--S 273 of 460 +a0354:= integrate(t0354,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 273 + +--S 274 of 460 +--m0354:= a0354-r0354 +--E 274 + +--S 275 of 460 +--d0354:= D(m0354,x) +--E 275 + +)clear all + +--S 276 of 460 +t0355:= (A+B*log(x))/(a-b*log(x))^(1/2) +--R +--R +--R B log(x) + A +--R (1) ----------------- +--R +--------------+ +--R \|- b log(x) + a +--R Type: Expression(Integer) +--E 276 + +--S 277 of 460 +r0355:= -1/2*(2*A*b+(2*a-b)*B)*exp(1)^(a/b)*%pi^(1/2)*_ + erf((a-b*log(x))^(1/2)/b^(1/2))/b^(3/2)-B*x*(a-b*log(x))^(1/2)/b +--R +--R +--R (2) +--R a +--R - +--------------+ +--R b +---+ \|- b log(x) + a +-+ +--------------+ +--R ((B - 2A)b - 2B a)%e \|%pi erf(-----------------) - 2B x\|b \|- b log(x) + a +--R +-+ +--R \|b +--R ----------------------------------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 277 + +--S 278 of 460 +a0355:= integrate(t0355,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 278 + +--S 279 of 460 +--m0355:= a0355-r0355 +--E 279 + +--S 280 of 460 +--d0355:= D(m0355,x) +--E 280 + +)clear all + +--S 281 of 460 +t0356:= log(x)*sin(a+b*x) +--R +--R +--R (1) log(x)sin(b x + a) +--R Type: Expression(Integer) +--E 281 + +--S 282 of 460 +r0356:= (cos(a)*Ci(b*x)-log(x)*cos(a+b*x)-sin(a)*Si(b*x))/b +--R +--R +--R - Si(b x)sin(a) - cos(b x + a)log(x) + Ci(b x)cos(a) +--R (2) ---------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 282 + +--S 283 of 460 +a0356:= integrate(t0356,x) +--R +--R +--R x +--R ++ +--R (3) | log(%R)sin(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 460 +--m0356:= a0356-r0356 +--E 284 + +--S 285 of 460 +--d0356:= D(m0356,x) +--E 285 + +)clear all + +--S 286 of 460 +t0357:= log(x)*sin(a+b*x)^2 +--R +--R +--R 2 +--R (1) log(x)sin(b x + a) +--R Type: Expression(Integer) +--E 286 + +--S 287 of 460 +r0357:= -1/4*(2*b*x-Ci(2*b*x)*sin(2*a)-2*log(x)*b*x+2*log(x)*cos(a+b*x)*_ + sin(a+b*x)-cos(2*a)*Si(2*b*x))/b +--R +--R +--R (2) +--R - 2cos(b x + a)log(x)sin(b x + a) + Ci(2b x)sin(2a) + 2b x log(x) +--R + +--R Si(2b x)cos(2a) - 2b x +--R / +--R 4b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 460 +a0357:= integrate(t0357,x) +--R +--R +--R x +--R ++ 2 +--R (3) | log(%R)sin(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 460 +--m0357:= a0357-r0357 +--E 289 + +--S 290 of 460 +--d0357:= D(m0357,x) +--E 290 + +)clear all + +--S 291 of 460 +t0358:= log(x)*sin(a+b*x)^3 +--R +--R +--R 3 +--R (1) log(x)sin(b x + a) +--R Type: Expression(Integer) +--E 291 + +--S 292 of 460 +r0358:= 1/12*(9*cos(a)*Ci(b*x)-cos(3*a)*Ci(3*b*x)-12*log(x)*cos(a+b*x)+_ + 4*log(x)*cos(a+b*x)^3-9*sin(a)*Si(b*x)+sin(3*a)*Si(3*b*x))/b +--R +--R +--R (2) +--R Si(3b x)sin(3a) - 9Si(b x)sin(a) +--R + +--R 3 +--R (4cos(b x + a) - 12cos(b x + a))log(x) - Ci(3b x)cos(3a) + 9Ci(b x)cos(a) +--R / +--R 12b +--R Type: Expression(Integer) +--E 292 + +--S 293 of 460 +a0358:= integrate(t0358,x) +--R +--R +--R x +--R ++ 3 +--R (3) | log(%R)sin(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 460 +--m0358:= a0358-r0358 +--E 294 + +--S 295 of 460 +--d0358:= D(m0358,x) +--E 295 + +)clear all + +--S 296 of 460 +t0359:= log(x)*cos(a+b*x) +--R +--R +--R (1) cos(b x + a)log(x) +--R Type: Expression(Integer) +--E 296 + +--S 297 of 460 +r0359:= -(Ci(b*x)*sin(a)-log(x)*sin(a+b*x)+cos(a)*Si(b*x))/b +--R +--R +--R log(x)sin(b x + a) - Ci(b x)sin(a) - Si(b x)cos(a) +--R (2) -------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 297 + +--S 298 of 460 +a0359:= integrate(t0359,x) +--R +--R +--R x +--R ++ +--R (3) | cos(%R b + a)log(%R)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 460 +--m0359:= a0359-r0359 +--E 299 + +--S 300 of 460 +--d0359:= D(m0359,x) +--E 300 + +)clear all + +--S 301 of 460 +t0360:= log(x)*cos(a+b*x)^2 +--R +--R +--R 2 +--R (1) cos(b x + a) log(x) +--R Type: Expression(Integer) +--E 301 + +--S 302 of 460 +r0360:= 1/4*(-2*b*x-Ci(2*b*x)*sin(2*a)+2*log(x)*b*x+2*log(x)*cos(a+b*x)*_ + sin(a+b*x)-cos(2*a)*Si(2*b*x))/b +--R +--R +--R (2) +--R 2cos(b x + a)log(x)sin(b x + a) - Ci(2b x)sin(2a) + 2b x log(x) +--R + +--R - Si(2b x)cos(2a) - 2b x +--R / +--R 4b +--R Type: Expression(Integer) +--E 302 + +--S 303 of 460 +a0360:= integrate(t0360,x) +--R +--R +--R x +--R ++ 2 +--R (3) | cos(%R b + a) log(%R)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 460 +--m0360:= a0360-r0360 +--E 304 + +--S 305 of 460 +--d0360:= D(m0360,x) +--E 305 + +)clear all + +--S 306 of 460 +t0361:= log(x)*cos(a+b*x)^3 +--R +--R +--R 3 +--R (1) cos(b x + a) log(x) +--R Type: Expression(Integer) +--E 306 + +--S 307 of 460 +r0361:= -1/12*(9*Ci(b*x)*sin(a)+Ci(3*b*x)*sin(3*a)-8*log(x)*sin(a+b*x)-_ + 4*log(x)*sin(a+b*x)*cos(a+b*x)^2+9*cos(a)*Si(b*x)+cos(3*a)*Si(3*b*x))/b +--R +--R +--R (2) +--R 2 +--R (4cos(b x + a) + 8)log(x)sin(b x + a) - Ci(3b x)sin(3a) - 9Ci(b x)sin(a) +--R + +--R - Si(3b x)cos(3a) - 9Si(b x)cos(a) +--R / +--R 12b +--R Type: Expression(Integer) +--E 307 + +--S 308 of 460 +a0361:= integrate(t0361,x) +--R +--R +--R x +--R ++ 3 +--R (3) | cos(%R b + a) log(%R)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 460 +--m0361:= a0361-r0361 +--E 309 + +--S 310 of 460 +--d0361:= D(m0361,x) +--E 310 + +)clear all + +--S 311 of 460 +t0362:= log(x)*sinh(a+b*x) +--R +--R +--R (1) log(x)sinh(b x + a) +--R Type: Expression(Integer) +--E 311 + +--S 312 of 460 +r0362:= (-cosh(a)*Chi(b*x)+log(x)*cosh(a+b*x)-sinh(a)*Shi(b*x))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 312 + +--S 313 of 460 +a0362:= integrate(t0362,x) +--R +--R +--R x +--R ++ +--R (2) | log(%R)sinh(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 460 +--m0362:= a0362-r0362 +--E 314 + +--S 315 of 460 +--d0362:= D(m0362,x) +--E 315 + +)clear all + +--S 316 of 460 +t0363:= log(x)*sinh(a+b*x)^3 +--R +--R +--R 3 +--R (1) log(x)sinh(b x + a) +--R Type: Expression(Integer) +--E 316 + +--S 317 of 460 +r0363:= 1/12*(9*cosh(a)*Chi(b*x)-cosh(3*a)*Chi(3*b*x)-12*log(x)*cosh(a+b*x)+_ + 4*log(x)*cosh(a+b*x)^3+9*sinh(a)*Shi(b*x)-sinh(3*a)*Shi(3*b*x))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 317 + +--S 318 of 460 +a0363:= integrate(t0363,x) +--R +--R +--R x +--R ++ 3 +--R (2) | log(%R)sinh(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 460 +--m0363:= a0363-r0363 +--E 319 + +--S 320 of 460 +--d0363:= D(m0363,x) +--E 320 + +)clear all + +--S 321 of 460 +t0364:= log(x)*cosh(a+b*x) +--R +--R +--R (1) cosh(b x + a)log(x) +--R Type: Expression(Integer) +--E 321 + +--S 322 of 460 +r0364:= (-Chi(b*x)*sinh(a)+log(x)*sinh(a+b*x)-cosh(a)*Shi(b*x))/b +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 322 + +--S 323 of 460 +a0364:= integrate(t0364,x) +--R +--R +--R x +--R ++ +--R (2) | cosh(%R b + a)log(%R)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 460 +--m0364:= a0364-r0364 +--E 324 + +--S 325 of 460 +--d0364:= D(m0364,x) +--E 325 + +)clear all + +--S 326 of 460 +t0365:= log(x)*cosh(a+b*x)^3 +--R +--R +--R 3 +--R (1) cosh(b x + a) log(x) +--R Type: Expression(Integer) +--E 326 + +--S 327 of 460 +r0365:= 1/12/b*(-9*Chi(b*x)*sinh(a)-Chi(3*b*x)*sinh(3*a)+8*log(x)*_ + sinh(a+b*x)+4*log(x)*sinh(a+b*x)*cosh(a+b*x)^2-_ + 9*cosh(a)*Shi(b*x)-cosh(3*a)*Shi(3*b*x)) +--R +--R There are no library operations named Chi +--R Use HyperDoc Browse or issue +--R )what op Chi +--R to learn if there is any operation containing " Chi " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named Chi +--R with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 327 + +--S 328 of 460 +a0365:= integrate(t0365,x) +--R +--R +--R x +--R ++ 3 +--R (2) | cosh(%R b + a) log(%R)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 460 +--m0365:= a0365-r0365 +--E 329 + +--S 330 of 460 +--d0365:= D(m0365,x) +--E 330 + +)clear all + +--S 331 of 460 +t0366:= x*(4+x^2)^(1/2)*log(x) +--R +--R +--R +------+ +--R | 2 +--R (1) x log(x)\|x + 4 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 460 +r0366:= -4/3*(4+x^2)^(1/2)-1/9*(4+x^2)^(3/2)+8/3*atanh(1/2*(4+x^2)^(1/2))+_ + 1/3*(4+x^2)^(3/2)*log(x) +--R +--R +--R +------+ +--R | 2 +------+ +--R \|x + 4 2 2 | 2 +--R 24atanh(---------) + ((3x + 12)log(x) - x - 16)\|x + 4 +--R 2 +--R (2) ---------------------------------------------------------- +--R 9 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 460 +a0366:= integrate(t0366,x) +--R +--R +--R (3) +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((24x + 24)\|x + 4 - 24x - 72x)log(\|x + 4 - x + 2) +--R + +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((- 24x - 24)\|x + 4 + 24x + 72x)log(\|x + 4 - x - 2) +--R + +--R +------+ +--R 5 3 5 3 | 2 +--R ((- 3x - 21x - 36x)log(x) + x + 19x + 48x)\|x + 4 +--R + +--R 6 4 2 6 4 2 +--R (3x + 27x + 72x + 48)log(x) - x - 21x - 84x - 64 +--R / +--R +------+ +--R 2 | 2 3 +--R (9x + 9)\|x + 4 - 9x - 27x +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 460 +m0366:= a0366-r0366 +--R +--R +--R +------+ +--R +------+ +------+ | 2 +--R | 2 | 2 \|x + 4 +--R 8log(\|x + 4 - x + 2) - 8log(\|x + 4 - x - 2) - 8atanh(---------) +--R 2 +--R (4) --------------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 460 +d0366:= D(m0366,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 460 +t0367:= x*log(x)/(-1+x^2)^(1/2) +--R +--R +--R x log(x) +--R (1) --------- +--R +------+ +--R | 2 +--R \|x - 1 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 460 +r0367:= -(-1+x^2)^(1/2)+atan((-1+x^2)^(1/2))+(-1+x^2)^(1/2)*log(x) +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (2) atan(\|x - 1 ) + (log(x) - 1)\|x - 1 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 460 +a0367:= integrate(t0367,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R (2\|x - 1 - 2x)atan(\|x - 1 - x) + (- x log(x) + x)\|x - 1 +--R + +--R 2 2 +--R (x - 1)log(x) - x + 1 +--R / +--R +------+ +--R | 2 +--R \|x - 1 - x +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 460 +m0367:= a0367-r0367 +--R +--R +--R +------+ +------+ +--R | 2 | 2 +--R (4) - atan(\|x - 1 ) + 2atan(\|x - 1 - x) +--R Type: Expression(Integer) +--E 339 + +--S 340 of 460 +d0367:= D(m0367,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 460 +t0368:= log(cos(x))*tan(x) +--R +--R +--R (1) tan(x)log(cos(x)) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 460 +r0368:= -1/2*log(cos(x))^2 +--R +--R +--R 2 +--R log(cos(x)) +--R (2) - ------------ +--R 2 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 460 +a0368:= integrate(t0368,x) +--R +--R +--R 2 +--R log(cos(x)) +--R (3) - ------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 460 +m0368:= a0368-r0368 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 460 +d0368:= D(m0368,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 460 +t0369:= cos(x)*log(cos(x)) +--R +--R +--R (1) cos(x)log(cos(x)) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 460 +r0369:= atanh(sin(x))-sin(x)+log(cos(x))*sin(x) +--R +--R +--R (2) sin(x)log(cos(x)) + atanh(sin(x)) - sin(x) +--R Type: Expression(Integer) +--E 347 + +--S 348 of 460 +a0369:= integrate(t0369,x) +--R +--R +--R log(sin(x) + 1) - log(sin(x) - 1) + 2sin(x)log(cos(x)) - 2sin(x) +--R (3) ---------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 460 +m0369:= a0369-r0369 +--R +--R +--R log(sin(x) + 1) - log(sin(x) - 1) - 2atanh(sin(x)) +--R (4) -------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 460 +d0369:= D(m0369,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 460 +t0370:= log(sin(x))*sin(x)^2 +--R +--R +--R 2 +--R (1) sin(x) log(sin(x)) +--R Type: Expression(Integer) +--E 351 + +--S 352 of 460 +r0370:= 1/4*x+1/4*%i*x^2-1/2*x*log(1-exp(1)^(2*%i*x))+_ + 1/4*%i*polylog(2,exp(1)^(2*%i*x))+1/4*cos(x)*sin(x)+_ + 1/2*log(sin(x))*(x-cos(x)*sin(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 352 + +--S 353 of 460 +a0370:= integrate(t0370,x) +--R +--R +--R x +--R ++ 2 +--R (2) | sin(%R) log(sin(%R))d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 460 +--m0370:= a0370-r0370 +--E 354 + +--S 355 of 460 +--d0370:= D(m0370,x) +--E 355 + +)clear all + +--S 356 of 460 +t0371:= log(sin(x))*sin(x)^3 +--R +--R +--R 3 +--R (1) sin(x) log(sin(x)) +--R Type: Expression(Integer) +--E 356 + +--S 357 of 460 +r0371:= -2/3*atanh(cos(x))+2/3*cos(x)-1/9*cos(x)^3-_ + 1/3*cos(x)*(3-cos(x)^2)*log(sin(x)) +--R +--R +--R 3 3 +--R (3cos(x) - 9cos(x))log(sin(x)) - 6atanh(cos(x)) - cos(x) + 6cos(x) +--R (2) -------------------------------------------------------------------- +--R 9 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 460 +a0371:= integrate(t0371,x) +--R +--R +--R (3) +--R 3 +--R (3cos(x) - 9cos(x))log(sin(x)) - 3log(cos(x) + 1) + 3log(cos(x) - 1) +--R + +--R 3 +--R - cos(x) + 6cos(x) +--R / +--R 9 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 460 +--m0371:= a0371-r0371 +--E 359 + +--S 360 of 460 +--d0371:= D(m0371,x) +--E 360 + +)clear all + +--S 361 of 460 +t0372:= log(sin(x^(1/2))) +--R +--R +--R +-+ +--R (1) log(sin(\|x )) +--R Type: Expression(Integer) +--E 361 + +--S 362 of 460 +r0372:= 1/3*%i*x^(3/2)-x*log(1-exp(2*%i*x^(1/2)))+x*log(sin(x^(1/2)))+_ + %i*x^(1/2)*polylog(2,exp(2*%i*x^(1/2)))-_ + 1/2*polylog(3,exp(2*%i*x^(1/2))) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 362 + +--S 363 of 460 +a0372:= integrate(t0372,x) +--R +--R +--R x +--R ++ +--+ +--R (2) | log(sin(\|%R ))d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 460 +--m0372:= a0372-r0372 +--E 364 + +--S 365 of 460 +--d0372:= D(m0372,x) +--E 365 + +)clear all + +--S 366 of 460 +t0373:= log(sin(x))*csc(x)^2 +--R +--R +--R 2 +--R (1) csc(x) log(sin(x)) +--R Type: Expression(Integer) +--E 366 + +--S 367 of 460 +r0373:= -x-cot(x)-cot(x)*log(sin(x)) +--R +--R +--R (2) - cot(x)log(sin(x)) - cot(x) - x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 460 +a0373:= integrate(t0373,x) +--R +--R +--R 2 +--R cos(x)sin(x)log(sin(x)) + cos(x)sin(x) - x cos(x) + x +--R (3) ------------------------------------------------------ +--R 2 +--R cos(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 460 +m0373:= a0373-r0373 +--R +--R +--R (4) +--R 2 +--R (cos(x)sin(x) + (cos(x) - 1)cot(x))log(sin(x)) + cos(x)sin(x) +--R + +--R 2 +--R (cos(x) - 1)cot(x) +--R / +--R 2 +--R cos(x) - 1 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 460 +d0373:= D(m0373,x) +--R +--R +--R (5) +--R 2 3 +--R (cos(x) + 1)sin(x) +--R + +--R 4 2 2 2 +--R ((- cos(x) + 2cos(x) - 1)cot(x) + cos(x) - 1)sin(x) +--R * +--R log(sin(x)) +--R + +--R 2 3 +--R (cos(x) + 1)sin(x) +--R + +--R 4 2 2 4 +--R ((- cos(x) + 2cos(x) - 1)cot(x) + cos(x) - 1)sin(x) +--R + +--R 5 3 +--R (cos(x) - 2cos(x) + cos(x))cot(x) +--R / +--R 4 2 +--R (cos(x) - 2cos(x) + 1)sin(x) +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 460 +t0374:= x*log(x)/(a+b*x+c*x^2) +--R +--R +--R x log(x) +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 371 + +--S 372 of 460 +r0374:= 1/2*(1-b/(b^2-4*a*c)^(1/2))*log(x)*_ + log((b-(b^2-4*a*c)^(1/2)+2*c*x)/(b-(b^2-4*a*c)^(1/2)))/c+_ + 1/2*(1+b/(b^2-4*a*c)^(1/2))*log(x)*log((b+(b^2-_ + 4*a*c)^(1/2)+2*c*x)/(b+(b^2-4*a*c)^(1/2)))/c+_ + 1/2*(1-b/(b^2-4*a*c)^(1/2))*_ + polylog(2,1-(b-(b^2-4*a*c)^(1/2)+2*c*x)/(b-(b^2-4*a*c)^(1/2)))/c+_ + 1/2*(1+b/(b^2-4*a*c)^(1/2))*_ + polylog(2,1-(b+(b^2-4*a*c)^(1/2)+2*c*x)/(b+(b^2-4*a*c)^(1/2)))/c +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 372 + +--S 373 of 460 +a0374:= integrate(t0374,x) +--R +--R +--R x +--R ++ %R log(%R) +--R (2) | --------------- d%R +--R ++ 2 +--R %R c + %R b + a +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 460 +--m0374:= a0374-r0374 +--E 374 + +--S 375 of 460 +--d0374:= D(m0374,x) +--E 375 + +)clear all + +--S 376 of 460 +t0375:= x^2*log(x)/(a+b*x+c*x^2) +--R +--R +--R 2 +--R x log(x) +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 376 + +--S 377 of 460 +r0375:= -x/c+x*log(x)/c+1/4*(b-(b^2-4*a*c)^(1/2))^2*log(x)*_ + log((b-(b^2-4*a*c)^(1/2)+2*c*x)/(b-(b^2-4*a*c)^(1/2)))/c^2/_ + (b^2-4*a*c)^(1/2)-1/4*(b+(b^2-4*a*c)^(1/2))^2*log(x)*_ + log((b+(b^2-4*a*c)^(1/2)+2*c*x)/(b+(b^2-4*a*c)^(1/2)))/c^2/_ + (b^2-4*a*c)^(1/2)+1/4*(b-(b^2-4*a*c)^(1/2))^2*_ + polylog(2,1-(b-(b^2-4*a*c)^(1/2)+2*c*x)/(b-(b^2-4*a*c)^(1/2)))/_ + c^2/(b^2-4*a*c)^(1/2)-1/4*(b+(b^2-4*a*c)^(1/2))^2*_ + polylog(2,1-(b+(b^2-4*a*c)^(1/2)+2*c*x)/(b+(b^2-4*a*c)^(1/2)))/_ + c^2/(b^2-4*a*c)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 377 + +--S 378 of 460 +a0375:= integrate(t0375,x) +--R +--R +--R x 2 +--R ++ %R log(%R) +--R (2) | --------------- d%R +--R ++ 2 +--R %R c + %R b + a +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 460 +--m0375:= a0375-r0375 +--E 379 + +--S 380 of 460 +--d0375:= D(m0375,x) +--E 380 + +)clear all + +--S 381 of 460 +t0376:= log(x)/x^2/(a+b*x+c*x^2) +--R +--R +--R log(x) +--R (1) ------------------ +--R 4 3 2 +--R c x + b x + a x +--R Type: Expression(Integer) +--E 381 + +--S 382 of 460 +r0376:= -2*c/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/x+_ + 2*c/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/x-2*c*log(x)/_ + (b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/x+_ + 2*c*log(x)/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))/x-_ + 2*c^2*log(x)^2/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))^2+_ + 2*c^2*log(x)^2/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))^2+_ + 4*c^2*log(x)*log((b-(b^2-4*a*c)^(1/2)+2*c*x)/_ + (b-(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))^2-_ + 4*c^2*log(x)*log((b+(b^2-4*a*c)^(1/2)+2*c*x)/_ + (b+(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))^2+_ + 4*c^2*polylog(2,1-(b-(b^2-4*a*c)^(1/2)+2*c*x)/_ + (b-(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))^2-_ + 4*c^2*polylog(2,1-(b+(b^2-4*a*c)^(1/2)+2*c*x)/_ + (b+(b^2-4*a*c)^(1/2)))/(b^2-4*a*c)^(1/2)/(b+(b^2-4*a*c)^(1/2))^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 382 + +--S 383 of 460 +a0376:= integrate(t0376,x) +--R +--R +--R x +--R ++ log(%R) +--R (2) | ------------------ d%R +--R ++ 4 3 2 +--R %R c + %R b + %R a +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 460 +--m0376:= a0376-r0376 +--E 384 + +--S 385 of 460 +--d0376:= D(m0376,x) +--E 385 + +)clear all + +--S 386 of 460 +t0377:= (2-log(x))*(3+log(x))^2/x +--R +--R +--R 3 2 +--R - log(x) - 4log(x) + 3log(x) + 18 +--R (1) ----------------------------------- +--R x +--R Type: Expression(Integer) +--E 386 + +--S 387 of 460 +r0377:= -1/12*(3+log(x))^3*(-11+3*log(x)) +--R +--R +--R 4 3 2 +--R - 3log(x) - 16log(x) + 18log(x) + 216log(x) + 297 +--R (2) ---------------------------------------------------- +--R 12 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 460 +a0377:= integrate(t0377,x) +--R +--R +--R 4 3 2 +--R - 3log(x) - 16log(x) + 18log(x) + 216log(x) +--R (3) ---------------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 460 +m0377:= a0377-r0377 +--R +--R +--R 99 +--R (4) - -- +--R 4 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 460 +d0377:= D(m0377,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 460 +t0378:= (1+log(x))^(1/2)/x/log(x) +--R +--R +--R +----------+ +--R \|log(x) + 1 +--R (1) ------------- +--R x log(x) +--R Type: Expression(Integer) +--E 391 + +--S 392 of 460 +r0378:= -2*atanh((1+log(x))^(1/2))+2*(1+log(x))^(1/2) +--R +--R +--R +----------+ +----------+ +--R (2) - 2atanh(\|log(x) + 1 ) + 2\|log(x) + 1 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 460 +a0378:= integrate(t0378,x) +--R +--R +--R +----------+ +----------+ +----------+ +--R (3) - log(\|log(x) + 1 + 1) + log(\|log(x) + 1 - 1) + 2\|log(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 460 +m0378:= a0378-r0378 +--R +--R +--R (4) +--R +----------+ +----------+ +----------+ +--R - log(\|log(x) + 1 + 1) + log(\|log(x) + 1 - 1) + 2atanh(\|log(x) + 1 ) +--R Type: Expression(Integer) +--E 394 + +--S 395 of 460 +d0378:= D(m0378,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 460 +t0379:= (log(a*x^n)^2)^p/x +--R +--R +--R n 2p +--R log(a x ) +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 396 + +--S 397 of 460 +r0379:= log(a*x^n)*(log(a*x^n)^2)^p/n/(1+2*p) +--R +--R +--R n n 2p +--R log(a x )log(a x ) +--R (2) -------------------- +--R 2n p + n +--R Type: Expression(Integer) +--E 397 + +--S 398 of 460 +a0379:= integrate(t0379,x) +--R +--R +--R 2p log(n log(x) + log(a)) +--R (n log(x) + log(a))%e +--R (3) ---------------------------------------------- +--R 2n p + n +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 460 +m0379:= a0379-r0379 +--R +--R +--R (4) +--R n n 2p 2p log(n log(x) + log(a)) +--R - log(a x )log(a x ) + (n log(x) + log(a))%e +--R ----------------------------------------------------------------------- +--R 2n p + n +--R Type: Expression(Integer) +--E 399 + +--S 400 of 460 +d0379:= D(m0379,x) +--R +--R +--R (5) +--R n - 1 n 2p n - 1 n n 2p - 1 +--R - x x log(a x ) - 2p x x log(a x )log(a x ) +--R + +--R n 2p log(n log(x) + log(a)) +--R (2p + 1)x %e +--R / +--R n +--R (2p + 1)x x +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 460 +t0380:= (log(a*x^n)^m)^p/x +--R +--R +--R n m p +--R log(a x ) +--R (1) ------------ +--R x +--R Type: Expression(Integer) +--E 401 + +--S 402 of 460 +r0380:= log(a*x^n)*(log(a*x^n)^m)^p/n/(1+m*p) +--R +--R +--R n n m p +--R log(a x )log(a x ) +--R (2) --------------------- +--R m n p + n +--R Type: Expression(Integer) +--E 402 + +--S 403 of 460 +a0380:= integrate(t0380,x) +--R +--R +--R m p log(n log(x) + log(a)) +--R (n log(x) + log(a))%e +--R (3) ----------------------------------------------- +--R m n p + n +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 460 +m0380:= a0380-r0380 +--R +--R +--R (4) +--R n n m p m p log(n log(x) + log(a)) +--R - log(a x )log(a x ) + (n log(x) + log(a))%e +--R ------------------------------------------------------------------------- +--R m n p + n +--R Type: Expression(Integer) +--E 404 + +--S 405 of 460 +d0380:= D(m0380,x) +--R +--R +--R (5) +--R n - 1 n m p n - 1 n n m p - 1 +--R - x x log(a x ) - m p x x log(a x )log(a x ) +--R + +--R n m p log(n log(x) + log(a)) +--R (m p + 1)x %e +--R / +--R n +--R (m p + 1)x x +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 460 +t0381:= (log(a*x^n)^2)^(1/2)/x +--R +--R +--R +----------+ +--R | n 2 +--R \|log(a x ) +--R (1) ------------- +--R x +--R Type: Expression(Integer) +--E 406 + +--S 407 of 460 +r0381:= 1/2*log(a*x^n)^2*csgn(log(a*x^n))/n +--R +--R There are no library operations named csgn +--R Use HyperDoc Browse or issue +--R )what op csgn +--R to learn if there is any operation containing " csgn " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named csgn +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 407 + +--S 408 of 460 +a0381:= integrate(t0381,x) +--R +--R +--R 2 +--R n log(x) + 2log(a)log(x) +--R (2) ------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 460 +m0381:= a0381-r0381 +--R +--R +--R 2 +--R n log(x) + 2log(a)log(x) - 2r0381 +--R (3) ---------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 460 +d0381:= D(m0381,x) +--R +--R +--R n log(x) + log(a) +--R (4) ----------------- +--R x +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 460 +t0382:= (b*log(a*x^n)^m)^p/x +--R +--R +--R n m p +--R (b log(a x ) ) +--R (1) --------------- +--R x +--R Type: Expression(Integer) +--E 411 + +--S 412 of 460 +r0382:= log(a*x^n)*(b*log(a*x^n)^m)^p/n/(1+m*p) +--R +--R +--R n n m p +--R log(a x )(b log(a x ) ) +--R (2) ------------------------ +--R m n p + n +--R Type: Expression(Integer) +--E 412 + +--S 413 of 460 +a0382:= integrate(t0382,x) +--R +--R +--R m p log(n log(x) + log(a)) + p log(b) +--R (n log(x) + log(a))%e +--R (3) ---------------------------------------------------------- +--R m n p + n +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 460 +m0382:= a0382-r0382 +--R +--R +--R (4) +--R n n m p +--R - log(a x )(b log(a x ) ) +--R + +--R m p log(n log(x) + log(a)) + p log(b) +--R (n log(x) + log(a))%e +--R / +--R m n p + n +--R Type: Expression(Integer) +--E 414 + +--S 415 of 460 +d0382:= D(m0382,x) +--R +--R +--R (5) +--R n - 1 n m p +--R - x x (b log(a x ) ) +--R + +--R n - 1 n n m - 1 n m p - 1 +--R - b m p x x log(a x )log(a x ) (b log(a x ) ) +--R + +--R n m p log(n log(x) + log(a)) + p log(b) +--R (m p + 1)x %e +--R / +--R n +--R (m p + 1)x x +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 460 +t0383:= 1/(-log(a*x^2))^(1/2) +--R +--R +--R 1 +--R (1) -------------- +--R +-----------+ +--R | 2 +--R \|- log(a x ) +--R Type: Expression(Integer) +--E 416 + +--S 417 of 460 +r0383:= -1/2*2^(1/2)*%pi^(1/2)*x*erf(1/2*(-log(a*x^2))^(1/2)*2^(1/2))/_ + (a*x^2)^(1/2) +--R +--R +--R +-----------+ +--R +-+ | 2 +--R +-+ +---+ \|2 \|- log(a x ) +--R x\|2 \|%pi erf(------------------) +--R 2 +--R (2) - ---------------------------------- +--R +----+ +--R | 2 +--R 2\|a x +--R Type: Expression(Integer) +--E 417 + +--S 418 of 460 +a0383:= integrate(t0383,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 418 + +--S 419 of 460 +--m0383:= a0383-r0383 +--E 419 + +--S 420 of 460 +--d0383:= D(m0383,x) +--E 420 + +)clear all + +--S 421 of 460 +t0384:= 1/(-log(a/x^2))^(1/2) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | a +--R |- log(--) +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 421 + +--S 422 of 460 +r0384:= 1/2*2^(1/2)*%pi^(1/2)*(a/x^2)^(1/2)*x*_ + erfi(1/2*(-log(a/x^2))^(1/2)*2^(1/2)) +--R +--R There are no library operations named erfi +--R Use HyperDoc Browse or issue +--R )what op erfi +--R to learn if there is any operation containing " erfi " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named erfi +--R with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 422 + +--S 423 of 460 +a0384:= integrate(t0384,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 423 + +--S 424 of 460 +--m0384:= a0384-r0384 +--E 424 + +--S 425 of 460 +--d0384:= D(m0384,x) +--E 425 + +)clear all + +--S 426 of 460 +t0385:= 1/(-log(a*x^n))^(1/2) +--R +--R +--R 1 +--R (1) -------------- +--R +-----------+ +--R | n +--R \|- log(a x ) +--R Type: Expression(Integer) +--E 426 + +--S 427 of 460 +r0385:= -%pi^(1/2)*x*erf((-log(a*x^n))^(1/2)/n^(1/2))/n^(1/2)/((a*x^n)^(1/n)) +--R +--R +--R +-----------+ +--R | n +--R +---+ \|- log(a x ) +--R x\|%pi erf(--------------) +--R +-+ +--R \|n +--R (2) - -------------------------- +--R 1 +--R - +--R +-+ n n +--R \|n (a x ) +--R Type: Expression(Integer) +--E 427 + +--S 428 of 460 +a0385:= integrate(t0385,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 428 + +--S 429 of 460 +--m0385:= a0385-r0385 +--E 429 + +--S 430 of 460 +--d0385:= D(m0385,x) +--E 430 + +)clear all + +--S 431 of 460 +t0386:= log(x^n)/(a+b*x) +--R +--R +--R n +--R log(x ) +--R (1) ------- +--R b x + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 460 +r0386:= 1/b*(log(x^n)*log((a+b*x)/a)+n*polylog(2,-b*x/a)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 432 + +--S 433 of 460 +a0386:= integrate(t0386,x) +--R +--R +--R x n +--R ++ log(%R ) +--R (2) | -------- d%R +--R ++ %R b + a +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 460 +--m0386:= a0386-r0386 +--E 434 + +--S 435 of 460 +--d0386:= D(m0386,x) +--E 435 + +)clear all + +--S 436 of 460 +t0387:= sin(x*log(x))+log(x)*sin(x*log(x)) +--R +--R +--R (1) (log(x) + 1)sin(x log(x)) +--R Type: Expression(Integer) +--E 436 + +--S 437 of 460 +r0387:= -cos(x*log(x)) +--R +--R +--R (2) - cos(x log(x)) +--R Type: Expression(Integer) +--E 437 + +--S 438 of 460 +a0387:= integrate(t0387,x) +--R +--R +--R (3) - cos(x log(x)) +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 460 +m0387:= a0387-r0387 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 460 +d0387:= D(m0387,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 460 +t0388:= log((1-x^2)/(1+x^2))/(1+x)^2 +--R +--R +--R 2 +--R - x + 1 +--R log(--------) +--R 2 +--R x + 1 +--R (1) ------------- +--R 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 460 +r0388:= -1/(1+x)-atan(x)+1/2*log(1-x)+1/2*log(1+x)-_ + log((1-x^2)/(1+x^2))/(1+x)-1/2*log(1+x^2) +--R +--R +--R (2) +--R 2 +--R 2 - x + 1 +--R (- x - 1)log(x + 1) + (x + 1)log(x + 1) - 2log(--------) +--R 2 +--R x + 1 +--R + +--R (x + 1)log(- x + 1) + (- 2x - 2)atan(x) - 2 +--R / +--R 2x + 2 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 460 +a0388:= integrate(t0388,x) +--R +--R +--R (3) +--R 2 +--R 2 2 - x + 1 +--R (- x - 1)log(x + 1) + (x + 1)log(x - 1) - 2log(--------) +--R 2 +--R x + 1 +--R + +--R (- 2x - 2)atan(x) - 2 +--R / +--R 2x + 2 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 460 +m0388:= a0388-r0388 +--R +--R +--R 2 +--R log(x - 1) - log(x + 1) - log(- x + 1) +--R (4) --------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 460 +d0388:= D(m0388,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 460 +t0389:= log((-1+x)/(1+x)) +--R +--R +--R x - 1 +--R (1) log(-----) +--R x + 1 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 460 +r0389:= x*log((-1+x)/(1+x))-log(-(-1+x)*(1+x)) +--R +--R +--R x - 1 2 +--R (2) x log(-----) - log(- x + 1) +--R x + 1 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 460 +a0389:= integrate(t0389,x) +--R +--R +--R 2 x - 1 +--R (3) - log(x - 1) + x log(-----) +--R x + 1 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 460 +m0389:= a0389-r0389 +--R +--R +--R 2 2 +--R (4) - log(x - 1) + log(- x + 1) +--R Type: Expression(Integer) +--E 449 + +--S 450 of 460 +d0389:= D(m0389,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 460 +t0390:= log(x)/(-1+x) +--R +--R +--R log(x) +--R (1) ------ +--R x - 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 460 +r0390:= -polylog(2,1-x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 452 + +--S 453 of 460 +a0390:= integrate(t0390,x) +--R +--R +--R (2) - dilog(x) +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 460 +--m0390:= a0390-r0390 +--E 454 + +--S 455 of 460 +--d0390:= D(m0390,x) +--E 455 + +)clear all + +--S 456 of 460 +t0391:= x*log(1-a-b*x)/(a+b*x) +--R +--R +--R x log(- b x - a + 1) +--R (1) -------------------- +--R b x + a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 460 +r0391:= -x/b-(1-a-b*x)*log(1-a-b*x)/b^2+a*polylog(2,a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 457 + +--S 458 of 460 +a0391:= integrate(t0391,x) +--R +--R +--R x +--R ++ %R log(- %R b - a + 1) +--R (2) | ---------------------- d%R +--R ++ %R b + a +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 460 +--m0391:= a0391-r0391 +--E 459 + +--S 460 of 460 +--d0391:= D(m0391,x) +--E 460 + +)spool +)lisp (bye) +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richlog300-391.input.pdf b/src/axiom-website/CATS/richlog300-391.input.pdf new file mode 100644 index 0000000..e35886f Binary files /dev/null and b/src/axiom-website/CATS/richlog300-391.input.pdf differ diff --git a/src/axiom-website/CATS/richrational.input.pamphlet b/src/axiom-website/CATS/richrational.input.pamphlet new file mode 100644 index 0000000..8c0f995 --- /dev/null +++ b/src/axiom-website/CATS/richrational.input.pamphlet @@ -0,0 +1,64072 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{405pt} +\begin{document} +\title{\$SPAD/src/input richrational.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{Summary} +\begin{verbatim} +========================================================================== +RATIONAL +========================================================================== +10 exact matches +98 differ by a constant +136 differ by a variable +all integrations succeeded. +axiom is visibly shorter in 57 cases, possibly others + +integrand rich axiom difference derivative difference derivative +0000 ok ok constant 0 +0001 ok ok constant 0 +0002 ok ok constant 0 +0003 ok ok constant 0 +0004 ok ok constant 0 +0005 ok ok constant 0 +0006 ok exact 0 0 +0007 ok exact 0 0 +0008 ok ok constant 0 +0009 ok ok constant 0 +0010 ok ok constant 0 +0011 ok ok constant 0 +0012 ok ok constant 0 +0013 ok ok constant 0 +0014 ok ok constant 0 +0015 ok ok constant 0 +0016 ok ok constant 0 +0017 ok ok constant 0 +0018 ok ok constant 0 +0019 ok exact 0 0 +0020 ok ok constant 0 +0021 ok ok constant 0 +0022 ok ok constant 0 +0023 ok ok constant 0 (axiom is shorter) +0024 ok ok constant 0 (axiom is shorter) +0025 ok ok constant 0 (axiom is shorter) +0026 ok ok var 0 +0027 ok ok constant 0 +0028 ok ok constant 0 +0029 ok ok constant 0 (axiom is shorter) +0030 ok ok constant 0 (axiom is shorter) +0031 ok ok constant 0 (axiom is shorter) +0032 ok ok constant 0 (axiom is shorter) +0033 ok ok constant 0 (axiom is shorter) +0034 ok ok constant 0 +0035 ok ok constant 0 +0036 ok ok constant 0 +0037 ok ok constant 0 (axiom is shorter) +0038 ok ok constant 0 (axiom is shorter) +0039 ok ok constant 0 (axiom is shorter) +0040 ok ok constant 0 (axiom is shorter) +0041 ok ok constant 0 (axiom is shorter) +0042 ok ok constant 0 (axiom is shorter) +0043 ok ok constant 0 (axiom is shorter) +0044 ok ok constant 0 (axiom is shorter) +0045 ok ok constant 0 (axiom is shorter) +0046 ok ok constant 0 (axiom is shorter) +0047 ok ok constant 0 (axiom is shorter) +0048 ok ok constant 0 (axiom is shorter) +0049 ok ok constant 0 (axiom is shorter) +0050 ok ok constant 0 (axiom is shorter) +0051 ok ok constant 0 (axiom is shorter) +0052 ok ok constant 0 (axiom is shorter) +0053 ok ok constant 0 (axiom is shorter) +0054 ok ok constant 0 (axiom is shorter) +0055 ok ok constant 0 (axiom is shorter) +0056 ok ok constant 0 (axiom is shorter) +0057 ok ok constant 0 (axiom is shorter) +0058 ok ok constant 0 (axiom is shorter) +0059 ok ok constant 0 (axiom is shorter) +0060 ok ok constant 0 (axiom is shorter) +0061 ok ok constant 0 +0062 ok exact 0 0 +0063 ok exact 0 0 +0064 ok ok constant 0 +0065 ok ok constant 0 +0066 ok ok constant 0 +0067 ok ok constant 0 +0068 ok ok constant 0 +0069 ok ok constant 0 +0070 ok ok constant 0 +0071 ok exact 0 0 +0072 ok exact 0 0 +0073 ok ok constant 0 +0074 ok ok constant 0 +0075 ok ok constant 0 +0076 ok ok constant 0 +0077 ok ok constant 0 (axiom is shorter) +0078 ok ok var 0 +0079 ok ok constant 0 (axiom is shorter) +0080 ok ok constant 0 (axiom is shorter) +0081 ok ok constant 0 (axiom is shorter) +0082 ok ok constant 0 (axiom is shorter) +0083 ok ok constant 0 (axiom is shorter) +0084 ok ok constant 0 (axiom is shorter) +0085 ok ok constant 0 (axiom is shorter) +0086 ok ok constant 0 (axiom is shorter) +0087 ok ok constant 0 (axiom is shorter) +0088 ok ok constant 0 (axiom is shorter) +0089 ok ok constant 0 (axiom is shorter) +0090 ok ok constant 0 (axiom is shorter) +0091 ok ok var 0 (axiom 2nd sol. is shorter) +0092 ok ok var 0 (two solutions) +0093 ok ok var 0 (two solutions) +0094 ok ok var 0 (two solutions) +0095 ok ok var 0 (two solutions) +0096 ok ok var 0 (two solutions) +0097 ok ok var 0 (two solutions) +0098 ok ok var 0 (two solutions) +0099 ok ok var 0 (two solutions) + +0100 ok ok var 0 (oddly differ by sign in log) +0101 ok ok var 0 (log vs atan expansion) +0102 ok ok var 0 (log vs atan expansion) +0103 ok ok var 0 (log vs atan expansion) +0104 ok ok var 0 (log vs atan expansion) +0105 ok ok var 0 +0106 ok ok var 0 (two solutions) +0107 ok ok var 0 (two solutions) +0108 ok ok var 0 (two solutions) +0109 ok ok var 0 (two solutions) +0110 ok ok var 0 (axiom 2nd sol. is shorter) +0111 ok ok constant 0 (axiom is shorter) +0112 ok ok constant 0 (axiom is shorter) +0113 ok ok constant 0 (axiom is shorter) +0114 ok ok constant 0 (axiom is shorter) +0115 ok ok var 0 +0116 ok ok var 0 +0117 ok ok var 0 +0118 ok ok var 0 +0119 ok ok var 0 +0120 ok ok var 0 +0121 ok ok var 0 +0122 ok ok var 0 +0123 ok ok constant 0 (axiom is shorter) +0124 ok ok constant 0 (axiom is shorter) +0125 ok ok constant 0 (axiom is shorter) +0126 ok ok var 0 +0127 ok ok var 0 +0128 ok ok var 0 +0129 ok ok var 0 +0130 ok ok var 0 +0131 ok ok var 0 +0132 ok ok var 0 +0133 ok ok var 0 +0134 ok ok var 0 +0135 ok ok var 0 +0136 ok ok var 0 +0137 ok ok var 0 +0138 ok ok var 0 +0139 ok ok var 0 +0140 ok ok var 0 +0141 ok ok var 0 +0142 ok ok var 0 +0143 ok ok var 0 +0144 ok ok var 0 +0145 ok ok var 0 +0146 ok ok var 0 +0147 ok ok var 0 +0148 ok ok constant 0 (axiom is shorter) +0149 ok ok constant 0 (axiom is shorter) +0150 ok ok var 0 (axiom is shorter) +0151 ok ok var 0 +0152 ok ok var 0 +0153 ok ok var 0 +0154 ok ok var 0 +0155 ok ok var 0 +0156 ok ok var 0 +0157 ok ok var 0 +0158 ok ok var 0 +0159 ok ok var 0 +0160 ok ok var 0 +0161 ok ok var 0 +0162 ok ok constant 0 +0163 ok ok constant 0 +0164 ok ok constant 0 (axiom is shorter) +0165 ok ok var var (axiom differentiates ok) +0166 ok ok var 0 +0167 ok ok var 0 +0168 ok ok var 0 +0169 ok ok var 0 +0170 ok ok var 0 +0171 ok ok var 0 +0172 ok ok var 0 +0173 ok ok var 0 +0174 ok ok var 0 +0175 ok ok var 0 +0176 ok ok var 0 +0177 ok ok var 0 +0178 ok ok var 0 +0179 ok ok var 0 +0180 ok ok var 0 +0181 ok ok var 0 +0182 ok ok var 0 +0183 ok ok var 0 +0184 ok ok constant 0 +0185 ok ok constant 0 +0186 ok ok var var (axiom differentiates ok) +0187 ok ok var 0 +0188 ok ok var 0 (two answers) +0189 ok ok var 0 +0190 ok ok var 0 (two answers) +0191 ok ok var 0 (two answers) +0192 ok ok var 0 +0193 ok ok var 0 +0194 ok ok var 0 (two answers) +0195 ok ok var 0 (two answers) +0196 ok ok var 0 (two answers) +0197 ok ok var 0 (two answers) +0198 ok ok var 0 (two answers) +0199 ok ok var 0 (two answers) + +0200 ok ok var 0 (two answers) +0201 ok ok var 0 (two answers) +0202 ok ok var 0 (two answers) +0203 ok ok var 0 (two answers) +0204 ok ok var 0 (two answers) +0205 ok ok var 0 (two answers) +0206 ok ok var 0 (two answers) +0207 ok ok var 0 (two answers) +0208 ok ok var 0 (two answers) +0209 ok ok var 0 (two answers) +0210 ok ok var 0 (two answers) +0211 ok ok var 0 (two answers) +0212 ok ok var 0 (two answers) +0213 ok ok var 0 (two answers ) +0214 ok ok var 0 +0215 ok ok var 0 (two answers) +0216 ok ok var 0 (two answers) +0217 ok ok var 0 (two answers) +0218 ok ok var 0 (two answers) +0219 ok ok var 0 (two answers) +0220 ok ok var 0 (two answers) +0221 ok ok var 0 (two answers) +0222 ok ok var 0 (two answers) +0223 ok ok var 0 (two answers) +0224 ok ok var 0 (two answers) +0225 ok ok constant 0 +0226 ok ok var 0 +0227 ok ok var 0 +0228 ok ok constant 0 +0229 ok ok var 0 +0230 ok ok var 0 +0231 ok ok var 0 +0232 ok ok var 0 +0233 ok ok var 0 +0234 ok ok var 0 +0235 ok ok var 0 +0236 ok ok var 0 (two answers) +0237 ok ok var 0 +0238 ok ok var 0 +0239 ok ok var 0 +0240 ok ok var bug? (rich differentiates ok) +0241 ok ok var bug? (NEITHER IS OK) +0242 ok ok var 0 +0243 ok ok var 0 +0244 ok ok var E(C(F(I))) +0245 ok ok var E(C(F(I))) +0246 ok ok var bug? (NEITHER IS OK) +0247 ok ok var bug? (rich differentiates ok) +0248 ok ok var 0 +0249 ok ok 0 0 +0250 ok ok 0 0 +0251 ok ok var 0 +0252 ok ok var 0 +0253 ok ok var 0 +0254 ok ok var 0 +0255 ok ok var 0 +0256 ok ok var 0 +0257 ok ok var 0 +0258 ok ok var 0 +0259 ok ok var 0 +0260 ok ok var 0 +0261 ok ok var bug? (NEITHER IS OK) +0262 ok ok var 0 +0263 ok ok var 0 +0264 ok ok var 0 +0265 ok ok var 0 +0266 ok ok var 0 +0267 ok ok var 0 +0268 ok ok var 0 +0269 ok ok var 0 +0270 ok ok var 0 +0271 ok ok var 0 +0272 ok ok var 0 +0273 ok exact 0 0 +0274 ok exact 0 0 +0275 ok exact 0 0 +0276 ok ok var 0 +\end{verbatim} +\begin{chunk}{*} +)set break resume +)sys rm -f richrational.output +)spool richrational.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1483 +t0000:= (5-2*x)^6*(2+3*x)^3*(-16+33*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R 57024x - 768960x + 4070736x - 10051008x + 8647828x + 8983380x +--R + +--R 4 3 2 +--R - 19081125x - 196250x + 11962500x - 75000x - 2000000 +--R Type: Polynomial(Integer) +--E 1 + +--S 2 of 1483 +r0000:= -1/2*(5-2*x)^7*(2+3*x)^4 +--R +--R +--R (2) +--R 11 10 9 8 7 6 +--R 5184x - 76896x + 452304x - 1256376x + 1235404x + 1497230x +--R + +--R 5 98125 4 3 2 +--R - 3816225x - ----- x + 3987500x - 37500x - 2000000x - 625000 +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 2 + +--S 3 of 1483 +a0000:=integrate(t0000,x) +--R +--R +--R (3) +--R 11 10 9 8 7 6 +--R 5184x - 76896x + 452304x - 1256376x + 1235404x + 1497230x +--R + +--R 5 98125 4 3 2 +--R - 3816225x - ----- x + 3987500x - 37500x - 2000000x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 3 + +--S 4 of 1483 +m0000:=a0000-r0000 +--R +--R +--R (4) 625000 +--R Type: Polynomial(Fraction(Integer)) +--E 4 + +--S 5 of 1483 +d0000:=D(m0000,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 5 + +--S 6 of 1483 +t0001:= x*(a+b*x)*(c+d*x)^16 +--R +--R +--R (6) +--R 16 18 16 15 17 15 2 14 16 +--R b d x + (a d + 16b c d )x + (16a c d + 120b c d )x +--R + +--R 2 14 3 13 15 3 13 4 12 14 +--R (120a c d + 560b c d )x + (560a c d + 1820b c d )x +--R + +--R 4 12 5 11 13 5 11 6 10 12 +--R (1820a c d + 4368b c d )x + (4368a c d + 8008b c d )x +--R + +--R 6 10 7 9 11 7 9 8 8 10 +--R (8008a c d + 11440b c d )x + (11440a c d + 12870b c d )x +--R + +--R 8 8 9 7 9 9 7 10 6 8 +--R (12870a c d + 11440b c d )x + (11440a c d + 8008b c d )x +--R + +--R 10 6 11 5 7 11 5 12 4 6 +--R (8008a c d + 4368b c d )x + (4368a c d + 1820b c d )x +--R + +--R 12 4 13 3 5 13 3 14 2 4 +--R (1820a c d + 560b c d )x + (560a c d + 120b c d )x +--R + +--R 14 2 15 3 15 16 2 16 +--R (120a c d + 16b c d)x + (16a c d + b c )x + a c x +--R Type: Polynomial(Integer) +--E 6 + +--S 7 of 1483 +r0001:= -1/5814*(c+d*x)^17*(-2*b*c^2+19*a*c*d+34*b*c*d*x-_ + 323*x*d^2*a-306*b*d^2*x^2)/d^3 +--R +--R +--R (7) +--R 1 19 19 1 19 8 18 18 16 18 120 2 17 17 +--R -- b d x + (-- a d + - b c d )x + (-- a c d + --- b c d )x +--R 19 18 9 17 17 +--R + +--R 15 2 17 3 16 16 112 3 16 364 4 15 15 +--R (-- a c d + 35b c d )x + (--- a c d + --- b c d )x +--R 2 3 3 +--R + +--R 4 15 5 14 14 5 14 6 13 13 +--R (130a c d + 312b c d )x + (336a c d + 616b c d )x +--R + +--R 2002 6 13 2860 7 12 12 7 12 8 11 11 +--R (---- a c d + ---- b c d )x + (1040a c d + 1170b c d )x +--R 3 3 +--R + +--R 8 11 9 10 10 11440 9 10 8008 10 9 9 +--R (1287a c d + 1144b c d )x + (----- a c d + ---- b c d )x +--R 9 9 +--R + +--R 10 9 11 8 8 11 8 12 7 7 +--R (1001a c d + 546b c d )x + (624a c d + 260b c d )x +--R + +--R 910 12 7 280 13 6 6 13 6 14 5 5 +--R (--- a c d + --- b c d )x + (112a c d + 24b c d )x +--R 3 3 +--R + +--R 14 5 15 4 4 16 15 4 1 16 3 3 1 16 3 2 +--R (30a c d + 4b c d )x + (-- a c d + - b c d )x + - a c d x +--R 3 3 2 +--R + +--R 1 18 1 19 +--R - --- a c d + ---- b c +--R 306 2907 +--R / +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 7 + +--S 8 of 1483 +a0001:=integrate(t0001,x) +--R +--R +--R (8) +--R 1 16 19 1 16 8 15 18 16 15 120 2 14 17 +--R -- b d x + (-- a d + - b c d )x + (-- a c d + --- b c d )x +--R 19 18 9 17 17 +--R + +--R 15 2 14 3 13 16 112 3 13 364 4 12 15 +--R (-- a c d + 35b c d )x + (--- a c d + --- b c d )x +--R 2 3 3 +--R + +--R 4 12 5 11 14 5 11 6 10 13 +--R (130a c d + 312b c d )x + (336a c d + 616b c d )x +--R + +--R 2002 6 10 2860 7 9 12 7 9 8 8 11 +--R (---- a c d + ---- b c d )x + (1040a c d + 1170b c d )x +--R 3 3 +--R + +--R 8 8 9 7 10 11440 9 7 8008 10 6 9 +--R (1287a c d + 1144b c d )x + (----- a c d + ---- b c d )x +--R 9 9 +--R + +--R 10 6 11 5 8 11 5 12 4 7 +--R (1001a c d + 546b c d )x + (624a c d + 260b c d )x +--R + +--R 910 12 4 280 13 3 6 13 3 14 2 5 +--R (--- a c d + --- b c d )x + (112a c d + 24b c d )x +--R 3 3 +--R + +--R 14 2 15 4 16 15 1 16 3 1 16 2 +--R (30a c d + 4b c d)x + (-- a c d + - b c )x + - a c x +--R 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 1483 +m0001:=a0001-r0001 +--R +--R +--R 1 18 1 19 +--R --- a c d - ---- b c +--R 306 2907 +--R (9) ----------------------- +--R 3 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 9 + +--S 10 of 1483 +d0001:=D(m0001,x) +--R +--R +--R (10) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 10 + +--S 11 of 1483 +t0002:= x*(a+b*x)^2*(c+d*x)^16 +--R +--R +--R (11) +--R 2 16 19 16 2 15 18 +--R b d x + (2a b d + 16b c d )x +--R + +--R 2 16 15 2 2 14 17 +--R (a d + 32a b c d + 120b c d )x +--R + +--R 2 15 2 14 2 3 13 16 +--R (16a c d + 240a b c d + 560b c d )x +--R + +--R 2 2 14 3 13 2 4 12 15 +--R (120a c d + 1120a b c d + 1820b c d )x +--R + +--R 2 3 13 4 12 2 5 11 14 +--R (560a c d + 3640a b c d + 4368b c d )x +--R + +--R 2 4 12 5 11 2 6 10 13 +--R (1820a c d + 8736a b c d + 8008b c d )x +--R + +--R 2 5 11 6 10 2 7 9 12 +--R (4368a c d + 16016a b c d + 11440b c d )x +--R + +--R 2 6 10 7 9 2 8 8 11 +--R (8008a c d + 22880a b c d + 12870b c d )x +--R + +--R 2 7 9 8 8 2 9 7 10 +--R (11440a c d + 25740a b c d + 11440b c d )x +--R + +--R 2 8 8 9 7 2 10 6 9 +--R (12870a c d + 22880a b c d + 8008b c d )x +--R + +--R 2 9 7 10 6 2 11 5 8 +--R (11440a c d + 16016a b c d + 4368b c d )x +--R + +--R 2 10 6 11 5 2 12 4 7 +--R (8008a c d + 8736a b c d + 1820b c d )x +--R + +--R 2 11 5 12 4 2 13 3 6 +--R (4368a c d + 3640a b c d + 560b c d )x +--R + +--R 2 12 4 13 3 2 14 2 5 +--R (1820a c d + 1120a b c d + 120b c d )x +--R + +--R 2 13 3 14 2 2 15 4 +--R (560a c d + 240a b c d + 16b c d)x +--R + +--R 2 14 2 15 2 16 3 2 15 16 2 2 16 +--R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x +--R Type: Polynomial(Integer) +--E 11 + +--S 12 of 1483 +r0002:= -1/58140*(c+d*x)^17*(3*b^2*c^3-40*a*b*c^2*d+190*a^2*c*d^2-_ + 51*d*b^2*c^2*x+680*a*b*c*d^2*x-3230*a^2*d^3*x+459*d^2*b^2*c*x^2-_ + 6120*d^3*a*b*x^2-2907*d^3*b^2*x^3)/d^4 +--R +--R +--R (12) +--R 1 2 20 20 2 20 16 2 19 19 +--R -- b d x + (-- a b d + -- b c d )x +--R 20 19 19 +--R + +--R 1 2 20 16 19 20 2 2 18 18 +--R (-- a d + -- a b c d + -- b c d )x +--R 18 9 3 +--R + +--R 16 2 19 240 2 18 560 2 3 17 17 +--R (-- a c d + --- a b c d + --- b c d )x +--R 17 17 17 +--R + +--R 15 2 2 18 3 17 455 2 4 16 16 +--R (-- a c d + 70a b c d + --- b c d )x +--R 2 4 +--R + +--R 112 2 3 17 728 4 16 1456 2 5 15 15 +--R (--- a c d + --- a b c d + ---- b c d )x +--R 3 3 5 +--R + +--R 2 4 16 5 15 2 6 14 14 +--R (130a c d + 624a b c d + 572b c d )x +--R + +--R 2 5 15 6 14 2 7 13 13 +--R (336a c d + 1232a b c d + 880b c d )x +--R + +--R 2002 2 6 14 5720 7 13 2145 2 8 12 12 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 3 3 2 +--R + +--R 2 7 13 8 12 2 9 11 11 +--R (1040a c d + 2340a b c d + 1040b c d )x +--R + +--R 2 8 12 9 11 4004 2 10 10 10 +--R (1287a c d + 2288a b c d + ---- b c d )x +--R 5 +--R + +--R 11440 2 9 11 16016 10 10 1456 2 11 9 9 +--R (----- a c d + ----- a b c d + ---- b c d )x +--R 9 9 3 +--R + +--R 2 10 10 11 9 455 2 12 8 8 +--R (1001a c d + 1092a b c d + --- b c d )x +--R 2 +--R + +--R 2 11 9 12 8 2 13 7 7 +--R (624a c d + 520a b c d + 80b c d )x +--R + +--R 910 2 12 8 560 13 7 2 14 6 6 +--R (--- a c d + --- a b c d + 20b c d )x +--R 3 3 +--R + +--R 2 13 7 14 6 16 2 15 5 5 +--R (112a c d + 48a b c d + -- b c d )x +--R 5 +--R + +--R 2 14 6 15 5 1 2 16 4 4 16 2 15 5 2 16 4 3 +--R (30a c d + 8a b c d + - b c d )x + (-- a c d + - a b c d )x +--R 4 3 3 +--R + +--R 1 2 16 4 2 1 2 18 2 2 19 1 2 20 +--R - a c d x - --- a c d + ---- a b c d - ----- b c +--R 2 306 2907 19380 +--R / +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 12 + +--S 13 of 1483 +a0002:=integrate(t0002,x) +--R +--R +--R (13) +--R 1 2 16 20 2 16 16 2 15 19 +--R -- b d x + (-- a b d + -- b c d )x +--R 20 19 19 +--R + +--R 1 2 16 16 15 20 2 2 14 18 +--R (-- a d + -- a b c d + -- b c d )x +--R 18 9 3 +--R + +--R 16 2 15 240 2 14 560 2 3 13 17 +--R (-- a c d + --- a b c d + --- b c d )x +--R 17 17 17 +--R + +--R 15 2 2 14 3 13 455 2 4 12 16 +--R (-- a c d + 70a b c d + --- b c d )x +--R 2 4 +--R + +--R 112 2 3 13 728 4 12 1456 2 5 11 15 +--R (--- a c d + --- a b c d + ---- b c d )x +--R 3 3 5 +--R + +--R 2 4 12 5 11 2 6 10 14 +--R (130a c d + 624a b c d + 572b c d )x +--R + +--R 2 5 11 6 10 2 7 9 13 +--R (336a c d + 1232a b c d + 880b c d )x +--R + +--R 2002 2 6 10 5720 7 9 2145 2 8 8 12 +--R (---- a c d + ---- a b c d + ---- b c d )x +--R 3 3 2 +--R + +--R 2 7 9 8 8 2 9 7 11 +--R (1040a c d + 2340a b c d + 1040b c d )x +--R + +--R 2 8 8 9 7 4004 2 10 6 10 +--R (1287a c d + 2288a b c d + ---- b c d )x +--R 5 +--R + +--R 11440 2 9 7 16016 10 6 1456 2 11 5 9 +--R (----- a c d + ----- a b c d + ---- b c d )x +--R 9 9 3 +--R + +--R 2 10 6 11 5 455 2 12 4 8 +--R (1001a c d + 1092a b c d + --- b c d )x +--R 2 +--R + +--R 2 11 5 12 4 2 13 3 7 +--R (624a c d + 520a b c d + 80b c d )x +--R + +--R 910 2 12 4 560 13 3 2 14 2 6 +--R (--- a c d + --- a b c d + 20b c d )x +--R 3 3 +--R + +--R 2 13 3 14 2 16 2 15 5 +--R (112a c d + 48a b c d + -- b c d)x +--R 5 +--R + +--R 2 14 2 15 1 2 16 4 16 2 15 2 16 3 1 2 16 2 +--R (30a c d + 8a b c d + - b c )x + (-- a c d + - a b c )x + - a c x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 1483 +m0002:=a0002-r0002 +--R +--R +--R 1 2 18 2 2 19 1 2 20 +--R --- a c d - ---- a b c d + ----- b c +--R 306 2907 19380 +--R (14) ----------------------------------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 14 + +--S 15 of 1483 +d0002:=D(m0002,x) +--R +--R +--R (15) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 15 + +--S 16 of 1483 +t0003:= x^2*(a+b*x)*(c+d*x)^16 +--R +--R +--R (16) +--R 16 19 16 15 18 15 2 14 17 +--R b d x + (a d + 16b c d )x + (16a c d + 120b c d )x +--R + +--R 2 14 3 13 16 3 13 4 12 15 +--R (120a c d + 560b c d )x + (560a c d + 1820b c d )x +--R + +--R 4 12 5 11 14 5 11 6 10 13 +--R (1820a c d + 4368b c d )x + (4368a c d + 8008b c d )x +--R + +--R 6 10 7 9 12 7 9 8 8 11 +--R (8008a c d + 11440b c d )x + (11440a c d + 12870b c d )x +--R + +--R 8 8 9 7 10 9 7 10 6 9 +--R (12870a c d + 11440b c d )x + (11440a c d + 8008b c d )x +--R + +--R 10 6 11 5 8 11 5 12 4 7 +--R (8008a c d + 4368b c d )x + (4368a c d + 1820b c d )x +--R + +--R 12 4 13 3 6 13 3 14 2 5 +--R (1820a c d + 560b c d )x + (560a c d + 120b c d )x +--R + +--R 14 2 15 4 15 16 3 16 2 +--R (120a c d + 16b c d)x + (16a c d + b c )x + a c x +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 1483 +r0003:= 1/58140*(c+d*x)^17*(20*a*c^2*d-3*b*c^3-340*a*c*d^2*x+51*d*b*c^2*x-_ + 459*d^2*b*c*x^2+3060*d^3*a*x^2+2907*d^3*b*x^3)/d^4 +--R +--R +--R (17) +--R 1 20 20 1 20 16 19 19 8 19 20 2 18 18 +--R -- b d x + (-- a d + -- b c d )x + (- a c d + -- b c d )x +--R 20 19 19 9 3 +--R + +--R 120 2 18 560 3 17 17 3 17 455 4 16 16 +--R (--- a c d + --- b c d )x + (35a c d + --- b c d )x +--R 17 17 4 +--R + +--R 364 4 16 1456 5 15 15 5 15 6 14 14 +--R (--- a c d + ---- b c d )x + (312a c d + 572b c d )x +--R 3 5 +--R + +--R 6 14 7 13 13 2860 7 13 2145 8 12 12 +--R (616a c d + 880b c d )x + (---- a c d + ---- b c d )x +--R 3 2 +--R + +--R 8 12 9 11 11 9 11 4004 10 10 10 +--R (1170a c d + 1040b c d )x + (1144a c d + ---- b c d )x +--R 5 +--R + +--R 8008 10 10 1456 11 9 9 11 9 455 12 8 8 +--R (---- a c d + ---- b c d )x + (546a c d + --- b c d )x +--R 9 3 2 +--R + +--R 12 8 13 7 7 280 13 7 14 6 6 +--R (260a c d + 80b c d )x + (--- a c d + 20b c d )x +--R 3 +--R + +--R 14 6 16 15 5 5 15 5 1 16 4 4 1 16 4 3 +--R (24a c d + -- b c d )x + (4a c d + - b c d )x + - a c d x +--R 5 4 3 +--R + +--R 1 19 1 20 +--R ---- a c d - ----- b c +--R 2907 19380 +--R / +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 17 + +--S 18 of 1483 +a0003:=integrate(t0003,x) +--R +--R +--R (18) +--R 1 16 20 1 16 16 15 19 8 15 20 2 14 18 +--R -- b d x + (-- a d + -- b c d )x + (- a c d + -- b c d )x +--R 20 19 19 9 3 +--R + +--R 120 2 14 560 3 13 17 3 13 455 4 12 16 +--R (--- a c d + --- b c d )x + (35a c d + --- b c d )x +--R 17 17 4 +--R + +--R 364 4 12 1456 5 11 15 5 11 6 10 14 +--R (--- a c d + ---- b c d )x + (312a c d + 572b c d )x +--R 3 5 +--R + +--R 6 10 7 9 13 2860 7 9 2145 8 8 12 +--R (616a c d + 880b c d )x + (---- a c d + ---- b c d )x +--R 3 2 +--R + +--R 8 8 9 7 11 9 7 4004 10 6 10 +--R (1170a c d + 1040b c d )x + (1144a c d + ---- b c d )x +--R 5 +--R + +--R 8008 10 6 1456 11 5 9 11 5 455 12 4 8 +--R (---- a c d + ---- b c d )x + (546a c d + --- b c d )x +--R 9 3 2 +--R + +--R 12 4 13 3 7 280 13 3 14 2 6 +--R (260a c d + 80b c d )x + (--- a c d + 20b c d )x +--R 3 +--R + +--R 14 2 16 15 5 15 1 16 4 1 16 3 +--R (24a c d + -- b c d)x + (4a c d + - b c )x + - a c x +--R 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 1483 +m0003:=a0003-r0003 +--R +--R +--R 1 19 1 20 +--R - ---- a c d + ----- b c +--R 2907 19380 +--R (19) --------------------------- +--R 4 +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 19 + +--S 20 of 1483 +d0003:=D(m0003,x) +--R +--R +--R (20) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 20 + +--S 21 of 1483 +t0004:= (b+2*c*x)*(a+b*x+c*x^2)^7 +--R +--R +--R (21) +--R 8 15 7 14 7 2 6 13 6 3 5 12 +--R 2c x + 15b c x + (14a c + 49b c )x + (91a b c + 91b c )x +--R + +--R 2 6 2 5 4 4 11 2 5 3 4 5 3 10 +--R (42a c + 252a b c + 105b c )x + (231a b c + 385a b c + 77b c )x +--R + +--R 3 5 2 2 4 4 3 6 2 9 +--R (70a c + 525a b c + 350a b c + 35b c )x +--R + +--R 3 4 2 3 3 5 2 7 8 +--R (315a b c + 630a b c + 189a b c + 9b c)x +--R + +--R 4 4 3 2 3 2 4 2 6 8 7 +--R (70a c + 560a b c + 420a b c + 56a b c + b )x +--R + +--R 4 3 3 3 2 2 5 7 6 +--R (245a b c + 490a b c + 147a b c + 7a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 5 +--R (42a c + 315a b c + 210a b c + 21a b )x +--R + +--R 5 2 4 3 3 5 4 6 2 5 2 4 4 3 +--R (105a b c + 175a b c + 35a b )x + (14a c + 84a b c + 35a b )x +--R + +--R 6 5 3 2 7 6 2 7 +--R (21a b c + 21a b )x + (2a c + 7a b )x + a b +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 1483 +r0004:= 1/8*(a+b*x+c*x^2)^8 +--R +--R +--R (22) +--R 1 8 16 7 15 7 7 2 6 14 6 3 5 13 +--R - c x + b c x + (a c + - b c )x + (7a b c + 7b c )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 12 2 5 3 4 5 3 11 +--R (- a c + 21a b c + -- b c )x + (21a b c + 35a b c + 7b c )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 10 +--R (7a c + --- a b c + 35a b c + - b c )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 9 +--R (35a b c + 70a b c + 21a b c + b c)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 8 +--R (-- a c + 70a b c + --- a b c + 7a b c + - b )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 7 +--R (35a b c + 70a b c + 21a b c + a b )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 6 5 2 4 3 3 5 5 +--R (7a c + --- a b c + 35a b c + - a b )x + (21a b c + 35a b c + 7a b )x +--R 2 2 +--R + +--R 7 6 2 5 2 35 4 4 4 6 5 3 3 7 7 6 2 2 +--R (- a c + 21a b c + -- a b )x + (7a b c + 7a b )x + (a c + - a b )x +--R 2 4 2 +--R + +--R 7 1 8 +--R a b x + - a +--R 8 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 1483 +a0004:=integrate(t0004,x) +--R +--R +--R (23) +--R 1 8 16 7 15 7 7 2 6 14 6 3 5 13 +--R - c x + b c x + (a c + - b c )x + (7a b c + 7b c )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 12 2 5 3 4 5 3 11 +--R (- a c + 21a b c + -- b c )x + (21a b c + 35a b c + 7b c )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 10 +--R (7a c + --- a b c + 35a b c + - b c )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 9 +--R (35a b c + 70a b c + 21a b c + b c)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 8 +--R (-- a c + 70a b c + --- a b c + 7a b c + - b )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 7 +--R (35a b c + 70a b c + 21a b c + a b )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 6 5 2 4 3 3 5 5 +--R (7a c + --- a b c + 35a b c + - a b )x + (21a b c + 35a b c + 7a b )x +--R 2 2 +--R + +--R 7 6 2 5 2 35 4 4 4 6 5 3 3 7 7 6 2 2 +--R (- a c + 21a b c + -- a b )x + (7a b c + 7a b )x + (a c + - a b )x +--R 2 4 2 +--R + +--R 7 +--R a b x +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 1483 +m0004:=a0004-r0004 +--R +--R +--R 1 8 +--R (24) - - a +--R 8 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 1483 +d0004:=D(m0004,x) +--R +--R +--R (25) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +--S 26 of 1483 +t0005:= (b+2*c*x+3*d*x^2)*(a+b*x+c*x^2+d*x^3)^7 +--R +--R +--R (26) +--R 8 23 7 22 7 2 6 21 +--R 3d x + 23c d x + (22b d + 77c d )x +--R + +--R 7 6 3 5 20 +--R (21a d + 147b c d + 147c d )x +--R + +--R 2 6 2 5 4 4 19 +--R ((140a c + 70b )d + 420b c d + 175c d )x +--R + +--R 6 2 2 5 3 4 5 3 18 +--R (133a b d + (399a c + 399b c)d + 665b c d + 133c d )x +--R + +--R 2 6 3 5 3 2 2 4 4 3 +--R 63a d + (756a b c + 126b )d + (630a c + 945b c )d + 630b c d +--R + +--R 6 2 +--R 63c d +--R * +--R 17 +--R x +--R + +--R 2 2 5 2 3 4 4 2 3 3 +--R (357a c + 357a b )d + (1785a b c + 595b c)d + (595a c + 1190b c )d +--R + +--R 5 2 7 +--R 357b c d + 17c d +--R * +--R 16 +--R x +--R + +--R 2 5 2 2 2 4 4 3 3 2 3 +--R 336a b d + (840a c + 1680a b c + 140b )d + (2240a b c + 1120b c )d +--R + +--R 5 2 4 2 6 8 +--R (336a c + 840b c )d + 112b c d + 2c +--R * +--R 15 +--R x +--R + +--R 3 5 2 3 4 2 3 2 2 4 3 +--R 105a d + (1575a b c + 525a b )d + (1050a c + 3150a b c + 525b c)d +--R + +--R 4 3 3 2 6 2 5 7 +--R (1575a b c + 1050b c )d + (105a c + 315b c )d + 15b c +--R * +--R 14 +--R x +--R + +--R 3 2 2 4 2 2 3 5 3 +--R (490a c + 735a b )d + (2940a b c + 1960a b c + 98b )d +--R + +--R 2 4 2 3 4 2 2 5 3 4 7 +--R (735a c + 2940a b c + 735b c )d + (588a b c + 490b c )d + 14a c +--R + +--R 2 6 +--R 49b c +--R * +--R 13 +--R x +--R + +--R 3 4 3 2 2 2 4 3 +--R 455a b d + (910a c + 2730a b c + 455a b )d +--R + +--R 2 3 3 2 5 2 +--R (2730a b c + 2730a b c + 273b c)d +--R + +--R 2 5 2 4 4 3 6 3 5 +--R (273a c + 1365a b c + 455b c )d + 91a b c + 91b c +--R * +--R 12 +--R x +--R + +--R 4 4 3 2 3 3 +--R 105a d + (1680a b c + 840a b )d +--R + +--R 3 3 2 2 2 4 6 2 +--R (840a c + 3780a b c + 1260a b c + 42b )d +--R + +--R 2 4 3 3 5 2 2 6 2 5 4 4 +--R (1260a b c + 1680a b c + 252b c )d + 42a c + 252a b c + 105b c +--R * +--R 11 +--R x +--R + +--R 4 3 2 3 3 2 2 3 5 2 +--R (385a c + 770a b )d + (2310a b c + 2310a b c + 231a b )d +--R + +--R 3 4 2 2 3 4 2 6 2 5 3 4 +--R (385a c + 2310a b c + 1155a b c + 77b c)d + 231a b c + 385a b c +--R + +--R 5 3 +--R 77b c +--R * +--R 10 +--R x +--R + +--R 4 3 4 2 3 2 2 4 2 +--R 350a b d + (525a c + 2100a b c + 525a b )d +--R + +--R 3 3 2 3 2 5 7 3 5 2 2 4 +--R (1400a b c + 2100a b c + 420a b c + 10b )d + 70a c + 525a b c +--R + +--R 4 3 6 2 +--R 350a b c + 35b c +--R * +--R 9 +--R x +--R + +--R 5 3 4 3 3 2 +--R 63a d + (945a b c + 630a b )d +--R + +--R 4 3 3 2 2 2 4 6 3 4 2 3 3 +--R (315a c + 1890a b c + 945a b c + 63a b )d + 315a b c + 630a b c +--R + +--R 5 2 7 +--R 189a b c + 9b c +--R * +--R 8 +--R x +--R + +--R 5 4 2 2 4 2 3 3 2 5 4 4 +--R (168a c + 420a b )d + (840a b c + 1120a b c + 168a b )d + 70a c +--R + +--R 3 2 3 2 4 2 6 8 +--R 560a b c + 420a b c + 56a b c + b +--R * +--R 7 +--R x +--R + +--R 5 2 5 2 4 2 3 4 4 3 3 3 2 +--R 147a b d + (147a c + 735a b c + 245a b )d + 245a b c + 490a b c +--R + +--R 2 5 7 +--R 147a b c + 7a b +--R * +--R 6 +--R x +--R + +--R 6 2 5 4 3 5 3 4 2 2 3 4 2 6 5 +--R (21a d + (252a b c + 210a b )d + 42a c + 315a b c + 210a b c + 21a b )x +--R + +--R 6 5 2 5 2 4 3 3 5 4 +--R ((35a c + 105a b )d + 105a b c + 175a b c + 35a b )x +--R + +--R 6 6 2 5 2 4 4 3 7 6 5 3 2 +--R (28a b d + 14a c + 84a b c + 35a b )x + (3a d + 21a b c + 21a b )x +--R + +--R 7 6 2 7 +--R (2a c + 7a b )x + a b +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 1483 +r0005:= 1/8*(a+b*x+c*x^2+d*x^3)^8 +--R +--R +--R (27) +--R 1 8 24 7 23 7 7 2 6 22 7 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (a d + 7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 +--R ((7a c + - b )d + 21b c d + -- c d )x +--R 2 4 +--R + +--R 6 2 2 5 3 4 5 3 19 +--R (7a b d + (21a c + 21b c)d + 35b c d + 7c d )x +--R + +--R 7 2 6 3 5 3 105 2 2 4 4 3 7 6 2 18 +--R (- a d + (42a b c + 7b )d + (35a c + --- b c )d + 35b c d + - c d )x +--R 2 2 2 +--R + +--R 2 2 5 2 3 4 4 2 3 3 +--R (21a c + 21a b )d + (105a b c + 35b c)d + (35a c + 70b c )d +--R + +--R 5 2 7 +--R 21b c d + c d +--R * +--R 17 +--R x +--R + +--R 2 5 105 2 2 2 35 4 4 3 3 2 3 +--R 21a b d + (--- a c + 105a b c + -- b )d + (140a b c + 70b c )d +--R 2 4 +--R + +--R 5 105 2 4 2 6 1 8 +--R (21a c + --- b c )d + 7b c d + - c +--R 2 8 +--R * +--R 16 +--R x +--R + +--R 3 5 2 3 4 2 3 2 2 4 3 +--R 7a d + (105a b c + 35a b )d + (70a c + 210a b c + 35b c)d +--R + +--R 4 3 3 2 6 2 5 7 +--R (105a b c + 70b c )d + (7a c + 21b c )d + b c +--R * +--R 15 +--R x +--R + +--R 3 105 2 2 4 2 2 3 5 3 +--R (35a c + --- a b )d + (210a b c + 140a b c + 7b )d +--R 2 +--R + +--R 105 2 4 2 3 105 4 2 2 5 3 4 7 +--R (--- a c + 210a b c + --- b c )d + (42a b c + 35b c )d + a c +--R 2 2 +--R + +--R 7 2 6 +--R - b c +--R 2 +--R * +--R 14 +--R x +--R + +--R 3 4 3 2 2 2 4 3 +--R 35a b d + (70a c + 210a b c + 35a b )d +--R + +--R 2 3 3 2 5 2 2 5 2 4 4 3 +--R (210a b c + 210a b c + 21b c)d + (21a c + 105a b c + 35b c )d +--R + +--R 6 3 5 +--R 7a b c + 7b c +--R * +--R 13 +--R x +--R + +--R 35 4 4 3 2 3 3 +--R -- a d + (140a b c + 70a b )d +--R 4 +--R + +--R 3 3 2 2 2 4 7 6 2 +--R (70a c + 315a b c + 105a b c + - b )d +--R 2 +--R + +--R 2 4 3 3 5 2 7 2 6 2 5 35 4 4 +--R (105a b c + 140a b c + 21b c )d + - a c + 21a b c + -- b c +--R 2 4 +--R * +--R 12 +--R x +--R + +--R 4 3 2 3 3 2 2 3 5 2 +--R (35a c + 70a b )d + (210a b c + 210a b c + 21a b )d +--R + +--R 3 4 2 2 3 4 2 6 2 5 3 4 5 3 +--R (35a c + 210a b c + 105a b c + 7b c)d + 21a b c + 35a b c + 7b c +--R * +--R 11 +--R x +--R + +--R 4 3 105 4 2 3 2 105 2 4 2 +--R 35a b d + (--- a c + 210a b c + --- a b )d +--R 2 2 +--R + +--R 3 3 2 3 2 5 7 3 5 105 2 2 4 4 3 +--R (140a b c + 210a b c + 42a b c + b )d + 7a c + --- a b c + 35a b c +--R 2 +--R + +--R 7 6 2 +--R - b c +--R 2 +--R * +--R 10 +--R x +--R + +--R 5 3 4 3 3 2 +--R 7a d + (105a b c + 70a b )d +--R + +--R 4 3 3 2 2 2 4 6 3 4 2 3 3 +--R (35a c + 210a b c + 105a b c + 7a b )d + 35a b c + 70a b c +--R + +--R 5 2 7 +--R 21a b c + b c +--R * +--R 9 +--R x +--R + +--R 5 105 4 2 2 4 2 3 3 2 5 35 4 4 +--R (21a c + --- a b )d + (105a b c + 140a b c + 21a b )d + -- a c +--R 2 4 +--R + +--R 3 2 3 105 2 4 2 6 1 8 +--R 70a b c + --- a b c + 7a b c + - b +--R 2 8 +--R * +--R 8 +--R x +--R + +--R 5 2 5 2 4 2 3 4 4 3 3 3 2 +--R 21a b d + (21a c + 105a b c + 35a b )d + 35a b c + 70a b c +--R + +--R 2 5 7 +--R 21a b c + a b +--R * +--R 7 +--R x +--R + +--R 7 6 2 5 4 3 5 3 105 4 2 2 3 4 7 2 6 6 +--R (- a d + (42a b c + 35a b )d + 7a c + --- a b c + 35a b c + - a b )x +--R 2 2 2 +--R + +--R 6 5 2 5 2 4 3 3 5 5 +--R ((7a c + 21a b )d + 21a b c + 35a b c + 7a b )x +--R + +--R 6 7 6 2 5 2 35 4 4 4 7 6 5 3 3 +--R (7a b d + - a c + 21a b c + -- a b )x + (a d + 7a b c + 7a b )x +--R 2 4 +--R + +--R 7 7 6 2 2 7 1 8 +--R (a c + - a b )x + a b x + - a +--R 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 1483 +a0005:=integrate(t0005,x) +--R +--R +--R (28) +--R 1 8 24 7 23 7 7 2 6 22 7 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (a d + 7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 +--R ((7a c + - b )d + 21b c d + -- c d )x +--R 2 4 +--R + +--R 6 2 2 5 3 4 5 3 19 +--R (7a b d + (21a c + 21b c)d + 35b c d + 7c d )x +--R + +--R 7 2 6 3 5 3 105 2 2 4 4 3 7 6 2 18 +--R (- a d + (42a b c + 7b )d + (35a c + --- b c )d + 35b c d + - c d )x +--R 2 2 2 +--R + +--R 2 2 5 2 3 4 4 2 3 3 +--R (21a c + 21a b )d + (105a b c + 35b c)d + (35a c + 70b c )d +--R + +--R 5 2 7 +--R 21b c d + c d +--R * +--R 17 +--R x +--R + +--R 2 5 105 2 2 2 35 4 4 3 3 2 3 +--R 21a b d + (--- a c + 105a b c + -- b )d + (140a b c + 70b c )d +--R 2 4 +--R + +--R 5 105 2 4 2 6 1 8 +--R (21a c + --- b c )d + 7b c d + - c +--R 2 8 +--R * +--R 16 +--R x +--R + +--R 3 5 2 3 4 2 3 2 2 4 3 +--R 7a d + (105a b c + 35a b )d + (70a c + 210a b c + 35b c)d +--R + +--R 4 3 3 2 6 2 5 7 +--R (105a b c + 70b c )d + (7a c + 21b c )d + b c +--R * +--R 15 +--R x +--R + +--R 3 105 2 2 4 2 2 3 5 3 +--R (35a c + --- a b )d + (210a b c + 140a b c + 7b )d +--R 2 +--R + +--R 105 2 4 2 3 105 4 2 2 5 3 4 7 +--R (--- a c + 210a b c + --- b c )d + (42a b c + 35b c )d + a c +--R 2 2 +--R + +--R 7 2 6 +--R - b c +--R 2 +--R * +--R 14 +--R x +--R + +--R 3 4 3 2 2 2 4 3 +--R 35a b d + (70a c + 210a b c + 35a b )d +--R + +--R 2 3 3 2 5 2 2 5 2 4 4 3 +--R (210a b c + 210a b c + 21b c)d + (21a c + 105a b c + 35b c )d +--R + +--R 6 3 5 +--R 7a b c + 7b c +--R * +--R 13 +--R x +--R + +--R 35 4 4 3 2 3 3 +--R -- a d + (140a b c + 70a b )d +--R 4 +--R + +--R 3 3 2 2 2 4 7 6 2 +--R (70a c + 315a b c + 105a b c + - b )d +--R 2 +--R + +--R 2 4 3 3 5 2 7 2 6 2 5 35 4 4 +--R (105a b c + 140a b c + 21b c )d + - a c + 21a b c + -- b c +--R 2 4 +--R * +--R 12 +--R x +--R + +--R 4 3 2 3 3 2 2 3 5 2 +--R (35a c + 70a b )d + (210a b c + 210a b c + 21a b )d +--R + +--R 3 4 2 2 3 4 2 6 2 5 3 4 5 3 +--R (35a c + 210a b c + 105a b c + 7b c)d + 21a b c + 35a b c + 7b c +--R * +--R 11 +--R x +--R + +--R 4 3 105 4 2 3 2 105 2 4 2 +--R 35a b d + (--- a c + 210a b c + --- a b )d +--R 2 2 +--R + +--R 3 3 2 3 2 5 7 3 5 105 2 2 4 4 3 +--R (140a b c + 210a b c + 42a b c + b )d + 7a c + --- a b c + 35a b c +--R 2 +--R + +--R 7 6 2 +--R - b c +--R 2 +--R * +--R 10 +--R x +--R + +--R 5 3 4 3 3 2 +--R 7a d + (105a b c + 70a b )d +--R + +--R 4 3 3 2 2 2 4 6 3 4 2 3 3 +--R (35a c + 210a b c + 105a b c + 7a b )d + 35a b c + 70a b c +--R + +--R 5 2 7 +--R 21a b c + b c +--R * +--R 9 +--R x +--R + +--R 5 105 4 2 2 4 2 3 3 2 5 35 4 4 +--R (21a c + --- a b )d + (105a b c + 140a b c + 21a b )d + -- a c +--R 2 4 +--R + +--R 3 2 3 105 2 4 2 6 1 8 +--R 70a b c + --- a b c + 7a b c + - b +--R 2 8 +--R * +--R 8 +--R x +--R + +--R 5 2 5 2 4 2 3 4 4 3 3 3 2 +--R 21a b d + (21a c + 105a b c + 35a b )d + 35a b c + 70a b c +--R + +--R 2 5 7 +--R 21a b c + a b +--R * +--R 7 +--R x +--R + +--R 7 6 2 5 4 3 5 3 105 4 2 2 3 4 7 2 6 6 +--R (- a d + (42a b c + 35a b )d + 7a c + --- a b c + 35a b c + - a b )x +--R 2 2 2 +--R + +--R 6 5 2 5 2 4 3 3 5 5 +--R ((7a c + 21a b )d + 21a b c + 35a b c + 7a b )x +--R + +--R 6 7 6 2 5 2 35 4 4 4 7 6 5 3 3 +--R (7a b d + - a c + 21a b c + -- a b )x + (a d + 7a b c + 7a b )x +--R 2 4 +--R + +--R 7 7 6 2 2 7 +--R (a c + - a b )x + a b x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 1483 +m0005:=a0005-r0005 +--R +--R +--R 1 8 +--R (29) - - a +--R 8 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 1483 +d0005:=D(m0005,x) +--R +--R +--R (30) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +--S 31 of 1483 +t0006:= (b+2*c*x+3*d*x^2)*(b*x+c*x^2+d*x^3)^7 +--R +--R +--R (31) +--R 8 23 7 22 7 2 6 21 6 3 5 20 +--R 3d x + 23c d x + (22b d + 77c d )x + (147b c d + 147c d )x +--R + +--R 2 6 2 5 4 4 19 2 5 3 4 5 3 18 +--R (70b d + 420b c d + 175c d )x + (399b c d + 665b c d + 133c d )x +--R + +--R 3 5 2 2 4 4 3 6 2 17 +--R (126b d + 945b c d + 630b c d + 63c d )x +--R + +--R 3 4 2 3 3 5 2 7 16 +--R (595b c d + 1190b c d + 357b c d + 17c d)x +--R + +--R 4 4 3 2 3 2 4 2 6 8 15 +--R (140b d + 1120b c d + 840b c d + 112b c d + 2c )x +--R + +--R 4 3 3 3 2 2 5 7 14 +--R (525b c d + 1050b c d + 315b c d + 15b c )x +--R + +--R 5 3 4 2 2 3 4 2 6 13 +--R (98b d + 735b c d + 490b c d + 49b c )x +--R + +--R 5 2 4 3 3 5 12 6 2 5 2 4 4 11 +--R (273b c d + 455b c d + 91b c )x + (42b d + 252b c d + 105b c )x +--R + +--R 6 5 3 10 7 6 2 9 7 8 8 7 +--R (77b c d + 77b c )x + (10b d + 35b c )x + 9b c x + b x +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 1483 +r0006:= 1/8*x^8*(b+c*x+d*x^2)^8 +--R +--R +--R (32) +--R 1 8 24 7 23 7 7 2 6 22 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 2 5 3 4 5 3 19 +--R (- b d + 21b c d + -- c d )x + (21b c d + 35b c d + 7c d )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 18 +--R (7b d + --- b c d + 35b c d + - c d )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 17 +--R (35b c d + 70b c d + 21b c d + c d)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 16 +--R (-- b d + 70b c d + --- b c d + 7b c d + - c )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 15 +--R (35b c d + 70b c d + 21b c d + b c )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 14 +--R (7b d + --- b c d + 35b c d + - b c )x +--R 2 2 +--R + +--R 5 2 4 3 3 5 13 7 6 2 5 2 35 4 4 12 +--R (21b c d + 35b c d + 7b c )x + (- b d + 21b c d + -- b c )x +--R 2 4 +--R + +--R 6 5 3 11 7 7 6 2 10 7 9 1 8 8 +--R (7b c d + 7b c )x + (b d + - b c )x + b c x + - b x +--R 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 1483 +a0006:=integrate(t0006,x) +--R +--R +--R (33) +--R 1 8 24 7 23 7 7 2 6 22 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 2 5 3 4 5 3 19 +--R (- b d + 21b c d + -- c d )x + (21b c d + 35b c d + 7c d )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 18 +--R (7b d + --- b c d + 35b c d + - c d )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 17 +--R (35b c d + 70b c d + 21b c d + c d)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 16 +--R (-- b d + 70b c d + --- b c d + 7b c d + - c )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 15 +--R (35b c d + 70b c d + 21b c d + b c )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 14 +--R (7b d + --- b c d + 35b c d + - b c )x +--R 2 2 +--R + +--R 5 2 4 3 3 5 13 7 6 2 5 2 35 4 4 12 +--R (21b c d + 35b c d + 7b c )x + (- b d + 21b c d + -- b c )x +--R 2 4 +--R + +--R 6 5 3 11 7 7 6 2 10 7 9 1 8 8 +--R (7b c d + 7b c )x + (b d + - b c )x + b c x + - b x +--R 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 1483 +m0006:=a0006-r0006 +--R +--R +--R (34) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 1483 +d0006:=D(m0006,x) +--R +--R +--R (35) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +--S 36 of 1483 +t0007:= (b+2*c*x+3*d*x^2)*x^7*(b+c*x+d*x^2)^7 +--R +--R +--R (36) +--R 8 23 7 22 7 2 6 21 6 3 5 20 +--R 3d x + 23c d x + (22b d + 77c d )x + (147b c d + 147c d )x +--R + +--R 2 6 2 5 4 4 19 2 5 3 4 5 3 18 +--R (70b d + 420b c d + 175c d )x + (399b c d + 665b c d + 133c d )x +--R + +--R 3 5 2 2 4 4 3 6 2 17 +--R (126b d + 945b c d + 630b c d + 63c d )x +--R + +--R 3 4 2 3 3 5 2 7 16 +--R (595b c d + 1190b c d + 357b c d + 17c d)x +--R + +--R 4 4 3 2 3 2 4 2 6 8 15 +--R (140b d + 1120b c d + 840b c d + 112b c d + 2c )x +--R + +--R 4 3 3 3 2 2 5 7 14 +--R (525b c d + 1050b c d + 315b c d + 15b c )x +--R + +--R 5 3 4 2 2 3 4 2 6 13 +--R (98b d + 735b c d + 490b c d + 49b c )x +--R + +--R 5 2 4 3 3 5 12 6 2 5 2 4 4 11 +--R (273b c d + 455b c d + 91b c )x + (42b d + 252b c d + 105b c )x +--R + +--R 6 5 3 10 7 6 2 9 7 8 8 7 +--R (77b c d + 77b c )x + (10b d + 35b c )x + 9b c x + b x +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 1483 +r0007:= 1/8*x^8*(b+c*x+d*x^2)^8 +--R +--R +--R (37) +--R 1 8 24 7 23 7 7 2 6 22 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 2 5 3 4 5 3 19 +--R (- b d + 21b c d + -- c d )x + (21b c d + 35b c d + 7c d )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 18 +--R (7b d + --- b c d + 35b c d + - c d )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 17 +--R (35b c d + 70b c d + 21b c d + c d)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 16 +--R (-- b d + 70b c d + --- b c d + 7b c d + - c )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 15 +--R (35b c d + 70b c d + 21b c d + b c )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 14 +--R (7b d + --- b c d + 35b c d + - b c )x +--R 2 2 +--R + +--R 5 2 4 3 3 5 13 7 6 2 5 2 35 4 4 12 +--R (21b c d + 35b c d + 7b c )x + (- b d + 21b c d + -- b c )x +--R 2 4 +--R + +--R 6 5 3 11 7 7 6 2 10 7 9 1 8 8 +--R (7b c d + 7b c )x + (b d + - b c )x + b c x + - b x +--R 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 37 + +--S 38 of 1483 +a0007:=integrate(t0007,x) +--R +--R +--R (38) +--R 1 8 24 7 23 7 7 2 6 22 6 3 5 21 +--R - d x + c d x + (b d + - c d )x + (7b c d + 7c d )x +--R 8 2 +--R + +--R 7 2 6 2 5 35 4 4 20 2 5 3 4 5 3 19 +--R (- b d + 21b c d + -- c d )x + (21b c d + 35b c d + 7c d )x +--R 2 4 +--R + +--R 3 5 105 2 2 4 4 3 7 6 2 18 +--R (7b d + --- b c d + 35b c d + - c d )x +--R 2 2 +--R + +--R 3 4 2 3 3 5 2 7 17 +--R (35b c d + 70b c d + 21b c d + c d)x +--R + +--R 35 4 4 3 2 3 105 2 4 2 6 1 8 16 +--R (-- b d + 70b c d + --- b c d + 7b c d + - c )x +--R 4 2 8 +--R + +--R 4 3 3 3 2 2 5 7 15 +--R (35b c d + 70b c d + 21b c d + b c )x +--R + +--R 5 3 105 4 2 2 3 4 7 2 6 14 +--R (7b d + --- b c d + 35b c d + - b c )x +--R 2 2 +--R + +--R 5 2 4 3 3 5 13 7 6 2 5 2 35 4 4 12 +--R (21b c d + 35b c d + 7b c )x + (- b d + 21b c d + -- b c )x +--R 2 4 +--R + +--R 6 5 3 11 7 7 6 2 10 7 9 1 8 8 +--R (7b c d + 7b c )x + (b d + - b c )x + b c x + - b x +--R 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 1483 +m0007:=a0007-r0007 +--R +--R +--R (39) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 39 + +--S 40 of 1483 +d0007:=D(m0007,x) +--R +--R +--R (40) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +--S 41 of 1483 +t0008:= (b+3*d*x^2)*(a+b*x+d*x^3)^7 +--R +--R +--R (41) +--R 8 23 7 21 7 20 2 6 19 6 18 +--R 3d x + 22b d x + 21a d x + 70b d x + 133a b d x +--R + +--R 2 6 3 5 17 2 5 16 2 5 4 4 15 +--R (63a d + 126b d )x + 357a b d x + (336a b d + 140b d )x +--R + +--R 3 5 3 4 14 2 2 4 5 3 13 +--R (105a d + 525a b d )x + (735a b d + 98b d )x +--R + +--R 3 4 4 3 12 4 4 2 3 3 6 2 11 +--R (455a b d + 455a b d )x + (105a d + 840a b d + 42b d )x +--R + +--R 3 2 3 5 2 10 4 3 2 4 2 7 9 +--R (770a b d + 231a b d )x + (350a b d + 525a b d + 10b d)x +--R + +--R 5 3 3 3 2 6 8 4 2 2 2 5 8 7 +--R (63a d + 630a b d + 63a b d)x + (420a b d + 168a b d + b )x +--R + +--R 5 2 3 4 7 6 6 2 4 3 2 6 5 +--R (147a b d + 245a b d + 7a b )x + (21a d + 210a b d + 21a b )x +--R + +--R 5 2 3 5 4 6 4 4 3 7 5 3 2 6 2 +--R (105a b d + 35a b )x + (28a b d + 35a b )x + (3a d + 21a b )x + 7a b x +--R + +--R 7 +--R a b +--R Type: Polynomial(Integer) +--E 41 + +--S 42 of 1483 +r0008:= 1/8*(a+b*x+d*x^3)^8 +--R +--R +--R (42) +--R 1 8 24 7 22 7 21 7 2 6 20 6 19 7 2 6 3 5 18 +--R - d x + b d x + a d x + - b d x + 7a b d x + (- a d + 7b d )x +--R 8 2 2 +--R + +--R 2 5 17 2 5 35 4 4 16 3 5 3 4 15 +--R 21a b d x + (21a b d + -- b d )x + (7a d + 35a b d )x +--R 4 +--R + +--R 105 2 2 4 5 3 14 3 4 4 3 13 +--R (--- a b d + 7b d )x + (35a b d + 35a b d )x +--R 2 +--R + +--R 35 4 4 2 3 3 7 6 2 12 3 2 3 5 2 11 +--R (-- a d + 70a b d + - b d )x + (70a b d + 21a b d )x +--R 4 2 +--R + +--R 4 3 105 2 4 2 7 10 5 3 3 3 2 6 9 +--R (35a b d + --- a b d + b d)x + (7a d + 70a b d + 7a b d)x +--R 2 +--R + +--R 105 4 2 2 2 5 1 8 8 5 2 3 4 7 7 +--R (--- a b d + 21a b d + - b )x + (21a b d + 35a b d + a b )x +--R 2 8 +--R + +--R 7 6 2 4 3 7 2 6 6 5 2 3 5 5 6 35 4 4 4 +--R (- a d + 35a b d + - a b )x + (21a b d + 7a b )x + (7a b d + -- a b )x +--R 2 2 4 +--R + +--R 7 5 3 3 7 6 2 2 7 1 8 +--R (a d + 7a b )x + - a b x + a b x + - a +--R 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 42 + +--S 43 of 1483 +a0008:=integrate(t0008,x) +--R +--R +--R (43) +--R 1 8 24 7 22 7 21 7 2 6 20 6 19 7 2 6 3 5 18 +--R - d x + b d x + a d x + - b d x + 7a b d x + (- a d + 7b d )x +--R 8 2 2 +--R + +--R 2 5 17 2 5 35 4 4 16 3 5 3 4 15 +--R 21a b d x + (21a b d + -- b d )x + (7a d + 35a b d )x +--R 4 +--R + +--R 105 2 2 4 5 3 14 3 4 4 3 13 +--R (--- a b d + 7b d )x + (35a b d + 35a b d )x +--R 2 +--R + +--R 35 4 4 2 3 3 7 6 2 12 3 2 3 5 2 11 +--R (-- a d + 70a b d + - b d )x + (70a b d + 21a b d )x +--R 4 2 +--R + +--R 4 3 105 2 4 2 7 10 5 3 3 3 2 6 9 +--R (35a b d + --- a b d + b d)x + (7a d + 70a b d + 7a b d)x +--R 2 +--R + +--R 105 4 2 2 2 5 1 8 8 5 2 3 4 7 7 +--R (--- a b d + 21a b d + - b )x + (21a b d + 35a b d + a b )x +--R 2 8 +--R + +--R 7 6 2 4 3 7 2 6 6 5 2 3 5 5 6 35 4 4 4 +--R (- a d + 35a b d + - a b )x + (21a b d + 7a b )x + (7a b d + -- a b )x +--R 2 2 4 +--R + +--R 7 5 3 3 7 6 2 2 7 +--R (a d + 7a b )x + - a b x + a b x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 43 + +--S 44 of 1483 +m0008:=a0008-r0008 +--R +--R +--R 1 8 +--R (44) - - a +--R 8 +--R Type: Polynomial(Fraction(Integer)) +--E 44 + +--S 45 of 1483 +d0008:=D(m0008,x) +--R +--R +--R (45) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 45 + +--S 46 of 1483 +t0009:= (2*c*x+3*d*x^2)*(a+c*x^2+d*x^3)^7 +--R +--R +--R (46) +--R 8 23 7 22 2 6 21 7 3 5 20 +--R 3d x + 23c d x + 77c d x + (21a d + 147c d )x +--R + +--R 6 4 4 19 2 5 5 3 18 +--R (140a c d + 175c d )x + (399a c d + 133c d )x +--R + +--R 2 6 3 4 6 2 17 2 5 4 3 7 16 +--R (63a d + 630a c d + 63c d )x + (357a c d + 595a c d + 17c d)x +--R + +--R 2 2 4 5 2 8 15 3 5 2 3 3 6 14 +--R (840a c d + 336a c d + 2c )x + (105a d + 1050a c d + 105a c d)x +--R + +--R 3 4 2 4 2 7 13 3 2 3 2 5 12 +--R (490a c d + 735a c d + 14a c )x + (910a c d + 273a c d)x +--R + +--R 4 4 3 3 2 2 6 11 4 3 3 4 10 +--R (105a d + 840a c d + 42a c )x + (385a c d + 385a c d)x +--R + +--R 4 2 2 3 5 9 5 3 4 3 8 5 2 4 4 7 +--R (525a c d + 70a c )x + (63a d + 315a c d)x + (168a c d + 70a c )x +--R + +--R 5 2 6 6 2 5 3 5 6 4 6 2 3 7 2 7 +--R 147a c d x + (21a d + 42a c )x + 35a c d x + 14a c x + 3a d x + 2a c x +--R Type: Polynomial(Integer) +--E 46 + +--S 47 of 1483 +r0009:= 1/8*(a+c*x^2+d*x^3)^8 +--R +--R +--R (47) +--R 1 8 24 7 23 7 2 6 22 7 3 5 21 6 35 4 4 20 +--R - d x + c d x + - c d x + (a d + 7c d )x + (7a c d + -- c d )x +--R 8 2 4 +--R + +--R 2 5 5 3 19 7 2 6 3 4 7 6 2 18 +--R (21a c d + 7c d )x + (- a d + 35a c d + - c d )x +--R 2 2 +--R + +--R 2 5 4 3 7 17 105 2 2 4 5 2 1 8 16 +--R (21a c d + 35a c d + c d)x + (--- a c d + 21a c d + - c )x +--R 2 8 +--R + +--R 3 5 2 3 3 6 15 3 4 105 2 4 2 7 14 +--R (7a d + 70a c d + 7a c d)x + (35a c d + --- a c d + a c )x +--R 2 +--R + +--R 3 2 3 2 5 13 35 4 4 3 3 2 7 2 6 12 +--R (70a c d + 21a c d)x + (-- a d + 70a c d + - a c )x +--R 4 2 +--R + +--R 4 3 3 4 11 105 4 2 2 3 5 10 5 3 4 3 9 +--R (35a c d + 35a c d)x + (--- a c d + 7a c )x + (7a d + 35a c d)x +--R 2 +--R + +--R 5 2 35 4 4 8 5 2 7 7 6 2 5 3 6 6 5 +--R (21a c d + -- a c )x + 21a c d x + (- a d + 7a c )x + 7a c d x +--R 4 2 +--R + +--R 7 6 2 4 7 3 7 2 1 8 +--R - a c x + a d x + a c x + - a +--R 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 47 + +--S 48 of 1483 +a0009:=integrate(t0009,x) +--R +--R +--R (48) +--R 1 8 24 7 23 7 2 6 22 7 3 5 21 6 35 4 4 20 +--R - d x + c d x + - c d x + (a d + 7c d )x + (7a c d + -- c d )x +--R 8 2 4 +--R + +--R 2 5 5 3 19 7 2 6 3 4 7 6 2 18 +--R (21a c d + 7c d )x + (- a d + 35a c d + - c d )x +--R 2 2 +--R + +--R 2 5 4 3 7 17 105 2 2 4 5 2 1 8 16 +--R (21a c d + 35a c d + c d)x + (--- a c d + 21a c d + - c )x +--R 2 8 +--R + +--R 3 5 2 3 3 6 15 3 4 105 2 4 2 7 14 +--R (7a d + 70a c d + 7a c d)x + (35a c d + --- a c d + a c )x +--R 2 +--R + +--R 3 2 3 2 5 13 35 4 4 3 3 2 7 2 6 12 +--R (70a c d + 21a c d)x + (-- a d + 70a c d + - a c )x +--R 4 2 +--R + +--R 4 3 3 4 11 105 4 2 2 3 5 10 5 3 4 3 9 +--R (35a c d + 35a c d)x + (--- a c d + 7a c )x + (7a d + 35a c d)x +--R 2 +--R + +--R 5 2 35 4 4 8 5 2 7 7 6 2 5 3 6 6 5 +--R (21a c d + -- a c )x + 21a c d x + (- a d + 7a c )x + 7a c d x +--R 4 2 +--R + +--R 7 6 2 4 7 3 7 2 +--R - a c x + a d x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 48 + +--S 49 of 1483 +m0009:=a0009-r0009 +--R +--R +--R 1 8 +--R (49) - - a +--R 8 +--R Type: Polynomial(Fraction(Integer)) +--E 49 + +--S 50 of 1483 +d0009:=D(m0009,x) +--R +--R +--R (50) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 50 + +--S 51 of 1483 +t0010:= x*(2*c+3*d*x)*(a+c*x^2+d*x^3)^7 +--R +--R +--R (51) +--R 8 23 7 22 2 6 21 7 3 5 20 +--R 3d x + 23c d x + 77c d x + (21a d + 147c d )x +--R + +--R 6 4 4 19 2 5 5 3 18 +--R (140a c d + 175c d )x + (399a c d + 133c d )x +--R + +--R 2 6 3 4 6 2 17 2 5 4 3 7 16 +--R (63a d + 630a c d + 63c d )x + (357a c d + 595a c d + 17c d)x +--R + +--R 2 2 4 5 2 8 15 3 5 2 3 3 6 14 +--R (840a c d + 336a c d + 2c )x + (105a d + 1050a c d + 105a c d)x +--R + +--R 3 4 2 4 2 7 13 3 2 3 2 5 12 +--R (490a c d + 735a c d + 14a c )x + (910a c d + 273a c d)x +--R + +--R 4 4 3 3 2 2 6 11 4 3 3 4 10 +--R (105a d + 840a c d + 42a c )x + (385a c d + 385a c d)x +--R + +--R 4 2 2 3 5 9 5 3 4 3 8 5 2 4 4 7 +--R (525a c d + 70a c )x + (63a d + 315a c d)x + (168a c d + 70a c )x +--R + +--R 5 2 6 6 2 5 3 5 6 4 6 2 3 7 2 7 +--R 147a c d x + (21a d + 42a c )x + 35a c d x + 14a c x + 3a d x + 2a c x +--R Type: Polynomial(Integer) +--E 51 + +--S 52 of 1483 +r0010:= 1/8*(a+c*x^2+d*x^3)^8 +--R +--R +--R (52) +--R 1 8 24 7 23 7 2 6 22 7 3 5 21 6 35 4 4 20 +--R - d x + c d x + - c d x + (a d + 7c d )x + (7a c d + -- c d )x +--R 8 2 4 +--R + +--R 2 5 5 3 19 7 2 6 3 4 7 6 2 18 +--R (21a c d + 7c d )x + (- a d + 35a c d + - c d )x +--R 2 2 +--R + +--R 2 5 4 3 7 17 105 2 2 4 5 2 1 8 16 +--R (21a c d + 35a c d + c d)x + (--- a c d + 21a c d + - c )x +--R 2 8 +--R + +--R 3 5 2 3 3 6 15 3 4 105 2 4 2 7 14 +--R (7a d + 70a c d + 7a c d)x + (35a c d + --- a c d + a c )x +--R 2 +--R + +--R 3 2 3 2 5 13 35 4 4 3 3 2 7 2 6 12 +--R (70a c d + 21a c d)x + (-- a d + 70a c d + - a c )x +--R 4 2 +--R + +--R 4 3 3 4 11 105 4 2 2 3 5 10 5 3 4 3 9 +--R (35a c d + 35a c d)x + (--- a c d + 7a c )x + (7a d + 35a c d)x +--R 2 +--R + +--R 5 2 35 4 4 8 5 2 7 7 6 2 5 3 6 6 5 +--R (21a c d + -- a c )x + 21a c d x + (- a d + 7a c )x + 7a c d x +--R 4 2 +--R + +--R 7 6 2 4 7 3 7 2 1 8 +--R - a c x + a d x + a c x + - a +--R 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 52 + +--S 53 of 1483 +a0010:=integrate(t0010,x) +--R +--R +--R (53) +--R 1 8 24 7 23 7 2 6 22 7 3 5 21 6 35 4 4 20 +--R - d x + c d x + - c d x + (a d + 7c d )x + (7a c d + -- c d )x +--R 8 2 4 +--R + +--R 2 5 5 3 19 7 2 6 3 4 7 6 2 18 +--R (21a c d + 7c d )x + (- a d + 35a c d + - c d )x +--R 2 2 +--R + +--R 2 5 4 3 7 17 105 2 2 4 5 2 1 8 16 +--R (21a c d + 35a c d + c d)x + (--- a c d + 21a c d + - c )x +--R 2 8 +--R + +--R 3 5 2 3 3 6 15 3 4 105 2 4 2 7 14 +--R (7a d + 70a c d + 7a c d)x + (35a c d + --- a c d + a c )x +--R 2 +--R + +--R 3 2 3 2 5 13 35 4 4 3 3 2 7 2 6 12 +--R (70a c d + 21a c d)x + (-- a d + 70a c d + - a c )x +--R 4 2 +--R + +--R 4 3 3 4 11 105 4 2 2 3 5 10 5 3 4 3 9 +--R (35a c d + 35a c d)x + (--- a c d + 7a c )x + (7a d + 35a c d)x +--R 2 +--R + +--R 5 2 35 4 4 8 5 2 7 7 6 2 5 3 6 6 5 +--R (21a c d + -- a c )x + 21a c d x + (- a d + 7a c )x + 7a c d x +--R 4 2 +--R + +--R 7 6 2 4 7 3 7 2 +--R - a c x + a d x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 53 + +--S 54 of 1483 +m0010:=a0010-r0010 +--R +--R +--R 1 8 +--R (54) - - a +--R 8 +--R Type: Polynomial(Fraction(Integer)) +--E 54 + +--S 55 of 1483 +d0010:=D(m0010,x) +--R +--R +--R (55) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 55 + +--S 56 of 1483 +t0011:= (-4+4*x+x^2)*(5-12*x+6*x^2+x^3) +--R +--R +--R 5 4 3 2 +--R (56) x + 10x + 8x - 67x + 68x - 20 +--R Type: Polynomial(Integer) +--E 56 + +--S 57 of 1483 +r0011:= 1/6*(5-12*x+6*x^2+x^3)^2 +--R +--R +--R 1 6 5 4 67 3 2 25 +--R (57) - x + 2x + 2x - -- x + 34x - 20x + -- +--R 6 3 6 +--R Type: Polynomial(Fraction(Integer)) +--E 57 + +--S 58 of 1483 +a0011:=integrate(t0011,x) +--R +--R +--R 1 6 5 4 67 3 2 +--R (58) - x + 2x + 2x - -- x + 34x - 20x +--R 6 3 +--R Type: Polynomial(Fraction(Integer)) +--E 58 + +--S 59 of 1483 +m0011:=a0011-r0011 +--R +--R +--R 25 +--R (59) - -- +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 59 + +--S 60 of 1483 +d0011:=D(m0011,x) +--R +--R +--R (60) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 60 + +--S 61 of 1483 +t0012:= (2*x+x^3)*(1+4*x^2+x^4) +--R +--R +--R 7 5 3 +--R (61) x + 6x + 9x + 2x +--R Type: Polynomial(Integer) +--E 61 + +--S 62 of 1483 +r0012:= 1/8*(1+4*x^2+x^4)^2 +--R +--R +--R 1 8 6 9 4 2 1 +--R (62) - x + x + - x + x + - +--R 8 4 8 +--R Type: Polynomial(Fraction(Integer)) +--E 62 + +--S 63 of 1483 +a0012:=integrate(t0012,x) +--R +--R +--R 1 8 6 9 4 2 +--R (63) - x + x + - x + x +--R 8 4 +--R Type: Polynomial(Fraction(Integer)) +--E 63 + +--S 64 of 1483 +m0012:=a0012-r0012 +--R +--R +--R 1 +--R (64) - - +--R 8 +--R Type: Polynomial(Fraction(Integer)) +--E 64 + +--S 65 of 1483 +d0012:=D(m0012,x) +--R +--R +--R (65) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 65 + +--S 66 of 1483 +t0013:= (a*x+b*x^7)^5 +--R +--R +--R 5 35 4 29 2 3 23 3 2 17 4 11 5 5 +--R (66) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 66 + +--S 67 of 1483 +r0013:= 1/36*(a+b*x^6)^6/b +--R +--R +--R (67) +--R 1 6 36 1 5 30 5 2 4 24 5 3 3 18 5 4 2 12 1 5 6 1 6 +--R -- b x + - a b x + -- a b x + - a b x + -- a b x + - a b x + -- a +--R 36 6 12 9 12 6 36 +--R ----------------------------------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 67 + +--S 68 of 1483 +a0013:=integrate(t0013,x) +--R +--R +--R 1 5 36 1 4 30 5 2 3 24 5 3 2 18 5 4 12 1 5 6 +--R (68) -- b x + - a b x + -- a b x + - a b x + -- a b x + - a x +--R 36 6 12 9 12 6 +--R Type: Polynomial(Fraction(Integer)) +--E 68 + +--S 69 of 1483 +m0013:=a0013-r0013 +--R +--R +--R 1 6 +--R -- a +--R 36 +--R (69) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 69 + +--S 70 of 1483 +d0013:=D(m0013,x) +--R +--R +--R (70) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 70 + +--S 71 of 1483 +t0014:= (a*x^2+b*x^13)^5 +--R +--R +--R 5 65 4 54 2 3 43 3 2 32 4 21 5 10 +--R (71) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 71 + +--S 72 of 1483 +r0014:= 1/66*(a+b*x^11)^6/b +--R +--R +--R (72) +--R 1 6 66 1 5 55 5 2 4 44 10 3 3 33 5 4 2 22 1 5 11 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 66 11 22 33 22 11 +--R + +--R 1 6 +--R -- a +--R 66 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 72 + +--S 73 of 1483 +a0014:=integrate(t0014,x) +--R +--R +--R (73) +--R 1 5 66 1 4 55 5 2 3 44 10 3 2 33 5 4 22 1 5 11 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 66 11 22 33 22 11 +--R Type: Polynomial(Fraction(Integer)) +--E 73 + +--S 74 of 1483 +m0014:=a0014-r0014 +--R +--R +--R 1 6 +--R -- a +--R 66 +--R (74) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 74 + +--S 75 of 1483 +d0014:=D(m0014,x) +--R +--R +--R (75) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 75 + +--S 76 of 1483 +t0015:= (a*x^3+b*x^19)^5 +--R +--R +--R 5 95 4 79 2 3 63 3 2 47 4 31 5 15 +--R (76) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 1483 +r0015:= 1/96*(a+b*x^16)^6/b +--R +--R +--R (77) +--R 1 6 96 1 5 80 5 2 4 64 5 3 3 48 5 4 2 32 1 5 16 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 96 16 32 24 32 16 +--R + +--R 1 6 +--R -- a +--R 96 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 1483 +a0015:=integrate(t0015,x) +--R +--R +--R (78) +--R 1 5 96 1 4 80 5 2 3 64 5 3 2 48 5 4 32 1 5 16 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 96 16 32 24 32 16 +--R Type: Polynomial(Fraction(Integer)) +--E 78 + +--S 79 of 1483 +m0015:=a0015-r0015 +--R +--R +--R 1 6 +--R -- a +--R 96 +--R (79) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 79 + +--S 80 of 1483 +d0015:=D(m0015,x) +--R +--R +--R (80) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 80 + +--S 81 of 1483 +t0016:= (a+b*x)*(1+(c+a*x+1/2*b*x^2)^4) +--R +--R +--R (81) +--R 1 5 9 9 4 8 1 4 2 3 7 7 3 7 3 2 6 +--R -- b x + -- a b x + (- b c + 2a b )x + (- a b c + - a b )x +--R 16 16 2 2 2 +--R + +--R 3 3 2 2 2 4 5 15 2 2 3 5 4 +--R (- b c + 9a b c + 3a b)x + (-- a b c + 10a b c + a )x +--R 2 2 +--R + +--R 2 3 2 2 4 3 3 3 2 2 4 2 3 +--R (2b c + 12a b c + 4a c)x + (6a b c + 6a c )x + (b c + 4a c + b)x +--R + +--R 4 +--R a c + a +--R Type: Polynomial(Fraction(Integer)) +--E 81 + +--S 82 of 1483 +r0016:= c+a*x+1/2*b*x^2+1/160*(2*c+2*a*x+b*x^2)^5 +--R +--R +--R (82) +--R 1 5 10 1 4 9 1 4 1 2 3 8 1 3 1 3 2 7 +--R --- b x + -- a b x + (-- b c + - a b )x + (- a b c + - a b )x +--R 160 16 16 4 2 2 +--R + +--R 1 3 2 3 2 2 1 4 6 3 2 2 3 1 5 5 +--R (- b c + - a b c + - a b)x + (- a b c + 2a b c + - a )x +--R 4 2 2 2 5 +--R + +--R 1 2 3 2 2 4 4 3 3 2 3 1 4 2 3 1 2 +--R (- b c + 3a b c + a c)x + (2a b c + 2a c )x + (- b c + 2a c + - b)x +--R 2 2 2 +--R + +--R 4 1 5 +--R (a c + a)x + - c + c +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 82 + +--S 83 of 1483 +a0016:=integrate(t0016,x) +--R +--R +--R (83) +--R 1 5 10 1 4 9 1 4 1 2 3 8 1 3 1 3 2 7 +--R --- b x + -- a b x + (-- b c + - a b )x + (- a b c + - a b )x +--R 160 16 16 4 2 2 +--R + +--R 1 3 2 3 2 2 1 4 6 3 2 2 3 1 5 5 +--R (- b c + - a b c + - a b)x + (- a b c + 2a b c + - a )x +--R 4 2 2 2 5 +--R + +--R 1 2 3 2 2 4 4 3 3 2 3 1 4 2 3 1 2 +--R (- b c + 3a b c + a c)x + (2a b c + 2a c )x + (- b c + 2a c + - b)x +--R 2 2 2 +--R + +--R 4 +--R (a c + a)x +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 of 1483 +m0016:=a0016-r0016 +--R +--R +--R 1 5 +--R (84) - - c - c +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 84 + +--S 85 of 1483 +d0016:=D(m0016,x) +--R +--R +--R (85) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +--S 86 of 1483 +t0017:= (a+c*x^2)*(1+(d+a*x+1/3*c*x^3)^5) +--R +--R +--R (86) +--R 1 6 17 16 5 15 5 5 14 35 2 4 13 65 4 12 +--R --- c x + --- a c x + -- c d x + -- a c x + -- a c d x +--R 243 243 81 81 81 +--R + +--R 10 4 2 40 3 3 11 110 2 3 10 100 3 2 25 4 2 9 +--R (-- c d + -- a c )x + --- a c d x + (--- a c d + -- a c )x +--R 27 27 27 27 9 +--R + +--R 10 3 3 3 2 8 40 2 2 2 8 5 7 70 2 3 35 4 6 +--R (-- c d + 10a c d)x + (-- a c d + - a c)x + (-- a c d + -- a c d)x +--R 9 3 3 9 3 +--R + +--R 5 2 4 3 2 6 5 50 2 3 5 4 20 4 4 2 3 +--R (- c d + 20a c d + a )x + (-- a c d + 5a d)x + (-- a c d + 10a d )x +--R 3 3 3 +--R + +--R 5 3 3 2 2 4 5 +--R (c d + 10a d + c)x + 5a d x + a d + a +--R Type: Polynomial(Fraction(Integer)) +--E 86 + +--S 87 of 1483 +r0017:= d+a*x+1/3*c*x^3+1/4374*(3*d+3*a*x+c*x^3)^6 +--R +--R +--R (87) +--R 1 6 18 1 5 16 1 5 15 5 2 4 14 5 4 13 +--R ---- c x + --- a c x + --- c d x + --- a c x + -- a c d x +--R 4374 243 243 162 81 +--R + +--R 5 4 2 10 3 3 12 10 2 3 11 10 3 2 5 4 2 10 +--R (--- c d + -- a c )x + -- a c d x + (-- a c d + -- a c )x +--R 162 81 27 27 18 +--R + +--R 10 3 3 10 3 2 9 5 2 2 2 1 5 8 10 2 3 5 4 7 +--R (-- c d + -- a c d)x + (- a c d + - a c)x + (-- a c d + - a c d)x +--R 81 9 3 3 9 3 +--R + +--R 5 2 4 10 3 2 1 6 6 10 2 3 5 5 +--R (-- c d + -- a c d + - a )x + (-- a c d + a d)x +--R 18 3 6 3 +--R + +--R 5 4 5 4 2 4 1 5 10 3 3 1 3 5 2 4 2 5 +--R (- a c d + - a d )x + (- c d + -- a d + - c)x + - a d x + (a d + a)x +--R 3 2 3 3 3 2 +--R + +--R 1 6 +--R - d + d +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 87 + +--S 88 of 1483 +a0017:=integrate(t0017,x) +--R +--R +--R (88) +--R 1 6 18 1 5 16 1 5 15 5 2 4 14 5 4 13 +--R ---- c x + --- a c x + --- c d x + --- a c x + -- a c d x +--R 4374 243 243 162 81 +--R + +--R 5 4 2 10 3 3 12 10 2 3 11 10 3 2 5 4 2 10 +--R (--- c d + -- a c )x + -- a c d x + (-- a c d + -- a c )x +--R 162 81 27 27 18 +--R + +--R 10 3 3 10 3 2 9 5 2 2 2 1 5 8 10 2 3 5 4 7 +--R (-- c d + -- a c d)x + (- a c d + - a c)x + (-- a c d + - a c d)x +--R 81 9 3 3 9 3 +--R + +--R 5 2 4 10 3 2 1 6 6 10 2 3 5 5 +--R (-- c d + -- a c d + - a )x + (-- a c d + a d)x +--R 18 3 6 3 +--R + +--R 5 4 5 4 2 4 1 5 10 3 3 1 3 5 2 4 2 5 +--R (- a c d + - a d )x + (- c d + -- a d + - c)x + - a d x + (a d + a)x +--R 3 2 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 88 + +--S 89 of 1483 +m0017:=a0017-r0017 +--R +--R +--R 1 6 +--R (89) - - d - d +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 89 + +--S 90 of 1483 +d0017:=D(m0017,x) +--R +--R +--R (90) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 90 + +--S 91 of 1483 +t0018:= (b*x+c*x^2)*(1+(d+1/2*b*x^2+1/3*c*x^3)^5) +--R +--R +--R (91) +--R 1 6 17 17 5 16 10 2 4 15 5 5 25 3 3 14 +--R --- c x + --- b c x + -- b c x + (-- c d + --- b c )x +--R 243 486 81 81 108 +--R + +--R 35 4 35 4 2 13 65 2 3 13 5 12 +--R (-- b c d + --- b c )x + (-- b c d + -- b c)x +--R 81 144 54 96 +--R + +--R 10 4 2 5 3 2 1 6 11 55 3 2 55 4 10 +--R (-- c d + - b c d + -- b )x + (-- b c d + -- b c d)x +--R 27 3 32 27 48 +--R + +--R 25 2 2 2 5 5 9 10 3 3 15 3 2 8 40 2 3 5 4 2 7 +--R (-- b c d + -- b d)x + (-- c d + -- b c d )x + (-- b c d + - b d )x +--R 6 16 9 4 9 4 +--R + +--R 35 2 3 6 5 2 4 5 3 3 5 25 4 4 5 2 4 3 5 2 +--R -- b c d x + (- c d + - b d )x + -- b c d x + - b d x + (c d + c)x +--R 6 3 2 6 2 +--R + +--R 5 +--R (b d + b)x +--R Type: Polynomial(Fraction(Integer)) +--E 91 + +--S 92 of 1483 +r0018:= d+1/2*b*x^2+1/3*c*x^3+1/279936*(6*d+3*b*x^2+2*c*x^3)^6 +--R +--R +--R (92) +--R 1 6 18 1 5 17 5 2 4 16 1 5 5 3 3 15 +--R ---- c x + --- b c x + --- b c x + (--- c d + --- b c )x +--R 4374 486 648 243 324 +--R + +--R 5 4 5 4 2 14 5 2 3 1 5 13 +--R (--- b c d + --- b c )x + (-- b c d + -- b c)x +--R 162 288 54 96 +--R + +--R 5 4 2 5 3 2 1 6 12 5 3 2 5 4 11 +--R (--- c d + -- b c d + --- b )x + (-- b c d + -- b c d)x +--R 162 36 384 27 48 +--R + +--R 5 2 2 2 1 5 10 10 3 3 5 3 2 9 5 2 3 5 4 2 8 +--R (-- b c d + -- b d)x + (-- c d + -- b c d )x + (- b c d + -- b d )x +--R 12 32 81 12 9 32 +--R + +--R 5 2 3 7 5 2 4 5 3 3 6 5 4 5 5 2 4 4 +--R - b c d x + (-- c d + -- b d )x + - b c d x + - b d x +--R 6 18 12 6 8 +--R + +--R 1 5 1 3 1 5 1 2 1 6 +--R (- c d + - c)x + (- b d + - b)x + - d + d +--R 3 3 2 2 6 +--R Type: Polynomial(Fraction(Integer)) +--E 92 + +--S 93 of 1483 +a0018:=integrate(t0018,x) +--R +--R +--R (93) +--R 1 6 18 1 5 17 5 2 4 16 1 5 5 3 3 15 +--R ---- c x + --- b c x + --- b c x + (--- c d + --- b c )x +--R 4374 486 648 243 324 +--R + +--R 5 4 5 4 2 14 5 2 3 1 5 13 +--R (--- b c d + --- b c )x + (-- b c d + -- b c)x +--R 162 288 54 96 +--R + +--R 5 4 2 5 3 2 1 6 12 5 3 2 5 4 11 +--R (--- c d + -- b c d + --- b )x + (-- b c d + -- b c d)x +--R 162 36 384 27 48 +--R + +--R 5 2 2 2 1 5 10 10 3 3 5 3 2 9 5 2 3 5 4 2 8 +--R (-- b c d + -- b d)x + (-- c d + -- b c d )x + (- b c d + -- b d )x +--R 12 32 81 12 9 32 +--R + +--R 5 2 3 7 5 2 4 5 3 3 6 5 4 5 5 2 4 4 +--R - b c d x + (-- c d + -- b d )x + - b c d x + - b d x +--R 6 18 12 6 8 +--R + +--R 1 5 1 3 1 5 1 2 +--R (- c d + - c)x + (- b d + - b)x +--R 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 93 + +--S 94 of 1483 +m0018:=a0018-r0018 +--R +--R +--R 1 6 +--R (94) - - d - d +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 94 + +--S 95 of 1483 +d0018:=D(m0018,x) +--R +--R +--R (95) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 95 + +--S 96 of 1483 +t0019:= (a+b*x+c*x^2)*(1+(a*x+1/2*b*x^2+1/3*c*x^3)^5) +--R +--R +--R (96) +--R 1 6 17 17 5 16 16 5 10 2 4 15 +--R --- c x + --- b c x + (--- a c + -- b c )x +--R 243 486 243 81 +--R + +--R 25 4 25 3 3 14 35 2 4 35 2 3 35 4 2 13 +--R (-- a b c + --- b c )x + (-- a c + -- a b c + --- b c )x +--R 54 108 81 27 144 +--R + +--R 65 2 3 65 3 2 13 5 12 +--R (-- a b c + -- a b c + -- b c)x +--R 27 36 96 +--R + +--R 40 3 3 2 2 2 5 4 1 6 11 +--R (-- a c + 5a b c + - a b c + -- b )x +--R 27 4 32 +--R + +--R 55 3 2 55 2 3 11 5 10 25 4 2 25 3 2 25 2 4 9 +--R (-- a b c + -- a b c + -- a b )x + (-- a c + -- a b c + -- a b )x +--R 9 12 32 9 3 16 +--R + +--R 15 4 15 3 3 8 8 5 4 2 7 7 5 6 6 5 2 +--R (-- a b c + -- a b )x + (- a c + 5a b )x + - a b x + a x + c x + b x + a +--R 2 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 96 + +--S 97 of 1483 +r0019:= a*x+1/2*b*x^2+1/3*c*x^3+1/279936*x^6*(6*a+3*b*x+2*c*x^2)^6 +--R +--R +--R (97) +--R 1 6 18 1 5 17 1 5 5 2 4 16 +--R ---- c x + --- b c x + (--- a c + --- b c )x +--R 4374 486 243 648 +--R + +--R 5 4 5 3 3 15 5 2 4 5 2 3 5 4 2 14 +--R (--- a b c + --- b c )x + (--- a c + -- a b c + --- b c )x +--R 162 324 162 54 288 +--R + +--R 5 2 3 5 3 2 1 5 13 +--R (-- a b c + -- a b c + -- b c)x +--R 27 36 96 +--R + +--R 10 3 3 5 2 2 2 5 4 1 6 12 +--R (-- a c + -- a b c + -- a b c + --- b )x +--R 81 12 48 384 +--R + +--R 5 3 2 5 2 3 1 5 11 5 4 2 5 3 2 5 2 4 10 +--R (- a b c + -- a b c + -- a b )x + (-- a c + - a b c + -- a b )x +--R 9 12 32 18 6 32 +--R + +--R 5 4 5 3 3 9 1 5 5 4 2 8 1 5 7 1 6 6 1 3 +--R (- a b c + -- a b )x + (- a c + - a b )x + - a b x + - a x + - c x +--R 6 12 3 8 2 6 3 +--R + +--R 1 2 +--R - b x + a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 1483 +a0019:=integrate(t0019,x) +--R +--R +--R (98) +--R 1 6 18 1 5 17 1 5 5 2 4 16 +--R ---- c x + --- b c x + (--- a c + --- b c )x +--R 4374 486 243 648 +--R + +--R 5 4 5 3 3 15 5 2 4 5 2 3 5 4 2 14 +--R (--- a b c + --- b c )x + (--- a c + -- a b c + --- b c )x +--R 162 324 162 54 288 +--R + +--R 5 2 3 5 3 2 1 5 13 +--R (-- a b c + -- a b c + -- b c)x +--R 27 36 96 +--R + +--R 10 3 3 5 2 2 2 5 4 1 6 12 +--R (-- a c + -- a b c + -- a b c + --- b )x +--R 81 12 48 384 +--R + +--R 5 3 2 5 2 3 1 5 11 5 4 2 5 3 2 5 2 4 10 +--R (- a b c + -- a b c + -- a b )x + (-- a c + - a b c + -- a b )x +--R 9 12 32 18 6 32 +--R + +--R 5 4 5 3 3 9 1 5 5 4 2 8 1 5 7 1 6 6 1 3 +--R (- a b c + -- a b )x + (- a c + - a b )x + - a b x + - a x + - c x +--R 6 12 3 8 2 6 3 +--R + +--R 1 2 +--R - b x + a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 1483 +m0019:=a0019-r0019 +--R +--R +--R (99) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 1483 +d0019:=D(m0019,x) +--R +--R +--R (100) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +--S 101 of 1483 +t0020:= (a+b*x+c*x^2)*(1+(d+a*x+1/2*b*x^2+1/3*c*x^3)^5) +--R +--R +--R (101) +--R 1 6 17 17 5 16 16 5 10 2 4 15 +--R --- c x + --- b c x + (--- a c + -- b c )x +--R 243 486 243 81 +--R + +--R 5 5 25 4 25 3 3 14 +--R (-- c d + -- a b c + --- b c )x +--R 81 54 108 +--R + +--R 35 4 35 2 4 35 2 3 35 4 2 13 +--R (-- b c d + -- a c + -- a b c + --- b c )x +--R 81 81 27 144 +--R + +--R 65 4 65 2 3 65 2 3 65 3 2 13 5 12 +--R ((-- a c + -- b c )d + -- a b c + -- a b c + -- b c)x +--R 81 54 27 36 96 +--R + +--R 10 4 2 40 3 5 3 2 40 3 3 2 2 2 5 4 1 6 11 +--R (-- c d + (-- a b c + - b c )d + -- a c + 5a b c + - a b c + -- b )x +--R 27 9 3 27 4 32 +--R + +--R 55 3 2 110 2 3 55 2 2 55 4 55 3 2 55 2 3 +--R -- b c d + (--- a c + -- a b c + -- b c)d + -- a b c + -- a b c +--R 27 27 6 48 9 12 +--R + +--R 11 5 +--R -- a b +--R 32 +--R * +--R 10 +--R x +--R + +--R 100 3 25 2 2 2 50 2 2 25 3 5 5 25 4 2 +--R (--- a c + -- b c )d + (-- a b c + -- a b c + -- b )d + -- a c +--R 27 6 3 3 16 9 +--R + +--R 25 3 2 25 2 4 +--R -- a b c + -- a b +--R 3 16 +--R * +--R 9 +--R x +--R + +--R 10 3 3 2 15 3 2 3 2 45 2 2 45 4 +--R -- c d + (15a b c + -- b c)d + (10a c + -- a b c + -- a b )d +--R 9 4 2 16 +--R + +--R 15 4 15 3 3 +--R -- a b c + -- a b +--R 2 4 +--R * +--R 8 +--R x +--R + +--R 40 2 3 40 2 2 2 5 4 2 80 3 2 3 8 5 +--R -- b c d + (-- a c + 20a b c + - b )d + (-- a b c + 10a b )d + - a c +--R 9 3 4 3 3 +--R + +--R 4 2 +--R 5a b +--R * +--R 7 +--R x +--R + +--R 70 2 35 2 3 2 35 3 2 35 4 35 3 2 +--R (-- a c + -- b c)d + (35a b c + -- a b )d + (-- a c + -- a b )d +--R 9 6 4 3 2 +--R + +--R 7 5 +--R - a b +--R 2 +--R * +--R 6 +--R x +--R + +--R 5 2 4 5 3 3 3 45 2 2 2 4 6 5 +--R (- c d + (20a b c + - b )d + (20a c + -- a b )d + 15a b d + a )x +--R 3 2 2 +--R + +--R 25 4 50 2 25 2 3 3 2 5 4 +--R (-- b c d + (-- a c + -- a b )d + 25a b d + 5a d)x +--R 6 3 2 +--R + +--R 20 5 2 4 2 3 4 2 3 +--R ((-- a c + - b )d + 20a b d + 10a d )x +--R 3 2 +--R + +--R 5 15 4 3 3 2 5 2 4 5 +--R (c d + -- a b d + 10a d + c)x + (b d + 5a d + b)x + a d + a +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 101 + +--S 102 of 1483 +r0020:= d+a*x+1/2*b*x^2+1/3*c*x^3+1/279936*(6*d+6*a*x+3*b*x^2+2*c*x^3)^6 +--R +--R +--R (102) +--R 1 6 18 1 5 17 1 5 5 2 4 16 +--R ---- c x + --- b c x + (--- a c + --- b c )x +--R 4374 486 243 648 +--R + +--R 1 5 5 4 5 3 3 15 +--R (--- c d + --- a b c + --- b c )x +--R 243 162 324 +--R + +--R 5 4 5 2 4 5 2 3 5 4 2 14 +--R (--- b c d + --- a c + -- a b c + --- b c )x +--R 162 162 54 288 +--R + +--R 5 4 5 2 3 5 2 3 5 3 2 1 5 13 +--R ((-- a c + -- b c )d + -- a b c + -- a b c + -- b c)x +--R 81 54 27 36 96 +--R + +--R 5 4 2 10 3 5 3 2 10 3 3 5 2 2 2 5 4 +--R --- c d + (-- a b c + -- b c )d + -- a c + -- a b c + -- a b c +--R 162 27 36 81 12 48 +--R + +--R 1 6 +--R --- b +--R 384 +--R * +--R 12 +--R x +--R + +--R 5 3 2 10 2 3 5 2 2 5 4 5 3 2 5 2 3 +--R -- b c d + (-- a c + - a b c + -- b c)d + - a b c + -- a b c +--R 27 27 6 48 9 12 +--R + +--R 1 5 +--R -- a b +--R 32 +--R * +--R 11 +--R x +--R + +--R 10 3 5 2 2 2 5 2 2 5 3 1 5 5 4 2 +--R (-- a c + -- b c )d + (- a b c + - a b c + -- b )d + -- a c +--R 27 12 3 6 32 18 +--R + +--R 5 3 2 5 2 4 +--R - a b c + -- a b +--R 6 32 +--R * +--R 10 +--R x +--R + +--R 10 3 3 5 2 5 3 2 10 3 2 5 2 2 5 4 +--R -- c d + (- a b c + -- b c)d + (-- a c + - a b c + -- a b )d +--R 81 3 12 9 2 16 +--R + +--R 5 4 5 3 3 +--R - a b c + -- a b +--R 6 12 +--R * +--R 9 +--R x +--R + +--R 5 2 3 5 2 2 5 2 5 4 2 10 3 5 2 3 1 5 +--R - b c d + (- a c + - a b c + -- b )d + (-- a b c + - a b )d + - a c +--R 9 3 2 32 3 4 3 +--R + +--R 5 4 2 +--R - a b +--R 8 +--R * +--R 8 +--R x +--R + +--R 10 2 5 2 3 2 5 3 2 5 4 5 3 2 1 5 7 +--R ((-- a c + - b c)d + (5a b c + - a b )d + (- a c + - a b )d + - a b)x +--R 9 6 4 3 2 2 +--R + +--R 5 2 4 10 5 3 3 10 3 15 2 2 2 5 4 1 6 6 +--R (-- c d + (-- a b c + -- b )d + (-- a c + -- a b )d + - a b d + - a )x +--R 18 3 12 3 4 2 6 +--R + +--R 5 4 10 2 5 2 3 3 2 5 5 +--R (- b c d + (-- a c + - a b )d + 5a b d + a d)x +--R 6 3 2 +--R + +--R 5 5 2 4 2 3 5 4 2 4 +--R ((- a c + - b )d + 5a b d + - a d )x +--R 3 8 2 +--R + +--R 1 5 5 4 10 3 3 1 3 1 5 5 2 4 1 2 +--R (- c d + - a b d + -- a d + - c)x + (- b d + - a d + - b)x +--R 3 2 3 3 2 2 2 +--R + +--R 5 1 6 +--R (a d + a)x + - d + d +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 102 + +--S 103 of 1483 +a0020:=integrate(t0020,x) +--R +--R +--R (103) +--R 1 6 18 1 5 17 1 5 5 2 4 16 +--R ---- c x + --- b c x + (--- a c + --- b c )x +--R 4374 486 243 648 +--R + +--R 1 5 5 4 5 3 3 15 +--R (--- c d + --- a b c + --- b c )x +--R 243 162 324 +--R + +--R 5 4 5 2 4 5 2 3 5 4 2 14 +--R (--- b c d + --- a c + -- a b c + --- b c )x +--R 162 162 54 288 +--R + +--R 5 4 5 2 3 5 2 3 5 3 2 1 5 13 +--R ((-- a c + -- b c )d + -- a b c + -- a b c + -- b c)x +--R 81 54 27 36 96 +--R + +--R 5 4 2 10 3 5 3 2 10 3 3 5 2 2 2 5 4 +--R --- c d + (-- a b c + -- b c )d + -- a c + -- a b c + -- a b c +--R 162 27 36 81 12 48 +--R + +--R 1 6 +--R --- b +--R 384 +--R * +--R 12 +--R x +--R + +--R 5 3 2 10 2 3 5 2 2 5 4 5 3 2 5 2 3 +--R -- b c d + (-- a c + - a b c + -- b c)d + - a b c + -- a b c +--R 27 27 6 48 9 12 +--R + +--R 1 5 +--R -- a b +--R 32 +--R * +--R 11 +--R x +--R + +--R 10 3 5 2 2 2 5 2 2 5 3 1 5 5 4 2 +--R (-- a c + -- b c )d + (- a b c + - a b c + -- b )d + -- a c +--R 27 12 3 6 32 18 +--R + +--R 5 3 2 5 2 4 +--R - a b c + -- a b +--R 6 32 +--R * +--R 10 +--R x +--R + +--R 10 3 3 5 2 5 3 2 10 3 2 5 2 2 5 4 +--R -- c d + (- a b c + -- b c)d + (-- a c + - a b c + -- a b )d +--R 81 3 12 9 2 16 +--R + +--R 5 4 5 3 3 +--R - a b c + -- a b +--R 6 12 +--R * +--R 9 +--R x +--R + +--R 5 2 3 5 2 2 5 2 5 4 2 10 3 5 2 3 1 5 +--R - b c d + (- a c + - a b c + -- b )d + (-- a b c + - a b )d + - a c +--R 9 3 2 32 3 4 3 +--R + +--R 5 4 2 +--R - a b +--R 8 +--R * +--R 8 +--R x +--R + +--R 10 2 5 2 3 2 5 3 2 5 4 5 3 2 1 5 7 +--R ((-- a c + - b c)d + (5a b c + - a b )d + (- a c + - a b )d + - a b)x +--R 9 6 4 3 2 2 +--R + +--R 5 2 4 10 5 3 3 10 3 15 2 2 2 5 4 1 6 6 +--R (-- c d + (-- a b c + -- b )d + (-- a c + -- a b )d + - a b d + - a )x +--R 18 3 12 3 4 2 6 +--R + +--R 5 4 10 2 5 2 3 3 2 5 5 +--R (- b c d + (-- a c + - a b )d + 5a b d + a d)x +--R 6 3 2 +--R + +--R 5 5 2 4 2 3 5 4 2 4 +--R ((- a c + - b )d + 5a b d + - a d )x +--R 3 8 2 +--R + +--R 1 5 5 4 10 3 3 1 3 1 5 5 2 4 1 2 +--R (- c d + - a b d + -- a d + - c)x + (- b d + - a d + - b)x +--R 3 2 3 3 2 2 2 +--R + +--R 5 +--R (a d + a)x +--R Type: Polynomial(Fraction(Integer)) +--E 103 + +--S 104 of 1483 +m0020:=a0020-r0020 +--R +--R +--R 1 6 +--R (104) - - d - d +--R 6 +--R Type: Polynomial(Fraction(Integer)) +--E 104 + +--S 105 of 1483 +d0020:=D(m0020,x) +--R +--R +--R (105) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 105 + +--S 106 of 1483 +t0021:= (2+3*x)^6*(1+(2+3*x)^7+(2+3*x)^14) +--R +--R +--R (106) +--R 20 19 18 17 +--R 3486784401x + 46490458680x + 294439571640x + 1177758286560x +--R + +--R 16 15 14 13 +--R 3336981811920x + 7118894532096x + 11864824220160x + 15819767221203x +--R + +--R 12 11 10 9 +--R 17138093246586x + 15233903651304x + 11171623917168x + 6770824454160x +--R + +--R 8 7 6 5 +--R 3385569848544x + 1389081063168x + 463107083481x + 123532587108x +--R + +--R 4 3 2 +--R 25748932860x + 4042307808x + 449706096x + 31617600x + 1056832 +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 1483 +r0021:= 1/21*(2+3*x)^7+1/42*(2+3*x)^14+1/63*(2+3*x)^21 +--R +--R +--R (107) +--R 1162261467 21 20 19 18 +--R ---------- x + 2324522934x + 15496819560x + 65431015920x +--R 7 +--R + +--R 17 16 15 15819767221203 14 +--R 196293047760x + 444930908256x + 790988281344x + -------------- x +--R 14 +--R + +--R 13 12 11 10 +--R 1318314865122x + 1269491970942x + 1015602174288x + 677082445416x +--R + +--R 9 8 7 6 +--R 376174427616x + 173635132896x + 66158154783x + 20588764518x +--R + +--R 5 4 3 2 2122112 +--R 5149786572x + 1010576952x + 149902032x + 15808800x + 1056832x + ------- +--R 63 +--R Type: Polynomial(Fraction(Integer)) +--E 107 + +--S 108 of 1483 +a0021:=integrate(t0021,x) +--R +--R +--R (108) +--R 1162261467 21 20 19 18 +--R ---------- x + 2324522934x + 15496819560x + 65431015920x +--R 7 +--R + +--R 17 16 15 15819767221203 14 +--R 196293047760x + 444930908256x + 790988281344x + -------------- x +--R 14 +--R + +--R 13 12 11 10 +--R 1318314865122x + 1269491970942x + 1015602174288x + 677082445416x +--R + +--R 9 8 7 6 +--R 376174427616x + 173635132896x + 66158154783x + 20588764518x +--R + +--R 5 4 3 2 +--R 5149786572x + 1010576952x + 149902032x + 15808800x + 1056832x +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 1483 +m0021:=a0021-r0021 +--R +--R +--R 2122112 +--R (109) - ------- +--R 63 +--R Type: Polynomial(Fraction(Integer)) +--E 109 + +--S 110 of 1483 +d0021:=D(m0021,x) +--R +--R +--R (110) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 110 + +--S 111 of 1483 +t0022:= (2+3*x)^6*(1+(2+3*x)^7+(2+3*x)^14)^2 +--R +--R +--R (111) +--R 34 33 32 +--R 16677181699666569x + 378016118525775564x + 4158177303783531204x +--R + +--R 31 30 +--R 29569260826905110784x + 152774514272343072384x +--R + +--R 29 28 +--R 611098057089372289536x + 1969093739510199599616x +--R + +--R 27 26 +--R 5250916653945060568950x + 11814562711582707057228x +--R + +--R 25 24 +--R 22753974480193166244840x + 37923300052713558858960x +--R + +--R 23 22 +--R 55161197358098322404160x + 70483846759795477607040x +--R + +--R 21 20 +--R 79520450781314886393600x + 79520847116576754110643x +--R + +--R 19 18 +--R 70685813958589477281960x + 55960416183860517516840x +--R + +--R 17 16 +--R 39502388988265540321440x + 24872768546728823564400x +--R + +--R 15 14 +--R 13964412385079287976448x + 6982756365625215229440x +--R + +--R 13 12 +--R 3103796605675782721446x + 1222900430946085012212x +--R + +--R 11 10 +--R 425448833766864577488x + 130036362517827878112x +--R + +--R 9 8 7 +--R 34689917186099544096x + 8009483060433484224x + 1583178214811622912x +--R + +--R 6 5 4 +--R 264090004030265049x + 36466108367328612x + 4057390785756924x +--R + +--R 3 2 +--R 349626718314720x + 21898634455152x + 887139656256x + 17451466816 +--R Type: Polynomial(Integer) +--E 111 + +--S 112 of 1483 +r0022:= 1/21*(2+3*x)^7+1/21*(2+3*x)^14+1/21*(2+3*x)^21+1/42*(2+3*x)^28+_ + 1/105*(2+3*x)^35 +--R +--R +--R (112) +--R 16677181699666569 35 34 33 +--R ----------------- x + 11118121133111046x + 126005372841925188x +--R 35 +--R + +--R 32 31 101849676181562048256 30 +--R 924039400840784712x + 4928210137817518464x + --------------------- x +--R 5 +--R + +--R 29 2625458326972530284475 28 +--R 67899784121041365504x + ---------------------- x +--R 14 +--R + +--R 27 26 +--R 437576396725285446564x + 875152864622814086340x +--R + +--R 7584660010542711771792 25 24 +--R ---------------------- x + 2298383223254096766840x +--R 5 +--R + +--R 23 22 +--R 3064515076512846852480x + 3614565944605222108800x +--R + +--R 26506949038858918036881 21 20 +--R ----------------------- x + 3534290697929473864098x +--R 7 +--R + +--R 19 18 +--R 2945285062308448290360x + 2194577166014752240080x +--R + +--R 17 16 +--R 1463104032160519033200x + 872775774067455498528x +--R + +--R 15 14 +--R 465517091041681015296x + 221699757548270194389x +--R + +--R 13 12 11 +--R 94069263918929616324x + 35454069480572048124x + 11821487501620716192x +--R + +--R 17344958593049772048 10 9 8 +--R -------------------- x + 889942562270387136x + 197897276851452864x +--R 5 +--R + +--R 7 6 4057390785756924 5 +--R 37727143432895007x + 6077684727888102x + ---------------- x +--R 5 +--R + +--R 4 3 2 +--R 87406679578680x + 7299544818384x + 443569828128x + 17451466816x +--R + +--R 35041395328 +--R ----------- +--R 105 +--R Type: Polynomial(Fraction(Integer)) +--E 112 + +--S 113 of 1483 +a0022:=integrate(t0022,x) +--R +--R +--R (113) +--R 16677181699666569 35 34 33 +--R ----------------- x + 11118121133111046x + 126005372841925188x +--R 35 +--R + +--R 32 31 101849676181562048256 30 +--R 924039400840784712x + 4928210137817518464x + --------------------- x +--R 5 +--R + +--R 29 2625458326972530284475 28 +--R 67899784121041365504x + ---------------------- x +--R 14 +--R + +--R 27 26 +--R 437576396725285446564x + 875152864622814086340x +--R + +--R 7584660010542711771792 25 24 +--R ---------------------- x + 2298383223254096766840x +--R 5 +--R + +--R 23 22 +--R 3064515076512846852480x + 3614565944605222108800x +--R + +--R 26506949038858918036881 21 20 +--R ----------------------- x + 3534290697929473864098x +--R 7 +--R + +--R 19 18 +--R 2945285062308448290360x + 2194577166014752240080x +--R + +--R 17 16 +--R 1463104032160519033200x + 872775774067455498528x +--R + +--R 15 14 +--R 465517091041681015296x + 221699757548270194389x +--R + +--R 13 12 11 +--R 94069263918929616324x + 35454069480572048124x + 11821487501620716192x +--R + +--R 17344958593049772048 10 9 8 +--R -------------------- x + 889942562270387136x + 197897276851452864x +--R 5 +--R + +--R 7 6 4057390785756924 5 +--R 37727143432895007x + 6077684727888102x + ---------------- x +--R 5 +--R + +--R 4 3 2 +--R 87406679578680x + 7299544818384x + 443569828128x + 17451466816x +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 1483 +m0022:=a0022-r0022 +--R +--R +--R 35041395328 +--R (114) - ----------- +--R 105 +--R Type: Polynomial(Fraction(Integer)) +--E 114 + +--S 115 of 1483 +d0022:=D(m0022,x) +--R +--R +--R (115) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 115 + +--S 116 of 1483 +t0023:= (a+b*x)^2/x^4 +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (116) ------------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 1483 +r0023:= -1/3*(a+b*x)^3/a/x^3 +--R +--R +--R 1 3 3 2 2 2 1 3 +--R - - b x - a b x - a b x - - a +--R 3 3 +--R (117) -------------------------------- +--R 3 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 117 + +--S 118 of 1483 +a0023:=integrate(t0023,x) +--R +--R +--R 2 2 2 +--R - 3b x - 3a b x - a +--R (118) --------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1483 +m0023:=a0023-r0023 +--R +--R +--R 3 +--R b +--R (119) -- +--R 3a +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1483 +d0023:=D(m0023,x) +--R +--R +--R (120) 0 +--R Type: Expression(Integer) +--E 120 + +--S 121 of 1483 +t0024:= x*(a+b*x)^3 +--R +--R +--R 3 4 2 3 2 2 3 +--R (121) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 121 + +--S 122 of 1483 +r0024:= -1/20*(a+b*x)^4*(a-4*b*x)/b^2 +--R +--R +--R 1 5 5 3 4 4 2 3 3 1 3 2 2 1 5 +--R - b x + - a b x + a b x + - a b x - -- a +--R 5 4 2 20 +--R (122) --------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 122 + +--S 123 of 1483 +a0024:=integrate(t0024,x) +--R +--R +--R 1 3 5 3 2 4 2 3 1 3 2 +--R (123) - b x + - a b x + a b x + - a x +--R 5 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +--S 124 of 1483 +m0024:=a0024-r0024 +--R +--R +--R 1 5 +--R -- a +--R 20 +--R (124) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 124 + +--S 125 of 1483 +d0024:=D(m0024,x) +--R +--R +--R (125) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 125 + +--S 126 of 1483 +t0025:= (a+b*x)^3/x^5 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (126) ---------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 1483 +r0025:= -1/4*(a+b*x)^4/a/x^4 +--R +--R +--R 1 4 4 3 3 3 2 2 2 3 1 4 +--R - - b x - a b x - - a b x - a b x - - a +--R 4 2 4 +--R (127) ------------------------------------------- +--R 4 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 127 + +--S 128 of 1483 +a0025:=integrate(t0025,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 4b x - 6a b x - 4a b x - a +--R (128) ------------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1483 +m0025:=a0025-r0025 +--R +--R +--R 4 +--R b +--R (129) -- +--R 4a +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1483 +d0025:=D(m0025,x) +--R +--R +--R (130) 0 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 1483 +t0026:= 1/x/(4+6*x) +--R +--R +--R 1 +--R (131) -------- +--R 2 +--R 6x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 1483 +r0026:= -1/2*atanh(1+3*x) +--R +--R +--R atanh(3x + 1) +--R (132) - ------------- +--R 2 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1483 +a0026:=integrate(t0026,x) +--R +--R +--R - log(3x + 2) + log(x) +--R (133) ---------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1483 +m0026:=a0026-r0026 +--R +--R +--R - log(3x + 2) + log(x) + 2atanh(3x + 1) +--R (134) --------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1483 +d0026:=D(m0026,x) +--R +--R +--R (135) 0 +--R Type: Expression(Integer) +--E 135 + +--S 136 of 1483 +t0027:= x^3*(a+b*x)^7 +--R +--R +--R (136) +--R 7 10 6 9 2 5 8 3 4 7 4 3 6 5 2 5 6 4 7 3 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 1483 +r0027:= -1/1320*(a+b*x)^8*(a^3-8*a^2*b*x+36*a*b^2*x^2-120*b^3*x^3)/b^4 +--R +--R +--R (137) +--R 1 11 11 7 10 10 7 2 9 9 35 3 8 8 4 7 7 7 5 6 6 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + - a b x +--R 11 10 3 8 2 +--R + +--R 7 6 5 5 1 7 4 4 1 11 +--R - a b x + - a b x - ---- a +--R 5 4 1320 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 137 + +--S 138 of 1483 +a0027:=integrate(t0027,x) +--R +--R +--R (138) +--R 1 7 11 7 6 10 7 2 5 9 35 3 4 8 4 3 7 7 5 2 6 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + - a b x +--R 11 10 3 8 2 +--R + +--R 7 6 5 1 7 4 +--R - a b x + - a x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 1483 +m0027:=a0027-r0027 +--R +--R +--R 1 11 +--R ---- a +--R 1320 +--R (139) -------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 139 + +--S 140 of 1483 +d0027:=D(m0027,x) +--R +--R +--R (140) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 140 + +--S 141 of 1483 +t0028:= x^2*(a+b*x)^7 +--R +--R +--R (141) +--R 7 9 6 8 2 5 7 3 4 6 4 3 5 5 2 4 6 3 7 2 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 141 + +--S 142 of 1483 +r0028:= 1/360*(a+b*x)^8*(a^2-8*a*b*x+36*b^2*x^2)/b^3 +--R +--R +--R (142) +--R 1 10 10 7 9 9 21 2 8 8 3 7 7 35 4 6 6 21 5 5 5 +--R -- b x + - a b x + -- a b x + 5a b x + -- a b x + -- a b x +--R 10 9 8 6 5 +--R + +--R 7 6 4 4 1 7 3 3 1 10 +--R - a b x + - a b x + --- a +--R 4 3 360 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 142 + +--S 143 of 1483 +a0028:=integrate(t0028,x) +--R +--R +--R (143) +--R 1 7 10 7 6 9 21 2 5 8 3 4 7 35 4 3 6 21 5 2 5 +--R -- b x + - a b x + -- a b x + 5a b x + -- a b x + -- a b x +--R 10 9 8 6 5 +--R + +--R 7 6 4 1 7 3 +--R - a b x + - a x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 143 + +--S 144 of 1483 +m0028:=a0028-r0028 +--R +--R +--R 1 10 +--R --- a +--R 360 +--R (144) - ------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 144 + +--S 145 of 1483 +d0028:=D(m0028,x) +--R +--R +--R (145) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 145 + +--S 146 of 1483 +t0029:= x*(a+b*x)^7 +--R +--R +--R (146) +--R 7 8 6 7 2 5 6 3 4 5 4 3 4 5 2 3 6 2 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a x +--R Type: Polynomial(Integer) +--E 146 + +--S 147 of 1483 +r0029:= -1/72*(a+b*x)^8*(a-8*b*x)/b^2 +--R +--R +--R (147) +--R 1 9 9 7 8 8 2 7 7 35 3 6 6 4 5 5 21 5 4 4 7 6 3 3 +--R - b x + - a b x + 3a b x + -- a b x + 7a b x + -- a b x + - a b x +--R 9 8 6 4 3 +--R + +--R 1 7 2 2 1 9 +--R - a b x - -- a +--R 2 72 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 147 + +--S 148 of 1483 +a0029:=integrate(t0029,x) +--R +--R +--R (148) +--R 1 7 9 7 6 8 2 5 7 35 3 4 6 4 3 5 21 5 2 4 7 6 3 +--R - b x + - a b x + 3a b x + -- a b x + 7a b x + -- a b x + - a b x +--R 9 8 6 4 3 +--R + +--R 1 7 2 +--R - a x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 148 + +--S 149 of 1483 +m0029:=a0029-r0029 +--R +--R +--R 1 9 +--R -- a +--R 72 +--R (149) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 149 + +--S 150 of 1483 +d0029:=D(m0029,x) +--R +--R +--R (150) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 150 + +--S 151 of 1483 +t0030:= (a+b*x)^7/x^9 +--R +--R +--R (151) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 1483 +r0030:= -1/8*(a+b*x)^8/a/x^8 +--R +--R +--R (152) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - - b x - a b x - - a b x - 7a b x - -- a b x - 7a b x - - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R - a b x - - a +--R 8 +--R / +--R 8 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 152 + +--S 153 of 1483 +a0030:=integrate(t0030,x) +--R +--R +--R (153) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - 8b x - 28a b x - 56a b x - 70a b x - 56a b x - 28a b x - 8a b x - a +--R ---------------------------------------------------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1483 +m0030:=a0030-r0030 +--R +--R +--R 8 +--R b +--R (154) -- +--R 8a +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1483 +d0030:=D(m0030,x) +--R +--R +--R (155) 0 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 1483 +t0031:= (a+b*x)^7/x^10 +--R +--R +--R (156) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 1483 +r0031:= -1/72*(a+b*x)^8*(8*a-b*x)/a^2/x^9 +--R +--R +--R (157) +--R 1 9 9 1 2 7 7 7 3 6 6 21 4 5 5 5 4 4 35 6 3 3 7 2 2 +--R -- b x - - a b x - - a b x - -- a b x - 7a b x - -- a b x - 3a b x +--R 72 2 3 4 6 +--R + +--R 7 8 1 9 +--R - - a b x - - a +--R 8 9 +--R / +--R 2 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 157 + +--S 158 of 1483 +a0031:=integrate(t0031,x) +--R +--R +--R (158) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 36b x - 168a b x - 378a b x - 504a b x - 420a b x - 216a b x +--R + +--R 6 7 +--R - 63a b x - 8a +--R / +--R 9 +--R 72x +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1483 +m0031:=a0031-r0031 +--R +--R +--R 9 +--R b +--R (159) - ---- +--R 2 +--R 72a +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1483 +d0031:=D(m0031,x) +--R +--R +--R (160) 0 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 1483 +t0032:= (a+b*x)^7/x^11 +--R +--R +--R (161) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 1483 +r0032:= -1/360*(a+b*x)^8*(36*a^2-8*a*b*x+b^2*x^2)/a^3/x^10 +--R +--R +--R (162) +--R 1 10 10 1 3 7 7 7 4 6 6 21 5 5 5 35 6 4 4 7 3 3 +--R - --- b x - - a b x - - a b x - -- a b x - -- a b x - 5a b x +--R 360 3 4 5 6 +--R + +--R 21 8 2 2 7 9 1 10 +--R - -- a b x - - a b x - -- a +--R 8 9 10 +--R / +--R 3 10 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +--S 163 of 1483 +a0032:=integrate(t0032,x) +--R +--R +--R (163) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 120b x - 630a b x - 1512a b x - 2100a b x - 1800a b x - 945a b x +--R + +--R 6 7 +--R - 280a b x - 36a +--R / +--R 10 +--R 360x +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1483 +m0032:=a0032-r0032 +--R +--R +--R 10 +--R b +--R (164) ----- +--R 3 +--R 360a +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1483 +d0032:=D(m0032,x) +--R +--R +--R (165) 0 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 1483 +t0033:= (a+b*x)^7/x^12 +--R +--R +--R (166) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1483 +r0033:= -1/1320*(a+b*x)^8*(120*a^3-36*a^2*b*x+8*a*b^2*x^2-b^3*x^3)/a^4/x^11 +--R +--R +--R (167) +--R 1 11 11 1 4 7 7 7 5 6 6 7 6 5 5 7 4 4 35 8 3 3 +--R ---- b x - - a b x - - a b x - - a b x - 5a b x - -- a b x +--R 1320 4 5 2 8 +--R + +--R 7 9 2 2 7 10 1 11 +--R - - a b x - -- a b x - -- a +--R 3 10 11 +--R / +--R 4 11 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 167 + +--S 168 of 1483 +a0033:=integrate(t0033,x) +--R +--R +--R (168) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R - 330b x - 1848a b x - 4620a b x - 6600a b x - 5775a b x +--R + +--R 5 2 2 6 7 +--R - 3080a b x - 924a b x - 120a +--R / +--R 11 +--R 1320x +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1483 +m0033:=a0033-r0033 +--R +--R +--R 11 +--R b +--R (169) - ------ +--R 4 +--R 1320a +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1483 +d0033:=D(m0033,x) +--R +--R +--R (170) 0 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1483 +t0034:= x^5/(a+b*x)^7 +--R +--R +--R (171) +--R 5 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1483 +r0034:= 1/6*x^6/a/(a+b*x)^6 +--R +--R +--R 1 6 +--R - x +--R 6 +--R (172) --------------------------------------------------------------- +--R 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R a b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 172 + +--S 173 of 1483 +a0034:=integrate(t0034,x) +--R +--R +--R (173) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a +--R ----------------------------------------------------------------------- +--R 12 6 11 5 2 10 4 3 9 3 4 8 2 5 7 6 6 +--R 6b x + 36a b x + 90a b x + 120a b x + 90a b x + 36a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1483 +m0034:=a0034-r0034 +--R +--R +--R 1 +--R (174) - ----- +--R 6 +--R 6a b +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1483 +d0034:=D(m0034,x) +--R +--R +--R (175) 0 +--R Type: Expression(Integer) +--E 175 + +--S 176 of 1483 +t0035:= x^4/(a+b*x)^7 +--R +--R +--R (176) +--R 4 +--R x +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1483 +r0035:= 1/30*x^5*(6*a+b*x)/a^2/(a+b*x)^6 +--R +--R +--R 1 6 1 5 +--R -- b x + - a x +--R 30 5 +--R (177) --------------------------------------------------------------- +--R 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 7 8 +--R a b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 177 + +--S 178 of 1483 +a0035:=integrate(t0035,x) +--R +--R +--R (178) +--R 4 4 3 3 2 2 2 3 4 +--R - 15b x - 20a b x - 15a b x - 6a b x - a +--R ---------------------------------------------------------------------------- +--R 11 6 10 5 2 9 4 3 8 3 4 7 2 5 6 6 5 +--R 30b x + 180a b x + 450a b x + 600a b x + 450a b x + 180a b x + 30a b +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1483 +m0035:=a0035-r0035 +--R +--R +--R 1 +--R (179) - ------ +--R 2 5 +--R 30a b +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1483 +d0035:=D(m0035,x) +--R +--R +--R (180) 0 +--R Type: Expression(Integer) +--E 180 + +--S 181 of 1483 +t0036:= (a+b*x)^2*(c+d*x) +--R +--R +--R 2 3 2 2 2 2 +--R (181) b d x + (2a b d + b c)x + (a d + 2a b c)x + a c +--R Type: Polynomial(Integer) +--E 181 + +--S 182 of 1483 +r0036:= -1/12*(a+b*x)^3*(-4*b*c+a*d-3*d*x*b)/b^2 +--R +--R +--R (182) +--R 1 4 4 2 3 1 4 3 1 2 2 3 2 2 2 1 4 +--R - b d x + (- a b d + - b c)x + (- a b d + a b c)x + a b c x - -- a d +--R 4 3 3 2 12 +--R + +--R 1 3 +--R - a b c +--R 3 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 182 + +--S 183 of 1483 +a0036:=integrate(t0036,x) +--R +--R +--R 1 2 4 2 1 2 3 1 2 2 2 +--R (183) - b d x + (- a b d + - b c)x + (- a d + a b c)x + a c x +--R 4 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 183 + +--S 184 of 1483 +m0036:=a0036-r0036 +--R +--R +--R 1 4 1 3 +--R -- a d - - a b c +--R 12 3 +--R (184) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 184 + +--S 185 of 1483 +d0036:=D(m0036,x) +--R +--R +--R (185) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 185 + +--S 186 of 1483 +t0037:= (a+b*x)^3*(c+d*x) +--R +--R +--R (186) +--R 3 4 2 3 3 2 2 2 3 2 3 +--R b d x + (3a b d + b c)x + (3a b d + 3a b c)x + (a d + 3a b c)x + a c +--R Type: Polynomial(Integer) +--E 186 + +--S 187 of 1483 +r0037:= -1/20*(a+b*x)^4*(-5*b*c+a*d-4*d*x*b)/b^2 +--R +--R +--R (187) +--R 1 5 5 3 4 1 5 4 2 3 4 3 +--R - b d x + (- a b d + - b c)x + (a b d + a b c)x +--R 5 4 4 +--R + +--R 1 3 2 3 2 3 2 3 2 1 5 1 4 +--R (- a b d + - a b c)x + a b c x - -- a d + - a b c +--R 2 2 20 4 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 187 + +--S 188 of 1483 +a0037:=integrate(t0037,x) +--R +--R +--R (188) +--R 1 3 5 3 2 1 3 4 2 2 3 1 3 3 2 2 +--R - b d x + (- a b d + - b c)x + (a b d + a b c)x + (- a d + - a b c)x +--R 5 4 4 2 2 +--R + +--R 3 +--R a c x +--R Type: Polynomial(Fraction(Integer)) +--E 188 + +--S 189 of 1483 +m0037:=a0037-r0037 +--R +--R +--R 1 5 1 4 +--R -- a d - - a b c +--R 20 4 +--R (189) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 189 + +--S 190 of 1483 +d0037:=D(m0037,x) +--R +--R +--R (190) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 190 + +--S 191 of 1483 +t0038:= (a+b*x)^4*(c+d*x) +--R +--R +--R (191) +--R 4 5 3 4 4 2 2 3 3 3 2 2 2 +--R b d x + (4a b d + b c)x + (6a b d + 4a b c)x + (4a b d + 6a b c)x +--R + +--R 4 3 4 +--R (a d + 4a b c)x + a c +--R Type: Polynomial(Integer) +--E 191 + +--S 192 of 1483 +r0038:= -1/30*(a+b*x)^5*(-6*b*c+a*d-5*d*x*b)/b^2 +--R +--R +--R (192) +--R 1 6 6 4 5 1 6 5 3 2 4 5 4 +--R - b d x + (- a b d + - b c)x + (- a b d + a b c)x +--R 6 5 5 2 +--R + +--R 4 3 3 2 4 3 1 4 2 3 3 2 4 2 1 6 1 5 +--R (- a b d + 2a b c)x + (- a b d + 2a b c)x + a b c x - -- a d + - a b c +--R 3 2 30 5 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 192 + +--S 193 of 1483 +a0038:=integrate(t0038,x) +--R +--R +--R (193) +--R 1 4 6 4 3 1 4 5 3 2 2 3 4 4 3 2 2 3 +--R - b d x + (- a b d + - b c)x + (- a b d + a b c)x + (- a b d + 2a b c)x +--R 6 5 5 2 3 +--R + +--R 1 4 3 2 4 +--R (- a d + 2a b c)x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +--S 194 of 1483 +m0038:=a0038-r0038 +--R +--R +--R 1 6 1 5 +--R -- a d - - a b c +--R 30 5 +--R (194) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 194 + +--S 195 of 1483 +d0038:=D(m0038,x) +--R +--R +--R (195) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 195 + +--S 196 of 1483 +t0039:= (a+b*x)^5*(c+d*x) +--R +--R +--R (196) +--R 5 6 4 5 5 2 3 4 4 3 2 2 3 3 +--R b d x + (5a b d + b c)x + (10a b d + 5a b c)x + (10a b d + 10a b c)x +--R + +--R 4 3 2 2 5 4 5 +--R (5a b d + 10a b c)x + (a d + 5a b c)x + a c +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 1483 +r0039:= -1/42*(a+b*x)^6*(-7*b*c+a*d-6*d*x*b)/b^2 +--R +--R +--R (197) +--R 1 7 7 5 6 1 7 6 2 5 6 5 +--R - b d x + (- a b d + - b c)x + (2a b d + a b c)x +--R 7 6 6 +--R + +--R 5 3 4 5 2 5 4 5 4 3 10 3 4 3 1 5 2 5 4 3 2 +--R (- a b d + - a b c)x + (- a b d + -- a b c)x + (- a b d + - a b c)x +--R 2 2 3 3 2 2 +--R + +--R 5 2 1 7 1 6 +--R a b c x - -- a d + - a b c +--R 42 6 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 197 + +--S 198 of 1483 +a0039:=integrate(t0039,x) +--R +--R +--R (198) +--R 1 5 7 5 4 1 5 6 2 3 4 5 5 3 2 5 2 3 4 +--R - b d x + (- a b d + - b c)x + (2a b d + a b c)x + (- a b d + - a b c)x +--R 7 6 6 2 2 +--R + +--R 5 4 10 3 2 3 1 5 5 4 2 5 +--R (- a b d + -- a b c)x + (- a d + - a b c)x + a c x +--R 3 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +--S 199 of 1483 +m0039:=a0039-r0039 +--R +--R +--R 1 7 1 6 +--R -- a d - - a b c +--R 42 6 +--R (199) ---------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 199 + +--S 200 of 1483 +d0039:=D(m0039,x) +--R +--R +--R (200) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 200 + +--S 201 of 1483 +t0040:= (a+b*x)^2*(c+d*x)^2 +--R +--R +--R (201) +--R 2 2 4 2 2 3 2 2 2 2 2 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 +--R (2a c d + 2a b c )x + a c +--R Type: Polynomial(Integer) +--E 201 + +--S 202 of 1483 +r0040:= 1/30*(a+b*x)^3*(10*b^2*c^2-5*a*b*c*d+a^2*d^2+15*b^2*c*d*x-_ + 3*b*a*d^2*x+6*b^2*d^2*x^2)/b^3 +--R +--R +--R (202) +--R 1 5 2 5 1 4 2 1 5 4 1 2 3 2 4 4 1 5 2 3 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 5 2 2 3 3 3 +--R + +--R 2 3 4 2 2 2 3 2 1 5 2 1 4 1 3 2 2 +--R (a b c d + a b c )x + a b c x + -- a d - - a b c d + - a b c +--R 30 6 3 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 202 + +--S 203 of 1483 +a0040:=integrate(t0040,x) +--R +--R +--R (203) +--R 1 2 2 5 1 2 1 2 4 1 2 2 4 1 2 2 3 +--R - b d x + (- a b d + - b c d)x + (- a d + - a b c d + - b c )x +--R 5 2 2 3 3 3 +--R + +--R 2 2 2 2 2 +--R (a c d + a b c )x + a c x +--R Type: Polynomial(Fraction(Integer)) +--E 203 + +--S 204 of 1483 +m0040:=a0040-r0040 +--R +--R +--R 1 5 2 1 4 1 3 2 2 +--R - -- a d + - a b c d - - a b c +--R 30 6 3 +--R (204) -------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 204 + +--S 205 of 1483 +d0040:=D(m0040,x) +--R +--R +--R (205) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 205 + +--S 206 of 1483 +t0041:= (a+b*x)^3*(c+d*x)^2 +--R +--R +--R (206) +--R 3 2 5 2 2 3 4 2 2 2 3 2 3 +--R b d x + (3a b d + 2b c d)x + (3a b d + 6a b c d + b c )x +--R + +--R 3 2 2 2 2 2 3 2 2 3 2 +--R (a d + 6a b c d + 3a b c )x + (2a c d + 3a b c )x + a c +--R Type: Polynomial(Integer) +--E 206 + +--S 207 of 1483 +r0041:= 1/60*(a+b*x)^4*(15*b^2*c^2-6*a*b*c*d+a^2*d^2+24*b^2*c*d*x-_ + 4*b*a*d^2*x+10*b^2*d^2*x^2)/b^3 +--R +--R +--R (207) +--R 1 6 2 6 3 5 2 2 6 5 3 2 4 2 3 5 1 6 2 4 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 3 2 2 4 5 2 3 3 3 3 2 4 2 2 3 3 2 +--R (- a b d + 2a b c d + a b c )x + (a b c d + - a b c )x + a b c x +--R 3 2 +--R + +--R 1 6 2 1 5 1 4 2 2 +--R -- a d - -- a b c d + - a b c +--R 60 10 4 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 207 + +--S 208 of 1483 +a0041:=integrate(t0041,x) +--R +--R +--R (208) +--R 1 3 2 6 3 2 2 2 3 5 3 2 2 3 2 1 3 2 4 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 6 5 5 4 2 4 +--R + +--R 1 3 2 2 2 2 3 3 3 2 2 2 3 2 +--R (- a d + 2a b c d + a b c )x + (a c d + - a b c )x + a c x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 208 + +--S 209 of 1483 +m0041:=a0041-r0041 +--R +--R +--R 1 6 2 1 5 1 4 2 2 +--R - -- a d + -- a b c d - - a b c +--R 60 10 4 +--R (209) --------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 209 + +--S 210 of 1483 +d0041:=D(m0041,x) +--R +--R +--R (210) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 210 + +--S 211 of 1483 +t0042:= (a+b*x)^4*(c+d*x)^2 +--R +--R +--R (211) +--R 4 2 6 3 2 4 5 2 2 2 3 4 2 4 +--R b d x + (4a b d + 2b c d)x + (6a b d + 8a b c d + b c )x +--R + +--R 3 2 2 2 3 2 3 4 2 3 2 2 2 2 +--R (4a b d + 12a b c d + 4a b c )x + (a d + 8a b c d + 6a b c )x +--R + +--R 4 3 2 4 2 +--R (2a c d + 4a b c )x + a c +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 1483 +r0042:= 1/105*(a+b*x)^5*(21*b^2*c^2-7*a*b*c*d+a^2*d^2+35*b^2*c*d*x-_ + 5*b*a*d^2*x+15*b^2*d^2*x^2)/b^3 +--R +--R +--R (212) +--R 1 7 2 7 2 6 2 1 7 6 6 2 5 2 8 6 1 7 2 5 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 7 3 3 5 5 5 +--R + +--R 3 4 2 2 5 6 2 4 1 4 3 2 8 3 4 2 5 2 3 +--R (a b d + 3a b c d + a b c )x + (- a b d + - a b c d + 2a b c )x +--R 3 3 +--R + +--R 4 3 3 4 2 2 4 3 2 1 7 2 1 6 1 5 2 2 +--R (a b c d + 2a b c )x + a b c x + --- a d - -- a b c d + - a b c +--R 105 15 5 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 212 + +--S 213 of 1483 +a0042:=integrate(t0042,x) +--R +--R +--R (213) +--R 1 4 2 7 2 3 2 1 4 6 6 2 2 2 8 3 1 4 2 5 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 7 3 3 5 5 5 +--R + +--R 3 2 2 2 3 2 4 1 4 2 8 3 2 2 2 3 +--R (a b d + 3a b c d + a b c )x + (- a d + - a b c d + 2a b c )x +--R 3 3 +--R + +--R 4 3 2 2 4 2 +--R (a c d + 2a b c )x + a c x +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 1483 +m0042:=a0042-r0042 +--R +--R +--R 1 7 2 1 6 1 5 2 2 +--R - --- a d + -- a b c d - - a b c +--R 105 15 5 +--R (214) ---------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 214 + +--S 215 of 1483 +d0042:=D(m0042,x) +--R +--R +--R (215) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 215 + +--S 216 of 1483 +t0043:= (a+b*x)^5*(c+d*x)^2 +--R +--R +--R (216) +--R 5 2 7 4 2 5 6 2 3 2 4 5 2 5 +--R b d x + (5a b d + 2b c d)x + (10a b d + 10a b c d + b c )x +--R + +--R 3 2 2 2 3 4 2 4 4 2 3 2 2 3 2 3 +--R (10a b d + 20a b c d + 5a b c )x + (5a b d + 20a b c d + 10a b c )x +--R + +--R 5 2 4 3 2 2 2 5 4 2 5 2 +--R (a d + 10a b c d + 10a b c )x + (2a c d + 5a b c )x + a c +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 1483 +r0043:= 1/168*(a+b*x)^6*(28*b^2*c^2-8*a*b*c*d+a^2*d^2+48*b^2*c*d*x-_ + 6*b*a*d^2*x+21*b^2*d^2*x^2)/b^3 +--R +--R +--R (217) +--R 1 8 2 8 5 7 2 2 8 7 5 2 6 2 5 7 1 8 2 6 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 8 7 7 3 3 6 +--R + +--R 3 5 2 2 6 7 2 5 5 4 4 2 3 5 5 2 6 2 4 +--R (2a b d + 4a b c d + a b c )x + (- a b d + 5a b c d + - a b c )x +--R 4 2 +--R + +--R 1 5 3 2 10 4 4 10 3 5 2 3 5 3 5 4 4 2 2 5 3 2 +--R (- a b d + -- a b c d + -- a b c )x + (a b c d + - a b c )x + a b c x +--R 3 3 3 2 +--R + +--R 1 8 2 1 7 1 6 2 2 +--R --- a d - -- a b c d + - a b c +--R 168 21 6 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 217 + +--S 218 of 1483 +a0043:=integrate(t0043,x) +--R +--R +--R (218) +--R 1 5 2 8 5 4 2 2 5 7 5 2 3 2 5 4 1 5 2 6 +--R - b d x + (- a b d + - b c d)x + (- a b d + - a b c d + - b c )x +--R 8 7 7 3 3 6 +--R + +--R 3 2 2 2 3 4 2 5 5 4 2 3 2 5 2 3 2 4 +--R (2a b d + 4a b c d + a b c )x + (- a b d + 5a b c d + - a b c )x +--R 4 2 +--R + +--R 1 5 2 10 4 10 3 2 2 3 5 5 4 2 2 5 2 +--R (- a d + -- a b c d + -- a b c )x + (a c d + - a b c )x + a c x +--R 3 3 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 1483 +m0043:=a0043-r0043 +--R +--R +--R 1 8 2 1 7 1 6 2 2 +--R - --- a d + -- a b c d - - a b c +--R 168 21 6 +--R (219) ---------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 219 + +--S 220 of 1483 +d0043:=D(m0043,x) +--R +--R +--R (220) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 220 + +--S 221 of 1483 +t0044:= (a+b*x)^3*(c+d*x)^3 +--R +--R +--R (221) +--R 3 3 6 2 3 3 2 5 2 3 2 2 3 2 4 +--R b d x + (3a b d + 3b c d )x + (3a b d + 9a b c d + 3b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 3 2 2 2 2 3 2 +--R (a d + 9a b c d + 9a b c d + b c )x + (3a c d + 9a b c d + 3a b c )x +--R + +--R 3 2 2 3 3 3 +--R (3a c d + 3a b c )x + a c +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 1483 +r0044:= 1/140*(b*c-a*d)^3*(a+b*x)^4/b^4+_ + 1/35*(b*c-a*d)^2*(a+b*x)^4*(c+d*x)/b^3+_ + 1/14*(b*c-a*d)*(a+b*x)^4*(c+d*x)^2/b^2+1/7*(a+b*x)^4*(c+d*x)^3/b +--R +--R +--R (222) +--R 1 7 3 7 1 6 3 1 7 2 6 3 2 5 3 9 6 2 3 7 2 5 +--R - b d x + (- a b d + - b c d )x + (- a b d + - a b c d + - b c d)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 4 3 9 2 5 2 9 6 2 1 7 3 4 +--R (- a b d + - a b c d + - a b c d + - b c )x +--R 4 4 4 4 +--R + +--R 3 4 2 2 5 2 6 3 3 3 3 4 2 3 2 5 3 2 3 4 3 +--R (a b c d + 3a b c d + a b c )x + (- a b c d + - a b c )x + a b c x +--R 2 2 +--R + +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R - --- a d + -- a b c d - -- a b c d + - a b c +--R 140 20 20 4 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 222 + +--S 223 of 1483 +a0044:=integrate(t0044,x) +--R +--R +--R (223) +--R 1 3 3 7 1 2 3 1 3 2 6 3 2 3 9 2 2 3 3 2 5 +--R - b d x + (- a b d + - b c d )x + (- a b d + - a b c d + - b c d)x +--R 7 2 2 5 5 5 +--R + +--R 1 3 3 9 2 2 9 2 2 1 3 3 4 +--R (- a d + - a b c d + - a b c d + - b c )x +--R 4 4 4 4 +--R + +--R 3 2 2 2 2 3 3 3 3 2 3 2 3 2 3 3 +--R (a c d + 3a b c d + a b c )x + (- a c d + - a b c )x + a c x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 1483 +m0044:=a0044-r0044 +--R +--R +--R 1 7 3 1 6 2 3 5 2 2 1 4 3 3 +--R --- a d - -- a b c d + -- a b c d - - a b c +--R 140 20 20 4 +--R (224) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 224 + +--S 225 of 1483 +d0044:=D(m0044,x) +--R +--R +--R (225) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 225 + +--S 226 of 1483 +t0045:= (a+b*x)^4*(c+d*x)^3 +--R +--R +--R (226) +--R 4 3 7 3 3 4 2 6 2 2 3 3 2 4 2 5 +--R b d x + (4a b d + 3b c d )x + (6a b d + 12a b c d + 3b c d)x +--R + +--R 3 3 2 2 2 3 2 4 3 4 +--R (4a b d + 18a b c d + 12a b c d + b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 3 +--R (a d + 12a b c d + 18a b c d + 4a b c )x +--R + +--R 4 2 3 2 2 2 3 2 4 2 3 3 4 3 +--R (3a c d + 12a b c d + 6a b c )x + (3a c d + 4a b c )x + a c +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 1483 +r0045:= 1/280*(b*c-a*d)^3*(a+b*x)^5/b^4+_ + 1/56*(b*c-a*d)^2*(a+b*x)^5*(c+d*x)/b^3+_ + 3/56*(b*c-a*d)*(a+b*x)^5*(c+d*x)^2/b^2+1/8*(a+b*x)^5*(c+d*x)^3/b +--R +--R +--R (227) +--R 1 8 3 8 4 7 3 3 8 2 7 2 6 3 7 2 1 8 2 6 +--R - b d x + (- a b d + - b c d )x + (a b d + 2a b c d + - b c d)x +--R 8 7 7 2 +--R + +--R 4 3 5 3 18 2 6 2 12 7 2 1 8 3 5 +--R (- a b d + -- a b c d + -- a b c d + - b c )x +--R 5 5 5 5 +--R + +--R 1 4 4 3 3 5 2 9 2 6 2 7 3 4 +--R (- a b d + 3a b c d + - a b c d + a b c )x +--R 4 2 +--R + +--R 4 4 2 3 5 2 2 6 3 3 3 4 4 2 3 5 3 2 4 4 3 +--R (a b c d + 4a b c d + 2a b c )x + (- a b c d + 2a b c )x + a b c x +--R 2 +--R + +--R 1 8 3 1 7 2 1 6 2 2 1 5 3 3 +--R - --- a d + -- a b c d - -- a b c d + - a b c +--R 280 35 10 5 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 227 + +--S 228 of 1483 +a0045:=integrate(t0045,x) +--R +--R +--R (228) +--R 1 4 3 8 4 3 3 3 4 2 7 2 2 3 3 2 1 4 2 6 +--R - b d x + (- a b d + - b c d )x + (a b d + 2a b c d + - b c d)x +--R 8 7 7 2 +--R + +--R 4 3 3 18 2 2 2 12 3 2 1 4 3 5 +--R (- a b d + -- a b c d + -- a b c d + - b c )x +--R 5 5 5 5 +--R + +--R 1 4 3 3 2 9 2 2 2 3 3 4 +--R (- a d + 3a b c d + - a b c d + a b c )x +--R 4 2 +--R + +--R 4 2 3 2 2 2 3 3 3 4 2 3 3 2 4 3 +--R (a c d + 4a b c d + 2a b c )x + (- a c d + 2a b c )x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 1483 +m0045:=a0045-r0045 +--R +--R +--R 1 8 3 1 7 2 1 6 2 2 1 5 3 3 +--R --- a d - -- a b c d + -- a b c d - - a b c +--R 280 35 10 5 +--R (229) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 229 + +--S 230 of 1483 +d0045:=D(m0045,x) +--R +--R +--R (230) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 230 + +--S 231 of 1483 +t0046:= (a+b*x)^5*(c+d*x)^3 +--R +--R +--R (231) +--R 5 3 8 4 3 5 2 7 2 3 3 4 2 5 2 6 +--R b d x + (5a b d + 3b c d )x + (10a b d + 15a b c d + 3b c d)x +--R + +--R 3 2 3 2 3 2 4 2 5 3 5 +--R (10a b d + 30a b c d + 15a b c d + b c )x +--R + +--R 4 3 3 2 2 2 3 2 4 3 4 +--R (5a b d + 30a b c d + 30a b c d + 5a b c )x +--R + +--R 5 3 4 2 3 2 2 2 3 3 3 +--R (a d + 15a b c d + 30a b c d + 10a b c )x +--R + +--R 5 2 4 2 3 2 3 2 5 2 4 3 5 3 +--R (3a c d + 15a b c d + 10a b c )x + (3a c d + 5a b c )x + a c +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 1483 +r0046:= 1/504*(b*c-a*d)^3*(a+b*x)^6/b^4+_ + 1/84*(b*c-a*d)^2*(a+b*x)^6*(c+d*x)/b^3+_ + 1/24*(b*c-a*d)*(a+b*x)^6*(c+d*x)^2/b^2+1/9*(a+b*x)^6*(c+d*x)^3/b +--R +--R +--R (232) +--R 1 9 3 9 5 8 3 3 9 2 8 +--R - b d x + (- a b d + - b c d )x +--R 9 8 8 +--R + +--R 10 2 7 3 15 8 2 3 9 2 7 +--R (-- a b d + -- a b c d + - b c d)x +--R 7 7 7 +--R + +--R 5 3 6 3 2 7 2 5 8 2 1 9 3 6 +--R (- a b d + 5a b c d + - a b c d + - b c )x +--R 3 2 6 +--R + +--R 4 5 3 3 6 2 2 7 2 8 3 5 +--R (a b d + 6a b c d + 6a b c d + a b c )x +--R + +--R 1 5 4 3 15 4 5 2 15 3 6 2 5 2 7 3 4 +--R (- a b d + -- a b c d + -- a b c d + - a b c )x +--R 4 4 2 2 +--R + +--R 5 4 2 4 5 2 10 3 6 3 3 3 5 4 2 5 4 5 3 2 5 4 3 +--R (a b c d + 5a b c d + -- a b c )x + (- a b c d + - a b c )x + a b c x +--R 3 2 2 +--R + +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R - --- a d + -- a b c d - -- a b c d + - a b c +--R 504 56 14 6 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 232 + +--S 233 of 1483 +a0046:=integrate(t0046,x) +--R +--R +--R (233) +--R 1 5 3 9 5 4 3 3 5 2 8 10 2 3 3 15 4 2 3 5 2 7 +--R - b d x + (- a b d + - b c d )x + (-- a b d + -- a b c d + - b c d)x +--R 9 8 8 7 7 7 +--R + +--R 5 3 2 3 2 3 2 5 4 2 1 5 3 6 +--R (- a b d + 5a b c d + - a b c d + - b c )x +--R 3 2 6 +--R + +--R 4 3 3 2 2 2 3 2 4 3 5 +--R (a b d + 6a b c d + 6a b c d + a b c )x +--R + +--R 1 5 3 15 4 2 15 3 2 2 5 2 3 3 4 +--R (- a d + -- a b c d + -- a b c d + - a b c )x +--R 4 4 2 2 +--R + +--R 5 2 4 2 10 3 2 3 3 3 5 2 5 4 3 2 5 3 +--R (a c d + 5a b c d + -- a b c )x + (- a c d + - a b c )x + a c x +--R 3 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 1483 +m0046:=a0046-r0046 +--R +--R +--R 1 9 3 1 8 2 1 7 2 2 1 6 3 3 +--R --- a d - -- a b c d + -- a b c d - - a b c +--R 504 56 14 6 +--R (234) ---------------------------------------------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 234 + +--S 235 of 1483 +d0046:=D(m0046,x) +--R +--R +--R (235) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 235 + +--S 236 of 1483 +t0047:= (a+b*x)^2/(c+d*x) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (236) ------------------ +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 1483 +r0047:= -b*(b*c-a*d)*x/d^2+1/2*(a+b*x)^2/d+(b*c-a*d)^2*log(c+d*x)/d^3 +--R +--R +--R (237) +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(d x + c) + b d x + (4a b d - 2b c d)x + a d +--R ---------------------------------------------------------------------------- +--R 3 +--R 2d +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1483 +a0047:=integrate(t0047,x) +--R +--R +--R (238) +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(d x + c) + b d x + (4a b d - 2b c d)x +--R --------------------------------------------------------------------- +--R 3 +--R 2d +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1483 +m0047:=a0047-r0047 +--R +--R +--R 2 +--R a +--R (239) - -- +--R 2d +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1483 +d0047:=D(m0047,x) +--R +--R +--R (240) 0 +--R Type: Expression(Integer) +--E 240 + +--S 241 of 1483 +t0048:= (a+b*x)^3/(c+d*x) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (241) ---------------------------- +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 1483 +r0048:= b*(b*c-a*d)^2*x/d^3-1/2*(b*c-a*d)*(a+b*x)^2/d^2+1/3*(a+b*x)^3/d-_ + (b*c-a*d)^3*log(c+d*x)/d^4 +--R +--R +--R (242) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )log(d x + c) + 2b d x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R (9a b d - 3b c d )x + (18a b d - 18a b c d + 6b c d)x + 5a d +--R + +--R 2 2 +--R - 3a b c d +--R / +--R 4 +--R 6d +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1483 +a0048:=integrate(t0048,x) +--R +--R +--R (243) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )log(d x + c) + 2b d x +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (9a b d - 3b c d )x + (18a b d - 18a b c d + 6b c d)x +--R / +--R 4 +--R 6d +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1483 +m0048:=a0048-r0048 +--R +--R +--R 3 2 +--R - 5a d + 3a b c +--R (244) --------------- +--R 2 +--R 6d +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1483 +d0048:=D(m0048,x) +--R +--R +--R (245) 0 +--R Type: Expression(Integer) +--E 245 + +--S 246 of 1483 +t0049:= (a+b*x)^4/(c+d*x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (246) -------------------------------------- +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1483 +r0049:= -b*(b*c-a*d)^3*x/d^4+1/2*(b*c-a*d)^2*(a+b*x)^2/d^3-_ + 1/3*(b*c-a*d)*(a+b*x)^3/d^2+1/4*(a+b*x)^4/d+(b*c-a*d)^4*log(c+d*x)/d^5 +--R +--R +--R (247) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a d - 48a b c d + 72a b c d - 48a b c d + 12b c )log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b d x + (16a b d - 4b c d )x + (36a b d - 24a b c d + 6b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (48a b d - 72a b c d + 48a b c d - 12b c d)x + 13a d - 16a b c d +--R + +--R 2 2 2 2 +--R 6a b c d +--R / +--R 5 +--R 12d +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1483 +a0049:=integrate(t0049,x) +--R +--R +--R (248) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (12a d - 48a b c d + 72a b c d - 48a b c d + 12b c )log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R 3b d x + (16a b d - 4b c d )x + (36a b d - 24a b c d + 6b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 +--R (48a b d - 72a b c d + 48a b c d - 12b c d)x +--R / +--R 5 +--R 12d +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1483 +m0049:=a0049-r0049 +--R +--R +--R 4 2 3 2 2 2 +--R - 13a d + 16a b c d - 6a b c +--R (249) ------------------------------ +--R 3 +--R 12d +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1483 +d0049:=D(m0049,x) +--R +--R +--R (250) 0 +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1483 +t0050:= (a+b*x)^5/(c+d*x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (251) -------------------------------------------------- +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1483 +r0050:= b*(b*c-a*d)^4*x/d^5-1/2*(b*c-a*d)^3*(a+b*x)^2/d^4+_ + 1/3*(b*c-a*d)^2*(a+b*x)^3/d^3-1/4*(b*c-a*d)*(a+b*x)^4/d^2+_ + 1/5*(a+b*x)^5/d-(b*c-a*d)^5*log(c+d*x)/d^6 +--R +--R +--R (252) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 5 5 +--R - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b d x + (75a b d - 15b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b d - 100a b c d + 20b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b d - 300a b c d + 150a b c d - 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (300a b d - 600a b c d + 600a b c d - 300a b c d + 60b c d)x + 77a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 +--R - 145a b c d + 110a b c d - 30a b c d +--R / +--R 6 +--R 60d +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1483 +a0050:=integrate(t0050,x) +--R +--R +--R (253) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 60a d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 5 5 +--R - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 +--R 12b d x + (75a b d - 15b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (200a b d - 100a b c d + 20b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (300a b d - 300a b c d + 150a b c d - 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (300a b d - 600a b c d + 600a b c d - 300a b c d + 60b c d)x +--R / +--R 6 +--R 60d +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1483 +m0050:=a0050-r0050 +--R +--R +--R 5 3 4 2 3 2 2 2 3 3 +--R - 77a d + 145a b c d - 110a b c d + 30a b c +--R (254) ---------------------------------------------- +--R 4 +--R 60d +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1483 +d0050:=D(m0050,x) +--R +--R +--R (255) 0 +--R Type: Expression(Integer) +--E 255 + +--S 256 of 1483 +t0051:= (a+b*x)^6/(c+d*x) +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (256) ------------------------------------------------------------- +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1483 +r0051:= -b*(b*c-a*d)^5*x/d^6+1/2*(b*c-a*d)^4*(a+b*x)^2/d^5-_ + 1/3*(b*c-a*d)^3*(a+b*x)^3/d^4+1/4*(b*c-a*d)^2*(a+b*x)^4/d^3-_ + 1/5*(b*c-a*d)*(a+b*x)^5/d^2+1/6*(a+b*x)^6/d+(b*c-a*d)^6*log(c+d*x)/d^7 +--R +--R +--R (257) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 60a d - 360a b c d + 900a b c d - 1200a b c d + 900a b c d +--R + +--R 5 5 6 6 +--R - 360a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b d x + (72a b d - 12b c d )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (225a b d - 90a b c d + 15b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b d - 300a b c d + 120a b c d - 20b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (450a b d - 600a b c d + 450a b c d - 180a b c d + 30b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 360a b d - 900a b c d + 1200a b c d - 900a b c d + 360a b c d +--R + +--R 6 5 +--R - 60b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 87a d - 222a b c d + 255a b c d - 140a b c d + 30a b c d +--R / +--R 7 +--R 60d +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1483 +a0051:=integrate(t0051,x) +--R +--R +--R (258) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 60a d - 360a b c d + 900a b c d - 1200a b c d + 900a b c d +--R + +--R 5 5 6 6 +--R - 360a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 +--R 10b d x + (72a b d - 12b c d )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (225a b d - 90a b c d + 15b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (400a b d - 300a b c d + 120a b c d - 20b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (450a b d - 600a b c d + 450a b c d - 180a b c d + 30b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 360a b d - 900a b c d + 1200a b c d - 900a b c d + 360a b c d +--R + +--R 6 5 +--R - 60b c d +--R * +--R x +--R / +--R 7 +--R 60d +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1483 +m0051:=a0051-r0051 +--R +--R +--R 6 4 5 3 4 2 2 2 3 3 3 2 4 4 +--R - 87a d + 222a b c d - 255a b c d + 140a b c d - 30a b c +--R (259) ------------------------------------------------------------ +--R 5 +--R 60d +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1483 +d0051:=D(m0051,x) +--R +--R +--R (260) 0 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1483 +t0052:= (a+b*x)^3/(c+d*x)^2 +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (261) ---------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1483 +r0052:= -2*b^2*(b*c-a*d)*x/d^3+1/2*b*(a+b*x)^2/d^2+(b*c-a*d)^3/d^4/(c+d*x)+_ + 3*b*(b*c-a*d)^2*log(c+d*x)/d^4 +--R +--R +--R (262) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b d - 12a b c d + 6b c d)x + 6a b c d - 12a b c d + 6b c ) +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 3 2 2 3 2 3 3 +--R b d x + (6a b d - 3b c d )x + (a b d + 6a b c d - 4b c d)x - 2a d +--R + +--R 2 2 2 2 3 3 +--R 7a b c d - 6a b c d + 2b c +--R / +--R 5 4 +--R 2d x + 2c d +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1483 +a0052:=integrate(t0052,x) +--R +--R +--R (263) +--R 2 3 2 2 3 2 2 2 2 2 3 3 +--R ((6a b d - 12a b c d + 6b c d)x + 6a b c d - 12a b c d + 6b c ) +--R * +--R log(d x + c) +--R + +--R 3 3 3 2 3 3 2 2 2 2 3 2 3 3 +--R b d x + (6a b d - 3b c d )x + (6a b c d - 4b c d)x - 2a d +--R + +--R 2 2 2 2 3 3 +--R 6a b c d - 6a b c d + 2b c +--R / +--R 5 4 +--R 2d x + 2c d +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1483 +m0052:=a0052-r0052 +--R +--R +--R 2 +--R a b +--R (264) - --- +--R 2 +--R 2d +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1483 +d0052:=D(m0052,x) +--R +--R +--R (265) 0 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 1483 +t0053:= (a+b*x)^4/(c+d*x)^2 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (266) -------------------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1483 +r0053:= 3*b^2*(b*c-a*d)^2*x/d^4-b*(b*c-a*d)*(a+b*x)^2/d^3+_ + 1/3*b*(a+b*x)^3/d^2-(b*c-a*d)^4/d^5/(c+d*x)-_ + 4*b*(b*c-a*d)^3*log(c+d*x)/d^5 +--R +--R +--R (267) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b d - 36a b c d + 36a b c d - 12b c d)x + 12a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b c d + 36a b c d - 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b d x + (6a b d - 2b c d )x + (18a b d - 18a b c d + 6b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (4a b d + 15a b c d - 24a b c d + 9b c d)x - 3a d + 16a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 21a b c d + 12a b c d - 3b c +--R / +--R 6 5 +--R 3d x + 3c d +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1483 +a0053:=integrate(t0053,x) +--R +--R +--R (268) +--R 3 4 2 2 3 3 2 2 4 3 3 3 +--R (12a b d - 36a b c d + 36a b c d - 12b c d)x + 12a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 36a b c d + 36a b c d - 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b d x + (6a b d - 2b c d )x + (18a b d - 18a b c d + 6b c d )x +--R + +--R 2 2 3 3 2 2 4 3 4 4 3 3 2 2 2 2 +--R (18a b c d - 24a b c d + 9b c d)x - 3a d + 12a b c d - 18a b c d +--R + +--R 3 3 4 4 +--R 12a b c d - 3b c +--R / +--R 6 5 +--R 3d x + 3c d +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1483 +m0053:=a0053-r0053 +--R +--R +--R 3 2 2 +--R - 4a b d + 3a b c +--R (269) ----------------- +--R 3 +--R 3d +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1483 +d0053:=D(m0053,x) +--R +--R +--R (270) 0 +--R Type: Expression(Integer) +--E 270 + +--S 271 of 1483 +t0054:= (a+b*x)^5/(c+d*x)^2 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (271) -------------------------------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1483 +r0054:= -4*b^2*(b*c-a*d)^3*x/d^5+3/2*b*(b*c-a*d)^2*(a+b*x)^2/d^4-_ + 2/3*b*(b*c-a*d)*(a+b*x)^3/d^3+1/4*b*(a+b*x)^4/d^2+_ + (b*c-a*d)^5/d^6/(c+d*x)+5*b*(b*c-a*d)^4*log(c+d*x)/d^6 +--R +--R +--R (272) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b d x + (20a b d - 5b c d )x + (60a b d - 40a b c d + 10b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b d - 180a b c d + 120a b c d - 30b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (29a b d + 76a b c d - 222a b c d + 180a b c d - 48b c d)x - 12a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 89a b c d - 164a b c d + 138a b c d - 60a b c d + 12b c +--R / +--R 7 6 +--R 12d x + 12c d +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1483 +a0054:=integrate(t0054,x) +--R +--R +--R (273) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d)x +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 3b d x + (20a b d - 5b c d )x + (60a b d - 40a b c d + 10b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (120a b d - 180a b c d + 120a b c d - 30b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (120a b c d - 240a b c d + 180a b c d - 48b c d)x - 12a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 60a b c d - 120a b c d + 120a b c d - 60a b c d + 12b c +--R / +--R 7 6 +--R 12d x + 12c d +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1483 +m0054:=a0054-r0054 +--R +--R +--R 4 2 3 2 2 3 2 +--R - 29a b d + 44a b c d - 18a b c +--R (274) --------------------------------- +--R 4 +--R 12d +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1483 +d0054:=D(m0054,x) +--R +--R +--R (275) 0 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1483 +t0055:= (a+b*x)^6/(c+d*x)^2 +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (276) ------------------------------------------------------------- +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1483 +r0055:= 5*b^2*(b*c-a*d)^4*x/d^6-2*b*(b*c-a*d)^3*(a+b*x)^2/d^5+_ + b*(b*c-a*d)^2*(a+b*x)^3/d^4-1/2*b*(b*c-a*d)*(a+b*x)^4/d^3+_ + 1/5*b*(a+b*x)^5/d^2-(b*c-a*d)^6/d^7/(c+d*x)-_ + 6*b*(b*c-a*d)^5*log(c+d*x)/d^7 +--R +--R +--R (277) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 60a b d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 6 5 +--R - 60b c d +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 60a b c d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 6 6 +--R - 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 2b d x + (15a b d - 3b c d )x + (50a b d - 25a b c d + 5b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b d - 100a b c d + 50a b c d - 10b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (150a b d - 300a b c d + 300a b c d - 150a b c d + 30b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 37a b d + 65a b c d - 330a b c d + 430a b c d - 240a b c d +--R + +--R 6 5 +--R 50b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a d + 97a b c d - 235a b c d + 270a b c d - 170a b c d +--R + +--R 5 5 6 6 +--R 60a b c d - 10b c +--R / +--R 8 7 +--R 10d x + 10c d +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1483 +a0055:=integrate(t0055,x) +--R +--R +--R (278) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 60a b d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 6 5 +--R - 60b c d +--R * +--R x +--R + +--R 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 +--R 60a b c d - 300a b c d + 600a b c d - 600a b c d + 300a b c d +--R + +--R 6 6 +--R - 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R 2b d x + (15a b d - 3b c d )x + (50a b d - 25a b c d + 5b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (100a b d - 100a b c d + 50a b c d - 10b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (150a b d - 300a b c d + 300a b c d - 150a b c d + 30b c d )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (150a b c d - 400a b c d + 450a b c d - 240a b c d + 50b c d)x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 10a d + 60a b c d - 150a b c d + 200a b c d - 150a b c d +--R + +--R 5 5 6 6 +--R 60a b c d - 10b c +--R / +--R 8 7 +--R 10d x + 10c d +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1483 +m0055:=a0055-r0055 +--R +--R +--R 5 3 4 2 2 3 3 2 2 4 3 +--R - 37a b d + 85a b c d - 70a b c d + 20a b c +--R (279) ---------------------------------------------- +--R 5 +--R 10d +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1483 +d0055:=D(m0055,x) +--R +--R +--R (280) 0 +--R Type: Expression(Integer) +--E 280 + +--S 281 of 1483 +t0056:= (a+b*x)^4/(c+d*x)^3 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (281) -------------------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1483 +r0056:= -3*b^3*(b*c-a*d)*x/d^4+1/2*b^2*(a+b*x)^2/d^3-_ + 1/2*(b*c-a*d)^4/d^5/(c+d*x)^2+4*b*(b*c-a*d)^3/d^5/(c+d*x)+_ + 6*b^2*(b*c-a*d)^2*log(c+d*x)/d^5 +--R +--R +--R (282) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b d - 24a b c d + 12b c d )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 4 4 +--R (24a b c d - 48a b c d + 24b c d)x + 12a b c d - 24a b c d + 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 2 2 4 3 3 4 2 2 2 +--R b d x + (8a b d - 4b c d )x + (a b d + 16a b c d - 11b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 8a b d + 26a b c d - 16a b c d + 2b c d)x - a d - 4a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R 19a b c d - 20a b c d + 7b c +--R / +--R 7 2 6 2 5 +--R 2d x + 4c d x + 2c d +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1483 +a0056:=integrate(t0056,x) +--R +--R +--R (283) +--R 2 2 4 3 3 4 2 2 2 +--R (12a b d - 24a b c d + 12b c d )x +--R + +--R 2 2 3 3 2 2 4 3 2 2 2 2 3 3 4 4 +--R (24a b c d - 48a b c d + 24b c d)x + 12a b c d - 24a b c d + 12b c +--R * +--R log(d x + c) +--R + +--R 4 4 4 3 4 4 3 3 3 3 4 2 2 2 +--R b d x + (8a b d - 4b c d )x + (16a b c d - 11b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 8a b d + 24a b c d - 16a b c d + 2b c d)x - a d - 4a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R 18a b c d - 20a b c d + 7b c +--R / +--R 7 2 6 2 5 +--R 2d x + 4c d x + 2c d +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1483 +m0056:=a0056-r0056 +--R +--R +--R 2 2 +--R a b +--R (284) - ---- +--R 3 +--R 2d +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1483 +d0056:=D(m0056,x) +--R +--R +--R (285) 0 +--R Type: Expression(Integer) +--E 285 + +--S 286 of 1483 +t0057:= (a+b*x)^5/(c+d*x)^3 +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (286) -------------------------------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1483 +r0057:= 6*b^3*(b*c-a*d)^2*x/d^5-3/2*b^2*(b*c-a*d)*(a+b*x)^2/d^4+_ + 1/3*b^2*(a+b*x)^3/d^3+1/2*(b*c-a*d)^5/d^6/(c+d*x)^2-_ + 5*b*(b*c-a*d)^4/d^6/(c+d*x)-10*b^2*(b*c-a*d)^3*log(c+d*x)/d^6 +--R +--R +--R (287) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b d - 180a b c d + 180a b c d - 60b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b c d - 360a b c d + 360a b c d - 120b c d)x + 60a b c d +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b c d + 180a b c d - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b d x + (15a b d - 5b c d )x + (60a b d - 60a b c d + 20b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (11a b d + 111a b c d - 165a b c d + 63b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b d + 142a b c d - 138a b c d + 30a b c d + 6b c d)x - 3a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b c d + 101a b c d - 159a b c d + 105a b c d - 27b c +--R / +--R 8 2 7 2 6 +--R 6d x + 12c d x + 6c d +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1483 +a0057:=integrate(t0057,x) +--R +--R +--R (288) +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (60a b d - 180a b c d + 180a b c d - 60b c d )x +--R + +--R 3 2 4 2 3 2 3 4 3 2 5 4 3 2 2 3 +--R (120a b c d - 360a b c d + 360a b c d - 120b c d)x + 60a b c d +--R + +--R 2 3 3 2 4 4 5 5 +--R - 180a b c d + 180a b c d - 60b c +--R * +--R log(d x + c) +--R + +--R 5 5 5 4 5 5 4 4 2 3 5 4 4 5 2 3 3 +--R 2b d x + (15a b d - 5b c d )x + (60a b d - 60a b c d + 20b c d )x +--R + +--R 2 3 4 4 2 3 5 3 2 2 +--R (120a b c d - 165a b c d + 63b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 30a b d + 120a b c d - 120a b c d + 30a b c d + 6b c d)x - 3a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 15a b c d + 90a b c d - 150a b c d + 105a b c d - 27b c +--R / +--R 8 2 7 2 6 +--R 6d x + 12c d x + 6c d +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1483 +m0057:=a0057-r0057 +--R +--R +--R 3 2 2 3 +--R - 11a b d + 9a b c +--R (289) ------------------ +--R 4 +--R 6d +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1483 +d0057:=D(m0057,x) +--R +--R +--R (290) 0 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1483 +t0058:= (a+b*x)^6/(c+d*x)^3 +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (291) ------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1483 +r0058:= -10*b^3*(b*c-a*d)^3*x/d^6+3*b^2*(b*c-a*d)^2*(a+b*x)^2/d^5-_ + b^2*(b*c-a*d)*(a+b*x)^3/d^4+1/4*b^2*(a+b*x)^4/d^3-_ + 1/2*(b*c-a*d)^6/d^7/(c+d*x)^2+6*b*(b*c-a*d)^5/d^7/(c+d*x)+_ + 15*b^2*(b*c-a*d)^4*log(c+d*x)/d^7 +--R +--R +--R (292) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b c d - 480a b c d + 720a b c d - 480a b c d + 120b c d)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b d x + (8a b d - 2b c d )x + (30a b d - 20a b c d + 5b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b d - 120a b c d + 80a b c d - 20b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (17a b d + 132a b c d - 318a b c d + 252a b c d - 68b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b d + 154a b c d - 216a b c d + 84a b c d + 24a b c d +--R + +--R 6 5 +--R - 16b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a d - 12a b c d + 107a b c d - 228a b c d + 222a b c d +--R + +--R 5 5 6 6 +--R - 108a b c d + 22b c +--R / +--R 9 2 8 2 7 +--R 4d x + 8c d x + 4c d +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1483 +a0058:=integrate(t0058,x) +--R +--R +--R (293) +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (60a b d - 240a b c d + 360a b c d - 240a b c d + 60b c d )x +--R + +--R 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (120a b c d - 480a b c d + 720a b c d - 480a b c d + 120b c d)x +--R + +--R 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R 60a b c d - 240a b c d + 360a b c d - 240a b c d + 60b c +--R * +--R log(d x + c) +--R + +--R 6 6 6 5 6 6 5 5 2 4 6 5 5 6 2 4 4 +--R b d x + (8a b d - 2b c d )x + (30a b d - 20a b c d + 5b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (80a b d - 120a b c d + 80a b c d - 20b c d )x +--R + +--R 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (160a b c d - 330a b c d + 252a b c d - 68b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 24a b d + 120a b c d - 160a b c d + 60a b c d + 24a b c d +--R + +--R 6 5 +--R - 16b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 2a d - 12a b c d + 90a b c d - 200a b c d + 210a b c d +--R + +--R 5 5 6 6 +--R - 108a b c d + 22b c +--R / +--R 9 2 8 2 7 +--R 4d x + 8c d x + 4c d +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1483 +m0058:=a0058-r0058 +--R +--R +--R 4 2 2 3 3 2 4 2 +--R - 17a b d + 28a b c d - 12a b c +--R (294) --------------------------------- +--R 5 +--R 4d +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1483 +d0058:=D(m0058,x) +--R +--R +--R (295) 0 +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1483 +t0059:= (a+b*x)^4/(c+d*x)^8 +--R +--R +--R (296) +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 1483 +r0059:= -1/105*(a+b*x)^5*(21*b^2*c^2-35*a*b*c*d+15*a^2*d^2+7*d*b^2*c*x-_ + 5*b*a*d^2*x+d^2*b^2*x^2)/(-b*c+a*d)^3/(c+d*x)^7 +--R +--R +--R (297) +--R 1 7 2 7 1 7 6 1 7 2 5 1 3 4 2 2 5 6 2 4 +--R - --- b d x - -- b c d x - - b c x + (- - a b d + a b c d - a b c )x +--R 105 15 5 3 +--R + +--R 4 3 2 8 3 4 2 5 2 3 6 5 2 2 4 3 3 4 2 2 +--R (- a b d + - a b c d - 2a b c )x + (- - a b d + 3a b c d - 2a b c )x +--R 3 5 +--R + +--R 2 6 2 8 5 2 4 3 2 1 7 2 1 6 1 5 2 2 +--R (- - a b d + - a b c d - a b c )x - - a d + - a b c d - - a b c +--R 3 5 7 3 5 +--R / +--R 3 10 2 9 2 2 8 3 3 7 7 +--R (a d - 3a b c d + 3a b c d - b c d )x +--R + +--R 3 9 2 2 8 2 3 7 3 4 6 6 +--R (7a c d - 21a b c d + 21a b c d - 7b c d )x +--R + +--R 3 2 8 2 3 7 2 4 6 3 5 5 5 +--R (21a c d - 63a b c d + 63a b c d - 21b c d )x +--R + +--R 3 3 7 2 4 6 2 5 5 3 6 4 4 +--R (35a c d - 105a b c d + 105a b c d - 35b c d )x +--R + +--R 3 4 6 2 5 5 2 6 4 3 7 3 3 +--R (35a c d - 105a b c d + 105a b c d - 35b c d )x +--R + +--R 3 5 5 2 6 4 2 7 3 3 8 2 2 +--R (21a c d - 63a b c d + 63a b c d - 21b c d )x +--R + +--R 3 6 4 2 7 3 2 8 2 3 9 3 7 3 2 8 2 +--R (7a c d - 21a b c d + 21a b c d - 7b c d)x + a c d - 3a b c d +--R + +--R 2 9 3 10 +--R 3a b c d - b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 297 + +--S 298 of 1483 +a0059:=integrate(t0059,x) +--R +--R +--R (298) +--R 4 4 4 3 4 4 3 3 +--R - 35b d x + (- 105a b d - 35b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 126a b d - 63a b c d - 21b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 3 3 +--R (- 70a b d - 42a b c d - 21a b c d - 7b c d)x - 15a d - 10a b c d +--R + +--R 2 2 2 2 3 3 4 4 +--R - 6a b c d - 3a b c d - b c +--R / +--R 12 7 11 6 2 10 5 3 9 4 4 8 3 +--R 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x +--R + +--R 5 7 2 6 6 7 5 +--R 2205c d x + 735c d x + 105c d +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1483 +m0059:=a0059-r0059 +--R +--R +--R 7 +--R b +--R (299) ----------------------------------------------- +--R 3 8 2 7 2 2 6 3 3 5 +--R 105a d - 315a b c d + 315a b c d - 105b c d +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1483 +d0059:=D(m0059,x) +--R +--R +--R (300) 0 +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1483 +t0060:= (a+b*x)^5/(c+d*x)^8 +--R +--R +--R (301) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1483 +r0060:= -1/42*(a+b*x)^6*(-7*b*c+6*a*d-d*b*x)/(-b*c+a*d)^2/(c+d*x)^7 +--R +--R +--R (302) +--R 1 7 7 1 7 6 1 2 5 6 5 5 3 4 5 2 5 4 +--R -- b d x + - b c x + (- - a b d + a b c)x + (- - a b d + - a b c)x +--R 42 6 2 3 2 +--R + +--R 5 4 3 10 3 4 3 5 2 5 4 3 2 5 6 5 2 +--R (- - a b d + -- a b c)x + (- 2a b d + - a b c)x + (- - a b d + a b c)x +--R 2 3 2 6 +--R + +--R 1 7 1 6 +--R - - a d + - a b c +--R 7 6 +--R / +--R 2 9 8 2 2 7 7 2 8 2 7 2 3 6 6 +--R (a d - 2a b c d + b c d )x + (7a c d - 14a b c d + 7b c d )x +--R + +--R 2 2 7 3 6 2 4 5 5 +--R (21a c d - 42a b c d + 21b c d )x +--R + +--R 2 3 6 4 5 2 5 4 4 +--R (35a c d - 70a b c d + 35b c d )x +--R + +--R 2 4 5 5 4 2 6 3 3 +--R (35a c d - 70a b c d + 35b c d )x +--R + +--R 2 5 4 6 3 2 7 2 2 2 6 3 7 2 2 8 +--R (21a c d - 42a b c d + 21b c d )x + (7a c d - 14a b c d + 7b c d)x +--R + +--R 2 7 2 8 2 9 +--R a c d - 2a b c d + b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 302 + +--S 303 of 1483 +a0060:=integrate(t0060,x) +--R +--R +--R (303) +--R 5 5 5 4 5 5 4 4 +--R - 21b d x + (- 70a b d - 35b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 105a b d - 70a b c d - 35b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (- 84a b d - 63a b c d - 42a b c d - 21b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 5 5 +--R (- 35a b d - 28a b c d - 21a b c d - 14a b c d - 7b c d)x - 6a d +--R + +--R 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R - 5a b c d - 4a b c d - 3a b c d - 2a b c d - b c +--R / +--R 13 7 12 6 2 11 5 3 10 4 4 9 3 5 8 2 +--R 42d x + 294c d x + 882c d x + 1470c d x + 1470c d x + 882c d x +--R + +--R 6 7 7 6 +--R 294c d x + 42c d +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1483 +m0060:=a0060-r0060 +--R +--R +--R 7 +--R b +--R (304) - ------------------------------ +--R 2 8 7 2 2 6 +--R 42a d - 84a b c d + 42b c d +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1483 +d0060:=D(m0060,x) +--R +--R +--R (305) 0 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1483 +t0061:= (a+b*x)^6/(c+d*x)^8 +--R +--R +--R (306) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 1483 +r0061:= 1/7*(a+b*x)^7/(b*c-a*d)/(c+d*x)^7 +--R +--R +--R (307) +--R 1 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 1 7 +--R - - b x - a b x - 3a b x - 5a b x - 5a b x - 3a b x - a b x - - a +--R 7 7 +--R / +--R 8 7 7 7 2 6 6 2 6 3 5 5 +--R (a d - b c d )x + (7a c d - 7b c d )x + (21a c d - 21b c d )x +--R + +--R 3 5 4 4 4 4 4 5 3 3 +--R (35a c d - 35b c d )x + (35a c d - 35b c d )x +--R + +--R 5 3 6 2 2 6 2 7 7 8 +--R (21a c d - 21b c d )x + (7a c d - 7b c d)x + a c d - b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 307 + +--S 308 of 1483 +a0061:=integrate(t0061,x) +--R +--R +--R (308) +--R 6 6 6 5 6 6 5 5 +--R - 7b d x + (- 21a b d - 21b c d )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 35a b d - 35a b c d - 35b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (- 35a b d - 35a b c d - 35a b c d - 35b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 2 +--R (- 21a b d - 21a b c d - 21a b c d - 21a b c d - 21b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 6 5 +--R (- 7a b d - 7a b c d - 7a b c d - 7a b c d - 7a b c d - 7b c d)x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 5 5 6 6 +--R - a d - a b c d - a b c d - a b c d - a b c d - a b c d - b c +--R / +--R 14 7 13 6 2 12 5 3 11 4 4 10 3 5 9 2 +--R 7d x + 49c d x + 147c d x + 245c d x + 245c d x + 147c d x +--R + +--R 6 8 7 7 +--R 49c d x + 7c d +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1483 +m0061:=a0061-r0061 +--R +--R +--R 7 +--R b +--R (309) --------------- +--R 8 7 +--R 7a d - 7b c d +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1483 +d0061:=D(m0061,x) +--R +--R +--R (310) 0 +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1483 +t0062:= (a+b*x)^7/(c+d*x)^8 +--R +--R +--R (311) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 1483 +r0062:= 1/7*(b*c-a*d)^7/d^8/(c+d*x)^7-7/6*b*(b*c-a*d)^6/d^8/(c+d*x)^6+_ + 21/5*b^2*(b*c-a*d)^5/d^8/(c+d*x)^5-_ + 35/4*b^3*(b*c-a*d)^4/d^8/(c+d*x)^4+_ + 35/3*b^4*(b*c-a*d)^3/d^8/(c+d*x)^3-_ + 21/2*b^5*(b*c-a*d)^2/d^8/(c+d*x)^2+_ + 7*b^6*(b*c-a*d)/d^8/(c+d*x)+b^7*log(c+d*x)/d^8 +--R +--R +--R (312) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(d x + c) +--R + +--R 6 7 7 6 6 +--R (- 2940a b d + 2940b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 4410a b d - 8820a b c d + 13230b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4900a b d - 7350a b c d - 14700a b c d + 26950b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 3675a b d - 4900a b c d - 7350a b c d - 14700a b c d +--R + +--R 7 4 3 +--R 30625b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1764a b d - 2205a b c d - 2940a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8820a b c d + 20139b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 490a b d - 588a b c d - 735a b c d - 980a b c d - 1470a b c d +--R + +--R 6 5 2 7 6 +--R - 2940a b c d + 7203b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d - 70a b c d - 84a b c d - 105a b c d - 140a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d - 420a b c d + 1089b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420d x + 2940c d x + 8820c d x + 14700c d x + 14700c d x +--R + +--R 5 10 2 6 9 7 8 +--R 8820c d x + 2940c d x + 420c d +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1483 +a0062:=integrate(t0062,x) +--R +--R +--R (313) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(d x + c) +--R + +--R 6 7 7 6 6 +--R (- 2940a b d + 2940b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 4410a b d - 8820a b c d + 13230b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4900a b d - 7350a b c d - 14700a b c d + 26950b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 3675a b d - 4900a b c d - 7350a b c d - 14700a b c d +--R + +--R 7 4 3 +--R 30625b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1764a b d - 2205a b c d - 2940a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8820a b c d + 20139b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 490a b d - 588a b c d - 735a b c d - 980a b c d - 1470a b c d +--R + +--R 6 5 2 7 6 +--R - 2940a b c d + 7203b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d - 70a b c d - 84a b c d - 105a b c d - 140a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d - 420a b c d + 1089b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420d x + 2940c d x + 8820c d x + 14700c d x + 14700c d x +--R + +--R 5 10 2 6 9 7 8 +--R 8820c d x + 2940c d x + 420c d +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1483 +m0062:=a0062-r0062 +--R +--R +--R (314) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1483 +d0062:=D(m0062,x) +--R +--R +--R (315) 0 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 1483 +t0063:= (a+b*x)^8/(c+d*x)^8 +--R +--R +--R (316) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 8 +--R 8a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1483 +r0063:= b^8*x/d^8-1/7*(b*c-a*d)^8/d^9/(c+d*x)^7+_ + 4/3*b*(b*c-a*d)^7/d^9/(c+d*x)^6-28/5*b^2*(b*c-a*d)^6/d^9/(c+d*x)^5+_ + 14*b^3*(b*c-a*d)^5/d^9/(c+d*x)^4-70/3*b^4*(b*c-a*d)^4/d^9/(c+d*x)^3+_ + 28*b^5*(b*c-a*d)^3/d^9/(c+d*x)^2-28*b^6*(b*c-a*d)^2/d^9/(c+d*x)-_ + 8*b^7*(b*c-a*d)*log(c+d*x)/d^9 +--R +--R +--R (317) +--R 7 8 8 7 7 7 7 8 2 6 6 +--R (840a b d - 840b c d )x + (5880a b c d - 5880b c d )x +--R + +--R 7 2 6 8 3 5 5 7 3 5 8 4 4 4 +--R (17640a b c d - 17640b c d )x + (29400a b c d - 29400b c d )x +--R + +--R 7 4 4 8 5 3 3 7 5 3 8 6 2 2 +--R (29400a b c d - 29400b c d )x + (17640a b c d - 17640b c d )x +--R + +--R 7 6 2 8 7 7 7 8 8 +--R (5880a b c d - 5880b c d)x + 840a b c d - 840b c +--R * +--R log(d x + c) +--R + +--R 8 8 8 8 7 7 2 6 8 7 7 8 2 6 6 +--R 105b d x + 735b c d x + (- 2940a b d + 5880a b c d - 735b c d )x +--R + +--R 3 5 8 2 6 7 7 2 6 8 3 5 5 +--R (- 2940a b d - 8820a b c d + 26460a b c d - 11025b c d )x +--R + +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 +--R - 2450a b d - 4900a b c d - 14700a b c d + 53900a b c d +--R + +--R 8 4 4 +--R - 28175b c d +--R * +--R 4 +--R x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 +--R - 1470a b d - 2450a b c d - 4900a b c d - 14700a b c d +--R + +--R 7 4 4 8 5 3 +--R 61250a b c d - 35525b c d +--R * +--R 3 +--R x +--R + +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 +--R - 588a b d - 882a b c d - 1470a b c d - 2940a b c d +--R + +--R 2 6 4 4 7 5 3 8 6 2 +--R - 8820a b c d + 40278a b c d - 24843b c d +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 140a b d - 196a b c d - 294a b c d - 490a b c d - 980a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R - 2940a b c d + 14406a b c d - 9261b c d +--R * +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R - 15a d - 20a b c d - 28a b c d - 42a b c d - 70a b c d +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R - 140a b c d - 420a b c d + 2178a b c d - 1443b c +--R / +--R 16 7 15 6 2 14 5 3 13 4 4 12 3 +--R 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x +--R + +--R 5 11 2 6 10 7 9 +--R 2205c d x + 735c d x + 105c d +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1483 +a0063:=integrate(t0063,x) +--R +--R +--R (318) +--R 7 8 8 7 7 7 7 8 2 6 6 +--R (840a b d - 840b c d )x + (5880a b c d - 5880b c d )x +--R + +--R 7 2 6 8 3 5 5 7 3 5 8 4 4 4 +--R (17640a b c d - 17640b c d )x + (29400a b c d - 29400b c d )x +--R + +--R 7 4 4 8 5 3 3 7 5 3 8 6 2 2 +--R (29400a b c d - 29400b c d )x + (17640a b c d - 17640b c d )x +--R + +--R 7 6 2 8 7 7 7 8 8 +--R (5880a b c d - 5880b c d)x + 840a b c d - 840b c +--R * +--R log(d x + c) +--R + +--R 8 8 8 8 7 7 2 6 8 7 7 8 2 6 6 +--R 105b d x + 735b c d x + (- 2940a b d + 5880a b c d - 735b c d )x +--R + +--R 3 5 8 2 6 7 7 2 6 8 3 5 5 +--R (- 2940a b d - 8820a b c d + 26460a b c d - 11025b c d )x +--R + +--R 4 4 8 3 5 7 2 6 2 6 7 3 5 +--R - 2450a b d - 4900a b c d - 14700a b c d + 53900a b c d +--R + +--R 8 4 4 +--R - 28175b c d +--R * +--R 4 +--R x +--R + +--R 5 3 8 4 4 7 3 5 2 6 2 6 3 5 +--R - 1470a b d - 2450a b c d - 4900a b c d - 14700a b c d +--R + +--R 7 4 4 8 5 3 +--R 61250a b c d - 35525b c d +--R * +--R 3 +--R x +--R + +--R 6 2 8 5 3 7 4 4 2 6 3 5 3 5 +--R - 588a b d - 882a b c d - 1470a b c d - 2940a b c d +--R + +--R 2 6 4 4 7 5 3 8 6 2 +--R - 8820a b c d + 40278a b c d - 24843b c d +--R * +--R 2 +--R x +--R + +--R 7 8 6 2 7 5 3 2 6 4 4 3 5 3 5 4 4 +--R - 140a b d - 196a b c d - 294a b c d - 490a b c d - 980a b c d +--R + +--R 2 6 5 3 7 6 2 8 7 +--R - 2940a b c d + 14406a b c d - 9261b c d +--R * +--R x +--R + +--R 8 8 7 7 6 2 2 6 5 3 3 5 4 4 4 4 +--R - 15a d - 20a b c d - 28a b c d - 42a b c d - 70a b c d +--R + +--R 3 5 5 3 2 6 6 2 7 7 8 8 +--R - 140a b c d - 420a b c d + 2178a b c d - 1443b c +--R / +--R 16 7 15 6 2 14 5 3 13 4 4 12 3 +--R 105d x + 735c d x + 2205c d x + 3675c d x + 3675c d x +--R + +--R 5 11 2 6 10 7 9 +--R 2205c d x + 735c d x + 105c d +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1483 +m0063:=a0063-r0063 +--R +--R +--R (319) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1483 +d0063:=D(m0063,x) +--R +--R +--R (320) 0 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1483 +t0064:= (a+b*x)^9/(c+d*x)^8 +--R +--R +--R (321) +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 2 2 8 9 +--R 36a b x + 9a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 1483 +r0064:= -8*b^8*(b*c-a*d)*x/d^9+1/2*b^7*(a+b*x)^2/d^8+_ + 1/7*(b*c-a*d)^9/d^10/(c+d*x)^7-3/2*b*(b*c-a*d)^8/d^10/(c+d*x)^6+_ + 36/5*b^2*(b*c-a*d)^7/d^10/(c+d*x)^5-_ + 21*b^3*(b*c-a*d)^6/d^10/(c+d*x)^4+42*b^4*(b*c-a*d)^5/d^10/(c+d*x)^3-_ + 63*b^5*(b*c-a*d)^4/d^10/(c+d*x)^2+84*b^6*(b*c-a*d)^3/d^10/(c+d*x)+_ + 36*b^7*(b*c-a*d)^2*log(c+d*x)/d^10 +--R +--R +--R (322) +--R 2 7 9 8 8 9 2 7 7 +--R (2520a b d - 5040a b c d + 2520b c d )x +--R + +--R 2 7 8 8 2 7 9 3 6 6 +--R (17640a b c d - 35280a b c d + 17640b c d )x +--R + +--R 2 7 2 7 8 3 6 9 4 5 5 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 3 6 8 4 5 9 5 4 4 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 4 5 8 5 4 9 6 3 3 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 5 4 8 6 3 9 7 2 2 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 6 3 8 7 2 9 8 2 7 7 2 +--R (17640a b c d - 35280a b c d + 17640b c d)x + 2520a b c d +--R + +--R 8 8 9 9 +--R - 5040a b c d + 2520b c +--R * +--R log(d x + c) +--R + +--R 9 9 9 8 9 9 8 8 +--R 35b d x + (630a b d - 315b c d )x +--R + +--R 2 7 9 8 8 9 2 7 7 +--R (35a b d + 4410a b c d - 3185b c d )x +--R + +--R 3 6 9 2 7 8 8 2 7 9 3 6 6 +--R (- 5880a b d + 17885a b c d - 4410a b c d - 4655b c d )x +--R + +--R 4 5 9 3 6 8 2 7 2 7 8 3 6 +--R - 4410a b d - 17640a b c d + 80115a b c d - 66150a b c d +--R + +--R 9 4 5 +--R 12495b c d +--R * +--R 5 +--R x +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 +--R - 2940a b d - 7350a b c d - 29400a b c d + 162925a b c d +--R + +--R 8 4 5 9 5 4 +--R - 169050a b c d + 50225b c d +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 5 2 7 3 6 3 6 +--R - 1470a b d - 2940a b c d - 7350a b c d - 29400a b c d +--R + +--R 2 7 4 5 8 5 4 9 6 3 +--R 184975a b c d - 213150a b c d + 72275b c d +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 +--R - 504a b d - 882a b c d - 1764a b c d - 4410a b c d +--R + +--R 3 6 4 5 2 7 5 4 8 6 3 9 7 2 +--R - 17640a b c d + 121569a b c d - 149058a b c d + 53949b c d +--R * +--R 2 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 4 5 4 5 +--R - 105a b d - 168a b c d - 294a b c d - 588a b c d - 1470a b c d +--R + +--R 3 6 5 4 2 7 6 3 8 7 2 9 8 +--R - 5880a b c d + 43463a b c d - 55566a b c d + 20923b c d +--R * +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 +--R - 10a d - 15a b c d - 24a b c d - 42a b c d - 84a b c d +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 +--R - 210a b c d - 840a b c d + 6569a b c d - 8658a b c d + 3349b c +--R / +--R 17 7 16 6 2 15 5 3 14 4 4 13 3 +--R 70d x + 490c d x + 1470c d x + 2450c d x + 2450c d x +--R + +--R 5 12 2 6 11 7 10 +--R 1470c d x + 490c d x + 70c d +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1483 +a0064:=integrate(t0064,x) +--R +--R +--R (323) +--R 2 7 9 8 8 9 2 7 7 +--R (2520a b d - 5040a b c d + 2520b c d )x +--R + +--R 2 7 8 8 2 7 9 3 6 6 +--R (17640a b c d - 35280a b c d + 17640b c d )x +--R + +--R 2 7 2 7 8 3 6 9 4 5 5 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 3 6 8 4 5 9 5 4 4 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 4 5 8 5 4 9 6 3 3 +--R (88200a b c d - 176400a b c d + 88200b c d )x +--R + +--R 2 7 5 4 8 6 3 9 7 2 2 +--R (52920a b c d - 105840a b c d + 52920b c d )x +--R + +--R 2 7 6 3 8 7 2 9 8 2 7 7 2 +--R (17640a b c d - 35280a b c d + 17640b c d)x + 2520a b c d +--R + +--R 8 8 9 9 +--R - 5040a b c d + 2520b c +--R * +--R log(d x + c) +--R + +--R 9 9 9 8 9 9 8 8 8 8 9 2 7 7 +--R 35b d x + (630a b d - 315b c d )x + (4410a b c d - 3185b c d )x +--R + +--R 3 6 9 2 7 8 8 2 7 9 3 6 6 +--R (- 5880a b d + 17640a b c d - 4410a b c d - 4655b c d )x +--R + +--R 4 5 9 3 6 8 2 7 2 7 8 3 6 +--R - 4410a b d - 17640a b c d + 79380a b c d - 66150a b c d +--R + +--R 9 4 5 +--R 12495b c d +--R * +--R 5 +--R x +--R + +--R 5 4 9 4 5 8 3 6 2 7 2 7 3 6 +--R - 2940a b d - 7350a b c d - 29400a b c d + 161700a b c d +--R + +--R 8 4 5 9 5 4 +--R - 169050a b c d + 50225b c d +--R * +--R 4 +--R x +--R + +--R 6 3 9 5 4 8 4 5 2 7 3 6 3 6 +--R - 1470a b d - 2940a b c d - 7350a b c d - 29400a b c d +--R + +--R 2 7 4 5 8 5 4 9 6 3 +--R 183750a b c d - 213150a b c d + 72275b c d +--R * +--R 3 +--R x +--R + +--R 7 2 9 6 3 8 5 4 2 7 4 5 3 6 +--R - 504a b d - 882a b c d - 1764a b c d - 4410a b c d +--R + +--R 3 6 4 5 2 7 5 4 8 6 3 9 7 2 +--R - 17640a b c d + 120834a b c d - 149058a b c d + 53949b c d +--R * +--R 2 +--R x +--R + +--R 8 9 7 2 8 6 3 2 7 5 4 3 6 4 5 4 5 +--R - 105a b d - 168a b c d - 294a b c d - 588a b c d - 1470a b c d +--R + +--R 3 6 5 4 2 7 6 3 8 7 2 9 8 +--R - 5880a b c d + 43218a b c d - 55566a b c d + 20923b c d +--R * +--R x +--R + +--R 9 9 8 8 7 2 2 7 6 3 3 6 5 4 4 5 +--R - 10a d - 15a b c d - 24a b c d - 42a b c d - 84a b c d +--R + +--R 4 5 5 4 3 6 6 3 2 7 7 2 8 8 9 9 +--R - 210a b c d - 840a b c d + 6534a b c d - 8658a b c d + 3349b c +--R / +--R 17 7 16 6 2 15 5 3 14 4 4 13 3 +--R 70d x + 490c d x + 1470c d x + 2450c d x + 2450c d x +--R + +--R 5 12 2 6 11 7 10 +--R 1470c d x + 490c d x + 70c d +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1483 +m0064:=a0064-r0064 +--R +--R +--R 2 7 +--R a b +--R (324) - ---- +--R 8 +--R 2d +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1483 +d0064:=D(m0064,x) +--R +--R +--R (325) 0 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 1483 +t0065:= (a+b*x)^7/(c+d*x) +--R +--R +--R (326) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 1483 +r0065:= b*(b*c-a*d)^6*x/d^7-1/2*(b*c-a*d)^5*(a+b*x)^2/d^6+_ + 1/3*(b*c-a*d)^4*(a+b*x)^3/d^5-1/4*(b*c-a*d)^3*(a+b*x)^4/d^4+_ + 1/5*(b*c-a*d)^2*(a+b*x)^5/d^3-1/6*(b*c-a*d)*(a+b*x)^6/d^2+_ + 1/7*(a+b*x)^7/d-(b*c-a*d)^7*log(c+d*x)/d^8 +--R +--R +--R (327) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a d - 2940a b c d + 8820a b c d - 14700a b c d + 14700a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 8820a b c d + 2940a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b d x + (490a b d - 70b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (1764a b d - 588a b c d + 84b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (3675a b d - 2205a b c d + 735a b c d - 105b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (4900a b d - 4900a b c d + 2940a b c d - 980a b c d + 140b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4410a b d - 7350a b c d + 7350a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R 1470a b c d - 210b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 2940a b d - 8820a b c d + 14700a b c d - 14700a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 8820a b c d - 2940a b c d + 420b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 669a d - 2163a b c d + 3339a b c d - 2765a b c d + 1190a b c d +--R + +--R 2 5 5 2 +--R - 210a b c d +--R / +--R 8 +--R 420d +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1483 +a0065:=integrate(t0065,x) +--R +--R +--R (328) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a d - 2940a b c d + 8820a b c d - 14700a b c d + 14700a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 8820a b c d + 2940a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 60b d x + (490a b d - 70b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (1764a b d - 588a b c d + 84b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (3675a b d - 2205a b c d + 735a b c d - 105b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (4900a b d - 4900a b c d + 2940a b c d - 980a b c d + 140b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 4410a b d - 7350a b c d + 7350a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R 1470a b c d - 210b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 2940a b d - 8820a b c d + 14700a b c d - 14700a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 8820a b c d - 2940a b c d + 420b c d +--R * +--R x +--R / +--R 8 +--R 420d +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1483 +m0065:=a0065-r0065 +--R +--R +--R (329) +--R 7 5 6 4 5 2 2 3 4 3 3 2 3 4 4 +--R - 669a d + 2163a b c d - 3339a b c d + 2765a b c d - 1190a b c d +--R + +--R 2 5 5 +--R 210a b c +--R / +--R 6 +--R 420d +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1483 +d0065:=D(m0065,x) +--R +--R +--R (330) 0 +--R Type: Expression(Integer) +--E 330 + +--S 331 of 1483 +t0066:= (a+b*x)^7/(c+d*x)^2 +--R +--R +--R (331) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 2 2 2 +--R d x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1483 +r0066:= -6*b^2*(b*c-a*d)^5*x/d^7+5/2*b*(b*c-a*d)^4*(a+b*x)^2/d^6-_ + 4/3*b*(b*c-a*d)^3*(a+b*x)^3/d^5+3/4*b*(b*c-a*d)^2*(a+b*x)^4/d^4-_ + 2/5*b*(b*c-a*d)*(a+b*x)^5/d^3+1/6*b*(a+b*x)^6/d^2+_ + (b*c-a*d)^7/d^8/(c+d*x)+7*b*(b*c-a*d)^6*log(c+d*x)/d^8 +--R +--R +--R (332) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b d - 2520a b c d + 6300a b c d - 8400a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b c d - 2520a b c d + 420b c d +--R * +--R x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a b c d - 2520a b c d + 6300a b c d - 8400a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 6300a b c d - 2520a b c d + 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b d x + (84a b d - 14b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (315a b d - 126a b c d + 21b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (700a b d - 525a b c d + 210a b c d - 35b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1050a b d - 1400a b c d + 1050a b c d - 420a b c d + 70b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b d - 3150a b c d + 4200a b c d - 3150a b c d +--R + +--R 6 4 3 7 5 2 +--R 1260a b c d - 210b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 309a b d + 306a b c d - 3015a b c d + 5620a b c d - 4890a b c d +--R + +--R 6 5 2 7 6 +--R 2100a b c d - 360b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d + 729a b c d - 2214a b c d + 3285a b c d - 2780a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 1410a b c d - 420a b c d + 60b c +--R / +--R 9 8 +--R 60d x + 60c d +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1483 +a0066:=integrate(t0066,x) +--R +--R +--R (333) +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R 420a b d - 2520a b c d + 6300a b c d - 8400a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 6300a b c d - 2520a b c d + 420b c d +--R * +--R x +--R + +--R 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 420a b c d - 2520a b c d + 6300a b c d - 8400a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 6300a b c d - 2520a b c d + 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b d x + (84a b d - 14b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (315a b d - 126a b c d + 21b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (700a b d - 525a b c d + 210a b c d - 35b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1050a b d - 1400a b c d + 1050a b c d - 420a b c d + 70b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 1260a b d - 3150a b c d + 4200a b c d - 3150a b c d +--R + +--R 6 4 3 7 5 2 +--R 1260a b c d - 210b c d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 1260a b c d - 4200a b c d + 6300a b c d - 5040a b c d +--R + +--R 6 5 2 7 6 +--R 2100a b c d - 360b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d + 420a b c d - 1260a b c d + 2100a b c d - 2100a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 1260a b c d - 420a b c d + 60b c +--R / +--R 9 8 +--R 60d x + 60c d +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1483 +m0066:=a0066-r0066 +--R +--R +--R 6 4 5 2 3 4 3 2 2 3 4 3 2 5 4 +--R - 309a b d + 954a b c d - 1185a b c d + 680a b c d - 150a b c +--R (334) ----------------------------------------------------------------- +--R 6 +--R 60d +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1483 +d0066:=D(m0066,x) +--R +--R +--R (335) 0 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1483 +t0067:= (a+b*x)^7/(c+d*x)^3 +--R +--R +--R (336) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 1483 +r0067:= 15*b^3*(b*c-a*d)^4*x/d^7-5*b^2*(b*c-a*d)^3*(a+b*x)^2/d^6+_ + 2*b^2*(b*c-a*d)^2*(a+b*x)^3/d^5-3/4*b^2*(b*c-a*d)*(a+b*x)^4/d^4+_ + 1/5*b^2*(a+b*x)^5/d^3+1/2*(b*c-a*d)^7/d^8/(c+d*x)^2-_ + 7*b*(b*c-a*d)^6/d^8/(c+d*x)-21*b^2*(b*c-a*d)^5*log(c+d*x)/d^8 +--R +--R +--R (337) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 420a b d - 2100a b c d + 4200a b c d - 4200a b c d +--R + +--R 6 4 3 7 5 2 +--R 2100a b c d - 420b c d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 840a b c d - 4200a b c d + 8400a b c d - 8400a b c d +--R + +--R 6 5 2 7 6 +--R 4200a b c d - 840b c d +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 420a b c d - 2100a b c d + 4200a b c d - 4200a b c d +--R + +--R 6 6 7 7 +--R 2100a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 4b d x + (35a b d - 7b c d )x + (140a b d - 70a b c d + 14b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (350a b d - 350a b c d + 175a b c d - 35b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (700a b d - 1400a b c d + 1400a b c d - 700a b c d + 140b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 159a b d + 1005a b c d - 3510a b c d + 4310a b c d - 2380a b c d +--R + +--R 7 5 2 +--R 500b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 +--R - 140a b d + 1158a b c d - 2190a b c d + 1380a b c d +--R + +--R 2 5 4 3 6 5 2 7 6 +--R 220a b c d - 560a b c d + 160b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a d - 70a b c d + 789a b c d - 2145a b c d + 2790a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1990a b c d + 770a b c d - 130b c +--R / +--R 10 2 9 2 8 +--R 20d x + 40c d x + 20c d +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1483 +a0067:=integrate(t0067,x) +--R +--R +--R (338) +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R 420a b d - 2100a b c d + 4200a b c d - 4200a b c d +--R + +--R 6 4 3 7 5 2 +--R 2100a b c d - 420b c d +--R * +--R 2 +--R x +--R + +--R 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R 840a b c d - 4200a b c d + 8400a b c d - 8400a b c d +--R + +--R 6 5 2 7 6 +--R 4200a b c d - 840b c d +--R * +--R x +--R + +--R 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R 420a b c d - 2100a b c d + 4200a b c d - 4200a b c d +--R + +--R 6 6 7 7 +--R 2100a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 4b d x + (35a b d - 7b c d )x + (140a b d - 70a b c d + 14b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (350a b d - 350a b c d + 175a b c d - 35b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (700a b d - 1400a b c d + 1400a b c d - 700a b c d + 140b c d )x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (1400a b c d - 3850a b c d + 4410a b c d - 2380a b c d + 500b c d )x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 140a b d + 840a b c d - 1400a b c d + 700a b c d + 420a b c d +--R + +--R 6 5 2 7 6 +--R - 560a b c d + 160b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a d - 70a b c d + 630a b c d - 1750a b c d + 2450a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1890a b c d + 770a b c d - 130b c +--R / +--R 10 2 9 2 8 +--R 20d x + 40c d x + 20c d +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1483 +m0067:=a0067-r0067 +--R +--R +--R 5 2 3 4 3 2 3 4 2 2 5 3 +--R - 159a b d + 395a b c d - 340a b c d + 100a b c +--R (339) -------------------------------------------------- +--R 6 +--R 20d +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1483 +d0067:=D(m0067,x) +--R +--R +--R (340) 0 +--R Type: Expression(Integer) +--E 340 + +--S 341 of 1483 +t0068:= (a+b*x)^7/(c+d*x)^4 +--R +--R +--R (341) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 1483 +r0068:= -20*b^4*(b*c-a*d)^3*x/d^7+5*b^3*(b*c-a*d)^2*(a+b*x)^2/d^6-_ + 4/3*b^3*(b*c-a*d)*(a+b*x)^3/d^5+1/4*b^3*(a+b*x)^4/d^4+_ + 1/3*(b*c-a*d)^7/d^8/(c+d*x)^3-7/2*b*(b*c-a*d)^6/d^8/(c+d*x)^2+_ + 21*b^2*(b*c-a*d)^5/d^8/(c+d*x)+35*b^3*(b*c-a*d)^4*log(c+d*x)/d^8 +--R +--R +--R (342) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b d - 1680a b c d + 2520a b c d - 1680a b c d +--R + +--R 7 4 3 +--R 420b c d +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 1260a b c d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 7 5 2 +--R 1260b c d +--R * +--R 2 +--R x +--R + +--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 1260a b c d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 7 6 +--R 1260b c d +--R * +--R x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b c d - 1680a b c d + 2520a b c d - 1680a b c d + 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 3b d x + (28a b d - 7b c d )x + (126a b d - 84a b c d + 21b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b d - 630a b c d + 420a b c d - 105b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (79a b d + 1124a b c d - 2586a b c d + 2044a b c d - 556b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 252a b d + 1497a b c d - 1668a b c d - 198a b c d +--R + +--R 6 4 3 7 5 2 +--R 1092a b c d - 408b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 42a b d - 252a b c d + 2127a b c d - 4188a b c d + 3582a b c d +--R + +--R 6 5 2 7 6 +--R - 1428a b c d + 222b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a d - 14a b c d - 84a b c d + 849a b c d - 1956a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 2034a b c d - 1036a b c d + 214b c +--R / +--R 11 3 10 2 2 9 3 8 +--R 12d x + 36c d x + 36c d x + 12c d +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1483 +a0068:=integrate(t0068,x) +--R +--R +--R (343) +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R 420a b d - 1680a b c d + 2520a b c d - 1680a b c d +--R + +--R 7 4 3 +--R 420b c d +--R * +--R 3 +--R x +--R + +--R 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R 1260a b c d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 7 5 2 +--R 1260b c d +--R * +--R 2 +--R x +--R + +--R 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R 1260a b c d - 5040a b c d + 7560a b c d - 5040a b c d +--R + +--R 7 6 +--R 1260b c d +--R * +--R x +--R + +--R 4 3 3 4 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b c d - 1680a b c d + 2520a b c d - 1680a b c d + 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 3b d x + (28a b d - 7b c d )x + (126a b d - 84a b c d + 21b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b d - 630a b c d + 420a b c d - 105b c d )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1260a b c d - 2646a b c d + 2044a b c d - 556b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 252a b d + 1260a b c d - 1260a b c d - 378a b c d +--R + +--R 6 4 3 7 5 2 +--R 1092a b c d - 408b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 42a b d - 252a b c d + 1890a b c d - 3780a b c d + 3402a b c d +--R + +--R 6 5 2 7 6 +--R - 1428a b c d + 222b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 4a d - 14a b c d - 84a b c d + 770a b c d - 1820a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R 1974a b c d - 1036a b c d + 214b c +--R / +--R 11 3 10 2 2 9 3 8 +--R 12d x + 36c d x + 36c d x + 12c d +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1483 +m0068:=a0068-r0068 +--R +--R +--R 4 3 2 3 4 2 5 2 +--R - 79a b d + 136a b c d - 60a b c +--R (344) ---------------------------------- +--R 6 +--R 12d +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1483 +d0068:=D(m0068,x) +--R +--R +--R (345) 0 +--R Type: Expression(Integer) +--E 345 + +--S 346 of 1483 +t0069:= (a+b*x)^7/(c+d*x)^5 +--R +--R +--R (346) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R d x + 5c d x + 10c d x + 10c d x + 5c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 1483 +r0069:= 15*b^5*(b*c-a*d)^2*x/d^7-5/2*b^4*(b*c-a*d)*(a+b*x)^2/d^6+_ + 1/3*b^4*(a+b*x)^3/d^5+1/4*(b*c-a*d)^7/d^8/(c+d*x)^4-_ + 7/3*b*(b*c-a*d)^6/d^8/(c+d*x)^3+21/2*b^2*(b*c-a*d)^5/d^8/(c+d*x)^2-_ + 35*b^3*(b*c-a*d)^4/d^8/(c+d*x)-35*b^4*(b*c-a*d)^3*log(c+d*x)/d^8 +--R +--R +--R (347) +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b d - 1260a b c d + 1260a b c d - 420b c d )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1680a b c d - 5040a b c d + 5040a b c d - 1680b c d )x +--R + +--R 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (2520a b c d - 7560a b c d + 7560a b c d - 2520b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 +--R (1680a b c d - 5040a b c d + 5040a b c d - 1680b c d)x +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b c d - 1260a b c d + 1260a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 4b d x + (42a b d - 14b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (252a b d - 252a b c d + 84b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (34a b d + 978a b c d - 1428a b c d + 556b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 420a b d + 1816a b c d - 1128a b c d - 672a b c d + 544b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 126a b d - 630a b c d + 3984a b c d - 5472a b c d +--R + +--R 6 4 3 7 5 2 +--R 2772a b c d - 444b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 28a b d - 84a b c d - 420a b c d + 3216a b c d - 5328a b c d +--R + +--R 6 5 2 7 6 +--R 3528a b c d - 856b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 3a d - 7a b c d - 21a b c d - 105a b c d + 909a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1647a b c d + 1197a b c d - 319b c +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12d x + 48c d x + 72c d x + 48c d x + 12c d +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1483 +a0069:=integrate(t0069,x) +--R +--R +--R (348) +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (420a b d - 1260a b c d + 1260a b c d - 420b c d )x +--R + +--R 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (1680a b c d - 5040a b c d + 5040a b c d - 1680b c d )x +--R + +--R 3 4 2 5 2 5 3 4 6 4 3 7 5 2 2 +--R (2520a b c d - 7560a b c d + 7560a b c d - 2520b c d )x +--R + +--R 3 4 3 4 2 5 4 3 6 5 2 7 6 +--R (1680a b c d - 5040a b c d + 5040a b c d - 1680b c d)x +--R + +--R 3 4 4 3 2 5 5 2 6 6 7 7 +--R 420a b c d - 1260a b c d + 1260a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 4b d x + (42a b d - 14b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (252a b d - 252a b c d + 84b c d )x +--R + +--R 2 5 6 6 2 5 7 3 4 4 +--R (1008a b c d - 1428a b c d + 556b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 420a b d + 1680a b c d - 1008a b c d - 672a b c d + 544b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 126a b d - 630a b c d + 3780a b c d - 5292a b c d +--R + +--R 6 4 3 7 5 2 +--R 2772a b c d - 444b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 28a b d - 84a b c d - 420a b c d + 3080a b c d - 5208a b c d +--R + +--R 6 5 2 7 6 +--R 3528a b c d - 856b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 3a d - 7a b c d - 21a b c d - 105a b c d + 875a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 1617a b c d + 1197a b c d - 319b c +--R / +--R 12 4 11 3 2 10 2 3 9 4 8 +--R 12d x + 48c d x + 72c d x + 48c d x + 12c d +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1483 +m0069:=a0069-r0069 +--R +--R +--R 3 4 2 5 +--R - 17a b d + 15a b c +--R (349) ------------------- +--R 6 +--R 6d +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1483 +d0069:=D(m0069,x) +--R +--R +--R (350) 0 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1483 +t0070:= (a+b*x)^7/(c+d*x)^6 +--R +--R +--R (351) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R d x + 6c d x + 15c d x + 20c d x + 15c d x + 6c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 1483 +r0070:= -6*b^6*(b*c-a*d)*x/d^7+1/2*b^5*(a+b*x)^2/d^6+_ + 1/5*(b*c-a*d)^7/d^8/(c+d*x)^5-7/4*b*(b*c-a*d)^6/d^8/(c+d*x)^4+_ + 7*b^2*(b*c-a*d)^5/d^8/(c+d*x)^3-35/2*b^3*(b*c-a*d)^4/d^8/(c+d*x)^2+_ + 35*b^4*(b*c-a*d)^3/d^8/(c+d*x)+21*b^5*(b*c-a*d)^2*log(c+d*x)/d^8 +--R +--R +--R (352) +--R 2 5 7 6 6 7 2 5 5 +--R (420a b d - 840a b c d + 420b c d )x +--R + +--R 2 5 6 6 2 5 7 3 4 4 +--R (2100a b c d - 4200a b c d + 2100b c d )x +--R + +--R 2 5 2 5 6 3 4 7 4 3 3 +--R (4200a b c d - 8400a b c d + 4200b c d )x +--R + +--R 2 5 3 4 6 4 3 7 5 2 2 +--R (4200a b c d - 8400a b c d + 4200b c d )x +--R + +--R 2 5 4 3 6 5 2 7 6 2 5 5 2 6 6 +--R (2100a b c d - 4200a b c d + 2100b c d)x + 420a b c d - 840a b c d +--R + +--R 7 7 +--R 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 +--R 10b d x + (140a b d - 70b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (10a b d + 700a b c d - 500b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 700a b d + 2150a b c d - 700a b c d - 400b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 350a b d - 1400a b c d + 6400a b c d - 5600a b c d + 1300b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 140a b d - 350a b c d - 1400a b c d + 7800a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8400a b c d + 2700b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 35a b d - 70a b c d - 175a b c d - 700a b c d + 4425a b c d +--R + +--R 6 5 2 7 6 +--R - 5250a b c d + 1875b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - 4a d - 7a b c d - 14a b c d - 35a b c d - 140a b c d + 969a b c d +--R + +--R 6 6 7 7 +--R - 1218a b c d + 459b c +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20d x + 100c d x + 200c d x + 200c d x + 100c d x + 20c d +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1483 +a0070:=integrate(t0070,x) +--R +--R +--R (353) +--R 2 5 7 6 6 7 2 5 5 +--R (420a b d - 840a b c d + 420b c d )x +--R + +--R 2 5 6 6 2 5 7 3 4 4 +--R (2100a b c d - 4200a b c d + 2100b c d )x +--R + +--R 2 5 2 5 6 3 4 7 4 3 3 +--R (4200a b c d - 8400a b c d + 4200b c d )x +--R + +--R 2 5 3 4 6 4 3 7 5 2 2 +--R (4200a b c d - 8400a b c d + 4200b c d )x +--R + +--R 2 5 4 3 6 5 2 7 6 2 5 5 2 6 6 +--R (2100a b c d - 4200a b c d + 2100b c d)x + 420a b c d - 840a b c d +--R + +--R 7 7 +--R 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 6 7 7 6 6 6 6 7 2 5 5 +--R 10b d x + (140a b d - 70b c d )x + (700a b c d - 500b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 700a b d + 2100a b c d - 700a b c d - 400b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 350a b d - 1400a b c d + 6300a b c d - 5600a b c d + 1300b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 140a b d - 350a b c d - 1400a b c d + 7700a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8400a b c d + 2700b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 35a b d - 70a b c d - 175a b c d - 700a b c d + 4375a b c d +--R + +--R 6 5 2 7 6 +--R - 5250a b c d + 1875b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - 4a d - 7a b c d - 14a b c d - 35a b c d - 140a b c d + 959a b c d +--R + +--R 6 6 7 7 +--R - 1218a b c d + 459b c +--R / +--R 13 5 12 4 2 11 3 3 10 2 4 9 5 8 +--R 20d x + 100c d x + 200c d x + 200c d x + 100c d x + 20c d +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1483 +m0070:=a0070-r0070 +--R +--R +--R 2 5 +--R a b +--R (354) - ---- +--R 6 +--R 2d +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1483 +d0070:=D(m0070,x) +--R +--R +--R (355) 0 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 1483 +t0071:= (a+b*x)^7/(c+d*x)^7 +--R +--R +--R (356) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R ------------------------------------------------------------------------ +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R d x + 7c d x + 21c d x + 35c d x + 35c d x + 21c d x + 7c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 1483 +r0071:= b^7*x/d^7+1/6*(b*c-a*d)^7/d^8/(c+d*x)^6-_ + 7/5*b*(b*c-a*d)^6/d^8/(c+d*x)^5+21/4*b^2*(b*c-a*d)^5/d^8/(c+d*x)^4-_ + 35/3*b^3*(b*c-a*d)^4/d^8/(c+d*x)^3+_ + 35/2*b^4*(b*c-a*d)^3/d^8/(c+d*x)^2-21*b^5*(b*c-a*d)^2/d^8/(c+d*x)-_ + 7*b^6*(b*c-a*d)*log(c+d*x)/d^8 +--R +--R +--R (357) +--R 6 7 7 6 6 6 6 7 2 5 5 +--R (420a b d - 420b c d )x + (2520a b c d - 2520b c d )x +--R + +--R 6 2 5 7 3 4 4 6 3 4 7 4 3 3 +--R (6300a b c d - 6300b c d )x + (8400a b c d - 8400b c d )x +--R + +--R 6 4 3 7 5 2 2 6 5 2 7 6 +--R (6300a b c d - 6300b c d )x + (2520a b c d - 2520b c d)x +--R + +--R 6 6 7 7 +--R 420a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 60b d x + 360b c d x + (- 1260a b d + 2520a b c d - 360b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1050a b d - 3150a b c d + 9450a b c d - 4050b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 700a b d - 1400a b c d - 4200a b c d + 15400a b c d +--R + +--R 7 4 3 +--R - 8200b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 315a b d - 525a b c d - 1050a b c d - 3150a b c d +--R + +--R 6 4 3 7 5 2 +--R 13125a b c d - 7725b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 84a b d - 126a b c d - 210a b c d - 420a b c d - 1260a b c d +--R + +--R 6 5 2 7 6 +--R 5754a b c d - 3594b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a d - 14a b c d - 21a b c d - 35a b c d - 70a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d + 1029a b c d - 669b c +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60d x + 360c d x + 900c d x + 1200c d x + 900c d x + 360c d x +--R + +--R 6 8 +--R 60c d +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1483 +a0071:=integrate(t0071,x) +--R +--R +--R (358) +--R 6 7 7 6 6 6 6 7 2 5 5 +--R (420a b d - 420b c d )x + (2520a b c d - 2520b c d )x +--R + +--R 6 2 5 7 3 4 4 6 3 4 7 4 3 3 +--R (6300a b c d - 6300b c d )x + (8400a b c d - 8400b c d )x +--R + +--R 6 4 3 7 5 2 2 6 5 2 7 6 +--R (6300a b c d - 6300b c d )x + (2520a b c d - 2520b c d)x +--R + +--R 6 6 7 7 +--R 420a b c d - 420b c +--R * +--R log(d x + c) +--R + +--R 7 7 7 7 6 6 2 5 7 6 6 7 2 5 5 +--R 60b d x + 360b c d x + (- 1260a b d + 2520a b c d - 360b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 1050a b d - 3150a b c d + 9450a b c d - 4050b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 700a b d - 1400a b c d - 4200a b c d + 15400a b c d +--R + +--R 7 4 3 +--R - 8200b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 315a b d - 525a b c d - 1050a b c d - 3150a b c d +--R + +--R 6 4 3 7 5 2 +--R 13125a b c d - 7725b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 84a b d - 126a b c d - 210a b c d - 420a b c d - 1260a b c d +--R + +--R 6 5 2 7 6 +--R 5754a b c d - 3594b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 10a d - 14a b c d - 21a b c d - 35a b c d - 70a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d + 1029a b c d - 669b c +--R / +--R 14 6 13 5 2 12 4 3 11 3 4 10 2 5 9 +--R 60d x + 360c d x + 900c d x + 1200c d x + 900c d x + 360c d x +--R + +--R 6 8 +--R 60c d +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1483 +m0071:=a0071-r0071 +--R +--R +--R (359) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1483 +d0071:=D(m0071,x) +--R +--R +--R (360) 0 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1483 +t0072:= (a+b*x)^7/(c+d*x)^8 +--R +--R +--R (361) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R / +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 6 2 2 +--R d x + 8c d x + 28c d x + 56c d x + 70c d x + 56c d x + 28c d x +--R + +--R 7 8 +--R 8c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 1483 +r0072:= 1/7*(b*c-a*d)^7/d^8/(c+d*x)^7-7/6*b*(b*c-a*d)^6/d^8/(c+d*x)^6+_ + 21/5*b^2*(b*c-a*d)^5/d^8/(c+d*x)^5-_ + 35/4*b^3*(b*c-a*d)^4/d^8/(c+d*x)^4+_ + 35/3*b^4*(b*c-a*d)^3/d^8/(c+d*x)^3-_ + 21/2*b^5*(b*c-a*d)^2/d^8/(c+d*x)^2+_ + 7*b^6*(b*c-a*d)/d^8/(c+d*x)+b^7*log(c+d*x)/d^8 +--R +--R +--R (362) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(d x + c) +--R + +--R 6 7 7 6 6 +--R (- 2940a b d + 2940b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 4410a b d - 8820a b c d + 13230b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4900a b d - 7350a b c d - 14700a b c d + 26950b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 3675a b d - 4900a b c d - 7350a b c d - 14700a b c d +--R + +--R 7 4 3 +--R 30625b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1764a b d - 2205a b c d - 2940a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8820a b c d + 20139b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 490a b d - 588a b c d - 735a b c d - 980a b c d - 1470a b c d +--R + +--R 6 5 2 7 6 +--R - 2940a b c d + 7203b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d - 70a b c d - 84a b c d - 105a b c d - 140a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d - 420a b c d + 1089b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420d x + 2940c d x + 8820c d x + 14700c d x + 14700c d x +--R + +--R 5 10 2 6 9 7 8 +--R 8820c d x + 2940c d x + 420c d +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1483 +a0072:=integrate(t0072,x) +--R +--R +--R (363) +--R 7 7 7 7 6 6 7 2 5 5 7 3 4 4 +--R 420b d x + 2940b c d x + 8820b c d x + 14700b c d x +--R + +--R 7 4 3 3 7 5 2 2 7 6 7 7 +--R 14700b c d x + 8820b c d x + 2940b c d x + 420b c +--R * +--R log(d x + c) +--R + +--R 6 7 7 6 6 +--R (- 2940a b d + 2940b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 4410a b d - 8820a b c d + 13230b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 4900a b d - 7350a b c d - 14700a b c d + 26950b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 +--R - 3675a b d - 4900a b c d - 7350a b c d - 14700a b c d +--R + +--R 7 4 3 +--R 30625b c d +--R * +--R 3 +--R x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 +--R - 1764a b d - 2205a b c d - 2940a b c d - 4410a b c d +--R + +--R 6 4 3 7 5 2 +--R - 8820a b c d + 20139b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 490a b d - 588a b c d - 735a b c d - 980a b c d - 1470a b c d +--R + +--R 6 5 2 7 6 +--R - 2940a b c d + 7203b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R - 60a d - 70a b c d - 84a b c d - 105a b c d - 140a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 210a b c d - 420a b c d + 1089b c +--R / +--R 15 7 14 6 2 13 5 3 12 4 4 11 3 +--R 420d x + 2940c d x + 8820c d x + 14700c d x + 14700c d x +--R + +--R 5 10 2 6 9 7 8 +--R 8820c d x + 2940c d x + 420c d +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 1483 +m0072:=a0072-r0072 +--R +--R +--R (364) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1483 +d0072:=D(m0072,x) +--R +--R +--R (365) 0 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1483 +t0073:= (a+b*x)^7/(c+d*x)^9 +--R +--R +--R (366) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R d x + 9c d x + 36c d x + 84c d x + 126c d x + 126c d x + 84c d x +--R + +--R 7 2 2 8 9 +--R 36c d x + 9c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 1483 +r0073:= 1/8*(a+b*x)^8/(b*c-a*d)/(c+d*x)^8 +--R +--R +--R (367) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 4 4 5 3 3 7 6 2 2 +--R - - b x - a b x - - a b x - 7a b x - -- a b x - 7a b x - - a b x +--R 8 2 4 2 +--R + +--R 7 1 8 +--R - a b x - - a +--R 8 +--R / +--R 9 8 8 8 2 7 7 2 7 3 6 6 +--R (a d - b c d )x + (8a c d - 8b c d )x + (28a c d - 28b c d )x +--R + +--R 3 6 4 5 5 4 5 5 4 4 +--R (56a c d - 56b c d )x + (70a c d - 70b c d )x +--R + +--R 5 4 6 3 3 6 3 7 2 2 7 2 8 +--R (56a c d - 56b c d )x + (28a c d - 28b c d )x + (8a c d - 8b c d)x +--R + +--R 8 9 +--R a c d - b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 367 + +--S 368 of 1483 +a0073:=integrate(t0073,x) +--R +--R +--R (368) +--R 7 7 7 6 7 7 6 6 +--R - 8b d x + (- 28a b d - 28b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 56a b d - 56a b c d - 56b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 70a b d - 70a b c d - 70a b c d - 70b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 56a b d - 56a b c d - 56a b c d - 56a b c d - 56b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 28a b d - 28a b c d - 28a b c d - 28a b c d - 28a b c d +--R + +--R 7 5 2 +--R - 28b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 6 5 2 +--R - 8a b d - 8a b c d - 8a b c d - 8a b c d - 8a b c d - 8a b c d +--R + +--R 7 6 +--R - 8b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 6 6 +--R - a d - a b c d - a b c d - a b c d - a b c d - a b c d - a b c d +--R + +--R 7 7 +--R - b c +--R / +--R 16 8 15 7 2 14 6 3 13 5 4 12 4 5 11 3 +--R 8d x + 64c d x + 224c d x + 448c d x + 560c d x + 448c d x +--R + +--R 6 10 2 7 9 8 8 +--R 224c d x + 64c d x + 8c d +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1483 +m0073:=a0073-r0073 +--R +--R +--R 8 +--R b +--R (369) --------------- +--R 9 8 +--R 8a d - 8b c d +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1483 +d0073:=D(m0073,x) +--R +--R +--R (370) 0 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1483 +t0074:= (a+b*x)^7/(c+d*x)^10 +--R +--R +--R (371) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x + a +--R / +--R 10 10 9 9 2 8 8 3 7 7 4 6 6 5 5 5 +--R d x + 10c d x + 45c d x + 120c d x + 210c d x + 252c d x +--R + +--R 6 4 4 7 3 3 8 2 2 9 10 +--R 210c d x + 120c d x + 45c d x + 10c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 1483 +r0074:= -1/72*(a+b*x)^8*(-9*b*c+8*a*d-b*d*x)/(-b*c+a*d)^2/(c+d*x)^9 +--R +--R +--R (372) +--R 1 9 9 1 9 8 1 2 7 8 7 7 3 6 7 2 7 6 +--R -- b d x + - b c x + (- - a b d + a b c)x + (- - a b d + - a b c)x +--R 72 8 2 3 2 +--R + +--R 21 4 5 3 6 5 5 4 35 4 5 4 +--R (- -- a b d + 7a b c)x + (- 7a b d + -- a b c)x +--R 4 4 +--R + +--R 35 6 3 5 4 3 7 2 7 6 3 2 7 8 7 2 +--R (- -- a b d + 7a b c)x + (- 3a b d + - a b c)x + (- - a b d + a b c)x +--R 6 2 8 +--R + +--R 1 9 1 8 +--R - - a d + - a b c +--R 9 8 +--R / +--R 2 11 10 2 2 9 9 2 10 2 9 2 3 8 8 +--R (a d - 2a b c d + b c d )x + (9a c d - 18a b c d + 9b c d )x +--R + +--R 2 2 9 3 8 2 4 7 7 +--R (36a c d - 72a b c d + 36b c d )x +--R + +--R 2 3 8 4 7 2 5 6 6 +--R (84a c d - 168a b c d + 84b c d )x +--R + +--R 2 4 7 5 6 2 6 5 5 +--R (126a c d - 252a b c d + 126b c d )x +--R + +--R 2 5 6 6 5 2 7 4 4 +--R (126a c d - 252a b c d + 126b c d )x +--R + +--R 2 6 5 7 4 2 8 3 3 +--R (84a c d - 168a b c d + 84b c d )x +--R + +--R 2 7 4 8 3 2 9 2 2 2 8 3 9 2 2 10 +--R (36a c d - 72a b c d + 36b c d )x + (9a c d - 18a b c d + 9b c d)x +--R + +--R 2 9 2 10 2 11 +--R a c d - 2a b c d + b c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 372 + +--S 373 of 1483 +a0074:=integrate(t0074,x) +--R +--R +--R (373) +--R 7 7 7 6 7 7 6 6 +--R - 36b d x + (- 168a b d - 84b c d )x +--R + +--R 2 5 7 6 6 7 2 5 5 +--R (- 378a b d - 252a b c d - 126b c d )x +--R + +--R 3 4 7 2 5 6 6 2 5 7 3 4 4 +--R (- 504a b d - 378a b c d - 252a b c d - 126b c d )x +--R + +--R 4 3 7 3 4 6 2 5 2 5 6 3 4 7 4 3 3 +--R (- 420a b d - 336a b c d - 252a b c d - 168a b c d - 84b c d )x +--R + +--R 5 2 7 4 3 6 3 4 2 5 2 5 3 4 6 4 3 +--R - 216a b d - 180a b c d - 144a b c d - 108a b c d - 72a b c d +--R + +--R 7 5 2 +--R - 36b c d +--R * +--R 2 +--R x +--R + +--R 6 7 5 2 6 4 3 2 5 3 4 3 4 2 5 4 3 +--R - 63a b d - 54a b c d - 45a b c d - 36a b c d - 27a b c d +--R + +--R 6 5 2 7 6 +--R - 18a b c d - 9b c d +--R * +--R x +--R + +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 2 5 5 2 +--R - 8a d - 7a b c d - 6a b c d - 5a b c d - 4a b c d - 3a b c d +--R + +--R 6 6 7 7 +--R - 2a b c d - b c +--R / +--R 17 9 16 8 2 15 7 3 14 6 4 13 5 +--R 72d x + 648c d x + 2592c d x + 6048c d x + 9072c d x +--R + +--R 5 12 4 6 11 3 7 10 2 8 9 9 8 +--R 9072c d x + 6048c d x + 2592c d x + 648c d x + 72c d +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1483 +m0074:=a0074-r0074 +--R +--R +--R 9 +--R b +--R (374) - -------------------------------- +--R 2 10 9 2 2 8 +--R 72a d - 144a b c d + 72b c d +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1483 +d0074:=D(m0074,x) +--R +--R +--R (375) 0 +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1483 +t0075:= (a+b*x)^5*(a*c+b*c*x)^3 +--R +--R +--R (376) +--R 8 3 8 7 3 7 2 6 3 6 3 5 3 5 4 4 3 4 5 3 3 3 +--R b c x + 8a b c x + 28a b c x + 56a b c x + 70a b c x + 56a b c x +--R + +--R 6 2 3 2 7 3 8 3 +--R 28a b c x + 8a b c x + a c +--R Type: Polynomial(Integer) +--E 376 + +--S 377 of 1483 +r0075:= 1/9*c^3*(a+b*x)^9/b +--R +--R +--R (377) +--R 1 9 3 9 8 3 8 2 7 3 7 28 3 6 3 6 4 5 3 5 5 4 3 4 +--R - b c x + a b c x + 4a b c x + -- a b c x + 14a b c x + 14a b c x +--R 9 3 +--R + +--R 28 6 3 3 3 7 2 3 2 8 3 1 9 3 +--R -- a b c x + 4a b c x + a b c x + - a c +--R 3 9 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 377 + +--S 378 of 1483 +a0075:=integrate(t0075,x) +--R +--R +--R (378) +--R 1 8 3 9 7 3 8 2 6 3 7 28 3 5 3 6 4 4 3 5 5 3 3 4 +--R - b c x + a b c x + 4a b c x + -- a b c x + 14a b c x + 14a b c x +--R 9 3 +--R + +--R 28 6 2 3 3 7 3 2 8 3 +--R -- a b c x + 4a b c x + a c x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 378 + +--S 379 of 1483 +m0075:=a0075-r0075 +--R +--R +--R 1 9 3 +--R - a c +--R 9 +--R (379) - ------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 379 + +--S 380 of 1483 +d0075:=D(m0075,x) +--R +--R +--R (380) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 380 + +--S 381 of 1483 +t0076:= (a+b*x)^5*(a*c+b*c*x)^2 +--R +--R +--R (381) +--R 7 2 7 6 2 6 2 5 2 5 3 4 2 4 4 3 2 3 5 2 2 2 +--R b c x + 7a b c x + 21a b c x + 35a b c x + 35a b c x + 21a b c x +--R + +--R 6 2 7 2 +--R 7a b c x + a c +--R Type: Polynomial(Integer) +--E 381 + +--S 382 of 1483 +r0076:= 1/8*c^2*(a+b*x)^8/b +--R +--R +--R (382) +--R 1 8 2 8 7 2 7 7 2 6 2 6 3 5 2 5 35 4 4 2 4 5 3 2 3 +--R - b c x + a b c x + - a b c x + 7a b c x + -- a b c x + 7a b c x +--R 8 2 4 +--R + +--R 7 6 2 2 2 7 2 1 8 2 +--R - a b c x + a b c x + - a c +--R 2 8 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 382 + +--S 383 of 1483 +a0076:=integrate(t0076,x) +--R +--R +--R (383) +--R 1 7 2 8 6 2 7 7 2 5 2 6 3 4 2 5 35 4 3 2 4 5 2 2 3 +--R - b c x + a b c x + - a b c x + 7a b c x + -- a b c x + 7a b c x +--R 8 2 4 +--R + +--R 7 6 2 2 7 2 +--R - a b c x + a c x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 383 + +--S 384 of 1483 +m0076:=a0076-r0076 +--R +--R +--R 1 8 2 +--R - a c +--R 8 +--R (384) - ------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 384 + +--S 385 of 1483 +d0076:=D(m0076,x) +--R +--R +--R (385) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 385 + +--S 386 of 1483 +t0077:= (a+b*x)^5*(a*c+b*c*x) +--R +--R +--R (386) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x + a c +--R Type: Polynomial(Integer) +--E 386 + +--S 387 of 1483 +r0077:= 1/7*c*(a+b*x)^7/b +--R +--R +--R (387) +--R 1 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - b c x + a b c x + 3a b c x + 5a b c x + 5a b c x + 3a b c x +--R 7 +--R + +--R 6 1 7 +--R a b c x + - a c +--R 7 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 387 + +--S 388 of 1483 +a0077:=integrate(t0077,x) +--R +--R +--R (388) +--R 1 6 7 5 6 2 4 5 3 3 4 4 2 3 5 2 6 +--R - b c x + a b c x + 3a b c x + 5a b c x + 5a b c x + 3a b c x + a c x +--R 7 +--R Type: Polynomial(Fraction(Integer)) +--E 388 + +--S 389 of 1483 +m0077:=a0077-r0077 +--R +--R +--R 1 7 +--R - a c +--R 7 +--R (389) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 389 + +--S 390 of 1483 +d0077:=D(m0077,x) +--R +--R +--R (390) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 390 + +--S 391 of 1483 +t0078:= 2/(-1+4*x^2) +--R +--R +--R 2 +--R (391) ------- +--R 2 +--R 4x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 1483 +r0078:= -atanh(2*x) +--R +--R +--R (392) - atanh(2x) +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1483 +a0078:=integrate(t0078,x) +--R +--R +--R - log(2x + 1) + log(2x - 1) +--R (393) --------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1483 +m0078:=a0078-r0078 +--R +--R +--R - log(2x + 1) + log(2x - 1) + 2atanh(2x) +--R (394) ---------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1483 +d0078:=D(m0078,x) +--R +--R +--R (395) 0 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 1483 +t0079:= x*(a+b*x^2)^2 +--R +--R +--R 2 5 3 2 +--R (396) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 396 + +--S 397 of 1483 +r0079:= 1/6*(a+b*x^2)^3/b +--R +--R +--R 1 3 6 1 2 4 1 2 2 1 3 +--R - b x + - a b x + - a b x + - a +--R 6 2 2 6 +--R (397) ----------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 397 + +--S 398 of 1483 +a0079:=integrate(t0079,x) +--R +--R +--R 1 2 6 1 4 1 2 2 +--R (398) - b x + - a b x + - a x +--R 6 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 398 + +--S 399 of 1483 +m0079:=a0079-r0079 +--R +--R +--R 1 3 +--R - a +--R 6 +--R (399) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 399 + +--S 400 of 1483 +d0079:=D(m0079,x) +--R +--R +--R (400) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 400 + +--S 401 of 1483 +t0080:= (a+b*x^2)^2/x^7 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (401) ------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 1483 +r0080:= -1/6*(a+b*x^2)^3/a/x^6 +--R +--R +--R 1 3 6 1 2 4 1 2 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 6 2 2 6 +--R (402) ------------------------------------- +--R 6 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 402 + +--S 403 of 1483 +a0080:=integrate(t0080,x) +--R +--R +--R 2 4 2 2 +--R - 3b x - 3a b x - a +--R (403) ---------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1483 +m0080:=a0080-r0080 +--R +--R +--R 3 +--R b +--R (404) -- +--R 6a +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1483 +d0080:=D(m0080,x) +--R +--R +--R (405) 0 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1483 +t0081:= x^3*(a+b*x^2)^3 +--R +--R +--R 3 9 2 7 2 5 3 3 +--R (406) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 406 + +--S 407 of 1483 +r0081:= -1/40*(a+b*x^2)^4*(a-4*b*x^2)/b^2 +--R +--R +--R 1 5 10 3 4 8 1 2 3 6 1 3 2 4 1 5 +--R -- b x + - a b x + - a b x + - a b x - -- a +--R 10 8 2 4 40 +--R (407) ------------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 407 + +--S 408 of 1483 +a0081:=integrate(t0081,x) +--R +--R +--R 1 3 10 3 2 8 1 2 6 1 3 4 +--R (408) -- b x + - a b x + - a b x + - a x +--R 10 8 2 4 +--R Type: Polynomial(Fraction(Integer)) +--E 408 + +--S 409 of 1483 +m0081:=a0081-r0081 +--R +--R +--R 1 5 +--R -- a +--R 40 +--R (409) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 409 + +--S 410 of 1483 +d0081:=D(m0081,x) +--R +--R +--R (410) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 410 + +--S 411 of 1483 +t0082:= x*(a+b*x^2)^3 +--R +--R +--R 3 7 2 5 2 3 3 +--R (411) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 411 + +--S 412 of 1483 +r0082:= 1/8*(a+b*x^2)^4/b +--R +--R +--R 1 4 8 1 3 6 3 2 2 4 1 3 2 1 4 +--R - b x + - a b x + - a b x + - a b x + - a +--R 8 2 4 2 8 +--R (412) ---------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 412 + +--S 413 of 1483 +a0082:=integrate(t0082,x) +--R +--R +--R 1 3 8 1 2 6 3 2 4 1 3 2 +--R (413) - b x + - a b x + - a b x + - a x +--R 8 2 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 413 + +--S 414 of 1483 +m0082:=a0082-r0082 +--R +--R +--R 1 4 +--R - a +--R 8 +--R (414) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 414 + +--S 415 of 1483 +d0082:=D(m0082,x) +--R +--R +--R (415) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 415 + +--S 416 of 1483 +t0083:= (a+b*x^2)^3/x^9 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (416) ----------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 1483 +r0083:= -1/8*(a+b*x^2)^4/a/x^8 +--R +--R +--R 1 4 8 1 3 6 3 2 2 4 1 3 2 1 4 +--R - - b x - - a b x - - a b x - - a b x - - a +--R 8 2 4 2 8 +--R (417) ------------------------------------------------ +--R 8 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 417 + +--S 418 of 1483 +a0083:=integrate(t0083,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 4b x - 6a b x - 4a b x - a +--R (418) -------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1483 +m0083:=a0083-r0083 +--R +--R +--R 4 +--R b +--R (419) -- +--R 8a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1483 +d0083:=D(m0083,x) +--R +--R +--R (420) 0 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1483 +t0084:= x^3*(a+b*x^2)^4 +--R +--R +--R 4 11 3 9 2 2 7 3 5 4 3 +--R (421) b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Polynomial(Integer) +--E 421 + +--S 422 of 1483 +r0084:= -1/60*(a+b*x^2)^5*(a-5*b*x^2)/b^2 +--R +--R +--R 1 6 12 2 5 10 3 2 4 8 2 3 3 6 1 4 2 4 1 6 +--R -- b x + - a b x + - a b x + - a b x + - a b x - -- a +--R 12 5 4 3 4 60 +--R (422) ------------------------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 422 + +--S 423 of 1483 +a0084:=integrate(t0084,x) +--R +--R +--R 1 4 12 2 3 10 3 2 2 8 2 3 6 1 4 4 +--R (423) -- b x + - a b x + - a b x + - a b x + - a x +--R 12 5 4 3 4 +--R Type: Polynomial(Fraction(Integer)) +--E 423 + +--S 424 of 1483 +m0084:=a0084-r0084 +--R +--R +--R 1 6 +--R -- a +--R 60 +--R (424) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 424 + +--S 425 of 1483 +d0084:=D(m0084,x) +--R +--R +--R (425) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 425 + +--S 426 of 1483 +t0085:= x*(a+b*x^2)^4 +--R +--R +--R 4 9 3 7 2 2 5 3 3 4 +--R (426) b x + 4a b x + 6a b x + 4a b x + a x +--R Type: Polynomial(Integer) +--E 426 + +--S 427 of 1483 +r0085:= 1/10*(a+b*x^2)^5/b +--R +--R +--R 1 5 10 1 4 8 2 3 6 3 2 4 1 4 2 1 5 +--R -- b x + - a b x + a b x + a b x + - a b x + -- a +--R 10 2 2 10 +--R (427) -------------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 427 + +--S 428 of 1483 +a0085:=integrate(t0085,x) +--R +--R +--R 1 4 10 1 3 8 2 2 6 3 4 1 4 2 +--R (428) -- b x + - a b x + a b x + a b x + - a x +--R 10 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 428 + +--S 429 of 1483 +m0085:=a0085-r0085 +--R +--R +--R 1 5 +--R -- a +--R 10 +--R (429) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 429 + +--S 430 of 1483 +d0085:=D(m0085,x) +--R +--R +--R (430) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 430 + +--S 431 of 1483 +t0086:= x^5*(a+b*x^2)^5 +--R +--R +--R 5 15 4 13 2 3 11 3 2 9 4 7 5 5 +--R (431) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 431 + +--S 432 of 1483 +r0086:= 1/336*(a+b*x^2)^6*(a^2-6*a*b*x^2+21*b^2*x^4)/b^3 +--R +--R +--R (432) +--R 1 8 16 5 7 14 5 2 6 12 3 5 10 5 4 4 8 1 5 3 6 1 8 +--R -- b x + -- a b x + - a b x + a b x + - a b x + - a b x + --- a +--R 16 14 6 8 6 336 +--R -------------------------------------------------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 432 + +--S 433 of 1483 +a0086:=integrate(t0086,x) +--R +--R +--R 1 5 16 5 4 14 5 2 3 12 3 2 10 5 4 8 1 5 6 +--R (433) -- b x + -- a b x + - a b x + a b x + - a b x + - a x +--R 16 14 6 8 6 +--R Type: Polynomial(Fraction(Integer)) +--E 433 + +--S 434 of 1483 +m0086:=a0086-r0086 +--R +--R +--R 1 8 +--R --- a +--R 336 +--R (434) - ------ +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 434 + +--S 435 of 1483 +d0086:=D(m0086,x) +--R +--R +--R (435) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 435 + +--S 436 of 1483 +t0087:= x^3*(a+b*x^2)^5 +--R +--R +--R 5 13 4 11 2 3 9 3 2 7 4 5 5 3 +--R (436) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 436 + +--S 437 of 1483 +r0087:= -1/84*(a+b*x^2)^6*(a-6*b*x^2)/b^2 +--R +--R +--R (437) +--R 1 7 14 5 6 12 2 5 10 5 3 4 8 5 4 3 6 1 5 2 4 1 7 +--R -- b x + -- a b x + a b x + - a b x + - a b x + - a b x - -- a +--R 14 12 4 6 4 84 +--R ------------------------------------------------------------------------ +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 437 + +--S 438 of 1483 +a0087:=integrate(t0087,x) +--R +--R +--R 1 5 14 5 4 12 2 3 10 5 3 2 8 5 4 6 1 5 4 +--R (438) -- b x + -- a b x + a b x + - a b x + - a b x + - a x +--R 14 12 4 6 4 +--R Type: Polynomial(Fraction(Integer)) +--E 438 + +--S 439 of 1483 +m0087:=a0087-r0087 +--R +--R +--R 1 7 +--R -- a +--R 84 +--R (439) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 439 + +--S 440 of 1483 +d0087:=D(m0087,x) +--R +--R +--R (440) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 440 + +--S 441 of 1483 +t0088:= x*(a+b*x^2)^5 +--R +--R +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (441) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 441 + +--S 442 of 1483 +r0088:= 1/12*(a+b*x^2)^6/b +--R +--R +--R (442) +--R 1 6 12 1 5 10 5 2 4 8 5 3 3 6 5 4 2 4 1 5 2 1 6 +--R -- b x + - a b x + - a b x + - a b x + - a b x + - a b x + -- a +--R 12 2 4 3 4 2 12 +--R ------------------------------------------------------------------------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 442 + +--S 443 of 1483 +a0088:=integrate(t0088,x) +--R +--R +--R 1 5 12 1 4 10 5 2 3 8 5 3 2 6 5 4 4 1 5 2 +--R (443) -- b x + - a b x + - a b x + - a b x + - a b x + - a x +--R 12 2 4 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 443 + +--S 444 of 1483 +m0088:=a0088-r0088 +--R +--R +--R 1 6 +--R -- a +--R 12 +--R (444) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 444 + +--S 445 of 1483 +d0088:=D(m0088,x) +--R +--R +--R (445) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 445 + +--S 446 of 1483 +t0089:= (a+b*x^2)^5/x^13 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (446) ---------------------------------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 1483 +r0089:= -1/12*(a+b*x^2)^6/a/x^12 +--R +--R +--R (447) +--R 1 6 12 1 5 10 5 2 4 8 5 3 3 6 5 4 2 4 1 5 2 1 6 +--R - -- b x - - a b x - - a b x - - a b x - - a b x - - a b x - -- a +--R 12 2 4 3 4 2 12 +--R -------------------------------------------------------------------------- +--R 12 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 447 + +--S 448 of 1483 +a0089:=integrate(t0089,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a +--R (448) -------------------------------------------------------- +--R 12 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 1483 +m0089:=a0089-r0089 +--R +--R +--R 6 +--R b +--R (449) --- +--R 12a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1483 +d0089:=D(m0089,x) +--R +--R +--R (450) 0 +--R Type: Expression(Integer) +--E 450 + +--S 451 of 1483 +t0090:= (a+b*x^2)^5/x^15 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (451) ---------------------------------------------------- +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 1483 +r0090:= -1/84*(a+b*x^2)^6*(6*a-b*x^2)/a^2/x^14 +--R +--R +--R (452) +--R 1 7 14 1 2 5 10 5 3 4 8 5 4 3 6 5 2 4 5 6 2 1 7 +--R -- b x - - a b x - - a b x - - a b x - a b x - -- a b x - -- a +--R 84 4 6 4 12 14 +--R ----------------------------------------------------------------------- +--R 2 14 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 452 + +--S 453 of 1483 +a0090:=integrate(t0090,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 21b x - 70a b x - 105a b x - 84a b x - 35a b x - 6a +--R (453) ------------------------------------------------------------ +--R 14 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 1483 +m0090:=a0090-r0090 +--R +--R +--R 7 +--R b +--R (454) - ---- +--R 2 +--R 84a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1483 +d0090:=D(m0090,x) +--R +--R +--R (455) 0 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1483 +t0091:= 1/(-1+a+a*x^2) +--R +--R +--R 1 +--R (456) ------------ +--R 2 +--R a x + a - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 1483 +r0091:= atanh((-a)^(1/2)*x/(-1+a)^(1/2))/(-1+a)^(1/2)/(-a)^(1/2) +--R +--R +--R +---+ +--R x\|- a +--R atanh(--------) +--R +-----+ +--R \|a - 1 +--R (457) --------------- +--R +---+ +-----+ +--R \|- a \|a - 1 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1483 +a0091:=integrate(t0091,x) +--R +--R +--R +--------+ +--R 2 | 2 2 +------+ +--R (a x - a + 1)\|- a + a + (2a - 2a)x | 2 +--R log(---------------------------------------) x\|a - a +--R 2 atan(----------) +--R a x + a - 1 a - 1 +--R (458) [--------------------------------------------,----------------] +--R +--------+ +------+ +--R | 2 | 2 +--R 2\|- a + a \|a - a +--R Type: Union(List(Expression(Integer)),...) +--E 458 + +--S 459 of 1483 +m0091a:=a0091.1-r0091 +--R +--R +--R (459) +--R +--------+ +--R 2 | 2 2 +--R +---+ +-----+ (a x - a + 1)\|- a + a + (2a - 2a)x +--R \|- a \|a - 1 log(---------------------------------------) +--R 2 +--R a x + a - 1 +--R + +--R +--------+ +---+ +--R | 2 x\|- a +--R - 2\|- a + a atanh(--------) +--R +-----+ +--R \|a - 1 +--R / +--R +--------+ +--R | 2 +---+ +-----+ +--R 2\|- a + a \|- a \|a - 1 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1483 +d0091a:=D(m0091a,x) +--R +--R +--R (460) 0 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1483 +m0091b:=a0091.2-r0091 +--R +--R +--R +------+ +--R +------+ +---+ | 2 +--R | 2 x\|- a +---+ +-----+ x\|a - a +--R - \|a - a atanh(--------) + \|- a \|a - 1 atan(----------) +--R +-----+ a - 1 +--R \|a - 1 +--R (461) ----------------------------------------------------------- +--R +------+ +--R +---+ +-----+ | 2 +--R \|- a \|a - 1 \|a - a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1483 +d0091b:=D(m0091b,x) +--R +--R +--R (462) 0 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1483 +t0092:= x^2/(a-b*x^2)^2 +--R +--R +--R 2 +--R x +--R (463) ------------------- +--R 2 4 2 2 +--R b x - 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 463 + +--S 464 of 1483 +r0092:= 1/2*x/b/(a-b*x^2)-1/2*atanh(b^(1/2)*x/a^(1/2))/a^(1/2)/b^(3/2) +--R +--R +--R +-+ +--R 2 x\|b +-+ +-+ +--R (- b x + a)atanh(-----) - x\|a \|b +--R +-+ +--R \|a +--R (464) ------------------------------------ +--R 2 2 +-+ +-+ +--R (2b x - 2a b)\|a \|b +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1483 +a0092:=integrate(t0092,x) +--R +--R +--R (465) +--R 2 +---+ +--R 2 (b x + a)\|a b - 2a b x +---+ +--R (b x - a)log(-------------------------) - 2x\|a b +--R 2 +--R b x - a +--R [---------------------------------------------------, +--R 2 2 +---+ +--R (4b x - 4a b)\|a b +--R +-----+ +--R 2 x\|- a b +-----+ +--R (- b x + a)atan(---------) - x\|- a b +--R a +--R ---------------------------------------] +--R 2 2 +-----+ +--R (2b x - 2a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 465 + +--S 466 of 1483 +m0092a:=a0092.1-r0092 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) + 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (466) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 4b\|a \|b \|a b +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1483 +d0092a:=D(m0092a,x) +--R +--R +--R (467) 0 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1483 +m0092b:=a0092.2-r0092 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R \|- a b atanh(-----) - \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (468) ---------------------------------------------- +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1483 +d0092b:=D(m0092b,x) +--R +--R +--R (469) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1483 +t0093:= 1/x^2/(a-b*x^2)^2 +--R +--R +--R 1 +--R (470) --------------------- +--R 2 6 4 2 2 +--R b x - 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 470 + +--S 471 of 1483 +r0093:= -1/a^2/x+1/2*b*x/a^2/(a-b*x^2)+_ + 3/2*b^(1/2)*atanh(b^(1/2)*x/a^(1/2))/a^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|b 2 +-+ +--R (3b x - 3a x)\|b atanh(-----) + (- 3b x + 2a)\|a +--R +-+ +--R \|a +--R (471) --------------------------------------------------- +--R 2 3 3 +-+ +--R (2a b x - 2a x)\|a +--R Type: Expression(Integer) +--E 471 + +--S 472 of 1483 +a0093:=integrate(t0093,x) +--R +--R +--R (472) +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +--R 3 |b \|a 2 +--R (3b x - 3a x) |- log(-------------------) - 6b x + 4a +--R \|a 2 +--R b x - a +--R [-------------------------------------------------------, +--R 2 3 3 +--R 4a b x - 4a x +--R +---+ +--R | b +--R +---+ a |- - +--R 3 | b \| a 2 +--R (- 3b x + 3a x) |- - atan(-------) - 3b x + 2a +--R \| a b x +--R ------------------------------------------------] +--R 2 3 3 +--R 2a b x - 2a x +--R Type: Union(List(Expression(Integer)),...) +--E 472 + +--S 473 of 1483 +m0093a:=a0093.1-r0093 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 3\|a |- log(-------------------) - 6\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (473) ----------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1483 +d0093a:=D(m0093a,x) +--R +--R +--R (474) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1483 +m0093b:=a0093.2-r0093 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 3\|b atanh(-----) - 3 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (475) ---------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1483 +d0093b:=D(m0093b,x) +--R +--R +--R (476) 0 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1483 +t0094:= x^2/(a-b*x^2)^3 +--R +--R +--R 2 +--R x +--R (477) - ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 477 + +--S 478 of 1483 +r0094:= 1/4*x/b/(a-b*x^2)^2-1/8*x/a/b/(a-b*x^2)-_ + 1/8*atanh(b^(1/2)*x/a^(1/2))/a^(3/2)/b^(3/2) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (- b x + 2a b x - a )atanh(-----) + (b x + a x)\|a \|b +--R +-+ +--R \|a +--R (478) ---------------------------------------------------------- +--R 3 4 2 2 2 3 +-+ +-+ +--R (8a b x - 16a b x + 8a b)\|a \|b +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1483 +a0094:=integrate(t0094,x) +--R +--R +--R (479) +--R 2 +---+ +--R 2 4 2 2 (b x + a)\|a b - 2a b x 3 +---+ +--R (b x - 2a b x + a )log(-------------------------) + (2b x + 2a x)\|a b +--R 2 +--R b x - a +--R [--------------------------------------------------------------------------, +--R 3 4 2 2 2 3 +---+ +--R (16a b x - 32a b x + 16a b)\|a b +--R +-----+ +--R 2 4 2 2 x\|- a b 3 +-----+ +--R (- b x + 2a b x - a )atan(---------) + (b x + a x)\|- a b +--R a +--R -------------------------------------------------------------] +--R 3 4 2 2 2 3 +-----+ +--R (8a b x - 16a b x + 8a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 479 + +--S 480 of 1483 +m0094a:=a0094.1-r0094 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) + 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (480) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 16a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1483 +d0094a:=D(m0094a,x) +--R +--R +--R (481) 0 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1483 +m0094b:=a0094.2-r0094 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R \|- a b atanh(-----) - \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (482) ---------------------------------------------- +--R +-----+ +-+ +-+ +--R 8a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1483 +d0094b:=D(m0094b,x) +--R +--R +--R (483) 0 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1483 +t0095:= 1/x^2/(a-b*x^2)^3 +--R +--R +--R 1 +--R (484) - ------------------------------- +--R 3 8 2 6 2 4 3 2 +--R b x - 3a b x + 3a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 484 + +--S 485 of 1483 +r0095:= -1/a^3/x+1/4*b*x/a^2/(a-b*x^2)^2+7/8*b*x/a^3/(a-b*x^2)+_ + 15/8*b^(1/2)*atanh(b^(1/2)*x/a^(1/2))/a^(7/2) +--R +--R +--R (485) +--R +-+ +--R 2 5 3 2 +-+ x\|b 2 4 2 2 +-+ +--R (15b x - 30a b x + 15a x)\|b atanh(-----) + (- 15b x + 25a b x - 8a )\|a +--R +-+ +--R \|a +--R ----------------------------------------------------------------------------- +--R 3 2 5 4 3 5 +-+ +--R (8a b x - 16a b x + 8a x)\|a +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1483 +a0095:=integrate(t0095,x) +--R +--R +--R (486) +--R [ +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +--R 2 5 3 2 |b \|a 2 4 +--R (15b x - 30a b x + 15a x) |- log(-------------------) - 30b x +--R \|a 2 +--R b x - a +--R + +--R 2 2 +--R 50a b x - 16a +--R / +--R 3 2 5 4 3 5 +--R 16a b x - 32a b x + 16a x +--R , +--R +---+ +--R | b +--R +---+ a |- - +--R 2 5 3 2 | b \| a 2 4 2 2 +--R (- 15b x + 30a b x - 15a x) |- - atan(-------) - 15b x + 25a b x - 8a +--R \| a b x +--R --------------------------------------------------------------------------] +--R 3 2 5 4 3 5 +--R 8a b x - 16a b x + 8a x +--R Type: Union(List(Expression(Integer)),...) +--E 486 + +--S 487 of 1483 +m0095a:=a0095.1-r0095 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 15\|a |- log(-------------------) - 30\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (487) ------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1483 +d0095a:=D(m0095a,x) +--R +--R +--R (488) 0 +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1483 +m0095b:=a0095.2-r0095 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 15\|b atanh(-----) - 15 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (489) ------------------------------------------------ +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1483 +d0095b:=D(m0095b,x) +--R +--R +--R (490) 0 +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1483 +t0096:= x^2/(a-b*x^2)^4 +--R +--R +--R 2 +--R x +--R (491) --------------------------------------- +--R 4 8 3 6 2 2 4 3 2 4 +--R b x - 4a b x + 6a b x - 4a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1483 +r0096:= 1/6*x/b/(a-b*x^2)^3-1/24*x/a/b/(a-b*x^2)^2-_ + 1/16*x/a^2/b/(a-b*x^2)-1/16*atanh(b^(1/2)*x/a^(1/2))/a^(5/2)/b^(3/2) +--R +--R +--R (492) +--R +-+ +--R 3 6 2 4 2 2 3 x\|b +--R (- 3b x + 9a b x - 9a b x + 3a )atanh(-----) +--R +-+ +--R \|a +--R + +--R 2 5 3 2 +-+ +-+ +--R (3b x - 8a b x - 3a x)\|a \|b +--R / +--R 2 4 6 3 3 4 4 2 2 5 +-+ +-+ +--R (48a b x - 144a b x + 144a b x - 48a b)\|a \|b +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1483 +a0096:=integrate(t0096,x) +--R +--R +--R (493) +--R [ +--R 2 +---+ +--R 3 6 2 4 2 2 3 (b x + a)\|a b - 2a b x +--R (3b x - 9a b x + 9a b x - 3a )log(-------------------------) +--R 2 +--R b x - a +--R + +--R 2 5 3 2 +---+ +--R (6b x - 16a b x - 6a x)\|a b +--R / +--R 2 4 6 3 3 4 4 2 2 5 +---+ +--R (96a b x - 288a b x + 288a b x - 96a b)\|a b +--R , +--R +--R +-----+ +--R 3 6 2 4 2 2 3 x\|- a b +--R (- 3b x + 9a b x - 9a b x + 3a )atan(---------) +--R a +--R + +--R 2 5 3 2 +-----+ +--R (3b x - 8a b x - 3a x)\|- a b +--R / +--R 2 4 6 3 3 4 4 2 2 5 +-----+ +--R (48a b x - 144a b x + 144a b x - 48a b)\|- a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 493 + +--S 494 of 1483 +m0096a:=a0096.1-r0096 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) + 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (494) ------------------------------------------------------------ +--R 2 +-+ +-+ +---+ +--R 32a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1483 +d0096a:=D(m0096a,x) +--R +--R +--R (495) 0 +--R Type: Expression(Integer) +--E 495 + +--S 496 of 1483 +m0096b:=a0096.2-r0096 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R \|- a b atanh(-----) - \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (496) ---------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 16a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1483 +d0096b:=D(m0096b,x) +--R +--R +--R (497) 0 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1483 +t0097:= 1/x^2/(a-b*x^2)^4 +--R +--R +--R 1 +--R (498) ------------------------------------------ +--R 4 10 3 8 2 2 6 3 4 4 2 +--R b x - 4a b x + 6a b x - 4a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 498 + +--S 499 of 1483 +r0097:= -1/a^4/x+1/6*b*x/a^2/(a-b*x^2)^3+11/24*b*x/a^3/(a-b*x^2)^2+_ + 19/16*b*x/a^4/(a-b*x^2)+35/16*b^(1/2)*atanh(b^(1/2)*x/a^(1/2))/a^(9/2) +--R +--R +--R (499) +--R +-+ +--R 3 7 2 5 2 3 3 +-+ x\|b +--R (105b x - 315a b x + 315a b x - 105a x)\|b atanh(-----) +--R +-+ +--R \|a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 105b x + 280a b x - 231a b x + 48a )\|a +--R / +--R 4 3 7 5 2 5 6 3 7 +-+ +--R (48a b x - 144a b x + 144a b x - 48a x)\|a +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1483 +a0097:=integrate(t0097,x) +--R +--R +--R (500) +--R [ +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +--R 3 7 2 5 2 3 3 |b \|a +--R (105b x - 315a b x + 315a b x - 105a x) |- log(-------------------) +--R \|a 2 +--R b x - a +--R + +--R 3 6 2 4 2 2 3 +--R - 210b x + 560a b x - 462a b x + 96a +--R / +--R 4 3 7 5 2 5 6 3 7 +--R 96a b x - 288a b x + 288a b x - 96a x +--R , +--R +--R +---+ +--R | b +--R +---+ a |- - +--R 3 7 2 5 2 3 3 | b \| a +--R (- 105b x + 315a b x - 315a b x + 105a x) |- - atan(-------) +--R \| a b x +--R + +--R 3 6 2 4 2 2 3 +--R - 105b x + 280a b x - 231a b x + 48a +--R / +--R 4 3 7 5 2 5 6 3 7 +--R 48a b x - 144a b x + 144a b x - 48a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 500 + +--S 501 of 1483 +m0097a:=a0097.1-r0097 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 35\|a |- log(-------------------) - 70\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (501) ------------------------------------------------------- +--R 4 +-+ +--R 32a \|a +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1483 +d0097a:=D(m0097a,x) +--R +--R +--R (502) 0 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1483 +m0097b:=a0097.2-r0097 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 35\|b atanh(-----) - 35 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (503) ------------------------------------------------ +--R 4 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1483 +d0097b:=D(m0097b,x) +--R +--R +--R (504) 0 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1483 +t0098:= x^2/(a-b*x^2)^5 +--R +--R +--R 2 +--R x +--R (505) - ---------------------------------------------------- +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 505 + +--S 506 of 1483 +r0098:= 1/8*x/b/(a-b*x^2)^4-1/48*x/a/b/(a-b*x^2)^3-_ + 5/192*x/a^2/b/(a-b*x^2)^2-5/128*x/a^3/b/(a-b*x^2)-_ + 5/128*atanh(b^(1/2)*x/a^(1/2))/a^(7/2)/b^(3/2) +--R +--R +--R (506) +--R +-+ +--R 4 8 3 6 2 2 4 3 2 4 x\|b +--R (- 15b x + 60a b x - 90a b x + 60a b x - 15a )atanh(-----) +--R +-+ +--R \|a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (15b x - 55a b x + 73a b x + 15a x)\|a \|b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +-+ +-+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a b)\|a \|b +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1483 +a0098:=integrate(t0098,x) +--R +--R +--R (507) +--R [ +--R 4 8 3 6 2 2 4 3 2 4 +--R (15b x - 60a b x + 90a b x - 60a b x + 15a ) +--R * +--R 2 +---+ +--R (b x + a)\|a b - 2a b x +--R log(-------------------------) +--R 2 +--R b x - a +--R + +--R 3 7 2 5 2 3 3 +---+ +--R (30b x - 110a b x + 146a b x + 30a x)\|a b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +---+ +--R (768a b x - 3072a b x + 4608a b x - 3072a b x + 768a b)\|a b +--R , +--R +--R +-----+ +--R 4 8 3 6 2 2 4 3 2 4 x\|- a b +--R (- 15b x + 60a b x - 90a b x + 60a b x - 15a )atan(---------) +--R a +--R + +--R 3 7 2 5 2 3 3 +-----+ +--R (15b x - 55a b x + 73a b x + 15a x)\|- a b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +-----+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a b)\|- a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 507 + +--S 508 of 1483 +m0098a:=a0098.1-r0098 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R 5\|a \|b log(-------------------------) + 10\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (508) -------------------------------------------------------------- +--R 3 +-+ +-+ +---+ +--R 256a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1483 +d0098a:=D(m0098a,x) +--R +--R +--R (509) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1483 +m0098b:=a0098.2-r0098 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R 5\|- a b atanh(-----) - 5\|a \|b atan(---------) +--R +-+ a +--R \|a +--R (510) ------------------------------------------------ +--R 3 +-----+ +-+ +-+ +--R 128a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 510 + +--S 511 of 1483 +d0098b:=D(m0098b,x) +--R +--R +--R (511) 0 +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1483 +t0099:= 1/x^2/(a-b*x^2)^5 +--R +--R +--R 1 +--R (512) - ------------------------------------------------------- +--R 5 12 4 10 2 3 8 3 2 6 4 4 5 2 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 512 + +--S 513 of 1483 +r0099:= -1/a^5/x+1/8*b*x/a^2/(a-b*x^2)^4+5/16*b*x/a^3/(a-b*x^2)^3+_ + 41/64*b*x/a^4/(a-b*x^2)^2+187/128*b*x/a^5/(a-b*x^2)+_ + 315/128*b^(1/2)*atanh(b^(1/2)*x/a^(1/2))/a^(11/2) +--R +--R +--R (513) +--R +-+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ x\|b +--R (315b x - 1260a b x + 1890a b x - 1260a b x + 315a x)\|b atanh(-----) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 315b x + 1155a b x - 1533a b x + 837a b x - 128a )\|a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +-+ +--R (128a b x - 512a b x + 768a b x - 512a b x + 128a x)\|a +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1483 +a0099:=integrate(t0099,x) +--R +--R +--R (514) +--R [ +--R +-+ +--R 4 9 3 7 2 2 5 3 3 4 |b +--R (315b x - 1260a b x + 1890a b x - 1260a b x + 315a x) |- +--R \|a +--R * +--R +-+ +--R |b 2 +--R 2a x |- + b x + a +--R \|a +--R log(-------------------) +--R 2 +--R b x - a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +--R - 630b x + 2310a b x - 3066a b x + 1674a b x - 256a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +--R 256a b x - 1024a b x + 1536a b x - 1024a b x + 256a x +--R , +--R +--R +---+ +--R 4 9 3 7 2 2 5 3 3 4 | b +--R (- 315b x + 1260a b x - 1890a b x + 1260a b x - 315a x) |- - +--R \| a +--R * +--R +---+ +--R | b +--R a |- - +--R \| a +--R atan(-------) +--R b x +--R + +--R 4 8 3 6 2 2 4 3 2 4 +--R - 315b x + 1155a b x - 1533a b x + 837a b x - 128a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +--R 128a b x - 512a b x + 768a b x - 512a b x + 128a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 514 + +--S 515 of 1483 +m0099a:=a0099.1-r0099 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 315\|a |- log(-------------------) - 630\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (515) --------------------------------------------------------- +--R 5 +-+ +--R 256a \|a +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1483 +d0099a:=D(m0099a,x) +--R +--R +--R (516) 0 +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1483 +m0099b:=a0099.2-r0099 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 315\|b atanh(-----) - 315 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (517) -------------------------------------------------- +--R 5 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1483 +d0099b:=D(m0099b,x) +--R +--R +--R (518) 0 +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1483 +t0100:= (a+b*x)/(1-x^2) +--R +--R +--R - b x - a +--R (519) --------- +--R 2 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 519 + +--S 520 of 1483 +r0100:= -1/2*(a+b)*log(1-x)+1/2*(a-b)*log(1+x) +--R +--R +--R (- b + a)log(x + 1) + (- b - a)log(- x + 1) +--R (520) ------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1483 +a0100:=integrate(t0100,x) +--R +--R +--R (- b + a)log(x + 1) + (- b - a)log(x - 1) +--R (521) ----------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 521 + +--S 522 of 1483 +m0100:=a0100-r0100 +--R +--R +--R (- b - a)log(x - 1) + (b + a)log(- x + 1) +--R (522) ----------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1483 +d0100:=D(m0100,x) +--R +--R +--R (523) 0 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1483 +t0101:= 1/(a+b*x)/(a^2-b^2*x^2) +--R +--R +--R 1 +--R (524) - -------------------------- +--R 3 3 2 2 2 3 +--R b x + a b x - a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 524 + +--S 525 of 1483 +r0101:= -1/2/a/b/(a+b*x)+1/2*atanh(b*x/a)/a^2/b +--R +--R +--R b x +--R (b x + a)atanh(---) - a +--R a +--R (525) ----------------------- +--R 2 2 3 +--R 2a b x + 2a b +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1483 +a0101:=integrate(t0101,x) +--R +--R +--R (b x + a)log(b x + a) + (- b x - a)log(b x - a) - 2a +--R (526) ---------------------------------------------------- +--R 2 2 3 +--R 4a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 526 + +--S 527 of 1483 +m0101:=a0101-r0101 +--R +--R +--R b x +--R log(b x + a) - log(b x - a) - 2atanh(---) +--R a +--R (527) ----------------------------------------- +--R 2 +--R 4a b +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1483 +d0101:=D(m0101,x) +--R +--R +--R (528) 0 +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1483 +t0102:= 1/(a+b*x)^2/(a^2-b^2*x^2) +--R +--R +--R 1 +--R (529) - ---------------------------- +--R 4 4 3 3 3 4 +--R b x + 2a b x - 2a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 529 + +--S 530 of 1483 +r0102:= -1/4/a/b/(a+b*x)^2-1/4/a^2/b/(a+b*x)+1/4*atanh(b*x/a)/a^3/b +--R +--R +--R 2 2 2 b x 2 +--R (b x + 2a b x + a )atanh(---) - a b x - 2a +--R a +--R (530) -------------------------------------------- +--R 3 3 2 4 2 5 +--R 4a b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1483 +a0102:=integrate(t0102,x) +--R +--R +--R (531) +--R 2 2 2 2 2 2 +--R (b x + 2a b x + a )log(b x + a) + (- b x - 2a b x - a )log(b x - a) +--R + +--R 2 +--R - 2a b x - 4a +--R / +--R 3 3 2 4 2 5 +--R 8a b x + 16a b x + 8a b +--R Type: Union(Expression(Integer),...) +--E 531 + +--S 532 of 1483 +m0102:=a0102-r0102 +--R +--R +--R b x +--R log(b x + a) - log(b x - a) - 2atanh(---) +--R a +--R (532) ----------------------------------------- +--R 3 +--R 8a b +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1483 +d0102:=D(m0102,x) +--R +--R +--R (533) 0 +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1483 +t0103:= (a+b*x)/(a^2-b^2*x^2)^2 +--R +--R +--R 1 +--R (534) -------------------------- +--R 3 3 2 2 2 3 +--R b x - a b x - a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 534 + +--S 535 of 1483 +r0103:= 1/2/a/b/(a-b*x)+1/2*atanh(b*x/a)/a^2/b +--R +--R +--R b x +--R (b x - a)atanh(---) - a +--R a +--R (535) ----------------------- +--R 2 2 3 +--R 2a b x - 2a b +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1483 +a0103:=integrate(t0103,x) +--R +--R +--R (b x - a)log(b x + a) + (- b x + a)log(b x - a) - 2a +--R (536) ---------------------------------------------------- +--R 2 2 3 +--R 4a b x - 4a b +--R Type: Union(Expression(Integer),...) +--E 536 + +--S 537 of 1483 +m0103:=a0103-r0103 +--R +--R +--R b x +--R log(b x + a) - log(b x - a) - 2atanh(---) +--R a +--R (537) ----------------------------------------- +--R 2 +--R 4a b +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1483 +d0103:=D(m0103,x) +--R +--R +--R (538) 0 +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1483 +t0104:= (a+b*x)^2/(a^2-b^2*x^2)^3 +--R +--R +--R 1 +--R (539) - ---------------------------- +--R 4 4 3 3 3 4 +--R b x - 2a b x + 2a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 539 + +--S 540 of 1483 +r0104:= 1/4/a/b/(a-b*x)^2+1/4/a^2/b/(a-b*x)+1/4*atanh(b*x/a)/a^3/b +--R +--R +--R 2 2 2 b x 2 +--R (b x - 2a b x + a )atanh(---) - a b x + 2a +--R a +--R (540) -------------------------------------------- +--R 3 3 2 4 2 5 +--R 4a b x - 8a b x + 4a b +--R Type: Expression(Integer) +--E 540 + +--S 541 of 1483 +a0104:=integrate(t0104,x) +--R +--R +--R (541) +--R 2 2 2 2 2 2 +--R (b x - 2a b x + a )log(b x + a) + (- b x + 2a b x - a )log(b x - a) +--R + +--R 2 +--R - 2a b x + 4a +--R / +--R 3 3 2 4 2 5 +--R 8a b x - 16a b x + 8a b +--R Type: Union(Expression(Integer),...) +--E 541 + +--S 542 of 1483 +m0104:=a0104-r0104 +--R +--R +--R b x +--R log(b x + a) - log(b x - a) - 2atanh(---) +--R a +--R (542) ----------------------------------------- +--R 3 +--R 8a b +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1483 +d0104:=D(m0104,x) +--R +--R +--R (543) 0 +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1483 +t0105:= (a+b*x^2)/(1-x^2) +--R +--R +--R 2 +--R - b x - a +--R (544) ---------- +--R 2 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 544 + +--S 545 of 1483 +r0105:= -b*x+(a+b)*atanh(x) +--R +--R +--R (545) (b + a)atanh(x) - b x +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1483 +a0105:=integrate(t0105,x) +--R +--R +--R (b + a)log(x + 1) + (- b - a)log(x - 1) - 2b x +--R (546) ---------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 546 + +--S 547 of 1483 +m0105:=a0105-r0105 +--R +--R +--R (b + a)log(x + 1) + (- b - a)log(x - 1) + (- 2b - 2a)atanh(x) +--R (547) ------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1483 +d0105:=D(m0105,x) +--R +--R +--R (548) 0 +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1483 +t0106:= (a+b*x^2)/(c+d*x^2)^3 +--R +--R +--R 2 +--R b x + a +--R (549) ----------------------------- +--R 3 6 2 4 2 2 3 +--R d x + 3c d x + 3c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 549 + +--S 550 of 1483 +r0106:= 1/4*a*x/c/(c+d*x^2)^2-1/4*b*x/d/(c+d*x^2)^2+_ + 1/8*(b*c+3*a*d)*x/c^2/d/(c+d*x^2)+_ + 1/8*(b*c+3*a*d)*atan(d^(1/2)*x/c^(1/2))/c^(5/2)/d^(3/2) +--R +--R +--R (550) +--R +-+ +--R 3 2 4 2 2 2 2 3 x\|d +--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c )atan(-----) +--R +-+ +--R \|c +--R + +--R 2 3 2 +-+ +-+ +--R ((3a d + b c d)x + (5a c d - b c )x)\|c \|d +--R / +--R 2 3 4 3 2 2 4 +-+ +-+ +--R (8c d x + 16c d x + 8c d)\|c \|d +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1483 +a0106:=integrate(t0106,x) +--R +--R +--R (551) +--R [ +--R 3 2 4 2 2 2 2 3 +--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c ) +--R * +--R 2 +-----+ +--R (d x - c)\|- c d + 2c d x +--R log(---------------------------) +--R 2 +--R d x + c +--R + +--R 2 3 2 +-----+ +--R ((6a d + 2b c d)x + (10a c d - 2b c )x)\|- c d +--R / +--R 2 3 4 3 2 2 4 +-----+ +--R (16c d x + 32c d x + 16c d)\|- c d +--R , +--R +--R 3 2 4 2 2 2 2 3 +--R ((3a d + b c d )x + (6a c d + 2b c d)x + 3a c d + b c ) +--R * +--R +---+ +--R x\|c d +--R atan(-------) +--R c +--R + +--R 2 3 2 +---+ +--R ((3a d + b c d)x + (5a c d - b c )x)\|c d +--R / +--R 2 3 4 3 2 2 4 +---+ +--R (8c d x + 16c d x + 8c d)\|c d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 551 + +--S 552 of 1483 +m0106a:=a0106.1-r0106 +--R +--R +--R (552) +--R 2 +-----+ +--R +-+ +-+ (d x - c)\|- c d + 2c d x +--R (3a d + b c)\|c \|d log(---------------------------) +--R 2 +--R d x + c +--R + +--R +-+ +--R +-----+ x\|d +--R (- 6a d - 2b c)\|- c d atan(-----) +--R +-+ +--R \|c +--R / +--R 2 +-----+ +-+ +-+ +--R 16c d\|- c d \|c \|d +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1483 +d0106a:=D(m0106a,x) +--R +--R +--R (553) 0 +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1483 +m0106b:=a0106.2-r0106 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|c d +---+ x\|d +--R (3a d + b c)\|c \|d atan(-------) + (- 3a d - b c)\|c d atan(-----) +--R c +-+ +--R \|c +--R (554) ------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8c d\|c \|d \|c d +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1483 +d0106b:=D(m0106b,x) +--R +--R +--R (555) 0 +--R Type: Expression(Integer) +--E 555 + +--S 556 of 1483 +t0107:= x^4*(a+b*x^2)/(c+d*x^2) +--R +--R +--R 6 4 +--R b x + a x +--R (556) ----------- +--R 2 +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 1483 +r0107:= c*(b*c-a*d)*x/d^3-1/3*(b*c-a*d)*x^3/d^2+1/5*b*x^5/d-_ + c^(3/2)*(b*c-a*d)*atan(d^(1/2)*x/c^(1/2))/d^(7/2) +--R +--R +--R (557) +--R +-+ +--R 2 +-+ x\|d +--R (15a c d - 15b c )\|c atan(-----) +--R +-+ +--R \|c +--R + +--R 2 5 2 3 2 +-+ +--R (3b d x + (5a d - 5b c d)x + (- 15a c d + 15b c )x)\|d +--R / +--R 3 +-+ +--R 15d \|d +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1483 +a0107:=integrate(t0107,x) +--R +--R +--R (558) +--R [ +--R +---+ +--R | c 2 +--R +---+ 2d x |- - + d x - c +--R 2 | c \| d 2 5 +--R (15a c d - 15b c ) |- - log(---------------------) + 6b d x +--R \| d 2 +--R d x + c +--R + +--R 2 3 2 +--R (10a d - 10b c d)x + (- 30a c d + 30b c )x +--R / +--R 3 +--R 30d +--R , +--R +--R +-+ +--R |c +--R +-+ |- +--R 2 |c \|d 2 5 2 3 +--R (- 15a c d + 15b c ) |- atan(----) + 3b d x + (5a d - 5b c d)x +--R \|d x +--R + +--R 2 +--R (- 15a c d + 15b c )x +--R / +--R 3 +--R 15d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 558 + +--S 559 of 1483 +m0107a:=a0107.1-r0107 +--R +--R +--R (559) +--R +---+ +--R | c 2 +--R +---+ 2d x |- - + d x - c +--R 2 | c +-+ \| d +--R (a c d - b c ) |- - \|d log(---------------------) +--R \| d 2 +--R d x + c +--R + +--R +-+ +--R 2 +-+ x\|d +--R (- 2a c d + 2b c )\|c atan(-----) +--R +-+ +--R \|c +--R / +--R 3 +-+ +--R 2d \|d +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1483 +d0107a:=D(m0107a,x) +--R +--R +--R (560) 0 +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1483 +m0107b:=a0107.2-r0107 +--R +--R +--R +-+ +--R |c +--R +-+ +-+ |- +--R 2 +-+ x\|d 2 |c +-+ \|d +--R (- a c d + b c )\|c atan(-----) + (- a c d + b c ) |- \|d atan(----) +--R +-+ \|d x +--R \|c +--R (561) -------------------------------------------------------------------- +--R 3 +-+ +--R d \|d +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1483 +d0107b:=D(m0107b,x) +--R +--R +--R (562) 0 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1483 +t0108:= x^2*(a+b*x^2)/(c+d*x^2) +--R +--R +--R 4 2 +--R b x + a x +--R (563) ----------- +--R 2 +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 563 + +--S 564 of 1483 +r0108:= -(b*c-a*d)*x/d^2+1/3*b*x^3/d+_ + c^(1/2)*(b*c-a*d)*atan(d^(1/2)*x/c^(1/2))/d^(5/2) +--R +--R +--R +-+ +--R +-+ x\|d 3 +-+ +--R (- 3a d + 3b c)\|c atan(-----) + (b d x + (3a d - 3b c)x)\|d +--R +-+ +--R \|c +--R (564) -------------------------------------------------------------- +--R 2 +-+ +--R 3d \|d +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1483 +a0108:=integrate(t0108,x) +--R +--R +--R (565) +--R +---+ +--R | c 2 +--R +---+ - 2d x |- - + d x - c +--R | c \| d 3 +--R (3a d - 3b c) |- - log(-----------------------) + 2b d x + (6a d - 6b c)x +--R \| d 2 +--R d x + c +--R [--------------------------------------------------------------------------, +--R 2 +--R 6d +--R +-+ +--R |c +--R +-+ |- +--R |c \|d 3 +--R (3a d - 3b c) |- atan(----) + b d x + (3a d - 3b c)x +--R \|d x +--R -----------------------------------------------------] +--R 2 +--R 3d +--R Type: Union(List(Expression(Integer)),...) +--E 565 + +--S 566 of 1483 +m0108a:=a0108.1-r0108 +--R +--R +--R (566) +--R +---+ +--R | c 2 +--R +---+ - 2d x |- - + d x - c +--R | c +-+ \| d +--R (a d - b c) |- - \|d log(-----------------------) +--R \| d 2 +--R d x + c +--R + +--R +-+ +--R +-+ x\|d +--R (2a d - 2b c)\|c atan(-----) +--R +-+ +--R \|c +--R / +--R 2 +-+ +--R 2d \|d +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1483 +d0108a:=D(m0108a,x) +--R +--R +--R (567) 0 +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1483 +m0108b:=a0108.2-r0108 +--R +--R +--R +-+ +--R |c +--R +-+ +-+ |- +--R +-+ x\|d |c +-+ \|d +--R (a d - b c)\|c atan(-----) + (a d - b c) |- \|d atan(----) +--R +-+ \|d x +--R \|c +--R (568) ---------------------------------------------------------- +--R 2 +-+ +--R d \|d +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1483 +d0108b:=D(m0108b,x) +--R +--R +--R (569) 0 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1483 +t0109:= (a+b*x^2)/x^2/(c+d*x^2) +--R +--R +--R 2 +--R b x + a +--R (570) ----------- +--R 4 2 +--R d x + c x +--R Type: Fraction(Polynomial(Integer)) +--E 570 + +--S 571 of 1483 +r0109:= -a/c/x+(b*c-a*d)*atan(d^(1/2)*x/c^(1/2))/c^(3/2)/d^(1/2) +--R +--R +--R +-+ +--R x\|d +-+ +-+ +--R (- a d + b c)x atan(-----) - a\|c \|d +--R +-+ +--R \|c +--R (571) -------------------------------------- +--R +-+ +-+ +--R c x\|c \|d +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1483 +a0109:=integrate(t0109,x) +--R +--R +--R (572) +--R 2 +-----+ +--R (d x - c)\|- c d - 2c d x +-----+ +--R (a d - b c)x log(---------------------------) - 2a\|- c d +--R 2 +--R d x + c +--R [----------------------------------------------------------, +--R +-----+ +--R 2c x\|- c d +--R +---+ +--R x\|c d +---+ +--R (- a d + b c)x atan(-------) - a\|c d +--R c +--R --------------------------------------] +--R +---+ +--R c x\|c d +--R Type: Union(List(Expression(Integer)),...) +--E 572 + +--S 573 of 1483 +m0109a:=a0109.1-r0109 +--R +--R +--R (573) +--R 2 +-----+ +--R +-+ +-+ (d x - c)\|- c d - 2c d x +--R (a d - b c)\|c \|d log(---------------------------) +--R 2 +--R d x + c +--R + +--R +-+ +--R +-----+ x\|d +--R (2a d - 2b c)\|- c d atan(-----) +--R +-+ +--R \|c +--R / +--R +-----+ +-+ +-+ +--R 2c\|- c d \|c \|d +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1483 +d0109a:=D(m0109a,x) +--R +--R +--R (574) 0 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1483 +m0109b:=a0109.2-r0109 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|c d +---+ x\|d +--R (- a d + b c)\|c \|d atan(-------) + (a d - b c)\|c d atan(-----) +--R c +-+ +--R \|c +--R (575) ----------------------------------------------------------------- +--R +-+ +-+ +---+ +--R c\|c \|d \|c d +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1483 +d0109b:=D(m0109b,x) +--R +--R +--R (576) 0 +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1483 +t0110:= (a+b*x^2)/x^4/(c+d*x^2) +--R +--R +--R 2 +--R b x + a +--R (577) ----------- +--R 6 4 +--R d x + c x +--R Type: Fraction(Polynomial(Integer)) +--E 577 + +--S 578 of 1483 +r0110:= -1/3*a/c/x^3-(b*c-a*d)/c^2/x-_ + d^(1/2)*(b*c-a*d)*atan(d^(1/2)*x/c^(1/2))/c^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|d 2 +-+ +--R (3a d - 3b c)x \|d atan(-----) + ((3a d - 3b c)x - a c)\|c +--R +-+ +--R \|c +--R (578) ------------------------------------------------------------ +--R 2 3 +-+ +--R 3c x \|c +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1483 +a0110:=integrate(t0110,x) +--R +--R +--R (579) +--R +---+ +--R | d 2 +--R +---+ 2c x |- - + d x - c +--R 3 | d \| c 2 +--R (3a d - 3b c)x |- - log(---------------------) + (6a d - 6b c)x - 2a c +--R \| c 2 +--R d x + c +--R [------------------------------------------------------------------------, +--R 2 3 +--R 6c x +--R +-+ +--R |d +--R +-+ c |- +--R 3 |d \|c 2 +--R (- 3a d + 3b c)x |- atan(-----) + (3a d - 3b c)x - a c +--R \|c d x +--R --------------------------------------------------------] +--R 2 3 +--R 3c x +--R Type: Union(List(Expression(Integer)),...) +--E 579 + +--S 580 of 1483 +m0110a:=a0110.1-r0110 +--R +--R +--R (580) +--R +---+ +--R | d 2 +--R +---+ 2c x |- - + d x - c +--R | d +-+ \| c +--R (a d - b c) |- - \|c log(---------------------) +--R \| c 2 +--R d x + c +--R + +--R +-+ +--R +-+ x\|d +--R (- 2a d + 2b c)\|d atan(-----) +--R +-+ +--R \|c +--R / +--R 2 +-+ +--R 2c \|c +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1483 +d0110a:=D(m0110a,x) +--R +--R +--R (581) 0 +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1483 +m0110b:=a0110.2-r0110 +--R +--R +--R +-+ +--R |d +--R +-+ +-+ c |- +--R +-+ x\|d +-+ |d \|c +--R (- a d + b c)\|d atan(-----) + (- a d + b c)\|c |- atan(-----) +--R +-+ \|c d x +--R \|c +--R (582) --------------------------------------------------------------- +--R 2 +-+ +--R c \|c +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1483 +d0110b:=D(m0110b,x) +--R +--R +--R (583) 0 +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1483 +t0111:= x^2*(a+b*x^3)^2 +--R +--R +--R 2 8 5 2 2 +--R (584) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 584 + +--S 585 of 1483 +r0111:= 1/9*(a+b*x^3)^3/b +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - b x + - a b x + - a b x + - a +--R 9 3 3 9 +--R (585) ----------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 585 + +--S 586 of 1483 +a0111:=integrate(t0111,x) +--R +--R +--R 1 2 9 1 6 1 2 3 +--R (586) - b x + - a b x + - a x +--R 9 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 586 + +--S 587 of 1483 +m0111:=a0111-r0111 +--R +--R +--R 1 3 +--R - a +--R 9 +--R (587) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 587 + +--S 588 of 1483 +d0111:=D(m0111,x) +--R +--R +--R (588) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 588 + +--S 589 of 1483 +t0112:= (a+b*x^3)^2/x^10 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (589) ------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 589 + +--S 590 of 1483 +r0112:= -1/9*(a+b*x^3)^3/a/x^9 +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - - b x - - a b x - - a b x - - a +--R 9 3 3 9 +--R (590) ------------------------------------- +--R 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 590 + +--S 591 of 1483 +a0112:=integrate(t0112,x) +--R +--R +--R 2 6 3 2 +--R - 3b x - 3a b x - a +--R (591) ---------------------- +--R 9 +--R 9x +--R Type: Union(Expression(Integer),...) +--E 591 + +--S 592 of 1483 +m0112:=a0112-r0112 +--R +--R +--R 3 +--R b +--R (592) -- +--R 9a +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1483 +d0112:=D(m0112,x) +--R +--R +--R (593) 0 +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1483 +t0113:= x^2*(a+b*x^3)^3 +--R +--R +--R 3 11 2 8 2 5 3 2 +--R (594) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 594 + +--S 595 of 1483 +r0113:= 1/12*(a+b*x^3)^4/b +--R +--R +--R 1 4 12 1 3 9 1 2 2 6 1 3 3 1 4 +--R -- b x + - a b x + - a b x + - a b x + -- a +--R 12 3 2 3 12 +--R (595) ------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 595 + +--S 596 of 1483 +a0113:=integrate(t0113,x) +--R +--R +--R 1 3 12 1 2 9 1 2 6 1 3 3 +--R (596) -- b x + - a b x + - a b x + - a x +--R 12 3 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 596 + +--S 597 of 1483 +m0113:=a0113-r0113 +--R +--R +--R 1 4 +--R -- a +--R 12 +--R (597) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 597 + +--S 598 of 1483 +d0113:=D(m0113,x) +--R +--R +--R (598) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 598 + +--S 599 of 1483 +t0114:= (a+b*x^3)^3/x^13 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (599) ----------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 599 + +--S 600 of 1483 +r0114:= -1/12*(a+b*x^3)^4/a/x^12 +--R +--R +--R 1 4 12 1 3 9 1 2 2 6 1 3 3 1 4 +--R - -- b x - - a b x - - a b x - - a b x - -- a +--R 12 3 2 3 12 +--R (600) --------------------------------------------------- +--R 12 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 600 + +--S 601 of 1483 +a0114:=integrate(t0114,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 4b x - 6a b x - 4a b x - a +--R (601) -------------------------------- +--R 12 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 601 + +--S 602 of 1483 +m0114:=a0114-r0114 +--R +--R +--R 4 +--R b +--R (602) --- +--R 12a +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1483 +d0114:=D(m0114,x) +--R +--R +--R (603) 0 +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1483 +t0115:= (a+b*x)^4/(c+d*x^3) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (604) -------------------------------------- +--R 3 +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 604 + +--S 605 of 1483 +r0115:= 4*a*b^3*x/d+1/2*b^4*x^2/d-1/3*b*(b^3*c-4*a^3*d)*atan(-1/3*3^(1/2)+_ + 2/3*d^(1/3)*x*3^(1/2)/c^(1/3))*3^(1/2)/c^(1/3)/d^(5/3)-_ + 1/3*a*(4*b^3*c-a^3*d)*atan(-1/3*3^(1/2)+_ + 2/3*d^(1/3)*x*3^(1/2)/c^(1/3))*3^(1/2)/c^(2/3)/d^(4/3)+_ + 1/3*b*(b^3*c-4*a^3*d)*log(c^(1/3)/d^(1/3)+x)/c^(1/3)/d^(5/3)-_ + 1/3*a*(4*b^3*c-a^3*d)*log(c^(1/3)/d^(1/3)+x)/c^(2/3)/d^(4/3)-_ + 1/6*b*(b^3*c-4*a^3*d)*log(c^(2/3)/d^(2/3)-_ + c^(1/3)*x/d^(1/3)+x^2)/c^(1/3)/d^(5/3)+_ + 1/6*a*(4*b^3*c-a^3*d)*log(c^(2/3)/d^(2/3)-_ + c^(1/3)*x/d^(1/3)+x^2)/c^(2/3)/d^(4/3)+2*a^2*b^2*log(c+d*x^3)/d +--R +--R +--R (605) +--R 4 3 3+-+ 3 4 3+-+ +--R ((- a d + 4a b c)\|d + (4a b d - b c)\|c ) +--R * +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R x \|d - x\|c \|d + \|c +--R log(---------------------------) +--R 3+-+2 +--R \|d +--R + +--R 3+-+ 3+-+ +--R 4 3 3+-+ 3 4 3+-+ x\|d + \|c +--R ((2a d - 8a b c)\|d + (- 8a b d + 2b c)\|c )log(------------) +--R 3+-+ +--R \|d +--R + +--R 4 3 +-+3+-+ 3 4 +-+3+-+ +--R ((2a d - 8a b c)\|3 \|d + (8a b d - 2b c)\|3 \|c ) +--R * +--R +-+3+-+ +-+3+-+ +--R 2x\|3 \|d - \|3 \|c +--R atan(---------------------) +--R 3+-+ +--R 3\|c +--R + +--R 2 2 3 4 2 3 3+-+2 3+-+2 +--R (12a b log(d x + c) + 3b x + 24a b x)\|c \|d +--R / +--R 3+-+2 3+-+2 +--R 6d \|c \|d +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1483 +a0115:=integrate(t0115,x) +--R +--R +--R (606) +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R - d |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 2 +--R - d %%F0 + 6a b +--R * +--R log +--R 3 2 4 4 3 3 8 4 5 3 2 3 2 6 3 2 +--R ((36a b c d - 9b c d )%%F0 - 3a c d - 48a b c d - 30a b c d ) +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3 2 4 4 3 3 2 +--R (- 36a b c d + 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (- 3a c d + 168a b c d - 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (2a d + 104a b c d - 104a b c d - 2b c )x - 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R - 48a b c d + 66a b c d + 8a b c +--R + +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R d |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 2 +--R - d %%F0 + 6a b +--R * +--R log +--R 3 2 4 4 3 3 8 4 5 3 2 3 +--R (- 36a b c d + 9b c d )%%F0 + 3a c d + 48a b c d +--R + +--R 2 6 3 2 +--R 30a b c d +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3 2 4 4 3 3 2 +--R (- 36a b c d + 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (- 3a c d + 168a b c d - 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (2a d + 104a b c d - 104a b c d - 2b c )x - 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R - 48a b c d + 66a b c d + 8a b c +--R + +--R 2d %%F0 +--R * +--R log +--R 3 2 4 4 3 3 2 +--R (36a b c d - 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (3a c d - 168a b c d + 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (a d + 52a b c d - 52a b c d - b c )x + 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R 48a b c d - 66a b c d - 8a b c +--R + +--R 4 2 3 +--R b x + 8a b x +--R / +--R 2d +--R Type: Union(Expression(Integer),...) +--E 606 + +--S 607 of 1483 +m0115:=a0115-r0115 +--R +--R +--R (607) +--R - +--R 3+-+2 3+-+2 +--R 3d \|c \|d +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3+-+2 3+-+2 2 2 3+-+2 3+-+2 +--R - 3d \|c \|d %%F + 18a b \|c \|d +--R * +--R log +--R 3 2 4 4 3 3 8 4 5 3 2 3 2 6 3 2 +--R ((36a b c d - 9b c d )%%F0 - 3a c d - 48a b c d - 30a b c d ) +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3 2 4 4 3 3 2 +--R (- 36a b c d + 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (- 3a c d + 168a b c d - 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (2a d + 104a b c d - 104a b c d - 2b c )x - 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R - 48a b c d + 66a b c d + 8a b c +--R + +--R 3+-+2 3+-+2 +--R 3d \|c \|d +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3+-+2 3+-+2 2 2 3+-+2 3+-+2 +--R - 3d \|c \|d %%F + 18a b \|c \|d +--R * +--R log +--R 3 2 4 4 3 3 8 4 5 3 2 3 +--R (- 36a b c d + 9b c d )%%F0 + 3a c d + 48a b c d +--R + +--R 2 6 3 2 +--R 30a b c d +--R * +--R +---------------------------------------------------------------+ +--R | 3 2 2 2 2 7 2 4 4 7 2 +--R |- 9c d %%F0 + 36a b c d %%F0 - 16a b d + 32a b c d - 16a b c +--R |--------------------------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3 2 4 4 3 3 2 +--R (- 36a b c d + 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (- 3a c d + 168a b c d - 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (2a d + 104a b c d - 104a b c d - 2b c )x - 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R - 48a b c d + 66a b c d + 8a b c +--R + +--R 3+-+2 3+-+2 +--R 6d \|c \|d %%F0 +--R * +--R log +--R 3 2 4 4 3 3 2 +--R (36a b c d - 9b c d )%%F0 +--R + +--R 8 4 5 3 2 3 2 6 3 2 +--R (3a c d - 168a b c d + 84a b c d )%%F0 +--R + +--R 12 4 9 3 3 3 9 3 12 4 10 2 3 +--R (a d + 52a b c d - 52a b c d - b c )x + 26a b c d +--R + +--R 7 5 2 2 4 8 3 11 4 +--R 48a b c d - 66a b c d - 8a b c +--R + +--R 4 3 3+-+ 3 4 3+-+ +--R ((a d - 4a b c)\|d + (- 4a b d + b c)\|c ) +--R * +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R x \|d - x\|c \|d + \|c +--R log(---------------------------) +--R 3+-+2 +--R \|d +--R + +--R 3+-+ 3+-+ +--R 4 3 3+-+ 3 4 3+-+ x\|d + \|c +--R ((- 2a d + 8a b c)\|d + (8a b d - 2b c)\|c )log(------------) +--R 3+-+ +--R \|d +--R + +--R 4 3 +-+3+-+ 3 4 +-+3+-+ +--R ((- 2a d + 8a b c)\|3 \|d + (- 8a b d + 2b c)\|3 \|c ) +--R * +--R +-+3+-+ +-+3+-+ +--R 2x\|3 \|d - \|3 \|c +--R atan(---------------------) +--R 3+-+ +--R 3\|c +--R + +--R 2 2 3 3+-+2 3+-+2 +--R - 12a b log(d x + c)\|c \|d +--R / +--R 3+-+2 3+-+2 +--R 6d \|c \|d +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1483 +d0115:=D(m0115,x) +--R +--R +--R (608) 0 +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1483 +t0116:= (1+x)^4/(c+d*x^3) +--R +--R +--R 4 3 2 +--R x + 4x + 6x + 4x + 1 +--R (609) ----------------------- +--R 3 +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 609 + +--S 610 of 1483 +r0116:= 4*x/d+1/2*x^2/d-1/3*(c-4*d)*atan(-1/3*3^(1/2)+_ + 2/3*d^(1/3)*x*3^(1/2)/c^(1/3))*3^(1/2)/c^(1/3)/d^(5/3)-_ + 1/3*(4*c-d)*atan(-1/3*3^(1/2)+_ + 2/3*d^(1/3)*x*3^(1/2)/c^(1/3))*3^(1/2)/c^(2/3)/d^(4/3)+_ + 1/3*(c-4*d)*log(c^(1/3)/d^(1/3)+x)/c^(1/3)/d^(5/3)-_ + 1/3*(4*c-d)*log(c^(1/3)/d^(1/3)+x)/c^(2/3)/d^(4/3)-_ + 1/6*(c-4*d)*log(c^(2/3)/d^(2/3)-c^(1/3)*x/d^(1/3)+_ + x^2)/c^(1/3)/d^(5/3)+1/6*(4*c-d)*log(c^(2/3)/d^(2/3)-_ + c^(1/3)*x/d^(1/3)+x^2)/c^(2/3)/d^(4/3)+2*log(c+d*x^3)/d +--R +--R +--R (610) +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ 3+-+ x \|d - x\|c \|d + \|c +--R ((- d + 4c)\|d + (4d - c)\|c )log(---------------------------) +--R 3+-+2 +--R \|d +--R + +--R 3+-+ 3+-+ +--R 3+-+ 3+-+ x\|d + \|c +--R ((2d - 8c)\|d + (- 8d + 2c)\|c )log(------------) +--R 3+-+ +--R \|d +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ +-+3+-+ 2x\|3 \|d - \|3 \|c +--R ((2d - 8c)\|3 \|d + (8d - 2c)\|3 \|c )atan(---------------------) +--R 3+-+ +--R 3\|c +--R + +--R 3 2 3+-+2 3+-+2 +--R (12log(d x + c) + 3x + 24x)\|c \|d +--R / +--R 3+-+2 3+-+2 +--R 6d \|c \|d +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1483 +a0116:=integrate(t0116,x) +--R +--R +--R (611) +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R (- d |----------------------------------------------- - d %%G0 + 6) +--R | 3 +--R \| 3c d +--R * +--R log +--R 2 4 3 3 4 2 3 3 2 +--R ((36c d - 9c d )%%G0 - 3c d - 48c d - 30c d ) +--R * +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 4 3 3 2 4 2 3 3 2 +--R (- 36c d + 9c d )%%G0 + (- 3c d + 168c d - 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (2d + 104c d - 104c d - 2c )x - 26c d - 48c d + 66c d + 8c +--R + +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R (d |----------------------------------------------- - d %%G0 + 6) +--R | 3 +--R \| 3c d +--R * +--R log +--R 2 4 3 3 4 2 3 3 2 +--R ((- 36c d + 9c d )%%G0 + 3c d + 48c d + 30c d ) +--R * +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 4 3 3 2 4 2 3 3 2 +--R (- 36c d + 9c d )%%G0 + (- 3c d + 168c d - 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (2d + 104c d - 104c d - 2c )x - 26c d - 48c d + 66c d + 8c +--R + +--R 2d %%G0 +--R * +--R log +--R 2 4 3 3 2 4 2 3 3 2 +--R (36c d - 9c d )%%G0 + (3c d - 168c d + 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (d + 52c d - 52c d - c )x + 26c d + 48c d - 66c d - 8c +--R + +--R 2 +--R x + 8x +--R / +--R 2d +--R Type: Union(Expression(Integer),...) +--E 611 + +--S 612 of 1483 +m0116:=a0116-r0116 +--R +--R +--R (612) +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R 3+-+2 3+-+2 |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R - 3d \|c \|d |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3d \|c \|d %%G + 18\|c \|d +--R * +--R log +--R 2 4 3 3 4 2 3 3 2 +--R ((36c d - 9c d )%%G0 - 3c d - 48c d - 30c d ) +--R * +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 4 3 3 2 4 2 3 3 2 +--R (- 36c d + 9c d )%%G0 + (- 3c d + 168c d - 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (2d + 104c d - 104c d - 2c )x - 26c d - 48c d + 66c d + 8c +--R + +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R 3+-+2 3+-+2 |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R 3d \|c \|d |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3d \|c \|d %%G + 18\|c \|d +--R * +--R log +--R 2 4 3 3 4 2 3 3 2 +--R ((- 36c d + 9c d )%%G0 + 3c d + 48c d + 30c d ) +--R * +--R +-----------------------------------------------+ +--R | 3 2 2 2 2 +--R |- 9c d %%G0 + 36c d %%G0 - 16d + 32c d - 16c +--R |----------------------------------------------- +--R | 3 +--R \| 3c d +--R + +--R 2 4 3 3 2 4 2 3 3 2 +--R (- 36c d + 9c d )%%G0 + (- 3c d + 168c d - 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (2d + 104c d - 104c d - 2c )x - 26c d - 48c d + 66c d + 8c +--R + +--R 3+-+2 3+-+2 +--R 6d \|c \|d %%G0 +--R * +--R log +--R 2 4 3 3 2 4 2 3 3 2 +--R (36c d - 9c d )%%G0 + (3c d - 168c d + 84c d )%%G0 +--R + +--R 4 3 3 4 3 2 2 3 4 +--R (d + 52c d - 52c d - c )x + 26c d + 48c d - 66c d - 8c +--R + +--R 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ 3+-+ x \|d - x\|c \|d + \|c +--R ((d - 4c)\|d + (- 4d + c)\|c )log(---------------------------) +--R 3+-+2 +--R \|d +--R + +--R 3+-+ 3+-+ +--R 3+-+ 3+-+ x\|d + \|c +--R ((- 2d + 8c)\|d + (8d - 2c)\|c )log(------------) +--R 3+-+ +--R \|d +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ +-+3+-+ 2x\|3 \|d - \|3 \|c +--R ((- 2d + 8c)\|3 \|d + (- 8d + 2c)\|3 \|c )atan(---------------------) +--R 3+-+ +--R 3\|c +--R + +--R 3 3+-+2 3+-+2 +--R - 12log(d x + c)\|c \|d +--R / +--R 3+-+2 3+-+2 +--R 6d \|c \|d +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1483 +d0116:=D(m0116,x) +--R +--R +--R (613) 0 +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1483 +t0117:= x^3/(a+b*(c+d*x)^3) +--R +--R +--R 3 +--R x +--R (614) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 614 + +--S 615 of 1483 +r0117:= (c+d*x)/b/d^4+3^(1/2)*c^2*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))/a^(1/3)/b^(2/3)/d^4-_ + 1/3*(a+b*c^3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/b^(4/3)/d^4-_ + c^2*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/b^(2/3)/d^4-_ + 1/3*(a+b*c^3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/b^(4/3)/d^4+_ + 1/2*c^2*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/b^(2/3)/d^4+1/6*(a+b*c^3)*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(2/3)/b^(4/3)/d^4-_ + c*log(a+b*(c+d*x)^3)/b/d^4 +--R +--R +--R (615) +--R 3 3+-+ 2 3+-+ +--R ((b c + a)\|b + 3b c \|a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3+-+ 2 3+-+ (d x + c)\|b + \|a +--R ((- 2b c - 2a)\|b - 6b c \|a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 +-+3+-+ 2 +-+3+-+ +--R ((- 2b c - 2a)\|3 \|b + 6b c \|3 \|a ) +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 3+-+2 +--R (- 6c log(b d x + 3b c d x + 3b c d x + b c + a) + 6d x + 6c)\|a \|b +--R / +--R 4 3+-+2 3+-+2 +--R 6b d \|a \|b +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1483 +a0117:=integrate(t0117,x) +--R +--R +--R (616) +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R 4 |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c 4 +--R (b d |--------------------------------------------- - b d %%H0 - 3c) +--R | 2 8 +--R \| a b d +--R * +--R log +--R 2 3 2 8 3 6 2 2 3 3 4 +--R (27a b c d %%H0 + (- 3a b c + 21a b c - 3a b)d ) +--R * +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R 27a b c d %%H0 + (3a b c + 60a b c + 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 +--R (2b c - 48a b c + 6a b c + 2a )d x + 2b c - 63a b c +--R + +--R 2 4 3 +--R 21a b c + 5a c +--R + +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R 4 |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c 4 +--R - b d |--------------------------------------------- - b d %%H0 +--R | 2 8 +--R \| a b d +--R + +--R - 3c +--R * +--R log +--R 2 3 2 8 3 6 2 2 3 3 4 +--R (- 27a b c d %%H0 + (3a b c - 21a b c + 3a b)d ) +--R * +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R 27a b c d %%H0 + (3a b c + 60a b c + 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 +--R (2b c - 48a b c + 6a b c + 2a )d x + 2b c - 63a b c +--R + +--R 2 4 3 +--R 21a b c + 5a c +--R + +--R 4 +--R 2b d %%H0 +--R * +--R log +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R - 27a b c d %%H0 + (- 3a b c - 60a b c - 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 2 4 +--R (b c - 24a b c + 3a b c + a )d x + b c - 9a b c - 12a b c +--R + +--R 3 +--R - 2a c +--R + +--R 2d x +--R / +--R 4 +--R 2b d +--R Type: Union(Expression(Integer),...) +--E 616 + +--S 617 of 1483 +m0117:=a0117-r0117 +--R +--R +--R (617) +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R 4 3+-+2 3+-+2 |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R 3b d \|a \|b |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 4 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3b d \|a \|b %% - 9c \|a \|b +--R * +--R log +--R 2 3 2 8 3 6 2 2 3 3 4 +--R (27a b c d %%H0 + (- 3a b c + 21a b c - 3a b)d ) +--R * +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R 27a b c d %%H0 + (3a b c + 60a b c + 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 +--R (2b c - 48a b c + 6a b c + 2a )d x + 2b c - 63a b c +--R + +--R 2 4 3 +--R 21a b c + 5a c +--R + +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R 4 3+-+2 3+-+2 |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R - 3b d \|a \|b |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 4 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3b d \|a \|b %% - 9c \|a \|b +--R * +--R log +--R 2 3 2 8 3 6 2 2 3 3 4 +--R (- 27a b c d %%H0 + (3a b c - 21a b c + 3a b)d ) +--R * +--R +---------------------------------------------+ +--R | 2 8 2 4 5 2 +--R |- 3a b d %%H0 - 6a b c d %%H0 + 4b c + a c +--R |--------------------------------------------- +--R | 2 8 +--R \| a b d +--R + +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R 27a b c d %%H0 + (3a b c + 60a b c + 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 +--R (2b c - 48a b c + 6a b c + 2a )d x + 2b c - 63a b c +--R + +--R 2 4 3 +--R 21a b c + 5a c +--R + +--R 3 3+-+ 2 3+-+ +--R ((- b c - a)\|b - 3b c \|a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3+-+ 2 3+-+ (d x + c)\|b + \|a +--R ((2b c + 2a)\|b + 6b c \|a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 4 3+-+2 3+-+2 +--R 6b d \|a \|b %%H0 +--R * +--R log +--R 2 3 2 8 2 3 6 2 2 3 3 4 +--R - 27a b c d %%H0 + (- 3a b c - 60a b c - 3a b)d %%H0 +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 2 4 +--R (b c - 24a b c + 3a b c + a )d x + b c - 9a b c - 12a b c +--R + +--R 3 +--R - 2a c +--R + +--R 3 +-+3+-+ 2 +-+3+-+ +--R ((2b c + 2a)\|3 \|b - 6b c \|3 \|a ) +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 3+-+2 +--R (6c log(b d x + 3b c d x + 3b c d x + b c + a) - 6c)\|a \|b +--R / +--R 4 3+-+2 3+-+2 +--R 6b d \|a \|b +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1483 +d0117:=D(m0117,x) +--R +--R +--R (618) 0 +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1483 +t0118:= x^2/(a+b*(c+d*x)^3) +--R +--R +--R 2 +--R x +--R (619) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 619 + +--S 620 of 1483 +r0118:= -2/3*c*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/b^(2/3)/d^3+_ + 1/3*c^2*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/b^(1/3)/d^3+_ + 2/3*c*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/b^(2/3)/d^3+_ + 1/3*c^2*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/b^(1/3)/d^3-_ + 1/3*c*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/b^(2/3)/d^3-1/6*c^2*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(2/3)/b^(1/3)/d^3+_ + 1/3*log(a+b*(c+d*x)^3)/b/d^3 +--R +--R +--R (620) +--R 2 3+-+ 3+-+ +--R (- b c \|b - 2b c\|a ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 2 3+-+ 3+-+ (d x + c)\|b + \|a +--R (2b c \|b + 4b c\|a )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 2 +-+3+-+ +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (2b c \|3 \|b - 4b c\|3 \|a )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 3+-+2 +--R 2log(b d x + 3b c d x + 3b c d x + b c + a)\|a \|b +--R / +--R 3 3+-+2 3+-+2 +--R 6b d \|a \|b +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1483 +a0118:=integrate(t0118,x) +--R +--R +--R (621) +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R 3 |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a 3 +--R (b d |---------------------------------------- - b d %%I0 + 1) +--R | 2 6 +--R \| 3a b d +--R * +--R log +--R 2 2 6 2 3 2 3 +--R (18a b d %%I0 + (3a b c - 6a b)d ) +--R * +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 2 2 6 2 2 3 2 3 2 5 2 +--R 18a b d %%I0 + (- 3a b c - 12a b)d %%I0 + (2b c - 16a b c )d x +--R + +--R 2 6 3 2 +--R 2b c - 23a b c + 2a +--R + +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R 3 |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a 3 +--R (- b d |---------------------------------------- - b d %%I0 + 1) +--R | 2 6 +--R \| 3a b d +--R * +--R log +--R 2 2 6 2 3 2 3 +--R (- 18a b d %%I0 + (- 3a b c + 6a b)d ) +--R * +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 2 2 6 2 2 3 2 3 2 5 2 +--R 18a b d %%I0 + (- 3a b c - 12a b)d %%I0 + (2b c - 16a b c )d x +--R + +--R 2 6 3 2 +--R 2b c - 23a b c + 2a +--R + +--R 3 +--R 2b d %%I0 +--R * +--R log +--R 2 2 6 2 2 3 2 3 2 5 2 +--R - 18a b d %%I0 + (3a b c + 12a b)d %%I0 + (b c - 8a b c )d x +--R + +--R 2 6 3 2 +--R b c - a b c - 2a +--R / +--R 3 +--R 2b d +--R Type: Union(Expression(Integer),...) +--E 621 + +--S 622 of 1483 +m0118:=a0118-r0118 +--R +--R +--R (622) +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R 3 3+-+2 3+-+2 |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R 3b d \|a \|b |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 3 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3b d \|a \|b %% + 3\|a \|b +--R * +--R log +--R 2 2 6 2 3 2 3 +--R (18a b d %%I0 + (3a b c - 6a b)d ) +--R * +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 2 2 6 2 2 3 2 3 2 5 2 +--R 18a b d %%I0 + (- 3a b c - 12a b)d %%I0 + (2b c - 16a b c )d x +--R + +--R 2 6 3 2 +--R 2b c - 23a b c + 2a +--R + +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R 3 3+-+2 3+-+2 |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R - 3b d \|a \|b |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 3 3+-+2 3+-+2 3+-+2 3+-+2 +--R - 3b d \|a \|b %% + 3\|a \|b +--R * +--R log +--R 2 2 6 2 3 2 3 +--R (- 18a b d %%I0 + (- 3a b c + 6a b)d ) +--R * +--R +----------------------------------------+ +--R | 2 6 2 3 3 +--R |- 9a b d %%I0 + 6a b d %%I0 + 8b c - a +--R |---------------------------------------- +--R | 2 6 +--R \| 3a b d +--R + +--R 2 2 6 2 2 3 2 3 2 5 2 +--R 18a b d %%I0 + (- 3a b c - 12a b)d %%I0 + (2b c - 16a b c )d x +--R + +--R 2 6 3 2 +--R 2b c - 23a b c + 2a +--R + +--R 2 3+-+ 3+-+ +--R (b c \|b + 2b c\|a ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 2 3+-+ 3+-+ (d x + c)\|b + \|a +--R (- 2b c \|b - 4b c\|a )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 3+-+2 3+-+2 +--R 6b d \|a \|b %%I0 +--R * +--R log +--R 2 2 6 2 2 3 2 3 2 5 2 +--R - 18a b d %%I0 + (3a b c + 12a b)d %%I0 + (b c - 8a b c )d x +--R + +--R 2 6 3 2 +--R b c - a b c - 2a +--R + +--R +-+3+-+ +-+3+-+ +--R 2 +-+3+-+ +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (- 2b c \|3 \|b + 4b c\|3 \|a )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 3+-+2 +--R - 2log(b d x + 3b c d x + 3b c d x + b c + a)\|a \|b +--R / +--R 3 3+-+2 3+-+2 +--R 6b d \|a \|b +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1483 +d0118:=D(m0118,x) +--R +--R +--R (623) 0 +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1483 +t0119:= x/(a+b*(c+d*x)^3) +--R +--R +--R x +--R (624) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 624 + +--S 625 of 1483 +r0119:= 1/3*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/b^(2/3)/d^2-_ + 1/3*c*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/b^(1/3)/d^2-_ + 1/3*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/b^(2/3)/d^2-_ + 1/3*c*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/b^(1/3)/d^2+_ + 1/6*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/b^(2/3)/d^2+1/6*c*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(2/3)/b^(1/3)/d^2 +--R +--R +--R (625) +--R 3+-+ 3+-+ +--R (c\|b + \|a ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+ 3+-+ (d x + c)\|b + \|a +--R (- 2c\|b - 2\|a )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (- 2c\|3 \|b + 2\|3 \|a )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R 2 3+-+2 3+-+2 +--R 6d \|a \|b +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1483 +a0119:=integrate(t0119,x) +--R +--R +--R (626) +--R +-------------------+ +--R | 4 2 +--R |- 9a b d %%J0 + 4c +--R ( |------------------- - %%J0) +--R | 4 +--R \| 3a b d +--R * +--R log +--R +-------------------+ +--R | 4 2 +--R 2 4 2 2 |- 9a b d %%J0 + 4c 2 4 2 +--R (9a b d %%J0 - 3a b c d ) |------------------- + 9a b d %%J0 +--R | 4 +--R \| 3a b d +--R + +--R 2 2 3 4 +--R 3a b c d %%J0 + (2b c - 2a)d x + 2b c - 4a c +--R + +--R +-------------------+ +--R | 4 2 +--R |- 9a b d %%J0 + 4c +--R (- |------------------- - %%J0) +--R | 4 +--R \| 3a b d +--R * +--R log +--R +-------------------+ +--R | 4 2 +--R 2 4 2 2 |- 9a b d %%J0 + 4c 2 4 2 +--R (- 9a b d %%J0 + 3a b c d ) |------------------- + 9a b d %%J0 +--R | 4 +--R \| 3a b d +--R + +--R 2 2 3 4 +--R 3a b c d %%J0 + (2b c - 2a)d x + 2b c - 4a c +--R + +--R 2 4 2 2 2 3 4 +--R 2%%J0 log(- 9a b d %%J0 - 3a b c d %%J0 + (b c - a)d x + b c + a c) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 626 + +--S 627 of 1483 +m0119:=a0119-r0119 +--R +--R +--R (627) +--R +-------------------+ +--R | 4 2 +--R 2 3+-+2 3+-+2 |- 9a b d %%J0 + 4c 2 3+-+2 3+-+2 +--R (3d \|a \|b |------------------ - 3d \|a \|b %%)0 +--R | 4 +--R \| 3a b d +--R * +--R log +--R +-------------------+ +--R | 4 2 +--R 2 4 2 2 |- 9a b d %%J0 + 4c 2 4 2 +--R (9a b d %%J0 - 3a b c d ) |------------------- + 9a b d %%J0 +--R | 4 +--R \| 3a b d +--R + +--R 2 2 3 4 +--R 3a b c d %%J0 + (2b c - 2a)d x + 2b c - 4a c +--R + +--R +-------------------+ +--R | 4 2 +--R 2 3+-+2 3+-+2 |- 9a b d %%J0 + 4c 2 3+-+2 3+-+2 +--R (- 3d \|a \|b |------------------ - 3d \|a \|b %%)0 +--R | 4 +--R \| 3a b d +--R * +--R log +--R +-------------------+ +--R | 4 2 +--R 2 4 2 2 |- 9a b d %%J0 + 4c 2 4 2 +--R (- 9a b d %%J0 + 3a b c d ) |------------------- + 9a b d %%J0 +--R | 4 +--R \| 3a b d +--R + +--R 2 2 3 4 +--R 3a b c d %%J0 + (2b c - 2a)d x + 2b c - 4a c +--R + +--R 3+-+ 3+-+ +--R (- c\|b - \|a ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+ 3+-+ (d x + c)\|b + \|a +--R (2c\|b + 2\|a )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 3+-+2 3+-+2 +--R 6d \|a \|b %%J0 +--R * +--R 2 4 2 2 2 3 4 +--R log(- 9a b d %%J0 - 3a b c d %%J0 + (b c - a)d x + b c + a c) +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (2c\|3 \|b - 2\|3 \|a )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R 2 3+-+2 3+-+2 +--R 6d \|a \|b +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1483 +d0119:=D(m0119,x) +--R +--R +--R (628) 0 +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1483 +t0120:= 1/(a+b*(c+d*x)^3) +--R +--R +--R 1 +--R (629) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 629 + +--S 630 of 1483 +r0120:= 1/3*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/b^(1/3)/d+_ + 1/3*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/b^(1/3)/d-_ + 1/6*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(2/3)/b^(1/3)/d +--R +--R +--R (630) +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R (d x + c)\|b + \|a +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R 2log(--------------------) + 2\|3 atan(------------------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R / +--R 3+-+2 3+-+ +--R 6d \|a \|b +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1483 +a0120:=integrate(t0120,x) +--R +--R +--R (631) +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R - \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +---+ +-+3| 2 +-+ +--R +-+ 3| 2 (2d x + 2c)\|3 \|a b - a\|3 +--R 2\|3 log((d x + c)\|a b + a) + 6atan(-----------------------------) +--R 3a +--R / +--R +---+ +--R +-+3| 2 +--R 6d\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 631 + +--S 632 of 1483 +m0120:=a0120-r0120 +--R +--R +--R (632) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3| 2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|a b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +---+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R - 2\|3 \|a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 6d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1483 +d0120:=D(m0120,x) +--R +--R +--R (633) 0 +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1483 +t0121:= 1/x/(a+b*(c+d*x)^3) +--R +--R +--R 1 +--R (634) -------------------------------------------- +--R 3 4 2 3 2 2 3 +--R b d x + 3b c d x + 3b c d x + (b c + a)x +--R Type: Fraction(Polynomial(Integer)) +--E 634 + +--S 635 of 1483 +r0121:= -1/3*b^(1/3)*c*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/(a+b*c^3)-_ + 1/3*b^(2/3)*c^2*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/(a+b*c^3)+_ + log(-d*x)/(a+b*c^3)+_ + 1/3*b^(1/3)*c*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/(a+b*c^3)-_ + 1/3*b^(2/3)*c^2*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/(a+b*c^3)-_ + 1/6*b^(1/3)*c*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/(a+b*c^3)+1/6*b^(2/3)*c^2*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(2/3)/(a+b*c^3)-_ + log(a+b*(c+d*x)^3)/(3*a+3*b*c^3) +--R +--R +--R (635) +--R 2 3+-+2 3+-+3+-+ +--R (c \|b - c\|a \|b ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 2 3+-+2 3+-+3+-+ (d x + c)\|b + \|a +--R (- 2c \|b + 2c\|a \|b )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 2 +-+3+-+2 +-+3+-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (- 2c \|3 \|b - 2c\|3 \|a \|b )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 +--R (- 2log(b d x + 3b c d x + 3b c d x + b c + a) + 6log(- d x))\|a +--R / +--R 3 3+-+2 +--R (6b c + 6a)\|a +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1483 +a0121:=integrate(t0121,x) +--R +--R +--R (636) +--R 3 +--R (- b c - a) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 3 +--R (- b c - a)%%L0 - 1 +--R * +--R log +--R 2 3 3 3 2 +--R ((9a b c + 9a )%%L0 + 3a b c + 3a ) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 9a b c - 9a )%%L0 + (3a b c - 6a )%%L0 + 2b c d x + 2b c - a +--R + +--R 3 +--R (b c + a) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 3 +--R (- b c - a)%%L0 - 1 +--R * +--R log +--R 2 3 3 3 2 +--R ((- 9a b c - 9a )%%L0 - 3a b c - 3a ) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 9a b c - 9a )%%L0 + (3a b c - 6a )%%L0 + 2b c d x + 2b c - a +--R + +--R 3 +--R (2b c + 2a)%%L0 +--R * +--R 2 3 3 2 3 2 2 3 +--R log((9a b c + 9a )%%L0 + (- 3a b c + 6a )%%L0 + b c d x + b c + a) +--R + +--R 2log(x) +--R / +--R 3 +--R 2b c + 2a +--R Type: Union(Expression(Integer),...) +--E 636 + +--S 637 of 1483 +m0121:=a0121-r0121 +--R +--R +--R (637) +--R 3 3+-+2 +--R (- 3b c - 3a)\|a +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 3 3+-+2 3+-+2 +--R (- 3b c - 3a)\|a %%L0 - 3\|a +--R * +--R log +--R 2 3 3 3 2 +--R ((9a b c + 9a )%%L0 + 3a b c + 3a ) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 9a b c - 9a )%%L0 + (3a b c - 6a )%%L0 + 2b c d x + 2b c - a +--R + +--R 3 3+-+2 +--R (3b c + 3a)\|a +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 3 3+-+2 3+-+2 +--R (- 3b c - 3a)\|a %%L0 - 3\|a +--R * +--R log +--R 2 3 3 3 2 +--R ((- 9a b c - 9a )%%L0 - 3a b c - 3a ) +--R * +--R ROOT +--R 2 6 2 3 3 2 3 2 +--R (- 9a b c - 18a b c - 9a )%%L0 + (- 6a b c - 6a )%%L0 +--R + +--R 3 +--R - 4b c - a +--R / +--R 2 6 2 3 3 +--R 3a b c + 6a b c + 3a +--R + +--R 2 3 3 2 3 2 2 3 +--R (- 9a b c - 9a )%%L0 + (3a b c - 6a )%%L0 + 2b c d x + 2b c - a +--R + +--R 3 3+-+2 +--R (6b c + 6a)\|a %%L0 +--R * +--R 2 3 3 2 3 2 2 3 +--R log((9a b c + 9a )%%L0 + (- 3a b c + 6a )%%L0 + b c d x + b c + a) +--R + +--R 2 3+-+2 3+-+3+-+ +--R (- c \|b + c\|a \|b ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 2 3+-+2 3+-+3+-+ (d x + c)\|b + \|a +--R (2c \|b - 2c\|a \|b )log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 2 +-+3+-+2 +-+3+-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R (2c \|3 \|b + 2c\|3 \|a \|b )atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 +--R 2log(b d x + 3b c d x + 3b c d x + b c + a) + 6log(x) +--R + +--R - 6log(- d x) +--R * +--R 3+-+2 +--R \|a +--R / +--R 3 3+-+2 +--R (6b c + 6a)\|a +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1483 +d0121:=D(m0121,x) +--R +--R +--R (638) 0 +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1483 +t0122:= 1/x^2/(a+b*(c+d*x)^3) +--R +--R +--R 1 +--R (639) --------------------------------------------- +--R 3 5 2 4 2 3 3 2 +--R b d x + 3b c d x + 3b c d x + (b c + a)x +--R Type: Fraction(Polynomial(Integer)) +--E 639 + +--S 640 of 1483 +r0122:= -1/(a+b*c^3)/x-1/3*b^(1/3)*(a-2*b*c^3)*d*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/(a+b*c^3)^2-_ + 1/3*b^(2/3)*c*(2*a-b*c^3)*d*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/(a+b*c^3)^2-_ + 3*b*c^2*d*log(-d*x)/(a+b*c^3)^2+_ + 1/3*b^(1/3)*(a-2*b*c^3)*d*log(a^(1/3)/b^(1/3)+c+_ + d*x)/a^(1/3)/(a+b*c^3)^2-_ + 1/3*b^(2/3)*c*(2*a-b*c^3)*d*log(a^(1/3)/b^(1/3)+c+_ + d*x)/a^(2/3)/(a+b*c^3)^2-_ + 1/6*b^(1/3)*(a-2*b*c^3)*d*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/(a+b*c^3)^2+_ + 1/6*b^(2/3)*c*(2*a-b*c^3)*d*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(2/3)/(a+b*c^3)^2+_ + b*c^2*d*log(a+b*(c+d*x)^3)/(a+b*c^3)^2 +--R +--R +--R (640) +--R 4 3+-+2 3 3+-+3+-+ +--R ((- b c + 2a c)d x \|b + (2b c - a)d x\|a \|b ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 4 3+-+2 3 3+-+3+-+ +--R ((2b c - 4a c)d x \|b + (- 4b c + 2a)d x\|a \|b ) +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 4 +-+3+-+2 3 +-+3+-+3+-+ +--R ((2b c - 4a c)d x\|3 \|b + (4b c - 2a)d x\|3 \|a \|b ) +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 3 3 2 2 2 3 +--R 6b c d x log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 3 +--R - 18b c d x log(- d x) - 6b c - 6a +--R * +--R 3+-+2 +--R \|a +--R / +--R 2 6 3 2 3+-+2 +--R (6b c + 12a b c + 6a )x \|a +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1483 +a0122:=integrate(t0122,x) +--R +--R +--R (641) +--R 2 6 3 2 +--R (- b c - 2a b c - a )x +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 6 3 2 2 +--R (- b c - 2a b c - a )x %%M0 + 3b c d x +--R * +--R log +--R 2 3 9 3 2 6 5 +--R (18a b c + 27a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (- 3a b c - 6a b c - 3a b c )d +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 3 9 3 2 6 5 2 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (- 3a b c + 48a b c - 30a b c )d %%M0 + (2b c - 2a b)d x +--R + +--R 3 7 2 4 2 2 +--R (2b c - 5a b c + 2a b c)d +--R + +--R 2 6 3 2 +--R (b c + 2a b c + a )x +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 6 3 2 2 +--R (- b c - 2a b c - a )x %%M0 + 3b c d x +--R * +--R log +--R 2 3 9 3 2 6 5 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (3a b c + 6a b c + 3a b c )d +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 3 9 3 2 6 5 2 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (- 3a b c + 48a b c - 30a b c )d %%M0 + (2b c - 2a b)d x +--R + +--R 3 7 2 4 2 2 +--R (2b c - 5a b c + 2a b c)d +--R + +--R 2 6 3 2 +--R (2b c + 4a b c + 2a )x %%M0 +--R * +--R log +--R 2 3 9 3 2 6 5 2 +--R (18a b c + 27a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (3a b c - 48a b c + 30a b c )d %%M0 + (b c - a b)d x +--R + +--R 3 7 2 4 2 2 +--R (b c + 5a b c - 5a b c)d +--R + +--R 2 3 +--R - 6b c d x log(x) - 2b c - 2a +--R / +--R 2 6 3 2 +--R (2b c + 4a b c + 2a )x +--R Type: Union(Expression(Integer),...) +--E 641 + +--S 642 of 1483 +m0122:=a0122-r0122 +--R +--R +--R (642) +--R 2 6 3 2 3+-+2 +--R (- 3b c - 6a b c - 3a )\|a +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 6 3 2 3+-+2 2 3+-+2 +--R (- 3b c - 6a b c - 3a )\|a %%M0 + 9b c d \|a +--R * +--R log +--R 2 3 9 3 2 6 5 +--R (18a b c + 27a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (- 3a b c - 6a b c - 3a b c )d +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 3 9 3 2 6 5 2 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (- 3a b c + 48a b c - 30a b c )d %%M0 + (2b c - 2a b)d x +--R + +--R 3 7 2 4 2 2 +--R (2b c - 5a b c + 2a b c)d +--R + +--R 2 6 3 2 3+-+2 +--R (3b c + 6a b c + 3a )\|a +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 6 3 2 3+-+2 2 3+-+2 +--R (- 3b c - 6a b c - 3a )\|a %%M0 + 9b c d \|a +--R * +--R log +--R 2 3 9 3 2 6 5 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (3a b c + 6a b c + 3a b c )d +--R * +--R ROOT +--R 4 12 2 3 9 3 2 6 4 3 5 2 +--R (- 9a b c - 36a b c - 54a b c - 36a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 +--R (18a b c + 36a b c + 18a b c )d %%M0 +--R + +--R 3 7 2 4 2 2 +--R (- 8b c + 11a b c - 8a b c)d +--R / +--R 4 12 2 3 9 3 2 6 4 3 5 +--R 3a b c + 12a b c + 18a b c + 12a b c + 3a +--R + +--R 2 3 9 3 2 6 5 2 +--R (- 18a b c - 27a b c + 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (- 3a b c + 48a b c - 30a b c )d %%M0 + (2b c - 2a b)d x +--R + +--R 3 7 2 4 2 2 +--R (2b c - 5a b c + 2a b c)d +--R + +--R 2 6 3 2 3+-+2 +--R (6b c + 12a b c + 6a )\|a %%M0 +--R * +--R log +--R 2 3 9 3 2 6 5 2 +--R (18a b c + 27a b c - 9a )%%M0 +--R + +--R 3 8 2 2 5 3 2 3 6 2 3 +--R (3a b c - 48a b c + 30a b c )d %%M0 + (b c - a b)d x +--R + +--R 3 7 2 4 2 2 +--R (b c + 5a b c - 5a b c)d +--R + +--R 4 3+-+2 3 3+-+3+-+ +--R ((b c - 2a c)d \|b + (- 2b c + a)d\|a \|b ) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 4 3+-+2 3 3+-+3+-+ +--R ((- 2b c + 4a c)d \|b + (4b c - 2a)d\|a \|b ) +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 4 +-+3+-+2 3 +-+3+-+3+-+ +--R ((- 2b c + 4a c)d\|3 \|b + (- 4b c + 2a)d\|3 \|a \|b ) +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 3 3 2 2 2 3 +--R - 6b c d log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 2 +--R - 18b c d log(x) + 18b c d log(- d x) +--R * +--R 3+-+2 +--R \|a +--R / +--R 2 6 3 2 3+-+2 +--R (6b c + 12a b c + 6a )\|a +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1483 +d0122:=D(m0122,x) +--R +--R +--R (643) 0 +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1483 +t0123:= (c+d*x)^3*(a+b*(c+d*x)^3) +--R +--R +--R (644) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R b d x + 6b c d x + 15b c d x + (20b c + a)d x + (15b c + 3a c)d x +--R + +--R 5 2 6 3 +--R (6b c + 3a c )d x + b c + a c +--R Type: Polynomial(Integer) +--E 644 + +--S 645 of 1483 +r0123:= 1/4*a*(c+d*x)^4/d+1/7*b*(c+d*x)^7/d +--R +--R +--R (645) +--R 1 7 7 6 6 2 5 5 3 1 4 4 4 3 3 +--R - b d x + b c d x + 3b c d x + (5b c + - a)d x + (5b c + a c)d x +--R 7 4 +--R + +--R 5 3 2 2 2 6 3 1 7 1 4 +--R (3b c + - a c )d x + (b c + a c )d x + - b c + - a c +--R 2 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 645 + +--S 646 of 1483 +a0123:=integrate(t0123,x) +--R +--R +--R (646) +--R 1 6 7 5 6 2 4 5 3 1 3 4 4 2 3 +--R - b d x + b c d x + 3b c d x + (5b c + - a)d x + (5b c + a c)d x +--R 7 4 +--R + +--R 5 3 2 2 6 3 +--R (3b c + - a c )d x + (b c + a c )x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 646 + +--S 647 of 1483 +m0123:=a0123-r0123 +--R +--R +--R 1 7 1 4 +--R - - b c - - a c +--R 7 4 +--R (647) ----------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 647 + +--S 648 of 1483 +d0123:=D(m0123,x) +--R +--R +--R (648) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 648 + +--S 649 of 1483 +t0124:= (c+d*x)^3*(a+b*(c+d*x)^3)^2 +--R +--R +--R (649) +--R 2 9 9 2 8 8 2 2 7 7 2 3 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 2a b)d x +--R + +--R 2 4 5 5 2 5 2 4 4 +--R (126b c + 12a b c)d x + (126b c + 30a b c )d x +--R + +--R 2 6 3 2 3 3 2 7 4 2 2 2 +--R (84b c + 40a b c + a )d x + (36b c + 30a b c + 3a c)d x +--R + +--R 2 8 5 2 2 2 9 6 2 3 +--R (9b c + 12a b c + 3a c )d x + b c + 2a b c + a c +--R Type: Polynomial(Integer) +--E 649 + +--S 650 of 1483 +r0124:= 1/4*a^2*(c+d*x)^4/d+2/7*a*b*(c+d*x)^7/d+1/10*b^2*(c+d*x)^10/d +--R +--R +--R (650) +--R 1 2 10 10 2 9 9 9 2 2 8 8 2 3 2 7 7 +--R -- b d x + b c d x + - b c d x + (12b c + - a b)d x +--R 10 2 7 +--R + +--R 2 4 6 6 126 2 5 2 5 5 +--R (21b c + 2a b c)d x + (--- b c + 6a b c )d x +--R 5 +--R + +--R 2 6 3 1 2 4 4 2 7 4 2 3 3 +--R (21b c + 10a b c + - a )d x + (12b c + 10a b c + a c)d x +--R 4 +--R + +--R 9 2 8 5 3 2 2 2 2 2 9 6 2 3 1 2 10 +--R (- b c + 6a b c + - a c )d x + (b c + 2a b c + a c )d x + -- b c +--R 2 2 10 +--R + +--R 2 7 1 2 4 +--R - a b c + - a c +--R 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 650 + +--S 651 of 1483 +a0124:=integrate(t0124,x) +--R +--R +--R (651) +--R 1 2 9 10 2 8 9 9 2 2 7 8 2 3 2 6 7 +--R -- b d x + b c d x + - b c d x + (12b c + - a b)d x +--R 10 2 7 +--R + +--R 2 4 5 6 126 2 5 2 4 5 +--R (21b c + 2a b c)d x + (--- b c + 6a b c )d x +--R 5 +--R + +--R 2 6 3 1 2 3 4 2 7 4 2 2 3 +--R (21b c + 10a b c + - a )d x + (12b c + 10a b c + a c)d x +--R 4 +--R + +--R 9 2 8 5 3 2 2 2 2 9 6 2 3 +--R (- b c + 6a b c + - a c )d x + (b c + 2a b c + a c )x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 651 + +--S 652 of 1483 +m0124:=a0124-r0124 +--R +--R +--R 1 2 10 2 7 1 2 4 +--R - -- b c - - a b c - - a c +--R 10 7 4 +--R (652) ------------------------------ +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 652 + +--S 653 of 1483 +d0124:=D(m0124,x) +--R +--R +--R (653) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 653 + +--S 654 of 1483 +t0125:= (c+d*x)^3*(a+b*(c+d*x)^3)^3 +--R +--R +--R (654) +--R 3 12 12 3 11 11 3 2 10 10 3 3 2 9 9 +--R b d x + 12b c d x + 66b c d x + (220b c + 3a b )d x +--R + +--R 3 4 2 8 8 3 5 2 2 7 7 +--R (495b c + 27a b c)d x + (792b c + 108a b c )d x +--R + +--R 3 6 2 3 2 6 6 3 7 2 4 2 5 5 +--R (924b c + 252a b c + 3a b)d x + (792b c + 378a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 4 4 +--R (495b c + 378a b c + 45a b c )d x +--R + +--R 3 9 2 6 2 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 2 2 +--R (66b c + 108a b c + 45a b c + 3a c)d x +--R + +--R 3 11 2 8 2 5 3 2 3 12 2 9 2 6 3 3 +--R (12b c + 27a b c + 18a b c + 3a c )d x + b c + 3a b c + 3a b c + a c +--R Type: Polynomial(Integer) +--E 654 + +--S 655 of 1483 +r0125:= 1/4*a^3*(c+d*x)^4/d+3/7/d*a^2*b*(c+d*x)^7+3/10/d*a*b^2*(c+d*x)^10+_ + 1/13/d*b^3*(c+d*x)^13 +--R +--R +--R (655) +--R 1 3 13 13 3 12 12 3 2 11 11 3 3 3 2 10 10 +--R -- b d x + b c d x + 6b c d x + (22b c + -- a b )d x +--R 13 10 +--R + +--R 3 4 2 9 9 3 5 27 2 2 8 8 +--R (55b c + 3a b c)d x + (99b c + -- a b c )d x +--R 2 +--R + +--R 3 6 2 3 3 2 7 7 3 7 2 4 2 6 6 +--R (132b c + 36a b c + - a b)d x + (132b c + 63a b c + 3a b c)d x +--R 7 +--R + +--R 3 8 378 2 5 2 2 5 5 +--R (99b c + --- a b c + 9a b c )d x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 4 4 +--R (55b c + 63a b c + 15a b c + - a )d x +--R 4 +--R + +--R 3 10 2 7 2 4 3 3 3 +--R (22b c + 36a b c + 15a b c + a c)d x +--R + +--R 3 11 27 2 8 2 5 3 3 2 2 2 +--R (6b c + -- a b c + 9a b c + - a c )d x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 1 3 13 3 2 10 3 2 7 +--R (b c + 3a b c + 3a b c + a c )d x + -- b c + -- a b c + - a b c +--R 13 10 7 +--R + +--R 1 3 4 +--R - a c +--R 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 655 + +--S 656 of 1483 +a0125:=integrate(t0125,x) +--R +--R +--R (656) +--R 1 3 12 13 3 11 12 3 2 10 11 3 3 3 2 9 10 +--R -- b d x + b c d x + 6b c d x + (22b c + -- a b )d x +--R 13 10 +--R + +--R 3 4 2 8 9 3 5 27 2 2 7 8 +--R (55b c + 3a b c)d x + (99b c + -- a b c )d x +--R 2 +--R + +--R 3 6 2 3 3 2 6 7 3 7 2 4 2 5 6 +--R (132b c + 36a b c + - a b)d x + (132b c + 63a b c + 3a b c)d x +--R 7 +--R + +--R 3 8 378 2 5 2 2 4 5 +--R (99b c + --- a b c + 9a b c )d x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 3 4 +--R (55b c + 63a b c + 15a b c + - a )d x +--R 4 +--R + +--R 3 10 2 7 2 4 3 2 3 +--R (22b c + 36a b c + 15a b c + a c)d x +--R + +--R 3 11 27 2 8 2 5 3 3 2 2 +--R (6b c + -- a b c + 9a b c + - a c )d x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 +--R (b c + 3a b c + 3a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 656 + +--S 657 of 1483 +m0125:=a0125-r0125 +--R +--R +--R 1 3 13 3 2 10 3 2 7 1 3 4 +--R - -- b c - -- a b c - - a b c - - a c +--R 13 10 7 4 +--R (657) ------------------------------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 657 + +--S 658 of 1483 +d0125:=D(m0125,x) +--R +--R +--R (658) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 658 + +--S 659 of 1483 +t0126:= (c+d*x)^4/(a+b*(c+d*x)^3) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R (659) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 659 + +--S 660 of 1483 +r0126:= 1/2*(c+d*x)^2/b/d-1/3*a^(2/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/b^(5/3)/d+_ + 1/3*a^(2/3)*log(a^(1/3)/b^(1/3)+c+d*x)/b^(5/3)/d-_ + 1/6*a^(2/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/b^(5/3)/d +--R +--R +--R (660) +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - \|a log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (d x + c)\|b + \|a +--R 2\|a log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 2\|3 \|a atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 2 2 3+-+2 +--R (3d x + 6c d x + 3c )\|b +--R / +--R 3+-+2 +--R 6b d \|b +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1483 +a0126:=integrate(t0126,x) +--R +--R +--R (661) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a |a +--R 2\|3 |-- log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |a |a |a 2 2 2 +--R - \|3 |-- log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R |a \|b 2 2 +-+ +--R 6 |-- atan(----------------------------------- + (3d x + 6c d x)\|3 +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression(Integer),...) +--E 661 + +--S 662 of 1483 +m0126:=a0126-r0126 +--R +--R +--R (662) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a 3+-+2 |a +--R 2\|3 |-- \|b log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|a log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 (d x + c)\|b + \|a +--R - 2\|3 \|a log(--------------------) +--R 3+-+ +--R \|b +--R + +--R - +--R +--+ +--R | 2 +--R +-+ |a 3+-+2 +--R \|3 |-- \|b +--R 3| 2 +--R \|b +--R * +--R +--+2 +--+ +--R | 2 | 2 +--R |a |a 2 2 2 +--R log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R 6\|a atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R |a 3+-+2 \|b 2 +-+3+-+2 +--R 6 |-- \|b atan(----------------------------------- - 3c \|3 \|b +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+3+-+2 +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1483 +d0126:=D(m0126,x) +--R +--R +--R (663) 0 +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1483 +t0127:= (c+d*x)^3/(a+b*(c+d*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (664) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 664 + +--S 665 of 1483 +r0127:= (c+d*x)/b/d-1/3*a^(1/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/b^(4/3)/d-_ + 1/3*a^(1/3)*log(a^(1/3)/b^(1/3)+c+d*x)/b^(4/3)/d+_ + 1/6*a^(1/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/b^(4/3)/d +--R +--R +--R (665) +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|a log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+ (d x + c)\|b + \|a +--R - 2\|a log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a 3+-+ +--R - 2\|3 \|a atan(------------------------------) + (6d x + 6c)\|b +--R 3+-+ +--R 3\|a +--R / +--R 3+-+ +--R 6b d\|b +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1483 +a0127:=integrate(t0127,x) +--R +--R +--R (666) +--R +---+ +---+2 +---+ +--R +-+ | a | a | a 2 2 2 +--R - \|3 3|- - log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R +-+ | a | a +--R 2\|3 3|- - log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R | a \| b +-+ +--R - 6 3|- - atan(---------------------------- + 6d x\|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression(Integer),...) +--E 666 + +--S 667 of 1483 +m0127:=a0127-r0127 +--R +--R +--R (667) +--R +---+ +---+2 +---+ +--R +-+ | a 3+-+ | a | a 2 2 2 +--R - \|3 3|- - \|b log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - \|3 \|a log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ (d x + c)\|b + \|a +--R 2\|3 \|a log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +---+ +--R +-+ | a 3+-+ | a +--R 2\|3 3|- - \|b log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R 6\|a atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R | a 3+-+ \| b +-+3+-+ +--R - 6 3|- - \|b atan(---------------------------- - 6c\|3 \|b +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1483 +d0127:=D(m0127,x) +--R +--R +--R (668) 0 +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1483 +t0128:= (c+d*x)/(a+b*(c+d*x)^3) +--R +--R +--R d x + c +--R (669) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 669 + +--S 670 of 1483 +r0128:= 1/3*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/b^(2/3)/d-_ + 1/3*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/b^(2/3)/d+_ + 1/6*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(1/3)/b^(2/3)/d +--R +--R +--R (670) +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +-+3+-+ +-+3+-+ +--R (d x + c)\|b + \|a +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R - 2log(--------------------) + 2\|3 atan(------------------------------) +--R 3+-+ 3+-+ +--R \|b 3\|a +--R / +--R 3+-+3+-+2 +--R 6d\|a \|b +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1483 +a0128:=integrate(t0128,x) +--R +--R +--R (671) +--R - +--R +-+ +--R \|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+ 3| 2 +--R 2\|3 log((d x + c)\|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 6d\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 671 + +--S 672 of 1483 +m0128:=a0128-r0128 +--R +--R +--R (672) +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R 2\|3 \|- a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|- a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1483 +d0128:=D(m0128,x) +--R +--R +--R (673) 0 +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1483 +t0129:= 1/(c+d*x)^2/(a+b*(c+d*x)^3) +--R +--R +--R (674) +--R 1 +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 +--R b d x + 5b c d x + 10b c d x + (10b c + a)d x + (5b c + 2a c)d x +--R + +--R 5 2 +--R b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 674 + +--S 675 of 1483 +r0129:= -1/a/d/(c+d*x)-1/3*b^(1/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(4/3)/d+_ + 1/3*b^(1/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(4/3)/d-_ + 1/6*b^(1/3)*log(a^(2/3)/b^(2/3)-_ + a^(1/3)*(c+d*x)/b^(1/3)+(c+d*x)^2)/a^(4/3)/d +--R +--R +--R (675) +--R 3+-+ +--R (- d x - c)\|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+ (d x + c)\|b + \|a +--R (2d x + 2c)\|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a 3+-+ +--R (- 2d x - 2c)\|3 \|b atan(------------------------------) - 6\|a +--R 3+-+ +--R 3\|a +--R / +--R 2 3+-+ +--R (6a d x + 6a c d)\|a +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1483 +a0129:=integrate(t0129,x) +--R +--R +--R (676) +--R +-+ +-+2 +--R +-+ |b |b +--R (2d x + 2c)\|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R +-+ +--R +-+ |b +--R (- d x - c)\|3 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +-+ +--R (6d x + 6c) 3|- atan(---------------------------------- - 6\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+ +--R (6a d x + 6a c d)\|3 +--R Type: Union(Expression(Integer),...) +--E 676 + +--S 677 of 1483 +m0129:=a0129-r0129 +--R +--R +--R (677) +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 2\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ (d x + c)\|b + \|a +--R - 2\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R \|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R 6\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R +-+3+-+ +--R 6a d\|3 \|a +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1483 +d0129:=D(m0129,x) +--R +--R +--R (678) 0 +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1483 +t0130:= 1/(c+d*x)^3/(a+b*(c+d*x)^3) +--R +--R +--R (679) +--R 1 +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R b d x + 6b c d x + 15b c d x + (20b c + a)d x + (15b c + 3a c)d x +--R + +--R 5 2 6 3 +--R (6b c + 3a c )d x + b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 679 + +--S 680 of 1483 +r0130:= -1/2/a/d/(c+d*x)^2-1/3*b^(2/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(5/3)/d-_ + 1/3*b^(2/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(5/3)/d+_ + 1/6*b^(2/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(5/3)/d +--R +--R +--R (680) +--R 2 2 2 3+-+2 +--R (d x + 2c d x + c )\|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 2 2 2 3+-+2 (d x + c)\|b + \|a +--R (- 2d x - 4c d x - 2c )\|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +-+3+-+ +-+3+-+ +--R 2 2 2 +-+3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R (- 2d x - 4c d x - 2c )\|3 \|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3+-+2 +--R - 3\|a +--R / +--R 3 2 2 2 3+-+2 +--R (6a d x + 12a c d x + 6a c d)\|a +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1483 +a0130:=integrate(t0130,x) +--R +--R +--R (681) +--R +----+ +--R | 2 +--R 2 2 2 +-+ | b +--R (- d x - 2c d x - c )\|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 2 2 +-+ | b | b +--R (2d x + 4c d x + 2c )\|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R 2 2 2 | b \| a +--R (- 6d x - 12c d x - 6c ) |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R +-+ +--R - 3\|3 +--R / +--R 3 2 2 2 +-+ +--R (6a d x + 12a c d x + 6a c d)\|3 +--R Type: Union(Expression(Integer),...) +--E 681 + +--S 682 of 1483 +m0130:=a0130-r0130 +--R +--R +--R (682) +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R \|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - \|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 (d x + c)\|b + \|a +--R 2\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 2\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R 6\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 6 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R +-+3+-+2 +--R 6a d\|3 \|a +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1483 +d0130:=D(m0130,x) +--R +--R +--R (683) 0 +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1483 +t0131:= (c+d*x)^4/(a+b*(c+d*x)^3)^2 +--R +--R +--R (684) +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 684 + +--S 685 of 1483 +r0131:= -1/3*(c+d*x)^2/b/d/(a+b*(c+d*x)^3)+2/9*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(1/3)/b^(5/3)/d-_ + 2/9*log(a^(1/3)/b^(1/3)+c+d*x)/a^(1/3)/b^(5/3)/d+_ + 1/9*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(1/3)/b^(5/3)/d +--R +--R +--R (685) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c + a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3 2 2 2 3 (d x + c)\|b + \|a +--R (- 2b d x - 6b c d x - 6b c d x - 2b c - 2a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 2 2 3+-+3+-+2 +--R (- 3d x - 6c d x - 3c )\|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3+-+3+-+2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|a \|b +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1483 +a0131:=integrate(t0131,x) +--R +--R +--R (686) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 3 2 2 2 3 +--R (- 6b d x - 18b c d x - 18b c d x - 6b c - 6a) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 2 2 +-+3| 2 +--R (- 3d x - 6c d x - 3c )\|3 \|- a b +--R / +--R +------+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 686 + +--S 687 of 1483 +m0131:=a0131-r0131 +--R +--R +--R (687) +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R 2\|3 \|- a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|- a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 9b d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1483 +d0131:=D(m0131,x) +--R +--R +--R (688) 0 +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1483 +t0132:= (c+d*x)^3/(a+b*(c+d*x)^3)^2 +--R +--R +--R (689) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 689 + +--S 690 of 1483 +r0132:= -1/3*(c+d*x)/b/d/(a+b*(c+d*x)^3)+1/9*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(2/3)/b^(4/3)/d+_ + 1/9*log(a^(1/3)/b^(1/3)+c+d*x)/a^(2/3)/b^(4/3)/d-_ + 1/18*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(2/3)/b^(4/3)/d +--R +--R +--R (690) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3 2 2 2 3 (d x + c)\|b + \|a +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3+-+2 3+-+ +--R (- 6d x - 6c)\|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3+-+2 3+-+ +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|a \|b +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1483 +a0132:=integrate(t0132,x) +--R +--R +--R (691) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 3 2 2 2 3 +-+ 3| 2 +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 log((d x + c)\|a b + a) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R (- 6d x - 6c)\|3 \|a b +--R / +--R +---+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 691 + +--S 692 of 1483 +m0132:=a0132-r0132 +--R +--R +--R (692) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3| 2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|a b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +---+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R - 2\|3 \|a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 18b d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1483 +d0132:=D(m0132,x) +--R +--R +--R (693) 0 +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1483 +t0133:= (c+d*x)/(a+b*(c+d*x)^3)^2 +--R +--R +--R (694) +--R d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 694 + +--S 695 of 1483 +r0133:= 1/3*(c+d*x)^2/a/d/(a+b*(c+d*x)^3)+1/9*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(4/3)/b^(2/3)/d-_ + 1/9*log(a^(1/3)/b^(1/3)+c+d*x)/a^(4/3)/b^(2/3)/d+_ + 1/18*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(4/3)/b^(2/3)/d +--R +--R +--R (695) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c + a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3 2 2 2 3 (d x + c)\|b + \|a +--R (- 2b d x - 6b c d x - 6b c d x - 2b c - 2a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 2 2 3+-+3+-+2 +--R (6d x + 12c d x + 6c )\|a \|b +--R / +--R 4 3 3 2 2 2 3 2 3+-+3+-+2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|a \|b +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1483 +a0133:=integrate(t0133,x) +--R +--R +--R (696) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 3 2 2 2 3 +--R (- 6b d x - 18b c d x - 18b c d x - 6b c - 6a) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 2 2 +-+3| 2 +--R (6d x + 12c d x + 6c )\|3 \|- a b +--R / +--R +------+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 696 + +--S 697 of 1483 +m0133:=a0133-r0133 +--R +--R +--R (697) +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R 2\|3 \|- a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|- a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 18a d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1483 +d0133:=D(m0133,x) +--R +--R +--R (698) 0 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1483 +t0134:= 1/(a+b*(c+d*x)^3)^2 +--R +--R +--R (699) +--R 1 +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 699 + +--S 700 of 1483 +r0134:= 1/3*(c+d*x)/a/d/(a+b*(c+d*x)^3)+2/9*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(5/3)/b^(1/3)/d+_ + 2/9*log(a^(1/3)/b^(1/3)+c+d*x)/a^(5/3)/b^(1/3)/d-_ + 1/9*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(5/3)/b^(1/3)/d +--R +--R +--R (700) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R 3 3 2 2 2 3 (d x + c)\|b + \|a +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +-+3+-+ +-+3+-+ +--R (2d x + 2c)\|3 \|b - \|3 \|a +--R atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3+-+2 3+-+ +--R (3d x + 3c)\|a \|b +--R / +--R 4 3 3 2 2 2 3 2 3+-+2 3+-+ +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|a \|b +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1483 +a0134:=integrate(t0134,x) +--R +--R +--R (701) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 3 2 2 2 3 +-+ 3| 2 +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 log((d x + c)\|a b + a) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R (3d x + 3c)\|3 \|a b +--R / +--R +---+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 701 + +--S 702 of 1483 +m0134:=a0134-r0134 +--R +--R +--R (702) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3| 2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|a b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +---+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R - 2\|3 \|a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 9a d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1483 +d0134:=D(m0134,x) +--R +--R +--R (703) 0 +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1483 +t0135:= 1/(c+d*x)^2/(a+b*(c+d*x)^3)^2 +--R +--R +--R (704) +--R 1 +--R / +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R b d x + 8b c d x + 28b c d x + (56b c + 2a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (70b c + 10a b c)d x + (56b c + 20a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 2 8 +--R (28b c + 20a b c + a )d x + (8b c + 10a b c + 2a c)d x + b c +--R + +--R 5 2 2 +--R 2a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 704 + +--S 705 of 1483 +r0135:= -1/a^2/d/(c+d*x)-1/3*b*(c+d*x)^2/a^2/d/(a+b*(c+d*x)^3)-_ + 4/9*b^(1/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(7/3)/d+_ + 4/9*b^(1/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(7/3)/d-_ + 2/9*b^(1/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(7/3)/d +--R +--R +--R (705) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R 3+-+ 3+-+ +--R 3+-+ (d x + c)\|b + \|a +--R \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - 4b d x - 16b c d x - 24b c d x + (- 16b c - 4a)d x - 4b c +--R + +--R - 4a c +--R * +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 \|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|a +--R / +--R 2 5 4 2 4 3 2 2 3 2 2 3 3 2 +--R 9a b d x + 36a b c d x + 54a b c d x + (36a b c + 9a )d x +--R + +--R 2 4 3 +--R (9a b c + 9a c)d +--R * +--R 3+-+ +--R \|a +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1483 +a0135:=integrate(t0135,x) +--R +--R +--R (706) +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 12b d x + 48b c d x + 72b c d x + (48b c + 12a)d x + 12b c +--R + +--R 12a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|3 +--R / +--R 2 5 4 2 4 3 2 2 3 2 2 3 3 2 +--R 9a b d x + 36a b c d x + 54a b c d x + (36a b c + 9a )d x +--R + +--R 2 4 3 +--R (9a b c + 9a c)d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 706 + +--S 707 of 1483 +m0135:=a0135-r0135 +--R +--R +--R (707) +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 4\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R 2\|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ (d x + c)\|b + \|a +--R - 4\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 2\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R 12\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 12\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 9a d\|3 \|a +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1483 +d0135:=D(m0135,x) +--R +--R +--R (708) 0 +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1483 +t0136:= 1/(c+d*x)^3/(a+b*(c+d*x)^3)^2 +--R +--R +--R (709) +--R 1 +--R / +--R 2 9 9 2 8 8 2 2 7 7 2 3 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 2a b)d x +--R + +--R 2 4 5 5 2 5 2 4 4 +--R (126b c + 12a b c)d x + (126b c + 30a b c )d x +--R + +--R 2 6 3 2 3 3 2 7 4 2 2 2 +--R (84b c + 40a b c + a )d x + (36b c + 30a b c + 3a c)d x +--R + +--R 2 8 5 2 2 2 9 6 2 3 +--R (9b c + 12a b c + 3a c )d x + b c + 2a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 709 + +--S 710 of 1483 +r0136:= -1/2/a^2/d/(c+d*x)^2-1/3*b*(c+d*x)/a^2/d/(a+b*(c+d*x)^3)-_ + 5/9*b^(2/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(8/3)/d-_ + 5/9*b^(2/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(8/3)/d+_ + 5/18*b^(2/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(8/3)/d +--R +--R +--R (710) +--R 5 5 4 4 2 3 3 3 2 2 +--R 5b d x + 25b c d x + 50b c d x + (50b c + 5a)d x +--R + +--R 4 5 2 +--R (25b c + 10a c)d x + 5b c + 5a c +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 10b d x - 50b c d x - 100b c d x + (- 100b c - 10a)d x +--R + +--R 4 5 2 +--R (- 50b c - 20a c)d x - 10b c - 10a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (d x + c)\|b + \|a +--R \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 10b d x - 50b c d x - 100b c d x + (- 100b c - 10a)d x +--R + +--R 4 5 2 +--R (- 50b c - 20a c)d x - 10b c - 10a c +--R * +--R +-+3+-+ +-+3+-+ +--R +-+3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 \|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 3 3 2 2 2 3 3+-+2 +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|a +--R / +--R 2 6 5 2 5 4 2 2 4 3 2 3 3 3 2 +--R 18a b d x + 90a b c d x + 180a b c d x + (180a b c + 18a )d x +--R + +--R 2 4 3 2 2 5 3 2 +--R (90a b c + 36a c)d x + (18a b c + 18a c )d +--R * +--R 3+-+2 +--R \|a +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1483 +a0136:=integrate(t0136,x) +--R +--R +--R (711) +--R 5 5 4 4 2 3 3 3 2 2 +--R - 5b d x - 25b c d x - 50b c d x + (- 50b c - 5a)d x +--R + +--R 4 5 2 +--R (- 25b c - 10a c)d x - 5b c - 5a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 10b d x + 50b c d x + 100b c d x + (100b c + 10a)d x +--R + +--R 4 5 2 +--R (50b c + 20a c)d x + 10b c + 10a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 30b d x - 150b c d x - 300b c d x + (- 300b c - 30a)d x +--R + +--R 4 5 2 +--R (- 150b c - 60a c)d x - 30b c - 30a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|3 +--R / +--R 2 6 5 2 5 4 2 2 4 3 2 3 3 3 2 +--R 18a b d x + 90a b c d x + 180a b c d x + (180a b c + 18a )d x +--R + +--R 2 4 3 2 2 5 3 2 +--R (90a b c + 36a c)d x + (18a b c + 18a c )d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 711 + +--S 712 of 1483 +m0136:=a0136-r0136 +--R +--R +--R (712) +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 5\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - 5\|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 (d x + c)\|b + \|a +--R 10\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 10\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R 30\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 30 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+3+-+2 +--R 18a d\|3 \|a +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1483 +d0136:=D(m0136,x) +--R +--R +--R (713) 0 +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1483 +t0137:= (c+d*x)^4/(a+b*(c+d*x)^3)^3 +--R +--R +--R (714) +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 714 + +--S 715 of 1483 +r0137:= -1/6*(c+d*x)^2/b/d/(a+b*(c+d*x)^3)^2+_ + 1/9*(c+d*x)^2/a/b/d/(a+b*(c+d*x)^3)+1/27*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(4/3)/b^(5/3)/d-_ + 1/27*log(a^(1/3)/b^(1/3)+c+d*x)/a^(4/3)/b^(5/3)/d+_ + 1/54*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(4/3)/b^(5/3)/d +--R +--R +--R (715) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +-+3+-+ +-+3+-+ +--R +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 6b d x + 30b c d x + 60b c d x + (60b c - 3a)d x +--R + +--R 4 5 2 +--R (30b c - 6a c)d x + 6b c - 3a c +--R * +--R 3+-+3+-+2 +--R \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R 3+-+3+-+2 +--R \|a \|b +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1483 +a0137:=integrate(t0137,x) +--R +--R +--R (716) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 90b c - 36a b c)d x + (- 36b c - 36a b c )d x - 6b c +--R + +--R 3 2 +--R - 12a b c - 6a +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 6b d x + 30b c d x + 60b c d x + (60b c - 3a)d x +--R + +--R 4 5 2 +--R (30b c - 6a c)d x + 6b c - 3a c +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 716 + +--S 717 of 1483 +m0137:=a0137-r0137 +--R +--R +--R (717) +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R 2\|3 \|- a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|- a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 54a b d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1483 +d0137:=D(m0137,x) +--R +--R +--R (718) 0 +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1483 +t0138:= (c+d*x)^3/(a+b*(c+d*x)^3)^3 +--R +--R +--R (719) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 719 + +--S 720 of 1483 +r0138:= -1/6*(c+d*x)/b/d/(a+b*(c+d*x)^3)^2+_ + 1/18*(c+d*x)/a/b/d/(a+b*(c+d*x)^3)+1/27*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(5/3)/b^(4/3)/d+_ + 1/27*log(a^(1/3)/b^(1/3)+c+d*x)/a^(5/3)/b^(4/3)/d-_ + 1/54*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(5/3)/b^(4/3)/d +--R +--R +--R (720) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +-+3+-+ +-+3+-+ +--R +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (3b d x + 12b c d x + 18b c d x + (12b c - 6a)d x + 3b c - 6a c) +--R * +--R 3+-+2 3+-+ +--R \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R 3+-+2 3+-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1483 +a0138:=integrate(t0138,x) +--R +--R +--R (721) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (3b d x + 12b c d x + 18b c d x + (12b c - 6a)d x + 3b c - 6a c) +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 721 + +--S 722 of 1483 +m0138:=a0138-r0138 +--R +--R +--R (722) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3| 2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|3 \|a b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +---+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R - 2\|3 \|a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 54a b d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1483 +d0138:=D(m0138,x) +--R +--R +--R (723) 0 +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1483 +t0139:= (c+d*x)/(a+b*(c+d*x)^3)^3 +--R +--R +--R (724) +--R d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 724 + +--S 725 of 1483 +r0139:= 1/6*(c+d*x)^2/a/d/(a+b*(c+d*x)^3)^2+_ + 2/9*(c+d*x)^2/a^2/d/(a+b*(c+d*x)^3)+2/27*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(7/3)/b^(2/3)/d-_ + 2/27*log(a^(1/3)/b^(1/3)+c+d*x)/a^(7/3)/b^(2/3)/d+_ + 1/27*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(7/3)/b^(2/3)/d +--R +--R +--R (725) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 4b d x - 24b c d x - 60b c d x + (- 80b c - 8a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 60b c - 24a b c)d x + (- 24b c - 24a b c )d x - 4b c - 8a b c +--R + +--R 2 +--R - 4a +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 4b d x + 24b c d x + 60b c d x + (80b c + 8a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (60b c + 24a b c)d x + (24b c + 24a b c )d x + 4b c + 8a b c + 4a +--R * +--R +-+3+-+ +-+3+-+ +--R +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d x + 60b c d x + 120b c d x + (120b c + 21a)d x +--R + +--R 4 5 2 +--R (60b c + 42a c)d x + 12b c + 21a c +--R * +--R 3+-+3+-+2 +--R \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R 3+-+3+-+2 +--R \|a \|b +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1483 +a0139:=integrate(t0139,x) +--R +--R +--R (726) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 4b d x + 24b c d x + 60b c d x + (80b c + 8a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (60b c + 24a b c)d x + (24b c + 24a b c )d x + 4b c + 8a b c + 4a +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 12b d x - 72b c d x - 180b c d x + (- 240b c - 24a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 180b c - 72a b c)d x + (- 72b c - 72a b c )d x - 12b c +--R + +--R 3 2 +--R - 24a b c - 12a +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d x + 60b c d x + 120b c d x + (120b c + 21a)d x +--R + +--R 4 5 2 +--R (60b c + 42a c)d x + 12b c + 21a c +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 726 + +--S 727 of 1483 +m0139:=a0139-r0139 +--R +--R +--R (727) +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R 2\|3 \|- a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 6\|- a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 27a d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1483 +d0139:=D(m0139,x) +--R +--R +--R (728) 0 +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1483 +t0140:= 1/(a+b*(c+d*x)^3)^3 +--R +--R +--R (729) +--R 1 +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 729 + +--S 730 of 1483 +r0140:= 1/6*(c+d*x)/a/d/(a+b*(c+d*x)^3)^2+_ + 5/18*(c+d*x)/a^2/d/(a+b*(c+d*x)^3)+5/27*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(8/3)/b^(1/3)/d+_ + 5/27*log(a^(1/3)/b^(1/3)+c+d*x)/a^(8/3)/b^(1/3)/d-_ + 5/54*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(8/3)/b^(1/3)/d +--R +--R +--R (730) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R 3+-+ 3+-+ +--R (d x + c)\|b + \|a +--R log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +-+3+-+ +-+3+-+ +--R +-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R 3+-+2 3+-+ +--R \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R 3+-+2 3+-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1483 +a0140:=integrate(t0140,x) +--R +--R +--R (731) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 30b d x + 180b c d x + 450b c d x + (600b c + 60a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (450b c + 180a b c)d x + (180b c + 180a b c )d x + 30b c +--R + +--R 3 2 +--R 60a b c + 30a +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 731 + +--S 732 of 1483 +m0140:=a0140-r0140 +--R +--R +--R (732) +--R - +--R +-+3+-+2 3+-+ +--R 5\|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 10\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3| 2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R 5\|3 \|a b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R +---+ 3+-+ 3+-+ +--R +-+3| 2 (d x + c)\|b + \|a +--R - 10\|3 \|a b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 30\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ +-+3+-+ +-+3+-+ +--R 3| 2 (2d x + 2c)\|3 \|b - \|3 \|a +--R - 30\|a b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 54a d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1483 +d0140:=D(m0140,x) +--R +--R +--R (733) 0 +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1483 +t0141:= 1/(c+d*x)^2/(a+b*(c+d*x)^3)^3 +--R +--R +--R (734) +--R 1 +--R / +--R 3 11 11 3 10 10 3 2 9 9 3 3 2 8 8 +--R b d x + 11b c d x + 55b c d x + (165b c + 3a b )d x +--R + +--R 3 4 2 7 7 3 5 2 2 6 6 +--R (330b c + 24a b c)d x + (462b c + 84a b c )d x +--R + +--R 3 6 2 3 2 5 5 3 7 2 4 2 4 4 +--R (462b c + 168a b c + 3a b)d x + (330b c + 210a b c + 15a b c)d x +--R + +--R 3 8 2 5 2 2 3 3 +--R (165b c + 168a b c + 30a b c )d x +--R + +--R 3 9 2 6 2 3 3 2 2 +--R (55b c + 84a b c + 30a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 3 11 2 8 2 5 +--R (11b c + 24a b c + 15a b c + 2a c)d x + b c + 3a b c + 3a b c +--R + +--R 3 2 +--R a c +--R Type: Fraction(Polynomial(Integer)) +--E 734 + +--S 735 of 1483 +r0141:= -1/a^3/d/(c+d*x)-1/6*b*(c+d*x)^2/a^2/d/(a+b*(c+d*x)^3)^2-_ + 5/9*b*(c+d*x)^2/a^3/d/(a+b*(c+d*x)^3)-_ + 14/27*b^(1/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(10/3)/d+_ + 14/27*b^(1/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(10/3)/d-_ + 7/27*b^(1/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(10/3)/d +--R +--R +--R (735) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R 3+-+ 3+-+ +--R 3+-+ (d x + c)\|b + \|a +--R \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 28b d x - 196b c d x - 588b c d x + (- 980b c - 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 980b c - 224a b c)d x + (- 588b c - 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 196b c - 224a b c - 28a )d x - 28b c - 56a b c - 28a c +--R * +--R +-+3+-+ +-+3+-+ +--R +-+3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 \|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R 3+-+ +--R \|a +--R / +--R 3 2 8 7 3 2 7 6 3 2 2 6 5 3 2 3 4 5 4 +--R 54a b d x + 378a b c d x + 1134a b c d x + (1890a b c + 108a b)d x +--R + +--R 3 2 4 4 4 3 3 2 5 4 2 3 2 +--R (1890a b c + 432a b c)d x + (1134a b c + 648a b c )d x +--R + +--R 3 2 6 4 3 5 2 3 2 7 4 4 5 +--R (378a b c + 432a b c + 54a )d x + (54a b c + 108a b c + 54a c)d +--R * +--R 3+-+ +--R \|a +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1483 +a0141:=integrate(t0141,x) +--R +--R +--R (736) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 84b d x + 588b c d x + 1764b c d x + (2940b c + 168a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (2940b c + 672a b c)d x + (1764b c + 1008a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (588b c + 672a b c + 84a )d x + 84b c + 168a b c + 84a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 8 7 3 2 7 6 3 2 2 6 5 3 2 3 4 5 4 +--R 54a b d x + 378a b c d x + 1134a b c d x + (1890a b c + 108a b)d x +--R + +--R 3 2 4 4 4 3 3 2 5 4 2 3 2 +--R (1890a b c + 432a b c)d x + (1134a b c + 648a b c )d x +--R + +--R 3 2 6 4 3 5 2 3 2 7 4 4 5 +--R (378a b c + 432a b c + 54a )d x + (54a b c + 108a b c + 54a c)d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 736 + +--S 737 of 1483 +m0141:=a0141-r0141 +--R +--R +--R (737) +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 14\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+ (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R 7\|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ (d x + c)\|b + \|a +--R - 14\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 7\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+ (2d x + 2c)\|3 \|b - \|3 \|a +--R 42\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 42\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 3 +-+3+-+ +--R 27a d\|3 \|a +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1483 +d0141:=D(m0141,x) +--R +--R +--R (738) 0 +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1483 +t0142:= 1/(c+d*x)^3/(a+b*(c+d*x)^3)^3 +--R +--R +--R (739) +--R 1 +--R / +--R 3 12 12 3 11 11 3 2 10 10 3 3 2 9 9 +--R b d x + 12b c d x + 66b c d x + (220b c + 3a b )d x +--R + +--R 3 4 2 8 8 3 5 2 2 7 7 +--R (495b c + 27a b c)d x + (792b c + 108a b c )d x +--R + +--R 3 6 2 3 2 6 6 3 7 2 4 2 5 5 +--R (924b c + 252a b c + 3a b)d x + (792b c + 378a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 4 4 +--R (495b c + 378a b c + 45a b c )d x +--R + +--R 3 9 2 6 2 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 2 2 +--R (66b c + 108a b c + 45a b c + 3a c)d x +--R + +--R 3 11 2 8 2 5 3 2 3 12 2 9 2 6 +--R (12b c + 27a b c + 18a b c + 3a c )d x + b c + 3a b c + 3a b c +--R + +--R 3 3 +--R a c +--R Type: Fraction(Polynomial(Integer)) +--E 739 + +--S 740 of 1483 +r0142:= -1/2/a^3/d/(c+d*x)^2-1/6*b*(c+d*x)/a^2/d/(a+b*(c+d*x)^3)^2-_ + 11/18*b*(c+d*x)/a^3/d/(a+b*(c+d*x)^3)-_ + 20/27*b^(2/3)*atan(-1/3*3^(1/2)+_ + 2/3*b^(1/3)*(c+d*x)*3^(1/2)/a^(1/3))*3^(1/2)/a^(11/3)/d-_ + 20/27*b^(2/3)*log(a^(1/3)/b^(1/3)+c+d*x)/a^(11/3)/d+_ + 10/27*b^(2/3)*log(a^(2/3)/b^(2/3)-a^(1/3)*(c+d*x)/b^(1/3)+_ + (c+d*x)^2)/a^(11/3)/d +--R +--R +--R (740) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 20b d x + 160b c d x + 560b c d x + (1120b c + 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (1400b c + 200a b c)d x + (1120b c + 400a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (560b c + 400a b c + 20a )d x + (160b c + 200a b c + 40a c)d x +--R + +--R 2 8 5 2 2 +--R 20b c + 40a b c + 20a c +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 40b d x - 320b c d x - 1120b c d x + (- 2240b c - 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 2800b c - 400a b c)d x + (- 2240b c - 800a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 1120b c - 800a b c - 40a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 320b c - 400a b c - 80a c)d x - 40b c - 80a b c - 40a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (d x + c)\|b + \|a +--R \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 40b d x - 320b c d x - 1120b c d x + (- 2240b c - 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 2800b c - 400a b c)d x + (- 2240b c - 800a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 1120b c - 800a b c - 40a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 320b c - 400a b c - 80a c)d x - 40b c - 80a b c - 40a c +--R * +--R +-+3+-+ +-+3+-+ +--R +-+3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R \|3 \|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R 3+-+2 +--R \|a +--R / +--R 3 2 9 8 3 2 8 7 3 2 2 7 6 3 2 3 4 6 5 +--R 54a b d x + 432a b c d x + 1512a b c d x + (3024a b c + 108a b)d x +--R + +--R 3 2 4 4 5 4 3 2 5 4 2 4 3 +--R (3780a b c + 540a b c)d x + (3024a b c + 1080a b c )d x +--R + +--R 3 2 6 4 3 5 3 2 +--R (1512a b c + 1080a b c + 54a )d x +--R + +--R 3 2 7 4 4 5 2 3 2 8 4 5 5 2 +--R (432a b c + 540a b c + 108a c)d x + (54a b c + 108a b c + 54a c )d +--R * +--R 3+-+2 +--R \|a +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1483 +a0142:=integrate(t0142,x) +--R +--R +--R (741) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 20b d x - 160b c d x - 560b c d x + (- 1120b c - 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 1400b c - 200a b c)d x + (- 1120b c - 400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 560b c - 400a b c - 20a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 160b c - 200a b c - 40a c)d x - 20b c - 40a b c - 20a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 40b d x + 320b c d x + 1120b c d x + (2240b c + 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (2800b c + 400a b c)d x + (2240b c + 800a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (1120b c + 800a b c + 40a )d x + (320b c + 400a b c + 80a c)d x +--R + +--R 2 8 5 2 2 +--R 40b c + 80a b c + 40a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 120b d x - 960b c d x - 3360b c d x + (- 6720b c - 240a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 8400b c - 1200a b c)d x + (- 6720b c - 2400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 3360b c - 2400a b c - 120a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 960b c - 1200a b c - 240a c)d x - 120b c - 240a b c - 120a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 9 8 3 2 8 7 3 2 2 7 6 3 2 3 4 6 5 +--R 54a b d x + 432a b c d x + 1512a b c d x + (3024a b c + 108a b)d x +--R + +--R 3 2 4 4 5 4 3 2 5 4 2 4 3 +--R (3780a b c + 540a b c)d x + (3024a b c + 1080a b c )d x +--R + +--R 3 2 6 4 3 5 3 2 +--R (1512a b c + 1080a b c + 54a )d x +--R + +--R 3 2 7 4 4 5 2 3 2 8 4 5 5 2 +--R (432a b c + 540a b c + 108a c)d x + (54a b c + 108a b c + 54a c )d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 741 + +--S 742 of 1483 +m0142:=a0142-r0142 +--R +--R +--R (742) +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 10\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R +-+3+-+2 (d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a +--R - 10\|3 \|b log(-------------------------------------------------------) +--R 3+-+2 +--R \|b +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 (d x + c)\|b + \|a +--R 20\|3 \|b log(--------------------) +--R 3+-+ +--R \|b +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 20\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +-+3+-+ +-+3+-+ +--R 3+-+2 (2d x + 2c)\|3 \|b - \|3 \|a +--R 60\|b atan(------------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 60 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 3 +-+3+-+2 +--R 27a d\|3 \|a +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1483 +d0142:=D(m0142,x) +--R +--R +--R (743) 0 +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1483 +t0143:= 1/(a+b*x^4) +--R +--R +--R 1 +--R (744) -------- +--R 4 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 744 + +--S 745 of 1483 +r0143:= 1/2*(atan((-b)^(1/4)*x/a^(1/4))+_ + atanh((-b)^(1/4)*x/a^(1/4)))/a^(3/4)/(-b)^(1/4) +--R +--R +--R 4+---+ 4+---+ +--R x\|- b x\|- b +--R atanh(-------) + atan(-------) +--R 4+-+ 4+-+ +--R \|a \|a +--R (745) ------------------------------ +--R 4+---+4+-+3 +--R 2\|- b \|a +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1483 +a0143:=integrate(t0143,x) +--R +--R +--R (746) +--R +--------+ +--------+ +--------+ +--------+ +--R | 1 | 1 | 1 | 1 +--R |- ------ log(4a |- ------ + x) - |- ------ log(- 4a |- ------ + x) +--R 4| 3 4| 3 4| 3 4| 3 +--R \| 256a b \| 256a b \| 256a b \| 256a b +--R + +--R +--------+ +--R | 1 +--R 4a |- ------ +--R +--------+ 4| 3 +--R | 1 \| 256a b +--R - 2 |- ------ atan(-------------) +--R 4| 3 x +--R \| 256a b +--R Type: Union(Expression(Integer),...) +--E 746 + +--S 747 of 1483 +m0143:=a0143-r0143 +--R +--R +--R (747) +--R +--------+ +--------+ +--R 4+---+ | 1 4+-+3 | 1 +--R 2\|- b |- ------ \|a log(4a |- ------ + x) +--R 4| 3 4| 3 +--R \| 256a b \| 256a b +--R + +--R +--------+ +--------+ 4+---+ +--R 4+---+ | 1 4+-+3 | 1 x\|- b +--R - 2\|- b |- ------ \|a log(- 4a |- ------ + x - atanh(-------) +--R 4| 3 4| 3 4+-+ +--R \| 256a b \| 256a b \|a +--R + +--R +--------+ +--R | 1 +--R 4a |- ------ +--R +--------+ 4| 3 4+---+ +--R 4+---+ | 1 4+-+3 \| 256a b x\|- b +--R - 4\|- b |- ------ \|a atan(------------- - atan(-------) +--R 4| 3 x 4+-+ +--R \| 256a b \|a +--R / +--R 4+---+4+-+3 +--R 2\|- b \|a +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1483 +d0143:=D(m0143,x) +--R +--R +--R (748) 0 +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1483 +t0144:= x^4/(a-b*x^4) +--R +--R +--R 4 +--R x +--R (749) - -------- +--R 4 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 749 + +--S 750 of 1483 +r0144:= 1/2/b^(5/4)*(-2*b^(1/4)*x+_ + a^(1/4)*atan(b^(1/4)*x/a^(1/4))+a^(1/4)*atanh(b^(1/4)*x/a^(1/4))) +--R +--R +--R 4+-+ 4+-+ +--R 4+-+ x\|b 4+-+ x\|b 4+-+ +--R \|a atanh(-----) + \|a atan(-----) - 2x\|b +--R 4+-+ 4+-+ +--R \|a \|a +--R (750) ------------------------------------------- +--R 4+-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1483 +a0144:=integrate(t0144,x) +--R +--R +--R (751) +--R +-----+ +-----+ +-----+ +-----+ +--R | a | a | a | a +--R b |----- log(4b |----- + x - b |----- log(- 4b |----- + x) +--R 4| 5 4| 5 4| 5 4| 5 +--R \|256b \|256b \|256b \|256b +--R + +--R +-----+ +--R | a +--R 4b |----- +--R +-----+ 4| 5 +--R | a \|256b +--R - 2b |----- atan(---------- - x +--R 4| 5 x +--R \|256b +--R / +--R b +--R Type: Union(Expression(Integer),...) +--E 751 + +--S 752 of 1483 +m0144:=a0144-r0144 +--R +--R +--R (752) +--R +-----+ +-----+ +-----+ +-----+ +--R | a 4+-+ | a | a 4+-+ | a +--R 2b |----- \|b log(4b |----- + x - 2b |----- \|b log(- 4b |----- + x) +--R 4| 5 4| 5 4| 5 4| 5 +--R \|256b \|256b \|256b \|256b +--R + +--R +-----+ +--R | a +--R 4b |----- +--R 4+-+ 4+-+ +-----+ 4| 5 +--R 4+-+ x\|b 4+-+ x\|b | a 4+-+ \|256b +--R - \|a atanh(-----) - \|a atan(-----) - 4b |----- \|b atan(----------) +--R 4+-+ 4+-+ 4| 5 x +--R \|a \|a \|256b +--R / +--R 4+-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1483 +d0144:=D(m0144,x) +--R +--R +--R (753) 0 +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1483 +t0145:= x^2/(a-b*x^4) +--R +--R +--R 2 +--R x +--R (754) - -------- +--R 4 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 754 + +--S 755 of 1483 +r0145:= -1/2*(atan(b^(1/4)*x/a^(1/4))-_ + atanh(b^(1/4)*x/a^(1/4)))/a^(1/4)/b^(3/4) +--R +--R +--R 4+-+ 4+-+ +--R x\|b x\|b +--R atanh(-----) - atan(-----) +--R 4+-+ 4+-+ +--R \|a \|a +--R (755) -------------------------- +--R 4+-+4+-+3 +--R 2\|a \|b +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1483 +a0145:=integrate(t0145,x) +--R +--R +--R (756) +--R +-------+ +-------+3 +--R | 1 2 | 1 +--R |------- log(64a b |------- + x) +--R 4| 3 4| 3 +--R \|256a b \|256a b +--R + +--R +-------+3 +--R 2 | 1 +--R 64a b |------- +--R +-------+ +-------+3 +-------+ 4| 3 +--R | 1 2 | 1 | 1 \|256a b +--R - |------- log(- 64a b |------- + x) + 2 |------- atan(-----------------) +--R 4| 3 4| 3 4| 3 x +--R \|256a b \|256a b \|256a b +--R Type: Union(Expression(Integer),...) +--E 756 + +--S 757 of 1483 +m0145:=a0145-r0145 +--R +--R +--R (757) +--R +-------+ +-------+3 +--R | 1 4+-+4+-+3 2 | 1 +--R 2 |------- \|a \|b log(64a b |------- + x) +--R 4| 3 4| 3 +--R \|256a b \|256a b +--R + +--R +-------+ +-------+3 4+-+ +--R | 1 4+-+4+-+3 2 | 1 x\|b +--R - 2 |------- \|a \|b log(- 64a b |------- + x - atanh(-----) +--R 4| 3 4| 3 4+-+ +--R \|256a b \|256a b \|a +--R + +--R +-------+3 +--R 2 | 1 +--R 64a b |------- +--R 4+-+ +-------+ 4| 3 +--R x\|b | 1 4+-+4+-+3 \|256a b +--R atan(-----) + 4 |------- \|a \|b atan(-----------------) +--R 4+-+ 4| 3 x +--R \|a \|256a b +--R / +--R 4+-+4+-+3 +--R 2\|a \|b +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1483 +d0145:=D(m0145,x) +--R +--R +--R (758) 0 +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1483 +t0146:= 1/(a-b*x^4) +--R +--R +--R 1 +--R (759) - -------- +--R 4 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 759 + +--S 760 of 1483 +r0146:= 1/2*(atan(b^(1/4)*x/a^(1/4))+_ + atanh(b^(1/4)*x/a^(1/4)))/a^(3/4)/b^(1/4) +--R +--R +--R 4+-+ 4+-+ +--R x\|b x\|b +--R atanh(-----) + atan(-----) +--R 4+-+ 4+-+ +--R \|a \|a +--R (760) -------------------------- +--R 4+-+3 4+-+ +--R 2\|a \|b +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1483 +a0146:=integrate(t0146,x) +--R +--R +--R (761) +--R +------+ +------+ +------+ +------+ +--R | 1 | 1 | 1 | 1 +--R |------ log(4a |------ + x) - |------ log(- 4a |------ + x) +--R 4| 3 4| 3 4| 3 4| 3 +--R \|256a b \|256a b \|256a b \|256a b +--R + +--R +------+ +--R | 1 +--R 4a |------ +--R +------+ 4| 3 +--R | 1 \|256a b +--R - 2 |------ atan(-----------) +--R 4| 3 x +--R \|256a b +--R Type: Union(Expression(Integer),...) +--E 761 + +--S 762 of 1483 +m0146:=a0146-r0146 +--R +--R +--R (762) +--R +------+ +------+ +--R | 1 4+-+3 4+-+ | 1 +--R 2 |------ \|a \|b log(4a |------ + x) +--R 4| 3 4| 3 +--R \|256a b \|256a b +--R + +--R +------+ +------+ 4+-+ 4+-+ +--R | 1 4+-+3 4+-+ | 1 x\|b x\|b +--R - 2 |------ \|a \|b log(- 4a |------ + - atanh(-----) - atan(-----) +--R 4| 3 4| 3 4+-+ 4+-+ +--R \|256a b \|256a b \|a \|a +--R + +--R +------+ +--R | 1 +--R 4a |------ +--R +------+ 4| 3 +--R | 1 4+-+3 4+-+ \|256a b +--R - 4 |------ \|a \|b atan(-----------) +--R 4| 3 x +--R \|256a b +--R / +--R 4+-+3 4+-+ +--R 2\|a \|b +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1483 +d0146:=D(m0146,x) +--R +--R +--R (763) 0 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1483 +t0147:= 1/x^4/(a-b*x^4) +--R +--R +--R 1 +--R (764) - ----------- +--R 8 4 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 764 + +--S 765 of 1483 +r0147:= -1/3/a/x^3+1/2*b^(3/4)*atan(b^(1/4)*x/a^(1/4))/a^(7/4)+_ + 1/2*b^(3/4)*atanh(b^(1/4)*x/a^(1/4))/a^(7/4) +--R +--R +--R 4+-+ 4+-+ +--R 3 4+-+3 x\|b 3 4+-+3 x\|b 4+-+3 +--R 3x \|b atanh(----- + 3x \|b atan(----- - 2\|a +--R 4+-+ 4+-+ +--R \|a \|a +--R (765) --------------------------------------------------- +--R 3 4+-+3 +--R 6a x \|a +--R Type: Expression(Integer) +--E 765 + +--S 766 of 1483 +a0147:=integrate(t0147,x) +--R +--R +--R (766) +--R +-----+ +-----+ +--R | 3 | 3 +--R 3 | b 2 | b +--R 3a x |----- log(4a |----- + b x) +--R 4| 7 4| 7 +--R \|256a \|256a +--R + +--R +-----+ +--R | 3 +--R 2 | b +--R +-----+ +-----+ +-----+ 4a |----- +--R | 3 | 3 | 3 4| 7 +--R 3 | b 2 | b 3 | b \|256a +--R - 3a x |----- log(- 4a |----- + b x - 6a x |----- atan(-----------) +--R 4| 7 4| 7 4| 7 b x +--R \|256a \|256a \|256a +--R + +--R - 1 +--R / +--R 3 +--R 3a x +--R Type: Union(Expression(Integer),...) +--E 766 + +--S 767 of 1483 +m0147:=a0147-r0147 +--R +--R +--R (767) +--R +-----+ +-----+ +--R | 3 | 3 +--R 4+-+3 | b 2 | b +--R 2a \|a |----- log(4a |----- + b x) +--R 4| 7 4| 7 +--R \|256a \|256a +--R + +--R +-----+ +-----+ +--R | 3 | 3 4+-+ +--R 4+-+3 | b 2 | b 4+-+3 x\|b +--R - 2a \|a |----- log(- 4a |----- + b x - \|b atanh(-----) +--R 4| 7 4| 7 4+-+ +--R \|256a \|256a \|a +--R + +--R +-----+ +--R | 3 +--R 2 | b +--R +-----+ 4a |----- +--R | 3 4| 7 4+-+ +--R 4+-+3 | b \|256a 4+-+3 x\|b +--R - 4a \|a |----- atan(----------- - \|b atan(-----) +--R 4| 7 b x 4+-+ +--R \|256a \|a +--R / +--R 4+-+3 +--R 2a \|a +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1483 +d0147:=D(m0147,x) +--R +--R +--R (768) 0 +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1483 +t0148:= x^3*(a+b*x^4)^2 +--R +--R +--R 2 11 7 2 3 +--R (769) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 769 + +--S 770 of 1483 +r0148:= 1/12*(a+b*x^4)^3/b +--R +--R +--R 1 3 12 1 2 8 1 2 4 1 3 +--R -- b x + - a b x + - a b x + -- a +--R 12 4 4 12 +--R (770) -------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 770 + +--S 771 of 1483 +a0148:=integrate(t0148,x) +--R +--R +--R 1 2 12 1 8 1 2 4 +--R (771) -- b x + - a b x + - a x +--R 12 4 4 +--R Type: Polynomial(Fraction(Integer)) +--E 771 + +--S 772 of 1483 +m0148:=a0148-r0148 +--R +--R +--R 1 3 +--R -- a +--R 12 +--R (772) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 772 + +--S 773 of 1483 +d0148:=D(m0148,x) +--R +--R +--R (773) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 773 + +--S 774 of 1483 +t0149:= x^3*(a+b*x^4)^3 +--R +--R +--R 3 15 2 11 2 7 3 3 +--R (774) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 774 + +--S 775 of 1483 +r0149:= 1/16*(a+b*x^4)^4/b +--R +--R +--R 1 4 16 1 3 12 3 2 2 8 1 3 4 1 4 +--R -- b x + - a b x + - a b x + - a b x + -- a +--R 16 4 8 4 16 +--R (775) -------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 775 + +--S 776 of 1483 +a0149:=integrate(t0149,x) +--R +--R +--R 1 3 16 1 2 12 3 2 8 1 3 4 +--R (776) -- b x + - a b x + - a b x + - a x +--R 16 4 8 4 +--R Type: Polynomial(Fraction(Integer)) +--E 776 + +--S 777 of 1483 +m0149:=a0149-r0149 +--R +--R +--R 1 4 +--R -- a +--R 16 +--R (777) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 777 + +--S 778 of 1483 +d0149:=D(m0149,x) +--R +--R +--R (778) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 778 + +--S 779 of 1483 +t0150:= (1+x^2)/(1+x^4) +--R +--R +--R 2 +--R x + 1 +--R (779) ------ +--R 4 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 779 + +--S 780 of 1483 +r0150:= 1/2*2^(1/2)*(atan(-1+x*2^(1/2))+atan(1+x*2^(1/2))) +--R +--R +--R +-+ +-+ +-+ +-+ +--R \|2 atan(x\|2 + 1) + \|2 atan(x\|2 - 1) +--R (780) ----------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1483 +a0150:=integrate(t0150,x) +--R +--R +--R +-+ 3 +--R x\|2 x + x +--R atan(-----) + atan(------) +--R 2 +-+ +--R \|2 +--R (781) -------------------------- +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 781 + +--S 782 of 1483 +m0150:=a0150-r0150 +--R +--R +--R +-+ 3 +--R +-+ +-+ x\|2 x + x +--R - atan(x\|2 + 1) - atan(x\|2 - 1) + atan(-----) + atan(------) +--R 2 +-+ +--R \|2 +--R (782) ---------------------------------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1483 +d0150:=D(m0150,x) +--R +--R +--R (783) 0 +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1483 +t0151:= (5+2*x^2)/(-1+x^4) +--R +--R +--R 2 +--R 2x + 5 +--R (784) ------- +--R 4 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 784 + +--S 785 of 1483 +r0151:= -3/2*atan(x)-7/2*atanh(x) +--R +--R +--R - 7atanh(x) - 3atan(x) +--R (785) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 785 + +--S 786 of 1483 +a0151:=integrate(t0151,x) +--R +--R +--R - 7log(x + 1) + 7log(x - 1) - 6atan(x) +--R (786) -------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 786 + +--S 787 of 1483 +m0151:=a0151-r0151 +--R +--R +--R - 7log(x + 1) + 7log(x - 1) + 14atanh(x) +--R (787) ---------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1483 +d0151:=D(m0151,x) +--R +--R +--R (788) 0 +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1483 +t0152:= (c+d*x^2)/(a-b*x^4) +--R +--R +--R 2 +--R - d x - c +--R (789) ---------- +--R 4 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 789 + +--S 790 of 1483 +r0152:= 1/2*(b^(1/2)*c-a^(1/2)*d)*atan(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+_ + 1/2*(b^(1/2)*c+a^(1/2)*d)*atanh(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4) +--R +--R +--R 4+-+ 4+-+ +--R +-+ +-+ x\|b +-+ +-+ x\|b +--R (c\|b + d\|a )atanh(-----) + (c\|b - d\|a )atan(-----) +--R 4+-+ 4+-+ +--R \|a \|a +--R (790) -------------------------------------------------------- +--R 4+-+3 4+-+3 +--R 2\|a \|b +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1483 +a0152:=integrate(t0152,x) +--R +--R +--R (791) +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (16a b d |----------------------- - 2a b c d - 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R - +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (16a b d |----------------------- + 2a b c d + 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (- 16a b d |----------------------- - 2a b c d - 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R - +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (- 16a b d |----------------------- + 2a b c d + 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 791 + +--S 792 of 1483 +m0152:=a0152-r0152 +--R +--R +--R (792) +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R 4+-+3 4+-+3 | \| 64a b +--R \|a \|b |------------------------------------ +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (16a b d |----------------------- - 2a b c d - 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R - +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R 4+-+3 4+-+3 | \| 64a b +--R \|a \|b |-------------------------------------- +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (16a b d |----------------------- + 2a b c d + 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R 4+-+3 4+-+3 | \| 64a b +--R \|a \|b |-------------------------------------- +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (- 16a b d |----------------------- - 2a b c d - 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +--------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |- 4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |-------------------------------------- +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R - +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R 4+-+3 4+-+3 | \| 64a b +--R \|a \|b |------------------------------------ +--R \| 2a b +--R * +--R log +--R +-----------------------+ +--R | 2 4 2 2 2 4 +--R 3 2 |a d + 2a b c d + b c 2 2 2 3 +--R (- 16a b d |----------------------- + 2a b c d + 2a b c ) +--R | 3 3 +--R \| 64a b +--R * +--R +------------------------------------+ +--R | +-----------------------+ +--R | | 2 4 2 2 2 4 +--R | |a d + 2a b c d + b c +--R |4a b |----------------------- + c d +--R | | 3 3 +--R | \| 64a b +--R |------------------------------------ +--R \| 2a b +--R + +--R 2 4 2 4 +--R (a d - b c )x +--R + +--R 4+-+ 4+-+ +--R +-+ +-+ x\|b +-+ +-+ x\|b +--R (- c\|b - d\|a )atanh(-----) + (- c\|b + d\|a )atan(-----) +--R 4+-+ 4+-+ +--R \|a \|a +--R / +--R 4+-+3 4+-+3 +--R 2\|a \|b +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1483 +d0152:=normalize(D(m0152,x)) +--R +--R +--R (793) 0 +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1483 +t0153:= (1+x+x^2+x^3)/(1+x^4) +--R +--R +--R 3 2 +--R x + x + x + 1 +--R (794) --------------- +--R 4 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 794 + +--S 795 of 1483 +r0153:= 1/2*atan(x^2)+1/2*atan(-1+x*2^(1/2))*2^(1/2)+_ + 1/2*atan(1+x*2^(1/2))*2^(1/2)+1/4*log(1+x^4) +--R +--R +--R (795) +--R 4 +-+ +-+ +-+ +-+ 2 +--R log(x + 1) + 2\|2 atan(x\|2 + 1) + 2\|2 atan(x\|2 - 1) + 2atan(x ) +--R --------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 795 + +--S 796 of 1483 +a0153:=integrate(t0153,x) +--R +--R +--R (796) +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R +---------+ (2\|2 - 2) |--------- +--R | +-+ | +-+ +--R |3\|2 + 4 \| 4\|2 +--R - 4 |--------- atan(-----------------------) +--R | +-+ +-+ +--R \| 4\|2 x\|2 - 1 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R +---------+ (2\|2 + 2) |--------- +--R | +-+ | +-+ +--R |3\|2 - 4 \| 4\|2 +-+ 2 +--R - 4 |--------- atan(-----------------------) + log(x\|2 + x + 1) +--R | +-+ +-+ +--R \| 4\|2 x\|2 + 1 +--R + +--R +-+ 2 +--R log(- x\|2 + x + 1) +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 796 + +--S 797 of 1483 +m0153:=a0153-r0153 +--R +--R +--R (797) +--R +---------+ +--R | +-+ +--R +-+ |3\|2 + 4 +--R +---------+ (2\|2 - 2) |--------- +--R | +-+ | +-+ +--R |3\|2 + 4 \| 4\|2 +--R - 4 |--------- atan(-----------------------) +--R | +-+ +-+ +--R \| 4\|2 x\|2 - 1 +--R + +--R +---------+ +--R | +-+ +--R +-+ |3\|2 - 4 +--R +---------+ (2\|2 + 2) |--------- +--R | +-+ | +-+ +--R |3\|2 - 4 \| 4\|2 +-+ 2 +--R - 4 |--------- atan(-----------------------) + log(x\|2 + x + 1) +--R | +-+ +-+ +--R \| 4\|2 x\|2 + 1 +--R + +--R 4 +-+ 2 +-+ +-+ +--R - log(x + 1) + log(- x\|2 + x + 1) - 2\|2 atan(x\|2 + 1) +--R + +--R +-+ +-+ 2 +--R - 2\|2 atan(x\|2 - 1) - 2atan(x ) +--R / +--R 4 +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1483 +d0153:=D(m0153,x) +--R +--R +--R (798) 0 +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1483 +t0154:= (c+d*x+e*x^2+f*x^3)/(a+b*x^4) +--R +--R +--R 3 2 +--R f x + e x + d x + c +--R (799) --------------------- +--R 4 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 799 + +--S 800 of 1483 +r0154:= 1/2*d*atan(b^(1/2)*x^2/a^(1/2))/a^(1/2)/b^(1/2)+1/4*(b^(1/2)*c+_ + a^(1/2)*e)*atan(-1+_ + 2^(1/2)*b^(1/4)*x/a^(1/4))*2^(1/2)/a^(3/4)/b^(3/4)+_ + 1/4*(b^(1/2)*c+_ + a^(1/2)*e)*atan(1+2^(1/2)*b^(1/4)*x/a^(1/4))*2^(1/2)/a^(3/4)/b^(3/4)-_ + 1/8*(b^(1/2)*c-a^(1/2)*e)*log(a^(1/2)/b^(1/2)-_ + 2^(1/2)*a^(1/4)*x/b^(1/4)+_ + x^2)*2^(1/2)/a^(3/4)/b^(3/4)+1/8*(b^(1/2)*c-_ + a^(1/2)*e)*log(a^(1/2)/b^(1/2)+2^(1/2)*a^(1/4)*x/b^(1/4)+_ + x^2)*2^(1/2)/a^(3/4)/b^(3/4)+1/4*f*log(a+b*x^4)/b +--R +--R +--R (800) +--R 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ +-+ 2 +-+ +-+ (x \|b + \|a )\|b + x\|2 \|a \|b +--R (- a b e\|2 \|b + b c\|2 \|a )log(-----------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ +-+ 2 +-+ +-+ (x \|b + \|a )\|b - x\|2 \|a \|b +--R (a b e\|2 \|b - b c\|2 \|a )log(-----------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ x\|2 \|b + \|a +--R (2a b e\|2 \|b + 2b c\|2 \|a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ x\|2 \|b - \|a +--R (2a b e\|2 \|b + 2b c\|2 \|a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+ +--R 4+-+3 4+-+3 x \|b 4 +-+4+-+3 +-+4+-+3 +--R 4b d \|a \|b atan(------ + 2f log(b x + a)\|a \|a \|b \|b +--R +-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 8b\|a \|a \|b \|b +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1483 +a0154:=integrate(t0154,x) +--R +--R +--R (801) +--R b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 - 6a b %%BT0 +--R + +--R 2 2 +--R 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R - b %%BT1 - b %%BT0 + f +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (2a b e - 2a b c e + 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f - 2a b c e + 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R 6a b c d e - 4a b c d + 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 32a b e + 32a b c e - 64a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e + 3a b c d e - 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 4a b c d e - a b c d e + (2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R - +--R b +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R - b %%BT1 - b %%BT0 + f +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 32a b e + 32a b c e - 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e + 8a b c d +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e + 8a b c d +--R * +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 2a b e + 2a b c e - 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e - 4a b c d)f + 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R - 2a b d e - 6a b c d e + 4a b c d - 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 32a b e + 32a b c e - 64a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e + 3a b c d e - 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 4a b c d e - a b c d e + (2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R 2b %%BT1 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (16a b e - 16a b c e + 32a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e + 16a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (64a b e - 64a b c e + 128a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 12a b e + 12a b c e - 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 24a b c d e + 16a b d e - 8a b c d)f - 4a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 4a b d e + 12a b c d e - 8a b c d + 4a b c +--R * +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 3 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 2 +--R (64a b e - 64a b c e + 128a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 3 2 4 +--R (- 24a b e + 24a b c e - 48a b c d )f - 16a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 +--R - 8a b d e + 16a b c e - 24a b c d e - 16a b c d +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (3a e - 3a b c e + 6a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R 5a b c e + a b d e - 4a b c e + 3a b c d e + 6a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 8a b c d e - 3a b c d e + (- 2a b d + a b c d)e +--R + +--R 3 3 3 +--R 3a b c d +--R + +--R 2b %%BT0 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 3 +--R (64a b e - 64a b c e + 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 48a b e + 48a b c e - 96a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e + 16a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (12a b e - 12a b c e + 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 24a b c d e + 16a b d e - 8a b c d)f + 12a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 4 5 +--R 12a b d e - 16a b c e + 36a b c d e + 8a b c d + 4a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R - 3a b c e - 3a b d e + 4a b c e - 9a b c d e - 2a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 3 2 2 2 5 3 4 3 3 3 +--R 3a b d e + 5a b c d e + (- 2a b d + 5a b c d)e - 5a b c d +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 801 + +--S 802 of 1483 +m0154:=a0154-r0154 +--R +--R +--R (802) +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 - 6a b %%BT0 +--R + +--R 2 2 +--R 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 4b\|a \|a \|b \|b %%BT1 - 4b\|a \|a \|b \|b %%BT0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4f\|a \|a \|b \|b +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (2a b e - 2a b c e + 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f - 2a b c e + 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R 6a b c d e - 4a b c d + 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 32a b e + 32a b c e - 64a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e + 3a b c d e - 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 4a b c d e - a b c d e + (2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R - +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 4b\|a \|a \|b \|b %%BT1 - 4b\|a \|a \|b \|b %%BT0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4f\|a \|a \|b \|b +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 32a b e + 32a b c e - 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e + 8a b c d +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e + 8a b c d +--R * +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 2a b e + 2a b c e - 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e - 4a b c d)f + 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R - 2a b d e - 6a b c d e + 4a b c d - 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BT1 + (- 4a b %%BT0 + 4a b f)%%BT1 +--R + +--R 2 2 2 2 +--R - 6a b %%BT0 + 4a b f %%BT0 - a f - 2b c e - b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e - 32a b c e + 64a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 32a b e + 32a b c e - 64a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e - 8a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e - 6a b c e + 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e + 4a b c d)f + 2a b c e - 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d - 2a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e + 3a b c d e - 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 4a b c d e - a b c d e + (2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R +-+4+-+3 +-+4+-+3 +--R 8b\|a \|a \|b \|b %%BT1 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (16a b e - 16a b c e + 32a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e + 16a b c d +--R * +--R 2 +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (64a b e - 64a b c e + 128a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 12a b e + 12a b c e - 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 24a b c d e + 16a b d e - 8a b c d)f - 4a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 4a b d e + 12a b c d e - 8a b c d + 4a b c +--R * +--R %%BT1 +--R + +--R 4 3 3 3 4 2 3 4 2 3 +--R (- 64a b e + 64a b c e - 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 2 +--R (64a b e - 64a b c e + 128a b c d )f %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 3 2 4 +--R (- 24a b e + 24a b c e - 48a b c d )f - 16a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 +--R - 8a b d e + 16a b c e - 24a b c d e - 16a b c d +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (3a e - 3a b c e + 6a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R 5a b c e + a b d e - 4a b c e + 3a b c d e + 6a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 8a b c d e - 3a b c d e + (- 2a b d + a b c d)e +--R + +--R 3 3 3 +--R 3a b c d +--R + +--R +-+4+-+3 +-+4+-+3 +--R 8b\|a \|a \|b \|b %%BT0 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 3 +--R (64a b e - 64a b c e + 128a b c d )%%BT0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 48a b e + 48a b c e - 96a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e + 16a b c d +--R * +--R 2 +--R %%BT0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (12a b e - 12a b c e + 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 24a b c d e + 16a b d e - 8a b c d)f + 12a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 4 5 +--R 12a b d e - 16a b c e + 36a b c d e + 8a b c d + 4a b c +--R * +--R %%BT0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e - a b c e + 8a b c d e + (- 4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d + b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R - 3a b c e - 3a b d e + 4a b c e - 9a b c d e - 2a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 3 2 2 2 5 3 4 3 3 3 +--R 3a b d e + 5a b c d e + (- 2a b d + 5a b c d)e - 5a b c d +--R + +--R 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ +-+ 2 +-+ +-+ (x \|b + \|a )\|b + x\|2 \|a \|b +--R (a b e\|2 \|b - b c\|2 \|a )log(-----------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ +-+ 2 +-+ +-+ (x \|b + \|a )\|b - x\|2 \|a \|b +--R (- a b e\|2 \|b + b c\|2 \|a )log(-----------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ x\|2 \|b + \|a +--R (- 2a b e\|2 \|b - 2b c\|2 \|a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ x\|2 \|b - \|a +--R (- 2a b e\|2 \|b - 2b c\|2 \|a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+ +--R 4+-+3 4+-+3 x \|b 4 +-+4+-+3 +-+4+-+3 +--R - 4b d \|a \|b atan(------ - 2f log(b x + a)\|a \|a \|b \|b +--R +-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 8b\|a \|a \|b \|b +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1483 +d0154:=normalize(D(m0154,x)) +--R +--R +--R (803) 0 +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1483 +t0155:= (1+x+x^2+x^3)/(a-b*x^4) +--R +--R +--R 3 2 +--R - x - x - x - 1 +--R (804) ----------------- +--R 4 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 804 + +--S 805 of 1483 +r0155:= -1/2*(a^(1/2)-b^(1/2))*atan(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+_ + 1/2*(a^(1/2)+b^(1/2))*atanh(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+_ + 1/2*atanh(b^(1/2)*x^2/a^(1/2))/a^(1/2)/b^(1/2)-1/4*log(a-b*x^4)/b +--R +--R +--R (805) +--R 4+-+ 2 +-+ +--R +-+ 2 +-+ x\|b 4+-+3 4+-+3 x \|b +--R (2a b\|b + 2b \|a )atanh(-----) + 2b \|a \|b atanh(------) +--R 4+-+ +-+ +--R \|a \|a +--R + +--R 4+-+ +--R +-+ 2 +-+ x\|b 4 +-+4+-+3 +-+4+-+3 +--R (- 2a b\|b + 2b \|a )atan(-----) - log(- b x + a)\|a \|a \|b \|b +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1483 +a0155:=integrate(t0155,x) +--R +--R +--R (806) +--R b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R - b %%BU1 - b %%BU0 - 1 +--R * +--R log +--R 3 3 2 3 3 2 2 3 3 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 + (- 8a b + 8a b )%%BU0 +--R + +--R 3 2 2 3 +--R 2a b - 4a b + 2a b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R 3 3 2 3 3 2 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (32a b %%BU0 + 32a b %%BU0 - 2a b - 4a b + 6a b)%%BU1 +--R + +--R 2 3 3 2 2 3 2 2 3 +--R (- 8a b + 8a b )%%BU0 + (- 2a b - 4a b + 6a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x + a b - 2a b + a +--R + +--R - +--R b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R - b %%BU1 - b %%BU0 - 1 +--R * +--R log +--R 3 3 2 3 3 2 2 3 3 2 +--R (- 32a b %%BU0 + 8a b - 8a b )%%BU1 + (8a b - 8a b )%%BU0 +--R + +--R 3 2 2 3 +--R - 2a b + 4a b - 2a b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R 3 3 2 3 3 2 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (32a b %%BU0 + 32a b %%BU0 - 2a b - 4a b + 6a b)%%BU1 +--R + +--R 2 3 3 2 2 3 2 2 3 +--R (- 8a b + 8a b )%%BU0 + (- 2a b - 4a b + 6a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x + a b - 2a b + a +--R + +--R 2b %%BU1 +--R * +--R log +--R 3 3 2 3 3 2 2 +--R (- 64a b %%BU0 + 16a b - 16a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (- 64a b %%BU0 - 64a b %%BU0 + 4a b + 8a b - 12a b)%%BU1 +--R + +--R 3 3 3 3 2 2 2 2 3 +--R - 64a b %%BU0 - 64a b %%BU0 + (24a b - 24a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x - 3a b + 6a b - 3a +--R + +--R 2b %%BU0 +--R * +--R log +--R 3 3 3 2 3 3 2 2 +--R 64a b %%BU0 + (16a b + 48a b )%%BU0 +--R + +--R 3 2 2 3 3 2 2 2 2 +--R (4a b - 16a b + 12a b)%%BU0 + (b - 2a b + a b)x + a b - 2a b +--R + +--R 3 +--R a +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 806 + +--S 807 of 1483 +m0155:=a0155-r0155 +--R +--R +--R (807) +--R +-+4+-+3 +-+4+-+3 +--R 2b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 2b\|a \|a \|b \|b %%BU1 - 2b\|a \|a \|b \|b %%BU0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R - 2\|a \|a \|b \|b +--R * +--R log +--R 3 3 2 3 3 2 2 3 3 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 + (- 8a b + 8a b )%%BU0 +--R + +--R 3 2 2 3 +--R 2a b - 4a b + 2a b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R 3 3 2 3 3 2 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (32a b %%BU0 + 32a b %%BU0 - 2a b - 4a b + 6a b)%%BU1 +--R + +--R 2 3 3 2 2 3 2 2 3 +--R (- 8a b + 8a b )%%BU0 + (- 2a b - 4a b + 6a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x + a b - 2a b + a +--R + +--R - +--R +-+4+-+3 +-+4+-+3 +--R 2b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 2b\|a \|a \|b \|b %%BU1 - 2b\|a \|a \|b \|b %%BU0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R - 2\|a \|a \|b \|b +--R * +--R log +--R 3 3 2 3 3 2 2 3 3 2 +--R (- 32a b %%BU0 + 8a b - 8a b )%%BU1 + (8a b - 8a b )%%BU0 +--R + +--R 3 2 2 3 +--R - 2a b + 4a b - 2a b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BU1 + (- 4a b %%BU0 - 4a b)%%BU1 - 6a b %%BU0 +--R + +--R - 4a b %%BU0 + 3b - a +--R / +--R 2 +--R 2a b +--R + +--R 3 3 2 3 3 2 2 +--R (32a b %%BU0 - 8a b + 8a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (32a b %%BU0 + 32a b %%BU0 - 2a b - 4a b + 6a b)%%BU1 +--R + +--R 2 3 3 2 2 3 2 2 3 +--R (- 8a b + 8a b )%%BU0 + (- 2a b - 4a b + 6a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x + a b - 2a b + a +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b %%BU1 +--R * +--R log +--R 3 3 2 3 3 2 2 +--R (- 64a b %%BU0 + 16a b - 16a b )%%BU1 +--R + +--R 3 3 2 3 2 3 2 2 3 +--R (- 64a b %%BU0 - 64a b %%BU0 + 4a b + 8a b - 12a b)%%BU1 +--R + +--R 3 3 3 3 2 2 2 2 3 +--R - 64a b %%BU0 - 64a b %%BU0 + (24a b - 24a b)%%BU0 +--R + +--R 3 2 2 2 2 3 +--R (b - 2a b + a b)x - 3a b + 6a b - 3a +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b %%BU0 +--R * +--R log +--R 3 3 3 2 3 3 2 2 +--R 64a b %%BU0 + (16a b + 48a b )%%BU0 +--R + +--R 3 2 2 3 3 2 2 2 2 +--R (4a b - 16a b + 12a b)%%BU0 + (b - 2a b + a b)x + a b - 2a b +--R + +--R 3 +--R a +--R + +--R 4+-+ 2 +-+ +--R +-+ 2 +-+ x\|b 4+-+3 4+-+3 x \|b +--R (- 2a b\|b - 2b \|a )atanh(-----) - 2b \|a \|b atanh(------) +--R 4+-+ +-+ +--R \|a \|a +--R + +--R 4+-+ +--R +-+ 2 +-+ x\|b 4 +-+4+-+3 +-+4+-+3 +--R (2a b\|b - 2b \|a )atan(-----) + log(- b x + a)\|a \|a \|b \|b +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1483 +d0155:=normalize(D(m0155,x)) +--R +--R +--R (808) 0 +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1483 +t0156:= (c+d*x+e*x^2+f*x^3)/(a-b*x^4) +--R +--R +--R 3 2 +--R - f x - e x - d x - c +--R (809) ----------------------- +--R 4 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 809 + +--S 810 of 1483 +r0156:= 1/2*(b^(1/2)*c-a^(1/2)*e)*atan(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+_ + 1/2*(b^(1/2)*c+a^(1/2)*e)*atanh(b^(1/4)*x/a^(1/4))/a^(3/4)/b^(3/4)+_ + 1/2*d*atanh(b^(1/2)*x^2/a^(1/2))/a^(1/2)/b^(1/2)-1/4*f*log(a-b*x^4)/b +--R +--R +--R (810) +--R 4+-+ 2 +-+ +--R +-+ 2 +-+ x\|b 4+-+3 4+-+3 x \|b +--R (2a b e\|b + 2b c\|a )atanh(-----) + 2b d \|a \|b atanh(------) +--R 4+-+ +-+ +--R \|a \|a +--R + +--R 4+-+ +--R +-+ 2 +-+ x\|b 4 +-+4+-+3 +-+4+-+3 +--R (- 2a b e\|b + 2b c\|a )atan(-----) - f log(- b x + a)\|a \|a \|b \|b +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1483 +a0156:=integrate(t0156,x) +--R +--R +--R (811) +--R b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 - 6a b %%BV0 +--R + +--R 2 2 +--R - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R - b %%BV1 - b %%BV0 - f +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e + 8a b c d +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e + 8a b c d +--R * +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (2a b e + 2a b c e - 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f + 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R - 2a b d e + 6a b c d e - 4a b c d - 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (32a b e + 32a b c e - 64a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e - 3a b c d e + 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 4a b c d e + a b c d e + (- 2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R - +--R b +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R - b %%BV1 - b %%BV0 - f +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 32a b e - 32a b c e + 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e - 8a b c d +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e - 8a b c d +--R * +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 2a b e - 2a b c e + 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e - 4a b c d)f - 2a b c e + 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d + 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (32a b e + 32a b c e - 64a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e - 3a b c d e + 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 4a b c d e + a b c d e + (- 2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R 2b %%BV1 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 16a b e - 16a b c e + 32a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e - 16a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 64a b e - 64a b c e + 128a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 12a b e - 12a b c e + 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (24a b c d e - 16a b d e - 8a b c d)f + 4a b c e - 4a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R 12a b c d e - 8a b c d - 4a b c +--R * +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 3 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 2 +--R (- 64a b e - 64a b c e + 128a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 3 2 4 +--R (- 24a b e - 24a b c e + 48a b c d )f + 16a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 +--R 8a b d e + 16a b c e - 24a b c d e - 16a b c d +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- 3a e - 3a b c e + 6a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R 5a b c e + a b d e + 4a b c e - 3a b c d e - 6a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 8a b c d e + 3a b c d e + (2a b d + a b c d)e +--R + +--R 3 3 3 +--R 3a b c d +--R + +--R 2b %%BV0 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 3 +--R (64a b e + 64a b c e - 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (48a b e + 48a b c e - 96a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e - 16a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (12a b e + 12a b c e - 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (24a b c d e - 16a b d e - 8a b c d)f - 12a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 4 5 +--R - 12a b d e - 16a b c e + 36a b c d e + 8a b c d - 4a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R - 3a b c e - 3a b d e - 4a b c e + 9a b c d e + 2a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 3 2 2 2 5 3 4 3 3 3 +--R 3a b d e - 5a b c d e + (2a b d + 5a b c d)e - 5a b c d +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 811 + +--S 812 of 1483 +m0156:=a0156-r0156 +--R +--R +--R (812) +--R +-+4+-+3 +-+4+-+3 +--R 2b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 - 6a b %%BV0 +--R + +--R 2 2 +--R - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 2b\|a \|a \|b \|b %%BV1 - 2b\|a \|a \|b \|b %%BV0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R - 2f\|a \|a \|b \|b +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e + 8a b c d +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R 16a b d e + 8a b c d +--R * +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (2a b e + 2a b c e - 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f + 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R - 2a b d e + 6a b c d e - 4a b c d - 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (32a b e + 32a b c e - 64a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e - 3a b c d e + 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 4a b c d e + a b c d e + (- 2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R - +--R +-+4+-+3 +-+4+-+3 +--R 2b\|a \|a \|b \|b +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R +-+4+-+3 +-+4+-+3 +-+4+-+3 +-+4+-+3 +--R - 2b\|a \|a \|b \|b %%BV1 - 2b\|a \|a \|b \|b %%BV0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R - 2f\|a \|a \|b \|b +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 32a b e - 32a b c e + 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e - 8a b c d +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 8a b e - 8a b c e + 16a b c d )f + 24a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 16a b d e - 8a b c d +--R * +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 2a b e - 2a b c e + 4a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (12a b c d e - 8a b d e - 4a b c d)f - 2a b c e + 2a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R - 6a b c d e + 4a b c d + 2a b c +--R * +--R ROOT +--R 2 2 2 +--R - 6a b %%BV1 + (- 4a b %%BV0 - 4a b f)%%BV1 +--R + +--R 2 2 2 2 +--R - 6a b %%BV0 - 4a b f %%BV0 - a f + 2b c e + b d +--R / +--R 2 +--R 2a b +--R + +--R 4 3 3 3 4 2 3 4 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (32a b e + 32a b c e - 64a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (32a b e + 32a b c e - 64a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV1 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 3 3 3 +--R (8a b e + 8a b c e - 16a b c d )f - 24a b c d e + 16a b d e +--R + +--R 2 4 3 +--R 8a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (6a b e + 6a b c e - 12a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (- 12a b c d e + 8a b d e + 4a b c d)f - 2a b c e +--R + +--R 3 2 2 3 2 3 2 2 2 3 4 4 5 +--R 2a b d e - 6a b c d e + 4a b c d + 2a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3a b c d e + 2a b d e + a b c d)f +--R + +--R 3 4 3 2 3 2 2 2 2 2 2 4 3 5 +--R (- a b c e + a b d e - 3a b c d e + 2a b c d + a b c )f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e + 4a b c d e + a b c d e + (- 2a b d - 3a b c d)e +--R + +--R 3 3 3 +--R a b c d +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b %%BV1 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (- 16a b e - 16a b c e + 32a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e - 16a b c d +--R * +--R 2 +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 2 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 +--R (- 64a b e - 64a b c e + 128a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (- 12a b e - 12a b c e + 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 3 2 2 3 +--R (24a b c d e - 16a b d e - 8a b c d)f + 4a b c e - 4a b d e +--R + +--R 2 3 2 2 2 3 4 4 5 +--R 12a b c d e - 8a b c d - 4a b c +--R * +--R %%BV1 +--R + +--R 4 3 3 3 4 2 3 4 2 3 +--R (- 64a b e - 64a b c e + 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 2 +--R (- 64a b e - 64a b c e + 128a b c d )f %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 3 2 4 +--R (- 24a b e - 24a b c e + 48a b c d )f + 16a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 +--R 8a b d e + 16a b c e - 24a b c d e - 16a b c d +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (- 3a e - 3a b c e + 6a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R 5a b c e + a b d e + 4a b c e - 3a b c d e - 6a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 2 3 2 2 3 2 2 2 5 3 4 +--R - a b d e - 8a b c d e + 3a b c d e + (2a b d + a b c d)e +--R + +--R 3 3 3 +--R 3a b c d +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b %%BV0 +--R * +--R log +--R 4 3 3 3 4 2 3 4 2 3 +--R (64a b e + 64a b c e - 128a b c d )%%BV0 +--R + +--R 4 2 3 3 3 2 3 3 2 3 3 2 +--R (48a b e + 48a b c e - 96a b c d )f + 48a b c d e +--R + +--R 3 3 3 2 4 3 +--R - 32a b d e - 16a b c d +--R * +--R 2 +--R %%BV0 +--R + +--R 4 3 3 2 2 3 2 2 2 +--R (12a b e + 12a b c e - 24a b c d )f +--R + +--R 3 2 2 3 2 3 2 3 3 3 2 4 +--R (24a b c d e - 16a b d e - 8a b c d)f - 12a b c e +--R + +--R 3 2 2 3 2 3 3 2 2 3 2 2 2 3 4 4 5 +--R - 12a b d e - 16a b c e + 36a b c d e + 8a b c d - 4a b c +--R * +--R %%BV0 +--R + +--R 3 6 2 2 2 4 2 2 2 3 2 2 4 3 4 2 +--R a b e + a b c e - 8a b c d e + (4a b d - a b c )e +--R + +--R 3 3 2 3 2 4 4 6 +--R 8a b c d e - 4a b c d - b c +--R * +--R x +--R + +--R 4 3 3 2 3 2 3 +--R (a e + a b c e - 2a b c d )f +--R + +--R 3 2 3 3 2 2 3 2 +--R (3a b c d e - 2a b d e - a b c d)f +--R + +--R 3 4 3 2 3 2 2 3 2 2 2 2 2 2 2 4 +--R - 3a b c e - 3a b d e - 4a b c e + 9a b c d e + 2a b c d +--R + +--R 3 5 +--R - a b c +--R * +--R f +--R + +--R 3 5 2 2 3 2 2 2 5 3 4 3 3 3 +--R 3a b d e - 5a b c d e + (2a b d + 5a b c d)e - 5a b c d +--R + +--R 4+-+ 2 +-+ +--R +-+ 2 +-+ x\|b 4+-+3 4+-+3 x \|b +--R (- 2a b e\|b - 2b c\|a )atanh(-----) - 2b d \|a \|b atanh(------) +--R 4+-+ +-+ +--R \|a \|a +--R + +--R 4+-+ +--R +-+ 2 +-+ x\|b 4 +-+4+-+3 +-+4+-+3 +--R (2a b e\|b - 2b c\|a )atan(-----) + f log(- b x + a)\|a \|a \|b \|b +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 +-+4+-+3 +--R 4b\|a \|a \|b \|b +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1483 +d0156:=normalize(D(m0156,x)) +--R +--R +--R (813) 0 +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1483 +t0157:= x^3/(a+b*(c+d*x)^4) +--R +--R +--R 3 +--R x +--R (814) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 814 + +--S 815 of 1483 +r0157:= 3/2*c^2*atan(b^(1/2)*(c+d*x)^2/a^(1/2))/a^(1/2)/b^(1/2)/d^4-_ + 1/4*c*(3*a^(1/2)+_ + b^(1/2)*c^2)*atan(-1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/_ + a^(3/4)/b^(3/4)/d^4-1/4*c*(3*a^(1/2)+_ + b^(1/2)*c^2)*atan(1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/_ + a^(3/4)/b^(3/4)/d^4-1/8*c*(3*a^(1/2)-_ + b^(1/2)*c^2)*log(a^(1/2)/b^(1/2)-2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(3/4)/d^4+1/8*c*(3*a^(1/2)-_ + b^(1/2)*c^2)*log(a^(1/2)/b^(1/2)+2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(3/4)/d^4+1/4*log(a+b*(c+d*x)^4)/b/d^4 +--R +--R +--R (815) +--R +-+ +-+ 2 3 +-+ +-+ +--R (3a b c\|2 \|b - b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+ +-+ 2 3 +-+ +-+ +--R (- 3a b c\|2 \|b + b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 3 +-+ +-+ (d x + c)\|2 \|b + \|a +--R (- 6a b c\|2 \|b - 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 3 +-+ +-+ (d x + c)\|2 \|b - \|a +--R (- 6a b c\|2 \|b - 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 2 4+-+3 4+-+3 (d x + 2c d x + c )\|b +--R 12b c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+4+-+3 +-+ +--R 2log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a)\|a \|a \|b +--R * +--R 4+-+3 +--R \|b +--R / +--R 4 +-+4+-+3 +-+4+-+3 +--R 8b d \|a \|a \|b \|b +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1483 +a0157:=integrate(t0157,x) +--R +--R +--R (816) +--R - +--R 4 +--R b d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 4 4 +--R - b d %%BW1 - b d %%BW0 + 1 +--R * +--R log +--R 3 4 4 4 3 12 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 24a b c + 528a b c - 216a b )d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 24a b c + 528a b c - 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 150a b c + 30a b c + 54a b)d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 118a b c - 1860a b c + 1230a b c + 27a +--R + +--R 4 +--R b d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 4 4 +--R - b d %%BW1 - b d %%BW0 + 1 +--R * +--R log +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 2a b c + 150a b c - 30a b c - 54a b)d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 118a b c - 1860a b c + 1230a b c + 27a +--R + +--R 4 +--R 2b d %%BW1 +--R * +--R log +--R 3 4 4 4 3 12 +--R (960a b c + 1728a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 48a b c + 1056a b c - 432a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (960a b c + 1728a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (- 960a b c - 1728a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 4a b c + 348a b c - 1116a b c + 324a b)d +--R * +--R %%BW1 +--R + +--R 3 4 4 4 3 12 3 3 3 4 4 2 8 2 +--R (960a b c + 1728a b )d %%BW0 + (- 960a b c - 1728a b )d %%BW0 +--R + +--R 2 3 8 3 2 4 4 4 +--R (1800a b c + 3600a b c + 648a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 206a b c - 48a b c + 846a b c - 81a +--R + +--R 4 +--R 2b d %%BW0 +--R * +--R log +--R 3 4 4 4 3 12 3 +--R (- 960a b c - 1728a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (- 48a b c + 2016a b c + 1296a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 4a b c - 1452a b c - 4716a b c - 324a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 26a b c - 444a b c - 390a b c + 27a +--R / +--R 4 +--R 2b d +--R Type: Union(Expression(Integer),...) +--E 816 + +--S 817 of 1483 +m0157:=a0157-r0157 +--R +--R +--R (817) +--R - +--R 4 +-+4+-+3 +-+4+-+3 +--R 4b d \|a \|a \|b \|b +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 4 +-+4+-+3 +-+4+-+3 4 +-+4+-+3 +-+4+-+3 +--R - 4b d \|a \|a \|b \|b %%BW1 - 4b d \|a \|a \|b \|b %%BW0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4\|a \|a \|b \|b +--R * +--R log +--R 3 4 4 4 3 12 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 24a b c + 528a b c - 216a b )d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 24a b c + 528a b c - 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 150a b c + 30a b c + 54a b)d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 118a b c - 1860a b c + 1230a b c + 27a +--R + +--R 4 +-+4+-+3 +-+4+-+3 +--R 4b d \|a \|a \|b \|b +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 4 +-+4+-+3 +-+4+-+3 4 +-+4+-+3 +-+4+-+3 +--R - 4b d \|a \|a \|b \|b %%BW1 - 4b d \|a \|a \|b \|b %%BW0 +--R + +--R +-+4+-+3 +-+4+-+3 +--R 4\|a \|a \|b \|b +--R * +--R log +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 2a b c + 150a b c - 30a b c - 54a b)d +--R * +--R ROOT +--R 2 8 2 2 8 4 +--R - 6a b d %%BW1 + (- 4a b d %%BW0 + 4a b d )%%BW1 +--R + +--R 2 8 2 4 4 +--R - 6a b d %%BW0 + 4a b d %%BW0 - 15b c - a +--R / +--R 2 8 +--R 2a b d +--R + +--R 3 4 4 4 3 12 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (24a b c - 528a b c + 216a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (- 480a b c - 864a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (480a b c + 864a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d +--R * +--R %%BW1 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (24a b c - 528a b c + 216a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (2a b c - 174a b c + 558a b c - 162a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 118a b c - 1860a b c + 1230a b c + 27a +--R + +--R 4 +-+4+-+3 +-+4+-+3 +--R 8b d \|a \|a \|b \|b %%BW1 +--R * +--R log +--R 3 4 4 4 3 12 +--R (960a b c + 1728a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 +--R (- 48a b c + 1056a b c - 432a b )d +--R * +--R 2 +--R %%BW1 +--R + +--R 3 4 4 4 3 12 2 +--R (960a b c + 1728a b )d %%BW0 +--R + +--R 3 3 4 4 2 8 +--R (- 960a b c - 1728a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 4a b c + 348a b c - 1116a b c + 324a b)d +--R * +--R %%BW1 +--R + +--R 3 4 4 4 3 12 3 3 3 4 4 2 8 2 +--R (960a b c + 1728a b )d %%BW0 + (- 960a b c - 1728a b )d %%BW0 +--R + +--R 2 3 8 3 2 4 4 4 +--R (1800a b c + 3600a b c + 648a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 206a b c - 48a b c + 846a b c - 81a +--R + +--R +-+ +-+ 2 3 +-+ +-+ +--R (- 3a b c\|2 \|b + b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+ +-+ 2 3 +-+ +-+ +--R (3a b c\|2 \|b - b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 4 +-+4+-+3 +-+4+-+3 +--R 8b d \|a \|a \|b \|b %%BW0 +--R * +--R log +--R 3 4 4 4 3 12 3 +--R (- 960a b c - 1728a b )d %%BW0 +--R + +--R 2 4 8 3 3 4 4 2 8 2 +--R (- 48a b c + 2016a b c + 1296a b )d %%BW0 +--R + +--R 4 12 2 3 8 3 2 4 4 4 +--R (- 4a b c - 1452a b c - 4716a b c - 324a b)d %%BW0 +--R + +--R 4 15 3 11 2 2 7 3 3 4 16 +--R (b c - 117a b c - 1053a b c + 729a b c )d x + b c +--R + +--R 3 12 2 2 8 3 4 4 +--R - 26a b c - 444a b c - 390a b c + 27a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 3 +-+ +-+ (d x + c)\|2 \|b + \|a +--R (6a b c\|2 \|b + 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 3 +-+ +-+ (d x + c)\|2 \|b - \|a +--R (6a b c\|2 \|b + 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 2 4+-+3 4+-+3 (d x + 2c d x + c )\|b +--R - 12b c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R + +--R - +--R 4 4 3 3 2 2 2 3 4 +-+4+-+3 +--R 2log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a)\|a \|a +--R * +--R +-+4+-+3 +--R \|b \|b +--R / +--R 4 +-+4+-+3 +-+4+-+3 +--R 8b d \|a \|a \|b \|b +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1483 +d0157:=normalize(D(m0157,x)) +--R +--R +--R (818) 0 +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1483 +t0158:= x^2/(a+b*(c+d*x)^4) +--R +--R +--R 2 +--R x +--R (819) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 819 + +--S 820 of 1483 +r0158:= -c*atan(b^(1/2)*(c+d*x)^2/a^(1/2))/a^(1/2)/b^(1/2)/d^3+_ + 1/4*(a^(1/2)+b^(1/2)*c^2)*atan(-1+2^(1/2)*b^(1/4)*(c+d*x)/_ + a^(1/4))*2^(1/2)/a^(3/4)/b^(3/4)/d^3+_ + 1/4*(a^(1/2)+b^(1/2)*c^2)*atan(1+2^(1/2)*b^(1/4)*(c+d*x)/_ + a^(1/4))*2^(1/2)/a^(3/4)/b^(3/4)/d^3+_ + 1/8*(a^(1/2)-b^(1/2)*c^2)*log(a^(1/2)/b^(1/2)-_ + 2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(3/4)/d^3-1/8*(a^(1/2)-_ + b^(1/2)*c^2)*log(a^(1/2)/b^(1/2)+2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(3/4)/d^3 +--R +--R +--R (820) +--R +-+ +-+ 2 +-+ +-+ +--R (- a\|2 \|b + b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+ +-+ 2 +-+ +-+ +--R (a\|2 \|b - b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ (d x + c)\|2 \|b + \|a +--R (2a\|2 \|b + 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ (d x + c)\|2 \|b - \|a +--R (2a\|2 \|b + 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 4+-+3 4+-+3 (d x + 2c d x + c )\|b +--R - 8c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R / +--R 3 +-+4+-+3 +-+4+-+3 +--R 8d \|a \|a \|b \|b +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1483 +a0158:=integrate(t0158,x) +--R +--R +--R (821) +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- - %%BX1 +--R | 6 +--R \| a b d +--R + +--R - %%BX0 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 2 3 7 3 2 3 6 3 10 2 2 6 3 2 3 +--R (16a b c - 80a b c )d %%BX0 + (2a b c - 40a b c + 6a b c )d +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (224a b c + 32a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 2 +--R (16a b c - 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 35a b c +--R + +--R 2 5 3 +--R - 81a b c + 3a c +--R + +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R - |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R - %%BX1 - %%BX0 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 +--R ((- 224a b c - 32a b )d %%BX0 + (- 16a b c + 80a b c )d ) +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 +--R (- 16a b c + 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (224a b c + 32a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 2 +--R (16a b c - 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 35a b c +--R + +--R 2 5 3 +--R - 81a b c + 3a c +--R + +--R 2%%BX1 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((- 448a b c - 64a b )d %%BX0 + (- 32a b c + 160a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (- 448a b c - 64a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (4a b c - 80a b c + 12a b c )d +--R * +--R %%BX1 +--R + +--R 3 3 4 4 2 9 3 2 2 6 3 2 3 +--R (- 448a b c - 64a b )d %%BX0 + (- 336a b c - 48a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 59a b c +--R + +--R 2 5 3 +--R 39a b c + 3a c +--R + +--R 2%%BX0 +--R * +--R log +--R 3 3 4 4 2 9 3 2 3 7 3 2 3 6 2 +--R (448a b c + 64a b )d %%BX0 + (- 32a b c + 160a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (4a b c + 256a b c + 60a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 2 5 +--R (b c - 33a b c - 33a b c + a )d x + b c - 3a b c - 9a b c +--R + +--R 3 +--R - 5a c +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 821 + +--S 822 of 1483 +m0158:=a0158-r0158 +--R +--R +--R (822) +--R 3 +-+4+-+3 +-+4+-+3 +--R 4d \|a \|a \|b \|b +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 +-+4+-+3 +-+4+-+3 3 +-+4+-+3 +-+4+-+3 +--R - 4d \|a \|a \|b \|b %%BX1 - 4d \|a \|a \|b \|b %%BX0 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 2 3 7 3 2 3 6 3 10 2 2 6 3 2 3 +--R (16a b c - 80a b c )d %%BX0 + (2a b c - 40a b c + 6a b c )d +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (224a b c + 32a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 2 +--R (16a b c - 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 35a b c +--R + +--R 2 5 3 +--R - 81a b c + 3a c +--R + +--R - +--R 3 +-+4+-+3 +-+4+-+3 +--R 4d \|a \|a \|b \|b +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 +-+4+-+3 +-+4+-+3 3 +-+4+-+3 +-+4+-+3 +--R - 4d \|a \|a \|b \|b %%BX1 - 4d \|a \|a \|b \|b %%BX0 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 +--R ((- 224a b c - 32a b )d %%BX0 + (- 16a b c + 80a b c )d ) +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 +--R (- 16a b c + 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R +----------------------------------------------------------+ +--R | 6 2 6 6 2 2 +--R |- 3a b d %%BX1 - 2a b d %%BX0 %%BX1 - 3a b d %%BX0 - 3c +--R |---------------------------------------------------------- +--R | 6 +--R \| a b d +--R + +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((224a b c + 32a b )d %%BX0 + (16a b c - 80a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (224a b c + 32a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d +--R * +--R %%BX1 +--R + +--R 2 3 7 3 2 3 6 2 +--R (16a b c - 80a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (- 2a b c + 40a b c - 6a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 35a b c +--R + +--R 2 5 3 +--R - 81a b c + 3a c +--R + +--R 3 +-+4+-+3 +-+4+-+3 +--R 8d \|a \|a \|b \|b %%BX1 +--R * +--R log +--R 3 3 4 4 2 9 2 3 7 3 2 3 6 2 +--R ((- 448a b c - 64a b )d %%BX0 + (- 32a b c + 160a b c )d )%%BX1 +--R + +--R 3 3 4 4 2 9 2 +--R (- 448a b c - 64a b )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (4a b c - 80a b c + 12a b c )d +--R * +--R %%BX1 +--R + +--R 3 3 4 4 2 9 3 2 2 6 3 2 3 +--R (- 448a b c - 64a b )d %%BX0 + (- 336a b c - 48a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 +--R (b c - 33a b c - 33a b c + a )d x + b c - 59a b c +--R + +--R 2 5 3 +--R 39a b c + 3a c +--R + +--R 3 +-+4+-+3 +-+4+-+3 +--R 8d \|a \|a \|b \|b %%BX0 +--R * +--R log +--R 3 3 4 4 2 9 3 2 3 7 3 2 3 6 2 +--R (448a b c + 64a b )d %%BX0 + (- 32a b c + 160a b c )d %%BX0 +--R + +--R 3 10 2 2 6 3 2 3 +--R (4a b c + 256a b c + 60a b c )d %%BX0 +--R + +--R 3 12 2 8 2 4 3 3 13 2 9 2 5 +--R (b c - 33a b c - 33a b c + a )d x + b c - 3a b c - 9a b c +--R + +--R 3 +--R - 5a c +--R + +--R +-+ +-+ 2 +-+ +-+ +--R (a\|2 \|b - b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+ +-+ 2 +-+ +-+ +--R (- a\|2 \|b + b c \|2 \|a ) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ (d x + c)\|2 \|b + \|a +--R (- 2a\|2 \|b - 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ 2 +-+ +-+ (d x + c)\|2 \|b - \|a +--R (- 2a\|2 \|b - 2b c \|2 \|a )atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 4+-+3 4+-+3 (d x + 2c d x + c )\|b +--R 8c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R / +--R 3 +-+4+-+3 +-+4+-+3 +--R 8d \|a \|a \|b \|b +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1483 +d0158:=normalize(D(m0158,x)) +--R +--R +--R (823) 0 +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1483 +t0159:= x/(a+b*(c+d*x)^4) +--R +--R +--R x +--R (824) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 824 + +--S 825 of 1483 +r0159:= 1/2*atan(b^(1/2)*(c+d*x)^2/a^(1/2))/a^(1/2)/b^(1/2)/d^2-_ + 1/4*c*atan(-1+2^(1/2)*b^(1/4)*(c+_ + d*x)/a^(1/4))*2^(1/2)/a^(3/4)/b^(1/4)/d^2-1/4*c*atan(1+_ + 2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/a^(3/4)/b^(1/4)/d^2+_ + 1/8*c*log(a^(1/2)/b^(1/2)-2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(1/4)/d^2-1/8*c*log(a^(1/2)/b^(1/2)+_ + 2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+(c+d*x)^2)*2^(1/2)/a^(3/4)/b^(1/4)/d^2 +--R +--R +--R (825) +--R - +--R +-+ +-+ +-+ +--R c\|2 \|a \|b +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+ +-+ +-+ +--R c\|2 \|a \|b +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ +-+ (d x + c)\|2 \|b + \|a +--R - 2c\|2 \|a \|b atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ +-+ (d x + c)\|2 \|b - \|a +--R - 2c\|2 \|a \|b atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 4+-+3 4+-+ (d x + 2c d x + c )\|b +--R 4\|a \|b atan(------------------------) +--R +-+ +--R \|a +--R / +--R 2 +-+4+-+3 +-+4+-+ +--R 8d \|a \|a \|b \|b +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1483 +a0159:=integrate(t0159,x) +--R +--R +--R (826) +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R - |-------------------------------------------------------- - %%BY1 +--R | 4 +--R \| 2a b d +--R + +--R - %%BY0 +--R * +--R log +--R 3 6 2 2 4 2 2 4 +--R (64a b d %%BY0 - 8a b c d )%%BY1 - 8a b c d %%BY0 +--R + +--R 4 2 2 +--R (2a b c - 4a )d +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 3 6 2 2 4 2 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 2 2 4 2 +--R (- 64a b d %%BY0 + (2a b c - 4a )d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 5 6 2 +--R (2a b c - 4a )d %%BY0 + (b c - 4a c)d x + b c - 5a c +--R + +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- - %%BY1 +--R | 4 +--R \| 2a b d +--R + +--R - %%BY0 +--R * +--R log +--R 3 6 2 2 4 2 2 4 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 +--R (- 2a b c + 4a )d +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 3 6 2 2 4 2 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 2 2 4 2 +--R (- 64a b d %%BY0 + (2a b c - 4a )d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 5 6 2 +--R (2a b c - 4a )d %%BY0 + (b c - 4a c)d x + b c - 5a c +--R + +--R 2%%BY1 +--R * +--R log +--R 3 6 2 2 4 2 +--R (128a b d %%BY0 - 16a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 3 6 3 +--R (128a b d %%BY0 + (- 4a b c + 8a )d )%%BY1 + 128a b d %%BY0 +--R + +--R 2 2 5 6 2 +--R 16a d %%BY0 + (b c - 4a c)d x + b c - 7a c +--R + +--R 2%%BY0 +--R * +--R log +--R 3 6 3 2 2 4 2 4 2 2 +--R - 128a b d %%BY0 - 16a b c d %%BY0 + (- 4a b c - 8a )d %%BY0 +--R + +--R 5 6 2 +--R (b c - 4a c)d x + b c + a c +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 826 + +--S 827 of 1483 +m0159:=a0159-r0159 +--R +--R +--R (827) +--R - +--R 2 +-+4+-+3 +-+4+-+ +--R 4d \|a \|a \|b \|b +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 2 +-+4+-+3 +-+4+-+ 2 +-+4+-+3 +-+4+-+ +--R - 4d \|a \|a \|b \|b %%BY1 - 4d \|a \|a \|b \|b %%BY0 +--R * +--R log +--R 3 6 2 2 4 2 2 4 +--R (64a b d %%BY0 - 8a b c d )%%BY1 - 8a b c d %%BY0 +--R + +--R 4 2 2 +--R (2a b c - 4a )d +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 3 6 2 2 4 2 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 2 2 4 2 +--R (- 64a b d %%BY0 + (2a b c - 4a )d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 5 6 2 +--R (2a b c - 4a )d %%BY0 + (b c - 4a c)d x + b c - 5a c +--R + +--R 2 +-+4+-+3 +-+4+-+ +--R 4d \|a \|a \|b \|b +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 2 +-+4+-+3 +-+4+-+ 2 +-+4+-+3 +-+4+-+ +--R - 4d \|a \|a \|b \|b %%BY1 - 4d \|a \|a \|b \|b %%BY0 +--R * +--R log +--R 3 6 2 2 4 2 2 4 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 +--R (- 2a b c + 4a )d +--R * +--R +--------------------------------------------------------+ +--R | 4 2 4 4 2 +--R |- 6a b d %%BY1 - 4a b d %%BY0 %%BY1 - 6a b d %%BY0 - 1 +--R |-------------------------------------------------------- +--R | 4 +--R \| 2a b d +--R + +--R 3 6 2 2 4 2 +--R (- 64a b d %%BY0 + 8a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 2 2 4 2 +--R (- 64a b d %%BY0 + (2a b c - 4a )d )%%BY1 + 8a b c d %%BY0 +--R + +--R 4 2 2 5 6 2 +--R (2a b c - 4a )d %%BY0 + (b c - 4a c)d x + b c - 5a c +--R + +--R 2 +-+4+-+3 +-+4+-+ +--R 8d \|a \|a \|b \|b %%BY1 +--R * +--R log +--R 3 6 2 2 4 2 +--R (128a b d %%BY0 - 16a b c d )%%BY1 +--R + +--R 3 6 2 4 2 2 3 6 3 +--R (128a b d %%BY0 + (- 4a b c + 8a )d )%%BY1 + 128a b d %%BY0 +--R + +--R 2 2 5 6 2 +--R 16a d %%BY0 + (b c - 4a c)d x + b c - 7a c +--R + +--R +-+ +-+ +-+ +--R c\|2 \|a \|b +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R - +--R +-+ +-+ +-+ +--R c\|2 \|a \|b +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 2 +-+4+-+3 +-+4+-+ +--R 8d \|a \|a \|b \|b %%BY0 +--R * +--R log +--R 3 6 3 2 2 4 2 4 2 2 +--R - 128a b d %%BY0 - 16a b c d %%BY0 + (- 4a b c - 8a )d %%BY0 +--R + +--R 5 6 2 +--R (b c - 4a c)d x + b c + a c +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ +-+ (d x + c)\|2 \|b + \|a +--R 2c\|2 \|a \|b atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ +-+ +-+ (d x + c)\|2 \|b - \|a +--R 2c\|2 \|a \|b atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 4+-+3 4+-+ (d x + 2c d x + c )\|b +--R - 4\|a \|b atan(------------------------) +--R +-+ +--R \|a +--R / +--R 2 +-+4+-+3 +-+4+-+ +--R 8d \|a \|a \|b \|b +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1483 +d0159:=normalize(D(m0159,x)) +--R +--R +--R (828) 0 +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1483 +t0160:= 1/(a+b*(c+d*x)^4) +--R +--R +--R 1 +--R (829) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 829 + +--S 830 of 1483 +r0160:= 1/4*atan(-1+2^(1/2)*b^(1/4)*(c+_ + d*x)/a^(1/4))*2^(1/2)/a^(3/4)/b^(1/4)/d+_ + 1/4*atan(1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/_ + a^(3/4)/b^(1/4)/d-1/8*log(a^(1/2)/b^(1/2)-2^(1/2)*_ + a^(1/4)*(c+d*x)/b^(1/4)+(c+d*x)^2)*2^(1/2)/a^(3/4)/b^(1/4)/d+_ + 1/8*log(a^(1/2)/b^(1/2)+2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/b^(1/4)/d +--R +--R +--R (830) +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R \|2 log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R - +--R +-+ +--R \|2 +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R +-+ (d x + c)\|2 \|b + \|a +-+ (d x + c)\|2 \|b - \|a +--R 2\|2 atan(------------------------) + 2\|2 atan(------------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R / +--R 4+-+3 4+-+ +--R 8d \|a \|b +--R Type: Expression(Integer) +--E 830 + +--S 831 of 1483 +a0160:=integrate(t0160,x) +--R +--R +--R (831) +--R +-----------+ +-----------+ +--R | 1 | 1 +--R |- --------- log(4a d |- --------- + d x + c) +--R 4| 3 4 4| 3 4 +--R \| 256a b d \| 256a b d +--R + +--R +-----------+ +-----------+ +--R | 1 | 1 +--R - |- --------- log(- 4a d |- --------- + d x + c) +--R 4| 3 4 4| 3 4 +--R \| 256a b d \| 256a b d +--R + +--R +-----------+ +--R | 1 +--R 4a d |- --------- +--R +-----------+ 4| 3 4 +--R | 1 \| 256a b d +--R - 2 |- --------- atan(------------------) +--R 4| 3 4 d x + c +--R \| 256a b d +--R Type: Union(Expression(Integer),...) +--E 831 + +--S 832 of 1483 +m0160:=a0160-r0160 +--R +--R +--R (832) +--R +-----------+ +-----------+ +--R | 1 4+-+3 4+-+ | 1 +--R 8d |- --------- \|a \|b log(4a d |- --------- + d x + c) +--R 4| 3 4 4| 3 4 +--R \| 256a b d \| 256a b d +--R + +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R - \|2 log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R +-+ ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R \|2 log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-----------+ +-----------+ +--R | 1 4+-+3 4+-+ | 1 +--R - 8d |- --------- \|a \|b log(- 4a d |- --------- + d x + c) +--R 4| 3 4 4| 3 4 +--R \| 256a b d \| 256a b d +--R + +--R +-+4+-+ 4+-+ +--R +-+ (d x + c)\|2 \|b + \|a +--R - 2\|2 atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R +-+ (d x + c)\|2 \|b - \|a +--R - 2\|2 atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-----------+ +--R | 1 +--R 4a d |- --------- +--R +-----------+ 4| 3 4 +--R | 1 4+-+3 4+-+ \| 256a b d +--R - 16d |- --------- \|a \|b atan(------------------) +--R 4| 3 4 d x + c +--R \| 256a b d +--R / +--R 4+-+3 4+-+ +--R 8d \|a \|b +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1483 +d0160:=normalize(D(m0160,x)) +--R +--R +--R (833) 0 +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1483 +t0161:= 1/x/(a+b*(c+d*x)^4) +--R +--R +--R 1 +--R (834) -------------------------------------------------------- +--R 4 5 3 4 2 2 3 3 2 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + (b c + a)x +--R Type: Fraction(Polynomial(Integer)) +--E 834 + +--S 835 of 1483 +r0161:= -1/2*b^(1/2)*c^2*atan(b^(1/2)*(c+d*x)^2/a^(1/2))/a^(1/2)/(a+b*c^4)-_ + 1/4*b^(1/4)*c*atan(-1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/_ + a^(1/4)/(a+b*c^4)-1/4*b^(3/4)*c^3*atan(-1+2^(1/2)*b^(1/4)*_ + (c+d*x)/a^(1/4))*2^(1/2)/a^(3/4)/(a+b*c^4)-1/4*b^(1/4)*c*_ + atan(1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*2^(1/2)/a^(1/4)/(a+b*c^4)-_ + 1/4*b^(3/4)*c^3*atan(1+2^(1/2)*b^(1/4)*(c+d*x)/a^(1/4))*_ + 2^(1/2)/a^(3/4)/(a+b*c^4)+log(-d*x)/(a+b*c^4)-1/8*b^(1/4)*c*_ + log(a^(1/2)/b^(1/2)-2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(1/4)/(a+b*c^4)+1/8*b^(3/4)*c^3*_ + log(a^(1/2)/b^(1/2)-2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+_ + (c+d*x)^2)*2^(1/2)/a^(3/4)/(a+b*c^4)+1/8*b^(1/4)*c*log(a^(1/2)/_ + b^(1/2)+2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+(c+d*x)^2)*_ + 2^(1/2)/a^(1/4)/(a+b*c^4)-1/8*b^(3/4)*c^3*log(a^(1/2)/b^(1/2)+_ + 2^(1/2)*a^(1/4)*(c+d*x)/b^(1/4)+(c+d*x)^2)*2^(1/2)/a^(3/4)/_ + (a+b*c^4)-log(a+b*(c+d*x)^4)/(4*a+4*b*c^4) +--R +--R +--R (835) +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ +--R (- c \|2 \|a \|b + c\|2 \|a \|a \|b) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ +--R (c \|2 \|a \|b - c\|2 \|a \|a \|b) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R +-+4+-+ 4+-+ +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ (d x + c)\|2 \|b + \|a +--R (- 2c \|2 \|a \|b - 2c\|2 \|a \|a \|b)atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ (d x + c)\|2 \|b - \|a +--R (- 2c \|2 \|a \|b - 2c\|2 \|a \|a \|b)atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 2 4+-+3 +-+ (d x + 2c d x + c )\|b +--R - 4c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - 2log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a) +--R + +--R 8log(- d x) +--R * +--R +-+4+-+3 +--R \|a \|a +--R / +--R 4 +-+4+-+3 +--R (8b c + 8a)\|a \|a +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1483 +a0161:=integrate(t0161,x) +--R +--R +--R (836) +--R 4 +--R (- b c - a) +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 4 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 + (- 4a b c - 4a )%%CA0 +--R + +--R 4 +--R - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 4 4 +--R (- b c - a)%%CA1 + (- b c - a)%%CA0 - 1 +--R * +--R log +--R 3 4 4 2 4 3 +--R ((32a b c + 32a )%%CA0 + 8a b c + 8a )%%CA1 +--R + +--R 2 4 3 4 2 +--R (8a b c + 8a )%%CA0 + 2a b c + 2a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 +--R + +--R 4 2 4 +--R (- 4a b c - 4a )%%CA0 - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 3 4 4 2 4 3 2 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((- 32a b c - 32a )%%CA0 - 32a %%CA0 + 2a b c - 6a )%%CA1 +--R + +--R 2 4 3 2 4 2 3 4 +--R (- 8a b c - 8a )%%CA0 + (2a b c - 6a )%%CA0 + b c d x + b c - a +--R + +--R 4 +--R (b c + a) +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 4 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 + (- 4a b c - 4a )%%CA0 +--R + +--R 4 +--R - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 4 4 +--R (- b c - a)%%CA1 + (- b c - a)%%CA0 - 1 +--R * +--R log +--R 3 4 4 2 4 3 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 2 4 3 4 2 +--R (- 8a b c - 8a )%%CA0 - 2a b c - 2a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 +--R + +--R 4 2 4 +--R (- 4a b c - 4a )%%CA0 - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 3 4 4 2 4 3 2 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((- 32a b c - 32a )%%CA0 - 32a %%CA0 + 2a b c - 6a )%%CA1 +--R + +--R 2 4 3 2 4 2 3 4 +--R (- 8a b c - 8a )%%CA0 + (2a b c - 6a )%%CA0 + b c d x + b c - a +--R + +--R 4 +--R (2b c + 2a)%%CA1 +--R * +--R log +--R 3 4 4 2 4 3 2 +--R ((64a b c + 64a )%%CA0 + 16a b c + 16a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((64a b c + 64a )%%CA0 + 64a %%CA0 - 4a b c + 12a )%%CA1 +--R + +--R 3 4 4 3 3 2 2 3 4 +--R (64a b c + 64a )%%CA0 + 64a %%CA0 + 24a %%CA0 + b c d x + b c +--R + +--R 3a +--R + +--R 4 +--R (2b c + 2a)%%CA0 +--R * +--R log +--R 3 4 4 3 2 4 3 2 +--R (- 64a b c - 64a )%%CA0 + (16a b c - 48a )%%CA0 +--R + +--R 4 2 3 4 +--R (- 4a b c - 12a )%%CA0 + b c d x + b c - a +--R + +--R 2log(x) +--R / +--R 4 +--R 2b c + 2a +--R Type: Union(Expression(Integer),...) +--E 836 + +--S 837 of 1483 +m0161:=a0161-r0161 +--R +--R +--R (837) +--R 4 +-+4+-+3 +--R (- 4b c - 4a)\|a \|a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 4 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 + (- 4a b c - 4a )%%CA0 +--R + +--R 4 +--R - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 4 +-+4+-+3 4 +-+4+-+3 +--R (- 4b c - 4a)\|a \|a %%CA1 + (- 4b c - 4a)\|a \|a %%CA0 +--R + +--R +-+4+-+3 +--R - 4\|a \|a +--R * +--R log +--R 3 4 4 2 4 3 +--R ((32a b c + 32a )%%CA0 + 8a b c + 8a )%%CA1 +--R + +--R 2 4 3 4 2 +--R (8a b c + 8a )%%CA0 + 2a b c + 2a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 +--R + +--R 4 2 4 +--R (- 4a b c - 4a )%%CA0 - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 3 4 4 2 4 3 2 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((- 32a b c - 32a )%%CA0 - 32a %%CA0 + 2a b c - 6a )%%CA1 +--R + +--R 2 4 3 2 4 2 3 4 +--R (- 8a b c - 8a )%%CA0 + (2a b c - 6a )%%CA0 + b c d x + b c - a +--R + +--R 4 +-+4+-+3 +--R (4b c + 4a)\|a \|a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 4 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 + (- 4a b c - 4a )%%CA0 +--R + +--R 4 +--R - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 4 +-+4+-+3 4 +-+4+-+3 +--R (- 4b c - 4a)\|a \|a %%CA1 + (- 4b c - 4a)\|a \|a %%CA0 +--R + +--R +-+4+-+3 +--R - 4\|a \|a +--R * +--R log +--R 3 4 4 2 4 3 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 2 4 3 4 2 +--R (- 8a b c - 8a )%%CA0 - 2a b c - 2a +--R * +--R ROOT +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA1 +--R + +--R 2 8 2 4 3 4 2 +--R ((- 4a b c - 8a b c - 4a )%%CA0 - 4a b c - 4a )%%CA1 +--R + +--R 2 8 2 4 3 2 +--R (- 6a b c - 12a b c - 6a )%%CA0 +--R + +--R 4 2 4 +--R (- 4a b c - 4a )%%CA0 - 3b c - a +--R / +--R 2 8 2 4 3 +--R 2a b c + 4a b c + 2a +--R + +--R 3 4 4 2 4 3 2 +--R ((- 32a b c - 32a )%%CA0 - 8a b c - 8a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((- 32a b c - 32a )%%CA0 - 32a %%CA0 + 2a b c - 6a )%%CA1 +--R + +--R 2 4 3 2 4 2 3 4 +--R (- 8a b c - 8a )%%CA0 + (2a b c - 6a )%%CA0 + b c d x + b c - a +--R + +--R 4 +-+4+-+3 +--R (8b c + 8a)\|a \|a %%CA1 +--R * +--R log +--R 3 4 4 2 4 3 2 +--R ((64a b c + 64a )%%CA0 + 16a b c + 16a )%%CA1 +--R + +--R 3 4 4 2 3 4 2 +--R ((64a b c + 64a )%%CA0 + 64a %%CA0 - 4a b c + 12a )%%CA1 +--R + +--R 3 4 4 3 3 2 2 3 4 +--R (64a b c + 64a )%%CA0 + 64a %%CA0 + 24a %%CA0 + b c d x + b c +--R + +--R 3a +--R + +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ +--R (c \|2 \|a \|b - c\|2 \|a \|a \|b) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (d x + c)\|2 \|a \|b +--R log(-------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ +--R (- c \|2 \|a \|b + c\|2 \|a \|a \|b) +--R * +--R 2 2 2 +-+ +-+ 4+-+ +-+4+-+ +-+ +--R ((d x + 2c d x + c )\|b + \|a )\|b + (- d x - c)\|2 \|a \|b +--R log(---------------------------------------------------------------) +--R +-+4+-+ +--R \|b \|b +--R + +--R 4 +-+4+-+3 +--R (8b c + 8a)\|a \|a %%CA0 +--R * +--R log +--R 3 4 4 3 2 4 3 2 +--R (- 64a b c - 64a )%%CA0 + (16a b c - 48a )%%CA0 +--R + +--R 4 2 3 4 +--R (- 4a b c - 12a )%%CA0 + b c d x + b c - a +--R + +--R +-+4+-+ 4+-+ +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ (d x + c)\|2 \|b + \|a +--R (2c \|2 \|a \|b + 2c\|2 \|a \|a \|b)atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 3 +-+ +-+4+-+3 +-+ +-+4+-+2 4+-+ (d x + c)\|2 \|b - \|a +--R (2c \|2 \|a \|b + 2c\|2 \|a \|a \|b)atan(------------------------) +--R 4+-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R 2 4+-+3 +-+ (d x + 2c d x + c )\|b +--R 4c \|a \|b atan(------------------------) +--R +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 2log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a) + 8log(x) +--R + +--R - 8log(- d x) +--R * +--R +-+4+-+3 +--R \|a \|a +--R / +--R 4 +-+4+-+3 +--R (8b c + 8a)\|a \|a +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1483 +d0161:=normalize(D(m0161,x)) +--R +--R +--R (838) 0 +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1483 +t0162:= (c+d*x)^3*(a+b*(c+d*x)^4)^3 +--R +--R +--R (839) +--R 3 15 15 3 14 14 3 2 13 13 3 3 12 12 +--R b d x + 15b c d x + 105b c d x + 455b c d x +--R + +--R 3 4 2 11 11 3 5 2 10 10 +--R (1365b c + 3a b )d x + (3003b c + 33a b c)d x +--R + +--R 3 6 2 2 9 9 3 7 2 3 8 8 +--R (5005b c + 165a b c )d x + (6435b c + 495a b c )d x +--R + +--R 3 8 2 4 2 7 7 3 9 2 5 2 6 6 +--R (6435b c + 990a b c + 3a b)d x + (5005b c + 1386a b c + 21a b c)d x +--R + +--R 3 10 2 6 2 2 5 5 +--R (3003b c + 1386a b c + 63a b c )d x +--R + +--R 3 11 2 7 2 3 4 4 +--R (1365b c + 990a b c + 105a b c )d x +--R + +--R 3 12 2 8 2 4 3 3 3 +--R (455b c + 495a b c + 105a b c + a )d x +--R + +--R 3 13 2 9 2 5 3 2 2 +--R (105b c + 165a b c + 63a b c + 3a c)d x +--R + +--R 3 14 2 10 2 6 3 2 3 15 2 11 2 7 +--R (15b c + 33a b c + 21a b c + 3a c )d x + b c + 3a b c + 3a b c +--R + +--R 3 3 +--R a c +--R Type: Polynomial(Integer) +--E 839 + +--S 840 of 1483 +r0162:= 1/16*(a+b*(c+d*x)^4)^4/b/d +--R +--R +--R (840) +--R 1 4 16 16 4 15 15 15 4 2 14 14 4 3 13 13 +--R -- b d x + b c d x + -- b c d x + 35b c d x +--R 16 2 +--R + +--R 455 4 4 1 3 12 12 4 5 3 11 11 +--R (--- b c + - a b )d x + (273b c + 3a b c)d x +--R 4 4 +--R + +--R 1001 4 6 33 3 2 10 10 4 7 3 3 9 9 +--R (---- b c + -- a b c )d x + (715b c + 55a b c )d x +--R 2 2 +--R + +--R 6435 4 8 495 3 4 3 2 2 8 8 +--R (---- b c + --- a b c + - a b )d x +--R 8 4 8 +--R + +--R 4 9 3 5 2 2 7 7 +--R (715b c + 198a b c + 3a b c)d x +--R + +--R 1001 4 10 3 6 21 2 2 2 6 6 +--R (---- b c + 231a b c + -- a b c )d x +--R 2 2 +--R + +--R 4 11 3 7 2 2 3 5 5 +--R (273b c + 198a b c + 21a b c )d x +--R + +--R 455 4 12 495 3 8 105 2 2 4 1 3 4 4 +--R (--- b c + --- a b c + --- a b c + - a b)d x +--R 4 4 4 4 +--R + +--R 4 13 3 9 2 2 5 3 3 3 +--R (35b c + 55a b c + 21a b c + a b c)d x +--R + +--R 15 4 14 33 3 10 21 2 2 6 3 3 2 2 2 +--R (-- b c + -- a b c + -- a b c + - a b c )d x +--R 2 2 2 2 +--R + +--R 4 15 3 11 2 2 7 3 3 1 4 16 1 3 12 +--R (b c + 3a b c + 3a b c + a b c )d x + -- b c + - a b c +--R 16 4 +--R + +--R 3 2 2 8 1 3 4 1 4 +--R - a b c + - a b c + -- a +--R 8 4 16 +--R / +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 840 + +--S 841 of 1483 +a0162:=integrate(t0162,x) +--R +--R +--R (841) +--R 1 3 15 16 3 14 15 15 3 2 13 14 3 3 12 13 +--R -- b d x + b c d x + -- b c d x + 35b c d x +--R 16 2 +--R + +--R 455 3 4 1 2 11 12 3 5 2 10 11 +--R (--- b c + - a b )d x + (273b c + 3a b c)d x +--R 4 4 +--R + +--R 1001 3 6 33 2 2 9 10 3 7 2 3 8 9 +--R (---- b c + -- a b c )d x + (715b c + 55a b c )d x +--R 2 2 +--R + +--R 6435 3 8 495 2 4 3 2 7 8 3 9 2 5 2 6 7 +--R (---- b c + --- a b c + - a b)d x + (715b c + 198a b c + 3a b c)d x +--R 8 4 8 +--R + +--R 1001 3 10 2 6 21 2 2 5 6 +--R (---- b c + 231a b c + -- a b c )d x +--R 2 2 +--R + +--R 3 11 2 7 2 3 4 5 +--R (273b c + 198a b c + 21a b c )d x +--R + +--R 455 3 12 495 2 8 105 2 4 1 3 3 4 +--R (--- b c + --- a b c + --- a b c + - a )d x +--R 4 4 4 4 +--R + +--R 3 13 2 9 2 5 3 2 3 +--R (35b c + 55a b c + 21a b c + a c)d x +--R + +--R 15 3 14 33 2 10 21 2 6 3 3 2 2 +--R (-- b c + -- a b c + -- a b c + - a c )d x +--R 2 2 2 2 +--R + +--R 3 15 2 11 2 7 3 3 +--R (b c + 3a b c + 3a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 841 + +--S 842 of 1483 +m0162:=a0162-r0162 +--R +--R +--R 1 4 16 1 3 12 3 2 2 8 1 3 4 1 4 +--R - -- b c - - a b c - - a b c - - a b c - -- a +--R 16 4 8 4 16 +--R (842) ---------------------------------------------------- +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 842 + +--S 843 of 1483 +d0162:=D(m0162,x) +--R +--R +--R (843) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 843 + +--S 844 of 1483 +t0163:= (c+d*x)^3*(a+b*(c+d*x)^4)^2 +--R +--R +--R (844) +--R 2 11 11 2 10 10 2 2 9 9 2 3 8 8 2 4 7 7 +--R b d x + 11b c d x + 55b c d x + 165b c d x + (330b c + 2a b)d x +--R + +--R 2 5 6 6 2 6 2 5 5 +--R (462b c + 14a b c)d x + (462b c + 42a b c )d x +--R + +--R 2 7 3 4 4 2 8 4 2 3 3 +--R (330b c + 70a b c )d x + (165b c + 70a b c + a )d x +--R + +--R 2 9 5 2 2 2 2 10 6 2 2 2 11 +--R (55b c + 42a b c + 3a c)d x + (11b c + 14a b c + 3a c )d x + b c +--R + +--R 7 2 3 +--R 2a b c + a c +--R Type: Polynomial(Integer) +--E 844 + +--S 845 of 1483 +r0163:= 1/12*(a+b*(c+d*x)^4)^3/b/d +--R +--R +--R (845) +--R 1 3 12 12 3 11 11 11 3 2 10 10 55 3 3 9 9 +--R -- b d x + b c d x + -- b c d x + -- b c d x +--R 12 2 3 +--R + +--R 165 3 4 1 2 8 8 3 5 2 7 7 3 6 2 2 6 6 +--R (--- b c + - a b )d x + (66b c + 2a b c)d x + (77b c + 7a b c )d x +--R 4 4 +--R + +--R 3 7 2 3 5 5 165 3 8 35 2 4 1 2 4 4 +--R (66b c + 14a b c )d x + (--- b c + -- a b c + - a b)d x +--R 4 2 4 +--R + +--R 55 3 9 2 5 2 3 3 11 3 10 2 6 3 2 2 2 2 +--R (-- b c + 14a b c + a b c)d x + (-- b c + 7a b c + - a b c )d x +--R 3 2 2 +--R + +--R 3 11 2 7 2 3 1 3 12 1 2 8 1 2 4 1 3 +--R (b c + 2a b c + a b c )d x + -- b c + - a b c + - a b c + -- a +--R 12 4 4 12 +--R / +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 845 + +--S 846 of 1483 +a0163:=integrate(t0163,x) +--R +--R +--R (846) +--R 1 2 11 12 2 10 11 11 2 2 9 10 55 2 3 8 9 +--R -- b d x + b c d x + -- b c d x + -- b c d x +--R 12 2 3 +--R + +--R 165 2 4 1 7 8 2 5 6 7 2 6 2 5 6 +--R (--- b c + - a b)d x + (66b c + 2a b c)d x + (77b c + 7a b c )d x +--R 4 4 +--R + +--R 2 7 3 4 5 165 2 8 35 4 1 2 3 4 +--R (66b c + 14a b c )d x + (--- b c + -- a b c + - a )d x +--R 4 2 4 +--R + +--R 55 2 9 5 2 2 3 11 2 10 6 3 2 2 2 +--R (-- b c + 14a b c + a c)d x + (-- b c + 7a b c + - a c )d x +--R 3 2 2 +--R + +--R 2 11 7 2 3 +--R (b c + 2a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 846 + +--S 847 of 1483 +m0163:=a0163-r0163 +--R +--R +--R 1 3 12 1 2 8 1 2 4 1 3 +--R - -- b c - - a b c - - a b c - -- a +--R 12 4 4 12 +--R (847) ---------------------------------------- +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 847 + +--S 848 of 1483 +d0163:=D(m0163,x) +--R +--R +--R (848) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 848 + +--S 849 of 1483 +t0164:= (c+d*x)^3*(a+b*(c+d*x)^4) +--R +--R +--R (849) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R b d x + 7b c d x + 21b c d x + 35b c d x + (35b c + a)d x +--R + +--R 5 2 2 6 2 7 3 +--R (21b c + 3a c)d x + (7b c + 3a c )d x + b c + a c +--R Type: Polynomial(Integer) +--E 849 + +--S 850 of 1483 +r0164:= 1/4*a*(c+d*x)^4/d+1/8*b*(c+d*x)^8/d +--R +--R +--R (850) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 1 4 4 +--R - b d x + b c d x + - b c d x + 7b c d x + (-- b c + - a)d x +--R 8 2 4 4 +--R + +--R 5 3 3 7 6 3 2 2 2 7 3 1 8 +--R (7b c + a c)d x + (- b c + - a c )d x + (b c + a c )d x + - b c +--R 2 2 8 +--R + +--R 1 4 +--R - a c +--R 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 850 + +--S 851 of 1483 +a0164:=integrate(t0164,x) +--R +--R +--R (851) +--R 1 7 8 6 7 7 2 5 6 3 4 5 35 4 1 3 4 +--R - b d x + b c d x + - b c d x + 7b c d x + (-- b c + - a)d x +--R 8 2 4 4 +--R + +--R 5 2 3 7 6 3 2 2 7 3 +--R (7b c + a c)d x + (- b c + - a c )d x + (b c + a c )x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 851 + +--S 852 of 1483 +m0164:=a0164-r0164 +--R +--R +--R 1 8 1 4 +--R - - b c - - a c +--R 8 4 +--R (852) ----------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 852 + +--S 853 of 1483 +d0164:=D(m0164,x) +--R +--R +--R (853) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 853 + +--S 854 of 1483 +t0165:= 1/(a+b*x^5) +--R +--R +--R 1 +--R (854) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 854 + +--S 855 of 1483 +r0165:= 1/10*(10-2*5^(1/2))^(1/2)*atan(-(5^(1/2)+1)/(10-2*5^(1/2))^(1/2)+_ + 2*2^(1/2)/(5-5^(1/2))^(1/2)*b^(1/5)*x/a^(1/5))/a^(4/5)/b^(1/5)+_ + 1/10*(10+2*5^(1/2))^(1/2)*atan(-(1-5^(1/2))/(10+2*5^(1/2))^(1/2)+_ + 2*2^(1/2)/(5+5^(1/2))^(1/2)*b^(1/5)*x/a^(1/5))/a^(4/5)/b^(1/5)+_ + 1/5*log(a^(1/5)/b^(1/5)+x)/a^(4/5)/b^(1/5)-_ + 1/20*(1-5^(1/2))*log(2*a^(2/5)/b^(2/5)-(1-5^(1/2))*a^(1/5)*x/b^(1/5)+_ + 2*x^2)/a^(4/5)/b^(1/5)-1/20*(5^(1/2)+1)*log(2*a^(2/5)/b^(2/5)-_ + (5^(1/2)+1)*a^(1/5)*x/b^(1/5)+2*x^2)/a^(4/5)/b^(1/5) +--R +--R +--R (855) +--R 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R +-+ 2x \|b + (x\|5 - x)\|a \|b + 2\|a +--R (\|5 - 1)log(---------------------------------------) +--R 5+-+2 +--R \|b +--R + +--R 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R +-+ 2x \|b + (- x\|5 - x)\|a \|b + 2\|a +--R (- \|5 - 1)log(-----------------------------------------) +--R 5+-+2 +--R \|b +--R + +--R 5+-+ 5+-+ +--R x\|b + \|a +--R 4log(------------) +--R 5+-+ +--R \|b +--R + +--R +----------+ +--R | +-+ +--R 2\|2\|5 + 10 +--R * +--R atan +--R +----------+ +--R +-+ 5+-+ | +-+ +--R (3\|5 - 5)\|a \|2\|5 + 10 +--R + +--R +--------+ +--R +-+ +-+ +-+ 5+-+ | +-+ +--R (- 2x\|2 \|5 + 10x\|2 )\|b \|\|5 + 5 +--R / +--R 5+-+ +--R 20\|a +--R + +--R +------------+ +--R | +-+ +--R 2\|- 2\|5 + 10 +--R * +--R atan +--R +----------+ +--R +-+ +-+ +-+ | +-+ 5+-+ +--R (2x\|2 \|5 + 10x\|2 )\|- \|5 + 5 \|b +--R + +--R +------------+ +--R +-+ | +-+ 5+-+ +--R (- 3\|5 - 5)\|- 2\|5 + 10 \|a +--R / +--R 5+-+ +--R 20\|a +--R / +--R 5+-+4 5+-+ +--R 20\|a \|b +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1483 +a0165:=integrate(t0165,x) +--R +--R +--R (856) +--R +---+ +--R 5| 4 +--R 5\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--R - 5\|a b %%CC1 - 5\|a b %%CC0 - 1 +--R * +--R log +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--R - 5a\|a b %%CC1 - 5a\|a b %%CC0 + 2x\|a b - a +--R + +--R - +--R +---+ +--R 5| 4 +--R 5\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--R - 5\|a b %%CC1 - 5\|a b %%CC0 - 1 +--R * +--R log +--R - +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--R - 5a\|a b %%CC1 - 5a\|a b %%CC0 + 2x\|a b - a +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--R 10\|a b %%CC1 log(5a %%CC1 + x) + 10\|a b %%CC0 log(5a %%CC0 + x) +--R + +--R +---+ +--R 5| 4 +--R 2log(x\|a b + a) +--R / +--R +---+ +--R 5| 4 +--R 10\|a b +--R Type: Union(Expression(Integer),...) +--E 856 + +--S 857 of 1483 +m0165:=a0165-r0165 +--R +--R +--R (857) +--R +---+ +--R 5+-+4 5+-+5| 4 +--R 10\|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5+-+4 5+-+5| 4 5+-+4 5+-+5| 4 5+-+4 5+-+ +--R - 10\|a \|b \|a b %%CC - 10\|a \|b \|a b %%CC - 2\|a \|b +--R * +--R log +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--R - 5a\|a b %%CC1 - 5a\|a b %%CC0 + 2x\|a b - a +--R + +--R - +--R +---+ +--R 5+-+4 5+-+5| 4 +--R 10\|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5+-+4 5+-+5| 4 5+-+4 5+-+5| 4 5+-+4 5+-+ +--R - 10\|a \|b \|a b %%CC - 10\|a \|b \|a b %%CC - 2\|a \|b +--R * +--R log +--R - +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--R - 75\|a b %%CC1 + (- 50\|a b %%CC0 - 10\|a b )%%CC1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--R - 75\|a b %%CC0 - 10\|a b %%CC0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--R - 5a\|a b %%CC1 - 5a\|a b %%CC0 + 2x\|a b - a +--R + +--R +---+ +--R 5+-+4 5+-+5| 4 +--R 20\|a \|b \|a b %%CC1 log(5a %%CC1 + x) +--R + +--R +---+ +---+ +--R 5+-+4 5+-+5| 4 5+-+4 5+-+ 5| 4 +--R 20\|a \|b \|a b %%CC0 log(5a %%CC0 + x + 4\|a \|b log(x\|a b + a) +--R + +--R +---+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R +-+ 5| 4 2x \|b + (x\|5 - x)\|a \|b + 2\|a +--R (- \|5 + 1)\|a b log(---------------------------------------) +--R 5+-+2 +--R \|b +--R + +--R +---+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R +-+ 5| 4 2x \|b + (- x\|5 - x)\|a \|b + 2\|a +--R (\|5 + 1)\|a b log(-----------------------------------------) +--R 5+-+2 +--R \|b +--R + +--R +---+ 5+-+ 5+-+ +--R 5| 4 x\|b + \|a +--R - 4\|a b log(------------) +--R 5+-+ +--R \|b +--R + +--R - +--R +---+ +----------+ +--R 5| 4 | +-+ +--R 2\|a b \|2\|5 + 10 +--R * +--R atan +--R +----------+ +--R +-+ 5+-+ | +-+ +--R (3\|5 - 5)\|a \|2\|5 + 10 +--R + +--R +--------+ +--R +-+ +-+ +-+ 5+-+ | +-+ +--R (- 2x\|2 \|5 + 10x\|2 )\|b \|\|5 + 5 +--R / +--R 5+-+ +--R 20\|a +--R + +--R - +--R +------------+ +---+ +--R | +-+ 5| 4 +--R 2\|- 2\|5 + 10 \|a b +--R * +--R atan +--R +----------+ +--R +-+ +-+ +-+ | +-+ 5+-+ +--R (2x\|2 \|5 + 10x\|2 )\|- \|5 + 5 \|b +--R + +--R +------------+ +--R +-+ | +-+ 5+-+ +--R (- 3\|5 - 5)\|- 2\|5 + 10 \|a +--R / +--R 5+-+ +--R 20\|a +--R / +--R +---+ +--R 5+-+4 5+-+5| 4 +--R 20\|a \|b \|a b +--R Type: Expression(Integer) +--E 857 + +--S 858 of 1483 +d0165:=normalize(D(m0165,x)) +--R +--R +--R (858) +--R +------------+ +----------+ +--R 2 | +-+ | +-+ 7 2 +-+ 5+-+4 +--R (a x \|- 2\|5 + 10 \|- \|5 + 5 + (2b x + 2a x )\|2 )\|b +--R + +--R +------------+ +----------+ +--R 6 | +-+ | +-+ +--R (- b x - a x)\|- 2\|5 + 10 \|- \|5 + 5 +--R + +--R 6 +-+ +-+ 6 +-+ +--R (- 3b x - 3a x)\|2 \|5 + (5b x + 5a x)\|2 +--R * +--R 5+-+5+-+3 +--R \|a \|b +--R + +--R +------------+ +----------+ +--R 5 | +-+ | +-+ 5 +-+ 5+-+2 5+-+2 +--R (b x \|- 2\|5 + 10 \|- \|5 + 5 + (2b x + 2a)\|2 )\|a \|b +--R + +--R 4 +-+ +-+ 4 +-+ 5+-+3 5+-+ +--R (- 3b x \|2 \|5 + 5b x \|2 )\|a \|b +--R + +--R 3 +-+ +-+ 3 +-+ 5+-+4 +--R (- 3b x \|2 \|5 + 5b x \|2 )\|a +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R +------------+ +----------+ +--R 7 2 +-+ | +-+ | +-+ 7 2 5+-+4 +--R ((2b x + 2a x )\|2 \|- 2\|5 + 10 \|- \|5 + 5 - 40b x - 80a x )\|b +--R + +--R +------------+ +--R 6 +-+ +-+ 6 +-+ | +-+ +--R ((3b x + 3a x)\|2 \|5 + (5b x + 5a x)\|2 )\|- 2\|5 + 10 +--R * +--R +----------+ +--R | +-+ 5+-+5+-+3 +--R \|- \|5 + 5 \|a \|b +--R + +--R +------------+ +----------+ +--R 5 +-+ | +-+ | +-+ 5 5+-+2 5+-+2 +--R ((2b x + 2a)\|2 \|- 2\|5 + 10 \|- \|5 + 5 - 80b x - 40a)\|a \|b +--R + +--R +------------+ +----------+ +--R 4 +-+ +-+ 4 +-+ | +-+ | +-+ 4 5+-+3 +--R ((3b x \|2 \|5 + 5b x \|2 )\|- 2\|5 + 10 \|- \|5 + 5 - 40b x )\|a +--R * +--R 5+-+ +--R \|b +--R + +--R +------------+ +----------+ +--R 3 +-+ +-+ 3 +-+ | +-+ | +-+ 3 5+-+4 +--R ((3b x \|2 \|5 + 5b x \|2 )\|- 2\|5 + 10 \|- \|5 + 5 - 40b x )\|a +--R / +--R +------------+ +----------+ +--R 7 2 2 | +-+ | +-+ 5+-+4 +--R (2a b x + 2a x )\|- 2\|5 + 10 \|- \|5 + 5 \|b +--R + +--R 6 2 +-+ +-+ 6 2 +-+ 5+-+5+-+3 +--R ((- 6a b x - 6a x)\|2 \|5 + (10a b x + 10a x)\|2 )\|a \|b +--R + +--R 2 8 3 +-+ +-+ 2 8 3 +-+ 5+-+4 +--R ((- 6b x - 6a b x )\|2 \|5 + (10b x + 10a b x )\|2 )\|a +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R 7 2 2 5+-+4 +--R (- 160a b x - 160a x )\|b +--R + +--R +------------+ +--R 6 2 +-+ +-+ 6 2 +-+ | +-+ +--R ((6a b x + 6a x)\|2 \|5 + (10a b x + 10a x)\|2 )\|- 2\|5 + 10 +--R * +--R +----------+ +--R | +-+ 5+-+5+-+3 +--R \|- \|5 + 5 \|a \|b +--R + +--R 5 2 5+-+2 5+-+2 2 9 4 5+-+3 5+-+ +--R (- 80a b x - 80a )\|a \|b + (- 80b x - 80a b x )\|a \|b +--R + +--R +------------+ +--R 2 8 3 +-+ +-+ 2 8 3 +-+ | +-+ +--R ((6b x + 6a b x )\|2 \|5 + (10b x + 10a b x )\|2 )\|- 2\|5 + 10 +--R * +--R +----------+ +--R | +-+ 5+-+4 +--R \|- \|5 + 5 \|a +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1483 +t0166:= 1/(1-x^5) +--R +--R +--R 1 +--R (859) - ------ +--R 5 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 859 + +--S 860 of 1483 +r0166:= 1/10*(10+2*5^(1/2))^(1/2)*atan((1-5^(1/2)+_ + 4*x)/(10+2*5^(1/2))^(1/2))+1/10*(10-2*5^(1/2))^(1/2)*atan((1+_ + 5^(1/2)+4*x)/(10-2*5^(1/2))^(1/2))-1/5*log(1-x)+1/20*(1-_ + 5^(1/2))*log(2+(1-5^(1/2))*x+2*x^2)+1/20*(5^(1/2)+1)*log(2+_ + (5^(1/2)+1)*x+2*x^2) +--R +--R +--R (860) +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 - 10x - 5)\|2\|5 + 10 +--R - 2\|2\|5 + 10 atan(-------------------------------------) +--R 20 +--R + +--R +------------+ +--R +------------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 + 10x + 5)\|- 2\|5 + 10 +--R 2\|- 2\|5 + 10 atan(---------------------------------------) +--R 20 +--R + +--R +-+ +-+ 2 +--R (\|5 + 1)log(x\|5 + 2x + x + 2) - 4log(- x + 1) +--R + +--R +-+ +-+ 2 +--R (- \|5 + 1)log(- x\|5 + 2x + x + 2) +--R / +--R 20 +--R Type: Expression(Integer) +--E 860 + +--S 861 of 1483 +a0166:=integrate(t0166,x) +--R +--R +--R (861) +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 2x + 1 +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 2x + 1 +--R + +--R 10%%CD1 log(5%%CD1 + x) + 10%%CD0 log(5%%CD0 + x) - 2log(x - 1) +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 861 + +--S 862 of 1483 +m0166:=a0166-r0166 +--R +--R +--R (862) +--R +-----------------------------------------------------------+ +--R | 2 2 +--R 2\|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 2x + 1 +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - 2\|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - \|- 75%%CD1 + (- 50%%CD0 + 10)%%CD1 - 75%%CD0 + 10%%CD0 - 3 +--R + +--R - 5%%CD1 - 5%%CD0 + 2x + 1 +--R + +--R 20%%CD1 log(5%%CD1 + x) + 20%%CD0 log(5%%CD0 + x) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 - 10x - 5)\|2\|5 + 10 +--R 2\|2\|5 + 10 atan(-------------------------------------) +--R 20 +--R + +--R +------------+ +--R +------------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 + 10x + 5)\|- 2\|5 + 10 +--R - 2\|- 2\|5 + 10 atan(---------------------------------------) +--R 20 +--R + +--R +-+ +-+ 2 +--R (- \|5 - 1)log(x\|5 + 2x + x + 2) - 4log(x - 1) + 4log(- x + 1) +--R + +--R +-+ +-+ 2 +--R (\|5 - 1)log(- x\|5 + 2x + x + 2) +--R / +--R 20 +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1483 +d0166:=D(m0166,x) +--R +--R +--R (863) 0 +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1483 +t0167:= 1/x^2/(1-x^5) +--R +--R +--R 1 +--R (864) - ------- +--R 7 2 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 864 + +--S 865 of 1483 +r0167:= -1/x-1/10*(10+2*5^(1/2))^(1/2)*atan((1-5^(1/2)+4*x)/_ + (10+2*5^(1/2))^(1/2))-1/10*(10-2*5^(1/2))^(1/2)*_ + atan((1+5^(1/2)+4*x)/(10-2*5^(1/2))^(1/2))-1/5*log(1-x)+_ + 1/20*(1-5^(1/2))*log(2+(1-5^(1/2))*x+2*x^2)+_ + 1/20*(5^(1/2)+1)*log(2+(5^(1/2)+1)*x+2*x^2) +--R +--R +--R (865) +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 - 10x - 5)\|2\|5 + 10 +--R 2x\|2\|5 + 10 atan(-------------------------------------) +--R 20 +--R + +--R +------------+ +--R +------------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 + 10x + 5)\|- 2\|5 + 10 +--R - 2x\|- 2\|5 + 10 atan(---------------------------------------) +--R 20 +--R + +--R +-+ +-+ 2 +--R (x\|5 + x)log(x\|5 + 2x + x + 2) - 4x log(- x + 1) +--R + +--R +-+ +-+ 2 +--R (- x\|5 + x)log(- x\|5 + 2x + x + 2) - 20 +--R / +--R 20x +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1483 +a0167:=integrate(t0167,x) +--R +--R +--R (866) +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - x\|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R - 5x %%CE1 - 5x %%CE0 + x +--R * +--R log +--R 25%%CE0 %%CE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R 2 2 +--R - 125%%CE0 %%CE1 + (- 125%%CE0 + 25%%CE0)%%CE1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--R x\|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R - 5x %%CE1 - 5x %%CE0 + x +--R * +--R log +--R - +--R 25%%CE0 %%CE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R 2 2 +--R - 125%%CE0 %%CE1 + (- 125%%CE0 + 25%%CE0)%%CE1 + 2x +--R + +--R 10x %%CE1 +--R * +--R log +--R 2 2 3 +--R 125%%CE0 %%CE1 + (125%%CE0 - 25%%CE0)%%CE1 + 125%%CE0 +--R + +--R 2 +--R - 25%%CE0 + 5%%CE0 + x +--R + +--R 3 2 +--R 10x %%CE0 log(- 125%%CE0 + 25%%CE0 - 5%%CE0 + x + 1) - 2x log(x - 1) - 10 +--R / +--R 10x +--R Type: Union(Expression(Integer),...) +--E 866 + +--S 867 of 1483 +m0167:=a0167-r0167 +--R +--R +--R (867) +--R +-----------------------------------------------------------+ +--R | 2 2 +--R - 2\|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2 +--R * +--R log +--R 25%%CE0 %%CE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R 2 2 +--R - 125%%CE0 %%CE1 + (- 125%%CE0 + 25%%CE0)%%CE1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--R 2\|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2 +--R * +--R log +--R - +--R 25%%CE0 %%CE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%CE1 + (- 50%%CE0 + 10)%%CE1 - 75%%CE0 + 10%%CE0 - 3 +--R + +--R 2 2 +--R - 125%%CE0 %%CE1 + (- 125%%CE0 + 25%%CE0)%%CE1 + 2x +--R + +--R 20%%CE1 +--R * +--R log +--R 2 2 3 +--R 125%%CE0 %%CE1 + (125%%CE0 - 25%%CE0)%%CE1 + 125%%CE0 +--R + +--R 2 +--R - 25%%CE0 + 5%%CE0 + x +--R + +--R 3 2 +--R 20%%CE0 log(- 125%%CE0 + 25%%CE0 - 5%%CE0 + x + 1) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 - 10x - 5)\|2\|5 + 10 +--R - 2\|2\|5 + 10 atan(-------------------------------------) +--R 20 +--R + +--R +------------+ +--R +------------+ +-+ | +-+ +--R | +-+ ((2x + 3)\|5 + 10x + 5)\|- 2\|5 + 10 +--R 2\|- 2\|5 + 10 atan(---------------------------------------) +--R 20 +--R + +--R +-+ +-+ 2 +--R (- \|5 - 1)log(x\|5 + 2x + x + 2) - 4log(x - 1) + 4log(- x + 1) +--R + +--R +-+ +-+ 2 +--R (\|5 - 1)log(- x\|5 + 2x + x + 2) +--R / +--R 20 +--R Type: Expression(Integer) +--E 867 + +--S 868 of 1483 +d0167:=D(m0167,x) +--R +--R +--R (868) 0 +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1483 +t0168:= x^8/(1-x^6) +--R +--R +--R 8 +--R x +--R (869) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 869 + +--S 870 of 1483 +r0168:= -1/3*x^3+1/3*atanh(x^3) +--R +--R +--R 3 3 +--R atanh(x ) - x +--R (870) -------------- +--R 3 +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1483 +a0168:=integrate(t0168,x) +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2x +--R (871) ------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 871 + +--S 872 of 1483 +m0168:=a0168-r0168 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (872) -------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1483 +d0168:=D(m0168,x) +--R +--R +--R (873) 0 +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1483 +t0169:= x^7/(1-x^6) +--R +--R +--R 7 +--R x +--R (874) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 874 + +--S 875 of 1483 +r0169:= -1/2*x^2+1/6*atan(1/3*(1+2*x^2)*3^(1/2)::EXPR(INT))*3^(1/2)-_ + 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) +--R +--R +--R 2 +-+ +--R 4 2 2 +-+ (2x + 1)\|3 2 +--R log(x + x + 1) - 2log(- x + 1) + 2\|3 atan(-------------) - 6x +--R 3 +--R (875) ------------------------------------------------------------------ +--R 12 +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1483 +a0169:=integrate(t0169,x) +--R +--R +--R (876) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 2 +-+ +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) - 6x \|3 +--R 3 +--R ------------------------------------------------------------------------ +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 876 + +--S 877 of 1483 +m0169:=a0169-r0169 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (877) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1483 +d0169:=D(m0169,x) +--R +--R +--R (878) 0 +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1483 +t0170:= x^5/(1-x^6) +--R +--R +--R 5 +--R x +--R (879) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 879 + +--S 880 of 1483 +r0170:= -1/6*log(1-x^6) +--R +--R +--R 6 +--R log(- x + 1) +--R (880) - ------------- +--R 6 +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1483 +a0170:=integrate(t0170,x) +--R +--R +--R 6 +--R log(x - 1) +--R (881) - ----------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 881 + +--S 882 of 1483 +m0170:=a0170-r0170 +--R +--R +--R 6 6 +--R - log(x - 1) + log(- x + 1) +--R (882) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1483 +d0170:=D(m0170,x) +--R +--R +--R (883) 0 +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1483 +t0171:= x^3/(1-x^6) +--R +--R +--R 3 +--R x +--R (884) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 884 + +--S 885 of 1483 +r0171:= -1/6*atan(1/3*(1+2*x^2)*3^(1/2)::EXPR(INT))*3^(1/2)-_ + 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) +--R +--R +--R 2 +-+ +--R 4 2 2 +-+ (2x + 1)\|3 +--R log(x + x + 1) - 2log(- x + 1) - 2\|3 atan(-------------) +--R 3 +--R (885) ------------------------------------------------------------ +--R 12 +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1483 +a0171:=integrate(t0171,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) - 6atan(-------------) +--R 3 +--R (886) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 886 + +--S 887 of 1483 +m0171:=a0171-r0171 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (887) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1483 +d0171:=D(m0171,x) +--R +--R +--R (888) 0 +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1483 +t0172:= x^2/(1-x^6) +--R +--R +--R 2 +--R x +--R (889) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 889 + +--S 890 of 1483 +r0172:= 1/3*atanh(x^3) +--R +--R +--R 3 +--R atanh(x ) +--R (890) --------- +--R 3 +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1483 +a0172:=integrate(t0172,x) +--R +--R +--R 3 3 +--R log(x + 1) - log(x - 1) +--R (891) ------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 891 + +--S 892 of 1483 +m0172:=a0172-r0172 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (892) -------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1483 +d0172:=D(m0172,x) +--R +--R +--R (893) 0 +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1483 +t0173:= x/(1-x^6) +--R +--R +--R x +--R (894) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 894 + +--S 895 of 1483 +r0173:= 1/6*atan(1/3*(1+2*x^2)*3^(1/2)::EXPR(INT))*3^(1/2)-_ + 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) +--R +--R +--R 2 +-+ +--R 4 2 2 +-+ (2x + 1)\|3 +--R log(x + x + 1) - 2log(- x + 1) + 2\|3 atan(-------------) +--R 3 +--R (895) ------------------------------------------------------------ +--R 12 +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1483 +a0173:=integrate(t0173,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) +--R 3 +--R (896) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 896 + +--S 897 of 1483 +m0173:=a0173-r0173 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (897) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1483 +d0173:=D(m0173,x) +--R +--R +--R (898) 0 +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1483 +t0174:= 1/x/(1-x^6) +--R +--R +--R 1 +--R (899) - ------ +--R 7 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 899 + +--S 900 of 1483 +r0174:= log(x)-1/6*log(1-x^6) +--R +--R +--R 6 +--R 6log(x) - log(- x + 1) +--R (900) ----------------------- +--R 6 +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1483 +a0174:=integrate(t0174,x) +--R +--R +--R 6 +--R - log(x - 1) + 6log(x) +--R (901) ----------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 901 + +--S 902 of 1483 +m0174:=a0174-r0174 +--R +--R +--R 6 6 +--R - log(x - 1) + log(- x + 1) +--R (902) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1483 +d0174:=D(m0174,x) +--R +--R +--R (903) 0 +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1483 +t0175:= 1/x^3/(1-x^6) +--R +--R +--R 1 +--R (904) - ------- +--R 9 3 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 904 + +--S 905 of 1483 +r0175:= -1/2/x^2-1/6*atan(1/3*(1+2*x^2)*3^(1/2)::EXPR(INT))*3^(1/2)-_ + 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) +--R +--R +--R (905) +--R 2 +-+ +--R 2 4 2 2 2 2 +-+ (2x + 1)\|3 +--R x log(x + x + 1) - 2x log(- x + 1) - 2x \|3 atan(-------------) - 6 +--R 3 +--R ---------------------------------------------------------------------- +--R 2 +--R 12x +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1483 +a0175:=integrate(t0175,x) +--R +--R +--R (906) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3 +-+ +--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) - 6x atan(-------------) - 6\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 2 +-+ +--R 12x \|3 +--R Type: Union(Expression(Integer),...) +--E 906 + +--S 907 of 1483 +m0175:=a0175-r0175 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (907) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1483 +d0175:=normalize(D(m0175,x)) +--R +--R +--R (908) 0 +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1483 +t0176:= 1/x^4/(1-x^6) +--R +--R +--R 1 +--R (909) - -------- +--R 10 4 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 909 + +--S 910 of 1483 +r0176:= -1/3/x^3+1/3*atanh(x^3) +--R +--R +--R 3 3 +--R x atanh(x ) - 1 +--R (910) --------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1483 +a0176:=integrate(t0176,x) +--R +--R +--R 3 3 3 3 +--R x log(x + 1) - x log(x - 1) - 2 +--R (911) --------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 911 + +--S 912 of 1483 +m0176:=a0176-r0176 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (912) -------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1483 +d0176:=D(m0176,x) +--R +--R +--R (913) 0 +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1483 +t0177:= 1/x^5/(1-x^6) +--R +--R +--R 1 +--R (914) - -------- +--R 11 5 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 914 + +--S 915 of 1483 +r0177:= -1/4/x^4+1/6*atan(1/3*(1+2*x^2)*3^(1/2)::EXPR(INT))*3^(1/2)-_ + 1/6*log(1-x^2)+1/12*log(1+x^2+x^4) +--R +--R +--R (915) +--R 2 +-+ +--R 4 4 2 4 2 4 +-+ (2x + 1)\|3 +--R x log(x + x + 1) - 2x log(- x + 1) + 2x \|3 atan(-------------) - 3 +--R 3 +--R ---------------------------------------------------------------------- +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1483 +a0177:=integrate(t0177,x) +--R +--R +--R (916) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3 +-+ +--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) + 6x atan(-------------) - 3\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 4 +-+ +--R 12x \|3 +--R Type: Union(Expression(Integer),...) +--E 916 + +--S 917 of 1483 +m0177:=a0177-r0177 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (917) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1483 +d0177:=normalize(D(m0177,x)) +--R +--R +--R (918) 0 +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1483 +t0178:= 1/(a+b*x^6) +--R +--R +--R 1 +--R (919) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 919 + +--S 920 of 1483 +r0178:= -1/12*(-4*atan(b^(1/6)*x/a^(1/6))-_ + 2*atan((-3^(1/2)*a^(1/6)+2*b^(1/6)*x)/a^(1/6))-_ + 2*atan((3^(1/2)*a^(1/6)+2*b^(1/6)*x)/a^(1/6))+log(-(-a^(1/3)+_ + 3^(1/2)*a^(1/6)*x*b^(1/6)-b^(1/3)*x^2)/b^(1/3))*3^(1/2)-_ + log(1/b^(1/3)*(a^(1/3)+3^(1/2)*a^(1/6)*x*b^(1/6)+_ + b^(1/3)*x^2))*3^(1/2))/a^(5/6)/b^(1/6) +--R +--R +--R (920) +--R +-+6+-+6+-+ 2 3+-+ 3+-+ +--R +-+ x\|3 \|a \|b + x \|b + \|a +--R \|3 log(-----------------------------) +--R 3+-+ +--R \|b +--R + +--R +-+6+-+6+-+ 2 3+-+ 3+-+ 6+-+ +-+6+-+ +--R +-+ - x\|3 \|a \|b + x \|b + \|a 2x\|b + \|3 \|a +--R - \|3 log(-------------------------------) + 2atan(-----------------) +--R 3+-+ 6+-+ +--R \|b \|a +--R + +--R 6+-+ +-+6+-+ 6+-+ +--R 2x\|b - \|3 \|a x\|b +--R 2atan(-----------------) + 4atan(-----) +--R 6+-+ 6+-+ +--R \|a \|a +--R / +--R 6+-+5 6+-+ +--R 12\|a \|b +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1483 +a0178:=integrate(t0178,x) +--R +--R +--R (921) +--R +----------+ +----------+2 +----------+ +--R | 1 2 | 1 | 1 2 +--R |- -------- log(36a |- -------- + 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+2 +----------+ +--R | 1 2 | 1 | 1 2 +--R - |- -------- log(36a |- -------- - 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 | 1 +--R 2 |- -------- log(6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 | 1 +--R - 2 |- -------- log(- 6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R 2\|3 |- -------- atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R - 2\|3 |- -------- atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- + x +--R 6| 5 +--R \| 46656a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 921 + +--S 922 of 1483 +m0178:=a0178-r0178 +--R +--R +--R (922) +--R +-+6+-+6+-+ 2 3+-+ 3+-+ +--R +-+ x\|3 \|a \|b + x \|b + \|a +--R - \|3 log(-----------------------------) +--R 3+-+ +--R \|b +--R + +--R +----------+ +----------+2 +----------+ +--R | 1 6+-+5 6+-+ 2 | 1 | 1 2 +--R 6 |- -------- \|a \|b log(36a |- -------- + 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+2 +----------+ +--R | 1 6+-+5 6+-+ 2 | 1 | 1 2 +--R - 6 |- -------- \|a \|b log(36a |- -------- - 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 6+-+5 6+-+ | 1 +--R 12 |- -------- \|a \|b log(6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 6+-+5 6+-+ | 1 +--R - 12 |- -------- \|a \|b log(- 6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-+6+-+6+-+ 2 3+-+ 3+-+ 6+-+ +-+6+-+ +--R +-+ - x\|3 \|a \|b + x \|b + \|a 2x\|b + \|3 \|a +--R \|3 log(-------------------------------) - 2atan(-----------------) +--R 3+-+ 6+-+ +--R \|b \|a +--R + +--R 6+-+ +-+6+-+ 6+-+ +--R 2x\|b - \|3 \|a x\|b +--R - 2atan(-----------------) - 4atan(-----) +--R 6+-+ 6+-+ +--R \|a \|a +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 6+-+5 6+-+ \| 46656a b +--R 12\|3 |- -------- \|a \|b atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 6+-+5 6+-+ \| 46656a b +--R - 12\|3 |- -------- \|a \|b atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- + x +--R 6| 5 +--R \| 46656a b +--R / +--R 6+-+5 6+-+ +--R 12\|a \|b +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1483 +d0178:=normalize(D(m0178,x)) +--R +--R +--R (923) 0 +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1483 +t0179:= 1/x^2/(a+b*x^6) +--R +--R +--R 1 +--R (924) ----------- +--R 8 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 924 + +--S 925 of 1483 +r0179:= -1/a/x-1/3*b^(1/6)*atan(b^(1/6)*x/a^(1/6))/a^(7/6)-_ + 1/6*b^(1/6)*atan(-3^(1/2)+2*b^(1/6)*x/a^(1/6))/a^(7/6)-_ + 1/6*b^(1/6)*atan(3^(1/2)+2*b^(1/6)*x/a^(1/6))/a^(7/6)-_ + 1/12*b^(1/6)*log(a^(1/3)/b^(1/3)-3^(1/2)*a^(1/6)*x/b^(1/6)+_ + x^2)*3^(1/2)/a^(7/6)+1/12*b^(1/6)*log(a^(1/3)/b^(1/3)+_ + 3^(1/2)*a^(1/6)*x/b^(1/6)+x^2)*3^(1/2)/a^(7/6) +--R +--R +--R (925) +--R 2 3+-+ 3+-+ 6+-+ +-+6+-+3+-+ +--R +-+6+-+ (x \|b + \|a )\|b + x\|3 \|a \|b +--R x\|3 \|b log(-----------------------------------) +--R 3+-+6+-+ +--R \|b \|b +--R + +--R 2 3+-+ 3+-+ 6+-+ +-+6+-+3+-+ +--R +-+6+-+ (x \|b + \|a )\|b - x\|3 \|a \|b +--R - x\|3 \|b log(-----------------------------------) +--R 3+-+6+-+ +--R \|b \|b +--R + +--R 6+-+ +-+6+-+ 6+-+ +-+6+-+ +--R 6+-+ 2x\|b + \|3 \|a 6+-+ 2x\|b - \|3 \|a +--R - 2x\|b atan(-----------------) - 2x\|b atan(-----------------) +--R 6+-+ 6+-+ +--R \|a \|a +--R + +--R 6+-+ +--R 6+-+ x\|b 6+-+ +--R - 4x\|b atan(-----) - 12\|a +--R 6+-+ +--R \|a +--R / +--R 6+-+ +--R 12a x\|a +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1483 +a0179:=integrate(t0179,x) +--R +--R +--R (926) +--R +---------+ +---------+5 +---------+4 +--R | b 6 | b 5 | b 2 +--R - a x |- ------- log(7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6 | b +--R - 2a x |- ------- log(7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6 | b +--R 2a x |- ------- log(- 7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +---------+4 +--R | b 6 | b 5 | b 2 +--R a x |- ------- log(- 7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R 2a x\|3 |- ------- atan(-------------------------) +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- - b x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R - 2a x\|3 |- ------- atan(------------------------- - 2 +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- + b x +--R 6| 7 +--R \| 46656a +--R / +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 926 + +--S 927 of 1483 +m0179:=a0179-r0179 +--R +--R +--R (927) +--R - +--R +---------+ +--R | b 6+-+ +--R 6a |- ------- \|a +--R 6| 7 +--R \| 46656a +--R * +--R +---------+5 +---------+4 +--R 6 | b 5 | b 2 +--R log(7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6+-+ 6 | b +--R - 12a |- ------- \|a log(7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R 2 3+-+ 3+-+ 6+-+ +-+6+-+3+-+ +--R +-+6+-+ (x \|b + \|a )\|b + x\|3 \|a \|b +--R - \|3 \|b log(-----------------------------------) +--R 3+-+6+-+ +--R \|b \|b +--R + +--R 2 3+-+ 3+-+ 6+-+ +-+6+-+3+-+ +--R +-+6+-+ (x \|b + \|a )\|b - x\|3 \|a \|b +--R \|3 \|b log(-----------------------------------) +--R 3+-+6+-+ +--R \|b \|b +--R + +--R +---------+ +---------+5 +--R | b 6+-+ 6 | b +--R 12a |- ------- \|a log(- 7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +--R | b 6+-+ +--R 6a |- ------- \|a +--R 6| 7 +--R \| 46656a +--R * +--R +---------+5 +---------+4 +--R 6 | b 5 | b 2 +--R log(- 7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R 6+-+ +-+6+-+ 6+-+ +-+6+-+ +--R 6+-+ 2x\|b + \|3 \|a 6+-+ 2x\|b - \|3 \|a +--R 2\|b atan(-----------------) + 2\|b atan(-----------------) +--R 6+-+ 6+-+ +--R \|a \|a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R 6+-+ +---------+ 6| 7 +--R 6+-+ x\|b +-+ | b 6+-+ \| 46656a +--R 4\|b atan(-----) + 12a\|3 |- ------- \|a atan(-------------------------) +--R 6+-+ 6| 7 +---------+5 +--R \|a \| 46656a 6 | b +--R 3888a |- ------- - b x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b 6+-+ \| 46656a +--R - 12a\|3 |- ------- \|a atan(-------------------------) +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- + b x +--R 6| 7 +--R \| 46656a +--R / +--R 6+-+ +--R 12a\|a +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1483 +d0179:=normalize(D(m0179,x)) +--R +--R +--R (928) 0 +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1483 +t0180:= 1/(a-b*x^6) +--R +--R +--R 1 +--R (929) - -------- +--R 6 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 929 + +--S 930 of 1483 +r0180:= 1/12*(2*atan(1/3*3^(1/2)*(-a^(1/6)+2*b^(1/6)*x)/a^(1/6))*3^(1/2)+_ + 2*atan(1/3*3^(1/2)*(a^(1/6)+2*b^(1/6)*x)/a^(1/6))*3^(1/2)+_ + 4*atanh(b^(1/6)*x/a^(1/6))-log(1/b^(1/3)*(a^(1/3)-_ + a^(1/6)*x*b^(1/6)+b^(1/3)*x^2))+log(1/b^(1/3)*(a^(1/3)+_ + a^(1/6)*x*b^(1/6)+b^(1/3)*x^2)))/a^(5/6)/b^(1/6) +--R +--R +--R (930) +--R 6+-+6+-+ 2 3+-+ 3+-+ 6+-+6+-+ 2 3+-+ 3+-+ +--R x\|a \|b + x \|b + \|a - x\|a \|b + x \|b + \|a +--R log(-------------------------) - log(---------------------------) +--R 3+-+ 3+-+ +--R \|b \|b +--R + +--R 6+-+ +-+6+-+ +-+6+-+ +--R x\|b +-+ 2x\|3 \|b + \|3 \|a +--R 4atanh(-----) + 2\|3 atan(---------------------) +--R 6+-+ 6+-+ +--R \|a 3\|a +--R + +--R +-+6+-+ +-+6+-+ +--R +-+ 2x\|3 \|b - \|3 \|a +--R 2\|3 atan(---------------------) +--R 6+-+ +--R 3\|a +--R / +--R 6+-+5 6+-+ +--R 12\|a \|b +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1483 +a0180:=integrate(t0180,x) +--R +--R +--R (931) +--R +--------+ +--------+2 +--------+ +--R | 1 2 | 1 | 1 2 +--R |-------- log(36a |-------- + 6a x |-------- + x ) +--R 6| 5 6| 5 6| 5 +--R \|46656a b \|46656a b \|46656a b +--R + +--R +--------+ +--------+2 +--------+ +--R | 1 2 | 1 | 1 2 +--R - |-------- log(36a |-------- - 6a x |-------- + x ) +--R 6| 5 6| 5 6| 5 +--R \|46656a b \|46656a b \|46656a b +--R + +--R +--------+ +--------+ +--------+ +--------+ +--R | 1 | 1 | 1 | 1 +--R 2 |-------- log(6a |-------- + x - 2 |-------- log(- 6a |-------- + x) +--R 6| 5 6| 5 6| 5 6| 5 +--R \|46656a b \|46656a b \|46656a b \|46656a b +--R + +--R +--------+ +--R +-+ | 1 +--R 3a\|3 |-------- +--R +--------+ 6| 5 +--R +-+ | 1 \|46656a b +--R 2\|3 |-------- atan(-----------------) +--R 6| 5 +--------+ +--R \|46656a b | 1 +--R 3a |-------- - x +--R 6| 5 +--R \|46656a b +--R + +--R +--------+ +--R +-+ | 1 +--R 3a\|3 |-------- +--R +--------+ 6| 5 +--R +-+ | 1 \|46656a b +--R - 2\|3 |-------- atan(-----------------) +--R 6| 5 +--------+ +--R \|46656a b | 1 +--R 3a |-------- + x +--R 6| 5 +--R \|46656a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 931 + +--S 932 of 1483 +m0180:=a0180-r0180 +--R +--R +--R (932) +--R 6+-+6+-+ 2 3+-+ 3+-+ +--R x\|a \|b + x \|b + \|a +--R - log(-------------------------) +--R 3+-+ +--R \|b +--R + +--R +--------+ +--------+2 +--------+ +--R | 1 6+-+5 6+-+ 2 | 1 | 1 2 +--R 6 |-------- \|a \|b log(36a |-------- + 6a x |-------- + x ) +--R 6| 5 6| 5 6| 5 +--R \|46656a b \|46656a b \|46656a b +--R + +--R +--------+ +--------+2 +--------+ +--R | 1 6+-+5 6+-+ 2 | 1 | 1 2 +--R - 6 |-------- \|a \|b log(36a |-------- - 6a x |-------- + x ) +--R 6| 5 6| 5 6| 5 +--R \|46656a b \|46656a b \|46656a b +--R + +--R +--------+ +--------+ +--R | 1 6+-+5 6+-+ | 1 +--R 12 |-------- \|a \|b log(6a |-------- + x) +--R 6| 5 6| 5 +--R \|46656a b \|46656a b +--R + +--R +--------+ +--------+ +--R | 1 6+-+5 6+-+ | 1 +--R - 12 |-------- \|a \|b log(- 6a |-------- + x) +--R 6| 5 6| 5 +--R \|46656a b \|46656a b +--R + +--R 6+-+6+-+ 2 3+-+ 3+-+ 6+-+ +--R - x\|a \|b + x \|b + \|a x\|b +--R log(---------------------------) - 4atanh(-----) +--R 3+-+ 6+-+ +--R \|b \|a +--R + +--R +-+6+-+ +-+6+-+ +-+6+-+ +-+6+-+ +--R +-+ 2x\|3 \|b + \|3 \|a +-+ 2x\|3 \|b - \|3 \|a +--R - 2\|3 atan(---------------------) - 2\|3 atan(---------------------) +--R 6+-+ 6+-+ +--R 3\|a 3\|a +--R + +--R +--------+ +--R +-+ | 1 +--R 3a\|3 |-------- +--R +--------+ 6| 5 +--R +-+ | 1 6+-+5 6+-+ \|46656a b +--R 12\|3 |-------- \|a \|b atan(-----------------) +--R 6| 5 +--------+ +--R \|46656a b | 1 +--R 3a |-------- - x +--R 6| 5 +--R \|46656a b +--R + +--R +--------+ +--R +-+ | 1 +--R 3a\|3 |-------- +--R +--------+ 6| 5 +--R +-+ | 1 6+-+5 6+-+ \|46656a b +--R - 12\|3 |-------- \|a \|b atan(-----------------) +--R 6| 5 +--------+ +--R \|46656a b | 1 +--R 3a |-------- + x +--R 6| 5 +--R \|46656a b +--R / +--R 6+-+5 6+-+ +--R 12\|a \|b +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1483 +d0180:=normalize(D(m0180,x)) +--R +--R +--R (933) 0 +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1483 +t0181:= 1/x^2/(a-b*x^6) +--R +--R +--R 1 +--R (934) - ----------- +--R 8 2 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 934 + +--S 935 of 1483 +r0181:= -1/12/a^(7/6)*(12*a^(1/6)+2*b^(1/6)*atan(1/3*3^(1/2)*(-a^(1/6)+_ + 2*b^(1/6)*x)/a^(1/6))*3^(1/2)*x+2*b^(1/6)*atan(1/3*3^(1/2)*_ + (a^(1/6)+2*b^(1/6)*x)/a^(1/6))*3^(1/2)*x-4*b^(1/6)*_ + atanh(b^(1/6)*x/a^(1/6))*x+b^(1/6)*log(1/b^(1/3)*(a^(1/3)-_ + a^(1/6)*x*b^(1/6)+b^(1/3)*x^2))*x-b^(1/6)*log(1/b^(1/3)*_ + (a^(1/3)+a^(1/6)*x*b^(1/6)+b^(1/3)*x^2))*x)/x +--R +--R +--R (935) +--R 6+-+6+-+ 2 3+-+ 3+-+ +--R 6+-+ x\|a \|b + x \|b + \|a +--R x\|b log(-------------------------) +--R 3+-+ +--R \|b +--R + +--R 6+-+6+-+ 2 3+-+ 3+-+ 6+-+ +--R 6+-+ - x\|a \|b + x \|b + \|a 6+-+ x\|b +--R - x\|b log(---------------------------) + 4x\|b atanh(-----) +--R 3+-+ 6+-+ +--R \|b \|a +--R + +--R +-+6+-+ +-+6+-+ +--R +-+6+-+ 2x\|3 \|b + \|3 \|a +--R - 2x\|3 \|b atan(---------------------) +--R 6+-+ +--R 3\|a +--R + +--R +-+6+-+ +-+6+-+ +--R +-+6+-+ 2x\|3 \|b - \|3 \|a 6+-+ +--R - 2x\|3 \|b atan(---------------------) - 12\|a +--R 6+-+ +--R 3\|a +--R / +--R 6+-+ +--R 12a x\|a +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1483 +a0181:=integrate(t0181,x) +--R +--R +--R (936) +--R +-------+ +-------+5 +-------+4 +--R | b 6 | b 5 | b 2 +--R a x |------- log(7776a x |------- + 1296a |------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \|46656a \|46656a \|46656a +--R + +--R +-------+ +-------+5 +--R | b 6 | b +--R 2a x |------- log(7776a |------- + b x) +--R 6| 7 6| 7 +--R \|46656a \|46656a +--R + +--R +-------+ +-------+5 +--R | b 6 | b +--R - 2a x |------- log(- 7776a |------- + b x) +--R 6| 7 6| 7 +--R \|46656a \|46656a +--R + +--R +-------+ +-------+5 +-------+4 +--R | b 6 | b 5 | b 2 +--R - a x |------- log(- 7776a x |------- + 1296a |------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \|46656a \|46656a \|46656a +--R + +--R +-------+5 +--R 6 +-+ | b +--R 3888a \|3 |------- +--R +-------+ 6| 7 +--R +-+ | b \|46656a +--R - 2a x\|3 |------- atan(-----------------------) +--R 6| 7 +-------+5 +--R \|46656a 6 | b +--R 3888a |------- - b x +--R 6| 7 +--R \|46656a +--R + +--R +-------+5 +--R 6 +-+ | b +--R 3888a \|3 |------- +--R +-------+ 6| 7 +--R +-+ | b \|46656a +--R 2a x\|3 |------- atan(----------------------- - 2 +--R 6| 7 +-------+5 +--R \|46656a 6 | b +--R 3888a |------- + b x +--R 6| 7 +--R \|46656a +--R / +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 936 + +--S 937 of 1483 +m0181:=a0181-r0181 +--R +--R +--R (937) +--R 6+-+6+-+ 2 3+-+ 3+-+ +--R 6+-+ x\|a \|b + x \|b + \|a +--R - \|b log(-------------------------) +--R 3+-+ +--R \|b +--R + +--R +-------+ +-------+5 +-------+4 +--R 6+-+ | b 6 | b 5 | b 2 +--R 6a\|a |------- log(7776a x |------- + 1296a |------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \|46656a \|46656a \|46656a +--R + +--R +-------+ +-------+5 +--R 6+-+ | b 6 | b +--R 12a\|a |------- log(7776a |------- + b x) +--R 6| 7 6| 7 +--R \|46656a \|46656a +--R + +--R +-------+ +-------+5 +--R 6+-+ | b 6 | b +--R - 12a\|a |------- log(- 7776a |------- + b x) +--R 6| 7 6| 7 +--R \|46656a \|46656a +--R + +--R +-------+ +-------+5 +-------+4 +--R 6+-+ | b 6 | b 5 | b 2 +--R - 6a\|a |------- log(- 7776a x |------- + 1296a |------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \|46656a \|46656a \|46656a +--R + +--R 6+-+6+-+ 2 3+-+ 3+-+ 6+-+ +--R 6+-+ - x\|a \|b + x \|b + \|a 6+-+ x\|b +--R \|b log(---------------------------) - 4\|b atanh(-----) +--R 3+-+ 6+-+ +--R \|b \|a +--R + +--R +-+6+-+ +-+6+-+ +--R +-+6+-+ 2x\|3 \|b + \|3 \|a +--R 2\|3 \|b atan(---------------------) +--R 6+-+ +--R 3\|a +--R + +--R +-+6+-+ +-+6+-+ +--R +-+6+-+ 2x\|3 \|b - \|3 \|a +--R 2\|3 \|b atan(---------------------) +--R 6+-+ +--R 3\|a +--R + +--R +-------+5 +--R 6 +-+ | b +--R 3888a \|3 |------- +--R +-------+ 6| 7 +--R +-+6+-+ | b \|46656a +--R - 12a\|3 \|a |------- atan(-----------------------) +--R 6| 7 +-------+5 +--R \|46656a 6 | b +--R 3888a |------- - b x +--R 6| 7 +--R \|46656a +--R + +--R +-------+5 +--R 6 +-+ | b +--R 3888a \|3 |------- +--R +-------+ 6| 7 +--R +-+6+-+ | b \|46656a +--R 12a\|3 \|a |------- atan(-----------------------) +--R 6| 7 +-------+5 +--R \|46656a 6 | b +--R 3888a |------- + b x +--R 6| 7 +--R \|46656a +--R / +--R 6+-+ +--R 12a\|a +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1483 +d0181:=normalize(D(m0181,x)) +--R +--R +--R (938) 0 +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1483 +t0182:= 1/(a-b*x^8) +--R +--R +--R 1 +--R (939) - -------- +--R 8 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 939 + +--S 940 of 1483 +r0182:= 1/16*(4*atan(b^(1/8)*x/a^(1/8))+2*atan((-a^(1/8)+2^(1/2)*_ + b^(1/8)*x)/a^(1/8))*2^(1/2)+2*atan((a^(1/8)+2^(1/2)*b^(1/8)*x)/_ + a^(1/8))*2^(1/2)+4*atanh(b^(1/8)*x/a^(1/8))-log((a^(1/4)-2^(1/2)*_ + a^(1/8)*x*b^(1/8)+x^2*b^(1/4))/b^(1/4))*2^(1/2)+log(1/b^(1/4)*_ + (a^(1/4)+2^(1/2)*a^(1/8)*x*b^(1/8)+x^2*b^(1/4)))*2^(1/2))/_ + a^(7/8)/b^(1/8) +--R +--R +--R (940) +--R +-+8+-+8+-+ 2 4+-+ 4+-+ +--R +-+ x\|2 \|a \|b + x \|b + \|a +--R \|2 log(-----------------------------) +--R 4+-+ +--R \|b +--R + +--R +-+8+-+8+-+ 2 4+-+ 4+-+ 8+-+ +--R +-+ - x\|2 \|a \|b + x \|b + \|a x\|b +--R - \|2 log(-------------------------------) + 4atanh(-----) +--R 4+-+ 8+-+ +--R \|b \|a +--R + +--R +-+8+-+ 8+-+ +-+8+-+ 8+-+ 8+-+ +--R +-+ x\|2 \|b + \|a +-+ x\|2 \|b - \|a x\|b +--R 2\|2 atan(----------------) + 2\|2 atan(----------------) + 4atan(-----) +--R 8+-+ 8+-+ 8+-+ +--R \|a \|a \|a +--R / +--R 8+-+7 8+-+ +--R 16\|a \|b +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1483 +a0182:=integrate(t0182,x) +--R +--R +--R (941) +--R +-----------+ +-----------+2 +-----------+ +--R | 1 2 | 1 +-+ | 1 2 +--R |----------- log(64a |----------- + 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 8| 7 +--R \|16777216a b \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+2 +-----------+ +--R | 1 2 | 1 +-+ | 1 2 +--R - |----------- log(64a |----------- - 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 8| 7 +--R \|16777216a b \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 | 1 +--R \|2 |----------- log(8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 | 1 +--R - \|2 |----------- log(- 8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R +-+ | 1 \|16777216a b +--R - 2\|2 |----------- atan(----------------) +--R 8| 7 x +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 \|16777216a b +--R 2 |----------- atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- - x\|2 +--R 8| 7 +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 \|16777216a b +--R - 2 |----------- atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- + x\|2 +--R 8| 7 +--R \|16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 941 + +--S 942 of 1483 +m0182:=a0182-r0182 +--R +--R +--R (942) +--R +-+8+-+8+-+ 2 4+-+ 4+-+ +--R x\|2 \|a \|b + x \|b + \|a +--R - log(-----------------------------) +--R 4+-+ +--R \|b +--R + +--R +-----------+ +--R | 1 8+-+7 8+-+ +--R 8 |----------- \|a \|b +--R 8| 7 +--R \|16777216a b +--R * +--R +-----------+2 +-----------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |----------- + 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R - +--R +-----------+ +--R | 1 8+-+7 8+-+ +--R 8 |----------- \|a \|b +--R 8| 7 +--R \|16777216a b +--R * +--R +-----------+2 +-----------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |----------- - 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 8+-+7 8+-+ | 1 +--R 8\|2 |----------- \|a \|b log(8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 8+-+7 8+-+ | 1 +--R - 8\|2 |----------- \|a \|b log(- 8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-+8+-+8+-+ 2 4+-+ 4+-+ 8+-+ +--R - x\|2 \|a \|b + x \|b + \|a +-+ x\|b +--R log(-------------------------------) - 2\|2 atanh(-----) +--R 4+-+ 8+-+ +--R \|b \|a +--R + +--R +-+8+-+ 8+-+ +-+8+-+ 8+-+ 8+-+ +--R x\|2 \|b + \|a x\|2 \|b - \|a +-+ x\|b +--R - 2atan(----------------) - 2atan(----------------) - 2\|2 atan(-----) +--R 8+-+ 8+-+ 8+-+ +--R \|a \|a \|a +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R +-+ | 1 8+-+7 8+-+ \|16777216a b +--R - 16\|2 |----------- \|a \|b atan(----------------) +--R 8| 7 x +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 8+-+7 8+-+ \|16777216a b +--R 16 |----------- \|a \|b atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- - x\|2 +--R 8| 7 +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 8+-+7 8+-+ \|16777216a b +--R - 16 |----------- \|a \|b atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- + x\|2 +--R 8| 7 +--R \|16777216a b +--R / +--R +-+8+-+7 8+-+ +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1483 +d0182:=normalize(D(m0182,x)) +--R +--R +--R (943) 0 +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1483 +t0183:= x^5/(9-x^12) +--R +--R +--R 5 +--R x +--R (944) - ------- +--R 12 +--R x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 944 + +--S 945 of 1483 +r0183:= 1/18*atanh(1/3*x^6) +--R +--R +--R 6 +--R x +--R atanh(--) +--R 3 +--R (945) --------- +--R 18 +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1483 +a0183:=integrate(t0183,x) +--R +--R +--R 6 6 +--R log(x + 3) - log(x - 3) +--R (946) ------------------------- +--R 36 +--R Type: Union(Expression(Integer),...) +--E 946 + +--S 947 of 1483 +m0183:=a0183-r0183 +--R +--R +--R 6 +--R 6 6 x +--R log(x + 3) - log(x - 3) - 2atanh(--) +--R 3 +--R (947) -------------------------------------- +--R 36 +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1483 +d0183:=D(m0183,x) +--R +--R +--R (948) 0 +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1483 +t0184:= (a+b/x^2)^3/x^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (949) ----------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 949 + +--S 950 of 1483 +r0184:= -1/8*(a+b/x^2)^4/b +--R +--R +--R 4 8 3 6 2 2 4 3 2 4 +--R - a x - 4a b x - 6a b x - 4a b x - b +--R (950) ----------------------------------------- +--R 8 +--R 8b x +--R Type: Fraction(Polynomial(Integer)) +--E 950 + +--S 951 of 1483 +a0184:=integrate(t0184,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 4a x - 6a b x - 4a b x - b +--R (951) -------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 951 + +--S 952 of 1483 +m0184:=a0184-r0184 +--R +--R +--R 4 +--R a +--R (952) -- +--R 8b +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1483 +d0184:=D(m0184,x) +--R +--R +--R (953) 0 +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1483 +t0185:= 1/x^3/(a+b/x^2)^3 +--R +--R +--R 3 +--R x +--R (954) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 954 + +--S 955 of 1483 +r0185:= 1/4/b/(a+b/x^2)^2 +--R +--R +--R 1 4 +--R - x +--R 4 +--R (955) --------------------- +--R 2 4 2 2 3 +--R a b x + 2a b x + b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 955 + +--S 956 of 1483 +a0185:=integrate(t0185,x) +--R +--R +--R 2 +--R - 2a x - b +--R (956) ----------------------- +--R 4 4 3 2 2 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 956 + +--S 957 of 1483 +m0185:=a0185-r0185 +--R +--R +--R 1 +--R (957) - ---- +--R 2 +--R 4a b +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1483 +d0185:=D(m0185,x) +--R +--R +--R (958) 0 +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1483 +t0186:= 1/(a+b/x^5) +--R +--R +--R 5 +--R x +--R (959) -------- +--R 5 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 959 + +--S 960 of 1483 +r0186:= x/a-1/10*(10-2*5^(1/2))^(1/2)*b^(1/5)*atan(-(5^(1/2)+1)/_ + (10-2*5^(1/2))^(1/2)+2*2^(1/2)/(5-5^(1/2))^(1/2)*a^(1/5)*x/b^(1/5))/_ + a^(6/5)-1/10*(10+2*5^(1/2))^(1/2)*b^(1/5)*atan(-(1-5^(1/2))/_ + (10+2*5^(1/2))^(1/2)+2*2^(1/2)/(5+5^(1/2))^(1/2)*a^(1/5)*x/b^(1/5))/_ + a^(6/5)-1/5*b^(1/5)*log(b^(1/5)/a^(1/5)+x)/a^(6/5)+_ + 1/20*(1-5^(1/2))*b^(1/5)*log(2*b^(2/5)/a^(2/5)-(1-5^(1/2))*b^(1/5)*x/_ + a^(1/5)+2*x^2)/a^(6/5)+1/20*(5^(1/2)+1)*b^(1/5)*_ + log(2*b^(2/5)/a^(2/5)-(5^(1/2)+1)*b^(1/5)*x/a^(1/5)+2*x^2)/a^(6/5) +--R +--R +--R (960) +--R 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R +-+ 5+-+ 2\|b + (x\|5 - x)\|a \|b + 2x \|a +--R (- \|5 + 1)\|b log(---------------------------------------) +--R 5+-+2 +--R \|a +--R + +--R 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R +-+ 5+-+ 2\|b + (- x\|5 - x)\|a \|b + 2x \|a +--R (\|5 + 1)\|b log(-----------------------------------------) +--R 5+-+2 +--R \|a +--R + +--R 5+-+ 5+-+ +--R 5+-+ \|b + x\|a +--R - 4\|b log(------------) +--R 5+-+ +--R \|a +--R + +--R - +--R +----------+ +--R 5+-+ | +-+ +--R 2\|b \|2\|5 + 10 +--R * +--R atan +--R +----------+ +--R +-+ 5+-+ | +-+ +--R (3\|5 - 5)\|b \|2\|5 + 10 +--R + +--R +--------+ +--R +-+ +-+ +-+ 5+-+ | +-+ +--R (- 2x\|2 \|5 + 10x\|2 )\|a \|\|5 + 5 +--R / +--R 5+-+ +--R 20\|b +--R + +--R +------------+ +--R | +-+ 5+-+ +--R 2\|- 2\|5 + 10 \|b +--R * +--R atan +--R +------------+ +--R +-+ | +-+ 5+-+ +--R (3\|5 + 5)\|- 2\|5 + 10 \|b +--R + +--R +----------+ +--R +-+ +-+ +-+ | +-+ 5+-+ +--R (- 2x\|2 \|5 - 10x\|2 )\|- \|5 + 5 \|a +--R / +--R 5+-+ +--R 20\|b +--R + +--R 5+-+ +--R 20x\|a +--R / +--R 5+-+ +--R 20a\|a +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1483 +a0186:=integrate(t0186,x) +--R +--R +--R (961) +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R - 5a %%CL1 - 5a %%CL0 - 5|- - +--R \| a +--R * +--R log +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CL1 + 5a %%CL0 + 5|- - + 2x +--R \| a +--R + +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b 2 2 +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 - 75a %%CL0 +--R \| a +--R + +--R +---+ +---+2 +--R | b | b +--R - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R - 5a %%CL1 - 5a %%CL0 - 5|- - +--R \| a +--R * +--R log +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CL1 + 5a %%CL0 + 5|- - + 2x +--R \| a +--R + +--R 10a %%CL1 log(- 5a %%CL1 + x) + 10a %%CL0 log(- 5a %%CL0 + x) +--R + +--R +---+ +---+ +--R | b | b +--R 2 5|- - log(- 5|- - + x + 10x +--R \| a \| a +--R / +--R 10a +--R Type: Union(Expression(Integer),...) +--E 961 + +--S 962 of 1483 +m0186:=a0186-r0186 +--R +--R +--R (962) +--R - +--R 5+-+ +--R 10a\|a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R 5+-+ 5+-+ | b 5+-+ +--R - 10a\|a %%CL1 - 10a\|a %%CL0 - 2 5|- - \|a +--R \| a +--R * +--R log +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CL1 + 5a %%CL0 + 5|- - + 2x +--R \| a +--R + +--R 5+-+ +--R 10a\|a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b 2 2 +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 - 75a %%CL0 +--R \| a +--R + +--R +---+ +---+2 +--R | b | b +--R - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R 5+-+ 5+-+ | b 5+-+ +--R - 10a\|a %%CL1 - 10a\|a %%CL0 - 2 5|- - \|a +--R \| a +--R * +--R log +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CL1 + (- 50a %%CL0 - 10a 5|- -)%%CL1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CL0 - 10a 5|- - %%CL - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CL1 + 5a %%CL0 + 5|- - + 2x +--R \| a +--R + +--R 5+-+ 5+-+ +--R 20a\|a %%CL1 log(- 5a %%CL1 + x) + 20a\|a %%CL0 log(- 5a %%CL0 + x) +--R + +--R 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R +-+ 5+-+ 2\|b + (x\|5 - x)\|a \|b + 2x \|a +--R (\|5 - 1)\|b log(---------------------------------------) +--R 5+-+2 +--R \|a +--R + +--R 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R +-+ 5+-+ 2\|b + (- x\|5 - x)\|a \|b + 2x \|a +--R (- \|5 - 1)\|b log(-----------------------------------------) +--R 5+-+2 +--R \|a +--R + +--R 5+-+ 5+-+ +---+ +---+ +--R 5+-+ \|b + x\|a | b 5+-+ | b +--R 4\|b log(------------) + 4 5|- - \|a log(- 5|- - + x) +--R 5+-+ \| a \| a +--R \|a +--R + +--R +----------+ +--R 5+-+ | +-+ +--R 2\|b \|2\|5 + 10 +--R * +--R atan +--R +----------+ +--R +-+ 5+-+ | +-+ +--R (3\|5 - 5)\|b \|2\|5 + 10 +--R + +--R +--------+ +--R +-+ +-+ +-+ 5+-+ | +-+ +--R (- 2x\|2 \|5 + 10x\|2 )\|a \|\|5 + 5 +--R / +--R 5+-+ +--R 20\|b +--R + +--R - +--R +------------+ +--R | +-+ 5+-+ +--R 2\|- 2\|5 + 10 \|b +--R * +--R atan +--R +------------+ +--R +-+ | +-+ 5+-+ +--R (3\|5 + 5)\|- 2\|5 + 10 \|b +--R + +--R +----------+ +--R +-+ +-+ +-+ | +-+ 5+-+ +--R (- 2x\|2 \|5 - 10x\|2 )\|- \|5 + 5 \|a +--R / +--R 5+-+ +--R 20\|b +--R / +--R 5+-+ +--R 20a\|a +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1483 +d0186:=normalize(D(m0186,x)) +--R +--R +--R (963) +--R +------------+ +----------+ +--R 5 | +-+ | +-+ 5 +-+ 5+-+2 5+-+4 +--R (a x \|- 2\|5 + 10 \|- \|5 + 5 + (2a x + 2b)\|2 )\|a \|b +--R + +--R +------------+ +----------+ +--R 6 | +-+ | +-+ +--R (- a x - b x)\|- 2\|5 + 10 \|- \|5 + 5 +--R + +--R 6 +-+ +-+ 6 +-+ +--R (- 3a x - 3b x)\|2 \|5 + (5a x + 5b x)\|2 +--R * +--R 5+-+3 5+-+3 +--R \|a \|b +--R + +--R +------------+ +----------+ +--R 2 | +-+ | +-+ 7 2 +-+ 5+-+4 5+-+2 +--R (b x \|- 2\|5 + 10 \|- \|5 + 5 + (2a x + 2b x )\|2 )\|a \|b +--R + +--R 3 +-+ +-+ 3 +-+ 5+-+ +--R (- 3a b x \|2 \|5 + 5a b x \|2 )\|b +--R + +--R 4 +-+ +-+ 4 +-+ 5+-+ +--R (- 3a b x \|2 \|5 + 5a b x \|2 )\|a +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R +------------+ +----------+ +--R 5 +-+ | +-+ | +-+ 5 5+-+2 5+-+4 +--R ((2a x + 2b)\|2 \|- 2\|5 + 10 \|- \|5 + 5 - 80a x - 40b)\|a \|b +--R + +--R +------------+ +--R 6 +-+ +-+ 6 +-+ | +-+ +--R ((3a x + 3b x)\|2 \|5 + (5a x + 5b x)\|2 )\|- 2\|5 + 10 +--R * +--R +----------+ +--R | +-+ 5+-+3 5+-+3 +--R \|- \|5 + 5 \|a \|b +--R + +--R +------------+ +----------+ +--R 7 2 +-+ | +-+ | +-+ 7 2 +--R ((2a x + 2b x )\|2 \|- 2\|5 + 10 \|- \|5 + 5 - 40a x - 80b x ) +--R * +--R 5+-+4 5+-+2 +--R \|a \|b +--R + +--R +------------+ +----------+ +--R 3 +-+ +-+ 3 +-+ | +-+ | +-+ +--R (3a b x \|2 \|5 + 5a b x \|2 )\|- 2\|5 + 10 \|- \|5 + 5 +--R + +--R 3 +--R - 40a b x +--R * +--R 5+-+ +--R \|b +--R + +--R +------------+ +----------+ +--R 4 +-+ +-+ 4 +-+ | +-+ | +-+ +--R (3a b x \|2 \|5 + 5a b x \|2 )\|- 2\|5 + 10 \|- \|5 + 5 +--R + +--R 4 +--R - 40a b x +--R * +--R 5+-+ +--R \|a +--R / +--R 2 6 +-+ +-+ 2 6 +-+ 5+-+3 5+-+3 +--R ((6a x + 6a b x)\|2 \|5 + (- 10a x - 10a b x)\|2 )\|a \|b +--R + +--R +------------+ +----------+ +--R 2 7 2 | +-+ | +-+ 5+-+4 5+-+2 +--R (- 2a x - 2a b x )\|- 2\|5 + 10 \|- \|5 + 5 \|a \|b +--R + +--R 3 8 2 3 +-+ +-+ 3 8 2 3 +-+ 5+-+ +--R ((6a x + 6a b x )\|2 \|5 + (- 10a x - 10a b x )\|2 )\|b +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R 2 5 5+-+2 5+-+4 +--R (80a x + 80a b)\|a \|b +--R + +--R +------------+ +--R 2 6 +-+ +-+ 2 6 +-+ | +-+ +--R ((- 6a x - 6a b x)\|2 \|5 + (- 10a x - 10a b x)\|2 )\|- 2\|5 + 10 +--R * +--R +----------+ +--R | +-+ 5+-+3 5+-+3 +--R \|- \|5 + 5 \|a \|b +--R + +--R 2 7 2 5+-+4 5+-+2 +--R (160a x + 160a b x )\|a \|b +--R + +--R 3 8 2 3 +-+ +-+ 3 8 2 3 +-+ +--R ((- 6a x - 6a b x )\|2 \|5 + (- 10a x - 10a b x )\|2 ) +--R * +--R +------------+ +----------+ +--R | +-+ | +-+ 5+-+ +--R \|- 2\|5 + 10 \|- \|5 + 5 \|b +--R + +--R 3 9 2 4 5+-+ +--R (80a x + 80a b x )\|a +--R Type: Expression(Integer) +--E 963 + +--S 964 of 1483 +t0187:= 1/(a+b/x^6) +--R +--R +--R 6 +--R x +--R (964) -------- +--R 6 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 964 + +--S 965 of 1483 +r0187:= x/a-1/3*b^(1/6)*atan(a^(1/6)*x/b^(1/6))/a^(7/6)-1/6*b^(1/6)*_ + atan(-3^(1/2)+2*a^(1/6)*x/b^(1/6))/a^(7/6)-1/6*b^(1/6)*_ + atan(3^(1/2)+2*a^(1/6)*x/b^(1/6))/a^(7/6)+1/12*b^(1/6)*_ + log(b^(1/3)/a^(1/3)-b^(1/6)*x*3^(1/2)/a^(1/6)+x^2)*3^(1/2)/a^(7/6)-_ + 1/12*b^(1/6)*log(b^(1/3)/a^(1/3)+b^(1/6)*x*3^(1/2)/a^(1/6)+_ + x^2)*3^(1/2)/a^(7/6) +--R +--R +--R (965) +--R +-+3+-+6+-+ 6+-+3+-+ 2 3+-+6+-+ +--R +-+6+-+ x\|3 \|a \|b + \|a \|b + x \|a \|a +--R - \|3 \|b log(-------------------------------------) +--R 3+-+6+-+ +--R \|a \|a +--R + +--R +-+3+-+6+-+ 6+-+3+-+ 2 3+-+6+-+ +--R +-+6+-+ - x\|3 \|a \|b + \|a \|b + x \|a \|a +--R \|3 \|b log(---------------------------------------) +--R 3+-+6+-+ +--R \|a \|a +--R + +--R +-+6+-+ 6+-+ +-+6+-+ 6+-+ +--R 6+-+ \|3 \|b + 2x\|a 6+-+ \|3 \|b - 2x\|a +--R - 2\|b atan(-----------------) + 2\|b atan(-----------------) +--R 6+-+ 6+-+ +--R \|b \|b +--R + +--R 6+-+ +--R 6+-+ x\|a 6+-+ +--R - 4\|b atan(-----) + 12x\|a +--R 6+-+ +--R \|b +--R / +--R 6+-+ +--R 12a\|a +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1483 +a0187:=integrate(t0187,x) +--R +--R +--R (966) +--R +---------+ +---------+2 +---------+ +--R | b 2 | b | b 2 +--R - a |- ------- log(36a |- ------- + 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+2 +---------+ +--R | b 2 | b | b 2 +--R a |- ------- log(36a |- ------- - 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b | b +--R - 2a |- ------- log(6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b | b +--R 2a |- ------- log(- 6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R - 2a\|3 |- ------- atan(------------------) +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- - x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R 2a\|3 |- ------- atan(------------------ + 2x +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- + x +--R 6| 7 +--R \| 46656a +--R / +--R 2a +--R Type: Union(Expression(Integer),...) +--E 966 + +--S 967 of 1483 +m0187:=a0187-r0187 +--R +--R +--R (967) +--R +-+3+-+6+-+ 6+-+3+-+ 2 3+-+6+-+ +--R +-+6+-+ x\|3 \|a \|b + \|a \|b + x \|a \|a +--R \|3 \|b log(-------------------------------------) +--R 3+-+6+-+ +--R \|a \|a +--R + +--R +---------+ +---------+2 +---------+ +--R | b 6+-+ 2 | b | b 2 +--R - 6a |- ------- \|a log(36a |- ------- + 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+2 +---------+ +--R | b 6+-+ 2 | b | b 2 +--R 6a |- ------- \|a log(36a |- ------- - 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b 6+-+ | b +--R - 12a |- ------- \|a log(6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b 6+-+ | b +--R 12a |- ------- \|a log(- 6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +-+3+-+6+-+ 6+-+3+-+ 2 3+-+6+-+ +--R +-+6+-+ - x\|3 \|a \|b + \|a \|b + x \|a \|a +--R - \|3 \|b log(---------------------------------------) +--R 3+-+6+-+ +--R \|a \|a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b 6+-+ \| 46656a +--R - 12a\|3 |- ------- \|a atan(------------------) +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- - x +--R 6| 7 +--R \| 46656a +--R + +--R +-+6+-+ 6+-+ +-+6+-+ 6+-+ +--R 6+-+ \|3 \|b + 2x\|a 6+-+ \|3 \|b - 2x\|a +--R 2\|b atan(-----------------) - 2\|b atan(-----------------) +--R 6+-+ 6+-+ +--R \|b \|b +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 6+-+ +--R +-+ | b 6+-+ \| 46656a 6+-+ x\|a +--R 12a\|3 |- ------- \|a atan(------------------ + 4\|b atan(-----) +--R 6| 7 +---------+ 6+-+ +--R \| 46656a | b \|b +--R 3a |- ------- + x +--R 6| 7 +--R \| 46656a +--R / +--R 6+-+ +--R 12a\|a +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1483 +d0187:=normalize(D(m0187,x)) +--R +--R +--R (968) 0 +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1483 +t0188:= (a+b/x^2)/(c+d/x^2) +--R +--R +--R 2 +--R a x + b +--R (969) -------- +--R 2 +--R c x + d +--R Type: Fraction(Polynomial(Integer)) +--E 969 + +--S 970 of 1483 +r0188:= a*x/c+(b*c-a*d)*atan(c^(1/2)*x/d^(1/2))/c^(3/2)/d^(1/2) +--R +--R +--R +-+ +--R x\|c +-+ +-+ +--R (- a d + b c)atan(-----) + a x\|c \|d +--R +-+ +--R \|d +--R (970) -------------------------------------- +--R +-+ +-+ +--R c\|c \|d +--R Type: Expression(Integer) +--E 970 + +--S 971 of 1483 +a0188:=integrate(t0188,x) +--R +--R +--R (971) +--R 2 +-----+ +--R (c x - d)\|- c d - 2c d x +-----+ +--R (a d - b c)log(---------------------------) + 2a x\|- c d +--R 2 +--R c x + d +--R [----------------------------------------------------------, +--R +-----+ +--R 2c\|- c d +--R +---+ +--R x\|c d +---+ +--R (- a d + b c)atan(-------) + a x\|c d +--R d +--R --------------------------------------] +--R +---+ +--R c\|c d +--R Type: Union(List(Expression(Integer)),...) +--E 971 + +--S 972 of 1483 +m0188a:=a0188.1-r0188 +--R +--R +--R (972) +--R 2 +-----+ +--R +-+ +-+ (c x - d)\|- c d - 2c d x +--R (a d - b c)\|c \|d log(---------------------------) +--R 2 +--R c x + d +--R + +--R +-+ +--R +-----+ x\|c +--R (2a d - 2b c)\|- c d atan(-----) +--R +-+ +--R \|d +--R / +--R +-----+ +-+ +-+ +--R 2c\|- c d \|c \|d +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1483 +d0188a:=D(m0188a,x) +--R +--R +--R (973) 0 +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1483 +m0188b:=a0188.2-r0188 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|c d +---+ x\|c +--R (- a d + b c)\|c \|d atan(-------) + (a d - b c)\|c d atan(-----) +--R d +-+ +--R \|d +--R (974) ----------------------------------------------------------------- +--R +-+ +-+ +---+ +--R c\|c \|d \|c d +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1483 +d0188b:=D(m0188b,x) +--R +--R +--R (975) 0 +--R Type: Expression(Integer) +--E 975 + +--S 976 of 1483 +t0189:= (a+b/x^3)/(c+d/x^3) +--R +--R +--R 3 +--R a x + b +--R (976) -------- +--R 3 +--R c x + d +--R Type: Fraction(Polynomial(Integer)) +--E 976 + +--S 977 of 1483 +r0189:= a*x/c+1/3*(b*c-a*d)*atan(-1/3*3^(1/2)+2/3*c^(1/3)*_ + x*3^(1/2)/d^(1/3))*3^(1/2)/c^(4/3)/d^(2/3)+1/3*(b*c-a*d)*_ + log(d^(1/3)/c^(1/3)+x)/c^(4/3)/d^(2/3)-1/6*(b*c-a*d)*_ + log(d^(2/3)/c^(2/3)-d^(1/3)*x/c^(1/3)+x^2)/c^(4/3)/d^(2/3) +--R +--R +--R (977) +--R 3+-+2 3+-+3+-+ 2 3+-+2 +--R \|d - x\|c \|d + x \|c +--R (a d - b c)log(---------------------------) +--R 3+-+2 +--R \|c +--R + +--R 3+-+ 3+-+ +--R \|d + x\|c +--R (- 2a d + 2b c)log(------------) +--R 3+-+ +--R \|c +--R + +--R +-+3+-+ +-+3+-+ +--R +-+ \|3 \|d - 2x\|3 \|c 3+-+3+-+2 +--R (2a d - 2b c)\|3 atan(---------------------) + 6a x\|c \|d +--R 3+-+ +--R 3\|d +--R / +--R 3+-+3+-+2 +--R 6c\|c \|d +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1483 +a0189:=integrate(t0189,x) +--R +--R +--R (978) +--R +------+2 +------+ +--R +-+ 2 3| 2 3| 2 2 +--R (- a d + b c)\|3 log(x \|- c d + d x\|- c d + d ) +--R + +--R +------+ +--R +-+ 3| 2 +--R (2a d - 2b c)\|3 log(x\|- c d - d) +--R + +--R +------+ +--R +-+3| 2 +-+ +------+ +--R 2x\|3 \|- c d + d\|3 +-+3| 2 +--R (- 6a d + 6b c)atan(-----------------------) + 6a x\|3 \|- c d +--R 3d +--R / +--R +------+ +--R +-+3| 2 +--R 6c\|3 \|- c d +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1483 +m0189:=a0189-r0189 +--R +--R +--R (979) +--R +------+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R +-+3| 2 \|d - x\|c \|d + x \|c +--R (- a d + b c)\|3 \|- c d log(---------------------------) +--R 3+-+2 +--R \|c +--R + +--R +------+ 3+-+ 3+-+ +--R +-+3| 2 \|d + x\|c +--R (2a d - 2b c)\|3 \|- c d log(------------) +--R 3+-+ +--R \|c +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2 +--R (- a d + b c)\|3 \|c \|d log(x \|- c d + d x\|- c d + d ) +--R + +--R +------+ +--R +-+3+-+3+-+2 3| 2 +--R (2a d - 2b c)\|3 \|c \|d log(x\|- c d - d) +--R + +--R +------+ +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- c d + d\|3 +--R (- 6a d + 6b c)\|c \|d atan(-----------------------) +--R 3d +--R + +--R +------+ +-+3+-+ +-+3+-+ +--R 3| 2 \|3 \|d - 2x\|3 \|c +--R (- 6a d + 6b c)\|- c d atan(---------------------) +--R 3+-+ +--R 3\|d +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6c\|3 \|- c d \|c \|d +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1483 +d0189:=D(m0189,x) +--R +--R +--R (980) 0 +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1483 +t0190:= 1/(a+b*(c+d*x)^2)^2 +--R +--R +--R (981) +--R 1 +--R / +--R 2 4 4 2 3 3 2 2 2 2 2 3 2 4 +--R b d x + 4b c d x + (6b c + 2a b)d x + (4b c + 4a b c)d x + b c +--R + +--R 2 2 +--R 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 981 + +--S 982 of 1483 +r0190:= 1/2*(c+d*x)/a/d/(a+b*c^2+2*b*c*d*x+b*d^2*x^2)+1/2*_ + atan(b^(1/2)*(c+d*x)/a^(1/2))/a^(3/2)/b^(1/2)/d +--R +--R +--R (982) +--R +-+ +--R 2 2 2 (d x + c)\|b +-+ +-+ +--R (b d x + 2b c d x + b c + a)atan(-------------) + (d x + c)\|a \|b +--R +-+ +--R \|a +--R --------------------------------------------------------------------- +--R 3 2 2 2 2 +-+ +-+ +--R (2a b d x + 4a b c d x + (2a b c + 2a )d)\|a \|b +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1483 +a0190:=integrate(t0190,x) +--R +--R +--R (983) +--R [ +--R 2 2 2 +--R (b d x + 2b c d x + b c + a) +--R * +--R 2 2 2 +-----+ +--R (b d x + 2b c d x + b c - a)\|- a b + 2a b d x + 2a b c +--R log(----------------------------------------------------------) +--R 2 2 2 +--R b d x + 2b c d x + b c + a +--R + +--R +-----+ +--R (2d x + 2c)\|- a b +--R / +--R 3 2 2 2 2 +-----+ +--R (4a b d x + 8a b c d x + (4a b c + 4a )d)\|- a b +--R , +--R +---+ +--R 2 2 2 (d x + c)\|a b +---+ +--R (b d x + 2b c d x + b c + a)atan(---------------) + (d x + c)\|a b +--R a +--R ---------------------------------------------------------------------] +--R 3 2 2 2 2 +---+ +--R (2a b d x + 4a b c d x + (2a b c + 2a )d)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 983 + +--S 984 of 1483 +m0190a:=a0190.1-r0190 +--R +--R +--R (984) +--R 2 2 2 +-----+ +--R +-+ +-+ (b d x + 2b c d x + b c - a)\|- a b + 2a b d x + 2a b c +--R \|a \|b log(----------------------------------------------------------) +--R 2 2 2 +--R b d x + 2b c d x + b c + a +--R + +--R +-+ +--R +-----+ (d x + c)\|b +--R - 2\|- a b atan(-------------) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 4a d\|- a b \|a \|b +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1483 +d0190a:=D(m0190a,x) +--R +--R +--R (985) 0 +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1483 +m0190b:=a0190.2-r0190 +--R +--R +--R +---+ +-+ +--R +-+ +-+ (d x + c)\|a b +---+ (d x + c)\|b +--R \|a \|b atan(---------------) - \|a b atan(-------------) +--R a +-+ +--R \|a +--R (986) --------------------------------------------------------- +--R +-+ +-+ +---+ +--R 2a d\|a \|b \|a b +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1483 +d0190b:=D(m0190b,x) +--R +--R +--R (987) 0 +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1483 +t0191:= 1/(a+b*(c+d*x)^2)^3 +--R +--R +--R (988) +--R 1 +--R / +--R 3 6 6 3 5 5 3 2 2 4 4 3 3 2 3 3 +--R b d x + 6b c d x + (15b c + 3a b )d x + (20b c + 12a b c)d x +--R + +--R 3 4 2 2 2 2 2 3 5 2 3 2 3 6 +--R (15b c + 18a b c + 3a b)d x + (6b c + 12a b c + 6a b c)d x + b c +--R + +--R 2 4 2 2 3 +--R 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 988 + +--S 989 of 1483 +r0191:= 1/4*(c+d*x)/a/d/(a+b*c^2+2*b*c*d*x+b*d^2*x^2)^2+_ + 3/8*(c+d*x)/a^2/d/(a+b*c^2+2*b*c*d*x+b*d^2*x^2)+_ + 3/8*atan(b^(1/2)*(c+d*x)/a^(1/2))/a^(5/2)/b^(1/2)/d +--R +--R +--R (989) +--R 2 4 4 2 3 3 2 2 2 2 2 3 +--R 3b d x + 12b c d x + (18b c + 6a b)d x + (12b c + 12a b c)d x +--R + +--R 2 4 2 2 +--R 3b c + 6a b c + 3a +--R * +--R +-+ +--R (d x + c)\|b +--R atan(-------------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +-+ +--R (3b d x + 9b c d x + (9b c + 5a)d x + 3b c + 5a c)\|a \|b +--R / +--R 2 2 5 4 2 2 4 3 2 2 2 3 3 2 +--R 8a b d x + 32a b c d x + (48a b c + 16a b)d x +--R + +--R 2 2 3 3 2 2 2 4 3 2 4 +--R (32a b c + 32a b c)d x + (8a b c + 16a b c + 8a )d +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1483 +a0191:=integrate(t0191,x) +--R +--R +--R (990) +--R [ +--R 2 4 4 2 3 3 2 2 2 2 2 3 +--R 3b d x + 12b c d x + (18b c + 6a b)d x + (12b c + 12a b c)d x +--R + +--R 2 4 2 2 +--R 3b c + 6a b c + 3a +--R * +--R 2 2 2 +-----+ +--R (b d x + 2b c d x + b c - a)\|- a b + 2a b d x + 2a b c +--R log(----------------------------------------------------------) +--R 2 2 2 +--R b d x + 2b c d x + b c + a +--R + +--R 3 3 2 2 2 3 +-----+ +--R (6b d x + 18b c d x + (18b c + 10a)d x + 6b c + 10a c)\|- a b +--R / +--R 2 2 5 4 2 2 4 3 2 2 2 3 3 2 +--R 16a b d x + 64a b c d x + (96a b c + 32a b)d x +--R + +--R 2 2 3 3 2 2 2 4 3 2 4 +--R (64a b c + 64a b c)d x + (16a b c + 32a b c + 16a )d +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 2 4 4 2 3 3 2 2 2 2 2 3 +--R 3b d x + 12b c d x + (18b c + 6a b)d x + (12b c + 12a b c)d x +--R + +--R 2 4 2 2 +--R 3b c + 6a b c + 3a +--R * +--R +---+ +--R (d x + c)\|a b +--R atan(---------------) +--R a +--R + +--R 3 3 2 2 2 3 +---+ +--R (3b d x + 9b c d x + (9b c + 5a)d x + 3b c + 5a c)\|a b +--R / +--R 2 2 5 4 2 2 4 3 2 2 2 3 3 2 +--R 8a b d x + 32a b c d x + (48a b c + 16a b)d x +--R + +--R 2 2 3 3 2 2 2 4 3 2 4 +--R (32a b c + 32a b c)d x + (8a b c + 16a b c + 8a )d +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 990 + +--S 991 of 1483 +m0191a:=a0191.1-r0191 +--R +--R +--R (991) +--R 2 2 2 +-----+ +--R +-+ +-+ (b d x + 2b c d x + b c - a)\|- a b + 2a b d x + 2a b c +--R 3\|a \|b log(----------------------------------------------------------) +--R 2 2 2 +--R b d x + 2b c d x + b c + a +--R + +--R +-+ +--R +-----+ (d x + c)\|b +--R - 6\|- a b atan(-------------) +--R +-+ +--R \|a +--R / +--R 2 +-----+ +-+ +-+ +--R 16a d\|- a b \|a \|b +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1483 +d0191a:=D(m0191a,x) +--R +--R +--R (992) 0 +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1483 +m0191b:=a0191.2-r0191 +--R +--R +--R +---+ +-+ +--R +-+ +-+ (d x + c)\|a b +---+ (d x + c)\|b +--R 3\|a \|b atan(---------------) - 3\|a b atan(-------------) +--R a +-+ +--R \|a +--R (993) ----------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a d\|a \|b \|a b +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1483 +d0191b:=D(m0191b,x) +--R +--R +--R (994) 0 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1483 +t0192:= 1/(1-(c+d*x)^2) +--R +--R +--R 1 +--R (995) - ---------------------- +--R 2 2 2 +--R d x + 2c d x + c - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 995 + +--S 996 of 1483 +r0192:= atanh(c+d*x)/d +--R +--R +--R atanh(d x + c) +--R (996) -------------- +--R d +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1483 +a0192:=integrate(t0192,x) +--R +--R +--R log(d x + c + 1) - log(d x + c - 1) +--R (997) ----------------------------------- +--R 2d +--R Type: Union(Expression(Integer),...) +--E 997 + +--S 998 of 1483 +m0192:=a0192-r0192 +--R +--R +--R log(d x + c + 1) - log(d x + c - 1) - 2atanh(d x + c) +--R (998) ----------------------------------------------------- +--R 2d +--R Type: Expression(Integer) +--E 998 + +--S 999 of 1483 +d0192:=D(m0192,x) +--R +--R +--R (999) 0 +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1483 +t0193:= 1/(1-(1+x)^2) +--R +--R +--R 1 +--R (1000) - ------- +--R 2 +--R x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1000 + +--S 1001 of 1483 +r0193:= atanh(1+x) +--R +--R +--R (1001) atanh(x + 1) +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1483 +a0193:=integrate(t0193,x) +--R +--R +--R log(x + 2) - log(x) +--R (1002) ------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1002 + +--S 1003 of 1483 +m0193:=a0193-r0193 +--R +--R +--R log(x + 2) - log(x) - 2atanh(x + 1) +--R (1003) ----------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1483 +d0193:=D(m0193,x) +--R +--R +--R (1004) 0 +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1483 +t0194:= x^3/(a+b*x+c*x^2) +--R +--R +--R 3 +--R x +--R (1005) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1005 + +--S 1006 of 1483 +r0194:= -b*x/c^2+1/2*x^2/c+b*(b^2-3*a*c)*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/c^3/(b^2-4*a*c)^(1/2)+_ + 1/2*(b^2-a*c)*log(a+b*x+c*x^2)/c^3 +--R +--R +--R (1006) +--R 3 2c x + b +--R (- 6a b c + 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 2 2 2 | 2 +--R ((- a c + b )log(c x + b x + a) + c x - 2b c x)\|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1483 +a0194:=integrate(t0194,x) +--R +--R +--R (1007) +--R [ +--R 3 +--R (3a b c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 2 2 2 | 2 +--R ((- a c + b )log(c x + b x + a) + c x - 2b c x)\|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 3 (2c x + b)\|4a c - b +--R (6a b c - 2b )atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 2 2 2 | 2 +--R ((- a c + b )log(c x + b x + a) + c x - 2b c x)\|4a c - b +--R / +--R +---------+ +--R 3 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1007 + +--S 1008 of 1483 +m0194a:=a0194.1-r0194 +--R +--R +--R (1008) +--R 3 +--R (3a b c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2c x + b +--R (6a b c - 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1483 +d0194a:=D(m0194a,x) +--R +--R +--R (1009) 0 +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1483 +m0194b:=a0194.2-r0194 +--R +--R +--R (1010) +--R +---------+ +--R 3 | 2 2c x + b +--R (3a b c - b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 3 | 2 (2c x + b)\|4a c - b +--R (3a b c - b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1483 +d0194b:=D(m0194b,x) +--R +--R +--R (1011) 0 +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1483 +t0195:= x^2/(a+b*x+c*x^2) +--R +--R +--R 2 +--R x +--R (1012) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1012 + +--S 1013 of 1483 +r0195:= x/c-(b^2-2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ + c^2/(b^2-4*a*c)^(1/2)-1/2*b*log(a+b*x+c*x^2)/c^2 +--R +--R +--R (1013) +--R 2 2c x + b +--R (4a c - 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R (- b log(c x + b x + a) + 2c x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1483 +a0195:=integrate(t0195,x) +--R +--R +--R (1014) +--R [ +--R 2 +--R (2a c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R (- b log(c x + b x + a) + 2c x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 (2c x + b)\|4a c - b +--R (- 4a c + 2b )atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (- b log(c x + b x + a) + 2c x)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1014 + +--S 1015 of 1483 +m0195a:=a0195.1-r0195 +--R +--R +--R (1015) +--R 2 +--R (2a c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2c x + b +--R (- 4a c + 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1483 +d0195a:=D(m0195a,x) +--R +--R +--R (1016) 0 +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1483 +m0195b:=a0195.2-r0195 +--R +--R +--R (1017) +--R +---------+ +--R 2 | 2 2c x + b +--R (- 2a c + b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (- 2a c + b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1483 +d0195b:=D(m0195b,x) +--R +--R +--R (1018) 0 +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1483 +t0196:= 1/((a/b)^(2/n)+x^2-2*(a/b)^(1/n)*x*cos((%pi-2*k*%pi)/n)) +--R +--R +--R 1 +--R (1019) ----------------------------------- +--R 2 1 +--R - - +--R a n (2k - 1)%pi a n 2 +--R (-) - 2x cos(-----------)(-) + x +--R b n b +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1483 +r0196:= -atan((-x+(a/b)^(1/n)*cos((%pi-2*k*%pi)/n))/((a/b)^(1/n))/_ + sin((%pi-2*k*%pi)/n))/((a/b)^(1/n))/sin((%pi-2*k*%pi)/n) +--R +--R +--R 1 +--R - +--R (2k - 1)%pi a n +--R cos(-----------)(-) - x +--R n b +--R atan(------------------------) +--R 1 +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R (1020) - ------------------------------ +--R 1 +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1483 +a0196:=integrate(t0196,x) +--R +--R +--R (1021) +--R [ +--R log +--R 2 2 +--R - +--R a n +--R - ((-) ) +--R b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (- cos(-----------) + 3cos(-----------) )((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))(-) +--R n n b +--R + +--R 2 (2k - 1)%pi 2 2 +--R - x cos(-----------) + x +--R n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 4 a n +--R - cos(-----------) ((-) ) +--R n b +--R * +--R +---------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R |(cos(-----------) - 1)(-) +--R \| n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2cos(-----------) - 2cos(-----------))(-) +--R n n b +--R + +--R (2k - 1)%pi 2 +--R - 2x cos(-----------) + 2x +--R n +--R * +--R 2 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 5 (2k - 1)%pi 3 a n +--R (- 2cos(-----------) + 2cos(-----------) )((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (2x cos(-----------) - 2x cos(-----------) )((-) ) +--R n n b +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R / +--R 2 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (- cos(-----------) - cos(-----------) )((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))(-) +--R n n b +--R + +--R 2 (2k - 1)%pi 2 2 +--R - x cos(-----------) + x +--R n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 4 a n +--R cos(-----------) ((-) ) +--R n b +--R / +--R +---------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R 2 |(cos(-----------) - 1)(-) +--R \| n b +--R , +--R +--R atan +--R 1 2 +--R - - +--R (2k - 1)%pi 3 a n (2k - 1)%pi 2 a n +--R (cos(-----------) (-) - x cos(-----------) + 2x)(-) +--R n b n b +--R + +--R 1 3 1 2 +--R - - +--R (2k - 1)%pi 3 a n (2k - 1)%pi 2 a n +--R - cos(-----------) ((-) ) - x cos(-----------) ((-) ) +--R n b n b +--R / +--R +-----------------------------+ +--R 2 | 2 +--R - | - +--R a n 2 | (2k - 1)%pi 2 a n +--R ((-) - x ) |(- cos(-----------) + 1)(-) +--R b \| n b +--R + +--R 1 +--R - +--R (2k - 1)%pi a n +--R cos(-----------)(-) + x +--R n b +--R - atan(--------------------------------) +--R +-----------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R |(- cos(-----------) + 1)(-) +--R \| n b +--R / +--R +-----------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R |(- cos(-----------) + 1)(-) +--R \| n b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1021 + +--S 1022 of 1483 +m0196a:=a0196.1-r0196 +--R +--R +--R (1022) +--R 1 +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R * +--R log +--R 2 2 +--R - +--R a n +--R - ((-) ) +--R b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (- cos(-----------) + 3cos(-----------) )((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))(-) +--R n n b +--R + +--R 2 (2k - 1)%pi 2 2 +--R - x cos(-----------) + x +--R n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 4 a n +--R - cos(-----------) ((-) ) +--R n b +--R * +--R +---------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R |(cos(-----------) - 1)(-) +--R \| n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2cos(-----------) - 2cos(-----------))(-) +--R n n b +--R + +--R (2k - 1)%pi 2 +--R - 2x cos(-----------) + 2x +--R n +--R * +--R 2 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 5 (2k - 1)%pi 3 a n +--R (- 2cos(-----------) + 2cos(-----------) )((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (2x cos(-----------) - 2x cos(-----------) )((-) ) +--R n n b +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R / +--R 2 2 +--R - +--R a n +--R ((-) ) +--R b +--R + +--R 1 2 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (- cos(-----------) - cos(-----------) )((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))(-) +--R n n b +--R + +--R 2 (2k - 1)%pi 2 2 +--R - x cos(-----------) + x +--R n +--R * +--R 2 +--R - +--R a n +--R (-) +--R b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 4 a n +--R cos(-----------) ((-) ) +--R n b +--R + +--R 1 +--R - +---------------------------+ +--R (2k - 1)%pi a n | 2 +--R cos(-----------)(-) - x | - +--R n b | (2k - 1)%pi 2 a n +--R 2atan(------------------------) |(cos(-----------) - 1)(-) +--R 1 \| n b +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R / +--R +---------------------------+ +--R 1 | 2 +--R - | - +--R (2k - 1)%pi a n | (2k - 1)%pi 2 a n +--R 2sin(-----------)(-) |(cos(-----------) - 1)(-) +--R n b \| n b +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1483 +d0196a:=normalize(D(m0196a,x)) +--R +--R +--R (1023) 0 +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1483 +m0196b:=a0196.2-r0196 +--R +--R +--R (1024) +--R 1 +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R * +--R atan +--R 1 2 +--R - - +--R (2k - 1)%pi 3 a n (2k - 1)%pi 2 a n +--R (cos(-----------) (-) - x cos(-----------) + 2x)(-) +--R n b n b +--R + +--R 1 3 1 2 +--R - - +--R (2k - 1)%pi 3 a n (2k - 1)%pi 2 a n +--R - cos(-----------) ((-) ) - x cos(-----------) ((-) ) +--R n b n b +--R / +--R +-----------------------------+ +--R 2 | 2 +--R - | - +--R a n 2 | (2k - 1)%pi 2 a n +--R ((-) - x ) |(- cos(-----------) + 1)(-) +--R b \| n b +--R + +--R 1 +--R - +--R 1 (2k - 1)%pi a n +--R - cos(-----------)(-) + x +--R (2k - 1)%pi a n n b +--R - sin(-----------)(-) atan(--------------------------------) +--R n b +-----------------------------+ +--R | 2 +--R | - +--R | (2k - 1)%pi 2 a n +--R |(- cos(-----------) + 1)(-) +--R \| n b +--R + +--R 1 +--R - +-----------------------------+ +--R (2k - 1)%pi a n | 2 +--R cos(-----------)(-) - x | - +--R n b | (2k - 1)%pi 2 a n +--R atan(------------------------) |(- cos(-----------) + 1)(-) +--R 1 \| n b +--R - +--R (2k - 1)%pi a n +--R sin(-----------)(-) +--R n b +--R / +--R +-----------------------------+ +--R 1 | 2 +--R - | - +--R (2k - 1)%pi a n | (2k - 1)%pi 2 a n +--R sin(-----------)(-) |(- cos(-----------) + 1)(-) +--R n b \| n b +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1483 +d0196b:=normalize(D(m0196b,x)) +--R +--R +--R (1025) 0 +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1483 +t0197:= 1/x^2/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (1026) ------------------ +--R 4 3 2 +--R c x + b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1026 + +--S 1027 of 1483 +r0197:= -1/a/x-(b^2-2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^2/_ + (b^2-4*a*c)^(1/2)-b*log(x)/a^2+1/2*b*log(a+b*x+c*x^2)/a^2 +--R +--R +--R (1027) +--R 2 2c x + b +--R (4a c - 2b )x atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R (b x log(c x + b x + a) - 2b x log(x) - 2a)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a x\|- 4a c + b +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1483 +a0197:=integrate(t0197,x) +--R +--R +--R (1028) +--R [ +--R 2 +--R (2a c - b )x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R (b x log(c x + b x + a) - 2b x log(x) - 2a)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a x\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 (2c x + b)\|4a c - b +--R (- 4a c + 2b )x atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (b x log(c x + b x + a) - 2b x log(x) - 2a)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2a x\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1028 + +--S 1029 of 1483 +m0197a:=a0197.1-r0197 +--R +--R +--R (1029) +--R 2 +--R (2a c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2c x + b +--R (- 4a c + 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a \|- 4a c + b +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1483 +d0197a:=D(m0197a,x) +--R +--R +--R (1030) 0 +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1483 +m0197b:=a0197.2-r0197 +--R +--R +--R (1031) +--R +---------+ +--R 2 | 2 2c x + b +--R (- 2a c + b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (- 2a c + b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R a \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1483 +d0197b:=D(m0197b,x) +--R +--R +--R (1032) 0 +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1483 +t0198:= 1/x^3/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (1033) ------------------ +--R 5 4 3 +--R c x + b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1033 + +--S 1034 of 1483 +r0198:= -1/2/a/x^2+b/a^2/x+b*(b^2-3*a*c)*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/a^3/(b^2-4*a*c)^(1/2)+(b^2-a*c)*_ + log(x)/a^3-1/2*(b^2-a*c)*log(a+b*x+c*x^2)/a^3 +--R +--R +--R (1034) +--R 3 2 2c x + b +--R (- 6a b c + 2b )x atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 +--R (a c - b )x log(c x + b x + a) + (- 2a c + 2b )x log(x) + 2a b x +--R + +--R 2 +--R - a +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 | 2 +--R 2a x \|- 4a c + b +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1483 +a0198:=integrate(t0198,x) +--R +--R +--R (1035) +--R [ +--R 3 2 +--R (3a b c - b )x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 +--R (a c - b )x log(c x + b x + a) + (- 2a c + 2b )x log(x) + 2a b x +--R + +--R 2 +--R - a +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 | 2 +--R 2a x \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 3 2 (2c x + b)\|4a c - b +--R (6a b c - 2b )x atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 2 2 +--R (a c - b )x log(c x + b x + a) + (- 2a c + 2b )x log(x) + 2a b x +--R + +--R 2 +--R - a +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 3 2 | 2 +--R 2a x \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1035 + +--S 1036 of 1483 +m0198a:=a0198.1-r0198 +--R +--R +--R (1036) +--R 3 +--R (3a b c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2c x + b +--R (6a b c - 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2a \|- 4a c + b +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1483 +d0198a:=D(m0198a,x) +--R +--R +--R (1037) 0 +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1483 +m0198b:=a0198.2-r0198 +--R +--R +--R (1038) +--R +---------+ +--R 3 | 2 2c x + b +--R (3a b c - b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 3 | 2 (2c x + b)\|4a c - b +--R (3a b c - b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R a \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1483 +d0198b:=D(m0198b,x) +--R +--R +--R (1039) 0 +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1483 +t0199:= x^3/(a+b*x+c*x^2)^2 +--R +--R +--R 3 +--R x +--R (1040) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1040 + +--S 1041 of 1483 +r0199:= -1/2*(b^2-a*c)/c^3/(a+b*x+c*x^2)+1/2*b*(b^2-3*a*c)*(b+2*c*x)/_ + c^3/(b^2-4*a*c)/(a+b*x+c*x^2)+3*b*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/c^2/(b^2-4*a*c)^(1/2)-2*b*(b^2-3*a*c)*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/c^2/(b^2-4*a*c)^(3/2)+_ + 1/2*log(a+b*x+c*x^2)/c^2 +--R +--R +--R (1041) +--R 2 3 2 2 4 2 3 +--R ((12a b c - 2b c)x + (12a b c - 2b )x + 12a b c - 2a b ) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 3 2 2 2 +--R ((4a c - b c)x + (4a b c - b )x + 4a c - a b )log(c x + b x + a) +--R + +--R 3 2 2 +--R (6a b c - 2b )x + 4a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 2 3 3 2 2 3 2 2 | 2 +--R ((8a c - 2b c )x + (8a b c - 2b c )x + 8a c - 2a b c )\|- 4a c + b +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1483 +a0199:=integrate(t0199,x) +--R +--R +--R (1042) +--R [ +--R 2 3 2 2 4 2 3 +--R ((6a b c - b c)x + (6a b c - b )x + 6a b c - a b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 3 2 2 2 +--R ((4a c - b c)x + (4a b c - b )x + 4a c - a b )log(c x + b x + a) +--R + +--R 3 2 2 +--R (6a b c - 2b )x + 4a c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 2 3 3 2 2 3 2 2 | 2 +--R ((8a c - 2b c )x + (8a b c - 2b c )x + 8a c - 2a b c )\|- 4a c + b +--R , +--R +--R 2 3 2 2 4 2 3 +--R ((- 12a b c + 2b c)x + (- 12a b c + 2b )x - 12a b c + 2a b ) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 3 2 2 2 +--R ((4a c - b c)x + (4a b c - b )x + 4a c - a b )log(c x + b x + a) +--R + +--R 3 2 2 +--R (6a b c - 2b )x + 4a c - 2a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 4 2 3 2 3 3 2 2 3 2 2 | 2 +--R ((8a c - 2b c )x + (8a b c - 2b c )x + 8a c - 2a b c )\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1042 + +--S 1043 of 1483 +m0199a:=a0199.1-r0199 +--R +--R +--R (1043) +--R 3 +--R (6a b c - b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2c x + b +--R (- 12a b c + 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 | 2 +--R (8a c - 2b c )\|- 4a c + b +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1483 +d0199a:=D(m0199a,x) +--R +--R +--R (1044) 0 +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1483 +m0199b:=a0199.2-r0199 +--R +--R +--R (1045) +--R +---------+ +--R 3 | 2 2c x + b +--R (- 6a b c + b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 3 | 2 (2c x + b)\|4a c - b +--R (- 6a b c + b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 3 2 2 | 2 | 2 +--R (4a c - b c )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1483 +d0199b:=D(m0199b,x) +--R +--R +--R (1046) 0 +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1483 +t0200:= x^2/(a+b*x+c*x^2)^2 +--R +--R +--R 2 +--R x +--R (1047) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1047 + +--S 1048 of 1483 +r0200:= -x/c/(a+b*x+c*x^2)-a*(b+2*c*x)/c/(b^2-4*a*c)/(a+b*x+c*x^2)+_ + 4*a*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(3/2) +--R +--R +--R (1048) +--R 2 2 2 2c x + b +--R (- 4a c x - 4a b c x - 4a c)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R ((- 2a c + b )x + a b)\|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 2 3 2 2 2 | 2 +--R ((4a c - b c )x + (4a b c - b c)x + 4a c - a b c)\|- 4a c + b +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1483 +a0200:=integrate(t0200,x) +--R +--R +--R (1049) +--R [ +--R 2 2 2 +--R (2a c x + 2a b c x + 2a c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R ((- 2a c + b )x + a b)\|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 2 3 2 2 2 | 2 +--R ((4a c - b c )x + (4a b c - b c)x + 4a c - a b c)\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 2 2 (2c x + b)\|4a c - b +--R (4a c x + 4a b c x + 4a c)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R ((- 2a c + b )x + a b)\|4a c - b +--R / +--R +---------+ +--R 3 2 2 2 2 3 2 2 2 | 2 +--R ((4a c - b c )x + (4a b c - b c)x + 4a c - a b c)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1049 + +--S 1050 of 1483 +m0200a:=a0200.1-r0200 +--R +--R +--R (1050) +--R 2a +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R 4a atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R (4a c - b )\|- 4a c + b +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1483 +d0200a:=D(m0200a,x) +--R +--R +--R (1051) 0 +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1483 +m0200b:=a0200.2-r0200 +--R +--R +--R (1052) +--R +---------+ +--R | 2 2c x + b +--R 4a\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R 4a\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R (4a c - b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1483 +d0200b:=D(m0200b,x) +--R +--R +--R (1053) 0 +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1483 +t0201:= 1/x^2/(a+b*x+c*x^2)^2 +--R +--R +--R 1 +--R (1054) ----------------------------------------------- +--R 2 6 5 2 4 3 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1054 + +--S 1055 of 1483 +r0201:= -1/a^2/x-1/2*b/a^2/(a+b*x+c*x^2)-1/2*(b^2-2*a*c)*(b+2*c*x)/_ + a^2/(b^2-4*a*c)/(a+b*x+c*x^2)+2*c*(b^2-2*a*c)*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^2/(b^2-4*a*c)^(3/2)-_ + 2*(b^2-a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^3/_ + (b^2-4*a*c)^(1/2)-2*b*log(x)/a^3+b*log(a+b*x+c*x^2)/a^3 +--R +--R +--R (1055) +--R 2 3 2 2 4 3 2 2 3 5 2 +--R (12a c - 12a b c + 2b c)x + (12a b c - 12a b c + 2b )x +--R + +--R 3 2 2 2 4 +--R (12a c - 12a b c + 2a b )x +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 3 2 4 2 2 3 +--R ((4a b c - b c)x + (4a b c - b )x + (4a b c - a b )x) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 2 4 2 2 3 +--R ((- 8a b c + 2b c)x + (- 8a b c + 2b )x + (- 8a b c + 2a b )x) +--R * +--R log(x) +--R + +--R 2 2 2 2 2 3 3 2 2 +--R (- 6a c + 2a b c)x + (- 7a b c + 2a b )x - 4a c + a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 2 3 4 3 3 2 5 4 2 | 2 +--R ((4a c - a b c)x + (4a b c - a b )x + (4a c - a b )x)\|- 4a c + b +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1483 +a0201:=integrate(t0201,x) +--R +--R +--R (1056) +--R [ +--R 2 3 2 2 4 3 2 2 3 5 2 +--R (6a c - 6a b c + b c)x + (6a b c - 6a b c + b )x +--R + +--R 3 2 2 2 4 +--R (6a c - 6a b c + a b )x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 3 2 4 2 2 3 +--R ((4a b c - b c)x + (4a b c - b )x + (4a b c - a b )x) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 2 4 2 2 3 +--R ((- 8a b c + 2b c)x + (- 8a b c + 2b )x + (- 8a b c + 2a b )x) +--R * +--R log(x) +--R + +--R 2 2 2 2 2 3 3 2 2 +--R (- 6a c + 2a b c)x + (- 7a b c + 2a b )x - 4a c + a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 2 3 2 3 4 3 3 2 5 4 2 | 2 +--R ((4a c - a b c)x + (4a b c - a b )x + (4a c - a b )x)\|- 4a c + b +--R , +--R +--R 2 3 2 2 4 3 2 2 3 5 2 +--R (- 12a c + 12a b c - 2b c)x + (- 12a b c + 12a b c - 2b )x +--R + +--R 3 2 2 2 4 +--R (- 12a c + 12a b c - 2a b )x +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 3 3 2 4 2 2 3 +--R ((4a b c - b c)x + (4a b c - b )x + (4a b c - a b )x) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 3 2 4 2 2 3 +--R ((- 8a b c + 2b c)x + (- 8a b c + 2b )x + (- 8a b c + 2a b )x) +--R * +--R log(x) +--R + +--R 2 2 2 2 2 3 3 2 2 +--R (- 6a c + 2a b c)x + (- 7a b c + 2a b )x - 4a c + a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 4 2 3 2 3 4 3 3 2 5 4 2 | 2 +--R ((4a c - a b c)x + (4a b c - a b )x + (4a c - a b )x)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1056 + +--S 1057 of 1483 +m0201a:=a0201.1-r0201 +--R +--R +--R (1057) +--R 2 2 2 4 +--R (6a c - 6a b c + b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 4 2c x + b +--R (- 12a c + 12a b c - 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 3 2 | 2 +--R (4a c - a b )\|- 4a c + b +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1483 +d0201a:=D(m0201a,x) +--R +--R +--R (1058) 0 +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1483 +m0201b:=a0201.2-r0201 +--R +--R +--R (1059) +--R +---------+ +--R 2 2 2 4 | 2 2c x + b +--R (- 12a c + 12a b c - 2b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 2 2 4 | 2 (2c x + b)\|4a c - b +--R (- 12a c + 12a b c - 2b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 4 3 2 | 2 | 2 +--R (4a c - a b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1483 +d0201b:=D(m0201b,x) +--R +--R +--R (1060) 0 +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1483 +t0202:= 1/x^3/(a+b*x+c*x^2)^2 +--R +--R +--R 1 +--R (1061) ----------------------------------------------- +--R 2 7 6 2 5 4 2 3 +--R c x + 2b c x + (2a c + b )x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1061 + +--S 1062 of 1483 +r0202:= -1/2/a^2/x^2+2*b/a^3/x+1/2*(b^2-a*c)/a^3/(a+b*x+c*x^2)+_ + 1/2*b*(b^2-3*a*c)*(b+2*c*x)/a^3/(b^2-4*a*c)/(a+b*x+c*x^2)-_ + 2*b*c*(b^2-3*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^3/_ + (b^2-4*a*c)^(3/2)+3*b*(b^2-2*a*c)*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/a^4/(b^2-4*a*c)^(1/2)+(3*b^2-2*a*c)*log(x)/a^4-_ + 1/2*(3*b^2-2*a*c)*log(a+b*x+c*x^2)/a^4 +--R +--R +--R (1062) +--R 2 3 3 2 5 4 2 2 2 4 6 3 +--R (- 60a b c + 40a b c - 6b c)x + (- 60a b c + 40a b c - 6b )x +--R + +--R 3 2 2 3 5 2 +--R (- 60a b c + 40a b c - 6a b )x +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (8a c - 14a b c + 3b c)x + (8a b c - 14a b c + 3b )x +--R + +--R 3 2 2 2 4 2 +--R (8a c - 14a b c + 3a b )x +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (- 16a c + 28a b c - 6b c)x + (- 16a b c + 28a b c - 6b )x +--R + +--R 3 2 2 2 4 2 +--R (- 16a c + 28a b c - 6a b )x +--R * +--R log(x) +--R + +--R 2 2 3 3 3 2 2 2 4 2 +--R (22a b c - 6a b c)x + (- 8a c + 25a b c - 6a b )x +--R + +--R 3 2 3 4 3 2 +--R (12a b c - 3a b )x - 4a c + a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 5 2 4 2 4 5 4 3 3 6 5 2 2 | 2 +--R ((8a c - 2a b c)x + (8a b c - 2a b )x + (8a c - 2a b )x )\|- 4a c + b +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1483 +a0202:=integrate(t0202,x) +--R +--R +--R (1063) +--R [ +--R 2 3 3 2 5 4 2 2 2 4 6 3 +--R (30a b c - 20a b c + 3b c)x + (30a b c - 20a b c + 3b )x +--R + +--R 3 2 2 3 5 2 +--R (30a b c - 20a b c + 3a b )x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (8a c - 14a b c + 3b c)x + (8a b c - 14a b c + 3b )x +--R + +--R 3 2 2 2 4 2 +--R (8a c - 14a b c + 3a b )x +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (- 16a c + 28a b c - 6b c)x + (- 16a b c + 28a b c - 6b )x +--R + +--R 3 2 2 2 4 2 +--R (- 16a c + 28a b c - 6a b )x +--R * +--R log(x) +--R + +--R 2 2 3 3 3 2 2 2 4 2 +--R (22a b c - 6a b c)x + (- 8a c + 25a b c - 6a b )x +--R + +--R 3 2 3 4 3 2 +--R (12a b c - 3a b )x - 4a c + a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 2 4 2 4 5 4 3 3 6 5 2 2 +--R ((8a c - 2a b c)x + (8a b c - 2a b )x + (8a c - 2a b )x ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 3 3 2 5 4 2 2 2 4 6 3 +--R (60a b c - 40a b c + 6b c)x + (60a b c - 40a b c + 6b )x +--R + +--R 3 2 2 3 5 2 +--R (60a b c - 40a b c + 6a b )x +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (8a c - 14a b c + 3b c)x + (8a b c - 14a b c + 3b )x +--R + +--R 3 2 2 2 4 2 +--R (8a c - 14a b c + 3a b )x +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 3 2 2 4 4 2 2 3 5 3 +--R (- 16a c + 28a b c - 6b c)x + (- 16a b c + 28a b c - 6b )x +--R + +--R 3 2 2 2 4 2 +--R (- 16a c + 28a b c - 6a b )x +--R * +--R log(x) +--R + +--R 2 2 3 3 3 2 2 2 4 2 +--R (22a b c - 6a b c)x + (- 8a c + 25a b c - 6a b )x +--R + +--R 3 2 3 4 3 2 +--R (12a b c - 3a b )x - 4a c + a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 5 2 4 2 4 5 4 3 3 6 5 2 2 | 2 +--R ((8a c - 2a b c)x + (8a b c - 2a b )x + (8a c - 2a b )x )\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1063 + +--S 1064 of 1483 +m0202a:=a0202.1-r0202 +--R +--R +--R (1064) +--R 2 2 3 5 +--R (30a b c - 20a b c + 3b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 5 2c x + b +--R (60a b c - 40a b c + 6b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 5 4 2 | 2 +--R (8a c - 2a b )\|- 4a c + b +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1483 +d0202a:=D(m0202a,x) +--R +--R +--R (1065) 0 +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1483 +m0202b:=a0202.2-r0202 +--R +--R +--R (1066) +--R +---------+ +--R 2 2 3 5 | 2 2c x + b +--R (30a b c - 20a b c + 3b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 2 3 5 | 2 (2c x + b)\|4a c - b +--R (30a b c - 20a b c + 3b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 5 4 2 | 2 | 2 +--R (4a c - a b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1483 +d0202b:=D(m0202b,x) +--R +--R +--R (1067) 0 +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1483 +t0203:= x^3/(a+b*x+c*x^2)^3 +--R +--R +--R (1068) +--R 3 +--R x +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1068 + +--S 1069 of 1483 +r0203:= -1/4*a/c^2/(a+b*x+c*x^2)^2-1/2*x^2/c/(a+b*x+c*x^2)^2+_ + 1/4*a*b*(b+2*c*x)/c^2/(b^2-4*a*c)/(a+b*x+c*x^2)^2-_ + 3/2*a*b*(b+2*c*x)/c/(b^2-4*a*c)^2/(a+b*x+c*x^2)+_ + 6*a*b*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(5/2) +--R +--R +--R (1069) +--R 3 4 2 2 3 2 2 3 2 2 2 +--R 12a b c x + 24a b c x + (24a b c + 12a b c)x + 24a b c x +--R + +--R 3 +--R 12a b c +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 2 4 2 2 3 3 +--R - 6a b c x + (- 16a c - a b c - b )x + (- 10a b c - 2a b )x - 8a c +--R + +--R 2 2 +--R - a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 5 2 4 4 3 4 2 4 3 3 5 2 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c )x +--R + +--R 3 4 4 2 6 2 3 3 2 3 2 5 4 3 +--R (64a c - 12a b c + 2b c)x + (64a b c - 32a b c + 4a b c)x + 32a c +--R + +--R 3 2 2 2 4 +--R - 16a b c + 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1483 +a0203:=integrate(t0203,x) +--R +--R +--R (1070) +--R [ +--R 3 4 2 2 3 2 2 3 2 2 2 3 +--R (6a b c x + 12a b c x + (12a b c + 6a b c)x + 12a b c x + 6a b c) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 4 2 2 3 +--R - 6a b c x + (- 16a c - a b c - b )x + (- 10a b c - 2a b )x +--R + +--R 3 2 2 +--R - 8a c - a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 5 2 4 4 3 4 2 4 3 3 5 2 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c )x +--R + +--R 3 4 4 2 6 2 3 3 2 3 2 5 +--R (64a c - 12a b c + 2b c)x + (64a b c - 32a b c + 4a b c)x +--R + +--R 4 3 3 2 2 2 4 +--R 32a c - 16a b c + 2a b c +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 3 4 2 2 3 2 2 3 2 2 2 +--R - 12a b c x - 24a b c x + (- 24a b c - 12a b c)x - 24a b c x +--R + +--R 3 +--R - 12a b c +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 3 2 2 2 4 2 2 3 +--R - 6a b c x + (- 16a c - a b c - b )x + (- 10a b c - 2a b )x +--R + +--R 3 2 2 +--R - 8a c - a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 2 5 2 4 4 3 4 2 4 3 3 5 2 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c )x +--R + +--R 3 4 4 2 6 2 3 3 2 3 2 5 +--R (64a c - 12a b c + 2b c)x + (64a b c - 32a b c + 4a b c)x +--R + +--R 4 3 3 2 2 2 4 +--R 32a c - 16a b c + 2a b c +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1070 + +--S 1071 of 1483 +m0203a:=a0203.1-r0203 +--R +--R +--R (1071) +--R 3a b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R - 6a b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 2 4 | 2 +--R (16a c - 8a b c + b )\|- 4a c + b +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1483 +d0203a:=D(m0203a,x) +--R +--R +--R (1072) 0 +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1483 +m0203b:=a0203.2-r0203 +--R +--R +--R (1073) +--R +---------+ +--R | 2 2c x + b +--R - 6a b\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R - 6a b\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 2 2 4 | 2 | 2 +--R (16a c - 8a b c + b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1483 +d0203b:=D(m0203b,x) +--R +--R +--R (1074) 0 +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1483 +t0204:= x^2/(a+b*x+c*x^2)^3 +--R +--R +--R (1075) +--R 2 +--R x +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1075 + +--S 1076 of 1483 +r0204:= 1/12*b/c^2/(a+b*x+c*x^2)^2-1/3*x/c/(a+b*x+c*x^2)^2-_ + 1/12*(b^2+2*a*c)*(b+2*c*x)/c^2/(b^2-4*a*c)/(a+b*x+c*x^2)^2+_ + 1/2*(2*a+b^2/c)*(b+2*c*x)/(b^2-4*a*c)^2/(a+b*x+c*x^2)-_ + 2*(b^2+2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(5/2) +--R +--R +--R (1076) +--R 3 2 2 4 2 3 3 +--R (- 8a c - 4b c )x + (- 16a b c - 8b c)x +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (- 16a c - 16a b c - 4b )x + (- 16a b c - 8a b )x - 8a c - 4a b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 3 2 2 2 2 +--R ((4a c + 2b c)x + (6a b c + 3b )x + (- 4a c + 10a b )x + 6a b) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 4 2 3 4 2 4 2 3 3 2 5 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c)x +--R + +--R 3 3 4 6 2 3 2 2 3 5 4 2 +--R (64a c - 12a b c + 2b )x + (64a b c - 32a b c + 4a b )x + 32a c +--R + +--R 3 2 2 4 +--R - 16a b c + 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1483 +a0204:=integrate(t0204,x) +--R +--R +--R (1077) +--R [ +--R 3 2 2 4 2 3 3 2 2 2 4 2 +--R (4a c + 2b c )x + (8a b c + 4b c)x + (8a c + 8a b c + 2b )x +--R + +--R 2 3 3 2 2 +--R (8a b c + 4a b )x + 4a c + 2a b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 3 2 2 2 2 +--R ((4a c + 2b c)x + (6a b c + 3b )x + (- 4a c + 10a b )x + 6a b) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 4 2 3 4 2 4 2 3 3 2 5 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c)x +--R + +--R 3 3 4 6 2 3 2 2 3 5 4 2 +--R (64a c - 12a b c + 2b )x + (64a b c - 32a b c + 4a b )x + 32a c +--R + +--R 3 2 2 4 +--R - 16a b c + 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 3 2 2 4 2 3 3 +--R (8a c + 4b c )x + (16a b c + 8b c)x +--R + +--R 2 2 2 4 2 2 3 3 2 2 +--R (16a c + 16a b c + 4b )x + (16a b c + 8a b )x + 8a c + 4a b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 3 3 2 2 2 2 +--R ((4a c + 2b c)x + (6a b c + 3b )x + (- 4a c + 10a b )x + 6a b) +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 2 4 2 3 4 2 4 2 3 3 2 5 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c)x +--R + +--R 3 3 4 6 2 3 2 2 3 5 4 2 +--R (64a c - 12a b c + 2b )x + (64a b c - 32a b c + 4a b )x + 32a c +--R + +--R 3 2 2 4 +--R - 16a b c + 2a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1077 + +--S 1078 of 1483 +m0204a:=a0204.1-r0204 +--R +--R +--R (1078) +--R 2 +--R (2a c + b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2c x + b +--R (4a c + 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 2 4 | 2 +--R (16a c - 8a b c + b )\|- 4a c + b +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1483 +d0204a:=D(m0204a,x) +--R +--R +--R (1079) 0 +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1483 +m0204b:=a0204.2-r0204 +--R +--R +--R (1080) +--R +---------+ +--R 2 | 2 2c x + b +--R (4a c + 2b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (4a c + 2b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 2 2 4 | 2 | 2 +--R (16a c - 8a b c + b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1483 +d0204b:=D(m0204b,x) +--R +--R +--R (1081) 0 +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1483 +t0205:= 1/(a+b*x+c*x^2)^3 +--R +--R +--R (1082) +--R 1 +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1082 + +--S 1083 of 1483 +r0205:= -1/2*(b+2*c*x)/(b^2-4*a*c)/(a+b*x+c*x^2)^2+_ + 3*c*(b+2*c*x)/(b^2-4*a*c)^2/(a+b*x+c*x^2)-_ + 12*c^2*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(5/2) +--R +--R +--R (1083) +--R 4 4 3 3 3 2 2 2 2 2 2 +--R (- 24c x - 48b c x + (- 48a c - 24b c )x - 48a b c x - 24a c ) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 3 2 2 2 2 3 | 2 +--R (12c x + 18b c x + (20a c + 4b c)x + 10a b c - b )\|- 4a c + b +--R / +--R 2 4 2 3 4 2 4 2 3 3 2 5 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c)x +--R + +--R 3 3 4 6 2 3 2 2 3 5 4 2 +--R (64a c - 12a b c + 2b )x + (64a b c - 32a b c + 4a b )x + 32a c +--R + +--R 3 2 2 4 +--R - 16a b c + 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1483 +a0205:=integrate(t0205,x) +--R +--R +--R (1084) +--R [ +--R 4 4 3 3 3 2 2 2 2 2 2 +--R (12c x + 24b c x + (24a c + 12b c )x + 24a b c x + 12a c ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 3 3 2 2 2 2 3 | 2 +--R (12c x + 18b c x + (20a c + 4b c)x + 10a b c - b )\|- 4a c + b +--R / +--R 2 4 2 3 4 2 4 2 3 3 2 5 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c)x +--R + +--R 3 3 4 6 2 3 2 2 3 5 4 2 +--R (64a c - 12a b c + 2b )x + (64a b c - 32a b c + 4a b )x + 32a c +--R + +--R 3 2 2 4 +--R - 16a b c + 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 4 4 3 3 3 2 2 2 2 2 2 +--R (24c x + 48b c x + (48a c + 24b c )x + 48a b c x + 24a c ) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 3 3 2 2 2 2 3 | 2 +--R (12c x + 18b c x + (20a c + 4b c)x + 10a b c - b )\|4a c - b +--R / +--R 2 4 2 3 4 2 4 2 3 3 2 5 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c)x +--R + +--R 3 3 4 6 2 3 2 2 3 5 4 2 +--R (64a c - 12a b c + 2b )x + (64a b c - 32a b c + 4a b )x + 32a c +--R + +--R 3 2 2 4 +--R - 16a b c + 2a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1084 + +--S 1085 of 1483 +m0205a:=a0205.1-r0205 +--R +--R +--R (1085) +--R 2 +--R 6c +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2c x + b +--R 12c atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 2 2 4 | 2 +--R (16a c - 8a b c + b )\|- 4a c + b +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1483 +d0205a:=D(m0205a,x) +--R +--R +--R (1086) 0 +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1483 +m0205b:=a0205.2-r0205 +--R +--R +--R (1087) +--R +---------+ +--R 2 | 2 2c x + b +--R 12c \|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R 12c \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 2 2 4 | 2 | 2 +--R (16a c - 8a b c + b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1483 +d0205b:=D(m0205b,x) +--R +--R +--R (1088) 0 +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1483 +t0206:= 1/x/(a+b*x+c*x^2)^3 +--R +--R +--R (1089) +--R 1 +--R / +--R 3 7 2 6 2 2 5 3 4 2 2 3 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 2 3 +--R 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1089 + +--S 1090 of 1483 +r0206:= 1/4/a/(a+b*x+c*x^2)^2+1/4*b*(b+2*c*x)/a/(b^2-4*a*c)/(a+b*x+c*x^2)^2+_ + 1/2/a^2/(a+b*x+c*x^2)-3/2*b*c*(b+2*c*x)/a/(b^2-4*a*c)^2/(a+b*x+c*x^2)+_ + 1/2*b*(b+2*c*x)/a^2/(b^2-4*a*c)/(a+b*x+c*x^2)+6*b*c^2*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a/(b^2-4*a*c)^(5/2)-_ + 2*b*c*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^2/(b^2-4*a*c)^(3/2)+_ + b*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^3/(b^2-4*a*c)^(1/2)+_ + log(x)/a^3-1/2*log(a+b*x+c*x^2)/a^3 +--R +--R +--R (1090) +--R 2 4 3 3 5 2 4 2 2 3 4 2 6 3 +--R (60a b c - 20a b c + 2b c )x + (120a b c - 40a b c + 4b c)x +--R + +--R 3 3 2 3 2 5 7 2 +--R (120a b c + 20a b c - 16a b c + 2b )x +--R + +--R 3 2 2 2 4 6 4 2 3 3 2 5 +--R (120a b c - 40a b c + 4a b )x + 60a b c - 20a b c + 2a b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 4 2 3 4 2 4 2 3 3 2 5 3 +--R (- 16a c + 8a b c - b c )x + (- 32a b c + 16a b c - 2b c)x +--R + +--R 3 3 4 6 2 3 2 2 3 5 +--R (- 32a c + 6a b c - b )x + (- 32a b c + 16a b c - 2a b )x +--R + +--R 4 2 3 2 2 4 +--R - 16a c + 8a b c - a b +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 4 2 3 4 2 4 2 3 3 2 5 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c)x +--R + +--R 3 3 4 6 2 3 2 2 3 5 +--R (64a c - 12a b c + 2b )x + (64a b c - 32a b c + 4a b )x +--R + +--R 4 2 3 2 2 4 +--R 32a c - 16a b c + 2a b +--R * +--R log(x) +--R + +--R 2 3 3 2 3 3 3 2 2 2 4 2 +--R (- 14a b c + 2a b c )x + (16a c - 29a b c + 4a b c)x +--R + +--R 3 2 2 3 5 4 2 3 2 2 4 +--R (- 2a b c - 12a b c + 2a b )x + 24a c - 21a b c + 3a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 4 4 2 3 3 4 2 4 5 3 4 3 2 3 5 3 +--R (32a c - 16a b c + 2a b c )x + (64a b c - 32a b c + 4a b c)x +--R + +--R 6 3 4 4 3 6 2 6 2 5 3 4 5 7 2 +--R (64a c - 12a b c + 2a b )x + (64a b c - 32a b c + 4a b )x + 32a c +--R + +--R 6 2 5 4 +--R - 16a b c + 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1483 +a0206:=integrate(t0206,x) +--R +--R +--R (1091) +--R [ +--R 2 4 3 3 5 2 4 2 2 3 4 2 6 3 +--R (30a b c - 10a b c + b c )x + (60a b c - 20a b c + 2b c)x +--R + +--R 3 3 2 3 2 5 7 2 +--R (60a b c + 10a b c - 8a b c + b )x +--R + +--R 3 2 2 2 4 6 4 2 3 3 2 5 +--R (60a b c - 20a b c + 2a b )x + 30a b c - 10a b c + a b +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 4 2 3 4 2 4 +--R (- 16a c + 8a b c - b c )x +--R + +--R 2 3 3 2 5 3 3 3 4 6 2 +--R (- 32a b c + 16a b c - 2b c)x + (- 32a c + 6a b c - b )x +--R + +--R 3 2 2 3 5 4 2 3 2 2 4 +--R (- 32a b c + 16a b c - 2a b )x - 16a c + 8a b c - a b +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 4 2 3 4 2 4 2 3 3 2 5 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c)x +--R + +--R 3 3 4 6 2 3 2 2 3 5 +--R (64a c - 12a b c + 2b )x + (64a b c - 32a b c + 4a b )x +--R + +--R 4 2 3 2 2 4 +--R 32a c - 16a b c + 2a b +--R * +--R log(x) +--R + +--R 2 3 3 2 3 3 3 2 2 2 4 2 +--R (- 14a b c + 2a b c )x + (16a c - 29a b c + 4a b c)x +--R + +--R 3 2 2 3 5 4 2 3 2 2 4 +--R (- 2a b c - 12a b c + 2a b )x + 24a c - 21a b c + 3a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 5 4 4 2 3 3 4 2 4 5 3 4 3 2 3 5 3 +--R (32a c - 16a b c + 2a b c )x + (64a b c - 32a b c + 4a b c)x +--R + +--R 6 3 4 4 3 6 2 6 2 5 3 4 5 7 2 +--R (64a c - 12a b c + 2a b )x + (64a b c - 32a b c + 4a b )x + 32a c +--R + +--R 6 2 5 4 +--R - 16a b c + 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 4 3 3 5 2 4 +--R (- 60a b c + 20a b c - 2b c )x +--R + +--R 2 2 3 4 2 6 3 +--R (- 120a b c + 40a b c - 4b c)x +--R + +--R 3 3 2 3 2 5 7 2 +--R (- 120a b c - 20a b c + 16a b c - 2b )x +--R + +--R 3 2 2 2 4 6 4 2 3 3 2 5 +--R (- 120a b c + 40a b c - 4a b )x - 60a b c + 20a b c - 2a b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 4 2 3 4 2 4 +--R (- 16a c + 8a b c - b c )x +--R + +--R 2 3 3 2 5 3 3 3 4 6 2 +--R (- 32a b c + 16a b c - 2b c)x + (- 32a c + 6a b c - b )x +--R + +--R 3 2 2 3 5 4 2 3 2 2 4 +--R (- 32a b c + 16a b c - 2a b )x - 16a c + 8a b c - a b +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 4 2 3 4 2 4 2 3 3 2 5 3 +--R (32a c - 16a b c + 2b c )x + (64a b c - 32a b c + 4b c)x +--R + +--R 3 3 4 6 2 3 2 2 3 5 +--R (64a c - 12a b c + 2b )x + (64a b c - 32a b c + 4a b )x +--R + +--R 4 2 3 2 2 4 +--R 32a c - 16a b c + 2a b +--R * +--R log(x) +--R + +--R 2 3 3 2 3 3 3 2 2 2 4 2 +--R (- 14a b c + 2a b c )x + (16a c - 29a b c + 4a b c)x +--R + +--R 3 2 2 3 5 4 2 3 2 2 4 +--R (- 2a b c - 12a b c + 2a b )x + 24a c - 21a b c + 3a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 5 4 4 2 3 3 4 2 4 5 3 4 3 2 3 5 3 +--R (32a c - 16a b c + 2a b c )x + (64a b c - 32a b c + 4a b c)x +--R + +--R 6 3 4 4 3 6 2 6 2 5 3 4 5 7 2 +--R (64a c - 12a b c + 2a b )x + (64a b c - 32a b c + 4a b )x + 32a c +--R + +--R 6 2 5 4 +--R - 16a b c + 2a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1091 + +--S 1092 of 1483 +m0206a:=a0206.1-r0206 +--R +--R +--R (1092) +--R 2 2 3 5 +--R (30a b c - 10a b c + b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 5 2c x + b +--R (- 60a b c + 20a b c - 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 5 2 4 2 3 4 | 2 +--R (32a c - 16a b c + 2a b )\|- 4a c + b +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1483 +d0206a:=D(m0206a,x) +--R +--R +--R (1093) 0 +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1483 +m0206b:=a0206.2-r0206 +--R +--R +--R (1094) +--R +---------+ +--R 2 2 3 5 | 2 2c x + b +--R (- 30a b c + 10a b c - b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 2 3 5 | 2 (2c x + b)\|4a c - b +--R (- 30a b c + 10a b c - b )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 5 2 4 2 3 4 | 2 | 2 +--R (16a c - 8a b c + a b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1483 +d0206b:=D(m0206b,x) +--R +--R +--R (1095) 0 +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1483 +t0207:= 1/x^2/(a+b*x+c*x^2)^3 +--R +--R +--R (1096) +--R 1 +--R / +--R 3 8 2 7 2 2 6 3 5 2 2 4 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 3 2 +--R 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1096 + +--S 1097 of 1483 +r0207:= -1/a^3/x-1/4*b/a^2/(a+b*x+c*x^2)^2-1/4*(b^2-2*a*c)*(b+2*c*x)/a^2/(b^2-_ + 4*a*c)/(a+b*x+c*x^2)^2-b/a^3/(a+b*x+c*x^2)+3/2*c*(b^2-2*a*c)*_ + (b+2*c*x)/a^2/(b^2-4*a*c)^2/(a+b*x+c*x^2)-(b^2-a*c)*_ + (b+2*c*x)/a^3/(b^2-4*a*c)/(a+b*x+c*x^2)-6*c^2*(b^2-2*a*c)*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^2/(b^2-4*a*c)^(5/2)-_ + (3*b^2-2*a*c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^4/_ + (b^2-4*a*c)^(1/2)+4*c*(b^2-a*c)*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/a^3/(b^2-4*a*c)^(3/2)-3*b*log(x)/a^4+_ + 3/2*b*log(a+b*x+c*x^2)/a^4 +--R +--R +--R (1097) +--R 3 5 2 2 4 4 3 6 2 5 +--R (120a c - 180a b c + 60a b c - 6b c )x +--R + +--R 3 4 2 3 3 5 2 7 4 +--R (240a b c - 360a b c + 120a b c - 12b c)x +--R + +--R 4 4 3 2 3 2 4 2 6 8 3 +--R (240a c - 240a b c - 60a b c + 48a b c - 6b )x +--R + +--R 4 3 3 3 2 2 5 7 2 +--R (240a b c - 360a b c + 120a b c - 12a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 +--R (120a c - 180a b c + 60a b c - 6a b )x +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 4 3 3 5 2 5 2 2 3 4 2 6 4 +--R (48a b c - 24a b c + 3b c )x + (96a b c - 48a b c + 6b c)x +--R + +--R 3 3 5 7 3 3 2 2 2 4 6 2 +--R (96a b c - 18a b c + 3b )x + (96a b c - 48a b c + 6a b )x +--R + +--R 4 2 3 3 2 5 +--R (48a b c - 24a b c + 3a b )x +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 4 3 3 5 2 5 +--R (- 96a b c + 48a b c - 6b c )x +--R + +--R 2 2 3 4 2 6 4 +--R (- 192a b c + 96a b c - 12b c)x +--R + +--R 3 3 5 7 3 +--R (- 192a b c + 36a b c - 6b )x +--R + +--R 3 2 2 2 4 6 2 +--R (- 192a b c + 96a b c - 12a b )x +--R + +--R 4 2 3 3 2 5 +--R (- 96a b c + 48a b c - 6a b )x +--R * +--R log(x) +--R + +--R 3 4 2 2 3 4 2 4 +--R (- 60a c + 42a b c - 6a b c )x +--R + +--R 3 3 2 3 2 5 3 +--R (- 138a b c + 87a b c - 12a b c)x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 100a c - 14a b c + 36a b c - 6a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 3 4 +--R (- 122a b c + 68a b c - 9a b )x - 32a c + 16a b c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 6 4 5 2 3 4 4 2 5 6 3 5 3 2 4 5 4 +--R (32a c - 16a b c + 2a b c )x + (64a b c - 32a b c + 4a b c)x +--R + +--R 7 3 5 4 4 6 3 7 2 6 3 5 5 2 +--R (64a c - 12a b c + 2a b )x + (64a b c - 32a b c + 4a b )x +--R + +--R 8 2 7 2 6 4 +--R (32a c - 16a b c + 2a b )x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1483 +a0207:=integrate(t0207,x) +--R +--R +--R (1098) +--R [ +--R 3 5 2 2 4 4 3 6 2 5 +--R (60a c - 90a b c + 30a b c - 3b c )x +--R + +--R 3 4 2 3 3 5 2 7 4 +--R (120a b c - 180a b c + 60a b c - 6b c)x +--R + +--R 4 4 3 2 3 2 4 2 6 8 3 +--R (120a c - 120a b c - 30a b c + 24a b c - 3b )x +--R + +--R 4 3 3 3 2 2 5 7 2 +--R (120a b c - 180a b c + 60a b c - 6a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 +--R (60a c - 90a b c + 30a b c - 3a b )x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 4 3 3 5 2 5 +--R (48a b c - 24a b c + 3b c )x +--R + +--R 2 2 3 4 2 6 4 3 3 5 7 3 +--R (96a b c - 48a b c + 6b c)x + (96a b c - 18a b c + 3b )x +--R + +--R 3 2 2 2 4 6 2 4 2 3 3 2 5 +--R (96a b c - 48a b c + 6a b )x + (48a b c - 24a b c + 3a b )x +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 4 3 3 5 2 5 +--R (- 96a b c + 48a b c - 6b c )x +--R + +--R 2 2 3 4 2 6 4 +--R (- 192a b c + 96a b c - 12b c)x +--R + +--R 3 3 5 7 3 +--R (- 192a b c + 36a b c - 6b )x +--R + +--R 3 2 2 2 4 6 2 +--R (- 192a b c + 96a b c - 12a b )x +--R + +--R 4 2 3 3 2 5 +--R (- 96a b c + 48a b c - 6a b )x +--R * +--R log(x) +--R + +--R 3 4 2 2 3 4 2 4 +--R (- 60a c + 42a b c - 6a b c )x +--R + +--R 3 3 2 3 2 5 3 +--R (- 138a b c + 87a b c - 12a b c)x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 100a c - 14a b c + 36a b c - 6a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 3 4 +--R (- 122a b c + 68a b c - 9a b )x - 32a c + 16a b c - 2a b +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 6 4 5 2 3 4 4 2 5 6 3 5 3 2 4 5 4 +--R (32a c - 16a b c + 2a b c )x + (64a b c - 32a b c + 4a b c)x +--R + +--R 7 3 5 4 4 6 3 7 2 6 3 5 5 2 +--R (64a c - 12a b c + 2a b )x + (64a b c - 32a b c + 4a b )x +--R + +--R 8 2 7 2 6 4 +--R (32a c - 16a b c + 2a b )x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 3 5 2 2 4 4 3 6 2 5 +--R (- 120a c + 180a b c - 60a b c + 6b c )x +--R + +--R 3 4 2 3 3 5 2 7 4 +--R (- 240a b c + 360a b c - 120a b c + 12b c)x +--R + +--R 4 4 3 2 3 2 4 2 6 8 3 +--R (- 240a c + 240a b c + 60a b c - 48a b c + 6b )x +--R + +--R 4 3 3 3 2 2 5 7 2 +--R (- 240a b c + 360a b c - 120a b c + 12a b )x +--R + +--R 5 3 4 2 2 3 4 2 6 +--R (- 120a c + 180a b c - 60a b c + 6a b )x +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 4 3 3 5 2 5 +--R (48a b c - 24a b c + 3b c )x +--R + +--R 2 2 3 4 2 6 4 3 3 5 7 3 +--R (96a b c - 48a b c + 6b c)x + (96a b c - 18a b c + 3b )x +--R + +--R 3 2 2 2 4 6 2 4 2 3 3 2 5 +--R (96a b c - 48a b c + 6a b )x + (48a b c - 24a b c + 3a b )x +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 4 3 3 5 2 5 +--R (- 96a b c + 48a b c - 6b c )x +--R + +--R 2 2 3 4 2 6 4 +--R (- 192a b c + 96a b c - 12b c)x +--R + +--R 3 3 5 7 3 +--R (- 192a b c + 36a b c - 6b )x +--R + +--R 3 2 2 2 4 6 2 +--R (- 192a b c + 96a b c - 12a b )x +--R + +--R 4 2 3 3 2 5 +--R (- 96a b c + 48a b c - 6a b )x +--R * +--R log(x) +--R + +--R 3 4 2 2 3 4 2 4 +--R (- 60a c + 42a b c - 6a b c )x +--R + +--R 3 3 2 3 2 5 3 +--R (- 138a b c + 87a b c - 12a b c)x +--R + +--R 4 3 3 2 2 2 4 6 2 +--R (- 100a c - 14a b c + 36a b c - 6a b )x +--R + +--R 4 2 3 3 2 5 5 2 4 2 3 4 +--R (- 122a b c + 68a b c - 9a b )x - 32a c + 16a b c - 2a b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 6 4 5 2 3 4 4 2 5 6 3 5 3 2 4 5 4 +--R (32a c - 16a b c + 2a b c )x + (64a b c - 32a b c + 4a b c)x +--R + +--R 7 3 5 4 4 6 3 7 2 6 3 5 5 2 +--R (64a c - 12a b c + 2a b )x + (64a b c - 32a b c + 4a b )x +--R + +--R 8 2 7 2 6 4 +--R (32a c - 16a b c + 2a b )x +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1098 + +--S 1099 of 1483 +m0207a:=a0207.1-r0207 +--R +--R +--R (1099) +--R 3 3 2 2 2 4 6 +--R (60a c - 90a b c + 30a b c - 3b ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 3 2 2 2 4 6 2c x + b +--R (- 120a c + 180a b c - 60a b c + 6b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 6 2 5 2 4 4 | 2 +--R (32a c - 16a b c + 2a b )\|- 4a c + b +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1483 +d0207a:=D(m0207a,x) +--R +--R +--R (1100) 0 +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1483 +m0207b:=a0207.2-r0207 +--R +--R +--R (1101) +--R +---------+ +--R 3 3 2 2 2 4 6 | 2 2c x + b +--R (- 60a c + 90a b c - 30a b c + 3b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 3 2 2 2 4 6 | 2 +--R (- 60a c + 90a b c - 30a b c + 3b )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 6 2 5 2 4 4 | 2 | 2 +--R (16a c - 8a b c + a b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1483 +d0207b:=D(m0207b,x) +--R +--R +--R (1102) 0 +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1483 +t0208:= x^3/(c+d*x+e*x^2)^4 +--R +--R +--R (1103) +--R 3 +--R x +--R / +--R 4 8 3 7 3 2 2 6 2 3 5 +--R e x + 4d e x + (4c e + 6d e )x + (12c d e + 4d e)x +--R + +--R 2 2 2 4 4 2 3 3 3 2 2 2 +--R (6c e + 12c d e + d )x + (12c d e + 4c d )x + (4c e + 6c d )x +--R + +--R 3 4 +--R 4c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1103 + +--S 1104 of 1483 +r0208:= -1/60*(d^2+5*c*e)/e^3/(c+d*x+e*x^2)^3+1/20*d*x/e^2/(c+d*x+e*x^2)^3-_ + 1/4*x^2/e/(c+d*x+e*x^2)^3+1/60*d*(d^2+6*c*e)*(d+2*e*x)/e^3/(d^2-_ + 4*c*e)/(c+d*x+e*x^2)^3-1/12*d*(d^2+6*c*e)*(d+2*e*x)/e^2/(d^2-_ + 4*c*e)^2/(c+d*x+e*x^2)^2+1/2*d*(6*c+d^2/e)*(d+2*e*x)/(d^2-4*c*e)^3/_ + (c+d*x+e*x^2)-2*d*(d^2+6*c*e)*_ + atanh((d+2*e*x)/(d^2-4*c*e)^(1/2))/(d^2-4*c*e)^(7/2) +--R +--R +--R (1104) +--R 4 3 3 6 2 3 4 2 5 +--R (72c d e + 12d e )x + (216c d e + 36d e )x +--R + +--R 2 3 3 2 5 4 2 2 2 4 6 3 +--R (216c d e + 252c d e + 36d e)x + (432c d e + 144c d e + 12d )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 4 +--R (216c d e + 252c d e + 36c d )x + (216c d e + 36c d )x + 72c d e +--R + +--R 3 3 +--R 12c d +--R * +--R 2e x + d +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4c e + d +--R + +--R 3 3 2 5 2 2 4 4 +--R (- 36c d e - 6d e )x + (- 90c d e - 15d e)x +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (- 96c d e - 82c d e - 11d )x + (- 96c e - 72c d e - 51c d )x +--R + +--R 3 2 3 4 3 2 +--R (- 60c d e - 60c d )x - 32c e - 22c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4c e + d +--R / +--R 3 6 2 2 5 4 4 6 3 6 +--R (384c e - 288c d e + 72c d e - 6d e )x +--R + +--R 3 5 2 3 4 5 3 7 2 5 +--R (1152c d e - 864c d e + 216c d e - 18d e )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 4 +--R (1152c e + 288c d e - 648c d e + 198c d e - 18d e)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 3 +--R (2304c d e - 1344c d e + 144c d e + 36c d e - 6d )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 2 +--R (1152c e + 288c d e - 648c d e + 198c d e - 18c d )x +--R + +--R 5 3 4 3 2 3 5 2 7 6 3 5 2 2 +--R (1152c d e - 864c d e + 216c d e - 18c d )x + 384c e - 288c d e +--R + +--R 4 4 3 6 +--R 72c d e - 6c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4c e + d +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1483 +a0208:=integrate(t0208,x) +--R +--R +--R (1105) +--R [ +--R 4 3 3 6 2 3 4 2 5 +--R (36c d e + 6d e )x + (108c d e + 18d e )x +--R + +--R 2 3 3 2 5 4 2 2 2 4 6 3 +--R (108c d e + 126c d e + 18d e)x + (216c d e + 72c d e + 6d )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 4 +--R (108c d e + 126c d e + 18c d )x + (108c d e + 18c d )x + 36c d e +--R + +--R 3 3 +--R 6c d +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2e x + 2d e x - 2c e + d )\|- 4c e + d + (- 8c e + 2d e)x +--R + +--R 3 +--R - 4c d e + d +--R / +--R 2 +--R e x + d x + c +--R + +--R 3 3 2 5 2 2 4 4 +--R (- 36c d e - 6d e )x + (- 90c d e - 15d e)x +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (- 96c d e - 82c d e - 11d )x + (- 96c e - 72c d e - 51c d )x +--R + +--R 3 2 3 4 3 2 +--R (- 60c d e - 60c d )x - 32c e - 22c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4c e + d +--R / +--R 3 6 2 2 5 4 4 6 3 6 +--R (384c e - 288c d e + 72c d e - 6d e )x +--R + +--R 3 5 2 3 4 5 3 7 2 5 +--R (1152c d e - 864c d e + 216c d e - 18d e )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 4 +--R (1152c e + 288c d e - 648c d e + 198c d e - 18d e)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 3 +--R (2304c d e - 1344c d e + 144c d e + 36c d e - 6d )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 2 +--R (1152c e + 288c d e - 648c d e + 198c d e - 18c d )x +--R + +--R 5 3 4 3 2 3 5 2 7 6 3 5 2 2 +--R (1152c d e - 864c d e + 216c d e - 18c d )x + 384c e - 288c d e +--R + +--R 4 4 3 6 +--R 72c d e - 6c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4c e + d +--R , +--R +--R 4 3 3 6 2 3 4 2 5 +--R (- 72c d e - 12d e )x + (- 216c d e - 36d e )x +--R + +--R 2 3 3 2 5 4 +--R (- 216c d e - 252c d e - 36d e)x +--R + +--R 2 2 2 4 6 3 +--R (- 432c d e - 144c d e - 12d )x +--R + +--R 3 2 2 3 5 2 3 2 2 4 +--R (- 216c d e - 252c d e - 36c d )x + (- 216c d e - 36c d )x +--R + +--R 4 3 3 +--R - 72c d e - 12c d +--R * +--R +---------+ +--R | 2 +--R (2e x + d)\|4c e - d +--R atan(----------------------) +--R 2 +--R 4c e - d +--R + +--R 3 3 2 5 2 2 4 4 +--R (- 36c d e - 6d e )x + (- 90c d e - 15d e)x +--R + +--R 2 2 3 5 3 3 2 2 2 4 2 +--R (- 96c d e - 82c d e - 11d )x + (- 96c e - 72c d e - 51c d )x +--R + +--R 3 2 3 4 3 2 +--R (- 60c d e - 60c d )x - 32c e - 22c d +--R * +--R +---------+ +--R | 2 +--R \|4c e - d +--R / +--R 3 6 2 2 5 4 4 6 3 6 +--R (384c e - 288c d e + 72c d e - 6d e )x +--R + +--R 3 5 2 3 4 5 3 7 2 5 +--R (1152c d e - 864c d e + 216c d e - 18d e )x +--R + +--R 4 5 3 2 4 2 4 3 6 2 8 4 +--R (1152c e + 288c d e - 648c d e + 198c d e - 18d e)x +--R + +--R 4 4 3 3 3 2 5 2 7 9 3 +--R (2304c d e - 1344c d e + 144c d e + 36c d e - 6d )x +--R + +--R 5 4 4 2 3 3 4 2 2 6 8 2 +--R (1152c e + 288c d e - 648c d e + 198c d e - 18c d )x +--R + +--R 5 3 4 3 2 3 5 2 7 6 3 5 2 2 +--R (1152c d e - 864c d e + 216c d e - 18c d )x + 384c e - 288c d e +--R + +--R 4 4 3 6 +--R 72c d e - 6c d +--R * +--R +---------+ +--R | 2 +--R \|4c e - d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1105 + +--S 1106 of 1483 +m0208a:=a0208.1-r0208 +--R +--R +--R (1106) +--R 3 +--R (6c d e + d ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2e x + 2d e x - 2c e + d )\|- 4c e + d + (- 8c e + 2d e)x +--R + +--R 3 +--R - 4c d e + d +--R / +--R 2 +--R e x + d x + c +--R + +--R 3 2e x + d +--R (- 12c d e - 2d )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4c e + d +--R / +--R +-----------+ +--R 3 3 2 2 2 4 6 | 2 +--R (64c e - 48c d e + 12c d e - d )\|- 4c e + d +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1483 +d0208a:=D(m0208a,x) +--R +--R +--R (1107) 0 +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1483 +m0208b:=a0208.2-r0208 +--R +--R +--R (1108) +--R +---------+ +--R 3 | 2 2e x + d +--R (- 12c d e - 2d )\|4c e - d atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4c e + d +--R + +--R +---------+ +--R +-----------+ | 2 +--R 3 | 2 (2e x + d)\|4c e - d +--R (- 12c d e - 2d )\|- 4c e + d atan(----------------------) +--R 2 +--R 4c e - d +--R / +--R +-----------+ +---------+ +--R 3 3 2 2 2 4 6 | 2 | 2 +--R (64c e - 48c d e + 12c d e - d )\|- 4c e + d \|4c e - d +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1483 +d0208b:=D(m0208b,x) +--R +--R +--R (1109) 0 +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1483 +t0209:= (d+e*x)^3/(a+b*x+c*x^2) +--R +--R +--R 3 3 2 2 2 3 +--R e x + 3d e x + 3d e x + d +--R (1110) ---------------------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1110 + +--S 1111 of 1483 +r0209:= e^2*(3*c*d-b*e)*x/c^2+1/2*e^3*x^2/c-(2*c*d-b*e)*(c^2*d^2+b^2*e^2-_ + c*e*(b*d+3*a*e))*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/c^3/(b^2-_ + 4*a*c)^(1/2)+1/2*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2-a*c*e^2)*_ + log(a+b*x+c*x^2)/c^3 +--R +--R +--R (1111) +--R 3 3 2 2 2 2 2 3 3 +--R ((- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d ) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 3 2 2 2 2 2 3 2 +--R ((- a c + b )e - 3b c d e + 3c d e)log(c x + b x + a) + c e x +--R + +--R 3 2 2 +--R (- 2b c e + 6c d e )x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1483 +a0209:=integrate(t0209,x) +--R +--R +--R (1112) +--R [ +--R 3 3 2 2 2 2 2 3 3 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 2 2 3 2 +--R ((- a c + b )e - 3b c d e + 3c d e)log(c x + b x + a) + c e x +--R + +--R 3 2 2 +--R (- 2b c e + 6c d e )x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R 3 3 2 2 2 2 2 3 3 +--R ((6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d ) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 3 2 2 2 2 2 3 2 +--R ((- a c + b )e - 3b c d e + 3c d e)log(c x + b x + a) + c e x +--R + +--R 3 2 2 +--R (- 2b c e + 6c d e )x +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 3 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1112 + +--S 1113 of 1483 +m0209a:=a0209.1-r0209 +--R +--R +--R (1113) +--R 3 3 2 2 2 2 2 3 3 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((6a b c - 2b )e + (- 12a c + 6b c)d e - 6b c d e + 4c d ) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1483 +d0209a:=D(m0209a,x) +--R +--R +--R (1114) 0 +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1483 +m0209b:=a0209.2-r0209 +--R +--R +--R (1115) +--R +---------+ +--R 3 3 2 2 2 2 2 3 3 | 2 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d )\|4a c - b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 3 2 2 2 2 2 3 3 +--R ((3a b c - b )e + (- 6a c + 3b c)d e - 3b c d e + 2c d ) +--R * +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R \|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1483 +d0209b:=D(m0209b,x) +--R +--R +--R (1116) 0 +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1483 +t0210:= (d+e*x)^2/(a+b*x+c*x^2) +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1117) ------------------ +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1117 + +--S 1118 of 1483 +r0210:= e^2*x/c-(b^2*e^2+2*c*(c*d^2-e*(b*d+a*e)))*atanh((b+2*c*x)/_ + (b^2-4*a*c)^(1/2))/c^2/(b^2-4*a*c)^(1/2)+_ + 1/2*e*(2*c*d-b*e)*log(a+b*x+c*x^2)/c^2 +--R +--R +--R (1118) +--R 2 2 2 2 2c x + b +--R ((4a c - 2b )e + 4b c d e - 4c d )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 2 2 | 2 +--R ((- b e + 2c d e)log(c x + b x + a) + 2c e x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1483 +a0210:=integrate(t0210,x) +--R +--R +--R (1119) +--R [ +--R 2 2 2 2 +--R ((2a c - b )e + 2b c d e - 2c d ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 2 2 | 2 +--R ((- b e + 2c d e)log(c x + b x + a) + 2c e x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 2 2 2 (2c x + b)\|4a c - b +--R ((- 4a c + 2b )e - 4b c d e + 4c d )atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 2 2 | 2 +--R ((- b e + 2c d e)log(c x + b x + a) + 2c e x)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1119 + +--S 1120 of 1483 +m0210a:=a0210.1-r0210 +--R +--R +--R (1120) +--R 2 2 2 2 +--R ((2a c - b )e + 2b c d e - 2c d ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2c x + b +--R ((- 4a c + 2b )e - 4b c d e + 4c d )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1483 +d0210a:=D(m0210a,x) +--R +--R +--R (1121) 0 +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1483 +m0210b:=a0210.2-r0210 +--R +--R +--R (1122) +--R +---------+ +--R 2 2 2 2 | 2 2c x + b +--R ((- 2a c + b )e - 2b c d e + 2c d )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 2 2 2 | 2 +--R ((- 2a c + b )e - 2b c d e + 2c d )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1122 + +--S 1123 of 1483 +d0210b:=D(m0210b,x) +--R +--R +--R (1123) 0 +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1483 +t0211:= (d+e*x)/(a+b*x+c*x^2) +--R +--R +--R e x + d +--R (1124) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1124 + +--S 1125 of 1483 +r0211:= -(2*d-b*e/c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(1/2)+_ + 1/2*e*log(a+b*x+c*x^2)/c +--R +--R +--R (1125) +--R +-----------+ +--R 2c x + b 2 | 2 +--R (2b e - 4c d)atanh(--------------) + e log(c x + b x + a)\|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R ------------------------------------------------------------------------ +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1483 +a0211:=integrate(t0211,x) +--R +--R +--R (1126) +--R [ +--R (b e - 2c d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R e log(c x + b x + a)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R (- 2b e + 4c d)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R e log(c x + b x + a)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2c\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1126 + +--S 1127 of 1483 +m0211a:=a0211.1-r0211 +--R +--R +--R (1127) +--R (b e - 2c d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R (- 2b e + 4c d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression(Integer) +--E 1127 + +--S 1128 of 1483 +d0211a:=D(m0211a,x) +--R +--R +--R (1128) 0 +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1483 +m0211b:=a0211.2-r0211 +--R +--R +--R (1129) +--R +---------+ +--R | 2 2c x + b +--R (- b e + 2c d)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R (- b e + 2c d)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R c\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1483 +d0211b:=D(m0211b,x) +--R +--R +--R (1130) 0 +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1483 +t0212:= 1/(d+e*x)^2/(a+b*x+c*x^2) +--R +--R +--R (1131) +--R 1 +--R / +--R 2 4 2 3 2 2 2 2 +--R c e x + (b e + 2c d e)x + (a e + 2b d e + c d )x + (2a d e + b d )x +--R + +--R 2 +--R a d +--R Type: Fraction(Polynomial(Integer)) +--E 1131 + +--S 1132 of 1483 +r0212:= -e/(c*d^2-e*(b*d-a*e))/(d+e*x)-(2*c^2*d^2+b^2*e^2-_ + 2*c*e*(b*d+a*e))*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ + (b^2-4*a*c)^(1/2)/(c*d^2-e*(b*d-a*e))^2+e*(2*c*d-b*e)*_ + log(d+e*x)/(c*d^2-e*(b*d-a*e))^2-1/2*e*(2*c*d-b*e)*_ + log(a+b*x+c*x^2)/(c*d^2-e*(b*d-a*e))^2 +--R +--R +--R (1132) +--R 2 3 2 2 2 2 2 2 +--R ((4a c - 2b )e + 4b c d e - 4c d e)x + (4a c - 2b )d e + 4b c d e +--R + +--R 2 3 +--R - 4c d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 2 +--R ((b e - 2c d e )x + b d e - 2c d e)log(c x + b x + a) +--R + +--R 3 2 2 2 3 +--R ((- 2b e + 4c d e )x - 2b d e + 4c d e)log(e x + d) - 2a e +--R + +--R 2 2 +--R 2b d e - 2c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 5 4 2 2 3 3 2 2 4 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x + 2a d e +--R + +--R 2 3 2 3 2 4 2 5 +--R - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1483 +a0212:=integrate(t0212,x) +--R +--R +--R (1133) +--R [ +--R 2 3 2 2 2 2 2 2 +--R ((2a c - b )e + 2b c d e - 2c d e)x + (2a c - b )d e + 2b c d e +--R + +--R 2 3 +--R - 2c d +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2 2 +--R ((b e - 2c d e )x + b d e - 2c d e)log(c x + b x + a) +--R + +--R 3 2 2 2 3 +--R ((- 2b e + 4c d e )x - 2b d e + 4c d e)log(e x + d) - 2a e +--R + +--R 2 2 +--R 2b d e - 2c d e +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 2 5 4 2 2 3 3 2 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x +--R + +--R 2 4 2 3 2 3 2 4 2 5 +--R 2a d e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 3 2 2 2 2 2 +--R ((- 4a c + 2b )e - 4b c d e + 4c d e)x + (- 4a c + 2b )d e +--R + +--R 2 2 3 +--R - 4b c d e + 4c d +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 2 2 2 2 +--R ((b e - 2c d e )x + b d e - 2c d e)log(c x + b x + a) +--R + +--R 3 2 2 2 3 +--R ((- 2b e + 4c d e )x - 2b d e + 4c d e)log(e x + d) - 2a e +--R + +--R 2 2 +--R 2b d e - 2c d e +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 2 5 4 2 2 3 3 2 2 4 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d e)x +--R + +--R 2 4 2 3 2 3 2 4 2 5 +--R 2a d e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1133 + +--S 1134 of 1483 +m0212a:=a0212.1-r0212 +--R +--R +--R (1134) +--R 2 2 2 2 +--R ((2a c - b )e + 2b c d e - 2c d ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2c x + b +--R ((- 4a c + 2b )e - 4b c d e + 4c d )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (2a e - 4a b d e + (4a c + 2b )d e - 4b c d e + 2c d )\|- 4a c + b +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1483 +d0212a:=D(m0212a,x) +--R +--R +--R (1135) 0 +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1483 +m0212b:=a0212.2-r0212 +--R +--R +--R (1136) +--R +---------+ +--R 2 2 2 2 | 2 2c x + b +--R ((- 2a c + b )e - 2b c d e + 2c d )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 2 2 2 | 2 +--R ((- 2a c + b )e - 2b c d e + 2c d )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +--R 2 4 3 2 2 2 3 2 4 | 2 +--R (a e - 2a b d e + (2a c + b )d e - 2b c d e + c d )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1483 +d0212b:=D(m0212b,x) +--R +--R +--R (1137) 0 +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1483 +t0213:= 2*((a/b)^(1/n)-x*cos((-1+2*k)*%pi/n))/((a/b)^(2/n)+x^2-_ + 2*(a/b)^(1/n)*x*cos((-1+2*k)*%pi/n)) +--R +--R +--R 1 +--R - +--R a n (2k - 1)%pi +--R 2(-) - 2x cos(-----------) +--R b n +--R (1138) ----------------------------------- +--R 2 1 +--R - - +--R a n (2k - 1)%pi a n 2 +--R (-) - 2x cos(-----------)(-) + x +--R b n b +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1483 +r0213:= -cos((1-2*k)*%pi/n)*log((a/b)^(2/n)+x^2-2*(a/b)^(1/n)*x*_ + cos((1-2*k)*%pi/n))+2*atan((x-(a/b)^(1/n)*cos((1-2*k)*%pi/n))*_ + csc((1-2*k)*%pi/n)/((a/b)^(1/n)))*sin((1-2*k)*%pi/n) +--R +--R +--R (1139) +--R 2 1 +--R - - +--R (2k - 1)%pi a n (2k - 1)%pi a n 2 +--R - cos(-----------)log((-) - 2x cos(-----------)(-) + x ) +--R n b n b +--R + +--R - +--R (2k - 1)%pi +--R 2sin(-----------) +--R n +--R * +--R 1 +--R - +--R (2k - 1)%pi (2k - 1)%pi a n (2k - 1)%pi +--R cos(-----------)csc(-----------)(-) - x csc(-----------) +--R n n b n +--R atan(---------------------------------------------------------) +--R 1 +--R - +--R a n +--R (-) +--R b +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1483 +a0213:=integrate(t0213,x) +--R +--R +--R (1140) +--R [ +--R +---------------------+ +--R | (2k - 1)%pi 2 +--R |cos(-----------) - 1 +--R \| n +--R * +--R log +--R 1 2 1 2 +--R - - - +--R (2k - 1)%pi a n a n a n +--R (- 2cos(-----------)((-) ) + 2x (-) )(-) +--R n b b b +--R + +--R 1 4 1 3 +--R - - +--R (2k - 1)%pi 3 a n (2k - 1)%pi 2 a n +--R 2cos(-----------) ((-) ) - 2x cos(-----------) ((-) ) +--R n b n b +--R * +--R +---------------------+ +--R | (2k - 1)%pi 2 +--R |cos(-----------) - 1 +--R \| n +--R + +--R 2 2 1 2 2 +--R - - - +--R a n (2k - 1)%pi 2 a n a n +--R - ((-) ) + 2cos(-----------) ((-) ) (-) +--R b n b b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (- 2cos(-----------) + cos(-----------) )((-) ) +--R n n b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R 2 (2k - 1)%pi 2 2 a n +--R (- x cos(-----------) + x )((-) ) +--R n b +--R / +--R 2 2 1 2 2 +--R - - - +--R a n (2k - 1)%pi 2 a n a n +--R ((-) ) - 2cos(-----------) ((-) ) (-) +--R b n b b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 2 a n +--R cos(-----------) ((-) ) +--R n b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R 2 (2k - 1)%pi 2 2 a n +--R (- x cos(-----------) + x )((-) ) +--R n b +--R + +--R - +--R (2k - 1)%pi +--R cos(-----------) +--R n +--R * +--R log +--R 2 2 1 2 2 +--R - - - +--R a n (2k - 1)%pi 2 a n a n +--R - ((-) ) + 2cos(-----------) ((-) ) (-) +--R b n b b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 2 a n +--R - cos(-----------) ((-) ) +--R n b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (- 2x cos(-----------) + 2x cos(-----------))((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R 2 (2k - 1)%pi 2 2 a n +--R (x cos(-----------) - x )((-) ) +--R n b +--R , +--R +--R - +--R +-----------------------+ +--R | (2k - 1)%pi 2 +--R 2 |- cos(-----------) + 1 +--R \| n +--R * +--R atan +--R 2 1 2 +--R - - +-----------------------+ +--R a n (2k - 1)%pi 2 a n | (2k - 1)%pi 2 +--R ((-) - cos(-----------) ((-) ) ) |- cos(-----------) + 1 +--R b n b \| n +--R / +--R 1 2 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (cos(-----------) - cos(-----------))((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 2 a n +--R (- x cos(-----------) + x)(-) +--R n b +--R + +--R - +--R (2k - 1)%pi +--R cos(-----------) +--R n +--R * +--R log +--R 2 2 1 2 2 +--R - - - +--R a n (2k - 1)%pi 2 a n a n +--R - ((-) ) + 2cos(-----------) ((-) ) (-) +--R b n b b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 2 a n +--R - cos(-----------) ((-) ) +--R n b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (- 2x cos(-----------) + 2x cos(-----------))((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R 2 (2k - 1)%pi 2 2 a n +--R (x cos(-----------) - x )((-) ) +--R n b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1140 + +--S 1141 of 1483 +m0213a:=a0213.1-r0213 +--R +--R +--R (1141) +--R +---------------------+ +--R | (2k - 1)%pi 2 +--R |cos(-----------) - 1 +--R \| n +--R * +--R log +--R 1 2 1 2 +--R - - - +--R (2k - 1)%pi a n a n a n +--R (- 2cos(-----------)((-) ) + 2x (-) )(-) +--R n b b b +--R + +--R 1 4 1 3 +--R - - +--R (2k - 1)%pi 3 a n (2k - 1)%pi 2 a n +--R 2cos(-----------) ((-) ) - 2x cos(-----------) ((-) ) +--R n b n b +--R * +--R +---------------------+ +--R | (2k - 1)%pi 2 +--R |cos(-----------) - 1 +--R \| n +--R + +--R 2 2 1 2 2 +--R - - - +--R a n (2k - 1)%pi 2 a n a n +--R - ((-) ) + 2cos(-----------) ((-) ) (-) +--R b n b b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 4 (2k - 1)%pi 2 a n +--R (- 2cos(-----------) + cos(-----------) )((-) ) +--R n n b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R 2 (2k - 1)%pi 2 2 a n +--R (- x cos(-----------) + x )((-) ) +--R n b +--R / +--R 2 2 1 2 2 1 4 +--R - - - - +--R a n (2k - 1)%pi 2 a n a n (2k - 1)%pi 2 a n +--R ((-) ) - 2cos(-----------) ((-) ) (-) + cos(-----------) ((-) ) +--R b n b b n b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (2x cos(-----------) - 2x cos(-----------))((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R 2 (2k - 1)%pi 2 2 a n +--R (- x cos(-----------) + x )((-) ) +--R n b +--R + +--R 2 1 +--R - - +--R (2k - 1)%pi a n (2k - 1)%pi a n 2 +--R cos(-----------)log((-) - 2x cos(-----------)(-) + x ) +--R n b n b +--R + +--R - +--R (2k - 1)%pi +--R cos(-----------) +--R n +--R * +--R log +--R 2 2 1 2 2 +--R - - - +--R a n (2k - 1)%pi 2 a n a n +--R - ((-) ) + 2cos(-----------) ((-) ) (-) +--R b n b b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 2 a n +--R - cos(-----------) ((-) ) +--R n b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (- 2x cos(-----------) + 2x cos(-----------))((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R 2 (2k - 1)%pi 2 2 a n +--R (x cos(-----------) - x )((-) ) +--R n b +--R + +--R (2k - 1)%pi +--R 2sin(-----------) +--R n +--R * +--R 1 +--R - +--R (2k - 1)%pi (2k - 1)%pi a n (2k - 1)%pi +--R cos(-----------)csc(-----------)(-) - x csc(-----------) +--R n n b n +--R atan(---------------------------------------------------------) +--R 1 +--R - +--R a n +--R (-) +--R b +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1483 +d0213a:=normalize(D(m0213a,x)) +--R +--R +--R (1142) 0 +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1483 +m0213b:=a0213.2-r0213 +--R +--R +--R (1143) +--R - +--R +-----------------------+ +--R | (2k - 1)%pi 2 +--R 2 |- cos(-----------) + 1 +--R \| n +--R * +--R atan +--R 2 1 2 +--R - - +-----------------------+ +--R a n (2k - 1)%pi 2 a n | (2k - 1)%pi 2 +--R ((-) - cos(-----------) ((-) ) ) |- cos(-----------) + 1 +--R b n b \| n +--R / +--R 1 2 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (cos(-----------) - cos(-----------))((-) ) +--R n n b +--R + +--R 1 +--R - +--R (2k - 1)%pi 2 a n +--R (- x cos(-----------) + x)(-) +--R n b +--R + +--R 2 1 +--R - - +--R (2k - 1)%pi a n (2k - 1)%pi a n 2 +--R cos(-----------)log((-) - 2x cos(-----------)(-) + x ) +--R n b n b +--R + +--R - +--R (2k - 1)%pi +--R cos(-----------) +--R n +--R * +--R log +--R 2 2 1 2 2 +--R - - - +--R a n (2k - 1)%pi 2 a n a n +--R - ((-) ) + 2cos(-----------) ((-) ) (-) +--R b n b b +--R + +--R 1 4 +--R - +--R (2k - 1)%pi 2 a n +--R - cos(-----------) ((-) ) +--R n b +--R + +--R 1 3 +--R - +--R (2k - 1)%pi 3 (2k - 1)%pi a n +--R (- 2x cos(-----------) + 2x cos(-----------))((-) ) +--R n n b +--R + +--R 1 2 +--R - +--R 2 (2k - 1)%pi 2 2 a n +--R (x cos(-----------) - x )((-) ) +--R n b +--R + +--R (2k - 1)%pi +--R 2sin(-----------) +--R n +--R * +--R 1 +--R - +--R (2k - 1)%pi (2k - 1)%pi a n (2k - 1)%pi +--R cos(-----------)csc(-----------)(-) - x csc(-----------) +--R n n b n +--R atan(---------------------------------------------------------) +--R 1 +--R - +--R a n +--R (-) +--R b +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1483 +d0213b:=normalize(D(m0213b,x)) +--R +--R +--R (1144) 0 +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1483 +t0214:= (d+e*x)^2/(a+b*x+c*x^2)^2 +--R +--R +--R 2 2 2 +--R e x + 2d e x + d +--R (1145) -------------------------------------------- +--R 2 4 3 2 2 2 +--R c x + 2b c x + (2a c + b )x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1145 + +--S 1146 of 1483 +r0214:= -(c*d^2-e*(b*d-a*e))*(b+2*c*x)/c/(b^2-4*a*c)/(a+b*x+c*x^2)-_ + e*(d+e*x)/c/(a+b*x+c*x^2)+4*(c*d^2-e*(b*d-a*e))*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(3/2) +--R +--R +--R (1146) +--R 2 2 2 3 2 2 +--R (- 4a c e + 4b c d e - 4c d )x +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 4a b c e + 4b c d e - 4b c d )x - 4a c e + 4a b c d e - 4a c d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 2 2 +--R (((- 2a c + b )e - 2b c d e + 2c d )x + a b e - 4a c d e + b c d ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 2 3 2 2 2 | 2 +--R ((4a c - b c )x + (4a b c - b c)x + 4a c - a b c)\|- 4a c + b +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1483 +a0214:=integrate(t0214,x) +--R +--R +--R (1147) +--R [ +--R 2 2 2 3 2 2 2 2 2 2 +--R (2a c e - 2b c d e + 2c d )x + (2a b c e - 2b c d e + 2b c d )x +--R + +--R 2 2 2 2 +--R 2a c e - 2a b c d e + 2a c d +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 2 2 +--R (((- 2a c + b )e - 2b c d e + 2c d )x + a b e - 4a c d e + b c d ) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 2 2 2 3 2 2 2 | 2 +--R ((4a c - b c )x + (4a b c - b c)x + 4a c - a b c)\|- 4a c + b +--R , +--R +--R 2 2 2 3 2 2 2 2 2 2 +--R (4a c e - 4b c d e + 4c d )x + (4a b c e - 4b c d e + 4b c d )x +--R + +--R 2 2 2 2 +--R 4a c e - 4a b c d e + 4a c d +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 2 2 2 +--R (((- 2a c + b )e - 2b c d e + 2c d )x + a b e - 4a c d e + b c d ) +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 3 2 2 2 2 3 2 2 2 | 2 +--R ((4a c - b c )x + (4a b c - b c)x + 4a c - a b c)\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1147 + +--S 1148 of 1483 +m0214a:=a0214.1-r0214 +--R +--R +--R (1148) +--R 2 2 +--R (2a e - 2b d e + 2c d ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2c x + b +--R (4a e - 4b d e + 4c d )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R (4a c - b )\|- 4a c + b +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1483 +d0214a:=D(m0214a,x) +--R +--R +--R (1149) 0 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1483 +m0214b:=a0214.2-r0214 +--R +--R +--R (1150) +--R +---------+ +--R 2 2 | 2 2c x + b +--R (4a e - 4b d e + 4c d )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 2 | 2 (2c x + b)\|4a c - b +--R (4a e - 4b d e + 4c d )\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R (4a c - b )\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1483 +d0214b:=D(m0214b,x) +--R +--R +--R (1151) 0 +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1483 +t0215:= 1/(d+e*x)/(a+b*x+c*x^2)^2 +--R +--R +--R (1152) +--R 1 +--R / +--R 2 5 2 4 2 3 +--R c e x + (2b c e + c d)x + ((2a c + b )e + 2b c d)x +--R + +--R 2 2 2 2 +--R (2a b e + (2a c + b )d)x + (a e + 2a b d)x + a d +--R Type: Fraction(Polynomial(Integer)) +--E 1152 + +--S 1153 of 1483 +r0215:= 1/2*e/(c*d^2-e*(b*d-a*e))/(a+b*x+c*x^2)-1/2*(2*c*d-b*e)*_ + (b+2*c*x)/(b^2-4*a*c)/(c*d^2-e*(b*d-a*e))/(a+b*x+c*x^2)-_ + e^2*(2*c*d-b*e)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ + (b^2-4*a*c)^(1/2)/(c*d^2-e*(b*d-a*e))^2+2*c*(2*c*d-b*e)*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(3/2)/_ + (c*d^2-e*(b*d-a*e))+e^3*log(d+e*x)/(c*d^2-e*(b*d-a*e))^2-_ + 1/2*e^3*log(a+b*x+c*x^2)/(c*d^2-e*(b*d-a*e))^2 +--R +--R +--R (1153) +--R 2 3 3 3 2 3 2 4 3 2 +--R ((12a b c - 2b c)e - 24a c d e + 12b c d e - 8c d )x +--R + +--R 2 4 3 2 2 2 2 2 3 3 +--R ((12a b c - 2b )e - 24a b c d e + 12b c d e - 8b c d )x +--R + +--R 2 3 3 2 2 2 2 2 3 3 +--R (12a b c - 2a b )e - 24a c d e + 12a b c d e - 8a c d +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 2 3 3 2 2 3 +--R ((- 4a c + b c)e x + (- 4a b c + b )e x + (- 4a c + a b )e ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 3 2 3 3 2 2 3 +--R ((8a c - 2b c)e x + (8a b c - 2b )e x + (8a c - 2a b )e ) +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 2 3 3 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d )x +--R + +--R 2 2 3 3 2 2 2 2 2 3 +--R (4a c - 2a b )e + (- 2a b c + 2b )d e + (4a c - 4b c)d e + 2b c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 2 4 2 2 3 3 +--R (8a c - 2a b c)e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (16a c + 4a b c - 2b c)d e + (- 16a b c + 4b c )d e +--R + +--R 4 2 3 4 +--R (8a c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 2 2 4 3 +--R (8a b c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (16a b c + 4a b c - 2b )d e + (- 16a b c + 4b c)d e +--R + +--R 3 3 2 4 +--R (8a b c - 2b c )d +--R * +--R x +--R + +--R 4 3 2 4 3 2 3 3 +--R (8a c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 +--R (8a c - 2a b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1483 +a0215:=integrate(t0215,x) +--R +--R +--R (1154) +--R [ +--R 2 3 3 3 2 3 2 4 3 2 +--R ((6a b c - b c)e - 12a c d e + 6b c d e - 4c d )x +--R + +--R 2 4 3 2 2 2 2 2 3 3 +--R ((6a b c - b )e - 12a b c d e + 6b c d e - 4b c d )x +--R + +--R 2 3 3 2 2 2 2 2 3 3 +--R (6a b c - a b )e - 12a c d e + 6a b c d e - 4a c d +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 2 3 3 2 2 3 +--R ((- 4a c + b c)e x + (- 4a b c + b )e x + (- 4a c + a b )e ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 3 2 3 3 2 2 3 +--R ((8a c - 2b c)e x + (8a b c - 2b )e x + (8a c - 2a b )e ) +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 2 3 3 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d )x +--R + +--R 2 2 3 3 2 2 2 2 2 3 +--R (4a c - 2a b )e + (- 2a b c + 2b )d e + (4a c - 4b c)d e + 2b c d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 2 4 2 2 3 3 +--R (8a c - 2a b c)e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (16a c + 4a b c - 2b c)d e + (- 16a b c + 4b c )d e +--R + +--R 4 2 3 4 +--R (8a c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 2 2 4 3 +--R (8a b c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (16a b c + 4a b c - 2b )d e + (- 16a b c + 4b c)d e +--R + +--R 3 3 2 4 +--R (8a b c - 2b c )d +--R * +--R x +--R + +--R 4 3 2 4 3 2 3 3 +--R (8a c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 +--R (8a c - 2a b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R , +--R +--R 2 3 3 3 2 3 2 4 3 2 +--R ((- 12a b c + 2b c)e + 24a c d e - 12b c d e + 8c d )x +--R + +--R 2 4 3 2 2 2 2 2 3 3 +--R ((- 12a b c + 2b )e + 24a b c d e - 12b c d e + 8b c d )x +--R + +--R 2 3 3 2 2 2 2 2 3 3 +--R (- 12a b c + 2a b )e + 24a c d e - 12a b c d e + 8a c d +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 3 2 3 3 2 2 3 +--R ((- 4a c + b c)e x + (- 4a b c + b )e x + (- 4a c + a b )e ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 2 2 3 2 3 3 2 2 3 +--R ((8a c - 2b c)e x + (8a b c - 2b )e x + (8a c - 2a b )e ) +--R * +--R log(e x + d) +--R + +--R 3 2 2 2 2 2 3 3 +--R (- 2a b c e + (4a c + 2b c)d e - 6b c d e + 4c d )x +--R + +--R 2 2 3 3 2 2 2 2 2 3 +--R (4a c - 2a b )e + (- 2a b c + 2b )d e + (4a c - 4b c)d e + 2b c d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R 3 2 2 2 4 2 2 3 3 +--R (8a c - 2a b c)e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 2 2 3 3 2 3 +--R (16a c + 4a b c - 2b c)d e + (- 16a b c + 4b c )d e +--R + +--R 4 2 3 4 +--R (8a c - 2b c )d +--R * +--R 2 +--R x +--R + +--R 3 2 3 4 2 2 4 3 +--R (8a b c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 2 2 3 5 2 2 2 2 4 3 +--R (16a b c + 4a b c - 2b )d e + (- 16a b c + 4b c)d e +--R + +--R 3 3 2 4 +--R (8a b c - 2b c )d +--R * +--R x +--R + +--R 4 3 2 4 3 2 3 3 +--R (8a c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 3 2 2 2 4 2 2 2 2 3 3 +--R (16a c + 4a b c - 2a b )d e + (- 16a b c + 4a b c)d e +--R + +--R 2 3 2 2 4 +--R (8a c - 2a b c )d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1154 + +--S 1155 of 1483 +m0215a:=a0215.1-r0215 +--R +--R +--R (1155) +--R 3 3 2 2 2 2 3 3 +--R ((6a b c - b )e - 12a c d e + 6b c d e - 4c d ) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 3 2 2 2 2 3 3 2c x + b +--R ((- 12a b c + 2b )e + 24a c d e - 12b c d e + 8c d )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R 3 2 2 4 2 3 3 +--R (8a c - 2a b )e + (- 16a b c + 4a b )d e +--R + +--R 2 2 2 4 2 2 2 3 3 3 2 2 4 +--R (16a c + 4a b c - 2b )d e + (- 16a b c + 4b c)d e + (8a c - 2b c )d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1483 +d0215a:=D(m0215a,x) +--R +--R +--R (1156) 0 +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1483 +m0215b:=a0215.2-r0215 +--R +--R +--R (1157) +--R +---------+ +--R 3 3 2 2 2 2 3 3 | 2 +--R ((- 6a b c + b )e + 12a c d e - 6b c d e + 4c d )\|4a c - b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 3 2 2 2 2 3 3 | 2 +--R ((- 6a b c + b )e + 12a c d e - 6b c d e + 4c d )\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R 3 2 2 4 2 3 3 2 2 2 4 2 2 +--R (4a c - a b )e + (- 8a b c + 2a b )d e + (8a c + 2a b c - b )d e +--R + +--R 2 3 3 3 2 2 4 +--R (- 8a b c + 2b c)d e + (4a c - b c )d +--R * +--R +-----------+ +---------+ +--R | 2 | 2 +--R \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1483 +d0215b:=D(m0215b,x) +--R +--R +--R (1158) 0 +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1483 +t0216:= x^4*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 5 4 +--R e x + d x +--R (1159) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1159 + +--S 1160 of 1483 +r0216:= (b^2*c*d-a*c^2*d-b^3*e+2*a*b*c*e)*x/c^4-_ + 1/2*(b*c*d-b^2*e+a*c*e)*x^2/c^3+1/3*(c*d-b*e)*x^3/c^2+_ + 1/4*e*x^4/c+(b^5*e-c*(b^4*d-4*a*b^2*c*d+2*a^2*c^2*d+5*a*b^3*e-_ + 5*a^2*b*c*e))*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ + c^5/(b^2-4*a*c)^(1/2)-1/2*(b^3*c*d-2*a*b*c^2*d-b^4*e+3*a*b^2*c*e-_ + a^2*c^2*e)*log(a+b*x+c*x^2)/c^5 +--R +--R +--R (1160) +--R 2 2 3 5 2 3 2 2 4 +--R ((60a b c - 60a b c + 12b )e + (- 24a c + 48a b c - 12b c)d) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 4 2 3 2 +--R ((6a c - 18a b c + 6b )e + (12a b c - 6b c)d)log(c x + b x + a) +--R + +--R 4 4 3 4 3 3 2 2 3 2 +--R 3c e x + (- 4b c e + 4c d)x + ((- 6a c + 6b c )e - 6b c d)x +--R + +--R 2 3 3 2 2 +--R ((24a b c - 12b c)e + (- 12a c + 12b c )d)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 5 | 2 +--R 12c \|- 4a c + b +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1483 +a0216:=integrate(t0216,x) +--R +--R +--R (1161) +--R [ +--R 2 2 3 5 2 3 2 2 4 +--R ((30a b c - 30a b c + 6b )e + (- 12a c + 24a b c - 6b c)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 4 2 3 2 +--R ((6a c - 18a b c + 6b )e + (12a b c - 6b c)d)log(c x + b x + a) +--R + +--R 4 4 3 4 3 3 2 2 3 2 +--R 3c e x + (- 4b c e + 4c d)x + ((- 6a c + 6b c )e - 6b c d)x +--R + +--R 2 3 3 2 2 +--R ((24a b c - 12b c)e + (- 12a c + 12b c )d)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 5 | 2 +--R 12c \|- 4a c + b +--R , +--R +--R 2 2 3 5 2 3 2 2 4 +--R ((- 60a b c + 60a b c - 12b )e + (24a c - 48a b c + 12b c)d) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 4 2 3 2 +--R ((6a c - 18a b c + 6b )e + (12a b c - 6b c)d)log(c x + b x + a) +--R + +--R 4 4 3 4 3 3 2 2 3 2 +--R 3c e x + (- 4b c e + 4c d)x + ((- 6a c + 6b c )e - 6b c d)x +--R + +--R 2 3 3 2 2 +--R ((24a b c - 12b c)e + (- 12a c + 12b c )d)x +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 5 | 2 +--R 12c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1161 + +--S 1162 of 1483 +m0216a:=a0216.1-r0216 +--R +--R +--R (1162) +--R 2 2 3 5 2 3 2 2 4 +--R ((5a b c - 5a b c + b )e + (- 2a c + 4a b c - b c)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 5 2 3 2 2 4 +--R ((- 10a b c + 10a b c - 2b )e + (4a c - 8a b c + 2b c)d) +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 5 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1483 +d0216a:=D(m0216a,x) +--R +--R +--R (1163) 0 +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1483 +m0216b:=a0216.2-r0216 +--R +--R +--R (1164) +--R +---------+ +--R 2 2 3 5 2 3 2 2 4 | 2 +--R ((- 5a b c + 5a b c - b )e + (2a c - 4a b c + b c)d)\|4a c - b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 2 3 5 2 3 2 2 4 | 2 +--R ((- 5a b c + 5a b c - b )e + (2a c - 4a b c + b c)d)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 5 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1483 +d0216b:=D(m0216b,x) +--R +--R +--R (1165) 0 +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1483 +t0217:= x^3*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 4 3 +--R e x + d x +--R (1166) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1166 + +--S 1167 of 1483 +r0217:= -(b*c*d-b^2*e+a*c*e)*x/c^3+1/2*(c*d-b*e)*x^2/c^2+1/3*e*x^3/c-_ + (b^4*e-c*(b^3*d-3*a*b*c*d+4*a*b^2*e-2*a^2*c*e))*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/c^4/(b^2-4*a*c)^(1/2)+_ + 1/2*(b^2*c*d-a*c^2*d-b^3*e+2*a*b*c*e)*log(a+b*x+c*x^2)/c^4 +--R +--R +--R (1167) +--R 2 2 2 4 2 3 2c x + b +--R ((- 12a c + 24a b c - 6b )e + (- 18a b c + 6b c)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 3 2 2 2 3 3 +--R ((6a b c - 3b )e + (- 3a c + 3b c)d)log(c x + b x + a) + 2c e x +--R + +--R 2 3 2 2 2 2 +--R (- 3b c e + 3c d)x + ((- 6a c + 6b c)e - 6b c d)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 | 2 +--R 6c \|- 4a c + b +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1483 +a0217:=integrate(t0217,x) +--R +--R +--R (1168) +--R [ +--R 2 2 2 4 2 3 +--R ((6a c - 12a b c + 3b )e + (9a b c - 3b c)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2 3 3 +--R ((6a b c - 3b )e + (- 3a c + 3b c)d)log(c x + b x + a) + 2c e x +--R + +--R 2 3 2 2 2 2 +--R (- 3b c e + 3c d)x + ((- 6a c + 6b c)e - 6b c d)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 | 2 +--R 6c \|- 4a c + b +--R , +--R +--R 2 2 2 4 2 3 +--R ((12a c - 24a b c + 6b )e + (18a b c - 6b c)d) +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 3 2 2 2 3 3 +--R ((6a b c - 3b )e + (- 3a c + 3b c)d)log(c x + b x + a) + 2c e x +--R + +--R 2 3 2 2 2 2 +--R (- 3b c e + 3c d)x + ((- 6a c + 6b c)e - 6b c d)x +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 4 | 2 +--R 6c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1168 + +--S 1169 of 1483 +m0217a:=a0217.1-r0217 +--R +--R +--R (1169) +--R 2 2 2 4 2 3 +--R ((2a c - 4a b c + b )e + (3a b c - b c)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 4 2 3 2c x + b +--R ((4a c - 8a b c + 2b )e + (6a b c - 2b c)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1483 +d0217a:=D(m0217a,x) +--R +--R +--R (1170) 0 +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1483 +m0217b:=a0217.2-r0217 +--R +--R +--R (1171) +--R +---------+ +--R 2 2 2 4 2 3 | 2 +--R ((2a c - 4a b c + b )e + (3a b c - b c)d)\|4a c - b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 2 2 4 2 3 | 2 +--R ((2a c - 4a b c + b )e + (3a b c - b c)d)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 4 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1483 +d0217b:=D(m0217b,x) +--R +--R +--R (1172) 0 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1483 +t0218:= x^2*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 3 2 +--R e x + d x +--R (1173) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1173 + +--S 1174 of 1483 +r0218:= (c*d-b*e)*x/c^2+1/2*e*x^2/c+(b^3*e-c*(b^2*d-2*a*c*d+3*a*b*e))*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/c^3/(b^2-4*a*c)^(1/2)-_ + 1/2*(b*c*d-b^2*e+a*c*e)*log(a+b*x+c*x^2)/c^3 +--R +--R +--R (1174) +--R 3 2 2 2c x + b +--R ((- 6a b c + 2b )e + (4a c - 2b c)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 2 +--R ((- a c + b )e - b c d)log(c x + b x + a) + c e x +--R + +--R 2 +--R (- 2b c e + 2c d)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 1483 +a0218:=integrate(t0218,x) +--R +--R +--R (1175) +--R [ +--R 3 2 2 +--R ((3a b c - b )e + (- 2a c + b c)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 2 +--R ((- a c + b )e - b c d)log(c x + b x + a) + c e x +--R + +--R 2 +--R (- 2b c e + 2c d)x +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 3 2 2 (2c x + b)\|4a c - b +--R ((6a b c - 2b )e + (- 4a c + 2b c)d)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 2 +--R ((- a c + b )e - b c d)log(c x + b x + a) + c e x +--R + +--R 2 +--R (- 2b c e + 2c d)x +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 3 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1175 + +--S 1176 of 1483 +m0218a:=a0218.1-r0218 +--R +--R +--R (1176) +--R 3 2 2 +--R ((3a b c - b )e + (- 2a c + b c)d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 3 2 2 2c x + b +--R ((6a b c - 2b )e + (- 4a c + 2b c)d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1483 +d0218a:=D(m0218a,x) +--R +--R +--R (1177) 0 +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1483 +m0218b:=a0218.2-r0218 +--R +--R +--R (1178) +--R +---------+ +--R 3 2 2 | 2 2c x + b +--R ((3a b c - b )e + (- 2a c + b c)d)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 3 2 2 | 2 +--R ((3a b c - b )e + (- 2a c + b c)d)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1483 +d0218b:=D(m0218b,x) +--R +--R +--R (1179) 0 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1483 +t0219:= x*(d+e*x)/(a+b*x+c*x^2) +--R +--R +--R 2 +--R e x + d x +--R (1180) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1180 + +--S 1181 of 1483 +r0219:= e*x/c-(b^2*e-c*(b*d+2*a*e))*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ + c^2/(b^2-4*a*c)^(1/2)+1/2*(c*d-b*e)*log(a+b*x+c*x^2)/c^2 +--R +--R +--R (1181) +--R 2 2c x + b +--R ((4a c - 2b )e + 2b c d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R ((- b e + c d)log(c x + b x + a) + 2c e x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1483 +a0219:=integrate(t0219,x) +--R +--R +--R (1182) +--R [ +--R 2 +--R ((2a c - b )e + b c d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R ((- b e + c d)log(c x + b x + a) + 2c e x)\|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 (2c x + b)\|4a c - b +--R ((- 4a c + 2b )e - 2b c d)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R ((- b e + c d)log(c x + b x + a) + 2c e x)\|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2c \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1182 + +--S 1183 of 1483 +m0219a:=a0219.1-r0219 +--R +--R +--R (1183) +--R 2 +--R ((2a c - b )e + b c d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2c x + b +--R ((- 4a c + 2b )e - 2b c d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2c \|- 4a c + b +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1483 +d0219a:=D(m0219a,x) +--R +--R +--R (1184) 0 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1483 +m0219b:=a0219.2-r0219 +--R +--R +--R (1185) +--R +---------+ +--R 2 | 2 2c x + b +--R ((- 2a c + b )e - b c d)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R ((- 2a c + b )e - b c d)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R c \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1483 +d0219b:=D(m0219b,x) +--R +--R +--R (1186) 0 +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1483 +t0220:= (d+e*x)/(a+b*x+c*x^2) +--R +--R +--R e x + d +--R (1187) -------------- +--R 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1187 + +--S 1188 of 1483 +r0220:= -(2*d-b*e/c)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/(b^2-4*a*c)^(1/2)+_ + 1/2*e*log(a+b*x+c*x^2)/c +--R +--R +--R (1188) +--R +-----------+ +--R 2c x + b 2 | 2 +--R (2b e - 4c d)atanh(--------------) + e log(c x + b x + a)\|- 4a c + b +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R ------------------------------------------------------------------------ +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1483 +a0220:=integrate(t0220,x) +--R +--R +--R (1189) +--R [ +--R (b e - 2c d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R e log(c x + b x + a)\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R (- 2b e + 4c d)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R e log(c x + b x + a)\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2c\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1189 + +--S 1190 of 1483 +m0220a:=a0220.1-r0220 +--R +--R +--R (1190) +--R (b e - 2c d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R (- 2b e + 4c d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2c\|- 4a c + b +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1483 +d0220a:=D(m0220a,x) +--R +--R +--R (1191) 0 +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1483 +m0220b:=a0220.2-r0220 +--R +--R +--R (1192) +--R +---------+ +--R | 2 2c x + b +--R (- b e + 2c d)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R (- b e + 2c d)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R c\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1483 +d0220b:=D(m0220b,x) +--R +--R +--R (1193) 0 +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1483 +t0221:= (d+e*x)/x/(a+b*x+c*x^2) +--R +--R +--R e x + d +--R (1194) ----------------- +--R 3 2 +--R c x + b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1194 + +--S 1195 of 1483 +r0221:= (b*d-2*a*e)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a/(b^2-4*a*c)^(1/2)+_ + d*log(x)/a-1/2*d*log(a+b*x+c*x^2)/a +--R +--R +--R (1195) +--R 2c x + b +--R (- 4a e + 2b d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 | 2 +--R (- d log(c x + b x + a) + 2d log(x))\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a\|- 4a c + b +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1483 +a0221:=integrate(t0221,x) +--R +--R +--R (1196) +--R [ +--R (2a e - b d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 | 2 +--R (- d log(c x + b x + a) + 2d log(x))\|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R (4a e - 2b d)atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 | 2 +--R (- d log(c x + b x + a) + 2d log(x))\|4a c - b +--R / +--R +---------+ +--R | 2 +--R 2a\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1196 + +--S 1197 of 1483 +m0221a:=a0221.1-r0221 +--R +--R +--R (1197) +--R (2a e - b d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2c x + b +--R (4a e - 2b d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R | 2 +--R 2a\|- 4a c + b +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1483 +d0221a:=D(m0221a,x) +--R +--R +--R (1198) 0 +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1483 +m0221b:=a0221.2-r0221 +--R +--R +--R (1199) +--R +---------+ +--R | 2 2c x + b +--R (2a e - b d)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R | 2 (2c x + b)\|4a c - b +--R (2a e - b d)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R | 2 | 2 +--R a\|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1483 +d0221b:=D(m0221b,x) +--R +--R +--R (1200) 0 +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1483 +t0222:= (d+e*x)/x^2/(a+b*x+c*x^2) +--R +--R +--R e x + d +--R (1201) ------------------ +--R 4 3 2 +--R c x + b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1201 + +--S 1202 of 1483 +r0222:= -d/a/x-(b^2*d-2*a*c*d-a*b*e)*atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/_ + a^2/(b^2-4*a*c)^(1/2)-(b*d-a*e)*log(x)/a^2+1/2*(b*d-a*e)*_ + log(a+b*x+c*x^2)/a^2 +--R +--R +--R (1202) +--R 2 2c x + b +--R (2a b e + (4a c - 2b )d)x atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 +--R ((- a e + b d)x log(c x + b x + a) + (2a e - 2b d)x log(x) - 2a d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a x\|- 4a c + b +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 1483 +a0222:=integrate(t0222,x) +--R +--R +--R (1203) +--R [ +--R 2 +--R (a b e + (2a c - b )d)x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 +--R ((- a e + b d)x log(c x + b x + a) + (2a e - 2b d)x log(x) - 2a d) +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a x\|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 (2c x + b)\|4a c - b +--R (- 2a b e + (- 4a c + 2b )d)x atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 +--R ((- a e + b d)x log(c x + b x + a) + (2a e - 2b d)x log(x) - 2a d) +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 2 | 2 +--R 2a x\|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1203 + +--S 1204 of 1483 +m0222a:=a0222.1-r0222 +--R +--R +--R (1204) +--R 2 +--R (a b e + (2a c - b )d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2c x + b +--R (- 2a b e + (- 4a c + 2b )d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 2a \|- 4a c + b +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1483 +d0222a:=D(m0222a,x) +--R +--R +--R (1205) 0 +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1483 +m0222b:=a0222.2-r0222 +--R +--R +--R (1206) +--R +---------+ +--R 2 | 2 2c x + b +--R (- a b e + (- 2a c + b )d)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (- a b e + (- 2a c + b )d)\|- 4a c + b atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R a \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1483 +d0222b:=D(m0222b,x) +--R +--R +--R (1207) 0 +--R Type: Expression(Integer) +--E 1207 + +--S 1208 of 1483 +t0223:= (d+e*x)/x^3/(a+b*x+c*x^2) +--R +--R +--R e x + d +--R (1208) ------------------ +--R 5 4 3 +--R c x + b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1208 + +--S 1209 of 1483 +r0223:= -1/2*d/a/x^2+(b*d-a*e)/a^2/x+(b^3*d-3*a*b*c*d-a*b^2*e+2*a^2*c*e)*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^3/(b^2-4*a*c)^(1/2)+_ + (b^2*d-a*c*d-a*b*e)*log(x)/a^3-1/2*(b^2*d-a*c*d-a*b*e)*_ + log(a+b*x+c*x^2)/a^3 +--R +--R +--R (1209) +--R 2 2 3 2 2c x + b +--R ((4a c - 2a b )e + (- 6a b c + 2b )d)x atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 2 +--R (a b e + (a c - b )d)x log(c x + b x + a) +--R + +--R 2 2 2 2 +--R (- 2a b e + (- 2a c + 2b )d)x log(x) + (- 2a e + 2a b d)x - a d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 | 2 +--R 2a x \|- 4a c + b +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1483 +a0223:=integrate(t0223,x) +--R +--R +--R (1210) +--R [ +--R 2 2 3 2 +--R ((2a c - a b )e + (- 3a b c + b )d)x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 2 +--R (a b e + (a c - b )d)x log(c x + b x + a) +--R + +--R 2 2 2 2 +--R (- 2a b e + (- 2a c + 2b )d)x log(x) + (- 2a e + 2a b d)x - a d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 2 | 2 +--R 2a x \|- 4a c + b +--R , +--R +--R +---------+ +--R | 2 +--R 2 2 3 2 (2c x + b)\|4a c - b +--R ((- 4a c + 2a b )e + (6a b c - 2b )d)x atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 2 +--R (a b e + (a c - b )d)x log(c x + b x + a) +--R + +--R 2 2 2 2 +--R (- 2a b e + (- 2a c + 2b )d)x log(x) + (- 2a e + 2a b d)x - a d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 3 2 | 2 +--R 2a x \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1210 + +--S 1211 of 1483 +m0223a:=a0223.1-r0223 +--R +--R +--R (1211) +--R 2 2 3 +--R ((2a c - a b )e + (- 3a b c + b )d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 2c x + b +--R ((- 4a c + 2a b )e + (6a b c - 2b )d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 3 | 2 +--R 2a \|- 4a c + b +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1483 +d0223a:=D(m0223a,x) +--R +--R +--R (1212) 0 +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 1483 +m0223b:=a0223.2-r0223 +--R +--R +--R (1213) +--R +---------+ +--R 2 2 3 | 2 2c x + b +--R ((- 2a c + a b )e + (3a b c - b )d)\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 2 3 | 2 +--R ((- 2a c + a b )e + (3a b c - b )d)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 3 | 2 | 2 +--R a \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1483 +d0223b:=D(m0223b,x) +--R +--R +--R (1214) 0 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1483 +t0224:= (d+e*x)/x^4/(a+b*x+c*x^2) +--R +--R +--R e x + d +--R (1215) ------------------ +--R 6 5 4 +--R c x + b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1215 + +--S 1216 of 1483 +r0224:= -1/3*d/a/x^3+1/2*(b*d-a*e)/a^2/x^2-(b^2*d-a*c*d-a*b*e)/a^3/x-_ + (b^4*d-4*a*b^2*c*d+2*a^2*c^2*d-a*b^3*e+3*a^2*b*c*e)*_ + atanh((b+2*c*x)/(b^2-4*a*c)^(1/2))/a^4/(b^2-4*a*c)^(1/2)-_ + (b^3*d-2*a*b*c*d-a*b^2*e+a^2*c*e)*log(x)/a^4+_ + 1/2*(b^3*d-2*a*b*c*d-a*b^2*e+a^2*c*e)*log(a+b*x+c*x^2)/a^4 +--R +--R +--R (1216) +--R 2 3 2 2 2 4 3 +--R ((- 18a b c + 6a b )e + (- 12a c + 24a b c - 6b )d)x +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R 2 2 3 3 2 +--R ((3a c - 3a b )e + (- 6a b c + 3b )d)x log(c x + b x + a) +--R + +--R 2 2 3 3 +--R ((- 6a c + 6a b )e + (12a b c - 6b )d)x log(x) +--R + +--R 2 2 2 2 3 2 3 +--R (6a b e + (6a c - 6a b )d)x + (- 3a e + 3a b d)x - 2a d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 3 | 2 +--R 6a x \|- 4a c + b +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1483 +a0224:=integrate(t0224,x) +--R +--R +--R (1217) +--R [ +--R 2 3 2 2 2 4 3 +--R ((9a b c - 3a b )e + (6a c - 12a b c + 3b )d)x +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 2 3 3 2 +--R ((3a c - 3a b )e + (- 6a b c + 3b )d)x log(c x + b x + a) +--R + +--R 2 2 3 3 +--R ((- 6a c + 6a b )e + (12a b c - 6b )d)x log(x) +--R + +--R 2 2 2 2 3 2 3 +--R (6a b e + (6a c - 6a b )d)x + (- 3a e + 3a b d)x - 2a d +--R * +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 3 | 2 +--R 6a x \|- 4a c + b +--R , +--R +--R 2 3 2 2 2 4 3 +--R ((18a b c - 6a b )e + (12a c - 24a b c + 6b )d)x +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R + +--R 2 2 3 3 2 +--R ((3a c - 3a b )e + (- 6a b c + 3b )d)x log(c x + b x + a) +--R + +--R 2 2 3 3 +--R ((- 6a c + 6a b )e + (12a b c - 6b )d)x log(x) +--R + +--R 2 2 2 2 3 2 3 +--R (6a b e + (6a c - 6a b )d)x + (- 3a e + 3a b d)x - 2a d +--R * +--R +---------+ +--R | 2 +--R \|4a c - b +--R / +--R +---------+ +--R 4 3 | 2 +--R 6a x \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1217 + +--S 1218 of 1483 +m0224a:=a0224.1-r0224 +--R +--R +--R (1218) +--R 2 3 2 2 2 4 +--R ((3a b c - a b )e + (2a c - 4a b c + b )d) +--R * +--R log +--R +-----------+ +--R 2 2 2 | 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (8a c - 2b c)x +--R + +--R 3 +--R 4a b c - b +--R / +--R 2 +--R c x + b x + a +--R + +--R 2 3 2 2 2 4 2c x + b +--R ((6a b c - 2a b )e + (4a c - 8a b c + 2b )d)atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 4 | 2 +--R 2a \|- 4a c + b +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1483 +d0224a:=D(m0224a,x) +--R +--R +--R (1219) 0 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1483 +m0224b:=a0224.2-r0224 +--R +--R +--R (1220) +--R +---------+ +--R 2 3 2 2 2 4 | 2 +--R ((3a b c - a b )e + (2a c - 4a b c + b )d)\|4a c - b +--R * +--R 2c x + b +--R atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 3 2 2 2 4 | 2 +--R ((3a b c - a b )e + (2a c - 4a b c + b )d)\|- 4a c + b +--R * +--R +---------+ +--R | 2 +--R (2c x + b)\|4a c - b +--R atan(----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 4 | 2 | 2 +--R a \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1483 +d0224b:=D(m0224b,x) +--R +--R +--R (1221) 0 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1483 +t0225:= (a+b*x)^3/(a*c+(b*c+a*d)*x+b*d*x^2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1222) ------------------ +--R d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1222 + +--S 1223 of 1483 +r0225:= -b*(b*c-a*d)*x/d^2+1/2*(a+b*x)^2/d+(b*c-a*d)^2*log(c+d*x)/d^3 +--R +--R +--R (1223) +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(d x + c) + b d x + (4a b d - 2b c d)x + a d +--R ---------------------------------------------------------------------------- +--R 3 +--R 2d +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1483 +a0225:=integrate(t0225,x) +--R +--R +--R (1224) +--R 2 2 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(d x + c) + b d x + (4a b d - 2b c d)x +--R --------------------------------------------------------------------- +--R 3 +--R 2d +--R Type: Union(Expression(Integer),...) +--E 1224 + +--S 1225 of 1483 +m0225:=a0225-r0225 +--R +--R +--R 2 +--R a +--R (1225) - -- +--R 2d +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1483 +d0225:=D(m0225,x) +--R +--R +--R (1226) 0 +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1483 +t0226:= 1/(2+5*x+3*x^2) +--R +--R +--R 1 +--R (1227) ------------ +--R 2 +--R 3x + 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1227 + +--S 1228 of 1483 +r0226:= -2*atanh(5+6*x) +--R +--R +--R (1228) - 2atanh(6x + 5) +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1483 +a0226:=integrate(t0226,x) +--R +--R +--R (1229) log(3x + 2) - log(x + 1) +--R Type: Union(Expression(Integer),...) +--E 1229 + +--S 1230 of 1483 +m0226:=a0226-r0226 +--R +--R +--R (1230) log(3x + 2) - log(x + 1) + 2atanh(6x + 5) +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1483 +d0226:=D(m0226,x) +--R +--R +--R (1231) 0 +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1483 +t0227:= 1/(2+5*x-3*x^2) +--R +--R +--R 1 +--R (1232) - ------------ +--R 2 +--R 3x - 5x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1232 + +--S 1233 of 1483 +r0227:= 2/7*atanh(-5/7+6/7*x) +--R +--R +--R 6x - 5 +--R 2atanh(------) +--R 7 +--R (1233) -------------- +--R 7 +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1483 +a0227:=integrate(t0227,x) +--R +--R +--R log(3x + 1) - log(x - 2) +--R (1234) ------------------------ +--R 7 +--R Type: Union(Expression(Integer),...) +--E 1234 + +--S 1235 of 1483 +m0227:=a0227-r0227 +--R +--R +--R 6x - 5 +--R log(3x + 1) - log(x - 2) - 2atanh(------) +--R 7 +--R (1235) ----------------------------------------- +--R 7 +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1483 +d0227:=D(m0227,x) +--R +--R +--R (1236) 0 +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1483 +t0228:= (b+2*c*x)^5/(a+b*x+c*x^2)^3 +--R +--R +--R (1237) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R 32c x + 80b c x + 80b c x + 40b c x + 10b c x + b +--R / +--R 3 6 2 5 2 2 4 3 3 2 2 2 +--R c x + 3b c x + (3a c + 3b c)x + (6a b c + b )x + (3a c + 3a b )x +--R + +--R 2 3 +--R 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1237 + +--S 1238 of 1483 +r0228:= -1/2*(b+2*c*x)^4/(a+b*x+c*x^2)^2-4*c*(b+2*c*x)^2/(a+b*x+c*x^2)+_ + 16*c^2*log(a+b*x+c*x^2) +--R +--R +--R (1238) +--R 4 4 3 3 3 2 2 2 2 2 2 +--R (32c x + 64b c x + (64a c + 32b c )x + 64a b c x + 32a c ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 4 4 3 3 3 2 2 2 2 3 +--R - 48c x - 96b c x + (- 32a c - 64b c )x + (- 32a b c - 16b c)x +--R + +--R 2 4 +--R - 8a b c - b +--R / +--R 2 4 3 2 2 2 +--R 2c x + 4b c x + (4a c + 2b )x + 4a b x + 2a +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1483 +a0228:=integrate(t0228,x) +--R +--R +--R (1239) +--R 4 4 3 3 3 2 2 2 2 2 2 +--R (32c x + 64b c x + (64a c + 32b c )x + 64a b c x + 32a c ) +--R * +--R 2 +--R log(c x + b x + a) +--R + +--R 3 2 2 2 2 3 2 2 2 4 +--R (64a c - 16b c )x + (64a b c - 16b c)x + 48a c - 8a b c - b +--R / +--R 2 4 3 2 2 2 +--R 2c x + 4b c x + (4a c + 2b )x + 4a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 1239 + +--S 1240 of 1483 +m0228:=a0228-r0228 +--R +--R +--R 2 +--R (1240) 24c +--R Type: Expression(Integer) +--E 1240 + +--S 1241 of 1483 +d0228:=D(m0228,x) +--R +--R +--R (1241) 0 +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1483 +t0229:= 1/(2+13*x+15*x^2) +--R +--R +--R 1 +--R (1242) -------------- +--R 2 +--R 15x + 13x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1242 + +--S 1243 of 1483 +r0229:= -2/7*atanh(13/7+30/7*x) +--R +--R +--R 30x + 13 +--R 2atanh(--------) +--R 7 +--R (1243) - ---------------- +--R 7 +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1483 +a0229:=integrate(t0229,x) +--R +--R +--R log(5x + 1) - log(3x + 2) +--R (1244) ------------------------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 1244 + +--S 1245 of 1483 +m0229:=a0229-r0229 +--R +--R +--R 30x + 13 +--R log(5x + 1) - log(3x + 2) + 2atanh(--------) +--R 7 +--R (1245) -------------------------------------------- +--R 7 +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1483 +d0229:=D(m0229,x) +--R +--R +--R (1246) 0 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1483 +t0230:= 1/x/(2/x+13+15*x) +--R +--R +--R 1 +--R (1247) -------------- +--R 2 +--R 15x + 13x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1247 + +--S 1248 of 1483 +r0230:= -2/7*atanh(13/7+30/7*x) +--R +--R +--R 30x + 13 +--R 2atanh(--------) +--R 7 +--R (1248) - ---------------- +--R 7 +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1483 +a0230:=integrate(t0230,x) +--R +--R +--R log(5x + 1) - log(3x + 2) +--R (1249) ------------------------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 1249 + +--S 1250 of 1483 +m0230:=a0230-r0230 +--R +--R +--R 30x + 13 +--R log(5x + 1) - log(3x + 2) + 2atanh(--------) +--R 7 +--R (1250) -------------------------------------------- +--R 7 +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1483 +d0230:=D(m0230,x) +--R +--R +--R (1251) 0 +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1483 +t0231:= 1/x^2/(2/x^2+13/x+15) +--R +--R +--R 1 +--R (1252) -------------- +--R 2 +--R 15x + 13x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1252 + +--S 1253 of 1483 +r0231:= 2/7*atanh(13/7+4/7/x) +--R +--R +--R 13x + 4 +--R 2atanh(-------) +--R 7x +--R (1253) --------------- +--R 7 +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1483 +a0231:=integrate(t0231,x) +--R +--R +--R log(5x + 1) - log(3x + 2) +--R (1254) ------------------------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 1254 + +--S 1255 of 1483 +m0231:=a0231-r0231 +--R +--R +--R 13x + 4 +--R log(5x + 1) - log(3x + 2) - 2atanh(-------) +--R 7x +--R (1255) ------------------------------------------- +--R 7 +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1483 +d0231:=D(m0231,x) +--R +--R +--R (1256) 0 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1483 +t0232:= x/(2*x+13*x^2+15*x^3) +--R +--R +--R 1 +--R (1257) -------------- +--R 2 +--R 15x + 13x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1257 + +--S 1258 of 1483 +r0232:= -2/7*atanh(13/7+30/7*x) +--R +--R +--R 30x + 13 +--R 2atanh(--------) +--R 7 +--R (1258) - ---------------- +--R 7 +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1483 +a0232:=integrate(t0232,x) +--R +--R +--R log(5x + 1) - log(3x + 2) +--R (1259) ------------------------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 1259 + +--S 1260 of 1483 +m0232:=a0232-r0232 +--R +--R +--R 30x + 13 +--R log(5x + 1) - log(3x + 2) + 2atanh(--------) +--R 7 +--R (1260) -------------------------------------------- +--R 7 +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1483 +d0232:=D(m0232,x) +--R +--R +--R (1261) 0 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1483 +t0233:= x^4/(a+b*x^2+c*x^4) +--R +--R +--R 4 +--R x +--R (1262) --------------- +--R 4 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1262 + +--S 1263 of 1483 +r0233:= x/c-1/2*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*atan(2^(1/2)*c^(1/2)*x/_ + (b-(b^2-4*a*c)^(1/2))^(1/2))*2^(1/2)/c^(3/2)/_ + (b-(b^2-4*a*c)^(1/2))^(1/2)-1/2*(b+(b^2-2*a*c)/_ + (b^2-4*a*c)^(1/2))*atan(2^(1/2)*c^(1/2)*x/_ + (b+(b^2-4*a*c)^(1/2))^(1/2))*2^(1/2)/c^(3/2)/_ + (b+(b^2-4*a*c)^(1/2))^(1/2) +--R +--R +--R (1263) +--R +------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 2 +-+ | | 2 +--R (- b\|2 \|- 4a c + b + (- 2a c + b )\|2 )\|\|- 4a c + b + b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atan(-----------------------) +--R +--------------------+ +--R | +-----------+ +--R | | 2 +--R \|- \|- 4a c + b + b +--R + +--R +--------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 2 +-+ | | 2 +--R (- b\|2 \|- 4a c + b + (2a c - b )\|2 )\|- \|- 4a c + b + b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b + b +--R + +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R 2x\|- 4a c + b \|c \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R / +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R 2c\|- 4a c + b \|c \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1483 +a0233:=integrate(t0233,x) +--R +--R +--R (1264) +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R c |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (16a b c - 4b c ) |-------------------- - 4a c + 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R - b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R - +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R c |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (16a b c - 4b c ) |-------------------- + 4a c - 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R b +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R c |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (- 16a b c + 4b c ) |-------------------- - 4a c + 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R - b +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R - +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R c |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 +--R (- 16a b c + 4b c ) |-------------------- + 4a c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 2 4 +--R - 5a b c + b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R 2x +--R / +--R 2c +--R Type: Union(Expression(Integer),...) +--E 1264 + +--S 1265 of 1483 +m0233:=a0233-r0233 +--R +--R +--R (1265) +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R c\|- 4a c + b \|c \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (16a b c - 4b c ) |-------------------- - 4a c + 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R - b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R - +--R +-----------+ +--R | 2 +-+ +--R c\|- 4a c + b \|c +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R +--------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (16a b c - 4b c ) |-------------------- + 4a c - 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R b +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R +-----------+ +--R | 2 +-+ +--R c\|- 4a c + b \|c +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R +--------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (- 16a b c + 4b c ) |-------------------- - 4a c + 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R - b +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R - +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R c\|- 4a c + b \|c \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 +--R (- 16a b c + 4b c ) |-------------------- + 4a c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 2 4 +--R - 5a b c + b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- - 3a b c + b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R +------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 2 +-+ | | 2 +--R (b\|2 \|- 4a c + b + (2a c - b )\|2 )\|\|- 4a c + b + b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atan(-----------------------) +--R +--------------------+ +--R | +-----------+ +--R | | 2 +--R \|- \|- 4a c + b + b +--R + +--R +--------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 2 +-+ | | 2 +--R (b\|2 \|- 4a c + b + (- 2a c + b )\|2 )\|- \|- 4a c + b + b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b + b +--R / +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R 2c\|- 4a c + b \|c \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1483 +d0233:=D(m0233,x) +--R +--R +--R (1266) 0 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1483 +t0234:= x^2/(a+b*x^2+c*x^4) +--R +--R +--R 2 +--R x +--R (1267) --------------- +--R 4 2 +--R c x + b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1267 + +--S 1268 of 1483 +r0234:= 1/2*2^(1/2)*(-(b-(b^2-4*a*c)^(1/2))^(1/2)*_ + atan(2^(1/2)*c^(1/2)*x/(b-(b^2-4*a*c)^(1/2))^(1/2))+_ + (b+(b^2-4*a*c)^(1/2))^(1/2)*_ + atan(2^(1/2)*c^(1/2)*x/(b+(b^2-4*a*c)^(1/2))^(1/2)))/_ + c^(1/2)/(b^2-4*a*c)^(1/2) +--R +--R +--R (1268) +--R +--------------------+ +--R | +-----------+ +-+ +-+ +--R +-+ | | 2 x\|2 \|c +--R - \|2 \|- \|- 4a c + b + b atan(-----------------------) +--R +--------------------+ +--R | +-----------+ +--R | | 2 +--R \|- \|- 4a c + b + b +--R + +--R +------------------+ +--R | +-----------+ +-+ +-+ +--R +-+ | | 2 x\|2 \|c +--R \|2 \|\|- 4a c + b + b atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b + b +--R / +--R +-----------+ +--R | 2 +-+ +--R 2\|- 4a c + b \|c +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1483 +a0234:=integrate(t0234,x) +--R +--R +--R (1269) +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R - +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R - +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1269 + +--S 1270 of 1483 +m0234:=a0234-r0234 +--R +--R +--R (1270) +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- + b +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 64a c - 16b c +--R \|- 4a c + b \|c |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R - +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- + b +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 64a c - 16b c +--R \|- 4a c + b \|c |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- + b +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 64a c - 16b c +--R \|- 4a c + b \|c |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R - +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- + b +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 64a c - 16b c +--R \|- 4a c + b \|c |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- + b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R +--------------------+ +--R | +-----------+ +-+ +-+ +--R +-+ | | 2 x\|2 \|c +--R \|2 \|- \|- 4a c + b + b atan(-----------------------) +--R +--------------------+ +--R | +-----------+ +--R | | 2 +--R \|- \|- 4a c + b + b +--R + +--R +------------------+ +--R | +-----------+ +-+ +-+ +--R +-+ | | 2 x\|2 \|c +--R - \|2 \|\|- 4a c + b + b atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b + b +--R / +--R +-----------+ +--R | 2 +-+ +--R 2\|- 4a c + b \|c +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1483 +d0234:=D(m0234,x) +--R +--R +--R (1271) 0 +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1483 +t0235:= 1/x^2/(a+b*x^2+c*x^4) +--R +--R +--R 1 +--R (1272) ------------------ +--R 6 4 2 +--R c x + b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1272 + +--S 1273 of 1483 +r0235:= -1/a/x-1/2*c^(1/2)*(1+b/(b^2-4*a*c)^(1/2))*_ + atan(2^(1/2)*c^(1/2)*x/(b-(b^2-4*a*c)^(1/2))^(1/2))*2^(1/2)/_ + a/(b-(b^2-4*a*c)^(1/2))^(1/2)-1/2*c^(1/2)*(1-b/(b^2-4*a*c)^(1/2))*_ + atan(2^(1/2)*c^(1/2)*x/(b+(b^2-4*a*c)^(1/2))^(1/2))*2^(1/2)/_ + a/(b+(b^2-4*a*c)^(1/2))^(1/2) +--R +--R +--R (1273) +--R +------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-+ | | 2 +--R (- x\|2 \|- 4a c + b - b x\|2 )\|c \|\|- 4a c + b + b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atan(-----------------------) +--R +--------------------+ +--R | +-----------+ +--R | | 2 +--R \|- \|- 4a c + b + b +--R + +--R +--------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-+ | | 2 +--R (- x\|2 \|- 4a c + b + b x\|2 )\|c \|- \|- 4a c + b + b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b + b +--R + +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 | | 2 | | 2 +--R - 2\|- 4a c + b \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R / +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 | | 2 | | 2 +--R 2a x\|- 4a c + b \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1483 +a0235:=integrate(t0235,x) +--R +--R +--R (1274) +--R - +--R +----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(16a c - 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R a x |---------------------------------------------------- +--R | 4 3 2 +--R \| 8a c - 2a b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 5 2 4 2 3 4 |- a c + 2a b c - b 2 2 +--R (32a c - 24a b c + 4a b ) |-------------------- + 4a b c +--R | 7 6 2 +--R \| 64a c - 16a b +--R + +--R 3 5 +--R - 5a b c + b +--R * +--R +----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(16a c - 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |---------------------------------------------------- +--R | 4 3 2 +--R \| 8a c - 2a b +--R + +--R 3 2 2 +--R (2a c - 2b c )x +--R + +--R +------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(- 16a c + 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R a x |------------------------------------------------------ +--R | 4 3 2 +--R \| 8a c - 2a b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 5 2 4 2 3 4 |- a c + 2a b c - b 2 2 +--R (32a c - 24a b c + 4a b ) |-------------------- - 4a b c +--R | 7 6 2 +--R \| 64a c - 16a b +--R + +--R 3 5 +--R 5a b c - b +--R * +--R +------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(- 16a c + 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |------------------------------------------------------ +--R | 4 3 2 +--R \| 8a c - 2a b +--R + +--R 3 2 2 +--R (2a c - 2b c )x +--R + +--R - +--R +------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(- 16a c + 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R a x |------------------------------------------------------ +--R | 4 3 2 +--R \| 8a c - 2a b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 5 2 4 2 3 4 |- a c + 2a b c - b +--R (- 32a c + 24a b c - 4a b ) |-------------------- +--R | 7 6 2 +--R \| 64a c - 16a b +--R + +--R 2 2 3 5 +--R 4a b c - 5a b c + b +--R * +--R +------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(- 16a c + 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |------------------------------------------------------ +--R | 4 3 2 +--R \| 8a c - 2a b +--R + +--R 3 2 2 +--R (2a c - 2b c )x +--R + +--R +----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(16a c - 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R a x |---------------------------------------------------- +--R | 4 3 2 +--R \| 8a c - 2a b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 5 2 4 2 3 4 |- a c + 2a b c - b 2 2 +--R (- 32a c + 24a b c - 4a b ) |-------------------- - 4a b c +--R | 7 6 2 +--R \| 64a c - 16a b +--R + +--R 3 5 +--R 5a b c - b +--R * +--R +----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(16a c - 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |---------------------------------------------------- +--R | 4 3 2 +--R \| 8a c - 2a b +--R + +--R 3 2 2 +--R (2a c - 2b c )x +--R + +--R - 2 +--R / +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 1274 + +--S 1275 of 1483 +m0235:=a0235-r0235 +--R +--R +--R (1275) +--R - +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 | | 2 | | 2 +--R a\|- 4a c + b \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R * +--R +----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(16a c - 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |---------------------------------------------------- +--R | 4 3 2 +--R \| 8a c - 2a b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 5 2 4 2 3 4 |- a c + 2a b c - b 2 2 +--R (32a c - 24a b c + 4a b ) |-------------------- + 4a b c +--R | 7 6 2 +--R \| 64a c - 16a b +--R + +--R 3 5 +--R - 5a b c + b +--R * +--R +----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(16a c - 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |---------------------------------------------------- +--R | 4 3 2 +--R \| 8a c - 2a b +--R + +--R 3 2 2 +--R (2a c - 2b c )x +--R + +--R +-----------+ +--R | 2 +--R a\|- 4a c + b +--R * +--R +------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(- 16a c + 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |------------------------------------------------------ +--R | 4 3 2 +--R \| 8a c - 2a b +--R * +--R +--------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 5 2 4 2 3 4 |- a c + 2a b c - b 2 2 +--R (32a c - 24a b c + 4a b ) |-------------------- - 4a b c +--R | 7 6 2 +--R \| 64a c - 16a b +--R + +--R 3 5 +--R 5a b c - b +--R * +--R +------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(- 16a c + 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |------------------------------------------------------ +--R | 4 3 2 +--R \| 8a c - 2a b +--R + +--R 3 2 2 +--R (2a c - 2b c )x +--R + +--R - +--R +-----------+ +--R | 2 +--R a\|- 4a c + b +--R * +--R +------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(- 16a c + 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |------------------------------------------------------ +--R | 4 3 2 +--R \| 8a c - 2a b +--R * +--R +--------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 5 2 4 2 3 4 |- a c + 2a b c - b +--R (- 32a c + 24a b c - 4a b ) |-------------------- +--R | 7 6 2 +--R \| 64a c - 16a b +--R + +--R 2 2 3 5 +--R 4a b c - 5a b c + b +--R * +--R +------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(- 16a c + 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |------------------------------------------------------ +--R | 4 3 2 +--R \| 8a c - 2a b +--R + +--R 3 2 2 +--R (2a c - 2b c )x +--R + +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 | | 2 | | 2 +--R a\|- 4a c + b \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R * +--R +----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(16a c - 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |---------------------------------------------------- +--R | 4 3 2 +--R \| 8a c - 2a b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 5 2 4 2 3 4 |- a c + 2a b c - b 2 2 +--R (- 32a c + 24a b c - 4a b ) |-------------------- - 4a b c +--R | 7 6 2 +--R \| 64a c - 16a b +--R + +--R 3 5 +--R 5a b c - b +--R * +--R +----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 3 2 |- a c + 2a b c - b 3 +--R |(16a c - 4a b ) |-------------------- - 3a b c + b +--R | | 7 6 2 +--R | \| 64a c - 16a b +--R |---------------------------------------------------- +--R | 4 3 2 +--R \| 8a c - 2a b +--R + +--R 3 2 2 +--R (2a c - 2b c )x +--R + +--R +------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-+ | | 2 +--R (\|2 \|- 4a c + b + b\|2 )\|c \|\|- 4a c + b + b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atan(-----------------------) +--R +--------------------+ +--R | +-----------+ +--R | | 2 +--R \|- \|- 4a c + b + b +--R + +--R +--------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ +-+ | | 2 +--R (\|2 \|- 4a c + b - b\|2 )\|c \|- \|- 4a c + b + b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b + b +--R / +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 | | 2 | | 2 +--R 2a\|- 4a c + b \|- \|- 4a c + b + b \|\|- 4a c + b + b +--R Type: Expression(Integer) +--E 1275 + +--S 1276 of 1483 +d0235:=D(m0235,x) +--R +--R +--R (1276) 0 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1483 +t0236:= 1/x^3/(a+b*x^2+c*x^4) +--R +--R +--R 1 +--R (1277) ------------------ +--R 7 5 3 +--R c x + b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1277 + +--S 1278 of 1483 +r0236:= -1/2/a/x^2-1/2*(b^2-2*a*c)*_ + atanh((b+2*c*x^2)/(b^2-4*a*c)^(1/2))/a^2/(b^2-4*a*c)^(1/2)-_ + b*log(x)/a^2+1/4*b*log(a+b*x^2+c*x^4)/a^2 +--R +--R +--R (1278) +--R 2 +--R 2 2 2c x + b +--R (4a c - 2b )x atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +-----------+ +--R 2 4 2 2 | 2 +--R (b x log(c x + b x + a) - 4b x log(x) - 2a)\|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R 4a x \|- 4a c + b +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1483 +a0236:=integrate(t0236,x) +--R +--R +--R (1279) +--R [ +--R 2 2 +--R (2a c - b )x +--R * +--R log +--R +-----------+ +--R 2 4 2 2 | 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b +--R + +--R 2 2 2 3 +--R (- 8a c + 2b c)x - 4a b c + b +--R / +--R 4 2 +--R c x + b x + a +--R + +--R +-----------+ +--R 2 4 2 2 | 2 +--R (b x log(c x + b x + a) - 4b x log(x) - 2a)\|- 4a c + b +--R / +--R +-----------+ +--R 2 2 | 2 +--R 4a x \|- 4a c + b +--R , +--R +--R +---------+ +--R 2 | 2 +--R 2 2 (2c x + b)\|4a c - b +--R (- 4a c + 2b )x atan(-----------------------) +--R 2 +--R 4a c - b +--R + +--R +---------+ +--R 2 4 2 2 | 2 +--R (b x log(c x + b x + a) - 4b x log(x) - 2a)\|4a c - b +--R / +--R +---------+ +--R 2 2 | 2 +--R 4a x \|4a c - b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1279 + +--S 1280 of 1483 +m0236a:=a0236.1-r0236 +--R +--R +--R (1280) +--R 2 +--R (2a c - b ) +--R * +--R log +--R +-----------+ +--R 2 4 2 2 | 2 2 2 2 +--R (2c x + 2b c x - 2a c + b )\|- 4a c + b + (- 8a c + 2b c)x +--R + +--R 3 +--R - 4a b c + b +--R / +--R 4 2 +--R c x + b x + a +--R + +--R 2 +--R 2 2c x + b +--R (- 4a c + 2b )atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R / +--R +-----------+ +--R 2 | 2 +--R 4a \|- 4a c + b +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1483 +d0236a:=D(m0236a,x) +--R +--R +--R (1281) 0 +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1483 +m0236b:=a0236.2-r0236 +--R +--R +--R (1282) +--R +---------+ 2 +--R 2 | 2 2c x + b +--R (- 2a c + b )\|4a c - b atanh(--------------) +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R + +--R +---------+ +--R +-----------+ 2 | 2 +--R 2 | 2 (2c x + b)\|4a c - b +--R (- 2a c + b )\|- 4a c + b atan(-----------------------) +--R 2 +--R 4a c - b +--R / +--R +-----------+ +---------+ +--R 2 | 2 | 2 +--R 2a \|- 4a c + b \|4a c - b +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 1483 +d0236b:=D(m0236b,x) +--R +--R +--R (1283) 0 +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1483 +t0237:= x^4/(a-b*x^2+c*x^4) +--R +--R +--R 4 +--R x +--R (1284) --------------- +--R 4 2 +--R c x - b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1284 + +--S 1285 of 1483 +r0237:= x/c+1/2*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ + atan(2^(1/2)*c^(1/2)*x/(-b+(b^2-4*a*c)^(1/2))^(1/2))*2^(1/2)/_ + c^(3/2)/(-b+(b^2-4*a*c)^(1/2))^(1/2)-1/2*(b+(b^2-2*a*c)/_ + (b^2-4*a*c)^(1/2))*atanh(2^(1/2)*c^(1/2)*x/_ + (b+(b^2-4*a*c)^(1/2))^(1/2))*2^(1/2)/c^(3/2)/_ + (b+(b^2-4*a*c)^(1/2))^(1/2) +--R +--R +--R (1285) +--R +------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 2 +-+ | | 2 +--R (- b\|2 \|- 4a c + b + (2a c - b )\|2 )\|\|- 4a c + b - b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atanh(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b + b +--R + +--R +------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 2 +-+ | | 2 +--R (b\|2 \|- 4a c + b + (2a c - b )\|2 )\|\|- 4a c + b + b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b - b +--R + +--R +------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R 2x\|- 4a c + b \|c \|\|- 4a c + b - b \|\|- 4a c + b + b +--R / +--R +------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R 2c\|- 4a c + b \|c \|\|- 4a c + b - b \|\|- 4a c + b + b +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1483 +a0237:=integrate(t0237,x) +--R +--R +--R (1286) +--R - +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R c |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (16a b c - 4b c ) |-------------------- + 4a c - 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R c |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (16a b c - 4b c ) |-------------------- - 4a c + 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R - b +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R - +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R c |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 +--R (- 16a b c + 4b c ) |-------------------- + 4a c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 2 4 +--R - 5a b c + b +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R c |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (- 16a b c + 4b c ) |-------------------- - 4a c + 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R - b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R 2x +--R / +--R 2c +--R Type: Union(Expression(Integer),...) +--E 1286 + +--S 1287 of 1483 +m0237:=a0237-r0237 +--R +--R +--R (1287) +--R - +--R +------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R c\|- 4a c + b \|c \|\|- 4a c + b - b \|\|- 4a c + b + b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (16a b c - 4b c ) |-------------------- + 4a c - 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R +-----------+ +--R | 2 +-+ +--R c\|- 4a c + b \|c +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R +------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|\|- 4a c + b - b \|\|- 4a c + b + b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (16a b c - 4b c ) |-------------------- - 4a c + 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R - b +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R - +--R +-----------+ +--R | 2 +-+ +--R c\|- 4a c + b \|c +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R +------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|\|- 4a c + b - b \|\|- 4a c + b + b +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 +--R (- 16a b c + 4b c ) |-------------------- + 4a c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 2 4 +--R - 5a b c + b +--R * +--R +-------------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(- 16a c + 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |------------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R +------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R c\|- 4a c + b \|c \|\|- 4a c + b - b \|\|- 4a c + b + b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R * +--R log +--R +--------------------+ +--R | 2 2 2 4 +--R 4 3 3 |- a c + 2a b c - b 2 2 2 +--R (- 16a b c + 4b c ) |-------------------- - 4a c + 5a b c +--R | 7 2 6 +--R \| 64a c - 16b c +--R + +--R 4 +--R - b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------+ +--R | | 2 2 2 4 +--R | 4 2 3 |- a c + 2a b c - b 3 +--R |(16a c - 4b c ) |-------------------- + 3a b c - b +--R | | 7 2 6 +--R | \| 64a c - 16b c +--R |----------------------------------------------------- +--R | 4 2 3 +--R \| 8a c - 2b c +--R + +--R 2 2 +--R (2a c - 2a b )x +--R + +--R +------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 2 +-+ | | 2 +--R (b\|2 \|- 4a c + b + (- 2a c + b )\|2 )\|\|- 4a c + b - b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atanh(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b + b +--R + +--R +------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 2 +-+ | | 2 +--R (- b\|2 \|- 4a c + b + (- 2a c + b )\|2 )\|\|- 4a c + b + b +--R * +--R +-+ +-+ +--R x\|2 \|c +--R atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b - b +--R / +--R +------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R 2c\|- 4a c + b \|c \|\|- 4a c + b - b \|\|- 4a c + b + b +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1483 +d0237:=D(m0237,x) +--R +--R +--R (1288) 0 +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1483 +t0238:= x^2/(a-b*x^2+c*x^4) +--R +--R +--R 2 +--R x +--R (1289) --------------- +--R 4 2 +--R c x - b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1289 + +--S 1290 of 1483 +r0238:= -1/2*2^(1/2)*(-(-b+(b^2-4*a*c)^(1/2))^(1/2)*_ + atan(2^(1/2)*c^(1/2)*x/(-b+(b^2-4*a*c)^(1/2))^(1/2))+_ + (b+(b^2-4*a*c)^(1/2))^(1/2)*atanh(2^(1/2)*c^(1/2)*_ + x/(b+(b^2-4*a*c)^(1/2))^(1/2)))/c^(1/2)/(b^2-4*a*c)^(1/2) +--R +--R +--R (1290) +--R +------------------+ +--R | +-----------+ +-+ +-+ +--R +-+ | | 2 x\|2 \|c +--R - \|2 \|\|- 4a c + b + b atanh(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b + b +--R + +--R +------------------+ +--R | +-----------+ +-+ +-+ +--R +-+ | | 2 x\|2 \|c +--R \|2 \|\|- 4a c + b - b atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b - b +--R / +--R +-----------+ +--R | 2 +-+ +--R 2\|- 4a c + b \|c +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1483 +a0238:=integrate(t0238,x) +--R +--R +--R (1291) +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R - +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R - +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1291 + +--S 1292 of 1483 +m0238:=a0238-r0238 +--R +--R +--R (1292) +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- - b +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 64a c - 16b c +--R \|- 4a c + b \|c |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R - +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- - b +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 64a c - 16b c +--R \|- 4a c + b \|c |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (16a c - 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- - b +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 64a c - 16b c +--R \|- 4a c + b \|c |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +-----------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(- 16a c + 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |----------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R - +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- - b +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 64a c - 16b c +--R \|- 4a c + b \|c |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R * +--R log +--R +-----------------+ +--R 2 2 | 1 +--R (- 16a c + 4b c) |- --------------- +--R | 3 2 2 +--R \| 64a c - 16b c +--R * +--R +---------------------------------------+ +--R | +-----------------+ +--R | 2 2 | 1 +--R |(16a c - 4b c) |- --------------- - b +--R | | 3 2 2 +--R | \| 64a c - 16b c +--R |--------------------------------------- +--R | 2 2 +--R \| 8a c - 2b c +--R + +--R x +--R + +--R +------------------+ +--R | +-----------+ +-+ +-+ +--R +-+ | | 2 x\|2 \|c +--R \|2 \|\|- 4a c + b + b atanh(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b + b +--R + +--R +------------------+ +--R | +-----------+ +-+ +-+ +--R +-+ | | 2 x\|2 \|c +--R - \|2 \|\|- 4a c + b - b atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4a c + b - b +--R / +--R +-----------+ +--R | 2 +-+ +--R 2\|- 4a c + b \|c +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1483 +d0238:=D(m0238,x) +--R +--R +--R (1293) 0 +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1483 +t0239:= 1/(a^2+b+2*a*x^2+x^4) +--R +--R +--R 1 +--R (1294) ------------------- +--R 4 2 2 +--R x + 2a x + b + a +--R Type: Fraction(Polynomial(Integer)) +--E 1294 + +--S 1295 of 1483 +r0239:= 1/2*atan(x/(a-(-b)^(1/2))^(1/2))/(a-(-b)^(1/2))^(1/2)/_ + (-b)^(1/2)-1/2*atan(x/(a+(-b)^(1/2))^(1/2))/_ + (a+(-b)^(1/2))^(1/2)/(-b)^(1/2) +--R +--R +--R (1295) +--R +----------+ +------------+ +--R | +---+ x | +---+ x +--R \|\|- b + a atan(---------------) - \|- \|- b + a atan(-------------) +--R +------------+ +----------+ +--R | +---+ | +---+ +--R \|- \|- b + a \|\|- b + a +--R ----------------------------------------------------------------------- +--R +------------+ +----------+ +--R +---+ | +---+ | +---+ +--R 2\|- b \|- \|- b + a \|\|- b + a +--R Type: Expression(Integer) +--E 1295 + +--S 1296 of 1483 +a0239:=integrate(t0239,x) +--R +--R +--R (1296) +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(8b + 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R * +--R log +--R +------------------------+ +--R 2 3 | 1 +--R ((16a b + 16a b) |- ---------------------- + 2b) +--R | 3 2 2 4 +--R \| 64b + 128a b + 64a b +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(8b + 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R + +--R x +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(- 8b - 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |--------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R * +--R log +--R +------------------------+ +--R 2 3 | 1 +--R ((16a b + 16a b) |- ---------------------- - 2b) +--R | 3 2 2 4 +--R \| 64b + 128a b + 64a b +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(- 8b - 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |--------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R + +--R x +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(- 8b - 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |--------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R * +--R log +--R +------------------------+ +--R 2 3 | 1 +--R ((- 16a b - 16a b) |- ---------------------- + 2b) +--R | 3 2 2 4 +--R \| 64b + 128a b + 64a b +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(- 8b - 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |--------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R + +--R x +--R + +--R - +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(8b + 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R * +--R log +--R +------------------------+ +--R 2 3 | 1 +--R ((- 16a b - 16a b) |- ---------------------- - 2b) +--R | 3 2 2 4 +--R \| 64b + 128a b + 64a b +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(8b + 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R + +--R x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1296 + +--S 1297 of 1483 +m0239:=a0239-r0239 +--R +--R +--R (1297) +--R +------------+ +----------+ +--R +---+ | +---+ | +---+ +--R \|- b \|- \|- b + a \|\|- b + a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(8b + 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R * +--R log +--R +------------------------+ +--R 2 3 | 1 +--R ((16a b + 16a b) |- ---------------------- + 2b) +--R | 3 2 2 4 +--R \| 64b + 128a b + 64a b +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(8b + 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R + +--R x +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(- 8b - 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R +---+ | \| 64b + 128a b + 64a b +--R \|- b |--------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R * +--R +------------+ +----------+ +--R | +---+ | +---+ +--R \|- \|- b + a \|\|- b + a +--R * +--R log +--R +------------------------+ +--R 2 3 | 1 +--R ((16a b + 16a b) |- ---------------------- - 2b) +--R | 3 2 2 4 +--R \| 64b + 128a b + 64a b +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(- 8b - 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |--------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R + +--R x +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(- 8b - 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +------------+ +--R +---+ | \| 64b + 128a b + 64a b | +---+ +--R \|- b |--------------------------------------------- \|- \|- b + a +--R | 2 2 +--R \| 4b + 4a b +--R * +--R +----------+ +--R | +---+ +--R \|\|- b + a +--R * +--R log +--R +------------------------+ +--R 2 3 | 1 +--R ((- 16a b - 16a b) |- ---------------------- + 2b) +--R | 3 2 2 4 +--R \| 64b + 128a b + 64a b +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(- 8b - 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |--------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R + +--R x +--R + +--R - +--R +------------+ +----------+ +--R +---+ | +---+ | +---+ +--R \|- b \|- \|- b + a \|\|- b + a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(8b + 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R * +--R log +--R +------------------------+ +--R 2 3 | 1 +--R ((- 16a b - 16a b) |- ---------------------- - 2b) +--R | 3 2 2 4 +--R \| 64b + 128a b + 64a b +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 2 | 1 +--R |(8b + 8a b) |- ---------------------- + a +--R | | 3 2 2 4 +--R | \| 64b + 128a b + 64a b +--R |------------------------------------------- +--R | 2 2 +--R \| 4b + 4a b +--R + +--R x +--R + +--R +----------+ +------------+ +--R | +---+ x | +---+ x +--R - \|\|- b + a atan(---------------) + \|- \|- b + a atan(-------------) +--R +------------+ +----------+ +--R | +---+ | +---+ +--R \|- \|- b + a \|\|- b + a +--R / +--R +------------+ +----------+ +--R +---+ | +---+ | +---+ +--R 2\|- b \|- \|- b + a \|\|- b + a +--R Type: Expression(Integer) +--E 1297 + +--S 1298 of 1483 +d0239:=D(m0239,x) +--R +--R +--R (1298) 0 +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1483 +t0240:= 1/(1+a^2+2*a*x^2+x^4) +--R +--R +--R 1 +--R (1299) ------------------- +--R 4 2 2 +--R x + 2a x + a + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1299 + +--S 1300 of 1483 +r0240:= -1/8*2^(1/2)*(2*atan(1/2*(2^(1/2)*(-a+(1+a^2)^(1/2))^(1/2)-2*x)*_ + 2^(1/2)/(a+(1+a^2)^(1/2))^(1/2))*(-a+(1+a^2)^(1/2))^(1/2)-2*_ + atan(1/2*(2^(1/2)*(-a+(1+a^2)^(1/2))^(1/2)+2*x)*2^(1/2)/_ + (a+(1+a^2)^(1/2))^(1/2))*(-a+(1+a^2)^(1/2))^(1/2)+log((1+a^2)^(1/2)-_ + 2^(1/2)*(-a+(1+a^2)^(1/2))^(1/2)*x+x^2)*(a+(1+a^2)^(1/2))^(1/2)-_ + log((1+a^2)^(1/2)+2^(1/2)*(-a+(1+a^2)^(1/2))^(1/2)*x+x^2)*_ + (a+(1+a^2)^(1/2))^(1/2))/(1+a^2)^(1/2)/(a+(1+a^2)^(1/2))^(1/2)/_ + (-a+(1+a^2)^(1/2))^(1/2) +--R +--R +--R (1300) +--R +-------------+ +-------------+ +--R | +------+ | +------+ +------+ +--R +-+ | | 2 +-+ | | 2 | 2 2 +--R \|2 \|\|a + 1 + a log(x\|2 \|\|a + 1 - a + \|a + 1 + x ) +--R + +--R +-------------+ +-------------+ +--R | +------+ | +------+ +------+ +--R +-+ | | 2 +-+ | | 2 | 2 2 +--R - \|2 \|\|a + 1 + a log(- x\|2 \|\|a + 1 - a + \|a + 1 + x ) +--R + +--R +-------------+ +--R +-------------+ | +------+ +--R | +------+ | | 2 +-+ +--R +-+ | | 2 \|\|a + 1 - a + x\|2 +--R 2\|2 \|\|a + 1 - a atan(------------------------) +--R +-------------+ +--R | +------+ +--R | | 2 +--R \|\|a + 1 + a +--R + +--R +-------------+ +--R +-------------+ | +------+ +--R | +------+ | | 2 +-+ +--R +-+ | | 2 \|\|a + 1 - a - x\|2 +--R - 2\|2 \|\|a + 1 - a atan(------------------------) +--R +-------------+ +--R | +------+ +--R | | 2 +--R \|\|a + 1 + a +--R / +--R +-------------+ +-------------+ +--R +------+ | +------+ | +------+ +--R | 2 | | 2 | | 2 +--R 8\|a + 1 \|\|a + 1 - a \|\|a + 1 + a +--R Type: Expression(Integer) +--E 1300 + +--S 1301 of 1483 +a0240:=integrate(t0240,x) +--R +--R +--R (1301) +--R - +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R |--------- cos(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R * +--R log +--R +-----------------+ 2 +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+2 atan(-----------------------------) +--R 2 | 1 a +--R (4a + 4) |--------- sin(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (32a + 32a)x |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R sin(-----------------------------------) +--R 2 +--R + +--R +-----------------+ 2 +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+2 atan(-----------------------------) +--R 2 | 1 a +--R (4a + 4) |--------- cos(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a 2 +--R - 4x |--------- cos(----------------------------------- + x +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R |--------- cos(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R * +--R log +--R +-----------------+ 2 +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+2 atan(-----------------------------) +--R 2 | 1 a +--R (4a + 4) |--------- sin(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (- 32a - 32a)x |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R sin(-----------------------------------) +--R 2 +--R + +--R +-----------------+ 2 +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+2 atan(-----------------------------) +--R 2 | 1 a +--R (4a + 4) |--------- cos(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a 2 +--R 4x |--------- cos(----------------------------------- + x +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R 2 |--------- sin(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R * +--R atan +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R 2 |--------- sin(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (16a + 16a) |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R cos(-----------------------------------) +--R 2 +--R / +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (16a + 16a) |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R sin(-----------------------------------) +--R 2 +--R + +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R - 2 |--------- cos(----------------------------------- - x +--R 4| 2 2 +--R \|16a + 16 +--R + +--R - +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R 2 |--------- sin(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R * +--R atan +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R 2 |--------- sin(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (16a + 16a) |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R cos(-----------------------------------) +--R 2 +--R / +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (16a + 16a) |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R sin(-----------------------------------) +--R 2 +--R + +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R - 2 |--------- cos(----------------------------------- + x +--R 4| 2 2 +--R \|16a + 16 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1301 + +--S 1302 of 1483 +m0240:=a0240-r0240 +--R +--R +--R (1302) +--R - +--R +-------------+ +-------------+ +--R +---------+ +------+ | +------+ | +------+ +--R | 1 | 2 | | 2 | | 2 +--R 4 |--------- \|a + 1 \|\|a + 1 - a \|\|a + 1 + a +--R 4| 2 +--R \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R cos(-----------------------------------) +--R 2 +--R * +--R log +--R +-----------------+ 2 +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+2 atan(-----------------------------) +--R 2 | 1 a +--R (4a + 4) |--------- sin(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (32a + 32a)x |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R sin(-----------------------------------) +--R 2 +--R + +--R +-----------------+ 2 +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+2 atan(-----------------------------) +--R 2 | 1 a +--R (4a + 4) |--------- cos(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a 2 +--R - 4x |--------- cos(----------------------------------- + x +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-------------+ +-------------+ +--R +---------+ +------+ | +------+ | +------+ +--R | 1 | 2 | | 2 | | 2 +--R 4 |--------- \|a + 1 \|\|a + 1 - a \|\|a + 1 + a +--R 4| 2 +--R \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R cos(-----------------------------------) +--R 2 +--R * +--R log +--R +-----------------+ 2 +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+2 atan(-----------------------------) +--R 2 | 1 a +--R (4a + 4) |--------- sin(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (- 32a - 32a)x |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R sin(-----------------------------------) +--R 2 +--R + +--R +-----------------+ 2 +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+2 atan(-----------------------------) +--R 2 | 1 a +--R (4a + 4) |--------- cos(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a 2 +--R 4x |--------- cos(----------------------------------- + x +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-------------+ +-------------+ +--R +---------+ +------+ | +------+ | +------+ +--R | 1 | 2 | | 2 | | 2 +--R 8 |--------- \|a + 1 \|\|a + 1 - a \|\|a + 1 + a +--R 4| 2 +--R \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R sin(-----------------------------------) +--R 2 +--R * +--R atan +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R 2 |--------- sin(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (16a + 16a) |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R cos(-----------------------------------) +--R 2 +--R / +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (16a + 16a) |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R sin(-----------------------------------) +--R 2 +--R + +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R - 2 |--------- cos(----------------------------------- - x +--R 4| 2 2 +--R \|16a + 16 +--R + +--R - +--R +-------------+ +-------------+ +--R +---------+ +------+ | +------+ | +------+ +--R | 1 | 2 | | 2 | | 2 +--R 8 |--------- \|a + 1 \|\|a + 1 - a \|\|a + 1 + a +--R 4| 2 +--R \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R sin(-----------------------------------) +--R 2 +--R * +--R atan +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R 2 |--------- sin(-----------------------------------) +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (16a + 16a) |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R cos(-----------------------------------) +--R 2 +--R / +--R +-----------------+ +---------+ +--R 3 | 1 | 1 +--R (16a + 16a) |----------------- |--------- +--R | 4 2 4| 2 +--R \|64a + 128a + 64 \|16a + 16 +--R * +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R atan(-----------------------------) +--R a +--R sin(-----------------------------------) +--R 2 +--R + +--R +-----------------+ +--R 2 | 1 +--R (8a + 8) |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R +---------+ atan(-----------------------------) +--R | 1 a +--R - 2 |--------- cos(----------------------------------- + x +--R 4| 2 2 +--R \|16a + 16 +--R + +--R +-------------+ +-------------+ +--R | +------+ | +------+ +------+ +--R +-+ | | 2 +-+ | | 2 | 2 2 +--R - \|2 \|\|a + 1 + a log(x\|2 \|\|a + 1 - a + \|a + 1 + x ) +--R + +--R +-------------+ +-------------+ +--R | +------+ | +------+ +------+ +--R +-+ | | 2 +-+ | | 2 | 2 2 +--R \|2 \|\|a + 1 + a log(- x\|2 \|\|a + 1 - a + \|a + 1 + x ) +--R + +--R +-------------+ +--R +-------------+ | +------+ +--R | +------+ | | 2 +-+ +--R +-+ | | 2 \|\|a + 1 - a + x\|2 +--R - 2\|2 \|\|a + 1 - a atan(------------------------) +--R +-------------+ +--R | +------+ +--R | | 2 +--R \|\|a + 1 + a +--R + +--R +-------------+ +--R +-------------+ | +------+ +--R | +------+ | | 2 +-+ +--R +-+ | | 2 \|\|a + 1 - a - x\|2 +--R 2\|2 \|\|a + 1 - a atan(------------------------) +--R +-------------+ +--R | +------+ +--R | | 2 +--R \|\|a + 1 + a +--R / +--R +-------------+ +-------------+ +--R +------+ | +------+ | +------+ +--R | 2 | | 2 | | 2 +--R 8\|a + 1 \|\|a + 1 - a \|\|a + 1 + a +--R Type: Expression(Integer) +--E 1302 + +--S 1303 of 1483 +d0240:=normalize(D(m0240,x)) +--R +--R +--R (1303) +--R 9 7 5 3 10 +--R (512a + 1568a + 1680a + 704a + 80a)x +--R + +--R 10 8 6 4 2 8 +--R (1024a + 3136a + 3360a + 1408a + 160a )x +--R + +--R 11 9 7 5 3 6 +--R (1024a + 2112a + 224a - 1952a - 1248a - 160a)x +--R + +--R 12 10 8 6 4 2 4 +--R (1024a + 8256a + 19040a + 18208a + 7200a + 800a )x +--R + +--R 13 11 9 7 5 3 2 +--R (512a + 544a - 2992a - 7360a - 6368a - 2272a - 240a)x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 10 +--R (- 64a - 132a - 78a - 10a)x +--R + +--R 8 6 4 2 8 +--R (- 128a - 264a - 156a - 20a )x +--R + +--R 9 7 5 3 6 +--R (- 256a - 528a - 312a - 40a )x +--R + +--R 10 8 6 4 2 4 +--R (128a - 120a - 636a - 448a - 60a )x +--R + +--R 11 9 7 5 3 2 +--R (- 192a - 524a - 434a - 54a + 58a + 10a)x +--R * +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 +--R + +--R 9 7 5 3 8 +--R (256a - 368a - 1056a - 432a )x +--R + +--R 10 8 6 4 6 +--R (512a - 736a - 2112a - 864a )x +--R + +--R 11 9 7 5 3 4 +--R (256a - 2160a - 2576a + 560a + 720a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 8 8 6 4 2 6 +--R (- 32a + 78a + 54a )x + (- 32a + 238a + 176a + 18a )x +--R + +--R 9 7 5 3 4 +--R (- 96a + 138a - 116a - 126a )x +--R + +--R 10 8 6 4 2 2 +--R (32a + 114a + 150a + 86a + 18a )x +--R * +--R 3 +--R %CW +--R + +--R 8 6 4 2 10 +--R (- 640a - 1792a - 1664a - 512a )x +--R + +--R 9 7 5 3 8 +--R (- 1280a - 3584a - 3328a - 1024a )x +--R + +--R 10 8 6 4 2 6 +--R (- 1280a - 2304a + 256a + 2304a + 1024a )x +--R + +--R 11 9 7 5 3 4 +--R (- 1280a - 9984a - 21248a - 17664a - 5120a )x +--R + +--R 12 10 8 6 4 2 2 +--R (- 640a - 512a + 3840a + 8192a + 6016a + 1536a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 6 4 2 10 7 5 3 8 +--R (80a + 144a + 64a )x + (160a + 288a + 128a )x +--R + +--R 8 6 4 6 9 7 5 3 4 +--R (320a + 576a + 256a )x + (- 160a + 192a + 736a + 384a )x +--R + +--R 10 8 6 4 2 2 +--R (240a + 592a + 400a - 16a - 64a )x +--R * +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 +--R + +--R 8 6 4 2 8 +--R (- 320a + 544a + 1152a + 288a )x +--R + +--R 9 7 5 3 6 +--R (- 640a + 1088a + 2304a + 576a )x +--R + +--R 10 8 6 4 2 4 +--R (- 320a + 2784a + 2464a - 1120a - 480a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 6 4 2 8 7 5 3 6 +--R (40a - 108a - 36a )x + (40a - 308a - 136a - 12a)x +--R + +--R 8 6 4 2 4 +--R (120a - 204a + 208a + 84a )x +--R + +--R 9 7 5 3 2 +--R (- 40a - 132a - 156a - 76a - 12a)x +--R * +--R 2 +--R %CW +--R + +--R 9 7 5 3 10 +--R (- 512a - 1440a - 1360a - 448a - 16a)x +--R + +--R 10 8 6 4 2 8 +--R (- 1024a - 2880a - 2720a - 896a - 32a )x +--R + +--R 11 9 7 5 3 6 +--R (- 1024a - 1856a + 160a + 1824a + 864a + 32a)x +--R + +--R 12 10 8 6 4 2 4 +--R (- 1024a - 8000a - 17120a - 14496a - 4512a - 160a )x +--R + +--R 13 11 9 7 5 3 2 +--R (- 512a - 416a + 3056a + 6592a + 4960a + 1376a + 48a)x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 10 8 6 4 2 8 +--R (64a + 116a + 54a + 2a)x + (128a + 232a + 108a + 4a )x +--R + +--R 9 7 5 3 6 +--R (256a + 464a + 216a + 8a )x +--R + +--R 10 8 6 4 2 4 +--R (- 128a + 152a + 588a + 320a + 12a )x +--R + +--R 11 9 7 5 3 2 +--R (192a + 476a + 330a - 2a - 50a - 2a)x +--R * +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 +--R + +--R 9 7 5 3 8 +--R (- 256a + 432a + 928a + 240a )x +--R + +--R 10 8 6 4 6 +--R (- 512a + 864a + 1856a + 480a )x +--R + +--R 11 9 7 5 3 4 +--R (- 256a + 2224a + 2000a - 880a - 400a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 8 8 6 4 2 6 +--R (32a - 86a - 30a )x + (32a - 246a - 112a - 10a )x +--R + +--R 9 7 5 3 4 +--R (96a - 162a + 164a + 70a )x +--R + +--R 10 8 6 4 2 2 +--R (- 32a - 106a - 126a - 62a - 10a )x +--R * +--R %CW +--R + +--R 8 6 4 2 10 +--R (128a + 352a + 320a + 96a )x +--R + +--R 9 7 5 3 8 +--R (256a + 704a + 640a + 192a )x +--R + +--R 10 8 6 4 2 6 +--R (256a + 448a - 64a - 448a - 192a )x +--R + +--R 11 9 7 5 3 4 +--R (256a + 1984a + 4160a + 3392a + 960a )x +--R + +--R 12 10 8 6 4 2 2 +--R (128a + 96a - 768a - 1600a - 1152a - 288a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 6 4 2 10 7 5 3 8 +--R (- 16a - 28a - 12a )x + (- 32a - 56a - 24a )x +--R + +--R 8 6 4 6 9 7 5 3 4 +--R (- 64a - 112a - 48a )x + (32a - 40a - 144a - 72a )x +--R + +--R 10 8 6 4 2 2 +--R (- 48a - 116a - 76a + 4a + 12a )x +--R * +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 +--R + +--R 8 6 4 2 8 9 7 5 3 6 +--R (64a - 112a - 224a - 48a )x + (128a - 224a - 448a - 96a )x +--R + +--R 10 8 6 4 2 4 +--R (64a - 560a - 464a + 240a + 80a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 6 4 2 8 7 5 3 6 +--R (- 8a + 22a + 6a )x + (- 8a + 62a + 24a + 2a)x +--R + +--R 8 6 4 2 4 9 7 5 3 2 +--R (- 24a + 42a - 44a - 14a )x + (8a + 26a + 30a + 14a + 2a)x +--R / +--R 9 7 5 3 10 +--R (4096a + 12544a + 13440a + 5632a + 640a)x +--R + +--R 10 8 6 4 2 8 +--R (8192a + 25088a + 26880a + 11264a + 1280a )x +--R + +--R 11 9 7 5 3 6 +--R (8192a + 33280a + 51968a + 38144a + 12544a + 1280a)x +--R + +--R 12 10 8 6 4 2 4 +--R (8192a + 33280a + 51968a + 38144a + 12544a + 1280a )x +--R + +--R 13 11 9 7 5 3 +--R 4096a + 20736a + 42624a + 45056a + 25344a + 6912a +--R + +--R 640a +--R * +--R 2 +--R x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 9 7 5 3 10 +--R (256a + 272a - 216a - 272a - 40a)x +--R + +--R 10 8 6 4 2 8 +--R (512a + 544a - 432a - 544a - 80a )x +--R + +--R 11 9 7 5 3 6 +--R (512a + 1056a + 112a - 976a - 624a - 80a)x +--R + +--R 12 10 8 6 4 2 4 +--R (512a + 1056a + 112a - 976a - 624a - 80a )x +--R + +--R 13 11 9 7 5 3 2 +--R (256a + 784a + 584a - 432a - 800a - 352a - 40a)x +--R * +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 +--R + +--R 9 7 5 3 8 +--R (2048a + 1152a - 2048a - 1152a )x +--R + +--R 10 8 6 4 6 +--R (4096a + 2304a - 4096a - 2304a )x +--R + +--R 11 9 7 5 3 4 +--R (2048a + 3200a - 896a - 3200a - 1152a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 12 8 6 4 2 10 +--R (16a + 41a + 34a + 9a)x + (32a + 82a + 68a + 18a )x +--R + +--R 9 7 5 3 8 +--R (112a + 79a + 473a + 309a + 27a)x +--R + +--R 10 8 6 4 2 6 +--R (192a + 44a + 796a + 532a + 36a )x +--R + +--R 11 9 7 5 3 4 +--R (112a + 191a + 552a + 782a + 336a + 27a)x +--R + +--R 12 10 8 6 4 2 2 13 11 +--R (32a + 146a + 264a + 236a + 104a + 18a )x + 16a + 89a +--R + +--R 9 7 5 3 +--R 205a + 250a + 170a + 61a + 9a +--R * +--R 3 +--R %CW +--R + +--R 8 6 4 2 10 +--R (- 5120a - 14336a - 13312a - 4096a )x +--R + +--R 9 7 5 3 8 +--R (- 10240a - 28672a - 26624a - 8192a )x +--R + +--R 10 8 6 4 2 6 +--R (- 10240a - 38912a - 55296a - 34816a - 8192a )x +--R + +--R 11 9 7 5 3 4 +--R (- 10240a - 38912a - 55296a - 34816a - 8192a )x +--R + +--R 12 10 8 6 4 2 2 +--R (- 5120a - 24576a - 47104a - 45056a - 21504a - 4096a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 8 6 4 2 10 +--R (- 320a - 256a + 320a + 256a )x +--R + +--R 9 7 5 3 8 +--R (- 640a - 512a + 640a + 512a )x +--R + +--R 10 8 6 4 2 6 +--R (- 640a - 1152a + 128a + 1152a + 512a )x +--R + +--R 11 9 7 5 3 4 +--R (- 640a - 1152a + 128a + 1152a + 512a )x +--R + +--R 12 10 8 6 4 2 2 +--R (- 320a - 896a - 512a + 640a + 832a + 256a )x +--R * +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 +--R + +--R 8 6 4 2 8 +--R (- 2560a - 768a + 2560a + 768a )x +--R + +--R 9 7 5 3 6 +--R (- 5120a - 1536a + 5120a + 1536a )x +--R + +--R 10 8 6 4 2 4 +--R (- 2560a - 3328a + 1792a + 3328a + 768a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 6 4 2 12 7 5 3 10 +--R (- 20a - 46a - 32a - 6)x + (- 40a - 92a - 64a - 12a)x +--R + +--R 8 6 4 2 8 +--R (- 140a - 62a - 586a - 234a - 18)x +--R + +--R 9 7 5 3 6 +--R (- 240a + 8a - 1016a - 392a - 24a)x +--R + +--R 10 8 6 4 2 4 +--R (- 140a - 202a - 648a - 820a - 252a - 18)x +--R + +--R 11 9 7 5 3 2 12 10 +--R (- 40a - 172a - 288a - 232a - 88a - 12a)x - 20a - 106a +--R + +--R 8 6 4 2 +--R - 230a - 260a - 160a - 50a - 6 +--R * +--R 2 +--R %CW +--R + +--R 9 7 5 3 10 +--R (- 4096a - 11520a - 10880a - 3584a - 128a)x +--R + +--R 10 8 6 4 2 8 +--R (- 8192a - 23040a - 21760a - 7168a - 256a )x +--R + +--R 11 9 7 5 3 6 +--R (- 8192a - 31232a - 44800a - 28928a - 7424a - 256a)x +--R + +--R 12 10 8 6 4 2 4 +--R (- 8192a - 31232a - 44800a - 28928a - 7424a - 256a )x +--R + +--R 13 11 9 7 5 +--R - 4096a - 19712a - 38016a - 36864a - 18176a +--R + +--R 3 +--R - 3840a - 128a +--R * +--R 2 +--R x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 9 7 5 3 10 +--R (- 256a - 208a + 248a + 208a + 8a)x +--R + +--R 10 8 6 4 2 8 +--R (- 512a - 416a + 496a + 416a + 16a )x +--R + +--R 11 9 7 5 3 6 +--R (- 512a - 928a + 80a + 912a + 432a + 16a)x +--R + +--R 12 10 8 6 4 2 4 +--R (- 512a - 928a + 80a + 912a + 432a + 16a )x +--R + +--R 13 11 9 7 5 3 2 +--R (- 256a - 720a - 424a + 496a + 672a + 224a + 8a)x +--R * +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 +--R + +--R 9 7 5 3 8 +--R (- 2048a - 640a + 2048a + 640a )x +--R + +--R 10 8 6 4 6 +--R (- 4096a - 1280a + 4096a + 1280a )x +--R + +--R 11 9 7 5 3 4 +--R (- 2048a - 2688a + 1408a + 2688a + 640a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 7 5 3 12 8 6 4 2 10 +--R (- 16a - 37a - 26a - 5a)x + (- 32a - 74a - 52a - 10a )x +--R + +--R 9 7 5 3 8 +--R (- 112a - 51a - 469a - 193a - 15a)x +--R + +--R 10 8 6 4 2 6 +--R (- 192a + 4a - 812a - 324a - 20a )x +--R + +--R 11 9 7 5 3 4 +--R (- 112a - 163a - 520a - 662a - 208a - 15a)x +--R + +--R 12 10 8 6 4 2 2 13 11 +--R (- 32a - 138a - 232a - 188a - 72a - 10a )x - 16a - 85a +--R + +--R 9 7 5 3 +--R - 185a - 210a - 130a - 41a - 5a +--R * +--R %CW +--R + +--R 8 6 4 2 10 +--R (1024a + 2816a + 2560a + 768a )x +--R + +--R 9 7 5 3 8 +--R (2048a + 5632a + 5120a + 1536a )x +--R + +--R 10 8 6 4 2 6 +--R (2048a + 7680a + 10752a + 6656a + 1536a )x +--R + +--R 11 9 7 5 3 4 +--R (2048a + 7680a + 10752a + 6656a + 1536a )x +--R + +--R 12 10 8 6 4 2 2 +--R (1024a + 4864a + 9216a + 8704a + 4096a + 768a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 8 6 4 2 10 9 7 5 3 8 +--R (64a + 48a - 64a - 48a )x + (128a + 96a - 128a - 96a )x +--R + +--R 10 8 6 4 2 6 +--R (128a + 224a - 32a - 224a - 96a )x +--R + +--R 11 9 7 5 3 4 +--R (128a + 224a - 32a - 224a - 96a )x +--R + +--R 12 10 8 6 4 2 2 +--R (64a + 176a + 96a - 128a - 160a - 48a )x +--R * +--R +---------+2 +--R | 1 +--R |--------- +--R 4| 2 +--R \|16a + 16 +--R + +--R 8 6 4 2 8 +--R (512a + 128a - 512a - 128a )x +--R + +--R 9 7 5 3 6 +--R (1024a + 256a - 1024a - 256a )x +--R + +--R 10 8 6 4 2 4 +--R (512a + 640a - 384a - 640a - 128a )x +--R * +--R +-----------------+ +--R | 1 +--R |----------------- +--R | 4 2 +--R \|64a + 128a + 64 +--R + +--R 6 4 2 12 7 5 3 10 +--R (4a + 9a + 6a + 1)x + (8a + 18a + 12a + 2a)x +--R + +--R 8 6 4 2 8 9 7 5 3 6 +--R (28a + 11a + 117a + 41a + 3)x + (48a - 4a + 204a + 68a + 4a)x +--R + +--R 10 8 6 4 2 4 +--R (28a + 39a + 128a + 158a + 44a + 3)x +--R + +--R 11 9 7 5 3 2 12 10 8 6 +--R (8a + 34a + 56a + 44a + 16a + 2a)x + 4a + 21a + 45a + 50a +--R + +--R 4 2 +--R 30a + 9a + 1 +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1483 +t0241:= (a+b*x^2)/(2+x^2+x^4) +--R +--R +--R 2 +--R b x + a +--R (1304) ----------- +--R 4 2 +--R x + x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1304 + +--S 1305 of 1483 +r0241:= -1/2*a*atan(((-1+2*2^(1/2))^(1/2)-2*x)/(1+2*2^(1/2))^(1/2))/_ + (2+4*2^(1/2))^(1/2)-1/2*b*atan(((-1+2*2^(1/2))^(1/2)-2*x)/_ + (1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2)+1/2*a*_ + atan(((-1+2*2^(1/2))^(1/2)+2*x)/(1+2*2^(1/2))^(1/2))/_ + (2+4*2^(1/2))^(1/2)+1/2*b*atan(((-1+2*2^(1/2))^(1/2)+2*x)/_ + (1+2*2^(1/2))^(1/2))/(1+2*2^(1/2))^(1/2)-1/4*a*log(2^(1/2)-_ + (-1+2*2^(1/2))^(1/2)*x+x^2)/(-2+4*2^(1/2))^(1/2)+1/4*b*log(2^(1/2)-_ + (-1+2*2^(1/2))^(1/2)*x+x^2)/(-1+2*2^(1/2))^(1/2)+1/4*a*log(2^(1/2)+_ + (-1+2*2^(1/2))^(1/2)*x+x^2)/(-2+4*2^(1/2))^(1/2)-1/4*b*log(2^(1/2)+_ + (-1+2*2^(1/2))^(1/2)*x+x^2)/(-1+2*2^(1/2))^(1/2) +--R +--R +--R (1305) +--R +---------+ +---------+ +---------+ +---------+ +---------+ +--R | +-+ | +-+ | +-+ | +-+ | +-+ +--R (- b\|2\|2 + 1 \|4\|2 - 2 + a\|2\|2 - 1 \|2\|2 + 1 )\|4\|2 + 2 +--R * +--R +---------+ +--R | +-+ +-+ 2 +--R log(x\|2\|2 - 1 + \|2 + x ) +--R + +--R +---------+ +---------+ +---------+ +---------+ +---------+ +--R | +-+ | +-+ | +-+ | +-+ | +-+ +--R (b\|2\|2 + 1 \|4\|2 - 2 - a\|2\|2 - 1 \|2\|2 + 1 )\|4\|2 + 2 +--R * +--R +---------+ +--R | +-+ +-+ 2 +--R log(- x\|2\|2 - 1 + \|2 + x ) +--R + +--R +---------+ +---------+ +---------+ +--R | +-+ | +-+ | +-+ +--R 2b\|2\|2 - 1 \|4\|2 - 2 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +---------+ +--R | +-+ | +-+ | +-+ +--R 2a\|2\|2 - 1 \|2\|2 + 1 \|4\|2 - 2 +--R * +--R +---------+ +---------+ +--R +-+ | +-+ +-+ | +-+ +--R ((2\|2 - 1)\|2\|2 - 1 + 4x\|2 - 2x)\|2\|2 + 1 +--R atan(---------------------------------------------------) +--R 7 +--R + +--R +---------+ +---------+ +---------+ +--R | +-+ | +-+ | +-+ +--R - 2b\|2\|2 - 1 \|4\|2 - 2 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +---------+ +--R | +-+ | +-+ | +-+ +--R - 2a\|2\|2 - 1 \|2\|2 + 1 \|4\|2 - 2 +--R * +--R +---------+ +---------+ +--R +-+ | +-+ +-+ | +-+ +--R ((2\|2 - 1)\|2\|2 - 1 - 4x\|2 + 2x)\|2\|2 + 1 +--R atan(---------------------------------------------------) +--R 7 +--R / +--R +---------+ +---------+ +---------+ +---------+ +--R | +-+ | +-+ | +-+ | +-+ +--R 4\|2\|2 - 1 \|2\|2 + 1 \|4\|2 - 2 \|4\|2 + 2 +--R Type: Expression(Integer) +--E 1305 + +--S 1306 of 1483 +a0241:=integrate(t0241,x) +--R +--R +--R (1306) +--R - +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +-------------------------------+ 2 2 +-+ +--R 4| 4 3 2 2 3 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + 5a b - 2a b + a cos(---------------------------) +--R 2 +--R * +--R log +--R +-------------------------------+2 +--R 2 2 4| 4 3 2 2 3 4 +--R (28b - 14a )\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ 2 +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R +-+4+--+4| 4 3 2 2 3 4 +--R (4b - a)x\|7 \|98 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+2 +--R 2 2 4| 4 3 2 2 3 4 +--R (28b - 14a )\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ 2 +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 2 3 4+--+4| 4 3 2 2 3 4 +--R (- 14a b + 7a )x\|98 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R 4 3 3 4 2 4+--+2 +--R (4b - 2a b + a b - a )x \|98 +--R + +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +-------------------------------+ 2 2 +-+ +--R 4| 4 3 2 2 3 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + 5a b - 2a b + a cos(---------------------------) +--R 2 +--R * +--R log +--R +-------------------------------+2 +--R 2 2 4| 4 3 2 2 3 4 +--R (28b - 14a )\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ 2 +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R +-+4+--+4| 4 3 2 2 3 4 +--R (- 4b + a)x\|7 \|98 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+2 +--R 2 2 4| 4 3 2 2 3 4 +--R (28b - 14a )\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ 2 +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 2 3 4+--+4| 4 3 2 2 3 4 +--R (14a b - 7a )x\|98 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R 4 3 3 4 2 4+--+2 +--R (4b - 2a b + a b - a )x \|98 +--R + +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +-------------------------------+ 2 2 +-+ +--R 4| 4 3 2 2 3 4 (2b - 8a b + a )\|7 +--R 2\|4b - 4a b + 5a b - 2a b + a sin(---------------------------) +--R 2 +--R * +--R atan +--R +-------------------------------+ +--R 2 3 +-+4| 4 3 2 2 3 4 +--R (14a b - 7a )\|7 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 4| 4 3 2 2 3 4 +--R (28b - 7a)\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a cos(---------------------------) +--R 2 +--R / +--R +-------------------------------+ +--R 4| 4 3 2 2 3 4 +--R (28b - 7a)\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 2 3 +-+4| 4 3 2 2 3 4 +--R (- 14a b + 7a )\|7 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R 4 3 3 4 +-+4+--+ +--R (- 8b + 4a b - 2a b + 2a )x\|7 \|98 +--R + +--R - +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +-------------------------------+ 2 2 +-+ +--R 4| 4 3 2 2 3 4 (2b - 8a b + a )\|7 +--R 2\|4b - 4a b + 5a b - 2a b + a sin(---------------------------) +--R 2 +--R * +--R atan +--R +-------------------------------+ +--R 2 3 +-+4| 4 3 2 2 3 4 +--R (14a b - 7a )\|7 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 4| 4 3 2 2 3 4 +--R (28b - 7a)\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a cos(---------------------------) +--R 2 +--R / +--R +-------------------------------+ +--R 4| 4 3 2 2 3 4 +--R (28b - 7a)\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 2 3 +-+4| 4 3 2 2 3 4 +--R (- 14a b + 7a )\|7 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R 4 3 3 4 +-+4+--+ +--R (8b - 4a b + 2a b - 2a )x\|7 \|98 +--R / +--R 4+--+ +--R 2\|98 +--R Type: Union(Expression(Integer),...) +--E 1306 + +--S 1307 of 1483 +m0241:=a0241-r0241 +--R +--R +--R (1307) +--R - +--R +-------------------------------+ +---------+ +---------+ +--R 4| 4 3 2 2 3 4 | +-+ | +-+ +--R 2\|4b - 4a b + 5a b - 2a b + a \|2\|2 - 1 \|2\|2 + 1 +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +---------+ +---------+ 2 2 +-+ +--R | +-+ | +-+ (2b - 8a b + a )\|7 +--R \|4\|2 - 2 \|4\|2 + 2 cos(---------------------------) +--R 2 +--R * +--R log +--R +-------------------------------+2 +--R 2 2 4| 4 3 2 2 3 4 +--R (28b - 14a )\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ 2 +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R +-+4+--+4| 4 3 2 2 3 4 +--R (4b - a)x\|7 \|98 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+2 +--R 2 2 4| 4 3 2 2 3 4 +--R (28b - 14a )\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ 2 +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 2 3 4+--+4| 4 3 2 2 3 4 +--R (- 14a b + 7a )x\|98 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R 4 3 3 4 2 4+--+2 +--R (4b - 2a b + a b - a )x \|98 +--R + +--R +-------------------------------+ +---------+ +---------+ +---------+ +--R 4| 4 3 2 2 3 4 | +-+ | +-+ | +-+ +--R 2\|4b - 4a b + 5a b - 2a b + a \|2\|2 - 1 \|2\|2 + 1 \|4\|2 - 2 +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +---------+ 2 2 +-+ +--R | +-+ (2b - 8a b + a )\|7 +--R \|4\|2 + 2 cos(---------------------------) +--R 2 +--R * +--R log +--R +-------------------------------+2 +--R 2 2 4| 4 3 2 2 3 4 +--R (28b - 14a )\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ 2 +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R +-+4+--+4| 4 3 2 2 3 4 +--R (- 4b + a)x\|7 \|98 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+2 +--R 2 2 4| 4 3 2 2 3 4 +--R (28b - 14a )\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ 2 +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 2 3 4+--+4| 4 3 2 2 3 4 +--R (14a b - 7a )x\|98 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R 4 3 3 4 2 4+--+2 +--R (4b - 2a b + a b - a )x \|98 +--R + +--R +-------------------------------+ +---------+ +---------+ +---------+ +--R 4| 4 3 2 2 3 4 | +-+ | +-+ | +-+ +--R 4\|4b - 4a b + 5a b - 2a b + a \|2\|2 - 1 \|2\|2 + 1 \|4\|2 - 2 +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +---------+ 2 2 +-+ +--R | +-+ (2b - 8a b + a )\|7 +--R \|4\|2 + 2 sin(---------------------------) +--R 2 +--R * +--R atan +--R +-------------------------------+ +--R 2 3 +-+4| 4 3 2 2 3 4 +--R (14a b - 7a )\|7 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 4| 4 3 2 2 3 4 +--R (28b - 7a)\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a cos(---------------------------) +--R 2 +--R / +--R +-------------------------------+ +--R 4| 4 3 2 2 3 4 +--R (28b - 7a)\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 2 3 +-+4| 4 3 2 2 3 4 +--R (- 14a b + 7a )\|7 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R 4 3 3 4 +-+4+--+ +--R (- 8b + 4a b - 2a b + 2a )x\|7 \|98 +--R + +--R - +--R +-------------------------------+ +---------+ +---------+ +--R 4| 4 3 2 2 3 4 | +-+ | +-+ +--R 4\|4b - 4a b + 5a b - 2a b + a \|2\|2 - 1 \|2\|2 + 1 +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +---------+ +---------+ 2 2 +-+ +--R | +-+ | +-+ (2b - 8a b + a )\|7 +--R \|4\|2 - 2 \|4\|2 + 2 sin(---------------------------) +--R 2 +--R * +--R atan +--R +-------------------------------+ +--R 2 3 +-+4| 4 3 2 2 3 4 +--R (14a b - 7a )\|7 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 4| 4 3 2 2 3 4 +--R (28b - 7a)\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a cos(---------------------------) +--R 2 +--R / +--R +-------------------------------+ +--R 4| 4 3 2 2 3 4 +--R (28b - 7a)\|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R +----------------+ 2 2 +-+ +--R | 4 2 2 4 (2b - 8a b + a )\|7 +--R \|4b - 4a b + a sin(---------------------------) +--R 2 +--R + +--R +-------------------------------+ +--R 2 3 +-+4| 4 3 2 2 3 4 +--R (- 14a b + 7a )\|7 \|4b - 4a b + 5a b - 2a b + a +--R * +--R +----------------+ +--R | 4 2 2 4 +--R 7\|4b - 4a b + a +--R atan(---------------------) +--R 2 2 +-+ +--R (2b - 8a b + a )\|7 +--R cos(---------------------------) +--R 2 +--R + +--R 4 3 3 4 +-+4+--+ +--R (8b - 4a b + 2a b - 2a )x\|7 \|98 +--R + +--R +---------+ +---------+ +---------+ +---------+ +--R 4+--+ | +-+ | +-+ 4+--+ | +-+ | +-+ +--R (b\|98 \|2\|2 + 1 \|4\|2 - 2 - a\|98 \|2\|2 - 1 \|2\|2 + 1 ) +--R * +--R +---------+ +---------+ +--R | +-+ | +-+ +-+ 2 +--R \|4\|2 + 2 log(x\|2\|2 - 1 + \|2 + x ) +--R + +--R +---------+ +---------+ +---------+ +---------+ +--R 4+--+ | +-+ | +-+ 4+--+ | +-+ | +-+ +--R (- b\|98 \|2\|2 + 1 \|4\|2 - 2 + a\|98 \|2\|2 - 1 \|2\|2 + 1 ) +--R * +--R +---------+ +---------+ +--R | +-+ | +-+ +-+ 2 +--R \|4\|2 + 2 log(- x\|2\|2 - 1 + \|2 + x ) +--R + +--R +---------+ +---------+ +---------+ +--R 4+--+ | +-+ | +-+ | +-+ +--R - 2b\|98 \|2\|2 - 1 \|4\|2 - 2 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +---------+ +--R 4+--+ | +-+ | +-+ | +-+ +--R - 2a\|98 \|2\|2 - 1 \|2\|2 + 1 \|4\|2 - 2 +--R * +--R +---------+ +---------+ +--R +-+ | +-+ +-+ | +-+ +--R ((2\|2 - 1)\|2\|2 - 1 + 4x\|2 - 2x)\|2\|2 + 1 +--R atan(---------------------------------------------------) +--R 7 +--R + +--R +---------+ +---------+ +---------+ +--R 4+--+ | +-+ | +-+ | +-+ +--R 2b\|98 \|2\|2 - 1 \|4\|2 - 2 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +---------+ +--R 4+--+ | +-+ | +-+ | +-+ +--R 2a\|98 \|2\|2 - 1 \|2\|2 + 1 \|4\|2 - 2 +--R * +--R +---------+ +---------+ +--R +-+ | +-+ +-+ | +-+ +--R ((2\|2 - 1)\|2\|2 - 1 - 4x\|2 + 2x)\|2\|2 + 1 +--R atan(---------------------------------------------------) +--R 7 +--R / +--R +---------+ +---------+ +---------+ +---------+ +--R 4+--+ | +-+ | +-+ | +-+ | +-+ +--R 4\|98 \|2\|2 - 1 \|2\|2 + 1 \|4\|2 - 2 \|4\|2 + 2 +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1483 +d0241:=normalize(D(m0241,x)) +--R +--R +--R (1308) +--R 2 9 3 8 4 7 +--R 35530880a b - 175567392a b + 486945536a b +--R + +--R 5 6 6 5 7 4 +--R - 663806528a b + 672982464a b - 409959088a b +--R + +--R 8 3 9 2 10 +--R 180379584a b - 48665232a b + 7429576a b +--R + +--R 11 +--R - 555170a +--R * +--R 8 +--R x +--R + +--R 2 9 3 8 4 7 +--R - 40376000a b + 199508400a b - 553347200a b +--R + +--R 5 6 6 5 7 4 +--R 754325600a b - 764752800a b + 465862600a b +--R + +--R 8 3 9 2 10 +--R - 204976800a b + 55301400a b - 8442700a b +--R + +--R 11 +--R 630875a +--R * +--R 6 +--R x +--R + +--R 2 9 3 8 4 7 +--R 71061760a b - 351134784a b + 973891072a b +--R + +--R 5 6 6 5 7 4 +--R - 1327613056a b + 1345964928a b - 819918176a b +--R + +--R 8 3 9 2 10 +--R 360759168a b - 97330464a b + 14859152a b +--R + +--R 11 +--R - 1110340a +--R * +--R 4 +--R x +--R + +--R 2 9 3 8 4 7 +--R - 80752000a b + 399016800a b - 1106694400a b +--R + +--R 5 6 6 5 7 4 +--R 1508651200a b - 1529505600a b + 931725200a b +--R + +--R 8 3 9 2 10 +--R - 409953600a b + 110602800a b - 16885400a b +--R + +--R 11 +--R 1261750a +--R * +--R 2 +--R x +--R * +--R +-+ +--R \|2 +--R + +--R 2 9 3 8 4 7 +--R - 40376000a b + 199508400a b - 553347200a b +--R + +--R 5 6 6 5 7 4 +--R 754325600a b - 764752800a b + 465862600a b +--R + +--R 8 3 9 2 10 +--R - 204976800a b + 55301400a b - 8442700a b +--R + +--R 11 +--R 630875a +--R * +--R 8 +--R x +--R + +--R 2 9 3 8 4 7 +--R 71061760a b - 351134784a b + 973891072a b +--R + +--R 5 6 6 5 7 4 +--R - 1327613056a b + 1345964928a b - 819918176a b +--R + +--R 8 3 9 2 10 +--R 360759168a b - 97330464a b + 14859152a b +--R + +--R 11 +--R - 1110340a +--R * +--R 6 +--R x +--R + +--R 2 9 3 8 4 7 +--R - 80752000a b + 399016800a b - 1106694400a b +--R + +--R 5 6 6 5 7 4 +--R 1508651200a b - 1529505600a b + 931725200a b +--R + +--R 8 3 9 2 10 +--R - 409953600a b + 110602800a b - 16885400a b +--R + +--R 11 +--R 1261750a +--R * +--R 4 +--R x +--R + +--R 2 9 3 8 4 7 +--R 142123520a b - 702269568a b + 1947782144a b +--R + +--R 5 6 6 5 7 4 +--R - 2655226112a b + 2691929856a b - 1639836352a b +--R + +--R 8 3 9 2 10 +--R 721518336a b - 194660928a b + 29718304a b +--R + +--R 11 +--R - 2220680a +--R * +--R 2 +--R x +--R * +--R +-------------------------------+2 +--R 4| 4 3 2 2 3 4 +--R \|4b - 4a b + 5a b - 2a b + a +--R + +--R 2 11 3 10 4 9 +--R 6228992a b - 64596224a b + 246498560a b +--R + +--R 5 8 6 7 7 6 +--R - 470138592a b + 557632768a b - 337301888a b +--R + +--R 8 5 9 4 10 3 +--R 53537792a b + 30222192a b - 22313984a b +--R + +--R 11 2 12 13 +--R 6341104a b - 799568a b + 36498a +--R * +--R 6 +--R x +--R + +--R 2 11 3 10 4 9 +--R - 7078400a b + 73404800a b - 280112000a b +--R + +--R 5 8 6 7 7 6 +--R 534248400a b - 633673600a b + 383297600a b +--R + +--R 8 5 9 4 10 3 +--R - 60838400a b - 34343400a b + 25356800a b +--R + +--R 11 2 12 13 +--R - 7205800a b + 908600a b - 41475a +--R * +--R 4 +--R x +--R * +--R +-+ +--R \|2 +--R + +--R 2 11 3 10 4 9 +--R - 7078400a b + 73404800a b - 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63995904a b + 40279680a b - 16869888a b + 5096448a b +--R + +--R 13 14 +--R - 870912a b + 88704a +--R * +--R 2 +--R x +--R + +--R 14 13 2 12 3 11 +--R - 22708224b + 111476736a b - 326172672a b + 539836416a b +--R + +--R 4 10 5 9 6 8 8 6 +--R - 644474880a b + 511967232a b - 249984000a b + 124992000a b +--R + +--R 9 5 10 4 11 3 12 2 +--R - 127991808a b + 80559360a b - 33739776a b + 10192896a b +--R + +--R 13 14 +--R - 1741824a b + 177408a +--R * +--R +-+4+--+2 +--R \|7 \|98 +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1483 +t0242:= (a+b*x^2)/(c+d*x^2+e*x^4) +--R +--R +--R 2 +--R b x + a +--R (1309) --------------- +--R 4 2 +--R e x + d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1309 + +--S 1310 of 1483 +r0242:= 1/2*(b-(b*d-2*a*e)/(d^2-4*c*e)^(1/2))*atan(2^(1/2)*e^(1/2)*x/_ + (d-(d^2-4*c*e)^(1/2))^(1/2))*2^(1/2)/e^(1/2)/_ + (d-(d^2-4*c*e)^(1/2))^(1/2)+1/2*(b+(b*d-2*a*e)/(d^2-4*c*e)^(1/2))*_ + atan(2^(1/2)*e^(1/2)*x/(d+(d^2-4*c*e)^(1/2))^(1/2))*2^(1/2)/_ + e^(1/2)/(d+(d^2-4*c*e)^(1/2))^(1/2) +--R +--R +--R (1310) +--R +------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R (b\|2 \|- 4c e + d + (2a e - b d)\|2 )\|\|- 4c e + d + d +--R * +--R +-+ +-+ +--R x\|2 \|e +--R atan(-----------------------) +--R +--------------------+ +--R | +-----------+ +--R | | 2 +--R \|- \|- 4c e + d + d +--R + +--R +--------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R (b\|2 \|- 4c e + d + (- 2a e + b d)\|2 )\|- \|- 4c e + d + d +--R * +--R +-+ +-+ +--R x\|2 \|e +--R atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4c e + d + d +--R / +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R 2\|- 4c e + d \|e \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1483 +a0242:=integrate(t0242,x) +--R +--R +--R (1311) +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c 2 +--R (16c e - 4c d e) |------------------------ + (a d - 4a b c)e +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 +--R b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R * +--R log +--R 2 3 2 3 2 2 +--R ((16a c d - 32b c )e + (- 4a c d + 8b c d )e) +--R * +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R |- a e + 2a b c e - b c +--R |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 3 2 3 2 2 2 2 2 +--R 4a c e + (- a d - 4a b c )e + a b c d +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (16c e - 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R + +--R 4 2 3 3 4 2 +--R (2a e - 2a b d e + 2a b c d - 2b c )x +--R + +--R - +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (- 16c e + 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R * +--R log +--R 2 3 2 3 2 2 +--R ((16a c d - 32b c )e + (- 4a c d + 8b c d )e) +--R * +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R |- a e + 2a b c e - b c +--R |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 3 2 3 2 2 2 2 2 +--R - 4a c e + (a d + 4a b c )e - a b c d +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (- 16c e + 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R + +--R 4 2 3 3 4 2 +--R (2a e - 2a b d e + 2a b c d - 2b c )x +--R + +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c 2 +--R (- 16c e + 4c d e) |------------------------ + (a d - 4a b c)e +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 +--R b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R * +--R log +--R 2 3 2 3 2 2 +--R ((- 16a c d + 32b c )e + (4a c d - 8b c d )e) +--R * +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R |- a e + 2a b c e - b c +--R |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 3 2 3 2 2 2 2 2 +--R 4a c e + (- a d - 4a b c )e + a b c d +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (- 16c e + 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R + +--R 4 2 3 3 4 2 +--R (2a e - 2a b d e + 2a b c d - 2b c )x +--R + +--R - +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (16c e - 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R * +--R log +--R 2 3 2 3 2 2 +--R ((- 16a c d + 32b c )e + (4a c d - 8b c d )e) +--R * +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R |- a e + 2a b c e - b c +--R |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 3 2 3 2 2 2 2 2 +--R - 4a c e + (a d + 4a b c )e - a b c d +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (16c e - 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R + +--R 4 2 3 3 4 2 +--R (2a e - 2a b d e + 2a b c d - 2b c )x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1311 + +--S 1312 of 1483 +m0242:=a0242-r0242 +--R +--R +--R (1312) +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R \|- 4c e + d \|e \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c 2 +--R (16c e - 4c d e) |------------------------ + (a d - 4a b c)e +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 +--R b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R * +--R log +--R 2 3 2 3 2 2 +--R ((16a c d - 32b c )e + (- 4a c d + 8b c d )e) +--R * +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R |- a e + 2a b c e - b c +--R |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 3 2 3 2 2 2 2 2 +--R 4a c e + (- a d - 4a b c )e + a b c d +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (16c e - 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R + +--R 4 2 3 3 4 2 +--R (2a e - 2a b d e + 2a b c d - 2b c )x +--R + +--R - +--R +-----------+ +--R | 2 +-+ +--R \|- 4c e + d \|e +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (- 16c e + 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R * +--R +--------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R * +--R log +--R 2 3 2 3 2 2 +--R ((16a c d - 32b c )e + (- 4a c d + 8b c d )e) +--R * +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R |- a e + 2a b c e - b c +--R |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 3 2 3 2 2 2 2 2 +--R - 4a c e + (a d + 4a b c )e - a b c d +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (- 16c e + 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R + +--R 4 2 3 3 4 2 +--R (2a e - 2a b d e + 2a b c d - 2b c )x +--R + +--R +-----------+ +--R | 2 +-+ +--R \|- 4c e + d \|e +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c 2 +--R (- 16c e + 4c d e) |------------------------ + (a d - 4a b c)e +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 +--R b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R * +--R +--------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R * +--R log +--R 2 3 2 3 2 2 +--R ((- 16a c d + 32b c )e + (4a c d - 8b c d )e) +--R * +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R |- a e + 2a b c e - b c +--R |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 3 2 3 2 2 2 2 2 +--R 4a c e + (- a d - 4a b c )e + a b c d +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (- 16c e + 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R + +--R 4 2 3 3 4 2 +--R (2a e - 2a b d e + 2a b c d - 2b c )x +--R + +--R - +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R \|- 4c e + d \|e \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (16c e - 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R * +--R log +--R 2 3 2 3 2 2 +--R ((- 16a c d + 32b c )e + (4a c d - 8b c d )e) +--R * +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R |- a e + 2a b c e - b c +--R |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 3 2 3 2 2 2 2 2 +--R - 4a c e + (a d + 4a b c )e - a b c d +--R * +--R ROOT +--R +------------------------+ +--R | 4 2 2 2 4 2 +--R 2 2 2 |- a e + 2a b c e - b c +--R (16c e - 4c d e) |------------------------ +--R | 3 3 2 2 2 +--R \| 64c e - 16c d e +--R + +--R 2 2 +--R (a d - 4a b c)e + b c d +--R / +--R 2 2 2 +--R 8c e - 2c d e +--R + +--R 4 2 3 3 4 2 +--R (2a e - 2a b d e + 2a b c d - 2b c )x +--R + +--R +------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R (- b\|2 \|- 4c e + d + (- 2a e + b d)\|2 )\|\|- 4c e + d + d +--R * +--R +-+ +-+ +--R x\|2 \|e +--R atan(-----------------------) +--R +--------------------+ +--R | +-----------+ +--R | | 2 +--R \|- \|- 4c e + d + d +--R + +--R +--------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R (- b\|2 \|- 4c e + d + (2a e - b d)\|2 )\|- \|- 4c e + d + d +--R * +--R +-+ +-+ +--R x\|2 \|e +--R atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4c e + d + d +--R / +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R | 2 +-+ | | 2 | | 2 +--R 2\|- 4c e + d \|e \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1483 +d0242:=D(m0242,x) +--R +--R +--R (1313) 0 +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1483 +t0243:= (a+b*x^2)/(c+d*x^2+e*x^4)^2 +--R +--R +--R 2 +--R b x + a +--R (1314) --------------------------------------------- +--R 2 8 6 2 4 2 2 +--R e x + 2d e x + (2c e + d )x + 2c d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1314 + +--S 1315 of 1483 +r0243:= -1/2*b*x*(d+2*e*x^2)/(d^2-4*c*e)/(c+d*x^2+e*x^4)+1/2*a*x*_ + (d^2-2*c*e+d*e*x^2)/c/(d^2-4*c*e)/(c+d*x^2+e*x^4)+1/2*b*d*e^(1/2)*_ + atan(2^(1/2)*e^(1/2)*x/(d-(d^2-4*c*e)^(1/2))^(1/2))*2^(1/2)/_ + (d^2-4*c*e)^(3/2)/(d-(d^2-4*c*e)^(1/2))^(1/2)+1/2*a*e^(1/2)*_ + (d^2-6*c*e)*atan(2^(1/2)*e^(1/2)*x/(d-(d^2-4*c*e)^(1/2))^(1/2))*_ + 2^(1/2)/c/(d^2-4*c*e)^(3/2)/(d-(d^2-4*c*e)^(1/2))^(1/2)+1/2*b*_ + e^(1/2)*(d-(d^2-4*c*e)^(1/2))^(1/2)*atan(2^(1/2)*e^(1/2)*x/_ + (d-(d^2-4*c*e)^(1/2))^(1/2))*2^(1/2)/(d^2-4*c*e)^(3/2)-1/4*a*d*_ + e^(1/2)*(d-(d^2-4*c*e)^(1/2))^(1/2)*atan(2^(1/2)*e^(1/2)*x/_ + (d-(d^2-4*c*e)^(1/2))^(1/2))*2^(1/2)/c/(d^2-4*c*e)^(3/2)-_ + 1/2*b*d*e^(1/2)*atan(2^(1/2)*e^(1/2)*x/_ + (d+(d^2-4*c*e)^(1/2))^(1/2))*2^(1/2)/(d^2-4*c*e)^(3/2)/_ + (d+(d^2-4*c*e)^(1/2))^(1/2)-1/2*a*e^(1/2)*(d^2-6*c*e)*_ + atan(2^(1/2)*e^(1/2)*x/(d+(d^2-4*c*e)^(1/2))^(1/2))*2^(1/2)/_ + c/(d^2-4*c*e)^(3/2)/(d+(d^2-4*c*e)^(1/2))^(1/2)-1/2*b*e^(1/2)*_ + (d+(d^2-4*c*e)^(1/2))^(1/2)*atan(2^(1/2)*e^(1/2)*x/_ + (d+(d^2-4*c*e)^(1/2))^(1/2))*2^(1/2)/(d^2-4*c*e)^(3/2)+1/4*a*d*_ + e^(1/2)*(d+(d^2-4*c*e)^(1/2))^(1/2)*atan(2^(1/2)*e^(1/2)*x/_ + (d+(d^2-4*c*e)^(1/2))^(1/2))*2^(1/2)/c/(d^2-4*c*e)^(3/2) +--R +--R +--R (1315) +--R 4 2 2 2 +-+ +--R ((- a d + 2b c)e x + (- a d + 2b c d)x - a c d + 2b c )\|2 +--R * +--R +-----------+ +--R | 2 +--R \|- 4c e + d +--R + +--R 2 2 4 +--R (12a c e + (- a d - 4b c d)e)x +--R + +--R 3 2 2 2 2 2 +--R (12a c d e - a d - 4b c d )x + 12a c e - a c d - 4b c d +--R * +--R +-+ +--R \|2 +--R * +--R +------------------+ +--R | +-----------+ +-+ +-+ +--R +-+ | | 2 x\|2 \|e +--R \|e \|\|- 4c e + d + d atan(-----------------------) +--R +--------------------+ +--R | +-----------+ +--R | | 2 +--R \|- \|- 4c e + d + d +--R + +--R 4 2 2 2 +-+ +--R ((- a d + 2b c)e x + (- a d + 2b c d)x - a c d + 2b c )\|2 +--R * +--R +-----------+ +--R | 2 +--R \|- 4c e + d +--R + +--R 2 2 4 +--R (- 12a c e + (a d + 4b c d)e)x +--R + +--R 3 2 2 2 2 2 +--R (- 12a c d e + a d + 4b c d )x - 12a c e + a c d + 4b c d +--R * +--R +-+ +--R \|2 +--R * +--R +--------------------+ +--R | +-----------+ +-+ +-+ +--R +-+ | | 2 x\|2 \|e +--R \|e \|- \|- 4c e + d + d atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4c e + d + d +--R + +--R +-----------+ +--R 3 2 | 2 +--R ((- 2a d + 4b c)e x + (4a c e - 2a d + 2b c d)x)\|- 4c e + d +--R * +--R +--------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R / +--R +-----------+ +--R 2 2 2 4 2 3 2 3 2 2 | 2 +--R ((16c e - 4c d e)x + (16c d e - 4c d )x + 16c e - 4c d )\|- 4c e + d +--R * +--R +--------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1483 +a0243:=integrate(t0243,x) +--R +--R +--R (1316) +--R 2 2 2 4 2 3 2 3 2 2 +--R ((4c e - c d e)x + (4c d e - c d )x + 4c e - c d ) +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (1024c e - 768c d e + 192c d e - 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 4 4 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e - a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 2 3 2 2 2 3 +--R (60a c d - 48a b c )e + (- 15a c d - 12a b c d + 12b c d)e +--R + +--R 2 5 4 2 2 3 +--R a d + 2a b c d + b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R * +--R log +--R 7 8 4 6 3 7 2 3 +--R (8192a c d - 4096b c )e + (- 7168a c d + 2048b c d )e +--R + +--R 5 5 2 4 7 5 6 3 9 +--R 2304a c d e + (- 320a c d - 128b c d )e + 16a c d +--R + +--R 4 8 +--R 16b c d +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 3 4 4 3 3 2 2 4 2 5 3 +--R 864a c e + (- 672a c d - 336a b c d - 96a b c )e +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 2 +--R (190a c d + 216a b c d + 96a b c d + 16b c d)e +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 8 +--R (- 23a c d - 45a b c d - 30a b c d - 8b c d )e + a d +--R + +--R 2 7 2 2 6 3 3 5 +--R 3a b c d + 3a b c d + b c d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (1024c e - 768c d e + 192c d e - 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 +--R (60a c d - 48a b c )e +--R + +--R 2 3 2 2 2 3 2 5 4 +--R (- 15a c d - 12a b c d + 12b c d)e + a d + 2a b c d +--R + +--R 2 2 3 +--R b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R + +--R 4 2 4 4 2 3 2 3 +--R 324a c e + (- 81a c d - 324a b c d)e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (5a d + 65a b c d + 84a b c d + 20a b c d - 4b c )e +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 +--R (- 3a b d - 9a b c d - 9a b c d - 3b c d )e +--R * +--R x +--R + +--R 2 2 2 4 2 3 2 3 2 2 +--R ((- 4c e + c d e)x + (- 4c d e + c d )x - 4c e + c d ) +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (- 1024c e + 768c d e - 192c d e + 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 4 4 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e - a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 2 3 2 2 2 3 +--R (60a c d - 48a b c )e + (- 15a c d - 12a b c d + 12b c d)e +--R + +--R 2 5 4 2 2 3 +--R a d + 2a b c d + b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R * +--R log +--R 7 8 4 6 3 7 2 3 +--R (8192a c d - 4096b c )e + (- 7168a c d + 2048b c d )e +--R + +--R 5 5 2 4 7 5 6 3 9 +--R 2304a c d e + (- 320a c d - 128b c d )e + 16a c d +--R + +--R 4 8 +--R 16b c d +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 3 4 4 3 3 2 2 4 2 5 3 +--R - 864a c e + (672a c d + 336a b c d + 96a b c )e +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 2 +--R (- 190a c d - 216a b c d - 96a b c d - 16b c d)e +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 8 +--R (23a c d + 45a b c d + 30a b c d + 8b c d )e - a d +--R + +--R 2 7 2 2 6 3 3 5 +--R - 3a b c d - 3a b c d - b c d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (- 1024c e + 768c d e - 192c d e + 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 +--R (60a c d - 48a b c )e +--R + +--R 2 3 2 2 2 3 2 5 4 +--R (- 15a c d - 12a b c d + 12b c d)e + a d + 2a b c d +--R + +--R 2 2 3 +--R b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R + +--R 4 2 4 4 2 3 2 3 +--R 324a c e + (- 81a c d - 324a b c d)e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (5a d + 65a b c d + 84a b c d + 20a b c d - 4b c )e +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 +--R (- 3a b d - 9a b c d - 9a b c d - 3b c d )e +--R * +--R x +--R + +--R 2 2 2 4 2 3 2 3 2 2 +--R ((4c e - c d e)x + (4c d e - c d )x + 4c e - c d ) +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (- 1024c e + 768c d e - 192c d e + 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 4 4 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e - a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 2 3 2 2 2 3 +--R (60a c d - 48a b c )e + (- 15a c d - 12a b c d + 12b c d)e +--R + +--R 2 5 4 2 2 3 +--R a d + 2a b c d + b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R * +--R log +--R 7 8 4 6 3 7 2 3 +--R (- 8192a c d + 4096b c )e + (7168a c d - 2048b c d )e +--R + +--R 5 5 2 4 7 5 6 3 9 +--R - 2304a c d e + (320a c d + 128b c d )e - 16a c d +--R + +--R 4 8 +--R - 16b c d +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 3 4 4 3 3 2 2 4 2 5 3 +--R 864a c e + (- 672a c d - 336a b c d - 96a b c )e +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 2 +--R (190a c d + 216a b c d + 96a b c d + 16b c d)e +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 8 +--R (- 23a c d - 45a b c d - 30a b c d - 8b c d )e + a d +--R + +--R 2 7 2 2 6 3 3 5 +--R 3a b c d + 3a b c d + b c d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (- 1024c e + 768c d e - 192c d e + 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 +--R (60a c d - 48a b c )e +--R + +--R 2 3 2 2 2 3 2 5 4 +--R (- 15a c d - 12a b c d + 12b c d)e + a d + 2a b c d +--R + +--R 2 2 3 +--R b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R + +--R 4 2 4 4 2 3 2 3 +--R 324a c e + (- 81a c d - 324a b c d)e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (5a d + 65a b c d + 84a b c d + 20a b c d - 4b c )e +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 +--R (- 3a b d - 9a b c d - 9a b c d - 3b c d )e +--R * +--R x +--R + +--R 2 2 2 4 2 3 2 3 2 2 +--R ((- 4c e + c d e)x + (- 4c d e + c d )x - 4c e + c d ) +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (1024c e - 768c d e + 192c d e - 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 4 4 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e - a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 2 3 2 2 2 3 +--R (60a c d - 48a b c )e + (- 15a c d - 12a b c d + 12b c d)e +--R + +--R 2 5 4 2 2 3 +--R a d + 2a b c d + b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R * +--R log +--R 7 8 4 6 3 7 2 3 +--R (- 8192a c d + 4096b c )e + (7168a c d - 2048b c d )e +--R + +--R 5 5 2 4 7 5 6 3 9 +--R - 2304a c d e + (320a c d + 128b c d )e - 16a c d +--R + +--R 4 8 +--R - 16b c d +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 3 4 4 3 3 2 2 4 2 5 3 +--R - 864a c e + (672a c d + 336a b c d + 96a b c )e +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 2 +--R (- 190a c d - 216a b c d - 96a b c d - 16b c d)e +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 8 +--R (23a c d + 45a b c d + 30a b c d + 8b c d )e - a d +--R + +--R 2 7 2 2 6 3 3 5 +--R - 3a b c d - 3a b c d - b c d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (1024c e - 768c d e + 192c d e - 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 +--R (60a c d - 48a b c )e +--R + +--R 2 3 2 2 2 3 2 5 4 +--R (- 15a c d - 12a b c d + 12b c d)e + a d + 2a b c d +--R + +--R 2 2 3 +--R b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R + +--R 4 2 4 4 2 3 2 3 +--R 324a c e + (- 81a c d - 324a b c d)e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (5a d + 65a b c d + 84a b c d + 20a b c d - 4b c )e +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 +--R (- 3a b d - 9a b c d - 9a b c d - 3b c d )e +--R * +--R x +--R + +--R 3 2 +--R (- a d + 2b c)e x + (2a c e - a d + b c d)x +--R / +--R 2 2 2 4 2 3 2 3 2 2 +--R (8c e - 2c d e)x + (8c d e - 2c d )x + 8c e - 2c d +--R Type: Union(Expression(Integer),...) +--E 1316 + +--S 1317 of 1483 +m0243:=a0243-r0243 +--R +--R +--R (1317) +--R +--------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (8c e - 2c d )\|- 4c e + d \|- \|- 4c e + d + d +--R * +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4c e + d + d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (1024c e - 768c d e + 192c d e - 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 4 4 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e - a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 2 3 2 2 2 3 +--R (60a c d - 48a b c )e + (- 15a c d - 12a b c d + 12b c d)e +--R + +--R 2 5 4 2 2 3 +--R a d + 2a b c d + b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R * +--R log +--R 7 8 4 6 3 7 2 3 +--R (8192a c d - 4096b c )e + (- 7168a c d + 2048b c d )e +--R + +--R 5 5 2 4 7 5 6 3 9 +--R 2304a c d e + (- 320a c d - 128b c d )e + 16a c d +--R + +--R 4 8 +--R 16b c d +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 3 4 4 3 3 2 2 4 2 5 3 +--R 864a c e + (- 672a c d - 336a b c d - 96a b c )e +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 2 +--R (190a c d + 216a b c d + 96a b c d + 16b c d)e +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 8 +--R (- 23a c d - 45a b c d - 30a b c d - 8b c d )e + a d +--R + +--R 2 7 2 2 6 3 3 5 +--R 3a b c d + 3a b c d + b c d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (1024c e - 768c d e + 192c d e - 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 +--R (60a c d - 48a b c )e +--R + +--R 2 3 2 2 2 3 2 5 4 +--R (- 15a c d - 12a b c d + 12b c d)e + a d + 2a b c d +--R + +--R 2 2 3 +--R b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R + +--R 4 2 4 4 2 3 2 3 +--R 324a c e + (- 81a c d - 324a b c d)e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (5a d + 65a b c d + 84a b c d + 20a b c d - 4b c )e +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 +--R (- 3a b d - 9a b c d - 9a b c d - 3b c d )e +--R * +--R x +--R + +--R +-----------+ +--R 2 2 | 2 +--R (- 8c e + 2c d )\|- 4c e + d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (- 1024c e + 768c d e - 192c d e + 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 4 4 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e - a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 2 3 2 2 2 3 +--R (60a c d - 48a b c )e + (- 15a c d - 12a b c d + 12b c d)e +--R + +--R 2 5 4 2 2 3 +--R a d + 2a b c d + b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R * +--R +--------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R * +--R log +--R 7 8 4 6 3 7 2 3 +--R (8192a c d - 4096b c )e + (- 7168a c d + 2048b c d )e +--R + +--R 5 5 2 4 7 5 6 3 9 +--R 2304a c d e + (- 320a c d - 128b c d )e + 16a c d +--R + +--R 4 8 +--R 16b c d +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 3 4 4 3 3 2 2 4 2 5 3 +--R - 864a c e + (672a c d + 336a b c d + 96a b c )e +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 2 +--R (- 190a c d - 216a b c d - 96a b c d - 16b c d)e +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 8 +--R (23a c d + 45a b c d + 30a b c d + 8b c d )e - a d +--R + +--R 2 7 2 2 6 3 3 5 +--R - 3a b c d - 3a b c d - b c d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (- 1024c e + 768c d e - 192c d e + 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 +--R (60a c d - 48a b c )e +--R + +--R 2 3 2 2 2 3 2 5 4 +--R (- 15a c d - 12a b c d + 12b c d)e + a d + 2a b c d +--R + +--R 2 2 3 +--R b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R + +--R 4 2 4 4 2 3 2 3 +--R 324a c e + (- 81a c d - 324a b c d)e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (5a d + 65a b c d + 84a b c d + 20a b c d - 4b c )e +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 +--R (- 3a b d - 9a b c d - 9a b c d - 3b c d )e +--R * +--R x +--R + +--R +-----------+ +--R 2 2 | 2 +--R (8c e - 2c d )\|- 4c e + d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (- 1024c e + 768c d e - 192c d e + 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 4 4 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e - a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 2 3 2 2 2 3 +--R (60a c d - 48a b c )e + (- 15a c d - 12a b c d + 12b c d)e +--R + +--R 2 5 4 2 2 3 +--R a d + 2a b c d + b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R * +--R +--------------------+ +------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R * +--R log +--R 7 8 4 6 3 7 2 3 +--R (- 8192a c d + 4096b c )e + (7168a c d - 2048b c d )e +--R + +--R 5 5 2 4 7 5 6 3 9 +--R - 2304a c d e + (320a c d + 128b c d )e - 16a c d +--R + +--R 4 8 +--R - 16b c d +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 3 4 4 3 3 2 2 4 2 5 3 +--R 864a c e + (- 672a c d - 336a b c d - 96a b c )e +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 2 +--R (190a c d + 216a b c d + 96a b c d + 16b c d)e +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 8 +--R (- 23a c d - 45a b c d - 30a b c d - 8b c d )e + a d +--R + +--R 2 7 2 2 6 3 3 5 +--R 3a b c d + 3a b c d + b c d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (- 1024c e + 768c d e - 192c d e + 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 +--R (60a c d - 48a b c )e +--R + +--R 2 3 2 2 2 3 2 5 4 +--R (- 15a c d - 12a b c d + 12b c d)e + a d + 2a b c d +--R + +--R 2 2 3 +--R b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R + +--R 4 2 4 4 2 3 2 3 +--R 324a c e + (- 81a c d - 324a b c d)e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (5a d + 65a b c d + 84a b c d + 20a b c d - 4b c )e +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 +--R (- 3a b d - 9a b c d - 9a b c d - 3b c d )e +--R * +--R x +--R + +--R +--------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (- 8c e + 2c d )\|- 4c e + d \|- \|- 4c e + d + d +--R * +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4c e + d + d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (1024c e - 768c d e + 192c d e - 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 4 4 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e - a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 2 3 2 2 2 3 +--R (60a c d - 48a b c )e + (- 15a c d - 12a b c d + 12b c d)e +--R + +--R 2 5 4 2 2 3 +--R a d + 2a b c d + b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R * +--R log +--R 7 8 4 6 3 7 2 3 +--R (- 8192a c d + 4096b c )e + (7168a c d - 2048b c d )e +--R + +--R 5 5 2 4 7 5 6 3 9 +--R - 2304a c d e + (320a c d + 128b c d )e - 16a c d +--R + +--R 4 8 +--R - 16b c d +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 3 4 4 3 3 2 2 4 2 5 3 +--R - 864a c e + (672a c d + 336a b c d + 96a b c )e +--R + +--R 3 2 4 2 3 3 2 4 2 3 5 2 +--R (- 190a c d - 216a b c d - 96a b c d - 16b c d)e +--R + +--R 3 6 2 2 5 2 3 4 3 4 3 3 8 +--R (23a c d + 45a b c d + 30a b c d + 8b c d )e - a d +--R + +--R 2 7 2 2 6 3 3 5 +--R - 3a b c d - 3a b c d - b c d +--R * +--R ROOT +--R 6 3 5 2 2 4 4 3 6 +--R (1024c e - 768c d e + 192c d e - 16c d ) +--R * +--R ROOT +--R 4 2 2 4 2 3 2 2 2 3 +--R - 81a c e + (18a c d + 36a b c d + 18a b c )e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R - a d - 4a b c d - 6a b c d - 4a b c d - b c +--R / +--R 9 3 8 2 2 7 4 6 6 +--R 16384c e - 12288c d e + 3072c d e - 256c d +--R + +--R 2 2 3 2 +--R (60a c d - 48a b c )e +--R + +--R 2 3 2 2 2 3 2 5 4 +--R (- 15a c d - 12a b c d + 12b c d)e + a d + 2a b c d +--R + +--R 2 2 3 +--R b c d +--R / +--R 6 3 5 2 2 4 4 3 6 +--R 512c e - 384c d e + 96c d e - 8c d +--R + +--R 4 2 4 4 2 3 2 3 +--R 324a c e + (- 81a c d - 324a b c d)e +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (5a d + 65a b c d + 84a b c d + 20a b c d - 4b c )e +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 +--R (- 3a b d - 9a b c d - 9a b c d - 3b c d )e +--R * +--R x +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +--R ((a d - 2b c)\|2 \|- 4c e + d + (- 12a c e + a d + 4b c d)\|2 )\|e +--R * +--R +------------------+ +--R | +-----------+ +-+ +-+ +--R | | 2 x\|2 \|e +--R \|\|- 4c e + d + d atan(-----------------------) +--R +--------------------+ +--R | +-----------+ +--R | | 2 +--R \|- \|- 4c e + d + d +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +-+ +--R ((a d - 2b c)\|2 \|- 4c e + d + (12a c e - a d - 4b c d)\|2 )\|e +--R * +--R +--------------------+ +--R | +-----------+ +-+ +-+ +--R | | 2 x\|2 \|e +--R \|- \|- 4c e + d + d atan(---------------------) +--R +------------------+ +--R | +-----------+ +--R | | 2 +--R \|\|- 4c e + d + d +--R / +--R +--------------------+ +------------------+ +--R +-----------+ | +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 | | 2 +--R (16c e - 4c d )\|- 4c e + d \|- \|- 4c e + d + d \|\|- 4c e + d + d +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1483 +d0243:=D(m0243,x) +--R +--R +--R (1318) 0 +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1483 +t0244:= 1/(2+x^3+x^6) +--R +--R +--R 1 +--R (1319) ----------- +--R 6 3 +--R x + x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1319 + +--S 1320 of 1483 +r0244:= 1/21*%i*atan(1/3*((1/2-1/2*%i*7^(1/2))^(1/3)-2*x)*3^(1/2)/_ + (1/2-1/2*%i*7^(1/2))^(1/3))*21^(1/2)/(1/2-1/2*%i*7^(1/2))^(2/3)-_ + 1/21*%i*atan(1/3*((1/2+1/2*%i*7^(1/2))^(1/3)-2*x)*3^(1/2)/_ + (1/2+1/2*%i*7^(1/2))^(1/3))*21^(1/2)/(1/2+1/2*%i*7^(1/2))^(2/3)-_ + 1/21*%i*log((1/2-1/2*%i*7^(1/2))^(1/3)+x)*7^(1/2)/_ + (1/2-1/2*%i*7^(1/2))^(2/3)+1/21*%i*log((1/2+1/2*%i*7^(1/2))^(1/3)+x)*_ + 7^(1/2)/(1/2+1/2*%i*7^(1/2))^(2/3)+1/42*%i*_ + log((1/2-1/2*%i*7^(1/2))^(2/3)-(1/2-1/2*%i*7^(1/2))^(1/3)*x+x^2)*_ + 2^(2/3)*7^(1/2)/(1-%i*7^(1/2))^(2/3)-1/42*%i*_ + log((1/2+1/2*%i*7^(1/2))^(2/3)-(1/2+1/2*%i*7^(1/2))^(1/3)*x+x^2)*_ + 2^(2/3)*7^(1/2)/(1+%i*7^(1/2))^(2/3) +--R +--R +--R (1320) +--R - +--R +------------+2 +--------------+2 +------------+2 +--R 1 3+-+2 +-+3| +-+ | 1 +-+ 1 |1 +-+ 1 +--R -- %i \|2 \|7 \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - +--R 42 \| 2 2 \|2 2 +--R * +--R +------------+2 +------------+ +--R |1 +-+ 1 |1 +-+ 1 2 +--R log(3|- %i\|7 + - - x 3|- %i\|7 + - + x ) +--R \|2 2 \|2 2 +--R + +--R +------------+2 +--------------+2 +----------+2 +--R 1 +-+3| +-+ | 1 +-+ 1 3| +-+ +--R -- %i\|7 \|- %i\|7 + 1 3|- - %i\|7 + - \|%i\|7 + 1 +--R 21 \| 2 2 +--R * +--R +------------+ +--R |1 +-+ 1 +--R log(3|- %i\|7 + - + x) +--R \|2 2 +--R + +--R +--------------+2 +------------+2 +----------+2 +--R 1 3+-+2 +-+ | 1 +-+ 1 |1 +-+ 1 3| +-+ +--R -- %i \|2 \|7 3|- - %i\|7 + - 3|- %i\|7 + - \|%i\|7 + 1 +--R 42 \| 2 2 \|2 2 +--R * +--R +--------------+2 +--------------+ +--R | 1 +-+ 1 | 1 +-+ 1 2 +--R log(3|- - %i\|7 + - - x 3|- - %i\|7 + - + x ) +--R \| 2 2 \| 2 2 +--R + +--R - +--R +------------+2 +------------+2 +----------+2 +--R 1 +-+3| +-+ |1 +-+ 1 3| +-+ +--R -- %i\|7 \|- %i\|7 + 1 3|- %i\|7 + - \|%i\|7 + 1 +--R 21 \|2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R log(3|- - %i\|7 + - + x) +--R \| 2 2 +--R + +--R - +--R +------------+2 +--------------+2 +----------+2 +--R 1 +--+3| +-+ | 1 +-+ 1 3| +-+ +--R -- %i\|21 \|- %i\|7 + 1 3|- - %i\|7 + - \|%i\|7 + 1 +--R 21 \| 2 2 +--R * +--R +------------+ +--R 1 +-+ |1 +-+ 1 2 +-+ +--R - \|3 3|- %i\|7 + - - - x\|3 +--R 3 \|2 2 3 +--R atan(-------------------------------) +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +------------+2 +------------+2 +----------+2 +--R 1 +--+3| +-+ |1 +-+ 1 3| +-+ +--R -- %i\|21 \|- %i\|7 + 1 3|- %i\|7 + - \|%i\|7 + 1 +--R 21 \|2 2 +--R * +--R +--------------+ +--R 1 +-+ | 1 +-+ 1 2 +-+ +--R - \|3 3|- - %i\|7 + - - - x\|3 +--R 3 \| 2 2 3 +--R atan(---------------------------------) +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R / +--R +------------+2 +--------------+2 +------------+2 +----------+2 +--R 3| +-+ | 1 +-+ 1 |1 +-+ 1 3| +-+ +--R \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - \|%i\|7 + 1 +--R \| 2 2 \|2 2 +--R Type: Expression(Complex(Fraction(Integer))) +--E 1320 + +--S 1321 of 1483 +a0244:=integrate(t0244,x) +--R +--R +--R (1321) +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|7 \|7 +--R (\|3 sin(----------) - cos(----------)) +--R 3 3 +--R * +--R log +--R 3 2 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ +-+ 6+----+ \|7 +--R 28sin(----------) + (x\|7 + 7x\|3 )\|1372 sin(----------) +--R 3 3 +--R + +--R 3 2 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ +-+ 6+----+ \|7 +--R 28cos(----------) + (x\|3 \|7 - 7x)\|1372 cos(----------) +--R 3 3 +--R + +--R 2 6+----+2 +--R 2x \|1372 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|7 \|7 +--R (- \|3 sin(----------) - cos(----------)) +--R 3 3 +--R * +--R log +--R 3 2 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ +-+ 6+----+ \|7 +--R 28sin(----------) + (x\|7 - 7x\|3 )\|1372 sin(----------) +--R 3 3 +--R + +--R 3 2 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ +-+ 6+----+ \|7 +--R 28cos(----------) + (- x\|3 \|7 - 7x)\|1372 cos(----------) +--R 3 3 +--R + +--R 2 6+----+2 +--R 2x \|1372 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|7 +--R 2cos(----------) +--R 3 +--R * +--R log +--R 3 2 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+6+----+ \|7 +--R 14sin(----------) - x\|7 \|1372 sin(----------) +--R 3 3 +--R + +--R 3 2 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 6+----+ \|7 2 6+----+2 +--R 14cos(----------) + 7x\|1372 cos(----------) + x \|1372 +--R 3 3 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|7 +--R 4sin(----------) +--R 3 +--R * +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|7 \|7 +--R 7\|7 sin(----------) + 7cos(----------) +--R 3 3 +--R atan(-------------------------------------------------------) +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ \|7 +-+6+----+ +--R 7sin(----------) - 7\|7 cos(----------) - 2x\|7 \|1372 +--R 3 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ \|7 +--R (2sin(----------) - 2\|3 cos(----------)) +--R 3 3 +--R * +--R atan +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ +-+ \|7 +-+ +-+ \|7 +--R (7\|7 + 7\|3 )sin(----------) + (- 7\|3 \|7 + 7)cos(----------) +--R 3 3 +--R / +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ +-+ \|7 +-+ +-+ \|7 +--R (7\|3 \|7 - 7)sin(----------) + (7\|7 + 7\|3 )cos(----------) +--R 3 3 +--R + +--R +-+6+----+ +--R - 4x\|7 \|1372 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ \|7 +--R (- 2sin(----------) - 2\|3 cos(----------)) +--R 3 3 +--R * +--R atan +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ +-+ \|7 +-+ +-+ \|7 +--R (7\|7 - 7\|3 )sin(----------) + (7\|3 \|7 + 7)cos(----------) +--R 3 3 +--R / +--R 3 +--R atan(----) +--R +-+ +--R +-+ +-+ \|7 +--R (7\|3 \|7 + 7)sin(----------) +--R 3 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ +-+ \|7 +-+6+----+ +--R (- 7\|7 + 7\|3 )cos(----------) + 4x\|7 \|1372 +--R 3 +--R / +--R 6+----+ +--R 6\|1372 +--R Type: Union(Expression(Integer),...) +--E 1321 + +--S 1322 of 1483 +m0244:=a0244-r0244 +--R +--R +--R (1322) +--R +------------+2 +--------------+2 +------------+2 +--R 1 +-+3| +-+ | 1 +-+ 1 |1 +-+ 1 +--R - \|3 \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - +--R 6 \| 2 2 \|2 2 +--R * +--R +----------+2 +--R 3| +-+ 1 3 +--R \|%i\|7 + 1 sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R - +--R +------------+2 +--------------+2 +------------+2 +--R 1 3| +-+ | 1 +-+ 1 |1 +-+ 1 +--R - \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - +--R 6 \| 2 2 \|2 2 +--R * +--R +----------+2 +--R 3| +-+ 1 3 +--R \|%i\|7 + 1 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R log +--R 1 3 2 +-+ +-+ 6+----+ 1 3 +--R 28sin(- atan(----)) + (x\|7 + 7x\|3 )\|1372 sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 1 3 2 +-+ +-+ 6+----+ 1 3 +--R 28cos(- atan(----)) + (x\|3 \|7 - 7x)\|1372 cos(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 2 6+----+2 +--R 2x \|1372 +--R + +--R - +--R +------------+2 +--------------+2 +------------+2 +--R 1 +-+3| +-+ | 1 +-+ 1 |1 +-+ 1 +--R - \|3 \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - +--R 6 \| 2 2 \|2 2 +--R * +--R +----------+2 +--R 3| +-+ 1 3 +--R \|%i\|7 + 1 sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R - +--R +------------+2 +--------------+2 +------------+2 +--R 1 3| +-+ | 1 +-+ 1 |1 +-+ 1 +--R - \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - +--R 6 \| 2 2 \|2 2 +--R * +--R +----------+2 +--R 3| +-+ 1 3 +--R \|%i\|7 + 1 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R log +--R 1 3 2 +-+ +-+ 6+----+ 1 3 +--R 28sin(- atan(----)) + (x\|7 - 7x\|3 )\|1372 sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 1 3 2 +-+ +-+ 6+----+ 1 3 +--R 28cos(- atan(----)) + (- x\|3 \|7 - 7x)\|1372 cos(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 2 6+----+2 +--R 2x \|1372 +--R + +--R +------------+2 +--------------+2 +------------+2 +----------+2 +--R 1 3| +-+ | 1 +-+ 1 |1 +-+ 1 3| +-+ +--R - \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - \|%i\|7 + 1 +--R 3 \| 2 2 \|2 2 +--R * +--R 1 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R log +--R 1 3 2 +-+6+----+ 1 3 +--R 14sin(- atan(----)) - x\|7 \|1372 sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 1 3 2 6+----+ 1 3 2 6+----+2 +--R 14cos(- atan(----)) + 7x\|1372 cos(- atan(----)) + x \|1372 +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R +------------+2 +--------------+2 +------------+2 +----------+2 +--R 2 3| +-+ | 1 +-+ 1 |1 +-+ 1 3| +-+ +--R - \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - \|%i\|7 + 1 +--R 3 \| 2 2 \|2 2 +--R * +--R 1 3 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R +-+ 1 3 1 3 +--R \|7 sin(- atan(----)) + cos(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R atan(----------------------------------------------------------) +--R 1 3 +-+ 1 3 2 +-+6+----+ +--R sin(- atan(----)) - \|7 cos(- atan(----)) - - x\|7 \|1372 +--R 3 +-+ 3 +-+ 7 +--R \|7 \|7 +--R + +--R +------------+2 +--------------+2 +------------+2 +----------+2 +--R 1 3| +-+ | 1 +-+ 1 |1 +-+ 1 3| +-+ +--R - \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - \|%i\|7 + 1 +--R 3 \| 2 2 \|2 2 +--R * +--R 1 3 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R - +--R +------------+2 +--------------+2 +------------+2 +--R 1 +-+3| +-+ | 1 +-+ 1 |1 +-+ 1 +--R - \|3 \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - +--R 3 \| 2 2 \|2 2 +--R * +--R +----------+2 +--R 3| +-+ 1 3 +--R \|%i\|7 + 1 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R atan +--R +-+ +-+ 1 3 +-+ +-+ 1 3 +--R (\|7 + \|3 )sin(- atan(----)) + (- \|3 \|7 + 1)cos(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R / +--R +-+ +-+ 1 3 +-+ +-+ 1 3 +--R (\|3 \|7 - 1)sin(- atan(----)) + (\|7 + \|3 )cos(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 4 +-+6+----+ +--R - - x\|7 \|1372 +--R 7 +--R + +--R - +--R +------------+2 +--------------+2 +------------+2 +--R 1 3| +-+ | 1 +-+ 1 |1 +-+ 1 +--R - \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - +--R 3 \| 2 2 \|2 2 +--R * +--R +----------+2 +--R 3| +-+ 1 3 +--R \|%i\|7 + 1 sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R - +--R +------------+2 +--------------+2 +------------+2 +--R 1 +-+3| +-+ | 1 +-+ 1 |1 +-+ 1 +--R - \|3 \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - +--R 3 \| 2 2 \|2 2 +--R * +--R +----------+2 +--R 3| +-+ 1 3 +--R \|%i\|7 + 1 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R atan +--R +-+ +-+ 1 3 +-+ +-+ 1 3 +--R (\|7 - \|3 )sin(- atan(----)) + (\|3 \|7 + 1)cos(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R / +--R +-+ +-+ 1 3 +--R (\|3 \|7 + 1)sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +-+ +-+ 1 3 4 +-+6+----+ +--R (- \|7 + \|3 )cos(- atan(----)) + - x\|7 \|1372 +--R 3 +-+ 7 +--R \|7 +--R + +--R +------------+2 +--------------+2 +--R 1 3+-+2 +-+6+----+3| +-+ | 1 +-+ 1 +--R -- %i \|2 \|7 \|1372 \|- %i\|7 + 1 3|- - %i\|7 + - +--R 42 \| 2 2 +--R * +--R +------------+2 +------------+2 +------------+ +--R |1 +-+ 1 |1 +-+ 1 |1 +-+ 1 2 +--R 3|- %i\|7 + - log(3|- %i\|7 + - - x 3|- %i\|7 + - + x ) +--R \|2 2 \|2 2 \|2 2 +--R + +--R - +--R +------------+2 +--------------+2 +----------+2 +--R 1 +-+6+----+3| +-+ | 1 +-+ 1 3| +-+ +--R -- %i\|7 \|1372 \|- %i\|7 + 1 3|- - %i\|7 + - \|%i\|7 + 1 +--R 21 \| 2 2 +--R * +--R +------------+ +--R |1 +-+ 1 +--R log(3|- %i\|7 + - + x) +--R \|2 2 +--R + +--R - +--R +--------------+2 +------------+2 +--R 1 3+-+2 +-+6+----+ | 1 +-+ 1 |1 +-+ 1 +--R -- %i \|2 \|7 \|1372 3|- - %i\|7 + - 3|- %i\|7 + - +--R 42 \| 2 2 \|2 2 +--R * +--R +----------+2 +--------------+2 +--------------+ +--R 3| +-+ | 1 +-+ 1 | 1 +-+ 1 2 +--R \|%i\|7 + 1 log(3|- - %i\|7 + - - x 3|- - %i\|7 + - + x ) +--R \| 2 2 \| 2 2 +--R + +--R +------------+2 +------------+2 +----------+2 +--R 1 +-+6+----+3| +-+ |1 +-+ 1 3| +-+ +--R -- %i\|7 \|1372 \|- %i\|7 + 1 3|- %i\|7 + - \|%i\|7 + 1 +--R 21 \|2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R log(3|- - %i\|7 + - + x) +--R \| 2 2 +--R + +--R +------------+2 +--------------+2 +----------+2 +--R 1 +--+6+----+3| +-+ | 1 +-+ 1 3| +-+ +--R -- %i\|21 \|1372 \|- %i\|7 + 1 3|- - %i\|7 + - \|%i\|7 + 1 +--R 21 \| 2 2 +--R * +--R +------------+ +--R 1 +-+ |1 +-+ 1 2 +-+ +--R - \|3 3|- %i\|7 + - - - x\|3 +--R 3 \|2 2 3 +--R atan(-------------------------------) +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R - +--R +------------+2 +------------+2 +----------+2 +--R 1 +--+6+----+3| +-+ |1 +-+ 1 3| +-+ +--R -- %i\|21 \|1372 \|- %i\|7 + 1 3|- %i\|7 + - \|%i\|7 + 1 +--R 21 \|2 2 +--R * +--R +--------------+ +--R 1 +-+ | 1 +-+ 1 2 +-+ +--R - \|3 3|- - %i\|7 + - - - x\|3 +--R 3 \| 2 2 3 +--R atan(---------------------------------) +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R / +--R +------------+2 +--------------+2 +------------+2 +----------+2 +--R 6+----+3| +-+ | 1 +-+ 1 |1 +-+ 1 3| +-+ +--R \|1372 \|- %i\|7 + 1 3|- - %i\|7 + - 3|- %i\|7 + - \|%i\|7 + 1 +--R \| 2 2 \|2 2 +--R Type: Expression(Complex(Fraction(Integer))) +--E 1322 + +--S 1323 of 1483 +d0244:=normalize(D(m0244,x)) +--R +--R +--R (1323) +--R 1 7 1 4 1 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x)\|2 \|7 +--R 336 336 168 +--R + +--R 1 7 1 4 1 3+-+2 +--R (-- x + -- x + -- x)\|2 +--R 48 48 24 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 336 336 168 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 48 48 24 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 6 1 3 1 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i)\|2 \|7 +--R 112 112 56 +--R + +--R 1 6 1 3 1 3+-+2 +--R (- -- x - -- x - --)\|2 +--R 48 48 24 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x )\|2 \|7 +--R 168 168 84 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 24 24 12 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x )\|2 \|7 +--R 168 168 84 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (-- x + -- x + -- x )\|2 +--R 24 24 12 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 1 7 1 4 1 3+-+2 +--R (-- x + -- x + -- x)\|2 +--R 24 24 12 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x)\|2 \|7 +--R 336 336 168 +--R + +--R 1 7 1 4 1 3+-+2 +--R (-- x + -- x + -- x)\|2 +--R 48 48 24 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 2 8 2 5 1 2 +--R - x + - x + - x +--R 3 3 3 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x )\|2 \|7 +--R 168 168 84 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 24 24 12 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 9 1 6 1 3 +-+ 7 9 7 6 1 3 +--R (- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x - - x +--R 84 84 42 12 12 6 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 7 1 4 1 +-+ +--+ +--R (- -- %i x - -- %i x - -- %i x)\|3 \|21 +--R 42 42 21 +--R + +--R 8 7 8 4 11 +-+ 1 7 1 4 1 +--R (-- %i x + -- %i x + -- %i x)\|7 - - x - - x - - x +--R 21 21 42 3 3 6 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 336 336 168 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 48 48 24 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 9 1 6 1 3 +-+ 7 9 7 6 1 3 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x - - x +--R 84 84 42 12 12 6 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x )\|2 \|7 +--R 168 168 84 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (-- x + -- x + -- x )\|2 +--R 24 24 12 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 10 1 7 +--R - x + - x +--R 2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 1 2 +-+ +--+ +--R (-- %i x + -- %i x + -- %i x )\|3 \|21 +--R 42 42 21 +--R + +--R 29 8 29 5 4 2 +-+ 1 8 1 5 +--R (- -- %i x - -- %i x - -- %i x )\|7 + - x + - x +--R 84 84 21 4 4 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 6 1 3 1 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i)\|2 \|7 +--R 112 112 56 +--R + +--R 1 6 1 3 1 3+-+2 +--R (- -- x - -- x - --)\|2 +--R 48 48 24 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 7 1 4 1 +-+ +--+ +--R (-- %i x + -- %i x + -- %i x)\|3 \|21 +--R 42 42 21 +--R + +--R 8 7 8 4 11 +-+ 1 7 1 4 1 +--R (- -- %i x - -- %i x - -- %i x)\|7 - - x - - x - - x +--R 21 21 42 3 3 6 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 1 7 1 4 1 3+-+2 +--R (-- x + -- x + -- x)\|2 +--R 24 24 12 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 8 1 5 1 2 +-+ +--+ +--R (- -- %i x - -- %i x - -- %i x )\|3 \|21 +--R 42 42 21 +--R + +--R 29 8 29 5 4 2 +-+ 1 8 1 5 +--R (-- %i x + -- %i x + -- %i x )\|7 + - x + - x +--R 84 84 21 4 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 6 1 3 1 +-+ +-+ +--+ 5 6 5 3 4 +--R (- -- x - -- x - --)\|3 \|7 \|21 + - x + - x + - +--R 42 42 21 3 3 3 +--R * +--R 1 3 12 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 1 7 1 4 1 3+-+2 +--R (- x + - x + - x)\|2 +--R 8 8 4 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 8 8 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 6 3 3 3 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i)\|2 \|7 +--R 56 56 28 +--R + +--R 1 6 1 3 1 3+-+2 +--R (- - x - - x - -)\|2 +--R 8 8 4 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 28 28 14 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 4 4 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 28 28 14 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (- x + - x + - x )\|2 +--R 4 4 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 7 3 4 3 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x)\|2 \|7 +--R 28 28 14 +--R + +--R 1 7 1 4 1 3+-+2 +--R (- x + - x + - x)\|2 +--R 4 4 2 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 1 7 1 4 1 3+-+2 +--R (- x + - x + - x)\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 8 5 2 +--R 4x + 4x + 2x +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 28 28 14 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 4 4 2 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 9 1 6 1 3 +-+ 7 9 7 6 3 +--R (- -- %i x - -- %i x - - %i x )\|7 - - x - - x - x +--R 14 14 7 2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 7 1 4 2 +-+ +--+ +--R (- - %i x - - %i x - - %i x)\|3 \|21 +--R 7 7 7 +--R + +--R 16 7 16 4 11 +-+ 7 4 +--R (-- %i x + -- %i x + -- %i x)\|7 - 2x - 2x - x +--R 7 7 7 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 9 1 6 1 3 +-+ 7 9 7 6 3 +--R (-- %i x + -- %i x + - %i x )\|7 - - x - - x - x +--R 14 14 7 2 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 28 28 14 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (- x + - x + - x )\|2 +--R 4 4 2 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 10 7 +--R 3x + 3x +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 2 2 +-+ +--+ +--R (- %i x + - %i x + - %i x )\|3 \|21 +--R 7 7 7 +--R + +--R 29 8 29 5 8 2 +-+ 3 8 3 5 +--R (- -- %i x - -- %i x - - %i x )\|7 + - x + - x +--R 14 14 7 2 2 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 3 6 3 3 3 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i)\|2 \|7 +--R 56 56 28 +--R + +--R 1 6 1 3 1 3+-+2 +--R (- - x - - x - -)\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 7 1 4 2 +-+ +--+ +--R (- %i x + - %i x + - %i x)\|3 \|21 +--R 7 7 7 +--R + +--R 16 7 16 4 11 +-+ 7 4 +--R (- -- %i x - -- %i x - -- %i x)\|7 - 2x - 2x - x +--R 7 7 7 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 7 3 4 3 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x)\|2 \|7 +--R 28 28 14 +--R + +--R 1 7 1 4 1 3+-+2 +--R (- x + - x + - x)\|2 +--R 4 4 2 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 8 1 5 2 2 +-+ +--+ +--R (- - %i x - - %i x - - %i x )\|3 \|21 +--R 7 7 7 +--R + +--R 29 8 29 5 8 2 +-+ 3 8 3 5 +--R (-- %i x + -- %i x + - %i x )\|7 + - x + - x +--R 14 14 7 2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 6 1 3 2 +-+ +-+ +--+ 6 3 +--R (- - x - - x - -)\|3 \|7 \|21 + 10x + 10x + 8 +--R 7 7 7 +--R * +--R 1 3 2 1 3 10 +--R cos(- atan(----)) sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 9408 9408 4704 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 9408 9408 4704 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 9 5 6 5 3 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 4704 4704 2352 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 4704 4704 2352 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 4704 4704 2352 +--R + +--R 5 12 5 9 5 6 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 4704 4704 2352 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 4704 4704 2352 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (- ---- %i x - ---- %i x - --- %i x )\|2 +--R 1568 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 9408 9408 4704 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 31 11 31 8 1 5 +-+6+----+3 +--R (---- x + ---- x + ---- x )\|7 \|1372 +--R 2352 2352 1176 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 4704 4704 2352 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 4704 4704 2352 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 13 12 13 9 1 6 +-+ 5 12 +--R (- ---- x - ---- x + --- x )\|7 - ---- %i x +--R 1176 1176 294 2352 +--R + +--R 5 9 5 6 +--R - ---- %i x - ---- %i x +--R 2352 1176 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 +-+ +-+ +--+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|3 \|7 \|21 +--R 8232 8232 4116 +--R + +--R 31 10 31 7 1 4 +-+ 257 10 +--R (- ---- x - ---- x - ---- x )\|7 + ---- %i x +--R 4704 4704 2352 4704 +--R + +--R 257 7 47 4 +--R ---- %i x + ---- %i x +--R 4704 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 9408 9408 4704 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 13 12 13 9 1 6 +-+ 5 12 +--R (- ---- x - ---- x + --- x )\|7 + ---- %i x +--R 1176 1176 294 2352 +--R + +--R 5 9 5 6 +--R ---- %i x + ---- %i x +--R 2352 1176 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 4704 4704 2352 +--R + +--R 5 12 5 9 5 6 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 4704 4704 2352 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 13 1 10 3 7 +-+6+----+3 +--R (--- x + --- x - --- x )\|7 \|1372 +--R 112 112 392 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 +-+ +-+ +--+ +--R (---- %i x + ---- %i x + ---- %i x )\|3 \|7 \|21 +--R 8232 8232 4116 +--R + +--R 1 11 1 8 3 5 +-+ 227 11 227 8 +--R (--- x + --- x - --- x )\|7 - ---- %i x - ---- %i x +--R 224 224 784 4704 4704 +--R + +--R 17 5 +--R - ---- %i x +--R 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 9 5 6 5 3 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 10 5 7 5 4 +-+ +-+ +--+ +--R (---- %i x + ---- %i x + ---- %i x )\|3 \|7 \|21 +--R 8232 8232 4116 +--R + +--R 31 10 31 7 1 4 +-+ 257 10 +--R (- ---- x - ---- x - ---- x )\|7 - ---- %i x +--R 4704 4704 2352 4704 +--R + +--R 257 7 47 4 +--R - ---- %i x - ---- %i x +--R 4704 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 4704 4704 2352 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (---- %i x + ---- %i x + --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 11 5 8 5 5 +-+ +-+ +--+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|3 \|7 \|21 +--R 8232 8232 4116 +--R + +--R 1 11 1 8 3 5 +-+ 227 11 227 8 +--R (--- x + --- x - --- x )\|7 + ---- %i x + ---- %i x +--R 224 224 784 4704 4704 +--R + +--R 17 5 +--R ---- %i x +--R 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 +-+ +--+ +--R (- ---- x - ---- x - --- x )\|3 \|21 +--R 1176 1176 588 +--R + +--R 41 9 41 6 11 3 +-+ +--R (---- x + ---- x + --- x )\|7 +--R 1176 1176 588 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 9 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 5 7 5 4 5 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x)\|2 \|7 +--R 112 112 56 +--R + +--R 5 7 5 4 5 3+-+2 +--R (-- x + -- x + - x)\|2 +--R 16 16 8 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x )\|2 \|7 +--R 112 112 56 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- -- x - -- x - - x )\|2 +--R 16 16 8 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 6 15 3 15 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i)\|2 \|7 +--R 112 112 56 +--R + +--R 5 6 5 3 5 3+-+2 +--R (- -- x - -- x - -)\|2 +--R 16 16 8 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 8 8 4 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 5 9 5 6 5 3 3+-+2 +--R (- x + - x + - x )\|2 +--R 8 8 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 7 15 4 15 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 5 7 5 4 5 3+-+2 +--R (- x + - x + - x)\|2 +--R 8 8 4 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 7 5 4 5 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x)\|2 \|7 +--R 112 112 56 +--R + +--R 5 7 5 4 5 3+-+2 +--R (-- x + -- x + - x)\|2 +--R 16 16 8 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 8 5 2 +--R 10x + 10x + 5x +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 9 5 6 5 3 +-+ 35 9 35 6 +--R (- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x +--R 28 28 14 4 4 +--R + +--R 5 3 +--R - - x +--R 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 7 5 4 5 +-+ +--+ +--R (- -- %i x - -- %i x - - %i x)\|3 \|21 +--R 14 14 7 +--R + +--R 40 7 40 4 55 +-+ 7 4 5 +--R (-- %i x + -- %i x + -- %i x)\|7 - 5x - 5x - - x +--R 7 7 14 2 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x )\|2 \|7 +--R 112 112 56 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- -- x - -- x - - x )\|2 +--R 16 16 8 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 9 5 6 5 3 +-+ 35 9 35 6 5 3 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x - - x +--R 28 28 14 4 4 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 5 9 5 6 5 3 3+-+2 +--R (- x + - x + - x )\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 15 10 15 7 +--R -- x + -- x +--R 2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 8 5 5 5 2 +-+ +--+ +--R (-- %i x + -- %i x + - %i x )\|3 \|21 +--R 14 14 7 +--R + +--R 145 8 145 5 20 2 +-+ 15 8 15 5 +--R (- --- %i x - --- %i x - -- %i x )\|7 + -- x + -- x +--R 28 28 7 4 4 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 15 6 15 3 15 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i)\|2 \|7 +--R 112 112 56 +--R + +--R 5 6 5 3 5 3+-+2 +--R (- -- x - -- x - -)\|2 +--R 16 16 8 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 7 5 4 5 +-+ +--+ +--R (-- %i x + -- %i x + - %i x)\|3 \|21 +--R 14 14 7 +--R + +--R 40 7 40 4 55 +-+ 7 4 5 +--R (- -- %i x - -- %i x - -- %i x)\|7 - 5x - 5x - - x +--R 7 7 14 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 7 15 4 15 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 5 7 5 4 5 3+-+2 +--R (- x + - x + - x)\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 8 5 5 5 2 +-+ +--+ +--R (- -- %i x - -- %i x - - %i x )\|3 \|21 +--R 14 14 7 +--R + +--R 145 8 145 5 20 2 +-+ 15 8 15 5 +--R (--- %i x + --- %i x + -- %i x )\|7 + -- x + -- x +--R 28 28 7 4 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 6 5 3 5 +-+ +-+ +--+ 6 3 +--R (- -- x - -- x - -)\|3 \|7 \|21 + 25x + 25x + 20 +--R 14 14 7 +--R * +--R 1 3 4 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 448 448 224 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 448 448 224 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 9 3 6 3 3 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 448 448 224 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 224 224 112 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 12 1 9 1 6 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 12 1 9 1 6 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 224 224 112 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 10 3 7 3 4 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 224 224 112 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 448 448 224 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 53 11 53 8 11 5 6+----+3 +--R (- --- x - --- x - --- x )\|1372 +--R 784 784 392 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 224 224 112 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 12 1 9 1 6 +-+ 23 12 +--R (--- %i x + --- %i x + --- %i x )\|7 + --- x +--R 784 784 392 392 +--R + +--R 23 9 1 6 +--R --- x + -- x +--R 392 98 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 10 1 7 1 4 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 392 392 196 +--R + +--R 61 10 61 7 19 4 +-+ 53 10 +--R (- ---- %i x - ---- %i x - --- %i x )\|7 + ---- x +--R 1568 1568 784 1568 +--R + +--R 53 7 11 4 +--R ---- x + --- x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 448 448 224 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 12 1 9 1 6 +-+ 23 12 +--R (- --- %i x - --- %i x - --- %i x )\|7 + --- x +--R 784 784 392 392 +--R + +--R 23 9 1 6 +--R --- x + -- x +--R 392 98 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 12 1 9 1 6 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 12 1 9 1 6 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 224 224 112 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 39 13 39 10 3 7 6+----+3 +--R (- --- x - --- x + --- x )\|1372 +--R 784 784 392 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 392 392 196 +--R + +--R 55 11 55 8 13 5 +-+ 39 11 +--R (---- %i x + ---- %i x + --- %i x )\|7 - ---- x +--R 1568 1568 784 1568 +--R + +--R 39 8 3 5 +--R - ---- x + --- x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 3 9 3 6 3 3 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 448 448 224 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 10 1 7 1 4 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 392 392 196 +--R + +--R 61 10 61 7 19 4 +-+ 53 10 +--R (---- %i x + ---- %i x + --- %i x )\|7 + ---- x +--R 1568 1568 784 1568 +--R + +--R 53 7 11 4 +--R ---- x + --- x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 10 3 7 3 4 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 224 224 112 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 11 1 8 1 5 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 392 392 196 +--R + +--R 55 11 55 8 13 5 +-+ 39 11 +--R (- ---- %i x - ---- %i x - --- %i x )\|7 - ---- x +--R 1568 1568 784 1568 +--R + +--R 39 8 3 5 +--R - ---- x + --- x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 +-+ +-+ +--+ 67 9 67 6 +--R (--- x + --- x + --- x )\|3 \|7 \|21 - --- x - --- x +--R 392 392 196 392 392 +--R + +--R 25 3 +--R - --- x +--R 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 3 8 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 5 7 5 4 5 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x)\|2 \|7 +--R 84 84 42 +--R + +--R 5 7 5 4 5 3+-+2 +--R (-- x + -- x + - x)\|2 +--R 12 12 6 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 84 84 42 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- -- x - -- x - - x )\|2 +--R 12 12 6 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 6 5 3 5 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i)\|2 \|7 +--R 28 28 14 +--R + +--R 5 6 5 3 5 3+-+2 +--R (- -- x - -- x - -)\|2 +--R 12 12 6 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 42 42 21 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 6 6 3 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 42 42 21 +--R + +--R 5 9 5 6 5 3 3+-+2 +--R (- x + - x + - x )\|2 +--R 6 6 3 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 7 5 4 5 3+-+2 +-+ +--R (- -- %i x - -- %i x - - %i x)\|2 \|7 +--R 14 14 7 +--R + +--R 5 7 5 4 5 3+-+2 +--R (- x + - x + - x)\|2 +--R 6 6 3 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 7 5 4 5 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x)\|2 \|7 +--R 84 84 42 +--R + +--R 5 7 5 4 5 3+-+2 +--R (-- x + -- x + - x)\|2 +--R 12 12 6 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 40 8 40 5 20 2 +--R -- x + -- x + -- x +--R 3 3 3 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 42 42 21 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 6 6 3 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 9 5 6 10 3 +-+ 35 9 35 6 +--R (- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x +--R 21 21 21 3 3 +--R + +--R 10 3 +--R - -- x +--R 3 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 10 7 10 4 20 +-+ +--+ +--R (- -- %i x - -- %i x - -- %i x)\|3 \|21 +--R 21 21 21 +--R + +--R 160 7 160 4 110 +-+ 20 7 20 4 10 +--R (--- %i x + --- %i x + --- %i x)\|7 - -- x - -- x - -- x +--R 21 21 21 3 3 3 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 84 84 42 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- -- x - -- x - - x )\|2 +--R 12 12 6 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 9 5 6 10 3 +-+ 35 9 35 6 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x +--R 21 21 21 3 3 +--R + +--R 10 3 +--R - -- x +--R 3 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 42 42 21 +--R + +--R 5 9 5 6 5 3 3+-+2 +--R (- x + - x + - x )\|2 +--R 6 6 3 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 10 7 +--R 10x + 10x +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 10 8 10 5 20 2 +-+ +--+ +--R (-- %i x + -- %i x + -- %i x )\|3 \|21 +--R 21 21 21 +--R + +--R 145 8 145 5 80 2 +-+ 8 5 +--R (- --- %i x - --- %i x - -- %i x )\|7 + 5x + 5x +--R 21 21 21 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 6 5 3 5 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i)\|2 \|7 +--R 28 28 14 +--R + +--R 5 6 5 3 5 3+-+2 +--R (- -- x - -- x - -)\|2 +--R 12 12 6 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 10 7 10 4 20 +-+ +--+ +--R (-- %i x + -- %i x + -- %i x)\|3 \|21 +--R 21 21 21 +--R + +--R 160 7 160 4 110 +-+ 20 7 20 4 10 +--R (- --- %i x - --- %i x - --- %i x)\|7 - -- x - -- x - -- x +--R 21 21 21 3 3 3 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 7 5 4 5 3+-+2 +-+ +--R (-- %i x + -- %i x + - %i x)\|2 \|7 +--R 14 14 7 +--R + +--R 5 7 5 4 5 3+-+2 +--R (- x + - x + - x)\|2 +--R 6 6 3 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 10 8 10 5 20 2 +-+ +--+ +--R (- -- %i x - -- %i x - -- %i x )\|3 \|21 +--R 21 21 21 +--R + +--R 145 8 145 5 80 2 +-+ 8 5 +--R (--- %i x + --- %i x + -- %i x )\|7 + 5x + 5x +--R 21 21 21 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 10 6 10 3 20 +-+ +-+ +--+ 100 6 100 3 80 +--R (- -- x - -- x - --)\|3 \|7 \|21 + --- x + --- x + -- +--R 21 21 21 3 3 3 +--R * +--R 1 3 6 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1176 1176 588 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 168 168 84 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1176 1176 588 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 168 168 84 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 392 392 196 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 168 168 84 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 588 588 294 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (-- x + -- x + -- x )\|2 +--R 84 84 42 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 12 1 9 1 6 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 588 588 294 +--R + +--R 1 12 1 9 1 6 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 84 84 42 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x )\|2 \|7 +--R 196 196 98 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 84 84 42 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1176 1176 588 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 168 168 84 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 53 11 53 8 11 5 6+----+3 +--R (- --- x - --- x - --- x )\|1372 +--R 294 294 147 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 588 588 294 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (-- x + -- x + -- x )\|2 +--R 84 84 42 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 12 1 9 1 6 +-+ 23 12 +--R (--- %i x + --- %i x + --- %i x )\|7 + --- x +--R 294 294 147 147 +--R + +--R 23 9 4 6 +--R --- x + --- x +--R 147 147 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 10 1 7 2 4 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 147 147 147 +--R + +--R 61 10 61 7 19 4 +-+ 53 10 +--R (- --- %i x - --- %i x - --- %i x )\|7 + --- x +--R 588 588 294 588 +--R + +--R 53 7 11 4 +--R --- x + --- x +--R 588 294 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1176 1176 588 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 168 168 84 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 12 1 9 1 6 +-+ 23 12 +--R (- --- %i x - --- %i x - --- %i x )\|7 + --- x +--R 294 294 147 147 +--R + +--R 23 9 4 6 +--R --- x + --- x +--R 147 147 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 12 1 9 1 6 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 588 588 294 +--R + +--R 1 12 1 9 1 6 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 84 84 42 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 13 13 13 10 1 7 6+----+3 +--R (- -- x - -- x + -- x )\|1372 +--R 98 98 49 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 2 5 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 147 147 147 +--R + +--R 55 11 55 8 13 5 +-+ 13 11 +--R (--- %i x + --- %i x + --- %i x )\|7 - --- x +--R 588 588 294 196 +--R + +--R 13 8 1 5 +--R - --- x + -- x +--R 196 98 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 392 392 196 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 168 168 84 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 10 1 7 2 4 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 147 147 147 +--R + +--R 61 10 61 7 19 4 +-+ 53 10 +--R (--- %i x + --- %i x + --- %i x )\|7 + --- x +--R 588 588 294 588 +--R + +--R 53 7 11 4 +--R --- x + --- x +--R 588 294 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x )\|2 \|7 +--R 196 196 98 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 84 84 42 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 11 1 8 2 5 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 147 147 147 +--R + +--R 55 11 55 8 13 5 +-+ 13 11 +--R (- --- %i x - --- %i x - --- %i x )\|7 - --- x +--R 588 588 294 196 +--R + +--R 13 8 1 5 +--R - --- x + -- x +--R 196 98 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 2 3 +-+ +-+ +--+ 67 9 67 6 +--R (--- x + --- x + --- x )\|3 \|7 \|21 - --- x - --- x +--R 147 147 147 147 147 +--R + +--R 50 3 +--R - --- x +--R 147 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 41 13 41 10 41 7 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 5376 5376 2688 +--R + +--R 41 13 41 10 41 7 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 768 768 384 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 14 41 11 41 8 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 5376 5376 2688 +--R + +--R 41 14 41 11 41 8 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 768 768 384 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 12 41 9 41 6 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1792 1792 896 +--R + +--R 41 12 41 9 41 6 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 768 768 384 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 41 14 41 11 41 8 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 2688 2688 1344 +--R + +--R 41 14 41 11 41 8 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 384 384 192 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 15 41 12 41 9 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 2688 2688 1344 +--R + +--R 41 15 41 12 41 9 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 384 384 192 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 13 41 10 41 7 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 896 896 448 +--R + +--R 41 13 41 10 41 7 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 384 384 192 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 41 13 41 10 41 7 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 5376 5376 2688 +--R + +--R 41 13 41 10 41 7 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 768 768 384 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 95 14 95 11 7 8 +--R -- x + -- x - -- x +--R 96 96 12 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 14 41 11 41 8 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 2688 2688 1344 +--R + +--R 41 14 41 11 41 8 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 384 384 192 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 41 15 41 12 41 9 +-+ 149 15 +--R (- ---- %i x - ---- %i x - --- %i x )\|7 - --- x +--R 1344 1344 672 192 +--R + +--R 149 12 97 9 +--R - --- x + -- x +--R 192 96 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 13 41 10 41 7 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 672 672 336 +--R + +--R 829 13 829 10 1 7 +-+ 95 13 95 10 +--R (---- %i x + ---- %i x - -- %i x )\|7 - --- x - --- x +--R 1344 1344 21 192 192 +--R + +--R 7 7 +--R -- x +--R 24 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 41 14 41 11 41 8 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 5376 5376 2688 +--R + +--R 41 14 41 11 41 8 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 768 768 384 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 41 15 41 12 41 9 +-+ 149 15 +--R (---- %i x + ---- %i x + --- %i x )\|7 - --- x +--R 1344 1344 672 192 +--R + +--R 149 12 97 9 +--R - --- x + -- x +--R 192 96 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 15 41 12 41 9 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 2688 2688 1344 +--R + +--R 41 15 41 12 41 9 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 384 384 192 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 9 16 9 13 23 10 +--R -- x + -- x - -- x +--R 16 16 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 14 41 11 41 8 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 672 672 336 +--R + +--R 353 14 353 11 155 8 +-+ 9 14 9 11 +--R (- --- %i x - --- %i x + --- %i x )\|7 + -- x + -- x +--R 672 672 672 32 32 +--R + +--R 23 8 +--R - -- x +--R 32 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 41 12 41 9 41 6 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1792 1792 896 +--R + +--R 41 12 41 9 41 6 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 768 768 384 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 41 13 41 10 41 7 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 672 672 336 +--R + +--R 829 13 829 10 1 7 +-+ 95 13 95 10 +--R (- ---- %i x - ---- %i x + -- %i x )\|7 - --- x - --- x +--R 1344 1344 21 192 192 +--R + +--R 7 7 +--R -- x +--R 24 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 13 41 10 41 7 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 896 896 448 +--R + +--R 41 13 41 10 41 7 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 384 384 192 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 41 14 41 11 41 8 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 672 672 336 +--R + +--R 353 14 353 11 155 8 +-+ 9 14 9 11 23 8 +--R (--- %i x + --- %i x - --- %i x )\|7 + -- x + -- x - -- x +--R 672 672 672 32 32 32 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 12 41 9 41 6 +-+ +-+ +--+ 17 12 17 9 13 6 +--R (- --- x - --- x - --- x )\|3 \|7 \|21 + -- x + -- x + -- x +--R 672 672 336 6 6 24 +--R * +--R 1 3 6 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- ---- x - ---- x - --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (- ---- %i x - ---- %i x - --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (---- x + ---- x + --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (---- %i x + ---- %i x + --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (---- x + ---- x + --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 15 9 15 6 15 3 3+-+2 +--R (- ---- %i x - ---- %i x - --- %i x )\|2 +--R 1568 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (--- x + --- x + --- x )\|2 \|7 +--R 784 784 392 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (--- %i x + --- %i x + --- %i x )\|2 +--R 784 784 392 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (- --- x - --- x - --- x )\|2 \|7 +--R 784 784 392 +--R + +--R 5 12 5 9 5 6 3+-+2 +--R (- --- %i x - --- %i x - --- %i x )\|2 +--R 784 784 392 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- --- x - --- x - --- x )\|2 \|7 +--R 784 784 392 +--R + +--R 15 10 15 7 15 4 3+-+2 +--R (--- %i x + --- %i x + --- %i x )\|2 +--R 784 784 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- ---- x - ---- x - --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (---- %i x + ---- %i x + --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 31 11 31 8 1 5 +-+6+----+3 +--R (- --- x - --- x - --- x )\|7 \|1372 +--R 392 392 196 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (--- x + --- x + --- x )\|2 \|7 +--R 784 784 392 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (- --- %i x - --- %i x - --- %i x )\|2 +--R 784 784 392 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 13 12 13 9 1 6 +-+ 5 12 +--R (--- x + --- x - -- x )\|7 + --- %i x +--R 196 196 49 392 +--R + +--R 5 9 5 6 +--R --- %i x + --- %i x +--R 392 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 +-+ +-+ +--+ +--R (---- %i x + ---- %i x + --- %i x )\|3 \|7 \|21 +--R 1372 1372 686 +--R + +--R 31 10 31 7 1 4 +-+ 257 10 257 7 +--R (--- x + --- x + --- x )\|7 - --- %i x - --- %i x +--R 784 784 392 784 784 +--R + +--R 47 4 +--R - --- %i x +--R 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (---- x + ---- x + --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (- ---- %i x - ---- %i x - --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 13 12 13 9 1 6 +-+ 5 12 +--R (--- x + --- x - -- x )\|7 - --- %i x +--R 196 196 49 392 +--R + +--R 5 9 5 6 +--R - --- %i x - --- %i x +--R 392 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (- --- x - --- x - --- x )\|2 \|7 +--R 784 784 392 +--R + +--R 5 12 5 9 5 6 3+-+2 +--R (--- %i x + --- %i x + --- %i x )\|2 +--R 784 784 392 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 3 13 3 10 9 7 +-+6+----+3 +--R (- -- x - -- x + --- x )\|7 \|1372 +--R 56 56 196 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 +-+ +-+ +--+ +--R (- ---- %i x - ---- %i x - --- %i x )\|3 \|7 \|21 +--R 1372 1372 686 +--R + +--R 3 11 3 8 9 5 +-+ 227 11 +--R (- --- x - --- x + --- x )\|7 + --- %i x +--R 112 112 392 784 +--R + +--R 227 8 17 5 +--R --- %i x + --- %i x +--R 784 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (---- x + ---- x + --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 15 9 15 6 15 3 3+-+2 +--R (---- %i x + ---- %i x + --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 10 5 7 5 4 +-+ +-+ +--+ +--R (- ---- %i x - ---- %i x - --- %i x )\|3 \|7 \|21 +--R 1372 1372 686 +--R + +--R 31 10 31 7 1 4 +-+ 257 10 257 7 +--R (--- x + --- x + --- x )\|7 + --- %i x + --- %i x +--R 784 784 392 784 784 +--R + +--R 47 4 +--R --- %i x +--R 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- --- x - --- x - --- x )\|2 \|7 +--R 784 784 392 +--R + +--R 15 10 15 7 15 4 3+-+2 +--R (- --- %i x - --- %i x - --- %i x )\|2 +--R 784 784 392 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 11 5 8 5 5 +-+ +-+ +--+ +--R (---- %i x + ---- %i x + --- %i x )\|3 \|7 \|21 +--R 1372 1372 686 +--R + +--R 3 11 3 8 9 5 +-+ 227 11 +--R (- --- x - --- x + --- x )\|7 - --- %i x +--R 112 112 392 784 +--R + +--R 227 8 17 5 +--R - --- %i x - --- %i x +--R 784 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 +-+ +--+ +--R (--- x + --- x + -- x )\|3 \|21 +--R 196 196 98 +--R + +--R 41 9 41 6 11 3 +-+ +--R (- --- x - --- x - -- x )\|7 +--R 196 196 98 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 4 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 5 13 5 10 5 7 3+-+2 +-+ +--R (- --- x - --- x - -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 5 13 5 10 5 7 3+-+2 +--R (- --- %i x - --- %i x - -- %i x )\|2 +--R 128 128 64 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 14 5 11 5 8 3+-+2 +-+ +--R (--- x + --- x + -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 5 14 5 11 5 8 3+-+2 +--R (--- %i x + --- %i x + -- %i x )\|2 +--R 128 128 64 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (--- x + --- x + -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 15 12 15 9 15 6 3+-+2 +--R (- --- %i x - --- %i x - -- %i x )\|2 +--R 128 128 64 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 14 5 11 5 8 3+-+2 +-+ +--R (-- x + -- x + -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 5 14 5 11 5 8 3+-+2 +--R (-- %i x + -- %i x + -- %i x )\|2 +--R 64 64 32 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 15 5 12 5 9 3+-+2 +-+ +--R (- -- x - -- x - -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 5 15 5 12 5 9 3+-+2 +--R (- -- %i x - -- %i x - -- %i x )\|2 +--R 64 64 32 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 13 5 10 5 7 3+-+2 +-+ +--R (- -- x - -- x - -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 15 13 15 10 15 7 3+-+2 +--R (-- %i x + -- %i x + -- %i x )\|2 +--R 64 64 32 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 13 5 10 5 7 3+-+2 +-+ +--R (- --- x - --- x - -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 5 13 5 10 5 7 3+-+2 +--R (--- %i x + --- %i x + -- %i x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 101 14 101 11 1 8 +-+ +--R (- --- x - --- x + -- x )\|7 +--R 112 112 14 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 14 5 11 5 8 3+-+2 +-+ +--R (-- x + -- x + -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 5 14 5 11 5 8 3+-+2 +--R (- -- %i x - -- %i x - -- %i x )\|2 +--R 64 64 32 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 167 15 167 12 43 9 +-+ 5 15 5 12 +--R (--- x + --- x - --- x )\|7 + -- %i x + -- %i x +--R 224 224 112 32 32 +--R + +--R 5 9 +--R -- %i x +--R 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 13 5 10 5 7 +-+ +-+ +--+ +--R (--- %i x + --- %i x + -- %i x )\|3 \|7 \|21 +--R 112 112 56 +--R + +--R 101 13 101 10 1 7 +-+ 121 13 121 10 +--R (--- x + --- x - -- x )\|7 - --- %i x - --- %i x +--R 224 224 28 32 32 +--R + +--R 7 +--R - %i x +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 14 5 11 5 8 3+-+2 +-+ +--R (--- x + --- x + -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 5 14 5 11 5 8 3+-+2 +--R (- --- %i x - --- %i x - -- %i x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 167 15 167 12 43 9 +-+ 5 15 5 12 +--R (--- x + --- x - --- x )\|7 - -- %i x - -- %i x +--R 224 224 112 32 32 +--R + +--R 5 9 +--R - -- %i x +--R 16 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 15 5 12 5 9 3+-+2 +-+ +--R (- -- x - -- x - -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 5 15 5 12 5 9 3+-+2 +--R (-- %i x + -- %i x + -- %i x )\|2 +--R 64 64 32 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 33 16 33 13 39 10 +-+ +--R (- -- x - -- x + -- x )\|7 +--R 56 56 56 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 14 5 11 5 8 +-+ +-+ +--+ +--R (- --- %i x - --- %i x - -- %i x )\|3 \|7 \|21 +--R 112 112 56 +--R + +--R 33 14 33 11 39 8 +-+ 53 14 53 11 +--R (- --- x - --- x + --- x )\|7 + -- %i x + -- %i x +--R 112 112 112 16 16 +--R + +--R 1 8 +--R -- %i x +--R 16 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (--- x + --- x + -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 15 12 15 9 15 6 3+-+2 +--R (--- %i x + --- %i x + -- %i x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 13 5 10 5 7 +-+ +-+ +--+ +--R (- --- %i x - --- %i x - -- %i x )\|3 \|7 \|21 +--R 112 112 56 +--R + +--R 101 13 101 10 1 7 +-+ 121 13 121 10 +--R (--- x + --- x - -- x )\|7 + --- %i x + --- %i x +--R 224 224 28 32 32 +--R + +--R 7 +--R %i x +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 13 5 10 5 7 3+-+2 +-+ +--R (- -- x - -- x - -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 15 13 15 10 15 7 3+-+2 +--R (- -- %i x - -- %i x - -- %i x )\|2 +--R 64 64 32 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 14 5 11 5 8 +-+ +-+ +--+ +--R (--- %i x + --- %i x + -- %i x )\|3 \|7 \|21 +--R 112 112 56 +--R + +--R 33 14 33 11 39 8 +-+ 53 14 53 11 +--R (- --- x - --- x + --- x )\|7 - -- %i x - -- %i x +--R 112 112 112 16 16 +--R + +--R 1 8 +--R - -- %i x +--R 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 +-+ +--+ 17 12 17 9 31 6 +-+ +--R (-- x + -- x + - x )\|3 \|21 + (- -- x - -- x - -- x )\|7 +--R 16 16 8 7 7 28 +--R * +--R 1 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 3 5 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 5 7 5 4 5 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x)\|2 \|7 +--R 112 112 56 +--R + +--R 5 7 5 4 5 3+-+2 +--R (-- x + -- x + - x)\|2 +--R 16 16 8 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x )\|2 \|7 +--R 112 112 56 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- -- x - -- x - - x )\|2 +--R 16 16 8 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 6 15 3 15 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i)\|2 \|7 +--R 112 112 56 +--R + +--R 5 6 5 3 5 3+-+2 +--R (- -- x - -- x - -)\|2 +--R 16 16 8 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 8 8 4 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 5 9 5 6 5 3 3+-+2 +--R (- x + - x + - x )\|2 +--R 8 8 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 7 15 4 15 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 5 7 5 4 5 3+-+2 +--R (- x + - x + - x)\|2 +--R 8 8 4 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 7 5 4 5 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x)\|2 \|7 +--R 112 112 56 +--R + +--R 5 7 5 4 5 3+-+2 +--R (-- x + -- x + - x)\|2 +--R 16 16 8 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 8 5 2 +--R 10x + 10x + 5x +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 9 5 6 5 3 +-+ 35 9 35 6 +--R (- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x +--R 28 28 14 4 4 +--R + +--R 5 3 +--R - - x +--R 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 7 5 4 5 +-+ +--+ +--R (- -- %i x - -- %i x - - %i x)\|3 \|21 +--R 14 14 7 +--R + +--R 40 7 40 4 55 +-+ 7 4 5 +--R (-- %i x + -- %i x + -- %i x)\|7 - 5x - 5x - - x +--R 7 7 14 2 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 8 5 5 5 2 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x )\|2 \|7 +--R 112 112 56 +--R + +--R 5 8 5 5 5 2 3+-+2 +--R (- -- x - -- x - - x )\|2 +--R 16 16 8 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 9 5 6 5 3 +-+ 35 9 35 6 5 3 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x - - x +--R 28 28 14 4 4 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 5 9 5 6 5 3 3+-+2 +--R (- x + - x + - x )\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 15 10 15 7 +--R -- x + -- x +--R 2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 8 5 5 5 2 +-+ +--+ +--R (-- %i x + -- %i x + - %i x )\|3 \|21 +--R 14 14 7 +--R + +--R 145 8 145 5 20 2 +-+ 15 8 15 5 +--R (- --- %i x - --- %i x - -- %i x )\|7 + -- x + -- x +--R 28 28 7 4 4 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 15 6 15 3 15 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i)\|2 \|7 +--R 112 112 56 +--R + +--R 5 6 5 3 5 3+-+2 +--R (- -- x - -- x - -)\|2 +--R 16 16 8 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 7 5 4 5 +-+ +--+ +--R (-- %i x + -- %i x + - %i x)\|3 \|21 +--R 14 14 7 +--R + +--R 40 7 40 4 55 +-+ 7 4 5 +--R (- -- %i x - -- %i x - -- %i x)\|7 - 5x - 5x - - x +--R 7 7 14 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 7 15 4 15 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 5 7 5 4 5 3+-+2 +--R (- x + - x + - x)\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 8 5 5 5 2 +-+ +--+ +--R (- -- %i x - -- %i x - - %i x )\|3 \|21 +--R 14 14 7 +--R + +--R 145 8 145 5 20 2 +-+ 15 8 15 5 +--R (--- %i x + --- %i x + -- %i x )\|7 + -- x + -- x +--R 28 28 7 4 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 6 5 3 5 +-+ +-+ +--+ 6 3 +--R (- -- x - -- x - -)\|3 \|7 \|21 + 25x + 25x + 20 +--R 14 14 7 +--R * +--R 1 3 8 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 224 224 112 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 224 224 112 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 9 3 6 3 3 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 224 224 112 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 784 784 392 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 112 112 56 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 12 1 9 1 6 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 784 784 392 +--R + +--R 1 12 1 9 1 6 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 112 112 56 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 10 3 7 3 4 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 784 784 392 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 112 112 56 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 224 224 112 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 53 11 53 8 11 5 6+----+3 +--R (- --- x - --- x - --- x )\|1372 +--R 392 392 196 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 784 784 392 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 112 112 56 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 12 1 9 1 6 +-+ 23 12 +--R (--- %i x + --- %i x + --- %i x )\|7 + --- x +--R 392 392 196 196 +--R + +--R 23 9 1 6 +--R --- x + -- x +--R 196 49 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 10 1 7 1 4 +-+ +--+ +--R (--- %i x + --- %i x + -- %i x )\|3 \|21 +--R 196 196 98 +--R + +--R 61 10 61 7 19 4 +-+ 53 10 +--R (- --- %i x - --- %i x - --- %i x )\|7 + --- x +--R 784 784 392 784 +--R + +--R 53 7 11 4 +--R --- x + --- x +--R 784 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 224 224 112 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 12 1 9 1 6 +-+ 23 12 +--R (- --- %i x - --- %i x - --- %i x )\|7 + --- x +--R 392 392 196 196 +--R + +--R 23 9 1 6 +--R --- x + -- x +--R 196 49 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 12 1 9 1 6 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 784 784 392 +--R + +--R 1 12 1 9 1 6 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 112 112 56 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 39 13 39 10 3 7 6+----+3 +--R (- --- x - --- x + --- x )\|1372 +--R 392 392 196 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 +-+ +--+ +--R (- --- %i x - --- %i x - -- %i x )\|3 \|21 +--R 196 196 98 +--R + +--R 55 11 55 8 13 5 +-+ 39 11 +--R (--- %i x + --- %i x + --- %i x )\|7 - --- x +--R 784 784 392 784 +--R + +--R 39 8 3 5 +--R - --- x + --- x +--R 784 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 3 9 3 6 3 3 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 224 224 112 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 10 1 7 1 4 +-+ +--+ +--R (- --- %i x - --- %i x - -- %i x )\|3 \|21 +--R 196 196 98 +--R + +--R 61 10 61 7 19 4 +-+ 53 10 +--R (--- %i x + --- %i x + --- %i x )\|7 + --- x +--R 784 784 392 784 +--R + +--R 53 7 11 4 +--R --- x + --- x +--R 784 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 10 3 7 3 4 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 784 784 392 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 112 112 56 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 11 1 8 1 5 +-+ +--+ +--R (--- %i x + --- %i x + -- %i x )\|3 \|21 +--R 196 196 98 +--R + +--R 55 11 55 8 13 5 +-+ 39 11 +--R (- --- %i x - --- %i x - --- %i x )\|7 - --- x +--R 784 784 392 784 +--R + +--R 39 8 3 5 +--R - --- x + --- x +--R 784 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 +-+ +-+ +--+ 67 9 67 6 +--R (--- x + --- x + -- x )\|3 \|7 \|21 - --- x - --- x +--R 196 196 98 196 196 +--R + +--R 25 3 +--R - -- x +--R 98 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 5 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 13 13 13 10 13 7 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1792 1792 896 +--R + +--R 13 13 13 10 13 7 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 256 256 128 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 13 14 13 11 13 8 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1792 1792 896 +--R + +--R 13 14 13 11 13 8 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 256 256 128 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 39 12 39 9 39 6 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1792 1792 896 +--R + +--R 13 12 13 9 13 6 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 256 256 128 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 13 14 13 11 13 8 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 896 896 448 +--R + +--R 13 14 13 11 13 8 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 128 128 64 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 13 15 13 12 13 9 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 896 896 448 +--R + +--R 13 15 13 12 13 9 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 128 128 64 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 39 13 39 10 39 7 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 896 896 448 +--R + +--R 13 13 13 10 13 7 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 13 13 13 10 13 7 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1792 1792 896 +--R + +--R 13 13 13 10 13 7 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 256 256 128 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 14 5 11 11 8 +--R -- x + -- x + -- x +--R 32 32 4 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 13 14 13 11 13 8 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 896 896 448 +--R + +--R 13 14 13 11 13 8 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 13 15 13 12 13 9 +-+ 23 15 +--R (--- %i x + --- %i x + --- %i x )\|7 - -- x +--R 448 448 224 64 +--R + +--R 23 12 101 9 +--R - -- x - --- x +--R 64 32 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 13 13 13 10 13 7 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 224 224 112 +--R + +--R 17 13 17 10 8 7 +-+ 5 13 5 10 +--R (- --- %i x - --- %i x + - %i x )\|7 - -- x - -- x +--R 448 448 7 64 64 +--R + +--R 11 7 +--R - -- x +--R 8 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 13 14 13 11 13 8 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1792 1792 896 +--R + +--R 13 14 13 11 13 8 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 256 256 128 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 13 15 13 12 13 9 +-+ 23 15 +--R (- --- %i x - --- %i x - --- %i x )\|7 - -- x +--R 448 448 224 64 +--R + +--R 23 12 101 9 +--R - -- x - --- x +--R 64 32 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 13 15 13 12 13 9 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 896 896 448 +--R + +--R 13 15 13 12 13 9 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 9 16 9 13 57 10 +--R -- x + -- x + -- x +--R 16 16 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 13 14 13 11 13 8 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 224 224 112 +--R + +--R 11 14 11 11 295 8 +-+ 9 14 9 11 +--R (- --- %i x - --- %i x - --- %i x )\|7 + -- x + -- x +--R 224 224 224 32 32 +--R + +--R 57 8 +--R -- x +--R 32 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 39 12 39 9 39 6 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1792 1792 896 +--R + +--R 13 12 13 9 13 6 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 256 256 128 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 13 13 13 10 13 7 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 224 224 112 +--R + +--R 17 13 17 10 8 7 +-+ 5 13 5 10 +--R (--- %i x + --- %i x - - %i x )\|7 - -- x - -- x +--R 448 448 7 64 64 +--R + +--R 11 7 +--R - -- x +--R 8 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 39 13 39 10 39 7 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 896 896 448 +--R + +--R 13 13 13 10 13 7 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 13 14 13 11 13 8 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 224 224 112 +--R + +--R 11 14 11 11 295 8 +-+ 9 14 9 11 +--R (--- %i x + --- %i x + --- %i x )\|7 + -- x + -- x +--R 224 224 224 32 32 +--R + +--R 57 8 +--R -- x +--R 32 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 13 12 13 9 13 6 +-+ +-+ +--+ 1 12 1 9 31 6 +--R (--- x + --- x + --- x )\|3 \|7 \|21 - - x - - x + -- x +--R 224 224 112 2 2 8 +--R * +--R 1 3 2 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 3 4 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- ---- x - ---- x - --- x )\|2 \|7 +--R 1176 1176 588 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (- ---- %i x - ---- %i x - --- %i x )\|2 +--R 1176 1176 588 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (---- x + ---- x + --- x )\|2 \|7 +--R 1176 1176 588 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (---- %i x + ---- %i x + --- %i x )\|2 +--R 1176 1176 588 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (---- x + ---- x + --- x )\|2 \|7 +--R 1176 1176 588 +--R + +--R 5 9 5 6 5 3 3+-+2 +--R (- --- %i x - --- %i x - --- %i x )\|2 +--R 392 392 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (--- x + --- x + --- x )\|2 \|7 +--R 588 588 294 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (--- %i x + --- %i x + --- %i x )\|2 +--R 588 588 294 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (- --- x - --- x - --- x )\|2 \|7 +--R 588 588 294 +--R + +--R 5 12 5 9 5 6 3+-+2 +--R (- --- %i x - --- %i x - --- %i x )\|2 +--R 588 588 294 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- --- x - --- x - --- x )\|2 \|7 +--R 588 588 294 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (--- %i x + --- %i x + -- %i x )\|2 +--R 196 196 98 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- ---- x - ---- x - --- x )\|2 \|7 +--R 1176 1176 588 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (---- %i x + ---- %i x + --- %i x )\|2 +--R 1176 1176 588 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 31 11 31 8 1 5 +-+6+----+3 +--R (- --- x - --- x - --- x )\|7 \|1372 +--R 294 294 147 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (--- x + --- x + --- x )\|2 \|7 +--R 588 588 294 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (- --- %i x - --- %i x - --- %i x )\|2 +--R 588 588 294 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 13 12 13 9 4 6 +-+ 5 12 +--R (--- x + --- x - --- x )\|7 + --- %i x +--R 147 147 147 294 +--R + +--R 5 9 5 6 +--R --- %i x + --- %i x +--R 294 147 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 10 4 +-+ +-+ +--+ +--R (---- %i x + ---- %i x + ---- %i x )\|3 \|7 \|21 +--R 1029 1029 1029 +--R + +--R 31 10 31 7 1 4 +-+ 257 10 257 7 +--R (--- x + --- x + --- x )\|7 - --- %i x - --- %i x +--R 588 588 294 588 588 +--R + +--R 47 4 +--R - --- %i x +--R 294 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (---- x + ---- x + --- x )\|2 \|7 +--R 1176 1176 588 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (- ---- %i x - ---- %i x - --- %i x )\|2 +--R 1176 1176 588 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 13 12 13 9 4 6 +-+ 5 12 +--R (--- x + --- x - --- x )\|7 - --- %i x +--R 147 147 147 294 +--R + +--R 5 9 5 6 +--R - --- %i x - --- %i x +--R 294 147 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (- --- x - --- x - --- x )\|2 \|7 +--R 588 588 294 +--R + +--R 5 12 5 9 5 6 3+-+2 +--R (--- %i x + --- %i x + --- %i x )\|2 +--R 588 588 294 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 13 1 10 3 7 +-+6+----+3 +--R (- -- x - -- x + -- x )\|7 \|1372 +--R 14 14 49 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 10 5 +-+ +-+ +--+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|3 \|7 \|21 +--R 1029 1029 1029 +--R + +--R 1 11 1 8 3 5 +-+ 227 11 227 8 +--R (- -- x - -- x + -- x )\|7 + --- %i x + --- %i x +--R 28 28 98 588 588 +--R + +--R 17 5 +--R --- %i x +--R 294 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (---- x + ---- x + --- x )\|2 \|7 +--R 1176 1176 588 +--R + +--R 5 9 5 6 5 3 3+-+2 +--R (--- %i x + --- %i x + --- %i x )\|2 +--R 392 392 196 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 10 5 7 10 4 +-+ +-+ +--+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|3 \|7 \|21 +--R 1029 1029 1029 +--R + +--R 31 10 31 7 1 4 +-+ 257 10 257 7 +--R (--- x + --- x + --- x )\|7 + --- %i x + --- %i x +--R 588 588 294 588 588 +--R + +--R 47 4 +--R --- %i x +--R 294 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- --- x - --- x - --- x )\|2 \|7 +--R 588 588 294 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (- --- %i x - --- %i x - -- %i x )\|2 +--R 196 196 98 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 11 5 8 10 5 +-+ +-+ +--+ +--R (---- %i x + ---- %i x + ---- %i x )\|3 \|7 \|21 +--R 1029 1029 1029 +--R + +--R 1 11 1 8 3 5 +-+ 227 11 227 8 +--R (- -- x - -- x + -- x )\|7 - --- %i x - --- %i x +--R 28 28 98 588 588 +--R + +--R 17 5 +--R - --- %i x +--R 294 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 10 3 +-+ +--+ +--R (--- x + --- x + --- x )\|3 \|21 +--R 147 147 147 +--R + +--R 41 9 41 6 22 3 +-+ +--R (- --- x - --- x - --- x )\|7 +--R 147 147 147 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 6 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 25 13 25 10 25 7 3+-+2 +-+ +--R (--- x + --- x + -- x )\|2 \|7 +--R 192 192 96 +--R + +--R 25 13 25 10 25 7 3+-+2 +--R (--- %i x + --- %i x + -- %i x )\|2 +--R 192 192 96 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 14 25 11 25 8 3+-+2 +-+ +--R (- --- x - --- x - -- x )\|2 \|7 +--R 192 192 96 +--R + +--R 25 14 25 11 25 8 3+-+2 +--R (- --- %i x - --- %i x - -- %i x )\|2 +--R 192 192 96 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 12 25 9 25 6 3+-+2 +-+ +--R (- --- x - --- x - -- x )\|2 \|7 +--R 192 192 96 +--R + +--R 25 12 25 9 25 6 3+-+2 +--R (-- %i x + -- %i x + -- %i x )\|2 +--R 64 64 32 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 25 14 25 11 25 8 3+-+2 +-+ +--R (- -- x - -- x - -- x )\|2 \|7 +--R 96 96 48 +--R + +--R 25 14 25 11 25 8 3+-+2 +--R (- -- %i x - -- %i x - -- %i x )\|2 +--R 96 96 48 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 15 25 12 25 9 3+-+2 +-+ +--R (-- x + -- x + -- x )\|2 \|7 +--R 96 96 48 +--R + +--R 25 15 25 12 25 9 3+-+2 +--R (-- %i x + -- %i x + -- %i x )\|2 +--R 96 96 48 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 13 25 10 25 7 3+-+2 +-+ +--R (-- x + -- x + -- x )\|2 \|7 +--R 96 96 48 +--R + +--R 25 13 25 10 25 7 3+-+2 +--R (- -- %i x - -- %i x - -- %i x )\|2 +--R 32 32 16 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 25 13 25 10 25 7 3+-+2 +-+ +--R (--- x + --- x + -- x )\|2 \|7 +--R 192 192 96 +--R + +--R 25 13 25 10 25 7 3+-+2 +--R (- --- %i x - --- %i x - -- %i x )\|2 +--R 192 192 96 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 505 14 505 11 5 8 +-+ +--R (--- x + --- x - -- x )\|7 +--R 168 168 21 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 14 25 11 25 8 3+-+2 +-+ +--R (- -- x - -- x - -- x )\|2 \|7 +--R 96 96 48 +--R + +--R 25 14 25 11 25 8 3+-+2 +--R (-- %i x + -- %i x + -- %i x )\|2 +--R 96 96 48 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 835 15 835 12 215 9 +-+ 25 15 +--R (- --- x - --- x + --- x )\|7 - -- %i x +--R 336 336 168 48 +--R + +--R 25 12 25 9 +--R - -- %i x - -- %i x +--R 48 24 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 13 25 10 25 7 +-+ +-+ +--+ +--R (- --- %i x - --- %i x - -- %i x )\|3 \|7 \|21 +--R 168 168 84 +--R + +--R 505 13 505 10 5 7 +-+ 605 13 605 10 +--R (- --- x - --- x + -- x )\|7 + --- %i x + --- %i x +--R 336 336 42 48 48 +--R + +--R 10 7 +--R -- %i x +--R 3 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 25 14 25 11 25 8 3+-+2 +-+ +--R (- --- x - --- x - -- x )\|2 \|7 +--R 192 192 96 +--R + +--R 25 14 25 11 25 8 3+-+2 +--R (--- %i x + --- %i x + -- %i x )\|2 +--R 192 192 96 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 835 15 835 12 215 9 +-+ 25 15 +--R (- --- x - --- x + --- x )\|7 + -- %i x +--R 336 336 168 48 +--R + +--R 25 12 25 9 +--R -- %i x + -- %i x +--R 48 24 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 15 25 12 25 9 3+-+2 +-+ +--R (-- x + -- x + -- x )\|2 \|7 +--R 96 96 48 +--R + +--R 25 15 25 12 25 9 3+-+2 +--R (- -- %i x - -- %i x - -- %i x )\|2 +--R 96 96 48 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 55 16 55 13 65 10 +-+ +--R (-- x + -- x - -- x )\|7 +--R 28 28 28 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 14 25 11 25 8 +-+ +-+ +--+ +--R (--- %i x + --- %i x + -- %i x )\|3 \|7 \|21 +--R 168 168 84 +--R + +--R 55 14 55 11 65 8 +-+ 265 14 265 11 +--R (-- x + -- x - -- x )\|7 - --- %i x - --- %i x +--R 56 56 56 24 24 +--R + +--R 5 8 +--R - -- %i x +--R 24 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 25 12 25 9 25 6 3+-+2 +-+ +--R (- --- x - --- x - -- x )\|2 \|7 +--R 192 192 96 +--R + +--R 25 12 25 9 25 6 3+-+2 +--R (- -- %i x - -- %i x - -- %i x )\|2 +--R 64 64 32 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 25 13 25 10 25 7 +-+ +-+ +--+ +--R (--- %i x + --- %i x + -- %i x )\|3 \|7 \|21 +--R 168 168 84 +--R + +--R 505 13 505 10 5 7 +-+ 605 13 605 10 +--R (- --- x - --- x + -- x )\|7 - --- %i x - --- %i x +--R 336 336 42 48 48 +--R + +--R 10 7 +--R - -- %i x +--R 3 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 13 25 10 25 7 3+-+2 +-+ +--R (-- x + -- x + -- x )\|2 \|7 +--R 96 96 48 +--R + +--R 25 13 25 10 25 7 3+-+2 +--R (-- %i x + -- %i x + -- %i x )\|2 +--R 32 32 16 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 25 14 25 11 25 8 +-+ +-+ +--+ +--R (- --- %i x - --- %i x - -- %i x )\|3 \|7 \|21 +--R 168 168 84 +--R + +--R 55 14 55 11 65 8 +-+ 265 14 265 11 +--R (-- x + -- x - -- x )\|7 + --- %i x + --- %i x +--R 56 56 56 24 24 +--R + +--R 5 8 +--R -- %i x +--R 24 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 12 25 9 25 6 +-+ +--+ +--R (- -- x - -- x - -- x )\|3 \|21 +--R 24 24 12 +--R + +--R 170 12 170 9 155 6 +-+ +--R (--- x + --- x + --- x )\|7 +--R 21 21 42 +--R * +--R 1 3 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 5 16 5 13 5 10 3+-+2 +-+ +--R (----- x + ----- x + ---- x )\|2 \|7 +--R 18816 18816 9408 +--R + +--R 5 16 5 13 5 10 3+-+2 +--R (----- %i x + ----- %i x + ---- %i x )\|2 +--R 18816 18816 9408 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 17 5 14 5 11 3+-+2 +-+ +--R (- ----- x - ----- x - ---- x )\|2 \|7 +--R 18816 18816 9408 +--R + +--R 5 17 5 14 5 11 3+-+2 +--R (- ----- %i x - ----- %i x - ---- %i x )\|2 +--R 18816 18816 9408 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 15 5 12 5 9 3+-+2 +-+ +--R (- ----- x - ----- x - ---- x )\|2 \|7 +--R 18816 18816 9408 +--R + +--R 5 15 5 12 5 9 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 6272 6272 3136 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 17 5 14 5 11 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 17 5 14 5 11 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 9408 9408 4704 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 18 5 15 5 12 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 18 5 15 5 12 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 9408 9408 4704 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 16 5 13 5 10 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 16 5 13 5 10 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 16 5 13 5 10 3+-+2 +-+ +--R (----- x + ----- x + ---- x )\|2 \|7 +--R 18816 18816 9408 +--R + +--R 5 16 5 13 5 10 3+-+2 +--R (- ----- %i x - ----- %i x - ---- %i x )\|2 +--R 18816 18816 9408 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 17 1 14 1 11 +-+6+----+3 +--R (--- x + --- x - --- x )\|7 \|1372 +--R 294 294 168 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 17 5 14 5 11 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 17 5 14 5 11 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 9408 9408 4704 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 11 18 11 15 19 12 +-+ 5 18 +--R (- ---- x - ---- x + ---- x )\|7 - ---- %i x +--R 4704 4704 2352 4704 +--R + +--R 5 15 5 12 +--R - ---- %i x - ---- %i x +--R 4704 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 16 5 13 5 10 +-+ +-+ +--+ +--R (- ----- %i x - ----- %i x - ---- %i x )\|3 \|7 \|21 +--R 16464 16464 8232 +--R + +--R 1 16 1 13 1 10 +-+ 19 16 +--R (- --- x - --- x + --- x )\|7 + ---- %i x +--R 588 588 336 1176 +--R + +--R 19 13 29 10 +--R ---- %i x - ---- %i x +--R 1176 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 17 5 14 5 11 3+-+2 +-+ +--R (- ----- x - ----- x - ---- x )\|2 \|7 +--R 18816 18816 9408 +--R + +--R 5 17 5 14 5 11 3+-+2 +--R (----- %i x + ----- %i x + ---- %i x )\|2 +--R 18816 18816 9408 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 11 18 11 15 19 12 +-+ 5 18 +--R (- ---- x - ---- x + ---- x )\|7 + ---- %i x +--R 4704 4704 2352 4704 +--R + +--R 5 15 5 12 +--R ---- %i x + ---- %i x +--R 4704 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 18 5 15 5 12 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 18 5 15 5 12 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 9408 9408 4704 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 19 1 16 1 13 +-+6+----+3 +--R (--- x + --- x - -- x )\|7 \|1372 +--R 784 784 98 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 17 5 14 5 11 +-+ +-+ +--+ +--R (----- %i x + ----- %i x + ---- %i x )\|3 \|7 \|21 +--R 16464 16464 8232 +--R + +--R 1 17 1 14 1 11 +-+ 61 17 +--R (---- x + ---- x - --- x )\|7 - ---- %i x +--R 1568 1568 196 4704 +--R + +--R 61 14 11 11 +--R - ---- %i x + --- %i x +--R 4704 588 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 15 5 12 5 9 3+-+2 +-+ +--R (- ----- x - ----- x - ---- x )\|2 \|7 +--R 18816 18816 9408 +--R + +--R 5 15 5 12 5 9 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 6272 6272 3136 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 16 5 13 5 10 +-+ +-+ +--+ +--R (----- %i x + ----- %i x + ---- %i x )\|3 \|7 \|21 +--R 16464 16464 8232 +--R + +--R 1 16 1 13 1 10 +-+ 19 16 +--R (- --- x - --- x + --- x )\|7 - ---- %i x +--R 588 588 336 1176 +--R + +--R 19 13 29 10 +--R - ---- %i x + ---- %i x +--R 1176 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 16 5 13 5 10 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 5 16 5 13 5 10 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 17 5 14 5 11 +-+ +-+ +--+ +--R (- ----- %i x - ----- %i x - ---- %i x )\|3 \|7 \|21 +--R 16464 16464 8232 +--R + +--R 1 17 1 14 1 11 +-+ 61 17 +--R (---- x + ---- x - --- x )\|7 + ---- %i x +--R 1568 1568 196 4704 +--R + +--R 61 14 11 11 +--R ---- %i x - --- %i x +--R 4704 588 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 15 5 12 5 9 +-+ +--+ +--R (- ---- x - ---- x - ---- x )\|3 \|21 +--R 2352 2352 1176 +--R + +--R 13 15 13 12 1 9 +-+ +--R (---- x + ---- x - --- x )\|7 +--R 1176 1176 294 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 3 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 1 7 1 4 1 3+-+2 +--R (- x + - x + - x)\|2 +--R 8 8 4 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 8 8 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 6 3 3 3 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i)\|2 \|7 +--R 56 56 28 +--R + +--R 1 6 1 3 1 3+-+2 +--R (- - x - - x - -)\|2 +--R 8 8 4 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 28 28 14 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 4 4 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 28 28 14 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (- x + - x + - x )\|2 +--R 4 4 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 7 3 4 3 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x)\|2 \|7 +--R 28 28 14 +--R + +--R 1 7 1 4 1 3+-+2 +--R (- x + - x + - x)\|2 +--R 4 4 2 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 1 7 1 4 1 3+-+2 +--R (- x + - x + - x)\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 8 5 2 +--R 4x + 4x + 2x +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 28 28 14 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 4 4 2 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 9 1 6 1 3 +-+ 7 9 7 6 3 +--R (- -- %i x - -- %i x - - %i x )\|7 - - x - - x - x +--R 14 14 7 2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 7 1 4 2 +-+ +--+ +--R (- - %i x - - %i x - - %i x)\|3 \|21 +--R 7 7 7 +--R + +--R 16 7 16 4 11 +-+ 7 4 +--R (-- %i x + -- %i x + -- %i x)\|7 - 2x - 2x - x +--R 7 7 7 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x )\|2 \|7 +--R 56 56 28 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- - x - - x - - x )\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 9 1 6 1 3 +-+ 7 9 7 6 3 +--R (-- %i x + -- %i x + - %i x )\|7 - - x - - x - x +--R 14 14 7 2 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x )\|2 \|7 +--R 28 28 14 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (- x + - x + - x )\|2 +--R 4 4 2 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 10 7 +--R 3x + 3x +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 2 2 +-+ +--+ +--R (- %i x + - %i x + - %i x )\|3 \|21 +--R 7 7 7 +--R + +--R 29 8 29 5 8 2 +-+ 3 8 3 5 +--R (- -- %i x - -- %i x - - %i x )\|7 + - x + - x +--R 14 14 7 2 2 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 3 6 3 3 3 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i)\|2 \|7 +--R 56 56 28 +--R + +--R 1 6 1 3 1 3+-+2 +--R (- - x - - x - -)\|2 +--R 8 8 4 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 7 1 4 2 +-+ +--+ +--R (- %i x + - %i x + - %i x)\|3 \|21 +--R 7 7 7 +--R + +--R 16 7 16 4 11 +-+ 7 4 +--R (- -- %i x - -- %i x - -- %i x)\|7 - 2x - 2x - x +--R 7 7 7 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 7 3 4 3 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x)\|2 \|7 +--R 28 28 14 +--R + +--R 1 7 1 4 1 3+-+2 +--R (- x + - x + - x)\|2 +--R 4 4 2 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 8 1 5 2 2 +-+ +--+ +--R (- - %i x - - %i x - - %i x )\|3 \|21 +--R 7 7 7 +--R + +--R 29 8 29 5 8 2 +-+ 3 8 3 5 +--R (-- %i x + -- %i x + - %i x )\|7 + - x + - x +--R 14 14 7 2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 6 1 3 2 +-+ +-+ +--+ 6 3 +--R (- - x - - x - -)\|3 \|7 \|21 + 10x + 10x + 8 +--R 7 7 7 +--R * +--R 1 3 10 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 11 13 11 10 11 7 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 256 256 128 +--R + +--R 77 13 77 10 77 7 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 256 256 128 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 11 14 11 11 11 8 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 256 256 128 +--R + +--R 77 14 77 11 77 8 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 256 256 128 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 33 12 33 9 33 6 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 256 256 128 +--R + +--R 77 12 77 9 77 6 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 256 256 128 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 11 14 11 11 11 8 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x )\|2 \|7 +--R 128 128 64 +--R + +--R 77 14 77 11 77 8 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 128 128 64 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 11 15 11 12 11 9 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x )\|2 \|7 +--R 128 128 64 +--R + +--R 77 15 77 12 77 9 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 128 128 64 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 33 13 33 10 33 7 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x )\|2 \|7 +--R 128 128 64 +--R + +--R 77 13 77 10 77 7 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 11 13 11 10 11 7 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 256 256 128 +--R + +--R 77 13 77 10 77 7 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 256 256 128 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 155 14 155 11 19 8 +--R --- x + --- x - -- x +--R 32 32 4 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 11 14 11 11 11 8 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x )\|2 \|7 +--R 128 128 64 +--R + +--R 77 14 77 11 77 8 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 11 15 11 12 11 9 +-+ 233 15 +--R (- -- %i x - -- %i x - -- %i x )\|7 - --- x +--R 64 64 32 64 +--R + +--R 233 12 229 9 +--R - --- x + --- x +--R 64 32 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 11 13 11 10 11 7 +-+ +--+ +--R (- -- %i x - -- %i x - -- %i x )\|3 \|21 +--R 32 32 16 +--R + +--R 199 13 199 10 7 +-+ 155 13 155 10 +--R (--- %i x + --- %i x - %i x )\|7 - --- x - --- x +--R 64 64 64 64 +--R + +--R 19 7 +--R -- x +--R 8 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 11 14 11 11 11 8 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 256 256 128 +--R + +--R 77 14 77 11 77 8 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 256 256 128 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 11 15 11 12 11 9 +-+ 233 15 +--R (-- %i x + -- %i x + -- %i x )\|7 - --- x +--R 64 64 32 64 +--R + +--R 233 12 229 9 +--R - --- x + --- x +--R 64 32 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 11 15 11 12 11 9 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x )\|2 \|7 +--R 128 128 64 +--R + +--R 77 15 77 12 77 9 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 39 16 39 13 153 10 +--R -- x + -- x - --- x +--R 16 16 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 11 14 11 11 11 8 +-+ +--+ +--R (-- %i x + -- %i x + -- %i x )\|3 \|21 +--R 32 32 16 +--R + +--R 83 14 83 11 65 8 +-+ 39 14 39 11 +--R (- -- %i x - -- %i x + -- %i x )\|7 + -- x + -- x +--R 32 32 32 32 32 +--R + +--R 153 8 +--R - --- x +--R 32 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 33 12 33 9 33 6 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 256 256 128 +--R + +--R 77 12 77 9 77 6 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 256 256 128 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 11 13 11 10 11 7 +-+ +--+ +--R (-- %i x + -- %i x + -- %i x )\|3 \|21 +--R 32 32 16 +--R + +--R 199 13 199 10 7 +-+ 155 13 155 10 +--R (- --- %i x - --- %i x + %i x )\|7 - --- x - --- x +--R 64 64 64 64 +--R + +--R 19 7 +--R -- x +--R 8 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 33 13 33 10 33 7 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x )\|2 \|7 +--R 128 128 64 +--R + +--R 77 13 77 10 77 7 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 11 14 11 11 11 8 +-+ +--+ +--R (- -- %i x - -- %i x - -- %i x )\|3 \|21 +--R 32 32 16 +--R + +--R 83 14 83 11 65 8 +-+ 39 14 39 11 +--R (-- %i x + -- %i x - -- %i x )\|7 + -- x + -- x +--R 32 32 32 32 32 +--R + +--R 153 8 +--R - --- x +--R 32 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 11 12 11 9 11 6 +-+ +-+ +--+ 29 12 29 9 1 6 +--R (- -- x - -- x - -- x )\|3 \|7 \|21 + -- x + -- x + - x +--R 32 32 16 2 2 8 +--R * +--R 1 3 4 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 16 1 13 1 10 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 1 16 1 13 1 10 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 896 896 448 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 17 1 14 1 11 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 1 17 1 14 1 11 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 896 896 448 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 15 3 12 3 9 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 1 15 1 12 1 9 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 896 896 448 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 17 1 14 1 11 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 17 1 14 1 11 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 448 448 224 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 18 1 15 1 12 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 18 1 15 1 12 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 448 448 224 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 16 3 13 3 10 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 16 1 13 1 10 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 448 448 224 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 16 1 13 1 10 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 1 16 1 13 1 10 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 896 896 448 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 17 1 14 5 11 6+----+3 +--R (- -- x - -- x + --- x )\|1372 +--R 49 49 392 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 17 1 14 1 11 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 17 1 14 1 11 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 448 448 224 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 18 1 15 1 12 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|7 +--R 1568 1568 784 +--R + +--R 25 18 25 15 17 12 +--R ---- x + ---- x - --- x +--R 1568 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 16 1 13 1 10 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 784 784 392 +--R + +--R 5 16 5 13 1 10 +-+ 1 16 +--R (- --- %i x - --- %i x + --- %i x )\|7 + -- x +--R 392 392 784 98 +--R + +--R 1 13 5 10 +--R -- x - --- x +--R 98 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 17 1 14 1 11 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 1 17 1 14 1 11 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 896 896 448 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 18 1 15 1 12 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|7 +--R 1568 1568 784 +--R + +--R 25 18 25 15 17 12 +--R ---- x + ---- x - --- x +--R 1568 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 18 1 15 1 12 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 18 1 15 1 12 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 448 448 224 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 9 19 9 16 3 13 6+----+3 +--R (- --- x - --- x + -- x )\|1372 +--R 784 784 98 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 17 1 14 1 11 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 784 784 392 +--R + +--R 17 17 17 14 1 11 +-+ 9 17 +--R (---- %i x + ---- %i x - --- %i x )\|7 - ---- x +--R 1568 1568 196 1568 +--R + +--R 9 14 3 11 +--R - ---- x + --- x +--R 1568 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 3 15 3 12 3 9 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 1 15 1 12 1 9 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 896 896 448 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 16 1 13 1 10 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 784 784 392 +--R + +--R 5 16 5 13 1 10 +-+ 1 16 +--R (--- %i x + --- %i x - --- %i x )\|7 + -- x +--R 392 392 784 98 +--R + +--R 1 13 5 10 +--R -- x - --- x +--R 98 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 16 3 13 3 10 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 16 1 13 1 10 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 448 448 224 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 17 1 14 1 11 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 784 784 392 +--R + +--R 17 17 17 14 1 11 +-+ 9 17 +--R (- ---- %i x - ---- %i x + --- %i x )\|7 - ---- x +--R 1568 1568 196 1568 +--R + +--R 9 14 3 11 +--R - ---- x + --- x +--R 1568 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 15 1 12 1 9 +-+ +-+ +--+ 23 15 23 12 +--R (--- x + --- x + --- x )\|3 \|7 \|21 - --- x - --- x +--R 784 784 392 392 392 +--R + +--R 1 9 +--R - -- x +--R 98 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 3 2 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 15 9 15 6 15 3 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (---- x + ---- x + --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (---- %i x + ---- %i x + --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (- ---- x - ---- x - --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 5 12 5 9 5 6 3+-+2 +--R (- ---- %i x - ---- %i x - --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- ---- x - ---- x - --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 15 10 15 7 15 4 3+-+2 +--R (---- %i x + ---- %i x + --- %i x )\|2 +--R 1568 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 5 10 5 7 5 4 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 31 11 31 8 1 5 +-+6+----+3 +--R (- --- x - --- x - --- x )\|7 \|1372 +--R 784 784 392 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (---- x + ---- x + --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (- ---- %i x - ---- %i x - --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 13 12 13 9 1 6 +-+ 5 12 +--R (--- x + --- x - -- x )\|7 + --- %i x +--R 392 392 98 784 +--R + +--R 5 9 5 6 +--R --- %i x + --- %i x +--R 784 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 +-+ +-+ +--+ +--R (---- %i x + ---- %i x + ---- %i x )\|3 \|7 \|21 +--R 2744 2744 1372 +--R + +--R 31 10 31 7 1 4 +-+ 257 10 +--R (---- x + ---- x + --- x )\|7 - ---- %i x +--R 1568 1568 784 1568 +--R + +--R 257 7 47 4 +--R - ---- %i x - --- %i x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 11 5 8 5 5 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 5 11 5 8 5 5 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 13 12 13 9 1 6 +-+ 5 12 +--R (--- x + --- x - -- x )\|7 - --- %i x +--R 392 392 98 784 +--R + +--R 5 9 5 6 +--R - --- %i x - --- %i x +--R 784 392 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (- ---- x - ---- x - --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 5 12 5 9 5 6 3+-+2 +--R (---- %i x + ---- %i x + --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 3 13 3 10 9 7 +-+6+----+3 +--R (- --- x - --- x + --- x )\|7 \|1372 +--R 112 112 392 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 +-+ +-+ +--+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|3 \|7 \|21 +--R 2744 2744 1372 +--R + +--R 3 11 3 8 9 5 +-+ 227 11 +--R (- --- x - --- x + --- x )\|7 + ---- %i x +--R 224 224 784 1568 +--R + +--R 227 8 17 5 +--R ---- %i x + --- %i x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 9 5 6 5 3 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 15 9 15 6 15 3 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 10 5 7 5 4 +-+ +-+ +--+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|3 \|7 \|21 +--R 2744 2744 1372 +--R + +--R 31 10 31 7 1 4 +-+ 257 10 +--R (---- x + ---- x + --- x )\|7 + ---- %i x +--R 1568 1568 784 1568 +--R + +--R 257 7 47 4 +--R ---- %i x + --- %i x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 10 5 7 5 4 3+-+2 +-+ +--R (- ---- x - ---- x - --- x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 15 10 15 7 15 4 3+-+2 +--R (- ---- %i x - ---- %i x - --- %i x )\|2 +--R 1568 1568 784 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 11 5 8 5 5 +-+ +-+ +--+ +--R (---- %i x + ---- %i x + ---- %i x )\|3 \|7 \|21 +--R 2744 2744 1372 +--R + +--R 3 11 3 8 9 5 +-+ 227 11 +--R (- --- x - --- x + --- x )\|7 - ---- %i x +--R 224 224 784 1568 +--R + +--R 227 8 17 5 +--R - ---- %i x - --- %i x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 +-+ +--+ +--R (--- x + --- x + --- x )\|3 \|21 +--R 392 392 196 +--R + +--R 41 9 41 6 11 3 +-+ +--R (- --- x - --- x - --- x )\|7 +--R 392 392 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 8 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 5 13 5 10 5 7 3+-+2 +-+ +--R (- --- x - --- x - -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 5 13 5 10 5 7 3+-+2 +--R (- --- %i x - --- %i x - -- %i x )\|2 +--R 128 128 64 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 14 5 11 5 8 3+-+2 +-+ +--R (--- x + --- x + -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 5 14 5 11 5 8 3+-+2 +--R (--- %i x + --- %i x + -- %i x )\|2 +--R 128 128 64 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (--- x + --- x + -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 15 12 15 9 15 6 3+-+2 +--R (- --- %i x - --- %i x - -- %i x )\|2 +--R 128 128 64 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 14 5 11 5 8 3+-+2 +-+ +--R (-- x + -- x + -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 5 14 5 11 5 8 3+-+2 +--R (-- %i x + -- %i x + -- %i x )\|2 +--R 64 64 32 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 15 5 12 5 9 3+-+2 +-+ +--R (- -- x - -- x - -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 5 15 5 12 5 9 3+-+2 +--R (- -- %i x - -- %i x - -- %i x )\|2 +--R 64 64 32 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 13 5 10 5 7 3+-+2 +-+ +--R (- -- x - -- x - -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 15 13 15 10 15 7 3+-+2 +--R (-- %i x + -- %i x + -- %i x )\|2 +--R 64 64 32 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 13 5 10 5 7 3+-+2 +-+ +--R (- --- x - --- x - -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 5 13 5 10 5 7 3+-+2 +--R (--- %i x + --- %i x + -- %i x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 101 14 101 11 1 8 +-+ +--R (- --- x - --- x + -- x )\|7 +--R 112 112 14 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 14 5 11 5 8 3+-+2 +-+ +--R (-- x + -- x + -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 5 14 5 11 5 8 3+-+2 +--R (- -- %i x - -- %i x - -- %i x )\|2 +--R 64 64 32 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 167 15 167 12 43 9 +-+ 5 15 5 12 +--R (--- x + --- x - --- x )\|7 + -- %i x + -- %i x +--R 224 224 112 32 32 +--R + +--R 5 9 +--R -- %i x +--R 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 13 5 10 5 7 +-+ +-+ +--+ +--R (--- %i x + --- %i x + -- %i x )\|3 \|7 \|21 +--R 112 112 56 +--R + +--R 101 13 101 10 1 7 +-+ 121 13 121 10 +--R (--- x + --- x - -- x )\|7 - --- %i x - --- %i x +--R 224 224 28 32 32 +--R + +--R 7 +--R - %i x +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 14 5 11 5 8 3+-+2 +-+ +--R (--- x + --- x + -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 5 14 5 11 5 8 3+-+2 +--R (- --- %i x - --- %i x - -- %i x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 167 15 167 12 43 9 +-+ 5 15 5 12 +--R (--- x + --- x - --- x )\|7 - -- %i x - -- %i x +--R 224 224 112 32 32 +--R + +--R 5 9 +--R - -- %i x +--R 16 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 15 5 12 5 9 3+-+2 +-+ +--R (- -- x - -- x - -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 5 15 5 12 5 9 3+-+2 +--R (-- %i x + -- %i x + -- %i x )\|2 +--R 64 64 32 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 33 16 33 13 39 10 +-+ +--R (- -- x - -- x + -- x )\|7 +--R 56 56 56 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 14 5 11 5 8 +-+ +-+ +--+ +--R (- --- %i x - --- %i x - -- %i x )\|3 \|7 \|21 +--R 112 112 56 +--R + +--R 33 14 33 11 39 8 +-+ 53 14 53 11 +--R (- --- x - --- x + --- x )\|7 + -- %i x + -- %i x +--R 112 112 112 16 16 +--R + +--R 1 8 +--R -- %i x +--R 16 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 12 5 9 5 6 3+-+2 +-+ +--R (--- x + --- x + -- x )\|2 \|7 +--R 128 128 64 +--R + +--R 15 12 15 9 15 6 3+-+2 +--R (--- %i x + --- %i x + -- %i x )\|2 +--R 128 128 64 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 13 5 10 5 7 +-+ +-+ +--+ +--R (- --- %i x - --- %i x - -- %i x )\|3 \|7 \|21 +--R 112 112 56 +--R + +--R 101 13 101 10 1 7 +-+ 121 13 121 10 +--R (--- x + --- x - -- x )\|7 + --- %i x + --- %i x +--R 224 224 28 32 32 +--R + +--R 7 +--R %i x +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 13 5 10 5 7 3+-+2 +-+ +--R (- -- x - -- x - -- x )\|2 \|7 +--R 64 64 32 +--R + +--R 15 13 15 10 15 7 3+-+2 +--R (- -- %i x - -- %i x - -- %i x )\|2 +--R 64 64 32 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 5 14 5 11 5 8 +-+ +-+ +--+ +--R (--- %i x + --- %i x + -- %i x )\|3 \|7 \|21 +--R 112 112 56 +--R + +--R 33 14 33 11 39 8 +-+ 53 14 53 11 +--R (- --- x - --- x + --- x )\|7 - -- %i x - -- %i x +--R 112 112 112 16 16 +--R + +--R 1 8 +--R - -- %i x +--R 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 12 5 9 5 6 +-+ +--+ 17 12 17 9 31 6 +-+ +--R (-- x + -- x + - x )\|3 \|21 + (- -- x - -- x - -- x )\|7 +--R 16 16 8 7 7 28 +--R * +--R 1 3 5 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 5 16 5 13 5 10 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 5 16 5 13 5 10 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 6272 6272 3136 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 17 5 14 5 11 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 5 17 5 14 5 11 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 6272 6272 3136 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 15 5 12 5 9 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 15 15 15 12 15 9 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 6272 6272 3136 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 17 5 14 5 11 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 5 17 5 14 5 11 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 18 5 15 5 12 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 5 18 5 15 5 12 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 16 5 13 5 10 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 15 16 15 13 15 10 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 5 16 5 13 5 10 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 5 16 5 13 5 10 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 6272 6272 3136 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 17 1 14 1 11 +-+6+----+3 +--R (- -- x - -- x + -- x )\|7 \|1372 +--R 98 98 56 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 17 5 14 5 11 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 5 17 5 14 5 11 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 11 18 11 15 19 12 +-+ 5 18 +--R (---- x + ---- x - --- x )\|7 + ---- %i x +--R 1568 1568 784 1568 +--R + +--R 5 15 5 12 +--R ---- %i x + --- %i x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 16 5 13 5 10 +-+ +-+ +--+ +--R (---- %i x + ---- %i x + ---- %i x )\|3 \|7 \|21 +--R 5488 5488 2744 +--R + +--R 1 16 1 13 1 10 +-+ 19 16 +--R (--- x + --- x - --- x )\|7 - --- %i x +--R 196 196 112 392 +--R + +--R 19 13 29 10 +--R - --- %i x + --- %i x +--R 392 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 17 5 14 5 11 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 5 17 5 14 5 11 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 6272 6272 3136 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 11 18 11 15 19 12 +-+ 5 18 +--R (---- x + ---- x - --- x )\|7 - ---- %i x +--R 1568 1568 784 1568 +--R + +--R 5 15 5 12 +--R - ---- %i x - --- %i x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 18 5 15 5 12 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 5 18 5 15 5 12 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 3 19 3 16 3 13 +-+6+----+3 +--R (- --- x - --- x + -- x )\|7 \|1372 +--R 784 784 98 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 17 5 14 5 11 +-+ +-+ +--+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|3 \|7 \|21 +--R 5488 5488 2744 +--R + +--R 3 17 3 14 3 11 +-+ 61 17 +--R (- ---- x - ---- x + --- x )\|7 + ---- %i x +--R 1568 1568 196 1568 +--R + +--R 61 14 11 11 +--R ---- %i x - --- %i x +--R 1568 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 15 5 12 5 9 3+-+2 +-+ +--R (---- x + ---- x + ---- x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 15 15 15 12 15 9 3+-+2 +--R (---- %i x + ---- %i x + ---- %i x )\|2 +--R 6272 6272 3136 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 16 5 13 5 10 +-+ +-+ +--+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|3 \|7 \|21 +--R 5488 5488 2744 +--R + +--R 1 16 1 13 1 10 +-+ 19 16 +--R (--- x + --- x - --- x )\|7 + --- %i x +--R 196 196 112 392 +--R + +--R 19 13 29 10 +--R --- %i x - --- %i x +--R 392 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 16 5 13 5 10 3+-+2 +-+ +--R (- ---- x - ---- x - ---- x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 15 16 15 13 15 10 3+-+2 +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 +--R 3136 3136 1568 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 5 17 5 14 5 11 +-+ +-+ +--+ +--R (---- %i x + ---- %i x + ---- %i x )\|3 \|7 \|21 +--R 5488 5488 2744 +--R + +--R 3 17 3 14 3 11 +-+ 61 17 +--R (- ---- x - ---- x + --- x )\|7 - ---- %i x +--R 1568 1568 196 1568 +--R + +--R 61 14 11 11 +--R - ---- %i x + --- %i x +--R 1568 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 15 5 12 5 9 +-+ +--+ +--R (--- x + --- x + --- x )\|3 \|21 +--R 784 784 392 +--R + +--R 13 15 13 12 1 9 +-+ +--R (- --- x - --- x + -- x )\|7 +--R 392 392 98 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 2 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 3 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x)\|2 \|7 +--R 336 336 168 +--R + +--R 1 7 1 4 1 3+-+2 +--R (-- x + -- x + -- x)\|2 +--R 48 48 24 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 336 336 168 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 48 48 24 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 6 1 3 1 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i)\|2 \|7 +--R 112 112 56 +--R + +--R 1 6 1 3 1 3+-+2 +--R (- -- x - -- x - --)\|2 +--R 48 48 24 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x )\|2 \|7 +--R 168 168 84 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 24 24 12 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x )\|2 \|7 +--R 168 168 84 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (-- x + -- x + -- x )\|2 +--R 24 24 12 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (- -- %i x - -- %i x - -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 1 7 1 4 1 3+-+2 +--R (-- x + -- x + -- x)\|2 +--R 24 24 12 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x)\|2 \|7 +--R 336 336 168 +--R + +--R 1 7 1 4 1 3+-+2 +--R (-- x + -- x + -- x)\|2 +--R 48 48 24 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 2 8 2 5 1 2 +--R - x + - x + - x +--R 3 3 3 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (--- %i x + --- %i x + -- %i x )\|2 \|7 +--R 168 168 84 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 24 24 12 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 9 1 6 1 3 +-+ 7 9 7 6 1 3 +--R (- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x - - x +--R 84 84 42 12 12 6 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 7 1 4 1 +-+ +--+ +--R (- -- %i x - -- %i x - -- %i x)\|3 \|21 +--R 42 42 21 +--R + +--R 8 7 8 4 11 +-+ 1 7 1 4 1 +--R (-- %i x + -- %i x + -- %i x)\|7 - - x - - x - - x +--R 21 21 42 3 3 6 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 8 1 5 1 2 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 336 336 168 +--R + +--R 1 8 1 5 1 2 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 48 48 24 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 9 1 6 1 3 +-+ 7 9 7 6 1 3 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x - - x +--R 84 84 42 12 12 6 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i x )\|2 \|7 +--R 168 168 84 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (-- x + -- x + -- x )\|2 +--R 24 24 12 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 10 1 7 +--R - x + - x +--R 2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 1 2 +-+ +--+ +--R (-- %i x + -- %i x + -- %i x )\|3 \|21 +--R 42 42 21 +--R + +--R 29 8 29 5 4 2 +-+ 1 8 1 5 +--R (- -- %i x - -- %i x - -- %i x )\|7 + - x + - x +--R 84 84 21 4 4 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 6 1 3 1 3+-+2 +-+ +--R (- --- %i x - --- %i x - -- %i)\|2 \|7 +--R 112 112 56 +--R + +--R 1 6 1 3 1 3+-+2 +--R (- -- x - -- x - --)\|2 +--R 48 48 24 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 7 1 4 1 +-+ +--+ +--R (-- %i x + -- %i x + -- %i x)\|3 \|21 +--R 42 42 21 +--R + +--R 8 7 8 4 11 +-+ 1 7 1 4 1 +--R (- -- %i x - -- %i x - -- %i x)\|7 - - x - - x - - x +--R 21 21 42 3 3 6 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 7 1 4 1 3+-+2 +-+ +--R (-- %i x + -- %i x + -- %i x)\|2 \|7 +--R 56 56 28 +--R + +--R 1 7 1 4 1 3+-+2 +--R (-- x + -- x + -- x)\|2 +--R 24 24 12 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 8 1 5 1 2 +-+ +--+ +--R (- -- %i x - -- %i x - -- %i x )\|3 \|21 +--R 42 42 21 +--R + +--R 29 8 29 5 4 2 +-+ 1 8 1 5 +--R (-- %i x + -- %i x + -- %i x )\|7 + - x + - x +--R 84 84 21 4 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 6 1 3 1 +-+ +-+ +--+ 5 6 5 3 4 +--R (- -- x - -- x - --)\|3 \|7 \|21 + - x + - x + - +--R 42 42 21 3 3 3 +--R * +--R 1 3 12 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (---- x + ---- x + --- x )\|2 +--R 1344 1344 672 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (- ---- x - ---- x - --- x )\|2 +--R 1344 1344 672 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (- ---- x - ---- x - --- x )\|2 +--R 1344 1344 672 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 4704 4704 2352 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 672 672 336 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 12 1 9 1 6 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 4704 4704 2352 +--R + +--R 1 12 1 9 1 6 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 672 672 336 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 672 672 336 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (---- x + ---- x + --- x )\|2 +--R 1344 1344 672 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 53 11 53 8 11 5 6+----+3 +--R (---- x + ---- x + ---- x )\|1372 +--R 2352 2352 1176 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 4704 4704 2352 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 672 672 336 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 12 1 9 1 6 +-+ 23 12 +--R (- ---- %i x - ---- %i x - ---- %i x )\|7 - ---- x +--R 2352 2352 1176 1176 +--R + +--R 23 9 1 6 +--R - ---- x - --- x +--R 1176 294 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 10 1 7 1 4 +-+ +--+ +--R (- ---- %i x - ---- %i x - --- %i x )\|3 \|21 +--R 1176 1176 588 +--R + +--R 61 10 61 7 19 4 +-+ 53 10 +--R (---- %i x + ---- %i x + ---- %i x )\|7 - ---- x +--R 4704 4704 2352 4704 +--R + +--R 53 7 11 4 +--R - ---- x - ---- x +--R 4704 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 11 1 8 1 5 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 1 11 1 8 1 5 3+-+2 +--R (- ---- x - ---- x - --- x )\|2 +--R 1344 1344 672 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 12 1 9 1 6 +-+ 23 12 +--R (---- %i x + ---- %i x + ---- %i x )\|7 - ---- x +--R 2352 2352 1176 1176 +--R + +--R 23 9 1 6 +--R - ---- x - --- x +--R 1176 294 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 12 1 9 1 6 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 4704 4704 2352 +--R + +--R 1 12 1 9 1 6 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 672 672 336 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 13 13 13 10 1 7 6+----+3 +--R (--- x + --- x - --- x )\|1372 +--R 784 784 392 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 +-+ +--+ +--R (---- %i x + ---- %i x + --- %i x )\|3 \|21 +--R 1176 1176 588 +--R + +--R 55 11 55 8 13 5 +-+ 13 11 +--R (- ---- %i x - ---- %i x - ---- %i x )\|7 + ---- x +--R 4704 4704 2352 1568 +--R + +--R 13 8 1 5 +--R ---- x - --- x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 9 1 6 1 3 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 9 1 6 1 3 3+-+2 +--R (- ---- x - ---- x - --- x )\|2 +--R 1344 1344 672 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 10 1 7 1 4 +-+ +--+ +--R (---- %i x + ---- %i x + --- %i x )\|3 \|21 +--R 1176 1176 588 +--R + +--R 61 10 61 7 19 4 +-+ 53 10 +--R (- ---- %i x - ---- %i x - ---- %i x )\|7 - ---- x +--R 4704 4704 2352 4704 +--R + +--R 53 7 11 4 +--R - ---- x - ---- x +--R 4704 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 10 1 7 1 4 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1568 1568 784 +--R + +--R 1 10 1 7 1 4 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 672 672 336 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 11 1 8 1 5 +-+ +--+ +--R (- ---- %i x - ---- %i x - --- %i x )\|3 \|21 +--R 1176 1176 588 +--R + +--R 55 11 55 8 13 5 +-+ 13 11 +--R (---- %i x + ---- %i x + ---- %i x )\|7 + ---- x +--R 4704 4704 2352 1568 +--R + +--R 13 8 1 5 +--R ---- x - --- x +--R 1568 784 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 +-+ +-+ +--+ 67 9 67 6 +--R (- ---- x - ---- x - --- x )\|3 \|7 \|21 + ---- x + ---- x +--R 1176 1176 588 1176 1176 +--R + +--R 25 3 +--R --- x +--R 588 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 9 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 23 13 23 10 23 7 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 5376 5376 2688 +--R + +--R 23 13 23 10 23 7 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 768 768 384 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 14 23 11 23 8 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 5376 5376 2688 +--R + +--R 23 14 23 11 23 8 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 768 768 384 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 12 23 9 23 6 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1792 1792 896 +--R + +--R 23 12 23 9 23 6 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 768 768 384 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 23 14 23 11 23 8 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 2688 2688 1344 +--R + +--R 23 14 23 11 23 8 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 384 384 192 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 15 23 12 23 9 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 2688 2688 1344 +--R + +--R 23 15 23 12 23 9 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 384 384 192 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 13 23 10 23 7 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 896 896 448 +--R + +--R 23 13 23 10 23 7 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 384 384 192 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 23 13 23 10 23 7 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 5376 5376 2688 +--R + +--R 23 13 23 10 23 7 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 768 768 384 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 65 14 65 11 1 8 +--R -- x + -- x - -- x +--R 96 96 12 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 14 23 11 23 8 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 2688 2688 1344 +--R + +--R 23 14 23 11 23 8 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 384 384 192 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 23 15 23 12 23 9 +-+ 107 15 +--R (- ---- %i x - ---- %i x - --- %i x )\|7 - --- x +--R 1344 1344 672 192 +--R + +--R 107 12 31 9 +--R - --- x + -- x +--R 192 96 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 13 23 10 23 7 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 672 672 336 +--R + +--R 547 13 547 10 2 7 +-+ 65 13 65 10 +--R (---- %i x + ---- %i x + -- %i x )\|7 - --- x - --- x +--R 1344 1344 21 192 192 +--R + +--R 1 7 +--R -- x +--R 24 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 23 14 23 11 23 8 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 5376 5376 2688 +--R + +--R 23 14 23 11 23 8 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 768 768 384 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 23 15 23 12 23 9 +-+ 107 15 +--R (---- %i x + ---- %i x + --- %i x )\|7 - --- x +--R 1344 1344 672 192 +--R + +--R 107 12 31 9 +--R - --- x + -- x +--R 192 96 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 15 23 12 23 9 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 2688 2688 1344 +--R + +--R 23 15 23 12 23 9 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 384 384 192 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 7 16 7 13 9 10 +--R -- x + -- x - -- x +--R 16 16 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 14 23 11 23 8 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 672 672 336 +--R + +--R 239 14 239 11 5 8 +-+ 7 14 7 11 +--R (- --- %i x - --- %i x + --- %i x )\|7 + -- x + -- x +--R 672 672 672 32 32 +--R + +--R 9 8 +--R - -- x +--R 32 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 23 12 23 9 23 6 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1792 1792 896 +--R + +--R 23 12 23 9 23 6 3+-+2 +--R (- --- x - --- x - --- x )\|2 +--R 768 768 384 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 23 13 23 10 23 7 +-+ +--+ +--R (--- %i x + --- %i x + --- %i x )\|3 \|21 +--R 672 672 336 +--R + +--R 547 13 547 10 2 7 +-+ 65 13 65 10 +--R (- ---- %i x - ---- %i x - -- %i x )\|7 - --- x - --- x +--R 1344 1344 21 192 192 +--R + +--R 1 7 +--R -- x +--R 24 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 13 23 10 23 7 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 896 896 448 +--R + +--R 23 13 23 10 23 7 3+-+2 +--R (--- x + --- x + --- x )\|2 +--R 384 384 192 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 23 14 23 11 23 8 +-+ +--+ +--R (- --- %i x - --- %i x - --- %i x )\|3 \|21 +--R 672 672 336 +--R + +--R 239 14 239 11 5 8 +-+ 7 14 7 11 9 8 +--R (--- %i x + --- %i x - --- %i x )\|7 + -- x + -- x - -- x +--R 672 672 672 32 32 32 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 12 23 9 23 6 +-+ +-+ +--+ 11 12 11 9 19 6 +--R (- --- x - --- x - --- x )\|3 \|7 \|21 + -- x + -- x + -- x +--R 672 672 336 6 6 24 +--R * +--R 1 3 6 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 16 1 13 1 10 3+-+2 +-+ +--R (----- %i x + ----- %i x + ---- %i x )\|2 \|7 +--R 18816 18816 9408 +--R + +--R 1 16 1 13 1 10 3+-+2 +--R (---- x + ---- x + ---- x )\|2 +--R 2688 2688 1344 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 17 1 14 1 11 3+-+2 +-+ +--R (- ----- %i x - ----- %i x - ---- %i x )\|2 \|7 +--R 18816 18816 9408 +--R + +--R 1 17 1 14 1 11 3+-+2 +--R (- ---- x - ---- x - ---- x )\|2 +--R 2688 2688 1344 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 15 1 12 1 9 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 1 15 1 12 1 9 3+-+2 +--R (- ---- x - ---- x - ---- x )\|2 +--R 2688 2688 1344 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 17 1 14 1 11 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 1 17 1 14 1 11 3+-+2 +--R (- ---- x - ---- x - --- x )\|2 +--R 1344 1344 672 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 18 1 15 1 12 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 1 18 1 15 1 12 3+-+2 +--R (---- x + ---- x + --- x )\|2 +--R 1344 1344 672 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 16 1 13 1 10 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 16 1 13 1 10 3+-+2 +--R (---- x + ---- x + --- x )\|2 +--R 1344 1344 672 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 16 1 13 1 10 3+-+2 +-+ +--R (- ----- %i x - ----- %i x - ---- %i x )\|2 \|7 +--R 18816 18816 9408 +--R + +--R 1 16 1 13 1 10 3+-+2 +--R (---- x + ---- x + ---- x )\|2 +--R 2688 2688 1344 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 17 1 14 5 11 6+----+3 +--R (--- x + --- x - ---- x )\|1372 +--R 147 147 1176 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 17 1 14 1 11 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 1 17 1 14 1 11 3+-+2 +--R (- ---- x - ---- x - --- x )\|2 +--R 1344 1344 672 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 18 1 15 1 12 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|7 +--R 4704 4704 2352 +--R + +--R 25 18 25 15 17 12 +--R - ---- x - ---- x + ---- x +--R 4704 4704 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 16 1 13 1 10 +-+ +--+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|3 \|21 +--R 2352 2352 1176 +--R + +--R 5 16 5 13 1 10 +-+ 1 16 +--R (---- %i x + ---- %i x - ---- %i x )\|7 - --- x +--R 1176 1176 2352 294 +--R + +--R 1 13 5 10 +--R - --- x + ---- x +--R 294 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 17 1 14 1 11 3+-+2 +-+ +--R (----- %i x + ----- %i x + ---- %i x )\|2 \|7 +--R 18816 18816 9408 +--R + +--R 1 17 1 14 1 11 3+-+2 +--R (- ---- x - ---- x - ---- x )\|2 +--R 2688 2688 1344 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 18 1 15 1 12 +-+ 25 18 +--R (---- %i x + ---- %i x + ---- %i x )\|7 - ---- x +--R 4704 4704 2352 4704 +--R + +--R 25 15 17 12 +--R - ---- x + ---- x +--R 4704 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 18 1 15 1 12 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 9408 9408 4704 +--R + +--R 1 18 1 15 1 12 3+-+2 +--R (---- x + ---- x + --- x )\|2 +--R 1344 1344 672 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 3 19 3 16 1 13 6+----+3 +--R (--- x + --- x - -- x )\|1372 +--R 784 784 98 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 17 1 14 1 11 +-+ +--+ +--R (---- %i x + ---- %i x + ---- %i x )\|3 \|21 +--R 2352 2352 1176 +--R + +--R 17 17 17 14 1 11 +-+ 3 17 +--R (- ---- %i x - ---- %i x + --- %i x )\|7 + ---- x +--R 4704 4704 588 1568 +--R + +--R 3 14 1 11 +--R ---- x - --- x +--R 1568 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 15 1 12 1 9 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|2 \|7 +--R 6272 6272 3136 +--R + +--R 1 15 1 12 1 9 3+-+2 +--R (- ---- x - ---- x - ---- x )\|2 +--R 2688 2688 1344 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 16 1 13 1 10 +-+ +--+ +--R (---- %i x + ---- %i x + ---- %i x )\|3 \|21 +--R 2352 2352 1176 +--R + +--R 5 16 5 13 1 10 +-+ 1 16 +--R (- ---- %i x - ---- %i x + ---- %i x )\|7 - --- x +--R 1176 1176 2352 294 +--R + +--R 1 13 5 10 +--R - --- x + ---- x +--R 294 2352 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 16 1 13 1 10 3+-+2 +-+ +--R (---- %i x + ---- %i x + ---- %i x )\|2 \|7 +--R 3136 3136 1568 +--R + +--R 1 16 1 13 1 10 3+-+2 +--R (---- x + ---- x + --- x )\|2 +--R 1344 1344 672 +--R * +--R +------------+ +--R 6+----+3 3| +-+ +--R \|1372 \|- %i\|7 + 1 +--R + +--R 1 17 1 14 1 11 +-+ +--+ +--R (- ---- %i x - ---- %i x - ---- %i x )\|3 \|21 +--R 2352 2352 1176 +--R + +--R 17 17 17 14 1 11 +-+ 3 17 +--R (---- %i x + ---- %i x - --- %i x )\|7 + ---- x +--R 4704 4704 588 1568 +--R + +--R 3 14 1 11 +--R ---- x - --- x +--R 1568 196 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 15 1 12 1 9 +-+ +-+ +--+ 23 15 +--R (- ---- x - ---- x - ---- x )\|3 \|7 \|21 + ---- x +--R 2352 2352 1176 1176 +--R + +--R 23 12 1 9 +--R ---- x + --- x +--R 1176 294 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R 1 3 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 19 1 16 1 13 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1344 1344 672 +--R + +--R 1 19 1 16 1 13 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 192 192 96 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 20 1 17 1 14 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1344 1344 672 +--R + +--R 1 20 1 17 1 14 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 192 192 96 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 18 1 15 1 12 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 448 448 224 +--R + +--R 1 18 1 15 1 12 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 192 192 96 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 20 1 17 1 14 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 672 672 336 +--R + +--R 1 20 1 17 1 14 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 96 96 48 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 21 1 18 1 15 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 672 672 336 +--R + +--R 1 21 1 18 1 15 3+-+2 +--R (-- x + -- x + -- x )\|2 +--R 96 96 48 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 19 1 16 1 13 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 224 224 112 +--R + +--R 1 19 1 16 1 13 3+-+2 +--R (-- x + -- x + -- x )\|2 +--R 96 96 48 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R * +--R +----------+ +--R 3| +-+ +--R \|%i\|7 + 1 +--R + +--R 1 19 1 16 1 13 3+-+2 +-+ +--R (- ---- %i x - ---- %i x - --- %i x )\|2 \|7 +--R 1344 1344 672 +--R + +--R 1 19 1 16 1 13 3+-+2 +--R (--- x + --- x + -- x )\|2 +--R 192 192 96 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 20 1 17 1 14 +--R -- x + -- x - - x +--R 24 24 6 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 20 1 17 1 14 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 672 672 336 +--R + +--R 1 20 1 17 1 14 3+-+2 +--R (- -- x - -- x - -- x )\|2 +--R 96 96 48 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 21 1 18 1 15 +-+ 1 21 1 18 +--R (- --- %i x - --- %i x - --- %i x )\|7 - -- x - -- x +--R 336 336 168 48 48 +--R + +--R 5 15 +--R -- x +--R 24 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 19 1 16 1 13 +-+ +--+ +--R (- --- %i x - --- %i x - -- %i x )\|3 \|21 +--R 168 168 84 +--R + +--R 11 19 11 16 5 13 +-+ 1 19 1 16 1 13 +--R (--- %i x + --- %i x - -- %i x )\|7 - -- x - -- x + -- x +--R 336 336 84 48 48 12 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 20 1 17 1 14 3+-+2 +-+ +--R (---- %i x + ---- %i x + --- %i x )\|2 \|7 +--R 1344 1344 672 +--R + +--R 1 20 1 17 1 14 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 192 192 96 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 21 1 18 1 15 +-+ 1 21 1 18 +--R (--- %i x + --- %i x + --- %i x )\|7 - -- x - -- x +--R 336 336 168 48 48 +--R + +--R 5 15 +--R -- x +--R 24 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 21 1 18 1 15 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 672 672 336 +--R + +--R 1 21 1 18 1 15 3+-+2 +--R (-- x + -- x + -- x )\|2 +--R 96 96 48 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 16 +--R - - x +--R 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 20 1 17 1 14 +-+ +--+ +--R (--- %i x + --- %i x + -- %i x )\|3 \|21 +--R 168 168 84 +--R + +--R 1 20 1 17 13 14 +-+ 1 14 +--R (- -- %i x - -- %i x + --- %i x )\|7 - - x +--R 42 42 168 8 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 18 1 15 1 12 3+-+2 +-+ +--R (- --- %i x - --- %i x - --- %i x )\|2 \|7 +--R 448 448 224 +--R + +--R 1 18 1 15 1 12 3+-+2 +--R (- --- x - --- x - -- x )\|2 +--R 192 192 96 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 19 1 16 1 13 +-+ +--+ +--R (--- %i x + --- %i x + -- %i x )\|3 \|21 +--R 168 168 84 +--R + +--R 11 19 11 16 5 13 +-+ 1 19 1 16 1 13 +--R (- --- %i x - --- %i x + -- %i x )\|7 - -- x - -- x + -- x +--R 336 336 84 48 48 12 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 19 1 16 1 13 3+-+2 +-+ +--R (--- %i x + --- %i x + --- %i x )\|2 \|7 +--R 224 224 112 +--R + +--R 1 19 1 16 1 13 3+-+2 +--R (-- x + -- x + -- x )\|2 +--R 96 96 48 +--R * +--R +------------+ +--R 3| +-+ +--R \|- %i\|7 + 1 +--R + +--R 1 20 1 17 1 14 +-+ +--+ +--R (- --- %i x - --- %i x - -- %i x )\|3 \|21 +--R 168 168 84 +--R + +--R 1 20 1 17 13 14 +-+ 1 14 +--R (-- %i x + -- %i x - --- %i x )\|7 - - x +--R 42 42 168 8 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 18 1 15 1 12 +-+ +-+ +--+ 1 18 1 15 1 12 +--R (- --- x - --- x - -- x )\|3 \|7 \|21 + - x + - x - - x +--R 168 168 84 6 6 6 +--R / +--R +--------------+2 +--R 8 5 2 | 1 +-+ 1 +--R (x + x + 2x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 9 6 3 | 1 +-+ 1 +--R (- x - x - 2x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 7 1 4 +-+ 1 7 1 4 +--R (- %i x + - %i x + %i x)\|7 - - x - - x - x +--R 2 2 2 2 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 9 6 3 | 1 +-+ 1 +--R (- x - x - 2x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 10 7 4 | 1 +-+ 1 +--R (x + x + 2x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 2 +-+ 1 8 1 5 2 +--R (- - %i x - - %i x - %i x )\|7 + - x + - x + x +--R 2 2 2 2 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 7 1 4 +-+ 1 7 1 4 +--R ((- - %i x - - %i x - %i x)\|7 - - x - - x - x) +--R 2 2 2 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 1 8 1 5 2 +-+ 1 8 1 5 2 | 1 +-+ 1 +--R ((- %i x + - %i x + %i x )\|7 + - x + - x + x ) 3|- - %i\|7 + - +--R 2 2 2 2 \| 2 2 +--R + +--R 6 3 +--R 2x + 2x + 4 +--R * +--R 1 3 12 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 8 5 2 | 1 +-+ 1 +--R (6x + 6x + 12x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 9 6 3 | 1 +-+ 1 +--R (- 6x - 6x - 12x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 7 4 +-+ 7 4 +--R (3%i x + 3%i x + 6%i x)\|7 - 3x - 3x - 6x +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 9 6 3 | 1 +-+ 1 +--R (- 6x - 6x - 12x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 10 7 4 | 1 +-+ 1 +--R (6x + 6x + 12x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 8 5 2 +-+ 8 5 2 +--R (- 3%i x - 3%i x - 6%i x )\|7 + 3x + 3x + 6x +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 7 4 +-+ 7 4 | 1 +-+ 1 +--R ((- 3%i x - 3%i x - 6%i x)\|7 - 3x - 3x - 6x) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 8 5 2 +-+ 8 5 2 | 1 +-+ 1 +--R ((3%i x + 3%i x + 6%i x )\|7 + 3x + 3x + 6x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 6 3 +--R 12x + 12x + 24 +--R * +--R 1 3 2 1 3 10 +--R cos(- atan(----)) sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R +--------------+2 +--R 5 11 5 8 5 5 +-+6+----+3 | 1 +-+ 1 +--R (--- x + --- x + -- x )\|7 \|1372 3|- - %i\|7 + - +--R 196 196 98 \| 2 2 +--R + +--R +--------------+ +--R 5 12 5 9 5 6 +-+6+----+3 | 1 +-+ 1 +--R (- --- x - --- x - -- x )\|7 \|1372 3|- - %i\|7 + - +--R 196 196 98 \| 2 2 +--R + +--R 5 10 5 7 5 4 +-+ 5 10 5 7 +--R (- --- x - --- x - --- x )\|7 + -- %i x + -- %i x +--R 392 392 196 56 56 +--R + +--R 5 4 +--R -- %i x +--R 28 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 5 12 5 9 5 6 +-+6+----+3 | 1 +-+ 1 +--R (- --- x - --- x - -- x )\|7 \|1372 3|- - %i\|7 + - +--R 196 196 98 \| 2 2 +--R + +--R +--------------+ +--R 5 13 5 10 5 7 +-+6+----+3 | 1 +-+ 1 +--R (--- x + --- x + -- x )\|7 \|1372 3|- - %i\|7 + - +--R 196 196 98 \| 2 2 +--R + +--R 5 11 5 8 5 5 +-+ 5 11 5 8 +--R (--- x + --- x + --- x )\|7 - -- %i x - -- %i x +--R 392 392 196 56 56 +--R + +--R 5 5 +--R - -- %i x +--R 28 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 10 5 7 5 4 +-+ 5 10 5 7 +--R (- --- x - --- x - --- x )\|7 - -- %i x - -- %i x +--R 392 392 196 56 56 +--R + +--R 5 4 +--R - -- %i x +--R 28 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 5 5 +-+ 5 11 5 8 5 5 +--R ((--- x + --- x + --- x )\|7 + -- %i x + -- %i x + -- %i x ) +--R 392 392 196 56 56 28 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 9 5 6 5 3 +-+6+----+3 +--R (-- x + -- x + -- x )\|7 \|1372 +--R 98 98 49 +--R * +--R 1 3 9 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 8 5 2 | 1 +-+ 1 +--R (15x + 15x + 30x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 9 6 3 | 1 +-+ 1 +--R (- 15x - 15x - 30x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 7 15 4 +-+ 15 7 15 4 +--R (-- %i x + -- %i x + 15%i x)\|7 - -- x - -- x - 15x +--R 2 2 2 2 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 9 6 3 | 1 +-+ 1 +--R (- 15x - 15x - 30x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 10 7 4 | 1 +-+ 1 +--R (15x + 15x + 30x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 8 15 5 2 +-+ 15 8 15 5 2 +--R (- -- %i x - -- %i x - 15%i x )\|7 + -- x + -- x + 15x +--R 2 2 2 2 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 15 7 15 4 +-+ 15 7 15 4 +--R ((- -- %i x - -- %i x - 15%i x)\|7 - -- x - -- x - 15x) +--R 2 2 2 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 8 15 5 2 +-+ 15 8 15 5 2 +--R ((-- %i x + -- %i x + 15%i x )\|7 + -- x + -- x + 15x ) +--R 2 2 2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 6 3 +--R 30x + 30x + 60 +--R * +--R 1 3 4 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 3 11 3 8 3 5 6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|1372 3|- - %i\|7 + - +--R 28 28 14 \| 2 2 +--R + +--R +--------------+ +--R 3 12 3 9 3 6 6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|1372 3|- - %i\|7 + - +--R 28 28 14 \| 2 2 +--R + +--R 3 10 3 7 3 4 +-+ 3 10 3 7 +--R (- -- %i x - -- %i x - -- %i x )\|7 + -- x + -- x +--R 56 56 28 56 56 +--R + +--R 3 4 +--R -- x +--R 28 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 3 12 3 9 3 6 6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|1372 3|- - %i\|7 + - +--R 28 28 14 \| 2 2 +--R + +--R +--------------+ +--R 3 13 3 10 3 7 6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|1372 3|- - %i\|7 + - +--R 28 28 14 \| 2 2 +--R + +--R 3 11 3 8 3 5 +-+ 3 11 3 8 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x +--R 56 56 28 56 56 +--R + +--R 3 5 +--R - -- x +--R 28 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 3 10 3 7 3 4 +-+ 3 10 3 7 +--R (-- %i x + -- %i x + -- %i x )\|7 + -- x + -- x +--R 56 56 28 56 56 +--R + +--R 3 4 +--R -- x +--R 28 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 11 3 8 3 5 +-+ 3 11 3 8 +--R (- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x +--R 56 56 28 56 56 +--R + +--R 3 5 +--R - -- x +--R 28 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 9 3 6 3 3 6+----+3 +--R (- -- x - -- x - - x )\|1372 +--R 14 14 7 +--R * +--R 1 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 3 8 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 8 5 2 | 1 +-+ 1 +--R (20x + 20x + 40x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 9 6 3 | 1 +-+ 1 +--R (- 20x - 20x - 40x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 7 4 +-+ 7 4 +--R (10%i x + 10%i x + 20%i x)\|7 - 10x - 10x - 20x +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 9 6 3 | 1 +-+ 1 +--R (- 20x - 20x - 40x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 10 7 4 | 1 +-+ 1 +--R (20x + 20x + 40x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 8 5 2 +-+ 8 5 2 +--R (- 10%i x - 10%i x - 20%i x )\|7 + 10x + 10x + 20x +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 7 4 +-+ 7 4 +--R ((- 10%i x - 10%i x - 20%i x)\|7 - 10x - 10x - 20x) +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 8 5 2 +-+ 8 5 2 +--R ((10%i x + 10%i x + 20%i x )\|7 + 10x + 10x + 20x ) +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 6 3 +--R 40x + 40x + 80 +--R * +--R 1 3 6 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 2 11 2 8 4 5 6+----+3 | 1 +-+ 1 +--R (- - x - - x - - x )\|1372 3|- - %i\|7 + - +--R 7 7 7 \| 2 2 +--R + +--R +--------------+ +--R 2 12 2 9 4 6 6+----+3 | 1 +-+ 1 +--R (- x + - x + - x )\|1372 3|- - %i\|7 + - +--R 7 7 7 \| 2 2 +--R + +--R 1 10 1 7 2 4 +-+ 1 10 1 7 +--R (- - %i x - - %i x - - %i x )\|7 + - x + - x +--R 7 7 7 7 7 +--R + +--R 2 4 +--R - x +--R 7 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 2 12 2 9 4 6 6+----+3 | 1 +-+ 1 +--R (- x + - x + - x )\|1372 3|- - %i\|7 + - +--R 7 7 7 \| 2 2 +--R + +--R +--------------+ +--R 2 13 2 10 4 7 6+----+3 | 1 +-+ 1 +--R (- - x - - x - - x )\|1372 3|- - %i\|7 + - +--R 7 7 7 \| 2 2 +--R + +--R 1 11 1 8 2 5 +-+ 1 11 1 8 2 5 +--R ((- %i x + - %i x + - %i x )\|7 - - x - - x - - x ) +--R 7 7 7 7 7 7 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 10 1 7 2 4 +-+ 1 10 1 7 2 4 +--R ((- %i x + - %i x + - %i x )\|7 + - x + - x + - x ) +--R 7 7 7 7 7 7 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 2 5 +-+ 1 11 1 8 2 5 +--R ((- - %i x - - %i x - - %i x )\|7 - - x - - x - - x ) +--R 7 7 7 7 7 7 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 4 9 4 6 8 3 6+----+3 +--R (- - x - - x - - x )\|1372 +--R 7 7 7 +--R * +--R 1 3 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 41 14 41 11 41 8 | 1 +-+ 1 +--R (-- x + -- x + -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R +--------------+ +--R 41 15 41 12 41 9 | 1 +-+ 1 +--R (- -- x - -- x - -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R 41 13 41 10 41 7 +-+ 41 13 41 10 41 7 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x - -- x +--R 32 32 16 32 32 16 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 41 15 41 12 41 9 | 1 +-+ 1 +--R (- -- x - -- x - -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R +--------------+ +--R 41 16 41 13 41 10 | 1 +-+ 1 +--R (-- x + -- x + -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R 41 14 41 11 41 8 +-+ 41 14 41 11 41 8 +--R (- -- %i x - -- %i x - -- %i x )\|7 + -- x + -- x + -- x +--R 32 32 16 32 32 16 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 41 13 41 10 41 7 +-+ 41 13 41 10 +--R (- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x +--R 32 32 16 32 32 +--R + +--R 41 7 +--R - -- x +--R 16 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 14 41 11 41 8 +-+ 41 14 41 11 41 8 +--R ((-- %i x + -- %i x + -- %i x )\|7 + -- x + -- x + -- x ) +--R 32 32 16 32 32 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 41 12 41 9 41 6 +--R -- x + -- x + -- x +--R 8 8 4 +--R * +--R 1 3 6 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 15 11 15 8 15 5 +-+6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|7 \|1372 3|- - %i\|7 + - +--R 98 98 49 \| 2 2 +--R + +--R +--------------+ +--R 15 12 15 9 15 6 +-+6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|7 \|1372 3|- - %i\|7 + - +--R 98 98 49 \| 2 2 +--R + +--R 15 10 15 7 15 4 +-+ 15 10 15 7 +--R (--- x + --- x + -- x )\|7 - -- %i x - -- %i x +--R 196 196 98 28 28 +--R + +--R 15 4 +--R - -- %i x +--R 14 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 15 12 15 9 15 6 +-+6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|7 \|1372 3|- - %i\|7 + - +--R 98 98 49 \| 2 2 +--R + +--R +--------------+ +--R 15 13 15 10 15 7 +-+6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|7 \|1372 3|- - %i\|7 + - +--R 98 98 49 \| 2 2 +--R + +--R 15 11 15 8 15 5 +-+ 15 11 15 8 +--R (- --- x - --- x - -- x )\|7 + -- %i x + -- %i x +--R 196 196 98 28 28 +--R + +--R 15 5 +--R -- %i x +--R 14 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 15 10 15 7 15 4 +-+ 15 10 15 7 +--R (--- x + --- x + -- x )\|7 + -- %i x + -- %i x +--R 196 196 98 28 28 +--R + +--R 15 4 +--R -- %i x +--R 14 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 11 15 8 15 5 +-+ 15 11 15 8 +--R (- --- x - --- x - -- x )\|7 - -- %i x - -- %i x +--R 196 196 98 28 28 +--R + +--R 15 5 +--R - -- %i x +--R 14 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 9 15 6 30 3 +-+6+----+3 +--R (- -- x - -- x - -- x )\|7 \|1372 +--R 49 49 49 +--R * +--R 1 3 4 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 15 14 15 11 15 8 +-+ | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|7 3|- - %i\|7 + - +--R 8 8 4 \| 2 2 +--R + +--R +--------------+ +--R 15 15 15 12 15 9 +-+ | 1 +-+ 1 +--R (-- x + -- x + -- x )\|7 3|- - %i\|7 + - +--R 8 8 4 \| 2 2 +--R + +--R 15 13 15 10 15 7 +-+ 105 13 105 10 +--R (-- x + -- x + -- x )\|7 - --- %i x - --- %i x +--R 16 16 8 16 16 +--R + +--R 105 7 +--R - --- %i x +--R 8 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 15 15 15 12 15 9 +-+ | 1 +-+ 1 +--R (-- x + -- x + -- x )\|7 3|- - %i\|7 + - +--R 8 8 4 \| 2 2 +--R + +--R +--------------+ +--R 15 16 15 13 15 10 +-+ | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|7 3|- - %i\|7 + - +--R 8 8 4 \| 2 2 +--R + +--R 15 14 15 11 15 8 +-+ 105 14 105 11 +--R (- -- x - -- x - -- x )\|7 + --- %i x + --- %i x +--R 16 16 8 16 16 +--R + +--R 105 8 +--R --- %i x +--R 8 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 15 13 15 10 15 7 +-+ 105 13 105 10 +--R (-- x + -- x + -- x )\|7 + --- %i x + --- %i x +--R 16 16 8 16 16 +--R + +--R 105 7 +--R --- %i x +--R 8 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 14 15 11 15 8 +-+ 105 14 105 11 +--R (- -- x - -- x - -- x )\|7 - --- %i x - --- %i x +--R 16 16 8 16 16 +--R + +--R 105 8 +--R - --- %i x +--R 8 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 12 15 9 15 6 +-+ +--R (- -- x - -- x - -- x )\|7 +--R 4 4 2 +--R * +--R 1 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 3 5 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 8 5 2 | 1 +-+ 1 +--R (15x + 15x + 30x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 9 6 3 | 1 +-+ 1 +--R (- 15x - 15x - 30x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 7 15 4 +-+ 15 7 15 4 +--R (-- %i x + -- %i x + 15%i x)\|7 - -- x - -- x - 15x +--R 2 2 2 2 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 9 6 3 | 1 +-+ 1 +--R (- 15x - 15x - 30x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 10 7 4 | 1 +-+ 1 +--R (15x + 15x + 30x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 8 15 5 2 +-+ 15 8 15 5 2 +--R (- -- %i x - -- %i x - 15%i x )\|7 + -- x + -- x + 15x +--R 2 2 2 2 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 15 7 15 4 +-+ 15 7 15 4 +--R ((- -- %i x - -- %i x - 15%i x)\|7 - -- x - -- x - 15x) +--R 2 2 2 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 8 15 5 2 +-+ 15 8 15 5 2 +--R ((-- %i x + -- %i x + 15%i x )\|7 + -- x + -- x + 15x ) +--R 2 2 2 2 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 6 3 +--R 30x + 30x + 60 +--R * +--R 1 3 8 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 3 11 3 8 3 5 6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - - x )\|1372 3|- - %i\|7 + - +--R 14 14 7 \| 2 2 +--R + +--R +--------------+ +--R 3 12 3 9 3 6 6+----+3 | 1 +-+ 1 +--R (-- x + -- x + - x )\|1372 3|- - %i\|7 + - +--R 14 14 7 \| 2 2 +--R + +--R 3 10 3 7 3 4 +-+ 3 10 3 7 +--R (- -- %i x - -- %i x - -- %i x )\|7 + -- x + -- x +--R 28 28 14 28 28 +--R + +--R 3 4 +--R -- x +--R 14 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 3 12 3 9 3 6 6+----+3 | 1 +-+ 1 +--R (-- x + -- x + - x )\|1372 3|- - %i\|7 + - +--R 14 14 7 \| 2 2 +--R + +--R +--------------+ +--R 3 13 3 10 3 7 6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - - x )\|1372 3|- - %i\|7 + - +--R 14 14 7 \| 2 2 +--R + +--R 3 11 3 8 3 5 +-+ 3 11 3 8 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x +--R 28 28 14 28 28 +--R + +--R 3 5 +--R - -- x +--R 14 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 3 10 3 7 3 4 +-+ 3 10 3 7 +--R (-- %i x + -- %i x + -- %i x )\|7 + -- x + -- x +--R 28 28 14 28 28 +--R + +--R 3 4 +--R -- x +--R 14 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 11 3 8 3 5 +-+ 3 11 3 8 +--R (- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x +--R 28 28 14 28 28 +--R + +--R 3 5 +--R - -- x +--R 14 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 9 3 6 6 3 6+----+3 +--R (- - x - - x - - x )\|1372 +--R 7 7 7 +--R * +--R 1 3 5 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 39 14 39 11 39 8 | 1 +-+ 1 +--R (- -- x - -- x - -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R +--------------+ +--R 39 15 39 12 39 9 | 1 +-+ 1 +--R (-- x + -- x + -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R 39 13 39 10 39 7 +-+ 39 13 39 10 +--R (- -- %i x - -- %i x - -- %i x )\|7 + -- x + -- x +--R 32 32 16 32 32 +--R + +--R 39 7 +--R -- x +--R 16 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 39 15 39 12 39 9 | 1 +-+ 1 +--R (-- x + -- x + -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R +--------------+ +--R 39 16 39 13 39 10 | 1 +-+ 1 +--R (- -- x - -- x - -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R 39 14 39 11 39 8 +-+ 39 14 39 11 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x +--R 32 32 16 32 32 +--R + +--R 39 8 +--R - -- x +--R 16 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 39 13 39 10 39 7 +-+ 39 13 39 10 +--R (-- %i x + -- %i x + -- %i x )\|7 + -- x + -- x +--R 32 32 16 32 32 +--R + +--R 39 7 +--R -- x +--R 16 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 39 14 39 11 39 8 +-+ 39 14 39 11 +--R (- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x +--R 32 32 16 32 32 +--R + +--R 39 8 +--R - -- x +--R 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 39 12 39 9 39 6 +--R - -- x - -- x - -- x +--R 8 8 4 +--R * +--R 1 3 2 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 3 4 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 10 11 10 8 20 5 +-+6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|7 \|1372 3|- - %i\|7 + - +--R 49 49 49 \| 2 2 +--R + +--R +--------------+ +--R 10 12 10 9 20 6 +-+6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|7 \|1372 3|- - %i\|7 + - +--R 49 49 49 \| 2 2 +--R + +--R 5 10 5 7 10 4 +-+ 5 10 5 7 +--R (-- x + -- x + -- x )\|7 - - %i x - - %i x +--R 49 49 49 7 7 +--R + +--R 10 4 +--R - -- %i x +--R 7 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 10 12 10 9 20 6 +-+6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|7 \|1372 3|- - %i\|7 + - +--R 49 49 49 \| 2 2 +--R + +--R +--------------+ +--R 10 13 10 10 20 7 +-+6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|7 \|1372 3|- - %i\|7 + - +--R 49 49 49 \| 2 2 +--R + +--R 5 11 5 8 10 5 +-+ 5 11 5 8 +--R (- -- x - -- x - -- x )\|7 + - %i x + - %i x +--R 49 49 49 7 7 +--R + +--R 10 5 +--R -- %i x +--R 7 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 10 5 7 10 4 +-+ 5 10 5 7 10 4 +--R ((-- x + -- x + -- x )\|7 + - %i x + - %i x + -- %i x ) +--R 49 49 49 7 7 7 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 11 5 8 10 5 +-+ 5 11 5 8 +--R (- -- x - -- x - -- x )\|7 - - %i x - - %i x +--R 49 49 49 7 7 +--R + +--R 10 5 +--R - -- %i x +--R 7 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 20 9 20 6 40 3 +-+6+----+3 +--R (- -- x - -- x - -- x )\|7 \|1372 +--R 49 49 49 +--R * +--R 1 3 6 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 25 14 25 11 25 8 +-+ | 1 +-+ 1 +--R (-- x + -- x + -- x )\|7 3|- - %i\|7 + - +--R 4 4 2 \| 2 2 +--R + +--R +--------------+ +--R 25 15 25 12 25 9 +-+ | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|7 3|- - %i\|7 + - +--R 4 4 2 \| 2 2 +--R + +--R 25 13 25 10 25 7 +-+ 175 13 175 10 +--R (- -- x - -- x - -- x )\|7 + --- %i x + --- %i x +--R 8 8 4 8 8 +--R + +--R 175 7 +--R --- %i x +--R 4 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 25 15 25 12 25 9 +-+ | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|7 3|- - %i\|7 + - +--R 4 4 2 \| 2 2 +--R + +--R +--------------+ +--R 25 16 25 13 25 10 +-+ | 1 +-+ 1 +--R (-- x + -- x + -- x )\|7 3|- - %i\|7 + - +--R 4 4 2 \| 2 2 +--R + +--R 25 14 25 11 25 8 +-+ 175 14 175 11 +--R (-- x + -- x + -- x )\|7 - --- %i x - --- %i x +--R 8 8 4 8 8 +--R + +--R 175 8 +--R - --- %i x +--R 4 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 25 13 25 10 25 7 +-+ 175 13 175 10 +--R (- -- x - -- x - -- x )\|7 - --- %i x - --- %i x +--R 8 8 4 8 8 +--R + +--R 175 7 +--R - --- %i x +--R 4 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 14 25 11 25 8 +-+ 175 14 175 11 +--R (-- x + -- x + -- x )\|7 + --- %i x + --- %i x +--R 8 8 4 8 8 +--R + +--R 175 8 +--R --- %i x +--R 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 25 12 25 9 6 +-+ +--R (-- x + -- x + 25x )\|7 +--R 2 2 +--R * +--R 1 3 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 5 17 5 14 5 11 +-+6+----+3 | 1 +-+ 1 +--R (--- x + --- x + --- x )\|7 \|1372 3|- - %i\|7 + - +--R 392 392 196 \| 2 2 +--R + +--R +--------------+ +--R 5 18 5 15 5 12 +-+6+----+3 | 1 +-+ 1 +--R (- --- x - --- x - --- x )\|7 \|1372 3|- - %i\|7 + - +--R 392 392 196 \| 2 2 +--R + +--R 5 16 5 13 5 10 +-+ 5 16 5 13 +--R (- --- x - --- x - --- x )\|7 + --- %i x + --- %i x +--R 784 784 392 112 112 +--R + +--R 5 10 +--R -- %i x +--R 56 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 5 18 5 15 5 12 +-+6+----+3 | 1 +-+ 1 +--R (- --- x - --- x - --- x )\|7 \|1372 3|- - %i\|7 + - +--R 392 392 196 \| 2 2 +--R + +--R +--------------+ +--R 5 19 5 16 5 13 +-+6+----+3 | 1 +-+ 1 +--R (--- x + --- x + --- x )\|7 \|1372 3|- - %i\|7 + - +--R 392 392 196 \| 2 2 +--R + +--R 5 17 5 14 5 11 +-+ 5 17 5 14 +--R (--- x + --- x + --- x )\|7 - --- %i x - --- %i x +--R 784 784 392 112 112 +--R + +--R 5 11 +--R - -- %i x +--R 56 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 5 16 5 13 5 10 +-+ 5 16 5 13 +--R (- --- x - --- x - --- x )\|7 - --- %i x - --- %i x +--R 784 784 392 112 112 +--R + +--R 5 10 +--R - -- %i x +--R 56 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 17 5 14 5 11 +-+ 5 17 5 14 +--R (--- x + --- x + --- x )\|7 + --- %i x + --- %i x +--R 784 784 392 112 112 +--R + +--R 5 11 +--R -- %i x +--R 56 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 5 15 5 12 5 9 +-+6+----+3 +--R (--- x + --- x + -- x )\|7 \|1372 +--R 196 196 98 +--R * +--R 1 3 3 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 8 5 2 | 1 +-+ 1 +--R (6x + 6x + 12x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 9 6 3 | 1 +-+ 1 +--R (- 6x - 6x - 12x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 7 4 +-+ 7 4 +--R (3%i x + 3%i x + 6%i x)\|7 - 3x - 3x - 6x +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 9 6 3 | 1 +-+ 1 +--R (- 6x - 6x - 12x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 10 7 4 | 1 +-+ 1 +--R (6x + 6x + 12x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 8 5 2 +-+ 8 5 2 +--R (- 3%i x - 3%i x - 6%i x )\|7 + 3x + 3x + 6x +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 7 4 +-+ 7 4 +--R ((- 3%i x - 3%i x - 6%i x)\|7 - 3x - 3x - 6x) +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 8 5 2 +-+ 8 5 2 +--R ((3%i x + 3%i x + 6%i x )\|7 + 3x + 3x + 6x ) +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 6 3 +--R 12x + 12x + 24 +--R * +--R 1 3 10 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 231 14 231 11 231 8 | 1 +-+ 1 +--R (--- x + --- x + --- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R +--------------+ +--R 231 15 231 12 231 9 | 1 +-+ 1 +--R (- --- x - --- x - --- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R 231 13 231 10 231 7 +-+ 231 13 231 10 +--R (--- %i x + --- %i x + --- %i x )\|7 - --- x - --- x +--R 32 32 16 32 32 +--R + +--R 231 7 +--R - --- x +--R 16 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 231 15 231 12 231 9 | 1 +-+ 1 +--R (- --- x - --- x - --- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R +--------------+ +--R 231 16 231 13 231 10 | 1 +-+ 1 +--R (--- x + --- x + --- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R 231 14 231 11 231 8 +-+ 231 14 +--R (- --- %i x - --- %i x - --- %i x )\|7 + --- x +--R 32 32 16 32 +--R + +--R 231 11 231 8 +--R --- x + --- x +--R 32 16 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 231 13 231 10 231 7 +-+ 231 13 +--R (- --- %i x - --- %i x - --- %i x )\|7 - --- x +--R 32 32 16 32 +--R + +--R 231 10 231 7 +--R - --- x - --- x +--R 32 16 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 231 14 231 11 231 8 +-+ 231 14 231 11 +--R (--- %i x + --- %i x + --- %i x )\|7 + --- x + --- x +--R 32 32 16 32 32 +--R + +--R 231 8 +--R --- x +--R 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 231 12 231 9 231 6 +--R --- x + --- x + --- x +--R 8 8 4 +--R * +--R 1 3 4 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 3 17 3 14 3 11 6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|1372 3|- - %i\|7 + - +--R 56 56 28 \| 2 2 +--R + +--R +--------------+ +--R 3 18 3 15 3 12 6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|1372 3|- - %i\|7 + - +--R 56 56 28 \| 2 2 +--R + +--R 3 16 3 13 3 10 +-+ 3 16 +--R (- --- %i x - --- %i x - -- %i x )\|7 + --- x +--R 112 112 56 112 +--R + +--R 3 13 3 10 +--R --- x + -- x +--R 112 56 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 3 18 3 15 3 12 6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|1372 3|- - %i\|7 + - +--R 56 56 28 \| 2 2 +--R + +--R +--------------+ +--R 3 19 3 16 3 13 6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|1372 3|- - %i\|7 + - +--R 56 56 28 \| 2 2 +--R + +--R 3 17 3 14 3 11 +-+ 3 17 +--R (--- %i x + --- %i x + -- %i x )\|7 - --- x +--R 112 112 56 112 +--R + +--R 3 14 3 11 +--R - --- x - -- x +--R 112 56 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 3 16 3 13 3 10 +-+ 3 16 3 13 +--R (--- %i x + --- %i x + -- %i x )\|7 + --- x + --- x +--R 112 112 56 112 112 +--R + +--R 3 10 +--R -- x +--R 56 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 17 3 14 3 11 +-+ 3 17 +--R (- --- %i x - --- %i x - -- %i x )\|7 - --- x +--R 112 112 56 112 +--R + +--R 3 14 3 11 +--R - --- x - -- x +--R 112 56 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 3 15 3 12 3 9 6+----+3 +--R (- -- x - -- x - -- x )\|1372 +--R 28 28 14 +--R * +--R 1 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 3 2 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 15 11 15 8 15 5 +-+6+----+3 | 1 +-+ 1 +--R (- --- x - --- x - -- x )\|7 \|1372 3|- - %i\|7 + - +--R 196 196 98 \| 2 2 +--R + +--R +--------------+ +--R 15 12 15 9 15 6 +-+6+----+3 | 1 +-+ 1 +--R (--- x + --- x + -- x )\|7 \|1372 3|- - %i\|7 + - +--R 196 196 98 \| 2 2 +--R + +--R 15 10 15 7 15 4 +-+ 15 10 15 7 +--R (--- x + --- x + --- x )\|7 - -- %i x - -- %i x +--R 392 392 196 56 56 +--R + +--R 15 4 +--R - -- %i x +--R 28 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 15 12 15 9 15 6 +-+6+----+3 | 1 +-+ 1 +--R (--- x + --- x + -- x )\|7 \|1372 3|- - %i\|7 + - +--R 196 196 98 \| 2 2 +--R + +--R +--------------+ +--R 15 13 15 10 15 7 +-+6+----+3 | 1 +-+ 1 +--R (- --- x - --- x - -- x )\|7 \|1372 3|- - %i\|7 + - +--R 196 196 98 \| 2 2 +--R + +--R 15 11 15 8 15 5 +-+ 15 11 15 8 +--R (- --- x - --- x - --- x )\|7 + -- %i x + -- %i x +--R 392 392 196 56 56 +--R + +--R 15 5 +--R -- %i x +--R 28 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 15 10 15 7 15 4 +-+ 15 10 15 7 +--R (--- x + --- x + --- x )\|7 + -- %i x + -- %i x +--R 392 392 196 56 56 +--R + +--R 15 4 +--R -- %i x +--R 28 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 11 15 8 15 5 +-+ 15 11 15 8 +--R (- --- x - --- x - --- x )\|7 - -- %i x - -- %i x +--R 392 392 196 56 56 +--R + +--R 15 5 +--R - -- %i x +--R 28 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 9 15 6 15 3 +-+6+----+3 +--R (- -- x - -- x - -- x )\|7 \|1372 +--R 98 98 49 +--R * +--R 1 3 8 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 15 14 15 11 15 8 +-+ | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|7 3|- - %i\|7 + - +--R 8 8 4 \| 2 2 +--R + +--R +--------------+ +--R 15 15 15 12 15 9 +-+ | 1 +-+ 1 +--R (-- x + -- x + -- x )\|7 3|- - %i\|7 + - +--R 8 8 4 \| 2 2 +--R + +--R 15 13 15 10 15 7 +-+ 105 13 105 10 +--R (-- x + -- x + -- x )\|7 - --- %i x - --- %i x +--R 16 16 8 16 16 +--R + +--R 105 7 +--R - --- %i x +--R 8 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 15 15 15 12 15 9 +-+ | 1 +-+ 1 +--R (-- x + -- x + -- x )\|7 3|- - %i\|7 + - +--R 8 8 4 \| 2 2 +--R + +--R +--------------+ +--R 15 16 15 13 15 10 +-+ | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|7 3|- - %i\|7 + - +--R 8 8 4 \| 2 2 +--R + +--R 15 14 15 11 15 8 +-+ 105 14 105 11 +--R (- -- x - -- x - -- x )\|7 + --- %i x + --- %i x +--R 16 16 8 16 16 +--R + +--R 105 8 +--R --- %i x +--R 8 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 15 13 15 10 15 7 +-+ 105 13 105 10 +--R (-- x + -- x + -- x )\|7 + --- %i x + --- %i x +--R 16 16 8 16 16 +--R + +--R 105 7 +--R --- %i x +--R 8 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 14 15 11 15 8 +-+ 105 14 105 11 +--R (- -- x - -- x - -- x )\|7 - --- %i x - --- %i x +--R 16 16 8 16 16 +--R + +--R 105 8 +--R - --- %i x +--R 8 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 12 15 9 15 6 +-+ +--R (- -- x - -- x - -- x )\|7 +--R 4 4 2 +--R * +--R 1 3 5 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 15 17 15 14 15 11 +-+6+----+3 | 1 +-+ 1 +--R (- --- x - --- x - --- x )\|7 \|1372 3|- - %i\|7 + - +--R 392 392 196 \| 2 2 +--R + +--R +--------------+ +--R 15 18 15 15 15 12 +-+6+----+3 | 1 +-+ 1 +--R (--- x + --- x + --- x )\|7 \|1372 3|- - %i\|7 + - +--R 392 392 196 \| 2 2 +--R + +--R 15 16 15 13 15 10 +-+ 15 16 +--R (--- x + --- x + --- x )\|7 - --- %i x +--R 784 784 392 112 +--R + +--R 15 13 15 10 +--R - --- %i x - -- %i x +--R 112 56 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 15 18 15 15 15 12 +-+6+----+3 | 1 +-+ 1 +--R (--- x + --- x + --- x )\|7 \|1372 3|- - %i\|7 + - +--R 392 392 196 \| 2 2 +--R + +--R +--------------+ +--R 15 19 15 16 15 13 +-+6+----+3 | 1 +-+ 1 +--R (- --- x - --- x - --- x )\|7 \|1372 3|- - %i\|7 + - +--R 392 392 196 \| 2 2 +--R + +--R 15 17 15 14 15 11 +-+ 15 17 +--R (- --- x - --- x - --- x )\|7 + --- %i x +--R 784 784 392 112 +--R + +--R 15 14 15 11 +--R --- %i x + -- %i x +--R 112 56 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 15 16 15 13 15 10 +-+ 15 16 15 13 +--R (--- x + --- x + --- x )\|7 + --- %i x + --- %i x +--R 784 784 392 112 112 +--R + +--R 15 10 +--R -- %i x +--R 56 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 17 15 14 15 11 +-+ 15 17 15 14 +--R (- --- x - --- x - --- x )\|7 - --- %i x - --- %i x +--R 784 784 392 112 112 +--R + +--R 15 11 +--R - -- %i x +--R 56 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 15 15 15 12 15 9 +-+6+----+3 +--R (- --- x - --- x - -- x )\|7 \|1372 +--R 196 196 98 +--R * +--R 1 3 2 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 3 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 8 5 2 | 1 +-+ 1 +--R (x + x + 2x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 9 6 3 | 1 +-+ 1 +--R (- x - x - 2x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 7 1 4 +-+ 1 7 1 4 +--R (- %i x + - %i x + %i x)\|7 - - x - - x - x +--R 2 2 2 2 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 9 6 3 | 1 +-+ 1 +--R (- x - x - 2x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 10 7 4 | 1 +-+ 1 +--R (x + x + 2x ) 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 8 1 5 2 +-+ 1 8 1 5 2 +--R (- - %i x - - %i x - %i x )\|7 + - x + - x + x +--R 2 2 2 2 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 7 1 4 +-+ 1 7 1 4 +--R ((- - %i x - - %i x - %i x)\|7 - - x - - x - x) +--R 2 2 2 2 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R +--------------+ +--R 1 8 1 5 2 +-+ 1 8 1 5 2 | 1 +-+ 1 +--R ((- %i x + - %i x + %i x )\|7 + - x + - x + x ) 3|- - %i\|7 + - +--R 2 2 2 2 \| 2 2 +--R + +--R 6 3 +--R 2x + 2x + 4 +--R * +--R 1 3 12 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 1 11 1 8 1 5 6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|1372 3|- - %i\|7 + - +--R 28 28 14 \| 2 2 +--R + +--R +--------------+ +--R 1 12 1 9 1 6 6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|1372 3|- - %i\|7 + - +--R 28 28 14 \| 2 2 +--R + +--R 1 10 1 7 1 4 +-+ 1 10 1 7 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x +--R 56 56 28 56 56 +--R + +--R 1 4 +--R - -- x +--R 28 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 1 12 1 9 1 6 6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|1372 3|- - %i\|7 + - +--R 28 28 14 \| 2 2 +--R + +--R +--------------+ +--R 1 13 1 10 1 7 6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|1372 3|- - %i\|7 + - +--R 28 28 14 \| 2 2 +--R + +--R 1 11 1 8 1 5 +-+ 1 11 1 8 +--R (- -- %i x - -- %i x - -- %i x )\|7 + -- x + -- x +--R 56 56 28 56 56 +--R + +--R 1 5 +--R -- x +--R 28 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 10 1 7 1 4 +-+ 1 10 1 7 1 4 +--R ((- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x - -- x ) +--R 56 56 28 56 56 28 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 11 1 8 1 5 +-+ 1 11 1 8 1 5 +--R ((-- %i x + -- %i x + -- %i x )\|7 + -- x + -- x + -- x ) +--R 56 56 28 56 56 28 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 9 1 6 1 3 6+----+3 +--R (-- x + -- x + - x )\|1372 +--R 14 14 7 +--R * +--R 1 3 9 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 23 14 23 11 23 8 | 1 +-+ 1 +--R (-- x + -- x + -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R +--------------+ +--R 23 15 23 12 23 9 | 1 +-+ 1 +--R (- -- x - -- x - -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R 23 13 23 10 23 7 +-+ 23 13 23 10 23 7 +--R (-- %i x + -- %i x + -- %i x )\|7 - -- x - -- x - -- x +--R 32 32 16 32 32 16 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 23 15 23 12 23 9 | 1 +-+ 1 +--R (- -- x - -- x - -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R +--------------+ +--R 23 16 23 13 23 10 | 1 +-+ 1 +--R (-- x + -- x + -- x ) 3|- - %i\|7 + - +--R 16 16 8 \| 2 2 +--R + +--R 23 14 23 11 23 8 +-+ 23 14 23 11 23 8 +--R (- -- %i x - -- %i x - -- %i x )\|7 + -- x + -- x + -- x +--R 32 32 16 32 32 16 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 23 13 23 10 23 7 +-+ 23 13 23 10 +--R (- -- %i x - -- %i x - -- %i x )\|7 - -- x - -- x +--R 32 32 16 32 32 +--R + +--R 23 7 +--R - -- x +--R 16 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 14 23 11 23 8 +-+ 23 14 23 11 23 8 +--R ((-- %i x + -- %i x + -- %i x )\|7 + -- x + -- x + -- x ) +--R 32 32 16 32 32 16 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 23 12 23 9 23 6 +--R -- x + -- x + -- x +--R 8 8 4 +--R * +--R 1 3 6 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 1 17 1 14 1 11 6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|1372 3|- - %i\|7 + - +--R 56 56 28 \| 2 2 +--R + +--R +--------------+ +--R 1 18 1 15 1 12 6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|1372 3|- - %i\|7 + - +--R 56 56 28 \| 2 2 +--R + +--R 1 16 1 13 1 10 +-+ 1 16 1 13 +--R (--- %i x + --- %i x + -- %i x )\|7 - --- x - --- x +--R 112 112 56 112 112 +--R + +--R 1 10 +--R - -- x +--R 56 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 1 18 1 15 1 12 6+----+3 | 1 +-+ 1 +--R (- -- x - -- x - -- x )\|1372 3|- - %i\|7 + - +--R 56 56 28 \| 2 2 +--R + +--R +--------------+ +--R 1 19 1 16 1 13 6+----+3 | 1 +-+ 1 +--R (-- x + -- x + -- x )\|1372 3|- - %i\|7 + - +--R 56 56 28 \| 2 2 +--R + +--R 1 17 1 14 1 11 +-+ 1 17 +--R (- --- %i x - --- %i x - -- %i x )\|7 + --- x +--R 112 112 56 112 +--R + +--R 1 14 1 11 +--R --- x + -- x +--R 112 56 +--R * +--R 6+----+3 +--R \|1372 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 16 1 13 1 10 +-+ 1 16 1 13 +--R (- --- %i x - --- %i x - -- %i x )\|7 - --- x - --- x +--R 112 112 56 112 112 +--R + +--R 1 10 +--R - -- x +--R 56 +--R * +--R +--------------+2 +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 17 1 14 1 11 +-+ 1 17 1 14 +--R (--- %i x + --- %i x + -- %i x )\|7 + --- x + --- x +--R 112 112 56 112 112 +--R + +--R 1 11 +--R -- x +--R 56 +--R * +--R +--------------+ +--R 6+----+3 | 1 +-+ 1 +--R \|1372 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 15 1 12 1 9 6+----+3 +--R (-- x + -- x + -- x )\|1372 +--R 28 28 14 +--R * +--R 1 3 3 +--R cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R +--------------+2 +--R 1 20 1 17 1 14 | 1 +-+ 1 +--R (- x + - x + - x ) 3|- - %i\|7 + - +--R 4 4 2 \| 2 2 +--R + +--R +--------------+ +--R 1 21 1 18 1 15 | 1 +-+ 1 +--R (- - x - - x - - x ) 3|- - %i\|7 + - +--R 4 4 2 \| 2 2 +--R + +--R 1 19 1 16 1 13 +-+ 1 19 1 16 1 13 +--R (- %i x + - %i x + - %i x )\|7 - - x - - x - - x +--R 8 8 4 8 8 4 +--R * +--R +------------+2 +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R +--------------+2 +--R 1 21 1 18 1 15 | 1 +-+ 1 +--R (- - x - - x - - x ) 3|- - %i\|7 + - +--R 4 4 2 \| 2 2 +--R + +--R +--------------+ +--R 1 22 1 19 1 16 | 1 +-+ 1 +--R (- x + - x + - x ) 3|- - %i\|7 + - +--R 4 4 2 \| 2 2 +--R + +--R 1 20 1 17 1 14 +-+ 1 20 1 17 1 14 +--R (- - %i x - - %i x - - %i x )\|7 + - x + - x + - x +--R 8 8 4 8 8 4 +--R * +--R +------------+ +--R |1 +-+ 1 +--R 3|- %i\|7 + - +--R \|2 2 +--R + +--R 1 19 1 16 1 13 +-+ 1 19 1 16 1 13 +--R ((- - %i x - - %i x - - %i x )\|7 - - x - - x - - x ) +--R 8 8 4 8 8 4 +--R * +--R +--------------+2 +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 20 1 17 1 14 +-+ 1 20 1 17 1 14 +--R ((- %i x + - %i x + - %i x )\|7 + - x + - x + - x ) +--R 8 8 4 8 8 4 +--R * +--R +--------------+ +--R | 1 +-+ 1 +--R 3|- - %i\|7 + - +--R \| 2 2 +--R + +--R 1 18 1 15 12 +--R - x + - x + x +--R 2 2 +--R Type: Expression(Complex(Fraction(Integer))) +--E 1323 + +--S 1324 of 1483 +t0245:= x^3/(2+x^3+x^6) +--R +--R +--R 3 +--R x +--R (1324) ----------- +--R 6 3 +--R x + x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1324 + +--S 1325 of 1483 +r0245:= -1/84*%i*7^(1/2)*(2*(4-4*%i*7^(1/2))^(1/3)*_ + atan(1/3*((4-4*%i*7^(1/2))^(1/3)-4*x)*3^(1/2)/_ + (4-4*%i*7^(1/2))^(1/3))*3^(1/2)-2*(4+4*%i*7^(1/2))^(1/3)*_ + atan(1/3*((4+4*%i*7^(1/2))^(1/3)-4*x)*3^(1/2)/_ + (4+4*%i*7^(1/2))^(1/3))*3^(1/2)-2*(4-4*%i*7^(1/2))^(1/3)*_ + log((4-4*%i*7^(1/2))^(1/3)+2*x)+2*(4+4*%i*7^(1/2))^(1/3)*_ + log((4+4*%i*7^(1/2))^(1/3)+2*x)+(4-4*%i*7^(1/2))^(1/3)*_ + log((4-4*%i*7^(1/2))^(2/3)-2*(4-4*%i*7^(1/2))^(1/3)*x+4*x^2)-_ + (4+4*%i*7^(1/2))^(1/3)*log((4+4*%i*7^(1/2))^(2/3)-_ + 2*(4+4*%i*7^(1/2))^(1/3)*x+4*x^2)) +--R +--R +--R (1325) +--R +-----------+ +-----------+2 +-----------+ +--R 1 +-+3| +-+ 3| +-+ 3| +-+ 2 +--R -- %i\|7 \|4%i\|7 + 4 log(\|4%i\|7 + 4 - 2x\|4%i\|7 + 4 + 4x ) +--R 84 +--R + +--R +-----------+ +-----------+ +--R 1 +-+3| +-+ 3| +-+ +--R - -- %i\|7 \|4%i\|7 + 4 log(\|4%i\|7 + 4 + 2x) +--R 42 +--R + +--R - +--R +-------------+ +--R 1 +-+3| +-+ +--R -- %i\|7 \|- 4%i\|7 + 4 +--R 84 +--R * +--R +-------------+2 +-------------+ +--R 3| +-+ 3| +-+ 2 +--R log(\|- 4%i\|7 + 4 - 2x\|- 4%i\|7 + 4 + 4x ) +--R + +--R +-------------+ +-------------+ +--R 1 +-+3| +-+ 3| +-+ +--R -- %i\|7 \|- 4%i\|7 + 4 log(\|- 4%i\|7 + 4 + 2x) +--R 42 +--R + +--R +-----------+ +--R 1 +-+3| +-+ 4 +-+ +--R +-----------+ - \|3 \|4%i\|7 + 4 - - x\|3 +--R 1 +-+ +-+3| +-+ 3 3 +--R -- %i\|3 \|7 \|4%i\|7 + 4 atan(------------------------------) +--R 42 +-----------+ +--R 3| +-+ +--R \|4%i\|7 + 4 +--R + +--R +-------------+ +--R 1 +-+3| +-+ 4 +-+ +--R +-------------+ - \|3 \|- 4%i\|7 + 4 - - x\|3 +--R 1 +-+ +-+3| +-+ 3 3 +--R - -- %i\|3 \|7 \|- 4%i\|7 + 4 atan(--------------------------------) +--R 42 +-------------+ +--R 3| +-+ +--R \|- 4%i\|7 + 4 +--R Type: Expression(Complex(Fraction(Integer))) +--E 1325 + +--S 1326 of 1483 +a0245:=integrate(t0245,x) +--R +--R +--R (1326) +--R 1 +--R atan(----) +--R +-+ +--R 6+-+ \|7 +--R 2\|2 cos(----------) +--R 3 +--R * +--R log +--R 1 2 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+2 \|7 6+-+ +-+6+---+ \|7 +--R 7\|2 sin(----------) + 2x\|2 \|7 \|343 sin(----------) +--R 3 3 +--R + +--R 1 2 +--R atan(----) +--R +-+ +--R 6+-+2 \|7 2 6+---+2 +--R 7\|2 cos(----------) + x \|343 +--R 3 +--R + +--R 1 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+ +-+ \|7 6+-+ \|7 +--R (- \|2 \|3 sin(----------) - \|2 cos(----------)) +--R 3 3 +--R * +--R log +--R 1 2 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+2 \|7 6+-+ +-+6+---+ \|7 +--R 7\|2 sin(----------) - x\|2 \|7 \|343 sin(----------) +--R 3 3 +--R + +--R 1 2 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+2 \|7 6+-+ +-+ +-+6+---+ \|7 +--R 7\|2 cos(----------) + x\|2 \|3 \|7 \|343 cos(----------) +--R 3 3 +--R + +--R 2 6+---+2 +--R x \|343 +--R + +--R 1 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+ +-+ \|7 6+-+ \|7 +--R (\|2 \|3 sin(----------) - \|2 cos(----------)) +--R 3 3 +--R * +--R log +--R 1 2 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+2 \|7 6+-+ +-+6+---+ \|7 +--R 7\|2 sin(----------) - x\|2 \|7 \|343 sin(----------) +--R 3 3 +--R + +--R 1 2 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+2 \|7 6+-+ +-+ +-+6+---+ \|7 +--R 7\|2 cos(----------) - x\|2 \|3 \|7 \|343 cos(----------) +--R 3 3 +--R + +--R 2 6+---+2 +--R x \|343 +--R + +--R 1 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+ \|7 6+-+ +-+ \|7 +--R (- 2\|2 sin(----------) + 2\|2 \|3 cos(----------)) +--R 3 3 +--R * +--R 1 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+ +-+ \|7 6+-+ \|7 +--R 7\|2 \|3 sin(----------) + 7\|2 cos(----------) +--R 3 3 +--R atan(--------------------------------------------------------------) +--R 1 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+ \|7 6+-+ +-+ \|7 +-+6+---+ +--R 7\|2 sin(----------) - 7\|2 \|3 cos(----------) - 2x\|7 \|343 +--R 3 3 +--R + +--R 1 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+ \|7 6+-+ +-+ \|7 +--R (2\|2 sin(----------) + 2\|2 \|3 cos(----------)) +--R 3 3 +--R * +--R 1 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+ +-+ \|7 6+-+ \|7 +--R 7\|2 \|3 sin(----------) - 7\|2 cos(----------) +--R 3 3 +--R atan(--------------------------------------------------------------) +--R 1 1 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6+-+ \|7 6+-+ +-+ \|7 +-+6+---+ +--R 7\|2 sin(----------) + 7\|2 \|3 cos(----------) - 2x\|7 \|343 +--R 3 3 +--R + +--R 1 +--R atan(----) +--R 1 +-+ +--R atan(----) 6+-+ \|7 +--R +-+ 7\|2 cos(----------) +--R 6+-+ \|7 3 +--R 4\|2 sin(----------)atan(----------------------------------) +--R 3 1 +--R atan(----) +--R +-+ +--R 6+-+ \|7 +-+6+---+ +--R 7\|2 sin(----------) + x\|7 \|343 +--R 3 +--R / +--R 6+---+ +--R 6\|343 +--R Type: Union(Expression(Integer),...) +--E 1326 + +--S 1327 of 1483 +m0245:=a0245-r0245 +--R +--R +--R (1327) +--R 1 6+-+ 1 1 +--R - \|2 cos(- atan(----)) +--R 3 3 +-+ +--R \|7 +--R * +--R log +--R 6+-+2 1 1 2 6+-+ 1 1 +--R 7\|2 sin(- atan(----)) + 14x\|2 sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 6+-+2 1 1 2 2 +--R 7\|2 cos(- atan(----)) + 7x +--R 3 +-+ +--R \|7 +--R + +--R 1 6+-+ +-+ 1 1 1 6+-+ 1 1 +--R (- - \|2 \|3 sin(- atan(----)) - - \|2 cos(- atan(----))) +--R 6 3 +-+ 6 3 +-+ +--R \|7 \|7 +--R * +--R log +--R 6+-+2 1 1 2 6+-+ 1 1 +--R 7\|2 sin(- atan(----)) - 7x\|2 sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 6+-+2 1 1 2 6+-+ +-+ 1 1 2 +--R 7\|2 cos(- atan(----)) + 7x\|2 \|3 cos(- atan(----)) + 7x +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 1 6+-+ +-+ 1 1 1 6+-+ 1 1 +--R (- \|2 \|3 sin(- atan(----)) - - \|2 cos(- atan(----))) +--R 6 3 +-+ 6 3 +-+ +--R \|7 \|7 +--R * +--R log +--R 6+-+2 1 1 2 6+-+ 1 1 +--R 7\|2 sin(- atan(----)) - 7x\|2 sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 6+-+2 1 1 2 6+-+ +-+ 1 1 2 +--R 7\|2 cos(- atan(----)) - 7x\|2 \|3 cos(- atan(----)) + 7x +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 1 6+-+ 1 1 1 6+-+ +-+ 1 1 +--R (- - \|2 sin(- atan(----)) + - \|2 \|3 cos(- atan(----))) +--R 3 3 +-+ 3 3 +-+ +--R \|7 \|7 +--R * +--R 6+-+ +-+ 1 1 6+-+ 1 1 +--R \|2 \|3 sin(- atan(----)) + \|2 cos(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R atan(------------------------------------------------------) +--R 6+-+ 1 1 6+-+ +-+ 1 1 +--R \|2 sin(- atan(----)) - \|2 \|3 cos(- atan(----)) - 2x +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 1 6+-+ 1 1 1 6+-+ +-+ 1 1 +--R (- \|2 sin(- atan(----)) + - \|2 \|3 cos(- atan(----))) +--R 3 3 +-+ 3 3 +-+ +--R \|7 \|7 +--R * +--R 6+-+ +-+ 1 1 6+-+ 1 1 +--R \|2 \|3 sin(- atan(----)) - \|2 cos(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R atan(------------------------------------------------------) +--R 6+-+ 1 1 6+-+ +-+ 1 1 +--R \|2 sin(- atan(----)) + \|2 \|3 cos(- atan(----)) - 2x +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 6+-+ 1 1 +--R \|2 cos(- atan(----)) +--R 3 +-+ +--R 2 6+-+ 1 1 \|7 +--R - \|2 sin(- atan(----))atan(-------------------------) +--R 3 3 +-+ 6+-+ 1 1 +--R \|7 \|2 sin(- atan(----)) + x +--R 3 +-+ +--R \|7 +--R + +--R +-----------+ +-----------+2 +-----------+ +--R 1 3| +-+ 3| +-+ 3| +-+ 2 +--R - -- %i\|4%i\|7 + 4 log(\|4%i\|7 + 4 - 2x\|4%i\|7 + 4 + 4x ) +--R 12 +--R + +--R +-----------+ +-----------+ +--R 1 3| +-+ 3| +-+ +--R - %i\|4%i\|7 + 4 log(\|4%i\|7 + 4 + 2x) +--R 6 +--R + +--R +-------------+ +-------------+2 +-------------+ +--R 1 3| +-+ 3| +-+ 3| +-+ 2 +--R -- %i\|- 4%i\|7 + 4 log(\|- 4%i\|7 + 4 - 2x\|- 4%i\|7 + 4 + 4x ) +--R 12 +--R + +--R +-------------+ +-------------+ +--R 1 3| +-+ 3| +-+ +--R - - %i\|- 4%i\|7 + 4 log(\|- 4%i\|7 + 4 + 2x) +--R 6 +--R + +--R +-----------+ +--R 1 +-+3| +-+ 4 +-+ +--R +-----------+ - \|3 \|4%i\|7 + 4 - - x\|3 +--R 1 +-+3| +-+ 3 3 +--R - - %i\|3 \|4%i\|7 + 4 atan(------------------------------) +--R 6 +-----------+ +--R 3| +-+ +--R \|4%i\|7 + 4 +--R + +--R +-------------+ +--R 1 +-+3| +-+ 4 +-+ +--R +-------------+ - \|3 \|- 4%i\|7 + 4 - - x\|3 +--R 1 +-+3| +-+ 3 3 +--R - %i\|3 \|- 4%i\|7 + 4 atan(--------------------------------) +--R 6 +-------------+ +--R 3| +-+ +--R \|- 4%i\|7 + 4 +--R / +--R +-+ +--R \|7 +--R Type: Expression(Complex(Fraction(Integer))) +--E 1327 + +--S 1328 of 1483 +d0245:=normalize(D(m0245,x)) +--R +--R +--R (1328) +--R 3 1 1 12 3 1 1 2 1 1 10 +--R - x sin(- atan(----)) - 6x cos(- atan(----)) sin(- atan(----)) +--R 3 +-+ 3 +-+ 3 +-+ +--R \|7 \|7 \|7 +--R + +--R 6 6+-+3 1 1 9 +--R - 2x \|2 sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 3 1 1 4 +--R - 15x cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 3 9 3 6 6 3 6+-+3 +-+ 1 1 +--R (- x + - x + - x )\|2 \|7 cos(- atan(----)) +--R 7 7 7 3 +-+ +--R \|7 +--R * +--R 1 1 8 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 3 1 1 6 +--R - 20x cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 8 9 8 6 16 3 6+-+3 +-+ 1 1 3 9 +--R (- x + - x + -- x )\|2 \|7 cos(- atan(----)) - 3x +--R 7 7 7 3 +-+ +--R \|7 +--R * +--R 1 1 6 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 6 6+-+3 1 1 4 +--R 12x \|2 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 6 12 6 9 12 6 +-+ 1 1 +--R (- x + - x + -- x )\|7 cos(- atan(----)) +--R 7 7 7 3 +-+ +--R \|7 +--R * +--R 1 1 5 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 3 1 1 8 +--R - 15x cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 6 9 6 6 12 3 6+-+3 +-+ 1 1 5 +--R (- x + - x + -- x )\|2 \|7 cos(- atan(----)) +--R 7 7 7 3 +-+ +--R \|7 +--R + +--R 9 1 1 2 +--R 9x cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 1 4 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 6 6+-+3 1 1 6 +--R 16x \|2 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 20 12 20 9 40 6 +-+ 1 1 3 12 6+-+3 +--R (- -- x - -- x - -- x )\|7 cos(- atan(----)) - x \|2 +--R 7 7 7 3 +-+ +--R \|7 +--R * +--R 1 1 3 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 3 1 1 10 9 1 1 4 +--R - 6x cos(- atan(----)) - 21x cos(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 3 15 3 12 3 9 6+-+3 +-+ 1 1 +--R (-- x + -- x + - x )\|2 \|7 cos(- atan(----)) +--R 14 14 7 3 +-+ +--R \|7 +--R * +--R 1 1 2 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 6 6+-+3 1 1 8 +--R 6x \|2 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 6 12 6 9 12 6 +-+ 1 1 5 +--R (- x + - x + -- x )\|7 cos(- atan(----)) +--R 7 7 7 3 +-+ +--R \|7 +--R + +--R 12 6+-+3 1 1 2 +--R 3x \|2 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 1 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 3 1 1 12 +--R - x cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 1 9 1 6 2 3 6+-+3 +-+ 1 1 9 9 1 1 6 +--R (- - x - - x - - x )\|2 \|7 cos(- atan(----)) - x cos(- atan(----)) +--R 7 7 7 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 1 15 1 12 1 9 6+-+3 +-+ 1 1 3 1 15 +--R (- -- x - -- x - - x )\|2 \|7 cos(- atan(----)) - - x +--R 14 14 7 3 +-+ 4 +--R \|7 +--R / +--R 6 3 1 1 12 +--R (x + x + 2)sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 6 3 1 1 2 1 1 10 +--R (6x + 6x + 12)cos(- atan(----)) sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 9 6 3 6+-+3 1 1 9 +--R (2x + 2x + 4x )\|2 sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 6 3 1 1 4 1 1 8 +--R (15x + 15x + 30)cos(- atan(----)) sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 6 3 1 1 6 12 9 6 +--R ((20x + 20x + 40)cos(- atan(----)) + 3x + 3x + 6x ) +--R 3 +-+ +--R \|7 +--R * +--R 1 1 6 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 9 6 3 6+-+3 1 1 4 1 1 5 +--R (- 12x - 12x - 24x )\|2 cos(- atan(----)) sin(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 6 3 1 1 8 +--R (15x + 15x + 30)cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 12 9 6 1 1 2 +--R (- 9x - 9x - 18x )cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 1 4 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 9 6 3 6+-+3 1 1 6 +--R (- 16x - 16x - 32x )\|2 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 15 12 9 6+-+3 +--R (x + x + 2x )\|2 +--R * +--R 1 1 3 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 6 3 1 1 10 +--R (6x + 6x + 12)cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 12 9 6 1 1 4 +--R (21x + 21x + 42x )cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 1 2 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 9 6 3 6+-+3 1 1 8 +--R (- 6x - 6x - 12x )\|2 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 15 12 9 6+-+3 1 1 2 +--R (- 3x - 3x - 6x )\|2 cos(- atan(----)) +--R 3 +-+ +--R \|7 +--R * +--R 1 1 +--R sin(- atan(----)) +--R 3 +-+ +--R \|7 +--R + +--R 6 3 1 1 12 12 9 6 1 1 6 +--R (x + x + 2)cos(- atan(----)) + (x + x + 2x )cos(- atan(----)) +--R 3 +-+ 3 +-+ +--R \|7 \|7 +--R + +--R 1 18 1 15 1 12 +--R - x + - x + - x +--R 4 4 2 +--R Type: Expression(Complex(Fraction(Integer))) +--E 1328 + +--S 1329 of 1483 +t0246:= x/(2+x^4+x^8) +--R +--R +--R x +--R (1329) ----------- +--R 8 4 +--R x + x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1329 + +--S 1330 of 1483 +r0246:= -1/4*atan(((-1+2*2^(1/2))^(1/2)-2*x^2)/(1+2*2^(1/2))^(1/2))/_ + (2+4*2^(1/2))^(1/2)+1/4*atan(((-1+2*2^(1/2))^(1/2)+2*x^2)/_ + (1+2*2^(1/2))^(1/2))/(2+4*2^(1/2))^(1/2)-1/8*log(2^(1/2)-_ + (-1+2*2^(1/2))^(1/2)*x^2+x^4)/(-2+4*2^(1/2))^(1/2)+_ + 1/8*log(2^(1/2)+(-1+2*2^(1/2))^(1/2)*x^2+x^4)/(-2+4*2^(1/2))^(1/2) +--R +--R +--R (1330) +--R +---------+ +---------+ +--R | +-+ 2 | +-+ +-+ 4 +--R \|4\|2 + 2 log(x \|2\|2 - 1 + \|2 + x ) +--R + +--R +---------+ +---------+ +--R | +-+ 2 | +-+ +-+ 4 +--R - \|4\|2 + 2 log(- x \|2\|2 - 1 + \|2 + x ) +--R + +--R +---------+ +---------+ +--R +---------+ +-+ | +-+ 2 +-+ 2 | +-+ +--R | +-+ ((2\|2 - 1)\|2\|2 - 1 + 4x \|2 - 2x )\|2\|2 + 1 +--R 2\|4\|2 - 2 atan(-----------------------------------------------------) +--R 7 +--R + +--R +---------+ +---------+ +--R +---------+ +-+ | +-+ 2 +-+ 2 | +-+ +--R | +-+ ((2\|2 - 1)\|2\|2 - 1 - 4x \|2 + 2x )\|2\|2 + 1 +--R - 2\|4\|2 - 2 atan(-----------------------------------------------------) +--R 7 +--R / +--R +---------+ +---------+ +--R | +-+ | +-+ +--R 8\|4\|2 - 2 \|4\|2 + 2 +--R Type: Expression(Integer) +--E 1330 + +--S 1331 of 1483 +a0246:=integrate(t0246,x) +--R +--R +--R (1331) +--R - +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R * +--R log +--R 7 2 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 2 +-+4+--+ \|7 +--R 14sin(----------) + x \|7 \|98 sin(----------) +--R 2 2 +--R + +--R 7 2 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 2 4+--+ \|7 4 4+--+2 +--R 14cos(----------) - 7x \|98 cos(---------- + x \|98 +--R 2 2 +--R + +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R * +--R log +--R 7 2 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 2 +-+4+--+ \|7 +--R 14sin(----------) - x \|7 \|98 sin(----------) +--R 2 2 +--R + +--R 7 2 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 2 4+--+ \|7 4 4+--+2 +--R 14cos(----------) + 7x \|98 cos(---------- + x \|98 +--R 2 2 +--R + +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R 2sin(----------) +--R 2 +--R * +--R 7 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|7 \|7 +--R 7\|7 sin(----------) + 7cos(----------) +--R 2 2 +--R atan(------------------------------------------------------) +--R 7 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ \|7 2 +-+4+--+ +--R 7sin(----------) - 7\|7 cos(----------) - 2x \|7 \|98 +--R 2 2 +--R + +--R - +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R 2sin(----------) +--R 2 +--R * +--R 7 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|7 \|7 +--R 7\|7 sin(----------) + 7cos(----------) +--R 2 2 +--R atan(------------------------------------------------------) +--R 7 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ \|7 2 +-+4+--+ +--R 7sin(----------) - 7\|7 cos(----------) + 2x \|7 \|98 +--R 2 2 +--R / +--R 4+--+ +--R 4\|98 +--R Type: Union(Expression(Integer),...) +--E 1331 + +--S 1332 of 1483 +m0246:=a0246-r0246 +--R +--R +--R (1332) +--R - +--R 7 +--R atan(----) +--R +---------+ +---------+ +-+ +--R | +-+ | +-+ \|7 +--R 2\|4\|2 - 2 \|4\|2 + 2 cos(----------) +--R 2 +--R * +--R log +--R 7 2 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 2 +-+4+--+ \|7 +--R 14sin(----------) + x \|7 \|98 sin(----------) +--R 2 2 +--R + +--R 7 2 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 2 4+--+ \|7 4 4+--+2 +--R 14cos(----------) - 7x \|98 cos(---------- + x \|98 +--R 2 2 +--R + +--R 7 +--R atan(----) +--R +---------+ +---------+ +-+ +--R | +-+ | +-+ \|7 +--R 2\|4\|2 - 2 \|4\|2 + 2 cos(----------) +--R 2 +--R * +--R log +--R 7 2 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 2 +-+4+--+ \|7 +--R 14sin(----------) - x \|7 \|98 sin(----------) +--R 2 2 +--R + +--R 7 2 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 2 4+--+ \|7 4 4+--+2 +--R 14cos(----------) + 7x \|98 cos(---------- + x \|98 +--R 2 2 +--R + +--R 7 +--R atan(----) +--R +---------+ +---------+ +-+ +--R | +-+ | +-+ \|7 +--R 4\|4\|2 - 2 \|4\|2 + 2 sin(----------) +--R 2 +--R * +--R 7 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|7 \|7 +--R 7\|7 sin(----------) + 7cos(----------) +--R 2 2 +--R atan(------------------------------------------------------) +--R 7 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ \|7 2 +-+4+--+ +--R 7sin(----------) - 7\|7 cos(----------) - 2x \|7 \|98 +--R 2 2 +--R + +--R - +--R 7 +--R atan(----) +--R +---------+ +---------+ +-+ +--R | +-+ | +-+ \|7 +--R 4\|4\|2 - 2 \|4\|2 + 2 sin(----------) +--R 2 +--R * +--R 7 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|7 \|7 +--R 7\|7 sin(----------) + 7cos(----------) +--R 2 2 +--R atan(------------------------------------------------------) +--R 7 7 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 +-+ \|7 2 +-+4+--+ +--R 7sin(----------) - 7\|7 cos(----------) + 2x \|7 \|98 +--R 2 2 +--R + +--R +---------+ +---------+ +--R 4+--+ | +-+ 2 | +-+ +-+ 4 +--R - \|98 \|4\|2 + 2 log(x \|2\|2 - 1 + \|2 + x ) +--R + +--R +---------+ +---------+ +--R 4+--+ | +-+ 2 | +-+ +-+ 4 +--R \|98 \|4\|2 + 2 log(- x \|2\|2 - 1 + \|2 + x ) +--R + +--R - +--R +---------+ +--R 4+--+ | +-+ +--R 2\|98 \|4\|2 - 2 +--R * +--R +---------+ +---------+ +--R +-+ | +-+ 2 +-+ 2 | +-+ +--R ((2\|2 - 1)\|2\|2 - 1 + 4x \|2 - 2x )\|2\|2 + 1 +--R atan(-----------------------------------------------------) +--R 7 +--R + +--R +---------+ +--R 4+--+ | +-+ +--R 2\|98 \|4\|2 - 2 +--R * +--R +---------+ +---------+ +--R +-+ | +-+ 2 +-+ 2 | +-+ +--R ((2\|2 - 1)\|2\|2 - 1 - 4x \|2 + 2x )\|2\|2 + 1 +--R atan(-----------------------------------------------------) +--R 7 +--R / +--R +---------+ +---------+ +--R 4+--+ | +-+ | +-+ +--R 8\|98 \|4\|2 - 2 \|4\|2 + 2 +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1483 +d0246:=normalize(D(m0246,x)) +--R +--R +--R (1333) +--R +---------+ +---------+ +--R 5 +-+ 5 4+--+2 | +-+ | +-+ +--R ((176x - 200x)\|2 - 200x + 352x)\|98 \|2\|2 + 1 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +--R 5 +-+ 5 4+--+2 | +-+ | +-+ +--R ((- 112x - 56x)\|2 + 56x + 224x)\|98 \|2\|2 - 1 \|4\|2 - 2 +--R + +--R 9 5 +-+ 9 5 4+--+2 +--R ((448x + 448x + 896x)\|2 - 1008x - 1008x - 2016x)\|98 +--R * +--R 7 8 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R +---------+ +--R 5 +-+ 5 4+--+2 | +-+ +--R ((704x - 800x)\|2 - 800x + 1408x)\|98 \|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +--R 5 +-+ 5 4+--+2 | +-+ +--R ((- 448x - 224x)\|2 + 224x + 896x)\|98 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 9 5 +-+ 9 5 4+--+2 +--R ((1792x + 1792x + 3584x)\|2 - 4032x - 4032x - 8064x)\|98 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +---------+ +--R 9 5 +-+ 9 5 | +-+ | +-+ +--R ((3696x - 4200x )\|2 - 4200x + 7392x )\|2\|2 + 1 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +--R 9 5 +-+ 9 5 | +-+ | +-+ +--R ((- 2352x - 1176x )\|2 + 1176x + 4704x )\|2\|2 - 1 \|4\|2 - 2 +--R + +--R 13 9 5 +-+ 13 9 5 +--R (7840x + 7840x + 15680x )\|2 - 17640x - 17640x - 35280x +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R +---------+ +---------+ +--R 9 5 +-+ 9 5 +-+ | +-+ | +-+ +--R ((2464x - 2800x )\|2 - 2800x + 4928x )\|7 \|2\|2 + 1 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +--R 9 5 +-+ 9 5 +-+ | +-+ | +-+ +--R ((- 1568x - 784x )\|2 + 784x + 3136x )\|7 \|2\|2 - 1 \|4\|2 - 2 +--R + +--R 13 9 5 +-+ 13 9 5 +-+ +--R ((4032x + 4032x + 8064x )\|2 - 9072x - 9072x - 18144x )\|7 +--R * +--R 7 7 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 \|7 +--R cos(----------)sin(----------) +--R 2 2 +--R + +--R +---------+ +--R 5 +-+ 5 4+--+2 | +-+ +--R ((1056x - 1200x)\|2 - 1200x + 2112x)\|98 \|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +--R 5 +-+ 5 4+--+2 | +-+ +--R ((- 672x - 336x)\|2 + 336x + 1344x)\|98 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 9 5 +-+ 9 5 4+--+2 +--R ((2688x + 2688x + 5376x)\|2 - 6048x - 6048x - 12096x)\|98 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +---------+ +--R 9 5 +-+ 9 5 | +-+ | +-+ +--R ((3696x - 4200x )\|2 - 4200x + 7392x )\|2\|2 + 1 \|4\|2 + 2 +--R + +--R +---------+ +--R 9 5 +-+ 9 5 | +-+ +--R ((- 2352x - 1176x )\|2 + 1176x + 4704x )\|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 13 9 5 +-+ 13 9 5 +--R (7840x + 7840x + 15680x )\|2 - 17640x - 17640x - 35280x +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +---------+ +--R 13 9 +-+ 13 9 4+--+2 | +-+ | +-+ +--R ((374x - 425x )\|2 - 425x + 748x )\|98 \|2\|2 + 1 \|4\|2 + 2 +--R + +--R +---------+ +--R 13 9 +-+ 13 9 4+--+2 | +-+ +--R ((- 238x - 119x )\|2 + 119x + 476x )\|98 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 17 13 9 +-+ 17 13 9 4+--+2 +--R ((560x + 560x + 1120x )\|2 - 1260x - 1260x - 2520x )\|98 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R +---------+ +--R 9 5 +-+ 9 5 +-+ | +-+ +--R ((4928x - 5600x )\|2 - 5600x + 9856x )\|7 \|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +--R 9 5 +-+ 9 5 +-+ | +-+ +--R ((- 3136x - 1568x )\|2 + 1568x + 6272x )\|7 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 13 9 5 +-+ 13 9 +--R (8064x + 8064x + 16128x )\|2 - 18144x - 18144x +--R + +--R 5 +--R - 36288x +--R * +--R +-+ +--R \|7 +--R * +--R 7 3 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +--R 13 9 +-+ 13 9 +-+4+--+2 | +-+ +--R ((264x - 300x )\|2 - 300x + 528x )\|7 \|98 \|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +--R 13 9 +-+ 13 9 +-+4+--+2 | +-+ +--R ((- 168x - 84x )\|2 + 84x + 336x )\|7 \|98 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 17 13 9 +-+ 17 13 9 +-+ +--R ((320x + 320x + 640x )\|2 - 720x - 720x - 1440x )\|7 +--R * +--R 4+--+2 +--R \|98 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R * +--R 7 3 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R +---------+ +--R 5 +-+ 5 4+--+2 | +-+ +--R ((704x - 800x)\|2 - 800x + 1408x)\|98 \|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +--R 5 +-+ 5 4+--+2 | +-+ +--R ((- 448x - 224x)\|2 + 224x + 896x)\|98 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 9 5 +-+ 9 5 4+--+2 +--R ((1792x + 1792x + 3584x)\|2 - 4032x - 4032x - 8064x)\|98 +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +--R 9 5 +-+ 9 5 | +-+ +--R ((- 3696x + 4200x )\|2 + 4200x - 7392x )\|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +---------+ +--R 9 5 +-+ 9 5 | +-+ | +-+ +--R ((2352x + 1176x )\|2 - 1176x - 4704x )\|2\|2 - 1 \|4\|2 - 2 +--R + +--R 13 9 5 +-+ 13 9 5 +--R (- 7840x - 7840x - 15680x )\|2 + 17640x + 17640x + 35280x +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +--R 13 9 +-+ 13 9 4+--+2 | +-+ +--R ((572x - 650x )\|2 - 650x + 1144x )\|98 \|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +--R 13 9 +-+ 13 9 4+--+2 | +-+ +--R ((- 364x - 182x )\|2 + 182x + 728x )\|98 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 17 13 9 +-+ 17 13 9 4+--+2 +--R ((224x + 224x + 448x )\|2 - 504x - 504x - 1008x )\|98 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +---------+ +--R 17 13 +-+ 17 13 | +-+ | +-+ +--R ((1848x - 2100x )\|2 - 2100x + 3696x )\|2\|2 + 1 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +--R 17 13 +-+ 17 13 | +-+ | +-+ +--R ((- 1176x - 588x )\|2 + 588x + 2352x )\|2\|2 - 1 \|4\|2 - 2 +--R + +--R 21 17 13 +-+ 21 17 13 +--R (1568x + 1568x + 3136x )\|2 - 3528x - 3528x - 7056x +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R +---------+ +--R 9 5 +-+ 9 5 +-+ | +-+ +--R ((2464x - 2800x )\|2 - 2800x + 4928x )\|7 \|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +--R 9 5 +-+ 9 5 +-+ | +-+ +--R ((- 1568x - 784x )\|2 + 784x + 3136x )\|7 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 13 9 5 +-+ 13 9 5 +-+ +--R ((4032x + 4032x + 8064x )\|2 - 9072x - 9072x - 18144x )\|7 +--R * +--R 7 5 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +--R 13 9 +-+ 13 9 +-+4+--+2 | +-+ +--R ((- 264x + 300x )\|2 + 300x - 528x )\|7 \|98 \|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +--R 13 9 +-+ 13 9 +-+4+--+2 | +-+ +--R ((168x + 84x )\|2 - 84x - 336x )\|7 \|98 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 17 13 9 +-+ 17 13 9 +--R ((- 320x - 320x - 640x )\|2 + 720x + 720x + 1440x ) +--R * +--R +-+4+--+2 +--R \|7 \|98 +--R * +--R 7 3 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +--R 17 13 +-+ 17 13 +-+ | +-+ +--R ((1232x - 1400x )\|2 - 1400x + 2464x )\|7 \|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +--R 17 13 +-+ 17 13 +-+ | +-+ +--R ((- 784x - 392x )\|2 + 392x + 1568x )\|7 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 21 17 13 +-+ 21 17 13 +-+ +--R ((448x + 448x + 896x )\|2 - 1008x - 1008x - 2016x )\|7 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R +---------+ +---------+ +--R 5 +-+ 5 4+--+2 | +-+ | +-+ +--R ((176x - 200x)\|2 - 200x + 352x)\|98 \|2\|2 + 1 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +--R 5 +-+ 5 4+--+2 | +-+ | +-+ +--R ((- 112x - 56x)\|2 + 56x + 224x)\|98 \|2\|2 - 1 \|4\|2 - 2 +--R + +--R 9 5 +-+ 9 5 4+--+2 +--R ((448x + 448x + 896x)\|2 - 1008x - 1008x - 2016x)\|98 +--R * +--R 7 8 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +---------+ +--R 9 5 +-+ 9 5 | +-+ | +-+ +--R ((- 3696x + 4200x )\|2 + 4200x - 7392x )\|2\|2 + 1 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +--R 9 5 +-+ 9 5 | +-+ | +-+ +--R ((2352x + 1176x )\|2 - 1176x - 4704x )\|2\|2 - 1 \|4\|2 - 2 +--R + +--R 13 9 5 +-+ 13 9 5 +--R (- 7840x - 7840x - 15680x )\|2 + 17640x + 17640x + 35280x +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +---------+ +--R 13 9 +-+ 13 9 4+--+2 | +-+ | +-+ +--R ((374x - 425x )\|2 - 425x + 748x )\|98 \|2\|2 + 1 \|4\|2 + 2 +--R + +--R +---------+ +--R 13 9 +-+ 13 9 4+--+2 | +-+ +--R ((- 238x - 119x )\|2 + 119x + 476x )\|98 \|2\|2 - 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 - 2 +--R + +--R 17 13 9 +-+ 17 13 9 4+--+2 +--R ((560x + 560x + 1120x )\|2 - 1260x - 1260x - 2520x )\|98 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +--R 17 13 +-+ 17 13 | +-+ +--R ((- 1848x + 2100x )\|2 + 2100x - 3696x )\|2\|2 + 1 +--R * +--R +---------+ +--R | +-+ +--R \|4\|2 + 2 +--R + +--R +---------+ +---------+ +--R 17 13 +-+ 17 13 | +-+ | +-+ +--R ((1176x + 588x )\|2 - 588x - 2352x )\|2\|2 - 1 \|4\|2 - 2 +--R + +--R 21 17 13 +-+ 21 17 13 +--R (- 1568x - 1568x - 3136x )\|2 + 3528x + 3528x + 7056x +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R +---------+ +---------+ +--R 21 17 +-+ 21 17 4+--+2 | +-+ | +-+ +--R ((44x - 50x )\|2 - 50x + 88x )\|98 \|2\|2 + 1 \|4\|2 + 2 +--R + +--R +---------+ +---------+ +--R 21 17 +-+ 21 17 4+--+2 | +-+ | +-+ +--R ((- 28x - 14x )\|2 + 14x + 56x )\|98 \|2\|2 - 1 \|4\|2 - 2 +--R / +--R 8 4 +-+ 8 4 4+--+2 +--R ((896x + 896x + 1792)\|2 - 2016x - 2016x - 4032)\|98 +--R * +--R 7 8 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R 8 4 +-+ 8 4 4+--+2 +--R ((3584x + 3584x + 7168)\|2 - 8064x - 8064x - 16128)\|98 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R 12 8 4 +-+ 12 8 4 +--R (18816x + 18816x + 37632x )\|2 - 42336x - 42336x - 84672x +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R 12 8 4 +-+ 12 8 4 +-+ +--R ((12544x + 12544x + 25088x )\|2 - 28224x - 28224x - 56448x )\|7 +--R * +--R 7 7 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|7 \|7 +--R cos(----------)sin(----------) +--R 2 2 +--R + +--R 8 4 +-+ 8 4 4+--+2 +--R ((5376x + 5376x + 10752)\|2 - 12096x - 12096x - 24192)\|98 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R 12 8 4 +-+ 12 8 4 +--R ((18816x + 18816x + 37632x )\|2 - 42336x - 42336x - 84672x ) +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R 16 12 8 +-+ 16 12 8 4+--+2 +--R ((1904x + 1904x + 3808x )\|2 - 4284x - 4284x - 8568x )\|98 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R 12 8 4 +-+ 12 8 +--R (25088x + 25088x + 50176x )\|2 - 56448x - 56448x +--R + +--R 4 +--R - 112896x +--R * +--R 7 3 +--R atan(----) +--R +-+ +--R +-+ \|7 +--R \|7 cos(----------) +--R 2 +--R + +--R 16 12 8 +-+ 16 12 8 +-+ +--R ((1344x + 1344x + 2688x )\|2 - 3024x - 3024x - 6048x )\|7 +--R * +--R 7 +--R atan(----) +--R +-+ +--R 4+--+2 \|7 +--R \|98 cos(----------) +--R 2 +--R * +--R 7 3 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R 8 4 +-+ 8 4 4+--+2 +--R ((3584x + 3584x + 7168)\|2 - 8064x - 8064x - 16128)\|98 +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R 12 8 4 +-+ 12 8 +--R (- 18816x - 18816x - 37632x )\|2 + 42336x + 42336x +--R + +--R 4 +--R 84672x +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R 16 12 8 +-+ 16 12 8 +--R ((2912x + 2912x + 5824x )\|2 - 6552x - 6552x - 13104x ) +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R 4+--+2 \|7 +--R \|98 cos(----------) +--R 2 +--R + +--R 20 16 12 +-+ 20 16 12 +--R (9408x + 9408x + 18816x )\|2 - 21168x - 21168x - 42336x +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R 12 8 4 +-+ 12 8 4 +--R ((12544x + 12544x + 25088x )\|2 - 28224x - 28224x - 56448x ) +--R * +--R 7 5 +--R atan(----) +--R +-+ +--R +-+ \|7 +--R \|7 cos(----------) +--R 2 +--R + +--R 16 12 8 +-+ 16 12 8 +--R ((- 1344x - 1344x - 2688x )\|2 + 3024x + 3024x + 6048x ) +--R * +--R 7 3 +--R atan(----) +--R +-+ +--R +-+4+--+2 \|7 +--R \|7 \|98 cos(----------) +--R 2 +--R + +--R 20 16 12 +-+ 20 16 +--R (6272x + 6272x + 12544x )\|2 - 14112x - 14112x +--R + +--R 12 +--R - 28224x +--R * +--R 7 +--R atan(----) +--R +-+ +--R +-+ \|7 +--R \|7 cos(----------) +--R 2 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R + +--R 8 4 +-+ 8 4 4+--+2 +--R ((896x + 896x + 1792)\|2 - 2016x - 2016x - 4032)\|98 +--R * +--R 7 8 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R 12 8 4 +-+ 12 8 4 +--R ((- 18816x - 18816x - 37632x )\|2 + 42336x + 42336x + 84672x ) +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R 16 12 8 +-+ 16 12 8 4+--+2 +--R ((1904x + 1904x + 3808x )\|2 - 4284x - 4284x - 8568x )\|98 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R 20 16 12 +-+ 20 16 12 +--R ((- 9408x - 9408x - 18816x )\|2 + 21168x + 21168x + 42336x ) +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R + +--R 24 20 16 +-+ 24 20 16 4+--+2 +--R ((224x + 224x + 448x )\|2 - 504x - 504x - 1008x )\|98 +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1483 +t0247:= x^4/(2+x^4+x^8) +--R +--R +--R 4 +--R x +--R (1334) ----------- +--R 8 4 +--R x + x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1334 + +--S 1335 of 1483 +r0247:= 1/8/(-1+2*2^(1/2))^(1/2)*(2*atan(((2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2)-2*x)/(2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2))*(2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2)-2*atan(((2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2)-2*x)/(2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2))*(2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2)-2*atan(((2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2)+2*x)/(2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2))*(2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2)+2*atan(((2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2)+2*x)/(2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2))*(2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2)-log(2^(1/4)-(2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2)*x+x^2)*(2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2)+log(2^(1/4)+(2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2)*x+x^2)*(2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2)+log(2^(1/4)-(2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2)*x+x^2)*(2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2)-log(2^(1/4)+(2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2)*x+x^2)*(2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2))/(2*2^(1/4)+_ + (-1+2*2^(1/2))^(1/2))^(1/2)/(2*2^(1/4)-_ + (-1+2*2^(1/2))^(1/2))^(1/2) +--R +--R +--R (1335) +--R +----------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (- 2\|2 - 1)\|2\|2 - 1 \|- \|2\|2 - 1 + 2\|2 +--R * +--R +--------------------+ +--R | +---------+ +--R | | +-+ 4+-+ 4+-+ 2 +--R log(x\|\|2\|2 - 1 + 2\|2 + \|2 + x ) +--R + +--R +--------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (2\|2 + 1)\|2\|2 - 1 \|\|2\|2 - 1 + 2\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ 4+-+ 2 +--R log(x\|- \|2\|2 - 1 + 2\|2 + \|2 + x ) +--R + +--R +--------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (- 2\|2 - 1)\|2\|2 - 1 \|\|2\|2 - 1 + 2\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ 4+-+ 2 +--R log(- x\|- \|2\|2 - 1 + 2\|2 + \|2 + x ) +--R + +--R +----------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (2\|2 + 1)\|2\|2 - 1 \|- \|2\|2 - 1 + 2\|2 +--R * +--R +--------------------+ +--R | +---------+ +--R | | +-+ 4+-+ 4+-+ 2 +--R log(- x\|\|2\|2 - 1 + 2\|2 + \|2 + x ) +--R + +--R +--------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (- 4\|2 - 2)\|2\|2 - 1 \|\|2\|2 - 1 + 2\|2 +--R * +--R atan +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((16\|2 - 92)\|2 - 50\|2 + 39)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (32\|2 - 184)\|2 + (- 100\|2 + 78)\|2 +--R * +--R +----------------------+ +--------------------+ +--R | +---------+ | +---------+ +--R | | +-+ 4+-+ | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 \|\|2\|2 - 1 + 2\|2 +--R + +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((32x\|2 - 184x)\|2 - 100x\|2 + 78x)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (64x\|2 - 368x)\|2 + (- 200x\|2 + 156x)\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 +--R / +--R 497 +--R + +--R +--------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (4\|2 + 2)\|2\|2 - 1 \|\|2\|2 - 1 + 2\|2 +--R * +--R atan +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((16\|2 - 92)\|2 - 50\|2 + 39)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (32\|2 - 184)\|2 + (- 100\|2 + 78)\|2 +--R * +--R +----------------------+ +--------------------+ +--R | +---------+ | +---------+ +--R | | +-+ 4+-+ | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 \|\|2\|2 - 1 + 2\|2 +--R + +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((- 32x\|2 + 184x)\|2 + 100x\|2 - 78x)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (- 64x\|2 + 368x)\|2 + (200x\|2 - 156x)\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 +--R / +--R 497 +--R + +--R +----------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (- 4\|2 - 2)\|2\|2 - 1 \|- \|2\|2 - 1 + 2\|2 +--R * +--R atan +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((16\|2 - 92)\|2 - 50\|2 + 39)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (- 32\|2 + 184)\|2 + (100\|2 - 78)\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 +--R + +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((32x\|2 - 184x)\|2 - 100x\|2 + 78x)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (- 64x\|2 + 368x)\|2 + (200x\|2 - 156x)\|2 +--R * +--R +--------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|\|2\|2 - 1 + 2\|2 +--R / +--R 497 +--R + +--R +----------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (4\|2 + 2)\|2\|2 - 1 \|- \|2\|2 - 1 + 2\|2 +--R * +--R atan +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((16\|2 - 92)\|2 - 50\|2 + 39)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (- 32\|2 + 184)\|2 + (100\|2 - 78)\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 +--R + +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((- 32x\|2 + 184x)\|2 + 100x\|2 - 78x)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (64x\|2 - 368x)\|2 + (- 200x\|2 + 156x)\|2 +--R * +--R +--------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|\|2\|2 - 1 + 2\|2 +--R / +--R 497 +--R / +--R +----------------------+ +--------------------+ +--R | +---------+ | +---------+ +--R | | +-+ 4+-+ | | +-+ 4+-+ +--R 56\|- \|2\|2 - 1 + 2\|2 \|\|2\|2 - 1 + 2\|2 +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1483 +a0247:=integrate(t0247,x) +--R +--R +--R (1336) +--R - +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R * +--R log +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 28 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R +-----------------------------------+ +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R +-+ | 2 2 +--R 4x\|7 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 28 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 2 +--R x +--R + +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R * +--R log +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R 28 |----------------------------------- sin(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R - +--R +-----------------------------------+ +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R +-+ | 2 2 +--R 4x\|7 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R 28 |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R 2 +--R x +--R + +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R 2 |----------------------------------- sin(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R * +--R atan +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R 14 |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R / +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R 14 |----------------------------------- sin(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R +-+ +--R - x\|7 +--R + +--R - +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R 2 |----------------------------------- sin(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R * +--R atan +--R +-----------------------------------+ +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 14 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R / +--R +-----------------------------------+ +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 14 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R +-+ +--R x\|7 +--R Type: Union(Expression(Integer),...) +--E 1336 + +--S 1337 of 1483 +m0247:=a0247-r0247 +--R +--R +--R (1337) +--R - +--R +----------------------+ +--------------------+ +--R | +---------+ | +---------+ +--R | | +-+ 4+-+ | | +-+ 4+-+ +--R 56\|- \|2\|2 - 1 + 2\|2 \|\|2\|2 - 1 + 2\|2 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R * +--R log +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 28 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R +-----------------------------------+ +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R +-+ | 2 2 +--R 4x\|7 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 28 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 2 +--R x +--R + +--R +----------------------+ +--------------------+ +--R | +---------+ | +---------+ +--R | | +-+ 4+-+ | | +-+ 4+-+ +--R 56\|- \|2\|2 - 1 + 2\|2 \|\|2\|2 - 1 + 2\|2 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R * +--R log +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 28 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R - +--R +-----------------------------------+ +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R +-+ | 2 2 +--R 4x\|7 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 28 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 2 +--R x +--R + +--R +----------------------+ +--------------------+ +--R | +---------+ | +---------+ +--R | | +-+ 4+-+ | | +-+ 4+-+ +--R 112\|- \|2\|2 - 1 + 2\|2 \|\|2\|2 - 1 + 2\|2 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- sin(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R * +--R atan +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R 14 |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R / +--R +-----------------------------------+ +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 14 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R +-+ +--R - x\|7 +--R + +--R - +--R +----------------------+ +--------------------+ +--R | +---------+ | +---------+ +--R | | +-+ 4+-+ | | +-+ 4+-+ +--R 112\|- \|2\|2 - 1 + 2\|2 \|\|2\|2 - 1 + 2\|2 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+ atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- sin(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R * +--R atan +--R +-----------------------------------+ +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 14 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R / +--R +-----------------------------------+ +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R 14 |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R +-+ +--R x\|7 +--R + +--R +----------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (2\|2 + 1)\|2\|2 - 1 \|- \|2\|2 - 1 + 2\|2 +--R * +--R +--------------------+ +--R | +---------+ +--R | | +-+ 4+-+ 4+-+ 2 +--R log(x\|\|2\|2 - 1 + 2\|2 + \|2 + x ) +--R + +--R +--------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (- 2\|2 - 1)\|2\|2 - 1 \|\|2\|2 - 1 + 2\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ 4+-+ 2 +--R log(x\|- \|2\|2 - 1 + 2\|2 + \|2 + x ) +--R + +--R +--------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (2\|2 + 1)\|2\|2 - 1 \|\|2\|2 - 1 + 2\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ 4+-+ 2 +--R log(- x\|- \|2\|2 - 1 + 2\|2 + \|2 + x ) +--R + +--R +----------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (- 2\|2 - 1)\|2\|2 - 1 \|- \|2\|2 - 1 + 2\|2 +--R * +--R +--------------------+ +--R | +---------+ +--R | | +-+ 4+-+ 4+-+ 2 +--R log(- x\|\|2\|2 - 1 + 2\|2 + \|2 + x ) +--R + +--R +--------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (4\|2 + 2)\|2\|2 - 1 \|\|2\|2 - 1 + 2\|2 +--R * +--R atan +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((16\|2 - 92)\|2 - 50\|2 + 39)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (32\|2 - 184)\|2 + (- 100\|2 + 78)\|2 +--R * +--R +----------------------+ +--------------------+ +--R | +---------+ | +---------+ +--R | | +-+ 4+-+ | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 \|\|2\|2 - 1 + 2\|2 +--R + +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((32x\|2 - 184x)\|2 - 100x\|2 + 78x)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (64x\|2 - 368x)\|2 + (- 200x\|2 + 156x)\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 +--R / +--R 497 +--R + +--R +--------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (- 4\|2 - 2)\|2\|2 - 1 \|\|2\|2 - 1 + 2\|2 +--R * +--R atan +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((16\|2 - 92)\|2 - 50\|2 + 39)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (32\|2 - 184)\|2 + (- 100\|2 + 78)\|2 +--R * +--R +----------------------+ +--------------------+ +--R | +---------+ | +---------+ +--R | | +-+ 4+-+ | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 \|\|2\|2 - 1 + 2\|2 +--R + +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((- 32x\|2 + 184x)\|2 + 100x\|2 - 78x)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (- 64x\|2 + 368x)\|2 + (200x\|2 - 156x)\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 +--R / +--R 497 +--R + +--R +----------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (4\|2 + 2)\|2\|2 - 1 \|- \|2\|2 - 1 + 2\|2 +--R * +--R atan +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((16\|2 - 92)\|2 - 50\|2 + 39)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (- 32\|2 + 184)\|2 + (100\|2 - 78)\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 +--R + +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((32x\|2 - 184x)\|2 - 100x\|2 + 78x)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (- 64x\|2 + 368x)\|2 + (200x\|2 - 156x)\|2 +--R * +--R +--------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|\|2\|2 - 1 + 2\|2 +--R / +--R 497 +--R + +--R +----------------------+ +--R +---------+ | +---------+ +--R +-+ | +-+ | | +-+ 4+-+ +--R (- 4\|2 - 2)\|2\|2 - 1 \|- \|2\|2 - 1 + 2\|2 +--R * +--R atan +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((16\|2 - 92)\|2 - 50\|2 + 39)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (- 32\|2 + 184)\|2 + (100\|2 - 78)\|2 +--R * +--R +----------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|- \|2\|2 - 1 + 2\|2 +--R + +--R +---------+ +--R +-+ 4+-+2 +-+ | +-+ +--R ((- 32x\|2 + 184x)\|2 + 100x\|2 - 78x)\|2\|2 - 1 +--R + +--R +-+ 4+-+3 +-+ 4+-+ +--R (64x\|2 - 368x)\|2 + (- 200x\|2 + 156x)\|2 +--R * +--R +--------------------+ +--R | +---------+ +--R | | +-+ 4+-+ +--R \|\|2\|2 - 1 + 2\|2 +--R / +--R 497 +--R / +--R +----------------------+ +--------------------+ +--R | +---------+ | +---------+ +--R | | +-+ 4+-+ | | +-+ 4+-+ +--R 56\|- \|2\|2 - 1 + 2\|2 \|\|2\|2 - 1 + 2\|2 +--R Type: Expression(Integer) +--E 1337 + +--S 1338 of 1483 +d0247:=normalize(D(m0247,x)) +--R +--R +--R (1338) +--R 7 4 7 2 7 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R 4 \|7 4 \|7 \|7 +--R - 14x sin(----------) - 28x cos(----------) sin(----------) +--R 2 2 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 4 \|7 +--R - 14x cos(----------) +--R 2 +--R * +--R 7 8 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 4 7 2 7 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R 4 \|7 4 \|7 \|7 +--R - 56x sin(----------) - 112x cos(----------) sin(----------) +--R 2 2 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 4 \|7 +--R - 56x cos(----------) +--R 2 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4+-+2 \|7 6 4+-+2 \|7 +--R (392x \|8 sin(----------) + 392x \|8 cos(----------)) +--R 2 2 +--R * +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (56x + 56x + 112x )\|7 \|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (56x + 56x + 112x )\|7 \|8 cos(----------) +--R 2 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R * +--R 7 5 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 4 7 2 7 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R 4 \|7 4 \|7 \|7 +--R - 84x sin(----------) - 168x cos(----------) sin(----------) +--R 2 2 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 4 \|7 +--R - 84x cos(----------) +--R 2 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4+-+2 \|7 6 4+-+2 \|7 +--R (392x \|8 sin(----------) + 392x \|8 cos(----------)) +--R 2 2 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4+-+2 \|7 8 4+-+2 \|7 +--R - 21x \|8 sin(----------) - 21x \|8 cos(----------) +--R 2 2 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (112x + 112x + 224x )\|7 \|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (112x + 112x + 224x )\|7 \|8 cos(----------) +--R 2 +--R * +--R 7 3 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 +-+4+-+2 \|7 +--R (- 4x - 4x - 8x )\|7 \|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 +-+4+-+2 \|7 +--R (- 4x - 4x - 8x )\|7 \|8 cos(----------) +--R 2 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R * +--R 7 3 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 4 7 2 7 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R 4 \|7 4 \|7 \|7 +--R - 56x sin(----------) - 112x cos(----------) sin(----------) +--R 2 2 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 4 \|7 +--R - 56x cos(----------) +--R 2 +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4+-+2 \|7 6 4+-+2 \|7 +--R (- 392x \|8 sin(----------) - 392x \|8 cos(----------)) +--R 2 2 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4+-+2 \|7 8 4+-+2 \|7 +--R (14x \|8 sin(----------) + 14x \|8 cos(----------)) +--R 2 2 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R 10 | 2 2 +--R 784x |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (56x + 56x + 112x )\|7 \|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 +-+4+-+2 \|7 +--R (56x + 56x + 112x )\|7 \|8 cos(----------) +--R 2 +--R * +--R 7 5 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 +-+4+-+2 \|7 +--R (4x + 4x + 8x )\|7 \|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 +-+4+-+2 \|7 +--R (4x + 4x + 8x )\|7 \|8 cos(----------) +--R 2 +--R * +--R 7 3 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 14 10 6 +-+ +--R (112x + 112x + 224x )\|7 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R * +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 4 7 2 7 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R 4 \|7 4 \|7 \|7 +--R - 14x sin(----------) - 28x cos(----------) sin(----------) +--R 2 2 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 4 \|7 +--R - 14x cos(----------) +--R 2 +--R * +--R 7 8 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4+-+2 \|7 6 4+-+2 \|7 +--R (- 392x \|8 sin(----------) - 392x \|8 cos(----------)) +--R 2 2 +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4+-+2 \|7 8 4+-+2 \|7 +--R (- 21x \|8 sin(----------) - 21x \|8 cos(----------)) +--R 2 2 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R - +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R 10 | 2 2 +--R 784x |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 12 +--R - 7x +--R / +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (14x + 14x + 28)sin(----------) +--R 2 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4 \|7 \|7 +--R (28x + 28x + 56)cos(----------) sin(----------) +--R 2 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (14x + 14x + 28)cos(----------) +--R 2 +--R * +--R 7 8 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (56x + 56x + 112)sin(----------) +--R 2 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4 \|7 \|7 +--R (112x + 112x + 224)cos(----------) sin(----------) +--R 2 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (56x + 56x + 112)cos(----------) +--R 2 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (- 392x - 392x - 784x )\|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (- 392x - 392x - 784x )\|8 cos(----------) +--R 2 +--R * +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R | 2 2 +--R |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (84x + 84x + 168)sin(----------) +--R 2 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4 \|7 \|7 +--R (168x + 168x + 336)cos(----------) sin(----------) +--R 2 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (84x + 84x + 168)cos(----------) +--R 2 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (- 392x - 392x - 784x )\|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (- 392x - 392x - 784x )\|8 cos(----------) +--R 2 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (21x + 21x + 42x )\|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (21x + 21x + 42x )\|8 cos(----------) +--R 2 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (56x + 56x + 112)sin(----------) +--R 2 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4 \|7 \|7 +--R (112x + 112x + 224)cos(----------) sin(----------) +--R 2 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (56x + 56x + 112)cos(----------) +--R 2 +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (392x + 392x + 784x )\|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (392x + 392x + 784x )\|8 cos(----------) +--R 2 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (- 14x - 14x - 28x )\|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (- 14x - 14x - 28x )\|8 cos(----------) +--R 2 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R 14 10 6 | 2 2 +--R (- 784x - 784x - 1568x ) |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R sin(---------------------) +--R 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (14x + 14x + 28)sin(----------) +--R 2 +--R + +--R 7 2 7 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 4 \|7 \|7 +--R (28x + 28x + 56)cos(----------) sin(----------) +--R 2 2 +--R + +--R 7 4 +--R atan(----) +--R +-+ +--R 8 4 \|7 +--R (14x + 14x + 28)cos(----------) +--R 2 +--R * +--R 7 8 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (392x + 392x + 784x )\|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 10 6 2 4+-+2 \|7 +--R (392x + 392x + 784x )\|8 cos(----------) +--R 2 +--R * +--R 7 6 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R +-----------------------------------+2 atan(---------------) +--R | 7 2 7 2 7 +--R | atan(----) atan(----) atan(----) +--R | +-+ +-+ +-+ +--R | \|7 \|7 \|7 +--R |sin(----------) + cos(----------) cos(----------) +--R | 2 2 2 +--R |----------------------------------- cos(---------------------) +--R 4| 4+-+2 2 +--R \| 196\|8 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (21x + 21x + 42x )\|8 sin(----------) +--R 2 +--R + +--R 7 2 +--R atan(----) +--R +-+ +--R 12 8 4 4+-+2 \|7 +--R (21x + 21x + 42x )\|8 cos(----------) +--R 2 +--R * +--R 7 4 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R +-----------------------------------+2 +--R | 7 2 7 2 +--R | atan(----) atan(----) +--R | +-+ +-+ +--R | \|7 \|7 +--R |sin(----------) + cos(----------) +--R 14 10 6 | 2 2 +--R (784x + 784x + 1568x ) |----------------------------------- +--R 4| 4+-+2 +--R \| 196\|8 +--R * +--R 7 2 +--R atan(----) +--R +-+ +--R \|7 +--R sin(----------) +--R 2 +--R atan(---------------) +--R 7 +--R atan(----) +--R +-+ +--R \|7 +--R cos(----------) +--R 2 +--R cos(---------------------) +--R 2 +--R + +--R 16 12 8 +--R 7x + 7x + 14x +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1483 +t0248:= x^3/(2+3*x^4+x^8) +--R +--R +--R 3 +--R x +--R (1339) ------------ +--R 8 4 +--R x + 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1339 + +--S 1340 of 1483 +r0248:= -1/2*atanh(3+2*x^4) +--R +--R +--R 4 +--R atanh(2x + 3) +--R (1340) - -------------- +--R 2 +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1483 +a0248:=integrate(t0248,x) +--R +--R +--R 4 4 +--R - log(x + 2) + log(x + 1) +--R (1341) --------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 1341 + +--S 1342 of 1483 +m0248:=a0248-r0248 +--R +--R +--R 4 4 4 +--R - log(x + 2) + log(x + 1) + 2atanh(2x + 3) +--R (1342) --------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 1483 +d0248:=D(m0248,x) +--R +--R +--R (1343) 0 +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1483 +t0249:= 1/x/(1+x^5+x^10) +--R +--R +--R 1 +--R (1344) ------------ +--R 11 6 +--R x + x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1344 + +--S 1345 of 1483 +r0249:= -1/15*atan(1/3*(1+2*x^5)*3^(1/2)::EXPR(INT))*3^(1/2)+log(x)-_ + 1/10*log(1+x^5+x^10) +--R +--R +--R 5 +-+ +--R 10 5 +-+ (2x + 1)\|3 +--R - 3log(x + x + 1) + 30log(x) - 2\|3 atan(-------------) +--R 3 +--R (1345) ---------------------------------------------------------- +--R 30 +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1483 +a0249:=integrate(t0249,x) +--R +--R +--R 5 +-+ +--R +-+ 10 5 +-+ (2x + 1)\|3 +--R - \|3 log(x + x + 1) + 10\|3 log(x) - 2atan(-------------) +--R 3 +--R (1346) ------------------------------------------------------------- +--R +-+ +--R 10\|3 +--R Type: Union(Expression(Integer),...) +--E 1346 + +--S 1347 of 1483 +m0249:=a0249-r0249 +--R +--R +--R (1347) 0 +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1483 +d0249:=D(m0249,x) +--R +--R +--R (1348) 0 +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1483 +t0250:= 1/(x+x^6+x^11) +--R +--R +--R 1 +--R (1349) ------------ +--R 11 6 +--R x + x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1349 + +--S 1350 of 1483 +r0250:= -1/15*atan(1/3*(1+2*x^5)*3^(1/2)::EXPR(INT))*3^(1/2)+log(x)-_ + 1/10*log(1+x^5+x^10) +--R +--R +--R 5 +-+ +--R 10 5 +-+ (2x + 1)\|3 +--R - 3log(x + x + 1) + 30log(x) - 2\|3 atan(-------------) +--R 3 +--R (1350) ---------------------------------------------------------- +--R 30 +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1483 +a0250:=integrate(t0250,x) +--R +--R +--R 5 +-+ +--R +-+ 10 5 +-+ (2x + 1)\|3 +--R - \|3 log(x + x + 1) + 10\|3 log(x) - 2atan(-------------) +--R 3 +--R (1351) ------------------------------------------------------------- +--R +-+ +--R 10\|3 +--R Type: Union(Expression(Integer),...) +--E 1351 + +--S 1352 of 1483 +m0250:=a0250-r0250 +--R +--R +--R (1352) 0 +--R Type: Expression(Integer) +--E 1352 + +--S 1353 of 1483 +d0250:=D(m0250,x) +--R +--R +--R (1353) 0 +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1483 +t0251:= (3+2*x)/(-2+x)/(5+x) +--R +--R +--R 2x + 3 +--R (1354) ------------ +--R 2 +--R x + 3x - 10 +--R Type: Fraction(Polynomial(Integer)) +--E 1354 + +--S 1355 of 1483 +r0251:= log(2-x)+log(5+x) +--R +--R +--R (1355) log(x + 5) + log(- x + 2) +--R Type: Expression(Integer) +--E 1355 + +--S 1356 of 1483 +a0251:=integrate(t0251,x) +--R +--R +--R 2 +--R (1356) log(x + 3x - 10) +--R Type: Union(Expression(Integer),...) +--E 1356 + +--S 1357 of 1483 +m0251:=a0251-r0251 +--R +--R +--R 2 +--R (1357) log(x + 3x - 10) - log(x + 5) - log(- x + 2) +--R Type: Expression(Integer) +--E 1357 + +--S 1358 of 1483 +d0251:=D(m0251,x) +--R +--R +--R (1358) 0 +--R Type: Expression(Integer) +--E 1358 + +--S 1359 of 1483 +t0252:= x/(-1+x^2) +--R +--R +--R x +--R (1359) ------ +--R 2 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1359 + +--S 1360 of 1483 +r0252:= 1/2*log(1-x^2) +--R +--R +--R 2 +--R log(- x + 1) +--R (1360) ------------- +--R 2 +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 1483 +a0252:=integrate(t0252,x) +--R +--R +--R 2 +--R log(x - 1) +--R (1361) ----------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1361 + +--S 1362 of 1483 +m0252:=a0252-r0252 +--R +--R +--R 2 2 +--R log(x - 1) - log(- x + 1) +--R (1362) --------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1362 + +--S 1363 of 1483 +d0252:=D(m0252,x) +--R +--R +--R (1363) 0 +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1483 +t0253:= 1/(-1+x^2)^2 +--R +--R +--R 1 +--R (1364) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1364 + +--S 1365 of 1483 +r0253:= x/(2-2*x^2)+1/2*atanh(x) +--R +--R +--R 2 +--R (x - 1)atanh(x) - x +--R (1365) -------------------- +--R 2 +--R 2x - 2 +--R Type: Expression(Integer) +--E 1365 + +--S 1366 of 1483 +a0253:=integrate(t0253,x) +--R +--R +--R 2 2 +--R (x - 1)log(x + 1) + (- x + 1)log(x - 1) - 2x +--R (1366) ---------------------------------------------- +--R 2 +--R 4x - 4 +--R Type: Union(Expression(Integer),...) +--E 1366 + +--S 1367 of 1483 +m0253:=a0253-r0253 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (1367) ----------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 1367 + +--S 1368 of 1483 +d0253:=D(m0253,x) +--R +--R +--R (1368) 0 +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1483 +t0254:= (-1+4*x^5)/(1+x+x^5)^2 +--R +--R +--R 5 +--R 4x - 1 +--R (1369) ----------------------------- +--R 10 6 5 2 +--R x + 2x + 2x + x + 2x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1369 + +--S 1370 of 1483 +r0254:= -x/(1+x+x^5) +--R +--R +--R x +--R (1370) - ---------- +--R 5 +--R x + x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1370 + +--S 1371 of 1483 +a0254:=integrate(t0254,x) +--R +--R +--R x +--R (1371) - ---------- +--R 5 +--R x + x + 1 +--R Type: Union(Expression(Integer),...) +--E 1371 + +--S 1372 of 1483 +m0254:=a0254-r0254 +--R +--R +--R (1372) 0 +--R Type: Expression(Integer) +--E 1372 + +--S 1373 of 1483 +d0254:=D(m0254,x) +--R +--R +--R (1373) 0 +--R Type: Expression(Integer) +--E 1373 + +--S 1374 of 1483 +t0255:= (5+3*x)/(1-x-x^2+x^3) +--R +--R +--R 3x + 5 +--R (1374) --------------- +--R 3 2 +--R x - x - x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1374 + +--S 1375 of 1483 +r0255:= 4/(1-x)+atanh(x) +--R +--R +--R (x - 1)atanh(x) - 4 +--R (1375) ------------------- +--R x - 1 +--R Type: Expression(Integer) +--E 1375 + +--S 1376 of 1483 +a0255:=integrate(t0255,x) +--R +--R +--R (x - 1)log(x + 1) + (- x + 1)log(x - 1) - 8 +--R (1376) ------------------------------------------- +--R 2x - 2 +--R Type: Union(Expression(Integer),...) +--E 1376 + +--S 1377 of 1483 +m0255:=a0255-r0255 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (1377) ----------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1377 + +--S 1378 of 1483 +d0255:=D(m0255,x) +--R +--R +--R (1378) 0 +--R Type: Expression(Integer) +--E 1378 + +--S 1379 of 1483 +t0256:= (3+2*x^2)/(1-2*x^2+x^4) +--R +--R +--R 2 +--R 2x + 3 +--R (1379) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1379 + +--S 1380 of 1483 +r0256:= 5*x/(2-2*x^2)+1/2*atanh(x) +--R +--R +--R 2 +--R (x - 1)atanh(x) - 5x +--R (1380) --------------------- +--R 2 +--R 2x - 2 +--R Type: Expression(Integer) +--E 1380 + +--S 1381 of 1483 +a0256:=integrate(t0256,x) +--R +--R +--R 2 2 +--R (x - 1)log(x + 1) + (- x + 1)log(x - 1) - 10x +--R (1381) ----------------------------------------------- +--R 2 +--R 4x - 4 +--R Type: Union(Expression(Integer),...) +--E 1381 + +--S 1382 of 1483 +m0256:=a0256-r0256 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (1382) ----------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 1382 + +--S 1383 of 1483 +d0256:=D(m0256,x) +--R +--R +--R (1383) 0 +--R Type: Expression(Integer) +--E 1383 + +--S 1384 of 1483 +t0257:= (x+x^2)/(4+x)/(-4+x^2) +--R +--R +--R 2 +--R x + x +--R (1384) ------------------ +--R 3 2 +--R x + 4x - 4x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 1384 + +--S 1385 of 1483 +r0257:= -1/2*atanh(1/2*x)+log(4+x) +--R +--R +--R x +--R 2log(x + 4) - atanh(-) +--R 2 +--R (1385) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 1385 + +--S 1386 of 1483 +a0257:=integrate(t0257,x) +--R +--R +--R 4log(x + 4) - log(x + 2) + log(x - 2) +--R (1386) ------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 1386 + +--S 1387 of 1483 +m0257:=a0257-r0257 +--R +--R +--R x +--R - log(x + 2) + log(x - 2) + 2atanh(-) +--R 2 +--R (1387) ------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 1387 + +--S 1388 of 1483 +d0257:=D(m0257,x) +--R +--R +--R (1388) 0 +--R Type: Expression(Integer) +--E 1388 + +--S 1389 of 1483 +t0258:= 1/(4-5*x^2+x^4) +--R +--R +--R 1 +--R (1389) ------------ +--R 4 2 +--R x - 5x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1389 + +--S 1390 of 1483 +r0258:= -1/6*atanh(1/2*x)+1/3*atanh(x) +--R +--R +--R x +--R 2atanh(x) - atanh(-) +--R 2 +--R (1390) -------------------- +--R 6 +--R Type: Expression(Integer) +--E 1390 + +--S 1391 of 1483 +a0258:=integrate(t0258,x) +--R +--R +--R - log(x + 2) + 2log(x + 1) - 2log(x - 1) + log(x - 2) +--R (1391) ----------------------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 1391 + +--S 1392 of 1483 +m0258:=a0258-r0258 +--R +--R +--R (1392) +--R x +--R - log(x + 2) + 2log(x + 1) - 2log(x - 1) + log(x - 2) - 4atanh(x) + 2atanh(-) +--R 2 +--R ----------------------------------------------------------------------------- +--R 12 +--R Type: Expression(Integer) +--E 1392 + +--S 1393 of 1483 +d0258:=D(m0258,x) +--R +--R +--R (1393) 0 +--R Type: Expression(Integer) +--E 1393 + +--S 1394 of 1483 +t0259:= x^2/(-1+x)^2/(1+x)^2 +--R +--R +--R 2 +--R x +--R (1394) ------------ +--R 4 2 +--R x - 2x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1394 + +--S 1395 of 1483 +r0259:= x/(2-2*x^2)-1/2*atanh(x) +--R +--R +--R 2 +--R (- x + 1)atanh(x) - x +--R (1395) ---------------------- +--R 2 +--R 2x - 2 +--R Type: Expression(Integer) +--E 1395 + +--S 1396 of 1483 +a0259:=integrate(t0259,x) +--R +--R +--R 2 2 +--R (- x + 1)log(x + 1) + (x - 1)log(x - 1) - 2x +--R (1396) ---------------------------------------------- +--R 2 +--R 4x - 4 +--R Type: Union(Expression(Integer),...) +--E 1396 + +--S 1397 of 1483 +m0259:=a0259-r0259 +--R +--R +--R - log(x + 1) + log(x - 1) + 2atanh(x) +--R (1397) ------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 1397 + +--S 1398 of 1483 +d0259:=D(m0259,x) +--R +--R +--R (1398) 0 +--R Type: Expression(Integer) +--E 1398 + +--S 1399 of 1483 +t0260:= x/(1+x^2)/(4+x^2) +--R +--R +--R x +--R (1399) ------------ +--R 4 2 +--R x + 5x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1399 + +--S 1400 of 1483 +r0260:= -1/3*atanh(5/3+2/3*x^2) +--R +--R +--R 2 +--R 2x + 5 +--R atanh(-------) +--R 3 +--R (1400) - -------------- +--R 3 +--R Type: Expression(Integer) +--E 1400 + +--S 1401 of 1483 +a0260:=integrate(t0260,x) +--R +--R +--R 2 2 +--R - log(x + 4) + log(x + 1) +--R (1401) --------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1401 + +--S 1402 of 1483 +m0260:=a0260-r0260 +--R +--R +--R 2 +--R 2 2 2x + 5 +--R - log(x + 4) + log(x + 1) + 2atanh(-------) +--R 3 +--R (1402) --------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1402 + +--S 1403 of 1483 +d0260:=D(m0260,x) +--R +--R +--R (1403) 0 +--R Type: Expression(Integer) +--E 1403 + +--S 1404 of 1483 +t0261:= 1/(2+2*x^2+x^4) +--R +--R +--R 1 +--R (1404) ------------ +--R 4 2 +--R x + 2x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1404 + +--S 1405 of 1483 +r0261:= -1/4*atan(((-2+2*2^(1/2))^(1/2)-2*x)/(2+2*2^(1/2))^(1/2))/_ + (1+2^(1/2))^(1/2)+1/4*atan(((-2+2*2^(1/2))^(1/2)+2*x)/_ + (2+2*2^(1/2))^(1/2))/(1+2^(1/2))^(1/2)-1/8*log(2^(1/2)-_ + (-2+2*2^(1/2))^(1/2)*x+x^2)/(2^(1/2)-1)^(1/2)+_ + 1/8*log(2^(1/2)+(-2+2*2^(1/2))^(1/2)*x+x^2)/(2^(1/2)-1)^(1/2) +--R +--R +--R (1405) +--R +--------+ +---------+ +--R | +-+ | +-+ +-+ 2 +--R \|\|2 + 1 log(x\|2\|2 - 2 + \|2 + x ) +--R + +--R +--------+ +---------+ +--R | +-+ | +-+ +-+ 2 +--R - \|\|2 + 1 log(- x\|2\|2 - 2 + \|2 + x ) +--R + +--R +---------+ +---------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 1)\|2\|2 - 2 + 2x\|2 - 2x)\|2\|2 + 2 +--R 2\|\|2 - 1 atan(--------------------------------------------------) +--R 2 +--R + +--R +---------+ +---------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 1)\|2\|2 - 2 - 2x\|2 + 2x)\|2\|2 + 2 +--R - 2\|\|2 - 1 atan(--------------------------------------------------) +--R 2 +--R / +--R +--------+ +--------+ +--R | +-+ | +-+ +--R 8\|\|2 - 1 \|\|2 + 1 +--R Type: Expression(Integer) +--E 1405 + +--S 1406 of 1483 +a0261:=integrate(t0261,x) +--R +--R +--R (1406) +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) + x\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R - x\|2 \|2 cos(---) + x +--R 8 +--R + +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) - x\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R x\|2 \|2 cos(---) + x +--R 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|2 sin(---) + \|2 cos(---) +--R 4+-+ %pi 8 8 +--R 2\|2 sin(---)atan(-----------------------------------) +--R 8 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) - x\|2 +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|2 sin(---) + \|2 cos(---) +--R 4+-+ %pi 8 8 +--R - 2\|2 sin(---)atan(-----------------------------------) +--R 8 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) + x\|2 +--R 8 8 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression(Integer),...) +--E 1406 + +--S 1407 of 1483 +m0261:=a0261-r0261 +--R +--R +--R (1407) +--R +--------+ +---------+ +--R +-+ | +-+ | +-+ +-+ 2 +--R - \|2 \|\|2 + 1 log(x\|2\|2 - 2 + \|2 + x ) +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|2 cos(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R log +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) + x\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R - x\|2 \|2 cos(---) + x +--R 8 +--R + +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|2 cos(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R log +--R 4+-+2 %pi 2 +-+4+-+ %pi 4+-+2 %pi 2 +--R \|2 sin(---) - x\|2 \|2 sin(---) + \|2 cos(---) +--R 8 8 8 +--R + +--R +-+4+-+ %pi 2 +--R x\|2 \|2 cos(---) + x +--R 8 +--R + +--R +--------+ +---------+ +--R +-+ | +-+ | +-+ +-+ 2 +--R \|2 \|\|2 + 1 log(- x\|2\|2 - 2 + \|2 + x ) +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 - 1 +--R * +--R +---------+ +---------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 1)\|2\|2 - 2 + 2x\|2 - 2x)\|2\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +---------+ +---------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 1)\|2\|2 - 2 - 2x\|2 + 2x)\|2\|2 + 2 +--R 2\|2 \|\|2 - 1 atan(--------------------------------------------------) +--R 2 +--R + +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R 4\|2 sin(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|2 sin(---) + \|2 cos(---) +--R 8 8 +--R atan(-----------------------------------) +--R 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) - x\|2 +--R 8 8 +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R 4\|2 sin(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|2 sin(---) + \|2 cos(---) +--R 8 8 +--R atan(-----------------------------------) +--R 4+-+ %pi 4+-+ %pi +-+ +--R \|2 sin(---) - \|2 cos(---) + x\|2 +--R 8 8 +--R / +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ +--R 8\|2 \|\|2 - 1 \|\|2 + 1 +--R Type: Expression(Integer) +--E 1407 + +--S 1408 of 1483 +d0261:=normalize(D(m0261,x)) +--R +--R +--R (1408) +--R 2 4+-+2 2 %pi 8 +--R ((20x - 28)\|2 - 28x + 40)sin(---) +--R 8 +--R + +--R 2 4+-+2 2 %pi 2 %pi 6 +--R ((80x - 112)\|2 - 112x + 160)cos(---) sin(---) +--R 8 8 +--R + +--R 4 2 4+-+2 4 2 %pi %pi 5 +--R ((- 112x + 160x )\|2 + 160x - 224x )cos(---)sin(---) +--R 8 8 +--R + +--R 2 4+-+2 2 %pi 4 6 4 4+-+2 +--R ((120x - 168)\|2 - 168x + 240)cos(---) + (20x - 28x )\|2 +--R 8 +--R + +--R 6 4 +--R - 28x + 40x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 4 2 4+-+2 4 2 %pi 3 %pi 3 +--R ((- 224x + 320x )\|2 + 320x - 448x )cos(---) sin(---) +--R 8 8 +--R + +--R 2 4+-+2 2 %pi 6 +--R ((80x - 112)\|2 - 112x + 160)cos(---) +--R 8 +--R + +--R 6 4 4+-+2 6 4 %pi 2 +--R ((200x - 280x )\|2 - 280x + 400x )cos(---) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4 2 4+-+2 4 2 %pi 5 +--R ((- 112x + 160x )\|2 + 160x - 224x )cos(---) +--R 8 +--R + +--R 8 6 4+-+2 8 6 %pi +--R ((- 56x + 80x )\|2 + 80x - 112x )cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 2 4+-+2 2 %pi 8 +--R ((20x - 28)\|2 - 28x + 40)cos(---) +--R 8 +--R + +--R 6 4 4+-+2 6 4 %pi 4 10 8 4+-+2 +--R ((20x - 28x )\|2 - 28x + 40x )cos(---) + (5x - 7x )\|2 +--R 8 +--R + +--R 10 8 +--R - 7x + 10x +--R * +--R +---------+ +----------+ +--R |4+-+2 | 4+-+2 +--R \|\|2 + 1 \|2\|2 + 2 +--R + +--R 2 4+-+2 2 %pi 8 +--R ((- 4x - 4)\|2 + 4x + 8)sin(---) +--R 8 +--R + +--R 2 4+-+2 2 %pi 2 %pi 6 +--R ((- 16x - 16)\|2 + 16x + 32)cos(---) sin(---) +--R 8 8 +--R + +--R 4 2 4+-+2 4 2 %pi %pi 5 +--R ((16x + 32x )\|2 - 32x - 32x )cos(---)sin(---) +--R 8 8 +--R + +--R 2 4+-+2 2 %pi 4 6 4 4+-+2 +--R ((- 24x - 24)\|2 + 24x + 48)cos(---) + (- 4x - 4x )\|2 +--R 8 +--R + +--R 6 4 +--R 4x + 8x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 4 2 4+-+2 4 2 %pi 3 %pi 3 +--R ((32x + 64x )\|2 - 64x - 64x )cos(---) sin(---) +--R 8 8 +--R + +--R 2 4+-+2 2 %pi 6 +--R ((- 16x - 16)\|2 + 16x + 32)cos(---) +--R 8 +--R + +--R 6 4 4+-+2 6 4 %pi 2 +--R ((- 40x - 40x )\|2 + 40x + 80x )cos(---) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 4 2 4+-+2 4 2 %pi 5 +--R ((16x + 32x )\|2 - 32x - 32x )cos(---) +--R 8 +--R + +--R 8 6 4+-+2 8 6 %pi +--R ((8x + 16x )\|2 - 16x - 16x )cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 2 4+-+2 2 %pi 8 +--R ((- 4x - 4)\|2 + 4x + 8)cos(---) +--R 8 +--R + +--R 6 4 4+-+2 6 4 %pi 4 10 8 4+-+2 10 +--R ((- 4x - 4x )\|2 + 4x + 8x )cos(---) + (- x - x )\|2 + x +--R 8 +--R + +--R 8 +--R 2x +--R * +--R +---------+ +----------+ +--R |4+-+2 | 4+-+2 +--R \|\|2 - 1 \|2\|2 - 2 +--R + +--R 4 2 4+-+2 4 2 %pi 8 +--R ((16x + 32x + 32)\|2 - 24x - 48x - 48)sin(---) +--R 8 +--R + +--R 4 2 4+-+2 4 2 %pi 2 +--R ((64x + 128x + 128)\|2 - 96x - 192x - 192)cos(---) +--R 8 +--R + +--R 6 4 2 4+-+2 6 4 2 +--R (- 12x - 24x - 24x )\|2 + 16x + 32x + 32x +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 6 4 2 4+-+2 6 4 2 %pi %pi 5 +--R ((- 72x - 144x - 144x )\|2 + 96x + 192x + 192x )cos(---)sin(---) +--R 8 8 +--R + +--R 4 2 4+-+2 4 2 %pi 4 +--R ((96x + 192x + 192)\|2 - 144x - 288x - 288)cos(---) +--R 8 +--R + +--R 6 4 2 4+-+2 6 4 2 %pi 2 +--R ((- 12x - 24x - 24x )\|2 + 16x + 32x + 32x )cos(---) +--R 8 +--R + +--R 8 6 4 4+-+2 8 6 4 +--R (8x + 16x + 16x )\|2 - 12x - 24x - 24x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 6 4 2 4+-+2 6 4 2 %pi 3 +--R ((- 144x - 288x - 288x )\|2 + 192x + 384x + 384x )cos(---) +--R 8 +--R + +--R 8 6 4 4+-+2 8 6 4 %pi +--R ((32x + 64x + 64x )\|2 - 48x - 96x - 96x )cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4 2 4+-+2 4 2 %pi 6 +--R ((64x + 128x + 128)\|2 - 96x - 192x - 192)cos(---) +--R 8 +--R + +--R 6 4 2 4+-+2 6 4 2 %pi 4 +--R ((12x + 24x + 24x )\|2 - 16x - 32x - 32x )cos(---) +--R 8 +--R + +--R 8 6 4 4+-+2 8 6 4 %pi 2 +--R ((80x + 160x + 160x )\|2 - 120x - 240x - 240x )cos(---) +--R 8 +--R + +--R 10 8 6 4+-+2 10 8 6 +--R (- 6x - 12x - 12x )\|2 + 8x + 16x + 16x +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 6 4 2 4+-+2 6 4 2 %pi 5 +--R ((- 72x - 144x - 144x )\|2 + 96x + 192x + 192x )cos(---) +--R 8 +--R + +--R 8 6 4 4+-+2 8 6 4 %pi 3 +--R ((- 32x - 64x - 64x )\|2 + 48x + 96x + 96x )cos(---) +--R 8 +--R + +--R 10 8 6 4+-+2 10 8 6 %pi +--R ((- 12x - 24x - 24x )\|2 + 16x + 32x + 32x )cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 4 2 4+-+2 4 2 %pi 8 +--R ((16x + 32x + 32)\|2 - 24x - 48x - 48)cos(---) +--R 8 +--R + +--R 6 4 2 4+-+2 6 4 2 %pi 6 +--R ((12x + 24x + 24x )\|2 - 16x - 32x - 32x )cos(---) +--R 8 +--R + +--R 8 6 4 4+-+2 8 6 4 %pi 4 +--R ((8x + 16x + 16x )\|2 - 12x - 24x - 24x )cos(---) +--R 8 +--R + +--R 10 8 6 4+-+2 10 8 6 %pi 2 +--R ((6x + 12x + 12x )\|2 - 8x - 16x - 16x )cos(---) +--R 8 +--R / +--R 4 2 4+-+2 4 2 %pi 8 +--R ((32x + 64x + 64)\|2 - 48x - 96x - 96)sin(---) +--R 8 +--R + +--R 4 2 4+-+2 4 2 %pi 2 %pi 6 +--R ((128x + 256x + 256)\|2 - 192x - 384x - 384)cos(---) sin(---) +--R 8 8 +--R + +--R 6 4 2 4+-+2 6 4 2 %pi %pi 5 +--R ((- 192x - 384x - 384x )\|2 + 256x + 512x + 512x )cos(---)sin(---) +--R 8 8 +--R + +--R 4 2 4+-+2 4 2 %pi 4 +--R ((192x + 384x + 384)\|2 - 288x - 576x - 576)cos(---) +--R 8 +--R + +--R 8 6 4 4+-+2 8 6 4 +--R (32x + 64x + 64x )\|2 - 48x - 96x - 96x +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 6 4 2 4+-+2 6 4 2 %pi 3 +--R ((- 384x - 768x - 768x )\|2 + 512x + 1024x + 1024x )cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 4 2 4+-+2 4 2 %pi 6 +--R ((128x + 256x + 256)\|2 - 192x - 384x - 384)cos(---) +--R 8 +--R + +--R 8 6 4 4+-+2 8 6 4 %pi 2 +--R ((320x + 640x + 640x )\|2 - 480x - 960x - 960x )cos(---) +--R 8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 6 4 2 4+-+2 6 4 2 %pi 5 +--R ((- 192x - 384x - 384x )\|2 + 256x + 512x + 512x )cos(---) +--R 8 +--R + +--R 10 8 6 4+-+2 10 8 6 %pi +--R ((- 96x - 192x - 192x )\|2 + 128x + 256x + 256x )cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 4 2 4+-+2 4 2 %pi 8 +--R ((32x + 64x + 64)\|2 - 48x - 96x - 96)cos(---) +--R 8 +--R + +--R 8 6 4 4+-+2 8 6 4 %pi 4 +--R ((32x + 64x + 64x )\|2 - 48x - 96x - 96x )cos(---) +--R 8 +--R + +--R 12 10 8 4+-+2 12 10 8 +--R (8x + 16x + 16x )\|2 - 12x - 24x - 24x +--R Type: Expression(Integer) +--E 1408 + +--S 1409 of 1483 +t0262:= x^5/(x-x^3) +--R +--R +--R 4 +--R x +--R (1409) - ------ +--R 2 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1409 + +--S 1410 of 1483 +r0262:= -x-1/3*x^3+atanh(x) +--R +--R +--R 3 +--R 3atanh(x) - x - 3x +--R (1410) ------------------- +--R 3 +--R Type: Expression(Integer) +--E 1410 + +--S 1411 of 1483 +a0262:=integrate(t0262,x) +--R +--R +--R 3 +--R 3log(x + 1) - 3log(x - 1) - 2x - 6x +--R (1411) ------------------------------------ +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1411 + +--S 1412 of 1483 +m0262:=a0262-r0262 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (1412) ----------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1412 + +--S 1413 of 1483 +d0262:=D(m0262,x) +--R +--R +--R (1413) 0 +--R Type: Expression(Integer) +--E 1413 + +--S 1414 of 1483 +t0263:= x^3/(x-x^3) +--R +--R +--R 2 +--R x +--R (1414) - ------ +--R 2 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1414 + +--S 1415 of 1483 +r0263:= -x+atanh(x) +--R +--R +--R (1415) atanh(x) - x +--R Type: Expression(Integer) +--E 1415 + +--S 1416 of 1483 +a0263:=integrate(t0263,x) +--R +--R +--R log(x + 1) - log(x - 1) - 2x +--R (1416) ---------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1416 + +--S 1417 of 1483 +m0263:=a0263-r0263 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (1417) ----------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1417 + +--S 1418 of 1483 +d0263:=D(m0263,x) +--R +--R +--R (1418) 0 +--R Type: Expression(Integer) +--E 1418 + +--S 1419 of 1483 +t0264:= x^2/(x-x^3) +--R +--R +--R x +--R (1419) - ------ +--R 2 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1419 + +--S 1420 of 1483 +r0264:= -1/2*log(1-x^2) +--R +--R +--R 2 +--R log(- x + 1) +--R (1420) - ------------- +--R 2 +--R Type: Expression(Integer) +--E 1420 + +--S 1421 of 1483 +a0264:=integrate(t0264,x) +--R +--R +--R 2 +--R log(x - 1) +--R (1421) - ----------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1421 + +--S 1422 of 1483 +m0264:=a0264-r0264 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (1422) ----------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1422 + +--S 1423 of 1483 +d0264:=D(m0264,x) +--R +--R +--R (1423) 0 +--R Type: Expression(Integer) +--E 1423 + +--S 1424 of 1483 +t0265:= 1/x/(x-x^3) +--R +--R +--R 1 +--R (1424) - ------- +--R 4 2 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1424 + +--S 1425 of 1483 +r0265:= -1/x+atanh(x) +--R +--R +--R x atanh(x) - 1 +--R (1425) -------------- +--R x +--R Type: Expression(Integer) +--E 1425 + +--S 1426 of 1483 +a0265:=integrate(t0265,x) +--R +--R +--R x log(x + 1) - x log(x - 1) - 2 +--R (1426) ------------------------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 1426 + +--S 1427 of 1483 +m0265:=a0265-r0265 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (1427) ----------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1427 + +--S 1428 of 1483 +d0265:=D(m0265,x) +--R +--R +--R (1428) 0 +--R Type: Expression(Integer) +--E 1428 + +--S 1429 of 1483 +t0266:= 1/x^3/(x-x^3) +--R +--R +--R 1 +--R (1429) - ------- +--R 6 4 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1429 + +--S 1430 of 1483 +r0266:= -1/3/x^3-1/x+atanh(x) +--R +--R +--R 3 2 +--R 3x atanh(x) - 3x - 1 +--R (1430) --------------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 1430 + +--S 1431 of 1483 +a0266:=integrate(t0266,x) +--R +--R +--R 3 3 2 +--R 3x log(x + 1) - 3x log(x - 1) - 6x - 2 +--R (1431) --------------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1431 + +--S 1432 of 1483 +m0266:=a0266-r0266 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (1432) ----------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1432 + +--S 1433 of 1483 +d0266:=D(m0266,x) +--R +--R +--R (1433) 0 +--R Type: Expression(Integer) +--E 1433 + +--S 1434 of 1483 +t0267:= (1-2*x^2)/(x^2-x^4) +--R +--R +--R 2 +--R 2x - 1 +--R (1434) ------- +--R 4 2 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1434 + +--S 1435 of 1483 +r0267:= -1/x-atanh(x) +--R +--R +--R - x atanh(x) - 1 +--R (1435) ---------------- +--R x +--R Type: Expression(Integer) +--E 1435 + +--S 1436 of 1483 +a0267:=integrate(t0267,x) +--R +--R +--R - x log(x + 1) + x log(x - 1) - 2 +--R (1436) --------------------------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 1436 + +--S 1437 of 1483 +m0267:=a0267-r0267 +--R +--R +--R - log(x + 1) + log(x - 1) + 2atanh(x) +--R (1437) ------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1437 + +--S 1438 of 1483 +d0267:=D(m0267,x) +--R +--R +--R (1438) 0 +--R Type: Expression(Integer) +--E 1438 + +--S 1439 of 1483 +t0268:= (1+x^6)/(x-x^7) +--R +--R +--R 6 +--R - x - 1 +--R (1439) -------- +--R 7 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1439 + +--S 1440 of 1483 +r0268:= log(x)-1/3*log(1-x^6) +--R +--R +--R 6 +--R 3log(x) - log(- x + 1) +--R (1440) ----------------------- +--R 3 +--R Type: Expression(Integer) +--E 1440 + +--S 1441 of 1483 +a0268:=integrate(t0268,x) +--R +--R +--R 6 +--R - log(x - 1) + 3log(x) +--R (1441) ----------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1441 + +--S 1442 of 1483 +m0268:=a0268-r0268 +--R +--R +--R 6 6 +--R - log(x - 1) + log(- x + 1) +--R (1442) ----------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1442 + +--S 1443 of 1483 +d0268:=D(m0268,x) +--R +--R +--R (1443) 0 +--R Type: Expression(Integer) +--E 1443 + +--S 1444 of 1483 +t0269:= (8+5*x^10)/(x-x^11) +--R +--R +--R 10 +--R - 5x - 8 +--R (1444) ---------- +--R 11 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1444 + +--S 1445 of 1483 +r0269:= 8*log(x)-13/10*log(1-x^10) +--R +--R +--R 10 +--R 80log(x) - 13log(- x + 1) +--R (1445) --------------------------- +--R 10 +--R Type: Expression(Integer) +--E 1445 + +--S 1446 of 1483 +a0269:=integrate(t0269,x) +--R +--R +--R 10 +--R - 13log(x - 1) + 80log(x) +--R (1446) --------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 1446 + +--S 1447 of 1483 +m0269:=a0269-r0269 +--R +--R +--R 10 10 +--R - 13log(x - 1) + 13log(- x + 1) +--R (1447) ----------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 1447 + +--S 1448 of 1483 +d0269:=D(m0269,x) +--R +--R +--R (1448) 0 +--R Type: Expression(Integer) +--E 1448 + +--S 1449 of 1483 +t0270:= (1+x^2)/x/(3+x^2) +--R +--R +--R 2 +--R x + 1 +--R (1449) ------- +--R 3 +--R x + 3x +--R Type: Fraction(Polynomial(Integer)) +--E 1449 + +--S 1450 of 1483 +r0270:= 1/3*log(x)+1/3*log(3+x^2) +--R +--R +--R 2 +--R log(x + 3) + log(x) +--R (1450) -------------------- +--R 3 +--R Type: Expression(Integer) +--E 1450 + +--S 1451 of 1483 +a0270:=integrate(t0270,x) +--R +--R +--R 3 +--R log(x + 3x) +--R (1451) ------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1451 + +--S 1452 of 1483 +m0270:=a0270-r0270 +--R +--R +--R 3 2 +--R log(x + 3x) - log(x + 3) - log(x) +--R (1452) ----------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1452 + +--S 1453 of 1483 +d0270:=D(m0270,x) +--R +--R +--R (1453) 0 +--R Type: Expression(Integer) +--E 1453 + +--S 1454 of 1483 +t0271:= (1+x^6)/x/(1-x^6) +--R +--R +--R 6 +--R - x - 1 +--R (1454) -------- +--R 7 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1454 + +--S 1455 of 1483 +r0271:= log(x)-1/3*log(1-x^6) +--R +--R +--R 6 +--R 3log(x) - log(- x + 1) +--R (1455) ----------------------- +--R 3 +--R Type: Expression(Integer) +--E 1455 + +--S 1456 of 1483 +a0271:=integrate(t0271,x) +--R +--R +--R 6 +--R - log(x - 1) + 3log(x) +--R (1456) ----------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1456 + +--S 1457 of 1483 +m0271:=a0271-r0271 +--R +--R +--R 6 6 +--R - log(x - 1) + log(- x + 1) +--R (1457) ----------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1457 + +--S 1458 of 1483 +d0271:=D(m0271,x) +--R +--R +--R (1458) 0 +--R Type: Expression(Integer) +--E 1458 + +--S 1459 of 1483 +t0272:= (x+x^2)/(-2*x-x^2+x^3) +--R +--R +--R 1 +--R (1459) ----- +--R x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1459 + +--S 1460 of 1483 +r0272:= log(2-x) +--R +--R +--R (1460) log(- x + 2) +--R Type: Expression(Integer) +--E 1460 + +--S 1461 of 1483 +a0272:=integrate(t0272,x) +--R +--R +--R (1461) log(x - 2) +--R Type: Union(Expression(Integer),...) +--E 1461 + +--S 1462 of 1483 +m0272:=a0272-r0272 +--R +--R +--R (1462) log(x - 2) - log(- x + 2) +--R Type: Expression(Integer) +--E 1462 + +--S 1463 of 1483 +d0272:=D(m0272,x) +--R +--R +--R (1463) 0 +--R Type: Expression(Integer) +--E 1463 + +--S 1464 of 1483 +t0273:= (b*c-a*d-2*a*e*x-b*e*x^2-3*a*f*x^2-2*b*f*x^3)/(c+d*x+e*x^2+f*x^3)^2 +--R +--R +--R (1464) +--R 3 2 +--R - 2b f x + (- 3a f - b e)x - 2a e x - a d + b c +--R / +--R 2 6 5 2 4 3 2 2 +--R f x + 2e f x + (2d f + e )x + (2c f + 2d e)x + (2c e + d )x + 2c d x +--R + +--R 2 +--R c +--R Type: Fraction(Polynomial(Integer)) +--E 1464 + +--S 1465 of 1483 +r0273:= (a+b*x)/(c+d*x+e*x^2+f*x^3) +--R +--R +--R b x + a +--R (1465) --------------------- +--R 3 2 +--R f x + e x + d x + c +--R Type: Fraction(Polynomial(Integer)) +--E 1465 + +--S 1466 of 1483 +a0273:=integrate(t0273,x) +--R +--R +--R b x + a +--R (1466) --------------------- +--R 3 2 +--R f x + e x + d x + c +--R Type: Union(Expression(Integer),...) +--E 1466 + +--S 1467 of 1483 +m0273:=a0273-r0273 +--R +--R +--R (1467) 0 +--R Type: Expression(Integer) +--E 1467 + +--S 1468 of 1483 +d0273:=D(m0273,x) +--R +--R +--R (1468) 0 +--R Type: Expression(Integer) +--E 1468 + +--S 1469 of 1483 +t0274:= (9-40*x-18*x^2+174*x^4+24*x^5+26*x^6-39*x^8)/(3+2*x^2+x^4)^3 +--R +--R +--R 8 6 5 4 2 +--R - 39x + 26x + 24x + 174x - 18x - 40x + 9 +--R (1469) --------------------------------------------- +--R 12 10 8 6 4 2 +--R x + 6x + 21x + 44x + 63x + 54x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 1469 + +--S 1470 of 1483 +r0274:= (2+3*x-4*x^2+13*x^5)/(3+2*x^2+x^4)^2 +--R +--R +--R 5 2 +--R 13x - 4x + 3x + 2 +--R (1470) -------------------------- +--R 8 6 4 2 +--R x + 4x + 10x + 12x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 1470 + +--S 1471 of 1483 +a0274:=integrate(t0274,x) +--R +--R +--R 5 2 +--R 13x - 4x + 3x + 2 +--R (1471) -------------------------- +--R 8 6 4 2 +--R x + 4x + 10x + 12x + 9 +--R Type: Union(Expression(Integer),...) +--E 1471 + +--S 1472 of 1483 +m0274:=a0274-r0274 +--R +--R +--R (1472) 0 +--R Type: Expression(Integer) +--E 1472 + +--S 1473 of 1483 +d0274:=D(m0274,x) +--R +--R +--R (1473) 0 +--R Type: Expression(Integer) +--E 1473 + +--S 1474 of 1483 +t0275:= (-3+10*x+4*x^3-30*x^5)/(3+x+x^4)^3-_ + 3*(1+4*x^3)*(2-3*x+5*x^2+x^4-5*x^6)/(3+x+x^4)^4 +--R +--R +--R (1474) +--R 9 7 6 5 4 3 2 +--R 30x - 8x - 15x - 140x + 34x - 12x - 5x + 36x - 15 +--R / +--R 16 13 12 10 9 8 7 6 5 4 +--R x + 4x + 12x + 6x + 36x + 54x + 4x + 36x + 108x + 109x +--R + +--R 3 2 +--R 12x + 54x + 108x + 81 +--R Type: Fraction(Polynomial(Integer)) +--E 1474 + +--S 1475 of 1483 +r0275:= (2-3*x+5*x^2+x^4-5*x^6)/(3+x+x^4)^3 +--R +--R +--R 6 4 2 +--R - 5x + x + 5x - 3x + 2 +--R (1475) --------------------------------------------------------- +--R 12 9 8 6 5 4 3 2 +--R x + 3x + 9x + 3x + 18x + 27x + x + 9x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 1475 + +--S 1476 of 1483 +a0275:=integrate(t0275,x) +--R +--R +--R 6 4 2 +--R - 5x + x + 5x - 3x + 2 +--R (1476) --------------------------------------------------------- +--R 12 9 8 6 5 4 3 2 +--R x + 3x + 9x + 3x + 18x + 27x + x + 9x + 27x + 27 +--R Type: Union(Expression(Integer),...) +--E 1476 + +--S 1477 of 1483 +m0275:=a0275-r0275 +--R +--R +--R (1477) 0 +--R Type: Expression(Integer) +--E 1477 + +--S 1478 of 1483 +d0275:=D(m0275,x) +--R +--R +--R (1478) 0 +--R Type: Expression(Integer) +--E 1478 + +--S 1479 of 1483 +t0276:= 1/(1+x^2)/(3+10*x/(1+x^2)) +--R +--R +--R 1 +--R (1479) ------------- +--R 2 +--R 3x + 10x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 1479 + +--S 1480 of 1483 +r0276:= -1/4*atanh(5/4+3/4*x) +--R +--R +--R 3x + 5 +--R atanh(------) +--R 4 +--R (1480) - ------------- +--R 4 +--R Type: Expression(Integer) +--E 1480 + +--S 1481 of 1483 +a0276:=integrate(t0276,x) +--R +--R +--R log(3x + 1) - log(x + 3) +--R (1481) ------------------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 1481 + +--S 1482 of 1483 +m0276:=a0276-r0276 +--R +--R +--R 3x + 5 +--R log(3x + 1) - log(x + 3) + 2atanh(------) +--R 4 +--R (1482) ----------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 1482 + +--S 1483 of 1483 +d0276:=D(m0276,x) +--R +--R +--R (1483) 0 +--R Type: Expression(Integer) +--E 1483 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richrational.input.pdf b/src/axiom-website/CATS/richrational.input.pdf new file mode 100644 index 0000000..3772b8c Binary files /dev/null and b/src/axiom-website/CATS/richrational.input.pdf differ diff --git a/src/axiom-website/CATS/richspecfunc000-022.input.pamphlet b/src/axiom-website/CATS/richspecfunc000-022.input.pamphlet new file mode 100644 index 0000000..c48ecc5 --- /dev/null +++ b/src/axiom-website/CATS/richspecfunc000-022.input.pamphlet @@ -0,0 +1,1119 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richspecfunc000-022.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richspecfunc000-022.output +)spool richspecfunc000-022.output +)set message auto off +)clear all + +--S 1 of 115 +t0000:= Gamma(n,a+b*x) +--R +--R +--R _ +--R (1) | (n,b x + a) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 115 +r0000:= (a+b*x)*Gamma(n,a+b*x)/b-Gamma(1+n,a+b*x)/b +--R +--R +--R _ _ +--R - | (n + 1,b x + a) + (b x + a)| (n,b x + a) +--R (2) -------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 115 +a0000:= integrate(t0000,x) +--R +--R +--R x +--R ++ _ +--R (3) | | (n,%K b + a)d%K +--R ++ +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 115 +--m0000:= a0000-r0000 +--E 4 + +--S 5 of 115 +--d0000:= D(m0000,x) +--E 5 + +--S 6 of 115 +t0001:= x*Gamma(n,a+b*x) +--R +--R +--R _ +--R (4) x| (n,b x + a) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 115 +r0001:= -1/2*(a^2/b^2-x^2)*Gamma(n,a+b*x)+a*Gamma(1+n,a+b*x)/b^2-1/2*_ + Gamma(2+n,a+b*x)/b^2 +--R +--R +--R _ _ 2 2 2 _ +--R - | (n + 2,b x + a) + 2a| (n + 1,b x + a) + (b x - a )| (n,b x + a) +--R (5) -------------------------------------------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 7 + +--S 8 of 115 +a0001:= integrate(t0001,x) +--R +--R +--R x +--R ++ _ +--R (6) | %K| (n,%K b + a)d%K +--R ++ +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 115 +--m0001:= a0001-r0001 +--E 9 + +--S 10 of 115 +--d0001:= D(m0001,x) +--E 10 + +--S 11 of 115 +t0002:= x^2*Gamma(n,a+b*x) +--R +--R +--R 2 _ +--R (7) x | (n,b x + a) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 115 +r0002:= -1/3*(-Gamma(n,a+b*x)*a^3-Gamma(n,a+b*x)*b^3*x^3+3*a^2*_ + Gamma(1+n,a+b*x)-3*a*Gamma(2+n,a+b*x)+Gamma(3+n,a+b*x))/b^3 +--R +--R +--R (8) +--R _ _ 2 _ +--R - | (n + 3,b x + a) + 3a| (n + 2,b x + a) - 3a | (n + 1,b x + a) +--R + +--R 3 3 3 _ +--R (b x + a )| (n,b x + a) +--R / +--R 3 +--R 3b +--R Type: Expression(Integer) +--E 12 + +--S 13 of 115 +a0002:= integrate(t0002,x) +--R +--R +--R x +--R ++ 2 _ +--R (9) | %K | (n,%K b + a)d%K +--R ++ +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 115 +--m0002:= a0002-r0002 +--E 14 + +--S 15 of 115 +--d0002:= D(m0002,x) +--E 15 + +--S 16 of 115 +t0003:= log(Gamma(a+b*x)) +--R +--R +--R _ +--R (10) log(| (b x + a)) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 115 +r0003:= x*log(Gamma(a+b*x))-x*logGamma(a+b*x)+Psi(-2,a+b*x)/b +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 115 +a0003:= integrate(t0003,x) +--R +--R +--R x +--R ++ _ +--R (11) | log(| (%K b + a))d%K +--R ++ +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 115 +--m0003:= a0003-r0003 +--E 19 + +--S 20 of 115 +--d0003:= D(m0003,x) +--E 20 + +--S 21 of 115 +t0004:= x*log(Gamma(a+b*x)) +--R +--R +--R _ +--R (12) x log(| (b x + a)) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 115 +r0004:= 1/2*x^2*log(Gamma(a+b*x))-1/2*x^2*logGamma(a+b*x)-_ + Psi(-3,a+b*x)/b^2+x*Psi(-2,a+b*x)/b +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 115 +a0004:= integrate(t0004,x) +--R +--R +--R x +--R ++ _ +--R (13) | %K log(| (%K b + a))d%K +--R ++ +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 115 +--m0004:= a0004-r0004 +--E 24 + +--S 25 of 115 +--d0004:= D(m0004,x) +--E 25 + +--S 26 of 115 +t0005:= x^2*log(Gamma(a+b*x)) +--R +--R +--R 2 _ +--R (14) x log(| (b x + a)) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 115 +r0005:= 1/3*x^3*log(Gamma(a+b*x))-1/3*x^3*logGamma(a+b*x)+2*_ + Psi(-4,a+b*x)/b^3-2*x*Psi(-3,a+b*x)/b^2+x^2*Psi(-2,a+b*x)/b +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 115 +a0005:= integrate(t0005,x) +--R +--R +--R x +--R ++ 2 _ +--R (15) | %K log(| (%K b + a))d%K +--R ++ +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 115 +--m0005:= a0005-r0005 +--E 29 + +--S 30 of 115 +--d0005:= D(m0005,x) +--E 30 + +--S 31 of 115 +t0006:= logGamma(a+b*x) +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 31 + +--S 32 of 115 +r0006:= Psi(-2,a+b*x)/b +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R Integer +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 115 +--a0006:= integrate(t0006,x) +--E 33 + +--S 34 of 115 +--m0006:= a0006-r0006 +--E 34 + +--S 35 of 115 +--d0006:= D(m0006,x) +--E 35 + +--S 36 of 115 +t0007:= x*logGamma(a+b*x) +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 36 + +--S 37 of 115 +r0007:= -(Psi(-3,a+b*x)-x*Psi(-2,a+b*x)*b)/b^2 +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R Integer +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 115 +--a0007:= integrate(t0007,x) +--E 38 + +--S 39 of 115 +--m0007:= a0007-r0007 +--E 39 + +--S 40 of 115 +--d0007:= D(m0007,x) +--E 40 + +--S 41 of 115 +t0008:= x^2*logGamma(a+b*x) +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 41 + +--S 42 of 115 +r0008:= 2*Psi(-4,a+b*x)/b^3-2*x*Psi(-3,a+b*x)/b^2+x^2*Psi(-2,a+b*x)/b +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R Integer +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 of 115 +--a0008:= integrate(t0008,x) +--E 43 + +--S 44 of 115 +--m0008:= a0008-r0008 +--E 44 + +--S 45 of 115 +--d0008:= D(m0008,x) +--E 45 + +--S 46 of 115 +t0009:= x*Psi(n,a+b*x) +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R Variable(n) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 46 + +--S 47 of 115 +r0009:= (-Psi(-2+n,a+b*x)+x*Psi(-1+n,a+b*x)*b)/b^2 +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R Polynomial(Integer) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 47 + +--S 48 of 115 +--a0009:= integrate(t0009,x) +--E 48 + +--S 49 of 115 +--m0009:= a0009-r0009 +--E 49 + +--S 50 of 115 +--d0009:= D(m0009,x) +--E 50 + +--S 51 of 115 +t0010:= x^2*Psi(1,a+b*x) +--R +--R There are no library operations named Psi +--R Use HyperDoc Browse or issue +--R )what op Psi +--R to learn if there is any operation containing " Psi " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Psi +--R with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 51 + +--S 52 of 115 +r0010:= (-2*x*logGamma(a+b*x)*b+2*Psi(-2,a+b*x)+x^2*Psi(a+b*x)*b^2)/b^3 +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 115 +--a0010:= integrate(t0010,x) +--E 53 + +--S 54 of 115 +--m0010:= a0010-r0010 +--E 54 + +--S 55 of 115 +--d0010:= D(m0010,x) +--E 55 + +--S 56 of 115 +t0011:= x*Zeta(2,a+b*x) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 56 + +--S 57 of 115 +r0011:= (-logGamma(a+b*x)+x*Psi(a+b*x)*b)/b^2 +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 115 +--a0011:= integrate(t0011,x) +--E 58 + +--S 59 of 115 +--m0011:= a0011-r0011 +--E 59 + +--S 60 of 115 +--d0011:= D(m0011,x) +--E 60 + +--S 61 of 115 +t0012:= x^2*Zeta(2,a+b*x) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 61 + +--S 62 of 115 +r0012:= (-2*x*logGamma(a+b*x)*b+2*Psi(-2,a+b*x)+x^2*Psi(a+b*x)*b^2)/b^3 +--R +--R There are 2 exposed and 0 unexposed library operations named +--R logGamma having 1 argument(s) but none was determined to be +--R applicable. Use HyperDoc Browse, or issue +--R )display op logGamma +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named +--R logGamma with argument type(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 115 +--a0012:= integrate(t0012,x) +--E 63 + +--S 64 of 115 +--m0012:= a0012-r0012 +--E 64 + +--S 65 of 115 +--d0012:= D(m0012,x) +--E 65 + +--S 66 of 115 +t0013:= Zeta(s,a+b*x) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Variable(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 66 + +--S 67 of 115 +r0013:= -Zeta(-1+s,a+b*x)/b/(-1+s) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Polynomial(Integer) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 of 115 +--a0013:= integrate(t0013,x) +--E 68 + +--S 69 of 115 +--m0013:= a0013-r0013 +--E 69 + +--S 70 of 115 +--d0013:= D(m0013,x) +--E 70 + +--S 71 of 115 +t0014:= x*Zeta(s,a+b*x) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Variable(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 71 + +--S 72 of 115 +r0014:= -Zeta(-2+s,a+b*x)/b^2/(1-s)/(2-s)+x*Zeta(-1+s,a+b*x)/b/(1-s) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Polynomial(Integer) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 72 + +--S 73 of 115 +--a0014:= integrate(t0014,x) +--E 73 + +--S 74 of 115 +--m0014:= a0014-r0014 +--E 74 + +--S 75 of 115 +--d0014:= D(m0014,x) +--E 75 + +--S 76 of 115 +t0015:= x^2*Zeta(s,a+b*x) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Variable(s) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 76 + +--S 77 of 115 +r0015:= 2*Zeta(-3+s,a+b*x)/b^3/(1-s)/(2-s)/(3-s)-_ + 2*x*Zeta(-2+s,a+b*x)/b^2/(1-s)/(2-s)+x^2*Zeta(-1+s,a+b*x)/b/(1-s) +--R +--R There are no library operations named Zeta +--R Use HyperDoc Browse or issue +--R )what op Zeta +--R to learn if there is any operation containing " Zeta " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named Zeta +--R with argument type(s) +--R Polynomial(Integer) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 115 +--a0015:= integrate(t0015,x) +--E 78 + +--S 79 of 115 +--m0015:= a0015-r0015 +--E 79 + +--S 80 of 115 +--d0015:= D(m0015,x) +--E 80 + +--S 81 of 115 +t0016:= polylog(n,a*x^m)/x +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable(n) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 81 + +--S 82 of 115 +r0016:= polylog(1+n,a*x^m)/m +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial(Integer) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 115 +--a0016:= integrate(t0016,x) +--E 83 + +--S 84 of 115 +--m0016:= a0016-r0016 +--E 84 + +--S 85 of 115 +--d0016:= D(m0016,x) +--E 85 + +--S 86 of 115 +t0017:= polylog(2,a+b*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 86 + +--S 87 of 115 +r0017:= -x-(1-a-b*x)*log(1-a-b*x)/b+(x+a/b)*polylog(2,a+b*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 115 +--a0017:= integrate(t0017,x) +--E 88 + +--S 89 of 115 +--m0017:= a0017-r0017 +--E 89 + +--S 90 of 115 +--d0017:= D(m0017,x) +--E 90 + +--S 91 of 115 +t0018:= polylog(n,a*f^x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable(n) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 91 + +--S 92 of 115 +r0018:= polylog(1+n,a*f^x)/log(f) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial(Integer) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 115 +--a0018:= integrate(t0018,x) +--E 93 + +--S 94 of 115 +--m0018:= a0018-r0018 +--E 94 + +--S 95 of 115 +--d0018:= D(m0018,x) +--E 95 + +--S 96 of 115 +t0019:= x*polylog(n,a*f^x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable(n) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 96 + +--S 97 of 115 +r0019:= 1/log(f)^2*(x*polylog(1+n,a*f^x)*log(f)-polylog(2+n,a*f^x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial(Integer) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 115 +--a0019:= integrate(t0019,x) +--E 98 + +--S 99 of 115 +--m0019:= a0019-r0019 +--E 99 + +--S 100 of 115 +--d0019:= D(m0019,x) +--E 100 + +--S 101 of 115 +t0020:= x^2*polylog(n,a*f^x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable(n) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 101 + +--S 102 of 115 +r0020:= 1/log(f)^3*(x^2*polylog(1+n,a*f^x)*log(f)^2-_ + 2*x*polylog(2+n,a*f^x)*log(f)+2*polylog(3+n,a*f^x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial(Integer) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 115 +--a0020:= integrate(t0020,x) +--E 103 + +--S 104 of 115 +--m0020:= a0020-r0020 +--E 104 + +--S 105 of 115 +--d0020:= D(m0020,x) +--E 105 + +--S 106 of 115 +t0021:= log(x)*polylog(n,a*x)/x +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable(n) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 106 + +--S 107 of 115 +r0021:= log(x)*polylog(1+n,a*x)-polylog(2+n,a*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial(Integer) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 115 +--a0021:= integrate(t0021,x) +--E 108 + +--S 109 of 115 +--m0021:= a0021-r0021 +--E 109 + +--S 110 of 115 +--d0021:= D(m0021,x) +--E 110 + +--S 111 of 115 +t0022:= log(x)^2*polylog(n,a*x)/x +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Variable(n) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 111 + +--S 112 of 115 +r0022:= log(x)^2*polylog(1+n,a*x)-2*log(x)*polylog(2+n,a*x)+2*polylog(3+n,a*x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R Polynomial(Integer) +--R Polynomial(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 112 + +--S 113 of 115 +--a0022:= integrate(t0022,x) +--E 113 + +--S 114 of 115 +--m0022:= a0022-r0022 +--E 114 + +--S 115 of 115 +--d0022:= D(m0022,x) +--E 115 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richspecfunc000-022.input.pdf b/src/axiom-website/CATS/richspecfunc000-022.input.pdf new file mode 100644 index 0000000..88f3001 Binary files /dev/null and b/src/axiom-website/CATS/richspecfunc000-022.input.pdf differ diff --git a/src/axiom-website/CATS/richtrig000-099.input.pamphlet b/src/axiom-website/CATS/richtrig000-099.input.pamphlet new file mode 100644 index 0000000..a04976b --- /dev/null +++ b/src/axiom-website/CATS/richtrig000-099.input.pamphlet @@ -0,0 +1,38216 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richtrig000-099.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig000-099.output +)spool richtrig000-099.output +)set message auto off +)clear all + +--S 1 of 520 +t0000:= sin(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (1) \|sin(b x + a) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 520 +r0000:= 2*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 520 +a0000:= integrate(t0000,x) +--R +--R +--R x +--R ++ +-------------+ +--R (2) | \|sin(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 520 +--m0000:= a0000-r0000 +--E 4 + +--S 5 of 520 +--d0000:= D(m0000,x) +--E 5 + +--S 6 of 520 +t0001:= sin(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (3) sin(b x + a)\|sin(b x + a) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 520 +r0001:= -2/3*(-EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)+_ + cos(a+b*x)*sin(a+b*x)^(1/2))/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 520 +a0001:= integrate(t0001,x) +--R +--R +--R x +--R ++ +-------------+ +--R (4) | sin(%R b + a)\|sin(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 520 +--m0001:= a0001-r0001 +--E 9 + +--S 10 of 520 +--d0001:= D(m0001,x) +--E 10 + +--S 11 of 520 +t0002:= sin(a+b*x)^(5/2) +--R +--R +--R 2 +------------+ +--R (5) sin(b x + a) \|sin(b x + a) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 520 +r0002:= -2/5*(-3*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)+_ + cos(a+b*x)*sin(a+b*x)^(3/2))/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 12 + +--S 13 of 520 +a0002:= integrate(t0002,x) +--R +--R +--R x +--R ++ 2 +-------------+ +--R (6) | sin(%R b + a) \|sin(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 520 +--m0002:= a0002-r0002 +--E 14 + +--S 15 of 520 +--d0002:= D(m0002,x) +--E 15 + +--S 16 of 520 +t0003:= 1/sin(a+b*x)^(1/2) +--R +--R +--R 1 +--R (7) --------------- +--R +------------+ +--R \|sin(b x + a) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 520 +r0003:= 2*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 17 + +--S 18 of 520 +a0003:= integrate(t0003,x) +--R +--R +--R x +--R ++ 1 +--R (8) | ---------------- d%R +--R ++ +-------------+ +--R \|sin(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 520 +--m0003:= a0003-r0003 +--E 19 + +--S 20 of 520 +--d0003:= D(m0003,x) +--E 20 + +--S 21 of 520 +t0004:= 1/sin(a+b*x)^(3/2) +--R +--R +--R 1 +--R (9) --------------------------- +--R +------------+ +--R sin(b x + a)\|sin(b x + a) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 520 +r0004:= -2*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)/b-_ + 2*cos(a+b*x)/b/sin(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 520 +a0004:= integrate(t0004,x) +--R +--R +--R x +--R ++ 1 +--R (10) | ----------------------------- d%R +--R ++ +-------------+ +--R sin(%R b + a)\|sin(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 520 +--m0004:= a0004-r0004 +--E 24 + +--S 25 of 520 +--d0004:= D(m0004,x) +--E 25 + +--S 26 of 520 +t0005:= 1/sin(a+b*x)^(5/2) +--R +--R +--R 1 +--R (11) ---------------------------- +--R 2 +------------+ +--R sin(b x + a) \|sin(b x + a) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 520 +r0005:= 2/3*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)/b-_ + 2/3*cos(a+b*x)/b/sin(a+b*x)^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 27 + +--S 28 of 520 +a0005:= integrate(t0005,x) +--R +--R +--R x +--R ++ 1 +--R (12) | ------------------------------ d%R +--R ++ 2 +-------------+ +--R sin(%R b + a) \|sin(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 520 +--m0005:= a0005-r0005 +--E 29 + +--S 30 of 520 +--d0005:= D(m0005,x) +--E 30 + +--S 31 of 520 +t0006:= (a*sin(x))^(1/2) +--R +--R +--R +--------+ +--R (13) \|a sin(x) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 520 +r0006:= 2*EllipticE(-1/4*%pi+1/2*x,2)*(a*sin(x))^(1/2)/sin(x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 520 +a0006:= integrate(t0006,x) +--R +--R +--R x +--R ++ +---------+ +--R (14) | \|a sin(%R) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 520 +--m0006:= a0006-r0006 +--E 34 + +--S 35 of 520 +--d0006:= D(m0006,x) +--E 35 + +--S 36 of 520 +t0007:= (a*sin(x)^3)^(1/2) +--R +--R +--R +---------+ +--R | 3 +--R (15) \|a sin(x) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 520 +r0007:= 2/3*(EllipticF(-1/4*%pi+1/2*x,2)-_ + cos(x)*sin(x)^(1/2))*(a*sin(x)^3)^(1/2)/sin(x)^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 37 + +--S 38 of 520 +a0007:= integrate(t0007,x) +--R +--R +--R x +----------+ +--R ++ | 3 +--R (16) | \|a sin(%R) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 520 +--m0007:= a0007-r0007 +--E 39 + +--S 40 of 520 +--d0007:= D(m0007,x) +--E 40 + +--S 41 of 520 +t0008:= (a*sin(x))^(3/2) +--R +--R +--R +--------+ +--R (17) a sin(x)\|a sin(x) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 520 +r0008:= 2/3*a^2*(EllipticF(-1/4*%pi+1/2*x,2)*sin(x)^(1/2)-_ + cos(x)*sin(x))/(a*sin(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 of 520 +a0008:= integrate(t0008,x) +--R +--R +--R x +--R ++ +---------+ +--R (18) | a sin(%R)\|a sin(%R) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 520 +--m0008:= a0008-r0008 +--E 44 + +--S 45 of 520 +--d0008:= D(m0008,x) +--E 45 + +--S 46 of 520 +t0009:= (a*sin(x)^3)^(3/2) +--R +--R +--R +---------+ +--R 3 | 3 +--R (19) a sin(x) \|a sin(x) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 520 +r0009:= 2/45*a*(a*sin(x)^3)^(1/2)*(21*EllipticE(-1/4*%pi+1/2*x,2)-_ + 7*cos(x)*sin(x)^(3/2)-5*cos(x)*sin(x)^(7/2))/sin(x)^(3/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 47 + +--S 48 of 520 +a0009:= integrate(t0009,x) +--R +--R +--R x +----------+ +--R ++ 3 | 3 +--R (20) | a sin(%R) \|a sin(%R) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 520 +--m0009:= a0009-r0009 +--E 49 + +--S 50 of 520 +--d0009:= D(m0009,x) +--E 50 + +--S 51 of 520 +t0010:= 1/(a*sin(x))^(1/2) +--R +--R +--R 1 +--R (21) ----------- +--R +--------+ +--R \|a sin(x) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 520 +r0010:= 2*EllipticF(-1/4*%pi+1/2*x,2)*sin(x)^(1/2)/(a*sin(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 520 +a0010:= integrate(t0010,x) +--R +--R +--R x +--R ++ 1 +--R (22) | ------------ d%R +--R ++ +---------+ +--R \|a sin(%R) +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 520 +--m0010:= a0010-r0010 +--E 54 + +--S 55 of 520 +--d0010:= D(m0010,x) +--E 55 + +--S 56 of 520 +t0011:= 1/(a*sin(x)^2)^(1/2) +--R +--R +--R 1 +--R (23) ------------ +--R +---------+ +--R | 2 +--R \|a sin(x) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 520 +r0011:= -atanh(cos(x))*sin(x)/(a*sin(x)^2)^(1/2) +--R +--R +--R sin(x)atanh(cos(x)) +--R (24) - ------------------- +--R +---------+ +--R | 2 +--R \|a sin(x) +--R Type: Expression(Integer) +--E 57 + +--S 58 of 520 +a0011:= integrate(t0011,x) +--R +--R +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R (25) --------------- +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 520 +m0011:= a0011-r0011 +--R +--R +--R +---------+ +--R sin(x) | 2 +-+ +--R log(----------)\|a sin(x) + sin(x)\|a atanh(cos(x)) +--R cos(x) + 1 +--R (26) ----------------------------------------------------- +--R +---------+ +--R +-+ | 2 +--R \|a \|a sin(x) +--R Type: Expression(Integer) +--E 59 + +--S 60 of 520 +d0011:= D(m0011,x) +--R +--R +--R +---------+ +--R 2 3 +-+ | 2 3 +--R ((cos(x) - 1)sin(x) + cos(x) - cos(x))\|a \|a sin(x) + a sin(x) +--R (27) -------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 +--R (a cos(x) - a)sin(x)\|a sin(x) +--R Type: Expression(Integer) +--E 60 + +--S 61 of 520 +t0012:= 1/(a*sin(x)^3)^(1/2) +--R +--R +--R 1 +--R (28) ------------ +--R +---------+ +--R | 3 +--R \|a sin(x) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 520 +r0012:= -2*(cos(x)+EllipticE(-1/4*%pi+1/2*x,2)*sin(x)^(1/2))*_ + sin(x)/(a*sin(x)^3)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 520 +a0012:= integrate(t0012,x) +--R +--R +--R x +--R ++ 1 +--R (29) | ------------- d%R +--R ++ +----------+ +--R | 3 +--R \|a sin(%R) +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 520 +--m0012:= a0012-r0012 +--E 64 + +--S 65 of 520 +--d0012:= D(m0012,x) +--E 65 + +--S 66 of 520 +t0013:= 1/(a+b*sin(c+d*x))^2 +--R +--R +--R 1 +--R (30) ---------------------------------------- +--R 2 2 2 +--R b sin(d x + c) + 2a b sin(d x + c) + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 520 +r0013:= 2*a*atan((b+a*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)/d+_ + b*cos(c+d*x)/(a^2-b^2)/d/(a+b*sin(c+d*x)) +--R +--R +--R (31) +--R d x + c +--R a tan(-------) + b +--R 2 2 +--R (- 2a b sin(d x + c) - 2a )atan(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R - b cos(d x + c)\|- b + a +--R / +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)d sin(d x + c) + (a b - a )d)\|- b + a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 520 +a0013:= integrate(t0013,x) +--R +--R +--R (32) +--R [ +--R 2 3 +--R (a b sin(d x + c) + a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (b - a )cos(d x + c) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(d x + c) + (b - a b)cos(d x + c) + b - a b +--R / +--R b sin(d x + c) + a +--R + +--R +-------+ +--R 2 | 2 2 +--R (- b sin(d x + c) - a b cos(d x + c) - a b)\|b - a +--R / +--R +-------+ +--R 3 3 2 2 4 | 2 2 +--R ((a b - a b)d sin(d x + c) + (a b - a )d)\|b - a +--R , +--R +--R 2 3 +--R (2a b sin(d x + c) + 2a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(d x + c) + b cos(d x + c) + b)\|- b + a +--R atan(-------------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R +---------+ +--R 2 | 2 2 +--R (- b sin(d x + c) - a b cos(d x + c) - a b)\|- b + a +--R / +--R +---------+ +--R 3 3 2 2 4 | 2 2 +--R ((a b - a b)d sin(d x + c) + (a b - a )d)\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 68 + +--S 69 of 520 +m0013a:= a0013.1-r0013 +--R +--R +--R (33) +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (b - a )cos(d x + c) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(d x + c) + (b - a b)cos(d x + c) + b - a b +--R / +--R b sin(d x + c) + a +--R + +--R d x + c +--R +-------+ a tan(-------) + b +---------+ +-------+ +--R 2 | 2 2 2 | 2 2 | 2 2 +--R 2a \|b - a atan(------------------) - b\|- b + a \|b - a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 3 | 2 2 | 2 2 +--R (a b - a )d\|- b + a \|b - a +--R Type: Expression(Integer) +--E 69 + +--S 70 of 520 +d0013a:= D(m0013a,x) +--R +--R +--R (34) +--R 3 3 3 2 2 2 +--R ((a b - a b)cos(d x + c) + a b )sin(d x + c) - a b cos(d x + c) +--R + +--R 2 2 +--R a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 2 2 2 3 2 +--R - 2a b sin(d x + c) - 2a b sin(d x + c) - 2a b cos(d x + c) +--R + +--R 3 3 +--R (- 2a b + 2a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 3 3 3 2 2 2 +--R ((a b - a b)cos(d x + c) + a b )sin(d x + c) - a b cos(d x + c) +--R + +--R 2 2 +--R a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 3 2 4 3 2 +--R ((a b - a b )cos(d x + c) + a b - a b )sin(d x + c) +--R + +--R 2 3 4 2 2 3 4 +--R (- a b + a b)cos(d x + c) + a b - a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 4 3 2 2 2 3 4 +--R (- 2a b + 2a b )sin(d x + c) + (- 2a b + 2a b)sin(d x + c) +--R + +--R 4 3 2 2 4 3 2 +--R (- 2a b + 2a b )cos(d x + c) + (- 2a b + 2a b )cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 3 2 4 3 2 +--R ((a b - a b )cos(d x + c) + a b - a b )sin(d x + c) +--R + +--R 2 3 4 2 2 3 4 +--R (- a b + a b)cos(d x + c) + a b - a b +--R / +--R 2 4 4 2 2 +--R (a b - a b )sin(d x + c) +--R + +--R 5 3 3 5 5 5 +--R ((a b - 2a b + a b)cos(d x + c) + a b - a b)sin(d x + c) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (a b - 2a b + a )cos(d x + c) + a b - a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 5 3 3 2 +--R (2a b - 2a b )sin(d x + c) +--R + +--R 6 2 4 4 2 6 4 2 +--R ((2b - 4a b + 2a b )cos(d x + c) + 2b - 2a b )sin(d x + c) +--R + +--R 5 3 3 5 5 3 3 +--R (2a b - 4a b + 2a b)cos(d x + c) + 2a b - 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 4 4 2 2 +--R (a b - a b )sin(d x + c) +--R + +--R 5 3 3 5 5 5 +--R ((a b - 2a b + a b)cos(d x + c) + a b - a b)sin(d x + c) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (a b - 2a b + a )cos(d x + c) + a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 4 3 6 2 +--R (a b - 2a b + a b)sin(d x + c) +--R + +--R 6 3 4 5 2 6 3 4 5 2 7 +--R ((a b - 2a b + a b )cos(d x + c) + a b - a b - a b + a ) +--R * +--R sin(d x + c) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (a b - 2a b + a b)cos(d x + c) + a b - 2a b + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 6 3 4 5 2 2 +--R (2a b - 4a b + 2a b )sin(d x + c) +--R + +--R 7 2 5 4 3 7 2 5 4 3 6 +--R ((2b - 4a b + 2a b )cos(d x + c) + 2b - 2a b - 2a b + 2a b) +--R * +--R sin(d x + c) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (2a b - 4a b + 2a b )cos(d x + c) + 2a b - 4a b + 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 5 4 3 6 2 +--R (a b - 2a b + a b)sin(d x + c) +--R + +--R 6 3 4 5 2 6 3 4 5 2 7 +--R ((a b - 2a b + a b )cos(d x + c) + a b - a b - a b + a )sin(d x + c) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (a b - 2a b + a b)cos(d x + c) + a b - 2a b + a b +--R Type: Expression(Integer) +--E 70 + +--S 71 of 520 +m0013b:= a0013.2-r0013 +--R +--R +--R (35) +--R +---------+ +--R | 2 2 +--R 2 (a sin(d x + c) + b cos(d x + c) + b)\|- b + a +--R 2a atan(-------------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R d x + c +--R a tan(-------) + b +---------+ +--R 2 2 | 2 2 +--R 2a atan(------------------) - b\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 3 | 2 2 +--R (a b - a )d\|- b + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 520 +d0013b:= D(m0013b,x) +--R +--R +--R (36) +--R 2 2 +--R - a sin(d x + c) + (2a b cos(d x + c) + 2a b)sin(d x + c) +--R + +--R 2 2 2 +--R - a cos(d x + c) + a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 +--R (- 4a b sin(d x + c) - 4a b cos(d x + c) - 4a b cos(d x + c)) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 +--R - a sin(d x + c) + (2a b cos(d x + c) + 2a b)sin(d x + c) +--R + +--R 2 2 2 +--R - a cos(d x + c) + a +--R / +--R 2 2 4 2 +--R (a b - a )sin(d x + c) +--R + +--R 3 3 3 3 +--R ((2a b - 2a b)cos(d x + c) + 2a b - 2a b)sin(d x + c) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (a b - a )cos(d x + c) + (2a b - 2a )cos(d x + c) + a b - a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 3 2 +--R (2a b - 2a b)sin(d x + c) +--R + +--R 4 2 2 4 2 2 +--R ((4b - 4a b )cos(d x + c) + 4b - 4a b )sin(d x + c) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b - 2a b)cos(d x + c) + (4a b - 4a b)cos(d x + c) + 2a b - 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 4 2 +--R (a b - a )sin(d x + c) +--R + +--R 3 3 3 3 +--R ((2a b - 2a b)cos(d x + c) + 2a b - 2a b)sin(d x + c) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (a b - a )cos(d x + c) + (2a b - 2a )cos(d x + c) + a b - a +--R Type: Expression(Integer) +--E 72 + +--S 73 of 520 +t0014:= 1/(a+b*sin(c+d*x))^3 +--R +--R +--R 1 +--R (37) ------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R b sin(d x + c) + 3a b sin(d x + c) + 3a b sin(d x + c) + a +--R Type: Expression(Integer) +--E 73 + +--S 74 of 520 +r0014:= (2*a^2+b^2)*atan((b+a*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/_ + (a^2-b^2)^(5/2)/d+1/2*b*cos(c+d*x)/(a^2-b^2)/d/(a+b*sin(c+d*x))^2+_ + 3/2*a*b*cos(c+d*x)/(a^2-b^2)^2/d/(a+b*sin(c+d*x)) +--R +--R +--R (38) +--R 4 2 2 2 3 3 2 2 4 +--R ((2b + 4a b )sin(d x + c) + (4a b + 8a b)sin(d x + c) + 2a b + 4a ) +--R * +--R d x + c +--R a tan(-------) + b +--R 2 +--R atan(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 3 2 | 2 2 +--R (3a b cos(d x + c)sin(d x + c) + (- b + 4a b)cos(d x + c))\|- b + a +--R / +--R 6 2 4 4 2 2 +--R (2b - 4a b + 2a b )d sin(d x + c) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (4a b - 8a b + 4a b)d sin(d x + c) + (2a b - 4a b + 2a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 74 + +--S 75 of 520 +a0014:= integrate(t0014,x) +--R +--R +--R (39) +--R [ +--R 3 3 5 2 4 4 2 2 2 4 +--R (2a b + 4a b)sin(d x + c) + (- a b - 2a b )cos(d x + c) + a b +--R + +--R 4 2 6 +--R 3a b + 2a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (b - a )cos(d x + c) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(d x + c) + (- b + a b)cos(d x + c) - b + a b +--R / +--R b sin(d x + c) + a +--R + +--R 3 2 4 3 2 +--R (3a b cos(d x + c) - 2a b + 8a b )sin(d x + c) +--R + +--R 5 2 3 2 2 3 4 5 +--R (b - 4a b )cos(d x + c) + (- a b + 4a b)cos(d x + c) - b +--R + +--R 2 3 4 +--R 3a b + 4a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 3 5 5 3 7 +--R (4a b - 8a b + 4a b)d sin(d x + c) +--R + +--R 2 6 4 4 6 2 2 +--R (- 2a b + 4a b - 2a b )d cos(d x + c) +--R + +--R 2 6 4 4 6 2 8 +--R (2a b - 2a b - 2a b + 2a )d +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 3 5 2 4 4 2 2 2 4 +--R (- 4a b - 8a b)sin(d x + c) + (2a b + 4a b )cos(d x + c) - 2a b +--R + +--R 4 2 6 +--R - 6a b - 4a +--R * +--R +---------+ +--R | 2 2 +--R (a sin(d x + c) + b cos(d x + c) + b)\|- b + a +--R atan(-------------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R 3 2 4 3 2 +--R (3a b cos(d x + c) - 2a b + 8a b )sin(d x + c) +--R + +--R 5 2 3 2 2 3 4 5 +--R (b - 4a b )cos(d x + c) + (- a b + 4a b)cos(d x + c) - b +--R + +--R 2 3 4 +--R 3a b + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 5 5 3 7 +--R (4a b - 8a b + 4a b)d sin(d x + c) +--R + +--R 2 6 4 4 6 2 2 +--R (- 2a b + 4a b - 2a b )d cos(d x + c) +--R + +--R 2 6 4 4 6 2 8 +--R (2a b - 2a b - 2a b + 2a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 75 + +--S 76 of 520 +m0014a:= a0014.1-r0014 +--R +--R +--R (40) +--R 3 5 5 3 3 +--R (2a b + 4a b )sin(d x + c) +--R + +--R 2 6 4 4 2 2 6 4 4 6 2 2 +--R ((- a b - 2a b )cos(d x + c) + a b + 7a b + 10a b )sin(d x + c) +--R + +--R 3 5 5 3 2 3 5 5 3 7 +--R ((- 2a b - 4a b )cos(d x + c) + 2a b + 8a b + 8a b)sin(d x + c) +--R + +--R 4 4 6 2 2 4 4 6 2 8 +--R (- a b - 2a b )cos(d x + c) + a b + 3a b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (b - a )cos(d x + c) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(d x + c) + (- b + a b)cos(d x + c) - b + a b +--R / +--R b sin(d x + c) + a +--R + +--R 3 5 5 3 3 +--R (- 4a b - 8a b )sin(d x + c) +--R + +--R 2 6 4 4 2 2 6 4 4 6 2 2 +--R ((2a b + 4a b )cos(d x + c) - 2a b - 14a b - 20a b )sin(d x + c) +--R + +--R 3 5 5 3 2 3 5 5 3 7 +--R ((4a b + 8a b )cos(d x + c) - 4a b - 16a b - 16a b)sin(d x + c) +--R + +--R 4 4 6 2 2 4 4 6 2 8 +--R (2a b + 4a b )cos(d x + c) - 2a b - 6a b - 4a +--R * +--R d x + c +--R +-------+ a tan(-------) + b +--R | 2 2 2 +--R \|b - a atan(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 4 6 3 4 3 +--R (3a b cos(d x + c) - 2a b + 8a b )sin(d x + c) +--R + +--R 7 2 5 2 2 5 4 3 7 +--R (b - 4a b )cos(d x + c) + (- a b + 4a b )cos(d x + c) - b +--R + +--R 2 5 4 3 +--R - a b + 20a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 4 3 6 3 4 2 +--R 3a b cos(d x + c) + (2a b - 8a b )cos(d x + c) +--R + +--R 3 4 6 3 4 5 2 +--R - 3a b cos(d x + c) - 2a b + 4a b + 16a b +--R * +--R sin(d x + c) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- a b + 4a b )cos(d x + c) + (a b - 4a b )cos(d x + c) +--R + +--R 2 5 4 3 2 5 4 3 6 +--R (a b - 4a b )cos(d x + c) - a b + 3a b + 4a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 3 7 5 5 7 3 3 +--R (4a b - 8a b + 4a b )d sin(d x + c) +--R + +--R 2 8 4 6 6 4 2 +--R (- 2a b + 4a b - 2a b )d cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 +--R (2a b + 6a b - 18a b + 10a b )d +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 7 5 5 7 3 2 3 7 7 3 9 +--R ((- 4a b + 8a b - 4a b )d cos(d x + c) + (4a b - 12a b + 8a b)d) +--R * +--R sin(d x + c) +--R + +--R 4 6 6 4 8 2 2 +--R (- 2a b + 4a b - 2a b )d cos(d x + c) +--R + +--R 4 6 6 4 8 2 10 +--R (2a b - 2a b - 2a b + 2a )d +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 520 +d0014a:= D(m0014a,x) +--R +--R +--R (41) +--R 4 7 7 +--R - 6a b sin(d x + c) +--R + +--R 3 8 2 3 8 5 6 3 8 +--R - 3a b cos(d x + c) + (- 6a b + 6a b )cos(d x + c) - 7a b +--R + +--R 5 6 +--R - 17a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 2 9 4 7 3 +--R (- 3a b + 3a b )cos(d x + c) +--R + +--R 2 9 4 7 2 +--R (- 2a b - 25a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 2 9 4 7 +--R (- 5a b - 20a b + 25a b )cos(d x + c) - 4a b - 23a b +--R + +--R 6 5 +--R - 15a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 10 3 8 5 6 3 +--R (5a b - 22a b + 17a b )cos(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (5a b - 7a b - 40a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 10 +--R (- 3a b - 15a b - 21a b + 39a b )cos(d x + c) - 3a b +--R + +--R 3 8 5 6 7 4 +--R - 20a b - 33a b - 4a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 11 2 9 4 7 5 +--R (- b - a b + 2a b )cos(d x + c) +--R + +--R 11 2 9 4 7 4 +--R (- b - 7a b - 22a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 3 +--R (2b + 18a b - 48a b + 28a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 2 +--R (2b + 30a b + 14a b - 4a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 11 +--R (- b - 9a b - 9a b - 11a b + 30a b )cos(d x + c) - b +--R + +--R 2 9 4 7 6 5 +--R - 15a b - 35a b - 39a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 10 3 8 6 +--R (a b + 5a b )cos(d x + c) +--R + +--R 10 3 8 5 6 5 +--R (- 3a b - 15a b + 18a b )cos(d x + c) +--R + +--R 10 3 8 5 6 4 +--R (- 6a b - 33a b - 51a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (6a b + 24a b - 42a b + 12a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 +--R (9a b + 53a b + 69a b + 22a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (- 3a b - 5a b + a b - 5a b + 12a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 +--R - 4a b - 21a b - 37a b - 34a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 9 4 7 7 2 9 4 7 6 +--R (3a b - 3a b )cos(d x + c) + (3a b + 9a b )cos(d x + c) +--R + +--R 4 7 6 5 5 +--R (- 33a b + 33a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 4 +--R (- 2a b - 59a b - 29a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 3 +--R (- a b + 35a b - 34a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 2 +--R (3a b + 63a b + 51a b + 12a b )cos(d x + c) +--R + +--R 2 9 4 7 8 3 10 2 9 4 7 +--R (- 2a b + a b - a b + 2a b)cos(d x + c) - 4a b - 13a b +--R + +--R 6 5 8 3 +--R - 23a b - 14a b +--R * +--R sin(d x + c) +--R + +--R 10 3 8 5 6 7 +--R (- 2a b + 7a b - 5a b )cos(d x + c) +--R + +--R 10 3 8 5 6 6 +--R (- 2a b + 6a b + 2a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 5 +--R (4a b - 10a b - 7a b + 13a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 4 +--R (4a b - 9a b - 21a b - 4a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 2a b + 3a b + 12a b - 13a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 2 3 8 +--R (- 2a b + 4a b + 23a b + 9a b + 2a b )cos(d x + c) - a b +--R + +--R 5 6 7 4 9 2 +--R - 4a b - 5a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 8 7 +--R - 12a b sin(d x + c) +--R + +--R 2 9 2 2 9 4 7 +--R - 6a b cos(d x + c) + (- 12a b + 12a b )cos(d x + c) +--R + +--R 2 9 4 7 +--R - 6a b - 18a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 10 3 8 3 +--R (- 6a b + 6a b )cos(d x + c) +--R + +--R 10 3 8 2 +--R (- 12a b - 66a b )cos(d x + c) +--R + +--R 10 3 8 5 6 10 3 8 +--R (- 2a b - 32a b + 34a b )cos(d x + c) + 8a b + 18a b +--R + +--R 5 6 +--R 34a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 11 2 9 4 +--R (2b + 4a b )cos(d x + c) +--R + +--R 11 2 9 4 7 3 +--R (2b - 52a b + 50a b )cos(d x + c) +--R + +--R 11 2 9 4 7 2 +--R (- 2b - 66a b - 136a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 11 2 9 +--R (2b + 10a b - 26a b + 14a b )cos(d x + c) + 4b + 40a b +--R + +--R 4 7 6 5 +--R 104a b + 92a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 10 3 8 4 +--R (- 4a b - 32a b )cos(d x + c) +--R + +--R 10 3 8 5 6 3 +--R (4a b - 116a b + 112a b )cos(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (12a b - 88a b - 80a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 10 +--R (12a b + 56a b - 28a b - 40a b )cos(d x + c) + 8a b +--R + +--R 3 8 5 6 7 4 +--R 84a b + 132a b + 76a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 11 2 9 6 +--R (2b + 10a b )cos(d x + c) +--R + +--R 2 9 4 7 5 +--R (- 24a b + 24a b )cos(d x + c) +--R + +--R 11 2 9 4 7 4 +--R (- 6b - 48a b - 90a b )cos(d x + c) +--R + +--R 4 7 6 5 3 +--R (- 96a b + 96a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 2 +--R (6b + 34a b + 22a b + 4a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 11 +--R (32a b + 64a b - 44a b - 52a b )cos(d x + c) - 2b +--R + +--R 2 9 4 7 6 5 8 3 +--R 12a b + 68a b + 62a b + 28a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 10 3 8 7 +--R (6a b - 6a b )cos(d x + c) +--R + +--R 10 3 8 6 +--R (6a b + 18a b )cos(d x + c) +--R + +--R 10 3 8 5 6 5 +--R (6a b - 60a b + 54a b )cos(d x + c) +--R + +--R 10 3 8 5 6 4 +--R (2a b - 104a b - 54a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 14a b + 38a b - 64a b + 40a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 +--R (- 6a b + 78a b + 50a b + 16a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R (2a b + 28a b + 22a b - 28a b - 24a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 +--R - 2a b + 8a b + 16a b + 10a b + 4a b +--R * +--R sin(d x + c) +--R + +--R 11 2 9 4 7 7 +--R (- 4b + 14a b - 10a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 +--R (- 4b + 12a b + 4a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 5 +--R (8b - 18a b - 12a b + 22a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 4 +--R (8b - 16a b - 38a b - 8a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 3 +--R (- 4b + 2a b + 16a b - 22a b + 8a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 2 +--R (- 4b + 4a b + 34a b + 10a b + 4a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 10 +--R (2a b + 6a b + 2a b - 6a b - 4a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 7 7 +--R - 6a b sin(d x + c) +--R + +--R 3 8 2 3 8 5 6 3 8 +--R - 3a b cos(d x + c) + (- 6a b + 6a b )cos(d x + c) - 7a b +--R + +--R 5 6 +--R - 17a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 2 9 4 7 3 2 9 4 7 2 +--R (- 3a b + 3a b )cos(d x + c) + (- 2a b - 25a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 2 9 4 7 6 5 +--R (- 5a b - 20a b + 25a b )cos(d x + c) - 4a b - 23a b - 15a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 10 3 8 5 6 3 +--R (5a b - 22a b + 17a b )cos(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (5a b - 7a b - 40a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 10 +--R (- 3a b - 15a b - 21a b + 39a b )cos(d x + c) - 3a b +--R + +--R 3 8 5 6 7 4 +--R - 20a b - 33a b - 4a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 11 2 9 4 7 5 +--R (- b - a b + 2a b )cos(d x + c) +--R + +--R 11 2 9 4 7 4 +--R (- b - 7a b - 22a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 3 +--R (2b + 18a b - 48a b + 28a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 2 +--R (2b + 30a b + 14a b - 4a b )cos(d x + c) +--R + +--R 11 2 9 4 7 6 5 8 3 11 +--R (- b - 9a b - 9a b - 11a b + 30a b )cos(d x + c) - b +--R + +--R 2 9 4 7 6 5 +--R - 15a b - 35a b - 39a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 10 3 8 6 +--R (a b + 5a b )cos(d x + c) +--R + +--R 10 3 8 5 6 5 +--R (- 3a b - 15a b + 18a b )cos(d x + c) +--R + +--R 10 3 8 5 6 4 +--R (- 6a b - 33a b - 51a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (6a b + 24a b - 42a b + 12a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 2 +--R (9a b + 53a b + 69a b + 22a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 10 +--R (- 3a b - 5a b + a b - 5a b + 12a b )cos(d x + c) - 4a b +--R + +--R 3 8 5 6 7 4 +--R - 21a b - 37a b - 34a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 9 4 7 7 2 9 4 7 6 +--R (3a b - 3a b )cos(d x + c) + (3a b + 9a b )cos(d x + c) +--R + +--R 4 7 6 5 5 +--R (- 33a b + 33a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 4 +--R (- 2a b - 59a b - 29a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 3 +--R (- a b + 35a b - 34a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 8 3 2 +--R (3a b + 63a b + 51a b + 12a b )cos(d x + c) +--R + +--R 2 9 4 7 8 3 10 2 9 4 7 +--R (- 2a b + a b - a b + 2a b)cos(d x + c) - 4a b - 13a b +--R + +--R 6 5 8 3 +--R - 23a b - 14a b +--R * +--R sin(d x + c) +--R + +--R 10 3 8 5 6 7 +--R (- 2a b + 7a b - 5a b )cos(d x + c) +--R + +--R 10 3 8 5 6 6 +--R (- 2a b + 6a b + 2a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 5 +--R (4a b - 10a b - 7a b + 13a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 4 +--R (4a b - 9a b - 21a b - 4a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 2a b + 3a b + 12a b - 13a b )cos(d x + c) +--R + +--R 10 3 8 5 6 7 4 9 2 2 3 8 +--R (- 2a b + 4a b + 23a b + 9a b + 2a b )cos(d x + c) - a b +--R + +--R 5 6 7 4 9 2 +--R - 4a b - 5a b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 8 6 6 7 +--R (6a b - 6a b )sin(d x + c) +--R + +--R 3 9 5 7 2 3 9 5 7 +--R (3a b - 3a b )cos(d x + c) + (6a b - 6a b )cos(d x + c) +--R + +--R 3 9 5 7 7 5 +--R 7a b + 10a b - 17a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 2 10 4 8 3 +--R (3a b - 3a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 2 +--R (2a b + 23a b - 25a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 2 10 4 8 6 6 +--R (5a b + 20a b - 25a b )cos(d x + c) + 4a b + 19a b - 8a b +--R + +--R 8 4 +--R - 15a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 11 3 9 5 7 3 +--R (- 5a b + 22a b - 17a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 5a b + 12a b + 33a b - 40a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 11 3 9 +--R (3a b + 15a b + 21a b - 39a b )cos(d x + c) + 3a b + 17a b +--R + +--R 5 7 7 5 9 3 +--R 13a b - 29a b - 4a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 12 2 10 4 8 5 +--R (b + a b - 2a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 4 +--R (b + 6a b + 15a b - 22a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 3 +--R (- 2b - 18a b + 48a b - 28a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 2 +--R (- 2b - 28a b + 16a b + 18a b - 4a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 12 +--R (b + 9a b + 9a b + 11a b - 30a b )cos(d x + c) + b +--R + +--R 2 10 4 8 6 6 8 4 +--R 14a b + 20a b + 4a b - 39a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 11 3 9 5 7 6 +--R (- a b - 4a b + 5a b )cos(d x + c) +--R + +--R 11 3 9 5 7 5 +--R (3a b + 15a b - 18a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 4 +--R (6a b + 27a b + 18a b - 51a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 3 +--R (- 6a b - 24a b + 42a b - 12a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 2 +--R (- 9a b - 44a b - 16a b + 47a b + 22a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (3a b + 5a b - a b + 5a b - 12a b )cos(d x + c) + 4a b +--R + +--R 3 9 5 7 7 5 9 3 +--R 17a b + 16a b - 3a b - 34a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 10 4 8 7 +--R (- 3a b + 3a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 6 +--R (- 3a b - 6a b + 9a b )cos(d x + c) +--R + +--R 4 8 6 6 5 +--R (33a b - 33a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 4 +--R (2a b + 57a b - 30a b - 29a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 3 +--R (a b - 35a b + 34a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 +--R (- 3a b - 60a b + 12a b + 39a b + 12a b )cos(d x + c) +--R + +--R 2 10 4 8 8 4 10 2 2 10 4 8 +--R (2a b - a b + a b - 2a b )cos(d x + c) + 4a b + 9a b +--R + +--R 6 6 8 4 10 2 +--R 10a b - 9a b - 14a b +--R * +--R sin(d x + c) +--R + +--R 11 3 9 5 7 7 +--R (2a b - 7a b + 5a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 6 +--R (2a b - 8a b + 4a b + 2a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 5 +--R (- 4a b + 10a b + 7a b - 13a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 4 +--R (- 4a b + 13a b + 12a b - 17a b - 4a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 3 +--R (2a b - 3a b - 12a b + 13a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 2 +--R (2a b - 6a b - 19a b + 14a b + 7a b + 2a b)cos(d x + c) +--R + +--R 3 9 5 7 7 5 9 3 11 +--R a b + 3a b + a b - 3a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 9 5 7 7 +--R (12a b - 12a b )sin(d x + c) +--R + +--R 2 10 4 8 2 2 10 4 8 +--R (6a b - 6a b )cos(d x + c) + (12a b - 12a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 +--R 6a b + 12a b - 18a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 11 3 9 3 +--R (6a b - 6a b )cos(d x + c) +--R + +--R 11 3 9 5 7 2 +--R (12a b + 54a b - 66a b )cos(d x + c) +--R + +--R 11 3 9 5 7 11 3 9 5 7 +--R (2a b + 32a b - 34a b )cos(d x + c) - 8a b - 10a b - 16a b +--R + +--R 7 5 +--R 34a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 12 2 10 4 8 4 +--R (- 2b - 2a b + 4a b )cos(d x + c) +--R + +--R 12 2 10 4 8 3 +--R (- 2b + 52a b - 50a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 2 +--R (2b + 64a b + 70a b - 136a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 12 2 10 +--R (- 2b - 10a b + 26a b - 14a b )cos(d x + c) - 4b - 36a b +--R + +--R 4 8 6 6 8 4 +--R - 64a b + 12a b + 92a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 11 3 9 5 7 4 +--R (4a b + 28a b - 32a b )cos(d x + c) +--R + +--R 11 3 9 5 7 3 +--R (- 4a b + 116a b - 112a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 12a b + 100a b - 8a b - 80a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 11 +--R (- 12a b - 56a b + 28a b + 40a b )cos(d x + c) - 8a b +--R + +--R 3 9 5 7 7 5 9 3 +--R - 76a b - 48a b + 56a b + 76a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 12 2 10 4 8 6 +--R (- 2b - 8a b + 10a b )cos(d x + c) +--R + +--R 2 10 4 8 5 +--R (24a b - 24a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 4 +--R (6b + 42a b + 42a b - 90a b )cos(d x + c) +--R + +--R 4 8 6 6 3 +--R (96a b - 96a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 2 +--R (- 6b - 28a b + 12a b + 18a b + 4a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 12 +--R (- 32a b - 64a b + 44a b + 52a b )cos(d x + c) + 2b +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R - 14a b - 56a b + 6a b + 34a b + 28a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 11 3 9 7 +--R (- 6a b + 6a b )cos(d x + c) +--R + +--R 11 3 9 5 7 6 +--R (- 6a b - 12a b + 18a b )cos(d x + c) +--R + +--R 11 3 9 5 7 5 +--R (- 6a b + 60a b - 54a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 4 +--R (- 2a b + 106a b - 50a b - 54a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 3 +--R (14a b - 38a b + 64a b - 40a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 2 +--R (6a b - 84a b + 28a b + 34a b + 16a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (- 2a b - 28a b - 22a b + 28a b + 24a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R 2a b - 10a b - 8a b + 6a b + 6a b + 4a b +--R * +--R sin(d x + c) +--R + +--R 12 2 10 4 8 7 +--R (4b - 14a b + 10a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 6 +--R (4b - 16a b + 8a b + 4a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 5 +--R (- 8b + 18a b + 12a b - 22a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 4 +--R (- 8b + 24a b + 22a b - 30a b - 8a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 3 +--R (4b - 2a b - 16a b + 22a b - 8a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 2 +--R (4b - 8a b - 30a b + 24a b + 6a b + 4a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (- 2a b - 6a b - 2a b + 6a b + 4a b )cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 8 6 6 7 +--R (6a b - 6a b )sin(d x + c) +--R + +--R 3 9 5 7 2 3 9 5 7 3 9 +--R (3a b - 3a b )cos(d x + c) + (6a b - 6a b )cos(d x + c) + 7a b +--R + +--R 5 7 7 5 +--R 10a b - 17a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 2 10 4 8 3 +--R (3a b - 3a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 2 +--R (2a b + 23a b - 25a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 2 10 4 8 6 6 +--R (5a b + 20a b - 25a b )cos(d x + c) + 4a b + 19a b - 8a b +--R + +--R 8 4 +--R - 15a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 11 3 9 5 7 3 +--R (- 5a b + 22a b - 17a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 5a b + 12a b + 33a b - 40a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 11 3 9 +--R (3a b + 15a b + 21a b - 39a b )cos(d x + c) + 3a b + 17a b +--R + +--R 5 7 7 5 9 3 +--R 13a b - 29a b - 4a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 12 2 10 4 8 5 +--R (b + a b - 2a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 4 +--R (b + 6a b + 15a b - 22a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 3 +--R (- 2b - 18a b + 48a b - 28a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 2 +--R (- 2b - 28a b + 16a b + 18a b - 4a b )cos(d x + c) +--R + +--R 12 2 10 4 8 6 6 8 4 12 2 10 +--R (b + 9a b + 9a b + 11a b - 30a b )cos(d x + c) + b + 14a b +--R + +--R 4 8 6 6 8 4 +--R 20a b + 4a b - 39a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 11 3 9 5 7 6 +--R (- a b - 4a b + 5a b )cos(d x + c) +--R + +--R 11 3 9 5 7 5 +--R (3a b + 15a b - 18a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 4 +--R (6a b + 27a b + 18a b - 51a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 3 +--R (- 6a b - 24a b + 42a b - 12a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 2 +--R (- 9a b - 44a b - 16a b + 47a b + 22a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (3a b + 5a b - a b + 5a b - 12a b )cos(d x + c) + 4a b +--R + +--R 3 9 5 7 7 5 9 3 +--R 17a b + 16a b - 3a b - 34a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 10 4 8 7 +--R (- 3a b + 3a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 6 +--R (- 3a b - 6a b + 9a b )cos(d x + c) +--R + +--R 4 8 6 6 5 +--R (33a b - 33a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 4 +--R (2a b + 57a b - 30a b - 29a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 3 +--R (a b - 35a b + 34a b )cos(d x + c) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 +--R (- 3a b - 60a b + 12a b + 39a b + 12a b )cos(d x + c) +--R + +--R 2 10 4 8 8 4 10 2 2 10 4 8 6 6 +--R (2a b - a b + a b - 2a b )cos(d x + c) + 4a b + 9a b + 10a b +--R + +--R 8 4 10 2 +--R - 9a b - 14a b +--R * +--R sin(d x + c) +--R + +--R 11 3 9 5 7 7 +--R (2a b - 7a b + 5a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 6 +--R (2a b - 8a b + 4a b + 2a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 5 +--R (- 4a b + 10a b + 7a b - 13a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 4 +--R (- 4a b + 13a b + 12a b - 17a b - 4a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 3 +--R (2a b - 3a b - 12a b + 13a b )cos(d x + c) +--R + +--R 11 3 9 5 7 7 5 9 3 11 2 3 9 +--R (2a b - 6a b - 19a b + 14a b + 7a b + 2a b)cos(d x + c) + a b +--R + +--R 5 7 7 5 9 3 11 +--R 3a b + a b - 3a b - 2a b +--R / +--R 4 10 6 8 8 6 6 +--R (8a b - 16a b + 8a b )sin(d x + c) +--R + +--R 3 11 5 9 7 7 2 +--R (- 8a b + 16a b - 8a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 3 11 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) + 16a b +--R + +--R 7 7 9 5 +--R - 48a b + 32a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 8 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 3 +--R (- 8a b + 24a b - 24a b + 8a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 2 +--R (- 12a b - 4a b + 44a b - 28a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (8a b + 8a b - 72a b + 88a b - 32a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R 10a b + 40a b - 60a b - 40a b + 50a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 13 3 11 5 9 7 7 5 +--R (2a b - 6a b + 6a b - 2a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 4 +--R (2a b + 2a b - 10a b + 6a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (- 4a b - 16a b + 72a b - 80a b + 28a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 2 +--R (- 4a b - 32a b + 40a b + 32a b - 36a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (2a b + 22a b - 28a b - 68a b + 122a b - 50a b ) +--R * +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R 2a b + 30a b + 20a b - 100a b + 10a b + 38a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (6a b - 18a b + 18a b - 6a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 4 +--R (6a b - 6a b - 6a b + 6a b )cos(d x + c) +--R + +--R 2 12 6 8 8 6 10 4 3 +--R (- 12a b + 72a b - 96a b + 36a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 2 +--R (- 12a b - 24a b + 64a b - 8a b - 20a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (6a b + 18a b - 52a b - 12a b + 78a b - 38a b ) +--R * +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R 6a b + 30a b - 20a b - 60a b + 30a b + 14a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 5 +--R (6a b - 18a b + 18a b - 6a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 4 +--R (6a b - 10a b + 2a b + 2a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (- 12a b + 16a b + 24a b - 48a b + 20a b )cos(d x + c) +--R + +--R 3 11 7 7 9 5 11 3 2 +--R (- 12a b + 32a b - 16a b - 4a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (6a b + 2a b - 28a b + 12a b + 22a b - 14a b) +--R * +--R cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R 6a b + 10a b - 20a b - 12a b + 14a b + 2a b +--R * +--R sin(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 5 +--R (2a b - 6a b + 6a b - 2a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 4 10 6 8 10 4 12 2 3 +--R (- 4a b + 8a b - 8a b + 4a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 2 +--R (- 4a b + 4a b + 4a b - 4a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cos(d x + c) +--R + +--R 4 10 8 6 12 2 +--R 2a b - 4a b + 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 11 5 9 7 7 6 +--R (16a b - 32a b + 16a b )sin(d x + c) +--R + +--R 2 12 4 10 6 8 2 +--R (- 16a b + 32a b - 16a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 2 12 +--R (16a b - 48a b + 48a b - 16a b )cos(d x + c) + 32a b +--R + +--R 6 8 8 6 +--R - 96a b + 64a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 13 3 11 5 9 4 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 3 +--R (- 16a b + 48a b - 48a b + 16a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 2 +--R (- 24a b - 8a b + 88a b - 56a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (16a b + 16a b - 144a b + 176a b - 64a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R 20a b + 80a b - 120a b - 80a b + 100a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 14 2 12 4 10 6 8 5 +--R (4b - 12a b + 12a b - 4a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 4 +--R (4b + 4a b - 20a b + 12a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 3 +--R (- 8b - 32a b + 144a b - 160a b + 56a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 2 +--R (- 8b - 64a b + 80a b + 64a b - 72a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R (4b + 44a b - 56a b - 136a b + 244a b - 100a b ) +--R * +--R cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R 4b + 60a b + 40a b - 200a b + 20a b + 76a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 13 3 11 5 9 7 7 5 +--R (12a b - 36a b + 36a b - 12a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 4 +--R (12a b - 12a b - 12a b + 12a b )cos(d x + c) +--R + +--R 13 5 9 7 7 9 5 3 +--R (- 24a b + 144a b - 192a b + 72a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (- 24a b - 48a b + 128a b - 16a b - 40a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (12a b + 36a b - 104a b - 24a b + 156a b - 76a b ) +--R * +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R 12a b + 60a b - 40a b - 120a b + 60a b + 28a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (12a b - 36a b + 36a b - 12a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 4 +--R (12a b - 20a b + 4a b + 4a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (- 24a b + 32a b + 48a b - 96a b + 40a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 2 12 6 8 8 6 10 4 2 +--R (- 24a b + 64a b - 32a b - 8a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (12a b + 4a b - 56a b + 24a b + 44a b - 28a b ) +--R * +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R 12a b + 20a b - 40a b - 24a b + 28a b + 4a b +--R * +--R sin(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 5 +--R (4a b - 12a b + 12a b - 4a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 4 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 3 11 5 9 9 5 11 3 3 +--R (- 8a b + 16a b - 16a b + 8a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 2 +--R (- 8a b + 8a b + 8a b - 8a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (4a b - 4a b - 8a b + 8a b + 4a b - 4a b)cos(d x + c) +--R + +--R 3 11 7 7 11 3 +--R 4a b - 8a b + 4a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 10 6 8 8 6 6 +--R (8a b - 16a b + 8a b )sin(d x + c) +--R + +--R 3 11 5 9 7 7 2 +--R (- 8a b + 16a b - 8a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 3 11 7 7 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) + 16a b - 48a b +--R + +--R 9 5 +--R 32a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 8 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 3 +--R (- 8a b + 24a b - 24a b + 8a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 2 +--R (- 12a b - 4a b + 44a b - 28a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (8a b + 8a b - 72a b + 88a b - 32a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R 10a b + 40a b - 60a b - 40a b + 50a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 13 3 11 5 9 7 7 5 +--R (2a b - 6a b + 6a b - 2a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 4 +--R (2a b + 2a b - 10a b + 6a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (- 4a b - 16a b + 72a b - 80a b + 28a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 2 +--R (- 4a b - 32a b + 40a b + 32a b - 36a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (2a b + 22a b - 28a b - 68a b + 122a b - 50a b ) +--R * +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R 2a b + 30a b + 20a b - 100a b + 10a b + 38a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (6a b - 18a b + 18a b - 6a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 4 +--R (6a b - 6a b - 6a b + 6a b )cos(d x + c) +--R + +--R 2 12 6 8 8 6 10 4 3 +--R (- 12a b + 72a b - 96a b + 36a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 2 +--R (- 12a b - 24a b + 64a b - 8a b - 20a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (6a b + 18a b - 52a b - 12a b + 78a b - 38a b ) +--R * +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R 6a b + 30a b - 20a b - 60a b + 30a b + 14a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 5 +--R (6a b - 18a b + 18a b - 6a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 4 +--R (6a b - 10a b + 2a b + 2a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (- 12a b + 16a b + 24a b - 48a b + 20a b )cos(d x + c) +--R + +--R 3 11 7 7 9 5 11 3 2 +--R (- 12a b + 32a b - 16a b - 4a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (6a b + 2a b - 28a b + 12a b + 22a b - 14a b)cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R 6a b + 10a b - 20a b - 12a b + 14a b + 2a b +--R * +--R sin(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 5 +--R (2a b - 6a b + 6a b - 2a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 4 10 6 8 10 4 12 2 3 +--R (- 4a b + 8a b - 8a b + 4a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 2 +--R (- 4a b + 4a b + 4a b - 4a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cos(d x + c) +--R + +--R 4 10 8 6 12 2 +--R 2a b - 4a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 11 6 9 8 7 10 5 6 +--R (- 8a b + 24a b - 24a b + 8a b )sin(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 2 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 3 12 +--R (- 8a b + 24a b - 24a b + 8a b )cos(d x + c) - 16a b +--R + +--R 5 10 7 8 9 6 11 4 +--R 16a b + 48a b - 80a b + 32a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 4 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 3 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 2 +--R (12a b - 8a b - 48a b + 72a b - 28a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (- 8a b - 8a b + 72a b - 88a b + 32a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 10a b - 30a b + 100a b - 20a b - 90a b + 50a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 14 3 12 5 10 7 8 5 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 14 5 10 7 8 9 6 4 +--R (- 2a b + 12a b - 16a b + 6a b )cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 3 +--R (4a b + 16a b - 72a b + 80a b - 28a b )cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (4a b + 28a b - 72a b + 8a b + 68a b - 36a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (- 2a b - 22a b + 28a b + 68a b - 122a b + 50a b ) +--R * +--R cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 2a b - 28a b + 10a b + 120a b - 110a b - 28a b +--R + +--R 13 2 +--R 38a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 2 13 4 11 8 7 10 5 4 +--R (- 6a b + 12a b - 12a b + 6a b )cos(d x + c) +--R + +--R 2 13 6 9 8 7 10 5 3 +--R (12a b - 72a b + 96a b - 36a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (12a b + 12a b - 88a b + 72a b + 12a b - 20a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (- 6a b - 18a b + 52a b + 12a b - 78a b + 38a b ) +--R * +--R cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 14 +--R - 6a b - 24a b + 50a b + 40a b - 90a b + 16a b + 14a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 11 4 4 +--R (- 6a b + 16a b - 12a b + 2a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 3 +--R (12a b - 16a b - 24a b + 48a b - 20a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (12a b - 12a b - 32a b + 48a b - 12a b - 4a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (- 6a b - 2a b + 28a b - 12a b - 22a b + 14a b ) +--R * +--R cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 15 +--R - 6a b - 4a b + 30a b - 8a b - 26a b + 12a b + 2a +--R * +--R sin(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 5 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 4 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 4 11 6 9 10 5 12 3 3 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 4 11 6 9 10 5 12 3 2 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R (- 2a b + 2a b + 4a b - 4a b - 2a b + 2a b)cos(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R - 2a b + 2a b + 4a b - 4a b - 2a b + 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 12 5 10 7 8 9 6 6 +--R (- 16a b + 48a b - 48a b + 16a b )sin(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 2 +--R (16a b - 48a b + 48a b - 16a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 2 13 +--R (- 16a b + 48a b - 48a b + 16a b )cos(d x + c) - 32a b +--R + +--R 4 11 6 9 8 7 10 5 +--R 32a b + 96a b - 160a b + 64a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 14 3 12 5 10 7 8 4 +--R (- 4a b + 12a b - 12a b + 4a b )cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 3 +--R (16a b - 48a b + 48a b - 16a b )cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 2 +--R (24a b - 16a b - 96a b + 144a b - 56a b )cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (- 16a b - 16a b + 144a b - 176a b + 64a b )cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 20a b - 60a b + 200a b - 40a b - 180a b + 100a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 15 2 13 4 11 6 9 5 +--R (- 4b + 12a b - 12a b + 4a b )cos(d x + c) +--R + +--R 15 4 11 6 9 8 7 4 +--R (- 4b + 24a b - 32a b + 12a b )cos(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 3 +--R (8b + 32a b - 144a b + 160a b - 56a b )cos(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R (8b + 56a b - 144a b + 16a b + 136a b - 72a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R (- 4b - 44a b + 56a b + 136a b - 244a b + 100a b ) +--R * +--R cos(d x + c) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 4b - 56a b + 20a b + 240a b - 220a b - 56a b + 76a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 14 3 12 5 10 7 8 5 +--R (- 12a b + 36a b - 36a b + 12a b )cos(d x + c) +--R + +--R 14 3 12 7 8 9 6 4 +--R (- 12a b + 24a b - 24a b + 12a b )cos(d x + c) +--R + +--R 14 5 10 7 8 9 6 3 +--R (24a b - 144a b + 192a b - 72a b )cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (24a b + 24a b - 176a b + 144a b + 24a b - 40a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (- 12a b - 36a b + 104a b + 24a b - 156a b + 76a b ) +--R * +--R cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 12a b - 48a b + 100a b + 80a b - 180a b + 32a b +--R + +--R 13 2 +--R 28a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 5 +--R (- 12a b + 36a b - 36a b + 12a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 10 5 4 +--R (- 12a b + 32a b - 24a b + 4a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 3 +--R (24a b - 32a b - 48a b + 96a b - 40a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (24a b - 24a b - 64a b + 96a b - 24a b - 8a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (- 12a b - 4a b + 56a b - 24a b - 44a b + 28a b ) +--R * +--R cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 14 +--R - 12a b - 8a b + 60a b - 16a b - 52a b + 24a b + 4a b +--R * +--R sin(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 5 +--R (- 4a b + 12a b - 12a b + 4a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 4 +--R (- 4a b + 12a b - 12a b + 4a b )cos(d x + c) +--R + +--R 3 12 5 10 9 6 11 4 3 +--R (8a b - 16a b + 16a b - 8a b )cos(d x + c) +--R + +--R 3 12 5 10 9 6 11 4 2 +--R (8a b - 16a b + 16a b - 8a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (- 4a b + 4a b + 8a b - 8a b - 4a b + 4a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R - 4a b + 4a b + 8a b - 8a b - 4a b + 4a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 11 6 9 8 7 10 5 6 +--R (- 8a b + 24a b - 24a b + 8a b )sin(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 2 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 3 12 5 10 +--R (- 8a b + 24a b - 24a b + 8a b )cos(d x + c) - 16a b + 16a b +--R + +--R 7 8 9 6 11 4 +--R 48a b - 80a b + 32a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 4 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 3 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 2 +--R (12a b - 8a b - 48a b + 72a b - 28a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 2 13 +--R (- 8a b - 8a b + 72a b - 88a b + 32a b )cos(d x + c) - 10a b +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R - 30a b + 100a b - 20a b - 90a b + 50a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 14 3 12 5 10 7 8 5 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 14 5 10 7 8 9 6 4 +--R (- 2a b + 12a b - 16a b + 6a b )cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 3 +--R (4a b + 16a b - 72a b + 80a b - 28a b )cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 2 +--R (4a b + 28a b - 72a b + 8a b + 68a b - 36a b )cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (- 2a b - 22a b + 28a b + 68a b - 122a b + 50a b ) +--R * +--R cos(d x + c) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 13 2 +--R - 2a b - 28a b + 10a b + 120a b - 110a b - 28a b + 38a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 2 13 4 11 8 7 10 5 4 +--R (- 6a b + 12a b - 12a b + 6a b )cos(d x + c) +--R + +--R 2 13 6 9 8 7 10 5 3 +--R (12a b - 72a b + 96a b - 36a b )cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (12a b + 12a b - 88a b + 72a b + 12a b - 20a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (- 6a b - 18a b + 52a b + 12a b - 78a b + 38a b ) +--R * +--R cos(d x + c) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 14 +--R - 6a b - 24a b + 50a b + 40a b - 90a b + 16a b + 14a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 11 4 4 +--R (- 6a b + 16a b - 12a b + 2a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 3 +--R (12a b - 16a b - 24a b + 48a b - 20a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 2 +--R (12a b - 12a b - 32a b + 48a b - 12a b - 4a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (- 6a b - 2a b + 28a b - 12a b - 22a b + 14a b )cos(d x + c) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 15 +--R - 6a b - 4a b + 30a b - 8a b - 26a b + 12a b + 2a +--R * +--R sin(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 5 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 4 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 4 11 6 9 10 5 12 3 3 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 4 11 6 9 10 5 12 3 2 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 4 11 +--R (- 2a b + 2a b + 4a b - 4a b - 2a b + 2a b)cos(d x + c) - 2a b +--R + +--R 6 9 8 7 10 5 12 3 14 +--R 2a b + 4a b - 4a b - 2a b + 2a b +--R Type: Expression(Integer) +--E 77 + +--S 78 of 520 +m0014b:= a0014.2-r0014 +--R +--R +--R (42) +--R 3 5 5 3 3 +--R (- 4a b - 8a b )sin(d x + c) +--R + +--R 2 6 4 4 2 2 6 4 4 6 2 2 +--R ((2a b + 4a b )cos(d x + c) - 2a b - 14a b - 20a b )sin(d x + c) +--R + +--R 3 5 5 3 2 3 5 5 3 7 +--R ((4a b + 8a b )cos(d x + c) - 4a b - 16a b - 16a b)sin(d x + c) +--R + +--R 4 4 6 2 2 4 4 6 2 8 +--R (2a b + 4a b )cos(d x + c) - 2a b - 6a b - 4a +--R * +--R +---------+ +--R | 2 2 +--R (a sin(d x + c) + b cos(d x + c) + b)\|- b + a +--R atan(-------------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R 3 5 5 3 3 +--R (- 4a b - 8a b )sin(d x + c) +--R + +--R 2 6 4 4 2 2 6 4 4 6 2 2 +--R ((2a b + 4a b )cos(d x + c) - 2a b - 14a b - 20a b )sin(d x + c) +--R + +--R 3 5 5 3 2 3 5 5 3 7 +--R ((4a b + 8a b )cos(d x + c) - 4a b - 16a b - 16a b)sin(d x + c) +--R + +--R 4 4 6 2 2 4 4 6 2 8 +--R (2a b + 4a b )cos(d x + c) - 2a b - 6a b - 4a +--R * +--R d x + c +--R a tan(-------) + b +--R 2 +--R atan(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 4 6 3 4 3 +--R (3a b cos(d x + c) - 2a b + 8a b )sin(d x + c) +--R + +--R 7 2 5 2 2 5 4 3 7 +--R (b - 4a b )cos(d x + c) + (- a b + 4a b )cos(d x + c) - b +--R + +--R 2 5 4 3 +--R - a b + 20a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 4 3 6 3 4 2 +--R 3a b cos(d x + c) + (2a b - 8a b )cos(d x + c) +--R + +--R 3 4 6 3 4 5 2 +--R - 3a b cos(d x + c) - 2a b + 4a b + 16a b +--R * +--R sin(d x + c) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- a b + 4a b )cos(d x + c) + (a b - 4a b )cos(d x + c) +--R + +--R 2 5 4 3 2 5 4 3 6 +--R (a b - 4a b )cos(d x + c) - a b + 3a b + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 7 5 5 7 3 3 +--R (4a b - 8a b + 4a b )d sin(d x + c) +--R + +--R 2 8 4 6 6 4 2 +--R (- 2a b + 4a b - 2a b )d cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 +--R (2a b + 6a b - 18a b + 10a b )d +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 7 5 5 7 3 2 3 7 7 3 9 +--R ((- 4a b + 8a b - 4a b )d cos(d x + c) + (4a b - 12a b + 8a b)d) +--R * +--R sin(d x + c) +--R + +--R 4 6 6 4 8 2 2 +--R (- 2a b + 4a b - 2a b )d cos(d x + c) +--R + +--R 4 6 6 4 8 2 10 +--R (2a b - 2a b - 2a b + 2a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 78 + +--S 79 of 520 +d0014b:= D(m0014b,x) +--R +--R +--R (43) +--R 4 6 8 +--R - 6a b sin(d x + c) +--R + +--R 3 7 2 3 7 3 7 5 5 +--R (- 3a b cos(d x + c) - 12a b cos(d x + c) - 9a b - 9a b ) +--R * +--R 7 +--R sin(d x + c) +--R + +--R 2 8 3 2 8 4 6 2 +--R - 6a b cos(d x + c) + (- 9a b - 39a b )cos(d x + c) +--R + +--R 2 8 4 6 2 8 4 6 6 4 +--R (- 10a b - 62a b )cos(d x + c) - 5a b - 30a b + 17a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 9 3 7 4 9 3 7 3 +--R (a b - a b )cos(d x + c) + (10a b - 40a b )cos(d x + c) +--R + +--R 9 3 7 5 5 2 +--R (8a b - 46a b - 85a b )cos(d x + c) +--R + +--R 9 3 7 5 5 9 3 7 +--R (- 6a b - 46a b - 128a b )cos(d x + c) - 5a b - 31a b +--R + +--R 5 5 7 3 +--R - 52a b + 46a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 10 2 8 5 +--R (- 2b - 4a b )cos(d x + c) +--R + +--R 10 2 8 4 6 4 +--R (- 2b - 5a b - 41a b )cos(d x + c) +--R + +--R 10 2 8 4 6 3 +--R (4b + 50a b - 90a b )cos(d x + c) +--R + +--R 10 2 8 4 6 6 4 2 +--R (4b + 54a b - 47a b - 47a b )cos(d x + c) +--R + +--R 10 2 8 4 6 6 4 10 2 8 +--R (- 2b - 26a b - 74a b - 138a b )cos(d x + c) - 2b - 29a b +--R + +--R 4 6 6 4 8 2 +--R - 72a b - 85a b + 38a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 9 3 7 6 9 3 7 5 +--R (a b + 5a b )cos(d x + c) + (- 8a b - 40a b )cos(d x + c) +--R + +--R 9 3 7 5 5 4 +--R (- 11a b - 50a b - 101a b )cos(d x + c) +--R + +--R 9 3 7 5 5 3 +--R (16a b + 100a b - 80a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 2 +--R (19a b + 121a b + 69a b + 22a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 9 3 7 +--R (- 8a b - 36a b - 52a b - 84a b )cos(d x + c) - 9a b - 52a b +--R + +--R 5 5 7 3 9 +--R - 100a b - 99a b + 14a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 8 7 2 8 4 6 6 +--R 6a b cos(d x + c) + (6a b - 3a b )cos(d x + c) +--R + +--R 2 8 4 6 5 +--R (- 6a b - 102a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 4 +--R (- 8a b - 115a b - 75a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 3 +--R (10a b + 128a b - 24a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (14a b + 171a b + 117a b + 34a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 2 8 +--R (- 10a b - 18a b - 16a b - 28a b )cos(d x + c) - 12a b +--R + +--R 4 6 6 4 8 2 10 +--R - 45a b - 82a b - 61a b + 2a +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 7 8 9 3 7 7 +--R 3a b cos(d x + c) + (- 4a b + 16a b )cos(d x + c) +--R + +--R 9 3 7 5 5 6 +--R (- 4a b + 17a b - 25a b )cos(d x + c) +--R + +--R 9 3 7 5 5 5 +--R (8a b - 12a b - 92a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 4 +--R (8a b - 25a b - 61a b - 24a b )cos(d x + c) +--R + +--R 9 5 5 3 +--R (- 4a b + 94a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 4a b + 11a b + 107a b + 55a b + 14a b)cos(d x + c) +--R + +--R 3 7 5 5 7 3 9 3 7 5 5 +--R (- 4a b - 2a b - 2a b - 4a b)cos(d x + c) - 6a b - 21a b +--R + +--R 7 3 9 +--R - 33a b - 18a b +--R * +--R sin(d x + c) +--R + +--R 2 8 4 6 8 2 8 4 6 7 +--R (- 2a b + 5a b )cos(d x + c) + (- 4a b + 10a b )cos(d x + c) +--R + +--R 2 8 6 4 6 +--R (2a b - 11a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 5 +--R (8a b - 12a b - 26a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (2a b - 8a b - 8a b - 4a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 3 +--R (- 4a b + 2a b + 26a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 10 2 4 6 6 4 +--R (- 2a b + 4a b + 23a b + 9a b + 2a )cos(d x + c) - a b - 4a b +--R + +--R 8 2 10 +--R - 5a b - 2a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 7 8 +--R - 12a b sin(d x + c) +--R + +--R 2 8 2 2 8 2 8 4 6 +--R (- 6a b cos(d x + c) - 24a b cos(d x + c) - 10a b - 2a b ) +--R * +--R 7 +--R sin(d x + c) +--R + +--R 9 3 9 3 7 2 +--R - 12a b cos(d x + c) + (- 26a b - 94a b )cos(d x + c) +--R + +--R 9 3 7 9 3 7 5 5 +--R (- 4a b - 92a b )cos(d x + c) + 14a b + 20a b + 98a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 10 2 8 4 10 2 8 3 +--R (4b + 2a b )cos(d x + c) + (4b - 112a b )cos(d x + c) +--R + +--R 10 2 8 4 6 2 +--R (- 4b - 152a b - 210a b )cos(d x + c) +--R + +--R 10 2 8 4 6 10 2 8 4 6 +--R (4b + 20a b - 96a b )cos(d x + c) + 8b + 74a b + 146a b +--R + +--R 6 4 +--R 192a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 9 3 7 4 9 3 7 3 +--R (- 4a b - 86a b )cos(d x + c) + (12a b - 324a b )cos(d x + c) +--R + +--R 9 3 7 5 5 2 +--R (24a b - 234a b - 102a b )cos(d x + c) +--R + +--R 9 3 7 5 5 9 3 7 +--R (28a b + 160a b + 52a b )cos(d x + c) + 20a b + 164a b +--R + +--R 5 5 7 3 +--R 204a b + 152a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 10 2 8 6 2 8 5 +--R (4b + 14a b )cos(d x + c) - 48a b cos(d x + c) +--R + +--R 10 2 8 4 6 4 +--R (- 12b - 102a b - 246a b )cos(d x + c) +--R + +--R 2 8 4 6 3 +--R (8a b - 416a b )cos(d x + c) +--R + +--R 10 2 8 6 4 2 +--R (12b + 106a b + 104a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 10 2 8 +--R (88a b + 328a b + 184a b )cos(d x + c) - 4b + 30a b +--R + +--R 4 6 6 4 8 2 +--R 158a b + 108a b + 56a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 9 7 9 3 7 6 +--R 12a b cos(d x + c) + (18a b + 6a b )cos(d x + c) +--R + +--R 9 3 7 5 +--R (12a b - 156a b )cos(d x + c) +--R + +--R 9 3 7 5 5 4 +--R (- 10a b - 252a b - 218a b )cos(d x + c) +--R + +--R 9 3 7 5 5 3 +--R (- 28a b + 48a b - 272a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 2 +--R (- 2a b + 238a b + 180a b + 136a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 9 +--R (4a b + 124a b + 296a b + 152a b )cos(d x + c) - 6a b +--R + +--R 3 7 5 5 7 3 9 +--R 24a b + 62a b + 20a b + 8a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 8 8 10 2 8 7 +--R 6a b cos(d x + c) + (- 8b + 32a b )cos(d x + c) +--R + +--R 10 2 8 4 6 6 +--R (- 8b + 40a b - 38a b )cos(d x + c) +--R + +--R 10 2 8 4 6 5 +--R (16b - 8a b - 152a b )cos(d x + c) +--R + +--R 10 2 8 4 6 6 4 4 +--R (16b - 52a b - 146a b - 88a b )cos(d x + c) +--R + +--R 10 2 8 4 6 6 4 3 +--R (- 8b - 32a b + 76a b - 96a b )cos(d x + c) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (- 8b + 8a b + 178a b + 108a b + 56a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 2 8 4 6 +--R (8a b + 76a b + 124a b + 56a b )cos(d x + c) - 2a b + 6a b +--R + +--R 6 4 +--R 8a b +--R * +--R sin(d x + c) +--R + +--R 9 3 7 8 9 3 7 7 +--R (- 4a b + 10a b )cos(d x + c) + (- 8a b + 20a b )cos(d x + c) +--R + +--R 9 3 7 5 5 6 +--R (4a b + 2a b - 18a b )cos(d x + c) +--R + +--R 9 3 7 5 5 5 +--R (16a b - 20a b - 44a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 4 +--R (4a b - 18a b - 24a b - 16a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 3 +--R (- 8a b - 4a b + 28a b - 16a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 4a b + 6a b + 42a b + 20a b + 8a b)cos(d x + c) +--R + +--R 3 7 5 5 7 3 9 +--R (4a b + 16a b + 20a b + 8a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 6 8 +--R - 6a b sin(d x + c) +--R + +--R 3 7 2 3 7 3 7 5 5 7 +--R (- 3a b cos(d x + c) - 12a b cos(d x + c) - 9a b - 9a b )sin(d x + c) +--R + +--R 2 8 3 2 8 4 6 2 +--R - 6a b cos(d x + c) + (- 9a b - 39a b )cos(d x + c) +--R + +--R 2 8 4 6 2 8 4 6 6 4 +--R (- 10a b - 62a b )cos(d x + c) - 5a b - 30a b + 17a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 9 3 7 4 9 3 7 3 +--R (a b - a b )cos(d x + c) + (10a b - 40a b )cos(d x + c) +--R + +--R 9 3 7 5 5 2 +--R (8a b - 46a b - 85a b )cos(d x + c) +--R + +--R 9 3 7 5 5 9 3 7 5 5 +--R (- 6a b - 46a b - 128a b )cos(d x + c) - 5a b - 31a b - 52a b +--R + +--R 7 3 +--R 46a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 10 2 8 5 +--R (- 2b - 4a b )cos(d x + c) +--R + +--R 10 2 8 4 6 4 +--R (- 2b - 5a b - 41a b )cos(d x + c) +--R + +--R 10 2 8 4 6 3 +--R (4b + 50a b - 90a b )cos(d x + c) +--R + +--R 10 2 8 4 6 6 4 2 +--R (4b + 54a b - 47a b - 47a b )cos(d x + c) +--R + +--R 10 2 8 4 6 6 4 10 2 8 +--R (- 2b - 26a b - 74a b - 138a b )cos(d x + c) - 2b - 29a b +--R + +--R 4 6 6 4 8 2 +--R - 72a b - 85a b + 38a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 9 3 7 6 9 3 7 5 +--R (a b + 5a b )cos(d x + c) + (- 8a b - 40a b )cos(d x + c) +--R + +--R 9 3 7 5 5 4 +--R (- 11a b - 50a b - 101a b )cos(d x + c) +--R + +--R 9 3 7 5 5 3 +--R (16a b + 100a b - 80a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 2 +--R (19a b + 121a b + 69a b + 22a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 9 3 7 +--R (- 8a b - 36a b - 52a b - 84a b )cos(d x + c) - 9a b - 52a b +--R + +--R 5 5 7 3 9 +--R - 100a b - 99a b + 14a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 8 7 2 8 4 6 6 +--R 6a b cos(d x + c) + (6a b - 3a b )cos(d x + c) +--R + +--R 2 8 4 6 5 +--R (- 6a b - 102a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 4 +--R (- 8a b - 115a b - 75a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 3 +--R (10a b + 128a b - 24a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (14a b + 171a b + 117a b + 34a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 2 8 4 6 +--R (- 10a b - 18a b - 16a b - 28a b )cos(d x + c) - 12a b - 45a b +--R + +--R 6 4 8 2 10 +--R - 82a b - 61a b + 2a +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 7 8 9 3 7 7 +--R 3a b cos(d x + c) + (- 4a b + 16a b )cos(d x + c) +--R + +--R 9 3 7 5 5 6 +--R (- 4a b + 17a b - 25a b )cos(d x + c) +--R + +--R 9 3 7 5 5 5 +--R (8a b - 12a b - 92a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 4 +--R (8a b - 25a b - 61a b - 24a b )cos(d x + c) +--R + +--R 9 5 5 3 +--R (- 4a b + 94a b )cos(d x + c) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 4a b + 11a b + 107a b + 55a b + 14a b)cos(d x + c) +--R + +--R 3 7 5 5 7 3 9 3 7 5 5 +--R (- 4a b - 2a b - 2a b - 4a b)cos(d x + c) - 6a b - 21a b +--R + +--R 7 3 9 +--R - 33a b - 18a b +--R * +--R sin(d x + c) +--R + +--R 2 8 4 6 8 2 8 4 6 7 +--R (- 2a b + 5a b )cos(d x + c) + (- 4a b + 10a b )cos(d x + c) +--R + +--R 2 8 6 4 6 2 8 4 6 6 4 5 +--R (2a b - 11a b )cos(d x + c) + (8a b - 12a b - 26a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (2a b - 8a b - 8a b - 4a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 3 +--R (- 4a b + 2a b + 26a b )cos(d x + c) +--R + +--R 2 8 4 6 6 4 8 2 10 2 4 6 6 4 +--R (- 2a b + 4a b + 23a b + 9a b + 2a )cos(d x + c) - a b - 4a b +--R + +--R 8 2 10 +--R - 5a b - 2a +--R / +--R 4 9 6 7 8 5 7 +--R (8a b - 16a b + 8a b )sin(d x + c) +--R + +--R 3 10 5 8 7 6 2 +--R (- 8a b + 16a b - 8a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 3 10 5 8 +--R (16a b - 32a b + 16a b )cos(d x + c) + 24a b - 16a b +--R + +--R 7 6 9 4 +--R - 40a b + 32a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 2 11 4 9 6 7 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 3 +--R (- 16a b + 32a b - 16a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 2 +--R (- 20a b + 20a b + 20a b - 20a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 2 11 +--R (16a b + 48a b - 144a b + 80a b )cos(d x + c) + 18a b +--R + +--R 4 9 6 7 10 3 +--R 64a b - 132a b + 50a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 12 3 10 5 8 5 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 4 +--R (4a b - 10a b + 8a b - 2a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 3 +--R (- 8a b - 56a b + 136a b - 72a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 8a b - 52a b + 124a b - 60a b - 4a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 +--R (4a b + 64a b + 24a b - 256a b + 164a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 11 2 +--R 4a b + 62a b + 32a b - 228a b + 92a b + 38a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 2 11 4 9 6 7 6 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 5 +--R (16a b - 32a b + 16a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 4 +--R (10a b - 42a b + 54a b - 22a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 3 +--R (- 32a b - 64a b + 224a b - 128a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 26a b - 32a b + 172a b - 144a b + 30a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R (16a b + 96a b - 64a b - 224a b + 176a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R 14a b + 78a b - 52a b - 172a b + 118a b + 14a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 3 10 5 8 7 6 6 +--R (6a b - 12a b + 6a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 5 +--R (24a b - 48a b + 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (6a b - 46a b + 74a b - 34a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 48a b - 16a b + 176a b - 112a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 30a b + 16a b + 92a b - 112a b + 34a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (24a b + 64a b - 96a b - 96a b + 104a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 13 +--R 18a b + 42a b - 68a b - 60a b + 66a b + 2a +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 9 6 7 8 5 6 +--R (6a b - 12a b + 6a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 5 +--R (16a b - 32a b + 16a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (- 2a b - 16a b + 38a b - 20a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 32a b + 16a b + 64a b - 48a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 14a b + 20a b + 16a b - 36a b + 14a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R (16a b + 16a b - 48a b - 16a b + 32a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R 10a b + 8a b - 28a b - 8a b + 18a b +--R * +--R sin(d x + c) +--R + +--R 5 8 7 6 9 4 6 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 5 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 5 8 9 4 11 2 4 +--R (- 2a b + 6a b - 4a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (- 8a b + 8a b + 8a b - 8a b )cos(d x + c) +--R + +--R 5 8 7 6 11 2 13 2 +--R (- 2a b + 4a b - 4a b + 2a )cos(d x + c) +--R + +--R 5 8 9 4 13 5 8 9 4 13 +--R (4a b - 8a b + 4a )cos(d x + c) + 2a b - 4a b + 2a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 10 5 8 7 6 7 +--R (16a b - 32a b + 16a b )sin(d x + c) +--R + +--R 2 11 4 9 6 7 2 +--R (- 16a b + 32a b - 16a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 2 11 4 9 +--R (32a b - 64a b + 32a b )cos(d x + c) + 48a b - 32a b +--R + +--R 6 7 8 5 +--R - 80a b + 64a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 12 3 10 5 8 4 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 12 3 10 5 8 3 +--R (- 32a b + 64a b - 32a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 2 +--R (- 40a b + 40a b + 40a b - 40a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 12 +--R (32a b + 96a b - 288a b + 160a b )cos(d x + c) + 36a b +--R + +--R 3 10 5 8 9 4 +--R 128a b - 264a b + 100a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 13 2 11 4 9 5 +--R (8b - 16a b + 8a b )cos(d x + c) +--R + +--R 13 2 11 4 9 6 7 4 +--R (8b - 20a b + 16a b - 4a b )cos(d x + c) +--R + +--R 13 2 11 4 9 6 7 3 +--R (- 16b - 112a b + 272a b - 144a b )cos(d x + c) +--R + +--R 13 2 11 4 9 6 7 8 5 2 +--R (- 16b - 104a b + 248a b - 120a b - 8a b )cos(d x + c) +--R + +--R 13 2 11 4 9 6 7 8 5 13 +--R (8b + 128a b + 48a b - 512a b + 328a b )cos(d x + c) + 8b +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R 124a b + 64a b - 456a b + 184a b + 76a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 12 3 10 5 8 6 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 12 3 10 5 8 5 +--R (32a b - 64a b + 32a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 4 +--R (20a b - 84a b + 108a b - 44a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 3 +--R (- 64a b - 128a b + 448a b - 256a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 52a b - 64a b + 344a b - 288a b + 60a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 +--R (32a b + 192a b - 128a b - 448a b + 352a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 11 2 +--R 28a b + 156a b - 104a b - 344a b + 236a b + 28a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 11 4 9 6 7 6 +--R (12a b - 24a b + 12a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 5 +--R (48a b - 96a b + 48a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 4 +--R (12a b - 92a b + 148a b - 68a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 3 +--R (- 96a b - 32a b + 352a b - 224a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 60a b + 32a b + 184a b - 224a b + 68a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R (48a b + 128a b - 192a b - 192a b + 208a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R 36a b + 84a b - 136a b - 120a b + 132a b + 4a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 10 5 8 7 6 6 +--R (12a b - 24a b + 12a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 5 +--R (32a b - 64a b + 32a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (- 4a b - 32a b + 76a b - 40a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 64a b + 32a b + 128a b - 96a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 28a b + 40a b + 32a b - 72a b + 28a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (32a b + 32a b - 96a b - 32a b + 64a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R 20a b + 16a b - 56a b - 16a b + 36a b +--R * +--R sin(d x + c) +--R + +--R 4 9 6 7 8 5 6 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 5 +--R (8a b - 16a b + 8a b )cos(d x + c) +--R + +--R 4 9 8 5 10 3 4 +--R (- 4a b + 12a b - 8a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 16a b + 16a b + 16a b - 16a b )cos(d x + c) +--R + +--R 4 9 6 7 10 3 12 2 +--R (- 4a b + 8a b - 8a b + 4a b)cos(d x + c) +--R + +--R 4 9 8 5 12 4 9 8 5 12 +--R (8a b - 16a b + 8a b)cos(d x + c) + 4a b - 8a b + 4a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 9 6 7 8 5 7 +--R (8a b - 16a b + 8a b )sin(d x + c) +--R + +--R 3 10 5 8 7 6 2 +--R (- 8a b + 16a b - 8a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 3 10 5 8 7 6 +--R (16a b - 32a b + 16a b )cos(d x + c) + 24a b - 16a b - 40a b +--R + +--R 9 4 +--R 32a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 2 11 4 9 6 7 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 3 +--R (- 16a b + 32a b - 16a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 2 +--R (- 20a b + 20a b + 20a b - 20a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 2 11 4 9 +--R (16a b + 48a b - 144a b + 80a b )cos(d x + c) + 18a b + 64a b +--R + +--R 6 7 10 3 +--R - 132a b + 50a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 12 3 10 5 8 5 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 4 +--R (4a b - 10a b + 8a b - 2a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 3 +--R (- 8a b - 56a b + 136a b - 72a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 8a b - 52a b + 124a b - 60a b - 4a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 12 +--R (4a b + 64a b + 24a b - 256a b + 164a b )cos(d x + c) + 4a b +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R 62a b + 32a b - 228a b + 92a b + 38a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 2 11 4 9 6 7 6 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 5 +--R (16a b - 32a b + 16a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 4 +--R (10a b - 42a b + 54a b - 22a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 3 +--R (- 32a b - 64a b + 224a b - 128a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 26a b - 32a b + 172a b - 144a b + 30a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R (16a b + 96a b - 64a b - 224a b + 176a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R 14a b + 78a b - 52a b - 172a b + 118a b + 14a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 3 10 5 8 7 6 6 +--R (6a b - 12a b + 6a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 5 +--R (24a b - 48a b + 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (6a b - 46a b + 74a b - 34a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 48a b - 16a b + 176a b - 112a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 30a b + 16a b + 92a b - 112a b + 34a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 3 10 +--R (24a b + 64a b - 96a b - 96a b + 104a b )cos(d x + c) + 18a b +--R + +--R 5 8 7 6 9 4 11 2 13 +--R 42a b - 68a b - 60a b + 66a b + 2a +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 9 6 7 8 5 6 +--R (6a b - 12a b + 6a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 5 +--R (16a b - 32a b + 16a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (- 2a b - 16a b + 38a b - 20a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 32a b + 16a b + 64a b - 48a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 14a b + 20a b + 16a b - 36a b + 14a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 4 9 +--R (16a b + 16a b - 48a b - 16a b + 32a b)cos(d x + c) + 10a b +--R + +--R 6 7 8 5 10 3 12 +--R 8a b - 28a b - 8a b + 18a b +--R * +--R sin(d x + c) +--R + +--R 5 8 7 6 9 4 6 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 5 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 5 8 9 4 11 2 4 +--R (- 2a b + 6a b - 4a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (- 8a b + 8a b + 8a b - 8a b )cos(d x + c) +--R + +--R 5 8 7 6 11 2 13 2 +--R (- 2a b + 4a b - 4a b + 2a )cos(d x + c) +--R + +--R 5 8 9 4 13 5 8 9 4 13 +--R (4a b - 8a b + 4a )cos(d x + c) + 2a b - 4a b + 2a +--R Type: Expression(Integer) +--E 79 + +--S 80 of 520 +t0015:= 1/(a+b*sin(c+d*x))^4 +--R +--R +--R (44) +--R 1 +--R / +--R 4 4 3 3 2 2 2 +--R b sin(d x + c) + 4a b sin(d x + c) + 6a b sin(d x + c) +--R + +--R 3 4 +--R 4a b sin(d x + c) + a +--R Type: Expression(Integer) +--E 80 + +--S 81 of 520 +r0015:= a*(2*a^2+3*b^2)*atan((b+a*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/_ + (a^2-b^2)^(7/2)/d+1/3*b*cos(c+d*x)/(a^2-b^2)/d/(a+b*sin(c+d*x))^3+_ + 5/6*a*b*cos(c+d*x)/(a^2-b^2)^2/d/(a+b*sin(c+d*x))^2+_ + 1/6*b*(11*a^2+4*b^2)*cos(c+d*x)/(a^2-b^2)^3/d/(a+b*sin(c+d*x)) +--R +--R +--R (45) +--R 5 3 3 3 2 4 4 2 2 +--R (- 18a b - 12a b )sin(d x + c) + (- 54a b - 36a b )sin(d x + c) +--R + +--R 3 3 5 4 2 6 +--R (- 54a b - 36a b)sin(d x + c) - 18a b - 12a +--R * +--R d x + c +--R a tan(-------) + b +--R 2 +--R atan(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 2 +--R (- 4b - 11a b )cos(d x + c)sin(d x + c) +--R + +--R 4 3 2 +--R (- 3a b - 27a b )cos(d x + c)sin(d x + c) +--R + +--R 5 2 3 4 +--R (- 2b + 5a b - 18a b)cos(d x + c) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 9 2 7 4 5 6 3 3 +--R (6b - 18a b + 18a b - 6a b )d sin(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (18a b - 54a b + 54a b - 18a b )d sin(d x + c) +--R + +--R 2 7 4 5 6 3 8 +--R (18a b - 54a b + 54a b - 18a b)d sin(d x + c) +--R + +--R 3 6 5 4 7 2 9 +--R (6a b - 18a b + 18a b - 6a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 520 +a0015:= integrate(t0015,x) +--R +--R +--R (46) +--R [ +--R 4 5 6 3 2 4 5 6 3 8 +--R ((9a b + 6a b )cos(d x + c) - 9a b - 33a b - 18a b)sin(d x + c) +--R + +--R 5 4 7 2 2 5 4 7 2 9 +--R (27a b + 18a b )cos(d x + c) - 27a b - 27a b - 6a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (b - a )cos(d x + c) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(d x + c) + (b - a b)cos(d x + c) + b - a b +--R / +--R b sin(d x + c) + a +--R + +--R 8 2 6 4 4 2 +--R (- 2b + 5a b - 18a b )cos(d x + c) +--R + +--R 4 4 6 2 8 2 6 4 4 6 2 +--R (3a b + 27a b )cos(d x + c) + 2b + a b + 3a b + 54a b +--R * +--R sin(d x + c) +--R + +--R 3 5 5 3 3 +--R (- 4a b - 11a b )cos(d x + c) +--R + +--R 7 3 5 5 3 2 +--R (- 6a b + 15a b - 54a b )cos(d x + c) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 +--R (6a b + 6a b + 18a b)cos(d x + c) + 6a b - 13a b + 49a b + 18a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 3 9 5 7 7 5 9 3 2 +--R (6a b - 18a b + 18a b - 6a b )d cos(d x + c) +--R + +--R 3 9 7 5 9 3 11 +--R (- 6a b + 36a b - 48a b + 18a b)d +--R * +--R sin(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cos(d x + c) +--R + +--R 4 8 6 6 8 4 12 +--R (- 18a b + 48a b - 36a b + 6a )d +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 4 5 6 3 2 4 5 6 3 8 +--R ((18a b + 12a b )cos(d x + c) - 18a b - 66a b - 36a b) +--R * +--R sin(d x + c) +--R + +--R 5 4 7 2 2 5 4 7 2 9 +--R (54a b + 36a b )cos(d x + c) - 54a b - 54a b - 12a +--R * +--R +---------+ +--R | 2 2 +--R (a sin(d x + c) + b cos(d x + c) + b)\|- b + a +--R atan(-------------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R 8 2 6 4 4 2 +--R (- 2b + 5a b - 18a b )cos(d x + c) +--R + +--R 4 4 6 2 8 2 6 4 4 6 2 +--R (3a b + 27a b )cos(d x + c) + 2b + a b + 3a b + 54a b +--R * +--R sin(d x + c) +--R + +--R 3 5 5 3 3 +--R (- 4a b - 11a b )cos(d x + c) +--R + +--R 7 3 5 5 3 2 +--R (- 6a b + 15a b - 54a b )cos(d x + c) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 +--R (6a b + 6a b + 18a b)cos(d x + c) + 6a b - 13a b + 49a b + 18a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 9 5 7 7 5 9 3 2 +--R (6a b - 18a b + 18a b - 6a b )d cos(d x + c) +--R + +--R 3 9 7 5 9 3 11 +--R (- 6a b + 36a b - 48a b + 18a b)d +--R * +--R sin(d x + c) +--R + +--R 4 8 6 6 8 4 10 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cos(d x + c) +--R + +--R 4 8 6 6 8 4 12 +--R (- 18a b + 48a b - 36a b + 6a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 82 + +--S 83 of 520 +m0015a:= a0015.1-r0015 +--R +--R +--R (47) +--R 4 8 6 6 2 4 8 6 6 8 4 4 +--R ((9a b + 6a b )cos(d x + c) - 9a b - 33a b - 18a b )sin(d x + c) +--R + +--R 5 7 7 5 2 5 7 7 5 9 3 +--R ((54a b + 36a b )cos(d x + c) - 54a b - 126a b - 60a b ) +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 6 8 4 2 6 6 8 4 10 2 +--R ((108a b + 72a b )cos(d x + c) - 108a b - 180a b - 72a b ) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 5 9 3 2 7 5 9 3 11 +--R ((90a b + 60a b )cos(d x + c) - 90a b - 114a b - 36a b) +--R * +--R sin(d x + c) +--R + +--R 8 4 10 2 2 8 4 10 2 12 +--R (27a b + 18a b )cos(d x + c) - 27a b - 27a b - 6a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (b - a )cos(d x + c) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(d x + c) + (b - a b)cos(d x + c) + b - a b +--R / +--R b sin(d x + c) + a +--R + +--R 4 8 6 6 2 4 8 6 6 8 4 +--R ((18a b + 12a b )cos(d x + c) - 18a b - 66a b - 36a b ) +--R * +--R 4 +--R sin(d x + c) +--R + +--R 5 7 7 5 2 5 7 7 5 9 3 +--R ((108a b + 72a b )cos(d x + c) - 108a b - 252a b - 120a b ) +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 6 8 4 2 6 6 8 4 10 2 +--R ((216a b + 144a b )cos(d x + c) - 216a b - 360a b - 144a b ) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 5 9 3 2 7 5 9 3 11 +--R ((180a b + 120a b )cos(d x + c) - 180a b - 228a b - 72a b) +--R * +--R sin(d x + c) +--R + +--R 8 4 10 2 2 8 4 10 2 12 +--R (54a b + 36a b )cos(d x + c) - 54a b - 54a b - 12a +--R * +--R d x + c +--R +-------+ a tan(-------) + b +--R | 2 2 2 +--R \|b - a atan(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 11 2 9 4 7 2 +--R (- 2b + 5a b - 18a b )cos(d x + c) +--R + +--R 4 7 6 5 11 2 9 4 7 6 5 +--R (3a b + 27a b )cos(d x + c) + 2b + a b + 3a b + 54a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (- 12a b + 30a b - 108a b )cos(d x + c) +--R + +--R 3 8 5 6 7 4 10 3 8 5 6 +--R (2a b - 8a b + 66a b )cos(d x + c) + 12a b - 10a b + 58a b +--R + +--R 7 4 +--R 180a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 4 7 6 5 3 +--R (3a b + 27a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 2 +--R (- 24a b + 60a b - 216a b )cos(d x + c) +--R + +--R 4 7 6 5 8 3 2 9 4 7 6 5 +--R (3a b - 46a b + 43a b )cos(d x + c) + 24a b - 36a b + 156a b +--R + +--R 8 3 +--R 216a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 8 5 6 7 4 3 +--R (2a b - 8a b + 66a b )cos(d x + c) +--R + +--R 3 8 5 6 7 4 2 +--R (- 20a b + 50a b - 180a b )cos(d x + c) +--R + +--R 3 8 5 6 7 4 3 8 5 6 +--R (- 2a b + 8a b - 66a b )cos(d x + c) + 20a b - 38a b +--R + +--R 7 4 9 2 +--R 150a b + 108a b +--R * +--R sin(d x + c) +--R + +--R 4 7 6 5 8 3 3 +--R (6a b - 19a b + 43a b )cos(d x + c) +--R + +--R 4 7 6 5 8 3 2 +--R (- 6a b + 15a b - 54a b )cos(d x + c) +--R + +--R 4 7 6 5 8 3 4 7 6 5 8 3 +--R (- 6a b + 19a b - 43a b )cos(d x + c) + 6a b - 13a b + 49a b +--R + +--R 10 +--R 18a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 3 12 5 10 7 8 9 6 2 +--R (6a b - 18a b + 18a b - 6a b )d cos(d x + c) +--R + +--R 3 12 7 8 9 6 11 4 +--R (- 6a b + 36a b - 48a b + 18a b )d +--R * +--R 4 +--R sin(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 2 +--R (36a b - 108a b + 108a b - 36a b )d cos(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R (- 36a b + 48a b + 72a b - 144a b + 60a b )d +--R * +--R 3 +--R sin(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 2 +--R (72a b - 216a b + 216a b - 72a b )d cos(d x + c) +--R + +--R 5 10 7 8 11 4 13 2 +--R (- 72a b + 144a b - 144a b + 72a b )d +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 2 +--R (60a b - 180a b + 180a b - 60a b )d cos(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 14 +--R (- 60a b + 144a b - 72a b - 48a b + 36a b)d +--R * +--R sin(d x + c) +--R + +--R 7 8 9 6 11 4 13 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cos(d x + c) +--R + +--R 7 8 9 6 11 4 15 +--R (- 18a b + 48a b - 36a b + 6a )d +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 83 + +--S 84 of 520 +--d0015a:= D(m0015a,x) +--E 84 + +--S 85 of 520 +m0015b:= a0015.2-r0015 +--R +--R +--R (48) +--R 4 8 6 6 2 4 8 6 6 8 4 +--R ((18a b + 12a b )cos(d x + c) - 18a b - 66a b - 36a b ) +--R * +--R 4 +--R sin(d x + c) +--R + +--R 5 7 7 5 2 5 7 7 5 9 3 +--R ((108a b + 72a b )cos(d x + c) - 108a b - 252a b - 120a b ) +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 6 8 4 2 6 6 8 4 10 2 +--R ((216a b + 144a b )cos(d x + c) - 216a b - 360a b - 144a b ) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 5 9 3 2 7 5 9 3 11 +--R ((180a b + 120a b )cos(d x + c) - 180a b - 228a b - 72a b) +--R * +--R sin(d x + c) +--R + +--R 8 4 10 2 2 8 4 10 2 12 +--R (54a b + 36a b )cos(d x + c) - 54a b - 54a b - 12a +--R * +--R +---------+ +--R | 2 2 +--R (a sin(d x + c) + b cos(d x + c) + b)\|- b + a +--R atan(-------------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R 4 8 6 6 2 4 8 6 6 8 4 +--R ((18a b + 12a b )cos(d x + c) - 18a b - 66a b - 36a b ) +--R * +--R 4 +--R sin(d x + c) +--R + +--R 5 7 7 5 2 5 7 7 5 9 3 +--R ((108a b + 72a b )cos(d x + c) - 108a b - 252a b - 120a b ) +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 6 8 4 2 6 6 8 4 10 2 +--R ((216a b + 144a b )cos(d x + c) - 216a b - 360a b - 144a b ) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 5 9 3 2 7 5 9 3 11 +--R ((180a b + 120a b )cos(d x + c) - 180a b - 228a b - 72a b) +--R * +--R sin(d x + c) +--R + +--R 8 4 10 2 2 8 4 10 2 12 +--R (54a b + 36a b )cos(d x + c) - 54a b - 54a b - 12a +--R * +--R d x + c +--R a tan(-------) + b +--R 2 +--R atan(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 11 2 9 4 7 2 +--R (- 2b + 5a b - 18a b )cos(d x + c) +--R + +--R 4 7 6 5 11 2 9 4 7 6 5 +--R (3a b + 27a b )cos(d x + c) + 2b + a b + 3a b + 54a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 10 3 8 5 6 2 +--R (- 12a b + 30a b - 108a b )cos(d x + c) +--R + +--R 3 8 5 6 7 4 10 3 8 5 6 +--R (2a b - 8a b + 66a b )cos(d x + c) + 12a b - 10a b + 58a b +--R + +--R 7 4 +--R 180a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 4 7 6 5 3 +--R (3a b + 27a b )cos(d x + c) +--R + +--R 2 9 4 7 6 5 2 +--R (- 24a b + 60a b - 216a b )cos(d x + c) +--R + +--R 4 7 6 5 8 3 2 9 4 7 6 5 +--R (3a b - 46a b + 43a b )cos(d x + c) + 24a b - 36a b + 156a b +--R + +--R 8 3 +--R 216a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 8 5 6 7 4 3 +--R (2a b - 8a b + 66a b )cos(d x + c) +--R + +--R 3 8 5 6 7 4 2 +--R (- 20a b + 50a b - 180a b )cos(d x + c) +--R + +--R 3 8 5 6 7 4 3 8 5 6 +--R (- 2a b + 8a b - 66a b )cos(d x + c) + 20a b - 38a b +--R + +--R 7 4 9 2 +--R 150a b + 108a b +--R * +--R sin(d x + c) +--R + +--R 4 7 6 5 8 3 3 +--R (6a b - 19a b + 43a b )cos(d x + c) +--R + +--R 4 7 6 5 8 3 2 +--R (- 6a b + 15a b - 54a b )cos(d x + c) +--R + +--R 4 7 6 5 8 3 4 7 6 5 8 3 +--R (- 6a b + 19a b - 43a b )cos(d x + c) + 6a b - 13a b + 49a b +--R + +--R 10 +--R 18a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 12 5 10 7 8 9 6 2 +--R (6a b - 18a b + 18a b - 6a b )d cos(d x + c) +--R + +--R 3 12 7 8 9 6 11 4 +--R (- 6a b + 36a b - 48a b + 18a b )d +--R * +--R 4 +--R sin(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 2 +--R (36a b - 108a b + 108a b - 36a b )d cos(d x + c) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R (- 36a b + 48a b + 72a b - 144a b + 60a b )d +--R * +--R 3 +--R sin(d x + c) +--R + +--R 5 10 7 8 9 6 11 4 2 +--R (72a b - 216a b + 216a b - 72a b )d cos(d x + c) +--R + +--R 5 10 7 8 11 4 13 2 +--R (- 72a b + 144a b - 144a b + 72a b )d +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 2 +--R (60a b - 180a b + 180a b - 60a b )d cos(d x + c) +--R + +--R 6 9 8 7 10 5 12 3 14 +--R (- 60a b + 144a b - 72a b - 48a b + 36a b)d +--R * +--R sin(d x + c) +--R + +--R 7 8 9 6 11 4 13 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cos(d x + c) +--R + +--R 7 8 9 6 11 4 15 +--R (- 18a b + 48a b - 36a b + 6a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 85 + +--S 86 of 520 +d0015b:= D(m0015b,x) +--R +--R +--R (49) +--R 3 11 5 9 2 3 11 5 9 7 7 +--R ((3a b + 27a b )cos(d x + c) + 3a b + 36a b + 81a b ) +--R * +--R 9 +--R sin(d x + c) +--R + +--R 2 12 4 10 4 +--R (- 9a b - 6a b )cos(d x + c) +--R + +--R 2 12 4 10 3 +--R (6a b + 54a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 2 +--R (26a b + 124a b + 210a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 2 12 4 10 +--R (6a b + 72a b + 162a b )cos(d x + c) - a b + 22a b +--R + +--R 6 8 8 6 +--R 207a b + 252a b +--R * +--R 8 +--R sin(d x + c) +--R + +--R 13 3 11 5 +--R (18a b + 12a b )cos(d x + c) +--R + +--R 13 3 11 5 9 4 +--R (18a b - 78a b - 60a b )cos(d x + c) +--R + +--R 13 3 11 5 9 3 +--R (- 32a b - 118a b + 330a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 2 +--R (- 32a b + 82a b + 894a b + 976a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 13 +--R (22a b + 146a b + 630a b + 882a b )cos(d x + c) + 22a b +--R + +--R 3 11 5 9 7 7 9 5 +--R 64a b + 86a b + 380a b + 168a b +--R * +--R 7 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 +--R (- 9a b - 6a b )cos(d x + c) +--R + +--R 2 12 4 10 5 +--R (174a b + 66a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 4 +--R (199a b - 187a b - 102a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 3 +--R (- 316a b - 946a b + 1082a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 2 +--R (- 337a b - 328a b + 2545a b + 2200a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 +--R (206a b + 828a b + 2050a b + 1956a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R 211a b + 547a b + 437a b + 241a b - 236a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 3 11 5 9 6 +--R (- 99a b - 141a b )cos(d x + c) +--R + +--R 13 3 11 5 9 5 +--R (- 8a b + 740a b + 258a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 4 +--R (- 8a b + 1023a b + 442a b + 583a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 3 +--R (12a b - 1292a b - 2930a b + 2230a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (12a b - 1541a b - 2719a b + 3189a b + 2319a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (- 4a b + 764a b + 2088a b + 3288a b + 2264a b ) +--R * +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 4a b + 829a b + 1946a b + 1388a b + 94a b - 413a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2 12 4 10 7 +--R (- 12a b - 108a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 6 +--R (- 22a b - 419a b - 564a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 5 +--R (- 28a b + 1864a b + 1044a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 4 +--R (- 6a b + 2889a b + 2765a b + 2152a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 3 +--R (72a b - 2852a b - 5022a b + 2702a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (58a b - 3867a b - 7076a b + 839a b + 926a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (- 32a b + 1476a b + 2758a b + 2724a b + 1474a b ) +--R * +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R - 30a b + 1777a b + 3689a b + 2329a b + 389a b - 234a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 3 11 5 9 8 +--R (- 6a b - 54a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 +--R (- 12a b + 24a b - 612a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 6 +--R (- 12a b - 16a b - 874a b - 718a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 5 +--R (24a b - 104a b + 2858a b + 2592a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 4 +--R (24a b + 8a b + 4400a b + 5306a b + 2622a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (- 12a b + 168a b - 3592a b - 5386a b + 1682a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 12a b + 88a b - 5450a b - 9376a b - 2184a b +--R + +--R 11 3 +--R - 106a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R (- 88a b + 1638a b + 1866a b + 1070a b + 554a b ) +--R * +--R cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R - 74a b + 2270a b + 3860a b + 2314a b + 570a b - 60a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 8 8 +--R (- 6a b + 18a b - 252a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 7 +--R (- 84a b + 320a b - 1316a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 6 +--R (- 66a b + 206a b - 1117a b - 28a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (168a b - 464a b + 2750a b + 3306a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (150a b - 260a b + 3813a b + 4927a b + 1300a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (- 84a b + 240a b - 2372a b - 4022a b + 418a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R - 78a b + 102a b - 4019a b - 7392a b - 2095a b +--R + +--R 12 2 +--R - 198a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R (- 96a b + 1006a b + 504a b + 146a b + 120a b ) +--R * +--R cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 +--R - 66a b + 1643a b + 2281a b + 1359a b + 309a b - 6a +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 11 5 9 7 7 8 +--R (- 36a b + 142a b - 406a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 7 +--R (- 180a b + 616a b - 1276a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 6 +--R (- 72a b + 284a b - 743a b + 471a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 5 +--R (360a b - 976a b + 1888a b + 1938a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R (252a b - 720a b + 2367a b + 1754a b + 307a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R (- 180a b + 396a b - 876a b - 1934a b + 14a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R - 144a b + 312a b - 1809a b - 2979a b - 690a b +--R + +--R 13 +--R - 60a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 13 +--R (- 36a b + 264a b - 4a b + 4a b + 12a b)cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 13 +--R - 18a b + 591a b + 754a b + 401a b + 72a b +--R * +--R sin(d x + c) +--R + +--R 4 10 6 8 8 6 8 +--R (- 54a b + 166a b - 232a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 7 +--R (- 108a b + 332a b - 464a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 6 +--R (54a b - 132a b + 45a b + 138a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 5 +--R (216a b - 596a b + 716a b + 384a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 4 +--R (54a b - 166a b + 475a b + 216a b + 36a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 3 +--R (- 108a b + 264a b - 252a b - 384a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 +--R (- 54a b + 132a b - 369a b - 462a b - 81a b - 6a ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 8 6 10 4 12 2 14 +--R 81a b + 108a b + 45a b + 6a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 12 4 10 2 2 12 4 10 6 8 +--R ((6a b + 54a b )cos(d x + c) + 6a b + 72a b + 162a b ) +--R * +--R 9 +--R sin(d x + c) +--R + +--R 13 3 11 4 +--R (- 36a b - 24a b )cos(d x + c) +--R + +--R 13 3 11 3 +--R (12a b + 108a b )cos(d x + c) +--R + +--R 13 3 11 5 9 2 +--R (88a b + 380a b + 492a b )cos(d x + c) +--R + +--R 13 3 11 5 9 13 3 11 +--R (12a b + 144a b + 324a b )cos(d x + c) - 20a b - 76a b +--R + +--R 5 9 7 7 +--R 180a b + 396a b +--R * +--R 8 +--R sin(d x + c) +--R + +--R 2 12 4 10 4 +--R (- 360a b - 240a b )cos(d x + c) +--R + +--R 14 2 12 4 10 3 +--R (8b + 28a b + 804a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 2 +--R (8b + 788a b + 2964a b + 2480a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 14 +--R (8b + 52a b + 792a b + 1548a b )cos(d x + c) + 8b +--R + +--R 2 12 4 10 6 8 8 6 +--R - 292a b - 1208a b - 740a b - 168a b +--R * +--R 7 +--R sin(d x + c) +--R + +--R 13 3 11 6 +--R (- 36a b - 24a b )cos(d x + c) +--R + +--R 13 3 11 5 +--R (- 48a b - 132a b )cos(d x + c) +--R + +--R 13 3 11 5 9 4 +--R (56a b - 1196a b - 600a b )cos(d x + c) +--R + +--R 13 3 11 5 9 3 +--R (160a b + 436a b + 3364a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 2 +--R (64a b + 2824a b + 9116a b + 5756a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 13 +--R (16a b - 408a b + 1064a b + 2688a b )cos(d x + c) + 44a b +--R + +--R 3 11 5 9 7 7 9 5 +--R - 1552a b - 4592a b - 3520a b - 1420a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 +--R (- 378a b - 402a b )cos(d x + c) +--R + +--R 14 2 12 4 10 5 +--R (- 16b - 284a b - 660a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 4 +--R (- 16b + 822a b - 508a b + 782a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 3 +--R (24b + 944a b + 2468a b + 8444a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 2 +--R (24b - 94a b + 3682a b + 13398a b + 6150a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 +--R (- 8b - 236a b - 2976a b - 1764a b + 1624a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R - 8b + 74a b - 3716a b - 8216a b - 5596a b - 1738a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 13 3 11 7 +--R (- 24a b - 216a b )cos(d x + c) +--R + +--R 13 3 11 5 9 6 +--R (- 44a b - 1540a b - 1596a b )cos(d x + c) +--R + +--R 13 3 11 5 9 5 +--R (- 56a b - 412a b - 672a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 4 +--R (- 12a b + 3744a b + 4948a b + 4820a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 3 +--R (144a b + 2576a b + 5916a b + 12364a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (116a b - 1560a b - 1144a b + 8380a b + 2368a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (- 64a b - 1188a b - 7684a b - 7092a b - 772a b ) +--R * +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 60a b + 116a b - 4580a b - 8140a b - 4160a b - 936a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 2 12 4 10 8 +--R (- 12a b - 108a b )cos(d x + c) +--R + +--R 14 2 12 4 10 7 +--R (- 24b + 48a b - 1224a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 6 +--R (- 24b - 32a b - 3116a b - 2348a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 5 +--R (48b - 208a b + 136a b + 1464a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 4 +--R (48b + 16a b + 7324a b + 11896a b + 6756a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 +--R (- 24b + 336a b + 3976a b + 7108a b + 10324a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 +--R - 24b + 176a b - 3844a b - 8144a b - 1008a b +--R + +--R 10 4 +--R - 596a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (- 176a b - 2304a b - 10428a b - 8960a b - 1652a b ) +--R * +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R - 148a b + 328a b - 3260a b - 4384a b - 1416a b - 240a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 13 3 11 5 9 8 +--R (- 12a b + 36a b - 504a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 +--R (- 168a b + 640a b - 2632a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 6 +--R (- 132a b + 412a b - 3656a b - 1004a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 5 +--R (336a b - 928a b + 1144a b + 3708a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (300a b - 520a b + 7536a b + 11828a b + 3956a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (- 168a b + 480a b + 3968a b + 3740a b + 4820a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 156a b + 204a b - 3592a b - 9912a b - 3512a b +--R + +--R 11 3 +--R - 792a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R (- 192a b - 2344a b - 7872a b - 5456a b - 936a b ) +--R * +--R cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R - 132a b + 352a b - 1336a b - 1080a b - 180a b - 24a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 8 8 +--R (- 72a b + 284a b - 812a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 7 +--R (- 360a b + 1232a b - 2552a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 6 +--R (- 144a b + 568a b - 2242a b + 438a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (720a b - 1952a b + 1940a b + 2652a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (504a b - 1440a b + 5166a b + 4588a b + 1142a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (- 360a b + 792a b + 1920a b + 380a b + 1228a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R - 288a b + 624a b - 2214a b - 4806a b - 1416a b +--R + +--R 12 2 +--R - 240a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R (- 72a b - 1308a b - 3032a b - 1588a b - 240a b ) +--R * +--R cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 +--R - 36a b + 102a b - 220a b - 86a b +--R * +--R sin(d x + c) +--R + +--R 3 11 5 9 7 7 8 +--R (- 108a b + 332a b - 464a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 7 +--R (- 216a b + 664a b - 928a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 6 +--R (108a b - 264a b - 72a b + 168a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 5 +--R (432a b - 1192a b + 1108a b + 552a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 4 +--R (108a b - 332a b + 1112a b + 648a b + 144a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (- 216a b + 528a b + 144a b - 120a b + 144a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (- 108a b + 264a b - 576a b - 816a b - 180a b - 24a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 7 7 9 5 11 3 13 +--R (- 324a b - 432a b - 180a b - 24a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 3 11 5 9 2 3 11 5 9 7 7 9 +--R ((3a b + 27a b )cos(d x + c) + 3a b + 36a b + 81a b )sin(d x + c) +--R + +--R 2 12 4 10 4 2 12 4 10 3 +--R (- 9a b - 6a b )cos(d x + c) + (6a b + 54a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 2 +--R (26a b + 124a b + 210a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 2 12 4 10 6 8 +--R (6a b + 72a b + 162a b )cos(d x + c) - a b + 22a b + 207a b +--R + +--R 8 6 +--R 252a b +--R * +--R 8 +--R sin(d x + c) +--R + +--R 13 3 11 5 +--R (18a b + 12a b )cos(d x + c) +--R + +--R 13 3 11 5 9 4 +--R (18a b - 78a b - 60a b )cos(d x + c) +--R + +--R 13 3 11 5 9 3 +--R (- 32a b - 118a b + 330a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 2 +--R (- 32a b + 82a b + 894a b + 976a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 13 +--R (22a b + 146a b + 630a b + 882a b )cos(d x + c) + 22a b +--R + +--R 3 11 5 9 7 7 9 5 +--R 64a b + 86a b + 380a b + 168a b +--R * +--R 7 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 2 12 4 10 5 +--R (- 9a b - 6a b )cos(d x + c) + (174a b + 66a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 4 +--R (199a b - 187a b - 102a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 3 +--R (- 316a b - 946a b + 1082a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 2 +--R (- 337a b - 328a b + 2545a b + 2200a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 2 12 +--R (206a b + 828a b + 2050a b + 1956a b )cos(d x + c) + 211a b +--R + +--R 4 10 6 8 8 6 10 4 +--R 547a b + 437a b + 241a b - 236a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 3 11 5 9 6 +--R (- 99a b - 141a b )cos(d x + c) +--R + +--R 13 3 11 5 9 5 +--R (- 8a b + 740a b + 258a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 4 +--R (- 8a b + 1023a b + 442a b + 583a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 3 +--R (12a b - 1292a b - 2930a b + 2230a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 2 +--R (12a b - 1541a b - 2719a b + 3189a b + 2319a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (- 4a b + 764a b + 2088a b + 3288a b + 2264a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 4a b + 829a b + 1946a b + 1388a b + 94a b - 413a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2 12 4 10 7 +--R (- 12a b - 108a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 6 +--R (- 22a b - 419a b - 564a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 5 +--R (- 28a b + 1864a b + 1044a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 4 +--R (- 6a b + 2889a b + 2765a b + 2152a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 3 +--R (72a b - 2852a b - 5022a b + 2702a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 2 +--R (58a b - 3867a b - 7076a b + 839a b + 926a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (- 32a b + 1476a b + 2758a b + 2724a b + 1474a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R - 30a b + 1777a b + 3689a b + 2329a b + 389a b - 234a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 3 11 5 9 8 +--R (- 6a b - 54a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 +--R (- 12a b + 24a b - 612a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 6 +--R (- 12a b - 16a b - 874a b - 718a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 5 +--R (24a b - 104a b + 2858a b + 2592a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 4 +--R (24a b + 8a b + 4400a b + 5306a b + 2622a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (- 12a b + 168a b - 3592a b - 5386a b + 1682a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 12a b + 88a b - 5450a b - 9376a b - 2184a b - 106a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R (- 88a b + 1638a b + 1866a b + 1070a b + 554a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R - 74a b + 2270a b + 3860a b + 2314a b + 570a b - 60a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 12 4 10 6 8 8 +--R (- 6a b + 18a b - 252a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 7 +--R (- 84a b + 320a b - 1316a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 6 +--R (- 66a b + 206a b - 1117a b - 28a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (168a b - 464a b + 2750a b + 3306a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 4 +--R (150a b - 260a b + 3813a b + 4927a b + 1300a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 3 +--R (- 84a b + 240a b - 2372a b - 4022a b + 418a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 78a b + 102a b - 4019a b - 7392a b - 2095a b - 198a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R (- 96a b + 1006a b + 504a b + 146a b + 120a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 +--R - 66a b + 1643a b + 2281a b + 1359a b + 309a b - 6a +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 11 5 9 7 7 8 +--R (- 36a b + 142a b - 406a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 7 +--R (- 180a b + 616a b - 1276a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 6 +--R (- 72a b + 284a b - 743a b + 471a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 5 +--R (360a b - 976a b + 1888a b + 1938a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 4 +--R (252a b - 720a b + 2367a b + 1754a b + 307a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (- 180a b + 396a b - 876a b - 1934a b + 14a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (- 144a b + 312a b - 1809a b - 2979a b - 690a b - 60a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 13 5 9 +--R (- 36a b + 264a b - 4a b + 4a b + 12a b)cos(d x + c) - 18a b +--R + +--R 7 7 9 5 11 3 13 +--R 591a b + 754a b + 401a b + 72a b +--R * +--R sin(d x + c) +--R + +--R 4 10 6 8 8 6 8 +--R (- 54a b + 166a b - 232a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 7 +--R (- 108a b + 332a b - 464a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 6 +--R (54a b - 132a b + 45a b + 138a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 5 +--R (216a b - 596a b + 716a b + 384a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 4 +--R (54a b - 166a b + 475a b + 216a b + 36a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 3 +--R (- 108a b + 264a b - 252a b - 384a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 2 +--R (- 54a b + 132a b - 369a b - 462a b - 81a b - 6a )cos(d x + c) +--R + +--R 8 6 10 4 12 2 14 +--R 81a b + 108a b + 45a b + 6a +--R / +--R 2 16 4 14 6 12 8 10 4 +--R (6a b - 18a b + 18a b - 6a b )cos(d x + c) +--R + +--R 2 16 6 12 8 10 10 8 2 2 16 +--R (- 12a b + 72a b - 96a b + 36a b )cos(d x + c) + 6a b +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R 18a b - 36a b - 60a b + 126a b - 54a b +--R * +--R 8 +--R sin(d x + c) +--R + +--R 17 3 15 5 13 7 11 5 +--R (12a b - 36a b + 36a b - 12a b )cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 4 +--R (12a b + 24a b - 144a b + 168a b - 60a b )cos(d x + c) +--R + +--R 17 5 13 7 11 9 9 3 +--R (- 24a b + 144a b - 192a b + 72a b )cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 +--R - 24a b - 120a b + 240a b + 240a b - 600a b +--R + +--R 11 7 +--R 264a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 11 7 +--R (12a b + 36a b - 72a b - 120a b + 252a b - 108a b ) +--R * +--R cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 11 7 +--R 12a b + 96a b + 12a b - 480a b + 228a b + 384a b +--R + +--R 13 5 +--R - 252a b +--R * +--R 7 +--R sin(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 6 +--R (6a b - 18a b + 18a b - 6a b )cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 5 +--R (132a b - 396a b + 396a b - 132a b )cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R (114a b - 144a b - 252a b + 480a b - 198a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R (- 264a b + 192a b + 1008a b - 1536a b + 600a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R - 246a b - 258a b + 1572a b - 708a b - 1038a b +--R + +--R 12 6 +--R 678a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R 132a b + 204a b - 792a b - 168a b + 1236a b +--R + +--R 12 6 +--R - 612a b +--R * +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 12 6 +--R 126a b + 420a b - 726a b - 1128a b + 1650a b + 132a b +--R + +--R 14 4 +--R - 474a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 6 +--R (60a b - 180a b + 180a b - 60a b )cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 5 +--R (588a b - 1764a b + 1764a b - 588a b )cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R (408a b - 1032a b + 648a b + 168a b - 192a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R (- 1176a b + 1536a b + 2448a b - 4800a b + 1992a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R - 996a b + 612a b + 3384a b - 3864a b + 108a b +--R + +--R 13 5 +--R 756a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R 588a b + 228a b - 2760a b + 1032a b + 2364a b +--R + +--R 13 5 +--R - 1452a b +--R * +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 13 5 +--R 528a b + 600a b - 2760a b - 144a b + 3072a b - 840a b +--R + +--R 15 3 +--R - 456a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 6 +--R (234a b - 702a b + 702a b - 234a b )cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 5 +--R (1380a b - 4140a b + 4140a b - 1380a b )cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R (678a b - 2292a b + 2808a b - 1452a b + 258a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R (- 2760a b + 4800a b + 2160a b - 7680a b + 3480a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R - 2058a b + 3210a b + 2460a b - 6060a b + 2190a b +--R + +--R 14 4 +--R 258a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R 1380a b - 660a b - 4440a b + 3480a b + 2100a b +--R + +--R 14 4 +--R - 1860a b +--R * +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R 1146a b - 216a b - 4110a b + 2400a b + 2430a b +--R + +--R 14 4 16 2 +--R - 1416a b - 234a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 6 +--R (456a b - 1368a b + 1368a b - 456a b )cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 5 +--R (1860a b - 5580a b + 5580a b - 1860a b )cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R (492a b - 2232a b + 3744a b - 2760a b + 756a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R (- 3720a b + 7680a b - 720a b - 6720a b + 3480a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R - 2352a b + 5088a b - 960a b - 4128a b + 2544a b +--R + +--R 15 3 +--R - 192a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R 1860a b - 2100a b - 3480a b + 4440a b + 660a b +--R + +--R 15 3 +--R - 1380a b +--R * +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R 1404a b - 1488a b - 2772a b + 3264a b + 660a b +--R + +--R 15 3 17 +--R - 1008a b - 60a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 6 +--R (474a b - 1422a b + 1422a b - 474a b )cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 5 +--R (1452a b - 4356a b + 4356a b - 1452a b )cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R (30a b - 768a b + 2124a b - 2064a b + 678a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R (- 2904a b + 6720a b - 2736a b - 3072a b + 1992a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R - 1482a b + 3810a b - 2340a b - 1020a b + 1230a b +--R + +--R 16 2 +--R - 198a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R 1452a b - 2364a b - 1032a b + 2760a b - 228a b +--R + +--R 16 2 +--R - 588a b +--R * +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 16 2 +--R 978a b - 1620a b - 618a b + 1800a b - 162a b - 372a b +--R + +--R 18 +--R - 6a +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 6 +--R (252a b - 756a b + 756a b - 252a b )cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 5 +--R (612a b - 1836a b + 1836a b - 612a b )cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 +--R (- 144a b + 168a b + 360a b - 648a b + 264a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 +--R (- 1224a b + 3072a b - 1872a b - 576a b + 600a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 +--R - 468a b + 1332a b - 1128a b + 72a b + 252a b +--R + +--R 17 +--R - 60a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 +--R 612a b - 1236a b + 168a b + 792a b - 204a b +--R + +--R 17 +--R - 132a b +--R * +--R cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 17 +--R 360a b - 744a b + 144a b + 432a b - 120a b - 72a b +--R * +--R sin(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 6 +--R (54a b - 162a b + 162a b - 54a b )cos(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 5 +--R (108a b - 324a b + 324a b - 108a b )cos(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 16 2 4 +--R (- 54a b + 126a b - 54a b - 54a b + 36a b )cos(d x + c) +--R + +--R 8 10 10 8 12 6 16 2 3 +--R (- 216a b + 576a b - 432a b + 72a b )cos(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 16 2 18 +--R (- 54a b + 162a b - 156a b + 36a b + 18a b - 6a ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 16 2 18 +--R (108a b - 252a b + 120a b + 72a b - 36a b - 12a ) +--R * +--R cos(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 16 2 18 +--R 54a b - 126a b + 60a b + 36a b - 18a b - 6a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 17 3 15 5 13 7 11 4 +--R (12a b - 36a b + 36a b - 12a b )cos(d x + c) +--R + +--R 17 5 13 7 11 9 9 2 17 +--R (- 24a b + 144a b - 192a b + 72a b )cos(d x + c) + 12a b +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R 36a b - 72a b - 120a b + 252a b - 108a b +--R * +--R 8 +--R sin(d x + c) +--R + +--R 18 2 16 4 14 6 12 5 +--R (24b - 72a b + 72a b - 24a b )cos(d x + c) +--R + +--R 18 2 16 4 14 6 12 8 10 4 +--R (24b + 48a b - 288a b + 336a b - 120a b )cos(d x + c) +--R + +--R 18 4 14 6 12 8 10 3 +--R (- 48b + 288a b - 384a b + 144a b )cos(d x + c) +--R + +--R 18 2 16 4 14 6 12 8 10 +--R - 48b - 240a b + 480a b + 480a b - 1200a b +--R + +--R 10 8 +--R 528a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 18 2 16 4 14 6 12 8 10 10 8 +--R (24b + 72a b - 144a b - 240a b + 504a b - 216a b ) +--R * +--R cos(d x + c) +--R + +--R 18 2 16 4 14 6 12 8 10 10 8 +--R 24b + 192a b + 24a b - 960a b + 456a b + 768a b +--R + +--R 12 6 +--R - 504a b +--R * +--R 7 +--R sin(d x + c) +--R + +--R 17 3 15 5 13 7 11 6 +--R (12a b - 36a b + 36a b - 12a b )cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 5 +--R (264a b - 792a b + 792a b - 264a b )cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 +--R (228a b - 288a b - 504a b + 960a b - 396a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 +--R (- 528a b + 384a b + 2016a b - 3072a b + 1200a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 +--R - 492a b - 516a b + 3144a b - 1416a b - 2076a b +--R + +--R 11 7 +--R 1356a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 +--R 264a b + 408a b - 1584a b - 336a b + 2472a b +--R + +--R 11 7 +--R - 1224a b +--R * +--R cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 11 7 +--R 252a b + 840a b - 1452a b - 2256a b + 3300a b + 264a b +--R + +--R 13 5 +--R - 948a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 6 +--R (120a b - 360a b + 360a b - 120a b )cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 5 +--R (1176a b - 3528a b + 3528a b - 1176a b )cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R (816a b - 2064a b + 1296a b + 336a b - 384a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R (- 2352a b + 3072a b + 4896a b - 9600a b + 3984a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R - 1992a b + 1224a b + 6768a b - 7728a b + 216a b +--R + +--R 12 6 +--R 1512a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R 1176a b + 456a b - 5520a b + 2064a b + 4728a b +--R + +--R 12 6 +--R - 2904a b +--R * +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R 1056a b + 1200a b - 5520a b - 288a b + 6144a b +--R + +--R 12 6 14 4 +--R - 1680a b - 912a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 6 +--R (468a b - 1404a b + 1404a b - 468a b )cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 5 +--R (2760a b - 8280a b + 8280a b - 2760a b )cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R (1356a b - 4584a b + 5616a b - 2904a b + 516a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R (- 5520a b + 9600a b + 4320a b - 15360a b + 6960a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R - 4116a b + 6420a b + 4920a b - 12120a b + 4380a b +--R + +--R 13 5 +--R 516a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R 2760a b - 1320a b - 8880a b + 6960a b + 4200a b +--R + +--R 13 5 +--R - 3720a b +--R * +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R 2292a b - 432a b - 8220a b + 4800a b + 4860a b +--R + +--R 13 5 15 3 +--R - 2832a b - 468a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 6 +--R (912a b - 2736a b + 2736a b - 912a b )cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 5 +--R (3720a b - 11160a b + 11160a b - 3720a b )cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R (984a b - 4464a b + 7488a b - 5520a b + 1512a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R (- 7440a b + 15360a b - 1440a b - 13440a b + 6960a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R - 4704a b + 10176a b - 1920a b - 8256a b + 5088a b +--R + +--R 14 4 +--R - 384a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R 3720a b - 4200a b - 6960a b + 8880a b + 1320a b +--R + +--R 14 4 +--R - 2760a b +--R * +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R 2808a b - 2976a b - 5544a b + 6528a b + 1320a b +--R + +--R 14 4 16 2 +--R - 2016a b - 120a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 6 +--R (948a b - 2844a b + 2844a b - 948a b )cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 5 +--R (2904a b - 8712a b + 8712a b - 2904a b )cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R (60a b - 1536a b + 4248a b - 4128a b + 1356a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R (- 5808a b + 13440a b - 5472a b - 6144a b + 3984a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R - 2964a b + 7620a b - 4680a b - 2040a b + 2460a b +--R + +--R 15 3 +--R - 396a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R 2904a b - 4728a b - 2064a b + 5520a b - 456a b +--R + +--R 15 3 +--R - 1176a b +--R * +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R 1956a b - 3240a b - 1236a b + 3600a b - 324a b +--R + +--R 15 3 17 +--R - 744a b - 12a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 6 +--R (504a b - 1512a b + 1512a b - 504a b )cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 5 +--R (1224a b - 3672a b + 3672a b - 1224a b )cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R (- 288a b + 336a b + 720a b - 1296a b + 528a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R (- 2448a b + 6144a b - 3744a b - 1152a b + 1200a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R - 936a b + 2664a b - 2256a b + 144a b + 504a b +--R + +--R 16 2 +--R - 120a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R 1224a b - 2472a b + 336a b + 1584a b - 408a b +--R + +--R 16 2 +--R - 264a b +--R * +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 16 2 +--R 720a b - 1488a b + 288a b + 864a b - 240a b - 144a b +--R * +--R sin(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 6 +--R (108a b - 324a b + 324a b - 108a b )cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 5 +--R (216a b - 648a b + 648a b - 216a b )cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 4 +--R (- 108a b + 252a b - 108a b - 108a b + 72a b )cos(d x + c) +--R + +--R 7 11 9 9 11 7 15 3 3 +--R (- 432a b + 1152a b - 864a b + 144a b )cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 17 +--R (- 108a b + 324a b - 312a b + 72a b + 36a b - 12a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 17 +--R (216a b - 504a b + 240a b + 144a b - 72a b - 24a b) +--R * +--R cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 17 +--R 108a b - 252a b + 120a b + 72a b - 36a b - 12a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 16 4 14 6 12 8 10 4 +--R (6a b - 18a b + 18a b - 6a b )cos(d x + c) +--R + +--R 2 16 6 12 8 10 10 8 2 2 16 +--R (- 12a b + 72a b - 96a b + 36a b )cos(d x + c) + 6a b +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R 18a b - 36a b - 60a b + 126a b - 54a b +--R * +--R 8 +--R sin(d x + c) +--R + +--R 17 3 15 5 13 7 11 5 +--R (12a b - 36a b + 36a b - 12a b )cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 4 +--R (12a b + 24a b - 144a b + 168a b - 60a b )cos(d x + c) +--R + +--R 17 5 13 7 11 9 9 3 +--R (- 24a b + 144a b - 192a b + 72a b )cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 11 7 +--R (- 24a b - 120a b + 240a b + 240a b - 600a b + 264a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 11 7 +--R (12a b + 36a b - 72a b - 120a b + 252a b - 108a b ) +--R * +--R cos(d x + c) +--R + +--R 17 3 15 5 13 7 11 9 9 11 7 13 5 +--R 12a b + 96a b + 12a b - 480a b + 228a b + 384a b - 252a b +--R * +--R 7 +--R sin(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 6 +--R (6a b - 18a b + 18a b - 6a b )cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 5 +--R (132a b - 396a b + 396a b - 132a b )cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 4 +--R (114a b - 144a b - 252a b + 480a b - 198a b )cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R (- 264a b + 192a b + 1008a b - 1536a b + 600a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R - 246a b - 258a b + 1572a b - 708a b - 1038a b +--R + +--R 12 6 +--R 678a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 12 6 +--R (132a b + 204a b - 792a b - 168a b + 1236a b - 612a b ) +--R * +--R cos(d x + c) +--R + +--R 2 16 4 14 6 12 8 10 10 8 12 6 +--R 126a b + 420a b - 726a b - 1128a b + 1650a b + 132a b +--R + +--R 14 4 +--R - 474a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 6 +--R (60a b - 180a b + 180a b - 60a b )cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 5 +--R (588a b - 1764a b + 1764a b - 588a b )cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 4 +--R (408a b - 1032a b + 648a b + 168a b - 192a b )cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R (- 1176a b + 1536a b + 2448a b - 4800a b + 1992a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R - 996a b + 612a b + 3384a b - 3864a b + 108a b +--R + +--R 13 5 +--R 756a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R 588a b + 228a b - 2760a b + 1032a b + 2364a b +--R + +--R 13 5 +--R - 1452a b +--R * +--R cos(d x + c) +--R + +--R 3 15 5 13 7 11 9 9 11 7 13 5 +--R 528a b + 600a b - 2760a b - 144a b + 3072a b - 840a b +--R + +--R 15 3 +--R - 456a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 6 +--R (234a b - 702a b + 702a b - 234a b )cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 5 +--R (1380a b - 4140a b + 4140a b - 1380a b )cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R (678a b - 2292a b + 2808a b - 1452a b + 258a b ) +--R * +--R 4 +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R (- 2760a b + 4800a b + 2160a b - 7680a b + 3480a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R - 2058a b + 3210a b + 2460a b - 6060a b + 2190a b +--R + +--R 14 4 +--R 258a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R 1380a b - 660a b - 4440a b + 3480a b + 2100a b +--R + +--R 14 4 +--R - 1860a b +--R * +--R cos(d x + c) +--R + +--R 4 14 6 12 8 10 10 8 12 6 14 4 +--R 1146a b - 216a b - 4110a b + 2400a b + 2430a b - 1416a b +--R + +--R 16 2 +--R - 234a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 6 +--R (456a b - 1368a b + 1368a b - 456a b )cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 5 +--R (1860a b - 5580a b + 5580a b - 1860a b )cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 4 +--R (492a b - 2232a b + 3744a b - 2760a b + 756a b )cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R (- 3720a b + 7680a b - 720a b - 6720a b + 3480a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R - 2352a b + 5088a b - 960a b - 4128a b + 2544a b +--R + +--R 15 3 +--R - 192a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R 1860a b - 2100a b - 3480a b + 4440a b + 660a b +--R + +--R 15 3 +--R - 1380a b +--R * +--R cos(d x + c) +--R + +--R 5 13 7 11 9 9 11 7 13 5 15 3 +--R 1404a b - 1488a b - 2772a b + 3264a b + 660a b - 1008a b +--R + +--R 17 +--R - 60a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 6 +--R (474a b - 1422a b + 1422a b - 474a b )cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 5 +--R (1452a b - 4356a b + 4356a b - 1452a b )cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 4 +--R (30a b - 768a b + 2124a b - 2064a b + 678a b )cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R (- 2904a b + 6720a b - 2736a b - 3072a b + 1992a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R - 1482a b + 3810a b - 2340a b - 1020a b + 1230a b +--R + +--R 16 2 +--R - 198a b +--R * +--R 2 +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R 1452a b - 2364a b - 1032a b + 2760a b - 228a b +--R + +--R 16 2 +--R - 588a b +--R * +--R cos(d x + c) +--R + +--R 6 12 8 10 10 8 12 6 14 4 16 2 +--R 978a b - 1620a b - 618a b + 1800a b - 162a b - 372a b +--R + +--R 18 +--R - 6a +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 6 +--R (252a b - 756a b + 756a b - 252a b )cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 5 +--R (612a b - 1836a b + 1836a b - 612a b )cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 4 +--R (- 144a b + 168a b + 360a b - 648a b + 264a b )cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 +--R (- 1224a b + 3072a b - 1872a b - 576a b + 600a b ) +--R * +--R 3 +--R cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 17 +--R (- 468a b + 1332a b - 1128a b + 72a b + 252a b - 60a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 17 +--R (612a b - 1236a b + 168a b + 792a b - 204a b - 132a b) +--R * +--R cos(d x + c) +--R + +--R 7 11 9 9 11 7 13 5 15 3 17 +--R 360a b - 744a b + 144a b + 432a b - 120a b - 72a b +--R * +--R sin(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 6 +--R (54a b - 162a b + 162a b - 54a b )cos(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 5 +--R (108a b - 324a b + 324a b - 108a b )cos(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 16 2 4 +--R (- 54a b + 126a b - 54a b - 54a b + 36a b )cos(d x + c) +--R + +--R 8 10 10 8 12 6 16 2 3 +--R (- 216a b + 576a b - 432a b + 72a b )cos(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 16 2 18 2 +--R (- 54a b + 162a b - 156a b + 36a b + 18a b - 6a )cos(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 16 2 18 +--R (108a b - 252a b + 120a b + 72a b - 36a b - 12a )cos(d x + c) +--R + +--R 8 10 10 8 12 6 14 4 16 2 18 +--R 54a b - 126a b + 60a b + 36a b - 18a b - 6a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 520 +t0016:= 1/(1+sin(c+d*x))^2 +--R +--R +--R 1 +--R (50) --------------------------------- +--R 2 +--R sin(d x + c) + 2sin(d x + c) + 1 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 520 +r0016:= 1/3/cos(c+d*x)^3/d*(2*sin(c+d*x)-2+cos(c+d*x)^2*sin(c+d*x)) +--R +--R +--R 2 +--R (cos(d x + c) + 2)sin(d x + c) - 2 +--R (51) ----------------------------------- +--R 3 +--R 3d cos(d x + c) +--R Type: Expression(Integer) +--E 88 + +--S 89 of 520 +a0016:= integrate(t0016,x) +--R +--R +--R (52) +--R 2 +--R (- 3cos(d x + c) - 3)sin(d x + c) + cos(d x + c) - 4cos(d x + c) - 5 +--R ---------------------------------------------------------------------------- +--R 2 +--R (3d cos(d x + c) + 6d)sin(d x + c) - 3d cos(d x + c) + 3d cos(d x + c) + 6d +--R Type: Union(Expression(Integer),...) +--E 89 + +--S 90 of 520 +m0016:= a0016-r0016 +--R +--R +--R (53) +--R 3 2 2 +--R (- cos(d x + c) - 2cos(d x + c) - 2cos(d x + c) - 4)sin(d x + c) +--R + +--R 4 3 5 +--R (- 2cos(d x + c) - 4cos(d x + c) )sin(d x + c) + cos(d x + c) +--R + +--R 4 3 2 +--R - 4cos(d x + c) - 5cos(d x + c) - 2cos(d x + c) + 2cos(d x + c) + 4 +--R / +--R 4 3 5 +--R (3d cos(d x + c) + 6d cos(d x + c) )sin(d x + c) - 3d cos(d x + c) +--R + +--R 4 3 +--R 3d cos(d x + c) + 6d cos(d x + c) +--R Type: Expression(Integer) +--E 90 + +--S 91 of 520 +d0016:= D(m0016,x) +--R +--R +--R (54) +--R 4 3 2 +--R - cos(d x + c) - 4cos(d x + c) - 10cos(d x + c) - 24cos(d x + c) +--R + +--R - 24 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 5 4 3 2 +--R 2cos(d x + c) + 5cos(d x + c) + 4cos(d x + c) + 10cos(d x + c) +--R + +--R - 24cos(d x + c) - 24 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 4 3 2 +--R - 3cos(d x + c) - 12cos(d x + c) - 6cos(d x + c) + 24cos(d x + c) +--R + +--R 24 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 5 4 +--R 2cos(d x + c) + 5cos(d x + c) + 2cos(d x + c) + 5cos(d x + c) +--R + +--R 3 2 +--R - 28cos(d x + c) - 34cos(d x + c) + 24cos(d x + c) + 24 +--R * +--R sin(d x + c) +--R + +--R 8 7 6 5 +--R cos(d x + c) + 4cos(d x + c) + 5cos(d x + c) + 4cos(d x + c) +--R + +--R 4 3 2 +--R 2cos(d x + c) - 8cos(d x + c) - 8cos(d x + c) +--R / +--R 6 5 4 2 +--R (3cos(d x + c) + 12cos(d x + c) + 12cos(d x + c) )sin(d x + c) +--R + +--R 7 6 5 4 +--R (- 6cos(d x + c) - 6cos(d x + c) + 24cos(d x + c) + 24cos(d x + c) ) +--R * +--R sin(d x + c) +--R + +--R 8 7 6 5 +--R 3cos(d x + c) - 6cos(d x + c) - 9cos(d x + c) + 12cos(d x + c) +--R + +--R 4 +--R 12cos(d x + c) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 520 +t0017:= 1/(1+sin(c+d*x))^3 +--R +--R +--R 1 +--R (55) -------------------------------------------------- +--R 3 2 +--R sin(d x + c) + 3sin(d x + c) + 3sin(d x + c) + 1 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 520 +r0017:= 1/15/cos(c+d*x)^5*(12*sin(c+d*x)+cos(c+d*x)^2*sin(c+d*x)-_ + 12+5*cos(c+d*x)^2+2*cos(c+d*x)^4*sin(c+d*x))/d +--R +--R +--R (56) +--R 4 2 2 +--R (2cos(d x + c) + cos(d x + c) + 12)sin(d x + c) + 5cos(d x + c) - 12 +--R ----------------------------------------------------------------------- +--R 5 +--R 15d cos(d x + c) +--R Type: Expression(Integer) +--E 93 + +--S 94 of 520 +a0017:= integrate(t0017,x) +--R +--R +--R (57) +--R 2 3 +--R (- 5cos(d x + c) + 20cos(d x + c) + 25)sin(d x + c) - 9cos(d x + c) +--R + +--R 2 +--R - 17cos(d x + c) + 23cos(d x + c) + 31 +--R / +--R 2 +--R (15d cos(d x + c) - 30d cos(d x + c) - 60d)sin(d x + c) +--R + +--R 3 2 +--R 15d cos(d x + c) + 45d cos(d x + c) - 30d cos(d x + c) - 60d +--R Type: Union(Expression(Integer),...) +--E 94 + +--S 95 of 520 +m0017:= a0017-r0017 +--R +--R +--R (58) +--R 6 5 4 3 +--R - 2cos(d x + c) + 4cos(d x + c) + 7cos(d x + c) + 2cos(d x + c) +--R + +--R 2 +--R - 8cos(d x + c) + 24cos(d x + c) + 48 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 5 +--R (- 7cos(d x + c) + 14cos(d x + c) + 28cos(d x + c) )sin(d x + c) +--R + +--R 8 7 6 5 +--R - 9cos(d x + c) - 17cos(d x + c) + 23cos(d x + c) + 26cos(d x + c) +--R + +--R 4 3 2 +--R - 15cos(d x + c) + 22cos(d x + c) + 56cos(d x + c) - 24cos(d x + c) - 48 +--R / +--R 7 6 5 +--R (15d cos(d x + c) - 30d cos(d x + c) - 60d cos(d x + c) )sin(d x + c) +--R + +--R 8 7 6 +--R 15d cos(d x + c) + 45d cos(d x + c) - 30d cos(d x + c) +--R + +--R 5 +--R - 60d cos(d x + c) +--R Type: Expression(Integer) +--E 95 + +--S 96 of 520 +d0017:= D(m0017,x) +--R +--R +--R (59) +--R 8 7 6 5 +--R - 2cos(d x + c) + 8cos(d x + c) + 5cos(d x + c) - 20cos(d x + c) +--R + +--R 4 3 2 +--R - 80cos(d x + c) + 192cos(d x + c) + 192cos(d x + c) +--R + +--R - 960cos(d x + c) - 960 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 9 8 7 6 +--R - 4cos(d x + c) + 6cos(d x + c) + 52cos(d x + c) + 57cos(d x + c) +--R + +--R 5 4 3 +--R - 52cos(d x + c) + 8cos(d x + c) + 864cos(d x + c) +--R + +--R 2 +--R 864cos(d x + c) - 960cos(d x + c) - 960 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 5 4 +--R - 45cos(d x + c) + 180cos(d x + c) + 240cos(d x + c) +--R + +--R 3 2 +--R - 960cos(d x + c) - 960cos(d x + c) + 960cos(d x + c) + 960 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 11 10 9 +--R - 4cos(d x + c) + 6cos(d x + c) + 56cos(d x + c) +--R + +--R 8 7 6 +--R 51cos(d x + c) - 104cos(d x + c) - 49cos(d x + c) +--R + +--R 5 4 3 +--R 916cos(d x + c) + 856cos(d x + c) - 1824cos(d x + c) +--R + +--R 2 +--R - 1824cos(d x + c) + 960cos(d x + c) + 960 +--R * +--R sin(d x + c) +--R + +--R 12 11 10 9 +--R 2cos(d x + c) - 8cos(d x + c) - 9cos(d x + c) + 36cos(d x + c) +--R + +--R 8 7 6 5 +--R 47cos(d x + c) - 60cos(d x + c) - 72cos(d x + c) + 224cos(d x + c) +--R + +--R 4 3 2 +--R 224cos(d x + c) - 192cos(d x + c) - 192cos(d x + c) +--R / +--R 10 9 8 +--R 15cos(d x + c) - 60cos(d x + c) - 60cos(d x + c) +--R + +--R 7 6 +--R 240cos(d x + c) + 240cos(d x + c) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 11 10 9 +--R 30cos(d x + c) + 30cos(d x + c) - 360cos(d x + c) +--R + +--R 8 7 6 +--R - 360cos(d x + c) + 480cos(d x + c) + 480cos(d x + c) +--R * +--R sin(d x + c) +--R + +--R 12 11 10 9 +--R 15cos(d x + c) + 90cos(d x + c) + 75cos(d x + c) - 300cos(d x + c) +--R + +--R 8 7 6 +--R - 300cos(d x + c) + 240cos(d x + c) + 240cos(d x + c) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 520 +t0018:= 1/(1+sin(c+d*x))^4 +--R +--R +--R 1 +--R (60) ------------------------------------------------------------------- +--R 4 3 2 +--R sin(d x + c) + 4sin(d x + c) + 6sin(d x + c) + 4sin(d x + c) + 1 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 520 +r0018:= 1/35/cos(c+d*x)^7*(40*sin(c+d*x)-8*cos(c+d*x)^2*sin(c+d*x)-_ + 40+28*cos(c+d*x)^2+cos(c+d*x)^4*sin(c+d*x)+_ + 2*cos(c+d*x)^6*sin(c+d*x))/d +--R +--R +--R (61) +--R 6 4 2 +--R (2cos(d x + c) + cos(d x + c) - 8cos(d x + c) + 40)sin(d x + c) +--R + +--R 2 +--R 28cos(d x + c) - 40 +--R / +--R 7 +--R 35d cos(d x + c) +--R Type: Expression(Integer) +--E 98 + +--S 99 of 520 +a0018:= integrate(t0018,x) +--R +--R +--R (62) +--R 3 2 +--R (- 14cos(d x + c) - 42cos(d x + c) + 63cos(d x + c) + 91)sin(d x + c) +--R + +--R 4 3 2 +--R 10cos(d x + c) - 44cos(d x + c) - 87cos(d x + c) + 68cos(d x + c) + 101 +--R / +--R 3 2 +--R (35d cos(d x + c) + 140d cos(d x + c) - 140d cos(d x + c) - 280d) +--R * +--R sin(d x + c) +--R + +--R 4 3 2 +--R - 35d cos(d x + c) + 105d cos(d x + c) + 280d cos(d x + c) +--R + +--R - 140d cos(d x + c) - 280d +--R Type: Union(Expression(Integer),...) +--E 99 + +--S 100 of 520 +m0018:= a0018-r0018 +--R +--R +--R (63) +--R 9 8 7 6 +--R - 2cos(d x + c) - 8cos(d x + c) + 7cos(d x + c) + 12cos(d x + c) +--R + +--R 5 4 3 +--R 12cos(d x + c) + 40cos(d x + c) - 72cos(d x + c) +--R + +--R 2 +--R - 224cos(d x + c) + 160cos(d x + c) + 320 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 10 9 8 +--R - 12cos(d x + c) - 48cos(d x + c) + 48cos(d x + c) +--R + +--R 7 +--R 96cos(d x + c) +--R * +--R sin(d x + c) +--R + +--R 11 10 9 8 +--R 10cos(d x + c) - 44cos(d x + c) - 87cos(d x + c) + 68cos(d x + c) +--R + +--R 7 6 5 4 +--R 101cos(d x + c) + 28cos(d x + c) - 84cos(d x + c) - 264cos(d x + c) +--R + +--R 3 2 +--R 232cos(d x + c) + 544cos(d x + c) - 160cos(d x + c) - 320 +--R / +--R 10 9 8 +--R 35d cos(d x + c) + 140d cos(d x + c) - 140d cos(d x + c) +--R + +--R 7 +--R - 280d cos(d x + c) +--R * +--R sin(d x + c) +--R + +--R 11 10 9 +--R - 35d cos(d x + c) + 105d cos(d x + c) + 280d cos(d x + c) +--R + +--R 8 7 +--R - 140d cos(d x + c) - 280d cos(d x + c) +--R Type: Expression(Integer) +--E 100 + +--S 101 of 520 +d0018:= D(m0018,x) +--R +--R +--R (64) +--R 12 11 10 +--R - 2cos(d x + c) - 16cos(d x + c) - 19cos(d x + c) +--R + +--R 9 8 7 +--R 72cos(d x + c) + 112cos(d x + c) + 336cos(d x + c) +--R + +--R 6 5 4 +--R 56cos(d x + c) - 4352cos(d x + c) - 4352cos(d x + c) +--R + +--R 3 2 +--R 16000cos(d x + c) + 16000cos(d x + c) - 17920cos(d x + c) - 17920 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 13 12 11 +--R 4cos(d x + c) + 18cos(d x + c) - 76cos(d x + c) +--R + +--R 10 9 8 +--R - 69cos(d x + c) + 152cos(d x + c) + 96cos(d x + c) +--R + +--R 7 6 5 +--R 1584cos(d x + c) + 1864cos(d x + c) - 11264cos(d x + c) +--R + +--R 4 3 2 +--R - 11264cos(d x + c) + 27520cos(d x + c) + 27520cos(d x + c) +--R + +--R - 17920cos(d x + c) - 17920 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 10 9 7 +--R 35cos(d x + c) + 280cos(d x + c) - 3920cos(d x + c) +--R + +--R 6 5 4 +--R - 3640cos(d x + c) + 17920cos(d x + c) + 17920cos(d x + c) +--R + +--R 3 2 +--R - 31360cos(d x + c) - 31360cos(d x + c) + 17920cos(d x + c) + 17920 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 15 14 13 +--R 4cos(d x + c) + 18cos(d x + c) - 80cos(d x + c) +--R + +--R 12 11 10 +--R - 87cos(d x + c) + 228cos(d x + c) + 165cos(d x + c) +--R + +--R 9 8 7 +--R 1432cos(d x + c) + 1768cos(d x + c) - 12848cos(d x + c) +--R + +--R 6 5 4 +--R - 13128cos(d x + c) + 38784cos(d x + c) + 38784cos(d x + c) +--R + +--R 3 2 +--R - 45440cos(d x + c) - 45440cos(d x + c) + 17920cos(d x + c) + 17920 +--R * +--R sin(d x + c) +--R + +--R 16 15 14 13 +--R 2cos(d x + c) + 16cos(d x + c) + 15cos(d x + c) - 104cos(d x + c) +--R + +--R 12 11 10 +--R - 113cos(d x + c) + 104cos(d x + c) + 152cos(d x + c) +--R + +--R 9 8 7 +--R 752cos(d x + c) + 712cos(d x + c) - 3200cos(d x + c) +--R + +--R 6 5 4 +--R - 3200cos(d x + c) + 4992cos(d x + c) + 4992cos(d x + c) +--R + +--R 3 2 +--R - 2560cos(d x + c) - 2560cos(d x + c) +--R / +--R 14 13 12 +--R 35cos(d x + c) + 280cos(d x + c) + 280cos(d x + c) +--R + +--R 11 10 9 +--R - 1680cos(d x + c) - 1680cos(d x + c) + 2240cos(d x + c) +--R + +--R 8 +--R 2240cos(d x + c) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 15 14 13 +--R - 70cos(d x + c) - 70cos(d x + c) + 1680cos(d x + c) +--R + +--R 12 11 10 +--R 1680cos(d x + c) - 5600cos(d x + c) - 5600cos(d x + c) +--R + +--R 9 8 +--R 4480cos(d x + c) + 4480cos(d x + c) +--R * +--R sin(d x + c) +--R + +--R 16 15 14 +--R 35cos(d x + c) - 210cos(d x + c) - 245cos(d x + c) +--R + +--R 13 12 11 +--R 1960cos(d x + c) + 1960cos(d x + c) - 3920cos(d x + c) +--R + +--R 10 9 8 +--R - 3920cos(d x + c) + 2240cos(d x + c) + 2240cos(d x + c) +--R Type: Expression(Integer) +--E 101 + +--S 102 of 520 +t0019:= 1/(1-sin(c+d*x))^2 +--R +--R +--R 1 +--R (65) --------------------------------- +--R 2 +--R sin(d x + c) - 2sin(d x + c) + 1 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 520 +r0019:= 1/3/d/cos(c+d*x)^3*(2*sin(c+d*x)+2+cos(c+d*x)^2*sin(c+d*x)) +--R +--R +--R 2 +--R (cos(d x + c) + 2)sin(d x + c) + 2 +--R (66) ----------------------------------- +--R 3 +--R 3d cos(d x + c) +--R Type: Expression(Integer) +--E 103 + +--S 104 of 520 +a0019:= integrate(t0019,x) +--R +--R +--R (67) +--R 2 +--R (3cos(d x + c) + 3)sin(d x + c) + cos(d x + c) - 4cos(d x + c) - 5 +--R ---------------------------------------------------------------------------- +--R 2 +--R (3d cos(d x + c) + 6d)sin(d x + c) + 3d cos(d x + c) - 3d cos(d x + c) - 6d +--R Type: Union(Expression(Integer),...) +--E 104 + +--S 105 of 520 +m0019:= a0019-r0019 +--R +--R +--R (68) +--R 3 2 2 +--R (- cos(d x + c) - 2cos(d x + c) - 2cos(d x + c) - 4)sin(d x + c) +--R + +--R 4 3 5 +--R (2cos(d x + c) + 4cos(d x + c) )sin(d x + c) + cos(d x + c) +--R + +--R 4 3 2 +--R - 4cos(d x + c) - 5cos(d x + c) - 2cos(d x + c) + 2cos(d x + c) + 4 +--R / +--R 4 3 5 +--R (3d cos(d x + c) + 6d cos(d x + c) )sin(d x + c) + 3d cos(d x + c) +--R + +--R 4 3 +--R - 3d cos(d x + c) - 6d cos(d x + c) +--R Type: Expression(Integer) +--E 105 + +--S 106 of 520 +d0019:= D(m0019,x) +--R +--R +--R (69) +--R 4 3 2 +--R - cos(d x + c) - 4cos(d x + c) - 10cos(d x + c) - 24cos(d x + c) +--R + +--R - 24 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 5 4 3 2 +--R - 2cos(d x + c) - 5cos(d x + c) - 4cos(d x + c) - 10cos(d x + c) +--R + +--R 24cos(d x + c) + 24 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 4 3 2 +--R - 3cos(d x + c) - 12cos(d x + c) - 6cos(d x + c) + 24cos(d x + c) +--R + +--R 24 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 5 4 +--R - 2cos(d x + c) - 5cos(d x + c) - 2cos(d x + c) - 5cos(d x + c) +--R + +--R 3 2 +--R 28cos(d x + c) + 34cos(d x + c) - 24cos(d x + c) - 24 +--R * +--R sin(d x + c) +--R + +--R 8 7 6 5 +--R cos(d x + c) + 4cos(d x + c) + 5cos(d x + c) + 4cos(d x + c) +--R + +--R 4 3 2 +--R 2cos(d x + c) - 8cos(d x + c) - 8cos(d x + c) +--R / +--R 6 5 4 2 +--R (3cos(d x + c) + 12cos(d x + c) + 12cos(d x + c) )sin(d x + c) +--R + +--R 7 6 5 4 +--R (6cos(d x + c) + 6cos(d x + c) - 24cos(d x + c) - 24cos(d x + c) ) +--R * +--R sin(d x + c) +--R + +--R 8 7 6 5 +--R 3cos(d x + c) - 6cos(d x + c) - 9cos(d x + c) + 12cos(d x + c) +--R + +--R 4 +--R 12cos(d x + c) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 520 +t0020:= 1/(1-sin(c+d*x))^3 +--R +--R +--R 1 +--R (70) - -------------------------------------------------- +--R 3 2 +--R sin(d x + c) - 3sin(d x + c) + 3sin(d x + c) - 1 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 520 +r0020:= 1/15/cos(c+d*x)^5*(12*sin(c+d*x)+cos(c+d*x)^2*sin(c+d*x)+12-_ + 5*cos(c+d*x)^2+2*cos(c+d*x)^4*sin(c+d*x))/d +--R +--R +--R (71) +--R 4 2 2 +--R (2cos(d x + c) + cos(d x + c) + 12)sin(d x + c) - 5cos(d x + c) + 12 +--R ----------------------------------------------------------------------- +--R 5 +--R 15d cos(d x + c) +--R Type: Expression(Integer) +--E 108 + +--S 109 of 520 +a0020:= integrate(t0020,x) +--R +--R +--R (72) +--R 2 3 +--R (5cos(d x + c) - 20cos(d x + c) - 25)sin(d x + c) - 9cos(d x + c) +--R + +--R 2 +--R - 17cos(d x + c) + 23cos(d x + c) + 31 +--R / +--R 2 +--R (15d cos(d x + c) - 30d cos(d x + c) - 60d)sin(d x + c) +--R + +--R 3 2 +--R - 15d cos(d x + c) - 45d cos(d x + c) + 30d cos(d x + c) + 60d +--R Type: Union(Expression(Integer),...) +--E 109 + +--S 110 of 520 +m0020:= a0020-r0020 +--R +--R +--R (73) +--R 6 5 4 3 +--R - 2cos(d x + c) + 4cos(d x + c) + 7cos(d x + c) + 2cos(d x + c) +--R + +--R 2 +--R - 8cos(d x + c) + 24cos(d x + c) + 48 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 5 +--R (7cos(d x + c) - 14cos(d x + c) - 28cos(d x + c) )sin(d x + c) +--R + +--R 8 7 6 5 +--R - 9cos(d x + c) - 17cos(d x + c) + 23cos(d x + c) + 26cos(d x + c) +--R + +--R 4 3 2 +--R - 15cos(d x + c) + 22cos(d x + c) + 56cos(d x + c) - 24cos(d x + c) - 48 +--R / +--R 7 6 5 +--R (15d cos(d x + c) - 30d cos(d x + c) - 60d cos(d x + c) )sin(d x + c) +--R + +--R 8 7 6 +--R - 15d cos(d x + c) - 45d cos(d x + c) + 30d cos(d x + c) +--R + +--R 5 +--R 60d cos(d x + c) +--R Type: Expression(Integer) +--E 110 + +--S 111 of 520 +d0020:= D(m0020,x) +--R +--R +--R (74) +--R 8 7 6 5 +--R - 2cos(d x + c) + 8cos(d x + c) + 5cos(d x + c) - 20cos(d x + c) +--R + +--R 4 3 2 +--R - 80cos(d x + c) + 192cos(d x + c) + 192cos(d x + c) +--R + +--R - 960cos(d x + c) - 960 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 9 8 7 6 +--R 4cos(d x + c) - 6cos(d x + c) - 52cos(d x + c) - 57cos(d x + c) +--R + +--R 5 4 3 +--R 52cos(d x + c) - 8cos(d x + c) - 864cos(d x + c) +--R + +--R 2 +--R - 864cos(d x + c) + 960cos(d x + c) + 960 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 5 4 +--R - 45cos(d x + c) + 180cos(d x + c) + 240cos(d x + c) +--R + +--R 3 2 +--R - 960cos(d x + c) - 960cos(d x + c) + 960cos(d x + c) + 960 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 11 10 9 8 +--R 4cos(d x + c) - 6cos(d x + c) - 56cos(d x + c) - 51cos(d x + c) +--R + +--R 7 6 5 +--R 104cos(d x + c) + 49cos(d x + c) - 916cos(d x + c) +--R + +--R 4 3 2 +--R - 856cos(d x + c) + 1824cos(d x + c) + 1824cos(d x + c) +--R + +--R - 960cos(d x + c) - 960 +--R * +--R sin(d x + c) +--R + +--R 12 11 10 9 +--R 2cos(d x + c) - 8cos(d x + c) - 9cos(d x + c) + 36cos(d x + c) +--R + +--R 8 7 6 5 +--R 47cos(d x + c) - 60cos(d x + c) - 72cos(d x + c) + 224cos(d x + c) +--R + +--R 4 3 2 +--R 224cos(d x + c) - 192cos(d x + c) - 192cos(d x + c) +--R / +--R 10 9 8 +--R 15cos(d x + c) - 60cos(d x + c) - 60cos(d x + c) +--R + +--R 7 6 +--R 240cos(d x + c) + 240cos(d x + c) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 11 10 9 +--R - 30cos(d x + c) - 30cos(d x + c) + 360cos(d x + c) +--R + +--R 8 7 6 +--R 360cos(d x + c) - 480cos(d x + c) - 480cos(d x + c) +--R * +--R sin(d x + c) +--R + +--R 12 11 10 9 +--R 15cos(d x + c) + 90cos(d x + c) + 75cos(d x + c) - 300cos(d x + c) +--R + +--R 8 7 6 +--R - 300cos(d x + c) + 240cos(d x + c) + 240cos(d x + c) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 520 +t0021:= 1/(1-sin(c+d*x))^4 +--R +--R +--R 1 +--R (75) ------------------------------------------------------------------- +--R 4 3 2 +--R sin(d x + c) - 4sin(d x + c) + 6sin(d x + c) - 4sin(d x + c) + 1 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 520 +r0021:= 1/35/cos(c+d*x)^7*(40*sin(c+d*x)-8*cos(c+d*x)^2*sin(c+d*x)+40-_ + 28*cos(c+d*x)^2+cos(c+d*x)^4*sin(c+d*x)+2*cos(c+d*x)^6*sin(c+d*x))/d +--R +--R +--R (76) +--R 6 4 2 +--R (2cos(d x + c) + cos(d x + c) - 8cos(d x + c) + 40)sin(d x + c) +--R + +--R 2 +--R - 28cos(d x + c) + 40 +--R / +--R 7 +--R 35d cos(d x + c) +--R Type: Expression(Integer) +--E 113 + +--S 114 of 520 +a0021:= integrate(t0021,x) +--R +--R +--R (77) +--R 3 2 +--R (14cos(d x + c) + 42cos(d x + c) - 63cos(d x + c) - 91)sin(d x + c) +--R + +--R 4 3 2 +--R 10cos(d x + c) - 44cos(d x + c) - 87cos(d x + c) + 68cos(d x + c) + 101 +--R / +--R 3 2 +--R (35d cos(d x + c) + 140d cos(d x + c) - 140d cos(d x + c) - 280d) +--R * +--R sin(d x + c) +--R + +--R 4 3 2 +--R 35d cos(d x + c) - 105d cos(d x + c) - 280d cos(d x + c) +--R + +--R 140d cos(d x + c) + 280d +--R Type: Union(Expression(Integer),...) +--E 114 + +--S 115 of 520 +m0021:= a0021-r0021 +--R +--R +--R (78) +--R 9 8 7 6 +--R - 2cos(d x + c) - 8cos(d x + c) + 7cos(d x + c) + 12cos(d x + c) +--R + +--R 5 4 3 +--R 12cos(d x + c) + 40cos(d x + c) - 72cos(d x + c) +--R + +--R 2 +--R - 224cos(d x + c) + 160cos(d x + c) + 320 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 10 9 8 +--R 12cos(d x + c) + 48cos(d x + c) - 48cos(d x + c) +--R + +--R 7 +--R - 96cos(d x + c) +--R * +--R sin(d x + c) +--R + +--R 11 10 9 8 +--R 10cos(d x + c) - 44cos(d x + c) - 87cos(d x + c) + 68cos(d x + c) +--R + +--R 7 6 5 4 +--R 101cos(d x + c) + 28cos(d x + c) - 84cos(d x + c) - 264cos(d x + c) +--R + +--R 3 2 +--R 232cos(d x + c) + 544cos(d x + c) - 160cos(d x + c) - 320 +--R / +--R 10 9 8 +--R 35d cos(d x + c) + 140d cos(d x + c) - 140d cos(d x + c) +--R + +--R 7 +--R - 280d cos(d x + c) +--R * +--R sin(d x + c) +--R + +--R 11 10 9 +--R 35d cos(d x + c) - 105d cos(d x + c) - 280d cos(d x + c) +--R + +--R 8 7 +--R 140d cos(d x + c) + 280d cos(d x + c) +--R Type: Expression(Integer) +--E 115 + +--S 116 of 520 +d0021:= D(m0021,x) +--R +--R +--R (79) +--R 12 11 10 +--R - 2cos(d x + c) - 16cos(d x + c) - 19cos(d x + c) +--R + +--R 9 8 7 +--R 72cos(d x + c) + 112cos(d x + c) + 336cos(d x + c) +--R + +--R 6 5 4 +--R 56cos(d x + c) - 4352cos(d x + c) - 4352cos(d x + c) +--R + +--R 3 2 +--R 16000cos(d x + c) + 16000cos(d x + c) - 17920cos(d x + c) - 17920 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 13 12 11 +--R - 4cos(d x + c) - 18cos(d x + c) + 76cos(d x + c) +--R + +--R 10 9 8 +--R 69cos(d x + c) - 152cos(d x + c) - 96cos(d x + c) +--R + +--R 7 6 5 +--R - 1584cos(d x + c) - 1864cos(d x + c) + 11264cos(d x + c) +--R + +--R 4 3 2 +--R 11264cos(d x + c) - 27520cos(d x + c) - 27520cos(d x + c) +--R + +--R 17920cos(d x + c) + 17920 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 10 9 7 +--R 35cos(d x + c) + 280cos(d x + c) - 3920cos(d x + c) +--R + +--R 6 5 4 +--R - 3640cos(d x + c) + 17920cos(d x + c) + 17920cos(d x + c) +--R + +--R 3 2 +--R - 31360cos(d x + c) - 31360cos(d x + c) + 17920cos(d x + c) + 17920 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 15 14 13 +--R - 4cos(d x + c) - 18cos(d x + c) + 80cos(d x + c) +--R + +--R 12 11 10 +--R 87cos(d x + c) - 228cos(d x + c) - 165cos(d x + c) +--R + +--R 9 8 7 +--R - 1432cos(d x + c) - 1768cos(d x + c) + 12848cos(d x + c) +--R + +--R 6 5 4 +--R 13128cos(d x + c) - 38784cos(d x + c) - 38784cos(d x + c) +--R + +--R 3 2 +--R 45440cos(d x + c) + 45440cos(d x + c) - 17920cos(d x + c) - 17920 +--R * +--R sin(d x + c) +--R + +--R 16 15 14 13 +--R 2cos(d x + c) + 16cos(d x + c) + 15cos(d x + c) - 104cos(d x + c) +--R + +--R 12 11 10 +--R - 113cos(d x + c) + 104cos(d x + c) + 152cos(d x + c) +--R + +--R 9 8 7 +--R 752cos(d x + c) + 712cos(d x + c) - 3200cos(d x + c) +--R + +--R 6 5 4 +--R - 3200cos(d x + c) + 4992cos(d x + c) + 4992cos(d x + c) +--R + +--R 3 2 +--R - 2560cos(d x + c) - 2560cos(d x + c) +--R / +--R 14 13 12 +--R 35cos(d x + c) + 280cos(d x + c) + 280cos(d x + c) +--R + +--R 11 10 9 +--R - 1680cos(d x + c) - 1680cos(d x + c) + 2240cos(d x + c) +--R + +--R 8 +--R 2240cos(d x + c) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 15 14 13 +--R 70cos(d x + c) + 70cos(d x + c) - 1680cos(d x + c) +--R + +--R 12 11 10 +--R - 1680cos(d x + c) + 5600cos(d x + c) + 5600cos(d x + c) +--R + +--R 9 8 +--R - 4480cos(d x + c) - 4480cos(d x + c) +--R * +--R sin(d x + c) +--R + +--R 16 15 14 +--R 35cos(d x + c) - 210cos(d x + c) - 245cos(d x + c) +--R + +--R 13 12 11 +--R 1960cos(d x + c) + 1960cos(d x + c) - 3920cos(d x + c) +--R + +--R 10 9 8 +--R - 3920cos(d x + c) + 2240cos(d x + c) + 2240cos(d x + c) +--R Type: Expression(Integer) +--E 116 + +--S 117 of 520 +t0022:= (a+b*sin(c+d*x))^(1/2) +--R +--R +--R +------------------+ +--R (80) \|b sin(d x + c) + a +--R Type: Expression(Integer) +--E 117 + +--S 118 of 520 +r0022:= 2*EllipticE(1/2*c-1/4*%pi+1/2*d*x,2*b/(a+b))*_ + (a+b*sin(c+d*x))^(1/2)/d/((a+b*sin(c+d*x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 118 + +--S 119 of 520 +a0022:= integrate(t0022,x) +--R +--R +--R x +--R ++ +-------------------+ +--R (81) | \|b sin(%R d + c) + a d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 119 + +--S 120 of 520 +--m0022:= a0022-r0022 +--E 120 + +--S 121 of 520 +--d0022:= D(m0022,x) +--E 121 + +--S 122 of 520 +t0023:= (a+b*sin(x))^(3/2) +--R +--R +--R +------------+ +--R (82) (b sin(x) + a)\|b sin(x) + a +--R Type: Expression(Integer) +--E 122 + +--S 123 of 520 +r0023:= 2/3*(4*a*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))-_ + a*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))-_ + b*cos(x)*((a+b*sin(x))/(a+b))^(1/2)+b*_ + EllipticF(-1/4*%pi+1/2*x,2*b/(a+b)))*(a+b*sin(x))^(1/2)/_ + ((a+b*sin(x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 123 + +--S 124 of 520 +a0023:= integrate(t0023,x) +--R +--R +--R x +--R ++ +-------------+ +--R (83) | (b sin(%R) + a)\|b sin(%R) + a d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 124 + +--S 125 of 520 +--m0023:= a0023-r0023 +--E 125 + +--S 126 of 520 +--d0023:= D(m0023,x) +--E 126 + +--S 127 of 520 +t0024:= 1/(a+b*sin(x))^(1/2) +--R +--R +--R 1 +--R (84) --------------- +--R +------------+ +--R \|b sin(x) + a +--R Type: Expression(Integer) +--E 127 + +--S 128 of 520 +r0024:= 2*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))*((a+b*sin(x))/(a+b))^(1/2)/_ + (a+b*sin(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 128 + +--S 129 of 520 +a0024:= integrate(t0024,x) +--R +--R +--R x +--R ++ 1 +--R (85) | ---------------- d%R +--R ++ +-------------+ +--R \|b sin(%R) + a +--R Type: Union(Expression(Integer),...) +--E 129 + +--S 130 of 520 +--m0024:= a0024-r0024 +--E 130 + +--S 131 of 520 +--d0024:= D(m0024,x) +--E 131 + +--S 132 of 520 +t0025:= 1/(a+b*sin(x))^(3/2) +--R +--R +--R 1 +--R (86) ----------------------------- +--R +------------+ +--R (b sin(x) + a)\|b sin(x) + a +--R Type: Expression(Integer) +--E 132 + +--S 133 of 520 +r0025:= 2*b*cos(x)/(a^2-b^2)/(a+b*sin(x))^(1/2)+_ + 2*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))*(a+b*sin(x))^(1/2)/_ + (a^2-b^2)/((a+b*sin(x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 133 + +--S 134 of 520 +a0025:= integrate(t0025,x) +--R +--R +--R x +--R ++ 1 +--R (87) | ------------------------------- d%R +--R ++ +-------------+ +--R (b sin(%R) + a)\|b sin(%R) + a +--R Type: Union(Expression(Integer),...) +--E 134 + +--S 135 of 520 +--m0025:= a0025-r0025 +--E 135 + +--S 136 of 520 +--d0025:= D(m0025,x) +--E 136 + +--S 137 of 520 +t0026:= 1/(a+b*sin(x))^(5/2) +--R +--R +--R 1 +--R (88) --------------------------------------------- +--R 2 2 2 +------------+ +--R (b sin(x) + 2a b sin(x) + a )\|b sin(x) + a +--R Type: Expression(Integer) +--E 137 + +--S 138 of 520 +r0026:= 2/3*b*cos(x)/(a^2-b^2)/(a+b*sin(x))^(3/2)+_ + 8/3*a*b*cos(x)/(a^2-b^2)^2/(a+b*sin(x))^(1/2)+_ + 8/3*a*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))*_ + (a+b*sin(x))^(1/2)/(a^2-b^2)^2/((a+b*sin(x))/(a+b))^(1/2)-_ + 2/3*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))*_ + ((a+b*sin(x))/(a+b))^(1/2)/(a^2-b^2)/(a+b*sin(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 138 + +--S 139 of 520 +a0026:= integrate(t0026,x) +--R +--R +--R x +--R ++ 1 +--R (89) | ------------------------------------------------ d%R +--R ++ 2 2 2 +-------------+ +--R (b sin(%R) + 2a b sin(%R) + a )\|b sin(%R) + a +--R Type: Union(Expression(Integer),...) +--E 139 + +--S 140 of 520 +--m0026:= a0026-r0026 +--E 140 + +--S 141 of 520 +--d0026:= D(m0026,x) +--E 141 + +--S 142 of 520 +t0027:= 1/(a+a*sin(c+d*x))^(1/2) +--R +--R +--R 1 +--R (90) --------------------- +--R +------------------+ +--R \|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 142 + +--S 143 of 520 +r0027:= -2*atanh(cos(1/2*c+1/4*%pi+1/2*d*x))*_ + sin(1/2*c+1/4*%pi+1/2*d*x)/d/(a+a*sin(c+d*x))^(1/2) +--R +--R +--R 2d x + %pi + 2c 2d x + %pi + 2c +--R 2sin(---------------)atanh(cos(---------------)) +--R 4 4 +--R (91) - ------------------------------------------------ +--R +------------------+ +--R d\|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 143 + +--S 144 of 520 +a0027:= integrate(t0027,x) +--R +--R +--R (92) +--R [ +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +--R (\|2 sin(d x + c) - \|2 cos(d x + c) - \|2 ) |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- cos(d x + c) - 1)sin(d x + c) + 3cos(d x + c) + 3 +--R / +--R (cos(d x + c) + 1)sin(d x + c) + cos(d x + c) + 1 +--R / +--R 2d +--R , +--R +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R log +--R (cos(d x + c) + 1)sin(d x + c) + cos(d x + c) + 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +--R (\|2 sin(d x + c) - \|2 cos(d x + c) - \|2 ) |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (cos(d x + c) + 1)sin(d x + c) - 3cos(d x + c) - 3 +--R / +--R 2d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 144 + +--S 145 of 520 +m0027a:= a0027.1-r0027 +--R +--R +--R (93) +--R +-+ +--R |2 +------------------+ +--R |- \|a sin(d x + c) + a +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +--R (\|2 sin(d x + c) - \|2 cos(d x + c) - \|2 ) |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- cos(d x + c) - 1)sin(d x + c) + 3cos(d x + c) + 3 +--R / +--R (cos(d x + c) + 1)sin(d x + c) + cos(d x + c) + 1 +--R + +--R 2d x + %pi + 2c 2d x + %pi + 2c +--R 4sin(---------------)atanh(cos(---------------)) +--R 4 4 +--R / +--R +------------------+ +--R 2d\|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 145 + +--S 146 of 520 +d0027a:= D(m0027a,x) +--R +--R +--R (94) +--R 2d x + %pi + 2c 2 2 +--R (4cos(---------------) - 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (4cos(---------------) - 4)cos(d x + c) +--R 4 +--R * +--R +-+ +--R |2 +------------------+ +--R |- \|a cos(d x + c) + a +--R \|a +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- \|2 cos(---------------) + \|2 )sin(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- \|2 cos(---------------) + \|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 2\|2 cos(---------------) + 2\|2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- \|2 cos(---------------) + \|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - \|2 cos(---------------) + \|2 +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 2\|2 cos(---------------) + 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 6\|2 cos(---------------) + 6\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 4\|2 cos(---------------) + 4\|2 )cos(d x + c) +--R 4 +--R * +--R +------------------+ +--R \|a sin(d x + c) + a +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (2cos(---------------) - 2cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R 2cos(---------------) - 2cos(---------------) +--R 4 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 2cos(---------------) + 2)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 2cos(---------------) + 2)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 4cos(---------------) + 4cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R - 4cos(---------------) + 4cos(---------------) +--R 4 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 2 +--R (6cos(---------------) - 6)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (6cos(---------------) - 6)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 6cos(---------------) + 6cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R - 6cos(---------------) + 6cos(---------------) +--R 4 4 +--R * +--R 2d x + %pi + 2c +--R atanh(cos(---------------)) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (2cos(d x + c) + 2)sin(---------------) sin(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 4cos(d x + c) - 4)sin(---------------) sin(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 6cos(d x + c) - 6)sin(---------------) +--R 4 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 2a\|2 cos(---------------) + 2a\|2 cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R - 2a\|2 cos(---------------) + 2a\|2 cos(---------------) +--R 4 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (2a\|2 cos(---------------) - 2a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (2a\|2 cos(---------------) - 2a\|2 )cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (2a\|2 cos(---------------) - 2a\|2 cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (2a\|2 cos(---------------) - 2a\|2 cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 2a\|2 cos(---------------) + 2a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 4a\|2 cos(---------------) + 4a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 2a\|2 cos(---------------) + 2a\|2 )cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (2a\|2 cos(---------------) - 2a\|2 cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (4a\|2 cos(---------------) - 4a\|2 cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R 2a\|2 cos(---------------) - 2a\|2 cos(---------------) +--R 4 4 +--R * +--R +-+ +--R |2 2d x + %pi + 2c +--R |- atanh(cos(---------------)) +--R \|a 4 +--R + +--R +-+ +-+ 2d x + %pi + 2c 2 2 +--R (- 2a\|2 cos(d x + c) - 2a\|2 )sin(---------------) sin(d x + c) +--R 4 +--R + +--R +-+ 2 +-+ 2d x + %pi + 2c 2 +--R (2a\|2 cos(d x + c) + 2a\|2 cos(d x + c))sin(---------------) +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R (2a\|2 cos(d x + c) + 4a\|2 cos(d x + c) + 2a\|2 ) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 2d x + %pi + 2c 2 +--R (2cos(---------------) - 2)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 2cos(---------------) - 2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 +--R (- 4cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 4cos(---------------) + 4 +--R 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R (- 6cos(---------------) + 6)cos(d x + c) - 6cos(---------------) +--R 4 4 +--R + +--R 6 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 2a\|2 cos(---------------) + 2a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 2a\|2 cos(---------------) + 2a\|2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (2a\|2 cos(---------------) - 2a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (2a\|2 cos(---------------) - 2a\|2 )cos(d x + c) +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (2a\|2 cos(---------------) - 2a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (4a\|2 cos(---------------) - 4a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 2a\|2 cos(---------------) - 2a\|2 +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------------+ +--R \|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 520 +m0027b:= a0027.2-r0027 +--R +--R +--R (95) +--R +-+ +--R |2 +------------------+ +--R |- \|a sin(d x + c) + a +--R \|a +--R * +--R log +--R (cos(d x + c) + 1)sin(d x + c) + cos(d x + c) + 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +--R (\|2 sin(d x + c) - \|2 cos(d x + c) - \|2 ) |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (cos(d x + c) + 1)sin(d x + c) - 3cos(d x + c) - 3 +--R + +--R 2d x + %pi + 2c 2d x + %pi + 2c +--R 4sin(---------------)atanh(cos(---------------)) +--R 4 4 +--R / +--R +------------------+ +--R 2d\|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 147 + +--S 148 of 520 +d0027b:= D(m0027b,x) +--R +--R +--R (96) +--R 2d x + %pi + 2c 2 4 +--R (- 2cos(---------------) + 2)sin(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 2cos(---------------) + 2)sin(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (2cos(---------------) - 2)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (4cos(---------------) - 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 2cos(---------------) - 2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 8cos(---------------) + 8)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 18cos(---------------) + 18)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 8cos(---------------) + 8)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 2cos(---------------) - 2 +--R 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 4 +--R (4cos(---------------) - 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (28cos(---------------) - 28)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (44cos(---------------) - 44)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (20cos(---------------) - 20)cos(d x + c) +--R 4 +--R * +--R +-+ +--R |2 +------------------+ +--R |- \|a cos(d x + c) + a +--R \|a +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- \|2 cos(---------------) + \|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - \|2 cos(---------------) + \|2 +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- \|2 cos(---------------) + \|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R \|2 cos(---------------) - \|2 +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (2\|2 cos(---------------) - 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (7\|2 cos(---------------) - 7\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 5\|2 cos(---------------) - 5\|2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 2\|2 cos(---------------) + 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 16\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 23\|2 cos(---------------) + 23\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 6\|2 cos(---------------) + 6\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 3\|2 cos(---------------) - 3\|2 +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (14\|2 cos(---------------) - 14\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (48\|2 cos(---------------) - 48\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (54\|2 cos(---------------) - 54\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (20\|2 cos(---------------) - 20\|2 )cos(d x + c) +--R 4 +--R * +--R +------------------+ +--R \|a sin(d x + c) + a +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 2 +--R (2cos(---------------) - 2cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (12cos(---------------) - 12cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R 10cos(---------------) - 10cos(---------------) +--R 4 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 2cos(---------------) + 2)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 12cos(---------------) + 12)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 10cos(---------------) + 10)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 26cos(---------------) + 26cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 44cos(---------------) + 44cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R - 18cos(---------------) + 18cos(---------------) +--R 4 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 3 +--R (28cos(---------------) - 28)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (56cos(---------------) - 56)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (28cos(---------------) - 28)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 3 +--R (8cos(---------------) - 8cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (14cos(---------------) - 14cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (4cos(---------------) - 4cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R - 2cos(---------------) + 2cos(---------------) +--R 4 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 8cos(---------------) + 8)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 42cos(---------------) + 42)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 60cos(---------------) + 60)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 26cos(---------------) + 26)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 3 +--R (8cos(---------------) - 8cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 2 +--R (42cos(---------------) - 42cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (60cos(---------------) - 60cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R 26cos(---------------) - 26cos(---------------) +--R 4 4 +--R * +--R 2d x + %pi + 2c +--R atanh(cos(---------------)) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 +--R (2cos(d x + c) + 12cos(d x + c) + 10)sin(---------------) +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 2d x + %pi + 2c 2 +--R (- 26cos(d x + c) - 44cos(d x + c) - 18)sin(---------------) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 +--R (8cos(d x + c) + 14cos(d x + c) + 4cos(d x + c) - 2) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) sin(d x + c) +--R 4 +--R + +--R 3 2 +--R (8cos(d x + c) + 42cos(d x + c) + 60cos(d x + c) + 26) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (4a\|2 cos(---------------) - 4a\|2 cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (8a\|2 cos(---------------) - 8a\|2 cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R 4a\|2 cos(---------------) - 4a\|2 cos(---------------) +--R 4 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 4a\|2 cos(---------------) + 4a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 8a\|2 cos(---------------) + 8a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 4a\|2 cos(---------------) + 4a\|2 )cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 4a\|2 cos(---------------) + 4a\|2 cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 20a\|2 cos(---------------) + 20a\|2 cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 28a\|2 cos(---------------) + 28a\|2 cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R - 12a\|2 cos(---------------) + 12a\|2 cos(---------------) +--R 4 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (4a\|2 cos(---------------) - 4a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (24a\|2 cos(---------------) - 24a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (36a\|2 cos(---------------) - 36a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (16a\|2 cos(---------------) - 16a\|2 )cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (8a\|2 cos(---------------) - 8a\|2 cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (12a\|2 cos(---------------) - 12a\|2 cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R - 4a\|2 cos(---------------) + 4a\|2 cos(---------------) +--R 4 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 12a\|2 cos(---------------) + 12a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 36a\|2 cos(---------------) + 36a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 36a\|2 cos(---------------) + 36a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 12a\|2 cos(---------------) + 12a\|2 )cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (12a\|2 cos(---------------) - 12a\|2 cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (36a\|2 cos(---------------) - 36a\|2 cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (36a\|2 cos(---------------) - 36a\|2 cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R 12a\|2 cos(---------------) - 12a\|2 cos(---------------) +--R 4 4 +--R * +--R +-+ +--R |2 2d x + %pi + 2c +--R |- atanh(cos(---------------)) +--R \|a 4 +--R + +--R +-+ 2 +-+ +-+ +--R (4a\|2 cos(d x + c) + 8a\|2 cos(d x + c) + 4a\|2 ) +--R * +--R 2d x + %pi + 2c 2 3 +--R sin(---------------) sin(d x + c) +--R 4 +--R + +--R +-+ 3 +-+ 2 +--R - 4a\|2 cos(d x + c) - 20a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 28a\|2 cos(d x + c) - 12a\|2 +--R * +--R 2d x + %pi + 2c 2 2 +--R sin(---------------) sin(d x + c) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R (8a\|2 cos(d x + c) + 12a\|2 cos(d x + c) - 4a\|2 ) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) sin(d x + c) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R 12a\|2 cos(d x + c) + 36a\|2 cos(d x + c) + 36a\|2 cos(d x + c) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 2d x + %pi + 2c 2 2 +--R (2cos(---------------) - 2)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (12cos(---------------) - 12)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 10cos(---------------) - 10 +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 26cos(---------------) + 26)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 44cos(---------------) + 44)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 18cos(---------------) + 18 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 3 +--R (8cos(---------------) - 8)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (14cos(---------------) - 14)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (4cos(---------------) - 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 2cos(---------------) + 2 +--R 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 3 +--R (8cos(---------------) - 8)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (42cos(---------------) - 42)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (60cos(---------------) - 60)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 26cos(---------------) - 26 +--R 4 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (4a\|2 cos(---------------) - 4a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (8a\|2 cos(---------------) - 8a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 4a\|2 cos(---------------) - 4a\|2 +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 4a\|2 cos(---------------) + 4a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 20a\|2 cos(---------------) + 20a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 28a\|2 cos(---------------) + 28a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 12a\|2 cos(---------------) + 12a\|2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (8a\|2 cos(---------------) - 8a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (12a\|2 cos(---------------) - 12a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 4a\|2 cos(---------------) + 4a\|2 +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (12a\|2 cos(---------------) - 12a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (36a\|2 cos(---------------) - 36a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (36a\|2 cos(---------------) - 36a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 12a\|2 cos(---------------) - 12a\|2 +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------------+ +--R \|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 148 + +--S 149 of 520 +t0028:= 1/(a+a*sin(c+d*x))^(3/2) +--R +--R +--R 1 +--R (97) ----------------------------------------- +--R +------------------+ +--R (a sin(d x + c) + a)\|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 149 + +--S 150 of 520 +r0028:= -1/2*cos(c+d*x)/d/(a+a*sin(c+d*x))^(3/2)-_ + 1/2*atanh(cos(1/2*c+1/4*%pi+1/2*d*x))*_ + sin(1/2*c+1/4*%pi+1/2*d*x)/a/d/(a+a*sin(c+d*x))^(1/2) +--R +--R +--R (98) +--R 2d x + %pi + 2c 2d x + %pi + 2c +--R (- sin(---------------)sin(d x + c) - sin(---------------)) +--R 4 4 +--R * +--R 2d x + %pi + 2c +--R atanh(cos(---------------)) +--R 4 +--R + +--R - cos(d x + c) +--R / +--R +------------------+ +--R (2a d sin(d x + c) + 2a d)\|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 520 +a0028:= integrate(t0028,x) +--R +--R +--R (99) +--R [ +--R +-+ +-+ +-+ 3 +--R (2\|2 cos(d x + c) + 2\|2 )sin(d x + c) - \|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - \|2 cos(d x + c) + 2\|2 cos(d x + c) + 2\|2 +--R * +--R +--+ +--R \|2a +--R * +--R log +--R +-+ +-+ +-+ +--+ +--R (\|2 sin(d x + c) - \|2 cos(d x + c) - \|2 )\|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- a cos(d x + c) - a)sin(d x + c) + 3a cos(d x + c) + 3a +--R / +--R (cos(d x + c) + 1)sin(d x + c) + cos(d x + c) + 1 +--R + +--R 2 +--R (- 4cos(d x + c)sin(d x + c) - 4cos(d x + c) - 4cos(d x + c)) +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 2 +-+ 2 +-+ 2 +-+ 3 +--R (16a d\|2 cos(d x + c) + 16a d\|2 )sin(d x + c) - 8a d\|2 cos(d x + c) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 8a d\|2 cos(d x + c) + 16a d\|2 cos(d x + c) + 16a d\|2 +--R , +--R +--R +-+ +-+ +-+ 3 +--R (- 2\|2 cos(d x + c) - 2\|2 )sin(d x + c) + \|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R \|2 cos(d x + c) - 2\|2 cos(d x + c) - 2\|2 +--R * +--R +----+ +--R \|- 2a +--R * +--R atan +--R +-+ +-+ +-+ +----+ +--R (\|2 sin(d x + c) - \|2 cos(d x + c) - \|2 )\|- 2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 4a cos(d x + c) + 4a +--R + +--R 2 +--R (- 2cos(d x + c)sin(d x + c) - 2cos(d x + c) - 2cos(d x + c)) +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 2 +-+ 2 +-+ 2 +-+ 3 +--R (8a d\|2 cos(d x + c) + 8a d\|2 )sin(d x + c) - 4a d\|2 cos(d x + c) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 4a d\|2 cos(d x + c) + 8a d\|2 cos(d x + c) + 8a d\|2 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 151 + +--S 152 of 520 +m0028a:= a0028.1-r0028 +--R +--R +--R (100) +--R +-+ +-+ 2 +--R (2\|2 cos(d x + c) + 2\|2 )sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - \|2 cos(d x + c) - \|2 cos(d x + c) + 4\|2 cos(d x + c) +--R + +--R +-+ +--R 4\|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - \|2 cos(d x + c) - \|2 cos(d x + c) + 2\|2 cos(d x + c) + 2\|2 +--R * +--R +--+ +------------------+ +--R \|2a \|a sin(d x + c) + a +--R * +--R log +--R +-+ +-+ +-+ +--+ +--R (\|2 sin(d x + c) - \|2 cos(d x + c) - \|2 )\|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- a cos(d x + c) - a)sin(d x + c) + 3a cos(d x + c) + 3a +--R / +--R (cos(d x + c) + 1)sin(d x + c) + cos(d x + c) + 1 +--R + +--R 2 +--R - 4cos(d x + c)sin(d x + c) +--R + +--R 2 2 +--R (- 4cos(d x + c) - 8cos(d x + c))sin(d x + c) - 4cos(d x + c) +--R + +--R - 4cos(d x + c) +--R * +--R +------------------+ +------------------+ +--R \|a cos(d x + c) + a \|a sin(d x + c) + a +--R + +--R +-+ +-+ 2d x + %pi + 2c 2 +--R (8a\|2 cos(d x + c) + 8a\|2 )sin(---------------)sin(d x + c) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 4a\|2 cos(d x + c) - 4a\|2 cos(d x + c) + 16a\|2 cos(d x + c) +--R + +--R +-+ +--R 16a\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------)sin(d x + c) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 4a\|2 cos(d x + c) - 4a\|2 cos(d x + c) + 8a\|2 cos(d x + c) +--R + +--R +-+ +--R 8a\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R * +--R 2d x + %pi + 2c +--R atanh(cos(---------------)) +--R 4 +--R + +--R +-+ 2 +-+ +--R (8a\|2 cos(d x + c) + 8a\|2 cos(d x + c))sin(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 4a\|2 cos(d x + c) - 4a\|2 cos(d x + c) + 8a\|2 cos(d x + c) +--R + +--R +-+ +--R 8a\|2 cos(d x + c) +--R / +--R 2 +-+ 2 +-+ 2 +--R (16a d\|2 cos(d x + c) + 16a d\|2 )sin(d x + c) +--R + +--R 2 +-+ 3 2 +-+ 2 +--R - 8a d\|2 cos(d x + c) - 8a d\|2 cos(d x + c) +--R + +--R 2 +-+ 2 +-+ +--R 32a d\|2 cos(d x + c) + 32a d\|2 +--R * +--R sin(d x + c) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 8a d\|2 cos(d x + c) - 8a d\|2 cos(d x + c) + 16a d\|2 cos(d x + c) +--R + +--R 2 +-+ +--R 16a d\|2 +--R * +--R +------------------+ +--R \|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 152 + +--S 153 of 520 +d0028a:= D(m0028a,x) +--R +--R +--R (101) +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (- 2\|2 cos(---------------) + 2\|2 )cos(d x + c)sin(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 3\|2 cos(---------------) + 3\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 12\|2 cos(---------------) + 12\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 6\|2 cos(---------------) + 6\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 16\|2 cos(---------------) - 16\|2 +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 4\|2 cos(---------------) + 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 16\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (28\|2 cos(---------------) - 28\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 64\|2 cos(---------------) - 64\|2 +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- \|2 cos(---------------) + \|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 2\|2 cos(---------------) + 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (10\|2 cos(---------------) - 10\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (48\|2 cos(---------------) - 48\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (116\|2 cos(---------------) - 116\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 96\|2 cos(---------------) - 96\|2 +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 4\|2 cos(---------------) + 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 10\|2 cos(---------------) + 10\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (24\|2 cos(---------------) - 24\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (120\|2 cos(---------------) - 120\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (150\|2 cos(---------------) - 150\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 64\|2 cos(---------------) - 64\|2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 7 +--R (2\|2 cos(---------------) - 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (6\|2 cos(---------------) - 6\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- \|2 cos(---------------) + \|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 14\|2 cos(---------------) + 14\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (17\|2 cos(---------------) - 17\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (92\|2 cos(---------------) - 92\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (82\|2 cos(---------------) - 82\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 16\|2 cos(---------------) - 16\|2 +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 7 +--R (2\|2 cos(---------------) - 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (6\|2 cos(---------------) - 6\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (2\|2 cos(---------------) - 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 6\|2 cos(---------------) + 6\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (4\|2 cos(---------------) - 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (24\|2 cos(---------------) - 24\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (16\|2 cos(---------------) - 16\|2 )cos(d x + c) +--R 4 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 2d x + %pi + 2c 2 +--R (4cos(---------------) - 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 8cos(---------------) - 8 +--R 4 +--R * +--R 6 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 3 +--R (6cos(---------------) - 6)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (12cos(---------------) - 12)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (20cos(---------------) - 20)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 24cos(---------------) - 24 +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 4cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 4cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (8cos(---------------) - 8)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 16cos(---------------) - 16 +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 5 +--R (2cos(---------------) - 2)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 4cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 56cos(---------------) + 56)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 104cos(---------------) + 104)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 72cos(---------------) + 72)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 16cos(---------------) + 16 +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 4cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (4cos(---------------) - 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (16cos(---------------) - 16)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 84cos(---------------) + 84)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 192cos(---------------) + 192)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 124cos(---------------) + 124)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 24cos(---------------) + 24 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 7 +--R (- 4cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 16cos(---------------) + 16)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 2cos(---------------) + 2)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (28cos(---------------) - 28)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 46cos(---------------) + 46)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 132cos(---------------) + 132)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 76cos(---------------) + 76)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 8cos(---------------) + 8 +--R 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 7 +--R (- 4cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 12cos(---------------) + 12)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 4cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (12cos(---------------) - 12)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 8cos(---------------) + 8)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 32cos(---------------) + 32)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 16cos(---------------) + 16)cos(d x + c) +--R 4 +--R * +--R +--+ +--R \|2a +--R * +--R +------------------+ +--R \|a sin(d x + c) + a +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (8\|2 cos(---------------) - 8\|2 cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R 8\|2 cos(---------------) - 8\|2 cos(---------------) +--R 4 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 8\|2 cos(---------------) + 8\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 8\|2 cos(---------------) + 8\|2 )cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 8\|2 cos(---------------) + 8\|2 cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 16\|2 cos(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 16\|2 cos(---------------) +--R 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (16\|2 cos(---------------) - 16\|2 cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R 24\|2 cos(---------------) - 24\|2 cos(---------------) +--R 4 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (8\|2 cos(---------------) - 8\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (16\|2 cos(---------------) - 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 8\|2 cos(---------------) + 8\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 16\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (2\|2 cos(---------------) - 2\|2 cos(---------------)) +--R 4 4 +--R * +--R 5 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (10\|2 cos(---------------) - 10\|2 cos(---------------)) +--R 4 4 +--R * +--R 4 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 8\|2 cos(---------------) + 8\|2 cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 48\|2 cos(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 48\|2 cos(---------------) +--R 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 16\|2 cos(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 16\|2 cos(---------------) +--R 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R 16\|2 cos(---------------) - 16\|2 cos(---------------) +--R 4 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (- 2\|2 cos(---------------) + 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 10\|2 cos(---------------) + 10\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (32\|2 cos(---------------) - 32\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (24\|2 cos(---------------) - 24\|2 )cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 2\|2 cos(---------------) + 2\|2 cos(---------------)) +--R 4 4 +--R * +--R 6 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (26\|2 cos(---------------) - 26\|2 cos(---------------)) +--R 4 4 +--R * +--R 4 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (24\|2 cos(---------------) - 24\|2 cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 48\|2 cos(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 48\|2 cos(---------------) +--R 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 64\|2 cos(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 64\|2 cos(---------------) +--R 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R - 16\|2 cos(---------------) + 16\|2 cos(---------------) +--R 4 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 7 +--R (2\|2 cos(---------------) - 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (2\|2 cos(---------------) - 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 16\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 24\|2 cos(---------------) + 24\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (16\|2 cos(---------------) - 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (40\|2 cos(---------------) - 40\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (16\|2 cos(---------------) - 16\|2 )cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 4\|2 cos(---------------) + 4\|2 cos(---------------)) +--R 4 4 +--R * +--R 6 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 6\|2 cos(---------------) + 6\|2 cos(---------------)) +--R 4 4 +--R * +--R 5 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (22\|2 cos(---------------) - 22\|2 cos(---------------)) +--R 4 4 +--R * +--R 4 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (40\|2 cos(---------------) - 40\|2 cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 16\|2 cos(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 16\|2 cos(---------------) +--R 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 56\|2 cos(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 56\|2 cos(---------------) +--R 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R - 24\|2 cos(---------------) + 24\|2 cos(---------------) +--R 4 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 7 +--R (2\|2 cos(---------------) - 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (4\|2 cos(---------------) - 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 6\|2 cos(---------------) + 6\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 16\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (16\|2 cos(---------------) - 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (8\|2 cos(---------------) - 8\|2 )cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 2\|2 cos(---------------) + 2\|2 cos(---------------)) +--R 4 4 +--R * +--R 6 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 4\|2 cos(---------------) + 4\|2 cos(---------------)) +--R 4 4 +--R * +--R 5 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (6\|2 cos(---------------) - 6\|2 cos(---------------)) +--R 4 4 +--R * +--R 4 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (16\|2 cos(---------------) - 16\|2 cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R (- 16\|2 cos(---------------) + 16\|2 cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +-+ 2d x + %pi + 2c +--R - 8\|2 cos(---------------) + 8\|2 cos(---------------) +--R 4 4 +--R * +--R +--+ 2d x + %pi + 2c +--R \|2a atanh(cos(---------------)) +--R 4 +--R + +--R +-+ +-+ 2d x + %pi + 2c 2 +--R (8\|2 cos(d x + c) + 8\|2 )sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 16\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 16\|2 cos(---------------) + 16\|2 +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 8\|2 cos(d x + c) - 16\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 16\|2 cos(d x + c) + 24\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (16\|2 cos(---------------) - 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (32\|2 cos(---------------) - 32\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 16\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 32\|2 cos(---------------) + 32\|2 +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +--R 2\|2 cos(d x + c) + 10\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 8\|2 cos(d x + c) - 48\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 16\|2 cos(d x + c) + 16\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 4\|2 cos(---------------) + 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 20\|2 cos(---------------) + 20\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 24\|2 cos(---------------) + 24\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (40\|2 cos(---------------) - 40\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (48\|2 cos(---------------) - 48\|2 )cos(d x + c) +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 4 +--R - 2\|2 cos(d x + c) + 26\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 24\|2 cos(d x + c) - 48\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 64\|2 cos(d x + c) - 16\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (4\|2 cos(---------------) - 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (28\|2 cos(---------------) - 28\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (16\|2 cos(---------------) - 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 48\|2 cos(---------------) + 48\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (8\|2 cos(---------------) - 8\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (80\|2 cos(---------------) - 80\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 32\|2 cos(---------------) - 32\|2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 5 +--R - 4\|2 cos(d x + c) - 6\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R 22\|2 cos(d x + c) + 40\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - 16\|2 cos(d x + c) - 56\|2 cos(d x + c) - 24\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 7 +--R (- 6\|2 cos(---------------) + 6\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (- 26\|2 cos(---------------) + 26\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 16\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (36\|2 cos(---------------) - 36\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (40\|2 cos(---------------) - 40\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (24\|2 cos(---------------) - 24\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (32\|2 cos(---------------) - 32\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 16\|2 cos(---------------) - 16\|2 +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 5 +--R - 2\|2 cos(d x + c) - 4\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ +--R 6\|2 cos(d x + c) + 16\|2 cos(d x + c) - 16\|2 cos(d x + c) +--R + +--R +-+ +--R - 8\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 8 +--R (6\|2 cos(---------------) - 6\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 7 +--R (12\|2 cos(---------------) - 12\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (- 18\|2 cos(---------------) + 18\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 48\|2 cos(---------------) + 48\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (48\|2 cos(---------------) - 48\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (24\|2 cos(---------------) - 24\|2 )cos(d x + c) +--R 4 +--R * +--R +--+ +--R \|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 8a cos(---------------) + 8a cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 16a cos(---------------) + 16a cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R - 8a cos(---------------) + 8a cos(---------------) +--R 4 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 3 +--R (8a cos(---------------) - 8a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (16a cos(---------------) - 16a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (8a cos(---------------) - 8a)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 4 +--R (8a cos(---------------) - 8a cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (16a cos(---------------) - 16a cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 16a cos(---------------) + 16a cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R - 8a cos(---------------) + 8a cos(---------------) +--R 4 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 8a cos(---------------) + 8a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 16a cos(---------------) + 16a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 8a cos(---------------) + 8a)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 2a cos(---------------) + 2a cos(---------------)) +--R 4 4 +--R * +--R 6 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 4a cos(---------------) + 4a cos(---------------)) +--R 4 4 +--R * +--R 5 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 2a cos(---------------) + 2a cos(---------------)) +--R 4 4 +--R * +--R 4 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (48a cos(---------------) - 48a cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (96a cos(---------------) - 96a cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R 48a cos(---------------) - 48a cos(---------------) +--R 4 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 7 +--R (2a cos(---------------) - 2a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (4a cos(---------------) - 4a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (10a cos(---------------) - 10a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (16a cos(---------------) - 16a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 40a cos(---------------) + 40a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 96a cos(---------------) + 96a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 48a cos(---------------) + 48a)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 6 +--R (2a cos(---------------) - 2a cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 5 +--R (4a cos(---------------) - 4a cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 46a cos(---------------) + 46a cos(---------------)) +--R 4 4 +--R * +--R 4 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 96a cos(---------------) + 96a cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (64a cos(---------------) - 64a cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (224a cos(---------------) - 224a cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R 112a cos(---------------) - 112a cos(---------------) +--R 4 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 7 +--R (- 4a cos(---------------) + 4a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 8a cos(---------------) + 8a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (36a cos(---------------) - 36a)cos(d x + c) +--R 4 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cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (24a cos(---------------) - 24a cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (176a cos(---------------) - 176a cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R 88a cos(---------------) - 88a cos(---------------) +--R 4 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 7 +--R (- 6a cos(---------------) + 6a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 12a cos(---------------) + 12a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (18a cos(---------------) - 18a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (48a cos(---------------) - 48a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 48a cos(---------------) + 48a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 24a cos(---------------) + 24a)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 6 +--R (6a cos(---------------) - 6a cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 5 +--R (12a cos(---------------) - 12a cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 4 +--R (- 18a cos(---------------) + 18a cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 3 +--R (- 48a cos(---------------) + 48a cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (48a cos(---------------) - 48a cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R 24a cos(---------------) - 24a cos(---------------) +--R 4 4 +--R * +--R 2d x + %pi + 2c +--R atanh(cos(---------------)) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 +--R (- 8a cos(d x + c) - 16a cos(d x + c) - 8a)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (16a cos(---------------) - 16a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (32a cos(---------------) - 32a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 16a cos(---------------) - 16a +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 4 3 +--R (8a cos(d x + c) + 16a cos(d x + c) - 16a cos(d x + c) - 8a) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 16a cos(---------------) + 16a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 32a cos(---------------) + 32a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 16a cos(---------------) + 16a)cos(d x + c) +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 5 4 +--R - 2a cos(d x + c) - 4a cos(d x + c) - 2a cos(d x + c) +--R + +--R 2 +--R 48a cos(d x + c) + 96a cos(d x + c) + 48a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (4a cos(---------------) - 4a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (8a cos(---------------) - 8a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (44a cos(---------------) - 44a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (80a cos(---------------) - 80a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 56a cos(---------------) + 56a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 192a cos(---------------) + 192a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 96a cos(---------------) + 96a +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 5 4 +--R 2a cos(d x + c) + 4a cos(d x + c) - 46a cos(d x + c) +--R + +--R 3 2 +--R - 96a cos(d x + c) + 64a cos(d x + c) + 224a cos(d x + c) + 112a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 32a cos(---------------) + 32a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 64a cos(---------------) + 64a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (24a cos(---------------) - 24a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (112a cos(---------------) - 112a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 72a cos(---------------) + 72a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 256a cos(---------------) + 256a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 128a cos(---------------) + 128a +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 5 4 +--R 10a cos(d x + c) + 20a cos(d x + c) - 54a cos(d x + c) +--R + +--R 3 2 +--R - 128a cos(d x + c) + 24a cos(d x + c) + 176a cos(d x + c) + 88a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 8 +--R (6a cos(---------------) - 6a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 7 +--R (12a cos(---------------) - 12a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (42a cos(---------------) - 42a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (72a cos(---------------) - 72a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 36a cos(---------------) + 36a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 144a cos(---------------) + 144a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 120a cos(---------------) + 120a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 96a cos(---------------) + 96a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 48a cos(---------------) + 48a +--R 4 +--R * +--R sin(d x + c) +--R + +--R 6 5 4 +--R 6a cos(d x + c) + 12a cos(d x + c) - 18a cos(d x + c) +--R + +--R 3 +--R - 48a cos(d x + c) + 48a cos(d x + c) + 24a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 8 +--R (- 18a cos(---------------) + 18a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 7 +--R (- 36a cos(---------------) + 36a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (54a cos(---------------) - 54a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (144a cos(---------------) - 144a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 144a cos(---------------) + 144a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 72a cos(---------------) + 72a)cos(d x + c) +--R 4 +--R / +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (32a\|2 cos(---------------) - 32a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 32a\|2 cos(---------------) - 32a\|2 +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 32a\|2 cos(---------------) + 32a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 64a\|2 cos(---------------) + 64a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (64a\|2 cos(---------------) - 64a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 96a\|2 cos(---------------) - 96a\|2 +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (8a\|2 cos(---------------) - 8a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (40a\|2 cos(---------------) - 40a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 32a\|2 cos(---------------) + 32a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 192a\|2 cos(---------------) + 192a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 64a\|2 cos(---------------) + 64a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 64a\|2 cos(---------------) - 64a\|2 +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (- 8a\|2 cos(---------------) + 8a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (104a\|2 cos(---------------) - 104a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (96a\|2 cos(---------------) - 96a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 192a\|2 cos(---------------) + 192a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 256a\|2 cos(---------------) + 256a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 64a\|2 cos(---------------) + 64a\|2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (- 16a\|2 cos(---------------) + 16a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 24a\|2 cos(---------------) + 24a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (88a\|2 cos(---------------) - 88a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (160a\|2 cos(---------------) - 160a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 64a\|2 cos(---------------) + 64a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 224a\|2 cos(---------------) + 224a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 96a\|2 cos(---------------) + 96a\|2 +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (- 8a\|2 cos(---------------) + 8a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 16a\|2 cos(---------------) + 16a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (24a\|2 cos(---------------) - 24a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (64a\|2 cos(---------------) - 64a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 64a\|2 cos(---------------) + 64a\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 32a\|2 cos(---------------) + 32a\|2 +--R 4 +--R * +--R +--+ +------------------+ +--R \|2a \|a cos(d x + c) + a +--R + +--R 2 2d x + %pi + 2c 2 2 2 +--R (- 32a cos(---------------) + 32a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R (- 64a cos(---------------) + 64a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R - 32a cos(---------------) + 32a +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2 2d x + %pi + 2c 2 2 4 +--R (32a cos(---------------) - 32a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 3 +--R (64a cos(---------------) - 64a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R (- 64a cos(---------------) + 64a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R - 32a cos(---------------) + 32a +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 2 2d x + %pi + 2c 2 2 6 +--R (- 8a cos(---------------) + 8a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 5 +--R (- 16a cos(---------------) + 16a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 4 +--R (- 8a cos(---------------) + 8a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 2 +--R (192a cos(---------------) - 192a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R (384a cos(---------------) - 384a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R 192a cos(---------------) - 192a +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 2d x + %pi + 2c 2 2 6 +--R (8a cos(---------------) - 8a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 5 +--R (16a cos(---------------) - 16a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 4 +--R (- 184a cos(---------------) + 184a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 3 +--R (- 384a cos(---------------) + 384a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 2 +--R (256a cos(---------------) - 256a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R (896a cos(---------------) - 896a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R 448a cos(---------------) - 448a +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 2d x + %pi + 2c 2 2 6 +--R (40a cos(---------------) - 40a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 5 +--R (80a cos(---------------) - 80a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 4 +--R (- 216a cos(---------------) + 216a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 3 +--R (- 512a cos(---------------) + 512a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 2 +--R (96a cos(---------------) - 96a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R (704a cos(---------------) - 704a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R 352a cos(---------------) - 352a +--R 4 +--R * +--R sin(d x + c) +--R + +--R 2 2d x + %pi + 2c 2 2 6 +--R (24a cos(---------------) - 24a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 5 +--R (48a cos(---------------) - 48a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 4 +--R (- 72a cos(---------------) + 72a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 3 +--R (- 192a cos(---------------) + 192a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R (192a cos(---------------) - 192a )cos(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 2 +--R 96a cos(---------------) - 96a +--R 4 +--R * +--R +------------------+ +--R \|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 153 + +--S 154 of 520 +m0028b:= a0028.2-r0028 +--R +--R +--R (102) +--R +-+ +-+ 2 +--R (- 2\|2 cos(d x + c) - 2\|2 )sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (\|2 cos(d x + c) + \|2 cos(d x + c) - 4\|2 cos(d x + c) - 4\|2 ) +--R * +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R \|2 cos(d x + c) + \|2 cos(d x + c) - 2\|2 cos(d x + c) - 2\|2 +--R * +--R +----+ +------------------+ +--R \|- 2a \|a sin(d x + c) + a +--R * +--R atan +--R +-+ +-+ +-+ +----+ +--R (\|2 sin(d x + c) - \|2 cos(d x + c) - \|2 )\|- 2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 4a cos(d x + c) + 4a +--R + +--R 2 +--R - 2cos(d x + c)sin(d x + c) +--R + +--R 2 2 +--R (- 2cos(d x + c) - 4cos(d x + c))sin(d x + c) - 2cos(d x + c) +--R + +--R - 2cos(d x + c) +--R * +--R +------------------+ +------------------+ +--R \|a cos(d x + c) + a \|a sin(d x + c) + a +--R + +--R +-+ +-+ 2d x + %pi + 2c 2 +--R (4a\|2 cos(d x + c) + 4a\|2 )sin(---------------)sin(d x + c) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 2a\|2 cos(d x + c) - 2a\|2 cos(d x + c) + 8a\|2 cos(d x + c) +--R + +--R +-+ +--R 8a\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------)sin(d x + c) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 2a\|2 cos(d x + c) - 2a\|2 cos(d x + c) + 4a\|2 cos(d x + c) +--R + +--R +-+ +--R 4a\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R * +--R 2d x + %pi + 2c +--R atanh(cos(---------------)) +--R 4 +--R + +--R +-+ 2 +-+ +--R (4a\|2 cos(d x + c) + 4a\|2 cos(d x + c))sin(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 2a\|2 cos(d x + c) - 2a\|2 cos(d x + c) + 4a\|2 cos(d x + c) +--R + +--R +-+ +--R 4a\|2 cos(d x + c) +--R / +--R 2 +-+ 2 +-+ 2 +--R (8a d\|2 cos(d x + c) + 8a d\|2 )sin(d x + c) +--R + +--R 2 +-+ 3 2 +-+ 2 +--R - 4a d\|2 cos(d x + c) - 4a d\|2 cos(d x + c) +--R + +--R 2 +-+ 2 +-+ +--R 16a d\|2 cos(d x + c) + 16a d\|2 +--R * +--R sin(d x + c) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 4a d\|2 cos(d x + c) - 4a d\|2 cos(d x + c) + 8a d\|2 cos(d x + c) +--R + +--R 2 +-+ +--R 8a d\|2 +--R * +--R +------------------+ +--R \|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 154 + +--S 155 of 520 +d0028b:= D(m0028b,x) +--R +--R +--R (103) +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (2\|2 cos(---------------) - 2\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 4\|2 cos(---------------) - 4\|2 +--R 4 +--R * +--R 7 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (3\|2 cos(---------------) - 3\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (4\|2 cos(---------------) - 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 4\|2 cos(---------------) + 4\|2 )cos(d x + c) +--R 4 +--R * +--R 6 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 5\|2 cos(---------------) + 5\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 3\|2 cos(---------------) + 3\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 24\|2 cos(---------------) + 24\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 90\|2 cos(---------------) + 90\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 60\|2 cos(---------------) + 60\|2 +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (\|2 cos(---------------) - \|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 4\|2 cos(---------------) + 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 38\|2 cos(---------------) + 38\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 168\|2 cos(---------------) + 168\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 296\|2 cos(---------------) + 296\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 160\|2 cos(---------------) + 160\|2 +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (- 5\|2 cos(---------------) + 5\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- \|2 cos(---------------) + 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2c 2 +-+ 3 +--R (- 81\|2 cos(---------------) + 81\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 348\|2 cos(---------------) + 348\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 324\|2 cos(---------------) + 324\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 96\|2 cos(---------------) + 96\|2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 7 +--R (- 4\|2 cos(---------------) + 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (- 17\|2 cos(---------------) + 17\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 7\|2 cos(---------------) + 7\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (29\|2 cos(---------------) - 29\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 47\|2 cos(---------------) + 47\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 168\|2 cos(---------------) + 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4 +--R * +--R 5 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (56cos(---------------) - 56cos(---------------)) +--R 4 4 +--R * +--R 4 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (144cos(---------------) - 144cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 80cos(---------------) + 80cos(---------------)) +--R 4 4 +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 320cos(---------------) + 320cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R - 160cos(---------------) + 160cos(---------------) +--R 4 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 7 +--R (4cos(---------------) - 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (14cos(---------------) - 14)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 38cos(---------------) + 38)cos(d x + c) 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2d x + %pi + 2c +--R (256cos(---------------) - 256cos(---------------)) +--R 4 4 +--R * +--R 3 +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 360cos(---------------) + 360cos(---------------)) +--R 4 4 +--R * +--R cos(d x + c) +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R - 200cos(---------------) + 200cos(---------------) +--R 4 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 8 +--R (- 2cos(---------------) + 2)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 7 +--R (6cos(---------------) - 6)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (34cos(---------------) - 34)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 22cos(---------------) + 22)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 136cos(---------------) + 136)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 24cos(---------------) + 24)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (152cos(---------------) - 152)cos(d x + c) 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sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 7 +--R (2cos(---------------) - 2cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 6 +--R (- 2cos(---------------) + 2cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 5 +--R (- 18cos(---------------) + 18cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 4 +--R (2cos(---------------) - 2cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 3 +--R (48cos(---------------) - 48cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c 2 +--R (16cos(---------------) - 16cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R (- 40cos(---------------) + 40cos(---------------))cos(d x + c) +--R 4 4 +--R + +--R 2d x + %pi + 2c 3 2d x + %pi + 2c +--R - 24cos(---------------) + 24cos(---------------) +--R 4 4 +--R * +--R 2d x + %pi + 2c +--R atanh(cos(---------------)) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (8cos(d x + c) + 8)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 16cos(---------------) + 16)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 16cos(---------------) + 16 +--R 4 +--R * +--R 6 +--R sin(d x + c) +--R + +--R 3 2 2d x + %pi + 2c 2 +--R (- 8cos(d x + c) - 24cos(d x + c) + 16)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (16cos(---------------) - 16)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (48cos(---------------) - 48)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (16cos(---------------) - 16)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 16cos(---------------) + 16 +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 5 4 3 +--R 2cos(d x + c) + 18cos(d x + c) + 16cos(d x + c) +--R + +--R 2 +--R - 80cos(d x + c) - 120cos(d x + c) - 40 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 4cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 36cos(---------------) + 36)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 72cos(---------------) + 72)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (88cos(---------------) - 88)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (224cos(---------------) - 224)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 96cos(---------------) - 96 +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 5 4 +--R - 4cos(d x + c) - 12cos(d x + c) + 56cos(d x + c) +--R + +--R 3 2 +--R 144cos(d x + c) - 80cos(d x + c) - 320cos(d x + c) - 160 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (8cos(---------------) - 8)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (52cos(---------------) - 52)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 4cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 192cos(---------------) + 192)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (48cos(---------------) - 48)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (416cos(---------------) - 416)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 224cos(---------------) - 224 +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 7 6 5 +--R 2cos(d x + c) - 10cos(d x + c) - 48cos(d x + c) +--R + +--R 4 3 +--R 60cos(d x + c) + 256cos(d x + c) - 360cos(d x + c) - 200 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 7 +--R (- 10cos(---------------) + 10)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 42cos(---------------) + 42)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 28cos(---------------) + 28)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (52cos(---------------) - 52)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (16cos(---------------) - 16)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (96cos(---------------) - 96)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (304cos(---------------) - 304)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 176cos(---------------) - 176 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 5 +--R 4cos(d x + c) - 8cos(d x + c) - 52cos(d x + c) +--R + +--R 4 3 2 +--R 24cos(d x + c) + 184cos(d x + c) + 40cos(d x + c) +--R + +--R - 192cos(d x + c) - 112 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 8 +--R (12cos(---------------) - 12)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 7 +--R (44cos(---------------) - 44)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 56cos(---------------) + 56)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 228cos(---------------) + 228)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 28cos(---------------) + 28)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (240cos(---------------) - 240)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (160cos(---------------) - 160)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (80cos(---------------) - 80)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 48cos(---------------) - 48 +--R 4 +--R * +--R sin(d x + c) +--R + +--R 7 6 5 +--R 2cos(d x + c) - 2cos(d x + c) - 18cos(d x + c) +--R + +--R 4 3 2 +--R 2cos(d x + c) + 48cos(d x + c) + 16cos(d x + c) +--R + +--R - 40cos(d x + c) - 24 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 9 +--R (- 6cos(---------------) + 6)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 8 +--R (6cos(---------------) - 6)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 7 +--R (54cos(---------------) - 54)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 6cos(---------------) + 6)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 144cos(---------------) + 144)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 48cos(---------------) + 48)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (120cos(---------------) - 120)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (72cos(---------------) - 72)cos(d x + c) +--R 4 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 2d x + %pi + 2c 2 +--R (32a cos(---------------) - 32a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 32a cos(---------------) - 32a +--R 4 +--R * +--R 6 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 32a cos(---------------) + 32a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 96a cos(---------------) + 96a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 64a cos(---------------) - 64a +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 5 +--R (8a cos(---------------) - 8a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (72a cos(---------------) - 72a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (64a cos(---------------) - 64a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 320a cos(---------------) + 320a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 480a cos(---------------) + 480a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 160a cos(---------------) + 160a +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 16a cos(---------------) + 16a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 48a cos(---------------) + 48a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (224a cos(---------------) - 224a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (576a cos(---------------) - 576a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 320a cos(---------------) + 320a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 1280a cos(---------------) + 1280a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 640a cos(---------------) + 640a +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 7 +--R (8a cos(---------------) - 8a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 40a cos(---------------) + 40a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 192a cos(---------------) + 192a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (240a cos(---------------) - 240a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (1024a cos(---------------) - 1024a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 1440a cos(---------------) + 1440a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 800a cos(---------------) + 800a +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 7 +--R (16a cos(---------------) - 16a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 32a cos(---------------) + 32a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 208a cos(---------------) + 208a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (96a cos(---------------) - 96a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (736a cos(---------------) - 736a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (160a cos(---------------) - 160a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 768a cos(---------------) + 768a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 448a cos(---------------) + 448a +--R 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 7 +--R (8a cos(---------------) - 8a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 8a cos(---------------) + 8a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 72a cos(---------------) + 72a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (8a cos(---------------) - 8a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (192a cos(---------------) - 192a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (64a cos(---------------) - 64a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 160a cos(---------------) + 160a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 96a cos(---------------) + 96a +--R 4 +--R * +--R +------------------+ +------------------+ +--R \|a cos(d x + c) + a \|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 155 + +--S 156 of 520 +t0029:= 1/(a+a*sin(c+d*x))^(5/2) +--R +--R +--R 1 +--R (104) ------------------------------------------------------------- +--R 2 2 2 2 +------------------+ +--R (a sin(d x + c) + 2a sin(d x + c) + a )\|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 520 +r0029:= -1/4*cos(c+d*x)/d/(a+a*sin(c+d*x))^(5/2)-_ + 3/16*cos(c+d*x)/a/d/(a+a*sin(c+d*x))^(3/2)-_ + 3/16*atanh(cos(1/2*c+1/4*%pi+1/2*d*x))*_ + sin(1/2*c+1/4*%pi+1/2*d*x)/a^2/d/(a+a*sin(c+d*x))^(1/2) +--R +--R +--R (105) +--R 2d x + %pi + 2c 2 +--R - 3sin(---------------)sin(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2d x + %pi + 2c +--R - 6sin(---------------)sin(d x + c) - 3sin(---------------) +--R 4 4 +--R * +--R 2d x + %pi + 2c +--R atanh(cos(---------------)) +--R 4 +--R + +--R - 3cos(d x + c)sin(d x + c) - 7cos(d x + c) +--R / +--R 2 2 2 2 +------------------+ +--R (16a d sin(d x + c) + 32a d sin(d x + c) + 16a d)\|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 157 + +--S 158 of 520 +a0029:= integrate(t0029,x) +--R +--R +--R (106) +--R [ +--R +-+ 3 +-+ 2 +-+ +--R 12\|2 cos(d x + c) + 12\|2 cos(d x + c) - 24\|2 cos(d x + c) +--R + +--R +-+ +--R - 24\|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 3\|2 cos(d x + c) - 3\|2 cos(d x + c) + 24\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R 24\|2 cos(d x + c) - 24\|2 cos(d x + c) - 24\|2 +--R * +--R +--+ +--R \|2a +--R * +--R log +--R +-+ +-+ +-+ +--+ +--R (\|2 sin(d x + c) - \|2 cos(d x + c) - \|2 )\|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- a cos(d x + c) - a)sin(d x + c) + 3a cos(d x + c) + 3a +--R / +--R (cos(d x + c) + 1)sin(d x + c) + cos(d x + c) + 1 +--R + +--R 3 2 +--R (- 12cos(d x + c) + 40cos(d x + c) + 80cos(d x + c))sin(d x + c) +--R + +--R 4 3 2 +--R - 12cos(d x + c) - 52cos(d x + c) + 40cos(d x + c) +--R + +--R 80cos(d x + c) +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 3 +-+ 3 3 +-+ 2 +--R 256a d\|2 cos(d x + c) + 256a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 +-+ +--R - 512a d\|2 cos(d x + c) - 512a d\|2 +--R * +--R sin(d x + c) +--R + +--R 3 +-+ 5 3 +-+ 4 +--R - 64a d\|2 cos(d x + c) - 64a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 3 +-+ 2 +--R 512a d\|2 cos(d x + c) + 512a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 +-+ +--R - 512a d\|2 cos(d x + c) - 512a d\|2 +--R , +--R +--R +-+ 3 +-+ 2 +--R - 12\|2 cos(d x + c) - 12\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 24\|2 cos(d x + c) + 24\|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 3\|2 cos(d x + c) + 3\|2 cos(d x + c) - 24\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - 24\|2 cos(d x + c) + 24\|2 cos(d x + c) + 24\|2 +--R * +--R +----+ +--R \|- 2a +--R * +--R atan +--R +-+ +-+ +-+ +----+ +--R (\|2 sin(d x + c) - \|2 cos(d x + c) - \|2 )\|- 2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 4a cos(d x + c) + 4a +--R + +--R 3 2 +--R (- 6cos(d x + c) + 20cos(d x + c) + 40cos(d x + c))sin(d x + c) +--R + +--R 4 3 2 +--R - 6cos(d x + c) - 26cos(d x + c) + 20cos(d x + c) + 40cos(d x + c) +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 3 +-+ 3 3 +-+ 2 +--R 128a d\|2 cos(d x + c) + 128a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 +-+ +--R - 256a d\|2 cos(d x + c) - 256a d\|2 +--R * +--R sin(d x + c) +--R + +--R 3 +-+ 5 3 +-+ 4 +--R - 32a d\|2 cos(d x + c) - 32a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 3 +-+ 2 +--R 256a d\|2 cos(d x + c) + 256a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 +-+ +--R - 256a d\|2 cos(d x + c) - 256a d\|2 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 158 + +--S 159 of 520 +--m0029a:= a0029.1-r0029 +--E 159 + +--S 160 of 520 +--d0029a:= D(m0029a,x) +--E 160 + +--S 161 of 520 +--m0029b:= a0029.2-r0029 +--E 161 + +--S 162 of 520 +--d0029b:= D(m0029b,x) +--E 162 + +--S 163 of 520 +t0030:= 1/(a-a*sin(c+d*x))^(1/2) +--R +--R +--R 1 +--R (107) ----------------------- +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 163 + +--S 164 of 520 +r0030:= 2*atanh(sin(1/2*c+1/4*%pi+1/2*d*x))*_ + cos(1/2*c+1/4*%pi+1/2*d*x)/d/(a-a*sin(c+d*x))^(1/2) +--R +--R +--R 2d x + %pi + 2c 2d x + %pi + 2c +--R 2cos(---------------)atanh(sin(---------------)) +--R 4 4 +--R (108) ------------------------------------------------ +--R +--------------------+ +--R d\|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 164 + +--S 165 of 520 +a0030:= integrate(t0030,x) +--R +--R +--R (109) +--R [ +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +--R (\|2 sin(d x + c) + \|2 cos(d x + c) + \|2 ) |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- cos(d x + c) - 1)sin(d x + c) - 3cos(d x + c) - 3 +--R / +--R (cos(d x + c) + 1)sin(d x + c) - cos(d x + c) - 1 +--R / +--R 2d +--R , +--R +--R - +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R log +--R (cos(d x + c) + 1)sin(d x + c) - cos(d x + c) - 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +--R (\|2 sin(d x + c) + \|2 cos(d x + c) + \|2 ) |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- cos(d x + c) - 1)sin(d x + c) - 3cos(d x + c) - 3 +--R / +--R 2d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 165 + +--S 166 of 520 +m0030a:= a0030.1-r0030 +--R +--R +--R (110) +--R +-+ +--R |2 +--------------------+ +--R |- \|- a sin(d x + c) + a +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +--R (\|2 sin(d x + c) + \|2 cos(d x + c) + \|2 ) |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- cos(d x + c) - 1)sin(d x + c) - 3cos(d x + c) - 3 +--R / +--R (cos(d x + c) + 1)sin(d x + c) - cos(d x + c) - 1 +--R + +--R 2d x + %pi + 2c 2d x + %pi + 2c +--R - 4cos(---------------)atanh(sin(---------------)) +--R 4 4 +--R / +--R +--------------------+ +--R 2d\|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 520 +d0030a:= D(m0030a,x) +--R +--R +--R (111) +--R 2 2d x + %pi + 2c 2 +--R (- 4cos(d x + c) - 4cos(d x + c))sin(---------------) +--R 4 +--R + +--R 2 +--R 4cos(d x + c) + 4cos(d x + c) +--R * +--R +-+ +--R |2 +--------------------+ +--R |- \|- a sin(d x + c) + a +--R \|a +--R + +--R 2d x + %pi + 2c 3 +--R (2cos(d x + c) + 2)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c +--R (- 2cos(d x + c) - 2)sin(---------------) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 3 +--R (4cos(d x + c) + 4)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 2cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c +--R (- 4cos(d x + c) - 4)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 2cos(---------------)cos(d x + c) +--R 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 3 +--R (- 6cos(d x + c) - 6)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 6cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 6cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c +--R (6cos(d x + c) + 6)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 6cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 6cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R atanh(sin(---------------)) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R (2cos(---------------) cos(d x + c) + 2cos(---------------) ) +--R 4 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R (4cos(---------------) cos(d x + c) + 4cos(---------------) ) +--R 4 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R - 6cos(---------------) cos(d x + c) - 6cos(---------------) +--R 4 4 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- \|2 sin(---------------) + \|2 )sin(d x + c) +--R 4 +--R + +--R +-+ +-+ 2d x + %pi + 2c 2 +--R (\|2 cos(d x + c) + 2\|2 )sin(---------------) +--R 4 +--R + +--R +-+ +-+ +--R - \|2 cos(d x + c) - 2\|2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ +-+ 2d x + %pi + 2c 2 +--R (- \|2 cos(d x + c) - \|2 )sin(---------------) +--R 4 +--R + +--R +-+ +-+ +--R \|2 cos(d x + c) + \|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (2\|2 cos(d x + c) + 6\|2 cos(d x + c) + 4\|2 cos(d x + c)) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 2\|2 cos(d x + c) - 6\|2 cos(d x + c) - 4\|2 cos(d x + c) +--R * +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R + +--R +-+ +-+ 2d x + %pi + 2c 3 +--R (- 2a\|2 cos(d x + c) - 2a\|2 )sin(---------------) +--R 4 +--R + +--R +-+ +-+ 2d x + %pi + 2c +--R (2a\|2 cos(d x + c) + 2a\|2 )sin(---------------) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2 +-+ 2d x + %pi + 2c 3 +--R (- 2a\|2 cos(d x + c) - 2a\|2 cos(d x + c))sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2 +-+ 2d x + %pi + 2c +--R (2a\|2 cos(d x + c) + 2a\|2 cos(d x + c))sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R (2a\|2 cos(d x + c) + 4a\|2 cos(d x + c) + 2a\|2 ) +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R (- 2a\|2 cos(d x + c) - 4a\|2 cos(d x + c) - 2a\|2 ) +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R +-+ +--R |2 2d x + %pi + 2c +--R |- atanh(sin(---------------)) +--R \|a 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 2a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 2a\|2 cos(---------------) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 2 +--R - 2a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 2a\|2 cos(---------------) cos(d x + c) +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 2 +--R 2a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2d x + %pi + 2c 2 +--R 4a\|2 cos(---------------) cos(d x + c) + 2a\|2 cos(---------------) +--R 4 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 2d x + %pi + 2c 2 +--R ((2cos(d x + c) + 2)sin(---------------) - 2cos(d x + c) - 2) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 +--R ((4cos(d x + c) + 4)sin(---------------) - 4cos(d x + c) - 4) +--R 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 +--R (- 6cos(d x + c) - 6)sin(---------------) + 6cos(d x + c) + 6 +--R 4 +--R * +--R +--------------------+ +------------------+ +--R \|- a sin(d x + c) + a \|a cos(d x + c) + a +--R + +--R +-+ +-+ 2d x + %pi + 2c 2 +--R (- 2a\|2 cos(d x + c) - 2a\|2 )sin(---------------) +--R 4 +--R + +--R +-+ +-+ +--R 2a\|2 cos(d x + c) + 2a\|2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2 +-+ 2d x + %pi + 2c 2 +--R (- 2a\|2 cos(d x + c) - 2a\|2 cos(d x + c))sin(---------------) +--R 4 +--R + +--R +-+ 2 +-+ +--R 2a\|2 cos(d x + c) + 2a\|2 cos(d x + c) +--R * +--R sin(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R (2a\|2 cos(d x + c) + 4a\|2 cos(d x + c) + 2a\|2 ) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R - 2a\|2 cos(d x + c) - 4a\|2 cos(d x + c) - 2a\|2 +--R * +--R +-+ +--R |2 +--------------------+ +--R |- \|- a sin(d x + c) + a +--R \|a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 520 +m0030b:= a0030.2-r0030 +--R +--R +--R (112) +--R - +--R +-+ +--R |2 +--------------------+ +--R |- \|- a sin(d x + c) + a +--R \|a +--R * +--R log +--R (cos(d x + c) + 1)sin(d x + c) - cos(d x + c) - 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +--R (\|2 sin(d x + c) + \|2 cos(d x + c) + \|2 ) |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- cos(d x + c) - 1)sin(d x + c) - 3cos(d x + c) - 3 +--R + +--R 2d x + %pi + 2c 2d x + %pi + 2c +--R - 4cos(---------------)atanh(sin(---------------)) +--R 4 4 +--R / +--R +--------------------+ +--R 2d\|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 168 + +--S 169 of 520 +d0030b:= D(m0030b,x) +--R +--R +--R (113) +--R 2d x + %pi + 2c 2 4 +--R (2sin(---------------) - 2)sin(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 2sin(---------------) + 2)sin(d x + c) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 +--R (- 2cos(d x + c) - 4cos(d x + c) - 2)sin(---------------) +--R 4 +--R + +--R 2 +--R 2cos(d x + c) + 4cos(d x + c) + 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 +--R (- 8cos(d x + c) - 18cos(d x + c) - 8cos(d x + c) + 2) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 3 2 +--R 8cos(d x + c) + 18cos(d x + c) + 8cos(d x + c) - 2 +--R * +--R sin(d x + c) +--R + +--R 4 3 2 +--R - 4cos(d x + c) - 28cos(d x + c) - 44cos(d x + c) +--R + +--R - 20cos(d x + c) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 4 3 2 +--R 4cos(d x + c) + 28cos(d x + c) + 44cos(d x + c) + 20cos(d x + c) +--R * +--R +-+ +--R |2 +--------------------+ +--R |- \|- a sin(d x + c) + a +--R \|a +--R + +--R 2 2d x + %pi + 2c 3 +--R (2cos(d x + c) + 12cos(d x + c) + 10)sin(---------------) +--R 4 +--R + +--R 2 2d x + %pi + 2c +--R (- 2cos(d x + c) - 12cos(d x + c) - 10)sin(---------------) +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 2d x + %pi + 2c 3 +--R (26cos(d x + c) + 44cos(d x + c) + 18)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 12cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 10cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2 2d x + %pi + 2c +--R (- 26cos(d x + c) - 44cos(d x + c) - 18)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 12cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 10cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 +--R (8cos(d x + c) + 14cos(d x + c) + 4cos(d x + c) - 2) +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 28cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 56cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 28cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 3 2 +--R (- 8cos(d x + c) - 14cos(d x + c) - 4cos(d x + c) + 2) +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 28cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 56cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 28cos(---------------)cos(d x + c) +--R 4 +--R * +--R sin(d x + c) +--R + +--R 3 2 +--R (- 8cos(d x + c) - 42cos(d x + c) - 60cos(d x + c) - 26) +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R 8cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 42cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 60cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 26cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 3 2 +--R (8cos(d x + c) + 42cos(d x + c) + 60cos(d x + c) + 26) +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R - 8cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 42cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 60cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 26cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R atanh(sin(---------------)) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R 2cos(---------------) cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R 12cos(---------------) cos(d x + c) + 10cos(---------------) +--R 4 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 2 +--R 26cos(---------------) cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R 44cos(---------------) cos(d x + c) + 18cos(---------------) +--R 4 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 3 +--R 8cos(---------------) cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R 14cos(---------------) cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R 4cos(---------------) cos(d x + c) - 2cos(---------------) +--R 4 4 +--R * +--R sin(d x + c) +--R + +--R 2d x + %pi + 2c 2 3 +--R - 8cos(---------------) cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R - 42cos(---------------) cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R - 60cos(---------------) cos(d x + c) - 26cos(---------------) +--R 4 4 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R +-+ +-+ 2d x + %pi + 2c 2 +--R (- \|2 cos(d x + c) - \|2 )sin(---------------) +--R 4 +--R + +--R +-+ +-+ +--R \|2 cos(d x + c) + \|2 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 2 +-+ 2d x + %pi + 2c 2 +--R (\|2 cos(d x + c) - \|2 )sin(---------------) +--R 4 +--R + +--R +-+ 2 +-+ +--R - \|2 cos(d x + c) + \|2 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R (2\|2 cos(d x + c) + 7\|2 cos(d x + c) + 5\|2 ) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R - 2\|2 cos(d x + c) - 7\|2 cos(d x + c) - 5\|2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R 2\|2 cos(d x + c) + 16\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R 23\|2 cos(d x + c) + 6\|2 cos(d x + c) - 3\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 2\|2 cos(d x + c) - 16\|2 cos(d x + c) - 23\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 6\|2 cos(d x + c) + 3\|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 14\|2 cos(d x + c) + 48\|2 cos(d x + c) + 54\|2 cos(d x + c) +--R + +--R +-+ +--R 20\|2 cos(d x + c) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 14\|2 cos(d x + c) - 48\|2 cos(d x + c) - 54\|2 cos(d x + c) +--R + +--R +-+ +--R - 20\|2 cos(d x + c) +--R * +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R + +--R +-+ 2 +-+ +-+ +--R (- 4a\|2 cos(d x + c) - 8a\|2 cos(d x + c) - 4a\|2 ) +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R (4a\|2 cos(d x + c) + 8a\|2 cos(d x + c) + 4a\|2 ) +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 4a\|2 cos(d x + c) - 20a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 28a\|2 cos(d x + c) - 12a\|2 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 8a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +--R 4a\|2 cos(d x + c) + 20a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 28a\|2 cos(d x + c) + 12a\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 8a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (- 8a\|2 cos(d x + c) - 12a\|2 cos(d x + c) + 4a\|2 ) +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 4 +--R - 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 24a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 36a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 16a\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R (8a\|2 cos(d x + c) + 12a\|2 cos(d x + c) - 4a\|2 ) +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 4 +--R 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R 24a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 36a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 16a\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 12a\|2 cos(d x + c) + 36a\|2 cos(d x + c) + 36a\|2 cos(d x + c) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 4 +--R - 12a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 36a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 36a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 12a\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +--R - 12a\|2 cos(d x + c) - 36a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 36a\|2 cos(d x + c) - 12a\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 4 +--R 12a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R 36a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 36a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 12a\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R +-+ +--R |2 2d x + %pi + 2c +--R |- atanh(sin(---------------)) +--R \|a 4 +--R + +--R +-+ 2d x + %pi + 2c 2 2 +--R - 4a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 8a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 4a\|2 cos(---------------) +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 3 +--R - 4a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 2 +--R - 20a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 28a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 12a\|2 cos(---------------) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 3 +--R - 8a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 2 +--R - 12a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 4a\|2 cos(---------------) +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 3 +--R 12a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 2 +--R 36a\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2d x + %pi + 2c 2 +--R 36a\|2 cos(---------------) cos(d x + c) + 12a\|2 cos(---------------) +--R 4 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R / +--R 2 2d x + %pi + 2c 2 +--R (2cos(d x + c) + 12cos(d x + c) + 10)sin(---------------) +--R 4 +--R + +--R 2 +--R - 2cos(d x + c) - 12cos(d x + c) - 10 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 2d x + %pi + 2c 2 +--R (26cos(d x + c) + 44cos(d x + c) + 18)sin(---------------) +--R 4 +--R + +--R 2 +--R - 26cos(d x + c) - 44cos(d x + c) - 18 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 +--R (8cos(d x + c) + 14cos(d x + c) + 4cos(d x + c) - 2) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 3 2 +--R - 8cos(d x + c) - 14cos(d x + c) - 4cos(d x + c) + 2 +--R * +--R sin(d x + c) +--R + +--R 3 2 +--R (- 8cos(d x + c) - 42cos(d x + c) - 60cos(d x + c) - 26) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 3 2 +--R 8cos(d x + c) + 42cos(d x + c) + 60cos(d x + c) + 26 +--R * +--R +--------------------+ +------------------+ +--R \|- a sin(d x + c) + a \|a cos(d x + c) + a +--R + +--R +-+ 2 +-+ +-+ +--R (- 4a\|2 cos(d x + c) - 8a\|2 cos(d x + c) - 4a\|2 ) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R 4a\|2 cos(d x + c) + 8a\|2 cos(d x + c) + 4a\|2 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 4a\|2 cos(d x + c) - 20a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 28a\|2 cos(d x + c) - 12a\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R 4a\|2 cos(d x + c) + 20a\|2 cos(d x + c) + 28a\|2 cos(d x + c) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (- 8a\|2 cos(d x + c) - 12a\|2 cos(d x + c) + 4a\|2 ) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(d x + c) + 12a\|2 cos(d x + c) - 4a\|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 12a\|2 cos(d x + c) + 36a\|2 cos(d x + c) + 36a\|2 cos(d x + c) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 12a\|2 cos(d x + c) - 36a\|2 cos(d x + c) - 36a\|2 cos(d x + c) +--R + +--R +-+ +--R - 12a\|2 +--R * +--R +-+ +--R |2 +--------------------+ +--R |- \|- a sin(d x + c) + a +--R \|a +--R Type: Expression(Integer) +--E 169 + +--S 170 of 520 +t0031:= 1/(a-a*sin(c+d*x))^(3/2) +--R +--R +--R 1 +--R (114) - ------------------------------------------- +--R +--------------------+ +--R (a sin(d x + c) - a)\|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 170 + +--S 171 of 520 +r0031:= 1/2*cos(c+d*x)/d/(a-a*sin(c+d*x))^(3/2)+_ + 1/2*atanh(sin(1/2*c+1/4*%pi+1/2*d*x))*_ + cos(1/2*c+1/4*%pi+1/2*d*x)/a/d/(a-a*sin(c+d*x))^(1/2) +--R +--R +--R (115) +--R 2d x + %pi + 2c 2d x + %pi + 2c +--R (cos(---------------)sin(d x + c) - cos(---------------)) +--R 4 4 +--R * +--R 2d x + %pi + 2c +--R atanh(sin(---------------)) +--R 4 +--R + +--R - cos(d x + c) +--R / +--R +--------------------+ +--R (2a d sin(d x + c) - 2a d)\|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 520 +a0031:= integrate(t0031,x) +--R +--R +--R (116) +--R [ +--R +-+ +-+ +-+ 3 +--R (2\|2 cos(d x + c) + 2\|2 )sin(d x + c) + \|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R \|2 cos(d x + c) - 2\|2 cos(d x + c) - 2\|2 +--R * +--R +--+ +--R \|2a +--R * +--R log +--R +-+ +-+ +-+ +--+ +--R (\|2 sin(d x + c) + \|2 cos(d x + c) + \|2 )\|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- a cos(d x + c) - a)sin(d x + c) - 3a cos(d x + c) - 3a +--R / +--R (cos(d x + c) + 1)sin(d x + c) - cos(d x + c) - 1 +--R + +--R 2 +--R (- 4cos(d x + c)sin(d x + c) + 4cos(d x + c) + 4cos(d x + c)) +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 2 +-+ 2 +-+ 2 +-+ 3 +--R (16a d\|2 cos(d x + c) + 16a d\|2 )sin(d x + c) + 8a d\|2 cos(d x + c) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 8a d\|2 cos(d x + c) - 16a d\|2 cos(d x + c) - 16a d\|2 +--R , +--R +--R +-+ +-+ +-+ 3 +--R (2\|2 cos(d x + c) + 2\|2 )sin(d x + c) + \|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R \|2 cos(d x + c) - 2\|2 cos(d x + c) - 2\|2 +--R * +--R +----+ +--R \|- 2a +--R * +--R atan +--R +-+ +-+ +-+ +----+ +--R (\|2 sin(d x + c) + \|2 cos(d x + c) + \|2 )\|- 2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 4a cos(d x + c) + 4a +--R + +--R 2 +--R (- 2cos(d x + c)sin(d x + c) + 2cos(d x + c) + 2cos(d x + c)) +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 2 +-+ 2 +-+ 2 +-+ 3 +--R (8a d\|2 cos(d x + c) + 8a d\|2 )sin(d x + c) + 4a d\|2 cos(d x + c) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 4a d\|2 cos(d x + c) - 8a d\|2 cos(d x + c) - 8a d\|2 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 172 + +--S 173 of 520 +m0031a:= a0031.1-r0031 +--R +--R +--R (117) +--R +-+ +-+ 2 +--R (2\|2 cos(d x + c) + 2\|2 )sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (\|2 cos(d x + c) + \|2 cos(d x + c) - 4\|2 cos(d x + c) - 4\|2 ) +--R * +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - \|2 cos(d x + c) - \|2 cos(d x + c) + 2\|2 cos(d x + c) + 2\|2 +--R * +--R +--+ +--------------------+ +--R \|2a \|- a sin(d x + c) + a +--R * +--R log +--R +-+ +-+ +-+ +--+ +--R (\|2 sin(d x + c) + \|2 cos(d x + c) + \|2 )\|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- a cos(d x + c) - a)sin(d x + c) - 3a cos(d x + c) - 3a +--R / +--R (cos(d x + c) + 1)sin(d x + c) - cos(d x + c) - 1 +--R + +--R 2 +--R - 4cos(d x + c)sin(d x + c) +--R + +--R 2 2 +--R (4cos(d x + c) + 8cos(d x + c))sin(d x + c) - 4cos(d x + c) +--R + +--R - 4cos(d x + c) +--R * +--R +--------------------+ +------------------+ +--R \|- a sin(d x + c) + a \|a cos(d x + c) + a +--R + +--R +-+ 2d x + %pi + 2c +--R - 8a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 8a\|2 cos(---------------) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 16a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 16a\|2 cos(---------------) +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +-+ 2d x + %pi + 2c +--R - 8a\|2 cos(---------------)cos(d x + c) - 8a\|2 cos(---------------) +--R 4 4 +--R * +--R 2d x + %pi + 2c +--R atanh(sin(---------------)) +--R 4 +--R + +--R +-+ 2 +-+ +--R (8a\|2 cos(d x + c) + 8a\|2 cos(d x + c))sin(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 4a\|2 cos(d x + c) + 4a\|2 cos(d x + c) - 8a\|2 cos(d x + c) +--R + +--R +-+ +--R - 8a\|2 cos(d x + c) +--R / +--R 2 +-+ 2 +-+ 2 +--R (16a d\|2 cos(d x + c) + 16a d\|2 )sin(d x + c) +--R + +--R 2 +-+ 3 2 +-+ 2 +--R 8a d\|2 cos(d x + c) + 8a d\|2 cos(d x + c) +--R + +--R 2 +-+ 2 +-+ +--R - 32a d\|2 cos(d x + c) - 32a d\|2 +--R * +--R sin(d x + c) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 8a d\|2 cos(d x + c) - 8a d\|2 cos(d x + c) + 16a d\|2 cos(d x + c) +--R + +--R 2 +-+ +--R 16a d\|2 +--R * +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 173 + +--S 174 of 520 +d0031a:= D(m0031a,x) +--R +--R +--R (118) +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 2\|2 cos(d x + c)sin(---------------) + 2\|2 cos(d x + c)) +--R 4 +--R * +--R 6 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 3\|2 cos(d x + c) + 12\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 6\|2 cos(d x + c) - 16\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +--R - 3\|2 cos(d x + c) - 12\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 6\|2 cos(d x + c) + 16\|2 +--R * +--R 5 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 4\|2 cos(d x + c) - 16\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 28\|2 cos(d x + c) + 64\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R 4\|2 cos(d x + c) + 16\|2 cos(d x + c) - 28\|2 cos(d x + c) +--R + +--R +-+ +--R - 64\|2 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +--R \|2 cos(d x + c) + 2\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 10\|2 cos(d x + c) - 48\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 116\|2 cos(d x + c) - 96\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 5 +-+ 4 +--R - \|2 cos(d x + c) - 2\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 10\|2 cos(d x + c) + 48\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 116\|2 cos(d x + c) + 96\|2 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +--R - 4\|2 cos(d x + c) - 10\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 24\|2 cos(d x + c) + 120\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 150\|2 cos(d x + c) + 64\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 5 +-+ 4 +--R 4\|2 cos(d x + c) + 10\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 24\|2 cos(d x + c) - 120\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 150\|2 cos(d x + c) - 64\|2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 7 +-+ 6 +--R - 2\|2 cos(d x + c) - 6\|2 cos(d x + c) +--R + +--R +-+ 5 +-+ 4 +--R \|2 cos(d x + c) + 14\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 17\|2 cos(d x + c) - 92\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 82\|2 cos(d x + c) - 16\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2\|2 cos(d x + c) + 6\|2 cos(d x + c) - \|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R - 14\|2 cos(d x + c) + 17\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R 92\|2 cos(d x + c) + 82\|2 cos(d x + c) + 16\|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2\|2 cos(d x + c) + 6\|2 cos(d x + c) + 2\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R - 6\|2 cos(d x + c) + 4\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +--R 24\|2 cos(d x + c) + 16\|2 cos(d x + c) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2\|2 cos(d x + c) - 6\|2 cos(d x + c) - 2\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 6\|2 cos(d x + c) - 4\|2 cos(d x + c) - 24\|2 cos(d x + c) +--R + +--R +-+ +--R - 16\|2 cos(d x + c) +--R * +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R + +--R +-+ +-+ 2d x + %pi + 2c 3 +--R (8\|2 cos(d x + c) + 8\|2 )sin(---------------) +--R 4 +--R + +--R +-+ +-+ 2d x + %pi + 2c +--R (- 8\|2 cos(d x + c) - 8\|2 )sin(---------------) +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 8\|2 cos(d x + c) + 16\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 16\|2 cos(d x + c) - 24\|2 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 8\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 8\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +--R - 8\|2 cos(d x + c) - 16\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 16\|2 cos(d x + c) + 24\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 8\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 8\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +--R 2\|2 cos(d x + c) + 10\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 8\|2 cos(d x + c) - 48\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 16\|2 cos(d x + c) + 16\|2 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 4 +--R 8\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 8\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 5 +-+ 4 +--R - 2\|2 cos(d x + c) - 10\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 8\|2 cos(d x + c) + 48\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 16\|2 cos(d x + c) - 16\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 4 +--R - 8\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 8\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 4 +--R 2\|2 cos(d x + c) - 26\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 24\|2 cos(d x + c) + 48\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 64\|2 cos(d x + c) + 16\|2 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 6 +--R 2\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 5 +--R 10\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 32\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 24\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 6 +-+ 4 +--R - 2\|2 cos(d x + c) + 26\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 24\|2 cos(d x + c) - 48\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 64\|2 cos(d x + c) - 16\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 6 +--R - 2\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 5 +--R - 10\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R 32\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 24\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 5 +--R - 4\|2 cos(d x + c) - 6\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R 22\|2 cos(d x + c) + 40\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - 16\|2 cos(d x + c) - 56\|2 cos(d x + c) - 24\|2 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 7 +--R 2\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 6 +--R 2\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 5 +--R - 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 4 +--R - 24\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 40\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 6 +-+ 5 +--R 4\|2 cos(d x + c) + 6\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R - 22\|2 cos(d x + c) - 40\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R 16\|2 cos(d x + c) + 56\|2 cos(d x + c) + 24\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 7 +--R - 2\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 6 +--R - 2\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 5 +--R 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 4 +--R 24\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 40\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 2\|2 cos(d x + c) + 4\|2 cos(d x + c) - 6\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ +-+ +--R - 16\|2 cos(d x + c) + 16\|2 cos(d x + c) + 8\|2 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 7 +--R - 2\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 6 +--R - 4\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 5 +--R 6\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 4 +--R 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 8\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 6 +-+ 5 +--R - 2\|2 cos(d x + c) - 4\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ +--R 6\|2 cos(d x + c) + 16\|2 cos(d x + c) - 16\|2 cos(d x + c) +--R + +--R +-+ +--R - 8\|2 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 7 +--R 2\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 6 +--R 4\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 5 +--R - 6\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 4 +--R - 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 16\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R 8\|2 cos(---------------)cos(d x + c) +--R 4 +--R * +--R +--+ 2d x + %pi + 2c +--R \|2a atanh(sin(---------------)) +--R 4 +--R + +--R +-+ +-+ 2d x + %pi + 2c 2 +--R (- 16\|2 cos(d x + c) - 16\|2 )sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (8\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 8\|2 cos(---------------) + 16\|2 +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 16\|2 cos(d x + c) - 32\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 16\|2 cos(d x + c) + 32\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (8\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (16\|2 cos(---------------) + 32\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 16\|2 cos(---------------) - 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 24\|2 cos(---------------) - 32\|2 +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +--R - 4\|2 cos(d x + c) - 20\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 24\|2 cos(d x + c) + 40\|2 cos(d x + c) +--R + +--R +-+ +--R 48\|2 cos(d x + c) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (2\|2 cos(---------------) + 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (10\|2 cos(---------------) + 20\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 8\|2 cos(---------------) + 24\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 48\|2 cos(---------------) - 40\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 16\|2 cos(---------------) - 48\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 16\|2 cos(---------------) +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 5 +--R - 4\|2 cos(d x + c) - 28\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R - 16\|2 cos(d x + c) + 48\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - 8\|2 cos(d x + c) - 80\|2 cos(d x + c) - 32\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (2\|2 cos(---------------) + 4\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 5 +--R 28\|2 cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (- 26\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 24\|2 cos(---------------) - 48\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (48\|2 cos(---------------) + 8\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (64\|2 cos(---------------) + 80\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R 16\|2 cos(---------------) + 32\|2 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 7 +-+ 6 +--R - 6\|2 cos(d x + c) - 26\|2 cos(d x + c) +--R + +--R +-+ 5 +-+ 4 +--R - 16\|2 cos(d x + c) + 36\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 40\|2 cos(d x + c) + 24\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 32\|2 cos(d x + c) + 16\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 7 +--R 6\|2 cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (- 4\|2 cos(---------------) + 26\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (- 6\|2 cos(---------------) + 16\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 4 +--R (22\|2 cos(---------------) - 36\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (40\|2 cos(---------------) - 40\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 2 +--R (- 16\|2 cos(---------------) - 24\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R (- 56\|2 cos(---------------) - 32\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ +--R - 24\|2 cos(---------------) - 16\|2 +--R 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 8 +-+ 7 +--R - 6\|2 cos(d x + c) - 12\|2 cos(d x + c) +--R + +--R +-+ 6 +-+ 5 +--R 18\|2 cos(d x + c) + 48\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 48\|2 cos(d x + c) - 24\|2 cos(d x + c) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 8 +-+ 7 +--R 6\|2 cos(d x + c) + 12\|2 cos(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 6 +--R (2\|2 cos(---------------) - 18\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 5 +--R (4\|2 cos(---------------) - 48\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 4 +--R - 6\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +-+ 3 +--R (- 16\|2 cos(---------------) + 48\|2 )cos(d x + c) +--R 4 +--R + +--R +-+ 2 +-+ 2d x + %pi + 2c 2 +--R 24\|2 cos(d x + c) + 16\|2 cos(---------------) cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 8\|2 cos(---------------) +--R 4 +--R * +--R +--+ +--R \|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 2d x + %pi + 2c 2 +--R ((4cos(d x + c) + 8)sin(---------------) - 4cos(d x + c) - 8) +--R 4 +--R * +--R 6 +--R sin(d x + c) +--R + +--R 3 2 +--R (- 6cos(d x + c) - 12cos(d x + c) - 20cos(d x + c) - 24) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 3 2 +--R 6cos(d x + c) + 12cos(d x + c) + 20cos(d x + c) + 24 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 4 3 +--R (- 4cos(d x + c) - 4cos(d x + c) + 8cos(d x + c) + 16) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 4 3 +--R 4cos(d x + c) + 4cos(d x + c) - 8cos(d x + c) - 16 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 5 4 3 +--R - 2cos(d x + c) + 4cos(d x + c) + 56cos(d x + c) +--R + +--R 2 +--R 104cos(d x + c) + 72cos(d x + c) + 16 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 5 4 3 +--R 2cos(d x + c) - 4cos(d x + c) - 56cos(d x + c) +--R + +--R 2 +--R - 104cos(d x + c) - 72cos(d x + c) - 16 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 5 4 +--R - 4cos(d x + c) + 4cos(d x + c) + 16cos(d x + c) +--R + +--R 3 2 +--R - 84cos(d x + c) - 192cos(d x + c) - 124cos(d x + c) - 24 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 6 5 4 +--R 4cos(d x + c) - 4cos(d x + c) - 16cos(d x + c) +--R + +--R 3 2 +--R 84cos(d x + c) + 192cos(d x + c) + 124cos(d x + c) + 24 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 5 +--R 4cos(d x + c) + 16cos(d x + c) + 2cos(d x + c) +--R + +--R 4 3 2 +--R - 28cos(d x + c) + 46cos(d x + c) + 132cos(d x + c) +--R + +--R 76cos(d x + c) + 8 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 7 6 5 +--R - 4cos(d x + c) - 16cos(d x + c) - 2cos(d x + c) +--R + +--R 4 3 2 +--R 28cos(d x + c) - 46cos(d x + c) - 132cos(d x + c) +--R + +--R - 76cos(d x + c) - 8 +--R * +--R sin(d x + c) +--R + +--R 7 6 5 +--R - 4cos(d x + c) - 12cos(d x + c) - 4cos(d x + c) +--R + +--R 4 3 2 +--R 12cos(d x + c) - 8cos(d x + c) - 32cos(d x + c) - 16cos(d x + c) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 7 6 5 4 +--R 4cos(d x + c) + 12cos(d x + c) + 4cos(d x + c) - 12cos(d x + c) +--R + +--R 3 2 +--R 8cos(d x + c) + 32cos(d x + c) + 16cos(d x + c) +--R * +--R +--+ +--------------------+ +--R \|2a \|- a sin(d x + c) + a +--R + +--R 2 2d x + %pi + 2c 3 +--R (- 8a cos(d x + c) - 16a cos(d x + c) - 8a)sin(---------------) +--R 4 +--R + +--R 2 2d x + %pi + 2c +--R (8a cos(d x + c) + 16a cos(d x + c) + 8a)sin(---------------) +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 4 3 +--R - 8a cos(d x + c) - 16a cos(d x + c) + 16a cos(d x + c) +--R + +--R 8a +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 8a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 16a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 8a cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 4 3 +--R (8a cos(d x + c) + 16a cos(d x + c) - 16a cos(d x + c) - 8a) +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 8a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 16a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 8a cos(---------------)cos(d x + c) +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 5 4 +--R - 2a cos(d x + c) - 4a cos(d x + c) - 2a cos(d x + c) +--R + +--R 2 +--R 48a cos(d x + c) + 96a cos(d x + c) + 48a +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R - 8a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R - 16a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 8a cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 6 5 4 +--R 2a cos(d x + c) + 4a cos(d x + c) + 2a cos(d x + c) +--R + +--R 2 +--R - 48a cos(d x + c) - 96a cos(d x + c) - 48a +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R 8a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R 16a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 8a cos(---------------)cos(d x + c) +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 5 4 +--R - 2a cos(d x + c) - 4a cos(d x + c) + 46a cos(d x + c) +--R + +--R 3 2 +--R 96a cos(d x + c) - 64a cos(d x + c) - 224a cos(d x + c) +--R + +--R - 112a +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R - 2a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R - 4a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R - 10a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R - 16a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 40a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 96a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 48a cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 6 5 4 +--R 2a cos(d x + c) + 4a cos(d x + c) - 46a cos(d x + c) +--R + +--R 3 2 +--R - 96a cos(d x + c) + 64a cos(d x + c) + 224a cos(d x + c) +--R + +--R 112a +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R 2a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R 4a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R 10a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R 16a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 40a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 96a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 48a cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 5 4 +--R 10a cos(d x + c) + 20a cos(d x + c) - 54a cos(d x + c) +--R + +--R 3 2 +--R - 128a cos(d x + c) + 24a cos(d x + c) + 176a cos(d x + c) +--R + +--R 88a +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R - 4a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R - 8a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R 36a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R 80a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 24a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 128a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 64a cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 6 5 4 +--R - 10a cos(d x + c) - 20a cos(d x + c) + 54a cos(d x + c) +--R + +--R 3 2 +--R 128a cos(d x + c) - 24a cos(d x + c) - 176a cos(d x + c) +--R + +--R - 88a +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R 4a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R 8a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R - 36a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R - 80a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 24a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 128a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 64a cos(---------------)cos(d x + c) +--R 4 +--R * +--R sin(d x + c) +--R + +--R 6 5 4 +--R - 6a cos(d x + c) - 12a cos(d x + c) + 18a cos(d x + c) +--R + +--R 3 +--R 48a cos(d x + c) - 48a cos(d x + c) - 24a +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R 6a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R 12a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R - 18a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R - 48a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 48a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 24a cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 6 5 4 +--R 6a cos(d x + c) + 12a cos(d x + c) - 18a cos(d x + c) +--R + +--R 3 +--R - 48a cos(d x + c) + 48a cos(d x + c) + 24a +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R - 6a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R - 12a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R 18a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R 48a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 48a cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 24a cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R atanh(sin(---------------)) +--R 4 +--R + +--R 2 2d x + %pi + 2c 2 +--R (16a cos(d x + c) + 32a cos(d x + c) + 16a)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 8a cos(---------------) - 16a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 16a cos(---------------) - 32a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 8a cos(---------------) - 16a +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 4 3 2 +--R (16a cos(d x + c) + 32a cos(d x + c) + 16a cos(d x + c) ) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 8a cos(---------------) - 16a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 2 +--R (- 16a cos(---------------) - 32a)cos(d x + c) - 16a cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R 16a cos(---------------) cos(d x + c) + 8a cos(---------------) +--R 4 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 5 4 +--R 4a cos(d x + c) + 8a cos(d x + c) + 44a cos(d x + c) +--R + +--R 3 2 +--R 80a cos(d x + c) - 56a cos(d x + c) - 192a cos(d x + c) - 96a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 2a cos(---------------) - 4a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 4a cos(---------------) - 8a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 3 +--R (- 2a cos(---------------) - 44a)cos(d x + c) - 80a cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (48a cos(---------------) + 56a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (96a cos(---------------) + 192a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 48a cos(---------------) + 96a +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 5 4 +--R 32a cos(d x + c) + 64a cos(d x + c) - 24a cos(d x + c) +--R + +--R 3 2 +--R - 112a cos(d x + c) + 72a cos(d x + c) + 256a cos(d x + c) + 128a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 2a cos(---------------) - 32a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 4a cos(---------------) - 64a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (46a cos(---------------) + 24a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (96a cos(---------------) + 112a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 64a cos(---------------) - 72a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 224a cos(---------------) - 256a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 112a cos(---------------) - 128a +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 7 6 +--R 6a cos(d x + c) + 12a cos(d x + c) + 42a cos(d x + c) +--R + +--R 5 4 3 +--R 72a cos(d x + c) - 36a cos(d x + c) - 144a cos(d x + c) +--R + +--R 2 +--R - 120a cos(d x + c) - 96a cos(d x + c) - 48a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 8 7 +--R - 6a cos(d x + c) - 12a cos(d x + c) +--R + +--R 2d x + %pi + 2c 2 6 +--R (10a cos(---------------) - 42a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (20a cos(---------------) - 72a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 54a cos(---------------) + 36a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 128a cos(---------------) + 144a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (24a cos(---------------) + 120a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (176a cos(---------------) + 96a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 88a cos(---------------) + 48a +--R 4 +--R * +--R sin(d x + c) +--R + +--R 8 7 6 +--R 18a cos(d x + c) + 36a cos(d x + c) - 54a cos(d x + c) +--R + +--R 5 3 2 +--R - 144a cos(d x + c) + 144a cos(d x + c) + 72a cos(d x + c) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 8 7 +--R - 18a cos(d x + c) - 36a cos(d x + c) +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 6a cos(---------------) + 54a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 12a cos(---------------) + 144a)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R 18a cos(---------------) cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 2 +--R (48a cos(---------------) - 144a)cos(d x + c) - 72a cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R - 48a cos(---------------) cos(d x + c) - 24a cos(---------------) +--R 4 4 +--R / +--R +-+ +-+ 2d x + %pi + 2c 2 +--R (32a\|2 cos(d x + c) + 32a\|2 )sin(---------------) +--R 4 +--R + +--R +-+ +-+ +--R - 32a\|2 cos(d x + c) - 32a\|2 +--R * +--R 5 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 32a\|2 cos(d x + c) + 64a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 64a\|2 cos(d x + c) - 96a\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +--R - 32a\|2 cos(d x + c) - 64a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 64a\|2 cos(d x + c) + 96a\|2 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +--R 8a\|2 cos(d x + c) + 40a\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 32a\|2 cos(d x + c) - 192a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 64a\|2 cos(d x + c) + 64a\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 5 +-+ 4 +--R - 8a\|2 cos(d x + c) - 40a\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 32a\|2 cos(d x + c) + 192a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 64a\|2 cos(d x + c) - 64a\|2 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 4 +--R 8a\|2 cos(d x + c) - 104a\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 96a\|2 cos(d x + c) + 192a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 256a\|2 cos(d x + c) + 64a\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 6 +-+ 4 +--R - 8a\|2 cos(d x + c) + 104a\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 96a\|2 cos(d x + c) - 192a\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 256a\|2 cos(d x + c) - 64a\|2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 5 +--R - 16a\|2 cos(d x + c) - 24a\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R 88a\|2 cos(d x + c) + 160a\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - 64a\|2 cos(d x + c) - 224a\|2 cos(d x + c) - 96a\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 6 +-+ 5 +--R 16a\|2 cos(d x + c) + 24a\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R - 88a\|2 cos(d x + c) - 160a\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R 64a\|2 cos(d x + c) + 224a\|2 cos(d x + c) + 96a\|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(d x + c) + 16a\|2 cos(d x + c) - 24a\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ +-+ +--R - 64a\|2 cos(d x + c) + 64a\|2 cos(d x + c) + 32a\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(d x + c) - 16a\|2 cos(d x + c) + 24a\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ +-+ +--R 64a\|2 cos(d x + c) - 64a\|2 cos(d x + c) - 32a\|2 +--R * +--R +--+ +--------------------+ +------------------+ +--R \|2a \|- a sin(d x + c) + a \|a cos(d x + c) + a +--R + +--R 2 2 2 2 +--R (- 32a cos(d x + c) - 64a cos(d x + c) - 32a ) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2 2 2 2 +--R 32a cos(d x + c) + 64a cos(d x + c) + 32a +--R * +--R 5 +--R sin(d x + c) +--R + +--R 2 4 2 3 2 +--R - 32a cos(d x + c) - 64a cos(d x + c) + 64a cos(d x + c) +--R + +--R 2 +--R 32a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2 4 2 3 2 2 +--R 32a cos(d x + c) + 64a cos(d x + c) - 64a cos(d x + c) - 32a +--R * +--R 4 +--R sin(d x + c) +--R + +--R 2 6 2 5 2 4 +--R - 8a cos(d x + c) - 16a cos(d x + c) - 8a cos(d x + c) +--R + +--R 2 2 2 2 +--R 192a cos(d x + c) + 384a cos(d x + c) + 192a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2 6 2 5 2 4 +--R 8a cos(d x + c) + 16a cos(d x + c) + 8a cos(d x + c) +--R + +--R 2 2 2 2 +--R - 192a cos(d x + c) - 384a cos(d x + c) - 192a +--R * +--R 3 +--R sin(d x + c) +--R + +--R 2 6 2 5 2 4 +--R - 8a cos(d x + c) - 16a cos(d x + c) + 184a cos(d x + c) +--R + +--R 2 3 2 2 2 +--R 384a cos(d x + c) - 256a cos(d x + c) - 896a cos(d x + c) +--R + +--R 2 +--R - 448a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2 6 2 5 2 4 +--R 8a cos(d x + c) + 16a cos(d x + c) - 184a cos(d x + c) +--R + +--R 2 3 2 2 2 +--R - 384a cos(d x + c) + 256a cos(d x + c) + 896a cos(d x + c) +--R + +--R 2 +--R 448a +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 6 2 5 2 4 +--R 40a cos(d x + c) + 80a cos(d x + c) - 216a cos(d x + c) +--R + +--R 2 3 2 2 2 +--R - 512a cos(d x + c) + 96a cos(d x + c) + 704a cos(d x + c) +--R + +--R 2 +--R 352a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2 6 2 5 2 4 +--R - 40a cos(d x + c) - 80a cos(d x + c) + 216a cos(d x + c) +--R + +--R 2 3 2 2 2 2 +--R 512a cos(d x + c) - 96a cos(d x + c) - 704a cos(d x + c) - 352a +--R * +--R sin(d x + c) +--R + +--R 2 6 2 5 2 4 +--R - 24a cos(d x + c) - 48a cos(d x + c) + 72a cos(d x + c) +--R + +--R 2 3 2 2 +--R 192a cos(d x + c) - 192a cos(d x + c) - 96a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2 6 2 5 2 4 +--R 24a cos(d x + c) + 48a cos(d x + c) - 72a cos(d x + c) +--R + +--R 2 3 2 2 +--R - 192a cos(d x + c) + 192a cos(d x + c) + 96a +--R * +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 174 + +--S 175 of 520 +m0031b:= a0031.2-r0031 +--R +--R +--R (119) +--R +-+ +-+ 2 +--R (2\|2 cos(d x + c) + 2\|2 )sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (\|2 cos(d x + c) + \|2 cos(d x + c) - 4\|2 cos(d x + c) - 4\|2 ) +--R * +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - \|2 cos(d x + c) - \|2 cos(d x + c) + 2\|2 cos(d x + c) + 2\|2 +--R * +--R +----+ +--------------------+ +--R \|- 2a \|- a sin(d x + c) + a +--R * +--R atan +--R +-+ +-+ +-+ +----+ +--R (\|2 sin(d x + c) + \|2 cos(d x + c) + \|2 )\|- 2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 4a cos(d x + c) + 4a +--R + +--R 2 +--R - 2cos(d x + c)sin(d x + c) +--R + +--R 2 2 +--R (2cos(d x + c) + 4cos(d x + c))sin(d x + c) - 2cos(d x + c) +--R + +--R - 2cos(d x + c) +--R * +--R +--------------------+ +------------------+ +--R \|- a sin(d x + c) + a \|a cos(d x + c) + a +--R + +--R +-+ 2d x + %pi + 2c +--R - 4a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +--R - 4a\|2 cos(---------------) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R - 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R - 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +-+ 2d x + %pi + 2c +--R 8a\|2 cos(---------------)cos(d x + c) + 8a\|2 cos(---------------) +--R 4 4 +--R * +--R sin(d x + c) +--R + +--R +-+ 2d x + %pi + 2c 3 +--R 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c 2 +--R 2a\|2 cos(---------------)cos(d x + c) +--R 4 +--R + +--R +-+ 2d x + %pi + 2c +-+ 2d x + %pi + 2c +--R - 4a\|2 cos(---------------)cos(d x + c) - 4a\|2 cos(---------------) +--R 4 4 +--R * +--R 2d x + %pi + 2c +--R atanh(sin(---------------)) +--R 4 +--R + +--R +-+ 2 +-+ +--R (4a\|2 cos(d x + c) + 4a\|2 cos(d x + c))sin(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 2a\|2 cos(d x + c) + 2a\|2 cos(d x + c) - 4a\|2 cos(d x + c) +--R + +--R +-+ +--R - 4a\|2 cos(d x + c) +--R / +--R 2 +-+ 2 +-+ 2 +--R (8a d\|2 cos(d x + c) + 8a d\|2 )sin(d x + c) +--R + +--R 2 +-+ 3 2 +-+ 2 +--R 4a d\|2 cos(d x + c) + 4a d\|2 cos(d x + c) +--R + +--R 2 +-+ 2 +-+ +--R - 16a d\|2 cos(d x + c) - 16a d\|2 +--R * +--R sin(d x + c) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 4a d\|2 cos(d x + c) - 4a d\|2 cos(d x + c) + 8a d\|2 cos(d x + c) +--R + +--R 2 +-+ +--R 8a d\|2 +--R * +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 175 + +--S 176 of 520 +d0031b:= D(m0031b,x) +--R +--R +--R (120) +--R 2d x + %pi + 2c 3 +--R (8cos(d x + c) + 8)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c +--R (- 8cos(d x + c) - 8)sin(---------------) +--R 4 +--R * +--R 6 +--R sin(d x + c) +--R + +--R 3 2 2d x + %pi + 2c 3 +--R (8cos(d x + c) + 24cos(d x + c) - 16)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 8cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 8cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 3 2 2d x + %pi + 2c +--R (- 8cos(d x + c) - 24cos(d x + c) + 16)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 8cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 8cos(---------------)cos(d x + c) +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 5 4 3 +--R 2cos(d x + c) + 18cos(d x + c) + 16cos(d x + c) +--R + +--R 2 +--R - 80cos(d x + c) - 120cos(d x + c) - 40 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R 8cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 24cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 8cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 8cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 5 4 3 +--R - 2cos(d x + c) - 18cos(d x + c) - 16cos(d x + c) +--R + +--R 2 +--R 80cos(d x + c) + 120cos(d x + c) + 40 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R - 8cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 24cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 8cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 8cos(---------------)cos(d x + c) +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 5 4 +--R 4cos(d x + c) + 12cos(d x + c) - 56cos(d x + c) +--R + +--R 3 2 +--R - 144cos(d x + c) + 80cos(d x + c) + 320cos(d x + c) +--R + +--R 160 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R 18cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R 24cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 56cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 112cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 48cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 6 5 4 +--R - 4cos(d x + c) - 12cos(d x + c) + 56cos(d x + c) +--R + +--R 3 2 +--R 144cos(d x + c) - 80cos(d x + c) - 320cos(d x + c) - 160 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R - 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R - 18cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R - 24cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 56cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 112cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 48cos(---------------)cos(d x + c) +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 7 6 5 +--R 2cos(d x + c) - 10cos(d x + c) - 48cos(d x + c) +--R + +--R 4 3 +--R 60cos(d x + c) + 256cos(d x + c) - 360cos(d x + c) - 200 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R 4cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R 14cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R - 38cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R - 120cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 24cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 208cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 112cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 7 6 5 +--R - 2cos(d x + c) + 10cos(d x + c) + 48cos(d x + c) +--R + +--R 4 3 +--R - 60cos(d x + c) - 256cos(d x + c) + 360cos(d x + c) +--R + +--R 200 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R - 4cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R - 14cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R 38cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R 120cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 24cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 208cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 112cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 5 +--R - 4cos(d x + c) + 8cos(d x + c) + 52cos(d x + c) +--R + +--R 4 3 2 +--R - 24cos(d x + c) - 184cos(d x + c) - 40cos(d x + c) +--R + +--R 192cos(d x + c) + 112 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 8 +--R 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R - 6cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R - 34cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R 22cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R 136cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 24cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 152cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 88cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 7 6 5 +--R 4cos(d x + c) - 8cos(d x + c) - 52cos(d x + c) +--R + +--R 4 3 2 +--R 24cos(d x + c) + 184cos(d x + c) + 40cos(d x + c) +--R + +--R - 192cos(d x + c) - 112 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 8 +--R - 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R 6cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R 34cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R - 22cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R - 136cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 24cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 152cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 88cos(---------------)cos(d x + c) +--R 4 +--R * +--R sin(d x + c) +--R + +--R 7 6 5 +--R 2cos(d x + c) - 2cos(d x + c) - 18cos(d x + c) +--R + +--R 4 3 2 +--R 2cos(d x + c) + 48cos(d x + c) + 16cos(d x + c) +--R + +--R - 40cos(d x + c) - 24 +--R * +--R 2d x + %pi + 2c 3 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 8 +--R - 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R 18cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R - 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R - 48cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R - 16cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 40cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R 24cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 7 6 5 +--R - 2cos(d x + c) + 2cos(d x + c) + 18cos(d x + c) +--R + +--R 4 3 2 +--R - 2cos(d x + c) - 48cos(d x + c) - 16cos(d x + c) +--R + +--R 40cos(d x + c) + 24 +--R * +--R 2d x + %pi + 2c +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 8 +--R 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 7 +--R - 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 6 +--R - 18cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 5 +--R 2cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 4 +--R 48cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 3 +--R 16cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 40cos(---------------)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c +--R - 24cos(---------------)cos(d x + c) +--R 4 +--R * +--R 2d x + %pi + 2c +--R atanh(sin(---------------)) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 16cos(d x + c) - 16)sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (8cos(---------------) + 16)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 8cos(---------------) + 16 +--R 4 +--R * +--R 6 +--R sin(d x + c) +--R + +--R 3 2 +--R (- 16cos(d x + c) - 48cos(d x + c) - 16cos(d x + c) + 16) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (8cos(---------------) + 16)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (24cos(---------------) + 48)cos(d x + c) + 16cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 16cos(---------------) - 16 +--R 4 +--R * +--R 5 +--R sin(d x + c) +--R + +--R 5 4 3 +--R - 4cos(d x + c) - 36cos(d x + c) - 72cos(d x + c) +--R + +--R 2 +--R 88cos(d x + c) + 224cos(d x + c) + 96 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (2cos(---------------) + 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (18cos(---------------) + 36)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (16cos(---------------) + 72)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 80cos(---------------) - 88)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 120cos(---------------) - 224)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 40cos(---------------) - 96 +--R 4 +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 5 4 +--R - 8cos(d x + c) - 52cos(d x + c) + 4cos(d x + c) +--R + +--R 3 2 +--R 192cos(d x + c) - 48cos(d x + c) - 416cos(d x + c) - 224 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (4cos(---------------) + 8)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (12cos(---------------) + 52)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 56cos(---------------) - 4)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 144cos(---------------) - 192)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (80cos(---------------) + 48)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (320cos(---------------) + 416)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 160cos(---------------) + 224 +--R 4 +--R * +--R 3 +--R sin(d x + c) +--R + +--R 7 6 5 +--R - 10cos(d x + c) - 42cos(d x + c) - 28cos(d x + c) +--R + +--R 4 3 2 +--R 52cos(d x + c) + 16cos(d x + c) + 96cos(d x + c) +--R + +--R 304cos(d x + c) + 176 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 2d x + %pi + 2c 2 7 +--R (2cos(---------------) + 10)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 10cos(---------------) + 42)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 48cos(---------------) + 28)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (60cos(---------------) - 52)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 2 +--R (256cos(---------------) - 16)cos(d x + c) - 96cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (- 360cos(---------------) - 304)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R - 200cos(---------------) - 176 +--R 4 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 7 6 +--R - 12cos(d x + c) - 44cos(d x + c) + 56cos(d x + c) +--R + +--R 5 4 3 +--R 228cos(d x + c) + 28cos(d x + c) - 240cos(d x + c) +--R + +--R 2 +--R - 160cos(d x + c) - 80cos(d x + c) - 48 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 8 2d x + %pi + 2c 2 7 +--R 12cos(d x + c) + (- 4cos(---------------) + 44)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (8cos(---------------) - 56)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (52cos(---------------) - 228)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (- 24cos(---------------) - 28)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (- 184cos(---------------) + 240)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (- 40cos(---------------) + 160)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R (192cos(---------------) + 80)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 +--R 112cos(---------------) + 48 +--R 4 +--R * +--R sin(d x + c) +--R + +--R 9 8 7 +--R - 6cos(d x + c) + 6cos(d x + c) + 54cos(d x + c) +--R + +--R 6 5 4 +--R - 6cos(d x + c) - 144cos(d x + c) - 48cos(d x + c) +--R + +--R 3 2 +--R 120cos(d x + c) + 72cos(d x + c) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 9 8 +--R 6cos(d x + c) - 6cos(d x + c) +--R + +--R 2d x + %pi + 2c 2 7 +--R (2cos(---------------) - 54)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 6 +--R (- 2cos(---------------) + 6)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 5 +--R (- 18cos(---------------) + 144)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 4 +--R (2cos(---------------) + 48)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 3 +--R (48cos(---------------) - 120)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2 +--R (16cos(---------------) - 72)cos(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2 2d x + %pi + 2c 2 +--R - 40cos(---------------) cos(d x + c) - 24cos(---------------) +--R 4 4 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R +-+ +-+ 2d x + %pi + 2c 2 +--R (2\|2 cos(d x + c) + 4\|2 )sin(---------------) +--R 4 +--R + +--R +-+ +-+ +--R - 2\|2 cos(d x + c) - 4\|2 +--R * +--R 7 +--R sin(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (- 3\|2 cos(d x + c) - 4\|2 cos(d x + c) + 4\|2 cos(d x + c)) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R 3\|2 cos(d x + c) + 4\|2 cos(d x + c) - 4\|2 cos(d x + c) +--R * +--R 6 +--R sin(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R - 5\|2 cos(d x + c) - 3\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - 24\|2 cos(d x + c) - 90\|2 cos(d x + c) - 60\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 5\|2 cos(d x + c) + 3\|2 cos(d x + c) + 24\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 90\|2 cos(d x + c) + 60\|2 +--R * +--R 5 +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +--R - \|2 cos(d x + c) + 4\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R 38\|2 cos(d x + c) + 168\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R 296\|2 cos(d x + c) + 160\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R \|2 cos(d x + c) - 4\|2 cos(d x + c) - 38\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - 168\|2 cos(d x + c) - 296\|2 cos(d x + c) - 160\|2 +--R * +--R 4 +--R sin(d x + c) +--R + +--R +-+ 6 +-+ 5 +--R - 5\|2 cos(d x + c) - \|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R 24\|2 cos(d x + c) - 78\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - 352\|2 cos(d x + c) - 434\|2 cos(d x + c) - 180\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 5\|2 cos(d x + c) + \|2 cos(d x + c) - 24\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 78\|2 cos(d x + c) + 352\|2 cos(d x + c) + 434\|2 cos(d x + c) +--R + +--R +-+ +--R 180\|2 +--R * +--R 3 +--R sin(d x + c) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2\|2 cos(d x + c) + 16\|2 cos(d x + c) + 7\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R - 46\|2 cos(d x + c) + 81\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R 348\|2 cos(d x + c) + 324\|2 cos(d x + c) + 96\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2\|2 cos(d x + c) - 16\|2 cos(d x + c) - 7\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 46\|2 cos(d x + c) - 81\|2 cos(d x + c) - 348\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 324\|2 cos(d x + c) - 96\|2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R +-+ 7 +-+ 6 +--R - 4\|2 cos(d x + c) - 17\|2 cos(d x + c) +--R + +--R +-+ 5 +-+ 4 +--R - 7\|2 cos(d x + c) + 29\|2 cos(d x + c) +--R + +--R +-+ 3 +-+ 2 +--R - 47\|2 cos(d x + c) - 168\|2 cos(d x + c) +--R + +--R +-+ +-+ +--R - 118\|2 cos(d x + c) - 20\|2 +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 4\|2 cos(d x + c) + 17\|2 cos(d x + c) + 7\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +--R - 29\|2 cos(d x + c) + 47\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R 168\|2 cos(d x + c) + 118\|2 cos(d x + c) + 20\|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2\|2 cos(d x + c) + 6\|2 cos(d x + c) + 2\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 6\|2 cos(d x + c) + 12\|2 cos(d x + c) + 32\|2 cos(d x + c) +--R + +--R +-+ +--R 16\|2 cos(d x + c) +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2\|2 cos(d x + c) - 6\|2 cos(d x + c) - 2\|2 cos(d x + c) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 6\|2 cos(d x + c) - 12\|2 cos(d x + c) - 32\|2 cos(d x + c) +--R + +--R +-+ +--R - 16\|2 cos(d x + c) +--R * +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R / +--R 2d x + %pi + 2c 2 +--R (32a cos(d x + c) + 32a)sin(---------------) - 32a cos(d x + c) +--R 4 +--R + +--R - 32a +--R * +--R 6 +--R sin(d x + c) +--R + +--R 3 2 2d x + %pi + 2c 2 +--R (32a cos(d x + c) + 96a cos(d x + c) - 64a)sin(---------------) +--R 4 +--R + +--R 3 2 +--R - 32a cos(d x + c) - 96a cos(d x + c) + 64a +--R * +--R 5 +--R sin(d x + c) +--R + +--R 5 4 3 +--R 8a cos(d x + c) + 72a cos(d x + c) + 64a cos(d x + c) +--R + +--R 2 +--R - 320a cos(d x + c) - 480a cos(d x + c) - 160a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 5 4 3 +--R - 8a cos(d x + c) - 72a cos(d x + c) - 64a cos(d x + c) +--R + +--R 2 +--R 320a cos(d x + c) + 480a cos(d x + c) + 160a +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 5 4 +--R 16a cos(d x + c) + 48a cos(d x + c) - 224a cos(d x + c) +--R + +--R 3 2 +--R - 576a cos(d x + c) + 320a cos(d x + c) + 1280a cos(d x + c) +--R + +--R 640a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 6 5 4 +--R - 16a cos(d x + c) - 48a cos(d x + c) + 224a cos(d x + c) +--R + +--R 3 2 +--R 576a cos(d x + c) - 320a cos(d x + c) - 1280a cos(d x + c) - 640a +--R * +--R 3 +--R sin(d x + c) +--R + +--R 7 6 5 +--R 8a cos(d x + c) - 40a cos(d x + c) - 192a cos(d x + c) +--R + +--R 4 3 +--R 240a cos(d x + c) + 1024a cos(d x + c) - 1440a cos(d x + c) +--R + +--R - 800a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 7 6 5 +--R - 8a cos(d x + c) + 40a cos(d x + c) + 192a cos(d x + c) +--R + +--R 4 3 +--R - 240a cos(d x + c) - 1024a cos(d x + c) + 1440a cos(d x + c) +--R + +--R 800a +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 5 +--R - 16a cos(d x + c) + 32a cos(d x + c) + 208a cos(d x + c) +--R + +--R 4 3 2 +--R - 96a cos(d x + c) - 736a cos(d x + c) - 160a cos(d x + c) +--R + +--R 768a cos(d x + c) + 448a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 7 6 5 +--R 16a cos(d x + c) - 32a cos(d x + c) - 208a cos(d x + c) +--R + +--R 4 3 2 +--R 96a cos(d x + c) + 736a cos(d x + c) + 160a cos(d x + c) +--R + +--R - 768a cos(d x + c) - 448a +--R * +--R sin(d x + c) +--R + +--R 7 6 5 +--R 8a cos(d x + c) - 8a cos(d x + c) - 72a cos(d x + c) +--R + +--R 4 3 2 +--R 8a cos(d x + c) + 192a cos(d x + c) + 64a cos(d x + c) +--R + +--R - 160a cos(d x + c) - 96a +--R * +--R 2d x + %pi + 2c 2 +--R sin(---------------) +--R 4 +--R + +--R 7 6 5 +--R - 8a cos(d x + c) + 8a cos(d x + c) + 72a cos(d x + c) +--R + +--R 4 3 2 +--R - 8a cos(d x + c) - 192a cos(d x + c) - 64a cos(d x + c) +--R + +--R 160a cos(d x + c) + 96a +--R * +--R +--------------------+ +------------------+ +--R \|- a sin(d x + c) + a \|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 176 + +--S 177 of 520 +t0032:= 1/(a-a*sin(c+d*x))^(5/2) +--R +--R +--R 1 +--R (121) --------------------------------------------------------------- +--R 2 2 2 2 +--------------------+ +--R (a sin(d x + c) - 2a sin(d x + c) + a )\|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 177 + +--S 178 of 520 +r0032:= 1/4*cos(c+d*x)/d/(a-a*sin(c+d*x))^(5/2)+_ + 3/16*cos(c+d*x)/a/d/(a-a*sin(c+d*x))^(3/2)+_ + 3/16*atanh(sin(1/2*c+1/4*%pi+1/2*d*x))*_ + cos(1/2*c+1/4*%pi+1/2*d*x)/a^2/d/(a-a*sin(c+d*x))^(1/2) +--R +--R +--R (122) +--R 2d x + %pi + 2c 2 +--R 3cos(---------------)sin(d x + c) +--R 4 +--R + +--R 2d x + %pi + 2c 2d x + %pi + 2c +--R - 6cos(---------------)sin(d x + c) + 3cos(---------------) +--R 4 4 +--R * +--R 2d x + %pi + 2c +--R atanh(sin(---------------)) +--R 4 +--R + +--R - 3cos(d x + c)sin(d x + c) + 7cos(d x + c) +--R / +--R 2 2 2 2 +--------------------+ +--R (16a d sin(d x + c) - 32a d sin(d x + c) + 16a d)\|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 178 + +--S 179 of 520 +a0032:= integrate(t0032,x) +--R +--R +--R (123) +--R [ +--R +-+ 3 +-+ 2 +-+ +--R 12\|2 cos(d x + c) + 12\|2 cos(d x + c) - 24\|2 cos(d x + c) +--R + +--R +-+ +--R - 24\|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 3\|2 cos(d x + c) + 3\|2 cos(d x + c) - 24\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - 24\|2 cos(d x + c) + 24\|2 cos(d x + c) + 24\|2 +--R * +--R +--+ +--R \|2a +--R * +--R log +--R +-+ +-+ +-+ +--+ +--R (\|2 sin(d x + c) + \|2 cos(d x + c) + \|2 )\|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R (- a cos(d x + c) - a)sin(d x + c) - 3a cos(d x + c) - 3a +--R / +--R (cos(d x + c) + 1)sin(d x + c) - cos(d x + c) - 1 +--R + +--R 3 2 +--R (- 12cos(d x + c) + 40cos(d x + c) + 80cos(d x + c))sin(d x + c) +--R + +--R 4 3 2 +--R 12cos(d x + c) + 52cos(d x + c) - 40cos(d x + c) - 80cos(d x + c) +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 3 +-+ 3 3 +-+ 2 +--R 256a d\|2 cos(d x + c) + 256a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 +-+ +--R - 512a d\|2 cos(d x + c) - 512a d\|2 +--R * +--R sin(d x + c) +--R + +--R 3 +-+ 5 3 +-+ 4 +--R 64a d\|2 cos(d x + c) + 64a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 3 +-+ 2 +--R - 512a d\|2 cos(d x + c) - 512a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 +-+ +--R 512a d\|2 cos(d x + c) + 512a d\|2 +--R , +--R +--R +-+ 3 +-+ 2 +-+ +--R 12\|2 cos(d x + c) + 12\|2 cos(d x + c) - 24\|2 cos(d x + c) +--R + +--R +-+ +--R - 24\|2 +--R * +--R sin(d x + c) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 3\|2 cos(d x + c) + 3\|2 cos(d x + c) - 24\|2 cos(d x + c) +--R + +--R +-+ 2 +-+ +-+ +--R - 24\|2 cos(d x + c) + 24\|2 cos(d x + c) + 24\|2 +--R * +--R +----+ +--R \|- 2a +--R * +--R atan +--R +-+ +-+ +-+ +----+ +--R (\|2 sin(d x + c) + \|2 cos(d x + c) + \|2 )\|- 2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 4a cos(d x + c) + 4a +--R + +--R 3 2 +--R (- 6cos(d x + c) + 20cos(d x + c) + 40cos(d x + c))sin(d x + c) +--R + +--R 4 3 2 +--R 6cos(d x + c) + 26cos(d x + c) - 20cos(d x + c) - 40cos(d x + c) +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R / +--R 3 +-+ 3 3 +-+ 2 +--R 128a d\|2 cos(d x + c) + 128a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 +-+ +--R - 256a d\|2 cos(d x + c) - 256a d\|2 +--R * +--R sin(d x + c) +--R + +--R 3 +-+ 5 3 +-+ 4 +--R 32a d\|2 cos(d x + c) + 32a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 3 +-+ 2 +--R - 256a d\|2 cos(d x + c) - 256a d\|2 cos(d x + c) +--R + +--R 3 +-+ 3 +-+ +--R 256a d\|2 cos(d x + c) + 256a d\|2 +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 179 + +--S 180 of 520 +--m0032a:= a0032.1-r0032 +--E 180 + +--S 181 of 520 +--d0032a:= D(m0032a,x) +--E 181 + +--S 182 of 520 +--m0032b:= a0032.2-r0032 +--E 182 + +--S 183 of 520 +--d0032b:= D(m0032b,x) +--E 183 + +--S 184 of 520 +t0033:= (b*sin(c+d*x))^(1/2) +--R +--R +--R +--------------+ +--R (124) \|b sin(d x + c) +--R Type: Expression(Integer) +--E 184 + +--S 185 of 520 +r0033:= 2*EllipticE(1/2*c-1/4*%pi+1/2*d*x,2)*_ + (b*sin(c+d*x))^(1/2)/d/sin(c+d*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 185 + +--S 186 of 520 +a0033:= integrate(t0033,x) +--R +--R +--R x +--R ++ +---------------+ +--R (125) | \|b sin(%R d + c) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 186 + +--S 187 of 520 +--m0033:= a0033-r0033 +--E 187 + +--S 188 of 520 +--d0033:= D(m0033,x) +--E 188 + +--S 189 of 520 +t0034:= (b*sin(c+d*x))^(3/2) +--R +--R +--R +--------------+ +--R (126) b sin(d x + c)\|b sin(d x + c) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 520 +r0034:= -2/3*b^2*(-EllipticF(1/2*c-1/4*%pi+1/2*d*x,2)*sin(c+d*x)^(1/2)+_ + cos(c+d*x)*sin(c+d*x))/d/(b*sin(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 190 + +--S 191 of 520 +a0034:= integrate(t0034,x) +--R +--R +--R x +--R ++ +---------------+ +--R (127) | b sin(%R d + c)\|b sin(%R d + c) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 191 + +--S 192 of 520 +--m0034:= a0034-r0034 +--E 192 + +--S 193 of 520 +--d0034:= D(m0034,x) +--E 193 + +--S 194 of 520 +t0035:= (b*sin(c+d*x))^(5/2) +--R +--R +--R 2 2 +--------------+ +--R (128) b sin(d x + c) \|b sin(d x + c) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 520 +r0035:= 2/5*b^2*(b*sin(c+d*x))^(1/2)*(3*EllipticE(1/2*c-1/4*%pi+1/2*d*x,2)-_ + cos(c+d*x)*sin(c+d*x)^(3/2))/d/sin(c+d*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 195 + +--S 196 of 520 +a0035:= integrate(t0035,x) +--R +--R +--R x +--R ++ 2 2 +---------------+ +--R (129) | b sin(%R d + c) \|b sin(%R d + c) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 196 + +--S 197 of 520 +--m0035:= a0035-r0035 +--E 197 + +--S 198 of 520 +--d0035:= D(m0035,x) +--E 198 + +--S 199 of 520 +t0036:= 1/(b*sin(c+d*x))^(1/2) +--R +--R +--R 1 +--R (130) ----------------- +--R +--------------+ +--R \|b sin(d x + c) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 520 +r0036:= 2*EllipticF(1/2*c-1/4*%pi+1/2*d*x,2)*_ + sin(c+d*x)^(1/2)/d/(b*sin(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 200 + +--S 201 of 520 +a0036:= integrate(t0036,x) +--R +--R +--R x +--R ++ 1 +--R (131) | ------------------ d%R +--R ++ +---------------+ +--R \|b sin(%R d + c) +--R Type: Union(Expression(Integer),...) +--E 201 + +--S 202 of 520 +--m0036:= a0036-r0036 +--E 202 + +--S 203 of 520 +--d0036:= D(m0036,x) +--E 203 + +--S 204 of 520 +t0037:= 1/(b*sin(c+d*x))^(3/2) +--R +--R +--R 1 +--R (132) ------------------------------- +--R +--------------+ +--R b sin(d x + c)\|b sin(d x + c) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 520 +r0037:= -2/b*(sin(c+d*x)^(1/2)*cos(c+d*x)+_ + EllipticE(1/2*c-1/4*%pi+1/2*d*x,2)*sin(c+d*x))/d/_ + (b*sin(c+d*x))^(1/2)/sin(c+d*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 205 + +--S 206 of 520 +a0037:= integrate(t0037,x) +--R +--R +--R x +--R ++ 1 +--R (133) | --------------------------------- d%R +--R ++ +---------------+ +--R b sin(%R d + c)\|b sin(%R d + c) +--R Type: Union(Expression(Integer),...) +--E 206 + +--S 207 of 520 +--m0037:= a0037-r0037 +--E 207 + +--S 208 of 520 +--d0037:= D(m0037,x) +--E 208 + +--S 209 of 520 +t0038:= 1/(b*sin(c+d*x))^(5/2) +--R +--R +--R 1 +--R (134) -------------------------------- +--R 2 2 +--------------+ +--R b sin(d x + c) \|b sin(d x + c) +--R Type: Expression(Integer) +--E 209 + +--S 210 of 520 +r0038:= 2/3*(-cos(c+d*x)+_ + EllipticF(1/2*c-1/4*%pi+1/2*d*x,2)*_ + sin(c+d*x)^(3/2))/b^2/d/sin(c+d*x)/(b*sin(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 210 + +--S 211 of 520 +a0038:= integrate(t0038,x) +--R +--R +--R x +--R ++ 1 +--R (135) | ---------------------------------- d%R +--R ++ 2 2 +---------------+ +--R b sin(%R d + c) \|b sin(%R d + c) +--R Type: Union(Expression(Integer),...) +--E 211 + +--S 212 of 520 +--m0038:= a0038-r0038 +--E 212 + +--S 213 of 520 +--d0038:= D(m0038,x) +--E 213 + +--S 214 of 520 +t0039:= x^2/(a+b*sin(x)) +--R +--R +--R 2 +--R x +--R (136) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 520 +r0039:= -(%i*x^2*log(-%i*(-%i*a+%i*(a^2-b^2)^(1/2)-_ + b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-_ + %i*x^2*log(-%i*(%i*a+%i*(a^2-b^2)^(1/2)+_ + b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+_ + 2*x*polylog(2,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 2*x*polylog(2,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+_ + 2*%i*polylog(3,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 2*%i*polylog(3,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 215 + +--S 216 of 520 +a0039:= integrate(t0039,x) +--R +--R +--R x 2 +--R ++ %R +--R (137) | ------------- d%R +--R ++ b sin(%R) + a +--R Type: Union(Expression(Integer),...) +--E 216 + +--S 217 of 520 +--m0039:= a0039-r0039 +--E 217 + +--S 218 of 520 +--d0039:= D(m0039,x) +--E 218 + +--S 219 of 520 +t0040:= x^3/(a+b*sin(x)) +--R +--R +--R 3 +--R x +--R (138) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 520 +r0040:= -(%i*x^3*log(-%i*(-%i*a+%i*(a^2-b^2)^(1/2)-b*exp(%i*x))/_ + (-a+(a^2-b^2)^(1/2)))-%i*x^3*log(-%i*(%i*a+%i*(a^2-b^2)^(1/2)+_ + b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+_ + 3*x^2*polylog(2,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 3*x^2*polylog(2,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+_ + 6*%i*x*polylog(3,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 6*%i*x*polylog(3,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))-_ + 6*polylog(4,-%i*b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))+_ + 6*polylog(4,%i*b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 220 + +--S 221 of 520 +a0040:= integrate(t0040,x) +--R +--R +--R x 3 +--R ++ %R +--R (139) | ------------- d%R +--R ++ b sin(%R) + a +--R Type: Union(Expression(Integer),...) +--E 221 + +--S 222 of 520 +--m0040:= a0040-r0040 +--E 222 + +--S 223 of 520 +--d0040:= D(m0040,x) +--E 223 + +--S 224 of 520 +t0041:= x/(a+a*sin(x)) +--R +--R +--R x +--R (140) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 520 +r0041:= 2*log(cos(-1/4*%pi+1/2*x))/a-x*cot(1/4*%pi+1/2*x)/a +--R +--R +--R 2x - %pi 2x + %pi +--R 2log(cos(--------)) - x cot(--------) +--R 4 4 +--R (141) ------------------------------------- +--R a +--R Type: Expression(Integer) +--E 225 + +--S 226 of 520 +a0041:= integrate(t0041,x) +--R +--R +--R (142) +--R sin(x) + cos(x) + 1 +--R (2sin(x) + 2cos(x) + 2)log(-------------------) +--R cos(x) + 1 +--R + +--R 2 +--R (- sin(x) - cos(x) - 1)log(----------) + x sin(x) - x cos(x) - x +--R cos(x) + 1 +--R / +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 226 + +--S 227 of 520 +m0041:= a0041-r0041 +--R +--R +--R (143) +--R sin(x) + cos(x) + 1 +--R (2sin(x) + 2cos(x) + 2)log(-------------------) +--R cos(x) + 1 +--R + +--R 2x - %pi +--R (- 2sin(x) - 2cos(x) - 2)log(cos(--------)) +--R 4 +--R + +--R 2 2x + %pi +--R (- sin(x) - cos(x) - 1)log(----------) + (x cot(--------) + x)sin(x) +--R cos(x) + 1 4 +--R + +--R 2x + %pi +--R (x cos(x) + x)cot(--------) - x cos(x) - x +--R 4 +--R / +--R a sin(x) + a cos(x) + a +--R Type: Expression(Integer) +--E 227 + +--S 228 of 520 +d0041:= D(m0041,x) +--R +--R +--R (144) +--R 2x - %pi 3 +--R 2cos(--------)sin(x) +--R 4 +--R + +--R 2x - %pi +--R (2cos(x) + 2)sin(--------) +--R 4 +--R + +--R 2x - %pi 2x - %pi 2x + %pi 2 +--R (- x cos(--------)cos(x) - x cos(--------))cot(--------) +--R 4 4 4 +--R + +--R 2x - %pi 2x - %pi 2x + %pi +--R (2cos(--------)cos(x) + 2cos(--------))cot(--------) +--R 4 4 4 +--R + +--R 2x - %pi 2x - %pi +--R (3x + 2)cos(--------)cos(x) + (3x + 2)cos(--------) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2 2x - %pi +--R (4cos(x) + 8cos(x) + 4)sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi +--R - 2x cos(--------)cos(x) - 4x cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi +--R - 2x cos(--------) +--R 4 +--R * +--R 2x + %pi 2 +--R cot(--------) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2x - %pi +--R (4cos(--------)cos(x) + 8cos(--------)cos(x) + 4cos(--------)) +--R 4 4 4 +--R * +--R 2x + %pi +--R cot(--------) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi +--R (- 2x + 2)cos(--------)cos(x) - 4x cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi +--R (- 2x - 2)cos(--------) +--R 4 +--R * +--R sin(x) +--R + +--R 3 2 2x - %pi +--R (2cos(x) + 6cos(x) + 6cos(x) + 2)sin(--------) +--R 4 +--R + +--R 2x - %pi 3 2x - %pi 2 +--R - x cos(--------)cos(x) - 3x cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2x - %pi +--R - 3x cos(--------)cos(x) - x cos(--------) +--R 4 4 +--R * +--R 2x + %pi 2 +--R cot(--------) +--R 4 +--R + +--R 2x - %pi 3 2x - %pi 2 2x - %pi +--R 2cos(--------)cos(x) + 6cos(--------)cos(x) + 6cos(--------)cos(x) +--R 4 4 4 +--R + +--R 2x - %pi +--R 2cos(--------) +--R 4 +--R * +--R 2x + %pi +--R cot(--------) +--R 4 +--R + +--R 2x - %pi 3 2x - %pi 2 +--R (3x + 2)cos(--------)cos(x) + (5x + 2)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2x - %pi +--R (x - 2)cos(--------)cos(x) + (- x - 2)cos(--------) +--R 4 4 +--R / +--R 2x - %pi 2x - %pi 2 +--R (2a cos(--------)cos(x) + 2a cos(--------))sin(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x - %pi 2x - %pi +--R (4a cos(--------)cos(x) + 8a cos(--------)cos(x) + 4a cos(--------)) +--R 4 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 3 2x - %pi 2 +--R 2a cos(--------)cos(x) + 6a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2x - %pi +--R 6a cos(--------)cos(x) + 2a cos(--------) +--R 4 4 +--R Type: Expression(Integer) +--E 228 + +--S 229 of 520 +t0042:= x/(a-a*sin(x)) +--R +--R +--R x +--R (145) - ------------ +--R a sin(x) - a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 520 +r0042:= 2*log(cos(1/4*%pi+1/2*x))/a+x*tan(1/4*%pi+1/2*x)/a +--R +--R +--R 2x + %pi 2x + %pi +--R 2log(cos(--------)) + x tan(--------) +--R 4 4 +--R (146) ------------------------------------- +--R a +--R Type: Expression(Integer) +--E 230 + +--S 231 of 520 +a0042:= integrate(t0042,x) +--R +--R +--R (147) +--R sin(x) - cos(x) - 1 +--R (2sin(x) - 2cos(x) - 2)log(-------------------) +--R cos(x) + 1 +--R + +--R 2 +--R (- sin(x) + cos(x) + 1)log(----------) - x sin(x) - x cos(x) - x +--R cos(x) + 1 +--R / +--R a sin(x) - a cos(x) - a +--R Type: Union(Expression(Integer),...) +--E 231 + +--S 232 of 520 +m0042:= a0042-r0042 +--R +--R +--R (148) +--R sin(x) - cos(x) - 1 +--R (2sin(x) - 2cos(x) - 2)log(-------------------) +--R cos(x) + 1 +--R + +--R 2x + %pi +--R (- 2sin(x) + 2cos(x) + 2)log(cos(--------)) +--R 4 +--R + +--R 2 +--R (- sin(x) + cos(x) + 1)log(----------) +--R cos(x) + 1 +--R + +--R 2x + %pi +--R (- x sin(x) + x cos(x) + x)tan(--------) - x sin(x) - x cos(x) - x +--R 4 +--R / +--R a sin(x) - a cos(x) - a +--R Type: Expression(Integer) +--E 232 + +--S 233 of 520 +d0042:= D(m0042,x) +--R +--R +--R (149) +--R 2x + %pi 2x + %pi 2 +--R (- x cos(--------)cos(x) - x cos(--------))sin(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi +--R 2x cos(--------)cos(x) + 4x cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R 2x cos(--------) +--R 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 3 2x + %pi 2 +--R - x cos(--------)cos(x) - 3x cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2x + %pi +--R - 3x cos(--------)cos(x) - x cos(--------) +--R 4 4 +--R * +--R 2x + %pi 2 +--R tan(--------) +--R 4 +--R + +--R 2x + %pi 2x + %pi 2 +--R (- 2cos(--------)cos(x) - 2cos(--------))sin(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi 2x + %pi +--R (4cos(--------)cos(x) + 8cos(--------)cos(x) + 4cos(--------))sin(x) +--R 4 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R - 2cos(--------)cos(x) - 6cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2x + %pi +--R - 6cos(--------)cos(x) - 2cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R tan(--------) +--R 4 +--R + +--R 2x + %pi 3 +--R 2cos(--------)sin(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (2cos(x) + 2)sin(--------) + (3x - 2)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R (3x - 2)cos(--------) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2 2x + %pi +--R (- 4cos(x) - 8cos(x) - 4)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi +--R (2x + 2)cos(--------)cos(x) + 4x cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R (2x - 2)cos(--------) +--R 4 +--R * +--R sin(x) +--R + +--R 3 2 2x + %pi +--R (2cos(x) + 6cos(x) + 6cos(x) + 2)sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (3x - 2)cos(--------)cos(x) + (5x - 2)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2x + %pi +--R (x + 2)cos(--------)cos(x) + (- x + 2)cos(--------) +--R 4 4 +--R / +--R 2x + %pi 2x + %pi 2 +--R (2a cos(--------)cos(x) + 2a cos(--------))sin(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi 2x + %pi +--R (- 4a cos(--------)cos(x) - 8a cos(--------)cos(x) - 4a cos(--------)) +--R 4 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 3 2x + %pi 2 +--R 2a cos(--------)cos(x) + 6a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2x + %pi +--R 6a cos(--------)cos(x) + 2a cos(--------) +--R 4 4 +--R Type: Expression(Integer) +--E 233 + +--S 234 of 520 +t0043:= x/(a+b*sin(x))^2 +--R +--R +--R x +--R (150) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 234 + +--S 235 of 520 +r0043:= -%i*a*x*log(1-%i*b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/_ + (a^2-b^2)^(3/2)+%i*a*x*log(1-%i*b*exp(1)^(%i*x)/_ + (a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-log(a+b*sin(x))/(a^2-b^2)-_ + a*polylog(2,%i*b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+_ + a*polylog(2,%i*b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+_ + b*x*cos(x)/(a^2-b^2)/(a+b*sin(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 235 + +--S 236 of 520 +a0043:= integrate(t0043,x) +--R +--R +--R x +--R ++ %R +--R (151) | ------------------------------ d%R +--R ++ 2 2 2 +--R b sin(%R) + 2a b sin(%R) + a +--R Type: Union(Expression(Integer),...) +--E 236 + +--S 237 of 520 +--m0043:= a0043-r0043 +--E 237 + +--S 238 of 520 +--d0043:= D(m0043,x) +--E 238 + +--S 239 of 520 +t0044:= x*(a+a*sin(c+d*x))^(1/2) +--R +--R +--R +------------------+ +--R (152) x\|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 239 + +--S 240 of 520 +r0044:= 2*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + csc(1/2*c+1/4*%pi+1/2*d*x)*(2*sin(1/2*c+1/4*%pi+1/2*d*x)-_ + d*x*cos(1/2*c+1/4*%pi+1/2*d*x))/d^2 +--R +--R +--R (153) +--R +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R 4\|2 csc(---------------)sin(---------------) +--R 4 4 +--R + +--R +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R - 2d x\|2 cos(---------------)csc(---------------) +--R 4 4 +--R * +--R +-----------------------+ +--R | 2d x + %pi + 2c 2 +--R |a sin(---------------) +--R \| 4 +--R / +--R 2 +--R d +--R Type: Expression(Integer) +--E 240 + +--S 241 of 520 +a0044:= integrate(t0044,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 241 + +--S 242 of 520 +--m0044:= a0044-r0044 +--E 242 + +--S 243 of 520 +--d0044:= D(m0044,x) +--E 243 + +--S 244 of 520 +t0045:= x^2*(a+a*sin(c+d*x))^(1/2) +--R +--R +--R 2 +------------------+ +--R (154) x \|a sin(d x + c) + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 520 +r0045:= 2*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + csc(1/2*c+1/4*%pi+1/2*d*x)*(4*d*x*sin(1/2*c+1/4*%pi+1/2*d*x)+_ + (8-d^2*x^2)*cos(1/2*c+1/4*%pi+1/2*d*x))/d^3 +--R +--R +--R (155) +--R +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R 8d x\|2 csc(---------------)sin(---------------) +--R 4 4 +--R + +--R 2 2 +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R (- 2d x + 16)\|2 cos(---------------)csc(---------------) +--R 4 4 +--R * +--R +-----------------------+ +--R | 2d x + %pi + 2c 2 +--R |a sin(---------------) +--R \| 4 +--R / +--R 3 +--R d +--R Type: Expression(Integer) +--E 245 + +--S 246 of 520 +a0045:= integrate(t0045,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 246 + +--S 247 of 520 +--m0045:= a0045-r0045 +--E 247 + +--S 248 of 520 +--d0045:= D(m0045,x) +--E 248 + +--S 249 of 520 +t0046:= x*(a-a*sin(c+d*x))^(1/2) +--R +--R +--R +--------------------+ +--R (156) x\|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 249 + +--S 250 of 520 +r0046:= 2*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + sec(1/2*c+1/4*%pi+1/2*d*x)*(2*cos(1/2*c+1/4*%pi+1/2*d*x)+_ + d*x*sin(1/2*c+1/4*%pi+1/2*d*x))/d^2 +--R +--R +--R (157) +--R +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R 2d x\|2 sec(---------------)sin(---------------) +--R 4 4 +--R + +--R +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R 4\|2 cos(---------------)sec(---------------) +--R 4 4 +--R * +--R +-----------------------+ +--R | 2d x + %pi + 2c 2 +--R |a cos(---------------) +--R \| 4 +--R / +--R 2 +--R d +--R Type: Expression(Integer) +--E 250 + +--S 251 of 520 +a0046:= integrate(t0046,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 251 + +--S 252 of 520 +--m0046:= a0046-r0046 +--E 252 + +--S 253 of 520 +--d0046:= D(m0046,x) +--E 253 + +--S 254 of 520 +t0047:= x^2*(a-a*sin(c+d*x))^(1/2) +--R +--R +--R 2 +--------------------+ +--R (158) x \|- a sin(d x + c) + a +--R Type: Expression(Integer) +--E 254 + +--S 255 of 520 +r0047:= 2*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + sec(1/2*c+1/4*%pi+1/2*d*x)*(4*d*x*cos(1/2*c+1/4*%pi+1/2*d*x)-_ + (8-d^2*x^2)*sin(1/2*c+1/4*%pi+1/2*d*x))/d^3 +--R +--R +--R (159) +--R 2 2 +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R (2d x - 16)\|2 sec(---------------)sin(---------------) +--R 4 4 +--R + +--R +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R 8d x\|2 cos(---------------)sec(---------------) +--R 4 4 +--R * +--R +-----------------------+ +--R | 2d x + %pi + 2c 2 +--R |a cos(---------------) +--R \| 4 +--R / +--R 3 +--R d +--R Type: Expression(Integer) +--E 255 + +--S 256 of 520 +a0047:= integrate(t0047,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 256 + +--S 257 of 520 +--m0047:= a0047-r0047 +--E 257 + +--S 258 of 520 +--d0047:= D(m0047,x) +--E 258 + +--S 259 of 520 +t0048:= (a+a*sin(c+d*x))^(1/2)/x +--R +--R +--R +------------------+ +--R \|a sin(d x + c) + a +--R (160) --------------------- +--R x +--R Type: Expression(Integer) +--E 259 + +--S 260 of 520 +r0048:= 2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + csc(1/2*c+1/4*%pi+1/2*d*x)*(sin(1/2*c+1/4*%pi)*Ci(1/2*d*x)+_ + cos(1/2*c+1/4*%pi)*Si(1/2*d*x)) +--R +--R +--R (161) +--R +-+ d x 2d x + %pi + 2c %pi + 2c +--R \|2 Ci(---)csc(---------------)sin(--------) +--R 2 4 4 +--R + +--R +-+ d x %pi + 2c 2d x + %pi + 2c +--R \|2 Si(---)cos(--------)csc(---------------) +--R 2 4 4 +--R * +--R +-----------------------+ +--R | 2d x + %pi + 2c 2 +--R |a sin(---------------) +--R \| 4 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 520 +a0048:= integrate(t0048,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 261 + +--S 262 of 520 +--m0048:= a0048-r0048 +--E 262 + +--S 263 of 520 +--d0048:= D(m0048,x) +--E 263 + +--S 264 of 520 +t0049:= (a+a*sin(c+d*x))^(1/2)/x^2 +--R +--R +--R +------------------+ +--R \|a sin(d x + c) + a +--R (162) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 520 +r0049:= -1/2*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + csc(1/2*c+1/4*%pi+1/2*d*x)*(2*sin(1/2*c+1/4*%pi+1/2*d*x)/x-_ + d*Ci(1/2*d*x)*cos(1/2*c+1/4*%pi)+d*sin(1/2*c+1/4*%pi)*Si(1/2*d*x)) +--R +--R +--R (163) +--R +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R - 2\|2 csc(---------------)sin(---------------) +--R 4 4 +--R + +--R +-+ d x 2d x + %pi + 2c %pi + 2c +--R - d x\|2 Si(---)csc(---------------)sin(--------) +--R 2 4 4 +--R + +--R +-+ d x %pi + 2c 2d x + %pi + 2c +--R d x\|2 Ci(---)cos(--------)csc(---------------) +--R 2 4 4 +--R * +--R +-----------------------+ +--R | 2d x + %pi + 2c 2 +--R |a sin(---------------) +--R \| 4 +--R / +--R 2x +--R Type: Expression(Integer) +--E 265 + +--S 266 of 520 +a0049:= integrate(t0049,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 266 + +--S 267 of 520 +--m0049:= a0049-r0049 +--E 267 + +--S 268 of 520 +--d0049:= D(m0049,x) +--E 268 + +--S 269 of 520 +t0050:= (a+a*sin(c+d*x))^(1/2)/x^3 +--R +--R +--R +------------------+ +--R \|a sin(d x + c) + a +--R (164) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 269 + +--S 270 of 520 +r0050:= -1/8*2^(1/2)*(a*sin(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + csc(1/2*c+1/4*%pi+1/2*d*x)*(4*sin(1/2*c+1/4*%pi+1/2*d*x)/x^2+_ + d^2*sin(1/2*c+1/4*%pi)*Ci(1/2*d*x)+_ + 2*d*cos(1/2*c+1/4*%pi+1/2*d*x)/x+d^2*cos(1/2*c+1/4*%pi)*Si(1/2*d*x)) +--R +--R +--R (165) +--R +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R - 4\|2 csc(---------------)sin(---------------) +--R 4 4 +--R + +--R 2 2 +-+ d x 2d x + %pi + 2c %pi + 2c +--R - d x \|2 Ci(---)csc(---------------)sin(--------) +--R 2 4 4 +--R + +--R +-+ 2d x + %pi + 2c 2 2 +-+ d x %pi + 2c +--R (- 2d x\|2 cos(---------------) - d x \|2 Si(---)cos(--------)) +--R 4 2 4 +--R * +--R 2d x + %pi + 2c +--R csc(---------------) +--R 4 +--R * +--R +-----------------------+ +--R | 2d x + %pi + 2c 2 +--R |a sin(---------------) +--R \| 4 +--R / +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 270 + +--S 271 of 520 +a0050:= integrate(t0050,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 271 + +--S 272 of 520 +--m0050:= a0050-r0050 +--E 272 + +--S 273 of 520 +--d0050:= D(m0050,x) +--E 273 + +--S 274 of 520 +t0051:= (a-a*sin(c+d*x))^(1/2)/x +--R +--R +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R (166) ----------------------- +--R x +--R Type: Expression(Integer) +--E 274 + +--S 275 of 520 +r0051:= 2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/4*%pi+_ + 1/2*d*x)*(cos(1/2*c+1/4*%pi)*Ci(1/2*d*x)-_ + sin(1/2*c+1/4*%pi)*Si(1/2*d*x)) +--R +--R +--R (167) +--R +-+ d x 2d x + %pi + 2c %pi + 2c +--R - \|2 Si(---)sec(---------------)sin(--------) +--R 2 4 4 +--R + +--R +-+ d x %pi + 2c 2d x + %pi + 2c +--R \|2 Ci(---)cos(--------)sec(---------------) +--R 2 4 4 +--R * +--R +-----------------------+ +--R | 2d x + %pi + 2c 2 +--R |a cos(---------------) +--R \| 4 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 520 +a0051:= integrate(t0051,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 276 + +--S 277 of 520 +--m0051:= a0051-r0051 +--E 277 + +--S 278 of 520 +--d0051:= D(m0051,x) +--E 278 + +--S 279 of 520 +t0052:= (a-a*sin(c+d*x))^(1/2)/x^2 +--R +--R +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R (168) ----------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 279 + +--S 280 of 520 +r0052:= -1/2*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + sec(1/2*c+1/4*%pi+1/2*d*x)*(2*cos(1/2*c+1/4*%pi+1/2*d*x)/x+_ + d*Ci(1/2*d*x)*sin(1/2*c+1/4*%pi)+d*cos(1/2*c+1/4*%pi)*Si(1/2*d*x)) +--R +--R +--R (169) +--R +-+ d x 2d x + %pi + 2c %pi + 2c +--R - d x\|2 Ci(---)sec(---------------)sin(--------) +--R 2 4 4 +--R + +--R +-+ 2d x + %pi + 2c +-+ d x %pi + 2c +--R (- 2\|2 cos(---------------) - d x\|2 Si(---)cos(--------)) +--R 4 2 4 +--R * +--R 2d x + %pi + 2c +--R sec(---------------) +--R 4 +--R * +--R +-----------------------+ +--R | 2d x + %pi + 2c 2 +--R |a cos(---------------) +--R \| 4 +--R / +--R 2x +--R Type: Expression(Integer) +--E 280 + +--S 281 of 520 +a0052:= integrate(t0052,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 281 + +--S 282 of 520 +--m0052:= a0052-r0052 +--E 282 + +--S 283 of 520 +--d0052:= D(m0052,x) +--E 283 + +--S 284 of 520 +t0053:= (a-a*sin(c+d*x))^(1/2)/x^3 +--R +--R +--R +--------------------+ +--R \|- a sin(d x + c) + a +--R (170) ----------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 284 + +--S 285 of 520 +r0053:= -1/8*2^(1/2)*(a*cos(1/2*c+1/4*%pi+1/2*d*x)^2)^(1/2)*_ + sec(1/2*c+1/4*%pi+1/2*d*x)*(4*cos(1/2*c+1/4*%pi+1/2*d*x)/x^2+_ + d^2*cos(1/2*c+1/4*%pi)*Ci(1/2*d*x)-_ + 2*d*sin(1/2*c+1/4*%pi+1/2*d*x)/x-d^2*sin(1/2*c+1/4*%pi)*Si(1/2*d*x)) +--R +--R +--R (171) +--R +-+ 2d x + %pi + 2c 2d x + %pi + 2c +--R 2d x\|2 sec(---------------)sin(---------------) +--R 4 4 +--R + +--R 2 2 +-+ d x 2d x + %pi + 2c %pi + 2c +--R d x \|2 Si(---)sec(---------------)sin(--------) +--R 2 4 4 +--R + +--R +-+ 2d x + %pi + 2c 2 2 +-+ d x %pi + 2c +--R (- 4\|2 cos(---------------) - d x \|2 Ci(---)cos(--------)) +--R 4 2 4 +--R * +--R 2d x + %pi + 2c +--R sec(---------------) +--R 4 +--R * +--R +-----------------------+ +--R | 2d x + %pi + 2c 2 +--R |a cos(---------------) +--R \| 4 +--R / +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 285 + +--S 286 of 520 +a0053:= integrate(t0053,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 286 + +--S 287 of 520 +--m0053:= a0053-r0053 +--E 287 + +--S 288 of 520 +--d0053:= D(m0053,x) +--E 288 + +--S 289 of 520 +t0054:= 1/(a+b*sin(x)^2)^2 +--R +--R +--R 1 +--R (172) ----------------------------- +--R 2 4 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 520 +r0054:= 1/2*(2*a+b)*atan((a+b)^(1/2)*tan(x)/a^(1/2))/a^(3/2)/(a+b)^(3/2)+_ + 1/2*b*tan(x)/a/(a+b)/(a+(a+b)*tan(x)^2) +--R +--R +--R (173) +--R +-----+ +--R 2 2 2 2 tan(x)\|b + a +--R ((b + 3a b + 2a )tan(x) + a b + 2a )atan(--------------) +--R +-+ +--R \|a +--R + +--R +-+ +-----+ +--R b tan(x)\|a \|b + a +--R / +--R 2 2 3 2 2 3 +-+ +-----+ +--R ((2a b + 4a b + 2a )tan(x) + 2a b + 2a )\|a \|b + a +--R Type: Expression(Integer) +--E 290 + +--S 291 of 520 +a0054:= integrate(t0054,x) +--R +--R +--R (174) +--R [ +--R 2 2 2 2 +--R ((b + 2a b)cos(x) - b - 3a b - 2a ) +--R * +--R log +--R +----------+ +--R 2 | 2 +--R ((- b - 2a)cos(x) + b + a)\|- a b - a +--R + +--R 2 +--R (2a b + 2a )cos(x)sin(x) +--R / +--R 2 +--R b cos(x) - b - a +--R + +--R +----------+ +--R | 2 +--R - 2b cos(x)sin(x)\|- a b - a +--R / +--R +----------+ +--R 2 2 2 2 2 3 | 2 +--R ((4a b + 4a b)cos(x) - 4a b - 8a b - 4a )\|- a b - a +--R , +--R +--R +--------+ +--R | 2 +--R 2 2 2 2 sin(x)\|a b + a +--R ((b + 2a b)cos(x) - b - 3a b - 2a )atan(-------------------------) +--R (2b + 2a)cos(x) + 2b + 2a +--R + +--R 2 2 2 2 +--R ((b + 2a b)cos(x) - b - 3a b - 2a ) +--R * +--R ((2b + a)cos(x) + 2b + 2a)sin(x) +--R atan(----------------------------------) +--R +--------+ +--R 2 | 2 +--R (cos(x) + 2cos(x) + 1)\|a b + a +--R + +--R +--------+ +--R | 2 +--R - b cos(x)sin(x)\|a b + a +--R / +--R +--------+ +--R 2 2 2 2 2 3 | 2 +--R ((2a b + 2a b)cos(x) - 2a b - 4a b - 2a )\|a b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 291 + +--S 292 of 520 +m0054a:= a0054.1-r0054 +--R +--R +--R (175) +--R 3 2 2 2 3 2 2 3 2 +--R ((b + 3a b + 2a b)cos(x) - b - 4a b - 5a b - 2a )tan(x) +--R + +--R 2 2 2 2 2 3 +--R (a b + 2a b)cos(x) - a b - 3a b - 2a +--R * +--R +-+ +-----+ +--R \|a \|b + a +--R * +--R +----------+ +--R 2 | 2 2 +--R ((- b - 2a)cos(x) + b + a)\|- a b - a + (2a b + 2a )cos(x)sin(x) +--R log(-------------------------------------------------------------------) +--R 2 +--R b cos(x) - b - a +--R + +--R 3 2 2 2 3 2 2 3 2 +--R ((- 2b - 6a b - 4a b)cos(x) + 2b + 8a b + 10a b + 4a )tan(x) +--R + +--R 2 2 2 2 2 3 +--R (- 2a b - 4a b)cos(x) + 2a b + 6a b + 4a +--R * +--R +----------+ +-----+ +--R | 2 tan(x)\|b + a +--R \|- a b - a atan(--------------) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 +--R (- 2b - 2a b)cos(x)sin(x)tan(x) + (- 2b cos(x) + 2b + 2a b)tan(x) +--R + +--R - 2a b cos(x)sin(x) +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- a b - a \|a \|b + a +--R / +--R 3 2 2 3 2 3 2 2 3 4 2 +--R ((4a b + 8a b + 4a b)cos(x) - 4a b - 12a b - 12a b - 4a )tan(x) +--R + +--R 2 2 3 2 2 2 3 4 +--R (4a b + 4a b)cos(x) - 4a b - 8a b - 4a +--R * +--R +----------+ +--R | 2 +-+ +-----+ +--R \|- a b - a \|a \|b + a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 520 +d0054a:= D(m0054a,x) +--R +--R +--R (176) +--R 3 2 2 2 3 2 2 3 2 +--R ((- b - 2a b - a b)cos(x) - b - 3a b - 3a b - a )sin(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- b - 2a b )cos(x) + (2b + 5a b + 3a b)cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 2b - 5a b - 4a b - a )cos(x) + b + 3a b + 3a b + a +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((- 2a b - 2a b)cos(x) - 2a b - 4a b - 2a )sin(x) +--R + +--R 3 2 6 3 2 2 4 +--R (- 2b - 4a b )cos(x) + (6b + 12a b + 6a b)cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 6b - 14a b - 10a b - 2a )cos(x) + 2b + 6a b + 6a b + 2a +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 2 3 2 3 2 6 +--R (- a b cos(x) - a b - a )sin(x) + (- b - 2a b )cos(x) +--R + +--R 3 2 2 4 3 2 2 3 2 3 +--R (3b + 7a b + 3a b)cos(x) + (- 3b - 8a b - 6a b - a )cos(x) + b +--R + +--R 2 2 3 +--R 3a b + 3a b + a +--R * +--R +----------+ +--R | 2 +--R \|- a b - a +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R ((b + 2a b + a b )cos(x) + (b + 3a b + 3a b + a b)cos(x)) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 5 3 2 2 3 3 +--R (b + 4a b + 3a b )cos(x) + (- 3a b - 6a b - 3a b)cos(x) +--R + +--R 4 3 2 2 3 +--R (- b - 3a b - 3a b - a b)cos(x) +--R * +--R sin(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3 2 2 3 3 2 2 3 3 +--R ((2a b + 2a b )cos(x) + (2a b + 4a b + 2a b)cos(x))sin(x) +--R + +--R 3 2 2 5 3 2 2 3 3 +--R (6a b + 6a b )cos(x) + (- 8a b - 14a b - 6a b)cos(x) +--R + +--R 3 2 2 3 +--R (2a b + 4a b + 2a b)cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 2 2 3 3 +--R (a b cos(x) + (a b + a b)cos(x))sin(x) +--R + +--R 3 2 2 5 3 2 2 3 3 +--R (2a b + 3a b )cos(x) + (- 4a b - 8a b - 3a b)cos(x) +--R + +--R 3 2 2 3 +--R (2a b + 5a b + 3a b)cos(x) +--R * +--R sin(x) +--R / +--R 5 4 2 3 3 2 6 +--R (b + 4a b + 5a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 3b - 13a b - 21a b - 15a b - 4a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (3b + 14a b + 26a b + 24a b + 11a b + 2a )cos(x) - b +--R + +--R 4 2 3 3 2 4 5 +--R - 5a b - 10a b - 10a b - 5a b - a +--R * +--R 4 +--R tan(x) +--R + +--R 4 2 3 3 2 6 +--R (2a b + 6a b + 4a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 6a b - 20a b - 22a b - 8a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 4 2 3 +--R (6a b + 22a b + 30a b + 18a b + 4a )cos(x) - 2a b - 8a b +--R + +--R 3 2 4 5 +--R - 12a b - 8a b - 2a +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 3 2 6 2 3 3 2 4 4 +--R (a b + 2a b )cos(x) + (- 3a b - 7a b - 4a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 4 5 +--R (3a b + 8a b + 7a b + 2a )cos(x) - a b - 3a b - 3a b - a +--R * +--R +----------+ +--R | 2 +--R \|- a b - a +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 2a b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (4a b + 16a b + 24a b + 16a b + 4a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 2a b - 10a b - 20a b - 20a b - 10a b - 2a )cos(x) +--R * +--R 4 +--R sin(x)tan(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- 4a b - 8a b - 4a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (8a b + 24a b + 24a b + 8a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 4a b - 16a b - 24a b - 16a b - 4a )cos(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 3 3 4 2 5 3 3 4 2 5 3 +--R (- 2a b - 2a b )cos(x) + (4a b + 8a b + 4a b)cos(x) +--R + +--R 3 3 4 2 5 6 +--R (- 2a b - 6a b - 6a b - 2a )cos(x) +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 293 + +--S 294 of 520 +m0054b:= a0054.2-r0054 +--R +--R +--R (177) +--R 3 2 2 2 3 2 2 3 2 +--R ((b + 3a b + 2a b)cos(x) - b - 4a b - 5a b - 2a )tan(x) +--R + +--R 2 2 2 2 2 3 +--R (a b + 2a b)cos(x) - a b - 3a b - 2a +--R * +--R +--------+ +--R | 2 +--R +-+ +-----+ sin(x)\|a b + a +--R \|a \|b + a atan(-------------------------) +--R (2b + 2a)cos(x) + 2b + 2a +--R + +--R 3 2 2 2 3 2 2 3 2 +--R ((- b - 3a b - 2a b)cos(x) + b + 4a b + 5a b + 2a )tan(x) +--R + +--R 2 2 2 2 2 3 +--R (- a b - 2a b)cos(x) + a b + 3a b + 2a +--R * +--R +--------+ +-----+ +--R | 2 tan(x)\|b + a +--R \|a b + a atan(--------------) +--R +-+ +--R \|a +--R + +--R 3 2 2 2 3 2 2 3 2 +--R ((b + 3a b + 2a b)cos(x) - b - 4a b - 5a b - 2a )tan(x) +--R + +--R 2 2 2 2 2 3 +--R (a b + 2a b)cos(x) - a b - 3a b - 2a +--R * +--R +-+ +-----+ ((2b + a)cos(x) + 2b + 2a)sin(x) +--R \|a \|b + a atan(----------------------------------) +--R +--------+ +--R 2 | 2 +--R (cos(x) + 2cos(x) + 1)\|a b + a +--R + +--R 2 2 2 2 2 +--R (- b - a b)cos(x)sin(x)tan(x) + (- b cos(x) + b + a b)tan(x) +--R + +--R - a b cos(x)sin(x) +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|a b + a +--R / +--R 3 2 2 3 2 3 2 2 3 4 2 +--R ((2a b + 4a b + 2a b)cos(x) - 2a b - 6a b - 6a b - 2a )tan(x) +--R + +--R 2 2 3 2 2 2 3 4 +--R (2a b + 2a b)cos(x) - 2a b - 4a b - 2a +--R * +--R +--------+ +--R +-+ +-----+ | 2 +--R \|a \|b + a \|a b + a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 520 +--d0054b:= D(m0054b,x) +--E 295 + +--S 296 of 520 +t0055:= (1+sin(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (178) \|sin(x) + 1 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 520 +r0055:= x +--R +--R +--R (179) x +--R Type: Variable(x) +--E 297 + +--S 298 of 520 +a0055:= integrate(t0055,x) +--R +--R +--R x +------------+ +--R ++ | 2 +--R (180) | \|sin(%R) + 1 d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 520 +--m0055:= a0055-r0055 +--E 299 + +--S 300 of 520 +--d0055:= D(m0055,x) +--E 300 + +--S 301 of 520 +t0056:= (-1-sin(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (181) \|- sin(x) - 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 520 +r0056:= (-3+cos(2*x))^(1/2)*x/(3-cos(2*x))^(1/2) +--R +--R +--R +-----------+ +--R x\|cos(2x) - 3 +--R (182) ---------------- +--R +-------------+ +--R \|- cos(2x) + 3 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 520 +a0056:= integrate(t0056,x) +--R +--R +--R (183) +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +--R (2(%e ) - 2%e ) +--R * +--R INTSIGN +--R , +--R x +--R , +--R +---+ 2 +--R +---+ %R\|- 1 +---+ +--R (2\|- 1 (%e ) + 2\|- 1 ) +--R * +--R +----------------------------------+ +--R | +---+ 4 +---+ 2 +--R | %R\|- 1 %R\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +--R %R\|- 1 %R\|- 1 %R\|- 1 +--R (%e ) - 6(%e ) + (%e ) +--R * +--R d%R +--R + +--R +--------------------------------+ +--R +---+ | +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ | x\|- 1 x\|- 1 +--R (- \|- 1 %e - \|- 1 )\|(%e ) - 6(%e ) + 1 +--R / +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +--R 2(%e ) - 2%e +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 520 +m0056:= a0056-r0056 +--R +--R +--R (184) +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +-------------+ +--R (2(%e ) - 2%e )\|- cos(2x) + 3 +--R * +--R INTSIGN +--R , +--R x +--R , +--R +---+ 2 +--R +---+ %R\|- 1 +---+ +--R (2\|- 1 (%e ) + 2\|- 1 ) +--R * +--R +----------------------------------+ +--R | +---+ 4 +---+ 2 +--R | %R\|- 1 %R\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +--R %R\|- 1 %R\|- 1 %R\|- 1 +--R (%e ) - 6(%e ) + (%e ) +--R * +--R d%R +--R + +--R +---+ +--R +---+ x\|- 1 +---+ +-------------+ +--R (- \|- 1 %e - \|- 1 )\|- cos(2x) + 3 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +-----------+ +--R (- 2x (%e ) + 2x %e )\|cos(2x) - 3 +--R / +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +-------------+ +--R (2(%e ) - 2%e )\|- cos(2x) + 3 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 520 +d0056:= D(m0056,x) +--R +--R +--R (185) +--R +---+ 4 +---+ 3 +--R x\|- 1 x\|- 1 +--R (- 2cos(2x) + 6)(%e ) + (4cos(2x) - 12)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R (- 2cos(2x) + 6)(%e ) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 7 +---+ 6 +---+ 5 +--R x\|- 1 x\|- 1 x\|- 1 +--R (%e ) - 2(%e ) - (%e ) +--R + +--R +---+ 4 +---+ 3 +--R +---+ x\|- 1 +---+ x\|- 1 +--R (4\|- 1 + 12)(%e ) + (- 8\|- 1 - 1)(%e ) +--R + +--R +---+ 2 +---+ +--R +---+ x\|- 1 +---+ x\|- 1 +---+ +--R (8\|- 1 - 2)(%e ) + (- 8\|- 1 + 1)%e + 4\|- 1 +--R * +--R +-------------+ +-----------+ +--R \|- cos(2x) + 3 \|cos(2x) - 3 +--R / +--R +---+ 4 +---+ 3 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +-------------+ +--R (2(%e ) - 4(%e ) + 2(%e ) )\|- cos(2x) + 3 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R +-----------+ | x\|- 1 x\|- 1 +--R \|cos(2x) - 3 \|(%e ) - 6(%e ) + 1 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 520 +t0057:= 1/(1+sin(x)^2)^(1/2) +--R +--R +--R 1 +--R (186) -------------- +--R +-----------+ +--R | 2 +--R \|sin(x) + 1 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 520 +r0057:= atanh(x) +--R +--R +--R (187) atanh(x) +--R Type: Expression(Integer) +--E 307 + +--S 308 of 520 +a0057:= integrate(t0057,x) +--R +--R +--R x +--R ++ 1 +--R (188) | --------------- d%R +--R ++ +------------+ +--R | 2 +--R \|sin(%R) + 1 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 520 +--m0057:= a0057-r0057 +--E 309 + +--S 310 of 520 +--d0057:= D(m0057,x) +--E 310 + +--S 311 of 520 +t0058:= 1/(-1-sin(x)^2)^(1/2) +--R +--R +--R 1 +--R (189) ---------------- +--R +-------------+ +--R | 2 +--R \|- sin(x) - 1 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 520 +r0058:= (3-cos(2*x))^(1/2)*atanh(x)/(-3+cos(2*x))^(1/2) +--R +--R +--R +-------------+ +--R atanh(x)\|- cos(2x) + 3 +--R (190) ------------------------ +--R +-----------+ +--R \|cos(2x) - 3 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 520 +a0058:= integrate(t0058,x) +--R +--R +--R +----------------------------------+ +--R | +---+ 4 +---+ 2 +--R x +---+ | %R\|- 1 %R\|- 1 +--R ++ 2\|- 1 \|(%e ) - 6(%e ) + 1 +--R (191) | ---------------------------------------------- d%R +--R ++ +---+ 6 +---+ 4 +---+ 2 +--R %R\|- 1 %R\|- 1 %R\|- 1 +--R (%e ) - 6(%e ) + (%e ) +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 520 +--m0058:= a0058-r0058 +--E 314 + +--S 315 of 520 +--d0058:= D(m0058,x) +--E 315 + +--S 316 of 520 +t0059:= x/(a+b*sin(x)^2) +--R +--R +--R x +--R (192) ------------- +--R 2 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 520 +r0059:= 1/4*(-2*%i*x*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)+_ + b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 2*%i*x*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)-_ + b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-_ + polylog(2,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + polylog(2,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/_ + a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 317 + +--S 318 of 520 +a0059:= integrate(t0059,x) +--R +--R +--R x +--R ++ %R +--R (193) | -------------- d%R +--R ++ 2 +--R b sin(%R) + a +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 520 +--m0059:= a0059-r0059 +--E 319 + +--S 320 of 520 +--d0059:= D(m0059,x) +--E 320 + +--S 321 of 520 +t0060:= x^2/(a+b*sin(x)^2) +--R +--R +--R 2 +--R x +--R (194) ------------- +--R 2 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 321 + +--S 322 of 520 +r0060:= -1/4*(2*%i*x^2*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)+_ + b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 2*%i*x^2*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)-_ + b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + 2*x*polylog(2,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 2*x*polylog(2,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + %i*polylog(3,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + %i*polylog(3,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/_ + a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 322 + +--S 323 of 520 +a0060:= integrate(t0060,x) +--R +--R +--R x 2 +--R ++ %R +--R (195) | -------------- d%R +--R ++ 2 +--R b sin(%R) + a +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 520 +--m0060:= a0060-r0060 +--E 324 + +--S 325 of 520 +--d0060:= D(m0060,x) +--E 325 + +--S 326 of 520 +t0061:= x^3/(a+b*sin(x)^2) +--R +--R +--R 3 +--R x +--R (196) ------------- +--R 2 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 520 +r0061:= -1/8*(4*%i*x^3*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)+_ + b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 4*%i*x^3*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)-_ + b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + 6*x^2*polylog(2,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 6*x^2*polylog(2,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + 6*%i*x*polylog(3,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 6*%i*x*polylog(3,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-_ + 3*polylog(4,-b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 3*polylog(4,b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/_ + a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 327 + +--S 328 of 520 +a0061:= integrate(t0061,x) +--R +--R +--R x 3 +--R ++ %R +--R (197) | -------------- d%R +--R ++ 2 +--R b sin(%R) + a +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 520 +--m0061:= a0061-r0061 +--E 329 + +--S 330 of 520 +--d0061:= D(m0061,x) +--E 330 + +--S 331 of 520 +t0062:= x*(sin(x)^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 +--R (198) x\|sin(x) +--R Type: Expression(Integer) +--E 331 + +--S 332 of 520 +r0062:= -csc(x)*(x*cos(x)-sin(x))*(sin(x)^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 +--R (199) (csc(x)sin(x) - x cos(x)csc(x))\|sin(x) +--R Type: Expression(Integer) +--E 332 + +--S 333 of 520 BUG? +a0062:= integrate(t0062,x) +--R +--R +--R (200) sin(x) - x cos(x) +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 520 +m0062:= a0062-r0062 +--R +--R +--R +-------+ +--R | 2 +--R (201) (- csc(x)sin(x) + x cos(x)csc(x))\|sin(x) + sin(x) - x cos(x) +--R Type: Expression(Integer) +--E 334 + +--S 335 of 520 +d0062:= D(m0062,x) +--R +--R +--R (202) +--R +-------+ +--R | 2 3 +--R x sin(x)\|sin(x) + (cot(x) - x)csc(x)sin(x) +--R + +--R 2 2 +--R (- x cos(x)cot(x) - cos(x))csc(x)sin(x) + x cos(x) csc(x)sin(x) +--R / +--R +-------+ +--R | 2 +--R \|sin(x) +--R Type: Expression(Integer) +--E 335 + +--S 336 of 520 +t0063:= 1/(a+b*sin(x)^3) +--R +--R +--R 1 +--R (203) ------------- +--R 3 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 336 + +--S 337 of 520 +r0063:= -2/3*atan(((-1)^(1/3)*b^(1/3)-a^(1/3)*tan(1/2*x))/_ + (a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/_ + (a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2)+2/3*_ + atan((b^(1/3)+a^(1/3)*tan(1/2*x))/(a^(2/3)-b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan(((-1)^(2/3)*b^(1/3)+_ + a^(1/3)*tan(1/2*x))/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2) +--R +--R +--R (204) +--R - +--R +---------------+ +-------------------+ +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+3+-+ x 3+-+ +--R \|- 1 \|b - tan(-)\|a +--R 2 +--R atan(-------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R 3+-+ x 3+-+ +--R +----------------------+ +-------------------+ \|b + tan(-)\|a +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 2 +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R 3+---+2 3+-+ x 3+-+ +--R +----------------------+ +---------------+ \|- 1 \|b + tan(-)\|a +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a atan(------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 520 +a0063:= integrate(t0063,x) +--R +--R +--R (205) +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EI0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EI0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EI0 +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--R (18a b - 18a )cos(x) + 18a b - 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EI0 + 4b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EI0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EI0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EI0 +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EI0 +--R + +--R 2 3 2 3 +--R (- 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EI0 + 4b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EI0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EI0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EI0 +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EI0 +--R + +--R 2 3 2 3 +--R (- 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EI0 + 4b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EI0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EI0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EI0 +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--R (18a b - 18a )cos(x) + 18a b - 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EI0 + 4b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--I \|4%%EI0 +--R * +--R log +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EI0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EI0 - 9a b cos(x) - 9a b +--R * +--R +------+ +--I \|4%%EI0 +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EI0 + 2b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I \|4%%EI0 +--R * +--R log +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EI0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EI0 + 9a b cos(x) + 9a b +--R * +--R +------+ +--I \|4%%EI0 +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EI0 + 2b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 520 +m0063:= a0063-r0063 +--R +--R +--R (206) +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EI0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EI0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EI0 +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--R (18a b - 18a )cos(x) + 18a b - 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EI0 + 4b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EI0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EI0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EI0 +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EI0 +--R + +--R 2 3 2 3 +--R (- 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EI0 + 4b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EI0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EI0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EI0 +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EI0 +--R + +--R 2 3 2 3 +--R (- 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EI0 + 4b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EI0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EI0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EI0 +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EI0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--R (18a b - 18a )cos(x) + 18a b - 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EI0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EI0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EI0 + 4b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +------+ +--I \|\|- 1 \|b + \|a \|4%%EI0 +--R * +--R log +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EI0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EI0 - 9a b cos(x) - 9a b +--R * +--R +------+ +--I \|4%%EI0 +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EI0 + 2b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%EI0 +--R * +--R log +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EI0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EI0 + 9a b cos(x) + 9a b +--R * +--R +------+ +--I \|4%%EI0 +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EI0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EI0 + 2b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R 3+---+3+-+ x 3+-+ +--R +---------------+ +-------------------+ \|- 1 \|b - tan(-)\|a +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 2 +--R 4\|- \|b + \|a \|\|- 1 \|b + \|a atan(-------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +-------------------+ +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 4\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+-+ x 3+-+ +--R \|b + tan(-)\|a +--R 2 +--R atan(------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R - +--R +----------------------+ +---------------+ +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 4\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 3+---+2 3+-+ x 3+-+ +--R \|- 1 \|b + tan(-)\|a +--R 2 +--R atan(------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 6\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 520 +--d0063:= D(m0063,x) +--E 340 + +--S 341 of 520 +t0064:= 1/(a+b*sin(x)^4) +--R +--R +--R 1 +--R (207) ------------- +--R 4 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 520 +r0064:= 1/2*atan((a^(1/2)-(-b)^(1/2))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/_ + (a^(1/2)-(-b)^(1/2))^(1/2)+1/2*_ + atan((a^(1/2)+(-b)^(1/2))^(1/2)*_ + tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)+(-b)^(1/2))^(1/2) +--R +--R +--R (208) +--R +-------------+ +--R +-------------+ | +-+ +---+ +--R | +-+ +---+ tan(x)\|\|a + \|- b +--R \|\|a - \|- b atan(----------------------) +--R 4+-+ +--R \|a +--R + +--R +-------------+ +--R +-------------+ | +-+ +---+ +--R | +-+ +---+ tan(x)\|\|a - \|- b +--R \|\|a + \|- b atan(----------------------) +--R 4+-+ +--R \|a +--R / +--R +-------------+ +-------------+ +--R 4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|a \|\|a - \|- b \|\|a + \|- b +--R Type: Expression(Integer) +--E 342 + +--S 343 of 520 +a0064:= integrate(t0064,x) +--R +--R +--R (209) +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 2 3 | b +--R ((32a b + 32a )sin(x) |- ---------------------- + 4a sin(x)) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 2 3 | b +--R (32a b + 32a )sin(x) |- ---------------------- +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R - 4a sin(x) +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 2 3 | b +--R (- 32a b - 32a )sin(x) |- ---------------------- +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 4a sin(x) +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +------------------------+ +--R 2 3 | b +--R (- 32a b - 32a )sin(x) |- ---------------------- +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R - 4a sin(x) +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 520 +m0064:= a0064-r0064 +--R +--R +--R (210) +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R log +--R +------------------------+ +--R 2 3 | b +--R ((32a b + 32a )sin(x) |- ---------------------- + 4a sin(x)) +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R 4+-+3 | \| 64a b + 128a b + 64a +--R \|a |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +-------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|\|a - \|- b \|\|a + \|- b +--R * +--R log +--R +------------------------+ +--R 2 3 | b +--R (32a b + 32a )sin(x) |- ---------------------- +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R - 4a sin(x) +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |--------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R log +--R +------------------------+ +--R 2 3 | b +--R (- 32a b - 32a )sin(x) |- ---------------------- +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R 4a sin(x) +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R log +--R +------------------------+ +--R 2 3 | b +--R (- 32a b - 32a )sin(x) |- ---------------------- +--R | 3 2 4 5 +--R \| 64a b + 128a b + 64a +--R + +--R - 4a sin(x) +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ +--R +-------------+ | +-+ +---+ +--R | +-+ +---+ tan(x)\|\|a + \|- b +--R - \|\|a - \|- b atan(----------------------) +--R 4+-+ +--R \|a +--R + +--R +-------------+ +--R +-------------+ | +-+ +---+ +--R | +-+ +---+ tan(x)\|\|a - \|- b +--R - \|\|a + \|- b atan(----------------------) +--R 4+-+ +--R \|a +--R / +--R +-------------+ +-------------+ +--R 4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|a \|\|a - \|- b \|\|a + \|- b +--R Type: Expression(Integer) +--E 344 + +--S 345 of 520 +d0064:= D(m0064,x) +--R +--R +--R (211) +--R 4 2 2 4 4 +--R ((b + a)sin(x) + (2b + 2a)cos(x) sin(x) + (b + a)cos(x) )tan(x) +--R + +--R 4 2 2 4 2 4 +--R ((- b - a)sin(x) - 2a cos(x) sin(x) - a cos(x) )tan(x) - b sin(x) +--R * +--R 4+-+2 +--R \|a +--R + +--R 4 2 2 4 4 +--R ((- b - a)sin(x) - 2a cos(x) sin(x) - a cos(x) )tan(x) +--R + +--R 4 2 2 4 2 +--R ((- b + a)sin(x) + 2a cos(x) sin(x) + a cos(x) )tan(x) +--R * +--R +-+ +--R \|a +--R / +--R 2 2 4 2 2 2 +--R (b + 2a b + a )sin(x) + (2a b + 2a )cos(x) sin(x) +--R + +--R 2 4 +--R (a b + a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 4 2 2 2 2 4 +--R (a b + a )sin(x) + 2a cos(x) sin(x) + a cos(x) +--R * +--R 4+-+2 +--R \|a +--R + +--R 2 4 2 2 2 2 4 2 +-+ +--R ((2a b + 2a )sin(x) + 4a cos(x) sin(x) + 2a cos(x) )tan(x) \|a +--R Type: Expression(Integer) +--E 345 + +--S 346 of 520 +t0065:= 1/(a+b*sin(x)^6) +--R +--R +--R 1 +--R (212) ------------- +--R 6 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 520 +r0065:= 1/3*atan((a^(1/3)+b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/_ + (a^(1/3)+b^(1/3))^(1/2)+1/3*atan((a^(1/3)-(-1)^(1/3)*b^(1/3))^(1/2)*_ + tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)-(-1)^(1/3)*b^(1/3))^(1/2)+_ + 1/3*atan((a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2)*_ + tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2) +--R +--R +--R (213) +--R +------------------+ +--R +-------------------+ +-----------+ |3+---+2 3+-+ 3+-+ +--R | 3+---+3+-+ 3+-+ |3+-+ 3+-+ tan(x)\|\|- 1 \|b + \|a +--R \|- \|- 1 \|b + \|a \|\|b + \|a atan(---------------------------) +--R 6+-+ +--R \|a +--R + +--R +-----------+ +--R +-------------------+ +------------------+ |3+-+ 3+-+ +--R | 3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|\|b + \|a +--R \|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(--------------------) +--R 6+-+ +--R \|a +--R + +--R +-------------------+ +--R +-----------+ +------------------+ | 3+---+3+-+ 3+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|- \|- 1 \|b + \|a +--R \|\|b + \|a \|\|- 1 \|b + \|a atan(----------------------------) +--R 6+-+ +--R \|a +--R / +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 520 +a0065:= integrate(t0065,x) +--R +--R +--R (214) +--R - +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 4 5 +--I (3888a b + 3888a )sin(x)%%EK0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 3 +--I (3888a b + 3888a )sin(x)%%EK0 + 324a sin(x)%%EK0 +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 4 5 +--I (3888a b + 3888a )sin(x)%%EK0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 3 +--I (- 3888a b - 3888a )sin(x)%%EK0 - 324a sin(x)%%EK0 +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 4 5 +--I (- 3888a b - 3888a )sin(x)%%EK0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 3 +--I (3888a b + 3888a )sin(x)%%EK0 + 324a sin(x)%%EK0 +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 4 5 +--I (- 3888a b - 3888a )sin(x)%%EK0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 3 +--I (- 3888a b - 3888a )sin(x)%%EK0 - 324a sin(x)%%EK0 +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I \|4%%EK0 +--R * +--R log +--R 4 5 2 3 +--I (7776a b + 7776a )sin(x)%%EK0 + 648a sin(x)%%EK0 +--R + +--R 18a sin(x) +--R * +--R +------+ +--I \|4%%EK0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--I \|4%%EK0 +--R * +--R log +--R 4 5 2 3 +--I (- 7776a b - 7776a )sin(x)%%EK0 - 648a sin(x)%%EK0 +--R + +--R - 18a sin(x) +--R * +--R +------+ +--I \|4%%EK0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 520 +m0065:= a0065-r0065 +--R +--R +--R (215) +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 4 5 +--I (3888a b + 3888a )sin(x)%%EK0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 3 +--I (3888a b + 3888a )sin(x)%%EK0 + 324a sin(x)%%EK0 +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 4 5 +--I (3888a b + 3888a )sin(x)%%EK0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 3 +--I (- 3888a b - 3888a )sin(x)%%EK0 - 324a sin(x)%%EK0 +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 4 5 +--I (- 3888a b - 3888a )sin(x)%%EK0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 3 +--I (3888a b + 3888a )sin(x)%%EK0 + 324a sin(x)%%EK0 +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 4 5 +--I (- 3888a b - 3888a )sin(x)%%EK0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 4 5 2 3 +--I (- 3888a b - 3888a )sin(x)%%EK0 - 324a sin(x)%%EK0 +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EK0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EK0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EK0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%EK0 +--R * +--R log +--R 4 5 2 3 +--I (7776a b + 7776a )sin(x)%%EK0 + 648a sin(x)%%EK0 +--R + +--R 18a sin(x) +--R * +--R +------+ +--I \|4%%EK0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%EK0 +--R * +--R log +--R 4 5 2 3 +--I (- 7776a b - 7776a )sin(x)%%EK0 - 648a sin(x)%%EK0 +--R + +--R - 18a sin(x) +--R * +--R +------+ +--I \|4%%EK0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------------------+ +--R +-------------------+ +-----------+ |3+---+2 3+-+ 3+-+ +--R | 3+---+3+-+ 3+-+ |3+-+ 3+-+ tan(x)\|\|- 1 \|b + \|a +--R - 2\|- \|- 1 \|b + \|a \|\|b + \|a atan(---------------------------) +--R 6+-+ +--R \|a +--R + +--R +-----------+ +--R +-------------------+ +------------------+ |3+-+ 3+-+ +--R | 3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|\|b + \|a +--R - 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(--------------------) +--R 6+-+ +--R \|a +--R + +--R +-------------------+ +--R +-----------+ +------------------+ | 3+---+3+-+ 3+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|- \|- 1 \|b + \|a +--R - 2\|\|b + \|a \|\|- 1 \|b + \|a atan(----------------------------) +--R 6+-+ +--R \|a +--R / +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 6\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 520 +d0065:= D(m0065,x) +--R +--R +--R (216) +--R 3+---+2 3+---+ 6 +--R ((6b + 15a)\|- 1 + (- 6b - 15a)\|- 1 + 6b + 15a)sin(x) +--R + +--R 3+---+2 3+---+ +--R ((18b + 45a)\|- 1 + (- 18b - 45a)\|- 1 + 18b + 45a) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 3+---+2 3+---+ +--R ((18b + 45a)\|- 1 + (- 18b - 45a)\|- 1 + 18b + 45a) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((6b + 15a)\|- 1 + (- 6b - 15a)\|- 1 + 6b + 15a)cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 3b - 3a)\|- 1 + (3b + 3a)\|- 1 - 3b - 3a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3a \|- 1 + 3a\|- 1 - 3a)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3b \|- 1 + 3b\|- 1 - 3b)sin(x) +--R * +--R 3+-+6+-+4 +--R \|a \|a +--R + +--R 3+---+2 3+---+ 6 +--R ((- 12b - 12a)\|- 1 + (12b + 12a)\|- 1 - 12b - 12a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 12a \|- 1 + 12a\|- 1 - 12a)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 12b + 6a)\|- 1 + (12b - 6a)\|- 1 - 12b + 6a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R (6a \|- 1 - 6a\|- 1 + 6a)cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 3+-+2 6+-+2 +--R \|a \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- b - 11a b - 10a )\|- 1 + (b + 11a b + 10a )\|- 1 - b +--R + +--R 2 +--R - 11a b - 10a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 3a b - 30a )\|- 1 + (3a b + 30a )\|- 1 - 3a b - 30a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 3a b - 30a )\|- 1 + (3a b + 30a )\|- 1 - 3a b - 30a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((- a b - 10a )\|- 1 + (a b + 10a )\|- 1 - a b - 10a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- b - 8a b + 20a )\|- 1 + (b + 8a b - 20a )\|- 1 - b +--R + +--R 2 +--R - 8a b + 20a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((6a b + 60a )\|- 1 + (- 6a b - 60a )\|- 1 + 6a b + 60a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((6a b + 60a )\|- 1 + (- 6a b - 60a )\|- 1 + 6a b + 60a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((2a b + 20a )\|- 1 + (- 2a b - 20a )\|- 1 + 2a b + 20a )cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 3+-+2 +--R \|b +--R + +--R 3+---+2 3+---+ 6 +--R ((15b + 6a)\|- 1 + (- 15b - 6a)\|- 1 + 15b + 6a)sin(x) +--R + +--R 3+---+2 3+---+ +--R ((45b + 18a)\|- 1 + (- 45b - 18a)\|- 1 + 45b + 18a) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 3+---+2 3+---+ +--R ((45b + 18a)\|- 1 + (- 45b - 18a)\|- 1 + 45b + 18a) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((15b + 6a)\|- 1 + (- 15b - 6a)\|- 1 + 15b + 6a)cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 3b - 3a)\|- 1 + (3b + 3a)\|- 1 - 3b - 3a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3a \|- 1 + 3a\|- 1 - 3a)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3b \|- 1 + 3b\|- 1 - 3b)sin(x) +--R * +--R 3+-+2 6+-+4 +--R \|a \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 2b - 10a b - 8a )\|- 1 + (2b + 10a b + 8a )\|- 1 +--R + +--R 2 2 +--R - 2b - 10a b - 8a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 6a b - 24a )\|- 1 + (6a b + 24a )\|- 1 - 6a b +--R + +--R 2 +--R - 24a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 6a b - 24a )\|- 1 + (6a b + 24a )\|- 1 - 6a b +--R + +--R 2 +--R - 24a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 2a b - 8a )\|- 1 + (2a b + 8a )\|- 1 - 2a b - 8a ) +--R * +--R 6 +--R cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 2b - 7a b + 4a )\|- 1 + (2b + 7a b - 4a )\|- 1 +--R + +--R 2 2 +--R - 2b - 7a b + 4a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (3a b + 12a )\|- 1 + (- 3a b - 12a )\|- 1 + 3a b +--R + +--R 2 +--R 12a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (3a b + 12a )\|- 1 + (- 3a b - 12a )\|- 1 + 3a b +--R + +--R 2 +--R 12a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((a b + 4a )\|- 1 + (- a b - 4a )\|- 1 + a b + 4a )cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 6+-+2 +--R \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 5b - 10a b - 5a )\|- 1 + (5b + 10a b + 5a )\|- 1 +--R + +--R 2 2 +--R - 5b - 10a b - 5a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 15a b - 15a )\|- 1 + (15a b + 15a )\|- 1 - 15a b +--R + +--R 2 +--R - 15a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 15a b - 15a )\|- 1 + (15a b + 15a )\|- 1 - 15a b +--R + +--R 2 +--R - 15a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 5a b - 5a )\|- 1 + (5a b + 5a )\|- 1 - 5a b - 5a ) +--R * +--R 6 +--R cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (- 5b + 5a b + 10a )\|- 1 + (5b - 5a b - 10a )\|- 1 +--R + +--R 2 2 +--R - 5b + 5a b + 10a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (30a b + 30a )\|- 1 + (- 30a b - 30a )\|- 1 + 30a b +--R + +--R 2 +--R 30a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (30a b + 30a )\|- 1 + (- 30a b - 30a )\|- 1 + 30a b +--R + +--R 2 +--R 30a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (10a b + 10a )\|- 1 + (- 10a b - 10a )\|- 1 + 10a b +--R + +--R 2 +--R 10a +--R * +--R 6 +--R cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 3+-+ +--R \|a +--R * +--R 3+-+ +--R \|b +--R + +--R 3+---+2 3+---+ 2 2 6 +--R (18a b \|- 1 - 18a b\|- 1 + 3b + 24a b + 3a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 2 4 +--R (54a b \|- 1 - 54a b\|- 1 + 9b + 72a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 2 +--R (54a b \|- 1 - 54a b\|- 1 + 9b + 72a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 2 6 +--R (18a b \|- 1 - 18a b\|- 1 + 3b + 24a b + 3a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 6 2 2 4 +--R (- 3b - 6a b - 3a )sin(x) + (- 9a b - 9a )cos(x) sin(x) +--R + +--R 2 4 2 2 6 +--R (- 9a b - 9a )cos(x) sin(x) + (- 3a b - 3a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 6 +--R (- 3b - 3a b)sin(x) +--R * +--R 6+-+4 +--R \|a +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 6b - 6a b)\|- 1 + (6b + 6a b)\|- 1 - 12b - 18a b +--R + +--R 2 +--R - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (- 18a b \|- 1 + 18a b\|- 1 - 36a b - 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (- 18a b \|- 1 + 18a b\|- 1 - 36a b - 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (- 6a b \|- 1 + 6a b\|- 1 - 12a b - 6a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 6 +--R ((- 6b + 3a b)\|- 1 + (6b - 3a b)\|- 1 - 12b + 3a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (9a b \|- 1 - 9a b\|- 1 + 18a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (9a b \|- 1 - 9a b\|- 1 + 18a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (3a b \|- 1 - 3a b\|- 1 + 6a b + 3a )cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 3+-+6+-+2 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 9b - 9a b)\|- 1 + (9b + 9a b)\|- 1 - 12b - 15a b +--R + +--R 2 +--R - 3a +--R * +--R 6 +--R sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (- 27a b \|- 1 + 27a b\|- 1 - 36a b - 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (- 27a b \|- 1 + 27a b\|- 1 - 36a b - 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (- 9a b \|- 1 + 9a b\|- 1 - 12a b - 3a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 9b + 18a b)\|- 1 + (9b - 18a b)\|- 1 - 12b + 21a b +--R + +--R 2 +--R 6a +--R * +--R 6 +--R sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (54a b \|- 1 - 54a b\|- 1 + 72a b + 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (54a b \|- 1 - 54a b\|- 1 + 72a b + 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (18a b \|- 1 - 18a b\|- 1 + 24a b + 6a )cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 3+-+2 +--R \|a +--R / +--R 2 2 3+---+2 +--R (6b + 21a b + 15a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 6b - 21a b - 15a )\|- 1 + 6b + 21a b + 15a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (18a b + 45a )\|- 1 + (- 18a b - 45a )\|- 1 + 18a b +--R + +--R 2 +--R 45a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (18a b + 45a )\|- 1 + (- 18a b - 45a )\|- 1 + 18a b +--R + +--R 2 +--R 45a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (6a b + 15a )\|- 1 + (- 6a b - 15a )\|- 1 + 6a b +--R + +--R 2 +--R 15a +--R * +--R 6 +--R cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((3a b + 3a )\|- 1 + (- 3a b - 3a )\|- 1 + 3a b + 3a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) +--R * +--R 3+-+6+-+4 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((18a b + 18a )\|- 1 + (- 18a b - 18a )\|- 1 + 18a b + 18a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) +--R * +--R 2 3+-+2 6+-+2 +--R tan(x) \|a \|a +--R + +--R 2 2 3 3+---+2 +--R (3a b + 33a b + 30a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 3a b - 33a b - 30a )\|- 1 + 3a b + 33a b + 30a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b + 90a )\|- 1 + (- 9a b - 90a )\|- 1 + 9a b + 90a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b + 90a )\|- 1 + (- 9a b - 90a )\|- 1 + 9a b + 90a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 6 +--R ((3a b + 30a )\|- 1 + (- 3a b - 30a )\|- 1 + 3a b + 30a )cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 3+-+2 +--R \|b +--R + +--R 2 2 3+---+2 +--R (15b + 21a b + 6a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 15b - 21a b - 6a )\|- 1 + 15b + 21a b + 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (45a b + 18a )\|- 1 + (- 45a b - 18a )\|- 1 + 45a b +--R + +--R 2 +--R 18a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (45a b + 18a )\|- 1 + (- 45a b - 18a )\|- 1 + 45a b +--R + +--R 2 +--R 18a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (15a b + 6a )\|- 1 + (- 15a b - 6a )\|- 1 + 15a b +--R + +--R 2 +--R 6a +--R * +--R 6 +--R cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((3a b + 3a )\|- 1 + (- 3a b - 3a )\|- 1 + 3a b + 3a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) +--R * +--R 3+-+2 6+-+4 +--R \|a \|a +--R + +--R 2 2 3 3+---+2 +--R (3a b + 15a b + 12a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 3a b - 15a b - 12a )\|- 1 + 3a b + 15a b + 12a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b + 36a )\|- 1 + (- 9a b - 36a )\|- 1 + 9a b + 36a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b + 36a )\|- 1 + (- 9a b - 36a )\|- 1 + 9a b + 36a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 6 +--R ((3a b + 12a )\|- 1 + (- 3a b - 12a )\|- 1 + 3a b + 12a )cos(x) +--R * +--R 2 6+-+2 +--R tan(x) \|a +--R + +--R 2 2 3 3+---+2 +--R (15a b + 30a b + 15a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 15a b - 30a b - 15a )\|- 1 + 15a b + 30a b + 15a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((45a b + 45a )\|- 1 + (- 45a b - 45a )\|- 1 + 45a b + 45a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((45a b + 45a )\|- 1 + (- 45a b - 45a )\|- 1 + 45a b + 45a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((15a b + 15a )\|- 1 + (- 15a b - 15a )\|- 1 + 15a b + 15a ) +--R * +--R 6 +--R cos(x) +--R * +--R 4 3+-+ +--R tan(x) \|a +--R * +--R 3+-+ +--R \|b +--R + +--R 2 2 3+---+2 2 2 3+---+ 3 +--R (18a b + 18a b)\|- 1 + (- 18a b - 18a b)\|- 1 + 3b +--R + +--R 2 2 3 +--R 27a b + 27a b + 3a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 2 4 +--R (54a b \|- 1 - 54a b\|- 1 + 9a b + 72a b + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 4 2 +--R (54a b \|- 1 - 54a b\|- 1 + 9a b + 72a b + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 6 +--R (18a b \|- 1 - 18a b\|- 1 + 3a b + 24a b + 3a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 6 2 3 2 4 +--R (3a b + 6a b + 3a )sin(x) + (9a b + 9a )cos(x) sin(x) +--R + +--R 2 3 4 2 2 3 6 +--R (9a b + 9a )cos(x) sin(x) + (3a b + 3a )cos(x) +--R * +--R 6+-+4 +--R \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (9a b + 9a b)\|- 1 + (- 9a b - 9a b)\|- 1 + 18a b + 27a b +--R + +--R 3 +--R 9a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 2 4 +--R (27a b \|- 1 - 27a b\|- 1 + 54a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 4 2 +--R (27a b \|- 1 - 27a b\|- 1 + 54a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 6 +--R (9a b \|- 1 - 9a b\|- 1 + 18a b + 9a )cos(x) +--R * +--R 2 3+-+6+-+2 +--R tan(x) \|a \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (27a b + 27a b)\|- 1 + (- 27a b - 27a b)\|- 1 + 36a b +--R + +--R 2 3 +--R 45a b + 9a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 2 4 +--R (81a b \|- 1 - 81a b\|- 1 + 108a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 4 2 +--R (81a b \|- 1 - 81a b\|- 1 + 108a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 6 +--R (27a b \|- 1 - 27a b\|- 1 + 36a b + 9a )cos(x) +--R * +--R 4 3+-+2 +--R tan(x) \|a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 520 +t0066:= 1/(a+b*sin(x)^8) +--R +--R +--R 1 +--R (217) ------------- +--R 8 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 520 +r0066:= 1/4*atan((a^(1/4)+(-b)^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/_ + (a^(1/4)+(-b)^(1/4))^(1/2)+1/4*atan((a^(1/2)-_ + a^(1/4)*(-b)^(1/4))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/_ + (a^(1/2)-a^(1/4)*(-b)^(1/4))^(1/2)+1/4*atan((a^(1/2)-_ + %i*a^(1/4)*(-b)^(1/4))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/_ + (a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2)+1/4*_ + atan((a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2)*_ + tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2) +--R +--R +--R (218) +--R +-------------------+ +---------------------+ +-------------+ +--R 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R tan(x)\|%i\|- b \|a + \|a +--R atan(----------------------------) +--R 4+-+ +--R \|a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +--R +-------------------+ |4+-+ 4+---+ +--R | 4+---+4+-+ +-+ tan(x)\|\|a + \|- b +--R \|%i\|- b \|a + \|a atan(----------------------) +--R 8+-+ +--R \|a +--R + +--R +-------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R +---------------------+ +--R | 4+---+4+-+ +-+ +--R tan(x)\|- %i\|- b \|a + \|a +--R atan(------------------------------) +--R 4+-+ +--R \|a +--R + +--R +---------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- %i\|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R tan(x)\|- \|- b \|a + \|a +--R atan(----------------------------) +--R 4+-+ +--R \|a +--R / +--R +-------------------+ +---------------------+ +-------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R 4\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R Type: Expression(Complex(Integer)) +--E 352 + +--S 353 of 520 +a0066:= integrate(t0066,x) +--R +--R +--R (219) +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%EL0 - 64a b - 64a ) +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 6 7 +--I (1048576a b + 1048576a )sin(x)%%EL0 %%EL1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 2 +--I (1048576a b + 1048576a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (1048576a b + 1048576a )sin(x)%%EL0 +--R + +--R 5 +--I 65536a sin(x)%%EL0 +--R * +--I %%EL1 +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EL0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 6 7 +--I (1048576a b + 1048576a )sin(x)%%EL0 %%EL1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 2 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 +--R + +--R 5 +--I - 65536a sin(x)%%EL0 +--R * +--I %%EL1 +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EL0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%EL0 - 64a b - 64a ) +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 6 7 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 %%EL1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 2 +--I (1048576a b + 1048576a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (1048576a b + 1048576a )sin(x)%%EL0 +--R + +--R 5 +--I 65536a sin(x)%%EL0 +--R * +--I %%EL1 +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EL0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 6 7 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 %%EL1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 2 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 +--R + +--R 5 +--I - 65536a sin(x)%%EL0 +--R * +--I %%EL1 +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EL0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--I \|4%%EL1 +--R * +--R log +--R 6 7 2 +--I (2097152a b + 2097152a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (2097152a b + 2097152a )sin(x)%%EL0 +--R + +--R 5 +--I 131072a sin(x)%%EL0 +--R * +--I %%EL1 +--R + +--R 6 7 3 +--I (2097152a b + 2097152a )sin(x)%%EL0 +--R + +--R 5 2 3 +--I 131072a sin(x)%%EL0 + 3072a sin(x)%%EL0 +--R * +--R +------+ +--I \|4%%EL1 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I \|4%%EL1 +--R * +--R log +--R 6 7 2 +--I (- 2097152a b - 2097152a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (- 2097152a b - 2097152a )sin(x)%%EL0 +--R + +--R 5 +--I - 131072a sin(x)%%EL0 +--R * +--I %%EL1 +--R + +--R 6 7 3 +--I (- 2097152a b - 2097152a )sin(x)%%EL0 +--R + +--R 5 2 3 +--I - 131072a sin(x)%%EL0 - 3072a sin(x)%%EL0 +--R * +--R +------+ +--I \|4%%EL1 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I \|4%%EL0 +--R * +--R log +--R 6 7 3 5 2 +--I (2097152a b + 2097152a )sin(x)%%EL0 + 131072a sin(x)%%EL0 +--R + +--R 3 +--I 3072a sin(x)%%EL0 + 32a sin(x) +--R * +--R +------+ +--I \|4%%EL0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--I \|4%%EL0 +--R * +--R log +--R 6 7 3 +--I (- 2097152a b - 2097152a )sin(x)%%EL0 +--R + +--R 5 2 3 +--I - 131072a sin(x)%%EL0 - 3072a sin(x)%%EL0 - 32a sin(x) +--R * +--R +------+ +--I \|4%%EL0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 520 +m0066:= a0066-r0066 +--R +--R +--R (220) +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%EL0 - 64a b - 64a ) +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 6 7 +--I (1048576a b + 1048576a )sin(x)%%EL0 %%EL1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 2 +--I (1048576a b + 1048576a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (1048576a b + 1048576a )sin(x)%%EL0 +--R + +--R 5 +--I 65536a sin(x)%%EL0 +--R * +--I %%EL1 +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EL0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 6 7 +--I (1048576a b + 1048576a )sin(x)%%EL0 %%EL1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 2 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 +--R + +--R 5 +--I - 65536a sin(x)%%EL0 +--R * +--I %%EL1 +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EL0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%EL0 - 64a b - 64a ) +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 6 7 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 %%EL1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 2 +--I (1048576a b + 1048576a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (1048576a b + 1048576a )sin(x)%%EL0 +--R + +--R 5 +--I 65536a sin(x)%%EL0 +--R * +--I %%EL1 +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EL0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 6 7 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 %%EL1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EL0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 6 7 2 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (- 1048576a b - 1048576a )sin(x)%%EL0 +--R + +--R 5 +--I - 65536a sin(x)%%EL0 +--R * +--I %%EL1 +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EL0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EL1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EL0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EL0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EL1 + (- 16a b - 16a )%%EL0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%EL1 +--R * +--R log +--R 6 7 2 +--I (2097152a b + 2097152a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (2097152a b + 2097152a )sin(x)%%EL0 +--R + +--R 5 +--I 131072a sin(x)%%EL0 +--R * +--I %%EL1 +--R + +--R 6 7 3 +--I (2097152a b + 2097152a )sin(x)%%EL0 +--R + +--R 5 2 3 +--I 131072a sin(x)%%EL0 + 3072a sin(x)%%EL0 +--R * +--R +------+ +--I \|4%%EL1 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%EL1 +--R * +--R log +--R 6 7 2 +--I (- 2097152a b - 2097152a )sin(x)%%EL0 %%EL1 +--R + +--R 6 7 2 +--I (- 2097152a b - 2097152a )sin(x)%%EL0 +--R + +--R 5 +--I - 131072a sin(x)%%EL0 +--R * +--I %%EL1 +--R + +--R 6 7 3 +--I (- 2097152a b - 2097152a )sin(x)%%EL0 +--R + +--R 5 2 3 +--I - 131072a sin(x)%%EL0 - 3072a sin(x)%%EL0 +--R * +--R +------+ +--I \|4%%EL1 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%EL0 +--R * +--R log +--R 6 7 3 5 2 +--I (2097152a b + 2097152a )sin(x)%%EL0 + 131072a sin(x)%%EL0 +--R + +--R 3 +--I 3072a sin(x)%%EL0 + 32a sin(x) +--R * +--R +------+ +--I \|4%%EL0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R 2\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +-------------------+ +--R |4+-+ 4+---+ | 4+---+4+-+ +-+ +------+ +--I \|\|a + \|- b \|%i\|- b \|a + \|a \|4%%EL0 +--R * +--R log +--R 6 7 3 +--I (- 2097152a b - 2097152a )sin(x)%%EL0 +--R + +--R 5 2 3 +--I - 131072a sin(x)%%EL0 - 3072a sin(x)%%EL0 - 32a sin(x) +--R * +--R +------+ +--I \|4%%EL0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +---------------------+ +-------------+ +--R 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R tan(x)\|%i\|- b \|a + \|a +--R atan(----------------------------) +--R 4+-+ +--R \|a +--R + +--R - +--R +-------------------+ +---------------------+ +--R 4+-+3 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------+ +--R +-------------------+ |4+-+ 4+---+ +--R | 4+---+4+-+ +-+ tan(x)\|\|a + \|- b +--R \|%i\|- b \|a + \|a atan(----------------------) +--R 8+-+ +--R \|a +--R + +--R - +--R +-------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R +---------------------+ +--R | 4+---+4+-+ +-+ +--R tan(x)\|- %i\|- b \|a + \|a +--R atan(------------------------------) +--R 4+-+ +--R \|a +--R + +--R - +--R +---------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- %i\|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R tan(x)\|- \|- b \|a + \|a +--R atan(----------------------------) +--R 4+-+ +--R \|a +--R / +--R +-------------------+ +---------------------+ +-------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R 4\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R Type: Expression(Complex(Integer)) +--E 354 + +--S 355 of 520 +d0066:= D(m0066,x) +--R +--R +--R (221) +--R 8 2 6 +--R (- 4b - 36a)sin(x) + (32b - 144a)cos(x) sin(x) +--R + +--R 4 4 6 2 +--R (48b - 216a)cos(x) sin(x) + (32b - 144a)cos(x) sin(x) +--R + +--R 8 +--R (8b - 36a)cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 8 2 6 +--R (4b + 52a)sin(x) + 208a cos(x) sin(x) +--R + +--R 4 4 6 2 8 +--R 312a cos(x) sin(x) + 208a cos(x) sin(x) + 52a cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 8 2 6 +--R (10b - 22a)sin(x) - 88a cos(x) sin(x) +--R + +--R 4 4 6 2 8 +--R - 132a cos(x) sin(x) - 88a cos(x) sin(x) - 22a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 8 2 6 +--R (- 6b + 2a)sin(x) + 8a cos(x) sin(x) +--R + +--R 4 4 6 2 8 +--R 12a cos(x) sin(x) + 8a cos(x) sin(x) + 2a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+3 +-+ +--R \|- b \|a +--R + +--R 2 2 8 +--R (- 7b - 26a b + 13a )sin(x) +--R + +--R 2 2 6 +--R (- 124a b + 52a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (- 186a b + 78a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (- 124a b + 52a )cos(x) sin(x) + (- 31a b + 13a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 8 +--R (- 3b + 18a b - 27a )sin(x) +--R + +--R 2 2 6 +--R (100a b - 108a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (150a b - 162a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (100a b - 108a )cos(x) sin(x) + (25a b - 27a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 8 +--R (b - 16a b + 15a )sin(x) +--R + +--R 2 2 6 +--R (- 28a b + 60a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (- 42a b + 90a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (- 28a b + 60a )cos(x) sin(x) + (- 7a b + 15a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 8 2 2 6 +--R (- 3b + 4a b - a )sin(x) + (4a b - 4a )cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 +--R (6a b - 6a )cos(x) sin(x) + (4a b - 4a )cos(x) sin(x) +--R + +--R 2 8 +--R (a b - a )cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+ +--R \|- b +--R * +--R 4+-+3 +--R \|a +--R + +--R 2 2 8 +--R (9b + 38a b - 3a )sin(x) +--R + +--R 2 2 6 +--R (164a b - 12a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (246a b - 18a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (164a b - 12a )cos(x) sin(x) + (41a b - 3a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 8 +--R (- 7b - 46a b + 9a )sin(x) +--R + +--R 2 2 6 +--R (- 172a b + 36a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (- 258a b + 54a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (- 172a b + 36a )cos(x) sin(x) + (- 43a b + 9a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 8 +--R (- 13b + 16a b - 3a )sin(x) +--R + +--R 2 2 6 +--R (76a b - 12a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (114a b - 18a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (76a b - 12a )cos(x) sin(x) + (19a b - 3a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 8 2 2 6 +--R (3b - 4a b + a )sin(x) + (- 4a b + 4a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (- 6a b + 6a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (- 4a b + 4a )cos(x) sin(x) + (- a b + a )cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 2 8 +--R (- 2b - 8a b + 26a )sin(x) +--R + +--R 2 2 6 +--R (- 72a b + 104a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (- 108a b + 156a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (- 72a b + 104a )cos(x) sin(x) + (- 18a b + 26a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (4a b - 44a )sin(x) + (32a b - 176a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (48a b - 264a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (32a b - 176a )cos(x) sin(x) + (8a b - 44a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 8 +--R (2b - 10a b + 20a )sin(x) +--R + +--R 2 2 6 +--R (- 8a b + 80a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (- 12a b + 120a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (- 8a b + 80a )cos(x) sin(x) + (- 2a b + 20a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (6a b - 2a )sin(x) - 8a cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R - 12a cos(x) sin(x) - 8a cos(x) sin(x) - 2a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+2 +--R \|- b +--R * +--R 4+-+2 +--R \|a +--R + +--R 2 2 8 +--R (6b + 24a b - 14a )sin(x) +--R + +--R 2 2 6 +--R (120a b - 56a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (180a b - 84a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (120a b - 56a )cos(x) sin(x) + (30a b - 14a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 8 +--R (- 2b - 24a b + 26a )sin(x) +--R + +--R 2 2 6 +--R (- 104a b + 104a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (- 156a b + 156a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (- 104a b + 104a )cos(x) sin(x) + (- 26a b + 26a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 8 +--R (- 8b + 10a b - 14a )sin(x) +--R + +--R 2 2 6 +--R (32a b - 56a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (48a b - 84a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (32a b - 56a )cos(x) sin(x) + (8a b - 14a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (- 6a b + 2a )sin(x) + 8a cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R 12a cos(x) sin(x) + 8a cos(x) sin(x) + 2a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+ +-+ +--R \|- b \|a +--R + +--R 2 2 8 +--R (- b + 2a b + 35a )sin(x) +--R + +--R 2 2 6 +--R (- 36a b + 140a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (- 54a b + 210a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (- 36a b + 140a )cos(x) sin(x) + (- 9a b + 35a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 8 +--R (- b - 2a b - 49a )sin(x) +--R + +--R 2 2 6 +--R (12a b - 196a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (18a b - 294a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (12a b - 196a )cos(x) sin(x) + (3a b - 49a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (- 10a b + 22a )sin(x) + 88a cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R 132a cos(x) sin(x) + 88a cos(x) sin(x) + 22a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (6a b - 2a )sin(x) - 8a cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R - 12a cos(x) sin(x) - 8a cos(x) sin(x) - 2a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+3 +--R \|- b +--R * +--R 4+-+ +--R \|a +--R + +--R 2 2 8 2 2 6 +--R (3b + 10a b - 25a )sin(x) + (76a b - 100a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (114a b - 150a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (76a b - 100a )cos(x) sin(x) + (19a b - 25a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 8 2 2 6 +--R (3b - 2a b + 43a )sin(x) + (- 36a b + 172a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (- 54a b + 258a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (- 36a b + 172a )cos(x) sin(x) + (- 9a b + 43a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (10a b - 22a )sin(x) - 88a cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R - 132a cos(x) sin(x) - 88a cos(x) sin(x) - 22a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (- 6a b + 2a )sin(x) + 8a cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R 12a cos(x) sin(x) + 8a cos(x) sin(x) + 2a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+2 +-+ +--R \|- b \|a +--R + +--R 2 2 3 8 +--R (- 8a b - 36a b + 4a )sin(x) +--R + +--R 2 2 3 2 6 +--R (16a b - 144a b + 16a )cos(x) sin(x) +--R + +--R 2 2 3 4 4 +--R (24a b - 216a b + 24a )cos(x) sin(x) +--R + +--R 2 2 3 6 2 +--R (16a b - 144a b + 16a )cos(x) sin(x) +--R + +--R 2 2 3 8 +--R (4a b - 36a b + 4a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (- 2a b + 40a b - 6a )sin(x) + (184a b - 24a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (276a b - 36a )cos(x) sin(x) + (184a b - 24a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (46a b - 6a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (4a b - 22a b + 6a )sin(x) + (- 64a b + 24a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (- 96a b + 36a )cos(x) sin(x) + (- 64a b + 24a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (- 16a b + 6a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 8 2 2 6 +--R (- 6a b + 2a b)sin(x) + 8a b cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R 12a b cos(x) sin(x) + 8a b cos(x) sin(x) + 2a b cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 8+-+6 +--R \|a +--R + +--R 2 2 8 2 2 6 +--R (- 2b + 2a )sin(x) + (- 8a b + 8a )cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 +--R (- 12a b + 12a )cos(x) sin(x) + (- 8a b + 8a )cos(x) sin(x) +--R + +--R 2 8 +--R (- 2a b + 2a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 8 2 2 6 +--R (- 2b - 4a b - 18a )sin(x) + (24a b - 72a )cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 +--R (36a b - 108a )cos(x) sin(x) + (24a b - 72a )cos(x) sin(x) +--R + +--R 2 8 +--R (6a b - 18a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 8 2 2 6 2 4 4 +--R 24a sin(x) + 96a cos(x) sin(x) + 144a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 96a cos(x) sin(x) + 24a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 8 2 2 6 2 4 4 +--R (8a b - 8a )sin(x) - 32a cos(x) sin(x) - 48a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R - 32a cos(x) sin(x) - 8a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 8 +--R - 4a b sin(x) +--R * +--R 4+---+2 +-+ +--R \|- b \|a +--R + +--R 2 2 3 8 2 3 2 6 +--R (3a b + 2a b - a )sin(x) + (12a b - 4a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (18a b - 6a )cos(x) sin(x) + (12a b - 4a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (3a b - a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (- 9a b - 22a b + 3a )sin(x) + (- 84a b + 12a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (- 126a b + 18a )cos(x) sin(x) + (- 84a b + 12a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (- 21a b + 3a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (- 9a b + 6a b - 9a )sin(x) + (60a b - 36a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (90a b - 54a )cos(x) sin(x) + (60a b - 36a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (15a b - 9a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (- a b - 14a b + 3a )sin(x) + (- 20a b + 12a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (- 30a b + 18a )cos(x) sin(x) + (- 20a b + 12a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (- 5a b + 3a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 8 +--R - 4a b sin(x) +--R * +--R 4+-+3 +--R \|a +--R + +--R 2 8 2 2 6 2 4 4 +--R (4a b + 4a )sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 16a cos(x) sin(x) + 4a cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (- 8a b - 24a )sin(x) - 96a cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R - 144a cos(x) sin(x) - 96a cos(x) sin(x) - 24a cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 8 2 2 6 2 4 4 +--R 24a sin(x) + 96a cos(x) sin(x) + 144a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 96a cos(x) sin(x) + 24a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 8 2 2 6 2 4 4 +--R (8a b - 8a )sin(x) - 32a cos(x) sin(x) - 48a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R - 32a cos(x) sin(x) - 8a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 8 +--R - 4a b sin(x) +--R * +--R 4+---+3 +-+ +--R \|- b \|a +--R + +--R 2 2 3 8 2 3 2 6 +--R (3a b + 2a b - a )sin(x) + (12a b - 4a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (18a b - 6a )cos(x) sin(x) + (12a b - 4a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (3a b - a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (a b - 2a b + 13a )sin(x) + (- 44a b + 52a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 66a b + 78a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 44a b + 52a )cos(x) sin(x) + (- 11a b + 13a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (a b + 6a b - 19a )sin(x) + (20a b - 76a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (30a b - 114a )cos(x) sin(x) + (20a b - 76a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (5a b - 19a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (3a b - 6a b + 7a )sin(x) + (- 4a b + 28a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (- 6a b + 42a )cos(x) sin(x) + (- 4a b + 28a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (- a b + 7a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 8 +--R 4a b sin(x) +--R * +--R 4+---+ +--R \|- b +--R * +--R 4+-+2 +--R \|a +--R + +--R 2 2 8 2 2 6 +--R (- 4a b - 4a b)sin(x) - 16a b cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R - 24a b cos(x) sin(x) - 16a b cos(x) sin(x) - 4a b cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (2a b + 12a b - 6a )sin(x) + (72a b - 24a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (108a b - 36a )cos(x) sin(x) + (72a b - 24a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (18a b - 6a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 8 +--R (- 6a b - 24a b + 6a )sin(x) +--R + +--R 2 3 2 6 +--R (- 72a b + 24a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 108a b + 36a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 72a b + 24a )cos(x) sin(x) + (- 18a b + 6a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 2 3 2 6 +--R (- 12a b - 4a )sin(x) + (16a b - 16a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (24a b - 24a )cos(x) sin(x) + (16a b - 16a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (4a b - 4a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 8 +--R - 4a b sin(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 2 3 8 2 3 2 6 +--R (a b - 2a b - 3a )sin(x) + (4a b - 12a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (6a b - 18a )cos(x) sin(x) + (4a b - 12a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (a b - 3a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 +--R (- a b + 2a b + 19a )sin(x) +--R + +--R 2 3 2 6 +--R (- 20a b + 76a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 30a b + 114a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 20a b + 76a )cos(x) sin(x) + (- 5a b + 19a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3 8 2 3 2 6 +--R (- 2a b - 22a )sin(x) + (8a b - 88a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (12a b - 132a )cos(x) sin(x) + (8a b - 88a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (2a b - 22a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 3 2 6 +--R (- 8a b + 8a )sin(x) + 32a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R 48a cos(x) sin(x) + 32a cos(x) sin(x) + 8a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 8 +--R 4a b sin(x) +--R * +--R 4+---+2 +--R \|- b +--R * +--R 4+-+ +--R \|a +--R + +--R 2 3 8 2 3 2 6 +--R (- 2a b + 2a )sin(x) + (- 8a b + 8a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (- 12a b + 12a )cos(x) sin(x) + (- 8a b + 8a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (- 2a b + 2a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (4a b + 8a b - 12a )sin(x) + (48a b - 48a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (72a b - 72a )cos(x) sin(x) + (48a b - 48a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (12a b - 12a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3 8 2 3 2 6 +--R (6a b + 18a )sin(x) + (- 24a b + 72a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (- 36a b + 108a )cos(x) sin(x) + (- 24a b + 72a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (- 6a b + 18a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 3 2 6 3 4 4 +--R (8a b - 8a )sin(x) - 32a cos(x) sin(x) - 48a cos(x) sin(x) +--R + +--R 3 6 2 3 8 +--R - 32a cos(x) sin(x) - 8a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 8 +--R - 4a b sin(x) +--R * +--R 4+---+ +-+ +--R \|- b \|a +--R + +--R 2 2 3 8 2 3 2 6 +--R (a b - 2a b - 3a )sin(x) + (4a b - 12a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (6a b - 18a )cos(x) sin(x) + (4a b - 12a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (a b - 3a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 2 3 2 6 +--R (a b + 6a b + 21a )sin(x) + (- 12a b + 84a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (- 18a b + 126a )cos(x) sin(x) + (- 12a b + 84a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (- 3a b + 21a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 3 8 3 2 6 3 4 4 +--R - 24a sin(x) - 96a cos(x) sin(x) - 144a cos(x) sin(x) +--R + +--R 3 6 2 3 8 +--R - 96a cos(x) sin(x) - 24a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 3 2 6 3 4 4 +--R (- 8a b + 8a )sin(x) + 32a cos(x) sin(x) + 48a cos(x) sin(x) +--R + +--R 3 6 2 3 8 +--R 32a cos(x) sin(x) + 8a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 8 +--R 4a b sin(x) +--R * +--R 4+---+3 +--R \|- b +--R / +--R 2 2 8 +--R (8b - 16a b - 24a )sin(x) +--R + +--R 2 2 6 +--R (32a b - 96a )cos(x) sin(x) +--R + +--R 2 4 4 +--R (48a b - 144a )cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R (32a b - 96a )cos(x) sin(x) + (8a b - 24a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (48a b + 48a )sin(x) + 192a cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R 288a cos(x) sin(x) + 192a cos(x) sin(x) + 48a cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (- 32a b - 32a )sin(x) - 128a cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R - 192a cos(x) sin(x) - 128a cos(x) sin(x) - 32a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (8a b + 8a )sin(x) + 32a cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 2 8 +--R 48a cos(x) sin(x) + 32a cos(x) sin(x) + 8a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+3 +-+ +--R \|- b \|a +--R + +--R 2 2 3 8 +--R (- 24a b - 16a b + 8a )sin(x) +--R + +--R 2 3 2 6 +--R (- 96a b + 32a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 144a b + 48a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 96a b + 32a )cos(x) sin(x) + (- 24a b + 8a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 +--R (28a b + 8a b - 20a )sin(x) +--R + +--R 2 3 2 6 +--R (112a b - 80a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (168a b - 120a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (112a b - 80a )cos(x) sin(x) + (28a b - 20a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 8 +--R (- 8a b + 16a b + 24a )sin(x) +--R + +--R 2 3 2 6 +--R (- 32a b + 96a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 48a b + 144a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 32a b + 96a )cos(x) sin(x) + (- 8a b + 24a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 2 3 2 6 +--R (4a b - 4a )sin(x) + (16a b - 16a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (24a b - 24a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (16a b - 16a )cos(x) sin(x) + (4a b - 4a )cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+ +--R \|- b +--R * +--R 4+-+3 +--R \|a +--R + +--R 2 2 8 2 2 6 +--R (32a b + 32a b)sin(x) + 128a b cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 +--R 192a b cos(x) sin(x) + 128a b cos(x) sin(x) +--R + +--R 2 8 +--R 32a b cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 +--R (- 36a b - 24a b + 12a )sin(x) +--R + +--R 2 3 2 6 +--R (- 144a b + 48a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 216a b + 72a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 144a b + 48a )cos(x) sin(x) + (- 36a b + 12a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 8 2 2 6 +--R (32a b + 32a b)sin(x) + 128a b cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 +--R 192a b cos(x) sin(x) + 128a b cos(x) sin(x) +--R + +--R 2 8 +--R 32a b cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 2 3 2 6 +--R (- 4a b + 4a )sin(x) + (- 16a b + 16a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 24a b + 24a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 16a b + 16a )cos(x) sin(x) + (- 4a b + 4a )cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 3 8 2 3 2 6 +--R (- 16a b + 16a )sin(x) + (- 64a b + 64a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 96a b + 96a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 64a b + 64a )cos(x) sin(x) + (- 16a b + 16a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 +--R (8a b - 32a b - 40a )sin(x) +--R + +--R 2 3 2 6 +--R (32a b - 160a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (48a b - 240a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (32a b - 160a )cos(x) sin(x) + (8a b - 40a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 8 +--R (- 4a b + 24a b + 28a )sin(x) +--R + +--R 2 3 2 6 +--R (- 16a b + 112a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 24a b + 168a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 16a b + 112a )cos(x) sin(x) + (- 4a b + 28a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 3 2 6 +--R (- 8a b - 8a )sin(x) - 32a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R - 48a cos(x) sin(x) - 32a cos(x) sin(x) - 8a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+2 +--R \|- b +--R * +--R 4+-+2 +--R \|a +--R + +--R 2 2 3 8 +--R (24a b + 16a b - 8a )sin(x) +--R + +--R 2 3 2 6 +--R (96a b - 32a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (144a b - 48a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (96a b - 32a )cos(x) sin(x) + (24a b - 8a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 3 8 2 3 2 6 +--R (- 24a b + 24a )sin(x) + (- 96a b + 96a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 144a b + 144a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 96a b + 96a )cos(x) sin(x) + (- 24a b + 24a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3 8 2 3 2 6 +--R (16a b - 16a )sin(x) + (64a b - 64a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (96a b - 96a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (64a b - 64a )cos(x) sin(x) + (16a b - 16a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 3 2 6 +--R (8a b + 8a )sin(x) + 32a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R 48a cos(x) sin(x) + 32a cos(x) sin(x) + 8a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+ +-+ +--R \|- b \|a +--R + +--R 2 2 3 8 +--R (- 8a b + 16a b + 24a )sin(x) +--R + +--R 2 3 2 6 +--R (- 32a b + 96a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 48a b + 144a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 32a b + 96a )cos(x) sin(x) + (- 8a b + 24a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 +--R (4a b - 40a b - 44a )sin(x) +--R + +--R 2 3 2 6 +--R (16a b - 176a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (24a b - 264a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (16a b - 176a )cos(x) sin(x) + (4a b - 44a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3 8 3 2 6 +--R (32a b + 32a )sin(x) + 128a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R 192a cos(x) sin(x) + 128a cos(x) sin(x) + 32a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 3 2 6 +--R (- 8a b - 8a )sin(x) - 32a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R - 48a cos(x) sin(x) - 32a cos(x) sin(x) - 8a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+3 +--R \|- b +--R * +--R 4+-+ +--R \|a +--R + +--R 2 3 8 2 3 2 6 +--R (16a b - 16a )sin(x) + (64a b - 64a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (96a b - 96a )cos(x) sin(x) + (64a b - 64a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (16a b - 16a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 +--R (- 12a b + 24a b + 36a )sin(x) +--R + +--R 2 3 2 6 +--R (- 48a b + 144a )cos(x) sin(x) +--R + +--R 2 3 4 4 +--R (- 72a b + 216a )cos(x) sin(x) +--R + +--R 2 3 6 2 2 3 8 +--R (- 48a b + 144a )cos(x) sin(x) + (- 12a b + 36a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3 8 3 2 6 +--R (- 32a b - 32a )sin(x) - 128a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R - 192a cos(x) sin(x) - 128a cos(x) sin(x) - 32a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 3 2 6 3 4 4 +--R (8a b + 8a )sin(x) + 32a cos(x) sin(x) + 48a cos(x) sin(x) +--R + +--R 3 6 2 3 8 +--R 32a cos(x) sin(x) + 8a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+---+2 +-+ +--R \|- b \|a +--R + +--R 3 2 2 3 4 8 +--R (4a b - 20a b - 20a b + 4a )sin(x) +--R + +--R 2 2 3 4 2 6 +--R (16a b - 96a b + 16a )cos(x) sin(x) +--R + +--R 2 2 3 4 4 4 +--R (24a b - 144a b + 24a )cos(x) sin(x) +--R + +--R 2 2 3 4 6 2 +--R (16a b - 96a b + 16a )cos(x) sin(x) +--R + +--R 2 2 3 4 8 +--R (4a b - 24a b + 4a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 2 3 8 3 2 6 +--R (48a b + 48a b)sin(x) + 192a b cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R 288a b cos(x) sin(x) + 192a b cos(x) sin(x) + 48a b cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 4 8 3 4 2 6 +--R (- 20a b - 8a b + 12a )sin(x) + (- 80a b + 48a )cos(x) sin(x) +--R + +--R 3 4 4 4 3 4 6 2 +--R (- 120a b + 72a )cos(x) sin(x) + (- 80a b + 48a )cos(x) sin(x) +--R + +--R 3 4 8 +--R (- 20a b + 12a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 3 8 3 2 6 +--R (8a b + 8a b)sin(x) + 32a b cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R 48a b cos(x) sin(x) + 32a b cos(x) sin(x) + 8a b cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 8+-+6 +--R \|a +--R + +--R 2 3 8 2 3 2 6 +--R (8a b - 8a )sin(x) + (32a b - 32a )cos(x) sin(x) +--R + +--R 2 3 4 4 2 3 6 2 +--R (48a b - 48a )cos(x) sin(x) + (32a b - 32a )cos(x) sin(x) +--R + +--R 2 3 8 +--R (8a b - 8a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3 8 3 2 6 +--R (24a b + 24a )sin(x) + 96a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R 144a cos(x) sin(x) + 96a cos(x) sin(x) + 24a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 3 2 6 +--R (- 16a b - 16a )sin(x) - 64a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R - 96a cos(x) sin(x) - 64a cos(x) sin(x) - 16a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 8 3 2 6 3 4 4 +--R (4a b + 4a )sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 3 6 2 3 8 +--R 16a cos(x) sin(x) + 4a cos(x) +--R * +--R 4+---+2 +-+ +--R \|- b \|a +--R + +--R 2 2 3 4 8 3 4 2 6 +--R (- 12a b - 8a b + 4a )sin(x) + (- 48a b + 16a )cos(x) sin(x) +--R + +--R 3 4 4 4 3 4 6 2 +--R (- 72a b + 24a )cos(x) sin(x) + (- 48a b + 16a )cos(x) sin(x) +--R + +--R 3 4 8 +--R (- 12a b + 4a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 8 3 2 6 +--R (24a b + 24a b)sin(x) + 96a b cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R 144a b cos(x) sin(x) + 96a b cos(x) sin(x) + 24a b cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 3 4 8 3 4 2 6 +--R (- 4a b + 8a b + 12a )sin(x) + (- 16a b + 48a )cos(x) sin(x) +--R + +--R 3 4 4 4 3 4 6 2 +--R (- 24a b + 72a )cos(x) sin(x) + (- 16a b + 48a )cos(x) sin(x) +--R + +--R 3 4 8 +--R (- 4a b + 12a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 8 3 2 6 3 4 4 +--R (4a b + 4a b)sin(x) + 16a b cos(x) sin(x) + 24a b cos(x) sin(x) +--R + +--R 3 6 2 3 8 +--R 16a b cos(x) sin(x) + 4a b cos(x) +--R * +--R 4+-+3 +--R \|a +--R + +--R 2 3 8 3 2 6 +--R (- 16a b - 16a )sin(x) - 64a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R - 96a cos(x) sin(x) - 64a cos(x) sin(x) - 16a cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3 8 3 2 6 +--R (24a b + 24a )sin(x) + 96a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R 144a cos(x) sin(x) + 96a cos(x) sin(x) + 24a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 8 3 2 6 +--R (- 16a b - 16a )sin(x) - 64a cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R - 96a cos(x) sin(x) - 64a cos(x) sin(x) - 16a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 8 3 2 6 3 4 4 +--R (4a b + 4a )sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 3 6 2 3 8 +--R 16a cos(x) sin(x) + 4a cos(x) +--R * +--R 4+---+3 +-+ +--R \|- b \|a +--R + +--R 2 2 3 4 8 +--R (- 12a b - 8a b + 4a )sin(x) +--R + +--R 3 4 2 6 +--R (- 48a b + 16a )cos(x) sin(x) +--R + +--R 3 4 4 4 +--R (- 72a b + 24a )cos(x) sin(x) +--R + +--R 3 4 6 2 3 4 8 +--R (- 48a b + 16a )cos(x) sin(x) + (- 12a b + 4a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 4 8 3 4 2 6 +--R (4a b - 16a b - 20a )sin(x) + (16a b - 80a )cos(x) sin(x) +--R + +--R 3 4 4 4 3 4 6 2 +--R (24a b - 120a )cos(x) sin(x) + (16a b - 80a )cos(x) sin(x) +--R + +--R 3 4 8 +--R (4a b - 20a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 3 4 8 +--R (- 4a b + 8a b + 12a )sin(x) +--R + +--R 3 4 2 6 +--R (- 16a b + 48a )cos(x) sin(x) +--R + +--R 3 4 4 4 +--R (- 24a b + 72a )cos(x) sin(x) +--R + +--R 3 4 6 2 3 4 8 +--R (- 16a b + 48a )cos(x) sin(x) + (- 4a b + 12a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 4 8 4 2 6 4 4 4 +--R (- 4a b - 4a )sin(x) - 16a cos(x) sin(x) - 24a cos(x) sin(x) +--R + +--R 4 6 2 4 8 +--R - 16a cos(x) sin(x) - 4a cos(x) +--R * +--R 4+---+ +--R \|- b +--R * +--R 4+-+2 +--R \|a +--R + +--R 2 2 3 8 3 2 6 +--R (16a b + 16a b)sin(x) + 64a b cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R 96a b cos(x) sin(x) + 64a b cos(x) sin(x) + 16a b cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 4 8 3 4 2 6 +--R (- 12a b + 12a )sin(x) + (- 48a b + 48a )cos(x) sin(x) +--R + +--R 3 4 4 4 +--R (- 72a b + 72a )cos(x) sin(x) +--R + +--R 3 4 6 2 3 4 8 +--R (- 48a b + 48a )cos(x) sin(x) + (- 12a b + 12a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 3 8 3 2 6 +--R (16a b + 16a b)sin(x) + 64a b cos(x) sin(x) +--R + +--R 3 4 4 3 6 2 3 8 +--R 96a b cos(x) sin(x) + 64a b cos(x) sin(x) + 16a b cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 4 8 4 2 6 4 4 4 +--R (4a b + 4a )sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 4 6 2 4 8 +--R 16a cos(x) sin(x) + 4a cos(x) +--R * +--R +-+ +--R \|a +--R + +--R 2 2 3 4 8 +--R (- 4a b + 8a b + 12a )sin(x) +--R + +--R 3 4 2 6 +--R (- 16a b + 48a )cos(x) sin(x) +--R + +--R 3 4 4 4 +--R (- 24a b + 72a )cos(x) sin(x) +--R + +--R 3 4 6 2 3 4 8 +--R (- 16a b + 48a )cos(x) sin(x) + (- 4a b + 12a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 4 8 3 4 2 6 +--R (4a b - 16a b - 20a )sin(x) + (16a b - 80a )cos(x) sin(x) +--R + +--R 3 4 4 4 3 4 6 2 +--R (24a b - 120a )cos(x) sin(x) + (16a b - 80a )cos(x) sin(x) +--R + +--R 3 4 8 +--R (4a b - 20a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3 4 8 4 2 6 +--R (16a b + 16a )sin(x) + 64a cos(x) sin(x) +--R + +--R 4 4 4 4 6 2 4 8 +--R 96a cos(x) sin(x) + 64a cos(x) sin(x) + 16a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 4 8 4 2 6 4 4 4 +--R (- 4a b - 4a )sin(x) - 16a cos(x) sin(x) - 24a cos(x) sin(x) +--R + +--R 4 6 2 4 8 +--R - 16a cos(x) sin(x) - 4a cos(x) +--R * +--R 4+---+2 +--R \|- b +--R * +--R 4+-+ +--R \|a +--R + +--R 2 2 4 8 3 4 2 6 +--R (8a b - 8a )sin(x) + (32a b - 32a )cos(x) sin(x) +--R + +--R 3 4 4 4 3 4 6 2 +--R (48a b - 48a )cos(x) sin(x) + (32a b - 32a )cos(x) sin(x) +--R + +--R 3 4 8 +--R (8a b - 8a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 4 8 3 4 2 6 +--R (- 12a b + 12a )sin(x) + (- 48a b + 48a )cos(x) sin(x) +--R + +--R 3 4 4 4 3 4 6 2 +--R (- 72a b + 72a )cos(x) sin(x) + (- 48a b + 48a )cos(x) sin(x) +--R + +--R 3 4 8 +--R (- 12a b + 12a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3 4 8 4 2 6 4 4 4 +--R (- 16a b - 16a )sin(x) - 64a cos(x) sin(x) - 96a cos(x) sin(x) +--R + +--R 4 6 2 4 8 +--R - 64a cos(x) sin(x) - 16a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 4 8 4 2 6 4 4 4 +--R (4a b + 4a )sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 4 6 2 4 8 +--R 16a cos(x) sin(x) + 4a cos(x) +--R * +--R 4+---+ +-+ +--R \|- b \|a +--R + +--R 2 2 3 4 8 3 4 2 6 +--R (- 4a b + 8a b + 12a )sin(x) + (- 16a b + 48a )cos(x) sin(x) +--R + +--R 3 4 4 4 3 4 6 2 +--R (- 24a b + 72a )cos(x) sin(x) + (- 16a b + 48a )cos(x) sin(x) +--R + +--R 3 4 8 +--R (- 4a b + 12a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 3 4 8 4 2 6 +--R (- 24a b - 24a )sin(x) - 96a cos(x) sin(x) +--R + +--R 4 4 4 4 6 2 4 8 +--R - 144a cos(x) sin(x) - 96a cos(x) sin(x) - 24a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3 4 8 4 2 6 4 4 4 +--R (16a b + 16a )sin(x) + 64a cos(x) sin(x) + 96a cos(x) sin(x) +--R + +--R 4 6 2 4 8 +--R 64a cos(x) sin(x) + 16a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 4 8 4 2 6 4 4 4 +--R (- 4a b - 4a )sin(x) - 16a cos(x) sin(x) - 24a cos(x) sin(x) +--R + +--R 4 6 2 4 8 +--R - 16a cos(x) sin(x) - 4a cos(x) +--R * +--R 4+---+3 +--R \|- b +--R Type: Expression(Complex(Integer)) +--E 355 + +--S 356 of 520 +t0067:= 1/(a-b*sin(x)^3) +--R +--R +--R 1 +--R (222) - ------------- +--R 3 +--R b sin(x) - a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 520 +r0067:= -2/3*atan((b^(1/3)-a^(1/3)*tan(1/2*x))/(a^(2/3)-b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)-2/3*atan(((-1)^(2/3)*b^(1/3)-_ + a^(1/3)*tan(1/2*x))/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+2/3*_ + atan(((-1)^(1/3)*b^(1/3)+a^(1/3)*tan(1/2*x))/_ + (a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/_ + (a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) +--R +--R +--R (223) +--R 3+---+3+-+ x 3+-+ +--R +---------------+ +-------------------+ \|- 1 \|b + tan(-)\|a +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 2 +--R 2\|- \|b + \|a \|\|- 1 \|b + \|a atan(-------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +-------------------+ +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+-+ x 3+-+ +--R \|b - tan(-)\|a +--R 2 +--R atan(------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R - +--R +----------------------+ +---------------+ +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 3+---+2 3+-+ x 3+-+ +--R \|- 1 \|b - tan(-)\|a +--R 2 +--R atan(------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 357 + +--S 358 of 520 +a0067:= integrate(t0067,x) +--R +--R +--R (224) +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EM0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EM0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EM0 +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--R (- 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EM0 + 4b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EM0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EM0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EM0 +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EM0 +--R + +--R 2 3 2 3 +--R (18a b - 18a )cos(x) + 18a b - 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EM0 + 4b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EM0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EM0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EM0 +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EM0 +--R + +--R 2 3 2 3 +--R (18a b - 18a )cos(x) + 18a b - 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EM0 + 4b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EM0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EM0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EM0 +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--R (- 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EM0 + 4b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--I \|4%%EM0 +--R * +--R log +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EM0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EM0 - 9a b cos(x) - 9a b +--R * +--R +------+ +--I \|4%%EM0 +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EM0 + 2b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I \|4%%EM0 +--R * +--R log +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EM0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EM0 + 9a b cos(x) + 9a b +--R * +--R +------+ +--I \|4%%EM0 +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EM0 + 2b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 520 +m0067:= a0067-r0067 +--R +--R +--R (225) +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EM0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EM0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EM0 +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--R (- 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EM0 + 4b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EM0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EM0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EM0 +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EM0 +--R + +--R 2 3 2 3 +--R (18a b - 18a )cos(x) + 18a b - 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EM0 + 4b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EM0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EM0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EM0 +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EM0 +--R + +--R 2 3 2 3 +--R (18a b - 18a )cos(x) + 18a b - 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EM0 + 4b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 3 3 5 3 3 5 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EM0 +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EM0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EM0 +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EM0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 3 2 5 3 2 5 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--R (- 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EM0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EM0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 3 2 5 3 2 5 2 +--I ((- 162a b + 162a )cos(x) - 162a b + 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((18a b + 36a )cos(x) + 18a b + 36a )%%EM0 + 4b sin(x) +--R + +--R 2a cos(x) + 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R +----------------------+ +---------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +------+ +--I \|\|- 1 \|b + \|a \|4%%EM0 +--R * +--R log +--R 3 3 5 3 3 5 2 +--I ((243a b - 243a b)cos(x) + 243a b - 243a b)%%EM0 +--R + +--R 3 3 +--I (- 81a b cos(x) - 81a b)%%EM0 - 9a b cos(x) - 9a b +--R * +--R +------+ +--I \|4%%EM0 +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EM0 + 2b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%EM0 +--R * +--R log +--R 3 3 5 3 3 5 2 +--I ((- 243a b + 243a b)cos(x) - 243a b + 243a b)%%EM0 +--R + +--R 3 3 +--I (81a b cos(x) + 81a b)%%EM0 + 9a b cos(x) + 9a b +--R * +--R +------+ +--I \|4%%EM0 +--R + +--R 3 2 5 3 2 5 2 +--I ((162a b - 162a )cos(x) + 162a b - 162a )%%EM0 +--R + +--R 2 3 2 3 +--I ((- 18a b - 36a )cos(x) - 18a b - 36a )%%EM0 + 2b sin(x) +--R + +--R - 2a cos(x) - 2a +--R / +--R cos(x) + 1 +--R + +--R - +--R +---------------+ +-------------------+ +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 4\|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+3+-+ x 3+-+ +--R \|- 1 \|b + tan(-)\|a +--R 2 +--R atan(-------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R 3+-+ x 3+-+ +--R +----------------------+ +-------------------+ \|b - tan(-)\|a +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 2 +--R 4\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R 3+---+2 3+-+ x 3+-+ +--R +----------------------+ +---------------+ \|- 1 \|b - tan(-)\|a +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 2 +--R 4\|- \|- 1 \|b + \|a \|- \|b + \|a atan(------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 6\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 359 + +--S 360 of 520 +--d0067:= D(m0067,x) +--E 360 + +--S 361 of 520 +t0068:= 1/(a-b*sin(x)^4) +--R +--R +--R 1 +--R (226) - ------------- +--R 4 +--R b sin(x) - a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 520 +r0068:= 1/2*atan((a^(1/2)-b^(1/2))^(1/2)*tan(x)/a^(1/4))/a^(3/4)/_ + (a^(1/2)-b^(1/2))^(1/2)+1/2*atan((a^(1/2)+b^(1/2))^(1/2)*_ + tan(x)/a^(1/4))/a^(3/4)/(a^(1/2)+b^(1/2))^(1/2) +--R +--R +--R (227) +--R +-----------+ +--R +-------------+ | +-+ +-+ +--R | +-+ +-+ tan(x)\|\|b + \|a +--R \|- \|b + \|a atan(--------------------) +--R 4+-+ +--R \|a +--R + +--R +-------------+ +--R +-----------+ | +-+ +-+ +--R | +-+ +-+ tan(x)\|- \|b + \|a +--R \|\|b + \|a atan(----------------------) +--R 4+-+ +--R \|a +--R / +--R +-------------+ +-----------+ +--R 4+-+3 | +-+ +-+ | +-+ +-+ +--R 2\|a \|- \|b + \|a \|\|b + \|a +--R Type: Expression(Integer) +--E 362 + +--S 363 of 520 +a0068:= integrate(t0068,x) +--R +--R +--R (228) +--R - +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 2 3 | b +--R ((32a b - 32a )sin(x) |---------------------- - 4a sin(x)) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 2 3 | b +--R ((32a b - 32a )sin(x) |---------------------- + 4a sin(x)) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 2 3 | b +--R (- 32a b + 32a )sin(x) |---------------------- +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R - 4a sin(x) +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R log +--R +----------------------+ +--R 2 3 | b +--R ((- 32a b + 32a )sin(x) |---------------------- + 4a sin(x)) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 520 +m0068:= a0068-r0068 +--R +--R +--R (229) +--R - +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- + 1 +--R +-------------+ | | 3 2 4 5 +--R 4+-+3 | +-+ +-+ | \|64a b - 128a b + 64a +--R \|a \|- \|b + \|a |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 2 3 | b +--R ((32a b - 32a )sin(x) |---------------------- - 4a sin(x)) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- + 1 +--R +-------------+ | | 3 2 4 5 +--R 4+-+3 | +-+ +-+ | \|64a b - 128a b + 64a +--R \|a \|- \|b + \|a |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 2 3 | b +--R ((32a b - 32a )sin(x) |---------------------- + 4a sin(x)) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- + 1 +--R +-------------+ | | 3 2 4 5 +--R 4+-+3 | +-+ +-+ | \|64a b - 128a b + 64a +--R \|a \|- \|b + \|a |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 2 3 | b +--R (- 32a b + 32a )sin(x) |---------------------- +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R + +--R - 4a sin(x) +--R * +--R +-------------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(- 8a b + 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- + 1 +--R +-------------+ | | 3 2 4 5 +--R 4+-+3 | +-+ +-+ | \|64a b - 128a b + 64a +--R \|a \|- \|b + \|a |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R * +--R +-----------+ +--R | +-+ +-+ +--R \|\|b + \|a +--R * +--R log +--R +----------------------+ +--R 2 3 | b +--R ((- 32a b + 32a )sin(x) |---------------------- + 4a sin(x)) +--R | 3 2 4 5 +--R \|64a b - 128a b + 64a +--R * +--R +-----------------------------------------+ +--R | +----------------------+ +--R | 2 | b +--R |(8a b - 8a ) |---------------------- + 1 +--R | | 3 2 4 5 +--R | \|64a b - 128a b + 64a +--R |----------------------------------------- +--R | 2 +--R \| 4a b - 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-----------+ +--R +-------------+ | +-+ +-+ +--R | +-+ +-+ tan(x)\|\|b + \|a +--R - \|- \|b + \|a atan(--------------------) +--R 4+-+ +--R \|a +--R + +--R +-------------+ +--R +-----------+ | +-+ +-+ +--R | +-+ +-+ tan(x)\|- \|b + \|a +--R - \|\|b + \|a atan(----------------------) +--R 4+-+ +--R \|a +--R / +--R +-------------+ +-----------+ +--R 4+-+3 | +-+ +-+ | +-+ +-+ +--R 2\|a \|- \|b + \|a \|\|b + \|a +--R Type: Expression(Integer) +--E 364 + +--S 365 of 520 +d0068:= D(m0068,x) +--R +--R +--R (230) +--R 4 2 2 4 +--R ((- b + a)sin(x) + (- 2b + 2a)cos(x) sin(x) + (- b + a)cos(x) ) +--R * +--R 4 +--R tan(x) +--R + +--R 4 2 2 4 2 4 +--R ((b - a)sin(x) - 2a cos(x) sin(x) - a cos(x) )tan(x) + b sin(x) +--R * +--R 4+-+2 +--R \|a +--R + +--R 4 2 2 4 4 +--R ((b - a)sin(x) - 2a cos(x) sin(x) - a cos(x) )tan(x) +--R + +--R 4 2 2 4 2 +--R ((b + a)sin(x) + 2a cos(x) sin(x) + a cos(x) )tan(x) +--R * +--R +-+ +--R \|a +--R / +--R 2 2 4 2 2 2 +--R (b - 2a b + a )sin(x) + (- 2a b + 2a )cos(x) sin(x) +--R + +--R 2 4 +--R (- a b + a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 4 2 2 2 2 4 +--R (- a b + a )sin(x) + 2a cos(x) sin(x) + a cos(x) +--R * +--R 4+-+2 +--R \|a +--R + +--R 2 4 2 2 2 2 4 2 +-+ +--R ((- 2a b + 2a )sin(x) + 4a cos(x) sin(x) + 2a cos(x) )tan(x) \|a +--R Type: Expression(Integer) +--E 365 + +--S 366 of 520 +t0069:= 1/(a-b*sin(x)^6) +--R +--R +--R 1 +--R (231) - ------------- +--R 6 +--R b sin(x) - a +--R Type: Expression(Integer) +--E 366 + +--S 367 of 520 +r0069:= 1/3*atan((a^(1/3)-b^(1/3))^(1/2)*tan(x)/a^(1/6))/a^(5/6)/_ + (a^(1/3)-b^(1/3))^(1/2)+1/3*atan((a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2)_ + *tan(x)/a^(1/6))/a^(5/6)/(a^(1/3)+(-1)^(1/3)*b^(1/3))^(1/2)+_ + 1/3*atan((a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2)*tan(x)/a^(1/6))/_ + a^(5/6)/(a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2) +--R +--R +--R (232) +--R +-----------------+ +--R +--------------------+ +-------------+ |3+---+3+-+ 3+-+ +--R | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ tan(x)\|\|- 1 \|b + \|a +--R \|- \|- 1 \|b + \|a \|- \|b + \|a atan(--------------------------) +--R 6+-+ +--R \|a +--R + +--R +-------------+ +--R +--------------------+ +-----------------+ | 3+-+ 3+-+ +--R | 3+---+2 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|- \|b + \|a +--R \|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(----------------------) +--R 6+-+ +--R \|a +--R + +--R +--------------------+ +--R +-------------+ +-----------------+ | 3+---+2 3+-+ 3+-+ +--R | 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|- \|- 1 \|b + \|a +--R \|- \|b + \|a \|\|- 1 \|b + \|a atan(-----------------------------) +--R 6+-+ +--R \|a +--R / +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 367 + +--S 368 of 520 +a0069:= integrate(t0069,x) +--R +--R +--R (233) +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 4 5 +--I (3888a b - 3888a )sin(x)%%EO0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 3 +--I (3888a b - 3888a )sin(x)%%EO0 - 324a sin(x)%%EO0 +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 4 5 +--I (3888a b - 3888a )sin(x)%%EO0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 3 +--I (- 3888a b + 3888a )sin(x)%%EO0 + 324a sin(x)%%EO0 +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 4 5 +--I (- 3888a b + 3888a )sin(x)%%EO0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 3 +--I (3888a b - 3888a )sin(x)%%EO0 - 324a sin(x)%%EO0 +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 4 5 +--I (- 3888a b + 3888a )sin(x)%%EO0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 3 +--I (- 3888a b + 3888a )sin(x)%%EO0 + 324a sin(x)%%EO0 +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--I \|4%%EO0 +--R * +--R log +--R 4 5 2 3 +--I (7776a b - 7776a )sin(x)%%EO0 - 648a sin(x)%%EO0 +--R + +--R - 18a sin(x) +--R * +--R +------+ +--I \|4%%EO0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I \|4%%EO0 +--R * +--R log +--R 4 5 2 3 +--I (- 7776a b + 7776a )sin(x)%%EO0 + 648a sin(x)%%EO0 +--R + +--R 18a sin(x) +--R * +--R +------+ +--I \|4%%EO0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 520 +m0069:= a0069-r0069 +--R +--R +--R (234) +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 4 5 +--I (3888a b - 3888a )sin(x)%%EO0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 3 +--I (3888a b - 3888a )sin(x)%%EO0 - 324a sin(x)%%EO0 +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 4 5 +--I (3888a b - 3888a )sin(x)%%EO0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 3 +--I (- 3888a b + 3888a )sin(x)%%EO0 + 324a sin(x)%%EO0 +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 4 5 +--I (- 3888a b + 3888a )sin(x)%%EO0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 3 +--I (3888a b - 3888a )sin(x)%%EO0 - 324a sin(x)%%EO0 +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 4 5 +--I (- 3888a b + 3888a )sin(x)%%EO0 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 4 5 2 3 +--I (- 3888a b + 3888a )sin(x)%%EO0 + 324a sin(x)%%EO0 +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%EO0 +--R * +--R log +--R 4 5 2 3 +--I (7776a b - 7776a )sin(x)%%EO0 - 648a sin(x)%%EO0 +--R + +--R - 18a sin(x) +--R * +--R +------+ +--I \|4%%EO0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I \|4%%EO0 +--R * +--R log +--R 4 5 2 3 +--I (- 7776a b + 7776a )sin(x)%%EO0 + 648a sin(x)%%EO0 +--R + +--R 18a sin(x) +--R * +--R +------+ +--I \|4%%EO0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +--------------------+ +-------------+ +--R | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R +-----------------+ +--R |3+---+3+-+ 3+-+ +--R tan(x)\|\|- 1 \|b + \|a +--R atan(--------------------------) +--R 6+-+ +--R \|a +--R + +--R - +--R +--------------------+ +-----------------+ +--R | 3+---+2 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +-------------+ +--R | 3+-+ 3+-+ +--R tan(x)\|- \|b + \|a +--R atan(----------------------) +--R 6+-+ +--R \|a +--R + +--R +--------------------+ +--R +-------------+ +-----------------+ | 3+---+2 3+-+ 3+-+ +--R | 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|- \|- 1 \|b + \|a +--R - 2\|- \|b + \|a \|\|- 1 \|b + \|a atan(-----------------------------) +--R 6+-+ +--R \|a +--R / +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 6\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 369 + +--S 370 of 520 +d0069:= D(m0069,x) +--R +--R +--R (235) +--R 3+---+2 3+---+ 6 +--R ((- 6b + 15a)\|- 1 + (6b - 15a)\|- 1 - 6b + 15a)sin(x) +--R + +--R 3+---+2 3+---+ +--R ((- 18b + 45a)\|- 1 + (18b - 45a)\|- 1 - 18b + 45a) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 3+---+2 3+---+ +--R ((- 18b + 45a)\|- 1 + (18b - 45a)\|- 1 - 18b + 45a) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 6b + 15a)\|- 1 + (6b - 15a)\|- 1 - 6b + 15a)cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((3b - 3a)\|- 1 + (- 3b + 3a)\|- 1 + 3b - 3a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (- 9a \|- 1 + 9a\|- 1 - 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3a \|- 1 + 3a\|- 1 - 3a)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R (3b \|- 1 - 3b\|- 1 + 3b)sin(x) +--R * +--R 3+-+6+-+4 +--R \|a \|a +--R + +--R 3+---+2 3+---+ 6 +--R ((12b - 12a)\|- 1 + (- 12b + 12a)\|- 1 + 12b - 12a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (- 36a \|- 1 + 36a\|- 1 - 36a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 12a \|- 1 + 12a\|- 1 - 12a)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((12b + 6a)\|- 1 + (- 12b - 6a)\|- 1 + 12b + 6a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (18a \|- 1 - 18a\|- 1 + 18a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R (6a \|- 1 - 6a\|- 1 + 6a)cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 3+-+2 6+-+2 +--R \|a \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- b + 11a b - 10a )\|- 1 + (b - 11a b + 10a )\|- 1 - b +--R + +--R 2 +--R 11a b - 10a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((3a b - 30a )\|- 1 + (- 3a b + 30a )\|- 1 + 3a b - 30a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((3a b - 30a )\|- 1 + (- 3a b + 30a )\|- 1 + 3a b - 30a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((a b - 10a )\|- 1 + (- a b + 10a )\|- 1 + a b - 10a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (- b + 8a b + 20a )\|- 1 + (b - 8a b - 20a )\|- 1 - b +--R + +--R 2 +--R 8a b + 20a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 6a b + 60a )\|- 1 + (6a b - 60a )\|- 1 - 6a b + 60a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 6a b + 60a )\|- 1 + (6a b - 60a )\|- 1 - 6a b + 60a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((- 2a b + 20a )\|- 1 + (2a b - 20a )\|- 1 - 2a b + 20a )cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 3+-+2 +--R \|b +--R + +--R 3+---+2 3+---+ 6 +--R ((15b - 6a)\|- 1 + (- 15b + 6a)\|- 1 + 15b - 6a)sin(x) +--R + +--R 3+---+2 3+---+ +--R ((45b - 18a)\|- 1 + (- 45b + 18a)\|- 1 + 45b - 18a) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 3+---+2 3+---+ +--R ((45b - 18a)\|- 1 + (- 45b + 18a)\|- 1 + 45b - 18a) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((15b - 6a)\|- 1 + (- 15b + 6a)\|- 1 + 15b - 6a)cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R ((- 3b + 3a)\|- 1 + (3b - 3a)\|- 1 - 3b + 3a)sin(x) +--R + +--R 3+---+2 3+---+ 2 4 +--R (9a \|- 1 - 9a\|- 1 + 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 4 2 +--R (9a \|- 1 - 9a\|- 1 + 9a)cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 6 +--R (3a \|- 1 - 3a\|- 1 + 3a)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3+---+2 3+---+ 6 +--R (- 3b \|- 1 + 3b\|- 1 - 3b)sin(x) +--R * +--R 3+-+2 6+-+4 +--R \|a \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (2b - 10a b + 8a )\|- 1 + (- 2b + 10a b - 8a )\|- 1 +--R + +--R 2 2 +--R 2b - 10a b + 8a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 6a b + 24a )\|- 1 + (6a b - 24a )\|- 1 - 6a b +--R + +--R 2 +--R 24a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 6a b + 24a )\|- 1 + (6a b - 24a )\|- 1 - 6a b +--R + +--R 2 +--R 24a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 2a b + 8a )\|- 1 + (2a b - 8a )\|- 1 - 2a b + 8a ) +--R * +--R 6 +--R cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (2b - 7a b - 4a )\|- 1 + (- 2b + 7a b + 4a )\|- 1 +--R + +--R 2 2 +--R 2b - 7a b - 4a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (3a b - 12a )\|- 1 + (- 3a b + 12a )\|- 1 + 3a b +--R + +--R 2 +--R - 12a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (3a b - 12a )\|- 1 + (- 3a b + 12a )\|- 1 + 3a b +--R + +--R 2 +--R - 12a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((a b - 4a )\|- 1 + (- a b + 4a )\|- 1 + a b - 4a )cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 6+-+2 +--R \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (5b - 10a b + 5a )\|- 1 + (- 5b + 10a b - 5a )\|- 1 +--R + +--R 2 2 +--R 5b - 10a b + 5a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 15a b + 15a )\|- 1 + (15a b - 15a )\|- 1 - 15a b +--R + +--R 2 +--R 15a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 15a b + 15a )\|- 1 + (15a b - 15a )\|- 1 - 15a b +--R + +--R 2 +--R 15a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 5a b + 5a )\|- 1 + (5a b - 5a )\|- 1 - 5a b + 5a ) +--R * +--R 6 +--R cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3+---+2 2 2 3+---+ +--R (5b + 5a b - 10a )\|- 1 + (- 5b - 5a b + 10a )\|- 1 +--R + +--R 2 2 +--R 5b + 5a b - 10a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (30a b - 30a )\|- 1 + (- 30a b + 30a )\|- 1 + 30a b +--R + +--R 2 +--R - 30a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (30a b - 30a )\|- 1 + (- 30a b + 30a )\|- 1 + 30a b +--R + +--R 2 +--R - 30a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (10a b - 10a )\|- 1 + (- 10a b + 10a )\|- 1 + 10a b +--R + +--R 2 +--R - 10a +--R * +--R 6 +--R cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 3+-+ +--R \|a +--R * +--R 3+-+ +--R \|b +--R + +--R 3+---+2 3+---+ 2 2 6 +--R (- 18a b \|- 1 + 18a b\|- 1 + 3b - 24a b + 3a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 2 4 +--R (- 54a b \|- 1 + 54a b\|- 1 + 9b - 72a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 2 +--R (- 54a b \|- 1 + 54a b\|- 1 + 9b - 72a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 2 6 +--R (- 18a b \|- 1 + 18a b\|- 1 + 3b - 24a b + 3a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 6 2 2 4 +--R (- 3b + 6a b - 3a )sin(x) + (9a b - 9a )cos(x) sin(x) +--R + +--R 2 4 2 2 6 +--R (9a b - 9a )cos(x) sin(x) + (3a b - 3a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 6 +--R (- 3b + 3a b)sin(x) +--R * +--R 6+-+4 +--R \|a +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 6b + 6a b)\|- 1 + (6b - 6a b)\|- 1 - 12b + 18a b +--R + +--R 2 +--R - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (18a b \|- 1 - 18a b\|- 1 + 36a b - 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (18a b \|- 1 - 18a b\|- 1 + 36a b - 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (6a b \|- 1 - 6a b\|- 1 + 12a b - 6a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 6 +--R ((- 6b - 3a b)\|- 1 + (6b + 3a b)\|- 1 - 12b + 3a )sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (- 9a b \|- 1 + 9a b\|- 1 - 18a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (- 9a b \|- 1 + 9a b\|- 1 - 18a b + 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (- 3a b \|- 1 + 3a b\|- 1 - 6a b + 3a )cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 3+-+6+-+2 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 9b + 9a b)\|- 1 + (9b - 9a b)\|- 1 - 12b + 15a b +--R + +--R 2 +--R - 3a +--R * +--R 6 +--R sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (27a b \|- 1 - 27a b\|- 1 + 36a b - 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (27a b \|- 1 - 27a b\|- 1 + 36a b - 9a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (9a b \|- 1 - 9a b\|- 1 + 12a b - 3a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 +--R (- 9b - 18a b)\|- 1 + (9b + 18a b)\|- 1 - 12b - 21a b +--R + +--R 2 +--R 6a +--R * +--R 6 +--R sin(x) +--R + +--R 3+---+2 3+---+ 2 2 4 +--R (- 54a b \|- 1 + 54a b\|- 1 - 72a b + 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 4 2 +--R (- 54a b \|- 1 + 54a b\|- 1 - 72a b + 18a )cos(x) sin(x) +--R + +--R 3+---+2 3+---+ 2 6 +--R (- 18a b \|- 1 + 18a b\|- 1 - 24a b + 6a )cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 3+-+2 +--R \|a +--R / +--R 2 2 3+---+2 +--R (6b - 21a b + 15a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (- 6b + 21a b - 15a )\|- 1 + 6b - 21a b + 15a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 18a b + 45a )\|- 1 + (18a b - 45a )\|- 1 - 18a b +--R + +--R 2 +--R 45a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 18a b + 45a )\|- 1 + (18a b - 45a )\|- 1 - 18a b +--R + +--R 2 +--R 45a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (- 6a b + 15a )\|- 1 + (6a b - 15a )\|- 1 - 6a b +--R + +--R 2 +--R 15a +--R * +--R 6 +--R cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((- 3a b + 3a )\|- 1 + (3a b - 3a )\|- 1 - 3a b + 3a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (9a \|- 1 - 9a \|- 1 + 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (3a \|- 1 - 3a \|- 1 + 3a )cos(x) +--R * +--R 3+-+6+-+4 +--R \|a \|a +--R + +--R 2 3+---+2 2 3+---+ 2 +--R ((- 18a b + 18a )\|- 1 + (18a b - 18a )\|- 1 - 18a b + 18a ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (54a \|- 1 - 54a \|- 1 + 54a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (18a \|- 1 - 18a \|- 1 + 18a )cos(x) +--R * +--R 2 3+-+2 6+-+2 +--R tan(x) \|a \|a +--R + +--R 2 2 3 3+---+2 +--R (3a b - 33a b + 30a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (- 3a b + 33a b - 30a )\|- 1 + 3a b - 33a b + 30a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((- 9a b + 90a )\|- 1 + (9a b - 90a )\|- 1 - 9a b + 90a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((- 9a b + 90a )\|- 1 + (9a b - 90a )\|- 1 - 9a b + 90a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 6 +--R ((- 3a b + 30a )\|- 1 + (3a b - 30a )\|- 1 - 3a b + 30a )cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 3+-+2 +--R \|b +--R + +--R 2 2 3+---+2 +--R (- 15b + 21a b - 6a )\|- 1 +--R + +--R 2 2 3+---+ 2 2 +--R (15b - 21a b + 6a )\|- 1 - 15b + 21a b - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (45a b - 18a )\|- 1 + (- 45a b + 18a )\|- 1 + 45a b +--R + +--R 2 +--R - 18a +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (45a b - 18a )\|- 1 + (- 45a b + 18a )\|- 1 + 45a b +--R + +--R 2 +--R - 18a +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ +--R (15a b - 6a )\|- 1 + (- 15a b + 6a )\|- 1 + 15a b +--R + +--R 2 +--R - 6a +--R * +--R 6 +--R cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R ((3a b - 3a )\|- 1 + (- 3a b + 3a )\|- 1 + 3a b - 3a )sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 4 +--R (- 9a \|- 1 + 9a \|- 1 - 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 4 2 +--R (- 9a \|- 1 + 9a \|- 1 - 9a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 6 +--R (- 3a \|- 1 + 3a \|- 1 - 3a )cos(x) +--R * +--R 3+-+2 6+-+4 +--R \|a \|a +--R + +--R 2 2 3 3+---+2 +--R (- 3a b + 15a b - 12a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (3a b - 15a b + 12a )\|- 1 - 3a b + 15a b - 12a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b - 36a )\|- 1 + (- 9a b + 36a )\|- 1 + 9a b - 36a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((9a b - 36a )\|- 1 + (- 9a b + 36a )\|- 1 + 9a b - 36a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 6 +--R ((3a b - 12a )\|- 1 + (- 3a b + 12a )\|- 1 + 3a b - 12a )cos(x) +--R * +--R 2 6+-+2 +--R tan(x) \|a +--R + +--R 2 2 3 3+---+2 +--R (- 15a b + 30a b - 15a )\|- 1 +--R + +--R 2 2 3 3+---+ 2 2 3 +--R (15a b - 30a b + 15a )\|- 1 - 15a b + 30a b - 15a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((45a b - 45a )\|- 1 + (- 45a b + 45a )\|- 1 + 45a b - 45a ) +--R * +--R 2 4 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((45a b - 45a )\|- 1 + (- 45a b + 45a )\|- 1 + 45a b - 45a ) +--R * +--R 4 2 +--R cos(x) sin(x) +--R + +--R 2 3 3+---+2 2 3 3+---+ 2 3 +--R ((15a b - 15a )\|- 1 + (- 15a b + 15a )\|- 1 + 15a b - 15a ) +--R * +--R 6 +--R cos(x) +--R * +--R 4 3+-+ +--R tan(x) \|a +--R * +--R 3+-+ +--R \|b +--R + +--R 2 2 3+---+2 2 2 3+---+ 3 +--R (18a b - 18a b)\|- 1 + (- 18a b + 18a b)\|- 1 - 3b +--R + +--R 2 2 3 +--R 27a b - 27a b + 3a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 2 +--R (- 54a b \|- 1 + 54a b\|- 1 + 9a b - 72a b + 9a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 4 +--R (- 54a b \|- 1 + 54a b\|- 1 + 9a b - 72a b + 9a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 2 3 6 +--R (- 18a b \|- 1 + 18a b\|- 1 + 3a b - 24a b + 3a )cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 2 2 3 6 2 3 2 4 +--R (3a b - 6a b + 3a )sin(x) + (- 9a b + 9a )cos(x) sin(x) +--R + +--R 2 3 4 2 2 3 6 +--R (- 9a b + 9a )cos(x) sin(x) + (- 3a b + 3a )cos(x) +--R * +--R 6+-+4 +--R \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 2 +--R (9a b - 9a b)\|- 1 + (- 9a b + 9a b)\|- 1 + 18a b - 27a b +--R + +--R 3 +--R 9a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 2 4 +--R (- 27a b \|- 1 + 27a b\|- 1 - 54a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 4 2 +--R (- 27a b \|- 1 + 27a b\|- 1 - 54a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 6 +--R (- 9a b \|- 1 + 9a b\|- 1 - 18a b + 9a )cos(x) +--R * +--R 2 3+-+6+-+2 +--R tan(x) \|a \|a +--R + +--R 2 2 3+---+2 2 2 3+---+ 2 +--R (27a b - 27a b)\|- 1 + (- 27a b + 27a b)\|- 1 + 36a b +--R + +--R 2 3 +--R - 45a b + 9a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 2 4 +--R (- 81a b \|- 1 + 81a b\|- 1 - 108a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 4 2 +--R (- 81a b \|- 1 + 81a b\|- 1 - 108a b + 27a )cos(x) sin(x) +--R + +--R 2 3+---+2 2 3+---+ 2 3 6 +--R (- 27a b \|- 1 + 27a b\|- 1 - 36a b + 9a )cos(x) +--R * +--R 4 3+-+2 +--R tan(x) \|a +--R Type: Expression(Integer) +--E 370 + +--S 371 of 520 +t0070:= 1/(a-b*sin(x)^8) +--R +--R +--R 1 +--R (236) - ------------- +--R 8 +--R b sin(x) - a +--R Type: Expression(Integer) +--E 371 + +--S 372 of 520 +r0070:= 1/4*atan((a^(1/4)-b^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/_ + (a^(1/4)-b^(1/4))^(1/2)+1/4*atan((a^(1/4)-%i*b^(1/4))^(1/2)*_ + tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)-%i*b^(1/4))^(1/2)+_ + 1/4*atan((a^(1/4)+%i*b^(1/4))^(1/2)*tan(x)/a^(1/8))/a^(7/8)/_ + (a^(1/4)+%i*b^(1/4))^(1/2)+1/4*atan((a^(1/4)+b^(1/4))^(1/2)*_ + tan(x)/a^(1/8))/a^(7/8)/(a^(1/4)+b^(1/4))^(1/2) +--R +--R +--R (237) +--R +-------------+ +---------------+ +-------------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R tan(x)\|\|b + \|a +--R atan(--------------------) +--R 8+-+ +--R \|a +--R + +--R +-------------+ +---------------+ +-----------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R \|- \|b + \|a \|- %i\|b + \|a \|\|b + \|a +--R * +--R +-------------+ +--R | 4+-+ 4+-+ +--R tan(x)\|%i\|b + \|a +--R atan(----------------------) +--R 8+-+ +--R \|a +--R + +--R +-------------+ +-------------+ +-----------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R \|- \|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +---------------+ +--R | 4+-+ 4+-+ +--R tan(x)\|- %i\|b + \|a +--R atan(------------------------) +--R 8+-+ +--R \|a +--R + +--R +---------------+ +-------------+ +-----------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +-------------+ +--R | 4+-+ 4+-+ +--R tan(x)\|- \|b + \|a +--R atan(----------------------) +--R 8+-+ +--R \|a +--R / +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 4\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R Type: Expression(Complex(Integer)) +--E 372 + +--S 373 of 520 +a0070:= integrate(t0070,x) +--R +--R +--R (238) +--R - +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 6 7 +--I (1048576a b - 1048576a )sin(x)%%EP0 %%EP1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 2 +--I (1048576a b - 1048576a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (1048576a b - 1048576a )sin(x)%%EP0 +--R + +--R 5 +--I - 65536a sin(x)%%EP0 +--R * +--I %%EP1 +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 6 7 +--I (1048576a b - 1048576a )sin(x)%%EP0 %%EP1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 2 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 +--R + +--R 5 +--I 65536a sin(x)%%EP0 +--R * +--I %%EP1 +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 6 7 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 %%EP1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 2 +--I (1048576a b - 1048576a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (1048576a b - 1048576a )sin(x)%%EP0 +--R + +--R 5 +--I - 65536a sin(x)%%EP0 +--R * +--I %%EP1 +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 6 7 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 %%EP1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 2 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 +--R + +--R 5 +--I 65536a sin(x)%%EP0 +--R * +--I %%EP1 +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I \|4%%EP1 +--R * +--R log +--R 6 7 2 +--I (2097152a b - 2097152a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (2097152a b - 2097152a )sin(x)%%EP0 +--R + +--R 5 +--I - 131072a sin(x)%%EP0 +--R * +--I %%EP1 +--R + +--R 6 7 3 5 2 +--I (2097152a b - 2097152a )sin(x)%%EP0 - 131072a sin(x)%%EP0 +--R + +--R 3 +--I - 3072a sin(x)%%EP0 +--R * +--R +------+ +--I \|4%%EP1 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--I \|4%%EP1 +--R * +--R log +--R 6 7 2 +--I (- 2097152a b + 2097152a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (- 2097152a b + 2097152a )sin(x)%%EP0 +--R + +--R 5 +--I 131072a sin(x)%%EP0 +--R * +--I %%EP1 +--R + +--R 6 7 3 +--I (- 2097152a b + 2097152a )sin(x)%%EP0 +--R + +--R 5 2 3 +--I 131072a sin(x)%%EP0 + 3072a sin(x)%%EP0 +--R * +--R +------+ +--I \|4%%EP1 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--I \|4%%EP0 +--R * +--R log +--R 6 7 3 +--I (2097152a b - 2097152a )sin(x)%%EP0 +--R + +--R 5 2 3 +--I - 131072a sin(x)%%EP0 - 3072a sin(x)%%EP0 - 32a sin(x) +--R * +--R +------+ +--I \|4%%EP0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I \|4%%EP0 +--R * +--R log +--R 6 7 3 +--I (- 2097152a b + 2097152a )sin(x)%%EP0 +--R + +--R 5 2 3 +--I 131072a sin(x)%%EP0 + 3072a sin(x)%%EP0 + 32a sin(x) +--R * +--R +------+ +--I \|4%%EP0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 520 +m0070:= a0070-r0070 +--R +--R +--R (239) +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 6 7 +--I (1048576a b - 1048576a )sin(x)%%EP0 %%EP1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 2 +--I (1048576a b - 1048576a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (1048576a b - 1048576a )sin(x)%%EP0 +--R + +--R 5 +--I - 65536a sin(x)%%EP0 +--R * +--I %%EP1 +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 6 7 +--I (1048576a b - 1048576a )sin(x)%%EP0 %%EP1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 2 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 +--R + +--R 5 +--I 65536a sin(x)%%EP0 +--R * +--I %%EP1 +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 6 7 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 %%EP1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 2 +--I (1048576a b - 1048576a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (1048576a b - 1048576a )sin(x)%%EP0 +--R + +--R 5 +--I - 65536a sin(x)%%EP0 +--R * +--I %%EP1 +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 6 7 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 %%EP1 +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 6 7 2 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (- 1048576a b + 1048576a )sin(x)%%EP0 +--R + +--R 5 +--I 65536a sin(x)%%EP0 +--R * +--I %%EP1 +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +------+ +--I \|4%%EP1 +--R * +--R log +--R 6 7 2 +--I (2097152a b - 2097152a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (2097152a b - 2097152a )sin(x)%%EP0 +--R + +--R 5 +--I - 131072a sin(x)%%EP0 +--R * +--I %%EP1 +--R + +--R 6 7 3 5 2 +--I (2097152a b - 2097152a )sin(x)%%EP0 - 131072a sin(x)%%EP0 +--R + +--R 3 +--I - 3072a sin(x)%%EP0 +--R * +--R +------+ +--I \|4%%EP1 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +------+ +--I \|\|b + \|a \|4%%EP1 +--R * +--R log +--R 6 7 2 +--I (- 2097152a b + 2097152a )sin(x)%%EP0 %%EP1 +--R + +--R 6 7 2 +--I (- 2097152a b + 2097152a )sin(x)%%EP0 +--R + +--R 5 +--I 131072a sin(x)%%EP0 +--R * +--I %%EP1 +--R + +--R 6 7 3 +--I (- 2097152a b + 2097152a )sin(x)%%EP0 +--R + +--R 5 2 3 +--I 131072a sin(x)%%EP0 + 3072a sin(x)%%EP0 +--R * +--R +------+ +--I \|4%%EP1 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +------+ +--I \|\|b + \|a \|4%%EP0 +--R * +--R log +--R 6 7 3 +--I (2097152a b - 2097152a )sin(x)%%EP0 +--R + +--R 5 2 3 +--I - 131072a sin(x)%%EP0 - 3072a sin(x)%%EP0 - 32a sin(x) +--R * +--R +------+ +--I \|4%%EP0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +------+ +--I \|4%%EP0 +--R * +--R log +--R 6 7 3 +--I (- 2097152a b + 2097152a )sin(x)%%EP0 +--R + +--R 5 2 3 +--I 131072a sin(x)%%EP0 + 3072a sin(x)%%EP0 + 32a sin(x) +--R * +--R +------+ +--I \|4%%EP0 +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R tan(x)\|\|b + \|a +--R atan(--------------------) +--R 8+-+ +--R \|a +--R + +--R - +--R +-------------+ +---------------+ +-----------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R \|- \|b + \|a \|- %i\|b + \|a \|\|b + \|a +--R * +--R +-------------+ +--R | 4+-+ 4+-+ +--R tan(x)\|%i\|b + \|a +--R atan(----------------------) +--R 8+-+ +--R \|a +--R + +--R - +--R +-------------+ +-------------+ +-----------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R \|- \|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +---------------+ +--R | 4+-+ 4+-+ +--R tan(x)\|- %i\|b + \|a +--R atan(------------------------) +--R 8+-+ +--R \|a +--R + +--R - +--R +---------------+ +-------------+ +-----------+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +-------------+ +--R | 4+-+ 4+-+ +--R tan(x)\|- \|b + \|a +--R atan(----------------------) +--R 8+-+ +--R \|a +--R / +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 4\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R Type: Expression(Complex(Integer)) +--E 374 + +--S 375 of 520 +d0070:= D(m0070,x) +--R +--R +--R (240) +--R 8 2 6 +--R (- b + a)sin(x) + (- 4b + 4a)cos(x) sin(x) +--R + +--R 4 4 6 2 +--R (- 6b + 6a)cos(x) sin(x) + (- 4b + 4a)cos(x) sin(x) +--R + +--R 8 +--R (- b + a)cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 8 2 6 4 4 +--R (b - a)sin(x) - 4a cos(x) sin(x) - 6a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 4a cos(x) sin(x) - a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 8 +--R b sin(x) +--R * +--R 8+-+6 +--R \|a +--R + +--R 8 2 6 4 4 +--R (3b - 3a)sin(x) - 12a cos(x) sin(x) - 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 12a cos(x) sin(x) - 3a cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 8 2 6 4 4 +--R (3b + a)sin(x) + 4a cos(x) sin(x) + 6a cos(x) sin(x) +--R + +--R 6 2 8 +--R 4a cos(x) sin(x) + a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+-+8+-+4 +--R \|a \|a +--R + +--R 8 2 6 4 4 +--R (3b - 3a)sin(x) - 12a cos(x) sin(x) - 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 12a cos(x) sin(x) - 3a cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 8 2 6 4 4 +--R (3b + 3a)sin(x) + 12a cos(x) sin(x) + 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R 12a cos(x) sin(x) + 3a cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 4+-+2 8+-+2 +--R \|a \|a +--R + +--R 8 2 6 4 4 +--R (b - a)sin(x) - 4a cos(x) sin(x) - 6a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 4a cos(x) sin(x) - a cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 8 2 6 4 4 +--R (b + 3a)sin(x) + 12a cos(x) sin(x) + 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R 12a cos(x) sin(x) + 3a cos(x) +--R * +--R 6 +--R tan(x) +--R * +--R 4+-+3 +--R \|a +--R / +--R 2 2 8 2 2 6 +--R (b - 2a b + a )sin(x) + (- 4a b + 4a )cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 +--R (- 6a b + 6a )cos(x) sin(x) + (- 4a b + 4a )cos(x) sin(x) +--R + +--R 2 8 +--R (- a b + a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 8 2 2 6 2 4 4 +--R (- a b + a )sin(x) + 4a cos(x) sin(x) + 6a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 4a cos(x) sin(x) + a cos(x) +--R * +--R 8+-+6 +--R \|a +--R + +--R 2 8 2 2 6 2 4 4 +--R (- 4a b + 4a )sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 16a cos(x) sin(x) + 4a cos(x) +--R * +--R 2 4+-+8+-+4 +--R tan(x) \|a \|a +--R + +--R 2 8 2 2 6 2 4 4 +--R (- 6a b + 6a )sin(x) + 24a cos(x) sin(x) + 36a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 24a cos(x) sin(x) + 6a cos(x) +--R * +--R 4 4+-+2 8+-+2 +--R tan(x) \|a \|a +--R + +--R 2 8 2 2 6 2 4 4 +--R (- 4a b + 4a )sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 16a cos(x) sin(x) + 4a cos(x) +--R * +--R 6 4+-+3 +--R tan(x) \|a +--R Type: Expression(Complex(Integer)) +--E 375 + +--S 376 of 520 +t0071:= 1/(1+sin(x)^3) +--R +--R +--R 1 +--R (241) ----------- +--R 3 +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 520 +r0071:= -2/3*atan(((-1)^(1/3)-tan(1/2*x))/(1-(-1)^(2/3))^(1/2))/_ + (1-(-1)^(2/3))^(1/2)+2/3*atan(((-1)^(2/3)+tan(1/2*x))/_ + (1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)-cos(x)/(3+3*sin(x)) +--R +--R +--R (242) +--R x 3+---+ +--R +----------+ tan(-) - \|- 1 +--R |3+---+ 2 +--R (2sin(x) + 2)\|\|- 1 + 1 atan(----------------) +--R +-------------+ +--R | 3+---+2 +--R \|- \|- 1 + 1 +--R + +--R x 3+---+2 +--R +-------------+ tan(-) + \|- 1 +--R | 3+---+2 2 +--R (2sin(x) + 2)\|- \|- 1 + 1 atan(----------------) +--R +----------+ +--R |3+---+ +--R \|\|- 1 + 1 +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R - cos(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R (3sin(x) + 3)\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 520 +a0071:= integrate(t0071,x) +--R +--R +--R (243) +--R %pi x 4 %pi x 2 x 2 %pi x x +--R - cos(---)sin(-) - 2cos(---)cos(-) sin(-) - 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R - cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (2\|3 + 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R - \|3 \|3 cos(---) + (\|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((4\|3 + 6)\|3 cos(-) - 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) - 2\|3 \|3 cos(---) + (2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +--R - 4\|3 \|3 cos(-)sin(---) +--R 2 12 +--R + +--R 4+-+ %pi 4+-+2 x +--R (- 12\|3 cos(---) - 4\|3 )cos(-) +--R 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +-+ 4+-+ +--R ((2\|3 + 3)\|3 cos(-) + 4\|3 \|3 cos(-) + (2\|3 - 3)\|3 ) +--R 2 2 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) - \|3 \|3 cos(---) + (\|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (- \|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R - cos(---)sin(-) - 2cos(---)cos(-) sin(-) - 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R - cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (2\|3 - 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R \|3 \|3 cos(---) + (- \|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((4\|3 - 6)\|3 cos(-) - 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) + 2\|3 \|3 cos(---) + (- 2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +--R - 4\|3 \|3 cos(-)sin(---) +--R 2 12 +--R + +--R 4+-+ %pi 4+-+2 x +--R (- 12\|3 cos(---) - 4\|3 )cos(-) +--R 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +-+ 4+-+ +--R ((2\|3 - 3)\|3 cos(-) + 4\|3 \|3 cos(-) + (2\|3 + 3)\|3 ) +--R 2 2 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) + \|3 \|3 cos(---) + (- \|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (\|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R cos(---)sin(-) + 2cos(---)cos(-) sin(-) + 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (- 2\|3 + 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R - \|3 \|3 cos(---) + (- \|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((- 4\|3 + 6)\|3 cos(-) + 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) - 2\|3 \|3 cos(---) + (- 2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi 4+-+2 x +--R (4\|3 \|3 cos(-)sin(---) + (12\|3 cos(---) - 4\|3 )cos(-)) +--R 2 12 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +--R (- 2\|3 + 3)\|3 cos(-) - 4\|3 \|3 cos(-) +--R 2 2 +--R + +--R +-+ 4+-+ +--R (- 2\|3 - 3)\|3 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) - \|3 \|3 cos(---) + (- \|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (\|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R cos(---)sin(-) + 2cos(---)cos(-) sin(-) + 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (- 2\|3 - 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R \|3 \|3 cos(---) + (\|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((- 4\|3 - 6)\|3 cos(-) + 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) + 2\|3 \|3 cos(---) + (2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi 4+-+2 x +--R (4\|3 \|3 cos(-)sin(---) + (12\|3 cos(---) - 4\|3 )cos(-)) +--R 2 12 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +--R (- 2\|3 - 3)\|3 cos(-) - 4\|3 \|3 cos(-) +--R 2 2 +--R + +--R +-+ 4+-+ +--R (- 2\|3 + 3)\|3 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) + \|3 \|3 cos(---) + (\|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (- \|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R 2sin(---)sin(-) + 4cos(-) sin(---)sin(-) + 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (2cos(-) + 2)sin(---) +--R 2 12 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (\|3 + 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (2\|3 + 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R - 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (\|3 + 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (\|3 - 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) + \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) + 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) - 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) + \|3 )cos(-) + (6cos(---) + 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) + \|3 +--R 12 +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R 2sin(---)sin(-) + 4cos(-) sin(---)sin(-) + 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (2cos(-) + 2)sin(---) +--R 2 12 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (\|3 - 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (2\|3 - 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R - 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (\|3 - 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (\|3 + 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) + \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) + 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) - 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) + \|3 )cos(-) + (6cos(---) + 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) + \|3 +--R 12 +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R - 2sin(---)sin(-) - 4cos(-) sin(---)sin(-) - 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (- 2cos(-) - 2)sin(---) +--R 2 12 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (- \|3 + 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (- 2\|3 + 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (- \|3 + 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) - 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (- \|3 - 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) - \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) - 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) - \|3 )cos(-) + (6cos(---) - 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) - \|3 +--R 12 +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R - 2sin(---)sin(-) - 4cos(-) sin(---)sin(-) - 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (- 2cos(-) - 2)sin(---) +--R 2 12 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (- \|3 - 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (- 2\|3 - 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (- \|3 - 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) - 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (- \|3 + 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) - \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) - 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) - \|3 )cos(-) + (6cos(---) - 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) - \|3 +--R 12 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ x 2 4+-+ x x +--R - 2\|3 sin(-) + (- 4\|3 cos(-) + 4\|3 )sin(-) - 8\|3 cos(-)sin(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ +--R - 2\|3 cos(-) - 4\|3 cos(-) - 2\|3 +--R 2 2 +--R / +--R 4+-+ x 4 4+-+ x 2 x 2 4+-+ x x 4+-+ x 4 +--R 6\|3 sin(-) + 12\|3 cos(-) sin(-) + 24\|3 cos(-)sin(-) + 6\|3 cos(-) +--R 2 2 2 2 2 2 +--R + +--R 4+-+ +--R 6\|3 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 520 +m0071:= a0071-r0071 +--R +--R +--R (244) +--R %pi x 4 %pi x 2 x 2 +--R - cos(---)sin(-) - 2cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x x %pi x 4 %pi +--R - 4cos(---)cos(-)sin(-) - cos(---)cos(-) - cos(---) +--R 12 2 2 12 2 12 +--R * +--R sin(x) +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R - cos(---)sin(-) - 2cos(---)cos(-) sin(-) - 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R - cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (2\|3 + 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R - \|3 \|3 cos(---) + (\|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((4\|3 + 6)\|3 cos(-) - 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) - 2\|3 \|3 cos(---) + (2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +--R - 4\|3 \|3 cos(-)sin(---) +--R 2 12 +--R + +--R 4+-+ %pi 4+-+2 x +--R (- 12\|3 cos(---) - 4\|3 )cos(-) +--R 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +-+ 4+-+ +--R ((2\|3 + 3)\|3 cos(-) + 4\|3 \|3 cos(-) + (2\|3 - 3)\|3 ) +--R 2 2 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) - \|3 \|3 cos(---) + (\|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (- \|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 x 2 +--R - cos(---)sin(-) - 2cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x x %pi x 4 %pi +--R - 4cos(---)cos(-)sin(-) - cos(---)cos(-) - cos(---) +--R 12 2 2 12 2 12 +--R * +--R sin(x) +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R - cos(---)sin(-) - 2cos(---)cos(-) sin(-) - 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R - cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (2\|3 - 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R \|3 \|3 cos(---) + (- \|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((4\|3 - 6)\|3 cos(-) - 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) + 2\|3 \|3 cos(---) + (- 2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +--R - 4\|3 \|3 cos(-)sin(---) +--R 2 12 +--R + +--R 4+-+ %pi 4+-+2 x +--R (- 12\|3 cos(---) - 4\|3 )cos(-) +--R 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +-+ 4+-+ +--R ((2\|3 - 3)\|3 cos(-) + 4\|3 \|3 cos(-) + (2\|3 + 3)\|3 ) +--R 2 2 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) + \|3 \|3 cos(---) + (- \|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (\|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R cos(---)sin(-) + 2cos(---)cos(-) sin(-) + 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R sin(x) +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R cos(---)sin(-) + 2cos(---)cos(-) sin(-) + 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (- 2\|3 + 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R - \|3 \|3 cos(---) + (- \|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((- 4\|3 + 6)\|3 cos(-) + 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) - 2\|3 \|3 cos(---) + (- 2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi 4+-+2 x +--R (4\|3 \|3 cos(-)sin(---) + (12\|3 cos(---) - 4\|3 )cos(-)) +--R 2 12 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +--R (- 2\|3 + 3)\|3 cos(-) - 4\|3 \|3 cos(-) +--R 2 2 +--R + +--R +-+ 4+-+ +--R (- 2\|3 - 3)\|3 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) - \|3 \|3 cos(---) + (- \|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (\|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R cos(---)sin(-) + 2cos(---)cos(-) sin(-) + 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R sin(x) +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R cos(---)sin(-) + 2cos(---)cos(-) sin(-) + 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (- 2\|3 - 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R \|3 \|3 cos(---) + (\|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((- 4\|3 - 6)\|3 cos(-) + 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) + 2\|3 \|3 cos(---) + (2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi 4+-+2 x +--R (4\|3 \|3 cos(-)sin(---) + (12\|3 cos(---) - 4\|3 )cos(-)) +--R 2 12 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +--R (- 2\|3 - 3)\|3 cos(-) - 4\|3 \|3 cos(-) +--R 2 2 +--R + +--R +-+ 4+-+ +--R (- 2\|3 + 3)\|3 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) + \|3 \|3 cos(---) + (\|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (- \|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 x 2 %pi x 2 +--R 2sin(---)sin(-) + 4cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x %pi x x 4 %pi +--R 8cos(-)sin(---)sin(-) + (2cos(-) + 2)sin(---) +--R 2 12 2 2 12 +--R * +--R sin(x) +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R 2sin(---)sin(-) + 4cos(-) sin(---)sin(-) + 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (2cos(-) + 2)sin(---) +--R 2 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (\|3 + 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (2\|3 + 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R - 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (\|3 + 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (\|3 - 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) + \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) + 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) - 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) + \|3 )cos(-) + (6cos(---) + 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) + \|3 +--R 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R 2sin(---)sin(-) + 4cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x %pi x x 4 %pi +--R 8cos(-)sin(---)sin(-) + (2cos(-) + 2)sin(---) +--R 2 12 2 2 12 +--R * +--R sin(x) +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R 2sin(---)sin(-) + 4cos(-) sin(---)sin(-) + 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (2cos(-) + 2)sin(---) +--R 2 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (\|3 - 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (2\|3 - 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R - 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (\|3 - 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (\|3 + 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) + \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) + 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) - 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) + \|3 )cos(-) + (6cos(---) + 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) + \|3 +--R 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R - 2sin(---)sin(-) - 4cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x %pi x x 4 %pi +--R - 8cos(-)sin(---)sin(-) + (- 2cos(-) - 2)sin(---) +--R 2 12 2 2 12 +--R * +--R sin(x) +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R - 2sin(---)sin(-) - 4cos(-) sin(---)sin(-) - 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (- 2cos(-) - 2)sin(---) +--R 2 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (- \|3 + 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (- 2\|3 + 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (- \|3 + 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) - 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (- \|3 - 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) - \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) - 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) - \|3 )cos(-) + (6cos(---) - 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) - \|3 +--R 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R - 2sin(---)sin(-) - 4cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x %pi x x 4 %pi +--R - 8cos(-)sin(---)sin(-) + (- 2cos(-) - 2)sin(---) +--R 2 12 2 2 12 +--R * +--R sin(x) +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R - 2sin(---)sin(-) - 4cos(-) sin(---)sin(-) - 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (- 2cos(-) - 2)sin(---) +--R 2 12 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (- \|3 - 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (- 2\|3 - 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (- \|3 - 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) - 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (- \|3 + 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) - \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) - 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) - \|3 )cos(-) + (6cos(---) - 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) - \|3 +--R 12 +--R + +--R 4+-+ x 4 4+-+ x 2 x 2 4+-+ x x +--R - 4\|3 sin(-) - 8\|3 cos(-) sin(-) - 16\|3 cos(-)sin(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ x 4 4+-+ +--R - 4\|3 cos(-) - 4\|3 +--R 2 +--R * +--R sin(x) +--R + +--R 4+-+ x 4 4+-+ x 2 x 2 4+-+ x x +--R - 4\|3 sin(-) - 8\|3 cos(-) sin(-) - 16\|3 cos(-)sin(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ x 4 4+-+ +--R - 4\|3 cos(-) - 4\|3 +--R 2 +--R * +--R x 3+---+ +--R +----------+ tan(-) - \|- 1 +--R |3+---+ 2 +--R \|\|- 1 + 1 atan(----------------) +--R +-------------+ +--R | 3+---+2 +--R \|- \|- 1 + 1 +--R + +--R 4+-+ x 4 4+-+ x 2 x 2 4+-+ x x +--R - 4\|3 sin(-) - 8\|3 cos(-) sin(-) - 16\|3 cos(-)sin(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ x 4 4+-+ +--R - 4\|3 cos(-) - 4\|3 +--R 2 +--R * +--R sin(x) +--R + +--R 4+-+ x 4 4+-+ x 2 x 2 4+-+ x x +--R - 4\|3 sin(-) - 8\|3 cos(-) sin(-) - 16\|3 cos(-)sin(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ x 4 4+-+ +--R - 4\|3 cos(-) - 4\|3 +--R 2 +--R * +--R x 3+---+2 +--R +-------------+ tan(-) + \|- 1 +--R | 3+---+2 2 +--R \|- \|- 1 + 1 atan(----------------) +--R +----------+ +--R |3+---+ +--R \|\|- 1 + 1 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ x 2 +--R - 2\|3 sin(-) + (- 4\|3 cos(-) + 4\|3 )sin(-) +--R 2 2 2 +--R + +--R 4+-+ x x 4+-+ x 4 4+-+ x 2 4+-+ +--R - 8\|3 cos(-)sin(-) - 2\|3 cos(-) - 4\|3 cos(-) - 2\|3 +--R 2 2 2 2 +--R * +--R sin(x) +--R + +--R 4+-+ 4+-+ x 4 +--R (2\|3 cos(x) - 2\|3 )sin(-) +--R 2 +--R + +--R 4+-+ x 2 4+-+ x 2 4+-+ x 2 +--R (4\|3 cos(-) cos(x) - 4\|3 cos(-) + 4\|3 )sin(-) +--R 2 2 2 +--R + +--R 4+-+ x 4+-+ x x +--R (8\|3 cos(-)cos(x) - 8\|3 cos(-))sin(-) +--R 2 2 2 +--R + +--R 4+-+ x 4 4+-+ 4+-+ x 4 4+-+ x 2 4+-+ +--R (2\|3 cos(-) + 2\|3 )cos(x) - 2\|3 cos(-) - 4\|3 cos(-) - 2\|3 +--R 2 2 2 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R 4+-+ x 4 4+-+ x 2 x 2 4+-+ x x +--R 6\|3 sin(-) + 12\|3 cos(-) sin(-) + 24\|3 cos(-)sin(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ x 4 4+-+ +--R 6\|3 cos(-) + 6\|3 +--R 2 +--R * +--R sin(x) +--R + +--R 4+-+ x 4 4+-+ x 2 x 2 4+-+ x x 4+-+ x 4 +--R 6\|3 sin(-) + 12\|3 cos(-) sin(-) + 24\|3 cos(-)sin(-) + 6\|3 cos(-) +--R 2 2 2 2 2 2 +--R + +--R 4+-+ +--R 6\|3 +--R * +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 520 +--d0071:= D(m0071,x) +--E 380 + +--S 381 of 520 +t0072:= 1/(1+sin(x)^4) +--R +--R +--R 1 +--R (245) ----------- +--R 4 +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 520 +r0072:= 1/2*atan((1-%i)^(1/2)*tan(x))/(1-%i)^(1/2)+_ + 1/2*atan((1+%i)^(1/2)*tan(x))/(1+%i)^(1/2) +--R +--R +--R +------+ +------+ +------+ +------+ +--R \|1 - %i atan(\|1 + %i tan(x)) + \|1 + %i atan(\|1 - %i tan(x)) +--R (246) --------------------------------------------------------------- +--R +------+ +------+ +--R 2\|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 382 + +--S 383 of 520 +a0072:= integrate(t0072,x) +--R +--R +--R (247) +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +-+4+-+ %pi x x 3 +--R (2\|2 \|2 cos(-)sin(---) + 2\|2 \|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (4\|2 cos(-) sin(---) + (4\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ x 3 %pi +-+4+-+ %pi x 3 x +--R (- 2\|2 \|2 cos(-) sin(---) - 2\|2 \|2 cos(---)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 4 +--R cos(-) +--R 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +-+4+-+ %pi x x 3 +--R (- 2\|2 \|2 cos(-)sin(---) - 2\|2 \|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 +--R (4\|2 cos(-) sin(---) + (4\|2 cos(---) - 2)cos(-) ) +--R 2 8 8 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x 3 %pi +-+4+-+ %pi x 3 x +--R (2\|2 \|2 cos(-) sin(---) + 2\|2 \|2 cos(---)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 4 +--R cos(-) +--R 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R - +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ x %pi 4+-+ %pi x x +--R (2\|2 cos(-)sin(---) - 2\|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R / +--R +-+ x 2 +--R \|2 sin(-) +--R 2 +--R + +--R 4+-+ x %pi 4+-+ %pi x x +--R (- 2\|2 cos(-)sin(---) - 2\|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R + +--R +-+ x 2 +--R - \|2 cos(-) +--R 2 +--R + +--R - +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ x %pi 4+-+ %pi x x +--R (2\|2 cos(-)sin(---) - 2\|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R / +--R +-+ x 2 +--R \|2 sin(-) +--R 2 +--R + +--R 4+-+ x %pi 4+-+ %pi x x +-+ x 2 +--R (2\|2 cos(-)sin(---) + 2\|2 cos(---)cos(-))sin(-) - \|2 cos(-) +--R 2 8 8 2 2 2 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 520 +m0072:= a0072-r0072 +--R +--R +--R (248) +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +-+4+-+ %pi x x 3 +--R (2\|2 \|2 cos(-)sin(---) + 2\|2 \|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (4\|2 cos(-) sin(---) + (4\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ x 3 %pi +-+4+-+ %pi x 3 x +--R (- 2\|2 \|2 cos(-) sin(---) - 2\|2 \|2 cos(---)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 4 +--R cos(-) +--R 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R - +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +-+4+-+ %pi x x 3 +--R (- 2\|2 \|2 cos(-)sin(---) - 2\|2 \|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 +--R (4\|2 cos(-) sin(---) + (4\|2 cos(---) - 2)cos(-) ) +--R 2 8 8 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x 3 %pi +-+4+-+ %pi x 3 x +--R (2\|2 \|2 cos(-) sin(---) + 2\|2 \|2 cos(---)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 4 +--R cos(-) +--R 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R +------+ +-+ +------+ +--R - 2\|1 - %i \|2 atan(\|1 + %i tan(x)) +--R + +--R +------+ +-+ +------+ +--R - 2\|1 + %i \|2 atan(\|1 - %i tan(x)) +--R + +--R - +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ x %pi 4+-+ %pi x x +--R (2\|2 cos(-)sin(---) - 2\|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R / +--R +-+ x 2 +--R \|2 sin(-) +--R 2 +--R + +--R 4+-+ x %pi 4+-+ %pi x x +--R (- 2\|2 cos(-)sin(---) - 2\|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R + +--R +-+ x 2 +--R - \|2 cos(-) +--R 2 +--R + +--R - +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 sin(---) +--R 8 +--R * +--R atan +--R 4+-+ x %pi 4+-+ %pi x x +--R (2\|2 cos(-)sin(---) - 2\|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R / +--R +-+ x 2 +--R \|2 sin(-) +--R 2 +--R + +--R 4+-+ x %pi 4+-+ %pi x x +-+ x 2 +--R (2\|2 cos(-)sin(---) + 2\|2 cos(---)cos(-))sin(-) - \|2 cos(-) +--R 2 8 8 2 2 2 +--R / +--R +------+ +------+ +-+ +--R 4\|1 - %i \|1 + %i \|2 +--R Type: Expression(Complex(Integer)) +--E 384 + +--S 385 of 520 +d0072:= D(m0072,x) +--R +--R +--R (249) +--R 4+-+2 %pi 2 4+-+2 %pi %pi 4+-+2 %pi 2 +--R (2\|2 sin(---) - 4\|2 cos(---)sin(---) - 2\|2 cos(---) - 2) +--R 8 8 8 8 +--R * +--R x 16 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 4 %pi x 2 %pi 3 +--R 16cos(-) sin(---) - 64cos(---)cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +--R (160cos(---) - 8\|2 )cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 3 4+-+2 %pi x 2 %pi +--R (64cos(---) + 80\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 2 +--R (16cos(---) + 8\|2 cos(---) + 16)cos(-) +--R 8 8 2 +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 4 %pi 6 4+-+2 %pi x 4 %pi 5 +--R 64\|2 cos(-) sin(---) - 384\|2 cos(---)cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi 2 x 4 %pi 4 +--R (64\|2 cos(---) - 160)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 3 %pi x 4 %pi 3 +--R (- 768\|2 cos(---) + 128cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 4 %pi 2 +--R (- 64\|2 cos(---) - 1600cos(---) + 8\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 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1024cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 6 %pi 5 +--R 2048\|2 cos(---)cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 4 x 6 %pi 4 +--R (1536cos(---) + 504)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 3 %pi x 6 %pi 3 +--R (4096\|2 cos(---) + 32cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 %pi 2 4+-+2 x 6 %pi 2 +--R (1024cos(---) + 5040cos(---) + 4\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi x 6 %pi +--R (2048\|2 cos(---) - 32cos(---) + 952\|2 cos(---))cos(-) sin(---) +--R 8 8 8 2 8 +--R + +--R %pi 8 %pi 4 4+-+2 %pi 2 x 6 +--R (256cos(---) + 504cos(---) - 4\|2 cos(---) + 112)cos(-) +--R 8 8 8 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 8 %pi 8 %pi 2 4+-+2 x 8 %pi 6 +--R - 1536cos(-) sin(---) + (- 6144cos(---) - 64\|2 )cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 8 %pi 5 +--R - 3712\|2 cos(---)cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 8 %pi 4 +--R (- 9216cos(---) - 64\|2 cos(---) - 736)cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 3 %pi x 8 %pi 3 +--R (- 7424\|2 cos(---) - 128cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 4+-+2 %pi 4 %pi 2 4+-+2 +--R (- 6144cos(---) + 64\|2 cos(---) - 7360cos(---) - 10\|2 ) +--R 8 8 8 +--R * +--R x 8 %pi 2 +--R cos(-) sin(---) +--R 2 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi x 8 +--R (- 3712\|2 cos(---) + 128cos(---) - 1260\|2 cos(---))cos(-) +--R 8 8 8 2 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R %pi 8 4+-+2 %pi 6 %pi 4 +--R - 1536cos(---) + 64\|2 cos(---) - 736cos(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R 10\|2 cos(---) - 140 +--R 8 +--R * +--R x 8 +--R cos(-) +--R 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 10 %pi 8 %pi 2 x 10 %pi 6 +--R 256cos(-) sin(---) + 1024cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 10 %pi 5 +--R 2048\|2 cos(---)cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 4 x 10 %pi 4 +--R (1536cos(---) + 504)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 3 %pi x 10 %pi 3 +--R (4096\|2 cos(---) + 32cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 6 %pi 2 4+-+2 x 10 %pi 2 +--R (1024cos(---) + 5040cos(---) + 4\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi x 10 %pi +--R (2048\|2 cos(---) - 32cos(---) + 952\|2 cos(---))cos(-) sin(---) +--R 8 8 8 2 8 +--R + +--R %pi 8 %pi 4 4+-+2 %pi 2 x 10 +--R (256cos(---) + 504cos(---) - 4\|2 cos(---) + 112)cos(-) +--R 8 8 8 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 12 %pi 6 4+-+2 %pi x 12 %pi 5 +--R 32\|2 cos(-) sin(---) - 192\|2 cos(---)cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi 2 x 12 %pi 4 +--R (32\|2 cos(---) - 144)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 3 %pi x 12 %pi 3 +--R (- 384\|2 cos(---) + 64cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 4 %pi 2 4+-+2 x 12 %pi 2 +--R (- 32\|2 cos(---) - 1440cos(---) + 4\|2 )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 5 %pi 3 4+-+2 %pi x 12 +--R (- 192\|2 cos(---) - 64cos(---) - 392\|2 cos(---))cos(-) +--R 8 8 8 2 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 4+-+2 %pi 6 %pi 4 4+-+2 %pi 2 x 12 +--R (- 32\|2 cos(---) - 144cos(---) - 4\|2 cos(---) - 56)cos(-) +--R 8 8 8 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 14 %pi 4 %pi x 14 %pi 3 +--R 8cos(-) sin(---) - 32cos(---)cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R %pi 2 4+-+2 x 14 %pi 2 +--R (80cos(---) - 4\|2 )cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 3 4+-+2 %pi x 14 %pi +--R (32cos(---) + 72\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 4 4+-+2 %pi 2 x 14 +--R (8cos(---) + 4\|2 cos(---) + 16)cos(-) +--R 8 8 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+2 x 16 %pi 2 4+-+2 %pi x 16 %pi +--R \|2 cos(-) sin(---) - 2\|2 cos(---)cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi 2 x 16 +--R (- \|2 cos(---) - 2)cos(-) +--R 8 2 +--R / +--R x 16 4+-+2 %pi x 2 %pi x 2 x 14 +--R 4sin(-) + (- 128\|2 cos(---)cos(-) sin(---) - 32cos(-) )sin(-) +--R 2 8 2 8 2 2 +--R + +--R x 4 %pi 4 %pi 2 x 4 %pi 2 +--R 256cos(-) sin(---) + 2560cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 4 %pi %pi 4 x 4 +--R 768\|2 cos(---)cos(-) sin(---) + (256cos(---) + 112)cos(-) +--R 8 2 8 8 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R 4+-+2 %pi x 6 %pi 5 x 6 %pi 4 +--R - 4096\|2 cos(---)cos(-) sin(---) - 1024cos(-) sin(---) +--R 8 2 8 2 8 +--R + +--R 4+-+2 %pi 3 x 6 %pi 3 +--R - 8192\|2 cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 2 x 6 %pi 2 +--R - 10240cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi x 6 %pi +--R (- 4096\|2 cos(---) - 1920\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 4 x 6 +--R (- 1024cos(---) - 224)cos(-) +--R 8 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 8 %pi 8 %pi 2 x 8 %pi 6 +--R 4096cos(-) sin(---) + 16384cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 8 %pi 5 +--R 8192\|2 cos(---)cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 4 x 8 %pi 4 +--R (24576cos(---) + 1536)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 3 x 8 %pi 3 +--R 16384\|2 cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 6 %pi 2 x 8 %pi 2 +--R (16384cos(---) + 15360cos(---) )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi x 8 %pi +--R (8192\|2 cos(---) + 2560\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 8 %pi 4 x 8 +--R (4096cos(---) + 1536cos(---) + 280)cos(-) +--R 8 8 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R 4+-+2 %pi x 10 %pi 5 x 10 %pi 4 +--R - 4096\|2 cos(---)cos(-) sin(---) - 1024cos(-) sin(---) +--R 8 2 8 2 8 +--R + +--R 4+-+2 %pi 3 x 10 %pi 3 +--R - 8192\|2 cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 2 x 10 %pi 2 +--R - 10240cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi x 10 %pi +--R (- 4096\|2 cos(---) - 1920\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 4 x 10 +--R (- 1024cos(---) - 224)cos(-) +--R 8 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 12 %pi 4 %pi 2 x 12 %pi 2 +--R 256cos(-) sin(---) + 2560cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 12 %pi %pi 4 x 12 +--R 768\|2 cos(---)cos(-) sin(---) + (256cos(---) + 112)cos(-) +--R 8 2 8 8 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+2 %pi x 14 %pi x 14 x 2 x 16 +--R (- 128\|2 cos(---)cos(-) sin(---) - 32cos(-) )sin(-) + 4cos(-) +--R 8 2 8 2 2 2 +--R * +--R 4 +--R tan(x) +--R + +--R x 16 4+-+2 %pi x 2 %pi x 2 x 14 +--R 4sin(-) + (- 128\|2 cos(---)cos(-) sin(---) - 32cos(-) )sin(-) +--R 2 8 2 8 2 2 +--R + +--R x 4 %pi 4 %pi 2 x 4 %pi 2 +--R 256cos(-) sin(---) + 2560cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 4 %pi %pi 4 x 4 +--R 768\|2 cos(---)cos(-) sin(---) + (256cos(---) + 112)cos(-) +--R 8 2 8 8 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R 4+-+2 %pi x 6 %pi 5 x 6 %pi 4 +--R - 4096\|2 cos(---)cos(-) sin(---) - 1024cos(-) sin(---) +--R 8 2 8 2 8 +--R + +--R 4+-+2 %pi 3 x 6 %pi 3 +--R - 8192\|2 cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 2 x 6 %pi 2 +--R - 10240cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi x 6 %pi +--R (- 4096\|2 cos(---) - 1920\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 4 x 6 +--R (- 1024cos(---) - 224)cos(-) +--R 8 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 8 %pi 8 %pi 2 x 8 %pi 6 +--R 4096cos(-) sin(---) + 16384cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 8 %pi 5 +--R 8192\|2 cos(---)cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 4 x 8 %pi 4 +--R (24576cos(---) + 1536)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 3 x 8 %pi 3 +--R 16384\|2 cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 6 %pi 2 x 8 %pi 2 +--R (16384cos(---) + 15360cos(---) )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi x 8 %pi +--R (8192\|2 cos(---) + 2560\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 8 %pi 4 x 8 +--R (4096cos(---) + 1536cos(---) + 280)cos(-) +--R 8 8 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R 4+-+2 %pi x 10 %pi 5 x 10 %pi 4 +--R - 4096\|2 cos(---)cos(-) sin(---) - 1024cos(-) sin(---) +--R 8 2 8 2 8 +--R + +--R 4+-+2 %pi 3 x 10 %pi 3 +--R - 8192\|2 cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 2 x 10 %pi 2 +--R - 10240cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi x 10 %pi +--R (- 4096\|2 cos(---) - 1920\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 4 x 10 +--R (- 1024cos(---) - 224)cos(-) +--R 8 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 12 %pi 4 %pi 2 x 12 %pi 2 +--R 256cos(-) sin(---) + 2560cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 12 %pi %pi 4 x 12 +--R 768\|2 cos(---)cos(-) sin(---) + (256cos(---) + 112)cos(-) +--R 8 2 8 8 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+2 %pi x 14 %pi x 14 x 2 x 16 +--R (- 128\|2 cos(---)cos(-) sin(---) - 32cos(-) )sin(-) + 4cos(-) +--R 8 2 8 2 2 2 +--R * +--R 2 +--R tan(x) +--R + +--R x 16 4+-+2 %pi x 2 %pi x 2 x 14 +--R 2sin(-) + (- 64\|2 cos(---)cos(-) sin(---) - 16cos(-) )sin(-) +--R 2 8 2 8 2 2 +--R + +--R x 4 %pi 4 %pi 2 x 4 %pi 2 +--R 128cos(-) sin(---) + 1280cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 4 %pi %pi 4 x 4 +--R 384\|2 cos(---)cos(-) sin(---) + (128cos(---) + 56)cos(-) +--R 8 2 8 8 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R 4+-+2 %pi x 6 %pi 5 x 6 %pi 4 +--R - 2048\|2 cos(---)cos(-) sin(---) - 512cos(-) sin(---) +--R 8 2 8 2 8 +--R + +--R 4+-+2 %pi 3 x 6 %pi 3 %pi 2 x 6 %pi 2 +--R - 4096\|2 cos(---) cos(-) sin(---) - 5120cos(---) cos(-) sin(---) +--R 8 2 8 8 2 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi x 6 %pi +--R (- 2048\|2 cos(---) - 960\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 4 x 6 +--R (- 512cos(---) - 112)cos(-) +--R 8 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 8 %pi 8 %pi 2 x 8 %pi 6 +--R 2048cos(-) sin(---) + 8192cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 8 %pi 5 +--R 4096\|2 cos(---)cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 4 x 8 %pi 4 +--R (12288cos(---) + 768)cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 3 x 8 %pi 3 +--R 8192\|2 cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 6 %pi 2 x 8 %pi 2 +--R (8192cos(---) + 7680cos(---) )cos(-) sin(---) +--R 8 8 2 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi x 8 %pi +--R (4096\|2 cos(---) + 1280\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 8 %pi 4 x 8 +--R (2048cos(---) + 768cos(---) + 140)cos(-) +--R 8 8 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R 4+-+2 %pi x 10 %pi 5 x 10 %pi 4 +--R - 2048\|2 cos(---)cos(-) sin(---) - 512cos(-) sin(---) +--R 8 2 8 2 8 +--R + +--R 4+-+2 %pi 3 x 10 %pi 3 +--R - 4096\|2 cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R %pi 2 x 10 %pi 2 +--R - 5120cos(---) cos(-) sin(---) +--R 8 2 8 +--R + +--R 4+-+2 %pi 5 4+-+2 %pi x 10 %pi +--R (- 2048\|2 cos(---) - 960\|2 cos(---))cos(-) sin(---) +--R 8 8 2 8 +--R + +--R %pi 4 x 10 +--R (- 512cos(---) - 112)cos(-) +--R 8 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 12 %pi 4 %pi 2 x 12 %pi 2 +--R 128cos(-) sin(---) + 1280cos(---) cos(-) sin(---) +--R 2 8 8 2 8 +--R + +--R 4+-+2 %pi x 12 %pi %pi 4 x 12 +--R 384\|2 cos(---)cos(-) sin(---) + (128cos(---) + 56)cos(-) +--R 8 2 8 8 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+2 %pi x 14 %pi x 14 x 2 x 16 +--R (- 64\|2 cos(---)cos(-) sin(---) - 16cos(-) )sin(-) + 2cos(-) +--R 8 2 8 2 2 2 +--R Type: Expression(Complex(Integer)) +--E 385 + +--S 386 of 520 +t0073:= 1/(1+sin(x)^8) +--R +--R +--R 1 +--R (250) ----------- +--R 8 +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 520 +r0073:= 1/4*atan((1-(-1)^(1/4))^(1/2)*tan(x))/(1-(-1)^(1/4))^(1/2)+_ + 1/4*atan((1+(-1)^(1/4))^(1/2)*tan(x))/(1+(-1)^(1/4))^(1/2)+_ + 1/4*atan((1-(-1)^(3/4))^(1/2)*tan(x))/(1-(-1)^(3/4))^(1/2)+_ + 1/4*atan((1+(-1)^(3/4))^(1/2)*tan(x))/(1+(-1)^(3/4))^(1/2) +--R +--R +--R (251) +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R atan(tan(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 - 1 +--R atan(tan(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 + 1 +--R atan(tan(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 - 1 +--R atan(tan(x) |----------------- ) +--R | +-+ +--R \| \|2 +--R / +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 4 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 520 +a0073:= integrate(t0073,x) +--R +--R +--R (252) +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +-+ x 8 +-+ x 2 x 6 +--R (\|2 + 2)sin(-) + (4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((6\|2 + 12)cos(-) - 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((4\|2 + 8)cos(-) + (12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (\|2 + 2)cos(-) + (- 2\|2 - 4)cos(-) + \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 3 +--R (1024\|2 + 1024)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 x +--R (- 1024\|2 - 1024)cos(-) sin(-) +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (2\|2 + 2)sin(-) + (8\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +-+ x 6 x 2 +--R (12\|2 + 12)cos(-) sin(-) + (8\|2 + 8)cos(-) sin(-) +--R 2 2 2 2 +--R + +--R +-+ x 8 +-+ +--R (2\|2 + 2)cos(-) - 2\|2 - 2 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (\|2 + 2)sin(-) + (4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((6\|2 + 12)cos(-) - 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((4\|2 + 8)cos(-) + (12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (\|2 + 2)cos(-) + (- 2\|2 - 4)cos(-) + \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (- 128\|2 - 128)sin(-) +--R 2 +--R + +--R +-+ x 2 x 6 +--R (- 512\|2 - 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 4 x 4 +--R (- 768\|2 - 768)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 6 x 2 +--R (- 512\|2 - 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 8 +-+ +--R (- 128\|2 - 128)cos(-) + 128\|2 + 128 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 3 +-+ x 3 x +--R (16\|2 + 16)cos(-)sin(-) + (- 16\|2 - 16)cos(-) sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +-+ x 8 +-+ x 2 x 6 +--R (\|2 + 2)sin(-) + (4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((6\|2 + 12)cos(-) - 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((4\|2 + 8)cos(-) + (12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (\|2 + 2)cos(-) + (- 2\|2 - 4)cos(-) + \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 3 +--R (1024\|2 + 1024)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 x +--R (- 1024\|2 - 1024)cos(-) sin(-) +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (- 2\|2 - 2)sin(-) + (- 8\|2 - 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +-+ x 6 x 2 +--R (- 12\|2 - 12)cos(-) sin(-) + (- 8\|2 - 8)cos(-) sin(-) +--R 2 2 2 2 +--R + +--R +-+ x 8 +-+ +--R (- 2\|2 - 2)cos(-) + 2\|2 + 2 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (\|2 + 2)sin(-) + (4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((6\|2 + 12)cos(-) - 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((4\|2 + 8)cos(-) + (12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (\|2 + 2)cos(-) + (- 2\|2 - 4)cos(-) + \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (128\|2 + 128)sin(-) + (512\|2 + 512)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +--R (768\|2 + 768)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +--R (512\|2 + 512)cos(-) sin(-) + (128\|2 + 128)cos(-) +--R 2 2 2 +--R + +--R +-+ +--R - 128\|2 - 128 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 3 +-+ x 3 x +--R (16\|2 + 16)cos(-)sin(-) + (- 16\|2 - 16)cos(-) sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +-+ x 8 +-+ x 2 x 6 +--R (\|2 + 2)sin(-) + (4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((6\|2 + 12)cos(-) - 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((4\|2 + 8)cos(-) + (12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (\|2 + 2)cos(-) + (- 2\|2 - 4)cos(-) + \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 3 +--R (- 1024\|2 - 1024)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 x +--R (1024\|2 + 1024)cos(-) sin(-) +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (2\|2 + 2)sin(-) + (8\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +-+ x 6 x 2 +--R (12\|2 + 12)cos(-) sin(-) + (8\|2 + 8)cos(-) sin(-) +--R 2 2 2 2 +--R + +--R +-+ x 8 +-+ +--R (2\|2 + 2)cos(-) - 2\|2 - 2 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (\|2 + 2)sin(-) + (4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((6\|2 + 12)cos(-) - 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((4\|2 + 8)cos(-) + (12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (\|2 + 2)cos(-) + (- 2\|2 - 4)cos(-) + \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (- 128\|2 - 128)sin(-) +--R 2 +--R + +--R +-+ x 2 x 6 +--R (- 512\|2 - 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 4 x 4 +--R (- 768\|2 - 768)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 6 x 2 +--R (- 512\|2 - 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 8 +-+ +--R (- 128\|2 - 128)cos(-) + 128\|2 + 128 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 3 +-+ x 3 x +--R (- 16\|2 - 16)cos(-)sin(-) + (16\|2 + 16)cos(-) sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +-+ x 8 +-+ x 2 x 6 +--R (\|2 + 2)sin(-) + (4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((6\|2 + 12)cos(-) - 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((4\|2 + 8)cos(-) + (12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (\|2 + 2)cos(-) + (- 2\|2 - 4)cos(-) + \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 3 +--R (- 1024\|2 - 1024)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 x +--R (1024\|2 + 1024)cos(-) sin(-) +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (- 2\|2 - 2)sin(-) + (- 8\|2 - 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +--R (- 12\|2 - 12)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +--R (- 8\|2 - 8)cos(-) sin(-) + (- 2\|2 - 2)cos(-) +--R 2 2 2 +--R + +--R +-+ +--R 2\|2 + 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (\|2 + 2)sin(-) + (4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((6\|2 + 12)cos(-) - 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((4\|2 + 8)cos(-) + (12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (\|2 + 2)cos(-) + (- 2\|2 - 4)cos(-) + \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (128\|2 + 128)sin(-) +--R 2 +--R + +--R +-+ x 2 x 6 +--R (512\|2 + 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 4 x 4 +--R (768\|2 + 768)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 6 x 2 +--R (512\|2 + 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 8 +-+ +--R (128\|2 + 128)cos(-) - 128\|2 - 128 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 3 +-+ x 3 x +--R (- 16\|2 - 16)cos(-)sin(-) + (16\|2 + 16)cos(-) sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +-+ x 8 +-+ x 2 x 6 +--R (- \|2 + 2)sin(-) + (- 4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((- 6\|2 + 12)cos(-) + 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((- 4\|2 + 8)cos(-) + (- 12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (- \|2 + 2)cos(-) + (2\|2 - 4)cos(-) - \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 3 +--R (1024\|2 - 1024)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 x +--R (- 1024\|2 + 1024)cos(-) sin(-) +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (2\|2 - 2)sin(-) + (8\|2 - 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +-+ x 6 x 2 +--R (12\|2 - 12)cos(-) sin(-) + (8\|2 - 8)cos(-) sin(-) +--R 2 2 2 2 +--R + +--R +-+ x 8 +-+ +--R (2\|2 - 2)cos(-) - 2\|2 + 2 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (- \|2 + 2)sin(-) + (- 4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((- 6\|2 + 12)cos(-) + 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((- 4\|2 + 8)cos(-) + (- 12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (- \|2 + 2)cos(-) + (2\|2 - 4)cos(-) - \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (- 128\|2 + 128)sin(-) +--R 2 +--R + +--R +-+ x 2 x 6 +--R (- 512\|2 + 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 4 x 4 +--R (- 768\|2 + 768)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 6 x 2 +--R (- 512\|2 + 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 8 +-+ +--R (- 128\|2 + 128)cos(-) + 128\|2 - 128 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 3 +-+ x 3 x +--R (16\|2 - 16)cos(-)sin(-) + (- 16\|2 + 16)cos(-) sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +-+ x 8 +-+ x 2 x 6 +--R (- \|2 + 2)sin(-) + (- 4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((- 6\|2 + 12)cos(-) + 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((- 4\|2 + 8)cos(-) + (- 12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (- \|2 + 2)cos(-) + (2\|2 - 4)cos(-) - \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 3 +--R (1024\|2 - 1024)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 x +--R (- 1024\|2 + 1024)cos(-) sin(-) +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (- 2\|2 + 2)sin(-) + (- 8\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +-+ x 6 x 2 +--R (- 12\|2 + 12)cos(-) sin(-) + (- 8\|2 + 8)cos(-) sin(-) +--R 2 2 2 2 +--R + +--R +-+ x 8 +-+ +--R (- 2\|2 + 2)cos(-) + 2\|2 - 2 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (- \|2 + 2)sin(-) + (- 4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((- 6\|2 + 12)cos(-) + 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((- 4\|2 + 8)cos(-) + (- 12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (- \|2 + 2)cos(-) + (2\|2 - 4)cos(-) - \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (128\|2 - 128)sin(-) + (512\|2 - 512)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +--R (768\|2 - 768)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +--R (512\|2 - 512)cos(-) sin(-) + (128\|2 - 128)cos(-) +--R 2 2 2 +--R + +--R +-+ +--R - 128\|2 + 128 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 3 +-+ x 3 x +--R (16\|2 - 16)cos(-)sin(-) + (- 16\|2 + 16)cos(-) sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +-+ x 8 +-+ x 2 x 6 +--R (- \|2 + 2)sin(-) + (- 4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((- 6\|2 + 12)cos(-) + 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((- 4\|2 + 8)cos(-) + (- 12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (- \|2 + 2)cos(-) + (2\|2 - 4)cos(-) - \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 3 +--R (- 1024\|2 + 1024)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 x +--R (1024\|2 - 1024)cos(-) sin(-) +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (2\|2 - 2)sin(-) + (8\|2 - 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +-+ x 6 x 2 +--R (12\|2 - 12)cos(-) sin(-) + (8\|2 - 8)cos(-) sin(-) +--R 2 2 2 2 +--R + +--R +-+ x 8 +-+ +--R (2\|2 - 2)cos(-) - 2\|2 + 2 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (- \|2 + 2)sin(-) + (- 4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((- 6\|2 + 12)cos(-) + 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((- 4\|2 + 8)cos(-) + (- 12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (- \|2 + 2)cos(-) + (2\|2 - 4)cos(-) - \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (- 128\|2 + 128)sin(-) +--R 2 +--R + +--R +-+ x 2 x 6 +--R (- 512\|2 + 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 4 x 4 +--R (- 768\|2 + 768)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 6 x 2 +--R (- 512\|2 + 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 8 +-+ +--R (- 128\|2 + 128)cos(-) + 128\|2 - 128 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 3 +-+ x 3 x +--R (- 16\|2 + 16)cos(-)sin(-) + (16\|2 - 16)cos(-) sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R +-+ x 8 +-+ x 2 x 6 +--R (- \|2 + 2)sin(-) + (- 4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((- 6\|2 + 12)cos(-) + 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((- 4\|2 + 8)cos(-) + (- 12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (- \|2 + 2)cos(-) + (2\|2 - 4)cos(-) - \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 3 +--R (- 1024\|2 + 1024)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 x +--R (1024\|2 - 1024)cos(-) sin(-) +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (- 2\|2 + 2)sin(-) + (- 8\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +--R (- 12\|2 + 12)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +--R (- 8\|2 + 8)cos(-) sin(-) + (- 2\|2 + 2)cos(-) +--R 2 2 2 +--R + +--R +-+ +--R 2\|2 - 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R (- \|2 + 2)sin(-) + (- 4\|2 + 8)cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 4 +--R ((- 6\|2 + 12)cos(-) + 2\|2 - 4)sin(-) +--R 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +--R ((- 4\|2 + 8)cos(-) + (- 12\|2 + 24)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 4 +-+ +--R (- \|2 + 2)cos(-) + (2\|2 - 4)cos(-) - \|2 + 2 +--R 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (128\|2 - 128)sin(-) +--R 2 +--R + +--R +-+ x 2 x 6 +--R (512\|2 - 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 4 x 4 +--R (768\|2 - 768)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 6 x 2 +--R (512\|2 - 512)cos(-) sin(-) +--R 2 2 +--R + +--R +-+ x 8 +-+ +--R (128\|2 - 128)cos(-) - 128\|2 + 128 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 3 +-+ x 3 x +--R (- 16\|2 + 16)cos(-)sin(-) + (16\|2 - 16)cos(-) sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x 8 +--R (64\|2 + 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 + 256)cos(-) - 128\|2 - 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 + 384)cos(-) + (- 128\|2 - 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 + 256)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 + 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 + 64)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 - 128)cos(-) - 64\|2 - 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 + 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 + 8)cos(-) + (- 8\|2 - 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 + 4)cos(-) + (8\|2 + 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 + 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R (- 256\|2 - 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((- 512\|2 - 512)cos(-) + (512\|2 + 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +--R (- 256\|2 - 256)cos(-) +--R 2 +--R + +--R +-+ x 3 +-+ x +--R (- 512\|2 - 512)cos(-) + (- 256\|2 - 256)cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +--R (\|2 + 1)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((4\|2 + 4)cos(-) - 2\|2 - 2)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 + 6)cos(-) + (- 2\|2 - 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ +--R ((4\|2 + 4)cos(-) + (2\|2 + 2)cos(-) + 2\|2 + 2) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 + 1)cos(-) + (2\|2 + 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 - 2)cos(-) - \|2 - 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x x 5 +--R (256\|2 + 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 + 512)cos(-) + (- 512\|2 - 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 + 256)cos(-) + (512\|2 + 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 + 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +--R (- \|2 - 1)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((- 4\|2 - 4)cos(-) + 2\|2 + 2)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((- 6\|2 - 6)cos(-) + (2\|2 + 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ +--R (- 4\|2 - 4)cos(-) + (- 2\|2 - 2)cos(-) - 2\|2 +--R 2 2 +--R + +--R - 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (- \|2 - 1)cos(-) + (- 2\|2 - 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (2\|2 + 2)cos(-) + \|2 + 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (64\|2 + 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 + 256)cos(-) - 128\|2 - 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 + 384)cos(-) + (- 128\|2 - 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 + 256)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 + 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 + 64)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 - 128)cos(-) - 64\|2 - 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 + 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 + 8)cos(-) + (- 8\|2 - 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 + 4)cos(-) + (8\|2 + 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 + 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x 8 +--R (64\|2 + 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 + 256)cos(-) - 128\|2 - 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 + 384)cos(-) + (- 128\|2 - 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 + 256)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 + 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 + 64)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 - 128)cos(-) - 64\|2 - 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 + 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 + 8)cos(-) + (- 8\|2 - 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 + 4)cos(-) + (8\|2 + 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 + 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R (- 256\|2 - 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((- 512\|2 - 512)cos(-) + (512\|2 + 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (- 256\|2 - 256)cos(-) + (- 512\|2 - 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (- 256\|2 - 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R (\|2 + 1)sin(-) + ((4\|2 + 4)cos(-) - 2\|2 - 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 + 6)cos(-) + (- 2\|2 - 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R ((4\|2 + 4)cos(-) + (2\|2 + 2)cos(-) + 2\|2 + 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 + 1)cos(-) + (2\|2 + 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 - 2)cos(-) - \|2 - 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R - 8cos(-)sin(-) - 16cos(-) sin(-) + (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x x 5 +--R (256\|2 + 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 + 512)cos(-) + (- 512\|2 - 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 + 256)cos(-) + (512\|2 + 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 + 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +--R (- \|2 - 1)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((- 4\|2 - 4)cos(-) + 2\|2 + 2)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((- 6\|2 - 6)cos(-) + (2\|2 + 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ +--R ((- 4\|2 - 4)cos(-) + (- 2\|2 - 2)cos(-) - 2\|2 - 2) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (- \|2 - 1)cos(-) + (- 2\|2 - 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (2\|2 + 2)cos(-) + \|2 + 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (64\|2 + 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 + 256)cos(-) - 128\|2 - 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 + 384)cos(-) + (- 128\|2 - 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 + 256)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 + 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 + 64)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 - 128)cos(-) - 64\|2 - 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 + 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 + 8)cos(-) + (- 8\|2 - 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 + 4)cos(-) + (8\|2 + 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 + 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x 8 +--R (64\|2 - 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 - 256)cos(-) - 128\|2 + 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 - 384)cos(-) + (- 128\|2 + 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 - 256)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 - 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 - 64)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 + 128)cos(-) - 64\|2 + 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 - 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 - 8)cos(-) + (- 8\|2 + 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 - 4)cos(-) + (8\|2 - 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 - 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R (- 256\|2 + 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((- 512\|2 + 512)cos(-) + (512\|2 - 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +--R (- 256\|2 + 256)cos(-) +--R 2 +--R + +--R +-+ x 3 +-+ x +--R (- 512\|2 + 512)cos(-) + (- 256\|2 + 256)cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +--R (\|2 - 1)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((4\|2 - 4)cos(-) - 2\|2 + 2)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 - 6)cos(-) + (- 2\|2 + 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ +--R ((4\|2 - 4)cos(-) + (2\|2 - 2)cos(-) + 2\|2 - 2) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 - 1)cos(-) + (2\|2 - 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 + 2)cos(-) - \|2 + 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x x 5 +--R (256\|2 - 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 - 512)cos(-) + (- 512\|2 + 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 - 256)cos(-) + (512\|2 - 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 - 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +--R (- \|2 + 1)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((- 4\|2 + 4)cos(-) + 2\|2 - 2)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((- 6\|2 + 6)cos(-) + (2\|2 - 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ +--R (- 4\|2 + 4)cos(-) + (- 2\|2 + 2)cos(-) - 2\|2 +--R 2 2 +--R + +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (- \|2 + 1)cos(-) + (- 2\|2 + 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (2\|2 - 2)cos(-) + \|2 - 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (64\|2 - 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 - 256)cos(-) - 128\|2 + 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 - 384)cos(-) + (- 128\|2 + 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 - 256)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 - 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 - 64)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 + 128)cos(-) - 64\|2 + 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 - 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 - 8)cos(-) + (- 8\|2 + 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 - 4)cos(-) + (8\|2 - 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 - 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x 8 +--R (64\|2 - 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 - 256)cos(-) - 128\|2 + 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 - 384)cos(-) + (- 128\|2 + 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 - 256)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 - 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 - 64)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 + 128)cos(-) - 64\|2 + 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 - 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 - 8)cos(-) + (- 8\|2 + 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 - 4)cos(-) + (8\|2 - 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 - 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R (- 256\|2 + 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((- 512\|2 + 512)cos(-) + (512\|2 - 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (- 256\|2 + 256)cos(-) + (- 512\|2 + 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (- 256\|2 + 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R (\|2 - 1)sin(-) + ((4\|2 - 4)cos(-) - 2\|2 + 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 - 6)cos(-) + (- 2\|2 + 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R ((4\|2 - 4)cos(-) + (2\|2 - 2)cos(-) + 2\|2 - 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 - 1)cos(-) + (2\|2 - 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 + 2)cos(-) - \|2 + 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R - 8cos(-)sin(-) - 16cos(-) sin(-) + (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x x 5 +--R (256\|2 - 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 - 512)cos(-) + (- 512\|2 + 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 - 256)cos(-) + (512\|2 - 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 - 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +--R (- \|2 + 1)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((- 4\|2 + 4)cos(-) + 2\|2 - 2)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((- 6\|2 + 6)cos(-) + (2\|2 - 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ +--R ((- 4\|2 + 4)cos(-) + (- 2\|2 + 2)cos(-) - 2\|2 + 2) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (- \|2 + 1)cos(-) + (- 2\|2 + 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (2\|2 - 2)cos(-) + \|2 - 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (64\|2 - 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 - 256)cos(-) - 128\|2 + 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 - 384)cos(-) + (- 128\|2 + 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 - 256)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 - 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 - 64)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 + 128)cos(-) - 64\|2 + 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 - 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 - 8)cos(-) + (- 8\|2 + 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 - 4)cos(-) + (8\|2 - 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 - 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x 8 +--R (64\|2 - 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 - 256)cos(-) - 128\|2 + 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 - 384)cos(-) + (- 128\|2 + 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 - 256)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 - 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 - 64)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 + 128)cos(-) - 64\|2 + 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (- 4\|2 + 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((- 8\|2 + 8)cos(-) + (8\|2 - 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (- 4\|2 + 4)cos(-) + (- 8\|2 + 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (- 4\|2 + 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R (256\|2 - 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 - 512)cos(-) + (- 512\|2 + 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 - 256)cos(-) + (512\|2 - 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 - 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R (\|2 - 1)sin(-) + ((4\|2 - 4)cos(-) - 2\|2 + 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 - 6)cos(-) + (- 2\|2 + 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R ((4\|2 - 4)cos(-) + (2\|2 - 2)cos(-) + 2\|2 - 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 - 1)cos(-) + (2\|2 - 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 + 2)cos(-) - \|2 + 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x x 5 +--R (256\|2 - 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 - 512)cos(-) + (- 512\|2 + 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 - 256)cos(-) + (512\|2 - 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 - 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R (\|2 - 1)sin(-) + ((4\|2 - 4)cos(-) - 2\|2 + 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 - 6)cos(-) + (- 2\|2 + 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R ((4\|2 - 4)cos(-) + (2\|2 - 2)cos(-) + 2\|2 - 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 - 1)cos(-) + (2\|2 - 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 + 2)cos(-) - \|2 + 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (- 64\|2 + 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((- 256\|2 + 256)cos(-) + 128\|2 - 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((- 384\|2 + 384)cos(-) + (128\|2 - 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (- 256\|2 + 256)cos(-) + (- 128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R - 128\|2 + 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (- 64\|2 + 64)cos(-) + (- 128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (128\|2 - 128)cos(-) + 64\|2 - 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 - 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 - 8)cos(-) + (- 8\|2 + 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 - 4)cos(-) + (8\|2 - 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 - 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x 8 +--R (64\|2 - 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 - 256)cos(-) - 128\|2 + 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 - 384)cos(-) + (- 128\|2 + 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 - 256)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 - 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 - 64)cos(-) + (128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 + 128)cos(-) - 64\|2 + 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (- 4\|2 + 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((- 8\|2 + 8)cos(-) + (8\|2 - 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (- 4\|2 + 4)cos(-) + (- 8\|2 + 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (- 4\|2 + 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R (256\|2 - 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 - 512)cos(-) + (- 512\|2 + 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 - 256)cos(-) + (512\|2 - 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 - 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +--R (\|2 - 1)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((4\|2 - 4)cos(-) - 2\|2 + 2)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 - 6)cos(-) + (- 2\|2 + 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ +--R ((4\|2 - 4)cos(-) + (2\|2 - 2)cos(-) + 2\|2 - 2) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 - 1)cos(-) + (2\|2 - 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 + 2)cos(-) - \|2 + 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 +--R - 8cos(-)sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 +--R + +--R x 5 x x +--R (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 +--R / +--R +-+ x x 5 +--R (256\|2 - 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 - 512)cos(-) + (- 512\|2 + 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 - 256)cos(-) + (512\|2 - 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 - 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +--R (\|2 - 1)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((4\|2 - 4)cos(-) - 2\|2 + 2)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 - 6)cos(-) + (- 2\|2 + 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ +--R ((4\|2 - 4)cos(-) + (2\|2 - 2)cos(-) + 2\|2 - 2) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 - 1)cos(-) + (2\|2 - 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 + 2)cos(-) - \|2 + 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (- 64\|2 + 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((- 256\|2 + 256)cos(-) + 128\|2 - 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((- 384\|2 + 384)cos(-) + (128\|2 - 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +--R (- 256\|2 + 256)cos(-) +--R 2 +--R + +--R +-+ x 4 +-+ +--R (- 128\|2 + 128)cos(-) - 128\|2 + 128 +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (- 64\|2 + 64)cos(-) + (- 128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (128\|2 - 128)cos(-) + 64\|2 - 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 - 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 - 8)cos(-) + (- 8\|2 + 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 - 4)cos(-) + (8\|2 - 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 - 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x 8 +--R (64\|2 + 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 + 256)cos(-) - 128\|2 - 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 + 384)cos(-) + (- 128\|2 - 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 + 256)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 + 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 + 64)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 - 128)cos(-) - 64\|2 - 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (- 4\|2 - 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((- 8\|2 - 8)cos(-) + (8\|2 + 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (- 4\|2 - 4)cos(-) + (- 8\|2 - 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (- 4\|2 - 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R (256\|2 + 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 + 512)cos(-) + (- 512\|2 - 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 + 256)cos(-) + (512\|2 + 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 + 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R (\|2 + 1)sin(-) + ((4\|2 + 4)cos(-) - 2\|2 - 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 + 6)cos(-) + (- 2\|2 - 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R ((4\|2 + 4)cos(-) + (2\|2 + 2)cos(-) + 2\|2 + 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 + 1)cos(-) + (2\|2 + 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 - 2)cos(-) - \|2 - 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x x 5 +--R (256\|2 + 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 + 512)cos(-) + (- 512\|2 - 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 + 256)cos(-) + (512\|2 + 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 + 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R (\|2 + 1)sin(-) + ((4\|2 + 4)cos(-) - 2\|2 - 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 + 6)cos(-) + (- 2\|2 - 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R ((4\|2 + 4)cos(-) + (2\|2 + 2)cos(-) + 2\|2 + 2)sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 + 1)cos(-) + (2\|2 + 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 - 2)cos(-) - \|2 - 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (- 64\|2 - 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((- 256\|2 - 256)cos(-) + 128\|2 + 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((- 384\|2 - 384)cos(-) + (128\|2 + 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (- 256\|2 - 256)cos(-) + (- 128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R - 128\|2 - 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (- 64\|2 - 64)cos(-) + (- 128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (128\|2 + 128)cos(-) + 64\|2 + 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 + 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 + 8)cos(-) + (- 8\|2 - 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 + 4)cos(-) + (8\|2 + 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 + 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x 8 +--R (64\|2 + 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((256\|2 + 256)cos(-) - 128\|2 - 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((384\|2 + 384)cos(-) + (- 128\|2 - 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +--R (256\|2 + 256)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ +--R 128\|2 + 128 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (64\|2 + 64)cos(-) + (128\|2 + 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 128\|2 - 128)cos(-) - 64\|2 - 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (- 4\|2 - 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((- 8\|2 - 8)cos(-) + (8\|2 + 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (- 4\|2 - 4)cos(-) + (- 8\|2 - 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (- 4\|2 - 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R (256\|2 + 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 + 512)cos(-) + (- 512\|2 - 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 + 256)cos(-) + (512\|2 + 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 + 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +--R (\|2 + 1)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((4\|2 + 4)cos(-) - 2\|2 - 2)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 + 6)cos(-) + (- 2\|2 - 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ +--R ((4\|2 + 4)cos(-) + (2\|2 + 2)cos(-) + 2\|2 + 2) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 + 1)cos(-) + (2\|2 + 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 - 2)cos(-) - \|2 - 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 +--R - 8cos(-)sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 +--R + +--R x 5 x x +--R (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 +--R / +--R +-+ x x 5 +--R (256\|2 + 256)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x +--R ((512\|2 + 512)cos(-) + (- 512\|2 - 512)cos(-)) +--R 2 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (256\|2 + 256)cos(-) + (512\|2 + 512)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (256\|2 + 256)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x 8 +--R (\|2 + 1)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((4\|2 + 4)cos(-) - 2\|2 - 2)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R ((6\|2 + 6)cos(-) + (- 2\|2 - 2)cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ +--R ((4\|2 + 4)cos(-) + (2\|2 + 2)cos(-) + 2\|2 + 2) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (\|2 + 1)cos(-) + (2\|2 + 2)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (- 2\|2 - 2)cos(-) - \|2 - 1 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +--R (- 64\|2 - 64)sin(-) +--R 2 +--R + +--R +-+ x 2 +-+ x 6 +--R ((- 256\|2 - 256)cos(-) + 128\|2 + 128)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +--R ((- 384\|2 - 384)cos(-) + (128\|2 + 128)cos(-) ) +--R 2 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +--R (- 256\|2 - 256)cos(-) +--R 2 +--R + +--R +-+ x 4 +-+ +--R (- 128\|2 - 128)cos(-) - 128\|2 - 128 +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +--R (- 64\|2 - 64)cos(-) + (- 128\|2 - 128)cos(-) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R (128\|2 + 128)cos(-) + 64\|2 + 64 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R |--------- +--R | +-+ +--R \| 4096\|2 +--R + +--R +-+ x x 5 +--R (4\|2 + 4)cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R ((8\|2 + 8)cos(-) + (- 8\|2 - 8)cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +--R (4\|2 + 4)cos(-) + (8\|2 + 8)cos(-) +--R 2 2 +--R + +--R +-+ x +--R (4\|2 + 4)cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R / +--R +-+ +--R 16\|2 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 520 +--m0073:= a0073-r0073 +--E 389 + +--S 390 of 520 +--d0073:= D(m0073,x) +--E 390 + +--S 391 of 520 +t0074:= 1/(1-sin(x)^3) +--R +--R +--R 1 +--R (253) - ----------- +--R 3 +--R sin(x) - 1 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 520 +r0074:= -2/3*atan(((-1)^(2/3)-tan(1/2*x))/(1+(-1)^(1/3))^(1/2))/_ + (1+(-1)^(1/3))^(1/2)+2/3*atan(((-1)^(1/3)+tan(1/2*x))/_ + (1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)+cos(x)/(3-3*sin(x)) +--R +--R +--R (254) +--R x 3+---+ +--R +----------+ tan(-) + \|- 1 +--R |3+---+ 2 +--R (2sin(x) - 2)\|\|- 1 + 1 atan(----------------) +--R +-------------+ +--R | 3+---+2 +--R \|- \|- 1 + 1 +--R + +--R x 3+---+2 +--R +-------------+ tan(-) - \|- 1 +--R | 3+---+2 2 +--R (2sin(x) - 2)\|- \|- 1 + 1 atan(----------------) +--R +----------+ +--R |3+---+ +--R \|\|- 1 + 1 +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R - cos(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R (3sin(x) - 3)\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 520 +a0074:= integrate(t0074,x) +--R +--R +--R (255) +--R %pi x 4 %pi x 2 x 2 %pi x x +--R cos(---)sin(-) + 2cos(---)cos(-) sin(-) - 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (2\|3 + 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R - \|3 \|3 cos(---) + (\|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((4\|3 + 6)\|3 cos(-) - 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) - 2\|3 \|3 cos(---) + (2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi 4+-+2 x +--R (4\|3 \|3 cos(-)sin(---) + (12\|3 cos(---) + 4\|3 )cos(-)) +--R 2 12 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +-+ 4+-+ +--R ((2\|3 + 3)\|3 cos(-) + 4\|3 \|3 cos(-) + (2\|3 - 3)\|3 ) +--R 2 2 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) - \|3 \|3 cos(---) + (\|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (- \|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R cos(---)sin(-) + 2cos(---)cos(-) sin(-) - 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (2\|3 - 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R \|3 \|3 cos(---) + (- \|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((4\|3 - 6)\|3 cos(-) - 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) + 2\|3 \|3 cos(---) + (- 2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi 4+-+2 x +--R (4\|3 \|3 cos(-)sin(---) + (12\|3 cos(---) + 4\|3 )cos(-)) +--R 2 12 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +-+ 4+-+ +--R ((2\|3 - 3)\|3 cos(-) + 4\|3 \|3 cos(-) + (2\|3 + 3)\|3 ) +--R 2 2 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) + \|3 \|3 cos(---) + (- \|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (\|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R - cos(---)sin(-) - 2cos(---)cos(-) sin(-) + 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R - cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (- 2\|3 + 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R - \|3 \|3 cos(---) + (- \|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((- 4\|3 + 6)\|3 cos(-) + 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) - 2\|3 \|3 cos(---) + (- 2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +--R - 4\|3 \|3 cos(-)sin(---) +--R 2 12 +--R + +--R 4+-+ %pi 4+-+2 x +--R (- 12\|3 cos(---) + 4\|3 )cos(-) +--R 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +--R (- 2\|3 + 3)\|3 cos(-) - 4\|3 \|3 cos(-) +--R 2 2 +--R + +--R +-+ 4+-+ +--R (- 2\|3 - 3)\|3 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) - \|3 \|3 cos(---) + (- \|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (\|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 x 2 %pi x x +--R - cos(---)sin(-) - 2cos(---)cos(-) sin(-) + 4cos(---)cos(-)sin(-) +--R 12 2 12 2 2 12 2 2 +--R + +--R %pi x 4 %pi +--R - cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 +-+ 4+-+ %pi %pi 2 +--R 3sin(---) + (- 2\|3 - 3)\|3 sin(---) + 3cos(---) +--R 12 12 12 +--R + +--R +-+4+-+ %pi +-+ 4+-+2 +--R \|3 \|3 cos(---) + (\|3 + 2)\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ 4+-+ x 2 +-+4+-+ %pi +--R ((- 4\|3 - 6)\|3 cos(-) + 4\|3 \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 2 +--R (6cos(---) + 2\|3 \|3 cos(---) + (2\|3 + 4)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 +--R - 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +--R - 4\|3 \|3 cos(-)sin(---) +--R 2 12 +--R + +--R 4+-+ %pi 4+-+2 x +--R (- 12\|3 cos(---) + 4\|3 )cos(-) +--R 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ 4+-+ x 4 +-+4+-+ x 2 +--R (- 2\|3 - 3)\|3 cos(-) - 4\|3 \|3 cos(-) +--R 2 2 +--R + +--R +-+ 4+-+ +--R (- 2\|3 + 3)\|3 +--R * +--R %pi +--R sin(---) +--R 12 +--R + +--R %pi 2 +-+4+-+ %pi +-+ 4+-+2 x 4 +--R (3cos(---) + \|3 \|3 cos(---) + (\|3 + 2)\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 x 2 %pi 2 +-+4+-+ %pi +--R 6cos(---) cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R +-+ 4+-+2 +--R (- \|3 + 2)\|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R - 2sin(---)sin(-) - 4cos(-) sin(---)sin(-) + 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (- 2cos(-) - 2)sin(---) +--R 2 12 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (\|3 + 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (2\|3 + 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R - 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (\|3 + 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (\|3 - 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) + \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) + 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) - 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) + \|3 )cos(-) + (6cos(---) + 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) + \|3 +--R 12 +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R - 2sin(---)sin(-) - 4cos(-) sin(---)sin(-) + 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (- 2cos(-) - 2)sin(---) +--R 2 12 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (\|3 - 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (2\|3 - 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R - 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (\|3 - 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (\|3 + 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) + \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) + 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) - 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) + \|3 )cos(-) + (6cos(---) + 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) + \|3 +--R 12 +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R 2sin(---)sin(-) + 4cos(-) sin(---)sin(-) - 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (2cos(-) + 2)sin(---) +--R 2 12 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (- \|3 + 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (- 2\|3 + 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (- \|3 + 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) - 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (- \|3 - 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) - \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) - 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) - \|3 )cos(-) + (6cos(---) - 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) - \|3 +--R 12 +--R + +--R %pi x 4 x 2 %pi x 2 x %pi x +--R 2sin(---)sin(-) + 4cos(-) sin(---)sin(-) - 8cos(-)sin(---)sin(-) +--R 12 2 2 12 2 2 12 2 +--R + +--R x 4 %pi +--R (2cos(-) + 2)sin(---) +--R 2 12 +--R * +--R atan +--R %pi +-+ %pi +-+ 4+-+ x 4 +--R (3sin(---) - \|3 cos(---) + (- \|3 - 2)\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +--R (6cos(-) - 6)sin(---) +--R 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) + (- 2\|3 - 4)\|3 )cos(-) + 2\|3 cos(---) +--R 12 2 12 +--R + +--R +-+4+-+ +--R 2\|3 \|3 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi +-+ 4+-+ x 4 +--R (- \|3 cos(---) + (- \|3 - 2)\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi +-+4+-+ x 2 +-+ %pi +--R (- 2\|3 cos(---) - 2\|3 \|3 )cos(-) - \|3 cos(---) +--R 12 2 12 +--R + +--R +-+ 4+-+ +--R (- \|3 + 2)\|3 +--R / +--R +-+ %pi %pi 4+-+ x 4 +--R (\|3 sin(---) + 3cos(---) - \|3 )sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi 4+-+ x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (6cos(---) - 2\|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 4+-+ +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 12 +--R + +--R %pi 4+-+ x 4 %pi 4+-+ x 2 +--R (3cos(---) - \|3 )cos(-) + (6cos(---) - 2\|3 )cos(-) +--R 12 2 12 2 +--R + +--R %pi 4+-+ +--R 3cos(---) - \|3 +--R 12 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ x 2 4+-+ x x +--R 2\|3 sin(-) + (4\|3 cos(-) - 4\|3 )sin(-) - 8\|3 cos(-)sin(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ +--R 2\|3 cos(-) + 4\|3 cos(-) + 2\|3 +--R 2 2 +--R / +--R 4+-+ x 4 4+-+ x 2 x 2 4+-+ x x 4+-+ x 4 +--R 6\|3 sin(-) + 12\|3 cos(-) sin(-) - 24\|3 cos(-)sin(-) + 6\|3 cos(-) +--R 2 2 2 2 2 2 +--R + +--R 4+-+ +--R 6\|3 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 520 +--m0074:= a0074-r0074 +--E 394 + +--S 395 of 520 +--d0074:= D(m0074,x) +--E 395 + +--S 396 of 520 +t0075:= 1/(1-sin(x)^6) +--R +--R +--R 1 +--R (256) - ----------- +--R 6 +--R sin(x) - 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 520 +r0075:= 1/3*atan((1+(-1)^(1/3))^(1/2)*tan(x))/(1+(-1)^(1/3))^(1/2)+_ + 1/3*atan((1-(-1)^(2/3))^(1/2)*tan(x))/(1-(-1)^(2/3))^(1/2)+1/3*tan(x) +--R +--R +--R (257) +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 atan(tan(x)\|\|- 1 + 1 ) +--R + +--R +----------+ +-------------+ +--R |3+---+ | 3+---+2 +--R \|\|- 1 + 1 atan(tan(x)\|- \|- 1 + 1 ) +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R tan(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R 3\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 520 +a0075:= integrate(t0075,x) +--R +--R +--R (258) +--R %pi x 8 %pi x 2 x 6 +--R cos(---)sin(-) + 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (6cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (4cos(---)cos(-) - 12cos(---)cos(-) )sin(-) + cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R 2cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) + 3\|3 sin(---) + 3cos(---) - \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 12cos(-) sin(---) + 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (12cos(---) - 4\|3 \|3 cos(---) + 4\|3 )cos(-) +--R 12 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (18cos(-) - 6)sin(---) + 18\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (18cos(---) - 6\|3 \|3 cos(---) + 6\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x 3 +--R (8\|3 \|3 cos(-)sin(---) + 24\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (12cos(-) + 36cos(-) )sin(---) + 12\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 6 +--R (12cos(---) - 4\|3 \|3 cos(---) + 4\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 +--R (36cos(---) - 12\|3 )cos(-) +--R 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x 3 %pi 4+-+ %pi x 3 x +--R (- 8\|3 \|3 cos(-) sin(---) - 24\|3 cos(---)cos(-) )sin(-) +--R 2 12 12 2 2 +--R + +--R x 8 x 4 %pi 2 +--R (3cos(-) - 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi +--R (3\|3 cos(-) - 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 8 +--R (3cos(---) - \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 +-+4+-+ %pi +--R (- 6cos(---) + 2\|3 )cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 %pi x 2 x 6 +--R - cos(---)sin(-) - 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (- 6cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (- 4cos(---)cos(-) + 12cos(---)cos(-) )sin(-) - cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R - 2cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) + 3\|3 sin(---) + 3cos(---) - \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 12cos(-) sin(---) + 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (12cos(---) - 4\|3 \|3 cos(---) + 4\|3 )cos(-) +--R 12 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (18cos(-) - 6)sin(---) + 18\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (18cos(---) - 6\|3 \|3 cos(---) + 6\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x 3 +--R (- 8\|3 \|3 cos(-)sin(---) - 24\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (12cos(-) + 36cos(-) )sin(---) + 12\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 6 +--R (12cos(---) - 4\|3 \|3 cos(---) + 4\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 +--R (36cos(---) - 12\|3 )cos(-) +--R 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x 3 %pi 4+-+ %pi x 3 x +--R (8\|3 \|3 cos(-) sin(---) + 24\|3 cos(---)cos(-) )sin(-) +--R 2 12 12 2 2 +--R + +--R x 8 x 4 %pi 2 +--R (3cos(-) - 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi +--R (3\|3 cos(-) - 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 8 +--R (3cos(---) - \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 +-+4+-+ %pi +--R (- 6cos(---) + 2\|3 )cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 %pi x 2 x 6 +--R cos(---)sin(-) + 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (6cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (4cos(---)cos(-) - 12cos(---)cos(-) )sin(-) + cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R 2cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) - 3\|3 sin(---) + 3cos(---) + \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 12cos(-) sin(---) - 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (12cos(---) + 4\|3 \|3 cos(---) + 4\|3 )cos(-) +--R 12 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (18cos(-) - 6)sin(---) - 18\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (18cos(---) + 6\|3 \|3 cos(---) + 6\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x 3 +--R (8\|3 \|3 cos(-)sin(---) + 24\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (12cos(-) + 36cos(-) )sin(---) - 12\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 6 +--R (12cos(---) + 4\|3 \|3 cos(---) + 4\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 +--R (36cos(---) - 12\|3 )cos(-) +--R 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x 3 %pi 4+-+ %pi x 3 x +--R (- 8\|3 \|3 cos(-) sin(---) - 24\|3 cos(---)cos(-) )sin(-) +--R 2 12 12 2 2 +--R + +--R x 8 x 4 %pi 2 +--R (3cos(-) - 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi +--R (- 3\|3 cos(-) + 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 8 +--R (3cos(---) + \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 +-+4+-+ %pi +--R (- 6cos(---) + 2\|3 )cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 %pi x 2 x 6 +--R - cos(---)sin(-) - 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (- 6cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (- 4cos(---)cos(-) + 12cos(---)cos(-) )sin(-) - cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R - 2cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) - 3\|3 sin(---) + 3cos(---) + \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 12cos(-) sin(---) - 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (12cos(---) + 4\|3 \|3 cos(---) + 4\|3 )cos(-) +--R 12 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (18cos(-) - 6)sin(---) - 18\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (18cos(---) + 6\|3 \|3 cos(---) + 6\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x 3 +--R (- 8\|3 \|3 cos(-)sin(---) - 24\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (12cos(-) + 36cos(-) )sin(---) - 12\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 6 +--R (12cos(---) + 4\|3 \|3 cos(---) + 4\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 +--R (36cos(---) - 12\|3 )cos(-) +--R 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x 3 %pi 4+-+ %pi x 3 x +--R (8\|3 \|3 cos(-) sin(---) + 24\|3 cos(---)cos(-) )sin(-) +--R 2 12 12 2 2 +--R + +--R x 8 x 4 %pi 2 +--R (3cos(-) - 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi +--R (- 3\|3 cos(-) + 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 8 +--R (3cos(---) + \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 +-+4+-+ %pi +--R (- 6cos(---) + 2\|3 )cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 x 2 %pi x 6 +--R - 2sin(---)sin(-) - 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (- 12cos(-) - 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (- 8cos(-) + 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (- 2cos(-) - 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R +-+ %pi %pi x 8 +--R (\|3 sin(---) + 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (4\|3 cos(-) - 2\|3 )sin(---) + 12cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 6cos(---) +--R 12 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x %pi +-+ %pi 4+-+ x x 5 +--R (12cos(-)sin(---) + (- 4\|3 cos(---) - 8\|3 )cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R +-+ x 4 +-+ x 2 %pi %pi x 4 +--R (6\|3 cos(-) - 2\|3 cos(-) )sin(---) + 18cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 +--R - 6cos(---)cos(-) +--R 12 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 3 x %pi +--R (24cos(-) - 24cos(-))sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 3 +-+ %pi x +--R (- 8\|3 cos(---) - 16\|3 )cos(-) + 8\|3 cos(---)cos(-) +--R 12 2 12 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ %pi +--R (4\|3 cos(-) + 2\|3 cos(-) + 2\|3 )sin(---) +--R 2 2 12 +--R + +--R %pi x 6 %pi x 4 %pi +--R 12cos(---)cos(-) + 6cos(---)cos(-) + 6cos(---) +--R 12 2 12 2 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 5 x 3 x %pi +--R (12cos(-) + 24cos(-) + 12cos(-))sin(---) +--R 2 2 2 12 +--R + +--R +-+ %pi 4+-+ x 5 +-+ %pi x 3 +--R (- 4\|3 cos(---) - 8\|3 )cos(-) - 8\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ x +--R (- 4\|3 cos(---) + 8\|3 )cos(-) +--R 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ %pi +--R (\|3 cos(-) + 2\|3 cos(-) - 2\|3 cos(-) - \|3 )sin(---) +--R 2 2 2 12 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R 3cos(---)cos(-) + 6cos(---)cos(-) - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi +-+ %pi 4+-+ x 8 +--R (3sin(---) - \|3 cos(---) - 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (12cos(-) - 6)sin(---) + (- 4\|3 cos(---) - 8\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi 4+-+ +--R 2\|3 cos(---) + 4\|3 +--R 12 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R +-+ x %pi %pi x x 5 +--R (- 4\|3 cos(-)sin(---) - 12cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi +--R (18cos(-) - 6cos(-) )sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +--R (- 6\|3 cos(---) - 12\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 2 4+-+ +--R (2\|3 cos(---) + 4\|3 )cos(-) - 4\|3 +--R 12 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 3 +-+ x %pi %pi x 3 +--R (- 8\|3 cos(-) + 8\|3 cos(-))sin(---) - 24cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x +--R 24cos(---)cos(-) +--R 12 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 %pi +--R (12cos(-) + 6cos(-) + 6)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 6 +--R (- 4\|3 cos(---) - 8\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 4 4+-+ x 2 +--R (- 2\|3 cos(---) - 4\|3 )cos(-) + 24\|3 cos(-) +--R 12 2 2 +--R + +--R +-+ %pi 4+-+ +--R - 2\|3 cos(---) + 4\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x %pi +--R (- 4\|3 cos(-) - 8\|3 cos(-) - 4\|3 cos(-))sin(---) +--R 2 2 2 12 +--R + +--R %pi x 5 %pi x 3 %pi x +--R - 12cos(---)cos(-) - 24cos(---)cos(-) - 12cos(---)cos(-) +--R 12 2 12 2 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 8 x 6 x 2 %pi +--R (3cos(-) + 6cos(-) - 6cos(-) - 3)sin(---) +--R 2 2 2 12 +--R + +--R +-+ %pi 4+-+ x 8 +--R (- \|3 cos(---) - 2\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 6 4+-+ x 4 +--R (- 2\|3 cos(---) - 4\|3 )cos(-) - 4\|3 cos(-) +--R 12 2 2 +--R + +--R +-+ %pi 4+-+ x 2 +-+ %pi 4+-+ +--R (2\|3 cos(---) - 4\|3 )cos(-) + \|3 cos(---) - 2\|3 +--R 12 2 12 +--R + +--R %pi x 8 x 2 %pi x 6 +--R 2sin(---)sin(-) + 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (12cos(-) + 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (8cos(-) - 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (2cos(-) + 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R +-+ %pi %pi x 8 +--R (\|3 sin(---) + 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (4\|3 cos(-) - 2\|3 )sin(---) + 12cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 6cos(---) +--R 12 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x %pi +-+ %pi 4+-+ x x 5 +--R (- 12cos(-)sin(---) + (4\|3 cos(---) + 8\|3 )cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R +-+ x 4 +-+ x 2 %pi %pi x 4 +--R (6\|3 cos(-) - 2\|3 cos(-) )sin(---) + 18cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 +--R - 6cos(---)cos(-) +--R 12 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 3 x %pi +--R (- 24cos(-) + 24cos(-))sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 3 +-+ %pi x +--R (8\|3 cos(---) + 16\|3 )cos(-) - 8\|3 cos(---)cos(-) +--R 12 2 12 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ %pi +--R (4\|3 cos(-) + 2\|3 cos(-) + 2\|3 )sin(---) +--R 2 2 12 +--R + +--R %pi x 6 %pi x 4 %pi +--R 12cos(---)cos(-) + 6cos(---)cos(-) + 6cos(---) +--R 12 2 12 2 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 5 x 3 x %pi +--R (- 12cos(-) - 24cos(-) - 12cos(-))sin(---) +--R 2 2 2 12 +--R + +--R +-+ %pi 4+-+ x 5 +-+ %pi x 3 +--R (4\|3 cos(---) + 8\|3 )cos(-) + 8\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ x +--R (4\|3 cos(---) - 8\|3 )cos(-) +--R 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ %pi +--R (\|3 cos(-) + 2\|3 cos(-) - 2\|3 cos(-) - \|3 )sin(---) +--R 2 2 2 12 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R 3cos(---)cos(-) + 6cos(---)cos(-) - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi +-+ %pi 4+-+ x 8 +--R (3sin(---) - \|3 cos(---) - 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (12cos(-) - 6)sin(---) + (- 4\|3 cos(---) - 8\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi 4+-+ +--R 2\|3 cos(---) + 4\|3 +--R 12 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R +-+ x %pi %pi x x 5 +--R (4\|3 cos(-)sin(---) + 12cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi +--R (18cos(-) - 6cos(-) )sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +--R (- 6\|3 cos(---) - 12\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 2 4+-+ +--R (2\|3 cos(---) + 4\|3 )cos(-) - 4\|3 +--R 12 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 3 +-+ x %pi %pi x 3 +--R (8\|3 cos(-) - 8\|3 cos(-))sin(---) + 24cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x +--R - 24cos(---)cos(-) +--R 12 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 %pi +--R (12cos(-) + 6cos(-) + 6)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 6 +--R (- 4\|3 cos(---) - 8\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 4 4+-+ x 2 +--R (- 2\|3 cos(---) - 4\|3 )cos(-) + 24\|3 cos(-) +--R 12 2 2 +--R + +--R +-+ %pi 4+-+ +--R - 2\|3 cos(---) + 4\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x %pi +--R (4\|3 cos(-) + 8\|3 cos(-) + 4\|3 cos(-))sin(---) +--R 2 2 2 12 +--R + +--R %pi x 5 %pi x 3 %pi x +--R 12cos(---)cos(-) + 24cos(---)cos(-) + 12cos(---)cos(-) +--R 12 2 12 2 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 8 x 6 x 2 %pi +--R (3cos(-) + 6cos(-) - 6cos(-) - 3)sin(---) +--R 2 2 2 12 +--R + +--R +-+ %pi 4+-+ x 8 +--R (- \|3 cos(---) - 2\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 6 4+-+ x 4 +--R (- 2\|3 cos(---) - 4\|3 )cos(-) - 4\|3 cos(-) +--R 12 2 2 +--R + +--R +-+ %pi 4+-+ x 2 +-+ %pi 4+-+ +--R (2\|3 cos(---) - 4\|3 )cos(-) + \|3 cos(---) - 2\|3 +--R 12 2 12 +--R + +--R %pi x 8 x 2 %pi x 6 +--R 2sin(---)sin(-) + 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (12cos(-) + 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (8cos(-) - 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (2cos(-) + 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R +-+ %pi %pi x 8 +--R (\|3 sin(---) + 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (4\|3 cos(-) - 2\|3 )sin(---) + 12cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 6cos(---) +--R 12 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x %pi +-+ %pi 4+-+ x x 5 +--R (12cos(-)sin(---) + (- 4\|3 cos(---) + 8\|3 )cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R +-+ x 4 +-+ x 2 %pi %pi x 4 +--R (6\|3 cos(-) - 2\|3 cos(-) )sin(---) + 18cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 +--R - 6cos(---)cos(-) +--R 12 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 3 x %pi +--R (24cos(-) - 24cos(-))sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 3 +-+ %pi x +--R (- 8\|3 cos(---) + 16\|3 )cos(-) + 8\|3 cos(---)cos(-) +--R 12 2 12 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ %pi +--R (4\|3 cos(-) + 2\|3 cos(-) + 2\|3 )sin(---) +--R 2 2 12 +--R + +--R %pi x 6 %pi x 4 %pi +--R 12cos(---)cos(-) + 6cos(---)cos(-) + 6cos(---) +--R 12 2 12 2 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 5 x 3 x %pi +--R (12cos(-) + 24cos(-) + 12cos(-))sin(---) +--R 2 2 2 12 +--R + +--R +-+ %pi 4+-+ x 5 +-+ %pi x 3 +--R (- 4\|3 cos(---) + 8\|3 )cos(-) - 8\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ x +--R (- 4\|3 cos(---) - 8\|3 )cos(-) +--R 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ %pi +--R (\|3 cos(-) + 2\|3 cos(-) - 2\|3 cos(-) - \|3 )sin(---) +--R 2 2 2 12 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R 3cos(---)cos(-) + 6cos(---)cos(-) - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi +-+ %pi 4+-+ x 8 +--R (3sin(---) - \|3 cos(---) + 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (12cos(-) - 6)sin(---) + (- 4\|3 cos(---) + 8\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi 4+-+ +--R 2\|3 cos(---) - 4\|3 +--R 12 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R +-+ x %pi %pi x x 5 +--R (- 4\|3 cos(-)sin(---) - 12cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi +--R (18cos(-) - 6cos(-) )sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +--R (- 6\|3 cos(---) + 12\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 2 4+-+ +--R (2\|3 cos(---) - 4\|3 )cos(-) + 4\|3 +--R 12 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 3 +-+ x %pi %pi x 3 +--R (- 8\|3 cos(-) + 8\|3 cos(-))sin(---) - 24cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x +--R 24cos(---)cos(-) +--R 12 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 %pi +--R (12cos(-) + 6cos(-) + 6)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 6 +--R (- 4\|3 cos(---) + 8\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 4 4+-+ x 2 +--R (- 2\|3 cos(---) + 4\|3 )cos(-) - 24\|3 cos(-) +--R 12 2 2 +--R + +--R +-+ %pi 4+-+ +--R - 2\|3 cos(---) - 4\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x %pi +--R (- 4\|3 cos(-) - 8\|3 cos(-) - 4\|3 cos(-))sin(---) +--R 2 2 2 12 +--R + +--R %pi x 5 %pi x 3 %pi x +--R - 12cos(---)cos(-) - 24cos(---)cos(-) - 12cos(---)cos(-) +--R 12 2 12 2 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 8 x 6 x 2 %pi +--R (3cos(-) + 6cos(-) - 6cos(-) - 3)sin(---) +--R 2 2 2 12 +--R + +--R +-+ %pi 4+-+ x 8 +--R (- \|3 cos(---) + 2\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 6 4+-+ x 4 +--R (- 2\|3 cos(---) + 4\|3 )cos(-) + 4\|3 cos(-) +--R 12 2 2 +--R + +--R +-+ %pi 4+-+ x 2 +-+ %pi 4+-+ +--R (2\|3 cos(---) + 4\|3 )cos(-) + \|3 cos(---) + 2\|3 +--R 12 2 12 +--R + +--R %pi x 8 x 2 %pi x 6 +--R - 2sin(---)sin(-) - 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (- 12cos(-) - 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (- 8cos(-) + 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (- 2cos(-) - 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R +-+ %pi %pi x 8 +--R (\|3 sin(---) + 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (4\|3 cos(-) - 2\|3 )sin(---) + 12cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 6cos(---) +--R 12 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x %pi +-+ %pi 4+-+ x x 5 +--R (- 12cos(-)sin(---) + (4\|3 cos(---) - 8\|3 )cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R +-+ x 4 +-+ x 2 %pi %pi x 4 +--R (6\|3 cos(-) - 2\|3 cos(-) )sin(---) + 18cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 +--R - 6cos(---)cos(-) +--R 12 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 3 x %pi +--R (- 24cos(-) + 24cos(-))sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 3 +-+ %pi x +--R (8\|3 cos(---) - 16\|3 )cos(-) - 8\|3 cos(---)cos(-) +--R 12 2 12 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ %pi +--R (4\|3 cos(-) + 2\|3 cos(-) + 2\|3 )sin(---) +--R 2 2 12 +--R + +--R %pi x 6 %pi x 4 %pi +--R 12cos(---)cos(-) + 6cos(---)cos(-) + 6cos(---) +--R 12 2 12 2 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 5 x 3 x %pi +--R (- 12cos(-) - 24cos(-) - 12cos(-))sin(---) +--R 2 2 2 12 +--R + +--R +-+ %pi 4+-+ x 5 +-+ %pi x 3 +--R (4\|3 cos(---) - 8\|3 )cos(-) + 8\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ x +--R (4\|3 cos(---) + 8\|3 )cos(-) +--R 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ %pi +--R (\|3 cos(-) + 2\|3 cos(-) - 2\|3 cos(-) - \|3 )sin(---) +--R 2 2 2 12 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R 3cos(---)cos(-) + 6cos(---)cos(-) - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi +-+ %pi 4+-+ x 8 +--R (3sin(---) - \|3 cos(---) + 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (12cos(-) - 6)sin(---) + (- 4\|3 cos(---) + 8\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi 4+-+ +--R 2\|3 cos(---) - 4\|3 +--R 12 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R +-+ x %pi %pi x x 5 +--R (4\|3 cos(-)sin(---) + 12cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi +--R (18cos(-) - 6cos(-) )sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +--R (- 6\|3 cos(---) + 12\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 2 4+-+ +--R (2\|3 cos(---) - 4\|3 )cos(-) + 4\|3 +--R 12 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+ x 3 +-+ x %pi %pi x 3 +--R (8\|3 cos(-) - 8\|3 cos(-))sin(---) + 24cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x +--R - 24cos(---)cos(-) +--R 12 2 +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 %pi +--R (12cos(-) + 6cos(-) + 6)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 6 +--R (- 4\|3 cos(---) + 8\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 4 4+-+ x 2 +--R (- 2\|3 cos(---) + 4\|3 )cos(-) - 24\|3 cos(-) +--R 12 2 2 +--R + +--R +-+ %pi 4+-+ +--R - 2\|3 cos(---) - 4\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x %pi +--R (4\|3 cos(-) + 8\|3 cos(-) + 4\|3 cos(-))sin(---) +--R 2 2 2 12 +--R + +--R %pi x 5 %pi x 3 %pi x +--R 12cos(---)cos(-) + 24cos(---)cos(-) + 12cos(---)cos(-) +--R 12 2 12 2 12 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R x 8 x 6 x 2 %pi +--R (3cos(-) + 6cos(-) - 6cos(-) - 3)sin(---) +--R 2 2 2 12 +--R + +--R +-+ %pi 4+-+ x 8 +--R (- \|3 cos(---) + 2\|3 )cos(-) +--R 12 2 +--R + +--R +-+ %pi 4+-+ x 6 4+-+ x 4 +--R (- 2\|3 cos(---) + 4\|3 )cos(-) + 4\|3 cos(-) +--R 12 2 2 +--R + +--R +-+ %pi 4+-+ x 2 +-+ %pi 4+-+ +--R (2\|3 cos(---) + 4\|3 )cos(-) + \|3 cos(---) + 2\|3 +--R 12 2 12 +--R + +--R 4+-+ x x 3 4+-+ x 3 x +--R - 32\|3 cos(-)sin(-) + 32\|3 cos(-) sin(-) +--R 2 2 2 2 +--R / +--R 4+-+ x 8 4+-+ x 2 x 6 4+-+ x 4 4+-+ x 4 +--R 12\|3 sin(-) + 48\|3 cos(-) sin(-) + (72\|3 cos(-) + 24\|3 )sin(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ x 6 4+-+ x 2 x 2 4+-+ x 8 4+-+ x 4 +--R (48\|3 cos(-) - 144\|3 cos(-) )sin(-) + 12\|3 cos(-) + 24\|3 cos(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 520 +--m0075:= a0075-r0075 +--E 399 + +--S 400 of 520 +--d0075:= D(m0075,x) +--E 400 + +--S 401 of 520 +t0076:= 1/(1-sin(x)^8) +--R +--R +--R 1 +--R (259) - ----------- +--R 8 +--R sin(x) - 1 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 520 +r0076:= 1/4*atan((1-%i)^(1/2)*tan(x))/(1-%i)^(1/2)+_ + 1/4*atan((1+%i)^(1/2)*tan(x))/(1+%i)^(1/2)+_ + 1/8*atan(2^(1/2)*tan(x))*2^(1/2)+1/4*tan(x) +--R +--R +--R (260) +--R +------+ +------+ +-+ +-+ +------+ +------+ +--R \|1 - %i \|1 + %i \|2 atan(\|2 tan(x)) + 2\|1 - %i atan(\|1 + %i tan(x)) +--R + +--R +------+ +------+ +------+ +------+ +--R 2\|1 + %i atan(\|1 - %i tan(x)) + 2\|1 - %i \|1 + %i tan(x) +--R / +--R +------+ +------+ +--R 8\|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 402 + +--S 403 of 520 +a0076:= integrate(t0076,x) +--R +--R +--R (261) +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 2 x 6 +--R \|2 \|2 cos(---)sin(-) + 4\|2 \|2 cos(---)cos(-) sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 4 +-+4+-+ %pi x 4 +--R (6\|2 \|2 cos(---)cos(-) + 2\|2 \|2 cos(---))sin(-) +--R 8 2 8 2 +--R + +--R +-+4+-+ %pi x 6 +-+4+-+ %pi x 2 x 2 +--R (4\|2 \|2 cos(---)cos(-) - 12\|2 \|2 cos(---)cos(-) )sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 4 +-+4+-+ %pi +--R \|2 \|2 cos(---)cos(-) + 2\|2 \|2 cos(---)cos(-) + \|2 \|2 cos(---) +--R 8 2 8 2 8 +--R * +--R log +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +-+4+-+ %pi x x 3 +--R (2\|2 \|2 cos(-)sin(---) + 2\|2 \|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (4\|2 cos(-) sin(---) + (4\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ x 3 %pi +-+4+-+ %pi x 3 x +--R (- 2\|2 \|2 cos(-) sin(---) - 2\|2 \|2 cos(---)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 4 +--R cos(-) +--R 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 2 x 6 +--R - \|2 \|2 cos(---)sin(-) - 4\|2 \|2 cos(---)cos(-) sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 4 +-+4+-+ %pi x 4 +--R (- 6\|2 \|2 cos(---)cos(-) - 2\|2 \|2 cos(---))sin(-) +--R 8 2 8 2 +--R + +--R +-+4+-+ %pi x 6 +-+4+-+ %pi x 2 x 2 +--R (- 4\|2 \|2 cos(---)cos(-) + 12\|2 \|2 cos(---)cos(-) )sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 4 +-+4+-+ %pi +--R - \|2 \|2 cos(---)cos(-) - 2\|2 \|2 cos(---)cos(-) - \|2 \|2 cos(---) +--R 8 2 8 2 8 +--R * +--R log +--R x 4 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi +-+4+-+ %pi x x 3 +--R (- 2\|2 \|2 cos(-)sin(---) - 2\|2 \|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (4\|2 cos(-) sin(---) + (4\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ x 3 %pi +-+4+-+ %pi x 3 x +--R (2\|2 \|2 cos(-) sin(---) + 2\|2 \|2 cos(---)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R x 4 +--R cos(-) +--R 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ x 2 %pi x 6 +--R - 2\|2 \|2 sin(---)sin(-) - 8\|2 \|2 cos(-) sin(---)sin(-) +--R 8 2 2 8 2 +--R + +--R +-+4+-+ x 4 +-+4+-+ %pi x 4 +--R (- 12\|2 \|2 cos(-) - 4\|2 \|2 )sin(---)sin(-) +--R 2 8 2 +--R + +--R +-+4+-+ x 6 +-+4+-+ x 2 %pi x 2 +--R (- 8\|2 \|2 cos(-) + 24\|2 \|2 cos(-) )sin(---)sin(-) +--R 2 2 8 2 +--R + +--R +-+4+-+ x 8 +-+4+-+ x 4 +-+4+-+ %pi +--R (- 2\|2 \|2 cos(-) - 4\|2 \|2 cos(-) - 2\|2 \|2 )sin(---) +--R 2 2 8 +--R * +--R atan +--R 4+-+ x %pi 4+-+ %pi x x +--R (2\|2 cos(-)sin(---) - 2\|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R / +--R +-+ x 2 +--R \|2 sin(-) +--R 2 +--R + +--R 4+-+ x %pi 4+-+ %pi x x +-+ x 2 +--R (- 2\|2 cos(-)sin(---) - 2\|2 cos(---)cos(-))sin(-) - \|2 cos(-) +--R 2 8 8 2 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ x 2 %pi x 6 +--R - 2\|2 \|2 sin(---)sin(-) - 8\|2 \|2 cos(-) sin(---)sin(-) +--R 8 2 2 8 2 +--R + +--R +-+4+-+ x 4 +-+4+-+ %pi x 4 +--R (- 12\|2 \|2 cos(-) - 4\|2 \|2 )sin(---)sin(-) +--R 2 8 2 +--R + +--R +-+4+-+ x 6 +-+4+-+ x 2 %pi x 2 +--R (- 8\|2 \|2 cos(-) + 24\|2 \|2 cos(-) )sin(---)sin(-) +--R 2 2 8 2 +--R + +--R +-+4+-+ x 8 +-+4+-+ x 4 +-+4+-+ %pi +--R (- 2\|2 \|2 cos(-) - 4\|2 \|2 cos(-) - 2\|2 \|2 )sin(---) +--R 2 2 8 +--R * +--R atan +--R 4+-+ x %pi 4+-+ %pi x x +--R (2\|2 cos(-)sin(---) - 2\|2 cos(---)cos(-))sin(-) +--R 2 8 8 2 2 +--R / +--R +-+ x 2 4+-+ x %pi 4+-+ %pi x x +--R \|2 sin(-) + (2\|2 cos(-)sin(---) + 2\|2 cos(---)cos(-))sin(-) +--R 2 2 8 8 2 2 +--R + +--R +-+ x 2 +--R - \|2 cos(-) +--R 2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 +-+ x 4 +--R - \|2 sin(-) - 4\|2 cos(-) sin(-) + (- 6\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +-+ x 8 +-+ x 4 +--R (- 4\|2 cos(-) + 12\|2 cos(-) )sin(-) - \|2 cos(-) - 2\|2 cos(-) +--R 2 2 2 2 2 +--R + +--R +-+ +--R - \|2 +--R * +--R +-+ x x +--R 4\|2 cos(-)sin(-) +--R 2 2 +--R atan(------------------) +--R x 2 x 2 +--R sin(-) - 8cos(-) +--R 2 2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 +-+ x 4 +--R - \|2 sin(-) - 4\|2 cos(-) sin(-) + (- 6\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +-+ x 8 +-+ x 4 +--R (- 4\|2 cos(-) + 12\|2 cos(-) )sin(-) - \|2 cos(-) - 2\|2 cos(-) +--R 2 2 2 2 2 +--R + +--R +-+ +--R - \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 18\|2 cos(-)sin(-) + (- 60\|2 cos(-) - 48\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (18\|2 cos(-) + 64\|2 cos(-) + 30\|2 cos(-))sin(-) +--R 2 2 2 2 +--R / +--R x 6 x 2 x 4 +--R 9sin(-) + (- 72cos(-) - 30)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 x 6 x 4 +--R (93cos(-) + 126cos(-) + 25)sin(-) - 2cos(-) - 12cos(-) +--R 2 2 2 2 2 +--R + +--R x 2 +--R - 18cos(-) +--R 2 +--R + +--R x x 3 x 3 x +--R - 32cos(-)sin(-) + 32cos(-) sin(-) +--R 2 2 2 2 +--R / +--R x 8 x 2 x 6 x 4 x 4 +--R 16sin(-) + 64cos(-) sin(-) + (96cos(-) + 32)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (64cos(-) - 192cos(-) )sin(-) + 16cos(-) + 32cos(-) + 16 +--R 2 2 2 2 2 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 520 +--m0076:= a0076-r0076 +--E 404 + +--S 405 of 520 +--d0076:= D(m0076,x) +--E 405 + +--S 406 of 520 +t0077:= sin(a+b*x+c*x^2)/x^2-b*cos(a+b*x+c*x^2)/x +--R +--R +--R 2 2 +--R sin(c x + b x + a) - b x cos(c x + b x + a) +--R (262) --------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 406 + +--S 407 of 520 +r0077:= c^(1/2)*2^(1/2)*%pi^(1/2)*cos(1/4*(b^2-4*a*c)/c)*_ + FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))+_ + c^(1/2)*2^(1/2)*%pi^(1/2)*_ + FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + sin(1/4*(b^2-4*a*c)/c)-sin(a+b*x+c*x^2)/x +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 407 + +--S 408 of 520 +a0077:= integrate(t0077,x) +--R +--R +--R x 2 2 +--R ++ sin(%R c + %R b + a) - %R b cos(%R c + %R b + a) +--R (263) | ------------------------------------------------ d%R +--R ++ 2 +--R %R +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 520 +--m0077:= a0077-r0077 +--E 409 + +--S 410 of 520 +--d0077:= D(m0077,x) +--E 410 + +--S 411 of 520 +t0078:= sin(a+b*x-c*x^2)/x^2-b*cos(a+b*x-c*x^2)/x +--R +--R +--R 2 2 +--R - sin(c x - b x - a) - b x cos(c x - b x - a) +--R (264) ----------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 411 + +--S 412 of 520 +r0078:= c^(1/2)*2^(1/2)*%pi^(1/2)*cos(1/4*(b^2+4*a*c)/c)*_ + FresnelC(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))+_ + c^(1/2)*2^(1/2)*%pi^(1/2)*_ + FresnelS(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + sin(1/4*(b^2+4*a*c)/c)-sin(a+b*x-c*x^2)/x +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 412 + +--S 413 of 520 +a0078:= integrate(t0078,x) +--R +--R +--R x 2 2 +--R ++ - sin(%R c - %R b - a) - %R b cos(%R c - %R b - a) +--R (265) | -------------------------------------------------- d%R +--R ++ 2 +--R %R +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 520 +--m0078:= a0078-r0078 +--E 414 + +--S 415 of 520 +--d0078:= D(m0078,x) +--E 415 + +--S 416 of 520 +t0079:= (d+e*x)^2*sin(a+b*x+c*x^2) +--R +--R +--R 2 2 2 2 +--R (266) (e x + 2d e x + d )sin(c x + b x + a) +--R Type: Expression(Integer) +--E 416 + +--S 417 of 520 +r0079:= -1/4*e*(4*c*d-b*e)*cos(a+b*x+c*x^2)/c^2-_ + 1/2*e^2*x*cos(a+b*x+c*x^2)/c+1/8*2^(1/2)*%pi^(1/2)*_ + FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*((2*c*d-b*e)^2*_ + cos(a-1/4*b^2/c)-2*c*e^2*sin(a-1/4*b^2/c))/c^(5/2)+_ + 1/8*2^(1/2)*%pi^(1/2)*_ + FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + (2*c*e^2*cos(a-1/4*b^2/c)+(2*c*d-b*e)^2*sin(a-1/4*b^2/c))/c^(5/2) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 417 + +--S 418 of 520 +a0079:= integrate(t0079,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--R (267) | (%R e + 2%R d e + d )sin(%R c + %R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 520 +--m0079:= a0079-r0079 +--E 419 + +--S 420 of 520 +--d0079:= D(m0079,x) +--E 420 + +--S 421 of 520 +t0080:= sin((a+b*x)/(c+d*x))^2 +--R +--R +--R b x + a 2 +--R (268) sin(-------) +--R d x + c +--R Type: Expression(Integer) +--E 421 + +--S 422 of 520 +r0080:= 1/2*x-1/2*(c+d*x)*cos(2*(a+b*x)/(c+d*x))/d+_ + (b*c-a*d)*Ci(-2*(b*c-a*d)/d/(c+d*x))*sin(2*b/d)/d^2+_ + (b*c-a*d)*cos(2*b/d)*Si(2*a/(c+d*x)-2*b*c/d/(c+d*x))/d^2 +--R +--R +--R (269) +--R 2a d - 2b c 2b 2 2b x + 2a +--R (- 2a d + 2b c)Ci(-----------)sin(--) + (- d x - c d)cos(---------) +--R 2 d d x + c +--R d x + c d +--R + +--R 2a d - 2b c 2b 2 +--R (- 2a d + 2b c)Si(-----------)cos(--) + d x +--R 2 d +--R d x + c d +--R / +--R 2 +--R 2d +--R Type: Expression(Integer) +--E 422 + +--S 423 of 520 +a0080:= integrate(t0080,x) +--R +--R +--R x +--R ++ %R b + a 2 +--R (270) | sin(--------) d%R +--R ++ %R d + c +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 520 +--m0080:= a0080-r0080 +--E 424 + +--S 425 of 520 +--d0080:= D(m0080,x) +--E 425 + +--S 426 of 520 +t0081:= sin(a+b*x^2)^2/x^3 +--R +--R +--R 2 2 +--R sin(b x + a) +--R (271) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 426 + +--S 427 of 520 +r0081:= 1/4*(-1+cos(2*a+2*b*x^2)+2*b*Ci(2*b*x^2)*sin(2*a)*x^2+_ + 2*b*cos(2*a)*Si(2*b*x^2)*x^2)/x^2 +--R +--R +--R 2 2 2 2 2 +--R 2b x Ci(2b x )sin(2a) + cos(2b x + 2a) + 2b x Si(2b x )cos(2a) - 1 +--R (272) ------------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 427 + +--S 428 of 520 +a0081:= integrate(t0081,x) +--R +--R +--R x 2 2 +--R ++ sin(%R b + a) +--R (273) | -------------- d%R +--R ++ 3 +--R %R +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 520 +--m0081:= a0081-r0081 +--E 429 + +--S 430 of 520 +--d0081:= D(m0081,x) +--E 430 + +--S 431 of 520 +t0082:= sin(a+b*x^2)^3/x^3 +--R +--R +--R 2 3 +--R sin(b x + a) +--R (274) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 431 + +--S 432 of 520 +r0082:= 3/8*b*cos(a)*Ci(b*x^2)-3/8*b*cos(3*a)*Ci(3*b*x^2)-_ + 3/8*sin(a+b*x^2)/x^2+1/8*sin(3*a+3*b*x^2)/x^2-_ + 3/8*b*sin(a)*Si(b*x^2)+3/8*b*sin(3*a)*Si(3*b*x^2) +--R +--R +--R (275) +--R 2 2 2 2 +--R sin(3b x + 3a) - 3sin(b x + a) + 3b x Si(3b x )sin(3a) +--R + +--R 2 2 2 2 2 2 +--R - 3b x Si(b x )sin(a) - 3b x Ci(3b x )cos(3a) + 3b x Ci(b x )cos(a) +--R / +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 432 + +--S 433 of 520 +a0082:= integrate(t0082,x) +--R +--R +--R x 2 3 +--R ++ sin(%R b + a) +--R (276) | -------------- d%R +--R ++ 3 +--R %R +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 520 +--m0082:= a0082-r0082 +--E 434 + +--S 435 of 520 +--d0082:= D(m0082,x) +--E 435 + +--S 436 of 520 +t0083:= sin(a+b*x^n) +--R +--R +--R n +--R (277) sin(b x + a) +--R Type: Expression(Integer) +--E 436 + +--S 437 of 520 +r0083:= -1/2*%i*x/n*(-exp(%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-%i*b*x^n)+(%i*b*x^n)^(-1/n)*exp(-%i*a)*Gamma(1/n,%i*b*x^n)) +--R +--R +--R (278) +--R 1 +--R - - +--R - %i a n n _ 1 n +--R - %i x %e (%i b x ) | (-,%i b x ) +--R n +--R + +--R 1 +--R - - +--R %i a n n _ 1 n +--R %i x %e (- %i b x ) | (-,- %i b x ) +--R n +--R / +--R 2n +--R Type: Expression(Complex(Integer)) +--E 437 + +--S 438 of 520 +a0083:= integrate(t0083,x) +--R +--R +--R x +--R ++ n +--R (279) | sin(b %R + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 520 +--m0083:= a0083-r0083 +--E 439 + +--S 440 of 520 +--d0083:= D(m0083,x) +--E 440 + +--S 441 of 520 +t0084:= sin(a+b*x^n)^2 +--R +--R +--R n 2 +--R (280) sin(b x + a) +--R Type: Expression(Integer) +--E 441 + +--S 442 of 520 +r0084:= 1/2*x/n*(2^(-(1+n)/n)*exp(2*%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-2*%i*b*x^n)+2^(-(1+n)/n)*exp(-2*%i*a)*(%i*b*x^n)^(-1/n)*_ + Gamma(1/n,2*%i*b*x^n)+n) +--R +--R +--R (281) +--R - n - 1 1 +--R ------- - - +--R - 2%i a n n n _ 1 n +--R x %e 2 (%i b x ) | (-,2%i b x ) +--R n +--R + +--R - n - 1 1 +--R ------- - - +--R 2%i a n n n _ 1 n +--R x %e 2 (- %i b x ) | (-,- 2%i b x ) + n x +--R n +--R / +--R 2n +--R Type: Expression(Complex(Integer)) +--E 442 + +--S 443 of 520 +a0084:= integrate(t0084,x) +--R +--R +--R x +--R ++ n 2 +--R (282) | sin(b %R + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 520 +--m0084:= a0084-r0084 +--E 444 + +--S 445 of 520 +--d0084:= D(m0084,x) +--E 445 + +--S 446 of 520 +t0085:= sin(a+b*x^n)^3 +--R +--R +--R n 3 +--R (283) sin(b x + a) +--R Type: Expression(Integer) +--E 446 + +--S 447 of 520 +r0085:= 1/8*%i/n*x*(3*exp(%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-%i*b*x^n)-3*(%i*b*x^n)^(-1/n)*exp(-%i*a)*_ + Gamma(1/n,%i*b*x^n)-exp(3*%i*a)*(-%i*b*x^n)^(-1/n)*3^(-1/n)*_ + Gamma(1/n,-3*%i*b*x^n)+(%i*b*x^n)^(-1/n)*3^(-1/n)*exp(-3*%i*a)*_ + Gamma(1/n,3*%i*b*x^n)) +--R +--R +--R (284) +--R 1 1 +--R - - - - +--R - 3%i a n n n _ 1 n +--R %i x %e 3 (%i b x ) | (-,3%i b x ) +--R n +--R + +--R 1 +--R - - +--R - %i a n n _ 1 n +--R - 3%i x %e (%i b x ) | (-,%i b x ) +--R n +--R + +--R 1 +--R - - +--R %i a n n _ 1 n +--R 3%i x %e (- %i b x ) | (-,- %i b x ) +--R n +--R + +--R 1 1 +--R - - - - +--R 3%i a n n n _ 1 n +--R - %i x %e 3 (- %i b x ) | (-,- 3%i b x ) +--R n +--R / +--R 8n +--R Type: Expression(Complex(Integer)) +--E 447 + +--S 448 of 520 +a0085:= integrate(t0085,x) +--R +--R +--R x +--R ++ n 3 +--R (285) | sin(b %R + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 520 +--m0085:= a0085-r0085 +--E 449 + +--S 450 of 520 +--d0085:= D(m0085,x) +--E 450 + +--S 451 of 520 +t0086:= x^m*sin(a+b*x^n) +--R +--R +--R m n +--R (286) x sin(b x + a) +--R Type: Expression(Integer) +--E 451 + +--S 452 of 520 +r0086:= 1/2*%i*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)-exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,%i*b*x^n))/n +--R +--R +--R (287) +--R - m - 1 +--R ------- +--R - %i a m n n _ m + 1 n +--R - %i %e x (%i b x ) | (-----,%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R %i a m n n _ m + 1 n +--R %i %e x (- %i b x ) | (-----,- %i b x ) +--R n +--R / +--R 2n +--R * +--R x +--R Type: UnivariatePolynomial(x,Expression(Complex(Integer))) +--E 452 + +--S 453 of 520 +a0086:= integrate(t0086,x) +--R +--R +--R x +--R ++ m n +--R (288) | %R sin(b %R + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 520 +--m0086:= a0086-r0086 +--E 454 + +--S 455 of 520 +--d0086:= D(m0086,x) +--E 455 + +--S 456 of 520 +t0087:= x^m*sin(a+b*x^n)^2 +--R +--R +--R m n 2 +--R (289) x sin(b x + a) +--R Type: Expression(Integer) +--E 456 + +--S 457 of 520 +r0087:= x^(1+m)/(2+2*m)+2^(-2-(1+m)/n)*exp(1)^(2*%i*a)*x^(1+m)*_ + Gamma((1+m)/n,-2*%i*b*x^n)/((-%i*b*x^n)^((1+m)/n))/n+_ + 2^(-2-(1+m)/n)*x^(1+m)*_ + Gamma((1+m)/n,2*%i*b*x^n)/(exp(1)^(2*%i*a))/((%i*b*x^n)^((1+m)/n))/n +--R +--R +--R (290) +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R n m + 1 n n _ m + 1 n +--R (2m + 2)2 x (- %i b x ) | (-----,2%i b x ) +--R n +--R + +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R 2%i a 2 n m + 1 n n _ m + 1 n +--R (2m + 2)(%e ) 2 x (%i b x ) | (-----,- 2%i b x ) +--R n +--R + +--R m + 1 m + 1 +--R ----- ----- +--R 2%i a m + 1 n n n n +--R n %e x (- %i b x ) (%i b x ) +--R / +--R m + 1 m + 1 +--R ----- ----- +--R 2%i a n n n n +--R (2m + 2)n %e (- %i b x ) (%i b x ) +--R Type: Expression(Complex(Integer)) +--E 457 + +--S 458 of 520 +a0087:= integrate(t0087,x) +--R +--R +--R x +--R ++ m n 2 +--R (291) | %R sin(b %R + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 520 +--m0087:= a0087-r0087 +--E 459 + +--S 460 of 520 +--d0087:= D(m0087,x) +--E 460 + +--S 461 of 520 +t0088:= x^m*sin(a+b*x^n)^3 +--R +--R +--R m n 3 +--R (292) x sin(b x + a) +--R Type: Expression(Integer) +--E 461 + +--S 462 of 520 +r0088:= -1/8*%i/n*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*_ + Gamma((1+m)/n,-3*%i*b*x^n)*exp(3*%i*a)-3*(-%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+_ + 3*exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,%i*b*x^n)-(%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*_ + Gamma((1+m)/n,3*%i*b*x^n)*exp(-3*%i*a)) +--R +--R +--R (293) +--R - m - 1 - m - 1 +--R ------- ------- +--R - 3%i a n m n n _ m + 1 n +--R %i x %e 3 x (%i b x ) | (-----,3%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R - %i a m n n _ m + 1 n +--R - 3%i x %e x (%i b x ) | (-----,%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R %i a m n n _ m + 1 n +--R 3%i x %e x (- %i b x ) | (-----,- %i b x ) +--R n +--R + +--R - m - 1 - m - 1 +--R ------- ------- +--R 3%i a n m n n _ m + 1 n +--R - %i x %e 3 x (- %i b x ) | (-----,- 3%i b x ) +--R n +--R / +--R 8n +--R Type: Expression(Complex(Integer)) +--E 462 + +--S 463 of 520 +a0088:= integrate(t0088,x) +--R +--R +--R x +--R ++ m n 3 +--R (294) | %R sin(b %R + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 520 +--m0088:= a0088-r0088 +--E 464 + +--S 465 of 520 +--d0088:= D(m0088,x) +--E 465 + +--S 466 of 520 +t0089:= x/sin(x)^(3/2)+x*sin(x)^(1/2) +--R +--R +--R 2 +--R x sin(x) + x +--R (295) --------------- +--R +------+ +--R sin(x)\|sin(x) +--R Type: Expression(Integer) +--E 466 + +--S 467 of 520 +r0089:= -2*(x*cos(x)-2*sin(x))/sin(x)^(1/2) +--R +--R +--R 4sin(x) - 2x cos(x) +--R (296) ------------------- +--R +------+ +--R \|sin(x) +--R Type: Expression(Integer) +--E 467 + +--S 468 of 520 +a0089:= integrate(t0089,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 468 + +--S 469 of 520 +--m0089:= a0089-r0089 +--E 469 + +--S 470 of 520 +--d0089:= D(m0089,x) +--E 470 + +--S 471 of 520 +t0090:= x/sin(x)^(5/2)-1/3*x/sin(x)^(1/2) +--R +--R +--R 2 +--R - x sin(x) + 3x +--R (297) ----------------- +--R 2 +------+ +--R 3sin(x) \|sin(x) +--R Type: Expression(Integer) +--E 471 + +--S 472 of 520 +r0090:= -2/3*(x*cos(x)+2*sin(x))/sin(x)^(3/2) +--R +--R +--R - 4sin(x) - 2x cos(x) +--R (298) --------------------- +--R +------+ +--R 3sin(x)\|sin(x) +--R Type: Expression(Integer) +--E 472 + +--S 473 of 520 +a0090:= integrate(t0090,x) +--R +--R +--R +------+ +--R (4sin(x) + 2x cos(x))\|sin(x) +--R (299) ------------------------------ +--R 2 +--R 3cos(x) - 3 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 520 +m0090:= a0090-r0090 +--R +--R +--R (300) +--R 3 2 2 3 +--R 4sin(x) + 2x cos(x)sin(x) + (4cos(x) - 4)sin(x) + 2x cos(x) - 2x cos(x) +--R --------------------------------------------------------------------------- +--R 2 +------+ +--R (3cos(x) - 3)sin(x)\|sin(x) +--R Type: Expression(Integer) +--E 474 + +--S 475 of 520 +d0090:= D(m0090,x) +--R +--R +--R (301) +--R 5 2 4 3 3 +--R 8cos(x)sin(x) + (2x cos(x) + 2x)sin(x) + (8cos(x) - 8cos(x))sin(x) +--R + +--R 4 2 2 6 4 +--R (- x cos(x) + 3x cos(x) - 2x)sin(x) - 3x cos(x) + 6x cos(x) +--R + +--R 2 +--R - 3x cos(x) +--R / +--R 4 2 2 +------+ +--R (3cos(x) - 6cos(x) + 3)sin(x) \|sin(x) +--R Type: Expression(Integer) +--E 475 + +--S 476 of 520 +t0091:= x/sin(x)^(7/2)+3/5*x*sin(x)^(1/2) +--R +--R +--R 4 +--R 3x sin(x) + 5x +--R (302) ----------------- +--R 3 +------+ +--R 5sin(x) \|sin(x) +--R Type: Expression(Integer) +--E 476 + +--S 477 of 520 +r0091:= 2/15*(16*sin(x)-18*sin(x)*cos(x)^2-12*x*cos(x)+_ + 9*x*cos(x)^3)/sin(x)^(5/2) +--R +--R +--R 2 3 +--R (- 36cos(x) + 32)sin(x) + 18x cos(x) - 24x cos(x) +--R (303) --------------------------------------------------- +--R 2 +------+ +--R 15sin(x) \|sin(x) +--R Type: Expression(Integer) +--E 477 + +--S 478 of 520 +a0091:= integrate(t0091,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 478 + +--S 479 of 520 +--m0091:= a0091-r0091 +--E 479 + +--S 480 of 520 +--d0091:= D(m0091,x) +--E 480 + +--S 481 of 520 +t0092:= x^2/sin(x)^(3/2)+x^2*sin(x)^(1/2) +--R +--R +--R 2 2 2 +--R x sin(x) + x +--R (304) --------------- +--R +------+ +--R sin(x)\|sin(x) +--R Type: Expression(Integer) +--E 481 + +--S 482 of 520 +r0092:= -16*EllipticE(-1/4*%pi+1/2*x,2)-2*x^2*cos(x)/sin(x)^(1/2)+_ + 8*x*sin(x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 482 + +--S 483 of 520 +a0092:= integrate(t0092,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 483 + +--S 484 of 520 +--m0092:= a0092-r0092 +--E 484 + +--S 485 of 520 +--d0092:= D(m0092,x) +--E 485 + +--S 486 of 520 +t0093:= sin(x)*(b-a/x^2)^(1/2)/(a-b*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |b x - a +--R sin(x) |-------- +--R | 2 +--R \| x +--R (305) ----------------- +--R +----------+ +--R | 2 +--R \|- b x + a +--R Type: Expression(Integer) +--E 486 + +--S 487 of 520 +r0093:= (b-a/x^2)^(1/2)*x*Si(x)/(a-b*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |b x - a +--R x Si(x) |-------- +--R | 2 +--R \| x +--R (306) ------------------ +--R +----------+ +--R | 2 +--R \|- b x + a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 520 +a0093:= integrate(t0093,x) +--R +--R +--R +--------+ +--R | 2 +--R |%R b - a +--R sin(%R) |-------- +--R x | 2 +--R ++ \| %R +--R (307) | ------------------ d%R +--R ++ +----------+ +--R | 2 +--R \|- %R b + a +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 520 +--m0093:= a0093-r0093 +--E 489 + +--S 490 of 520 +--d0093:= D(m0093,x) +--E 490 + +--S 491 of 520 +t0094:= sin(a+b*log(c*x^n)) +--R +--R +--R n +--R (308) sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 491 + +--S 492 of 520 +r0094:= x*(-b*n*cos(a+b*log(c*x^n))+sin(a+b*log(c*x^n)))/(1+b^2*n^2) +--R +--R +--R n n +--R x sin(b log(c x ) + a) - b n x cos(b log(c x ) + a) +--R (309) --------------------------------------------------- +--R 2 2 +--R b n + 1 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 520 +a0094:= integrate(t0094,x) +--R +--R +--R (310) +--R x sin(b n log(x) + b log(c) + a) - b n x cos(b n log(x) + b log(c) + a) +--R ----------------------------------------------------------------------- +--R 2 2 +--R b n + 1 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 520 +m0094:= a0094-r0094 +--R +--R +--R (311) +--R n n +--R - x sin(b log(c x ) + a) + b n x cos(b log(c x ) + a) +--R + +--R x sin(b n log(x) + b log(c) + a) - b n x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n + 1 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 520 +d0094:= D(m0094,x) +--R +--R +--R (312) +--R n 2 2 n - 1 n +--R (- x - b n x x )sin(b log(c x ) + a) +--R + +--R n n - 1 n +--R (b n x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n + 1)x sin(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n + 1)x +--R Type: Expression(Integer) +--E 495 + +--S 496 of 520 +t0095:= x*sin(a+b*log(c*x^n)) +--R +--R +--R n +--R (313) x sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 496 + +--S 497 of 520 +r0095:= x^2*(-b*n*cos(a+b*log(c*x^n))+2*sin(a+b*log(c*x^n)))/(4+b^2*n^2) +--R +--R +--R 2 n 2 n +--R 2x sin(b log(c x ) + a) - b n x cos(b log(c x ) + a) +--R (314) ---------------------------------------------------- +--R 2 2 +--R b n + 4 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 520 +a0095:= integrate(t0095,x) +--R +--R +--R (315) +--R 2 2 +--R 2x sin(b n log(x) + b log(c) + a) - b n x cos(b n log(x) + b log(c) + a) +--R ------------------------------------------------------------------------ +--R 2 2 +--R b n + 4 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 520 +m0095:= a0095-r0095 +--R +--R +--R (316) +--R 2 n 2 n +--R - 2x sin(b log(c x ) + a) + b n x cos(b log(c x ) + a) +--R + +--R 2 2 +--R 2x sin(b n log(x) + b log(c) + a) - b n x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n + 4 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 520 +d0095:= D(m0095,x) +--R +--R +--R (317) +--R n 2 2 2 n - 1 n +--R (- 4x x - b n x x )sin(b log(c x ) + a) +--R + +--R n 2 n - 1 n +--R (2b n x x - 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n + 4)x x sin(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n + 4)x +--R Type: Expression(Integer) +--E 500 + +--S 501 of 520 +t0096:= x^2*sin(a+b*log(c*x^n)) +--R +--R +--R 2 n +--R (318) x sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 501 + +--S 502 of 520 +r0096:= x^3*(-b*n*cos(a+b*log(c*x^n))+3*sin(a+b*log(c*x^n)))/(9+b^2*n^2) +--R +--R +--R 3 n 3 n +--R 3x sin(b log(c x ) + a) - b n x cos(b log(c x ) + a) +--R (319) ---------------------------------------------------- +--R 2 2 +--R b n + 9 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 520 +a0096:= integrate(t0096,x) +--R +--R +--R (320) +--R 3 3 +--R 3x sin(b n log(x) + b log(c) + a) - b n x cos(b n log(x) + b log(c) + a) +--R ------------------------------------------------------------------------ +--R 2 2 +--R b n + 9 +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 520 +m0096:= a0096-r0096 +--R +--R +--R (321) +--R 3 n 3 n +--R - 3x sin(b log(c x ) + a) + b n x cos(b log(c x ) + a) +--R + +--R 3 3 +--R 3x sin(b n log(x) + b log(c) + a) - b n x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n + 9 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 520 +d0096:= D(m0096,x) +--R +--R +--R (322) +--R 2 n 2 2 3 n - 1 n +--R (- 9x x - b n x x )sin(b log(c x ) + a) +--R + +--R 2 n 3 n - 1 n +--R (3b n x x - 3b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 2 n +--R (b n + 9)x x sin(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n + 9)x +--R Type: Expression(Integer) +--E 505 + +--S 506 of 520 +t0097:= sin(a+b*log(c*x^n))/x^2 +--R +--R +--R n +--R sin(b log(c x ) + a) +--R (323) -------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 506 + +--S 507 of 520 +r0097:= -1/(1+b^2*n^2)/x*(sin(a+b*log(c*x^n))+b*n*cos(a+b*log(c*x^n))) +--R +--R +--R n n +--R - sin(b log(c x ) + a) - b n cos(b log(c x ) + a) +--R (324) ------------------------------------------------- +--R 2 2 +--R (b n + 1)x +--R Type: Expression(Integer) +--E 507 + +--S 508 of 520 +a0097:= integrate(t0097,x) +--R +--R +--R (325) +--R - sin(b n log(x) + b log(c) + a) - b n cos(b n log(x) + b log(c) + a) +--R --------------------------------------------------------------------- +--R 2 2 +--R (b n + 1)x +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 520 +m0097:= a0097-r0097 +--R +--R +--R (326) +--R n n +--R sin(b log(c x ) + a) + b n cos(b log(c x ) + a) +--R + +--R - sin(b n log(x) + b log(c) + a) - b n cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R (b n + 1)x +--R Type: Expression(Integer) +--E 509 + +--S 510 of 520 +d0097:= D(m0097,x) +--R +--R +--R (327) +--R n 2 2 n - 1 n +--R (- x - b n x x )sin(b log(c x ) + a) +--R + +--R n n - 1 n +--R (- b n x + b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n + 1)x sin(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (b n + 1)x x +--R Type: Expression(Integer) +--E 510 + +--S 511 of 520 +t0098:= x^m*sin(a+b*log(c*x^n)) +--R +--R +--R m n +--R (328) x sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 511 + +--S 512 of 520 +r0098:= -b*n*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)+_ + (1+m)*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+b^2*n^2) +--R +--R +--R m + 1 n m + 1 n +--R (m + 1)x sin(b log(c x ) + a) - b n x cos(b log(c x ) + a) +--R (329) ------------------------------------------------------------------ +--R 2 2 2 +--R b n + m + 2m + 1 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 520 +a0098:= integrate(t0098,x) +--R +--R +--R (330) +--R m log(x) +--R (m + 1)x %e sin(b n log(x) + b log(c) + a) +--R + +--R m log(x) +--R - b n x cos(b n log(x) + b log(c) + a)%e +--R / +--R 2 2 2 +--R b n + m + 2m + 1 +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 520 +m0098:= a0098-r0098 +--R +--R +--R (331) +--R m + 1 n m + 1 n +--R (- m - 1)x sin(b log(c x ) + a) + b n x cos(b log(c x ) + a) +--R + +--R m log(x) +--R (m + 1)x %e sin(b n log(x) + b log(c) + a) +--R + +--R m log(x) +--R - b n x cos(b n log(x) + b log(c) + a)%e +--R / +--R 2 2 2 +--R b n + m + 2m + 1 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 520 +d0098:= D(m0098,x) +--R +--R +--R (332) +--R 2 m n 2 2 m + 1 n - 1 n +--R ((- m - 2m - 1)x x - b n x x )sin(b log(c x ) + a) +--R + +--R m n m + 1 n - 1 n +--R ((b m + b)n x x + (- b m - b)n x x )cos(b log(c x ) + a) +--R + +--R 2 2 2 n m log(x) +--R (b n + m + 2m + 1)x %e sin(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (b n + m + 2m + 1)x +--R Type: Expression(Integer) +--E 515 + +--S 516 of 520 +t0099:= sin(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (333) sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 516 + +--S 517 of 520 +r0099:= -x*(-2*b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-_ + 1+cos(a+b*log(c*x^n))^2)/(1+4*b^2*n^2) +--R +--R +--R (334) +--R n n +--R - 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 2 +--R - x cos(b log(c x ) + a) + (2b n + 1)x +--R / +--R 2 2 +--R 4b n + 1 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 520 +a0099:= integrate(t0099,x) +--R +--R +--R (335) +--R - 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R - x cos(b n log(x) + b log(c) + a) + (2b n + 1)x +--R / +--R 2 2 +--R 4b n + 1 +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 520 +m0099:= a0099-r0099 +--R +--R +--R (336) +--R n n n 2 +--R 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) + x cos(b log(c x ) + a) +--R + +--R - 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 +--R - x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R 4b n + 1 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 520 +d0099:= D(m0099,x) +--R +--R +--R (337) +--R 2 2 n - 1 n 2 +--R - 2b n x x sin(b log(c x ) + a) +--R + +--R n n - 1 n n +--R (2b n x - 2b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n 2 +--R (x + 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R 2b n x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 +--R (- 2b n - 1)x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (4b n + 1)x +--R Type: Expression(Integer) +--E 520 +)spool + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richtrig000-099.input.pdf b/src/axiom-website/CATS/richtrig000-099.input.pdf new file mode 100644 index 0000000..d5dae75 Binary files /dev/null and b/src/axiom-website/CATS/richtrig000-099.input.pdf differ diff --git a/src/axiom-website/CATS/richtrig100-199.input.pamphlet b/src/axiom-website/CATS/richtrig100-199.input.pamphlet new file mode 100644 index 0000000..5a2a090 --- /dev/null +++ b/src/axiom-website/CATS/richtrig100-199.input.pamphlet @@ -0,0 +1,15093 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richtrig100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig100-199.output +)spool richtrig100-199.output +)set message test on +)set message auto off +)clear all + +--S 1 of 504 +t0100:= x*sin(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (1) x sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 504 +r0100:= -1/4*x^2*(-b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-_ + 2+2*cos(a+b*log(c*x^n))^2)/(1+b^2*n^2) +--R +--R +--R (2) +--R 2 n n +--R - 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 n 2 2 2 2 +--R - 2x cos(b log(c x ) + a) + (b n + 2)x +--R / +--R 2 2 +--R 4b n + 4 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 504 +a0100:= integrate(t0100,x) +--R +--R +--R (3) +--R 2 +--R - 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 +--R - 2x cos(b n log(x) + b log(c) + a) + (b n + 2)x +--R / +--R 2 2 +--R 4b n + 4 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 504 +m0100:= a0100-r0100 +--R +--R +--R (4) +--R 2 n n 2 n 2 +--R b n x cos(b log(c x ) + a)sin(b log(c x ) + a) + x cos(b log(c x ) + a) +--R + +--R 2 +--R - b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R - x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R 2b n + 2 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 504 +d0100:= D(m0100,x) +--R +--R +--R (5) +--R 2 2 2 n - 1 n 2 +--R - b n x x sin(b log(c x ) + a) +--R + +--R n 2 n - 1 n n +--R (2b n x x - 2b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 2 n - 1 n 2 +--R (2x x + b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R b n x x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 +--R (- b n - 2)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (2b n + 2)x +--R Type: Expression(Integer) +--E 5 + +--S 6 of 504 +t0101:= x^2*sin(a+b*log(c*x^n))^2 +--R +--R +--R 2 n 2 +--R (6) x sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 504 +r0101:= -1/3*x^3*(-2*b^2*n^2+6*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))-_ + 9+9*cos(a+b*log(c*x^n))^2)/(9+4*b^2*n^2) +--R +--R +--R (7) +--R 3 n n +--R - 6b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 3 n 2 2 2 3 +--R - 9x cos(b log(c x ) + a) + (2b n + 9)x +--R / +--R 2 2 +--R 12b n + 27 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 504 +a0101:= integrate(t0101,x) +--R +--R +--R (8) +--R 3 +--R - 6b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 3 2 2 2 3 +--R - 9x cos(b n log(x) + b log(c) + a) + (2b n + 9)x +--R / +--R 2 2 +--R 12b n + 27 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 504 +m0101:= a0101-r0101 +--R +--R +--R (9) +--R 3 n n +--R 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 3 n 2 +--R 3x cos(b log(c x ) + a) +--R + +--R 3 +--R - 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 3 2 +--R - 3x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R 4b n + 9 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 504 +d0101:= D(m0101,x) +--R +--R +--R (10) +--R 2 2 3 n - 1 n 2 +--R - 2b n x x sin(b log(c x ) + a) +--R + +--R 2 n 3 n - 1 n n +--R (6b n x x - 6b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 n 2 2 3 n - 1 n 2 +--R (9x x + 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 2 n 2 +--R 2b n x x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 +--R (- 2b n - 9)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (4b n + 9)x +--R Type: Expression(Integer) +--E 10 + +--S 11 of 504 +t0102:= sin(a+b*log(c*x^n))^2/x^2 +--R +--R +--R n 2 +--R sin(b log(c x ) + a) +--R (11) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 504 +r0102:= -1/(1+4*b^2*n^2)/x*(2*b^2*n^2+2*b*n*cos(a+b*log(c*x^n))*_ + sin(a+b*log(c*x^n))+1-cos(a+b*log(c*x^n))^2) +--R +--R +--R (12) +--R n n n 2 +--R - 2b n cos(b log(c x ) + a)sin(b log(c x ) + a) + cos(b log(c x ) + a) +--R + +--R 2 2 +--R - 2b n - 1 +--R / +--R 2 2 +--R (4b n + 1)x +--R Type: Expression(Integer) +--E 12 + +--S 13 of 504 +a0102:= integrate(t0102,x) +--R +--R +--R (13) +--R - 2b n cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R cos(b n log(x) + b log(c) + a) - 2b n - 1 +--R / +--R 2 2 +--R (4b n + 1)x +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 504 +m0102:= a0102-r0102 +--R +--R +--R (14) +--R n n n 2 +--R 2b n cos(b log(c x ) + a)sin(b log(c x ) + a) - cos(b log(c x ) + a) +--R + +--R - 2b n cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 +--R cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R (4b n + 1)x +--R Type: Expression(Integer) +--E 14 + +--S 15 of 504 +d0102:= D(m0102,x) +--R +--R +--R (15) +--R 2 2 n - 1 n 2 +--R - 2b n x x sin(b log(c x ) + a) +--R + +--R n n - 1 n n +--R (- 2b n x + 2b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n 2 +--R (x + 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R 2b n x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 +--R (- 2b n - 1)x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (4b n + 1)x x +--R Type: Expression(Integer) +--E 15 + +--S 16 of 504 +t0103:= x^m*sin(a+b*log(c*x^n))^2 +--R +--R +--R m n 2 +--R (16) x sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 504 +r0103:= 2*b^2*n^2*x^(1+m)/(1+m)/((1+m)^2+4*b^2*n^2)-_ + 2*b*n*x^(1+m)*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))/((1+m)^2+_ + 4*b^2*n^2)+(1+m)*x^(1+m)*sin(a+b*log(c*x^n))^2/((1+m)^2+4*b^2*n^2) +--R +--R +--R (17) +--R 2 m + 1 n 2 +--R (m + 2m + 1)x sin(b log(c x ) + a) +--R + +--R m + 1 n n 2 2 m + 1 +--R (- 2b m - 2b)n x cos(b log(c x ) + a)sin(b log(c x ) + a) + 2b n x +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n + m + 3m + 3m + 1 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 504 +a0103:= integrate(t0103,x) +--R +--R +--R (18) +--R m log(x) +--R (- 2b m - 2b)n x cos(b n log(x) + b log(c) + a)%e +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- m - 2m - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (2b n + m + 2m + 1)x +--R * +--R m log(x) +--R %e +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n + m + 3m + 3m + 1 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 504 +m0103:= a0103-r0103 +--R +--R +--R (19) +--R 2 m + 1 n 2 +--R (- m - 2m - 1)x sin(b log(c x ) + a) +--R + +--R m + 1 n n +--R (2b m + 2b)n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R m log(x) +--R (- 2b m - 2b)n x cos(b n log(x) + b log(c) + a)%e +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R (- m - 2m - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (2b n + m + 2m + 1)x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m + 1 +--R - 2b n x +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n + m + 3m + 3m + 1 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 504 +d0103:= D(m0103,x) +--R +--R +--R (20) +--R 2 m n 2 2 m + 1 n - 1 n 2 +--R ((- m - 2m - 1)x x - 2b n x x )sin(b log(c x ) + a) +--R + +--R m n m + 1 n - 1 n +--R ((2b m + 2b)n x x + (- 2b m - 2b)n x x )cos(b log(c x ) + a) +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 2 2 m + 1 n - 1 n 2 +--R 2b n x x cos(b log(c x ) + a) +--R + +--R 2 2 n m log(x) 2 +--R 2b n x %e sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 +--R (- 2b n - m - 2m - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n +--R (2b n + m + 2m + 1)x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m n +--R - 2b n x x +--R / +--R 2 2 2 n +--R (4b n + m + 2m + 1)x +--R Type: Expression(Integer) +--E 20 + +--S 21 of 504 +t0104:= sin(a+b*log(c*x^n))^3 +--R +--R +--R n 3 +--R (21) sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 504 +r0104:= -6*b^3*n^3*x*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)+_ + 6*b^2*n^2*x*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)-_ + 3*b*n*x*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(1+9*b^2*n^2)+_ + x*sin(a+b*log(c*x^n))^3/(1+9*b^2*n^2) +--R +--R +--R (22) +--R 2 2 n 3 +--R (b n + 1)x sin(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (- 3b n - 3b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R 6b n x sin(b log(c x ) + a) - 6b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 9b n + 10b n + 1 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 504 +a0104:= integrate(t0104,x) +--R +--R +--R (23) +--R 2 2 2 2 2 +--R ((- b n - 1)x cos(b n log(x) + b log(c) + a) + (7b n + 1)x) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n + 3b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 9b n - 3b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 10b n + 1 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 504 +m0104:= a0104-r0104 +--R +--R +--R (24) +--R 2 2 n 3 +--R (- b n - 1)x sin(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (3b n + 3b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R - 6b n x sin(b log(c x ) + a) + 6b n x cos(b log(c x ) + a) +--R + +--R 2 2 2 2 2 +--R ((- b n - 1)x cos(b n log(x) + b log(c) + a) + (7b n + 1)x) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n + 3b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 9b n - 3b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 10b n + 1 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 504 +d0104:= D(m0104,x) +--R +--R +--R (25) +--R 2 2 n 4 4 2 2 n - 1 n 3 +--R ((- b n - 1)x + (- 3b n - 3b n )x x )sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R ((3b n + 3b n)x + (- 3b n - 3b n)x x )cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 4 4 2 2 n - 1 n 2 2 2 n +--R (6b n + 6b n )x x cos(b log(c x ) + a) - 6b n x +--R + +--R 4 4 n - 1 +--R - 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R (6b n x - 6b n x x )cos(b log(c x ) + a) +--R + +--R 3 3 n +--R (2b n + 2b n)x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 2 +--R (- 9b n - 10b n - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (9b n + 10b n + 1)x +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 n 3 +--R (2b n + 2b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 n +--R (- 2b n - 2b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (9b n + 10b n + 1)x +--R Type: Expression(Integer) +--E 25 + +--S 26 of 504 +t0105:= x*sin(a+b*log(c*x^n))^3 +--R +--R +--R n 3 +--R (26) x sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 504 +r0105:= -6*b^3*n^3*x^2*cos(a+b*log(c*x^n))/(4+b^2*n^2)/(4+9*b^2*n^2)+_ + 12*b^2*n^2*x^2*sin(a+b*log(c*x^n))/(4+b^2*n^2)/(4+9*b^2*n^2)-_ + 3*b*n*x^2*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(4+9*b^2*n^2)+_ + 2*x^2*sin(a+b*log(c*x^n))^3/(4+9*b^2*n^2) +--R +--R +--R (27) +--R 2 2 2 n 3 +--R (2b n + 8)x sin(b log(c x ) + a) +--R + +--R 3 3 2 n n 2 +--R (- 3b n - 12b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 2 n 3 3 2 n +--R 12b n x sin(b log(c x ) + a) - 6b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 9b n + 40b n + 16 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 504 +a0105:= integrate(t0105,x) +--R +--R +--R (28) +--R 2 2 2 2 2 2 2 +--R ((- 2b n - 8)x cos(b n log(x) + b log(c) + a) + (14b n + 8)x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n + 12b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 9b n - 12b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 40b n + 16 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 504 +m0105:= a0105-r0105 +--R +--R +--R (29) +--R 2 2 2 n 3 +--R (- 2b n - 8)x sin(b log(c x ) + a) +--R + +--R 3 3 2 n n 2 +--R (3b n + 12b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 2 n 3 3 2 n +--R - 12b n x sin(b log(c x ) + a) + 6b n x cos(b log(c x ) + a) +--R + +--R 2 2 2 2 2 2 2 +--R ((- 2b n - 8)x cos(b n log(x) + b log(c) + a) + (14b n + 8)x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n + 12b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 9b n - 12b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 40b n + 16 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 504 +d0105:= D(m0105,x) +--R +--R +--R (30) +--R 2 2 n 4 4 2 2 2 n - 1 n 3 +--R ((- 4b n - 16)x x + (- 3b n - 12b n )x x )sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 2 n - 1 n +--R ((6b n + 24b n)x x + (- 6b n - 24b n)x x )cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 4 4 2 2 2 n - 1 n 2 2 2 n +--R (6b n + 24b n )x x cos(b log(c x ) + a) - 24b n x x +--R + +--R 4 4 2 n - 1 +--R - 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 2 n - 1 n +--R (12b n x x - 12b n x x )cos(b log(c x ) + a) +--R + +--R 3 3 n +--R (4b n + 16b n)x x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 2 +--R (- 9b n - 40b n - 16)x x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (9b n + 40b n + 16)x x +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 n 3 +--R (4b n + 16b n)x x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 n +--R (- 4b n - 16b n)x x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (9b n + 40b n + 16)x +--R Type: Expression(Integer) +--E 30 + +--S 31 of 504 +t0106:= x^2*sin(a+b*log(c*x^n))^3 +--R +--R +--R 2 n 3 +--R (31) x sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 504 +r0106:= -2/3*b^3*n^3*x^3*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(9+b^2*n^2)+_ + 2*b^2*n^2*x^3*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(9+b^2*n^2)-_ + b*n*x^3*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(3+3*b^2*n^2)+_ + x^3*sin(a+b*log(c*x^n))^3/(3+3*b^2*n^2) +--R +--R +--R (32) +--R 2 2 3 n 3 +--R (b n + 9)x sin(b log(c x ) + a) +--R + +--R 3 3 3 n n 2 +--R (- b n - 9b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 3 n 3 3 3 n +--R 6b n x sin(b log(c x ) + a) - 2b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 3b n + 30b n + 27 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 504 +a0106:= integrate(t0106,x) +--R +--R +--R (33) +--R 2 2 3 2 2 2 3 +--R ((- b n - 9)x cos(b n log(x) + b log(c) + a) + (7b n + 9)x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 3 +--R (b n + 9b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (- 3b n - 9b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 3b n + 30b n + 27 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 504 +m0106:= a0106-r0106 +--R +--R +--R (34) +--R 2 2 3 n 3 +--R (- b n - 9)x sin(b log(c x ) + a) +--R + +--R 3 3 3 n n 2 +--R (b n + 9b n)x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 3 n 3 3 3 n +--R - 6b n x sin(b log(c x ) + a) + 2b n x cos(b log(c x ) + a) +--R + +--R 2 2 3 2 2 2 3 +--R ((- b n - 9)x cos(b n log(x) + b log(c) + a) + (7b n + 9)x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 3 +--R (b n + 9b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (- 3b n - 9b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 3b n + 30b n + 27 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 504 +d0106:= D(m0106,x) +--R +--R +--R (35) +--R 2 2 2 n 4 4 2 2 3 n - 1 n 3 +--R ((- 3b n - 27)x x + (- b n - 9b n )x x )sin(b log(c x ) + a) +--R + +--R 3 3 2 n 3 3 3 n - 1 n +--R ((3b n + 27b n)x x + (- 3b n - 27b n)x x )cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 4 4 2 2 3 n - 1 n 2 2 2 2 n +--R (2b n + 18b n )x x cos(b log(c x ) + a) - 18b n x x +--R + +--R 4 4 3 n - 1 +--R - 2b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 3 3 2 n 3 3 3 n - 1 n +--R (6b n x x - 6b n x x )cos(b log(c x ) + a) +--R + +--R 3 3 2 n +--R (2b n + 18b n)x x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 n 2 +--R (- 3b n - 30b n - 27)x x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 n +--R (3b n + 30b n + 27)x x +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 n 3 +--R (2b n + 18b n)x x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 n +--R (- 2b n - 18b n)x x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (3b n + 30b n + 27)x +--R Type: Expression(Integer) +--E 35 + +--S 36 of 504 +t0107:= sin(a+b*log(c*x^n))^3/x^2 +--R +--R +--R n 3 +--R sin(b log(c x ) + a) +--R (36) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 504 +r0107:= -6*b^3*n^3*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)/x-_ + 6*b^2*n^2*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)/x-_ + 3*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))^2/(1+9*b^2*n^2)/x-_ + sin(a+b*log(c*x^n))^3/(1+9*b^2*n^2)/x +--R +--R +--R (37) +--R 2 2 n 3 +--R (- b n - 1)sin(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (- 3b n - 3b n)cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R - 6b n sin(b log(c x ) + a) - 6b n cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R (9b n + 10b n + 1)x +--R Type: Expression(Integer) +--E 37 + +--S 38 of 504 +a0107:= integrate(t0107,x) +--R +--R +--R (38) +--R 2 2 2 2 2 +--R ((b n + 1)cos(b n log(x) + b log(c) + a) - 7b n - 1) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n + 3b n)cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 9b n - 3b n)cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R (9b n + 10b n + 1)x +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 504 +m0107:= a0107-r0107 +--R +--R +--R (39) +--R 2 2 n 3 +--R (b n + 1)sin(b log(c x ) + a) +--R + +--R 3 3 n n 2 +--R (3b n + 3b n)cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 2 n 3 3 n +--R 6b n sin(b log(c x ) + a) + 6b n cos(b log(c x ) + a) +--R + +--R 2 2 2 2 2 +--R ((b n + 1)cos(b n log(x) + b log(c) + a) - 7b n - 1) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 +--R (3b n + 3b n)cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R (- 9b n - 3b n)cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R (9b n + 10b n + 1)x +--R Type: Expression(Integer) +--E 39 + +--S 40 of 504 +d0107:= D(m0107,x) +--R +--R +--R (40) +--R 2 2 n 4 4 2 2 n - 1 n 3 +--R ((- b n - 1)x + (- 3b n - 3b n )x x )sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R ((- 3b n - 3b n)x + (3b n + 3b n)x x )cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 4 4 2 2 n - 1 n 2 2 2 n +--R (6b n + 6b n )x x cos(b log(c x ) + a) - 6b n x +--R + +--R 4 4 n - 1 +--R - 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n +--R (- 6b n x + 6b n x x )cos(b log(c x ) + a) +--R + +--R 3 3 n +--R (- 2b n - 2b n)x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 2 +--R (- 9b n - 10b n - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (9b n + 10b n + 1)x +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 n 3 +--R (- 2b n - 2b n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 n +--R (2b n + 2b n)x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 n +--R (9b n + 10b n + 1)x x +--R Type: Expression(Integer) +--E 40 + +--S 41 of 504 +t0108:= x^m*sin(a+b*log(c*x^n))^3 +--R +--R +--R m n 3 +--R (41) x sin(b log(c x ) + a) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 504 +r0108:= -6*b^3*n^3*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)/((1+m)^2+_ + 9*b^2*n^2)+6*b^2*(1+m)*n^2*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+_ + b^2*n^2)/((1+m)^2+9*b^2*n^2)-3*b*n*x^(1+m)*cos(a+b*log(c*x^n))*_ + sin(a+b*log(c*x^n))^2/((1+m)^2+9*b^2*n^2)+(1+m)*x^(1+m)*_ + sin(a+b*log(c*x^n))^3/((1+m)^2+9*b^2*n^2) +--R +--R +--R (42) +--R 2 2 2 3 2 m + 1 n 3 +--R ((b m + b )n + m + 3m + 3m + 1)x sin(b log(c x ) + a) +--R + +--R 3 3 2 m + 1 n +--R (- 3b n + (- 3b m - 6b m - 3b)n)x cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 2 2 2 m + 1 n 3 3 m + 1 n +--R (6b m + 6b )n x sin(b log(c x ) + a) - 6b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 504 +a0108:= integrate(t0108,x) +--R +--R +--R (43) +--R 2 2 2 3 2 2 +--R ((- b m - b )n - m - 3m - 3m - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((7b m + 7b )n + m + 3m + 3m + 1)x +--R * +--R m log(x) +--R %e sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n + (3b m + 6b m + 3b)n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 9b n + (- 3b m - 6b m - 3b)n)x cos(b n log(x) + b log(c) + a) +--R * +--R m log(x) +--R %e +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 504 +m0108:= a0108-r0108 +--R +--R +--R (44) +--R 2 2 2 3 2 m + 1 n 3 +--R ((- b m - b )n - m - 3m - 3m - 1)x sin(b log(c x ) + a) +--R + +--R 3 3 2 m + 1 n +--R (3b n + (3b m + 6b m + 3b)n)x cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 2 2 2 m + 1 n +--R (- 6b m - 6b )n x sin(b log(c x ) + a) +--R + +--R 3 3 m + 1 n +--R 6b n x cos(b log(c x ) + a) +--R + +--R 2 2 2 3 2 2 +--R ((- b m - b )n - m - 3m - 3m - 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 +--R ((7b m + 7b )n + m + 3m + 3m + 1)x +--R * +--R m log(x) +--R %e sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 3 +--R (3b n + (3b m + 6b m + 3b)n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 2 +--R (- 9b n + (- 3b m - 6b m - 3b)n)x cos(b n log(x) + b log(c) + a) +--R * +--R m log(x) +--R %e +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 504 +d0108:= D(m0108,x) +--R +--R +--R (45) +--R 2 2 2 2 2 4 3 2 m n +--R ((- b m - 2b m - b )n - m - 4m - 6m - 4m - 1)x x +--R + +--R 4 4 2 2 2 2 2 m + 1 n - 1 +--R (- 3b n + (- 3b m - 6b m - 3b )n )x x +--R * +--R n 3 +--R sin(b log(c x ) + a) +--R + +--R 3 3 3 3 2 m n +--R ((3b m + 3b )n + (3b m + 9b m + 9b m + 3b)n)x x +--R + +--R 3 3 3 3 2 m + 1 n - 1 +--R ((- 3b m - 3b )n + (- 3b m - 9b m - 9b m - 3b)n)x x +--R * +--R n n 2 +--R cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 4 4 2 2 2 2 2 m + 1 n - 1 n 2 +--R (6b n + (6b m + 12b m + 6b )n )x x cos(b log(c x ) + a) +--R + +--R 2 2 2 2 2 m n 4 4 m + 1 n - 1 +--R (- 6b m - 12b m - 6b )n x x - 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 3 3 3 m n 3 3 3 m + 1 n - 1 n +--R ((6b m + 6b )n x x + (- 6b m - 6b )n x x )cos(b log(c x ) + a) +--R + +--R 3 3 3 3 2 n +--R ((2b m + 2b )n + (2b m + 6b m + 6b m + 2b)n)x +--R * +--R m log(x) 2 +--R cos(b n log(x) + b log(c) + a)%e sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 n +--R (- 9b n + (- 10b m - 20b m - 10b )n - m - 4m - 6m - 4m - 1)x +--R * +--R 2 +--R cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 n +--R (9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1)x +--R * +--R m log(x) +--R %e sin(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 3 2 n +--R ((2b m + 2b )n + (2b m + 6b m + 6b m + 2b)n)x +--R * +--R 3 +--R cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 3 3 2 n +--R ((- 2b m - 2b )n + (- 2b m - 6b m - 6b m - 2b)n)x +--R * +--R cos(b n log(x) + b log(c) + a) +--R * +--R m log(x) +--R %e +--R / +--R 4 4 2 2 2 2 2 4 3 2 n +--R (9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1)x +--R Type: Expression(Integer) +--E 45 + +--S 46 of 504 +t0109:= sin(log(9+17*x)) +--R +--R +--R (46) sin(log(17x + 9)) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 504 +r0109:= -1/34*(9+17*x)*(cos(log(9+17*x))-sin(log(9+17*x))) +--R +--R +--R (17x + 9)sin(log(17x + 9)) + (- 17x - 9)cos(log(17x + 9)) +--R (47) --------------------------------------------------------- +--R 34 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 504 +a0109:= integrate(t0109,x) +--R +--R +--R (17x + 9)sin(log(17x + 9)) + (- 17x - 9)cos(log(17x + 9)) +--R (48) --------------------------------------------------------- +--R 34 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 504 +m0109:= a0109-r0109 +--R +--R +--R (49) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 504 +d0109:= D(m0109,x) +--R +--R +--R (50) 0 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 504 +t0110:= cos(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (51) \|cos(b x + a) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 504 +r0110:= 2*EllipticE(1/2*a+1/2*b*x,2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 504 +a0110:= integrate(t0110,x) +--R +--R +--R x +--R ++ +-------------+ +--R (52) | \|cos(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 504 +--m0110:= a0110-r0110 +--E 54 + +--S 55 of 504 +--d0110:= D(m0110,x) +--E 55 + +--S 56 of 504 +t0111:= cos(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (53) cos(b x + a)\|cos(b x + a) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 504 +r0111:= 2/3*(EllipticF(1/2*a+1/2*b*x,2)+cos(a+b*x)^(1/2)*sin(a+b*x))/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 504 +a0111:= integrate(t0111,x) +--R +--R +--R x +--R ++ +-------------+ +--R (54) | cos(%H b + a)\|cos(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 504 +--m0111:= a0111-r0111 +--E 59 + +--S 60 of 504 +--d0111:= D(m0111,x) +--E 60 + +--S 61 of 504 +t0112:= cos(a+b*x)^(5/2) +--R +--R +--R 2 +------------+ +--R (55) cos(b x + a) \|cos(b x + a) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 504 +r0112:= 2/5*(3*EllipticE(1/2*a+1/2*b*x,2)+cos(a+b*x)^(3/2)*sin(a+b*x))/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 504 +a0112:= integrate(t0112,x) +--R +--R +--R x +--R ++ 2 +-------------+ +--R (56) | cos(%H b + a) \|cos(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 504 +--m0112:= a0112-r0112 +--E 64 + +--S 65 of 504 +--d0112:= D(m0112,x) +--E 65 + +--S 66 of 504 +t0113:= 1/cos(a+b*x)^(1/2) +--R +--R +--R 1 +--R (57) --------------- +--R +------------+ +--R \|cos(b x + a) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 504 +r0113:= 2*EllipticF(1/2*a+1/2*b*x,2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 of 504 +a0113:= integrate(t0113,x) +--R +--R +--R x +--R ++ 1 +--R (58) | ---------------- d%H +--R ++ +-------------+ +--R \|cos(%H b + a) +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 504 +--m0113:= a0113-r0113 +--E 69 + +--S 70 of 504 +--d0113:= D(m0113,x) +--E 70 + +--S 71 of 504 +t0114:= 1/cos(a+b*x)^(3/2) +--R +--R +--R 1 +--R (59) --------------------------- +--R +------------+ +--R cos(b x + a)\|cos(b x + a) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 504 +r0114:= -2*EllipticE(1/2*a+1/2*b*x,2)/b+2*sin(a+b*x)/b/cos(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 72 + +--S 73 of 504 +a0114:= integrate(t0114,x) +--R +--R +--R x +--R ++ 1 +--R (60) | ----------------------------- d%H +--R ++ +-------------+ +--R cos(%H b + a)\|cos(%H b + a) +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 504 +--m0114:= a0114-r0114 +--E 74 + +--S 75 of 504 +--d0114:= D(m0114,x) +--E 75 + +--S 76 of 504 +t0115:= 1/cos(a+b*x)^(5/2) +--R +--R +--R 1 +--R (61) ---------------------------- +--R 2 +------------+ +--R cos(b x + a) \|cos(b x + a) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 504 +r0115:= 2/3*EllipticF(1/2*a+1/2*b*x,2)/b+2/3*sin(a+b*x)/b/cos(a+b*x)^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 504 +a0115:= integrate(t0115,x) +--R +--R +--R x +--R ++ 1 +--R (62) | ------------------------------ d%H +--R ++ 2 +-------------+ +--R cos(%H b + a) \|cos(%H b + a) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 504 +--m0115:= a0115-r0115 +--E 79 + +--S 80 of 504 +--d0115:= D(m0115,x) +--E 80 + +--S 81 of 504 +t0116:= (a*cos(x))^(1/2) +--R +--R +--R +--------+ +--R (63) \|a cos(x) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 504 +r0116:= 2*(a*cos(x))^(1/2)*EllipticE(1/2*x,2)/cos(x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 504 +a0116:= integrate(t0116,x) +--R +--R +--R x +--R ++ +---------+ +--R (64) | \|a cos(%H) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 504 +--m0116:= a0116-r0116 +--E 84 + +--S 85 of 504 +--d0116:= D(m0116,x) +--E 85 + +--S 86 of 504 +t0117:= (a*cos(x)^3)^(1/2) +--R +--R +--R +---------+ +--R | 3 +--R (65) \|a cos(x) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 504 +r0117:= 2/3*(a*cos(x)^3)^(1/2)*_ + (EllipticF(1/2*x,2)+cos(x)^(1/2)*sin(x))/cos(x)^(3/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 504 +a0117:= integrate(t0117,x) +--R +--R +--R x +----------+ +--R ++ | 3 +--R (66) | \|a cos(%H) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 504 +--m0117:= a0117-r0117 +--E 89 + +--S 90 of 504 +--d0117:= D(m0117,x) +--E 90 + +--S 91 of 504 +t0118:= (a*cos(x))^(3/2) +--R +--R +--R +--------+ +--R (67) a cos(x)\|a cos(x) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 504 +r0118:= 2/3*a^2*(cos(x)^(1/2)*_ + EllipticF(1/2*x,2)+cos(x)*sin(x))/(a*cos(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 504 +a0118:= integrate(t0118,x) +--R +--R +--R x +--R ++ +---------+ +--R (68) | a cos(%H)\|a cos(%H) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 504 +--m0118:= a0118-r0118 +--E 94 + +--S 95 of 504 +--d0118:= D(m0118,x) +--E 95 + +--S 96 of 504 +t0119:= (a*cos(x)^3)^(3/2) +--R +--R +--R +---------+ +--R 3 | 3 +--R (69) a cos(x) \|a cos(x) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 504 +r0119:= 2/45*a*(a*cos(x)^3)^(1/2)*_ + (21*EllipticE(1/2*x,2)+7*cos(x)^(3/2)*sin(x)+_ + 5*cos(x)^(7/2)*sin(x))/cos(x)^(3/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 504 +a0119:= integrate(t0119,x) +--R +--R +--R x +----------+ +--R ++ 3 | 3 +--R (70) | a cos(%H) \|a cos(%H) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 504 +--m0119:= a0119-r0119 +--E 99 + +--S 100 of 504 +--d0119:= D(m0119,x) +--E 100 + +--S 101 of 504 +t0120:= 1/(a*cos(x))^(1/2) +--R +--R +--R 1 +--R (71) ----------- +--R +--------+ +--R \|a cos(x) +--R Type: Expression(Integer) +--E 101 + +--S 102 of 504 +r0120:= 2*cos(x)^(1/2)*EllipticF(1/2*x,2)/(a*cos(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 504 +a0120:= integrate(t0120,x) +--R +--R +--R x +--R ++ 1 +--R (72) | ------------ d%H +--R ++ +---------+ +--R \|a cos(%H) +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 504 +--m0120:= a0120-r0120 +--E 104 + +--S 105 of 504 +--d0120:= D(m0120,x) +--E 105 + +--S 106 of 504 +t0121:= 1/(a*cos(x)^2)^(1/2) +--R +--R +--R 1 +--R (73) ------------ +--R +---------+ +--R | 2 +--R \|a cos(x) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 504 +r0121:= atanh(sin(x))*cos(x)/(a*cos(x)^2)^(1/2) +--R +--R +--R cos(x)atanh(sin(x)) +--R (74) ------------------- +--R +---------+ +--R | 2 +--R \|a cos(x) +--R Type: Expression(Integer) +--E 107 + +--S 108 of 504 +a0121:= integrate(t0121,x) +--R +--R +--R +---+ +-+ +--R sin(x) - cos(x) - 1 sin(x)\|- a \|a +--R log(-------------------) 2atan(----------------) +--R sin(x) + cos(x) + 1 a cos(x) + a +--R (75) [------------------------,- -----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 108 + +--S 109 of 504 +m0121a:= a0121.1-r0121 +--R +--R +--R +---------+ +--R sin(x) - cos(x) - 1 | 2 +-+ +--R log(-------------------)\|a cos(x) - cos(x)\|a atanh(sin(x)) +--R sin(x) + cos(x) + 1 +--R (76) -------------------------------------------------------------- +--R +---------+ +--R +-+ | 2 +--R \|a \|a cos(x) +--R Type: Expression(Integer) +--E 109 + +--S 110 of 504 +d0121a:= D(m0121a,x) +--R +--R +--R (77) +--R 4 2 2 2 +-+ +--R (2sin(x) + (2cos(x) + 2cos(x) - 2)sin(x) - 2cos(x) - 2cos(x))\|a +--R * +--R +---------+ +--R | 2 +--R \|a cos(x) +--R + +--R 2 2 4 3 2 +--R a cos(x) sin(x) - a cos(x) - 2a cos(x) - a cos(x) +--R / +--R 4 2 2 2 +--R a sin(x) + (- a cos(x) - 2a cos(x) - 2a)sin(x) + a cos(x) +--R + +--R 2a cos(x) + a +--R * +--R +---------+ +--R | 2 +--R \|a cos(x) +--R Type: Expression(Integer) +--E 110 + +--S 111 of 504 +m0121b:= a0121.2-r0121 +--R +--R +--R +---+ +-+ +---------+ +--R sin(x)\|- a \|a | 2 +---+ +--R - 2atan(----------------)\|a cos(x) - cos(x)\|- a atanh(sin(x)) +--R a cos(x) + a +--R (78) ----------------------------------------------------------------- +--R +---------+ +--R +---+ | 2 +--R \|- a \|a cos(x) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 504 +d0121b:= D(m0121b,x) +--R +--R +--R (79) +--R 4 2 2 2 +-+ +--R (2sin(x) + (2cos(x) + 2cos(x) - 2)sin(x) - 2cos(x) - 2cos(x))\|a +--R * +--R +---------+ +--R | 2 +--R \|a cos(x) +--R + +--R 2 2 4 3 2 +--R a cos(x) sin(x) - a cos(x) - 2a cos(x) - a cos(x) +--R / +--R 4 2 2 2 +--R a sin(x) + (- a cos(x) - 2a cos(x) - 2a)sin(x) + a cos(x) +--R + +--R 2a cos(x) + a +--R * +--R +---------+ +--R | 2 +--R \|a cos(x) +--R Type: Expression(Integer) +--E 112 + +--S 113 of 504 +t0122:= 1/(a*cos(x)^3)^(1/2) +--R +--R +--R 1 +--R (80) ------------ +--R +---------+ +--R | 3 +--R \|a cos(x) +--R Type: Expression(Integer) +--E 113 + +--S 114 of 504 +r0122:= -2*cos(x)*(cos(x)^(1/2)*EllipticE(1/2*x,2)-sin(x))/(a*cos(x)^3)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 114 + +--S 115 of 504 +a0122:= integrate(t0122,x) +--R +--R +--R x +--R ++ 1 +--R (81) | ------------- d%H +--R ++ +----------+ +--R | 3 +--R \|a cos(%H) +--R Type: Union(Expression(Integer),...) +--E 115 + +--S 116 of 504 +--m0122:= a0122-r0122 +--E 116 + +--S 117 of 504 +--d0122:= D(m0122,x) +--E 117 + +--S 118 of 504 +t0123:= 1/(a+b*cos(c+d*x))^4 +--R +--R +--R (82) +--R 1 +--R / +--R 4 4 3 3 2 2 2 +--R b cos(d x + c) + 4a b cos(d x + c) + 6a b cos(d x + c) +--R + +--R 3 4 +--R 4a b cos(d x + c) + a +--R Type: Expression(Integer) +--E 118 + +--S 119 of 504 +r0123:= a*(2*a^2+3*b^2)*atan((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/_ + (a^2-b^2)^(7/2)/d-1/3*b*sin(c+d*x)/(a^2-b^2)/d/_ + (a+b*cos(c+d*x))^3-5/6*a*b*sin(c+d*x)/(a^2-b^2)^2/d/_ + (a+b*cos(c+d*x))^2-1/6*b*(11*a^2+4*b^2)*sin(c+d*x)/_ + (a^2-b^2)^3/d/(a+b*cos(c+d*x)) +--R +--R +--R (83) +--R 5 3 3 3 2 4 4 2 2 +--R (18a b + 12a b )cos(d x + c) + (54a b + 36a b )cos(d x + c) +--R + +--R 3 3 5 4 2 6 +--R (54a b + 36a b)cos(d x + c) + 18a b + 12a +--R * +--R d x + c +--R (b - a)tan(-------) +--R 2 +--R atan(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 2 4 3 2 5 +--R (4b + 11a b )cos(d x + c) + (3a b + 27a b )cos(d x + c) + 2b +--R + +--R 2 3 4 +--R - 5a b + 18a b +--R * +--R +---------+ +--R | 2 2 +--R sin(d x + c)\|- b + a +--R / +--R 9 2 7 4 5 6 3 3 +--R (6b - 18a b + 18a b - 6a b )d cos(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cos(d x + c) +--R + +--R 2 7 4 5 6 3 8 +--R (18a b - 54a b + 54a b - 18a b)d cos(d x + c) +--R + +--R 3 6 5 4 7 2 9 +--R (6a b - 18a b + 18a b - 6a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 119 + +--S 120 of 504 +a0123:= integrate(t0123,x) +--R +--R +--R (84) +--R [ +--R 5 3 3 3 2 4 4 2 2 +--R (9a b + 6a b )cos(d x + c) + (27a b + 18a b )cos(d x + c) +--R + +--R 3 3 5 4 2 6 +--R (27a b + 18a b)cos(d x + c) + 9a b + 6a +--R * +--R +-------+ +--R | 2 2 2 2 +--R (- a cos(d x + c) - b)\|b - a + (b - a )sin(d x + c) +--R log(--------------------------------------------------------) +--R b cos(d x + c) + a +--R + +--R 5 2 3 2 4 3 2 5 +--R (4b + 11a b )cos(d x + c) + (3a b + 27a b )cos(d x + c) + 2b +--R + +--R 2 3 4 +--R - 5a b + 18a b +--R * +--R +-------+ +--R | 2 2 +--R sin(d x + c)\|b - a +--R / +--R 9 2 7 4 5 6 3 3 +--R (6b - 18a b + 18a b - 6a b )d cos(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cos(d x + c) +--R + +--R 2 7 4 5 6 3 8 +--R (18a b - 54a b + 54a b - 18a b)d cos(d x + c) +--R + +--R 3 6 5 4 7 2 9 +--R (6a b - 18a b + 18a b - 6a )d +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 5 3 3 3 2 4 4 2 2 +--R (- 18a b - 12a b )cos(d x + c) + (- 54a b - 36a b )cos(d x + c) +--R + +--R 3 3 5 4 2 6 +--R (- 54a b - 36a b)cos(d x + c) - 18a b - 12a +--R * +--R +---------+ +--R | 2 2 +--R sin(d x + c)\|- b + a +--R atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R + +--R 5 2 3 2 4 3 2 5 +--R (4b + 11a b )cos(d x + c) + (3a b + 27a b )cos(d x + c) + 2b +--R + +--R 2 3 4 +--R - 5a b + 18a b +--R * +--R +---------+ +--R | 2 2 +--R sin(d x + c)\|- b + a +--R / +--R 9 2 7 4 5 6 3 3 +--R (6b - 18a b + 18a b - 6a b )d cos(d x + c) +--R + +--R 8 3 6 5 4 7 2 2 +--R (18a b - 54a b + 54a b - 18a b )d cos(d x + c) +--R + +--R 2 7 4 5 6 3 8 +--R (18a b - 54a b + 54a b - 18a b)d cos(d x + c) +--R + +--R 3 6 5 4 7 2 9 +--R (6a b - 18a b + 18a b - 6a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 120 + +--S 121 of 504 +m0123a:= a0123.1-r0123 +--R +--R +--R (85) +--R +---------+ +--R 2 3 | 2 2 +--R (3a b + 2a )\|- b + a +--R * +--R +-------+ +--R | 2 2 2 2 +--R (- a cos(d x + c) - b)\|b - a + (b - a )sin(d x + c) +--R log(--------------------------------------------------------) +--R b cos(d x + c) + a +--R + +--R d x + c +--R +-------+ (b - a)tan(-------) +--R 2 3 | 2 2 2 +--R (- 6a b - 4a )\|b - a atan(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 6 2 4 4 2 6 | 2 2 | 2 2 +--R (2b - 6a b + 6a b - 2a )d\|- b + a \|b - a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 504 +d0123a:= D(m0123a,x) +--R +--R +--R (86) +--R 4 2 3 3 2 4 2 +--R (- 3a b + 3a b - 2a b + 2a b)sin(d x + c) +--R + +--R 4 3 2 2 +--R (- 3a b - 2a b )cos(d x + c) +--R + +--R 4 2 3 3 2 4 2 3 4 +--R (- 3a b - 3a b - 2a b - 2a b)cos(d x + c) - 3a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 4 2 3 3 2 4 2 +--R (3a b + 3a b + 2a b + 2a b)sin(d x + c) +--R + +--R 4 3 2 2 +--R (3a b + 2a b )cos(d x + c) +--R + +--R 4 2 3 3 2 4 2 3 4 +--R (- 3a b + 3a b - 2a b + 2a b)cos(d x + c) - 3a b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 3 3 5 5 3 3 5 +--R ((3a b - a b - 2a b)cos(d x + c) + 3a b - a b - 2a b)sin(d x + c) +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 5 3 3 5 5 3 3 5 +--R ((3a b - a b - 2a b)cos(d x + c) - 3a b + a b + 2a b)sin(d x + c) +--R / +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (2a b - 2a b - 6a b + 6a b + 6a b - 6a b - 2a b + 2a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 9 8 2 7 3 6 6 3 7 2 8 9 +--R (2b - 2a b - 4a b + 4a b + 4a b - 4a b - 2a b + 2a ) +--R * +--R cos(d x + c) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R 2a b - 2a b - 6a b + 6a b + 6a b - 6a b - 2a b + 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (- 2a b - 2a b + 6a b + 6a b - 6a b - 6a b + 2a b + 2a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 9 8 2 7 3 6 6 3 7 2 8 9 +--R (- 2b - 2a b + 4a b + 4a b - 4a b - 4a b + 2a b + 2a ) +--R * +--R cos(d x + c) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R - 2a b - 2a b + 6a b + 6a b - 6a b - 6a b + 2a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 2b + 2a b + 8a b - 8a b - 12a b + 12a b + 8a b - 8a b +--R + +--R 8 2 9 +--R - 2a b + 2a b +--R * +--R cos(d x + c) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 2a b + 2a b + 8a b - 8a b - 12a b + 12a b + 8a b - 8a b +--R + +--R 9 10 +--R - 2a b + 2a +--R * +--R d x + c 2 +--R sin(d x + c)tan(-------) +--R 2 +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 2b + 2a b - 8a b - 8a b + 12a b + 12a b - 8a b - 8a b +--R + +--R 8 2 9 +--R 2a b + 2a b +--R * +--R cos(d x + c) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 2a b + 2a b - 8a b - 8a b + 12a b + 12a b - 8a b - 8a b +--R + +--R 9 10 +--R 2a b + 2a +--R * +--R sin(d x + c) +--R Type: Expression(Integer) +--E 122 + +--S 123 of 504 +m0123b:= a0123.2-r0123 +--R +--R +--R (87) +--R +---------+ +--R | 2 2 +--R 2 3 sin(d x + c)\|- b + a +--R (- 3a b - 2a )atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R + +--R d x + c +--R (b - a)tan(-------) +--R 2 3 2 +--R (- 3a b - 2a )atan(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 6 2 4 4 2 6 | 2 2 +--R (b - 3a b + 3a b - a )d\|- b + a +--R Type: Expression(Integer) +--E 123 + +--S 124 of 504 +d0123b:= D(m0123b,x) +--R +--R +--R (88) +--R 3 2 2 3 4 2 +--R (3a b - 3a b + 2a b - 2a )sin(d x + c) +--R + +--R 3 2 2 3 4 2 +--R (9a b - 3a b + 6a b - 2a )cos(d x + c) +--R + +--R 3 3 3 2 2 3 4 +--R (12a b + 8a b)cos(d x + c) + 3a b + 3a b + 2a b + 2a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 2 2 3 4 2 +--R (- 9a b - 3a b - 6a b - 2a )sin(d x + c) +--R + +--R 3 2 2 3 4 2 3 2 2 3 4 +--R (- 3a b - 3a b - 2a b - 2a )cos(d x + c) + 3a b + 3a b + 2a b + 2a +--R / +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (2b - 4a b - 4a b + 12a b - 12a b + 4a b + 4a b - 2a ) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- 2b + 8a b - 12a b + 8a b - 2a )cos(d x + c) +--R + +--R 8 2 6 4 4 6 2 8 8 2 6 +--R (- 4b + 16a b - 24a b + 16a b - 4a )cos(d x + c) - 2b + 8a b +--R + +--R 4 4 6 2 8 +--R - 12a b + 8a b - 2a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- 2b + 8a b - 12a b + 8a b - 2a )sin(d x + c) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a )cos(d x + c) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R (4b + 8a b - 8a b - 24a b + 24a b + 8a b - 8a b - 4a )cos(d x + c) +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 +--R 2b + 4a b - 4a b - 12a b + 12a b + 4a b - 4a b - 2a +--R Type: Expression(Integer) +--E 124 + +--S 125 of 504 +t0124:= (a+b*cos(c+d*x))^(1/2) +--R +--R +--R +------------------+ +--R (89) \|b cos(d x + c) + a +--R Type: Expression(Integer) +--E 125 + +--S 126 of 504 +r0124:= 2*(a+b*cos(c+d*x))^(1/2)*_ + EllipticE(1/2*c+1/2*d*x,2*b/(a+b))/d/((a+b*cos(c+d*x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 126 + +--S 127 of 504 +a0124:= integrate(t0124,x) +--R +--R +--R x +--R ++ +-------------------+ +--R (90) | \|b cos(%H d + c) + a d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 127 + +--S 128 of 504 +--m0124:= a0124-r0124 +--E 128 + +--S 129 of 504 +--d0124:= D(m0124,x) +--E 129 + +--S 130 of 504 +t0125:= 1/(a+b*cos(x))^(1/2) +--R +--R +--R 1 +--R (91) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression(Integer) +--E 130 + +--S 131 of 504 +r0125:= 2*((a+b*cos(x))/(a+b))^(1/2)*_ + EllipticF(1/2*x,2*b/(a+b))/(a+b*cos(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 131 + +--S 132 of 504 +a0125:= integrate(t0125,x) +--R +--R +--R x +--R ++ 1 +--R (92) | ---------------- d%H +--R ++ +-------------+ +--R \|b cos(%H) + a +--R Type: Union(Expression(Integer),...) +--E 132 + +--S 133 of 504 +--m0125:= a0125-r0125 +--E 133 + +--S 134 of 504 +--d0125:= D(m0125,x) +--E 134 + +--S 135 of 504 +t0126:= 1/(a+b*cos(x))^(3/2) +--R +--R +--R 1 +--R (93) ----------------------------- +--R +------------+ +--R (b cos(x) + a)\|b cos(x) + a +--R Type: Expression(Integer) +--E 135 + +--S 136 of 504 +r0126:= 2*(a+b*cos(x))^(1/2)*_ + EllipticE(1/2*x,2*b/(a+b))/(a^2-b^2)/((a+b*cos(x))/(a+b))^(1/2)-_ + 2*b*sin(x)/(a^2-b^2)/(a+b*cos(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 136 + +--S 137 of 504 +a0126:= integrate(t0126,x) +--R +--R +--R x +--R ++ 1 +--R (94) | ------------------------------- d%H +--R ++ +-------------+ +--R (b cos(%H) + a)\|b cos(%H) + a +--R Type: Union(Expression(Integer),...) +--E 137 + +--S 138 of 504 +--m0126:= a0126-r0126 +--E 138 + +--S 139 of 504 +--d0126:= D(m0126,x) +--E 139 + +--S 140 of 504 +t0127:= 1/(a+b*cos(x))^(5/2) +--R +--R +--R 1 +--R (95) --------------------------------------------- +--R 2 2 2 +------------+ +--R (b cos(x) + 2a b cos(x) + a )\|b cos(x) + a +--R Type: Expression(Integer) +--E 140 + +--S 141 of 504 +r0127:= 8/3*a*(a+b*cos(x))^(1/2)*EllipticE(1/2*x,2*b/(a+b))/_ + (a^2-b^2)^2/((a+b*cos(x))/(a+b))^(1/2)-_ + 2/3*((a+b*cos(x))/(a+b))^(1/2)*EllipticF(1/2*x,2*b/(a+b))/_ + (a^2-b^2)/(a+b*cos(x))^(1/2)-2/3*b*sin(x)/_ + (a^2-b^2)/(a+b*cos(x))^(3/2)-8/3*a*b*sin(x)/(a^2-b^2)^2/_ + (a+b*cos(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 141 + +--S 142 of 504 +a0127:= integrate(t0127,x) +--R +--R +--R x +--R ++ 1 +--R (96) | ------------------------------------------------ d%H +--R ++ 2 2 2 +-------------+ +--R (b cos(%H) + 2a b cos(%H) + a )\|b cos(%H) + a +--R Type: Union(Expression(Integer),...) +--E 142 + +--S 143 of 504 +--m0127:= a0127-r0127 +--E 143 + +--S 144 of 504 +--d0127:= D(m0127,x) +--E 144 + +--S 145 of 504 +t0128:= (a+a*cos(c+d*x))^(1/2) +--R +--R +--R +------------------+ +--R (97) \|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 145 + +--S 146 of 504 +r0128:= 2*a*sin(c+d*x)/d/(a+a*cos(c+d*x))^(1/2) +--R +--R +--R 2a sin(d x + c) +--R (98) ---------------------- +--R +------------------+ +--R d\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 504 +a0128:= integrate(t0128,x) +--R +--R +--R +------------------+ +--R 2sin(d x + c)\|a cos(d x + c) + a +--R (99) ---------------------------------- +--R d cos(d x + c) + d +--R Type: Union(Expression(Integer),...) +--E 147 + +--S 148 of 504 +m0128:= a0128-r0128 +--R +--R +--R (100) 0 +--R Type: Expression(Integer) +--E 148 + +--S 149 of 504 +d0128:= D(m0128,x) +--R +--R +--R (101) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 504 +t0129:= (a+a*cos(c+d*x))^(3/2) +--R +--R +--R +------------------+ +--R (102) (a cos(d x + c) + a)\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 504 +r0129:= 2/3*a^2*sin(c+d*x)*(5+cos(c+d*x))/(a*(1+cos(c+d*x)))^(1/2)/d +--R +--R +--R 2 2 +--R (2a cos(d x + c) + 10a )sin(d x + c) +--R (103) ------------------------------------ +--R +------------------+ +--R 3d\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 151 + +--S 152 of 504 +a0129:= integrate(t0129,x) +--R +--R +--R +------------------+ +--R (2a cos(d x + c) + 10a)sin(d x + c)\|a cos(d x + c) + a +--R (104) -------------------------------------------------------- +--R 3d cos(d x + c) + 3d +--R Type: Union(Expression(Integer),...) +--E 152 + +--S 153 of 504 +m0129:= a0129-r0129 +--R +--R +--R (105) 0 +--R Type: Expression(Integer) +--E 153 + +--S 154 of 504 +d0129:= D(m0129,x) +--R +--R +--R (106) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 504 +t0130:= (a+a*cos(c+d*x))^(5/2) +--R +--R +--R 2 2 2 2 +------------------+ +--R (107) (a cos(d x + c) + 2a cos(d x + c) + a )\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 155 + +--S 156 of 504 +r0130:= 2/15*a^3*sin(c+d*x)*(43+14*cos(c+d*x)+_ + 3*cos(c+d*x)^2)/(a*(1+cos(c+d*x)))^(1/2)/d +--R +--R +--R 3 2 3 3 +--R (6a cos(d x + c) + 28a cos(d x + c) + 86a )sin(d x + c) +--R (108) -------------------------------------------------------- +--R +------------------+ +--R 15d\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 504 +a0130:= integrate(t0130,x) +--R +--R +--R (109) +--R 2 2 2 2 +------------------+ +--R (6a cos(d x + c) + 28a cos(d x + c) + 86a )sin(d x + c)\|a cos(d x + c) + a +--R ----------------------------------------------------------------------------- +--R 15d cos(d x + c) + 15d +--R Type: Union(Expression(Integer),...) +--E 157 + +--S 158 of 504 +m0130:= a0130-r0130 +--R +--R +--R (110) 0 +--R Type: Expression(Integer) +--E 158 + +--S 159 of 504 +d0130:= D(m0130,x) +--R +--R +--R (111) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 504 +t0131:= 1/(a+a*cos(c+d*x))^(1/2) +--R +--R +--R 1 +--R (112) --------------------- +--R +------------------+ +--R \|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 160 + +--S 161 of 504 +r0131:= 2*atanh(sin(1/2*c+1/2*d*x))*cos(1/2*c+1/2*d*x)/d/_ + (a+a*cos(c+d*x))^(1/2) +--R +--R +--R d x + c d x + c +--R 2cos(-------)atanh(sin(-------)) +--R 2 2 +--R (113) -------------------------------- +--R +------------------+ +--R d\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 504 +a0131:= integrate(t0131,x) +--R +--R +--R (114) +--R [ +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R log +--R +-+ +--R |2 +------------------+ 2 +--R 2sin(d x + c) |- \|a cos(d x + c) + a - cos(d x + c) +--R \|a +--R + +--R 2cos(d x + c) + 3 +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R / +--R 2d +--R , +--R +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R log +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R / +--R +-+ +--R |2 +------------------+ 2 +--R 2sin(d x + c) |- \|a cos(d x + c) + a + cos(d x + c) +--R \|a +--R + +--R - 2cos(d x + c) - 3 +--R / +--R 2d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 162 + +--S 163 of 504 +m0131a:= a0131.1-r0131 +--R +--R +--R (115) +--R +-+ +--R |2 +------------------+ +--R |- \|a cos(d x + c) + a +--R \|a +--R * +--R log +--R +-+ +--R |2 +------------------+ 2 +--R 2sin(d x + c) |- \|a cos(d x + c) + a - cos(d x + c) +--R \|a +--R + +--R 2cos(d x + c) + 3 +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R + +--R d x + c d x + c +--R - 4cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R +------------------+ +--R 2d\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 163 + +--S 164 of 504 +d0131a:= D(m0131a,x) +--R +--R +--R (116) +--R d x + c d x + c 2 d x + c 2 +--R (2cos(-------)sin(-------) - 2cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (- 2cos(d x + c) - 2)sin(-------) +--R 2 +--R + +--R d x + c +--R (2cos(d x + c) + 2)sin(-------) +--R 2 +--R * +--R sin(d x + c) +--R * +--R +-+ +--R |2 d x + c +--R |- atanh(sin(-------)) +--R \|a 2 +--R + +--R d x + c 2 +--R (- 2cos(d x + c) - 2)sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 2cos(-------) + 2)cos(d x + c) - 2cos(-------) + 2 +--R 2 2 +--R * +--R +-+ +--R |2 +--R sin(d x + c) |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 d x + c +--R - cos(-------)cos(d x + c) + 2cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R 3cos(-------) +--R 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c +--R cos(-------)cos(d x + c) - 2cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R - 3cos(-------) +--R 2 +--R * +--R sin(d x + c) +--R + +--R 3 2 d x + c 3 +--R (cos(d x + c) - cos(d x + c) - 5cos(d x + c) - 3)sin(-------) +--R 2 +--R + +--R 3 2 d x + c +--R (- cos(d x + c) + cos(d x + c) + 5cos(d x + c) + 3)sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 2 +--R ((- 3cos(d x + c) - 3)sin(-------) + 3cos(d x + c) + 3)sin(d x + c) +--R 2 +--R + +--R 3 2 d x + c 2 +--R (- 2cos(d x + c) - 4cos(d x + c) - 2cos(d x + c))sin(-------) +--R 2 +--R + +--R d x + c 2 3 d x + c 2 2 +--R (cos(-------) + 2)cos(d x + c) + (- cos(-------) + 4)cos(d x + c) +--R 2 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 5cos(-------) + 2)cos(d x + c) - 3cos(-------) +--R 2 2 +--R / +--R 3 2 d x + c 2 +--R (cos(d x + c) - cos(d x + c) - 5cos(d x + c) - 3)sin(-------) +--R 2 +--R + +--R 3 2 +--R - cos(d x + c) + cos(d x + c) + 5cos(d x + c) + 3 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 2 d x + c 2 +--R (- 2a cos(d x + c) - 4a cos(d x + c) - 2a)sin(-------) +--R 2 +--R + +--R 2 +--R 2a cos(d x + c) + 4a cos(d x + c) + 2a +--R * +--R +-+ +--R |2 +--R sin(d x + c) |- +--R \|a +--R Type: Expression(Integer) +--E 164 + +--S 165 of 504 +m0131b:= a0131.2-r0131 +--R +--R +--R (117) +--R +-+ +--R |2 +------------------+ +--R |- \|a cos(d x + c) + a +--R \|a +--R * +--R log +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R / +--R +-+ +--R |2 +------------------+ 2 +--R 2sin(d x + c) |- \|a cos(d x + c) + a + cos(d x + c) +--R \|a +--R + +--R - 2cos(d x + c) - 3 +--R + +--R d x + c d x + c +--R - 4cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R +------------------+ +--R 2d\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 165 + +--S 166 of 504 +d0131b:= D(m0131b,x) +--R +--R +--R (118) +--R d x + c d x + c d x + c 2 +--R (- 4cos(-------)cos(d x + c) + 12cos(-------))sin(-------) +--R 2 2 2 +--R + +--R d x + c d x + c +--R 4cos(-------)cos(d x + c) - 12cos(-------) +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 d x + c 3 +--R (4cos(d x + c) - 8cos(d x + c) - 12)sin(-------) +--R 2 +--R + +--R 2 d x + c +--R (- 4cos(d x + c) + 8cos(d x + c) + 12)sin(-------) +--R 2 +--R * +--R sin(d x + c) +--R * +--R +-+ +--R |2 d x + c +--R |- atanh(sin(-------)) +--R \|a 2 +--R + +--R d x + c 2 3 +--R (- 6sin(-------) + 6)sin(d x + c) +--R 2 +--R + +--R 2 d x + c 2 +--R (- 2cos(d x + c) - 8cos(d x + c) - 6)sin(-------) +--R 2 +--R + +--R d x + c 2 2 +--R (4cos(-------) + 2)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 8cos(-------) + 8)cos(d x + c) - 12cos(-------) + 6 +--R 2 2 +--R * +--R sin(d x + c) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c d x + c 2 d x + c 3 +--R (- 8cos(-------)sin(-------) + 8cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (8cos(d x + c) + 8)sin(-------) +--R 2 +--R + +--R d x + c +--R (- 8cos(d x + c) - 8)sin(-------) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R d x + c 3 d x + c 2 +--R - cos(-------)cos(d x + c) + 5cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c d x + c +--R - 3cos(-------)cos(d x + c) - 9cos(-------) +--R 2 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 3 d x + c 2 +--R cos(-------)cos(d x + c) - 5cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c d x + c +--R 3cos(-------)cos(d x + c) + 9cos(-------) +--R 2 2 +--R * +--R sin(d x + c) +--R + +--R 4 3 2 +--R cos(d x + c) - 4cos(d x + c) - 2cos(d x + c) + 12cos(d x + c) +--R + +--R 9 +--R * +--R d x + c 3 +--R sin(-------) +--R 2 +--R + +--R 4 3 2 +--R - cos(d x + c) + 4cos(d x + c) + 2cos(d x + c) +--R + +--R - 12cos(d x + c) - 9 +--R * +--R d x + c +--R sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R 2 d x + c 2 +--R (- 3cos(d x + c) + 14cos(d x + c) + 17)sin(-------) +--R 2 +--R + +--R 2 d x + c 2 d x + c 2 +--R 3cos(d x + c) + (8cos(-------) - 14)cos(d x + c) + 8cos(-------) +--R 2 2 +--R + +--R - 17 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 3 2 +--R (- 2cos(d x + c) + 2cos(d x + c) + 10cos(d x + c) + 6cos(d x + c)) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 4 d x + c 2 3 +--R (cos(-------) + 2)cos(d x + c) + (- 4cos(-------) - 2)cos(d x + c) +--R 2 2 +--R + +--R d x + c 2 2 d x + c 2 +--R (- 2cos(-------) - 10)cos(d x + c) + (12cos(-------) - 6)cos(d x + c) +--R 2 2 +--R + +--R d x + c 2 +--R 9cos(-------) +--R 2 +--R / +--R d x + c 2 2 +--R ((8cos(d x + c) + 8)sin(-------) - 8cos(d x + c) - 8)sin(d x + c) +--R 2 +--R + +--R 4 3 2 +--R cos(d x + c) - 4cos(d x + c) - 2cos(d x + c) + 12cos(d x + c) +--R + +--R 9 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R 4 3 2 +--R - cos(d x + c) + 4cos(d x + c) + 2cos(d x + c) - 12cos(d x + c) - 9 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 3 2 +--R (4a cos(d x + c) - 4a cos(d x + c) - 20a cos(d x + c) - 12a) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R 3 2 +--R - 4a cos(d x + c) + 4a cos(d x + c) + 20a cos(d x + c) + 12a +--R * +--R +-+ +--R |2 +--R sin(d x + c) |- +--R \|a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 504 +t0132:= 1/(a+a*cos(c+d*x))^(3/2) +--R +--R +--R 1 +--R (119) ----------------------------------------- +--R +------------------+ +--R (a cos(d x + c) + a)\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 504 +r0132:= 1/2*atanh(sin(1/2*c+1/2*d*x))*_ + cos(1/2*c+1/2*d*x)/a/d/(a+a*cos(c+d*x))^(1/2)+_ + 1/2*sin(c+d*x)/d/(a+a*cos(c+d*x))^(3/2) +--R +--R +--R (120) +--R d x + c d x + c d x + c +--R (cos(-------)cos(d x + c) + cos(-------))atanh(sin(-------)) + sin(d x + c) +--R 2 2 2 +--R --------------------------------------------------------------------------- +--R +------------------+ +--R (2a d cos(d x + c) + 2a d)\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 168 + +--S 169 of 504 +a0132:= integrate(t0132,x) +--R +--R +--R (121) +--R [ +--R 2 +--+ +--R (cos(d x + c) + 2cos(d x + c) + 1)\|2a +--R * +--R log +--R +--+ +------------------+ 2 +--R 2sin(d x + c)\|2a \|a cos(d x + c) + a - a cos(d x + c) +--R + +--R 2a cos(d x + c) + 3a +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R + +--R +------------------+ +--R 4sin(d x + c)\|a cos(d x + c) + a +--R / +--R 2 2 2 2 +--R 8a d cos(d x + c) + 16a d cos(d x + c) + 8a d +--R , +--R +--R 2 +----+ +--R (- cos(d x + c) - 2cos(d x + c) - 1)\|- 2a +--R * +--R +----+ +------------------+ +--R sin(d x + c)\|- 2a \|a cos(d x + c) + a +--R atan(----------------------------------------) +--R 2a cos(d x + c) + 2a +--R + +--R +------------------+ +--R 2sin(d x + c)\|a cos(d x + c) + a +--R / +--R 2 2 2 2 +--R 4a d cos(d x + c) + 8a d cos(d x + c) + 4a d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 169 + +--S 170 of 504 +m0132a:= a0132.1-r0132 +--R +--R +--R (122) +--R +--+ +------------------+ +--R \|2a \|a cos(d x + c) + a +--R * +--R log +--R +--+ +------------------+ 2 +--R 2sin(d x + c)\|2a \|a cos(d x + c) + a - a cos(d x + c) +--R + +--R 2a cos(d x + c) + 3a +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R + +--R d x + c d x + c +--R - 4a cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R 2 +------------------+ +--R 8a d\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 170 + +--S 171 of 504 +d0132a:= D(m0132a,x) +--R +--R +--R (123) +--R d x + c d x + c 2 d x + c 2 +--R (2cos(-------)sin(-------) - 2cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (- 2cos(d x + c) - 2)sin(-------) +--R 2 +--R + +--R d x + c +--R (2cos(d x + c) + 2)sin(-------) +--R 2 +--R * +--R sin(d x + c) +--R * +--R +--+ d x + c +--R \|2a atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 +--R (- 2cos(d x + c) - 2)sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 2cos(-------) + 2)cos(d x + c) - 2cos(-------) + 2 +--R 2 2 +--R * +--R +--+ +--R sin(d x + c)\|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 d x + c +--R - a cos(-------)cos(d x + c) + 2a cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R 3a cos(-------) +--R 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c +--R a cos(-------)cos(d x + c) - 2a cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R - 3a cos(-------) +--R 2 +--R * +--R sin(d x + c) +--R + +--R 3 2 +--R (a cos(d x + c) - a cos(d x + c) - 5a cos(d x + c) - 3a) +--R * +--R d x + c 3 +--R sin(-------) +--R 2 +--R + +--R 3 2 +--R (- a cos(d x + c) + a cos(d x + c) + 5a cos(d x + c) + 3a) +--R * +--R d x + c +--R sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 +--R ((- 3a cos(d x + c) - 3a)sin(-------) + 3a cos(d x + c) + 3a) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 d x + c 2 +--R (- 2a cos(d x + c) - 4a cos(d x + c) - 2a cos(d x + c))sin(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (a cos(-------) + 2a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- a cos(-------) + 4a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 5a cos(-------) + 2a)cos(d x + c) - 3a cos(-------) +--R 2 2 +--R / +--R 2 3 2 2 2 2 +--R (4a cos(d x + c) - 4a cos(d x + c) - 20a cos(d x + c) - 12a ) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R 2 3 2 2 2 2 +--R - 4a cos(d x + c) + 4a cos(d x + c) + 20a cos(d x + c) + 12a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 2 2 2 2 d x + c 2 +--R (- 8a cos(d x + c) - 16a cos(d x + c) - 8a )sin(-------) +--R 2 +--R + +--R 2 2 2 2 +--R 8a cos(d x + c) + 16a cos(d x + c) + 8a +--R * +--R +--+ +--R sin(d x + c)\|2a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 504 +m0132b:= a0132.2-r0132 +--R +--R +--R (124) +--R - +--R +----+ +------------------+ +--R \|- 2a \|a cos(d x + c) + a +--R * +--R +----+ +------------------+ +--R sin(d x + c)\|- 2a \|a cos(d x + c) + a +--R atan(----------------------------------------) +--R 2a cos(d x + c) + 2a +--R + +--R d x + c d x + c +--R - 2a cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R 2 +------------------+ +--R 4a d\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 504 +d0132b:= D(m0132b,x) +--R +--R +--R (125) +--R d x + c d x + c 2 d x + c 3 +--R (- cos(-------)sin(-------) + cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (cos(d x + c) + 1)sin(-------) +--R 2 +--R + +--R d x + c +--R (- cos(d x + c) - 1)sin(-------) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R d x + c d x + c d x + c 2 +--R (2cos(-------)cos(d x + c) + 2cos(-------))sin(-------) +--R 2 2 2 +--R + +--R d x + c d x + c +--R - 2cos(-------)cos(d x + c) - 2cos(-------) +--R 2 2 +--R * +--R sin(d x + c) +--R + +--R 2 d x + c 3 +--R (- 2cos(d x + c) - 4cos(d x + c) - 2)sin(-------) +--R 2 +--R + +--R 2 d x + c +--R (2cos(d x + c) + 4cos(d x + c) + 2)sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- cos(d x + c) - 1)sin(-------) + (cos(-------) + 1)cos(d x + c) +--R 2 2 +--R + +--R d x + c 2 +--R cos(-------) + 1 +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 d x + c 2 +--R (- 2cos(d x + c) - 4cos(d x + c) - 2cos(d x + c))sin(-------) +--R 2 +--R + +--R 3 d x + c 2 2 +--R 2cos(d x + c) + (- 2cos(-------) + 4)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 4cos(-------) + 2)cos(d x + c) - 2cos(-------) +--R 2 2 +--R / +--R d x + c 2 +--R ((4a cos(d x + c) + 4a)sin(-------) - 4a cos(d x + c) - 4a) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 d x + c 2 +--R (- 8a cos(d x + c) - 16a cos(d x + c) - 8a)sin(-------) +--R 2 +--R + +--R 2 +--R 8a cos(d x + c) + 16a cos(d x + c) + 8a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 173 + +--S 174 of 504 +t0133:= 1/(a+a*cos(c+d*x))^(5/2) +--R +--R +--R 1 +--R (126) ------------------------------------------------------------- +--R 2 2 2 2 +------------------+ +--R (a cos(d x + c) + 2a cos(d x + c) + a )\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 174 + +--S 175 of 504 +r0133:= 3/16*atanh(sin(1/2*c+1/2*d*x))*cos(1/2*c+1/2*d*x)/a^2/d/_ + (a+a*cos(c+d*x))^(1/2)+1/4*sin(c+d*x)/d/_ + (a+a*cos(c+d*x))^(5/2)+3/16*sin(c+d*x)/a/d/(a+a*cos(c+d*x))^(3/2) +--R +--R +--R (127) +--R d x + c 2 d x + c +--R 3cos(-------)cos(d x + c) + 6cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R 3cos(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R (3cos(d x + c) + 7)sin(d x + c) +--R / +--R 2 2 2 2 +------------------+ +--R (16a d cos(d x + c) + 32a d cos(d x + c) + 16a d)\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 175 + +--S 176 of 504 +a0133:= integrate(t0133,x) +--R +--R +--R (128) +--R [ +--R 3 2 +--+ +--R (3cos(d x + c) + 9cos(d x + c) + 9cos(d x + c) + 3)\|2a +--R * +--R log +--R +--+ +------------------+ 2 +--R 2sin(d x + c)\|2a \|a cos(d x + c) + a - a cos(d x + c) +--R + +--R 2a cos(d x + c) + 3a +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R + +--R +------------------+ +--R (12cos(d x + c) + 28)sin(d x + c)\|a cos(d x + c) + a +--R / +--R 3 3 3 2 3 3 +--R 64a d cos(d x + c) + 192a d cos(d x + c) + 192a d cos(d x + c) + 64a d +--R , +--R +--R 3 2 +----+ +--R (- 3cos(d x + c) - 9cos(d x + c) - 9cos(d x + c) - 3)\|- 2a +--R * +--R +----+ +------------------+ +--R sin(d x + c)\|- 2a \|a cos(d x + c) + a +--R atan(----------------------------------------) +--R 2a cos(d x + c) + 2a +--R + +--R +------------------+ +--R (6cos(d x + c) + 14)sin(d x + c)\|a cos(d x + c) + a +--R / +--R 3 3 3 2 3 3 +--R 32a d cos(d x + c) + 96a d cos(d x + c) + 96a d cos(d x + c) + 32a d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 176 + +--S 177 of 504 +m0133a:= a0133.1-r0133 +--R +--R +--R (129) +--R +--+ +------------------+ +--R 3\|2a \|a cos(d x + c) + a +--R * +--R log +--R +--+ +------------------+ 2 +--R 2sin(d x + c)\|2a \|a cos(d x + c) + a - a cos(d x + c) +--R + +--R 2a cos(d x + c) + 3a +--R / +--R 2 +--R cos(d x + c) + 2cos(d x + c) + 1 +--R + +--R d x + c d x + c +--R - 12a cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R 3 +------------------+ +--R 64a d\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 177 + +--S 178 of 504 +d0133a:= D(m0133a,x) +--R +--R +--R (130) +--R d x + c d x + c 2 d x + c 2 +--R (6cos(-------)sin(-------) - 6cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (- 6cos(d x + c) - 6)sin(-------) +--R 2 +--R + +--R d x + c +--R (6cos(d x + c) + 6)sin(-------) +--R 2 +--R * +--R sin(d x + c) +--R * +--R +--+ d x + c +--R \|2a atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 +--R (- 6cos(d x + c) - 6)sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 6cos(-------) + 6)cos(d x + c) - 6cos(-------) + 6 +--R 2 2 +--R * +--R +--+ +--R sin(d x + c)\|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 d x + c +--R - 3a cos(-------)cos(d x + c) + 6a cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R 9a cos(-------) +--R 2 +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 d x + c +--R 3a cos(-------)cos(d x + c) - 6a cos(-------)cos(d x + c) +--R 2 2 +--R + +--R d x + c +--R - 9a cos(-------) +--R 2 +--R * +--R sin(d x + c) +--R + +--R 3 2 +--R (3a cos(d x + c) - 3a cos(d x + c) - 15a cos(d x + c) - 9a) +--R * +--R d x + c 3 +--R sin(-------) +--R 2 +--R + +--R 3 2 +--R (- 3a cos(d x + c) + 3a cos(d x + c) + 15a cos(d x + c) + 9a) +--R * +--R d x + c +--R sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 +--R ((- 9a cos(d x + c) - 9a)sin(-------) + 9a cos(d x + c) + 9a) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 d x + c 2 +--R (- 6a cos(d x + c) - 12a cos(d x + c) - 6a cos(d x + c))sin(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (3a cos(-------) + 6a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 3a cos(-------) + 12a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 15a cos(-------) + 6a)cos(d x + c) - 9a cos(-------) +--R 2 2 +--R / +--R 3 3 3 2 3 3 +--R (32a cos(d x + c) - 32a cos(d x + c) - 160a cos(d x + c) - 96a ) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R 3 3 3 2 3 3 +--R - 32a cos(d x + c) + 32a cos(d x + c) + 160a cos(d x + c) + 96a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R 3 2 3 3 d x + c 2 +--R (- 64a cos(d x + c) - 128a cos(d x + c) - 64a )sin(-------) +--R 2 +--R + +--R 3 2 3 3 +--R 64a cos(d x + c) + 128a cos(d x + c) + 64a +--R * +--R +--+ +--R sin(d x + c)\|2a +--R Type: Expression(Integer) +--E 178 + +--S 179 of 504 +m0133b:= a0133.2-r0133 +--R +--R +--R (131) +--R - +--R +----+ +------------------+ +--R 3\|- 2a \|a cos(d x + c) + a +--R * +--R +----+ +------------------+ +--R sin(d x + c)\|- 2a \|a cos(d x + c) + a +--R atan(----------------------------------------) +--R 2a cos(d x + c) + 2a +--R + +--R d x + c d x + c +--R - 6a cos(-------)atanh(sin(-------)) +--R 2 2 +--R / +--R 3 +------------------+ +--R 32a d\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 179 + +--S 180 of 504 +d0133b:= D(m0133b,x) +--R +--R +--R (132) +--R d x + c d x + c 2 d x + c 3 +--R (- 3cos(-------)sin(-------) + 3cos(-------))sin(d x + c) +--R 2 2 2 +--R + +--R d x + c 3 +--R (3cos(d x + c) + 3)sin(-------) +--R 2 +--R + +--R d x + c +--R (- 3cos(d x + c) - 3)sin(-------) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R d x + c d x + c d x + c 2 +--R (6cos(-------)cos(d x + c) + 6cos(-------))sin(-------) +--R 2 2 2 +--R + +--R d x + c d x + c +--R - 6cos(-------)cos(d x + c) - 6cos(-------) +--R 2 2 +--R * +--R sin(d x + c) +--R + +--R 2 d x + c 3 +--R (- 6cos(d x + c) - 12cos(d x + c) - 6)sin(-------) +--R 2 +--R + +--R 2 d x + c +--R (6cos(d x + c) + 12cos(d x + c) + 6)sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(sin(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 3cos(d x + c) - 3)sin(-------) + (3cos(-------) + 3)cos(d x + c) +--R 2 2 +--R + +--R d x + c 2 +--R 3cos(-------) + 3 +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 d x + c 2 +--R (- 6cos(d x + c) - 12cos(d x + c) - 6cos(d x + c))sin(-------) +--R 2 +--R + +--R 3 d x + c 2 2 +--R 6cos(d x + c) + (- 6cos(-------) + 12)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 12cos(-------) + 6)cos(d x + c) - 6cos(-------) +--R 2 2 +--R / +--R 2 2 d x + c 2 2 2 +--R ((32a cos(d x + c) + 32a )sin(-------) - 32a cos(d x + c) - 32a ) +--R 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 2 2 2 2 d x + c 2 +--R (- 64a cos(d x + c) - 128a cos(d x + c) - 64a )sin(-------) +--R 2 +--R + +--R 2 2 2 2 +--R 64a cos(d x + c) + 128a cos(d x + c) + 64a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 180 + +--S 181 of 504 +t0134:= 1/(a-a*cos(c+d*x))^(3/2) +--R +--R +--R 1 +--R (133) - ------------------------------------------- +--R +--------------------+ +--R (a cos(d x + c) - a)\|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 181 + +--S 182 of 504 +r0134:= -1/2*atanh(cos(1/2*c+1/2*d*x))*sin(1/2*c+1/2*d*x)/a/d/_ + (a-a*cos(c+d*x))^(1/2)-1/2*sin(c+d*x)/d/(a-a*cos(c+d*x))^(3/2) +--R +--R +--R d x + c d x + c +--R (- cos(d x + c) + 1)sin(-------)atanh(cos(-------)) + sin(d x + c) +--R 2 2 +--R (134) ------------------------------------------------------------------ +--R +--------------------+ +--R (2a d cos(d x + c) - 2a d)\|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 182 + +--S 183 of 504 +a0134:= integrate(t0134,x) +--R +--R +--R (135) +--R [ +--R +--+ +--R (cos(d x + c) - 1)\|2a +--R * +--R +--+ +------------------+ +--R 2\|2a \|a cos(d x + c) + a - a cos(d x + c) - 3a +--R log(-------------------------------------------------) +--R cos(d x + c) - 1 +--R + +--R +------------------+ +--R 4\|a cos(d x + c) + a +--R / +--R 2 2 +--R 8a d cos(d x + c) - 8a d +--R , +--R +--R +----+ +------------------+ +--R +----+ \|- 2a \|a cos(d x + c) + a +--R (cos(d x + c) - 1)\|- 2a atan(----------------------------) +--R 2a +--R + +--R +------------------+ +--R 2\|a cos(d x + c) + a +--R / +--R 2 2 +--R 4a d cos(d x + c) - 4a d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 183 + +--S 184 of 504 +m0134a:= a0134.1-r0134 +--R +--R +--R (136) +--R +--+ +--------------------+ +--R (cos(d x + c) - 1)\|2a \|- a cos(d x + c) + a +--R * +--R +--+ +------------------+ +--R 2\|2a \|a cos(d x + c) + a - a cos(d x + c) - 3a +--R log(-------------------------------------------------) +--R cos(d x + c) - 1 +--R + +--R +--------------------+ +------------------+ +--R 4\|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R d x + c d x + c +--R (4a cos(d x + c) - 4a)sin(-------)atanh(cos(-------)) - 4a sin(d x + c) +--R 2 2 +--R / +--R 2 2 +--------------------+ +--R (8a d cos(d x + c) - 8a d)\|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 184 + +--S 185 of 504 +d0134a:= D(m0134a,x) +--R +--R +--R (137) +--R d x + c 2 d x + c 2 +--R ((- 4cos(-------) + 4)cos(d x + c) - 12cos(-------) + 12) +--R 2 2 +--R * +--R +--------------------+ +--R sin(d x + c)\|- a cos(d x + c) + a +--R + +--R d x + c 2 2 d x + c 2 +--R ((2cos(-------) - 2)cos(d x + c) - 2cos(-------) + 2) +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 3 +--R (2cos(-------) - 2cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 2cos(-------) + 2cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c d x + c 3 +--R (- 2cos(-------) + 2cos(-------))cos(d x + c) + 2cos(-------) +--R 2 2 2 +--R + +--R d x + c +--R - 2cos(-------) +--R 2 +--R * +--R +--+ d x + c +--R \|2a atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R ((- 6cos(-------) + 6)cos(d x + c) - 6cos(-------) + 6) +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 +--R (2cos(d x + c) - 2cos(d x + c) - 2cos(d x + c) + 2) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (- 4cos(-------) + 4)cos(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (4cos(-------) - 4)cos(d x + c) +--R 2 +--R * +--R +--+ +--R \|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 d x + c 2 +--R ((8cos(-------) - 8)cos(d x + c) + 8cos(-------) - 8)sin(d x + c) +--R 2 2 +--R * +--R +--+ +--------------------+ +--R \|2a \|- a cos(d x + c) + a +--R + +--R d x + c 2 3 +--R (- a cos(-------) + a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 3a cos(-------) + 3a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (a cos(-------) - a)cos(d x + c) + 3a cos(-------) - 3a +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 4 +--R (- a cos(-------) + a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 2a cos(-------) + 2a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (4a cos(-------) - 4a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c d x + c 3 +--R (2a cos(-------) - 2a cos(-------))cos(d x + c) - 3a cos(-------) +--R 2 2 2 +--R + +--R d x + c +--R 3a cos(-------) +--R 2 +--R * +--R d x + c +--R atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 2 +--R (3a cos(-------) - 3a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (12a cos(-------) - 12a)cos(d x + c) + 9a cos(-------) - 9a +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 3 2 +--R - a cos(d x + c) - 2a cos(d x + c) + 4a cos(d x + c) +--R + +--R 2a cos(d x + c) - 3a +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 4 +--R (2a cos(-------) - 2a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (6a cos(-------) - 6a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 2a cos(-------) + 2a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 6a cos(-------) + 6a)cos(d x + c) +--R 2 +--R / +--R d x + c 2 3 +--R (8a cos(-------) - 8a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 8a cos(-------) + 8a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 8a cos(-------) + 8a)cos(d x + c) + 8a cos(-------) - 8a +--R 2 2 +--R * +--R +--+ +--------------------+ +------------------+ +--R \|2a \|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R 2 d x + c 2 2 4 +--R (- 4a cos(-------) + 4a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 3 +--R (- 8a cos(-------) + 8a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (16a cos(-------) - 16a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 2 +--R (8a cos(-------) - 8a )cos(d x + c) - 12a cos(-------) + 12a +--R 2 2 +--R * +--R +--------------------+ +--R \|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 185 + +--S 186 of 504 +m0134b:= a0134.2-r0134 +--R +--R +--R (138) +--R +----+ +--------------------+ +--R (cos(d x + c) - 1)\|- 2a \|- a cos(d x + c) + a +--R * +--R +----+ +------------------+ +--R \|- 2a \|a cos(d x + c) + a +--R atan(----------------------------) +--R 2a +--R + +--R +--------------------+ +------------------+ +--R 2\|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R d x + c d x + c +--R (2a cos(d x + c) - 2a)sin(-------)atanh(cos(-------)) - 2a sin(d x + c) +--R 2 2 +--R / +--R 2 2 +--------------------+ +--R (4a d cos(d x + c) - 4a d)\|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 186 + +--S 187 of 504 +d0134b:= D(m0134b,x) +--R +--R +--R (139) +--R d x + c 2 d x + c 2 +--R ((cos(-------) - 1)cos(d x + c) - cos(-------) + 1) +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 2 +--R (cos(-------) - cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c d x + c 3 +--R (- 2cos(-------) + 2cos(-------))cos(d x + c) + cos(-------) +--R 2 2 2 +--R + +--R d x + c +--R - cos(-------) +--R 2 +--R * +--R d x + c +--R atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 2 +--R (- 3cos(-------) + 3)sin(d x + c) +--R 2 +--R + +--R 2 d x + c 2 +--R (cos(d x + c) - 2cos(d x + c) + 1)sin(-------) +--R 2 +--R + +--R d x + c 2 2 d x + c 2 +--R (- 2cos(-------) + 2)cos(d x + c) + (2cos(-------) - 2)cos(d x + c) +--R 2 2 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 +--------------------+ +--R (4cos(-------) - 4)sin(d x + c)\|- a cos(d x + c) + a +--R 2 +--R / +--R d x + c 2 2 +--R (4a cos(-------) - 4a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 8a cos(-------) + 8a)cos(d x + c) + 4a cos(-------) - 4a +--R 2 2 +--R * +--R +--------------------+ +------------------+ +--R \|- a cos(d x + c) + a \|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 187 + +--S 188 of 504 +t0135:= 1/(a-a*cos(c+d*x))^(5/2) +--R +--R +--R 1 +--R (140) --------------------------------------------------------------- +--R 2 2 2 2 +--------------------+ +--R (a cos(d x + c) - 2a cos(d x + c) + a )\|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 188 + +--S 189 of 504 +r0135:= -3/16*atanh(cos(1/2*c+1/2*d*x))*sin(1/2*c+1/2*d*x)/a^2/d/_ + (a-a*cos(c+d*x))^(1/2)-1/4*sin(c+d*x)/d/_ + (a-a*cos(c+d*x))^(5/2)-3/16*sin(c+d*x)/a/d/(a-a*cos(c+d*x))^(3/2) +--R +--R +--R (141) +--R 2 d x + c d x + c +--R (- 3cos(d x + c) + 6cos(d x + c) - 3)sin(-------)atanh(cos(-------)) +--R 2 2 +--R + +--R (3cos(d x + c) - 7)sin(d x + c) +--R / +--R 2 2 2 2 +--------------------+ +--R (16a d cos(d x + c) - 32a d cos(d x + c) + 16a d)\|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 189 + +--S 190 of 504 +a0135:= integrate(t0135,x) +--R +--R +--R (142) +--R [ +--R 2 +--+ +--R (3cos(d x + c) - 6cos(d x + c) + 3)\|2a +--R * +--R +--+ +------------------+ +--R 2\|2a \|a cos(d x + c) + a - a cos(d x + c) - 3a +--R log(-------------------------------------------------) +--R cos(d x + c) - 1 +--R + +--R +------------------+ +--R (12cos(d x + c) - 28)\|a cos(d x + c) + a +--R / +--R 3 2 3 3 +--R 64a d cos(d x + c) - 128a d cos(d x + c) + 64a d +--R , +--R +--R 2 +----+ +--R (3cos(d x + c) - 6cos(d x + c) + 3)\|- 2a +--R * +--R +----+ +------------------+ +--R \|- 2a \|a cos(d x + c) + a +--R atan(----------------------------) +--R 2a +--R + +--R +------------------+ +--R (6cos(d x + c) - 14)\|a cos(d x + c) + a +--R / +--R 3 2 3 3 +--R 32a d cos(d x + c) - 64a d cos(d x + c) + 32a d +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 190 + +--S 191 of 504 +m0135a:= a0135.1-r0135 +--R +--R +--R (143) +--R 2 +--+ +--------------------+ +--R (3cos(d x + c) - 6cos(d x + c) + 3)\|2a \|- a cos(d x + c) + a +--R * +--R +--+ +------------------+ +--R 2\|2a \|a cos(d x + c) + a - a cos(d x + c) - 3a +--R log(-------------------------------------------------) +--R cos(d x + c) - 1 +--R + +--R +--------------------+ +------------------+ +--R (12cos(d x + c) - 28)\|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R 2 d x + c +--R (12a cos(d x + c) - 24a cos(d x + c) + 12a)sin(-------) +--R 2 +--R * +--R d x + c +--R atanh(cos(-------)) +--R 2 +--R + +--R (- 12a cos(d x + c) + 28a)sin(d x + c) +--R / +--R 3 2 3 3 +--------------------+ +--R (64a d cos(d x + c) - 128a d cos(d x + c) + 64a d)\|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 191 + +--S 192 of 504 +d0135a:= D(m0135a,x) +--R +--R +--R (144) +--R d x + c 2 d x + c 2 +--R ((32cos(-------) - 32)cos(d x + c) + 96cos(-------) - 96) +--R 2 2 +--R * +--R +--------------------+ +--R sin(d x + c)\|- a cos(d x + c) + a +--R + +--R d x + c 2 3 +--R (6cos(-------) - 6)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 6cos(-------) + 6)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 6cos(-------) + 6)cos(d x + c) + 6cos(-------) - 6 +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 4 +--R (6cos(-------) - 6cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (- 12cos(-------) + 12cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c d x + c 3 +--R (12cos(-------) - 12cos(-------))cos(d x + c) - 6cos(-------) +--R 2 2 2 +--R + +--R d x + c +--R 6cos(-------) +--R 2 +--R * +--R +--+ d x + c +--R \|2a atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 2 +--R (- 18cos(-------) + 18)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (40cos(-------) - 40)cos(d x + c) + 58cos(-------) - 58 +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 3 +--R (6cos(d x + c) - 12cos(d x + c) + 12cos(d x + c) - 6) +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 4 +--R (- 12cos(-------) + 12)cos(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (28cos(-------) - 28)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (12cos(-------) - 12)cos(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 28cos(-------) + 28)cos(d x + c) +--R 2 +--R * +--R +--+ +--R \|2a +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 d x + c 2 +--R ((- 64cos(-------) + 64)cos(d x + c) - 64cos(-------) + 64) +--R 2 2 +--R * +--R +--+ +--------------------+ +--R sin(d x + c)\|2a \|- a cos(d x + c) + a +--R + +--R d x + c 2 4 +--R (- 3a cos(-------) + 3a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 6a cos(-------) + 6a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (12a cos(-------) - 12a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (6a cos(-------) - 6a)cos(d x + c) - 9a cos(-------) + 9a +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 5 +--R (- 3a cos(-------) + 3a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 4 +--R (- 3a cos(-------) + 3a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 3 +--R (18a cos(-------) - 18a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 6a cos(-------) + 6a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R (- 15a cos(-------) + 15a cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c +--R 9a cos(-------) - 9a cos(-------) +--R 2 2 +--R * +--R d x + c +--R atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 3 +--R (9a cos(-------) - 9a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (7a cos(-------) - 7a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 89a cos(-------) + 89a)cos(d x + c) - 87a cos(-------) + 87a +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 5 4 3 +--R - 3a cos(d x + c) - 3a cos(d x + c) + 18a cos(d x + c) +--R + +--R 2 +--R - 6a cos(d x + c) - 15a cos(d x + c) + 9a +--R * +--R d x + c 2 +--R sin(-------) +--R 2 +--R + +--R d x + c 2 5 +--R (6a cos(-------) - 6a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 4 +--R (4a cos(-------) - 4a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 3 +--R (- 48a cos(-------) + 48a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (- 4a cos(-------) + 4a)cos(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (42a cos(-------) - 42a)cos(d x + c) +--R 2 +--R / +--R 2 d x + c 2 2 4 +--R (64a cos(-------) - 64a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 3 +--R (- 128a cos(-------) + 128a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 2 +--R (128a cos(-------) - 128a )cos(d x + c) - 64a cos(-------) + 64a +--R 2 2 +--R * +--R +--+ +--------------------+ +------------------+ +--R \|2a \|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R 3 d x + c 2 3 5 +--R (- 32a cos(-------) + 32a )cos(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 4 +--R (- 32a cos(-------) + 32a )cos(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 +--R (192a cos(-------) - 192a )cos(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 2 +--R (- 64a cos(-------) + 64a )cos(d x + c) +--R 2 +--R + +--R 3 d x + c 2 3 3 d x + c 2 3 +--R (- 160a cos(-------) + 160a )cos(d x + c) + 96a cos(-------) - 96a +--R 2 2 +--R * +--R +--------------------+ +--R \|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 192 + +--S 193 of 504 +m0135b:= a0135.2-r0135 +--R +--R +--R (145) +--R 2 +----+ +--------------------+ +--R (3cos(d x + c) - 6cos(d x + c) + 3)\|- 2a \|- a cos(d x + c) + a +--R * +--R +----+ +------------------+ +--R \|- 2a \|a cos(d x + c) + a +--R atan(----------------------------) +--R 2a +--R + +--R +--------------------+ +------------------+ +--R (6cos(d x + c) - 14)\|- a cos(d x + c) + a \|a cos(d x + c) + a +--R + +--R 2 d x + c d x + c +--R (6a cos(d x + c) - 12a cos(d x + c) + 6a)sin(-------)atanh(cos(-------)) +--R 2 2 +--R + +--R (- 6a cos(d x + c) + 14a)sin(d x + c) +--R / +--R 3 2 3 3 +--------------------+ +--R (32a d cos(d x + c) - 64a d cos(d x + c) + 32a d)\|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 193 + +--S 194 of 504 +d0135b:= D(m0135b,x) +--R +--R +--R (146) +--R d x + c 2 2 +--R (3cos(-------) - 3)cos(d x + c) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R (- 6cos(-------) + 6)cos(d x + c) + 3cos(-------) - 3 +--R 2 2 +--R * +--R d x + c +--R sin(-------)sin(d x + c) +--R 2 +--R + +--R d x + c 3 d x + c 3 +--R (3cos(-------) - 3cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c 2 +--R (- 9cos(-------) + 9cos(-------))cos(d x + c) +--R 2 2 +--R + +--R d x + c 3 d x + c d x + c 3 +--R (9cos(-------) - 9cos(-------))cos(d x + c) - 3cos(-------) +--R 2 2 2 +--R + +--R d x + c +--R 3cos(-------) +--R 2 +--R * +--R d x + c +--R atanh(cos(-------)) +--R 2 +--R + +--R d x + c 2 d x + c 2 +--R ((- 9cos(-------) + 9)cos(d x + c) + 29cos(-------) - 29) +--R 2 2 +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 2 d x + c 2 +--R (3cos(d x + c) - 9cos(d x + c) + 9cos(d x + c) - 3)sin(-------) +--R 2 +--R + +--R d x + c 2 3 +--R (- 6cos(-------) + 6)cos(d x + c) +--R 2 +--R + +--R d x + c 2 2 +--R (20cos(-------) - 20)cos(d x + c) +--R 2 +--R + +--R d x + c 2 +--R (- 14cos(-------) + 14)cos(d x + c) +--R 2 +--R * +--R +------------------+ +--R \|a cos(d x + c) + a +--R + +--R d x + c 2 +--------------------+ +--R (- 32cos(-------) + 32)sin(d x + c)\|- a cos(d x + c) + a +--R 2 +--R / +--R 2 d x + c 2 2 3 +--R (32a cos(-------) - 32a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 +--R (- 96a cos(-------) + 96a )cos(d x + c) +--R 2 +--R + +--R 2 d x + c 2 2 2 d x + c 2 2 +--R (96a cos(-------) - 96a )cos(d x + c) - 32a cos(-------) + 32a +--R 2 2 +--R * +--R +--------------------+ +------------------+ +--R \|- a cos(d x + c) + a \|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 194 + +--S 195 of 504 +t0136:= (b*cos(c+d*x))^(1/2) +--R +--R +--R +--------------+ +--R (147) \|b cos(d x + c) +--R Type: Expression(Integer) +--E 195 + +--S 196 of 504 +r0136:= 2*(b*cos(c+d*x))^(1/2)*EllipticE(1/2*c+1/2*d*x,2)/d/cos(c+d*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 196 + +--S 197 of 504 +a0136:= integrate(t0136,x) +--R +--R +--R x +--R ++ +---------------+ +--R (148) | \|b cos(%H d + c) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 197 + +--S 198 of 504 +--m0136:= a0136-r0136 +--E 198 + +--S 199 of 504 +--d0136:= D(m0136,x) +--E 199 + +--S 200 of 504 +t0137:= (b*cos(c+d*x))^(3/2) +--R +--R +--R +--------------+ +--R (149) b cos(d x + c)\|b cos(d x + c) +--R Type: Expression(Integer) +--E 200 + +--S 201 of 504 +r0137:= 2/3*b^2*(cos(c+d*x)^(1/2)*EllipticF(1/2*c+1/2*d*x,2)+_ + cos(c+d*x)*sin(c+d*x))/d/(b*cos(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 201 + +--S 202 of 504 +a0137:= integrate(t0137,x) +--R +--R +--R x +--R ++ +---------------+ +--R (150) | b cos(%H d + c)\|b cos(%H d + c) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 202 + +--S 203 of 504 +--m0137:= a0137-r0137 +--E 203 + +--S 204 of 504 +--d0137:= D(m0137,x) +--E 204 + +--S 205 of 504 +t0138:= (b*cos(c+d*x))^(5/2) +--R +--R +--R 2 2 +--------------+ +--R (151) b cos(d x + c) \|b cos(d x + c) +--R Type: Expression(Integer) +--E 205 + +--S 206 of 504 +r0138:= 2/5*b^2*(b*cos(c+d*x))^(1/2)*(3*EllipticE(1/2*c+1/2*d*x,2)+_ + cos(c+d*x)^(3/2)*sin(c+d*x))/d/cos(c+d*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 206 + +--S 207 of 504 +a0138:= integrate(t0138,x) +--R +--R +--R x +--R ++ 2 2 +---------------+ +--R (152) | b cos(%H d + c) \|b cos(%H d + c) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 207 + +--S 208 of 504 +--m0138:= a0138-r0138 +--E 208 + +--S 209 of 504 +--d0138:= D(m0138,x) +--E 209 + +--S 210 of 504 +t0139:= 1/(b*cos(c+d*x))^(1/2) +--R +--R +--R 1 +--R (153) ----------------- +--R +--------------+ +--R \|b cos(d x + c) +--R Type: Expression(Integer) +--E 210 + +--S 211 of 504 +r0139:= 2*cos(c+d*x)^(1/2)*EllipticF(1/2*c+1/2*d*x,2)/d/(b*cos(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 504 +a0139:= integrate(t0139,x) +--R +--R +--R x +--R ++ 1 +--R (154) | ------------------ d%H +--R ++ +---------------+ +--R \|b cos(%H d + c) +--R Type: Union(Expression(Integer),...) +--E 212 + +--S 213 of 504 +--m0139:= a0139-r0139 +--E 213 + +--S 214 of 504 +--d0139:= D(m0139,x) +--E 214 + +--S 215 of 504 +t0140:= 1/(b*cos(c+d*x))^(3/2) +--R +--R +--R 1 +--R (155) ------------------------------- +--R +--------------+ +--R b cos(d x + c)\|b cos(d x + c) +--R Type: Expression(Integer) +--E 215 + +--S 216 of 504 +r0140:= -2/b*(cos(c+d*x)*EllipticE(1/2*c+1/2*d*x,2)-_ + sin(c+d*x)*cos(c+d*x)^(1/2))/d/cos(c+d*x)^(1/2)/(b*cos(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 216 + +--S 217 of 504 +a0140:= integrate(t0140,x) +--R +--R +--R x +--R ++ 1 +--R (156) | --------------------------------- d%H +--R ++ +---------------+ +--R b cos(%H d + c)\|b cos(%H d + c) +--R Type: Union(Expression(Integer),...) +--E 217 + +--S 218 of 504 +--m0140:= a0140-r0140 +--E 218 + +--S 219 of 504 +--d0140:= D(m0140,x) +--E 219 + +--S 220 of 504 +t0141:= 1/(b*cos(c+d*x))^(5/2) +--R +--R +--R 1 +--R (157) -------------------------------- +--R 2 2 +--------------+ +--R b cos(d x + c) \|b cos(d x + c) +--R Type: Expression(Integer) +--E 220 + +--S 221 of 504 +r0141:= 2/3/b^2*(cos(c+d*x)^(3/2)*EllipticF(1/2*c+1/2*d*x,2)+_ + sin(c+d*x))/d/cos(c+d*x)/(b*cos(c+d*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 221 + +--S 222 of 504 +a0141:= integrate(t0141,x) +--R +--R +--R x +--R ++ 1 +--R (158) | ---------------------------------- d%H +--R ++ 2 2 +---------------+ +--R b cos(%H d + c) \|b cos(%H d + c) +--R Type: Union(Expression(Integer),...) +--E 222 + +--S 223 of 504 +--m0141:= a0141-r0141 +--E 223 + +--S 224 of 504 +--d0141:= D(m0141,x) +--E 224 + +--S 225 of 504 +t0142:= x^2/(a+b*cos(x)) +--R +--R +--R 2 +--R x +--R (159) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 225 + +--S 226 of 504 +r0142:= -(%i*x^2*log((-a+(a^2-b^2)^(1/2)-b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-_ + %i*x^2*log((a+(a^2-b^2)^(1/2)+b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+_ + 2*x*polylog(2,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 2*x*polylog(2,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+_ + 2*%i*polylog(3,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 2*%i*polylog(3,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 226 + +--S 227 of 504 +a0142:= integrate(t0142,x) +--R +--R +--R x 2 +--R ++ %H +--R (160) | ------------- d%H +--R ++ b cos(%H) + a +--R Type: Union(Expression(Integer),...) +--E 227 + +--S 228 of 504 +--m0142:= a0142-r0142 +--E 228 + +--S 229 of 504 +--d0142:= D(m0142,x) +--E 229 + +--S 230 of 504 +t0143:= x^3/(a+b*cos(x)) +--R +--R +--R 3 +--R x +--R (161) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 230 + +--S 231 of 504 +r0143:= -(%i*x^3*log((-a+(a^2-b^2)^(1/2)-b*exp(%i*x))/(-a+(a^2-b^2)^(1/2)))-_ + %i*x^3*log((a+(a^2-b^2)^(1/2)+b*exp(%i*x))/(a+(a^2-b^2)^(1/2)))+_ + 3*x^2*polylog(2,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 3*x^2*polylog(2,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))+_ + 6*%i*x*polylog(3,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))-_ + 6*%i*x*polylog(3,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2)))-_ + 6*polylog(4,b*exp(%i*x)/(-a+(a^2-b^2)^(1/2)))+_ + 6*polylog(4,-b*exp(%i*x)/(a+(a^2-b^2)^(1/2))))/(a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 231 + +--S 232 of 504 +a0143:= integrate(t0143,x) +--R +--R +--R x 3 +--R ++ %H +--R (162) | ------------- d%H +--R ++ b cos(%H) + a +--R Type: Union(Expression(Integer),...) +--E 232 + +--S 233 of 504 +--m0143:= a0143-r0143 +--E 233 + +--S 234 of 504 +--d0143:= D(m0143,x) +--E 234 + +--S 235 of 504 +t0144:= x/(a-a*cos(x)) +--R +--R +--R x +--R (163) - ------------ +--R a cos(x) - a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 504 +r0144:= -x*cot(1/2*x)/a+2*log(sin(1/2*x))/a +--R +--R +--R x x +--R 2log(sin(-)) - x cot(-) +--R 2 2 +--R (164) ----------------------- +--R a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 504 +a0144:= integrate(t0144,x) +--R +--R +--R sin(x) 2 +--R 2sin(x)log(----------) - sin(x)log(----------) - x cos(x) - x +--R cos(x) + 1 cos(x) + 1 +--R (165) ------------------------------------------------------------- +--R a sin(x) +--R Type: Union(Expression(Integer),...) +--E 237 + +--S 238 of 504 +m0144:= a0144-r0144 +--R +--R +--R (166) +--R sin(x) x 2 +--R 2sin(x)log(----------) - 2sin(x)log(sin(-)) - sin(x)log(----------) +--R cos(x) + 1 2 cos(x) + 1 +--R + +--R x +--R x cot(-)sin(x) - x cos(x) - x +--R 2 +--R / +--R a sin(x) +--R Type: Expression(Integer) +--E 238 + +--S 239 of 504 +d0144:= D(m0144,x) +--R +--R +--R (167) +--R x 3 +--R 2sin(-)sin(x) +--R 2 +--R + +--R x 2 x x +--R ((- x cos(x) - x)cot(-) + (2cos(x) + 2)cot(-) + x cos(x) + x)sin(-) +--R 2 2 2 +--R + +--R x x +--R - 2cos(-)cos(x) - 2cos(-) +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 x 3 2 x +--R (2cos(x) - 2)sin(-)sin(x) + (2x cos(x) + 4x cos(x) + 2x cos(x))sin(-) +--R 2 2 +--R / +--R x 2 +--R (2a cos(x) + 2a)sin(-)sin(x) +--R 2 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 504 +t0145:= x/(a+b*cos(x))^2 +--R +--R +--R x +--R (168) ---------------------------- +--R 2 2 2 +--R b cos(x) + 2a b cos(x) + a +--R Type: Expression(Integer) +--E 240 + +--S 241 of 504 +r0145:= -%i*a*x*log(1+b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+_ + %i*a*x*log(1+b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-_ + log(a+b*cos(x))/(a^2-b^2)-_ + a*polylog(2,-b*exp(1)^(%i*x)/(a-(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)+_ + a*polylog(2,-b*exp(1)^(%i*x)/(a+(a^2-b^2)^(1/2)))/(a^2-b^2)^(3/2)-_ + b*x*sin(x)/(a^2-b^2)/(a+b*cos(x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 241 + +--S 242 of 504 +a0145:= integrate(t0145,x) +--R +--R +--R x +--R ++ %H +--R (169) | ------------------------------ d%H +--R ++ 2 2 2 +--R b cos(%H) + 2a b cos(%H) + a +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 504 +--m0145:= a0145-r0145 +--E 243 + +--S 244 of 504 +--d0145:= D(m0145,x) +--E 244 + +--S 245 of 504 +t0146:= x*(a+a*cos(c+d*x))^(1/2) +--R +--R +--R +------------------+ +--R (170) x\|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 245 + +--S 246 of 504 +r0146:= 2*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*_ + sec(1/2*c+1/2*d*x)*(2*cos(1/2*c+1/2*d*x)+d*x*sin(1/2*c+1/2*d*x))/d^2 +--R +--R +--R (171) +--R +-+ d x + c d x + c +-+ d x + c d x + c +--R (2d x\|2 sec(-------)sin(-------) + 4\|2 cos(-------)sec(-------)) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R / +--R 2 +--R d +--R Type: Expression(Integer) +--E 246 + +--S 247 of 504 +a0146:= integrate(t0146,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 247 + +--S 248 of 504 +--m0146:= a0146-r0146 +--E 248 + +--S 249 of 504 +--d0146:= D(m0146,x) +--E 249 + +--S 250 of 504 +t0147:= x^2*(a+a*cos(c+d*x))^(1/2) +--R +--R +--R 2 +------------------+ +--R (172) x \|a cos(d x + c) + a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 504 +r0147:= 2*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*_ + (4*d*x*cos(1/2*c+1/2*d*x)-(8-d^2*x^2)*sin(1/2*c+1/2*d*x))/d^3 +--R +--R +--R (173) +--R 2 2 +-+ d x + c d x + c +--R (2d x - 16)\|2 sec(-------)sin(-------) +--R 2 2 +--R + +--R +-+ d x + c d x + c +--R 8d x\|2 cos(-------)sec(-------) +--R 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R / +--R 3 +--R d +--R Type: Expression(Integer) +--E 251 + +--S 252 of 504 +a0147:= integrate(t0147,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 252 + +--S 253 of 504 +--m0147:= a0147-r0147 +--E 253 + +--S 254 of 504 +--d0147:= D(m0147,x) +--E 254 + +--S 255 of 504 +t0148:= (a+a*cos(c+d*x))^(1/2)/x +--R +--R +--R +------------------+ +--R \|a cos(d x + c) + a +--R (174) --------------------- +--R x +--R Type: Expression(Integer) +--E 255 + +--S 256 of 504 +r0148:= 2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*_ + (cos(1/2*c)*Ci(1/2*d*x)-sin(1/2*c)*Si(1/2*d*x)) +--R +--R +--R (175) +--R +-+ d x d x + c c +-+ d x c d x + c +--R (- \|2 Si(---)sec(-------)sin(-) + \|2 Ci(---)cos(-)sec(-------)) +--R 2 2 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 504 +a0148:= integrate(t0148,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 257 + +--S 258 of 504 +--m0148:= a0148-r0148 +--E 258 + +--S 259 of 504 +--d0148:= D(m0148,x) +--E 259 + +--S 260 of 504 +t0149:= (a+a*cos(c+d*x))^(1/2)/x^2 +--R +--R +--R +------------------+ +--R \|a cos(d x + c) + a +--R (176) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 260 + +--S 261 of 504 +r0149:= -1/2*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*_ + (2*cos(1/2*c+1/2*d*x)/x+d*Ci(1/2*d*x)*sin(1/2*c)+_ + d*cos(1/2*c)*Si(1/2*d*x))*2^(1/2) +--R +--R +--R (177) +--R +-+ d x d x + c c +--R - d x\|2 Ci(---)sec(-------)sin(-) +--R 2 2 2 +--R + +--R +-+ d x + c +-+ d x c d x + c +--R (- 2\|2 cos(-------) - d x\|2 Si(---)cos(-))sec(-------) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R / +--R 2x +--R Type: Expression(Integer) +--E 261 + +--S 262 of 504 +a0149:= integrate(t0149,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 262 + +--S 263 of 504 +--m0149:= a0149-r0149 +--E 263 + +--S 264 of 504 +--d0149:= D(m0149,x) +--E 264 + +--S 265 of 504 +t0150:= (a+a*cos(c+d*x))^(1/2)/x^3 +--R +--R +--R +------------------+ +--R \|a cos(d x + c) + a +--R (178) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 265 + +--S 266 of 504 +r0150:= -1/8*2^(1/2)*(a*cos(1/2*c+1/2*d*x)^2)^(1/2)*sec(1/2*c+1/2*d*x)*_ + (4*cos(1/2*c+1/2*d*x)/x^2+d^2*cos(1/2*c)*Ci(1/2*d*x)-_ + 2*d*sin(1/2*c+1/2*d*x)/x-d^2*sin(1/2*c)*Si(1/2*d*x)) +--R +--R +--R (179) +--R +-+ d x + c d x + c 2 2 +-+ d x d x + c c +--R 2d x\|2 sec(-------)sin(-------) + d x \|2 Si(---)sec(-------)sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ d x + c 2 2 +-+ d x c d x + c +--R (- 4\|2 cos(-------) - d x \|2 Ci(---)cos(-))sec(-------) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a cos(-------) +--R \| 2 +--R / +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 266 + +--S 267 of 504 +a0150:= integrate(t0150,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 267 + +--S 268 of 504 +--m0150:= a0150-r0150 +--E 268 + +--S 269 of 504 +--d0150:= D(m0150,x) +--E 269 + +--S 270 of 504 +t0151:= x*(a-a*cos(c+d*x))^(1/2) +--R +--R +--R +--------------------+ +--R (180) x\|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 270 + +--S 271 of 504 +r0151:= -2*2^(1/2)*csc(1/2*c+1/2*d*x)*(d*x*cos(1/2*c+1/2*d*x)-_ + 2*sin(1/2*c+1/2*d*x))*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)/d^2 +--R +--R +--R (181) +--R +-+ d x + c d x + c +-+ d x + c d x + c +--R (4\|2 csc(-------)sin(-------) - 2d x\|2 cos(-------)csc(-------)) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R / +--R 2 +--R d +--R Type: Expression(Integer) +--E 271 + +--S 272 of 504 +a0151:= integrate(t0151,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 272 + +--S 273 of 504 +--m0151:= a0151-r0151 +--E 273 + +--S 274 of 504 +--d0151:= D(m0151,x) +--E 274 + +--S 275 of 504 +t0152:= x^2*(a-a*cos(c+d*x))^(1/2) +--R +--R +--R 2 +--------------------+ +--R (182) x \|- a cos(d x + c) + a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 504 +r0152:= 2*2^(1/2)*csc(1/2*c+1/2*d*x)*(8*cos(1/2*c+1/2*d*x)-_ + d*x*(d*x*cos(1/2*c+1/2*d*x)-4*sin(1/2*c+1/2*d*x)))*_ + (a*sin(1/2*c+1/2*d*x)^2)^(1/2)/d^3 +--R +--R +--R (183) +--R +-+ d x + c d x + c +--R 8d x\|2 csc(-------)sin(-------) +--R 2 2 +--R + +--R 2 2 +-+ d x + c d x + c +--R (- 2d x + 16)\|2 cos(-------)csc(-------) +--R 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R / +--R 3 +--R d +--R Type: Expression(Integer) +--E 276 + +--S 277 of 504 +a0152:= integrate(t0152,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 277 + +--S 278 of 504 +--m0152:= a0152-r0152 +--E 278 + +--S 279 of 504 +--d0152:= D(m0152,x) +--E 279 + +--S 280 of 504 +t0153:= (a-a*cos(c+d*x))^(1/2)/x +--R +--R +--R +--------------------+ +--R \|- a cos(d x + c) + a +--R (184) ----------------------- +--R x +--R Type: Expression(Integer) +--E 280 + +--S 281 of 504 +r0153:= 2^(1/2)*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*_ + (Ci(1/2*d*x)*sin(1/2*c)+cos(1/2*c)*Si(1/2*d*x)) +--R +--R +--R (185) +--R +-+ d x d x + c c +-+ d x c d x + c +--R (\|2 Ci(---)csc(-------)sin(-) + \|2 Si(---)cos(-)csc(-------)) +--R 2 2 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 504 +a0153:= integrate(t0153,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 282 + +--S 283 of 504 +--m0153:= a0153-r0153 +--E 283 + +--S 284 of 504 +--d0153:= D(m0153,x) +--E 284 + +--S 285 of 504 +t0154:= (a-a*cos(c+d*x))^(1/2)/x^2 +--R +--R +--R +--------------------+ +--R \|- a cos(d x + c) + a +--R (186) ----------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 285 + +--S 286 of 504 +r0154:= 1/2*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*_ + (d*cos(1/2*c)*Ci(1/2*d*x)-2*sin(1/2*c+1/2*d*x)/x-_ + d*sin(1/2*c)*Si(1/2*d*x))*2^(1/2) +--R +--R +--R (187) +--R +-+ d x + c d x + c +-+ d x d x + c c +--R - 2\|2 csc(-------)sin(-------) - d x\|2 Si(---)csc(-------)sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ d x c d x + c +--R d x\|2 Ci(---)cos(-)csc(-------) +--R 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R / +--R 2x +--R Type: Expression(Integer) +--E 286 + +--S 287 of 504 +a0154:= integrate(t0154,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 287 + +--S 288 of 504 +--m0154:= a0154-r0154 +--E 288 + +--S 289 of 504 +--d0154:= D(m0154,x) +--E 289 + +--S 290 of 504 +t0155:= (a-a*cos(c+d*x))^(1/2)/x^3 +--R +--R +--R +--------------------+ +--R \|- a cos(d x + c) + a +--R (188) ----------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 290 + +--S 291 of 504 +r0155:= -1/8*2^(1/2)*csc(1/2*c+1/2*d*x)*(a*sin(1/2*c+1/2*d*x)^2)^(1/2)*_ + (2*d*cos(1/2*c+1/2*d*x)/x+d^2*Ci(1/2*d*x)*sin(1/2*c)+_ + 4*sin(1/2*c+1/2*d*x)/x^2+d^2*cos(1/2*c)*Si(1/2*d*x)) +--R +--R +--R (189) +--R +-+ d x + c d x + c 2 2 +-+ d x d x + c c +--R - 4\|2 csc(-------)sin(-------) - d x \|2 Ci(---)csc(-------)sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ d x + c 2 2 +-+ d x c d x + c +--R (- 2d x\|2 cos(-------) - d x \|2 Si(---)cos(-))csc(-------) +--R 2 2 2 2 +--R * +--R +---------------+ +--R | d x + c 2 +--R |a sin(-------) +--R \| 2 +--R / +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 291 + +--S 292 of 504 +a0155:= integrate(t0155,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 292 + +--S 293 of 504 +--m0155:= a0155-r0155 +--E 293 + +--S 294 of 504 +--d0155:= D(m0155,x) +--E 294 + +--S 295 of 504 +t0156:= (1+cos(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (190) \|cos(x) + 1 +--R Type: Expression(Integer) +--E 295 + +--S 296 of 504 +r0156:= 2^(1/2)*EllipticE(x,1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Variable(x) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 296 + +--S 297 of 504 +a0156:= integrate(t0156,x) +--R +--R +--R x +------------+ +--R ++ | 2 +--R (191) | \|cos(%H) + 1 d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 297 + +--S 298 of 504 +--m0156:= a0156-r0156 +--E 298 + +--S 299 of 504 +--d0156:= D(m0156,x) +--E 299 + +--S 300 of 504 +t0157:= (-1-cos(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (192) \|- cos(x) - 1 +--R Type: Expression(Integer) +--E 300 + +--S 301 of 504 +r0157:= 2^(1/2)*(-3-cos(2*x))^(1/2)*EllipticE(x,1/2)/(3+cos(2*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Variable(x) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 301 + +--S 302 of 504 +a0157:= integrate(t0157,x) +--R +--R +--R (193) +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +--R (2(%e ) - 2%e ) +--R * +--R +----------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x %H\|- 1 | %H\|- 1 %H\|- 1 +--R ++ (4(%e ) + 4)\|(%e ) + 6(%e ) + 1 +--R | --------------------------------------------------------- d%H +--R ++ +---+ 6 +---+ 4 +---+ 2 +--R %H\|- 1 %H\|- 1 %H\|- 1 +--R (%e ) + 6(%e ) + (%e ) +--R + +--R +--------------------------------+ +--R +---+ | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (%e + 1)\|(%e ) + 6(%e ) + 1 +--R / +--R +---+ 2 +---+ +--R x\|- 1 x\|- 1 +--R 2(%e ) - 2%e +--R Type: Union(Expression(Integer),...) +--E 302 + +--S 303 of 504 +--m0157:= a0157-r0157 +--E 303 + +--S 304 of 504 +--d0157:= D(m0157,x) +--E 304 + +--S 305 of 504 +t0158:= 1/(1+cos(x)^2)^(1/2) +--R +--R +--R 1 +--R (194) -------------- +--R +-----------+ +--R | 2 +--R \|cos(x) + 1 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 504 +r0158:= 1/2*EllipticF(x,1/2)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Variable(x) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 306 + +--S 307 of 504 +a0158:= integrate(t0158,x) +--R +--R +--R x +--R ++ 1 +--R (195) | --------------- d%H +--R ++ +------------+ +--R | 2 +--R \|cos(%H) + 1 +--R Type: Union(Expression(Integer),...) +--E 307 + +--S 308 of 504 +--m0158:= a0158-r0158 +--E 308 + +--S 309 of 504 +--d0158:= D(m0158,x) +--E 309 + +--S 310 of 504 +t0159:= 1/(-1-cos(x)^2)^(1/2) +--R +--R +--R 1 +--R (196) ---------------- +--R +-------------+ +--R | 2 +--R \|- cos(x) - 1 +--R Type: Expression(Integer) +--E 310 + +--S 311 of 504 +r0159:= 1/2*(3+cos(2*x))^(1/2)*EllipticF(x,1/2)*2^(1/2)/(-3-cos(2*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Variable(x) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 311 + +--S 312 of 504 +a0159:= integrate(t0159,x) +--R +--R +--R +----------------------------------+ +--R | +---+ 4 +---+ 2 +--R x | %H\|- 1 %H\|- 1 +--R ++ 2\|(%e ) + 6(%e ) + 1 +--R (197) | ---------------------------------------------- d%H +--R ++ +---+ 6 +---+ 4 +---+ 2 +--R %H\|- 1 %H\|- 1 %H\|- 1 +--R (%e ) + 6(%e ) + (%e ) +--R Type: Union(Expression(Integer),...) +--E 312 + +--S 313 of 504 +--m0159:= a0159-r0159 +--E 313 + +--S 314 of 504 +--d0159:= D(m0159,x) +--E 314 + +--S 315 of 504 +t0160:= x/(a+b*cos(x)^2) +--R +--R +--R x +--R (198) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 315 + +--S 316 of 504 +r0160:= -1/4*(2*%i*x*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-b*exp(2*%i*x))/_ + (-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*%i*x*log((2*a+b+2*a^(1/2)*_ + (a+b)^(1/2)+b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + polylog(2,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*_ + (a+b)^(1/2))))/a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 316 + +--S 317 of 504 +a0160:= integrate(t0160,x) +--R +--R +--R x +--R ++ %H +--R (199) | -------------- d%H +--R ++ 2 +--R b cos(%H) + a +--R Type: Union(Expression(Integer),...) +--E 317 + +--S 318 of 504 +--m0160:= a0160-r0160 +--E 318 + +--S 319 of 504 +--d0160:= D(m0160,x) +--E 319 + +--S 320 of 504 +t0161:= x^2/(a+b*cos(x)^2) +--R +--R +--R 2 +--R x +--R (200) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 320 + +--S 321 of 504 +r0161:= -1/4*(2*%i*x^2*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-_ + b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 2*%i*x^2*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+b*exp(2*%i*x))/_ + (2*a+b+2*a^(1/2)*(a+b)^(1/2)))+2*x*polylog(2,b*exp(2*%i*x)/_ + (-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-2*x*_ + polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + %i*polylog(3,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + %i*polylog(3,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/_ + a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 321 + +--S 322 of 504 +a0161:= integrate(t0161,x) +--R +--R +--R x 2 +--R ++ %H +--R (201) | -------------- d%H +--R ++ 2 +--R b cos(%H) + a +--R Type: Union(Expression(Integer),...) +--E 322 + +--S 323 of 504 +--m0161:= a0161-r0161 +--E 323 + +--S 324 of 504 +--d0161:= D(m0161,x) +--E 324 + +--S 325 of 504 +t0162:= x^3/(a+b*cos(x)^2) +--R +--R +--R 3 +--R x +--R (202) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 504 +r0162:= 1/8*(-4*%i*x^3*log((-2*a-b+2*a^(1/2)*(a+b)^(1/2)-_ + b*exp(2*%i*x))/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 4*%i*x^3*log((2*a+b+2*a^(1/2)*(a+b)^(1/2)+_ + b*exp(2*%i*x))/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-_ + 6*x^2*polylog(2,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 6*x^2*polylog(2,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))-_ + 6*%i*x*polylog(3,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))+_ + 6*%i*x*polylog(3,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2)))+_ + 3*polylog(4,b*exp(2*%i*x)/(-2*a-b+2*a^(1/2)*(a+b)^(1/2)))-_ + 3*polylog(4,-b*exp(2*%i*x)/(2*a+b+2*a^(1/2)*(a+b)^(1/2))))/_ + a^(1/2)/(a+b)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 326 + +--S 327 of 504 +a0162:= integrate(t0162,x) +--R +--R +--R x 3 +--R ++ %H +--R (203) | -------------- d%H +--R ++ 2 +--R b cos(%H) + a +--R Type: Union(Expression(Integer),...) +--E 327 + +--S 328 of 504 +--m0162:= a0162-r0162 +--E 328 + +--S 329 of 504 +--d0162:= D(m0162,x) +--E 329 + +--S 330 of 504 +t0163:= 1/(a+b*cos(x)^3) +--R +--R +--R 1 +--R (204) ------------- +--R 3 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 504 +r0163:= 2/3*atan((a^(1/3)-b^(1/3))*tan(1/2*x)/(a^(2/3)-b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan((a^(1/3)-(-1)^(2/3)*_ + b^(1/3))*tan(1/2*x)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2))/a^(2/3)/_ + (a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+2/3*atan((a^(1/3)+(-1)^(1/3)*_ + b^(1/3))*tan(1/2*x)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) +--R +--R +--R (205) +--R +---------------+ +-------------------+ +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+ x 3+-+ x 3+-+ +--R \|- 1 tan(-)\|b + tan(-)\|a +--R 2 2 +--R atan(-----------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R - +--R +----------------------+ +-------------------+ +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 3+-+ x 3+-+ +--R tan(-)\|b - tan(-)\|a +--R 2 2 +--R atan(-----------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R - +--R +----------------------+ +---------------+ +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 3+---+2 x 3+-+ x 3+-+ +--R \|- 1 tan(-)\|b - tan(-)\|a +--R 2 2 +--R atan(------------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 504 +a0163:= integrate(t0163,x) +--R +--R +--R (206) +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--I ((243a b - 243a )cos(x) + 243a b - 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R (27a b - 27a )cos(x) + 27a b - 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--I ((243a b - 243a )cos(x) + 243a b - 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--I ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EJ0 +--R + +--R 2 2 +--R (6a b - 3a )cos(x) + 6a b - 3a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--I ((243a b - 243a )cos(x) + 243a b - 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R (27a b - 27a )cos(x) + 27a b - 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--I ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--I ((27a b + 54a )cos(x) + 27a b + 54a )%%EJ0 +--R + +--R 2 2 +--R (- 6a b + 3a )cos(x) - 6a b + 3a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--I ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R (- 27a b + 27a )cos(x) - 27a b + 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--I ((243a b - 243a )cos(x) + 243a b - 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--I ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EJ0 +--R + +--R 2 2 +--R (6a b - 3a )cos(x) + 6a b - 3a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--I ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--R (- 27a b + 27a )cos(x) - 27a b + 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--I ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--I ((27a b + 54a )cos(x) + 27a b + 54a )%%EJ0 +--R + +--R 2 2 +--R (- 6a b + 3a )cos(x) - 6a b + 3a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EJ0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EJ0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EJ0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--I \|4%%EJ0 +--R * +--R log +--R 4 2 6 4 2 6 2 +--I ((243a b - 243a )cos(x) + 243a b - 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--I ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EJ0 +--R + +--R 2 2 +--R (- 3a b - 3a )cos(x) - 3a b - 3a +--R * +--R +------+ +--I \|4%%EJ0 +--R + +--R 2b sin(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I \|4%%EJ0 +--R * +--R log +--R 4 2 6 4 2 6 2 +--I ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EJ0 +--R + +--R 2 2 4 2 2 4 +--I ((27a b + 54a )cos(x) + 27a b + 54a )%%EJ0 +--R + +--R 2 2 +--R (3a b + 3a )cos(x) + 3a b + 3a +--R * +--R +------+ +--I \|4%%EJ0 +--R + +--R 2b sin(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 332 + +--S 333 of 504 +--m0163:= a0163-r0163 +--E 333 + +--S 334 of 504 +--d0163:= D(m0163,x) +--E 334 + +--S 335 of 504 +t0164:= 1/(a+b*cos(x)^4) +--R +--R +--R 1 +--R (207) ------------- +--R 4 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 504 +r0164:= 1/2*atan(a^(1/4)*tan(x)/(a^(1/2)-(-b)^(1/2))^(1/2))/a^(3/4)/_ + (a^(1/2)-(-b)^(1/2))^(1/2)+1/2*atan(a^(1/4)*tan(x)/(a^(1/2)+_ + (-b)^(1/2))^(1/2))/a^(3/4)/(a^(1/2)+(-b)^(1/2))^(1/2) +--R +--R +--R (208) +--R +-------------+ 4+-+ +--R | +-+ +---+ tan(x)\|a +--R \|\|a + \|- b atan(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a - \|- b +--R + +--R +-------------+ 4+-+ +--R | +-+ +---+ tan(x)\|a +--R \|\|a - \|- b atan(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R / +--R +-------------+ +-------------+ +--R 4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|a \|\|a - \|- b \|\|a + \|- b +--R Type: Expression(Integer) +--E 336 + +--S 337 of 504 +a0164:= integrate(t0164,x) +--R +--R +--R (209) +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R 4a sin(x) |------------------------------------------- - 2cos(x) +--R | 2 +--R \| 4a b + 4a +--R log(-----------------------------------------------------------------) +--R cos(x) + 1 +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R 4a sin(x) |--------------------------------------------- - 2cos(x) +--R | 2 +--R \| 4a b + 4a +--R log(-------------------------------------------------------------------) +--R cos(x) + 1 +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R - 4a sin(x) |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R log +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R - 4a sin(x) |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 337 + +--S 338 of 504 +m0164:= a0164-r0164 +--R +--R +--R (210) +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R 4a sin(x) |------------------------------------------- - 2cos(x) +--R | 2 +--R \| 4a b + 4a +--R log(-----------------------------------------------------------------) +--R cos(x) + 1 +--R + +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |--------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R 4a sin(x) |--------------------------------------------- - 2cos(x) +--R | 2 +--R \| 4a b + 4a +--R log(-------------------------------------------------------------------) +--R cos(x) + 1 +--R + +--R - +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R 4+-+3 | \| 64a b + 128a b + 64a +--R \|a |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +-------------+ +--R | +-+ +---+ | +-+ +---+ +--R \|\|a - \|- b \|\|a + \|- b +--R * +--R log +--R +---------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(- 8a b - 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R - 4a sin(x) |--------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +-------------+ +--R 4+-+3 | \| 64a b + 128a b + 64a | +-+ +---+ +--R \|a |------------------------------------------- \|\|a - \|- b +--R | 2 +--R \| 4a b + 4a +--R * +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R * +--R log +--R +-------------------------------------------+ +--R | +------------------------+ +--R | 2 | b +--R |(8a b + 8a ) |- ---------------------- - 1 +--R | | 3 2 4 5 +--R | \| 64a b + 128a b + 64a +--R - 4a sin(x) |------------------------------------------- +--R | 2 +--R \| 4a b + 4a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ 4+-+ +--R | +-+ +---+ tan(x)\|a +--R - \|\|a + \|- b atan(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a - \|- b +--R + +--R +-------------+ 4+-+ +--R | +-+ +---+ tan(x)\|a +--R - \|\|a - \|- b atan(----------------) +--R +-------------+ +--R | +-+ +---+ +--R \|\|a + \|- b +--R / +--R +-------------+ +-------------+ +--R 4+-+3 | +-+ +---+ | +-+ +---+ +--R 2\|a \|\|a - \|- b \|\|a + \|- b +--R Type: Expression(Integer) +--E 338 + +--S 339 of 504 +d0164:= D(m0164,x) +--R +--R +--R (211) +--R 4 4 +--R - b cos(x) tan(x) +--R + +--R 4 2 2 4 2 +--R (- a sin(x) - 2a cos(x) sin(x) + (- b - a)cos(x) )tan(x) +--R + +--R 4 2 2 4 +--R (b + a)sin(x) + (2b + 2a)cos(x) sin(x) + (b + a)cos(x) +--R * +--R 4+-+2 +--R \|a +--R + +--R 4 2 2 4 2 4 +--R (a sin(x) + 2a cos(x) sin(x) + (- b + a)cos(x) )tan(x) - a sin(x) +--R + +--R 2 2 4 +--R - 2a cos(x) sin(x) + (- b - a)cos(x) +--R * +--R +-+ +--R \|a +--R / +--R 2 4 2 2 2 2 4 4 +--R (a sin(x) + 2a cos(x) sin(x) + (a b + a )cos(x) )tan(x) +--R + +--R 2 4 2 2 2 +--R (a b + a )sin(x) + (2a b + 2a )cos(x) sin(x) +--R + +--R 2 2 4 +--R (b + 2a b + a )cos(x) +--R * +--R 4+-+2 +--R \|a +--R + +--R 2 4 2 2 2 2 4 2 +-+ +--R (2a sin(x) + 4a cos(x) sin(x) + (2a b + 2a )cos(x) )tan(x) \|a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 504 +t0165:= 1/(a+b*cos(x)^6) +--R +--R +--R 1 +--R (212) ------------- +--R 6 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 504 +r0165:= 1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+_ + b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-_ + (-1)^(1/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-_ + (-1)^(1/3)*b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+_ + (-1)^(2/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+(-1)^(2/3)*b^(1/3))^(1/2) +--R +--R +--R (213) +--R +-----------+ +------------------+ 6+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|a +--R \|\|b + \|a \|\|- 1 \|b + \|a atan(----------------------) +--R +-------------------+ +--R | 3+---+3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +-------------------+ +------------------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|a +--R \|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(--------------) +--R +-----------+ +--R |3+-+ 3+-+ +--R \|\|b + \|a +--R + +--R +-------------------+ +-----------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+-+ 3+-+ tan(x)\|a +--R \|- \|- 1 \|b + \|a \|\|b + \|a atan(---------------------) +--R +------------------+ +--R |3+---+2 3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 504 +a0165:= integrate(t0165,x) +--R +--R +--R (214) +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ 6a sin(x)\|4%%EL0 - 2cos(x) +--I \|4%%EL0 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ - 6a sin(x)\|4%%EL0 - 2cos(x) +--I - \|4%%EL0 log(------------------------------) +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 342 + +--S 343 of 504 +m0165:= a0165-r0165 +--R +--R +--R (215) +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b - 2592a b - 1296a )%%EL0 +--R + +--R 2 3 +--I (- 72a b - 72a )%%EL0 - 4b - a +--R / +--R 3 2 4 5 +--R 432a b + 864a b + 432a +--R + +--R 2 +--I (- 12a b - 12a )%%EL0 - 1 +--R / +--R 2 +--R 6a b + 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I +------+ 6a sin(x)\|4%%EL0 - 2cos(x) +--I \|4%%EL0 log(----------------------------) +--R cos(x) + 1 +--R + +--R - +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I +------+ - 6a sin(x)\|4%%EL0 - 2cos(x) +--I \|4%%EL0 log(------------------------------) +--R cos(x) + 1 +--R + +--R +-----------+ +------------------+ 6+-+ +--R |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|a +--R - 2\|\|b + \|a \|\|- 1 \|b + \|a atan(----------------------) +--R +-------------------+ +--R | 3+---+3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +-------------------+ +------------------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+---+2 3+-+ 3+-+ tan(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(--------------) +--R +-----------+ +--R |3+-+ 3+-+ +--R \|\|b + \|a +--R + +--R +-------------------+ +-----------+ 6+-+ +--R | 3+---+3+-+ 3+-+ |3+-+ 3+-+ tan(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|\|b + \|a atan(---------------------) +--R +------------------+ +--R |3+---+2 3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +-------------------+ +-----------+ +------------------+ +--R 6+-+5 | 3+---+3+-+ 3+-+ |3+-+ 3+-+ |3+---+2 3+-+ 3+-+ +--R 6\|a \|- \|- 1 \|b + \|a \|\|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 504 +--d0165:= D(m0165,x) +--E 344 + +--S 345 of 504 +t0166:= 1/(a+b*cos(x)^8) +--R +--R +--R 1 +--R (216) ------------- +--R 8 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 345 + +--S 346 of 504 +r0166:= 1/4*atan(a^(1/8)*tan(x)/(a^(1/4)+(-b)^(1/4))^(1/2))/a^(7/8)/_ + (a^(1/4)+(-b)^(1/4))^(1/2)+1/4*atan(a^(1/4)*tan(x)/(a^(1/2)-_ + a^(1/4)*(-b)^(1/4))^(1/2))/a^(3/4)/(a^(1/2)-a^(1/4)*_ + (-b)^(1/4))^(1/2)+1/4*atan(a^(1/4)*tan(x)/(a^(1/2)-%i*a^(1/4)*_ + (-b)^(1/4))^(1/2))/a^(3/4)/(a^(1/2)-%i*a^(1/4)*(-b)^(1/4))^(1/2)+_ + 1/4*atan(a^(1/4)*tan(x)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2))/_ + a^(3/4)/(a^(1/2)+%i*a^(1/4)*(-b)^(1/4))^(1/2) +--R +--R +--R (217) +--R +---------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- %i\|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R 4+-+ +--R tan(x)\|a +--R atan(----------------------) +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|- \|- b \|a + \|a +--R + +--R +-------------------+ +-------------+ +-------------------+ +--R 8+-+7 | 4+---+4+-+ +-+ |4+-+ 4+---+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|\|a + \|- b \|%i\|- b \|a + \|a +--R * +--R 4+-+ +--R tan(x)\|a +--R atan(------------------------) +--R +---------------------+ +--R | 4+---+4+-+ +-+ +--R \|- %i\|- b \|a + \|a +--R + +--R +-------------------+ +---------------------+ +--R 4+-+3 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a +--R * +--R +-------------------+ 8+-+ +--R | 4+---+4+-+ +-+ tan(x)\|a +--R \|%i\|- b \|a + \|a atan(----------------) +--R +-------------+ +--R |4+-+ 4+---+ +--R \|\|a + \|- b +--R + +--R +-------------------+ +---------------------+ +-------------+ +--R 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R 4+-+ +--R tan(x)\|a +--R atan(----------------------) +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R / +--R +-------------------+ +---------------------+ +-------------+ +--R 4+-+3 8+-+7 | 4+---+4+-+ +-+ | 4+---+4+-+ +-+ |4+-+ 4+---+ +--R 4\|a \|a \|- \|- b \|a + \|a \|- %i\|- b \|a + \|a \|\|a + \|- b +--R * +--R +-------------------+ +--R | 4+---+4+-+ +-+ +--R \|%i\|- b \|a + \|a +--R Type: Expression(Complex(Integer)) +--E 346 + +--S 347 of 504 +a0166:= integrate(t0166,x) +--R +--R +--R (218) +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%EM0 - 64a b - 64a ) +--R * +--I %%EM1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EM0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EM1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b - 2048a b - 1024a )%%EM0 - 64a b - 64a ) +--R * +--I %%EM1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EM0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EM1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EM0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EM1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EM0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EM1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b - 2048a b - 1024a )%%EM0 - 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EM1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM1 +--R + +--R 3 2 4 5 +--I (- 1024a b - 2048a b - 1024a )%%EM0 +--R + +--R 2 3 +--R - 64a b - 64a +--R * +--I %%EM1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b - 3072a b - 1536a )%%EM0 +--R + +--R 2 3 +--I (- 64a b - 64a )%%EM0 - 3b - a +--R / +--R 3 2 4 5 +--R 512a b + 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b - 16a )%%EM1 + (- 16a b - 16a )%%EM0 - 1 +--R / +--R 2 +--R 8a b + 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ 8a sin(x)\|4%%EM1 - 2cos(x) +--I \|4%%EM1 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ - 8a sin(x)\|4%%EM1 - 2cos(x) +--I - \|4%%EM1 log(------------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ 8a sin(x)\|4%%EM0 - 2cos(x) +--I \|4%%EM0 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ - 8a sin(x)\|4%%EM0 - 2cos(x) +--I - \|4%%EM0 log(------------------------------) +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 347 + +--S 348 of 504 +--m0166:= a0166-r0166 +--E 348 + +--S 349 of 504 +--d0166:= D(m0166,x) +--E 349 + +--S 350 of 504 +t0167:= 1/(a-b*cos(x)^3) +--R +--R +--R 1 +--R (219) - ------------- +--R 3 +--R b cos(x) - a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 504 +r0167:= 2/3*atan((a^(1/3)+b^(1/3))*tan(1/2*x)/(a^(2/3)-b^(2/3))^(1/2))/_ + a^(2/3)/(a^(2/3)-b^(2/3))^(1/2)+2/3*atan((a^(1/3)+_ + (-1)^(2/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)+(-1)^(1/3)*_ + b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)+(-1)^(1/3)*b^(2/3))^(1/2)+_ + 2/3*atan((a^(1/3)-(-1)^(1/3)*b^(1/3))*tan(1/2*x)/(a^(2/3)-_ + (-1)^(2/3)*b^(2/3))^(1/2))/a^(2/3)/(a^(2/3)-(-1)^(2/3)*b^(2/3))^(1/2) +--R +--R +--R (220) +--R - +--R +---------------+ +-------------------+ +--R | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R 3+---+ x 3+-+ x 3+-+ +--R \|- 1 tan(-)\|b - tan(-)\|a +--R 2 2 +--R atan(-----------------------------) +--R +----------------------+ +--R | 3+---+2 3+-+2 3+-+2 +--R \|- \|- 1 \|b + \|a +--R + +--R +----------------------+ +-------------------+ +--R | 3+---+2 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a +--R * +--R x 3+-+ x 3+-+ +--R tan(-)\|b + tan(-)\|a +--R 2 2 +--R atan(-----------------------) +--R +---------------+ +--R | 3+-+2 3+-+2 +--R \|- \|b + \|a +--R + +--R +----------------------+ +---------------+ +--R | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 +--R 2\|- \|- 1 \|b + \|a \|- \|b + \|a +--R * +--R 3+---+2 x 3+-+ x 3+-+ +--R \|- 1 tan(-)\|b + tan(-)\|a +--R 2 2 +--R atan(------------------------------) +--R +-------------------+ +--R |3+---+3+-+2 3+-+2 +--R \|\|- 1 \|b + \|a +--R / +--R +----------------------+ +---------------+ +-------------------+ +--R 3+-+2 | 3+---+2 3+-+2 3+-+2 | 3+-+2 3+-+2 |3+---+3+-+2 3+-+2 +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 504 +a0167:= integrate(t0167,x) +--R +--R +--R (221) +--R - +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--I ((243a b - 243a )cos(x) + 243a b - 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R (27a b - 27a )cos(x) + 27a b - 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--I ((243a b - 243a )cos(x) + 243a b - 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--I ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EN0 +--R + +--R 2 2 +--R (- 6a b - 3a )cos(x) - 6a b - 3a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--I ((243a b - 243a )cos(x) + 243a b - 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R (27a b - 27a )cos(x) + 27a b - 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--I ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--I ((27a b + 54a )cos(x) + 27a b + 54a )%%EN0 +--R + +--R 2 2 +--R (6a b + 3a )cos(x) + 6a b + 3a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--I ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R (- 27a b + 27a )cos(x) - 27a b + 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--I ((243a b - 243a )cos(x) + 243a b - 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--I ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EN0 +--R + +--R 2 2 +--R (- 6a b - 3a )cos(x) - 6a b - 3a +--R * +--R ROOT +--R 2 2 +--R (- 6b + 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R * +--R log +--R 4 2 6 4 2 6 +--I ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--R (- 27a b + 27a )cos(x) - 27a b + 27a +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 4 2 6 4 2 6 2 +--I ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--I ((27a b + 54a )cos(x) + 27a b + 54a )%%EN0 +--R + +--R 2 2 +--R (6a b + 3a )cos(x) + 6a b + 3a +--R * +--R ROOT +--R 2 2 +--R (6b - 6a ) +--R * +--R ROOT +--R 2 4 4 2 6 2 +--I (- 81a b + 162a b - 81a )%%EN0 +--R + +--R 2 2 4 2 2 +--I (18a b - 18a )%%EN0 + 4b - a +--R / +--R 2 4 4 2 6 +--R 27a b - 54a b + 27a +--R + +--R 2 2 +--I (- 6b + 6a )%%EN0 + 2 +--R / +--R 2 2 +--R 3b - 3a +--R + +--R 4b sin(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I \|4%%EN0 +--R * +--R log +--R 4 2 6 4 2 6 2 +--I ((243a b - 243a )cos(x) + 243a b - 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--I ((- 27a b - 54a )cos(x) - 27a b - 54a )%%EN0 +--R + +--R 2 2 +--R (3a b - 3a )cos(x) + 3a b - 3a +--R * +--R +------+ +--I \|4%%EN0 +--R + +--R 2b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +------+ +--I \|4%%EN0 +--R * +--R log +--R 4 2 6 4 2 6 2 +--I ((- 243a b + 243a )cos(x) - 243a b + 243a )%%EN0 +--R + +--R 2 2 4 2 2 4 +--I ((27a b + 54a )cos(x) + 27a b + 54a )%%EN0 +--R + +--R 2 2 +--R (- 3a b + 3a )cos(x) - 3a b + 3a +--R * +--R +------+ +--I \|4%%EN0 +--R + +--R 2b sin(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 352 + +--S 353 of 504 +--m0167:= a0167-r0167 +--E 353 + +--S 354 of 504 +--d0167:= D(m0167,x) +--E 354 + +--S 355 of 504 +t0168:= 1/(a-b*cos(x)^6) +--R +--R +--R 1 +--R (222) - ------------- +--R 6 +--R b cos(x) - a +--R Type: Expression(Integer) +--E 355 + +--S 356 of 504 +r0168:= 1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-b^(1/3))^(1/2))/a^(5/6)/_ + (a^(1/3)-b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)+_ + (-1)^(1/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)+(-1)^(1/3)*_ + b^(1/3))^(1/2)+1/3*atan(a^(1/6)*tan(x)/(a^(1/3)-_ + (-1)^(2/3)*b^(1/3))^(1/2))/a^(5/6)/(a^(1/3)-(-1)^(2/3)*b^(1/3))^(1/2) +--R +--R +--R (223) +--R +-------------+ +-----------------+ 6+-+ +--R | 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|a +--R \|- \|b + \|a \|\|- 1 \|b + \|a atan(-----------------------) +--R +--------------------+ +--R | 3+---+2 3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +--------------------+ +-----------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|a +--R \|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(----------------) +--R +-------------+ +--R | 3+-+ 3+-+ +--R \|- \|b + \|a +--R + +--R +--------------------+ +-------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ tan(x)\|a +--R \|- \|- 1 \|b + \|a \|- \|b + \|a atan(--------------------) +--R +-----------------+ +--R |3+---+3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 504 +a0168:= integrate(t0168,x) +--R +--R +--R (224) +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ 6a sin(x)\|4%%EO0 - 2cos(x) +--I \|4%%EO0 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ - 6a sin(x)\|4%%EO0 - 2cos(x) +--I - \|4%%EO0 log(------------------------------) +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 357 + +--S 358 of 504 +m0168:= a0168-r0168 +--R +--R +--R (225) +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (- 12a b + 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R * +--R log +--R - +--R 6a sin(x) +--R * +--R ROOT +--R 2 +--R (12a b - 12a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1296a b + 2592a b - 1296a )%%EO0 +--R + +--R 2 3 +--I (72a b - 72a )%%EO0 + 4b - a +--R / +--R 3 2 4 5 +--R 432a b - 864a b + 432a +--R + +--R 2 +--I (- 12a b + 12a )%%EO0 + 1 +--R / +--R 2 +--R 6a b - 6a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I +------+ 6a sin(x)\|4%%EO0 - 2cos(x) +--I \|4%%EO0 log(----------------------------) +--R cos(x) + 1 +--R + +--R - +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 3\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R * +--R +------+ +--I +------+ - 6a sin(x)\|4%%EO0 - 2cos(x) +--I \|4%%EO0 log(------------------------------) +--R cos(x) + 1 +--R + +--R +-------------+ +-----------------+ 6+-+ +--R | 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|a +--R - 2\|- \|b + \|a \|\|- 1 \|b + \|a atan(-----------------------) +--R +--------------------+ +--R | 3+---+2 3+-+ 3+-+ +--R \|- \|- 1 \|b + \|a +--R + +--R +--------------------+ +-----------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ |3+---+3+-+ 3+-+ tan(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|\|- 1 \|b + \|a atan(----------------) +--R +-------------+ +--R | 3+-+ 3+-+ +--R \|- \|b + \|a +--R + +--R +--------------------+ +-------------+ 6+-+ +--R | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ tan(x)\|a +--R - 2\|- \|- 1 \|b + \|a \|- \|b + \|a atan(--------------------) +--R +-----------------+ +--R |3+---+3+-+ 3+-+ +--R \|\|- 1 \|b + \|a +--R / +--R +--------------------+ +-------------+ +-----------------+ +--R 6+-+5 | 3+---+2 3+-+ 3+-+ | 3+-+ 3+-+ |3+---+3+-+ 3+-+ +--R 6\|a \|- \|- 1 \|b + \|a \|- \|b + \|a \|\|- 1 \|b + \|a +--R Type: Expression(Integer) +--E 358 + +--S 359 of 504 +--d0168:= D(m0168,x) +--E 359 + +--S 360 of 504 +t0169:= 1/(a-b*cos(x)^8) +--R +--R +--R 1 +--R (226) - ------------- +--R 8 +--R b cos(x) - a +--R Type: Expression(Integer) +--E 360 + +--S 361 of 504 +r0169:= 1/4*atan(a^(1/8)*tan(x)/(a^(1/4)-b^(1/4))^(1/2))/a^(7/8)/_ + (a^(1/4)-b^(1/4))^(1/2)+1/4*atan(a^(1/8)*tan(x)/_ + (a^(1/4)-%i*b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)-%i*b^(1/4))^(1/2)+_ + 1/4*atan(a^(1/8)*tan(x)/(a^(1/4)+%i*b^(1/4))^(1/2))/a^(7/8)/_ + (a^(1/4)+%i*b^(1/4))^(1/2)+1/4*atan(a^(1/8)*tan(x)/_ + (a^(1/4)+b^(1/4))^(1/2))/a^(7/8)/(a^(1/4)+b^(1/4))^(1/2) +--R +--R +--R (227) +--R +---------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a atan(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|- \|b + \|a +--R + +--R +-------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R \|- \|b + \|a \|%i\|b + \|a \|\|b + \|a atan(------------------) +--R +---------------+ +--R | 4+-+ 4+-+ +--R \|- %i\|b + \|a +--R + +--R +-------------+ +---------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R \|- \|b + \|a \|- %i\|b + \|a \|\|b + \|a atan(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|%i\|b + \|a +--R + +--R +-------------+ +---------------+ +-------------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ tan(x)\|a +--R \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a atan(--------------) +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R / +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 4\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R Type: Expression(Complex(Integer)) +--E 361 + +--S 362 of 504 +a0169:= integrate(t0169,x) +--R +--R +--R (228) +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ 8a sin(x)\|4%%EP1 - 2cos(x) +--I \|4%%EP1 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ - 8a sin(x)\|4%%EP1 - 2cos(x) +--I - \|4%%EP1 log(------------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ 8a sin(x)\|4%%EP0 - 2cos(x) +--I \|4%%EP0 log(----------------------------) +--R cos(x) + 1 +--R + +--R +------+ +--I +------+ - 8a sin(x)\|4%%EP0 - 2cos(x) +--I - \|4%%EP0 log(------------------------------) +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 362 + +--S 363 of 504 +m0169:= a0169-r0169 +--R +--R +--R (229) +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 3 +--I ((- 1024a b + 2048a b - 1024a )%%EP0 + 64a b - 64a ) +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (- 16a b + 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1024a b + 2048a b - 1024a )%%EP0 + 64a b +--R + +--R 3 +--R - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R * +--R log +--R - +--R 8a sin(x) +--R * +--R ROOT +--R 2 +--R (16a b - 16a ) +--R * +--R ROOT +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP1 +--R + +--R 3 2 4 5 +--I (- 1024a b + 2048a b - 1024a )%%EP0 +--R + +--R 2 3 +--R 64a b - 64a +--R * +--I %%EP1 +--R + +--R 3 2 4 5 2 +--I (- 1536a b + 3072a b - 1536a )%%EP0 +--R + +--R 2 3 +--I (64a b - 64a )%%EP0 + 3b - a +--R / +--R 3 2 4 5 +--R 512a b - 1024a b + 512a +--R + +--R 2 2 +--I (- 16a b + 16a )%%EP1 + (- 16a b + 16a )%%EP0 + 1 +--R / +--R 2 +--R 8a b - 8a +--R + +--R - 2cos(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +------+ +--I +------+ 8a sin(x)\|4%%EP1 - 2cos(x) +--I \|4%%EP1 log(----------------------------) +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +------+ +--I |4+-+ 4+-+ +------+ - 8a sin(x)\|4%%EP1 - 2cos(x) +--I \|\|b + \|a \|4%%EP1 log(------------------------------) +--R cos(x) + 1 +--R + +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R * +--R +------+ +--I +------+ 8a sin(x)\|4%%EP0 - 2cos(x) +--I \|4%%EP0 log(----------------------------) +--R cos(x) + 1 +--R + +--R - +--R +-------------+ +---------------+ +-------------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ +--R 2\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a +--R * +--R +-----------+ +------+ +--I |4+-+ 4+-+ +------+ - 8a sin(x)\|4%%EP0 - 2cos(x) +--I \|\|b + \|a \|4%%EP0 log(------------------------------) +--R cos(x) + 1 +--R + +--R +---------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R - \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a atan(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|- \|b + \|a +--R + +--R +-------------+ +-------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R - \|- \|b + \|a \|%i\|b + \|a \|\|b + \|a atan(------------------) +--R +---------------+ +--R | 4+-+ 4+-+ +--R \|- %i\|b + \|a +--R + +--R +-------------+ +---------------+ +-----------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ tan(x)\|a +--R - \|- \|b + \|a \|- %i\|b + \|a \|\|b + \|a atan(----------------) +--R +-------------+ +--R | 4+-+ 4+-+ +--R \|%i\|b + \|a +--R + +--R +-------------+ +---------------+ +-------------+ 8+-+ +--R | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ tan(x)\|a +--R - \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a atan(--------------) +--R +-----------+ +--R |4+-+ 4+-+ +--R \|\|b + \|a +--R / +--R +-------------+ +---------------+ +-------------+ +-----------+ +--R 8+-+7 | 4+-+ 4+-+ | 4+-+ 4+-+ | 4+-+ 4+-+ |4+-+ 4+-+ +--R 4\|a \|- \|b + \|a \|- %i\|b + \|a \|%i\|b + \|a \|\|b + \|a +--R Type: Expression(Complex(Integer)) +--E 363 + +--S 364 of 504 +d0169:= D(m0169,x) +--R +--R +--R (230) +--R 8 8 +--R b cos(x) tan(x) +--R + +--R 8 2 6 4 4 +--R - a sin(x) - 4a cos(x) sin(x) - 6a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 4a cos(x) sin(x) + (b - a)cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 8 2 6 +--R (- b + a)sin(x) + (- 4b + 4a)cos(x) sin(x) +--R + +--R 4 4 6 2 +--R (- 6b + 6a)cos(x) sin(x) + (- 4b + 4a)cos(x) sin(x) +--R + +--R 8 +--R (- b + a)cos(x) +--R * +--R 8+-+6 +--R \|a +--R + +--R 8 2 6 4 4 +--R a sin(x) + 4a cos(x) sin(x) + 6a cos(x) sin(x) +--R + +--R 6 2 8 +--R 4a cos(x) sin(x) + (3b + a)cos(x) +--R * +--R 6 +--R tan(x) +--R + +--R 8 2 6 4 4 +--R - 3a sin(x) - 12a cos(x) sin(x) - 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 12a cos(x) sin(x) + (3b - 3a)cos(x) +--R * +--R 4 +--R tan(x) +--R * +--R 4+-+8+-+4 +--R \|a \|a +--R + +--R 8 2 6 4 4 +--R 3a sin(x) + 12a cos(x) sin(x) + 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R 12a cos(x) sin(x) + (3b + 3a)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 8 2 6 4 4 +--R - 3a sin(x) - 12a cos(x) sin(x) - 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 12a cos(x) sin(x) + (3b - 3a)cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R 4+-+2 8+-+2 +--R \|a \|a +--R + +--R 8 2 6 4 4 +--R 3a sin(x) + 12a cos(x) sin(x) + 18a cos(x) sin(x) +--R + +--R 6 2 8 +--R 12a cos(x) sin(x) + (b + 3a)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 8 2 6 4 4 +--R - a sin(x) - 4a cos(x) sin(x) - 6a cos(x) sin(x) +--R + +--R 6 2 8 +--R - 4a cos(x) sin(x) + (b - a)cos(x) +--R * +--R 4+-+3 +--R \|a +--R / +--R 2 8 2 2 6 2 4 4 +--R a sin(x) + 4a cos(x) sin(x) + 6a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 4a cos(x) sin(x) + (- a b + a )cos(x) +--R * +--R 8 +--R tan(x) +--R + +--R 2 8 2 2 6 +--R (- a b + a )sin(x) + (- 4a b + 4a )cos(x) sin(x) +--R + +--R 2 4 4 2 6 2 +--R (- 6a b + 6a )cos(x) sin(x) + (- 4a b + 4a )cos(x) sin(x) +--R + +--R 2 2 8 +--R (b - 2a b + a )cos(x) +--R * +--R 8+-+6 +--R \|a +--R + +--R 2 8 2 2 6 2 4 4 +--R 4a sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 16a cos(x) sin(x) + (- 4a b + 4a )cos(x) +--R * +--R 6 4+-+8+-+4 +--R tan(x) \|a \|a +--R + +--R 2 8 2 2 6 2 4 4 +--R 6a sin(x) + 24a cos(x) sin(x) + 36a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 24a cos(x) sin(x) + (- 6a b + 6a )cos(x) +--R * +--R 4 4+-+2 8+-+2 +--R tan(x) \|a \|a +--R + +--R 2 8 2 2 6 2 4 4 +--R 4a sin(x) + 16a cos(x) sin(x) + 24a cos(x) sin(x) +--R + +--R 2 6 2 2 8 +--R 16a cos(x) sin(x) + (- 4a b + 4a )cos(x) +--R * +--R 2 4+-+3 +--R tan(x) \|a +--R Type: Expression(Complex(Integer)) +--E 364 + +--S 365 of 504 +t0170:= 1/(1+cos(x)^3) +--R +--R +--R 1 +--R (231) ----------- +--R 3 +--R cos(x) + 1 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 504 +r0170:= -2/3*atan((-1)^(2/3)*(1+(-1)^(1/3))^(1/2)*tan(1/2*x))/_ + (1+(-1)^(1/3))^(1/2)+2/3*atan((-1)^(1/3)*(1-(-1)^(2/3))^(1/2)*_ + tan(1/2*x))/(1-(-1)^(2/3))^(1/2)+sin(x)/(3*cos(x)+3) +--R +--R +--R (232) +--R +-------------+ +----------+ +--R | 3+---+2 3+---+2 x |3+---+ +--R (- 2cos(x) - 2)\|- \|- 1 + 1 atan(\|- 1 tan(-)\|\|- 1 + 1 ) +--R 2 +--R + +--R +----------+ +-------------+ +--R |3+---+ 3+---+ x | 3+---+2 +--R (2cos(x) + 2)\|\|- 1 + 1 atan(\|- 1 tan(-)\|- \|- 1 + 1 ) +--R 2 +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R sin(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R (3cos(x) + 3)\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 504 +a0170:= integrate(t0170,x) +--R +--R +--R (233) +--R %pi x 4 %pi x 2 %pi x 2 +--R cos(---)sin(-) + (2cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R sin(---) + \|3 sin(---) + cos(---) - \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (2cos(-) - 2)sin(---) + 2\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (2cos(---) - 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 2cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (4\|3 \|3 cos(-)sin(---) + 4\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 4+-+ x 4 4+-+ %pi +--R (cos(-) + 2cos(-) + 1)sin(---) + (\|3 cos(-) - \|3 )sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (cos(---) - \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (2cos(---) - 2\|3 )cos(-) + cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R - cos(---)sin(-) + (- 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R - cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R sin(---) + \|3 sin(---) + cos(---) - \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (2cos(-) - 2)sin(---) + 2\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (2cos(---) - 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 2cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (- 4\|3 \|3 cos(-)sin(---) - 4\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 4+-+ x 4 4+-+ %pi +--R (cos(-) + 2cos(-) + 1)sin(---) + (\|3 cos(-) - \|3 )sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (cos(---) - \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (2cos(---) - 2\|3 )cos(-) + cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R cos(---)sin(-) + (2cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R sin(---) - \|3 sin(---) + cos(---) + \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (2cos(-) - 2)sin(---) - 2\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (2cos(---) + 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 2cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (4\|3 \|3 cos(-)sin(---) + 4\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (- \|3 cos(-) + \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (cos(---) + \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (2cos(---) - 2\|3 )cos(-) + cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R - cos(---)sin(-) + (- 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R - cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R sin(---) - \|3 sin(---) + cos(---) + \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (2cos(-) - 2)sin(---) - 2\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (2cos(---) + 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 2cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (- 4\|3 \|3 cos(-)sin(---) - 4\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (- \|3 cos(-) + \|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (cos(---) + \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (2cos(---) - 2\|3 )cos(-) + cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 x 2 %pi x 2 +--R 2sin(---)sin(-) + (4cos(-) - 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (2cos(-) + 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (sin(---) - \|3 cos(---) + 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (2cos(-) - 2)sin(---) + (- 2\|3 cos(---) + 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (- \|3 cos(---) + 2\|3 )cos(-) - 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R - \|3 cos(---) - 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) + cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + 2cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 2cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi %pi x 4 +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) + cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 %pi +--R 2cos(---)cos(-) + cos(---) +--R 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R - 2sin(---)sin(-) + (- 4cos(-) + 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (- 2cos(-) - 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (sin(---) - \|3 cos(---) + 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (2cos(-) - 2)sin(---) + (- 2\|3 cos(---) + 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (- \|3 cos(---) + 2\|3 )cos(-) - 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R - \|3 cos(---) - 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) + cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + 2cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 2cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R 2sin(---)sin(-) + (4cos(-) - 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (2cos(-) + 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (sin(---) - \|3 cos(---) - 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (2cos(-) - 2)sin(---) + (- 2\|3 cos(---) - 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (- \|3 cos(---) - 2\|3 )cos(-) - 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R - \|3 cos(---) + 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) + cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + 2cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 2cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi %pi x 4 +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) + cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 %pi +--R 2cos(---)cos(-) + cos(---) +--R 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R - 2sin(---)sin(-) + (- 4cos(-) + 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (- 2cos(-) - 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (sin(---) - \|3 cos(---) - 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (2cos(-) - 2)sin(---) + (- 2\|3 cos(---) - 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (cos(-) + 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (- \|3 cos(---) - 2\|3 )cos(-) - 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R - \|3 cos(---) + 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) + cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) + 2cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R - 2cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R + +--R 4+-+ x x +--R 8\|3 cos(-)sin(-) +--R 2 2 +--R / +--R 4+-+ x 4 4+-+ x 2 4+-+ x 2 4+-+ x 4 +--R 6\|3 sin(-) + (12\|3 cos(-) - 12\|3 )sin(-) + 6\|3 cos(-) +--R 2 2 2 2 +--R + +--R 4+-+ x 2 4+-+ +--R 12\|3 cos(-) + 6\|3 +--R 2 +--R Type: Union(Expression(Integer),...) +--E 367 + +--S 368 of 504 +t0171:= 1/(1+cos(x)^4) +--R +--R +--R 1 +--R (234) ----------- +--R 4 +--R cos(x) + 1 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 504 +r0171:= 1/2*atan(tan(x)/(1-%i)^(1/2))/(1-%i)^(1/2)+_ + 1/2*atan(tan(x)/(1+%i)^(1/2))/(1+%i)^(1/2) +--R +--R +--R +------+ tan(x) +------+ tan(x) +--R \|1 + %i atan(---------) + \|1 - %i atan(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R (235) --------------------------------------------------- +--R +------+ +------+ +--R 2\|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 369 + +--S 370 of 504 +a0171:= integrate(t0171,x) +--R +--R +--R (236) +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) + 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R - 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R - +--R 4+-+ %pi +--R \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) - 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) ) +--R 2 8 8 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R - +--R 4+-+ %pi +--R 2\|2 sin(---) +--R 8 +--R * +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 2 8 2 +--R atan(-----------------------------------------------------) +--R +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) - 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R + +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 4+-+ %pi 2 8 2 +--R - 2\|2 sin(---)atan(-----------------------------------------------------) +--R 8 +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) + 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R / +--R +-+ +--R 4\|2 +--R Type: Union(Expression(Integer),...) +--E 370 + +--S 371 of 504 +m0171:= a0171-r0171 +--R +--R +--R (237) +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) + 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R - 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R - +--R +------+ +------+4+-+ %pi +--R \|1 - %i \|1 + %i \|2 cos(---) +--R 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) - 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) ) +--R 2 8 8 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R +------+ +-+ tan(x) +------+ +-+ tan(x) +--R - 2\|1 + %i \|2 atan(---------) - 2\|1 - %i \|2 atan(---------) +--R +------+ +------+ +--R \|1 - %i \|1 + %i +--R + +--R - +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 sin(---) +--R 8 +--R * +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 2 8 2 +--R atan(-----------------------------------------------------) +--R +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) - 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R + +--R - +--R +------+ +------+4+-+ %pi +--R 2\|1 - %i \|1 + %i \|2 sin(---) +--R 8 +--R * +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 2 8 2 +--R atan(-----------------------------------------------------) +--R +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) + 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R / +--R +------+ +------+ +-+ +--R 4\|1 - %i \|1 + %i \|2 +--R Type: Expression(Complex(Integer)) +--E 371 + +--S 372 of 504 +--d0171:= D(m0171,x) +--E 372 + +--S 373 of 504 +t0172:= 1/(1+cos(x)^8) +--R +--R +--R 1 +--R (238) ----------- +--R 8 +--R cos(x) + 1 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 504 +r0172:= 1/4*atan(tan(x)/(1-(-1)^(1/4))^(1/2))/(1-(-1)^(1/4))^(1/2)+_ + 1/4*atan(tan(x)/(1+(-1)^(1/4))^(1/2))/(1+(-1)^(1/4))^(1/2)+_ + 1/4*atan(tan(x)/(1-(-1)^(3/4))^(1/2))/(1-(-1)^(3/4))^(1/2)+_ + 1/4*atan(tan(x)/(1+(-1)^(3/4))^(1/2))/(1+(-1)^(3/4))^(1/2) +--R +--R +--R (239) +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tan(x) +--R atan(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 - 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 + \|- 1 - 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tan(x) +--R atan(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 - \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 + 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tan(x) +--R atan(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 - 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R + +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R tan(x) +--R atan(--------------------) +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R / +--R +-----------------+ +-----------------+ +-----------------+ +--R | +-+ +---+ | +-+ +---+ | +-+ +---+ +--R |\|2 - \|- 1 - 1 |\|2 - \|- 1 + 1 |\|2 + \|- 1 - 1 +--R 4 |----------------- |----------------- |----------------- +--R | +-+ | +-+ | +-+ +--R \| \|2 \| \|2 \| \|2 +--R * +--R +-----------------+ +--R | +-+ +---+ +--R |\|2 + \|- 1 + 1 +--R |----------------- +--R | +-+ +--R \| \|2 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 504 +a0172:= integrate(t0172,x) +--R +--R +--R (240) +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R 2\|2 sin(-) + 8\|2 cos(-) sin(-) + 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R 8\|2 cos(-) sin(-) + 2\|2 cos(-) - 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 + 4 +--R (16\|2 cos(-)sin(-) - 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R 2\|2 sin(-) + 8\|2 cos(-) sin(-) + 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R 8\|2 cos(-) sin(-) + 2\|2 cos(-) - 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 + 4 +--R (- 16\|2 cos(-)sin(-) + 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R - 2\|2 sin(-) - 8\|2 cos(-) sin(-) - 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R - 8\|2 cos(-) sin(-) - 2\|2 cos(-) + 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 + 4 +--R (16\|2 cos(-)sin(-) - 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R - 2\|2 sin(-) - 8\|2 cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +-+ x 6 x 2 +--R - 12\|2 cos(-) sin(-) - 8\|2 cos(-) sin(-) +--R 2 2 2 2 +--R + +--R +-+ x 8 +-+ +--R - 2\|2 cos(-) + 2\|2 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 + 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 + 4 +--R (- 16\|2 cos(-)sin(-) + 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R 2\|2 sin(-) + 8\|2 cos(-) sin(-) + 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R 8\|2 cos(-) sin(-) + 2\|2 cos(-) - 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 - 4 +--R (16\|2 cos(-)sin(-) - 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R 2\|2 sin(-) + 8\|2 cos(-) sin(-) + 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R 8\|2 cos(-) sin(-) + 2\|2 cos(-) - 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 - 4 +--R (- 16\|2 cos(-)sin(-) + 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 x 4 +--R - 2\|2 sin(-) - 8\|2 cos(-) sin(-) - 12\|2 cos(-) sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 x 2 +-+ x 8 +-+ +--R - 8\|2 cos(-) sin(-) - 2\|2 cos(-) + 2\|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 - 4 +--R (16\|2 cos(-)sin(-) - 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R log +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +--R - 2\|2 sin(-) - 8\|2 cos(-) sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 x 4 +-+ x 6 x 2 +--R - 12\|2 cos(-) sin(-) - 8\|2 cos(-) sin(-) +--R 2 2 2 2 +--R + +--R +-+ x 8 +-+ +--R - 2\|2 cos(-) + 2\|2 +--R 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R sin(-) + 4cos(-) sin(-) + (6cos(-) - 2)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (4cos(-) + 12cos(-) )sin(-) + cos(-) - 2cos(-) + 1 +--R 2 2 2 2 2 +--R * +--R +---------+ 2 +--R | +-+ +--R |3\|2 - 4 +--R +---------+2 atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +---------+ +--R | +-+ +--R +-+ x x 3 +-+ x 3 x |4\|2 - 4 +--R (- 16\|2 cos(-)sin(-) + 16\|2 cos(-) sin(-)) |--------- +--R 2 2 2 2 4| +-+ +--R \| \|2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R atan(64 |--------- ) +--R | +-+ +--R \| 4096\|2 +--R cos(--------------------) +--R 2 +--R + +--R x 8 x 2 x 6 x 4 x 4 +--R 2sin(-) + 8cos(-) sin(-) + (12cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (8cos(-) - 24cos(-) )sin(-) + 2cos(-) + 4cos(-) + 2 +--R 2 2 2 2 2 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R - 4\|2 cos(-)sin(-) + (- 8\|2 cos(-) + 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (- 4\|2 cos(-) - 8\|2 cos(-) - 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 +--R - 8cos(-)sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 +--R + +--R x 5 x x +--R (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R - 4\|2 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R (- 8\|2 cos(-) + 8\|2 cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (- 4\|2 cos(-) - 8\|2 cos(-) - 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R - 4\|2 cos(-)sin(-) + (- 8\|2 cos(-) + 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (- 4\|2 cos(-) - 8\|2 cos(-) - 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 +--R - 8cos(-)sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 +--R + +--R x 5 x x +--R (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +--R - 4\|2 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 3 +-+ x x 3 +--R (- 8\|2 cos(-) + 8\|2 cos(-))sin(-) +--R 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (- 4\|2 cos(-) - 8\|2 cos(-) - 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R - \|2 sin(-) + (- 4\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (- 6\|2 cos(-) + 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (- 4\|2 cos(-) - 2\|2 cos(-) - 2\|2 )sin(-) - \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R - 2\|2 cos(-) + 2\|2 cos(-) + \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R - \|2 sin(-) + (- 4\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (- 6\|2 cos(-) + 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (- 4\|2 cos(-) - 2\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R - \|2 cos(-) - 2\|2 cos(-) + 2\|2 cos(-) + \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 +--R - 8cos(-)sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 +--R + +--R x 5 x x +--R (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 + 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 + 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R + +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R - \|2 sin(-) + (- 4\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (- 6\|2 cos(-) + 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (- 4\|2 cos(-) - 2\|2 cos(-) - 2\|2 )sin(-) - \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R - 2\|2 cos(-) + 2\|2 cos(-) + \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 x 5 x x +--R 8cos(-)sin(-) + 16cos(-) sin(-) + (8cos(-) - 8cos(-))sin(-) +--R 2 2 2 2 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +-+ x 8 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) + \|2 cos(-) +--R 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 +-+ +--R 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R 2sin(-) + (8cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (12cos(-) - 4cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (8cos(-) + 4cos(-) - 24cos(-) - 4)sin(-) + 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4cos(-) + 4cos(-) + 4cos(-) + 2 +--R 2 2 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R 2 |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R * +--R atan +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R - \|2 sin(-) + (- 4\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (- 6\|2 cos(-) + 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (- 4\|2 cos(-) - 2\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R - \|2 cos(-) - 2\|2 cos(-) + 2\|2 cos(-) + \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x x 5 x 3 x 3 +--R - 8cos(-)sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 +--R + +--R x 5 x x +--R (- 8cos(-) + 8cos(-))sin(-) +--R 2 2 2 +--R / +--R +-+ x 8 +-+ x 2 +-+ x 6 +--R \|2 sin(-) + (4\|2 cos(-) - 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 4 +-+ x 2 x 4 +--R (6\|2 cos(-) - 2\|2 cos(-) )sin(-) +--R 2 2 2 +--R + +--R +-+ x 6 +-+ x 4 +-+ x 2 +--R (4\|2 cos(-) + 2\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 +--R + +--R +-+ x 8 +-+ x 6 +-+ x 2 +-+ +--R \|2 cos(-) + 2\|2 cos(-) - 2\|2 cos(-) - \|2 +--R 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- sin(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R +-+ x x 5 +-+ x 3 +-+ x x 3 +--R 4\|2 cos(-)sin(-) + (8\|2 cos(-) - 8\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 5 +-+ x 3 +-+ x x +--R (4\|2 cos(-) + 8\|2 cos(-) + 4\|2 cos(-))sin(-) +--R 2 2 2 2 +--R * +--R +---------+ +--R | +-+ +--R |3\|2 - 4 +--R +---------+ atan(64 |--------- ) +--R | +-+ | +-+ +--R |4\|2 - 4 \| 4096\|2 +--R |--------- cos(--------------------) +--R 4| +-+ 2 +--R \| \|2 +--R + +--R x 8 x 2 x 6 +--R - 2sin(-) + (- 8cos(-) + 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (- 12cos(-) + 4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 +--R (- 8cos(-) - 4cos(-) + 24cos(-) + 4)sin(-) - 2cos(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4cos(-) - 4cos(-) - 4cos(-) - 2 +--R 2 2 2 +--R / +--R +-+ +--R 16\|2 +--R Type: Union(Expression(Integer),...) +--E 375 + +--S 376 of 504 +t0173:= 1/(1-cos(x)^3) +--R +--R +--R 1 +--R (241) - ----------- +--R 3 +--R cos(x) - 1 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 504 +r0173:= 2/3*atan((1-(-1)^(1/3))*tan(1/2*x)/(1-(-1)^(2/3))^(1/2))/_ + (1-(-1)^(2/3))^(1/2)+2/3*atan((1+(-1)^(2/3))*tan(1/2*x)/_ + (1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)-sin(x)/(3-3*cos(x)) +--R +--R +--R (242) +--R 3+---+ x +--R +----------+ (\|- 1 - 1)tan(-) +--R |3+---+ 2 +--R (- 2cos(x) + 2)\|\|- 1 + 1 atan(------------------) +--R +-------------+ +--R | 3+---+2 +--R \|- \|- 1 + 1 +--R + +--R 3+---+2 x +--R +-------------+ (\|- 1 + 1)tan(-) +--R | 3+---+2 2 +--R (2cos(x) - 2)\|- \|- 1 + 1 atan(-------------------) +--R +----------+ +--R |3+---+ +--R \|\|- 1 + 1 +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R sin(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R (3cos(x) - 3)\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 504 +a0173:= integrate(t0173,x) +--R +--R +--R (243) +--R %pi x 4 %pi x 2 %pi x 2 +--R - cos(---)sin(-) + (- 2cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R - cos(---)cos(-) + 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) + 3\|3 sin(---) + 3cos(---) + \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (6cos(-) - 6)sin(---) + 6\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (6cos(---) + 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (4\|3 \|3 cos(-)sin(---) - 12\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (3\|3 cos(-) - 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (3cos(---) + \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (6cos(---) - 2\|3 )cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R cos(---)sin(-) + (2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) - 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) + 3\|3 sin(---) + 3cos(---) + \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (6cos(-) - 6)sin(---) + 6\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (6cos(---) + 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (- 4\|3 \|3 cos(-)sin(---) + 12\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (3\|3 cos(-) - 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (3cos(---) + \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (6cos(---) - 2\|3 )cos(-) + 3cos(---) - \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R - cos(---)sin(-) + (- 2cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R - cos(---)cos(-) + 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) - 3\|3 sin(---) + 3cos(---) - \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (6cos(-) - 6)sin(---) - 6\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (6cos(---) - 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (4\|3 \|3 cos(-)sin(---) - 12\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (- 3\|3 cos(-) + 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (3cos(---) - \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (6cos(---) - 2\|3 )cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 %pi x 2 %pi x 2 +--R cos(---)sin(-) + (2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R %pi x 4 %pi x 2 %pi +--R cos(---)cos(-) - 2cos(---)cos(-) + cos(---) +--R 12 2 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 +-+4+-+ %pi +--R 3sin(---) - 3\|3 sin(---) + 3cos(---) - \|3 \|3 cos(---) +--R 12 12 12 12 +--R + +--R 4+-+2 +--R \|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R (6cos(-) - 6)sin(---) - 6\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 2 +--R (6cos(---) - 2\|3 \|3 cos(---) + 2\|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 +--R - 6cos(---) + 2\|3 +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R +-+4+-+ x %pi 4+-+ %pi x x +--R (- 4\|3 \|3 cos(-)sin(---) + 12\|3 cos(---)cos(-))sin(-) +--R 2 12 12 2 2 +--R + +--R x 4 x 2 %pi 2 +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 4 4+-+ %pi +--R (- 3\|3 cos(-) + 3\|3 )sin(---) +--R 2 12 +--R + +--R %pi 2 +-+4+-+ %pi 4+-+2 x 4 +--R (3cos(---) - \|3 \|3 cos(---) + \|3 )cos(-) +--R 12 12 2 +--R + +--R %pi 2 4+-+2 x 2 %pi 2 +-+4+-+ %pi +--R (6cos(---) - 2\|3 )cos(-) + 3cos(---) + \|3 \|3 cos(---) +--R 12 2 12 12 +--R + +--R 4+-+2 +--R \|3 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R %pi x 4 x 2 %pi x 2 +--R 2sin(---)sin(-) + (4cos(-) + 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (2cos(-) - 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (3sin(---) + \|3 cos(---) + 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (6cos(-) - 6)sin(---) + (2\|3 cos(---) + 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R - 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (\|3 cos(---) + 2\|3 )cos(-) + 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R \|3 cos(---) - 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) - 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) - 6cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi %pi x 4 +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) - 3cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 %pi +--R - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R - 2sin(---)sin(-) + (- 4cos(-) - 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (- 2cos(-) + 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (3sin(---) + \|3 cos(---) + 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (6cos(-) - 6)sin(---) + (2\|3 cos(---) + 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R - 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (\|3 cos(---) + 2\|3 )cos(-) + 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R \|3 cos(---) - 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) - 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) - 6cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi x 4 %pi x 2 %pi +--R - 3cos(---)cos(-) - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R 2sin(---)sin(-) + (4cos(-) + 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (2cos(-) - 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (3sin(---) + \|3 cos(---) - 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (6cos(-) - 6)sin(---) + (2\|3 cos(---) - 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R - 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (\|3 cos(---) - 2\|3 )cos(-) + 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R \|3 cos(---) + 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) - 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) - 6cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R + +--R +-+ x 4 +-+ x 2 +-+ %pi %pi x 4 +--R (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) - 3cos(---)cos(-) +--R 2 2 12 12 2 +--R + +--R %pi x 2 %pi +--R - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 +--R + +--R %pi x 4 x 2 %pi x 2 +--R - 2sin(---)sin(-) + (- 4cos(-) - 4)sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 x 2 %pi +--R (- 2cos(-) + 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi +-+ %pi 4+-+ x 4 +--R (3sin(---) + \|3 cos(---) - 2\|3 )sin(-) +--R 12 12 2 +--R + +--R x 2 %pi +-+ %pi 4+-+ x 2 +--R (6cos(-) - 6)sin(---) + (2\|3 cos(---) - 4\|3 )cos(-) +--R 2 12 12 2 +--R + +--R +-+ %pi +--R - 2\|3 cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 4 x 2 %pi +--R (3cos(-) + 6cos(-) + 3)sin(---) +--R 2 2 12 +--R + +--R +-+ %pi 4+-+ x 4 +-+ %pi x 2 +--R (\|3 cos(---) - 2\|3 )cos(-) + 2\|3 cos(---)cos(-) +--R 12 2 12 2 +--R + +--R +-+ %pi 4+-+ +--R \|3 cos(---) + 2\|3 +--R 12 +--R / +--R +-+ %pi %pi x 4 +--R (\|3 sin(---) - 3cos(---))sin(-) +--R 12 12 2 +--R + +--R +-+ x 2 +-+ %pi %pi x 2 +--R (2\|3 cos(-) - 2\|3 )sin(---) - 6cos(---)cos(-) +--R 2 12 12 2 +--R + +--R %pi +--R 6cos(---) +--R 12 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ x x +-+ x 4 +-+ x 2 +-+ %pi +--R 8\|3 cos(-)sin(-) + (\|3 cos(-) + 2\|3 cos(-) + \|3 )sin(---) +--R 2 2 2 2 12 +--R + +--R %pi x 4 %pi x 2 %pi +--R - 3cos(---)cos(-) - 6cos(---)cos(-) - 3cos(---) +--R 12 2 12 2 12 +--R + +--R 4+-+ x x +--R - 8\|3 cos(-)sin(-) +--R 2 2 +--R / +--R 4+-+ x 4 4+-+ x 2 4+-+ x 2 4+-+ x 4 +--R 6\|3 sin(-) + (12\|3 cos(-) + 12\|3 )sin(-) + 6\|3 cos(-) +--R 2 2 2 2 +--R + +--R 4+-+ x 2 4+-+ +--R - 12\|3 cos(-) + 6\|3 +--R 2 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 504 +t0174:= 1/(1-cos(x)^6) +--R +--R +--R 1 +--R (244) - ----------- +--R 6 +--R cos(x) - 1 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 504 +r0174:= 1/3*atan(tan(x)/(1+(-1)^(1/3))^(1/2))/(1+(-1)^(1/3))^(1/2)+_ + 1/3*atan(tan(x)/(1-(-1)^(2/3))^(1/2))/(1-(-1)^(2/3))^(1/2)-1/3*cot(x) +--R +--R +--R (245) +--R +----------+ +-------------+ +--R |3+---+ tan(x) | 3+---+2 tan(x) +--R \|\|- 1 + 1 atan(----------------) + \|- \|- 1 + 1 atan(-------------) +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R \|- \|- 1 + 1 \|\|- 1 + 1 +--R + +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R - cot(x)\|- \|- 1 + 1 \|\|- 1 + 1 +--R / +--R +-------------+ +----------+ +--R | 3+---+2 |3+---+ +--R 3\|- \|- 1 + 1 \|\|- 1 + 1 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 504 +a0174:= integrate(t0174,x) +--R +--R +--R (246) +--R %pi x 8 %pi x 2 x 6 +--R cos(---)sin(-) + 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (6cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (4cos(---)cos(-) + 12cos(---)cos(-) )sin(-) + cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R - 2cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 4+-+2 x 8 +--R (sin(---) + 2\|3 sin(---) + cos(---) + \|3 )sin(-) +--R 12 12 12 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 4cos(-) sin(---) + 8\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) +--R 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (6cos(-) - 2)sin(---) + 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (6cos(---) + 6\|3 )cos(-) - 2cos(---) + 2\|3 +--R 12 2 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x x 3 +--R 16\|3 cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (4cos(-) + 12cos(-) )sin(---) + 8\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 6 %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) + (12cos(---) - 12\|3 )cos(-) +--R 12 2 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x 3 x +--R - 16\|3 cos(---)cos(-) sin(-) +--R 12 2 2 +--R + +--R x 8 x 4 %pi 2 +--R (cos(-) - 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi %pi 2 4+-+2 x 8 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (cos(---) + \|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (- 2cos(---) + 2\|3 )cos(-) + cos(---) + \|3 +--R 12 2 12 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 %pi x 2 x 6 +--R - cos(---)sin(-) - 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (- 6cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (- 4cos(---)cos(-) - 12cos(---)cos(-) )sin(-) - cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R 2cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 4+-+2 x 8 +--R (sin(---) + 2\|3 sin(---) + cos(---) + \|3 )sin(-) +--R 12 12 12 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 4cos(-) sin(---) + 8\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) +--R 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (6cos(-) - 2)sin(---) + 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (6cos(---) + 6\|3 )cos(-) - 2cos(---) + 2\|3 +--R 12 2 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x x 3 +--R - 16\|3 cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (4cos(-) + 12cos(-) )sin(---) + 8\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 6 %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) + (12cos(---) - 12\|3 )cos(-) +--R 12 2 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x 3 x x 8 x 4 %pi 2 +--R 16\|3 cos(---)cos(-) sin(-) + (cos(-) - 2cos(-) + 1)sin(---) +--R 12 2 2 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi %pi 2 4+-+2 x 8 +--R (2\|3 cos(-) - 2\|3 )sin(---) + (cos(---) + \|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (- 2cos(---) + 2\|3 )cos(-) + cos(---) + \|3 +--R 12 2 12 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 %pi x 2 x 6 +--R cos(---)sin(-) + 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (6cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (4cos(---)cos(-) + 12cos(---)cos(-) )sin(-) + cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R - 2cos(---)cos(-) + cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 4+-+2 x 8 +--R (sin(---) - 2\|3 sin(---) + cos(---) + \|3 )sin(-) +--R 12 12 12 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 4cos(-) sin(---) - 8\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) +--R 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (6cos(-) - 2)sin(---) - 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (6cos(---) + 6\|3 )cos(-) - 2cos(---) + 2\|3 +--R 12 2 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x x 3 +--R 16\|3 cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (4cos(-) + 12cos(-) )sin(---) - 8\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 6 %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) + (12cos(---) - 12\|3 )cos(-) +--R 12 2 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x 3 x +--R - 16\|3 cos(---)cos(-) sin(-) +--R 12 2 2 +--R + +--R x 8 x 4 %pi 2 +--R (cos(-) - 2cos(-) + 1)sin(---) +--R 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi %pi 2 4+-+2 x 8 +--R (- 2\|3 cos(-) + 2\|3 )sin(---) + (cos(---) + \|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (- 2cos(---) + 2\|3 )cos(-) + cos(---) + \|3 +--R 12 2 12 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 %pi x 2 x 6 +--R - cos(---)sin(-) - 4cos(---)cos(-) sin(-) +--R 12 2 12 2 2 +--R + +--R %pi x 4 %pi x 4 +--R (- 6cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 +--R + +--R %pi x 6 %pi x 2 x 2 %pi x 8 +--R (- 4cos(---)cos(-) - 12cos(---)cos(-) )sin(-) - cos(---)cos(-) +--R 12 2 12 2 2 12 2 +--R + +--R %pi x 4 %pi +--R 2cos(---)cos(-) - cos(---) +--R 12 2 12 +--R * +--R log +--R %pi 2 4+-+ %pi %pi 2 4+-+2 x 8 +--R (sin(---) - 2\|3 sin(---) + cos(---) + \|3 )sin(-) +--R 12 12 12 2 +--R + +--R x 2 %pi 2 4+-+ x 2 %pi +--R 4cos(-) sin(---) - 8\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) +--R 12 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 4 %pi 2 4+-+ x 4 %pi +--R (6cos(-) - 2)sin(---) - 12\|3 cos(-) sin(---) +--R 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (6cos(---) + 6\|3 )cos(-) - 2cos(---) + 2\|3 +--R 12 2 12 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x x 3 +--R - 16\|3 cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 6 x 2 %pi 2 4+-+ x 6 %pi +--R (4cos(-) + 12cos(-) )sin(---) - 8\|3 cos(-) sin(---) +--R 2 2 12 2 12 +--R + +--R %pi 2 4+-+2 x 6 %pi 2 4+-+2 x 2 +--R (4cos(---) + 4\|3 )cos(-) + (12cos(---) - 12\|3 )cos(-) +--R 12 2 12 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 4+-+ %pi x 3 x x 8 x 4 %pi 2 +--R 16\|3 cos(---)cos(-) sin(-) + (cos(-) - 2cos(-) + 1)sin(---) +--R 12 2 2 2 2 12 +--R + +--R 4+-+ x 8 4+-+ %pi %pi 2 4+-+2 x 8 +--R (- 2\|3 cos(-) + 2\|3 )sin(---) + (cos(---) + \|3 )cos(-) +--R 2 12 12 2 +--R + +--R %pi 2 4+-+2 x 4 %pi 2 4+-+2 +--R (- 2cos(---) + 2\|3 )cos(-) + cos(---) + \|3 +--R 12 2 12 +--R / +--R x 8 x 2 x 6 +--R sin(-) + (4cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 4 +--R (6cos(-) - 4cos(-) + 6)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 2 x 8 x 6 +--R (4cos(-) + 4cos(-) - 4cos(-) - 4)sin(-) + cos(-) + 4cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 4cos(-) + 1 +--R 2 2 +--R + +--R %pi x 8 x 2 %pi x 6 +--R - 2sin(---)sin(-) - 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (- 12cos(-) + 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (- 8cos(-) - 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (- 2cos(-) + 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi x 8 %pi x 2 %pi x 6 +--R cos(---)sin(-) + (4cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x %pi 4+-+ x x 5 +--R (4cos(-)sin(---) - 4\|3 cos(-))sin(-) +--R 2 12 2 2 +--R + +--R %pi x 4 %pi x 2 x 4 +--R (6cos(---)cos(-) - 2cos(---)cos(-) )sin(-) +--R 12 2 12 2 2 +--R + +--R x 3 x %pi 4+-+ x 3 x 3 +--R ((8cos(-) - 8cos(-))sin(---) - 8\|3 cos(-) )sin(-) +--R 2 2 12 2 2 +--R + +--R %pi x 6 %pi x 4 %pi x 2 +--R (4cos(---)cos(-) + 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x 5 x 3 x %pi 4+-+ x 5 +--R (4cos(-) + 8cos(-) + 4cos(-))sin(---) - 4\|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x +--R 4\|3 cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi 4+-+ x 8 +--R (sin(---) - \|3 )sin(-) +--R 12 2 +--R + +--R x 2 %pi 4+-+ x 2 4+-+ x 6 +--R ((4cos(-) - 2)sin(---) - 4\|3 cos(-) + 2\|3 )sin(-) +--R 2 12 2 2 +--R + +--R %pi x x 5 +--R - 4cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 4 x 2 %pi 4+-+ x 4 4+-+ x 2 +--R (6cos(-) - 2cos(-) )sin(---) - 6\|3 cos(-) + 2\|3 cos(-) +--R 2 2 12 2 2 +--R + +--R 4+-+ +--R - 2\|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R %pi x 3 %pi x x 3 +--R (- 8cos(---)cos(-) + 8cos(---)cos(-))sin(-) +--R 12 2 12 2 2 +--R + +--R x 6 x 4 %pi 4+-+ x 6 +--R (4cos(-) + 2cos(-) + 2)sin(---) - 4\|3 cos(-) +--R 2 2 12 2 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ +--R - 2\|3 cos(-) + 12\|3 cos(-) + 2\|3 +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R %pi x 5 %pi x 3 %pi x x +--R (- 4cos(---)cos(-) - 8cos(---)cos(-) - 4cos(---)cos(-))sin(-) +--R 12 2 12 2 12 2 2 +--R + +--R x 8 x 6 x 2 %pi 4+-+ x 8 +--R (cos(-) + 2cos(-) - 2cos(-) - 1)sin(---) - \|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x 6 4+-+ x 4 4+-+ x 2 4+-+ +--R - 2\|3 cos(-) - 2\|3 cos(-) - 2\|3 cos(-) - \|3 +--R 2 2 2 +--R + +--R %pi x 8 x 2 %pi x 6 +--R 2sin(---)sin(-) + 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (12cos(-) - 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (8cos(-) + 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (2cos(-) - 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi x 8 %pi x 2 %pi x 6 +--R cos(---)sin(-) + (4cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x %pi 4+-+ x x 5 +--R (- 4cos(-)sin(---) + 4\|3 cos(-))sin(-) +--R 2 12 2 2 +--R + +--R %pi x 4 %pi x 2 x 4 +--R (6cos(---)cos(-) - 2cos(---)cos(-) )sin(-) +--R 12 2 12 2 2 +--R + +--R x 3 x %pi 4+-+ x 3 x 3 +--R ((- 8cos(-) + 8cos(-))sin(---) + 8\|3 cos(-) )sin(-) +--R 2 2 12 2 2 +--R + +--R %pi x 6 %pi x 4 %pi x 2 +--R (4cos(---)cos(-) + 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x 5 x 3 x %pi 4+-+ x 5 +--R (- 4cos(-) - 8cos(-) - 4cos(-))sin(---) + 4\|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x +--R - 4\|3 cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi 4+-+ x 8 +--R (sin(---) - \|3 )sin(-) +--R 12 2 +--R + +--R x 2 %pi 4+-+ x 2 4+-+ x 6 +--R ((4cos(-) - 2)sin(---) - 4\|3 cos(-) + 2\|3 )sin(-) +--R 2 12 2 2 +--R + +--R %pi x x 5 +--R 4cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 4 x 2 %pi 4+-+ x 4 4+-+ x 2 +--R (6cos(-) - 2cos(-) )sin(---) - 6\|3 cos(-) + 2\|3 cos(-) +--R 2 2 12 2 2 +--R + +--R 4+-+ +--R - 2\|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R %pi x 3 %pi x x 3 +--R (8cos(---)cos(-) - 8cos(---)cos(-))sin(-) +--R 12 2 12 2 2 +--R + +--R x 6 x 4 %pi 4+-+ x 6 +--R (4cos(-) + 2cos(-) + 2)sin(---) - 4\|3 cos(-) +--R 2 2 12 2 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ +--R - 2\|3 cos(-) + 12\|3 cos(-) + 2\|3 +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R %pi x 5 %pi x 3 %pi x x +--R (4cos(---)cos(-) + 8cos(---)cos(-) + 4cos(---)cos(-))sin(-) +--R 12 2 12 2 12 2 2 +--R + +--R x 8 x 6 x 2 %pi 4+-+ x 8 +--R (cos(-) + 2cos(-) - 2cos(-) - 1)sin(---) - \|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x 6 4+-+ x 4 4+-+ x 2 4+-+ +--R - 2\|3 cos(-) - 2\|3 cos(-) - 2\|3 cos(-) - \|3 +--R 2 2 2 +--R + +--R %pi x 8 x 2 %pi x 6 +--R 2sin(---)sin(-) + 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (12cos(-) - 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (8cos(-) + 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (2cos(-) - 4cos(-) + 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi x 8 %pi x 2 %pi x 6 +--R cos(---)sin(-) + (4cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x %pi 4+-+ x x 5 +--R (4cos(-)sin(---) + 4\|3 cos(-))sin(-) +--R 2 12 2 2 +--R + +--R %pi x 4 %pi x 2 x 4 +--R (6cos(---)cos(-) - 2cos(---)cos(-) )sin(-) +--R 12 2 12 2 2 +--R + +--R x 3 x %pi 4+-+ x 3 x 3 +--R ((8cos(-) - 8cos(-))sin(---) + 8\|3 cos(-) )sin(-) +--R 2 2 12 2 2 +--R + +--R %pi x 6 %pi x 4 %pi x 2 +--R (4cos(---)cos(-) + 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x 5 x 3 x %pi 4+-+ x 5 +--R (4cos(-) + 8cos(-) + 4cos(-))sin(---) + 4\|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x +--R - 4\|3 cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi 4+-+ x 8 +--R (sin(---) + \|3 )sin(-) +--R 12 2 +--R + +--R x 2 %pi 4+-+ x 2 4+-+ x 6 +--R ((4cos(-) - 2)sin(---) + 4\|3 cos(-) - 2\|3 )sin(-) +--R 2 12 2 2 +--R + +--R %pi x x 5 +--R - 4cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 4 x 2 %pi 4+-+ x 4 4+-+ x 2 +--R (6cos(-) - 2cos(-) )sin(---) + 6\|3 cos(-) - 2\|3 cos(-) +--R 2 2 12 2 2 +--R + +--R 4+-+ +--R 2\|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R %pi x 3 %pi x x 3 +--R (- 8cos(---)cos(-) + 8cos(---)cos(-))sin(-) +--R 12 2 12 2 2 +--R + +--R x 6 x 4 %pi 4+-+ x 6 +--R (4cos(-) + 2cos(-) + 2)sin(---) + 4\|3 cos(-) +--R 2 2 12 2 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ +--R 2\|3 cos(-) - 12\|3 cos(-) - 2\|3 +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R %pi x 5 %pi x 3 %pi x x +--R (- 4cos(---)cos(-) - 8cos(---)cos(-) - 4cos(---)cos(-))sin(-) +--R 12 2 12 2 12 2 2 +--R + +--R x 8 x 6 x 2 %pi 4+-+ x 8 +--R (cos(-) + 2cos(-) - 2cos(-) - 1)sin(---) + \|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x 6 4+-+ x 4 4+-+ x 2 4+-+ +--R 2\|3 cos(-) + 2\|3 cos(-) + 2\|3 cos(-) + \|3 +--R 2 2 2 +--R + +--R %pi x 8 x 2 %pi x 6 +--R - 2sin(---)sin(-) - 8cos(-) sin(---)sin(-) +--R 12 2 2 12 2 +--R + +--R x 4 %pi x 4 +--R (- 12cos(-) + 4)sin(---)sin(-) +--R 2 12 2 +--R + +--R x 6 x 2 %pi x 2 +--R (- 8cos(-) - 24cos(-) )sin(---)sin(-) +--R 2 2 12 2 +--R + +--R x 8 x 4 %pi +--R (- 2cos(-) + 4cos(-) - 2)sin(---) +--R 2 2 12 +--R * +--R atan +--R %pi x 8 %pi x 2 %pi x 6 +--R cos(---)sin(-) + (4cos(---)cos(-) - 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x %pi 4+-+ x x 5 +--R (- 4cos(-)sin(---) - 4\|3 cos(-))sin(-) +--R 2 12 2 2 +--R + +--R %pi x 4 %pi x 2 x 4 +--R (6cos(---)cos(-) - 2cos(---)cos(-) )sin(-) +--R 12 2 12 2 2 +--R + +--R x 3 x %pi 4+-+ x 3 x 3 +--R ((- 8cos(-) + 8cos(-))sin(---) - 8\|3 cos(-) )sin(-) +--R 2 2 12 2 2 +--R + +--R %pi x 6 %pi x 4 %pi x 2 +--R (4cos(---)cos(-) + 2cos(---)cos(-) + 2cos(---))sin(-) +--R 12 2 12 2 12 2 +--R + +--R x 5 x 3 x %pi 4+-+ x 5 +--R (- 4cos(-) - 8cos(-) - 4cos(-))sin(---) - 4\|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x +--R 4\|3 cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R %pi x 8 %pi x 6 %pi x 2 %pi +--R cos(---)cos(-) + 2cos(---)cos(-) - 2cos(---)cos(-) - cos(---) +--R 12 2 12 2 12 2 12 +--R / +--R %pi 4+-+ x 8 +--R (sin(---) + \|3 )sin(-) +--R 12 2 +--R + +--R x 2 %pi 4+-+ x 2 4+-+ x 6 +--R ((4cos(-) - 2)sin(---) + 4\|3 cos(-) - 2\|3 )sin(-) +--R 2 12 2 2 +--R + +--R %pi x x 5 +--R 4cos(---)cos(-)sin(-) +--R 12 2 2 +--R + +--R x 4 x 2 %pi 4+-+ x 4 4+-+ x 2 +--R (6cos(-) - 2cos(-) )sin(---) + 6\|3 cos(-) - 2\|3 cos(-) +--R 2 2 12 2 2 +--R + +--R 4+-+ +--R 2\|3 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R %pi x 3 %pi x x 3 +--R (8cos(---)cos(-) - 8cos(---)cos(-))sin(-) +--R 12 2 12 2 2 +--R + +--R x 6 x 4 %pi 4+-+ x 6 +--R (4cos(-) + 2cos(-) + 2)sin(---) + 4\|3 cos(-) +--R 2 2 12 2 +--R + +--R 4+-+ x 4 4+-+ x 2 4+-+ +--R 2\|3 cos(-) - 12\|3 cos(-) - 2\|3 +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R %pi x 5 %pi x 3 %pi x x +--R (4cos(---)cos(-) + 8cos(---)cos(-) + 4cos(---)cos(-))sin(-) +--R 12 2 12 2 12 2 2 +--R + +--R x 8 x 6 x 2 %pi 4+-+ x 8 +--R (cos(-) + 2cos(-) - 2cos(-) - 1)sin(---) + \|3 cos(-) +--R 2 2 2 12 2 +--R + +--R 4+-+ x 6 4+-+ x 4 4+-+ x 2 4+-+ +--R 2\|3 cos(-) + 2\|3 cos(-) + 2\|3 cos(-) + \|3 +--R 2 2 2 +--R + +--R 4+-+ x x 3 4+-+ x 3 x +--R 32\|3 cos(-)sin(-) - 32\|3 cos(-) sin(-) +--R 2 2 2 2 +--R / +--R 4+-+ x 8 4+-+ x 2 x 6 4+-+ x 4 4+-+ x 4 +--R 12\|3 sin(-) + 48\|3 cos(-) sin(-) + (72\|3 cos(-) - 24\|3 )sin(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ x 6 4+-+ x 2 x 2 4+-+ x 8 4+-+ x 4 +--R (48\|3 cos(-) + 144\|3 cos(-) )sin(-) + 12\|3 cos(-) - 24\|3 cos(-) +--R 2 2 2 2 2 +--R + +--R 4+-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 504 +t0175:= 1/(1-cos(x)^8) +--R +--R +--R 1 +--R (247) - ----------- +--R 8 +--R cos(x) - 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 504 +r0175:= 1/4*atan(tan(x)/(1-%i)^(1/2))/(1-%i)^(1/2)+_ + 1/4*atan(tan(x)/(1+%i)^(1/2))/(1+%i)^(1/2)+_ + 1/8*atan(1/2*2^(1/2)*tan(x))*2^(1/2)-1/4*cot(x) +--R +--R +--R (248) +--R +-+ +--R +------+ +------+ +-+ \|2 tan(x) +------+ tan(x) +--R \|1 - %i \|1 + %i \|2 atan(----------) + 2\|1 + %i atan(---------) +--R 2 +------+ +--R \|1 - %i +--R + +--R +------+ tan(x) +------+ +------+ +--R 2\|1 - %i atan(---------) - 2\|1 - %i \|1 + %i cot(x) +--R +------+ +--R \|1 + %i +--R / +--R +------+ +------+ +--R 8\|1 - %i \|1 + %i +--R Type: Expression(Complex(Integer)) +--E 383 + +--S 384 of 504 +a0175:= integrate(t0175,x) +--R +--R +--R (249) +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 2 x 6 +--R \|2 \|2 cos(---)sin(-) + 4\|2 \|2 cos(---)cos(-) sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 4 +-+4+-+ %pi x 4 +--R (6\|2 \|2 cos(---)cos(-) - 2\|2 \|2 cos(---))sin(-) +--R 8 2 8 2 +--R + +--R +-+4+-+ %pi x 6 +-+4+-+ %pi x 2 x 2 +--R (4\|2 \|2 cos(---)cos(-) + 12\|2 \|2 cos(---)cos(-) )sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 4 +-+4+-+ %pi +--R \|2 \|2 cos(---)cos(-) - 2\|2 \|2 cos(---)cos(-) + \|2 \|2 cos(---) +--R 8 2 8 2 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) + 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R - 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 2 x 6 +--R - \|2 \|2 cos(---)sin(-) - 4\|2 \|2 cos(---)cos(-) sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 4 +-+4+-+ %pi x 4 +--R (- 6\|2 \|2 cos(---)cos(-) + 2\|2 \|2 cos(---))sin(-) +--R 8 2 8 2 +--R + +--R +-+4+-+ %pi x 6 +-+4+-+ %pi x 2 x 2 +--R (- 4\|2 \|2 cos(---)cos(-) - 12\|2 \|2 cos(---)cos(-) )sin(-) +--R 8 2 8 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ %pi x 4 +-+4+-+ %pi +--R - \|2 \|2 cos(---)cos(-) + 2\|2 \|2 cos(---)cos(-) - \|2 \|2 cos(---) +--R 8 2 8 2 8 +--R * +--R log +--R x 4 +-+4+-+ %pi x x 3 +--R sin(-) - 2\|2 \|2 cos(---)cos(-)sin(-) +--R 2 8 2 2 +--R + +--R 4+-+2 x 2 %pi 2 4+-+2 %pi 2 x 2 x 2 +--R (2\|2 cos(-) sin(---) + (2\|2 cos(---) - 2)cos(-) )sin(-) +--R 2 8 8 2 2 +--R + +--R +-+4+-+ %pi x 3 x x 4 +--R 2\|2 \|2 cos(---)cos(-) sin(-) + cos(-) +--R 8 2 2 2 +--R / +--R x 4 x 2 x 2 x 4 x 2 +--R sin(-) + (- 2cos(-) - 2)sin(-) + cos(-) + 2cos(-) + 1 +--R 2 2 2 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ x 2 %pi x 6 +--R - 2\|2 \|2 sin(---)sin(-) - 8\|2 \|2 cos(-) sin(---)sin(-) +--R 8 2 2 8 2 +--R + +--R +-+4+-+ x 4 +-+4+-+ %pi x 4 +--R (- 12\|2 \|2 cos(-) + 4\|2 \|2 )sin(---)sin(-) +--R 2 8 2 +--R + +--R +-+4+-+ x 6 +-+4+-+ x 2 %pi x 2 +--R (- 8\|2 \|2 cos(-) - 24\|2 \|2 cos(-) )sin(---)sin(-) +--R 2 2 8 2 +--R + +--R +-+4+-+ x 8 +-+4+-+ x 4 +-+4+-+ %pi +--R (- 2\|2 \|2 cos(-) + 4\|2 \|2 cos(-) - 2\|2 \|2 )sin(---) +--R 2 2 8 +--R * +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 2 8 2 +--R atan(-----------------------------------------------------) +--R +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) - 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R + +--R +-+4+-+ %pi x 8 +-+4+-+ x 2 %pi x 6 +--R - 2\|2 \|2 sin(---)sin(-) - 8\|2 \|2 cos(-) sin(---)sin(-) +--R 8 2 2 8 2 +--R + +--R +-+4+-+ x 4 +-+4+-+ %pi x 4 +--R (- 12\|2 \|2 cos(-) + 4\|2 \|2 )sin(---)sin(-) +--R 2 8 2 +--R + +--R +-+4+-+ x 6 +-+4+-+ x 2 %pi x 2 +--R (- 8\|2 \|2 cos(-) - 24\|2 \|2 cos(-) )sin(---)sin(-) +--R 2 2 8 2 +--R + +--R +-+4+-+ x 8 +-+4+-+ x 4 +-+4+-+ %pi +--R (- 2\|2 \|2 cos(-) + 4\|2 \|2 cos(-) - 2\|2 \|2 )sin(---) +--R 2 2 8 +--R * +--R 4+-+ x %pi x +--R 2\|2 cos(-)sin(---)sin(-) +--R 2 8 2 +--R atan(-----------------------------------------------------) +--R +-+ x 2 4+-+ %pi x x +-+ x 2 +--R \|2 sin(-) + 2\|2 cos(---)cos(-)sin(-) - \|2 cos(-) +--R 2 8 2 2 2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 +-+ x 4 +--R - \|2 sin(-) - 4\|2 cos(-) sin(-) + (- 6\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +-+ x 8 +-+ x 4 +--R (- 4\|2 cos(-) - 12\|2 cos(-) )sin(-) - \|2 cos(-) + 2\|2 cos(-) +--R 2 2 2 2 2 +--R + +--R +-+ +--R - \|2 +--R * +--R +-+ x x +--R 2\|2 cos(-)sin(-) +--R 2 2 +--R atan(------------------) +--R x 2 x 2 +--R sin(-) - 2cos(-) +--R 2 2 +--R + +--R +-+ x 8 +-+ x 2 x 6 +-+ x 4 +-+ x 4 +--R - \|2 sin(-) - 4\|2 cos(-) sin(-) + (- 6\|2 cos(-) + 2\|2 )sin(-) +--R 2 2 2 2 2 +--R + +--R +-+ x 6 +-+ x 2 x 2 +-+ x 8 +-+ x 4 +--R (- 4\|2 cos(-) - 12\|2 cos(-) )sin(-) - \|2 cos(-) + 2\|2 cos(-) +--R 2 2 2 2 2 +--R + +--R +-+ +--R - \|2 +--R * +--R atan +--R +-+ x x 3 +-+ x 3 +-+ x x +--R 12\|2 cos(-)sin(-) + (- 4\|2 cos(-) - 12\|2 cos(-))sin(-) +--R 2 2 2 2 2 +--R / +--R x 2 x 4 x 4 x 2 x 2 x 6 +--R 9cos(-) sin(-) + (- 6cos(-) - 18cos(-) - 8)sin(-) + cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 6cos(-) + 9cos(-) +--R 2 2 +--R + +--R x x 3 x 3 x +--R 32cos(-)sin(-) - 32cos(-) sin(-) +--R 2 2 2 2 +--R / +--R x 8 x 2 x 6 x 4 x 4 +--R 16sin(-) + 64cos(-) sin(-) + (96cos(-) - 32)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 2 x 8 x 4 +--R (64cos(-) + 192cos(-) )sin(-) + 16cos(-) - 32cos(-) + 16 +--R 2 2 2 2 2 +--R Type: Union(Expression(Integer),...) +--E 384 + +--S 385 of 504 +t0176:= cos(a+b*x+c*x^2)/x^2+b*sin(a+b*x+c*x^2)/x +--R +--R +--R 2 2 +--R b x sin(c x + b x + a) + cos(c x + b x + a) +--R (250) --------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 385 + +--S 386 of 504 +r0176:= -cos(a+b*x+c*x^2)/x-c^(1/2)*2^(1/2)*%pi^(1/2)*_ + cos(1/4*(b^2-4*a*c)/c)*FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/_ + %pi^(1/2))+c^(1/2)*2^(1/2)*%pi^(1/2)*_ + FresnelC(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + sin(1/4*(b^2-4*a*c)/c) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 386 + +--S 387 of 504 +a0176:= integrate(t0176,x) +--R +--R +--R x 2 2 +--R ++ %H b sin(%H c + %H b + a) + cos(%H c + %H b + a) +--R (251) | ------------------------------------------------ d%H +--R ++ 2 +--R %H +--R Type: Union(Expression(Integer),...) +--E 387 + +--S 388 of 504 +--m0176:= a0176-r0176 +--E 388 + +--S 389 of 504 +--d0176:= D(m0176,x) +--E 389 + +--S 390 of 504 +t0177:= cos(a+b*x-c*x^2)/x^2+b*sin(a+b*x-c*x^2)/x +--R +--R +--R 2 2 +--R - b x sin(c x - b x - a) + cos(c x - b x - a) +--R (252) ----------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 390 + +--S 391 of 504 +r0177:= -cos(a+b*x-c*x^2)/x+c^(1/2)*2^(1/2)*%pi^(1/2)*_ + cos(1/4*(b^2+4*a*c)/c)*_ + FresnelS(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))-_ + c^(1/2)*2^(1/2)*%pi^(1/2)*_ + FresnelC(1/2*(b-2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + sin(1/4*(b^2+4*a*c)/c) +--R +--R There are no library operations named FresnelS +--R Use HyperDoc Browse or issue +--R )what op FresnelS +--R to learn if there is any operation containing " FresnelS " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R FresnelS with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 391 + +--S 392 of 504 +a0177:= integrate(t0177,x) +--R +--R +--R x 2 2 +--R ++ - %H b sin(%H c - %H b - a) + cos(%H c - %H b - a) +--R (253) | -------------------------------------------------- d%H +--R ++ 2 +--R %H +--R Type: Union(Expression(Integer),...) +--E 392 + +--S 393 of 504 +--m0177:= a0177-r0177 +--E 393 + +--S 394 of 504 +--d0177:= D(m0177,x) +--E 394 + +--S 395 of 504 +t0178:= (d+e*x)^2*cos(a+b*x+c*x^2) +--R +--R +--R 2 2 2 2 +--R (254) (e x + 2d e x + d )cos(c x + b x + a) +--R Type: Expression(Integer) +--E 395 + +--S 396 of 504 +r0178:= 1/8*2^(1/2)*%pi^(1/2)*FresnelC(1/2*(b+2*c*x)/c^(1/2)*_ + 2^(1/2)/%pi^(1/2))*((2*c*d-b*e)^2*cos(a-1/4*b^2/c)-_ + 2*c*e^2*sin(a-1/4*b^2/c))/c^(5/2)-1/8*2^(1/2)*%pi^(1/2)*_ + FresnelS(1/2*(b+2*c*x)/c^(1/2)*2^(1/2)/%pi^(1/2))*_ + (2*c*e^2*cos(a-1/4*b^2/c)+(2*c*d-b*e)^2*sin(a-1/4*b^2/c))/c^(5/2)+_ + 1/4*e*(4*c*d-b*e)*sin(a+b*x+c*x^2)/c^2+1/2*e^2*x*sin(a+b*x+c*x^2)/c +--R +--R There are no library operations named FresnelC +--R Use HyperDoc Browse or issue +--R )what op FresnelC +--R to learn if there is any operation containing " FresnelC " in its +--R name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R FresnelC with argument type(s) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 396 + +--S 397 of 504 +a0178:= integrate(t0178,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--R (255) | (%H e + 2%H d e + d )cos(%H c + %H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 397 + +--S 398 of 504 +--m0178:= a0178-r0178 +--E 398 + +--S 399 of 504 +--d0178:= D(m0178,x) +--E 399 + +--S 400 of 504 +t0179:= cos((a+b*x)/(c+d*x))^2 +--R +--R +--R b x + a 2 +--R (256) cos(-------) +--R d x + c +--R Type: Expression(Integer) +--E 400 + +--S 401 of 504 +r0179:= 1/2*x+1/2*(c+d*x)*cos(2*(a+b*x)/(c+d*x))/d-(b*c-a*d)*_ + Ci(-2*(b*c-a*d)/d/(c+d*x))*sin(2*b/d)/d^2-(b*c-a*d)*_ + cos(2*b/d)*Si(2*a/(c+d*x)-2*b*c/d/(c+d*x))/d^2 +--R +--R +--R (257) +--R 2a d - 2b c 2b 2 2b x + 2a +--R (2a d - 2b c)Ci(-----------)sin(--) + (d x + c d)cos(---------) +--R 2 d d x + c +--R d x + c d +--R + +--R 2a d - 2b c 2b 2 +--R (2a d - 2b c)Si(-----------)cos(--) + d x +--R 2 d +--R d x + c d +--R / +--R 2 +--R 2d +--R Type: Expression(Integer) +--E 401 + +--S 402 of 504 +a0179:= integrate(t0179,x) +--R +--R +--R x +--R ++ %H b + a 2 +--R (258) | cos(--------) d%H +--R ++ %H d + c +--R Type: Union(Expression(Integer),...) +--E 402 + +--S 403 of 504 +--m0179:= a0179-r0179 +--E 403 + +--S 404 of 504 +--d0179:= D(m0179,x) +--E 404 + +--S 405 of 504 +t0180:= cos(a+b*x^2)^2/x^3 +--R +--R +--R 2 2 +--R cos(b x + a) +--R (259) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 405 + +--S 406 of 504 +r0180:= -1/4*(1+cos(2*a+2*b*x^2)+2*b*Ci(2*b*x^2)*sin(2*a)*x^2+_ + 2*b*cos(2*a)*Si(2*b*x^2)*x^2)/x^2 +--R +--R +--R (260) +--R 2 2 2 2 2 +--R - 2b x Ci(2b x )sin(2a) - cos(2b x + 2a) - 2b x Si(2b x )cos(2a) - 1 +--R --------------------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 406 + +--S 407 of 504 +a0180:= integrate(t0180,x) +--R +--R +--R x 2 2 +--R ++ cos(%H b + a) +--R (261) | -------------- d%H +--R ++ 3 +--R %H +--R Type: Union(Expression(Integer),...) +--E 407 + +--S 408 of 504 +--m0180:= a0180-r0180 +--E 408 + +--S 409 of 504 +--d0180:= D(m0180,x) +--E 409 + +--S 410 of 504 +t0181:= cos(a+b*x^2)^3/x +--R +--R +--R 2 3 +--R cos(b x + a) +--R (262) -------------- +--R x +--R Type: Expression(Integer) +--E 410 + +--S 411 of 504 +r0181:= 3/8*cos(a)*Ci(b*x^2)+1/8*cos(3*a)*Ci(3*b*x^2)-_ + 3/8*sin(a)*Si(b*x^2)-1/8*sin(3*a)*Si(3*b*x^2) +--R +--R +--R (263) +--R 2 2 2 2 +--R - Si(3b x )sin(3a) - 3Si(b x )sin(a) + Ci(3b x )cos(3a) + 3Ci(b x )cos(a) +--R ------------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 504 +a0181:= integrate(t0181,x) +--R +--R +--R x 2 3 +--R ++ cos(%H b + a) +--R (264) | -------------- d%H +--R ++ %H +--R Type: Union(Expression(Integer),...) +--E 412 + +--S 413 of 504 +--m0181:= a0181-r0181 +--E 413 + +--S 414 of 504 +--d0181:= D(m0181,x) +--E 414 + +--S 415 of 504 +t0182:= cos(a+b*x^2)^3/x^3 +--R +--R +--R 2 3 +--R cos(b x + a) +--R (265) -------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 415 + +--S 416 of 504 +r0182:= -1/8*(3*cos(a+b*x^2)+cos(3*a+3*b*x^2)+3*b*Ci(b*x^2)*sin(a)*x^2+_ + 3*b*Ci(3*b*x^2)*sin(3*a)*x^2+3*b*cos(a)*Si(b*x^2)*x^2+_ + 3*b*cos(3*a)*Si(3*b*x^2)*x^2)/x^2 +--R +--R +--R (266) +--R 2 2 2 2 2 +--R - 3b x Ci(3b x )sin(3a) - 3b x Ci(b x )sin(a) - cos(3b x + 3a) +--R + +--R 2 2 2 2 2 +--R - 3cos(b x + a) - 3b x Si(3b x )cos(3a) - 3b x Si(b x )cos(a) +--R / +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 416 + +--S 417 of 504 +a0182:= integrate(t0182,x) +--R +--R +--R x 2 3 +--R ++ cos(%H b + a) +--R (267) | -------------- d%H +--R ++ 3 +--R %H +--R Type: Union(Expression(Integer),...) +--E 417 + +--S 418 of 504 +--m0182:= a0182-r0182 +--E 418 + +--S 419 of 504 +--d0182:= D(m0182,x) +--E 419 + +--S 420 of 504 +t0183:= cos(a+b*x^n) +--R +--R +--R n +--R (268) cos(b x + a) +--R Type: Expression(Integer) +--E 420 + +--S 421 of 504 +r0183:= -1/2*x/n*(exp(%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-%i*b*x^n)+(%i*b*x^n)^(-1/n)*exp(-%i*a)*_ + Gamma(1/n,%i*b*x^n)) +--R +--R +--R (269) +--R 1 1 +--R - - - - +--R - %i a n n _ 1 n %i a n n _ 1 n +--R - x %e (%i b x ) | (-,%i b x ) - x %e (- %i b x ) | (-,- %i b x ) +--R n n +--R ----------------------------------------------------------------------------- +--R 2n +--R Type: Expression(Complex(Integer)) +--E 421 + +--S 422 of 504 +a0183:= integrate(t0183,x) +--R +--R +--R x +--R ++ n +--R (270) | cos(b %H + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 422 + +--S 423 of 504 +--m0183:= a0183-r0183 +--E 423 + +--S 424 of 504 +--d0183:= D(m0183,x) +--E 424 + +--S 425 of 504 +t0184:= cos(a+b*x^n)^2 +--R +--R +--R n 2 +--R (271) cos(b x + a) +--R Type: Expression(Integer) +--E 425 + +--S 426 of 504 +r0184:= -1/2*x/n*(2^(-(1+n)/n)*exp(2*%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-2*%i*b*x^n)+2^(-(1+n)/n)*exp(-2*%i*a)*(%i*b*x^n)^(-1/n)*_ + Gamma(1/n,2*%i*b*x^n)-n) +--R +--R +--R (272) +--R - n - 1 1 +--R ------- - - +--R - 2%i a n n n _ 1 n +--R - x %e 2 (%i b x ) | (-,2%i b x ) +--R n +--R + +--R - n - 1 1 +--R ------- - - +--R 2%i a n n n _ 1 n +--R - x %e 2 (- %i b x ) | (-,- 2%i b x ) + n x +--R n +--R / +--R 2n +--R Type: Expression(Complex(Integer)) +--E 426 + +--S 427 of 504 +a0184:= integrate(t0184,x) +--R +--R +--R x +--R ++ n 2 +--R (273) | cos(b %H + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 427 + +--S 428 of 504 +--m0184:= a0184-r0184 +--E 428 + +--S 429 of 504 +--d0184:= D(m0184,x) +--E 429 + +--S 430 of 504 +t0185:= cos(a+b*x^n)^3 +--R +--R +--R n 3 +--R (274) cos(b x + a) +--R Type: Expression(Integer) +--E 430 + +--S 431 of 504 +r0185:= -1/8*x/n*(3*exp(%i*a)*(-%i*b*x^n)^(-1/n)*_ + Gamma(1/n,-%i*b*x^n)+3*(%i*b*x^n)^(-1/n)*exp(-%i*a)*_ + Gamma(1/n,%i*b*x^n)+exp(3*%i*a)*(-%i*b*x^n)^(-1/n)*3^(-1/n)*_ + Gamma(1/n,-3*%i*b*x^n)+(%i*b*x^n)^(-1/n)*3^(-1/n)*exp(-3*%i*a)*_ + Gamma(1/n,3*%i*b*x^n)) +--R +--R +--R (275) +--R 1 1 +--R - - - - +--R - 3%i a n n n _ 1 n +--R - x %e 3 (%i b x ) | (-,3%i b x ) +--R n +--R + +--R 1 +--R - - +--R - %i a n n _ 1 n +--R - 3x %e (%i b x ) | (-,%i b x ) +--R n +--R + +--R 1 +--R - - +--R %i a n n _ 1 n +--R - 3x %e (- %i b x ) | (-,- %i b x ) +--R n +--R + +--R 1 1 +--R - - - - +--R 3%i a n n n _ 1 n +--R - x %e 3 (- %i b x ) | (-,- 3%i b x ) +--R n +--R / +--R 8n +--R Type: Expression(Complex(Integer)) +--E 431 + +--S 432 of 504 +a0185:= integrate(t0185,x) +--R +--R +--R x +--R ++ n 3 +--R (276) | cos(b %H + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 432 + +--S 433 of 504 +--m0185:= a0185-r0185 +--E 433 + +--S 434 of 504 +--d0185:= D(m0185,x) +--E 434 + +--S 435 of 504 +t0186:= x^m*cos(a+b*x^n) +--R +--R +--R m n +--R (277) x cos(b x + a) +--R Type: Expression(Integer) +--E 435 + +--S 436 of 504 +r0186:= -1/2*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+exp(-%i*a)*(%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,%i*b*x^n))/n +--R +--R +--R (278) +--R - m - 1 +--R ------- +--R - %i a m n n _ m + 1 n +--R - x %e x (%i b x ) | (-----,%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R %i a m n n _ m + 1 n +--R - x %e x (- %i b x ) | (-----,- %i b x ) +--R n +--R / +--R 2n +--R Type: Expression(Complex(Integer)) +--E 436 + +--S 437 of 504 +a0186:= integrate(t0186,x) +--R +--R +--R x +--R ++ m n +--R (279) | %H cos(b %H + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 437 + +--S 438 of 504 +--m0186:= a0186-r0186 +--E 438 + +--S 439 of 504 +--d0186:= D(m0186,x) +--E 439 + +--S 440 of 504 +t0187:= x^m*cos(a+b*x^n)^2 +--R +--R +--R m n 2 +--R (280) x cos(b x + a) +--R Type: Expression(Integer) +--E 440 + +--S 441 of 504 +r0187:= x^(1+m)/(2+2*m)-2^(-2-(1+m)/n)*exp(1)^(2*%i*a)*x^(1+m)*_ + Gamma((1+m)/n,-2*%i*b*x^n)/((-%i*b*x^n)^((1+m)/n))/n-_ + 2^(-2-(1+m)/n)*x^(1+m)*_ + Gamma((1+m)/n,2*%i*b*x^n)/(exp(1)^(2*%i*a))/((%i*b*x^n)^((1+m)/n))/n +--R +--R +--R (281) +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R n m + 1 n n _ m + 1 n +--R (- 2m - 2)2 x (- %i b x ) | (-----,2%i b x ) +--R n +--R + +--R - 2n - m - 1 m + 1 +--R ------------ ----- +--R 2%i a 2 n m + 1 n n _ m + 1 n +--R (- 2m - 2)(%e ) 2 x (%i b x ) | (-----,- 2%i b x ) +--R n +--R + +--R m + 1 m + 1 +--R ----- ----- +--R 2%i a m + 1 n n n n +--R n %e x (- %i b x ) (%i b x ) +--R / +--R m + 1 m + 1 +--R ----- ----- +--R 2%i a n n n n +--R (2m + 2)n %e (- %i b x ) (%i b x ) +--R Type: Expression(Complex(Integer)) +--E 441 + +--S 442 of 504 +a0187:= integrate(t0187,x) +--R +--R +--R x +--R ++ m n 2 +--R (282) | %H cos(b %H + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 442 + +--S 443 of 504 +--m0187:= a0187-r0187 +--E 443 + +--S 444 of 504 +--d0187:= D(m0187,x) +--E 444 + +--S 445 of 504 +t0188:= x^m*cos(a+b*x^n)^3 +--R +--R +--R m n 3 +--R (283) x cos(b x + a) +--R Type: Expression(Integer) +--E 445 + +--S 446 of 504 +r0188:= -1/8*x*x^m*((-%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*_ + Gamma((1+m)/n,-3*%i*b*x^n)*exp(3*%i*a)+3*(-%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,-%i*b*x^n)*exp(%i*a)+3*exp(-%i*a)*_ + (%i*b*x^n)^(-(1+m)/n)*_ + Gamma((1+m)/n,%i*b*x^n)+(%i*b*x^n)^(-(1+m)/n)*3^(-(1+m)/n)*_ + Gamma((1+m)/n,3*%i*b*x^n)*exp(-3*%i*a))/n +--R +--R +--R (284) +--R - m - 1 - m - 1 +--R ------- ------- +--R - 3%i a n m n n _ m + 1 n +--R - x %e 3 x (%i b x ) | (-----,3%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R - %i a m n n _ m + 1 n +--R - 3x %e x (%i b x ) | (-----,%i b x ) +--R n +--R + +--R - m - 1 +--R ------- +--R %i a m n n _ m + 1 n +--R - 3x %e x (- %i b x ) | (-----,- %i b x ) +--R n +--R + +--R - m - 1 - m - 1 +--R ------- ------- +--R 3%i a n m n n _ m + 1 n +--R - x %e 3 x (- %i b x ) | (-----,- 3%i b x ) +--R n +--R / +--R 8n +--R Type: Expression(Complex(Integer)) +--E 446 + +--S 447 of 504 +a0188:= integrate(t0188,x) +--R +--R +--R x +--R ++ m n 3 +--R (285) | %H cos(b %H + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 447 + +--S 448 of 504 +--m0188:= a0188-r0188 +--E 448 + +--S 449 of 504 +--d0188:= D(m0188,x) +--E 449 + +--S 450 of 504 +t0189:= x/cos(x)^(3/2)+x*cos(x)^(1/2) +--R +--R +--R 2 +--R x cos(x) + x +--R (286) --------------- +--R +------+ +--R cos(x)\|cos(x) +--R Type: Expression(Integer) +--E 450 + +--S 451 of 504 +r0189:= 2*(2*cos(x)+x*sin(x))/cos(x)^(1/2) +--R +--R +--R 2x sin(x) + 4cos(x) +--R (287) ------------------- +--R +------+ +--R \|cos(x) +--R Type: Expression(Integer) +--E 451 + +--S 452 of 504 +a0189:= integrate(t0189,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 452 + +--S 453 of 504 +--m0189:= a0189-r0189 +--E 453 + +--S 454 of 504 +--d0189:= D(m0189,x) +--E 454 + +--S 455 of 504 +t0190:= x/cos(x)^(5/2)-1/3*x/cos(x)^(1/2) +--R +--R +--R 2 +--R - x cos(x) + 3x +--R (288) ----------------- +--R 2 +------+ +--R 3cos(x) \|cos(x) +--R Type: Expression(Integer) +--E 455 + +--S 456 of 504 +r0190:= -2/3*(2*cos(x)-x*sin(x))/cos(x)^(3/2) +--R +--R +--R 2x sin(x) - 4cos(x) +--R (289) ------------------- +--R +------+ +--R 3cos(x)\|cos(x) +--R Type: Expression(Integer) +--E 456 + +--S 457 of 504 +a0190:= integrate(t0190,x) +--R +--R +--R +------+ +--R (2x sin(x) - 4cos(x))\|cos(x) +--R (290) ------------------------------ +--R 2 +--R 3cos(x) +--R Type: Union(Expression(Integer),...) +--E 457 + +--S 458 of 504 +m0190:= a0190-r0190 +--R +--R +--R (291) 0 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 504 +d0190:= D(m0190,x) +--R +--R +--R (292) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 504 +t0191:= x/cos(x)^(7/2)+3/5*x*cos(x)^(1/2) +--R +--R +--R 4 +--R 3x cos(x) + 5x +--R (293) ----------------- +--R 3 +------+ +--R 5cos(x) \|cos(x) +--R Type: Expression(Integer) +--E 460 + +--S 461 of 504 +r0191:= 2/15*(-2*cos(x)+18*cos(x)^3+_ + 3*x*sin(x)+9*x*sin(x)*cos(x)^2)/cos(x)^(5/2) +--R +--R +--R 2 3 +--R (18x cos(x) + 6x)sin(x) + 36cos(x) - 4cos(x) +--R (294) ---------------------------------------------- +--R 2 +------+ +--R 15cos(x) \|cos(x) +--R Type: Expression(Integer) +--E 461 + +--S 462 of 504 +a0191:= integrate(t0191,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 462 + +--S 463 of 504 +--m0191:= a0191-r0191 +--E 463 + +--S 464 of 504 +--d0191:= D(m0191,x) +--E 464 + +--S 465 of 504 +t0192:= x^2/cos(x)^(3/2)+x^2*cos(x)^(1/2) +--R +--R +--R 2 2 2 +--R x cos(x) + x +--R (295) --------------- +--R +------+ +--R cos(x)\|cos(x) +--R Type: Expression(Integer) +--E 465 + +--S 466 of 504 +r0192:= 8*x*cos(x)^(1/2)-16*EllipticE(1/2*x,2)+2*x^2*sin(x)/cos(x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 466 + +--S 467 of 504 +a0192:= integrate(t0192,x) +--R +--R +--RDaly Bug +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 467 + +--S 468 of 504 +--m0192:= a0192-r0192 +--E 468 + +--S 469 of 504 +--d0192:= D(m0192,x) +--E 469 + +--S 470 of 504 +t0193:= cos(a+b*log(c*x^n)) +--R +--R +--R n +--R (296) cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 470 + +--S 471 of 504 +r0193:= x*(cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(1+b^2*n^2) +--R +--R +--R n n +--R b n x sin(b log(c x ) + a) + x cos(b log(c x ) + a) +--R (297) --------------------------------------------------- +--R 2 2 +--R b n + 1 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 504 +a0193:= integrate(t0193,x) +--R +--R +--R (298) +--R b n x sin(b n log(x) + b log(c) + a) + x cos(b n log(x) + b log(c) + a) +--R ----------------------------------------------------------------------- +--R 2 2 +--R b n + 1 +--R Type: Union(Expression(Integer),...) +--E 472 + +--S 473 of 504 +m0193:= a0193-r0193 +--R +--R +--R (299) +--R n n +--R - b n x sin(b log(c x ) + a) - x cos(b log(c x ) + a) +--R + +--R b n x sin(b n log(x) + b log(c) + a) + x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n + 1 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 504 +d0193:= D(m0193,x) +--R +--R +--R (300) +--R n n - 1 n +--R (- b n x + b n x x )sin(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n +--R (- x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n + 1)x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n + 1)x +--R Type: Expression(Integer) +--E 474 + +--S 475 of 504 +t0194:= x*cos(a+b*log(c*x^n)) +--R +--R +--R n +--R (301) x cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 475 + +--S 476 of 504 +r0194:= x^2*(2*cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(4+b^2*n^2) +--R +--R +--R 2 n 2 n +--R b n x sin(b log(c x ) + a) + 2x cos(b log(c x ) + a) +--R (302) ---------------------------------------------------- +--R 2 2 +--R b n + 4 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 504 +a0194:= integrate(t0194,x) +--R +--R +--R (303) +--R 2 2 +--R b n x sin(b n log(x) + b log(c) + a) + 2x cos(b n log(x) + b log(c) + a) +--R ------------------------------------------------------------------------ +--R 2 2 +--R b n + 4 +--R Type: Union(Expression(Integer),...) +--E 477 + +--S 478 of 504 +m0194:= a0194-r0194 +--R +--R +--R (304) +--R 2 n 2 n +--R - b n x sin(b log(c x ) + a) - 2x cos(b log(c x ) + a) +--R + +--R 2 2 +--R b n x sin(b n log(x) + b log(c) + a) + 2x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n + 4 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 504 +d0194:= D(m0194,x) +--R +--R +--R (305) +--R n 2 n - 1 n +--R (- 2b n x x + 2b n x x )sin(b log(c x ) + a) +--R + +--R n 2 2 2 n - 1 n +--R (- 4x x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n + 4)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n + 4)x +--R Type: Expression(Integer) +--E 479 + +--S 480 of 504 +t0195:= x^2*cos(a+b*log(c*x^n)) +--R +--R +--R 2 n +--R (306) x cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 480 + +--S 481 of 504 +r0195:= x^3*(3*cos(a+b*log(c*x^n))+b*n*sin(a+b*log(c*x^n)))/(9+b^2*n^2) +--R +--R +--R 3 n 3 n +--R b n x sin(b log(c x ) + a) + 3x cos(b log(c x ) + a) +--R (307) ---------------------------------------------------- +--R 2 2 +--R b n + 9 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 504 +a0195:= integrate(t0195,x) +--R +--R +--R (308) +--R 3 3 +--R b n x sin(b n log(x) + b log(c) + a) + 3x cos(b n log(x) + b log(c) + a) +--R ------------------------------------------------------------------------ +--R 2 2 +--R b n + 9 +--R Type: Union(Expression(Integer),...) +--E 482 + +--S 483 of 504 +m0195:= a0195-r0195 +--R +--R +--R (309) +--R 3 n 3 n +--R - b n x sin(b log(c x ) + a) - 3x cos(b log(c x ) + a) +--R + +--R 3 3 +--R b n x sin(b n log(x) + b log(c) + a) + 3x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R b n + 9 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 504 +d0195:= D(m0195,x) +--R +--R +--R (310) +--R 2 n 3 n - 1 n +--R (- 3b n x x + 3b n x x )sin(b log(c x ) + a) +--R + +--R 2 n 2 2 3 n - 1 n +--R (- 9x x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 2 n +--R (b n + 9)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (b n + 9)x +--R Type: Expression(Integer) +--E 484 + +--S 485 of 504 +t0196:= cos(a+b*log(c*x^n))/x^2 +--R +--R +--R n +--R cos(b log(c x ) + a) +--R (311) -------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 485 + +--S 486 of 504 +r0196:= -1/(1+b^2*n^2)/x*(cos(a+b*log(c*x^n))-b*n*sin(a+b*log(c*x^n))) +--R +--R +--R n n +--R b n sin(b log(c x ) + a) - cos(b log(c x ) + a) +--R (312) ----------------------------------------------- +--R 2 2 +--R (b n + 1)x +--R Type: Expression(Integer) +--E 486 + +--S 487 of 504 +a0196:= integrate(t0196,x) +--R +--R +--R b n sin(b n log(x) + b log(c) + a) - cos(b n log(x) + b log(c) + a) +--R (313) ------------------------------------------------------------------- +--R 2 2 +--R (b n + 1)x +--R Type: Union(Expression(Integer),...) +--E 487 + +--S 488 of 504 +m0196:= a0196-r0196 +--R +--R +--R (314) +--R n n +--R - b n sin(b log(c x ) + a) + cos(b log(c x ) + a) +--R + +--R b n sin(b n log(x) + b log(c) + a) - cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R (b n + 1)x +--R Type: Expression(Integer) +--E 488 + +--S 489 of 504 +d0196:= D(m0196,x) +--R +--R +--R (315) +--R n n - 1 n +--R (b n x - b n x x )sin(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n +--R (- x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n +--R (b n + 1)x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (b n + 1)x x +--R Type: Expression(Integer) +--E 489 + +--S 490 of 504 +t0197:= x^m*cos(a+b*log(c*x^n)) +--R +--R +--R m n +--R (316) x cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 490 + +--S 491 of 504 +r0197:= (1+m)*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)+_ + b*n*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+b^2*n^2) +--R +--R +--R m + 1 n m + 1 n +--R b n x sin(b log(c x ) + a) + (m + 1)x cos(b log(c x ) + a) +--R (317) ------------------------------------------------------------------ +--R 2 2 2 +--R b n + m + 2m + 1 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 504 +a0197:= integrate(t0197,x) +--R +--R +--R (318) +--R m log(x) +--R b n x %e sin(b n log(x) + b log(c) + a) +--R + +--R m log(x) +--R (m + 1)x cos(b n log(x) + b log(c) + a)%e +--R / +--R 2 2 2 +--R b n + m + 2m + 1 +--R Type: Union(Expression(Integer),...) +--E 492 + +--S 493 of 504 +m0197:= a0197-r0197 +--R +--R +--R (319) +--R m + 1 n m + 1 n +--R - b n x sin(b log(c x ) + a) + (- m - 1)x cos(b log(c x ) + a) +--R + +--R m log(x) +--R b n x %e sin(b n log(x) + b log(c) + a) +--R + +--R m log(x) +--R (m + 1)x cos(b n log(x) + b log(c) + a)%e +--R / +--R 2 2 2 +--R b n + m + 2m + 1 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 504 +d0197:= D(m0197,x) +--R +--R +--R (320) +--R m n m + 1 n - 1 n +--R ((- b m - b)n x x + (b m + b)n x x )sin(b log(c x ) + a) +--R + +--R 2 m n 2 2 m + 1 n - 1 n +--R ((- m - 2m - 1)x x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 2 n m log(x) +--R (b n + m + 2m + 1)x cos(b n log(x) + b log(c) + a)%e +--R / +--R 2 2 2 n +--R (b n + m + 2m + 1)x +--R Type: Expression(Integer) +--E 494 + +--S 495 of 504 +t0198:= cos(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (321) cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 495 + +--S 496 of 504 +r0198:= x*(2*b^2*n^2+cos(a+b*log(c*x^n))^2+_ + 2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n)))/(1+4*b^2*n^2) +--R +--R +--R (322) +--R n n n 2 +--R 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) + x cos(b log(c x ) + a) +--R + +--R 2 2 +--R 2b n x +--R / +--R 2 2 +--R 4b n + 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 504 +a0198:= integrate(t0198,x) +--R +--R +--R (323) +--R 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R x cos(b n log(x) + b log(c) + a) + 2b n x +--R / +--R 2 2 +--R 4b n + 1 +--R Type: Union(Expression(Integer),...) +--E 497 + +--S 498 of 504 +m0198:= a0198-r0198 +--R +--R +--R (324) +--R n n +--R - 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 +--R - x cos(b log(c x ) + a) +--R + +--R 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 +--R x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R 4b n + 1 +--R Type: Expression(Integer) +--E 498 + +--S 499 of 504 +d0198:= D(m0198,x) +--R +--R +--R (325) +--R 2 2 n - 1 n 2 +--R 2b n x x sin(b log(c x ) + a) +--R + +--R n n - 1 n n +--R (- 2b n x + 2b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n 2 +--R (- x - 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R - 2b n x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 +--R (2b n + 1)x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (4b n + 1)x +--R Type: Expression(Integer) +--E 499 + +--S 500 of 504 +t0199:= x*cos(a+b*log(c*x^n))^2 +--R +--R +--R n 2 +--R (326) x cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 500 + +--S 501 of 504 +r0199:= 1/4/(1+b^2*n^2)*x^2*(b^2*n^2+2*cos(a+b*log(c*x^n))^2+_ + 2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))) +--R +--R +--R (327) +--R 2 n n +--R 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 n 2 2 2 2 +--R 2x cos(b log(c x ) + a) + b n x +--R / +--R 2 2 +--R 4b n + 4 +--R Type: Expression(Integer) +--E 501 + +--S 502 of 504 +a0199:= integrate(t0199,x) +--R +--R +--R (328) +--R 2 +--R 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 2 +--R 2x cos(b n log(x) + b log(c) + a) + b n x +--R / +--R 2 2 +--R 4b n + 4 +--R Type: Union(Expression(Integer),...) +--E 502 + +--S 503 of 504 +m0199:= a0199-r0199 +--R +--R +--R (329) +--R 2 n n +--R - b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 n 2 +--R - x cos(b log(c x ) + a) +--R + +--R 2 +--R b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R 2b n + 2 +--R Type: Expression(Integer) +--E 503 + +--S 504 of 504 +d0199:= D(m0199,x) +--R +--R +--R (330) +--R 2 2 2 n - 1 n 2 +--R b n x x sin(b log(c x ) + a) +--R + +--R n 2 n - 1 n n +--R (- 2b n x x + 2b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 2 n - 1 n 2 +--R (- 2x x - b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R - b n x x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 +--R (b n + 2)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (2b n + 2)x +--R Type: Expression(Integer) +--E 504 +)spool + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richtrig100-199.input.pdf b/src/axiom-website/CATS/richtrig100-199.input.pdf new file mode 100644 index 0000000..07a255c Binary files /dev/null and b/src/axiom-website/CATS/richtrig100-199.input.pdf differ diff --git a/src/axiom-website/CATS/richtrig200-299.input.pamphlet b/src/axiom-website/CATS/richtrig200-299.input.pamphlet new file mode 100644 index 0000000..8a9723f --- /dev/null +++ b/src/axiom-website/CATS/richtrig200-299.input.pamphlet @@ -0,0 +1,32584 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richtrig200-299.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig200-299.output +)spool richtrig200-299.output +)set message auto off +)clear all + +--S 1 of 510 +t0200:= x^2*cos(a+b*log(c*x^n))^2 +--R +--R +--R 2 n 2 +--R (1) x cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 510 +r0200:= 1/3/(9+4*b^2*n^2)*x^3*(2*b^2*n^2+9*cos(a+b*log(c*x^n))^2+_ + 6*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))) +--R +--R +--R (2) +--R 3 n n +--R 6b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 3 n 2 2 2 3 +--R 9x cos(b log(c x ) + a) + 2b n x +--R / +--R 2 2 +--R 12b n + 27 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 510 +a0200:= integrate(t0200,x) +--R +--R +--R (3) +--R 3 +--R 6b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 3 2 2 2 3 +--R 9x cos(b n log(x) + b log(c) + a) + 2b n x +--R / +--R 2 2 +--R 12b n + 27 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 510 +m0200:= a0200-r0200 +--R +--R +--R (4) +--R 3 n n +--R - 2b n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 3 n 2 +--R - 3x cos(b log(c x ) + a) +--R + +--R 3 +--R 2b n x cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 3 2 +--R 3x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R 4b n + 9 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 510 +d0200:= D(m0200,x) +--R +--R +--R (5) +--R 2 2 3 n - 1 n 2 +--R 2b n x x sin(b log(c x ) + a) +--R + +--R 2 n 3 n - 1 n n +--R (- 6b n x x + 6b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 n 2 2 3 n - 1 n 2 +--R (- 9x x - 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 2 n 2 +--R - 2b n x x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 +--R (2b n + 9)x x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 n +--R (4b n + 9)x +--R Type: Expression(Integer) +--E 5 + +--S 6 of 510 +t0201:= cos(a+b*log(c*x^n))^2/x^2 +--R +--R +--R n 2 +--R cos(b log(c x ) + a) +--R (6) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 510 +r0201:= -1/(1+4*b^2*n^2)/x*(2*b^2*n^2+cos(a+b*log(c*x^n))^2-_ + 2*b*n*cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))) +--R +--R +--R (7) +--R n n n 2 2 2 +--R 2b n cos(b log(c x ) + a)sin(b log(c x ) + a) - cos(b log(c x ) + a) - 2b n +--R ----------------------------------------------------------------------------- +--R 2 2 +--R (4b n + 1)x +--R Type: Expression(Integer) +--E 7 + +--S 8 of 510 +a0201:= integrate(t0201,x) +--R +--R +--R (8) +--R 2b n cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R - cos(b n log(x) + b log(c) + a) - 2b n +--R / +--R 2 2 +--R (4b n + 1)x +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 510 +m0201:= a0201-r0201 +--R +--R +--R (9) +--R n n n 2 +--R - 2b n cos(b log(c x ) + a)sin(b log(c x ) + a) + cos(b log(c x ) + a) +--R + +--R 2b n cos(b n log(x) + b log(c) + a)sin(b n log(x) + b log(c) + a) +--R + +--R 2 +--R - cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 +--R (4b n + 1)x +--R Type: Expression(Integer) +--E 9 + +--S 10 of 510 +d0201:= D(m0201,x) +--R +--R +--R (10) +--R 2 2 n - 1 n 2 +--R 2b n x x sin(b log(c x ) + a) +--R + +--R n n - 1 n n +--R (2b n x - 2b n x x )cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R n 2 2 n - 1 n 2 +--R (- x - 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 2 +--R - 2b n x sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 n 2 +--R (2b n + 1)x cos(b n log(x) + b log(c) + a) +--R / +--R 2 2 2 n +--R (4b n + 1)x x +--R Type: Expression(Integer) +--E 10 + +--S 11 of 510 +t0202:= x^m*cos(a+b*log(c*x^n))^2 +--R +--R +--R m n 2 +--R (11) x cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 510 +r0202:= 2*b^2*n^2*x^(1+m)/(1+m)/((1+m)^2+4*b^2*n^2)+(1+m)*x^(1+m)*_ + cos(a+b*log(c*x^n))^2/((1+m)^2+4*b^2*n^2)+2*b*n*x^(1+m)*_ + cos(a+b*log(c*x^n))*sin(a+b*log(c*x^n))/((1+m)^2+4*b^2*n^2) +--R +--R +--R (12) +--R m + 1 n n +--R (2b m + 2b)n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 m + 1 n 2 2 2 m + 1 +--R (m + 2m + 1)x cos(b log(c x ) + a) + 2b n x +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n + m + 3m + 3m + 1 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 510 +a0202:= integrate(t0202,x) +--R +--R +--R (13) +--R m log(x) +--R (2b m + 2b)n x cos(b n log(x) + b log(c) + a)%e +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 m log(x) +--R ((m + 2m + 1)x cos(b n log(x) + b log(c) + a) + 2b n x)%e +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n + m + 3m + 3m + 1 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 510 +m0202:= a0202-r0202 +--R +--R +--R (14) +--R m + 1 n n +--R (- 2b m - 2b)n x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 2 m + 1 n 2 +--R (- m - 2m - 1)x cos(b log(c x ) + a) +--R + +--R m log(x) +--R (2b m + 2b)n x cos(b n log(x) + b log(c) + a)%e +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 2 m log(x) +--R ((m + 2m + 1)x cos(b n log(x) + b log(c) + a) + 2b n x)%e +--R + +--R 2 2 m + 1 +--R - 2b n x +--R / +--R 2 2 2 3 2 +--R (4b m + 4b )n + m + 3m + 3m + 1 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 510 +d0202:= D(m0202,x) +--R +--R +--R (15) +--R 2 2 m + 1 n - 1 n 2 +--R 2b n x x sin(b log(c x ) + a) +--R + +--R m n m + 1 n - 1 n +--R ((- 2b m - 2b)n x x + (2b m + 2b)n x x )cos(b log(c x ) + a) +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 2 m n 2 2 m + 1 n - 1 n 2 +--R ((- m - 2m - 1)x x - 2b n x x )cos(b log(c x ) + a) +--R + +--R 2 2 n m log(x) 2 +--R - 2b n x %e sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 n 2 2 2 n +--R ((2b n + m + 2m + 1)x cos(b n log(x) + b log(c) + a) + 2b n x ) +--R * +--R m log(x) +--R %e +--R + +--R 2 2 m n +--R - 2b n x x +--R / +--R 2 2 2 n +--R (4b n + m + 2m + 1)x +--R Type: Expression(Integer) +--E 15 + +--S 16 of 510 +t0203:= cos(a+b*log(c*x^n))^3 +--R +--R +--R n 3 +--R (16) cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 510 +r0203:= 6*b^2*n^2*x*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)+_ + x*cos(a+b*log(c*x^n))^3/(1+9*b^2*n^2)+6*b^3*n^3*x*_ + sin(a+b*log(c*x^n))/(1+b^2*n^2)/(1+9*b^2*n^2)+_ + 3*b*n*x*cos(a+b*log(c*x^n))^2*sin(a+b*log(c*x^n))/(1+9*b^2*n^2) +--R +--R +--R (17) +--R 3 3 n 2 3 3 n +--R ((3b n + 3b n)x cos(b log(c x ) + a) + 6b n x)sin(b log(c x ) + a) +--R + +--R 2 2 n 3 2 2 n +--R (b n + 1)x cos(b log(c x ) + a) + 6b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 9b n + 10b n + 1 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 510 +a0203:= integrate(t0203,x) +--R +--R +--R (18) +--R 3 3 2 3 3 +--R ((3b n + 3b n)x cos(b n log(x) + b log(c) + a) + 6b n x) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (b n + 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R 6b n x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 10b n + 1 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 510 +m0203:= a0203-r0203 +--R +--R +--R (19) +--R 3 3 n 2 3 3 n +--R ((- 3b n - 3b n)x cos(b log(c x ) + a) - 6b n x)sin(b log(c x ) + a) +--R + +--R 2 2 n 3 2 2 n +--R (- b n - 1)x cos(b log(c x ) + a) - 6b n x cos(b log(c x ) + a) +--R + +--R 3 3 2 3 3 +--R ((3b n + 3b n)x cos(b n log(x) + b log(c) + a) + 6b n x) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (b n + 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R 6b n x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 10b n + 1 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 510 +d0203:= D(m0203,x) +--R +--R +--R (20) +--R 4 4 2 2 n - 1 n n 2 +--R (6b n + 6b n )x x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n 2 +--R ((- 3b n - 3b n)x + (3b n + 3b n)x x )cos(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 +--R - 6b n x + 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 2 2 n 4 4 2 2 n - 1 n 3 +--R ((- b n - 1)x + (- 3b n - 3b n )x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 4 4 n - 1 n +--R (- 6b n x - 6b n x x )cos(b log(c x ) + a) +--R + +--R 4 4 2 2 n +--R (- 6b n - 6b n )x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 3 +--R (3b n + 4b n + 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (6b n + 6b n )x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (9b n + 10b n + 1)x +--R Type: Expression(Integer) +--E 20 + +--S 21 of 510 +t0204:= x*cos(a+b*log(c*x^n))^3 +--R +--R +--R n 3 +--R (21) x cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 510 +r0204:= x^2*(12*b^2*n^2*cos(a+b*log(c*x^n))+8*cos(a+b*log(c*x^n))^3+_ + 2*cos(a+b*log(c*x^n))^3*b^2*n^2+6*b^3*n^3*sin(a+b*log(c*x^n))+_ + 12*b*n*cos(a+b*log(c*x^n))^2*sin(a+b*log(c*x^n))+_ + 3*b^3*n^3*cos(a+b*log(c*x^n))^2*_ + sin(a+b*log(c*x^n)))/(4+b^2*n^2)/(4+9*b^2*n^2) +--R +--R +--R (22) +--R 3 3 2 n 2 3 3 2 n +--R ((3b n + 12b n)x cos(b log(c x ) + a) + 6b n x )sin(b log(c x ) + a) +--R + +--R 2 2 2 n 3 2 2 2 n +--R (2b n + 8)x cos(b log(c x ) + a) + 12b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 9b n + 40b n + 16 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 510 +a0204:= integrate(t0204,x) +--R +--R +--R (23) +--R 3 3 2 2 3 3 2 +--R ((3b n + 12b n)x cos(b n log(x) + b log(c) + a) + 6b n x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 +--R (2b n + 8)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R 12b n x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 40b n + 16 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 510 +m0204:= a0204-r0204 +--R +--R +--R (24) +--R 3 3 2 n 2 3 3 2 n +--R ((- 3b n - 12b n)x cos(b log(c x ) + a) - 6b n x )sin(b log(c x ) + a) +--R + +--R 2 2 2 n 3 2 2 2 n +--R (- 2b n - 8)x cos(b log(c x ) + a) - 12b n x cos(b log(c x ) + a) +--R + +--R 3 3 2 2 3 3 2 +--R ((3b n + 12b n)x cos(b n log(x) + b log(c) + a) + 6b n x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 +--R (2b n + 8)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R 12b n x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 9b n + 40b n + 16 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 510 +d0204:= D(m0204,x) +--R +--R +--R (25) +--R 4 4 2 2 2 n - 1 n n 2 +--R (6b n + 24b n )x x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 2 n - 1 +--R ((- 6b n - 24b n)x x + (6b n + 24b n)x x ) +--R * +--R n 2 +--R cos(b log(c x ) + a) +--R + +--R 3 3 n 3 3 2 n - 1 +--R - 12b n x x + 12b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 2 2 n 4 4 2 2 2 n - 1 n 3 +--R ((- 4b n - 16)x x + (- 3b n - 12b n )x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 4 4 2 n - 1 n +--R (- 24b n x x - 6b n x x )cos(b log(c x ) + a) +--R + +--R 4 4 2 2 n +--R (- 6b n - 24b n )x x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 3 +--R (3b n + 16b n + 16)x x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (6b n + 24b n )x x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (9b n + 40b n + 16)x +--R Type: Expression(Integer) +--E 25 + +--S 26 of 510 +t0205:= x^2*cos(a+b*log(c*x^n))^3 +--R +--R +--R 2 n 3 +--R (26) x cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 510 +r0205:= 2*b^2*n^2*x^3*cos(a+b*log(c*x^n))/(1+b^2*n^2)/(9+b^2*n^2)+_ + x^3*cos(a+b*log(c*x^n))^3/(3+3*b^2*n^2)+2/3*b^3*n^3*_ + x^3*sin(a+b*log(c*x^n))/(1+b^2*n^2)/(9+b^2*n^2)+b*n*_ + x^3*cos(a+b*log(c*x^n))^2*sin(a+b*log(c*x^n))/(3+3*b^2*n^2) +--R +--R +--R (27) +--R 3 3 3 n 2 3 3 3 n +--R ((b n + 9b n)x cos(b log(c x ) + a) + 2b n x )sin(b log(c x ) + a) +--R + +--R 2 2 3 n 3 2 2 3 n +--R (b n + 9)x cos(b log(c x ) + a) + 6b n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R 3b n + 30b n + 27 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 510 +a0205:= integrate(t0205,x) +--R +--R +--R (28) +--R 3 3 3 2 3 3 3 +--R ((b n + 9b n)x cos(b n log(x) + b log(c) + a) + 2b n x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 3 +--R (b n + 9)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R 6b n x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 3b n + 30b n + 27 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 510 +m0205:= a0205-r0205 +--R +--R +--R (29) +--R 3 3 3 n 2 3 3 3 n +--R ((- b n - 9b n)x cos(b log(c x ) + a) - 2b n x )sin(b log(c x ) + a) +--R + +--R 2 2 3 n 3 2 2 3 n +--R (- b n - 9)x cos(b log(c x ) + a) - 6b n x cos(b log(c x ) + a) +--R + +--R 3 3 3 2 3 3 3 +--R ((b n + 9b n)x cos(b n log(x) + b log(c) + a) + 2b n x ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 3 +--R (b n + 9)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R 6b n x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R 3b n + 30b n + 27 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 510 +d0205:= D(m0205,x) +--R +--R +--R (30) +--R 4 4 2 2 3 n - 1 n n 2 +--R (2b n + 18b n )x x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 3 3 2 n 3 3 3 n - 1 +--R ((- 3b n - 27b n)x x + (3b n + 27b n)x x ) +--R * +--R n 2 +--R cos(b log(c x ) + a) +--R + +--R 3 3 2 n 3 3 3 n - 1 +--R - 6b n x x + 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 2 2 2 n 4 4 2 2 3 n - 1 n 3 +--R ((- 3b n - 27)x x + (- b n - 9b n )x x )cos(b log(c x ) + a) +--R + +--R 2 2 2 n 4 4 3 n - 1 n +--R (- 18b n x x - 2b n x x )cos(b log(c x ) + a) +--R + +--R 4 4 2 2 2 n +--R (- 2b n - 18b n )x x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 n 3 +--R (b n + 12b n + 27)x x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 n +--R (2b n + 18b n )x x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 n +--R (3b n + 30b n + 27)x +--R Type: Expression(Integer) +--E 30 + +--S 31 of 510 +t0206:= cos(a+b*log(c*x^n))^3/x^2 +--R +--R +--R n 3 +--R cos(b log(c x ) + a) +--R (31) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 510 +r0206:= -1/(1+b^2*n^2)/(1+9*b^2*n^2)/x*(6*b^2*n^2*cos(a+b*log(c*x^n))+_ + cos(a+b*log(c*x^n))^3+cos(a+b*log(c*x^n))^3*b^2*n^2-_ + 6*b^3*n^3*sin(a+b*log(c*x^n))-3*b*n*cos(a+b*log(c*x^n))^2*_ + sin(a+b*log(c*x^n))-3*b^3*n^3*cos(a+b*log(c*x^n))^2*_ + sin(a+b*log(c*x^n))) +--R +--R +--R (32) +--R 3 3 n 2 3 3 n +--R ((3b n + 3b n)cos(b log(c x ) + a) + 6b n )sin(b log(c x ) + a) +--R + +--R 2 2 n 3 2 2 n +--R (- b n - 1)cos(b log(c x ) + a) - 6b n cos(b log(c x ) + a) +--R / +--R 4 4 2 2 +--R (9b n + 10b n + 1)x +--R Type: Expression(Integer) +--E 32 + +--S 33 of 510 +a0206:= integrate(t0206,x) +--R +--R +--R (33) +--R 3 3 2 3 3 +--R ((3b n + 3b n)cos(b n log(x) + b log(c) + a) + 6b n ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (- b n - 1)cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R - 6b n cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R (9b n + 10b n + 1)x +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 510 +m0206:= a0206-r0206 +--R +--R +--R (34) +--R 3 3 n 2 3 3 n +--R ((- 3b n - 3b n)cos(b log(c x ) + a) - 6b n )sin(b log(c x ) + a) +--R + +--R 2 2 n 3 2 2 n +--R (b n + 1)cos(b log(c x ) + a) + 6b n cos(b log(c x ) + a) +--R + +--R 3 3 2 3 3 +--R ((3b n + 3b n)cos(b n log(x) + b log(c) + a) + 6b n ) +--R * +--R sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 3 +--R (- b n - 1)cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 +--R - 6b n cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 +--R (9b n + 10b n + 1)x +--R Type: Expression(Integer) +--E 34 + +--S 35 of 510 +d0206:= D(m0206,x) +--R +--R +--R (35) +--R 4 4 2 2 n - 1 n n 2 +--R (6b n + 6b n )x x cos(b log(c x ) + a)sin(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 n 2 +--R ((3b n + 3b n)x + (- 3b n - 3b n)x x )cos(b log(c x ) + a) +--R + +--R 3 3 n 3 3 n - 1 +--R 6b n x - 6b n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 2 2 n 4 4 2 2 n - 1 n 3 +--R ((- b n - 1)x + (- 3b n - 3b n )x x )cos(b log(c x ) + a) +--R + +--R 2 2 n 4 4 n - 1 n +--R (- 6b n x - 6b n x x )cos(b log(c x ) + a) +--R + +--R 4 4 2 2 n +--R (- 6b n - 6b n )x cos(b n log(x) + b log(c) + a) +--R * +--R 2 +--R sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n 3 +--R (3b n + 4b n + 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 n +--R (6b n + 6b n )x cos(b n log(x) + b log(c) + a) +--R / +--R 4 4 2 2 2 n +--R (9b n + 10b n + 1)x x +--R Type: Expression(Integer) +--E 35 + +--S 36 of 510 +t0207:= x^m*cos(a+b*log(c*x^n))^3 +--R +--R +--R m n 3 +--R (36) x cos(b log(c x ) + a) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 510 +r0207:= 6*b^2*(1+m)*n^2*x^(1+m)*cos(a+b*log(c*x^n))/((1+m)^2+_ + b^2*n^2)/((1+m)^2+9*b^2*n^2)+(1+m)*x^(1+m)*_ + cos(a+b*log(c*x^n))^3/((1+m)^2+9*b^2*n^2)+_ + 6*b^3*n^3*x^(1+m)*sin(a+b*log(c*x^n))/((1+m)^2+b^2*n^2)/((1+m)^2+_ + 9*b^2*n^2)+3*b*n*x^(1+m)*cos(a+b*log(c*x^n))^2*_ + sin(a+b*log(c*x^n))/((1+m)^2+9*b^2*n^2) +--R +--R +--R (37) +--R 3 3 2 m + 1 n 2 +--R (3b n + (3b m + 6b m + 3b)n)x cos(b log(c x ) + a) +--R + +--R 3 3 m + 1 +--R 6b n x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 2 2 2 3 2 m + 1 n 3 +--R ((b m + b )n + m + 3m + 3m + 1)x cos(b log(c x ) + a) +--R + +--R 2 2 2 m + 1 n +--R (6b m + 6b )n x cos(b log(c x ) + a) +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 510 +a0207:= integrate(t0207,x) +--R +--R +--R (38) +--R 3 3 2 2 +--R (3b n + (3b m + 6b m + 3b)n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R 6b n x +--R * +--R m log(x) +--R %e sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 3 +--R ((b m + b )n + m + 3m + 3m + 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (6b m + 6b )n x cos(b n log(x) + b log(c) + a) +--R * +--R m log(x) +--R %e +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 510 +m0207:= a0207-r0207 +--R +--R +--R (39) +--R 3 3 2 m + 1 n 2 +--R (- 3b n + (- 3b m - 6b m - 3b)n)x cos(b log(c x ) + a) +--R + +--R 3 3 m + 1 +--R - 6b n x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 2 2 2 3 2 m + 1 n 3 +--R ((- b m - b )n - m - 3m - 3m - 1)x cos(b log(c x ) + a) +--R + +--R 2 2 2 m + 1 n +--R (- 6b m - 6b )n x cos(b log(c x ) + a) +--R + +--R 3 3 2 2 +--R (3b n + (3b m + 6b m + 3b)n)x cos(b n log(x) + b log(c) + a) +--R + +--R 3 3 +--R 6b n x +--R * +--R m log(x) +--R %e sin(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 3 2 3 +--R ((b m + b )n + m + 3m + 3m + 1)x cos(b n log(x) + b log(c) + a) +--R + +--R 2 2 2 +--R (6b m + 6b )n x cos(b n log(x) + b log(c) + a) +--R * +--R m log(x) +--R %e +--R / +--R 4 4 2 2 2 2 2 4 3 2 +--R 9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 510 +d0207:= D(m0207,x) +--R +--R +--R (40) +--R 4 4 2 2 2 2 2 m + 1 n - 1 n +--R (6b n + (6b m + 12b m + 6b )n )x x cos(b log(c x ) + a) +--R * +--R n 2 +--R sin(b log(c x ) + a) +--R + +--R 3 3 3 3 2 m n +--R ((- 3b m - 3b )n + (- 3b m - 9b m - 9b m - 3b)n)x x +--R + +--R 3 3 3 3 2 m + 1 n - 1 +--R ((3b m + 3b )n + (3b m + 9b m + 9b m + 3b)n)x x +--R * +--R n 2 +--R cos(b log(c x ) + a) +--R + +--R 3 3 3 m n 3 3 3 m + 1 n - 1 +--R (- 6b m - 6b )n x x + (6b m + 6b )n x x +--R * +--R n +--R sin(b log(c x ) + a) +--R + +--R 2 2 2 2 2 4 3 2 m n +--R ((- b m - 2b m - b )n - m - 4m - 6m - 4m - 1)x x +--R + +--R 4 4 2 2 2 2 2 m + 1 n - 1 +--R (- 3b n + (- 3b m - 6b m - 3b )n )x x +--R * +--R n 3 +--R cos(b log(c x ) + a) +--R + +--R 2 2 2 2 2 m n 4 4 m + 1 n - 1 n +--R ((- 6b m - 12b m - 6b )n x x - 6b n x x )cos(b log(c x ) + a) +--R + +--R 4 4 2 2 2 2 2 n +--R (- 6b n + (- 6b m - 12b m - 6b )n )x cos(b n log(x) + b log(c) + a) +--R * +--R m log(x) 2 +--R %e sin(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 4 3 2 n +--R (3b n + (4b m + 8b m + 4b )n + m + 4m + 6m + 4m + 1)x +--R * +--R 3 +--R cos(b n log(x) + b log(c) + a) +--R + +--R 4 4 2 2 2 2 2 n +--R (6b n + (6b m + 12b m + 6b )n )x cos(b n log(x) + b log(c) + a) +--R * +--R m log(x) +--R %e +--R / +--R 4 4 2 2 2 2 2 4 3 2 n +--R (9b n + (10b m + 20b m + 10b )n + m + 4m + 6m + 4m + 1)x +--R Type: Expression(Integer) +--E 40 + +--S 41 of 510 +t0208:= tan(a+b*x) +--R +--R +--R (41) tan(b x + a) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 510 +r0208:= -log(cos(a+b*x))/b +--R +--R +--R log(cos(b x + a)) +--R (42) - ----------------- +--R b +--R Type: Expression(Integer) +--E 42 + +--S 43 of 510 +a0208:= integrate(t0208,x) +--R +--R +--R 2 +--R log(tan(b x + a) + 1) +--R (43) ---------------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 510 +m0208:= a0208-r0208 +--R +--R +--R 2 +--R log(tan(b x + a) + 1) + 2log(cos(b x + a)) +--R (44) ------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 44 + +--S 45 of 510 +d0208:= D(m0208,x) +--R +--R +--R cos(b x + a)tan(b x + a) - sin(b x + a) +--R (45) --------------------------------------- +--R cos(b x + a) +--R Type: Expression(Integer) +--E 45 + +--S 46 of 510 +t0209:= tan(a+b*x)^2 +--R +--R +--R 2 +--R (46) tan(b x + a) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 510 +r0209:= -x+tan(a+b*x)/b +--R +--R +--R tan(b x + a) - b x +--R (47) ------------------ +--R b +--R Type: Expression(Integer) +--E 47 + +--S 48 of 510 +a0209:= integrate(t0209,x) +--R +--R +--R tan(b x + a) - b x +--R (48) ------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 510 +m0209:= a0209-r0209 +--R +--R +--R (49) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 510 +d0209:= D(m0209,x) +--R +--R +--R (50) 0 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 510 +t0210:= x*tan(a+b*x) +--R +--R +--R (51) x tan(b x + a) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 510 +r0210:= -1/2*(-%i*x^2*b^2+2*x*log(1+exp(2*%i*(a+b*x)))*b-_ + %i*polylog(2,-exp(2*%i*(a+b*x))))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 510 +a0210:= integrate(t0210,x) +--R +--R +--R x +--R ++ +--R (52) | %H tan(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 510 +m0210:= a0210-r0210 +--R +--R +--R x +--R ++ +--R (53) | %H tan(%H b + a)d%H - r0210 +--R ++ +--R Type: Expression(Integer) +--E 54 + +--S 55 of 510 +d0210:= D(m0210,x) +--R +--R +--R (54) x tan(b x + a) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 510 +t0211:= x*tan(a+b*x)^3 +--R +--R +--R 3 +--R (55) x tan(b x + a) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 510 +r0211:= -1/2*%i*x^2+x*log(1+exp(1)^(2*%i*a+2*%i*b*x))/b-_ + 1/2*%i*polylog(2,-exp(1)^(2*%i*a+2*%i*b*x))/b^2+_ + 1/2*x*sec(a+b*x)^2/b-1/2*tan(a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 510 +a0211:= integrate(t0211,x) +--R +--R +--R x +--R ++ 3 +--R (56) | %H tan(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 510 +m0211:= a0211-r0211 +--R +--R +--R x +--R ++ 3 +--R (57) | %H tan(%H b + a) d%H - r0211 +--R ++ +--R Type: Expression(Integer) +--E 59 + +--S 60 of 510 +d0211:= D(m0211,x) +--R +--R +--R 3 +--R (58) x tan(b x + a) +--R Type: Expression(Integer) +--E 60 + +--S 61 of 510 +t0212:= x^2*tan(a+b*x) +--R +--R +--R 2 +--R (59) x tan(b x + a) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 510 +r0212:= -1/6*(-2*%i*x^3*b^3+6*x^2*log(1+exp(2*%i*(a+b*x)))*b^2-_ + 6*%i*x*polylog(2,-exp(2*%i*(a+b*x)))*b+_ + 3*polylog(3,-exp(2*%i*(a+b*x))))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 510 +a0212:= integrate(t0212,x) +--R +--R +--R x +--R ++ 2 +--R (60) | %H tan(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 510 +m0212:= a0212-r0212 +--R +--R +--R x +--R ++ 2 +--R (61) | %H tan(%H b + a)d%H - r0212 +--R ++ +--R Type: Expression(Integer) +--E 64 + +--S 65 of 510 +d0212:= D(m0212,x) +--R +--R +--R 2 +--R (62) x tan(b x + a) +--R Type: Expression(Integer) +--E 65 + +--S 66 of 510 +t0213:= x^2*tan(a+b*x)^2 +--R +--R +--R 2 2 +--R (63) x tan(b x + a) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 510 +r0213:= 1/3*(-3*%i*x^2*b^2-b^3*x^3+6*x*log(1+exp(2*%i*(a+b*x)))*b-_ + 3*%i*polylog(2,-exp(2*%i*(a+b*x)))+3*x^2*tan(a+b*x)*b^2)/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 of 510 +a0213:= integrate(t0213,x) +--R +--R +--R x +--R ++ 2 2 +--R (64) | %H tan(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 510 +m0213:= a0213-r0213 +--R +--R +--R x +--R ++ 2 2 +--R (65) | %H tan(%H b + a) d%H - r0213 +--R ++ +--R Type: Expression(Integer) +--E 69 + +--S 70 of 510 +d0213:= D(m0213,x) +--R +--R +--R 2 2 +--R (66) x tan(b x + a) +--R Type: Expression(Integer) +--E 70 + +--S 71 of 510 +t0214:= x^2*tan(a+b*x)^3 +--R +--R +--R 2 3 +--R (67) x tan(b x + a) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 510 +r0214:= -1/3*%i*x^3+x^2*log(1+exp(1)^(2*%i*a+2*%i*b*x))/b-_ + log(cos(a+b*x))/b^3-%i*x*polylog(2,-exp(1)^(2*%i*a+2*%i*b*x))/b^2+_ + 1/2*polylog(3,-exp(1)^(2*%i*a+2*%i*b*x))/b^3+_ + 1/2*x^2*sec(a+b*x)^2/b-x*tan(a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 72 + +--S 73 of 510 +a0214:= integrate(t0214,x) +--R +--R +--R x +--R ++ 2 3 +--R (68) | %H tan(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 510 +m0214:= a0214-r0214 +--R +--R +--R x +--R ++ 2 3 +--R (69) | %H tan(%H b + a) d%H - r0214 +--R ++ +--R Type: Expression(Integer) +--E 74 + +--S 75 of 510 +d0214:= D(m0214,x) +--R +--R +--R 2 3 +--R (70) x tan(b x + a) +--R Type: Expression(Integer) +--E 75 + +--S 76 of 510 +t0215:= x^3*tan(a+b*x) +--R +--R +--R 3 +--R (71) x tan(b x + a) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 510 +r0215:= -1/4*(-%i*x^4*b^4+4*x^3*log(1+exp(2*%i*(a+b*x)))*b^3-_ + 6*%i*x^2*polylog(2,-exp(2*%i*(a+b*x)))*b^2+_ + 6*x*polylog(3,-exp(2*%i*(a+b*x)))*b+_ + 3*%i*polylog(4,-exp(2*%i*(a+b*x))))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 510 +a0215:= integrate(t0215,x) +--R +--R +--R x +--R ++ 3 +--R (72) | %H tan(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 510 +m0215:= a0215-r0215 +--R +--R +--R x +--R ++ 3 +--R (73) | %H tan(%H b + a)d%H - r0215 +--R ++ +--R Type: Expression(Integer) +--E 79 + +--S 80 of 510 +d0215:= D(m0215,x) +--R +--R +--R 3 +--R (74) x tan(b x + a) +--R Type: Expression(Integer) +--E 80 + +--S 81 of 510 +t0216:= x^3*tan(a+b*x)^2 +--R +--R +--R 3 2 +--R (75) x tan(b x + a) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 510 +r0216:= 1/4*(-4*%i*x^3*b^3-x^4*b^4+12*x^2*log(1+exp(2*%i*(a+b*x)))*b^2-_ + 12*%i*x*polylog(2,-exp(2*%i*(a+b*x)))*b+_ + 6*polylog(3,-exp(2*%i*(a+b*x)))+4*x^3*tan(a+b*x)*b^3)/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 510 +a0216:= integrate(t0216,x) +--R +--R +--R x +--R ++ 3 2 +--R (76) | %H tan(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 510 +m0216:= a0216-r0216 +--R +--R +--R x +--R ++ 3 2 +--R (77) | %H tan(%H b + a) d%H - r0216 +--R ++ +--R Type: Expression(Integer) +--E 84 + +--S 85 of 510 +d0216:= D(m0216,x) +--R +--R +--R 3 2 +--R (78) x tan(b x + a) +--R Type: Expression(Integer) +--E 85 + +--S 86 of 510 +t0217:= x^3*tan(a+b*x)^3 +--R +--R +--R 3 3 +--R (79) x tan(b x + a) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 510 +r0217:= 3/2*%i*x^2/b^2-1/4*%i*x^4-3*x*log(1+exp(1)^(2*%i*a+2*%i*b*x))/b^3+_ + x^3*log(1+exp(1)^(2*%i*a+2*%i*b*x))/b+_ + 3/2*%i*(1-b^2*x^2)*polylog(2,-exp(1)^(2*%i*a+2*%i*b*x))/b^4+_ + 3/2*x*polylog(3,-exp(1)^(2*%i*a+2*%i*b*x))/b^3+_ + 3/4*%i*polylog(4,-exp(1)^(2*%i*a+2*%i*b*x))/b^4+_ + 1/2*x^3*sec(a+b*x)^2/b-3/2*x^2*tan(a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 510 +a0217:= integrate(t0217,x) +--R +--R +--R x +--R ++ 3 3 +--R (80) | %H tan(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 510 +m0217:= a0217-r0217 +--R +--R +--R x +--R ++ 3 3 +--R (81) | %H tan(%H b + a) d%H - r0217 +--R ++ +--R Type: Expression(Integer) +--E 89 + +--S 90 of 510 +d0217:= D(m0217,x) +--R +--R +--R 3 3 +--R (82) x tan(b x + a) +--R Type: Expression(Integer) +--E 90 + +--S 91 of 510 +t0218:= (a*tan(x)^2)^(1/2) +--R +--R +--R +---------+ +--R | 2 +--R (83) \|a tan(x) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 510 +r0218:= -cot(x)*log(cos(x))*(a*tan(x)^2)^(1/2) +--R +--R +--R +---------+ +--R | 2 +--R (84) - cot(x)log(cos(x))\|a tan(x) +--R Type: Expression(Integer) +--E 92 + +--S 93 of 510 +a0218:= integrate(t0218,x) +--R +--R +--R +-+ 2 +--R \|a log(tan(x) + 1) +--R (85) -------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 510 +m0218:= a0218-r0218 +--R +--R +--R +---------+ +--R | 2 +-+ 2 +--R 2cot(x)log(cos(x))\|a tan(x) + \|a log(tan(x) + 1) +--R (86) ----------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 510 +d0218:= D(m0218,x) +--R +--R +--R (87) +--R +---------+ +--R +-+ | 2 +--R cos(x)tan(x)\|a \|a tan(x) +--R + +--R 3 2 2 +--R a cos(x)cot(x)tan(x) + (- a cos(x)cot(x) - a cos(x))tan(x) +--R + +--R a cos(x)cot(x)tan(x) +--R * +--R log(cos(x)) +--R + +--R 2 +--R - a cot(x)sin(x)tan(x) +--R / +--R +---------+ +--R | 2 +--R cos(x)\|a tan(x) +--R Type: Expression(Integer) +--E 95 + +--S 96 of 510 +t0219:= (a*tan(x)^3)^(1/2) +--R +--R +--R +---------+ +--R | 3 +--R (88) \|a tan(x) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 510 +r0219:= -1/4*(2*2^(1/2)*atan(-1+2^(1/2)*tan(x)^(1/2))+_ + 2*2^(1/2)*atan(1+2^(1/2)*tan(x)^(1/2))-_ + log(1-2^(1/2)*tan(x)^(1/2)+tan(x))*2^(1/2)+_ + log(1+2^(1/2)*tan(x)^(1/2)+tan(x))*2^(1/2)-8*tan(x)^(1/2))*_ + (a*tan(x)^3)^(1/2)/tan(x)^(3/2) +--R +--R +--R (89) +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R - \|2 \|a tan(x) log(\|2 \|tan(x) + tan(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R \|2 \|a tan(x) log(- \|2 \|tan(x) + tan(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R - 2\|2 \|a tan(x) atan(\|2 \|tan(x) + 1) +--R + +--R +---------+ +---------+ +--R +-+ | 3 +-+ +------+ +------+ | 3 +--R - 2\|2 \|a tan(x) atan(\|2 \|tan(x) - 1) + 8\|tan(x) \|a tan(x) +--R / +--R +------+ +--R 4tan(x)\|tan(x) +--R Type: Expression(Integer) +--E 97 + +--S 98 of 510 +a0219:= integrate(t0219,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 98 + +--S 99 of 510 +m0219:= a0219-r0219 +--R +--R +--R (90) +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R \|2 \|a tan(x) log(\|2 \|tan(x) + tan(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R - \|2 \|a tan(x) log(- \|2 \|tan(x) + tan(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R 2\|2 \|a tan(x) atan(\|2 \|tan(x) + 1) +--R + +--R +---------+ +---------+ +--R +-+ | 3 +-+ +------+ +------+ | 3 +--R 2\|2 \|a tan(x) atan(\|2 \|tan(x) - 1) - 8\|tan(x) \|a tan(x) +--R + +--R +------+ +--R 4a0219 tan(x)\|tan(x) +--R / +--R +------+ +--R 4tan(x)\|tan(x) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 510 +d0219:= D(m0219,x) +--R +--R +--R 3 +--R a tan(x) +--R (91) - ------------ +--R +---------+ +--R | 3 +--R \|a tan(x) +--R Type: Expression(Integer) +--E 100 + +--S 101 of 510 +t0220:= (a*tan(x)^3)^(3/2) +--R +--R +--R +---------+ +--R 3 | 3 +--R (92) a tan(x) \|a tan(x) +--R Type: Expression(Integer) +--E 101 + +--S 102 of 510 +r0220:= 1/84*a*(a*tan(x)^3)^(1/2)*(42*2^(1/2)*atan(-1+2^(1/2)*tan(x)^(1/2))+_ + 42*2^(1/2)*atan(1+2^(1/2)*tan(x)^(1/2))+21*log(1-2^(1/2)*_ + tan(x)^(1/2)+tan(x))*2^(1/2)-21*log(1+2^(1/2)*tan(x)^(1/2)+_ + tan(x))*2^(1/2)-56*tan(x)^(3/2)+24*tan(x)^(7/2))/tan(x)^(3/2) +--R +--R +--R (93) +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R - 21a\|2 \|a tan(x) log(\|2 \|tan(x) + tan(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R 21a\|2 \|a tan(x) log(- \|2 \|tan(x) + tan(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R 42a\|2 \|a tan(x) atan(\|2 \|tan(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R 42a\|2 \|a tan(x) atan(\|2 \|tan(x) - 1) +--R + +--R +---------+ +--R 3 +------+ | 3 +--R (24a tan(x) - 56a tan(x))\|tan(x) \|a tan(x) +--R / +--R +------+ +--R 84tan(x)\|tan(x) +--R Type: Expression(Integer) +--E 102 + +--S 103 of 510 +a0220:= integrate(t0220,x) +--R +--R +--R (94) +--R 2 7 2 5 2 3 2 +--R (19712a cos(x) - 25984a cos(x) + 3724a cos(x) + 294a cos(x))sin(x) +--R + +--R 2 10 2 8 2 6 2 4 +--R - 10240a cos(x) + 26112a cos(x) - 9664a cos(x) - 8536a cos(x) +--R + +--R 2 2 2 +--R 2182a cos(x) + 6a +--R * +--R +--------+ +--R |a sin(x) +--R |-------- +--R \| cos(x) +--R + +--R 2 +-+ 9 2 +-+ 7 2 +-+ 5 +--R 5120a \|2 cos(x) - 21632a \|2 cos(x) + 17824a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ +--R - 150a \|2 cos(x) - 672a \|2 cos(x) +--R * +--R sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R 5120a \|2 cos(x) - 4480a \|2 cos(x) - 12768a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 2 2 +-+ +--R 14686a \|2 cos(x) - 2506a \|2 cos(x) - 42a \|2 +--R * +--R +-+ +--R \|a +--R / +--R +-+ 9 +-+ 7 +-+ 5 +--R (10752\|2 cos(x) - 10752\|2 cos(x) - 2352\|2 cos(x) )sin(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 9408\|2 cos(x) - 9408\|2 cos(x) - 147\|2 cos(x) +--R * +--R +--------+ +--R +-+ |a sin(x) +--R \|a |-------- +--R \| cos(x) +--R + +--R 9 7 5 3 +--R (- 10752a cos(x) + 4032a cos(x) + 7728a cos(x) + 21a cos(x) )sin(x) +--R + +--R 10 8 6 4 +--R 10752a cos(x) - 28224a cos(x) + 16464a cos(x) + 1029a cos(x) +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 510 +m0220:= a0220-r0220 +--R +--R +--R (95) +--R 9 7 5 +--R (21504a cos(x) - 21504a cos(x) - 4704a cos(x) )sin(x) +--R + +--R 8 6 4 +--R 18816a cos(x) - 18816a cos(x) - 294a cos(x) +--R * +--R +--------+ +--R +-+ |a sin(x) +--R \|a |-------- +--R \| cos(x) +--R + +--R 2 +-+ 9 2 +-+ 7 2 +-+ 5 +--R - 10752a \|2 cos(x) + 4032a \|2 cos(x) + 7728a \|2 cos(x) +--R + +--R 2 +-+ 3 +--R 21a \|2 cos(x) +--R * +--R sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R 10752a \|2 cos(x) - 28224a \|2 cos(x) + 16464a \|2 cos(x) +--R + +--R 2 +-+ 4 +--R 1029a \|2 cos(x) +--R * +--R +---------+ +--R | 3 +-+ +------+ +--R \|a tan(x) log(\|2 \|tan(x) + tan(x) + 1) +--R + +--R 9 7 5 +--R (- 21504a cos(x) + 21504a cos(x) + 4704a cos(x) )sin(x) +--R + +--R 8 6 4 +--R - 18816a cos(x) + 18816a cos(x) + 294a cos(x) +--R * +--R +--------+ +--R +-+ |a sin(x) +--R \|a |-------- +--R \| cos(x) +--R + +--R 2 +-+ 9 2 +-+ 7 2 +-+ 5 +--R 10752a \|2 cos(x) - 4032a \|2 cos(x) - 7728a \|2 cos(x) +--R + +--R 2 +-+ 3 +--R - 21a \|2 cos(x) +--R * +--R sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R - 10752a \|2 cos(x) + 28224a \|2 cos(x) - 16464a \|2 cos(x) +--R + +--R 2 +-+ 4 +--R - 1029a \|2 cos(x) +--R * +--R +---------+ +--R | 3 +-+ +------+ +--R \|a tan(x) log(- \|2 \|tan(x) + tan(x) + 1) +--R + +--R 9 7 5 +--R (- 43008a cos(x) + 43008a cos(x) + 9408a cos(x) )sin(x) +--R + +--R 8 6 4 +--R - 37632a cos(x) + 37632a cos(x) + 588a cos(x) +--R * +--R +--------+ +--R +-+ |a sin(x) +--R \|a |-------- +--R \| cos(x) +--R + +--R 2 +-+ 9 2 +-+ 7 2 +-+ 5 +--R 21504a \|2 cos(x) - 8064a \|2 cos(x) - 15456a \|2 cos(x) +--R + +--R 2 +-+ 3 +--R - 42a \|2 cos(x) +--R * +--R sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R - 21504a \|2 cos(x) + 56448a \|2 cos(x) - 32928a \|2 cos(x) +--R + +--R 2 +-+ 4 +--R - 2058a \|2 cos(x) +--R * +--R +---------+ +--R | 3 +-+ +------+ +--R \|a tan(x) atan(\|2 \|tan(x) + 1) +--R + +--R 9 7 5 +--R (- 43008a cos(x) + 43008a cos(x) + 9408a cos(x) )sin(x) +--R + +--R 8 6 4 +--R - 37632a cos(x) + 37632a cos(x) + 588a cos(x) +--R * +--R +--------+ +--R +-+ |a sin(x) +--R \|a |-------- +--R \| cos(x) +--R + +--R 2 +-+ 9 2 +-+ 7 2 +-+ 5 +--R 21504a \|2 cos(x) - 8064a \|2 cos(x) - 15456a \|2 cos(x) +--R + +--R 2 +-+ 3 +--R - 42a \|2 cos(x) +--R * +--R sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R - 21504a \|2 cos(x) + 56448a \|2 cos(x) - 32928a \|2 cos(x) +--R + +--R 2 +-+ 4 +--R - 2058a \|2 cos(x) +--R * +--R +---------+ +--R | 3 +-+ +------+ +--R \|a tan(x) atan(\|2 \|tan(x) - 1) +--R + +--R +-+ 9 +-+ 7 +--R - 12288a\|2 cos(x) + 12288a\|2 cos(x) +--R + +--R +-+ 5 +--R 2688a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 10752a\|2 cos(x) + 10752a\|2 cos(x) + 168a\|2 cos(x) +--R * +--R 3 +--R tan(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R (28672a\|2 cos(x) - 28672a\|2 cos(x) - 6272a\|2 cos(x) ) +--R * +--R sin(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 25088a\|2 cos(x) - 25088a\|2 cos(x) - 392a\|2 cos(x) +--R * +--R tan(x) +--R * +--R +--------+ +--R +-+ |a sin(x) +--R \|a |-------- +--R \| cos(x) +--R + +--R 2 9 2 7 2 5 2 3 +--R (12288a cos(x) - 4608a cos(x) - 8832a cos(x) - 24a cos(x) ) +--R * +--R sin(x) +--R + +--R 2 10 2 8 2 6 2 4 +--R - 12288a cos(x) + 32256a cos(x) - 18816a cos(x) - 1176a cos(x) +--R * +--R 3 +--R tan(x) +--R + +--R 2 9 2 7 2 5 +--R - 28672a cos(x) + 10752a cos(x) + 20608a cos(x) +--R + +--R 2 3 +--R 56a cos(x) +--R * +--R sin(x) +--R + +--R 2 10 2 8 2 6 2 4 +--R 28672a cos(x) - 75264a cos(x) + 43904a cos(x) + 2744a cos(x) +--R * +--R tan(x) +--R * +--R +---------+ +--R +------+ | 3 +--R \|tan(x) \|a tan(x) +--R + +--R 2 7 2 5 2 3 +--R 78848a cos(x) - 103936a cos(x) + 14896a cos(x) +--R + +--R 2 +--R 1176a cos(x) +--R * +--R sin(x) +--R + +--R 2 10 2 8 2 6 +--R - 40960a cos(x) + 104448a cos(x) - 38656a cos(x) +--R + +--R 2 4 2 2 2 +--R - 34144a cos(x) + 8728a cos(x) + 24a +--R * +--R +--------+ +--R |a sin(x) +--R tan(x) |-------- +--R \| cos(x) +--R + +--R 2 +-+ 9 2 +-+ 7 2 +-+ 5 +--R 20480a \|2 cos(x) - 86528a \|2 cos(x) + 71296a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ +--R - 600a \|2 cos(x) - 2688a \|2 cos(x) +--R * +--R sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R 20480a \|2 cos(x) - 17920a \|2 cos(x) - 51072a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 2 2 +-+ +--R 58744a \|2 cos(x) - 10024a \|2 cos(x) - 168a \|2 +--R * +--R +-+ +--R tan(x)\|a +--R * +--R +------+ +--R \|tan(x) +--R / +--R +-+ 9 +-+ 7 +-+ 5 +--R (43008\|2 cos(x) - 43008\|2 cos(x) - 9408\|2 cos(x) )sin(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 37632\|2 cos(x) - 37632\|2 cos(x) - 588\|2 cos(x) +--R * +--R +--------+ +--R +-+ |a sin(x) +--R tan(x)\|a |-------- +--R \| cos(x) +--R + +--R 9 7 5 +--R - 43008a cos(x) + 16128a cos(x) + 30912a cos(x) +--R + +--R 3 +--R 84a cos(x) +--R * +--R sin(x) +--R + +--R 10 8 6 4 +--R 43008a cos(x) - 112896a cos(x) + 65856a cos(x) + 4116a cos(x) +--R * +--R tan(x) +--R * +--R +------+ +--R \|tan(x) +--R Type: Expression(Integer) +--E 104 + +--S 105 of 510 +d0220:= D(m0220,x) +--R +--R +--R (96) +--R +-+ 13 +-+ 11 +--R 20185088a\|2 cos(x) - 53215232a\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +--R 42463232a\|2 cos(x) - 6422528a\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +--R - 1737344a\|2 cos(x) - 131712a\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 16 +-+ 14 +--R 5242880a\|2 cos(x) + 17825792a\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R - 42418176a\|2 cos(x) - 11026432a\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +--R 42969600a\|2 cos(x) - 9787392a\|2 cos(x) +--R + +--R +-+ 4 +-+ 2 +--R - 2428468a\|2 cos(x) - 10878a\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 17 +-+ 15 +--R 5242880a\|2 cos(x) - 17825792a\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R 55361536a\|2 cos(x) - 77529088a\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +--R 22661632a\|2 cos(x) + 21704704a\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 9367988a\|2 cos(x) - 225246a\|2 cos(x) - 294a\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 18 +-+ 16 +--R 5242880a\|2 cos(x) - 9437184a\|2 cos(x) +--R + +--R +-+ 14 +-+ 12 +--R - 16203776a\|2 cos(x) + 66830336a\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +--R - 81737216a\|2 cos(x) + 43075584a\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 7317556a\|2 cos(x) - 444542a\|2 cos(x) - 8232a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 19 +-+ 17 +--R 5242880a\|2 cos(x) - 21233664a\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +--R 34652160a\|2 cos(x) - 29126656a\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 13371904a\|2 cos(x) - 3273088a\|2 cos(x) + 381388a\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +--R - 14966a\|2 cos(x) + 42a\|2 cos(x) +--R * +--R +--------+ +--R +-+ |a sin(x) +--R \|a |-------- +--R \| cos(x) +--R + +--R 2 15 2 13 2 11 +--R - 2621440a cos(x) - 45350912a cos(x) + 119726080a cos(x) +--R + +--R 2 9 2 7 2 5 +--R - 76083200a cos(x) - 5539072a cos(x) + 7667072a cos(x) +--R + +--R 2 3 2 +--R 1015574a cos(x) + 735a cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 16 2 14 2 12 +--R - 10485760a cos(x) + 29360128a cos(x) - 108036096a cos(x) +--R + +--R 2 10 2 8 2 6 +--R 208044032a cos(x) - 139740160a cos(x) + 11812864a cos(x) +--R + +--R 2 4 2 2 2 +--R 8758232a cos(x) + 131694a cos(x) + 21a +--R * +--R 3 +--R sin(x) +--R + +--R 2 17 2 15 2 13 +--R - 5242880a cos(x) + 9961472a cos(x) - 147456a cos(x) +--R + +--R 2 11 2 9 2 7 +--R - 43655168a cos(x) + 90682880a cos(x) - 67244800a cos(x) +--R + +--R 2 5 2 3 2 +--R 15080492a cos(x) + 557620a cos(x) + 3381a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 18 2 16 2 14 +--R - 10485760a cos(x) + 39845888a cos(x) - 60325888a cos(x) +--R + +--R 2 12 2 10 2 8 +--R 46333952a cos(x) - 19031040a cos(x) + 4035584a cos(x) +--R + +--R 2 6 2 4 2 2 +--R - 382760a cos(x) + 10006a cos(x) - 3a cos(x) +--R * +--R sin(x) +--R + +--R 2 19 2 17 2 15 +--R - 2621440a cos(x) + 11272192a cos(x) - 19734528a cos(x) +--R + +--R 2 13 2 11 2 9 +--R 18042880a cos(x) - 9184512a cos(x) + 2564992a cos(x) +--R + +--R 2 7 2 5 2 3 +--R - 358890a cos(x) + 19453a cos(x) - 147a cos(x) +--R * +--R +---------+ +--R | 3 +--R \|a tan(x) +--R + +--R 2 16 2 14 2 12 +--R - 11010048a cos(x) + 22020096a cos(x) - 6193152a cos(x) +--R + +--R 2 10 2 8 +--R - 4816896a cos(x) - 526848a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 17 2 15 2 13 +--R - 5505024a cos(x) - 15138816a cos(x) + 45674496a cos(x) +--R + +--R 2 11 2 9 2 7 +--R - 17697792a cos(x) - 7367808a cos(x) - 81312a cos(x) +--R + +--R 2 5 +--R - 21a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 18 2 16 2 14 +--R 11010048a cos(x) - 33030144a cos(x) + 11354112a cos(x) +--R + +--R 2 12 2 10 2 8 +--R 32342016a cos(x) - 20622336a cos(x) - 1053696a cos(x) +--R + +--R 2 6 +--R - 4116a cos(x) +--R * +--R sin(x) +--R + +--R 2 19 2 17 2 15 +--R - 5505024a cos(x) + 28901376a cos(x) - 54792192a cos(x) +--R + +--R 2 13 2 11 2 9 +--R 43201536a cos(x) - 10141824a cos(x) - 1613472a cos(x) +--R + +--R 2 7 +--R - 50421a cos(x) +--R * +--R +--------+ +--R 6 |a sin(x) +--R tan(x) |-------- +--R \| cos(x) +--R + +--R 2 +-+ 16 2 +-+ 14 +--R 11010048a \|2 cos(x) - 15138816a \|2 cos(x) +--R + +--R 2 +-+ 12 2 +-+ 10 +--R - 6193152a \|2 cos(x) + 8795136a \|2 cos(x) +--R + +--R 2 +-+ 8 2 +-+ 6 +--R 1752576a \|2 cos(x) + 4704a \|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 +-+ 17 2 +-+ 15 +--R - 11010048a \|2 cos(x) + 49545216a \|2 cos(x) +--R + +--R 2 +-+ 13 2 +-+ 11 +--R - 56598528a \|2 cos(x) + 6021120a \|2 cos(x) +--R + +--R 2 +-+ 9 2 +-+ 7 2 +-+ 5 +--R 11703552a \|2 cos(x) + 357504a \|2 cos(x) + 294a \|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 +-+ 16 2 +-+ 14 +--R - 9633792a \|2 cos(x) + 34922496a \|2 cos(x) +--R + +--R 2 +-+ 12 2 +-+ 10 +--R - 39889920a \|2 cos(x) + 13434624a \|2 cos(x) +--R + +--R 2 +-+ 8 2 +-+ 6 +--R 1152480a \|2 cos(x) + 14406a \|2 cos(x) +--R * +--R sin(x) +--R * +--R 6 +-+ +--R tan(x) \|a +--R / +--R 16 14 12 +--R 11010048cos(x) - 22020096cos(x) + 6193152cos(x) +--R + +--R 10 8 +--R 4816896cos(x) + 526848cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 17 15 13 +--R 5505024cos(x) + 15138816cos(x) - 45674496cos(x) +--R + +--R 11 9 7 5 +--R 17697792cos(x) + 7367808cos(x) + 81312cos(x) + 21cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 18 16 14 +--R - 11010048cos(x) + 33030144cos(x) - 11354112cos(x) +--R + +--R 12 10 8 +--R - 32342016cos(x) + 20622336cos(x) + 1053696cos(x) +--R + +--R 6 +--R 4116cos(x) +--R * +--R sin(x) +--R + +--R 19 17 15 +--R 5505024cos(x) - 28901376cos(x) + 54792192cos(x) +--R + +--R 13 11 9 7 +--R - 43201536cos(x) + 10141824cos(x) + 1613472cos(x) + 50421cos(x) +--R * +--R +--------+ +--R |a sin(x) +--R |-------- +--R \| cos(x) +--R + +--R +-+ 16 +-+ 14 +--R - 11010048\|2 cos(x) + 15138816\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 6193152\|2 cos(x) - 8795136\|2 cos(x) - 1752576\|2 cos(x) +--R + +--R +-+ 6 +--R - 4704\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 17 +-+ 15 +--R 11010048\|2 cos(x) - 49545216\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R 56598528\|2 cos(x) - 6021120\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 11703552\|2 cos(x) - 357504\|2 cos(x) - 294\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 16 +-+ 14 +--R 9633792\|2 cos(x) - 34922496\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R 39889920\|2 cos(x) - 13434624\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +--R - 1152480\|2 cos(x) - 14406\|2 cos(x) +--R * +--R sin(x) +--R * +--R +-+ +--R \|a +--R * +--R +---------+ +--R | 3 +--R \|a tan(x) +--R Type: Expression(Integer) +--E 105 + +--S 106 of 510 +t0221:= 1/(a*tan(x)^2)^(1/2) +--R +--R +--R 1 +--R (97) ------------ +--R +---------+ +--R | 2 +--R \|a tan(x) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 510 +r0221:= log(sin(x))*tan(x)/(a*tan(x)^2)^(1/2) +--R +--R +--R tan(x)log(sin(x)) +--R (98) ----------------- +--R +---------+ +--R | 2 +--R \|a tan(x) +--R Type: Expression(Integer) +--E 107 + +--S 108 of 510 +a0221:= integrate(t0221,x) +--R +--R +--R 2 +--R - log(tan(x) + 1) + 2log(tan(x)) +--R (99) --------------------------------- +--R +-+ +--R 2\|a +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 510 +m0221:= a0221-r0221 +--R +--R +--R (100) +--R +---------+ +--R 2 | 2 +-+ +--R (- log(tan(x) + 1) + 2log(tan(x)))\|a tan(x) - 2tan(x)\|a log(sin(x)) +--R ------------------------------------------------------------------------ +--R +---------+ +--R +-+ | 2 +--R 2\|a \|a tan(x) +--R Type: Expression(Integer) +--E 109 + +--S 110 of 510 +d0221:= D(m0221,x) +--R +--R +--R +---------+ +--R +-+ | 2 2 +--R sin(x)\|a \|a tan(x) - a cos(x)tan(x) +--R (101) ---------------------------------------- +--R +---------+ +--R | 2 +--R a sin(x)tan(x)\|a tan(x) +--R Type: Expression(Integer) +--E 110 + +--S 111 of 510 +t0222:= 1/(a*tan(x)^3)^(1/2) +--R +--R +--R 1 +--R (102) ------------ +--R +---------+ +--R | 3 +--R \|a tan(x) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 510 +r0222:= -1/2/(a*tan(x)^3)^(1/2)*(4-(-2^(1/2)*atan(-1+2^(1/2)*tan(x)^(1/2))-_ + 2^(1/2)*atan(1+2^(1/2)*tan(x)^(1/2))-_ + 1/2*log(1-2^(1/2)*tan(x)^(1/2)+tan(x))*2^(1/2)+_ + 1/2*log(1+2^(1/2)*tan(x)^(1/2)+tan(x))*2^(1/2))*tan(x)^(1/2))*tan(x) +--R +--R +--R (103) +--R +-+ +------+ +-+ +------+ +--R \|2 tan(x)\|tan(x) log(\|2 \|tan(x) + tan(x) + 1) +--R + +--R +-+ +------+ +-+ +------+ +--R - \|2 tan(x)\|tan(x) log(- \|2 \|tan(x) + tan(x) + 1) +--R + +--R +-+ +------+ +-+ +------+ +--R - 2\|2 tan(x)\|tan(x) atan(\|2 \|tan(x) + 1) +--R + +--R +-+ +------+ +-+ +------+ +--R - 2\|2 tan(x)\|tan(x) atan(\|2 \|tan(x) - 1) - 8tan(x) +--R / +--R +---------+ +--R | 3 +--R 4\|a tan(x) +--R Type: Expression(Integer) +--E 112 + +--S 113 of 510 +a0222:= integrate(t0222,x) +--R +--R +--R +--------+ +--R 2 |a sin(x) +-+ +-+ 2 +-+ +-+ +--R 2cos(x) |-------- + (- \|2 cos(x)sin(x) - \|2 cos(x) + \|2 )\|a +--R \| cos(x) +--R (104) ------------------------------------------------------------------- +--R +--------+ +--R +-+ +-+ |a sin(x) 2 +--R \|2 cos(x)sin(x)\|a |-------- - a cos(x)sin(x) + a cos(x) - a +--R \| cos(x) +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 510 +m0222:= a0222-r0222 +--R +--R +--R (105) +--R +--------+ +--R +-+ |a sin(x) +--R - 2cos(x)sin(x)tan(x)\|a |-------- +--R \| cos(x) +--R + +--R +-+ +-+ 2 +-+ +--R (a\|2 cos(x)sin(x) - a\|2 cos(x) + a\|2 )tan(x) +--R * +--R +------+ +-+ +------+ +--R \|tan(x) log(\|2 \|tan(x) + tan(x) + 1) +--R + +--R +--------+ +--R +-+ |a sin(x) +--R 2cos(x)sin(x)tan(x)\|a |-------- +--R \| cos(x) +--R + +--R +-+ +-+ 2 +-+ +--R (- a\|2 cos(x)sin(x) + a\|2 cos(x) - a\|2 )tan(x) +--R * +--R +------+ +-+ +------+ +--R \|tan(x) log(- \|2 \|tan(x) + tan(x) + 1) +--R + +--R +--------+ +--R +-+ |a sin(x) +--R 4cos(x)sin(x)tan(x)\|a |-------- +--R \| cos(x) +--R + +--R +-+ +-+ 2 +-+ +--R (- 2a\|2 cos(x)sin(x) + 2a\|2 cos(x) - 2a\|2 )tan(x) +--R * +--R +------+ +-+ +------+ +--R \|tan(x) atan(\|2 \|tan(x) + 1) +--R + +--R +--------+ +--R +-+ |a sin(x) +--R 4cos(x)sin(x)tan(x)\|a |-------- +--R \| cos(x) +--R + +--R +-+ +-+ 2 +-+ +--R (- 2a\|2 cos(x)sin(x) + 2a\|2 cos(x) - 2a\|2 )tan(x) +--R * +--R +------+ +-+ +------+ +--R \|tan(x) atan(\|2 \|tan(x) - 1) +--R + +--R +--------+ +--R 2 |a sin(x) +--R 8cos(x) |-------- +--R \| cos(x) +--R + +--R +-+ +-+ 2 +-+ +-+ +--R (- 4\|2 cos(x)sin(x) - 4\|2 cos(x) + 4\|2 )\|a +--R * +--R +---------+ +--R | 3 +--R \|a tan(x) +--R + +--R +--------+ +--R +-+ +-+ |a sin(x) +--R 8\|2 cos(x)sin(x)tan(x)\|a |-------- +--R \| cos(x) +--R + +--R 2 +--R (- 8a cos(x)sin(x) + 8a cos(x) - 8a)tan(x) +--R / +--R +--------+ +--R +-+ +-+ |a sin(x) 2 +--R (4\|2 cos(x)sin(x)\|a |-------- - 4a cos(x)sin(x) + 4a cos(x) - 4a) +--R \| cos(x) +--R * +--R +---------+ +--R | 3 +--R \|a tan(x) +--R Type: Expression(Integer) +--E 114 + +--S 115 of 510 +d0222:= D(m0222,x) +--R +--R +--R (106) +--R +-+ 2 3 +-+ 3 +-+ 2 +--R - 2\|2 cos(x) sin(x) + (- 2\|2 cos(x) - 2\|2 cos(x))sin(x) +--R + +--R +-+ 4 +-+ 5 +-+ 3 +--R - 2\|2 cos(x) sin(x) - 2\|2 cos(x) + 2\|2 cos(x) +--R * +--R +--------+ +--R +-+ |a sin(x) +--R \|a |-------- +--R \| cos(x) +--R + +--R 4 2 3 +--R a cos(x)sin(x) + (4a cos(x) + a)sin(x) +--R + +--R 3 2 4 2 +--R (2a cos(x) + 3a cos(x))sin(x) + (4a cos(x) - 3a cos(x) )sin(x) +--R + +--R 5 3 +--R a cos(x) - a cos(x) +--R * +--R +---------+ +--R | 3 +--R \|a tan(x) +--R + +--R 2 3 3 2 +--R - 2a cos(x) sin(x) - a cos(x) sin(x) +--R + +--R 4 2 5 3 +--R (2a cos(x) - 2a cos(x) )sin(x) - a cos(x) + 2a cos(x) - a cos(x) +--R * +--R +--------+ +--R |a sin(x) +--R |-------- +--R \| cos(x) +--R + +--R +-+ 2 3 +-+ 3 +-+ 2 +-+ +--R (2a\|2 cos(x) sin(x) + (- 2a\|2 cos(x) + 2a\|2 cos(x))sin(x) )\|a +--R / +--R 2 3 3 2 +--R 2a cos(x) sin(x) + a cos(x) sin(x) +--R + +--R 4 2 5 3 +--R (- 2a cos(x) + 2a cos(x) )sin(x) + a cos(x) - 2a cos(x) + a cos(x) +--R * +--R +--------+ +--R |a sin(x) +--R |-------- +--R \| cos(x) +--R + +--R +-+ 2 3 +-+ 3 +-+ 2 +-+ +--R (- 2a\|2 cos(x) sin(x) + (2a\|2 cos(x) - 2a\|2 cos(x))sin(x) )\|a +--R * +--R +---------+ +--R | 3 +--R \|a tan(x) +--R Type: Expression(Integer) +--E 115 + +--S 116 of 510 +t0223:= (1+%i*tan(x))^2 +--R +--R +--R 2 +--R (107) - tan(x) + 2%i tan(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 116 + +--S 117 of 510 +r0223:= 2*x-2*%i*log(cos(x))-tan(x) +--R +--R +--R (108) - 2%i log(cos(x)) - tan(x) + 2x +--R Type: Expression(Complex(Integer)) +--E 117 + +--S 118 of 510 +a0223:= integrate(t0223,x) +--R +--R +--R 2 +--R (109) %i log(tan(x) + 1) - tan(x) + 2x +--R Type: Union(Expression(Complex(Integer)),...) +--E 118 + +--S 119 of 510 +m0223:= a0223-r0223 +--R +--R +--R 2 +--R (110) %i log(tan(x) + 1) + 2%i log(cos(x)) +--R Type: Expression(Complex(Integer)) +--E 119 + +--S 120 of 510 +d0223:= D(m0223,x) +--R +--R +--R 2%i cos(x)tan(x) - 2%i sin(x) +--R (111) ----------------------------- +--R cos(x) +--R Type: Expression(Complex(Integer)) +--E 120 + +--S 121 of 510 +t0224:= 1/(1+%i*tan(x)) +--R +--R +--R %i +--R (112) - ----------- +--R tan(x) - %i +--R Type: Expression(Complex(Integer)) +--E 121 + +--S 122 of 510 +r0224:= 1/2*x+%i/(2+2*%i*tan(x)) +--R +--R +--R x tan(x) - %i x + 1 +--R (113) ------------------- +--R 2tan(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 122 + +--S 123 of 510 +a0224:= integrate(t0224,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 123 + +--S 124 of 510 +m0224:= a0224-r0224 +--R +--R +--R (- x + 2a0224)tan(x) + %i x - 2%i a0224 - 1 +--R (114) ------------------------------------------- +--R 2tan(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 124 + +--S 125 of 510 +d0224:= D(m0224,x) +--R +--R +--R %i +--R (115) ----------- +--R tan(x) - %i +--R Type: Expression(Complex(Integer)) +--E 125 + +--S 126 of 510 +t0225:= (a+b*tan(x))^3 +--R +--R +--R 3 3 2 2 2 3 +--R (116) b tan(x) + 3a b tan(x) + 3a b tan(x) + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 510 +r0225:= a^3*x-3*a*b^2*x-3*a^2*b*log(cos(x))+b^3*log(cos(x))+_ + 3*a*b^2*tan(x)+1/2*b^3*tan(x)^2 +--R +--R +--R 3 2 3 2 2 2 3 +--R (2b - 6a b)log(cos(x)) + b tan(x) + 6a b tan(x) + (- 6a b + 2a )x +--R (117) -------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 510 +a0225:= integrate(t0225,x) +--R +--R +--R (118) +--R 3 2 2 3 2 2 2 3 +--R (- b + 3a b)log(tan(x) + 1) + b tan(x) + 6a b tan(x) + (- 6a b + 2a )x +--R -------------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 510 +m0225:= a0225-r0225 +--R +--R +--R 3 2 2 3 2 +--R (- b + 3a b)log(tan(x) + 1) + (- 2b + 6a b)log(cos(x)) +--R (119) --------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 510 +d0225:= D(m0225,x) +--R +--R +--R 3 2 3 2 +--R (- b + 3a b)cos(x)tan(x) + (b - 3a b)sin(x) +--R (120) --------------------------------------------- +--R cos(x) +--R Type: Expression(Integer) +--E 130 + +--S 131 of 510 +t0226:= 1/(4-6*tan(x)) +--R +--R +--R 1 +--R (121) - ----------- +--R 6tan(x) - 4 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 510 +r0226:= 1/13*x-3/26*log(2*cos(x)-3*sin(x)) +--R +--R +--R - 3log(- 3sin(x) + 2cos(x)) + 2x +--R (122) -------------------------------- +--R 26 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 510 +a0226:= integrate(t0226,x) +--R +--R +--R 2 +--R 3log(tan(x) + 1) - 6log(3tan(x) - 2) + 4x +--R (123) ------------------------------------------ +--R 52 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 510 +m0226:= a0226-r0226 +--R +--R +--R 2 +--R 3log(tan(x) + 1) - 6log(3tan(x) - 2) + 6log(- 3sin(x) + 2cos(x)) +--R (124) ----------------------------------------------------------------- +--R 52 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 510 +d0226:= D(m0226,x) +--R +--R +--R 3cos(x)tan(x) - 3sin(x) +--R (125) ------------------------------------------------ +--R (18sin(x) - 12cos(x))tan(x) - 12sin(x) + 8cos(x) +--R Type: Expression(Integer) +--E 135 + +--S 136 of 510 +t0227:= 1/(a+b*tan(x)) +--R +--R +--R 1 +--R (126) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 136 + +--S 137 of 510 +r0227:= (a*x+b*log(a*cos(x)+b*sin(x)))/(a^2+b^2) +--R +--R +--R b log(b sin(x) + a cos(x)) + a x +--R (127) -------------------------------- +--R 2 2 +--R b + a +--R Type: Expression(Integer) +--E 137 + +--S 138 of 510 +a0227:= integrate(t0227,x) +--R +--R +--R 2 +--R - b log(tan(x) + 1) + 2b log(b tan(x) + a) + 2a x +--R (128) -------------------------------------------------- +--R 2 2 +--R 2b + 2a +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 510 +m0227:= a0227-r0227 +--R +--R +--R (129) +--R 2 +--R - b log(tan(x) + 1) + 2b log(b tan(x) + a) - 2b log(b sin(x) + a cos(x)) +--R ------------------------------------------------------------------------- +--R 2 2 +--R 2b + 2a +--R Type: Expression(Integer) +--E 139 + +--S 140 of 510 +d0227:= D(m0227,x) +--R +--R +--R - b cos(x)tan(x) + b sin(x) +--R (130) ----------------------------------------------------- +--R 2 2 +--R (b sin(x) + a b cos(x))tan(x) + a b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 140 + +--S 141 of 510 +t0228:= 1/(a+b*tan(x))^2 +--R +--R +--R 1 +--R (131) ---------------------------- +--R 2 2 2 +--R b tan(x) + 2a b tan(x) + a +--R Type: Expression(Integer) +--E 141 + +--S 142 of 510 +r0228:= (a^2-b^2)*x/(a^2+b^2)^2+2*a*b*log(a*cos(x)+b*sin(x))/_ + (a^2+b^2)^2-b/(a^2+b^2)/(a+b*tan(x)) +--R +--R +--R (132) +--R 2 2 3 2 +--R (2a b tan(x) + 2a b)log(b sin(x) + a cos(x)) + (- b + a b)x tan(x) +--R + +--R 2 3 3 2 +--R (- a b + a )x - b - a b +--R / +--R 5 2 3 4 4 3 2 5 +--R (b + 2a b + a b)tan(x) + a b + 2a b + a +--R Type: Expression(Integer) +--E 142 + +--S 143 of 510 +a0228:= integrate(t0228,x) +--R +--R +--R (133) +--R 2 2 2 +--R (- a b tan(x) - a b)log(tan(x) + 1) +--R + +--R 2 2 3 2 +--R (2a b tan(x) + 2a b)log(b tan(x) + a) + (- b + a b)x tan(x) +--R + +--R 2 3 3 2 +--R (- a b + a )x - b - a b +--R / +--R 5 2 3 4 4 3 2 5 +--R (b + 2a b + a b)tan(x) + a b + 2a b + a +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 510 +m0228:= a0228-r0228 +--R +--R +--R (134) +--R 2 +--R - a b log(tan(x) + 1) + 2a b log(b tan(x) + a) +--R + +--R - 2a b log(b sin(x) + a cos(x)) +--R / +--R 4 2 2 4 +--R b + 2a b + a +--R Type: Expression(Integer) +--E 144 + +--S 145 of 510 +d0228:= D(m0228,x) +--R +--R +--R (135) +--R - 2a b cos(x)tan(x) + 2a b sin(x) +--R / +--R 4 2 2 3 3 3 3 +--R ((b + a b )sin(x) + (a b + a b)cos(x))tan(x) + (a b + a b)sin(x) +--R + +--R 2 2 4 +--R (a b + a )cos(x) +--R Type: Expression(Integer) +--E 145 + +--S 146 of 510 +t0229:= 1/(a+b*tan(x))^3 +--R +--R +--R 1 +--R (136) ------------------------------------------- +--R 3 3 2 2 2 3 +--R b tan(x) + 3a b tan(x) + 3a b tan(x) + a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 510 +r0229:= a*(a^2-3*b^2)*x/(a^2+b^2)^3+b*(3*a^2-b^2)*log(a*cos(x)+b*sin(x))/_ + (a^2+b^2)^3-1/2*b/(a^2+b^2)/(a+b*tan(x))^2-_ + 2*a*b/(a^2+b^2)^2/(a+b*tan(x)) +--R +--R +--R (137) +--R 5 2 3 2 4 3 2 2 3 4 +--R ((- 2b + 6a b )tan(x) + (- 4a b + 12a b )tan(x) - 2a b + 6a b) +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 6a b + 2a b )x tan(x) + ((- 12a b + 4a b)x - 4a b - 4a b )tan(x) +--R + +--R 3 2 5 5 2 3 4 +--R (- 6a b + 2a )x - b - 6a b - 5a b +--R / +--R 8 2 6 4 4 6 2 2 +--R (2b + 6a b + 6a b + 2a b )tan(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 8 +--R (4a b + 12a b + 12a b + 4a b)tan(x) + 2a b + 6a b + 6a b + 2a +--R Type: Expression(Integer) +--E 147 + +--S 148 of 510 +a0229:= integrate(t0229,x) +--R +--R +--R (138) +--R 5 2 3 2 4 3 2 2 3 4 +--R ((b - 3a b )tan(x) + (2a b - 6a b )tan(x) + a b - 3a b) +--R * +--R 2 +--R log(tan(x) + 1) +--R + +--R 5 2 3 2 4 3 2 2 3 4 +--R ((- 2b + 6a b )tan(x) + (- 4a b + 12a b )tan(x) - 2a b + 6a b) +--R * +--R log(b tan(x) + a) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 6a b + 2a b )x tan(x) + ((- 12a b + 4a b)x - 4a b - 4a b )tan(x) +--R + +--R 3 2 5 5 2 3 4 +--R (- 6a b + 2a )x - b - 6a b - 5a b +--R / +--R 8 2 6 4 4 6 2 2 +--R (2b + 6a b + 6a b + 2a b )tan(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 8 +--R (4a b + 12a b + 12a b + 4a b)tan(x) + 2a b + 6a b + 6a b + 2a +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 510 +m0229:= a0229-r0229 +--R +--R +--R (139) +--R 3 2 2 3 2 +--R (b - 3a b)log(tan(x) + 1) + (- 2b + 6a b)log(b tan(x) + a) +--R + +--R 3 2 +--R (2b - 6a b)log(b sin(x) + a cos(x)) +--R / +--R 6 2 4 4 2 6 +--R 2b + 6a b + 6a b + 2a +--R Type: Expression(Integer) +--E 149 + +--S 150 of 510 +d0229:= D(m0229,x) +--R +--R +--R (140) +--R 3 2 3 2 +--R (b - 3a b)cos(x)tan(x) + (- b + 3a b)sin(x) +--R / +--R 6 2 4 4 2 5 3 3 5 +--R ((b + 2a b + a b )sin(x) + (a b + 2a b + a b)cos(x))tan(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (a b + 2a b + a b)sin(x) + (a b + 2a b + a )cos(x) +--R Type: Expression(Integer) +--E 150 + +--S 151 of 510 +t0230:= (a+b*tan(x))^(1/2) +--R +--R +--R +------------+ +--R (141) \|b tan(x) + a +--R Type: Expression(Integer) +--E 151 + +--S 152 of 510 +r0230:= b*((a-(-b^2)^(1/2))^(1/2)*atanh((a+b*tan(x))^(1/2)/_ + (a-(-b^2)^(1/2))^(1/2))-(a+(-b^2)^(1/2))^(1/2)*_ + atanh((a+b*tan(x))^(1/2)/(a+(-b^2)^(1/2))^(1/2)))/(-b^2)^(1/2) +--R +--R +--R (142) +--R +-------------+ +--R | +----+ +------------+ +--R | | 2 \|b tan(x) + a +--R b\|- \|- b + a atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- b + a +--R + +--R +-----------+ +--R | +----+ +------------+ +--R | | 2 \|b tan(x) + a +--R - b\|\|- b + a atanh(---------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- b + a +--R / +--R +----+ +--R | 2 +--R \|- b +--R Type: Expression(Integer) +--E 152 + +--S 153 of 510 +a0230:= integrate(t0230,x) +--R +--R +--R >> Error detected within library code: +--R ker2trigs: cannot convert kernel to gaussian function +--R +--R Continuing to read the file... +--R +--E 153 + +--S 154 of 510 +m0230:= a0230-r0230 +--R +--R +--R (143) +--R +-------------+ +--R | +----+ +------------+ +--R | | 2 \|b tan(x) + a +--R - b\|- \|- b + a atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- b + a +--R + +--R +-----------+ +--R | +----+ +------------+ +----+ +--R | | 2 \|b tan(x) + a | 2 +--R b\|\|- b + a atanh(---------------) + a0230\|- b +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- b + a +--R / +--R +----+ +--R | 2 +--R \|- b +--R Type: Expression(Integer) +--E 154 + +--S 155 of 510 +d0230:= D(m0230,x) +--R +--R +--R - b tan(x) - a +--R (144) --------------- +--R +------------+ +--R \|b tan(x) + a +--R Type: Expression(Integer) +--E 155 + +--S 156 of 510 +t0231:= 1/(a+b*tan(x))^(1/2) +--R +--R +--R 1 +--R (145) --------------- +--R +------------+ +--R \|b tan(x) + a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 510 +r0231:= b*atanh((a+b*tan(x))^(1/2)/(a-(-b^2)^(1/2))^(1/2))/(-b^2)^(1/2)/_ + (a-(-b^2)^(1/2))^(1/2)-b*atanh((a+b*tan(x))^(1/2)/_ + (a+(-b^2)^(1/2))^(1/2))/(-b^2)^(1/2)/(a+(-b^2)^(1/2))^(1/2) +--R +--R +--R (146) +--R +-----------+ +--R | +----+ +------------+ +--R | | 2 \|b tan(x) + a +--R b\|\|- b + a atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- b + a +--R + +--R +-------------+ +--R | +----+ +------------+ +--R | | 2 \|b tan(x) + a +--R - b\|- \|- b + a atanh(---------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- b + a +--R / +--R +-------------+ +-----------+ +--R +----+ | +----+ | +----+ +--R | 2 | | 2 | | 2 +--R \|- b \|- \|- b + a \|\|- b + a +--R Type: Expression(Integer) +--E 157 + +--S 158 of 510 +a0231:= integrate(t0231,x) +--R +--R +--R >> Error detected within library code: +--R ker2trigs: cannot convert kernel to gaussian function +--R +--R Continuing to read the file... +--R +--E 158 + +--S 159 of 510 +m0231:= a0231-r0231 +--R +--R +--R (147) +--R +-----------+ +--R | +----+ +------------+ +--R | | 2 \|b tan(x) + a +--R - b\|\|- b + a atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- b + a +--R + +--R +-------------+ +--R | +----+ +------------+ +--R | | 2 \|b tan(x) + a +--R b\|- \|- b + a atanh(---------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- b + a +--R + +--R +-------------+ +-----------+ +--R +----+ | +----+ | +----+ +--R | 2 | | 2 | | 2 +--R a0231\|- b \|- \|- b + a \|\|- b + a +--R / +--R +-------------+ +-----------+ +--R +----+ | +----+ | +----+ +--R | 2 | | 2 | | 2 +--R \|- b \|- \|- b + a \|\|- b + a +--R Type: Expression(Integer) +--E 159 + +--S 160 of 510 +d0231:= D(m0231,x) +--R +--R +--R 1 +--R (148) - --------------- +--R +------------+ +--R \|b tan(x) + a +--R Type: Expression(Integer) +--E 160 + +--S 161 of 510 +t0232:= (a+b*tan(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (149) \|b tan(x) + a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 510 +r0232:= (a-b)^(1/2)*atan((a-b)^(1/2)*tan(x)/(a+b*tan(x)^2)^(1/2))+_ + b^(1/2)*atanh(cot(x)*(a+b*tan(x)^2)^(1/2)/b^(1/2)) +--R +--R +--R +-------------+ +--R | 2 +-------+ +--R +-+ cot(x)\|b tan(x) + a +-------+ tan(x)\|- b + a +--R (150) \|b atanh(----------------------) + \|- b + a atan(----------------) +--R +-+ +-------------+ +--R \|b | 2 +--R \|b tan(x) + a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 510 +a0232:= integrate(t0232,x) +--R +--R +--R (151) +--R [ +--R (b - a) +--R * +--R log +--R 3 +-----+ +--R ((8b - 8a)cos(x) + (- 8b + 4a)cos(x))sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (- 16b + 24a b - 8a )cos(x) + 8b +--R + +--R 2 +--R - 8a b + a +--R + +--R +-----+ +-+ +--R 2\|b - a \|b +--R * +--R log +--R 3 2 2 3 7 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 5 +--R (320b - 800a b + 640a b - 160a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 256b + 512a b - 304a b + 48a )cos(x) +--R + +--R 3 2 2 3 +--R (64b - 96a b + 36a b - 2a )cos(x) +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 2 2 3 9 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 7 +--R (384b - 960a b + 768a b - 192a )cos(x) +--R + +--R 3 2 2 3 5 +--R (- 448b + 896a b - 528a b + 80a )cos(x) +--R + +--R 3 2 2 3 3 +--R (256b - 384a b + 144a b - 8a )cos(x) +--R + +--R 3 2 2 +--R (- 64b + 64a b - 12a b)cos(x) +--R * +--R +-----+ +--R sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 8 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (448b - 1120a b + 896a b - 224a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 576b + 1152a b - 688a b + 112a )cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R (320b - 480a b + 188a b - 14a )cos(x) - 64b + 64a b +--R + +--R 2 +--R - 12a b +--R * +--R +-----+ +-+ +--R \|b - a \|b +--R + +--R 4 3 2 2 3 4 10 +--R (- 128b + 512a b - 768a b + 512a b - 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (512b - 1792a b + 2304a b - 1280a b + 256a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 832b + 2496a b - 2656a b + 1152a b - 160a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (704b - 1760a b + 1472a b - 448a b + 32a )cos(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (- 320b + 640a b - 388a b + 68a b - a )cos(x) + 64b +--R + +--R 3 2 2 3 +--R - 96a b + 36a b - 2a b +--R / +--R 3 2 2 3 9 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 7 +--R (- 384b + 960a b - 768a b + 192a )cos(x) +--R + +--R 3 2 2 3 5 +--R (384b - 768a b + 464a b - 80a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 128b + 192a b - 80a b + 8a )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R sin(x)\|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4 3 2 2 3 4 10 +--R (128b - 512a b + 768a b - 512a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 512b + 1792a b - 2304a b + 1280a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (768b - 2304a b + 2464a b - 1088a b + 160a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 512b + 1280a b - 1088a b + 352a b - 32a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (128b - 256a b + 160a b - 32a b + a )cos(x) +--R / +--R +-----+ +--R 4\|b - a +--R , +--R +--R (b - a) +--R * +--R log +--R 3 +-----+ +--R ((8b - 8a)cos(x) + (- 8b + 4a)cos(x))sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (- 16b + 24a b - 8a )cos(x) + 8b +--R + +--R 2 +--R - 8a b + a +--R + +--R - +--R +---+ +-----+ +--R 4\|- b \|b - a +--R * +--R atan +--R +--------------------+ +--R | 2 +--R +---+ |(- b + a)cos(x) + b +--R cos(x)sin(x)\|- b |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 +---+ +-----+ +--R cos(x) \|- b \|b - a +--R / +--R b +--R / +--R +-----+ +--R 4\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 163 + +--S 164 of 510 +m0232a:= a0232.1-r0232 +--R +--R +--R (152) +--R (b - a) +--R * +--R log +--R 3 +-----+ +--R ((8b - 8a)cos(x) + (- 8b + 4a)cos(x))sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (- 16b + 24a b - 8a )cos(x) + 8b +--R + +--R 2 +--R - 8a b + a +--R + +--R +-----+ +-+ +--R 2\|b - a \|b +--R * +--R log +--R 3 2 2 3 7 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 5 +--R (320b - 800a b + 640a b - 160a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 256b + 512a b - 304a b + 48a )cos(x) +--R + +--R 3 2 2 3 +--R (64b - 96a b + 36a b - 2a )cos(x) +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 2 2 3 9 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 7 +--R (384b - 960a b + 768a b - 192a )cos(x) +--R + +--R 3 2 2 3 5 +--R (- 448b + 896a b - 528a b + 80a )cos(x) +--R + +--R 3 2 2 3 3 +--R (256b - 384a b + 144a b - 8a )cos(x) +--R + +--R 3 2 2 +--R (- 64b + 64a b - 12a b)cos(x) +--R * +--R +-----+ +--R sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 8 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (448b - 1120a b + 896a b - 224a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 576b + 1152a b - 688a b + 112a )cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R (320b - 480a b + 188a b - 14a )cos(x) - 64b + 64a b +--R + +--R 2 +--R - 12a b +--R * +--R +-----+ +-+ +--R \|b - a \|b +--R + +--R 4 3 2 2 3 4 10 +--R (- 128b + 512a b - 768a b + 512a b - 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (512b - 1792a b + 2304a b - 1280a b + 256a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 832b + 2496a b - 2656a b + 1152a b - 160a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (704b - 1760a b + 1472a b - 448a b + 32a )cos(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (- 320b + 640a b - 388a b + 68a b - a )cos(x) + 64b +--R + +--R 3 2 2 3 +--R - 96a b + 36a b - 2a b +--R / +--R 3 2 2 3 9 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 7 +--R (- 384b + 960a b - 768a b + 192a )cos(x) +--R + +--R 3 2 2 3 5 +--R (384b - 768a b + 464a b - 80a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 128b + 192a b - 80a b + 8a )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R sin(x)\|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4 3 2 2 3 4 10 +--R (128b - 512a b + 768a b - 512a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 512b + 1792a b - 2304a b + 1280a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (768b - 2304a b + 2464a b - 1088a b + 160a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 512b + 1280a b - 1088a b + 352a b - 32a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (128b - 256a b + 160a b - 32a b + a )cos(x) +--R + +--R +-------------+ +--R | 2 +--R +-----+ +-+ cot(x)\|b tan(x) + a +--R - 4\|b - a \|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R +-------+ +--R +-------+ +-----+ tan(x)\|- b + a +--R - 4\|- b + a \|b - a atan(----------------) +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R / +--R +-----+ +--R 4\|b - a +--R Type: Expression(Integer) +--E 164 + +--S 165 of 510 +--d0232a:= D(m0232a,x) +--E 165 + +--S 166 of 510 +m0232b:= a0232.2-r0232 +--R +--R +--R (153) +--R (b - a) +--R * +--R log +--R 3 +-----+ +--R ((8b - 8a)cos(x) + (- 8b + 4a)cos(x))sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (- 16b + 24a b - 8a )cos(x) + 8b +--R + +--R 2 +--R - 8a b + a +--R + +--R +-------------+ +--R | 2 +--R +-----+ +-+ cot(x)\|b tan(x) + a +--R - 4\|b - a \|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R - +--R +---+ +-----+ +--R 4\|- b \|b - a +--R * +--R atan +--R +--------------------+ +--R | 2 +--R +---+ |(- b + a)cos(x) + b 2 +---+ +-----+ +--R cos(x)sin(x)\|- b |-------------------- + cos(x) \|- b \|b - a +--R | 2 +--R \| cos(x) +--R ----------------------------------------------------------------- +--R b +--R + +--R +-------+ +--R +-------+ +-----+ tan(x)\|- b + a +--R - 4\|- b + a \|b - a atan(----------------) +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R / +--R +-----+ +--R 4\|b - a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 510 +d0232b:= D(m0232b,x) +--R +--R +--R (154) +--R 4 3 2 2 3 4 +--R (- 6b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 4 3 2 2 3 2 +--R (6b - 13a b + 8a b - a b)cos(x) +--R * +--R 2 4 +--R cot(x) sin(x) +--R + +--R 4 3 2 2 3 6 +--R (24b - 72a b + 72a b - 24a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 44b + 98a b - 64a b + 10a b)cos(x) +--R + +--R 4 3 2 2 2 +--R (20b - 30a b + 10a b )cos(x) +--R * +--R 2 2 +--R cot(x) sin(x) +--R + +--R 4 3 2 2 3 8 +--R (- 2b + 6a b - 6a b + 2a b)cos(x) +--R + +--R 4 3 2 2 3 6 +--R (10b - 21a b + 12a b - a b)cos(x) +--R + +--R 4 3 2 2 4 4 3 2 +--R (- 14b + 20a b - 6a b )cos(x) + (6b - 5a b )cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 4 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (6a b - 13a b + 8a b - a )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 3 4 +--R (6b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 6b + 13a b - 8a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 4 6 +--R (24a b - 72a b + 72a b - 24a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 44a b + 98a b - 64a b + 10a )cos(x) +--R + +--R 3 2 2 3 2 +--R (20a b - 30a b + 10a b)cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 3 6 +--R (- 24b + 72a b - 72a b + 24a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (44b - 98a b + 64a b - 10a b)cos(x) +--R + +--R 4 3 2 2 2 +--R (- 20b + 30a b - 10a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 8 +--R (- 2a b + 6a b - 6a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 6 +--R (10a b - 21a b + 12a b - a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 2 +--R (- 14a b + 20a b - 6a b)cos(x) + (6a b - 5a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 3 8 +--R (2b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 6 +--R (- 10b + 21a b - 12a b + a b)cos(x) +--R + +--R 4 3 2 2 4 4 3 2 +--R (14b - 20a b + 6a b )cos(x) + (- 6b + 5a b )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- 20b + 60a b - 60a b + 20a b)cos(x) +--R + +--R 4 3 2 2 3 3 +--R (36b - 78a b + 48a b - 6a b)cos(x) +--R + +--R 4 3 2 2 +--R (- 16b + 24a b - 8a b )cos(x) +--R * +--R 2 3 +--R cot(x) sin(x) +--R + +--R 4 3 2 2 3 7 +--R (12b - 36a b + 36a b - 12a b)cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- 40b + 86a b - 52a b + 6a b)cos(x) +--R + +--R 4 3 2 2 3 +--R (44b - 58a b + 14a b )cos(x) +--R + +--R 4 3 2 2 +--R (- 16b + 8a b + 2a b )cos(x) +--R * +--R 2 +--R cot(x) sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 5 +--R (- 20a b + 60a b - 60a b + 20a )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (36a b - 78a b + 48a b - 6a )cos(x) +--R + +--R 3 2 2 3 +--R (- 16a b + 24a b - 8a b)cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 3 5 +--R (20b - 60a b + 60a b - 20a b)cos(x) +--R + +--R 4 3 2 2 3 3 +--R (- 36b + 78a b - 48a b + 6a b)cos(x) +--R + +--R 4 3 2 2 +--R (16b - 24a b + 8a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 4 7 +--R (12a b - 36a b + 36a b - 12a )cos(x) +--R + +--R 3 2 2 3 4 5 +--R (- 40a b + 86a b - 52a b + 6a )cos(x) +--R + +--R 3 2 2 3 3 +--R (44a b - 58a b + 14a b)cos(x) +--R + +--R 3 2 2 3 +--R (- 16a b + 8a b + 2a b)cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 3 7 +--R (- 12b + 36a b - 36a b + 12a b)cos(x) +--R + +--R 4 3 2 2 3 5 +--R (40b - 86a b + 52a b - 6a b)cos(x) +--R + +--R 4 3 2 2 3 +--R (- 44b + 58a b - 14a b )cos(x) +--R + +--R 4 3 2 2 +--R (16b - 8a b - 2a b )cos(x) +--R * +--R sin(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R + +--R 4 3 2 2 5 +--R (8b - 16a b + 8a b )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 16b + 20a b - 4a b )cos(x) + (8b - 4a b )cos(x) +--R * +--R 3 +--R cot(x)sin(x) +--R + +--R 4 3 2 2 7 +--R (- 24b + 48a b - 24a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (40b - 60a b + 20a b )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 8b + 8a b - 2a b )cos(x) + (- 8b + 4a b )cos(x) +--R * +--R cot(x)sin(x) +--R * +--R 3 +--R tan(x) +--R + +--R 3 2 2 3 5 +--R (- 8a b + 16a b - 8a b)cos(x) +--R + +--R 3 2 2 3 3 3 2 2 +--R (16a b - 20a b + 4a b)cos(x) + (- 8a b + 4a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 5 +--R (- 8b + 16a b - 8a b )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (16b - 20a b + 4a b )cos(x) + (- 8b + 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 7 +--R (24a b - 48a b + 24a b)cos(x) +--R + +--R 3 2 2 3 5 +--R (- 40a b + 60a b - 20a b)cos(x) +--R + +--R 3 2 2 3 3 3 2 2 +--R (8a b - 8a b + 2a b)cos(x) + (8a b - 4a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 7 +--R (24b - 48a b + 24a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (- 40b + 60a b - 20a b )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (8b - 8a b + 2a b )cos(x) + (8b - 4a b )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 2 5 +--R (8b - 16a b + 8a b )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 16b + 20a b - 4a b )cos(x) + (8b - 4a b )cos(x) +--R * +--R 3 +--R cot(x)sin(x) +--R + +--R 4 3 2 2 7 +--R (- 24b + 48a b - 24a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (40b - 60a b + 20a b )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 8b + 8a b - 2a b )cos(x) + (- 8b + 4a b )cos(x) +--R * +--R cot(x)sin(x) +--R * +--R tan(x) +--R + +--R 2 2 3 4 5 +--R (- 8a b + 16a b - 8a )cos(x) +--R + +--R 2 2 3 4 3 2 2 3 +--R (16a b - 20a b + 4a )cos(x) + (- 8a b + 4a b)cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 5 4 3 2 2 3 +--R (- 8b + 16a b - 8a b )cos(x) + (16b - 20a b + 4a b )cos(x) +--R + +--R 4 3 +--R (- 8b + 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 4 7 +--R (24a b - 48a b + 24a )cos(x) +--R + +--R 2 2 3 4 5 +--R (- 40a b + 60a b - 20a )cos(x) +--R + +--R 2 2 3 4 3 2 2 3 +--R (8a b - 8a b + 2a )cos(x) + (8a b - 4a b)cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 7 +--R (24b - 48a b + 24a b )cos(x) +--R + +--R 4 3 2 2 5 4 3 2 2 3 +--R (- 40b + 60a b - 20a b )cos(x) + (8b - 8a b + 2a b )cos(x) +--R + +--R 4 3 +--R (8b - 4a b )cos(x) +--R * +--R sin(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (24b - 72a b + 72a b - 24a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 56b + 128a b - 88a b + 16a b )cos(x) +--R + +--R 5 4 2 3 3 2 2 5 4 2 3 +--R (40b - 64a b + 25a b - a b )cos(x) - 8b + 8a b - a b +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 8b + 24a b - 24a b + 8a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 2 3 3 2 4 +--R (16b - 40a b + 32a b - 8a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 4 2 3 2 5 4 2 3 +--R (- 16b + 24a b - 8a b )cos(x) + 8b - 8a b + a b +--R * +--R cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 24a b + 72a b - 72a b + 24a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (56a b - 128a b + 88a b - 16a b)cos(x) +--R + +--R 4 2 3 3 2 4 2 4 2 3 +--R (- 40a b + 64a b - 25a b + a b)cos(x) + 8a b - 8a b +--R + +--R 3 2 +--R a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 24b + 72a b - 72a b + 24a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (56b - 128a b + 88a b - 16a b )cos(x) +--R + +--R 5 4 2 3 3 2 2 5 4 2 3 +--R (- 40b + 64a b - 25a b + a b )cos(x) + 8b - 8a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 4 8 +--R (8a b - 24a b + 24a b - 8a b)cos(x) +--R + +--R 4 2 3 3 2 4 6 3 2 4 4 +--R (- 16a b + 40a b - 32a b + 8a b)cos(x) + (a b - a b)cos(x) +--R + +--R 4 2 3 3 2 2 4 2 3 3 2 +--R (16a b - 24a b + 8a b )cos(x) - 8a b + 8a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 2 3 3 2 8 +--R (8b - 24a b + 24a b - 8a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 2 3 3 2 4 +--R (- 16b + 40a b - 32a b + 8a b )cos(x) + (a b - a b )cos(x) +--R + +--R 5 4 2 3 2 5 4 2 3 +--R (16b - 24a b + 8a b )cos(x) - 8b + 8a b - a b +--R * +--R 2 +--R tan(x) +--R + +--R 5 4 2 3 3 2 6 +--R (24b - 72a b + 72a b - 24a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 56b + 128a b - 88a b + 16a b )cos(x) +--R + +--R 5 4 2 3 3 2 2 5 4 2 3 +--R (40b - 64a b + 25a b - a b )cos(x) - 8b + 8a b - a b +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 8b + 24a b - 24a b + 8a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 2 3 3 2 4 +--R (16b - 40a b + 32a b - 8a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 4 2 3 2 5 4 2 3 +--R (- 16b + 24a b - 8a b )cos(x) + 8b - 8a b + a b +--R * +--R cot(x) +--R * +--R tan(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 24a b + 72a b - 72a b + 24a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (56a b - 128a b + 88a b - 16a )cos(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 4 +--R (- 40a b + 64a b - 25a b + a )cos(x) + 8a b - 8a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 24b + 72a b - 72a b + 24a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (56b - 128a b + 88a b - 16a b )cos(x) +--R + +--R 5 4 2 3 3 2 2 5 4 2 3 +--R (- 40b + 64a b - 25a b + a b )cos(x) + 8b - 8a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 5 8 +--R (8a b - 24a b + 24a b - 8a )cos(x) +--R + +--R 2 3 3 2 4 5 6 4 5 4 +--R (- 16a b + 40a b - 32a b + 8a )cos(x) + (a b - a )cos(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 +--R (16a b - 24a b + 8a b)cos(x) - 8a b + 8a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 2 3 3 2 8 +--R (8b - 24a b + 24a b - 8a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 2 3 3 2 4 +--R (- 16b + 40a b - 32a b + 8a b )cos(x) + (a b - a b )cos(x) +--R + +--R 5 4 2 3 2 5 4 2 3 +--R (16b - 24a b + 8a b )cos(x) - 8b + 8a b - a b +--R / +--R 3 2 2 5 +--R (8b - 16a b + 8a b)cos(x) +--R + +--R 3 2 2 3 3 2 +--R (- 16b + 20a b - 4a b)cos(x) + (8b - 4a b )cos(x) +--R * +--R 2 3 +--R cot(x) sin(x) +--R + +--R 3 2 2 7 +--R (- 24b + 48a b - 24a b)cos(x) +--R + +--R 3 2 2 5 +--R (40b - 60a b + 20a b)cos(x) +--R + +--R 3 2 2 3 3 2 +--R (- 8b + 8a b - 2a b)cos(x) + (- 8b + 4a b )cos(x) +--R * +--R 2 +--R cot(x) sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 5 +--R (8a b - 16a b + 8a )cos(x) +--R + +--R 2 2 3 3 2 2 +--R (- 16a b + 20a b - 4a )cos(x) + (8a b - 4a b)cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 2 5 3 2 2 3 +--R (- 8b + 16a b - 8a b)cos(x) + (16b - 20a b + 4a b)cos(x) +--R + +--R 3 2 +--R (- 8b + 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 7 +--R (- 24a b + 48a b - 24a )cos(x) +--R + +--R 2 2 3 5 +--R (40a b - 60a b + 20a )cos(x) +--R + +--R 2 2 3 3 2 2 +--R (- 8a b + 8a b - 2a )cos(x) + (- 8a b + 4a b)cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 2 7 +--R (24b - 48a b + 24a b)cos(x) +--R + +--R 3 2 2 5 3 2 2 3 +--R (- 40b + 60a b - 20a b)cos(x) + (8b - 8a b + 2a b)cos(x) +--R + +--R 3 2 +--R (8b - 4a b )cos(x) +--R * +--R sin(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4 3 2 2 3 6 +--R (24b - 72a b + 72a b - 24a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 56b + 128a b - 88a b + 16a b)cos(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (40b - 64a b + 25a b - a b)cos(x) - 8b + 8a b - a b +--R * +--R 2 2 +--R cot(x) sin(x) +--R + +--R 4 3 2 2 3 8 +--R (- 8b + 24a b - 24a b + 8a b)cos(x) +--R + +--R 4 3 2 2 3 6 2 2 3 4 +--R (16b - 40a b + 32a b - 8a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (- 16b + 24a b - 8a b )cos(x) + 8b - 8a b + a b +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 6 +--R (24a b - 72a b + 72a b - 24a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 56a b + 128a b - 88a b + 16a )cos(x) +--R + +--R 3 2 2 3 4 2 3 2 2 3 +--R (40a b - 64a b + 25a b - a )cos(x) - 8a b + 8a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 3 6 +--R (- 24b + 72a b - 72a b + 24a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (56b - 128a b + 88a b - 16a b)cos(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 +--R (- 40b + 64a b - 25a b + a b)cos(x) + 8b - 8a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 8 +--R (- 8a b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 6 3 4 4 +--R (16a b - 40a b + 32a b - 8a )cos(x) + (- a b + a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 16a b + 24a b - 8a b)cos(x) + 8a b - 8a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 3 8 +--R (8b - 24a b + 24a b - 8a b)cos(x) +--R + +--R 4 3 2 2 3 6 2 2 3 4 +--R (- 16b + 40a b - 32a b + 8a b)cos(x) + (a b - a b)cos(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (16b - 24a b + 8a b )cos(x) - 8b + 8a b - a b +--R * +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 510 +t0233:= 1/(a+b*tan(x)^2)^(1/2) +--R +--R +--R 1 +--R (155) ---------------- +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R Type: Expression(Integer) +--E 168 + +--S 169 of 510 +r0233:= atan((a-b)^(1/2)*tan(x)/(a+b*tan(x)^2)^(1/2))/(a-b)^(1/2) +--R +--R +--R +-------+ +--R tan(x)\|- b + a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R (156) ---------------------- +--R +-------+ +--R \|- b + a +--R Type: Expression(Integer) +--E 169 + +--S 170 of 510 +a0233:= integrate(t0233,x) +--R +--R +--R (157) +--R - +--R log +--R 3 +-----+ +--R ((8b - 8a)cos(x) + (- 8b + 4a)cos(x))sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (- 16b + 24a b - 8a )cos(x) + 8b +--R + +--R 2 +--R - 8a b + a +--R / +--R +-----+ +--R 4\|b - a +--R Type: Union(Expression(Integer),...) +--E 170 + +--S 171 of 510 +m0233:= a0233-r0233 +--R +--R +--R (158) +--R - +--R +-------+ +--R \|- b + a +--R * +--R log +--R 3 +-----+ +--R ((8b - 8a)cos(x) + (- 8b + 4a)cos(x))sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (- 16b + 24a b - 8a )cos(x) +--R + +--R 2 2 +--R 8b - 8a b + a +--R + +--R +-------+ +--R +-----+ tan(x)\|- b + a +--R - 4\|b - a atan(----------------) +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R / +--R +-------+ +-----+ +--R 4\|- b + a \|b - a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 510 +d0233:= D(m0233,x) +--R +--R +--R (159) +--R 4 2 +-----+ +--R ((8b - 8a)cos(x) + (- 8b + 4a)cos(x) )sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 3 2 2 2 +--R ((- 6b + 12a b - 6a )cos(x) + (6b - 7a b + a )cos(x))sin(x) +--R + +--R 2 2 5 2 2 3 +--R (2b - 4a b + 2a )cos(x) + (- 4b + 5a b - a )cos(x) +--R + +--R 2 +--R (2b - a b)cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R + +--R 2 2 5 2 2 3 +--R (- 8b + 16a b - 8a )cos(x) + (16b - 24a b + 8a )cos(x) +--R + +--R 2 2 +--R (- 8b + 8a b - a )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (- 16b + 20a b - 4a )cos(x) + 8b +--R + +--R - 4a b +--R * +--R +-----+ +--R sin(x)\|b - a +--R / +--R 2 2 5 2 2 3 +--R (8b - 16a b + 8a )cos(x) + (- 16b + 24a b - 8a )cos(x) +--R + +--R 2 2 +--R (8b - 8a b + a )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 2 +--R (- 8b + 16a b - 8a )cos(x) + (16b - 20a b + 4a )cos(x) - 8b +--R + +--R 4a b +--R * +--R +-----+ +--R sin(x)\|b - a +--R * +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 510 +t0234:= (-1-tan(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (160) (- tan(x) - 1)\|- tan(x) - 1 +--R Type: Expression(Integer) +--E 173 + +--S 174 of 510 +r0234:= -1/2*cos(x)*(-sec(x)^2)^(1/2)*(atanh(sin(x))+sec(x)*tan(x)) +--R +--R +--R +---------+ +--R | 2 +--R (- cos(x)atanh(sin(x)) - cos(x)sec(x)tan(x))\|- sec(x) +--R (161) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 510 +a0234:= integrate(t0234,x) +--R +--R +--R (162) +--R +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ +--R (- \|- 1 (%e ) - 2\|- 1 (%e ) - \|- 1 ) +--R * +--R +---+ +--R x\|- 1 +---+ +--R log(%e + \|- 1 ) +--R + +--R +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ +--R (\|- 1 (%e ) + 2\|- 1 (%e ) + \|- 1 ) +--R * +--R +---+ +--R x\|- 1 +---+ +--R log(%e - \|- 1 ) +--R + +--R +---+ 3 +---+ +--R x\|- 1 x\|- 1 +--R - 2(%e ) + 2%e +--R / +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 4(%e ) + 2 +--R Type: Union(Expression(Integer),...) +--E 175 + +--S 176 of 510 +m0234:= a0234-r0234 +--R +--R +--R (163) +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R (cos(x)(%e ) + 2cos(x)(%e ) + cos(x))atanh(sin(x)) +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R (cos(x)(%e ) + 2cos(x)(%e ) + cos(x))sec(x)tan(x) +--R * +--R +---------+ +--R | 2 +--R \|- sec(x) +--R + +--R +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ +--R (- \|- 1 (%e ) - 2\|- 1 (%e ) - \|- 1 ) +--R * +--R +---+ +--R x\|- 1 +---+ +--R log(%e + \|- 1 ) +--R + +--R +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ +--R (\|- 1 (%e ) + 2\|- 1 (%e ) + \|- 1 ) +--R * +--R +---+ +--R x\|- 1 +---+ +--R log(%e - \|- 1 ) +--R + +--R +---+ 3 +---+ +--R x\|- 1 x\|- 1 +--R - 2(%e ) + 2%e +--R / +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 4(%e ) + 2 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 510 +d0234:= D(m0234,x) +--R +--R +--R (164) +--R +---+ 3 +---+ 3 +---------+ +--R +---+ x\|- 1 2 +---+ x\|- 1 | 2 +--R (- 16\|- 1 (%e ) sin(x) + 16\|- 1 (%e ) )\|- sec(x) +--R + +--R +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 +--R - cos(x)(%e ) - 3cos(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R - 3cos(x)(%e ) - cos(x) +--R * +--R 2 2 +--R sec(x) sin(x) +--R + +--R +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 +--R cos(x)(%e ) + 3cos(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 3cos(x)(%e ) + cos(x) +--R * +--R 2 +--R sec(x) +--R * +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 2 3 +--R ((%e ) + 3(%e ) + 3(%e ) + 1)sec(x) sin(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 2 +--R (- (%e ) - 3(%e ) - 3(%e ) - 1)sec(x) sin(x) +--R * +--R atanh(sin(x)) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - 3cos(x)(%e ) - 9cos(x)(%e ) - 9cos(x)(%e ) +--R + +--R - 3cos(x) +--R * +--R 3 2 +--R sec(x) sin(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R 3cos(x)(%e ) + 9cos(x)(%e ) + 9cos(x)(%e ) +--R + +--R 3cos(x) +--R * +--R 3 +--R sec(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 3 3 +--R ((%e ) + 3(%e ) + 3(%e ) + 1)sec(x) sin(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 3 +--R (- (%e ) - 3(%e ) - 3(%e ) - 1)sec(x) sin(x) +--R * +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - cos(x)(%e ) - 3cos(x)(%e ) - 3cos(x)(%e ) +--R + +--R - cos(x) +--R * +--R 3 2 +--R sec(x) sin(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R cos(x)(%e ) + 3cos(x)(%e ) + 3cos(x)(%e ) +--R + +--R cos(x) +--R * +--R 3 +--R sec(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 x\|- 1 +--R cos(x) (%e ) + 3cos(x) (%e ) + 3cos(x) (%e ) +--R + +--R 2 +--R cos(x) +--R * +--R 2 +--R sec(x) +--R / +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 2 +--R (2(%e ) + 6(%e ) + 6(%e ) + 2)sin(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - 2(%e ) - 6(%e ) - 6(%e ) - 2 +--R * +--R +---------+ +--R | 2 +--R \|- sec(x) +--R Type: Expression(Integer) +--E 177 + +--S 178 of 510 +t0235:= (a+b*tan(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (165) (b tan(x) + a)\|b tan(x) + a +--R Type: Expression(Integer) +--E 178 + +--S 179 of 510 +r0235:= (a-b)^(3/2)*atan((a-b)^(1/2)*tan(x)/(a+b*tan(x)^2)^(1/2))+_ + 3/2*a*b^(1/2)*atanh(cot(x)*(a+b*tan(x)^2)^(1/2)/b^(1/2))-_ + b^(3/2)*atanh(cot(x)*(a+b*tan(x)^2)^(1/2)/b^(1/2))+_ + 1/2*b*tan(x)*(a+b*tan(x)^2)^(1/2) +--R +--R +--R (166) +--R +-------------+ +--R | 2 +--R +-+ cot(x)\|b tan(x) + a +--R (- 2b + 3a)\|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R +-------+ +-------------+ +--R +-------+ tan(x)\|- b + a | 2 +--R (- 2b + 2a)\|- b + a atan(----------------) + b tan(x)\|b tan(x) + a +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 510 +a0235:= integrate(t0235,x) +--R +--R +--R (167) +--R [ +--R 3 2 2 3 5 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 3 +--R (8b - 20a b + 16a b - 4a )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R sin(x) |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (16b - 40a b + 32a b - 8a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 8b + 16a b - 9a b + a )cos(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R log +--R 2 3 2 +--R ((128b - 128a b)cos(x) + (- 128b + 64a b)cos(x))sin(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 4 +--R (128b - 256a b + 128a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 256b + 384a b - 128a b)cos(x) + 128b - 128a b + 16a b +--R / +--R b - a +--R + +--R 2 2 5 2 2 3 +--R ((16b - 40a b + 24a )cos(x) + (- 16b + 32a b - 12a )cos(x) ) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ +-+ |(- b + a)cos(x) + b +--R sin(x)\|b - a \|b |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (16b - 56a b + 64a b - 24a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 32b + 96a b - 88a b + 24a )cos(x) +--R + +--R 3 2 2 3 2 +--R (16b - 40a b + 26a b - 3a )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R log +--R 3 2 2 3 7 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 5 +--R (- 320b + 800a b - 640a b + 160a )cos(x) +--R + +--R 3 2 2 3 3 +--R (256b - 512a b + 304a b - 48a )cos(x) +--R + +--R 3 2 2 3 +--R (- 64b + 96a b - 36a b + 2a )cos(x) +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 2 2 3 9 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 7 +--R (384b - 960a b + 768a b - 192a )cos(x) +--R + +--R 3 2 2 3 5 +--R (- 448b + 896a b - 528a b + 80a )cos(x) +--R + +--R 3 2 2 3 3 +--R (256b - 384a b + 144a b - 8a )cos(x) +--R + +--R 3 2 2 +--R (- 64b + 64a b - 12a b)cos(x) +--R * +--R +-----+ +--R sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 8 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (- 448b + 1120a b - 896a b + 224a )cos(x) +--R + +--R 3 2 2 3 4 +--R (576b - 1152a b + 688a b - 112a )cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 320b + 480a b - 188a b + 14a )cos(x) + 64b - 64a b +--R + +--R 2 +--R 12a b +--R * +--R +-----+ +-+ +--R \|b - a \|b +--R + +--R 4 3 2 2 3 4 10 +--R (- 128b + 512a b - 768a b + 512a b - 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (512b - 1792a b + 2304a b - 1280a b + 256a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 832b + 2496a b - 2656a b + 1152a b - 160a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (704b - 1760a b + 1472a b - 448a b + 32a )cos(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (- 320b + 640a b - 388a b + 68a b - a )cos(x) + 64b +--R + +--R 3 2 2 3 +--R - 96a b + 36a b - 2a b +--R / +--R 3 2 2 3 9 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 7 +--R (- 384b + 960a b - 768a b + 192a )cos(x) +--R + +--R 3 2 2 3 5 +--R (384b - 768a b + 464a b - 80a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 128b + 192a b - 80a b + 8a )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R sin(x)\|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4 3 2 2 3 4 10 +--R (128b - 512a b + 768a b - 512a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 512b + 1792a b - 2304a b + 1280a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (768b - 2304a b + 2464a b - 1088a b + 160a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 512b + 1280a b - 1088a b + 352a b - 32a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (128b - 256a b + 160a b - 32a b + a )cos(x) +--R + +--R 3 2 2 3 5 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 8b + 20a b - 16a b + 4a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 3 3 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (16b - 16a b + 2a b)cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R sin(x) |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 16b + 40a b - 32a b + 8a )cos(x) +--R + +--R 3 2 2 3 2 +--R (8b - 16a b + 9a b - a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (32b - 32a b + 6a b)cos(x) +--R + +--R 3 2 +--R - 16b + 8a b +--R * +--R +-----+ +--R \|b - a +--R / +--R 5 3 +-----+ +--R ((32b - 32a)cos(x) + (- 32b + 16a)cos(x) )sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 6 2 2 4 +--R (32b - 64a b + 32a )cos(x) + (- 64b + 96a b - 32a )cos(x) +--R + +--R 2 2 2 +--R (32b - 32a b + 4a )cos(x) +--R , +--R +--R 3 2 2 3 5 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 3 +--R (8b - 20a b + 16a b - 4a )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R sin(x) |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (16b - 40a b + 32a b - 8a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 8b + 16a b - 9a b + a )cos(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R log +--R 2 3 2 +--R ((128b - 128a b)cos(x) + (- 128b + 64a b)cos(x))sin(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 4 +--R (128b - 256a b + 128a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 256b + 384a b - 128a b)cos(x) + 128b - 128a b + 16a b +--R / +--R b - a +--R + +--R 2 2 5 2 2 3 +--R ((32b - 80a b + 48a )cos(x) + (- 32b + 64a b - 24a )cos(x) ) +--R * +--R +--------------------+ +--R | 2 +--R +---+ +-----+ |(- b + a)cos(x) + b +--R sin(x)\|- b \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 112a b + 128a b - 48a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 64b + 192a b - 176a b + 48a )cos(x) +--R + +--R 3 2 2 3 2 +--R (32b - 80a b + 52a b - 6a )cos(x) +--R * +--R +---+ +--R \|- b +--R * +--R +--------------------+ +--R | 2 +--R +---+ |(- b + a)cos(x) + b 2 +---+ +-----+ +--R cos(x)sin(x)\|- b |-------------------- + cos(x) \|- b \|b - a +--R | 2 +--R \| cos(x) +--R atan(-----------------------------------------------------------------) +--R b +--R + +--R 3 2 2 3 5 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 8b + 20a b - 16a b + 4a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 3 3 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (16b - 16a b + 2a b)cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R sin(x) |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 16b + 40a b - 32a b + 8a )cos(x) +--R + +--R 3 2 2 3 2 +--R (8b - 16a b + 9a b - a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (32b - 32a b + 6a b)cos(x) +--R + +--R 3 2 +--R - 16b + 8a b +--R * +--R +-----+ +--R \|b - a +--R / +--R 5 3 +-----+ +--R ((32b - 32a)cos(x) + (- 32b + 16a)cos(x) )sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 6 2 2 4 +--R (32b - 64a b + 32a )cos(x) + (- 64b + 96a b - 32a )cos(x) +--R + +--R 2 2 2 +--R (32b - 32a b + 4a )cos(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 180 + +--S 181 of 510 +m0235a:= a0235.1-r0235 +--R +--R +--R (168) +--R 3 2 2 3 5 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 3 +--R (8b - 20a b + 16a b - 4a )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R sin(x) |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (16b - 40a b + 32a b - 8a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 8b + 16a b - 9a b + a )cos(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R log +--R 2 3 2 +--R ((128b - 128a b)cos(x) + (- 128b + 64a b)cos(x))sin(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 4 +--R (128b - 256a b + 128a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 256b + 384a b - 128a b)cos(x) + 128b - 128a b + 16a b +--R / +--R b - a +--R + +--R 2 2 5 2 2 3 +--R ((16b - 40a b + 24a )cos(x) + (- 16b + 32a b - 12a )cos(x) ) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ +-+ |(- b + a)cos(x) + b +--R sin(x)\|b - a \|b |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (16b - 56a b + 64a b - 24a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 32b + 96a b - 88a b + 24a )cos(x) +--R + +--R 3 2 2 3 2 +--R (16b - 40a b + 26a b - 3a )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R log +--R 3 2 2 3 7 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 5 +--R (- 320b + 800a b - 640a b + 160a )cos(x) +--R + +--R 3 2 2 3 3 +--R (256b - 512a b + 304a b - 48a )cos(x) +--R + +--R 3 2 2 3 +--R (- 64b + 96a b - 36a b + 2a )cos(x) +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 2 2 3 9 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 7 +--R (384b - 960a b + 768a b - 192a )cos(x) +--R + +--R 3 2 2 3 5 +--R (- 448b + 896a b - 528a b + 80a )cos(x) +--R + +--R 3 2 2 3 3 +--R (256b - 384a b + 144a b - 8a )cos(x) +--R + +--R 3 2 2 +--R (- 64b + 64a b - 12a b)cos(x) +--R * +--R +-----+ +--R sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 8 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (- 448b + 1120a b - 896a b + 224a )cos(x) +--R + +--R 3 2 2 3 4 +--R (576b - 1152a b + 688a b - 112a )cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 320b + 480a b - 188a b + 14a )cos(x) + 64b - 64a b +--R + +--R 2 +--R 12a b +--R * +--R +-----+ +-+ +--R \|b - a \|b +--R + +--R 4 3 2 2 3 4 10 +--R (- 128b + 512a b - 768a b + 512a b - 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (512b - 1792a b + 2304a b - 1280a b + 256a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 832b + 2496a b - 2656a b + 1152a b - 160a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (704b - 1760a b + 1472a b - 448a b + 32a )cos(x) +--R + +--R 4 3 2 2 3 4 2 4 +--R (- 320b + 640a b - 388a b + 68a b - a )cos(x) + 64b +--R + +--R 3 2 2 3 +--R - 96a b + 36a b - 2a b +--R / +--R 3 2 2 3 9 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 7 +--R (- 384b + 960a b - 768a b + 192a )cos(x) +--R + +--R 3 2 2 3 5 +--R (384b - 768a b + 464a b - 80a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 128b + 192a b - 80a b + 8a )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R sin(x)\|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 4 3 2 2 3 4 10 +--R (128b - 512a b + 768a b - 512a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 512b + 1792a b - 2304a b + 1280a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (768b - 2304a b + 2464a b - 1088a b + 160a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 512b + 1280a b - 1088a b + 352a b - 32a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (128b - 256a b + 160a b - 32a b + a )cos(x) +--R + +--R 2 2 5 2 2 3 +--R ((32b - 80a b + 48a )cos(x) + (- 32b + 64a b - 24a )cos(x) ) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ +-+ |(- b + a)cos(x) + b +--R sin(x)\|b - a \|b |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 112a b + 128a b - 48a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 64b + 192a b - 176a b + 48a )cos(x) +--R + +--R 3 2 2 3 2 +--R (32b - 80a b + 52a b - 6a )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R +-------------+ +--R | 2 +--R cot(x)\|b tan(x) + a +--R atanh(----------------------) +--R +-+ +--R \|b +--R + +--R 2 2 5 2 2 3 +--R ((32b - 64a b + 32a )cos(x) + (- 32b + 48a b - 16a )cos(x) ) +--R * +--R +--------------------+ +--R | 2 +--R +-------+ +-----+ |(- b + a)cos(x) + b +--R sin(x)\|- b + a \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 96a b + 96a b - 32a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 64b + 160a b - 128a b + 32a )cos(x) +--R + +--R 3 2 2 3 2 +--R (32b - 64a b + 36a b - 4a )cos(x) +--R * +--R +-------+ +--R \|- b + a +--R * +--R +-------+ +--R tan(x)\|- b + a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R + +--R 2 5 2 3 +--R ((- 16b + 16a b)cos(x) + (16b - 8a b)cos(x) )sin(x)tan(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 16b + 32a b - 16a b)cos(x) + (32b - 48a b + 16a b)cos(x) +--R + +--R 3 2 2 2 +--R (- 16b + 16a b - 2a b)cos(x) +--R * +--R tan(x) +--R * +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R + +--R 3 2 2 3 5 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 8b + 20a b - 16a b + 4a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 3 3 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (16b - 16a b + 2a b)cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R sin(x) |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 16b + 40a b - 32a b + 8a )cos(x) +--R + +--R 3 2 2 3 2 +--R (8b - 16a b + 9a b - a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (32b - 32a b + 6a b)cos(x) +--R + +--R 3 2 +--R - 16b + 8a b +--R * +--R +-----+ +--R \|b - a +--R / +--R 5 3 +-----+ +--R ((32b - 32a)cos(x) + (- 32b + 16a)cos(x) )sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 6 2 2 4 +--R (32b - 64a b + 32a )cos(x) + (- 64b + 96a b - 32a )cos(x) +--R + +--R 2 2 2 +--R (32b - 32a b + 4a )cos(x) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 510 +--d0235a:= D(m0235a,x) +--E 182 + +--S 183 of 510 +m0235b:= a0235.2-r0235 +--R +--R +--R (169) +--R 3 2 2 3 5 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 3 +--R (8b - 20a b + 16a b - 4a )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R sin(x) |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (16b - 40a b + 32a b - 8a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 8b + 16a b - 9a b + a )cos(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R log +--R 2 3 2 +--R ((128b - 128a b)cos(x) + (- 128b + 64a b)cos(x))sin(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 4 +--R (128b - 256a b + 128a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 256b + 384a b - 128a b)cos(x) + 128b - 128a b + 16a b +--R / +--R b - a +--R + +--R 2 2 5 2 2 3 +--R ((32b - 80a b + 48a )cos(x) + (- 32b + 64a b - 24a )cos(x) ) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ +-+ |(- b + a)cos(x) + b +--R sin(x)\|b - a \|b |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 112a b + 128a b - 48a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 64b + 192a b - 176a b + 48a )cos(x) +--R + +--R 3 2 2 3 2 +--R (32b - 80a b + 52a b - 6a )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R +-------------+ +--R | 2 +--R cot(x)\|b tan(x) + a +--R atanh(----------------------) +--R +-+ +--R \|b +--R + +--R 2 2 5 2 2 3 +--R ((32b - 80a b + 48a )cos(x) + (- 32b + 64a b - 24a )cos(x) ) +--R * +--R +--------------------+ +--R | 2 +--R +---+ +-----+ |(- b + a)cos(x) + b +--R sin(x)\|- b \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 112a b + 128a b - 48a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 64b + 192a b - 176a b + 48a )cos(x) +--R + +--R 3 2 2 3 2 +--R (32b - 80a b + 52a b - 6a )cos(x) +--R * +--R +---+ +--R \|- b +--R * +--R +--------------------+ +--R | 2 +--R +---+ |(- b + a)cos(x) + b 2 +---+ +-----+ +--R cos(x)sin(x)\|- b |-------------------- + cos(x) \|- b \|b - a +--R | 2 +--R \| cos(x) +--R atan(-----------------------------------------------------------------) +--R b +--R + +--R 2 2 5 2 2 3 +--R ((32b - 64a b + 32a )cos(x) + (- 32b + 48a b - 16a )cos(x) ) +--R * +--R +--------------------+ +--R | 2 +--R +-------+ +-----+ |(- b + a)cos(x) + b +--R sin(x)\|- b + a \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 96a b + 96a b - 32a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 64b + 160a b - 128a b + 32a )cos(x) +--R + +--R 3 2 2 3 2 +--R (32b - 64a b + 36a b - 4a )cos(x) +--R * +--R +-------+ +--R \|- b + a +--R * +--R +-------+ +--R tan(x)\|- b + a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R + +--R 2 5 2 3 +--R ((- 16b + 16a b)cos(x) + (16b - 8a b)cos(x) )sin(x)tan(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 16b + 32a b - 16a b)cos(x) + (32b - 48a b + 16a b)cos(x) +--R + +--R 3 2 2 2 +--R (- 16b + 16a b - 2a b)cos(x) +--R * +--R tan(x) +--R * +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R + +--R 3 2 2 3 5 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 8b + 20a b - 16a b + 4a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 3 3 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (16b - 16a b + 2a b)cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R sin(x) |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 16b + 40a b - 32a b + 8a )cos(x) +--R + +--R 3 2 2 3 2 +--R (8b - 16a b + 9a b - a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (32b - 32a b + 6a b)cos(x) +--R + +--R 3 2 +--R - 16b + 8a b +--R * +--R +-----+ +--R \|b - a +--R / +--R 5 3 +-----+ +--R ((32b - 32a)cos(x) + (- 32b + 16a)cos(x) )sin(x)\|b - a +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 2 2 6 2 2 4 +--R (32b - 64a b + 32a )cos(x) + (- 64b + 96a b - 32a )cos(x) +--R + +--R 2 2 2 +--R (32b - 32a b + 4a )cos(x) +--R Type: Expression(Integer) +--E 183 + +--S 184 of 510 +d0235b:= D(m0235b,x) +--R +--R +--R (170) +--R 9 8 2 7 3 6 4 5 +--R 768b - 6144a b + 21504a b - 43008a b + 53760a b +--R + +--R 5 4 6 3 7 2 8 +--R - 43008a b + 21504a b - 6144a b + 768a b +--R * +--R 13 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 4096b + 29056a b - 89216a b + 154496a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 164480a b + 109696a b - 44416a b + 9856a b +--R + +--R 8 +--R - 896a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 9728b - 60032a b + 157760a b - 229120a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 199360a b - 105088a b + 32192a b - 5120a b + 320a b +--R * +--R 9 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 13312b + 70272a b - 154240a b + 181344a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 122528a b + 47424a b - 9920a b + 992a b - 32a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 11008b - 49024a b + 88000a b - 81056a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 40352a b - 10528a b + 1312a b - 64a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 5120b + 18944a b - 27264a b + 19136a b +--R + +--R 4 5 5 4 6 3 +--R - 6720a b + 1088a b - 64a b +--R * +--R 3 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 1024b - 3072a b + 3456a b - 1792a b + 416a b +--R + +--R 5 4 +--R - 32a b +--R * +--R cos(x) +--R * +--R 2 6 +--R cot(x) sin(x) +--R + +--R 9 8 2 7 3 6 +--R - 8960b + 71680a b - 250880a b + 501760a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 627200a b + 501760a b - 250880a b + 71680a b +--R + +--R 8 +--R - 8960a b +--R * +--R 15 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 53504b - 387200a b + 1214848a b - 2154112a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 2354560a b - 1618304a b + 679040a b - 157568a b +--R + +--R 8 +--R 15232a b +--R * +--R 13 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 136704b + 884736a b - 2454080a b + 3792768a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 3549120a b + 2040064a b - 693696a b + 124800a b +--R + +--R 8 +--R - 8768a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 193024b - 1102080a b + 2657216a b - 3504288a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 2732704a b - 1268800a b + 333824a b - 43552a b +--R + +--R 8 +--R 1952a b +--R * +--R 9 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 161536b + 800768a b - 1643968a b + 1800640a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 1128804a b + 403128a b - 76560a b + 6472a b +--R + +--R 8 +--R - 140a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 79104b - 334464a b + 570560a b - 501280a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 239804a b - 60598a b + 7162a b - 290a b + 2a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 20480b + 72704a b - 100608a b + 68096a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 23016a b + 3456a b - 153a b + a b +--R * +--R 3 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 2048b - 6144a b + 6912a b - 3584a b + 848a b +--R + +--R 5 4 6 3 +--R - 80a b + 2a b +--R * +--R cos(x) +--R * +--R 2 4 +--R cot(x) sin(x) +--R + +--R 9 8 2 7 3 6 +--R 6400b - 51200a b + 179200a b - 358400a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 448000a b - 358400a b + 179200a b - 51200a b +--R + +--R 8 +--R 6400a b +--R * +--R 17 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 44544b + 328320a b - 1048448a b + 1890432a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 2098560a b + 1462144a b - 620160a b + 144768a b +--R + +--R 8 +--R - 13952a b +--R * +--R 15 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 128768b - 870016a b + 2519104a b - 4062976a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 3965120a b - 2373248a b + 837056a b - 154624a b +--R + +--R 8 +--R 10816a b +--R * +--R 13 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 196608b + 1211136a b - 3157504a b + 4513696a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 3824736a b + 1932352a b - 551872a b + 77088a b +--R + +--R 8 +--R - 3552a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 162560b - 909568a b + 2122624a b - 2666016a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 1935840a b - 808368a b + 180112a b - 17648a b +--R + +--R 8 +--R 464a b +--R * +--R 9 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 58880b + 303232a b - 640000a b + 711200a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 443160a b + 151292a b - 25156a b + 1492a b +--R + +--R 8 +--R - 20a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 7936b + 25472a b - 27456a b + 7328a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 6152a b - 4332a b + 808a b - 36a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 13312b - 46592a b + 62848a b - 40640a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 12608a b - 1560a b + 24a b + a b +--R * +--R 3 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 3072b + 9216a b - 10368a b + 5376a b - 1264a b +--R + +--R 5 4 6 3 +--R 112a b - 2a b +--R * +--R cos(x) +--R * +--R 2 2 +--R cot(x) sin(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 256b + 2048a b - 7168a b + 14336a b - 17920a b +--R + +--R 5 4 6 3 7 2 8 +--R 14336a b - 7168a b + 2048a b - 256a b +--R * +--R 19 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 2304b - 17280a b + 55936a b - 101760a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 113280a b - 78464a b + 32640a b - 7296a b + 640a b +--R * +--R 17 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 8448b + 59136a b - 176448a b + 291456a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 288960a b + 173568a b - 60096a b + 10368a b +--R + +--R 8 +--R - 576a b +--R * +--R 15 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 16640b - 108160a b + 295744a b - 440672a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 386272a b - 199488a b + 56832a b - 7392a b + 224a b +--R * +--R 13 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 19200b + 115200a b - 286336a b + 380800a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 290972a b + 126712a b - 28864a b + 2696a b +--R + +--R 8 +--R - 36a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 13056b - 71808a b + 160512a b - 187584a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 122148a b - 43342a b + 7474a b - 458a b + 2a b +--R * +--R 9 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 4864b + 24320a b - 48192a b + 48384a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 25916a b + 7092a b - 859a b + 35a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 768b - 3456a b + 5952a b - 4960a b + 2076a b +--R + +--R 5 4 6 3 7 2 +--R - 422a b + 42a b - a b +--R * +--R 5 +--R cos(x) +--R + +--R 4 5 5 4 6 3 3 +--R (- 8a b + 8a b - a b )cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R 8 2 7 3 6 4 5 +--R 768a b - 6144a b + 21504a b - 43008a b +--R + +--R 5 4 6 3 7 2 8 9 +--R 53760a b - 43008a b + 21504a b - 6144a b + 768a +--R * +--R 13 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 4096a b + 29056a b - 89216a b + 154496a b +--R + +--R 5 4 6 3 7 2 8 9 +--R - 164480a b + 109696a b - 44416a b + 9856a b - 896a +--R * +--R 11 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 9728a b - 60032a b + 157760a b - 229120a b +--R + +--R 5 4 6 3 7 2 8 9 +--R 199360a b - 105088a b + 32192a b - 5120a b + 320a +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 13312a b + 70272a b - 154240a b + 181344a b +--R + +--R 5 4 6 3 7 2 8 9 +--R - 122528a b + 47424a b - 9920a b + 992a b - 32a +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 11008a b - 49024a b + 88000a b - 81056a b +--R + +--R 5 4 6 3 7 2 8 +--R 40352a b - 10528a b + 1312a b - 64a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 5120a b + 18944a b - 27264a b + 19136a b +--R + +--R 5 4 6 3 7 2 +--R - 6720a b + 1088a b - 64a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 1024a b - 3072a b + 3456a b - 1792a b + 416a b +--R + +--R 6 3 +--R - 32a b +--R * +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 768b + 6144a b - 21504a b + 43008a b - 53760a b +--R + +--R 5 4 6 3 7 2 8 +--R 43008a b - 21504a b + 6144a b - 768a b +--R * +--R 13 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 4096b - 29056a b + 89216a b - 154496a b + 164480a b +--R + +--R 5 4 6 3 7 2 8 +--R - 109696a b + 44416a b - 9856a b + 896a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 9728b + 60032a b - 157760a b + 229120a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 199360a b + 105088a b - 32192a b + 5120a b - 320a b +--R * +--R 9 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 13312b - 70272a b + 154240a b - 181344a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 122528a b - 47424a b + 9920a b - 992a b + 32a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 11008b + 49024a b - 88000a b + 81056a b - 40352a b +--R + +--R 5 4 6 3 7 2 +--R 10528a b - 1312a b + 64a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 5120b - 18944a b + 27264a b - 19136a b + 6720a b +--R + +--R 5 4 6 3 +--R - 1088a b + 64a b +--R * +--R 3 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 1024b + 3072a b - 3456a b + 1792a b - 416a b +--R + +--R 5 4 +--R 32a b +--R * +--R cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 8960a b + 71680a b - 250880a b + 501760a b +--R + +--R 5 4 6 3 7 2 8 +--R - 627200a b + 501760a b - 250880a b + 71680a b +--R + +--R 9 +--R - 8960a +--R * +--R 15 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 53504a b - 387200a b + 1214848a b - 2154112a b +--R + +--R 5 4 6 3 7 2 8 +--R 2354560a b - 1618304a b + 679040a b - 157568a b +--R + +--R 9 +--R 15232a +--R * +--R 13 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 136704a b + 884736a b - 2454080a b + 3792768a b +--R + +--R 5 4 6 3 7 2 8 +--R - 3549120a b + 2040064a b - 693696a b + 124800a b +--R + +--R 9 +--R - 8768a +--R * +--R 11 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 193024a b - 1102080a b + 2657216a b - 3504288a b +--R + +--R 5 4 6 3 7 2 8 +--R 2732704a b - 1268800a b + 333824a b - 43552a b +--R + +--R 9 +--R 1952a +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 161536a b + 800768a b - 1643968a b + 1800640a b +--R + +--R 5 4 6 3 7 2 8 +--R - 1128804a b + 403128a b - 76560a b + 6472a b +--R + +--R 9 +--R - 140a +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 79104a b - 334464a b + 570560a b - 501280a b +--R + +--R 5 4 6 3 7 2 8 9 +--R 239804a b - 60598a b + 7162a b - 290a b + 2a +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 20480a b + 72704a b - 100608a b + 68096a b +--R + +--R 5 4 6 3 7 2 8 +--R - 23016a b + 3456a b - 153a b + a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 2048a b - 6144a b + 6912a b - 3584a b + 848a b +--R + +--R 6 3 7 2 +--R - 80a b + 2a b +--R * +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 8960b - 71680a b + 250880a b - 501760a b + 627200a b +--R + +--R 5 4 6 3 7 2 8 +--R - 501760a b + 250880a b - 71680a b + 8960a b +--R * +--R 15 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 53504b + 387200a b - 1214848a b + 2154112a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 2354560a b + 1618304a b - 679040a b + 157568a b +--R + +--R 8 +--R - 15232a b +--R * +--R 13 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 136704b - 884736a b + 2454080a b - 3792768a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 3549120a b - 2040064a b + 693696a b - 124800a b +--R + +--R 8 +--R 8768a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 193024b + 1102080a b - 2657216a b + 3504288a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 2732704a b + 1268800a b - 333824a b + 43552a b +--R + +--R 8 +--R - 1952a b +--R * +--R 9 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 161536b - 800768a b + 1643968a b - 1800640a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 1128804a b - 403128a b + 76560a b - 6472a b + 140a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 79104b + 334464a b - 570560a b + 501280a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 239804a b + 60598a b - 7162a b + 290a b - 2a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 20480b - 72704a b + 100608a b - 68096a b + 23016a b +--R + +--R 5 4 6 3 7 2 +--R - 3456a b + 153a b - a b +--R * +--R 3 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 2048b + 6144a b - 6912a b + 3584a b - 848a b +--R + +--R 5 4 6 3 +--R 80a b - 2a b +--R * +--R cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 8 2 7 3 6 4 5 +--R 6400a b - 51200a b + 179200a b - 358400a b +--R + +--R 5 4 6 3 7 2 8 +--R 448000a b - 358400a b + 179200a b - 51200a b +--R + +--R 9 +--R 6400a +--R * +--R 17 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 44544a b + 328320a b - 1048448a b + 1890432a b +--R + +--R 5 4 6 3 7 2 8 +--R - 2098560a b + 1462144a b - 620160a b + 144768a b +--R + +--R 9 +--R - 13952a +--R * +--R 15 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 128768a b - 870016a b + 2519104a b - 4062976a b +--R + +--R 5 4 6 3 7 2 8 +--R 3965120a b - 2373248a b + 837056a b - 154624a b +--R + +--R 9 +--R 10816a +--R * +--R 13 +--R cos(x) +--R + +--R 8 2 7 3 6 +--R - 196608a b + 1211136a b - 3157504a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 4513696a b - 3824736a b + 1932352a b - 551872a b +--R + +--R 8 9 +--R 77088a b - 3552a +--R * +--R 11 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 162560a b - 909568a b + 2122624a b - 2666016a b +--R + +--R 5 4 6 3 7 2 8 +--R 1935840a b - 808368a b + 180112a b - 17648a b +--R + +--R 9 +--R 464a +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 58880a b + 303232a b - 640000a b + 711200a b +--R + +--R 5 4 6 3 7 2 8 9 +--R - 443160a b + 151292a b - 25156a b + 1492a b - 20a +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 7936a b + 25472a b - 27456a b + 7328a b +--R + +--R 5 4 6 3 7 2 8 +--R 6152a b - 4332a b + 808a b - 36a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 13312a b - 46592a b + 62848a b - 40640a b +--R + +--R 5 4 6 3 7 2 8 +--R 12608a b - 1560a b + 24a b + a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 3072a b + 9216a b - 10368a b + 5376a b +--R + +--R 5 4 6 3 7 2 +--R - 1264a b + 112a b - 2a b +--R * +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 2 7 3 6 +--R - 6400b + 51200a b - 179200a b + 358400a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 448000a b + 358400a b - 179200a b + 51200a b +--R + +--R 8 +--R - 6400a b +--R * +--R 17 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 44544b - 328320a b + 1048448a b - 1890432a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 2098560a b - 1462144a b + 620160a b - 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2304b + 17280a b - 55936a b + 101760a b - 113280a b +--R + +--R 5 4 6 3 7 2 8 +--R 78464a b - 32640a b + 7296a b - 640a b +--R * +--R 17 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 8448b - 59136a b + 176448a b - 291456a b + 288960a b +--R + +--R 5 4 6 3 7 2 8 +--R - 173568a b + 60096a b - 10368a b + 576a b +--R * +--R 15 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 16640b + 108160a b - 295744a b + 440672a b - 386272a b +--R + +--R 5 4 6 3 7 2 8 +--R 199488a b - 56832a b + 7392a b - 224a b +--R * +--R 13 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 19200b - 115200a b + 286336a b - 380800a b + 290972a b +--R + +--R 5 4 6 3 7 2 8 +--R - 126712a b + 28864a b - 2696a b + 36a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 13056b + 71808a b - 160512a b + 187584a b - 122148a b +--R + +--R 5 4 6 3 7 2 8 +--R 43342a b - 7474a b + 458a b - 2a b +--R * +--R 9 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 4864b - 24320a b + 48192a b - 48384a b + 25916a b +--R + +--R 5 4 6 3 7 2 +--R - 7092a b + 859a b - 35a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 768b + 3456a b - 5952a b + 4960a b - 2076a b + 422a b +--R + +--R 6 3 7 2 +--R - 42a b + a b +--R * +--R 5 +--R cos(x) +--R + +--R 4 5 5 4 6 3 3 +--R (8a b - 8a b + a b )cos(x) +--R * +--R +--------------------+ +--R | 2 +--R |(- b + a)cos(x) + b +--R |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 9 8 2 7 3 6 +--R 4096b - 32768a b + 114688a b - 229376a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 286720a b - 229376a b + 114688a b - 32768a b +--R + +--R 8 +--R 4096a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 25088b + 179456a b - 555776a b + 971008a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 1043200a b + 702208a b - 286976a b + 64256a b +--R + +--R 8 +--R - 5888a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 67584b - 425728a b + 1145024a b - 1707392a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 1531200a b - 835584a b + 266048a b - 43904a b +--R + +--R 8 +--R 2752a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 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1087488a b + 375232a b - 66176a b +--R + +--R 8 +--R 4160a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 109056b + 683008a b - 1801536a b + 2590656a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 2192000a b + 1094016a b - 303168a b + 39616a b +--R + +--R 8 +--R - 1536a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 116736b - 668160a b + 1582464a b - 1999488a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 1444784a b - 591352a b + 126024a b - 11240a b +--R + +--R 8 +--R 232a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 66048b + 347904a b - 739456a b + 813952a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 492624a b + 159176a b - 24108a b + 1216a b +--R + +--R 8 +--R - 12a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 9216b - 53504a b + 112960a b - 114432a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 58936a b - 14512a b + 1358a b - 22a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 10752b - 35328a b + 44992a b - 27840a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 8528a b - 1108a b + 22a b - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 6144b + 18432a b - 20736a b + 10752a b +--R + +--R 4 5 5 4 +--R - 2488a b + 188a b +--R * +--R 2 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 1024b - 2560a b + 2304a b - 896a b + 144a b - 8a b +--R * +--R 2 +--R cot(x) sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 8 2 7 3 6 4 5 +--R 4096a b - 32768a b + 114688a b - 229376a b +--R + +--R 5 4 6 3 7 2 8 +--R 286720a b - 229376a b + 114688a b - 32768a b +--R + +--R 9 +--R 4096a +--R * +--R 14 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 25088a b + 179456a b - 555776a b + 971008a b +--R + +--R 5 4 6 3 7 2 8 +--R - 1043200a b + 702208a b - 286976a b + 64256a b +--R + +--R 9 +--R - 5888a +--R * +--R 12 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 67584a b - 425728a b + 1145024a b - 1707392a b +--R + +--R 5 4 6 3 7 2 8 +--R 1531200a b - 835584a b + 266048a b - 43904a b +--R + +--R 9 +--R 2752a +--R * +--R 10 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 104448a b + 569600a b - 1301184a b + 1608448a b +--R + +--R 5 4 6 3 7 2 8 +--R - 1158720a b + 487168a b - 112960a b + 12544a b +--R + +--R 9 +--R - 448a +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 100352a b - 465152a b + 879936a b - 870336a b +--R + +--R 5 4 6 3 7 2 8 9 +--R 478968a b - 144376a b + 21976a b - 1384a b + 16a +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 59904a b + 231424a b - 352576a b + 267712a b +--R + +--R 5 4 6 3 7 2 8 +--R - 105472a b + 20444a b - 1656a b + 28a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 20480a b - 64512a b + 76800a b - 42752a b +--R + +--R 5 4 6 3 7 2 +--R 11112a b - 1156a b + 28a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 3072a b + 7680a b - 6912a b + 2688a b - 416a b +--R + +--R 6 3 +--R 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 2 7 3 6 +--R - 4096b + 32768a b - 114688a b + 229376a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 286720a b + 229376a b - 114688a b + 32768a b +--R + +--R 8 +--R - 4096a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 25088b - 179456a b + 555776a b - 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28a b +--R * +--R 2 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 3072b - 7680a b + 6912a b - 2688a b + 416a b - 16a b +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 10240a b + 81920a b - 286720a b + 573440a b +--R + +--R 5 4 6 3 7 2 8 +--R - 716800a b + 573440a b - 286720a b + 81920a b +--R + +--R 9 +--R - 10240a +--R * +--R 16 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 70656a b - 514560a b + 1623552a b - 2892288a b +--R + +--R 5 4 6 3 7 2 8 +--R 3171840a b - 2182656a b + 913920a b - 210432a b +--R + +--R 9 +--R 19968a +--R * +--R 14 +--R cos(x) +--R + +--R 8 2 7 3 6 +--R - 207872a b + 1366016a b - 3844352a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 6020608a b - 5697280a b + 3300352a b - 1124096a b +--R + +--R 8 9 +--R 200192a b - 13568a +--R * +--R 12 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R 335872a b - 1970176a b + 4881024a b - 6611776a b +--R + +--R 5 4 6 3 7 2 8 +--R 5288640a b - 2509952a b + 669696a b - 87104a b +--R + +--R 9 +--R 3776a +--R * +--R 10 +--R cos(x) +--R + +--R 8 2 7 3 6 +--R - 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1582464a b + 1999488a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 1444784a b + 591352a b - 126024a b + 11240a b +--R + +--R 8 +--R - 232a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 66048b - 347904a b + 739456a b - 813952a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 492624a b - 159176a b + 24108a b - 1216a b + 12a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 9216b + 53504a b - 112960a b + 114432a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 58936a b + 14512a b - 1358a b + 22a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 10752b + 35328a b - 44992a b + 27840a b - 8528a b +--R + +--R 5 4 6 3 7 2 +--R 1108a b - 22a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 6144b - 18432a b + 20736a b - 10752a b + 2488a b +--R + +--R 5 4 +--R - 188a b +--R * +--R 2 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 1024b + 2560a b - 2304a b + 896a b - 144a b + 8a b +--R * +--R sin(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R + +--R 9 8 2 7 3 6 4 5 +--R - 1024b + 6144a b - 15360a b + 20480a b - 15360a b +--R + +--R 5 4 6 3 +--R 6144a b - 1024a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 5120b - 27136a b + 58880a b - 66560a b + 40960a b +--R + +--R 5 4 6 3 +--R - 12800a b + 1536a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 10240b + 47104a b - 86784a b + 80896a b - 39424a b +--R + +--R 5 4 6 3 +--R 9216a b - 768a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 10240b - 39936a b + 60672a b - 44928a b + 16512a b +--R + +--R 5 4 6 3 +--R - 2688a b + 128a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 5120b + 16384a b - 19712a b + 11008a b - 2816a b +--R + +--R 5 4 +--R 256a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (1024b - 2560a b + 2304a b - 896a b + 128a b )cos(x) +--R * +--R 2 5 +--R cot(x) sin(x) +--R + +--R 9 8 2 7 3 6 +--R 10240b - 61440a b + 153600a b - 204800a b +--R + +--R 4 5 5 4 6 3 +--R 153600a b - 61440a b + 10240a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 53248b + 287744a b - 640000a b + 747520a b +--R + +--R 4 5 5 4 6 3 +--R - 481280a b + 160768a b - 21504a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 112640b - 541696a b + 1056512a b - 1061888a b +--R + +--R 4 5 5 4 6 3 +--R 573952a b - 155648a b + 16128a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 122880b + 518144a b - 870144a b + 735488a b +--R + +--R 4 5 5 4 6 3 +--R - 323840a b + 68352a b - 5120a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 71680b - 260096a b + 367360a b - 253184a b +--R + +--R 4 5 5 4 6 3 +--R 86896a b - 13280a b + 624a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 20480b + 62464a b - 71936a b + 38656a b - 9632a b +--R + +--R 5 4 6 3 +--R 952a b - 24a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 2048b - 5120a b + 4608a b - 1792a b + 304a b +--R + +--R 5 4 +--R - 24a b +--R * +--R 4 +--R cos(x) +--R * +--R 2 3 +--R cot(x) sin(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 5120b + 30720a b - 76800a b + 102400a b - 76800a b +--R + +--R 5 4 6 3 +--R 30720a b - 5120a b +--R * +--R 18 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 27648b - 152064a b + 345600a b - 414720a b +--R + +--R 4 5 5 4 6 3 +--R 276480a b - 96768a b + 13824a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 58368b + 291840a b - 597504a b + 638976a b +--R + +--R 4 5 5 4 6 3 +--R - 374784a b + 113664a b - 13824a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 56320b - 253440a b + 463104a b - 438144a b +--R + +--R 4 5 5 4 6 3 +--R 225408a b - 59520a b + 6272a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 15360b + 61440a b - 101376a b + 89088a b +--R + +--R 4 5 5 4 6 3 +--R - 44304a b + 11808a b - 1296a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 15360b + 53760a b - 70656a b + 42240a b - 10512a b +--R + +--R 5 4 6 3 +--R 408a b + 120a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 13312b - 39936a b + 44544a b - 22528a b + 4944a b +--R + +--R 5 4 6 3 +--R - 336a b - 4a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 3072b + 7680a b - 6912a b + 2688a b - 432a b +--R + +--R 5 4 +--R 24a b +--R * +--R 4 +--R cos(x) +--R * +--R 2 +--R cot(x) sin(x) +--R * +--R 6 +--R tan(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 1024b + 4608a b - 6144a b - 2560a b + 15360a b +--R + +--R 5 4 6 3 7 2 +--R - 16896a b + 8192a b - 1536a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 5120b - 19456a b + 18176a b + 21760a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 58880a b + 48640a b - 17664a b + 2304a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 10240b + 31744a b - 16128a b - 49280a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 81920a b - 49920a b + 13056a b - 1152a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 10240b - 24576a b + 768a b + 46080a b - 50880a b +--R + +--R 5 4 6 3 7 2 +--R 22080a b - 3904a b + 192a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 5120b + 8704a b + 4864a b - 18560a b +--R + +--R 4 5 5 4 6 3 +--R 13696a b - 3968a b + 384a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 1024b - 1024a b - 1536a b + 2560a b - 1216a b +--R + +--R 5 4 +--R 192a b +--R * +--R 4 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 1024b - 6144a b + 15360a b - 20480a b + 15360a b +--R + +--R 5 4 6 3 +--R - 6144a b + 1024a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 5120b + 27136a b - 58880a b + 66560a b - 40960a b +--R + +--R 5 4 6 3 +--R 12800a b - 1536a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 10240b - 47104a b + 86784a b - 80896a b + 39424a b +--R + +--R 5 4 6 3 +--R - 9216a b + 768a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 10240b + 39936a b - 60672a b + 44928a b - 16512a b +--R + +--R 5 4 6 3 +--R 2688a b - 128a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 5120b - 16384a b + 19712a b - 11008a b + 2816a b +--R + +--R 5 4 +--R - 256a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 1024b + 2560a b - 2304a b + 896a b - 128a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 9 8 2 7 3 6 +--R 10240b - 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933120a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 898560a b - 511488a b + 158976a b - 20736a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 58368b + 379392a b - 1035264a b + 1535232a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 1333248a b + 675840a b - 184320a b + 20736a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R 56320b - 337920a b + 843264a b - 1132800a b +--R + +--R 4 5 5 4 6 3 7 2 +--R 882624a b - 397632a b + 95552a b - 9408a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 15360b + 84480a b - 193536a b + 241152a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 177936a b + 78264a b - 19008a b + 1944a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 15360b + 76800a b - 151296a b + 148224a b +--R + +--R 4 5 5 4 6 3 7 2 +--R - 73872a b + 16176a b - 492a b - 180a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 13312b - 59904a b + 104448a b - 89344a b + 38736a b +--R + +--R 5 4 6 3 7 2 +--R - 7752a b + 500a b + 6a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 3072b + 12288a b - 18432a b + 13056a b - 4464a b +--R + +--R 5 4 6 3 +--R 672a b - 36a b +--R * +--R 4 +--R cos(x) +--R * +--R cot(x)sin(x) +--R * +--R tan(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 1024a b + 6144a b - 15360a b + 20480a b - 15360a b +--R + +--R 8 9 +--R 6144a b - 1024a +--R * +--R 14 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 5120a b - 27136a b + 58880a b - 66560a b + 40960a b +--R + +--R 8 9 +--R - 12800a b + 1536a +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 10240a b + 47104a b - 86784a b + 80896a b +--R + +--R 7 2 8 9 +--R - 39424a b + 9216a b - 768a +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 10240a b - 39936a b + 60672a b - 44928a b + 16512a b +--R + +--R 8 9 +--R - 2688a b + 128a +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 5120a b + 16384a b - 19712a b + 11008a b - 2816a b +--R + +--R 8 +--R 256a b +--R * +--R 6 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 4 +--R (1024a b - 2560a b + 2304a b - 896a b + 128a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 1024b - 6656a b + 17920a b - 25088a b + 17920a b +--R + +--R 5 4 6 3 7 2 8 +--R - 3584a b - 3584a b + 2560a b - 512a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 5120b + 29696a b - 69888a b + 82432a b - 44800a b +--R + +--R 6 3 7 2 8 +--R 12544a b - 5632a b + 768a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 10240b - 52224a b + 105216a b - 100736a b + 36480a b +--R + +--R 5 4 6 3 7 2 8 +--R 11520a b - 14336a b + 4224a b - 384a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 10240b + 45056a b - 75520a b + 55296a b - 8640a b +--R + +--R 5 4 6 3 7 2 8 +--R - 11520a b + 6784a b - 1280a b + 64a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 5120b - 18944a b + 25344a b - 12672a b - 1536a b +--R + +--R 5 4 6 3 7 2 +--R 3840a b - 1280a b + 128a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 1024b + 3072a b - 3072a b + 768a b + 576a b - 384a b +--R + +--R 6 3 +--R 64a b +--R * +--R 4 +--R cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R 10240a b - 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24a b +--R * +--R 4 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 10240b + 66560a b - 179200a b + 250880a b - 179200a b +--R + +--R 5 4 6 3 7 2 8 +--R 35840a b + 35840a b - 25600a b + 5120a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 53248b - 314368a b + 757248a b - 923648a b + 535040a b +--R + +--R 5 4 6 3 7 2 8 +--R - 27648a b - 138752a b + 69632a b - 10752a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 +--R - 112640b + 598016a b - 1271040a b + 1319296a b +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 576640a b - 88320a b + 193024a b - 69760a b + 8064a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 122880b - 579584a b + 1067776a b - 911488a b + 256512a b +--R + +--R 5 4 6 3 7 2 8 +--R 137472a b - 122624a b + 31616a b - 2560a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 71680b + 295936a b - 461568a b + 306816a b - 29808a b +--R + +--R 5 4 6 3 7 2 8 +--R - 69864a b + 36184a b - 6328a b + 312a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 20480b - 72704a b + 92928a b - 43392a b - 7008a b +--R + +--R 5 4 6 3 7 2 8 +--R 13560a b - 4316a b + 464a b - 12a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 2048b + 6144a b - 6144a b + 1536a b + 1104a b +--R + +--R 5 4 6 3 7 2 +--R - 720a b + 140a b - 12a b +--R * +--R 4 +--R cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 5120a b + 30720a b - 76800a b + 102400a b +--R + +--R 7 2 8 9 +--R - 76800a b + 30720a b - 5120a +--R * +--R 18 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R 27648a b - 152064a b + 345600a b - 414720a b +--R + +--R 7 2 8 9 +--R 276480a b - 96768a b + 13824a +--R * +--R 16 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 58368a b + 291840a b - 597504a b + 638976a b +--R + +--R 7 2 8 9 +--R - 374784a b + 113664a b - 13824a +--R * +--R 14 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R 56320a b - 253440a b + 463104a b - 438144a b +--R + +--R 7 2 8 9 +--R 225408a b - 59520a b + 6272a +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 15360a b + 61440a b - 101376a b + 89088a b +--R + +--R 7 2 8 9 +--R - 44304a b + 11808a b - 1296a +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 15360a b + 53760a b - 70656a b + 42240a b +--R + +--R 7 2 8 9 +--R - 10512a b + 408a b + 120a +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 13312a b - 39936a b + 44544a b - 22528a b + 4944a b +--R + +--R 8 9 +--R - 336a b - 4a +--R * +--R 6 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 3072a b + 7680a b - 6912a b + 2688a b - 432a b +--R + +--R 8 +--R 24a b +--R * +--R 4 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 5120b - 33280a b + 89600a b - 125440a b + 89600a b +--R + +--R 5 4 6 3 7 2 8 +--R - 17920a b - 17920a b + 12800a b - 2560a b +--R * +--R 18 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 27648b + 165888a b - 407808a b + 511488a b - 311040a b +--R + +--R 5 4 6 3 7 2 8 +--R 27648a b + 76032a b - 41472a b + 6912a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 58368b - 321024a b + 714240a b - 791808a b + 395520a b +--R + +--R 5 4 6 3 7 2 8 +--R 18432a b - 116736a b + 49920a b - 6912a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 56320b + 281600a b - 561664a b + 542976a b - 212928a b +--R + +--R 5 4 6 3 7 2 8 +--R - 46848a b + 76672a b - 26624a b + 3136a b +--R * +--R 12 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 15360b - 69120a b + 124416a b - 109056a b + 38160a b +--R + +--R 5 4 6 3 7 2 8 +--R 10584a b - 14952a b + 5256a b - 648a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 15360b - 61440a b + 89856a b - 50688a b - 3696a b +--R + +--R 5 4 6 3 7 2 8 +--R 15456a b - 5172a b + 264a b + 60a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 13312b + 46592a b - 57856a b + 24832a b + 6064a b +--R + +--R 5 4 6 3 7 2 8 +--R - 8456a b + 2308a b - 170a b - 2a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 3072b - 9216a b + 9216a b - 2304a b - 1680a b + 1104a b +--R + +--R 6 3 7 2 +--R - 204a b + 12a b +--R * +--R 4 +--R cos(x) +--R * +--R sin(x) +--R * +--R +--------------------+ +--R | 2 +--R +-----+ |(- b + a)cos(x) + b +--R \|b - a |-------------------- +--R | 2 +--R \| cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 5120b + 35840a b - 107520a b + 179200a b - 179200a b +--R + +--R 5 5 6 4 7 3 +--R 107520a b - 35840a b + 5120a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 28672b - 181248a b + 485376a b - 711680a b + 614400a b +--R + +--R 5 5 6 4 7 3 +--R - 310272a b + 83968a b - 9216a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 66560b + 375808a b - 886400a b + 1124480a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 820480a b + 339200a b - 71808a b + 5760a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 81920b - 407552a b + 832512a b - 894336a b + 536064a b +--R + +--R 5 5 6 4 7 3 +--R - 174336a b + 27136a b - 1408a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 56320b + 242688a b - 420096a b + 371328a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 175584a b + 42144a b - 4256a b + 96a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 20480b - 74752a b + 106496a b - 74368a b + 26048a b +--R + +--R 5 5 6 4 +--R - 4096a b + 192a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 3072b + 9216a b - 10368a b + 5376a b - 1248a b +--R + +--R 5 5 +--R 96a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 4 +--R cot(x) sin(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 10240b - 71680a b + 215040a b - 358400a b + 358400a b +--R + +--R 5 5 6 4 7 3 +--R - 215040a b + 71680a b - 10240a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 59392b + 380928a b - 1038336a b + 1556480a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 1382400a b + 724992a b - 206848a b + 24576a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 141312b - 823296a b + 2018304a b - 2688000a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 2088960a b - 940032a b + 224256a b - 21504a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 174080b + 911360a b - 1983744a b + 2311296a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 1542144a b + 581376a b - 112384a b + 8320a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 112640b - 522240a b + 992256a b - 991104a b + 553968a b +--R + +--R 5 5 6 4 7 3 +--R - 169680a b + 25552a b - 1392a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 30720b + 122880a b - 198144a b + 164736a b - 74928a b +--R + +--R 5 5 6 4 7 3 +--R 18240a b - 2160a b + 96a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 2048b + 8192a b - 12288a b + 8576a b - 2672a b +--R + +--R 5 5 6 4 7 3 +--R 192a b + 50a b - 2a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 2048b - 6144a b + 6912a b - 3584a b + 816a b - 48a b +--R + +--R 6 4 +--R - 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 2 +--R cot(x) sin(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 1024b + 7168a b - 21504a b + 35840a b - 35840a b +--R + +--R 5 5 6 4 7 3 +--R 21504a b - 7168a b + 1024a b +--R * +--R 19 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 6144b - 39936a b + 110592a b - 168960a b + 153600a b +--R + +--R 5 5 6 4 7 3 +--R - 82944a b + 24576a b - 3072a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 14336b + 86016a b - 218496a b + 304000a b - 249600a b +--R + +--R 5 5 6 4 7 3 +--R 120576a b - 31616a b + 3456a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 78848a b + 182784a b - 231168a b + 172032a b +--R + +--R 5 5 6 4 7 3 +--R - 75264a b + 17920a b - 1792a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 1920a b + 7680a b - 11952a b + 8976a b - 3216a b +--R + +--R 7 3 +--R 432a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 14336b + 64512a b - 116736a b + 107520a b - 52128a b +--R + +--R 5 5 6 4 7 3 +--R 12048a b - 832a b - 48a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 57344a b + 91008a b - 72320a b + 29696a b +--R + +--R 5 5 6 4 7 3 +--R - 5760a b + 382a b + 2a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 6144b + 21504a b - 29184a b + 19200a b - 6240a b +--R + +--R 5 5 6 4 +--R 912a b - 48a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 1024b - 3072a b + 3456a b - 1792a b + 432a b - 48a b +--R + +--R 6 4 +--R 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R 6 +--R tan(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 5120b + 28160a b - 53760a b + 17920a b + 89600a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 161280a b + 125440a b - 48640a b + 7680a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 28672b - 138240a b + 213504a b + 16384a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 453120a b + 611328a b - 381440a b + 116736a b +--R + +--R 8 2 +--R - 13824a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 66560b + 275968a b - 322688a b - 205120a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 866240a b - 891520a b + 436992a b - 101952a b +--R + +--R 8 2 +--R 8640a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 81920b - 284672a b + 221184a b + 354432a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 805440a b + 629760a b - 234368a b + 39296a b +--R + +--R 8 2 +--R - 2112a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 56320b + 158208a b - 56064a b - 258816a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 381408a b - 221232a b + 58960a b - 6288a b + 144a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 20480b - 44032a b - 5632a b + 85376a b - 85504a b +--R + +--R 5 5 6 4 7 3 +--R 34976a b - 5952a b + 288a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 3072b + 4608a b + 3456a b - 10176a b + 6816a b +--R + +--R 5 5 6 4 +--R - 1776a b + 144a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 5120b - 35840a b + 107520a b - 179200a b + 179200a b +--R + +--R 5 5 6 4 7 3 +--R - 107520a b + 35840a b - 5120a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 28672b + 181248a b - 485376a b + 711680a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 614400a b + 310272a b - 83968a b + 9216a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 66560b - 375808a b + 886400a b - 1124480a b + 820480a b +--R + +--R 5 5 6 4 7 3 +--R - 339200a b + 71808a b - 5760a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 81920b + 407552a b - 832512a b + 894336a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 536064a b + 174336a b - 27136a b + 1408a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 56320b - 242688a b + 420096a b - 371328a b + 175584a b +--R + +--R 5 5 6 4 7 3 +--R - 42144a b + 4256a b - 96a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 20480b + 74752a b - 106496a b + 74368a b - 26048a b +--R + +--R 5 5 6 4 +--R 4096a b - 192a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R (3072b - 9216a b + 10368a b - 5376a b + 1248a b - 96a b ) +--R * +--R 3 +--R cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 10 9 2 8 3 7 +--R 10240b - 56320a b + 107520a b - 35840a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 179200a b + 322560a b - 250880a b + 97280a b +--R + +--R 8 2 +--R - 15360a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 59392b + 291840a b - 466944a b - 1024a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 952320a b - 1348608a b + 880640a b - 285696a b +--R + +--R 8 2 +--R 36864a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 141312b - 611328a b + 783360a b + 339456a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 1943040a b + 2193408a b - 1185792a b + 314880a b +--R + +--R 8 2 +--R - 32256a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 174080b + 650240a b - 616704a b - 664320a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 1924800a b - 1731840a b + 759680a b - 160256a b +--R + +--R 8 2 +--R 12480a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 112640b - 353280a b + 208896a b + 497280a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 932688a b + 661272a b - 228968a b + 36936a b +--R + +--R 8 2 +--R - 2088a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 30720b + 76800a b - 13824a b - 132480a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 172176a b - 94152a b + 25200a b - 3144a b + 144a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 3 7 4 6 5 5 +--R - 2048b + 5120a b - 9856a b + 10192a b - 3816a b +--R + +--R 6 4 7 3 8 2 +--R 338a b + 73a b - 3a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 2048b - 3072a b - 2304a b + 6784a b - 4560a b +--R + +--R 5 5 6 4 7 3 +--R 1176a b - 74a b - 3a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 10240b + 71680a b - 215040a b + 358400a b - 358400a b +--R + +--R 5 5 6 4 7 3 +--R 215040a b - 71680a b + 10240a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 59392b - 380928a b + 1038336a b - 1556480a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 1382400a b - 724992a b + 206848a b - 24576a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 141312b + 823296a b - 2018304a b + 2688000a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 2088960a b + 940032a b - 224256a b + 21504a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 174080b - 911360a b + 1983744a b - 2311296a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 1542144a b - 581376a b + 112384a b - 8320a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 112640b + 522240a b - 992256a b + 991104a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 553968a b + 169680a b - 25552a b + 1392a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 30720b - 122880a b + 198144a b - 164736a b + 74928a b +--R + +--R 5 5 6 4 7 3 +--R - 18240a b + 2160a b - 96a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 2048b - 8192a b + 12288a b - 8576a b + 2672a b +--R + +--R 5 5 6 4 7 3 +--R - 192a b - 50a b + 2a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R - 2048b + 6144a b - 6912a b + 3584a b - 816a b + 48a b +--R + +--R 6 4 +--R 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 1024b + 5632a b - 10752a b + 3584a b + 17920a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 32256a b + 25088a b - 9728a b + 1536a b +--R * +--R 19 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 6144b - 30720a b + 50688a b - 3072a b - 99840a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 147456a b - 99840a b + 33792a b - 4608a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 14336b + 64512a b - 89472a b - 23744a b + 206400a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 253824a b + 149248a b - 43968a b + 5184a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 57344a b + 64512a b + 43008a b - 174720a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 182784a b - 94976a b + 25088a b - 2688a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 1920a b + 4800a b - 432a b - 8952a b + 10248a b +--R + +--R 7 3 8 2 +--R - 4392a b + 648a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 14336b + 43008a b - 19968a b - 67584a b + 109152a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 66144a b + 17240a b - 1296a b - 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 35840a b + 4992a b + 64192a b - 78784a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 38784a b - 8258a b + 575a b + 3a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 6144b + 12288a b + 3072a b - 24576a b + 22560a b +--R + +--R 5 5 6 4 7 3 +--R - 8448a b + 1320a b - 72a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 1024b - 1536a b - 1152a b + 3392a b - 2256a b + 600a b +--R + +--R 6 4 7 3 +--R - 70a b + 3a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 1024b - 7168a b + 21504a b - 35840a b + 35840a b +--R + +--R 5 5 6 4 7 3 +--R - 21504a b + 7168a b - 1024a b +--R * +--R 19 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 6144b + 39936a b - 110592a b + 168960a b - 153600a b +--R + +--R 5 5 6 4 7 3 +--R 82944a b - 24576a b + 3072a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 86016a b + 218496a b - 304000a b + 249600a b +--R + +--R 5 5 6 4 7 3 +--R - 120576a b + 31616a b - 3456a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 14336b + 78848a b - 182784a b + 231168a b - 172032a b +--R + +--R 5 5 6 4 7 3 +--R 75264a b - 17920a b + 1792a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (1920a b - 7680a b + 11952a b - 8976a b + 3216a b - 432a b ) +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 64512a b + 116736a b - 107520a b + 52128a b +--R + +--R 5 5 6 4 7 3 +--R - 12048a b + 832a b + 48a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 14336b + 57344a b - 91008a b + 72320a b - 29696a b +--R + +--R 5 5 6 4 7 3 +--R 5760a b - 382a b - 2a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 6144b - 21504a b + 29184a b - 19200a b + 6240a b - 912a b +--R + +--R 6 4 +--R 48a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R - 1024b + 3072a b - 3456a b + 1792a b - 432a b + 48a b +--R + +--R 6 4 +--R - 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 5120b + 43520a b - 161280a b + 340480a b - 448000a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 376320a b - 197120a b + 58880a b - 7680a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 28672b - 224256a b + 757248a b - 1439744a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 1681920a b - 1231872a b + 549376a b - 135168a b + 13824a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 66560b + 475648a b - 1450112a b + 2454080a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 2507200a b + 1569920a b - 580608a b + 113472a b +--R + +--R 8 2 +--R - 8640a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 81920b - 530432a b + 1443840a b - 2143104a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 1877568a b - 978432a b + 288640a b - 42112a b + 2112a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 56320b + 327168a b - 784128a b + 1001472a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 732576a b + 305520a b - 67472a b + 6480a b - 144a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 20480b - 105472a b + 218624a b - 234112a b + 137600a b +--R + +--R 5 5 6 4 7 3 +--R - 43168a b + 6336a b - 288a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 3072b + 13824a b - 24192a b + 20928a b - 9312a b +--R + +--R 5 5 6 4 +--R 1968a b - 144a b +--R * +--R 3 +--R cos(x) +--R * +--R 4 +--R cot(x)sin(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 10240b - 87040a b + 322560a b - 680960a b + 896000a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 752640a b + 394240a b - 117760a b + 15360a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 59392b + 470016a b - 1609728a b + 3113984a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 3717120a b + 2798592a b - 1294336a b + 334848a b +--R + +--R 8 2 +--R - 36864a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 141312b - 1035264a b + 3253248a b - 5715456a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 6120960a b - 4073472a b + 1634304a b - 357888a b +--R + +--R 8 2 +--R 32256a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 174080b + 1172480a b - 3350784a b + 5286912a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 5009088a b + 2894592a b - 984448a b + 176896a b +--R + +--R 8 2 +--R - 12480a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 112640b - 691200a b + 1775616a b - 2479488a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 2040624a b - 1000632a b + 280072a b - 39720a b + 2088a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 30720b + 168960a b - 382464a b + 461952a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 322032a b + 130632a b - 29520a b + 3336a b - 144a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 2048b + 11264a b - 24576a b + 27008a b - 15536a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 4200a b - 238a b - 77a b + 3a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 2048b - 9216a b + 16128a b - 13952a b + 6192a b +--R + +--R 5 5 6 4 7 3 +--R - 1272a b + 70a b + 3a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 1024b + 8704a b - 32256a b + 68096a b - 89600a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 75264a b - 39424a b + 11776a b - 1536a b +--R * +--R 19 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 6144b - 49152a b + 170496a b - 334848a b + 407040a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 313344a b + 148992a b - 39936a b + 4608a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 14336b + 107520a b - 347520a b + 631744a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 705600a b + 494976a b - 212480a b + 50880a b - 5184a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 100352a b + 301056a b - 505344a b + 518784a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 333312a b + 130816a b - 28672a b + 2688a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 1920a b + 10560a b - 23472a b + 26904a b - 16680a b +--R + +--R 7 3 8 2 +--R 5256a b - 648a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 14336b + 86016a b - 213504a b + 282624a b - 213408a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 90240a b - 18904a b + 1200a b + 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 78848a b + 177024a b - 208832a b + 138176a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 50304a b + 9022a b - 571a b - 3a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 6144b + 30720a b - 61440a b + 62976a b - 35040a b +--R + +--R 5 5 6 4 7 3 +--R 10272a b - 1416a b + 72a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 1024b - 4608a b + 8064a b - 6976a b + 3120a b - 696a b +--R + +--R 6 4 7 3 +--R 74a b - 3a b +--R * +--R 3 +--R cos(x) +--R * +--R cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R 9 2 8 3 7 4 6 +--R - 5120a b + 28160a b - 53760a b + 17920a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 89600a b - 161280a b + 125440a b - 48640a b + 7680a b +--R * +--R 15 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R 28672a b - 138240a b + 213504a b + 16384a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 453120a b + 611328a b - 381440a b + 116736a b +--R + +--R 9 +--R - 13824a b +--R * +--R 13 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R - 66560a b + 275968a b - 322688a b - 205120a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 866240a b - 891520a b + 436992a b - 101952a b + 8640a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R 81920a b - 284672a b + 221184a b + 354432a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 805440a b + 629760a b - 234368a b + 39296a b +--R + +--R 9 +--R - 2112a b +--R * +--R 9 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R - 56320a b + 158208a b - 56064a b - 258816a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 381408a b - 221232a b + 58960a b - 6288a b + 144a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 20480a b - 44032a b - 5632a b + 85376a b - 85504a b +--R + +--R 6 4 7 3 8 2 +--R 34976a b - 5952a b + 288a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 3072a b + 4608a b + 3456a b - 10176a b + 6816a b +--R + +--R 6 4 7 3 +--R - 1776a b + 144a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 10240b - 76800a b + 250880a b - 465920a b + 537600a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 394240a b + 179200a b - 46080a b + 5120a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 57344b + 391168a b - 1152000a b + 1908736a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 1940480a b + 1234944a b - 478208a b + 102400a b +--R + +--R 8 2 +--R - 9216a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 133120b - 818176a b + 2148608a b - 3135360a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 2765440a b - 1498880a b + 482816a b - 83328a b + 5760a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 163840b + 897024a b - 2072576a b + 2621184a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 1966464a b + 884736a b - 228608a b + 29952a b - 1408a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 112640b - 541696a b + 1082880a b - 1162752a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 722496a b - 259872a b + 50656a b - 4448a b + 96a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 40960b + 169984a b - 287744a b + 255232a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 126464a b + 34240a b - 4480a b + 192a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 6144b - 21504a b + 29952a b - 21120a b + 7872a b +--R + +--R 5 5 6 4 +--R - 1440a b + 96a b +--R * +--R 3 +--R cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 9 2 8 3 7 4 6 +--R 10240a b - 56320a b + 107520a b - 35840a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 179200a b + 322560a b - 250880a b + 97280a b +--R + +--R 9 +--R - 15360a b +--R * +--R 17 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R - 59392a b + 291840a b - 466944a b - 1024a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 952320a b - 1348608a b + 880640a b - 285696a b +--R + +--R 9 +--R 36864a b +--R * +--R 15 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R 141312a b - 611328a b + 783360a b + 339456a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 1943040a b + 2193408a b - 1185792a b + 314880a b +--R + +--R 9 +--R - 32256a b +--R * +--R 13 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R - 174080a b + 650240a b - 616704a b - 664320a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 1924800a b - 1731840a b + 759680a b - 160256a b +--R + +--R 9 +--R 12480a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R 112640a b - 353280a b + 208896a b + 497280a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 932688a b + 661272a b - 228968a b + 36936a b +--R + +--R 9 +--R - 2088a b +--R * +--R 9 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R - 30720a b + 76800a b - 13824a b - 132480a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 172176a b - 94152a b + 25200a b - 3144a b + 144a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 2 8 4 6 5 5 6 4 +--R - 2048a b + 5120a b - 9856a b + 10192a b - 3816a b +--R + +--R 7 3 8 2 9 +--R 338a b + 73a b - 3a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 2048a b - 3072a b - 2304a b + 6784a b - 4560a b +--R + +--R 6 4 7 3 8 2 +--R 1176a b - 74a b - 3a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 2 8 3 7 +--R - 20480b + 153600a b - 501760a b + 931840a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 1075200a b + 788480a b - 358400a b + 92160a b - 10240a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 118784b - 821248a b + 2457600a b - 4151296a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 4321280a b - 2832384a b + 1138688a b - 256000a b +--R + +--R 8 2 +--R 24576a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 282624b + 1787904a b - 4859904a b + 7394304a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 6865920a b + 3969024a b - 1388544a b + 267264a b +--R + +--R 8 2 +--R - 21504a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 348160b - 1996800a b + 4878848a b - 6606336a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 5395584a b - 2704896a b + 806144a b - 129024a b + 8320a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 225280b + 1157120a b - 2506752a b + 2974464a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 2099040a b + 893328a b - 220784a b + 28336a b - 1392a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 61440b - 276480a b + 519168a b - 527616a b + 314592a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 111408a b + 22560a b - 2352a b + 96a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 4096b - 18432a b + 32768a b - 29440a b + 13920a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 3056a b + 92a b + 54a b - 2a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 4096b + 14336a b - 19968a b + 14080a b - 5216a b +--R + +--R 5 5 6 4 7 3 +--R 912a b - 44a b - 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 1024a b + 5632a b - 10752a b + 3584a b + 17920a b +--R + +--R 6 4 7 3 8 2 9 +--R - 32256a b + 25088a b - 9728a b + 1536a b +--R * +--R 19 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 6144a b - 30720a b + 50688a b - 3072a b - 99840a b +--R + +--R 6 4 7 3 8 2 9 +--R 147456a b - 99840a b + 33792a b - 4608a b +--R * +--R 17 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 14336a b + 64512a b - 89472a b - 23744a b + 206400a b +--R + +--R 6 4 7 3 8 2 9 +--R - 253824a b + 149248a b - 43968a b + 5184a b +--R * +--R 15 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 14336a b - 57344a b + 64512a b + 43008a b - 174720a b +--R + +--R 6 4 7 3 8 2 9 +--R 182784a b - 94976a b + 25088a b - 2688a b +--R * +--R 13 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 1920a b + 4800a b - 432a b - 8952a b + 10248a b +--R + +--R 8 2 9 +--R - 4392a b + 648a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 14336a b + 43008a b - 19968a b - 67584a b + 109152a b +--R + +--R 6 4 7 3 8 2 9 +--R - 66144a b + 17240a b - 1296a b - 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 14336a b - 35840a b + 4992a b + 64192a b - 78784a b +--R + +--R 6 4 7 3 8 2 9 +--R 38784a b - 8258a b + 575a b + 3a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 6144a b + 12288a b + 3072a b - 24576a b + 22560a b +--R + +--R 6 4 7 3 8 2 +--R - 8448a b + 1320a b - 72a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 1024a b - 1536a b - 1152a b + 3392a b - 2256a b +--R + +--R 6 4 7 3 8 2 +--R 600a b - 70a b + 3a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 2048b - 15360a b + 50176a b - 93184a b + 107520a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 78848a b + 35840a b - 9216a b + 1024a b +--R * +--R 19 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 12288b + 86016a b - 261120a b + 448512a b - 476160a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 319488a b - 132096a b + 30720a b - 3072a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 28672b - 186368a b + 523008a b - 826496a b + 803200a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 490752a b + 183808a b - 38528a b + 3456a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 28672b + 172032a b - 444416a b + 645120a b - 575232a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 322560a b - 111104a b + 21504a b - 1792a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 3840a b - 17280a b + 31584a b - 29904a b + 15408a b +--R + +--R 7 3 8 2 +--R - 4080a b + 432a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 28672b - 143360a b + 297984a b - 331776a b + 211776a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 76224a b + 13712a b - 736a b - 48a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 28672b + 129024a b - 239360a b + 235648a b - 131712a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 41216a b - 6524a b + 378a b + 2a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 12288b - 49152a b + 79872a b - 67584a b + 31680a b +--R + +--R 5 5 6 4 7 3 +--R - 8064a b + 1008a b - 48a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R - 2048b + 7168a b - 9984a b + 7040a b - 2656a b + 528a b +--R + +--R 6 4 7 3 +--R - 52a b + 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 5120b + 43520a b - 161280a b + 340480a b - 448000a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 376320a b - 197120a b + 58880a b - 7680a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 28672b - 224256a b + 757248a b - 1439744a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 1681920a b - 1231872a b + 549376a b - 135168a b + 13824a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 66560b + 475648a b - 1450112a b + 2454080a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 2507200a b + 1569920a b - 580608a b + 113472a b +--R + +--R 8 2 +--R - 8640a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 81920b - 530432a b + 1443840a b - 2143104a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 1877568a b - 978432a b + 288640a b - 42112a b + 2112a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 56320b + 327168a b - 784128a b + 1001472a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 732576a b + 305520a b - 67472a b + 6480a b - 144a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 20480b - 105472a b + 218624a b - 234112a b + 137600a b +--R + +--R 5 5 6 4 7 3 +--R - 43168a b + 6336a b - 288a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 3072b + 13824a b - 24192a b + 20928a b - 9312a b +--R + +--R 5 5 6 4 +--R 1968a b - 144a b +--R * +--R 3 +--R cos(x) +--R * +--R 4 +--R cot(x)sin(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 10240b - 87040a b + 322560a b - 680960a b + 896000a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 752640a b + 394240a b - 117760a b + 15360a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 59392b + 470016a b - 1609728a b + 3113984a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 3717120a b + 2798592a b - 1294336a b + 334848a b +--R + +--R 8 2 +--R - 36864a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 141312b - 1035264a b + 3253248a b - 5715456a b +--R + +--R 4 6 5 5 6 4 7 3 +--R 6120960a b - 4073472a b + 1634304a b - 357888a b +--R + +--R 8 2 +--R 32256a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 174080b + 1172480a b - 3350784a b + 5286912a b +--R + +--R 4 6 5 5 6 4 7 3 +--R - 5009088a b + 2894592a b - 984448a b + 176896a b +--R + +--R 8 2 +--R - 12480a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R 112640b - 691200a b + 1775616a b - 2479488a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 2040624a b - 1000632a b + 280072a b - 39720a b + 2088a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 30720b + 168960a b - 382464a b + 461952a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 322032a b + 130632a b - 29520a b + 3336a b - 144a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 2048b + 11264a b - 24576a b + 27008a b - 15536a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 4200a b - 238a b - 77a b + 3a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 2048b - 9216a b + 16128a b - 13952a b + 6192a b +--R + +--R 5 5 6 4 7 3 +--R - 1272a b + 70a b + 3a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 1024b + 8704a b - 32256a b + 68096a b - 89600a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 75264a b - 39424a b + 11776a b - 1536a b +--R * +--R 19 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 6144b - 49152a b + 170496a b - 334848a b + 407040a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 313344a b + 148992a b - 39936a b + 4608a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 14336b + 107520a b - 347520a b + 631744a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 705600a b + 494976a b - 212480a b + 50880a b - 5184a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 100352a b + 301056a b - 505344a b + 518784a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 333312a b + 130816a b - 28672a b + 2688a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 1920a b + 10560a b - 23472a b + 26904a b - 16680a b +--R + +--R 7 3 8 2 +--R 5256a b - 648a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 14336b + 86016a b - 213504a b + 282624a b - 213408a b +--R + +--R 5 5 6 4 7 3 8 2 +--R 90240a b - 18904a b + 1200a b + 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 78848a b + 177024a b - 208832a b + 138176a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 50304a b + 9022a b - 571a b - 3a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 6144b + 30720a b - 61440a b + 62976a b - 35040a b +--R + +--R 5 5 6 4 7 3 +--R 10272a b - 1416a b + 72a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 1024b - 4608a b + 8064a b - 6976a b + 3120a b - 696a b +--R + +--R 6 4 7 3 +--R 74a b - 3a b +--R * +--R 3 +--R cos(x) +--R * +--R cot(x) +--R * +--R tan(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 5120a b + 35840a b - 107520a b + 179200a b - 179200a b +--R + +--R 8 2 9 10 +--R 107520a b - 35840a b + 5120a +--R * +--R 15 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 28672a b - 181248a b + 485376a b - 711680a b + 614400a b +--R + +--R 8 2 9 10 +--R - 310272a b + 83968a b - 9216a +--R * +--R 13 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 +--R - 66560a b + 375808a b - 886400a b + 1124480a b +--R + +--R 7 3 8 2 9 10 +--R - 820480a b + 339200a b - 71808a b + 5760a +--R * +--R 11 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 81920a b - 407552a b + 832512a b - 894336a b + 536064a b +--R + +--R 8 2 9 10 +--R - 174336a b + 27136a b - 1408a +--R * +--R 9 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 +--R - 56320a b + 242688a b - 420096a b + 371328a b +--R + +--R 7 3 8 2 9 10 +--R - 175584a b + 42144a b - 4256a b + 96a +--R * +--R 7 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 20480a b - 74752a b + 106496a b - 74368a b + 26048a b +--R + +--R 8 2 9 +--R - 4096a b + 192a b +--R * +--R 5 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 3072a b + 9216a b - 10368a b + 5376a b - 1248a b +--R + +--R 8 2 +--R 96a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 5120b - 38400a b + 122880a b - 215040a b + 215040a b +--R + +--R 5 5 7 3 8 2 9 +--R - 107520a b + 30720a b - 15360a b + 2560a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 28672b + 195584a b - 561664a b + 863744a b - 727552a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 261632a b + 68096a b - 103936a b + 37376a b - 4608a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 66560b - 409088a b + 1041024a b - 1379776a b + 939520a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R - 187200a b - 168832a b + 127936a b - 33024a b + 2880a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 81920b + 448512a b - 995328a b + 1106816a b - 566976a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R - 4800a b + 153728a b - 72192a b + 12864a b - 704a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 56320b - 270848a b + 513280a b - 460032a b + 151200a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 55728a b - 62464a b + 18848a b - 2080a b + 48a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 20480b + 84992a b - 133632a b + 90240a b - 9984a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 20064a b + 10784a b - 1952a b + 96a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 3072b - 10752a b + 13440a b - 5952a b - 1248a b + 1968a b +--R + +--R 6 4 7 3 +--R - 576a b + 48a b +--R * +--R 3 +--R cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 10240a b - 71680a b + 215040a b - 358400a b + 358400a b +--R + +--R 8 2 9 10 +--R - 215040a b + 71680a b - 10240a +--R * +--R 17 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 +--R - 59392a b + 380928a b - 1038336a b + 1556480a b +--R + +--R 7 3 8 2 9 10 +--R - 1382400a b + 724992a b - 206848a b + 24576a +--R * +--R 15 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 +--R 141312a b - 823296a b + 2018304a b - 2688000a b +--R + +--R 7 3 8 2 9 10 +--R 2088960a b - 940032a b + 224256a b - 21504a +--R * +--R 13 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 +--R - 174080a b + 911360a b - 1983744a b + 2311296a b +--R + +--R 7 3 8 2 9 10 +--R - 1542144a b + 581376a b - 112384a b + 8320a +--R * +--R 11 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 +--R 112640a b - 522240a b + 992256a b - 991104a b +--R + +--R 7 3 8 2 9 10 +--R 553968a b - 169680a b + 25552a b - 1392a +--R * +--R 9 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 +--R - 30720a b + 122880a b - 198144a b + 164736a b +--R + +--R 7 3 8 2 9 10 +--R - 74928a b + 18240a b - 2160a b + 96a +--R * +--R 7 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 2048a b + 8192a b - 12288a b + 8576a b - 2672a b +--R + +--R 8 2 9 10 +--R 192a b + 50a b - 2a +--R * +--R 5 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 2048a b - 6144a b + 6912a b - 3584a b + 816a b - 48a b +--R + +--R 9 +--R - 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 10240b + 76800a b - 245760a b + 430080a b - 430080a b +--R + +--R 5 5 7 3 8 2 9 +--R 215040a b - 61440a b + 30720a b - 5120a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 59392b - 410624a b + 1199104a b - 1885184a b + 1641472a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R - 637952a b - 121856a b + 234496a b - 91136a b + 12288a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 +--R - 141312b + 893952a b - 2359296a b + 3285504a b +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 2423808a b + 640512a b + 350208a b - 336384a b + 101376a b +--R + +--R 9 +--R - 10752a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 174080b - 998400a b + 2352384a b - 2847488a b + 1705920a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R - 196800a b - 368000a b + 226176a b - 52032a b + 4160a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 112640b + 578560a b - 1197056a b + 1226112a b - 553392a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R - 48888a b + 166592a b - 70672a b + 12080a b - 696a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 30720b - 138240a b + 244224a b - 202368a b + 58224a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 26664a b - 26184a b + 7944a b - 1032a b + 48a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 2048b - 9216a b + 15360a b - 10624a b + 816a b + 2760a b +--R + +--R 6 4 7 3 8 2 9 +--R - 1290a b + 123a b + 24a b - a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R - 2048b + 7168a b - 8960a b + 3968a b + 848a b - 1336a b +--R + +--R 6 4 7 3 8 2 +--R 386a b - 25a b - a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 1024a b + 7168a b - 21504a b + 35840a b - 35840a b +--R + +--R 8 2 9 10 +--R 21504a b - 7168a b + 1024a +--R * +--R 19 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 6144a b - 39936a b + 110592a b - 168960a b + 153600a b +--R + +--R 8 2 9 10 +--R - 82944a b + 24576a b - 3072a +--R * +--R 17 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 14336a b + 86016a b - 218496a b + 304000a b - 249600a b +--R + +--R 8 2 9 10 +--R 120576a b - 31616a b + 3456a +--R * +--R 15 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 14336a b - 78848a b + 182784a b - 231168a b + 172032a b +--R + +--R 8 2 9 10 +--R - 75264a b + 17920a b - 1792a +--R * +--R 13 +--R cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 10 +--R (- 1920a b + 7680a b - 11952a b + 8976a b - 3216a b + 432a ) +--R * +--R 11 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 14336a b + 64512a b - 116736a b + 107520a b - 52128a b +--R + +--R 8 2 9 10 +--R 12048a b - 832a b - 48a +--R * +--R 9 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 14336a b - 57344a b + 91008a b - 72320a b + 29696a b +--R + +--R 8 2 9 10 +--R - 5760a b + 382a b + 2a +--R * +--R 7 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 6144a b + 21504a b - 29184a b + 19200a b - 6240a b +--R + +--R 8 2 9 +--R 912a b - 48a b +--R * +--R 5 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 1024a b - 3072a b + 3456a b - 1792a b + 432a b - 48a b +--R + +--R 9 +--R 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 1024b - 7680a b + 24576a b - 43008a b + 43008a b - 21504a b +--R + +--R 7 3 8 2 9 +--R 6144a b - 3072a b + 512a b +--R * +--R 19 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 6144b + 43008a b - 127488a b + 204288a b - 182784a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 75264a b + 10752a b - 26112a b + 10752a b - 1536a b +--R * +--R 17 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 93184a b + 254336a b - 370240a b + 292352a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R - 93376a b - 32896a b + 41024a b - 14080a b + 1728a b +--R * +--R 15 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 14336b + 86016a b - 215040a b + 283136a b - 196224a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 45696a b + 30464a b - 26880a b + 8064a b - 896a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 1920a b - 8640a b + 14832a b - 11112a b + 1728a b + 2448a b +--R + +--R 8 2 9 +--R - 1392a b + 216a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 14336b - 71680a b + 141824a b - 133632a b + 47520a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 15648a b - 19208a b + 5656a b - 440a b - 24a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R - 14336b + 64512a b - 112512a b + 89152a b - 20352a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R - 15552a b + 11586a b - 2691a b + 192a b + a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 6144b - 24576a b + 36864a b - 23040a b + 1248a b + 5568a b +--R + +--R 6 4 7 3 8 2 +--R - 2616a b + 432a b - 24a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R - 1024b + 3584a b - 4480a b + 1984a b + 400a b - 632a b +--R + +--R 6 4 7 3 8 2 +--R 190a b - 23a b + a b +--R * +--R 3 +--R cos(x) +--R / +--R 7 6 2 5 3 4 4 3 +--R 1024b - 6144a b + 15360a b - 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382a b - 2a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 6144b - 21504a b + 29184a b - 19200a b + 6240a b +--R + +--R 5 3 6 2 +--R - 912a b + 48a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 1024b + 3072a b - 3456a b + 1792a b - 432a b +--R + +--R 5 3 6 2 +--R 48a b - 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 5120a b - 35840a b + 107520a b - 179200a b + 179200a b +--R + +--R 6 2 7 8 +--R - 107520a b + 35840a b - 5120a +--R * +--R 15 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 28672a b + 181248a b - 485376a b + 711680a b +--R + +--R 5 3 6 2 7 8 +--R - 614400a b + 310272a b - 83968a b + 9216a +--R * +--R 13 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R 66560a b - 375808a b + 886400a b - 1124480a b +--R + +--R 5 3 6 2 7 8 +--R 820480a b - 339200a b + 71808a b - 5760a +--R * +--R 11 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 81920a b + 407552a b - 832512a b + 894336a b +--R + +--R 5 3 6 2 7 8 +--R - 536064a b + 174336a b - 27136a b + 1408a +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R 56320a b - 242688a b + 420096a b - 371328a b +--R + +--R 5 3 6 2 7 8 +--R 175584a b - 42144a b + 4256a b - 96a +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 20480a b + 74752a b - 106496a b + 74368a b +--R + +--R 5 3 6 2 7 +--R - 26048a b + 4096a b - 192a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 3072a b - 9216a b + 10368a b - 5376a b + 1248a b +--R + +--R 6 2 +--R - 96a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 5120b + 35840a b - 107520a b + 179200a b - 179200a b +--R + +--R 5 3 6 2 7 +--R 107520a b - 35840a b + 5120a b +--R * +--R 15 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 28672b - 181248a b + 485376a b - 711680a b + 614400a b +--R + +--R 5 3 6 2 7 +--R - 310272a b + 83968a b - 9216a b +--R * +--R 13 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 66560b + 375808a b - 886400a b + 1124480a b - 820480a b +--R + +--R 5 3 6 2 7 +--R 339200a b - 71808a b + 5760a b +--R * +--R 11 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 81920b - 407552a b + 832512a b - 894336a b + 536064a b +--R + +--R 5 3 6 2 7 +--R - 174336a b + 27136a b - 1408a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 56320b + 242688a b - 420096a b + 371328a b - 175584a b +--R + +--R 5 3 6 2 7 +--R 42144a b - 4256a b + 96a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 20480b - 74752a b + 106496a b - 74368a b + 26048a b +--R + +--R 5 3 6 2 +--R - 4096a b + 192a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R (- 3072b + 9216a b - 10368a b + 5376a b - 1248a b + 96a b ) +--R * +--R 3 +--R cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 10240a b + 71680a b - 215040a b + 358400a b +--R + +--R 5 3 6 2 7 8 +--R - 358400a b + 215040a b - 71680a b + 10240a +--R * +--R 17 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R 59392a b - 380928a b + 1038336a b - 1556480a b +--R + +--R 5 3 6 2 7 8 +--R 1382400a b - 724992a b + 206848a b - 24576a +--R * +--R 15 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 141312a b + 823296a b - 2018304a b + 2688000a b +--R + +--R 5 3 6 2 7 8 +--R - 2088960a b + 940032a b - 224256a b + 21504a +--R * +--R 13 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R 174080a b - 911360a b + 1983744a b - 2311296a b +--R + +--R 5 3 6 2 7 8 +--R 1542144a b - 581376a b + 112384a b - 8320a +--R * +--R 11 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 112640a b + 522240a b - 992256a b + 991104a b +--R + +--R 5 3 6 2 7 8 +--R - 553968a b + 169680a b - 25552a b + 1392a +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R 30720a b - 122880a b + 198144a b - 164736a b +--R + +--R 5 3 6 2 7 8 +--R 74928a b - 18240a b + 2160a b - 96a +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 2048a b - 8192a b + 12288a b - 8576a b + 2672a b +--R + +--R 6 2 7 8 +--R - 192a b - 50a b + 2a +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 2048a b + 6144a b - 6912a b + 3584a b - 816a b +--R + +--R 6 2 7 +--R 48a b + 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 10240b - 71680a b + 215040a b - 358400a b + 358400a b +--R + +--R 5 3 6 2 7 +--R - 215040a b + 71680a b - 10240a b +--R * +--R 17 +--R cos(x) +--R + +--R 8 7 2 6 3 5 +--R - 59392b + 380928a b - 1038336a b + 1556480a b +--R + +--R 4 4 5 3 6 2 7 +--R - 1382400a b + 724992a b - 206848a b + 24576a b +--R * +--R 15 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 141312b - 823296a b + 2018304a b - 2688000a b + 2088960a b +--R + +--R 5 3 6 2 7 +--R - 940032a b + 224256a b - 21504a b +--R * +--R 13 +--R cos(x) +--R + +--R 8 7 2 6 3 5 +--R - 174080b + 911360a b - 1983744a b + 2311296a b +--R + +--R 4 4 5 3 6 2 7 +--R - 1542144a b + 581376a b - 112384a b + 8320a b +--R * +--R 11 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 112640b - 522240a b + 992256a b - 991104a b + 553968a b +--R + +--R 5 3 6 2 7 +--R - 169680a b + 25552a b - 1392a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 30720b + 122880a b - 198144a b + 164736a b - 74928a b +--R + +--R 5 3 6 2 7 +--R 18240a b - 2160a b + 96a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 2048b + 8192a b - 12288a b + 8576a b - 2672a b + 192a b +--R + +--R 6 2 7 +--R 50a b - 2a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 2048b - 6144a b + 6912a b - 3584a b + 816a b - 48a b +--R + +--R 6 2 +--R - 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 1024a b - 7168a b + 21504a b - 35840a b + 35840a b +--R + +--R 6 2 7 8 +--R - 21504a b + 7168a b - 1024a +--R * +--R 19 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 6144a b + 39936a b - 110592a b + 168960a b - 153600a b +--R + +--R 6 2 7 8 +--R 82944a b - 24576a b + 3072a +--R * +--R 17 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 14336a b - 86016a b + 218496a b - 304000a b + 249600a b +--R + +--R 6 2 7 8 +--R - 120576a b + 31616a b - 3456a +--R * +--R 15 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 14336a b + 78848a b - 182784a b + 231168a b - 172032a b +--R + +--R 6 2 7 8 +--R 75264a b - 17920a b + 1792a +--R * +--R 13 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (1920a b - 7680a b + 11952a b - 8976a b + 3216a b - 432a ) +--R * +--R 11 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 14336a b - 64512a b + 116736a b - 107520a b + 52128a b +--R + +--R 6 2 7 8 +--R - 12048a b + 832a b + 48a +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 14336a b + 57344a b - 91008a b + 72320a b - 29696a b +--R + +--R 6 2 7 8 +--R 5760a b - 382a b - 2a +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 6144a b - 21504a b + 29184a b - 19200a b + 6240a b +--R + +--R 6 2 7 +--R - 912a b + 48a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 1024a b + 3072a b - 3456a b + 1792a b - 432a b + 48a b +--R + +--R 7 +--R - 2a b +--R * +--R 3 +--R cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 1024b + 7168a b - 21504a b + 35840a b - 35840a b + 21504a b +--R + +--R 6 2 7 +--R - 7168a b + 1024a b +--R * +--R 19 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 6144b - 39936a b + 110592a b - 168960a b + 153600a b +--R + +--R 5 3 6 2 7 +--R - 82944a b + 24576a b - 3072a b +--R * +--R 17 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 14336b + 86016a b - 218496a b + 304000a b - 249600a b +--R + +--R 5 3 6 2 7 +--R 120576a b - 31616a b + 3456a b +--R * +--R 15 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 14336b - 78848a b + 182784a b - 231168a b + 172032a b +--R + +--R 5 3 6 2 7 +--R - 75264a b + 17920a b - 1792a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (- 1920a b + 7680a b - 11952a b + 8976a b - 3216a b + 432a b) +--R * +--R 11 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 14336b + 64512a b - 116736a b + 107520a b - 52128a b +--R + +--R 5 3 6 2 7 +--R 12048a b - 832a b - 48a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 14336b - 57344a b + 91008a b - 72320a b + 29696a b - 5760a b +--R + +--R 6 2 7 +--R 382a b + 2a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 6144b + 21504a b - 29184a b + 19200a b - 6240a b + 912a b +--R + +--R 6 2 +--R - 48a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R (1024b - 3072a b + 3456a b - 1792a b + 432a b - 48a b + 2a b ) +--R * +--R 3 +--R cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|b tan(x) + a +--R Type: Expression(Integer) +--E 184 + +--S 185 of 510 +t0236:= cot(a+b*x) +--R +--R +--R (171) cot(b x + a) +--R Type: Expression(Integer) +--E 185 + +--S 186 of 510 +r0236:= log(sin(a+b*x))/b +--R +--R +--R log(sin(b x + a)) +--R (172) ----------------- +--R b +--R Type: Expression(Integer) +--E 186 + +--S 187 of 510 +a0236:= integrate(t0236,x) +--R +--R +--R sin(2b x + 2a) 2 +--R 2log(------------------) - log(------------------) +--R cos(2b x + 2a) + 1 cos(2b x + 2a) + 1 +--R (173) -------------------------------------------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 187 + +--S 188 of 510 +m0236:= a0236-r0236 +--R +--R +--R (174) +--R sin(2b x + 2a) 2 +--R 2log(------------------) - 2log(sin(b x + a)) - log(------------------) +--R cos(2b x + 2a) + 1 cos(2b x + 2a) + 1 +--R ----------------------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 188 + +--S 189 of 510 +d0236:= D(m0236,x) +--R +--R +--R (175) +--R 2 +--R sin(b x + a)sin(2b x + 2a) +--R + +--R (- cos(b x + a)cos(2b x + 2a) - cos(b x + a))sin(2b x + 2a) +--R + +--R 2 +--R (2cos(2b x + 2a) + 2cos(2b x + 2a))sin(b x + a) +--R / +--R (cos(2b x + 2a) + 1)sin(b x + a)sin(2b x + 2a) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 510 +t0237:= cot(a+b*x)^2 +--R +--R +--R 2 +--R (176) cot(b x + a) +--R Type: Expression(Integer) +--E 190 + +--S 191 of 510 +r0237:= -x-cot(a+b*x)/b +--R +--R +--R - cot(b x + a) - b x +--R (177) -------------------- +--R b +--R Type: Expression(Integer) +--E 191 + +--S 192 of 510 +a0237:= integrate(t0237,x) +--R +--R +--R - b x sin(2b x + 2a) - cos(2b x + 2a) - 1 +--R (178) ----------------------------------------- +--R b sin(2b x + 2a) +--R Type: Union(Expression(Integer),...) +--E 192 + +--S 193 of 510 +m0237:= a0237-r0237 +--R +--R +--R cot(b x + a)sin(2b x + 2a) - cos(2b x + 2a) - 1 +--R (179) ----------------------------------------------- +--R b sin(2b x + 2a) +--R Type: Expression(Integer) +--E 193 + +--S 194 of 510 +d0237:= D(m0237,x) +--R +--R +--R (180) +--R 2 2 2 +--R (- cot(b x + a) + 1)sin(2b x + 2a) + 2cos(2b x + 2a) + 2cos(2b x + 2a) +--R ------------------------------------------------------------------------- +--R 2 +--R sin(2b x + 2a) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 510 +t0238:= x*cot(a+b*x) +--R +--R +--R (181) x cot(b x + a) +--R Type: Expression(Integer) +--E 195 + +--S 196 of 510 +r0238:= -1/2*%i*x^2+x*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b-_ + 1/2*%i*polylog(2,exp(1)^(2*%i*a+2*%i*b*x))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 196 + +--S 197 of 510 +a0238:= integrate(t0238,x) +--R +--R +--R x +--R ++ +--R (182) | %H cot(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 197 + +--S 198 of 510 +m0238:= a0238-r0238 +--R +--R +--R x +--R ++ +--R (183) | %H cot(%H b + a)d%H - r0238 +--R ++ +--R Type: Expression(Integer) +--E 198 + +--S 199 of 510 +d0238:= D(m0238,x) +--R +--R +--R (184) x cot(b x + a) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 510 +t0239:= x*cot(a+b*x)^2 +--R +--R +--R 2 +--R (185) x cot(b x + a) +--R Type: Expression(Integer) +--E 200 + +--S 201 of 510 +r0239:= -1/2*x^2-x*cot(a+b*x)/b+log(sin(a+b*x))/b^2 +--R +--R +--R 2 2 +--R 2log(sin(b x + a)) - 2b x cot(b x + a) - b x +--R (186) --------------------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 201 + +--S 202 of 510 +a0239:= integrate(t0239,x) +--R +--R +--R (187) +--R sin(2b x + 2a) +--R 2sin(2b x + 2a)log(------------------) +--R cos(2b x + 2a) + 1 +--R + +--R 2 2 2 +--R - sin(2b x + 2a)log(------------------) - b x sin(2b x + 2a) +--R cos(2b x + 2a) + 1 +--R + +--R - 2b x cos(2b x + 2a) - 2b x +--R / +--R 2 +--R 2b sin(2b x + 2a) +--R Type: Union(Expression(Integer),...) +--E 202 + +--S 203 of 510 +m0239:= a0239-r0239 +--R +--R +--R (188) +--R sin(2b x + 2a) +--R 2sin(2b x + 2a)log(------------------) - 2sin(2b x + 2a)log(sin(b x + a)) +--R cos(2b x + 2a) + 1 +--R + +--R 2 +--R - sin(2b x + 2a)log(------------------) + 2b x cot(b x + a)sin(2b x + 2a) +--R cos(2b x + 2a) + 1 +--R + +--R - 2b x cos(2b x + 2a) - 2b x +--R / +--R 2 +--R 2b sin(2b x + 2a) +--R Type: Expression(Integer) +--E 203 + +--S 204 of 510 +d0239:= D(m0239,x) +--R +--R +--R (189) +--R 3 +--R sin(b x + a)sin(2b x + 2a) +--R + +--R 2 +--R (- b x cos(2b x + 2a) - b x)cot(b x + a) +--R + +--R (cos(2b x + 2a) + 1)cot(b x + a) + b x cos(2b x + 2a) + b x +--R * +--R sin(b x + a) +--R + +--R - cos(b x + a)cos(2b x + 2a) - cos(b x + a) +--R * +--R 2 +--R sin(2b x + 2a) +--R + +--R 2 +--R (cos(2b x + 2a) - 1)sin(b x + a)sin(2b x + 2a) +--R + +--R 3 2 +--R (2b x cos(2b x + 2a) + 4b x cos(2b x + 2a) + 2b x cos(2b x + 2a)) +--R * +--R sin(b x + a) +--R / +--R 2 +--R (b cos(2b x + 2a) + b)sin(b x + a)sin(2b x + 2a) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 510 +t0240:= x*cot(a+b*x)^3 +--R +--R +--R 3 +--R (190) x cot(b x + a) +--R Type: Expression(Integer) +--E 205 + +--S 206 of 510 +r0240:= 1/2*%i*x^2-1/2*cot(a+b*x)/b^2-1/2*x*csc(a+b*x)^2/b-_ + x*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b+_ + 1/2*%i*polylog(2,exp(1)^(2*%i*a+2*%i*b*x))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 206 + +--S 207 of 510 +a0240:= integrate(t0240,x) +--R +--R +--R x +--R ++ 3 +--R (191) | %H cot(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 207 + +--S 208 of 510 +m0240:= a0240-r0240 +--R +--R +--R x +--R ++ 3 +--R (192) | %H cot(%H b + a) d%H - r0240 +--R ++ +--R Type: Expression(Integer) +--E 208 + +--S 209 of 510 +d0240:= D(m0240,x) +--R +--R +--R 3 +--R (193) x cot(b x + a) +--R Type: Expression(Integer) +--E 209 + +--S 210 of 510 +t0241:= x^2*cot(a+b*x) +--R +--R +--R 2 +--R (194) x cot(b x + a) +--R Type: Expression(Integer) +--E 210 + +--S 211 of 510 +r0241:= 1/6*(-2*%i*x^3*b^3+6*x^2*log(1-exp(2*%i*(a+b*x)))*b^2-_ + 6*%i*x*polylog(2,exp(2*%i*(a+b*x)))*b+_ + 3*polylog(3,exp(2*%i*(a+b*x))))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 211 + +--S 212 of 510 +a0241:= integrate(t0241,x) +--R +--R +--R x +--R ++ 2 +--R (195) | %H cot(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 212 + +--S 213 of 510 +m0241:= a0241-r0241 +--R +--R +--R x +--R ++ 2 +--R (196) | %H cot(%H b + a)d%H - r0241 +--R ++ +--R Type: Expression(Integer) +--E 213 + +--S 214 of 510 +d0241:= D(m0241,x) +--R +--R +--R 2 +--R (197) x cot(b x + a) +--R Type: Expression(Integer) +--E 214 + +--S 215 of 510 +t0242:= x^2*cot(a+b*x)^2 +--R +--R +--R 2 2 +--R (198) x cot(b x + a) +--R Type: Expression(Integer) +--E 215 + +--S 216 of 510 +r0242:= 1/3*(-3*%i*x^2*b^2-b^3*x^3-3*x^2*cot(a+b*x)*b^2+_ + 6*x*log(1-exp(2*%i*(a+b*x)))*b-3*%i*polylog(2,exp(2*%i*(a+b*x))))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 216 + +--S 217 of 510 +a0242:= integrate(t0242,x) +--R +--R +--R x +--R ++ 2 2 +--R (199) | %H cot(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 217 + +--S 218 of 510 +m0242:= a0242-r0242 +--R +--R +--R x +--R ++ 2 2 +--R (200) | %H cot(%H b + a) d%H - r0242 +--R ++ +--R Type: Expression(Integer) +--E 218 + +--S 219 of 510 +d0242:= D(m0242,x) +--R +--R +--R 2 2 +--R (201) x cot(b x + a) +--R Type: Expression(Integer) +--E 219 + +--S 220 of 510 +t0243:= x^2*cot(a+b*x)^3 +--R +--R +--R 2 3 +--R (202) x cot(b x + a) +--R Type: Expression(Integer) +--E 220 + +--S 221 of 510 +r0243:= 1/3*%i*x^3-x*cot(a+b*x)/b^2-1/2*x^2*csc(a+b*x)^2/b-_ + x^2*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b+log(sin(a+b*x))/b^3+_ + %i*x*polylog(2,exp(1)^(2*%i*a+2*%i*b*x))/b^2-_ + 1/2*polylog(3,exp(1)^(2*%i*a+2*%i*b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 221 + +--S 222 of 510 +a0243:= integrate(t0243,x) +--R +--R +--R x +--R ++ 2 3 +--R (203) | %H cot(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 222 + +--S 223 of 510 +m0243:= a0243-r0243 +--R +--R +--R x +--R ++ 2 3 +--R (204) | %H cot(%H b + a) d%H - r0243 +--R ++ +--R Type: Expression(Integer) +--E 223 + +--S 224 of 510 +d0243:= D(m0243,x) +--R +--R +--R 2 3 +--R (205) x cot(b x + a) +--R Type: Expression(Integer) +--E 224 + +--S 225 of 510 +t0244:= x^3*cot(a+b*x) +--R +--R +--R 3 +--R (206) x cot(b x + a) +--R Type: Expression(Integer) +--E 225 + +--S 226 of 510 +r0244:= 1/4*(-%i*x^4*b^4+4*x^3*log(1-exp(2*%i*(a+b*x)))*b^3-_ + 6*%i*x^2*polylog(2,exp(2*%i*(a+b*x)))*b^2+_ + 6*x*polylog(3,exp(2*%i*(a+b*x)))*b+_ + 3*%i*polylog(4,exp(2*%i*(a+b*x))))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 226 + +--S 227 of 510 +a0244:= integrate(t0244,x) +--R +--R +--R x +--R ++ 3 +--R (207) | %H cot(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 227 + +--S 228 of 510 +m0244:= a0244-r0244 +--R +--R +--R x +--R ++ 3 +--R (208) | %H cot(%H b + a)d%H - r0244 +--R ++ +--R Type: Expression(Integer) +--E 228 + +--S 229 of 510 +d0244:= D(m0244,x) +--R +--R +--R 3 +--R (209) x cot(b x + a) +--R Type: Expression(Integer) +--E 229 + +--S 230 of 510 +t0245:= x^3*cot(a+b*x)^2 +--R +--R +--R 3 2 +--R (210) x cot(b x + a) +--R Type: Expression(Integer) +--E 230 + +--S 231 of 510 +r0245:= 1/4*(-4*%i*x^3*b^3-x^4*b^4-4*x^3*cot(a+b*x)*b^3+12*x^2*_ + log(1-exp(2*%i*(a+b*x)))*b^2-12*%i*x*_ + polylog(2,exp(2*%i*(a+b*x)))*b+6*polylog(3,exp(2*%i*(a+b*x))))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 231 + +--S 232 of 510 +a0245:= integrate(t0245,x) +--R +--R +--R x +--R ++ 3 2 +--R (211) | %H cot(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 232 + +--S 233 of 510 +m0245:= a0245-r0245 +--R +--R +--R x +--R ++ 3 2 +--R (212) | %H cot(%H b + a) d%H - r0245 +--R ++ +--R Type: Expression(Integer) +--E 233 + +--S 234 of 510 +d0245:= D(m0245,x) +--R +--R +--R 3 2 +--R (213) x cot(b x + a) +--R Type: Expression(Integer) +--E 234 + +--S 235 of 510 +t0246:= x^3*cot(a+b*x)^3 +--R +--R +--R 3 3 +--R (214) x cot(b x + a) +--R Type: Expression(Integer) +--E 235 + +--S 236 of 510 +r0246:= -3/2*%i*x^2/b^2+1/4*%i*x^4-3/2*x^2*cot(a+b*x)/b^2-_ + 1/2*x^3*csc(a+b*x)^2/b+3*x*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b^3-_ + x^3*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b-3/2*%i*(1-b^2*x^2)*_ + polylog(2,exp(1)^(2*%i*a+2*%i*b*x))/b^4-3/2*x*_ + polylog(3,exp(1)^(2*%i*a+2*%i*b*x))/b^3-3/4*%i*_ + polylog(4,exp(1)^(2*%i*a+2*%i*b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 236 + +--S 237 of 510 +a0246:= integrate(t0246,x) +--R +--R +--R x +--R ++ 3 3 +--R (215) | %H cot(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 237 + +--S 238 of 510 +m0246:= a0246-r0246 +--R +--R +--R x +--R ++ 3 3 +--R (216) | %H cot(%H b + a) d%H - r0246 +--R ++ +--R Type: Expression(Integer) +--E 238 + +--S 239 of 510 +d0246:= D(m0246,x) +--R +--R +--R 3 3 +--R (217) x cot(b x + a) +--R Type: Expression(Integer) +--E 239 + +--S 240 of 510 +t0247:= (a*cot(x)^2)^(1/2) +--R +--R +--R +---------+ +--R | 2 +--R (218) \|a cot(x) +--R Type: Expression(Integer) +--E 240 + +--S 241 of 510 +r0247:= (a*cot(x)^2)^(1/2)*log(sin(x))*tan(x) +--R +--R +--R +---------+ +--R | 2 +--R (219) tan(x)log(sin(x))\|a cot(x) +--R Type: Expression(Integer) +--E 241 + +--S 242 of 510 +a0247:= integrate(t0247,x) +--R +--R +--R +-+ sin(2x) +-+ 2 +--R 2\|a log(-----------) - \|a log(-----------) +--R cos(2x) + 1 cos(2x) + 1 +--R (220) -------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 510 +m0247:= a0247-r0247 +--R +--R +--R (221) +--R +---------+ +--R | 2 +-+ sin(2x) +--R - 2tan(x)log(sin(x))\|a cot(x) + 2\|a log(-----------) +--R cos(2x) + 1 +--R + +--R +-+ 2 +--R - \|a log(-----------) +--R cos(2x) + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 243 + +--S 244 of 510 +d0247:= D(m0247,x) +--R +--R +--R (222) +--R +---------+ +--R 2 2 +-+ | 2 +--R (sin(x)sin(2x) + (2cos(2x) + 2cos(2x))sin(x))\|a \|a cot(x) +--R + +--R 2 2 +--R (- a cos(2x) - a)cot(x) sin(x)sin(2x)tan(x) +--R + +--R 3 +--R ((a cos(2x) + a)cot(x) + (a cos(2x) + a)cot(x))sin(x)sin(2x)tan(x) +--R + +--R 2 +--R (- a cos(2x) - a)cot(x) sin(x)sin(2x) +--R * +--R log(sin(x)) +--R + +--R 2 +--R (- a cos(x)cos(2x) - a cos(x))cot(x) sin(2x)tan(x) +--R / +--R +---------+ +--R | 2 +--R (cos(2x) + 1)sin(x)sin(2x)\|a cot(x) +--R Type: Expression(Integer) +--E 244 + +--S 245 of 510 +t0248:= (a*cot(x)^3)^(1/2) +--R +--R +--R +---------+ +--R | 3 +--R (223) \|a cot(x) +--R Type: Expression(Integer) +--E 245 + +--S 246 of 510 +r0248:= 1/4*(a*cot(x)^3)^(1/2)*(2*2^(1/2)*atan(-1+2^(1/2)*cot(x)^(1/2))+_ + 2*2^(1/2)*atan(1+2^(1/2)*cot(x)^(1/2))-8*cot(x)^(1/2)-_ + log(1-2^(1/2)*cot(x)^(1/2)+cot(x))*2^(1/2)+_ + log(1+2^(1/2)*cot(x)^(1/2)+cot(x))*2^(1/2))/cot(x)^(3/2) +--R +--R +--R (224) +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R \|2 \|a cot(x) log(\|2 \|cot(x) + cot(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R - \|2 \|a cot(x) log(- \|2 \|cot(x) + cot(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R 2\|2 \|a cot(x) atan(\|2 \|cot(x) + 1) +--R + +--R +---------+ +---------+ +--R +-+ | 3 +-+ +------+ +------+ | 3 +--R 2\|2 \|a cot(x) atan(\|2 \|cot(x) - 1) - 8\|cot(x) \|a cot(x) +--R / +--R +------+ +--R 4cot(x)\|cot(x) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 510 +a0248:= integrate(t0248,x) +--R +--R +--R >> System error: +--R Cannot take first of an empty list +--R +--R Continuing to read the file... +--R +--E 247 + +--S 248 of 510 +m0248:= a0248-r0248 +--R +--R +--R (225) +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R - \|2 \|a cot(x) log(\|2 \|cot(x) + cot(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R \|2 \|a cot(x) log(- \|2 \|cot(x) + cot(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R - 2\|2 \|a cot(x) atan(\|2 \|cot(x) + 1) +--R + +--R +---------+ +---------+ +--R +-+ | 3 +-+ +------+ +------+ | 3 +--R - 2\|2 \|a cot(x) atan(\|2 \|cot(x) - 1) + 8\|cot(x) \|a cot(x) +--R + +--R +------+ +--R 4a0248 cot(x)\|cot(x) +--R / +--R +------+ +--R 4cot(x)\|cot(x) +--R Type: Expression(Integer) +--E 248 + +--S 249 of 510 +d0248:= D(m0248,x) +--R +--R +--R 3 +--R a cot(x) +--R (226) - ------------ +--R +---------+ +--R | 3 +--R \|a cot(x) +--R Type: Expression(Integer) +--E 249 + +--S 250 of 510 +t0249:= (a*cot(x)^3)^(3/2) +--R +--R +--R +---------+ +--R 3 | 3 +--R (227) a cot(x) \|a cot(x) +--R Type: Expression(Integer) +--E 250 + +--S 251 of 510 +r0249:= -1/84*a*(a*cot(x)^3)^(1/2)*(42*2^(1/2)*_ + atan(-1+2^(1/2)*cot(x)^(1/2))+42*2^(1/2)*_ + atan(1+2^(1/2)*cot(x)^(1/2))-56*cot(x)^(3/2)+24*cot(x)^(7/2)+_ + 21*log(1-2^(1/2)*cot(x)^(1/2)+cot(x))*2^(1/2)-_ + 21*log(1+2^(1/2)*cot(x)^(1/2)+cot(x))*2^(1/2))/cot(x)^(3/2) +--R +--R +--R (228) +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R 21a\|2 \|a cot(x) log(\|2 \|cot(x) + cot(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R - 21a\|2 \|a cot(x) log(- \|2 \|cot(x) + cot(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R - 42a\|2 \|a cot(x) atan(\|2 \|cot(x) + 1) +--R + +--R +---------+ +--R +-+ | 3 +-+ +------+ +--R - 42a\|2 \|a cot(x) atan(\|2 \|cot(x) - 1) +--R + +--R +---------+ +--R 3 +------+ | 3 +--R (- 24a cot(x) + 56a cot(x))\|cot(x) \|a cot(x) +--R / +--R +------+ +--R 84cot(x)\|cot(x) +--R Type: Expression(Integer) +--E 251 + +--S 252 of 510 +a0249:= integrate(t0249,x) +--R +--R +--R (229) +--R 2 10 2 8 2 6 2 4 +--R 10240a cos(x) - 25088a cos(x) + 7616a cos(x) + 16744a cos(x) +--R + +--R 2 2 2 +--R - 9366a cos(x) - 140a +--R * +--R sin(x) +--R + +--R 2 9 2 7 2 5 2 3 +--R - 19712a cos(x) + 52864a cos(x) - 44044a cos(x) + 8638a cos(x) +--R + +--R 2 +--R 2254a cos(x) +--R * +--R +--------+ +--R |a cos(x) +--R |-------- +--R \| sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R 5120a \|2 cos(x) - 21120a \|2 cos(x) + 20512a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 2 2 +-+ +--R - 702a \|2 cos(x) - 3758a \|2 cos(x) - 10a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 11 2 +-+ 9 2 +-+ 7 +--R - 5120a \|2 cos(x) + 3968a \|2 cos(x) + 17504a \|2 cos(x) +--R + +--R 2 +-+ 5 2 +-+ 3 2 +-+ +--R - 25270a \|2 cos(x) + 8428a \|2 cos(x) + 490a \|2 cos(x) +--R * +--R +---+ +--R \|- a +--R / +--R +-+ 8 +-+ 6 +-+ 4 +--R 9408\|2 cos(x) - 28224\|2 cos(x) + 28077\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 9114\|2 cos(x) - 147\|2 +--R * +--R sin(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 10752\|2 cos(x) - 43008\|2 cos(x) + 62160\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 35952\|2 cos(x) + 3696\|2 cos(x) + 2352\|2 cos(x) +--R * +--R +--------+ +--R +---+ |a cos(x) +--R \|- a |-------- +--R \| sin(x) +--R + +--R 10 8 6 4 +--R - 10752a cos(x) + 25536a cos(x) - 11088a cos(x) - 11403a cos(x) +--R + +--R 2 +--R 7686a cos(x) + 21a +--R * +--R sin(x) +--R + +--R 11 9 7 5 +--R - 10752a cos(x) + 49728a cos(x) - 83664a cos(x) + 60123a cos(x) +--R + +--R 3 +--R - 14406a cos(x) - 1029a cos(x) +--R Type: Union(Expression(Integer),...) +--E 252 + +--S 253 of 510 +m0249:= a0249-r0249 +--R +--R +--R (230) +--R 8 6 4 +--R - 18816a cos(x) + 56448a cos(x) - 56154a cos(x) +--R + +--R 2 +--R 18228a cos(x) + 294a +--R * +--R sin(x) +--R + +--R 11 9 7 +--R - 21504a cos(x) + 86016a cos(x) - 124320a cos(x) +--R + +--R 5 3 +--R 71904a cos(x) - 7392a cos(x) - 4704a cos(x) +--R * +--R +--------+ +--R +---+ |a cos(x) +--R \|- a |-------- +--R \| sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R 10752a \|2 cos(x) - 25536a \|2 cos(x) + 11088a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 2 2 +-+ +--R 11403a \|2 cos(x) - 7686a \|2 cos(x) - 21a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 11 2 +-+ 9 2 +-+ 7 +--R 10752a \|2 cos(x) - 49728a \|2 cos(x) + 83664a \|2 cos(x) +--R + +--R 2 +-+ 5 2 +-+ 3 2 +-+ +--R - 60123a \|2 cos(x) + 14406a \|2 cos(x) + 1029a \|2 cos(x) +--R * +--R +---------+ +--R | 3 +-+ +------+ +--R \|a cot(x) log(\|2 \|cot(x) + cot(x) + 1) +--R + +--R 8 6 4 +--R 18816a cos(x) - 56448a cos(x) + 56154a cos(x) +--R + +--R 2 +--R - 18228a cos(x) - 294a +--R * +--R sin(x) +--R + +--R 11 9 7 +--R 21504a cos(x) - 86016a cos(x) + 124320a cos(x) +--R + +--R 5 3 +--R - 71904a cos(x) + 7392a cos(x) + 4704a cos(x) +--R * +--R +--------+ +--R +---+ |a cos(x) +--R \|- a |-------- +--R \| sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R - 10752a \|2 cos(x) + 25536a \|2 cos(x) - 11088a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 2 2 +-+ +--R - 11403a \|2 cos(x) + 7686a \|2 cos(x) + 21a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 11 2 +-+ 9 2 +-+ 7 +--R - 10752a \|2 cos(x) + 49728a \|2 cos(x) - 83664a \|2 cos(x) +--R + +--R 2 +-+ 5 2 +-+ 3 2 +-+ +--R 60123a \|2 cos(x) - 14406a \|2 cos(x) - 1029a \|2 cos(x) +--R * +--R +---------+ +--R | 3 +-+ +------+ +--R \|a cot(x) log(- \|2 \|cot(x) + cot(x) + 1) +--R + +--R 8 6 4 +--R 37632a cos(x) - 112896a cos(x) + 112308a cos(x) +--R + +--R 2 +--R - 36456a cos(x) - 588a +--R * +--R sin(x) +--R + +--R 11 9 7 +--R 43008a cos(x) - 172032a cos(x) + 248640a cos(x) +--R + +--R 5 3 +--R - 143808a cos(x) + 14784a cos(x) + 9408a cos(x) +--R * +--R +--------+ +--R +---+ |a cos(x) +--R \|- a |-------- +--R \| sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R - 21504a \|2 cos(x) + 51072a \|2 cos(x) - 22176a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 2 2 +-+ +--R - 22806a \|2 cos(x) + 15372a \|2 cos(x) + 42a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 11 2 +-+ 9 2 +-+ 7 +--R - 21504a \|2 cos(x) + 99456a \|2 cos(x) - 167328a \|2 cos(x) +--R + +--R 2 +-+ 5 2 +-+ 3 2 +-+ +--R 120246a \|2 cos(x) - 28812a \|2 cos(x) - 2058a \|2 cos(x) +--R * +--R +---------+ +--R | 3 +-+ +------+ +--R \|a cot(x) atan(\|2 \|cot(x) + 1) +--R + +--R 8 6 4 +--R 37632a cos(x) - 112896a cos(x) + 112308a cos(x) +--R + +--R 2 +--R - 36456a cos(x) - 588a +--R * +--R sin(x) +--R + +--R 11 9 7 +--R 43008a cos(x) - 172032a cos(x) + 248640a cos(x) +--R + +--R 5 3 +--R - 143808a cos(x) + 14784a cos(x) + 9408a cos(x) +--R * +--R +--------+ +--R +---+ |a cos(x) +--R \|- a |-------- +--R \| sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R - 21504a \|2 cos(x) + 51072a \|2 cos(x) - 22176a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 2 2 +-+ +--R - 22806a \|2 cos(x) + 15372a \|2 cos(x) + 42a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 11 2 +-+ 9 2 +-+ 7 +--R - 21504a \|2 cos(x) + 99456a \|2 cos(x) - 167328a \|2 cos(x) +--R + +--R 2 +-+ 5 2 +-+ 3 2 +-+ +--R 120246a \|2 cos(x) - 28812a \|2 cos(x) - 2058a \|2 cos(x) +--R * +--R +---------+ +--R | 3 +-+ +------+ +--R \|a cot(x) atan(\|2 \|cot(x) - 1) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 10752a\|2 cos(x) - 32256a\|2 cos(x) + 32088a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 10416a\|2 cos(x) - 168a\|2 +--R * +--R 3 +--R cot(x) +--R + +--R +-+ 8 +-+ 6 +--R - 25088a\|2 cos(x) + 75264a\|2 cos(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R - 74872a\|2 cos(x) + 24304a\|2 cos(x) + 392a\|2 +--R * +--R cot(x) +--R * +--R sin(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 12288a\|2 cos(x) - 49152a\|2 cos(x) + 71040a\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 41088a\|2 cos(x) + 4224a\|2 cos(x) + 2688a\|2 cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R +-+ 11 +-+ 9 +--R - 28672a\|2 cos(x) + 114688a\|2 cos(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 165760a\|2 cos(x) + 95872a\|2 cos(x) - 9856a\|2 cos(x) +--R + +--R +-+ +--R - 6272a\|2 cos(x) +--R * +--R cot(x) +--R * +--R +--------+ +--R +---+ |a cos(x) +--R \|- a |-------- +--R \| sin(x) +--R + +--R 2 10 2 8 2 6 +--R - 12288a cos(x) + 29184a cos(x) - 12672a cos(x) +--R + +--R 2 4 2 2 2 +--R - 13032a cos(x) + 8784a cos(x) + 24a +--R * +--R 3 +--R cot(x) +--R + +--R 2 10 2 8 2 6 +--R 28672a cos(x) - 68096a cos(x) + 29568a cos(x) +--R + +--R 2 4 2 2 2 +--R 30408a cos(x) - 20496a cos(x) - 56a +--R * +--R cot(x) +--R * +--R sin(x) +--R + +--R 2 11 2 9 2 7 +--R - 12288a cos(x) + 56832a cos(x) - 95616a cos(x) +--R + +--R 2 5 2 3 2 +--R 68712a cos(x) - 16464a cos(x) - 1176a cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 2 11 2 9 2 7 +--R 28672a cos(x) - 132608a cos(x) + 223104a cos(x) +--R + +--R 2 5 2 3 2 +--R - 160328a cos(x) + 38416a cos(x) + 2744a cos(x) +--R * +--R cot(x) +--R * +--R +---------+ +--R +------+ | 3 +--R \|cot(x) \|a cot(x) +--R + +--R 2 10 2 8 2 6 +--R 40960a cos(x) - 100352a cos(x) + 30464a cos(x) +--R + +--R 2 4 2 2 2 +--R 66976a cos(x) - 37464a cos(x) - 560a +--R * +--R cot(x)sin(x) +--R + +--R 2 9 2 7 2 5 +--R - 78848a cos(x) + 211456a cos(x) - 176176a cos(x) +--R + +--R 2 3 2 +--R 34552a cos(x) + 9016a cos(x) +--R * +--R cot(x) +--R * +--R +--------+ +--R |a cos(x) +--R |-------- +--R \| sin(x) +--R + +--R 2 +-+ 10 2 +-+ 8 2 +-+ 6 +--R 20480a \|2 cos(x) - 84480a \|2 cos(x) + 82048a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 2 2 +-+ +--R - 2808a \|2 cos(x) - 15032a \|2 cos(x) - 40a \|2 +--R * +--R cot(x)sin(x) +--R + +--R 2 +-+ 11 2 +-+ 9 +--R - 20480a \|2 cos(x) + 15872a \|2 cos(x) +--R + +--R 2 +-+ 7 2 +-+ 5 2 +-+ 3 +--R 70016a \|2 cos(x) - 101080a \|2 cos(x) + 33712a \|2 cos(x) +--R + +--R 2 +-+ +--R 1960a \|2 cos(x) +--R * +--R cot(x) +--R * +--R +---+ +--R \|- a +--R * +--R +------+ +--R \|cot(x) +--R / +--R +-+ 8 +-+ 6 +-+ 4 +--R 37632\|2 cos(x) - 112896\|2 cos(x) + 112308\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 36456\|2 cos(x) - 588\|2 +--R * +--R cot(x)sin(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 43008\|2 cos(x) - 172032\|2 cos(x) + 248640\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 143808\|2 cos(x) + 14784\|2 cos(x) + 9408\|2 cos(x) +--R * +--R cot(x) +--R * +--R +--------+ +--R +---+ |a cos(x) +--R \|- a |-------- +--R \| sin(x) +--R + +--R 10 8 6 +--R - 43008a cos(x) + 102144a cos(x) - 44352a cos(x) +--R + +--R 4 2 +--R - 45612a cos(x) + 30744a cos(x) + 84a +--R * +--R cot(x)sin(x) +--R + +--R 11 9 7 +--R - 43008a cos(x) + 198912a cos(x) - 334656a cos(x) +--R + +--R 5 3 +--R 240492a cos(x) - 57624a cos(x) - 4116a cos(x) +--R * +--R cot(x) +--R * +--R +------+ +--R \|cot(x) +--R Type: Expression(Integer) +--E 253 + +--S 254 of 510 +d0249:= D(m0249,x) +--R +--R +--R (231) +--R +-+ 15 +-+ 13 +--R 9175040a\|2 cos(x) - 22020096a\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +--R 24399872a\|2 cos(x) - 24485888a\|2 cos(x) +--R + +--R +-+ 7 +-+ 5 +--R 17492608a\|2 cos(x) - 4528384a\|2 cos(x) +--R + +--R +-+ 3 +-+ +--R - 24724a\|2 cos(x) - 196a\|2 cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 18 +-+ 16 +--R - 5242880a\|2 cos(x) + 22544384a\|2 cos(x) +--R + +--R +-+ 14 +-+ 12 +--R - 8962048a\|2 cos(x) - 88121344a\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +--R 159368704a\|2 cos(x) - 97816832a\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R 16486708a\|2 cos(x) + 1723862a\|2 cos(x) + 19110a\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 19 +-+ 17 +--R 5242880a\|2 cos(x) + 7864320a\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +--R - 120799232a\|2 cos(x) + 278634496a\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +--R - 258696704a\|2 cos(x) + 87071488a\|2 cos(x) +--R + +--R +-+ 7 +-+ 5 +--R 7177548a\|2 cos(x) - 6162702a\|2 cos(x) +--R + +--R +-+ 3 +-+ +--R - 331996a\|2 cos(x) - 98a\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 20 +-+ 18 +--R - 5242880a\|2 cos(x) + 5767168a\|2 cos(x) +--R + +--R +-+ 16 +-+ 14 +--R 34553856a\|2 cos(x) - 87760896a\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R 76318208a\|2 cos(x) - 25619712a\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 3794484a\|2 cos(x) - 2948498a\|2 cos(x) + 1138270a\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 21 +-+ 19 +--R 5242880a\|2 cos(x) - 28573696a\|2 cos(x) +--R + +--R +-+ 17 +-+ 15 +--R 65847296a\|2 cos(x) - 83144704a\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R 62200320a\|2 cos(x) - 27733888a\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 6985804a\|2 cos(x) - 858746a\|2 cos(x) + 34832a\|2 cos(x) +--R + +--R +-+ 3 +--R - 98a\|2 cos(x) +--R * +--R sin(x) +--R * +--R +--------+ +--R +---+ |a cos(x) +--R \|- a |-------- +--R \| sin(x) +--R + +--R 2 18 2 16 2 14 +--R 2621440a cos(x) - 2359296a cos(x) - 15130624a cos(x) +--R + +--R 2 12 2 10 2 8 +--R 69144576a cos(x) - 115370752a cos(x) + 78913408a cos(x) +--R + +--R 2 6 2 4 2 2 +--R - 17379222a cos(x) - 432229a cos(x) - 3773a cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 19 2 17 2 15 +--R - 10485760a cos(x) + 44040192a cos(x) + 2064384a cos(x) +--R + +--R 2 13 2 11 2 9 +--R - 203685888a cos(x) + 297106432a cos(x) - 139654144a cos(x) +--R + +--R 2 7 2 5 2 3 2 +--R 1823192a cos(x) + 8659898a cos(x) + 131649a cos(x) + 21a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 20 2 18 2 16 +--R 5242880a cos(x) + 26738688a cos(x) - 187023360a cos(x) +--R + +--R 2 14 2 12 2 10 +--R 358932480a cos(x) - 292935168a cos(x) + 86458624a cos(x) +--R + +--R 2 8 2 6 2 4 +--R 7002324a cos(x) - 3276728a cos(x) - 1139397a cos(x) +--R + +--R 2 2 +--R - 343a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 21 2 19 2 17 +--R - 10485760a cos(x) + 54525952a cos(x) - 119046144a cos(x) +--R + +--R 2 15 2 13 2 11 +--R 141066240a cos(x) - 97707008a cos(x) + 39510016a cos(x) +--R + +--R 2 9 2 7 2 5 2 3 +--R - 8711976a cos(x) + 872034a cos(x) - 23375a cos(x) + 21a cos(x) +--R * +--R sin(x) +--R + +--R 2 22 2 20 2 18 +--R 2621440a cos(x) - 14942208a cos(x) + 36249600a cos(x) +--R + +--R 2 16 2 14 2 12 +--R - 48607232a cos(x) + 39089408a cos(x) - 19081856a cos(x) +--R + +--R 2 10 2 8 2 6 2 4 +--R 5423978a cos(x) - 797867a cos(x) + 45080a cos(x) - 343a cos(x) +--R * +--R +---------+ +--R | 3 +--R \|a cot(x) +--R + +--R 2 18 2 16 2 14 +--R - 5505024a cos(x) + 20643840a cos(x) - 21762048a cos(x) +--R + +--R 2 12 2 10 2 8 +--R - 6472704a cos(x) + 23275392a cos(x) - 7437024a cos(x) +--R + +--R 2 6 2 4 2 2 2 +--R - 5563509a cos(x) + 2805663a cos(x) + 15393a cos(x) + 21a +--R * +--R 6 4 +--R cot(x) sin(x) +--R + +--R 2 19 2 17 2 15 +--R - 11010048a cos(x) + 66060288a cos(x) - 143474688a cos(x) +--R + +--R 2 13 2 11 2 9 +--R 111820800a cos(x) + 50555904a cos(x) - 146485248a cos(x) +--R + +--R 2 7 2 5 2 3 +--R 91052052a cos(x) - 17473596a cos(x) - 1041348a cos(x) +--R + +--R 2 +--R - 4116a cos(x) +--R * +--R 6 3 +--R cot(x) sin(x) +--R + +--R 2 20 2 18 2 16 +--R - 5505024a cos(x) + 64684032a cos(x) - 273616896a cos(x) +--R + +--R 2 14 2 12 2 10 +--R 584285184a cos(x) - 695796864a cos(x) + 457130016a cos(x) +--R + +--R 2 8 2 6 2 4 +--R - 139547541a cos(x) + 2536191a cos(x) + 5714625a cos(x) +--R + +--R 2 2 +--R 116277a cos(x) +--R * +--R 6 2 +--R cot(x) sin(x) +--R + +--R 2 21 2 19 2 17 +--R 11010048a cos(x) - 77070336a cos(x) + 226394112a cos(x) +--R + +--R 2 15 2 13 2 11 +--R - 356450304a cos(x) + 313625088a cos(x) - 137507328a cos(x) +--R + +--R 2 9 2 7 2 5 +--R 10085376a cos(x) + 12622848a cos(x) - 2182656a cos(x) +--R + +--R 2 3 +--R - 526848a cos(x) +--R * +--R 6 +--R cot(x) sin(x) +--R * +--R +--------+ +--R |a cos(x) +--R |-------- +--R \| sin(x) +--R + +--R 2 +-+ 17 2 +-+ 15 +--R 9633792a \|2 cos(x) - 42147840a \|2 cos(x) +--R + +--R 2 +-+ 13 2 +-+ 11 +--R 65178624a \|2 cos(x) - 32024832a \|2 cos(x) +--R + +--R 2 +-+ 9 2 +-+ 7 +--R - 17898720a \|2 cos(x) + 23967174a \|2 cos(x) +--R + +--R 2 +-+ 5 2 +-+ 3 2 +-+ +--R - 6581778a \|2 cos(x) - 126126a \|2 cos(x) - 294a \|2 cos(x) +--R * +--R 6 3 +--R cot(x) sin(x) +--R + +--R 2 +-+ 20 2 +-+ 18 +--R 11010048a \|2 cos(x) - 49545216a \|2 cos(x) +--R + +--R 2 +-+ 16 2 +-+ 14 +--R 56598528a \|2 cos(x) + 72253440a \|2 cos(x) +--R + +--R 2 +-+ 12 2 +-+ 10 +--R - 246527232a \|2 cos(x) + 249142656a \|2 cos(x) +--R + +--R 2 +-+ 8 2 +-+ 6 +--R - 107627814a \|2 cos(x) + 11833458a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 2 +--R 2843022a \|2 cos(x) + 19110a \|2 cos(x) +--R * +--R 6 2 +--R cot(x) sin(x) +--R + +--R 2 +-+ 21 2 +-+ 19 +--R 11010048a \|2 cos(x) - 83951616a \|2 cos(x) +--R + +--R 2 +-+ 17 2 +-+ 15 +--R 269058048a \|2 cos(x) - 466400256a \|2 cos(x) +--R + +--R 2 +-+ 13 2 +-+ 11 +--R 463959552a \|2 cos(x) - 251483232a \|2 cos(x) +--R + +--R 2 +-+ 9 2 +-+ 7 +--R 53757312a \|2 cos(x) + 8100288a \|2 cos(x) +--R + +--R 2 +-+ 5 2 +-+ 3 +--R - 3819648a \|2 cos(x) - 230496a \|2 cos(x) +--R * +--R 6 +--R cot(x) sin(x) +--R * +--R +---+ +--R \|- a +--R / +--R 18 16 14 +--R 5505024cos(x) - 20643840cos(x) + 21762048cos(x) +--R + +--R 12 10 8 +--R 6472704cos(x) - 23275392cos(x) + 7437024cos(x) +--R + +--R 6 4 2 +--R 5563509cos(x) - 2805663cos(x) - 15393cos(x) - 21 +--R * +--R 4 +--R sin(x) +--R + +--R 19 17 15 +--R 11010048cos(x) - 66060288cos(x) + 143474688cos(x) +--R + +--R 13 11 9 +--R - 111820800cos(x) - 50555904cos(x) + 146485248cos(x) +--R + +--R 7 5 3 +--R - 91052052cos(x) + 17473596cos(x) + 1041348cos(x) + 4116cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 20 18 16 +--R 5505024cos(x) - 64684032cos(x) + 273616896cos(x) +--R + +--R 14 12 10 +--R - 584285184cos(x) + 695796864cos(x) - 457130016cos(x) +--R + +--R 8 6 4 +--R 139547541cos(x) - 2536191cos(x) - 5714625cos(x) +--R + +--R 2 +--R - 116277cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 21 19 17 +--R - 11010048cos(x) + 77070336cos(x) - 226394112cos(x) +--R + +--R 15 13 11 +--R 356450304cos(x) - 313625088cos(x) + 137507328cos(x) +--R + +--R 9 7 5 +--R - 10085376cos(x) - 12622848cos(x) + 2182656cos(x) +--R + +--R 3 +--R 526848cos(x) +--R * +--R sin(x) +--R * +--R +--------+ +--R |a cos(x) +--R |-------- +--R \| sin(x) +--R + +--R +-+ 17 +-+ 15 +--R - 9633792\|2 cos(x) + 42147840\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R - 65178624\|2 cos(x) + 32024832\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 17898720\|2 cos(x) - 23967174\|2 cos(x) + 6581778\|2 cos(x) +--R + +--R +-+ 3 +-+ +--R 126126\|2 cos(x) + 294\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 20 +-+ 18 +--R - 11010048\|2 cos(x) + 49545216\|2 cos(x) +--R + +--R +-+ 16 +-+ 14 +--R - 56598528\|2 cos(x) - 72253440\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R 246527232\|2 cos(x) - 249142656\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 107627814\|2 cos(x) - 11833458\|2 cos(x) - 2843022\|2 cos(x) +--R + +--R +-+ 2 +--R - 19110\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 21 +-+ 19 +--R - 11010048\|2 cos(x) + 83951616\|2 cos(x) +--R + +--R +-+ 17 +-+ 15 +--R - 269058048\|2 cos(x) + 466400256\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R - 463959552\|2 cos(x) + 251483232\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 53757312\|2 cos(x) - 8100288\|2 cos(x) + 3819648\|2 cos(x) +--R + +--R +-+ 3 +--R 230496\|2 cos(x) +--R * +--R sin(x) +--R * +--R +---+ +--R \|- a +--R * +--R +---------+ +--R | 3 +--R \|a cot(x) +--R Type: Expression(Integer) +--E 254 + +--S 255 of 510 +t0250:= 1/(a*cot(x)^2)^(1/2) +--R +--R +--R 1 +--R (232) ------------ +--R +---------+ +--R | 2 +--R \|a cot(x) +--R Type: Expression(Integer) +--E 255 + +--S 256 of 510 +r0250:= -cot(x)*log(cos(x))/(a*cot(x)^2)^(1/2) +--R +--R +--R cot(x)log(cos(x)) +--R (233) - ----------------- +--R +---------+ +--R | 2 +--R \|a cot(x) +--R Type: Expression(Integer) +--E 256 + +--S 257 of 510 +a0250:= integrate(t0250,x) +--R +--R +--R 2 +--R log(-----------) +--R cos(2x) + 1 +--R (234) ---------------- +--R +-+ +--R 2\|a +--R Type: Union(Expression(Integer),...) +--E 257 + +--S 258 of 510 +m0250:= a0250-r0250 +--R +--R +--R +---------+ +--R 2 | 2 +-+ +--R log(-----------)\|a cot(x) + 2cot(x)\|a log(cos(x)) +--R cos(2x) + 1 +--R (235) ----------------------------------------------------- +--R +---------+ +--R +-+ | 2 +--R 2\|a \|a cot(x) +--R Type: Expression(Integer) +--E 258 + +--S 259 of 510 +d0250:= D(m0250,x) +--R +--R +--R +---------+ +--R +-+ | 2 +--R cos(x)sin(2x)\|a \|a cot(x) + (- a cos(2x) - a)cot(x)sin(x) +--R (236) ------------------------------------------------------------- +--R +---------+ +--R | 2 +--R (a cos(x)cos(2x) + a cos(x))\|a cot(x) +--R Type: Expression(Integer) +--E 259 + +--S 260 of 510 +t0251:= 1/(a*cot(x)^3)^(1/2) +--R +--R +--R 1 +--R (237) ------------ +--R +---------+ +--R | 3 +--R \|a cot(x) +--R Type: Expression(Integer) +--E 260 + +--S 261 of 510 +r0251:= 1/2/(a*cot(x)^3)^(1/2)*cot(x)*(4-cot(x)^(1/2)*(-2^(1/2)*_ + atan(-1+2^(1/2)*cot(x)^(1/2))-2^(1/2)*atan(1+2^(1/2)*cot(x)^(1/2))-_ + 1/2*log(1-2^(1/2)*cot(x)^(1/2)+cot(x))*2^(1/2)+_ + 1/2*log(1+2^(1/2)*cot(x)^(1/2)+cot(x))*2^(1/2))) +--R +--R +--R (238) +--R +-+ +------+ +-+ +------+ +--R - \|2 cot(x)\|cot(x) log(\|2 \|cot(x) + cot(x) + 1) +--R + +--R +-+ +------+ +-+ +------+ +--R \|2 cot(x)\|cot(x) log(- \|2 \|cot(x) + cot(x) + 1) +--R + +--R +-+ +------+ +-+ +------+ +--R 2\|2 cot(x)\|cot(x) atan(\|2 \|cot(x) + 1) +--R + +--R +-+ +------+ +-+ +------+ +--R 2\|2 cot(x)\|cot(x) atan(\|2 \|cot(x) - 1) + 8cot(x) +--R / +--R +---------+ +--R | 3 +--R 4\|a cot(x) +--R Type: Expression(Integer) +--E 261 + +--S 262 of 510 +a0251:= integrate(t0251,x) +--R +--R +--R (239) +--R +--------+ +--R 2 |a cos(x) +--R (- 2cos(x) + 2)sin(x) |-------- +--R \| sin(x) +--R + +--R +-+ 2 +-+ 3 +-+ +---+ +--R (- \|2 cos(x) sin(x) + \|2 cos(x) - \|2 cos(x))\|- a +--R / +--R +--------+ +--R +-+ 3 +-+ +---+ |a cos(x) 2 3 +--R (\|2 cos(x) - \|2 cos(x))\|- a |-------- - a cos(x) sin(x) - a cos(x) +--R \| sin(x) +--R + +--R a cos(x) +--R Type: Union(Expression(Integer),...) +--E 262 + +--S 263 of 510 +m0251:= a0251-r0251 +--R +--R +--R (240) +--R +--------+ +--R 3 +---+ |a cos(x) +--R (2cos(x) - 2cos(x))cot(x)\|- a |-------- +--R \| sin(x) +--R + +--R +-+ 2 +-+ 3 +-+ +--R - a\|2 cos(x) cot(x)sin(x) + (- a\|2 cos(x) + a\|2 cos(x))cot(x) +--R * +--R +------+ +-+ +------+ +--R \|cot(x) log(\|2 \|cot(x) + cot(x) + 1) +--R + +--R +--------+ +--R 3 +---+ |a cos(x) +--R (- 2cos(x) + 2cos(x))cot(x)\|- a |-------- +--R \| sin(x) +--R + +--R +-+ 2 +-+ 3 +-+ +--R a\|2 cos(x) cot(x)sin(x) + (a\|2 cos(x) - a\|2 cos(x))cot(x) +--R * +--R +------+ +-+ +------+ +--R \|cot(x) log(- \|2 \|cot(x) + cot(x) + 1) +--R + +--R +--------+ +--R 3 +---+ |a cos(x) +--R (- 4cos(x) + 4cos(x))cot(x)\|- a |-------- +--R \| sin(x) +--R + +--R +-+ 2 +-+ 3 +-+ +--R 2a\|2 cos(x) cot(x)sin(x) + (2a\|2 cos(x) - 2a\|2 cos(x))cot(x) +--R * +--R +------+ +-+ +------+ +--R \|cot(x) atan(\|2 \|cot(x) + 1) +--R + +--R +--------+ +--R 3 +---+ |a cos(x) +--R (- 4cos(x) + 4cos(x))cot(x)\|- a |-------- +--R \| sin(x) +--R + +--R +-+ 2 +-+ 3 +-+ +--R 2a\|2 cos(x) cot(x)sin(x) + (2a\|2 cos(x) - 2a\|2 cos(x))cot(x) +--R * +--R +------+ +-+ +------+ +--R \|cot(x) atan(\|2 \|cot(x) - 1) +--R + +--R +--------+ +--R 2 |a cos(x) +--R (- 8cos(x) + 8)sin(x) |-------- +--R \| sin(x) +--R + +--R +-+ 2 +-+ 3 +-+ +---+ +--R (- 4\|2 cos(x) sin(x) + 4\|2 cos(x) - 4\|2 cos(x))\|- a +--R * +--R +---------+ +--R | 3 +--R \|a cot(x) +--R + +--R +--------+ +--R +-+ 3 +-+ +---+ |a cos(x) +--R (- 8\|2 cos(x) + 8\|2 cos(x))cot(x)\|- a |-------- +--R \| sin(x) +--R + +--R 2 3 +--R 8a cos(x) cot(x)sin(x) + (8a cos(x) - 8a cos(x))cot(x) +--R / +--R +--------+ +--R +-+ 3 +-+ +---+ |a cos(x) 2 +--R (4\|2 cos(x) - 4\|2 cos(x))\|- a |-------- - 4a cos(x) sin(x) +--R \| sin(x) +--R + +--R 3 +--R - 4a cos(x) + 4a cos(x) +--R * +--R +---------+ +--R | 3 +--R \|a cot(x) +--R Type: Expression(Integer) +--E 263 + +--S 264 of 510 +d0251:= D(m0251,x) +--R +--R +--R (241) +--R +-+ 3 +-+ 4 +--R (2\|2 cos(x) + 2\|2 cos(x))sin(x) +--R + +--R +-+ 4 +-+ 2 +-+ 3 +--R (- 2\|2 cos(x) + 4\|2 cos(x) - 2\|2 )sin(x) +--R + +--R +-+ 5 +-+ 3 2 +--R (2\|2 cos(x) - 2\|2 cos(x) )sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R (- 2\|2 cos(x) + 4\|2 cos(x) - 2\|2 cos(x) )sin(x) +--R * +--R +--------+ +--R +---+ |a cos(x) +--R \|- a |-------- +--R \| sin(x) +--R + +--R 3 4 +--R (- a cos(x) - 3a cos(x))sin(x) +--R + +--R 4 2 3 +--R (4a cos(x) - a cos(x) + a)sin(x) +--R + +--R 5 3 2 +--R (- 2a cos(x) + 3a cos(x) - a cos(x))sin(x) +--R + +--R 6 4 2 7 5 +--R (4a cos(x) - 5a cos(x) + a cos(x) )sin(x) - a cos(x) + 2a cos(x) +--R + +--R 3 +--R - a cos(x) +--R * +--R +---------+ +--R | 3 +--R \|a cot(x) +--R + +--R 3 4 4 2 3 +--R - a cos(x) sin(x) + (- 2a cos(x) + 2a cos(x) )sin(x) +--R + +--R 5 3 2 +--R (- a cos(x) + 2a cos(x) - a cos(x))sin(x) +--R + +--R 6 4 2 +--R (2a cos(x) - 4a cos(x) + 2a cos(x) )sin(x) +--R * +--R +--------+ +--R |a cos(x) +--R |-------- +--R \| sin(x) +--R + +--R +-+ 5 +-+ 3 2 +--R (2a\|2 cos(x) - 2a\|2 cos(x) )sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R (2a\|2 cos(x) - 4a\|2 cos(x) + 2a\|2 cos(x) )sin(x) +--R * +--R +---+ +--R \|- a +--R / +--R 3 4 4 2 3 +--R a cos(x) sin(x) + (2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 5 3 2 +--R (a cos(x) - 2a cos(x) + a cos(x))sin(x) +--R + +--R 6 4 2 +--R (- 2a cos(x) + 4a cos(x) - 2a cos(x) )sin(x) +--R * +--R +--------+ +--R |a cos(x) +--R |-------- +--R \| sin(x) +--R + +--R +-+ 5 +-+ 3 2 +--R (- 2a\|2 cos(x) + 2a\|2 cos(x) )sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R (- 2a\|2 cos(x) + 4a\|2 cos(x) - 2a\|2 cos(x) )sin(x) +--R * +--R +---+ +--R \|- a +--R * +--R +---------+ +--R | 3 +--R \|a cot(x) +--R Type: Expression(Integer) +--E 264 + +--S 265 of 510 +t0252:= (1+%i*cot(x))^3 +--R +--R +--R 3 2 +--R (242) - %i cot(x) - 3cot(x) + 3%i cot(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 265 + +--S 266 of 510 +r0252:= 4*x+3*cot(x)+1/2*%i*cot(x)^2+4*%i*log(sin(x)) +--R +--R +--R 1 2 +--R (243) 4%i log(sin(x)) + - %i cot(x) + 3cot(x) + 4x +--R 2 +--R Type: Expression(Complex(Fraction(Integer))) +--E 266 + +--S 267 of 510 +a0252:= integrate(t0252,x) +--R +--R +--R (244) +--R sin(2x) +--R (8%i cos(2x) - 8%i)log(-----------) +--R cos(2x) + 1 +--R + +--R 2 +--R (- 4%i cos(2x) + 4%i)log(-----------) - 6sin(2x) + (8x - %i)cos(2x) - 8x +--R cos(2x) + 1 +--R + +--R - %i +--R / +--R 2cos(2x) - 2 +--R Type: Union(Expression(Complex(Integer)),...) +--E 267 + +--S 268 of 510 +m0252:= a0252-r0252 +--R +--R +--R (245) +--R sin(2x) +--R (4%i cos(2x) - 4%i)log(-----------) + (- 4%i cos(2x) + 4%i)log(sin(x)) +--R cos(2x) + 1 +--R + +--R 2 +--R (- 2%i cos(2x) + 2%i)log(-----------) - 3sin(2x) +--R cos(2x) + 1 +--R + +--R 1 1 2 1 +--R (- - %i cos(2x) + - %i)cot(x) + (- 3cos(2x) + 3)cot(x) - - %i cos(2x) +--R 2 2 2 +--R + +--R 1 +--R - - %i +--R 2 +--R / +--R cos(2x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 268 + +--S 269 of 510 +d0252:= D(m0252,x) +--R +--R +--R (246) +--R 3 +--R (- 6cos(2x) - 6)sin(x)sin(2x) +--R + +--R 2 2 +--R (4%i cos(2x) - 10%i cos(2x) + 2%i)sin(x)sin(2x) +--R + +--R 3 2 3 +--R (%i cos(2x) - %i cos(2x) - %i cos(2x) + %i)cot(x) +--R + +--R 3 2 2 +--R (3cos(2x) - 3cos(2x) - 3cos(2x) + 3)cot(x) +--R + +--R 3 2 3 +--R (%i cos(2x) - %i cos(2x) - %i cos(2x) + %i)cot(x) - 3cos(2x) +--R + +--R 2 +--R - 3cos(2x) + 3cos(2x) + 3 +--R * +--R sin(x) +--R + +--R 3 2 +--R - 4%i cos(x)cos(2x) + 4%i cos(x)cos(2x) + 4%i cos(x)cos(2x) +--R + +--R - 4%i cos(x) +--R * +--R sin(2x) +--R + +--R 4 3 2 +--R (8%i cos(2x) - 8%i cos(2x) - 8%i cos(2x) + 8%i cos(2x))sin(x) +--R / +--R 3 2 +--R (cos(2x) - cos(2x) - cos(2x) + 1)sin(x)sin(2x) +--R Type: Expression(Complex(Fraction(Integer))) +--E 269 + +--S 270 of 510 +t0253:= (1+%i*cot(x))^2 +--R +--R +--R 2 +--R (247) - cot(x) + 2%i cot(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 270 + +--S 271 of 510 +r0253:= 2*x+cot(x)+2*%i*log(sin(x)) +--R +--R +--R (248) 2%i log(sin(x)) + cot(x) + 2x +--R Type: Expression(Complex(Integer)) +--E 271 + +--S 272 of 510 +a0253:= integrate(t0253,x) +--R +--R +--R (249) +--R sin(2x) 2 +--R 2%i sin(2x)log(-----------) - %i sin(2x)log(-----------) + 2x sin(2x) +--R cos(2x) + 1 cos(2x) + 1 +--R + +--R cos(2x) + 1 +--R / +--R sin(2x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 272 + +--S 273 of 510 +m0253:= a0253-r0253 +--R +--R +--R (250) +--R sin(2x) +--R 2%i sin(2x)log(-----------) - 2%i sin(2x)log(sin(x)) +--R cos(2x) + 1 +--R + +--R 2 +--R - %i sin(2x)log(-----------) - cot(x)sin(2x) + cos(2x) + 1 +--R cos(2x) + 1 +--R / +--R sin(2x) +--R Type: Expression(Complex(Integer)) +--E 273 + +--S 274 of 510 +d0253:= D(m0253,x) +--R +--R +--R (251) +--R 3 +--R 2%i sin(x)sin(2x) +--R + +--R 2 +--R ((cos(2x) + 1)cot(x) - cos(2x) - 1)sin(x) - 2%i cos(x)cos(2x) +--R + +--R - 2%i cos(x) +--R * +--R 2 +--R sin(2x) +--R + +--R 2 +--R (4%i cos(2x) + 4%i cos(2x))sin(x)sin(2x) +--R + +--R 3 2 +--R (- 2cos(2x) - 4cos(2x) - 2cos(2x))sin(x) +--R / +--R 2 +--R (cos(2x) + 1)sin(x)sin(2x) +--R Type: Expression(Complex(Integer)) +--E 274 + +--S 275 of 510 +t0254:= 1/(1+%i*cot(x)) +--R +--R +--R %i +--R (252) - ----------- +--R cot(x) - %i +--R Type: Expression(Complex(Integer)) +--E 275 + +--S 276 of 510 +r0254:= 1/2*x-%i/(2+2*%i*cot(x)) +--R +--R +--R x cot(x) - %i x - 1 +--R (253) ------------------- +--R 2cot(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 276 + +--S 277 of 510 +a0254:= integrate(t0254,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 277 + +--S 278 of 510 +m0254:= a0254-r0254 +--R +--R +--R (- x + 2a0254)cot(x) + %i x - 2%i a0254 + 1 +--R (254) ------------------------------------------- +--R 2cot(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 278 + +--S 279 of 510 +d0254:= D(m0254,x) +--R +--R +--R %i +--R (255) ----------- +--R cot(x) - %i +--R Type: Expression(Complex(Integer)) +--E 279 + +--S 280 of 510 +t0255:= (a+b*cot(x))^3 +--R +--R +--R 3 3 2 2 2 3 +--R (256) b cot(x) + 3a b cot(x) + 3a b cot(x) + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 510 +r0255:= a^3*x-3*a*b^2*x-3*a*b^2*cot(x)-1/2*b^3*cot(x)^2+_ + 3*a^2*b*log(sin(x))-b^3*log(sin(x)) +--R +--R +--R (257) +--R 3 2 3 2 2 2 3 +--R (- 2b + 6a b)log(sin(x)) - b cot(x) - 6a b cot(x) + (- 6a b + 2a )x +--R ---------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 510 +a0255:= integrate(t0255,x) +--R +--R +--R (258) +--R 3 2 3 2 sin(2x) +--R ((- 2b + 6a b)cos(2x) + 2b - 6a b)log(-----------) +--R cos(2x) + 1 +--R + +--R 3 2 3 2 2 2 +--R ((b - 3a b)cos(2x) - b + 3a b)log(-----------) + 6a b sin(2x) +--R cos(2x) + 1 +--R + +--R 2 3 3 2 3 3 +--R ((- 6a b + 2a )x + b )cos(2x) + (6a b - 2a )x + b +--R / +--R 2cos(2x) - 2 +--R Type: Union(Expression(Integer),...) +--E 282 + +--S 283 of 510 +m0255:= a0255-r0255 +--R +--R +--R (259) +--R 3 2 3 2 sin(2x) +--R ((- 2b + 6a b)cos(2x) + 2b - 6a b)log(-----------) +--R cos(2x) + 1 +--R + +--R 3 2 3 2 +--R ((2b - 6a b)cos(2x) - 2b + 6a b)log(sin(x)) +--R + +--R 3 2 3 2 2 2 +--R ((b - 3a b)cos(2x) - b + 3a b)log(-----------) + 6a b sin(2x) +--R cos(2x) + 1 +--R + +--R 3 3 2 2 2 3 3 +--R (b cos(2x) - b )cot(x) + (6a b cos(2x) - 6a b )cot(x) + b cos(2x) + b +--R / +--R 2cos(2x) - 2 +--R Type: Expression(Integer) +--E 283 + +--S 284 of 510 +d0255:= D(m0255,x) +--R +--R +--R (260) +--R 2 2 3 +--R (6a b cos(2x) + 6a b )sin(x)sin(2x) +--R + +--R 3 2 2 3 2 3 2 2 +--R ((- b + 3a b)cos(2x) + (4b - 6a b)cos(2x) + b + 3a b)sin(x)sin(2x) +--R + +--R 3 3 3 2 3 3 3 +--R (- b cos(2x) + b cos(2x) + b cos(2x) - b )cot(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 3a b cos(2x) + 3a b cos(2x) + 3a b cos(2x) - 3a b )cot(x) +--R + +--R 3 3 3 2 3 3 +--R (- b cos(2x) + b cos(2x) + b cos(2x) - b )cot(x) +--R + +--R 2 3 2 2 2 2 +--R 3a b cos(2x) + 3a b cos(2x) - 3a b cos(2x) - 3a b +--R * +--R sin(x) +--R + +--R 3 2 3 3 2 2 +--R (b - 3a b)cos(x)cos(2x) + (- b + 3a b)cos(x)cos(2x) +--R + +--R 3 2 3 2 +--R (- b + 3a b)cos(x)cos(2x) + (b - 3a b)cos(x) +--R * +--R sin(2x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 2b + 6a b)cos(2x) + (2b - 6a b)cos(2x) + (2b - 6a b)cos(2x) +--R + +--R 3 2 +--R (- 2b + 6a b)cos(2x) +--R * +--R sin(x) +--R / +--R 3 2 +--R (cos(2x) - cos(2x) - cos(2x) + 1)sin(x)sin(2x) +--R Type: Expression(Integer) +--E 284 + +--S 285 of 510 +t0256:= (a+b*cot(x))^2 +--R +--R +--R 2 2 2 +--R (261) b cot(x) + 2a b cot(x) + a +--R Type: Expression(Integer) +--E 285 + +--S 286 of 510 +r0256:= a^2*x-b^2*x-b^2*cot(x)+2*a*b*log(sin(x)) +--R +--R +--R 2 2 2 +--R (262) 2a b log(sin(x)) - b cot(x) + (- b + a )x +--R Type: Expression(Integer) +--E 286 + +--S 287 of 510 +a0256:= integrate(t0256,x) +--R +--R +--R (263) +--R sin(2x) 2 +--R 2a b sin(2x)log(-----------) - a b sin(2x)log(-----------) +--R cos(2x) + 1 cos(2x) + 1 +--R + +--R 2 2 2 2 +--R (- b + a )x sin(2x) - b cos(2x) - b +--R / +--R sin(2x) +--R Type: Union(Expression(Integer),...) +--E 287 + +--S 288 of 510 +m0256:= a0256-r0256 +--R +--R +--R (264) +--R sin(2x) +--R 2a b sin(2x)log(-----------) - 2a b sin(2x)log(sin(x)) +--R cos(2x) + 1 +--R + +--R 2 2 2 2 +--R - a b sin(2x)log(-----------) + b cot(x)sin(2x) - b cos(2x) - b +--R cos(2x) + 1 +--R / +--R sin(2x) +--R Type: Expression(Integer) +--E 288 + +--S 289 of 510 +d0256:= D(m0256,x) +--R +--R +--R (265) +--R 3 +--R 2a b sin(x)sin(2x) +--R + +--R 2 2 2 2 2 +--R ((- b cos(2x) - b )cot(x) + b cos(2x) + b )sin(x) +--R + +--R - 2a b cos(x)cos(2x) - 2a b cos(x) +--R * +--R 2 +--R sin(2x) +--R + +--R 2 +--R (4a b cos(2x) + 4a b cos(2x))sin(x)sin(2x) +--R + +--R 2 3 2 2 2 +--R (2b cos(2x) + 4b cos(2x) + 2b cos(2x))sin(x) +--R / +--R 2 +--R (cos(2x) + 1)sin(x)sin(2x) +--R Type: Expression(Integer) +--E 289 + +--S 290 of 510 +t0257:= 1/(4-6*cot(x)) +--R +--R +--R 1 +--R (266) - ----------- +--R 6cot(x) - 4 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 510 +r0257:= 1/13*x+3/26*log(-3*cos(x)+2*sin(x)) +--R +--R +--R 3log(2sin(x) - 3cos(x)) + 2x +--R (267) ---------------------------- +--R 26 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 510 +a0257:= integrate(t0257,x) +--R +--R +--R 2sin(2x) - 3cos(2x) - 3 2 +--R 6log(-----------------------) - 3log(-----------) + 4x +--R cos(2x) + 1 cos(2x) + 1 +--R (268) ------------------------------------------------------ +--R 52 +--R Type: Union(Expression(Integer),...) +--E 292 + +--S 293 of 510 +m0257:= a0257-r0257 +--R +--R +--R (269) +--R 2sin(2x) - 3cos(2x) - 3 2 +--R 6log(-----------------------) - 6log(2sin(x) - 3cos(x)) - 3log(-----------) +--R cos(2x) + 1 cos(2x) + 1 +--R --------------------------------------------------------------------------- +--R 52 +--R Type: Expression(Integer) +--E 293 + +--S 294 of 510 +d0257:= D(m0257,x) +--R +--R +--R (270) +--R 2 +--R (12sin(x) - 18cos(x))sin(2x) + (- 39cos(x)cos(2x) - 39cos(x))sin(2x) +--R + +--R 2 2 +--R (51cos(2x) + 78cos(2x) + 27)sin(x) - 18cos(x)cos(2x) + 18cos(x) +--R / +--R ((104cos(2x) + 104)sin(x) - 156cos(x)cos(2x) - 156cos(x))sin(2x) +--R + +--R 2 2 +--R (- 156cos(2x) - 312cos(2x) - 156)sin(x) + 234cos(x)cos(2x) +--R + +--R 468cos(x)cos(2x) + 234cos(x) +--R Type: Expression(Integer) +--E 294 + +--S 295 of 510 +t0258:= 1/(a+b*cot(x)) +--R +--R +--R 1 +--R (271) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 295 + +--S 296 of 510 +r0258:= -(-a*x+b*log(b*cos(x)+a*sin(x)))/(a^2+b^2) +--R +--R +--R - b log(a sin(x) + b cos(x)) + a x +--R (272) ---------------------------------- +--R 2 2 +--R b + a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 510 +a0258:= integrate(t0258,x) +--R +--R +--R a sin(2x) + b cos(2x) + b 2 +--R - 2b log(-------------------------) + b log(-----------) + 2a x +--R cos(2x) + 1 cos(2x) + 1 +--R (273) --------------------------------------------------------------- +--R 2 2 +--R 2b + 2a +--R Type: Union(Expression(Integer),...) +--E 297 + +--S 298 of 510 +m0258:= a0258-r0258 +--R +--R +--R (274) +--R a sin(2x) + b cos(2x) + b +--R - 2b log(-------------------------) + 2b log(a sin(x) + b cos(x)) +--R cos(2x) + 1 +--R + +--R 2 +--R b log(-----------) +--R cos(2x) + 1 +--R / +--R 2 2 +--R 2b + 2a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 510 +d0258:= D(m0258,x) +--R +--R +--R (275) +--R 2 2 2 +--R (- a b sin(x) - a b cos(x))sin(2x) +--R + +--R 3 2 3 2 +--R ((b + a b)cos(x)cos(2x) + (b + a b)cos(x))sin(2x) +--R + +--R 3 2 2 3 2 3 +--R ((- b - 2a b)cos(2x) + (- 2b - 2a b)cos(2x) - b )sin(x) +--R + +--R 2 2 2 +--R - a b cos(x)cos(2x) + a b cos(x) +--R / +--R 2 2 4 2 2 4 3 3 +--R ((a b + a )cos(2x) + a b + a )sin(x) + (a b + a b)cos(x)cos(2x) +--R + +--R 3 3 +--R (a b + a b)cos(x) +--R * +--R sin(2x) +--R + +--R 3 3 2 3 3 3 3 +--R ((a b + a b)cos(2x) + (2a b + 2a b)cos(2x) + a b + a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 4 2 2 +--R (b + a b )cos(x)cos(2x) + (2b + 2a b )cos(x)cos(2x) + (b + a b )cos(x) +--R Type: Expression(Integer) +--E 299 + +--S 300 of 510 +t0259:= 1/(a+b*cot(x))^2 +--R +--R +--R 1 +--R (276) ---------------------------- +--R 2 2 2 +--R b cot(x) + 2a b cot(x) + a +--R Type: Expression(Integer) +--E 300 + +--S 301 of 510 +r0259:= (a^2-b^2)*x/(a^2+b^2)^2+b/(a^2+b^2)/_ + (a+b*cot(x))-2*a*b*log(b*cos(x)+a*sin(x))/(a^2+b^2)^2 +--R +--R +--R (277) +--R 2 2 3 2 +--R (- 2a b cot(x) - 2a b)log(a sin(x) + b cos(x)) + (- b + a b)x cot(x) +--R + +--R 2 3 3 2 +--R (- a b + a )x + b + a b +--R / +--R 5 2 3 4 4 3 2 5 +--R (b + 2a b + a b)cot(x) + a b + 2a b + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 510 +a0259:= integrate(t0259,x) +--R +--R +--R (278) +--R 3 2 2 2 2 a sin(2x) + b cos(2x) + b +--R (- 2a b sin(2x) - 2a b cos(2x) - 2a b )log(-------------------------) +--R cos(2x) + 1 +--R + +--R 3 2 2 2 2 2 +--R (a b sin(2x) + a b cos(2x) + a b )log(-----------) +--R cos(2x) + 1 +--R + +--R 2 2 4 3 3 4 2 2 +--R (- a b + a )x sin(2x) + ((- a b + a b)x - b - a b )cos(2x) +--R + +--R 3 3 4 2 2 +--R (- a b + a b)x - b - a b +--R / +--R 2 4 4 2 6 5 3 3 5 5 3 3 +--R (a b + 2a b + a )sin(2x) + (a b + 2a b + a b)cos(2x) + a b + 2a b +--R + +--R 5 +--R a b +--R Type: Union(Expression(Integer),...) +--E 302 + +--S 303 of 510 +m0259:= a0259-r0259 +--R +--R +--R (279) +--R 3 2 4 2 3 2 3 +--R (- 2a b cot(x) - 2a b)sin(2x) + (- 2a b cos(2x) - 2a b )cot(x) +--R + +--R 3 2 3 2 +--R - 2a b cos(2x) - 2a b +--R * +--R a sin(2x) + b cos(2x) + b +--R log(-------------------------) +--R cos(2x) + 1 +--R + +--R 3 2 4 2 3 2 3 +--R (2a b cot(x) + 2a b)sin(2x) + (2a b cos(2x) + 2a b )cot(x) +--R + +--R 3 2 3 2 +--R 2a b cos(2x) + 2a b +--R * +--R log(a sin(x) + b cos(x)) +--R + +--R 3 2 4 2 3 2 3 3 2 +--R (a b cot(x) + a b)sin(2x) + (a b cos(2x) + a b )cot(x) + a b cos(2x) +--R + +--R 3 2 +--R a b +--R * +--R 2 +--R log(-----------) +--R cos(2x) + 1 +--R + +--R 2 3 4 5 2 3 5 2 3 +--R (- a b - a b)sin(2x) + ((- b - a b )cos(2x) - b - a b )cot(x) +--R + +--R 4 3 2 4 3 2 +--R (- 2a b - 2a b )cos(2x) - 2a b - 2a b +--R / +--R 2 5 4 3 6 3 4 5 2 7 +--R ((a b + 2a b + a b)cot(x) + a b + 2a b + a )sin(2x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R ((a b + 2a b + a b )cos(2x) + a b + 2a b + a b )cot(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (a b + 2a b + a b)cos(2x) + a b + 2a b + a b +--R Type: Expression(Integer) +--E 303 + +--S 304 of 510 +d0259:= D(m0259,x) +--R +--R +--R (280) +--R 4 3 2 5 2 6 3 4 2 +--R (- 2a b cot(x) - 4a b cot(x) - 2a b)sin(x) - 2a b cos(x)cot(x) +--R + +--R 4 3 5 2 +--R - 4a b cos(x)cot(x) - 2a b cos(x) +--R * +--R 3 +--R sin(2x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 2 +--R ((2a b - a b - a b )cos(2x) + 2a b - a b - a b )cot(x) +--R + +--R 2 5 2 5 3 4 5 2 3 4 5 2 +--R (4a b cos(2x) + 4a b )cot(x) + (a b - a b )cos(2x) + a b - a b +--R * +--R sin(x) +--R + +--R 7 2 5 4 3 7 2 5 4 3 2 +--R ((2b + a b + a b )cos(x)cos(2x) + (2b + a b + a b )cos(x))cot(x) +--R + +--R 6 3 4 5 2 +--R (4a b + 4a b + 4a b )cos(x)cos(2x) +--R + +--R 6 3 4 5 2 +--R (4a b + 4a b + 4a b )cos(x) +--R * +--R cot(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (a b + a b + 2a b)cos(x)cos(2x) + (a b + a b + 2a b)cos(x) +--R * +--R 2 +--R sin(2x) +--R + +--R 2 5 4 3 2 2 5 4 3 2 5 +--R (- 4a b - 6a b )cos(2x) + (- 8a b - 8a b )cos(2x) - 4a b +--R + +--R 4 3 +--R - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 2 3 4 5 2 3 4 +--R ((- 4a b - 8a b )cos(2x) + (- 8a b - 8a b )cos(2x) - 4a b ) +--R * +--R cot(x) +--R + +--R 2 5 4 3 6 2 +--R (- 2a b - 4a b - 4a b)cos(2x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (- 4a b - 8a b - 4a b)cos(2x) - 2a b - 4a b +--R * +--R sin(x) +--R + +--R 3 4 2 3 4 2 +--R (- 2a b cos(x)cos(2x) + 2a b cos(x))cot(x) +--R + +--R 2 5 2 2 5 4 3 +--R 4a b cos(x)cos(2x) + (8a b + 8a b )cos(x)cos(2x) +--R + +--R 2 5 4 3 +--R (4a b + 8a b )cos(x) +--R * +--R cot(x) +--R + +--R 6 2 6 5 2 +--R - 2a b cos(x)cos(2x) + (- 4a b + 4a b )cos(x)cos(2x) +--R + +--R 6 5 2 +--R (- 2a b + 4a b )cos(x) +--R * +--R sin(2x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- a b - 3a b )cos(2x) + (- 5a b - 7a b )cos(2x) +--R + +--R 6 3 4 6 3 4 +--R (- 7a b - 5a b )cos(2x) - 3a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 3 2 5 4 3 2 +--R - 4a b cos(2x) + (- 4a b - 8a b )cos(2x) +--R + +--R 2 5 4 3 2 5 +--R (- 8a b - 4a b )cos(2x) - 4a b +--R * +--R cot(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R (- a b - a b - 2a b )cos(2x) + (- 3a b - 5a b - 4a b )cos(2x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (- 3a b - 7a b - 2a b )cos(2x) - a b - 3a b +--R * +--R sin(x) +--R + +--R 7 2 5 3 7 2 5 2 +--R (b - a b )cos(x)cos(2x) + (b - a b )cos(x)cos(2x) +--R + +--R 7 2 5 7 2 5 +--R (- b + a b )cos(x)cos(2x) + (- b + a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 6 3 4 2 +--R 4a b cos(x)cos(2x) + (8a b + 4a b )cos(x)cos(2x) +--R + +--R 6 3 4 3 4 +--R (4a b + 8a b )cos(x)cos(2x) + 4a b cos(x) +--R * +--R cot(x) +--R + +--R 7 2 5 3 7 2 5 4 3 2 +--R (- b + a b )cos(x)cos(2x) + (- 3b + a b + 2a b )cos(x)cos(2x) +--R + +--R 7 2 5 4 3 7 2 5 4 3 +--R (- 3b - a b + 4a b )cos(x)cos(2x) + (- b - a b + 2a b )cos(x) +--R / +--R 3 6 5 4 7 2 3 6 5 4 7 2 2 +--R ((a b + 2a b + a b )cos(2x) + a b + 2a b + a b )cot(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R ((2a b + 4a b + 2a b)cos(2x) + 2a b + 4a b + 2a b)cot(x) +--R + +--R 5 4 7 2 9 5 4 7 2 9 +--R (a b + 2a b + a )cos(2x) + a b + 2a b + a +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R ((a b + 2a b + a b )cos(x)cos(2x) + (a b + 2a b + a b )cos(x)) +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 5 4 7 2 +--R (2a b + 4a b + 2a b )cos(x)cos(2x) +--R + +--R 3 6 5 4 7 2 +--R (2a b + 4a b + 2a b )cos(x) +--R * +--R cot(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (a b + 2a b + a b)cos(x)cos(2x) + (a b + 2a b + a b)cos(x) +--R * +--R 2 +--R sin(2x) +--R + +--R 2 7 4 5 6 3 2 +--R (2a b + 4a b + 2a b )cos(2x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (4a b + 8a b + 4a b )cos(2x) + 2a b + 4a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 5 4 7 2 2 +--R (4a b + 8a b + 4a b )cos(2x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (8a b + 16a b + 8a b )cos(2x) + 4a b + 8a b + 4a b +--R * +--R cot(x) +--R + +--R 4 5 6 3 8 2 4 5 6 3 8 +--R (2a b + 4a b + 2a b)cos(2x) + (4a b + 8a b + 4a b)cos(2x) +--R + +--R 4 5 6 3 8 +--R 2a b + 4a b + 2a b +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 2 +--R (2a b + 4a b + 2a b )cos(x)cos(2x) +--R + +--R 8 3 6 5 4 +--R (4a b + 8a b + 4a b )cos(x)cos(2x) +--R + +--R 8 3 6 5 4 +--R (2a b + 4a b + 2a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 6 3 2 +--R (4a b + 8a b + 4a b )cos(x)cos(2x) +--R + +--R 2 7 4 5 6 3 +--R (8a b + 16a b + 8a b )cos(x)cos(2x) +--R + +--R 2 7 4 5 6 3 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R cot(x) +--R + +--R 3 6 5 4 7 2 2 +--R (2a b + 4a b + 2a b )cos(x)cos(2x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (4a b + 8a b + 4a b )cos(x)cos(2x) + (2a b + 4a b + 2a b )cos(x) +--R * +--R sin(2x) +--R + +--R 8 3 6 5 4 3 8 3 6 5 4 2 +--R (a b + 2a b + a b )cos(2x) + (3a b + 6a b + 3a b )cos(2x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 +--R (3a b + 6a b + 3a b )cos(2x) + a b + 2a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 6 3 3 +--R (2a b + 4a b + 2a b )cos(2x) +--R + +--R 2 7 4 5 6 3 2 +--R (6a b + 12a b + 6a b )cos(2x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (6a b + 12a b + 6a b )cos(2x) + 2a b + 4a b + 2a b +--R * +--R cot(x) +--R + +--R 3 6 5 4 7 2 3 3 6 5 4 7 2 2 +--R (a b + 2a b + a b )cos(2x) + (3a b + 6a b + 3a b )cos(2x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (3a b + 6a b + 3a b )cos(2x) + a b + 2a b + a b +--R * +--R sin(x) +--R + +--R 9 2 7 4 5 3 +--R (b + 2a b + a b )cos(x)cos(2x) +--R + +--R 9 2 7 4 5 2 +--R (3b + 6a b + 3a b )cos(x)cos(2x) +--R + +--R 9 2 7 4 5 9 2 7 4 5 +--R (3b + 6a b + 3a b )cos(x)cos(2x) + (b + 2a b + a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 5 4 3 +--R (2a b + 4a b + 2a b )cos(x)cos(2x) +--R + +--R 8 3 6 5 4 2 +--R (6a b + 12a b + 6a b )cos(x)cos(2x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 +--R (6a b + 12a b + 6a b )cos(x)cos(2x) + (2a b + 4a b + 2a b )cos(x) +--R * +--R cot(x) +--R + +--R 2 7 4 5 6 3 3 +--R (a b + 2a b + a b )cos(x)cos(2x) +--R + +--R 2 7 4 5 6 3 2 +--R (3a b + 6a b + 3a b )cos(x)cos(2x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (3a b + 6a b + 3a b )cos(x)cos(2x) + (a b + 2a b + a b )cos(x) +--R Type: Expression(Integer) +--E 304 + +--S 305 of 510 +t0260:= 1/(a+b*cot(x))^3 +--R +--R +--R 1 +--R (281) ------------------------------------------- +--R 3 3 2 2 2 3 +--R b cot(x) + 3a b cot(x) + 3a b cot(x) + a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 510 +r0260:= a*(a^2-3*b^2)*x/(a^2+b^2)^3+1/2*b/(a^2+b^2)/(a+b*cot(x))^2+_ + 2*a*b/(a^2+b^2)^2/(a+b*cot(x))-b*(3*a^2-b^2)*log(b*cos(x)+_ + a*sin(x))/(a^2+b^2)^3 +--R +--R +--R (282) +--R 5 2 3 2 4 3 2 2 3 4 +--R ((2b - 6a b )cot(x) + (4a b - 12a b )cot(x) + 2a b - 6a b) +--R * +--R log(a sin(x) + b cos(x)) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 6a b + 2a b )x cot(x) + ((- 12a b + 4a b)x + 4a b + 4a b )cot(x) +--R + +--R 3 2 5 5 2 3 4 +--R (- 6a b + 2a )x + b + 6a b + 5a b +--R / +--R 8 2 6 4 4 6 2 2 +--R (2b + 6a b + 6a b + 2a b )cot(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 8 +--R (4a b + 12a b + 12a b + 4a b)cot(x) + 2a b + 6a b + 6a b + 2a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 510 +a0260:= integrate(t0260,x) +--R +--R +--R (283) +--R 3 4 5 2 2 5 4 3 6 2 5 +--R (4a b - 12a b )sin(2x) + (2a b - 8a b + 6a b)cos(2x) + 2a b +--R + +--R 4 3 6 +--R - 4a b - 6a b +--R * +--R a sin(2x) + b cos(2x) + b +--R log(-------------------------) +--R cos(2x) + 1 +--R + +--R 3 4 5 2 2 5 4 3 6 2 5 +--R (- 2a b + 6a b )sin(2x) + (- a b + 4a b - 3a b)cos(2x) - a b +--R + +--R 4 3 6 +--R 2a b + 3a b +--R * +--R 2 +--R log(-----------) +--R cos(2x) + 1 +--R + +--R 4 3 6 6 3 4 5 2 +--R ((- 12a b + 4a b)x - 2a b - 8a b - 6a b )sin(2x) +--R + +--R 3 4 5 2 7 7 2 5 4 3 +--R ((- 6a b + 8a b - 2a )x - b - 6a b - 5a b )cos(2x) +--R + +--R 3 4 5 2 7 7 2 5 4 3 +--R (- 6a b - 4a b + 2a )x - b - 6a b - 5a b +--R / +--R 3 7 5 5 7 3 9 +--R (4a b + 12a b + 12a b + 4a b)sin(2x) +--R + +--R 2 8 4 6 8 2 10 2 8 4 6 6 4 8 2 +--R (2a b + 4a b - 4a b - 2a )cos(2x) + 2a b + 8a b + 12a b + 8a b +--R + +--R 10 +--R 2a +--R Type: Union(Expression(Integer),...) +--E 307 + +--S 308 of 510 +m0260:= a0260-r0260 +--R +--R +--R (284) +--R 3 6 5 4 2 4 5 6 3 5 4 7 2 +--R ((4a b - 12a b )cot(x) + (8a b - 24a b )cot(x) + 4a b - 12a b ) +--R * +--R sin(2x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 2 +--R ((2a b - 8a b + 6a b )cos(2x) + 2a b - 4a b - 6a b )cot(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R ((4a b - 16a b + 12a b )cos(2x) + 4a b - 8a b - 12a b )cot(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (2a b - 8a b + 6a b)cos(2x) + 2a b - 4a b - 6a b +--R * +--R a sin(2x) + b cos(2x) + b +--R log(-------------------------) +--R cos(2x) + 1 +--R + +--R 3 6 5 4 2 4 5 6 3 5 4 +--R (- 4a b + 12a b )cot(x) + (- 8a b + 24a b )cot(x) - 4a b +--R + +--R 7 2 +--R 12a b +--R * +--R sin(2x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 2 +--R ((- 2a b + 8a b - 6a b )cos(2x) - 2a b + 4a b + 6a b )cot(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R ((- 4a b + 16a b - 12a b )cos(2x) - 4a b + 8a b + 12a b )cot(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (- 2a b + 8a b - 6a b)cos(2x) - 2a b + 4a b + 6a b +--R * +--R log(a sin(x) + b cos(x)) +--R + +--R 3 6 5 4 2 4 5 6 3 5 4 +--R (- 2a b + 6a b )cot(x) + (- 4a b + 12a b )cot(x) - 2a b +--R + +--R 7 2 +--R 6a b +--R * +--R sin(2x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 2 +--R ((- a b + 4a b - 3a b )cos(2x) - a b + 2a b + 3a b )cot(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R ((- 2a b + 8a b - 6a b )cos(2x) - 2a b + 4a b + 6a b )cot(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (- a b + 4a b - 3a b)cos(2x) - a b + 2a b + 3a b +--R * +--R 2 +--R log(-----------) +--R cos(2x) + 1 +--R + +--R 8 3 6 5 4 2 2 7 4 5 6 3 +--R (- 2a b - 8a b - 6a b )cot(x) + (- 4a b - 24a b - 20a b )cot(x) +--R + +--R 3 6 5 4 7 2 +--R - 4a b - 20a b - 16a b +--R * +--R sin(2x) +--R + +--R 9 2 7 4 5 9 2 7 4 5 2 +--R ((- b - 6a b - 5a b )cos(2x) - b - 6a b - 5a b )cot(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (- 2a b - 16a b - 10a b + 4a b )cos(2x) - 2a b - 16a b - 18a b +--R + +--R 7 2 +--R - 4a b +--R * +--R cot(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 8 +--R (- 2a b - 11a b - 4a b + 5a b)cos(2x) - 2a b - 13a b - 16a b - 5a b +--R / +--R 3 9 5 7 7 5 9 3 2 +--R (4a b + 12a b + 12a b + 4a b )cot(x) +--R + +--R 4 8 6 6 8 4 10 2 5 7 7 5 9 3 +--R (8a b + 24a b + 24a b + 8a b )cot(x) + 4a b + 12a b + 12a b +--R + +--R 11 +--R 4a b +--R * +--R sin(2x) +--R + +--R 2 10 4 8 8 4 10 2 2 10 4 8 6 6 +--R (2a b + 4a b - 4a b - 2a b )cos(2x) + 2a b + 8a b + 12a b +--R + +--R 8 4 10 2 +--R 8a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 9 5 7 9 3 11 3 9 5 7 7 5 +--R (4a b + 8a b - 8a b - 4a b)cos(2x) + 4a b + 16a b + 24a b +--R + +--R 9 3 11 +--R 16a b + 4a b +--R * +--R cot(x) +--R + +--R 4 8 6 6 10 2 12 4 8 6 6 8 4 10 2 +--R (2a b + 4a b - 4a b - 2a )cos(2x) + 2a b + 8a b + 12a b + 8a b +--R + +--R 12 +--R 2a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 510 +d0260:= D(m0260,x) +--R +--R +--R (285) +--R 4 8 6 6 3 5 7 7 5 2 +--R (4a b - 12a b )cot(x) + (12a b - 36a b )cot(x) +--R + +--R 6 6 8 4 7 5 9 3 +--R (12a b - 36a b )cot(x) + 4a b - 12a b +--R * +--R sin(x) +--R + +--R 3 9 5 7 3 4 8 6 6 2 +--R (4a b - 12a b )cos(x)cot(x) + (12a b - 36a b )cos(x)cot(x) +--R + +--R 5 7 7 5 6 6 8 4 +--R (12a b - 36a b )cos(x)cot(x) + (4a b - 12a b )cos(x) +--R * +--R 4 +--R sin(2x) +--R + +--R 3 9 5 7 7 5 3 9 5 7 7 5 +--R ((10a b - 12a b + 10a b )cos(2x) + 10a b - 4a b - 14a b ) +--R * +--R 3 +--R cot(x) +--R + +--R 4 8 6 6 8 4 4 8 6 6 8 4 +--R ((26a b - 28a b + 42a b )cos(2x) + 26a b - 4a b - 30a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 5 7 7 5 9 3 5 7 7 5 9 3 +--R ((22a b - 20a b + 54a b )cos(2x) + 22a b + 4a b - 18a b ) +--R * +--R cot(x) +--R + +--R 4 8 6 6 8 4 10 2 4 8 6 6 +--R (- 4a b - 6a b - 16a b + 18a b )cos(2x) - 4a b - 6a b +--R + +--R 8 4 10 2 +--R - 8a b - 6a b +--R * +--R sin(x) +--R + +--R 2 10 4 8 6 6 +--R (6a b - 4a b + 22a b )cos(x)cos(2x) +--R + +--R 2 10 4 8 6 6 +--R (6a b + 4a b - 2a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 3 9 5 7 7 5 +--R (14a b - 4a b + 78a b )cos(x)cos(2x) +--R + +--R 3 9 5 7 7 5 +--R (14a b + 20a b + 6a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 8 6 6 8 4 +--R (10a b + 4a b + 90a b )cos(x)cos(2x) +--R + +--R 4 8 6 6 8 4 +--R (10a b + 28a b + 18a b )cos(x) +--R * +--R cot(x) +--R + +--R 3 9 5 7 7 5 9 3 +--R (- 4a b - 10a b - 8a b + 30a b )cos(x)cos(2x) +--R + +--R 3 9 5 7 9 3 +--R (- 4a b - 10a b + 6a b )cos(x) +--R * +--R 3 +--R sin(2x) +--R + +--R 2 10 4 8 6 6 8 4 2 +--R (11a b - 13a b - 19a b + 5a b )cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 2 10 4 8 +--R (24a b - 18a b - 36a b + 6a b )cos(2x) + 13a b - 5a b +--R + +--R 6 6 8 4 +--R - 13a b - 11a b +--R * +--R 3 +--R cot(x) +--R + +--R 3 9 5 7 7 5 9 3 2 +--R (25a b - 19a b - 41a b + 3a b )cos(2x) +--R + +--R 3 9 5 7 7 5 9 3 3 9 5 7 +--R (56a b - 22a b - 60a b + 18a b )cos(2x) + 31a b - 3a b +--R + +--R 7 5 9 3 +--R - 7a b - 21a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 8 6 6 8 4 10 2 2 +--R (17a b + a b - 25a b - 9a b )cos(2x) +--R + +--R 4 8 6 6 8 4 10 2 4 8 6 6 +--R (40a b + 10a b - 12a b + 18a b )cos(2x) + 23a b + 9a b +--R + +--R 8 4 10 2 +--R 25a b - 9a b +--R * +--R cot(x) +--R + +--R 3 9 5 7 7 5 9 3 11 2 +--R (- 8a b - 17a b - 5a b + a b - 3a b)cos(2x) +--R + +--R 3 9 5 7 7 5 9 3 11 3 9 +--R (- 16a b - 40a b - 34a b - 4a b + 6a b)cos(2x) - 8a b +--R + +--R 5 7 7 5 9 3 11 +--R - 23a b - 29a b - a b - 3a b +--R * +--R sin(x) +--R + +--R 11 3 9 5 7 7 5 2 +--R (3a b + 7a b - 3a b - 7a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 +--R (8a b + 14a b + 12a b + 6a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 +--R (5a b + 7a b + 19a b + a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 2 10 4 8 6 6 8 4 2 +--R (a b + 41a b + 7a b - 33a b )cos(x)cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 +--R (8a b + 74a b + 84a b + 18a b )cos(x)cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 +--R (7a b + 33a b + 89a b + 15a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 3 9 5 7 7 5 9 3 2 +--R (- 7a b + 61a b + 23a b - 45a b )cos(x)cos(2x) +--R + +--R 3 9 5 7 7 5 9 3 +--R (- 8a b + 106a b + 132a b + 18a b )cos(x)cos(2x) +--R + +--R 3 9 5 7 7 5 9 3 +--R (- a b + 45a b + 121a b + 27a b )cos(x) +--R * +--R cot(x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 +--R (- 8a b - 25a b + 15a b + 17a b - 15a b )cos(x)cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (- 16a b - 56a b - 2a b + 44a b + 6a b )cos(x)cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (- 8a b - 31a b - 17a b + 31a b + 9a b )cos(x) +--R * +--R 2 +--R sin(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 3 +--R (4a b - 12a b - 6a b + 40a b - 2a b )cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 2 +--R (14a b - 34a b - 36a b + 14a b + 2a b )cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (16a b - 28a b - 54a b - 40a b + 2a b )cos(2x) + 6a b +--R + +--R 3 9 5 7 7 5 9 3 +--R - 6a b - 24a b - 14a b - 2a b +--R * +--R 3 +--R cot(x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 3 +--R (7a b - 20a b - 16a b + 104a b - 3a b )cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 +--R (27a b - 66a b - 74a b + 22a b + 3a b )cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (33a b - 60a b - 104a b - 104a b + 3a b )cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R 13a b - 14a b - 46a b - 22a b - 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 9 5 7 7 5 9 3 3 +--R (2a b - 4a b - 14a b + 88a b )cos(2x) +--R + +--R 3 9 5 7 7 5 9 3 2 +--R (12a b - 30a b - 40a b + 2a b )cos(2x) +--R + +--R 3 9 5 7 7 5 9 3 3 9 5 7 +--R (18a b - 36a b - 46a b - 88a b )cos(2x) + 8a b - 10a b +--R + +--R 7 5 9 3 +--R - 20a b - 2a b +--R * +--R cot(x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 3 +--R (- 5a b - 10a b + 6a b + 6a b + 27a b )cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 +--R (- 15a b - 40a b - 24a b + 4a b + 3a b )cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 10 +--R (- 15a b - 50a b - 66a b - 26a b - 27a b )cos(2x) - 5a b +--R + +--R 4 8 6 6 8 4 10 2 +--R - 20a b - 36a b - 24a b - 3a b +--R * +--R sin(x) +--R + +--R 12 2 10 4 8 6 6 8 4 3 +--R (- b + 4a b - 4a b + 24a b + a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 2 +--R (- b + 2a b - 2a b - 6a b - a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (b - 4a b + 4a b - 24a b - a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (b - 2a b + 2a b + 6a b + a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 11 3 9 5 7 7 5 9 3 3 +--R (- 8a b + 28a b - 10a b + 56a b + 6a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 2 +--R (- 18a b + 42a b + 28a b - 38a b - 6a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (- 12a b + 12a b + 70a b - 56a b - 6a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (- 2a b - 2a b + 32a b + 38a b + 6a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 3 +--R (- 13a b + 44a b - 8a b + 40a b + 9a b )cos(x)cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 +--R (- 33a b + 78a b + 62a b - 58a b - 9a b )cos(x)cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (- 27a b + 36a b + 128a b - 40a b - 9a b )cos(x)cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (- 7a b + 2a b + 58a b + 58a b + 9a b )cos(x) +--R * +--R cot(x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 3 +--R (- 5a b - 15a b + 22a b + 8a b + 11a b + 3a b)cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 2 +--R (- 15a b - 55a b + 12a b + 38a b - 17a b - 3a b)cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (- 15a b - 65a b - 42a b + 32a b - 11a b - 3a b)cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (- 5a b - 25a b - 32a b + 2a b + 17a b + 3a b)cos(x) +--R * +--R sin(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 4 +--R (b + a b + 11a b + 19a b - 8a b )cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 3 +--R (4b - 4a b + 10a b + 24a b + 6a b )cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 2 +--R (6b - 14a b - 24a b - 10a b + 10a b )cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 12 2 10 +--R (4b - 12a b - 34a b - 24a b - 6a b )cos(2x) + b - 3a b +--R + +--R 4 8 6 6 8 4 +--R - 11a b - 9a b - 2a b +--R * +--R 3 +--R cot(x) +--R + +--R 11 3 9 5 7 7 5 9 3 4 +--R (2a b + 7a b + 31a b + 53a b - 21a b )cos(2x) +--R + +--R 11 5 7 7 5 9 3 3 +--R (8a b + 34a b + 60a b + 18a b )cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 2 +--R (12a b - 30a b - 52a b - 34a b + 24a b )cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (8a b - 32a b - 82a b - 60a b - 18a b )cos(2x) + 2a b +--R + +--R 3 9 5 7 7 5 9 3 +--R - 9a b - 27a b - 19a b - 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 4 +--R (a b + 11a b + 29a b + 49a b - 18a b )cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 3 +--R (4a b + 12a b + 38a b + 48a b + 18a b )cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 +--R (6a b - 18a b - 32a b - 38a b + 18a b )cos(2x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 10 +--R (4a b - 28a b - 62a b - 48a b - 18a b )cos(2x) + a b +--R + +--R 4 8 6 6 8 4 +--R - 9a b - 21a b - 11a b +--R * +--R cot(x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 4 +--R (- a b - a b + 7a b + 11a b + 14a b - 6a b)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 3 +--R (- 4a b - 8a b + 8a b + 22a b + 16a b + 6a b)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 2 +--R (- 6a b - 18a b - 18a b - 4a b - 8a b + 6a b)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 11 +--R (- 4a b - 16a b - 32a b - 30a b - 16a b - 6a b)cos(2x) - a b +--R + +--R 3 9 5 7 7 5 9 3 +--R - 5a b - 13a b - 15a b - 6a b +--R * +--R sin(x) +--R + +--R 11 3 9 5 7 7 5 4 +--R (5a b + 9a b + 15a b - 5a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 3 +--R (8a b + 14a b + 12a b + 6a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 2a b - 4a b - 14a b + 4a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 +--R (- 8a b - 14a b - 12a b - 6a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 +--R (- 3a b - 5a b - a b + a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 12 2 10 4 8 6 6 8 4 4 +--R (- b + 19a b + 25a b + 41a b - 12a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 3 +--R (- 4b + 36a b + 46a b + 24a b + 18a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 2 +--R (- 6b + 6a b + 8a b - 46a b + 6a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (- 4b - 20a b - 22a b - 24a b - 18a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 +--R (- b - 9a b - 9a b + 5a b + 6a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 11 3 9 5 7 7 5 9 3 4 +--R (- 2a b + 23a b + 23a b + 37a b - 9a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 3 +--R (- 8a b + 48a b + 50a b + 12a b + 18a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 12a b + 18a b + 28a b - 50a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (- 8a b - 16a b - 2a b - 12a b - 18a b )cos(x)cos(2x) +--R + +--R 11 3 9 5 7 7 5 9 3 +--R (- 2a b - 9a b - 3a b + 13a b + 9a b )cos(x) +--R * +--R cot(x) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 4 +--R (- b - 2a b + 11a b + 9a b + 10a b - 3a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 3 +--R (- 4b - 12a b + 20a b + 26a b + 4a b + 6a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 2 +--R (- 6b - 24a b - 6a b + 16a b - 12a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (- 4b - 20a b - 28a b - 10a b - 4a b - 6a b )cos(x)cos(2x) +--R + +--R 12 2 10 4 8 6 6 8 4 10 2 +--R (- b - 6a b - 13a b - 9a b + 2a b + 3a b )cos(x) +--R / +--R 4 11 6 9 8 7 10 5 4 11 6 9 +--R (4a b + 12a b + 12a b + 4a b )cos(2x) + 4a b + 12a b +--R + +--R 8 7 10 5 +--R 12a b + 4a b +--R * +--R 3 +--R cot(x) +--R + +--R 5 10 7 8 9 6 11 4 5 10 +--R (12a b + 36a b + 36a b + 12a b )cos(2x) + 12a b +--R + +--R 7 8 9 6 11 4 +--R 36a b + 36a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 9 8 7 10 5 12 3 6 9 +--R (12a b + 36a b + 36a b + 12a b )cos(2x) + 12a b +--R + +--R 8 7 10 5 12 3 +--R 36a b + 36a b + 12a b +--R * +--R cot(x) +--R + +--R 7 8 9 6 11 4 13 2 7 8 9 6 +--R (4a b + 12a b + 12a b + 4a b )cos(2x) + 4a b + 12a b +--R + +--R 11 4 13 2 +--R 12a b + 4a b +--R * +--R sin(x) +--R + +--R 3 12 5 10 7 8 9 6 +--R (4a b + 12a b + 12a b + 4a b )cos(x)cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 +--R (4a b + 12a b + 12a b + 4a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 4 11 6 9 8 7 10 5 +--R (12a b + 36a b + 36a b + 12a b )cos(x)cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 +--R (12a b + 36a b + 36a b + 12a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 5 10 7 8 9 6 11 4 +--R (12a b + 36a b + 36a b + 12a b )cos(x)cos(2x) +--R + +--R 5 10 7 8 9 6 11 4 +--R (12a b + 36a b + 36a b + 12a b )cos(x) +--R * +--R cot(x) +--R + +--R 6 9 8 7 10 5 12 3 +--R (4a b + 12a b + 12a b + 4a b )cos(x)cos(2x) +--R + +--R 6 9 8 7 10 5 12 3 +--R (4a b + 12a b + 12a b + 4a b )cos(x) +--R * +--R 3 +--R sin(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 2 +--R (8a b + 20a b + 12a b - 4a b - 4a b )cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 3 12 +--R (16a b + 48a b + 48a b + 16a b )cos(2x) + 8a b +--R + +--R 5 10 7 8 9 6 11 4 +--R 28a b + 36a b + 20a b + 4a b +--R * +--R 3 +--R cot(x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 2 +--R (24a b + 60a b + 36a b - 12a b - 12a b )cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 4 11 +--R (48a b + 144a b + 144a b + 48a b )cos(2x) + 24a b +--R + +--R 6 9 8 7 10 5 12 3 +--R 84a b + 108a b + 60a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 10 7 8 9 6 11 4 13 2 2 +--R (24a b + 60a b + 36a b - 12a b - 12a b )cos(2x) +--R + +--R 5 10 7 8 9 6 11 4 5 10 +--R (48a b + 144a b + 144a b + 48a b )cos(2x) + 24a b +--R + +--R 7 8 9 6 11 4 13 2 +--R 84a b + 108a b + 60a b + 12a b +--R * +--R cot(x) +--R + +--R 6 9 8 7 10 5 12 3 14 2 +--R (8a b + 20a b + 12a b - 4a b - 4a b)cos(2x) +--R + +--R 6 9 8 7 10 5 12 3 6 9 8 7 +--R (16a b + 48a b + 48a b + 16a b )cos(2x) + 8a b + 28a b +--R + +--R 10 5 12 3 14 +--R 36a b + 20a b + 4a b +--R * +--R sin(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 2 +--R (8a b + 20a b + 12a b - 4a b - 4a b )cos(x)cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 +--R (16a b + 48a b + 48a b + 16a b )cos(x)cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (8a b + 28a b + 36a b + 20a b + 4a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 2 +--R (24a b + 60a b + 36a b - 12a b - 12a b )cos(x)cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 +--R (48a b + 144a b + 144a b + 48a b )cos(x)cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R (24a b + 84a b + 108a b + 60a b + 12a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 2 +--R (24a b + 60a b + 36a b - 12a b - 12a b )cos(x)cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 +--R (48a b + 144a b + 144a b + 48a b )cos(x)cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R (24a b + 84a b + 108a b + 60a b + 12a b )cos(x) +--R * +--R cot(x) +--R + +--R 5 10 7 8 9 6 11 4 13 2 2 +--R (8a b + 20a b + 12a b - 4a b - 4a b )cos(x)cos(2x) +--R + +--R 5 10 7 8 9 6 11 4 +--R (16a b + 48a b + 48a b + 16a b )cos(x)cos(2x) +--R + +--R 5 10 7 8 9 6 11 4 13 2 +--R (8a b + 28a b + 36a b + 20a b + 4a b )cos(x) +--R * +--R 2 +--R sin(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 3 +--R (5a b + 9a b - 2a b - 10a b - 3a b + a b )cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 2 +--R (15a b + 39a b + 26a b - 6a b - 9a b - a b )cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (15a b + 51a b + 62a b + 30a b + 3a b - a b )cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R 5a b + 21a b + 34a b + 26a b + 9a b + a b +--R * +--R 3 +--R cot(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (15a b + 27a b - 6a b - 30a b - 9a b + 3a b ) +--R * +--R 3 +--R cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (45a b + 117a b + 78a b - 18a b - 27a b - 3a b ) +--R * +--R 2 +--R cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (45a b + 153a b + 186a b + 90a b + 9a b - 3a b ) +--R * +--R cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R 15a b + 63a b + 102a b + 78a b + 27a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 3 +--R (15a b + 27a b - 6a b - 30a b - 9a b + 3a b)cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R (45a b + 117a b + 78a b - 18a b - 27a b - 3a b) +--R * +--R 2 +--R cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R (45a b + 153a b + 186a b + 90a b + 9a b - 3a b) +--R * +--R cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R 15a b + 63a b + 102a b + 78a b + 27a b + 3a b +--R * +--R cot(x) +--R + +--R 5 10 7 8 9 6 11 4 13 2 15 3 +--R (5a b + 9a b - 2a b - 10a b - 3a b + a )cos(2x) +--R + +--R 5 10 7 8 9 6 11 4 13 2 15 2 +--R (15a b + 39a b + 26a b - 6a b - 9a b - a )cos(2x) +--R + +--R 5 10 7 8 9 6 11 4 13 2 15 +--R (15a b + 51a b + 62a b + 30a b + 3a b - a )cos(2x) +--R + +--R 5 10 7 8 9 6 11 4 13 2 15 +--R 5a b + 21a b + 34a b + 26a b + 9a b + a +--R * +--R sin(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 3 +--R (5a b + 9a b - 2a b - 10a b - 3a b + a b )cos(x)cos(2x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (15a b + 39a b + 26a b - 6a b - 9a b - a b )cos(x) +--R * +--R 2 +--R cos(2x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (15a b + 51a b + 62a b + 30a b + 3a b - a b )cos(x) +--R * +--R cos(2x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (5a b + 21a b + 34a b + 26a b + 9a b + a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (15a b + 27a b - 6a b - 30a b - 9a b + 3a b )cos(x) +--R * +--R 3 +--R cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (45a b + 117a b + 78a b - 18a b - 27a b - 3a b )cos(x) +--R * +--R 2 +--R cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (45a b + 153a b + 186a b + 90a b + 9a b - 3a b )cos(x) +--R * +--R cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (15a b + 63a b + 102a b + 78a b + 27a b + 3a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (15a b + 27a b - 6a b - 30a b - 9a b + 3a b )cos(x) +--R * +--R 3 +--R cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (45a b + 117a b + 78a b - 18a b - 27a b - 3a b )cos(x) +--R * +--R 2 +--R cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (45a b + 153a b + 186a b + 90a b + 9a b - 3a b )cos(x) +--R * +--R cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (15a b + 63a b + 102a b + 78a b + 27a b + 3a b )cos(x) +--R * +--R cot(x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 3 +--R (5a b + 9a b - 2a b - 10a b - 3a b + a b)cos(x)cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 2 +--R (15a b + 39a b + 26a b - 6a b - 9a b - a b)cos(x)cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R (15a b + 51a b + 62a b + 30a b + 3a b - a b)cos(x)cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R (5a b + 21a b + 34a b + 26a b + 9a b + a b)cos(x) +--R * +--R sin(2x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 4 +--R (a b + a b - 2a b - 2a b + a b + a b )cos(2x) +--R + +--R 14 3 12 7 8 9 6 3 +--R (4a b + 8a b - 8a b - 4a b )cos(2x) +--R + +--R 14 3 12 5 10 9 6 11 4 2 +--R (6a b + 18a b + 16a b - 6a b - 2a b )cos(2x) +--R + +--R 14 3 12 5 10 7 8 9 6 14 +--R (4a b + 16a b + 24a b + 16a b + 4a b )cos(2x) + a b +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R 5a b + 10a b + 10a b + 5a b + a b +--R * +--R 3 +--R cot(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 4 +--R (3a b + 3a b - 6a b - 6a b + 3a b + 3a b )cos(2x) +--R + +--R 2 13 4 11 8 7 10 5 3 +--R (12a b + 24a b - 24a b - 12a b )cos(2x) +--R + +--R 2 13 4 11 6 9 10 5 12 3 2 +--R (18a b + 54a b + 48a b - 18a b - 6a b )cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 2 13 +--R (12a b + 48a b + 72a b + 48a b + 12a b )cos(2x) + 3a b +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R 15a b + 30a b + 30a b + 15a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 4 +--R (3a b + 3a b - 6a b - 6a b + 3a b + 3a b )cos(2x) +--R + +--R 3 12 5 10 9 6 11 4 3 +--R (12a b + 24a b - 24a b - 12a b )cos(2x) +--R + +--R 3 12 5 10 7 8 11 4 13 2 2 +--R (18a b + 54a b + 48a b - 18a b - 6a b )cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 3 12 +--R (12a b + 48a b + 72a b + 48a b + 12a b )cos(2x) + 3a b +--R + +--R 5 10 7 8 9 6 11 4 13 2 +--R 15a b + 30a b + 30a b + 15a b + 3a b +--R * +--R cot(x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 4 +--R (a b + a b - 2a b - 2a b + a b + a b)cos(2x) +--R + +--R 4 11 6 9 10 5 12 3 3 +--R (4a b + 8a b - 8a b - 4a b )cos(2x) +--R + +--R 4 11 6 9 8 7 12 3 14 2 +--R (6a b + 18a b + 16a b - 6a b - 2a b)cos(2x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 4 11 6 9 +--R (4a b + 16a b + 24a b + 16a b + 4a b )cos(2x) + a b + 5a b +--R + +--R 8 7 10 5 12 3 14 +--R 10a b + 10a b + 5a b + a b +--R * +--R sin(x) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 4 +--R (b + a b - 2a b - 2a b + a b + a b )cos(x)cos(2x) +--R + +--R 15 2 13 6 9 8 7 3 +--R (4b + 8a b - 8a b - 4a b )cos(x)cos(2x) +--R + +--R 15 2 13 4 11 8 7 10 5 2 +--R (6b + 18a b + 16a b - 6a b - 2a b )cos(x)cos(2x) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R (4b + 16a b + 24a b + 16a b + 4a b )cos(x)cos(2x) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R (b + 5a b + 10a b + 10a b + 5a b + a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 4 +--R (3a b + 3a b - 6a b - 6a b + 3a b + 3a b )cos(x)cos(2x) +--R + +--R 14 3 12 7 8 9 6 3 +--R (12a b + 24a b - 24a b - 12a b )cos(x)cos(2x) +--R + +--R 14 3 12 5 10 9 6 11 4 2 +--R (18a b + 54a b + 48a b - 18a b - 6a b )cos(x)cos(2x) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (12a b + 48a b + 72a b + 48a b + 12a b )cos(x)cos(2x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (3a b + 15a b + 30a b + 30a b + 15a b + 3a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 4 +--R (3a b + 3a b - 6a b - 6a b + 3a b + 3a b )cos(x)cos(2x) +--R + +--R 2 13 4 11 8 7 10 5 3 +--R (12a b + 24a b - 24a b - 12a b )cos(x)cos(2x) +--R + +--R 2 13 4 11 6 9 10 5 12 3 2 +--R (18a b + 54a b + 48a b - 18a b - 6a b )cos(x)cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (12a b + 48a b + 72a b + 48a b + 12a b )cos(x)cos(2x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (3a b + 15a b + 30a b + 30a b + 15a b + 3a b )cos(x) +--R * +--R cot(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 4 +--R (a b + a b - 2a b - 2a b + a b + a b )cos(x)cos(2x) +--R + +--R 3 12 5 10 9 6 11 4 3 +--R (4a b + 8a b - 8a b - 4a b )cos(x)cos(2x) +--R + +--R 3 12 5 10 7 8 11 4 13 2 2 +--R (6a b + 18a b + 16a b - 6a b - 2a b )cos(x)cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R (4a b + 16a b + 24a b + 16a b + 4a b )cos(x)cos(2x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (a b + 5a b + 10a b + 10a b + 5a b + a b )cos(x) +--R Type: Expression(Integer) +--E 309 + +--S 310 of 510 +t0261:= (a+b*cot(x))^(1/2) +--R +--R +--R +------------+ +--R (286) \|b cot(x) + a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 510 +r0261:= -b*((a-(-b^2)^(1/2))^(1/2)*atanh((a+b*cot(x))^(1/2)/_ + (a-(-b^2)^(1/2))^(1/2))-(a+(-b^2)^(1/2))^(1/2)*_ + atanh((a+b*cot(x))^(1/2)/(a+(-b^2)^(1/2))^(1/2)))/(-b^2)^(1/2) +--R +--R +--R (287) +--R +-------------+ +--R | +----+ +------------+ +--R | | 2 \|b cot(x) + a +--R - b\|- \|- b + a atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- b + a +--R + +--R +-----------+ +--R | +----+ +------------+ +--R | | 2 \|b cot(x) + a +--R b\|\|- b + a atanh(---------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- b + a +--R / +--R +----+ +--R | 2 +--R \|- b +--R Type: Expression(Integer) +--E 311 + +--S 312 of 510 +a0261:= integrate(t0261,x) +--R +--R +--R >> Error detected within library code: +--R ker2trigs: cannot convert kernel to gaussian function +--R +--R Continuing to read the file... +--R +--E 312 + +--S 313 of 510 +m0261:= a0261-r0261 +--R +--R +--R (288) +--R +-------------+ +--R | +----+ +------------+ +--R | | 2 \|b cot(x) + a +--R b\|- \|- b + a atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- b + a +--R + +--R +-----------+ +--R | +----+ +------------+ +----+ +--R | | 2 \|b cot(x) + a | 2 +--R - b\|\|- b + a atanh(---------------) + a0261\|- b +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- b + a +--R / +--R +----+ +--R | 2 +--R \|- b +--R Type: Expression(Integer) +--E 313 + +--S 314 of 510 +d0261:= D(m0261,x) +--R +--R +--R - b cot(x) - a +--R (289) --------------- +--R +------------+ +--R \|b cot(x) + a +--R Type: Expression(Integer) +--E 314 + +--S 315 of 510 +t0262:= 1/(a+b*cot(x))^(1/2) +--R +--R +--R 1 +--R (290) --------------- +--R +------------+ +--R \|b cot(x) + a +--R Type: Expression(Integer) +--E 315 + +--S 316 of 510 +r0262:= -b*atanh((a+b*cot(x))^(1/2)/(a-(-b^2)^(1/2))^(1/2))/(-b^2)^(1/2)/_ + (a-(-b^2)^(1/2))^(1/2)+b*atanh((a+b*cot(x))^(1/2)/_ + (a+(-b^2)^(1/2))^(1/2))/(-b^2)^(1/2)/(a+(-b^2)^(1/2))^(1/2) +--R +--R +--R (291) +--R +-----------+ +--R | +----+ +------------+ +--R | | 2 \|b cot(x) + a +--R - b\|\|- b + a atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- b + a +--R + +--R +-------------+ +--R | +----+ +------------+ +--R | | 2 \|b cot(x) + a +--R b\|- \|- b + a atanh(---------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- b + a +--R / +--R +-------------+ +-----------+ +--R +----+ | +----+ | +----+ +--R | 2 | | 2 | | 2 +--R \|- b \|- \|- b + a \|\|- b + a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 510 +a0262:= integrate(t0262,x) +--R +--R +--R >> Error detected within library code: +--R ker2trigs: cannot convert kernel to gaussian function +--R +--R Continuing to read the file... +--R +--E 317 + +--S 318 of 510 +m0262:= a0262-r0262 +--R +--R +--R (292) +--R +-----------+ +--R | +----+ +------------+ +--R | | 2 \|b cot(x) + a +--R b\|\|- b + a atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- b + a +--R + +--R +-------------+ +--R | +----+ +------------+ +--R | | 2 \|b cot(x) + a +--R - b\|- \|- b + a atanh(---------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- b + a +--R + +--R +-------------+ +-----------+ +--R +----+ | +----+ | +----+ +--R | 2 | | 2 | | 2 +--R a0262\|- b \|- \|- b + a \|\|- b + a +--R / +--R +-------------+ +-----------+ +--R +----+ | +----+ | +----+ +--R | 2 | | 2 | | 2 +--R \|- b \|- \|- b + a \|\|- b + a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 510 +d0262:= D(m0262,x) +--R +--R +--R 1 +--R (293) - --------------- +--R +------------+ +--R \|b cot(x) + a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 510 +t0263:= (a+b*cot(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (294) \|b cot(x) + a +--R Type: Expression(Integer) +--E 320 + +--S 321 of 510 +r0263:= -(a-b)^(1/2)*atan((a-b)^(1/2)*cot(x)/(a+b*cot(x)^2)^(1/2))-_ + b^(1/2)*atanh((a+b*cot(x)^2)^(1/2)*tan(x)/b^(1/2)) +--R +--R +--R (295) +--R +-------------+ +--R | 2 +-------+ +--R +-+ tan(x)\|b cot(x) + a +-------+ cot(x)\|- b + a +--R - \|b atanh(----------------------) - \|- b + a atan(----------------) +--R +-+ +-------------+ +--R \|b | 2 +--R \|b cot(x) + a +--R Type: Expression(Integer) +--E 321 + +--S 322 of 510 +a0263:= integrate(t0263,x) +--R +--R +--R (296) +--R [ +--R +-----+ +-+ +--R 2\|b - a \|b +--R * +--R log +--R 3 2 2 3 8 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (64b - 352a b + 512a b - 224a )cos(x) +--R + +--R 2 2 3 4 2 3 2 +--R (64a b - 176a b + 112a )cos(x) + (12a b - 14a )cos(x) +--R * +--R +-+ +--R \|b +--R + +--R 3 2 2 3 10 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 8 +--R (128b - 576a b + 768a b - 320a )cos(x) +--R + +--R 3 2 2 3 6 +--R (- 64b + 320a b - 528a b + 272a )cos(x) +--R + +--R 2 2 3 4 +--R (- 64a b + 144a b - 88a )cos(x) +--R + +--R 2 3 2 +--R (- 12a b + 8a )cos(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 8 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (- 64b + 416a b - 640a b + 288a )cos(x) +--R + +--R 2 2 3 4 +--R (- 96a b + 304a b - 208a )cos(x) +--R + +--R 2 3 2 3 +--R (- 36a b + 50a )cos(x) - 2a +--R * +--R +-----+ +-+ +--R \|b - a \|b +--R + +--R 4 3 2 2 3 4 10 +--R (128b - 512a b + 768a b - 512a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 128b + 768a b - 1536a b + 1280a b - 384a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (64b - 448a b + 1120a b - 1152a b + 416a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (96a b - 352a b + 448a b - 192a )cos(x) +--R + +--R 2 2 3 4 2 3 4 +--R (36a b - 68a b + 33a )cos(x) + 2a b - a +--R / +--R 3 2 2 3 10 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 8 +--R (- 128b + 576a b - 768a b + 320a )cos(x) +--R + +--R 2 2 3 6 +--R (- 192a b + 464a b - 272a )cos(x) +--R + +--R 2 3 4 3 2 +--R (- 80a b + 88a )cos(x) - 8a cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ |(b - a)cos(x) + a +--R \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 4 3 2 2 3 4 10 +--R (- 128b + 512a b - 768a b + 512a b - 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (128b - 768a b + 1536a b - 1280a b + 384a )cos(x) +--R + +--R 3 2 2 3 4 6 +--R (256a b - 928a b + 1088a b - 416a )cos(x) +--R + +--R 2 2 3 4 4 3 4 2 4 +--R (160a b - 352a b + 192a )cos(x) + (32a b - 33a )cos(x) + a +--R + +--R (- b + a) +--R * +--R log +--R +------------------+ +--R | 2 +--R 4 2 +-----+ |(b - a)cos(x) + a +--R ((- 8b + 8a)cos(x) - 4a cos(x) )\|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (8a b - 8a )cos(x) + a +--R / +--R +-----+ +--R 4\|b - a +--R , +--R +--R (- b + a) +--R * +--R log +--R +------------------+ +--R | 2 +--R 4 2 +-----+ |(b - a)cos(x) + a +--R ((- 8b + 8a)cos(x) - 4a cos(x) )\|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (8a b - 8a )cos(x) + a +--R + +--R +---+ +-----+ +--R 4\|- b \|b - a +--R * +--R atan +--R +------------------+ +--R | 2 +--R 2 +---+ |(b - a)cos(x) + a 2 +---+ +-----+ +--R cos(x) \|- b |------------------ + (- cos(x) + 1)\|- b \|b - a +--R | 2 +--R \| cos(x) +--R ------------------------------------------------------------------ +--R b +--R / +--R +-----+ +--R 4\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 322 + +--S 323 of 510 +m0263a:= a0263.1-r0263 +--R +--R +--R (297) +--R +-----+ +-+ +--R 2\|b - a \|b +--R * +--R log +--R 3 2 2 3 8 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (64b - 352a b + 512a b - 224a )cos(x) +--R + +--R 2 2 3 4 2 3 2 +--R (64a b - 176a b + 112a )cos(x) + (12a b - 14a )cos(x) +--R * +--R +-+ +--R \|b +--R + +--R 3 2 2 3 10 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 8 +--R (128b - 576a b + 768a b - 320a )cos(x) +--R + +--R 3 2 2 3 6 +--R (- 64b + 320a b - 528a b + 272a )cos(x) +--R + +--R 2 2 3 4 2 3 2 +--R (- 64a b + 144a b - 88a )cos(x) + (- 12a b + 8a )cos(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 8 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (- 64b + 416a b - 640a b + 288a )cos(x) +--R + +--R 2 2 3 4 2 3 2 +--R (- 96a b + 304a b - 208a )cos(x) + (- 36a b + 50a )cos(x) +--R + +--R 3 +--R - 2a +--R * +--R +-----+ +-+ +--R \|b - a \|b +--R + +--R 4 3 2 2 3 4 10 +--R (128b - 512a b + 768a b - 512a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 128b + 768a b - 1536a b + 1280a b - 384a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (64b - 448a b + 1120a b - 1152a b + 416a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (96a b - 352a b + 448a b - 192a )cos(x) +--R + +--R 2 2 3 4 2 3 4 +--R (36a b - 68a b + 33a )cos(x) + 2a b - a +--R / +--R 3 2 2 3 10 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 8 +--R (- 128b + 576a b - 768a b + 320a )cos(x) +--R + +--R 2 2 3 6 +--R (- 192a b + 464a b - 272a )cos(x) +--R + +--R 2 3 4 3 2 +--R (- 80a b + 88a )cos(x) - 8a cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ |(b - a)cos(x) + a +--R \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 4 3 2 2 3 4 10 +--R (- 128b + 512a b - 768a b + 512a b - 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (128b - 768a b + 1536a b - 1280a b + 384a )cos(x) +--R + +--R 3 2 2 3 4 6 +--R (256a b - 928a b + 1088a b - 416a )cos(x) +--R + +--R 2 2 3 4 4 3 4 2 4 +--R (160a b - 352a b + 192a )cos(x) + (32a b - 33a )cos(x) + a +--R + +--R (- b + a) +--R * +--R log +--R +------------------+ +--R | 2 +--R 4 2 +-----+ |(b - a)cos(x) + a +--R ((- 8b + 8a)cos(x) - 4a cos(x) )\|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (8a b - 8a )cos(x) + a +--R + +--R +-------------+ +--R | 2 +--R +-----+ +-+ tan(x)\|b cot(x) + a +--R 4\|b - a \|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R +-------+ +--R +-------+ +-----+ cot(x)\|- b + a +--R 4\|- b + a \|b - a atan(----------------) +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R / +--R +-----+ +--R 4\|b - a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 510 +d0263a:= D(m0263a,x) +--R +--R +--R (298) +--R 14 13 2 12 +--R 134217728b - 1744830464a b + 10468982784a b +--R + +--R 3 11 4 10 +--R - 38386270208a b + 95965675520a b +--R + +--R 5 9 6 8 +--R - 172738215936a b + 230317621248a b +--R + +--R 7 7 8 6 +--R - 230317621248a b + 172738215936a b +--R + +--R 9 5 10 4 +--R - 95965675520a b + 38386270208a b +--R + +--R 11 3 12 2 +--R - 10468982784a b + 1744830464a b +--R + +--R 13 +--R - 134217728a b +--R * +--R 29 +--R cos(x) +--R + +--R 14 13 +--R - 67108864b + 1778384896a b +--R + +--R 2 12 3 11 +--R - 16106127360a b + 78987132928a b +--R + +--R 4 10 5 9 +--R - 247296163840a b + 534824091648a b +--R + +--R 6 8 7 7 +--R - 832686784512a b + 952274780160a b +--R + +--R 8 6 9 5 +--R - 803897081856a b + 496437821440a b +--R + +--R 10 4 11 3 +--R - 218506461184a b + 65028489216a b +--R + +--R 12 2 13 +--R - 11744051200a b + 973078528a b +--R * +--R 27 +--R cos(x) +--R + +--R 13 2 12 +--R - 436207616a b + 7952400384a b +--R + +--R 3 11 4 10 +--R - 58686701568a b + 245450670080a b +--R + +--R 5 9 6 8 +--R - 664377753600a b + 1242386399232a b +--R + +--R 7 7 8 6 +--R - 1658729791488a b + 1601150386176a b +--R + +--R 9 5 10 4 +--R - 1112832737280a b + 544420659200a b +--R + +--R 11 3 12 2 +--R - 178274697216a b + 35131490304a b +--R + +--R 13 +--R - 3154116608a b +--R * +--R 25 +--R cos(x) +--R + +--R 2 12 3 11 +--R - 1254096896a b + 18570280960a b +--R + +--R 4 10 5 9 +--R - 116727480320a b + 421810667520a b +--R + +--R 6 8 7 7 +--R - 986877788160a b + 1582187937792a b +--R + +--R 8 6 9 5 +--R - 1782746972160a b + 1416647147520a b +--R + +--R 10 4 11 3 +--R - 779951800320a b + 283860008960a b +--R + +--R 12 2 13 +--R - 61547216896a b + 6029312000a b +--R * +--R 23 +--R cos(x) +--R + +--R 3 11 4 10 +--R - 2099249152a b + 26442465280a b +--R + +--R 5 9 6 8 +--R - 143515975680a b + 448108953600a b +--R + +--R 7 7 8 6 +--R - 898640117760a b + 1215707480064a b +--R + +--R 9 5 10 4 +--R - 1127539015680a b + 709707694080a b +--R + +--R 11 3 12 2 +--R - 290665267200a b + 70042255360a b +--R + +--R 13 +--R - 7549222912a b +--R * +--R 21 +--R cos(x) +--R + +--R 4 10 5 9 +--R - 2266234880a b + 24632229888a b +--R + +--R 6 8 7 7 +--R - 115473383424a b + 308974977024a b +--R + +--R 8 6 9 5 +--R - 522768089088a b + 582073712640a b +--R + +--R 10 4 11 3 +--R - 427586224128a b + 200195702784a b +--R + +--R 12 2 13 +--R - 54285041664a b + 6502350848a b +--R * +--R 19 +--R cos(x) +--R + +--R 5 9 6 8 +--R - 1651113984a b + 15495069696a b +--R + +--R 7 7 8 6 +--R - 62234296320a b + 140471697408a b +--R + +--R 9 5 10 4 +--R - 195593502720a b + 172477906944a b +--R + +--R 11 3 12 2 +--R - 94240505856a b + 29212016640a b +--R + +--R 13 +--R - 3937271808a b +--R * +--R 17 +--R cos(x) +--R + +--R 6 8 7 7 +--R - 825556992a b + 6636208128a b +--R + +--R 8 6 9 5 +--R - 22480551936a b + 41754132480a b +--R + +--R 10 4 11 3 +--R - 46040678400a b + 30196334592a b +--R + +--R 12 2 13 +--R - 10922754048a b + 1682866176a b +--R * +--R 15 +--R cos(x) +--R + +--R 7 7 8 6 9 5 +--R - 282427392a b + 1914531840a b - 5336248320a b +--R + +--R 10 4 11 3 +--R 7848222720a b - 6436085760a b +--R + +--R 12 2 13 +--R 2794401792a b - 502394880a b +--R * +--R 13 +--R cos(x) +--R + +--R 8 6 9 5 10 4 +--R - 64722944a b + 360954880a b - 796590080a b +--R + +--R 11 3 12 2 13 +--R 871270400a b - 472975360a b + 102063104a b +--R * +--R 11 +--R cos(x) +--R + +--R 9 5 10 4 11 3 +--R - 9518080a b + 42025984a b - 68969472a b +--R + +--R 12 2 13 +--R 49933312a b - 13471744a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 4 11 3 12 2 +--R - 832832a b + 2734368a b - 2970240a b +--R + +--R 13 +--R 1068704a b +--R * +--R 7 +--R cos(x) +--R + +--R 11 3 12 2 13 5 +--R (- 37856a b + 82264a b - 44408a b)cos(x) +--R + +--R 12 2 13 3 13 +--R (- 676a b + 730a b)cos(x) - 2a b cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 13 2 12 3 11 +--R 134217728a b - 1744830464a b + 10468982784a b +--R + +--R 4 10 5 9 +--R - 38386270208a b + 95965675520a b +--R + +--R 6 8 7 7 +--R - 172738215936a b + 230317621248a b +--R + +--R 8 6 9 5 +--R - 230317621248a b + 172738215936a b +--R + +--R 10 4 11 3 +--R - 95965675520a b + 38386270208a b +--R + +--R 12 2 13 14 +--R - 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2950390874112a b + 1237420343296a b +--R + +--R 13 2 14 15 +--R - 353428832256a b + 61605937152a b - 4949278720a +--R * +--R 28 +--R cos(x) +--R + +--R 14 2 13 3 12 +--R 67108864a b - 2248146944a b + 28554821632a b +--R + +--R 4 11 5 10 6 9 +--R - 197132288000a b + 859630993408a b - 2563021733888a b +--R + +--R 7 8 8 7 9 6 +--R 5467828912128a b - 8563829243904a b + 9965666304000a b +--R + +--R 10 5 11 4 12 3 +--R - 8619563155456a b + 5476318183424a b - 2485947203584a b +--R + +--R 13 2 14 15 +--R 764067971072a b - 142606336000a b + 12213813248a +--R * +--R 26 +--R cos(x) +--R + +--R 2 13 3 12 4 11 +--R 436207616a b - 9424601088a b + 88621449216a b +--R + +--R 5 10 6 9 7 8 +--R - 484067246080a b + 1728016547840a b - 4287883640832a b +--R + +--R 8 7 9 6 10 5 +--R 7653216485376a b - 9994352197632a b + 9584687185920a b +--R + +--R 11 4 12 3 13 2 +--R - 6686627594240a b + 3306386620416a b - 1099537317888a b +--R + +--R 14 15 +--R 220768239616a b - 20240138240a +--R * +--R 24 +--R cos(x) +--R + +--R 3 12 4 11 5 10 +--R 1254096896a b - 21296578560a b + 162391916544a b +--R + +--R 6 9 7 8 8 7 +--R - 733877895168a b + 2190422310912a b - 4556178063360a b +--R + +--R 9 6 10 5 11 4 +--R 6785096220672a b - 7302861029376a b + 5647937568768a b +--R + +--R 12 3 13 2 14 +--R - 3065734234112a b + 1110168305664a b - 241093312512a b +--R + +--R 15 +--R 23770693632a +--R * +--R 22 +--R cos(x) +--R + +--R 4 11 5 10 6 9 +--R 2099249152a b - 29758324736a b + 190596775936a b +--R + +--R 7 8 8 7 9 6 +--R - 725734195200a b + 1822636376064a b - 3168631259136a b +--R + +--R 10 5 11 4 12 3 +--R 3891589545984a b - 3378056134656a b + 2032289710080a b +--R + +--R 13 2 14 15 +--R - 807583350784a b + 190901387264a b - 20349779968a +--R * +--R 20 +--R cos(x) +--R + +--R 5 10 6 9 7 8 +--R 2266234880a b - 27416461312a b + 149339897856a b +--R + +--R 8 7 9 6 10 5 +--R - 480944848896a b + 1012170227712a b - 1452830883840a b +--R + +--R 11 4 12 3 13 2 +--R 1439442665472a b - 971796381696a b + 427825299456a b +--R + +--R 14 15 +--R - 110918500352a b + 12862750720a +--R * +--R 18 +--R cos(x) +--R + +--R 6 9 7 8 8 7 +--R 1651113984a b - 17146183680a b + 79443984384a b +--R + +--R 9 6 10 5 11 4 +--R - 215069503488a b + 374239272960a b - 433500770304a b +--R + +--R 12 3 13 2 14 +--R 333953679360a b - 164877225984a b + 47318704128a b +--R + +--R 15 +--R - 6013071360a +--R * +--R 16 +--R cos(x) +--R + +--R 7 8 8 7 9 6 +--R 825556992a b - 7331414016a b + 28644237312a b +--R + +--R 10 5 11 4 12 3 +--R - 64206622720a b + 90180055040a b - 81170440192a b +--R + +--R 13 2 14 15 +--R 45677756416a b - 14681280512a b + 2062151680a +--R * +--R 14 +--R cos(x) +--R + +--R 8 7 9 6 10 5 +--R 282427392a b - 2120468480a b + 6866515968a b +--R + +--R 11 4 12 3 13 2 +--R - 12419224064a b + 13536147456a b - 8882205696a b +--R + +--R 14 15 +--R 3246104576a b - 509297152a +--R * +--R 12 +--R cos(x) +--R + +--R 9 6 10 5 11 4 +--R 64722944a b - 402834432a b + 1051235328a b +--R + +--R 12 3 13 2 14 15 +--R - 1471708160a b + 1165212672a b - 494407680a b + 87779328a +--R * +--R 10 +--R cos(x) +--R + +--R 10 5 11 4 12 3 13 2 +--R 9518080a b - 47617856a b + 95762368a b - 96786248a b +--R + +--R 14 15 +--R 49166416a b - 10042760a +--R * +--R 8 +--R cos(x) +--R + +--R 11 4 12 3 13 2 14 +--R 832832a b - 3188640a b + 4582032a b - 2929864a b +--R + +--R 15 +--R 703640a +--R * +--R 6 +--R cos(x) +--R + +--R 12 3 13 2 14 15 4 +--R (37856a b - 101868a b + 90276a b - 26265a )cos(x) +--R + +--R 13 2 14 15 2 14 15 +--R (676a b - 1070a b + 394a )cos(x) + 2a b - a +--R * +--R 2 +--R tan(x) +--R + +--R 15 14 2 13 +--R 134217728b - 1879048192a b + 12213813248a b +--R + +--R 3 12 4 11 5 10 +--R - 48855252992a b + 134351945728a b - 268703891456a b +--R + +--R 6 9 7 8 8 7 +--R 403055837184a b - 460635242496a b + 403055837184a b +--R + +--R 9 6 10 5 11 4 +--R - 268703891456a b + 134351945728a b - 48855252992a b +--R + +--R 12 3 13 2 14 +--R 12213813248a b - 1879048192a b + 134217728a b +--R * +--R 32 +--R cos(x) +--R + +--R 15 14 2 13 +--R - 268435456b + 4697620480a b - 36641439744a b +--R + +--R 3 12 4 11 5 10 +--R 170993385472a b - 537407782912a b + 1209167511552a b +--R + +--R 6 9 7 8 8 7 +--R - 2015279185920a b + 2533493833728a b - 2418335023104a b +--R + +--R 9 6 10 5 11 4 +--R 1746575294464a b - 940463620096a b + 366414397440a b +--R + +--R 12 3 13 2 14 +--R - 97710505984a b + 15971909632a b - 1207959552a b +--R * +--R 30 +--R cos(x) +--R + +--R 15 14 2 13 +--R 201326592b - 4630511616a b + 44811943936a b +--R + +--R 3 12 4 11 5 10 +--R - 249846300672a b + 913519411200a b - 2344515272704a b +--R + +--R 6 9 7 8 8 7 +--R 4389876006912a b - 6125562888192a b + 6426747469824a b +--R + +--R 9 6 10 5 11 4 +--R - 5060343889920a b + 2950390874112a b - 1237420343296a b +--R + +--R 12 3 13 2 14 +--R 353428832256a b - 61605937152a b + 4949278720a b +--R * +--R 28 +--R cos(x) +--R + +--R 15 14 2 13 +--R - 67108864b + 2248146944a b - 28554821632a b +--R + +--R 3 12 4 11 5 10 +--R 197132288000a b - 859630993408a b + 2563021733888a b +--R + +--R 6 9 7 8 8 7 +--R - 5467828912128a b + 8563829243904a b - 9965666304000a b +--R + +--R 9 6 10 5 11 4 +--R 8619563155456a b - 5476318183424a b + 2485947203584a b +--R + +--R 12 3 13 2 14 +--R - 764067971072a b + 142606336000a b - 12213813248a b +--R * +--R 26 +--R cos(x) +--R + +--R 14 2 13 3 12 +--R - 436207616a b + 9424601088a b - 88621449216a b +--R + +--R 4 11 5 10 6 9 +--R 484067246080a b - 1728016547840a b + 4287883640832a b +--R + +--R 7 8 8 7 9 6 +--R - 7653216485376a b + 9994352197632a b - 9584687185920a b +--R + +--R 10 5 11 4 12 3 +--R 6686627594240a b - 3306386620416a b + 1099537317888a b +--R + +--R 13 2 14 +--R - 220768239616a b + 20240138240a b +--R * +--R 24 +--R cos(x) +--R + +--R 2 13 3 12 4 11 +--R - 1254096896a b + 21296578560a b - 162391916544a b +--R + +--R 5 10 6 9 7 8 +--R 733877895168a b - 2190422310912a b + 4556178063360a b +--R + +--R 8 7 9 6 10 5 +--R - 6785096220672a b + 7302861029376a b - 5647937568768a b +--R + +--R 11 4 12 3 13 2 +--R 3065734234112a b - 1110168305664a b + 241093312512a b +--R + +--R 14 +--R - 23770693632a b +--R * +--R 22 +--R cos(x) +--R + +--R 3 12 4 11 5 10 +--R - 2099249152a b + 29758324736a b - 190596775936a b +--R + +--R 6 9 7 8 8 7 +--R 725734195200a b - 1822636376064a b + 3168631259136a b +--R + +--R 9 6 10 5 11 4 +--R - 3891589545984a b + 3378056134656a b - 2032289710080a b +--R + +--R 12 3 13 2 14 +--R 807583350784a b - 190901387264a b + 20349779968a b +--R * +--R 20 +--R cos(x) +--R + +--R 4 11 5 10 6 9 +--R - 2266234880a b + 27416461312a b - 149339897856a b +--R + +--R 7 8 8 7 9 6 +--R 480944848896a b - 1012170227712a b + 1452830883840a b +--R + +--R 10 5 11 4 12 3 +--R - 1439442665472a b + 971796381696a b - 427825299456a b +--R + +--R 13 2 14 +--R 110918500352a b - 12862750720a b +--R * +--R 18 +--R cos(x) +--R + +--R 5 10 6 9 7 8 +--R - 1651113984a b + 17146183680a b - 79443984384a b +--R + +--R 8 7 9 6 10 5 +--R 215069503488a b - 374239272960a b + 433500770304a b +--R + +--R 11 4 12 3 13 2 +--R - 333953679360a b + 164877225984a b - 47318704128a b +--R + +--R 14 +--R 6013071360a b +--R * +--R 16 +--R cos(x) +--R + +--R 6 9 7 8 8 7 +--R - 825556992a b + 7331414016a b - 28644237312a b +--R + +--R 9 6 10 5 11 4 +--R 64206622720a b - 90180055040a b + 81170440192a b +--R + +--R 12 3 13 2 14 +--R - 45677756416a b + 14681280512a b - 2062151680a b +--R * +--R 14 +--R cos(x) +--R + +--R 7 8 8 7 9 6 +--R - 282427392a b + 2120468480a b - 6866515968a b +--R + +--R 10 5 11 4 12 3 +--R 12419224064a b - 13536147456a b + 8882205696a b +--R + +--R 13 2 14 +--R - 3246104576a b + 509297152a b +--R * +--R 12 +--R cos(x) +--R + +--R 8 7 9 6 10 5 11 4 +--R - 64722944a b + 402834432a b - 1051235328a b + 1471708160a b +--R + +--R 12 3 13 2 14 +--R - 1165212672a b + 494407680a b - 87779328a b +--R * +--R 10 +--R cos(x) +--R + +--R 9 6 10 5 11 4 12 3 +--R - 9518080a b + 47617856a b - 95762368a b + 96786248a b +--R + +--R 13 2 14 +--R - 49166416a b + 10042760a b +--R * +--R 8 +--R cos(x) +--R + +--R 10 5 11 4 12 3 13 2 +--R - 832832a b + 3188640a b - 4582032a b + 2929864a b +--R + +--R 14 +--R - 703640a b +--R * +--R 6 +--R cos(x) +--R + +--R 11 4 12 3 13 2 14 4 +--R (- 37856a b + 101868a b - 90276a b + 26265a b)cos(x) +--R + +--R 12 3 13 2 14 2 13 2 14 +--R (- 676a b + 1070a b - 394a b)cos(x) - 2a b + a b +--R * +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R Type: Expression(Integer) +--E 324 + +--S 325 of 510 +m0263b:= a0263.2-r0263 +--R +--R +--R (299) +--R (- b + a) +--R * +--R log +--R +------------------+ +--R | 2 +--R 4 2 +-----+ |(b - a)cos(x) + a +--R ((- 8b + 8a)cos(x) - 4a cos(x) )\|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (8a b - 8a )cos(x) + a +--R + +--R +-------------+ +--R | 2 +--R +-----+ +-+ tan(x)\|b cot(x) + a +--R 4\|b - a \|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R +---+ +-----+ +--R 4\|- b \|b - a +--R * +--R +------------------+ +--R | 2 +--R 2 +---+ |(b - a)cos(x) + a 2 +---+ +-----+ +--R cos(x) \|- b |------------------ + (- cos(x) + 1)\|- b \|b - a +--R | 2 +--R \| cos(x) +--R atan(------------------------------------------------------------------) +--R b +--R + +--R +-------+ +--R +-------+ +-----+ cot(x)\|- b + a +--R 4\|- b + a \|b - a atan(----------------) +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R / +--R +-----+ +--R 4\|b - a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 510 +d0263b:= D(m0263b,x) +--R +--R +--R (300) +--R 3 2 2 5 2 2 3 +--R (8b - 16a b + 8a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 +--R a b cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 3 5 2 3 3 3 +--R (8a b - 16a b + 8a )cos(x) + (8a b - 8a )cos(x) + a cos(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 3 2 2 5 2 2 3 +--R (- 8b + 16a b - 8a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 2 +--R - a b cos(x) +--R * +--R sin(x) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 5 +--R (- 8b + 16a b - 8a b)cos(x) +--R + +--R 2 2 3 2 +--R (- 12a b + 12a b)cos(x) - 4a b cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 3 5 2 3 3 +--R (- 8a b + 16a b - 8a )cos(x) + (- 12a b + 12a )cos(x) +--R + +--R 3 +--R - 4a cos(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 3 2 2 5 2 2 3 +--R (8b - 16a b + 8a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 2 +--R 4a b cos(x) +--R * +--R sin(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R + +--R 2 2 6 2 2 4 +--R (- 8a b + 8a b)cos(x) + (8a b - 12a b)cos(x) +--R + +--R 2 2 +--R 4a b cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 6 2 3 4 3 2 +--R (- 8a b + 8a )cos(x) + (8a b - 12a )cos(x) + 4a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 6 3 2 4 2 2 +--R ((8b - 8a b )cos(x) + (- 8b + 12a b )cos(x) - 4a b cos(x) ) +--R * +--R 3 +--R cot(x) +--R + +--R 3 2 6 3 2 4 2 2 +--R ((8b - 8a b )cos(x) + (- 8b + 12a b )cos(x) - 4a b cos(x) ) +--R * +--R cot(x) +--R * +--R tan(x) +--R + +--R 3 2 6 3 2 4 2 2 +--R ((- 8b + 8a b )cos(x) + (8b - 12a b )cos(x) + 4a b cos(x) ) +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 6 3 2 4 2 2 +--R (- 8b + 8a b )cos(x) + (8b - 12a b )cos(x) + 4a b cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ |(b - a)cos(x) + a +--R \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 3 2 2 3 4 2 2 3 2 3 +--R (- 8a b + 24a b - 16a b)cos(x) + (- 8a b + 9a b)cos(x) - a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 3 4 6 2 2 3 4 4 +--R (8a b - 16a b + 8a )cos(x) + (- 8a b + 24a b - 16a )cos(x) +--R + +--R 3 4 2 4 +--R (- 8a b + 9a )cos(x) - a +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 2 6 4 3 2 2 4 +--R (- 8b + 16a b - 8a b )cos(x) + (8b - 24a b + 16a b )cos(x) +--R + +--R 3 2 2 2 2 2 +--R (8a b - 9a b )cos(x) + a b +--R * +--R 3 +--R cot(x) +--R + +--R 4 3 2 2 6 4 3 2 2 4 +--R (- 8b + 16a b - 8a b )cos(x) + (8b - 24a b + 16a b )cos(x) +--R + +--R 3 2 2 2 2 2 +--R (8a b - 9a b )cos(x) + a b +--R * +--R cot(x) +--R * +--R tan(x) +--R + +--R 4 3 2 2 6 4 3 2 2 4 +--R (8b - 16a b + 8a b )cos(x) + (- 8b + 24a b - 16a b )cos(x) +--R + +--R 3 2 2 2 2 2 +--R (- 8a b + 9a b )cos(x) - a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 2 6 4 3 2 2 4 +--R (8b - 16a b + 8a b )cos(x) + (- 8b + 24a b - 16a b )cos(x) +--R + +--R 3 2 2 2 2 2 +--R (- 8a b + 9a b )cos(x) - a b +--R / +--R 2 6 2 4 2 +--R ((8b - 8a b)cos(x) + (- 8b + 12a b)cos(x) - 4a b cos(x) ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 2 4 2 2 +--R (8a b - 8a )cos(x) + (- 8a b + 12a )cos(x) - 4a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 6 2 4 2 +--R (- 8b + 8a b)cos(x) + (8b - 12a b)cos(x) + 4a b cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ |(b - a)cos(x) + a +--R \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 8b + 16a b - 8a b)cos(x) + (8b - 24a b + 16a b)cos(x) +--R + +--R 2 2 2 2 +--R (8a b - 9a b)cos(x) + a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 3 6 2 2 3 4 +--R (- 8a b + 16a b - 8a )cos(x) + (8a b - 24a b + 16a )cos(x) +--R + +--R 2 3 2 3 +--R (8a b - 9a )cos(x) + a +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (8b - 16a b + 8a b)cos(x) + (- 8b + 24a b - 16a b)cos(x) +--R + +--R 2 2 2 2 +--R (- 8a b + 9a b)cos(x) - a b +--R * +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 510 +t0264:= 1/(a+b*cot(x)^2)^(1/2) +--R +--R +--R 1 +--R (301) ---------------- +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R Type: Expression(Integer) +--E 327 + +--S 328 of 510 +r0264:= -atan((a-b)^(1/2)*cot(x)/(a+b*cot(x)^2)^(1/2))/(a-b)^(1/2) +--R +--R +--R +-------+ +--R cot(x)\|- b + a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R (302) - ---------------------- +--R +-------+ +--R \|- b + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 510 +a0264:= integrate(t0264,x) +--R +--R +--R (303) +--R log +--R +------------------+ +--R | 2 +--R 4 2 +-----+ |(b - a)cos(x) + a +--R ((- 8b + 8a)cos(x) - 4a cos(x) )\|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (8a b - 8a )cos(x) + a +--R / +--R +-----+ +--R 4\|b - a +--R Type: Union(Expression(Integer),...) +--E 329 + +--S 330 of 510 +m0264:= a0264-r0264 +--R +--R +--R (304) +--R +-------+ +--R \|- b + a +--R * +--R log +--R +------------------+ +--R | 2 +--R 4 2 +-----+ |(b - a)cos(x) + a +--R ((- 8b + 8a)cos(x) - 4a cos(x) )\|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 +--R (8b - 16a b + 8a )cos(x) + (8a b - 8a )cos(x) + a +--R + +--R +-------+ +--R +-----+ cot(x)\|- b + a +--R 4\|b - a atan(----------------) +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R / +--R +-------+ +-----+ +--R 4\|- b + a \|b - a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 510 +d0264:= D(m0264,x) +--R +--R +--R (305) +--R +------------------+ +--R | 2 +--R 4 2 +-----+ |(b - a)cos(x) + a +--R ((- 8b + 8a)cos(x) - 4a cos(x) )sin(x)\|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 4 2 2 2 +--R ((8b - 16a b + 8a )cos(x) + (8a b - 8a )cos(x) + a )sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R + +--R 2 2 5 2 3 2 +--R ((- 8b + 16a b - 8a )cos(x) + (- 8a b + 8a )cos(x) - a cos(x)) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 5 2 3 2 +-----+ +--R ((8b - 16a b + 8a )cos(x) + (12a b - 12a )cos(x) + 4a cos(x))\|b - a +--R / +--R 2 2 5 2 3 2 +--R ((8b - 16a b + 8a )cos(x) + (8a b - 8a )cos(x) + a cos(x)) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 5 2 3 2 +--R ((- 8b + 16a b - 8a )cos(x) + (- 12a b + 12a )cos(x) - 4a cos(x)) +--R * +--R +-----+ +--R \|b - a +--R * +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 510 +t0265:= (-1-cot(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (306) (- cot(x) - 1)\|- cot(x) - 1 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 510 +r0265:= 1/2*(-csc(x)^2)^(1/2)*(atanh(cos(x))+cot(x)*csc(x))*sin(x) +--R +--R +--R +---------+ +--R | 2 +--R (sin(x)atanh(cos(x)) + cot(x)csc(x)sin(x))\|- csc(x) +--R (307) ------------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 333 + +--S 334 of 510 +a0265:= integrate(t0265,x) +--R +--R +--R (308) +--R +---+ 4 +---+ 2 +---+ +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R (- \|- 1 (%e ) + 2\|- 1 (%e ) - \|- 1 )log(%e + 1) +--R + +--R +---+ 4 +---+ 2 +---+ +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R (\|- 1 (%e ) - 2\|- 1 (%e ) + \|- 1 )log(%e - 1) +--R + +--R +---+ 3 +---+ +--R +---+ x\|- 1 +---+ x\|- 1 +--R 2\|- 1 (%e ) + 2\|- 1 %e +--R / +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) - 4(%e ) + 2 +--R Type: Union(Expression(Integer),...) +--E 334 + +--S 335 of 510 +m0265:= a0265-r0265 +--R +--R +--R (309) +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R (- (%e ) + 2(%e ) - 1)sin(x)atanh(cos(x)) +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R - cot(x)csc(x)(%e ) + 2cot(x)csc(x)(%e ) +--R + +--R - cot(x)csc(x) +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 +--R \|- csc(x) +--R + +--R +---+ 4 +---+ 2 +---+ +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R (- \|- 1 (%e ) + 2\|- 1 (%e ) - \|- 1 )log(%e + 1) +--R + +--R +---+ 4 +---+ 2 +---+ +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R (\|- 1 (%e ) - 2\|- 1 (%e ) + \|- 1 )log(%e - 1) +--R + +--R +---+ 3 +---+ +--R +---+ x\|- 1 +---+ x\|- 1 +--R 2\|- 1 (%e ) + 2\|- 1 %e +--R / +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) - 4(%e ) + 2 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 510 +d0265:= D(m0265,x) +--R +--R +--R (310) +--R +---+ 3 +---------+ +--R 2 x\|- 1 | 2 +--R (16cos(x) - 16)(%e ) \|- csc(x) +--R + +--R +---+ 6 +--R 2 2 x\|- 1 +--R (- cos(x) + 1)cot(x)csc(x) (%e ) +--R + +--R +---+ 4 +--R 2 2 x\|- 1 +--R (3cos(x) - 3)cot(x)csc(x) (%e ) +--R + +--R +---+ 2 +--R 2 2 x\|- 1 +--R (- 3cos(x) + 3)cot(x)csc(x) (%e ) +--R + +--R 2 2 +--R (cos(x) - 1)cot(x)csc(x) +--R * +--R sin(x) +--R + +--R +---+ 6 +--R 3 2 x\|- 1 +--R (cos(x) - cos(x))csc(x) (%e ) +--R + +--R +---+ 4 +--R 3 2 x\|- 1 +--R (- 3cos(x) + 3cos(x))csc(x) (%e ) +--R + +--R +---+ 2 +--R 3 2 x\|- 1 3 2 +--R (3cos(x) - 3cos(x))csc(x) (%e ) + (- cos(x) + cos(x))csc(x) +--R * +--R atanh(cos(x)) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 x\|- 1 +--R csc(x) (%e ) - 3csc(x) (%e ) + 3csc(x) (%e ) +--R + +--R 2 +--R - csc(x) +--R * +--R 2 +--R sin(x) +--R + +--R +---+ 6 +--R 2 2 2 3 x\|- 1 +--R ((- 3cos(x) + 3)cot(x) - cos(x) + 1)csc(x) (%e ) +--R + +--R +---+ 4 +--R 2 2 2 3 x\|- 1 +--R ((9cos(x) - 9)cot(x) + 3cos(x) - 3)csc(x) (%e ) +--R + +--R +---+ 2 +--R 2 2 2 3 x\|- 1 +--R ((- 9cos(x) + 9)cot(x) - 3cos(x) + 3)csc(x) (%e ) +--R + +--R 2 2 2 3 +--R ((3cos(x) - 3)cot(x) + cos(x) - 1)csc(x) +--R * +--R sin(x) +--R + +--R +---+ 6 +--R 3 3 x\|- 1 +--R (cos(x) - cos(x))cot(x)csc(x) (%e ) +--R + +--R +---+ 4 +--R 3 3 x\|- 1 +--R (- 3cos(x) + 3cos(x))cot(x)csc(x) (%e ) +--R + +--R +---+ 2 +--R 3 3 x\|- 1 +--R (3cos(x) - 3cos(x))cot(x)csc(x) (%e ) +--R + +--R 3 3 +--R (- cos(x) + cos(x))cot(x)csc(x) +--R / +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (2cos(x) - 2)(%e ) + (- 6cos(x) + 6)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (6cos(x) - 6)(%e ) - 2cos(x) + 2 +--R * +--R +---------+ +--R | 2 +--R \|- csc(x) +--R Type: Expression(Integer) +--E 336 + +--S 337 of 510 +t0266:= (a+b*cot(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (311) (b cot(x) + a)\|b cot(x) + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 510 +r0266:= -(a-b)^(3/2)*atan((a-b)^(1/2)*cot(x)/(a+b*cot(x)^2)^(1/2))-_ + 3/2*a*b^(1/2)*atanh((a+b*cot(x)^2)^(1/2)*tan(x)/b^(1/2))+_ + b^(3/2)*atanh((a+b*cot(x)^2)^(1/2)*tan(x)/b^(1/2))-_ + 1/2*b*cot(x)*(a+b*cot(x)^2)^(1/2) +--R +--R +--R (312) +--R +-------------+ +--R | 2 +--R +-+ tan(x)\|b cot(x) + a +--R (2b - 3a)\|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R +-------+ +-------------+ +--R +-------+ cot(x)\|- b + a | 2 +--R (2b - 2a)\|- b + a atan(----------------) - b cot(x)\|b cot(x) + a +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 338 + +--S 339 of 510 +a0266:= integrate(t0266,x) +--R +--R +--R (313) +--R [ +--R 2 2 6 2 2 4 +--R (16b - 40a b + 24a )cos(x) + (- 16b + 48a b - 36a )cos(x) +--R + +--R 2 2 +--R (- 8a b + 12a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ +-+ |(b - a)cos(x) + a +--R \|b - a \|b |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (- 16b + 56a b - 64a b + 24a )cos(x) +--R + +--R 3 2 2 3 4 +--R (16b - 72a b + 104a b - 48a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (16a b - 42a b + 27a )cos(x) + 2a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R log +--R 3 2 2 3 8 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (- 64b + 352a b - 512a b + 224a )cos(x) +--R + +--R 2 2 3 4 +--R (- 64a b + 176a b - 112a )cos(x) +--R + +--R 2 3 2 +--R (- 12a b + 14a )cos(x) +--R * +--R +-+ +--R \|b +--R + +--R 3 2 2 3 10 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 8 +--R (128b - 576a b + 768a b - 320a )cos(x) +--R + +--R 3 2 2 3 6 +--R (- 64b + 320a b - 528a b + 272a )cos(x) +--R + +--R 2 2 3 4 +--R (- 64a b + 144a b - 88a )cos(x) +--R + +--R 2 3 2 +--R (- 12a b + 8a )cos(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 8 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (64b - 416a b + 640a b - 288a )cos(x) +--R + +--R 2 2 3 4 2 3 2 +--R (96a b - 304a b + 208a )cos(x) + (36a b - 50a )cos(x) +--R + +--R 3 +--R 2a +--R * +--R +-----+ +-+ +--R \|b - a \|b +--R + +--R 4 3 2 2 3 4 10 +--R (128b - 512a b + 768a b - 512a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 128b + 768a b - 1536a b + 1280a b - 384a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (64b - 448a b + 1120a b - 1152a b + 416a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (96a b - 352a b + 448a b - 192a )cos(x) +--R + +--R 2 2 3 4 2 3 4 +--R (36a b - 68a b + 33a )cos(x) + 2a b - a +--R / +--R 3 2 2 3 10 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 8 +--R (- 128b + 576a b - 768a b + 320a )cos(x) +--R + +--R 2 2 3 6 +--R (- 192a b + 464a b - 272a )cos(x) +--R + +--R 2 3 4 3 2 +--R (- 80a b + 88a )cos(x) - 8a cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ |(b - a)cos(x) + a +--R \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 4 3 2 2 3 4 10 +--R (- 128b + 512a b - 768a b + 512a b - 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (128b - 768a b + 1536a b - 1280a b + 384a )cos(x) +--R + +--R 3 2 2 3 4 6 +--R (256a b - 928a b + 1088a b - 416a )cos(x) +--R + +--R 2 2 3 4 4 3 4 2 4 +--R (160a b - 352a b + 192a )cos(x) + (32a b - 33a )cos(x) + a +--R + +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 8b + 28a b - 32a b + 12a )cos(x) +--R + +--R 2 2 3 2 +--R (- 4a b + 8a b - 4a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (8b - 32a b + 40a b - 16a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (8a b - 17a b + 9a )cos(x) + a b - a +--R * +--R +-----+ +--R \|b - a +--R * +--R log +--R 2 4 2 +-----+ +--R ((- 128b + 128a b)cos(x) - 64a b cos(x) )\|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 4 2 2 2 +--R (128b - 256a b + 128a b)cos(x) + (128a b - 128a b)cos(x) +--R + +--R 2 +--R 16a b +--R / +--R b - a +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (8b - 28a b + 32a b - 12a )cos(x) +--R + +--R 2 2 3 2 +--R (4a b - 8a b + 4a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 4 2 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (- 8a b + 6a b)cos(x) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 8b + 32a b - 40a b + 16a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 8a b + 17a b - 9a )cos(x) - a b + a +--R * +--R log(4b) +--R + +--R 3 2 2 4 2 2 2 2 +--R (16b - 24a b + 8a b)cos(x) + (16a b - 10a b)cos(x) + 2a b +--R * +--R +-----+ +--R \|b - a +--R / +--R 6 4 2 +-----+ +--R ((32b - 32a)cos(x) + (- 32b + 48a)cos(x) - 16a cos(x) )\|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 6 2 2 4 +--R (- 32b + 64a b - 32a )cos(x) + (32b - 96a b + 64a )cos(x) +--R + +--R 2 2 2 +--R (32a b - 36a )cos(x) + 4a +--R , +--R +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 8b + 28a b - 32a b + 12a )cos(x) +--R + +--R 2 2 3 2 +--R (- 4a b + 8a b - 4a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (8b - 32a b + 40a b - 16a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (8a b - 17a b + 9a )cos(x) + a b - a +--R * +--R +-----+ +--R \|b - a +--R * +--R log +--R 2 4 2 +-----+ +--R ((- 128b + 128a b)cos(x) - 64a b cos(x) )\|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 4 2 2 2 +--R (128b - 256a b + 128a b)cos(x) + (128a b - 128a b)cos(x) +--R + +--R 2 +--R 16a b +--R / +--R b - a +--R + +--R 2 2 6 2 2 4 +--R (- 32b + 80a b - 48a )cos(x) + (32b - 96a b + 72a )cos(x) +--R + +--R 2 2 +--R (16a b - 24a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R +---+ +-----+ |(b - a)cos(x) + a +--R \|- b \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 112a b + 128a b - 48a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 32b + 144a b - 208a b + 96a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 32a b + 84a b - 54a )cos(x) - 4a b + 6a +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +------------------+ +--R | 2 +--R 2 +---+ |(b - a)cos(x) + a 2 +---+ +-----+ +--R cos(x) \|- b |------------------ + (- cos(x) + 1)\|- b \|b - a +--R | 2 +--R \| cos(x) +--R ------------------------------------------------------------------ +--R b +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (8b - 28a b + 32a b - 12a )cos(x) +--R + +--R 2 2 3 2 +--R (4a b - 8a b + 4a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 4 2 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (- 8a b + 6a b)cos(x) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 8b + 32a b - 40a b + 16a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 8a b + 17a b - 9a )cos(x) - a b + a +--R * +--R log(4b) +--R + +--R 3 2 2 4 2 2 2 2 +--R (16b - 24a b + 8a b)cos(x) + (16a b - 10a b)cos(x) + 2a b +--R * +--R +-----+ +--R \|b - a +--R / +--R 6 4 2 +-----+ +--R ((32b - 32a)cos(x) + (- 32b + 48a)cos(x) - 16a cos(x) )\|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 6 2 2 4 +--R (- 32b + 64a b - 32a )cos(x) + (32b - 96a b + 64a )cos(x) +--R + +--R 2 2 2 +--R (32a b - 36a )cos(x) + 4a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 339 + +--S 340 of 510 +m0266a:= a0266.1-r0266 +--R +--R +--R (314) +--R 2 2 6 2 2 4 +--R (16b - 40a b + 24a )cos(x) + (- 16b + 48a b - 36a )cos(x) +--R + +--R 2 2 +--R (- 8a b + 12a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ +-+ |(b - a)cos(x) + a +--R \|b - a \|b |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (- 16b + 56a b - 64a b + 24a )cos(x) +--R + +--R 3 2 2 3 4 +--R (16b - 72a b + 104a b - 48a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (16a b - 42a b + 27a )cos(x) + 2a b - 3a +--R * +--R +-+ +--R \|b +--R * +--R log +--R 3 2 2 3 8 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (- 64b + 352a b - 512a b + 224a )cos(x) +--R + +--R 2 2 3 4 +--R (- 64a b + 176a b - 112a )cos(x) +--R + +--R 2 3 2 +--R (- 12a b + 14a )cos(x) +--R * +--R +-+ +--R \|b +--R + +--R 3 2 2 3 10 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 8 +--R (128b - 576a b + 768a b - 320a )cos(x) +--R + +--R 3 2 2 3 6 +--R (- 64b + 320a b - 528a b + 272a )cos(x) +--R + +--R 2 2 3 4 2 3 2 +--R (- 64a b + 144a b - 88a )cos(x) + (- 12a b + 8a )cos(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 8 +--R (- 128b + 384a b - 384a b + 128a )cos(x) +--R + +--R 3 2 2 3 6 +--R (64b - 416a b + 640a b - 288a )cos(x) +--R + +--R 2 2 3 4 2 3 2 3 +--R (96a b - 304a b + 208a )cos(x) + (36a b - 50a )cos(x) + 2a +--R * +--R +-----+ +-+ +--R \|b - a \|b +--R + +--R 4 3 2 2 3 4 10 +--R (128b - 512a b + 768a b - 512a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 128b + 768a b - 1536a b + 1280a b - 384a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (64b - 448a b + 1120a b - 1152a b + 416a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (96a b - 352a b + 448a b - 192a )cos(x) +--R + +--R 2 2 3 4 2 3 4 +--R (36a b - 68a b + 33a )cos(x) + 2a b - a +--R / +--R 3 2 2 3 10 +--R (128b - 384a b + 384a b - 128a )cos(x) +--R + +--R 3 2 2 3 8 +--R (- 128b + 576a b - 768a b + 320a )cos(x) +--R + +--R 2 2 3 6 +--R (- 192a b + 464a b - 272a )cos(x) +--R + +--R 2 3 4 3 2 +--R (- 80a b + 88a )cos(x) - 8a cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ |(b - a)cos(x) + a +--R \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 4 3 2 2 3 4 10 +--R (- 128b + 512a b - 768a b + 512a b - 128a )cos(x) +--R + +--R 4 3 2 2 3 4 8 +--R (128b - 768a b + 1536a b - 1280a b + 384a )cos(x) +--R + +--R 3 2 2 3 4 6 +--R (256a b - 928a b + 1088a b - 416a )cos(x) +--R + +--R 2 2 3 4 4 3 4 2 4 +--R (160a b - 352a b + 192a )cos(x) + (32a b - 33a )cos(x) + a +--R + +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 8b + 28a b - 32a b + 12a )cos(x) +--R + +--R 2 2 3 2 +--R (- 4a b + 8a b - 4a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (8b - 32a b + 40a b - 16a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (8a b - 17a b + 9a )cos(x) + a b - a +--R * +--R +-----+ +--R \|b - a +--R * +--R log +--R 2 4 2 +-----+ +--R ((- 128b + 128a b)cos(x) - 64a b cos(x) )\|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 4 2 2 2 +--R (128b - 256a b + 128a b)cos(x) + (128a b - 128a b)cos(x) +--R + +--R 2 +--R 16a b +--R / +--R b - a +--R + +--R 2 2 6 2 2 4 +--R (- 32b + 80a b - 48a )cos(x) + (32b - 96a b + 72a )cos(x) +--R + +--R 2 2 +--R (16a b - 24a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ +-+ |(b - a)cos(x) + a +--R \|b - a \|b |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 112a b + 128a b - 48a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 32b + 144a b - 208a b + 96a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 32a b + 84a b - 54a )cos(x) - 4a b + 6a +--R * +--R +-+ +--R \|b +--R * +--R +-------------+ +--R | 2 +--R tan(x)\|b cot(x) + a +--R atanh(----------------------) +--R +-+ +--R \|b +--R + +--R 2 2 6 2 2 4 +--R (- 32b + 64a b - 32a )cos(x) + (32b - 80a b + 48a )cos(x) +--R + +--R 2 2 +--R (16a b - 16a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-------+ +-----+ |(b - a)cos(x) + a +--R \|- b + a \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 96a b + 96a b - 32a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 32b + 128a b - 160a b + 64a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 32a b + 68a b - 36a )cos(x) - 4a b + 4a +--R * +--R +-------+ +--R \|- b + a +--R * +--R +-------+ +--R cot(x)\|- b + a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R + +--R 2 6 2 4 2 +--R ((16b - 16a b)cos(x) + (- 16b + 24a b)cos(x) - 8a b cos(x) ) +--R * +--R +------------------+ +--R | 2 +--R +-----+ |(b - a)cos(x) + a +--R cot(x)\|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 16b + 32a b - 16a b)cos(x) + (16b - 48a b + 32a b)cos(x) +--R + +--R 2 2 2 2 +--R (16a b - 18a b)cos(x) + 2a b +--R * +--R cot(x) +--R * +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 2 +--R (8b - 28a b + 32a b - 12a )cos(x) + (4a b - 8a b + 4a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 4 2 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (- 8a b + 6a b)cos(x) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 8b + 32a b - 40a b + 16a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 8a b + 17a b - 9a )cos(x) - a b + a +--R * +--R log(4b) +--R + +--R 3 2 2 4 2 2 2 2 +--R (16b - 24a b + 8a b)cos(x) + (16a b - 10a b)cos(x) + 2a b +--R * +--R +-----+ +--R \|b - a +--R / +--R 6 4 2 +-----+ +--R ((32b - 32a)cos(x) + (- 32b + 48a)cos(x) - 16a cos(x) )\|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 6 2 2 4 +--R (- 32b + 64a b - 32a )cos(x) + (32b - 96a b + 64a )cos(x) +--R + +--R 2 2 2 +--R (32a b - 36a )cos(x) + 4a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 510 +--d0266a:= D(m0266a,x) +--E 341 + +--S 342 of 510 +m0266b:= a0266.2-r0266 +--R +--R +--R (315) +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 8b + 28a b - 32a b + 12a )cos(x) +--R + +--R 2 2 3 2 +--R (- 4a b + 8a b - 4a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (8b - 32a b + 40a b - 16a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (8a b - 17a b + 9a )cos(x) + a b - a +--R * +--R +-----+ +--R \|b - a +--R * +--R log +--R 2 4 2 +-----+ +--R ((- 128b + 128a b)cos(x) - 64a b cos(x) )\|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 4 2 2 2 +--R (128b - 256a b + 128a b)cos(x) + (128a b - 128a b)cos(x) +--R + +--R 2 +--R 16a b +--R / +--R b - a +--R + +--R 2 2 6 2 2 4 +--R (- 32b + 80a b - 48a )cos(x) + (32b - 96a b + 72a )cos(x) +--R + +--R 2 2 +--R (16a b - 24a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ +-+ |(b - a)cos(x) + a +--R \|b - a \|b |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 112a b + 128a b - 48a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 32b + 144a b - 208a b + 96a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 32a b + 84a b - 54a )cos(x) - 4a b + 6a +--R * +--R +-+ +--R \|b +--R * +--R +-------------+ +--R | 2 +--R tan(x)\|b cot(x) + a +--R atanh(----------------------) +--R +-+ +--R \|b +--R + +--R 2 2 6 2 2 4 +--R (- 32b + 80a b - 48a )cos(x) + (32b - 96a b + 72a )cos(x) +--R + +--R 2 2 +--R (16a b - 24a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R +---+ +-----+ |(b - a)cos(x) + a +--R \|- b \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 112a b + 128a b - 48a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 32b + 144a b - 208a b + 96a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 32a b + 84a b - 54a )cos(x) - 4a b + 6a +--R * +--R +---+ +--R \|- b +--R * +--R +------------------+ +--R | 2 +--R 2 +---+ |(b - a)cos(x) + a 2 +---+ +-----+ +--R cos(x) \|- b |------------------ + (- cos(x) + 1)\|- b \|b - a +--R | 2 +--R \| cos(x) +--R atan(------------------------------------------------------------------) +--R b +--R + +--R 2 2 6 2 2 4 +--R (- 32b + 64a b - 32a )cos(x) + (32b - 80a b + 48a )cos(x) +--R + +--R 2 2 +--R (16a b - 16a )cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-------+ +-----+ |(b - a)cos(x) + a +--R \|- b + a \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (32b - 96a b + 96a b - 32a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 32b + 128a b - 160a b + 64a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 32a b + 68a b - 36a )cos(x) - 4a b + 4a +--R * +--R +-------+ +--R \|- b + a +--R * +--R +-------+ +--R cot(x)\|- b + a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R + +--R 2 6 2 4 2 +--R ((16b - 16a b)cos(x) + (- 16b + 24a b)cos(x) - 8a b cos(x) ) +--R * +--R +------------------+ +--R | 2 +--R +-----+ |(b - a)cos(x) + a +--R cot(x)\|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- 16b + 32a b - 16a b)cos(x) + (16b - 48a b + 32a b)cos(x) +--R + +--R 2 2 2 2 +--R (16a b - 18a b)cos(x) + 2a b +--R * +--R cot(x) +--R * +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R + +--R 3 2 2 3 6 +--R (- 8b + 24a b - 24a b + 8a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 2 +--R (8b - 28a b + 32a b - 12a )cos(x) + (4a b - 8a b + 4a )cos(x) +--R * +--R log(4b) +--R + +--R 3 2 2 4 2 2 2 +--R (- 16b + 24a b - 8a b)cos(x) + (- 8a b + 6a b)cos(x) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 3 2 2 3 6 +--R (8b - 24a b + 24a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 8b + 32a b - 40a b + 16a )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 8a b + 17a b - 9a )cos(x) - a b + a +--R * +--R log(4b) +--R + +--R 3 2 2 4 2 2 2 2 +--R (16b - 24a b + 8a b)cos(x) + (16a b - 10a b)cos(x) + 2a b +--R * +--R +-----+ +--R \|b - a +--R / +--R 6 4 2 +-----+ +--R ((32b - 32a)cos(x) + (- 32b + 48a)cos(x) - 16a cos(x) )\|b - a +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 2 2 6 2 2 4 +--R (- 32b + 64a b - 32a )cos(x) + (32b - 96a b + 64a )cos(x) +--R + +--R 2 2 2 +--R (32a b - 36a )cos(x) + 4a +--R Type: Expression(Integer) +--E 342 + +--S 343 of 510 +d0266b:= D(m0266b,x) +--R +--R +--R (316) +--R 8 7 2 6 3 5 +--R - 4096b + 28672a b - 86016a b + 143360a b +--R + +--R 4 4 5 3 6 2 7 +--R - 143360a b + 86016a b - 28672a b + 4096a b +--R * +--R 15 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 16384a b + 98304a b - 245760a b + 327680a b +--R + +--R 5 3 6 2 7 +--R - 245760a b + 98304a b - 16384a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R - 26112a b + 130560a b - 261120a b + 261120a b +--R + +--R 6 2 7 +--R - 130560a b + 26112a b +--R * +--R 11 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R - 20992a b + 83968a b - 125952a b + 83968a b +--R + +--R 7 +--R - 20992a b +--R * +--R 9 +--R cos(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (- 8848a b + 26544a b - 26544a b + 8848a b)cos(x) +--R + +--R 5 3 6 2 7 5 +--R (- 1824a b + 3648a b - 1824a b)cos(x) +--R + +--R 6 2 7 3 7 +--R (- 146a b + 146a b)cos(x) - 2a b cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 4096a b + 28672a b - 86016a b + 143360a b +--R + +--R 5 3 6 2 7 8 +--R - 143360a b + 86016a b - 28672a b + 4096a +--R * +--R 15 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R - 16384a b + 98304a b - 245760a b + 327680a b +--R + +--R 6 2 7 8 +--R - 245760a b + 98304a b - 16384a +--R * +--R 13 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R - 26112a b + 130560a b - 261120a b + 261120a b +--R + +--R 7 8 +--R - 130560a b + 26112a +--R * +--R 11 +--R cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (- 20992a b + 83968a b - 125952a b + 83968a b - 20992a ) +--R * +--R 9 +--R cos(x) +--R + +--R 5 3 6 2 7 8 7 +--R (- 8848a b + 26544a b - 26544a b + 8848a )cos(x) +--R + +--R 6 2 7 8 5 +--R (- 1824a b + 3648a b - 1824a )cos(x) +--R + +--R 7 8 3 8 +--R (- 146a b + 146a )cos(x) - 2a cos(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 4096b - 28672a b + 86016a b - 143360a b + 143360a b +--R + +--R 5 3 6 2 7 +--R - 86016a b + 28672a b - 4096a b +--R * +--R 15 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R 16384a b - 98304a b + 245760a b - 327680a b +--R + +--R 5 3 6 2 7 +--R 245760a b - 98304a b + 16384a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R 26112a b - 130560a b + 261120a b - 261120a b +--R + +--R 6 2 7 +--R 130560a b - 26112a b +--R * +--R 11 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (20992a b - 83968a b + 125952a b - 83968a b + 20992a b) +--R * +--R 9 +--R cos(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (8848a b - 26544a b + 26544a b - 8848a b)cos(x) +--R + +--R 5 3 6 2 7 5 +--R (1824a b - 3648a b + 1824a b)cos(x) +--R + +--R 6 2 7 3 7 +--R (146a b - 146a b)cos(x) + 2a b cos(x) +--R * +--R sin(x) +--R * +--R +------------------+ +--R | 2 +--R |(b - a)cos(x) + a +--R |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 8 7 2 6 3 5 +--R 4096b - 28672a b + 86016a b - 143360a b +--R + +--R 4 4 5 3 6 2 7 +--R 143360a b - 86016a b + 28672a b - 4096a b +--R * +--R 15 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R 18432a b - 110592a b + 276480a b - 368640a b +--R + +--R 5 3 6 2 7 +--R 276480a b - 110592a b + 18432a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R 33792a b - 168960a b + 337920a b - 337920a b +--R + +--R 6 2 7 +--R 168960a b - 33792a b +--R * +--R 11 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R 32256a b - 129024a b + 193536a b - 129024a b +--R + +--R 7 +--R 32256a b +--R * +--R 9 +--R cos(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (16944a b - 50832a b + 50832a b - 16944a b)cos(x) +--R + +--R 5 3 6 2 7 5 +--R (4728a b - 9456a b + 4728a b)cos(x) +--R + +--R 6 2 7 3 7 +--R (608a b - 608a b)cos(x) + 24a b cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 6 3 5 4 4 +--R 4096a b - 28672a b + 86016a b - 143360a b +--R + +--R 5 3 6 2 7 8 +--R 143360a b - 86016a b + 28672a b - 4096a +--R * +--R 15 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R 18432a b - 110592a b + 276480a b - 368640a b +--R + +--R 6 2 7 8 +--R 276480a b - 110592a b + 18432a +--R * +--R 13 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R 33792a b - 168960a b + 337920a b - 337920a b +--R + +--R 7 8 +--R 168960a b - 33792a +--R * +--R 11 +--R cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (32256a b - 129024a b + 193536a b - 129024a b + 32256a ) +--R * +--R 9 +--R cos(x) +--R + +--R 5 3 6 2 7 8 7 +--R (16944a b - 50832a b + 50832a b - 16944a )cos(x) +--R + +--R 6 2 7 8 5 +--R (4728a b - 9456a b + 4728a )cos(x) +--R + +--R 7 8 3 8 +--R (608a b - 608a )cos(x) + 24a cos(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 8 7 2 6 3 5 +--R - 4096b + 28672a b - 86016a b + 143360a b +--R + +--R 4 4 5 3 6 2 7 +--R - 143360a b + 86016a b - 28672a b + 4096a b +--R * +--R 15 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 18432a b + 110592a b - 276480a b + 368640a b +--R + +--R 5 3 6 2 7 +--R - 276480a b + 110592a b - 18432a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R - 33792a b + 168960a b - 337920a b + 337920a b +--R + +--R 6 2 7 +--R - 168960a b + 33792a b +--R * +--R 11 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R - 32256a b + 129024a b - 193536a b + 129024a b +--R + +--R 7 +--R - 32256a b +--R * +--R 9 +--R cos(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (- 16944a b + 50832a b - 50832a b + 16944a b)cos(x) +--R + +--R 5 3 6 2 7 5 +--R (- 4728a b + 9456a b - 4728a b)cos(x) +--R + +--R 6 2 7 3 7 +--R (- 608a b + 608a b)cos(x) - 24a b cos(x) +--R * +--R sin(x) +--R * +--R +-----+ +--R \|b - a +--R * +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R + +--R 8 7 2 6 3 5 4 4 +--R - 4096b + 20480a b - 40960a b + 40960a b - 20480a b +--R + +--R 5 3 +--R 4096a b +--R * +--R 16 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 8192b - 51200a b + 122880a b - 143360a b + 81920a b +--R + +--R 5 3 +--R - 18432a b +--R * +--R 14 +--R cos(x) +--R + +--R 8 7 2 6 3 5 +--R - 4096b + 40960a b - 132096a b + 191488a b +--R + +--R 4 4 5 3 +--R - 130048a b + 33792a b +--R * +--R 12 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 10240a b + 59392a b - 120320a b + 103424a b +--R + +--R 5 3 +--R - 32256a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 8 +--R (- 9216a b + 34816a b - 42544a b + 16944a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 +--R (- 3584a b + 8288a b - 4728a b )cos(x) +--R + +--R 4 4 5 3 4 5 3 2 +--R (- 560a b + 608a b )cos(x) - 24a b cos(x) +--R * +--R 6 +--R cot(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 4096b + 14336a b - 10240a b - 20480a b + 40960a b +--R + +--R 5 3 6 2 +--R - 26624a b + 6144a b +--R * +--R 16 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 8192b - 38912a b + 46080a b + 40960a b - 133120a b +--R + +--R 5 3 6 2 +--R 104448a b - 27648a b +--R * +--R 14 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 4096b + 34816a b - 70656a b - 6656a b + 157184a b +--R + +--R 5 3 6 2 +--R - 161280a b + 50688a b +--R * +--R 12 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 10240a b + 44032a b - 31232a b - 77056a b +--R + +--R 5 3 6 2 +--R 122880a b - 48384a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 9216a b + 20992a b + 9680a b - 46872a b + 25416a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 6 +--R (- 3584a b + 2912a b + 7704a b - 7092a b )cos(x) +--R + +--R 4 4 5 3 6 2 4 +--R (- 560a b - 232a b + 912a b )cos(x) +--R + +--R 5 3 6 2 2 +--R (- 24a b - 36a b )cos(x) +--R * +--R 4 +--R cot(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 4096a b + 14336a b - 10240a b - 20480a b +--R + +--R 5 3 6 2 7 +--R 40960a b - 26624a b + 6144a b +--R * +--R 16 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 8192a b - 38912a b + 46080a b + 40960a b - 133120a b +--R + +--R 6 2 7 +--R 104448a b - 27648a b +--R * +--R 14 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 4096a b + 34816a b - 70656a b - 6656a b +--R + +--R 5 3 6 2 7 +--R 157184a b - 161280a b + 50688a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R - 10240a b + 44032a b - 31232a b - 77056a b +--R + +--R 6 2 7 +--R 122880a b - 48384a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 9216a b + 20992a b + 9680a b - 46872a b + 25416a b) +--R * +--R 8 +--R cos(x) +--R + +--R 4 4 5 3 6 2 7 6 +--R (- 3584a b + 2912a b + 7704a b - 7092a b)cos(x) +--R + +--R 5 3 6 2 7 4 +--R (- 560a b - 232a b + 912a b)cos(x) +--R + +--R 6 2 7 2 +--R (- 24a b - 36a b)cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R - 4096a b + 20480a b - 40960a b + 40960a b - 20480a b +--R + +--R 8 +--R 4096a +--R * +--R 16 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 8192a b - 51200a b + 122880a b - 143360a b + 81920a b +--R + +--R 8 +--R - 18432a +--R * +--R 14 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R - 4096a b + 40960a b - 132096a b + 191488a b - 130048a b +--R + +--R 8 +--R 33792a +--R * +--R 12 +--R cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (- 10240a b + 59392a b - 120320a b + 103424a b - 32256a ) +--R * +--R 10 +--R cos(x) +--R + +--R 5 3 6 2 7 8 8 +--R (- 9216a b + 34816a b - 42544a b + 16944a )cos(x) +--R + +--R 6 2 7 8 6 +--R (- 3584a b + 8288a b - 4728a )cos(x) +--R + +--R 7 8 4 8 2 +--R (- 560a b + 608a )cos(x) - 24a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 4096b + 26624a b - 71680a b + 102400a b - 81920a b +--R + +--R 5 3 6 2 +--R 34816a b - 6144a b +--R * +--R 16 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 8192b - 63488a b + 199680a b - 327680a b + 296960a b +--R + +--R 5 3 6 2 +--R - 141312a b + 27648a b +--R * +--R 14 +--R cos(x) +--R + +--R 8 7 2 6 3 5 +--R - 4096b + 47104a b - 193536a b + 389632a b +--R + +--R 4 4 5 3 6 2 +--R - 417280a b + 228864a b - 50688a b +--R * +--R 12 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 10240a b + 74752a b - 209408a b + 283904a b +--R + +--R 5 3 6 2 +--R - 187392a b + 48384a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R - 9216a b + 48640a b - 94768a b + 80760a b +--R + +--R 6 2 +--R - 25416a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 6 +--R (- 3584a b + 13664a b - 17160a b + 7092a b )cos(x) +--R + +--R 4 4 5 3 6 2 4 +--R (- 560a b + 1448a b - 912a b )cos(x) +--R + +--R 5 3 6 2 2 +--R (- 24a b + 36a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 4096b + 26624a b - 71680a b + 102400a b - 81920a b +--R + +--R 5 3 6 2 +--R 34816a b - 6144a b +--R * +--R 16 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 8192b - 63488a b + 199680a b - 327680a b + 296960a b +--R + +--R 5 3 6 2 +--R - 141312a b + 27648a b +--R * +--R 14 +--R cos(x) +--R + +--R 8 7 2 6 3 5 +--R - 4096b + 47104a b - 193536a b + 389632a b +--R + +--R 4 4 5 3 6 2 +--R - 417280a b + 228864a b - 50688a b +--R * +--R 12 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 10240a b + 74752a b - 209408a b + 283904a b +--R + +--R 5 3 6 2 +--R - 187392a b + 48384a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R - 9216a b + 48640a b - 94768a b + 80760a b +--R + +--R 6 2 +--R - 25416a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 6 +--R (- 3584a b + 13664a b - 17160a b + 7092a b )cos(x) +--R + +--R 4 4 5 3 6 2 4 +--R (- 560a b + 1448a b - 912a b )cos(x) +--R + +--R 5 3 6 2 2 +--R (- 24a b + 36a b )cos(x) +--R * +--R cot(x) +--R * +--R tan(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 4096b - 20480a b + 40960a b - 40960a b + 20480a b +--R + +--R 5 3 +--R - 4096a b +--R * +--R 16 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 8192b + 51200a b - 122880a b + 143360a b - 81920a b +--R + +--R 5 3 +--R 18432a b +--R * +--R 14 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 4096b - 40960a b + 132096a b - 191488a b + 130048a b +--R + +--R 5 3 +--R - 33792a b +--R * +--R 12 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (10240a b - 59392a b + 120320a b - 103424a b + 32256a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 8 +--R (9216a b - 34816a b + 42544a b - 16944a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 +--R (3584a b - 8288a b + 4728a b )cos(x) +--R + +--R 4 4 5 3 4 5 3 2 +--R (560a b - 608a b )cos(x) + 24a b cos(x) +--R * +--R 4 +--R cot(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 8192b - 45056a b + 102400a b - 122880a b + 81920a b +--R + +--R 5 3 6 2 +--R - 28672a b + 4096a b +--R * +--R 16 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 16384b + 110592a b - 296960a b + 409600a b - 307200a b +--R + +--R 5 3 6 2 +--R 118784a b - 18432a b +--R * +--R 14 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 8192b - 86016a b + 305152a b - 515072a b + 451584a b +--R + +--R 5 3 6 2 +--R - 197632a b + 33792a b +--R * +--R 12 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 20480a b - 129024a b + 300032a b - 327168a b + 167936a b +--R + +--R 6 2 +--R - 32256a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (18432a b - 78848a b + 119904a b - 76432a b + 16944a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 6 +--R (7168a b - 20160a b + 17744a b - 4728a b )cos(x) +--R + +--R 4 4 5 3 6 2 4 5 3 6 2 2 +--R (1120a b - 1776a b + 608a b )cos(x) + (48a b - 24a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 4096b - 22528a b + 49152a b - 51200a b + 20480a b + 6144a b +--R + +--R 6 2 7 +--R - 8192a b + 2048a b +--R * +--R 16 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 8192b + 55296a b - 144384a b + 179200a b - 92160a b +--R + +--R 5 3 6 2 7 +--R - 12288a b + 31744a b - 9216a b +--R * +--R 14 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 4096b - 43008a b + 150528a b - 237056a b + 159744a b +--R + +--R 5 3 6 2 7 +--R - 3072a b - 48128a b + 16896a b +--R * +--R 12 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 10240a b - 64512a b + 144896a b - 133888a b + 23808a b +--R + +--R 6 2 7 +--R 35584a b - 16128a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 9216a b - 39424a b + 55344a b - 20808a b - 12800a b +--R + +--R 7 +--R 8472a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 6 +--R (3584a b - 10080a b + 7080a b + 1780a b - 2364a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 4 +--R (560a b - 888a b + 24a b + 304a b)cos(x) +--R + +--R 5 3 6 2 7 2 +--R (24a b - 12a b - 12a b)cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ |(b - a)cos(x) + a +--R \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 4096b - 24576a b + 61440a b - 81920a b + 61440a b +--R + +--R 5 4 6 3 +--R - 24576a b + 4096a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 8192b + 61440a b - 184320a b + 286720a b - 245760a b +--R + +--R 5 4 6 3 +--R 110592a b - 20480a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 4096b - 49152a b + 198144a b - 382976a b + 390144a b +--R + +--R 5 4 6 3 +--R - 202752a b + 42496a b +--R * +--R 12 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 12288a b - 89088a b + 240640a b - 310272a b + 193536a b +--R + +--R 6 3 +--R - 47104a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R (13824a b - 69632a b + 127632a b - 101664a b + 29840a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 6 +--R (7168a b - 24864a b + 28368a b - 10672a b )cos(x) +--R + +--R 4 5 5 4 6 3 4 +--R (1680a b - 3648a b + 1970a b )cos(x) +--R + +--R 5 4 6 3 2 6 3 +--R (144a b - 148a b )cos(x) + 2a b +--R * +--R 6 +--R cot(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 4096b - 18432a b + 24576a b + 10240a b - 61440a b +--R + +--R 5 4 6 3 7 2 +--R 67584a b - 32768a b + 6144a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 8192b + 49152a b - 92160a b + 10240a b + 184320a b +--R + +--R 5 4 6 3 7 2 +--R - 258048a b + 145408a b - 30720a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 4096b - 43008a b + 124416a b - 85760a b - 184320a b +--R + +--R 5 4 6 3 7 2 +--R 382464a b - 261632a b + 63744a b +--R * +--R 12 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 12288a b - 70656a b + 107008a b + 50688a b - 271872a b +--R + +--R 6 3 7 2 +--R 243200a b - 70656a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 13824a b - 48896a b + 23184a b + 89784a b - 122656a b +--R + +--R 7 2 +--R 44760a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 6 +--R (7168a b - 14112a b - 8928a b + 31880a b - 16008a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 4 +--R (1680a b - 1128a b - 3502a b + 2955a b )cos(x) +--R + +--R 5 4 6 3 7 2 2 6 3 7 2 +--R (144a b + 68a b - 222a b )cos(x) + 2a b + 3a b +--R * +--R 4 +--R cot(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 4096a b - 18432a b + 24576a b + 10240a b - 61440a b +--R + +--R 6 3 7 2 8 +--R 67584a b - 32768a b + 6144a b +--R * +--R 16 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 8192a b + 49152a b - 92160a b + 10240a b + 184320a b +--R + +--R 6 3 7 2 8 +--R - 258048a b + 145408a b - 30720a b +--R * +--R 14 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 4096a b - 43008a b + 124416a b - 85760a b - 184320a b +--R + +--R 6 3 7 2 8 +--R 382464a b - 261632a b + 63744a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 12288a b - 70656a b + 107008a b + 50688a b - 271872a b +--R + +--R 7 2 8 +--R 243200a b - 70656a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 13824a b - 48896a b + 23184a b + 89784a b - 122656a b +--R + +--R 8 +--R 44760a b +--R * +--R 8 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 6 +--R (7168a b - 14112a b - 8928a b + 31880a b - 16008a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 4 +--R (1680a b - 1128a b - 3502a b + 2955a b)cos(x) +--R + +--R 6 3 7 2 8 2 7 2 8 +--R (144a b + 68a b - 222a b)cos(x) + 2a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 4096a b - 24576a b + 61440a b - 81920a b + 61440a b +--R + +--R 8 9 +--R - 24576a b + 4096a +--R * +--R 16 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 8192a b + 61440a b - 184320a b + 286720a b - 245760a b +--R + +--R 8 9 +--R 110592a b - 20480a +--R * +--R 14 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 4096a b - 49152a b + 198144a b - 382976a b + 390144a b +--R + +--R 8 9 +--R - 202752a b + 42496a +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 12288a b - 89088a b + 240640a b - 310272a b + 193536a b +--R + +--R 9 +--R - 47104a +--R * +--R 10 +--R cos(x) +--R + +--R 5 4 6 3 7 2 8 9 8 +--R (13824a b - 69632a b + 127632a b - 101664a b + 29840a )cos(x) +--R + +--R 6 3 7 2 8 9 6 +--R (7168a b - 24864a b + 28368a b - 10672a )cos(x) +--R + +--R 7 2 8 9 4 8 9 2 9 +--R (1680a b - 3648a b + 1970a )cos(x) + (144a b - 148a )cos(x) + 2a +--R * +--R 2 +--R tan(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 4096b - 30720a b + 98304a b - 174080a b + 184320a b +--R + +--R 5 4 6 3 7 2 +--R - 116736a b + 40960a b - 6144a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 8192b + 73728a b - 276480a b + 563200a b - 675840a b +--R + +--R 5 4 6 3 7 2 +--R 479232a b - 186368a b + 30720a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 4096b - 55296a b + 271872a b - 680192a b + 964608a b +--R + +--R 5 4 6 3 7 2 +--R - 787968a b + 346624a b - 63744a b +--R * +--R 12 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 12288a b - 107520a b + 374272a b - 671232a b + 658944a b +--R + +--R 6 3 7 2 +--R - 337408a b + 70656a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 13824a b - 90368a b + 232080a b - 293112a b + 182336a b +--R + +--R 7 2 +--R - 44760a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 6 +--R (7168a b - 35616a b + 65664a b - 53224a b + 16008a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 4 +--R (1680a b - 6168a b + 7442a b - 2955a b )cos(x) +--R + +--R 5 4 6 3 7 2 2 6 3 7 2 +--R (144a b - 364a b + 222a b )cos(x) + 2a b - 3a b +--R * +--R 3 +--R cot(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 4096b - 30720a b + 98304a b - 174080a b + 184320a b +--R + +--R 5 4 6 3 7 2 +--R - 116736a b + 40960a b - 6144a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 8192b + 73728a b - 276480a b + 563200a b - 675840a b +--R + +--R 5 4 6 3 7 2 +--R 479232a b - 186368a b + 30720a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 4096b - 55296a b + 271872a b - 680192a b + 964608a b +--R + +--R 5 4 6 3 7 2 +--R - 787968a b + 346624a b - 63744a b +--R * +--R 12 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 12288a b - 107520a b + 374272a b - 671232a b + 658944a b +--R + +--R 6 3 7 2 +--R - 337408a b + 70656a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 13824a b - 90368a b + 232080a b - 293112a b + 182336a b +--R + +--R 7 2 +--R - 44760a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 6 +--R (7168a b - 35616a b + 65664a b - 53224a b + 16008a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 4 +--R (1680a b - 6168a b + 7442a b - 2955a b )cos(x) +--R + +--R 5 4 6 3 7 2 2 6 3 7 2 +--R (144a b - 364a b + 222a b )cos(x) + 2a b - 3a b +--R * +--R cot(x) +--R * +--R tan(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 4096b + 24576a b - 61440a b + 81920a b - 61440a b +--R + +--R 5 4 6 3 +--R 24576a b - 4096a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 8192b - 61440a b + 184320a b - 286720a b + 245760a b +--R + +--R 5 4 6 3 +--R - 110592a b + 20480a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 4096b + 49152a b - 198144a b + 382976a b - 390144a b +--R + +--R 5 4 6 3 +--R 202752a b - 42496a b +--R * +--R 12 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12288a b + 89088a b - 240640a b + 310272a b - 193536a b +--R + +--R 6 3 +--R 47104a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R (- 13824a b + 69632a b - 127632a b + 101664a b - 29840a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 6 +--R (- 7168a b + 24864a b - 28368a b + 10672a b )cos(x) +--R + +--R 4 5 5 4 6 3 4 +--R (- 1680a b + 3648a b - 1970a b )cos(x) +--R + +--R 5 4 6 3 2 6 3 +--R (- 144a b + 148a b )cos(x) - 2a b +--R * +--R 4 +--R cot(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 8192b + 53248a b - 147456a b + 225280a b - 204800a b +--R + +--R 5 4 6 3 7 2 +--R 110592a b - 32768a b + 4096a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 16384b - 131072a b + 430080a b - 757760a b + 778240a b +--R + +--R 5 4 6 3 7 2 +--R - 466944a b + 151552a b - 20480a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 8192b + 102400a b - 445440a b + 964096a b - 1163264a b +--R + +--R 5 4 6 3 7 2 +--R 795648a b - 287744a b + 42496a b +--R * +--R 12 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 24576a b + 190464a b - 570368a b + 861184a b - 697344a b +--R + +--R 6 3 7 2 +--R 287744a b - 47104a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 27648a b + 153088a b - 324896a b + 330960a b - 161344a b +--R + +--R 7 2 +--R 29840a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 6 +--R (- 14336a b + 56896a b - 81600a b + 49712a b - 10672a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 4 +--R (- 3360a b + 8976a b - 7588a b + 1970a b )cos(x) +--R + +--R 5 4 6 3 7 2 2 6 3 7 2 +--R (- 288a b + 440a b - 148a b )cos(x) - 4a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 4096b + 26624a b - 71680a b + 100352a b - 71680a b + 14336a b +--R + +--R 6 3 7 2 8 +--R 14336a b - 10240a b + 2048a b +--R * +--R 16 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 8192b - 65536a b + 210944a b - 348160a b + 296960a b - 90112a b +--R + +--R 6 3 7 2 8 +--R - 47104a b + 45056a b - 10240a b +--R * +--R 14 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 4096b + 51200a b - 220672a b + 457472a b - 482560a b +--R + +--R 5 4 6 3 7 2 8 +--R 206336a b + 51200a b - 80128a b + 21248a b +--R * +--R 12 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12288a b + 95232a b - 279040a b + 386048a b - 228352a b +--R + +--R 6 3 7 2 8 +--R - 11264a b + 73216a b - 23552a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 13824a b + 76544a b - 155536a b + 130664a b - 16856a b +--R + +--R 7 2 8 +--R - 35912a b + 14920a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R (- 7168a b + 28448a b - 37216a b + 12424a b + 8848a b - 5336a b) +--R * +--R 6 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 4 +--R (- 1680a b + 4488a b - 2954a b - 839a b + 985a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 2 6 3 7 2 8 +--R (- 144a b + 220a b - 2a b - 74a b)cos(x) - 2a b + a b + a b +--R / +--R 6 5 2 4 3 3 4 2 +--R 4096b - 20480a b + 40960a b - 40960a b + 20480a b +--R + +--R 5 +--R - 4096a b +--R * +--R 16 +--R cos(x) +--R + +--R 6 5 2 4 3 3 +--R - 8192b + 51200a b - 122880a b + 143360a b +--R + +--R 4 2 5 +--R - 81920a b + 18432a b +--R * +--R 14 +--R cos(x) +--R + +--R 6 5 2 4 3 3 +--R 4096b - 40960a b + 132096a b - 191488a b +--R + +--R 4 2 5 +--R 130048a b - 33792a b +--R * +--R 12 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 +--R 10240a b - 59392a b + 120320a b - 103424a b +--R + +--R 5 +--R 32256a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (9216a b - 34816a b + 42544a b - 16944a b)cos(x) +--R + +--R 3 3 4 2 5 6 +--R (3584a b - 8288a b + 4728a b)cos(x) +--R + +--R 4 2 5 4 5 2 +--R (560a b - 608a b)cos(x) + 24a b cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 4096a b - 20480a b + 40960a b - 40960a b + 20480a b +--R + +--R 6 +--R - 4096a +--R * +--R 16 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R - 8192a b + 51200a b - 122880a b + 143360a b - 81920a b +--R + +--R 6 +--R 18432a +--R * +--R 14 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 4096a b - 40960a b + 132096a b - 191488a b + 130048a b +--R + +--R 6 +--R - 33792a +--R * +--R 12 +--R cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (10240a b - 59392a b + 120320a b - 103424a b + 32256a ) +--R * +--R 10 +--R cos(x) +--R + +--R 3 3 4 2 5 6 8 +--R (9216a b - 34816a b + 42544a b - 16944a )cos(x) +--R + +--R 4 2 5 6 6 5 6 4 +--R (3584a b - 8288a b + 4728a )cos(x) + (560a b - 608a )cos(x) +--R + +--R 6 2 +--R 24a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 4096b + 20480a b - 40960a b + 40960a b - 20480a b +--R + +--R 5 +--R 4096a b +--R * +--R 16 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R 8192b - 51200a b + 122880a b - 143360a b + 81920a b +--R + +--R 5 +--R - 18432a b +--R * +--R 14 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 4096b + 40960a b - 132096a b + 191488a b - 130048a b +--R + +--R 5 +--R 33792a b +--R * +--R 12 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 10240a b + 59392a b - 120320a b + 103424a b - 32256a b) +--R * +--R 10 +--R cos(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (- 9216a b + 34816a b - 42544a b + 16944a b)cos(x) +--R + +--R 3 3 4 2 5 6 +--R (- 3584a b + 8288a b - 4728a b)cos(x) +--R + +--R 4 2 5 4 5 2 +--R (- 560a b + 608a b)cos(x) - 24a b cos(x) +--R * +--R +------------------+ +--R | 2 +--R +-----+ |(b - a)cos(x) + a +--R \|b - a |------------------ +--R | 2 +--R \| cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 4096b + 24576a b - 61440a b + 81920a b - 61440a b +--R + +--R 5 2 6 +--R 24576a b - 4096a b +--R * +--R 16 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 8192b - 61440a b + 184320a b - 286720a b + 245760a b +--R + +--R 5 2 6 +--R - 110592a b + 20480a b +--R * +--R 14 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 4096b + 49152a b - 198144a b + 382976a b - 390144a b +--R + +--R 5 2 6 +--R 202752a b - 42496a b +--R * +--R 12 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 +--R - 12288a b + 89088a b - 240640a b + 310272a b +--R + +--R 5 2 6 +--R - 193536a b + 47104a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 13824a b + 69632a b - 127632a b + 101664a b +--R + +--R 6 +--R - 29840a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 7168a b + 24864a b - 28368a b + 10672a b)cos(x) +--R + +--R 4 3 5 2 6 4 +--R (- 1680a b + 3648a b - 1970a b)cos(x) +--R + +--R 5 2 6 2 6 +--R (- 144a b + 148a b)cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 4096a b + 24576a b - 61440a b + 81920a b - 61440a b +--R + +--R 6 7 +--R 24576a b - 4096a +--R * +--R 16 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 8192a b - 61440a b + 184320a b - 286720a b + 245760a b +--R + +--R 6 7 +--R - 110592a b + 20480a +--R * +--R 14 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 4096a b + 49152a b - 198144a b + 382976a b - 390144a b +--R + +--R 6 7 +--R 202752a b - 42496a +--R * +--R 12 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 12288a b + 89088a b - 240640a b + 310272a b - 193536a b +--R + +--R 7 +--R 47104a +--R * +--R 10 +--R cos(x) +--R + +--R 3 4 4 3 5 2 6 7 8 +--R (- 13824a b + 69632a b - 127632a b + 101664a b - 29840a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 7168a b + 24864a b - 28368a b + 10672a )cos(x) +--R + +--R 5 2 6 7 4 6 7 2 +--R (- 1680a b + 3648a b - 1970a )cos(x) + (- 144a b + 148a )cos(x) +--R + +--R 7 +--R - 2a +--R * +--R 2 +--R tan(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 4096b - 24576a b + 61440a b - 81920a b + 61440a b - 24576a b +--R + +--R 6 +--R 4096a b +--R * +--R 16 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 8192b + 61440a b - 184320a b + 286720a b - 245760a b +--R + +--R 5 2 6 +--R 110592a b - 20480a b +--R * +--R 14 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 4096b - 49152a b + 198144a b - 382976a b + 390144a b +--R + +--R 5 2 6 +--R - 202752a b + 42496a b +--R * +--R 12 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 12288a b - 89088a b + 240640a b - 310272a b + 193536a b +--R + +--R 6 +--R - 47104a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 8 +--R (13824a b - 69632a b + 127632a b - 101664a b + 29840a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (7168a b - 24864a b + 28368a b - 10672a b)cos(x) +--R + +--R 4 3 5 2 6 4 5 2 6 2 6 +--R (1680a b - 3648a b + 1970a b)cos(x) + (144a b - 148a b)cos(x) + 2a b +--R * +--R +-------------+ +--R | 2 +--R \|b cot(x) + a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 510 +t0267:= sec(a+b*x) +--R +--R +--R (317) sec(b x + a) +--R Type: Expression(Integer) +--E 344 + +--S 345 of 510 +r0267:= atanh(sin(a+b*x))/b +--R +--R +--R atanh(sin(b x + a)) +--R (318) ------------------- +--R b +--R Type: Expression(Integer) +--E 345 + +--S 346 of 510 +a0267:= integrate(t0267,x) +--R +--R +--R (319) +--R sin(b x + a) + cos(b x + a) + 1 sin(b x + a) - cos(b x + a) - 1 +--R log(-------------------------------) - log(-------------------------------) +--R cos(b x + a) + 1 cos(b x + a) + 1 +--R --------------------------------------------------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 346 + +--S 347 of 510 +m0267:= a0267-r0267 +--R +--R +--R (320) +--R sin(b x + a) + cos(b x + a) + 1 +--R log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R - log(-------------------------------) - atanh(sin(b x + a)) +--R cos(b x + a) + 1 +--R / +--R b +--R Type: Expression(Integer) +--E 347 + +--S 348 of 510 +d0267:= D(m0267,x) +--R +--R +--R (321) +--R 4 2 2 +--R - 2sin(b x + a) + (- 2cos(b x + a) - cos(b x + a) + 2)sin(b x + a) +--R + +--R 3 +--R - cos(b x + a) + cos(b x + a) +--R / +--R 4 2 2 +--R sin(b x + a) + (- cos(b x + a) - 2cos(b x + a) - 2)sin(b x + a) +--R + +--R 2 +--R cos(b x + a) + 2cos(b x + a) + 1 +--R Type: Expression(Integer) +--E 348 + +--S 349 of 510 +t0268:= sec(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (322) \|sec(b x + a) +--R Type: Expression(Integer) +--E 349 + +--S 350 of 510 +r0268:= 2*cos(a+b*x)^(1/2)*EllipticF(1/2*a+1/2*b*x,2)*sec(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 350 + +--S 351 of 510 +a0268:= integrate(t0268,x) +--R +--R +--R x +--R ++ +-------------+ +--R (323) | \|sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 351 + +--S 352 of 510 +m0268:= a0268-r0268 +--R +--R +--R x +--R ++ +-------------+ +--R (324) | \|sec(%H b + a) d%H - r0268 +--R ++ +--R Type: Expression(Integer) +--E 352 + +--S 353 of 510 +d0268:= D(m0268,x) +--R +--R +--R +------------+ +--R (325) \|sec(b x + a) +--R Type: Expression(Integer) +--E 353 + +--S 354 of 510 +t0269:= sec(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (326) sec(b x + a)\|sec(b x + a) +--R Type: Expression(Integer) +--E 354 + +--S 355 of 510 +r0269:= -2*(1/cos(a+b*x))^(1/2)*(cos(a+b*x)^(1/2)*_ + EllipticE(1/2*a+1/2*b*x,2)-sin(a+b*x))/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 355 + +--S 356 of 510 +a0269:= integrate(t0269,x) +--R +--R +--R x +--R ++ +-------------+ +--R (327) | sec(%H b + a)\|sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 356 + +--S 357 of 510 +m0269:= a0269-r0269 +--R +--R +--R x +--R ++ +-------------+ +--R (328) | sec(%H b + a)\|sec(%H b + a) d%H - r0269 +--R ++ +--R Type: Expression(Integer) +--E 357 + +--S 358 of 510 +d0269:= D(m0269,x) +--R +--R +--R +------------+ +--R (329) sec(b x + a)\|sec(b x + a) +--R Type: Expression(Integer) +--E 358 + +--S 359 of 510 +t0270:= sec(a+b*x)^(5/2) +--R +--R +--R 2 +------------+ +--R (330) sec(b x + a) \|sec(b x + a) +--R Type: Expression(Integer) +--E 359 + +--S 360 of 510 +r0270:= 2/3*(1/cos(a+b*x))^(1/2)*(cos(a+b*x)^(3/2)*_ + EllipticF(1/2*a+1/2*b*x,2)+sin(a+b*x))/cos(a+b*x)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 360 + +--S 361 of 510 +a0270:= integrate(t0270,x) +--R +--R +--R x +--R ++ 2 +-------------+ +--R (331) | sec(%H b + a) \|sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 361 + +--S 362 of 510 +m0270:= a0270-r0270 +--R +--R +--R x +--R ++ 2 +-------------+ +--R (332) | sec(%H b + a) \|sec(%H b + a) d%H - r0270 +--R ++ +--R Type: Expression(Integer) +--E 362 + +--S 363 of 510 +d0270:= D(m0270,x) +--R +--R +--R 2 +------------+ +--R (333) sec(b x + a) \|sec(b x + a) +--R Type: Expression(Integer) +--E 363 + +--S 364 of 510 +t0271:= 1/sec(a+b*x)^(1/2) +--R +--R +--R 1 +--R (334) --------------- +--R +------------+ +--R \|sec(b x + a) +--R Type: Expression(Integer) +--E 364 + +--S 365 of 510 +r0271:= 2*cos(a+b*x)^(1/2)*EllipticE(1/2*a+1/2*b*x,2)*sec(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 365 + +--S 366 of 510 +a0271:= integrate(t0271,x) +--R +--R +--R x +--R ++ 1 +--R (335) | ---------------- d%H +--R ++ +-------------+ +--R \|sec(%H b + a) +--R Type: Union(Expression(Integer),...) +--E 366 + +--S 367 of 510 +m0271:= a0271-r0271 +--R +--R +--R x +--R ++ 1 +--R (336) | ---------------- d%H - r0271 +--R ++ +-------------+ +--R \|sec(%H b + a) +--R Type: Expression(Integer) +--E 367 + +--S 368 of 510 +d0271:= D(m0271,x) +--R +--R +--R 1 +--R (337) --------------- +--R +------------+ +--R \|sec(b x + a) +--R Type: Expression(Integer) +--E 368 + +--S 369 of 510 +t0272:= 1/sec(a+b*x)^(3/2) +--R +--R +--R 1 +--R (338) --------------------------- +--R +------------+ +--R sec(b x + a)\|sec(b x + a) +--R Type: Expression(Integer) +--E 369 + +--S 370 of 510 +r0272:= 2/3*(EllipticF(1/2*a+1/2*b*x,2)+_ + sin(a+b*x)*cos(a+b*x)^(1/2))/cos(a+b*x)^(1/2)/(1/cos(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 370 + +--S 371 of 510 +a0272:= integrate(t0272,x) +--R +--R +--R x +--R ++ 1 +--R (339) | ----------------------------- d%H +--R ++ +-------------+ +--R sec(%H b + a)\|sec(%H b + a) +--R Type: Union(Expression(Integer),...) +--E 371 + +--S 372 of 510 +m0272:= a0272-r0272 +--R +--R +--R x +--R ++ 1 +--R (340) | ----------------------------- d%H - r0272 +--R ++ +-------------+ +--R sec(%H b + a)\|sec(%H b + a) +--R Type: Expression(Integer) +--E 372 + +--S 373 of 510 +d0272:= D(m0272,x) +--R +--R +--R 1 +--R (341) --------------------------- +--R +------------+ +--R sec(b x + a)\|sec(b x + a) +--R Type: Expression(Integer) +--E 373 + +--S 374 of 510 +t0273:= 1/sec(a+b*x)^(5/2) +--R +--R +--R 1 +--R (342) ---------------------------- +--R 2 +------------+ +--R sec(b x + a) \|sec(b x + a) +--R Type: Expression(Integer) +--E 374 + +--S 375 of 510 +r0273:= 2/5*(3*EllipticE(1/2*a+1/2*b*x,2)+_ + sin(a+b*x)*cos(a+b*x)^(3/2))/cos(a+b*x)^(1/2)/(1/cos(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 375 + +--S 376 of 510 +a0273:= integrate(t0273,x) +--R +--R +--R x +--R ++ 1 +--R (343) | ------------------------------ d%H +--R ++ 2 +-------------+ +--R sec(%H b + a) \|sec(%H b + a) +--R Type: Union(Expression(Integer),...) +--E 376 + +--S 377 of 510 +m0273:= a0273-r0273 +--R +--R +--R x +--R ++ 1 +--R (344) | ------------------------------ d%H - r0273 +--R ++ 2 +-------------+ +--R sec(%H b + a) \|sec(%H b + a) +--R Type: Expression(Integer) +--E 377 + +--S 378 of 510 +d0273:= D(m0273,x) +--R +--R +--R 1 +--R (345) ---------------------------- +--R 2 +------------+ +--R sec(b x + a) \|sec(b x + a) +--R Type: Expression(Integer) +--E 378 + +--S 379 of 510 +t0274:= (c*sec(a+b*x))^(1/2) +--R +--R +--R +--------------+ +--R (346) \|c sec(b x + a) +--R Type: Expression(Integer) +--E 379 + +--S 380 of 510 +r0274:= 2*cos(a+b*x)^(1/2)*EllipticF(1/2*a+1/2*b*x,2)*(c*sec(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 380 + +--S 381 of 510 +a0274:= integrate(t0274,x) +--R +--R +--R x +--R ++ +---------------+ +--R (347) | \|c sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 510 +m0274:= a0274-r0274 +--R +--R +--R x +--R ++ +---------------+ +--R (348) | \|c sec(%H b + a) d%H - r0274 +--R ++ +--R Type: Expression(Integer) +--E 382 + +--S 383 of 510 +d0274:= D(m0274,x) +--R +--R +--R +--------------+ +--R (349) \|c sec(b x + a) +--R Type: Expression(Integer) +--E 383 + +--S 384 of 510 +t0275:= (c*sec(a+b*x))^(3/2) +--R +--R +--R +--------------+ +--R (350) c sec(b x + a)\|c sec(b x + a) +--R Type: Expression(Integer) +--E 384 + +--S 385 of 510 +r0275:= -2*c^2*(cos(a+b*x)^(1/2)*_ + EllipticE(1/2*a+1/2*b*x,2)-sin(a+b*x))/cos(a+b*x)/(c/cos(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 385 + +--S 386 of 510 +a0275:= integrate(t0275,x) +--R +--R +--R x +--R ++ +---------------+ +--R (351) | c sec(%H b + a)\|c sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 510 +m0275:= a0275-r0275 +--R +--R +--R x +--R ++ +---------------+ +--R (352) | c sec(%H b + a)\|c sec(%H b + a) d%H - r0275 +--R ++ +--R Type: Expression(Integer) +--E 387 + +--S 388 of 510 +d0275:= D(m0275,x) +--R +--R +--R +--------------+ +--R (353) c sec(b x + a)\|c sec(b x + a) +--R Type: Expression(Integer) +--E 388 + +--S 389 of 510 +t0276:= (c*sec(a+b*x))^(5/2) +--R +--R +--R 2 2 +--------------+ +--R (354) c sec(b x + a) \|c sec(b x + a) +--R Type: Expression(Integer) +--E 389 + +--S 390 of 510 +r0276:= 2/3*c^2*(c/cos(a+b*x))^(1/2)*(cos(a+b*x)^(3/2)*_ + EllipticF(1/2*a+1/2*b*x,2)+sin(a+b*x))/cos(a+b*x)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 390 + +--S 391 of 510 +a0276:= integrate(t0276,x) +--R +--R +--R x +--R ++ 2 2 +---------------+ +--R (355) | c sec(%H b + a) \|c sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 510 +m0276:= a0276-r0276 +--R +--R +--R x +--R ++ 2 2 +---------------+ +--R (356) | c sec(%H b + a) \|c sec(%H b + a) d%H - r0276 +--R ++ +--R Type: Expression(Integer) +--E 392 + +--S 393 of 510 +d0276:= D(m0276,x) +--R +--R +--R 2 2 +--------------+ +--R (357) c sec(b x + a) \|c sec(b x + a) +--R Type: Expression(Integer) +--E 393 + +--S 394 of 510 +t0277:= 1/(c*sec(a+b*x))^(1/2) +--R +--R +--R 1 +--R (358) ----------------- +--R +--------------+ +--R \|c sec(b x + a) +--R Type: Expression(Integer) +--E 394 + +--S 395 of 510 +r0277:= 2*EllipticE(1/2*a+1/2*b*x,2)/b/cos(a+b*x)^(1/2)/(c*sec(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 395 + +--S 396 of 510 +a0277:= integrate(t0277,x) +--R +--R +--R x +--R ++ 1 +--R (359) | ------------------ d%H +--R ++ +---------------+ +--R \|c sec(%H b + a) +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 510 +m0277:= a0277-r0277 +--R +--R +--R x +--R ++ 1 +--R (360) | ------------------ d%H - r0277 +--R ++ +---------------+ +--R \|c sec(%H b + a) +--R Type: Expression(Integer) +--E 397 + +--S 398 of 510 +d0277:= D(m0277,x) +--R +--R +--R 1 +--R (361) ----------------- +--R +--------------+ +--R \|c sec(b x + a) +--R Type: Expression(Integer) +--E 398 + +--S 399 of 510 +t0278:= 1/(c*sec(a+b*x))^(3/2) +--R +--R +--R 1 +--R (362) ------------------------------- +--R +--------------+ +--R c sec(b x + a)\|c sec(b x + a) +--R Type: Expression(Integer) +--E 399 + +--S 400 of 510 +r0278:= 2/3/c*(EllipticF(1/2*a+1/2*b*x,2)+sin(a+b*x)*_ + cos(a+b*x)^(1/2))/cos(a+b*x)^(1/2)/b/(c/cos(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 400 + +--S 401 of 510 +a0278:= integrate(t0278,x) +--R +--R +--R x +--R ++ 1 +--R (363) | --------------------------------- d%H +--R ++ +---------------+ +--R c sec(%H b + a)\|c sec(%H b + a) +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 510 +m0278:= a0278-r0278 +--R +--R +--R x +--R ++ 1 +--R (364) | --------------------------------- d%H - r0278 +--R ++ +---------------+ +--R c sec(%H b + a)\|c sec(%H b + a) +--R Type: Expression(Integer) +--E 402 + +--S 403 of 510 +d0278:= D(m0278,x) +--R +--R +--R 1 +--R (365) ------------------------------- +--R +--------------+ +--R c sec(b x + a)\|c sec(b x + a) +--R Type: Expression(Integer) +--E 403 + +--S 404 of 510 +t0279:= 1/(c*sec(a+b*x))^(5/2) +--R +--R +--R 1 +--R (366) -------------------------------- +--R 2 2 +--------------+ +--R c sec(b x + a) \|c sec(b x + a) +--R Type: Expression(Integer) +--E 404 + +--S 405 of 510 +r0279:= 2/5/c^2*(3*EllipticE(1/2*a+1/2*b*x,2)+_ + sin(a+b*x)*cos(a+b*x)^(3/2))/cos(a+b*x)^(1/2)/b/(c/cos(a+b*x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 405 + +--S 406 of 510 +a0279:= integrate(t0279,x) +--R +--R +--R x +--R ++ 1 +--R (367) | ---------------------------------- d%H +--R ++ 2 2 +---------------+ +--R c sec(%H b + a) \|c sec(%H b + a) +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 510 +m0279:= a0279-r0279 +--R +--R +--R x +--R ++ 1 +--R (368) | ---------------------------------- d%H - r0279 +--R ++ 2 2 +---------------+ +--R c sec(%H b + a) \|c sec(%H b + a) +--R Type: Expression(Integer) +--E 407 + +--S 408 of 510 +d0279:= D(m0279,x) +--R +--R +--R 1 +--R (369) -------------------------------- +--R 2 2 +--------------+ +--R c sec(b x + a) \|c sec(b x + a) +--R Type: Expression(Integer) +--E 408 + +--S 409 of 510 +t0280:= x*sec(a+b*x) +--R +--R +--R (370) x sec(b x + a) +--R Type: Expression(Integer) +--E 409 + +--S 410 of 510 +r0280:= %i*(-2*x*atan(exp(%i*(a+b*x)))*b+polylog(2,-%i*exp(%i*(a+b*x)))-_ + polylog(2,%i*exp(%i*(a+b*x))))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 410 + +--S 411 of 510 +a0280:= integrate(t0280,x) +--R +--R +--R x +--R ++ +--R (371) | %H sec(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 510 +m0280:= a0280-r0280 +--R +--R +--R x +--R ++ +--R (372) | %H sec(%H b + a)d%H - r0280 +--R ++ +--R Type: Expression(Integer) +--E 412 + +--S 413 of 510 +d0280:= D(m0280,x) +--R +--R +--R (373) x sec(b x + a) +--R Type: Expression(Integer) +--E 413 + +--S 414 of 510 +t0281:= x^2*sec(a+b*x) +--R +--R +--R 2 +--R (374) x sec(b x + a) +--R Type: Expression(Integer) +--E 414 + +--S 415 of 510 +r0281:= -2*(%i*x^2*atan(exp(%i*(a+b*x)))*b^2-_ + %i*x*polylog(2,-%i*exp(%i*(a+b*x)))*b+_ + %i*x*polylog(2,%i*exp(%i*(a+b*x)))*b+_ + polylog(3,-%i*exp(%i*(a+b*x)))-polylog(3,%i*exp(%i*(a+b*x))))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 415 + +--S 416 of 510 +a0281:= integrate(t0281,x) +--R +--R +--R x +--R ++ 2 +--R (375) | %H sec(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 416 + +--S 417 of 510 +m0281:= a0281-r0281 +--R +--R +--R x +--R ++ 2 +--R (376) | %H sec(%H b + a)d%H - r0281 +--R ++ +--R Type: Expression(Integer) +--E 417 + +--S 418 of 510 +d0281:= D(m0281,x) +--R +--R +--R 2 +--R (377) x sec(b x + a) +--R Type: Expression(Integer) +--E 418 + +--S 419 of 510 +t0282:= x^3*sec(a+b*x) +--R +--R +--R 3 +--R (378) x sec(b x + a) +--R Type: Expression(Integer) +--E 419 + +--S 420 of 510 +r0282:= -(2*%i*x^3*atan(exp(%i*(a+b*x)))*b^3-_ + 3*%i*x^2*polylog(2,-%i*exp(%i*(a+b*x)))*b^2+_ + 3*%i*x^2*polylog(2,%i*exp(%i*(a+b*x)))*b^2+_ + 6*x*polylog(3,-%i*exp(%i*(a+b*x)))*b-_ + 6*x*polylog(3,%i*exp(%i*(a+b*x)))*b+_ + 6*%i*polylog(4,-%i*exp(%i*(a+b*x)))-_ + 6*%i*polylog(4,%i*exp(%i*(a+b*x))))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 420 + +--S 421 of 510 +a0282:= integrate(t0282,x) +--R +--R +--R x +--R ++ 3 +--R (379) | %H sec(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 510 +m0282:= a0282-r0282 +--R +--R +--R x +--R ++ 3 +--R (380) | %H sec(%H b + a)d%H - r0282 +--R ++ +--R Type: Expression(Integer) +--E 422 + +--S 423 of 510 +d0282:= D(m0282,x) +--R +--R +--R 3 +--R (381) x sec(b x + a) +--R Type: Expression(Integer) +--E 423 + +--S 424 of 510 +t0283:= x^2*sec(a+b*x)^2 +--R +--R +--R 2 2 +--R (382) x sec(b x + a) +--R Type: Expression(Integer) +--E 424 + +--S 425 of 510 +r0283:= (-%i*x^2*b^2+2*x*log(1+exp(2*%i*(a+b*x)))*b-_ + %i*polylog(2,-exp(2*%i*(a+b*x)))+x^2*tan(a+b*x)*b^2)/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 425 + +--S 426 of 510 +a0283:= integrate(t0283,x) +--R +--R +--R x +--R ++ 2 2 +--R (383) | %H sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 426 + +--S 427 of 510 +m0283:= a0283-r0283 +--R +--R +--R x +--R ++ 2 2 +--R (384) | %H sec(%H b + a) d%H - r0283 +--R ++ +--R Type: Expression(Integer) +--E 427 + +--S 428 of 510 +d0283:= D(m0283,x) +--R +--R +--R 2 2 +--R (385) x sec(b x + a) +--R Type: Expression(Integer) +--E 428 + +--S 429 of 510 +t0284:= x^3*sec(a+b*x)^2 +--R +--R +--R 3 2 +--R (386) x sec(b x + a) +--R Type: Expression(Integer) +--E 429 + +--S 430 of 510 +r0284:= 1/2*(-2*%i*x^3*b^3+6*x^2*log(1+exp(2*%i*(a+b*x)))*b^2-_ + 6*%i*x*polylog(2,-exp(2*%i*(a+b*x)))*b+_ + 3*polylog(3,-exp(2*%i*(a+b*x)))+2*x^3*tan(a+b*x)*b^3)/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 430 + +--S 431 of 510 +a0284:= integrate(t0284,x) +--R +--R +--R x +--R ++ 3 2 +--R (387) | %H sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 431 + +--S 432 of 510 +m0284:= a0284-r0284 +--R +--R +--R x +--R ++ 3 2 +--R (388) | %H sec(%H b + a) d%H - r0284 +--R ++ +--R Type: Expression(Integer) +--E 432 + +--S 433 of 510 +d0284:= D(m0284,x) +--R +--R +--R 3 2 +--R (389) x sec(b x + a) +--R Type: Expression(Integer) +--E 433 + +--S 434 of 510 +t0285:= x*sec(a+b*x)^3 +--R +--R +--R 3 +--R (390) x sec(b x + a) +--R Type: Expression(Integer) +--E 434 + +--S 435 of 510 +r0285:= -%i*x*atan(exp(1)^(%i*b*x+%i*a))/b+_ + 1/2*%i*polylog(2,-%i*exp(1)^(%i*b*x+%i*a))/b^2-_ + 1/2*%i*polylog(2,%i*exp(1)^(%i*b*x+%i*a))/b^2-_ + 1/2*sec(a+b*x)/b^2+1/2*x*sec(a+b*x)*tan(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 435 + +--S 436 of 510 +a0285:= integrate(t0285,x) +--R +--R +--R x +--R ++ 3 +--R (391) | %H sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 510 +m0285:= a0285-r0285 +--R +--R +--R x +--R ++ 3 +--R (392) | %H sec(%H b + a) d%H - r0285 +--R ++ +--R Type: Expression(Integer) +--E 437 + +--S 438 of 510 +d0285:= D(m0285,x) +--R +--R +--R 3 +--R (393) x sec(b x + a) +--R Type: Expression(Integer) +--E 438 + +--S 439 of 510 +t0286:= x^2*sec(a+b*x)^3 +--R +--R +--R 2 3 +--R (394) x sec(b x + a) +--R Type: Expression(Integer) +--E 439 + +--S 440 of 510 +r0286:= -%i*x^2*atan(exp(1)^(%i*b*x+%i*a))/b+atanh(sin(a+b*x))/b^3+_ + %i*x*polylog(2,-%i*exp(1)^(%i*b*x+%i*a))/b^2-_ + %i*x*polylog(2,%i*exp(1)^(%i*b*x+%i*a))/b^2-_ + polylog(3,-%i*exp(1)^(%i*b*x+%i*a))/b^3+_ + polylog(3,%i*exp(1)^(%i*b*x+%i*a))/b^3-_ + x*sec(a+b*x)/b^2+1/2*x^2*sec(a+b*x)*tan(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 440 + +--S 441 of 510 +a0286:= integrate(t0286,x) +--R +--R +--R x +--R ++ 2 3 +--R (395) | %H sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 510 +m0286:= a0286-r0286 +--R +--R +--R x +--R ++ 2 3 +--R (396) | %H sec(%H b + a) d%H - r0286 +--R ++ +--R Type: Expression(Integer) +--E 442 + +--S 443 of 510 +d0286:= D(m0286,x) +--R +--R +--R 2 3 +--R (397) x sec(b x + a) +--R Type: Expression(Integer) +--E 443 + +--S 444 of 510 +t0287:= (c+d*x)*sec(a+b*x) +--R +--R +--R (398) (d x + c)sec(b x + a) +--R Type: Expression(Integer) +--E 444 + +--S 445 of 510 +r0287:= -%i*(2*atan(exp(%i*(a+b*x)))*c*b+2*atan(exp(%i*(a+b*x)))*d*x*b-_ + d*polylog(2,-%i*exp(%i*(a+b*x)))+d*polylog(2,%i*exp(%i*(a+b*x))))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 445 + +--S 446 of 510 +a0287:= integrate(t0287,x) +--R +--R +--R x +--R ++ +--R (399) | (%H d + c)sec(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 510 +m0287:= a0287-r0287 +--R +--R +--R x +--R ++ +--R (400) | (%H d + c)sec(%H b + a)d%H - r0287 +--R ++ +--R Type: Expression(Integer) +--E 447 + +--S 448 of 510 +d0287:= D(m0287,x) +--R +--R +--R (401) (d x + c)sec(b x + a) +--R Type: Expression(Integer) +--E 448 + +--S 449 of 510 +t0288:= (c+d*x)^2*sec(a+b*x) +--R +--R +--R 2 2 2 +--R (402) (d x + 2c d x + c )sec(b x + a) +--R Type: Expression(Integer) +--E 449 + +--S 450 of 510 +r0288:= -2*%i*(c+d*x)^2*atan(exp(1)^(%i*b*x+%i*a))/b+_ + 2*%i*d*(c+d*x)*polylog(2,-%i*exp(1)^(%i*b*x+%i*a))/b^2-_ + 2*%i*d*(c+d*x)*polylog(2,%i*exp(1)^(%i*b*x+%i*a))/b^2-_ + 2*d^2*polylog(3,-%i*exp(1)^(%i*b*x+%i*a))/b^3+_ + 2*d^2*polylog(3,%i*exp(1)^(%i*b*x+%i*a))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 450 + +--S 451 of 510 +a0288:= integrate(t0288,x) +--R +--R +--R x +--R ++ 2 2 2 +--R (403) | (%H d + 2%H c d + c )sec(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 510 +m0288:= a0288-r0288 +--R +--R +--R x +--R ++ 2 2 2 +--R (404) | (%H d + 2%H c d + c )sec(%H b + a)d%H - r0288 +--R ++ +--R Type: Expression(Integer) +--E 452 + +--S 453 of 510 +d0288:= D(m0288,x) +--R +--R +--R 2 2 2 +--R (405) (d x + 2c d x + c )sec(b x + a) +--R Type: Expression(Integer) +--E 453 + +--S 454 of 510 +t0289:= (c+d*x)^3*sec(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R (406) (d x + 3c d x + 3c d x + c )sec(b x + a) +--R Type: Expression(Integer) +--E 454 + +--S 455 of 510 +r0289:= -2*%i*(c+d*x)^3*atan(exp(1)^(%i*b*x+%i*a))/b+_ + 3*%i*d*(c+d*x)^2*polylog(2,-%i*exp(1)^(%i*b*x+%i*a))/b^2-_ + 3*%i*d*(c+d*x)^2*polylog(2,%i*exp(1)^(%i*b*x+%i*a))/b^2-_ + 6*d^2*(c+d*x)*polylog(3,-%i*exp(1)^(%i*b*x+%i*a))/b^3+_ + 6*d^2*(c+d*x)*polylog(3,%i*exp(1)^(%i*b*x+%i*a))/b^3-_ + 6*%i*d^3*polylog(4,-%i*exp(1)^(%i*b*x+%i*a))/b^4+_ + 6*%i*d^3*polylog(4,%i*exp(1)^(%i*b*x+%i*a))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 455 + +--S 456 of 510 +a0289:= integrate(t0289,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 +--R (407) | (%H d + 3%H c d + 3%H c d + c )sec(%H b + a)d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 510 +m0289:= a0289-r0289 +--R +--R +--R x +--R ++ 3 3 2 2 2 3 +--R (408) | (%H d + 3%H c d + 3%H c d + c )sec(%H b + a)d%H - r0289 +--R ++ +--R Type: Expression(Integer) +--E 457 + +--S 458 of 510 +d0289:= D(m0289,x) +--R +--R +--R 3 3 2 2 2 3 +--R (409) (d x + 3c d x + 3c d x + c )sec(b x + a) +--R Type: Expression(Integer) +--E 458 + +--S 459 of 510 +t0290:= (c+d*x)^2*sec(a+b*x)^2 +--R +--R +--R 2 2 2 2 +--R (410) (d x + 2c d x + c )sec(b x + a) +--R Type: Expression(Integer) +--E 459 + +--S 460 of 510 +r0290:= -%i*(c+d*x)^2/b+2*d*(c+d*x)*log(1+exp(1)^(2*%i*a+2*%i*b*x))/b^2-_ + %i*d^2*polylog(2,-exp(1)^(2*%i*a+2*%i*b*x))/b^3+(c+d*x)^2*tan(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 460 + +--S 461 of 510 +a0290:= integrate(t0290,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--R (411) | (%H d + 2%H c d + c )sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 510 +m0290:= a0290-r0290 +--R +--R +--R x +--R ++ 2 2 2 2 +--R (412) | (%H d + 2%H c d + c )sec(%H b + a) d%H - r0290 +--R ++ +--R Type: Expression(Integer) +--E 462 + +--S 463 of 510 +d0290:= D(m0290,x) +--R +--R +--R 2 2 2 2 +--R (413) (d x + 2c d x + c )sec(b x + a) +--R Type: Expression(Integer) +--E 463 + +--S 464 of 510 +t0291:= (c+d*x)^3*sec(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 2 +--R (414) (d x + 3c d x + 3c d x + c )sec(b x + a) +--R Type: Expression(Integer) +--E 464 + +--S 465 of 510 +r0291:= -%i*(c+d*x)^3/b+3*d*(c+d*x)^2*log(1+exp(1)^(2*%i*a+2*%i*b*x))/b^2-_ + 3*%i*d^2*(c+d*x)*polylog(2,-exp(1)^(2*%i*a+2*%i*b*x))/b^3+_ + 3/2*d^3*polylog(3,-exp(1)^(2*%i*a+2*%i*b*x))/b^4+(c+d*x)^3*tan(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 465 + +--S 466 of 510 +a0291:= integrate(t0291,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 2 +--R (415) | (%H d + 3%H c d + 3%H c d + c )sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 510 +m0291:= a0291-r0291 +--R +--R +--R x +--R ++ 3 3 2 2 2 3 2 +--R (416) | (%H d + 3%H c d + 3%H c d + c )sec(%H b + a) d%H - r0291 +--R ++ +--R Type: Expression(Integer) +--E 467 + +--S 468 of 510 +d0291:= D(m0291,x) +--R +--R +--R 3 3 2 2 2 3 2 +--R (417) (d x + 3c d x + 3c d x + c )sec(b x + a) +--R Type: Expression(Integer) +--E 468 + +--S 469 of 510 +t0292:= (c+d*x)*sec(a+b*x)^3 +--R +--R +--R 3 +--R (418) (d x + c)sec(b x + a) +--R Type: Expression(Integer) +--E 469 + +--S 470 of 510 +r0292:= -%i*(c+d*x)*atan(exp(1)^(%i*b*x+%i*a))/b+_ + 1/2*%i*d*polylog(2,-%i*exp(1)^(%i*b*x+%i*a))/b^2-_ + 1/2*%i*d*polylog(2,%i*exp(1)^(%i*b*x+%i*a))/b^2-_ + 1/2*d*sec(a+b*x)/b^2+1/2*(c+d*x)*sec(a+b*x)*tan(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 470 + +--S 471 of 510 +a0292:= integrate(t0292,x) +--R +--R +--R x +--R ++ 3 +--R (419) | (%H d + c)sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 510 +m0292:= a0292-r0292 +--R +--R +--R x +--R ++ 3 +--R (420) | (%H d + c)sec(%H b + a) d%H - r0292 +--R ++ +--R Type: Expression(Integer) +--E 472 + +--S 473 of 510 +d0292:= D(m0292,x) +--R +--R +--R 3 +--R (421) (d x + c)sec(b x + a) +--R Type: Expression(Integer) +--E 473 + +--S 474 of 510 +t0293:= (c+d*x)^2*sec(a+b*x)^3 +--R +--R +--R 2 2 2 3 +--R (422) (d x + 2c d x + c )sec(b x + a) +--R Type: Expression(Integer) +--E 474 + +--S 475 of 510 +r0293:= -%i*(c+d*x)^2*atan(exp(1)^(%i*b*x+%i*a))/b+_ + d^2*atanh(sin(a+b*x))/b^3+%i*d*(c+d*x)*_ + polylog(2,-%i*exp(1)^(%i*b*x+%i*a))/b^2-%i*d*(c+d*x)*_ + polylog(2,%i*exp(1)^(%i*b*x+%i*a))/b^2-d^2*_ + polylog(3,-%i*exp(1)^(%i*b*x+%i*a))/b^3+d^2*_ + polylog(3,%i*exp(1)^(%i*b*x+%i*a))/b^3-d*(c+d*x)*_ + sec(a+b*x)/b^2+1/2*(c+d*x)^2*sec(a+b*x)*tan(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 475 + +--S 476 of 510 +a0293:= integrate(t0293,x) +--R +--R +--R x +--R ++ 2 2 2 3 +--R (423) | (%H d + 2%H c d + c )sec(%H b + a) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 510 +m0293:= a0293-r0293 +--R +--R +--R x +--R ++ 2 2 2 3 +--R (424) | (%H d + 2%H c d + c )sec(%H b + a) d%H - r0293 +--R ++ +--R Type: Expression(Integer) +--E 477 + +--S 478 of 510 +d0293:= D(m0293,x) +--R +--R +--R 2 2 2 3 +--R (425) (d x + 2c d x + c )sec(b x + a) +--R Type: Expression(Integer) +--E 478 + +--S 479 of 510 +t0294:= (sec(x)^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 +--R (426) \|sec(x) +--R Type: Expression(Integer) +--E 479 + +--S 480 of 510 +r0294:= asinh(tan(x)) +--R +--R +--R (427) asinh(tan(x)) +--R Type: Expression(Integer) +--E 480 + +--S 481 of 510 +a0294:= integrate(t0294,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (428) - log(-------------------) + log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 510 +m0294:= a0294-r0294 +--R +--R +--R (429) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - log(-------------------) + log(-------------------) - asinh(tan(x)) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 510 +d0294:= D(m0294,x) +--R +--R +--R (430) +--R +-----------+ +--R 2 2 | 2 +--R (2sin(x) + 2cos(x) + 2cos(x))\|tan(x) + 1 +--R + +--R 2 2 2 2 2 +--R (- sin(x) + cos(x) + 2cos(x) + 1)tan(x) - sin(x) + cos(x) + 2cos(x) +--R + +--R 1 +--R / +--R +-----------+ +--R 2 2 | 2 +--R (sin(x) - cos(x) - 2cos(x) - 1)\|tan(x) + 1 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 510 +t0295:= (a*sec(x)^2)^(1/2) +--R +--R +--R +---------+ +--R | 2 +--R (431) \|a sec(x) +--R Type: Expression(Integer) +--E 484 + +--S 485 of 510 +r0295:= atanh(sin(x))*cos(x)*(a*sec(x)^2)^(1/2) +--R +--R +--R +---------+ +--R | 2 +--R (432) cos(x)atanh(sin(x))\|a sec(x) +--R Type: Expression(Integer) +--E 485 + +--S 486 of 510 +a0295:= integrate(t0295,x) +--R +--R +--R +---+ +-+ +--R +-+ sin(x) - cos(x) - 1 +---+ (cos(x) + 1)\|- a \|a +--R (433) [\|a log(-------------------),2\|- a atan(----------------------)] +--R sin(x) + cos(x) + 1 a sin(x) +--R Type: Union(List(Expression(Integer)),...) +--E 486 + +--S 487 of 510 +m0295a:= a0295.1-r0295 +--R +--R +--R +---------+ +--R | 2 +-+ sin(x) - cos(x) - 1 +--R (434) - cos(x)atanh(sin(x))\|a sec(x) + \|a log(-------------------) +--R sin(x) + cos(x) + 1 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 510 +d0295a:= D(m0295a,x) +--R +--R +--R (435) +--R 4 2 2 2 +-+ +--R (2sin(x) + (2cos(x) + 2cos(x) - 2)sin(x) - 2cos(x) - 2cos(x))\|a +--R * +--R +---------+ +--R | 2 +--R \|a sec(x) +--R + +--R 2 4 +--R - a cos(x)sec(x) sin(x) +--R + +--R 3 2 2 2 +--R (a cos(x) + 2a cos(x) + 2a cos(x))sec(x) sin(x) +--R + +--R 3 2 2 +--R (- a cos(x) - 2a cos(x) - a cos(x))sec(x) +--R * +--R tan(x) +--R + +--R 2 5 2 2 3 +--R a sec(x) sin(x) + (- a cos(x) - 2a cos(x) - 2a)sec(x) sin(x) +--R + +--R 2 2 +--R (a cos(x) + 2a cos(x) + a)sec(x) sin(x) +--R * +--R atanh(sin(x)) +--R + +--R 2 2 2 4 3 2 2 +--R a cos(x) sec(x) sin(x) + (- a cos(x) - 2a cos(x) - a cos(x) )sec(x) +--R / +--R 4 2 2 2 +--R (sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1) +--R * +--R +---------+ +--R | 2 +--R \|a sec(x) +--R Type: Expression(Integer) +--E 488 + +--S 489 of 510 +m0295b:= a0295.2-r0295 +--R +--R +--R (436) +--R +---------+ +---+ +-+ +--R | 2 +---+ (cos(x) + 1)\|- a \|a +--R - cos(x)atanh(sin(x))\|a sec(x) + 2\|- a atan(----------------------) +--R a sin(x) +--R Type: Expression(Integer) +--E 489 + +--S 490 of 510 +d0295b:= D(m0295b,x) +--R +--R +--R (437) +--R 4 2 2 2 +-+ +--R (2sin(x) + (2cos(x) + 2cos(x) - 2)sin(x) - 2cos(x) - 2cos(x))\|a +--R * +--R +---------+ +--R | 2 +--R \|a sec(x) +--R + +--R 2 4 +--R - a cos(x)sec(x) sin(x) +--R + +--R 3 2 2 2 +--R (a cos(x) + 2a cos(x) + 2a cos(x))sec(x) sin(x) +--R + +--R 3 2 2 +--R (- a cos(x) - 2a cos(x) - a cos(x))sec(x) +--R * +--R tan(x) +--R + +--R 2 5 2 2 3 +--R a sec(x) sin(x) + (- a cos(x) - 2a cos(x) - 2a)sec(x) sin(x) +--R + +--R 2 2 +--R (a cos(x) + 2a cos(x) + a)sec(x) sin(x) +--R * +--R atanh(sin(x)) +--R + +--R 2 2 2 4 3 2 2 +--R a cos(x) sec(x) sin(x) + (- a cos(x) - 2a cos(x) - a cos(x) )sec(x) +--R / +--R 4 2 2 2 +--R (sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1) +--R * +--R +---------+ +--R | 2 +--R \|a sec(x) +--R Type: Expression(Integer) +--E 490 + +--S 491 of 510 +t0296:= (a*sec(x)^3)^(1/2) +--R +--R +--R +---------+ +--R | 3 +--R (438) \|a sec(x) +--R Type: Expression(Integer) +--E 491 + +--S 492 of 510 +r0296:= -2*cos(x)*(a*sec(x)^3)^(1/2)*(cos(x)^(1/2)*EllipticE(1/2*x,2)-sin(x)) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 492 + +--S 493 of 510 +a0296:= integrate(t0296,x) +--R +--R +--R x +----------+ +--R ++ | 3 +--R (439) | \|a sec(%H) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 510 +m0296:= a0296-r0296 +--R +--R +--R x +----------+ +--R ++ | 3 +--R (440) | \|a sec(%H) d%H - r0296 +--R ++ +--R Type: Expression(Integer) +--E 494 + +--S 495 of 510 +d0296:= D(m0296,x) +--R +--R +--R +---------+ +--R | 3 +--R (441) \|a sec(x) +--R Type: Expression(Integer) +--E 495 + +--S 496 of 510 +t0297:= (sec(x)^2)^(3/2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (442) sec(x) \|sec(x) +--R Type: Expression(Integer) +--E 496 + +--S 497 of 510 +r0297:= 1/2*asinh(tan(x))+1/2*(sec(x)^2)^(1/2)*tan(x) +--R +--R +--R +-------+ +--R | 2 +--R tan(x)\|sec(x) + asinh(tan(x)) +--R (443) -------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 510 +a0297:= integrate(t0297,x) +--R +--R +--R (444) +--R 2 sin(x) + cos(x) + 1 2 sin(x) - cos(x) - 1 +--R - cos(x) log(-------------------) + cos(x) log(-------------------) - sin(x) +--R cos(x) + 1 cos(x) + 1 +--R ---------------------------------------------------------------------------- +--R 2 +--R 2cos(x) +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 510 +m0297:= a0297-r0297 +--R +--R +--R (445) +--R +-------+ +--R 2 | 2 2 sin(x) + cos(x) + 1 +--R - cos(x) tan(x)\|sec(x) - cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 sin(x) - cos(x) - 1 2 +--R cos(x) log(-------------------) - cos(x) asinh(tan(x)) - sin(x) +--R cos(x) + 1 +--R / +--R 2 +--R 2cos(x) +--R Type: Expression(Integer) +--E 499 + +--S 500 of 510 +d0297:= D(m0297,x) +--R +--R +--R (446) +--R 4 3 2 2 5 +--R - 2sin(x) + (2cos(x) + cos(x) + 4cos(x) + 2)sin(x) + 2cos(x) +--R + +--R 4 3 2 +--R 3cos(x) + 2cos(x) + cos(x) +--R * +--R +-------+ +--R | 2 +--R \|sec(x) +--R + +--R 3 2 2 +--R - 2cos(x) sec(x) sin(x) +--R + +--R 5 4 3 2 +--R (2cos(x) + 4cos(x) + 2cos(x) )sec(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 5 4 3 2 +--R - cos(x) sec(x) sin(x) + (cos(x) + 2cos(x) + cos(x) )sec(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 1 +--R + +--R 3 2 5 4 3 2 +--R (- cos(x) sin(x) + cos(x) + 2cos(x) + cos(x) )tan(x) +--R + +--R 3 2 5 4 3 +--R - cos(x) sin(x) + cos(x) + 2cos(x) + cos(x) +--R * +--R +-------+ +--R | 2 +--R \|sec(x) +--R / +--R +-------+ +-----------+ +--R 3 2 5 4 3 | 2 | 2 +--R (2cos(x) sin(x) - 2cos(x) - 4cos(x) - 2cos(x) )\|sec(x) \|tan(x) + 1 +--R Type: Expression(Integer) +--E 500 + +--S 501 of 510 +t0298:= (a*sec(x)^2)^(3/2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (447) a sec(x) \|a sec(x) +--R Type: Expression(Integer) +--E 501 + +--S 502 of 510 +r0298:= 1/2*a*cos(x)*(a*sec(x)^2)^(1/2)*(atanh(sin(x))+sec(x)*tan(x)) +--R +--R +--R +---------+ +--R | 2 +--R (a cos(x)atanh(sin(x)) + a cos(x)sec(x)tan(x))\|a sec(x) +--R (448) ---------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 510 +a0298:= integrate(t0298,x) +--R +--R +--R 2 +-+ sin(x) - cos(x) - 1 +-+ +--R a cos(x) \|a log(-------------------) - a sin(x)\|a +--R sin(x) + cos(x) + 1 +--R (449) ---------------------------------------------------- +--R 2 +--R 2cos(x) +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 510 +m0298:= a0298-r0298 +--R +--R +--R (450) +--R +---------+ +--R 3 3 | 2 +--R (- a cos(x) atanh(sin(x)) - a cos(x) sec(x)tan(x))\|a sec(x) +--R + +--R 2 +-+ sin(x) - cos(x) - 1 +-+ +--R a cos(x) \|a log(-------------------) - a sin(x)\|a +--R sin(x) + cos(x) + 1 +--R / +--R 2 +--R 2cos(x) +--R Type: Expression(Integer) +--E 504 + +--S 505 of 510 +d0298:= D(m0298,x) +--R +--R +--R (451) +--R 6 3 2 4 +--R - 2a sin(x) + (2a cos(x) + a cos(x) + 4a cos(x) + 4a)sin(x) +--R + +--R 5 4 2 5 +--R (2a cos(x) + 3a cos(x) - 4a cos(x) - 2a)sin(x) - 2a cos(x) +--R + +--R 4 3 2 +--R - 3a cos(x) - 2a cos(x) - a cos(x) +--R * +--R +---------+ +--R +-+ | 2 +--R \|a \|a sec(x) +--R + +--R 2 4 2 4 +--R - a cos(x) sec(x) sin(x) +--R + +--R 2 6 2 5 2 4 2 2 +--R (a cos(x) + 2a cos(x) + 2a cos(x) )sec(x) sin(x) +--R + +--R 2 6 2 5 2 4 2 +--R (- a cos(x) - 2a cos(x) - a cos(x) )sec(x) +--R * +--R tan(x) +--R + +--R 2 3 2 5 +--R a cos(x) sec(x) sin(x) +--R + +--R 2 5 2 4 2 3 2 3 +--R (- a cos(x) - 2a cos(x) - 2a cos(x) )sec(x) sin(x) +--R + +--R 2 5 2 4 2 3 2 +--R (a cos(x) + 2a cos(x) + a cos(x) )sec(x) sin(x) +--R * +--R atanh(sin(x)) +--R + +--R 2 4 3 4 +--R - 3a cos(x) sec(x) sin(x) +--R + +--R 2 6 2 5 2 4 3 2 +--R (3a cos(x) + 6a cos(x) + 6a cos(x) )sec(x) sin(x) +--R + +--R 2 6 2 5 2 4 3 +--R (- 3a cos(x) - 6a cos(x) - 3a cos(x) )sec(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 3 5 +--R a cos(x) sec(x) sin(x) +--R + +--R 2 5 2 4 2 3 3 3 +--R (- a cos(x) - 2a cos(x) - 2a cos(x) )sec(x) sin(x) +--R + +--R 2 5 2 4 2 3 3 +--R (a cos(x) + 2a cos(x) + a cos(x) )sec(x) sin(x) +--R * +--R tan(x) +--R + +--R 2 4 3 4 +--R - a cos(x) sec(x) sin(x) +--R + +--R 2 6 2 5 2 4 3 2 5 2 2 +--R ((a cos(x) + 2a cos(x) + 2a cos(x) )sec(x) + a cos(x) sec(x) )sin(x) +--R + +--R 2 6 2 5 2 4 3 +--R (- a cos(x) - 2a cos(x) - a cos(x) )sec(x) +--R + +--R 2 7 2 6 2 5 2 +--R (- a cos(x) - 2a cos(x) - a cos(x) )sec(x) +--R / +--R 3 4 5 4 3 2 5 +--R 2cos(x) sin(x) + (- 2cos(x) - 4cos(x) - 4cos(x) )sin(x) + 2cos(x) +--R + +--R 4 3 +--R 4cos(x) + 2cos(x) +--R * +--R +---------+ +--R | 2 +--R \|a sec(x) +--R Type: Expression(Integer) +--E 505 + +--S 506 of 510 +t0299:= (a*sec(x)^3)^(3/2) +--R +--R +--R +---------+ +--R 3 | 3 +--R (452) a sec(x) \|a sec(x) +--R Type: Expression(Integer) +--E 506 + +--S 507 of 510 +r0299:= 2/21*a*cos(x)*(a*sec(x)^3)^(1/2)*(5*cos(x)^(1/2)*EllipticF(1/2*x,2)+_ + 5*tan(x)+3*sec(x)^2*tan(x)) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 507 + +--S 508 of 510 +a0299:= integrate(t0299,x) +--R +--R +--R x +----------+ +--R ++ 3 | 3 +--R (453) | a sec(%H) \|a sec(%H) d%H +--R ++ +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 510 +m0299:= a0299-r0299 +--R +--R +--R x +----------+ +--R ++ 3 | 3 +--R (454) | a sec(%H) \|a sec(%H) d%H - r0299 +--R ++ +--R Type: Expression(Integer) +--E 509 + +--S 510 of 510 +d0299:= D(m0299,x) +--R +--R +--R +---------+ +--R 3 | 3 +--R (455) a sec(x) \|a sec(x) +--R Type: Expression(Integer) +--E 510 + +)spool + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richtrig200-299.input.pdf b/src/axiom-website/CATS/richtrig200-299.input.pdf new file mode 100644 index 0000000..fe301dd Binary files /dev/null and b/src/axiom-website/CATS/richtrig200-299.input.pdf differ diff --git a/src/axiom-website/CATS/richtrig300-399.input.pamphlet b/src/axiom-website/CATS/richtrig300-399.input.pamphlet new file mode 100644 index 0000000..0eefcf5 --- /dev/null +++ b/src/axiom-website/CATS/richtrig300-399.input.pamphlet @@ -0,0 +1,76546 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richtrig300-399.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig300-399.output +)spool richtrig300-399.output +)set message auto off +)clear all + +--S 1 of 528 +t0300:= 1/(a*sec(x)^3)^(1/2) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | 3 +--R \|a sec(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 528 +r0300:= 2/3*sec(x)*(EllipticF(1/2*x,2)/cos(x)^(1/2)+sin(x))/(a*sec(x)^3)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 2 + +--S 3 of 528 +a0300:= integrate(t0300,x) +--R +--R +--R x +--R ++ 1 +--R (2) | ------------- d%R +--R ++ +----------+ +--R | 3 +--R \|a sec(%R) +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 528 +m0300:= a0300-r0300 +--R +--R +--R x +--R ++ 1 +--R (3) | ------------- d%R - r0300 +--R ++ +----------+ +--R | 3 +--R \|a sec(%R) +--R Type: Expression(Integer) +--E 4 + +--S 5 of 528 +d0300:= D(m0300,x) +--R +--R +--R 1 +--R (4) ------------ +--R +---------+ +--R | 3 +--R \|a sec(x) +--R Type: Expression(Integer) +--E 5 + +--S 6 of 528 +t0301:= 1/(a-a*sec(c+d*x)) +--R +--R +--R 1 +--R (5) - ------------------ +--R a sec(d x + c) - a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 528 +r0301:= x/a+sin(c+d*x)/a/d/(1-cos(c+d*x)) +--R +--R +--R - sin(d x + c) + d x cos(d x + c) - d x +--R (6) --------------------------------------- +--R a d cos(d x + c) - a d +--R Type: Expression(Integer) +--E 7 + +--S 8 of 528 +a0301:= integrate(t0301,x) +--R +--R +--R d x sin(d x + c) + cos(d x + c) + 1 +--R (7) ----------------------------------- +--R a d sin(d x + c) +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 528 +m0301:= a0301-r0301 +--R +--R +--R 2 2 +--R sin(d x + c) + cos(d x + c) - 1 +--R (8) ------------------------------------ +--R (a d cos(d x + c) - a d)sin(d x + c) +--R Type: Expression(Integer) +--E 9 + +--S 10 of 528 +d0301:= D(m0301,x) +--R +--R +--R (9) +--R 4 2 4 +--R sin(d x + c) + (cos(d x + c) - 1)sin(d x + c) - cos(d x + c) +--R + +--R 3 2 +--R cos(d x + c) + cos(d x + c) - cos(d x + c) +--R / +--R 2 2 +--R (a cos(d x + c) - 2a cos(d x + c) + a)sin(d x + c) +--R Type: Expression(Integer) +--E 10 + +--S 11 of 528 +t0302:= (3+3*sec(x))^(1/2) +--R +--R +--R +-----------+ +--R (10) \|3sec(x) + 3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 528 +r0302:= 2*3^(1/2)*atan((-1+sec(x))^(1/2))*tan(x)/(-1+sec(x))^(1/2)/(1+sec(x))^(1/2) +--R +--R +--R +-+ +----------+ +--R 2\|3 tan(x)atan(\|sec(x) - 1 ) +--R (11) ------------------------------ +--R +----------+ +----------+ +--R \|sec(x) - 1 \|sec(x) + 1 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 528 +a0302:= integrate(t0302,x) +--R +--R +--R (12) 0 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 528 +m0302:= a0302-r0302 +--R +--R +--R +-+ +----------+ +--R 2\|3 tan(x)atan(\|sec(x) - 1 ) +--R (13) - ------------------------------ +--R +----------+ +----------+ +--R \|sec(x) - 1 \|sec(x) + 1 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 528 +d0302:= D(m0302,x) +--R +--R +--R (14) +--R +-+ 2 +-+ 2 +-+ +----------+ +--R (2\|3 tan(x) - 2\|3 sec(x) + 2\|3 )atan(\|sec(x) - 1 ) +--R + +--R +-+ +-+ 2 +----------+ +--R (- \|3 sec(x) - \|3 )tan(x) \|sec(x) - 1 +--R / +--R 2 +----------+ +----------+ +--R (sec(x) - 1)\|sec(x) - 1 \|sec(x) + 1 +--R Type: Expression(Integer) +--E 15 + +--S 16 of 528 +t0303:= (3-3*sec(x))^(1/2) +--R +--R +--R +-------------+ +--R (15) \|- 3sec(x) + 3 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 528 +r0303:= 2*3^(1/2)*atan((-1-sec(x))^(1/2))*tan(x)/(-1-sec(x))^(1/2)/(1-sec(x))^(1/2) +--R +--R +--R +-+ +------------+ +--R 2\|3 tan(x)atan(\|- sec(x) - 1 ) +--R (16) -------------------------------- +--R +------------+ +------------+ +--R \|- sec(x) - 1 \|- sec(x) + 1 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 528 +a0303:= integrate(t0303,x) +--R +--R +--R +-+ +-+ +--R +-+ 2\|3 cos(x) + \|3 +--R (17) \|3 atan(-----------------------) +--R +-------------+ +--R |- 3cos(x) - 3 +--R 2cos(x) |------------- +--R \| cos(x) +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 528 +m0303:= a0303-r0303 +--R +--R +--R (18) +--R +-+ +------------+ +--R - 2\|3 tan(x)atan(\|- sec(x) - 1 ) +--R + +--R +-+ +-+ +--R +-+ +------------+ +------------+ 2\|3 cos(x) + \|3 +--R \|3 \|- sec(x) - 1 \|- sec(x) + 1 atan(-----------------------) +--R +-------------+ +--R |- 3cos(x) - 3 +--R 2cos(x) |------------- +--R \| cos(x) +--R / +--R +------------+ +------------+ +--R \|- sec(x) - 1 \|- sec(x) + 1 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 528 +d0303:= D(m0303,x) +--R +--R +--R (19) +--R +-------------+ +--R +-+ 2 +-+ 2 +-+ |- 3cos(x) - 3 +--R (2\|3 cos(x)tan(x) - 2\|3 cos(x)sec(x) + 2\|3 cos(x)) |------------- +--R \| cos(x) +--R * +--R +------------+ +--R atan(\|- sec(x) - 1 ) +--R + +--R +-------------+ +--R +-+ +-+ 2 +------------+ |- 3cos(x) - 3 +--R (\|3 cos(x)sec(x) - \|3 cos(x))tan(x) \|- sec(x) - 1 |------------- +--R \| cos(x) +--R + +--R 2 +------------+ +------------+ +--R (- 3sec(x) + 3)sin(x)\|- sec(x) - 1 \|- sec(x) + 1 +--R / +--R +-------------+ +--R 2 +------------+ +------------+ |- 3cos(x) - 3 +--R (cos(x)sec(x) - cos(x))\|- sec(x) - 1 \|- sec(x) + 1 |------------- +--R \| cos(x) +--R Type: Expression(Integer) +--E 20 + +--S 21 of 528 +t0304:= (a+a*sec(x))^(1/2) +--R +--R +--R +------------+ +--R (20) \|a sec(x) + a +--R Type: Expression(Integer) +--E 21 + +--S 22 of 528 +r0304:= 2*a*atan((-1+sec(x))^(1/2))*tan(x)/(-1+sec(x))^(1/2)/(a+a*sec(x))^(1/2) +--R +--R +--R +----------+ +--R 2a tan(x)atan(\|sec(x) - 1 ) +--R (21) ---------------------------- +--R +----------+ +------------+ +--R \|sec(x) - 1 \|a sec(x) + a +--R Type: Expression(Integer) +--E 22 + +--S 23 of 528 +a0304:= integrate(t0304,x) +--R +--R +--R (22) +--R [ +--R +---+ +--R \|- a +--R * +--R log +--R +------------+ +--R 2 +---+ |a cos(x) + a 3 +--R (- 8cos(x) + 4cos(x))sin(x)\|- a |------------ + 8a cos(x) +--R \| cos(x) +--R + +--R - 7a cos(x) + a +--R / +--R cos(x) + 1 +--R / +--R 2 +--R , +--R +------------+ +--R +-+ |a cos(x) + a +--R 2cos(x)sin(x)\|a |------------ +--R +-+ \| cos(x) +--R \|a atan(--------------------------------)] +--R 2 +--R 2a cos(x) + a cos(x) - a +--R Type: Union(List(Expression(Integer)),...) +--E 23 + +--S 24 of 528 +m0304a:= a0304.1-r0304 +--R +--R +--R (23) +--R +---+ +----------+ +------------+ +--R \|- a \|sec(x) - 1 \|a sec(x) + a +--R * +--R log +--R +------------+ +--R 2 +---+ |a cos(x) + a 3 +--R (- 8cos(x) + 4cos(x))sin(x)\|- a |------------ + 8a cos(x) +--R \| cos(x) +--R + +--R - 7a cos(x) + a +--R / +--R cos(x) + 1 +--R + +--R +----------+ +--R - 4a tan(x)atan(\|sec(x) - 1 ) +--R / +--R +----------+ +------------+ +--R 2\|sec(x) - 1 \|a sec(x) + a +--R Type: Expression(Integer) +--E 24 + +--S 25 of 528 +d0304a:= D(m0304a,x) +--R +--R +--R (24) +--R 4 2 2 +--R (16a cos(x) - 14a cos(x) + 2a cos(x))tan(x) +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 14a cos(x) - 2a cos(x))sec(x) + 16a cos(x) +--R + +--R 2 +--R - 14a cos(x) + 2a cos(x) +--R * +--R +------------+ +--R |a cos(x) + a +--R |------------ +--R \| cos(x) +--R + +--R 3 2 2 +--R (- 16a cos(x) - 8a cos(x) + 8a cos(x))sin(x)tan(x) +--R + +--R 3 2 2 3 +--R (16a cos(x) + 8a cos(x) - 8a cos(x))sec(x) - 16a cos(x) +--R + +--R 2 +--R - 8a cos(x) + 8a cos(x) +--R * +--R sin(x) +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R atan(\|sec(x) - 1 ) +--R + +--R 3 2 2 3 2 +--R (- 8cos(x) - 4cos(x) + 4cos(x))sec(x) + 8cos(x) + 4cos(x) +--R + +--R - 4cos(x) +--R * +--R +------------+ +--R +---+ |a cos(x) + a +--R sin(x)\|- a |------------ +--R \| cos(x) +--R + +--R 2 2 2 +--R (- 4a cos(x) - 6a cos(x) + a)sec(x) + 4a cos(x) + 6a cos(x) +--R + +--R - a +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (4a cos(x) + 2a cos(x) - 2a cos(x) )sec(x) - 4a cos(x) +--R + +--R 3 2 +--R - 2a cos(x) + 2a cos(x) +--R * +--R +----------+ +------------+ +--R \|sec(x) - 1 \|a sec(x) + a +--R + +--R 4 2 4 +--R (- 8a cos(x) + 7a cos(x) - a cos(x))sec(x) - 8a cos(x) +--R + +--R 2 +--R 7a cos(x) - a cos(x) +--R * +--R +------------+ +--R 2 |a cos(x) + a +--R tan(x) |------------ +--R \| cos(x) +--R + +--R 3 2 3 +--R (8a cos(x) + 4a cos(x) - 4a cos(x))sec(x) + 8a cos(x) +--R + +--R 2 +--R 4a cos(x) - 4a cos(x) +--R * +--R 2 +---+ +--R sin(x)tan(x) \|- a +--R * +--R +----------+ +--R \|sec(x) - 1 +--R / +--R 4 2 2 4 2 +--R (8cos(x) - 7cos(x) + cos(x))sec(x) - 8cos(x) + 7cos(x) +--R + +--R - cos(x) +--R * +--R +------------+ +--R |a cos(x) + a +--R |------------ +--R \| cos(x) +--R + +--R 3 2 2 3 2 +--R (- 8cos(x) - 4cos(x) + 4cos(x))sec(x) + 8cos(x) + 4cos(x) +--R + +--R - 4cos(x) +--R * +--R +---+ +--R sin(x)\|- a +--R * +--R +----------+ +------------+ +--R \|sec(x) - 1 \|a sec(x) + a +--R Type: Expression(Integer) +--E 25 + +--S 26 of 528 +m0304b:= a0304.2-r0304 +--R +--R +--R (25) +--R +----------+ +--R - 2a tan(x)atan(\|sec(x) - 1 ) +--R + +--R +------------+ +--R +-+ |a cos(x) + a +--R 2cos(x)sin(x)\|a |------------ +--R +-+ +----------+ +------------+ \| cos(x) +--R \|a \|sec(x) - 1 \|a sec(x) + a atan(--------------------------------) +--R 2 +--R 2a cos(x) + a cos(x) - a +--R / +--R +----------+ +------------+ +--R \|sec(x) - 1 \|a sec(x) + a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 528 +d0304b:= D(m0304b,x) +--R +--R +--R (26) +--R 2 2 4 2 2 +--R (8a cos(x) sin(x) + 8a cos(x) - 6a cos(x) + 2a cos(x))tan(x) +--R + +--R 2 2 2 2 +--R (- 8a cos(x) sec(x) + 8a cos(x) )sin(x) +--R + +--R 4 2 2 4 +--R (- 8a cos(x) + 6a cos(x) - 2a cos(x))sec(x) + 8a cos(x) +--R + +--R 2 +--R - 6a cos(x) + 2a cos(x) +--R * +--R +------------+ +--R |a cos(x) + a +----------+ +--R |------------ atan(\|sec(x) - 1 ) +--R \| cos(x) +--R + +--R 2 2 2 +--R ((4a cos(x) + 2a cos(x) + a)sec(x) - 4a cos(x) - 2a cos(x) - a) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (4a cos(x) + 2a cos(x) - 2a cos(x) )sec(x) - 4a cos(x) +--R + +--R 3 2 +--R - 2a cos(x) + 2a cos(x) +--R * +--R +----------+ +------------+ +--R \|sec(x) - 1 \|a sec(x) + a +--R + +--R 2 2 2 +--R (- 4a cos(x) sec(x) - 4a cos(x) )sin(x) +--R + +--R 4 2 4 +--R (- 4a cos(x) + 3a cos(x) - a cos(x))sec(x) - 4a cos(x) +--R + +--R 2 +--R 3a cos(x) - a cos(x) +--R * +--R +------------+ +--R 2 |a cos(x) + a +----------+ +--R tan(x) |------------ \|sec(x) - 1 +--R \| cos(x) +--R / +--R 2 2 2 2 +--R (4cos(x) sec(x) - 4cos(x) )sin(x) +--R + +--R 4 2 2 4 2 +--R (4cos(x) - 3cos(x) + cos(x))sec(x) - 4cos(x) + 3cos(x) - cos(x) +--R * +--R +------------+ +--R |a cos(x) + a +----------+ +------------+ +--R |------------ \|sec(x) - 1 \|a sec(x) + a +--R \| cos(x) +--R Type: Expression(Integer) +--E 27 + +--S 28 of 528 +t0305:= (a-a*sec(x))^(1/2) +--R +--R +--R +--------------+ +--R (27) \|- a sec(x) + a +--R Type: Expression(Integer) +--E 28 + +--S 29 of 528 +r0305:= 2*a*atan((-1-sec(x))^(1/2))*tan(x)/(-1-sec(x))^(1/2)/(a-a*sec(x))^(1/2) +--R +--R +--R +------------+ +--R 2a tan(x)atan(\|- sec(x) - 1 ) +--R (28) -------------------------------- +--R +--------------+ +------------+ +--R \|- a sec(x) + a \|- sec(x) - 1 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 528 +a0305:= integrate(t0305,x) +--R +--R +--R (29) +--R - +--R +----+ +--R \|- 4a +--R * +--R log +--R +--------------+ +--R 2 +----+ |- a cos(x) - a 2 +--R (4cos(x) + 2cos(x))\|- 4a |-------------- - 8a cos(x) +--R \| cos(x) +--R + +--R - 8a cos(x) - a +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 30 + +--S 31 of 528 +m0305:= a0305-r0305 +--R +--R +--R (30) +--R - +--R +----+ +--------------+ +------------+ +--R \|- 4a \|- a sec(x) + a \|- sec(x) - 1 +--R * +--R log +--R +--------------+ +--R 2 +----+ |- a cos(x) - a 2 +--R (4cos(x) + 2cos(x))\|- 4a |-------------- - 8a cos(x) +--R \| cos(x) +--R + +--R - 8a cos(x) - a +--R + +--R +------------+ +--R - 8a tan(x)atan(\|- sec(x) - 1 ) +--R / +--R +--------------+ +------------+ +--R 4\|- a sec(x) + a \|- sec(x) - 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 528 +d0305:= D(m0305,x) +--R +--R +--R (31) +--R 3 2 2 +--R (16a cos(x) + 16a cos(x) + 2a cos(x))tan(x) +--R + +--R 3 2 2 3 +--R (- 16a cos(x) - 16a cos(x) - 2a cos(x))sec(x) + 16a cos(x) +--R + +--R 2 +--R 16a cos(x) + 2a cos(x) +--R * +--R +--------------+ +--R |- a cos(x) - a +--R |-------------- +--R \| cos(x) +--R + +--R 3 2 2 +--R (8a cos(x) + 12a cos(x) + 4a cos(x))tan(x) +--R + +--R 3 2 2 3 +--R (- 8a cos(x) - 12a cos(x) - 4a cos(x))sec(x) + 8a cos(x) +--R + +--R 2 +--R 12a cos(x) + 4a cos(x) +--R * +--R +----+ +--R \|- 4a +--R * +--R +------------+ +--R atan(\|- sec(x) - 1 ) +--R + +--R 2 2 2 +----+ +--R ((4cos(x) + 2cos(x))sec(x) - 4cos(x) - 2cos(x))sin(x)\|- 4a +--R * +--R +--------------+ +--R \|- a sec(x) + a +--R + +--R 3 2 3 +--R (8a cos(x) + 8a cos(x) + a cos(x))sec(x) - 8a cos(x) +--R + +--R 2 +--R - 8a cos(x) - a cos(x) +--R * +--R 2 +--R tan(x) +--R * +--R +--------------+ +--R +------------+ |- a cos(x) - a +--R \|- sec(x) - 1 |-------------- +--R \| cos(x) +--R + +--R 2 2 2 +--R (- 8a cos(x) - 8a cos(x) - a)sec(x) + 8a cos(x) + 8a cos(x) +--R + +--R a +--R * +--R +--------------+ +--R sin(x)\|- a sec(x) + a +--R + +--R 3 2 3 +--R (4a cos(x) + 6a cos(x) + 2a cos(x))sec(x) - 4a cos(x) +--R + +--R 2 +--R - 6a cos(x) - 2a cos(x) +--R * +--R 2 +----+ +--R tan(x) \|- 4a +--R * +--R +------------+ +--R \|- sec(x) - 1 +--R / +--R 3 2 2 3 2 +--R ((8cos(x) + 8cos(x) + cos(x))sec(x) - 8cos(x) - 8cos(x) - cos(x)) +--R * +--R +--------------+ +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a sec(x) + a \|- sec(x) - 1 |-------------- +--R \| cos(x) +--R + +--R 3 2 2 3 2 +--R (4cos(x) + 6cos(x) + 2cos(x))sec(x) - 4cos(x) - 6cos(x) +--R + +--R - 2cos(x) +--R * +--R +----+ +--------------+ +------------+ +--R \|- 4a \|- a sec(x) + a \|- sec(x) - 1 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 528 +t0306:= (a+b*sec(c+d*x))^3 +--R +--R +--R 3 3 2 2 2 3 +--R (32) b sec(d x + c) + 3a b sec(d x + c) + 3a b sec(d x + c) + a +--R Type: Expression(Integer) +--E 33 + +--S 34 of 528 +r0306:= a^3*x+3*a^2*b*atanh(sin(c+d*x))/d+1/2*b^3*_ + atanh(sin(c+d*x))/d+3*a*b^2*tan(c+d*x)/d+_ + 1/2*b^3*sec(c+d*x)*tan(c+d*x)/d +--R +--R +--R (33) +--R 3 2 3 2 +--R (b + 6a b)atanh(sin(d x + c)) + (b sec(d x + c) + 6a b )tan(d x + c) +--R + +--R 3 +--R 2a d x +--R / +--R 2d +--R Type: Expression(Integer) +--E 34 + +--S 35 of 528 +a0306:= integrate(t0306,x) +--R +--R +--R (34) +--R 3 2 2 sin(d x + c) + cos(d x + c) + 1 +--R (b + 6a b)cos(d x + c) log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R 3 2 2 sin(d x + c) - cos(d x + c) - 1 +--R (- b - 6a b)cos(d x + c) log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R 2 3 3 2 +--R (6a b cos(d x + c) + b )sin(d x + c) + 2a d x cos(d x + c) +--R / +--R 2 +--R 2d cos(d x + c) +--R Type: Union(Expression(Integer),...) +--E 35 + +--S 36 of 528 +m0306:= a0306-r0306 +--R +--R +--R (35) +--R 3 2 2 sin(d x + c) + cos(d x + c) + 1 +--R (b + 6a b)cos(d x + c) log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R 3 2 2 sin(d x + c) - cos(d x + c) - 1 +--R (- b - 6a b)cos(d x + c) log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R 3 2 2 +--R (- b - 6a b)cos(d x + c) atanh(sin(d x + c)) +--R + +--R 3 2 2 2 +--R (- b cos(d x + c) sec(d x + c) - 6a b cos(d x + c) )tan(d x + c) +--R + +--R 2 3 +--R (6a b cos(d x + c) + b )sin(d x + c) +--R / +--R 2 +--R 2d cos(d x + c) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 528 +d0306:= D(m0306,x) +--R +--R +--R (36) +--R 3 3 2 3 4 +--R (- 2b cos(d x + c) sec(d x + c) - 6a b cos(d x + c) )sin(d x + c) +--R + +--R 3 5 3 4 3 3 +--R (2b cos(d x + c) + 4b cos(d x + c) + 4b cos(d x + c) ) +--R * +--R sec(d x + c) +--R + +--R 2 5 2 4 2 3 +--R 6a b cos(d x + c) + 12a b cos(d x + c) + 12a b cos(d x + c) +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 5 3 4 3 3 +--R (- 2b cos(d x + c) - 4b cos(d x + c) - 2b cos(d x + c) ) +--R * +--R sec(d x + c) +--R + +--R 2 5 2 4 2 3 +--R - 6a b cos(d x + c) - 12a b cos(d x + c) - 6a b cos(d x + c) +--R * +--R 2 +--R tan(d x + c) +--R + +--R 2 3 6 +--R (6a b cos(d x + c) + 2b )sin(d x + c) +--R + +--R 3 3 3 2 2 3 +--R - b cos(d x + c) sec(d x + c) + (- 2b - 6a b - 12a b)cos(d x + c) +--R + +--R 3 2 2 3 2 3 +--R (- b - 12a b )cos(d x + c) + (- 4b - 12a b )cos(d x + c) - 4b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 3 5 3 4 3 3 +--R (b cos(d x + c) + 2b cos(d x + c) + 2b cos(d x + c) )sec(d x + c) +--R + +--R 3 2 5 3 2 4 +--R (- 2b - 12a b)cos(d x + c) + (- 2b - 6a b)cos(d x + c) +--R + +--R 2 2 3 2 2 +--R (6a b + 12a b)cos(d x + c) + 12a b cos(d x + c) +--R + +--R 3 2 3 +--R (4b + 6a b )cos(d x + c) + 2b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 5 3 4 3 3 +--R (- b cos(d x + c) - 2b cos(d x + c) - b cos(d x + c) )sec(d x + c) +--R + +--R 3 2 6 3 2 4 3 3 +--R (- b - 6a b)cos(d x + c) + (2b + 6a b)cos(d x + c) + 2b cos(d x + c) +--R + +--R 3 2 +--R b cos(d x + c) +--R / +--R 3 4 +--R 2cos(d x + c) sin(d x + c) +--R + +--R 5 4 3 2 +--R (- 2cos(d x + c) - 4cos(d x + c) - 4cos(d x + c) )sin(d x + c) +--R + +--R 5 4 3 +--R 2cos(d x + c) + 4cos(d x + c) + 2cos(d x + c) +--R Type: Expression(Integer) +--E 37 + +--S 38 of 528 +t0307:= (a+b*sec(c+d*x))^2 +--R +--R +--R 2 2 2 +--R (37) b sec(d x + c) + 2a b sec(d x + c) + a +--R Type: Expression(Integer) +--E 38 + +--S 39 of 528 +r0307:= a^2*x+2*a*b*atanh(sin(c+d*x))/d+b^2*tan(c+d*x)/d +--R +--R +--R 2 2 +--R 2a b atanh(sin(d x + c)) + b tan(d x + c) + a d x +--R (38) ------------------------------------------------- +--R d +--R Type: Expression(Integer) +--E 39 + +--S 40 of 528 +a0307:= integrate(t0307,x) +--R +--R +--R (39) +--R sin(d x + c) + cos(d x + c) + 1 +--R 2a b cos(d x + c)log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R sin(d x + c) - cos(d x + c) - 1 2 +--R - 2a b cos(d x + c)log(-------------------------------) + b sin(d x + c) +--R cos(d x + c) + 1 +--R + +--R 2 +--R a d x cos(d x + c) +--R / +--R d cos(d x + c) +--R Type: Union(Expression(Integer),...) +--E 40 + +--S 41 of 528 +m0307:= a0307-r0307 +--R +--R +--R (40) +--R sin(d x + c) + cos(d x + c) + 1 +--R 2a b cos(d x + c)log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R sin(d x + c) - cos(d x + c) - 1 +--R - 2a b cos(d x + c)log(-------------------------------) +--R cos(d x + c) + 1 +--R + +--R 2 +--R - 2a b cos(d x + c)atanh(sin(d x + c)) - b cos(d x + c)tan(d x + c) +--R + +--R 2 +--R b sin(d x + c) +--R / +--R d cos(d x + c) +--R Type: Expression(Integer) +--E 41 + +--S 42 of 528 +d0307:= D(m0307,x) +--R +--R +--R (41) +--R 2 2 4 +--R - b cos(d x + c) sin(d x + c) +--R + +--R 2 4 2 3 2 2 2 +--R (b cos(d x + c) + 2b cos(d x + c) + 2b cos(d x + c) )sin(d x + c) +--R + +--R 2 4 2 3 2 2 +--R - b cos(d x + c) - 2b cos(d x + c) - b cos(d x + c) +--R * +--R 2 +--R tan(d x + c) +--R + +--R 2 6 +--R b sin(d x + c) +--R + +--R 2 2 2 2 4 +--R ((- b - 4a b)cos(d x + c) - 2b cos(d x + c) - 2b )sin(d x + c) +--R + +--R 4 3 2 2 +--R - 4a b cos(d x + c) - 2a b cos(d x + c) + (b + 4a b)cos(d x + c) +--R + +--R 2 2 +--R 2b cos(d x + c) + b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 5 3 +--R - 2a b cos(d x + c) + 2a b cos(d x + c) +--R / +--R 2 4 +--R cos(d x + c) sin(d x + c) +--R + +--R 4 3 2 2 +--R (- cos(d x + c) - 2cos(d x + c) - 2cos(d x + c) )sin(d x + c) +--R + +--R 4 3 2 +--R cos(d x + c) + 2cos(d x + c) + cos(d x + c) +--R Type: Expression(Integer) +--E 42 + +--S 43 of 528 +t0308:= 1/(3+5*sec(c+d*x)) +--R +--R +--R 1 +--R (42) ----------------- +--R 5sec(d x + c) + 3 +--R Type: Expression(Integer) +--E 43 + +--S 44 of 528 +r0308:= 1/3*x-5/6*atan(1/2*tan(1/2*c+1/2*d*x))/d +--R +--R +--R d x + c +--R tan(-------) +--R 2 +--R - 5atan(------------) + 2d x +--R 2 +--R (43) ---------------------------- +--R 6d +--R Type: Expression(Integer) +--E 44 + +--S 45 of 528 +a0308:= integrate(t0308,x) +--R +--R +--R sin(d x + c) +--R - 5atan(-----------------) + 2d x +--R 2cos(d x + c) + 2 +--R (44) --------------------------------- +--R 6d +--R Type: Union(Expression(Integer),...) +--E 45 + +--S 46 of 528 +m0308:= a0308-r0308 +--R +--R +--R d x + c +--R tan(-------) +--R 2 sin(d x + c) +--R 5atan(------------) - 5atan(-----------------) +--R 2 2cos(d x + c) + 2 +--R (45) ---------------------------------------------- +--R 6d +--R Type: Expression(Integer) +--E 46 + +--S 47 of 528 +d0308:= D(m0308,x) +--R +--R +--R (46) +--R 2 2 d x + c 2 +--R (- 5sin(d x + c) + 10cos(d x + c) + 30cos(d x + c) + 20)tan(-------) +--R 2 +--R + +--R 2 2 +--R - 35sin(d x + c) - 20cos(d x + c) + 20 +--R / +--R 2 2 d x + c 2 +--R (6sin(d x + c) + 24cos(d x + c) + 48cos(d x + c) + 24)tan(-------) +--R 2 +--R + +--R 2 2 +--R 24sin(d x + c) + 96cos(d x + c) + 192cos(d x + c) + 96 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 528 +t0309:= 1/(5+3*sec(c+d*x)) +--R +--R +--R 1 +--R (47) ----------------- +--R 3sec(d x + c) + 5 +--R Type: Expression(Integer) +--E 48 + +--S 49 of 528 +r0309:= 1/5*x-3/10*atanh(1/2*tan(1/2*c+1/2*d*x))/d +--R +--R +--R d x + c +--R tan(-------) +--R 2 +--R - 3atanh(------------) + 2d x +--R 2 +--R (48) ----------------------------- +--R 10d +--R Type: Expression(Integer) +--E 49 + +--S 50 of 528 +a0309:= integrate(t0309,x) +--R +--R +--R (49) +--R sin(d x + c) + 2cos(d x + c) + 2 +--R - 3log(--------------------------------) +--R cos(d x + c) + 1 +--R + +--R sin(d x + c) - 2cos(d x + c) - 2 +--R 3log(--------------------------------) + 4d x +--R cos(d x + c) + 1 +--R / +--R 20d +--R Type: Union(Expression(Integer),...) +--E 50 + +--S 51 of 528 +m0309:= a0309-r0309 +--R +--R +--R (50) +--R sin(d x + c) + 2cos(d x + c) + 2 +--R - 3log(--------------------------------) +--R cos(d x + c) + 1 +--R + +--R d x + c +--R tan(-------) +--R sin(d x + c) - 2cos(d x + c) - 2 2 +--R 3log(--------------------------------) + 6atanh(------------) +--R cos(d x + c) + 1 2 +--R / +--R 20d +--R Type: Expression(Integer) +--E 51 + +--S 52 of 528 +d0309:= D(m0309,x) +--R +--R +--R (51) +--R 2 2 d x + c 2 +--R (3sin(d x + c) + 18cos(d x + c) + 30cos(d x + c) + 12)tan(-------) +--R 2 +--R + +--R 2 2 +--R - 27sin(d x + c) - 12cos(d x + c) + 12 +--R / +--R 2 2 d x + c 2 +--R (10sin(d x + c) - 40cos(d x + c) - 80cos(d x + c) - 40)tan(-------) +--R 2 +--R + +--R 2 2 +--R - 40sin(d x + c) + 160cos(d x + c) + 320cos(d x + c) + 160 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 528 +t0310:= 1/(a+b*sec(c+d*x))^2 +--R +--R +--R 1 +--R (52) ---------------------------------------- +--R 2 2 2 +--R b sec(d x + c) + 2a b sec(d x + c) + a +--R Type: Expression(Integer) +--E 53 + +--S 54 of 528 +r0310:= x/a^2-2*b^3*atanh((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/a^2/_ + (a^2-b^2)^(3/2)/d-4*b*atanh((a-b)*tan(1/2*c+1/2*d*x)/_ + (a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)/d+b^2*sin(c+d*x)/a/(a^2-b^2)/d/(b+a*cos(c+d*x)) +--R +--R +--R (53) +--R d x + c +--R (b - a)tan(-------) +--R 3 3 4 2 2 2 +--R ((2a b - 4a b)cos(d x + c) + 2b - 4a b )atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 3 2 +--R (- a b sin(d x + c) + (a b - a )d x cos(d x + c) + (b - a b)d x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d cos(d x + c) + (a b - a b)d)\|- b + a +--R Type: Expression(Integer) +--E 54 + +--S 55 of 528 +a0310:= integrate(t0310,x) +--R +--R +--R (54) +--R [ +--R 3 3 4 2 2 +--R ((a b - 2a b)cos(d x + c) + b - 2a b ) +--R * +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(d x + c) - a)\|- b + a + (- b + a )sin(d x + c) +--R log(------------------------------------------------------------) +--R a cos(d x + c) + b +--R + +--R 2 2 3 3 2 +--R (- a b sin(d x + c) + (a b - a )d x cos(d x + c) + (b - a b)d x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d cos(d x + c) + (a b - a b)d)\|- b + a +--R , +--R +--R 3 3 4 2 2 +--R ((- 2a b + 4a b)cos(d x + c) - 2b + 4a b ) +--R * +--R +-------+ +--R | 2 2 +--R sin(d x + c)\|b - a +--R atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R + +--R 2 2 3 3 2 +--R (- a b sin(d x + c) + (a b - a )d x cos(d x + c) + (b - a b)d x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d cos(d x + c) + (a b - a b)d)\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 55 + +--S 56 of 528 +m0310a:= a0310.1-r0310 +--R +--R +--R (55) +--R 3 2 +--R (b - 2a b) +--R * +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(d x + c) - a)\|- b + a + (- b + a )sin(d x + c) +--R log(------------------------------------------------------------) +--R a cos(d x + c) + b +--R + +--R d x + c +--R (b - a)tan(-------) +--R 3 2 2 +--R (- 2b + 4a b)atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 4 | 2 2 +--R (a b - a )d\|- b + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 528 +d0310a:= D(m0310a,x) +--R +--R +--R (56) +--R 4 3 2 2 3 2 +--R (- b + a b + 2a b - 2a b)sin(d x + c) +--R + +--R 3 3 2 +--R (a b - 2a b)cos(d x + c) +--R + +--R 4 3 2 2 3 4 2 2 +--R (b + a b - 2a b - 2a b)cos(d x + c) + b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (- b - a b + 2a b + 2a b)sin(d x + c) +--R + +--R 3 3 2 +--R (- a b + 2a b)cos(d x + c) +--R + +--R 4 3 2 2 3 4 2 2 +--R (- b + a b + 2a b - 2a b)cos(d x + c) + b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 4 5 2 3 4 +--R ((b - 3a b + 2a b)cos(d x + c) + b - 3a b + 2a b)sin(d x + c) +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 5 2 3 4 5 2 3 4 +--R ((b - 3a b + 2a b)cos(d x + c) - b + 3a b - 2a b)sin(d x + c) +--R / +--R 2 4 3 3 4 2 5 2 +--R (a b - a b - a b + a b)cos(d x + c) +--R + +--R 5 2 4 5 6 2 4 3 3 4 2 5 +--R (a b - a b - a b + a )cos(d x + c) + a b - a b - a b + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 4 3 3 4 2 5 2 +--R (a b + a b - a b - a b)cos(d x + c) +--R + +--R 5 2 4 5 6 2 4 3 3 4 2 5 +--R (a b + a b - a b - a )cos(d x + c) + a b + a b - a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 +--R (a b - a b - 2a b + 2a b + a b - a )cos(d x + c) + a b - a b +--R + +--R 3 4 4 3 5 2 6 +--R - 2a b + 2a b + a b - a b +--R * +--R d x + c 2 +--R sin(d x + c)tan(-------) +--R 2 +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 2 5 +--R (a b + a b - 2a b - 2a b + a b + a )cos(d x + c) + a b + a b +--R + +--R 3 4 4 3 5 2 6 +--R - 2a b - 2a b + a b + a b +--R * +--R sin(d x + c) +--R Type: Expression(Integer) +--E 57 + +--S 58 of 528 +m0310b:= a0310.2-r0310 +--R +--R +--R (57) +--R d x + c +--R +-------+ (b - a)tan(-------) +--R 3 2 | 2 2 2 +--R (- 2b + 4a b)\|b - a atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 2 | 2 2 sin(d x + c)\|b - a +--R (- 2b + 4a b)\|- b + a atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R / +--R +---------+ +-------+ +--R 2 2 4 | 2 2 | 2 2 +--R (a b - a )d\|- b + a \|b - a +--R Type: Expression(Integer) +--E 58 + +--S 59 of 528 +d0310b:= D(m0310b,x) +--R +--R +--R (58) +--R 4 3 2 2 3 2 +--R (- b + a b + 2a b - 2a b)sin(d x + c) +--R + +--R 4 3 2 2 3 2 +--R (- b + 3a b + 2a b - 6a b)cos(d x + c) +--R + +--R 3 3 4 3 2 2 3 +--R (4a b - 8a b)cos(d x + c) + b + a b - 2a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (- b - 3a b + 2a b + 6a b)sin(d x + c) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (- b - a b + 2a b + 2a b)cos(d x + c) + b + a b - 2a b - 2a b +--R / +--R 2 4 3 3 5 6 2 +--R (a b - 2a b + 2a b - a )sin(d x + c) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (a b - 2a b + a )cos(d x + c) + (2a b - 4a b + 2a )cos(d x + c) +--R + +--R 2 4 4 2 6 +--R a b - 2a b + a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 4 4 2 6 2 +--R (a b - 2a b + a )sin(d x + c) +--R + +--R 2 4 3 3 5 6 2 +--R (a b + 2a b - 2a b - a )cos(d x + c) +--R + +--R 2 4 3 3 5 6 2 4 3 3 5 6 +--R (2a b + 4a b - 4a b - 2a )cos(d x + c) + a b + 2a b - 2a b - a +--R Type: Expression(Integer) +--E 59 + +--S 60 of 528 +t0311:= 1/(a+b*sec(c+d*x))^3 +--R +--R +--R 1 +--R (59) ------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R b sec(d x + c) + 3a b sec(d x + c) + 3a b sec(d x + c) + a +--R Type: Expression(Integer) +--E 60 + +--S 61 of 528 +r0311:= x/a^3-6*b^3*atanh((a-b)*tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/a^3/_ + (a^2-b^2)^(3/2)/d-6*b*atanh((a-b)*tan(1/2*c+1/2*d*x)/_ + (a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)/d-b^3*(a^2+2*b^2)*atanh((a-b)*_ + tan(1/2*c+1/2*d*x)/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(5/2)/d-_ + 1/2*b^3*sin(c+d*x)/a^2/(a^2-b^2)/d/(b+a*cos(c+d*x))^2+_ + 3/2*b^4*sin(c+d*x)/a^2/(a^2-b^2)^2/d/(b+a*cos(c+d*x))+_ + 3*b^2*sin(c+d*x)/a^2/(a^2-b^2)/d/(b+a*cos(c+d*x)) +--R +--R +--R (60) +--R 2 5 4 3 6 2 +--R (4a b - 10a b + 12a b)cos(d x + c) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (8a b - 20a b + 24a b )cos(d x + c) + 4b - 10a b + 12a b +--R * +--R d x + c +--R (b - a)tan(-------) +--R 2 +--R atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 5 3 3 +--R ((- 3a b + 6a b )cos(d x + c) - 2a b + 5a b )sin(d x + c) +--R + +--R 2 4 4 2 6 2 +--R (2a b - 4a b + 2a )d x cos(d x + c) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (4a b - 8a b + 4a b)d x cos(d x + c) + (2b - 4a b + 2a b )d x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 7 2 9 2 +--R (2a b - 4a b + 2a )d cos(d x + c) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 +--R (4a b - 8a b + 4a b)d cos(d x + c) + (2a b - 4a b + 2a b )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 528 +a0311:= integrate(t0311,x) +--R +--R +--R (61) +--R [ +--R 2 5 4 3 6 2 +--R (2a b - 5a b + 6a b)cos(d x + c) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (4a b - 10a b + 12a b )cos(d x + c) + 2b - 5a b + 6a b +--R * +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(d x + c) - a)\|- b + a + (- b + a )sin(d x + c) +--R log(------------------------------------------------------------) +--R a cos(d x + c) + b +--R + +--R 2 4 4 2 5 3 3 +--R ((- 3a b + 6a b )cos(d x + c) - 2a b + 5a b )sin(d x + c) +--R + +--R 2 4 4 2 6 2 +--R (2a b - 4a b + 2a )d x cos(d x + c) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (4a b - 8a b + 4a b)d x cos(d x + c) + (2b - 4a b + 2a b )d x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 7 2 9 2 +--R (2a b - 4a b + 2a )d cos(d x + c) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 +--R (4a b - 8a b + 4a b)d cos(d x + c) + (2a b - 4a b + 2a b )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 2 5 4 3 6 2 +--R (- 4a b + 10a b - 12a b)cos(d x + c) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (- 8a b + 20a b - 24a b )cos(d x + c) - 4b + 10a b - 12a b +--R * +--R +-------+ +--R | 2 2 +--R sin(d x + c)\|b - a +--R atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R + +--R 2 4 4 2 5 3 3 +--R ((- 3a b + 6a b )cos(d x + c) - 2a b + 5a b )sin(d x + c) +--R + +--R 2 4 4 2 6 2 +--R (2a b - 4a b + 2a )d x cos(d x + c) +--R + +--R 5 3 3 5 6 2 4 4 2 +--R (4a b - 8a b + 4a b)d x cos(d x + c) + (2b - 4a b + 2a b )d x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 5 4 7 2 9 2 +--R (2a b - 4a b + 2a )d cos(d x + c) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 +--R (4a b - 8a b + 4a b)d cos(d x + c) + (2a b - 4a b + 2a b )d +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 62 + +--S 63 of 528 +m0311a:= a0311.1-r0311 +--R +--R +--R (62) +--R 5 2 3 4 +--R (2b - 5a b + 6a b) +--R * +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(d x + c) - a)\|- b + a + (- b + a )sin(d x + c) +--R log(------------------------------------------------------------) +--R a cos(d x + c) + b +--R + +--R d x + c +--R (b - a)tan(-------) +--R 5 2 3 4 2 +--R (- 4b + 10a b - 12a b)atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 4 5 2 7 | 2 2 +--R (2a b - 4a b + 2a )d\|- b + a +--R Type: Expression(Integer) +--E 63 + +--S 64 of 528 +d0311a:= D(m0311a,x) +--R +--R +--R (63) +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2b + 2a b + 5a b - 5a b - 6a b + 6a b)sin(d x + c) +--R + +--R 5 3 3 5 2 +--R (2a b - 5a b + 6a b)cos(d x + c) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (2b + 2a b - 5a b - 5a b + 6a b + 6a b)cos(d x + c) + 2b +--R + +--R 2 4 4 2 +--R - 5a b + 6a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2b - 2a b + 5a b + 5a b - 6a b - 6a b)sin(d x + c) +--R + +--R 5 3 3 5 2 +--R (- 2a b + 5a b - 6a b)cos(d x + c) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 2b + 2a b + 5a b - 5a b - 6a b + 6a b)cos(d x + c) + 2b +--R + +--R 2 4 4 2 +--R - 5a b + 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (2b - 7a b + 11a b - 6a b)cos(d x + c) + 2b - 7a b + 11a b +--R + +--R 6 +--R - 6a b +--R * +--R d x + c 2 +--R sin(d x + c)tan(-------) +--R 2 +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (2b - 7a b + 11a b - 6a b)cos(d x + c) - 2b + 7a b - 11a b +--R + +--R 6 +--R 6a b +--R * +--R sin(d x + c) +--R / +--R 3 6 4 5 5 4 6 3 7 2 8 2 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a b)cos(d x + c) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (2a b - 2a b - 2a b + 2a b - 2a b + 2a b + 2a b - 2a ) +--R * +--R cos(d x + c) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 2a b - 2a b - 4a b + 4a b + 2a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 2 +--R (2a b + 2a b - 4a b - 4a b + 2a b + 2a b)cos(d x + c) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 +--R (2a b + 2a b - 2a b - 2a b - 2a b - 2a b + 2a b + 2a ) +--R * +--R cos(d x + c) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 2a b + 2a b - 4a b - 4a b + 2a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R (2a b - 2a b - 6a b + 6a b + 6a b - 6a b - 2a b + 2a ) +--R * +--R cos(d x + c) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 2a b - 2a b - 6a b + 6a b + 6a b - 6a b - 2a b + 2a b +--R * +--R d x + c 2 +--R sin(d x + c)tan(-------) +--R 2 +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 +--R (2a b + 2a b - 6a b - 6a b + 6a b + 6a b - 2a b - 2a ) +--R * +--R cos(d x + c) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 2a b + 2a b - 6a b - 6a b + 6a b + 6a b - 2a b - 2a b +--R * +--R sin(d x + c) +--R Type: Expression(Integer) +--E 64 + +--S 65 of 528 +m0311b:= a0311.2-r0311 +--R +--R +--R (64) +--R d x + c +--R +-------+ (b - a)tan(-------) +--R 5 2 3 4 | 2 2 2 +--R (- 2b + 5a b - 6a b)\|b - a atanh(-------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 5 2 3 4 | 2 2 sin(d x + c)\|b - a +--R (- 2b + 5a b - 6a b)\|- b + a atan(---------------------------) +--R (b + a)cos(d x + c) + b + a +--R / +--R +---------+ +-------+ +--R 3 4 5 2 7 | 2 2 | 2 2 +--R (a b - 2a b + a )d\|- b + a \|b - a +--R Type: Expression(Integer) +--E 65 + +--S 66 of 528 +d0311b:= D(m0311b,x) +--R +--R +--R (65) +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2b + 2a b + 5a b - 5a b - 6a b + 6a b)sin(d x + c) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2b + 6a b + 5a b - 15a b - 6a b + 18a b)cos(d x + c) +--R + +--R 5 3 3 5 6 5 2 4 3 3 +--R (8a b - 20a b + 24a b)cos(d x + c) + 2b + 2a b - 5a b - 5a b +--R + +--R 4 2 5 +--R 6a b + 6a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 2b - 6a b + 5a b + 15a b - 6a b - 18a b)sin(d x + c) +--R + +--R 6 5 2 4 3 3 4 2 5 2 6 5 +--R (- 2b - 2a b + 5a b + 5a b - 6a b - 6a b)cos(d x + c) + 2b + 2a b +--R + +--R 2 4 3 3 4 2 5 +--R - 5a b - 5a b + 6a b + 6a b +--R / +--R 3 6 4 5 5 4 6 3 7 2 8 9 2 +--R (2a b - 4a b - 2a b + 8a b - 2a b - 4a b + 2a )sin(d x + c) +--R + +--R 3 6 5 4 7 2 9 2 +--R (2a b - 6a b + 6a b - 2a )cos(d x + c) +--R + +--R 3 6 5 4 7 2 9 3 6 5 4 7 2 +--R (4a b - 12a b + 12a b - 4a )cos(d x + c) + 2a b - 6a b + 6a b +--R + +--R 9 +--R - 2a +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 6 5 4 7 2 9 2 +--R (2a b - 6a b + 6a b - 2a )sin(d x + c) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 2 +--R (2a b + 4a b - 2a b - 8a b - 2a b + 4a b + 2a )cos(d x + c) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 3 6 +--R (4a b + 8a b - 4a b - 16a b - 4a b + 8a b + 4a )cos(d x + c) + 2a b +--R + +--R 4 5 5 4 6 3 7 2 8 9 +--R 4a b - 2a b - 8a b - 2a b + 4a b + 2a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 528 +t0312:= (1+sec(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (66) \|sec(x) + 1 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 528 +r0312:= asinh(1/2*2^(1/2)*tan(x))+atan(tan(x)/(2+tan(x)^2)^(1/2)) +--R +--R +--R +-+ +--R tan(x) \|2 tan(x) +--R (67) atan(--------------) + asinh(----------) +--R +-----------+ 2 +--R | 2 +--R \|tan(x) + 2 +--R Type: Expression(Integer) +--E 68 + +--S 69 of 528 +a0312:= integrate(t0312,x) +--R +--R +--R (68) +--R - +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((- cos(x) - 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R sin(x) +--R - atan(------) +--R cos(x) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 69 + +--S 70 of 528 +m0312:= a0312-r0312 +--R +--R +--R (69) +--R - +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((- cos(x) - 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R +-+ +--R tan(x) sin(x) \|2 tan(x) +--R - 2atan(--------------) - atan(------) - 2asinh(----------) +--R +-----------+ cos(x) 2 +--R | 2 +--R \|tan(x) + 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 528 +d0312:= D(m0312,x) +--R +--R +--R (70) +--R 17 16 15 14 +--R - 1024cos(x) - 1024cos(x) - 768cos(x) - 768cos(x) +--R + +--R 13 12 11 10 +--R 1280cos(x) + 1280cos(x) + 816cos(x) + 816cos(x) +--R + +--R 9 8 7 6 +--R - 540cos(x) - 540cos(x) - 275cos(x) - 275cos(x) +--R + +--R 5 4 3 2 +--R 72cos(x) + 72cos(x) + 30cos(x) + 30cos(x) + cos(x) + 1 +--R * +--R 4 +--R sin(x) +--R + +--R 19 18 17 16 +--R - 2048cos(x) - 2048cos(x) - 2048cos(x) - 2048cos(x) +--R + +--R 15 14 13 12 +--R 896cos(x) + 896cos(x) + 384cos(x) + 384cos(x) +--R + +--R 11 10 9 8 +--R - 264cos(x) - 264cos(x) + 632cos(x) + 632cos(x) +--R + +--R 7 6 5 4 3 +--R 238cos(x) + 238cos(x) - 176cos(x) - 176cos(x) - 60cos(x) +--R + +--R 2 +--R - 60cos(x) - 2cos(x) - 2 +--R * +--R 2 +--R sin(x) +--R + +--R 21 20 19 18 +--R - 1024cos(x) - 1024cos(x) - 1280cos(x) - 1280cos(x) +--R + +--R 17 16 15 14 +--R 1152cos(x) + 1152cos(x) + 1488cos(x) + 1488cos(x) +--R + +--R 13 12 11 10 +--R - 524cos(x) - 524cos(x) - 533cos(x) - 533cos(x) +--R + +--R 9 8 7 6 5 +--R 132cos(x) + 132cos(x) + 39cos(x) + 39cos(x) - 17cos(x) +--R + +--R 4 3 2 +--R - 17cos(x) + 6cos(x) + 6cos(x) + cos(x) + 1 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 17 15 13 11 +--R 2048cos(x) + 2560cos(x) - 2048cos(x) - 2976cos(x) +--R + +--R 9 7 5 3 +--R 600cos(x) + 1130cos(x) - 6cos(x) - 138cos(x) - 16cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 19 17 15 13 +--R 4096cos(x) + 6144cos(x) - 256cos(x) - 1920cos(x) +--R + +--R 11 9 7 5 3 +--R 464cos(x) - 1064cos(x) - 1124cos(x) + 268cos(x) + 284cos(x) +--R + +--R 32cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 21 19 17 15 +--R 2048cos(x) + 3584cos(x) - 1280cos(x) - 4320cos(x) +--R + +--R 13 11 9 7 5 +--R - 72cos(x) + 1774cos(x) + 70cos(x) - 244cos(x) + 34cos(x) +--R + +--R 3 +--R - 2cos(x) - 8cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R + +--R 17 16 15 14 +--R - 1024cos(x) - 1024cos(x) - 1536cos(x) - 1536cos(x) +--R + +--R 13 12 11 10 +--R 320cos(x) + 320cos(x) + 1184cos(x) + 1184cos(x) +--R + +--R 9 8 7 6 5 +--R 188cos(x) + 188cos(x) - 222cos(x) - 222cos(x) - 62cos(x) +--R + +--R 4 3 2 +--R - 62cos(x) - 2cos(x) - 2cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 16 15 14 +--R 2048cos(x) + 2048cos(x) + 3072cos(x) + 3072cos(x) +--R + +--R 13 12 11 10 +--R - 896cos(x) - 896cos(x) - 2624cos(x) - 2624cos(x) +--R + +--R 9 8 7 6 +--R - 184cos(x) - 184cos(x) + 636cos(x) + 636cos(x) +--R + +--R 5 4 3 2 +--R 90cos(x) + 90cos(x) - 30cos(x) - 30cos(x) - 2cos(x) - 2 +--R * +--R 2 +--R sin(x) +--R + +--R 21 20 19 18 +--R 1024cos(x) + 1024cos(x) + 1536cos(x) + 1536cos(x) +--R + +--R 17 16 15 14 +--R - 1344cos(x) - 1344cos(x) - 2464cos(x) - 2464cos(x) +--R + +--R 13 12 11 10 +--R 644cos(x) + 644cos(x) + 1470cos(x) + 1470cos(x) +--R + +--R 9 8 7 6 5 +--R - 134cos(x) - 134cos(x) - 378cos(x) - 378cos(x) + 6cos(x) +--R + +--R 4 3 2 +--R 6cos(x) + 34cos(x) + 34cos(x) + 2cos(x) + 2 +--R * +--R 2 +--R tan(x) +--R + +--R 17 16 15 14 +--R - 2048cos(x) - 2048cos(x) - 3072cos(x) - 3072cos(x) +--R + +--R 13 12 11 10 +--R 640cos(x) + 640cos(x) + 2368cos(x) + 2368cos(x) +--R + +--R 9 8 7 6 5 +--R 376cos(x) + 376cos(x) - 444cos(x) - 444cos(x) - 124cos(x) +--R + +--R 4 3 2 +--R - 124cos(x) - 4cos(x) - 4cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 16 15 14 +--R 4096cos(x) + 4096cos(x) + 6144cos(x) + 6144cos(x) +--R + +--R 13 12 11 10 +--R - 1792cos(x) - 1792cos(x) - 5248cos(x) - 5248cos(x) +--R + +--R 9 8 7 6 +--R - 368cos(x) - 368cos(x) + 1272cos(x) + 1272cos(x) +--R + +--R 5 4 3 2 +--R 180cos(x) + 180cos(x) - 60cos(x) - 60cos(x) - 4cos(x) - 4 +--R * +--R 2 +--R sin(x) +--R + +--R 21 20 19 18 +--R 2048cos(x) + 2048cos(x) + 3072cos(x) + 3072cos(x) +--R + +--R 17 16 15 14 +--R - 2688cos(x) - 2688cos(x) - 4928cos(x) - 4928cos(x) +--R + +--R 13 12 11 10 +--R 1288cos(x) + 1288cos(x) + 2940cos(x) + 2940cos(x) +--R + +--R 9 8 7 6 5 +--R - 268cos(x) - 268cos(x) - 756cos(x) - 756cos(x) + 12cos(x) +--R + +--R 4 3 2 +--R 12cos(x) + 68cos(x) + 68cos(x) + 4cos(x) + 4 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 17 15 13 11 +--R 2048cos(x) + 4096cos(x) + 640cos(x) - 2944cos(x) +--R + +--R 9 7 5 3 +--R - 1368cos(x) + 448cos(x) + 312cos(x) + 32cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 15 13 11 +--R - 4096cos(x) - 8192cos(x) - 768cos(x) + 6656cos(x) +--R + +--R 9 7 5 3 +--R 2544cos(x) - 1504cos(x) - 688cos(x) + 56cos(x) + 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 21 19 17 15 +--R - 2048cos(x) - 4096cos(x) + 1408cos(x) + 6528cos(x) +--R + +--R 13 11 9 7 5 +--R 728cos(x) - 3968cos(x) - 880cos(x) + 1088cos(x) + 256cos(x) +--R + +--R 3 +--R - 112cos(x) - 24cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 17 15 13 11 +--R 4096cos(x) + 8192cos(x) + 1280cos(x) - 5888cos(x) +--R + +--R 9 7 5 3 +--R - 2736cos(x) + 896cos(x) + 624cos(x) + 64cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 15 13 11 +--R - 8192cos(x) - 16384cos(x) - 1536cos(x) + 13312cos(x) +--R + +--R 9 7 5 3 +--R 5088cos(x) - 3008cos(x) - 1376cos(x) + 112cos(x) + 48cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 21 19 17 15 +--R - 4096cos(x) - 8192cos(x) + 2816cos(x) + 13056cos(x) +--R + +--R 13 11 9 7 5 +--R 1456cos(x) - 7936cos(x) - 1760cos(x) + 2176cos(x) + 512cos(x) +--R + +--R 3 +--R - 224cos(x) - 48cos(x) +--R / +--R 17 16 15 14 +--R 1024cos(x) + 1024cos(x) + 1536cos(x) + 1536cos(x) +--R + +--R 13 12 11 10 +--R - 320cos(x) - 320cos(x) - 1184cos(x) - 1184cos(x) +--R + +--R 9 8 7 6 5 +--R - 188cos(x) - 188cos(x) + 222cos(x) + 222cos(x) + 62cos(x) +--R + +--R 4 3 2 +--R 62cos(x) + 2cos(x) + 2cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 16 15 14 +--R - 2048cos(x) - 2048cos(x) - 3072cos(x) - 3072cos(x) +--R + +--R 13 12 11 10 +--R 896cos(x) + 896cos(x) + 2624cos(x) + 2624cos(x) +--R + +--R 9 8 7 6 5 +--R 184cos(x) + 184cos(x) - 636cos(x) - 636cos(x) - 90cos(x) +--R + +--R 4 3 2 +--R - 90cos(x) + 30cos(x) + 30cos(x) + 2cos(x) + 2 +--R * +--R 2 +--R sin(x) +--R + +--R 21 20 19 18 +--R - 1024cos(x) - 1024cos(x) - 1536cos(x) - 1536cos(x) +--R + +--R 17 16 15 14 +--R 1344cos(x) + 1344cos(x) + 2464cos(x) + 2464cos(x) +--R + +--R 13 12 11 10 +--R - 644cos(x) - 644cos(x) - 1470cos(x) - 1470cos(x) +--R + +--R 9 8 7 6 5 +--R 134cos(x) + 134cos(x) + 378cos(x) + 378cos(x) - 6cos(x) +--R + +--R 4 3 2 +--R - 6cos(x) - 34cos(x) - 34cos(x) - 2cos(x) - 2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 17 15 13 11 +--R - 2048cos(x) - 4096cos(x) - 640cos(x) + 2944cos(x) +--R + +--R 9 7 5 3 +--R 1368cos(x) - 448cos(x) - 312cos(x) - 32cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 17 15 13 11 +--R 4096cos(x) + 8192cos(x) + 768cos(x) - 6656cos(x) +--R + +--R 9 7 5 3 +--R - 2544cos(x) + 1504cos(x) + 688cos(x) - 56cos(x) - 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 21 19 17 15 13 +--R 2048cos(x) + 4096cos(x) - 1408cos(x) - 6528cos(x) - 728cos(x) +--R + +--R 11 9 7 5 3 +--R 3968cos(x) + 880cos(x) - 1088cos(x) - 256cos(x) + 112cos(x) +--R + +--R 24cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 528 +t0313:= (1-sec(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (71) \|- sec(x) + 1 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 528 +r0313:= -cot(x)*log(cos(x))*(-tan(x)^2)^(1/2) +--R +--R +--R +---------+ +--R | 2 +--R (72) - cot(x)log(cos(x))\|- tan(x) +--R Type: Expression(Integer) +--E 73 + +--S 74 of 528 +a0313:= integrate(t0313,x) +--R +--R +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R (73) atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R Type: Union(Expression(Integer),...) +--E 74 + +--S 75 of 528 +m0313:= a0313-r0313 +--R +--R +--R (74) +--R +---------+ +--R | 2 +--R cot(x)log(cos(x))\|- tan(x) +--R + +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R Type: Expression(Integer) +--E 75 + +--S 76 of 528 +d0313:= D(m0313,x) +--R +--R +--R (75) +--R x 6 x 2 x 4 +--R - cos(x)sin(-) + (- 3cos(-) + 2)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 6 x 4 x 2 +--R (- 3cos(-) - 1)cos(x)sin(-) + (- cos(-) - 2cos(-) + 3cos(-) )cos(x) +--R 2 2 2 2 2 +--R * +--R +---------+ +--R | 2 +--R \|- tan(x) +--R + +--R x 6 x 2 x 4 +--R - cos(x)cot(x)sin(-) + (- 3cos(-) + 2)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (- 3cos(-) + 12cos(-) - 1)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (- cos(-) - 6cos(-) - 9cos(-) )cos(x)cot(x) +--R 2 2 2 +--R * +--R 3 +--R tan(x) +--R + +--R 2 x 6 +--R (cos(x)cot(x) + cos(x))sin(-) +--R 2 +--R + +--R x 2 2 x 2 x 4 +--R ((3cos(-) - 2)cos(x)cot(x) + (3cos(-) - 2)cos(x))sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 +--R (3cos(-) - 12cos(-) + 1)cos(x)cot(x) +--R 2 2 +--R + +--R x 4 x 2 +--R (3cos(-) - 12cos(-) + 1)cos(x) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 x 2 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cos(x)cot(x) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cos(x) +--R 2 2 2 +--R * +--R 2 +--R tan(x) +--R + +--R x 6 x 2 x 4 +--R - cos(x)cot(x)sin(-) + (- 3cos(-) + 2)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (- 3cos(-) + 12cos(-) - 1)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (- cos(-) - 6cos(-) - 9cos(-) )cos(x)cot(x) +--R 2 2 2 +--R * +--R tan(x) +--R * +--R log(cos(x)) +--R + +--R x 6 x 2 x 4 +--R cot(x)sin(-) + (3cos(-) - 2)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (3cos(-) - 12cos(-) + 1)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cot(x) +--R 2 2 2 +--R * +--R 2 +--R sin(x)tan(x) +--R / +--R x 6 x 2 x 4 +--R cos(x)sin(-) + (3cos(-) - 2)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (3cos(-) - 12cos(-) + 1)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cos(x) +--R 2 2 2 +--R * +--R +---------+ +--R | 2 +--R \|- tan(x) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 528 +t0314:= (-1+sec(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (76) \|sec(x) - 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 528 +r0314:= -cot(x)*log(cos(x))*(tan(x)^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 +--R (77) - cot(x)log(cos(x))\|tan(x) +--R Type: Expression(Integer) +--E 78 + +--S 79 of 528 +a0314:= integrate(t0314,x) +--R +--R +--R 2 2cos(x) +--R (78) - log(----------) + log(- ----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 79 + +--S 80 of 528 +m0314:= a0314-r0314 +--R +--R +--R +-------+ +--R | 2 2 2cos(x) +--R (79) cot(x)log(cos(x))\|tan(x) - log(----------) + log(- ----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 80 + +--S 81 of 528 +d0314:= D(m0314,x) +--R +--R +--R (80) +--R +-------+ +--R | 2 +--R - sin(x)\|tan(x) +--R + +--R 3 2 2 +--R cos(x)cot(x)tan(x) + (- cos(x)cot(x) - cos(x))tan(x) +--R + +--R cos(x)cot(x)tan(x) +--R * +--R log(cos(x)) +--R + +--R 2 +--R - cot(x)sin(x)tan(x) +--R / +--R +-------+ +--R | 2 +--R cos(x)\|tan(x) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 528 +t0315:= (-1-sec(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (81) \|- sec(x) - 1 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 528 +r0315:= atan(cot(x)*(-2-tan(x)^2)^(1/2))-atanh(tan(x)/(-2-tan(x)^2)^(1/2)) +--R +--R +--R +-------------+ +--R tan(x) | 2 +--R (82) - atanh(----------------) + atan(cot(x)\|- tan(x) - 2 ) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R Type: Expression(Integer) +--E 83 + +--S 84 of 528 +a0315:= integrate(t0315,x) +--R +--R +--R (83) +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) + 2\|- 1 - 1) +--R + +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R - +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 2\|- 1 - 1) +--R + +--R - +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 84 + +--S 85 of 528 +m0315:= a0315-r0315 +--R +--R +--R (84) +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) + 2\|- 1 - 1) +--R + +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R - +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 2\|- 1 - 1) +--R + +--R - +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R + +--R +-------------+ +--R tan(x) | 2 +--R 2atanh(----------------) - 2atan(cot(x)\|- tan(x) - 2 ) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 85 + +--S 86 of 528 +d0315:= D(m0315,x) +--R +--R +--R (85) +--R +---+ 6 +---+ 4 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R - \|- 1 cot(x) (%e ) - 9\|- 1 cot(x) (%e ) +--R + +--R +---+ 2 +--R +---+ 2 x\|- 1 +---+ 2 +--R - 21\|- 1 cot(x) (%e ) - 9\|- 1 cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (- 2\|- 1 cot(x) + \|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (- 18\|- 1 cot(x) + 9\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +--R (- 42\|- 1 cot(x) + 21\|- 1 )(%e ) - 18\|- 1 cot(x) +--R + +--R +---+ +--R 9\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - cot(x)(%e ) - 7cot(x)(%e ) - 13cot(x)(%e ) +--R + +--R - 7cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (2cot(x) + 1)(%e ) + (14cot(x) + 7)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (26cot(x) + 13)(%e ) + 14cot(x) + 7 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - cot(x)(%e ) - 7cot(x)(%e ) - 13cot(x)(%e ) +--R + +--R - 7cot(x) +--R * +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (4cot(x) + 1)(%e ) + (28cot(x) + 7)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (52cot(x) + 13)(%e ) + 28cot(x) + 7 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R \|- 1 cot(x) (%e ) + 12\|- 1 cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R 44\|- 1 cot(x) (%e ) + 48\|- 1 cot(x) (%e ) +--R + +--R +---+ 2 +--R 7\|- 1 cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 8 +--R +---+ 2 +---+ x\|- 1 +--R (2\|- 1 cot(x) - \|- 1 )(%e ) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (24\|- 1 cot(x) - 12\|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (88\|- 1 cot(x) - 44\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +---+ +--R (96\|- 1 cot(x) - 48\|- 1 )(%e ) + 14\|- 1 cot(x) - 7\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 x\|- 1 +--R cot(x)(%e ) + 10cot(x)(%e ) + 30cot(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 30cot(x)(%e ) + 9cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (- 2cot(x) - 1)(%e ) + (- 20cot(x) - 10)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 +--R (- 60cot(x) - 30)(%e ) + (- 60cot(x) - 30)(%e ) +--R + +--R 2 +--R - 18cot(x) - 9 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 x\|- 1 +--R cot(x)(%e ) + 10cot(x)(%e ) + 30cot(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 30cot(x)(%e ) + 9cot(x) +--R * +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (- 4cot(x) - 1)(%e ) + (- 40cot(x) - 10)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 +--R (- 120cot(x) - 30)(%e ) + (- 120cot(x) - 30)(%e ) +--R + +--R 2 +--R - 36cot(x) - 9 +--R / +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R cot(x) (%e ) + 7cot(x) (%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R 13cot(x) (%e ) + 7cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (2cot(x) - 1)(%e ) + (14cot(x) - 7)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (26cot(x) - 13)(%e ) + 14cot(x) - 7 +--R * +--R +--------------------------------+ +--R +-------------+ | +---+ 4 +---+ 2 +--R | 2 | x\|- 1 x\|- 1 +--R \|- tan(x) - 2 \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R - cot(x) (%e ) - 10cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 +--R - 30cot(x) (%e ) - 30cot(x) (%e ) - 9cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (- 2cot(x) + 1)(%e ) + (- 20cot(x) + 10)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 +--R (- 60cot(x) + 30)(%e ) + (- 60cot(x) + 30)(%e ) +--R + +--R 2 +--R - 18cot(x) + 9 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 528 +t0316:= (a+b*sec(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (86) \|b sec(x) + a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 528 +r0316:= a^(1/2)*atan(a^(1/2)*tan(x)/(a+b*sec(x)^2)^(1/2))+_ + b^(1/2)*atanh(cot(x)*(a+b*sec(x)^2)^(1/2)/b^(1/2)) +--R +--R +--R +-------------+ +--R | 2 +-+ +--R +-+ cot(x)\|b sec(x) + a +-+ tan(x)\|a +--R (87) \|b atanh(----------------------) + \|a atan(----------------) +--R +-+ +-------------+ +--R \|b | 2 +--R \|b sec(x) + a +--R Type: Expression(Integer) +--E 88 + +--S 89 of 528 +a0316:= integrate(t0316,x) +--R +--R +--R (88) +--R [ +--R +-+ +-+ +--R \|a \|b +--R * +--R log +--R 4 9 4 8 3 7 +--R 128a cos(x) + 128a cos(x) + 256a b cos(x) +--R + +--R 3 6 2 2 5 2 2 4 +--R 256a b cos(x) + 160a b cos(x) + 160a b cos(x) +--R + +--R 3 3 3 2 4 4 +--R 32a b cos(x) + 32a b cos(x) + b cos(x) + b +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 4 10 3 4 9 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 8 +--R (- 96a b + 224a b)cos(x) +--R + +--R 2 2 3 7 +--R (- 96a b + 224a b)cos(x) +--R + +--R 3 2 2 6 +--R (- 40a b + 232a b )cos(x) +--R + +--R 3 2 2 5 4 3 4 +--R (- 40a b + 232a b )cos(x) + (- 4b + 84a b )cos(x) +--R + +--R 4 3 3 4 2 4 +--R (- 4b + 84a b )cos(x) + 8b cos(x) + 8b cos(x) +--R * +--R +-+ +--R \|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 7 2 2 5 +--R - 256a cos(x) - 640a b cos(x) - 544a b cos(x) +--R + +--R 3 3 4 +--R - 176a b cos(x) - 16b cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 8 +--R (128a b - 128a )cos(x) + (256a b - 512a b)cos(x) +--R + +--R 2 3 3 2 6 4 2 3 4 +--R (160a b - 672a b )cos(x) + (32a b - 352a b )cos(x) +--R + +--R 5 4 2 5 +--R (b - 65a b )cos(x) - 2b +--R / +--R 3 10 3 9 2 8 2 7 +--R 64a cos(x) + 64a cos(x) + 96a b cos(x) + 96a b cos(x) +--R + +--R 2 6 2 5 3 4 3 3 +--R 40a b cos(x) + 40a b cos(x) + 4b cos(x) + 4b cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 8 2 2 6 +--R - 128a cos(x) - 256a b cos(x) - 160a b cos(x) +--R + +--R 3 4 4 2 +--R - 32a b cos(x) - b cos(x) +--R + +--R a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R sin(x) +--R - a atan(------) +--R cos(x) +--R / +--R +-+ +--R 2\|a +--R , +--R +--R a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R - +--R +---+ +-+ +--R 2\|- b \|a +--R * +--R atan +--R +---------------------+ +--R | 2 +--R +---+ | 4a cos(x) + 4b +--R (cos(x) + 1)sin(x)\|- b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +---------------------+ +--R | 2 +--R 2 +-+ | 4a cos(x) + 4b 2 +--R (cos(x) + cos(x))\|a |--------------------- - 2a cos(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - 2b +--R + +--R sin(x) +--R - a atan(------) +--R cos(x) +--R / +--R +-+ +--R 2\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 89 + +--S 90 of 528 +m0316a:= a0316.1-r0316 +--R +--R +--R (89) +--R +-+ +-+ +--R \|a \|b +--R * +--R log +--R 4 9 4 8 3 7 +--R 128a cos(x) + 128a cos(x) + 256a b cos(x) +--R + +--R 3 6 2 2 5 2 2 4 +--R 256a b cos(x) + 160a b cos(x) + 160a b cos(x) +--R + +--R 3 3 3 2 4 4 +--R 32a b cos(x) + 32a b cos(x) + b cos(x) + b +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 4 10 3 4 9 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 8 2 2 3 7 +--R (- 96a b + 224a b)cos(x) + (- 96a b + 224a b)cos(x) +--R + +--R 3 2 2 6 +--R (- 40a b + 232a b )cos(x) +--R + +--R 3 2 2 5 4 3 4 +--R (- 40a b + 232a b )cos(x) + (- 4b + 84a b )cos(x) +--R + +--R 4 3 3 4 2 4 +--R (- 4b + 84a b )cos(x) + 8b cos(x) + 8b cos(x) +--R * +--R +-+ +--R \|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 7 2 2 5 +--R - 256a cos(x) - 640a b cos(x) - 544a b cos(x) +--R + +--R 3 3 4 +--R - 176a b cos(x) - 16b cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 8 +--R (128a b - 128a )cos(x) + (256a b - 512a b)cos(x) +--R + +--R 2 3 3 2 6 4 2 3 4 +--R (160a b - 672a b )cos(x) + (32a b - 352a b )cos(x) +--R + +--R 5 4 2 5 +--R (b - 65a b )cos(x) - 2b +--R / +--R 3 10 3 9 2 8 2 7 +--R 64a cos(x) + 64a cos(x) + 96a b cos(x) + 96a b cos(x) +--R + +--R 2 6 2 5 3 4 3 3 +--R 40a b cos(x) + 40a b cos(x) + 4b cos(x) + 4b cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 8 2 2 6 +--R - 128a cos(x) - 256a b cos(x) - 160a b cos(x) +--R + +--R 3 4 4 2 +--R - 32a b cos(x) - b cos(x) +--R + +--R +-------------+ +--R | 2 +--R +-+ +-+ cot(x)\|b sec(x) + a +--R - 2\|a \|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R +-+ +--R tan(x)\|a sin(x) +--R - 2a atan(----------------) - a atan(------) +--R +-------------+ cos(x) +--R | 2 +--R \|b sec(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 90 + +--S 91 of 528 +--d0316a:= D(m0316a,x) +--E 91 + +--S 92 of 528 +m0316b:= a0316.2-r0316 +--R +--R +--R (90) +--R +-------------+ +--R | 2 +--R +-+ +-+ cot(x)\|b sec(x) + a +--R - 2\|a \|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R - +--R +---+ +-+ +--R 2\|- b \|a +--R * +--R atan +--R +---------------------+ +--R | 2 +--R +---+ | 4a cos(x) + 4b +--R (cos(x) + 1)sin(x)\|- b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +---------------------+ +--R | 2 +--R 2 +-+ | 4a cos(x) + 4b 2 +--R (cos(x) + cos(x))\|a |--------------------- - 2a cos(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - 2b +--R + +--R +-+ +--R tan(x)\|a sin(x) +--R - 2a atan(----------------) - a atan(------) +--R +-------------+ cos(x) +--R | 2 +--R \|b sec(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 92 + +--S 93 of 528 +d0316b:= D(m0316b,x) +--R +--R +--R (91) +--R 7 2 16 7 2 15 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 6 3 7 2 14 +--R (- 6144a b + 4608a b )cos(x) +--R + +--R 6 3 7 2 13 +--R (- 6144a b + 4608a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (- 6912a b + 13056a b - 3456a b )cos(x) +--R + +--R 5 4 6 3 7 2 11 +--R (- 6912a b + 13056a b - 3456a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (- 3584a b + 13536a b - 9216a b + 864a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 9 +--R (- 3584a b + 13536a b - 9216a b + 864a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 8 +--R (- 840a b + 6192a b - 8736a b + 2160a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 +--R (- 840a b + 6192a b - 8736a b + 2160a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 +--R (- 72a b + 1170a b - 3456a b + 1854a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 5 +--R (- 72a b + 1170a b - 3456a b + 1854a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (- a b + 63a b - 495a b + 617a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (- a b + 63a b - 495a b + 617a b )cos(x) +--R + +--R 2 7 3 6 2 2 7 3 6 +--R (- 12a b + 60a b )cos(x) + (- 12a b + 60a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 16 8 15 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 7 2 8 14 +--R (- 6144a b + 4608a b)cos(x) +--R + +--R 7 2 8 13 +--R (- 6144a b + 4608a b)cos(x) +--R + +--R 6 3 7 2 8 12 +--R (- 6912a b + 13056a b - 3456a b)cos(x) +--R + +--R 6 3 7 2 8 11 +--R (- 6912a b + 13056a b - 3456a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 10 +--R (- 3584a b + 13536a b - 9216a b + 864a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 3584a b + 13536a b - 9216a b + 864a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 840a b + 6192a b - 8736a b + 2160a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 7 +--R (- 840a b + 6192a b - 8736a b + 2160a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 6 +--R (- 72a b + 1170a b - 3456a b + 1854a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 5 +--R (- 72a b + 1170a b - 3456a b + 1854a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 4 +--R (- a b + 63a b - 495a b + 617a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 3 +--R (- a b + 63a b - 495a b + 617a b )cos(x) +--R + +--R 3 6 4 5 2 3 6 4 5 +--R (- 12a b + 60a b )cos(x) + (- 12a b + 60a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 16 7 2 15 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 6 3 7 2 14 6 3 7 2 13 +--R (6144a b - 4608a b )cos(x) + (6144a b - 4608a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (6912a b - 13056a b + 3456a b )cos(x) +--R + +--R 5 4 6 3 7 2 11 +--R (6912a b - 13056a b + 3456a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (3584a b - 13536a b + 9216a b - 864a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 9 +--R (3584a b - 13536a b + 9216a b - 864a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 8 +--R (840a b - 6192a b + 8736a b - 2160a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 +--R (840a b - 6192a b + 8736a b - 2160a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 +--R (72a b - 1170a b + 3456a b - 1854a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 5 +--R (72a b - 1170a b + 3456a b - 1854a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (a b - 63a b + 495a b - 617a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (a b - 63a b + 495a b - 617a b )cos(x) +--R + +--R 2 7 3 6 2 2 7 3 6 +--R (12a b - 60a b )cos(x) + (12a b - 60a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 7 2 18 7 2 17 +--R - 4096a b cos(x) - 4096a b cos(x) +--R + +--R 6 3 7 2 8 16 +--R (- 14336a b + 10752a b - 512a b)cos(x) +--R + +--R 6 3 7 2 8 15 +--R (- 14336a b + 10752a b - 512a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (- 19968a b + 34560a b - 13184a b + 640a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 13 +--R (- 19968a b + 34560a b - 13184a b + 640a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 14080a b + 42976a b - 36064a b + 8032a b +--R + +--R 8 +--R - 96a b +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 14080a b + 42976a b - 36064a b + 8032a b +--R + +--R 8 +--R - 96a b +--R * +--R 11 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 5264a b + 25968a b - 38608a b + 18896a b +--R + +--R 7 2 8 +--R - 1592a b - 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 5264a b + 25968a b - 38608a b + 18896a b +--R + +--R 7 2 8 +--R - 1592a b - 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R - 984a b + 7818a b - 19106a b + 17534a b +--R + +--R 6 3 7 2 +--R - 3710a b - 192a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R - 984a b + 7818a b - 19106a b + 17534a b +--R + +--R 6 3 7 2 +--R - 3710a b - 192a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 74a b + 1059a b - 4224a b + 7058a b - 3214a b +--R + +--R 6 3 +--R - 173a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 74a b + 1059a b - 4224a b + 7058a b - 3214a b +--R + +--R 6 3 +--R - 173a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - b + 45a b - 332a b + 1060a b - 1115a b +--R + +--R 5 4 +--R - 57a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - b + 45a b - 332a b + 1060a b - 1115a b +--R + +--R 5 4 +--R - 57a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 2 +--R (- 4a b + 28a b - 116a b - 4a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R (- 4a b + 28a b - 116a b - 4a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 18 8 17 +--R - 4096a b cos(x) - 4096a b cos(x) +--R + +--R 7 2 8 9 16 +--R (- 14336a b + 10752a b - 512a )cos(x) +--R + +--R 7 2 8 9 15 +--R (- 14336a b + 10752a b - 512a )cos(x) +--R + +--R 6 3 7 2 8 9 14 +--R (- 19968a b + 34560a b - 13184a b + 640a )cos(x) +--R + +--R 6 3 7 2 8 9 13 +--R (- 19968a b + 34560a b - 13184a b + 640a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 14080a b + 42976a b - 36064a b + 8032a b - 96a ) +--R * +--R 12 +--R cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 14080a b + 42976a b - 36064a b + 8032a b - 96a ) +--R * +--R 11 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 5264a b + 25968a b - 38608a b + 18896a b +--R + +--R 8 9 +--R - 1592a b - 72a +--R * +--R 10 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 5264a b + 25968a b - 38608a b + 18896a b +--R + +--R 8 9 +--R - 1592a b - 72a +--R * +--R 9 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 984a b + 7818a b - 19106a b + 17534a b +--R + +--R 7 2 8 +--R - 3710a b - 192a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 984a b + 7818a b - 19106a b + 17534a b +--R + +--R 7 2 8 +--R - 3710a b - 192a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 74a b + 1059a b - 4224a b + 7058a b - 3214a b +--R + +--R 7 2 +--R - 173a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 74a b + 1059a b - 4224a b + 7058a b - 3214a b +--R + +--R 7 2 +--R - 173a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - a b + 45a b - 332a b + 1060a b - 1115a b +--R + +--R 6 3 +--R - 57a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - a b + 45a b - 332a b + 1060a b - 1115a b +--R + +--R 6 3 +--R - 57a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 2 +--R (- 4a b + 28a b - 116a b - 4a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R (- 4a b + 28a b - 116a b - 4a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 18 7 2 17 +--R 4096a b cos(x) + 4096a b cos(x) +--R + +--R 6 3 7 2 8 16 +--R (14336a b - 10752a b + 512a b)cos(x) +--R + +--R 6 3 7 2 8 15 +--R (14336a b - 10752a b + 512a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (19968a b - 34560a b + 13184a b - 640a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 13 +--R (19968a b - 34560a b + 13184a b - 640a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (14080a b - 42976a b + 36064a b - 8032a b + 96a b) +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (14080a b - 42976a b + 36064a b - 8032a b + 96a b) +--R * +--R 11 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 5264a b - 25968a b + 38608a b - 18896a b + 1592a b +--R + +--R 8 +--R 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 5264a b - 25968a b + 38608a b - 18896a b + 1592a b +--R + +--R 8 +--R 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 984a b - 7818a b + 19106a b - 17534a b + 3710a b +--R + +--R 7 2 +--R 192a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 984a b - 7818a b + 19106a b - 17534a b + 3710a b +--R + +--R 7 2 +--R 192a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 74a b - 1059a b + 4224a b - 7058a b + 3214a b +--R + +--R 6 3 +--R 173a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 74a b - 1059a b + 4224a b - 7058a b + 3214a b +--R + +--R 6 3 +--R 173a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 4 +--R (b - 45a b + 332a b - 1060a b + 1115a b + 57a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 3 +--R (b - 45a b + 332a b - 1060a b + 1115a b + 57a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 2 +--R (4a b - 28a b + 116a b + 4a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R (4a b - 28a b + 116a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 20 7 2 19 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 6 3 7 2 8 18 +--R (- 8192a b + 6144a b - 512a b)cos(x) +--R + +--R 6 3 7 2 8 17 +--R (- 8192a b + 6144a b - 512a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (- 13056a b + 23552a b - 9216a b + 1152a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 15 +--R (- 13056a b + 23552a b - 9216a b + 1152a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 10496a b + 35456a b - 29536a b + 8448a b - 864a b) +--R * +--R 14 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 10496a b + 35456a b - 29536a b + 8448a b - 864a b) +--R * +--R 13 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 4424a b + 26304a b - 39824a b + 20736a b - 4248a b +--R + +--R 8 +--R 216a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 4424a b + 26304a b - 39824a b + 20736a b - 4248a b +--R + +--R 8 +--R 216a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 912a b + 9816a b - 26354a b + 23592a b - 8070a b +--R + +--R 7 2 +--R 864a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 912a b + 9816a b - 26354a b + 23592a b - 8070a b +--R + +--R 7 2 +--R 864a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 73a b + 1644a b - 8403a b + 13295a b - 7452a b +--R + +--R 6 3 +--R 1341a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 73a b + 1644a b - 8403a b + 13295a b - 7452a b +--R + +--R 6 3 +--R 1341a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R (- b + 84a b - 1066a b + 3434a b - 3393a b + 998a b ) +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R (- b + 84a b - 1066a b + 3434a b - 3393a b + 998a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (- 25a b + 291a b - 655a b + 349a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (- 25a b + 291a b - 655a b + 349a b )cos(x) +--R + +--R 2 7 3 6 2 2 7 3 6 +--R (- 28a b + 44a b )cos(x) + (- 28a b + 44a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 20 8 19 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 7 2 8 9 18 +--R (- 8192a b + 6144a b - 512a )cos(x) +--R + +--R 7 2 8 9 17 +--R (- 8192a b + 6144a b - 512a )cos(x) +--R + +--R 6 3 7 2 8 9 16 +--R (- 13056a b + 23552a b - 9216a b + 1152a )cos(x) +--R + +--R 6 3 7 2 8 9 15 +--R (- 13056a b + 23552a b - 9216a b + 1152a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 10496a b + 35456a b - 29536a b + 8448a b - 864a ) +--R * +--R 14 +--R cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 10496a b + 35456a b - 29536a b + 8448a b - 864a ) +--R * +--R 13 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 4424a b + 26304a b - 39824a b + 20736a b - 4248a b +--R + +--R 9 +--R 216a +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 4424a b + 26304a b - 39824a b + 20736a b - 4248a b +--R + +--R 9 +--R 216a +--R * +--R 11 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 912a b + 9816a b - 26354a b + 23592a b - 8070a b +--R + +--R 8 +--R 864a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 912a b + 9816a b - 26354a b + 23592a b - 8070a b +--R + +--R 8 +--R 864a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 73a b + 1644a b - 8403a b + 13295a b - 7452a b +--R + +--R 7 2 +--R 1341a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 73a b + 1644a b - 8403a b + 13295a b - 7452a b +--R + +--R 7 2 +--R 1341a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - a b + 84a b - 1066a b + 3434a b - 3393a b +--R + +--R 6 3 +--R 998a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - a b + 84a b - 1066a b + 3434a b - 3393a b +--R + +--R 6 3 +--R 998a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 4 +--R (- 25a b + 291a b - 655a b + 349a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 3 +--R (- 25a b + 291a b - 655a b + 349a b )cos(x) +--R + +--R 3 6 4 5 2 3 6 4 5 +--R (- 28a b + 44a b )cos(x) + (- 28a b + 44a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 20 7 2 19 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 6 3 7 2 8 18 +--R (8192a b - 6144a b + 512a b)cos(x) +--R + +--R 6 3 7 2 8 17 +--R (8192a b - 6144a b + 512a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (13056a b - 23552a b + 9216a b - 1152a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 15 +--R (13056a b - 23552a b + 9216a b - 1152a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 14 +--R (10496a b - 35456a b + 29536a b - 8448a b + 864a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 13 +--R (10496a b - 35456a b + 29536a b - 8448a b + 864a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 4424a b - 26304a b + 39824a b - 20736a b + 4248a b +--R + +--R 8 +--R - 216a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 4424a b - 26304a b + 39824a b - 20736a b + 4248a b +--R + +--R 8 +--R - 216a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 912a b - 9816a b + 26354a b - 23592a b + 8070a b +--R + +--R 7 2 +--R - 864a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 912a b - 9816a b + 26354a b - 23592a b + 8070a b +--R + +--R 7 2 +--R - 864a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 73a b - 1644a b + 8403a b - 13295a b + 7452a b +--R + +--R 6 3 +--R - 1341a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 73a b - 1644a b + 8403a b - 13295a b + 7452a b +--R + +--R 6 3 +--R - 1341a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 +--R (b - 84a b + 1066a b - 3434a b + 3393a b - 998a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 5 +--R (b - 84a b + 1066a b - 3434a b + 3393a b - 998a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (25a b - 291a b + 655a b - 349a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 3 +--R (25a b - 291a b + 655a b - 349a b )cos(x) +--R + +--R 2 7 3 6 2 2 7 3 6 +--R (28a b - 44a b )cos(x) + (28a b - 44a b )cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 7 2 16 6 3 7 2 14 +--R 4096a b cos(x) + (14336a b - 9216a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (19456a b - 30720a b + 6912a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (12800a b - 38976a b + 21888a b - 1728a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 8 +--R (4144a b - 23232a b + 25824a b - 5184a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 +--R (584a b - 6420a b + 13776a b - 5652a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (24a b - 672a b + 3144a b - 2656a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (- 12a b + 216a b - 476a b )cos(x) - 16a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 16 7 2 8 14 +--R 4096a b cos(x) + (14336a b - 9216a b)cos(x) +--R + +--R 6 3 7 2 8 12 +--R (19456a b - 30720a b + 6912a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 10 +--R (12800a b - 38976a b + 21888a b - 1728a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (4144a b - 23232a b + 25824a b - 5184a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 6 +--R (584a b - 6420a b + 13776a b - 5652a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 4 +--R (24a b - 672a b + 3144a b - 2656a b )cos(x) +--R + +--R 2 7 3 6 4 5 2 3 6 +--R (- 12a b + 216a b - 476a b )cos(x) - 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 16 6 3 7 2 14 +--R - 4096a b cos(x) + (- 14336a b + 9216a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (- 19456a b + 30720a b - 6912a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (- 12800a b + 38976a b - 21888a b + 1728a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 8 +--R (- 4144a b + 23232a b - 25824a b + 5184a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 +--R (- 584a b + 6420a b - 13776a b + 5652a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 4 +--R (- 24a b + 672a b - 3144a b + 2656a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (12a b - 216a b + 476a b )cos(x) + 16a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 2 18 +--R 8192a b cos(x) +--R + +--R 6 3 7 2 8 16 +--R (32768a b - 21504a b + 1024a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (53248a b - 79872a b + 26880a b - 1280a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R 45056a b - 117824a b + 85184a b - 16704a b +--R + +--R 8 +--R 192a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R 21088a b - 87616a b + 110048a b - 45664a b +--R + +--R 7 2 8 +--R 3280a b + 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R 5312a b - 34340a b + 69412a b - 52036a b +--R + +--R 6 3 7 2 +--R 8988a b + 456a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 632a b - 6704a b + 21408a b - 27880a b + 9752a b +--R + +--R 6 3 +--R 520a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 24b - 532a b + 2820a b - 6564a b + 4708a b +--R + +--R 5 4 +--R 248a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (- 8b + 104a b - 480a b + 888a b + 40a b )cos(x) +--R + +--R 2 7 +--R 32a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 18 +--R 8192a b cos(x) +--R + +--R 7 2 8 9 16 +--R (32768a b - 21504a b + 1024a )cos(x) +--R + +--R 6 3 7 2 8 9 14 +--R (53248a b - 79872a b + 26880a b - 1280a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (45056a b - 117824a b + 85184a b - 16704a b + 192a ) +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R 21088a b - 87616a b + 110048a b - 45664a b +--R + +--R 8 9 +--R 3280a b + 144a +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R 5312a b - 34340a b + 69412a b - 52036a b +--R + +--R 7 2 8 +--R 8988a b + 456a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 632a b - 6704a b + 21408a b - 27880a b + 9752a b +--R + +--R 7 2 +--R 520a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 24a b - 532a b + 2820a b - 6564a b + 4708a b +--R + +--R 6 3 +--R 248a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 2 +--R (- 8a b + 104a b - 480a b + 888a b + 40a b )cos(x) +--R + +--R 3 6 +--R 32a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 18 +--R - 8192a b cos(x) +--R + +--R 6 3 7 2 8 16 +--R (- 32768a b + 21504a b - 1024a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (- 53248a b + 79872a b - 26880a b + 1280a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 45056a b + 117824a b - 85184a b + 16704a b - 192a b) +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 21088a b + 87616a b - 110048a b + 45664a b +--R + +--R 7 2 8 +--R - 3280a b - 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 5312a b + 34340a b - 69412a b + 52036a b - 8988a b +--R + +--R 7 2 +--R - 456a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 632a b + 6704a b - 21408a b + 27880a b - 9752a b +--R + +--R 6 3 +--R - 520a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 24b + 532a b - 2820a b + 6564a b - 4708a b +--R + +--R 5 4 +--R - 248a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 2 7 +--R (8b - 104a b + 480a b - 888a b - 40a b )cos(x) - 32a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 20 6 3 7 2 8 18 +--R 4096a b cos(x) + (18432a b - 12288a b + 1024a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (33792a b - 53248a b + 18944a b - 2304a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (32256a b - 92928a b + 68160a b - 18048a b + 1728a b) +--R * +--R 14 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 16944a b - 82944a b + 106944a b - 49632a b + 9360a b +--R + +--R 8 +--R - 432a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 4728a b - 39536a b + 86260a b - 65952a b + 20172a b +--R + +--R 7 2 +--R - 1944a b +--R * +--R 10 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 608a b - 9456a b + 36204a b - 45964a b + 22020a b +--R + +--R 6 3 +--R - 3492a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 24b - 912a b + 7100a b - 16260a b + 12684a b +--R + +--R 5 4 +--R - 3148a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 16b + 452a b - 2436a b + 3564a b - 1452a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (- 76a b + 360a b - 300a b )cos(x) - 16a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 20 7 2 8 9 18 +--R 4096a b cos(x) + (18432a b - 12288a b + 1024a )cos(x) +--R + +--R 6 3 7 2 8 9 16 +--R (33792a b - 53248a b + 18944a b - 2304a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (32256a b - 92928a b + 68160a b - 18048a b + 1728a ) +--R * +--R 14 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 16944a b - 82944a b + 106944a b - 49632a b + 9360a b +--R + +--R 9 +--R - 432a +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 4728a b - 39536a b + 86260a b - 65952a b + 20172a b +--R + +--R 8 +--R - 1944a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 608a b - 9456a b + 36204a b - 45964a b + 22020a b +--R + +--R 7 2 +--R - 3492a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 24a b - 912a b + 7100a b - 16260a b + 12684a b +--R + +--R 6 3 +--R - 3148a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 4 +--R (- 16a b + 452a b - 2436a b + 3564a b - 1452a b )cos(x) +--R + +--R 2 7 3 6 4 5 2 3 6 +--R (- 76a b + 360a b - 300a b )cos(x) - 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 20 6 3 7 2 8 18 +--R - 4096a b cos(x) + (- 18432a b + 12288a b - 1024a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (- 33792a b + 53248a b - 18944a b + 2304a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 32256a b + 92928a b - 68160a b + 18048a b - 1728a b) +--R * +--R 14 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 16944a b + 82944a b - 106944a b + 49632a b - 9360a b +--R + +--R 8 +--R 432a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 4728a b + 39536a b - 86260a b + 65952a b - 20172a b +--R + +--R 7 2 +--R 1944a b +--R * +--R 10 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 608a b + 9456a b - 36204a b + 45964a b - 22020a b +--R + +--R 6 3 +--R 3492a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 24b + 912a b - 7100a b + 16260a b - 12684a b +--R + +--R 5 4 +--R 3148a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (16b - 452a b + 2436a b - 3564a b + 1452a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (76a b - 360a b + 300a b )cos(x) + 16a b +--R * +--R +-+ +--R \|a +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 6 3 16 6 3 15 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 5 4 6 3 14 5 4 6 3 13 +--R (7168a b - 4096a b )cos(x) + (7168a b - 4096a b )cos(x) +--R + +--R 4 5 5 4 6 3 12 +--R (9728a b - 13312a b + 2816a b )cos(x) +--R + +--R 4 5 5 4 6 3 11 +--R (9728a b - 13312a b + 2816a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 10 +--R (6400a b - 16384a b + 8320a b - 768a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 9 +--R (6400a b - 16384a b + 8320a b - 768a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 8 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 5 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (12b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (12b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 9 8 2 7 3 6 2 +--R (- 4b + 44a b - 60a b + 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 +--R (- 4b + 44a b - 60a b + 20a b )cos(x) +--R * +--R 2 4 +--R cot(x)sec(x) sin(x) +--R + +--R 6 3 7 2 18 6 3 7 2 17 +--R (2048a b - 2048a b )cos(x) + (2048a b - 2048a b )cos(x) +--R + +--R 5 4 6 3 7 2 16 +--R (7168a b - 15360a b + 4096a b )cos(x) +--R + +--R 5 4 6 3 7 2 15 +--R (7168a b - 15360a b + 4096a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 14 +--R (9728a b - 37376a b + 24320a b - 2816a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 13 +--R (9728a b - 37376a b + 24320a b - 2816a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a b ) +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 7 2 +--R - 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 7 2 +--R - 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 6 3 +--R - 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 6 3 +--R - 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 12b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 5 4 +--R - 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 12b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 5 4 +--R - 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 20b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (- 20b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 9 8 2 7 3 6 2 +--R (4b - 76a b + 156a b - 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 +--R (4b - 76a b + 156a b - 20a b )cos(x) +--R * +--R 2 2 +--R cot(x)sec(x) sin(x) +--R + +--R 7 2 20 7 2 19 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 6 3 7 2 18 +--R (- 9216a b + 6144a b )cos(x) +--R + +--R 6 3 7 2 17 +--R (- 9216a b + 6144a b )cos(x) +--R + +--R 5 4 6 3 7 2 16 +--R (- 16896a b + 26624a b - 6912a b )cos(x) +--R + +--R 5 4 6 3 7 2 15 +--R (- 16896a b + 26624a b - 6912a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 14 +--R (- 16128a b + 46464a b - 28800a b + 3456a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 13 +--R (- 16128a b + 46464a b - 28800a b + 3456a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a b ) +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 6 +--R (- 12b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 +--R (- 12b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 +--R (8b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 9 8 2 7 3 6 3 +--R (8b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 8 2 7 2 8 2 7 +--R (32a b - 96a b )cos(x) + (32a b - 96a b )cos(x) +--R * +--R 2 +--R cot(x)sec(x) +--R * +--R tan(x) +--R + +--R 6 3 7 2 16 +--R (- 2048a b - 2048a b )cos(x) +--R + +--R 6 3 7 2 15 +--R (- 2048a b - 2048a b )cos(x) +--R + +--R 5 4 6 3 7 2 14 +--R (- 7168a b - 3072a b + 4096a b )cos(x) +--R + +--R 5 4 6 3 7 2 13 +--R (- 7168a b - 3072a b + 4096a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 12 +--R (- 9728a b + 3584a b + 10496a b - 2816a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 11 +--R (- 9728a b + 3584a b + 10496a b - 2816a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 6400a b + 9984a b + 8064a b - 7552a b + 768a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 6400a b + 9984a b + 8064a b - 7552a b + 768a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 2072a b + 7336a b + 416a b - 7008a b + 1912a b +--R + +--R 7 2 +--R - 72a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 2072a b + 7336a b + 416a b - 7008a b + 1912a b +--R + +--R 7 2 +--R - 72a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 292a b + 2188a b - 1792a b - 2512a b + 1604a b +--R + +--R 6 3 +--R - 156a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 292a b + 2188a b - 1792a b - 2512a b + 1604a b +--R + +--R 6 3 +--R - 156a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 232a b - 584a b - 224a b + 500a b +--R + +--R 5 4 +--R - 104a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 232a b - 584a b - 224a b + 500a b +--R + +--R 5 4 +--R - 104a b +--R * +--R 3 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (4b - 40a b + 16a b + 40a b - 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R (4b - 40a b + 16a b + 40a b - 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 16 6 3 15 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 5 4 6 3 14 +--R (- 7168a b + 4096a b )cos(x) +--R + +--R 5 4 6 3 13 +--R (- 7168a b + 4096a b )cos(x) +--R + +--R 4 5 5 4 6 3 12 +--R (- 9728a b + 13312a b - 2816a b )cos(x) +--R + +--R 4 5 5 4 6 3 11 +--R (- 9728a b + 13312a b - 2816a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 10 +--R (- 6400a b + 16384a b - 8320a b + 768a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 9 +--R (- 6400a b + 16384a b - 8320a b + 768a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 8 +--R (- 2072a b + 9408a b - 8992a b + 1984a b - 72a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 +--R (- 2072a b + 9408a b - 8992a b + 1984a b - 72a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 +--R (- 292a b + 2480a b - 4272a b + 1760a b - 156a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 5 +--R (- 292a b + 2480a b - 4272a b + 1760a b - 156a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 12b + 244a b - 828a b + 604a b - 104a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (- 12b + 244a b - 828a b + 604a b - 104a b )cos(x) +--R + +--R 9 8 2 7 3 6 2 +--R (4b - 44a b + 60a b - 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 +--R (4b - 44a b + 60a b - 20a b )cos(x) +--R * +--R 2 +--R sec(x) +--R + +--R 7 2 8 16 +--R (- 2048a b - 2048a b)cos(x) +--R + +--R 7 2 8 15 +--R (- 2048a b - 2048a b)cos(x) +--R + +--R 6 3 7 2 8 14 +--R (- 7168a b - 3072a b + 4096a b)cos(x) +--R + +--R 6 3 7 2 8 13 +--R (- 7168a b - 3072a b + 4096a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 12 +--R (- 9728a b + 3584a b + 10496a b - 2816a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 11 +--R (- 9728a b + 3584a b + 10496a b - 2816a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 6400a b + 9984a b + 8064a b - 7552a b + 768a b) +--R * +--R 10 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 9 +--R (- 6400a b + 9984a b + 8064a b - 7552a b + 768a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 2072a b + 7336a b + 416a b - 7008a b + 1912a b +--R + +--R 8 +--R - 72a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 2072a b + 7336a b + 416a b - 7008a b + 1912a b +--R + +--R 8 +--R - 72a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 292a b + 2188a b - 1792a b - 2512a b + 1604a b +--R + +--R 7 2 +--R - 156a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 292a b + 2188a b - 1792a b - 2512a b + 1604a b +--R + +--R 7 2 +--R - 156a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12a b + 232a b - 584a b - 224a b + 500a b +--R + +--R 6 3 +--R - 104a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12a b + 232a b - 584a b - 224a b + 500a b +--R + +--R 6 3 +--R - 104a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 2 +--R (4a b - 40a b + 16a b + 40a b - 20a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R (4a b - 40a b + 16a b + 40a b - 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 8 18 +--R (- 2048a b + 2048a b)cos(x) +--R + +--R 6 3 8 17 +--R (- 2048a b + 2048a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (- 7168a b + 8192a b + 11264a b - 4096a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 15 +--R (- 7168a b + 8192a b + 11264a b - 4096a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 9728a b + 27648a b + 13056a b - 21504a b +--R + +--R 8 +--R 2816a b +--R * +--R 14 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 +--R - 9728a b + 27648a b + 13056a b - 21504a b +--R + +--R 8 +--R 2816a b +--R * +--R 13 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 6400a b + 35712a b - 9472a b - 36992a b +--R + +--R 7 2 8 +--R 13824a b - 768a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 6400a b + 35712a b - 9472a b - 36992a b +--R + +--R 7 2 8 +--R 13824a b - 768a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R - 2072a b + 21888a b - 27656a b - 23936a b +--R + +--R 6 3 7 2 8 +--R 24280a b - 3328a b + 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 +--R - 2072a b + 21888a b - 27656a b - 23936a b +--R + +--R 6 3 7 2 8 +--R 24280a b - 3328a b + 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 292a b + 6352a b - 19020a b - 1096a b +--R + +--R 5 4 6 3 7 2 +--R 18988a b - 5352a b + 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 +--R - 292a b + 6352a b - 19020a b - 1096a b +--R + +--R 5 4 6 3 7 2 +--R 18988a b - 5352a b + 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 740a b - 5116a b + 4544a b + 6212a b +--R + +--R 5 4 6 3 +--R - 3940a b + 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 740a b - 5116a b + 4544a b + 6212a b +--R + +--R 5 4 6 3 +--R - 3940a b + 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 20b - 444a b + 1360a b + 416a b - 1284a b +--R + +--R 5 4 +--R 124a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 20b - 444a b + 1360a b + 416a b - 1284a b +--R + +--R 5 4 +--R 124a b +--R * +--R 3 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (- 4b + 72a b - 80a b - 136a b + 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R (- 4b + 72a b - 80a b - 136a b + 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 7 2 18 +--R (- 2048a b + 2048a b )cos(x) +--R + +--R 6 3 7 2 17 +--R (- 2048a b + 2048a b )cos(x) +--R + +--R 5 4 6 3 7 2 16 +--R (- 7168a b + 15360a b - 4096a b )cos(x) +--R + +--R 5 4 6 3 7 2 15 +--R (- 7168a b + 15360a b - 4096a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 14 +--R (- 9728a b + 37376a b - 24320a b + 2816a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 13 +--R (- 9728a b + 37376a b - 24320a b + 2816a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 6400a b + 42112a b - 51584a b + 14592a b - 768a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 6400a b + 42112a b - 51584a b + 14592a b - 768a b ) +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 2072a b + 23960a b - 51616a b + 27680a b - 3400a b +--R + +--R 7 2 +--R 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 2072a b + 23960a b - 51616a b + 27680a b - 3400a b +--R + +--R 7 2 +--R 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 292a b + 6644a b - 25664a b + 24568a b - 5580a b +--R + +--R 6 3 +--R 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 292a b + 6644a b - 25664a b + 24568a b - 5580a b +--R + +--R 6 3 +--R 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 752a b - 5868a b + 10412a b - 4200a b +--R + +--R 5 4 +--R 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R - 12b + 752a b - 5868a b + 10412a b - 4200a b +--R + +--R 5 4 +--R 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (20b - 464a b + 1824a b - 1408a b + 124a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (20b - 464a b + 1824a b - 1408a b + 124a b )cos(x) +--R + +--R 9 8 2 7 3 6 2 +--R (- 4b + 76a b - 156a b + 20a b )cos(x) +--R + +--R 9 8 2 7 3 6 +--R (- 4b + 76a b - 156a b + 20a b )cos(x) +--R * +--R 2 +--R sec(x) +--R + +--R 7 2 9 18 7 2 9 17 +--R (- 2048a b + 2048a )cos(x) + (- 2048a b + 2048a )cos(x) +--R + +--R 6 3 7 2 8 9 16 +--R (- 7168a b + 8192a b + 11264a b - 4096a )cos(x) +--R + +--R 6 3 7 2 8 9 15 +--R (- 7168a b + 8192a b + 11264a b - 4096a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 9728a b + 27648a b + 13056a b - 21504a b + 2816a ) +--R * +--R 14 +--R cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 9728a b + 27648a b + 13056a b - 21504a b + 2816a ) +--R * +--R 13 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 6400a b + 35712a b - 9472a b - 36992a b + 13824a b +--R + +--R 9 +--R - 768a +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 6400a b + 35712a b - 9472a b - 36992a b + 13824a b +--R + +--R 9 +--R - 768a +--R * +--R 11 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 2072a b + 21888a b - 27656a b - 23936a b +--R + +--R 7 2 8 9 +--R 24280a b - 3328a b + 72a +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 +--R - 2072a b + 21888a b - 27656a b - 23936a b +--R + +--R 7 2 8 9 +--R 24280a b - 3328a b + 72a +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 292a b + 6352a b - 19020a b - 1096a b + 18988a b +--R + +--R 7 2 8 +--R - 5352a b + 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 292a b + 6352a b - 19020a b - 1096a b + 18988a b +--R + +--R 7 2 8 +--R - 5352a b + 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12a b + 740a b - 5116a b + 4544a b + 6212a b +--R + +--R 6 3 7 2 +--R - 3940a b + 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12a b + 740a b - 5116a b + 4544a b + 6212a b +--R + +--R 6 3 7 2 +--R - 3940a b + 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 20a b - 444a b + 1360a b + 416a b - 1284a b +--R + +--R 6 3 +--R 124a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 20a b - 444a b + 1360a b + 416a b - 1284a b +--R + +--R 6 3 +--R 124a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 2 +--R (- 4a b + 72a b - 80a b - 136a b + 20a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R (- 4a b + 72a b - 80a b - 136a b + 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 8 20 7 2 8 19 +--R (2048a b + 2048a b)cos(x) + (2048a b + 2048a b)cos(x) +--R + +--R 6 3 7 2 8 18 +--R (9216a b + 3072a b - 6144a b)cos(x) +--R + +--R 6 3 7 2 8 17 +--R (9216a b + 3072a b - 6144a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 16 +--R (16896a b - 9728a b - 19712a b + 6912a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 15 +--R (16896a b - 9728a b - 19712a b + 6912a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (16128a b - 30336a b - 17664a b + 25344a b - 3456a b) +--R * +--R 14 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (16128a b - 30336a b - 17664a b + 25344a b - 3456a b) +--R * +--R 13 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 8472a b - 33000a b + 6240a b + 33888a b - 13176a b +--R + +--R 8 +--R 648a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 8472a b - 33000a b + 6240a b + 33888a b - 13176a b +--R + +--R 8 +--R 648a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 2364a b - 17404a b + 19832a b + 17928a b - 19188a b +--R + +--R 7 2 +--R 2484a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 2364a b - 17404a b + 19832a b + 17928a b - 19188a b +--R + +--R 7 2 +--R 2484a b +--R * +--R 9 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 304a b - 4424a b + 12192a b + 304a b - 12944a b +--R + +--R 6 3 +--R 3672a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 304a b - 4424a b + 12192a b + 304a b - 12944a b +--R + +--R 6 3 +--R 3672a b +--R * +--R 7 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 12b - 444a b + 2904a b - 2904a b - 3684a b +--R + +--R 5 4 +--R 2580a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 +--R 12b - 444a b + 2904a b - 2904a b - 3684a b +--R + +--R 5 4 +--R 2580a b +--R * +--R 5 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 8b + 208a b - 768a b - 144a b + 840a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (- 8b + 208a b - 768a b - 144a b + 840a b )cos(x) +--R + +--R 8 2 7 3 6 2 +--R (- 32a b + 64a b + 96a b )cos(x) +--R + +--R 8 2 7 3 6 +--R (- 32a b + 64a b + 96a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 20 7 2 19 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 6 3 7 2 18 6 3 7 2 17 +--R (9216a b - 6144a b )cos(x) + (9216a b - 6144a b )cos(x) +--R + +--R 5 4 6 3 7 2 16 +--R (16896a b - 26624a b + 6912a b )cos(x) +--R + +--R 5 4 6 3 7 2 15 +--R (16896a b - 26624a b + 6912a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 14 +--R (16128a b - 46464a b + 28800a b - 3456a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 13 +--R (16128a b - 46464a b + 28800a b - 3456a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 12 +--R (8472a b - 41472a b + 47712a b - 13824a b + 648a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 11 +--R (8472a b - 41472a b + 47712a b - 13824a b + 648a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 10 +--R (2364a b - 19768a b + 39600a b - 21672a b + 2484a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 9 +--R (2364a b - 19768a b + 39600a b - 21672a b + 2484a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 8 +--R (304a b - 4728a b + 16920a b - 16616a b + 3672a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 7 +--R (304a b - 4728a b + 16920a b - 16616a b + 3672a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 6 +--R (12b - 456a b + 3360a b - 6264a b + 2580a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 +--R (12b - 456a b + 3360a b - 6264a b + 2580a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 +--R (- 8b + 216a b - 984a b + 840a b )cos(x) +--R + +--R 9 8 2 7 3 6 3 +--R (- 8b + 216a b - 984a b + 840a b )cos(x) +--R + +--R 8 2 7 2 8 2 7 +--R (- 32a b + 96a b )cos(x) + (- 32a b + 96a b )cos(x) +--R * +--R 2 +--R sec(x) +--R + +--R 8 9 20 8 9 19 +--R (2048a b + 2048a )cos(x) + (2048a b + 2048a )cos(x) +--R + +--R 7 2 8 9 18 +--R (9216a b + 3072a b - 6144a )cos(x) +--R + +--R 7 2 8 9 17 +--R (9216a b + 3072a b - 6144a )cos(x) +--R + +--R 6 3 7 2 8 9 16 +--R (16896a b - 9728a b - 19712a b + 6912a )cos(x) +--R + +--R 6 3 7 2 8 9 15 +--R (16896a b - 9728a b - 19712a b + 6912a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 14 +--R (16128a b - 30336a b - 17664a b + 25344a b - 3456a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 13 +--R (16128a b - 30336a b - 17664a b + 25344a b - 3456a )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 8472a b - 33000a b + 6240a b + 33888a b - 13176a b +--R + +--R 9 +--R 648a +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R 8472a b - 33000a b + 6240a b + 33888a b - 13176a b +--R + +--R 9 +--R 648a +--R * +--R 11 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 2364a b - 17404a b + 19832a b + 17928a b - 19188a b +--R + +--R 8 +--R 2484a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 2364a b - 17404a b + 19832a b + 17928a b - 19188a b +--R + +--R 8 +--R 2484a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 304a b - 4424a b + 12192a b + 304a b - 12944a b +--R + +--R 7 2 +--R 3672a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 304a b - 4424a b + 12192a b + 304a b - 12944a b +--R + +--R 7 2 +--R 3672a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R (12a b - 444a b + 2904a b - 2904a b - 3684a b + 2580a b ) +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R (12a b - 444a b + 2904a b - 2904a b - 3684a b + 2580a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 4 +--R (- 8a b + 208a b - 768a b - 144a b + 840a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 3 +--R (- 8a b + 208a b - 768a b - 144a b + 840a b )cos(x) +--R + +--R 2 7 3 6 4 5 2 +--R (- 32a b + 64a b + 96a b )cos(x) +--R + +--R 2 7 3 6 4 5 +--R (- 32a b + 64a b + 96a b )cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 7 3 16 6 4 7 3 14 +--R - 4096a b cos(x) + (- 16384a b + 8192a b )cos(x) +--R + +--R 5 5 6 4 7 3 12 +--R (- 26112a b + 30720a b - 5632a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 10 +--R (- 20992a b + 45056a b - 19456a b + 1536a b )cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 +--R (- 8848a b + 32384a b - 25600a b + 4736a b - 144a b )cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 6 +--R (- 1824a b + 11616a b - 15808a b + 5312a b - 384a b )cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 4 +--R (- 146a b + 1848a b - 4500a b + 2568a b - 346a b )cos(x) +--R + +--R 10 9 2 8 3 7 4 6 2 9 +--R (- 2b + 88a b - 476a b + 472a b - 114a b )cos(x) - 8a b +--R + +--R 2 8 3 7 +--R 16a b - 8a b +--R * +--R 2 4 +--R cot(x)sec(x) sin(x) +--R + +--R 7 3 8 2 18 +--R (- 4096a b + 4096a b )cos(x) +--R + +--R 6 4 7 3 8 2 16 +--R (- 16384a b + 32768a b - 8192a b )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 14 +--R (- 26112a b + 89600a b - 52736a b + 5632a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (- 20992a b + 118016a b - 126464a b + 32000a b - 1536a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 8848a b + 82448a b - 149248a b + 69248a b - 7568a b +--R + +--R 8 2 +--R 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 1824a b + 30304a b - 92768a b + 73520a b - 14368a b +--R + +--R 7 3 +--R 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 146a b + 5258a b - 29268a b + 40076a b - 13226a b +--R + +--R 6 4 +--R 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R (- 2b + 316a b - 3964a b + 10392a b - 5986a b + 460a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 2 9 +--R (2b - 136a b + 964a b - 1144a b + 122a b )cos(x) + 8a b +--R + +--R 2 8 3 7 +--R - 48a b + 8a b +--R * +--R 2 2 +--R cot(x)sec(x) sin(x) +--R + +--R 8 2 20 7 3 8 2 18 +--R 4096a b cos(x) + (20480a b - 12288a b )cos(x) +--R + +--R 6 4 7 3 8 2 16 +--R (42496a b - 59392a b + 13824a b )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 14 +--R (47104a b - 118016a b + 64512a b - 6912a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (29840a b - 123520a b + 122496a b - 31104a b + 1296a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R (10672a b - 72240a b + 120576a b - 56304a b + 5616a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 8 +--R (1970a b - 22920a b + 64572a b - 51880a b + 9666a b )cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 +--R (148a b - 3456a b + 17832a b - 25184a b + 8292a b )cos(x) +--R + +--R 10 9 2 8 3 7 4 6 4 +--R (2b - 168a b + 2076a b - 5896a b + 3602a b )cos(x) +--R + +--R 9 2 8 3 7 2 2 8 +--R (48a b - 480a b + 688a b )cos(x) + 32a b +--R * +--R 2 +--R cot(x)sec(x) +--R * +--R tan(x) +--R + +--R 7 3 8 2 16 +--R (4096a b + 4096a b )cos(x) +--R + +--R 6 4 7 3 8 2 14 +--R (16384a b + 8192a b - 8192a b )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 12 +--R (26112a b - 4608a b - 25088a b + 5632a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (20992a b - 24064a b - 25600a b + 17920a b - 1536a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 8848a b - 23536a b - 6784a b + 20864a b - 4592a b +--R + +--R 8 2 +--R 144a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 1824a b - 9792a b + 4192a b + 10496a b - 4928a b +--R + +--R 7 3 +--R 384a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 146a b - 1702a b + 2652a b + 1932a b - 2222a b +--R + +--R 6 4 +--R 346a b +--R * +--R 4 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 2 +--R (2b - 86a b + 388a b + 4a b - 358a b + 114a b )cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R 8a b - 8a b - 8a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 16 6 4 7 3 14 +--R 4096a b cos(x) + (16384a b - 8192a b )cos(x) +--R + +--R 5 5 6 4 7 3 12 +--R (26112a b - 30720a b + 5632a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 10 +--R (20992a b - 45056a b + 19456a b - 1536a b )cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 +--R (8848a b - 32384a b + 25600a b - 4736a b + 144a b )cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 6 +--R (1824a b - 11616a b + 15808a b - 5312a b + 384a b )cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 4 +--R (146a b - 1848a b + 4500a b - 2568a b + 346a b )cos(x) +--R + +--R 10 9 2 8 3 7 4 6 2 9 +--R (2b - 88a b + 476a b - 472a b + 114a b )cos(x) + 8a b +--R + +--R 2 8 3 7 +--R - 16a b + 8a b +--R * +--R 2 +--R sec(x) +--R + +--R 8 2 9 16 +--R (4096a b + 4096a b)cos(x) +--R + +--R 7 3 8 2 9 14 +--R (16384a b + 8192a b - 8192a b)cos(x) +--R + +--R 6 4 7 3 8 2 9 12 +--R (26112a b - 4608a b - 25088a b + 5632a b)cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 10 +--R (20992a b - 24064a b - 25600a b + 17920a b - 1536a b)cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 8848a b - 23536a b - 6784a b + 20864a b - 4592a b +--R + +--R 9 +--R 144a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 1824a b - 9792a b + 4192a b + 10496a b - 4928a b +--R + +--R 8 2 +--R 384a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R (146a b - 1702a b + 2652a b + 1932a b - 2222a b + 346a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 2 +--R (2a b - 86a b + 388a b + 4a b - 358a b + 114a b )cos(x) +--R + +--R 2 8 3 7 4 6 5 5 +--R 8a b - 8a b - 8a b + 8a b +--R * +--R 2 +--R cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 9 18 +--R (4096a b - 4096a b)cos(x) +--R + +--R 6 4 7 3 8 2 9 16 +--R (16384a b - 16384a b - 24576a b + 8192a b)cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 +--R (26112a b - 63488a b - 36864a b + 47104a b - 5632a b) +--R * +--R 14 +--R cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 20992a b - 97024a b + 8448a b + 94464a b - 30464a b +--R + +--R 9 +--R 1536a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 8848a b - 73600a b + 66800a b + 80000a b - 61680a b +--R + +--R 8 2 9 +--R 7424a b - 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 1824a b - 28480a b + 62464a b + 19248a b - 59152a b +--R + +--R 7 3 8 2 +--R 13840a b - 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 146a b - 5112a b + 24010a b - 10808a b - 26850a b +--R + +--R 6 4 7 3 +--R 12496a b - 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 +--R 2b - 314a b + 3648a b - 6428a b - 4406a b +--R + +--R 5 5 6 4 +--R 5526a b - 460a b +--R * +--R 4 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R (- 2b + 134a b - 828a b + 180a b + 1022a b - 122a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 +--R - 8a b + 40a b + 40a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 8 2 18 +--R (4096a b - 4096a b )cos(x) +--R + +--R 6 4 7 3 8 2 16 +--R (16384a b - 32768a b + 8192a b )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 14 +--R (26112a b - 89600a b + 52736a b - 5632a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (20992a b - 118016a b + 126464a b - 32000a b + 1536a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 8848a b - 82448a b + 149248a b - 69248a b + 7568a b +--R + +--R 8 2 +--R - 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 1824a b - 30304a b + 92768a b - 73520a b + 14368a b +--R + +--R 7 3 +--R - 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R 146a b - 5258a b + 29268a b - 40076a b + 13226a b +--R + +--R 6 4 +--R - 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R (2b - 316a b + 3964a b - 10392a b + 5986a b - 460a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 2 9 +--R (- 2b + 136a b - 964a b + 1144a b - 122a b )cos(x) - 8a b +--R + +--R 2 8 3 7 +--R 48a b - 8a b +--R * +--R 2 +--R sec(x) +--R + +--R 8 2 10 18 +--R (4096a b - 4096a )cos(x) +--R + +--R 7 3 8 2 9 10 16 +--R (16384a b - 16384a b - 24576a b + 8192a )cos(x) +--R + +--R 6 4 7 3 8 2 9 10 14 +--R (26112a b - 63488a b - 36864a b + 47104a b - 5632a )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 +--R 20992a b - 97024a b + 8448a b + 94464a b - 30464a b +--R + +--R 10 +--R 1536a +--R * +--R 12 +--R cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R 8848a b - 73600a b + 66800a b + 80000a b - 61680a b +--R + +--R 9 10 +--R 7424a b - 144a +--R * +--R 10 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 1824a b - 28480a b + 62464a b + 19248a b - 59152a b +--R + +--R 8 2 9 +--R 13840a b - 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 146a b - 5112a b + 24010a b - 10808a b - 26850a b +--R + +--R 7 3 8 2 +--R 12496a b - 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 2a b - 314a b + 3648a b - 6428a b - 4406a b + 5526a b +--R + +--R 7 3 +--R - 460a b +--R * +--R 4 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R (- 2a b + 134a b - 828a b + 180a b + 1022a b - 122a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 +--R - 8a b + 40a b + 40a b - 8a b +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 9 20 +--R (- 4096a b - 4096a b)cos(x) +--R + +--R 7 3 8 2 9 18 +--R (- 20480a b - 8192a b + 12288a b)cos(x) +--R + +--R 6 4 7 3 8 2 9 16 +--R (- 42496a b + 16896a b + 45568a b - 13824a b)cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 +--R (- 47104a b + 70912a b + 53504a b - 57600a b + 6912a b) +--R * +--R 14 +--R cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 29840a b + 93680a b + 1024a b - 91392a b + 29808a b +--R + +--R 9 +--R - 1296a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 10672a b + 61568a b - 48336a b - 64272a b + 50688a b +--R + +--R 8 2 +--R - 5616a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 1970a b + 20950a b - 41652a b - 12692a b + 42214a b +--R + +--R 7 3 +--R - 9666a b +--R * +--R 8 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 148a b + 3308a b - 14376a b + 7352a b + 16892a b +--R + +--R 6 4 +--R - 8292a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R (- 2b + 166a b - 1908a b + 3820a b + 2294a b - 3602a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 2 2 8 3 7 +--R (- 48a b + 432a b - 208a b - 688a b )cos(x) - 32a b - 32a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 2 20 7 3 8 2 18 +--R - 4096a b cos(x) + (- 20480a b + 12288a b )cos(x) +--R + +--R 6 4 7 3 8 2 16 +--R (- 42496a b + 59392a b - 13824a b )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 14 +--R (- 47104a b + 118016a b - 64512a b + 6912a b )cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (- 29840a b + 123520a b - 122496a b + 31104a b - 1296a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 10 +--R (- 10672a b + 72240a b - 120576a b + 56304a b - 5616a b )cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 8 +--R (- 1970a b + 22920a b - 64572a b + 51880a b - 9666a b )cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 +--R (- 148a b + 3456a b - 17832a b + 25184a b - 8292a b )cos(x) +--R + +--R 10 9 2 8 3 7 4 6 4 +--R (- 2b + 168a b - 2076a b + 5896a b - 3602a b )cos(x) +--R + +--R 9 2 8 3 7 2 2 8 +--R (- 48a b + 480a b - 688a b )cos(x) - 32a b +--R * +--R 2 +--R sec(x) +--R + +--R 9 10 20 +--R (- 4096a b - 4096a )cos(x) +--R + +--R 8 2 9 10 18 +--R (- 20480a b - 8192a b + 12288a )cos(x) +--R + +--R 7 3 8 2 9 10 16 +--R (- 42496a b + 16896a b + 45568a b - 13824a )cos(x) +--R + +--R 6 4 7 3 8 2 9 10 14 +--R (- 47104a b + 70912a b + 53504a b - 57600a b + 6912a )cos(x) +--R + +--R 5 5 6 4 7 3 8 2 9 +--R - 29840a b + 93680a b + 1024a b - 91392a b + 29808a b +--R + +--R 10 +--R - 1296a +--R * +--R 12 +--R cos(x) +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R - 10672a b + 61568a b - 48336a b - 64272a b + 50688a b +--R + +--R 9 +--R - 5616a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 1970a b + 20950a b - 41652a b - 12692a b + 42214a b +--R + +--R 8 2 +--R - 9666a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 148a b + 3308a b - 14376a b + 7352a b + 16892a b +--R + +--R 7 3 +--R - 8292a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R (- 2a b + 166a b - 1908a b + 3820a b + 2294a b - 3602a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 2 8 3 7 4 6 5 5 2 3 7 4 6 +--R (- 48a b + 432a b - 208a b - 688a b )cos(x) - 32a b - 32a b +--R * +--R 2 +--R cot(x) +--R / +--R 6 2 16 6 2 15 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 5 3 6 2 14 +--R (7168a b - 4096a b )cos(x) +--R + +--R 5 3 6 2 13 +--R (7168a b - 4096a b )cos(x) +--R + +--R 4 4 5 3 6 2 12 +--R (9728a b - 13312a b + 2816a b )cos(x) +--R + +--R 4 4 5 3 6 2 11 +--R (9728a b - 13312a b + 2816a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 10 +--R (6400a b - 16384a b + 8320a b - 768a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 9 +--R (6400a b - 16384a b + 8320a b - 768a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 8 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 5 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 4 +--R (12b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (12b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 8 7 2 6 3 5 2 +--R (- 4b + 44a b - 60a b + 20a b )cos(x) +--R + +--R 8 7 2 6 3 5 +--R (- 4b + 44a b - 60a b + 20a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 7 16 7 15 +--R 2048a b cos(x) + 2048a b cos(x) +--R + +--R 6 2 7 14 6 2 7 13 +--R (7168a b - 4096a b)cos(x) + (7168a b - 4096a b)cos(x) +--R + +--R 5 3 6 2 7 12 +--R (9728a b - 13312a b + 2816a b)cos(x) +--R + +--R 5 3 6 2 7 11 +--R (9728a b - 13312a b + 2816a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 10 +--R (6400a b - 16384a b + 8320a b - 768a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 9 +--R (6400a b - 16384a b + 8320a b - 768a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 7 +--R (2072a b - 9408a b + 8992a b - 1984a b + 72a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 6 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 5 +--R (292a b - 2480a b + 4272a b - 1760a b + 156a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 4 +--R (12a b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 3 +--R (12a b - 244a b + 828a b - 604a b + 104a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 2 +--R (- 4a b + 44a b - 60a b + 20a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R (- 4a b + 44a b - 60a b + 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 16 6 2 15 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 5 3 6 2 14 +--R (- 7168a b + 4096a b )cos(x) +--R + +--R 5 3 6 2 13 +--R (- 7168a b + 4096a b )cos(x) +--R + +--R 4 4 5 3 6 2 12 +--R (- 9728a b + 13312a b - 2816a b )cos(x) +--R + +--R 4 4 5 3 6 2 11 +--R (- 9728a b + 13312a b - 2816a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 10 +--R (- 6400a b + 16384a b - 8320a b + 768a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 9 +--R (- 6400a b + 16384a b - 8320a b + 768a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 8 +--R (- 2072a b + 9408a b - 8992a b + 1984a b - 72a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (- 2072a b + 9408a b - 8992a b + 1984a b - 72a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 +--R (- 292a b + 2480a b - 4272a b + 1760a b - 156a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 5 +--R (- 292a b + 2480a b - 4272a b + 1760a b - 156a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 4 +--R (- 12b + 244a b - 828a b + 604a b - 104a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (- 12b + 244a b - 828a b + 604a b - 104a b )cos(x) +--R + +--R 8 7 2 6 3 5 2 +--R (4b - 44a b + 60a b - 20a b )cos(x) +--R + +--R 8 7 2 6 3 5 +--R (4b - 44a b + 60a b - 20a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 2 7 18 6 2 7 17 +--R (2048a b - 2048a b)cos(x) + (2048a b - 2048a b)cos(x) +--R + +--R 5 3 6 2 7 16 +--R (7168a b - 15360a b + 4096a b)cos(x) +--R + +--R 5 3 6 2 7 15 +--R (7168a b - 15360a b + 4096a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (9728a b - 37376a b + 24320a b - 2816a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 13 +--R (9728a b - 37376a b + 24320a b - 2816a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a b) +--R * +--R 12 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a b) +--R * +--R 11 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 7 +--R - 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 7 +--R - 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 6 2 +--R - 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 6 2 +--R - 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 12b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 5 3 +--R - 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 12b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 5 3 +--R - 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 4 +--R (- 20b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (- 20b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 8 7 2 6 3 5 2 +--R (4b - 76a b + 156a b - 20a b )cos(x) +--R + +--R 8 7 2 6 3 5 +--R (4b - 76a b + 156a b - 20a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 7 8 18 7 8 17 +--R (2048a b - 2048a )cos(x) + (2048a b - 2048a )cos(x) +--R + +--R 6 2 7 8 16 +--R (7168a b - 15360a b + 4096a )cos(x) +--R + +--R 6 2 7 8 15 +--R (7168a b - 15360a b + 4096a )cos(x) +--R + +--R 5 3 6 2 7 8 14 +--R (9728a b - 37376a b + 24320a b - 2816a )cos(x) +--R + +--R 5 3 6 2 7 8 13 +--R (9728a b - 37376a b + 24320a b - 2816a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a ) +--R * +--R 12 +--R cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (6400a b - 42112a b + 51584a b - 14592a b + 768a ) +--R * +--R 11 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 8 +--R - 72a +--R * +--R 10 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 2072a b - 23960a b + 51616a b - 27680a b + 3400a b +--R + +--R 8 +--R - 72a +--R * +--R 9 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 7 +--R - 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 292a b - 6644a b + 25664a b - 24568a b + 5580a b +--R + +--R 7 +--R - 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 12a b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 6 2 +--R - 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 12a b - 752a b + 5868a b - 10412a b + 4200a b +--R + +--R 6 2 +--R - 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 4 +--R (- 20a b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 3 +--R (- 20a b + 464a b - 1824a b + 1408a b - 124a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 2 +--R (4a b - 76a b + 156a b - 20a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R (4a b - 76a b + 156a b - 20a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 7 18 6 2 7 17 +--R (- 2048a b + 2048a b)cos(x) + (- 2048a b + 2048a b)cos(x) +--R + +--R 5 3 6 2 7 16 +--R (- 7168a b + 15360a b - 4096a b)cos(x) +--R + +--R 5 3 6 2 7 15 +--R (- 7168a b + 15360a b - 4096a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (- 9728a b + 37376a b - 24320a b + 2816a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 13 +--R (- 9728a b + 37376a b - 24320a b + 2816a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 6400a b + 42112a b - 51584a b + 14592a b - 768a b) +--R * +--R 12 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 6400a b + 42112a b - 51584a b + 14592a b - 768a b) +--R * +--R 11 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2072a b + 23960a b - 51616a b + 27680a b - 3400a b +--R + +--R 7 +--R 72a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2072a b + 23960a b - 51616a b + 27680a b - 3400a b +--R + +--R 7 +--R 72a b +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 292a b + 6644a b - 25664a b + 24568a b - 5580a b +--R + +--R 6 2 +--R 228a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 292a b + 6644a b - 25664a b + 24568a b - 5580a b +--R + +--R 6 2 +--R 228a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 12b + 752a b - 5868a b + 10412a b - 4200a b +--R + +--R 5 3 +--R 260a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 12b + 752a b - 5868a b + 10412a b - 4200a b +--R + +--R 5 3 +--R 260a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 4 +--R (20b - 464a b + 1824a b - 1408a b + 124a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (20b - 464a b + 1824a b - 1408a b + 124a b )cos(x) +--R + +--R 8 7 2 6 3 5 2 +--R (- 4b + 76a b - 156a b + 20a b )cos(x) +--R + +--R 8 7 2 6 3 5 +--R (- 4b + 76a b - 156a b + 20a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 20 7 19 +--R - 2048a b cos(x) - 2048a b cos(x) +--R + +--R 6 2 7 18 6 2 7 17 +--R (- 9216a b + 6144a b)cos(x) + (- 9216a b + 6144a b)cos(x) +--R + +--R 5 3 6 2 7 16 +--R (- 16896a b + 26624a b - 6912a b)cos(x) +--R + +--R 5 3 6 2 7 15 +--R (- 16896a b + 26624a b - 6912a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (- 16128a b + 46464a b - 28800a b + 3456a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 13 +--R (- 16128a b + 46464a b - 28800a b + 3456a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a b) +--R * +--R 12 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a b) +--R * +--R 11 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 6 +--R (- 12b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 +--R (- 12b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 +--R (8b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 8 7 2 6 3 5 3 +--R (8b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 7 2 6 2 7 2 6 +--R (32a b - 96a b )cos(x) + (32a b - 96a b )cos(x) +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 20 8 19 +--R - 2048a cos(x) - 2048a cos(x) +--R + +--R 7 8 18 7 8 17 +--R (- 9216a b + 6144a )cos(x) + (- 9216a b + 6144a )cos(x) +--R + +--R 6 2 7 8 16 +--R (- 16896a b + 26624a b - 6912a )cos(x) +--R + +--R 6 2 7 8 15 +--R (- 16896a b + 26624a b - 6912a )cos(x) +--R + +--R 5 3 6 2 7 8 14 +--R (- 16128a b + 46464a b - 28800a b + 3456a )cos(x) +--R + +--R 5 3 6 2 7 8 13 +--R (- 16128a b + 46464a b - 28800a b + 3456a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 11 +--R (- 8472a b + 41472a b - 47712a b + 13824a b - 648a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b) +--R * +--R 10 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 2364a b + 19768a b - 39600a b + 21672a b - 2484a b) +--R * +--R 9 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 304a b + 4728a b - 16920a b + 16616a b - 3672a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 +--R (- 12a b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 5 +--R (- 12a b + 456a b - 3360a b + 6264a b - 2580a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 4 +--R (8a b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 3 +--R (8a b - 216a b + 984a b - 840a b )cos(x) +--R + +--R 2 6 3 5 2 2 6 3 5 +--R (32a b - 96a b )cos(x) + (32a b - 96a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 20 7 19 6 2 7 18 +--R 2048a b cos(x) + 2048a b cos(x) + (9216a b - 6144a b)cos(x) +--R + +--R 6 2 7 17 +--R (9216a b - 6144a b)cos(x) +--R + +--R 5 3 6 2 7 16 +--R (16896a b - 26624a b + 6912a b)cos(x) +--R + +--R 5 3 6 2 7 15 +--R (16896a b - 26624a b + 6912a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (16128a b - 46464a b + 28800a b - 3456a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 13 +--R (16128a b - 46464a b + 28800a b - 3456a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 12 +--R (8472a b - 41472a b + 47712a b - 13824a b + 648a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 11 +--R (8472a b - 41472a b + 47712a b - 13824a b + 648a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 10 +--R (2364a b - 19768a b + 39600a b - 21672a b + 2484a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 9 +--R (2364a b - 19768a b + 39600a b - 21672a b + 2484a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 8 +--R (304a b - 4728a b + 16920a b - 16616a b + 3672a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 7 +--R (304a b - 4728a b + 16920a b - 16616a b + 3672a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 6 +--R (12b - 456a b + 3360a b - 6264a b + 2580a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 +--R (12b - 456a b + 3360a b - 6264a b + 2580a b )cos(x) +--R + +--R 8 7 2 6 3 5 4 +--R (- 8b + 216a b - 984a b + 840a b )cos(x) +--R + +--R 8 7 2 6 3 5 3 +--R (- 8b + 216a b - 984a b + 840a b )cos(x) +--R + +--R 7 2 6 2 7 2 6 +--R (- 32a b + 96a b )cos(x) + (- 32a b + 96a b )cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 7 2 16 6 3 7 2 14 +--R - 4096a b cos(x) + (- 16384a b + 8192a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (- 26112a b + 30720a b - 5632a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (- 20992a b + 45056a b - 19456a b + 1536a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 8848a b + 32384a b - 25600a b + 4736a b - 144a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R (- 1824a b + 11616a b - 15808a b + 5312a b - 384a b ) +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 4 +--R (- 146a b + 1848a b - 4500a b + 2568a b - 346a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 8 +--R (- 2b + 88a b - 476a b + 472a b - 114a b )cos(x) - 8a b +--R + +--R 2 7 3 6 +--R 16a b - 8a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 16 7 2 8 14 +--R - 4096a b cos(x) + (- 16384a b + 8192a b)cos(x) +--R + +--R 6 3 7 2 8 12 +--R (- 26112a b + 30720a b - 5632a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 10 +--R (- 20992a b + 45056a b - 19456a b + 1536a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 8 +--R (- 8848a b + 32384a b - 25600a b + 4736a b - 144a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 1824a b + 11616a b - 15808a b + 5312a b - 384a b ) +--R * +--R 6 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 4 +--R (- 146a b + 1848a b - 4500a b + 2568a b - 346a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 2 2 7 +--R (- 2a b + 88a b - 476a b + 472a b - 114a b )cos(x) - 8a b +--R + +--R 3 6 4 5 +--R 16a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 16 6 3 7 2 14 +--R 4096a b cos(x) + (16384a b - 8192a b )cos(x) +--R + +--R 5 4 6 3 7 2 12 +--R (26112a b - 30720a b + 5632a b )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 10 +--R (20992a b - 45056a b + 19456a b - 1536a b )cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R (8848a b - 32384a b + 25600a b - 4736a b + 144a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 6 +--R (1824a b - 11616a b + 15808a b - 5312a b + 384a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 4 +--R (146a b - 1848a b + 4500a b - 2568a b + 346a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 8 +--R (2b - 88a b + 476a b - 472a b + 114a b )cos(x) + 8a b +--R + +--R 2 7 3 6 +--R - 16a b + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 2 8 18 +--R (- 4096a b + 4096a b)cos(x) +--R + +--R 6 3 7 2 8 16 +--R (- 16384a b + 32768a b - 8192a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (- 26112a b + 89600a b - 52736a b + 5632a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 20992a b + 118016a b - 126464a b + 32000a b - 1536a b) +--R * +--R 12 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 8848a b + 82448a b - 149248a b + 69248a b - 7568a b +--R + +--R 8 +--R 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 1824a b + 30304a b - 92768a b + 73520a b - 14368a b +--R + +--R 7 2 +--R 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 146a b + 5258a b - 29268a b + 40076a b - 13226a b +--R + +--R 6 3 +--R 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R (- 2b + 316a b - 3964a b + 10392a b - 5986a b + 460a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 8 +--R (2b - 136a b + 964a b - 1144a b + 122a b )cos(x) + 8a b +--R + +--R 2 7 3 6 +--R - 48a b + 8a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 8 9 18 +--R (- 4096a b + 4096a )cos(x) +--R + +--R 7 2 8 9 16 +--R (- 16384a b + 32768a b - 8192a )cos(x) +--R + +--R 6 3 7 2 8 9 14 +--R (- 26112a b + 89600a b - 52736a b + 5632a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 20992a b + 118016a b - 126464a b + 32000a b - 1536a ) +--R * +--R 12 +--R cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 +--R - 8848a b + 82448a b - 149248a b + 69248a b - 7568a b +--R + +--R 9 +--R 144a +--R * +--R 10 +--R cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R - 1824a b + 30304a b - 92768a b + 73520a b - 14368a b +--R + +--R 8 +--R 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 146a b + 5258a b - 29268a b + 40076a b - 13226a b +--R + +--R 7 2 +--R 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 2a b + 316a b - 3964a b + 10392a b - 5986a b +--R + +--R 6 3 +--R 460a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 2 2 7 +--R (2a b - 136a b + 964a b - 1144a b + 122a b )cos(x) + 8a b +--R + +--R 3 6 4 5 +--R - 48a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 8 18 +--R (4096a b - 4096a b)cos(x) +--R + +--R 6 3 7 2 8 16 +--R (16384a b - 32768a b + 8192a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (26112a b - 89600a b + 52736a b - 5632a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 12 +--R (20992a b - 118016a b + 126464a b - 32000a b + 1536a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 8848a b - 82448a b + 149248a b - 69248a b + 7568a b +--R + +--R 8 +--R - 144a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R 1824a b - 30304a b + 92768a b - 73520a b + 14368a b +--R + +--R 7 2 +--R - 528a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 146a b - 5258a b + 29268a b - 40076a b + 13226a b +--R + +--R 6 3 +--R - 730a b +--R * +--R 6 +--R cos(x) +--R + +--R 9 8 2 7 3 6 4 5 5 4 4 +--R (2b - 316a b + 3964a b - 10392a b + 5986a b - 460a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 2 8 +--R (- 2b + 136a b - 964a b + 1144a b - 122a b )cos(x) - 8a b +--R + +--R 2 7 3 6 +--R 48a b - 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 20 7 2 8 18 +--R 4096a b cos(x) + (20480a b - 12288a b)cos(x) +--R + +--R 6 3 7 2 8 16 +--R (42496a b - 59392a b + 13824a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (47104a b - 118016a b + 64512a b - 6912a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 12 +--R (29840a b - 123520a b + 122496a b - 31104a b + 1296a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 10 +--R (10672a b - 72240a b + 120576a b - 56304a b + 5616a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 8 +--R (1970a b - 22920a b + 64572a b - 51880a b + 9666a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 +--R (148a b - 3456a b + 17832a b - 25184a b + 8292a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (2b - 168a b + 2076a b - 5896a b + 3602a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (48a b - 480a b + 688a b )cos(x) + 32a b +--R * +--R 2 2 +--R cot(x) sec(x) +--R + +--R 9 20 8 9 18 +--R 4096a cos(x) + (20480a b - 12288a )cos(x) +--R + +--R 7 2 8 9 16 +--R (42496a b - 59392a b + 13824a )cos(x) +--R + +--R 6 3 7 2 8 9 14 +--R (47104a b - 118016a b + 64512a b - 6912a )cos(x) +--R + +--R 5 4 6 3 7 2 8 9 12 +--R (29840a b - 123520a b + 122496a b - 31104a b + 1296a )cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 10 +--R (10672a b - 72240a b + 120576a b - 56304a b + 5616a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R (1970a b - 22920a b + 64572a b - 51880a b + 9666a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 6 +--R (148a b - 3456a b + 17832a b - 25184a b + 8292a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 4 +--R (2a b - 168a b + 2076a b - 5896a b + 3602a b )cos(x) +--R + +--R 2 7 3 6 4 5 2 3 6 +--R (48a b - 480a b + 688a b )cos(x) + 32a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 20 7 2 8 18 +--R - 4096a b cos(x) + (- 20480a b + 12288a b)cos(x) +--R + +--R 6 3 7 2 8 16 +--R (- 42496a b + 59392a b - 13824a b)cos(x) +--R + +--R 5 4 6 3 7 2 8 14 +--R (- 47104a b + 118016a b - 64512a b + 6912a b)cos(x) +--R + +--R 4 5 5 4 6 3 7 2 8 12 +--R (- 29840a b + 123520a b - 122496a b + 31104a b - 1296a b)cos(x) +--R + +--R 3 6 4 5 5 4 6 3 7 2 10 +--R (- 10672a b + 72240a b - 120576a b + 56304a b - 5616a b )cos(x) +--R + +--R 2 7 3 6 4 5 5 4 6 3 8 +--R (- 1970a b + 22920a b - 64572a b + 51880a b - 9666a b )cos(x) +--R + +--R 8 2 7 3 6 4 5 5 4 6 +--R (- 148a b + 3456a b - 17832a b + 25184a b - 8292a b )cos(x) +--R + +--R 9 8 2 7 3 6 4 5 4 +--R (- 2b + 168a b - 2076a b + 5896a b - 3602a b )cos(x) +--R + +--R 8 2 7 3 6 2 2 7 +--R (- 48a b + 480a b - 688a b )cos(x) - 32a b +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R Type: Expression(Integer) +--E 93 + +--S 94 of 528 +t0317:= 1/(1+sec(x)^2)^(1/2) +--R +--R +--R 1 +--R (92) -------------- +--R +-----------+ +--R | 2 +--R \|sec(x) + 1 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 528 +r0317:= atan(tan(x)/(2+tan(x)^2)^(1/2)) +--R +--R +--R tan(x) +--R (93) atan(--------------) +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 528 +a0317:= integrate(t0317,x) +--R +--R +--R (94) +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R sin(x) +--R - atan(------) +--R cos(x) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 96 + +--S 97 of 528 +m0317:= a0317-r0317 +--R +--R +--R (95) +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R tan(x) sin(x) +--R - 2atan(--------------) - atan(------) +--R +-----------+ cos(x) +--R | 2 +--R \|tan(x) + 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 528 +d0317:= D(m0317,x) +--R +--R +--R (96) +--R 13 12 11 10 +--R 64cos(x) + 64cos(x) + 112cos(x) + 112cos(x) +--R + +--R 9 8 7 6 5 +--R - 40cos(x) - 40cos(x) - 89cos(x) - 89cos(x) + 6cos(x) +--R + +--R 4 3 2 +--R 6cos(x) + 16cos(x) + 16cos(x) + cos(x) + 1 +--R * +--R 2 +--R sin(x) +--R + +--R 15 14 13 12 11 +--R 64cos(x) + 64cos(x) + 48cos(x) + 48cos(x) - 88cos(x) +--R + +--R 10 9 8 7 6 +--R - 88cos(x) - 49cos(x) - 49cos(x) + 43cos(x) + 43cos(x) +--R + +--R 5 4 3 2 +--R 14cos(x) + 14cos(x) - 7cos(x) - 7cos(x) - cos(x) - 1 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 13 11 9 7 5 +--R - 128cos(x) - 288cos(x) - 16cos(x) + 238cos(x) + 58cos(x) +--R + +--R 3 +--R - 50cos(x) - 12cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 15 13 11 9 7 +--R - 128cos(x) - 160cos(x) + 144cos(x) + 190cos(x) - 60cos(x) +--R + +--R 5 3 +--R - 72cos(x) + 10cos(x) + 8cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R + +--R 15 14 13 12 +--R - 256cos(x) - 256cos(x) - 256cos(x) - 256cos(x) +--R + +--R 11 10 9 8 7 +--R 192cos(x) + 192cos(x) + 192cos(x) + 192cos(x) - 34cos(x) +--R + +--R 6 5 4 3 2 +--R - 34cos(x) - 34cos(x) - 34cos(x) - 2cos(x) - 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 16 13 12 11 +--R - 256cos(x) - 256cos(x) + 448cos(x) + 448cos(x) - 64cos(x) +--R + +--R 10 9 8 7 6 +--R - 64cos(x) - 258cos(x) - 258cos(x) + 60cos(x) + 60cos(x) +--R + +--R 5 4 3 2 +--R 50cos(x) + 50cos(x) - 12cos(x) - 12cos(x) - 2cos(x) - 2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 15 13 11 9 7 +--R 512cos(x) + 768cos(x) - 192cos(x) - 608cos(x) - 64cos(x) +--R + +--R 5 3 +--R 120cos(x) + 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 15 13 11 9 +--R 512cos(x) + 256cos(x) - 960cos(x) - 288cos(x) + 672cos(x) +--R + +--R 7 5 +--R 80cos(x) - 192cos(x) + 16cos(x) +--R / +--R 15 14 13 12 +--R 256cos(x) + 256cos(x) + 256cos(x) + 256cos(x) +--R + +--R 11 10 9 8 +--R - 192cos(x) - 192cos(x) - 192cos(x) - 192cos(x) +--R + +--R 7 6 5 4 3 +--R 34cos(x) + 34cos(x) + 34cos(x) + 34cos(x) + 2cos(x) +--R + +--R 2 +--R 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 16 13 12 11 +--R 256cos(x) + 256cos(x) - 448cos(x) - 448cos(x) + 64cos(x) +--R + +--R 10 9 8 7 6 +--R 64cos(x) + 258cos(x) + 258cos(x) - 60cos(x) - 60cos(x) +--R + +--R 5 4 3 2 +--R - 50cos(x) - 50cos(x) + 12cos(x) + 12cos(x) + 2cos(x) + 2 +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 15 13 11 9 7 +--R - 512cos(x) - 768cos(x) + 192cos(x) + 608cos(x) + 64cos(x) +--R + +--R 5 3 +--R - 120cos(x) - 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 15 13 11 9 +--R - 512cos(x) - 256cos(x) + 960cos(x) + 288cos(x) - 672cos(x) +--R + +--R 7 5 +--R - 80cos(x) + 192cos(x) - 16cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R Type: Expression(Integer) +--E 98 + +--S 99 of 528 +t0318:= 1/(1-sec(x)^2)^(1/2) +--R +--R +--R 1 +--R (97) ---------------- +--R +-------------+ +--R | 2 +--R \|- sec(x) + 1 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 528 +r0318:= log(sin(x))*tan(x)/(-tan(x)^2)^(1/2) +--R +--R +--R tan(x)log(sin(x)) +--R (98) ----------------- +--R +---------+ +--R | 2 +--R \|- tan(x) +--R Type: Expression(Integer) +--E 100 + +--S 101 of 528 +a0318:= integrate(t0318,x) +--R +--R +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R (99) atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R Type: Union(Expression(Integer),...) +--E 101 + +--S 102 of 528 +m0318:= a0318-r0318 +--R +--R +--R (100) +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +---------+ +--R 2 2 2 2 2 | 2 +--R atan(-------------------------------------------)\|- tan(x) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R + +--R - tan(x)log(sin(x)) +--R / +--R +---------+ +--R | 2 +--R \|- tan(x) +--R Type: Expression(Integer) +--E 102 + +--S 103 of 528 +d0318:= D(m0318,x) +--R +--R +--R (101) +--R x 6 x 2 x 4 x 4 x 2 +--R - sin(-) + (- 3cos(-) + 2)sin(-) + (- 3cos(-) - 1)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - cos(-) - 2cos(-) + 3cos(-) +--R 2 2 2 +--R * +--R +---------+ +--R | 2 +--R sin(x)\|- tan(x) +--R + +--R x 6 x 2 x 4 +--R - cos(x)sin(-) + (- 3cos(-) + 2)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (- 3cos(-) + 12cos(-) - 1)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (- cos(-) - 6cos(-) - 9cos(-) )cos(x) +--R 2 2 2 +--R * +--R tan(x) +--R / +--R x 6 x 2 x 4 x 4 x 2 x 2 +--R sin(-) + (3cos(-) - 2)sin(-) + (3cos(-) - 12cos(-) + 1)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R cos(-) + 6cos(-) + 9cos(-) +--R 2 2 2 +--R * +--R +---------+ +--R | 2 +--R sin(x)\|- tan(x) +--R Type: Expression(Integer) +--E 103 + +--S 104 of 528 +t0319:= 1/(-1+sec(x)^2)^(1/2) +--R +--R +--R 1 +--R (102) -------------- +--R +-----------+ +--R | 2 +--R \|sec(x) - 1 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 528 +r0319:= log(sin(x))*tan(x)/(tan(x)^2)^(1/2) +--R +--R +--R tan(x)log(sin(x)) +--R (103) ----------------- +--R +-------+ +--R | 2 +--R \|tan(x) +--R Type: Expression(Integer) +--E 105 + +--S 106 of 528 +a0319:= integrate(t0319,x) +--R +--R +--R sin(x) 2 +--R (104) - log(----------) + log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 106 + +--S 107 of 528 +m0319:= a0319-r0319 +--R +--R +--R +-------+ +--R sin(x) 2 | 2 +--R (- log(----------) + log(----------))\|tan(x) - tan(x)log(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (105) ------------------------------------------------------------------- +--R +-------+ +--R | 2 +--R \|tan(x) +--R Type: Expression(Integer) +--E 107 + +--S 108 of 528 +d0319:= D(m0319,x) +--R +--R +--R +-------+ +--R | 2 +--R - cos(x)\|tan(x) - cos(x)tan(x) +--R (106) --------------------------------- +--R +-------+ +--R | 2 +--R sin(x)\|tan(x) +--R Type: Expression(Integer) +--E 108 + +--S 109 of 528 +t0320:= 1/(-1-sec(x)^2)^(1/2) +--R +--R +--R 1 +--R (107) ---------------- +--R +-------------+ +--R | 2 +--R \|- sec(x) - 1 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 528 +r0320:= atanh(tan(x)/(-2-tan(x)^2)^(1/2)) +--R +--R +--R tan(x) +--R (108) atanh(----------------) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 528 +a0320:= integrate(t0320,x) +--R +--R +--R (109) +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R - log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 111 + +--S 112 of 528 +m0320:= a0320-r0320 +--R +--R +--R (110) +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R - log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R + +--R tan(x) +--R - 2atanh(----------------) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 528 +d0320:= D(m0320,x) +--R +--R +--R (111) +--R +---+ 6 +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R \|- 1 (%e ) + 7\|- 1 (%e ) + 11\|- 1 (%e ) +--R + +--R +---+ +--R 5\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) - 9(%e ) - 19(%e ) - 3 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R - \|- 1 (%e ) - 10\|- 1 (%e ) - 28\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 22\|- 1 (%e ) - 3\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (%e ) + 12(%e ) + 42(%e ) + 36(%e ) + 5 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +-------------+ +--R x\|- 1 x\|- 1 x\|- 1 | 2 +--R ((%e ) + 9(%e ) + 19(%e ) + 3)\|- tan(x) - 2 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) - 12(%e ) - 42(%e ) - 36(%e ) - 5) +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R Type: Expression(Integer) +--E 113 + +--S 114 of 528 +t0321:= 1/(a+b*sec(x)^2)^(1/2) +--R +--R +--R 1 +--R (112) ---------------- +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R Type: Expression(Integer) +--E 114 + +--S 115 of 528 +r0321:= atan(a^(1/2)*tan(x)/(a+b*sec(x)^2)^(1/2))/a^(1/2) +--R +--R +--R +-+ +--R tan(x)\|a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R (113) ---------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 115 + +--S 116 of 528 +a0321:= integrate(t0321,x) +--R +--R +--R (114) +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x))\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R sin(x) +--R - atan(------) +--R cos(x) +--R / +--R +-+ +--R 2\|a +--R Type: Union(Expression(Integer),...) +--E 116 + +--S 117 of 528 +m0321:= a0321-r0321 +--R +--R +--R (115) +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x))\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R +-+ +--R tan(x)\|a sin(x) +--R - 2atan(----------------) - atan(------) +--R +-------------+ cos(x) +--R | 2 +--R \|b sec(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 117 + +--S 118 of 528 +d0321:= D(m0321,x) +--R +--R +--R (116) +--R 5 13 5 12 4 5 11 +--R 512a cos(x) + 512a cos(x) + (1536a b - 640a )cos(x) +--R + +--R 4 5 10 +--R (1536a b - 640a )cos(x) +--R + +--R 3 2 4 5 9 +--R (1568a b - 1984a b + 96a )cos(x) +--R + +--R 3 2 4 5 8 +--R (1568a b - 1984a b + 96a )cos(x) +--R + +--R 2 3 3 2 4 5 7 +--R (640a b - 1936a b + 512a b + 72a )cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (640a b - 1936a b + 512a b + 72a )cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (90a b - 680a b + 554a b + 84a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (90a b - 680a b + 554a b + 84a b)cos(x) +--R + +--R 5 4 2 3 3 2 3 +--R (2b - 64a b + 170a b + 20a b )cos(x) +--R + +--R 5 4 2 3 3 2 2 4 4 +--R (2b - 64a b + 170a b + 20a b )cos(x) + 8a b cos(x) + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 15 5 14 4 5 13 +--R 512a cos(x) + 512a cos(x) + (1536a b - 1152a )cos(x) +--R + +--R 4 5 12 3 2 4 5 11 +--R (1536a b - 1152a )cos(x) + (1696a b - 3264a b + 864a )cos(x) +--R + +--R 3 2 4 5 10 +--R (1696a b - 3264a b + 864a )cos(x) +--R + +--R 2 3 3 2 4 5 9 +--R (832a b - 3312a b + 2304a b - 216a )cos(x) +--R + +--R 2 3 3 2 4 5 8 +--R (832a b - 3312a b + 2304a b - 216a )cos(x) +--R + +--R 4 2 3 3 2 4 7 +--R (170a b - 1416a b + 2130a b - 540a b)cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (170a b - 1416a b + 2130a b - 540a b)cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (10b - 222a b + 774a b - 450a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (10b - 222a b + 774a b - 450a b )cos(x) +--R + +--R 5 4 2 3 3 +--R (- 6b + 84a b - 134a b )cos(x) +--R + +--R 5 4 2 3 2 4 4 +--R (- 6b + 84a b - 134a b )cos(x) - 8a b cos(x) - 8a b +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 13 5 6 11 +--R - 1024a cos(x) + (- 3584a b + 1280a )cos(x) +--R + +--R 4 2 5 6 9 +--R (- 4544a b + 4608a b - 192a )cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (- 2528a b + 5696a b - 1120a b - 144a )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 580a b + 2880a b - 1596a b - 240a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 38a b + 522a b - 778a b - 106a b )cos(x) +--R + +--R 5 2 4 3 3 +--R (16a b - 104a b - 8a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 15 5 6 13 +--R - 1024a cos(x) + (- 3584a b + 2304a )cos(x) +--R + +--R 4 2 5 6 11 +--R (- 4800a b + 7680a b - 1728a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (- 3040a b + 9600a b - 5472a b + 432a )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 900a b + 5472a b - 6348a b + 1296a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 102a b + 1350a b - 3210a b + 1386a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 2b + 102a b - 630a b + 610a b )cos(x) +--R + +--R 5 2 4 +--R (- 24a b + 88a b )cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 6 15 6 14 5 6 13 +--R - 2048a cos(x) - 2048a cos(x) + (- 6144a b + 4096a )cos(x) +--R + +--R 5 6 12 +--R (- 6144a b + 4096a )cos(x) +--R + +--R 4 2 5 6 11 +--R (- 6912a b + 11264a b - 2816a )cos(x) +--R + +--R 4 2 5 6 10 +--R (- 6912a b + 11264a b - 2816a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (- 3584a b + 11264a b - 6912a b + 768a )cos(x) +--R + +--R 3 3 4 2 5 6 8 +--R (- 3584a b + 11264a b - 6912a b + 768a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (- 840a b + 4928a b - 5888a b + 1600a b - 72a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 840a b + 4928a b - 5888a b + 1600a b - 72a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 72a b + 880a b - 2016a b + 1056a b - 120a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- 72a b + 880a b - 2016a b + 1056a b - 120a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- b + 44a b - 234a b + 228a b - 53a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- b + 44a b - 234a b + 228a b - 53a b )cos(x) +--R + +--R 5 2 4 3 3 5 2 4 3 3 +--R (- 4a b + 8a b - 4a b )cos(x) - 4a b + 8a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 17 6 16 5 6 15 +--R - 2048a cos(x) - 2048a cos(x) + (- 6144a b + 6144a )cos(x) +--R + +--R 5 6 14 +--R (- 6144a b + 6144a )cos(x) +--R + +--R 4 2 5 6 13 +--R (- 6912a b + 17408a b - 6912a )cos(x) +--R + +--R 4 2 5 6 12 +--R (- 6912a b + 17408a b - 6912a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (- 3584a b + 18048a b - 18432a b + 3456a )cos(x) +--R + +--R 3 3 4 2 5 6 10 +--R (- 3584a b + 18048a b - 18432a b + 3456a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (- 840a b + 8256a b - 17472a b + 8640a b - 648a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 8 +--R (- 840a b + 8256a b - 17472a b + 8640a b - 648a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (- 72a b + 1560a b - 6912a b + 7416a b - 1512a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 72a b + 1560a b - 6912a b + 7416a b - 1512a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b + 84a b - 990a b + 2468a b - 1161a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- b + 84a b - 990a b + 2468a b - 1161a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (- 24a b + 240a b - 312a b )cos(x) +--R + +--R 5 2 4 3 3 2 2 4 2 4 +--R (- 24a b + 240a b - 312a b )cos(x) - 16a b cos(x) - 16a b +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 15 5 6 13 +--R 4096a cos(x) + (14336a b - 8192a )cos(x) +--R + +--R 4 2 5 6 11 +--R (19456a b - 26624a b + 5632a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (12800a b - 32768a b + 16640a b - 1536a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (4144a b - 18816a b + 17984a b - 3968a b + 144a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (584a b - 4960a b + 8544a b - 3520a b + 312a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (24b - 488a b + 1656a b - 1208a b + 208a b )cos(x) +--R + +--R 6 5 2 4 3 3 +--R (- 8b + 88a b - 120a b + 40a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 17 5 6 15 +--R 4096a cos(x) + (14336a b - 12288a )cos(x) +--R + +--R 4 2 5 6 13 +--R (19456a b - 40960a b + 13824a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (12800a b - 51968a b + 43776a b - 6912a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (4144a b - 30976a b + 51648a b - 20736a b + 1296a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (584a b - 8560a b + 27552a b - 22608a b + 3672a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (24b - 896a b + 6288a b - 10624a b + 3672a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 16b + 432a b - 1904a b + 1488a b )cos(x) +--R + +--R 5 2 4 +--R (- 64a b + 192a b )cos(x) +--R * +--R +-+ +--R \|a +--R / +--R 6 15 6 14 5 6 13 +--R 2048a cos(x) + 2048a cos(x) + (6144a b - 4096a )cos(x) +--R + +--R 5 6 12 +--R (6144a b - 4096a )cos(x) +--R + +--R 4 2 5 6 11 +--R (6912a b - 11264a b + 2816a )cos(x) +--R + +--R 4 2 5 6 10 +--R (6912a b - 11264a b + 2816a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (3584a b - 11264a b + 6912a b - 768a )cos(x) +--R + +--R 3 3 4 2 5 6 8 +--R (3584a b - 11264a b + 6912a b - 768a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (840a b - 4928a b + 5888a b - 1600a b + 72a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (840a b - 4928a b + 5888a b - 1600a b + 72a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (72a b - 880a b + 2016a b - 1056a b + 120a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (72a b - 880a b + 2016a b - 1056a b + 120a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (b - 44a b + 234a b - 228a b + 53a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (b - 44a b + 234a b - 228a b + 53a b )cos(x) +--R + +--R 5 2 4 3 3 5 2 4 3 3 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 8a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 17 6 16 5 6 15 +--R 2048a cos(x) + 2048a cos(x) + (6144a b - 6144a )cos(x) +--R + +--R 5 6 14 4 2 5 6 13 +--R (6144a b - 6144a )cos(x) + (6912a b - 17408a b + 6912a )cos(x) +--R + +--R 4 2 5 6 12 +--R (6912a b - 17408a b + 6912a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (3584a b - 18048a b + 18432a b - 3456a )cos(x) +--R + +--R 3 3 4 2 5 6 10 +--R (3584a b - 18048a b + 18432a b - 3456a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (840a b - 8256a b + 17472a b - 8640a b + 648a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 8 +--R (840a b - 8256a b + 17472a b - 8640a b + 648a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (72a b - 1560a b + 6912a b - 7416a b + 1512a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (72a b - 1560a b + 6912a b - 7416a b + 1512a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b - 84a b + 990a b - 2468a b + 1161a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (b - 84a b + 990a b - 2468a b + 1161a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (24a b - 240a b + 312a b )cos(x) +--R + +--R 5 2 4 3 3 2 2 4 2 4 +--R (24a b - 240a b + 312a b )cos(x) + 16a b cos(x) + 16a b +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 15 5 6 13 +--R - 4096a cos(x) + (- 14336a b + 8192a )cos(x) +--R + +--R 4 2 5 6 11 +--R (- 19456a b + 26624a b - 5632a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (- 12800a b + 32768a b - 16640a b + 1536a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (- 4144a b + 18816a b - 17984a b + 3968a b - 144a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 584a b + 4960a b - 8544a b + 3520a b - 312a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 24b + 488a b - 1656a b + 1208a b - 208a b )cos(x) +--R + +--R 6 5 2 4 3 3 +--R (8b - 88a b + 120a b - 40a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 17 5 6 15 +--R - 4096a cos(x) + (- 14336a b + 12288a )cos(x) +--R + +--R 4 2 5 6 13 +--R (- 19456a b + 40960a b - 13824a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (- 12800a b + 51968a b - 43776a b + 6912a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (- 4144a b + 30976a b - 51648a b + 20736a b - 1296a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 7 +--R (- 584a b + 8560a b - 27552a b + 22608a b - 3672a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 24b + 896a b - 6288a b + 10624a b - 3672a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (16b - 432a b + 1904a b - 1488a b )cos(x) +--R + +--R 5 2 4 +--R (64a b - 192a b )cos(x) +--R * +--R +-+ +--R \|a +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R Type: Expression(Integer) +--E 118 + +--S 119 of 528 +t0322:= (1+sec(x)^2)^(3/2) +--R +--R +--R +-----------+ +--R 2 | 2 +--R (117) (sec(x) + 1)\|sec(x) + 1 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 528 +r0322:= 2*asinh(1/2*2^(1/2)*tan(x))+atan(tan(x)/(2+tan(x)^2)^(1/2))+_ + 1/2*tan(x)*(2+tan(x)^2)^(1/2) +--R +--R +--R +-----------+ +-+ +--R tan(x) | 2 \|2 tan(x) +--R 2atan(--------------) + tan(x)\|tan(x) + 2 + 4asinh(----------) +--R +-----------+ 2 +--R | 2 +--R \|tan(x) + 2 +--R (118) ----------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 120 + +--S 121 of 528 +a0322:= integrate(t0322,x) +--R +--R +--R (119) +--R 6 5 4 3 +--R (- 16cos(x) - 16cos(x) - 8cos(x) - 8cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 32cos(x) + 32cos(x) + 4cos(x) +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (16cos(x) + 16cos(x) + 8cos(x) + 8cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) - 32cos(x) - 4cos(x) +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((- cos(x) - 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (8cos(x) + 8cos(x) + 4cos(x) + 4cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 16cos(x) - 16cos(x) - 2cos(x) +--R * +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R 6 5 4 3 sin(x) +--R (- 8cos(x) - 8cos(x) - 4cos(x) - 4cos(x) )atan(------) +--R cos(x) +--R + +--R 5 4 3 2 +--R (8cos(x) + 8cos(x) + 8cos(x) + 8cos(x) + cos(x) + 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 sin(x) +--R (16cos(x) + 16cos(x) + 2cos(x) )atan(------) +--R cos(x) +--R + +--R 5 3 +--R (- 16cos(x) - 24cos(x) - 8cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (16cos(x) + 16cos(x) + 8cos(x) + 8cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) - 32cos(x) - 4cos(x) +--R Type: Union(Expression(Integer),...) +--E 121 + +--S 122 of 528 +m0322:= a0322-r0322 +--R +--R +--R (120) +--R 6 5 4 3 +--R (- 16cos(x) - 16cos(x) - 8cos(x) - 8cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 32cos(x) + 32cos(x) + 4cos(x) +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (16cos(x) + 16cos(x) + 8cos(x) + 8cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) - 32cos(x) - 4cos(x) +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | 4cos(x) + 4 +--R ((- cos(x) - 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) + 2cos(x) + 2 +--R + +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (8cos(x) + 8cos(x) + 4cos(x) + 4cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 16cos(x) - 16cos(x) - 2cos(x) +--R * +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 4 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R 6 5 4 3 +--R (- 16cos(x) - 16cos(x) - 8cos(x) - 8cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 32cos(x) + 32cos(x) + 4cos(x) +--R * +--R tan(x) +--R atan(--------------) +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R + +--R 6 5 4 3 +--R (- 8cos(x) - 8cos(x) - 4cos(x) - 4cos(x) )tan(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R (16cos(x) + 16cos(x) + 2cos(x) )tan(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R + +--R 6 5 4 3 sin(x) +--R (- 8cos(x) - 8cos(x) - 4cos(x) - 4cos(x) )atan(------) +--R cos(x) +--R + +--R +-+ +--R 6 5 4 3 \|2 tan(x) +--R (- 32cos(x) - 32cos(x) - 16cos(x) - 16cos(x) )asinh(----------) +--R 2 +--R + +--R 5 4 3 2 +--R (8cos(x) + 8cos(x) + 8cos(x) + 8cos(x) + cos(x) + 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 sin(x) +--R (16cos(x) + 16cos(x) + 2cos(x) )atan(------) +--R cos(x) +--R + +--R +-+ +--R 6 4 2 \|2 tan(x) +--R (64cos(x) + 64cos(x) + 8cos(x) )asinh(----------) +--R 2 +--R + +--R 5 3 +--R (- 16cos(x) - 24cos(x) - 8cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 6 5 4 3 | 4cos(x) + 4 +--R (16cos(x) + 16cos(x) + 8cos(x) + 8cos(x) ) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) - 32cos(x) - 4cos(x) +--R Type: Expression(Integer) +--E 122 + +--S 123 of 528 +d0322:= D(m0322,x) +--R +--R +--R (121) +--R 26 25 24 +--R 131072cos(x) + 131072cos(x) + 655360cos(x) +--R + +--R 23 22 21 +--R 655360cos(x) + 1122304cos(x) + 1122304cos(x) +--R + +--R 20 19 18 +--R 589824cos(x) + 589824cos(x) - 428544cos(x) +--R + +--R 17 16 15 +--R - 428544cos(x) - 634368cos(x) - 634368cos(x) +--R + +--R 14 13 12 +--R - 183872cos(x) - 183872cos(x) + 80512cos(x) +--R + +--R 11 10 9 8 +--R 80512cos(x) + 63954cos(x) + 63954cos(x) + 14898cos(x) +--R + +--R 7 6 5 4 +--R 14898cos(x) + 1324cos(x) + 1324cos(x) + 32cos(x) +--R + +--R 3 +--R 32cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 28 27 26 +--R - 393216cos(x) - 393216cos(x) - 1245184cos(x) +--R + +--R 25 24 23 +--R - 1245184cos(x) - 1646592cos(x) - 1646592cos(x) +--R + +--R 22 21 20 +--R - 1241088cos(x) - 1241088cos(x) - 211456cos(x) +--R + +--R 19 18 17 +--R - 211456cos(x) + 900864cos(x) + 900864cos(x) +--R + +--R 16 15 14 +--R 948544cos(x) + 948544cos(x) + 165344cos(x) +--R + +--R 13 12 11 +--R 165344cos(x) - 217414cos(x) - 217414cos(x) +--R + +--R 10 9 8 7 +--R - 111339cos(x) - 111339cos(x) - 7462cos(x) - 7462cos(x) +--R + +--R 6 5 4 3 +--R 4678cos(x) + 4678cos(x) + 815cos(x) + 815cos(x) +--R + +--R 2 +--R 28cos(x) + 28cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 30 29 28 +--R - 1179648cos(x) - 1179648cos(x) - 4063232cos(x) +--R + +--R 27 26 25 +--R - 4063232cos(x) - 4857856cos(x) - 4857856cos(x) +--R + +--R 24 23 22 +--R - 1359872cos(x) - 1359872cos(x) + 2152960cos(x) +--R + +--R 21 20 19 +--R 2152960cos(x) + 2220544cos(x) + 2220544cos(x) +--R + +--R 18 17 16 +--R 540736cos(x) + 540736cos(x) - 328448cos(x) +--R + +--R 15 14 13 +--R - 328448cos(x) - 193122cos(x) - 193122cos(x) +--R + +--R 12 11 10 9 +--R 8602cos(x) + 8602cos(x) + 5348cos(x) + 5348cos(x) +--R + +--R 8 7 6 5 +--R - 14858cos(x) - 14858cos(x) - 6604cos(x) - 6604cos(x) +--R + +--R 4 3 2 +--R - 862cos(x) - 862cos(x) - 28cos(x) - 28cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 31 30 +--R - 655360cos(x) - 655360cos(x) - 2162688cos(x) +--R + +--R 29 28 27 +--R - 2162688cos(x) - 1695744cos(x) - 1695744cos(x) +--R + +--R 26 25 24 +--R 1617920cos(x) + 1617920cos(x) + 2812416cos(x) +--R + +--R 23 22 21 +--R 2812416cos(x) + 316672cos(x) + 316672cos(x) +--R + +--R 20 19 18 +--R - 1303872cos(x) - 1303872cos(x) - 566368cos(x) +--R + +--R 17 16 15 +--R - 566368cos(x) + 186358cos(x) + 186358cos(x) +--R + +--R 14 13 12 11 +--R 160887cos(x) + 160887cos(x) + 13740cos(x) + 13740cos(x) +--R + +--R 10 9 8 7 +--R - 12277cos(x) - 12277cos(x) - 3781cos(x) - 3781cos(x) +--R + +--R 6 5 4 3 +--R - 402cos(x) - 402cos(x) - 13cos(x) - 13cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 26 24 22 +--R - 262144cos(x) - 1441792cos(x) - 2867200cos(x) +--R + +--R 20 18 16 +--R - 2154496cos(x) + 476160cos(x) + 1748480cos(x) +--R + +--R 14 12 10 8 +--R 878464cos(x) - 74816cos(x) - 212484cos(x) - 74438cos(x) +--R + +--R 6 4 2 +--R - 10362cos(x) - 510cos(x) - 4cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 28 26 24 +--R 786432cos(x) + 2883584cos(x) + 4440064cos(x) +--R + +--R 22 20 18 +--R 3866624cos(x) + 1377280cos(x) - 1770496cos(x) +--R + +--R 16 14 12 +--R - 2772352cos(x) - 1072896cos(x) + 407660cos(x) +--R + +--R 10 8 6 4 +--R 422940cos(x) + 84166cos(x) - 11108cos(x) - 4972cos(x) +--R + +--R 2 +--R - 382cos(x) - 4 +--R * +--R 4 +--R sin(x) +--R + +--R 30 28 26 +--R 2359296cos(x) + 9306112cos(x) + 13484032cos(x) +--R + +--R 24 22 20 +--R 6709248cos(x) - 3744768cos(x) - 6579712cos(x) +--R + +--R 18 16 14 +--R - 2799488cos(x) + 432960cos(x) + 715684cos(x) +--R + +--R 12 10 8 6 +--R 102078cos(x) - 34002cos(x) + 31048cos(x) + 26318cos(x) +--R + +--R 4 2 +--R 5714cos(x) + 388cos(x) + 4 +--R * +--R 2 +--R sin(x) +--R + +--R 32 30 28 26 +--R 1310720cos(x) + 4980736cos(x) + 5390336cos(x) - 1998848cos(x) +--R + +--R 24 22 20 +--R - 7447552cos(x) - 2962432cos(x) + 2750848cos(x) +--R + +--R 18 16 14 12 +--R 2315776cos(x) - 57676cos(x) - 537124cos(x) - 136318cos(x) +--R + +--R 10 8 6 4 2 +--R 26904cos(x) + 17354cos(x) + 2874cos(x) + 176cos(x) + 2cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R + +--R 28 27 26 +--R - 262144cos(x) - 262144cos(x) - 917504cos(x) +--R + +--R 25 24 23 +--R - 917504cos(x) - 1032192cos(x) - 1032192cos(x) +--R + +--R 22 21 20 +--R - 90112cos(x) - 90112cos(x) + 656384cos(x) +--R + +--R 19 18 17 +--R 656384cos(x) + 435712cos(x) + 435712cos(x) +--R + +--R 16 15 14 13 +--R 7040cos(x) + 7040cos(x) - 88896cos(x) - 88896cos(x) +--R + +--R 12 11 10 9 +--R - 34692cos(x) - 34692cos(x) - 5054cos(x) - 5054cos(x) +--R + +--R 8 7 6 5 +--R - 254cos(x) - 254cos(x) - 2cos(x) - 2cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 27 26 +--R 524288cos(x) + 524288cos(x) + 1835008cos(x) +--R + +--R 25 24 23 +--R 1835008cos(x) + 1998848cos(x) + 1998848cos(x) +--R + +--R 22 21 20 +--R - 16384cos(x) - 16384cos(x) - 1476608cos(x) +--R + +--R 19 18 17 +--R - 1476608cos(x) - 822272cos(x) - 822272cos(x) +--R + +--R 16 15 14 +--R 120064cos(x) + 120064cos(x) + 224896cos(x) +--R + +--R 13 12 11 10 +--R 224896cos(x) + 53256cos(x) + 53256cos(x) - 3588cos(x) +--R + +--R 9 8 7 6 +--R - 3588cos(x) - 2374cos(x) - 2374cos(x) - 190cos(x) +--R + +--R 5 4 3 +--R - 190cos(x) - 2cos(x) - 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 31 30 29 +--R 262144cos(x) + 262144cos(x) + 917504cos(x) + 917504cos(x) +--R + +--R 28 27 26 25 +--R 770048cos(x) + 770048cos(x) - 761856cos(x) - 761856cos(x) +--R + +--R 24 23 22 +--R - 1426432cos(x) - 1426432cos(x) - 165376cos(x) +--R + +--R 21 20 19 +--R - 165376cos(x) + 764032cos(x) + 764032cos(x) +--R + +--R 18 17 16 15 +--R 341312cos(x) + 341312cos(x) - 139516cos(x) - 139516cos(x) +--R + +--R 14 13 12 11 +--R - 114818cos(x) - 114818cos(x) - 4614cos(x) - 4614cos(x) +--R + +--R 10 9 8 7 +--R 11526cos(x) + 11526cos(x) + 2822cos(x) + 2822cos(x) +--R + +--R 6 5 4 3 +--R 194cos(x) + 194cos(x) + 2cos(x) + 2cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 28 27 26 +--R - 1048576cos(x) - 1048576cos(x) - 3670016cos(x) +--R + +--R 25 24 23 +--R - 3670016cos(x) - 4128768cos(x) - 4128768cos(x) +--R + +--R 22 21 20 +--R - 360448cos(x) - 360448cos(x) + 2625536cos(x) +--R + +--R 19 18 17 +--R 2625536cos(x) + 1742848cos(x) + 1742848cos(x) +--R + +--R 16 15 14 +--R 28160cos(x) + 28160cos(x) - 355584cos(x) +--R + +--R 13 12 11 +--R - 355584cos(x) - 138768cos(x) - 138768cos(x) +--R + +--R 10 9 8 7 +--R - 20216cos(x) - 20216cos(x) - 1016cos(x) - 1016cos(x) +--R + +--R 6 5 +--R - 8cos(x) - 8cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 27 26 +--R 2097152cos(x) + 2097152cos(x) + 7340032cos(x) +--R + +--R 25 24 23 +--R 7340032cos(x) + 7995392cos(x) + 7995392cos(x) +--R + +--R 22 21 20 +--R - 65536cos(x) - 65536cos(x) - 5906432cos(x) +--R + +--R 19 18 17 +--R - 5906432cos(x) - 3289088cos(x) - 3289088cos(x) +--R + +--R 16 15 14 +--R 480256cos(x) + 480256cos(x) + 899584cos(x) +--R + +--R 13 12 11 +--R 899584cos(x) + 213024cos(x) + 213024cos(x) +--R + +--R 10 9 8 7 +--R - 14352cos(x) - 14352cos(x) - 9496cos(x) - 9496cos(x) +--R + +--R 6 5 4 3 +--R - 760cos(x) - 760cos(x) - 8cos(x) - 8cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 31 30 +--R 1048576cos(x) + 1048576cos(x) + 3670016cos(x) +--R + +--R 29 28 27 +--R 3670016cos(x) + 3080192cos(x) + 3080192cos(x) +--R + +--R 26 25 24 +--R - 3047424cos(x) - 3047424cos(x) - 5705728cos(x) +--R + +--R 23 22 21 +--R - 5705728cos(x) - 661504cos(x) - 661504cos(x) +--R + +--R 20 19 18 +--R 3056128cos(x) + 3056128cos(x) + 1365248cos(x) +--R + +--R 17 16 15 +--R 1365248cos(x) - 558064cos(x) - 558064cos(x) +--R + +--R 14 13 12 11 +--R - 459272cos(x) - 459272cos(x) - 18456cos(x) - 18456cos(x) +--R + +--R 10 9 8 7 +--R 46104cos(x) + 46104cos(x) + 11288cos(x) + 11288cos(x) +--R + +--R 6 5 4 3 +--R 776cos(x) + 776cos(x) + 8cos(x) + 8cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 28 27 26 +--R - 1048576cos(x) - 1048576cos(x) - 3670016cos(x) +--R + +--R 25 24 23 +--R - 3670016cos(x) - 4128768cos(x) - 4128768cos(x) +--R + +--R 22 21 20 +--R - 360448cos(x) - 360448cos(x) + 2625536cos(x) +--R + +--R 19 18 17 +--R 2625536cos(x) + 1742848cos(x) + 1742848cos(x) +--R + +--R 16 15 14 13 +--R 28160cos(x) + 28160cos(x) - 355584cos(x) - 355584cos(x) +--R + +--R 12 11 10 9 +--R - 138768cos(x) - 138768cos(x) - 20216cos(x) - 20216cos(x) +--R + +--R 8 7 6 5 +--R - 1016cos(x) - 1016cos(x) - 8cos(x) - 8cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 27 26 +--R 2097152cos(x) + 2097152cos(x) + 7340032cos(x) +--R + +--R 25 24 23 +--R 7340032cos(x) + 7995392cos(x) + 7995392cos(x) +--R + +--R 22 21 20 +--R - 65536cos(x) - 65536cos(x) - 5906432cos(x) +--R + +--R 19 18 17 +--R - 5906432cos(x) - 3289088cos(x) - 3289088cos(x) +--R + +--R 16 15 14 13 +--R 480256cos(x) + 480256cos(x) + 899584cos(x) + 899584cos(x) +--R + +--R 12 11 10 9 +--R 213024cos(x) + 213024cos(x) - 14352cos(x) - 14352cos(x) +--R + +--R 8 7 6 5 4 +--R - 9496cos(x) - 9496cos(x) - 760cos(x) - 760cos(x) - 8cos(x) +--R + +--R 3 +--R - 8cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 31 30 29 +--R 1048576cos(x) + 1048576cos(x) + 3670016cos(x) + 3670016cos(x) +--R + +--R 28 27 26 25 +--R 3080192cos(x) + 3080192cos(x) - 3047424cos(x) - 3047424cos(x) +--R + +--R 24 23 22 21 +--R - 5705728cos(x) - 5705728cos(x) - 661504cos(x) - 661504cos(x) +--R + +--R 20 19 18 17 +--R 3056128cos(x) + 3056128cos(x) + 1365248cos(x) + 1365248cos(x) +--R + +--R 16 15 14 13 +--R - 558064cos(x) - 558064cos(x) - 459272cos(x) - 459272cos(x) +--R + +--R 12 11 10 9 +--R - 18456cos(x) - 18456cos(x) + 46104cos(x) + 46104cos(x) +--R + +--R 8 7 6 5 4 +--R 11288cos(x) + 11288cos(x) + 776cos(x) + 776cos(x) + 8cos(x) +--R + +--R 3 +--R 8cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 28 26 24 +--R 524288cos(x) + 2097152cos(x) + 2916352cos(x) +--R + +--R 22 20 18 +--R 1015808cos(x) - 1386496cos(x) - 1478656cos(x) +--R + +--R 16 14 12 +--R - 315648cos(x) + 217856cos(x) + 142152cos(x) +--R + +--R 10 8 6 +--R 31104cos(x) + 2680cos(x) + 64cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 26 24 +--R - 1048576cos(x) - 4194304cos(x) - 5701632cos(x) +--R + +--R 22 20 18 +--R - 1572864cos(x) + 3280896cos(x) + 2981888cos(x) +--R + +--R 16 14 12 10 +--R 292352cos(x) - 643072cos(x) - 276496cos(x) - 16832cos(x) +--R + +--R 8 6 4 +--R 9872cos(x) + 1656cos(x) + 56cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 30 28 26 +--R - 524288cos(x) - 2097152cos(x) - 2392064cos(x) + 950272cos(x) +--R + +--R 24 22 20 18 +--R 3713024cos(x) + 1527808cos(x) - 1603328cos(x) - 1382144cos(x) +--R + +--R 16 14 12 10 +--R 88504cos(x) + 386304cos(x) + 86288cos(x) - 29568cos(x) +--R + +--R 8 6 4 +--R - 14336cos(x) - 1776cos(x) - 56cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 28 26 24 +--R 2097152cos(x) + 8388608cos(x) + 11665408cos(x) +--R + +--R 22 20 18 +--R 4063232cos(x) - 5545984cos(x) - 5914624cos(x) +--R + +--R 16 14 12 +--R - 1262592cos(x) + 871424cos(x) + 568608cos(x) +--R + +--R 10 8 6 +--R 124416cos(x) + 10720cos(x) + 256cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 26 24 +--R - 4194304cos(x) - 16777216cos(x) - 22806528cos(x) +--R + +--R 22 20 18 +--R - 6291456cos(x) + 13123584cos(x) + 11927552cos(x) +--R + +--R 16 14 12 +--R 1169408cos(x) - 2572288cos(x) - 1105984cos(x) +--R + +--R 10 8 6 4 +--R - 67328cos(x) + 39488cos(x) + 6624cos(x) + 224cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 30 28 +--R - 2097152cos(x) - 8388608cos(x) - 9568256cos(x) +--R + +--R 26 24 22 +--R 3801088cos(x) + 14852096cos(x) + 6111232cos(x) +--R + +--R 20 18 16 +--R - 6413312cos(x) - 5528576cos(x) + 354016cos(x) +--R + +--R 14 12 10 8 +--R 1545216cos(x) + 345152cos(x) - 118272cos(x) - 57344cos(x) +--R + +--R 6 4 +--R - 7104cos(x) - 224cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 28 26 24 +--R 2097152cos(x) + 8388608cos(x) + 11665408cos(x) +--R + +--R 22 20 18 16 +--R 4063232cos(x) - 5545984cos(x) - 5914624cos(x) - 1262592cos(x) +--R + +--R 14 12 10 8 +--R 871424cos(x) + 568608cos(x) + 124416cos(x) + 10720cos(x) +--R + +--R 6 +--R 256cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 26 24 +--R - 4194304cos(x) - 16777216cos(x) - 22806528cos(x) +--R + +--R 22 20 18 +--R - 6291456cos(x) + 13123584cos(x) + 11927552cos(x) +--R + +--R 16 14 12 10 +--R 1169408cos(x) - 2572288cos(x) - 1105984cos(x) - 67328cos(x) +--R + +--R 8 6 4 +--R 39488cos(x) + 6624cos(x) + 224cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 30 28 26 +--R - 2097152cos(x) - 8388608cos(x) - 9568256cos(x) + 3801088cos(x) +--R + +--R 24 22 20 18 +--R 14852096cos(x) + 6111232cos(x) - 6413312cos(x) - 5528576cos(x) +--R + +--R 16 14 12 10 +--R 354016cos(x) + 1545216cos(x) + 345152cos(x) - 118272cos(x) +--R + +--R 8 6 4 +--R - 57344cos(x) - 7104cos(x) - 224cos(x) +--R / +--R 28 27 26 +--R 262144cos(x) + 262144cos(x) + 917504cos(x) +--R + +--R 25 24 23 +--R 917504cos(x) + 1032192cos(x) + 1032192cos(x) +--R + +--R 22 21 20 19 +--R 90112cos(x) + 90112cos(x) - 656384cos(x) - 656384cos(x) +--R + +--R 18 17 16 15 +--R - 435712cos(x) - 435712cos(x) - 7040cos(x) - 7040cos(x) +--R + +--R 14 13 12 11 +--R 88896cos(x) + 88896cos(x) + 34692cos(x) + 34692cos(x) +--R + +--R 10 9 8 7 6 +--R 5054cos(x) + 5054cos(x) + 254cos(x) + 254cos(x) + 2cos(x) +--R + +--R 5 +--R 2cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 27 26 +--R - 524288cos(x) - 524288cos(x) - 1835008cos(x) +--R + +--R 25 24 23 +--R - 1835008cos(x) - 1998848cos(x) - 1998848cos(x) +--R + +--R 22 21 20 +--R 16384cos(x) + 16384cos(x) + 1476608cos(x) +--R + +--R 19 18 17 +--R 1476608cos(x) + 822272cos(x) + 822272cos(x) +--R + +--R 16 15 14 +--R - 120064cos(x) - 120064cos(x) - 224896cos(x) +--R + +--R 13 12 11 10 +--R - 224896cos(x) - 53256cos(x) - 53256cos(x) + 3588cos(x) +--R + +--R 9 8 7 6 +--R 3588cos(x) + 2374cos(x) + 2374cos(x) + 190cos(x) +--R + +--R 5 4 3 +--R 190cos(x) + 2cos(x) + 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 31 30 29 +--R - 262144cos(x) - 262144cos(x) - 917504cos(x) - 917504cos(x) +--R + +--R 28 27 26 25 +--R - 770048cos(x) - 770048cos(x) + 761856cos(x) + 761856cos(x) +--R + +--R 24 23 22 21 +--R 1426432cos(x) + 1426432cos(x) + 165376cos(x) + 165376cos(x) +--R + +--R 20 19 18 17 +--R - 764032cos(x) - 764032cos(x) - 341312cos(x) - 341312cos(x) +--R + +--R 16 15 14 13 +--R 139516cos(x) + 139516cos(x) + 114818cos(x) + 114818cos(x) +--R + +--R 12 11 10 9 +--R 4614cos(x) + 4614cos(x) - 11526cos(x) - 11526cos(x) +--R + +--R 8 7 6 5 4 +--R - 2822cos(x) - 2822cos(x) - 194cos(x) - 194cos(x) - 2cos(x) +--R + +--R 3 +--R - 2cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 28 26 24 +--R - 524288cos(x) - 2097152cos(x) - 2916352cos(x) +--R + +--R 22 20 18 +--R - 1015808cos(x) + 1386496cos(x) + 1478656cos(x) +--R + +--R 16 14 12 10 +--R 315648cos(x) - 217856cos(x) - 142152cos(x) - 31104cos(x) +--R + +--R 8 6 +--R - 2680cos(x) - 64cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 28 26 24 +--R 1048576cos(x) + 4194304cos(x) + 5701632cos(x) +--R + +--R 22 20 18 +--R 1572864cos(x) - 3280896cos(x) - 2981888cos(x) +--R + +--R 16 14 12 10 +--R - 292352cos(x) + 643072cos(x) + 276496cos(x) + 16832cos(x) +--R + +--R 8 6 4 +--R - 9872cos(x) - 1656cos(x) - 56cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 32 30 28 26 +--R 524288cos(x) + 2097152cos(x) + 2392064cos(x) - 950272cos(x) +--R + +--R 24 22 20 18 +--R - 3713024cos(x) - 1527808cos(x) + 1603328cos(x) + 1382144cos(x) +--R + +--R 16 14 12 10 +--R - 88504cos(x) - 386304cos(x) - 86288cos(x) + 29568cos(x) +--R + +--R 8 6 4 +--R 14336cos(x) + 1776cos(x) + 56cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 2 +--R Type: Expression(Integer) +--E 123 + +--S 124 of 528 +t0323:= (1-sec(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (122) (- sec(x) + 1)\|- sec(x) + 1 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 528 +r0323:= -1/2*cot(x)*(-tan(x)^2)^(1/2)*(2*log(cos(x))+tan(x)^2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 2cot(x)log(cos(x)) - cot(x)tan(x) )\|- tan(x) +--R (123) -------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 125 + +--S 126 of 528 +a0323:= integrate(t0323,x) +--R +--R +--R (124) +--R x 16 x 2 x 14 x 4 x 12 +--R sin(-) + 8cos(-) sin(-) + (28cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 x 8 x 4 x 8 +--R (56cos(-) - 8cos(-) )sin(-) + (70cos(-) - 68cos(-) + 6)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (56cos(-) - 112cos(-) - 40cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (28cos(-) - 68cos(-) + 164cos(-) + 4)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (8cos(-) - 8cos(-) - 40cos(-) - 24cos(-) )sin(-) + cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R * +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R + +--R x x 11 x 3 x 9 x 5 x 7 +--R - 8cos(-)sin(-) - 24cos(-) sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 7 x 5 x 9 x x 3 +--R 16cos(-) sin(-) + (24cos(-) + 8cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R x 11 x 3 x +--R (8cos(-) - 8cos(-) )sin(-) +--R 2 2 2 +--R / +--R x 16 x 2 x 14 x 4 x 12 +--R sin(-) + 8cos(-) sin(-) + (28cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 x 8 x 4 x 8 +--R (56cos(-) - 8cos(-) )sin(-) + (70cos(-) - 68cos(-) + 6)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (56cos(-) - 112cos(-) - 40cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (28cos(-) - 68cos(-) + 164cos(-) + 4)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (8cos(-) - 8cos(-) - 40cos(-) - 24cos(-) )sin(-) + cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R 4cos(-) + 6cos(-) + 4cos(-) + 1 +--R 2 2 2 +--R Type: Union(Expression(Integer),...) +--E 126 + +--S 127 of 528 +m0323:= a0323-r0323 +--R +--R +--R (125) +--R x 16 x 2 x 14 +--R 2cot(x)sin(-) + 16cos(-) cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 12 +--R (56cos(-) + 8)cot(x)sin(-) +--R 2 2 +--R + +--R x 6 x 2 x 10 +--R (112cos(-) - 16cos(-) )cot(x)sin(-) +--R 2 2 2 +--R + +--R x 8 x 4 x 8 +--R (140cos(-) - 136cos(-) + 12)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (112cos(-) - 224cos(-) - 80cos(-) )cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (56cos(-) - 136cos(-) + 328cos(-) + 8)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 +--R (16cos(-) - 16cos(-) - 80cos(-) - 48cos(-) )cot(x)sin(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 12 x 8 x 4 +--R (2cos(-) + 8cos(-) + 12cos(-) + 8cos(-) + 2)cot(x) +--R 2 2 2 2 +--R * +--R log(cos(x)) +--R + +--R x 16 x 2 x 14 +--R cot(x)sin(-) + 8cos(-) cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 12 +--R (28cos(-) + 4)cot(x)sin(-) +--R 2 2 +--R + +--R x 6 x 2 x 10 +--R (56cos(-) - 8cos(-) )cot(x)sin(-) +--R 2 2 2 +--R + +--R x 8 x 4 x 8 +--R (70cos(-) - 68cos(-) + 6)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (56cos(-) - 112cos(-) - 40cos(-) )cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (28cos(-) - 68cos(-) + 164cos(-) + 4)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 +--R (8cos(-) - 8cos(-) - 40cos(-) - 24cos(-) )cot(x)sin(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 12 x 8 x 4 +--R (cos(-) + 4cos(-) + 6cos(-) + 4cos(-) + 1)cot(x) +--R 2 2 2 2 +--R * +--R 2 +--R tan(x) +--R * +--R +---------+ +--R | 2 +--R \|- tan(x) +--R + +--R x 16 x 2 x 14 x 4 x 12 +--R 2sin(-) + 16cos(-) sin(-) + (56cos(-) + 8)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 +--R (112cos(-) - 16cos(-) )sin(-) +--R 2 2 2 +--R + +--R x 8 x 4 x 8 +--R (140cos(-) - 136cos(-) + 12)sin(-) +--R 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (112cos(-) - 224cos(-) - 80cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (56cos(-) - 136cos(-) + 328cos(-) + 8)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (16cos(-) - 16cos(-) - 80cos(-) - 48cos(-) )sin(-) + 2cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R 8cos(-) + 12cos(-) + 8cos(-) + 2 +--R 2 2 2 +--R * +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R + +--R x x 11 x 3 x 9 x 5 x 7 +--R - 16cos(-)sin(-) - 48cos(-) sin(-) - 32cos(-) sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 7 x 5 x 9 x x 3 +--R 32cos(-) sin(-) + (48cos(-) + 16cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R x 11 x 3 x +--R (16cos(-) - 16cos(-) )sin(-) +--R 2 2 2 +--R / +--R x 16 x 2 x 14 x 4 x 12 +--R 2sin(-) + 16cos(-) sin(-) + (56cos(-) + 8)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 x 8 x 4 x 8 +--R (112cos(-) - 16cos(-) )sin(-) + (140cos(-) - 136cos(-) + 12)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (112cos(-) - 224cos(-) - 80cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (56cos(-) - 136cos(-) + 328cos(-) + 8)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (16cos(-) - 16cos(-) - 80cos(-) - 48cos(-) )sin(-) + 2cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R 8cos(-) + 12cos(-) + 8cos(-) + 2 +--R 2 2 2 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 528 +d0323:= D(m0323,x) +--R +--R +--R (126) +--R x 30 x 2 x 28 +--R - 2cos(x)sin(-) + (- 30cos(-) + 4)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (- 210cos(-) + 48cos(-) - 6)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (- 910cos(-) + 260cos(-) - 38cos(-) + 8)cos(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (- 2730cos(-) + 832cos(-) - 20cos(-) - 80cos(-) - 18)cos(x) +--R 2 2 2 2 +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 6006cos(-) + 1716cos(-) + 572cos(-) - 320cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 586cos(-) + 28 +--R 2 +--R * +--R x 20 +--R cos(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 10010cos(-) + 2288cos(-) + 2750cos(-) + 1040cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 2722cos(-) - 1248cos(-) - 54 +--R 2 2 +--R * +--R x 18 +--R cos(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 12870cos(-) + 1716cos(-) + 6798cos(-) + 7624cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 1174cos(-) - 6348cos(-) + 978cos(-) + 80 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)sin(-) +--R 2 +--R + +--R x 16 x 12 x 10 x 8 +--R - 12870cos(-) + 10824cos(-) + 17888cos(-) - 14900cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 6080cos(-) + 3432cos(-) - 672cos(-) - 86 +--R 2 2 2 +--R * +--R x 14 +--R cos(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 10010cos(-) - 1716cos(-) + 11880cos(-) + 21952cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 39900cos(-) + 5016cos(-) + 9000cos(-) + 2656cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 262cos(-) + 92 +--R 2 +--R * +--R x 12 +--R cos(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 6006cos(-) - 2288cos(-) + 9174cos(-) + 14624cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 47740cos(-) + 1408cos(-) + 17388cos(-) - 8736cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 3214cos(-) + 304cos(-) - 66 +--R 2 2 +--R * +--R x 10 +--R cos(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 2730cos(-) - 1716cos(-) + 4950cos(-) + 4120cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 6 +--R - 29908cos(-) - 16152cos(-) + 19324cos(-) + 6942cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 4748cos(-) - 50cos(-) + 40 +--R 2 2 +--R * +--R x 8 +--R cos(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R - 910cos(-) - 832cos(-) + 1804cos(-) - 656cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 8346cos(-) - 12864cos(-) + 14408cos(-) + 8736cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 17346cos(-) - 6272cos(-) - 3924cos(-) - 144cos(-) - 22 +--R 2 2 2 2 +--R * +--R x 6 +--R cos(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 210cos(-) - 260cos(-) + 412cos(-) - 640cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 370cos(-) + 1036cos(-) + 8904cos(-) - 2656cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 3602cos(-) + 4532cos(-) + 6812cos(-) - 608cos(-) + 78cos(-) +--R 2 2 2 2 2 +--R + +--R 4 +--R * +--R x 4 +--R cos(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 22 x 20 +--R - 30cos(-) - 48cos(-) + 50cos(-) - 48cos(-) + 698cos(-) +--R 2 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 2400cos(-) + 3226cos(-) + 672cos(-) - 1242cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 1200cos(-) - 3658cos(-) + 528cos(-) + 190cos(-) - 2 +--R 2 2 2 2 +--R * +--R x 2 +--R cos(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R - 2cos(-) - 4cos(-) + 2cos(-) + 24cos(-) + 94cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 36cos(-) + 194cos(-) - 80cos(-) + 74cos(-) - 156cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R - 74cos(-) - 72cos(-) - 38cos(-) - 4cos(-) + 6cos(-) +--R 2 2 2 2 2 +--R * +--R cos(x) +--R * +--R +---------+ +--R | 2 +--R \|- tan(x) +--R + +--R x 30 x 2 x 28 +--R - 2cos(x)cot(x)sin(-) + (- 30cos(-) + 4)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (- 210cos(-) + 72cos(-) - 14)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (- 910cos(-) + 540cos(-) - 102cos(-) + 24)cos(x)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (- 2730cos(-) + 2320cos(-) - 228cos(-) + 192cos(-) - 42) +--R 2 2 2 2 +--R * +--R x 22 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 6006cos(-) + 6468cos(-) + 220cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 78cos(-) + 60 +--R 2 +--R * +--R x 20 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 10010cos(-) + 12408cos(-) + 2310cos(-) - 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 282cos(-) + 72cos(-) - 70 +--R 2 2 +--R * +--R x 18 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 12870cos(-) + 16764cos(-) + 5742cos(-) - 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 1422cos(-) - 1764cos(-) + 90cos(-) + 80 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 +--R - 12870cos(-) + 15840cos(-) + 7656cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 34176cos(-) + 4188cos(-) + 5856cos(-) + 744cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 192cos(-) - 70 +--R 2 +--R * +--R x 14 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 10010cos(-) + 9900cos(-) + 5544cos(-) - 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 10164cos(-) + 31608cos(-) - 1144cos(-) - 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 150cos(-) + 60 +--R 2 +--R * +--R x 12 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 6006cos(-) + 3256cos(-) + 990cos(-) - 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 16884cos(-) + 35376cos(-) - 13236cos(-) + 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 1410cos(-) - 168cos(-) - 42 +--R 2 2 +--R * +--R x 10 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 2730cos(-) - 396cos(-) - 2090cos(-) + 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 17052cos(-) + 3096cos(-) - 25812cos(-) - 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 9426cos(-) - 1452cos(-) + 30cos(-) + 24 +--R 2 2 2 +--R * +--R x 8 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R - 910cos(-) - 1008cos(-) - 2244cos(-) + 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 9582cos(-) - 11808cos(-) - 17080cos(-) + 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 39150cos(-) + 12432cos(-) + 1596cos(-) - 14 +--R 2 2 2 +--R * +--R x 6 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 210cos(-) - 500cos(-) - 1092cos(-) + 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 2298cos(-) - 2100cos(-) - 984cos(-) - 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 12222cos(-) - 8796cos(-) - 8100cos(-) - 912cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 42cos(-) + 4 +--R 2 +--R * +--R x 4 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R - 30cos(-) - 120cos(-) - 278cos(-) - 174cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1224cos(-) + 1482cos(-) + 2496cos(-) + 3158cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 1944cos(-) + 2382cos(-) + 576cos(-) + 630cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 24cos(-) - 2 +--R 2 +--R * +--R x 2 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 +--R - 2cos(-) - 12cos(-) - 30cos(-) - 72cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 138cos(-) - 180cos(-) - 310cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 390cos(-) - 180cos(-) - 282cos(-) - 72cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 110cos(-) - 12cos(-) - 18cos(-) +--R 2 2 2 +--R * +--R cos(x)cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R 2 x 30 +--R (2cos(x)cot(x) + 2cos(x))sin(-) +--R 2 +--R + +--R x 2 2 x 2 x 28 +--R ((30cos(-) - 4)cos(x)cot(x) + (30cos(-) - 4)cos(x))sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 +--R (210cos(-) - 72cos(-) + 14)cos(x)cot(x) +--R 2 2 +--R + +--R x 4 x 2 +--R (210cos(-) - 72cos(-) + 14)cos(x) +--R 2 2 +--R * +--R x 26 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 x 2 2 +--R (910cos(-) - 540cos(-) + 102cos(-) - 24)cos(x)cot(x) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (910cos(-) - 540cos(-) + 102cos(-) - 24)cos(x) +--R 2 2 2 +--R * +--R x 24 +--R sin(-) +--R 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 228cos(-) - 192cos(-) + 42) +--R 2 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 228cos(-) - 192cos(-) + 42) +--R 2 2 2 2 +--R * +--R cos(x) +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 6006cos(-) - 6468cos(-) - 220cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 78cos(-) - 60 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 10 x 8 x 6 x 4 +--R 6006cos(-) - 6468cos(-) - 220cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 78cos(-) - 60 +--R 2 +--R * +--R cos(x) +--R * +--R x 20 +--R sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) - 2310cos(-) + 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 282cos(-) - 72cos(-) + 70 +--R 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) - 2310cos(-) + 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 282cos(-) - 72cos(-) + 70 +--R 2 2 +--R * +--R cos(x) +--R * +--R x 18 +--R sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 +--R 12870cos(-) - 16764cos(-) - 5742cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 19320cos(-) - 1422cos(-) + 1764cos(-) - 90cos(-) - 80 +--R 2 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 14 x 12 x 10 +--R 12870cos(-) - 16764cos(-) - 5742cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 19320cos(-) - 1422cos(-) + 1764cos(-) - 90cos(-) - 80 +--R 2 2 2 2 +--R * +--R cos(x) +--R * +--R x 16 +--R sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 +--R 12870cos(-) - 15840cos(-) - 7656cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 34176cos(-) - 4188cos(-) - 5856cos(-) - 744cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 192cos(-) + 70 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 16 x 14 x 12 +--R 12870cos(-) - 15840cos(-) - 7656cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 34176cos(-) - 4188cos(-) - 5856cos(-) - 744cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 192cos(-) + 70 +--R 2 +--R * +--R cos(x) +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 +--R 10010cos(-) - 9900cos(-) - 5544cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R 32928cos(-) - 10164cos(-) - 31608cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 1144cos(-) + 1536cos(-) - 150cos(-) - 60 +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 18 x 16 x 14 +--R 10010cos(-) - 9900cos(-) - 5544cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R 32928cos(-) - 10164cos(-) - 31608cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 1144cos(-) + 1536cos(-) - 150cos(-) - 60 +--R 2 2 2 +--R * +--R cos(x) +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) - 990cos(-) + 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 +--R - 16884cos(-) - 35376cos(-) + 13236cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 9024cos(-) - 1410cos(-) + 168cos(-) + 42 +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) - 990cos(-) + 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 +--R - 16884cos(-) - 35376cos(-) + 13236cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 9024cos(-) - 1410cos(-) + 168cos(-) + 42 +--R 2 2 2 +--R * +--R cos(x) +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 2090cos(-) - 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 +--R - 17052cos(-) - 3096cos(-) + 25812cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 61920cos(-) + 9426cos(-) + 1452cos(-) - 30cos(-) - 24 +--R 2 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 2090cos(-) - 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 +--R - 17052cos(-) - 3096cos(-) + 25812cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 61920cos(-) + 9426cos(-) + 1452cos(-) - 30cos(-) - 24 +--R 2 2 2 2 +--R * +--R cos(x) +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 2244cos(-) - 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 +--R - 9582cos(-) + 11808cos(-) + 17080cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 +--R - 43968cos(-) - 39150cos(-) - 12432cos(-) +--R 2 2 2 +--R + +--R x 4 +--R - 1596cos(-) + 14 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 2244cos(-) - 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 +--R - 9582cos(-) + 11808cos(-) + 17080cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 +--R - 43968cos(-) - 39150cos(-) - 12432cos(-) +--R 2 2 2 +--R + +--R x 4 +--R - 1596cos(-) + 14 +--R 2 +--R * +--R cos(x) +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1092cos(-) - 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 2298cos(-) + 2100cos(-) + 984cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 12160cos(-) + 12222cos(-) + 8796cos(-) + 8100cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 912cos(-) + 42cos(-) - 4 +--R 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1092cos(-) - 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 2298cos(-) + 2100cos(-) + 984cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 12160cos(-) + 12222cos(-) + 8796cos(-) + 8100cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 912cos(-) + 42cos(-) - 4 +--R 2 2 +--R * +--R cos(x) +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R 30cos(-) + 120cos(-) + 278cos(-) + 174cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 1224cos(-) - 1482cos(-) - 2496cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 3158cos(-) - 1944cos(-) - 2382cos(-) - 576cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 630cos(-) - 24cos(-) + 2 +--R 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 28 x 26 x 24 x 20 +--R 30cos(-) + 120cos(-) + 278cos(-) + 174cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 1224cos(-) - 1482cos(-) - 2496cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 3158cos(-) - 1944cos(-) - 2382cos(-) - 576cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 630cos(-) - 24cos(-) + 2 +--R 2 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 +--R 2cos(-) + 12cos(-) + 30cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 138cos(-) + 180cos(-) + 310cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 390cos(-) + 180cos(-) + 282cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 110cos(-) + 12cos(-) + 18cos(-) +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 30 x 28 x 26 x 24 +--R 2cos(-) + 12cos(-) + 30cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 138cos(-) + 180cos(-) + 310cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 390cos(-) + 180cos(-) + 282cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 110cos(-) + 12cos(-) + 18cos(-) +--R 2 2 2 +--R * +--R cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R x 30 x 2 x 28 +--R - 2cos(x)cot(x)sin(-) + (- 30cos(-) + 4)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (- 210cos(-) + 72cos(-) - 14)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (- 910cos(-) + 540cos(-) - 102cos(-) + 24)cos(x)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (- 2730cos(-) + 2320cos(-) - 228cos(-) + 192cos(-) - 42) +--R 2 2 2 2 +--R * +--R x 22 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 6006cos(-) + 6468cos(-) + 220cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 78cos(-) + 60 +--R 2 +--R * +--R x 20 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 10010cos(-) + 12408cos(-) + 2310cos(-) - 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 282cos(-) + 72cos(-) - 70 +--R 2 2 +--R * +--R x 18 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 12870cos(-) + 16764cos(-) + 5742cos(-) - 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 1422cos(-) - 1764cos(-) + 90cos(-) + 80 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 +--R - 12870cos(-) + 15840cos(-) + 7656cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 34176cos(-) + 4188cos(-) + 5856cos(-) + 744cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 192cos(-) - 70 +--R 2 +--R * +--R x 14 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 10010cos(-) + 9900cos(-) + 5544cos(-) - 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 10164cos(-) + 31608cos(-) - 1144cos(-) - 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 150cos(-) + 60 +--R 2 +--R * +--R x 12 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 6006cos(-) + 3256cos(-) + 990cos(-) - 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 16884cos(-) + 35376cos(-) - 13236cos(-) + 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 1410cos(-) - 168cos(-) - 42 +--R 2 2 +--R * +--R x 10 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 2730cos(-) - 396cos(-) - 2090cos(-) + 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 17052cos(-) + 3096cos(-) - 25812cos(-) - 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 9426cos(-) - 1452cos(-) + 30cos(-) + 24 +--R 2 2 2 +--R * +--R x 8 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R - 910cos(-) - 1008cos(-) - 2244cos(-) + 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 9582cos(-) - 11808cos(-) - 17080cos(-) + 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 39150cos(-) + 12432cos(-) + 1596cos(-) - 14 +--R 2 2 2 +--R * +--R x 6 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 210cos(-) - 500cos(-) - 1092cos(-) + 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 2298cos(-) - 2100cos(-) - 984cos(-) - 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 12222cos(-) - 8796cos(-) - 8100cos(-) - 912cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 42cos(-) + 4 +--R 2 +--R * +--R x 4 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R - 30cos(-) - 120cos(-) - 278cos(-) - 174cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1224cos(-) + 1482cos(-) + 2496cos(-) + 3158cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 1944cos(-) + 2382cos(-) + 576cos(-) + 630cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 24cos(-) - 2 +--R 2 +--R * +--R x 2 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 +--R - 2cos(-) - 12cos(-) - 30cos(-) - 72cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 138cos(-) - 180cos(-) - 310cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 390cos(-) - 180cos(-) - 282cos(-) - 72cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 110cos(-) - 12cos(-) - 18cos(-) +--R 2 2 2 +--R * +--R cos(x)cot(x) +--R * +--R tan(x) +--R * +--R log(cos(x)) +--R + +--R x 30 x 2 x 28 +--R - 3cos(x)cot(x)sin(-) + (- 45cos(-) + 6)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (- 315cos(-) + 108cos(-) - 21)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (- 1365cos(-) + 810cos(-) - 153cos(-) + 36)cos(x)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (- 4095cos(-) + 3480cos(-) - 342cos(-) + 288cos(-) - 63)cos(x) +--R 2 2 2 2 +--R * +--R x 22 +--R cot(x)sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 9009cos(-) + 9702cos(-) + 330cos(-) - 360cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 117cos(-) + 90 +--R 2 +--R * +--R x 20 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 15015cos(-) + 18612cos(-) + 3465cos(-) - 8064cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 423cos(-) + 108cos(-) - 105 +--R 2 2 +--R * +--R x 18 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 19305cos(-) + 25146cos(-) + 8613cos(-) - 28980cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 2133cos(-) - 2646cos(-) + 135cos(-) + 120 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 19305cos(-) + 23760cos(-) + 11484cos(-) - 51264cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 6282cos(-) + 8784cos(-) + 1116cos(-) - 288cos(-) - 105 +--R 2 2 2 2 +--R * +--R x 14 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 15015cos(-) + 14850cos(-) + 8316cos(-) - 49392cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 15246cos(-) + 47412cos(-) - 1716cos(-) - 2304cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 225cos(-) + 90 +--R 2 +--R * +--R x 12 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 9009cos(-) + 4884cos(-) + 1485cos(-) - 21888cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 25326cos(-) + 53064cos(-) - 19854cos(-) + 13536cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 2115cos(-) - 252cos(-) - 63 +--R 2 2 +--R * +--R x 10 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 4095cos(-) - 594cos(-) - 3135cos(-) + 2556cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 25578cos(-) + 4644cos(-) - 38718cos(-) - 92880cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 14139cos(-) - 2178cos(-) + 45cos(-) + 36 +--R 2 2 2 +--R * +--R x 8 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R - 1365cos(-) - 1512cos(-) - 3366cos(-) + 7200cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 14373cos(-) - 17712cos(-) - 25620cos(-) + 65952cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 58725cos(-) + 18648cos(-) + 2394cos(-) - 21 +--R 2 2 2 +--R * +--R x 6 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 315cos(-) - 750cos(-) - 1638cos(-) + 2520cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 3447cos(-) - 3150cos(-) - 1476cos(-) - 18240cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 18333cos(-) - 13194cos(-) - 12150cos(-) - 1368cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 63cos(-) + 6 +--R 2 +--R * +--R x 4 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R - 45cos(-) - 180cos(-) - 417cos(-) - 261cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1836cos(-) + 2223cos(-) + 3744cos(-) + 4737cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 2916cos(-) + 3573cos(-) + 864cos(-) + 945cos(-) + 36cos(-) +--R 2 2 2 2 2 +--R + +--R - 3 +--R * +--R x 2 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R - 3cos(-) - 18cos(-) - 45cos(-) - 108cos(-) - 207cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 270cos(-) - 465cos(-) - 360cos(-) - 585cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 x 4 +--R - 270cos(-) - 423cos(-) - 108cos(-) - 165cos(-) - 18cos(-) +--R 2 2 2 2 2 +--R + +--R x 2 +--R - 27cos(-) +--R 2 +--R * +--R cos(x)cot(x) +--R * +--R 5 +--R tan(x) +--R + +--R 2 x 30 +--R (cos(x)cot(x) + cos(x))sin(-) +--R 2 +--R + +--R x 2 2 x 2 x 28 +--R ((15cos(-) - 2)cos(x)cot(x) + (15cos(-) - 2)cos(x))sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 +--R (105cos(-) - 36cos(-) + 7)cos(x)cot(x) +--R 2 2 +--R + +--R x 4 x 2 +--R (105cos(-) - 36cos(-) + 7)cos(x) +--R 2 2 +--R * +--R x 26 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 x 2 2 +--R (455cos(-) - 270cos(-) + 51cos(-) - 12)cos(x)cot(x) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (455cos(-) - 270cos(-) + 51cos(-) - 12)cos(x) +--R 2 2 2 +--R * +--R x 24 +--R sin(-) +--R 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (1365cos(-) - 1160cos(-) + 114cos(-) - 96cos(-) + 21)cos(x) +--R 2 2 2 2 +--R * +--R 2 +--R cot(x) +--R + +--R x 8 x 6 x 4 x 2 +--R (1365cos(-) - 1160cos(-) + 114cos(-) - 96cos(-) + 21)cos(x) +--R 2 2 2 2 +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 3003cos(-) - 3234cos(-) - 110cos(-) + 120cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 39cos(-) - 30 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 10 x 8 x 6 x 4 +--R 3003cos(-) - 3234cos(-) - 110cos(-) + 120cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 39cos(-) - 30 +--R 2 +--R * +--R cos(x) +--R * +--R x 20 +--R sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 5005cos(-) - 6204cos(-) - 1155cos(-) + 2688cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 141cos(-) - 36cos(-) + 35 +--R 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 12 x 10 x 8 x 6 +--R 5005cos(-) - 6204cos(-) - 1155cos(-) + 2688cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 141cos(-) - 36cos(-) + 35 +--R 2 2 +--R * +--R cos(x) +--R * +--R x 18 +--R sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 6435cos(-) - 8382cos(-) - 2871cos(-) + 9660cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 711cos(-) + 882cos(-) - 45cos(-) - 40 +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 14 x 12 x 10 x 8 +--R 6435cos(-) - 8382cos(-) - 2871cos(-) + 9660cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 711cos(-) + 882cos(-) - 45cos(-) - 40 +--R 2 2 2 +--R * +--R cos(x) +--R * +--R x 16 +--R sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 6435cos(-) - 7920cos(-) - 3828cos(-) + 17088cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 2094cos(-) - 2928cos(-) - 372cos(-) + 96cos(-) + 35 +--R 2 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 16 x 14 x 12 x 10 +--R 6435cos(-) - 7920cos(-) - 3828cos(-) + 17088cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 2094cos(-) - 2928cos(-) - 372cos(-) + 96cos(-) + 35 +--R 2 2 2 2 +--R * +--R cos(x) +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 5005cos(-) - 4950cos(-) - 2772cos(-) + 16464cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 5082cos(-) - 15804cos(-) + 572cos(-) + 768cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 75cos(-) - 30 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 18 x 16 x 14 x 12 +--R 5005cos(-) - 4950cos(-) - 2772cos(-) + 16464cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 5082cos(-) - 15804cos(-) + 572cos(-) + 768cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 75cos(-) - 30 +--R 2 +--R * +--R cos(x) +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 3003cos(-) - 1628cos(-) - 495cos(-) + 7296cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 8442cos(-) - 17688cos(-) + 6618cos(-) - 4512cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 705cos(-) + 84cos(-) + 21 +--R 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 20 x 18 x 16 x 14 +--R 3003cos(-) - 1628cos(-) - 495cos(-) + 7296cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 8442cos(-) - 17688cos(-) + 6618cos(-) - 4512cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 705cos(-) + 84cos(-) + 21 +--R 2 2 +--R * +--R cos(x) +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 1365cos(-) + 198cos(-) + 1045cos(-) - 852cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 8526cos(-) - 1548cos(-) + 12906cos(-) + 30960cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4713cos(-) + 726cos(-) - 15cos(-) - 12 +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 22 x 20 x 18 x 16 +--R 1365cos(-) + 198cos(-) + 1045cos(-) - 852cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 8526cos(-) - 1548cos(-) + 12906cos(-) + 30960cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 4713cos(-) + 726cos(-) - 15cos(-) - 12 +--R 2 2 2 +--R * +--R cos(x) +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 455cos(-) + 504cos(-) + 1122cos(-) - 2400cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 4791cos(-) + 5904cos(-) + 8540cos(-) - 21984cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R - 19575cos(-) - 6216cos(-) - 798cos(-) + 7 +--R 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 24 x 22 x 20 x 18 +--R 455cos(-) + 504cos(-) + 1122cos(-) - 2400cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 4791cos(-) + 5904cos(-) + 8540cos(-) - 21984cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R - 19575cos(-) - 6216cos(-) - 798cos(-) + 7 +--R 2 2 2 +--R * +--R cos(x) +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 105cos(-) + 250cos(-) + 546cos(-) - 840cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 1149cos(-) + 1050cos(-) + 492cos(-) + 6080cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 6111cos(-) + 4398cos(-) + 4050cos(-) + 456cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 21cos(-) - 2 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 26 x 24 x 22 x 20 +--R 105cos(-) + 250cos(-) + 546cos(-) - 840cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 1149cos(-) + 1050cos(-) + 492cos(-) + 6080cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 6111cos(-) + 4398cos(-) + 4050cos(-) + 456cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 21cos(-) - 2 +--R 2 +--R * +--R cos(x) +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R 15cos(-) + 60cos(-) + 139cos(-) + 87cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 612cos(-) - 741cos(-) - 1248cos(-) - 1579cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 972cos(-) - 1191cos(-) - 288cos(-) - 315cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 12cos(-) + 1 +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 28 x 26 x 24 x 20 +--R 15cos(-) + 60cos(-) + 139cos(-) + 87cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 612cos(-) - 741cos(-) - 1248cos(-) - 1579cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 972cos(-) - 1191cos(-) - 288cos(-) - 315cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 12cos(-) + 1 +--R 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R cos(-) + 6cos(-) + 15cos(-) + 36cos(-) + 69cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 90cos(-) + 155cos(-) + 120cos(-) + 195cos(-) + 90cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 141cos(-) + 36cos(-) + 55cos(-) + 6cos(-) + 9cos(-) +--R 2 2 2 2 2 +--R * +--R 2 +--R cos(x)cot(x) +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R cos(-) + 6cos(-) + 15cos(-) + 36cos(-) + 69cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 90cos(-) + 155cos(-) + 120cos(-) + 195cos(-) + 90cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 141cos(-) + 36cos(-) + 55cos(-) + 6cos(-) + 9cos(-) +--R 2 2 2 2 2 +--R * +--R cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R x 30 x 2 x 28 +--R - 3cos(x)cot(x)sin(-) + (- 45cos(-) + 6)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (- 315cos(-) + 108cos(-) - 21)cos(x)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (- 1365cos(-) + 810cos(-) - 153cos(-) + 36)cos(x)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (- 4095cos(-) + 3480cos(-) - 342cos(-) + 288cos(-) - 63)cos(x) +--R 2 2 2 2 +--R * +--R x 22 +--R cot(x)sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 9009cos(-) + 9702cos(-) + 330cos(-) - 360cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 117cos(-) + 90 +--R 2 +--R * +--R x 20 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 15015cos(-) + 18612cos(-) + 3465cos(-) - 8064cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 423cos(-) + 108cos(-) - 105 +--R 2 2 +--R * +--R x 18 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 19305cos(-) + 25146cos(-) + 8613cos(-) - 28980cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 2133cos(-) - 2646cos(-) + 135cos(-) + 120 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 19305cos(-) + 23760cos(-) + 11484cos(-) - 51264cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 6282cos(-) + 8784cos(-) + 1116cos(-) - 288cos(-) - 105 +--R 2 2 2 2 +--R * +--R x 14 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 15015cos(-) + 14850cos(-) + 8316cos(-) - 49392cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 15246cos(-) + 47412cos(-) - 1716cos(-) - 2304cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 225cos(-) + 90 +--R 2 +--R * +--R x 12 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 9009cos(-) + 4884cos(-) + 1485cos(-) - 21888cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 25326cos(-) + 53064cos(-) - 19854cos(-) + 13536cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 2115cos(-) - 252cos(-) - 63 +--R 2 2 +--R * +--R x 10 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R - 4095cos(-) - 594cos(-) - 3135cos(-) + 2556cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 25578cos(-) + 4644cos(-) - 38718cos(-) - 92880cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 14139cos(-) - 2178cos(-) + 45cos(-) + 36 +--R 2 2 2 +--R * +--R x 8 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R - 1365cos(-) - 1512cos(-) - 3366cos(-) + 7200cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 14373cos(-) - 17712cos(-) - 25620cos(-) + 65952cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 58725cos(-) + 18648cos(-) + 2394cos(-) - 21 +--R 2 2 2 +--R * +--R x 6 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 315cos(-) - 750cos(-) - 1638cos(-) + 2520cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 3447cos(-) - 3150cos(-) - 1476cos(-) - 18240cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 18333cos(-) - 13194cos(-) - 12150cos(-) - 1368cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 63cos(-) + 6 +--R 2 +--R * +--R x 4 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R - 45cos(-) - 180cos(-) - 417cos(-) - 261cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1836cos(-) + 2223cos(-) + 3744cos(-) + 4737cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 2916cos(-) + 3573cos(-) + 864cos(-) + 945cos(-) + 36cos(-) +--R 2 2 2 2 2 +--R + +--R - 3 +--R * +--R x 2 +--R cos(x)cot(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R - 3cos(-) - 18cos(-) - 45cos(-) - 108cos(-) - 207cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 +--R - 270cos(-) - 465cos(-) - 360cos(-) - 585cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 x 4 +--R - 270cos(-) - 423cos(-) - 108cos(-) - 165cos(-) - 18cos(-) +--R 2 2 2 2 2 +--R + +--R x 2 +--R - 27cos(-) +--R 2 +--R * +--R cos(x)cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R x 30 x 2 x 28 +--R 2cot(x)sin(-) + (30cos(-) - 4)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (210cos(-) - 72cos(-) + 14)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (910cos(-) - 540cos(-) + 102cos(-) - 24)cot(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 228cos(-) - 192cos(-) + 42)cot(x) +--R 2 2 2 2 +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 6006cos(-) - 6468cos(-) - 220cos(-) + 240cos(-) + 78cos(-) +--R 2 2 2 2 2 +--R + +--R - 60 +--R * +--R x 20 +--R cot(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) - 2310cos(-) + 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 282cos(-) - 72cos(-) + 70 +--R 2 2 +--R * +--R x 18 +--R cot(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 12870cos(-) - 16764cos(-) - 5742cos(-) + 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 1422cos(-) + 1764cos(-) - 90cos(-) - 80 +--R 2 2 2 +--R * +--R x 16 +--R cot(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 12870cos(-) - 15840cos(-) - 7656cos(-) + 34176cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 4188cos(-) - 5856cos(-) - 744cos(-) + 192cos(-) + 70 +--R 2 2 2 2 +--R * +--R x 14 +--R cot(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 10010cos(-) - 9900cos(-) - 5544cos(-) + 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 10164cos(-) - 31608cos(-) + 1144cos(-) + 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 150cos(-) - 60 +--R 2 +--R * +--R x 12 +--R cot(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) - 990cos(-) + 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 16884cos(-) - 35376cos(-) + 13236cos(-) - 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 1410cos(-) + 168cos(-) + 42 +--R 2 2 +--R * +--R x 10 +--R cot(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 2090cos(-) - 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 17052cos(-) - 3096cos(-) + 25812cos(-) + 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 9426cos(-) + 1452cos(-) - 30cos(-) - 24 +--R 2 2 2 +--R * +--R x 8 +--R cot(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 2244cos(-) - 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 9582cos(-) + 11808cos(-) + 17080cos(-) - 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R - 39150cos(-) - 12432cos(-) - 1596cos(-) + 14 +--R 2 2 2 +--R * +--R x 6 +--R cot(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1092cos(-) - 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 2298cos(-) + 2100cos(-) + 984cos(-) + 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 12222cos(-) + 8796cos(-) + 8100cos(-) + 912cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 42cos(-) - 4 +--R 2 +--R * +--R x 4 +--R cot(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R 30cos(-) + 120cos(-) + 278cos(-) + 174cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 1224cos(-) - 1482cos(-) - 2496cos(-) - 3158cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 1944cos(-) - 2382cos(-) - 576cos(-) - 630cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 24cos(-) + 2 +--R 2 +--R * +--R x 2 +--R cot(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R 2cos(-) + 12cos(-) + 30cos(-) + 72cos(-) + 138cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 180cos(-) + 310cos(-) + 240cos(-) + 390cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 x 4 +--R 180cos(-) + 282cos(-) + 72cos(-) + 110cos(-) + 12cos(-) +--R 2 2 2 2 2 +--R + +--R x 2 +--R 18cos(-) +--R 2 +--R * +--R cot(x) +--R * +--R 2 +--R sin(x)tan(x) +--R / +--R x 30 x 2 x 28 +--R 2cos(x)sin(-) + (30cos(-) - 4)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (210cos(-) - 72cos(-) + 14)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (910cos(-) - 540cos(-) + 102cos(-) - 24)cos(x)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 228cos(-) - 192cos(-) + 42)cos(x) +--R 2 2 2 2 +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 6006cos(-) - 6468cos(-) - 220cos(-) + 240cos(-) + 78cos(-) +--R 2 2 2 2 2 +--R + +--R - 60 +--R * +--R x 20 +--R cos(x)sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) - 2310cos(-) + 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 282cos(-) - 72cos(-) + 70 +--R 2 2 +--R * +--R x 18 +--R cos(x)sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 12870cos(-) - 16764cos(-) - 5742cos(-) + 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 1422cos(-) + 1764cos(-) - 90cos(-) - 80 +--R 2 2 2 +--R * +--R x 16 +--R cos(x)sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 12870cos(-) - 15840cos(-) - 7656cos(-) + 34176cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 4188cos(-) - 5856cos(-) - 744cos(-) + 192cos(-) + 70 +--R 2 2 2 2 +--R * +--R x 14 +--R cos(x)sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 10010cos(-) - 9900cos(-) - 5544cos(-) + 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 10164cos(-) - 31608cos(-) + 1144cos(-) + 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 150cos(-) - 60 +--R 2 +--R * +--R x 12 +--R cos(x)sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) - 990cos(-) + 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 16884cos(-) - 35376cos(-) + 13236cos(-) - 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 1410cos(-) + 168cos(-) + 42 +--R 2 2 +--R * +--R x 10 +--R cos(x)sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 2090cos(-) - 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R - 17052cos(-) - 3096cos(-) + 25812cos(-) + 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 9426cos(-) + 1452cos(-) - 30cos(-) - 24 +--R 2 2 2 +--R * +--R x 8 +--R cos(x)sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 2244cos(-) - 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 9582cos(-) + 11808cos(-) + 17080cos(-) - 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R - 39150cos(-) - 12432cos(-) - 1596cos(-) + 14 +--R 2 2 2 +--R * +--R x 6 +--R cos(x)sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1092cos(-) - 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 2298cos(-) + 2100cos(-) + 984cos(-) + 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 12222cos(-) + 8796cos(-) + 8100cos(-) + 912cos(-) + 42cos(-) +--R 2 2 2 2 2 +--R + +--R - 4 +--R * +--R x 4 +--R cos(x)sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 x 18 +--R 30cos(-) + 120cos(-) + 278cos(-) + 174cos(-) - 1224cos(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 1482cos(-) - 2496cos(-) - 3158cos(-) - 1944cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 2382cos(-) - 576cos(-) - 630cos(-) - 24cos(-) + 2 +--R 2 2 2 2 +--R * +--R x 2 +--R cos(x)sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R 2cos(-) + 12cos(-) + 30cos(-) + 72cos(-) + 138cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 180cos(-) + 310cos(-) + 240cos(-) + 390cos(-) + 180cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 282cos(-) + 72cos(-) + 110cos(-) + 12cos(-) + 18cos(-) +--R 2 2 2 2 2 +--R * +--R cos(x) +--R * +--R +---------+ +--R | 2 +--R \|- tan(x) +--R Type: Expression(Integer) +--E 128 + +--S 129 of 528 +t0324:= (-1+sec(x)^2)^(3/2) +--R +--R +--R +-----------+ +--R 2 | 2 +--R (127) (sec(x) - 1)\|sec(x) - 1 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 528 +r0324:= 1/2*cot(x)*(tan(x)^2)^(1/2)*(2*log(cos(x))+tan(x)^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (2cot(x)log(cos(x)) + cot(x)tan(x) )\|tan(x) +--R (128) ---------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 528 +a0324:= integrate(t0324,x) +--R +--R +--R 2 2 2 2cos(x) 2 +--R 2cos(x) log(----------) - 2cos(x) log(- ----------) + cos(x) - 1 +--R cos(x) + 1 cos(x) + 1 +--R (129) ----------------------------------------------------------------- +--R 2 +--R 2cos(x) +--R Type: Union(Expression(Integer),...) +--E 131 + +--S 132 of 528 +m0324:= a0324-r0324 +--R +--R +--R (130) +--R +-------+ +--R 2 2 2 | 2 +--R (- 2cos(x) cot(x)log(cos(x)) - cos(x) cot(x)tan(x) )\|tan(x) +--R + +--R 2 2 2 2cos(x) 2 +--R 2cos(x) log(----------) - 2cos(x) log(- ----------) + cos(x) - 1 +--R cos(x) + 1 cos(x) + 1 +--R / +--R 2 +--R 2cos(x) +--R Type: Expression(Integer) +--E 132 + +--S 133 of 528 +d0324:= D(m0324,x) +--R +--R +--R (131) +--R +-------+ +--R 2 | 2 +--R (2cos(x) - 2)sin(x)\|tan(x) +--R + +--R 3 3 3 2 3 2 +--R - 2cos(x) cot(x)tan(x) + (2cos(x) cot(x) + 2cos(x) )tan(x) +--R + +--R 3 +--R - 2cos(x) cot(x)tan(x) +--R * +--R log(cos(x)) +--R + +--R 3 5 3 2 3 4 +--R - 3cos(x) cot(x)tan(x) + (cos(x) cot(x) + cos(x) )tan(x) +--R + +--R 3 3 2 2 +--R - 3cos(x) cot(x)tan(x) + 2cos(x) cot(x)sin(x)tan(x) +--R / +--R +-------+ +--R 3 | 2 +--R 2cos(x) \|tan(x) +--R Type: Expression(Integer) +--E 133 + +--S 134 of 528 +t0325:= (-1-sec(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (132) (- sec(x) - 1)\|- sec(x) - 1 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 528 +r0325:= -2*atan(cot(x)*(-2-tan(x)^2)^(1/2))+_ + atanh(tan(x)/(-2-tan(x)^2)^(1/2))-1/2*tan(x)*(-2-tan(x)^2)^(1/2) +--R +--R +--R (133) +--R +-------------+ +--R tan(x) | 2 +--R 2atanh(----------------) - 4atan(cot(x)\|- tan(x) - 2 ) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +-------------+ +--R | 2 +--R - tan(x)\|- tan(x) - 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 135 + +--S 136 of 528 +a0325:= integrate(t0325,x) +--R +--R +--R (134) +--R +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) - 20\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 28\|- 1 (%e ) - 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) + 32\|- 1 (%e ) + 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R 64\|- 1 (%e ) + 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) + 2\|- 1 - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) - 5(%e ) - 7(%e ) - 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (%e ) + 8(%e ) + 18(%e ) + 16(%e ) + 5 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) + 20\|- 1 (%e ) + 28\|- 1 (%e ) +--R + +--R +---+ +--R 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) - 32\|- 1 (%e ) - 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 64\|- 1 (%e ) - 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 2\|- 1 - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R ((%e ) + 5(%e ) + 7(%e ) + 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) - 8(%e ) - 18(%e ) - 16(%e ) - 5 +--R * +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R + +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +---+ 4 +--R x\|- 1 | x\|- 1 x\|- 1 x\|- 1 +--R (- 8(%e ) - 8)\|(%e ) + 6(%e ) + 1 + 8(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 32(%e ) + 8 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (2(%e ) + 10(%e ) + 14(%e ) + 6) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - 2(%e ) - 16(%e ) - 36(%e ) - 32(%e ) - 10 +--R Type: Union(Expression(Integer),...) +--E 136 + +--S 137 of 528 +m0325:= a0325-r0325 +--R +--R +--R (135) +--R +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) - 20\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 28\|- 1 (%e ) - 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) + 32\|- 1 (%e ) + 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R 64\|- 1 (%e ) + 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) + 2\|- 1 - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) - 5(%e ) - 7(%e ) - 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (%e ) + 8(%e ) + 18(%e ) + 16(%e ) + 5 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) + 20\|- 1 (%e ) + 28\|- 1 (%e ) +--R + +--R +---+ +--R 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) - 32\|- 1 (%e ) - 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 64\|- 1 (%e ) - 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) + 6(%e ) + 1 - (%e ) - 2\|- 1 - 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R ((%e ) + 5(%e ) + 7(%e ) + 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) - 8(%e ) - 18(%e ) - 16(%e ) - 5 +--R * +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) - 2)\|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) + 8(%e ) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (- 2(%e ) - 10(%e ) - 14(%e ) - 6) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R 2(%e ) + 16(%e ) + 36(%e ) + 32(%e ) + 10 +--R * +--R tan(x) +--R atanh(----------------) +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (4(%e ) + 20(%e ) + 28(%e ) + 12) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - 4(%e ) - 32(%e ) - 72(%e ) - 64(%e ) - 20 +--R * +--R +-------------+ +--R | 2 +--R atan(cot(x)\|- tan(x) - 2 ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R ((%e ) + 5(%e ) + 7(%e ) + 3)tan(x) +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 2 +--R x\|- 1 +--R - 8(%e ) - 8 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) - 8(%e ) - 18(%e ) - 16(%e ) - 5) +--R * +--R +-------------+ +--R | 2 +--R tan(x)\|- tan(x) - 2 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 8(%e ) + 32(%e ) + 8 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (2(%e ) + 10(%e ) + 14(%e ) + 6) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - 2(%e ) - 16(%e ) - 36(%e ) - 32(%e ) - 10 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 528 +d0325:= D(m0325,x) +--R +--R +--R (136) +--R +---+ 18 +---+ 16 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R \|- 1 cot(x) (%e ) + 27\|- 1 cot(x) (%e ) +--R + +--R +---+ 14 +--R +---+ 2 x\|- 1 +--R 302\|- 1 cot(x) (%e ) +--R + +--R +---+ 12 +--R +---+ 2 x\|- 1 +--R 1806\|- 1 cot(x) (%e ) +--R + +--R +---+ 10 +--R +---+ 2 x\|- 1 +--R 6216\|- 1 cot(x) (%e ) +--R + +--R +---+ 8 +--R +---+ 2 x\|- 1 +--R 12348\|- 1 cot(x) (%e ) +--R + +--R +---+ 6 +--R +---+ 2 x\|- 1 +--R 13482\|- 1 cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R 7290\|- 1 cot(x) (%e ) + 1663\|- 1 cot(x) (%e ) +--R + +--R +---+ 2 +--R 129\|- 1 cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 18 +--R +---+ 2 +---+ x\|- 1 +--R (2\|- 1 cot(x) - \|- 1 )(%e ) +--R + +--R +---+ 16 +--R +---+ 2 +---+ x\|- 1 +--R (54\|- 1 cot(x) - 27\|- 1 )(%e ) +--R + +--R +---+ 14 +--R +---+ 2 +---+ x\|- 1 +--R (604\|- 1 cot(x) - 302\|- 1 )(%e ) +--R + +--R +---+ 12 +--R +---+ 2 +---+ x\|- 1 +--R (3612\|- 1 cot(x) - 1806\|- 1 )(%e ) +--R + +--R +---+ 10 +--R +---+ 2 +---+ x\|- 1 +--R (12432\|- 1 cot(x) - 6216\|- 1 )(%e ) +--R + +--R +---+ 8 +--R +---+ 2 +---+ x\|- 1 +--R (24696\|- 1 cot(x) - 12348\|- 1 )(%e ) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (26964\|- 1 cot(x) - 13482\|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (14580\|- 1 cot(x) - 7290\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +--R (3326\|- 1 cot(x) - 1663\|- 1 )(%e ) + 258\|- 1 cot(x) +--R + +--R +---+ +--R - 129\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R - cot(x) (%e ) - 21cot(x) (%e ) +--R + +--R +---+ 14 +---+ 12 +--R 2 x\|- 1 2 x\|- 1 +--R - 182cot(x) (%e ) - 850cot(x) (%e ) +--R + +--R +---+ 10 +---+ 8 +--R 2 x\|- 1 2 x\|- 1 +--R - 2352cot(x) (%e ) - 4004cot(x) (%e ) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R - 4210cot(x) (%e ) - 2646cot(x) (%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R - 903cot(x) (%e ) - 127cot(x) +--R * +--R 6 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R (- 4cot(x) + 1)(%e ) + (- 84cot(x) + 21)(%e ) +--R + +--R +---+ 14 +--R 2 x\|- 1 +--R (- 728cot(x) + 182)(%e ) +--R + +--R +---+ 12 +--R 2 x\|- 1 +--R (- 3400cot(x) + 850)(%e ) +--R + +--R +---+ 10 +--R 2 x\|- 1 +--R (- 9408cot(x) + 2352)(%e ) +--R + +--R +---+ 8 +--R 2 x\|- 1 +--R (- 16016cot(x) + 4004)(%e ) +--R + +--R +---+ 6 +--R 2 x\|- 1 +--R (- 16840cot(x) + 4210)(%e ) +--R + +--R +---+ 4 +--R 2 x\|- 1 +--R (- 10584cot(x) + 2646)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (- 3612cot(x) + 903)(%e ) - 508cot(x) + 127 +--R * +--R 4 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R x\|- 1 x\|- 1 +--R 2cot(x)(%e ) + 42cot(x)(%e ) +--R + +--R +---+ 14 +---+ 12 +--R x\|- 1 x\|- 1 +--R 364cot(x)(%e ) + 1700cot(x)(%e ) +--R + +--R +---+ 10 +---+ 8 +--R x\|- 1 x\|- 1 +--R 4704cot(x)(%e ) + 8008cot(x)(%e ) +--R + +--R +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 +--R 8420cot(x)(%e ) + 5292cot(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 1806cot(x)(%e ) + 254cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R - 8cot(x) (%e ) - 168cot(x) (%e ) +--R + +--R +---+ 14 +---+ 12 +--R 2 x\|- 1 2 x\|- 1 +--R - 1456cot(x) (%e ) - 6800cot(x) (%e ) +--R + +--R +---+ 10 +---+ 8 +--R 2 x\|- 1 2 x\|- 1 +--R - 18816cot(x) (%e ) - 32032cot(x) (%e ) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R - 33680cot(x) (%e ) - 21168cot(x) (%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R - 7224cot(x) (%e ) - 1016cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R x\|- 1 x\|- 1 +--R 2cot(x)(%e ) + 42cot(x)(%e ) +--R + +--R +---+ 14 +---+ 12 +--R x\|- 1 x\|- 1 +--R 364cot(x)(%e ) + 1700cot(x)(%e ) +--R + +--R +---+ 10 +---+ 8 +--R x\|- 1 x\|- 1 +--R 4704cot(x)(%e ) + 8008cot(x)(%e ) +--R + +--R +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 +--R 8420cot(x)(%e ) + 5292cot(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R 1806cot(x)(%e ) + 254cot(x) +--R * +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R (- 8cot(x) - 2)(%e ) + (- 168cot(x) - 42)(%e ) +--R + +--R +---+ 14 +--R 2 x\|- 1 +--R (- 1456cot(x) - 364)(%e ) +--R + +--R +---+ 12 +--R 2 x\|- 1 +--R (- 6800cot(x) - 1700)(%e ) +--R + +--R +---+ 10 +--R 2 x\|- 1 +--R (- 18816cot(x) - 4704)(%e ) +--R + +--R +---+ 8 +--R 2 x\|- 1 +--R (- 32032cot(x) - 8008)(%e ) +--R + +--R +---+ 6 +--R 2 x\|- 1 +--R (- 33680cot(x) - 8420)(%e ) +--R + +--R +---+ 4 +--R 2 x\|- 1 +--R (- 21168cot(x) - 5292)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (- 7224cot(x) - 1806)(%e ) - 1016cot(x) - 254 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 20 +---+ 18 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R - \|- 1 cot(x) (%e ) - 30\|- 1 cot(x) (%e ) +--R + +--R +---+ 16 +---+ 14 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R - 379\|- 1 cot(x) (%e ) - 2616\|- 1 cot(x) (%e ) +--R + +--R +---+ 12 +--R +---+ 2 x\|- 1 +--R - 10706\|- 1 cot(x) (%e ) +--R + +--R +---+ 10 +--R +---+ 2 x\|- 1 +--R - 26388\|- 1 cot(x) (%e ) +--R + +--R +---+ 8 +---+ 6 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R - 38118\|- 1 cot(x) (%e ) - 30168\|- 1 cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R +---+ 2 x\|- 1 +---+ 2 x\|- 1 +--R - 11789\|- 1 cot(x) (%e ) - 2046\|- 1 cot(x) (%e ) +--R + +--R +---+ 2 +--R - 127\|- 1 cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 20 +--R +---+ 2 +---+ x\|- 1 +--R (- 2\|- 1 cot(x) + \|- 1 )(%e ) +--R + +--R +---+ 18 +--R +---+ 2 +---+ x\|- 1 +--R (- 60\|- 1 cot(x) + 30\|- 1 )(%e ) +--R + +--R +---+ 16 +--R +---+ 2 +---+ x\|- 1 +--R (- 758\|- 1 cot(x) + 379\|- 1 )(%e ) +--R + +--R +---+ 14 +--R +---+ 2 +---+ x\|- 1 +--R (- 5232\|- 1 cot(x) + 2616\|- 1 )(%e ) +--R + +--R +---+ 12 +--R +---+ 2 +---+ x\|- 1 +--R (- 21412\|- 1 cot(x) + 10706\|- 1 )(%e ) +--R + +--R +---+ 10 +--R +---+ 2 +---+ x\|- 1 +--R (- 52776\|- 1 cot(x) + 26388\|- 1 )(%e ) +--R + +--R +---+ 8 +--R +---+ 2 +---+ x\|- 1 +--R (- 76236\|- 1 cot(x) + 38118\|- 1 )(%e ) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (- 60336\|- 1 cot(x) + 30168\|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (- 23578\|- 1 cot(x) + 11789\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +--R (- 4092\|- 1 cot(x) + 2046\|- 1 )(%e ) - 254\|- 1 cot(x) +--R + +--R +---+ +--R 127\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R cot(x) (%e ) + 24cot(x) (%e ) +--R + +--R +---+ 16 +---+ 14 +--R 2 x\|- 1 2 x\|- 1 +--R 241cot(x) (%e ) + 1324cot(x) (%e ) +--R + +--R +---+ 12 +---+ 10 +--R 2 x\|- 1 2 x\|- 1 +--R 4382cot(x) (%e ) + 9100cot(x) (%e ) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R 11998cot(x) (%e ) + 9908cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 +--R 4881cot(x) (%e ) + 1276cot(x) (%e ) + 129cot(x) +--R * +--R 6 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R (4cot(x) - 1)(%e ) + (96cot(x) - 24)(%e ) +--R + +--R +---+ 16 +---+ 14 +--R 2 x\|- 1 2 x\|- 1 +--R (964cot(x) - 241)(%e ) + (5296cot(x) - 1324)(%e ) +--R + +--R +---+ 12 +--R 2 x\|- 1 +--R (17528cot(x) - 4382)(%e ) +--R + +--R +---+ 10 +--R 2 x\|- 1 +--R (36400cot(x) - 9100)(%e ) +--R + +--R +---+ 8 +--R 2 x\|- 1 +--R (47992cot(x) - 11998)(%e ) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (39632cot(x) - 9908)(%e ) + (19524cot(x) - 4881)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (5104cot(x) - 1276)(%e ) + 516cot(x) - 129 +--R * +--R 4 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R x\|- 1 x\|- 1 +--R - 2cot(x)(%e ) - 48cot(x)(%e ) +--R + +--R +---+ 16 +---+ 14 +--R x\|- 1 x\|- 1 +--R - 482cot(x)(%e ) - 2648cot(x)(%e ) +--R + +--R +---+ 12 +---+ 10 +--R x\|- 1 x\|- 1 +--R - 8764cot(x)(%e ) - 18200cot(x)(%e ) +--R + +--R +---+ 8 +---+ 6 +--R x\|- 1 x\|- 1 +--R - 23996cot(x)(%e ) - 19816cot(x)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R - 9762cot(x)(%e ) - 2552cot(x)(%e ) - 258cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R 8cot(x) (%e ) + 192cot(x) (%e ) +--R + +--R +---+ 16 +---+ 14 +--R 2 x\|- 1 2 x\|- 1 +--R 1928cot(x) (%e ) + 10592cot(x) (%e ) +--R + +--R +---+ 12 +---+ 10 +--R 2 x\|- 1 2 x\|- 1 +--R 35056cot(x) (%e ) + 72800cot(x) (%e ) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R 95984cot(x) (%e ) + 79264cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 +--R 39048cot(x) (%e ) + 10208cot(x) (%e ) + 1032cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R x\|- 1 x\|- 1 +--R - 2cot(x)(%e ) - 48cot(x)(%e ) +--R + +--R +---+ 16 +---+ 14 +--R x\|- 1 x\|- 1 +--R - 482cot(x)(%e ) - 2648cot(x)(%e ) +--R + +--R +---+ 12 +---+ 10 +--R x\|- 1 x\|- 1 +--R - 8764cot(x)(%e ) - 18200cot(x)(%e ) +--R + +--R +---+ 8 +---+ 6 +--R x\|- 1 x\|- 1 +--R - 23996cot(x)(%e ) - 19816cot(x)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R - 9762cot(x)(%e ) - 2552cot(x)(%e ) - 258cot(x) +--R * +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R (8cot(x) + 2)(%e ) + (192cot(x) + 48)(%e ) +--R + +--R +---+ 16 +---+ 14 +--R 2 x\|- 1 2 x\|- 1 +--R (1928cot(x) + 482)(%e ) + (10592cot(x) + 2648)(%e ) +--R + +--R +---+ 12 +---+ 10 +--R 2 x\|- 1 2 x\|- 1 +--R (35056cot(x) + 8764)(%e ) + (72800cot(x) + 18200)(%e ) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (95984cot(x) + 23996)(%e ) + (79264cot(x) + 19816)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 +--R (39048cot(x) + 9762)(%e ) + (10208cot(x) + 2552)(%e ) +--R + +--R 2 +--R 1032cot(x) + 258 +--R / +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R cot(x) (%e ) + 21cot(x) (%e ) +--R + +--R +---+ 14 +---+ 12 +--R 2 x\|- 1 2 x\|- 1 +--R 182cot(x) (%e ) + 850cot(x) (%e ) +--R + +--R +---+ 10 +---+ 8 +--R 2 x\|- 1 2 x\|- 1 +--R 2352cot(x) (%e ) + 4004cot(x) (%e ) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R 4210cot(x) (%e ) + 2646cot(x) (%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R 903cot(x) (%e ) + 127cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R (2cot(x) - 1)(%e ) + (42cot(x) - 21)(%e ) +--R + +--R +---+ 14 +---+ 12 +--R 2 x\|- 1 2 x\|- 1 +--R (364cot(x) - 182)(%e ) + (1700cot(x) - 850)(%e ) +--R + +--R +---+ 10 +---+ 8 +--R 2 x\|- 1 2 x\|- 1 +--R (4704cot(x) - 2352)(%e ) + (8008cot(x) - 4004)(%e ) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (8420cot(x) - 4210)(%e ) + (5292cot(x) - 2646)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (1806cot(x) - 903)(%e ) + 254cot(x) - 127 +--R * +--R +--------------------------------+ +--R +-------------+ | +---+ 4 +---+ 2 +--R | 2 | x\|- 1 x\|- 1 +--R \|- tan(x) - 2 \|(%e ) + 6(%e ) + 1 +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R - cot(x) (%e ) - 24cot(x) (%e ) +--R + +--R +---+ 16 +---+ 14 +--R 2 x\|- 1 2 x\|- 1 +--R - 241cot(x) (%e ) - 1324cot(x) (%e ) +--R + +--R +---+ 12 +---+ 10 +--R 2 x\|- 1 2 x\|- 1 +--R - 4382cot(x) (%e ) - 9100cot(x) (%e ) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R - 11998cot(x) (%e ) - 9908cot(x) (%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 +--R - 4881cot(x) (%e ) - 1276cot(x) (%e ) - 129cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R (- 2cot(x) + 1)(%e ) + (- 48cot(x) + 24)(%e ) +--R + +--R +---+ 16 +--R 2 x\|- 1 +--R (- 482cot(x) + 241)(%e ) +--R + +--R +---+ 14 +--R 2 x\|- 1 +--R (- 2648cot(x) + 1324)(%e ) +--R + +--R +---+ 12 +--R 2 x\|- 1 +--R (- 8764cot(x) + 4382)(%e ) +--R + +--R +---+ 10 +--R 2 x\|- 1 +--R (- 18200cot(x) + 9100)(%e ) +--R + +--R +---+ 8 +--R 2 x\|- 1 +--R (- 23996cot(x) + 11998)(%e ) +--R + +--R +---+ 6 +--R 2 x\|- 1 +--R (- 19816cot(x) + 9908)(%e ) +--R + +--R +---+ 4 +--R 2 x\|- 1 +--R (- 9762cot(x) + 4881)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (- 2552cot(x) + 1276)(%e ) - 258cot(x) + 129 +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) - 2 +--R Type: Expression(Integer) +--E 138 + +--S 139 of 528 +t0326:= (a+b*sec(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (137) (b sec(x) + a)\|b sec(x) + a +--R Type: Expression(Integer) +--E 139 + +--S 140 of 528 +r0326:= a^(3/2)*atan(a^(1/2)*tan(x)/(a+b*sec(x)^2)^(1/2))+_ + 3/2*a*b^(1/2)*atanh(cot(x)*(a+b*sec(x)^2)^(1/2)/b^(1/2))+_ + 1/2*b^(3/2)*atanh(cot(x)*(a+b*sec(x)^2)^(1/2)/b^(1/2))+_ + 1/2*b*(a+b*sec(x)^2)^(1/2)*tan(x) +--R +--R +--R (138) +--R +-------------+ +--R | 2 +-+ +--R +-+ cot(x)\|b sec(x) + a +-+ tan(x)\|a +--R (b + 3a)\|b atanh(----------------------) + 2a\|a atan(----------------) +--R +-+ +-------------+ +--R \|b | 2 +--R \|b sec(x) + a +--R + +--R +-------------+ +--R | 2 +--R b tan(x)\|b sec(x) + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 140 + +--S 141 of 528 +a0326:= integrate(t0326,x) +--R +--R +--R (139) +--R [ +--R 2 6 2 5 +--R (4a b + 12a )cos(x) + (4a b + 12a )cos(x) +--R + +--R 2 4 2 3 +--R (2b + 6a b)cos(x) + (2b + 6a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ +-+ | 4a cos(x) + 4b +--R \|a \|b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a b)cos(x) +--R + +--R 3 2 2 +--R (- b - 3a b )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 9 4 8 3 7 +--R 128a cos(x) + 128a cos(x) + 256a b cos(x) +--R + +--R 3 6 2 2 5 2 2 4 +--R 256a b cos(x) + 160a b cos(x) + 160a b cos(x) +--R + +--R 3 3 3 2 4 4 +--R 32a b cos(x) + 32a b cos(x) + b cos(x) + b +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 4 10 3 4 9 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 8 +--R (- 96a b + 224a b)cos(x) +--R + +--R 2 2 3 7 +--R (- 96a b + 224a b)cos(x) +--R + +--R 3 2 2 6 +--R (- 40a b + 232a b )cos(x) +--R + +--R 3 2 2 5 4 3 4 +--R (- 40a b + 232a b )cos(x) + (- 4b + 84a b )cos(x) +--R + +--R 4 3 3 4 2 4 +--R (- 4b + 84a b )cos(x) + 8b cos(x) + 8b cos(x) +--R * +--R +-+ +--R \|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 7 2 2 5 +--R - 256a cos(x) - 640a b cos(x) - 544a b cos(x) +--R + +--R 3 3 4 +--R - 176a b cos(x) - 16b cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 8 +--R (128a b - 128a )cos(x) + (256a b - 512a b)cos(x) +--R + +--R 2 3 3 2 6 4 2 3 4 +--R (160a b - 672a b )cos(x) + (32a b - 352a b )cos(x) +--R + +--R 5 4 2 5 +--R (b - 65a b )cos(x) - 2b +--R / +--R 3 10 3 9 2 8 2 7 +--R 64a cos(x) + 64a cos(x) + 96a b cos(x) + 96a b cos(x) +--R + +--R 2 6 2 5 3 4 3 3 +--R 40a b cos(x) + 40a b cos(x) + 4b cos(x) + 4b cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 8 2 2 6 +--R - 128a cos(x) - 256a b cos(x) - 160a b cos(x) +--R + +--R 3 4 4 2 +--R - 32a b cos(x) - b cos(x) +--R + +--R 3 6 3 5 2 4 2 3 +--R (8a cos(x) + 8a cos(x) + 4a b cos(x) + 4a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (- 16a cos(x) - 16a b cos(x) - 2a b cos(x) )\|a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R 3 6 3 5 2 4 2 3 +--R (- 8a cos(x) - 8a cos(x) - 4a b cos(x) - 4a b cos(x) ) +--R * +--R sin(x) +--R atan(------) +--R cos(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a b cos(x) + 8a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R b cos(x) + b +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ sin(x) +--R (16a cos(x) + 16a b cos(x) + 2a b cos(x) )\|a atan(------) +--R cos(x) +--R + +--R 2 5 2 3 3 +-+ +--R (- 16a b cos(x) - 24a b cos(x) - 8b cos(x))sin(x)\|a +--R / +--R 6 5 4 3 +-+ +--R (16a cos(x) + 16a cos(x) + 8b cos(x) + 8b cos(x) )\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 4 2 2 +--R - 32a cos(x) - 32a b cos(x) - 4b cos(x) +--R , +--R +--R 3 6 3 5 2 4 2 3 +--R (8a cos(x) + 8a cos(x) + 4a b cos(x) + 4a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (- 16a cos(x) - 16a b cos(x) - 2a b cos(x) )\|a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R 2 6 2 5 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a )cos(x) +--R + +--R 2 4 2 3 +--R (- 4b - 12a b)cos(x) + (- 4b - 12a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +---+ +-+ | 4a cos(x) + 4b +--R \|- b \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (16a b + 48a )cos(x) + (16a b + 48a b)cos(x) +--R + +--R 3 2 2 +--R (2b + 6a b )cos(x) +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +---------------------+ +--R | 2 +--R +---+ | 4a cos(x) + 4b +--R (cos(x) + 1)sin(x)\|- b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +---------------------+ +--R | 2 +--R 2 +-+ | 4a cos(x) + 4b 2 +--R (cos(x) + cos(x))\|a |--------------------- - 2a cos(x) - 2b +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 3 5 2 4 2 3 +--R (- 8a cos(x) - 8a cos(x) - 4a b cos(x) - 4a b cos(x) ) +--R * +--R sin(x) +--R atan(------) +--R cos(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a b cos(x) + 8a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R b cos(x) + b +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ sin(x) +--R (16a cos(x) + 16a b cos(x) + 2a b cos(x) )\|a atan(------) +--R cos(x) +--R + +--R 2 5 2 3 3 +-+ +--R (- 16a b cos(x) - 24a b cos(x) - 8b cos(x))sin(x)\|a +--R / +--R 6 5 4 3 +-+ +--R (16a cos(x) + 16a cos(x) + 8b cos(x) + 8b cos(x) )\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 4 2 2 +--R - 32a cos(x) - 32a b cos(x) - 4b cos(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 141 + +--S 142 of 528 +m0326a:= a0326.1-r0326 +--R +--R +--R (140) +--R 2 6 2 5 2 4 +--R (4a b + 12a )cos(x) + (4a b + 12a )cos(x) + (2b + 6a b)cos(x) +--R + +--R 2 3 +--R (2b + 6a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ +-+ | 4a cos(x) + 4b +--R \|a \|b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a b)cos(x) +--R + +--R 3 2 2 +--R (- b - 3a b )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 9 4 8 3 7 +--R 128a cos(x) + 128a cos(x) + 256a b cos(x) +--R + +--R 3 6 2 2 5 2 2 4 +--R 256a b cos(x) + 160a b cos(x) + 160a b cos(x) +--R + +--R 3 3 3 2 4 4 +--R 32a b cos(x) + 32a b cos(x) + b cos(x) + b +--R * +--R +-+ +--R sin(x)\|b +--R + +--R 3 4 10 3 4 9 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 8 2 2 3 7 +--R (- 96a b + 224a b)cos(x) + (- 96a b + 224a b)cos(x) +--R + +--R 3 2 2 6 +--R (- 40a b + 232a b )cos(x) +--R + +--R 3 2 2 5 4 3 4 +--R (- 40a b + 232a b )cos(x) + (- 4b + 84a b )cos(x) +--R + +--R 4 3 3 4 2 4 +--R (- 4b + 84a b )cos(x) + 8b cos(x) + 8b cos(x) +--R * +--R +-+ +--R \|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 7 2 2 5 +--R - 256a cos(x) - 640a b cos(x) - 544a b cos(x) +--R + +--R 3 3 4 +--R - 176a b cos(x) - 16b cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 8 +--R (128a b - 128a )cos(x) + (256a b - 512a b)cos(x) +--R + +--R 2 3 3 2 6 4 2 3 4 +--R (160a b - 672a b )cos(x) + (32a b - 352a b )cos(x) +--R + +--R 5 4 2 5 +--R (b - 65a b )cos(x) - 2b +--R / +--R 3 10 3 9 2 8 2 7 +--R 64a cos(x) + 64a cos(x) + 96a b cos(x) + 96a b cos(x) +--R + +--R 2 6 2 5 3 4 3 3 +--R 40a b cos(x) + 40a b cos(x) + 4b cos(x) + 4b cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 8 2 2 6 +--R - 128a cos(x) - 256a b cos(x) - 160a b cos(x) +--R + +--R 3 4 4 2 +--R - 32a b cos(x) - b cos(x) +--R + +--R 2 6 2 5 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a )cos(x) +--R + +--R 2 4 2 3 +--R (- 4b - 12a b)cos(x) + (- 4b - 12a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ +-+ | 4a cos(x) + 4b +--R \|a \|b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (16a b + 48a )cos(x) + (16a b + 48a b)cos(x) +--R + +--R 3 2 2 +--R (2b + 6a b )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R +-------------+ +--R | 2 +--R cot(x)\|b sec(x) + a +--R atanh(----------------------) +--R +-+ +--R \|b +--R + +--R 3 6 3 5 2 4 2 3 +--R (8a cos(x) + 8a cos(x) + 4a b cos(x) + 4a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (- 16a cos(x) - 16a b cos(x) - 2a b cos(x) )\|a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R 3 6 3 5 2 4 2 3 +--R (- 16a cos(x) - 16a cos(x) - 8a b cos(x) - 8a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (32a cos(x) + 32a b cos(x) + 4a b cos(x) )\|a +--R * +--R +-+ +--R tan(x)\|a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 6 5 2 4 2 3 +-+ +--R (- 8a b cos(x) - 8a b cos(x) - 4b cos(x) - 4b cos(x) )tan(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 2 4 3 2 +--R (16a b cos(x) + 16a b cos(x) + 2b cos(x) )tan(x) +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 3 6 3 5 2 4 2 3 sin(x) +--R (- 8a cos(x) - 8a cos(x) - 4a b cos(x) - 4a b cos(x) )atan(------) +--R cos(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a b cos(x) + 8a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R b cos(x) + b +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ sin(x) +--R (16a cos(x) + 16a b cos(x) + 2a b cos(x) )\|a atan(------) +--R cos(x) +--R + +--R 2 5 2 3 3 +-+ +--R (- 16a b cos(x) - 24a b cos(x) - 8b cos(x))sin(x)\|a +--R / +--R 6 5 4 3 +-+ +--R (16a cos(x) + 16a cos(x) + 8b cos(x) + 8b cos(x) )\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 4 2 2 +--R - 32a cos(x) - 32a b cos(x) - 4b cos(x) +--R Type: Expression(Integer) +--E 142 + +--S 143 of 528 +--d0326a:= D(m0326a,x) +--E 143 + +--S 144 of 528 +m0326b:= a0326.2-r0326 +--R +--R +--R (141) +--R 2 6 2 5 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a )cos(x) +--R + +--R 2 4 2 3 +--R (- 4b - 12a b)cos(x) + (- 4b - 12a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +-+ +-+ | 4a cos(x) + 4b +--R \|a \|b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (16a b + 48a )cos(x) + (16a b + 48a b)cos(x) +--R + +--R 3 2 2 +--R (2b + 6a b )cos(x) +--R * +--R +-+ +--R \|b +--R * +--R +-------------+ +--R | 2 +--R cot(x)\|b sec(x) + a +--R atanh(----------------------) +--R +-+ +--R \|b +--R + +--R 3 6 3 5 2 4 2 3 +--R (8a cos(x) + 8a cos(x) + 4a b cos(x) + 4a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (- 16a cos(x) - 16a b cos(x) - 2a b cos(x) )\|a +--R * +--R atan +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (b - a)cos(x) + b - a)sin(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (- 6a b + 2a )cos(x))sin(x) +--R / +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (b - 3a)cos(x) + (b - 3a)cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R +-+ | 4a cos(x) + 4b +--R \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 +--R - 8a cos(x) + (- 6a b + 6a )cos(x) + 4a b +--R + +--R 2 6 2 5 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a )cos(x) +--R + +--R 2 4 2 3 +--R (- 4b - 12a b)cos(x) + (- 4b - 12a b)cos(x) +--R * +--R +---------------------+ +--R | 2 +--R +---+ +-+ | 4a cos(x) + 4b +--R \|- b \|a |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 4 +--R (16a b + 48a )cos(x) + (16a b + 48a b)cos(x) +--R + +--R 3 2 2 +--R (2b + 6a b )cos(x) +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +---------------------+ +--R | 2 +--R +---+ | 4a cos(x) + 4b +--R (cos(x) + 1)sin(x)\|- b |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +---------------------+ +--R | 2 +--R 2 +-+ | 4a cos(x) + 4b 2 +--R (cos(x) + cos(x))\|a |--------------------- - 2a cos(x) - 2b +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 3 5 2 4 2 3 +--R (- 16a cos(x) - 16a cos(x) - 8a b cos(x) - 8a b cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ +--R (32a cos(x) + 32a b cos(x) + 4a b cos(x) )\|a +--R * +--R +-+ +--R tan(x)\|a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 6 5 2 4 2 3 +-+ +--R (- 8a b cos(x) - 8a b cos(x) - 4b cos(x) - 4b cos(x) )tan(x)\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 2 4 3 2 +--R (16a b cos(x) + 16a b cos(x) + 2b cos(x) )tan(x) +--R * +--R +-------------+ +--R | 2 +--R \|b sec(x) + a +--R + +--R 3 6 3 5 2 4 2 3 sin(x) +--R (- 8a cos(x) - 8a cos(x) - 4a b cos(x) - 4a b cos(x) )atan(------) +--R cos(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a b cos(x) + 8a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R b cos(x) + b +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 4 2 2 +-+ sin(x) +--R (16a cos(x) + 16a b cos(x) + 2a b cos(x) )\|a atan(------) +--R cos(x) +--R + +--R 2 5 2 3 3 +-+ +--R (- 16a b cos(x) - 24a b cos(x) - 8b cos(x))sin(x)\|a +--R / +--R 6 5 4 3 +-+ +--R (16a cos(x) + 16a cos(x) + 8b cos(x) + 8b cos(x) )\|a +--R * +--R +---------------------+ +--R | 2 +--R | 4a cos(x) + 4b +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 6 4 2 2 +--R - 32a cos(x) - 32a b cos(x) - 4b cos(x) +--R Type: Expression(Integer) +--E 144 + +--S 145 of 528 +--d0326b:= D(m0326b,x) +--E 145 + +--S 146 of 528 +t0327:= x/sec(x)^(3/2)-1/3*x*sec(x)^(1/2) +--R +--R +--R 2 +--R - x sec(x) + 3x +--R (142) ---------------- +--R +------+ +--R 3sec(x)\|sec(x) +--R Type: Expression(Integer) +--E 146 + +--S 147 of 528 +r0327:= 2/9*(2*cos(x)+3*x*sin(x))/(1/cos(x))^(1/2) +--R +--R +--R 6x sin(x) + 4cos(x) +--R (143) ------------------- +--R +------+ +--R | 1 +--R 9 |------ +--R \|cos(x) +--R Type: Expression(Integer) +--E 147 + +--S 148 of 528 +a0327:= integrate(t0327,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 148 + +--S 149 of 528 +m0327:= a0327-r0327 +--R +--R +--R +------+ +--R | 1 +--R 9a0327 |------ - 6x sin(x) - 4cos(x) +--R \|cos(x) +--R (144) ------------------------------------- +--R +------+ +--R | 1 +--R 9 |------ +--R \|cos(x) +--R Type: Expression(Integer) +--E 149 + +--S 150 of 528 +d0327:= D(m0327,x) +--R +--R +--R 2 2 +--R x sin(x) - 2x cos(x) +--R (145) ---------------------- +--R +------+ +--R | 1 +--R 3cos(x) |------ +--R \|cos(x) +--R Type: Expression(Integer) +--E 150 + +--S 151 of 528 +t0328:= x/sec(x)^(5/2)-3/5*x/sec(x)^(1/2) +--R +--R +--R 2 +--R - 3x sec(x) + 5x +--R (146) ----------------- +--R 2 +------+ +--R 5sec(x) \|sec(x) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 528 +r0328:= 4/25/sec(x)^(5/2)+2/5*x*sin(x)/sec(x)^(3/2) +--R +--R +--R 10x sec(x)sin(x) + 4 +--R (147) -------------------- +--R 2 +------+ +--R 25sec(x) \|sec(x) +--R Type: Expression(Integer) +--E 152 + +--S 153 of 528 +a0328:= integrate(t0328,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 153 + +--S 154 of 528 +m0328:= a0328-r0328 +--R +--R +--R 2 +------+ +--R 25a0328 sec(x) \|sec(x) - 10x sec(x)sin(x) - 4 +--R (148) ----------------------------------------------- +--R 2 +------+ +--R 25sec(x) \|sec(x) +--R Type: Expression(Integer) +--E 154 + +--S 155 of 528 +d0328:= D(m0328,x) +--R +--R +--R (3x sec(x)sin(x) + 2)tan(x) - 2sec(x)sin(x) - 2x cos(x)sec(x) +--R (149) ------------------------------------------------------------- +--R 2 +------+ +--R 5sec(x) \|sec(x) +--R Type: Expression(Integer) +--E 155 + +--S 156 of 528 +t0329:= x/sec(x)^(7/2)-5/21*x*sec(x)^(1/2) +--R +--R +--R 4 +--R - 5x sec(x) + 21x +--R (150) ------------------ +--R 3 +------+ +--R 21sec(x) \|sec(x) +--R Type: Expression(Integer) +--E 156 + +--S 157 of 528 +r0329:= 2/441*(18*cos(x)^3+70*cos(x)+63*x*sin(x)*cos(x)^2+_ + 105*x*sin(x))/(1/cos(x))^(1/2) +--R +--R +--R 2 3 +--R (126x cos(x) + 210x)sin(x) + 36cos(x) + 140cos(x) +--R (151) --------------------------------------------------- +--R +------+ +--R | 1 +--R 441 |------ +--R \|cos(x) +--R Type: Expression(Integer) +--E 157 + +--S 158 of 528 +a0329:= integrate(t0329,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 158 + +--S 159 of 528 +m0329:= a0329-r0329 +--R +--R +--R (152) +--R +------+ +--R | 1 2 3 +--R 441a0329 |------ + (- 126x cos(x) - 210x)sin(x) - 36cos(x) - 140cos(x) +--R \|cos(x) +--R ------------------------------------------------------------------------- +--R +------+ +--R | 1 +--R 441 |------ +--R \|cos(x) +--R Type: Expression(Integer) +--E 159 + +--S 160 of 528 +d0329:= D(m0329,x) +--R +--R +--R 2 2 4 2 +--R (15x cos(x) + 5x)sin(x) - 6x cos(x) - 10x cos(x) +--R (153) ---------------------------------------------------- +--R +------+ +--R | 1 +--R 21cos(x) |------ +--R \|cos(x) +--R Type: Expression(Integer) +--E 160 + +--S 161 of 528 +t0330:= x^2/sec(x)^(3/2)-1/3*x^2*sec(x)^(1/2) +--R +--R +--R 2 2 2 +--R - x sec(x) + 3x +--R (154) ----------------- +--R +------+ +--R 3sec(x)\|sec(x) +--R Type: Expression(Integer) +--E 161 + +--S 162 of 528 +r0330:= 2/27*(12*x*cos(x)^(3/2)-8*EllipticF(1/2*x,2)-8*cos(x)^(1/2)*sin(x)+_ + 9*x^2*sin(x)*cos(x)^(1/2))/cos(x)^(1/2)/(1/cos(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 162 + +--S 163 of 528 +a0330:= integrate(t0330,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 163 + +--S 164 of 528 +m0330:= a0330-r0330 +--R +--R +--R (155) - r0330 + a0330 +--R Type: Polynomial(Integer) +--E 164 + +--S 165 of 528 +d0330:= D(m0330,x) +--R +--R +--R (156) 0 +--R Type: Polynomial(Integer) +--E 165 + +--S 166 of 528 +t0331:= sec(x^(1/2))/x^(1/2) +--R +--R +--R +-+ +--R sec(\|x ) +--R (157) --------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 166 + +--S 167 of 528 +r0331:= 2*atanh(sin(x^(1/2))) +--R +--R +--R +-+ +--R (158) 2atanh(sin(\|x )) +--R Type: Expression(Integer) +--E 167 + +--S 168 of 528 +a0331:= integrate(t0331,x) +--R +--R +--R +-+ +-+ +--R (159) log(sin(\|x ) + 1) - log(sin(\|x ) - 1) +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 528 +m0331:= a0331-r0331 +--R +--R +--R +-+ +-+ +-+ +--R (160) log(sin(\|x ) + 1) - log(sin(\|x ) - 1) - 2atanh(sin(\|x )) +--R Type: Expression(Integer) +--E 169 + +--S 170 of 528 +d0331:= D(m0331,x) +--R +--R +--R (161) 0 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 528 +t0332:= csc(a+b*x) +--R +--R +--R (162) csc(b x + a) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 528 +r0332:= -atanh(cos(a+b*x))/b +--R +--R +--R atanh(cos(b x + a)) +--R (163) - ------------------- +--R b +--R Type: Expression(Integer) +--E 172 + +--S 173 of 528 +a0332:= integrate(t0332,x) +--R +--R +--R sin(b x + a) +--R log(----------------) +--R cos(b x + a) + 1 +--R (164) --------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 528 +m0332:= a0332-r0332 +--R +--R +--R sin(b x + a) +--R log(----------------) + atanh(cos(b x + a)) +--R cos(b x + a) + 1 +--R (165) ------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 174 + +--S 175 of 528 +d0332:= D(m0332,x) +--R +--R +--R 2 3 +--R cos(b x + a)sin(b x + a) + cos(b x + a) - cos(b x + a) +--R (166) -------------------------------------------------------- +--R 2 +--R (cos(b x + a) - 1)sin(b x + a) +--R Type: Expression(Integer) +--E 175 + +--S 176 of 528 +t0333:= csc(a+b*x)^3 +--R +--R +--R 3 +--R (167) csc(b x + a) +--R Type: Expression(Integer) +--E 176 + +--S 177 of 528 +r0333:= -1/2*atanh(cos(a+b*x))/b-1/2*cot(a+b*x)*csc(a+b*x)/b +--R +--R +--R - atanh(cos(b x + a)) - cot(b x + a)csc(b x + a) +--R (168) ------------------------------------------------ +--R 2b +--R Type: Expression(Integer) +--E 177 + +--S 178 of 528 +a0333:= integrate(t0333,x) +--R +--R +--R 2 sin(b x + a) +--R (cos(b x + a) - 1)log(----------------) + cos(b x + a) +--R cos(b x + a) + 1 +--R (169) ------------------------------------------------------- +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 528 +m0333:= a0333-r0333 +--R +--R +--R (170) +--R 2 sin(b x + a) +--R (cos(b x + a) - 1)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 2 +--R (cos(b x + a) - 1)atanh(cos(b x + a)) +--R + +--R 2 +--R (cos(b x + a) - 1)cot(b x + a)csc(b x + a) + cos(b x + a) +--R / +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Expression(Integer) +--E 179 + +--S 180 of 528 +d0333:= D(m0333,x) +--R +--R +--R (171) +--R 3 2 2 +--R (cos(b x + a) + cos(b x + a) - cos(b x + a) + 1)sin(b x + a) +--R + +--R 4 2 2 4 +--R (- 2cos(b x + a) + 4cos(b x + a) - 2)cot(b x + a) - cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) - 1 +--R * +--R csc(b x + a)sin(b x + a) +--R + +--R 5 3 +--R cos(b x + a) - 2cos(b x + a) + cos(b x + a) +--R / +--R 4 2 +--R (2cos(b x + a) - 4cos(b x + a) + 2)sin(b x + a) +--R Type: Expression(Integer) +--E 180 + +--S 181 of 528 +t0334:= csc(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (172) \|csc(b x + a) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 528 +r0334:= 2*csc(a+b*x)^(1/2)*_ + EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 182 + +--S 183 of 528 +a0334:= integrate(t0334,x) +--R +--R +--R x +--R ++ +-------------+ +--R (173) | \|csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 528 +m0334:= a0334-r0334 +--R +--R +--R x +--R ++ +-------------+ +--R (174) | \|csc(%R b + a) d%R - r0334 +--R ++ +--R Type: Expression(Integer) +--E 184 + +--S 185 of 528 +d0334:= D(m0334,x) +--R +--R +--R +------------+ +--R (175) \|csc(b x + a) +--R Type: Expression(Integer) +--E 185 + +--S 186 of 528 +t0335:= csc(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (176) csc(b x + a)\|csc(b x + a) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 528 +r0335:= -2*(1/sin(a+b*x))^(1/2)*(cos(a+b*x)+_ + EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(1/2))/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 187 + +--S 188 of 528 +a0335:= integrate(t0335,x) +--R +--R +--R x +--R ++ +-------------+ +--R (177) | csc(%R b + a)\|csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 528 +m0335:= a0335-r0335 +--R +--R +--R x +--R ++ +-------------+ +--R (178) | csc(%R b + a)\|csc(%R b + a) d%R - r0335 +--R ++ +--R Type: Expression(Integer) +--E 189 + +--S 190 of 528 +d0335:= D(m0335,x) +--R +--R +--R +------------+ +--R (179) csc(b x + a)\|csc(b x + a) +--R Type: Expression(Integer) +--E 190 + +--S 191 of 528 +t0336:= csc(a+b*x)^(5/2) +--R +--R +--R 2 +------------+ +--R (180) csc(b x + a) \|csc(b x + a) +--R Type: Expression(Integer) +--E 191 + +--S 192 of 528 +r0336:= 2/3*(1/sin(a+b*x))^(1/2)*(-cos(a+b*x)+_ + EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(3/2))/b/sin(a+b*x) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 192 + +--S 193 of 528 +a0336:= integrate(t0336,x) +--R +--R +--R x +--R ++ 2 +-------------+ +--R (181) | csc(%R b + a) \|csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 528 +m0336:= a0336-r0336 +--R +--R +--R x +--R ++ 2 +-------------+ +--R (182) | csc(%R b + a) \|csc(%R b + a) d%R - r0336 +--R ++ +--R Type: Expression(Integer) +--E 194 + +--S 195 of 528 +d0336:= D(m0336,x) +--R +--R +--R 2 +------------+ +--R (183) csc(b x + a) \|csc(b x + a) +--R Type: Expression(Integer) +--E 195 + +--S 196 of 528 +t0337:= 1/csc(a+b*x)^(1/2) +--R +--R +--R 1 +--R (184) --------------- +--R +------------+ +--R \|csc(b x + a) +--R Type: Expression(Integer) +--E 196 + +--S 197 of 528 +r0337:= 2*csc(a+b*x)^(1/2)*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*_ + sin(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 197 + +--S 198 of 528 +a0337:= integrate(t0337,x) +--R +--R +--R x +--R ++ 1 +--R (185) | ---------------- d%R +--R ++ +-------------+ +--R \|csc(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 528 +m0337:= a0337-r0337 +--R +--R +--R x +--R ++ 1 +--R (186) | ---------------- d%R - r0337 +--R ++ +-------------+ +--R \|csc(%R b + a) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 528 +d0337:= D(m0337,x) +--R +--R +--R 1 +--R (187) --------------- +--R +------------+ +--R \|csc(b x + a) +--R Type: Expression(Integer) +--E 200 + +--S 201 of 528 +t0338:= 1/csc(a+b*x)^(3/2) +--R +--R +--R 1 +--R (188) --------------------------- +--R +------------+ +--R csc(b x + a)\|csc(b x + a) +--R Type: Expression(Integer) +--E 201 + +--S 202 of 528 +r0338:= 2/3*(-cos(a+b*x)*sin(a+b*x)^(1/2)+_ + EllipticF(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/_ + (1/sin(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 202 + +--S 203 of 528 +a0338:= integrate(t0338,x) +--R +--R +--R x +--R ++ 1 +--R (189) | ----------------------------- d%R +--R ++ +-------------+ +--R csc(%R b + a)\|csc(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 528 +m0338:= a0338-r0338 +--R +--R +--R x +--R ++ 1 +--R (190) | ----------------------------- d%R - r0338 +--R ++ +-------------+ +--R csc(%R b + a)\|csc(%R b + a) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 528 +d0338:= D(m0338,x) +--R +--R +--R 1 +--R (191) --------------------------- +--R +------------+ +--R csc(b x + a)\|csc(b x + a) +--R Type: Expression(Integer) +--E 205 + +--S 206 of 528 +t0339:= 1/csc(a+b*x)^(5/2) +--R +--R +--R 1 +--R (192) ---------------------------- +--R 2 +------------+ +--R csc(b x + a) \|csc(b x + a) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 528 +r0339:= 2/5*(-cos(a+b*x)*sin(a+b*x)^(3/2)+_ + 3*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2))/_ + sin(a+b*x)^(1/2)/(1/sin(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 207 + +--S 208 of 528 +a0339:= integrate(t0339,x) +--R +--R +--R x +--R ++ 1 +--R (193) | ------------------------------ d%R +--R ++ 2 +-------------+ +--R csc(%R b + a) \|csc(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 528 +m0339:= a0339-r0339 +--R +--R +--R x +--R ++ 1 +--R (194) | ------------------------------ d%R - r0339 +--R ++ 2 +-------------+ +--R csc(%R b + a) \|csc(%R b + a) +--R Type: Expression(Integer) +--E 209 + +--S 210 of 528 +d0339:= D(m0339,x) +--R +--R +--R 1 +--R (195) ---------------------------- +--R 2 +------------+ +--R csc(b x + a) \|csc(b x + a) +--R Type: Expression(Integer) +--E 210 + +--S 211 of 528 +t0340:= (c*csc(a+b*x))^(1/2) +--R +--R +--R +--------------+ +--R (196) \|c csc(b x + a) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 528 +r0340:= 2*(c*csc(a+b*x))^(1/2)*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)*_ + sin(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 212 + +--S 213 of 528 +a0340:= integrate(t0340,x) +--R +--R +--R x +--R ++ +---------------+ +--R (197) | \|c csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 528 +m0340:= a0340-r0340 +--R +--R +--R x +--R ++ +---------------+ +--R (198) | \|c csc(%R b + a) d%R - r0340 +--R ++ +--R Type: Expression(Integer) +--E 214 + +--S 215 of 528 +d0340:= D(m0340,x) +--R +--R +--R +--------------+ +--R (199) \|c csc(b x + a) +--R Type: Expression(Integer) +--E 215 + +--S 216 of 528 +t0341:= (c*csc(a+b*x))^(3/2) +--R +--R +--R +--------------+ +--R (200) c csc(b x + a)\|c csc(b x + a) +--R Type: Expression(Integer) +--E 216 + +--S 217 of 528 +r0341:= -2*c^2*(cos(a+b*x)+EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*_ + sin(a+b*x)^(1/2))/sin(a+b*x)/(c/sin(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 217 + +--S 218 of 528 +a0341:= integrate(t0341,x) +--R +--R +--R x +--R ++ +---------------+ +--R (201) | c csc(%R b + a)\|c csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 528 +m0341:= a0341-r0341 +--R +--R +--R x +--R ++ +---------------+ +--R (202) | c csc(%R b + a)\|c csc(%R b + a) d%R - r0341 +--R ++ +--R Type: Expression(Integer) +--E 219 + +--S 220 of 528 +d0341:= D(m0341,x) +--R +--R +--R +--------------+ +--R (203) c csc(b x + a)\|c csc(b x + a) +--R Type: Expression(Integer) +--E 220 + +--S 221 of 528 +t0342:= (c*csc(a+b*x))^(5/2) +--R +--R +--R 2 2 +--------------+ +--R (204) c csc(b x + a) \|c csc(b x + a) +--R Type: Expression(Integer) +--E 221 + +--S 222 of 528 +r0342:= 2/3*c^2*(c/sin(a+b*x))^(1/2)*(-cos(a+b*x)+_ + EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(3/2))/b/sin(a+b*x) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 222 + +--S 223 of 528 +a0342:= integrate(t0342,x) +--R +--R +--R x +--R ++ 2 2 +---------------+ +--R (205) | c csc(%R b + a) \|c csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 528 +m0342:= a0342-r0342 +--R +--R +--R x +--R ++ 2 2 +---------------+ +--R (206) | c csc(%R b + a) \|c csc(%R b + a) d%R - r0342 +--R ++ +--R Type: Expression(Integer) +--E 224 + +--S 225 of 528 +d0342:= D(m0342,x) +--R +--R +--R 2 2 +--------------+ +--R (207) c csc(b x + a) \|c csc(b x + a) +--R Type: Expression(Integer) +--E 225 + +--S 226 of 528 +t0343:= 1/(c*csc(a+b*x))^(1/2) +--R +--R +--R 1 +--R (208) ----------------- +--R +--------------+ +--R \|c csc(b x + a) +--R Type: Expression(Integer) +--E 226 + +--S 227 of 528 +r0343:= 2*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)/b/(c*csc(a+b*x))^(1/2)/_ + sin(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 528 +a0343:= integrate(t0343,x) +--R +--R +--R x +--R ++ 1 +--R (209) | ------------------ d%R +--R ++ +---------------+ +--R \|c csc(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 528 +m0343:= a0343-r0343 +--R +--R +--R x +--R ++ 1 +--R (210) | ------------------ d%R - r0343 +--R ++ +---------------+ +--R \|c csc(%R b + a) +--R Type: Expression(Integer) +--E 229 + +--S 230 of 528 +d0343:= D(m0343,x) +--R +--R +--R 1 +--R (211) ----------------- +--R +--------------+ +--R \|c csc(b x + a) +--R Type: Expression(Integer) +--E 230 + +--S 231 of 528 +t0344:= 1/(c*csc(a+b*x))^(3/2) +--R +--R +--R 1 +--R (212) ------------------------------- +--R +--------------+ +--R c csc(b x + a)\|c csc(b x + a) +--R Type: Expression(Integer) +--E 231 + +--S 232 of 528 +r0344:= 2/3/c*(-cos(a+b*x)*sin(a+b*x)^(1/2)+_ + EllipticF(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/_ + (c/sin(a+b*x))^(1/2)/b +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 232 + +--S 233 of 528 +a0344:= integrate(t0344,x) +--R +--R +--R x +--R ++ 1 +--R (213) | --------------------------------- d%R +--R ++ +---------------+ +--R c csc(%R b + a)\|c csc(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 528 +m0344:= a0344-r0344 +--R +--R +--R x +--R ++ 1 +--R (214) | --------------------------------- d%R - r0344 +--R ++ +---------------+ +--R c csc(%R b + a)\|c csc(%R b + a) +--R Type: Expression(Integer) +--E 234 + +--S 235 of 528 +d0344:= D(m0344,x) +--R +--R +--R 1 +--R (215) ------------------------------- +--R +--------------+ +--R c csc(b x + a)\|c csc(b x + a) +--R Type: Expression(Integer) +--E 235 + +--S 236 of 528 +t0345:= 1/(c*csc(a+b*x))^(5/2) +--R +--R +--R 1 +--R (216) -------------------------------- +--R 2 2 +--------------+ +--R c csc(b x + a) \|c csc(b x + a) +--R Type: Expression(Integer) +--E 236 + +--S 237 of 528 +r0345:= 2/5*(-cos(a+b*x)*sin(a+b*x)^(3/2)+_ + 3*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/_ + (c/sin(a+b*x))^(1/2)/b/c^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 528 +a0345:= integrate(t0345,x) +--R +--R +--R x +--R ++ 1 +--R (217) | ---------------------------------- d%R +--R ++ 2 2 +---------------+ +--R c csc(%R b + a) \|c csc(%R b + a) +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 528 +m0345:= a0345-r0345 +--R +--R +--R x +--R ++ 1 +--R (218) | ---------------------------------- d%R - r0345 +--R ++ 2 2 +---------------+ +--R c csc(%R b + a) \|c csc(%R b + a) +--R Type: Expression(Integer) +--E 239 + +--S 240 of 528 +d0345:= D(m0345,x) +--R +--R +--R 1 +--R (219) -------------------------------- +--R 2 2 +--------------+ +--R c csc(b x + a) \|c csc(b x + a) +--R Type: Expression(Integer) +--E 240 + +--S 241 of 528 +t0346:= x*csc(a+b*x) +--R +--R +--R (220) x csc(b x + a) +--R Type: Expression(Integer) +--E 241 + +--S 242 of 528 +r0346:= -(2*x*atanh(exp(%i*(a+b*x)))*b-%i*polylog(2,-exp(%i*(a+b*x)))+_ + %i*polylog(2,exp(%i*(a+b*x))))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 242 + +--S 243 of 528 +a0346:= integrate(t0346,x) +--R +--R +--R x +--R ++ +--R (221) | %R csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 528 +m0346:= a0346-r0346 +--R +--R +--R x +--R ++ +--R (222) | %R csc(%R b + a)d%R - r0346 +--R ++ +--R Type: Expression(Integer) +--E 244 + +--S 245 of 528 +d0346:= D(m0346,x) +--R +--R +--R (223) x csc(b x + a) +--R Type: Expression(Integer) +--E 245 + +--S 246 of 528 +t0347:= x^2*csc(a+b*x) +--R +--R +--R 2 +--R (224) x csc(b x + a) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 528 +r0347:= -2*(x^2*atanh(exp(%i*(a+b*x)))*b^2-%i*polylog(2,-exp(%i*(a+b*x)))*_ + x*b+%i*polylog(2,exp(%i*(a+b*x)))*x*b+polylog(3,-exp(%i*(a+b*x)))-_ + polylog(3,exp(%i*(a+b*x))))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 247 + +--S 248 of 528 +a0347:= integrate(t0347,x) +--R +--R +--R x +--R ++ 2 +--R (225) | %R csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 528 +m0347:= a0347-r0347 +--R +--R +--R x +--R ++ 2 +--R (226) | %R csc(%R b + a)d%R - r0347 +--R ++ +--R Type: Expression(Integer) +--E 249 + +--S 250 of 528 +d0347:= D(m0347,x) +--R +--R +--R 2 +--R (227) x csc(b x + a) +--R Type: Expression(Integer) +--E 250 + +--S 251 of 528 +t0348:= x^3*csc(a+b*x) +--R +--R +--R 3 +--R (228) x csc(b x + a) +--R Type: Expression(Integer) +--E 251 + +--S 252 of 528 +r0348:= -(2*x^3*atanh(exp(%i*(a+b*x)))*b^3-_ + 3*%i*polylog(2,-exp(%i*(a+b*x)))*x^2*b^2+_ + 3*%i*polylog(2,exp(%i*(a+b*x)))*x^2*b^2+_ + 6*polylog(3,-exp(%i*(a+b*x)))*x*b-_ + 6*polylog(3,exp(%i*(a+b*x)))*x*b+_ + 6*%i*polylog(4,-exp(%i*(a+b*x)))-_ + 6*%i*polylog(4,exp(%i*(a+b*x))))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 252 + +--S 253 of 528 +a0348:= integrate(t0348,x) +--R +--R +--R x +--R ++ 3 +--R (229) | %R csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 528 +m0348:= a0348-r0348 +--R +--R +--R x +--R ++ 3 +--R (230) | %R csc(%R b + a)d%R - r0348 +--R ++ +--R Type: Expression(Integer) +--E 254 + +--S 255 of 528 +d0348:= D(m0348,x) +--R +--R +--R 3 +--R (231) x csc(b x + a) +--R Type: Expression(Integer) +--E 255 + +--S 256 of 528 +t0349:= x^2*csc(a+b*x)^2 +--R +--R +--R 2 2 +--R (232) x csc(b x + a) +--R Type: Expression(Integer) +--E 256 + +--S 257 of 528 +r0349:= -(%i*x^2*b^2+x^2*cot(a+b*x)*b^2-_ + 2*x*log(1-exp(2*%i*(a+b*x)))*b+%i*polylog(2,exp(2*%i*(a+b*x))))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 257 + +--S 258 of 528 +a0349:= integrate(t0349,x) +--R +--R +--R x +--R ++ 2 2 +--R (233) | %R csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 528 +m0349:= a0349-r0349 +--R +--R +--R x +--R ++ 2 2 +--R (234) | %R csc(%R b + a) d%R - r0349 +--R ++ +--R Type: Expression(Integer) +--E 259 + +--S 260 of 528 +d0349:= D(m0349,x) +--R +--R +--R 2 2 +--R (235) x csc(b x + a) +--R Type: Expression(Integer) +--E 260 + +--S 261 of 528 +t0350:= x^3*csc(a+b*x)^2 +--R +--R +--R 3 2 +--R (236) x csc(b x + a) +--R Type: Expression(Integer) +--E 261 + +--S 262 of 528 +r0350:= -1/2*(2*%i*x^3*b^3+2*x^3*cot(a+b*x)*b^3-_ + 6*x^2*log(1-exp(2*%i*(a+b*x)))*b^2+_ + 6*%i*x*polylog(2,exp(2*%i*(a+b*x)))*b-_ + 3*polylog(3,exp(2*%i*(a+b*x))))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 262 + +--S 263 of 528 +a0350:= integrate(t0350,x) +--R +--R +--R x +--R ++ 3 2 +--R (237) | %R csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 528 +m0350:= a0350-r0350 +--R +--R +--R x +--R ++ 3 2 +--R (238) | %R csc(%R b + a) d%R - r0350 +--R ++ +--R Type: Expression(Integer) +--E 264 + +--S 265 of 528 +d0350:= D(m0350,x) +--R +--R +--R 3 2 +--R (239) x csc(b x + a) +--R Type: Expression(Integer) +--E 265 + +--S 266 of 528 +t0351:= x*csc(a+b*x)^3 +--R +--R +--R 3 +--R (240) x csc(b x + a) +--R Type: Expression(Integer) +--E 266 + +--S 267 of 528 +r0351:= -x*atanh(exp(1)^(%i*b*x+%i*a))/b-1/2*csc(a+b*x)/b^2-_ + 1/2*x*cot(a+b*x)*csc(a+b*x)/b+_ + 1/2*%i*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-_ + 1/2*%i*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 528 +a0351:= integrate(t0351,x) +--R +--R +--R x +--R ++ 3 +--R (241) | %R csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 528 +m0351:= a0351-r0351 +--R +--R +--R x +--R ++ 3 +--R (242) | %R csc(%R b + a) d%R - r0351 +--R ++ +--R Type: Expression(Integer) +--E 269 + +--S 270 of 528 +d0351:= D(m0351,x) +--R +--R +--R 3 +--R (243) x csc(b x + a) +--R Type: Expression(Integer) +--E 270 + +--S 271 of 528 +t0352:= x^2*csc(a+b*x)^3 +--R +--R +--R 2 3 +--R (244) x csc(b x + a) +--R Type: Expression(Integer) +--E 271 + +--S 272 of 528 +r0352:= -x^2*atanh(exp(1)^(%i*b*x+%i*a))/b-atanh(cos(a+b*x))/b^3-_ + x*csc(a+b*x)/b^2-1/2*x^2*cot(a+b*x)*csc(a+b*x)/b+_ + %i*x*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-_ + %i*x*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2-_ + polylog(3,-exp(1)^(%i*b*x+%i*a))/b^3+_ + polylog(3,exp(1)^(%i*b*x+%i*a))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 272 + +--S 273 of 528 +a0352:= integrate(t0352,x) +--R +--R +--R x +--R ++ 2 3 +--R (245) | %R csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 528 +m0352:= a0352-r0352 +--R +--R +--R x +--R ++ 2 3 +--R (246) | %R csc(%R b + a) d%R - r0352 +--R ++ +--R Type: Expression(Integer) +--E 274 + +--S 275 of 528 +d0352:= D(m0352,x) +--R +--R +--R 2 3 +--R (247) x csc(b x + a) +--R Type: Expression(Integer) +--E 275 + +--S 276 of 528 +t0353:= (c+d*x)*csc(a+b*x) +--R +--R +--R (248) (d x + c)csc(b x + a) +--R Type: Expression(Integer) +--E 276 + +--S 277 of 528 +r0353:= (-2*atanh(exp(%i*(a+b*x)))*c*b-2*atanh(exp(%i*(a+b*x)))*d*x*b+_ + %i*d*polylog(2,-exp(%i*(a+b*x)))-%i*d*polylog(2,exp(%i*(a+b*x))))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 277 + +--S 278 of 528 +a0353:= integrate(t0353,x) +--R +--R +--R x +--R ++ +--R (249) | (%R d + c)csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 528 +m0353:= a0353-r0353 +--R +--R +--R x +--R ++ +--R (250) | (%R d + c)csc(%R b + a)d%R - r0353 +--R ++ +--R Type: Expression(Integer) +--E 279 + +--S 280 of 528 +d0353:= D(m0353,x) +--R +--R +--R (251) (d x + c)csc(b x + a) +--R Type: Expression(Integer) +--E 280 + +--S 281 of 528 +t0354:= (c+d*x)^2*csc(a+b*x) +--R +--R +--R 2 2 2 +--R (252) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression(Integer) +--E 281 + +--S 282 of 528 +r0354:= -2*(c+d*x)^2*atanh(exp(1)^(%i*b*x+%i*a))/b+_ + 2*%i*d*(c+d*x)*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-_ + 2*%i*d*(c+d*x)*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2-_ + 2*d^2*polylog(3,-exp(1)^(%i*b*x+%i*a))/b^3+_ + 2*d^2*polylog(3,exp(1)^(%i*b*x+%i*a))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 528 +a0354:= integrate(t0354,x) +--R +--R +--R x +--R ++ 2 2 2 +--R (253) | (%R d + 2%R c d + c )csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 528 +m0354:= a0354-r0354 +--R +--R +--R x +--R ++ 2 2 2 +--R (254) | (%R d + 2%R c d + c )csc(%R b + a)d%R - r0354 +--R ++ +--R Type: Expression(Integer) +--E 284 + +--S 285 of 528 +d0354:= D(m0354,x) +--R +--R +--R 2 2 2 +--R (255) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression(Integer) +--E 285 + +--S 286 of 528 +t0355:= (c+d*x)^3*csc(a+b*x) +--R +--R +--R 3 3 2 2 2 3 +--R (256) (d x + 3c d x + 3c d x + c )csc(b x + a) +--R Type: Expression(Integer) +--E 286 + +--S 287 of 528 +r0355:= -2*(c+d*x)^3*atanh(exp(1)^(%i*b*x+%i*a))/b+_ + 3*%i*d*(c+d*x)^2*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-_ + 3*%i*d*(c+d*x)^2*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2-_ + 6*d^2*(c+d*x)*polylog(3,-exp(1)^(%i*b*x+%i*a))/b^3+_ + 6*d^2*(c+d*x)*polylog(3,exp(1)^(%i*b*x+%i*a))/b^3-_ + 6*%i*d^3*polylog(4,-exp(1)^(%i*b*x+%i*a))/b^4+_ + 6*%i*d^3*polylog(4,exp(1)^(%i*b*x+%i*a))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 287 + +--S 288 of 528 +a0355:= integrate(t0355,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 +--R (257) | (%R d + 3%R c d + 3%R c d + c )csc(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 528 +m0355:= a0355-r0355 +--R +--R +--R x +--R ++ 3 3 2 2 2 3 +--R (258) | (%R d + 3%R c d + 3%R c d + c )csc(%R b + a)d%R - r0355 +--R ++ +--R Type: Expression(Integer) +--E 289 + +--S 290 of 528 +d0355:= D(m0355,x) +--R +--R +--R 3 3 2 2 2 3 +--R (259) (d x + 3c d x + 3c d x + c )csc(b x + a) +--R Type: Expression(Integer) +--E 290 + +--S 291 of 528 +t0356:= (c+d*x)^2*csc(a+b*x)^2 +--R +--R +--R 2 2 2 2 +--R (260) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression(Integer) +--E 291 + +--S 292 of 528 +r0356:= -%i*(c+d*x)^2/b-(c+d*x)^2*cot(a+b*x)/b+_ + 2*d*(c+d*x)*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b^2-_ + %i*d^2*polylog(2,exp(1)^(2*%i*a+2*%i*b*x))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 292 + +--S 293 of 528 +a0356:= integrate(t0356,x) +--R +--R +--R x +--R ++ 2 2 2 2 +--R (261) | (%R d + 2%R c d + c )csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 528 +m0356:= a0356-r0356 +--R +--R +--R x +--R ++ 2 2 2 2 +--R (262) | (%R d + 2%R c d + c )csc(%R b + a) d%R - r0356 +--R ++ +--R Type: Expression(Integer) +--E 294 + +--S 295 of 528 +d0356:= D(m0356,x) +--R +--R +--R 2 2 2 2 +--R (263) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression(Integer) +--E 295 + +--S 296 of 528 +t0357:= (c+d*x)^3*csc(a+b*x)^2 +--R +--R +--R 3 3 2 2 2 3 2 +--R (264) (d x + 3c d x + 3c d x + c )csc(b x + a) +--R Type: Expression(Integer) +--E 296 + +--S 297 of 528 +r0357:= -%i*(c+d*x)^3/b-(c+d*x)^3*cot(a+b*x)/b+_ + 3*d*(c+d*x)^2*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b^2-_ + 3*%i*d^2*(c+d*x)*polylog(2,exp(1)^(2*%i*a+2*%i*b*x))/b^3+_ + 3/2*d^3*polylog(3,exp(1)^(2*%i*a+2*%i*b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 297 + +--S 298 of 528 +a0357:= integrate(t0357,x) +--R +--R +--R x +--R ++ 3 3 2 2 2 3 2 +--R (265) | (%R d + 3%R c d + 3%R c d + c )csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 528 +m0357:= a0357-r0357 +--R +--R +--R x +--R ++ 3 3 2 2 2 3 2 +--R (266) | (%R d + 3%R c d + 3%R c d + c )csc(%R b + a) d%R - r0357 +--R ++ +--R Type: Expression(Integer) +--E 299 + +--S 300 of 528 +d0357:= D(m0357,x) +--R +--R +--R 3 3 2 2 2 3 2 +--R (267) (d x + 3c d x + 3c d x + c )csc(b x + a) +--R Type: Expression(Integer) +--E 300 + +--S 301 of 528 +t0358:= (c+d*x)*csc(a+b*x)^3 +--R +--R +--R 3 +--R (268) (d x + c)csc(b x + a) +--R Type: Expression(Integer) +--E 301 + +--S 302 of 528 +r0358:= -(c+d*x)*atanh(exp(1)^(%i*b*x+%i*a))/b-1/2*d*csc(a+b*x)/b^2-_ + 1/2*(c+d*x)*cot(a+b*x)*csc(a+b*x)/b+_ + 1/2*%i*d*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-_ + 1/2*%i*d*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 302 + +--S 303 of 528 +a0358:= integrate(t0358,x) +--R +--R +--R x +--R ++ 3 +--R (269) | (%R d + c)csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 528 +m0358:= a0358-r0358 +--R +--R +--R x +--R ++ 3 +--R (270) | (%R d + c)csc(%R b + a) d%R - r0358 +--R ++ +--R Type: Expression(Integer) +--E 304 + +--S 305 of 528 +d0358:= D(m0358,x) +--R +--R +--R 3 +--R (271) (d x + c)csc(b x + a) +--R Type: Expression(Integer) +--E 305 + +--S 306 of 528 +t0359:= (c+d*x)^2*csc(a+b*x)^3 +--R +--R +--R 2 2 2 3 +--R (272) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression(Integer) +--E 306 + +--S 307 of 528 +r0359:= -(c+d*x)^2*atanh(exp(1)^(%i*b*x+%i*a))/b-d^2*atanh(cos(a+b*x))/b^3-_ + d*(c+d*x)*csc(a+b*x)/b^2-1/2*(c+d*x)^2*cot(a+b*x)*csc(a+b*x)/b+_ + %i*d*(c+d*x)*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^2-_ + %i*d*(c+d*x)*polylog(2,exp(1)^(%i*b*x+%i*a))/b^2-_ + d^2*polylog(3,-exp(1)^(%i*b*x+%i*a))/b^3+_ + d^2*polylog(3,exp(1)^(%i*b*x+%i*a))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 307 + +--S 308 of 528 +a0359:= integrate(t0359,x) +--R +--R +--R x +--R ++ 2 2 2 3 +--R (273) | (%R d + 2%R c d + c )csc(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 528 +m0359:= a0359-r0359 +--R +--R +--R x +--R ++ 2 2 2 3 +--R (274) | (%R d + 2%R c d + c )csc(%R b + a) d%R - r0359 +--R ++ +--R Type: Expression(Integer) +--E 309 + +--S 310 of 528 +d0359:= D(m0359,x) +--R +--R +--R 2 2 2 3 +--R (275) (d x + 2c d x + c )csc(b x + a) +--R Type: Expression(Integer) +--E 310 + +--S 311 of 528 +t0360:= (csc(x)^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 +--R (276) \|csc(x) +--R Type: Expression(Integer) +--E 311 + +--S 312 of 528 +r0360:= -acsch(tan(x)) +--R +--R +--R (277) - acsch(tan(x)) +--R Type: Expression(Integer) +--E 312 + +--S 313 of 528 +a0360:= integrate(t0360,x) +--R +--R +--R sin(x) +--R (278) log(----------) +--R cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 528 +m0360:= a0360-r0360 +--R +--R +--R sin(x) +--R (279) log(----------) + acsch(tan(x)) +--R cos(x) + 1 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 528 +d0360:= D(m0360,x) +--R +--R +--R (280) +--R +-----------+ +--R 2 2 | 2 +--R (sin(x) + cos(x) + cos(x))tan(x)\|tan(x) + 1 +--R + +--R 2 +--R (- cos(x) - 1)sin(x)tan(x) + (- cos(x) - 1)sin(x) +--R / +--R +-----------+ +--R | 2 +--R (cos(x) + 1)sin(x)tan(x)\|tan(x) + 1 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 528 +t0361:= (a*csc(x)^2)^(1/2) +--R +--R +--R +---------+ +--R | 2 +--R (281) \|a csc(x) +--R Type: Expression(Integer) +--E 316 + +--S 317 of 528 +r0361:= -atanh(cos(x))*(a*csc(x)^2)^(1/2)*sin(x) +--R +--R +--R +---------+ +--R | 2 +--R (282) - sin(x)atanh(cos(x))\|a csc(x) +--R Type: Expression(Integer) +--E 317 + +--S 318 of 528 +a0361:= integrate(t0361,x) +--R +--R +--R +-+ sin(x) +--R (283) \|a log(----------) +--R cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 528 +m0361:= a0361-r0361 +--R +--R +--R +---------+ +--R | 2 +-+ sin(x) +--R (284) sin(x)atanh(cos(x))\|a csc(x) + \|a log(----------) +--R cos(x) + 1 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 528 +d0361:= D(m0361,x) +--R +--R +--R (285) +--R +---------+ +--R 2 3 +-+ | 2 +--R ((cos(x) - 1)sin(x) + cos(x) - cos(x))\|a \|a csc(x) +--R + +--R 2 2 2 +--R (- a cos(x) + a)cot(x)csc(x) sin(x) +--R + +--R 3 2 +--R (a cos(x) - a cos(x))csc(x) sin(x) +--R * +--R atanh(cos(x)) +--R + +--R 2 3 +--R a csc(x) sin(x) +--R / +--R +---------+ +--R 2 | 2 +--R (cos(x) - 1)sin(x)\|a csc(x) +--R Type: Expression(Integer) +--E 320 + +--S 321 of 528 +t0362:= (a*csc(x)^3)^(1/2) +--R +--R +--R +---------+ +--R | 3 +--R (286) \|a csc(x) +--R Type: Expression(Integer) +--E 321 + +--S 322 of 528 +r0362:= -2*(a*csc(x)^3)^(1/2)*(cos(x)+_ + EllipticE(-1/4*%pi+1/2*x,2)*sin(x)^(1/2))*sin(x) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 322 + +--S 323 of 528 +a0362:= integrate(t0362,x) +--R +--R +--R x +----------+ +--R ++ | 3 +--R (287) | \|a csc(%R) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 528 +m0362:= a0362-r0362 +--R +--R +--R x +----------+ +--R ++ | 3 +--R (288) | \|a csc(%R) d%R - r0362 +--R ++ +--R Type: Expression(Integer) +--E 324 + +--S 325 of 528 +d0362:= D(m0362,x) +--R +--R +--R +---------+ +--R | 3 +--R (289) \|a csc(x) +--R Type: Expression(Integer) +--E 325 + +--S 326 of 528 +t0363:= (csc(x)^2)^(3/2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (290) csc(x) \|csc(x) +--R Type: Expression(Integer) +--E 326 + +--S 327 of 528 +r0363:= -1/2*acsch(tan(x))-1/2*cot(x)*(csc(x)^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 +--R - cot(x)\|csc(x) - acsch(tan(x)) +--R (291) ---------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 528 +a0363:= integrate(t0363,x) +--R +--R +--R 2 sin(x) +--R (cos(x) - 1)log(----------) + cos(x) +--R cos(x) + 1 +--R (292) ------------------------------------- +--R 2 +--R 2cos(x) - 2 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 528 +m0363:= a0363-r0363 +--R +--R +--R (293) +--R +-------+ +--R 2 | 2 2 sin(x) +--R (cos(x) - 1)cot(x)\|csc(x) + (cos(x) - 1)log(----------) +--R cos(x) + 1 +--R + +--R 2 +--R (cos(x) - 1)acsch(tan(x)) + cos(x) +--R / +--R 2 +--R 2cos(x) - 2 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 528 +d0363:= D(m0363,x) +--R +--R +--R (294) +--R 3 2 5 3 +--R ((cos(x) - cos(x) + 2)sin(x) + cos(x) - 2cos(x) + cos(x))tan(x) +--R * +--R +-------+ +--R | 2 +--R \|csc(x) +--R + +--R 4 2 2 4 2 +--R ((- 2cos(x) + 4cos(x) - 2)cot(x) - cos(x) + 2cos(x) - 1) +--R * +--R 2 +--R csc(x) sin(x)tan(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) + 1 +--R + +--R 4 2 2 +--R (- cos(x) + 2cos(x) - 1)sin(x)tan(x) +--R + +--R 4 2 +--R (- cos(x) + 2cos(x) - 1)sin(x) +--R * +--R +-------+ +--R | 2 +--R \|csc(x) +--R / +--R +-------+ +-----------+ +--R 4 2 | 2 | 2 +--R (2cos(x) - 4cos(x) + 2)sin(x)tan(x)\|csc(x) \|tan(x) + 1 +--R Type: Expression(Integer) +--E 330 + +--S 331 of 528 +t0364:= (a*csc(x)^2)^(3/2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (295) a csc(x) \|a csc(x) +--R Type: Expression(Integer) +--E 331 + +--S 332 of 528 +r0364:= -1/2*a*(a*csc(x)^2)^(1/2)*(atanh(cos(x))+cot(x)*csc(x))*sin(x) +--R +--R +--R +---------+ +--R | 2 +--R (- a sin(x)atanh(cos(x)) - a cot(x)csc(x)sin(x))\|a csc(x) +--R (296) ------------------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 528 +a0364:= integrate(t0364,x) +--R +--R +--R 2 +-+ sin(x) +-+ +--R (a cos(x) - a)\|a log(----------) + a cos(x)\|a +--R cos(x) + 1 +--R (297) ------------------------------------------------- +--R 2 +--R 2cos(x) - 2 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 528 +m0364:= a0364-r0364 +--R +--R +--R (298) +--R 2 +--R (a cos(x) - a)sin(x)atanh(cos(x)) +--R + +--R 2 +--R (a cos(x) - a)cot(x)csc(x)sin(x) +--R * +--R +---------+ +--R | 2 +--R \|a csc(x) +--R + +--R 2 +-+ sin(x) +-+ +--R (a cos(x) - a)\|a log(----------) + a cos(x)\|a +--R cos(x) + 1 +--R / +--R 2 +--R 2cos(x) - 2 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 528 +d0364:= D(m0364,x) +--R +--R +--R (299) +--R 3 2 5 3 +--R (a cos(x) - a cos(x) + 2a)sin(x) + a cos(x) - 2a cos(x) +--R + +--R a cos(x) +--R * +--R +---------+ +--R +-+ | 2 +--R \|a \|a csc(x) +--R + +--R 2 4 2 2 2 2 2 +--R (- a cos(x) + 2a cos(x) - a )cot(x)csc(x) sin(x) +--R + +--R 2 5 2 3 2 2 +--R (a cos(x) - 2a cos(x) + a cos(x))csc(x) sin(x) +--R * +--R atanh(cos(x)) +--R + +--R 2 2 2 2 3 +--R (a cos(x) - a )csc(x) sin(x) +--R + +--R 2 4 2 2 2 2 2 4 2 2 +--R (- 3a cos(x) + 6a cos(x) - 3a )cot(x) - a cos(x) + 2a cos(x) +--R + +--R 2 +--R - a +--R * +--R 3 2 +--R csc(x) sin(x) +--R + +--R 2 5 2 3 2 3 +--R (a cos(x) - 2a cos(x) + a cos(x))cot(x)csc(x) sin(x) +--R / +--R +---------+ +--R 4 2 | 2 +--R (2cos(x) - 4cos(x) + 2)sin(x)\|a csc(x) +--R Type: Expression(Integer) +--E 335 + +--S 336 of 528 +t0365:= (a*csc(x)^3)^(3/2) +--R +--R +--R +---------+ +--R 3 | 3 +--R (300) a csc(x) \|a csc(x) +--R Type: Expression(Integer) +--E 336 + +--S 337 of 528 +r0365:= -2/21*a*(a*csc(x)^3)^(1/2)*(5*cot(x)+3*cot(x)*csc(x)^2-_ + 5*EllipticF(-1/4*%pi+1/2*x,2)*sin(x)^(1/2))*sin(x) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 337 + +--S 338 of 528 +a0365:= integrate(t0365,x) +--R +--R +--R x +----------+ +--R ++ 3 | 3 +--R (301) | a csc(%R) \|a csc(%R) d%R +--R ++ +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 528 +m0365:= a0365-r0365 +--R +--R +--R x +----------+ +--R ++ 3 | 3 +--R (302) | a csc(%R) \|a csc(%R) d%R - r0365 +--R ++ +--R Type: Expression(Integer) +--E 339 + +--S 340 of 528 +d0365:= D(m0365,x) +--R +--R +--R +---------+ +--R 3 | 3 +--R (303) a csc(x) \|a csc(x) +--R Type: Expression(Integer) +--E 340 + +--S 341 of 528 +t0366:= 1/(a*csc(x)^2)^(1/2) +--R +--R +--R 1 +--R (304) ------------ +--R +---------+ +--R | 2 +--R \|a csc(x) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 528 +r0366:= -cot(x)/(a*csc(x)^2)^(1/2) +--R +--R +--R cot(x) +--R (305) - ------------ +--R +---------+ +--R | 2 +--R \|a csc(x) +--R Type: Expression(Integer) +--E 342 + +--S 343 of 528 +a0366:= integrate(t0366,x) +--R +--R +--R cos(x) +--R (306) - ------ +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 528 +m0366:= a0366-r0366 +--R +--R +--R +---------+ +--R | 2 +-+ +--R - cos(x)\|a csc(x) + cot(x)\|a +--R (307) --------------------------------- +--R +---------+ +--R +-+ | 2 +--R \|a \|a csc(x) +--R Type: Expression(Integer) +--E 344 + +--S 345 of 528 +d0366:= D(m0366,x) +--R +--R +--R +---------+ +--R +-+ | 2 +--R sin(x)\|a \|a csc(x) - a +--R (308) -------------------------- +--R +---------+ +--R | 2 +--R a\|a csc(x) +--R Type: Expression(Integer) +--E 345 + +--S 346 of 528 +t0367:= 1/(a*csc(x)^3)^(1/2) +--R +--R +--R 1 +--R (309) ------------ +--R +---------+ +--R | 3 +--R \|a csc(x) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 528 +r0367:= -2/3*csc(x)*(cos(x)-_ + EllipticF(-1/4*%pi+1/2*x,2)/sin(x)^(1/2))/(a*csc(x)^3)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 347 + +--S 348 of 528 +a0367:= integrate(t0367,x) +--R +--R +--R x +--R ++ 1 +--R (310) | ------------- d%R +--R ++ +----------+ +--R | 3 +--R \|a csc(%R) +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 528 +m0367:= a0367-r0367 +--R +--R +--R x +--R ++ 1 +--R (311) | ------------- d%R - r0367 +--R ++ +----------+ +--R | 3 +--R \|a csc(%R) +--R Type: Expression(Integer) +--E 349 + +--S 350 of 528 +d0367:= D(m0367,x) +--R +--R +--R 1 +--R (312) ------------ +--R +---------+ +--R | 3 +--R \|a csc(x) +--R Type: Expression(Integer) +--E 350 + +--S 351 of 528 +t0368:= 1/(a+a*csc(c+d*x)) +--R +--R +--R 1 +--R (313) ------------------ +--R a csc(d x + c) + a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 528 +r0368:= x/a+cos(c+d*x)/a/d/(1+sin(c+d*x)) +--R +--R +--R d x sin(d x + c) + cos(d x + c) + d x +--R (314) ------------------------------------- +--R a d sin(d x + c) + a d +--R Type: Expression(Integer) +--E 352 + +--S 353 of 528 +a0368:= integrate(t0368,x) +--R +--R +--R d x sin(d x + c) + (d x + 2)cos(d x + c) + d x + 2 +--R (315) -------------------------------------------------- +--R a d sin(d x + c) + a d cos(d x + c) + a d +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 528 +m0368:= a0368-r0368 +--R +--R +--R (316) +--R 2 +--R (cos(d x + c) + 2)sin(d x + c) - cos(d x + c) + cos(d x + c) + 2 +--R / +--R 2 +--R a d sin(d x + c) + (a d cos(d x + c) + 2a d)sin(d x + c) +--R + +--R a d cos(d x + c) + a d +--R Type: Expression(Integer) +--E 354 + +--S 355 of 528 +d0368:= D(m0368,x) +--R +--R +--R (317) +--R 4 3 +--R - sin(d x + c) + (2cos(d x + c) - 1)sin(d x + c) +--R + +--R 2 +--R (2cos(d x + c) + 1)sin(d x + c) +--R + +--R 3 2 +--R (2cos(d x + c) - cos(d x + c) - 2cos(d x + c) + 1)sin(d x + c) +--R + +--R 4 3 2 +--R cos(d x + c) + 2cos(d x + c) - cos(d x + c) - 2cos(d x + c) +--R / +--R 4 3 +--R a sin(d x + c) + (2a cos(d x + c) + 4a)sin(d x + c) +--R + +--R 2 2 +--R (a cos(d x + c) + 6a cos(d x + c) + 6a)sin(d x + c) +--R + +--R 2 2 +--R (2a cos(d x + c) + 6a cos(d x + c) + 4a)sin(d x + c) + a cos(d x + c) +--R + +--R 2a cos(d x + c) + a +--R Type: Expression(Integer) +--E 355 + +--S 356 of 528 +t0369:= 1/(a-a*csc(c+d*x)) +--R +--R +--R 1 +--R (318) - ------------------ +--R a csc(d x + c) - a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 528 +r0369:= x/a-cos(c+d*x)/a/d/(1-sin(c+d*x)) +--R +--R +--R d x sin(d x + c) + cos(d x + c) - d x +--R (319) ------------------------------------- +--R a d sin(d x + c) - a d +--R Type: Expression(Integer) +--E 357 + +--S 358 of 528 +a0369:= integrate(t0369,x) +--R +--R +--R d x sin(d x + c) + (- d x + 2)cos(d x + c) - d x + 2 +--R (320) ---------------------------------------------------- +--R a d sin(d x + c) - a d cos(d x + c) - a d +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 528 +m0369:= a0369-r0369 +--R +--R +--R (321) +--R 2 +--R (cos(d x + c) + 2)sin(d x + c) + cos(d x + c) - cos(d x + c) - 2 +--R / +--R 2 +--R a d sin(d x + c) + (- a d cos(d x + c) - 2a d)sin(d x + c) +--R + +--R a d cos(d x + c) + a d +--R Type: Expression(Integer) +--E 359 + +--S 360 of 528 +d0369:= D(m0369,x) +--R +--R +--R (322) +--R 4 3 +--R - sin(d x + c) + (- 2cos(d x + c) + 1)sin(d x + c) +--R + +--R 2 +--R (2cos(d x + c) + 1)sin(d x + c) +--R + +--R 3 2 +--R (- 2cos(d x + c) + cos(d x + c) + 2cos(d x + c) - 1)sin(d x + c) +--R + +--R 4 3 2 +--R cos(d x + c) + 2cos(d x + c) - cos(d x + c) - 2cos(d x + c) +--R / +--R 4 3 +--R a sin(d x + c) + (- 2a cos(d x + c) - 4a)sin(d x + c) +--R + +--R 2 2 +--R (a cos(d x + c) + 6a cos(d x + c) + 6a)sin(d x + c) +--R + +--R 2 2 +--R (- 2a cos(d x + c) - 6a cos(d x + c) - 4a)sin(d x + c) + a cos(d x + c) +--R + +--R 2a cos(d x + c) + a +--R Type: Expression(Integer) +--E 360 + +--S 361 of 528 +t0370:= (3+3*csc(x))^(1/2) +--R +--R +--R +-----------+ +--R (323) \|3csc(x) + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 528 +r0370:= -2*3^(1/2)*atan((-1+csc(x))^(1/2))*cot(x)/_ + (-1+csc(x))^(1/2)/(1+csc(x))^(1/2) +--R +--R +--R +-+ +----------+ +--R 2\|3 cot(x)atan(\|csc(x) - 1 ) +--R (324) - ------------------------------ +--R +----------+ +----------+ +--R \|csc(x) - 1 \|csc(x) + 1 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 528 +a0370:= integrate(t0370,x) +--R +--R +--R +-------------+ +--R +-+ +-+ +-+ |- 9cos(x) - 9 +--R (2\|3 sin(x) + 2\|3 cos(x) - 2\|3 ) 4|------------- +--R +-+ \| 4cos(x) - 4 +--R (325) \|3 atan(---------------------------------------------------) +--R +-------------+2 +--R |- 9cos(x) - 9 +--R (2cos(x) - 2) 4|------------- - 3sin(x) + 3 +--R \| 4cos(x) - 4 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 528 +m0370:= a0370-r0370 +--R +--R +--R (326) +--R +-+ +----------+ +--R 2\|3 cot(x)atan(\|csc(x) - 1 ) +--R + +--R +-+ +----------+ +----------+ +--R \|3 \|csc(x) - 1 \|csc(x) + 1 +--R * +--R +-------------+ +--R +-+ +-+ +-+ |- 9cos(x) - 9 +--R (2\|3 sin(x) + 2\|3 cos(x) - 2\|3 ) 4|------------- +--R \| 4cos(x) - 4 +--R atan(---------------------------------------------------) +--R +-------------+2 +--R |- 9cos(x) - 9 +--R (2cos(x) - 2) 4|------------- - 3sin(x) + 3 +--R \| 4cos(x) - 4 +--R / +--R +----------+ +----------+ +--R \|csc(x) - 1 \|csc(x) + 1 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 528 +d0370:= D(m0370,x) +--R +--R +--R (327) +--R +-+ 2 +-+ +-+ 2 +--R (- 8\|3 cos(x) + 16\|3 cos(x) - 8\|3 )csc(x) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ 2 +--R (8\|3 cos(x) - 16\|3 cos(x) + 8\|3 )cot(x) + 8\|3 cos(x) +--R + +--R +-+ +-+ +--R - 16\|3 cos(x) + 8\|3 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2 +--R (- 32\|3 cos(x) + 64\|3 cos(x) - 32\|3 cos(x))csc(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2 +--R (32\|3 cos(x) - 64\|3 cos(x) + 32\|3 cos(x))cot(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 32\|3 cos(x) - 64\|3 cos(x) + 32\|3 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 16\|3 cos(x) + 64\|3 cos(x) - 80\|3 cos(x) +--R + +--R +-+ +--R 32\|3 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 16\|3 cos(x) - 64\|3 cos(x) + 80\|3 cos(x) +--R + +--R +-+ +--R - 32\|3 cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 16\|3 cos(x) - 64\|3 cos(x) + 80\|3 cos(x) - 32\|3 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 2 +--R - 32\|3 cos(x) + 64\|3 cos(x) - 32\|3 cos(x) +--R + +--R +-+ +-+ +--R - 32\|3 cos(x) + 32\|3 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 2 +--R 32\|3 cos(x) - 64\|3 cos(x) + 32\|3 cos(x) +--R + +--R +-+ +-+ +--R 32\|3 cos(x) - 32\|3 +--R * +--R 2 +--R cot(x) +--R + +--R +-+ 5 +-+ 4 +-+ 2 +-+ +--R 32\|3 cos(x) - 64\|3 cos(x) + 32\|3 cos(x) + 32\|3 cos(x) +--R + +--R +-+ +--R - 32\|3 +--R * +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8\|3 cos(x) + 48\|3 cos(x) - 40\|3 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 64\|3 cos(x) + 64\|3 cos(x) + 32\|3 cos(x) - 32\|3 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 8\|3 cos(x) - 48\|3 cos(x) + 40\|3 cos(x) + 64\|3 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 64\|3 cos(x) - 32\|3 cos(x) + 32\|3 +--R * +--R 2 +--R cot(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 8\|3 cos(x) - 48\|3 cos(x) + 40\|3 cos(x) + 64\|3 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 64\|3 cos(x) - 32\|3 cos(x) + 32\|3 +--R * +--R +-------------+3 +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 2 +-+ 2 +--R (24\|3 cos(x) - 24\|3 )csc(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (- 24\|3 cos(x) + 24\|3 )cot(x) - 24\|3 cos(x) + 24\|3 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 48\|3 cos(x) + 48\|3 )csc(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (48\|3 cos(x) - 48\|3 )cot(x) + 48\|3 cos(x) - 48\|3 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2 +-+ 2 +--R (24\|3 cos(x) - 24\|3 )csc(x) +--R + +--R +-+ 2 +-+ 2 +-+ 2 +-+ +--R (- 24\|3 cos(x) + 24\|3 )cot(x) - 24\|3 cos(x) + 24\|3 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 48\|3 cos(x) + 96\|3 cos(x) - 48\|3 )csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (48\|3 cos(x) - 96\|3 cos(x) + 48\|3 )cot(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 48\|3 cos(x) - 96\|3 cos(x) + 48\|3 +--R * +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 24\|3 cos(x) + 96\|3 cos(x) - 120\|3 cos(x) + 48\|3 ) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (24\|3 cos(x) - 96\|3 cos(x) + 120\|3 cos(x) - 48\|3 )cot(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R 24\|3 cos(x) - 96\|3 cos(x) + 120\|3 cos(x) - 48\|3 +--R * +--R +-------------+ +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +--R atan(\|csc(x) - 1 ) +--R + +--R 2 2 2 +--R (- 12cos(x) - 6cos(x) + 18)csc(x) + 12cos(x) + 6cos(x) +--R + +--R - 18 +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (24cos(x) - 6cos(x) - 18)csc(x) - 24cos(x) + 6cos(x) +--R + +--R 18 +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 +--R (- 42cos(x) + 42cos(x) + 12cos(x) - 12)csc(x) + 42cos(x) +--R + +--R 2 +--R - 42cos(x) - 12cos(x) + 12 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (24cos(x) - 6cos(x) - 12cos(x) - 30cos(x) + 24)csc(x) +--R + +--R 5 4 3 2 +--R - 24cos(x) + 6cos(x) + 12cos(x) + 30cos(x) - 24 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (12cos(x) - 36cos(x) - 12cos(x) + 60cos(x) - 24cos(x))csc(x) +--R + +--R 6 5 4 3 +--R - 12cos(x) + 36cos(x) + 12cos(x) - 60cos(x) + 24cos(x) +--R * +--R +-------------+2 +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R + +--R 2 5 +--R (9csc(x) - 9)sin(x) +--R + +--R 2 2 2 +--R ((- 18cos(x) + 9cos(x) - 18)csc(x) + 18cos(x) - 9cos(x) + 18) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 +--R (- 36cos(x) + 27cos(x) + 9cos(x) + 27)csc(x) + 36cos(x) +--R + +--R 2 +--R - 27cos(x) - 9cos(x) - 27 +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 +--R (45cos(x) - 54cos(x) - 18cos(x) + 18)csc(x) - 45cos(x) +--R + +--R 2 +--R 54cos(x) + 18cos(x) - 18 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R - 36cos(x) + 18cos(x) + 63cos(x) + 27cos(x) - 36cos(x) +--R + +--R - 36 +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R 36cos(x) - 18cos(x) - 63cos(x) - 27cos(x) + 36cos(x) + 36 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 18cos(x) + 36cos(x) - 54cos(x) - 72cos(x) + 36cos(x) +--R + +--R 36cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 18cos(x) - 36cos(x) + 54cos(x) + 72cos(x) - 36cos(x) - 36cos(x) +--R * +--R +----------+ +----------+ +--R \|csc(x) - 1 \|csc(x) + 1 +--R + +--R +-+ 2 +-+ +-+ 2 +--R (- 4\|3 cos(x) + 8\|3 cos(x) - 4\|3 )cot(x) csc(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R (- 4\|3 cos(x) + 8\|3 cos(x) - 4\|3 )cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2 +--R (- 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x))cot(x) csc(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2 +--R (- 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x))cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8\|3 cos(x) + 32\|3 cos(x) - 40\|3 cos(x) +--R + +--R +-+ +--R 16\|3 cos(x) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8\|3 cos(x) + 32\|3 cos(x) - 40\|3 cos(x) +--R + +--R +-+ +--R 16\|3 cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 2 +--R - 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x) +--R + +--R +-+ +-+ +--R - 16\|3 cos(x) + 16\|3 +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 2 +--R - 16\|3 cos(x) + 32\|3 cos(x) - 16\|3 cos(x) +--R + +--R +-+ +-+ +--R - 16\|3 cos(x) + 16\|3 +--R * +--R 2 +--R cot(x) +--R * +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 4\|3 cos(x) + 24\|3 cos(x) - 20\|3 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 32\|3 cos(x) + 32\|3 cos(x) + 16\|3 cos(x) - 16\|3 +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 4\|3 cos(x) + 24\|3 cos(x) - 20\|3 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 32\|3 cos(x) + 32\|3 cos(x) + 16\|3 cos(x) - 16\|3 +--R * +--R 2 +--R cot(x) +--R * +--R +-------------+3 +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 2 +-+ 2 +--R (12\|3 cos(x) - 12\|3 )cot(x) csc(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|3 cos(x) - 12\|3 )cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 24\|3 cos(x) + 24\|3 )cot(x) csc(x) +--R + +--R +-+ 2 +-+ 2 +--R (- 24\|3 cos(x) + 24\|3 )cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|3 cos(x) - 12\|3 )cot(x) csc(x) +--R + +--R +-+ 2 +-+ 2 +--R (12\|3 cos(x) - 12\|3 )cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 24\|3 cos(x) + 48\|3 cos(x) - 24\|3 )cot(x) csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 24\|3 cos(x) + 48\|3 cos(x) - 24\|3 )cot(x) +--R * +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ +--R (- 12\|3 cos(x) + 48\|3 cos(x) - 60\|3 cos(x) + 24\|3 ) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +-+ 2 +--R (- 12\|3 cos(x) + 48\|3 cos(x) - 60\|3 cos(x) + 24\|3 )cot(x) +--R * +--R +-------------+ +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +--R \|csc(x) - 1 +--R / +--R 2 2 2 4 +--R ((4cos(x) - 8cos(x) + 4)csc(x) - 4cos(x) + 8cos(x) - 4)sin(x) +--R + +--R 3 2 2 3 +--R (16cos(x) - 32cos(x) + 16cos(x))csc(x) - 16cos(x) +--R + +--R 2 +--R 32cos(x) - 16cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (8cos(x) - 32cos(x) + 40cos(x) - 16cos(x))csc(x) - 8cos(x) +--R + +--R 3 2 +--R 32cos(x) - 40cos(x) + 16cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 2 +--R (16cos(x) - 32cos(x) + 16cos(x) + 16cos(x) - 16)csc(x) +--R + +--R 5 4 2 +--R - 16cos(x) + 32cos(x) - 16cos(x) - 16cos(x) + 16 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) - 24cos(x) + 20cos(x) + 32cos(x) - 32cos(x) +--R + +--R - 16cos(x) + 16 +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 4cos(x) + 24cos(x) - 20cos(x) - 32cos(x) + 32cos(x) +--R + +--R 16cos(x) - 16 +--R * +--R +-------------+3 +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 4 +--R ((- 12cos(x) + 12)csc(x) + 12cos(x) - 12)sin(x) +--R + +--R 2 2 2 3 +--R ((24cos(x) - 24)csc(x) - 24cos(x) + 24)sin(x) +--R + +--R 2 2 2 2 +--R ((- 12cos(x) + 12)csc(x) + 12cos(x) - 12)sin(x) +--R + +--R 4 2 2 4 2 +--R (24cos(x) - 48cos(x) + 24)csc(x) - 24cos(x) + 48cos(x) +--R + +--R - 24 +--R * +--R sin(x) +--R + +--R 6 4 2 2 6 +--R (12cos(x) - 48cos(x) + 60cos(x) - 24)csc(x) - 12cos(x) +--R + +--R 4 2 +--R 48cos(x) - 60cos(x) + 24 +--R * +--R +-------------+ +--R |- 9cos(x) - 9 +--R 4|------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +----------+ +--R \|csc(x) - 1 \|csc(x) + 1 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 528 +t0371:= (3-3*csc(x))^(1/2) +--R +--R +--R +-------------+ +--R (328) \|- 3csc(x) + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 528 +r0371:= -2*3^(1/2)*atan((-1-csc(x))^(1/2))*cot(x)/_ + (-1-csc(x))^(1/2)/(1-csc(x))^(1/2) +--R +--R +--R +-+ +------------+ +--R 2\|3 cot(x)atan(\|- csc(x) - 1 ) +--R (329) - -------------------------------- +--R +------------+ +------------+ +--R \|- csc(x) - 1 \|- csc(x) + 1 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 528 +a0371:= integrate(t0371,x) +--R +--R +--R (330) 0 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 528 +m0371:= a0371-r0371 +--R +--R +--R +-+ +------------+ +--R 2\|3 cot(x)atan(\|- csc(x) - 1 ) +--R (331) -------------------------------- +--R +------------+ +------------+ +--R \|- csc(x) - 1 \|- csc(x) + 1 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 528 +d0371:= D(m0371,x) +--R +--R +--R (332) +--R +-+ 2 +-+ 2 +-+ +------------+ +--R (- 2\|3 csc(x) + 2\|3 cot(x) + 2\|3 )atan(\|- csc(x) - 1 ) +--R + +--R +-+ 2 +-+ 2 +------------+ +--R (\|3 cot(x) csc(x) - \|3 cot(x) )\|- csc(x) - 1 +--R / +--R 2 +------------+ +------------+ +--R (csc(x) - 1)\|- csc(x) - 1 \|- csc(x) + 1 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 528 +t0372:= (a+a*csc(x))^(1/2) +--R +--R +--R +------------+ +--R (333) \|a csc(x) + a +--R Type: Expression(Integer) +--E 371 + +--S 372 of 528 +r0372:= -2*a*atan((-1+csc(x))^(1/2))*cot(x)/(-1+csc(x))^(1/2)/_ + (a+a*csc(x))^(1/2) +--R +--R +--R +----------+ +--R 2a cot(x)atan(\|csc(x) - 1 ) +--R (334) - ---------------------------- +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R Type: Expression(Integer) +--E 372 + +--S 373 of 528 +a0372:= integrate(t0372,x) +--R +--R +--R (335) +--R [ +--R +---+ +--R \|- a +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((- 8cos(x) + 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((8cos(x) - 12)sin(x) - 8cos(x) - 4cos(x) + 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R - 4a sin(x) - 4a cos(x) + 5a +--R / +--R 2 +--R , +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) + 2cos(x) - 2)\|a 4|--------------- +--R +-+ \| 4cos(x) - 4 +--R \|a atan(-----------------------------------------------)] +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- - a sin(x) + a +--R \| 4cos(x) - 4 +--R Type: Union(List(Expression(Integer)),...) +--E 373 + +--S 374 of 528 +m0372a:= a0372.1-r0372 +--R +--R +--R (336) +--R +---+ +----------+ +------------+ +--R \|- a \|csc(x) - 1 \|a csc(x) + a +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((- 8cos(x) + 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((8cos(x) - 12)sin(x) - 8cos(x) - 4cos(x) + 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R - 4a sin(x) - 4a cos(x) + 5a +--R + +--R +----------+ +--R 4a cot(x)atan(\|csc(x) - 1 ) +--R / +--R +----------+ +------------+ +--R 2\|csc(x) - 1 \|a csc(x) + a +--R Type: Expression(Integer) +--E 374 + +--S 375 of 528 +d0372a:= D(m0372a,x) +--R +--R +--R (337) +--R 2 2 +--R (- 32a cos(x) + 64a cos(x) - 32a)csc(x) +--R + +--R 2 2 2 +--R (32a cos(x) - 64a cos(x) + 32a)cot(x) + 32a cos(x) +--R + +--R - 64a cos(x) + 32a +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- 32a cos(x) + 64a cos(x) + 8a cos(x) - 80a cos(x) + 40a) +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R (32a cos(x) - 64a cos(x) - 8a cos(x) + 80a cos(x) - 40a) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 +--R 32a cos(x) - 64a cos(x) - 8a cos(x) + 80a cos(x) - 40a +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 16a cos(x) - 16a cos(x) + 16a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R - 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 16a cos(x) - 16a cos(x) + 16a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R 16a cos(x) - 16a cos(x) - 16a cos(x) + 16a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 24a cos(x) + 16a cos(x) - 24a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 24a cos(x) - 16a cos(x) + 24a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R 16a cos(x) - 24a cos(x) - 16a cos(x) + 24a +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (16a cos(x) + 8a cos(x) - 40a cos(x) - 8a cos(x) + 24a ) +--R * +--R 2 +--R csc(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- 16a cos(x) - 8a cos(x) + 40a cos(x) + 8a cos(x) - 24a ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R - 16a cos(x) - 8a cos(x) + 40a cos(x) + 8a cos(x) - 24a +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R atan(\|csc(x) - 1 ) +--R + +--R 3 2 2 3 +--R (- 16cos(x) + 32cos(x) - 16cos(x))csc(x) + 16cos(x) +--R + +--R 2 +--R - 32cos(x) + 16cos(x) +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (8cos(x) - 16cos(x) + 8cos(x))csc(x) - 8cos(x) + 16cos(x) +--R + +--R - 8cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ |- a cos(x) - a +--R \|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x))sin(x) +--R + +--R 2 2 2 +--R ((- 4a cos(x) + 4a cos(x))csc(x) + 4a cos(x) - 4a cos(x)) +--R * +--R sin(x) +--R + +--R 4 3 2 2 +--R (- 4a cos(x) + 4a cos(x) + 4a cos(x) - 4a cos(x))csc(x) +--R + +--R 4 3 2 +--R 4a cos(x) - 4a cos(x) - 4a cos(x) + 4a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +---+ |- a cos(x) - a +--R \|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R (4a cos(x) - 2a cos(x) - a )csc(x) - 4a cos(x) + 2a cos(x) +--R + +--R 2 +--R a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 2 2 3 2 +--R (- 8a cos(x) + 9a cos(x) - a )csc(x) + 8a cos(x) - 9a cos(x) +--R + +--R 2 +--R a +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- 4a cos(x) + 6a cos(x) + 4a cos(x) - 6a cos(x))csc(x) +--R + +--R 2 4 2 3 2 2 2 +--R 4a cos(x) - 6a cos(x) - 4a cos(x) + 6a cos(x) +--R * +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R + +--R 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a)cot(x) csc(x) +--R + +--R 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a)cot(x) +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- 16a cos(x) + 32a cos(x) + 4a cos(x) - 40a cos(x) + 20a) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 4 3 2 +--R (- 16a cos(x) + 32a cos(x) + 4a cos(x) - 40a cos(x) + 20a) +--R * +--R 2 +--R cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) - 8a cos(x) - 8a cos(x) + 8a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) - 8a cos(x) - 8a cos(x) + 8a )cot(x) +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a )cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 12a cos(x) + 8a cos(x) - 12a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 12a cos(x) + 8a cos(x) - 12a )cot(x) +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (8a cos(x) + 4a cos(x) - 20a cos(x) - 4a cos(x) + 12a ) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (8a cos(x) + 4a cos(x) - 20a cos(x) - 4a cos(x) + 12a )cot(x) +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +--R \|csc(x) - 1 +--R / +--R 2 2 2 +--R ((16cos(x) - 32cos(x) + 16)csc(x) - 16cos(x) + 32cos(x) - 16) +--R * +--R sin(x) +--R + +--R 4 3 2 2 +--R (16cos(x) - 32cos(x) - 4cos(x) + 40cos(x) - 20)csc(x) +--R + +--R 4 3 2 +--R - 16cos(x) + 32cos(x) + 4cos(x) - 40cos(x) + 20 +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 2 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a)csc(x) +--R + +--R 3 2 +--R 8a cos(x) - 8a cos(x) - 8a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 3 2 2 3 +--R (8a cos(x) - 8a cos(x) - 8a cos(x) + 8a)csc(x) - 8a cos(x) +--R + +--R 2 +--R 8a cos(x) + 8a cos(x) - 8a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 2 +--R (8a cos(x) - 12a cos(x) - 8a cos(x) + 12a)csc(x) +--R + +--R 3 2 +--R - 8a cos(x) + 12a cos(x) + 8a cos(x) - 12a +--R * +--R sin(x) +--R + +--R 4 3 2 2 +--R (- 8a cos(x) - 4a cos(x) + 20a cos(x) + 4a cos(x) - 12a)csc(x) +--R + +--R 4 3 2 +--R 8a cos(x) + 4a cos(x) - 20a cos(x) - 4a cos(x) + 12a +--R * +--R +---+ +--R \|- a +--R * +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R Type: Expression(Integer) +--E 375 + +--S 376 of 528 +m0372b:= a0372.2-r0372 +--R +--R +--R (338) +--R +----------+ +--R 2a cot(x)atan(\|csc(x) - 1 ) +--R + +--R +-+ +----------+ +------------+ +--R \|a \|csc(x) - 1 \|a csc(x) + a +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) + 2cos(x) - 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- - a sin(x) + a +--R \| 4cos(x) - 4 +--R / +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R Type: Expression(Integer) +--E 376 + +--S 377 of 528 +d0372b:= D(m0372b,x) +--R +--R +--R (339) +--R 2 2 +--R (- 8a cos(x) + 16a cos(x) - 8a)csc(x) +--R + +--R 2 2 2 +--R (8a cos(x) - 16a cos(x) + 8a)cot(x) + 8a cos(x) +--R + +--R - 16a cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 +--R (- 32a cos(x) + 64a cos(x) - 32a cos(x))csc(x) +--R + +--R 3 2 2 3 +--R (32a cos(x) - 64a cos(x) + 32a cos(x))cot(x) + 32a cos(x) +--R + +--R 2 +--R - 64a cos(x) + 32a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 +--R (- 16a cos(x) + 64a cos(x) - 80a cos(x) + 32a cos(x)) +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 2 +--R (16a cos(x) - 64a cos(x) + 80a cos(x) - 32a cos(x))cot(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 64a cos(x) + 80a cos(x) - 32a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 +--R - 32a cos(x) + 64a cos(x) - 32a cos(x) - 32a cos(x) +--R + +--R 32a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 2 +--R 32a cos(x) - 64a cos(x) + 32a cos(x) + 32a cos(x) +--R + +--R - 32a +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 2 +--R 32a cos(x) - 64a cos(x) + 32a cos(x) + 32a cos(x) - 32a +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R - 8a cos(x) + 48a cos(x) - 40a cos(x) - 64a cos(x) +--R + +--R 2 +--R 64a cos(x) + 32a cos(x) - 32a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 48a cos(x) + 40a cos(x) + 64a cos(x) +--R + +--R 2 +--R - 64a cos(x) - 32a cos(x) + 32a +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 48a cos(x) + 40a cos(x) + 64a cos(x) +--R + +--R 2 +--R - 64a cos(x) - 32a cos(x) + 32a +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R (8a cos(x) - 8a )csc(x) + (- 8a cos(x) + 8a )cot(x) +--R + +--R 2 2 2 +--R - 8a cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 16a cos(x) + 16a )csc(x) + (16a cos(x) - 16a )cot(x) +--R + +--R 2 2 2 +--R 16a cos(x) - 16a +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (8a cos(x) - 8a )csc(x) + (- 8a cos(x) + 8a )cot(x) +--R + +--R 2 2 2 +--R - 8a cos(x) + 8a +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 2 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a )csc(x) +--R + +--R 2 4 2 2 2 2 2 4 +--R (16a cos(x) - 32a cos(x) + 16a )cot(x) + 16a cos(x) +--R + +--R 2 2 2 +--R - 32a cos(x) + 16a +--R * +--R sin(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 8a cos(x) + 32a cos(x) - 40a cos(x) + 16a )csc(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (8a cos(x) - 32a cos(x) + 40a cos(x) - 16a )cot(x) +--R + +--R 2 6 2 4 2 2 2 +--R 8a cos(x) - 32a cos(x) + 40a cos(x) - 16a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +--R atan(\|csc(x) - 1 ) +--R + +--R 2 2 2 +--R (- 4a cos(x) - 2a cos(x) + 6a)csc(x) + 4a cos(x) +--R + +--R 2a cos(x) - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 +--R (8a cos(x) - 2a cos(x) - 6a)csc(x) - 8a cos(x) +--R + +--R 2 +--R 2a cos(x) + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 +--R (- 14a cos(x) + 14a cos(x) + 4a cos(x) - 4a)csc(x) +--R + +--R 3 2 +--R 14a cos(x) - 14a cos(x) - 4a cos(x) + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R (8a cos(x) - 2a cos(x) - 4a cos(x) - 10a cos(x) + 8a) +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 2a cos(x) + 4a cos(x) + 10a cos(x) - 8a +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R 4a cos(x) - 12a cos(x) - 4a cos(x) + 20a cos(x) +--R + +--R - 8a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R - 4a cos(x) + 12a cos(x) + 4a cos(x) - 20a cos(x) + 8a cos(x) +--R * +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 5 +--R (a csc(x) - a )sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 2a cos(x) + a cos(x) - 2a )csc(x) + 2a cos(x) - a cos(x) +--R + +--R 2 +--R 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 4a cos(x) + 3a cos(x) + a cos(x) + 3a )csc(x) + 4a cos(x) +--R + +--R 2 2 2 2 +--R - 3a cos(x) - a cos(x) - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (5a cos(x) - 6a cos(x) - 2a cos(x) + 2a )csc(x) - 5a cos(x) +--R + +--R 2 2 2 2 +--R 6a cos(x) + 2a cos(x) - 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 4a cos(x) + 2a cos(x) + 7a cos(x) + 3a cos(x) +--R + +--R 2 2 +--R - 4a cos(x) - 4a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R 4a cos(x) - 2a cos(x) - 7a cos(x) - 3a cos(x) + 4a cos(x) + 4a +--R * +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 2a cos(x) + 4a cos(x) - 6a cos(x) - 8a cos(x) + 4a cos(x) +--R + +--R 2 +--R 4a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R - 2a cos(x) - 4a cos(x) + 6a cos(x) + 8a cos(x) - 4a cos(x) +--R + +--R 2 +--R - 4a cos(x) +--R * +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R + +--R 2 2 +--R (- 4a cos(x) + 8a cos(x) - 4a)cot(x) csc(x) +--R + +--R 2 2 +--R (- 4a cos(x) + 8a cos(x) - 4a)cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a cos(x))cot(x) csc(x) +--R + +--R 3 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a cos(x))cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 +--R (- 8a cos(x) + 32a cos(x) - 40a cos(x) + 16a cos(x)) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 4 3 2 2 +--R (- 8a cos(x) + 32a cos(x) - 40a cos(x) + 16a cos(x))cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 +--R - 16a cos(x) + 32a cos(x) - 16a cos(x) - 16a cos(x) +--R + +--R 16a +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 5 4 2 +--R - 16a cos(x) + 32a cos(x) - 16a cos(x) - 16a cos(x) +--R + +--R 16a +--R * +--R 2 +--R cot(x) +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R - 4a cos(x) + 24a cos(x) - 20a cos(x) - 32a cos(x) +--R + +--R 2 +--R 32a cos(x) + 16a cos(x) - 16a +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 6 5 4 3 +--R - 4a cos(x) + 24a cos(x) - 20a cos(x) - 32a cos(x) +--R + +--R 2 +--R 32a cos(x) + 16a cos(x) - 16a +--R * +--R 2 +--R cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R ((4a cos(x) - 4a )cot(x) csc(x) + (4a cos(x) - 4a )cot(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 2 2 +--R (- 8a cos(x) + 8a )cot(x) csc(x) +--R + +--R 2 2 2 2 +--R (- 8a cos(x) + 8a )cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((4a cos(x) - 4a )cot(x) csc(x) + (4a cos(x) - 4a )cot(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 2 2 2 +--R (- 8a cos(x) + 16a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 4 2 2 2 2 +--R (- 8a cos(x) + 16a cos(x) - 8a )cot(x) +--R * +--R sin(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 4a cos(x) + 16a cos(x) - 20a cos(x) + 8a )cot(x) csc(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 4a cos(x) + 16a cos(x) - 20a cos(x) + 8a )cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +--R \|csc(x) - 1 +--R / +--R 2 2 2 4 +--R ((4cos(x) - 8cos(x) + 4)csc(x) - 4cos(x) + 8cos(x) - 4)sin(x) +--R + +--R 3 2 2 3 +--R (16cos(x) - 32cos(x) + 16cos(x))csc(x) - 16cos(x) +--R + +--R 2 +--R 32cos(x) - 16cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (8cos(x) - 32cos(x) + 40cos(x) - 16cos(x))csc(x) - 8cos(x) +--R + +--R 3 2 +--R 32cos(x) - 40cos(x) + 16cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 2 +--R (16cos(x) - 32cos(x) + 16cos(x) + 16cos(x) - 16)csc(x) +--R + +--R 5 4 2 +--R - 16cos(x) + 32cos(x) - 16cos(x) - 16cos(x) + 16 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) - 24cos(x) + 20cos(x) + 32cos(x) - 32cos(x) +--R + +--R - 16cos(x) + 16 +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 4cos(x) + 24cos(x) - 20cos(x) - 32cos(x) + 32cos(x) +--R + +--R 16cos(x) - 16 +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 4 +--R ((- 4a cos(x) + 4a)csc(x) + 4a cos(x) - 4a)sin(x) +--R + +--R 2 2 2 3 +--R ((8a cos(x) - 8a)csc(x) - 8a cos(x) + 8a)sin(x) +--R + +--R 2 2 2 2 +--R ((- 4a cos(x) + 4a)csc(x) + 4a cos(x) - 4a)sin(x) +--R + +--R 4 2 2 4 +--R (8a cos(x) - 16a cos(x) + 8a)csc(x) - 8a cos(x) +--R + +--R 2 +--R 16a cos(x) - 8a +--R * +--R sin(x) +--R + +--R 6 4 2 2 6 +--R (4a cos(x) - 16a cos(x) + 20a cos(x) - 8a)csc(x) - 4a cos(x) +--R + +--R 4 2 +--R 16a cos(x) - 20a cos(x) + 8a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +----------+ +------------+ +--R \|csc(x) - 1 \|a csc(x) + a +--R Type: Expression(Integer) +--E 377 + +--S 378 of 528 +t0373:= (a-a*csc(x))^(1/2) +--R +--R +--R +--------------+ +--R (340) \|- a csc(x) + a +--R Type: Expression(Integer) +--E 378 + +--S 379 of 528 +r0373:= -2*a*atan((-1-csc(x))^(1/2))*cot(x)/(-1-csc(x))^(1/2)/_ + (a-a*csc(x))^(1/2) +--R +--R +--R +------------+ +--R 2a cot(x)atan(\|- csc(x) - 1 ) +--R (341) - -------------------------------- +--R +--------------+ +------------+ +--R \|- a csc(x) + a \|- csc(x) - 1 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 528 +a0373:= integrate(t0373,x) +--R +--R +--R (342) +--R [ +--R +---+ +--R \|- a +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((8cos(x) - 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((- 8cos(x) + 12)sin(x) - 8cos(x) - 4cos(x) + 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R 4a sin(x) - 4a cos(x) + 5a +--R / +--R 2 +--R , +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) - 2cos(x) + 2)\|a 4|--------------- +--R +-+ \| 4cos(x) - 4 +--R - \|a atan(-----------------------------------------------)] +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- + a sin(x) + a +--R \| 4cos(x) - 4 +--R Type: Union(List(Expression(Integer)),...) +--E 380 + +--S 381 of 528 +m0373a:= a0373.1-r0373 +--R +--R +--R (343) +--R +---+ +--------------+ +------------+ +--R \|- a \|- a csc(x) + a \|- csc(x) - 1 +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((8cos(x) - 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((- 8cos(x) + 12)sin(x) - 8cos(x) - 4cos(x) + 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R 4a sin(x) - 4a cos(x) + 5a +--R + +--R +------------+ +--R 4a cot(x)atan(\|- csc(x) - 1 ) +--R / +--R +--------------+ +------------+ +--R 2\|- a csc(x) + a \|- csc(x) - 1 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 528 +d0373a:= D(m0373a,x) +--R +--R +--R (344) +--R 2 2 +--R (- 32a cos(x) + 64a cos(x) - 32a)csc(x) +--R + +--R 2 2 2 +--R (32a cos(x) - 64a cos(x) + 32a)cot(x) + 32a cos(x) +--R + +--R - 64a cos(x) + 32a +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (32a cos(x) - 64a cos(x) - 8a cos(x) + 80a cos(x) - 40a) +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R (- 32a cos(x) + 64a cos(x) + 8a cos(x) - 80a cos(x) + 40a) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 +--R - 32a cos(x) + 64a cos(x) + 8a cos(x) - 80a cos(x) + 40a +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 16a cos(x) - 16a cos(x) + 16a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R - 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 16a cos(x) - 16a cos(x) + 16a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R - 16a cos(x) + 16a cos(x) + 16a cos(x) - 16a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (- 16a cos(x) + 24a cos(x) + 16a cos(x) - 24a )csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (16a cos(x) - 24a cos(x) - 16a cos(x) + 24a )cot(x) +--R + +--R 2 3 2 2 2 2 +--R 16a cos(x) - 24a cos(x) - 16a cos(x) + 24a +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- 16a cos(x) - 8a cos(x) + 40a cos(x) + 8a cos(x) - 24a ) +--R * +--R 2 +--R csc(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (16a cos(x) + 8a cos(x) - 40a cos(x) - 8a cos(x) + 24a ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R 16a cos(x) + 8a cos(x) - 40a cos(x) - 8a cos(x) + 24a +--R * +--R +---+ +--R \|- a +--R * +--R +------------+ +--R atan(\|- csc(x) - 1 ) +--R + +--R 3 2 2 3 +--R (16cos(x) - 32cos(x) + 16cos(x))csc(x) - 16cos(x) +--R + +--R 2 +--R 32cos(x) - 16cos(x) +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (8cos(x) - 16cos(x) + 8cos(x))csc(x) - 8cos(x) + 16cos(x) +--R + +--R - 8cos(x) +--R * +--R +---+ +--------------+ +--R \|- a \|- a csc(x) + a +--R + +--R 2 2 +--R (16a cos(x) - 32a cos(x) + 16a)cot(x) csc(x) +--R + +--R 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a)cot(x) +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- 16a cos(x) + 32a cos(x) + 4a cos(x) - 40a cos(x) + 20a) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 4 3 2 2 +--R (16a cos(x) - 32a cos(x) - 4a cos(x) + 40a cos(x) - 20a)cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +------------+ |- a cos(x) - a +--R \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x))sin(x) +--R + +--R 2 2 2 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x))sin(x) +--R + +--R 4 3 2 2 +--R (- 4a cos(x) + 4a cos(x) + 4a cos(x) - 4a cos(x))csc(x) +--R + +--R 4 3 2 +--R 4a cos(x) - 4a cos(x) - 4a cos(x) + 4a cos(x) +--R * +--R +---+ +--------------+ +--R \|- a \|- a csc(x) + a +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) - 8a cos(x) - 8a cos(x) + 8a )cot(x) +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) - 8a cos(x) - 8a cos(x) + 8a )cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R +------------+ |- a cos(x) - a +--R \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R (4a cos(x) - 2a cos(x) - a )csc(x) - 4a cos(x) + 2a cos(x) +--R + +--R 2 +--R a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 2 2 3 2 +--R (8a cos(x) - 9a cos(x) + a )csc(x) - 8a cos(x) + 9a cos(x) +--R + +--R 2 +--R - a +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- 4a cos(x) + 6a cos(x) + 4a cos(x) - 6a cos(x))csc(x) +--R + +--R 2 4 2 3 2 2 2 +--R 4a cos(x) - 6a cos(x) - 4a cos(x) + 6a cos(x) +--R * +--R +--------------+ +--R \|- a csc(x) + a +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) - 12a cos(x) - 8a cos(x) + 12a )cot(x) csc(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) + 12a cos(x) + 8a cos(x) - 12a )cot(x) +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (8a cos(x) + 4a cos(x) - 20a cos(x) - 4a cos(x) + 12a ) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (- 8a cos(x) - 4a cos(x) + 20a cos(x) + 4a cos(x) - 12a )cot(x) +--R * +--R +---+ +--R \|- a +--R * +--R +------------+ +--R \|- csc(x) - 1 +--R / +--R 2 2 2 +--R ((16cos(x) - 32cos(x) + 16)csc(x) - 16cos(x) + 32cos(x) - 16) +--R * +--R sin(x) +--R + +--R 4 3 2 2 +--R (- 16cos(x) + 32cos(x) + 4cos(x) - 40cos(x) + 20)csc(x) +--R + +--R 4 3 2 +--R 16cos(x) - 32cos(x) - 4cos(x) + 40cos(x) - 20 +--R * +--R +---------------+3 +--R | 2 2 +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a csc(x) + a \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 2 3 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a)csc(x) + 8a cos(x) +--R + +--R 2 +--R - 8a cos(x) - 8a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 3 2 2 3 +--R (- 8a cos(x) + 8a cos(x) + 8a cos(x) - 8a)csc(x) + 8a cos(x) +--R + +--R 2 +--R - 8a cos(x) - 8a cos(x) + 8a +--R * +--R +---------------+ +--R | 2 2 +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a csc(x) + a \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 2 3 +--R (8a cos(x) - 12a cos(x) - 8a cos(x) + 12a)csc(x) - 8a cos(x) +--R + +--R 2 +--R 12a cos(x) + 8a cos(x) - 12a +--R * +--R sin(x) +--R + +--R 4 3 2 2 +--R (8a cos(x) + 4a cos(x) - 20a cos(x) - 4a cos(x) + 12a)csc(x) +--R + +--R 4 3 2 +--R - 8a cos(x) - 4a cos(x) + 20a cos(x) + 4a cos(x) - 12a +--R * +--R +---+ +--------------+ +------------+ +--R \|- a \|- a csc(x) + a \|- csc(x) - 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 528 +m0373b:= a0373.2-r0373 +--R +--R +--R (345) +--R +------------+ +--R 2a cot(x)atan(\|- csc(x) - 1 ) +--R + +--R - +--R +-+ +--------------+ +------------+ +--R \|a \|- a csc(x) + a \|- csc(x) - 1 +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) - 2cos(x) + 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- + a sin(x) + a +--R \| 4cos(x) - 4 +--R / +--R +--------------+ +------------+ +--R \|- a csc(x) + a \|- csc(x) - 1 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 528 +d0373b:= D(m0373b,x) +--R +--R +--R (346) +--R 2 2 +--R (- 8a cos(x) + 16a cos(x) - 8a)csc(x) +--R + +--R 2 2 2 +--R (8a cos(x) - 16a cos(x) + 8a)cot(x) + 8a cos(x) +--R + +--R - 16a cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 +--R (32a cos(x) - 64a cos(x) + 32a cos(x))csc(x) +--R + +--R 3 2 2 +--R (- 32a cos(x) + 64a cos(x) - 32a cos(x))cot(x) +--R + +--R 3 2 +--R - 32a cos(x) + 64a cos(x) - 32a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 +--R (- 16a cos(x) + 64a cos(x) - 80a cos(x) + 32a cos(x)) +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 2 +--R (16a cos(x) - 64a cos(x) + 80a cos(x) - 32a cos(x))cot(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 64a cos(x) + 80a cos(x) - 32a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 +--R 32a cos(x) - 64a cos(x) + 32a cos(x) + 32a cos(x) +--R + +--R - 32a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 2 +--R - 32a cos(x) + 64a cos(x) - 32a cos(x) - 32a cos(x) +--R + +--R 32a +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 2 +--R - 32a cos(x) + 64a cos(x) - 32a cos(x) - 32a cos(x) + 32a +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R - 8a cos(x) + 48a cos(x) - 40a cos(x) - 64a cos(x) +--R + +--R 2 +--R 64a cos(x) + 32a cos(x) - 32a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 48a cos(x) + 40a cos(x) + 64a cos(x) +--R + +--R 2 +--R - 64a cos(x) - 32a cos(x) + 32a +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 48a cos(x) + 40a cos(x) + 64a cos(x) +--R + +--R 2 +--R - 64a cos(x) - 32a cos(x) + 32a +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R (8a cos(x) - 8a )csc(x) + (- 8a cos(x) + 8a )cot(x) +--R + +--R 2 2 2 +--R - 8a cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (16a cos(x) - 16a )csc(x) + (- 16a cos(x) + 16a )cot(x) +--R + +--R 2 2 2 +--R - 16a cos(x) + 16a +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (8a cos(x) - 8a )csc(x) + (- 8a cos(x) + 8a )cot(x) +--R + +--R 2 2 2 +--R - 8a cos(x) + 8a +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 2 2 2 +--R (16a cos(x) - 32a cos(x) + 16a )csc(x) +--R + +--R 2 4 2 2 2 2 2 4 +--R (- 16a cos(x) + 32a cos(x) - 16a )cot(x) - 16a cos(x) +--R + +--R 2 2 2 +--R 32a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 8a cos(x) + 32a cos(x) - 40a cos(x) + 16a )csc(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (8a cos(x) - 32a cos(x) + 40a cos(x) - 16a )cot(x) +--R + +--R 2 6 2 4 2 2 2 +--R 8a cos(x) - 32a cos(x) + 40a cos(x) - 16a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +------------+ +--R atan(\|- csc(x) - 1 ) +--R + +--R 2 2 +--R (4a cos(x) - 8a cos(x) + 4a)cot(x) csc(x) +--R + +--R 2 2 +--R (- 4a cos(x) + 8a cos(x) - 4a)cot(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 +--R (- 16a cos(x) + 32a cos(x) - 16a cos(x))cot(x) csc(x) +--R + +--R 3 2 2 +--R (16a cos(x) - 32a cos(x) + 16a cos(x))cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 +--R (8a cos(x) - 32a cos(x) + 40a cos(x) - 16a cos(x))cot(x) +--R * +--R csc(x) +--R + +--R 4 3 2 2 +--R (- 8a cos(x) + 32a cos(x) - 40a cos(x) + 16a cos(x))cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 +--R (- 16a cos(x) + 32a cos(x) - 16a cos(x) - 16a cos(x) + 16a) +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 5 4 2 2 +--R (16a cos(x) - 32a cos(x) + 16a cos(x) + 16a cos(x) - 16a)cot(x) +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R 4a cos(x) - 24a cos(x) + 20a cos(x) + 32a cos(x) +--R + +--R 2 +--R - 32a cos(x) - 16a cos(x) + 16a +--R * +--R 2 +--R cot(x) csc(x) +--R + +--R 6 5 4 3 +--R - 4a cos(x) + 24a cos(x) - 20a cos(x) - 32a cos(x) +--R + +--R 2 +--R 32a cos(x) + 16a cos(x) - 16a +--R * +--R 2 +--R cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +------------+ |- a cos(x) - a +--R \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 +--R (4a cos(x) + 2a cos(x) - 6a)csc(x) - 4a cos(x) - 2a cos(x) +--R + +--R 6a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (8a cos(x) - 2a cos(x) - 6a)csc(x) - 8a cos(x) + 2a cos(x) +--R + +--R 6a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 +--R (14a cos(x) - 14a cos(x) - 4a cos(x) + 4a)csc(x) - 14a cos(x) +--R + +--R 2 +--R 14a cos(x) + 4a cos(x) - 4a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (8a cos(x) - 2a cos(x) - 4a cos(x) - 10a cos(x) + 8a)csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 2a cos(x) + 4a cos(x) + 10a cos(x) - 8a +--R * +--R sin(x) +--R + +--R 6 5 4 3 +--R (- 4a cos(x) + 12a cos(x) + 4a cos(x) - 20a cos(x) + 8a cos(x)) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 4a cos(x) - 12a cos(x) - 4a cos(x) + 20a cos(x) - 8a cos(x) +--R * +--R +---------------+2 +--R | 2 2 +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a csc(x) + a \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 4a cos(x) + 4a )cot(x) csc(x) + (4a cos(x) - 4a )cot(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 8a cos(x) + 8a )cot(x) csc(x) + (8a cos(x) - 8a )cot(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((- 4a cos(x) + 4a )cot(x) csc(x) + (4a cos(x) - 4a )cot(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 2 2 2 +--R (- 8a cos(x) + 16a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 4 2 2 2 2 +--R (8a cos(x) - 16a cos(x) + 8a )cot(x) +--R * +--R sin(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (4a cos(x) - 16a cos(x) + 20a cos(x) - 8a )cot(x) csc(x) +--R + +--R 2 6 2 4 2 2 2 2 +--R (- 4a cos(x) + 16a cos(x) - 20a cos(x) + 8a )cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R +------------+ |- a cos(x) - a +--R \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 5 +--R (a csc(x) - a )sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (2a cos(x) - a cos(x) + 2a )csc(x) - 2a cos(x) + a cos(x) +--R + +--R 2 +--R - 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 4a cos(x) + 3a cos(x) + a cos(x) + 3a )csc(x) + 4a cos(x) +--R + +--R 2 2 2 2 +--R - 3a cos(x) - a cos(x) - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 2 3 +--R (- 5a cos(x) + 6a cos(x) + 2a cos(x) - 2a )csc(x) + 5a cos(x) +--R + +--R 2 2 2 2 +--R - 6a cos(x) - 2a cos(x) + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 4a cos(x) + 2a cos(x) + 7a cos(x) + 3a cos(x) +--R + +--R 2 2 +--R - 4a cos(x) - 4a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R 4a cos(x) - 2a cos(x) - 7a cos(x) - 3a cos(x) + 4a cos(x) + 4a +--R * +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R - 2a cos(x) - 4a cos(x) + 6a cos(x) + 8a cos(x) - 4a cos(x) +--R + +--R 2 +--R - 4a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 2a cos(x) + 4a cos(x) - 6a cos(x) - 8a cos(x) + 4a cos(x) +--R + +--R 2 +--R 4a cos(x) +--R * +--R +--------------+ +------------+ +--R \|- a csc(x) + a \|- csc(x) - 1 +--R / +--R 2 2 2 4 +--R ((4cos(x) - 8cos(x) + 4)csc(x) - 4cos(x) + 8cos(x) - 4)sin(x) +--R + +--R 3 2 2 3 +--R (- 16cos(x) + 32cos(x) - 16cos(x))csc(x) + 16cos(x) +--R + +--R 2 +--R - 32cos(x) + 16cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (8cos(x) - 32cos(x) + 40cos(x) - 16cos(x))csc(x) - 8cos(x) +--R + +--R 3 2 +--R 32cos(x) - 40cos(x) + 16cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 2 +--R (- 16cos(x) + 32cos(x) - 16cos(x) - 16cos(x) + 16)csc(x) +--R + +--R 5 4 2 +--R 16cos(x) - 32cos(x) + 16cos(x) + 16cos(x) - 16 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) - 24cos(x) + 20cos(x) + 32cos(x) - 32cos(x) +--R + +--R - 16cos(x) + 16 +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 4cos(x) + 24cos(x) - 20cos(x) - 32cos(x) + 32cos(x) + 16cos(x) +--R + +--R - 16 +--R * +--R +---------------+3 +--R | 2 2 +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a csc(x) + a \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 2 2 4 +--R ((- 4a cos(x) + 4a)csc(x) + 4a cos(x) - 4a)sin(x) +--R + +--R 2 2 2 3 +--R ((- 8a cos(x) + 8a)csc(x) + 8a cos(x) - 8a)sin(x) +--R + +--R 2 2 2 2 +--R ((- 4a cos(x) + 4a)csc(x) + 4a cos(x) - 4a)sin(x) +--R + +--R 4 2 2 4 +--R (- 8a cos(x) + 16a cos(x) - 8a)csc(x) + 8a cos(x) +--R + +--R 2 +--R - 16a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 6 4 2 2 6 +--R (4a cos(x) - 16a cos(x) + 20a cos(x) - 8a)csc(x) - 4a cos(x) +--R + +--R 4 2 +--R 16a cos(x) - 20a cos(x) + 8a +--R * +--R +---------------+ +--R | 2 2 +--R +--------------+ +------------+ |- a cos(x) - a +--R \|- a csc(x) + a \|- csc(x) - 1 4|--------------- +--R \| 4cos(x) - 4 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 528 +t0374:= 1/(a+a*csc(x))^(1/2) +--R +--R +--R 1 +--R (347) --------------- +--R +------------+ +--R \|a csc(x) + a +--R Type: Expression(Integer) +--E 385 + +--S 386 of 528 +r0374:= -(2^(1/2)*atan(2^(1/2)*a^(1/2)/(-a+a*csc(x))^(1/2))+_ + 2*atan((-a+a*csc(x))^(1/2)/a^(1/2)))*(-a+a*csc(x))^(1/2)*_ + (a+a*csc(x))^(1/2)*tan(x)/a^(3/2) +--R +--R +--R (348) +--R +------------+ +--R +------------+ +------------+ \|a csc(x) - a +--R - 2tan(x)\|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +------------+ +------------+ \|2 \|a +--R - \|2 tan(x)\|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +------------+ +--R \|a csc(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 386 + +--S 387 of 528 +a0374:= integrate(t0374,x) +--R +--R +--R (349) +--R [ +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((- 8cos(x) + 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((- 8cos(x) + 12)sin(x) + 8cos(x) + 4cos(x) - 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R - 4a sin(x) - 4a cos(x) + 5a +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ (sin(x) - cos(x) + 1) |- 4|--------------- +--R +---+ |2 \|a \| 4cos(x) - 4 +--R - 2\|- a |- atan(-------------------------------------------) +--R \|a cos(x) +--R / +--R +---+ +--R 2\|- a +--R , +--R +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) + 2cos(x) - 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- - a sin(x) + a +--R \| 4cos(x) - 4 +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ 2a |- 4|--------------- +--R |2 +-+ \|a \| 4cos(x) - 4 +--R - |- \|a atan(------------------------) +--R \|a +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 2 4|--------------- - a +--R \| 4cos(x) - 4 +--R / +--R +-+ +--R \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 387 + +--S 388 of 528 +m0374a:= a0374.1-r0374 +--R +--R +--R (350) +--R +-+ +--R a\|a +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((- 8cos(x) + 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((- 8cos(x) + 12)sin(x) + 8cos(x) + 4cos(x) - 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R - 4a sin(x) - 4a cos(x) + 5a +--R + +--R +------------+ +--R +---+ +------------+ +------------+ \|a csc(x) - a +--R 4tan(x)\|- a \|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +-+ +--R \|a +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ (sin(x) - cos(x) + 1) |- 4|--------------- +--R +---+ |2 +-+ \|a \| 4cos(x) - 4 +--R - 2a\|- a |- \|a atan(-------------------------------------------) +--R \|a cos(x) +--R + +--R +-+ +-+ +--R +-+ +---+ +------------+ +------------+ \|2 \|a +--R 2\|2 tan(x)\|- a \|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +------------+ +--R \|a csc(x) - a +--R / +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression(Integer) +--E 388 + +--S 389 of 528 +d0374a:= D(m0374a,x) +--R +--R +--R (351) +--R 6 5 4 3 +--R 32cos(x) - 80cos(x) + 16cos(x) + 80cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) + 48cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R - 32cos(x) + 16cos(x) + 96cos(x) - 64cos(x) +--R + +--R 3 2 +--R - 64cos(x) + 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) - 16cos(x) - 96cos(x) + 64cos(x) + 64cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 5 4 3 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) +--R + +--R 2 +--R 48cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) - 16cos(x) - 96cos(x) + 64cos(x) + 64cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 6 5 4 3 2 +--R (32cos(x) - 80cos(x) + 16cos(x) + 80cos(x) - 48cos(x) ) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) + 48cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 32cos(x) + 16cos(x) + 96cos(x) - 64cos(x) - 64cos(x) +--R + +--R 2 +--R 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) - 16cos(x) - 96cos(x) + 64cos(x) + 64cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 32a cos(x) - 16a)csc(x) + 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 32a cos(x) - 16a cos(x) - 64a cos(x) + 32a cos(x) +--R + +--R 32a cos(x) - 16a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 32a cos(x) + 16a cos(x) + 64a cos(x) - 32a cos(x) +--R + +--R - 32a cos(x) + 16a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R - 16a cos(x) + 16a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R - 16a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 7 5 4 3 +--R 16a cos(x) - 68a cos(x) + 20a cos(x) + 84a cos(x) +--R + +--R 2 +--R - 36a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 7 5 4 3 +--R - 16a cos(x) + 68a cos(x) - 20a cos(x) - 84a cos(x) +--R + +--R 2 +--R 36a cos(x) + 32a cos(x) - 16a +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 2 3 +--R (16a cos(x) - 32a cos(x) + 16a)cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R - 32a cos(x) + 16a cos(x) + 64a cos(x) - 32a cos(x) +--R + +--R - 32a cos(x) + 16a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 5 4 3 +--R - 16a cos(x) + 68a cos(x) - 20a cos(x) - 84a cos(x) +--R + +--R 2 +--R 36a cos(x) + 32a cos(x) - 16a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 32a cos(x) - 16a)csc(x) + 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 32a cos(x) - 16a cos(x) - 64a cos(x) + 32a cos(x) +--R + +--R 32a cos(x) - 16a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 32a cos(x) + 16a cos(x) + 64a cos(x) - 32a cos(x) +--R + +--R - 32a cos(x) + 16a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 16a cos(x) + 16a cos(x) + 32a cos(x) - 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 7 5 4 3 +--R 16a cos(x) - 68a cos(x) + 20a cos(x) + 84a cos(x) +--R + +--R 2 +--R - 36a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 7 5 4 3 +--R - 16a cos(x) + 68a cos(x) - 20a cos(x) - 84a cos(x) +--R + +--R 2 +--R 36a cos(x) + 32a cos(x) - 16a +--R * +--R +---------------+2 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 40a cos(x) - 8a cos(x) +--R + +--R - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 48a cos(x) - 24a cos(x) - 96a cos(x) + 48a cos(x) +--R + +--R 48a cos(x) - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 48a cos(x) + 24a cos(x) + 96a cos(x) - 48a cos(x) +--R + +--R - 48a cos(x) + 24a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R - 48a cos(x) + 24a cos(x) + 120a cos(x) +--R + +--R 3 2 +--R - 48a cos(x) - 96a cos(x) + 24a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 16a cos(x) - 8a cos(x) - 64a cos(x) + 40a cos(x) +--R + +--R 3 2 +--R 80a cos(x) - 56a cos(x) - 32a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 16a cos(x) + 8a cos(x) + 64a cos(x) - 40a cos(x) +--R + +--R 3 2 +--R - 80a cos(x) + 56a cos(x) + 32a cos(x) - 24a +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 +--R (16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a) +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R - 48a cos(x) + 24a cos(x) + 96a cos(x) - 48a cos(x) +--R + +--R - 48a cos(x) + 24a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 +--R - 16a cos(x) + 8a cos(x) + 64a cos(x) - 40a cos(x) +--R + +--R 3 2 +--R - 80a cos(x) + 56a cos(x) + 32a cos(x) - 24a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 40a cos(x) - 8a cos(x) +--R + +--R - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 48a cos(x) - 24a cos(x) - 96a cos(x) + 48a cos(x) +--R + +--R 48a cos(x) - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 48a cos(x) + 24a cos(x) + 96a cos(x) - 48a cos(x) +--R + +--R - 48a cos(x) + 24a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 48a cos(x) + 24a cos(x) + 120a cos(x) - 48a cos(x) +--R + +--R 2 +--R - 96a cos(x) + 24a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 16a cos(x) - 8a cos(x) - 64a cos(x) + 40a cos(x) +--R + +--R 3 2 +--R 80a cos(x) - 56a cos(x) - 32a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 16a cos(x) + 8a cos(x) + 64a cos(x) - 40a cos(x) +--R + +--R 3 2 +--R - 80a cos(x) + 56a cos(x) + 32a cos(x) - 24a +--R * +--R +---------------+ +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) - 8a cos(x) + 8a cos(x) + 8a )csc(x) +--R + +--R 2 3 2 2 2 2 +--R 8a cos(x) + 8a cos(x) - 8a cos(x) - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 8a cos(x) + 8a cos(x) + 18a cos(x) - 14a cos(x) +--R + +--R 2 2 +--R - 10a cos(x) + 6a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a cos(x) - 8a cos(x) - 18a cos(x) + 14a cos(x) +--R + +--R 2 2 +--R 10a cos(x) - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 8a cos(x) - 8a cos(x) - 28a cos(x) + 16a cos(x) +--R + +--R 2 2 2 2 +--R 32a cos(x) - 8a cos(x) - 12a +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 8a cos(x) + 16a cos(x) + 26a cos(x) - 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 28a cos(x) + 36a cos(x) + 10a cos(x) - 10a +--R * +--R 2 +--R csc(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 8a cos(x) - 16a cos(x) - 26a cos(x) + 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 28a cos(x) - 36a cos(x) - 10a cos(x) + 10a +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) + 8a cos(x) - 8a cos(x) - 8a )cot(x)csc(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a cos(x) - 8a cos(x) - 18a cos(x) + 14a cos(x) +--R + +--R 2 2 +--R 10a cos(x) - 6a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 8a cos(x) - 16a cos(x) - 26a cos(x) + 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 28a cos(x) - 36a cos(x) - 10a cos(x) + 10a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) - 8a cos(x) + 8a cos(x) + 8a )csc(x) +--R + +--R 2 3 2 2 2 2 +--R 8a cos(x) + 8a cos(x) - 8a cos(x) - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 8a cos(x) + 8a cos(x) + 18a cos(x) - 14a cos(x) +--R + +--R 2 2 +--R - 10a cos(x) + 6a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a cos(x) - 8a cos(x) - 18a cos(x) + 14a cos(x) +--R + +--R 2 2 +--R 10a cos(x) - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 8a cos(x) - 8a cos(x) - 28a cos(x) + 16a cos(x) +--R + +--R 2 2 2 2 +--R 32a cos(x) - 8a cos(x) - 12a +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 8a cos(x) + 16a cos(x) + 26a cos(x) - 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 28a cos(x) + 36a cos(x) + 10a cos(x) - 10a +--R * +--R 2 +--R csc(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 8a cos(x) - 16a cos(x) - 26a cos(x) + 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 28a cos(x) - 36a cos(x) - 10a cos(x) + 10a +--R * +--R +-+ +--R \|a +--R * +--R +------------+ +--R \|a csc(x) - a +--R atan(---------------) +--R +-+ +--R \|a +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 40\|2 cos(x) + 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 40\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 16\|2 cos(x) + 8\|2 cos(x) + 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 8\|2 cos(x) - 48\|2 cos(x) + 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 32\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 16\|2 cos(x) - 8\|2 cos(x) - 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 32\|2 cos(x) + 32\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 40\|2 cos(x) + 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 40\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 16\|2 cos(x) + 8\|2 cos(x) + 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 8\|2 cos(x) - 48\|2 cos(x) + 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 32\|2 cos(x) - 24\|2 cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 )csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16a\|2 cos(x) - 8a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 8a\|2 cos(x) + 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 34a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 42a\|2 cos(x) - 18a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 34a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 42a\|2 cos(x) + 18a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 3 +--R (8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 )cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 34a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 42a\|2 cos(x) + 18a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 )csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16a\|2 cos(x) - 8a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 8a\|2 cos(x) + 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 34a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 42a\|2 cos(x) - 18a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 34a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 42a\|2 cos(x) + 18a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R +---------------+2 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 4a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R 4a\|2 cos(x) + 12a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 24a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 24a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 24a\|2 cos(x) - 48a\|2 cos(x) + 12a\|2 cos(x) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 20a\|2 cos(x) + 40a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 16a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 20a\|2 cos(x) - 40a\|2 cos(x) + 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R 16a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R 4a\|2 cos(x) + 12a\|2 +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 24a\|2 cos(x) + 12a\|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 20a\|2 cos(x) - 40a\|2 cos(x) + 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R 16a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 4a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 24a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 24a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 48a\|2 cos(x) + 12a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 20a\|2 cos(x) + 40a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 16a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 32a\|2 cos(x) - 20a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 40a\|2 cos(x) + 28a\|2 cos(x) + 16a\|2 cos(x) - 12a\|2 +--R * +--R +---------------+ +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 4a \|2 cos(x) - 4a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 4a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 +--R * +--R 3 +--R sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 7a \|2 cos(x) - 5a \|2 cos(x) + 3a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 7a \|2 cos(x) + 5a \|2 cos(x) - 3a \|2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R 8a \|2 cos(x) + 16a \|2 cos(x) - 4a \|2 cos(x) +--R + +--R 2 +-+ +--R - 6a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 6a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R - 4a \|2 cos(x) + 8a \|2 cos(x) + 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R - 21a \|2 cos(x) - 14a \|2 cos(x) + 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R 5a \|2 cos(x) - 5a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R 4a \|2 cos(x) - 8a \|2 cos(x) - 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R 21a \|2 cos(x) + 14a \|2 cos(x) - 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R - 5a \|2 cos(x) + 5a \|2 +--R * +--R 2 +--R tan(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R (4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 ) +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 7a \|2 cos(x) + 5a \|2 cos(x) - 3a \|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 6a \|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R 4a \|2 cos(x) - 8a \|2 cos(x) - 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R 21a \|2 cos(x) + 14a \|2 cos(x) - 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R - 5a \|2 cos(x) + 5a \|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 4a \|2 cos(x) - 4a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 4a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 +--R * +--R 3 +--R sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 7a \|2 cos(x) - 5a \|2 cos(x) + 3a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 7a \|2 cos(x) + 5a \|2 cos(x) - 3a \|2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 8a \|2 cos(x) + 16a \|2 cos(x) - 4a \|2 cos(x) - 6a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) + 6a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R - 4a \|2 cos(x) + 8a \|2 cos(x) + 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R - 21a \|2 cos(x) - 14a \|2 cos(x) + 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R 5a \|2 cos(x) - 5a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R 4a \|2 cos(x) - 8a \|2 cos(x) - 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R 21a \|2 cos(x) + 14a \|2 cos(x) - 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R - 5a \|2 cos(x) + 5a \|2 +--R * +--R +-+ +--R \|a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(---------------) +--R +------------+ +--R \|a csc(x) - a +--R + +--R 3 2 3 +--R (- 16cos(x) + 8cos(x) + 24cos(x) - 16)sin(x) +--R + +--R 5 4 3 2 +--R (- 24cos(x) + 20cos(x) + 34cos(x) - 28cos(x) - 6cos(x) + 4) +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 16cos(x) - 40cos(x) - 2cos(x) + 70cos(x) - 34cos(x) +--R + +--R - 30cos(x) + 20 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 8cos(x) - 4cos(x) + 40cos(x) - 16cos(x) - 32cos(x) +--R + +--R 2 +--R 20cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 +--R (- 4cos(x) + 4cos(x))sin(x) +--R + +--R 4 3 2 3 +--R (8cos(x) - 4cos(x) - 8cos(x) + 4cos(x))sin(x) +--R + +--R 5 3 7 6 +--R (4cos(x) - 8cos(x) + 4cos(x))sin(x) + 4cos(x) - 12cos(x) +--R + +--R 4 3 2 +--R 20cos(x) - 8cos(x) - 8cos(x) + 4cos(x) +--R * +--R +---------------+2 +--R | 2 2 +--R +---+ |- a cos(x) - a +--R \|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 4 +--R (4a cos(x) + 2a cos(x) - 3a cos(x) - a)sin(x) +--R + +--R 4 2 3 +--R (- 8a cos(x) + 3a cos(x) + 5a)sin(x) +--R + +--R 5 4 3 2 +--R 16a cos(x) - 8a cos(x) - 27a cos(x) + 11a cos(x) +--R + +--R 11a cos(x) - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 4a cos(x) - 19a cos(x) + 2a cos(x) +--R + +--R 2 +--R 20a cos(x) + 2a cos(x) - 9a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 4a cos(x) + 2a cos(x) + 2a cos(x) - 4a cos(x) + 8a cos(x) +--R + +--R 2 +--R 2a cos(x) - 6a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 3 +--R (4a cos(x) - 4a cos(x) - 18a cos(x) + 2a cos(x) + 12a)sin(x) +--R + +--R 5 4 2 2 +--R (- 2a cos(x) - 10a cos(x) + 10a cos(x) + 2a cos(x))sin(x) +--R + +--R 6 5 4 3 +--R 4a cos(x) - 6a cos(x) - 22a cos(x) + 8a cos(x) +--R + +--R 2 +--R 30a cos(x) - 2a cos(x) - 12a +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R - 6a cos(x) - 10a cos(x) + 10a cos(x) + 20a cos(x) +--R + +--R 3 2 +--R - 2a cos(x) - 10a cos(x) - 2a cos(x) +--R * +--R +---+ +--R \|- a +--R * +--R +------------+ +------------+ +--R \|a csc(x) - a \|a csc(x) + a +--R + +--R 6 5 4 3 2 +--R (- 16cos(x) + 40cos(x) - 8cos(x) - 40cos(x) + 24cos(x) ) +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 3 +--R 16cos(x) - 8cos(x) - 48cos(x) + 32cos(x) + 32cos(x) +--R + +--R 2 +--R - 24cos(x) +--R * +--R cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ |- a cos(x) - a +--R tan(x)\|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 2 3 +--R (8a cos(x) - 16a cos(x) + 8a)cot(x)sin(x) +--R + +--R 5 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 32a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) + 8a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 8a cos(x) - 16a cos(x) + 8a cos(x) +--R + +--R 2 +--R 16a cos(x) - 8a +--R * +--R cot(x)sin(x) +--R + +--R 7 5 4 3 +--R - 8a cos(x) + 34a cos(x) - 10a cos(x) - 42a cos(x) +--R + +--R 2 +--R 18a cos(x) + 16a cos(x) - 8a +--R * +--R cot(x) +--R * +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R tan(x) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 +--R (8a cos(x) - 4a cos(x) - 20a cos(x) + 4a cos(x) + 12a)cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R - 24a cos(x) + 12a cos(x) + 48a cos(x) - 24a cos(x) +--R + +--R - 24a cos(x) + 12a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 6 5 4 3 +--R 24a cos(x) - 12a cos(x) - 60a cos(x) + 24a cos(x) +--R + +--R 2 +--R 48a cos(x) - 12a cos(x) - 12a +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 +--R - 8a cos(x) + 4a cos(x) + 32a cos(x) - 20a cos(x) +--R + +--R 3 2 +--R - 40a cos(x) + 28a cos(x) + 16a cos(x) - 12a +--R * +--R cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R +---+ |- a cos(x) - a +--R tan(x)\|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 3 +--R (4a cos(x) + 4a cos(x) - 4a cos(x) - 4a )cot(x)sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 +--R 4a cos(x) - 4a cos(x) - 9a cos(x) + 7a cos(x) + 5a cos(x) +--R + +--R 2 +--R - 3a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 4a cos(x) + 4a cos(x) + 14a cos(x) - 8a cos(x) +--R + +--R 2 2 2 2 +--R - 16a cos(x) + 4a cos(x) + 6a +--R * +--R cot(x)sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 4a cos(x) - 8a cos(x) - 13a cos(x) + 21a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 14a cos(x) - 18a cos(x) - 5a cos(x) + 5a +--R * +--R cot(x) +--R * +--R tan(x) +--R * +--R +------------+ +--R \|a csc(x) - a +--R / +--R 6 5 4 3 2 +--R (16cos(x) - 40cos(x) + 8cos(x) + 40cos(x) - 24cos(x) )sin(x) +--R + +--R 7 6 5 4 3 +--R - 16cos(x) + 8cos(x) + 48cos(x) - 32cos(x) - 32cos(x) +--R + +--R 2 +--R 24cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ |- a cos(x) - a +--R \|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 2 3 +--R (- 8a cos(x) + 16a cos(x) - 8a)sin(x) +--R + +--R 5 4 3 2 +--R 16a cos(x) - 8a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) - 8a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 8a cos(x) + 8a cos(x) + 16a cos(x) - 8a cos(x) +--R + +--R 2 +--R - 16a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 7 5 4 3 2 +--R 8a cos(x) - 34a cos(x) + 10a cos(x) + 42a cos(x) - 18a cos(x) +--R + +--R - 16a cos(x) + 8a +--R * +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 3 +--R (- 8a cos(x) + 4a cos(x) + 20a cos(x) - 4a cos(x) - 12a)sin(x) +--R + +--R 5 4 3 2 +--R 24a cos(x) - 12a cos(x) - 48a cos(x) + 24a cos(x) +--R + +--R 24a cos(x) - 12a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 24a cos(x) + 12a cos(x) + 60a cos(x) - 24a cos(x) +--R + +--R 2 +--R - 48a cos(x) + 12a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 8a cos(x) - 4a cos(x) - 32a cos(x) + 20a cos(x) + 40a cos(x) +--R + +--R 2 +--R - 28a cos(x) - 16a cos(x) + 12a +--R * +--R +---------------+ +--R | 2 2 +--R +---+ |- a cos(x) - a +--R \|- a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 3 +--R (- 4a cos(x) - 4a cos(x) + 4a cos(x) + 4a )sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 +--R - 4a cos(x) + 4a cos(x) + 9a cos(x) - 7a cos(x) - 5a cos(x) +--R + +--R 2 +--R 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 4a cos(x) - 4a cos(x) - 14a cos(x) + 8a cos(x) + 16a cos(x) +--R + +--R 2 2 +--R - 4a cos(x) - 6a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 2 3 +--R - 4a cos(x) + 8a cos(x) + 13a cos(x) - 21a cos(x) - 14a cos(x) +--R + +--R 2 2 2 2 +--R 18a cos(x) + 5a cos(x) - 5a +--R * +--R +------------+ +------------+ +--R \|a csc(x) - a \|a csc(x) + a +--R Type: Expression(Integer) +--E 389 + +--S 390 of 528 +m0374b:= a0374.2-r0374 +--R +--R +--R (352) +--R +------------+ +--R +------------+ +------------+ \|a csc(x) - a +--R 2tan(x)\|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +-+ +--R \|a +--R + +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) + 2cos(x) - 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R a atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- - a sin(x) + a +--R \| 4cos(x) - 4 +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ 2a |- 4|--------------- +--R |2 +-+ \|a \| 4cos(x) - 4 +--R - a |- \|a atan(------------------------) +--R \|a +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 2 4|--------------- - a +--R \| 4cos(x) - 4 +--R + +--R +-+ +-+ +--R +-+ +------------+ +------------+ \|2 \|a +--R \|2 tan(x)\|a csc(x) - a \|a csc(x) + a atan(---------------) +--R +------------+ +--R \|a csc(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 390 + +--S 391 of 528 +d0374b:= D(m0374b,x) +--R +--R +--R (353) +--R 3 2 3 4 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 3 +--R ((- 32cos(x) + 32cos(x))csc(x) + 32cos(x) - 32cos(x)) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 3 2 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 5 3 2 5 +--R (- 32cos(x) + 64cos(x) - 32cos(x))csc(x) + 32cos(x) +--R + +--R 3 +--R - 64cos(x) + 32cos(x) +--R * +--R sin(x) +--R + +--R 7 5 3 2 +--R (- 16cos(x) + 64cos(x) - 80cos(x) + 32cos(x))csc(x) +--R + +--R 7 5 3 +--R 16cos(x) - 64cos(x) + 80cos(x) - 32cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 4 +--R (- 16cos(x) + 16cos(x))cot(x)csc(x) sin(x) +--R + +--R 3 2 3 +--R (32cos(x) - 32cos(x))cot(x)csc(x) sin(x) +--R + +--R 3 2 2 +--R (- 16cos(x) + 16cos(x))cot(x)csc(x) sin(x) +--R + +--R 5 3 2 +--R (32cos(x) - 64cos(x) + 32cos(x))cot(x)csc(x) sin(x) +--R + +--R 7 5 3 2 +--R (16cos(x) - 64cos(x) + 80cos(x) - 32cos(x))cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 3 2 3 4 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 3 3 +--R ((- 32cos(x) + 32cos(x))csc(x) + 32cos(x) - 32cos(x))sin(x) +--R + +--R 3 2 3 2 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 5 3 2 5 +--R (- 32cos(x) + 64cos(x) - 32cos(x))csc(x) + 32cos(x) +--R + +--R 3 +--R - 64cos(x) + 32cos(x) +--R * +--R sin(x) +--R + +--R 7 5 3 2 +--R (- 16cos(x) + 64cos(x) - 80cos(x) + 32cos(x))csc(x) +--R + +--R 7 5 3 +--R 16cos(x) - 64cos(x) + 80cos(x) - 32cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 3 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x)) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 4 +--R (16a cos(x) - 16a cos(x) )csc(x) - 16a cos(x) +--R + +--R 2 +--R 16a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 16a cos(x) ) +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 3 2 +--R 16a cos(x) - 32a cos(x) - 16a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 4 3 2 +--R - 16a cos(x) + 32a cos(x) + 16a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 4a cos(x) - 16a cos(x) - 20a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R 32a cos(x) - 16a cos(x) - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 4 +--R (- 4a cos(x) + 4a cos(x))cot(x)csc(x) sin(x) +--R + +--R 4 2 2 3 +--R (- 16a cos(x) + 16a cos(x) )cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R (- 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) ) +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 4 3 2 +--R - 16a cos(x) + 32a cos(x) + 16a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 3 2 3 4 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x))sin(x) +--R + +--R 4 2 2 4 +--R (16a cos(x) - 16a cos(x) )csc(x) - 16a cos(x) +--R + +--R 2 +--R 16a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 16a cos(x) )csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 3 2 +--R 16a cos(x) - 32a cos(x) - 16a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 4 3 2 +--R - 16a cos(x) + 32a cos(x) + 16a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 4a cos(x) - 16a cos(x) - 20a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R 32a cos(x) - 16a cos(x) - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +------------+ +--R \|a csc(x) - a +--R atan(---------------) +--R +-+ +--R \|a +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (- 16\|2 cos(x) + 16\|2 cos(x))csc(x) + 16\|2 cos(x) +--R + +--R +-+ +--R - 16\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 16\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x))csc(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 16\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 8\|2 cos(x) + 32\|2 cos(x) - 40\|2 cos(x) +--R + +--R +-+ +--R 16\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) - 16\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 3 +-+ 2 4 +--R (- 8\|2 cos(x) + 8\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 3 +-+ 2 3 +--R (16\|2 cos(x) - 16\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 3 +-+ 2 2 +--R (- 8\|2 cos(x) + 8\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (16\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x))cot(x)csc(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) +--R + +--R +-+ +--R - 16\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (- 16\|2 cos(x) + 16\|2 cos(x))csc(x) + 16\|2 cos(x) +--R + +--R +-+ +--R - 16\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (- 16\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x))csc(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 16\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 8\|2 cos(x) + 32\|2 cos(x) - 40\|2 cos(x) + 16\|2 cos(x)) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) - 16\|2 cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (2a\|2 cos(x) - 2a\|2 cos(x))csc(x) - 2a\|2 cos(x) +--R + +--R +-+ +--R 2a\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 2 +-+ 4 +--R (8a\|2 cos(x) - 8a\|2 cos(x) )csc(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R - 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2a\|2 cos(x) - 8a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ +--R - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ +--R 8a\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 3 +-+ 2 4 +--R (- 2a\|2 cos(x) + 2a\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 4 +-+ 2 2 3 +--R (- 8a\|2 cos(x) + 8a\|2 cos(x) )cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R - 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ +--R 8a\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (2a\|2 cos(x) - 2a\|2 cos(x))csc(x) - 2a\|2 cos(x) +--R + +--R +-+ +--R 2a\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 2 +-+ 4 +--R (8a\|2 cos(x) - 8a\|2 cos(x) )csc(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R - 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2a\|2 cos(x) - 8a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(---------------) +--R +------------+ +--R \|a csc(x) - a +--R + +--R 5 +--R (4cos(x) + 2)sin(x) +--R + +--R 3 2 4 +--R (4cos(x) + 6cos(x) - 12cos(x) - 8)sin(x) +--R + +--R 4 3 2 3 +--R (8cos(x) - 2cos(x) - 14cos(x) + 6cos(x) + 4)sin(x) +--R + +--R 4 3 2 2 +--R (- 2cos(x) - 4cos(x) - 12cos(x) + 4cos(x) + 16)sin(x) +--R + +--R 6 5 4 3 2 +--R (8cos(x) - 6cos(x) - 28cos(x) + 6cos(x) + 36cos(x) - 16) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R - 4cos(x) - 8cos(x) + 12cos(x) + 16cos(x) - 8cos(x) - 8cos(x) +--R * +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 5 +--R (- a cos(x) - a)sin(x) +--R + +--R 3 2 4 +--R (- 2a cos(x) - a cos(x) + 5a cos(x) + 4a)sin(x) +--R + +--R 4 3 2 3 +--R (4a cos(x) + 9a cos(x) + 4a cos(x) - 3a cos(x) - 2a)sin(x) +--R + +--R 4 3 2 2 +--R (- 3a cos(x) + a cos(x) + 2a cos(x) - 10a cos(x) - 8a)sin(x) +--R + +--R 6 5 4 3 2 +--R 4a cos(x) + 10a cos(x) + 3a cos(x) - 17a cos(x) - 14a cos(x) +--R + +--R 8a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 2a cos(x) - 2a cos(x) - 10a cos(x) - 2a cos(x) + 8a cos(x) +--R + +--R 2 +--R 4a cos(x) +--R * +--R +------------+ +------------+ +--R \|a csc(x) - a \|a csc(x) + a +--R + +--R 3 4 +--R (- 8cos(x) + 8cos(x))cot(x)sin(x) +--R + +--R 3 3 +--R (16cos(x) - 16cos(x))cot(x)sin(x) +--R + +--R 3 2 +--R (- 8cos(x) + 8cos(x))cot(x)sin(x) +--R + +--R 5 3 +--R (16cos(x) - 32cos(x) + 16cos(x))cot(x)sin(x) +--R + +--R 7 5 3 +--R (8cos(x) - 32cos(x) + 40cos(x) - 16cos(x))cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R tan(x) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 +--R (- 2a cos(x) + 2a cos(x))cot(x)sin(x) +--R + +--R 4 2 3 +--R (- 8a cos(x) + 8a cos(x) )cot(x)sin(x) +--R + +--R 5 4 3 2 +--R (- 4a cos(x) + 8a cos(x) + 4a cos(x) - 8a cos(x) )cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 3 2 +--R - 8a cos(x) + 16a cos(x) + 8a cos(x) - 8a cos(x) +--R + +--R - 8a cos(x) +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 +--R - 2a cos(x) + 8a cos(x) + 10a cos(x) - 16a cos(x) +--R + +--R 3 2 +--R - 16a cos(x) + 8a cos(x) + 8a cos(x) +--R * +--R cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R tan(x) 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +------------+ +--R \|a csc(x) - a +--R / +--R 3 4 3 3 +--R (8cos(x) - 8cos(x))sin(x) + (- 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 +--R (8cos(x) - 8cos(x))sin(x) +--R + +--R 5 3 7 5 +--R (- 16cos(x) + 32cos(x) - 16cos(x))sin(x) - 8cos(x) + 32cos(x) +--R + +--R 3 +--R - 40cos(x) + 16cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 4 2 3 +--R (2a cos(x) - 2a cos(x))sin(x) + (8a cos(x) - 8a cos(x) )sin(x) +--R + +--R 5 4 3 2 2 +--R (4a cos(x) - 8a cos(x) - 4a cos(x) + 8a cos(x) )sin(x) +--R + +--R 6 4 3 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 8a cos(x) + 8a cos(x)) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 2a cos(x) - 8a cos(x) - 10a cos(x) + 16a cos(x) + 16a cos(x) +--R + +--R 2 +--R - 8a cos(x) - 8a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +------------+ +------------+ +--R \|a csc(x) - a \|a csc(x) + a +--R Type: Expression(Integer) +--E 391 + +--S 392 of 528 +t0375:= 1/(a-a*csc(x))^(1/2) +--R +--R +--R 1 +--R (354) ----------------- +--R +--------------+ +--R \|- a csc(x) + a +--R Type: Expression(Integer) +--E 392 + +--S 393 of 528 +r0375:= -(2^(1/2)*atan(2^(1/2)*a^(1/2)/(-a-a*csc(x))^(1/2))+_ + 2*atan((-a-a*csc(x))^(1/2)/a^(1/2)))*(-a-a*csc(x))^(1/2)*_ + (a-a*csc(x))^(1/2)*tan(x)/a^(3/2) +--R +--R +--R (355) +--R +--------------+ +--R +--------------+ +--------------+ \|- a csc(x) - a +--R - 2tan(x)\|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +--------------+ +--------------+ \|2 \|a +--R - \|2 tan(x)\|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +--------------+ +--R \|- a csc(x) - a +--R / +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 393 + +--S 394 of 528 +a0375:= integrate(t0375,x) +--R +--R +--R (356) +--R [ +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((8cos(x) - 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((8cos(x) - 12)sin(x) + 8cos(x) + 4cos(x) - 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R 4a sin(x) - 4a cos(x) + 5a +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ (sin(x) + cos(x) - 1) |- 4|--------------- +--R +---+ |2 \|a \| 4cos(x) - 4 +--R 2\|- a |- atan(-------------------------------------------) +--R \|a cos(x) +--R / +--R +---+ +--R 2\|- a +--R , +--R +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) - 2cos(x) + 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R - atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- + a sin(x) + a +--R \| 4cos(x) - 4 +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ 2a |- 4|--------------- +--R |2 +-+ \|a \| 4cos(x) - 4 +--R - |- \|a atan(------------------------) +--R \|a +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 2 4|--------------- - a +--R \| 4cos(x) - 4 +--R / +--R +-+ +--R \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 394 + +--S 395 of 528 +m0375a:= a0375.1-r0375 +--R +--R +--R (357) +--R +-+ +--R a\|a +--R * +--R log +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R ((8cos(x) - 8)sin(x) + 8cos(x) - 8) 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +---+ +--R ((8cos(x) - 12)sin(x) + 8cos(x) + 4cos(x) - 12)\|- a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +--R 4a sin(x) - 4a cos(x) + 5a +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ (sin(x) + cos(x) - 1) |- 4|--------------- +--R +---+ |2 +-+ \|a \| 4cos(x) - 4 +--R 2a\|- a |- \|a atan(-------------------------------------------) +--R \|a cos(x) +--R + +--R +--------------+ +--R +---+ +--------------+ +--------------+ \|- a csc(x) - a +--R 4tan(x)\|- a \|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +---+ +--------------+ +--------------+ \|2 \|a +--R 2\|2 tan(x)\|- a \|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +--------------+ +--R \|- a csc(x) - a +--R / +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression(Integer) +--E 395 + +--S 396 of 528 +d0375a:= D(m0375a,x) +--R +--R +--R (358) +--R 6 5 4 3 +--R 32cos(x) - 80cos(x) + 16cos(x) + 80cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) + 48cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) - 16cos(x) - 96cos(x) + 64cos(x) + 64cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 32cos(x) + 16cos(x) + 96cos(x) - 64cos(x) - 64cos(x) +--R + +--R 2 +--R 48cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 5 4 3 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) +--R + +--R 2 +--R 48cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 +--R - 32cos(x) + 16cos(x) + 96cos(x) - 64cos(x) +--R + +--R 3 2 +--R - 64cos(x) + 48cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 6 5 4 3 2 +--R (32cos(x) - 80cos(x) + 16cos(x) + 80cos(x) - 48cos(x) ) +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 80cos(x) - 16cos(x) - 80cos(x) + 48cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) - 16cos(x) - 96cos(x) + 64cos(x) + 64cos(x) +--R + +--R 2 +--R - 48cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 32cos(x) + 16cos(x) + 96cos(x) - 64cos(x) - 64cos(x) +--R + +--R 2 +--R 48cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 32a cos(x) - 16a)csc(x) + 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 +--R - 32a cos(x) + 16a cos(x) + 64a cos(x) +--R + +--R 2 +--R - 32a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R 32a cos(x) - 16a cos(x) - 64a cos(x) + 32a cos(x) +--R + +--R 32a cos(x) - 16a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R - 16a cos(x) + 16a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R - 16a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 7 5 4 3 +--R - 16a cos(x) + 68a cos(x) - 20a cos(x) - 84a cos(x) +--R + +--R 2 +--R 36a cos(x) + 32a cos(x) - 16a +--R * +--R 2 +--R csc(x) +--R + +--R 7 5 4 3 +--R 16a cos(x) - 68a cos(x) + 20a cos(x) + 84a cos(x) +--R + +--R 2 +--R - 36a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 2 3 +--R (16a cos(x) - 32a cos(x) + 16a)cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R 32a cos(x) - 16a cos(x) - 64a cos(x) + 32a cos(x) +--R + +--R 32a cos(x) - 16a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 5 4 3 +--R 16a cos(x) - 68a cos(x) + 20a cos(x) + 84a cos(x) +--R + +--R 2 +--R - 36a cos(x) - 32a cos(x) + 16a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 32a cos(x) - 16a)csc(x) + 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R - 32a cos(x) + 16a cos(x) + 64a cos(x) - 32a cos(x) +--R + +--R - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R 32a cos(x) - 16a cos(x) - 64a cos(x) + 32a cos(x) +--R + +--R 32a cos(x) - 16a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 16a cos(x) + 16a cos(x) + 32a cos(x) - 16a cos(x) +--R + +--R 2 +--R - 32a cos(x) + 16a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 16a cos(x) - 16a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R 32a cos(x) - 16a +--R * +--R sin(x) +--R + +--R 7 5 4 3 +--R - 16a cos(x) + 68a cos(x) - 20a cos(x) - 84a cos(x) +--R + +--R 2 +--R 36a cos(x) + 32a cos(x) - 16a +--R * +--R 2 +--R csc(x) +--R + +--R 7 5 4 3 +--R 16a cos(x) - 68a cos(x) + 20a cos(x) + 84a cos(x) +--R + +--R 2 +--R - 36a cos(x) - 32a cos(x) + 16a +--R * +--R +---------------+2 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 40a cos(x) - 8a cos(x) +--R + +--R - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 +--R - 48a cos(x) + 24a cos(x) + 96a cos(x) +--R + +--R 2 +--R - 48a cos(x) - 48a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R 48a cos(x) - 24a cos(x) - 96a cos(x) + 48a cos(x) +--R + +--R 48a cos(x) - 24a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R - 48a cos(x) + 24a cos(x) + 120a cos(x) +--R + +--R 3 2 +--R - 48a cos(x) - 96a cos(x) + 24a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R - 16a cos(x) + 8a cos(x) + 64a cos(x) - 40a cos(x) +--R + +--R 3 2 +--R - 80a cos(x) + 56a cos(x) + 32a cos(x) - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R 16a cos(x) - 8a cos(x) - 64a cos(x) + 40a cos(x) +--R + +--R 3 2 +--R 80a cos(x) - 56a cos(x) - 32a cos(x) + 24a +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 +--R (16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a) +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R 48a cos(x) - 24a cos(x) - 96a cos(x) + 48a cos(x) +--R + +--R 48a cos(x) - 24a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 +--R 16a cos(x) - 8a cos(x) - 64a cos(x) + 40a cos(x) +--R + +--R 3 2 +--R 80a cos(x) - 56a cos(x) - 32a cos(x) + 24a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 40a cos(x) - 8a cos(x) +--R + +--R - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 4 3 2 +--R 16a cos(x) - 8a cos(x) - 40a cos(x) + 8a cos(x) + 24a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R - 48a cos(x) + 24a cos(x) + 96a cos(x) - 48a cos(x) +--R + +--R - 48a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R 48a cos(x) - 24a cos(x) - 96a cos(x) + 48a cos(x) +--R + +--R 48a cos(x) - 24a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 48a cos(x) + 24a cos(x) + 120a cos(x) - 48a cos(x) +--R + +--R 2 +--R - 96a cos(x) + 24a cos(x) + 24a +--R * +--R 2 +--R csc(x) +--R + +--R 6 5 4 3 +--R 48a cos(x) - 24a cos(x) - 120a cos(x) + 48a cos(x) +--R + +--R 2 +--R 96a cos(x) - 24a cos(x) - 24a +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R - 16a cos(x) + 8a cos(x) + 64a cos(x) - 40a cos(x) +--R + +--R 3 2 +--R - 80a cos(x) + 56a cos(x) + 32a cos(x) - 24a +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R 16a cos(x) - 8a cos(x) - 64a cos(x) + 40a cos(x) +--R + +--R 3 2 +--R 80a cos(x) - 56a cos(x) - 32a cos(x) + 24a +--R * +--R +---------------+ +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) - 8a cos(x) + 8a cos(x) + 8a )csc(x) +--R + +--R 2 3 2 2 2 2 +--R 8a cos(x) + 8a cos(x) - 8a cos(x) - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a cos(x) - 8a cos(x) - 18a cos(x) + 14a cos(x) +--R + +--R 2 2 +--R 10a cos(x) - 6a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 8a cos(x) + 8a cos(x) + 18a cos(x) - 14a cos(x) +--R + +--R 2 2 +--R - 10a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 8a cos(x) - 8a cos(x) - 28a cos(x) + 16a cos(x) +--R + +--R 2 2 2 2 +--R 32a cos(x) - 8a cos(x) - 12a +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 8a cos(x) - 16a cos(x) - 26a cos(x) + 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 28a cos(x) - 36a cos(x) - 10a cos(x) + 10a +--R * +--R 2 +--R csc(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 8a cos(x) + 16a cos(x) + 26a cos(x) - 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 28a cos(x) + 36a cos(x) + 10a cos(x) - 10a +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 2 2 2 2 2 +--R (8a cos(x) + 8a cos(x) - 8a cos(x) - 8a )cot(x)csc(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 8a cos(x) + 8a cos(x) + 18a cos(x) - 14a cos(x) +--R + +--R 2 2 +--R - 10a cos(x) + 6a +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 8a cos(x) + 16a cos(x) + 26a cos(x) - 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 28a cos(x) + 36a cos(x) + 10a cos(x) - 10a +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 8a cos(x) - 8a cos(x) + 8a cos(x) + 8a )csc(x) +--R + +--R 2 3 2 2 2 2 +--R 8a cos(x) + 8a cos(x) - 8a cos(x) - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R 8a cos(x) - 8a cos(x) - 18a cos(x) + 14a cos(x) +--R + +--R 2 2 +--R 10a cos(x) - 6a +--R * +--R 2 +--R csc(x) +--R + +--R 2 5 2 4 2 3 2 2 +--R - 8a cos(x) + 8a cos(x) + 18a cos(x) - 14a cos(x) +--R + +--R 2 2 +--R - 10a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R 8a cos(x) - 8a cos(x) - 28a cos(x) + 16a cos(x) +--R + +--R 2 2 2 2 +--R 32a cos(x) - 8a cos(x) - 12a +--R * +--R 2 +--R csc(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 8a cos(x) + 8a cos(x) + 28a cos(x) - 16a cos(x) +--R + +--R 2 2 2 2 +--R - 32a cos(x) + 8a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R 8a cos(x) - 16a cos(x) - 26a cos(x) + 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 28a cos(x) - 36a cos(x) - 10a cos(x) + 10a +--R * +--R 2 +--R csc(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 8a cos(x) + 16a cos(x) + 26a cos(x) - 42a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 28a cos(x) + 36a cos(x) + 10a cos(x) - 10a +--R * +--R +-+ +--R \|a +--R * +--R +--------------+ +--R \|- a csc(x) - a +--R atan(-----------------) +--R +-+ +--R \|a +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 40\|2 cos(x) + 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 40\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 16\|2 cos(x) - 8\|2 cos(x) - 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 32\|2 cos(x) + 32\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 16\|2 cos(x) + 8\|2 cos(x) + 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 16\|2 cos(x) + 8\|2 cos(x) + 48\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 40\|2 cos(x) + 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 40\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 40\|2 cos(x) - 8\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 40\|2 cos(x) + 24\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 16\|2 cos(x) - 8\|2 cos(x) - 48\|2 cos(x) + 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R 32\|2 cos(x) - 24\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 16\|2 cos(x) + 8\|2 cos(x) + 48\|2 cos(x) - 32\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +--R - 32\|2 cos(x) + 24\|2 cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 )csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16a\|2 cos(x) - 8a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 8a\|2 cos(x) + 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 34a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 42a\|2 cos(x) + 18a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 34a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 42a\|2 cos(x) - 18a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 3 +--R (8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 )cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16a\|2 cos(x) - 8a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 34a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 42a\|2 cos(x) - 18a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +--R (- 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 )csc(x) +--R + +--R +-+ 4 +-+ 2 +-+ +--R 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 16a\|2 cos(x) - 8a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 8a\|2 cos(x) + 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 8a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +--R - 8a\|2 cos(x) + 34a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 42a\|2 cos(x) + 18a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 34a\|2 cos(x) + 10a\|2 cos(x) + 42a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 18a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 +--R * +--R +---------------+2 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 4a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R 4a\|2 cos(x) + 12a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 24a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 24a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 24a\|2 cos(x) - 48a\|2 cos(x) + 12a\|2 cos(x) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 20a\|2 cos(x) - 40a\|2 cos(x) + 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R 16a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 20a\|2 cos(x) + 40a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 16a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R 4a\|2 cos(x) + 12a\|2 +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 24a\|2 cos(x) - 12a\|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 20a\|2 cos(x) + 40a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 16a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 20a\|2 cos(x) +--R + +--R +-+ +-+ +--R - 4a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 20a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ +--R 12a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 24a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 48a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 24a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 24a\|2 cos(x) + 12a\|2 cos(x) + 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 24a\|2 cos(x) - 48a\|2 cos(x) + 12a\|2 cos(x) + 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R 24a\|2 cos(x) - 12a\|2 cos(x) - 60a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 24a\|2 cos(x) + 48a\|2 cos(x) - 12a\|2 cos(x) - 12a\|2 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 8a\|2 cos(x) + 4a\|2 cos(x) + 32a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 20a\|2 cos(x) - 40a\|2 cos(x) + 28a\|2 cos(x) +--R + +--R +-+ +-+ +--R 16a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R 8a\|2 cos(x) - 4a\|2 cos(x) - 32a\|2 cos(x) + 20a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 40a\|2 cos(x) - 28a\|2 cos(x) - 16a\|2 cos(x) + 12a\|2 +--R * +--R +---------------+ +--R | 2 2 +--R +---+ +-+ |- a cos(x) - a +--R \|- a \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 4a \|2 cos(x) - 4a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 4a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 +--R * +--R 3 +--R sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 7a \|2 cos(x) + 5a \|2 cos(x) - 3a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 7a \|2 cos(x) - 5a \|2 cos(x) + 3a \|2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R 8a \|2 cos(x) + 16a \|2 cos(x) - 4a \|2 cos(x) +--R + +--R 2 +-+ +--R - 6a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 6a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R 4a \|2 cos(x) - 8a \|2 cos(x) - 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R 21a \|2 cos(x) + 14a \|2 cos(x) - 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R - 5a \|2 cos(x) + 5a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R - 4a \|2 cos(x) + 8a \|2 cos(x) + 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R - 21a \|2 cos(x) - 14a \|2 cos(x) + 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R 5a \|2 cos(x) - 5a \|2 +--R * +--R 2 +--R tan(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R (4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 ) +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 7a \|2 cos(x) - 5a \|2 cos(x) + 3a \|2 +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 6a \|2 +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R - 4a \|2 cos(x) + 8a \|2 cos(x) + 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R - 21a \|2 cos(x) - 14a \|2 cos(x) + 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R 5a \|2 cos(x) - 5a \|2 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ +--R - 4a \|2 cos(x) - 4a \|2 cos(x) + 4a \|2 cos(x) +--R + +--R 2 +-+ +--R 4a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 4a \|2 cos(x) + 4a \|2 cos(x) - 4a \|2 cos(x) - 4a \|2 +--R * +--R 3 +--R sin(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R 7a \|2 cos(x) + 5a \|2 cos(x) - 3a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 5 2 +-+ 4 2 +-+ 3 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 9a \|2 cos(x) +--R + +--R 2 +-+ 2 2 +-+ 2 +-+ +--R - 7a \|2 cos(x) - 5a \|2 cos(x) + 3a \|2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R 4a \|2 cos(x) - 4a \|2 cos(x) - 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R 8a \|2 cos(x) + 16a \|2 cos(x) - 4a \|2 cos(x) - 6a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 6 2 +-+ 5 2 +-+ 4 +--R - 4a \|2 cos(x) + 4a \|2 cos(x) + 14a \|2 cos(x) +--R + +--R 2 +-+ 3 2 +-+ 2 2 +-+ 2 +-+ +--R - 8a \|2 cos(x) - 16a \|2 cos(x) + 4a \|2 cos(x) + 6a \|2 +--R * +--R sin(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R 4a \|2 cos(x) - 8a \|2 cos(x) - 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R 21a \|2 cos(x) + 14a \|2 cos(x) - 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R - 5a \|2 cos(x) + 5a \|2 +--R * +--R 2 +--R csc(x) +--R + +--R 2 +-+ 7 2 +-+ 6 2 +-+ 5 +--R - 4a \|2 cos(x) + 8a \|2 cos(x) + 13a \|2 cos(x) +--R + +--R 2 +-+ 4 2 +-+ 3 2 +-+ 2 +--R - 21a \|2 cos(x) - 14a \|2 cos(x) + 18a \|2 cos(x) +--R + +--R 2 +-+ 2 +-+ +--R 5a \|2 cos(x) - 5a \|2 +--R * +--R +-+ +--R \|a +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(-----------------) +--R +--------------+ +--R \|- a csc(x) - a +--R + +--R 3 2 3 +--R (16cos(x) - 8cos(x) - 24cos(x) + 16)sin(x) +--R + +--R 5 4 3 2 +--R (- 24cos(x) + 20cos(x) + 34cos(x) - 28cos(x) - 6cos(x) + 4) +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 16cos(x) + 40cos(x) + 2cos(x) - 70cos(x) + 34cos(x) +--R + +--R 30cos(x) - 20 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 8cos(x) - 4cos(x) + 40cos(x) - 16cos(x) - 32cos(x) +--R + +--R 2 +--R 20cos(x) +--R * +--R +--------------+ +--------------+ +--R \|- a csc(x) - a \|- a csc(x) + a +--R + +--R 6 5 4 3 2 +--R (- 16cos(x) + 40cos(x) - 8cos(x) - 40cos(x) + 24cos(x) ) +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 3 +--R - 16cos(x) + 8cos(x) + 48cos(x) - 32cos(x) - 32cos(x) +--R + +--R 2 +--R 24cos(x) +--R * +--R cot(x) +--R * +--R +---+ +--------------+ +--R tan(x)\|- a \|- a csc(x) - a +--R * +--R +---------------+3 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 +--R (- 4cos(x) + 4cos(x))sin(x) +--R + +--R 4 3 2 3 +--R (- 8cos(x) + 4cos(x) + 8cos(x) - 4cos(x))sin(x) +--R + +--R 5 3 7 6 +--R (- 4cos(x) + 8cos(x) - 4cos(x))sin(x) + 4cos(x) - 12cos(x) +--R + +--R 4 3 2 +--R 20cos(x) - 8cos(x) - 8cos(x) + 4cos(x) +--R * +--R +---+ +--------------+ +--------------+ +--R \|- a \|- a csc(x) - a \|- a csc(x) + a +--R + +--R 4 2 3 +--R (8a cos(x) - 16a cos(x) + 8a)cot(x)sin(x) +--R + +--R 5 4 3 2 +--R 16a cos(x) - 8a cos(x) - 32a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) - 8a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 6 5 4 3 +--R 8a cos(x) - 8a cos(x) - 16a cos(x) + 8a cos(x) +--R + +--R 2 +--R 16a cos(x) - 8a +--R * +--R cot(x)sin(x) +--R + +--R 7 5 4 3 +--R 8a cos(x) - 34a cos(x) + 10a cos(x) + 42a cos(x) +--R + +--R 2 +--R - 18a cos(x) - 16a cos(x) + 8a +--R * +--R cot(x) +--R * +--R +--------------+ +--R tan(x)\|- a csc(x) - a +--R * +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 4 +--R (4a cos(x) + 2a cos(x) - 3a cos(x) - a)sin(x) +--R + +--R 4 2 3 +--R (8a cos(x) - 3a cos(x) - 5a)sin(x) +--R + +--R 5 4 3 2 +--R 16a cos(x) - 8a cos(x) - 27a cos(x) + 11a cos(x) +--R + +--R 11a cos(x) - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 8a cos(x) + 4a cos(x) + 19a cos(x) - 2a cos(x) +--R + +--R 2 +--R - 20a cos(x) - 2a cos(x) + 9a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 4a cos(x) + 2a cos(x) + 2a cos(x) - 4a cos(x) + 8a cos(x) +--R + +--R 2 +--R 2a cos(x) - 6a cos(x) +--R * +--R +--------------+ +--------------+ +--R \|- a csc(x) - a \|- a csc(x) + a +--R + +--R 4 3 2 +--R (8a cos(x) - 4a cos(x) - 20a cos(x) + 4a cos(x) + 12a)cot(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 24a cos(x) - 12a cos(x) - 48a cos(x) + 24a cos(x) +--R + +--R 24a cos(x) - 12a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 6 5 4 3 +--R 24a cos(x) - 12a cos(x) - 60a cos(x) + 24a cos(x) +--R + +--R 2 +--R 48a cos(x) - 12a cos(x) - 12a +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 +--R 8a cos(x) - 4a cos(x) - 32a cos(x) + 20a cos(x) +--R + +--R 3 2 +--R 40a cos(x) - 28a cos(x) - 16a cos(x) + 12a +--R * +--R cot(x) +--R * +--R +---+ +--------------+ +--R tan(x)\|- a \|- a csc(x) - a +--R * +--R +---------------+ +--R | 2 2 +--R |- a cos(x) - a +--R 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 3 +--R (- 4a cos(x) + 4a cos(x) + 18a cos(x) - 2a cos(x) - 12a)sin(x) +--R + +--R 5 4 2 2 +--R (- 2a cos(x) - 10a cos(x) + 10a cos(x) + 2a cos(x))sin(x) +--R + +--R 6 5 4 3 +--R - 4a cos(x) + 6a cos(x) + 22a cos(x) - 8a cos(x) +--R + +--R 2 +--R - 30a cos(x) + 2a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 6a cos(x) - 10a cos(x) + 10a cos(x) + 20a cos(x) - 2a cos(x) +--R + +--R 2 +--R - 10a cos(x) - 2a cos(x) +--R * +--R +---+ +--------------+ +--------------+ +--R \|- a \|- a csc(x) - a \|- a csc(x) + a +--R + +--R 2 3 2 2 2 2 3 +--R (4a cos(x) + 4a cos(x) - 4a cos(x) - 4a )cot(x)sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 +--R - 4a cos(x) + 4a cos(x) + 9a cos(x) - 7a cos(x) - 5a cos(x) +--R + +--R 2 +--R 3a +--R * +--R 2 +--R cot(x)sin(x) +--R + +--R 2 6 2 5 2 4 2 3 +--R - 4a cos(x) + 4a cos(x) + 14a cos(x) - 8a cos(x) +--R + +--R 2 2 2 2 +--R - 16a cos(x) + 4a cos(x) + 6a +--R * +--R cot(x)sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 4a cos(x) + 8a cos(x) + 13a cos(x) - 21a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 14a cos(x) + 18a cos(x) + 5a cos(x) - 5a +--R * +--R cot(x) +--R * +--R +--------------+ +--R tan(x)\|- a csc(x) - a +--R / +--R 6 5 4 3 2 +--R (16cos(x) - 40cos(x) + 8cos(x) + 40cos(x) - 24cos(x) )sin(x) +--R + +--R 7 6 5 4 3 2 +--R 16cos(x) - 8cos(x) - 48cos(x) + 32cos(x) + 32cos(x) - 24cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +---+ +--------------+ +--------------+ |- a cos(x) - a +--R \|- a \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 2 3 +--R (- 8a cos(x) + 16a cos(x) - 8a)sin(x) +--R + +--R 5 4 3 2 +--R - 16a cos(x) + 8a cos(x) + 32a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) + 8a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 8a cos(x) + 8a cos(x) + 16a cos(x) - 8a cos(x) +--R + +--R 2 +--R - 16a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 7 5 4 3 2 +--R - 8a cos(x) + 34a cos(x) - 10a cos(x) - 42a cos(x) + 18a cos(x) +--R + +--R 16a cos(x) - 8a +--R * +--R +---------------+2 +--R | 2 2 +--R +--------------+ +--------------+ |- a cos(x) - a +--R \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 4 3 2 3 +--R (- 8a cos(x) + 4a cos(x) + 20a cos(x) - 4a cos(x) - 12a)sin(x) +--R + +--R 5 4 3 2 +--R - 24a cos(x) + 12a cos(x) + 48a cos(x) - 24a cos(x) +--R + +--R - 24a cos(x) + 12a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 24a cos(x) + 12a cos(x) + 60a cos(x) - 24a cos(x) +--R + +--R 2 +--R - 48a cos(x) + 12a cos(x) + 12a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 8a cos(x) + 4a cos(x) + 32a cos(x) - 20a cos(x) - 40a cos(x) +--R + +--R 2 +--R 28a cos(x) + 16a cos(x) - 12a +--R * +--R +---------------+ +--R | 2 2 +--R +---+ +--------------+ +--------------+ |- a cos(x) - a +--R \|- a \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 2 3 2 2 2 2 3 +--R (- 4a cos(x) - 4a cos(x) + 4a cos(x) + 4a )sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 +--R 4a cos(x) - 4a cos(x) - 9a cos(x) + 7a cos(x) + 5a cos(x) +--R + +--R 2 +--R - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 4a cos(x) - 4a cos(x) - 14a cos(x) + 8a cos(x) + 16a cos(x) +--R + +--R 2 2 +--R - 4a cos(x) - 6a +--R * +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 2 3 +--R 4a cos(x) - 8a cos(x) - 13a cos(x) + 21a cos(x) + 14a cos(x) +--R + +--R 2 2 2 2 +--R - 18a cos(x) - 5a cos(x) + 5a +--R * +--R +--------------+ +--------------+ +--R \|- a csc(x) - a \|- a csc(x) + a +--R Type: Expression(Integer) +--E 396 + +--S 397 of 528 +m0375b:= a0375.2-r0375 +--R +--R +--R (359) +--R +--------------+ +--R +--------------+ +--------------+ \|- a csc(x) - a +--R 2tan(x)\|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +-+ +--R \|a +--R + +--R +-+ +-+ +--R +-+ +--------------+ +--------------+ \|2 \|a +--R \|2 tan(x)\|- a csc(x) - a \|- a csc(x) + a atan(-----------------) +--R +--------------+ +--R \|- a csc(x) - a +--R + +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R (2sin(x) - 2cos(x) + 2)\|a 4|--------------- +--R \| 4cos(x) - 4 +--R - a atan(-----------------------------------------------) +--R +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R (2cos(x) - 2) 4|--------------- + a sin(x) + a +--R \| 4cos(x) - 4 +--R + +--R +---------------+ +--R +-+ | 2 2 +--R |2 |- a cos(x) - a +--R +-+ 2a |- 4|--------------- +--R |2 +-+ \|a \| 4cos(x) - 4 +--R - a |- \|a atan(------------------------) +--R \|a +---------------+2 +--R | 2 2 +--R |- a cos(x) - a +--R 2 4|--------------- - a +--R \| 4cos(x) - 4 +--R / +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 528 +d0375b:= D(m0375b,x) +--R +--R +--R (360) +--R 3 2 3 4 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 3 3 +--R ((32cos(x) - 32cos(x))csc(x) - 32cos(x) + 32cos(x))sin(x) +--R + +--R 3 2 3 2 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 5 3 2 5 +--R (32cos(x) - 64cos(x) + 32cos(x))csc(x) - 32cos(x) +--R + +--R 3 +--R 64cos(x) - 32cos(x) +--R * +--R sin(x) +--R + +--R 7 5 3 2 +--R (- 16cos(x) + 64cos(x) - 80cos(x) + 32cos(x))csc(x) +--R + +--R 7 5 3 +--R 16cos(x) - 64cos(x) + 80cos(x) - 32cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 4 +--R (- 16cos(x) + 16cos(x))cot(x)csc(x) sin(x) +--R + +--R 3 2 3 +--R (- 32cos(x) + 32cos(x))cot(x)csc(x) sin(x) +--R + +--R 3 2 2 +--R (- 16cos(x) + 16cos(x))cot(x)csc(x) sin(x) +--R + +--R 5 3 2 +--R (- 32cos(x) + 64cos(x) - 32cos(x))cot(x)csc(x) sin(x) +--R + +--R 7 5 3 2 +--R (16cos(x) - 64cos(x) + 80cos(x) - 32cos(x))cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 3 2 3 4 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 3 3 +--R ((32cos(x) - 32cos(x))csc(x) - 32cos(x) + 32cos(x))sin(x) +--R + +--R 3 2 3 2 +--R ((16cos(x) - 16cos(x))csc(x) - 16cos(x) + 16cos(x))sin(x) +--R + +--R 5 3 2 5 +--R (32cos(x) - 64cos(x) + 32cos(x))csc(x) - 32cos(x) +--R + +--R 3 +--R 64cos(x) - 32cos(x) +--R * +--R sin(x) +--R + +--R 7 5 3 2 +--R (- 16cos(x) + 64cos(x) - 80cos(x) + 32cos(x))csc(x) +--R + +--R 7 5 3 +--R 16cos(x) - 64cos(x) + 80cos(x) - 32cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 2 3 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x)) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 16a cos(x) )csc(x) + 16a cos(x) +--R + +--R 2 +--R - 16a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 16a cos(x) ) +--R * +--R 2 +--R csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 3 +--R - 16a cos(x) + 32a cos(x) + 16a cos(x) +--R + +--R 2 +--R - 16a cos(x) - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 4 3 2 +--R 16a cos(x) - 32a cos(x) - 16a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 4a cos(x) - 16a cos(x) - 20a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R 32a cos(x) - 16a cos(x) - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 4 +--R (- 4a cos(x) + 4a cos(x))cot(x)csc(x) sin(x) +--R + +--R 4 2 2 3 +--R (16a cos(x) - 16a cos(x) )cot(x)csc(x) sin(x) +--R + +--R 5 4 3 2 +--R (- 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) ) +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 6 4 3 2 +--R 16a cos(x) - 32a cos(x) - 16a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 3 2 3 4 +--R ((4a cos(x) - 4a cos(x))csc(x) - 4a cos(x) + 4a cos(x))sin(x) +--R + +--R 4 2 2 4 +--R (- 16a cos(x) + 16a cos(x) )csc(x) + 16a cos(x) +--R + +--R 2 +--R - 16a cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 16a cos(x) )csc(x) +--R + +--R 5 4 3 2 +--R - 8a cos(x) + 16a cos(x) + 8a cos(x) - 16a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 3 2 +--R - 16a cos(x) + 32a cos(x) + 16a cos(x) - 16a cos(x) +--R + +--R - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 6 4 3 2 +--R 16a cos(x) - 32a cos(x) - 16a cos(x) + 16a cos(x) +--R + +--R 16a cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 +--R 4a cos(x) - 16a cos(x) - 20a cos(x) + 32a cos(x) +--R + +--R 3 2 +--R 32a cos(x) - 16a cos(x) - 16a cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R 7 6 5 4 +--R - 4a cos(x) + 16a cos(x) + 20a cos(x) - 32a cos(x) +--R + +--R 3 2 +--R - 32a cos(x) + 16a cos(x) + 16a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +--------------+ +--R \|- a csc(x) - a +--R atan(-----------------) +--R +-+ +--R \|a +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (16\|2 cos(x) - 16\|2 cos(x))csc(x) - 16\|2 cos(x) +--R + +--R +-+ +--R 16\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (16\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x))csc(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 16\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 8\|2 cos(x) + 32\|2 cos(x) - 40\|2 cos(x) +--R + +--R +-+ +--R 16\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) - 16\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 3 +-+ 2 4 +--R (- 8\|2 cos(x) + 8\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 3 +-+ 2 3 +--R (- 16\|2 cos(x) + 16\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 3 +-+ 2 2 +--R (- 8\|2 cos(x) + 8\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 16\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x))cot(x) +--R * +--R 2 +--R csc(x) sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) +--R + +--R +-+ +--R - 16\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (16\|2 cos(x) - 16\|2 cos(x))csc(x) - 16\|2 cos(x) +--R + +--R +-+ +--R 16\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (8\|2 cos(x) - 8\|2 cos(x))csc(x) - 8\|2 cos(x) +--R + +--R +-+ +--R 8\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 3 +-+ 2 +--R (16\|2 cos(x) - 32\|2 cos(x) + 16\|2 cos(x))csc(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R - 16\|2 cos(x) + 32\|2 cos(x) - 16\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R (- 8\|2 cos(x) + 32\|2 cos(x) - 40\|2 cos(x) + 16\|2 cos(x)) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +-+ +--R 8\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) - 16\|2 cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (2a\|2 cos(x) - 2a\|2 cos(x))csc(x) - 2a\|2 cos(x) +--R + +--R +-+ +--R 2a\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 2 +-+ 4 +--R (- 8a\|2 cos(x) + 8a\|2 cos(x) )csc(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R - 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2a\|2 cos(x) - 8a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ +--R - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ +--R 8a\|2 cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ 3 +-+ 2 4 +--R (- 2a\|2 cos(x) + 2a\|2 cos(x))cot(x)csc(x) sin(x) +--R + +--R +-+ 4 +-+ 2 2 3 +--R (8a\|2 cos(x) - 8a\|2 cos(x) )cot(x)csc(x) sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 16a\|2 cos(x) - 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ +--R 8a\|2 cos(x) +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (2a\|2 cos(x) - 2a\|2 cos(x))csc(x) - 2a\|2 cos(x) +--R + +--R +-+ +--R 2a\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 4 +-+ 2 2 +-+ 4 +--R (- 8a\|2 cos(x) + 8a\|2 cos(x) )csc(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +--R - 8a\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 cos(x) +--R + +--R +-+ 2 +--R 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R - 4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R - 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 6 +-+ 4 +-+ 3 +--R 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R 2a\|2 cos(x) - 8a\|2 cos(x) - 10a\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 16a\|2 cos(x) + 16a\|2 cos(x) - 8a\|2 cos(x) - 8a\|2 cos(x) +--R * +--R 2 +--R csc(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +-+ 4 +--R - 2a\|2 cos(x) + 8a\|2 cos(x) + 10a\|2 cos(x) - 16a\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 16a\|2 cos(x) + 8a\|2 cos(x) + 8a\|2 cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +-+ |- a cos(x) - a +--R \|a 4|--------------- +--R \| 4cos(x) - 4 +--R * +--R +-+ +-+ +--R \|2 \|a +--R atan(-----------------) +--R +--------------+ +--R \|- a csc(x) - a +--R + +--R 3 4 +--R (- 8cos(x) + 8cos(x))cot(x)sin(x) +--R + +--R 3 3 +--R (- 16cos(x) + 16cos(x))cot(x)sin(x) +--R + +--R 3 2 +--R (- 8cos(x) + 8cos(x))cot(x)sin(x) +--R + +--R 5 3 +--R (- 16cos(x) + 32cos(x) - 16cos(x))cot(x)sin(x) +--R + +--R 7 5 3 +--R (8cos(x) - 32cos(x) + 40cos(x) - 16cos(x))cot(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +--------------+ |- a cos(x) - a +--R tan(x)\|- a csc(x) - a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 5 3 2 4 +--R (4cos(x) + 2)sin(x) + (- 4cos(x) - 6cos(x) + 12cos(x) + 8)sin(x) +--R + +--R 4 3 2 3 +--R (8cos(x) - 2cos(x) - 14cos(x) + 6cos(x) + 4)sin(x) +--R + +--R 4 3 2 2 +--R (2cos(x) + 4cos(x) + 12cos(x) - 4cos(x) - 16)sin(x) +--R + +--R 6 5 4 3 2 +--R (8cos(x) - 6cos(x) - 28cos(x) + 6cos(x) + 36cos(x) - 16)sin(x) +--R + +--R 7 6 5 4 3 2 +--R 4cos(x) + 8cos(x) - 12cos(x) - 16cos(x) + 8cos(x) + 8cos(x) +--R * +--R +---------------+2 +--R | 2 2 +--R +--------------+ +--------------+ |- a cos(x) - a +--R \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 +--R (- 2a cos(x) + 2a cos(x))cot(x)sin(x) +--R + +--R 4 2 3 +--R (8a cos(x) - 8a cos(x) )cot(x)sin(x) +--R + +--R 5 4 3 2 2 +--R (- 4a cos(x) + 8a cos(x) + 4a cos(x) - 8a cos(x) )cot(x)sin(x) +--R + +--R 6 4 3 2 +--R (8a cos(x) - 16a cos(x) - 8a cos(x) + 8a cos(x) + 8a cos(x)) +--R * +--R cot(x)sin(x) +--R + +--R 7 6 5 4 +--R - 2a cos(x) + 8a cos(x) + 10a cos(x) - 16a cos(x) +--R + +--R 3 2 +--R - 16a cos(x) + 8a cos(x) + 8a cos(x) +--R * +--R cot(x) +--R * +--R +---------------+ +--R | 2 2 +--R +--------------+ |- a cos(x) - a +--R tan(x)\|- a csc(x) - a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 5 +--R (- a cos(x) - a)sin(x) +--R + +--R 3 2 4 +--R (2a cos(x) + a cos(x) - 5a cos(x) - 4a)sin(x) +--R + +--R 4 3 2 3 +--R (4a cos(x) + 9a cos(x) + 4a cos(x) - 3a cos(x) - 2a)sin(x) +--R + +--R 4 3 2 2 +--R (3a cos(x) - a cos(x) - 2a cos(x) + 10a cos(x) + 8a)sin(x) +--R + +--R 6 5 4 3 2 +--R 4a cos(x) + 10a cos(x) + 3a cos(x) - 17a cos(x) - 14a cos(x) +--R + +--R 8a cos(x) + 8a +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 2a cos(x) + 2a cos(x) + 10a cos(x) + 2a cos(x) - 8a cos(x) +--R + +--R 2 +--R - 4a cos(x) +--R * +--R +--------------+ +--------------+ +--R \|- a csc(x) - a \|- a csc(x) + a +--R / +--R 3 4 3 3 +--R (8cos(x) - 8cos(x))sin(x) + (16cos(x) - 16cos(x))sin(x) +--R + +--R 3 2 +--R (8cos(x) - 8cos(x))sin(x) +--R + +--R 5 3 7 5 +--R (16cos(x) - 32cos(x) + 16cos(x))sin(x) - 8cos(x) + 32cos(x) +--R + +--R 3 +--R - 40cos(x) + 16cos(x) +--R * +--R +---------------+3 +--R | 2 2 +--R +--------------+ +--------------+ |- a cos(x) - a +--R \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R + +--R 3 4 4 2 3 +--R (2a cos(x) - 2a cos(x))sin(x) + (- 8a cos(x) + 8a cos(x) )sin(x) +--R + +--R 5 4 3 2 2 +--R (4a cos(x) - 8a cos(x) - 4a cos(x) + 8a cos(x) )sin(x) +--R + +--R 6 4 3 2 +--R (- 8a cos(x) + 16a cos(x) + 8a cos(x) - 8a cos(x) - 8a cos(x)) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 2a cos(x) - 8a cos(x) - 10a cos(x) + 16a cos(x) + 16a cos(x) +--R + +--R 2 +--R - 8a cos(x) - 8a cos(x) +--R * +--R +---------------+ +--R | 2 2 +--R +--------------+ +--------------+ |- a cos(x) - a +--R \|- a csc(x) - a \|- a csc(x) + a 4|--------------- +--R \| 4cos(x) - 4 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 528 +t0376:= (a+b*csc(c+d*x))^3 +--R +--R +--R 3 3 2 2 2 3 +--R (361) b csc(d x + c) + 3a b csc(d x + c) + 3a b csc(d x + c) + a +--R Type: Expression(Integer) +--E 399 + +--S 400 of 528 +r0376:= a^3*x-3*a^2*b*atanh(cos(c+d*x))/d-_ + 1/2*b^3*atanh(cos(c+d*x))/d-3*a*b^2*cot(c+d*x)/d-_ + 1/2*b^3*cot(c+d*x)*csc(c+d*x)/d +--R +--R +--R (362) +--R 3 2 3 +--R (- b - 6a b)atanh(cos(d x + c)) - b cot(d x + c)csc(d x + c) +--R + +--R 2 3 +--R - 6a b cot(d x + c) + 2a d x +--R / +--R 2d +--R Type: Expression(Integer) +--E 400 + +--S 401 of 528 +a0376:= integrate(t0376,x) +--R +--R +--R (363) +--R 3 2 2 3 2 sin(d x + c) +--R ((b + 6a b)cos(d x + c) - b - 6a b)log(----------------) +--R cos(d x + c) + 1 +--R + +--R 2 3 2 3 +--R 6a b cos(d x + c)sin(d x + c) + 2a d x cos(d x + c) + b cos(d x + c) +--R + +--R 3 +--R - 2a d x +--R / +--R 2 +--R 2d cos(d x + c) - 2d +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 528 +m0376:= a0376-r0376 +--R +--R +--R (364) +--R 3 2 2 3 2 sin(d x + c) +--R ((b + 6a b)cos(d x + c) - b - 6a b)log(----------------) +--R cos(d x + c) + 1 +--R + +--R 3 2 2 3 2 +--R ((b + 6a b)cos(d x + c) - b - 6a b)atanh(cos(d x + c)) +--R + +--R 2 +--R 6a b cos(d x + c)sin(d x + c) +--R + +--R 3 2 3 +--R (b cos(d x + c) - b )cot(d x + c)csc(d x + c) +--R + +--R 2 2 2 3 +--R (6a b cos(d x + c) - 6a b )cot(d x + c) + b cos(d x + c) +--R / +--R 2 +--R 2d cos(d x + c) - 2d +--R Type: Expression(Integer) +--E 402 + +--S 403 of 528 +d0376:= D(m0376,x) +--R +--R +--R (365) +--R 2 2 2 3 +--R (6a b cos(d x + c) + 6a b )sin(d x + c) +--R + +--R 3 2 3 3 2 +--R (b + 6a b)cos(d x + c) + b cos(d x + c) +--R + +--R 3 2 3 +--R (- b - 6a b)cos(d x + c) + b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 4 3 2 3 2 +--R (- 2b cos(d x + c) + 4b cos(d x + c) - 2b )cot(d x + c) +--R + +--R 3 4 3 2 3 +--R - b cos(d x + c) + 2b cos(d x + c) - b +--R * +--R csc(d x + c) +--R + +--R 2 4 2 2 2 2 +--R (- 6a b cos(d x + c) + 12a b cos(d x + c) - 6a b )cot(d x + c) +--R + +--R 2 2 2 +--R 6a b cos(d x + c) - 6a b +--R * +--R sin(d x + c) +--R + +--R 3 2 5 3 2 3 +--R (b + 6a b)cos(d x + c) + (- 2b - 12a b)cos(d x + c) +--R + +--R 3 2 +--R (b + 6a b)cos(d x + c) +--R / +--R 4 2 +--R (2cos(d x + c) - 4cos(d x + c) + 2)sin(d x + c) +--R Type: Expression(Integer) +--E 403 + +--S 404 of 528 +t0377:= (a+b*csc(c+d*x))^2 +--R +--R +--R 2 2 2 +--R (366) b csc(d x + c) + 2a b csc(d x + c) + a +--R Type: Expression(Integer) +--E 404 + +--S 405 of 528 +r0377:= a^2*x-2*a*b*atanh(cos(c+d*x))/d-b^2*cot(c+d*x)/d +--R +--R +--R 2 2 +--R - 2a b atanh(cos(d x + c)) - b cot(d x + c) + a d x +--R (367) --------------------------------------------------- +--R d +--R Type: Expression(Integer) +--E 405 + +--S 406 of 528 +a0377:= integrate(t0377,x) +--R +--R +--R (368) +--R sin(d x + c) 2 2 +--R 2a b sin(d x + c)log(----------------) + a d x sin(d x + c) - b cos(d x + c) +--R cos(d x + c) + 1 +--R ---------------------------------------------------------------------------- +--R d sin(d x + c) +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 528 +m0377:= a0377-r0377 +--R +--R +--R (369) +--R sin(d x + c) +--R 2a b sin(d x + c)log(----------------) +--R cos(d x + c) + 1 +--R + +--R 2 +--R 2a b sin(d x + c)atanh(cos(d x + c)) + b cot(d x + c)sin(d x + c) +--R + +--R 2 +--R - b cos(d x + c) +--R / +--R d sin(d x + c) +--R Type: Expression(Integer) +--E 407 + +--S 408 of 528 +d0377:= D(m0377,x) +--R +--R +--R (370) +--R 3 +--R 2a b cos(d x + c)sin(d x + c) +--R + +--R 2 2 2 2 2 +--R (- b cos(d x + c) + b )cot(d x + c) sin(d x + c) +--R + +--R 3 2 4 +--R (2a b cos(d x + c) - 2a b cos(d x + c))sin(d x + c) + b cos(d x + c) +--R + +--R 2 2 +--R - b cos(d x + c) +--R / +--R 2 2 +--R (cos(d x + c) - 1)sin(d x + c) +--R Type: Expression(Integer) +--E 408 + +--S 409 of 528 +t0378:= 1/(3+5*csc(c+d*x)) +--R +--R +--R 1 +--R (371) ----------------- +--R 5csc(d x + c) + 3 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 528 +r0378:= 1/3*x-5/6*atan(3/4+5/4*tan(1/2*c+1/2*d*x))/d +--R +--R +--R d x + c +--R 5tan(-------) + 3 +--R 2 +--R - 5atan(-----------------) + 2d x +--R 4 +--R (372) --------------------------------- +--R 6d +--R Type: Expression(Integer) +--E 410 + +--S 411 of 528 +a0378:= integrate(t0378,x) +--R +--R +--R 5sin(d x + c) + 3cos(d x + c) + 3 +--R - 5atan(---------------------------------) + 2d x +--R 4cos(d x + c) + 4 +--R (373) ------------------------------------------------- +--R 6d +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 528 +m0378:= a0378-r0378 +--R +--R +--R d x + c +--R 5tan(-------) + 3 +--R 2 5sin(d x + c) + 3cos(d x + c) + 3 +--R 5atan(-----------------) - 5atan(---------------------------------) +--R 4 4cos(d x + c) + 4 +--R (374) ------------------------------------------------------------------- +--R 6d +--R Type: Expression(Integer) +--E 412 + +--S 413 of 528 +d0378:= D(m0378,x) +--R +--R +--R (375) +--R 2 +--R - 25sin(d x + c) + (30cos(d x + c) + 30)sin(d x + c) +--R + +--R 2 +--R - 25cos(d x + c) + 25 +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 d x + c +--R (- 60sin(d x + c) - 60cos(d x + c) - 60cos(d x + c))tan(-------) +--R 2 +--R + +--R 2 2 +--R - 25sin(d x + c) + (30cos(d x + c) + 30)sin(d x + c) - 25cos(d x + c) +--R + +--R 25 +--R / +--R 2 2 +--R 75sin(d x + c) + (90cos(d x + c) + 90)sin(d x + c) + 75cos(d x + c) +--R + +--R 150cos(d x + c) + 75 +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 +--R 90sin(d x + c) + (108cos(d x + c) + 108)sin(d x + c) +--R + +--R 2 +--R 90cos(d x + c) + 180cos(d x + c) + 90 +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 +--R 75sin(d x + c) + (90cos(d x + c) + 90)sin(d x + c) + 75cos(d x + c) +--R + +--R 150cos(d x + c) + 75 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 528 +t0379:= 1/(5+3*csc(c+d*x)) +--R +--R +--R 1 +--R (376) ----------------- +--R 3csc(d x + c) + 5 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 528 +r0379:= 1/5*x+3/10*atanh(5/4+3/4*tan(1/2*c+1/2*d*x))/d +--R +--R +--R d x + c +--R 3tan(-------) + 5 +--R 2 +--R 3atanh(-----------------) + 2d x +--R 4 +--R (377) -------------------------------- +--R 10d +--R Type: Expression(Integer) +--E 415 + +--S 416 of 528 +a0379:= integrate(t0379,x) +--R +--R +--R (378) +--R 3sin(d x + c) + cos(d x + c) + 1 +--R - 3log(--------------------------------) +--R cos(d x + c) + 1 +--R + +--R sin(d x + c) + 3cos(d x + c) + 3 +--R 3log(--------------------------------) + 4d x +--R cos(d x + c) + 1 +--R / +--R 20d +--R Type: Union(Expression(Integer),...) +--E 416 + +--S 417 of 528 +m0379:= a0379-r0379 +--R +--R +--R (379) +--R 3sin(d x + c) + cos(d x + c) + 1 +--R - 3log(--------------------------------) +--R cos(d x + c) + 1 +--R + +--R d x + c +--R 3tan(-------) + 5 +--R sin(d x + c) + 3cos(d x + c) + 3 2 +--R 3log(--------------------------------) - 6atanh(-----------------) +--R cos(d x + c) + 1 4 +--R / +--R 20d +--R Type: Expression(Integer) +--E 417 + +--S 418 of 528 +d0379:= D(m0379,x) +--R +--R +--R (380) +--R 2 2 +--R - 9sin(d x + c) + (30cos(d x + c) + 30)sin(d x + c) - 9cos(d x + c) +--R + +--R 9 +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 d x + c +--R (- 60sin(d x + c) - 60cos(d x + c) - 60cos(d x + c))tan(-------) +--R 2 +--R + +--R 2 2 +--R - 9sin(d x + c) + (30cos(d x + c) + 30)sin(d x + c) - 9cos(d x + c) + 9 +--R / +--R 2 +--R 45sin(d x + c) + (150cos(d x + c) + 150)sin(d x + c) +--R + +--R 2 +--R 45cos(d x + c) + 90cos(d x + c) + 45 +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 +--R 150sin(d x + c) + (500cos(d x + c) + 500)sin(d x + c) +--R + +--R 2 +--R 150cos(d x + c) + 300cos(d x + c) + 150 +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 +--R 45sin(d x + c) + (150cos(d x + c) + 150)sin(d x + c) + 45cos(d x + c) +--R + +--R 90cos(d x + c) + 45 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 528 +t0380:= 1/(a+b*csc(c+d*x)) +--R +--R +--R 1 +--R (381) ------------------ +--R b csc(d x + c) + a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 528 +r0380:= x/a+2*b*atanh((a+b*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/a/_ + (a^2-b^2)^(1/2)/d +--R +--R +--R d x + c +--R b tan(-------) + a +---------+ +--R 2 | 2 2 +--R 2b atanh(------------------) + d x\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (382) ---------------------------------------------- +--R +---------+ +--R | 2 2 +--R a d\|- b + a +--R Type: Expression(Integer) +--E 420 + +--S 421 of 528 +a0380:= integrate(t0380,x) +--R +--R +--R (383) +--R [ +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R +---------+ +--R | 2 2 +--R d x\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R a d\|- b + a +--R , +--R +-------+ +--R | 2 2 +-------+ +--R (b sin(d x + c) + a cos(d x + c) + a)\|b - a | 2 2 +--R - 2b atan(-----------------------------------------------) + d x\|b - a +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R --------------------------------------------------------------------------] +--R +-------+ +--R | 2 2 +--R a d\|b - a +--R Type: Union(List(Expression(Integer)),...) +--E 421 + +--S 422 of 528 +m0380a:= a0380.1-r0380 +--R +--R +--R (384) +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R d x + c +--R b tan(-------) + a +--R 2 +--R - 2b atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R | 2 2 +--R a d\|- b + a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 528 +d0380a:= D(m0380a,x) +--R +--R +--R (385) +--R 3 2 2 2 2 +--R ((- b + a b)cos(d x + c) + a b)sin(d x + c) - a b cos(d x + c) +--R + +--R 2 +--R a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 2 2 2 +--R - 2a b sin(d x + c) - 2a b sin(d x + c) - 2a b cos(d x + c) +--R + +--R 3 2 +--R (2b - 2a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 3 2 2 2 2 2 +--R ((- b + a b)cos(d x + c) + a b)sin(d x + c) - a b cos(d x + c) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 3 3 +--R ((- a b + a b)cos(d x + c) - a b + a b)sin(d x + c) +--R + +--R 4 2 2 2 4 2 2 +--R (b - a b )cos(d x + c) - b + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 3 2 4 2 2 +--R (2a b - 2a b)sin(d x + c) + (2b - 2a b )sin(d x + c) +--R + +--R 3 3 2 3 3 +--R (2a b - 2a b)cos(d x + c) + (2a b - 2a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 3 3 3 3 +--R ((- a b + a b)cos(d x + c) - a b + a b)sin(d x + c) +--R + +--R 4 2 2 2 4 2 2 +--R (b - a b )cos(d x + c) - b + a b +--R / +--R 2 2 2 +--R a b sin(d x + c) +--R + +--R 3 3 3 3 +--R ((- a b + a b)cos(d x + c) + a b + a b)sin(d x + c) +--R + +--R 4 2 2 2 2 +--R (- b + a b )cos(d x + c) + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 2 +--R 2a b sin(d x + c) +--R + +--R 2 2 4 2 2 4 +--R ((- 2a b + 2a )cos(d x + c) + 2a b + 2a )sin(d x + c) +--R + +--R 3 3 3 +--R (- 2a b + 2a b)cos(d x + c) + 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 2 +--R a b sin(d x + c) +--R + +--R 3 3 3 3 +--R ((- a b + a b)cos(d x + c) + a b + a b)sin(d x + c) +--R + +--R 4 2 2 2 2 +--R (- b + a b )cos(d x + c) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 2 2 +--R (- a b + a b )sin(d x + c) +--R + +--R 2 3 4 5 4 +--R ((- a b + a b)cos(d x + c) - b + a b)sin(d x + c) +--R + +--R 4 3 2 4 3 2 +--R (- a b + a b )cos(d x + c) - a b + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 3 4 2 +--R (- 2a b + 2a b)sin(d x + c) +--R + +--R 3 2 5 4 5 +--R ((- 2a b + 2a )cos(d x + c) - 2a b + 2a )sin(d x + c) +--R + +--R 2 3 4 2 3 4 +--R (- 2a b + 2a b)cos(d x + c) - 2a b + 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 3 2 2 +--R (- a b + a b )sin(d x + c) +--R + +--R 2 3 4 5 4 +--R ((- a b + a b)cos(d x + c) - b + a b)sin(d x + c) +--R + +--R 4 3 2 4 3 2 +--R (- a b + a b )cos(d x + c) - a b + a b +--R Type: Expression(Integer) +--E 423 + +--S 424 of 528 +m0380b:= a0380.2-r0380 +--R +--R +--R (386) +--R d x + c +--R +-------+ b tan(-------) + a +--R | 2 2 2 +--R - 2b\|b - a atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sin(d x + c) + a cos(d x + c) + a)\|b - a +--R - 2b\|- b + a atan(-----------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R a d\|- b + a \|b - a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 528 +d0380b:= D(m0380b,x) +--R +--R +--R (387) +--R 2 2 +--R - b sin(d x + c) + (2a b cos(d x + c) + 2a b)sin(d x + c) +--R + +--R 2 2 2 +--R - b cos(d x + c) + b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 +--R (- 4a b sin(d x + c) - 4a b cos(d x + c) - 4a b cos(d x + c)) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 +--R - b sin(d x + c) + (2a b cos(d x + c) + 2a b)sin(d x + c) +--R + +--R 2 2 2 +--R - b cos(d x + c) + b +--R / +--R 2 2 2 2 +--R a b sin(d x + c) + (2a b cos(d x + c) + 2a b)sin(d x + c) +--R + +--R 2 2 2 2 +--R a b cos(d x + c) + 2a b cos(d x + c) + a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 2 3 3 +--R 2a b sin(d x + c) + (4a cos(d x + c) + 4a )sin(d x + c) +--R + +--R 2 2 2 2 +--R 2a b cos(d x + c) + 4a b cos(d x + c) + 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 2 2 2 +--R a b sin(d x + c) + (2a b cos(d x + c) + 2a b)sin(d x + c) +--R + +--R 2 2 2 2 +--R a b cos(d x + c) + 2a b cos(d x + c) + a b +--R Type: Expression(Integer) +--E 425 + +--S 426 of 528 +t0381:= 1/(a+b*csc(c+d*x))^2 +--R +--R +--R 1 +--R (388) ---------------------------------------- +--R 2 2 2 +--R b csc(d x + c) + 2a b csc(d x + c) + a +--R Type: Expression(Integer) +--E 426 + +--S 427 of 528 +r0381:= x/a^2+2*b^3*atanh((a+b*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/_ + a^2/(a^2-b^2)^(3/2)/d+4*b*atanh((a+b*tan(1/2*c+1/2*d*x))/_ + (a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)/d-_ + b^2*cos(c+d*x)/a/(a^2-b^2)/d/(b+a*sin(c+d*x)) +--R +--R +--R (389) +--R d x + c +--R b tan(-------) + a +--R 3 3 4 2 2 2 +--R ((2a b - 4a b)sin(d x + c) + 2b - 4a b )atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 3 2 +--R ((a b - a )d x sin(d x + c) + a b cos(d x + c) + (b - a b)d x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d sin(d x + c) + (a b - a b)d)\|- b + a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 528 +a0381:= integrate(t0381,x) +--R +--R +--R (390) +--R [ +--R 3 3 4 2 2 +--R ((a b - 2a b)sin(d x + c) + b - 2a b ) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R 2 3 2 2 +--R ((a b - a )d x + a b)sin(d x + c) + a b cos(d x + c) +--R + +--R 3 2 2 +--R (b - a b)d x + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d sin(d x + c) + (a b - a b)d)\|- b + a +--R , +--R +--R 3 3 4 2 2 +--R ((- 2a b + 4a b)sin(d x + c) - 2b + 4a b ) +--R * +--R +-------+ +--R | 2 2 +--R (b sin(d x + c) + a cos(d x + c) + a)\|b - a +--R atan(-----------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R 2 3 2 2 +--R ((a b - a )d x + a b)sin(d x + c) + a b cos(d x + c) +--R + +--R 3 2 2 +--R (b - a b)d x + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 3 2 5 2 3 4 | 2 2 +--R ((a b - a )d sin(d x + c) + (a b - a b)d)\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 428 + +--S 429 of 528 +m0381a:= a0381.1-r0381 +--R +--R +--R (391) +--R 3 2 +--R (b - 2a b) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R d x + c +--R b tan(-------) + a +---------+ +--R 3 2 2 | 2 2 +--R (- 2b + 4a b)atanh(------------------) + a b\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 4 | 2 2 +--R (a b - a )d\|- b + a +--R Type: Expression(Integer) +--E 429 + +--S 430 of 528 +d0381a:= D(m0381a,x) +--R +--R +--R (392) +--R 5 2 3 4 2 3 4 +--R ((- b + 3a b - 2a b)cos(d x + c) + a b - 2a b)sin(d x + c) +--R + +--R 4 3 2 2 4 3 2 +--R (- a b + 2a b )cos(d x + c) + a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 2 3 4 2 4 3 2 +--R (- 2a b + 4a b)sin(d x + c) + (- 2a b + 4a b )sin(d x + c) +--R + +--R 2 3 4 2 5 2 3 4 +--R (- 2a b + 4a b)cos(d x + c) + (2b - 6a b + 4a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 5 2 3 4 2 3 4 +--R ((- b + 3a b - 2a b)cos(d x + c) + a b - 2a b)sin(d x + c) +--R + +--R 4 3 2 2 4 3 2 +--R (- a b + 2a b )cos(d x + c) + a b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 3 3 5 5 3 3 5 +--R ((- a b + 3a b - 2a b)cos(d x + c) - a b + 3a b - 2a b) +--R * +--R sin(d x + c) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (b - 3a b + 2a b )cos(d x + c) - b + 3a b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 5 3 3 5 2 +--R (2a b - 6a b + 4a b)sin(d x + c) +--R + +--R 6 2 4 4 2 +--R (2b - 6a b + 4a b )sin(d x + c) +--R + +--R 5 3 3 5 2 +--R (2a b - 6a b + 4a b)cos(d x + c) +--R + +--R 5 3 3 5 +--R (2a b - 6a b + 4a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 5 3 3 5 5 3 3 5 +--R ((- a b + 3a b - 2a b)cos(d x + c) - a b + 3a b - 2a b)sin(d x + c) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (b - 3a b + 2a b )cos(d x + c) - b + 3a b - 2a b +--R / +--R 3 4 5 2 2 +--R (a b - a b )sin(d x + c) +--R + +--R 2 5 4 3 6 2 5 6 +--R ((- a b + 2a b - a b)cos(d x + c) + a b - a b)sin(d x + c) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (- a b + 2a b - a b )cos(d x + c) + a b - a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 4 3 6 2 +--R (2a b - 2a b)sin(d x + c) +--R + +--R 3 4 5 2 7 3 4 7 +--R ((- 2a b + 4a b - 2a )cos(d x + c) + 2a b - 2a )sin(d x + c) +--R + +--R 2 5 4 3 6 4 3 6 +--R (- 2a b + 4a b - 2a b)cos(d x + c) + 2a b - 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 3 4 5 2 2 +--R (a b - a b )sin(d x + c) +--R + +--R 2 5 4 3 6 2 5 6 +--R ((- a b + 2a b - a b)cos(d x + c) + a b - a b)sin(d x + c) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (- a b + 2a b - a b )cos(d x + c) + a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )sin(d x + c) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 +--R ((- a b + 2a b - a b)cos(d x + c) - a b + a b + a b - a b) +--R * +--R sin(d x + c) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (- a b + 2a b - a b )cos(d x + c) - a b + 2a b - a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 5 5 3 7 2 +--R (- 2a b + 4a b - 2a b)sin(d x + c) +--R + +--R 4 4 6 2 8 2 6 4 4 6 2 8 +--R ((- 2a b + 4a b - 2a )cos(d x + c) - 2a b + 2a b + 2a b - 2a ) +--R * +--R sin(d x + c) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (- 2a b + 4a b - 2a b)cos(d x + c) - 2a b + 4a b - 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )sin(d x + c) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 +--R ((- a b + 2a b - a b)cos(d x + c) - a b + a b + a b - a b) +--R * +--R sin(d x + c) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (- a b + 2a b - a b )cos(d x + c) - a b + 2a b - a b +--R Type: Expression(Integer) +--E 430 + +--S 431 of 528 +m0381b:= a0381.2-r0381 +--R +--R +--R (393) +--R d x + c +--R +-------+ b tan(-------) + a +--R 3 2 | 2 2 2 +--R (- 2b + 4a b)\|b - a atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 2 | 2 2 +--R (- 2b + 4a b)\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (b sin(d x + c) + a cos(d x + c) + a)\|b - a +--R atan(-----------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R a b\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 2 4 | 2 2 | 2 2 +--R (a b - a )d\|- b + a \|b - a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 528 +d0381b:= D(m0381b,x) +--R +--R +--R (394) +--R 4 2 2 2 +--R (- b + 2a b )sin(d x + c) +--R + +--R 3 3 3 3 +--R ((2a b - 4a b)cos(d x + c) + 2a b - 4a b)sin(d x + c) +--R + +--R 4 2 2 2 4 2 2 +--R (- b + 2a b )cos(d x + c) + b - 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 3 2 3 3 2 +--R (- 4a b + 8a b)sin(d x + c) + (- 4a b + 8a b)cos(d x + c) +--R + +--R 3 3 +--R (- 4a b + 8a b)cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 4 2 2 2 +--R (- b + 2a b )sin(d x + c) +--R + +--R 3 3 3 3 +--R ((2a b - 4a b)cos(d x + c) + 2a b - 4a b)sin(d x + c) +--R + +--R 4 2 2 2 4 2 2 +--R (- b + 2a b )cos(d x + c) + b - 2a b +--R / +--R 2 4 4 2 2 +--R (a b - a b )sin(d x + c) +--R + +--R 3 3 5 3 3 5 +--R ((2a b - 2a b)cos(d x + c) + 2a b - 2a b)sin(d x + c) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(d x + c) + (2a b - 2a b )cos(d x + c) + a b - a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 3 3 5 2 +--R (2a b - 2a b)sin(d x + c) +--R + +--R 4 2 6 4 2 6 +--R ((4a b - 4a )cos(d x + c) + 4a b - 4a )sin(d x + c) +--R + +--R 3 3 5 2 3 3 5 3 3 5 +--R (2a b - 2a b)cos(d x + c) + (4a b - 4a b)cos(d x + c) + 2a b - 2a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 2 4 4 2 2 +--R (a b - a b )sin(d x + c) +--R + +--R 3 3 5 3 3 5 +--R ((2a b - 2a b)cos(d x + c) + 2a b - 2a b)sin(d x + c) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(d x + c) + (2a b - 2a b )cos(d x + c) + a b - a b +--R Type: Expression(Integer) +--E 432 + +--S 433 of 528 +t0382:= 1/(a+b*csc(c+d*x))^3 +--R +--R +--R 1 +--R (395) ------------------------------------------------------------- +--R 3 3 2 2 2 3 +--R b csc(d x + c) + 3a b csc(d x + c) + 3a b csc(d x + c) + a +--R Type: Expression(Integer) +--E 433 + +--S 434 of 528 +r0382:= x/a^3+6*b^3*atanh((a+b*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/a^3/_ + (a^2-b^2)^(3/2)/d+6*b*atanh((a+b*tan(1/2*c+1/2*d*x))/_ + (a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)/d+b^3*(a^2+2*b^2)*_ + atanh((a+b*tan(1/2*c+1/2*d*x))/(a^2-b^2)^(1/2))/a^3/_ + (a^2-b^2)^(5/2)/d+1/2*b^3*cos(c+d*x)/a^2/(a^2-b^2)/d/_ + (b+a*sin(c+d*x))^2-3/2*b^4*cos(c+d*x)/a^2/(a^2-b^2)^2/d/_ + (b+a*sin(c+d*x))-3*b^2*cos(c+d*x)/a^2/(a^2-b^2)/d/(b+a*sin(c+d*x)) +--R +--R +--R (396) +--R 2 5 4 3 6 2 +--R (4a b - 10a b + 12a b)sin(d x + c) +--R + +--R 6 3 4 5 2 7 2 5 4 3 +--R (8a b - 20a b + 24a b )sin(d x + c) + 4b - 10a b + 12a b +--R * +--R d x + c +--R b tan(-------) + a +--R 2 +--R atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 6 2 +--R (2a b - 4a b + 2a )d x sin(d x + c) +--R + +--R 2 4 4 2 5 3 3 5 +--R ((3a b - 6a b )cos(d x + c) + (4a b - 8a b + 4a b)d x)sin(d x + c) +--R + +--R 5 3 3 6 2 4 4 2 +--R (2a b - 5a b )cos(d x + c) + (2b - 4a b + 2a b )d x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 4 7 2 9 2 +--R (2a b - 4a b + 2a )d sin(d x + c) +--R + +--R 4 5 6 3 8 3 6 5 4 7 2 +--R (4a b - 8a b + 4a b)d sin(d x + c) + (2a b - 4a b + 2a b )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 528 +a0382:= integrate(t0382,x) +--R +--R +--R (397) +--R [ +--R 6 3 4 5 2 +--R (4a b - 10a b + 12a b )sin(d x + c) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 6 +--R (- 2a b + 5a b - 6a b)cos(d x + c) + 2b - 3a b + a b + 6a b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R 2 4 4 2 5 3 3 5 2 4 +--R (3a b - 6a b )cos(d x + c) + (4a b - 8a b + 4a b)d x + 4a b +--R + +--R 4 2 +--R - 10a b +--R * +--R sin(d x + c) +--R + +--R 2 4 4 2 6 3 3 5 2 +--R ((- 2a b + 4a b - 2a )d x - 2a b + 5a b)cos(d x + c) +--R + +--R 5 3 3 6 2 4 4 2 6 +--R (2a b - 5a b )cos(d x + c) + (2b - 2a b - 2a b + 2a )d x +--R + +--R 5 3 3 5 +--R 2a b - 3a b - 5a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 5 6 3 8 +--R (4a b - 8a b + 4a b)d sin(d x + c) +--R + +--R 5 4 7 2 9 2 3 6 5 4 7 2 9 +--R (- 2a b + 4a b - 2a )d cos(d x + c) + (2a b - 2a b - 2a b + 2a )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 6 3 4 5 2 +--R (- 8a b + 20a b - 24a b )sin(d x + c) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 6 +--R (4a b - 10a b + 12a b)cos(d x + c) - 4b + 6a b - 2a b - 12a b +--R * +--R +-------+ +--R | 2 2 +--R (b sin(d x + c) + a cos(d x + c) + a)\|b - a +--R atan(-----------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R 2 4 4 2 5 3 3 5 2 4 +--R (3a b - 6a b )cos(d x + c) + (4a b - 8a b + 4a b)d x + 4a b +--R + +--R 4 2 +--R - 10a b +--R * +--R sin(d x + c) +--R + +--R 2 4 4 2 6 3 3 5 2 +--R ((- 2a b + 4a b - 2a )d x - 2a b + 5a b)cos(d x + c) +--R + +--R 5 3 3 6 2 4 4 2 6 +--R (2a b - 5a b )cos(d x + c) + (2b - 2a b - 2a b + 2a )d x +--R + +--R 5 3 3 5 +--R 2a b - 3a b - 5a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 5 6 3 8 +--R (4a b - 8a b + 4a b)d sin(d x + c) +--R + +--R 5 4 7 2 9 2 3 6 5 4 7 2 9 +--R (- 2a b + 4a b - 2a )d cos(d x + c) + (2a b - 2a b - 2a b + 2a )d +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 435 + +--S 436 of 528 +m0382a:= a0382.1-r0382 +--R +--R +--R (398) +--R 3 6 5 4 7 2 3 +--R (4a b - 10a b + 12a b )sin(d x + c) +--R + +--R 4 5 6 3 8 2 2 7 4 5 6 3 +--R (- 2a b + 5a b - 6a b)cos(d x + c) + 10a b - 23a b + 25a b +--R + +--R 8 +--R 6a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 6 5 4 7 2 2 8 3 6 +--R (- 4a b + 10a b - 12a b )cos(d x + c) + 8a b - 16a b +--R + +--R 5 4 7 2 +--R 14a b + 12a b +--R * +--R sin(d x + c) +--R + +--R 2 7 4 5 6 3 2 9 2 7 4 5 6 3 +--R (- 2a b + 5a b - 6a b )cos(d x + c) + 2b - 3a b + a b + 6a b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(d x + c) + (- b + a )cos(d x + c) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(d x + c) + (- a b + a )cos(d x + c) - a b + a +--R / +--R a sin(d x + c) + b +--R + +--R 3 6 5 4 7 2 3 +--R (- 8a b + 20a b - 24a b )sin(d x + c) +--R + +--R 4 5 6 3 8 2 2 7 4 5 6 3 +--R (4a b - 10a b + 12a b)cos(d x + c) - 20a b + 46a b - 50a b +--R + +--R 8 +--R - 12a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 6 5 4 7 2 2 8 3 6 5 4 +--R (8a b - 20a b + 24a b )cos(d x + c) - 16a b + 32a b - 28a b +--R + +--R 7 2 +--R - 24a b +--R * +--R sin(d x + c) +--R + +--R 2 7 4 5 6 3 2 9 2 7 4 5 6 3 +--R (4a b - 10a b + 12a b )cos(d x + c) - 4b + 6a b - 2a b - 12a b +--R * +--R d x + c +--R b tan(-------) + a +--R 2 +--R atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 6 2 4 4 6 2 3 +--R ((3a b - 6a b )cos(d x + c) + 4a b - 10a b )sin(d x + c) +--R + +--R 5 3 7 2 3 5 5 3 +--R (- 2a b + 5a b)cos(d x + c) + (2a b - 5a b )cos(d x + c) +--R + +--R 3 5 5 3 7 +--R 10a b - 23a b - 5a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (3a b - 6a b )cos(d x + c) + (- 4a b + 10a b )cos(d x + c) +--R + +--R 4 4 6 2 2 6 4 4 6 2 +--R (- 3a b + 6a b )cos(d x + c) + 8a b - 16a b - 10a b +--R * +--R sin(d x + c) +--R + +--R 3 5 5 3 3 3 5 5 3 2 +--R (2a b - 5a b )cos(d x + c) + (- 2a b + 5a b )cos(d x + c) +--R + +--R 3 5 5 3 7 3 5 5 3 +--R (- 2a b + 5a b )cos(d x + c) + 2a b - 3a b - 5a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 6 5 8 3 10 3 +--R (4a b - 8a b + 4a b)d sin(d x + c) +--R + +--R 7 4 9 2 11 2 +--R (- 2a b + 4a b - 2a )d cos(d x + c) +--R + +--R 5 6 7 4 9 2 11 +--R (10a b - 18a b + 6a b + 2a )d +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 5 8 3 10 2 +--R (- 4a b + 8a b - 4a b)d cos(d x + c) +--R + +--R 4 7 6 5 10 +--R (8a b - 12a b + 4a b)d +--R * +--R sin(d x + c) +--R + +--R 5 6 7 4 9 2 2 +--R (- 2a b + 4a b - 2a b )d cos(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 +--R (2a b - 2a b - 2a b + 2a b )d +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 528 +d0382a:= D(m0382a,x) +--R +--R +--R (399) +--R 6 7 8 5 7 +--R (- 6a b + 12a b )sin(d x + c) +--R + +--R 7 6 9 4 2 +--R (- 3a b + 6a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 5 8 7 6 +--R (6a b - 18a b + 12a b )cos(d x + c) - 13a b + 19a b +--R + +--R 9 4 +--R 18a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 6 7 8 5 10 3 3 +--R (3a b - 9a b + 6a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 2 +--R (- 23a b + 44a b + 6a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 9 +--R (5a b - 10a b - 25a b + 30a b )cos(d x + c) - 9a b +--R + +--R 6 7 8 5 10 3 +--R 17a b + 4a b + 30a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (31a b - 98a b + 91a b - 24a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 38a b + 55a b + 49a b - 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (- 15a b + 45a b - 81a b + 27a b + 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R - 2a b + 39a b - 70a b + 69a b + 24a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 7 8 5 10 3 12 5 +--R (- 2a b + 7a b - 11a b + 6a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 8a b + 13a b + 19a b + 6a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 3 +--R (50a b - 162a b + 156a b - 32a b - 12a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 38a b + 40a b + 60a b - 92a b - 12a b)cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R (- 24a b + 53a b - 39a b - 39a b + 43a b + 6a b) +--R * +--R cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R 57a b - 97a b + 51a b + 73a b + 6a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 6 +--R (a b - a b - 6a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 5 +--R (12a b - 33a b + 9a b + 12a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (3a b - 21a b + 78a b + 30a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 3 +--R (30a b - 108a b + 126a b - 24a b - 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (- 28a b + 15a b + 61a b - 159a b - 42a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 11 2 +--R (- 12a b + 17a b + 11a b - 43a b + 15a b + 12a b ) +--R * +--R cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R 40a b - 53a b + 9a b + 82a b + 18a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 7 8 5 10 3 7 +--R (- 3a b + 9a b - 6a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 6 +--R (- 3a b + 9a b - 18a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 5 +--R (15a b - 45a b + 12a b + 18a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (11a b - 31a b + 56a b + 54a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 3 +--R (6a b - 32a b + 61a b - 17a b - 18a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 12a b - 3a b + 45a b - 105a b - 54a b )cos(d x + c) +--R + +--R 13 2 11 4 9 6 7 8 5 10 3 +--R (- 2b + a b + 6a b - 7a b - 4a b + 6a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R 14a b - 13a b - 5a b + 40a b + 18a b +--R * +--R sin(d x + c) +--R + +--R 5 8 7 6 9 4 7 +--R (- a b + 5a b - 4a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 6 +--R (- 2a b + 6a b - 10a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 5 +--R (5a b - 17a b + 4a b + 8a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (4a b - 9a b + 9a b + 26a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 5a b + 18a b - 9a b - 4a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 2a b - 3a b + 13a b - 22a b - 22a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 +--R 2a b - a b - 2a b + 7a b + 6a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 7 6 9 4 7 +--R (- 12a b + 24a b )sin(d x + c) +--R + +--R 8 5 10 3 2 +--R (- 6a b + 12a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 6 7 8 5 +--R (12a b - 36a b + 24a b )cos(d x + c) - 42a b + 78a b +--R + +--R 10 3 +--R - 12a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 3 +--R (6a b - 18a b + 12a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 2 +--R (- 30a b + 48a b + 60a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 5 8 +--R (26a b - 76a b + 38a b + 12a b )cos(d x + c) - 82a b +--R + +--R 7 6 9 4 11 2 +--R 162a b - 104a b - 36a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 8 5 10 3 12 4 +--R (- 4a b + 10a b - 12a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 3 +--R (46a b - 140a b + 94a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 2 +--R (- 20a b - 6a b + 206a b + 24a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 9 +--R (34a b - 118a b + 134a b - 50a b )cos(d x + c) - 104a b +--R + +--R 6 7 8 5 10 3 12 +--R 208a b - 160a b - 172a b - 12a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 4 +--R (- 28a b + 52a b + 12a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (44a b - 136a b + 32a b + 60a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 4a b - 20a b + 144a b + 36a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (52a b - 188a b + 280a b - 84a b - 60a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R - 76a b + 132a b - 60a b - 248a b - 48a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 8 5 10 3 12 6 +--R (2a b - 2a b - 12a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 5 +--R (36a b - 108a b + 84a b - 12a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 6a b - 24a b + 150a b + 24a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 3 +--R (- 12a b + 12a b - 60a b + 36a b + 24a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 16a b + 26a b + 26a b - 90a b - 12a b)cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R (52a b - 160a b + 200a b + 40a b - 120a b - 12a b) +--R * +--R cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R - 28a b + 34a b + 16a b - 132a b - 58a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 7 +--R (- 6a b + 18a b - 12a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 6 +--R (- 6a b + 18a b - 36a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 5 +--R (42a b - 132a b + 90a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (18a b - 64a b + 130a b + 72a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 3 +--R (- 28a b + 52a b - 14a b - 46a b + 36a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (- 16a b + 22a b + 18a b - 126a b - 36a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 11 2 +--R (24a b - 56a b + 38a b + 80a b - 62a b - 24a b ) +--R * +--R cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 +--R - 4a b + 2a b + 8a b - 20a b - 22a b +--R * +--R sin(d x + c) +--R + +--R 6 7 8 5 10 3 7 +--R (- 2a b + 10a b - 8a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 6 +--R (- 4a b + 12a b - 20a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 5 +--R (14a b - 48a b + 30a b + 4a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (8a b - 22a b + 28a b + 40a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 3 +--R (- 8a b + 10a b + 20a b - 38a b + 16a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 4a b + 2a b + 14a b - 40a b - 20a b )cos(d x + c) +--R + +--R 13 2 11 4 9 6 7 8 5 10 3 +--R (4b - 6a b - 2a b + 18a b - 2a b - 12a b )cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 6 7 8 5 7 +--R (- 6a b + 12a b )sin(d x + c) +--R + +--R 7 6 9 4 2 +--R (- 3a b + 6a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 5 8 7 6 9 4 +--R (6a b - 18a b + 12a b )cos(d x + c) - 13a b + 19a b + 18a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 6 7 8 5 10 3 3 +--R (3a b - 9a b + 6a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 2 +--R (- 23a b + 44a b + 6a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 9 6 7 +--R (5a b - 10a b - 25a b + 30a b )cos(d x + c) - 9a b + 17a b +--R + +--R 8 5 10 3 +--R 4a b + 30a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (31a b - 98a b + 91a b - 24a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 38a b + 55a b + 49a b - 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (- 15a b + 45a b - 81a b + 27a b + 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R - 2a b + 39a b - 70a b + 69a b + 24a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 7 8 5 10 3 12 5 +--R (- 2a b + 7a b - 11a b + 6a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 8a b + 13a b + 19a b + 6a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 3 +--R (50a b - 162a b + 156a b - 32a b - 12a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 38a b + 40a b + 60a b - 92a b - 12a b)cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R (- 24a b + 53a b - 39a b - 39a b + 43a b + 6a b) +--R * +--R cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R 57a b - 97a b + 51a b + 73a b + 6a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 6 +--R (a b - a b - 6a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 5 +--R (12a b - 33a b + 9a b + 12a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (3a b - 21a b + 78a b + 30a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 3 +--R (30a b - 108a b + 126a b - 24a b - 24a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 28a b + 15a b + 61a b - 159a b - 42a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 11 2 +--R (- 12a b + 17a b + 11a b - 43a b + 15a b + 12a b ) +--R * +--R cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R 40a b - 53a b + 9a b + 82a b + 18a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 7 8 5 10 3 7 +--R (- 3a b + 9a b - 6a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 6 +--R (- 3a b + 9a b - 18a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 5 +--R (15a b - 45a b + 12a b + 18a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (11a b - 31a b + 56a b + 54a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 3 +--R (6a b - 32a b + 61a b - 17a b - 18a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 12a b - 3a b + 45a b - 105a b - 54a b )cos(d x + c) +--R + +--R 13 2 11 4 9 6 7 8 5 10 3 +--R (- 2b + a b + 6a b - 7a b - 4a b + 6a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R 14a b - 13a b - 5a b + 40a b + 18a b +--R * +--R sin(d x + c) +--R + +--R 5 8 7 6 9 4 7 +--R (- a b + 5a b - 4a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 6 +--R (- 2a b + 6a b - 10a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 5 +--R (5a b - 17a b + 4a b + 8a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (4a b - 9a b + 9a b + 26a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 5a b + 18a b - 9a b - 4a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 2 12 +--R (- 2a b - 3a b + 13a b - 22a b - 22a b )cos(d x + c) + 2a b +--R + +--R 3 10 5 8 7 6 9 4 +--R - a b - 2a b + 7a b + 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 9 7 7 9 5 7 +--R (6a b - 18a b + 12a b )sin(d x + c) +--R + +--R 6 8 8 6 10 4 2 +--R (3a b - 9a b + 6a b )cos(d x + c) +--R + +--R 6 8 8 6 10 4 4 10 6 8 8 6 +--R (6a b - 18a b + 12a b )cos(d x + c) + 13a b - 32a b + a b +--R + +--R 10 4 +--R 18a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 7 7 9 5 11 3 3 +--R (3a b - 9a b + 6a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 2 +--R (23a b - 67a b + 38a b + 6a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 3 11 5 9 +--R (5a b - 10a b - 25a b + 30a b )cos(d x + c) + 9a b - 26a b +--R + +--R 7 7 9 5 11 3 +--R 13a b - 26a b + 30a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 3 +--R (31a b - 98a b + 91a b - 24a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 2 +--R (38a b - 93a b + 6a b + 73a b - 24a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R (- 15a b + 45a b - 81a b + 27a b + 24a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R 2a b - 41a b + 109a b - 139a b + 45a b + 24a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 7 7 9 5 11 3 13 5 +--R (- 2a b + 7a b - 11a b + 6a b)cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 13 4 +--R (8a b - 21a b - 6a b + 13a b + 6a b)cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 13 3 +--R (50a b - 162a b + 156a b - 32a b - 12a b)cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (38a b - 78a b - 20a b + 152a b - 80a b - 12a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (- 24a b + 53a b - 39a b - 39a b + 43a b + 6a b) +--R * +--R cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R - 57a b + 154a b - 148a b - 22a b + 67a b + 6a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 6 +--R (- a b + 2a b + 5a b - 6a b )cos(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 5 +--R (12a b - 33a b + 9a b + 12a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 4 +--R (- 3a b + 24a b - 99a b + 48a b + 30a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 3 +--R (30a b - 108a b + 126a b - 24a b - 24a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (28a b - 43a b - 46a b + 220a b - 117a b - 42a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 12a b + 17a b + 11a b - 43a b + 15a b + 12a b ) +--R * +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R - 40a b + 93a b - 62a b - 73a b + 64a b + 18a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 7 9 5 11 3 7 +--R (- 3a b + 9a b - 6a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 6 +--R (3a b - 12a b + 27a b - 18a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 5 +--R (15a b - 45a b + 12a b + 18a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 4 +--R (- 11a b + 42a b - 87a b + 2a b + 54a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (6a b - 32a b + 61a b - 17a b - 18a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (12a b - 9a b - 48a b + 150a b - 51a b - 54a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 2a b + a b + 6a b - 7a b - 4a b + 6a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 14a b + 27a b - 8a b - 45a b + 22a b + 18a b +--R * +--R sin(d x + c) +--R + +--R 6 8 8 6 10 4 7 +--R (- a b + 5a b - 4a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 6 +--R (2a b - 8a b + 16a b - 10a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 5 +--R (5a b - 17a b + 4a b + 8a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 4 +--R (- 4a b + 13a b - 18a b - 17a b + 26a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 3 +--R (- 5a b + 18a b - 9a b - 4a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 10 4 2 14 +--R (2b + a b - 16a b + 35a b - 22a b )cos(d x + c) - 2b +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R 3a b + a b - 9a b + a b + 6a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 6 8 8 6 10 4 7 +--R (12a b - 36a b + 24a b )sin(d x + c) +--R + +--R 7 7 9 5 11 3 2 +--R (6a b - 18a b + 12a b )cos(d x + c) +--R + +--R 7 7 9 5 11 3 5 9 7 7 +--R (12a b - 36a b + 24a b )cos(d x + c) + 42a b - 120a b +--R + +--R 9 5 11 3 +--R 90a b - 12a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 8 6 10 4 12 2 3 +--R (6a b - 18a b + 12a b )cos(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 2 +--R (30a b - 78a b - 12a b + 60a b )cos(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 4 10 +--R (26a b - 76a b + 38a b + 12a b )cos(d x + c) + 82a b +--R + +--R 6 8 8 6 10 4 12 2 +--R - 244a b + 266a b - 68a b - 36a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 7 7 9 5 11 3 13 4 +--R (4a b - 14a b + 22a b - 12a b)cos(d x + c) +--R + +--R 7 7 9 5 11 3 3 +--R (46a b - 140a b + 94a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 13 2 +--R (20a b - 14a b - 212a b + 182a b + 24a b)cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 3 11 +--R (34a b - 118a b + 134a b - 50a b )cos(d x + c) + 104a b +--R + +--R 5 9 7 7 9 5 11 3 13 +--R - 312a b + 368a b + 12a b - 160a b - 12a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 4 +--R (28a b - 80a b + 40a b + 12a b )cos(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 3 +--R (44a b - 136a b + 32a b + 60a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 2 +--R (4a b + 16a b - 164a b + 108a b + 36a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R (52a b - 188a b + 280a b - 84a b - 60a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R 76a b - 208a b + 192a b + 188a b - 200a b - 48a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 7 7 9 5 11 3 13 6 +--R (- 2a b + 4a b + 10a b - 12a b)cos(d x + c) +--R + +--R 7 7 9 5 11 3 13 5 +--R (36a b - 108a b + 84a b - 12a b)cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 13 4 +--R (6a b + 18a b - 174a b + 126a b + 24a b)cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 13 3 +--R (- 12a b + 12a b - 60a b + 36a b + 24a b)cos(d x + c) +--R + +--R 3 11 5 9 9 5 11 3 13 2 +--R (16a b - 42a b + 116a b - 78a b - 12a b)cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (52a b - 160a b + 200a b + 40a b - 120a b - 12a b) +--R * +--R cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R 28a b - 62a b + 18a b + 148a b - 74a b - 58a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 6 10 4 12 2 7 +--R (- 6a b + 18a b - 12a b )cos(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 6 +--R (6a b - 24a b + 54a b - 36a b )cos(d x + c) +--R + +--R 6 8 8 6 10 4 5 +--R (42a b - 132a b + 90a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 4 +--R (- 18a b + 82a b - 194a b + 58a b + 72a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 3 +--R (- 28a b + 52a b - 14a b - 46a b + 36a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (16a b - 38a b + 4a b + 144a b - 90a b - 36a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (24a b - 56a b + 38a b + 80a b - 62a b - 24a b ) +--R * +--R cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R 4b - 6a b - 6a b + 28a b + 2a b - 22a b +--R * +--R sin(d x + c) +--R + +--R 7 7 9 5 11 3 7 +--R (- 2a b + 10a b - 8a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 6 +--R (4a b - 16a b + 32a b - 20a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 5 +--R (14a b - 48a b + 30a b + 4a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 4 +--R (- 8a b + 30a b - 50a b - 12a b + 40a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (- 8a b + 10a b + 20a b - 38a b + 16a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 2 +--R (4a b - 6a b - 12a b + 54a b - 20a b - 20a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (4a b - 6a b - 2a b + 18a b - 2a b - 12a b )cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 5 9 7 7 9 5 7 +--R (6a b - 18a b + 12a b )sin(d x + c) +--R + +--R 6 8 8 6 10 4 2 +--R (3a b - 9a b + 6a b )cos(d x + c) +--R + +--R 6 8 8 6 10 4 4 10 6 8 8 6 +--R (6a b - 18a b + 12a b )cos(d x + c) + 13a b - 32a b + a b +--R + +--R 10 4 +--R 18a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 7 7 9 5 11 3 3 +--R (3a b - 9a b + 6a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 2 +--R (23a b - 67a b + 38a b + 6a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 3 11 5 9 +--R (5a b - 10a b - 25a b + 30a b )cos(d x + c) + 9a b - 26a b +--R + +--R 7 7 9 5 11 3 +--R 13a b - 26a b + 30a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 3 +--R (31a b - 98a b + 91a b - 24a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 2 +--R (38a b - 93a b + 6a b + 73a b - 24a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R (- 15a b + 45a b - 81a b + 27a b + 24a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R 2a b - 41a b + 109a b - 139a b + 45a b + 24a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 7 7 9 5 11 3 13 5 +--R (- 2a b + 7a b - 11a b + 6a b)cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 13 4 +--R (8a b - 21a b - 6a b + 13a b + 6a b)cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 13 3 +--R (50a b - 162a b + 156a b - 32a b - 12a b)cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 2 +--R (38a b - 78a b - 20a b + 152a b - 80a b - 12a b)cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (- 24a b + 53a b - 39a b - 39a b + 43a b + 6a b)cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R - 57a b + 154a b - 148a b - 22a b + 67a b + 6a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 6 +--R (- a b + 2a b + 5a b - 6a b )cos(d x + c) +--R + +--R 6 8 8 6 10 4 12 2 5 +--R (12a b - 33a b + 9a b + 12a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 4 +--R (- 3a b + 24a b - 99a b + 48a b + 30a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 12 2 3 +--R (30a b - 108a b + 126a b - 24a b - 24a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (28a b - 43a b - 46a b + 220a b - 117a b - 42a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 12a b + 17a b + 11a b - 43a b + 15a b + 12a b ) +--R * +--R cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R - 40a b + 93a b - 62a b - 73a b + 64a b + 18a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 7 9 5 11 3 7 +--R (- 3a b + 9a b - 6a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 6 +--R (3a b - 12a b + 27a b - 18a b )cos(d x + c) +--R + +--R 5 9 7 7 9 5 11 3 5 +--R (15a b - 45a b + 12a b + 18a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 4 +--R (- 11a b + 42a b - 87a b + 2a b + 54a b )cos(d x + c) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (6a b - 32a b + 61a b - 17a b - 18a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 2 +--R (12a b - 9a b - 48a b + 150a b - 51a b - 54a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 2a b + a b + 6a b - 7a b - 4a b + 6a b )cos(d x + c) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 14a b + 27a b - 8a b - 45a b + 22a b + 18a b +--R * +--R sin(d x + c) +--R + +--R 6 8 8 6 10 4 7 +--R (- a b + 5a b - 4a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 6 +--R (2a b - 8a b + 16a b - 10a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 5 +--R (5a b - 17a b + 4a b + 8a b )cos(d x + c) +--R + +--R 2 12 4 10 6 8 8 6 10 4 4 +--R (- 4a b + 13a b - 18a b - 17a b + 26a b )cos(d x + c) +--R + +--R 4 10 6 8 8 6 10 4 3 +--R (- 5a b + 18a b - 9a b - 4a b )cos(d x + c) +--R + +--R 14 2 12 4 10 6 8 10 4 2 14 2 12 +--R (2b + a b - 16a b + 35a b - 22a b )cos(d x + c) - 2b + 3a b +--R + +--R 4 10 6 8 8 6 10 4 +--R a b - 9a b + a b + 6a b +--R / +--R 8 8 10 6 12 4 6 +--R (8a b - 16a b + 8a b )sin(d x + c) +--R + +--R 9 7 11 5 13 3 2 +--R (- 8a b + 16a b - 8a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 7 9 +--R (- 8a b + 24a b - 24a b + 8a b )cos(d x + c) + 32a b +--R + +--R 9 7 13 3 +--R - 48a b + 16a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 10 6 12 4 14 2 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 3 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 2 +--R (- 28a b + 44a b - 4a b - 12a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 +--R (- 32a b + 88a b - 72a b + 8a b + 8a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 +--R 50a b - 40a b - 60a b + 40a b + 10a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 9 7 11 5 13 3 15 5 +--R (- 2a b + 6a b - 6a b + 2a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 4 +--R (6a b - 10a b + 2a b + 2a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 3 +--R (28a b - 80a b + 72a b - 16a b - 4a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 2 +--R (- 36a b + 32a b + 40a b - 32a b - 4a b)cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 15 +--R (- 50a b + 122a b - 68a b - 28a b + 22a b + 2a b) +--R * +--R cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 15 +--R 38a b + 10a b - 100a b + 20a b + 30a b + 2a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 4 +--R (6a b - 6a b - 6a b + 6a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 14 2 3 +--R (36a b - 96a b + 72a b - 12a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 +--R (- 20a b - 8a b + 64a b - 24a b - 12a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 14 2 +--R (- 38a b + 78a b - 12a b - 52a b + 18a b + 6a b ) +--R * +--R cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 14 2 +--R 14a b + 30a b - 60a b - 20a b + 30a b + 6a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 4 +--R (2a b + 2a b - 10a b + 6a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 3 +--R (20a b - 48a b + 24a b + 16a b - 12a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 13 3 2 +--R (- 4a b - 16a b + 32a b - 12a b )cos(d x + c) +--R + +--R 3 13 5 11 7 9 9 7 11 5 13 3 +--R (- 14a b + 22a b + 12a b - 28a b + 2a b + 6a b ) +--R * +--R cos(d x + c) +--R + +--R 3 13 5 11 7 9 9 7 11 5 13 3 +--R 2a b + 14a b - 12a b - 20a b + 10a b + 6a b +--R * +--R sin(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 5 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 4 12 6 10 10 6 12 4 3 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 2 +--R (- 4a b + 4a b + 4a b - 4a b )cos(d x + c) +--R + +--R 2 14 4 12 6 10 8 8 10 6 12 4 +--R (- 2a b + 2a b + 4a b - 4a b - 2a b + 2a b ) +--R * +--R cos(d x + c) +--R + +--R 4 12 8 8 12 4 +--R 2a b - 4a b + 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 9 7 11 5 13 3 6 +--R (16a b - 32a b + 16a b )sin(d x + c) +--R + +--R 10 6 12 4 14 2 2 +--R (- 16a b + 32a b - 16a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 8 8 +--R (- 16a b + 48a b - 48a b + 16a b )cos(d x + c) + 64a b +--R + +--R 10 6 14 2 +--R - 96a b + 32a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 11 5 13 3 15 4 +--R (4a b - 8a b + 4a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 3 +--R (16a b - 48a b + 48a b - 16a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 2 +--R (- 56a b + 88a b - 8a b - 24a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 +--R (- 64a b + 176a b - 144a b + 16a b + 16a b) +--R * +--R cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 +--R 100a b - 80a b - 120a b + 80a b + 20a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 10 6 12 4 14 2 16 5 +--R (- 4a b + 12a b - 12a b + 4a )cos(d x + c) +--R + +--R 10 6 12 4 14 2 16 4 +--R (12a b - 20a b + 4a b + 4a )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 16 3 +--R (56a b - 160a b + 144a b - 32a b - 8a )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 16 2 +--R (- 72a b + 64a b + 80a b - 64a b - 8a )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 +--R - 100a b + 244a b - 136a b - 56a b + 44a b +--R + +--R 16 +--R 4a +--R * +--R cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 16 +--R 76a b + 20a b - 200a b + 40a b + 60a b + 4a +--R * +--R 3 +--R sin(d x + c) +--R + +--R 9 7 11 5 13 3 15 5 +--R (- 12a b + 36a b - 36a b + 12a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 4 +--R (12a b - 12a b - 12a b + 12a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 15 3 +--R (72a b - 192a b + 144a b - 24a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 +--R (- 40a b - 16a b + 128a b - 48a b - 24a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 +--R - 76a b + 156a b - 24a b - 104a b + 36a b +--R + +--R 15 +--R 12a b +--R * +--R cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 15 +--R 28a b + 60a b - 120a b - 40a b + 60a b + 12a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 5 +--R (- 12a b + 36a b - 36a b + 12a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 4 +--R (4a b + 4a b - 20a b + 12a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 3 +--R (40a b - 96a b + 48a b + 32a b - 24a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 14 2 2 +--R (- 8a b - 32a b + 64a b - 24a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 14 2 +--R (- 28a b + 44a b + 24a b - 56a b + 4a b + 12a b ) +--R * +--R cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 14 2 +--R 4a b + 28a b - 24a b - 40a b + 20a b + 12a b +--R * +--R sin(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 5 +--R (- 4a b + 12a b - 12a b + 4a b )cos(d x + c) +--R + +--R 9 7 11 5 13 3 4 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 5 11 7 9 11 5 13 3 3 +--R (8a b - 16a b + 16a b - 8a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 2 +--R (- 8a b + 8a b + 8a b - 8a b )cos(d x + c) +--R + +--R 3 13 5 11 7 9 9 7 11 5 13 3 +--R (- 4a b + 4a b + 8a b - 8a b - 4a b + 4a b )cos(d x + c) +--R + +--R 5 11 9 7 13 3 +--R 4a b - 8a b + 4a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 8 8 10 6 12 4 6 +--R (8a b - 16a b + 8a b )sin(d x + c) +--R + +--R 9 7 11 5 13 3 2 +--R (- 8a b + 16a b - 8a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 7 9 +--R (- 8a b + 24a b - 24a b + 8a b )cos(d x + c) + 32a b +--R + +--R 9 7 13 3 +--R - 48a b + 16a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 10 6 12 4 14 2 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 3 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 2 +--R (- 28a b + 44a b - 4a b - 12a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 +--R (- 32a b + 88a b - 72a b + 8a b + 8a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 +--R 50a b - 40a b - 60a b + 40a b + 10a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 9 7 11 5 13 3 15 5 +--R (- 2a b + 6a b - 6a b + 2a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 4 +--R (6a b - 10a b + 2a b + 2a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 3 +--R (28a b - 80a b + 72a b - 16a b - 4a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 2 +--R (- 36a b + 32a b + 40a b - 32a b - 4a b)cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 15 +--R (- 50a b + 122a b - 68a b - 28a b + 22a b + 2a b) +--R * +--R cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 15 +--R 38a b + 10a b - 100a b + 20a b + 30a b + 2a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 4 +--R (6a b - 6a b - 6a b + 6a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 14 2 3 +--R (36a b - 96a b + 72a b - 12a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 2 +--R (- 20a b - 8a b + 64a b - 24a b - 12a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 14 2 +--R (- 38a b + 78a b - 12a b - 52a b + 18a b + 6a b ) +--R * +--R cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 14 2 +--R 14a b + 30a b - 60a b - 20a b + 30a b + 6a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 4 +--R (2a b + 2a b - 10a b + 6a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 3 +--R (20a b - 48a b + 24a b + 16a b - 12a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 13 3 2 +--R (- 4a b - 16a b + 32a b - 12a b )cos(d x + c) +--R + +--R 3 13 5 11 7 9 9 7 11 5 13 3 +--R (- 14a b + 22a b + 12a b - 28a b + 2a b + 6a b ) +--R * +--R cos(d x + c) +--R + +--R 3 13 5 11 7 9 9 7 11 5 13 3 +--R 2a b + 14a b - 12a b - 20a b + 10a b + 6a b +--R * +--R sin(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 5 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 4 12 6 10 10 6 12 4 3 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 2 +--R (- 4a b + 4a b + 4a b - 4a b )cos(d x + c) +--R + +--R 2 14 4 12 6 10 8 8 10 6 12 4 +--R (- 2a b + 2a b + 4a b - 4a b - 2a b + 2a b )cos(d x + c) +--R + +--R 4 12 8 8 12 4 +--R 2a b - 4a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 7 10 9 8 11 6 13 4 6 +--R (- 8a b + 24a b - 24a b + 8a b )sin(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 2 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 6 11 +--R (- 8a b + 24a b - 24a b + 8a b )cos(d x + c) - 32a b +--R + +--R 8 9 10 7 12 5 14 3 +--R 80a b - 48a b - 16a b + 16a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 9 8 11 6 13 4 15 2 4 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 9 8 11 6 13 4 15 2 3 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 15 2 2 +--R (28a b - 72a b + 48a b + 8a b - 12a b )cos(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 15 2 +--R (- 32a b + 88a b - 72a b + 8a b + 8a b )cos(d x + c) +--R + +--R 5 12 7 10 9 8 11 6 13 4 15 2 +--R - 50a b + 90a b + 20a b - 100a b + 30a b + 10a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 10 7 12 5 14 3 16 5 +--R (- 2a b + 6a b - 6a b + 2a b)cos(d x + c) +--R + +--R 8 9 10 7 12 5 16 4 +--R (- 6a b + 16a b - 12a b + 2a b)cos(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 16 3 +--R (28a b - 80a b + 72a b - 16a b - 4a b)cos(d x + c) +--R + +--R 6 11 8 9 10 7 12 5 14 3 16 +--R (36a b - 68a b - 8a b + 72a b - 28a b - 4a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 6 11 8 9 10 7 12 5 14 3 16 +--R (- 50a b + 122a b - 68a b - 28a b + 22a b + 2a b) +--R * +--R cos(d x + c) +--R + +--R 4 13 6 11 8 9 10 7 12 5 14 3 +--R - 38a b + 28a b + 110a b - 120a b - 10a b + 28a b +--R + +--R 16 +--R 2a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 9 8 11 6 13 4 15 2 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 7 10 9 8 13 4 15 2 4 +--R (- 6a b + 12a b - 12a b + 6a b )cos(d x + c) +--R + +--R 7 10 9 8 11 6 15 2 3 +--R (36a b - 96a b + 72a b - 12a b )cos(d x + c) +--R + +--R 5 12 7 10 9 8 11 6 13 4 15 2 +--R (20a b - 12a b - 72a b + 88a b - 12a b - 12a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 5 12 7 10 9 8 11 6 13 4 15 2 +--R (- 38a b + 78a b - 12a b - 52a b + 18a b + 6a b ) +--R * +--R cos(d x + c) +--R + +--R 3 14 5 12 7 10 9 8 11 6 13 4 15 2 +--R - 14a b - 16a b + 90a b - 40a b - 50a b + 24a b + 6a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 6 11 10 7 12 5 14 3 4 +--R (- 2a b + 12a b - 16a b + 6a b )cos(d x + c) +--R + +--R 6 11 8 9 10 7 12 5 14 3 3 +--R (20a b - 48a b + 24a b + 16a b - 12a b )cos(d x + c) +--R + +--R 4 13 6 11 8 9 10 7 12 5 14 3 +--R (4a b + 12a b - 48a b + 32a b + 12a b - 12a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 4 13 6 11 8 9 10 7 12 5 14 3 +--R (- 14a b + 22a b + 12a b - 28a b + 2a b + 6a b ) +--R * +--R cos(d x + c) +--R + +--R 2 15 4 13 6 11 8 9 10 7 12 5 14 3 +--R - 2a b - 12a b + 26a b + 8a b - 30a b + 4a b + 6a b +--R * +--R sin(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 5 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 4 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 5 12 7 10 11 6 13 4 3 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 5 12 7 10 11 6 13 4 2 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 3 14 5 12 7 10 9 8 11 6 13 4 +--R (- 2a b + 2a b + 4a b - 4a b - 2a b + 2a b )cos(d x + c) +--R + +--R 3 14 5 12 7 10 9 8 11 6 13 4 +--R - 2a b + 2a b + 4a b - 4a b - 2a b + 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 8 9 10 7 12 5 14 3 6 +--R (- 16a b + 48a b - 48a b + 16a b )sin(d x + c) +--R + +--R 9 8 11 6 13 4 15 2 2 +--R (16a b - 48a b + 48a b - 16a b )cos(d x + c) +--R + +--R 9 8 11 6 13 4 15 2 7 10 +--R (- 16a b + 48a b - 48a b + 16a b )cos(d x + c) - 64a b +--R + +--R 9 8 11 6 13 4 15 2 +--R 160a b - 96a b - 32a b + 32a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 10 7 12 5 14 3 16 4 +--R (- 4a b + 12a b - 12a b + 4a b)cos(d x + c) +--R + +--R 10 7 12 5 14 3 16 3 +--R (16a b - 48a b + 48a b - 16a b)cos(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 16 2 +--R (56a b - 144a b + 96a b + 16a b - 24a b)cos(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 16 +--R (- 64a b + 176a b - 144a b + 16a b + 16a b)cos(d x + c) +--R + +--R 6 11 8 9 10 7 12 5 14 3 16 +--R - 100a b + 180a b + 40a b - 200a b + 60a b + 20a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 11 6 13 4 15 2 17 5 +--R (- 4a b + 12a b - 12a b + 4a )cos(d x + c) +--R + +--R 9 8 11 6 13 4 17 4 +--R (- 12a b + 32a b - 24a b + 4a )cos(d x + c) +--R + +--R 9 8 11 6 13 4 15 2 17 3 +--R (56a b - 160a b + 144a b - 32a b - 8a )cos(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 15 2 17 +--R (72a b - 136a b - 16a b + 144a b - 56a b - 8a ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 15 2 17 +--R (- 100a b + 244a b - 136a b - 56a b + 44a b + 4a ) +--R * +--R cos(d x + c) +--R + +--R 5 12 7 10 9 8 11 6 13 4 15 2 17 +--R - 76a b + 56a b + 220a b - 240a b - 20a b + 56a b + 4a +--R * +--R 3 +--R sin(d x + c) +--R + +--R 10 7 12 5 14 3 16 5 +--R (- 12a b + 36a b - 36a b + 12a b)cos(d x + c) +--R + +--R 8 9 10 7 14 3 16 4 +--R (- 12a b + 24a b - 24a b + 12a b)cos(d x + c) +--R + +--R 8 9 10 7 12 5 16 3 +--R (72a b - 192a b + 144a b - 24a b)cos(d x + c) +--R + +--R 6 11 8 9 10 7 12 5 14 3 16 +--R (40a b - 24a b - 144a b + 176a b - 24a b - 24a b) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 6 11 8 9 10 7 12 5 14 3 16 +--R (- 76a b + 156a b - 24a b - 104a b + 36a b + 12a b) +--R * +--R cos(d x + c) +--R + +--R 4 13 6 11 8 9 10 7 12 5 14 3 +--R - 28a b - 32a b + 180a b - 80a b - 100a b + 48a b +--R + +--R 16 +--R 12a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 9 8 11 6 13 4 15 2 5 +--R (- 12a b + 36a b - 36a b + 12a b )cos(d x + c) +--R + +--R 7 10 11 6 13 4 15 2 4 +--R (- 4a b + 24a b - 32a b + 12a b )cos(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 15 2 3 +--R (40a b - 96a b + 48a b + 32a b - 24a b )cos(d x + c) +--R + +--R 5 12 7 10 9 8 11 6 13 4 15 2 +--R (8a b + 24a b - 96a b + 64a b + 24a b - 24a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 5 12 7 10 9 8 11 6 13 4 15 2 +--R (- 28a b + 44a b + 24a b - 56a b + 4a b + 12a b ) +--R * +--R cos(d x + c) +--R + +--R 3 14 5 12 7 10 9 8 11 6 13 4 15 2 +--R - 4a b - 24a b + 52a b + 16a b - 60a b + 8a b + 12a b +--R * +--R sin(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 5 +--R (- 4a b + 12a b - 12a b + 4a b )cos(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 4 +--R (- 4a b + 12a b - 12a b + 4a b )cos(d x + c) +--R + +--R 6 11 8 9 12 5 14 3 3 +--R (8a b - 16a b + 16a b - 8a b )cos(d x + c) +--R + +--R 6 11 8 9 12 5 14 3 2 +--R (8a b - 16a b + 16a b - 8a b )cos(d x + c) +--R + +--R 4 13 6 11 8 9 10 7 12 5 14 3 +--R (- 4a b + 4a b + 8a b - 8a b - 4a b + 4a b )cos(d x + c) +--R + +--R 4 13 6 11 8 9 10 7 12 5 14 3 +--R - 4a b + 4a b + 8a b - 8a b - 4a b + 4a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 7 10 9 8 11 6 13 4 6 +--R (- 8a b + 24a b - 24a b + 8a b )sin(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 2 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 6 11 8 9 +--R (- 8a b + 24a b - 24a b + 8a b )cos(d x + c) - 32a b + 80a b +--R + +--R 10 7 12 5 14 3 +--R - 48a b - 16a b + 16a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 9 8 11 6 13 4 15 2 4 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 9 8 11 6 13 4 15 2 3 +--R (8a b - 24a b + 24a b - 8a b )cos(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 15 2 2 +--R (28a b - 72a b + 48a b + 8a b - 12a b )cos(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 15 2 +--R (- 32a b + 88a b - 72a b + 8a b + 8a b )cos(d x + c) +--R + +--R 5 12 7 10 9 8 11 6 13 4 15 2 +--R - 50a b + 90a b + 20a b - 100a b + 30a b + 10a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 10 7 12 5 14 3 16 5 +--R (- 2a b + 6a b - 6a b + 2a b)cos(d x + c) +--R + +--R 8 9 10 7 12 5 16 4 +--R (- 6a b + 16a b - 12a b + 2a b)cos(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 16 3 +--R (28a b - 80a b + 72a b - 16a b - 4a b)cos(d x + c) +--R + +--R 6 11 8 9 10 7 12 5 14 3 16 2 +--R (36a b - 68a b - 8a b + 72a b - 28a b - 4a b)cos(d x + c) +--R + +--R 6 11 8 9 10 7 12 5 14 3 16 +--R (- 50a b + 122a b - 68a b - 28a b + 22a b + 2a b) +--R * +--R cos(d x + c) +--R + +--R 4 13 6 11 8 9 10 7 12 5 14 3 16 +--R - 38a b + 28a b + 110a b - 120a b - 10a b + 28a b + 2a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 9 8 11 6 13 4 15 2 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 7 10 9 8 13 4 15 2 4 +--R (- 6a b + 12a b - 12a b + 6a b )cos(d x + c) +--R + +--R 7 10 9 8 11 6 15 2 3 +--R (36a b - 96a b + 72a b - 12a b )cos(d x + c) +--R + +--R 5 12 7 10 9 8 11 6 13 4 15 2 +--R (20a b - 12a b - 72a b + 88a b - 12a b - 12a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 5 12 7 10 9 8 11 6 13 4 15 2 +--R (- 38a b + 78a b - 12a b - 52a b + 18a b + 6a b ) +--R * +--R cos(d x + c) +--R + +--R 3 14 5 12 7 10 9 8 11 6 13 4 15 2 +--R - 14a b - 16a b + 90a b - 40a b - 50a b + 24a b + 6a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 9 10 7 12 5 14 3 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(d x + c) +--R + +--R 6 11 10 7 12 5 14 3 4 +--R (- 2a b + 12a b - 16a b + 6a b )cos(d x + c) +--R + +--R 6 11 8 9 10 7 12 5 14 3 3 +--R (20a b - 48a b + 24a b + 16a b - 12a b )cos(d x + c) +--R + +--R 4 13 6 11 8 9 10 7 12 5 14 3 +--R (4a b + 12a b - 48a b + 32a b + 12a b - 12a b ) +--R * +--R 2 +--R cos(d x + c) +--R + +--R 4 13 6 11 8 9 10 7 12 5 14 3 +--R (- 14a b + 22a b + 12a b - 28a b + 2a b + 6a b ) +--R * +--R cos(d x + c) +--R + +--R 2 15 4 13 6 11 8 9 10 7 12 5 14 3 +--R - 2a b - 12a b + 26a b + 8a b - 30a b + 4a b + 6a b +--R * +--R sin(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 5 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 7 10 9 8 11 6 13 4 4 +--R (- 2a b + 6a b - 6a b + 2a b )cos(d x + c) +--R + +--R 5 12 7 10 11 6 13 4 3 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 5 12 7 10 11 6 13 4 2 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 3 14 5 12 7 10 9 8 11 6 13 4 +--R (- 2a b + 2a b + 4a b - 4a b - 2a b + 2a b )cos(d x + c) +--R + +--R 3 14 5 12 7 10 9 8 11 6 13 4 +--R - 2a b + 2a b + 4a b - 4a b - 2a b + 2a b +--R Type: Expression(Integer) +--E 437 + +--S 438 of 528 +m0382b:= a0382.2-r0382 +--R +--R +--R (400) +--R 3 6 5 4 7 2 3 +--R (- 8a b + 20a b - 24a b )sin(d x + c) +--R + +--R 4 5 6 3 8 2 2 7 4 5 6 3 +--R (4a b - 10a b + 12a b)cos(d x + c) - 20a b + 46a b - 50a b +--R + +--R 8 +--R - 12a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 6 5 4 7 2 2 8 3 6 5 4 +--R (8a b - 20a b + 24a b )cos(d x + c) - 16a b + 32a b - 28a b +--R + +--R 7 2 +--R - 24a b +--R * +--R sin(d x + c) +--R + +--R 2 7 4 5 6 3 2 9 2 7 4 5 6 3 +--R (4a b - 10a b + 12a b )cos(d x + c) - 4b + 6a b - 2a b - 12a b +--R * +--R d x + c +--R +-------+ b tan(-------) + a +--R | 2 2 2 +--R \|b - a atanh(------------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 6 5 4 7 2 3 +--R (- 8a b + 20a b - 24a b )sin(d x + c) +--R + +--R 4 5 6 3 8 2 2 7 4 5 6 3 +--R (4a b - 10a b + 12a b)cos(d x + c) - 20a b + 46a b - 50a b +--R + +--R 8 +--R - 12a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 3 6 5 4 7 2 2 8 3 6 5 4 +--R (8a b - 20a b + 24a b )cos(d x + c) - 16a b + 32a b - 28a b +--R + +--R 7 2 +--R - 24a b +--R * +--R sin(d x + c) +--R + +--R 2 7 4 5 6 3 2 9 2 7 4 5 6 3 +--R (4a b - 10a b + 12a b )cos(d x + c) - 4b + 6a b - 2a b - 12a b +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sin(d x + c) + a cos(d x + c) + a)\|b - a +--R \|- b + a atan(-----------------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(d x + c) + b - a +--R + +--R 4 4 6 2 4 4 6 2 3 +--R ((3a b - 6a b )cos(d x + c) + 4a b - 10a b )sin(d x + c) +--R + +--R 5 3 7 2 3 5 5 3 +--R (- 2a b + 5a b)cos(d x + c) + (2a b - 5a b )cos(d x + c) +--R + +--R 3 5 5 3 7 +--R 10a b - 23a b - 5a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (3a b - 6a b )cos(d x + c) + (- 4a b + 10a b )cos(d x + c) +--R + +--R 4 4 6 2 2 6 4 4 6 2 +--R (- 3a b + 6a b )cos(d x + c) + 8a b - 16a b - 10a b +--R * +--R sin(d x + c) +--R + +--R 3 5 5 3 3 3 5 5 3 2 +--R (2a b - 5a b )cos(d x + c) + (- 2a b + 5a b )cos(d x + c) +--R + +--R 3 5 5 3 7 3 5 5 3 +--R (- 2a b + 5a b )cos(d x + c) + 2a b - 3a b - 5a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 6 5 8 3 10 3 +--R (4a b - 8a b + 4a b)d sin(d x + c) +--R + +--R 7 4 9 2 11 2 +--R (- 2a b + 4a b - 2a )d cos(d x + c) +--R + +--R 5 6 7 4 9 2 11 +--R (10a b - 18a b + 6a b + 2a )d +--R * +--R 2 +--R sin(d x + c) +--R + +--R 6 5 8 3 10 2 +--R (- 4a b + 8a b - 4a b)d cos(d x + c) +--R + +--R 4 7 6 5 10 +--R (8a b - 12a b + 4a b)d +--R * +--R sin(d x + c) +--R + +--R 5 6 7 4 9 2 2 +--R (- 2a b + 4a b - 2a b )d cos(d x + c) +--R + +--R 3 8 5 6 7 4 9 2 +--R (2a b - 2a b - 2a b + 2a b )d +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 438 + +--S 439 of 528 +d0382b:= D(m0382b,x) +--R +--R +--R (401) +--R 6 7 8 5 8 +--R (- 6a b + 12a b )sin(d x + c) +--R + +--R 7 6 9 4 2 7 6 9 4 +--R (- 3a b + 6a b )cos(d x + c) + (- 12a b + 24a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 +--R - 21a b + 33a b + 6a b +--R * +--R 7 +--R sin(d x + c) +--R + +--R 8 5 10 3 3 +--R (- 6a b + 12a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 2 +--R (- 21a b + 33a b + 36a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 4 9 6 7 +--R (- 22a b + 34a b + 60a b )cos(d x + c) - 41a b + 78a b +--R + +--R 8 5 10 3 +--R - 55a b + 36a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 4 +--R (- 5a b + 11a b - 6a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 3 +--R (- 68a b + 146a b - 48a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 23a b - 20a b + 202a b - 36a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 10 +--R (20a b - 50a b + 162a b + 48a b )cos(d x + c) - 52a b +--R + +--R 5 8 7 6 9 4 11 2 +--R 154a b - 197a b + 95a b + 42a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 8 5 10 3 12 5 +--R (4a b - 10a b + 12a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 37a b + 77a b - 4a b + 12a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 3 +--R (- 162a b + 358a b - 136a b - 24a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 19a b - 85a b + 312a b - 148a b - 24a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R (78a b - 118a b + 122a b + 146a b + 12a b)cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R - 38a b + 187a b - 258a b + 95a b + 152a b + 12a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 6 +--R (a b - a b - 6a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 5 +--R (- 20a b + 32a b + 36a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (- 25a b + 32a b + 101a b + 54a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (- 160a b + 380a b - 184a b - 72a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 34a b - 63a b + 275a b - 319a b - 90a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (72a b - 68a b - 12a b + 152a b + 36a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 11 2 +--R - 14a b + 141a b - 182a b + 40a b + 219a b + 42a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 8 5 10 3 7 +--R (6a b - 12a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 6 +--R (- 21a b + 48a b - 30a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 5 +--R (- 54a b + 102a b + 60a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (15a b - 47a b + 116a b + 114a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 72a b + 208a b - 166a b - 84a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 34a b - 27a b + 183a b - 320a b - 138a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 13 +--R (28a b - 8a b - 42a b + 58a b + 36a b )cos(d x + c) - 2b +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R 67a b - 74a b - 3a b + 156a b + 54a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 9 4 8 7 6 9 4 7 +--R (3a b - 6a b )cos(d x + c) + (8a b - 20a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 6 +--R (- 23a b + 55a b - 20a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 5 +--R (- 40a b + 84a b + 52a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (18a b - 35a b + 31a b + 88a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 12a b + 62a b - 96a b - 44a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 14a b - 13a b + 79a b - 143a b - 92a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 12 +--R (4a b + 2a b - 10a b + 4a b + 12a b )cos(d x + c) + 18a b +--R + +--R 3 10 5 8 7 6 9 4 +--R - 15a b - 9a b + 54a b + 30a b +--R * +--R sin(d x + c) +--R + +--R 6 7 8 5 8 6 7 8 5 7 +--R (a b - 4a b )cos(d x + c) + (2a b - 8a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 6 +--R (- 7a b + 18a b - 2a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 5 +--R (- 10a b + 24a b + 16a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 4 +--R (4a b - 4a b - 4a b + 22a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 3 +--R (10a b - 26a b - 8a b )cos(d x + c) +--R + +--R 13 2 11 4 9 6 7 8 5 2 13 +--R (- 2b - 3a b + 13a b - 22a b - 22a b )cos(d x + c) + 2b +--R + +--R 2 11 4 9 6 7 8 5 +--R - a b - 2a b + 7a b + 6a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 7 6 9 4 8 +--R (- 12a b + 24a b )sin(d x + c) +--R + +--R 8 5 10 3 2 +--R (- 6a b + 12a b )cos(d x + c) +--R + +--R 8 5 10 3 6 7 8 5 10 3 +--R (- 24a b + 48a b )cos(d x + c) - 58a b + 106a b - 36a b +--R * +--R 7 +--R sin(d x + c) +--R + +--R 9 4 11 2 3 +--R (- 12a b + 24a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 2 +--R (- 26a b + 26a b + 120a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 5 8 7 6 +--R (- 76a b + 148a b + 24a b )cos(d x + c) - 146a b + 268a b +--R + +--R 9 4 11 2 +--R - 182a b - 72a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 8 5 10 3 12 4 +--R (- 14a b + 32a b - 24a b)cos(d x + c) +--R + +--R 8 5 10 3 3 +--R (- 104a b + 212a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 2 +--R (- 6a b - 100a b + 424a b + 48a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 4 9 6 7 +--R (- 120a b + 268a b - 76a b )cos(d x + c) - 204a b + 358a b +--R + +--R 8 5 10 3 12 +--R - 230a b - 320a b - 24a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 4 +--R (- 70a b + 136a b + 24a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 3 +--R (- 180a b + 372a b + 120a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 30a b - 54a b + 324a b + 72a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 10 +--R (- 172a b + 440a b - 388a b - 120a b )cos(d x + c) - 152a b +--R + +--R 5 8 7 6 9 4 11 2 +--R 228a b - 44a b - 476a b - 96a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 8 5 10 3 12 6 +--R (- 2a b + 8a b - 24a b)cos(d x + c) +--R + +--R 8 5 10 3 12 5 +--R (- 72a b + 144a b - 24a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 6a b - 66a b + 384a b + 48a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 3 +--R (- 64a b + 184a b + 240a b + 48a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 128a b + 192a b + 2a b - 264a b - 24a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R (- 208a b + 488a b - 472a b - 384a b - 24a b)cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R - 56a b + 60a b + 70a b - 294a b - 128a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 9 4 11 2 7 +--R (12a b - 24a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 6 +--R (- 54a b + 126a b - 96a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 5 +--R (- 156a b + 324a b - 24a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (98a b - 276a b + 466a b + 192a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (80a b - 48a b + 100a b + 120a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 136a b + 204a b + 2a b - 526a b - 96a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R (- 152a b + 280a b - 196a b - 436a b - 72a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 +--R - 8a b + 4a b + 34a b - 72a b - 66a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 5 10 3 8 8 5 10 3 7 +--R (6a b - 12a b )cos(d x + c) + (16a b - 40a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 6 +--R (- 58a b + 140a b - 76a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 5 +--R (- 112a b + 248a b + 8a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (76a b - 166a b + 172a b + 188a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (72a b - 52a b - 64a b + 104a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 56a b + 60a b + 62a b - 308a b - 100a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R (- 56a b + 68a b - 4a b - 200a b - 72a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 +--R 4a b - 6a b - 10a b +--R * +--R sin(d x + c) +--R + +--R 7 6 9 4 8 7 6 9 4 7 +--R (2a b - 8a b )cos(d x + c) + (4a b - 16a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 6 +--R (- 18a b + 46a b - 16a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 5 +--R (- 28a b + 68a b + 8a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (16a b - 24a b + 6a b + 56a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (16a b - 4a b - 44a b + 32a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 8a b + 4a b + 18a b - 54a b - 32a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 +--R (- 8a b + 4a b + 8a b - 28a b - 24a b )cos(d x + c) +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 6 7 8 5 8 +--R (- 6a b + 12a b )sin(d x + c) +--R + +--R 7 6 9 4 2 7 6 9 4 +--R (- 3a b + 6a b )cos(d x + c) + (- 12a b + 24a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 +--R - 21a b + 33a b + 6a b +--R * +--R 7 +--R sin(d x + c) +--R + +--R 8 5 10 3 3 +--R (- 6a b + 12a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 2 +--R (- 21a b + 33a b + 36a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 4 9 6 7 8 5 +--R (- 22a b + 34a b + 60a b )cos(d x + c) - 41a b + 78a b - 55a b +--R + +--R 10 3 +--R 36a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 4 +--R (- 5a b + 11a b - 6a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 3 +--R (- 68a b + 146a b - 48a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 23a b - 20a b + 202a b - 36a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 10 5 8 +--R (20a b - 50a b + 162a b + 48a b )cos(d x + c) - 52a b + 154a b +--R + +--R 7 6 9 4 11 2 +--R - 197a b + 95a b + 42a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 8 5 10 3 12 5 +--R (4a b - 10a b + 12a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 4 +--R (- 37a b + 77a b - 4a b + 12a b)cos(d x + c) +--R + +--R 6 7 8 5 10 3 12 3 +--R (- 162a b + 358a b - 136a b - 24a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 19a b - 85a b + 312a b - 148a b - 24a b)cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 12 +--R (78a b - 118a b + 122a b + 146a b + 12a b)cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R - 38a b + 187a b - 258a b + 95a b + 152a b + 12a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 7 6 9 4 11 2 6 +--R (a b - a b - 6a b )cos(d x + c) +--R + +--R 7 6 9 4 11 2 5 +--R (- 20a b + 32a b + 36a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (- 25a b + 32a b + 101a b + 54a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (- 160a b + 380a b - 184a b - 72a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 34a b - 63a b + 275a b - 319a b - 90a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 11 2 12 +--R (72a b - 68a b - 12a b + 152a b + 36a b )cos(d x + c) - 14a b +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R 141a b - 182a b + 40a b + 219a b + 42a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 8 5 10 3 7 +--R (6a b - 12a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 6 +--R (- 21a b + 48a b - 30a b )cos(d x + c) +--R + +--R 6 7 8 5 10 3 5 +--R (- 54a b + 102a b + 60a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (15a b - 47a b + 116a b + 114a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 72a b + 208a b - 166a b - 84a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 34a b - 27a b + 183a b - 320a b - 138a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 10 3 13 +--R (28a b - 8a b - 42a b + 58a b + 36a b )cos(d x + c) - 2b +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R 67a b - 74a b - 3a b + 156a b + 54a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 7 6 9 4 8 7 6 9 4 7 +--R (3a b - 6a b )cos(d x + c) + (8a b - 20a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 6 +--R (- 23a b + 55a b - 20a b )cos(d x + c) +--R + +--R 5 8 7 6 9 4 5 +--R (- 40a b + 84a b + 52a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (18a b - 35a b + 31a b + 88a b )cos(d x + c) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 12a b + 62a b - 96a b - 44a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 14a b - 13a b + 79a b - 143a b - 92a b )cos(d x + c) +--R + +--R 12 3 10 5 8 7 6 9 4 12 +--R (4a b + 2a b - 10a b + 4a b + 12a b )cos(d x + c) + 18a b +--R + +--R 3 10 5 8 7 6 9 4 +--R - 15a b - 9a b + 54a b + 30a b +--R * +--R sin(d x + c) +--R + +--R 6 7 8 5 8 6 7 8 5 7 +--R (a b - 4a b )cos(d x + c) + (2a b - 8a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 6 +--R (- 7a b + 18a b - 2a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 5 +--R (- 10a b + 24a b + 16a b )cos(d x + c) +--R + +--R 2 11 4 9 6 7 8 5 4 +--R (4a b - 4a b - 4a b + 22a b )cos(d x + c) +--R + +--R 4 9 6 7 8 5 3 +--R (10a b - 26a b - 8a b )cos(d x + c) +--R + +--R 13 2 11 4 9 6 7 8 5 2 13 2 11 +--R (- 2b - 3a b + 13a b - 22a b - 22a b )cos(d x + c) + 2b - a b +--R + +--R 4 9 6 7 8 5 +--R - 2a b + 7a b + 6a b +--R / +--R 8 8 10 6 12 4 7 +--R (8a b - 16a b + 8a b )sin(d x + c) +--R + +--R 9 7 11 5 13 3 2 +--R (- 8a b + 16a b - 8a b )cos(d x + c) +--R + +--R 9 7 11 5 13 3 7 9 9 7 +--R (16a b - 32a b + 16a b )cos(d x + c) + 32a b - 40a b +--R + +--R 11 5 13 3 +--R - 16a b + 24a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 10 6 12 4 14 2 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 10 6 12 4 14 2 3 +--R (- 16a b + 32a b - 16a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 2 +--R (- 20a b + 20a b + 20a b - 20a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 6 10 +--R (80a b - 144a b + 48a b + 16a b )cos(d x + c) + 50a b +--R + +--R 10 6 12 4 14 2 +--R - 132a b + 64a b + 18a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 11 5 13 3 15 5 +--R (4a b - 8a b + 4a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 4 +--R (- 2a b + 8a b - 10a b + 4a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 3 +--R (- 72a b + 136a b - 56a b - 8a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 2 +--R (- 4a b - 60a b + 124a b - 52a b - 8a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 +--R (164a b - 256a b + 24a b + 64a b + 4a b)cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 15 +--R 38a b + 92a b - 228a b + 32a b + 62a b + 4a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 10 6 12 4 14 2 6 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 10 6 12 4 14 2 5 +--R (16a b - 32a b + 16a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 4 +--R (- 22a b + 54a b - 42a b + 10a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 3 +--R (- 128a b + 224a b - 64a b - 32a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 2 +--R (30a b - 144a b + 172a b - 32a b - 26a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 +--R (176a b - 224a b - 64a b + 96a b + 16a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 14 2 +--R 14a b + 118a b - 172a b - 52a b + 78a b + 14a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 9 7 11 5 13 3 6 +--R (6a b - 12a b + 6a b )cos(d x + c) +--R + +--R 9 7 11 5 13 3 5 +--R (24a b - 48a b + 24a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 4 +--R (- 34a b + 74a b - 46a b + 6a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 3 +--R (- 112a b + 176a b - 16a b - 48a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 2 +--R (34a b - 112a b + 92a b + 16a b - 30a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 +--R (104a b - 96a b - 96a b + 64a b + 24a b )cos(d x + c) +--R + +--R 3 13 5 11 7 9 9 7 11 5 13 3 +--R 2a b + 66a b - 60a b - 68a b + 42a b + 18a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 8 10 6 12 4 6 +--R (6a b - 12a b + 6a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 5 +--R (16a b - 32a b + 16a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 4 +--R (- 20a b + 38a b - 16a b - 2a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 3 +--R (- 48a b + 64a b + 16a b - 32a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 2 +--R (14a b - 36a b + 16a b + 20a b - 14a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 +--R (32a b - 16a b - 48a b + 16a b + 16a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 +--R 18a b - 8a b - 28a b + 8a b + 10a b +--R * +--R sin(d x + c) +--R + +--R 7 9 9 7 11 5 6 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 5 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 5 11 7 9 11 5 4 +--R (- 4a b + 6a b - 2a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 3 +--R (- 8a b + 8a b + 8a b - 8a b )cos(d x + c) +--R + +--R 3 13 5 11 9 7 11 5 2 +--R (2a b - 4a b + 4a b - 2a b )cos(d x + c) +--R + +--R 3 13 7 9 11 5 3 13 7 9 11 5 +--R (4a b - 8a b + 4a b )cos(d x + c) + 2a b - 4a b + 2a b +--R * +--R d x + c 2 +--R tan(-------) +--R 2 +--R + +--R 9 7 11 5 13 3 7 +--R (16a b - 32a b + 16a b )sin(d x + c) +--R + +--R 10 6 12 4 14 2 2 +--R (- 16a b + 32a b - 16a b )cos(d x + c) +--R + +--R 10 6 12 4 14 2 8 8 10 6 +--R (32a b - 64a b + 32a b )cos(d x + c) + 64a b - 80a b +--R + +--R 12 4 14 2 +--R - 32a b + 48a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 11 5 13 3 15 4 +--R (4a b - 8a b + 4a b)cos(d x + c) +--R + +--R 11 5 13 3 15 3 +--R (- 32a b + 64a b - 32a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 2 +--R (- 40a b + 40a b + 40a b - 40a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 7 9 +--R (160a b - 288a b + 96a b + 32a b)cos(d x + c) + 100a b +--R + +--R 11 5 13 3 15 +--R - 264a b + 128a b + 36a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 12 4 14 2 16 5 +--R (8a b - 16a b + 8a )cos(d x + c) +--R + +--R 10 6 12 4 14 2 16 4 +--R (- 4a b + 16a b - 20a b + 8a )cos(d x + c) +--R + +--R 10 6 12 4 14 2 16 3 +--R (- 144a b + 272a b - 112a b - 16a )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 16 2 +--R (- 8a b - 120a b + 248a b - 104a b - 16a )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 16 +--R (328a b - 512a b + 48a b + 128a b + 8a )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 16 +--R 76a b + 184a b - 456a b + 64a b + 124a b + 8a +--R * +--R 4 +--R sin(d x + c) +--R + +--R 11 5 13 3 15 6 +--R (4a b - 8a b + 4a b)cos(d x + c) +--R + +--R 11 5 13 3 15 5 +--R (32a b - 64a b + 32a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 4 +--R (- 44a b + 108a b - 84a b + 20a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 3 +--R (- 256a b + 448a b - 128a b - 64a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 2 +--R (60a b - 288a b + 344a b - 64a b - 52a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 +--R (352a b - 448a b - 128a b + 192a b + 32a b)cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 15 +--R 28a b + 236a b - 344a b - 104a b + 156a b + 28a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 10 6 12 4 14 2 6 +--R (12a b - 24a b + 12a b )cos(d x + c) +--R + +--R 10 6 12 4 14 2 5 +--R (48a b - 96a b + 48a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 4 +--R (- 68a b + 148a b - 92a b + 12a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 3 +--R (- 224a b + 352a b - 32a b - 96a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 2 +--R (68a b - 224a b + 184a b + 32a b - 60a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 +--R (208a b - 192a b - 192a b + 128a b + 48a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 14 2 +--R 4a b + 132a b - 120a b - 136a b + 84a b + 36a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 9 7 11 5 13 3 6 +--R (12a b - 24a b + 12a b )cos(d x + c) +--R + +--R 9 7 11 5 13 3 5 +--R (32a b - 64a b + 32a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 4 +--R (- 40a b + 76a b - 32a b - 4a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 3 +--R (- 96a b + 128a b + 32a b - 64a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 2 +--R (28a b - 72a b + 32a b + 40a b - 28a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 +--R (64a b - 32a b - 96a b + 32a b + 32a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 +--R 36a b - 16a b - 56a b + 16a b + 20a b +--R * +--R sin(d x + c) +--R + +--R 8 8 10 6 12 4 6 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 5 +--R (8a b - 16a b + 8a b )cos(d x + c) +--R + +--R 6 10 8 8 12 4 4 +--R (- 8a b + 12a b - 4a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 3 +--R (- 16a b + 16a b + 16a b - 16a b )cos(d x + c) +--R + +--R 4 12 6 10 10 6 12 4 2 +--R (4a b - 8a b + 8a b - 4a b )cos(d x + c) +--R + +--R 4 12 8 8 12 4 4 12 8 8 12 4 +--R (8a b - 16a b + 8a b )cos(d x + c) + 4a b - 8a b + 4a b +--R * +--R d x + c +--R tan(-------) +--R 2 +--R + +--R 8 8 10 6 12 4 7 +--R (8a b - 16a b + 8a b )sin(d x + c) +--R + +--R 9 7 11 5 13 3 2 +--R (- 8a b + 16a b - 8a b )cos(d x + c) +--R + +--R 9 7 11 5 13 3 7 9 9 7 11 5 +--R (16a b - 32a b + 16a b )cos(d x + c) + 32a b - 40a b - 16a b +--R + +--R 13 3 +--R 24a b +--R * +--R 6 +--R sin(d x + c) +--R + +--R 10 6 12 4 14 2 4 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 10 6 12 4 14 2 3 +--R (- 16a b + 32a b - 16a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 2 +--R (- 20a b + 20a b + 20a b - 20a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 6 10 +--R (80a b - 144a b + 48a b + 16a b )cos(d x + c) + 50a b +--R + +--R 10 6 12 4 14 2 +--R - 132a b + 64a b + 18a b +--R * +--R 5 +--R sin(d x + c) +--R + +--R 11 5 13 3 15 5 +--R (4a b - 8a b + 4a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 4 +--R (- 2a b + 8a b - 10a b + 4a b)cos(d x + c) +--R + +--R 9 7 11 5 13 3 15 3 +--R (- 72a b + 136a b - 56a b - 8a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 2 +--R (- 4a b - 60a b + 124a b - 52a b - 8a b)cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 15 5 11 +--R (164a b - 256a b + 24a b + 64a b + 4a b)cos(d x + c) + 38a b +--R + +--R 7 9 9 7 11 5 13 3 15 +--R 92a b - 228a b + 32a b + 62a b + 4a b +--R * +--R 4 +--R sin(d x + c) +--R + +--R 10 6 12 4 14 2 6 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 10 6 12 4 14 2 5 +--R (16a b - 32a b + 16a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 4 +--R (- 22a b + 54a b - 42a b + 10a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 14 2 3 +--R (- 128a b + 224a b - 64a b - 32a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 2 +--R (30a b - 144a b + 172a b - 32a b - 26a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 14 2 +--R (176a b - 224a b - 64a b + 96a b + 16a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 14 2 +--R 14a b + 118a b - 172a b - 52a b + 78a b + 14a b +--R * +--R 3 +--R sin(d x + c) +--R + +--R 9 7 11 5 13 3 6 +--R (6a b - 12a b + 6a b )cos(d x + c) +--R + +--R 9 7 11 5 13 3 5 +--R (24a b - 48a b + 24a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 4 +--R (- 34a b + 74a b - 46a b + 6a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 13 3 3 +--R (- 112a b + 176a b - 16a b - 48a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 2 +--R (34a b - 112a b + 92a b + 16a b - 30a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 13 3 3 13 +--R (104a b - 96a b - 96a b + 64a b + 24a b )cos(d x + c) + 2a b +--R + +--R 5 11 7 9 9 7 11 5 13 3 +--R 66a b - 60a b - 68a b + 42a b + 18a b +--R * +--R 2 +--R sin(d x + c) +--R + +--R 8 8 10 6 12 4 6 +--R (6a b - 12a b + 6a b )cos(d x + c) +--R + +--R 8 8 10 6 12 4 5 +--R (16a b - 32a b + 16a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 4 +--R (- 20a b + 38a b - 16a b - 2a b )cos(d x + c) +--R + +--R 6 10 8 8 10 6 12 4 3 +--R (- 48a b + 64a b + 16a b - 32a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 2 +--R (14a b - 36a b + 16a b + 20a b - 14a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 +--R (32a b - 16a b - 48a b + 16a b + 16a b )cos(d x + c) +--R + +--R 4 12 6 10 8 8 10 6 12 4 +--R 18a b - 8a b - 28a b + 8a b + 10a b +--R * +--R sin(d x + c) +--R + +--R 7 9 9 7 11 5 6 +--R (2a b - 4a b + 2a b )cos(d x + c) +--R + +--R 7 9 9 7 11 5 5 +--R (4a b - 8a b + 4a b )cos(d x + c) +--R + +--R 5 11 7 9 11 5 4 +--R (- 4a b + 6a b - 2a b )cos(d x + c) +--R + +--R 5 11 7 9 9 7 11 5 3 +--R (- 8a b + 8a b + 8a b - 8a b )cos(d x + c) +--R + +--R 3 13 5 11 9 7 11 5 2 +--R (2a b - 4a b + 4a b - 2a b )cos(d x + c) +--R + +--R 3 13 7 9 11 5 3 13 7 9 11 5 +--R (4a b - 8a b + 4a b )cos(d x + c) + 2a b - 4a b + 2a b +--R Type: Expression(Integer) +--E 439 + +--S 440 of 528 +t0383:= (1+csc(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (402) \|csc(x) + 1 +--R Type: Expression(Integer) +--E 440 + +--S 441 of 528 +r0383:= -asinh(1/2*2^(1/2)*cot(x))-atan(cot(x)/(2+cot(x)^2)^(1/2)) +--R +--R +--R +-+ +--R cot(x) \|2 cot(x) +--R (403) - atan(--------------) - asinh(----------) +--R +-----------+ 2 +--R | 2 +--R \|cot(x) + 2 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 528 +a0383:= integrate(t0383,x) +--R +--R +--R (404) +--R - +--R log +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R ((cos(x) + 1)sin(x) + cos(x) + cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) - 2cos(x) + 4 +--R + +--R log +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) - 2cos(x) + 4 +--R + +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R - atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 442 + +--S 443 of 528 +m0383:= a0383-r0383 +--R +--R +--R (405) +--R - +--R log +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R ((cos(x) + 1)sin(x) + cos(x) + cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) - 2cos(x) + 4 +--R + +--R log +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) - 2cos(x) + 4 +--R + +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R - atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R + +--R +-+ +--R cot(x) \|2 cot(x) +--R 2atan(--------------) + 2asinh(----------) +--R +-----------+ 2 +--R | 2 +--R \|cot(x) + 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 528 +d0383:= D(m0383,x) +--R +--R +--R (406) +--R 7 6 5 4 3 +--R - 16cos(x) - 16cos(x) + 48cos(x) + 48cos(x) - 36cos(x) +--R + +--R 2 +--R - 36cos(x) + 8cos(x) + 8 +--R * +--R 11 +--R sin(x) +--R + +--R 9 8 7 6 +--R 448cos(x) + 448cos(x) - 2144cos(x) - 2144cos(x) +--R + +--R 5 4 3 2 +--R 3356cos(x) + 3356cos(x) - 1892cos(x) - 1892cos(x) +--R + +--R 348cos(x) + 348 +--R * +--R 9 +--R sin(x) +--R + +--R 11 10 9 8 +--R - 1120cos(x) - 1120cos(x) + 7616cos(x) + 7616cos(x) +--R + +--R 7 6 5 4 +--R - 19008cos(x) - 19008cos(x) + 20892cos(x) + 20892cos(x) +--R + +--R 3 2 +--R - 9501cos(x) - 9501cos(x) + 1486cos(x) + 1486 +--R * +--R 7 +--R sin(x) +--R + +--R 13 12 11 10 +--R 448cos(x) + 448cos(x) - 4256cos(x) - 4256cos(x) +--R + +--R 9 8 7 6 +--R 15648cos(x) + 15648cos(x) - 27900cos(x) - 27900cos(x) +--R + +--R 5 4 3 2 +--R 24494cos(x) + 24494cos(x) - 9456cos(x) - 9456cos(x) +--R + +--R 1289cos(x) + 1289 +--R * +--R 5 +--R sin(x) +--R + +--R 15 14 13 12 +--R - 16cos(x) - 16cos(x) + 272cos(x) + 272cos(x) +--R + +--R 11 10 9 8 +--R - 1628cos(x) - 1628cos(x) + 4700cos(x) + 4700cos(x) +--R + +--R 7 6 5 4 +--R - 7101cos(x) - 7101cos(x) + 5466cos(x) + 5466cos(x) +--R + +--R 3 2 +--R - 1874cos(x) - 1874cos(x) + 228cos(x) + 228 +--R * +--R 3 +--R sin(x) +--R + +--R 13 12 11 10 9 +--R 4cos(x) + 4cos(x) - 32cos(x) - 32cos(x) + 100cos(x) +--R + +--R 8 7 6 5 +--R 100cos(x) - 152cos(x) - 152cos(x) + 113cos(x) +--R + +--R 4 3 2 +--R 113cos(x) - 36cos(x) - 36cos(x) + 4cos(x) + 4 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 8 6 4 2 10 +--R (256cos(x) - 1248cos(x) + 2000cos(x) - 1168cos(x) + 224)sin(x) +--R + +--R 10 8 6 4 +--R - 1792cos(x) + 12096cos(x) - 30144cos(x) + 33400cos(x) +--R + +--R 2 +--R - 15584cos(x) + 2528 +--R * +--R 8 +--R sin(x) +--R + +--R 12 10 8 6 +--R 1792cos(x) - 16128cos(x) + 56960cos(x) - 98888cos(x) +--R + +--R 4 2 +--R 85936cos(x) - 33660cos(x) + 4728 +--R * +--R 6 +--R sin(x) +--R + +--R 14 12 10 8 +--R - 256cos(x) + 3264cos(x) - 16512cos(x) + 42760cos(x) +--R + +--R 6 4 2 +--R - 60216cos(x) + 44632cos(x) - 15304cos(x) + 1904 +--R * +--R 4 +--R sin(x) +--R + +--R 14 12 10 8 +--R - 32cos(x) + 368cos(x) - 1704cos(x) + 4072cos(x) +--R + +--R 6 4 2 +--R - 5308cos(x) + 3632cos(x) - 1136cos(x) + 128 +--R * +--R 2 +--R sin(x) +--R * +--R +-----------+ +--R | 2 +--R \|cot(x) + 2 +--R + +--R 9 8 7 6 +--R - 128cos(x) - 128cos(x) + 496cos(x) + 496cos(x) +--R + +--R 5 4 3 2 +--R - 632cos(x) - 632cos(x) + 320cos(x) + 320cos(x) +--R + +--R - 56cos(x) - 56 +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 7 6 5 +--R - 256cos(x) - 256cos(x) + 992cos(x) + 992cos(x) - 1264cos(x) +--R + +--R 4 3 2 +--R - 1264cos(x) + 640cos(x) + 640cos(x) - 112cos(x) - 112 +--R * +--R 9 +--R sin(x) +--R + +--R 11 10 9 8 +--R 896cos(x) + 896cos(x) - 5152cos(x) - 5152cos(x) +--R + +--R 7 6 5 4 +--R 10816cos(x) + 10816cos(x) - 10140cos(x) - 10140cos(x) +--R + +--R 3 2 +--R 4212cos(x) + 4212cos(x) - 632cos(x) - 632 +--R * +--R 2 +--R cot(x) +--R + +--R 11 10 9 8 +--R 1792cos(x) + 1792cos(x) - 10304cos(x) - 10304cos(x) +--R + +--R 7 6 5 4 +--R 21632cos(x) + 21632cos(x) - 20280cos(x) - 20280cos(x) +--R + +--R 3 2 +--R 8424cos(x) + 8424cos(x) - 1264cos(x) - 1264 +--R * +--R 7 +--R sin(x) +--R + +--R 13 12 11 10 +--R - 896cos(x) - 896cos(x) + 7168cos(x) + 7168cos(x) +--R + +--R 9 8 7 6 +--R - 22208cos(x) - 22208cos(x) + 33508cos(x) + 33508cos(x) +--R + +--R 5 4 3 2 +--R - 25396cos(x) - 25396cos(x) + 9006cos(x) + 9006cos(x) +--R + +--R - 1182cos(x) - 1182 +--R * +--R 2 +--R cot(x) +--R + +--R 13 12 11 10 +--R - 1792cos(x) - 1792cos(x) + 14336cos(x) + 14336cos(x) +--R + +--R 9 8 7 6 +--R - 44416cos(x) - 44416cos(x) + 67016cos(x) + 67016cos(x) +--R + +--R 5 4 3 2 +--R - 50792cos(x) - 50792cos(x) + 18012cos(x) + 18012cos(x) +--R + +--R - 2364cos(x) - 2364 +--R * +--R 5 +--R sin(x) +--R + +--R 15 14 13 12 +--R 128cos(x) + 128cos(x) - 1504cos(x) - 1504cos(x) +--R + +--R 11 10 9 8 +--R 6880cos(x) + 6880cos(x) - 15876cos(x) - 15876cos(x) +--R + +--R 7 6 5 4 +--R 19736cos(x) + 19736cos(x) - 12952cos(x) - 12952cos(x) +--R + +--R 3 2 +--R 4064cos(x) + 4064cos(x) - 476cos(x) - 476 +--R * +--R 2 +--R cot(x) +--R + +--R 15 14 13 12 +--R 256cos(x) + 256cos(x) - 3008cos(x) - 3008cos(x) +--R + +--R 11 10 9 8 +--R 13760cos(x) + 13760cos(x) - 31752cos(x) - 31752cos(x) +--R + +--R 7 6 5 4 +--R 39472cos(x) + 39472cos(x) - 25904cos(x) - 25904cos(x) +--R + +--R 3 2 +--R 8128cos(x) + 8128cos(x) - 952cos(x) - 952 +--R * +--R 3 +--R sin(x) +--R + +--R 15 14 13 12 +--R 16cos(x) + 16cos(x) - 168cos(x) - 168cos(x) +--R + +--R 11 10 9 8 +--R 700cos(x) + 700cos(x) - 1488cos(x) - 1488cos(x) +--R + +--R 7 6 5 4 +--R 1714cos(x) + 1714cos(x) - 1042cos(x) - 1042cos(x) +--R + +--R 3 2 +--R 300cos(x) + 300cos(x) - 32cos(x) - 32 +--R * +--R 2 +--R cot(x) +--R + +--R 15 14 13 12 +--R 32cos(x) + 32cos(x) - 336cos(x) - 336cos(x) +--R + +--R 11 10 9 8 +--R 1400cos(x) + 1400cos(x) - 2976cos(x) - 2976cos(x) +--R + +--R 7 6 5 4 +--R 3428cos(x) + 3428cos(x) - 2084cos(x) - 2084cos(x) +--R + +--R 3 2 +--R 600cos(x) + 600cos(x) - 64cos(x) - 64 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 8 6 4 2 2 +--R (- 32cos(x) + 128cos(x) - 168cos(x) + 88cos(x) - 16)cot(x) +--R + +--R 8 6 4 2 +--R - 64cos(x) + 256cos(x) - 336cos(x) + 176cos(x) - 32 +--R * +--R 10 +--R sin(x) +--R + +--R 10 8 6 4 +--R 896cos(x) - 5184cos(x) + 11000cos(x) - 10496cos(x) +--R + +--R 2 +--R 4480cos(x) - 696 +--R * +--R 2 +--R cot(x) +--R + +--R 10 8 6 4 +--R 1792cos(x) - 10368cos(x) + 22000cos(x) - 20992cos(x) +--R + +--R 2 +--R 8960cos(x) - 1392 +--R * +--R 8 +--R sin(x) +--R + +--R 12 10 8 6 +--R - 2240cos(x) + 17472cos(x) - 53248cos(x) + 79800cos(x) +--R + +--R 4 2 +--R - 60786cos(x) + 21974cos(x) - 2972 +--R * +--R 2 +--R cot(x) +--R + +--R 12 10 8 6 +--R - 4480cos(x) + 34944cos(x) - 106496cos(x) + 159600cos(x) +--R + +--R 4 2 +--R - 121572cos(x) + 43948cos(x) - 5944 +--R * +--R 6 +--R sin(x) +--R + +--R 14 12 10 8 +--R 896cos(x) - 9408cos(x) + 39808cos(x) - 87096cos(x) +--R + +--R 6 4 2 +--R 104788cos(x) - 67900cos(x) + 21490cos(x) - 2578 +--R * +--R 2 +--R cot(x) +--R + +--R 14 12 10 8 +--R 1792cos(x) - 18816cos(x) + 79616cos(x) - 174192cos(x) +--R + +--R 6 4 2 +--R 209576cos(x) - 135800cos(x) + 42980cos(x) - 5156 +--R * +--R 4 +--R sin(x) +--R + +--R 16 14 12 10 +--R - 32cos(x) + 576cos(x) - 3800cos(x) + 12656cos(x) +--R + +--R 8 6 4 2 +--R - 23602cos(x) + 25134cos(x) - 14680cos(x) + 4204cos(x) - 456 +--R * +--R 2 +--R cot(x) +--R + +--R 16 14 12 10 +--R - 64cos(x) + 1152cos(x) - 7600cos(x) + 25312cos(x) +--R + +--R 8 6 4 2 +--R - 47204cos(x) + 50268cos(x) - 29360cos(x) + 8408cos(x) - 912 +--R * +--R 2 +--R sin(x) +--R + +--R 14 12 10 8 6 +--R 8cos(x) - 72cos(x) + 264cos(x) - 504cos(x) + 530cos(x) +--R + +--R 4 2 +--R - 298cos(x) + 80cos(x) - 8 +--R * +--R 2 +--R cot(x) +--R + +--R 14 12 10 8 6 +--R 16cos(x) - 144cos(x) + 528cos(x) - 1008cos(x) + 1060cos(x) +--R + +--R 4 2 +--R - 596cos(x) + 160cos(x) - 16 +--R / +--R 9 8 7 6 5 +--R 128cos(x) + 128cos(x) - 496cos(x) - 496cos(x) + 632cos(x) +--R + +--R 4 3 2 +--R 632cos(x) - 320cos(x) - 320cos(x) + 56cos(x) + 56 +--R * +--R 9 +--R sin(x) +--R + +--R 11 10 9 8 +--R - 896cos(x) - 896cos(x) + 5152cos(x) + 5152cos(x) +--R + +--R 7 6 5 4 +--R - 10816cos(x) - 10816cos(x) + 10140cos(x) + 10140cos(x) +--R + +--R 3 2 +--R - 4212cos(x) - 4212cos(x) + 632cos(x) + 632 +--R * +--R 7 +--R sin(x) +--R + +--R 13 12 11 10 +--R 896cos(x) + 896cos(x) - 7168cos(x) - 7168cos(x) +--R + +--R 9 8 7 6 +--R 22208cos(x) + 22208cos(x) - 33508cos(x) - 33508cos(x) +--R + +--R 5 4 3 2 +--R 25396cos(x) + 25396cos(x) - 9006cos(x) - 9006cos(x) +--R + +--R 1182cos(x) + 1182 +--R * +--R 5 +--R sin(x) +--R + +--R 15 14 13 12 +--R - 128cos(x) - 128cos(x) + 1504cos(x) + 1504cos(x) +--R + +--R 11 10 9 8 +--R - 6880cos(x) - 6880cos(x) + 15876cos(x) + 15876cos(x) +--R + +--R 7 6 5 4 +--R - 19736cos(x) - 19736cos(x) + 12952cos(x) + 12952cos(x) +--R + +--R 3 2 +--R - 4064cos(x) - 4064cos(x) + 476cos(x) + 476 +--R * +--R 3 +--R sin(x) +--R + +--R 15 14 13 12 +--R - 16cos(x) - 16cos(x) + 168cos(x) + 168cos(x) +--R + +--R 11 10 9 8 +--R - 700cos(x) - 700cos(x) + 1488cos(x) + 1488cos(x) +--R + +--R 7 6 5 4 +--R - 1714cos(x) - 1714cos(x) + 1042cos(x) + 1042cos(x) +--R + +--R 3 2 +--R - 300cos(x) - 300cos(x) + 32cos(x) + 32 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 8 6 4 2 10 +--R (32cos(x) - 128cos(x) + 168cos(x) - 88cos(x) + 16)sin(x) +--R + +--R 10 8 6 4 +--R - 896cos(x) + 5184cos(x) - 11000cos(x) + 10496cos(x) +--R + +--R 2 +--R - 4480cos(x) + 696 +--R * +--R 8 +--R sin(x) +--R + +--R 12 10 8 6 +--R 2240cos(x) - 17472cos(x) + 53248cos(x) - 79800cos(x) +--R + +--R 4 2 +--R 60786cos(x) - 21974cos(x) + 2972 +--R * +--R 6 +--R sin(x) +--R + +--R 14 12 10 8 +--R - 896cos(x) + 9408cos(x) - 39808cos(x) + 87096cos(x) +--R + +--R 6 4 2 +--R - 104788cos(x) + 67900cos(x) - 21490cos(x) + 2578 +--R * +--R 4 +--R sin(x) +--R + +--R 16 14 12 10 +--R 32cos(x) - 576cos(x) + 3800cos(x) - 12656cos(x) +--R + +--R 8 6 4 2 +--R 23602cos(x) - 25134cos(x) + 14680cos(x) - 4204cos(x) + 456 +--R * +--R 2 +--R sin(x) +--R + +--R 14 12 10 8 6 +--R - 8cos(x) + 72cos(x) - 264cos(x) + 504cos(x) - 530cos(x) +--R + +--R 4 2 +--R 298cos(x) - 80cos(x) + 8 +--R * +--R +-----------+ +--R | 2 +--R \|cot(x) + 2 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 528 +t0384:= (1-csc(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (407) \|- csc(x) + 1 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 528 +r0384:= (-cot(x)^2)^(1/2)*log(sin(x))*tan(x) +--R +--R +--R +---------+ +--R | 2 +--R (408) tan(x)log(sin(x))\|- cot(x) +--R Type: Expression(Integer) +--E 446 + +--S 447 of 528 +a0384:= integrate(t0384,x) +--R +--R +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R (409) - atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R Type: Union(Expression(Integer),...) +--E 447 + +--S 448 of 528 +m0384:= a0384-r0384 +--R +--R +--R (410) +--R +---------+ +--R | 2 +--R - tan(x)log(sin(x))\|- cot(x) +--R + +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R - atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 528 +d0384:= D(m0384,x) +--R +--R +--R (411) +--R x 6 x 2 x 4 x 4 x 2 x 6 +--R sin(-) + (3cos(-) - 2)sin(-) + (3cos(-) + 1)sin(-) + cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 2 +--R 2cos(-) - 3cos(-) +--R 2 2 +--R * +--R +---------+ +--R | 2 +--R sin(x)\|- cot(x) +--R + +--R 2 x 6 x 2 2 x 4 +--R cot(x) sin(-) + (3cos(-) - 2)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 x 2 +--R (3cos(-) - 12cos(-) + 1)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cot(x) +--R 2 2 2 +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 3 x 6 +--R (- cot(x) - cot(x))sin(-) +--R 2 +--R + +--R x 2 3 x 2 x 4 +--R ((- 3cos(-) + 2)cot(x) + (- 3cos(-) + 2)cot(x))sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 3 +--R (- 3cos(-) + 12cos(-) - 1)cot(x) +--R 2 2 +--R + +--R x 4 x 2 +--R (- 3cos(-) + 12cos(-) - 1)cot(x) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 x 2 3 +--R (- cos(-) - 6cos(-) - 9cos(-) )cot(x) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (- cos(-) - 6cos(-) - 9cos(-) )cot(x) +--R 2 2 2 +--R * +--R sin(x)tan(x) +--R + +--R 2 x 6 x 2 2 x 4 +--R cot(x) sin(-) + (3cos(-) - 2)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 x 2 +--R (3cos(-) - 12cos(-) + 1)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cot(x) +--R 2 2 2 +--R * +--R sin(x) +--R * +--R log(sin(x)) +--R + +--R 2 x 6 x 2 2 x 4 +--R cos(x)cot(x) sin(-) + (3cos(-) - 2)cos(x)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 x 2 +--R (3cos(-) - 12cos(-) + 1)cos(x)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cos(x)cot(x) +--R 2 2 2 +--R * +--R tan(x) +--R / +--R x 6 x 2 x 4 x 4 x 2 x 2 +--R sin(-) + (3cos(-) - 2)sin(-) + (3cos(-) - 12cos(-) + 1)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R cos(-) + 6cos(-) + 9cos(-) +--R 2 2 2 +--R * +--R +---------+ +--R | 2 +--R sin(x)\|- cot(x) +--R Type: Expression(Integer) +--E 449 + +--S 450 of 528 +t0385:= (-1+csc(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (412) \|csc(x) - 1 +--R Type: Expression(Integer) +--E 450 + +--S 451 of 528 +r0385:= (cot(x)^2)^(1/2)*log(sin(x))*tan(x) +--R +--R +--R +-------+ +--R | 2 +--R (413) tan(x)log(sin(x))\|cot(x) +--R Type: Expression(Integer) +--E 451 + +--S 452 of 528 +a0385:= integrate(t0385,x) +--R +--R +--R sin(x) 2 +--R (414) - log(----------) + log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 452 + +--S 453 of 528 +m0385:= a0385-r0385 +--R +--R +--R +-------+ +--R | 2 sin(x) 2 +--R (415) - tan(x)log(sin(x))\|cot(x) - log(----------) + log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 528 +d0385:= D(m0385,x) +--R +--R +--R (416) +--R +-------+ +--R | 2 +--R - cos(x)\|cot(x) +--R + +--R 2 2 3 +--R - cot(x) sin(x)tan(x) + (cot(x) + cot(x))sin(x)tan(x) +--R + +--R 2 +--R - cot(x) sin(x) +--R * +--R log(sin(x)) +--R + +--R 2 +--R - cos(x)cot(x) tan(x) +--R / +--R +-------+ +--R | 2 +--R sin(x)\|cot(x) +--R Type: Expression(Integer) +--E 454 + +--S 455 of 528 +t0386:= (-1-csc(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (417) \|- csc(x) - 1 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 528 +r0386:= -atan((-2-cot(x)^2)^(1/2)*tan(x))+atanh(cot(x)/(-2-cot(x)^2)^(1/2)) +--R +--R +--R +-------------+ +--R cot(x) | 2 +--R (418) atanh(----------------) - atan(tan(x)\|- cot(x) - 2 ) +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 528 +a0386:= integrate(t0386,x) +--R +--R +--R (419) +--R - +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) + 2\|- 1 + 1) +--R + +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) + 1) +--R + +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) - 2\|- 1 + 1) +--R + +--R - +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) + 2)\|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) - 8(%e ) - 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 457 + +--S 458 of 528 +m0386:= a0386-r0386 +--R +--R +--R (420) +--R - +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) + 2\|- 1 + 1) +--R + +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) + 1) +--R + +--R +---+ +--R 2\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) - 2\|- 1 + 1) +--R + +--R - +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) + 2)\|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) - 8(%e ) - 2 +--R + +--R +-------------+ +--R cot(x) | 2 +--R - 2atanh(----------------) + 2atan(tan(x)\|- cot(x) - 2 ) +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 528 +d0386:= D(m0386,x) +--R +--R +--R (421) +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (- \|- 1 cot(x) - 2\|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (9\|- 1 cot(x) + 18\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +--R (- 21\|- 1 cot(x) - 42\|- 1 )(%e ) + 9\|- 1 cot(x) +--R + +--R +---+ +--R 18\|- 1 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R \|- 1 (%e ) - 9\|- 1 (%e ) + 21\|- 1 (%e ) +--R + +--R +---+ +--R - 9\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (2cot(x) + 4)(%e ) + (- 14cot(x) - 28)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (26cot(x) + 52)(%e ) - 14cot(x) - 28 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 6 +--R 3 x\|- 1 +--R (- cot(x) - cot(x))(%e ) +--R + +--R +---+ 4 +--R 3 x\|- 1 +--R (7cot(x) + 7cot(x))(%e ) +--R + +--R +---+ 2 +--R 3 x\|- 1 3 +--R (- 13cot(x) - 13cot(x))(%e ) + 7cot(x) + 7cot(x) +--R * +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (cot(x) + 1)(%e ) + (- 7cot(x) - 7)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (13cot(x) + 13)(%e ) - 7cot(x) - 7 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +--R +---+ 2 +---+ x\|- 1 +--R (\|- 1 cot(x) + 2\|- 1 )(%e ) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (- 12\|- 1 cot(x) - 24\|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (44\|- 1 cot(x) + 88\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +--R (- 48\|- 1 cot(x) - 96\|- 1 )(%e ) + 7\|- 1 cot(x) +--R + +--R +---+ +--R 14\|- 1 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R - \|- 1 (%e ) + 12\|- 1 (%e ) - 44\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R 48\|- 1 (%e ) - 7\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (- 2cot(x) - 4)(%e ) + (20cot(x) + 40)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 +--R (- 60cot(x) - 120)(%e ) + (60cot(x) + 120)(%e ) +--R + +--R 2 +--R - 18cot(x) - 36 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +--R 3 x\|- 1 3 x\|- 1 +--R (cot(x) + cot(x))(%e ) + (- 10cot(x) - 10cot(x))(%e ) +--R + +--R +---+ 4 +--R 3 x\|- 1 +--R (30cot(x) + 30cot(x))(%e ) +--R + +--R +---+ 2 +--R 3 x\|- 1 3 +--R (- 30cot(x) - 30cot(x))(%e ) + 9cot(x) + 9cot(x) +--R * +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (- cot(x) - 1)(%e ) + (10cot(x) + 10)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 2 +--R (- 30cot(x) - 30)(%e ) + (30cot(x) + 30)(%e ) - 9cot(x) +--R + +--R - 9 +--R / +--R +---+ 6 +---+ 4 +--R 2 x\|- 1 2 x\|- 1 +--R (cot(x) + 2)(%e ) + (- 7cot(x) - 14)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (13cot(x) + 26)(%e ) - 7cot(x) - 14 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) + 7(%e ) - 13(%e ) + 7 +--R * +--R +--------------------------------+ +--R +-------------+ | +---+ 4 +---+ 2 +--R | 2 | x\|- 1 x\|- 1 +--R \|- cot(x) - 2 \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +--R 2 x\|- 1 2 x\|- 1 +--R (- cot(x) - 2)(%e ) + (10cot(x) + 20)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 2 x\|- 1 2 x\|- 1 +--R (- 30cot(x) - 60)(%e ) + (30cot(x) + 60)(%e ) +--R + +--R 2 +--R - 9cot(x) - 18 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (%e ) - 10(%e ) + 30(%e ) - 30(%e ) + 9 +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 528 +t0387:= (a+b*csc(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R (422) \|b csc(x) + a +--R Type: Expression(Integer) +--E 460 + +--S 461 of 528 +r0387:= -a^(1/2)*atan(a^(1/2)*cot(x)/(a+b*csc(x)^2)^(1/2))-_ + b^(1/2)*atanh((a+b*csc(x)^2)^(1/2)*tan(x)/b^(1/2)) +--R +--R +--R +-------------+ +--R | 2 +-+ +--R +-+ tan(x)\|b csc(x) + a +-+ cot(x)\|a +--R (423) - \|b atanh(----------------------) - \|a atan(----------------) +--R +-+ +-------------+ +--R \|b | 2 +--R \|b csc(x) + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 528 +a0387:= integrate(t0387,x) +--R +--R +--R (424) +--R [ +--R +-+ +-+ +--R \|a \|b +--R * +--R log +--R 4 10 4 9 +--R 128a cos(x) + 128a cos(x) +--R + +--R 3 4 8 3 4 7 +--R (- 256a b - 512a )cos(x) + (- 256a b - 512a )cos(x) +--R + +--R 2 2 3 4 6 +--R (160a b + 768a b + 768a )cos(x) +--R + +--R 2 2 3 4 5 +--R (160a b + 768a b + 768a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 32a b - 320a b - 768a b - 512a )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (- 32a b - 320a b - 768a b - 512a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (b + 32a b + 160a b + 256a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (b + 32a b + 160a b + 256a b + 128a )cos(x) +--R * +--R +-+ +--R \|b +--R + +--R 3 4 9 3 4 8 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 4 7 +--R (96a b + 32a b - 256a )cos(x) +--R + +--R 2 2 3 4 6 +--R (96a b + 32a b - 256a )cos(x) +--R + +--R 3 2 2 3 4 5 +--R (- 40a b - 56a b + 288a b + 384a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 40a b - 56a b + 288a b + 384a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (4b - 4a b - 176a b - 416a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (4b - 4a b - 176a b - 416a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (4b + 44a b + 136a b + 160a b + 64a )cos(x) + 4b +--R + +--R 3 2 2 3 4 +--R 44a b + 136a b + 160a b + 64a +--R * +--R +-+ +--R sin(x)\|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 4 7 +--R - 256a cos(x) + (640a b + 1024a )cos(x) +--R + +--R 2 2 3 4 5 +--R (- 544a b - 1920a b - 1536a )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (176a b + 1088a b + 1920a b + 1024a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 16b - 176a b - 544a b - 640a b - 256a )cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 5 8 +--R (- 128a b + 128a )cos(x) + (256a b + 128a b - 640a )cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 160a b - 352a b + 768a b + 1280a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (32a b + 128a b - 480a b - 1792a b - 1280a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- b + a b + 224a b + 992a b + 1408a b + 640a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R - b - 33a b - 192a b - 416a b - 384a b - 128a +--R / +--R 3 9 3 8 2 3 7 +--R 64a cos(x) + 64a cos(x) + (- 96a b - 256a )cos(x) +--R + +--R 2 3 6 +--R (- 96a b - 256a )cos(x) +--R + +--R 2 2 3 5 +--R (40a b + 288a b + 384a )cos(x) +--R + +--R 2 2 3 4 +--R (40a b + 288a b + 384a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 4b - 80a b - 288a b - 256a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 4b - 80a b - 288a b - 256a )cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (4b + 40a b + 96a b + 64a )cos(x) + 4b + 40a b + 96a b +--R + +--R 3 +--R 64a +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 4 8 +--R 128a cos(x) + (- 256a b - 640a )cos(x) +--R + +--R 2 2 3 4 6 +--R (160a b + 1024a b + 1280a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 32a b - 480a b - 1536a b - 1280a )cos(x) +--R + +--R 4 3 2 2 3 4 2 4 3 +--R (b + 64a b + 480a b + 1024a b + 640a )cos(x) - b - 32a b +--R + +--R 2 2 3 4 +--R - 160a b - 256a b - 128a +--R + +--R a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a 2 +-+ +--R (cos(x) + 1)sin(x) |---------------------- + (2cos(x) - 2)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------------) +--R +----------------------+ +--R | 2 +--R 2 |- 4a cos(x) + 4b + 4a +-+ +--R (cos(x) + cos(x)) |---------------------- - 2cos(x)sin(x)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R a +--R * +--R atan +--R 4 3 2 +--R 4a cos(x) + 4a cos(x) + (- b - 3a)cos(x) +--R + +--R (- b - 3a)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (6a b + 6a )cos(x))sin(x) +--R / +--R 3 2 +--R (4a cos(x) + 4a cos(x) + (- b - a)cos(x) - b - a)sin(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 2 +--R 8a cos(x) + (- 6a b - 10a )cos(x) + 2a b + 2a +--R / +--R +-+ +--R 2\|a +--R , +--R +--R a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a 2 +-+ +--R (cos(x) + 1)sin(x) |---------------------- + (2cos(x) - 2)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------------) +--R +----------------------+ +--R | 2 +--R 2 |- 4a cos(x) + 4b + 4a +-+ +--R (cos(x) + cos(x)) |---------------------- - 2cos(x)sin(x)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R a +--R * +--R atan +--R 4 3 2 +--R 4a cos(x) + 4a cos(x) + (- b - 3a)cos(x) +--R + +--R (- b - 3a)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (6a b + 6a )cos(x))sin(x) +--R / +--R 3 2 +--R (4a cos(x) + 4a cos(x) + (- b - a)cos(x) - b - a)sin(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 2 +--R 8a cos(x) + (- 6a b - 10a )cos(x) + 2a b + 2a +--R + +--R - +--R +---+ +-+ +--R 2\|- b \|a +--R * +--R atan +--R +----------------------+ +--R | 2 +--R 2 +---+ |- 4a cos(x) + 4b + 4a +--R (cos(x) + cos(x))\|- b |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R (cos(x) + 1)sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2a cos(x) - 2b - 2a +--R / +--R +-+ +--R 2\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 462 + +--S 463 of 528 +m0387a:= a0387.1-r0387 +--R +--R +--R (425) +--R +-+ +-+ +--R \|a \|b +--R * +--R log +--R 4 10 4 9 3 4 8 +--R 128a cos(x) + 128a cos(x) + (- 256a b - 512a )cos(x) +--R + +--R 3 4 7 +--R (- 256a b - 512a )cos(x) +--R + +--R 2 2 3 4 6 +--R (160a b + 768a b + 768a )cos(x) +--R + +--R 2 2 3 4 5 +--R (160a b + 768a b + 768a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 32a b - 320a b - 768a b - 512a )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (- 32a b - 320a b - 768a b - 512a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (b + 32a b + 160a b + 256a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (b + 32a b + 160a b + 256a b + 128a )cos(x) +--R * +--R +-+ +--R \|b +--R + +--R 3 4 9 3 4 8 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 4 7 +--R (96a b + 32a b - 256a )cos(x) +--R + +--R 2 2 3 4 6 +--R (96a b + 32a b - 256a )cos(x) +--R + +--R 3 2 2 3 4 5 +--R (- 40a b - 56a b + 288a b + 384a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 40a b - 56a b + 288a b + 384a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (4b - 4a b - 176a b - 416a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (4b - 4a b - 176a b - 416a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (4b + 44a b + 136a b + 160a b + 64a )cos(x) + 4b +--R + +--R 3 2 2 3 4 +--R 44a b + 136a b + 160a b + 64a +--R * +--R +-+ +--R sin(x)\|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 4 7 +--R - 256a cos(x) + (640a b + 1024a )cos(x) +--R + +--R 2 2 3 4 5 +--R (- 544a b - 1920a b - 1536a )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (176a b + 1088a b + 1920a b + 1024a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 16b - 176a b - 544a b - 640a b - 256a )cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 5 8 +--R (- 128a b + 128a )cos(x) + (256a b + 128a b - 640a )cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 160a b - 352a b + 768a b + 1280a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (32a b + 128a b - 480a b - 1792a b - 1280a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (- b + a b + 224a b + 992a b + 1408a b + 640a )cos(x) - b +--R + +--R 4 2 3 3 2 4 5 +--R - 33a b - 192a b - 416a b - 384a b - 128a +--R / +--R 3 9 3 8 2 3 7 +--R 64a cos(x) + 64a cos(x) + (- 96a b - 256a )cos(x) +--R + +--R 2 3 6 2 2 3 5 +--R (- 96a b - 256a )cos(x) + (40a b + 288a b + 384a )cos(x) +--R + +--R 2 2 3 4 +--R (40a b + 288a b + 384a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 4b - 80a b - 288a b - 256a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 4b - 80a b - 288a b - 256a )cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (4b + 40a b + 96a b + 64a )cos(x) + 4b + 40a b + 96a b +--R + +--R 3 +--R 64a +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 4 8 +--R 128a cos(x) + (- 256a b - 640a )cos(x) +--R + +--R 2 2 3 4 6 +--R (160a b + 1024a b + 1280a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 32a b - 480a b - 1536a b - 1280a )cos(x) +--R + +--R 4 3 2 2 3 4 2 4 3 +--R (b + 64a b + 480a b + 1024a b + 640a )cos(x) - b - 32a b +--R + +--R 2 2 3 4 +--R - 160a b - 256a b - 128a +--R + +--R +-------------+ +--R | 2 +--R +-+ +-+ tan(x)\|b csc(x) + a +--R 2\|a \|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a 2 +-+ +--R (cos(x) + 1)sin(x) |---------------------- + (2cos(x) - 2)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R a atan(----------------------------------------------------------------) +--R +----------------------+ +--R | 2 +--R 2 |- 4a cos(x) + 4b + 4a +-+ +--R (cos(x) + cos(x)) |---------------------- - 2cos(x)sin(x)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R a +--R * +--R atan +--R 4 3 2 +--R 4a cos(x) + 4a cos(x) + (- b - 3a)cos(x) +--R + +--R (- b - 3a)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (6a b + 6a )cos(x))sin(x) +--R / +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (- b - a)cos(x) - b - a)sin(x)\|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 2 +--R 8a cos(x) + (- 6a b - 10a )cos(x) + 2a b + 2a +--R + +--R +-+ +--R cot(x)\|a +--R 2a atan(----------------) +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 463 + +--S 464 of 528 +--d0387a:= D(m0387a,x) +--E 464 + +--S 465 of 528 +m0387b:= a0387.2-r0387 +--R +--R +--R (426) +--R +-------------+ +--R | 2 +--R +-+ +-+ tan(x)\|b csc(x) + a +--R 2\|a \|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a 2 +-+ +--R (cos(x) + 1)sin(x) |---------------------- + (2cos(x) - 2)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R a atan(----------------------------------------------------------------) +--R +----------------------+ +--R | 2 +--R 2 |- 4a cos(x) + 4b + 4a +-+ +--R (cos(x) + cos(x)) |---------------------- - 2cos(x)sin(x)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R a +--R * +--R atan +--R 4 3 2 +--R 4a cos(x) + 4a cos(x) + (- b - 3a)cos(x) +--R + +--R (- b - 3a)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (6a b + 6a )cos(x))sin(x) +--R / +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (- b - a)cos(x) - b - a)sin(x)\|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 2 +--R 8a cos(x) + (- 6a b - 10a )cos(x) + 2a b + 2a +--R + +--R - +--R +---+ +-+ +--R 2\|- b \|a +--R * +--R atan +--R +----------------------+ +--R | 2 +--R 2 +---+ |- 4a cos(x) + 4b + 4a +--R (cos(x) + cos(x))\|- b |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a 2 +--R (cos(x) + 1)sin(x)\|a |---------------------- + 2a cos(x) +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R - 2b - 2a +--R + +--R +-+ +--R cot(x)\|a +--R 2a atan(----------------) +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 465 + +--S 466 of 528 +d0387b:= D(m0387b,x) +--R +--R +--R (427) +--R 4 3 5 2 6 9 +--R (- 64a b - 192a b - 128a b)cos(x) +--R + +--R 4 3 5 2 6 8 +--R (- 64a b - 192a b - 128a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (144a b + 608a b + 784a b + 320a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (144a b + 608a b + 784a b + 320a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 104a b - 576a b - 1104a b - 896a b - 264a b) +--R * +--R 5 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 104a b - 576a b - 1104a b - 896a b - 264a b) +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 26a b + 184a b + 476a b + 584a b + 346a b +--R + +--R 6 +--R 80a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 26a b + 184a b + 476a b + 584a b + 346a b +--R + +--R 6 +--R 80a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2b - 18a b - 60a b - 100a b - 90a b +--R + +--R 5 2 6 +--R - 42a b - 8a b +--R * +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 2b - 18a b - 60a b - 100a b - 90a b - 42a b +--R + +--R 6 +--R - 8a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 9 +--R (- 64a b - 192a b - 128a )cos(x) +--R + +--R 5 2 6 7 8 +--R (- 64a b - 192a b - 128a )cos(x) +--R + +--R 4 3 5 2 6 7 7 +--R (144a b + 608a b + 784a b + 320a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (144a b + 608a b + 784a b + 320a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 5 +--R (- 104a b - 576a b - 1104a b - 896a b - 264a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- 104a b - 576a b - 1104a b - 896a b - 264a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (26a b + 184a b + 476a b + 584a b + 346a b + 80a ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (26a b + 184a b + 476a b + 584a b + 346a b + 80a ) +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 2a b - 18a b - 60a b - 100a b - 90a b - 42a b +--R + +--R 7 +--R - 8a +--R * +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R - 2a b - 18a b - 60a b - 100a b - 90a b - 42a b - 8a +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 5 2 6 11 +--R (- 64a b + 448a b + 896a b)cos(x) +--R + +--R 4 3 5 2 6 10 +--R (- 64a b + 448a b + 896a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 9 +--R (112a b - 1248a b - 4368a b - 3136a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 8 +--R (112a b - 1248a b - 4368a b - 3136a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 40a b + 1424a b + 6672a b + 9296a b +--R + +--R 6 +--R 4088a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 40a b + 1424a b + 6672a b + 9296a b +--R + +--R 6 +--R 4088a b +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 +--R - 10a b - 740a b - 4180a b - 8588a b +--R + +--R 5 2 6 +--R - 7546a b - 2408a b +--R * +--R 5 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 +--R - 10a b - 740a b - 4180a b - 8588a b +--R + +--R 5 2 6 +--R - 7546a b - 2408a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 2b + 132a b + 972a b + 2760a b + 3738a b +--R + +--R 5 2 6 +--R 2436a b + 616a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 2b + 132a b + 972a b + 2760a b + 3738a b +--R + +--R 5 2 6 +--R 2436a b + 616a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 6b - 66a b - 260a b - 500a b - 510a b +--R + +--R 5 2 6 +--R - 266a b - 56a b +--R * +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 6b - 66a b - 260a b - 500a b - 510a b +--R + +--R 5 2 6 +--R - 266a b - 56a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 11 +--R (- 64a b + 448a b + 896a )cos(x) +--R + +--R 5 2 6 7 10 +--R (- 64a b + 448a b + 896a )cos(x) +--R + +--R 4 3 5 2 6 7 9 +--R (112a b - 1248a b - 4368a b - 3136a )cos(x) +--R + +--R 4 3 5 2 6 7 8 +--R (112a b - 1248a b - 4368a b - 3136a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (- 40a b + 1424a b + 6672a b + 9296a b + 4088a ) +--R * +--R 7 +--R cos(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (- 40a b + 1424a b + 6672a b + 9296a b + 4088a ) +--R * +--R 6 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 10a b - 740a b - 4180a b - 8588a b - 7546a b +--R + +--R 7 +--R - 2408a +--R * +--R 5 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 10a b - 740a b - 4180a b - 8588a b - 7546a b +--R + +--R 7 +--R - 2408a +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 2a b + 132a b + 972a b + 2760a b + 3738a b +--R + +--R 6 7 +--R 2436a b + 616a +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 2a b + 132a b + 972a b + 2760a b + 3738a b +--R + +--R 6 7 +--R 2436a b + 616a +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 6a b - 66a b - 260a b - 500a b - 510a b +--R + +--R 6 7 +--R - 266a b - 56a +--R * +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 6a b - 66a b - 260a b - 500a b - 510a b - 266a b +--R + +--R 7 +--R - 56a +--R * +--R 6 +--R sin(x) +--R + +--R 4 3 5 2 6 13 +--R (64a b + 448a b - 896a b)cos(x) +--R + +--R 4 3 5 2 6 12 +--R (64a b + 448a b - 896a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 11 +--R (- 208a b - 1504a b + 1456a b + 4032a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 10 +--R (- 208a b - 1504a b + 1456a b + 4032a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (232a b + 1824a b - 304a b - 8736a b - 7224a b) +--R * +--R 9 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (232a b + 1824a b - 304a b - 8736a b - 7224a b) +--R * +--R 8 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 +--R - 98a b - 912a b - 300a b + 7280a b +--R + +--R 5 2 6 +--R 13230a b + 6496a b +--R * +--R 7 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 +--R - 98a b - 912a b - 300a b + 7280a b +--R + +--R 5 2 6 +--R 13230a b + 6496a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 10b + 154a b + 24a b - 2940a b - 8350a b +--R + +--R 5 2 6 +--R - 8554a b - 3024a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 10b + 154a b + 24a b - 2940a b - 8350a b +--R + +--R 5 2 6 +--R - 8554a b - 3024a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 8b + 4a b + 472a b + 1950a b + 3212a b +--R + +--R 5 2 6 +--R 2394a b + 672a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 8b + 4a b + 472a b + 1950a b + 3212a b +--R + +--R 5 2 6 +--R 2394a b + 672a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 20a b - 130a b - 326a b - 398a b - 238a b +--R + +--R 6 +--R - 56a b +--R * +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 20a b - 130a b - 326a b - 398a b - 238a b +--R + +--R 6 +--R - 56a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 13 +--R (64a b + 448a b - 896a )cos(x) +--R + +--R 5 2 6 7 12 +--R (64a b + 448a b - 896a )cos(x) +--R + +--R 4 3 5 2 6 7 11 +--R (- 208a b - 1504a b + 1456a b + 4032a )cos(x) +--R + +--R 4 3 5 2 6 7 10 +--R (- 208a b - 1504a b + 1456a b + 4032a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 9 +--R (232a b + 1824a b - 304a b - 8736a b - 7224a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 8 +--R (232a b + 1824a b - 304a b - 8736a b - 7224a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 98a b - 912a b - 300a b + 7280a b + 13230a b +--R + +--R 7 +--R 6496a +--R * +--R 7 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 98a b - 912a b - 300a b + 7280a b + 13230a b +--R + +--R 7 +--R 6496a +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 10a b + 154a b + 24a b - 2940a b - 8350a b +--R + +--R 6 7 +--R - 8554a b - 3024a +--R * +--R 5 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 10a b + 154a b + 24a b - 2940a b - 8350a b +--R + +--R 6 7 +--R - 8554a b - 3024a +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 8a b + 4a b + 472a b + 1950a b + 3212a b +--R + +--R 6 7 +--R 2394a b + 672a +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 8a b + 4a b + 472a b + 1950a b + 3212a b +--R + +--R 6 7 +--R 2394a b + 672a +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 20a b - 130a b - 326a b - 398a b - 238a b +--R + +--R 7 +--R - 56a +--R * +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R - 20a b - 130a b - 326a b - 398a b - 238a b - 56a +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 5 2 6 15 +--R (64a b - 192a b + 128a b)cos(x) +--R + +--R 4 3 5 2 6 14 +--R (64a b - 192a b + 128a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 13 +--R (- 176a b + 352a b + 464a b - 704a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 12 +--R (- 176a b + 352a b + 464a b - 704a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (168a b - 176a b - 1296a b + 272a b + 1608a b) +--R * +--R 11 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (168a b - 176a b - 1296a b + 272a b + 1608a b) +--R * +--R 10 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 62a b + 12a b + 1028a b + 900a b - 1918a b +--R + +--R 6 +--R - 1960a b +--R * +--R 9 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 62a b + 12a b + 1028a b + 900a b - 1918a b +--R + +--R 6 +--R - 1960a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 6b + 4a b - 328a b - 728a b + 638a b +--R + +--R 5 2 6 +--R 2392a b + 1360a b +--R * +--R 7 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 6b + 4a b - 328a b - 728a b + 638a b +--R + +--R 5 2 6 +--R 2392a b + 1360a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2b + 30a b + 152a b - 70a b - 978a b +--R + +--R 5 2 6 +--R - 1316a b - 528a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2b + 30a b + 152a b - 70a b - 978a b +--R + +--R 5 2 6 +--R - 1316a b - 528a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 8a b + 2a b + 148a b + 362a b + 328a b +--R + +--R 6 +--R 104a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 8a b + 2a b + 148a b + 362a b + 328a b +--R + +--R 6 +--R 104a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (- 6a b - 26a b - 42a b - 30a b - 8a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 6a b - 26a b - 42a b - 30a b - 8a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 15 +--R (64a b - 192a b + 128a )cos(x) +--R + +--R 5 2 6 7 14 +--R (64a b - 192a b + 128a )cos(x) +--R + +--R 4 3 5 2 6 7 13 +--R (- 176a b + 352a b + 464a b - 704a )cos(x) +--R + +--R 4 3 5 2 6 7 12 +--R (- 176a b + 352a b + 464a b - 704a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 11 +--R (168a b - 176a b - 1296a b + 272a b + 1608a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 10 +--R (168a b - 176a b - 1296a b + 272a b + 1608a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 62a b + 12a b + 1028a b + 900a b - 1918a b +--R + +--R 7 +--R - 1960a +--R * +--R 9 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 62a b + 12a b + 1028a b + 900a b - 1918a b +--R + +--R 7 +--R - 1960a +--R * +--R 8 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 6a b + 4a b - 328a b - 728a b + 638a b + 2392a b +--R + +--R 7 +--R 1360a +--R * +--R 7 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 6a b + 4a b - 328a b - 728a b + 638a b + 2392a b +--R + +--R 7 +--R 1360a +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 2a b + 30a b + 152a b - 70a b - 978a b +--R + +--R 6 7 +--R - 1316a b - 528a +--R * +--R 5 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 2a b + 30a b + 152a b - 70a b - 978a b +--R + +--R 6 7 +--R - 1316a b - 528a +--R * +--R 4 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (- 8a b + 2a b + 148a b + 362a b + 328a b + 104a ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (- 8a b + 2a b + 148a b + 362a b + 328a b + 104a ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 4 4 3 5 2 6 7 3 4 +--R (- 6a b - 26a b - 42a b - 30a b - 8a )cos(x) - 6a b +--R + +--R 4 3 5 2 6 7 +--R - 26a b - 42a b - 30a b - 8a +--R * +--R 2 +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 5 2 6 9 +--R (64a b + 192a b + 128a b)cos(x) +--R + +--R 4 3 5 2 6 8 +--R (64a b + 192a b + 128a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (- 144a b - 608a b - 784a b - 320a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 144a b - 608a b - 784a b - 320a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 5 +--R (104a b + 576a b + 1104a b + 896a b + 264a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (104a b + 576a b + 1104a b + 896a b + 264a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 26a b - 184a b - 476a b - 584a b - 346a b - 80a b) +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 26a b - 184a b - 476a b - 584a b - 346a b - 80a b) +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (2b + 18a b + 60a b + 100a b + 90a b + 42a b + 8a b) +--R * +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 2b + 18a b + 60a b + 100a b + 90a b + 42a b + 8a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 5 2 6 11 +--R (64a b - 448a b - 896a b)cos(x) +--R + +--R 4 3 5 2 6 10 +--R (64a b - 448a b - 896a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 9 +--R (- 112a b + 1248a b + 4368a b + 3136a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 8 +--R (- 112a b + 1248a b + 4368a b + 3136a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (40a b - 1424a b - 6672a b - 9296a b - 4088a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (40a b - 1424a b - 6672a b - 9296a b - 4088a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 10a b + 740a b + 4180a b + 8588a b + 7546a b +--R + +--R 6 +--R 2408a b +--R * +--R 5 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 10a b + 740a b + 4180a b + 8588a b + 7546a b +--R + +--R 6 +--R 2408a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2b - 132a b - 972a b - 2760a b - 3738a b +--R + +--R 5 2 6 +--R - 2436a b - 616a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2b - 132a b - 972a b - 2760a b - 3738a b +--R + +--R 5 2 6 +--R - 2436a b - 616a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 6b + 66a b + 260a b + 500a b + 510a b + 266a b +--R + +--R 6 +--R 56a b +--R * +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 6b + 66a b + 260a b + 500a b + 510a b + 266a b + 56a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 3 5 2 6 13 +--R (- 64a b - 448a b + 896a b)cos(x) +--R + +--R 4 3 5 2 6 12 +--R (- 64a b - 448a b + 896a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 11 +--R (208a b + 1504a b - 1456a b - 4032a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 10 +--R (208a b + 1504a b - 1456a b - 4032a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 9 +--R (- 232a b - 1824a b + 304a b + 8736a b + 7224a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 8 +--R (- 232a b - 1824a b + 304a b + 8736a b + 7224a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 98a b + 912a b + 300a b - 7280a b - 13230a b +--R + +--R 6 +--R - 6496a b +--R * +--R 7 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 98a b + 912a b + 300a b - 7280a b - 13230a b +--R + +--R 6 +--R - 6496a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 10b - 154a b - 24a b + 2940a b + 8350a b +--R + +--R 5 2 6 +--R 8554a b + 3024a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 10b - 154a b - 24a b + 2940a b + 8350a b +--R + +--R 5 2 6 +--R 8554a b + 3024a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 8b - 4a b - 472a b - 1950a b - 3212a b - 2394a b +--R + +--R 6 +--R - 672a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 8b - 4a b - 472a b - 1950a b - 3212a b - 2394a b +--R + +--R 6 +--R - 672a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (20a b + 130a b + 326a b + 398a b + 238a b + 56a b) +--R * +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 20a b + 130a b + 326a b + 398a b + 238a b + 56a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 5 2 6 15 +--R (- 64a b + 192a b - 128a b)cos(x) +--R + +--R 4 3 5 2 6 14 +--R (- 64a b + 192a b - 128a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 13 +--R (176a b - 352a b - 464a b + 704a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 12 +--R (176a b - 352a b - 464a b + 704a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 11 +--R (- 168a b + 176a b + 1296a b - 272a b - 1608a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 10 +--R (- 168a b + 176a b + 1296a b - 272a b - 1608a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (62a b - 12a b - 1028a b - 900a b + 1918a b + 1960a b) +--R * +--R 9 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (62a b - 12a b - 1028a b - 900a b + 1918a b + 1960a b) +--R * +--R 8 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 6b - 4a b + 328a b + 728a b - 638a b - 2392a b +--R + +--R 6 +--R - 1360a b +--R * +--R 7 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 6b - 4a b + 328a b + 728a b - 638a b - 2392a b +--R + +--R 6 +--R - 1360a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 2b - 30a b - 152a b + 70a b + 978a b + 1316a b +--R + +--R 6 +--R 528a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 2b - 30a b - 152a b + 70a b + 978a b + 1316a b +--R + +--R 6 +--R 528a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 3 +--R (8a b - 2a b - 148a b - 362a b - 328a b - 104a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 +--R (8a b - 2a b - 148a b - 362a b - 328a b - 104a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 +--R (6a b + 26a b + 42a b + 30a b + 8a b)cos(x) + 6a b +--R + +--R 3 4 4 3 5 2 6 +--R 26a b + 42a b + 30a b + 8a b +--R * +--R 2 +--R sin(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 5 3 6 2 7 8 +--R (32a b + 64a b + 32a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 6 +--R (- 80a b - 240a b - 240a b - 80a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 4 +--R (66a b + 264a b + 396a b + 264a b + 66a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 20a b - 100a b - 200a b - 200a b - 100a b +--R + +--R 7 +--R - 20a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 2a b + 12a b + 30a b + 40a b + 30a b + 12a b + 2a b +--R * +--R 2 +--R csc(x) +--R + +--R 6 2 7 8 8 +--R (32a b + 64a b + 32a )cos(x) +--R + +--R 5 3 6 2 7 8 6 +--R (- 80a b - 240a b - 240a b - 80a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 4 +--R (66a b + 264a b + 396a b + 264a b + 66a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (- 20a b - 100a b - 200a b - 200a b - 100a b - 20a ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R 2a b + 12a b + 30a b + 40a b + 30a b + 12a b + 2a +--R * +--R 9 +--R sin(x) +--R + +--R 5 3 6 2 7 10 +--R (- 128a b - 896a b - 896a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (416a b + 3328a b + 6048a b + 3136a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R - 488a b - 4448a b - 11520a b - 11648a b +--R + +--R 7 +--R - 4088a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 240a b + 2540a b + 8588a b + 12924a b + 9044a b +--R + +--R 7 +--R 2408a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 42a b - 560a b - 2436a b - 4984a b - 5306a b +--R + +--R 6 2 7 +--R - 2856a b - 616a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 2b + 38a b + 216a b + 580a b + 850a b + 702a b +--R + +--R 6 2 7 +--R 308a b + 56a b +--R * +--R 2 +--R csc(x) +--R + +--R 6 2 7 8 10 +--R (- 128a b - 896a b - 896a )cos(x) +--R + +--R 5 3 6 2 7 8 8 +--R (416a b + 3328a b + 6048a b + 3136a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 6 +--R (- 488a b - 4448a b - 11520a b - 11648a b - 4088a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 240a b + 2540a b + 8588a b + 12924a b + 9044a b +--R + +--R 8 +--R 2408a +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 42a b - 560a b - 2436a b - 4984a b - 5306a b +--R + +--R 7 8 +--R - 2856a b - 616a +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 2a b + 38a b + 216a b + 580a b + 850a b + 702a b +--R + +--R 7 8 +--R 308a b + 56a +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 7 12 +--R (- 320a b + 2240a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 10 +--R (960a b + 800a b - 8960a b - 10080a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 +--R - 1028a b - 1520a b + 13560a b + 31920a b +--R + +--R 7 +--R 18060a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 456a b + 756a b - 10620a b - 37380a b - 42700a b +--R + +--R 7 +--R - 16240a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 72a b - 24a b + 4398a b + 19640a b + 33910a b +--R + +--R 6 2 7 +--R 26180a b + 7560a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 4b - 8a b - 708a b - 4136a b - 9980a b +--R + +--R 5 3 6 2 7 +--R - 12000a b - 7140a b - 1680a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 30a b + 260a b + 880a b + 1520a b + 1430a b +--R + +--R 6 2 7 +--R 700a b + 140a b +--R * +--R 2 +--R csc(x) +--R + +--R 6 2 8 12 +--R (- 320a b + 2240a )cos(x) +--R + +--R 5 3 6 2 7 8 10 +--R (960a b + 800a b - 8960a b - 10080a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (- 1028a b - 1520a b + 13560a b + 31920a b + 18060a ) +--R * +--R 8 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 456a b + 756a b - 10620a b - 37380a b - 42700a b +--R + +--R 8 +--R - 16240a +--R * +--R 6 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 72a b - 24a b + 4398a b + 19640a b + 33910a b +--R + +--R 7 8 +--R 26180a b + 7560a +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 4a b - 8a b - 708a b - 4136a b - 9980a b - 12000a b +--R + +--R 7 8 +--R - 7140a b - 1680a +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 30a b + 260a b + 880a b + 1520a b + 1430a b + 700a b +--R + +--R 8 +--R 140a +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 6 2 7 14 +--R (- 128a b + 896a b - 896a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 12 +--R (352a b - 2688a b - 672a b + 4928a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 328a b + 3296a b + 5664a b - 8064a b - 11256a b) +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 112a b - 2092a b - 6812a b + 3172a b + 21308a b +--R + +--R 7 +--R 13720a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 10a b + 648a b + 3168a b + 360a b - 15150a b +--R + +--R 6 2 7 +--R - 22512a b - 9520a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 2b - 58a b - 516a b - 176a b + 5170a b +--R + +--R 5 3 6 2 7 +--R 12786a b + 11592a b + 3696a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 24a b + 8a b - 746a b - 2764a b - 4106a b +--R + +--R 6 2 7 +--R - 2800a b - 728a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 30a b + 174a b + 398a b + 450a b + 252a b + 56a b +--R * +--R 2 +--R csc(x) +--R + +--R 6 2 7 8 14 +--R (- 128a b + 896a b - 896a )cos(x) +--R + +--R 5 3 6 2 7 8 12 +--R (352a b - 2688a b - 672a b + 4928a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 10 +--R (- 328a b + 3296a b + 5664a b - 8064a b - 11256a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 112a b - 2092a b - 6812a b + 3172a b + 21308a b +--R + +--R 8 +--R 13720a +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 10a b + 648a b + 3168a b + 360a b - 15150a b +--R + +--R 7 8 +--R - 22512a b - 9520a +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 2a b - 58a b - 516a b - 176a b + 5170a b + 12786a b +--R + +--R 7 8 +--R 11592a b + 3696a +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 24a b + 8a b - 746a b - 2764a b - 4106a b - 2800a b +--R + +--R 8 +--R - 728a +--R * +--R 2 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R 30a b + 174a b + 398a b + 450a b + 252a b + 56a +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 6 2 7 16 +--R (32a b - 64a b + 32a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (- 112a b + 80a b + 240a b - 208a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 12 +--R (146a b + 104a b - 612a b - 184a b + 578a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 84a b - 208a b + 436a b + 940a b - 448a b +--R + +--R 7 +--R - 892a b +--R * +--R 10 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 18a b + 100a b - 96a b - 784a b - 348a b +--R + +--R 6 2 7 +--R 1080a b + 830a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 3 5 4 4 5 3 6 2 +--R - 12a b + 236a b + 368a b - 360a b - 976a b +--R + +--R 7 +--R - 472a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 2a b - 20a b - 80a b + 32a b + 372a b + 440a b +--R + +--R 7 +--R 158a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 4 4 5 3 6 2 7 2 +--R (4a b - 52a b - 116a b - 96a b - 28a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 2a b + 8a b + 12a b + 8a b + 2a b +--R * +--R 2 +--R csc(x) +--R + +--R 6 2 7 8 16 +--R (32a b - 64a b + 32a )cos(x) +--R + +--R 5 3 6 2 7 8 14 +--R (- 112a b + 80a b + 240a b - 208a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (146a b + 104a b - 612a b - 184a b + 578a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (- 84a b - 208a b + 436a b + 940a b - 448a b - 892a ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 18a b + 100a b - 96a b - 784a b - 348a b + 1080a b +--R + +--R 8 +--R 830a +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 4 4 5 3 6 2 7 8 +--R (- 12a b + 236a b + 368a b - 360a b - 976a b - 472a ) +--R * +--R 6 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 2a b - 20a b - 80a b + 32a b + 372a b + 440a b +--R + +--R 8 +--R 158a +--R * +--R 4 +--R cos(x) +--R + +--R 3 5 5 3 6 2 7 8 2 4 4 +--R (4a b - 52a b - 116a b - 96a b - 28a )cos(x) + 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b + 12a b + 8a b + 2a +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 3 6 2 7 8 +--R (- 32a b - 64a b - 32a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 6 +--R (80a b + 240a b + 240a b + 80a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 4 +--R (- 66a b - 264a b - 396a b - 264a b - 66a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b + 100a b + 200a b + 200a b + 100a b + 20a b)cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R - 2a b - 12a b - 30a b - 40a b - 30a b - 12a b - 2a b +--R * +--R 9 +--R sin(x) +--R + +--R 5 3 6 2 7 10 +--R (128a b + 896a b + 896a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (- 416a b - 3328a b - 6048a b - 3136a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 6 +--R (488a b + 4448a b + 11520a b + 11648a b + 4088a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 240a b - 2540a b - 8588a b - 12924a b - 9044a b +--R + +--R 7 +--R - 2408a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 42a b + 560a b + 2436a b + 4984a b + 5306a b + 2856a b +--R + +--R 7 +--R 616a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 2b - 38a b - 216a b - 580a b - 850a b - 702a b - 308a b +--R + +--R 7 +--R - 56a b +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 7 12 +--R (320a b - 2240a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 10 +--R (- 960a b - 800a b + 8960a b + 10080a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (1028a b + 1520a b - 13560a b - 31920a b - 18060a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 456a b - 756a b + 10620a b + 37380a b + 42700a b +--R + +--R 7 +--R 16240a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 72a b + 24a b - 4398a b - 19640a b - 33910a b +--R + +--R 6 2 7 +--R - 26180a b - 7560a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 4b + 8a b + 708a b + 4136a b + 9980a b + 12000a b +--R + +--R 6 2 7 +--R 7140a b + 1680a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 30a b - 260a b - 880a b - 1520a b - 1430a b - 700a b +--R + +--R 7 +--R - 140a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 6 2 7 14 +--R (128a b - 896a b + 896a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 12 +--R (- 352a b + 2688a b + 672a b - 4928a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 10 +--R (328a b - 3296a b - 5664a b + 8064a b + 11256a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 112a b + 2092a b + 6812a b - 3172a b - 21308a b +--R + +--R 7 +--R - 13720a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 10a b - 648a b - 3168a b - 360a b + 15150a b + 22512a b +--R + +--R 7 +--R 9520a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 2b + 58a b + 516a b + 176a b - 5170a b - 12786a b +--R + +--R 6 2 7 +--R - 11592a b - 3696a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 24a b - 8a b + 746a b + 2764a b + 4106a b + 2800a b +--R + +--R 7 +--R 728a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 30a b - 174a b - 398a b - 450a b - 252a b - 56a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 6 2 7 16 +--R (- 32a b + 64a b - 32a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (112a b - 80a b - 240a b + 208a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 12 +--R (- 146a b - 104a b + 612a b + 184a b - 578a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 10 +--R (84a b + 208a b - 436a b - 940a b + 448a b + 892a b)cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 18a b - 100a b + 96a b + 784a b + 348a b - 1080a b +--R + +--R 7 +--R - 830a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 3 5 4 4 5 3 6 2 7 6 +--R (12a b - 236a b - 368a b + 360a b + 976a b + 472a b)cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 20a b + 80a b - 32a b - 372a b - 440a b +--R + +--R 7 +--R - 158a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 4 4 5 3 6 2 7 2 3 5 +--R (- 4a b + 52a b + 116a b + 96a b + 28a b)cos(x) - 2a b +--R + +--R 4 4 5 3 6 2 7 +--R - 8a b - 12a b - 8a b - 2a b +--R * +--R sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R + +--R 4 4 5 3 6 2 7 9 +--R (- 16a b - 48a b - 48a b - 16a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 +--R (- 16a b - 48a b - 48a b - 16a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 7 +--R (24a b + 112a b + 192a b + 144a b + 40a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 6 +--R (24a b + 112a b + 192a b + 144a b + 40a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 9a b - 69a b - 186a b - 234a b - 141a b +--R + +--R 7 +--R - 33a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 9a b - 69a b - 186a b - 234a b - 141a b +--R + +--R 7 +--R - 33a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R a b + 15a b + 60a b + 110a b + 105a b + 51a b +--R + +--R 7 +--R 10a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R a b + 15a b + 60a b + 110a b + 105a b + 51a b +--R + +--R 7 +--R 10a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - a b - 6a b - 15a b - 20a b - 15a b - 6a b +--R + +--R 7 +--R - a b +--R * +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R - a b - 6a b - 15a b - 20a b - 15a b - 6a b - a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 3 6 2 7 8 9 +--R (- 16a b - 48a b - 48a b - 16a )cos(x) +--R + +--R 5 3 6 2 7 8 8 +--R (- 16a b - 48a b - 48a b - 16a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 7 +--R (24a b + 112a b + 192a b + 144a b + 40a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 6 +--R (24a b + 112a b + 192a b + 144a b + 40a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 5 +--R (- 9a b - 69a b - 186a b - 234a b - 141a b - 33a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (- 9a b - 69a b - 186a b - 234a b - 141a b - 33a )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (a b + 15a b + 60a b + 110a b + 105a b + 51a b + 10a ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (a b + 15a b + 60a b + 110a b + 105a b + 51a b + 10a ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (- a b - 6a b - 15a b - 20a b - 15a b - 6a b - a )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R - a b - 6a b - 15a b - 20a b - 15a b - 6a b - a +--R * +--R 8 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 11 +--R (64a b + 512a b + 896a b + 448a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 10 +--R (64a b + 512a b + 896a b + 448a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 144a b - 1360a b - 3792a b - 4144a b - 1568a b) +--R * +--R 9 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 144a b - 1360a b - 3792a b - 4144a b - 1568a b) +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 100a b + 1172a b + 4704a b + 8336a b + 6748a b +--R + +--R 7 +--R 2044a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 100a b + 1172a b + 4704a b + 8336a b + 6748a b +--R + +--R 7 +--R 2044a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 20a b - 362a b - 2156a b - 5700a b - 7484a b +--R + +--R 6 2 7 +--R - 4802a b - 1204a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 20a b - 362a b - 2156a b - 5700a b - 7484a b +--R + +--R 6 2 7 +--R - 4802a b - 1204a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R b + 39a b + 370a b + 1418a b + 2717a b +--R + +--R 5 3 6 2 7 +--R 2779a b + 1456a b + 308a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R b + 39a b + 370a b + 1418a b + 2717a b +--R + +--R 5 3 6 2 7 +--R 2779a b + 1456a b + 308a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - b - 19a b - 108a b - 290a b - 425a b - 351a b +--R + +--R 6 2 7 +--R - 154a b - 28a b +--R * +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - b - 19a b - 108a b - 290a b - 425a b - 351a b +--R + +--R 6 2 7 +--R - 154a b - 28a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 3 6 2 7 8 11 +--R (64a b + 512a b + 896a b + 448a )cos(x) +--R + +--R 5 3 6 2 7 8 10 +--R (64a b + 512a b + 896a b + 448a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 9 +--R (- 144a b - 1360a b - 3792a b - 4144a b - 1568a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 8 +--R (- 144a b - 1360a b - 3792a b - 4144a b - 1568a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 100a b + 1172a b + 4704a b + 8336a b + 6748a b +--R + +--R 8 +--R 2044a +--R * +--R 7 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 100a b + 1172a b + 4704a b + 8336a b + 6748a b +--R + +--R 8 +--R 2044a +--R * +--R 6 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 20a b - 362a b - 2156a b - 5700a b - 7484a b +--R + +--R 7 8 +--R - 4802a b - 1204a +--R * +--R 5 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 20a b - 362a b - 2156a b - 5700a b - 7484a b +--R + +--R 7 8 +--R - 4802a b - 1204a +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R a b + 39a b + 370a b + 1418a b + 2717a b + 2779a b +--R + +--R 7 8 +--R 1456a b + 308a +--R * +--R 3 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R a b + 39a b + 370a b + 1418a b + 2717a b + 2779a b +--R + +--R 7 8 +--R 1456a b + 308a +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - a b - 19a b - 108a b - 290a b - 425a b - 351a b +--R + +--R 7 8 +--R - 154a b - 28a +--R * +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - a b - 19a b - 108a b - 290a b - 425a b - 351a b +--R + +--R 7 8 +--R - 154a b - 28a +--R * +--R 6 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 13 +--R (160a b + 160a b - 1120a b - 1120a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 12 +--R (160a b + 160a b - 1120a b - 1120a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 320a b - 720a b + 2960a b + 8400a b + 5040a b) +--R * +--R 11 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 320a b - 720a b + 2960a b + 8400a b + 5040a b) +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 194a b + 714a b - 2900a b - 15460a b - 21070a b +--R + +--R 7 +--R - 9030a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 194a b + 714a b - 2900a b - 15460a b - 21070a b +--R + +--R 7 +--R - 9030a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 34a b - 212a b + 1472a b + 11660a b + 26250a b +--R + +--R 6 2 7 +--R 24360a b + 8120a b +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 34a b - 212a b + 1472a b + 11660a b + 26250a b +--R + +--R 6 2 7 +--R 24360a b + 8120a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 2b + 30a b - 321a b - 3819a b - 12865a b +--R + +--R 5 3 6 2 7 +--R - 19475a b - 13860a b - 3780a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 2b + 30a b - 321a b - 3819a b - 12865a b +--R + +--R 5 3 6 2 7 +--R - 19475a b - 13860a b - 3780a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 2b + 19a b + 469a b + 2393a b + 5425a b +--R + +--R 5 3 6 2 7 +--R 6280a b + 3640a b + 840a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 2b + 19a b + 469a b + 2393a b + 5425a b +--R + +--R 5 3 6 2 7 +--R 6280a b + 3640a b + 840a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 15a b - 130a b - 440a b - 760a b - 715a b +--R + +--R 6 2 7 +--R - 350a b - 70a b +--R * +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 15a b - 130a b - 440a b - 760a b - 715a b +--R + +--R 6 2 7 +--R - 350a b - 70a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 3 6 2 7 8 13 +--R (160a b + 160a b - 1120a b - 1120a )cos(x) +--R + +--R 5 3 6 2 7 8 12 +--R (160a b + 160a b - 1120a b - 1120a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 11 +--R (- 320a b - 720a b + 2960a b + 8400a b + 5040a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 10 +--R (- 320a b - 720a b + 2960a b + 8400a b + 5040a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 194a b + 714a b - 2900a b - 15460a b - 21070a b +--R + +--R 8 +--R - 9030a +--R * +--R 9 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 194a b + 714a b - 2900a b - 15460a b - 21070a b +--R + +--R 8 +--R - 9030a +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 34a b - 212a b + 1472a b + 11660a b + 26250a b +--R + +--R 7 8 +--R 24360a b + 8120a +--R * +--R 7 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 34a b - 212a b + 1472a b + 11660a b + 26250a b +--R + +--R 7 8 +--R 24360a b + 8120a +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 2a b + 30a b - 321a b - 3819a b - 12865a b +--R + +--R 6 2 7 8 +--R - 19475a b - 13860a b - 3780a +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 2a b + 30a b - 321a b - 3819a b - 12865a b +--R + +--R 6 2 7 8 +--R - 19475a b - 13860a b - 3780a +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 2a b + 19a b + 469a b + 2393a b + 5425a b +--R + +--R 6 2 7 8 +--R 6280a b + 3640a b + 840a +--R * +--R 3 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 2a b + 19a b + 469a b + 2393a b + 5425a b +--R + +--R 6 2 7 8 +--R 6280a b + 3640a b + 840a +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 15a b - 130a b - 440a b - 760a b - 715a b - 350a b +--R + +--R 8 +--R - 70a +--R * +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 15a b - 130a b - 440a b - 760a b - 715a b - 350a b +--R + +--R 8 +--R - 70a +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 5 3 7 15 +--R (64a b - 384a b + 448a b)cos(x) +--R + +--R 4 4 5 3 7 14 +--R (64a b - 384a b + 448a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 112a b + 784a b + 1680a b - 1680a b - 2464a b) +--R * +--R 13 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 112a b + 784a b + 1680a b - 1680a b - 2464a b) +--R * +--R 12 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 52a b - 636a b - 3184a b - 480a b + 7644a b +--R + +--R 7 +--R 5628a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 52a b - 636a b - 3184a b - 480a b + 7644a b +--R + +--R 7 +--R 5628a b +--R * +--R 10 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 4a b + 242a b + 2116a b + 2636a b - 6276a b +--R + +--R 6 2 7 +--R - 13902a b - 6860a b +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 4a b + 242a b + 2116a b + 2636a b - 6276a b +--R + +--R 6 2 7 +--R - 13902a b - 6860a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R b - 25a b - 540a b - 1464a b + 1935a b +--R + +--R 5 3 6 2 7 +--R 10893a b + 12768a b + 4760a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R b - 25a b - 540a b - 1464a b + 1935a b +--R + +--R 5 3 6 2 7 +--R 10893a b + 12768a b + 4760a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - b + 41a b + 250a b - 262a b - 3545a b +--R + +--R 5 3 6 2 7 +--R - 7359a b - 6132a b - 1848a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - b + 41a b + 250a b - 262a b - 3545a b +--R + +--R 5 3 6 2 7 +--R - 7359a b - 6132a b - 1848a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 12a b + 11a b + 445a b + 1509a b + 2151a b +--R + +--R 6 2 7 +--R 1428a b + 364a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 12a b + 11a b + 445a b + 1509a b + 2151a b +--R + +--R 6 2 7 +--R 1428a b + 364a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 15a b - 87a b - 199a b - 225a b - 126a b +--R + +--R 7 +--R - 28a b +--R * +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 15a b - 87a b - 199a b - 225a b - 126a b - 28a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 3 6 2 8 15 +--R (64a b - 384a b + 448a )cos(x) +--R + +--R 5 3 6 2 8 14 +--R (64a b - 384a b + 448a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 13 +--R (- 112a b + 784a b + 1680a b - 1680a b - 2464a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (- 112a b + 784a b + 1680a b - 1680a b - 2464a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (52a b - 636a b - 3184a b - 480a b + 7644a b + 5628a ) +--R * +--R 11 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (52a b - 636a b - 3184a b - 480a b + 7644a b + 5628a ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 4a b + 242a b + 2116a b + 2636a b - 6276a b +--R + +--R 7 8 +--R - 13902a b - 6860a +--R * +--R 9 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 4a b + 242a b + 2116a b + 2636a b - 6276a b +--R + +--R 7 8 +--R - 13902a b - 6860a +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R a b - 25a b - 540a b - 1464a b + 1935a b + 10893a b +--R + +--R 7 8 +--R 12768a b + 4760a +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R a b - 25a b - 540a b - 1464a b + 1935a b + 10893a b +--R + +--R 7 8 +--R 12768a b + 4760a +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - a b + 41a b + 250a b - 262a b - 3545a b - 7359a b +--R + +--R 7 8 +--R - 6132a b - 1848a +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - a b + 41a b + 250a b - 262a b - 3545a b - 7359a b +--R + +--R 7 8 +--R - 6132a b - 1848a +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 12a b + 11a b + 445a b + 1509a b + 2151a b +--R + +--R 7 8 +--R 1428a b + 364a +--R * +--R 3 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 12a b + 11a b + 445a b + 1509a b + 2151a b +--R + +--R 7 8 +--R 1428a b + 364a +--R * +--R 2 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R (- 15a b - 87a b - 199a b - 225a b - 126a b - 28a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R - 15a b - 87a b - 199a b - 225a b - 126a b - 28a +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 17 +--R (- 16a b + 16a b + 16a b - 16a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 16 +--R (- 16a b + 16a b + 16a b - 16a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 15 +--R (40a b + 32a b - 144a b - 32a b + 104a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 14 +--R (40a b + 32a b - 144a b - 32a b + 104a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (- 33a b - 109a b + 126a b + 382a b - 109a b - 289a b) +--R * +--R 13 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (- 33a b - 109a b + 126a b + 382a b - 109a b - 289a b) +--R * +--R 12 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 9a b + 77a b + 28a b - 434a b - 371a b + 469a b +--R + +--R 7 +--R 446a b +--R * +--R 11 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 9a b + 77a b + 28a b - 434a b - 371a b + 469a b +--R + +--R 7 +--R 446a b +--R * +--R 10 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 15a b - 43a b + 148a b + 449a b - 22a b - 710a b +--R + +--R 7 +--R - 415a b +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 15a b - 43a b + 148a b + 449a b - 22a b - 710a b +--R + +--R 7 +--R - 415a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 7a b - 11a b - 145a b - 143a b + 302a b + 554a b +--R + +--R 7 +--R 236a b +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 7a b - 11a b - 145a b - 143a b + 302a b + 554a b +--R + +--R 7 +--R 236a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - a b + 12a b + 38a b - 39a b - 218a b - 233a b +--R + +--R 7 +--R - 79a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - a b + 12a b + 38a b - 39a b - 218a b - 233a b +--R + +--R 7 +--R - 79a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 +--R (- 2a b + a b + 29a b + 61a b + 49a b + 14a b)cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (- 2a b + a b + 29a b + 61a b + 49a b + 14a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 3 5 4 4 +--R (- a b - 4a b - 6a b - 4a b - a b)cos(x) - a b - 4a b +--R + +--R 5 3 6 2 7 +--R - 6a b - 4a b - a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 3 6 2 7 8 17 +--R (- 16a b + 16a b + 16a b - 16a )cos(x) +--R + +--R 5 3 6 2 7 8 16 +--R (- 16a b + 16a b + 16a b - 16a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 15 +--R (40a b + 32a b - 144a b - 32a b + 104a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 14 +--R (40a b + 32a b - 144a b - 32a b + 104a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 13 +--R (- 33a b - 109a b + 126a b + 382a b - 109a b - 289a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 12 +--R (- 33a b - 109a b + 126a b + 382a b - 109a b - 289a )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (9a b + 77a b + 28a b - 434a b - 371a b + 469a b + 446a ) +--R * +--R 11 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (9a b + 77a b + 28a b - 434a b - 371a b + 469a b + 446a ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 15a b - 43a b + 148a b + 449a b - 22a b - 710a b +--R + +--R 8 +--R - 415a +--R * +--R 9 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 15a b - 43a b + 148a b + 449a b - 22a b - 710a b +--R + +--R 8 +--R - 415a +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (7a b - 11a b - 145a b - 143a b + 302a b + 554a b + 236a ) +--R * +--R 7 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (7a b - 11a b - 145a b - 143a b + 302a b + 554a b + 236a ) +--R * +--R 6 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (- a b + 12a b + 38a b - 39a b - 218a b - 233a b - 79a ) +--R * +--R 5 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 +--R (- a b + 12a b + 38a b - 39a b - 218a b - 233a b - 79a ) +--R * +--R 4 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (- 2a b + a b + 29a b + 61a b + 49a b + 14a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 2 +--R (- 2a b + a b + 29a b + 61a b + 49a b + 14a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 4 4 5 3 6 2 +--R (- a b - 4a b - 6a b - 4a b - a )cos(x) - a b - 4a b - 6a b +--R + +--R 7 8 +--R - 4a b - a +--R * +--R 2 +--R tan(x) +--R + +--R 4 4 5 3 6 2 9 +--R (16a b + 32a b + 16a b )cos(x) +--R + +--R 4 4 5 3 6 2 8 +--R (16a b + 32a b + 16a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 24a b - 88a b - 104a b - 40a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 6 +--R (- 24a b - 88a b - 104a b - 40a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 5 +--R (9a b + 60a b + 126a b + 108a b + 33a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 4 +--R (9a b + 60a b + 126a b + 108a b + 33a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 3 +--R (- a b - 14a b - 46a b - 64a b - 41a b - 10a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 +--R (- a b - 14a b - 46a b - 64a b - 41a b - 10a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R (a b + 5a b + 10a b + 10a b + 5a b + a b )cos(x) + a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 5a b + 10a b + 10a b + 5a b + a b +--R * +--R 2 8 +--R cot(x)csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 11 +--R (- 64a b - 448a b - 448a b )cos(x) +--R + +--R 4 4 5 3 6 2 10 +--R (- 64a b - 448a b - 448a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 9 +--R (144a b + 1216a b + 2576a b + 1568a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 8 +--R (144a b + 1216a b + 2576a b + 1568a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 100a b - 1072a b - 3632a b - 4704a b - 2044a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 100a b - 1072a b - 3632a b - 4704a b - 2044a b ) +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 20a b + 342a b + 1814a b + 3886a b + 3598a b +--R + +--R 6 2 +--R 1204a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 20a b + 342a b + 1814a b + 3886a b + 3598a b +--R + +--R 6 2 +--R 1204a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - b - 38a b - 332a b - 1086a b - 1631a b - 1148a b +--R + +--R 6 2 +--R - 308a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - b - 38a b - 332a b - 1086a b - 1631a b - 1148a b +--R + +--R 6 2 +--R - 308a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R b + 18a b + 90a b + 200a b + 225a b + 126a b +--R + +--R 6 2 +--R 28a b +--R * +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R b + 18a b + 90a b + 200a b + 225a b + 126a b + 28a b +--R * +--R 2 6 +--R cot(x)csc(x) sin(x) +--R + +--R 4 4 6 2 13 +--R (- 160a b + 1120a b )cos(x) +--R + +--R 4 4 6 2 12 +--R (- 160a b + 1120a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 11 +--R (320a b + 400a b - 3360a b - 5040a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 10 +--R (320a b + 400a b - 3360a b - 5040a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 194a b - 520a b + 3420a b + 12040a b + 9030a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 194a b - 520a b + 3420a b + 12040a b + 9030a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 34a b + 178a b - 1650a b - 10010a b - 16240a b +--R + +--R 6 2 +--R - 8120a b +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 34a b + 178a b - 1650a b - 10010a b - 16240a b +--R + +--R 6 2 +--R - 8120a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 2b - 28a b + 349a b + 3470a b + 9395a b +--R + +--R 5 3 6 2 +--R 10080a b + 3780a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 2b - 28a b + 349a b + 3470a b + 9395a b +--R + +--R 5 3 6 2 +--R 10080a b + 3780a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 2b - 21a b - 448a b - 1945a b - 3480a b - 2800a b +--R + +--R 6 2 +--R - 840a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 2b - 21a b - 448a b - 1945a b - 3480a b - 2800a b +--R + +--R 6 2 +--R - 840a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (15a b + 115a b + 325a b + 435a b + 280a b + 70a b ) +--R * +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 15a b + 115a b + 325a b + 435a b + 280a b + 70a b +--R * +--R 2 4 +--R cot(x)csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 15 +--R (- 64a b + 448a b - 448a b )cos(x) +--R + +--R 4 4 5 3 6 2 14 +--R (- 64a b + 448a b - 448a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 13 +--R (112a b - 896a b - 784a b + 2464a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 12 +--R (112a b - 896a b - 784a b + 2464a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 11 +--R (- 52a b + 688a b + 2496a b - 2016a b - 5628a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 10 +--R (- 52a b + 688a b + 2496a b - 2016a b - 5628a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 4a b - 246a b - 1870a b - 766a b + 7042a b +--R + +--R 6 2 +--R 6860a b +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 4a b - 246a b - 1870a b - 766a b + 7042a b +--R + +--R 6 2 +--R 6860a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - b + 26a b + 514a b + 950a b - 2885a b - 8008a b +--R + +--R 6 2 +--R - 4760a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - b + 26a b + 514a b + 950a b - 2885a b - 8008a b +--R + +--R 6 2 +--R - 4760a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R b - 42a b - 208a b + 470a b + 3075a b + 4284a b +--R + +--R 6 2 +--R 1848a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R b - 42a b - 208a b + 470a b + 3075a b + 4284a b +--R + +--R 6 2 +--R 1848a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (12a b - 23a b - 422a b - 1087a b - 1064a b - 364a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (12a b - 23a b - 422a b - 1087a b - 1064a b - 364a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 6 +--R (15a b + 72a b + 127a b + 98a b + 28a b )cos(x) + 15a b +--R + +--R 3 5 4 4 5 3 6 2 +--R 72a b + 127a b + 98a b + 28a b +--R * +--R 2 2 +--R cot(x)csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 17 +--R (16a b - 32a b + 16a b )cos(x) +--R + +--R 4 4 5 3 6 2 16 +--R (16a b - 32a b + 16a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 15 +--R (- 40a b + 8a b + 136a b - 104a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 14 +--R (- 40a b + 8a b + 136a b - 104a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 13 +--R (33a b + 76a b - 202a b - 180a b + 289a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 12 +--R (33a b + 76a b - 202a b - 180a b + 289a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 9a b - 68a b + 40a b + 394a b - 23a b - 446a b ) +--R * +--R 11 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 9a b - 68a b + 40a b + 394a b - 23a b - 446a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (15a b + 28a b - 176a b - 273a b + 295a b + 415a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (15a b + 28a b - 176a b - 273a b + 295a b + 415a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 7a b + 18a b + 127a b + 16a b - 318a b - 236a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 7a b + 18a b + 127a b + 16a b - 318a b - 236a b ) +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 5 +--R (a b - 13a b - 25a b + 64a b + 154a b + 79a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 4 +--R (a b - 13a b - 25a b + 64a b + 154a b + 79a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 3 +--R (2a b - 3a b - 26a b - 35a b - 14a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (2a b - 3a b - 26a b - 35a b - 14a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 3 5 4 4 5 3 +--R (a b + 3a b + 3a b + a b )cos(x) + a b + 3a b + 3a b +--R + +--R 6 2 +--R a b +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 4 4 5 3 6 2 9 +--R (- 16a b - 32a b - 16a b )cos(x) +--R + +--R 4 4 5 3 6 2 8 +--R (- 16a b - 32a b - 16a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (24a b + 88a b + 104a b + 40a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 6 +--R (24a b + 88a b + 104a b + 40a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 5 +--R (- 9a b - 60a b - 126a b - 108a b - 33a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 4 +--R (- 9a b - 60a b - 126a b - 108a b - 33a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 3 +--R (a b + 14a b + 46a b + 64a b + 41a b + 10a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 +--R (a b + 14a b + 46a b + 64a b + 41a b + 10a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R (- a b - 5a b - 10a b - 10a b - 5a b - a b )cos(x) - a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 5a b - 10a b - 10a b - 5a b - a b +--R * +--R 2 8 +--R csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 11 +--R (64a b + 448a b + 448a b )cos(x) +--R + +--R 4 4 5 3 6 2 10 +--R (64a b + 448a b + 448a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 9 +--R (- 144a b - 1216a b - 2576a b - 1568a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 8 +--R (- 144a b - 1216a b - 2576a b - 1568a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R (100a b + 1072a b + 3632a b + 4704a b + 2044a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 6 +--R (100a b + 1072a b + 3632a b + 4704a b + 2044a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 20a b - 342a b - 1814a b - 3886a b - 3598a b +--R + +--R 6 2 +--R - 1204a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 20a b - 342a b - 1814a b - 3886a b - 3598a b +--R + +--R 6 2 +--R - 1204a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R b + 38a b + 332a b + 1086a b + 1631a b + 1148a b +--R + +--R 6 2 +--R 308a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R b + 38a b + 332a b + 1086a b + 1631a b + 1148a b +--R + +--R 6 2 +--R 308a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R (- b - 18a b - 90a b - 200a b - 225a b - 126a b - 28a b ) +--R * +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - b - 18a b - 90a b - 200a b - 225a b - 126a b - 28a b +--R * +--R 2 6 +--R csc(x) sin(x) +--R + +--R 4 4 6 2 13 4 4 6 2 12 +--R (160a b - 1120a b )cos(x) + (160a b - 1120a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 11 +--R (- 320a b - 400a b + 3360a b + 5040a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 10 +--R (- 320a b - 400a b + 3360a b + 5040a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 9 +--R (194a b + 520a b - 3420a b - 12040a b - 9030a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 8 +--R (194a b + 520a b - 3420a b - 12040a b - 9030a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 34a b - 178a b + 1650a b + 10010a b + 16240a b +--R + +--R 6 2 +--R 8120a b +--R * +--R 7 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 34a b - 178a b + 1650a b + 10010a b + 16240a b +--R + +--R 6 2 +--R 8120a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 2b + 28a b - 349a b - 3470a b - 9395a b - 10080a b +--R + +--R 6 2 +--R - 3780a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 2b + 28a b - 349a b - 3470a b - 9395a b - 10080a b +--R + +--R 6 2 +--R - 3780a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 2b + 21a b + 448a b + 1945a b + 3480a b + 2800a b +--R + +--R 6 2 +--R 840a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 2b + 21a b + 448a b + 1945a b + 3480a b + 2800a b +--R + +--R 6 2 +--R 840a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 15a b - 115a b - 325a b - 435a b - 280a b - 70a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 15a b - 115a b - 325a b - 435a b - 280a b - 70a b +--R * +--R 2 4 +--R csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 15 +--R (64a b - 448a b + 448a b )cos(x) +--R + +--R 4 4 5 3 6 2 14 +--R (64a b - 448a b + 448a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 13 +--R (- 112a b + 896a b + 784a b - 2464a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 12 +--R (- 112a b + 896a b + 784a b - 2464a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 11 +--R (52a b - 688a b - 2496a b + 2016a b + 5628a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 10 +--R (52a b - 688a b - 2496a b + 2016a b + 5628a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 4a b + 246a b + 1870a b + 766a b - 7042a b - 6860a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 4a b + 246a b + 1870a b + 766a b - 7042a b - 6860a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R b - 26a b - 514a b - 950a b + 2885a b + 8008a b +--R + +--R 6 2 +--R 4760a b +--R * +--R 7 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R b - 26a b - 514a b - 950a b + 2885a b + 8008a b +--R + +--R 6 2 +--R 4760a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - b + 42a b + 208a b - 470a b - 3075a b - 4284a b +--R + +--R 6 2 +--R - 1848a b +--R * +--R 5 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - b + 42a b + 208a b - 470a b - 3075a b - 4284a b +--R + +--R 6 2 +--R - 1848a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 12a b + 23a b + 422a b + 1087a b + 1064a b + 364a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 12a b + 23a b + 422a b + 1087a b + 1064a b + 364a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 6 +--R (- 15a b - 72a b - 127a b - 98a b - 28a b )cos(x) - 15a b +--R + +--R 3 5 4 4 5 3 6 2 +--R - 72a b - 127a b - 98a b - 28a b +--R * +--R 2 2 +--R csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 17 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 4 4 5 3 6 2 16 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 15 +--R (40a b - 8a b - 136a b + 104a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 14 +--R (40a b - 8a b - 136a b + 104a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 13 +--R (- 33a b - 76a b + 202a b + 180a b - 289a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 12 +--R (- 33a b - 76a b + 202a b + 180a b - 289a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 11 +--R (9a b + 68a b - 40a b - 394a b + 23a b + 446a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 10 +--R (9a b + 68a b - 40a b - 394a b + 23a b + 446a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 15a b - 28a b + 176a b + 273a b - 295a b - 415a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 15a b - 28a b + 176a b + 273a b - 295a b - 415a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R (7a b - 18a b - 127a b - 16a b + 318a b + 236a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 6 +--R (7a b - 18a b - 127a b - 16a b + 318a b + 236a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 5 +--R (- a b + 13a b + 25a b - 64a b - 154a b - 79a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 4 +--R (- a b + 13a b + 25a b - 64a b - 154a b - 79a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 3 +--R (- 2a b + 3a b + 26a b + 35a b + 14a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (- 2a b + 3a b + 26a b + 35a b + 14a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 3 5 4 4 5 3 6 2 +--R (- a b - 3a b - 3a b - a b )cos(x) - a b - 3a b - 3a b - a b +--R * +--R 2 +--R csc(x) +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 4 5 3 6 2 7 10 +--R (- 128a b - 512a b - 640a b - 256a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (288a b + 1632a b + 3296a b + 2848a b + 896a b) +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 208a b - 1648a b - 4864a b - 6784a b - 4528a b +--R + +--R 7 +--R - 1168a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 52a b + 628a b + 2680a b + 5480a b + 5860a b +--R + +--R 6 2 7 +--R 3172a b + 688a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 4b - 92a b - 576a b - 1640a b - 2500a b +--R + +--R 5 3 6 2 7 +--R - 2124a b - 952a b - 176a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 4b + 40a b + 156a b + 320a b + 380a b + 264a b +--R + +--R 6 2 7 +--R 100a b + 16a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 3 6 2 7 8 10 +--R (- 128a b - 512a b - 640a b - 256a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 8 +--R (288a b + 1632a b + 3296a b + 2848a b + 896a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R - 208a b - 1648a b - 4864a b - 6784a b - 4528a b +--R + +--R 8 +--R - 1168a +--R * +--R 6 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 52a b + 628a b + 2680a b + 5480a b + 5860a b +--R + +--R 7 8 +--R 3172a b + 688a +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 4a b - 92a b - 576a b - 1640a b - 2500a b +--R + +--R 6 2 7 8 +--R - 2124a b - 952a b - 176a +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 4a b + 40a b + 156a b + 320a b + 380a b + 264a b +--R + +--R 7 8 +--R 100a b + 16a +--R * +--R 7 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 12 +--R (- 128a b + 768a b + 2688a b + 1792a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (224a b - 2144a b - 12000a b - 17696a b - 8064a b) +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 +--R - 80a b + 2544a b + 18464a b + 43168a b +--R + +--R 6 2 7 +--R 41776a b + 14448a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 20a b - 1420a b - 12608a b - 41728a b +--R + +--R 5 3 6 2 7 +--R - 64204a b - 46676a b - 12992a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 4b + 288a b + 3708a b + 17304a b + 38532a b +--R + +--R 5 3 6 2 7 +--R 44616a b + 26012a b + 6048a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 16b - 412a b - 2860a b - 8984a b - 15016a b +--R + +--R 5 3 6 2 7 +--R - 13900a b - 6748a b - 1344a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 12b + 144a b + 652a b + 1520a b + 2020a b + 1552a b +--R + +--R 6 2 7 +--R 644a b + 112a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 3 6 2 7 8 12 +--R (- 128a b + 768a b + 2688a b + 1792a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 10 +--R (224a b - 2144a b - 12000a b - 17696a b - 8064a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R - 80a b + 2544a b + 18464a b + 43168a b + 41776a b +--R + +--R 8 +--R 14448a +--R * +--R 8 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 20a b - 1420a b - 12608a b - 41728a b - 64204a b +--R + +--R 7 8 +--R - 46676a b - 12992a +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 4a b + 288a b + 3708a b + 17304a b + 38532a b +--R + +--R 6 2 7 8 +--R 44616a b + 26012a b + 6048a +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 16a b - 412a b - 2860a b - 8984a b - 15016a b +--R + +--R 6 2 7 8 +--R - 13900a b - 6748a b - 1344a +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 12a b + 144a b + 652a b + 1520a b + 2020a b + 1552a b +--R + +--R 7 8 +--R 644a b + 112a +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 14 +--R (128a b + 1024a b - 896a b - 1792a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 416a b - 3552a b - 1120a b + 11872a b + 9856a b) +--R * +--R 12 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 464a b + 4528a b + 6464a b - 17984a b - 42896a b +--R + +--R 7 +--R - 22512a b +--R * +--R 10 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 +--R - 196a b - 2484a b - 6536a b + 10920a b +--R + +--R 5 3 6 2 7 +--R 59100a b + 71372a b + 27440a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 20b + 524a b + 2376a b - 3408a b - 36540a b +--R + +--R 5 3 6 2 7 +--R - 74828a b - 62608a b - 19040a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 36b - 336a b + 596a b + 10676a b + 32904a b +--R + +--R 5 3 6 2 7 +--R 45020a b + 29288a b + 7392a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 16b - 32a b - 1252a b - 5756a b - 11772a b +--R + +--R 5 3 6 2 7 +--R - 12484a b - 6720a b - 1456a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 40a b + 300a b + 912a b + 1448a b + 1272a b +--R + +--R 6 2 7 +--R 588a b + 112a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 3 6 2 7 8 14 +--R (128a b + 1024a b - 896a b - 1792a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 12 +--R (- 416a b - 3552a b - 1120a b + 11872a b + 9856a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 464a b + 4528a b + 6464a b - 17984a b - 42896a b +--R + +--R 8 +--R - 22512a +--R * +--R 10 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 196a b - 2484a b - 6536a b + 10920a b + 59100a b +--R + +--R 7 8 +--R 71372a b + 27440a +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 20a b + 524a b + 2376a b - 3408a b - 36540a b +--R + +--R 6 2 7 8 +--R - 74828a b - 62608a b - 19040a +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 36a b - 336a b + 596a b + 10676a b + 32904a b +--R + +--R 6 2 7 8 +--R 45020a b + 29288a b + 7392a +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 16a b - 32a b - 1252a b - 5756a b - 11772a b +--R + +--R 6 2 7 8 +--R - 12484a b - 6720a b - 1456a +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 40a b + 300a b + 912a b + 1448a b + 1272a b + 588a b +--R + +--R 8 +--R 112a +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 16 +--R (128a b - 256a b - 128a b + 256a b)cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R (- 352a b + 224a b + 1888a b - 352a b - 1664a b) +--R * +--R 14 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 336a b + 336a b - 3296a b - 3680a b + 4240a b +--R + +--R 7 +--R 4624a b +--R * +--R 12 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 124a b - 436a b + 2096a b + 6800a b + 12a b +--R + +--R 6 2 7 +--R - 11516a b - 7136a b +--R * +--R 10 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 12b + 144a b - 548a b - 4192a b - 4036a b +--R + +--R 5 3 6 2 7 +--R 8096a b + 15260a b + 6640a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 16b + 36a b + 1012a b + 2276a b - 1916a b +--R + +--R 5 3 6 2 7 +--R - 10648a b - 11192a b - 3776a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 4b - 72a b - 376a b + 136a b + 3116a b +--R + +--R 5 3 6 2 7 +--R 5968a b + 4552a b + 1264a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 3 5 4 4 5 3 6 2 +--R 16a b - 364a b - 1156a b - 1524a b - 940a b +--R + +--R 7 +--R - 224a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R 12a b + 64a b + 136a b + 144a b + 76a b + 16a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 3 6 2 7 8 16 +--R (128a b - 256a b - 128a b + 256a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 14 +--R (- 352a b + 224a b + 1888a b - 352a b - 1664a )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 +--R 336a b + 336a b - 3296a b - 3680a b + 4240a b +--R + +--R 8 +--R 4624a +--R * +--R 12 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 124a b - 436a b + 2096a b + 6800a b + 12a b +--R + +--R 7 8 +--R - 11516a b - 7136a +--R * +--R 10 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 12a b + 144a b - 548a b - 4192a b - 4036a b +--R + +--R 6 2 7 8 +--R 8096a b + 15260a b + 6640a +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 16a b + 36a b + 1012a b + 2276a b - 1916a b +--R + +--R 6 2 7 8 +--R - 10648a b - 11192a b - 3776a +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 4a b - 72a b - 376a b + 136a b + 3116a b + 5968a b +--R + +--R 7 8 +--R 4552a b + 1264a +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 4 4 5 3 6 2 7 8 +--R (16a b - 364a b - 1156a b - 1524a b - 940a b - 224a ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 5 4 4 5 3 6 2 7 8 +--R 12a b + 64a b + 136a b + 144a b + 76a b + 16a +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 4 5 3 6 2 10 +--R (128a b + 384a b + 256a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 8 +--R (- 288a b - 1344a b - 1952a b - 896a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 6 +--R (208a b + 1440a b + 3424a b + 3360a b + 1168a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 52a b - 576a b - 2104a b - 3376a b - 2484a b +--R + +--R 6 2 +--R - 688a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 4b + 88a b + 488a b + 1152a b + 1348a b + 776a b +--R + +--R 6 2 +--R 176a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 4b - 36a b - 120a b - 200a b - 180a b - 84a b - 16a b +--R * +--R 2 7 +--R cot(x)csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 12 +--R (128a b - 896a b - 1792a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 10 +--R (- 224a b + 2368a b + 9632a b + 8064a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (80a b - 2624a b - 15840a b - 27328a b - 14448a b ) +--R * +--R 8 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 20a b + 1400a b + 11208a b + 30520a b + 33684a b +--R + +--R 6 2 +--R 12992a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 4b - 284a b - 3424a b - 13880a b - 24652a b +--R + +--R 5 3 6 2 +--R - 19964a b - 6048a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 16b + 396a b + 2464a b + 6520a b + 8496a b +--R + +--R 5 3 6 2 +--R 5404a b + 1344a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 12b - 132a b - 520a b - 1000a b - 1020a b - 532a b +--R + +--R 6 2 +--R - 112a b +--R * +--R 2 5 +--R cot(x)csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 14 +--R (- 128a b - 896a b + 1792a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 12 +--R (416a b + 3136a b - 2016a b - 9856a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R (- 464a b - 4064a b - 2400a b + 20384a b + 22512a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 196a b + 2288a b + 4248a b - 15168a b - 43932a b +--R + +--R 6 2 +--R - 27440a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 20b - 504a b - 1872a b + 5280a b + 31260a b +--R + +--R 5 3 6 2 +--R 43568a b + 19040a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R 36b + 300a b - 896a b - 9780a b - 23124a b +--R + +--R 5 3 6 2 +--R - 21896a b - 7392a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 16b + 48a b + 1204a b + 4552a b + 7220a b +--R + +--R 5 3 6 2 +--R 5264a b + 1456a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 40a b - 260a b - 652a b - 796a b - 476a b - 112a b +--R * +--R 2 3 +--R cot(x)csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 16 +--R (- 128a b + 384a b - 256a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 14 +--R (352a b - 576a b - 1312a b + 1664a b )cos(x) +--R + +--R 2 6 4 4 5 3 6 2 12 +--R (- 336a b + 3296a b + 384a b - 4624a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R 124a b + 312a b - 2408a b - 4392a b + 4380a b +--R + +--R 6 2 +--R 7136a b +--R * +--R 10 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 +--R - 12b - 132a b + 680a b + 3512a b + 524a b +--R + +--R 5 3 6 2 +--R - 8620a b - 6640a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 16b - 52a b - 960a b - 1316a b + 3232a b + 7416a b +--R + +--R 6 2 +--R 3776a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 4b + 76a b + 300a b - 436a b - 2680a b - 3288a b +--R + +--R 6 2 +--R - 1264a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (- 16a b + 16a b + 348a b + 808a b + 716a b + 224a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 12a b - 52a b - 84a b - 60a b - 16a b +--R * +--R 2 +--R cot(x)csc(x) sin(x) +--R * +--R tan(x) +--R + +--R 4 4 5 3 6 2 10 +--R (- 128a b - 384a b - 256a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 8 +--R (288a b + 1344a b + 1952a b + 896a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 6 +--R (- 208a b - 1440a b - 3424a b - 3360a b - 1168a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R (52a b + 576a b + 2104a b + 3376a b + 2484a b + 688a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 4b - 88a b - 488a b - 1152a b - 1348a b - 776a b +--R + +--R 6 2 +--R - 176a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 4b + 36a b + 120a b + 200a b + 180a b + 84a b + 16a b +--R * +--R 2 7 +--R csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 12 +--R (- 128a b + 896a b + 1792a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 10 +--R (224a b - 2368a b - 9632a b - 8064a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 8 +--R (- 80a b + 2624a b + 15840a b + 27328a b + 14448a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 20a b - 1400a b - 11208a b - 30520a b - 33684a b +--R + +--R 6 2 +--R - 12992a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 4b + 284a b + 3424a b + 13880a b + 24652a b + 19964a b +--R + +--R 6 2 +--R 6048a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 16b - 396a b - 2464a b - 6520a b - 8496a b - 5404a b +--R + +--R 6 2 +--R - 1344a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 12b + 132a b + 520a b + 1000a b + 1020a b + 532a b + 112a b +--R * +--R 2 5 +--R csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 14 +--R (128a b + 896a b - 1792a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 12 +--R (- 416a b - 3136a b + 2016a b + 9856a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 10 +--R (464a b + 4064a b + 2400a b - 20384a b - 22512a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 196a b - 2288a b - 4248a b + 15168a b + 43932a b +--R + +--R 6 2 +--R 27440a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 20b + 504a b + 1872a b - 5280a b - 31260a b - 43568a b +--R + +--R 6 2 +--R - 19040a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 36b - 300a b + 896a b + 9780a b + 23124a b + 21896a b +--R + +--R 6 2 +--R 7392a b +--R * +--R 4 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 16b - 48a b - 1204a b - 4552a b - 7220a b - 5264a b +--R + +--R 6 2 +--R - 1456a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 40a b + 260a b + 652a b + 796a b + 476a b + 112a b +--R * +--R 2 3 +--R csc(x) sin(x) +--R + +--R 4 4 5 3 6 2 16 +--R (128a b - 384a b + 256a b )cos(x) +--R + +--R 3 5 4 4 5 3 6 2 14 +--R (- 352a b + 576a b + 1312a b - 1664a b )cos(x) +--R + +--R 2 6 4 4 5 3 6 2 12 +--R (336a b - 3296a b - 384a b + 4624a b )cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 124a b - 312a b + 2408a b + 4392a b - 4380a b +--R + +--R 6 2 +--R - 7136a b +--R * +--R 10 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 12b + 132a b - 680a b - 3512a b - 524a b + 8620a b +--R + +--R 6 2 +--R 6640a b +--R * +--R 8 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 16b + 52a b + 960a b + 1316a b - 3232a b - 7416a b +--R + +--R 6 2 +--R - 3776a b +--R * +--R 6 +--R cos(x) +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 4b - 76a b - 300a b + 436a b + 2680a b + 3288a b +--R + +--R 6 2 +--R 1264a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 +--R (16a b - 16a b - 348a b - 808a b - 716a b - 224a b )cos(x) +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R 12a b + 52a b + 84a b + 60a b + 16a b +--R * +--R 2 +--R csc(x) sin(x) +--R * +--R +-+ +--R \|a +--R / +--R 4 3 5 2 6 9 +--R (16a b + 32a b + 16a b)cos(x) +--R + +--R 4 3 5 2 6 8 +--R (16a b + 32a b + 16a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (- 24a b - 88a b - 104a b - 40a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 24a b - 88a b - 104a b - 40a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 5 +--R (9a b + 60a b + 126a b + 108a b + 33a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (9a b + 60a b + 126a b + 108a b + 33a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- a b - 14a b - 46a b - 64a b - 41a b - 10a b) +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- a b - 14a b - 46a b - 64a b - 41a b - 10a b) +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (a b + 5a b + 10a b + 10a b + 5a b + a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R a b + 5a b + 10a b + 10a b + 5a b + a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 9 +--R (16a b + 32a b + 16a )cos(x) +--R + +--R 5 2 6 7 8 +--R (16a b + 32a b + 16a )cos(x) +--R + +--R 4 3 5 2 6 7 7 +--R (- 24a b - 88a b - 104a b - 40a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 24a b - 88a b - 104a b - 40a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 5 +--R (9a b + 60a b + 126a b + 108a b + 33a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (9a b + 60a b + 126a b + 108a b + 33a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 3 +--R (- a b - 14a b - 46a b - 64a b - 41a b - 10a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 2 +--R (- a b - 14a b - 46a b - 64a b - 41a b - 10a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 2 5 +--R (a b + 5a b + 10a b + 10a b + 5a b + a )cos(x) + a b +--R + +--R 3 4 4 3 5 2 6 7 +--R 5a b + 10a b + 10a b + 5a b + a +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 5 2 6 11 +--R (- 64a b - 448a b - 448a b)cos(x) +--R + +--R 4 3 5 2 6 10 +--R (- 64a b - 448a b - 448a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 9 +--R (144a b + 1216a b + 2576a b + 1568a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 8 +--R (144a b + 1216a b + 2576a b + 1568a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 100a b - 1072a b - 3632a b - 4704a b +--R + +--R 6 +--R - 2044a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 100a b - 1072a b - 3632a b - 4704a b +--R + +--R 6 +--R - 2044a b +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 20a b + 342a b + 1814a b + 3886a b + 3598a b +--R + +--R 6 +--R 1204a b +--R * +--R 5 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 20a b + 342a b + 1814a b + 3886a b + 3598a b +--R + +--R 6 +--R 1204a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - b - 38a b - 332a b - 1086a b - 1631a b +--R + +--R 5 2 6 +--R - 1148a b - 308a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - b - 38a b - 332a b - 1086a b - 1631a b +--R + +--R 5 2 6 +--R - 1148a b - 308a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R b + 18a b + 90a b + 200a b + 225a b + 126a b +--R + +--R 6 +--R 28a b +--R * +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R b + 18a b + 90a b + 200a b + 225a b + 126a b +--R + +--R 6 +--R 28a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 11 +--R (- 64a b - 448a b - 448a )cos(x) +--R + +--R 5 2 6 7 10 +--R (- 64a b - 448a b - 448a )cos(x) +--R + +--R 4 3 5 2 6 7 9 +--R (144a b + 1216a b + 2576a b + 1568a )cos(x) +--R + +--R 4 3 5 2 6 7 8 +--R (144a b + 1216a b + 2576a b + 1568a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 7 +--R (- 100a b - 1072a b - 3632a b - 4704a b - 2044a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 6 +--R (- 100a b - 1072a b - 3632a b - 4704a b - 2044a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R 20a b + 342a b + 1814a b + 3886a b + 3598a b +--R + +--R 7 +--R 1204a +--R * +--R 5 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R 20a b + 342a b + 1814a b + 3886a b + 3598a b +--R + +--R 7 +--R 1204a +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - a b - 38a b - 332a b - 1086a b - 1631a b +--R + +--R 6 7 +--R - 1148a b - 308a +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - a b - 38a b - 332a b - 1086a b - 1631a b +--R + +--R 6 7 +--R - 1148a b - 308a +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R a b + 18a b + 90a b + 200a b + 225a b + 126a b +--R + +--R 7 +--R 28a +--R * +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R a b + 18a b + 90a b + 200a b + 225a b + 126a b + 28a +--R * +--R 6 +--R sin(x) +--R + +--R 4 3 6 13 +--R (- 160a b + 1120a b)cos(x) +--R + +--R 4 3 6 12 +--R (- 160a b + 1120a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 11 +--R (320a b + 400a b - 3360a b - 5040a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 10 +--R (320a b + 400a b - 3360a b - 5040a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 194a b - 520a b + 3420a b + 12040a b +--R + +--R 6 +--R 9030a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 194a b - 520a b + 3420a b + 12040a b +--R + +--R 6 +--R 9030a b +--R * +--R 8 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 34a b + 178a b - 1650a b - 10010a b - 16240a b +--R + +--R 6 +--R - 8120a b +--R * +--R 7 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 34a b + 178a b - 1650a b - 10010a b - 16240a b +--R + +--R 6 +--R - 8120a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2b - 28a b + 349a b + 3470a b + 9395a b +--R + +--R 5 2 6 +--R 10080a b + 3780a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2b - 28a b + 349a b + 3470a b + 9395a b +--R + +--R 5 2 6 +--R 10080a b + 3780a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 2b - 21a b - 448a b - 1945a b - 3480a b +--R + +--R 5 2 6 +--R - 2800a b - 840a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 2b - 21a b - 448a b - 1945a b - 3480a b +--R + +--R 5 2 6 +--R - 2800a b - 840a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 15a b + 115a b + 325a b + 435a b + 280a b +--R + +--R 6 +--R 70a b +--R * +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 15a b + 115a b + 325a b + 435a b + 280a b + 70a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 7 13 5 2 7 12 +--R (- 160a b + 1120a )cos(x) + (- 160a b + 1120a )cos(x) +--R + +--R 4 3 5 2 6 7 11 +--R (320a b + 400a b - 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448a )cos(x) +--R + +--R 5 2 6 7 14 +--R (- 64a b + 448a b - 448a )cos(x) +--R + +--R 4 3 5 2 6 7 13 +--R (112a b - 896a b - 784a b + 2464a )cos(x) +--R + +--R 4 3 5 2 6 7 12 +--R (112a b - 896a b - 784a b + 2464a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 11 +--R (- 52a b + 688a b + 2496a b - 2016a b - 5628a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 10 +--R (- 52a b + 688a b + 2496a b - 2016a b - 5628a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 246a b - 1870a b - 766a b + 7042a b + 6860a ) +--R * +--R 9 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 246a b - 1870a b - 766a b + 7042a b + 6860a ) +--R * +--R 8 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - a b + 26a b + 514a b + 950a b - 2885a b +--R + +--R 6 7 +--R - 8008a b - 4760a +--R * +--R 7 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - a b + 26a b + 514a b + 950a b - 2885a b +--R + +--R 6 7 +--R - 8008a b - 4760a +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R a b - 42a b - 208a b + 470a b + 3075a b + 4284a b +--R + +--R 7 +--R 1848a +--R * +--R 5 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R a b - 42a b - 208a b + 470a b + 3075a b + 4284a b +--R + +--R 7 +--R 1848a +--R * +--R 4 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (12a b - 23a b - 422a b - 1087a b - 1064a b - 364a ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (12a b - 23a b - 422a b - 1087a b - 1064a b - 364a ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 4 4 3 5 2 6 7 3 4 +--R (15a b + 72a b + 127a b + 98a b + 28a )cos(x) + 15a b +--R + +--R 4 3 5 2 6 7 +--R 72a b + 127a b + 98a b + 28a +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 5 2 6 17 +--R (16a b - 32a b + 16a b)cos(x) +--R + +--R 4 3 5 2 6 16 +--R (16a b - 32a b + 16a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 15 +--R (- 40a b + 8a b + 136a b - 104a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 14 +--R (- 40a b + 8a b + 136a b - 104a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 13 +--R (33a b + 76a b - 202a b - 180a b + 289a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 12 +--R (33a b + 76a b - 202a b - 180a b + 289a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 9a b - 68a b + 40a b + 394a b - 23a b - 446a b) +--R * +--R 11 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 9a b - 68a b + 40a b + 394a b - 23a b - 446a b) +--R * +--R 10 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (15a b + 28a b - 176a b - 273a b + 295a b + 415a b) +--R * +--R 9 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (15a b + 28a b - 176a b - 273a b + 295a b + 415a b) +--R * +--R 8 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 7a b + 18a b + 127a b + 16a b - 318a b - 236a b) +--R * +--R 7 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 7a b + 18a b + 127a b + 16a b - 318a b - 236a b) +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 5 +--R (a b - 13a b - 25a b + 64a b + 154a b + 79a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 4 +--R (a b - 13a b - 25a b + 64a b + 154a b + 79a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (2a b - 3a b - 26a b - 35a b - 14a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 +--R (2a b - 3a b - 26a b - 35a b - 14a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 3 4 4 3 5 2 +--R (a b + 3a b + 3a b + a b)cos(x) + a b + 3a b + 3a b +--R + +--R 6 +--R a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 17 +--R (16a b - 32a b + 16a )cos(x) +--R + +--R 5 2 6 7 16 +--R (16a b - 32a b + 16a )cos(x) +--R + +--R 4 3 5 2 6 7 15 +--R (- 40a b + 8a b + 136a b - 104a )cos(x) +--R + +--R 4 3 5 2 6 7 14 +--R (- 40a b + 8a b + 136a b - 104a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 13 +--R (33a b + 76a b - 202a b - 180a b + 289a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 12 +--R (33a b + 76a b - 202a b - 180a b + 289a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 11 +--R (- 9a b - 68a b + 40a b + 394a b - 23a b - 446a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 10 +--R (- 9a b - 68a b + 40a b + 394a b - 23a b - 446a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 9 +--R (15a b + 28a b - 176a b - 273a b + 295a b + 415a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 8 +--R (15a b + 28a b - 176a b - 273a b + 295a b + 415a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 7 +--R (- 7a b + 18a b + 127a b + 16a b - 318a b - 236a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 +--R (- 7a b + 18a b + 127a b + 16a b - 318a b - 236a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 5 +--R (a b - 13a b - 25a b + 64a b + 154a b + 79a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 4 +--R (a b - 13a b - 25a b + 64a b + 154a b + 79a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (2a b - 3a b - 26a b - 35a b - 14a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 2 +--R (2a b - 3a b - 26a b - 35a b - 14a )cos(x) +--R + +--R 4 3 5 2 6 7 4 3 5 2 6 7 +--R (a b + 3a b + 3a b + a )cos(x) + a b + 3a b + 3a b + a +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 5 2 6 9 +--R (- 16a b - 32a b - 16a b)cos(x) +--R + +--R 4 3 5 2 6 8 +--R (- 16a b - 32a b - 16a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (24a b + 88a b + 104a b + 40a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (24a b + 88a b + 104a b + 40a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 5 +--R (- 9a b - 60a b - 126a b - 108a b - 33a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 4 +--R (- 9a b - 60a b - 126a b - 108a b - 33a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 3 +--R (a b + 14a b + 46a b + 64a b + 41a b + 10a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 +--R (a b + 14a b + 46a b + 64a b + 41a b + 10a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 6 +--R (- a b - 5a b - 10a b - 10a b - 5a b - a b)cos(x) - a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 5a b - 10a b - 10a b - 5a b - a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 5 2 6 11 +--R (64a b + 448a b + 448a b)cos(x) +--R + +--R 4 3 5 2 6 10 +--R (64a b + 448a b + 448a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 9 +--R (- 144a b - 1216a b - 2576a b - 1568a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 8 +--R (- 144a b - 1216a b - 2576a b - 1568a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (100a b + 1072a b + 3632a b + 4704a b + 2044a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (100a b + 1072a b + 3632a b + 4704a b + 2044a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 20a b - 342a b - 1814a b - 3886a b - 3598a b +--R + +--R 6 +--R - 1204a b +--R * +--R 5 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 20a b - 342a b - 1814a b - 3886a b - 3598a b +--R + +--R 6 +--R - 1204a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R b + 38a b + 332a b + 1086a b + 1631a b + 1148a b +--R + +--R 6 +--R 308a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R b + 38a b + 332a b + 1086a b + 1631a b + 1148a b +--R + +--R 6 +--R 308a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - b - 18a b - 90a b - 200a b - 225a b - 126a b +--R + +--R 6 +--R - 28a b +--R * +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - b - 18a b - 90a b - 200a b - 225a b - 126a b - 28a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 3 6 13 4 3 6 12 +--R (160a b - 1120a b)cos(x) + (160a b - 1120a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 11 +--R (- 320a b - 400a b + 3360a b + 5040a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 10 +--R (- 320a b - 400a b + 3360a b + 5040a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 9 +--R (194a b + 520a b - 3420a b - 12040a b - 9030a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 8 +--R (194a b + 520a b - 3420a b - 12040a b - 9030a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 34a b - 178a b + 1650a b + 10010a b + 16240a b +--R + +--R 6 +--R 8120a b +--R * +--R 7 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 34a b - 178a b + 1650a b + 10010a b + 16240a b +--R + +--R 6 +--R 8120a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 2b + 28a b - 349a b - 3470a b - 9395a b - 10080a b +--R + +--R 6 +--R - 3780a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 2b + 28a b - 349a b - 3470a b - 9395a b - 10080a b +--R + +--R 6 +--R - 3780a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 2b + 21a b + 448a b + 1945a b + 3480a b + 2800a b +--R + +--R 6 +--R 840a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 2b + 21a b + 448a b + 1945a b + 3480a b + 2800a b +--R + +--R 6 +--R 840a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 15a b - 115a b - 325a b - 435a b - 280a b - 70a b) +--R * +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 15a b - 115a b - 325a b - 435a b - 280a b - 70a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 5 2 6 15 +--R (64a b - 448a b + 448a b)cos(x) +--R + +--R 4 3 5 2 6 14 +--R (64a b - 448a b + 448a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 13 +--R (- 112a b + 896a b + 784a b - 2464a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 12 +--R (- 112a b + 896a b + 784a b - 2464a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 11 +--R (52a b - 688a b - 2496a b + 2016a b + 5628a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 10 +--R (52a b - 688a b - 2496a b + 2016a b + 5628a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 4a b + 246a b + 1870a b + 766a b - 7042a b - 6860a b) +--R * +--R 9 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 4a b + 246a b + 1870a b + 766a b - 7042a b - 6860a b) +--R * +--R 8 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R b - 26a b - 514a b - 950a b + 2885a b + 8008a b +--R + +--R 6 +--R 4760a b +--R * +--R 7 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R b - 26a b - 514a b - 950a b + 2885a b + 8008a b +--R + +--R 6 +--R 4760a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - b + 42a b + 208a b - 470a b - 3075a b - 4284a b +--R + +--R 6 +--R - 1848a b +--R * +--R 5 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - b + 42a b + 208a b - 470a b - 3075a b - 4284a b +--R + +--R 6 +--R - 1848a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 12a b + 23a b + 422a b + 1087a b + 1064a b + 364a b) +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (- 12a b + 23a b + 422a b + 1087a b + 1064a b + 364a b) +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 5 +--R (- 15a b - 72a b - 127a b - 98a b - 28a b)cos(x) - 15a b +--R + +--R 3 4 4 3 5 2 6 +--R - 72a b - 127a b - 98a b - 28a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 5 2 6 17 +--R (- 16a b + 32a b - 16a b)cos(x) +--R + +--R 4 3 5 2 6 16 +--R (- 16a b + 32a b - 16a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 15 +--R (40a b - 8a b - 136a b + 104a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 14 +--R (40a b - 8a b - 136a b + 104a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 13 +--R (- 33a b - 76a b + 202a b + 180a b - 289a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 12 +--R (- 33a b - 76a b + 202a b + 180a b - 289a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 11 +--R (9a b + 68a b - 40a b - 394a b + 23a b + 446a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 10 +--R (9a b + 68a b - 40a b - 394a b + 23a b + 446a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 9 +--R (- 15a b - 28a b + 176a b + 273a b - 295a b - 415a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 8 +--R (- 15a b - 28a b + 176a b + 273a b - 295a b - 415a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (7a b - 18a b - 127a b - 16a b + 318a b + 236a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 6 +--R (7a b - 18a b - 127a b - 16a b + 318a b + 236a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 5 +--R (- a b + 13a b + 25a b - 64a b - 154a b - 79a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 4 +--R (- a b + 13a b + 25a b - 64a b - 154a b - 79a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 3 +--R (- 2a b + 3a b + 26a b + 35a b + 14a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 2 +--R (- 2a b + 3a b + 26a b + 35a b + 14a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 3 4 4 3 5 2 6 +--R (- a b - 3a b - 3a b - a b)cos(x) - a b - 3a b - 3a b - a b +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 3 5 2 6 10 +--R (128a b + 384a b + 256a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 8 +--R (- 288a b - 1344a b - 1952a b - 896a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (208a b + 1440a b + 3424a b + 3360a b + 1168a b) +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 52a b - 576a b - 2104a b - 3376a b - 2484a b +--R + +--R 6 +--R - 688a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 4b + 88a b + 488a b + 1152a b + 1348a b +--R + +--R 5 2 6 +--R 776a b + 176a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 4b - 36a b - 120a b - 200a b - 180a b - 84a b +--R + +--R 6 +--R - 16a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 10 +--R (128a b + 384a b + 256a )cos(x) +--R + +--R 4 3 5 2 6 7 8 +--R (- 288a b - 1344a b - 1952a b - 896a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 6 +--R (208a b + 1440a b + 3424a b + 3360a b + 1168a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 52a b - 576a b - 2104a b - 3376a b - 2484a b +--R + +--R 7 +--R - 688a +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 4a b + 88a b + 488a b + 1152a b + 1348a b + 776a b +--R + +--R 7 +--R 176a +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R - 4a b - 36a b - 120a b - 200a b - 180a b - 84a b - 16a +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 5 2 6 12 +--R (128a b - 896a b - 1792a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 10 +--R (- 224a b + 2368a b + 9632a b + 8064a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R 80a b - 2624a b - 15840a b - 27328a b +--R + +--R 6 +--R - 14448a b +--R * +--R 8 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 +--R 20a b + 1400a b + 11208a b + 30520a b +--R + +--R 5 2 6 +--R 33684a b + 12992a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 4b - 284a b - 3424a b - 13880a b - 24652a b +--R + +--R 5 2 6 +--R - 19964a b - 6048a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 16b + 396a b + 2464a b + 6520a b + 8496a b +--R + +--R 5 2 6 +--R 5404a b + 1344a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 12b - 132a b - 520a b - 1000a b - 1020a b +--R + +--R 5 2 6 +--R - 532a b - 112a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 12 +--R (128a b - 896a b - 1792a )cos(x) +--R + +--R 4 3 5 2 6 7 10 +--R (- 224a b + 2368a b + 9632a b + 8064a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 8 +--R (80a b - 2624a b - 15840a b - 27328a b - 14448a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R 20a b + 1400a b + 11208a b + 30520a b + 33684a b +--R + +--R 7 +--R 12992a +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 4a b - 284a b - 3424a b - 13880a b - 24652a b +--R + +--R 6 7 +--R - 19964a b - 6048a +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 16a b + 396a b + 2464a b + 6520a b + 8496a b +--R + +--R 6 7 +--R 5404a b + 1344a +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 12a b - 132a b - 520a b - 1000a b - 1020a b - 532a b +--R + +--R 7 +--R - 112a +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 5 2 6 14 +--R (- 128a b - 896a b + 1792a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 12 +--R (416a b + 3136a b - 2016a b - 9856a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R - 464a b - 4064a b - 2400a b + 20384a b +--R + +--R 6 +--R 22512a b +--R * +--R 10 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 +--R 196a b + 2288a b + 4248a b - 15168a b +--R + +--R 5 2 6 +--R - 43932a b - 27440a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 20b - 504a b - 1872a b + 5280a b + 31260a b +--R + +--R 5 2 6 +--R 43568a b + 19040a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 36b + 300a b - 896a b - 9780a b - 23124a b +--R + +--R 5 2 6 +--R - 21896a b - 7392a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 16b + 48a b + 1204a b + 4552a b + 7220a b +--R + +--R 5 2 6 +--R 5264a b + 1456a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 40a b - 260a b - 652a b - 796a b - 476a b - 112a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 14 +--R (- 128a b - 896a b + 1792a )cos(x) +--R + +--R 4 3 5 2 6 7 12 +--R (416a b + 3136a b - 2016a b - 9856a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R (- 464a b - 4064a b - 2400a b + 20384a b + 22512a ) +--R * +--R 10 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R 196a b + 2288a b + 4248a b - 15168a b - 43932a b +--R + +--R 7 +--R - 27440a +--R * +--R 8 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 20a b - 504a b - 1872a b + 5280a b + 31260a b +--R + +--R 6 7 +--R 43568a b + 19040a +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 36a b + 300a b - 896a b - 9780a b - 23124a b +--R + +--R 6 7 +--R - 21896a b - 7392a +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 16a b + 48a b + 1204a b + 4552a b + 7220a b +--R + +--R 6 7 +--R 5264a b + 1456a +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R - 40a b - 260a b - 652a b - 796a b - 476a b - 112a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 5 2 6 16 +--R (- 128a b + 384a b - 256a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 14 +--R (352a b - 576a b - 1312a b + 1664a b)cos(x) +--R + +--R 2 5 4 3 5 2 6 12 +--R (- 336a b + 3296a b + 384a b - 4624a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 124a b + 312a b - 2408a b - 4392a b + 4380a b +--R + +--R 6 +--R 7136a b +--R * +--R 10 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 12b - 132a b + 680a b + 3512a b + 524a b +--R + +--R 5 2 6 +--R - 8620a b - 6640a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 16b - 52a b - 960a b - 1316a b + 3232a b +--R + +--R 5 2 6 +--R 7416a b + 3776a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 4b + 76a b + 300a b - 436a b - 2680a b +--R + +--R 5 2 6 +--R - 3288a b - 1264a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 16a b + 16a b + 348a b + 808a b + 716a b +--R + +--R 6 +--R 224a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 12a b - 52a b - 84a b - 60a b - 16a b +--R * +--R 2 +--R csc(x) +--R + +--R 5 2 6 7 16 +--R (- 128a b + 384a b - 256a )cos(x) +--R + +--R 4 3 5 2 6 7 14 +--R (352a b - 576a b - 1312a b + 1664a )cos(x) +--R + +--R 3 4 5 2 6 7 12 +--R (- 336a b + 3296a b + 384a b - 4624a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R 124a b + 312a b - 2408a b - 4392a b + 4380a b +--R + +--R 7 +--R 7136a +--R * +--R 10 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 12a b - 132a b + 680a b + 3512a b + 524a b +--R + +--R 6 7 +--R - 8620a b - 6640a +--R * +--R 8 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 16a b - 52a b - 960a b - 1316a b + 3232a b +--R + +--R 6 7 +--R 7416a b + 3776a +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 4a b + 76a b + 300a b - 436a b - 2680a b +--R + +--R 6 7 +--R - 3288a b - 1264a +--R * +--R 4 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (- 16a b + 16a b + 348a b + 808a b + 716a b + 224a ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 4 4 3 5 2 6 7 +--R - 12a b - 52a b - 84a b - 60a b - 16a +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 5 2 6 10 +--R (- 128a b - 384a b - 256a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 8 +--R (288a b + 1344a b + 1952a b + 896a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (- 208a b - 1440a b - 3424a b - 3360a b - 1168a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R (52a b + 576a b + 2104a b + 3376a b + 2484a b + 688a b) +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 4b - 88a b - 488a b - 1152a b - 1348a b - 776a b +--R + +--R 6 +--R - 176a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 4b + 36a b + 120a b + 200a b + 180a b + 84a b + 16a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 5 2 6 12 +--R (- 128a b + 896a b + 1792a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 10 +--R (224a b - 2368a b - 9632a b - 8064a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 8 +--R (- 80a b + 2624a b + 15840a b + 27328a b + 14448a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 20a b - 1400a b - 11208a b - 30520a b - 33684a b +--R + +--R 6 +--R - 12992a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 4b + 284a b + 3424a b + 13880a b + 24652a b +--R + +--R 5 2 6 +--R 19964a b + 6048a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 16b - 396a b - 2464a b - 6520a b - 8496a b +--R + +--R 5 2 6 +--R - 5404a b - 1344a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 12b + 132a b + 520a b + 1000a b + 1020a b + 532a b + 112a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 5 2 6 14 +--R (128a b + 896a b - 1792a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 12 +--R (- 416a b - 3136a b + 2016a b + 9856a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 10 +--R (464a b + 4064a b + 2400a b - 20384a b - 22512a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 196a b - 2288a b - 4248a b + 15168a b + 43932a b +--R + +--R 6 +--R 27440a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R 20b + 504a b + 1872a b - 5280a b - 31260a b +--R + +--R 5 2 6 +--R - 43568a b - 19040a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 +--R - 36b - 300a b + 896a b + 9780a b + 23124a b +--R + +--R 5 2 6 +--R 21896a b + 7392a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 16b - 48a b - 1204a b - 4552a b - 7220a b - 5264a b +--R + +--R 6 +--R - 1456a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 40a b + 260a b + 652a b + 796a b + 476a b + 112a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 5 2 6 16 +--R (128a b - 384a b + 256a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 14 +--R (- 352a b + 576a b + 1312a b - 1664a b)cos(x) +--R + +--R 2 5 4 3 5 2 6 12 +--R (336a b - 3296a b - 384a b + 4624a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 +--R - 124a b - 312a b + 2408a b + 4392a b - 4380a b +--R + +--R 6 +--R - 7136a b +--R * +--R 10 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 12b + 132a b - 680a b - 3512a b - 524a b + 8620a b +--R + +--R 6 +--R 6640a b +--R * +--R 8 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 16b + 52a b + 960a b + 1316a b - 3232a b - 7416a b +--R + +--R 6 +--R - 3776a b +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 4b - 76a b - 300a b + 436a b + 2680a b + 3288a b +--R + +--R 6 +--R 1264a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 2 +--R (16a b - 16a b - 348a b - 808a b - 716a b - 224a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R 12a b + 52a b + 84a b + 60a b + 16a b +--R * +--R sin(x) +--R * +--R +-+ +--R \|a +--R * +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 528 +t0388:= 1/(1+csc(x)^2)^(1/2) +--R +--R +--R 1 +--R (428) -------------- +--R +-----------+ +--R | 2 +--R \|csc(x) + 1 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 528 +r0388:= -atan(cot(x)/(2+cot(x)^2)^(1/2)) +--R +--R +--R cot(x) +--R (429) - atan(--------------) +--R +-----------+ +--R | 2 +--R \|cot(x) + 2 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 528 +a0388:= integrate(t0388,x) +--R +--R +--R (430) +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R - atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 469 + +--S 470 of 528 +m0388:= a0388-r0388 +--R +--R +--R (431) +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R - atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R + +--R cot(x) +--R 2atan(--------------) +--R +-----------+ +--R | 2 +--R \|cot(x) + 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 528 +d0388:= D(m0388,x) +--R +--R +--R (432) +--R 7 6 5 4 3 +--R - 16cos(x) - 16cos(x) + 48cos(x) + 48cos(x) - 36cos(x) +--R + +--R 2 +--R - 36cos(x) + 8cos(x) + 8 +--R * +--R 9 +--R sin(x) +--R + +--R 9 8 7 6 +--R 240cos(x) + 240cos(x) - 1136cos(x) - 1136cos(x) +--R + +--R 5 4 3 2 +--R 1752cos(x) + 1752cos(x) - 964cos(x) - 964cos(x) +--R + +--R 172cos(x) + 172 +--R * +--R 7 +--R sin(x) +--R + +--R 11 10 9 8 +--R - 240cos(x) - 240cos(x) + 1680cos(x) + 1680cos(x) +--R + +--R 7 6 5 4 +--R - 4264cos(x) - 4264cos(x) + 4688cos(x) + 4688cos(x) +--R + +--R 3 2 +--R - 2073cos(x) - 2073cos(x) + 310cos(x) + 310 +--R * +--R 5 +--R sin(x) +--R + +--R 13 12 11 10 +--R 16cos(x) + 16cos(x) - 208cos(x) - 208cos(x) +--R + +--R 9 8 7 6 +--R 920cos(x) + 920cos(x) - 1836cos(x) - 1836cos(x) +--R + +--R 5 4 3 2 +--R 1705cos(x) + 1705cos(x) - 652cos(x) - 652cos(x) +--R + +--R 85cos(x) + 85 +--R * +--R 3 +--R sin(x) +--R + +--R 11 10 9 8 7 +--R - 4cos(x) - 4cos(x) + 24cos(x) + 24cos(x) - 52cos(x) +--R + +--R 6 5 4 3 2 +--R - 52cos(x) + 48cos(x) + 48cos(x) - 17cos(x) - 17cos(x) +--R + +--R 2cos(x) + 2 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 8 6 4 2 8 +--R (192cos(x) - 928cos(x) + 1472cos(x) - 848cos(x) + 160)sin(x) +--R + +--R 10 8 6 4 +--R - 640cos(x) + 4320cos(x) - 10720cos(x) + 11736cos(x) +--R + +--R 2 +--R - 5328cos(x) + 832 +--R * +--R 6 +--R sin(x) +--R + +--R 12 10 8 6 +--R 192cos(x) - 1888cos(x) + 7104cos(x) - 12848cos(x) +--R + +--R 4 2 +--R 11340cos(x) - 4348cos(x) + 584 +--R * +--R 4 +--R sin(x) +--R + +--R 12 10 8 6 +--R 32cos(x) - 288cos(x) + 1000cos(x) - 1672cos(x) +--R + +--R 4 2 +--R 1356cos(x) - 468cos(x) + 56 +--R * +--R 2 +--R sin(x) +--R * +--R +-----------+ +--R | 2 +--R \|cot(x) + 2 +--R + +--R 9 8 7 6 5 +--R - 96cos(x) - 96cos(x) + 464cos(x) + 464cos(x) - 736cos(x) +--R + +--R 4 3 2 +--R - 736cos(x) + 424cos(x) + 424cos(x) - 80cos(x) - 80 +--R * +--R 7 +--R sin(x) +--R + +--R 11 10 9 8 +--R 320cos(x) + 320cos(x) - 2160cos(x) - 2160cos(x) +--R + +--R 7 6 5 4 +--R 5360cos(x) + 5360cos(x) - 5868cos(x) - 5868cos(x) +--R + +--R 3 2 +--R 2664cos(x) + 2664cos(x) - 416cos(x) - 416 +--R * +--R 5 +--R sin(x) +--R + +--R 13 12 11 10 +--R - 96cos(x) - 96cos(x) + 944cos(x) + 944cos(x) +--R + +--R 9 8 7 6 +--R - 3552cos(x) - 3552cos(x) + 6424cos(x) + 6424cos(x) +--R + +--R 5 4 3 2 +--R - 5670cos(x) - 5670cos(x) + 2174cos(x) + 2174cos(x) +--R + +--R - 292cos(x) - 292 +--R * +--R 3 +--R sin(x) +--R + +--R 13 12 11 10 +--R - 16cos(x) - 16cos(x) + 144cos(x) + 144cos(x) +--R + +--R 9 8 7 6 5 +--R - 500cos(x) - 500cos(x) + 836cos(x) + 836cos(x) - 678cos(x) +--R + +--R 4 3 2 +--R - 678cos(x) + 234cos(x) + 234cos(x) - 28cos(x) - 28 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 8 6 4 2 8 +--R (- 32cos(x) + 160cos(x) - 264cos(x) + 160cos(x) - 32)sin(x) +--R + +--R 10 8 6 4 2 +--R 480cos(x) - 3232cos(x) + 8048cos(x) - 8936cos(x) + 4200cos(x) +--R + +--R - 688 +--R * +--R 6 +--R sin(x) +--R + +--R 12 10 8 6 +--R - 480cos(x) + 4320cos(x) - 15248cos(x) + 26432cos(x) +--R + +--R 4 2 +--R - 22898cos(x) + 8912cos(x) - 1240 +--R * +--R 4 +--R sin(x) +--R + +--R 14 12 10 8 6 +--R 32cos(x) - 480cos(x) + 2672cos(x) - 7352cos(x) + 10754cos(x) +--R + +--R 4 2 +--R - 8124cos(x) + 2778cos(x) - 340 +--R * +--R 2 +--R sin(x) +--R + +--R 12 10 8 6 4 +--R - 8cos(x) + 64cos(x) - 200cos(x) + 304cos(x) - 226cos(x) +--R + +--R 2 +--R 72cos(x) - 8 +--R / +--R 9 8 7 6 5 +--R 96cos(x) + 96cos(x) - 464cos(x) - 464cos(x) + 736cos(x) +--R + +--R 4 3 2 +--R 736cos(x) - 424cos(x) - 424cos(x) + 80cos(x) + 80 +--R * +--R 7 +--R sin(x) +--R + +--R 11 10 9 8 +--R - 320cos(x) - 320cos(x) + 2160cos(x) + 2160cos(x) +--R + +--R 7 6 5 4 +--R - 5360cos(x) - 5360cos(x) + 5868cos(x) + 5868cos(x) +--R + +--R 3 2 +--R - 2664cos(x) - 2664cos(x) + 416cos(x) + 416 +--R * +--R 5 +--R sin(x) +--R + +--R 13 12 11 10 +--R 96cos(x) + 96cos(x) - 944cos(x) - 944cos(x) +--R + +--R 9 8 7 6 +--R 3552cos(x) + 3552cos(x) - 6424cos(x) - 6424cos(x) +--R + +--R 5 4 3 2 +--R 5670cos(x) + 5670cos(x) - 2174cos(x) - 2174cos(x) +--R + +--R 292cos(x) + 292 +--R * +--R 3 +--R sin(x) +--R + +--R 13 12 11 10 +--R 16cos(x) + 16cos(x) - 144cos(x) - 144cos(x) +--R + +--R 9 8 7 6 5 +--R 500cos(x) + 500cos(x) - 836cos(x) - 836cos(x) + 678cos(x) +--R + +--R 4 3 2 +--R 678cos(x) - 234cos(x) - 234cos(x) + 28cos(x) + 28 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 8 6 4 2 8 +--R (32cos(x) - 160cos(x) + 264cos(x) - 160cos(x) + 32)sin(x) +--R + +--R 10 8 6 4 +--R - 480cos(x) + 3232cos(x) - 8048cos(x) + 8936cos(x) +--R + +--R 2 +--R - 4200cos(x) + 688 +--R * +--R 6 +--R sin(x) +--R + +--R 12 10 8 6 +--R 480cos(x) - 4320cos(x) + 15248cos(x) - 26432cos(x) +--R + +--R 4 2 +--R 22898cos(x) - 8912cos(x) + 1240 +--R * +--R 4 +--R sin(x) +--R + +--R 14 12 10 8 +--R - 32cos(x) + 480cos(x) - 2672cos(x) + 7352cos(x) +--R + +--R 6 4 2 +--R - 10754cos(x) + 8124cos(x) - 2778cos(x) + 340 +--R * +--R 2 +--R sin(x) +--R + +--R 12 10 8 6 4 +--R 8cos(x) - 64cos(x) + 200cos(x) - 304cos(x) + 226cos(x) +--R + +--R 2 +--R - 72cos(x) + 8 +--R * +--R +-----------+ +--R | 2 +--R \|cot(x) + 2 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 528 +t0389:= 1/(1-csc(x)^2)^(1/2) +--R +--R +--R 1 +--R (433) ---------------- +--R +-------------+ +--R | 2 +--R \|- csc(x) + 1 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 528 +r0389:= -cot(x)*log(cos(x))/(-cot(x)^2)^(1/2) +--R +--R +--R cot(x)log(cos(x)) +--R (434) - ----------------- +--R +---------+ +--R | 2 +--R \|- cot(x) +--R Type: Expression(Integer) +--E 473 + +--S 474 of 528 +a0389:= integrate(t0389,x) +--R +--R +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R (435) - atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R Type: Union(Expression(Integer),...) +--E 474 + +--S 475 of 528 +m0389:= a0389-r0389 +--R +--R +--R (436) +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +---------+ +--R 2 2 2 2 2 | 2 +--R - atan(-------------------------------------------)\|- cot(x) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R + +--R cot(x)log(cos(x)) +--R / +--R +---------+ +--R | 2 +--R \|- cot(x) +--R Type: Expression(Integer) +--E 475 + +--S 476 of 528 +d0389:= D(m0389,x) +--R +--R +--R (437) +--R x 6 x 2 x 4 +--R cos(x)sin(-) + (3cos(-) - 2)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 6 x 4 x 2 +--R (3cos(-) + 1)cos(x)sin(-) + (cos(-) + 2cos(-) - 3cos(-) )cos(x) +--R 2 2 2 2 2 +--R * +--R +---------+ +--R | 2 +--R \|- cot(x) +--R + +--R x 6 x 2 x 4 +--R - cot(x)sin(-) + (- 3cos(-) + 2)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (- 3cos(-) + 12cos(-) - 1)cot(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (- cos(-) - 6cos(-) - 9cos(-) )cot(x) +--R 2 2 2 +--R * +--R sin(x) +--R / +--R x 6 x 2 x 4 +--R cos(x)sin(-) + (3cos(-) - 2)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 2 +--R (3cos(-) - 12cos(-) + 1)cos(x)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (cos(-) + 6cos(-) + 9cos(-) )cos(x) +--R 2 2 2 +--R * +--R +---------+ +--R | 2 +--R \|- cot(x) +--R Type: Expression(Integer) +--E 476 + +--S 477 of 528 +t0390:= 1/(-1+csc(x)^2)^(1/2) +--R +--R +--R 1 +--R (438) -------------- +--R +-----------+ +--R | 2 +--R \|csc(x) - 1 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 528 +r0390:= -cot(x)*log(cos(x))/(cot(x)^2)^(1/2) +--R +--R +--R cot(x)log(cos(x)) +--R (439) - ----------------- +--R +-------+ +--R | 2 +--R \|cot(x) +--R Type: Expression(Integer) +--E 478 + +--S 479 of 528 +a0390:= integrate(t0390,x) +--R +--R +--R 2 2cos(x) +--R (440) - log(----------) + log(- ----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 479 + +--S 480 of 528 +m0390:= a0390-r0390 +--R +--R +--R (441) +--R +-------+ +--R 2 2cos(x) | 2 +--R (- log(----------) + log(- ----------))\|cot(x) + cot(x)log(cos(x)) +--R cos(x) + 1 cos(x) + 1 +--R --------------------------------------------------------------------- +--R +-------+ +--R | 2 +--R \|cot(x) +--R Type: Expression(Integer) +--E 480 + +--S 481 of 528 +d0390:= D(m0390,x) +--R +--R +--R +-------+ +--R | 2 +--R - sin(x)\|cot(x) - cot(x)sin(x) +--R (442) --------------------------------- +--R +-------+ +--R | 2 +--R cos(x)\|cot(x) +--R Type: Expression(Integer) +--E 481 + +--S 482 of 528 +t0391:= 1/(-1-csc(x)^2)^(1/2) +--R +--R +--R 1 +--R (443) ---------------- +--R +-------------+ +--R | 2 +--R \|- csc(x) - 1 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 528 +r0391:= -atanh(cot(x)/(-2-cot(x)^2)^(1/2)) +--R +--R +--R cot(x) +--R (444) - atanh(----------------) +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 528 +a0391:= integrate(t0391,x) +--R +--R +--R (445) +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R - log(\|(%e ) - 6(%e ) + 1 - (%e ) + 1) +--R + +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) + 2)\|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) - 8(%e ) - 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 484 + +--S 485 of 528 +m0391:= a0391-r0391 +--R +--R +--R (446) +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R - log(\|(%e ) - 6(%e ) + 1 - (%e ) + 1) +--R + +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) + 2)\|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) - 8(%e ) - 2 +--R + +--R cot(x) +--R 2atanh(----------------) +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 485 + +--S 486 of 528 +d0391:= D(m0391,x) +--R +--R +--R (447) +--R +---+ 6 +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R \|- 1 (%e ) - 7\|- 1 (%e ) + 11\|- 1 (%e ) +--R + +--R +---+ +--R - 5\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) + 9(%e ) - 19(%e ) + 3 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R - \|- 1 (%e ) + 10\|- 1 (%e ) - 28\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R 22\|- 1 (%e ) - 3\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (%e ) - 12(%e ) + 42(%e ) - 36(%e ) + 5 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +-------------+ +--R x\|- 1 x\|- 1 x\|- 1 | 2 +--R ((%e ) - 9(%e ) + 19(%e ) - 3)\|- cot(x) - 2 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) + 12(%e ) - 42(%e ) + 36(%e ) - 5) +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 528 +t0392:= 1/(a+b*csc(x)^2)^(1/2) +--R +--R +--R 1 +--R (448) ---------------- +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 528 +r0392:= -atan(a^(1/2)*cot(x)/(a+b*csc(x)^2)^(1/2))/a^(1/2) +--R +--R +--R +-+ +--R cot(x)\|a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R (449) - ---------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 488 + +--S 489 of 528 +a0392:= integrate(t0392,x) +--R +--R +--R (450) +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a 2 +-+ +--R (cos(x) + 1)sin(x) |---------------------- + (2cos(x) - 2)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------------) +--R +----------------------+ +--R | 2 +--R 2 |- 4a cos(x) + 4b + 4a +-+ +--R (cos(x) + cos(x)) |---------------------- - 2cos(x)sin(x)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R atan +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (- b - 3a)cos(x) + (- b - 3a)cos(x)) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (6a b + 6a )cos(x))sin(x) +--R / +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (- b - a)cos(x) - b - a)sin(x)\|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 2 +--R 8a cos(x) + (- 6a b - 10a )cos(x) + 2a b + 2a +--R / +--R +-+ +--R 2\|a +--R Type: Union(Expression(Integer),...) +--E 489 + +--S 490 of 528 +m0392:= a0392-r0392 +--R +--R +--R (451) +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a 2 +-+ +--R (cos(x) + 1)sin(x) |---------------------- + (2cos(x) - 2)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------------) +--R +----------------------+ +--R | 2 +--R 2 |- 4a cos(x) + 4b + 4a +-+ +--R (cos(x) + cos(x)) |---------------------- - 2cos(x)sin(x)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R atan +--R 4 3 2 +--R (4a cos(x) + 4a cos(x) + (- b - 3a)cos(x) + (- b - 3a)cos(x)) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (6a b + 6a )cos(x))sin(x) +--R / +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (- b - a)cos(x) - b - a)sin(x)\|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 2 +--R 8a cos(x) + (- 6a b - 10a )cos(x) + 2a b + 2a +--R + +--R +-+ +--R cot(x)\|a +--R 2atan(----------------) +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 490 + +--S 491 of 528 +d0392:= D(m0392,x) +--R +--R +--R (452) +--R 4 2 5 6 7 +--R (16a b + 32a b + 16a )cos(x) +--R + +--R 4 2 5 6 6 +--R (16a b + 32a b + 16a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 24a b - 72a b - 72a b - 24a )cos(x) +--R + +--R 3 3 4 2 5 6 4 +--R (- 24a b - 72a b - 72a b - 24a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (9a b + 36a b + 54a b + 36a b + 9a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (9a b + 36a b + 54a b + 36a b + 9a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- a b - 5a b - 10a b - 10a b - 5a b - a )cos(x) - a b +--R + +--R 2 4 3 3 4 2 5 6 +--R - 5a b - 10a b - 10a b - 5a b - a +--R * +--R 9 +--R sin(x) +--R + +--R 4 2 5 6 9 +--R (- 64a b - 448a b - 448a )cos(x) +--R + +--R 4 2 5 6 8 +--R (- 64a b - 448a b - 448a )cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (144a b + 1152a b + 2128a b + 1120a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (144a b + 1152a b + 2128a b + 1120a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 100a b - 928a b - 2480a b - 2576a b - 924a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 100a b - 928a b - 2480a b - 2576a b - 924a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (20a b + 242a b + 886a b + 1406a b + 1022a b + 280a ) +--R * +--R 3 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (20a b + 242a b + 886a b + 1406a b + 1022a b + 280a ) +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - b - 18a b - 90a b - 200a b - 225a b - 126a b +--R + +--R 6 +--R - 28a +--R * +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R - b - 18a b - 90a b - 200a b - 225a b - 126a b - 28a +--R * +--R 7 +--R sin(x) +--R + +--R 4 2 6 11 4 2 6 10 +--R (- 160a b + 1120a )cos(x) + (- 160a b + 1120a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (320a b + 240a b - 3360a b - 3920a )cos(x) +--R + +--R 3 3 4 2 5 6 8 +--R (320a b + 240a b - 3360a b - 3920a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (- 194a b - 200a b + 3660a b + 8680a b + 5110a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 194a b - 200a b + 3660a b + 8680a b + 5110a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (34a b - 16a b - 1850a b - 6350a b - 7560a b - 3010a ) +--R * +--R 5 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (34a b - 16a b - 1850a b - 6350a b - 7560a b - 3010a ) +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 2b + 6a b + 333a b + 1620a b + 3045a b + 2520a b +--R + +--R 6 +--R 770a +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 2b + 6a b + 333a b + 1620a b + 3045a b + 2520a b +--R + +--R 6 +--R 770a +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 15a b - 115a b - 325a b - 435a b - 280a b - 70a ) +--R * +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 15a b - 115a b - 325a b - 435a b - 280a b - 70a +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 5 6 13 +--R (- 64a b + 448a b - 448a )cos(x) +--R + +--R 4 2 5 6 12 +--R (- 64a b + 448a b - 448a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (112a b - 960a b - 336a b + 2016a )cos(x) +--R + +--R 3 3 4 2 5 6 10 +--R (112a b - 960a b - 336a b + 2016a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (- 52a b + 800a b + 1536a b - 2352a b - 3612a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 8 +--R (- 52a b + 800a b + 1536a b - 2352a b - 3612a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (4a b - 298a b - 1070a b + 770a b + 4690a b + 3248a ) +--R * +--R 7 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (4a b - 298a b - 1070a b + 770a b + 4690a b + 3248a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - b + 30a b + 216a b - 120a b - 2115a b - 3318a b +--R + +--R 6 +--R - 1512a +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - b + 30a b + 216a b - 120a b - 2115a b - 3318a b +--R + +--R 6 +--R - 1512a +--R * +--R 4 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 12a b + 8a b + 350a b + 960a b + 966a b + 336a ) +--R * +--R 3 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 12a b + 8a b + 350a b + 960a b + 966a b + 336a ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 3 3 4 2 5 6 2 4 +--R (- 15a b - 72a b - 127a b - 98a b - 28a )cos(x) - 15a b +--R + +--R 3 3 4 2 5 6 +--R - 72a b - 127a b - 98a b - 28a +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 6 15 +--R (16a b - 32a b + 16a )cos(x) +--R + +--R 4 2 5 6 14 +--R (16a b - 32a b + 16a )cos(x) +--R + +--R 3 3 4 2 5 6 13 +--R (- 40a b + 24a b + 104a b - 88a )cos(x) +--R + +--R 3 3 4 2 5 6 12 +--R (- 40a b + 24a b + 104a b - 88a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 11 +--R (33a b + 36a b - 178a b - 76a b + 201a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 10 +--R (33a b + 36a b - 178a b - 76a b + 201a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 9 +--R (- 9a b - 35a b + 76a b + 216a b - 99a b - 245a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 8 +--R (- 9a b - 35a b + 76a b + 216a b - 99a b - 245a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (6a b - 7a b - 100a b - 57a b + 196a b + 170a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (6a b - 7a b - 100a b - 57a b + 196a b + 170a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- a b + 11a b + 27a b - 41a b - 122a b - 66a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (- a b + 11a b + 27a b - 41a b - 122a b - 66a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- 2a b + 2a b + 23a b + 32a b + 13a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (- 2a b + 2a b + 23a b + 32a b + 13a )cos(x) +--R + +--R 3 3 4 2 5 6 3 3 4 2 5 6 +--R (- a b - 3a b - 3a b - a )cos(x) - a b - 3a b - 3a b - a +--R * +--R sin(x) +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 2 5 6 8 +--R (128a b + 384a b + 256a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (- 288a b - 1216a b - 1568a b - 640a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (208a b + 1152a b + 2208a b + 1792a b + 528a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 52a b - 368a b - 952a b - 1168a b - 692a b - 160a ) +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 4b + 36a b + 120a b + 200a b + 180a b + 84a b + 16a +--R * +--R 8 +--R sin(x) +--R + +--R 4 2 5 6 10 +--R (128a b - 896a b - 1792a )cos(x) +--R + +--R 3 3 4 2 5 6 8 +--R (- 224a b + 2496a b + 8736a b + 6272a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (80a b - 2848a b - 13344a b - 18592a b - 8176a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 20a b + 1480a b + 8360a b + 17176a b + 15092a b +--R + +--R 6 +--R 4816a +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 4b - 264a b - 1944a b - 5520a b - 7476a b +--R + +--R 5 6 +--R - 4872a b - 1232a +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 12b + 132a b + 520a b + 1000a b + 1020a b + 532a b + 112a +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 5 6 12 +--R (- 128a b - 896a b + 1792a )cos(x) +--R + +--R 3 3 4 2 5 6 10 +--R (416a b + 3008a b - 2912a b - 8064a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 8 +--R (- 464a b - 3648a b + 608a b + 17472a b + 14448a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 196a b + 1824a b + 600a b - 14560a b - 26460a b +--R + +--R 6 +--R - 12992a +--R * +--R 6 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 20b - 308a b - 48a b + 5880a b + 16700a b +--R + +--R 5 6 +--R 17108a b + 6048a +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 16b - 8a b - 944a b - 3900a b - 6424a b - 4788a b +--R + +--R 6 +--R - 1344a +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 40a b + 260a b + 652a b + 796a b + 476a b + 112a +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 6 14 +--R (- 128a b + 384a b - 256a )cos(x) +--R + +--R 3 3 4 2 5 6 12 +--R (352a b - 704a b - 928a b + 1408a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 10 +--R (- 336a b + 352a b + 2592a b - 544a b - 3216a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (124a b - 24a b - 2056a b - 1800a b + 3836a b + 3920a ) +--R * +--R 8 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 12b - 8a b + 656a b + 1456a b - 1276a b - 4784a b +--R + +--R 6 +--R - 2720a +--R * +--R 6 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 4b - 60a b - 304a b + 140a b + 1956a b + 2632a b +--R + +--R 6 +--R 1056a +--R * +--R 4 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (16a b - 4a b - 296a b - 724a b - 656a b - 208a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R 12a b + 52a b + 84a b + 60a b + 16a +--R * +--R 2 +--R sin(x) +--R * +--R +-+ +--R \|a +--R * +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R + +--R 4 2 5 6 9 +--R (- 64a b - 192a b - 128a )cos(x) +--R + +--R 4 2 5 6 8 +--R (- 64a b - 192a b - 128a )cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (144a b + 608a b + 784a b + 320a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (144a b + 608a b + 784a b + 320a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 104a b - 576a b - 1104a b - 896a b - 264a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 104a b - 576a b - 1104a b - 896a b - 264a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (26a b + 184a b + 476a b + 584a b + 346a b + 80a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (26a b + 184a b + 476a b + 584a b + 346a b + 80a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 2b - 18a b - 60a b - 100a b - 90a b - 42a b - 8a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R - 2b - 18a b - 60a b - 100a b - 90a b - 42a b - 8a +--R * +--R 7 +--R sin(x) +--R + +--R 4 2 5 6 11 +--R (- 64a b + 448a b + 896a )cos(x) +--R + +--R 4 2 5 6 10 +--R (- 64a b + 448a b + 896a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (112a b - 1248a b - 4368a b - 3136a )cos(x) +--R + +--R 3 3 4 2 5 6 8 +--R (112a b - 1248a b - 4368a b - 3136a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (- 40a b + 1424a b + 6672a b + 9296a b + 4088a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (- 40a b + 1424a b + 6672a b + 9296a b + 4088a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 10a b - 740a b - 4180a b - 8588a b - 7546a b - 2408a ) +--R * +--R 5 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 10a b - 740a b - 4180a b - 8588a b - 7546a b - 2408a ) +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 2b + 132a b + 972a b + 2760a b + 3738a b + 2436a b +--R + +--R 6 +--R 616a +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 2b + 132a b + 972a b + 2760a b + 3738a b + 2436a b +--R + +--R 6 +--R 616a +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 6b - 66a b - 260a b - 500a b - 510a b - 266a b - 56a ) +--R * +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R - 6b - 66a b - 260a b - 500a b - 510a b - 266a b - 56a +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 5 6 13 +--R (64a b + 448a b - 896a )cos(x) +--R + +--R 4 2 5 6 12 +--R (64a b + 448a b - 896a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (- 208a b - 1504a b + 1456a b + 4032a )cos(x) +--R + +--R 3 3 4 2 5 6 10 +--R (- 208a b - 1504a b + 1456a b + 4032a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (232a b + 1824a b - 304a b - 8736a b - 7224a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 8 +--R (232a b + 1824a b - 304a b - 8736a b - 7224a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 98a b - 912a b - 300a b + 7280a b + 13230a b + 6496a ) +--R * +--R 7 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 98a b - 912a b - 300a b + 7280a b + 13230a b + 6496a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 10b + 154a b + 24a b - 2940a b - 8350a b - 8554a b +--R + +--R 6 +--R - 3024a +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 10b + 154a b + 24a b - 2940a b - 8350a b - 8554a b +--R + +--R 6 +--R - 3024a +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 8b + 4a b + 472a b + 1950a b + 3212a b + 2394a b +--R + +--R 6 +--R 672a +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 8b + 4a b + 472a b + 1950a b + 3212a b + 2394a b +--R + +--R 6 +--R 672a +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 20a b - 130a b - 326a b - 398a b - 238a b - 56a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R - 20a b - 130a b - 326a b - 398a b - 238a b - 56a +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 6 15 +--R (64a b - 192a b + 128a )cos(x) +--R + +--R 4 2 5 6 14 +--R (64a b - 192a b + 128a )cos(x) +--R + +--R 3 3 4 2 5 6 13 +--R (- 176a b + 352a b + 464a b - 704a )cos(x) +--R + +--R 3 3 4 2 5 6 12 +--R (- 176a b + 352a b + 464a b - 704a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 11 +--R (168a b - 176a b - 1296a b + 272a b + 1608a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 10 +--R (168a b - 176a b - 1296a b + 272a b + 1608a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 62a b + 12a b + 1028a b + 900a b - 1918a b - 1960a ) +--R * +--R 9 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 62a b + 12a b + 1028a b + 900a b - 1918a b - 1960a ) +--R * +--R 8 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (6b + 4a b - 328a b - 728a b + 638a b + 2392a b + 1360a ) +--R * +--R 7 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (6b + 4a b - 328a b - 728a b + 638a b + 2392a b + 1360a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 2b + 30a b + 152a b - 70a b - 978a b - 1316a b - 528a ) +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 2b + 30a b + 152a b - 70a b - 978a b - 1316a b - 528a ) +--R * +--R 4 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 8a b + 2a b + 148a b + 362a b + 328a b + 104a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (- 8a b + 2a b + 148a b + 362a b + 328a b + 104a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 2 4 3 3 +--R (- 6a b - 26a b - 42a b - 30a b - 8a )cos(x) - 6a b - 26a b +--R + +--R 4 2 5 6 +--R - 42a b - 30a b - 8a +--R * +--R sin(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 5 2 6 7 8 +--R (32a b + 64a b + 32a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 80a b - 240a b - 240a b - 80a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (66a b + 264a b + 396a b + 264a b + 66a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 2 +--R (- 20a b - 100a b - 200a b - 200a b - 100a b - 20a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R 2a b + 12a b + 30a b + 40a b + 30a b + 12a b + 2a +--R * +--R 8 +--R sin(x) +--R + +--R 5 2 6 7 10 +--R (- 128a b - 896a b - 896a )cos(x) +--R + +--R 4 3 5 2 6 7 8 +--R (416a b + 3328a b + 6048a b + 3136a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 6 +--R (- 488a b - 4448a b - 11520a b - 11648a b - 4088a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 4 +--R (240a b + 2540a b + 8588a b + 12924a b + 9044a b + 2408a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 42a b - 560a b - 2436a b - 4984a b - 5306a b - 2856a b +--R + +--R 7 +--R - 616a +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R 2b + 38a b + 216a b + 580a b + 850a b + 702a b + 308a b + 56a +--R * +--R 6 +--R sin(x) +--R + +--R 5 2 7 12 +--R (- 320a b + 2240a )cos(x) +--R + +--R 4 3 5 2 6 7 10 +--R (960a b + 800a b - 8960a b - 10080a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 8 +--R (- 1028a b - 1520a b + 13560a b + 31920a b + 18060a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (456a b + 756a b - 10620a b - 37380a b - 42700a b - 16240a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 72a b - 24a b + 4398a b + 19640a b + 33910a b + 26180a b +--R + +--R 7 +--R 7560a +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 4b - 8a b - 708a b - 4136a b - 9980a b - 12000a b - 7140a b +--R + +--R 7 +--R - 1680a +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R 30a b + 260a b + 880a b + 1520a b + 1430a b + 700a b + 140a +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 6 7 14 +--R (- 128a b + 896a b - 896a )cos(x) +--R + +--R 4 3 5 2 6 7 12 +--R (352a b - 2688a b - 672a b + 4928a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 10 +--R (- 328a b + 3296a b + 5664a b - 8064a b - 11256a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (112a b - 2092a b - 6812a b + 3172a b + 21308a b + 13720a ) +--R * +--R 8 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 10a b + 648a b + 3168a b + 360a b - 15150a b - 22512a b +--R + +--R 7 +--R - 9520a +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 2b - 58a b - 516a b - 176a b + 5170a b + 12786a b +--R + +--R 6 7 +--R 11592a b + 3696a +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (24a b + 8a b - 746a b - 2764a b - 4106a b - 2800a b - 728a ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R 30a b + 174a b + 398a b + 450a b + 252a b + 56a +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 6 7 16 +--R (32a b - 64a b + 32a )cos(x) +--R + +--R 4 3 5 2 6 7 14 +--R (- 112a b + 80a b + 240a b - 208a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 12 +--R (146a b + 104a b - 612a b - 184a b + 578a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 10 +--R (- 84a b - 208a b + 436a b + 940a b - 448a b - 892a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 8 +--R (18a b + 100a b - 96a b - 784a b - 348a b + 1080a b + 830a )cos(x) +--R + +--R 6 3 4 4 3 5 2 6 7 6 +--R (- 12a b + 236a b + 368a b - 360a b - 976a b - 472a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 4 +--R (2a b - 20a b - 80a b + 32a b + 372a b + 440a b + 158a )cos(x) +--R + +--R 2 5 4 3 5 2 6 7 2 3 4 4 3 5 2 +--R (4a b - 52a b - 116a b - 96a b - 28a )cos(x) + 2a b + 8a b + 12a b +--R + +--R 6 7 +--R 8a b + 2a +--R / +--R 4 2 5 6 9 +--R (64a b + 192a b + 128a )cos(x) +--R + +--R 4 2 5 6 8 +--R (64a b + 192a b + 128a )cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (- 144a b - 608a b - 784a b - 320a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (- 144a b - 608a b - 784a b - 320a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (104a b + 576a b + 1104a b + 896a b + 264a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (104a b + 576a b + 1104a b + 896a b + 264a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 26a b - 184a b - 476a b - 584a b - 346a b - 80a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (- 26a b - 184a b - 476a b - 584a b - 346a b - 80a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (2b + 18a b + 60a b + 100a b + 90a b + 42a b + 8a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 2b + 18a b + 60a b + 100a b + 90a b + 42a b + 8a +--R * +--R 7 +--R sin(x) +--R + +--R 4 2 5 6 11 +--R (64a b - 448a b - 896a )cos(x) +--R + +--R 4 2 5 6 10 +--R (64a b - 448a b - 896a )cos(x) +--R + +--R 3 3 4 2 5 6 9 +--R (- 112a b + 1248a b + 4368a b + 3136a )cos(x) +--R + +--R 3 3 4 2 5 6 8 +--R (- 112a b + 1248a b + 4368a b + 3136a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 7 +--R (40a b - 1424a b - 6672a b - 9296a b - 4088a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 6 +--R (40a b - 1424a b - 6672a b - 9296a b - 4088a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (10a b + 740a b + 4180a b + 8588a b + 7546a b + 2408a ) +--R * +--R 5 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (10a b + 740a b + 4180a b + 8588a b + 7546a b + 2408a ) +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 2b - 132a b - 972a b - 2760a b - 3738a b - 2436a b +--R + +--R 6 +--R - 616a +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 2b - 132a b - 972a b - 2760a b - 3738a b - 2436a b +--R + +--R 6 +--R - 616a +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (6b + 66a b + 260a b + 500a b + 510a b + 266a b + 56a ) +--R * +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R 6b + 66a b + 260a b + 500a b + 510a b + 266a b + 56a +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 5 6 13 +--R (- 64a b - 448a b + 896a )cos(x) +--R + +--R 4 2 5 6 12 +--R (- 64a b - 448a b + 896a )cos(x) +--R + +--R 3 3 4 2 5 6 11 +--R (208a b + 1504a b - 1456a b - 4032a )cos(x) +--R + +--R 3 3 4 2 5 6 10 +--R (208a b + 1504a b - 1456a b - 4032a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (- 232a b - 1824a b + 304a b + 8736a b + 7224a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 8 +--R (- 232a b - 1824a b + 304a b + 8736a b + 7224a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (98a b + 912a b + 300a b - 7280a b - 13230a b - 6496a ) +--R * +--R 7 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (98a b + 912a b + 300a b - 7280a b - 13230a b - 6496a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 10b - 154a b - 24a b + 2940a b + 8350a b + 8554a b +--R + +--R 6 +--R 3024a +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 10b - 154a b - 24a b + 2940a b + 8350a b + 8554a b +--R + +--R 6 +--R 3024a +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 8b - 4a b - 472a b - 1950a b - 3212a b - 2394a b +--R + +--R 6 +--R - 672a +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 8b - 4a b - 472a b - 1950a b - 3212a b - 2394a b +--R + +--R 6 +--R - 672a +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (20a b + 130a b + 326a b + 398a b + 238a b + 56a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R 20a b + 130a b + 326a b + 398a b + 238a b + 56a +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 6 15 +--R (- 64a b + 192a b - 128a )cos(x) +--R + +--R 4 2 5 6 14 +--R (- 64a b + 192a b - 128a )cos(x) +--R + +--R 3 3 4 2 5 6 13 +--R (176a b - 352a b - 464a b + 704a )cos(x) +--R + +--R 3 3 4 2 5 6 12 +--R (176a b - 352a b - 464a b + 704a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 11 +--R (- 168a b + 176a b + 1296a b - 272a b - 1608a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 10 +--R (- 168a b + 176a b + 1296a b - 272a b - 1608a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (62a b - 12a b - 1028a b - 900a b + 1918a b + 1960a ) +--R * +--R 9 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (62a b - 12a b - 1028a b - 900a b + 1918a b + 1960a ) +--R * +--R 8 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 6b - 4a b + 328a b + 728a b - 638a b - 2392a b +--R + +--R 6 +--R - 1360a +--R * +--R 7 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 6b - 4a b + 328a b + 728a b - 638a b - 2392a b +--R + +--R 6 +--R - 1360a +--R * +--R 6 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (2b - 30a b - 152a b + 70a b + 978a b + 1316a b + 528a ) +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (2b - 30a b - 152a b + 70a b + 978a b + 1316a b + 528a ) +--R * +--R 4 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (8a b - 2a b - 148a b - 362a b - 328a b - 104a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (8a b - 2a b - 148a b - 362a b - 328a b - 104a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 2 4 3 3 +--R (6a b + 26a b + 42a b + 30a b + 8a )cos(x) + 6a b + 26a b +--R + +--R 4 2 5 6 +--R 42a b + 30a b + 8a +--R * +--R sin(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 5 2 6 7 8 +--R (- 32a b - 64a b - 32a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (80a b + 240a b + 240a b + 80a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- 66a b - 264a b - 396a b - 264a b - 66a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 2 +--R (20a b + 100a b + 200a b + 200a b + 100a b + 20a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R - 2a b - 12a b - 30a b - 40a b - 30a b - 12a b - 2a +--R * +--R 8 +--R sin(x) +--R + +--R 5 2 6 7 10 +--R (128a b + 896a b + 896a )cos(x) +--R + +--R 4 3 5 2 6 7 8 +--R (- 416a b - 3328a b - 6048a b - 3136a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 6 +--R (488a b + 4448a b + 11520a b + 11648a b + 4088a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (- 240a b - 2540a b - 8588a b - 12924a b - 9044a b - 2408a ) +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 42a b + 560a b + 2436a b + 4984a b + 5306a b + 2856a b +--R + +--R 7 +--R 616a +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 2b - 38a b - 216a b - 580a b - 850a b - 702a b - 308a b +--R + +--R 7 +--R - 56a +--R * +--R 6 +--R sin(x) +--R + +--R 5 2 7 12 +--R (320a b - 2240a )cos(x) +--R + +--R 4 3 5 2 6 7 10 +--R (- 960a b - 800a b + 8960a b + 10080a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 8 +--R (1028a b + 1520a b - 13560a b - 31920a b - 18060a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - 456a b - 756a b + 10620a b + 37380a b + 42700a b +--R + +--R 7 +--R 16240a +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 72a b + 24a b - 4398a b - 19640a b - 33910a b - 26180a b +--R + +--R 7 +--R - 7560a +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 4b + 8a b + 708a b + 4136a b + 9980a b + 12000a b +--R + +--R 6 7 +--R 7140a b + 1680a +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R - 30a b - 260a b - 880a b - 1520a b - 1430a b - 700a b - 140a +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 6 7 14 +--R (128a b - 896a b + 896a )cos(x) +--R + +--R 4 3 5 2 6 7 12 +--R (- 352a b + 2688a b + 672a b - 4928a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 10 +--R (328a b - 3296a b - 5664a b + 8064a b + 11256a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R (- 112a b + 2092a b + 6812a b - 3172a b - 21308a b - 13720a ) +--R * +--R 8 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 10a b - 648a b - 3168a b - 360a b + 15150a b + 22512a b +--R + +--R 7 +--R 9520a +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 2b + 58a b + 516a b + 176a b - 5170a b - 12786a b +--R + +--R 6 7 +--R - 11592a b - 3696a +--R * +--R 4 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 24a b - 8a b + 746a b + 2764a b + 4106a b + 2800a b +--R + +--R 7 +--R 728a +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 +--R - 30a b - 174a b - 398a b - 450a b - 252a b - 56a +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 6 7 16 +--R (- 32a b + 64a b - 32a )cos(x) +--R + +--R 4 3 5 2 6 7 14 +--R (112a b - 80a b - 240a b + 208a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 12 +--R (- 146a b - 104a b + 612a b + 184a b - 578a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 10 +--R (84a b + 208a b - 436a b - 940a b + 448a b + 892a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (- 18a b - 100a b + 96a b + 784a b + 348a b - 1080a b - 830a ) +--R * +--R 8 +--R cos(x) +--R + +--R 6 3 4 4 3 5 2 6 7 6 +--R (12a b - 236a b - 368a b + 360a b + 976a b + 472a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 4 +--R (- 2a b + 20a b + 80a b - 32a b - 372a b - 440a b - 158a )cos(x) +--R + +--R 2 5 4 3 5 2 6 7 2 3 4 4 3 +--R (- 4a b + 52a b + 116a b + 96a b + 28a )cos(x) - 2a b - 8a b +--R + +--R 5 2 6 7 +--R - 12a b - 8a b - 2a +--R * +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R Type: Expression(Integer) +--E 491 + +--S 492 of 528 +t0393:= (1+csc(x)^2)^(3/2) +--R +--R +--R +-----------+ +--R 2 | 2 +--R (453) (csc(x) + 1)\|csc(x) + 1 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 528 +r0393:= -2*asinh(1/2*2^(1/2)*cot(x))-atan(cot(x)/(2+cot(x)^2)^(1/2))-_ + 1/2*cot(x)*(2+cot(x)^2)^(1/2) +--R +--R +--R +-----------+ +-+ +--R cot(x) | 2 \|2 cot(x) +--R - 2atan(--------------) - cot(x)\|cot(x) + 2 - 4asinh(----------) +--R +-----------+ 2 +--R | 2 +--R \|cot(x) + 2 +--R (454) ------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 528 +a0393:= integrate(t0393,x) +--R +--R +--R (455) +--R 5 4 3 2 +--R (- 16cos(x) - 16cos(x) + 40cos(x) + 40cos(x) - 24cos(x) - 24) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 32cos(x) - 128cos(x) + 164cos(x) - 68 +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R ((cos(x) + 1)sin(x) + cos(x) + cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) - 2cos(x) + 4 +--R + +--R 5 4 3 2 +--R (16cos(x) + 16cos(x) - 40cos(x) - 40cos(x) + 24cos(x) + 24) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) + 128cos(x) - 164cos(x) + 68 +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) - 2cos(x) + 4 +--R + +--R 5 4 3 2 +--R (- 8cos(x) - 8cos(x) + 20cos(x) + 20cos(x) - 12cos(x) - 12) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 16cos(x) - 64cos(x) + 82cos(x) - 34 +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 5 4 3 2 +--R (- 8cos(x) - 8cos(x) + 20cos(x) + 20cos(x) - 12cos(x) - 12) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 16cos(x) - 64cos(x) + 82cos(x) - 34 +--R * +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R + +--R 6 5 4 3 2 +--R (- 8cos(x) - 8cos(x) + 24cos(x) + 24cos(x) - 17cos(x) - 17cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 5 3 +--R (- 16cos(x) + 56cos(x) - 48cos(x))sin(x) +--R / +--R 5 4 3 2 +--R (16cos(x) + 16cos(x) - 40cos(x) - 40cos(x) + 24cos(x) + 24)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) + 128cos(x) - 164cos(x) + 68 +--R Type: Union(Expression(Integer),...) +--E 494 + +--S 495 of 528 +m0393:= a0393-r0393 +--R +--R +--R (456) +--R 5 4 3 2 +--R (- 16cos(x) - 16cos(x) + 40cos(x) + 40cos(x) - 24cos(x) - 24) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 32cos(x) - 128cos(x) + 164cos(x) - 68 +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R ((cos(x) + 1)sin(x) + cos(x) + cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R 2cos(x)sin(x) - 2cos(x) + 4 +--R + +--R 5 4 3 2 +--R (16cos(x) + 16cos(x) - 40cos(x) - 40cos(x) + 24cos(x) + 24) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) + 128cos(x) - 164cos(x) + 68 +--R * +--R log +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R ((cos(x) + 1)sin(x) - cos(x) - cos(x)) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 +--R - 2cos(x)sin(x) - 2cos(x) + 4 +--R + +--R 5 4 3 2 +--R (- 8cos(x) - 8cos(x) + 20cos(x) + 20cos(x) - 12cos(x) - 12) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 16cos(x) - 64cos(x) + 82cos(x) - 34 +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 5 4 3 2 +--R (- 8cos(x) - 8cos(x) + 20cos(x) + 20cos(x) - 12cos(x) - 12) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R 16cos(x) - 64cos(x) + 82cos(x) - 34 +--R * +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R + +--R 5 4 3 2 +--R (16cos(x) + 16cos(x) - 40cos(x) - 40cos(x) + 24cos(x) + 24) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) + 128cos(x) - 164cos(x) + 68 +--R * +--R cot(x) +--R atan(--------------) +--R +-----------+ +--R | 2 +--R \|cot(x) + 2 +--R + +--R 5 4 3 2 +--R (8cos(x) + 8cos(x) - 20cos(x) - 20cos(x) + 12cos(x) + 12)cot(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R (- 16cos(x) + 64cos(x) - 82cos(x) + 34)cot(x) +--R * +--R +-----------+ +--R | 2 +--R \|cot(x) + 2 +--R + +--R 5 4 3 2 +--R (32cos(x) + 32cos(x) - 80cos(x) - 80cos(x) + 48cos(x) + 48) +--R * +--R +-+ +--R \|2 cot(x) +--R sin(x)asinh(----------) +--R 2 +--R + +--R 6 5 4 3 2 +--R - 8cos(x) - 8cos(x) + 24cos(x) + 24cos(x) - 17cos(x) - 17cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ +--R 6 4 2 \|2 cot(x) +--R (- 64cos(x) + 256cos(x) - 328cos(x) + 136)asinh(----------) +--R 2 +--R + +--R 5 3 +--R (- 16cos(x) + 56cos(x) - 48cos(x))sin(x) +--R / +--R 5 4 3 2 +--R (16cos(x) + 16cos(x) - 40cos(x) - 40cos(x) + 24cos(x) + 24)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 32cos(x) + 128cos(x) - 164cos(x) + 68 +--R Type: Expression(Integer) +--E 495 + +--S 496 of 528 +d0393:= D(m0393,x) +--R +--R +--R (457) +--R 15 14 13 12 +--R - 1024cos(x) - 1024cos(x) + 10240cos(x) + 10240cos(x) +--R + +--R 11 10 9 8 +--R - 42496cos(x) - 42496cos(x) + 94208cos(x) + 94208cos(x) +--R + +--R 7 6 5 4 +--R - 119360cos(x) - 119360cos(x) + 85376cos(x) + 85376cos(x) +--R + +--R 3 2 +--R - 31488cos(x) - 31488cos(x) + 4608cos(x) + 4608 +--R * +--R 13 +--R sin(x) +--R + +--R 17 16 15 +--R 46080cos(x) + 46080cos(x) - 535552cos(x) +--R + +--R 14 13 12 +--R - 535552cos(x) + 2654464cos(x) + 2654464cos(x) +--R + +--R 11 10 9 +--R - 7291648cos(x) - 7291648cos(x) + 12060432cos(x) +--R + +--R 8 7 6 +--R 12060432cos(x) - 12190352cos(x) - 12190352cos(x) +--R + +--R 5 4 3 +--R 7268100cos(x) + 7268100cos(x) - 2305872cos(x) +--R + +--R 2 +--R - 2305872cos(x) + 296464cos(x) + 296464 +--R * +--R 11 +--R sin(x) +--R + +--R 19 18 17 +--R - 215040cos(x) - 215040cos(x) + 2875392cos(x) +--R + +--R 16 15 14 +--R 2875392cos(x) - 16726272cos(x) - 16726272cos(x) +--R + +--R 13 12 11 +--R 55341568cos(x) + 55341568cos(x) - 114202560cos(x) +--R + +--R 10 9 8 +--R - 114202560cos(x) + 151421856cos(x) + 151421856cos(x) +--R + +--R 7 6 5 +--R - 127862732cos(x) - 127862732cos(x) + 65536828cos(x) +--R + +--R 4 3 2 +--R 65536828cos(x) - 18249572cos(x) - 18249572cos(x) +--R + +--R 2088504cos(x) + 2088504 +--R * +--R 9 +--R sin(x) +--R + +--R 21 20 19 +--R 215040cos(x) + 215040cos(x) - 3311616cos(x) +--R + +--R 18 17 16 +--R - 3311616cos(x) + 22503936cos(x) + 22503936cos(x) +--R + +--R 15 14 13 +--R - 88596480cos(x) - 88596480cos(x) + 222921504cos(x) +--R + +--R 12 11 10 +--R 222921504cos(x) - 372688704cos(x) - 372688704cos(x) +--R + +--R 9 8 7 +--R 416461200cos(x) + 416461200cos(x) - 304378284cos(x) +--R + +--R 6 5 4 +--R - 304378284cos(x) + 137582997cos(x) + 137582997cos(x) +--R + +--R 3 2 +--R - 34232392cos(x) - 34232392cos(x) + 3530396cos(x) + 3530396 +--R * +--R 7 +--R sin(x) +--R + +--R 23 22 21 +--R - 46080cos(x) - 46080cos(x) + 841728cos(x) +--R + +--R 20 19 18 +--R 841728cos(x) - 6819840cos(x) - 6819840cos(x) +--R + +--R 17 16 15 +--R 32308736cos(x) + 32308736cos(x) - 99219776cos(x) +--R + +--R 14 13 12 +--R - 99219776cos(x) + 206709024cos(x) + 206709024cos(x) +--R + +--R 11 10 9 +--R - 296710832cos(x) - 296710832cos(x) + 291513244cos(x) +--R + +--R 8 7 6 +--R 291513244cos(x) - 190360182cos(x) - 190360182cos(x) +--R + +--R 5 4 3 +--R 77707516cos(x) + 77707516cos(x) - 17574633cos(x) +--R + +--R 2 +--R - 17574633cos(x) + 1653202cos(x) + 1653202 +--R * +--R 5 +--R sin(x) +--R + +--R 25 24 23 22 +--R 1024cos(x) + 1024cos(x) - 27648cos(x) - 27648cos(x) +--R + +--R 21 20 19 +--R 306432cos(x) + 306432cos(x) - 1912064cos(x) +--R + +--R 18 17 16 +--R - 1912064cos(x) + 7602256cos(x) + 7602256cos(x) +--R + +--R 15 14 13 +--R - 20437168cos(x) - 20437168cos(x) + 38177516cos(x) +--R + +--R 12 11 10 +--R 38177516cos(x) - 49868420cos(x) - 49868420cos(x) +--R + +--R 9 8 7 +--R 45001749cos(x) + 45001749cos(x) - 27139540cos(x) +--R + +--R 6 5 4 +--R - 27139540cos(x) + 10255110cos(x) + 10255110cos(x) +--R + +--R 3 2 +--R - 2145416cos(x) - 2145416cos(x) + 186312cos(x) + 186312 +--R * +--R 3 +--R sin(x) +--R + +--R 23 22 21 20 +--R - 256cos(x) - 256cos(x) + 4096cos(x) + 4096cos(x) +--R + +--R 19 18 17 +--R - 29248cos(x) - 29248cos(x) + 122688cos(x) +--R + +--R 16 15 14 +--R 122688cos(x) - 334724cos(x) - 334724cos(x) +--R + +--R 13 12 11 +--R 620776cos(x) + 620776cos(x) - 793716cos(x) +--R + +--R 10 9 8 +--R - 793716cos(x) + 693872cos(x) + 693872cos(x) +--R + +--R 7 6 5 +--R - 401825cos(x) - 401825cos(x) + 144518cos(x) +--R + +--R 4 3 2 +--R 144518cos(x) - 28492cos(x) - 28492cos(x) + 2312cos(x) + 2312 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 16 14 12 +--R 20480cos(x) - 241664cos(x) + 1217024cos(x) +--R + +--R 10 8 6 +--R - 3399936cos(x) + 5726336cos(x) - 5904064cos(x) +--R + +--R 4 2 +--R 3599488cos(x) - 1171712cos(x) + 155136 +--R * +--R 12 +--R sin(x) +--R + +--R 18 16 14 +--R - 245760cos(x) + 3311616cos(x) - 19429376cos(x) +--R + +--R 12 10 8 +--R 64904704cos(x) - 135403392cos(x) + 181804064cos(x) +--R + +--R 6 4 2 +--R - 155813328cos(x) + 81311600cos(x) - 23151616cos(x) + 2721472 +--R * +--R 10 +--R sin(x) +--R + +--R 20 18 16 +--R 516096cos(x) - 7913472cos(x) + 53627904cos(x) +--R + +--R 14 12 10 +--R - 210905600cos(x) + 531091456cos(x) - 890489920cos(x) +--R + +--R 8 6 4 +--R 1000504352cos(x) - 737549928cos(x) + 337651504cos(x) +--R + +--R 2 +--R - 85549024cos(x) + 9034816 +--R * +--R 8 +--R sin(x) +--R + +--R 22 20 18 +--R - 245760cos(x) + 4337664cos(x) - 34166784cos(x) +--R + +--R 16 14 12 +--R 158196736cos(x) - 477072640cos(x) + 980334976cos(x) +--R + +--R 10 8 6 +--R - 1393969280cos(x) + 1362777000cos(x) - 889898528cos(x) +--R + +--R 4 2 +--R 365407500cos(x) - 83728304cos(x) + 8036784 +--R * +--R 6 +--R sin(x) +--R + +--R 24 22 20 +--R 20480cos(x) - 446464cos(x) + 4305408cos(x) +--R + +--R 18 16 14 +--R - 24354048cos(x) + 90074496cos(x) - 229303296cos(x) +--R + +--R 12 10 8 +--R 411061472cos(x) - 520804600cos(x) + 460100008cos(x) +--R + +--R 6 4 2 +--R - 274035048cos(x) + 103201848cos(x) - 21737344cos(x) + 1918432 +--R * +--R 4 +--R sin(x) +--R + +--R 24 22 20 18 +--R 2048cos(x) - 40960cos(x) + 366080cos(x) - 1932672cos(x) +--R + +--R 16 14 12 +--R 6703968cos(x) - 16059696cos(x) + 27149320cos(x) +--R + +--R 10 8 6 +--R - 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31893280cos(x) +--R + +--R 6 4 2 +--R 23631912cos(x) - 10801024cos(x) + 2750568cos(x) - 296464 +--R * +--R 4 +--R cot(x) +--R + +--R 18 16 14 +--R 368640cos(x) - 4284416cos(x) + 21604352cos(x) +--R + +--R 12 10 8 +--R - 61880320cos(x) + 110624896cos(x) - 127573120cos(x) +--R + +--R 6 4 2 +--R 94527648cos(x) - 43204096cos(x) + 11002272cos(x) - 1185856 +--R * +--R 2 +--R cot(x) +--R + +--R 18 16 14 +--R 368640cos(x) - 4284416cos(x) + 21604352cos(x) +--R + +--R 12 10 8 +--R - 61880320cos(x) + 110624896cos(x) - 127573120cos(x) +--R + +--R 6 4 2 +--R 94527648cos(x) - 43204096cos(x) + 11002272cos(x) - 1185856 +--R * +--R 10 +--R sin(x) +--R + +--R 20 18 16 +--R - 430080cos(x) + 5750784cos(x) - 33882624cos(x) +--R + +--R 14 12 10 +--R 115573760cos(x) - 252076416cos(x) + 366184256cos(x) +--R + +--R 8 6 4 +--R - 357449496cos(x) + 230469304cos(x) - 93433312cos(x) +--R + +--R 2 +--R 21382328cos(x) - 2088504 +--R * +--R 4 +--R cot(x) +--R + +--R 20 18 16 +--R - 1720320cos(x) + 23003136cos(x) - 135530496cos(x) +--R + +--R 14 12 10 +--R 462295040cos(x) - 1008305664cos(x) + 1464737024cos(x) +--R + +--R 8 6 4 +--R - 1429797984cos(x) + 921877216cos(x) - 373733248cos(x) +--R + +--R 2 +--R 85529312cos(x) - 8354016 +--R * +--R 2 +--R cot(x) +--R + +--R 20 18 16 +--R - 1720320cos(x) + 23003136cos(x) - 135530496cos(x) +--R + +--R 14 12 10 +--R 462295040cos(x) - 1008305664cos(x) + 1464737024cos(x) +--R + +--R 8 6 4 +--R - 1429797984cos(x) + 921877216cos(x) - 373733248cos(x) +--R + +--R 2 +--R 85529312cos(x) - 8354016 +--R * +--R 8 +--R sin(x) +--R + +--R 22 20 18 +--R 430080cos(x) - 6623232cos(x) + 45437952cos(x) +--R + +--R 16 14 12 +--R - 182956032cos(x) + 479324736cos(x) - 855606912cos(x) +--R + +--R 10 8 6 +--R 1058306400cos(x) - 903365976cos(x) + 518869578cos(x) +--R + +--R 4 2 +--R - 189814184cos(x) + 39527986cos(x) - 3530396 +--R * +--R 4 +--R cot(x) +--R + +--R 22 20 18 +--R 1720320cos(x) - 26492928cos(x) + 181751808cos(x) +--R + +--R 16 14 12 +--R - 731824128cos(x) + 1917298944cos(x) - 3422427648cos(x) +--R + +--R 10 8 6 +--R 4233225600cos(x) - 3613463904cos(x) + 2075478312cos(x) +--R + +--R 4 2 +--R - 759256736cos(x) + 158111944cos(x) - 14121584 +--R * +--R 2 +--R cot(x) +--R + +--R 22 20 18 +--R 1720320cos(x) - 26492928cos(x) + 181751808cos(x) +--R + +--R 16 14 12 +--R - 731824128cos(x) + 1917298944cos(x) - 3422427648cos(x) +--R + +--R 10 8 6 +--R 4233225600cos(x) - 3613463904cos(x) + 2075478312cos(x) +--R + +--R 4 2 +--R - 759256736cos(x) + 158111944cos(x) - 14121584 +--R * +--R 6 +--R sin(x) +--R + +--R 24 22 20 +--R - 92160cos(x) + 1683456cos(x) - 13731840cos(x) +--R + +--R 18 16 14 +--R 66116608cos(x) - 209080960cos(x) + 456752704cos(x) +--R + +--R 12 10 8 +--R - 705191904cos(x) + 772904056cos(x) - 594386892cos(x) +--R + +--R 6 4 2 +--R 311108464cos(x) - 104482766cos(x) + 20054436cos(x) - 1653202 +--R * +--R 4 +--R cot(x) +--R + +--R 24 22 20 +--R - 368640cos(x) + 6733824cos(x) - 54927360cos(x) +--R + +--R 18 16 14 +--R 264466432cos(x) - 836323840cos(x) + 1827010816cos(x) +--R + +--R 12 10 8 +--R - 2820767616cos(x) + 3091616224cos(x) - 2377547568cos(x) +--R + +--R 6 4 2 +--R 1244433856cos(x) - 417931064cos(x) + 80217744cos(x) - 6612808 +--R * +--R 2 +--R cot(x) +--R + +--R 24 22 20 +--R - 368640cos(x) + 6733824cos(x) - 54927360cos(x) +--R + +--R 18 16 14 +--R 264466432cos(x) - 836323840cos(x) + 1827010816cos(x) +--R + +--R 12 10 8 +--R - 2820767616cos(x) + 3091616224cos(x) - 2377547568cos(x) +--R + +--R 6 4 2 +--R 1244433856cos(x) - 417931064cos(x) + 80217744cos(x) - 6612808 +--R * +--R 4 +--R sin(x) +--R + +--R 26 24 22 20 +--R 2048cos(x) - 55296cos(x) + 614912cos(x) - 3875328cos(x) +--R + +--R 18 16 14 +--R 15714976cos(x) - 43677536cos(x) + 85953144cos(x) +--R + +--R 12 10 8 +--R - 121414952cos(x) + 123002306cos(x) - 88018304cos(x) +--R + +--R 6 4 2 +--R 43035270cos(x) - 13519812cos(x) + 2424884cos(x) - 186312 +--R * +--R 4 +--R cot(x) +--R + +--R 26 24 22 +--R 8192cos(x) - 221184cos(x) + 2459648cos(x) +--R + +--R 20 18 16 +--R - 15501312cos(x) + 62859904cos(x) - 174710144cos(x) +--R + +--R 14 12 10 +--R 343812576cos(x) - 485659808cos(x) + 492009224cos(x) +--R + +--R 8 6 4 +--R - 352073216cos(x) + 172141080cos(x) - 54079248cos(x) +--R + +--R 2 +--R 9699536cos(x) - 745248 +--R * +--R 2 +--R cot(x) +--R + +--R 26 24 22 20 +--R 8192cos(x) - 221184cos(x) + 2459648cos(x) - 15501312cos(x) +--R + +--R 18 16 14 +--R 62859904cos(x) - 174710144cos(x) + 343812576cos(x) +--R + +--R 12 10 8 +--R - 485659808cos(x) + 492009224cos(x) - 352073216cos(x) +--R + +--R 6 4 2 +--R 172141080cos(x) - 54079248cos(x) + 9699536cos(x) - 745248 +--R * +--R 2 +--R sin(x) +--R + +--R 24 22 20 18 +--R - 512cos(x) + 8192cos(x) - 59008cos(x) + 252544cos(x) +--R + +--R 16 14 12 +--R - 713608cos(x) + 1398608cos(x) - 1942768cos(x) +--R + +--R 10 8 6 4 +--R 1918624cos(x) - 1329322cos(x) + 625436cos(x) - 187834cos(x) +--R + +--R 2 +--R 31960cos(x) - 2312 +--R * +--R 4 +--R cot(x) +--R + +--R 24 22 20 18 +--R - 2048cos(x) + 32768cos(x) - 236032cos(x) + 1010176cos(x) +--R + +--R 16 14 12 +--R - 2854432cos(x) + 5594432cos(x) - 7771072cos(x) +--R + +--R 10 8 6 4 +--R 7674496cos(x) - 5317288cos(x) + 2501744cos(x) - 751336cos(x) +--R + +--R 2 +--R 127840cos(x) - 9248 +--R * +--R 2 +--R cot(x) +--R + +--R 24 22 20 18 +--R - 2048cos(x) + 32768cos(x) - 236032cos(x) + 1010176cos(x) +--R + +--R 16 14 12 10 +--R - 2854432cos(x) + 5594432cos(x) - 7771072cos(x) + 7674496cos(x) +--R + +--R 8 6 4 2 +--R - 5317288cos(x) + 2501744cos(x) - 751336cos(x) + 127840cos(x) - 9248 +--R / +--R 17 16 15 14 +--R 10240cos(x) + 10240cos(x) - 100352cos(x) - 100352cos(x) +--R + +--R 13 12 11 +--R 418048cos(x) + 418048cos(x) - 964224cos(x) +--R + +--R 10 9 8 +--R - 964224cos(x) + 1342528cos(x) + 1342528cos(x) +--R + +--R 7 6 5 +--R - 1151328cos(x) - 1151328cos(x) + 591552cos(x) +--R + +--R 4 3 2 +--R 591552cos(x) - 165856cos(x) - 165856cos(x) + 19392cos(x) +--R + +--R 19392 +--R * +--R 11 +--R sin(x) +--R + +--R 19 18 17 +--R - 122880cos(x) - 122880cos(x) + 1410048cos(x) +--R + +--R 16 15 14 +--R 1410048cos(x) - 7017472cos(x) - 7017472cos(x) +--R + +--R 13 12 11 +--R 19827456cos(x) + 19827456cos(x) - 34941376cos(x) +--R + +--R 10 9 8 +--R - 34941376cos(x) + 39682448cos(x) + 39682448cos(x) +--R + +--R 7 6 5 +--R - 28917128cos(x) - 28917128cos(x) + 12972856cos(x) +--R + +--R 4 3 2 +--R 12972856cos(x) - 3234136cos(x) - 3234136cos(x) +--R + +--R 340184cos(x) + 340184 +--R * +--R 9 +--R sin(x) +--R + +--R 21 20 19 +--R 258048cos(x) + 258048cos(x) - 3440640cos(x) +--R + +--R 18 17 16 +--R - 3440640cos(x) + 20190720cos(x) + 20190720cos(x) +--R + +--R 15 14 13 +--R - 68512000cos(x) - 68512000cos(x) + 148454400cos(x) +--R + +--R 12 11 10 +--R 148454400cos(x) - 213923616cos(x) - 213923616cos(x) +--R + +--R 9 8 7 +--R 206775760cos(x) + 206775760cos(x) - 131726772cos(x) +--R + +--R 6 5 4 +--R - 131726772cos(x) + 52617728cos(x) + 52617728cos(x) +--R + +--R 3 2 +--R - 11822980cos(x) - 11822980cos(x) + 1129352cos(x) + 1129352 +--R * +--R 7 +--R sin(x) +--R + +--R 23 22 21 +--R - 122880cos(x) - 122880cos(x) + 1923072cos(x) +--R + +--R 20 19 18 +--R 1923072cos(x) - 13360128cos(x) - 13360128cos(x) +--R + +--R 17 16 15 +--R 54301184cos(x) + 54301184cos(x) - 143171200cos(x) +--R + +--R 14 13 12 +--R - 143171200cos(x) + 256448960cos(x) + 256448960cos(x) +--R + +--R 11 10 9 +--R - 317375296cos(x) - 317375296cos(x) + 270228244cos(x) +--R + +--R 8 7 6 +--R 270228244cos(x) - 154296744cos(x) - 154296744cos(x) +--R + +--R 5 4 3 +--R 55890826cos(x) + 55890826cos(x) - 11470636cos(x) +--R + +--R 2 +--R - 11470636cos(x) + 1004598cos(x) + 1004598 +--R * +--R 5 +--R sin(x) +--R + +--R 25 24 23 22 +--R 10240cos(x) + 10240cos(x) - 202752cos(x) - 202752cos(x) +--R + +--R 21 20 19 +--R 1757440cos(x) + 1757440cos(x) - 8864896cos(x) +--R + +--R 18 17 16 +--R - 8864896cos(x) + 29054656cos(x) + 29054656cos(x) +--R + +--R 15 14 13 +--R - 65224960cos(x) - 65224960cos(x) + 102752816cos(x) +--R + +--R 12 11 10 +--R 102752816cos(x) - 114204316cos(x) - 114204316cos(x) +--R + +--R 9 8 7 +--R 88556812cos(x) + 88556812cos(x) - 46475320cos(x) +--R + +--R 6 5 4 +--R - 46475320cos(x) + 15557448cos(x) + 15557448cos(x) +--R + +--R 3 2 +--R - 2956972cos(x) - 2956972cos(x) + 239804cos(x) + 239804 +--R * +--R 3 +--R sin(x) +--R + +--R 25 24 23 22 +--R 1024cos(x) + 1024cos(x) - 18432cos(x) - 18432cos(x) +--R + +--R 21 20 19 +--R 147200cos(x) + 147200cos(x) - 690368cos(x) +--R + +--R 18 17 16 +--R - 690368cos(x) + 2117424cos(x) + 2117424cos(x) +--R + +--R 15 14 13 +--R - 4468984cos(x) - 4468984cos(x) + 6640708cos(x) +--R + +--R 12 11 10 +--R 6640708cos(x) - 6976572cos(x) - 6976572cos(x) +--R + +--R 9 8 7 +--R 5118330cos(x) + 5118330cos(x) - 2540420cos(x) +--R + +--R 6 5 4 +--R - 2540420cos(x) + 802614cos(x) + 802614cos(x) +--R + +--R 3 2 +--R - 143404cos(x) - 143404cos(x) + 10880cos(x) + 10880 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 16 14 12 10 +--R 2048cos(x) - 20480cos(x) + 87040cos(x) - 204800cos(x) +--R + +--R 8 6 4 2 +--R 290944cos(x) - 254720cos(x) + 133760cos(x) - 38400cos(x) + 4608 +--R * +--R 12 +--R sin(x) +--R + +--R 18 16 14 +--R - 92160cos(x) + 1071104cos(x) - 5401088cos(x) +--R + +--R 12 10 8 +--R 15470080cos(x) - 27656224cos(x) + 31893280cos(x) +--R + +--R 6 4 2 +--R - 23631912cos(x) + 10801024cos(x) - 2750568cos(x) + 296464 +--R * +--R 10 +--R sin(x) +--R + +--R 20 18 16 +--R 430080cos(x) - 5750784cos(x) + 33882624cos(x) +--R + +--R 14 12 10 +--R - 115573760cos(x) + 252076416cos(x) - 366184256cos(x) +--R + +--R 8 6 4 +--R 357449496cos(x) - 230469304cos(x) + 93433312cos(x) +--R + +--R 2 +--R - 21382328cos(x) + 2088504 +--R * +--R 8 +--R sin(x) +--R + +--R 22 20 18 +--R - 430080cos(x) + 6623232cos(x) - 45437952cos(x) +--R + +--R 16 14 12 +--R 182956032cos(x) - 479324736cos(x) + 855606912cos(x) +--R + +--R 10 8 6 +--R - 1058306400cos(x) + 903365976cos(x) - 518869578cos(x) +--R + +--R 4 2 +--R 189814184cos(x) - 39527986cos(x) + 3530396 +--R * +--R 6 +--R sin(x) +--R + +--R 24 22 20 +--R 92160cos(x) - 1683456cos(x) + 13731840cos(x) +--R + +--R 18 16 14 +--R - 66116608cos(x) + 209080960cos(x) - 456752704cos(x) +--R + +--R 12 10 8 +--R 705191904cos(x) - 772904056cos(x) + 594386892cos(x) +--R + +--R 6 4 2 +--R - 311108464cos(x) + 104482766cos(x) - 20054436cos(x) + 1653202 +--R * +--R 4 +--R sin(x) +--R + +--R 26 24 22 20 +--R - 2048cos(x) + 55296cos(x) - 614912cos(x) + 3875328cos(x) +--R + +--R 18 16 14 +--R - 15714976cos(x) + 43677536cos(x) - 85953144cos(x) +--R + +--R 12 10 8 +--R 121414952cos(x) - 123002306cos(x) + 88018304cos(x) +--R + +--R 6 4 2 +--R - 43035270cos(x) + 13519812cos(x) - 2424884cos(x) + 186312 +--R * +--R 2 +--R sin(x) +--R + +--R 24 22 20 18 +--R 512cos(x) - 8192cos(x) + 59008cos(x) - 252544cos(x) +--R + +--R 16 14 12 10 +--R 713608cos(x) - 1398608cos(x) + 1942768cos(x) - 1918624cos(x) +--R + +--R 8 6 4 2 +--R 1329322cos(x) - 625436cos(x) + 187834cos(x) - 31960cos(x) + 2312 +--R * +--R +-----------+ +--R | 2 +--R \|cot(x) + 2 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 528 +t0394:= (1-csc(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (458) (- csc(x) + 1)\|- csc(x) + 1 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 528 +r0394:= 1/2*(-cot(x)^2)^(1/2)*(cot(x)^2+2*log(sin(x)))*tan(x) +--R +--R +--R +---------+ +--R 2 | 2 +--R (2tan(x)log(sin(x)) + cot(x) tan(x))\|- cot(x) +--R (459) ------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 498 + +--S 499 of 528 +a0394:= integrate(t0394,x) +--R +--R +--R (460) +--R x 16 x 2 x 14 x 4 x 12 +--R - sin(-) - 8cos(-) sin(-) + (- 28cos(-) + 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 +--R (- 56cos(-) - 8cos(-) )sin(-) +--R 2 2 2 +--R + +--R x 8 x 4 x 8 +--R (- 70cos(-) - 68cos(-) - 6)sin(-) +--R 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (- 56cos(-) - 112cos(-) + 40cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (- 28cos(-) - 68cos(-) - 164cos(-) + 4)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (- 8cos(-) - 8cos(-) + 40cos(-) - 24cos(-) )sin(-) - cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R 4cos(-) - 6cos(-) + 4cos(-) - 1 +--R 2 2 2 +--R * +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R + +--R x x 11 x 3 x 9 x 5 x 7 +--R - 8cos(-)sin(-) - 24cos(-) sin(-) - 16cos(-) sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 7 x 5 x 9 x x 3 +--R 16cos(-) sin(-) + (24cos(-) + 8cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R x 11 x 3 x +--R (8cos(-) - 8cos(-) )sin(-) +--R 2 2 2 +--R / +--R x 16 x 2 x 14 x 4 x 12 +--R sin(-) + 8cos(-) sin(-) + (28cos(-) - 4)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 x 8 x 4 x 8 +--R (56cos(-) + 8cos(-) )sin(-) + (70cos(-) + 68cos(-) + 6)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (56cos(-) + 112cos(-) - 40cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (28cos(-) + 68cos(-) + 164cos(-) - 4)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (8cos(-) + 8cos(-) - 40cos(-) + 24cos(-) )sin(-) + cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R - 4cos(-) + 6cos(-) - 4cos(-) + 1 +--R 2 2 2 +--R Type: Union(Expression(Integer),...) +--E 499 + +--S 500 of 528 +m0394:= a0394-r0394 +--R +--R +--R (461) +--R x 16 x 2 x 14 x 4 x 12 +--R - 2sin(-) - 16cos(-) sin(-) + (- 56cos(-) + 8)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 +--R (- 112cos(-) - 16cos(-) )sin(-) +--R 2 2 2 +--R + +--R x 8 x 4 x 8 +--R (- 140cos(-) - 136cos(-) - 12)sin(-) +--R 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (- 112cos(-) - 224cos(-) + 80cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (- 56cos(-) - 136cos(-) - 328cos(-) + 8)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 +--R (- 16cos(-) - 16cos(-) + 80cos(-) - 48cos(-) )sin(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 12 x 8 x 4 +--R - 2cos(-) + 8cos(-) - 12cos(-) + 8cos(-) - 2 +--R 2 2 2 2 +--R * +--R tan(x)log(sin(x)) +--R + +--R 2 x 16 x 2 2 x 14 +--R - cot(x) sin(-) - 8cos(-) cot(x) sin(-) +--R 2 2 2 +--R + +--R x 4 2 x 12 +--R (- 28cos(-) + 4)cot(x) sin(-) +--R 2 2 +--R + +--R x 6 x 2 2 x 10 +--R (- 56cos(-) - 8cos(-) )cot(x) sin(-) +--R 2 2 2 +--R + +--R x 8 x 4 2 x 8 +--R (- 70cos(-) - 68cos(-) - 6)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 10 x 6 x 2 2 x 6 +--R (- 56cos(-) - 112cos(-) + 40cos(-) )cot(x) sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 2 x 4 +--R (- 28cos(-) - 68cos(-) - 164cos(-) + 4)cot(x) sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 2 x 2 +--R (- 8cos(-) - 8cos(-) + 40cos(-) - 24cos(-) )cot(x) sin(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 12 x 8 x 4 2 +--R (- cos(-) + 4cos(-) - 6cos(-) + 4cos(-) - 1)cot(x) +--R 2 2 2 2 +--R * +--R tan(x) +--R * +--R +---------+ +--R | 2 +--R \|- cot(x) +--R + +--R x 16 x 2 x 14 x 4 x 12 +--R - 2sin(-) - 16cos(-) sin(-) + (- 56cos(-) + 8)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 +--R (- 112cos(-) - 16cos(-) )sin(-) +--R 2 2 2 +--R + +--R x 8 x 4 x 8 +--R (- 140cos(-) - 136cos(-) - 12)sin(-) +--R 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (- 112cos(-) - 224cos(-) + 80cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (- 56cos(-) - 136cos(-) - 328cos(-) + 8)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 +--R (- 16cos(-) - 16cos(-) + 80cos(-) - 48cos(-) )sin(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 12 x 8 x 4 +--R - 2cos(-) + 8cos(-) - 12cos(-) + 8cos(-) - 2 +--R 2 2 2 2 +--R * +--R x x 3 x 3 x x +--R 2cos(-)sin(-) + (2cos(-) - 2cos(-))sin(-) +--R 2 2 2 2 2 +--R atan(-------------------------------------------) +--R x 4 x 2 x 4 x 2 +--R sin(-) - sin(-) - cos(-) - 3cos(-) +--R 2 2 2 2 +--R + +--R x x 11 x 3 x 9 x 5 x 7 +--R - 16cos(-)sin(-) - 48cos(-) sin(-) - 32cos(-) sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 7 x 5 x 9 x x 3 +--R 32cos(-) sin(-) + (48cos(-) + 16cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R x 11 x 3 x +--R (16cos(-) - 16cos(-) )sin(-) +--R 2 2 2 +--R / +--R x 16 x 2 x 14 x 4 x 12 +--R 2sin(-) + 16cos(-) sin(-) + (56cos(-) - 8)sin(-) +--R 2 2 2 2 2 +--R + +--R x 6 x 2 x 10 x 8 x 4 x 8 +--R (112cos(-) + 16cos(-) )sin(-) + (140cos(-) + 136cos(-) + 12)sin(-) +--R 2 2 2 2 2 2 +--R + +--R x 10 x 6 x 2 x 6 +--R (112cos(-) + 224cos(-) - 80cos(-) )sin(-) +--R 2 2 2 2 +--R + +--R x 12 x 8 x 4 x 4 +--R (56cos(-) + 136cos(-) + 328cos(-) - 8)sin(-) +--R 2 2 2 2 +--R + +--R x 14 x 10 x 6 x 2 x 2 x 16 +--R (16cos(-) + 16cos(-) - 80cos(-) + 48cos(-) )sin(-) + 2cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 12 x 8 x 4 +--R - 8cos(-) + 12cos(-) - 8cos(-) + 2 +--R 2 2 2 +--R Type: Expression(Integer) +--E 500 + +--S 501 of 528 +d0394:= D(m0394,x) +--R +--R +--R (462) +--R x 30 x 2 x 28 +--R 2sin(-) + (30cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (210cos(-) - 48cos(-) - 2)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (910cos(-) - 260cos(-) - 2cos(-) + 8)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 x 22 +--R (2730cos(-) - 832cos(-) + 100cos(-) - 80cos(-) + 10)sin(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 6006cos(-) - 1716cos(-) + 660cos(-) - 320cos(-) - 386cos(-) +--R 2 2 2 2 2 +--R + +--R - 28 +--R * +--R x 20 +--R sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 2288cos(-) + 2090cos(-) + 1040cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 2138cos(-) + 1248cos(-) - 26 +--R 2 2 +--R * +--R x 18 +--R sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 12870cos(-) - 1716cos(-) + 4026cos(-) + 7624cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4446cos(-) + 6348cos(-) - 546cos(-) + 80 +--R 2 2 2 +--R * +--R x 16 +--R sin(-) +--R 2 +--R + +--R x 16 x 12 x 10 x 8 +--R 12870cos(-) + 5016cos(-) + 17888cos(-) - 5660cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 6080cos(-) - 4392cos(-) - 672cos(-) + 6 +--R 2 2 2 +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 10010cos(-) + 1716cos(-) + 3960cos(-) + 21952cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 9044cos(-) - 5016cos(-) - 5864cos(-) + 2656cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 650cos(-) - 92 +--R 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) + 2288cos(-) + 1650cos(-) + 14624cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R - 16884cos(-) - 1408cos(-) + 564cos(-) - 8736cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 1538cos(-) - 304cos(-) + 26 +--R 2 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 1716cos(-) - 110cos(-) + 4120cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 6 +--R - 20668cos(-) + 16152cos(-) - 1372cos(-) + 10674cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 4748cos(-) + 170cos(-) + 40 +--R 2 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 832cos(-) - 572cos(-) - 656cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 13966cos(-) + 12864cos(-) - 11272cos(-) + 8736cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 13614cos(-) + 6272cos(-) + 4484cos(-) - 144cos(-) - 18 +--R 2 2 2 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 260cos(-) - 332cos(-) - 640cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 4490cos(-) - 1036cos(-) - 9864cos(-) - 2656cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 5278cos(-) - 4532cos(-) - 6252cos(-) - 608cos(-) + 90cos(-) +--R 2 2 2 2 2 +--R + +--R - 4 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 22 x 20 +--R 30cos(-) + 48cos(-) - 90cos(-) - 48cos(-) - 274cos(-) +--R 2 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 2400cos(-) - 2794cos(-) + 672cos(-) - 854cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 1200cos(-) + 3778cos(-) + 528cos(-) + 202cos(-) + 2 +--R 2 2 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R 2cos(-) + 4cos(-) - 10cos(-) + 24cos(-) + 122cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R - 36cos(-) - 274cos(-) - 80cos(-) + 166cos(-) + 156cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 34cos(-) - 72cos(-) - 34cos(-) + 4cos(-) - 6cos(-) +--R 2 2 2 2 2 +--R * +--R +---------+ +--R | 2 +--R sin(x)\|- cot(x) +--R + +--R 2 x 30 x 2 2 x 28 +--R 2cot(x) sin(-) + (30cos(-) - 4)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 x 26 +--R (210cos(-) - 72cos(-) - 10)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 2 x 24 +--R (910cos(-) - 540cos(-) - 18cos(-) + 24)cot(x) sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 468cos(-) + 192cos(-) + 18) +--R 2 2 2 2 +--R * +--R 2 x 22 +--R cot(x) sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 6006cos(-) - 6468cos(-) + 3476cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 186cos(-) - 60 +--R 2 +--R * +--R 2 x 20 +--R cot(x) sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) + 12210cos(-) - 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 258cos(-) - 72cos(-) - 10 +--R 2 2 +--R * +--R 2 x 18 +--R cot(x) sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 12870cos(-) - 16764cos(-) + 26730cos(-) - 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 5178cos(-) + 1764cos(-) + 342cos(-) + 80 +--R 2 2 2 +--R * +--R 2 x 16 +--R cot(x) sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 12870cos(-) - 15840cos(-) + 39864cos(-) - 34176cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 23988cos(-) - 5856cos(-) - 1704cos(-) - 192cos(-) - 10 +--R 2 2 2 2 +--R * +--R 2 x 14 +--R cot(x) sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 10010cos(-) - 9900cos(-) + 41976cos(-) - 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 48636cos(-) - 31608cos(-) + 4280cos(-) - 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 198cos(-) - 60 +--R 2 +--R * +--R 2 x 12 +--R cot(x) sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) + 31482cos(-) - 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 55356cos(-) - 35376cos(-) + 31188cos(-) + 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 1902cos(-) + 168cos(-) + 18 +--R 2 2 +--R * +--R 2 x 10 +--R cot(x) sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 16610cos(-) + 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 36852cos(-) - 3096cos(-) + 43764cos(-) - 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 5790cos(-) + 1452cos(-) + 42cos(-) + 24 +--R 2 2 2 +--R * +--R 2 x 8 +--R cot(x) sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 5940cos(-) + 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 13338cos(-) + 11808cos(-) + 20216cos(-) + 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 42786cos(-) - 12432cos(-) - 1260cos(-) - 10 +--R 2 2 2 +--R * +--R 2 x 6 +--R cot(x) sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1332cos(-) + 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1758cos(-) + 2100cos(-) + 24cos(-) - 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 11730cos(-) + 8796cos(-) + 8436cos(-) - 912cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 30cos(-) - 4 +--R 2 +--R * +--R 2 x 4 +--R cot(x) sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R 30cos(-) + 120cos(-) + 158cos(-) - 282cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 1224cos(-) - 1050cos(-) + 2496cos(-) + 2810cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 1944cos(-) - 2310cos(-) + 576cos(-) + 642cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 24cos(-) + 2 +--R 2 +--R * +--R 2 x 2 +--R cot(x) sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R 2cos(-) + 12cos(-) + 6cos(-) - 72cos(-) - 78cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 180cos(-) + 230cos(-) - 240cos(-) - 330cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 180cos(-) + 258cos(-) - 72cos(-) - 106cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 12cos(-) + 18cos(-) +--R 2 2 +--R * +--R 2 +--R cot(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 3 x 30 +--R (- 2cot(x) - 2cot(x))sin(-) +--R 2 +--R + +--R x 2 3 x 2 x 28 +--R ((- 30cos(-) + 4)cot(x) + (- 30cos(-) + 4)cot(x))sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 3 +--R (- 210cos(-) + 72cos(-) + 10)cot(x) +--R 2 2 +--R + +--R x 4 x 2 +--R (- 210cos(-) + 72cos(-) + 10)cot(x) +--R 2 2 +--R * +--R x 26 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 x 2 3 +--R (- 910cos(-) + 540cos(-) + 18cos(-) - 24)cot(x) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R (- 910cos(-) + 540cos(-) + 18cos(-) - 24)cot(x) +--R 2 2 2 +--R * +--R x 24 +--R sin(-) +--R 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 2730cos(-) + 2320cos(-) - 468cos(-) - 192cos(-) +--R 2 2 2 2 +--R + +--R - 18 +--R * +--R 3 +--R cot(x) +--R + +--R x 8 x 6 x 4 x 2 +--R - 2730cos(-) + 2320cos(-) - 468cos(-) - 192cos(-) +--R 2 2 2 2 +--R + +--R - 18 +--R * +--R cot(x) +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 6006cos(-) + 6468cos(-) - 3476cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 186cos(-) + 60 +--R 2 +--R * +--R 3 +--R cot(x) +--R + +--R x 10 x 8 x 6 x 4 +--R - 6006cos(-) + 6468cos(-) - 3476cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 186cos(-) + 60 +--R 2 +--R * +--R cot(x) +--R * +--R x 20 +--R sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 +--R - 10010cos(-) + 12408cos(-) - 12210cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 5376cos(-) + 258cos(-) + 72cos(-) + 10 +--R 2 2 2 +--R * +--R 3 +--R cot(x) +--R + +--R x 12 x 10 x 8 +--R - 10010cos(-) + 12408cos(-) - 12210cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 5376cos(-) + 258cos(-) + 72cos(-) + 10 +--R 2 2 2 +--R * +--R cot(x) +--R * +--R x 18 +--R sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 +--R - 12870cos(-) + 16764cos(-) - 26730cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 19320cos(-) - 5178cos(-) - 1764cos(-) - 342cos(-) - 80 +--R 2 2 2 2 +--R * +--R 3 +--R cot(x) +--R + +--R x 14 x 12 x 10 +--R - 12870cos(-) + 16764cos(-) - 26730cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 19320cos(-) - 5178cos(-) - 1764cos(-) - 342cos(-) - 80 +--R 2 2 2 2 +--R * +--R cot(x) +--R * +--R x 16 +--R sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 +--R - 12870cos(-) + 15840cos(-) - 39864cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 34176cos(-) - 23988cos(-) + 5856cos(-) + 1704cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 192cos(-) + 10 +--R 2 +--R * +--R 3 +--R cot(x) +--R + +--R x 16 x 14 x 12 +--R - 12870cos(-) + 15840cos(-) - 39864cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 34176cos(-) - 23988cos(-) + 5856cos(-) + 1704cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 192cos(-) + 10 +--R 2 +--R * +--R cot(x) +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 +--R - 10010cos(-) + 9900cos(-) - 41976cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R 32928cos(-) - 48636cos(-) + 31608cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4280cos(-) + 1536cos(-) + 198cos(-) + 60 +--R 2 2 2 +--R * +--R 3 +--R cot(x) +--R + +--R x 18 x 16 x 14 +--R - 10010cos(-) + 9900cos(-) - 41976cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R 32928cos(-) - 48636cos(-) + 31608cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 4280cos(-) + 1536cos(-) + 198cos(-) + 60 +--R 2 2 2 +--R * +--R cot(x) +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 +--R - 6006cos(-) + 3256cos(-) - 31482cos(-) +--R 2 2 2 +--R + +--R x 14 x 12 x 10 +--R 14592cos(-) - 55356cos(-) + 35376cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 31188cos(-) - 9024cos(-) - 1902cos(-) - 168cos(-) +--R 2 2 2 2 +--R + +--R - 18 +--R * +--R 3 +--R cot(x) +--R + +--R x 20 x 18 x 16 +--R - 6006cos(-) + 3256cos(-) - 31482cos(-) +--R 2 2 2 +--R + +--R x 14 x 12 x 10 +--R 14592cos(-) - 55356cos(-) + 35376cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 31188cos(-) - 9024cos(-) - 1902cos(-) - 168cos(-) +--R 2 2 2 2 +--R + +--R - 18 +--R * +--R cot(x) +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 +--R - 2730cos(-) - 396cos(-) - 16610cos(-) +--R 2 2 2 +--R + +--R x 16 x 14 x 12 +--R - 1704cos(-) - 36852cos(-) + 3096cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 +--R - 43764cos(-) + 61920cos(-) + 5790cos(-) +--R 2 2 2 +--R + +--R x 4 x 2 +--R - 1452cos(-) - 42cos(-) - 24 +--R 2 2 +--R * +--R 3 +--R cot(x) +--R + +--R x 22 x 20 x 18 +--R - 2730cos(-) - 396cos(-) - 16610cos(-) +--R 2 2 2 +--R + +--R x 16 x 14 x 12 +--R - 1704cos(-) - 36852cos(-) + 3096cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 +--R - 43764cos(-) + 61920cos(-) + 5790cos(-) +--R 2 2 2 +--R + +--R x 4 x 2 +--R - 1452cos(-) - 42cos(-) - 24 +--R 2 2 +--R * +--R cot(x) +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 +--R - 910cos(-) - 1008cos(-) - 5940cos(-) +--R 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 4800cos(-) - 13338cos(-) - 11808cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R - 20216cos(-) - 43968cos(-) - 42786cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 +--R 12432cos(-) + 1260cos(-) + 10 +--R 2 2 +--R * +--R 3 +--R cot(x) +--R + +--R x 24 x 22 x 20 +--R - 910cos(-) - 1008cos(-) - 5940cos(-) +--R 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 4800cos(-) - 13338cos(-) - 11808cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R - 20216cos(-) - 43968cos(-) - 42786cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 +--R 12432cos(-) + 1260cos(-) + 10 +--R 2 2 +--R * +--R cot(x) +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 210cos(-) - 500cos(-) - 1332cos(-) - 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 1758cos(-) - 2100cos(-) - 24cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 12160cos(-) + 11730cos(-) - 8796cos(-) - 8436cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 912cos(-) + 30cos(-) + 4 +--R 2 2 +--R * +--R 3 +--R cot(x) +--R + +--R x 26 x 24 x 22 x 20 +--R - 210cos(-) - 500cos(-) - 1332cos(-) - 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 1758cos(-) - 2100cos(-) - 24cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 12160cos(-) + 11730cos(-) - 8796cos(-) - 8436cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 912cos(-) + 30cos(-) + 4 +--R 2 2 +--R * +--R cot(x) +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R - 30cos(-) - 120cos(-) - 158cos(-) + 282cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1224cos(-) + 1050cos(-) - 2496cos(-) - 2810cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 1944cos(-) + 2310cos(-) - 576cos(-) - 642cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 24cos(-) - 2 +--R 2 +--R * +--R 3 +--R cot(x) +--R + +--R x 28 x 26 x 24 x 20 +--R - 30cos(-) - 120cos(-) - 158cos(-) + 282cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1224cos(-) + 1050cos(-) - 2496cos(-) - 2810cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 1944cos(-) + 2310cos(-) - 576cos(-) - 642cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 24cos(-) - 2 +--R 2 +--R * +--R cot(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 +--R - 2cos(-) - 12cos(-) - 6cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 78cos(-) - 180cos(-) - 230cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 330cos(-) - 180cos(-) - 258cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 106cos(-) - 12cos(-) - 18cos(-) +--R 2 2 2 +--R * +--R 3 +--R cot(x) +--R + +--R x 30 x 28 x 26 x 24 +--R - 2cos(-) - 12cos(-) - 6cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 78cos(-) - 180cos(-) - 230cos(-) + 240cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 330cos(-) - 180cos(-) - 258cos(-) + 72cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 106cos(-) - 12cos(-) - 18cos(-) +--R 2 2 2 +--R * +--R cot(x) +--R * +--R sin(x)tan(x) +--R + +--R 2 x 30 x 2 2 x 28 +--R 2cot(x) sin(-) + (30cos(-) - 4)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 x 26 +--R (210cos(-) - 72cos(-) - 10)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 2 x 24 +--R (910cos(-) - 540cos(-) - 18cos(-) + 24)cot(x) sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 468cos(-) + 192cos(-) + 18) +--R 2 2 2 2 +--R * +--R 2 x 22 +--R cot(x) sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 6006cos(-) - 6468cos(-) + 3476cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 186cos(-) - 60 +--R 2 +--R * +--R 2 x 20 +--R cot(x) sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) + 12210cos(-) - 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 258cos(-) - 72cos(-) - 10 +--R 2 2 +--R * +--R 2 x 18 +--R cot(x) sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 12870cos(-) - 16764cos(-) + 26730cos(-) - 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 5178cos(-) + 1764cos(-) + 342cos(-) + 80 +--R 2 2 2 +--R * +--R 2 x 16 +--R cot(x) sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 12870cos(-) - 15840cos(-) + 39864cos(-) - 34176cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 23988cos(-) - 5856cos(-) - 1704cos(-) - 192cos(-) - 10 +--R 2 2 2 2 +--R * +--R 2 x 14 +--R cot(x) sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 10010cos(-) - 9900cos(-) + 41976cos(-) - 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 48636cos(-) - 31608cos(-) + 4280cos(-) - 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 198cos(-) - 60 +--R 2 +--R * +--R 2 x 12 +--R cot(x) sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) + 31482cos(-) - 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 55356cos(-) - 35376cos(-) + 31188cos(-) + 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 1902cos(-) + 168cos(-) + 18 +--R 2 2 +--R * +--R 2 x 10 +--R cot(x) sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 16610cos(-) + 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 36852cos(-) - 3096cos(-) + 43764cos(-) - 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 5790cos(-) + 1452cos(-) + 42cos(-) + 24 +--R 2 2 2 +--R * +--R 2 x 8 +--R cot(x) sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 5940cos(-) + 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 13338cos(-) + 11808cos(-) + 20216cos(-) + 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 42786cos(-) - 12432cos(-) - 1260cos(-) - 10 +--R 2 2 2 +--R * +--R 2 x 6 +--R cot(x) sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1332cos(-) + 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1758cos(-) + 2100cos(-) + 24cos(-) - 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 11730cos(-) + 8796cos(-) + 8436cos(-) - 912cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 30cos(-) - 4 +--R 2 +--R * +--R 2 x 4 +--R cot(x) sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R 30cos(-) + 120cos(-) + 158cos(-) - 282cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 1224cos(-) - 1050cos(-) + 2496cos(-) + 2810cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 1944cos(-) - 2310cos(-) + 576cos(-) + 642cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 24cos(-) + 2 +--R 2 +--R * +--R 2 x 2 +--R cot(x) sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R 2cos(-) + 12cos(-) + 6cos(-) - 72cos(-) - 78cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 180cos(-) + 230cos(-) - 240cos(-) - 330cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 180cos(-) + 258cos(-) - 72cos(-) - 106cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 12cos(-) + 18cos(-) +--R 2 2 +--R * +--R 2 +--R cot(x) +--R * +--R sin(x) +--R * +--R log(sin(x)) +--R + +--R 4 x 30 x 2 4 x 28 +--R cot(x) sin(-) + (15cos(-) - 2)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 4 x 26 +--R (105cos(-) - 36cos(-) - 5)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 4 x 24 +--R (455cos(-) - 270cos(-) - 9cos(-) + 12)cot(x) sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 4 +--R (1365cos(-) - 1160cos(-) + 234cos(-) + 96cos(-) + 9)cot(x) +--R 2 2 2 2 +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 3003cos(-) - 3234cos(-) + 1738cos(-) - 120cos(-) - 93cos(-) +--R 2 2 2 2 2 +--R + +--R - 30 +--R * +--R 4 x 20 +--R cot(x) sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 5005cos(-) - 6204cos(-) + 6105cos(-) - 2688cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 129cos(-) - 36cos(-) - 5 +--R 2 2 +--R * +--R 4 x 18 +--R cot(x) sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 6435cos(-) - 8382cos(-) + 13365cos(-) - 9660cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 2589cos(-) + 882cos(-) + 171cos(-) + 40 +--R 2 2 2 +--R * +--R 4 x 16 +--R cot(x) sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 6435cos(-) - 7920cos(-) + 19932cos(-) - 17088cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 11994cos(-) - 2928cos(-) - 852cos(-) - 96cos(-) - 5 +--R 2 2 2 2 +--R * +--R 4 x 14 +--R cot(x) sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 5005cos(-) - 4950cos(-) + 20988cos(-) - 16464cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 24318cos(-) - 15804cos(-) + 2140cos(-) - 768cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 99cos(-) - 30 +--R 2 +--R * +--R 4 x 12 +--R cot(x) sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 3003cos(-) - 1628cos(-) + 15741cos(-) - 7296cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 27678cos(-) - 17688cos(-) + 15594cos(-) + 4512cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 951cos(-) + 84cos(-) + 9 +--R 2 2 +--R * +--R 4 x 10 +--R cot(x) sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 1365cos(-) + 198cos(-) + 8305cos(-) + 852cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 18426cos(-) - 1548cos(-) + 21882cos(-) - 30960cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 2895cos(-) + 726cos(-) + 21cos(-) + 12 +--R 2 2 2 +--R * +--R 4 x 8 +--R cot(x) sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 455cos(-) + 504cos(-) + 2970cos(-) + 2400cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 6669cos(-) + 5904cos(-) + 10108cos(-) + 21984cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 21393cos(-) - 6216cos(-) - 630cos(-) - 5 +--R 2 2 2 +--R * +--R 4 x 6 +--R cot(x) sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 105cos(-) + 250cos(-) + 666cos(-) + 840cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 879cos(-) + 1050cos(-) + 12cos(-) - 6080cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 5865cos(-) + 4398cos(-) + 4218cos(-) - 456cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 15cos(-) - 2 +--R 2 +--R * +--R 4 x 4 +--R cot(x) sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 x 18 +--R 15cos(-) + 60cos(-) + 79cos(-) - 141cos(-) - 612cos(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 525cos(-) + 1248cos(-) + 1405cos(-) - 972cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 1155cos(-) + 288cos(-) + 321cos(-) - 12cos(-) + 1 +--R 2 2 2 2 +--R * +--R 4 x 2 +--R cot(x) sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R cos(-) + 6cos(-) + 3cos(-) - 36cos(-) - 39cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 90cos(-) + 115cos(-) - 120cos(-) - 165cos(-) + 90cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 129cos(-) - 36cos(-) - 53cos(-) + 6cos(-) + 9cos(-) +--R 2 2 2 2 2 +--R * +--R 4 +--R cot(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 5 3 x 30 +--R (- 3cot(x) - 3cot(x) )sin(-) +--R 2 +--R + +--R x 2 5 x 2 3 x 28 +--R ((- 45cos(-) + 6)cot(x) + (- 45cos(-) + 6)cot(x) )sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 5 +--R (- 315cos(-) + 108cos(-) + 15)cot(x) +--R 2 2 +--R + +--R x 4 x 2 3 +--R (- 315cos(-) + 108cos(-) + 15)cot(x) +--R 2 2 +--R * +--R x 26 +--R sin(-) +--R 2 +--R + +--R x 6 x 4 x 2 5 +--R (- 1365cos(-) + 810cos(-) + 27cos(-) - 36)cot(x) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 3 +--R (- 1365cos(-) + 810cos(-) + 27cos(-) - 36)cot(x) +--R 2 2 2 +--R * +--R x 24 +--R sin(-) +--R 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 4095cos(-) + 3480cos(-) - 702cos(-) - 288cos(-) +--R 2 2 2 2 +--R + +--R - 27 +--R * +--R 5 +--R cot(x) +--R + +--R x 8 x 6 x 4 x 2 +--R - 4095cos(-) + 3480cos(-) - 702cos(-) - 288cos(-) +--R 2 2 2 2 +--R + +--R - 27 +--R * +--R 3 +--R cot(x) +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 9009cos(-) + 9702cos(-) - 5214cos(-) + 360cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 279cos(-) + 90 +--R 2 +--R * +--R 5 +--R cot(x) +--R + +--R x 10 x 8 x 6 x 4 +--R - 9009cos(-) + 9702cos(-) - 5214cos(-) + 360cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 279cos(-) + 90 +--R 2 +--R * +--R 3 +--R cot(x) +--R * +--R x 20 +--R sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 +--R - 15015cos(-) + 18612cos(-) - 18315cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 8064cos(-) + 387cos(-) + 108cos(-) + 15 +--R 2 2 2 +--R * +--R 5 +--R cot(x) +--R + +--R x 12 x 10 x 8 +--R - 15015cos(-) + 18612cos(-) - 18315cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 8064cos(-) + 387cos(-) + 108cos(-) + 15 +--R 2 2 2 +--R * +--R 3 +--R cot(x) +--R * +--R x 18 +--R sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 +--R - 19305cos(-) + 25146cos(-) - 40095cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 28980cos(-) - 7767cos(-) - 2646cos(-) - 513cos(-) - 120 +--R 2 2 2 2 +--R * +--R 5 +--R cot(x) +--R + +--R x 14 x 12 x 10 +--R - 19305cos(-) + 25146cos(-) - 40095cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 28980cos(-) - 7767cos(-) - 2646cos(-) - 513cos(-) - 120 +--R 2 2 2 2 +--R * +--R 3 +--R cot(x) +--R * +--R x 16 +--R sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 +--R - 19305cos(-) + 23760cos(-) - 59796cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 51264cos(-) - 35982cos(-) + 8784cos(-) + 2556cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 288cos(-) + 15 +--R 2 +--R * +--R 5 +--R cot(x) +--R + +--R x 16 x 14 x 12 +--R - 19305cos(-) + 23760cos(-) - 59796cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 51264cos(-) - 35982cos(-) + 8784cos(-) + 2556cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 288cos(-) + 15 +--R 2 +--R * +--R 3 +--R cot(x) +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 +--R - 15015cos(-) + 14850cos(-) - 62964cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R 49392cos(-) - 72954cos(-) + 47412cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 6420cos(-) + 2304cos(-) + 297cos(-) + 90 +--R 2 2 2 +--R * +--R 5 +--R cot(x) +--R + +--R x 18 x 16 x 14 +--R - 15015cos(-) + 14850cos(-) - 62964cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R 49392cos(-) - 72954cos(-) + 47412cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 6420cos(-) + 2304cos(-) + 297cos(-) + 90 +--R 2 2 2 +--R * +--R 3 +--R cot(x) +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 +--R - 9009cos(-) + 4884cos(-) - 47223cos(-) +--R 2 2 2 +--R + +--R x 14 x 12 x 10 +--R 21888cos(-) - 83034cos(-) + 53064cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 46782cos(-) - 13536cos(-) - 2853cos(-) - 252cos(-) +--R 2 2 2 2 +--R + +--R - 27 +--R * +--R 5 +--R cot(x) +--R + +--R x 20 x 18 x 16 +--R - 9009cos(-) + 4884cos(-) - 47223cos(-) +--R 2 2 2 +--R + +--R x 14 x 12 x 10 +--R 21888cos(-) - 83034cos(-) + 53064cos(-) +--R 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 46782cos(-) - 13536cos(-) - 2853cos(-) - 252cos(-) +--R 2 2 2 2 +--R + +--R - 27 +--R * +--R 3 +--R cot(x) +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 +--R - 4095cos(-) - 594cos(-) - 24915cos(-) +--R 2 2 2 +--R + +--R x 16 x 14 x 12 +--R - 2556cos(-) - 55278cos(-) + 4644cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 +--R - 65646cos(-) + 92880cos(-) + 8685cos(-) +--R 2 2 2 +--R + +--R x 4 x 2 +--R - 2178cos(-) - 63cos(-) - 36 +--R 2 2 +--R * +--R 5 +--R cot(x) +--R + +--R x 22 x 20 x 18 +--R - 4095cos(-) - 594cos(-) - 24915cos(-) +--R 2 2 2 +--R + +--R x 16 x 14 x 12 +--R - 2556cos(-) - 55278cos(-) + 4644cos(-) +--R 2 2 2 +--R + +--R x 10 x 8 x 6 +--R - 65646cos(-) + 92880cos(-) + 8685cos(-) +--R 2 2 2 +--R + +--R x 4 x 2 +--R - 2178cos(-) - 63cos(-) - 36 +--R 2 2 +--R * +--R 3 +--R cot(x) +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 +--R - 1365cos(-) - 1512cos(-) - 8910cos(-) +--R 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 7200cos(-) - 20007cos(-) - 17712cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R - 30324cos(-) - 65952cos(-) - 64179cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 +--R 18648cos(-) + 1890cos(-) + 15 +--R 2 2 +--R * +--R 5 +--R cot(x) +--R + +--R x 24 x 22 x 20 +--R - 1365cos(-) - 1512cos(-) - 8910cos(-) +--R 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 7200cos(-) - 20007cos(-) - 17712cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R - 30324cos(-) - 65952cos(-) - 64179cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 +--R 18648cos(-) + 1890cos(-) + 15 +--R 2 2 +--R * +--R 3 +--R cot(x) +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R - 315cos(-) - 750cos(-) - 1998cos(-) - 2520cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 2637cos(-) - 3150cos(-) - 36cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R 18240cos(-) + 17595cos(-) - 13194cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 12654cos(-) + 1368cos(-) + 45cos(-) + 6 +--R 2 2 2 +--R * +--R 5 +--R cot(x) +--R + +--R x 26 x 24 x 22 x 20 +--R - 315cos(-) - 750cos(-) - 1998cos(-) - 2520cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 +--R - 2637cos(-) - 3150cos(-) - 36cos(-) +--R 2 2 2 +--R + +--R x 12 x 10 x 8 +--R 18240cos(-) + 17595cos(-) - 13194cos(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 12654cos(-) + 1368cos(-) + 45cos(-) + 6 +--R 2 2 2 +--R * +--R 3 +--R cot(x) +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R - 45cos(-) - 180cos(-) - 237cos(-) + 423cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1836cos(-) + 1575cos(-) - 3744cos(-) - 4215cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 2916cos(-) + 3465cos(-) - 864cos(-) - 963cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 36cos(-) - 3 +--R 2 +--R * +--R 5 +--R cot(x) +--R + +--R x 28 x 26 x 24 x 20 +--R - 45cos(-) - 180cos(-) - 237cos(-) + 423cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1836cos(-) + 1575cos(-) - 3744cos(-) - 4215cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 2916cos(-) + 3465cos(-) - 864cos(-) - 963cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R 36cos(-) - 3 +--R 2 +--R * +--R 3 +--R cot(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 +--R - 3cos(-) - 18cos(-) - 9cos(-) + 108cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 117cos(-) - 270cos(-) - 345cos(-) + 360cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 495cos(-) - 270cos(-) - 387cos(-) + 108cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 159cos(-) - 18cos(-) - 27cos(-) +--R 2 2 2 +--R * +--R 5 +--R cot(x) +--R + +--R x 30 x 28 x 26 x 24 +--R - 3cos(-) - 18cos(-) - 9cos(-) + 108cos(-) +--R 2 2 2 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 117cos(-) - 270cos(-) - 345cos(-) + 360cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 495cos(-) - 270cos(-) - 387cos(-) + 108cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 159cos(-) - 18cos(-) - 27cos(-) +--R 2 2 2 +--R * +--R 3 +--R cot(x) +--R * +--R sin(x) +--R + +--R 2 x 30 x 2 2 x 28 +--R 2cos(x)cot(x) sin(-) + (30cos(-) - 4)cos(x)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 2 x 26 +--R (210cos(-) - 72cos(-) - 10)cos(x)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 2 x 24 +--R (910cos(-) - 540cos(-) - 18cos(-) + 24)cos(x)cot(x) sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R (2730cos(-) - 2320cos(-) + 468cos(-) + 192cos(-) + 18)cos(x) +--R 2 2 2 2 +--R * +--R 2 x 22 +--R cot(x) sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 6006cos(-) - 6468cos(-) + 3476cos(-) - 240cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 186cos(-) - 60 +--R 2 +--R * +--R 2 x 20 +--R cos(x)cot(x) sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) + 12210cos(-) - 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 258cos(-) - 72cos(-) - 10 +--R 2 2 +--R * +--R 2 x 18 +--R cos(x)cot(x) sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 12870cos(-) - 16764cos(-) + 26730cos(-) - 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 5178cos(-) + 1764cos(-) + 342cos(-) + 80 +--R 2 2 2 +--R * +--R 2 x 16 +--R cos(x)cot(x) sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 12870cos(-) - 15840cos(-) + 39864cos(-) - 34176cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 23988cos(-) - 5856cos(-) - 1704cos(-) - 192cos(-) - 10 +--R 2 2 2 2 +--R * +--R 2 x 14 +--R cos(x)cot(x) sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 10010cos(-) - 9900cos(-) + 41976cos(-) - 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 48636cos(-) - 31608cos(-) + 4280cos(-) - 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 198cos(-) - 60 +--R 2 +--R * +--R 2 x 12 +--R cos(x)cot(x) sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) + 31482cos(-) - 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 55356cos(-) - 35376cos(-) + 31188cos(-) + 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 1902cos(-) + 168cos(-) + 18 +--R 2 2 +--R * +--R 2 x 10 +--R cos(x)cot(x) sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 16610cos(-) + 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 36852cos(-) - 3096cos(-) + 43764cos(-) - 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 5790cos(-) + 1452cos(-) + 42cos(-) + 24 +--R 2 2 2 +--R * +--R 2 x 8 +--R cos(x)cot(x) sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 5940cos(-) + 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 13338cos(-) + 11808cos(-) + 20216cos(-) + 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 42786cos(-) - 12432cos(-) - 1260cos(-) - 10 +--R 2 2 2 +--R * +--R 2 x 6 +--R cos(x)cot(x) sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1332cos(-) + 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1758cos(-) + 2100cos(-) + 24cos(-) - 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 11730cos(-) + 8796cos(-) + 8436cos(-) - 912cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 30cos(-) - 4 +--R 2 +--R * +--R 2 x 4 +--R cos(x)cot(x) sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 +--R 30cos(-) + 120cos(-) + 158cos(-) - 282cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R - 1224cos(-) - 1050cos(-) + 2496cos(-) + 2810cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 1944cos(-) - 2310cos(-) + 576cos(-) + 642cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 24cos(-) + 2 +--R 2 +--R * +--R 2 x 2 +--R cos(x)cot(x) sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R 2cos(-) + 12cos(-) + 6cos(-) - 72cos(-) - 78cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 180cos(-) + 230cos(-) - 240cos(-) - 330cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 x 4 +--R 180cos(-) + 258cos(-) - 72cos(-) - 106cos(-) + 12cos(-) +--R 2 2 2 2 2 +--R + +--R x 2 +--R 18cos(-) +--R 2 +--R * +--R 2 +--R cos(x)cot(x) +--R * +--R tan(x) +--R + +--R 4 x 30 x 2 4 x 28 +--R cot(x) sin(-) + (15cos(-) - 2)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 4 x 26 +--R (105cos(-) - 36cos(-) - 5)cot(x) sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 4 x 24 +--R (455cos(-) - 270cos(-) - 9cos(-) + 12)cot(x) sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 4 +--R (1365cos(-) - 1160cos(-) + 234cos(-) + 96cos(-) + 9)cot(x) +--R 2 2 2 2 +--R * +--R x 22 +--R sin(-) +--R 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 3003cos(-) - 3234cos(-) + 1738cos(-) - 120cos(-) - 93cos(-) +--R 2 2 2 2 2 +--R + +--R - 30 +--R * +--R 4 x 20 +--R cot(x) sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 5005cos(-) - 6204cos(-) + 6105cos(-) - 2688cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 129cos(-) - 36cos(-) - 5 +--R 2 2 +--R * +--R 4 x 18 +--R cot(x) sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 6435cos(-) - 8382cos(-) + 13365cos(-) - 9660cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 2589cos(-) + 882cos(-) + 171cos(-) + 40 +--R 2 2 2 +--R * +--R 4 x 16 +--R cot(x) sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 6435cos(-) - 7920cos(-) + 19932cos(-) - 17088cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 11994cos(-) - 2928cos(-) - 852cos(-) - 96cos(-) - 5 +--R 2 2 2 2 +--R * +--R 4 x 14 +--R cot(x) sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 5005cos(-) - 4950cos(-) + 20988cos(-) - 16464cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 24318cos(-) - 15804cos(-) + 2140cos(-) - 768cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 99cos(-) - 30 +--R 2 +--R * +--R 4 x 12 +--R cot(x) sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 3003cos(-) - 1628cos(-) + 15741cos(-) - 7296cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 27678cos(-) - 17688cos(-) + 15594cos(-) + 4512cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 951cos(-) + 84cos(-) + 9 +--R 2 2 +--R * +--R 4 x 10 +--R cot(x) sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 1365cos(-) + 198cos(-) + 8305cos(-) + 852cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 18426cos(-) - 1548cos(-) + 21882cos(-) - 30960cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 2895cos(-) + 726cos(-) + 21cos(-) + 12 +--R 2 2 2 +--R * +--R 4 x 8 +--R cot(x) sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 455cos(-) + 504cos(-) + 2970cos(-) + 2400cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 6669cos(-) + 5904cos(-) + 10108cos(-) + 21984cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 21393cos(-) - 6216cos(-) - 630cos(-) - 5 +--R 2 2 2 +--R * +--R 4 x 6 +--R cot(x) sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 105cos(-) + 250cos(-) + 666cos(-) + 840cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 879cos(-) + 1050cos(-) + 12cos(-) - 6080cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 5865cos(-) + 4398cos(-) + 4218cos(-) - 456cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 15cos(-) - 2 +--R 2 +--R * +--R 4 x 4 +--R cot(x) sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 x 18 +--R 15cos(-) + 60cos(-) + 79cos(-) - 141cos(-) - 612cos(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 525cos(-) + 1248cos(-) + 1405cos(-) - 972cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 1155cos(-) + 288cos(-) + 321cos(-) - 12cos(-) + 1 +--R 2 2 2 2 +--R * +--R 4 x 2 +--R cot(x) sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R cos(-) + 6cos(-) + 3cos(-) - 36cos(-) - 39cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 90cos(-) + 115cos(-) - 120cos(-) - 165cos(-) + 90cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 129cos(-) - 36cos(-) - 53cos(-) + 6cos(-) + 9cos(-) +--R 2 2 2 2 2 +--R * +--R 4 +--R cot(x) +--R * +--R sin(x) +--R / +--R x 30 x 2 x 28 +--R 2sin(-) + (30cos(-) - 4)sin(-) +--R 2 2 2 +--R + +--R x 4 x 2 x 26 +--R (210cos(-) - 72cos(-) - 10)sin(-) +--R 2 2 2 +--R + +--R x 6 x 4 x 2 x 24 +--R (910cos(-) - 540cos(-) - 18cos(-) + 24)sin(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 x 22 +--R (2730cos(-) - 2320cos(-) + 468cos(-) + 192cos(-) + 18)sin(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 6006cos(-) - 6468cos(-) + 3476cos(-) - 240cos(-) - 186cos(-) +--R 2 2 2 2 2 +--R + +--R - 60 +--R * +--R x 20 +--R sin(-) +--R 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 10010cos(-) - 12408cos(-) + 12210cos(-) - 5376cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R - 258cos(-) - 72cos(-) - 10 +--R 2 2 +--R * +--R x 18 +--R sin(-) +--R 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 12870cos(-) - 16764cos(-) + 26730cos(-) - 19320cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R 5178cos(-) + 1764cos(-) + 342cos(-) + 80 +--R 2 2 2 +--R * +--R x 16 +--R sin(-) +--R 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 12870cos(-) - 15840cos(-) + 39864cos(-) - 34176cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R 23988cos(-) - 5856cos(-) - 1704cos(-) - 192cos(-) - 10 +--R 2 2 2 2 +--R * +--R x 14 +--R sin(-) +--R 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 10010cos(-) - 9900cos(-) + 41976cos(-) - 32928cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R 48636cos(-) - 31608cos(-) + 4280cos(-) - 1536cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 198cos(-) - 60 +--R 2 +--R * +--R x 12 +--R sin(-) +--R 2 +--R + +--R x 20 x 18 x 16 x 14 +--R 6006cos(-) - 3256cos(-) + 31482cos(-) - 14592cos(-) +--R 2 2 2 2 +--R + +--R x 12 x 10 x 8 x 6 +--R 55356cos(-) - 35376cos(-) + 31188cos(-) + 9024cos(-) +--R 2 2 2 2 +--R + +--R x 4 x 2 +--R 1902cos(-) + 168cos(-) + 18 +--R 2 2 +--R * +--R x 10 +--R sin(-) +--R 2 +--R + +--R x 22 x 20 x 18 x 16 +--R 2730cos(-) + 396cos(-) + 16610cos(-) + 1704cos(-) +--R 2 2 2 2 +--R + +--R x 14 x 12 x 10 x 8 +--R 36852cos(-) - 3096cos(-) + 43764cos(-) - 61920cos(-) +--R 2 2 2 2 +--R + +--R x 6 x 4 x 2 +--R - 5790cos(-) + 1452cos(-) + 42cos(-) + 24 +--R 2 2 2 +--R * +--R x 8 +--R sin(-) +--R 2 +--R + +--R x 24 x 22 x 20 x 18 +--R 910cos(-) + 1008cos(-) + 5940cos(-) + 4800cos(-) +--R 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R 13338cos(-) + 11808cos(-) + 20216cos(-) + 43968cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 +--R 42786cos(-) - 12432cos(-) - 1260cos(-) - 10 +--R 2 2 2 +--R * +--R x 6 +--R sin(-) +--R 2 +--R + +--R x 26 x 24 x 22 x 20 +--R 210cos(-) + 500cos(-) + 1332cos(-) + 1680cos(-) +--R 2 2 2 2 +--R + +--R x 18 x 16 x 14 x 12 +--R 1758cos(-) + 2100cos(-) + 24cos(-) - 12160cos(-) +--R 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 +--R - 11730cos(-) + 8796cos(-) + 8436cos(-) - 912cos(-) +--R 2 2 2 2 +--R + +--R x 2 +--R - 30cos(-) - 4 +--R 2 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 28 x 26 x 24 x 20 x 18 +--R 30cos(-) + 120cos(-) + 158cos(-) - 282cos(-) - 1224cos(-) +--R 2 2 2 2 2 +--R + +--R x 16 x 14 x 12 x 10 +--R - 1050cos(-) + 2496cos(-) + 2810cos(-) - 1944cos(-) +--R 2 2 2 2 +--R + +--R x 8 x 6 x 4 x 2 +--R - 2310cos(-) + 576cos(-) + 642cos(-) - 24cos(-) + 2 +--R 2 2 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 30 x 28 x 26 x 24 x 22 +--R 2cos(-) + 12cos(-) + 6cos(-) - 72cos(-) - 78cos(-) +--R 2 2 2 2 2 +--R + +--R x 20 x 18 x 16 x 14 x 12 +--R 180cos(-) + 230cos(-) - 240cos(-) - 330cos(-) + 180cos(-) +--R 2 2 2 2 2 +--R + +--R x 10 x 8 x 6 x 4 x 2 +--R 258cos(-) - 72cos(-) - 106cos(-) + 12cos(-) + 18cos(-) +--R 2 2 2 2 2 +--R * +--R +---------+ +--R | 2 +--R sin(x)\|- cot(x) +--R Type: Expression(Integer) +--E 501 + +--S 502 of 528 +t0395:= (-1+csc(x)^2)^(3/2) +--R +--R +--R +-----------+ +--R 2 | 2 +--R (463) (csc(x) - 1)\|csc(x) - 1 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 528 +r0395:= -1/2*(cot(x)^2)^(1/2)*(cot(x)^2+2*log(sin(x)))*tan(x) +--R +--R +--R +-------+ +--R 2 | 2 +--R (- 2tan(x)log(sin(x)) - cot(x) tan(x))\|cot(x) +--R (464) ------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 503 + +--S 504 of 528 +a0395:= integrate(t0395,x) +--R +--R +--R (465) +--R 2 sin(x) 2 2 2 +--R (4cos(x) - 4)log(----------) + (- 4cos(x) + 4)log(----------) - cos(x) - 1 +--R cos(x) + 1 cos(x) + 1 +--R ----------------------------------------------------------------------------- +--R 2 +--R 4cos(x) - 4 +--R Type: Union(Expression(Integer),...) +--E 504 + +--S 505 of 528 +m0395:= a0395-r0395 +--R +--R +--R (466) +--R +-------+ +--R 2 2 2 | 2 +--R ((4cos(x) - 4)tan(x)log(sin(x)) + (2cos(x) - 2)cot(x) tan(x))\|cot(x) +--R + +--R 2 sin(x) 2 2 2 +--R (4cos(x) - 4)log(----------) + (- 4cos(x) + 4)log(----------) - cos(x) +--R cos(x) + 1 cos(x) + 1 +--R + +--R - 1 +--R / +--R 2 +--R 4cos(x) - 4 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 528 +d0395:= D(m0395,x) +--R +--R +--R (467) +--R +-------+ +--R 2 5 3 | 2 +--R (- 2cos(x)sin(x) + 2cos(x) - 4cos(x) + 2cos(x))\|cot(x) +--R + +--R 4 2 2 2 +--R (2cos(x) - 4cos(x) + 2)cot(x) sin(x)tan(x) +--R + +--R 4 2 3 +--R (- 2cos(x) + 4cos(x) - 2)cot(x) +--R + +--R 4 2 +--R (- 2cos(x) + 4cos(x) - 2)cot(x) +--R * +--R sin(x)tan(x) +--R + +--R 4 2 2 +--R (2cos(x) - 4cos(x) + 2)cot(x) sin(x) +--R * +--R log(sin(x)) +--R + +--R 4 2 4 2 +--R (cos(x) - 2cos(x) + 1)cot(x) sin(x)tan(x) +--R + +--R 4 2 5 +--R (- 3cos(x) + 6cos(x) - 3)cot(x) +--R + +--R 4 2 3 +--R (- 3cos(x) + 6cos(x) - 3)cot(x) +--R * +--R sin(x) +--R + +--R 5 3 2 +--R (2cos(x) - 4cos(x) + 2cos(x))cot(x) +--R * +--R tan(x) +--R + +--R 4 2 4 +--R (cos(x) - 2cos(x) + 1)cot(x) sin(x) +--R / +--R +-------+ +--R 4 2 | 2 +--R (2cos(x) - 4cos(x) + 2)sin(x)\|cot(x) +--R Type: Expression(Integer) +--E 506 + +--S 507 of 528 +t0396:= (-1-csc(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (468) (- csc(x) - 1)\|- csc(x) - 1 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 528 +r0396:= 2*atan((-2-cot(x)^2)^(1/2)*tan(x))-atanh(cot(x)/(-2-cot(x)^2)^(1/2))+_ + 1/2*cot(x)*(-2-cot(x)^2)^(1/2) +--R +--R +--R (469) +--R +-------------+ +--R cot(x) | 2 +--R - 2atanh(----------------) + 4atan(tan(x)\|- cot(x) - 2 ) +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R + +--R +-------------+ +--R | 2 +--R cot(x)\|- cot(x) - 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 508 + +--S 509 of 528 +a0396:= integrate(t0396,x) +--R +--R +--R (470) +--R +---+ 6 +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) - 20\|- 1 (%e ) + 28\|- 1 (%e ) +--R + +--R +---+ +--R - 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) + 32\|- 1 (%e ) - 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R 64\|- 1 (%e ) - 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) + 2\|- 1 + 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) + 5(%e ) - 7(%e ) + 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (%e ) - 8(%e ) + 18(%e ) - 16(%e ) + 5 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) + 1) +--R + +--R +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) + 20\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 28\|- 1 (%e ) + 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) - 32\|- 1 (%e ) + 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 64\|- 1 (%e ) + 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) - 2\|- 1 + 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R ((%e ) - 5(%e ) + 7(%e ) - 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) + 8(%e ) - 18(%e ) + 16(%e ) - 5 +--R * +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) + 2)\|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) - 8(%e ) - 2 +--R + +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +---+ 4 +--R x\|- 1 | x\|- 1 x\|- 1 x\|- 1 +--R (- 8(%e ) + 8)\|(%e ) - 6(%e ) + 1 + 8(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R - 32(%e ) + 8 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (2(%e ) - 10(%e ) + 14(%e ) - 6) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - 2(%e ) + 16(%e ) - 36(%e ) + 32(%e ) - 10 +--R Type: Union(Expression(Integer),...) +--E 509 + +--S 510 of 528 +m0396:= a0396-r0396 +--R +--R +--R (471) +--R +---+ 6 +---+ 4 +---+ 2 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) - 20\|- 1 (%e ) + 28\|- 1 (%e ) +--R + +--R +---+ +--R - 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) + 32\|- 1 (%e ) - 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R 64\|- 1 (%e ) - 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) + 2\|- 1 + 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (- (%e ) + 5(%e ) - 7(%e ) + 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R (%e ) - 8(%e ) + 18(%e ) - 16(%e ) + 5 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) + 1) +--R + +--R +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 4\|- 1 (%e ) + 20\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 28\|- 1 (%e ) + 12\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R 4\|- 1 (%e ) - 32\|- 1 (%e ) + 72\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 64\|- 1 (%e ) + 20\|- 1 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +---+ 2 +--R | x\|- 1 x\|- 1 x\|- 1 +---+ +--R log(\|(%e ) - 6(%e ) + 1 - (%e ) - 2\|- 1 + 1) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R ((%e ) - 5(%e ) + 7(%e ) - 3) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) + 8(%e ) - 18(%e ) + 16(%e ) - 5 +--R * +--R log +--R +--------------------------------+ +--R +---+ 2 | +---+ 4 +---+ 2 +--R x\|- 1 | x\|- 1 x\|- 1 +--R (- 2(%e ) + 2)\|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 2(%e ) - 8(%e ) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (2(%e ) - 10(%e ) + 14(%e ) - 6) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - 2(%e ) + 16(%e ) - 36(%e ) + 32(%e ) - 10 +--R * +--R cot(x) +--R atanh(----------------) +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (- 4(%e ) + 20(%e ) - 28(%e ) + 12) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R 4(%e ) - 32(%e ) + 72(%e ) - 64(%e ) + 20 +--R * +--R +-------------+ +--R | 2 +--R atan(tan(x)\|- cot(x) - 2 ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - cot(x)(%e ) + 5cot(x)(%e ) - 7cot(x)(%e ) +--R + +--R 3cot(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R + +--R +---+ 2 +--R x\|- 1 +--R - 8(%e ) + 8 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 x\|- 1 +--R cot(x)(%e ) - 8cot(x)(%e ) + 18cot(x)(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R - 16cot(x)(%e ) + 5cot(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R + +--R +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 +--R 8(%e ) - 32(%e ) + 8 +--R / +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R (2(%e ) - 10(%e ) + 14(%e ) - 6) +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 8 +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 x\|- 1 +--R - 2(%e ) + 16(%e ) - 36(%e ) + 32(%e ) - 10 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 528 +d0396:= D(m0396,x) +--R +--R +--R (472) +--R +---+ 18 +--R +---+ 2 +---+ x\|- 1 +--R (\|- 1 cot(x) + 2\|- 1 )(%e ) +--R + +--R +---+ 16 +--R +---+ 2 +---+ x\|- 1 +--R (- 27\|- 1 cot(x) - 54\|- 1 )(%e ) +--R + +--R +---+ 14 +--R +---+ 2 +---+ x\|- 1 +--R (302\|- 1 cot(x) + 604\|- 1 )(%e ) +--R + +--R +---+ 12 +--R +---+ 2 +---+ x\|- 1 +--R (- 1806\|- 1 cot(x) - 3612\|- 1 )(%e ) +--R + +--R +---+ 10 +--R +---+ 2 +---+ x\|- 1 +--R (6216\|- 1 cot(x) + 12432\|- 1 )(%e ) +--R + +--R +---+ 8 +--R +---+ 2 +---+ x\|- 1 +--R (- 12348\|- 1 cot(x) - 24696\|- 1 )(%e ) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (13482\|- 1 cot(x) + 26964\|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (- 7290\|- 1 cot(x) - 14580\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +--R (1663\|- 1 cot(x) + 3326\|- 1 )(%e ) +--R + +--R +---+ 2 +---+ +--R - 129\|- 1 cot(x) - 258\|- 1 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - \|- 1 (%e ) + 27\|- 1 (%e ) +--R + +--R +---+ 14 +---+ 12 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 302\|- 1 (%e ) + 1806\|- 1 (%e ) +--R + +--R +---+ 10 +---+ 8 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 6216\|- 1 (%e ) + 12348\|- 1 (%e ) +--R + +--R +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 13482\|- 1 (%e ) + 7290\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 1663\|- 1 (%e ) + 129\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R + +--R +---+ 18 +--R 6 4 2 x\|- 1 +--R (- cot(x) - 4cot(x) - 8cot(x) - 8)(%e ) +--R + +--R +---+ 16 +--R 6 4 2 x\|- 1 +--R (21cot(x) + 84cot(x) + 168cot(x) + 168)(%e ) +--R + +--R +---+ 14 +--R 6 4 2 x\|- 1 +--R (- 182cot(x) - 728cot(x) - 1456cot(x) - 1456)(%e ) +--R + +--R +---+ 12 +--R 6 4 2 x\|- 1 +--R (850cot(x) + 3400cot(x) + 6800cot(x) + 6800)(%e ) +--R + +--R +---+ 10 +--R 6 4 2 x\|- 1 +--R (- 2352cot(x) - 9408cot(x) - 18816cot(x) - 18816)(%e ) +--R + +--R +---+ 8 +--R 6 4 2 x\|- 1 +--R (4004cot(x) + 16016cot(x) + 32032cot(x) + 32032)(%e ) +--R + +--R +---+ 6 +--R 6 4 2 x\|- 1 +--R (- 4210cot(x) - 16840cot(x) - 33680cot(x) - 33680)(%e ) +--R + +--R +---+ 4 +--R 6 4 2 x\|- 1 +--R (2646cot(x) + 10584cot(x) + 21168cot(x) + 21168)(%e ) +--R + +--R +---+ 2 +--R 6 4 2 x\|- 1 +--R (- 903cot(x) - 3612cot(x) - 7224cot(x) - 7224)(%e ) +--R + +--R 6 4 2 +--R 127cot(x) + 508cot(x) + 1016cot(x) + 1016 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 18 +--R 3 x\|- 1 +--R (2cot(x) + 2cot(x))(%e ) +--R + +--R +---+ 16 +--R 3 x\|- 1 +--R (- 42cot(x) - 42cot(x))(%e ) +--R + +--R +---+ 14 +--R 3 x\|- 1 +--R (364cot(x) + 364cot(x))(%e ) +--R + +--R +---+ 12 +--R 3 x\|- 1 +--R (- 1700cot(x) - 1700cot(x))(%e ) +--R + +--R +---+ 10 +--R 3 x\|- 1 +--R (4704cot(x) + 4704cot(x))(%e ) +--R + +--R +---+ 8 +--R 3 x\|- 1 +--R (- 8008cot(x) - 8008cot(x))(%e ) +--R + +--R +---+ 6 +--R 3 x\|- 1 +--R (8420cot(x) + 8420cot(x))(%e ) +--R + +--R +---+ 4 +--R 3 x\|- 1 +--R (- 5292cot(x) - 5292cot(x))(%e ) +--R + +--R +---+ 2 +--R 3 x\|- 1 3 +--R (1806cot(x) + 1806cot(x))(%e ) - 254cot(x) - 254cot(x) +--R * +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +--R 4 x\|- 1 4 x\|- 1 +--R (cot(x) - 2)(%e ) + (- 21cot(x) + 42)(%e ) +--R + +--R +---+ 14 +---+ 12 +--R 4 x\|- 1 4 x\|- 1 +--R (182cot(x) - 364)(%e ) + (- 850cot(x) + 1700)(%e ) +--R + +--R +---+ 10 +--R 4 x\|- 1 +--R (2352cot(x) - 4704)(%e ) +--R + +--R +---+ 8 +---+ 6 +--R 4 x\|- 1 4 x\|- 1 +--R (- 4004cot(x) + 8008)(%e ) + (4210cot(x) - 8420)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 4 x\|- 1 4 x\|- 1 +--R (- 2646cot(x) + 5292)(%e ) + (903cot(x) - 1806)(%e ) +--R + +--R 4 +--R - 127cot(x) + 254 +--R * +--R +--------------------------------+ +--R | +---+ 4 +---+ 2 +--R | x\|- 1 x\|- 1 +--R \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 20 +--R +---+ 2 +---+ x\|- 1 +--R (- \|- 1 cot(x) - 2\|- 1 )(%e ) +--R + +--R +---+ 18 +--R +---+ 2 +---+ x\|- 1 +--R (30\|- 1 cot(x) + 60\|- 1 )(%e ) +--R + +--R +---+ 16 +--R +---+ 2 +---+ x\|- 1 +--R (- 379\|- 1 cot(x) - 758\|- 1 )(%e ) +--R + +--R +---+ 14 +--R +---+ 2 +---+ x\|- 1 +--R (2616\|- 1 cot(x) + 5232\|- 1 )(%e ) +--R + +--R +---+ 12 +--R +---+ 2 +---+ x\|- 1 +--R (- 10706\|- 1 cot(x) - 21412\|- 1 )(%e ) +--R + +--R +---+ 10 +--R +---+ 2 +---+ x\|- 1 +--R (26388\|- 1 cot(x) + 52776\|- 1 )(%e ) +--R + +--R +---+ 8 +--R +---+ 2 +---+ x\|- 1 +--R (- 38118\|- 1 cot(x) - 76236\|- 1 )(%e ) +--R + +--R +---+ 6 +--R +---+ 2 +---+ x\|- 1 +--R (30168\|- 1 cot(x) + 60336\|- 1 )(%e ) +--R + +--R +---+ 4 +--R +---+ 2 +---+ x\|- 1 +--R (- 11789\|- 1 cot(x) - 23578\|- 1 )(%e ) +--R + +--R +---+ 2 +--R +---+ 2 +---+ x\|- 1 +---+ 2 +--R (2046\|- 1 cot(x) + 4092\|- 1 )(%e ) - 127\|- 1 cot(x) +--R + +--R +---+ +--R - 254\|- 1 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +---+ 16 +--R +---+ x\|- 1 +---+ x\|- 1 +---+ x\|- 1 +--R \|- 1 (%e ) - 30\|- 1 (%e ) + 379\|- 1 (%e ) +--R + +--R +---+ 14 +---+ 12 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 2616\|- 1 (%e ) + 10706\|- 1 (%e ) +--R + +--R +---+ 10 +---+ 8 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 26388\|- 1 (%e ) + 38118\|- 1 (%e ) +--R + +--R +---+ 6 +---+ 4 +--R +---+ x\|- 1 +---+ x\|- 1 +--R - 30168\|- 1 (%e ) + 11789\|- 1 (%e ) +--R + +--R +---+ 2 +--R +---+ x\|- 1 +---+ +--R - 2046\|- 1 (%e ) + 127\|- 1 +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R + +--R +---+ 20 +--R 6 4 2 x\|- 1 +--R (cot(x) + 4cot(x) + 8cot(x) + 8)(%e ) +--R + +--R +---+ 18 +--R 6 4 2 x\|- 1 +--R (- 24cot(x) - 96cot(x) - 192cot(x) - 192)(%e ) +--R + +--R +---+ 16 +--R 6 4 2 x\|- 1 +--R (241cot(x) + 964cot(x) + 1928cot(x) + 1928)(%e ) +--R + +--R +---+ 14 +--R 6 4 2 x\|- 1 +--R (- 1324cot(x) - 5296cot(x) - 10592cot(x) - 10592)(%e ) +--R + +--R +---+ 12 +--R 6 4 2 x\|- 1 +--R (4382cot(x) + 17528cot(x) + 35056cot(x) + 35056)(%e ) +--R + +--R +---+ 10 +--R 6 4 2 x\|- 1 +--R (- 9100cot(x) - 36400cot(x) - 72800cot(x) - 72800)(%e ) +--R + +--R +---+ 8 +--R 6 4 2 x\|- 1 +--R (11998cot(x) + 47992cot(x) + 95984cot(x) + 95984)(%e ) +--R + +--R +---+ 6 +--R 6 4 2 x\|- 1 +--R (- 9908cot(x) - 39632cot(x) - 79264cot(x) - 79264)(%e ) +--R + +--R +---+ 4 +--R 6 4 2 x\|- 1 +--R (4881cot(x) + 19524cot(x) + 39048cot(x) + 39048)(%e ) +--R + +--R +---+ 2 +--R 6 4 2 x\|- 1 +--R (- 1276cot(x) - 5104cot(x) - 10208cot(x) - 10208)(%e ) +--R + +--R 6 4 2 +--R 129cot(x) + 516cot(x) + 1032cot(x) + 1032 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 20 +--R 3 x\|- 1 +--R (- 2cot(x) - 2cot(x))(%e ) +--R + +--R +---+ 18 +--R 3 x\|- 1 +--R (48cot(x) + 48cot(x))(%e ) +--R + +--R +---+ 16 +--R 3 x\|- 1 +--R (- 482cot(x) - 482cot(x))(%e ) +--R + +--R +---+ 14 +--R 3 x\|- 1 +--R (2648cot(x) + 2648cot(x))(%e ) +--R + +--R +---+ 12 +--R 3 x\|- 1 +--R (- 8764cot(x) - 8764cot(x))(%e ) +--R + +--R +---+ 10 +--R 3 x\|- 1 +--R (18200cot(x) + 18200cot(x))(%e ) +--R + +--R +---+ 8 +--R 3 x\|- 1 +--R (- 23996cot(x) - 23996cot(x))(%e ) +--R + +--R +---+ 6 +--R 3 x\|- 1 +--R (19816cot(x) + 19816cot(x))(%e ) +--R + +--R +---+ 4 +--R 3 x\|- 1 +--R (- 9762cot(x) - 9762cot(x))(%e ) +--R + +--R +---+ 2 +--R 3 x\|- 1 3 +--R (2552cot(x) + 2552cot(x))(%e ) - 258cot(x) - 258cot(x) +--R * +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +--R 4 x\|- 1 4 x\|- 1 +--R (- cot(x) + 2)(%e ) + (24cot(x) - 48)(%e ) +--R + +--R +---+ 16 +---+ 14 +--R 4 x\|- 1 4 x\|- 1 +--R (- 241cot(x) + 482)(%e ) + (1324cot(x) - 2648)(%e ) +--R + +--R +---+ 12 +---+ 10 +--R 4 x\|- 1 4 x\|- 1 +--R (- 4382cot(x) + 8764)(%e ) + (9100cot(x) - 18200)(%e ) +--R + +--R +---+ 8 +---+ 6 +--R 4 x\|- 1 4 x\|- 1 +--R (- 11998cot(x) + 23996)(%e ) + (9908cot(x) - 19816)(%e ) +--R + +--R +---+ 4 +---+ 2 +--R 4 x\|- 1 4 x\|- 1 +--R (- 4881cot(x) + 9762)(%e ) + (1276cot(x) - 2552)(%e ) +--R + +--R 4 +--R - 129cot(x) + 258 +--R / +--R +---+ 18 +---+ 16 +--R 2 x\|- 1 2 x\|- 1 +--R (cot(x) + 2)(%e ) + (- 21cot(x) - 42)(%e ) +--R + +--R +---+ 14 +--R 2 x\|- 1 +--R (182cot(x) + 364)(%e ) +--R + +--R +---+ 12 +--R 2 x\|- 1 +--R (- 850cot(x) - 1700)(%e ) +--R + +--R +---+ 10 +--R 2 x\|- 1 +--R (2352cot(x) + 4704)(%e ) +--R + +--R +---+ 8 +--R 2 x\|- 1 +--R (- 4004cot(x) - 8008)(%e ) +--R + +--R +---+ 6 +--R 2 x\|- 1 +--R (4210cot(x) + 8420)(%e ) +--R + +--R +---+ 4 +--R 2 x\|- 1 +--R (- 2646cot(x) - 5292)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (903cot(x) + 1806)(%e ) - 127cot(x) - 254 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 18 +---+ 16 +---+ 14 +--R x\|- 1 x\|- 1 x\|- 1 +--R - (%e ) + 21(%e ) - 182(%e ) +--R + +--R +---+ 12 +---+ 10 +---+ 8 +--R x\|- 1 x\|- 1 x\|- 1 +--R 850(%e ) - 2352(%e ) + 4004(%e ) +--R + +--R +---+ 6 +---+ 4 +---+ 2 +--R x\|- 1 x\|- 1 x\|- 1 +--R - 4210(%e ) + 2646(%e ) - 903(%e ) + 127 +--R * +--R +--------------------------------+ +--R +-------------+ | +---+ 4 +---+ 2 +--R | 2 | x\|- 1 x\|- 1 +--R \|- cot(x) - 2 \|(%e ) - 6(%e ) + 1 +--R + +--R +---+ 20 +---+ 18 +--R 2 x\|- 1 2 x\|- 1 +--R (- cot(x) - 2)(%e ) + (24cot(x) + 48)(%e ) +--R + +--R +---+ 16 +--R 2 x\|- 1 +--R (- 241cot(x) - 482)(%e ) +--R + +--R +---+ 14 +--R 2 x\|- 1 +--R (1324cot(x) + 2648)(%e ) +--R + +--R +---+ 12 +--R 2 x\|- 1 +--R (- 4382cot(x) - 8764)(%e ) +--R + +--R +---+ 10 +--R 2 x\|- 1 +--R (9100cot(x) + 18200)(%e ) +--R + +--R +---+ 8 +--R 2 x\|- 1 +--R (- 11998cot(x) - 23996)(%e ) +--R + +--R +---+ 6 +--R 2 x\|- 1 +--R (9908cot(x) + 19816)(%e ) +--R + +--R +---+ 4 +--R 2 x\|- 1 +--R (- 4881cot(x) - 9762)(%e ) +--R + +--R +---+ 2 +--R 2 x\|- 1 2 +--R (1276cot(x) + 2552)(%e ) - 129cot(x) - 258 +--R * +--R 2 +--R tan(x) +--R + +--R +---+ 20 +---+ 18 +---+ 16 +--R x\|- 1 x\|- 1 x\|- 1 +--R (%e ) - 24(%e ) + 241(%e ) +--R + +--R +---+ 14 +---+ 12 +---+ 10 +--R x\|- 1 x\|- 1 x\|- 1 +--R - 1324(%e ) + 4382(%e ) - 9100(%e ) +--R + +--R +---+ 8 +---+ 6 +---+ 4 +--R x\|- 1 x\|- 1 x\|- 1 +--R 11998(%e ) - 9908(%e ) + 4881(%e ) +--R + +--R +---+ 2 +--R x\|- 1 +--R - 1276(%e ) + 129 +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) - 2 +--R Type: Expression(Integer) +--E 511 + +--S 512 of 528 +t0397:= (a+b*csc(x)^2)^(3/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (473) (b csc(x) + a)\|b csc(x) + a +--R Type: Expression(Integer) +--E 512 + +--S 513 of 528 +r0397:= -a^(3/2)*atan(a^(1/2)*cot(x)/(a+b*csc(x)^2)^(1/2))-_ + 3/2*a*b^(1/2)*atanh((a+b*csc(x)^2)^(1/2)*tan(x)/b^(1/2))-_ + 1/2*b^(3/2)*atanh((a+b*csc(x)^2)^(1/2)*tan(x)/b^(1/2))-_ + 1/2*b*cot(x)*(a+b*csc(x)^2)^(1/2) +--R +--R +--R (474) +--R +-------------+ +--R | 2 +--R +-+ tan(x)\|b csc(x) + a +--R (- b - 3a)\|b atanh(----------------------) +--R +-+ +--R \|b +--R + +--R +-+ +-------------+ +--R +-+ cot(x)\|a | 2 +--R - 2a\|a atan(----------------) - b cot(x)\|b csc(x) + a +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 513 + +--S 514 of 528 +a0397:= integrate(t0397,x) +--R +--R +--R (475) +--R [ +--R 2 5 2 4 +--R (4a b + 12a )cos(x) + (4a b + 12a )cos(x) +--R + +--R 2 2 3 2 2 2 +--R (- 2b - 14a b - 24a )cos(x) + (- 2b - 14a b - 24a )cos(x) +--R + +--R 2 2 2 2 +--R (2b + 10a b + 12a )cos(x) + 2b + 10a b + 12a +--R * +--R +----------------------+ +--R | 2 +--R +-+ +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a \|b |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 3 4 +--R (8a b + 24a )cos(x) + (- 8a b - 48a b - 72a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + 19a b + 72a b + 72a )cos(x) - b - 11a b - 32a b - 24a +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 10 4 9 +--R 128a cos(x) + 128a cos(x) +--R + +--R 3 4 8 3 4 7 +--R (- 256a b - 512a )cos(x) + (- 256a b - 512a )cos(x) +--R + +--R 2 2 3 4 6 +--R (160a b + 768a b + 768a )cos(x) +--R + +--R 2 2 3 4 5 +--R (160a b + 768a b + 768a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 32a b - 320a b - 768a b - 512a )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (- 32a b - 320a b - 768a b - 512a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (b + 32a b + 160a b + 256a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (b + 32a b + 160a b + 256a b + 128a )cos(x) +--R * +--R +-+ +--R \|b +--R + +--R 3 4 9 3 4 8 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 4 7 +--R (96a b + 32a b - 256a )cos(x) +--R + +--R 2 2 3 4 6 +--R (96a b + 32a b - 256a )cos(x) +--R + +--R 3 2 2 3 4 5 +--R (- 40a b - 56a b + 288a b + 384a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 40a b - 56a b + 288a b + 384a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (4b - 4a b - 176a b - 416a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (4b - 4a b - 176a b - 416a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (4b + 44a b + 136a b + 160a b + 64a )cos(x) + 4b +--R + +--R 3 2 2 3 4 +--R 44a b + 136a b + 160a b + 64a +--R * +--R +-+ +--R sin(x)\|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 4 7 +--R - 256a cos(x) + (640a b + 1024a )cos(x) +--R + +--R 2 2 3 4 5 +--R (- 544a b - 1920a b - 1536a )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (176a b + 1088a b + 1920a b + 1024a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 16b - 176a b - 544a b - 640a b - 256a )cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 5 8 +--R (- 128a b + 128a )cos(x) + (256a b + 128a b - 640a )cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 160a b - 352a b + 768a b + 1280a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (32a b + 128a b - 480a b - 1792a b - 1280a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- b + a b + 224a b + 992a b + 1408a b + 640a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R - b - 33a b - 192a b - 416a b - 384a b - 128a +--R / +--R 3 9 3 8 2 3 7 +--R 64a cos(x) + 64a cos(x) + (- 96a b - 256a )cos(x) +--R + +--R 2 3 6 +--R (- 96a b - 256a )cos(x) +--R + +--R 2 2 3 5 +--R (40a b + 288a b + 384a )cos(x) +--R + +--R 2 2 3 4 +--R (40a b + 288a b + 384a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 4b - 80a b - 288a b - 256a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 4b - 80a b - 288a b - 256a )cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (4b + 40a b + 96a b + 64a )cos(x) + 4b + 40a b + 96a b +--R + +--R 3 +--R 64a +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 4 8 +--R 128a cos(x) + (- 256a b - 640a )cos(x) +--R + +--R 2 2 3 4 6 +--R (160a b + 1024a b + 1280a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 32a b - 480a b - 1536a b - 1280a )cos(x) +--R + +--R 4 3 2 2 3 4 2 4 3 +--R (b + 64a b + 480a b + 1024a b + 640a )cos(x) - b - 32a b +--R + +--R 2 2 3 4 +--R - 160a b - 256a b - 128a +--R + +--R 3 5 3 4 2 3 3 +--R 8a cos(x) + 8a cos(x) + (- 4a b - 16a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 4a b - 16a )cos(x) + (4a b + 8a )cos(x) + 4a b + 8a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R sin(x) |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 3 4 +--R 16a cos(x) + (- 16a b - 48a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 32a b + 48a )cos(x) - 2a b - 16a b - 16a +--R * +--R +-+ +--R \|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a 2 +-+ +--R (cos(x) + 1)sin(x) |---------------------- + (2cos(x) - 2)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------------) +--R +----------------------+ +--R | 2 +--R 2 |- 4a cos(x) + 4b + 4a +-+ +--R (cos(x) + cos(x)) |---------------------- - 2cos(x)sin(x)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 5 3 4 2 3 3 +--R 8a cos(x) + 8a cos(x) + (- 4a b - 16a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 4a b - 16a )cos(x) + (4a b + 8a )cos(x) + 4a b + 8a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R sin(x) |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 3 4 +--R 16a cos(x) + (- 16a b - 48a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 32a b + 48a )cos(x) - 2a b - 16a b - 16a +--R * +--R +-+ +--R \|a +--R * +--R atan +--R 4 3 2 +--R 4a cos(x) + 4a cos(x) + (- b - 3a)cos(x) +--R + +--R (- b - 3a)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (6a b + 6a )cos(x))sin(x) +--R / +--R 3 2 +--R (4a cos(x) + 4a cos(x) + (- b - a)cos(x) - b - a)sin(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 2 +--R 8a cos(x) + (- 6a b - 10a )cos(x) + 2a b + 2a +--R + +--R 2 6 2 5 2 2 4 +--R 8a b cos(x) + 8a b cos(x) + (- 8a b - 16a b)cos(x) +--R + +--R 2 2 3 3 2 2 2 +--R (- 8a b - 16a b)cos(x) + (b + 8a b + 8a b)cos(x) +--R + +--R 3 2 2 +--R (b + 8a b + 8a b)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 5 2 2 3 +--R - 16a b cos(x) + (24a b + 32a b)cos(x) +--R + +--R 3 2 2 +--R (- 8b - 24a b - 16a b)cos(x) +--R * +--R +-+ +--R sin(x)\|a +--R / +--R 5 4 3 +--R 16a cos(x) + 16a cos(x) + (- 8b - 32a)cos(x) +--R + +--R 2 +--R (- 8b - 32a)cos(x) + (8b + 16a)cos(x) + 8b + 16a +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 6 2 4 2 2 2 +--R 32a cos(x) + (- 32a b - 96a )cos(x) + (4b + 64a b + 96a )cos(x) +--R + +--R 2 2 +--R - 4b - 32a b - 32a +--R , +--R +--R 3 5 3 4 2 3 3 +--R 8a cos(x) + 8a cos(x) + (- 4a b - 16a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 4a b - 16a )cos(x) + (4a b + 8a )cos(x) + 4a b + 8a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R sin(x) |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 3 4 +--R 16a cos(x) + (- 16a b - 48a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 32a b + 48a )cos(x) - 2a b - 16a b - 16a +--R * +--R +-+ +--R \|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a 2 +-+ +--R (cos(x) + 1)sin(x) |---------------------- + (2cos(x) - 2)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------------) +--R +----------------------+ +--R | 2 +--R 2 |- 4a cos(x) + 4b + 4a +-+ +--R (cos(x) + cos(x)) |---------------------- - 2cos(x)sin(x)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 5 3 4 2 3 3 +--R 8a cos(x) + 8a cos(x) + (- 4a b - 16a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 4a b - 16a )cos(x) + (4a b + 8a )cos(x) + 4a b + 8a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R sin(x) |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 3 4 +--R 16a cos(x) + (- 16a b - 48a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 32a b + 48a )cos(x) - 2a b - 16a b - 16a +--R * +--R +-+ +--R \|a +--R * +--R atan +--R 4 3 2 +--R 4a cos(x) + 4a cos(x) + (- b - 3a)cos(x) +--R + +--R (- b - 3a)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (6a b + 6a )cos(x))sin(x) +--R / +--R 3 2 +--R (4a cos(x) + 4a cos(x) + (- b - a)cos(x) - b - a)sin(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 2 +--R 8a cos(x) + (- 6a b - 10a )cos(x) + 2a b + 2a +--R + +--R 2 5 2 4 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a )cos(x) +--R + +--R 2 2 3 2 2 2 +--R (4b + 28a b + 48a )cos(x) + (4b + 28a b + 48a )cos(x) +--R + +--R 2 2 2 2 +--R (- 4b - 20a b - 24a )cos(x) - 4b - 20a b - 24a +--R * +--R +----------------------+ +--R | 2 +--R +---+ +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|- b \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 3 4 +--R (- 16a b - 48a )cos(x) + (16a b + 96a b + 144a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 2b - 38a b - 144a b - 144a )cos(x) + 2b + 22a b + 64a b +--R + +--R 3 +--R 48a +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +----------------------+ +--R | 2 +--R 2 +---+ |- 4a cos(x) + 4b + 4a +--R (cos(x) + cos(x))\|- b |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a 2 +--R (cos(x) + 1)sin(x)\|a |---------------------- + 2a cos(x) +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R - 2b - 2a +--R + +--R 2 6 2 5 2 2 4 +--R 8a b cos(x) + 8a b cos(x) + (- 8a b - 16a b)cos(x) +--R + +--R 2 2 3 3 2 2 2 +--R (- 8a b - 16a b)cos(x) + (b + 8a b + 8a b)cos(x) +--R + +--R 3 2 2 +--R (b + 8a b + 8a b)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 5 2 2 3 +--R - 16a b cos(x) + (24a b + 32a b)cos(x) +--R + +--R 3 2 2 +--R (- 8b - 24a b - 16a b)cos(x) +--R * +--R +-+ +--R sin(x)\|a +--R / +--R 5 4 3 +--R 16a cos(x) + 16a cos(x) + (- 8b - 32a)cos(x) +--R + +--R 2 +--R (- 8b - 32a)cos(x) + (8b + 16a)cos(x) + 8b + 16a +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 6 2 4 2 2 2 +--R 32a cos(x) + (- 32a b - 96a )cos(x) + (4b + 64a b + 96a )cos(x) +--R + +--R 2 2 +--R - 4b - 32a b - 32a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 514 + +--S 515 of 528 +m0397a:= a0397.1-r0397 +--R +--R +--R (476) +--R 2 5 2 4 +--R (4a b + 12a )cos(x) + (4a b + 12a )cos(x) +--R + +--R 2 2 3 2 2 2 +--R (- 2b - 14a b - 24a )cos(x) + (- 2b - 14a b - 24a )cos(x) +--R + +--R 2 2 2 2 +--R (2b + 10a b + 12a )cos(x) + 2b + 10a b + 12a +--R * +--R +----------------------+ +--R | 2 +--R +-+ +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a \|b |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 3 4 +--R (8a b + 24a )cos(x) + (- 8a b - 48a b - 72a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (b + 19a b + 72a b + 72a )cos(x) - b - 11a b - 32a b - 24a +--R * +--R +-+ +--R \|b +--R * +--R log +--R 4 10 4 9 3 4 8 +--R 128a cos(x) + 128a cos(x) + (- 256a b - 512a )cos(x) +--R + +--R 3 4 7 +--R (- 256a b - 512a )cos(x) +--R + +--R 2 2 3 4 6 +--R (160a b + 768a b + 768a )cos(x) +--R + +--R 2 2 3 4 5 +--R (160a b + 768a b + 768a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 32a b - 320a b - 768a b - 512a )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (- 32a b - 320a b - 768a b - 512a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (b + 32a b + 160a b + 256a b + 128a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (b + 32a b + 160a b + 256a b + 128a )cos(x) +--R * +--R +-+ +--R \|b +--R + +--R 3 4 9 3 4 8 +--R (- 64a b + 64a )cos(x) + (- 64a b + 64a )cos(x) +--R + +--R 2 2 3 4 7 +--R (96a b + 32a b - 256a )cos(x) +--R + +--R 2 2 3 4 6 +--R (96a b + 32a b - 256a )cos(x) +--R + +--R 3 2 2 3 4 5 +--R (- 40a b - 56a b + 288a b + 384a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 40a b - 56a b + 288a b + 384a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (4b - 4a b - 176a b - 416a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (4b - 4a b - 176a b - 416a b - 256a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (4b + 44a b + 136a b + 160a b + 64a )cos(x) + 4b +--R + +--R 3 2 2 3 4 +--R 44a b + 136a b + 160a b + 64a +--R * +--R +-+ +--R sin(x)\|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 9 3 4 7 +--R - 256a cos(x) + (640a b + 1024a )cos(x) +--R + +--R 2 2 3 4 5 +--R (- 544a b - 1920a b - 1536a )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (176a b + 1088a b + 1920a b + 1024a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 16b - 176a b - 544a b - 640a b - 256a )cos(x) +--R * +--R +-+ +-+ +--R sin(x)\|a \|b +--R + +--R 4 5 10 3 2 4 5 8 +--R (- 128a b + 128a )cos(x) + (256a b + 128a b - 640a )cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 160a b - 352a b + 768a b + 1280a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (32a b + 128a b - 480a b - 1792a b - 1280a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 +--R (- b + a b + 224a b + 992a b + 1408a b + 640a )cos(x) - b +--R + +--R 4 2 3 3 2 4 5 +--R - 33a b - 192a b - 416a b - 384a b - 128a +--R / +--R 3 9 3 8 2 3 7 +--R 64a cos(x) + 64a cos(x) + (- 96a b - 256a )cos(x) +--R + +--R 2 3 6 2 2 3 5 +--R (- 96a b - 256a )cos(x) + (40a b + 288a b + 384a )cos(x) +--R + +--R 2 2 3 4 +--R (40a b + 288a b + 384a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 4b - 80a b - 288a b - 256a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 4b - 80a b - 288a b - 256a )cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (4b + 40a b + 96a b + 64a )cos(x) + 4b + 40a b + 96a b +--R + +--R 3 +--R 64a +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 4 10 3 4 8 +--R 128a cos(x) + (- 256a b - 640a )cos(x) +--R + +--R 2 2 3 4 6 +--R (160a b + 1024a b + 1280a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 32a b - 480a b - 1536a b - 1280a )cos(x) +--R + +--R 4 3 2 2 3 4 2 4 3 +--R (b + 64a b + 480a b + 1024a b + 640a )cos(x) - b - 32a b +--R + +--R 2 2 3 4 +--R - 160a b - 256a b - 128a +--R + +--R 2 5 2 4 +--R (8a b + 24a )cos(x) + (8a b + 24a )cos(x) +--R + +--R 2 2 3 2 2 2 +--R (- 4b - 28a b - 48a )cos(x) + (- 4b - 28a b - 48a )cos(x) +--R + +--R 2 2 2 2 +--R (4b + 20a b + 24a )cos(x) + 4b + 20a b + 24a +--R * +--R +----------------------+ +--R | 2 +--R +-+ +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a \|b |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 3 4 +--R (16a b + 48a )cos(x) + (- 16a b - 96a b - 144a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (2b + 38a b + 144a b + 144a )cos(x) - 2b - 22a b - 64a b +--R + +--R 3 +--R - 48a +--R * +--R +-+ +--R \|b +--R * +--R +-------------+ +--R | 2 +--R tan(x)\|b csc(x) + a +--R atanh(----------------------) +--R +-+ +--R \|b +--R + +--R 3 5 3 4 2 3 3 +--R 8a cos(x) + 8a cos(x) + (- 4a b - 16a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 4a b - 16a )cos(x) + (4a b + 8a )cos(x) + 4a b + 8a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R sin(x) |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 3 4 +--R 16a cos(x) + (- 16a b - 48a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 32a b + 48a )cos(x) - 2a b - 16a b - 16a +--R * +--R +-+ +--R \|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a 2 +-+ +--R (cos(x) + 1)sin(x) |---------------------- + (2cos(x) - 2)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------------) +--R +----------------------+ +--R | 2 +--R 2 |- 4a cos(x) + 4b + 4a +-+ +--R (cos(x) + cos(x)) |---------------------- - 2cos(x)sin(x)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 5 3 4 2 3 3 +--R 8a cos(x) + 8a cos(x) + (- 4a b - 16a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 4a b - 16a )cos(x) + (4a b + 8a )cos(x) + 4a b + 8a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R sin(x) |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 3 4 +--R 16a cos(x) + (- 16a b - 48a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 32a b + 48a )cos(x) - 2a b - 16a b - 16a +--R * +--R +-+ +--R \|a +--R * +--R atan +--R 4 3 2 +--R 4a cos(x) + 4a cos(x) + (- b - 3a)cos(x) +--R + +--R (- b - 3a)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (6a b + 6a )cos(x))sin(x) +--R / +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (- b - a)cos(x) - b - a)sin(x)\|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 2 +--R 8a cos(x) + (- 6a b - 10a )cos(x) + 2a b + 2a +--R + +--R 3 5 3 4 2 3 3 +--R 16a cos(x) + 16a cos(x) + (- 8a b - 32a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 8a b - 32a )cos(x) + (8a b + 16a )cos(x) + 8a b + 16a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R sin(x) |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 3 4 +--R 32a cos(x) + (- 32a b - 96a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (4a b + 64a b + 96a )cos(x) - 4a b - 32a b - 32a +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R cot(x)\|a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R + +--R 5 4 2 3 +--R 8a b cos(x) + 8a b cos(x) + (- 4b - 16a b)cos(x) +--R + +--R 2 2 2 2 +--R (- 4b - 16a b)cos(x) + (4b + 8a b)cos(x) + 4b + 8a b +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R cot(x)sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 6 2 2 4 +--R 16a b cos(x) + (- 16a b - 48a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2b + 32a b + 48a b)cos(x) - 2b - 16a b - 16a b +--R * +--R cot(x) +--R * +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R + +--R 2 6 2 5 2 2 4 +--R 8a b cos(x) + 8a b cos(x) + (- 8a b - 16a b)cos(x) +--R + +--R 2 2 3 3 2 2 2 +--R (- 8a b - 16a b)cos(x) + (b + 8a b + 8a b)cos(x) +--R + +--R 3 2 2 +--R (b + 8a b + 8a b)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 5 2 2 3 +--R - 16a b cos(x) + (24a b + 32a b)cos(x) +--R + +--R 3 2 2 +--R (- 8b - 24a b - 16a b)cos(x) +--R * +--R +-+ +--R sin(x)\|a +--R / +--R 5 4 3 2 +--R 16a cos(x) + 16a cos(x) + (- 8b - 32a)cos(x) + (- 8b - 32a)cos(x) +--R + +--R (8b + 16a)cos(x) + 8b + 16a +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 6 2 4 2 2 2 2 +--R 32a cos(x) + (- 32a b - 96a )cos(x) + (4b + 64a b + 96a )cos(x) - 4b +--R + +--R 2 +--R - 32a b - 32a +--R Type: Expression(Integer) +--E 515 + +--S 516 of 528 +--d0397a:= D(m0397a,x) +--E 516 + +--S 517 of 528 +m0397b:= a0397.2-r0397 +--R +--R +--R (477) +--R 2 5 2 4 +--R (8a b + 24a )cos(x) + (8a b + 24a )cos(x) +--R + +--R 2 2 3 2 2 2 +--R (- 4b - 28a b - 48a )cos(x) + (- 4b - 28a b - 48a )cos(x) +--R + +--R 2 2 2 2 +--R (4b + 20a b + 24a )cos(x) + 4b + 20a b + 24a +--R * +--R +----------------------+ +--R | 2 +--R +-+ +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a \|b |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 3 4 +--R (16a b + 48a )cos(x) + (- 16a b - 96a b - 144a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (2b + 38a b + 144a b + 144a )cos(x) - 2b - 22a b - 64a b +--R + +--R 3 +--R - 48a +--R * +--R +-+ +--R \|b +--R * +--R +-------------+ +--R | 2 +--R tan(x)\|b csc(x) + a +--R atanh(----------------------) +--R +-+ +--R \|b +--R + +--R 3 5 3 4 2 3 3 +--R 8a cos(x) + 8a cos(x) + (- 4a b - 16a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 4a b - 16a )cos(x) + (4a b + 8a )cos(x) + 4a b + 8a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R sin(x) |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 3 4 +--R 16a cos(x) + (- 16a b - 48a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 32a b + 48a )cos(x) - 2a b - 16a b - 16a +--R * +--R +-+ +--R \|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a 2 +-+ +--R (cos(x) + 1)sin(x) |---------------------- + (2cos(x) - 2)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------------) +--R +----------------------+ +--R | 2 +--R 2 |- 4a cos(x) + 4b + 4a +-+ +--R (cos(x) + cos(x)) |---------------------- - 2cos(x)sin(x)\|a +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 5 3 4 2 3 3 +--R 8a cos(x) + 8a cos(x) + (- 4a b - 16a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 4a b - 16a )cos(x) + (4a b + 8a )cos(x) + 4a b + 8a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R sin(x) |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 3 4 +--R 16a cos(x) + (- 16a b - 48a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b + 32a b + 48a )cos(x) - 2a b - 16a b - 16a +--R * +--R +-+ +--R \|a +--R * +--R atan +--R 4 3 2 +--R 4a cos(x) + 4a cos(x) + (- b - 3a)cos(x) +--R + +--R (- b - 3a)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 2 +--R (- 8a cos(x) + (6a b + 6a )cos(x))sin(x) +--R / +--R 3 2 +-+ +--R (4a cos(x) + 4a cos(x) + (- b - a)cos(x) - b - a)sin(x)\|a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 4 2 2 2 +--R 8a cos(x) + (- 6a b - 10a )cos(x) + 2a b + 2a +--R + +--R 2 5 2 4 +--R (- 8a b - 24a )cos(x) + (- 8a b - 24a )cos(x) +--R + +--R 2 2 3 2 2 2 +--R (4b + 28a b + 48a )cos(x) + (4b + 28a b + 48a )cos(x) +--R + +--R 2 2 2 2 +--R (- 4b - 20a b - 24a )cos(x) - 4b - 20a b - 24a +--R * +--R +----------------------+ +--R | 2 +--R +---+ +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|- b \|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 3 6 2 2 3 4 +--R (- 16a b - 48a )cos(x) + (16a b + 96a b + 144a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 2b - 38a b - 144a b - 144a )cos(x) + 2b + 22a b + 64a b +--R + +--R 3 +--R 48a +--R * +--R +---+ +--R \|- b +--R * +--R atan +--R +----------------------+ +--R | 2 +--R 2 +---+ |- 4a cos(x) + 4b + 4a +--R (cos(x) + cos(x))\|- b |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R +---+ +-+ +--R - 2cos(x)sin(x)\|- b \|a +--R / +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a 2 +--R (cos(x) + 1)sin(x)\|a |---------------------- + 2a cos(x) +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R - 2b - 2a +--R + +--R 3 5 3 4 2 3 3 +--R 16a cos(x) + 16a cos(x) + (- 8a b - 32a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 8a b - 32a )cos(x) + (8a b + 16a )cos(x) + 8a b + 16a +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R sin(x) |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 3 6 2 3 4 +--R 32a cos(x) + (- 32a b - 96a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (4a b + 64a b + 96a )cos(x) - 4a b - 32a b - 32a +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R cot(x)\|a +--R atan(----------------) +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R + +--R 5 4 2 3 +--R 8a b cos(x) + 8a b cos(x) + (- 4b - 16a b)cos(x) +--R + +--R 2 2 2 2 +--R (- 4b - 16a b)cos(x) + (4b + 8a b)cos(x) + 4b + 8a b +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R cot(x)sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 6 2 2 4 +--R 16a b cos(x) + (- 16a b - 48a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 +--R (2b + 32a b + 48a b)cos(x) - 2b - 16a b - 16a b +--R * +--R cot(x) +--R * +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R + +--R 2 6 2 5 2 2 4 +--R 8a b cos(x) + 8a b cos(x) + (- 8a b - 16a b)cos(x) +--R + +--R 2 2 3 3 2 2 2 +--R (- 8a b - 16a b)cos(x) + (b + 8a b + 8a b)cos(x) +--R + +--R 3 2 2 +--R (b + 8a b + 8a b)cos(x) +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 5 2 2 3 +--R - 16a b cos(x) + (24a b + 32a b)cos(x) +--R + +--R 3 2 2 +--R (- 8b - 24a b - 16a b)cos(x) +--R * +--R +-+ +--R sin(x)\|a +--R / +--R 5 4 3 2 +--R 16a cos(x) + 16a cos(x) + (- 8b - 32a)cos(x) + (- 8b - 32a)cos(x) +--R + +--R (8b + 16a)cos(x) + 8b + 16a +--R * +--R +----------------------+ +--R | 2 +--R +-+ |- 4a cos(x) + 4b + 4a +--R sin(x)\|a |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 2 6 2 4 2 2 2 2 +--R 32a cos(x) + (- 32a b - 96a )cos(x) + (4b + 64a b + 96a )cos(x) - 4b +--R + +--R 2 +--R - 32a b - 32a +--R Type: Expression(Integer) +--E 517 + +--S 518 of 528 +d0397b:= D(m0397b,x) +--R +--R +--R (478) +--R 9 3 10 2 11 17 +--R (- 12288a b - 32768a b - 20480a b)cos(x) +--R + +--R 9 3 10 2 11 16 +--R (- 12288a b - 32768a b - 20480a b)cos(x) +--R + +--R 8 4 9 3 10 2 11 +--R (63488a b + 251904a b + 321536a b + 133120a b) +--R * +--R 15 +--R cos(x) +--R + +--R 8 4 9 3 10 2 11 +--R (63488a b + 251904a b + 321536a b + 133120a b) +--R * +--R 14 +--R cos(x) +--R + +--R 7 5 8 4 9 3 +--R - 137984a b - 734208a b - 1422336a b +--R + +--R 10 2 11 +--R - 1196032a b - 369920a b +--R * +--R 13 +--R cos(x) +--R + +--R 7 5 8 4 9 3 +--R - 137984a b - 734208a b - 1422336a b +--R + +--R 10 2 11 +--R - 1196032a b - 369920a b +--R * +--R 12 +--R cos(x) +--R + +--R 6 6 7 5 8 4 +--R 163712a b + 1103104a b + 2887936a b +--R + +--R 9 3 10 2 11 +--R 3692288a b + 2314624a b + 570880a b +--R * +--R 11 +--R cos(x) +--R + +--R 6 6 7 5 8 4 +--R 163712a b + 1103104a b + 2887936a b +--R + +--R 9 3 10 2 11 +--R 3692288a b + 2314624a b + 570880a b +--R * +--R 10 +--R cos(x) +--R + +--R 5 7 6 6 7 5 +--R - 115104a b - 947584a b - 3151168a b +--R + +--R 8 4 9 3 10 2 +--R - 5450240a b - 5192992a b - 2592640a b +--R + +--R 11 +--R - 531200a b +--R * +--R 9 +--R cos(x) +--R + +--R 5 7 6 6 7 5 +--R - 115104a b - 947584a b - 3151168a b +--R + +--R 8 4 9 3 10 2 +--R - 5450240a b - 5192992a b - 2592640a b +--R + +--R 11 +--R - 531200a b +--R * +--R 8 +--R cos(x) +--R + +--R 4 8 5 7 6 6 +--R 48688a b + 478016a b + 1943072a b +--R + +--R 7 5 8 4 9 3 +--R 4267968a b + 5497392a b + 4167296a b +--R + +--R 10 2 11 +--R 1726208a b + 302080a b +--R * +--R 7 +--R cos(x) +--R + +--R 4 8 5 7 6 6 +--R 48688a b + 478016a b + 1943072a b +--R + +--R 7 5 8 4 9 3 +--R 4267968a b + 5497392a b + 4167296a b +--R + +--R 10 2 11 +--R 1726208a b + 302080a b +--R * +--R 6 +--R cos(x) +--R + +--R 3 9 4 8 5 7 +--R - 11984a b - 137936a b - 667616a b +--R + +--R 6 6 7 5 8 4 +--R - 1789600a b - 2922640a b - 2990224a b +--R + +--R 9 3 10 2 11 +--R - 1877696a b - 663296a b - 101120a b +--R * +--R 5 +--R cos(x) +--R + +--R 3 9 4 8 5 7 +--R - 11984a b - 137936a b - 667616a b +--R + +--R 6 6 7 5 8 4 +--R - 1789600a b - 2922640a b - 2990224a b +--R + +--R 9 3 10 2 11 +--R - 1877696a b - 663296a b - 101120a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 10 3 9 4 8 5 7 +--R 1552a b + 20704a b + 117104a b + 372672a b +--R + +--R 6 6 7 5 8 4 9 3 +--R 740720a b + 958432a b + 810384a b + 433024a b +--R + +--R 10 2 11 +--R 132992a b + 17920a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 10 3 9 4 8 5 7 +--R 1552a b + 20704a b + 117104a b + 372672a b +--R + +--R 6 6 7 5 8 4 9 3 +--R 740720a b + 958432a b + 810384a b + 433024a b +--R + +--R 10 2 11 +--R 132992a b + 17920a b +--R * +--R 2 +--R cos(x) +--R + +--R 11 2 10 3 9 4 8 +--R - 80a b - 1232a b - 8048a b - 29840a b +--R + +--R 5 7 6 6 7 5 8 4 +--R - 70224a b - 110320a b - 117712a b - 84528a b +--R + +--R 9 3 10 2 11 +--R - 39200a b - 10624a b - 1280a b +--R * +--R cos(x) +--R + +--R 11 2 10 3 9 4 8 +--R - 80a b - 1232a b - 8048a b - 29840a b +--R + +--R 5 7 6 6 7 5 8 4 +--R - 70224a b - 110320a b - 117712a b - 84528a b +--R + +--R 9 3 10 2 11 +--R - 39200a b - 10624a b - 1280a b +--R * +--R 2 +--R csc(x) +--R + +--R 10 2 11 12 17 +--R (- 12288a b - 32768a b - 20480a )cos(x) +--R + +--R 10 2 11 12 16 +--R (- 12288a b - 32768a b - 20480a )cos(x) +--R + +--R 9 3 10 2 11 12 +--R (63488a b + 251904a b + 321536a b + 133120a ) +--R * +--R 15 +--R cos(x) +--R + +--R 9 3 10 2 11 12 +--R (63488a b + 251904a b + 321536a b + 133120a ) +--R * +--R 14 +--R cos(x) +--R + +--R 8 4 9 3 10 2 +--R - 137984a b - 734208a b - 1422336a b +--R + +--R 11 12 +--R - 1196032a b - 369920a +--R * +--R 13 +--R cos(x) +--R + +--R 8 4 9 3 10 2 +--R - 137984a b - 734208a b - 1422336a b +--R + +--R 11 12 +--R - 1196032a b - 369920a +--R * +--R 12 +--R cos(x) +--R + +--R 7 5 8 4 9 3 10 2 +--R 163712a b + 1103104a b + 2887936a b + 3692288a b +--R + +--R 11 12 +--R 2314624a b + 570880a +--R * +--R 11 +--R cos(x) +--R + +--R 7 5 8 4 9 3 10 2 +--R 163712a b + 1103104a b + 2887936a b + 3692288a b +--R + +--R 11 12 +--R 2314624a b + 570880a +--R * +--R 10 +--R cos(x) +--R + +--R 6 6 7 5 8 4 9 3 +--R - 115104a b - 947584a b - 3151168a b - 5450240a b +--R + +--R 10 2 11 12 +--R - 5192992a b - 2592640a b - 531200a +--R * +--R 9 +--R cos(x) +--R + +--R 6 6 7 5 8 4 9 3 +--R - 115104a b - 947584a b - 3151168a b - 5450240a b +--R + +--R 10 2 11 12 +--R - 5192992a b - 2592640a b - 531200a +--R * +--R 8 +--R cos(x) +--R + +--R 5 7 6 6 7 5 8 4 +--R 48688a b + 478016a b + 1943072a b + 4267968a b +--R + +--R 9 3 10 2 11 12 +--R 5497392a b + 4167296a b + 1726208a b + 302080a +--R * +--R 7 +--R cos(x) +--R + +--R 5 7 6 6 7 5 8 4 +--R 48688a b + 478016a b + 1943072a b + 4267968a b +--R + +--R 9 3 10 2 11 12 +--R 5497392a b + 4167296a b + 1726208a b + 302080a +--R * +--R 6 +--R cos(x) +--R + +--R 4 8 5 7 6 6 7 5 +--R - 11984a b - 137936a b - 667616a b - 1789600a b +--R + +--R 8 4 9 3 10 2 +--R - 2922640a b - 2990224a b - 1877696a b +--R + +--R 11 12 +--R - 663296a b - 101120a +--R * +--R 5 +--R cos(x) +--R + +--R 4 8 5 7 6 6 7 5 +--R - 11984a b - 137936a b - 667616a b - 1789600a b +--R + +--R 8 4 9 3 10 2 +--R - 2922640a b - 2990224a b - 1877696a b +--R + +--R 11 12 +--R - 663296a b - 101120a +--R * +--R 4 +--R cos(x) +--R + +--R 3 9 4 8 5 7 6 6 +--R 1552a b + 20704a b + 117104a b + 372672a b +--R + +--R 7 5 8 4 9 3 10 2 +--R 740720a b + 958432a b + 810384a b + 433024a b +--R + +--R 11 12 +--R 132992a b + 17920a +--R * +--R 3 +--R cos(x) +--R + +--R 3 9 4 8 5 7 6 6 +--R 1552a b + 20704a b + 117104a b + 372672a b +--R + +--R 7 5 8 4 9 3 10 2 +--R 740720a b + 958432a b + 810384a b + 433024a b +--R + +--R 11 12 +--R 132992a b + 17920a +--R * +--R 2 +--R cos(x) +--R + +--R 2 10 3 9 4 8 5 7 +--R - 80a b - 1232a b - 8048a b - 29840a b +--R + +--R 6 6 7 5 8 4 9 3 +--R - 70224a b - 110320a b - 117712a b - 84528a b +--R + +--R 10 2 11 12 +--R - 39200a b - 10624a b - 1280a +--R * +--R cos(x) +--R + +--R 2 10 3 9 4 8 5 7 6 6 +--R - 80a b - 1232a b - 8048a b - 29840a b - 70224a b +--R + +--R 7 5 8 4 9 3 10 2 +--R - 110320a b - 117712a b - 84528a b - 39200a b +--R + +--R 11 12 +--R - 10624a b - 1280a +--R * +--R 10 +--R sin(x) +--R + +--R 9 3 10 2 11 19 +--R (16384a b + 196608a b + 245760a b)cos(x) +--R + +--R 9 3 10 2 11 18 +--R (16384a b + 196608a b + 245760a b)cos(x) +--R + +--R 8 4 9 3 10 2 +--R - 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2237932a b - 4631620a b - 648704a b + 6948096a b +--R + +--R 12 13 +--R 7478784a b + 2416128a +--R * +--R 12 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R - 780a b - 15888a b - 95736a b - 124192a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 676368a b + 2484632a b + 2064076a b - 3112448a b +--R + +--R 11 2 12 13 +--R - 7523712a b - 5581824a b - 1469952a +--R * +--R 10 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 36a b + 1220a b + 11656a b + 27464a b - 119352a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 718712a b - 1110260a b + 553836a b + 3863296a b +--R + +--R 11 2 12 13 +--R 5039488a b + 2905600a b + 647680a +--R * +--R 8 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 24a b - 476a b - 1920a b + 12440a b + 109008a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 255848a b - 10048a b - 1121068a b - 2280448a b +--R + +--R 11 2 12 13 +--R - 2161408a b - 1031168a b - 199936a +--R * +--R 6 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 4a b + 28a b - 592a b - 7200a b - 23920a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 768a b + 193772a b + 546612a b + 750592a b +--R + +--R 11 2 12 13 +--R 575232a b + 236288a b + 40704a +--R * +--R 4 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R 8a b + 136a b + 596a b - 1376a b - 18560a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 64648a b - 119292a b - 130816a b - 85824a b +--R + +--R 12 13 +--R - 31232a b - 4864a +--R * +--R 2 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 4a b + 84a b + 680a b + 2792a b + 6676a b + 9924a b +--R + +--R 10 3 11 2 12 13 +--R 9344a b + 5440a b + 1792a b + 256a +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 10 3 11 2 12 16 +--R (- 4096a b - 8192a b - 4096a b)cos(x) +--R + +--R 9 4 10 3 11 2 12 14 +--R (22528a b + 71680a b + 75776a b + 26624a b)cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R - 52480a b - 230400a b - 377344a b - 273408a b +--R + +--R 12 +--R - 73984a b +--R * +--R 12 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 67328a b + 378880a b + 846848a b + 940544a b +--R + +--R 11 2 12 +--R 519424a b + 114176a b +--R * +--R 10 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 51776a b - 356864a b - 1015936a b - 1530624a b +--R + +--R 10 3 11 2 12 +--R - 1288256a b - 574720a b - 106240a b +--R * +--R 8 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 24320a b + 198912a b + 690176a b + 1318400a b +--R + +--R 9 4 10 3 11 2 12 +--R 1498880a b + 1015040a b + 379392a b + 60416a b +--R * +--R 6 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R - 6784a b - 64256a b - 263296a b - 610304a b - 876160a b +--R + +--R 9 4 10 3 11 2 12 +--R - 798464a b - 451456a b - 144896a b - 20224a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R 1024a b + 11008a b + 51968a b + 141568a b + 245504a b +--R + +--R 8 5 9 4 10 3 11 2 12 +--R 281344a b + 213248a b + 103168a b + 28928a b + 3584a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 64a b - 768a b - 4096a b - 12800a b - 25984a b +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R - 35840a b - 34048a b - 22016a b - 9280a b - 2304a b +--R + +--R 12 +--R - 256a b +--R * +--R 11 +--R sin(x) +--R + +--R 10 3 11 2 12 18 +--R (53248a b + 221184a b + 184320a b)cos(x) +--R + +--R 9 4 10 3 11 2 12 +--R (- 313344a b - 1730560a b - 2783232a b - 1382400a b) +--R * +--R 16 +--R cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R 790784a b + 5499904a b + 12986880a b + 12801024a b +--R + +--R 12 +--R 4527360a b +--R * +--R 14 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R - 1115904a b - 9452288a b - 29496832a b - 43536896a b +--R + +--R 11 2 12 +--R - 30843648a b - 8467200a b +--R * +--R 12 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 962176a b + 9716608a b + 37942976a b + 74979584a b +--R + +--R 10 3 11 2 12 +--R 80104512a b + 44232192a b + 9918720a b +--R * +--R 10 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R - 520032a b - 6178912a b - 29238560a b - 72928992a b +--R + +--R 9 4 10 3 11 2 12 +--R - 104843776a b - 87579968a b - 39585024a b - 7499520a b +--R * +--R 8 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R 173732a b + 2412176a b + 13562456a b + 41224336a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 75064484a b + 84566528a b + 57910400a b + 22136832a b +--R + +--R 12 +--R 3628800a b +--R * +--R 6 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R - 33964a b - 550620a b - 3636920a b - 13178424a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 29303900a b - 41871404a b - 38704640a b - 22428800a b +--R + +--R 11 2 12 +--R - 7421184a b - 1071360a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R 3436a b + 65544a b + 506516a b + 2159216a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 5728788a b + 10001416a b + 11728684a b + 9175296a b +--R + +--R 10 3 11 2 12 +--R 4602176a b + 1340928a b + 172800a b +--R * +--R 2 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 132a b - 3036a b - 27604a b - 137740a b - 430092a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 896084a b - 1283996a b - 1274244a b - 862720a b +--R + +--R 10 3 11 2 12 +--R - 380992a b - 99072a b - 11520a b +--R * +--R 9 +--R sin(x) +--R + +--R 10 3 11 2 12 20 +--R (57344a b - 344064a b - 860160a b)cos(x) +--R + +--R 9 4 10 3 11 2 12 +--R (- 315392a b + 1863680a b + 8687616a b + 7311360a b) +--R * +--R 18 +--R cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R 730624a b - 4601856a b - 32736256a b - 54491136a b +--R + +--R 12 +--R - 27578880a b +--R * +--R 16 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R - 922112a b + 6960128a b + 66275328a b + 165401600a b +--R + +--R 11 2 12 +--R 167526912a b + 60641280a b +--R * +--R 14 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 683392a b - 7174912a b - 82348800a b - 273989632a b +--R + +--R 10 3 11 2 12 +--R - 418151552a b - 304442880a b - 85800960a b +--R * +--R 12 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R - 297024a b + 5153792a b + 66147392a b + 274560128a b +--R + +--R 9 4 10 3 11 2 12 +--R 562420096a b + 619431680a b + 352160256a b + 81285120a b +--R * +--R 10 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R 70000a b - 2500352a b - 34557952a b - 171911104a b +--R + +--R 8 5 9 4 10 3 +--R - 444352048a b - 660023168a b - 569269120a b +--R + +--R 11 2 12 +--R - 265606656a b - 51932160a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R - 6608a b + 766952a b + 11375960a b + 66387832a b +--R + +--R 7 6 8 5 9 4 +--R 209001624a b + 394263488a b + 460244736a b +--R + +--R 10 3 11 2 12 +--R 326534656a b + 129271296a b + 21934080a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 308a b - 134424a b - 2187640a b - 14901248a b +--R + +--R 6 7 7 6 8 5 +--R - 56119444a b - 130024136a b - 193667616a b +--R + +--R 9 4 10 3 11 2 12 +--R - 186527488a b - 112524160a b - 38717952a b - 5806080a b +--R * +--R 4 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 +--R 88a b + 11392a b + 211992a b + 1704832a b +--R + +--R 5 8 6 7 7 6 8 5 +--R 7656072a b + 21437888a b + 39455112a b + 48679232a b +--R + +--R 9 4 10 3 11 2 12 +--R 39976832a b + 21004032a b + 6397440a b + 860160a b +--R * +--R 2 +--R cos(x) +--R + +--R 13 12 2 11 3 10 4 9 +--R - 4b - 336a b - 7484a b - 73016a b - 395116a b +--R + +--R 5 8 6 7 7 6 8 5 +--R - 1333408a b - 2985508a b - 4571864a b - 4825136a b +--R + +--R 9 4 10 3 11 2 12 +--R - 3459456a b - 1611904a b - 440832a b - 53760a b +--R * +--R 7 +--R sin(x) +--R + +--R 10 3 11 2 12 22 +--R (- 57344a b - 344064a b + 860160a b)cos(x) +--R + +--R 9 4 10 3 11 2 12 20 +--R (372736a b + 2666496a b - 3010560a b - 8171520a b)cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R - 1046016a b - 8787968a b - 236544a b + 39610368a b +--R + +--R 12 +--R 34890240a b +--R * +--R 18 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 1653248a b + 16170496a b + 16966656a b - 78296064a b +--R + +--R 11 2 12 +--R - 167634432a b - 88220160a b +--R * +--R 16 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 1608960a b - 18266624a b - 36361344a b + 80704512a b +--R + +--R 10 3 11 2 12 +--R 344202880a b + 389910528a b + 146442240a b +--R * +--R 14 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 989568a b + 13079360a b + 37782144a b - 46524224a b +--R + +--R 9 4 10 3 11 2 +--R - 398290816a b - 730731904a b - 571705344a b +--R + +--R 12 +--R - 167086080a b +--R * +--R 12 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 379528a b - 5901984a b - 22262288a b + 16098720a b +--R + +--R 8 5 9 4 10 3 +--R 289095320a b + 758171904a b + 925051008a b +--R + +--R 11 2 12 +--R 556351488a b + 133217280a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 86168a b + 1611088a b + 7503224a b - 4820376a b +--R + +--R 7 6 8 5 9 4 +--R - 138061840a b - 475102904a b - 799811712a b +--R + +--R 10 3 11 2 12 +--R - 741888896a b - 363783168a b - 73866240a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 10400a b - 243496a b - 1344788a b + 1852912a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 43335564a b + 182367232a b + 394907504a b + 502014464a b +--R + +--R 10 3 11 2 12 +--R 378514304a b + 157151232a b + 27740160a b +--R * +--R 6 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 +--R 536a b + 17072a b + 105164a b - 512540a b +--R + +--R 5 8 6 7 7 6 8 5 +--R - 8329684a b - 40863796a b - 109141856a b - 178724016a b +--R + +--R 9 4 10 3 11 2 12 +--R - 184797312a b - 118034560a b - 42620928a b - 6666240a b +--R * +--R 4 +--R cos(x) +--R + +--R 13 12 2 11 3 10 4 9 +--R - 8b - 376a b - 1772a b + 60512a b + 821608a b +--R + +--R 5 8 6 7 7 6 8 5 +--R 4660248a b + 15100404a b + 30883296a b + 41385464a b +--R + +--R 9 4 10 3 11 2 12 +--R 36382976a b + 20261248a b + 6494208a b + 913920a b +--R * +--R 2 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 60a b - 2180a b - 29160a b - 195840a b - 774284a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 1959908a b - 3314320a b - 3800280a b - 2925440a b +--R + +--R 10 3 11 2 12 +--R - 1450624a b - 419328a b - 53760a b +--R * +--R 5 +--R sin(x) +--R + +--R 10 3 11 2 12 24 +--R (- 53248a b + 221184a b - 184320a b)cos(x) +--R + +--R 9 4 10 3 11 2 12 22 +--R (325632a b - 985088a b - 866304a b + 1935360a b)cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R - 858368a b + 1620992a b + 6931968a b - 2792448a b +--R + +--R 12 +--R - 9227520a b +--R * +--R 20 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 1272576a b - 947200a b - 16630784a b - 11693568a b +--R + +--R 11 2 12 +--R 27705600a b + 26380800a b +--R * +--R 18 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 1160512a b - 469760a b + 21099904a b + 40420096a b +--R + +--R 10 3 11 2 12 +--R - 20497216a b - 90236160a b - 50284800a b +--R * +--R 16 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 668480a b + 1037312a b - 16393280a b - 55202176a b +--R + +--R 9 4 10 3 11 2 12 +--R - 21304960a b + 120361472a b + 170284032a b + 67184640a b +--R * +--R 14 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 240208a b - 643328a b + 8303296a b + 42182080a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 48694736a b - 76492416a b - 237750016a b - 210373632a b +--R + +--R 12 +--R - 64350720a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 51184a b + 191352a b - 2790968a b - 19453048a b +--R + +--R 7 6 8 5 9 4 +--R - 37167384a b + 21138592a b + 179380096a b +--R + +--R 10 3 11 2 12 +--R 270569984a b + 177348096a b + 44375040a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 5812a b - 26872a b + 598736a b + 5360192a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 14403300a b - 590856a b - 81426640a b - 185635456a b +--R + +--R 10 3 11 2 12 +--R - 195332992a b - 102643200a b - 21772800a b +--R * +--R 8 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R 280a b + 1424a b - 71768a b - 809712a b - 2847760a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 465888a b + 23570640a b + 73476416a b + 109474944a b +--R + +--R 10 3 11 2 12 +--R 90502656a b + 39951360a b + 7372800a b +--R * +--R 6 +--R cos(x) +--R + +--R 13 12 2 11 3 10 4 9 +--R - 4b - 16a b + 3564a b + 54520a b + 243176a b +--R + +--R 5 8 6 7 7 6 8 5 +--R - 96352a b - 4330312a b - 16624720a b - 32502224a b +--R + +--R 9 4 10 3 11 2 12 +--R - 37531520a b - 25904384a b - 9916416a b - 1624320a b +--R * +--R 4 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 48a b - 1088a b - 5504a b + 32328a b + 430664a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 1913464a b + 4703240a b + 7144864a b + 6893184a b +--R + +--R 10 3 11 2 12 +--R 4127744a b + 1403136a b + 207360a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 60a b - 1560a b - 15672a b - 80928a b - 247612a b +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R - 482536a b - 617904a b - 519808a b - 277312a b - 85248a b +--R + +--R 12 +--R - 11520a b +--R * +--R 3 +--R sin(x) +--R + +--R 10 3 11 2 12 26 +--R (4096a b - 8192a b + 4096a b)cos(x) +--R + +--R 9 4 10 3 11 2 12 24 +--R (- 26624a b + 14336a b + 59392a b - 47104a b)cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R 75008a b + 76800a b - 265728a b - 130048a b +--R + +--R 12 +--R 248064a b +--R * +--R 22 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R - 119552a b - 326400a b + 303616a b + 1033728a b +--R + +--R 11 2 12 +--R - 165632a b - 791296a b +--R * +--R 20 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 117888a b + 548480a b + 174016a b - 1942784a b +--R + +--R 10 3 11 2 12 +--R - 1733312a b + 1600000a b + 1703680a b +--R * +--R 18 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R - 73760a b - 510432a b - 726368a b + 1570592a b +--R + +--R 9 4 10 3 11 2 12 +--R 4172672a b + 559296a b - 4344576a b - 2610432a b +--R * +--R 16 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R 28804a b + 281872a b + 733688a b - 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9856a b - 59904a b - 127232a b - 114176a b +--R + +--R 10 3 +--R - 36992a b +--R * +--R 13 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 9856a b - 59904a b - 127232a b - 114176a b +--R + +--R 10 3 +--R - 36992a b +--R * +--R 12 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 6784a b + 60416a b + 194560a b + 292096a b +--R + +--R 9 4 10 3 +--R 208256a b + 57088a b +--R * +--R 11 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 6784a b + 60416a b + 194560a b + 292096a b +--R + +--R 9 4 10 3 +--R 208256a b + 57088a b +--R * +--R 10 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 2464a b - 31744a b - 146240a b - 325504a b +--R + +--R 8 5 9 4 10 3 +--R - 380064a b - 224640a b - 53120a b +--R * +--R 9 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 2464a b - 31744a b - 146240a b - 325504a b +--R + +--R 8 5 9 4 10 3 +--R - 380064a b - 224640a b - 53120a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 448a b + 8832a b + 57472a b + 179456a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 305344a b + 290944a b + 146176a b + 30208a b +--R * +--R 7 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 448a b + 8832a b + 57472a b + 179456a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 305344a b + 290944a b + 146176a b + 30208a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 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32a b - 320a b - 1376a b - 3328a b - 4960a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 4672a b - 2720a b - 896a b - 128a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 5 9 4 10 3 17 +--R (- 1024a b - 2048a b - 1024a b )cos(x) +--R + +--R 8 5 9 4 10 3 16 +--R (- 1024a b - 2048a b - 1024a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 15 +--R (3584a b + 13824a b + 16896a b + 6656a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 14 +--R (3584a b + 13824a b + 16896a b + 6656a b )cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 4928a b - 29952a b - 63616a b - 57088a b +--R + +--R 10 3 +--R - 18496a b +--R * +--R 13 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 4928a b - 29952a b - 63616a b - 57088a b +--R + +--R 10 3 +--R - 18496a b +--R * +--R 12 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 3392a b + 30208a b + 97280a b + 146048a b +--R + +--R 9 4 10 3 +--R 104128a b + 28544a b +--R * +--R 11 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 3392a b + 30208a b + 97280a b + 146048a b +--R + +--R 9 4 10 3 +--R 104128a b + 28544a b +--R * +--R 10 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 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14784a b - 89856a b - 190848a b +--R + +--R 10 3 11 2 +--R - 171264a b - 55488a b +--R * +--R 13 +--R cos(x) +--R + +--R 7 6 8 5 9 4 +--R - 14784a b - 89856a b - 190848a b +--R + +--R 10 3 11 2 +--R - 171264a b - 55488a b +--R * +--R 12 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 10176a b + 90624a b + 291840a b + 438144a b +--R + +--R 10 3 11 2 +--R 312384a b + 85632a b +--R * +--R 11 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 10176a b + 90624a b + 291840a b + 438144a b +--R + +--R 10 3 11 2 +--R 312384a b + 85632a b +--R * +--R 10 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R - 3696a b - 47616a b - 219360a b - 488256a b +--R + +--R 9 4 10 3 11 2 +--R - 570096a b - 336960a b - 79680a b +--R * +--R 9 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R - 3696a b - 47616a b - 219360a b - 488256a b +--R + +--R 9 4 10 3 11 2 +--R - 570096a b - 336960a b - 79680a b +--R * +--R 8 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R 672a b + 13248a b + 86208a b + 269184a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 458016a b + 436416a b + 219264a b + 45312a b +--R * +--R 7 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R 672a b + 13248a b + 86208a b + 269184a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 458016a b + 436416a b + 219264a b + 45312a b +--R * +--R 6 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R - 48a b - 1824a b - 17472a b - 75264a b +--R + +--R 7 6 8 5 9 4 +--R - 176304a b - 240864a b - 192288a b +--R + +--R 10 3 11 2 +--R - 83328a b - 15168a b +--R * +--R 5 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R - 48a b - 1824a b - 17472a b - 75264a b +--R + +--R 7 6 8 5 9 4 +--R - 176304a b - 240864a b - 192288a b +--R + +--R 10 3 11 2 +--R - 83328a b - 15168a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 96a b + 1632a b + 9984a b + 31488a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 58080a b + 65376a b + 44352a b + 16704a b +--R + +--R 11 2 +--R 2688a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 96a b + 1632a b + 9984a b + 31488a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 58080a b + 65376a b + 44352a b + 16704a b +--R + +--R 11 2 +--R 2688a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R - 48a b - 480a b - 2064a b - 4992a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 7440a b - 7008a b - 4080a b - 1344a b +--R + +--R 11 2 +--R - 192a b +--R * +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 480a b - 2064a b - 4992a b - 7440a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 7008a b - 4080a b - 1344a b - 192a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R - 1024a b - 7168a b - 13312a b - 9216a b +--R + +--R 12 +--R - 2048a b +--R * +--R 17 +--R cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R - 1024a b - 7168a b - 13312a b - 9216a b +--R + +--R 12 +--R - 2048a b +--R * +--R 16 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 3584a b + 31744a b + 93184a b + 118784a b +--R + +--R 11 2 12 +--R 67072a b + 13312a b +--R * +--R 15 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 3584a b + 31744a b + 93184a b + 118784a b +--R + +--R 11 2 12 +--R 67072a b + 13312a b +--R * +--R 14 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 4928a b - 54592a b - 223232a b - 435072a b +--R + +--R 10 3 11 2 12 +--R - 431168a b - 206656a b - 36992a b +--R * +--R 13 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 4928a b - 54592a b - 223232a b - 435072a b +--R + +--R 10 3 11 2 12 +--R - 431168a b - 206656a b - 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554030a b - 582770a b - 412352a b +--R + +--R 11 2 12 13 +--R - 187616a b - 49536a b - 5760a +--R * +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 33a b - 825a b - 8320a b - 46092a b - 158561a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 359769a b - 554030a b - 582770a b - 412352a b +--R + +--R 11 2 12 13 +--R - 187616a b - 49536a b - 5760a +--R * +--R 8 +--R sin(x) +--R + +--R 8 5 9 4 10 3 21 +--R (28672a b - 172032a b - 430080a b )cos(x) +--R + +--R 8 5 9 4 10 3 20 +--R (28672a b - 172032a b - 430080a b )cos(x) +--R + +--R 7 6 8 5 9 4 +--R - 100352a b + 587776a b + 3483648a b +--R + +--R 10 3 +--R 3655680a b +--R * +--R 19 +--R cos(x) +--R + +--R 7 6 8 5 9 4 +--R - 100352a b + 587776a b + 3483648a b +--R + +--R 10 3 +--R 3655680a b +--R * +--R 18 +--R cos(x) +--R + +--R 6 7 7 6 8 5 +--R 135936a b - 896000a b - 9314816a b +--R + +--R 9 4 10 3 +--R - 20794368a b - 13789440a b +--R * +--R 17 +--R cos(x) +--R + +--R 6 7 7 6 8 5 +--R 135936a b - 896000a b - 9314816a b +--R + +--R 9 4 10 3 +--R - 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1536a b + 50688a b - 35328a b ) +--R * +--R 25 +--R cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R (- 13824a b - 1536a b + 50688a b - 35328a b ) +--R * +--R 24 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 25536a b + 66816a b - 113280a b - 162048a b +--R + +--R 11 2 +--R 186048a b +--R * +--R 23 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 25536a b + 66816a b - 113280a b - 162048a b +--R + +--R 11 2 +--R 186048a b +--R * +--R 22 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 24768a b - 143424a b - 34176a b + 569472a b +--R + +--R 10 3 11 2 +--R 183360a b - 593472a b +--R * +--R 21 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 24768a b - 143424a b - 34176a b + 569472a b +--R + +--R 10 3 11 2 +--R 183360a b - 593472a b +--R * +--R 20 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 13344a b + 136416a b + 275280a b - 462528a b +--R + +--R 9 4 10 3 11 2 +--R - 1292880a b + 320640a b + 1277760a b +--R * +--R 19 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 13344a b + 136416a b + 275280a b - 462528a b +--R + +--R 9 4 10 3 11 2 +--R - 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1024a b + 5120a b - 3072a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 26 +--R (- 1024a b - 1024a b + 5120a b - 3072a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 4608a b + 14336a b - 15360a b - 38912a b +--R + +--R 11 2 +--R 35328a b +--R * +--R 25 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 4608a b + 14336a b - 15360a b - 38912a b +--R + +--R 11 2 +--R 35328a b +--R * +--R 24 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 8512a b - 47808a b - 29056a b + 167296a b +--R + +--R 10 3 11 2 +--R 100032a b - 186048a b +--R * +--R 23 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 8512a b - 47808a b - 29056a b + 167296a b +--R + +--R 10 3 11 2 +--R 100032a b - 186048a b +--R * +--R 22 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 8256a b + 72576a b + 154816a b - 155648a b +--R + +--R 9 4 10 3 11 2 +--R - 630592a b + 14464a b + 593472a b +--R * +--R 21 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 8256a b + 72576a b + 154816a b - 155648a b +--R + +--R 9 4 10 3 11 2 +--R - 630592a b + 14464a b + 593472a b +--R * +--R 20 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 4448a b - 58816a b - 228176a b - 121104a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 893488a b + 1186000a b - 746560a b - 1277760a b +--R * +--R 19 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 4448a b - 58816a b - 228176a b - 121104a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 893488a b + 1186000a b - 746560a b - 1277760a b +--R * +--R 18 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 1288a b + 26256a b + 163168a b + 308000a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 430744a b - 1974960a b - 980112a b + 2234880a b +--R + +--R 11 2 +--R 1957824a b +--R * +--R 17 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 1288a b + 26256a b + 163168a b + 308000a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 430744a b - 1974960a b - 980112a b + 2234880a b +--R + +--R 11 2 +--R 1957824a b +--R * +--R 16 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 177a b - 6151a b - 61050a b - 215934a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 49749a b + 1310405a b + 2303424a b - 469440a b +--R + +--R 10 3 11 2 +--R - 3716736a b - 2192256a b +--R * +--R 15 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 177a b - 6151a b - 61050a b - 215934a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 49749a b + 1310405a b + 2303424a b - 469440a b +--R + +--R 10 3 11 2 +--R - 3716736a b - 2192256a b +--R * +--R 14 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R 9a b + 656a b + 11395a b + 69128a b + 112471a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 390392a b - 1621123a b - 1257408a b + 2188608a b +--R + +--R 10 3 11 2 +--R 4068096a b + 1812096a b +--R * +--R 13 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R 9a b + 656a b + 11395a b + 69128a b + 112471a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 390392a b - 1621123a b - 1257408a b + 2188608a b +--R + +--R 10 3 11 2 +--R 4068096a b + 1812096a b +--R * +--R 12 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 24a b - 904a b - 10056a b - 35229a b + 42451a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 532649a b + 1013129a b - 198240a b - 2721696a b +--R + +--R 10 3 11 2 +--R - 3074688a b - 1102464a b +--R * +--R 11 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 24a b - 904a b - 10056a b - 35229a b + 42451a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 532649a b + 1013129a b - 198240a b - 2721696a b +--R + +--R 10 3 11 2 +--R - 3074688a b - 1102464a b +--R * +--R 10 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R 22a b + 556a b + 3951a b + 786a b - 86334a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 307974a b - 217471a b + 810592a b + 1933600a b +--R + +--R 10 3 11 2 +--R 1615360a b + 485760a b +--R * +--R 9 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R 22a b + 556a b + 3951a b + 786a b - 86334a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 307974a b - 217471a b + 810592a b + 1933600a b +--R + +--R 10 3 11 2 +--R 1615360a b + 485760a b +--R * +--R 8 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 8a b - 137a b - 251a b + 6632a b + 41512a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 68605a b - 112081a b - 575936a b - 857664a b +--R + +--R 10 3 11 2 +--R - 577600a b - 149952a b +--R * +--R 7 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 8a b - 137a b - 251a b + 6632a b + 41512a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 68605a b - 112081a b - 575936a b - 857664a b +--R + +--R 10 3 11 2 +--R - 577600a b - 149952a b +--R * +--R 6 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R a b + 4a b - 211a b - 2232a b - 6341a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 8724a b + 87287a b + 205120a b + 233600a b +--R + +--R 10 3 11 2 +--R 133248a b + 30528a b +--R * +--R 5 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R a b + 4a b - 211a b - 2232a b - 6341a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 8724a b + 87287a b + 205120a b + 233600a b +--R + +--R 10 3 11 2 +--R 133248a b + 30528a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 2a b + 34a b + 135a b - 621a b - 6561a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 21869a b - 37456a b - 35504a b - 17728a b +--R + +--R 11 2 +--R - 3648a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 2a b + 34a b + 135a b - 621a b - 6561a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 21869a b - 37456a b - 35504a b - 17728a b +--R + +--R 11 2 +--R - 3648a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R a b + 22a b + 188a b + 810a b + 1955a b + 2768a b +--R + +--R 9 4 10 3 11 2 +--R 2288a b + 1024a b + 192a b +--R * +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R a b + 22a b + 188a b + 810a b + 1955a b + 2768a b +--R + +--R 9 4 10 3 11 2 +--R 2288a b + 1024a b + 192a b +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R tan(x) +--R + +--R 8 5 9 4 10 3 17 +--R (2048a b + 4096a b + 2048a b )cos(x) +--R + +--R 8 5 9 4 10 3 16 +--R (2048a b + 4096a b + 2048a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 15 +--R (- 7168a b - 27648a b - 33792a b - 13312a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 14 +--R (- 7168a b - 27648a b - 33792a b - 13312a b )cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 9856a b + 59904a b + 127232a b + 114176a b +--R + +--R 10 3 +--R 36992a b +--R * +--R 13 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 9856a b + 59904a b + 127232a b + 114176a b +--R + +--R 10 3 +--R 36992a b +--R * +--R 12 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R - 6784a b - 60416a b - 194560a b - 292096a b +--R + +--R 9 4 10 3 +--R - 208256a b - 57088a b +--R * +--R 11 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R - 6784a b - 60416a b - 194560a b - 292096a b +--R + +--R 9 4 10 3 +--R - 208256a b - 57088a b +--R * +--R 10 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R 2464a b + 31744a b + 146240a b + 325504a b +--R + +--R 8 5 9 4 10 3 +--R 380064a b + 224640a b + 53120a b +--R * +--R 9 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R 2464a b + 31744a b + 146240a b + 325504a b +--R + +--R 8 5 9 4 10 3 +--R 380064a b + 224640a b + 53120a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R - 448a b - 8832a b - 57472a b - 179456a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 305344a b - 290944a b - 146176a b - 30208a b +--R * +--R 7 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R - 448a b - 8832a b - 57472a b - 179456a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 305344a b - 290944a b - 146176a b - 30208a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R 32a b + 1216a b + 11648a b + 50176a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 117536a b + 160576a b + 128192a b + 55552a b +--R + +--R 10 3 +--R 10112a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R 32a b + 1216a b + 11648a b + 50176a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 117536a b + 160576a b + 128192a b + 55552a b +--R + +--R 10 3 +--R 10112a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 64a b - 1088a b - 6656a b - 20992a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 38720a b - 43584a b - 29568a b - 11136a b +--R + +--R 10 3 +--R - 1792a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 64a b - 1088a b - 6656a b - 20992a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 38720a b - 43584a b - 29568a b - 11136a b +--R + +--R 10 3 +--R - 1792a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 32a b + 320a b + 1376a b + 3328a b + 4960a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 4672a b + 2720a b + 896a b + 128a b +--R * +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 32a b + 320a b + 1376a b + 3328a b + 4960a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 4672a b + 2720a b + 896a b + 128a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 4 10 3 11 2 17 +--R (- 3072a b - 6144a b - 3072a b )cos(x) +--R + +--R 9 4 10 3 11 2 16 +--R (- 3072a b - 6144a b - 3072a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 15 +--R (10752a b + 41472a b + 50688a b + 19968a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 14 +--R (10752a b + 41472a b + 50688a b + 19968a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R - 14784a b - 89856a b - 190848a b - 171264a b +--R + +--R 11 2 +--R - 55488a b +--R * +--R 13 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R - 14784a b - 89856a b - 190848a b - 171264a b +--R + +--R 11 2 +--R - 55488a b +--R * +--R 12 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 10176a b + 90624a b + 291840a b + 438144a b +--R + +--R 10 3 11 2 +--R 312384a b + 85632a b +--R * +--R 11 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 10176a b + 90624a b + 291840a b + 438144a b +--R + +--R 10 3 11 2 +--R 312384a b + 85632a b +--R * +--R 10 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R - 3696a b - 47616a b - 219360a b - 488256a b +--R + +--R 9 4 10 3 11 2 +--R - 570096a b - 336960a b - 79680a b +--R * +--R 9 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R - 3696a b - 47616a b - 219360a b - 488256a b +--R + +--R 9 4 10 3 11 2 +--R - 570096a b - 336960a b - 79680a b +--R * +--R 8 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R 672a b + 13248a b + 86208a b + 269184a b + 458016a b +--R + +--R 9 4 10 3 11 2 +--R 436416a b + 219264a b + 45312a b +--R * +--R 7 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R 672a b + 13248a b + 86208a b + 269184a b + 458016a b +--R + +--R 9 4 10 3 11 2 +--R 436416a b + 219264a b + 45312a b +--R * +--R 6 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 1824a b - 17472a b - 75264a b - 176304a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 240864a b - 192288a b - 83328a b - 15168a b +--R * +--R 5 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 1824a b - 17472a b - 75264a b - 176304a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 240864a b - 192288a b - 83328a b - 15168a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R 96a b + 1632a b + 9984a b + 31488a b + 58080a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 65376a b + 44352a b + 16704a b + 2688a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R 96a b + 1632a b + 9984a b + 31488a b + 58080a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 65376a b + 44352a b + 16704a b + 2688a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 480a b - 2064a b - 4992a b - 7440a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 7008a b - 4080a b - 1344a b - 192a b +--R * +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 48a b - 480a b - 2064a b - 4992a b - 7440a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 7008a b - 4080a b - 1344a b - 192a b +--R * +--R 2 +--R csc(x) +--R + +--R 9 4 10 3 11 2 17 +--R (1024a b + 2048a b + 1024a b )cos(x) +--R + +--R 9 4 10 3 11 2 16 +--R (1024a b + 2048a b + 1024a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 15 +--R (- 3584a b - 13824a b - 16896a b - 6656a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 14 +--R (- 3584a b - 13824a b - 16896a b - 6656a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 4928a b + 29952a b + 63616a b + 57088a b +--R + +--R 11 2 +--R 18496a b +--R * +--R 13 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 4928a b + 29952a b + 63616a b + 57088a b +--R + +--R 11 2 +--R 18496a b +--R * +--R 12 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 3392a b - 30208a b - 97280a b - 146048a b +--R + +--R 10 3 11 2 +--R - 104128a b - 28544a b +--R * +--R 11 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 3392a b - 30208a b - 97280a b - 146048a b +--R + +--R 10 3 11 2 +--R - 104128a b - 28544a b +--R * +--R 10 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 1232a b + 15872a b + 73120a b + 162752a b +--R + +--R 9 4 10 3 11 2 +--R 190032a b + 112320a b + 26560a b +--R * +--R 9 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 1232a b + 15872a b + 73120a b + 162752a b +--R + +--R 9 4 10 3 11 2 +--R 190032a b + 112320a b + 26560a b +--R * +--R 8 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R - 224a b - 4416a b - 28736a b - 89728a b - 152672a b +--R + +--R 9 4 10 3 11 2 +--R - 145472a b - 73088a b - 15104a b +--R * +--R 7 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R - 224a b - 4416a b - 28736a b - 89728a b - 152672a b +--R + +--R 9 4 10 3 11 2 +--R - 145472a b - 73088a b - 15104a b +--R * +--R 6 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R 16a b + 608a b + 5824a b + 25088a b + 58768a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 80288a b + 64096a b + 27776a b + 5056a b +--R * +--R 5 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R 16a b + 608a b + 5824a b + 25088a b + 58768a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 80288a b + 64096a b + 27776a b + 5056a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 32a b - 544a b - 3328a b - 10496a b - 19360a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 21792a b - 14784a b - 5568a b - 896a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 32a b - 544a b - 3328a b - 10496a b - 19360a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 21792a b - 14784a b - 5568a b - 896a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R 16a b + 160a b + 688a b + 1664a b + 2480a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 2336a b + 1360a b + 448a b + 64a b +--R * +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 16a b + 160a b + 688a b + 1664a b + 2480a b + 2336a b +--R + +--R 9 4 10 3 11 2 +--R 1360a b + 448a b + 64a b +--R * +--R 2 +--R cot(x) +--R + +--R 10 3 11 2 12 17 +--R (- 1024a b - 2048a b - 1024a b)cos(x) +--R + +--R 10 3 11 2 12 16 +--R (- 1024a b - 2048a b - 1024a b)cos(x) +--R + +--R 9 4 10 3 11 2 12 15 +--R (3584a b + 13824a b + 16896a b + 6656a b)cos(x) +--R + +--R 9 4 10 3 11 2 12 14 +--R (3584a b + 13824a b + 16896a b + 6656a b)cos(x) +--R + +--R 8 5 9 4 10 3 11 2 12 +--R (- 4928a b - 29952a b - 63616a b - 57088a b - 18496a b) +--R * +--R 13 +--R cos(x) +--R + +--R 8 5 9 4 10 3 11 2 12 +--R (- 4928a b - 29952a b - 63616a b - 57088a b - 18496a b) +--R * +--R 12 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R 3392a b + 30208a b + 97280a b + 146048a b + 104128a b +--R + +--R 12 +--R 28544a b +--R * +--R 11 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R 3392a b + 30208a b + 97280a b + 146048a b + 104128a b +--R + +--R 12 +--R 28544a b +--R * +--R 10 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 1232a b - 15872a b - 73120a b - 162752a b - 190032a b +--R + +--R 11 2 12 +--R - 112320a b - 26560a b +--R * +--R 9 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 1232a b - 15872a b - 73120a b - 162752a b - 190032a b +--R + +--R 11 2 12 +--R - 112320a b - 26560a b +--R * +--R 8 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 +--R 224a b + 4416a b + 28736a b + 89728a b + 152672a b +--R + +--R 10 3 11 2 12 +--R 145472a b + 73088a b + 15104a b +--R * +--R 7 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 +--R 224a b + 4416a b + 28736a b + 89728a b + 152672a b +--R + +--R 10 3 11 2 12 +--R 145472a b + 73088a b + 15104a b +--R * +--R 6 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R - 16a b - 608a b - 5824a b - 25088a b - 58768a b +--R + +--R 9 4 10 3 11 2 12 +--R - 80288a b - 64096a b - 27776a b - 5056a b +--R * +--R 5 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R - 16a b - 608a b - 5824a b - 25088a b - 58768a b +--R + +--R 9 4 10 3 11 2 12 +--R - 80288a b - 64096a b - 27776a b - 5056a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R 32a b + 544a b + 3328a b + 10496a b + 19360a b +--R + +--R 9 4 10 3 11 2 12 +--R 21792a b + 14784a b + 5568a b + 896a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R 32a b + 544a b + 3328a b + 10496a b + 19360a b +--R + +--R 9 4 10 3 11 2 12 +--R 21792a b + 14784a b + 5568a b + 896a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 16a b - 160a b - 688a b - 1664a b - 2480a b - 2336a b +--R + +--R 10 3 11 2 12 +--R - 1360a b - 448a b - 64a b +--R * +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 16a b - 160a b - 688a b - 1664a b - 2480a b - 2336a b +--R + +--R 10 3 11 2 12 +--R - 1360a b - 448a b - 64a b +--R * +--R 10 +--R sin(x) +--R + +--R 8 5 9 4 10 3 19 +--R (- 26624a b - 110592a b - 92160a b )cos(x) +--R + +--R 8 5 9 4 10 3 18 +--R (- 26624a b - 110592a b - 92160a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R (103424a b + 644096a b + 1207296a b + 691200a b ) +--R * +--R 17 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R (103424a b + 644096a b + 1207296a b + 691200a b ) +--R * +--R 16 +--R cos(x) +--R + +--R 6 7 7 6 8 5 +--R - 161920a b - 1404416a b - 4207872a b +--R + +--R 9 4 10 3 +--R - 5202432a b - 2263680a b +--R * +--R 15 +--R cos(x) +--R + +--R 6 7 7 6 8 5 +--R - 161920a b - 1404416a b - 4207872a b +--R + +--R 9 4 10 3 +--R - 5202432a b - 2263680a b +--R * +--R 14 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 130688a b + 1533312a b + 6581504a b + 13050112a b +--R + +--R 9 4 10 3 +--R 12092544a b + 4233600a b +--R * +--R 13 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 130688a b + 1533312a b + 6581504a b + 13050112a b +--R + +--R 9 4 10 3 +--R 12092544a b + 4233600a b +--R * +--R 12 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 57792a b - 917952a b - 5410912a b - 15450752a b +--R + +--R 8 5 9 4 10 3 +--R - 22920864a b - 16978176a b - 4959360a b +--R * +--R 11 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 57792a b - 917952a b - 5410912a b - 15450752a b +--R + +--R 8 5 9 4 10 3 +--R - 22920864a b - 16978176a b - 4959360a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 13744a b + 305456a b + 2457296a b + 9663856a b +--R + +--R 7 6 8 5 9 4 +--R 20632384a b + 24396064a b + 15011712a b +--R + +--R 10 3 +--R 3749760a b +--R * +--R 9 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 13744a b + 305456a b + 2457296a b + 9663856a b +--R + +--R 7 6 8 5 9 4 +--R 20632384a b + 24396064a b + 15011712a b +--R + +--R 10 3 +--R 3749760a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 1586a b - 54184a b - 611116a b - 3276200a b +--R + +--R 6 7 7 6 8 5 +--R - 9606962a b - 16289280a b - 15935296a b +--R + +--R 9 4 10 3 +--R - 8349696a b - 1814400a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 1586a b - 54184a b - 611116a b - 3276200a b +--R + +--R 6 7 7 6 8 5 +--R - 9606962a b - 16289280a b - 15935296a b +--R + +--R 9 4 10 3 +--R - 8349696a b - 1814400a b +--R * +--R 6 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 +--R 66a b + 4558a b + 78100a b + 582588a b +--R + +--R 5 8 6 7 7 6 8 5 +--R 2311850a b + 5347510a b + 7455360a b + 6175552a b +--R + +--R 9 4 10 3 +--R 2800512a b + 535680a b +--R * +--R 5 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 +--R 66a b + 4558a b + 78100a b + 582588a b +--R + +--R 5 8 6 7 7 6 8 5 +--R 2311850a b + 5347510a b + 7455360a b + 6175552a b +--R + +--R 9 4 10 3 +--R 2800512a b + 535680a b +--R * +--R 4 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 +--R - 132a b - 4358a b - 48624a b - 264692a b +--R + +--R 5 8 6 7 7 6 +--R - 818652a b - 1541430a b - 1804160a b +--R + +--R 8 5 9 4 10 3 +--R - 1283872a b - 509184a b - 86400a b +--R * +--R 3 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 +--R - 132a b - 4358a b - 48624a b - 264692a b +--R + +--R 5 8 6 7 7 6 +--R - 818652a b - 1541430a b - 1804160a b +--R + +--R 8 5 9 4 10 3 +--R - 1283872a b - 509184a b - 86400a b +--R * +--R 2 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 +--R 66a b + 1386a b + 10964a b + 45556a b +--R + +--R 5 8 6 7 7 6 8 5 +--R 112970a b + 176546a b + 175936a b + 108704a b +--R + +--R 9 4 10 3 +--R 38016a b + 5760a b +--R * +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R 66a b + 1386a b + 10964a b + 45556a b + 112970a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 176546a b + 175936a b + 108704a b + 38016a b +--R + +--R 10 3 +--R 5760a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 4 10 3 11 2 19 +--R (39936a b + 165888a b + 138240a b )cos(x) +--R + +--R 9 4 10 3 11 2 18 +--R (39936a b + 165888a b + 138240a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R (- 155136a b - 966144a b - 1810944a b - 1036800a b ) +--R * +--R 17 +--R cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R (- 155136a b - 966144a b - 1810944a b - 1036800a b ) +--R * +--R 16 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 242880a b + 2106624a b + 6311808a b + 7803648a b +--R + +--R 11 2 +--R 3395520a b +--R * +--R 15 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 242880a b + 2106624a b + 6311808a b + 7803648a b +--R + +--R 11 2 +--R 3395520a b +--R * +--R 14 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 196032a b - 2299968a b - 9872256a b - 19575168a b +--R + +--R 10 3 11 2 +--R - 18138816a b - 6350400a b +--R * +--R 13 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 196032a b - 2299968a b - 9872256a b - 19575168a b +--R + +--R 10 3 11 2 +--R - 18138816a b - 6350400a b +--R * +--R 12 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 86688a b + 1376928a b + 8116368a b + 23176128a b +--R + +--R 9 4 10 3 11 2 +--R 34381296a b + 25467264a b + 7439040a b +--R * +--R 11 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 86688a b + 1376928a b + 8116368a b + 23176128a b +--R + +--R 9 4 10 3 11 2 +--R 34381296a b + 25467264a b + 7439040a b +--R * +--R 10 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 20616a b - 458184a b - 3685944a b - 14495784a b +--R + +--R 8 5 9 4 10 3 +--R - 30948576a b - 36594096a b - 22517568a b +--R + +--R 11 2 +--R - 5624640a b +--R * +--R 9 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 20616a b - 458184a b - 3685944a b - 14495784a b +--R + +--R 8 5 9 4 10 3 +--R - 30948576a b - 36594096a b - 22517568a b +--R + +--R 11 2 +--R - 5624640a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 2379a b + 81276a b + 916674a b + 4914300a b +--R + +--R 7 6 8 5 9 4 +--R 14410443a b + 24433920a b + 23902944a b +--R + +--R 10 3 11 2 +--R 12524544a b + 2721600a b +--R * +--R 7 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 2379a b + 81276a b + 916674a b + 4914300a b +--R + +--R 7 6 8 5 9 4 +--R 14410443a b + 24433920a b + 23902944a b +--R + +--R 10 3 11 2 +--R 12524544a b + 2721600a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 99a b - 6837a b - 117150a b - 873882a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 3467775a b - 8021265a b - 11183040a b - 9263328a b +--R + +--R 10 3 11 2 +--R - 4200768a b - 803520a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 99a b - 6837a b - 117150a b - 873882a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 3467775a b - 8021265a b - 11183040a b - 9263328a b +--R + +--R 10 3 11 2 +--R - 4200768a b - 803520a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R 198a b + 6537a b + 72936a b + 397038a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 1227978a b + 2312145a b + 2706240a b + 1925808a b +--R + +--R 10 3 11 2 +--R 763776a b + 129600a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R 198a b + 6537a b + 72936a b + 397038a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 1227978a b + 2312145a b + 2706240a b + 1925808a b +--R + +--R 10 3 11 2 +--R 763776a b + 129600a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 99a b - 2079a b - 16446a b - 68334a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 169455a b - 264819a b - 263904a b - 163056a b +--R + +--R 10 3 11 2 +--R - 57024a b - 8640a b +--R * +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 99a b - 2079a b - 16446a b - 68334a b - 169455a b +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R - 264819a b - 263904a b - 163056a b - 57024a b - 8640a b +--R * +--R 2 +--R csc(x) +--R + +--R 9 4 10 3 11 2 19 +--R (- 13312a b - 55296a b - 46080a b )cos(x) +--R + +--R 9 4 10 3 11 2 18 +--R (- 13312a b - 55296a b - 46080a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 17 +--R (51712a b + 322048a b + 603648a b + 345600a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 16 +--R (51712a b + 322048a b + 603648a b + 345600a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R - 80960a b - 702208a b - 2103936a b - 2601216a b +--R + +--R 11 2 +--R - 1131840a b +--R * +--R 15 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R - 80960a b - 702208a b - 2103936a b - 2601216a b +--R + +--R 11 2 +--R - 1131840a b +--R * +--R 14 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 65344a b + 766656a b + 3290752a b + 6525056a b +--R + +--R 10 3 11 2 +--R 6046272a b + 2116800a b +--R * +--R 13 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R 65344a b + 766656a b + 3290752a b + 6525056a b +--R + +--R 10 3 11 2 +--R 6046272a b + 2116800a b +--R * +--R 12 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R - 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4b - 368a b - 12108a b - 147276a b +--R + +--R 4 9 5 8 6 7 +--R - 875008a b - 2934900a b - 5955488a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 7472192a b - 5674368a b - 2392320a b - 430080a b +--R * +--R 3 +--R cos(x) +--R + +--R 13 12 2 11 3 10 +--R - 4b - 368a b - 12108a b - 147276a b +--R + +--R 4 9 5 8 6 7 +--R - 875008a b - 2934900a b - 5955488a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 7472192a b - 5674368a b - 2392320a b - 430080a b +--R * +--R 2 +--R cos(x) +--R + +--R 13 12 2 11 3 10 4 9 +--R 2b + 164a b + 3412a b + 29520a b + 135106a b +--R + +--R 5 8 6 7 7 6 8 5 +--R 366972a b + 623704a b + 671552a b + 445760a b +--R + +--R 9 4 10 3 +--R 166656a b + 26880a b +--R * +--R cos(x) +--R + +--R 13 12 2 11 3 10 4 9 +--R 2b + 164a b + 3412a b + 29520a b + 135106a b +--R + +--R 5 8 6 7 7 6 8 5 +--R 366972a b + 623704a b + 671552a b + 445760a b +--R + +--R 9 4 10 3 +--R 166656a b + 26880a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 4 10 3 11 2 21 +--R (43008a b - 258048a b - 645120a b )cos(x) +--R + +--R 9 4 10 3 11 2 20 +--R (43008a b - 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76457220a b - 176326752a b - 223505184a b +--R + +--R 10 3 11 2 +--R - 146708352a b - 38949120a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R 60a b + 8142a b + 295890a b + 3688314a b +--R + +--R 6 7 7 6 8 5 +--R 21539274a b + 68064336a b + 123506880a b +--R + +--R 9 4 10 3 11 2 +--R 128682624a b + 71551872a b + 16450560a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R 60a b + 8142a b + 295890a b + 3688314a b +--R + +--R 6 7 7 6 8 5 +--R 21539274a b + 68064336a b + 123506880a b +--R + +--R 9 4 10 3 11 2 +--R 128682624a b + 71551872a b + 16450560a b +--R * +--R 6 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 +--R - 3a b - 366a b - 21078a b - 393372a b +--R + +--R 5 8 6 7 7 6 +--R - 3203223a b - 13749150a b - 34151640a b +--R + +--R 8 5 9 4 10 3 +--R - 50855616a b - 44806944a b - 21538944a b +--R + +--R 11 2 +--R - 4354560a b +--R * +--R 5 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 +--R - 3a b - 366a b - 21078a b - 393372a b +--R + +--R 5 8 6 7 7 6 +--R - 3203223a b - 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45a b - 1080a b - 9549a b - 40518a b - 95124a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 131136a b - 106032a b - 46656a b - 8640a b +--R * +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 45a b - 1080a b - 9549a b - 40518a b - 95124a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 131136a b - 106032a b - 46656a b - 8640a b +--R * +--R 2 +--R csc(x) +--R + +--R 9 4 10 3 11 2 25 +--R (13312a b - 55296a b + 46080a b )cos(x) +--R + +--R 9 4 10 3 11 2 24 +--R (13312a b - 55296a b + 46080a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R (- 54784a b + 135680a b + 308736a b - 483840a b ) +--R * +--R 23 +--R cos(x) +--R + +--R 8 5 9 4 10 3 11 2 +--R (- 54784a b + 135680a b + 308736a b - 483840a b ) +--R * +--R 22 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 91712a b - 51968a b - 1272192a b - 177408a b +--R + +--R 11 2 +--R 2306880a b +--R * +--R 21 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 91712a b - 51968a b - 1272192a b - 177408a b +--R + +--R 11 2 +--R 2306880a b +--R * +--R 20 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 79936a b - 139008a b + 1713152a b + 3467136a b +--R + +--R 10 3 11 2 +--R - 3188160a b - 6595200a b +--R * +--R 19 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 79936a b - 139008a b + 1713152a b + 3467136a b +--R + +--R 10 3 11 2 +--R - 3188160a b - 6595200a b +--R * +--R 18 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 38544a b + 184384a b - 1101280a b - 5691328a b +--R + +--R 9 4 10 3 11 2 +--R - 2577392a b + 13106880a b + 12571200a b +--R * +--R 17 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 38544a b + 184384a b - 1101280a b - 5691328a b +--R + +--R 9 4 10 3 11 2 +--R - 2577392a b + 13106880a b + 12571200a b +--R * +--R 16 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 10096a b - 94848a b + 356304a b + 4247648a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 7697280a b - 6852224a b - 26880768a b - 16796160a b +--R * +--R 15 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 10096a b - 94848a b + 356304a b + 4247648a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 7697280a b - 6852224a b - 26880768a b - 16796160a b +--R * +--R 14 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 1316a b + 23712a b - 50160a b - 1707312a b +--R + +--R 7 6 8 5 9 4 +--R - 6098564a b - 2205056a b + 21068992a b +--R + +--R 10 3 11 2 +--R 34691328a b + 16087680a b +--R * +--R 13 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 1316a b + 23712a b - 50160a b - 1707312a b +--R + +--R 7 6 8 5 9 4 +--R - 6098564a b - 2205056a b + 21068992a b +--R + +--R 10 3 11 2 +--R 34691328a b + 16087680a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 68a b - 2846a b - 450a b + 375230a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 2320574a b + 3466040a b - 7149184a b - 27677312a b +--R + +--R 10 3 11 2 +--R - 30063744a b - 11093760a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 68a b - 2846a b - 450a b + 375230a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 2320574a b + 3466040a b - 7149184a b - 27677312a b +--R + +--R 10 3 11 2 +--R - 30063744a b - 11093760a b +--R * +--R 10 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R a b + 138a b + 872a b - 41220a b - 448217a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 1298774a b + 825668a b + 10944768a b + 21534304a b +--R + +--R 10 3 11 2 +--R 17746560a b + 5443200a b +--R * +--R 9 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R a b + 138a b + 872a b - 41220a b - 448217a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 1298774a b + 825668a b + 10944768a b + 21534304a b +--R + +--R 10 3 11 2 +--R 17746560a b + 5443200a b +--R * +--R 8 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 2a b - 60a b + 1778a b + 40320a b + 204984a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 54076a b - 2316560a b - 7505792a b - 10474368a b +--R + +--R 10 3 11 2 +--R - 7015680a b - 1843200a b +--R * +--R 7 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 2a b - 60a b + 1778a b + 40320a b + 204984a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 54076a b - 2316560a b - 7505792a b - 10474368a b +--R + +--R 10 3 11 2 +--R - 7015680a b - 1843200a b +--R * +--R 6 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R a b - 22a b - 1353a b - 12804a b - 12974a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 266916a b + 1326212a b + 2808960a b + 3109952a b +--R + +--R 10 3 11 2 +--R 1764864a b + 406080a b +--R * +--R 5 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R a b - 22a b - 1353a b - 12804a b - 12974a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 266916a b + 1326212a b + 2808960a b + 3109952a b +--R + +--R 10 3 11 2 +--R 1764864a b + 406080a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 12a b + 218a b + 178a b - 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54076a b + 2316560a b + 7505792a b + 10474368a b +--R + +--R 11 2 12 +--R 7015680a b + 1843200a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - a b + 22a b + 1353a b + 12804a b + 12974a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 266916a b - 1326212a b - 2808960a b - 3109952a b +--R + +--R 11 2 12 +--R - 1764864a b - 406080a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - a b + 22a b + 1353a b + 12804a b + 12974a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 266916a b - 1326212a b - 2808960a b - 3109952a b +--R + +--R 11 2 12 +--R - 1764864a b - 406080a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 12a b - 218a b - 178a b + 15742a b + 109738a b +--R + +--R 8 5 9 4 10 3 11 2 12 +--R 333576a b + 549760a b + 511232a b + 252864a b + 51840a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 12a b - 218a b - 178a b + 15742a b + 109738a b +--R + +--R 8 5 9 4 10 3 11 2 12 +--R 333576a b + 549760a b + 511232a b + 252864a b + 51840a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R - 15a b - 360a b - 3183a b - 13506a b - 31708a b +--R + +--R 9 4 10 3 11 2 12 +--R - 43712a b - 35344a b - 15552a b - 2880a b +--R * +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 15a b - 360a b - 3183a b - 13506a b - 31708a b - 43712a b +--R + +--R 10 3 11 2 12 +--R - 35344a b - 15552a b - 2880a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 5 9 4 10 3 27 +--R (- 2048a b + 4096a b - 2048a b )cos(x) +--R + +--R 8 5 9 4 10 3 26 +--R (- 2048a b + 4096a b - 2048a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 25 +--R (9216a b + 1024a b - 33792a b + 23552a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 24 +--R (9216a b + 1024a b - 33792a b + 23552a b )cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 17024a b - 44544a b + 75520a b + 108032a b +--R + +--R 10 3 +--R - 124032a b +--R * +--R 23 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 17024a b - 44544a b + 75520a b + 108032a b +--R + +--R 10 3 +--R - 124032a b +--R * +--R 22 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 16512a b + 95616a b + 22784a b - 379648a b +--R + +--R 9 4 10 3 +--R - 122240a b + 395648a b +--R * +--R 21 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 16512a b + 95616a b + 22784a b - 379648a b +--R + +--R 9 4 10 3 +--R - 122240a b + 395648a b +--R * +--R 20 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 8896a b - 90944a b - 183520a b + 308352a b +--R + +--R 8 5 9 4 10 3 +--R 861920a b - 213760a b - 851840a b +--R * +--R 19 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 +--R - 8896a b - 90944a b - 183520a b + 308352a b +--R + +--R 8 5 9 4 10 3 +--R 861920a b - 213760a b - 851840a b +--R * +--R 18 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 2576a b + 44784a b + 191984a b + 40048a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 981632a b - 1005024a b + 1054848a b + 1305216a b +--R * +--R 17 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 +--R 2576a b + 44784a b + 191984a b + 40048a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 981632a b - 1005024a b + 1054848a b + 1305216a b +--R * +--R 16 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 +--R - 354a b - 11240a b - 88380a b - 166728a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 400686a b + 1418752a b + 350592a b - 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48a b - 1664a b - 15120a b - 25098a b +--R + +--R 5 8 6 7 7 6 8 5 +--R 160196a b + 584710a b + 272128a b - 1212864a b +--R + +--R 9 4 10 3 +--R - 1804800a b - 734976a b +--R * +--R 10 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R 44a b + 980a b + 4962a b - 13314a b - 132726a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 217770a b + 218368a b + 966080a b + 968960a b +--R + +--R 10 3 +--R 323840a b +--R * +--R 9 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R 44a b + 980a b + 4962a b - 13314a b - 132726a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 217770a b + 218368a b + 966080a b + 968960a b +--R + +--R 10 3 +--R 323840a b +--R * +--R 8 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 16a b - 226a b + 176a b + 12736a b + 44816a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 2762a b - 232448a b - 454528a b - 351744a b +--R + +--R 10 3 +--R - 99968a b +--R * +--R 7 +--R cos(x) +--R + +--R 12 2 11 3 10 4 9 5 8 +--R - 16a b - 226a b + 176a b + 12736a b + 44816a b +--R + +--R 6 7 7 6 8 5 9 4 +--R 2762a b - 232448a b - 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6144a b + 3072a b )cos(x) +--R + +--R 9 4 10 3 11 2 26 +--R (3072a b - 6144a b + 3072a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 25 +--R (- 13824a b - 1536a b + 50688a b - 35328a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 24 +--R (- 13824a b - 1536a b + 50688a b - 35328a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 25536a b + 66816a b - 113280a b - 162048a b +--R + +--R 11 2 +--R 186048a b +--R * +--R 23 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 +--R 25536a b + 66816a b - 113280a b - 162048a b +--R + +--R 11 2 +--R 186048a b +--R * +--R 22 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 24768a b - 143424a b - 34176a b + 569472a b +--R + +--R 10 3 11 2 +--R 183360a b - 593472a b +--R * +--R 21 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 +--R - 24768a b - 143424a b - 34176a b + 569472a b +--R + +--R 10 3 11 2 +--R 183360a b - 593472a b +--R * +--R 20 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 13344a b + 136416a b + 275280a b - 462528a b +--R + +--R 9 4 10 3 11 2 +--R - 1292880a b + 320640a b + 1277760a b +--R * +--R 19 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 +--R 13344a b + 136416a b + 275280a b - 462528a b +--R + +--R 9 4 10 3 11 2 +--R - 1292880a b + 320640a b + 1277760a b +--R * +--R 18 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R - 3864a b - 67176a b - 287976a b - 60072a b + 1472448a b +--R + +--R 9 4 10 3 11 2 +--R 1507536a b - 1582272a b - 1957824a b +--R * +--R 17 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R - 3864a b - 67176a b - 287976a b - 60072a b + 1472448a b +--R + +--R 9 4 10 3 11 2 +--R 1507536a b - 1582272a b - 1957824a b +--R * +--R 16 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R 531a b + 16860a b + 132570a b + 250092a b - 601029a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 2128128a b - 525888a b + 2985984a b + 2192256a b +--R * +--R 15 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R 531a b + 16860a b + 132570a b + 250092a b - 601029a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 2128128a b - 525888a b + 2985984a b + 2192256a b +--R * +--R 14 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 27a b - 1887a b - 28524a b - 121812a b + 28023a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 1087107a b + 1602048a b - 1033920a b - 3464064a b +--R + +--R 11 2 +--R - 1812096a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 27a b - 1887a b - 28524a b - 121812a b + 28023a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 1087107a b + 1602048a b - 1033920a b - 3464064a b +--R + +--R 11 2 +--R - 1812096a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 72a b + 2496a b + 22680a b + 37647a b - 240294a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 877065a b - 408192a b + 1819296a b + 2707200a b +--R + +--R 11 2 +--R 1102464a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 72a b + 2496a b + 22680a b + 37647a b - 240294a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 877065a b - 408192a b + 1819296a b + 2707200a b +--R + +--R 11 2 +--R 1102464a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 66a b - 1470a b - 7443a b + 19971a b + 199089a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 326655a b - 327552a b - 1449120a b - 1453440a b +--R + +--R 11 2 +--R - 485760a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 66a b - 1470a b - 7443a b + 19971a b + 199089a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 326655a b - 327552a b - 1449120a b - 1453440a b +--R + +--R 11 2 +--R - 485760a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 24a b + 339a b - 264a b - 19104a b - 67224a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 4143a b + 348672a b + 681792a b + 527616a b +--R + +--R 11 2 +--R 149952a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 24a b + 339a b - 264a b - 19104a b - 67224a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 4143a b + 348672a b + 681792a b + 527616a b +--R + +--R 11 2 +--R 149952a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 3a b - 3a b + 642a b + 4770a b + 4713a b - 40311a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 140928a b - 192576a b - 123072a b - 30528a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 3a b - 3a b + 642a b + 4770a b + 4713a b - 40311a b +--R + +--R 8 5 9 4 10 3 11 2 +--R - 140928a b - 192576a b - 123072a b - 30528a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 6a b - 84a b - 153a b + 2322a b + 12717a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 27456a b + 30000a b + 16512a b + 3648a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 6a b - 84a b - 153a b + 2322a b + 12717a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 27456a b + 30000a b + 16512a b + 3648a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 3a b - 57a b - 393a b - 1251a b - 2112a b - 1968a b +--R + +--R 10 3 11 2 +--R - 960a b - 192a b +--R * +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 3a b - 57a b - 393a b - 1251a b - 2112a b - 1968a b +--R + +--R 10 3 11 2 +--R - 960a b - 192a b +--R * +--R 2 +--R csc(x) +--R + +--R 9 4 10 3 11 2 27 +--R (- 1024a b + 2048a b - 1024a b )cos(x) +--R + +--R 9 4 10 3 11 2 26 +--R (- 1024a b + 2048a b - 1024a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 25 +--R (4608a b + 512a b - 16896a b + 11776a b )cos(x) +--R + +--R 8 5 9 4 10 3 11 2 24 +--R (4608a b + 512a b - 16896a b + 11776a b )cos(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R (- 8512a b - 22272a b + 37760a b + 54016a b - 62016a b ) +--R * +--R 23 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R (- 8512a b - 22272a b + 37760a b + 54016a b - 62016a b ) +--R * +--R 22 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R 8256a b + 47808a b + 11392a b - 189824a b - 61120a b +--R + +--R 11 2 +--R 197824a b +--R * +--R 21 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R 8256a b + 47808a b + 11392a b - 189824a b - 61120a b +--R + +--R 11 2 +--R 197824a b +--R * +--R 20 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 +--R - 4448a b - 45472a b - 91760a b + 154176a b + 430960a b +--R + +--R 10 3 11 2 +--R - 106880a b - 425920a b +--R * +--R 19 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 +--R - 4448a b - 45472a b - 91760a b + 154176a b + 430960a b +--R + +--R 10 3 11 2 +--R - 106880a b - 425920a b +--R * +--R 18 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R 1288a b + 22392a b + 95992a b + 20024a b - 490816a b +--R + +--R 9 4 10 3 11 2 +--R - 502512a b + 527424a b + 652608a b +--R * +--R 17 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R 1288a b + 22392a b + 95992a b + 20024a b - 490816a b +--R + +--R 9 4 10 3 11 2 +--R - 502512a b + 527424a b + 652608a b +--R * +--R 16 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 177a b - 5620a b - 44190a b - 83364a b + 200343a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 709376a b + 175296a b - 995328a b - 730752a b +--R * +--R 15 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 177a b - 5620a b - 44190a b - 83364a b + 200343a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 709376a b + 175296a b - 995328a b - 730752a b +--R * +--R 14 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 9a b + 629a b + 9508a b + 40604a b - 9341a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 362369a b - 534016a b + 344640a b + 1154688a b +--R + +--R 11 2 +--R 604032a b +--R * +--R 13 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 9a b + 629a b + 9508a b + 40604a b - 9341a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 362369a b - 534016a b + 344640a b + 1154688a b +--R + +--R 11 2 +--R 604032a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 24a b - 832a b - 7560a b - 12549a b + 80098a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 292355a b + 136064a b - 606432a b - 902400a b +--R + +--R 11 2 +--R - 367488a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 24a b - 832a b - 7560a b - 12549a b + 80098a b +--R + +--R 7 6 8 5 9 4 10 3 +--R 292355a b + 136064a b - 606432a b - 902400a b +--R + +--R 11 2 +--R - 367488a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 22a b + 490a b + 2481a b - 6657a b - 66363a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 108885a b + 109184a b + 483040a b + 484480a b +--R + +--R 11 2 +--R 161920a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R 22a b + 490a b + 2481a b - 6657a b - 66363a b +--R + +--R 7 6 8 5 9 4 10 3 +--R - 108885a b + 109184a b + 483040a b + 484480a b +--R + +--R 11 2 +--R 161920a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 8a b - 113a b + 88a b + 6368a b + 22408a b +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R 1381a b - 116224a b - 227264a b - 175872a b - 49984a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 +--R - 8a b - 113a b + 88a b + 6368a b + 22408a b +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R 1381a b - 116224a b - 227264a b - 175872a b - 49984a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R a b + a b - 214a b - 1590a b - 1571a b + 13437a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 46976a b + 64192a b + 41024a b + 10176a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R a b + a b - 214a b - 1590a b - 1571a b + 13437a b +--R + +--R 8 5 9 4 10 3 11 2 +--R 46976a b + 64192a b + 41024a b + 10176a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 2a b + 28a b + 51a b - 774a b - 4239a b - 9152a b +--R + +--R 9 4 10 3 11 2 +--R - 10000a b - 5504a b - 1216a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 2a b + 28a b + 51a b - 774a b - 4239a b - 9152a b +--R + +--R 9 4 10 3 11 2 +--R - 10000a b - 5504a b - 1216a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R a b + 19a b + 131a b + 417a b + 704a b + 656a b +--R + +--R 10 3 11 2 +--R 320a b + 64a b +--R * +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 10 3 +--R a b + 19a b + 131a b + 417a b + 704a b + 656a b + 320a b +--R + +--R 11 2 +--R 64a b +--R * +--R 2 +--R cot(x) +--R + +--R 10 3 11 2 12 27 +--R (1024a b - 2048a b + 1024a b)cos(x) +--R + +--R 10 3 11 2 12 26 +--R (1024a b - 2048a b + 1024a b)cos(x) +--R + +--R 9 4 10 3 11 2 12 25 +--R (- 4608a b - 512a b + 16896a b - 11776a b)cos(x) +--R + +--R 9 4 10 3 11 2 12 24 +--R (- 4608a b - 512a b + 16896a b - 11776a b)cos(x) +--R + +--R 8 5 9 4 10 3 11 2 12 23 +--R (8512a b + 22272a b - 37760a b - 54016a b + 62016a b)cos(x) +--R + +--R 8 5 9 4 10 3 11 2 12 22 +--R (8512a b + 22272a b - 37760a b - 54016a b + 62016a b)cos(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R - 8256a b - 47808a b - 11392a b + 189824a b + 61120a b +--R + +--R 12 +--R - 197824a b +--R * +--R 21 +--R cos(x) +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R - 8256a b - 47808a b - 11392a b + 189824a b + 61120a b +--R + +--R 12 +--R - 197824a b +--R * +--R 20 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R 4448a b + 45472a b + 91760a b - 154176a b - 430960a b +--R + +--R 11 2 12 +--R 106880a b + 425920a b +--R * +--R 19 +--R cos(x) +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R 4448a b + 45472a b + 91760a b - 154176a b - 430960a b +--R + +--R 11 2 12 +--R 106880a b + 425920a b +--R * +--R 18 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 +--R - 1288a b - 22392a b - 95992a b - 20024a b + 490816a b +--R + +--R 10 3 11 2 12 +--R 502512a b - 527424a b - 652608a b +--R * +--R 17 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 +--R - 1288a b - 22392a b - 95992a b - 20024a b + 490816a b +--R + +--R 10 3 11 2 12 +--R 502512a b - 527424a b - 652608a b +--R * +--R 16 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R 177a b + 5620a b + 44190a b + 83364a b - 200343a b +--R + +--R 9 4 10 3 11 2 12 +--R - 709376a b - 175296a b + 995328a b + 730752a b +--R * +--R 15 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 +--R 177a b + 5620a b + 44190a b + 83364a b - 200343a b +--R + +--R 9 4 10 3 11 2 12 +--R - 709376a b - 175296a b + 995328a b + 730752a b +--R * +--R 14 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 9a b - 629a b - 9508a b - 40604a b + 9341a b + 362369a b +--R + +--R 9 4 10 3 11 2 12 +--R 534016a b - 344640a b - 1154688a b - 604032a b +--R * +--R 13 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 9a b - 629a b - 9508a b - 40604a b + 9341a b + 362369a b +--R + +--R 9 4 10 3 11 2 12 +--R 534016a b - 344640a b - 1154688a b - 604032a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 24a b + 832a b + 7560a b + 12549a b - 80098a b - 292355a b +--R + +--R 9 4 10 3 11 2 12 +--R - 136064a b + 606432a b + 902400a b + 367488a b +--R * +--R 11 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 24a b + 832a b + 7560a b + 12549a b - 80098a b - 292355a b +--R + +--R 9 4 10 3 11 2 12 +--R - 136064a b + 606432a b + 902400a b + 367488a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 22a b - 490a b - 2481a b + 6657a b + 66363a b +--R + +--R 8 5 9 4 10 3 11 2 12 +--R 108885a b - 109184a b - 483040a b - 484480a b - 161920a b +--R * +--R 9 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 +--R - 22a b - 490a b - 2481a b + 6657a b + 66363a b +--R + +--R 8 5 9 4 10 3 11 2 12 +--R 108885a b - 109184a b - 483040a b - 484480a b - 161920a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 8a b + 113a b - 88a b - 6368a b - 22408a b - 1381a b +--R + +--R 9 4 10 3 11 2 12 +--R 116224a b + 227264a b + 175872a b + 49984a b +--R * +--R 7 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R 8a b + 113a b - 88a b - 6368a b - 22408a b - 1381a b +--R + +--R 9 4 10 3 11 2 12 +--R 116224a b + 227264a b + 175872a b + 49984a b +--R * +--R 6 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - a b - a b + 214a b + 1590a b + 1571a b - 13437a b +--R + +--R 9 4 10 3 11 2 12 +--R - 46976a b - 64192a b - 41024a b - 10176a b +--R * +--R 5 +--R cos(x) +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - a b - a b + 214a b + 1590a b + 1571a b - 13437a b +--R + +--R 9 4 10 3 11 2 12 +--R - 46976a b - 64192a b - 41024a b - 10176a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 2a b - 28a b - 51a b + 774a b + 4239a b + 9152a b +--R + +--R 10 3 11 2 12 +--R 10000a b + 5504a b + 1216a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 2a b - 28a b - 51a b + 774a b + 4239a b + 9152a b +--R + +--R 10 3 11 2 12 +--R 10000a b + 5504a b + 1216a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - a b - 19a b - 131a b - 417a b - 704a b - 656a b +--R + +--R 11 2 12 +--R - 320a b - 64a b +--R * +--R cos(x) +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 11 2 +--R - a b - 19a b - 131a b - 417a b - 704a b - 656a b - 320a b +--R + +--R 12 +--R - 64a b +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 8 5 9 4 10 3 18 +--R (- 24576a b - 65536a b - 40960a b )cos(x) +--R + +--R 7 6 8 5 9 4 +--R 102400a b + 462848a b + 667648a b +--R + +--R 10 3 +--R 307200a b +--R * +--R 16 +--R cos(x) +--R + +--R 6 7 7 6 8 5 +--R - 173568a b - 1157120a b - 2746368a b +--R + +--R 9 4 10 3 +--R - 2768896a b - 1006080a b +--R * +--R 14 +--R cos(x) +--R + +--R 5 8 6 7 7 6 +--R 153856a b + 1427456a b + 4936192a b +--R + +--R 8 5 9 4 10 3 +--R 8062464a b + 6281472a b + 1881600a b +--R * +--R 12 +--R cos(x) +--R + +--R 4 9 5 8 6 7 +--R - 76352a b - 968704a b - 4627072a b +--R + +--R 7 6 8 5 9 4 +--R - 10921984a b - 13655872a b - 8672768a b +--R + +--R 10 3 +--R - 2204160a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 10 4 9 5 8 +--R 21024a b + 371392a b + 2408128a b +--R + +--R 6 7 7 6 8 5 +--R 7797760a b + 13993760a b + 14162496a b +--R + +--R 9 4 10 3 +--R 7575296a b + 1666560a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 11 3 10 4 9 +--R - 2944a b - 78208a b - 697984a b +--R + +--R 5 8 6 7 7 6 +--R - 3040768a b - 7427968a b - 10714240a b +--R + +--R 8 5 9 4 10 3 +--R - 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2464a b - 31744a b - 146240a b - 325504a b +--R + +--R 8 3 9 2 10 +--R - 380064a b - 224640a b - 53120a b +--R * +--R 8 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 7 4 +--R 448a b + 8832a b + 57472a b + 179456a b + 305344a b +--R + +--R 8 3 9 2 10 +--R 290944a b + 146176a b + 30208a b +--R * +--R 7 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 7 4 +--R 448a b + 8832a b + 57472a b + 179456a b + 305344a b +--R + +--R 8 3 9 2 10 +--R 290944a b + 146176a b + 30208a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R - 32a b - 1216a b - 11648a b - 50176a b - 117536a b +--R + +--R 7 4 8 3 9 2 10 +--R - 160576a b - 128192a b - 55552a b - 10112a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R - 32a b - 1216a b - 11648a b - 50176a b - 117536a b +--R + +--R 7 4 8 3 9 2 10 +--R - 160576a b - 128192a b - 55552a b - 10112a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R 64a b + 1088a b + 6656a b + 20992a b + 38720a b +--R + +--R 7 4 8 3 9 2 10 +--R 43584a b + 29568a b + 11136a b + 1792a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R 64a b + 1088a b + 6656a b + 20992a b + 38720a b +--R + +--R 7 4 8 3 9 2 10 +--R 43584a b + 29568a b + 11136a b + 1792a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R - 32a b - 320a b - 1376a b - 3328a b - 4960a b +--R + +--R 7 4 8 3 9 2 10 +--R - 4672a b - 2720a b - 896a b - 128a b +--R * +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 +--R - 32a b - 320a b - 1376a b - 3328a b - 4960a b - 4672a b +--R + +--R 8 3 9 2 10 +--R - 2720a b - 896a b - 128a b +--R * +--R 10 +--R sin(x) +--R + +--R 8 3 9 2 10 19 +--R (26624a b + 110592a b + 92160a b)cos(x) +--R + +--R 8 3 9 2 10 18 +--R (26624a b + 110592a b + 92160a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 17 +--R (- 103424a b - 644096a b - 1207296a b - 691200a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 16 +--R (- 103424a b - 644096a b - 1207296a b - 691200a b)cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R 161920a b + 1404416a b + 4207872a b + 5202432a b +--R + +--R 10 +--R 2263680a b +--R * +--R 15 +--R cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R 161920a b + 1404416a b + 4207872a b + 5202432a b +--R + +--R 10 +--R 2263680a b +--R * +--R 14 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R - 130688a b - 1533312a b - 6581504a b - 13050112a b +--R + +--R 9 2 10 +--R - 12092544a b - 4233600a b +--R * +--R 13 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R - 130688a b - 1533312a b - 6581504a b - 13050112a b +--R + +--R 9 2 10 +--R - 12092544a b - 4233600a b +--R * +--R 12 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R 57792a b + 917952a b + 5410912a b + 15450752a b +--R + +--R 8 3 9 2 10 +--R 22920864a b + 16978176a b + 4959360a b +--R * +--R 11 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R 57792a b + 917952a b + 5410912a b + 15450752a b +--R + +--R 8 3 9 2 10 +--R 22920864a b + 16978176a b + 4959360a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R - 13744a b - 305456a b - 2457296a b - 9663856a b +--R + +--R 7 4 8 3 9 2 10 +--R - 20632384a b - 24396064a b - 15011712a b - 3749760a b +--R * +--R 9 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R - 13744a b - 305456a b - 2457296a b - 9663856a b +--R + +--R 7 4 8 3 9 2 10 +--R - 20632384a b - 24396064a b - 15011712a b - 3749760a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 +--R 1586a b + 54184a b + 611116a b + 3276200a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 9606962a b + 16289280a b + 15935296a b + 8349696a b +--R + +--R 10 +--R 1814400a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 +--R 1586a b + 54184a b + 611116a b + 3276200a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 9606962a b + 16289280a b + 15935296a b + 8349696a b +--R + +--R 10 +--R 1814400a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 66a b - 4558a b - 78100a b - 582588a b - 2311850a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 5347510a b - 7455360a b - 6175552a b - 2800512a b +--R + +--R 10 +--R - 535680a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 66a b - 4558a b - 78100a b - 582588a b - 2311850a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 5347510a b - 7455360a b - 6175552a b - 2800512a b +--R + +--R 10 +--R - 535680a b +--R * +--R 4 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 132a b + 4358a b + 48624a b + 264692a b + 818652a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 1541430a b + 1804160a b + 1283872a b + 509184a b +--R + +--R 10 +--R 86400a b +--R * +--R 3 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 132a b + 4358a b + 48624a b + 264692a b + 818652a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 1541430a b + 1804160a b + 1283872a b + 509184a b +--R + +--R 10 +--R 86400a b +--R * +--R 2 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 66a b - 1386a b - 10964a b - 45556a b - 112970a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 176546a b - 175936a b - 108704a b - 38016a b - 5760a b +--R * +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 66a b - 1386a b - 10964a b - 45556a b - 112970a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 176546a b - 175936a b - 108704a b - 38016a b - 5760a b +--R * +--R 8 +--R sin(x) +--R + +--R 8 3 9 2 10 21 +--R (28672a b - 172032a b - 430080a b)cos(x) +--R + +--R 8 3 9 2 10 20 +--R (28672a b - 172032a b - 430080a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 19 +--R (- 100352a b + 587776a b + 3483648a b + 3655680a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 18 +--R (- 100352a b + 587776a b + 3483648a b + 3655680a b)cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R 135936a b - 896000a b - 9314816a b - 20794368a b +--R + +--R 10 +--R - 13789440a b +--R * +--R 17 +--R cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R 135936a b - 896000a b - 9314816a b - 20794368a b +--R + +--R 10 +--R - 13789440a b +--R * +--R 16 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R - 88832a b + 842240a b + 12601344a b + 44939776a b +--R + +--R 9 2 10 +--R 62635776a b + 30320640a b +--R * +--R 15 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R - 88832a b + 842240a b + 12601344a b + 44939776a b +--R + +--R 9 2 10 +--R 62635776a b + 30320640a b +--R * +--R 14 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R 28096a b - 534400a b - 9911168a b - 50168832a b +--R + +--R 8 3 9 2 10 +--R - 111001408a b - 112707840a b - 42900480a b +--R * +--R 13 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R 28096a b - 534400a b - 9911168a b - 50168832a b +--R + +--R 8 3 9 2 10 +--R - 111001408a b - 112707840a b - 42900480a b +--R * +--R 12 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R - 3488a b + 216320a b + 4699424a b + 31964224a b +--R + +--R 7 4 8 3 9 2 10 +--R 100880192a b + 162617728a b + 129792768a b + 40642560a b +--R * +--R 11 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R - 3488a b + 216320a b + 4699424a b + 31964224a b +--R + +--R 7 4 8 3 9 2 10 +--R 100880192a b + 162617728a b + 129792768a b + 40642560a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 +--R - 72a b - 49280a b - 1307712a b - 11837536a b +--R + +--R 6 5 7 4 8 3 +--R - 50971480a b - 117551168a b - 149003456a b +--R + +--R 9 2 10 +--R - 97805568a b - 25966080a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 +--R - 72a b - 49280a b - 1307712a b - 11837536a b +--R + +--R 6 5 7 4 8 3 +--R - 50971480a b - 117551168a b - 149003456a b +--R + +--R 9 2 10 +--R - 97805568a b - 25966080a b +--R * +--R 8 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 +--R 40a b + 5428a b + 197260a b + 2458876a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 14359516a b + 45376224a b + 82337920a b + 85788416a b +--R + +--R 9 2 10 +--R 47701248a b + 10967040a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 +--R 40a b + 5428a b + 197260a b + 2458876a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 14359516a b + 45376224a b + 82337920a b + 85788416a b +--R + +--R 9 2 10 +--R 47701248a b + 10967040a b +--R * +--R 6 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 2b - 244a b - 14052a b - 262248a b - 2135482a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 9166100a b - 22767760a b - 33903744a b - 29871296a b +--R + +--R 9 2 10 +--R - 14359296a b - 2903040a b +--R * +--R 5 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 2b - 244a b - 14052a b - 262248a b - 2135482a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 9166100a b - 22767760a b - 33903744a b - 29871296a b +--R + +--R 9 2 10 +--R - 14359296a b - 2903040a b +--R * +--R 4 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 4b + 368a b + 12108a b + 147276a b + 875008a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 2934900a b + 5955488a b + 7472192a b + 5674368a b +--R + +--R 9 2 10 +--R 2392320a b + 430080a b +--R * +--R 3 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 4b + 368a b + 12108a b + 147276a b + 875008a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 2934900a b + 5955488a b + 7472192a b + 5674368a b +--R + +--R 9 2 10 +--R 2392320a b + 430080a b +--R * +--R 2 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 2b - 164a b - 3412a b - 29520a b - 135106a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 366972a b - 623704a b - 671552a b - 445760a b +--R + +--R 9 2 10 +--R - 166656a b - 26880a b +--R * +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 2b - 164a b - 3412a b - 29520a b - 135106a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 366972a b - 623704a b - 671552a b - 445760a b +--R + +--R 9 2 10 +--R - 166656a b - 26880a b +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 9 2 10 23 +--R (- 28672a b - 172032a b + 430080a b)cos(x) +--R + +--R 8 3 9 2 10 22 +--R (- 28672a b - 172032a b + 430080a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 21 +--R (129024a b + 989184a b - 645120a b - 4085760a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 20 +--R (129024a b + 989184a b - 645120a b - 4085760a b)cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R - 236288a b - 2300928a b - 2182656a b + 12493824a b +--R + +--R 10 +--R 17445120a b +--R * +--R 19 +--R cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R - 236288a b - 2300928a b - 2182656a b + 12493824a b +--R + +--R 10 +--R 17445120a b +--R * +--R 18 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R 225024a b + 2809600a b + 7028224a b - 12569088a b +--R + +--R 9 2 10 +--R - 56238336a b - 44110080a b +--R * +--R 17 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R 225024a b + 2809600a b + 7028224a b - 12569088a b +--R + +--R 9 2 10 +--R - 56238336a b - 44110080a b +--R * +--R 16 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R - 118144a b - 1943808a b - 8177728a b + 2082304a b +--R + +--R 8 3 9 2 10 +--R 72414272a b + 134313984a b + 73221120a b +--R * +--R 15 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R - 118144a b - 1943808a b - 8177728a b + 2082304a b +--R + +--R 8 3 9 2 10 +--R 72414272a b + 134313984a b + 73221120a b +--R * +--R 14 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R 33472a b + 765088a b + 4868800a b + 4696672a b +--R + +--R 7 4 8 3 9 2 10 +--R - 48025152a b - 166104512a b - 200051712a b - 83543040a b +--R * +--R 13 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R 33472a b + 765088a b + 4868800a b + 4696672a b +--R + +--R 7 4 8 3 9 2 10 +--R - 48025152a b - 166104512a b - 200051712a b - 83543040a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 +--R - 4676a b - 163344a b - 1563720a b - 3518192a b +--R + +--R 6 5 7 4 8 3 +--R 17833100a b + 108244864a b + 218783040a b +--R + +--R 9 2 10 +--R 196890624a b + 66608640a b +--R * +--R 11 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 +--R - 4676a b - 163344a b - 1563720a b - 3518192a b +--R + +--R 6 5 7 4 8 3 +--R 17833100a b + 108244864a b + 218783040a b +--R + +--R 9 2 10 +--R 196890624a b + 66608640a b +--R * +--R 10 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 +--R 260a b + 17000a b + 261804a b + 1028596a b +--R + +--R 5 6 6 5 7 4 +--R - 3845744a b - 40294812a b - 122881472a b +--R + +--R 8 3 9 2 10 +--R - 180263104a b - 129959424a b - 36933120a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 +--R 260a b + 17000a b + 261804a b + 1028596a b +--R + +--R 5 6 6 5 7 4 +--R - 3845744a b - 40294812a b - 122881472a b +--R + +--R 8 3 9 2 10 +--R - 180263104a b - 129959424a b - 36933120a b +--R * +--R 8 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 4b - 700a b - 20554a b - 137984a b + 489722a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 8620832a b + 37645880a b + 80914176a b + 94053568a b +--R + +--R 9 2 10 +--R 56641536a b + 13870080a b +--R * +--R 7 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 4b - 700a b - 20554a b - 137984a b + 489722a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 8620832a b + 37645880a b + 80914176a b + 94053568a b +--R + +--R 9 2 10 +--R 56641536a b + 13870080a b +--R * +--R 6 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 8b + 590a b + 7782a b - 35918a b - 998838a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 6118816a b - 18379992a b - 31016384a b - 29970752a b +--R + +--R 9 2 10 +--R - 15504384a b - 3333120a b +--R * +--R 5 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 8b + 590a b + 7782a b - 35918a b - 998838a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 6118816a b - 18379992a b - 31016384a b - 29970752a b +--R + +--R 9 2 10 +--R - 15504384a b - 3333120a b +--R * +--R 4 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 4b - 120a b + 1478a b + 54460a b + 469206a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 1942736a b + 4549948a b + 6358912a b + 5265344a b +--R + +--R 9 2 10 +--R 2386944a b + 456960a b +--R * +--R 3 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 4b - 120a b + 1478a b + 54460a b + 469206a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 1942736a b + 4549948a b + 6358912a b + 5265344a b +--R + +--R 9 2 10 +--R 2386944a b + 456960a b +--R * +--R 2 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 30a b - 1030a b - 12490a b - 71910a b - 230832a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 446380a b - 533568a b - 386624a b - 155904a b +--R + +--R 10 +--R - 26880a b +--R * +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 30a b - 1030a b - 12490a b - 71910a b - 230832a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 446380a b - 533568a b - 386624a b - 155904a b - 26880a b +--R * +--R 4 +--R sin(x) +--R + +--R 8 3 9 2 10 25 +--R (- 26624a b + 110592a b - 92160a b)cos(x) +--R + +--R 8 3 9 2 10 24 +--R (- 26624a b + 110592a b - 92160a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 23 +--R (109568a b - 271360a b - 617472a b + 967680a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 22 +--R (109568a b - 271360a b - 617472a b + 967680a b)cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R - 183424a b + 103936a b + 2544384a b + 354816a b +--R + +--R 10 +--R - 4613760a b +--R * +--R 21 +--R cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R - 183424a b + 103936a b + 2544384a b + 354816a b +--R + +--R 10 +--R - 4613760a b +--R * +--R 20 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R 159872a b + 278016a b - 3426304a b - 6934272a b +--R + +--R 9 2 10 +--R 6376320a b + 13190400a b +--R * +--R 19 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R 159872a b + 278016a b - 3426304a b - 6934272a b +--R + +--R 9 2 10 +--R 6376320a b + 13190400a b +--R * +--R 18 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R - 77088a b - 368768a b + 2202560a b + 11382656a b +--R + +--R 8 3 9 2 10 +--R 5154784a b - 26213760a b - 25142400a b +--R * +--R 17 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R - 77088a b - 368768a b + 2202560a b + 11382656a b +--R + +--R 8 3 9 2 10 +--R 5154784a b - 26213760a b - 25142400a b +--R * +--R 16 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R 20192a b + 189696a b - 712608a b - 8495296a b +--R + +--R 7 4 8 3 9 2 10 +--R - 15394560a b + 13704448a b + 53761536a b + 33592320a b +--R * +--R 15 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R 20192a b + 189696a b - 712608a b - 8495296a b +--R + +--R 7 4 8 3 9 2 10 +--R - 15394560a b + 13704448a b + 53761536a b + 33592320a b +--R * +--R 14 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 +--R - 2632a b - 47424a b + 100320a b + 3414624a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 12197128a b + 4410112a b - 42137984a b - 69382656a b +--R + +--R 10 +--R - 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2b - 276a b - 1744a b + 82440a b + 896434a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 2597548a b - 1651336a b - 21889536a b - 43068608a b +--R + +--R 9 2 10 +--R - 35493120a b - 10886400a b +--R * +--R 8 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 4b + 120a b - 3556a b - 80640a b - 409968a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 108152a b + 4633120a b + 15011584a b + 20948736a b +--R + +--R 9 2 10 +--R 14031360a b + 3686400a b +--R * +--R 7 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 4b + 120a b - 3556a b - 80640a b - 409968a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 108152a b + 4633120a b + 15011584a b + 20948736a b +--R + +--R 9 2 10 +--R 14031360a b + 3686400a b +--R * +--R 6 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 2b + 44a b + 2706a b + 25608a b + 25948a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 533832a b - 2652424a b - 5617920a b - 6219904a b +--R + +--R 9 2 10 +--R - 3529728a b - 812160a b +--R * +--R 5 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 2b + 44a b + 2706a b + 25608a b + 25948a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 533832a b - 2652424a b - 5617920a b - 6219904a b +--R + +--R 9 2 10 +--R - 3529728a b - 812160a b +--R * +--R 4 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 24a b - 436a b - 356a b + 31484a b + 219476a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 667152a b + 1099520a b + 1022464a b + 505728a b +--R + +--R 10 +--R 103680a b +--R * +--R 3 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 24a b - 436a b - 356a b + 31484a b + 219476a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 667152a b + 1099520a b + 1022464a b + 505728a b +--R + +--R 10 +--R 103680a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R - 30a b - 720a b - 6366a b - 27012a b - 63416a b +--R + +--R 7 4 8 3 9 2 10 +--R - 87424a b - 70688a b - 31104a b - 5760a b +--R * +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R - 30a b - 720a b - 6366a b - 27012a b - 63416a b +--R + +--R 7 4 8 3 9 2 10 +--R - 87424a b - 70688a b - 31104a b - 5760a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 9 2 10 27 +--R (2048a b - 4096a b + 2048a b)cos(x) +--R + +--R 8 3 9 2 10 26 +--R (2048a b - 4096a b + 2048a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 25 +--R (- 9216a b - 1024a b + 33792a b - 23552a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 24 +--R (- 9216a b - 1024a b + 33792a b - 23552a b)cos(x) +--R + +--R 6 5 7 4 8 3 9 2 10 +--R (17024a b + 44544a b - 75520a b - 108032a b + 124032a b) +--R * +--R 23 +--R cos(x) +--R + +--R 6 5 7 4 8 3 9 2 10 +--R (17024a b + 44544a b - 75520a b - 108032a b + 124032a b) +--R * +--R 22 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R - 16512a b - 95616a b - 22784a b + 379648a b + 122240a b +--R + +--R 10 +--R - 395648a b +--R * +--R 21 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R - 16512a b - 95616a b - 22784a b + 379648a b + 122240a b +--R + +--R 10 +--R - 395648a b +--R * +--R 20 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 8 3 +--R 8896a b + 90944a b + 183520a b - 308352a b - 861920a b +--R + +--R 9 2 10 +--R 213760a b + 851840a b +--R * +--R 19 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 8 3 +--R 8896a b + 90944a b + 183520a b - 308352a b - 861920a b +--R + +--R 9 2 10 +--R 213760a b + 851840a b +--R * +--R 18 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 7 4 +--R - 2576a b - 44784a b - 191984a b - 40048a b + 981632a b +--R + +--R 8 3 9 2 10 +--R 1005024a b - 1054848a b - 1305216a b +--R * +--R 17 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 7 4 +--R - 2576a b - 44784a b - 191984a b - 40048a b + 981632a b +--R + +--R 8 3 9 2 10 +--R 1005024a b - 1054848a b - 1305216a b +--R * +--R 16 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R 354a b + 11240a b + 88380a b + 166728a b - 400686a b +--R + +--R 7 4 8 3 9 2 10 +--R - 1418752a b - 350592a b + 1990656a b + 1461504a b +--R * +--R 15 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R 354a b + 11240a b + 88380a b + 166728a b - 400686a b +--R + +--R 7 4 8 3 9 2 10 +--R - 1418752a b - 350592a b + 1990656a b + 1461504a b +--R * +--R 14 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 18a b - 1258a b - 19016a b - 81208a b + 18682a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 724738a b + 1068032a b - 689280a b - 2309376a b - 1208064a b +--R * +--R 13 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 18a b - 1258a b - 19016a b - 81208a b + 18682a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 724738a b + 1068032a b - 689280a b - 2309376a b - 1208064a b +--R * +--R 12 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 48a b + 1664a b + 15120a b + 25098a b - 160196a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 584710a b - 272128a b + 1212864a b + 1804800a b +--R + +--R 10 +--R 734976a b +--R * +--R 11 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 48a b + 1664a b + 15120a b + 25098a b - 160196a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 584710a b - 272128a b + 1212864a b + 1804800a b +--R + +--R 10 +--R 734976a b +--R * +--R 10 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 44a b - 980a b - 4962a b + 13314a b + 132726a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 217770a b - 218368a b - 966080a b - 968960a b - 323840a b +--R * +--R 9 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 44a b - 980a b - 4962a b + 13314a b + 132726a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 217770a b - 218368a b - 966080a b - 968960a b - 323840a b +--R * +--R 8 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 16a b + 226a b - 176a b - 12736a b - 44816a b - 2762a b +--R + +--R 7 4 8 3 9 2 10 +--R 232448a b + 454528a b + 351744a b + 99968a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 16a b + 226a b - 176a b - 12736a b - 44816a b - 2762a b +--R + +--R 7 4 8 3 9 2 10 +--R 232448a b + 454528a b + 351744a b + 99968a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R - 2a b - 2a b + 428a b + 3180a b + 3142a b - 26874a b +--R + +--R 7 4 8 3 9 2 10 +--R - 93952a b - 128384a b - 82048a b - 20352a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R - 2a b - 2a b + 428a b + 3180a b + 3142a b - 26874a b +--R + +--R 7 4 8 3 9 2 10 +--R - 93952a b - 128384a b - 82048a b - 20352a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 +--R - 4a b - 56a b - 102a b + 1548a b + 8478a b + 18304a b +--R + +--R 8 3 9 2 10 +--R 20000a b + 11008a b + 2432a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 +--R - 4a b - 56a b - 102a b + 1548a b + 8478a b + 18304a b +--R + +--R 8 3 9 2 10 +--R 20000a b + 11008a b + 2432a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 7 4 8 3 +--R - 2a b - 38a b - 262a b - 834a b - 1408a b - 1312a b +--R + +--R 9 2 10 +--R - 640a b - 128a b +--R * +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 7 4 8 3 +--R - 2a b - 38a b - 262a b - 834a b - 1408a b - 1312a b +--R + +--R 9 2 10 +--R - 640a b - 128a b +--R * +--R +----------------------+ +--R | 2 +--R |- 4a cos(x) + 4b + 4a +--R |---------------------- +--R | 2 +--R \| cos(x) + 2cos(x) + 1 +--R + +--R 8 3 9 2 10 18 +--R (24576a b + 65536a b + 40960a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 +--R (- 102400a b - 462848a b - 667648a b - 307200a b) +--R * +--R 16 +--R cos(x) +--R + +--R 6 5 7 4 8 3 +--R 173568a b + 1157120a b + 2746368a b +--R + +--R 9 2 10 +--R 2768896a b + 1006080a b +--R * +--R 14 +--R cos(x) +--R + +--R 5 6 6 5 7 4 +--R - 153856a b - 1427456a b - 4936192a b +--R + +--R 8 3 9 2 10 +--R - 8062464a b - 6281472a b - 1881600a b +--R * +--R 12 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R 76352a b + 968704a b + 4627072a b + 10921984a b +--R + +--R 8 3 9 2 10 +--R 13655872a b + 8672768a b + 2204160a b +--R * +--R 10 +--R cos(x) +--R + +--R 3 8 4 7 5 6 +--R - 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80b - 4376a b - 76096a b - 604752a b - 2644400a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 6993880a b - 11693056a b - 12458496a b - 8212992a b +--R + +--R 9 2 10 +--R - 3056640a b - 491520a b +--R * +--R 2 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 40b + 1512a b + 18480a b + 110800a b + 385288a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 841160a b + 1192992a b + 1100800a b + 638720a b +--R + +--R 9 2 10 +--R 211968a b + 30720a b +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 10 22 +--R (114688a b - 1032192a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 20 +--R (- 516096a b - 860160a b + 5677056a b + 9805824a b)cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R 957440a b + 3383296a b - 10579968a b - 48513024a b +--R + +--R 10 +--R - 41868288a b +--R * +--R 18 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R - 942592a b - 5394432a b + 8193024a b + 96531456a b +--R + +--R 9 2 10 +--R 184149504a b + 105864192a b +--R * +--R 16 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R 528256a b + 4473600a b - 1588480a b - 103022080a b +--R + +--R 8 3 9 2 10 +--R - 332495744a b - 407973888a b - 175730688a b +--R * +--R 14 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R - 168192a b - 2064000a b - 1360320a b + 65917056a b +--R + +--R 7 4 8 3 9 2 10 +--R 323539776a b + 640954496a b + 582543360a b + 200503296a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 +--R 28704a b + 528640a b + 873792a b - 26496640a b +--R + +--R 6 5 7 4 8 3 +--R - 185868512a b - 532823424a b - 772227456a b +--R + +--R 9 2 10 +--R - 558157824a b - 159860736a b +--R * +--R 10 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 +--R - 2264a b - 71472a b - 201424a b + 6655600a b +--R + +--R 5 6 6 5 7 4 +--R 64324232a b + 253156320a b + 525366464a b +--R + +--R 8 3 9 2 10 +--R 602831488a b + 361718784a b + 88639488a b +--R * +--R 8 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 56b + 4512a b + 22224a b - 974848a b - 12991304a b +--R + +--R 5 6 6 5 7 4 +--R - 68914976a b - 195021248a b - 319329024a b +--R + +--R 8 3 9 2 10 +--R - 303538816a b - 155602944a b - 33288192a b +--R * +--R 6 +--R cos(x) +--R + +--R 11 10 2 9 3 8 +--R - 88b - 1104a b + 72576a b + 1405120a b +--R + +--R 4 7 5 6 6 5 7 4 +--R 10169016a b + 38617712a b + 85989440a b + 116410560a b +--R + +--R 8 3 9 2 10 +--R 94392704a b + 42190848a b + 7999488a b +--R * +--R 4 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 8b - 2272a b - 69456a b - 714048a b - 3669272a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 10916768a b - 20042336a b - 23099776a b - 16306304a b +--R + +--R 9 2 10 +--R - 6451200a b - 1096704a b +--R * +--R 2 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 24b + 1128a b + 17424a b + 124752a b + 497912a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 1215752a b + 1894752a b + 1897280a b + 1183616a b +--R + +--R 9 2 10 +--R 419328a b + 64512a b +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 9 2 10 24 +--R (32768a b - 393216a b + 491520a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 +--R (- 131072a b + 1687552a b + 1130496a b - 5160960a b) +--R * +--R 22 +--R cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R 206848a b - 3166208a b - 9854976a b + 8896512a b +--R + +--R 10 +--R 24606720a b +--R * +--R 20 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R - 160768a b + 3452928a b + 20893696a b + 10881024a b +--R + +--R 9 2 10 +--R - 66247680a b - 70348800a b +--R * +--R 18 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R 61440a b - 2413824a b - 22577664a b - 42300928a b +--R + +--R 8 3 9 2 10 +--R 54902528a b + 203996160a b + 134092800a b +--R * +--R 16 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R - 9024a b + 1090816a b + 14255808a b + 48027520a b +--R + +--R 7 4 8 3 9 2 10 +--R 3848448a b - 231184384a b - 376270848a b - 179159040a b +--R * +--R 14 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 +--R - 352a b - 298688a b - 5369216a b - 27897664a b +--R + +--R 6 5 7 4 8 3 +--R - 32814368a b + 127875328a b + 426632192a b +--R + +--R 9 2 10 +--R 459583488a b + 171601920a b +--R * +--R 12 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 +--R 168a b + 43136a b + 1151344a b + 8950464a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 21026920a b - 34537152a b - 253383424a b - 472619008a b +--R + +--R 9 2 10 +--R - 385173504a b - 118333440a b +--R * +--R 10 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 8b - 2584a b - 125120a b - 1535536a b - 5952808a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 3601528a b + 85867552a b + 250708224a b + 337312256a b +--R + +--R 9 2 10 +--R 222382080a b + 58060800a b +--R * +--R 8 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 48b + 5544a b + 125856a b + 796792a b + 71712a b +--R + +--R 5 6 6 5 7 4 +--R - 16996656a b - 73293056a b - 145847552a b +--R + +--R 8 3 9 2 10 +--R - 155854848a b - 86568960a b - 19660800a b +--R * +--R 6 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 72b - 3928a b - 44856a b - 20776a b + 1907856a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 11579312a b + 32244000a b + 50121472a b + 44778496a b +--R + +--R 9 2 10 +--R 21540864a b + 4331520a b +--R * +--R 4 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 32b + 720a b - 944a b - 108104a b - 883872a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 3356536a b - 7223232a b - 9339136a b - 7204864a b +--R + +--R 9 2 10 +--R - 3062784a b - 552960a b +--R * +--R 2 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 80a b + 2280a b + 23992a b + 123608a b + 361880a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 646624a b + 721152a b + 491264a b + 187392a b + 30720a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 9 2 10 26 +--R (- 24576a b + 65536a b - 40960a b)cos(x) +--R + +--R 7 4 8 3 9 2 10 24 +--R (118784a b - 94208a b - 479232a b + 471040a b)cos(x) +--R + +--R 6 5 7 4 8 3 9 2 +--R - 239104a b - 325632a b + 1677312a b + 1081344a b +--R + +--R 10 +--R - 2480640a b +--R * +--R 22 +--R cos(x) +--R + +--R 5 6 6 5 7 4 8 3 +--R 258304a b + 1026048a b - 1525248a b - 6572544a b +--R + +--R 9 2 10 +--R 1140992a b + 7912960a b +--R * +--R 20 +--R cos(x) +--R + +--R 4 7 5 6 6 5 7 4 +--R - 160576a b - 1185536a b - 397440a b + 9412096a b +--R + +--R 8 3 9 2 10 +--R 11348160a b - 12311040a b - 17036800a b +--R * +--R 18 +--R cos(x) +--R + +--R 3 8 4 7 5 6 6 5 +--R 57056a b + 705472a b + 1524224a b - 5703808a b +--R + +--R 7 4 8 3 9 2 10 +--R - 20464480a b - 4863168a b + 33907968a b + 26104320a b +--R * +--R 16 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 +--R - 10784a b - 225792a b - 1028928a b + 1240320a b +--R + +--R 6 5 7 4 8 3 9 2 +--R 15042912a b + 21291776a b - 17650944a b - 54736896a b +--R + +--R 10 +--R - 29230080a b +--R * +--R 14 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 +--R 920a b + 36624a b + 310992a b + 182704a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 5590472a b - 17212832a b - 5665408a b + 41016576a b +--R + +--R 9 2 10 +--R 59023872a b + 24161280a b +--R * +--R 12 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 24b - 2560a b - 43360a b - 124032a b + 1065000a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 6424496a b + 8768480a b - 12320512a b - 45355392a b +--R + +--R 9 2 10 +--R - 44227584a b - 14699520a b +--R * +--R 10 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 56b + 2400a b + 17584a b - 94392a b - 1203544a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 3238584a b + 626400a b + 16923584a b + 30791040a b +--R + +--R 9 2 10 +--R 23114240a b + 6476800a b +--R * +--R 8 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R - 40b - 768a b + 2904a b + 105632a b + 504528a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 339616a b - 3311072a b - 10371840a b - 13363456a b +--R + +--R 9 2 10 +--R - 8239104a b - 1999360a b +--R * +--R 6 +--R cos(x) +--R + +--R 11 10 2 9 3 8 4 7 +--R 8b - 24a b - 3512a b - 31040a b - 47872a b +--R + +--R 5 6 6 5 7 4 8 3 +--R 355400a b + 1774368a b + 3509120a b + 3601152a b +--R + +--R 9 2 10 +--R 1897728a b + 407040a b +--R * +--R 4 +--R cos(x) +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 32a b + 520a b + 1056a b - 20984a b - 144208a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 409824a b - 628480a b - 545088a b - 252416a b +--R + +--R 10 +--R - 48640a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 +--R 24a b + 520a b + 4200a b + 16440a b + 35872a b + 46240a b +--R + +--R 8 3 9 2 10 +--R 35136a b + 14592a b + 2560a b +--R * +--R sin(x) +--R * +--R +-+ +--R \|a +--R * +--R +-------------+ +--R | 2 +--R \|b csc(x) + a +--R Type: Expression(Integer) +--E 518 + +--S 519 of 528 +t0398:= x/csc(x)^(3/2)-1/3*x*csc(x)^(1/2) +--R +--R +--R 2 +--R - x csc(x) + 3x +--R (479) ---------------- +--R +------+ +--R 3csc(x)\|csc(x) +--R Type: Expression(Integer) +--E 519 + +--S 520 of 528 +r0398:= -2/9*(-2*sin(x)+3*x*cos(x))/(1/sin(x))^(1/2) +--R +--R +--R 4sin(x) - 6x cos(x) +--R (480) ------------------- +--R +------+ +--R | 1 +--R 9 |------ +--R \|sin(x) +--R Type: Expression(Integer) +--E 520 + +--S 521 of 528 +a0398:= integrate(t0398,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 521 + +--S 522 of 528 +m0398:= a0398-r0398 +--R +--R +--R +------+ +--R | 1 +--R 9a0398 |------ - 4sin(x) + 6x cos(x) +--R \|sin(x) +--R (481) ------------------------------------- +--R +------+ +--R | 1 +--R 9 |------ +--R \|sin(x) +--R Type: Expression(Integer) +--E 522 + +--S 523 of 528 +d0398:= D(m0398,x) +--R +--R +--R 2 2 +--R - 2x sin(x) + x cos(x) +--R (482) ------------------------ +--R +------+ +--R | 1 +--R 3sin(x) |------ +--R \|sin(x) +--R Type: Expression(Integer) +--E 523 + +--S 524 of 528 +t0399:= x/csc(x)^(5/2)-3/5*x/csc(x)^(1/2) +--R +--R +--R 2 +--R - 3x csc(x) + 5x +--R (483) ----------------- +--R 2 +------+ +--R 5csc(x) \|csc(x) +--R Type: Expression(Integer) +--E 524 + +--S 525 of 528 +r0399:= 4/25/csc(x)^(5/2)-2/5*x*cos(x)/csc(x)^(3/2) +--R +--R +--R - 10x cos(x)csc(x) + 4 +--R (484) ---------------------- +--R 2 +------+ +--R 25csc(x) \|csc(x) +--R Type: Expression(Integer) +--E 525 + +--S 526 of 528 +a0399:= integrate(t0399,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 526 + +--S 527 of 528 +m0399:= a0399-r0399 +--R +--R +--R 2 +------+ +--R 25a0399 csc(x) \|csc(x) + 10x cos(x)csc(x) - 4 +--R (485) ----------------------------------------------- +--R 2 +------+ +--R 25csc(x) \|csc(x) +--R Type: Expression(Integer) +--E 527 + +--S 528 of 528 +d0399:= D(m0399,x) +--R +--R +--R - 2x csc(x)sin(x) + (3x cos(x)cot(x) + 2cos(x))csc(x) - 2cot(x) +--R (486) --------------------------------------------------------------- +--R 2 +------+ +--R 5csc(x) \|csc(x) +--R Type: Expression(Integer) +--E 528 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richtrig300-399.input.pdf b/src/axiom-website/CATS/richtrig300-399.input.pdf new file mode 100644 index 0000000..8fdc200 Binary files /dev/null and b/src/axiom-website/CATS/richtrig300-399.input.pdf differ diff --git a/src/axiom-website/CATS/richtrig400-499.input.pamphlet b/src/axiom-website/CATS/richtrig400-499.input.pamphlet new file mode 100644 index 0000000..3efaddf --- /dev/null +++ b/src/axiom-website/CATS/richtrig400-499.input.pamphlet @@ -0,0 +1,33043 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richtrig400-499.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig400-499.output +)spool richtrig400-499.output +)set message auto off +)clear all + +--S 1 of 546 +t0400:= x/csc(x)^(7/2)-5/21*x*csc(x)^(1/2) +--R +--R +--R 4 +--R - 5x csc(x) + 21x +--R (1) ------------------ +--R 3 +------+ +--R 21csc(x) \|csc(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 546 +r0400:= 2/441*(88*sin(x)-18*sin(x)*cos(x)^2-168*x*cos(x)+_ + 63*x*cos(x)^3)/(1/sin(x))^(1/2) +--R +--R +--R 2 3 +--R (- 36cos(x) + 176)sin(x) + 126x cos(x) - 336x cos(x) +--R (2) ------------------------------------------------------ +--R +------+ +--R | 1 +--R 441 |------ +--R \|sin(x) +--R Type: Expression(Integer) +--E 2 + +--S 3 of 546 +a0400:= integrate(t0400,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 3 + +--S 4 of 546 +m0400:= a0400-r0400 +--R +--R +--R (3) +--R +------+ +--R | 1 2 3 +--R 441a0400 |------ + (36cos(x) - 176)sin(x) - 126x cos(x) + 336x cos(x) +--R \|sin(x) +--R ------------------------------------------------------------------------ +--R +------+ +--R | 1 +--R 441 |------ +--R \|sin(x) +--R Type: Expression(Integer) +--E 4 + +--S 5 of 546 +d0400:= D(m0400,x) +--R +--R +--R (4) +--R 3 2 2 +--R - 24cos(x)sin(x) + (126x cos(x) - 112x)sin(x) +--R + +--R 3 4 2 +--R (- 24cos(x) + 24cos(x))sin(x) - 21x cos(x) + 56x cos(x) +--R / +--R +------+ +--R | 1 +--R 147sin(x) |------ +--R \|sin(x) +--R Type: Expression(Integer) +--E 5 + +--S 6 of 546 +t0401:= x^2/csc(x)^(3/2)-1/3*x^2*csc(x)^(1/2) +--R +--R +--R 2 2 2 +--R - x csc(x) + 3x +--R (5) ----------------- +--R +------+ +--R 3csc(x)\|csc(x) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 546 +r0401:= -2/27*(-12*x*sin(x)^(3/2)-8*cos(x)*sin(x)^(1/2)+_ + 9*x^2*cos(x)*sin(x)^(1/2)+8*_ + EllipticF(-1/4*%pi+1/2*x,2))/sin(x)^(1/2)/(1/sin(x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 7 + +--S 8 of 546 +a0401:= integrate(t0401,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 8 + +--S 9 of 546 +m0401:= a0401-r0401 +--R +--R +--R (6) - r0401 + a0401 +--R Type: Polynomial(Integer) +--E 9 + +--S 10 of 546 +d0401:= D(m0401,x) +--R +--R +--R (7) 0 +--R Type: Polynomial(Integer) +--E 10 + +--S 11 of 546 +t0402:= csc(x^(1/2))^3/x^(1/2) +--R +--R +--R +-+ 3 +--R csc(\|x ) +--R (8) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 546 +r0402:= -atanh(cos(x^(1/2)))-cot(x^(1/2))*csc(x^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R (9) - atanh(cos(\|x )) - cot(\|x )csc(\|x ) +--R Type: Expression(Integer) +--E 12 + +--S 13 of 546 +a0402:= integrate(t0402,x) +--R +--R +--R (10) +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- cos(\|x ) + 1)log(cos(\|x ) + 1) + (cos(\|x ) - 1)log(cos(\|x ) - 1) +--R + +--R +-+ +--R 2cos(\|x ) +--R / +--R +-+ 2 +--R 2cos(\|x ) - 2 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 546 +m0402:= a0402-r0402 +--R +--R +--R (11) +--R +-+ 2 +-+ +-+ 2 +-+ +--R (- cos(\|x ) + 1)log(cos(\|x ) + 1) + (cos(\|x ) - 1)log(cos(\|x ) - 1) +--R + +--R +-+ 2 +-+ +-+ 2 +-+ +-+ +--R (2cos(\|x ) - 2)atanh(cos(\|x )) + (2cos(\|x ) - 2)cot(\|x )csc(\|x ) +--R + +--R +-+ +--R 2cos(\|x ) +--R / +--R +-+ 2 +--R 2cos(\|x ) - 2 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 546 +d0402:= D(m0402,x) +--R +--R +--R (12) +--R +-+ 2 +-+ +--R (cos(\|x ) + 1)sin(\|x ) +--R + +--R +-+ 4 +-+ 2 +-+ 2 +-+ 4 +--R (- 2cos(\|x ) + 4cos(\|x ) - 2)cot(\|x ) - cos(\|x ) +--R + +--R +-+ 2 +--R 2cos(\|x ) - 1 +--R * +--R +-+ +--R csc(\|x ) +--R / +--R +-+ +-+ 4 +-+ +-+ 2 +-+ +--R 2\|x cos(\|x ) - 4\|x cos(\|x ) + 2\|x +--R Type: Expression(Integer) +--E 15 + +--S 16 of 546 +t0403:= sin(x)^2/(a+b*sin(x)) +--R +--R +--R 2 +--R sin(x) +--R (13) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 546 +r0403:= -a*x/b^2+2*a^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2/_ + (a^2-b^2)^(1/2)-cos(x)/b +--R +--R +--R x +--R a tan(-) + b +---------+ +--R 2 2 | 2 2 +--R 2a atan(------------) + (- b cos(x) - a x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (14) ------------------------------------------------------ +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 17 + +--S 18 of 546 +a0403:= integrate(t0403,x) +--R +--R +--R (15) +--R [ +--R 2 +--R a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R | 2 2 +--R (- b cos(x) - a x)\|b - a +--R / +--R +-------+ +--R 2 | 2 2 +--R b \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 (a sin(x) + b cos(x) + b)\|- b + a +--R - 2a atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R | 2 2 +--R (- b cos(x) - a x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 18 + +--S 19 of 546 +m0403a:= a0403.1-r0403 +--R +--R +--R (16) +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R 2 | 2 2 2 +--R - 2a \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R b \|- b + a \|b - a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 546 +d0403a:= D(m0403a,x) +--R +--R +--R (17) +--R 2 2 4 2 2 3 2 3 x 2 +--R (((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b)tan(-) +--R 2 +--R + +--R 2 2 2 3 2 2 2 2 2 4 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (2a b - 2a )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 2 3 2 3 +--R ((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 4 2 3 4 3 2 5 2 3 2 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b +--R + +--R 5 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 3 2 5 +--R (- 2a b + 2a b)sin(x) + (- 2a b + 2a )sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 3 4 3 2 5 2 3 2 5 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b - a +--R / +--R 2 3 2 4 3 2 4 3 2 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (a b - a b)cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 5 2 3 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 4 3 2 4 +--R (2a b - 2a b )cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 3 2 4 3 2 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (a b - a b)cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 +--R (- 2a b + 2a b )sin(x) +--R + +--R 6 2 4 6 4 2 5 3 3 +--R ((- 2b + 2a b )cos(x) - 2b + 2a b )sin(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 +--R - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- a b + a b )cos(x) - a b + a b +--R Type: Expression(Integer) +--E 20 + +--S 21 of 546 +m0403b:= a0403.2-r0403 +--R +--R +--R (18) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R 2 (a sin(x) + b cos(x) + b)\|- b + a 2 2 +--R - 2a atan(-------------------------------------) - 2a atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R ------------------------------------------------------------------------ +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 21 + +--S 22 of 546 +d0403b:= D(m0403b,x) +--R +--R +--R (19) +--R 3 2 2 2 3 2 3 x 2 +--R (a sin(x) + (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a )tan(-) +--R 2 +--R + +--R 2 2 2 2 2 x 3 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + a sin(x) +--R 2 +--R + +--R 2 2 3 2 3 +--R (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R Type: Expression(Integer) +--E 22 + +--S 23 of 546 +t0404:= sin(x)^3/(a+b*sin(x)) +--R +--R +--R 3 +--R sin(x) +--R (20) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 23 + +--S 24 of 546 +r0404:= a^2*x/b^3+1/2*x/b-2*a^3*atan((b+a*tan(1/2*x))/_ + (a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(1/2)+a*cos(x)/b^2-1/2*cos(x)*sin(x)/b +--R +--R +--R (21) +--R x +--R a tan(-) + b +--R 3 2 +--R - 4a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- b cos(x)sin(x) + 2a b cos(x) + (b + 2a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression(Integer) +--E 24 + +--S 25 of 546 +a0404:= integrate(t0404,x) +--R +--R +--R (22) +--R [ +--R 3 +--R 2a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (- b cos(x)sin(x) + 2a b cos(x) + (b + 2a )x)\|b - a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2b \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 3 (a sin(x) + b cos(x) + b)\|- b + a +--R 4a atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- b cos(x)sin(x) + 2a b cos(x) + (b + 2a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 25 + +--S 26 of 546 +m0404a:= a0404.1-r0404 +--R +--R +--R (23) +--R +---------+ +--R 3 | 2 2 +--R a \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R 3 | 2 2 2 +--R 2a \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 3 | 2 2 | 2 2 +--R b \|- b + a \|b - a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 546 +d0404a:= D(m0404a,x) +--R +--R +--R (24) +--R 3 2 5 3 2 4 2 4 x 2 +--R (((a b - a )cos(x) + a b )sin(x) - a b cos(x) + a b)tan(-) +--R 2 +--R + +--R 3 2 2 4 3 2 2 +--R - 2a b sin(x) - 2a b sin(x) - 2a b cos(x) +--R + +--R 3 2 5 +--R (- 2a b + 2a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 5 3 2 4 2 4 +--R ((a b - a )cos(x) + a b )sin(x) - a b cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 3 5 3 3 5 4 2 6 2 4 2 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b +--R + +--R 6 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 2 4 2 6 +--R (- 2a b + 2a b)sin(x) + (- 2a b + 2a )sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 5 3 3 5 4 2 6 2 4 2 6 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b - a +--R / +--R 2 4 2 5 3 3 5 3 3 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 4 4 2 2 4 +--R (a b - a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 2 4 6 2 4 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 5 3 3 5 +--R (2a b - 2a b )cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 5 3 3 5 3 3 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 4 4 2 2 4 +--R (a b - a b )cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 4 3 2 6 3 4 6 5 2 +--R (a b - a b )sin(x) + ((a b - a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (a b - a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 2 7 2 5 7 4 3 +--R (2a b - 2a b )sin(x) + ((2b - 2a b )cos(x) + 2b - 2a b )sin(x) +--R + +--R 6 3 4 6 3 4 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 6 3 4 6 5 2 +--R (a b - a b )sin(x) + ((a b - a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (a b - a b )cos(x) + a b - a b +--R Type: Expression(Integer) +--E 27 + +--S 28 of 546 +m0404b:= a0404.2-r0404 +--R +--R +--R (25) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R 3 (a sin(x) + b cos(x) + b)\|- b + a 3 2 +--R 2a atan(-------------------------------------) + 2a atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R ---------------------------------------------------------------------- +--R +---------+ +--R 3 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 28 + +--S 29 of 546 +d0404b:= D(m0404b,x) +--R +--R +--R (26) +--R 4 2 3 3 4 2 4 x 2 +--R (- a sin(x) + (2a b cos(x) + 2a b)sin(x) - a cos(x) + a )tan(-) +--R 2 +--R + +--R 3 2 3 2 3 x 4 2 +--R (- 4a b sin(x) - 4a b cos(x) - 4a b cos(x))tan(-) - a sin(x) +--R 2 +--R + +--R 3 3 4 2 4 +--R (2a b cos(x) + 2a b)sin(x) - a cos(x) + a +--R / +--R 2 3 2 4 4 2 3 2 2 3 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 3 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 5 4 2 4 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 4 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 4 2 3 2 2 3 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 3 +--R a b +--R Type: Expression(Integer) +--E 29 + +--S 30 of 546 +t0405:= sin(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R sin(x) +--R (27) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 30 + +--S 31 of 546 +r0405:= -a^3*x/b^4-1/2*a*x/b^2+2*a^4*atan((b+a*tan(1/2*x))/_ + (a^2-b^2)^(1/2))/b^4/(a^2-b^2)^(1/2)-a^2*cos(x)/b^3-cos(x)/b+_ + 1/3*cos(x)^3/b+1/2*a*cos(x)*sin(x)/b^2 +--R +--R +--R (28) +--R x +--R a tan(-) + b +--R 4 2 +--R 12a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 3 2 +--R 3a b cos(x)sin(x) + 2b cos(x) + (- 6b - 6a b)cos(x) +--R + +--R 2 3 +--R (- 3a b - 6a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6b \|- b + a +--R Type: Expression(Integer) +--E 31 + +--S 32 of 546 +a0405:= integrate(t0405,x) +--R +--R +--R (29) +--R [ +--R 4 +--R 6a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 2 3 3 3 2 +--R 3a b cos(x)sin(x) + 2b cos(x) + (- 6b - 6a b)cos(x) +--R + +--R 2 3 +--R (- 3a b - 6a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6b \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 4 (a sin(x) + b cos(x) + b)\|- b + a +--R - 12a atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 3 3 2 +--R 3a b cos(x)sin(x) + 2b cos(x) + (- 6b - 6a b)cos(x) +--R + +--R 2 3 +--R (- 3a b - 6a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6b \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 32 + +--S 33 of 546 +m0405a:= a0405.1-r0405 +--R +--R +--R (30) +--R +---------+ +--R 4 | 2 2 +--R a \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R 4 | 2 2 2 +--R - 2a \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 4 | 2 2 | 2 2 +--R b \|- b + a \|b - a +--R Type: Expression(Integer) +--E 33 + +--S 34 of 546 +d0405a:= D(m0405a,x) +--R +--R +--R (31) +--R 4 2 6 4 2 5 2 5 x 2 +--R (((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b)tan(-) +--R 2 +--R + +--R 4 2 2 5 4 2 2 4 2 6 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (2a b - 2a )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 4 2 5 2 5 +--R ((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 3 6 4 3 6 5 2 7 2 5 2 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b +--R + +--R 7 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 6 2 5 2 7 +--R (- 2a b + 2a b)sin(x) + (- 2a b + 2a )sin(x) +--R + +--R 4 3 6 2 4 3 6 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 6 4 3 6 5 2 7 2 5 2 7 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b - a +--R / +--R 2 5 2 6 3 4 6 3 4 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 5 4 3 2 5 +--R (a b - a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 7 2 5 7 2 5 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 6 3 4 6 +--R (2a b - 2a b )cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 2 6 3 4 6 3 4 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 5 4 3 2 5 +--R (a b - a b )cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 6 4 4 2 7 3 5 7 5 3 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 6 4 4 2 6 4 4 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 2 +--R (- 2a b + 2a b )sin(x) +--R + +--R 8 2 6 8 4 4 7 3 5 +--R ((- 2b + 2a b )cos(x) - 2b + 2a b )sin(x) + (- 2a b + 2a b )cos(x) +--R + +--R 7 3 5 +--R - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 2 7 3 5 7 5 3 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 6 4 4 2 6 4 4 +--R (- a b + a b )cos(x) - a b + a b +--R Type: Expression(Integer) +--E 34 + +--S 35 of 546 +m0405b:= a0405.2-r0405 +--R +--R +--R (32) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R 4 (a sin(x) + b cos(x) + b)\|- b + a 4 2 +--R - 2a atan(-------------------------------------) - 2a atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R ------------------------------------------------------------------------ +--R +---------+ +--R 4 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 35 + +--S 36 of 546 +d0405b:= D(m0405b,x) +--R +--R +--R (33) +--R 5 2 4 4 5 2 5 x 2 +--R (a sin(x) + (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a )tan(-) +--R 2 +--R + +--R 4 2 4 2 4 x 5 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + a sin(x) +--R 2 +--R + +--R 4 4 5 2 5 +--R (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a +--R / +--R 2 4 2 5 5 2 4 2 2 4 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 4 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 5 2 5 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 5 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 5 5 2 4 2 2 4 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 4 +--R a b +--R Type: Expression(Integer) +--E 36 + +--S 37 of 546 +t0406:= sin(x)/(a+a*sin(x)) +--R +--R +--R sin(x) +--R (34) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 546 +r0406:= x/a+cos(x)/a/(1+sin(x)) +--R +--R +--R x sin(x) + cos(x) + x +--R (35) --------------------- +--R a sin(x) + a +--R Type: Expression(Integer) +--E 38 + +--S 39 of 546 +a0406:= integrate(t0406,x) +--R +--R +--R x sin(x) + (x + 2)cos(x) + x + 2 +--R (36) -------------------------------- +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 39 + +--S 40 of 546 +m0406:= a0406-r0406 +--R +--R +--R 2 +--R (cos(x) + 2)sin(x) - cos(x) + cos(x) + 2 +--R (37) ------------------------------------------------ +--R 2 +--R a sin(x) + (a cos(x) + 2a)sin(x) + a cos(x) + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 546 +d0406:= D(m0406,x) +--R +--R +--R (38) +--R 4 3 2 +--R - sin(x) + (2cos(x) - 1)sin(x) + (2cos(x) + 1)sin(x) +--R + +--R 3 2 4 3 2 +--R (2cos(x) - cos(x) - 2cos(x) + 1)sin(x) + cos(x) + 2cos(x) - cos(x) +--R + +--R - 2cos(x) +--R / +--R 4 3 2 2 +--R a sin(x) + (2a cos(x) + 4a)sin(x) + (a cos(x) + 6a cos(x) + 6a)sin(x) +--R + +--R 2 2 +--R (2a cos(x) + 6a cos(x) + 4a)sin(x) + a cos(x) + 2a cos(x) + a +--R Type: Expression(Integer) +--E 41 + +--S 42 of 546 +t0407:= sin(x)^2/(a+a*sin(x)) +--R +--R +--R 2 +--R sin(x) +--R (39) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 42 + +--S 43 of 546 +r0407:= -(cos(x)^2+x*cos(x)-sin(x)+1)/a/cos(x) +--R +--R +--R 2 +--R sin(x) - cos(x) - x cos(x) - 1 +--R (40) ------------------------------- +--R a cos(x) +--R Type: Expression(Integer) +--E 43 + +--S 44 of 546 +a0407:= integrate(t0407,x) +--R +--R +--R 2 +--R (- cos(x) - x - 1)sin(x) - cos(x) + (- x - 4)cos(x) - x - 3 +--R (41) ------------------------------------------------------------ +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 44 + +--S 45 of 546 +m0407:= a0407-r0407 +--R +--R +--R 2 2 +--R - sin(x) - 2cos(x)sin(x) - 3cos(x) - 2cos(x) + 1 +--R (42) -------------------------------------------------- +--R 2 +--R a cos(x)sin(x) + a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 45 + +--S 46 of 546 +d0407:= D(m0407,x) +--R +--R +--R (43) +--R 4 3 2 +--R - sin(x) + (- 2cos(x) - 1)sin(x) + sin(x) +--R + +--R 3 2 4 2 +--R (- 2cos(x) - cos(x) + 2cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 2 3 2 4 +--R a cos(x) sin(x) + (2a cos(x) + 2a cos(x) )sin(x) + a cos(x) +--R + +--R 3 2 +--R 2a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 546 +t0408:= sin(x)^3/(a+a*sin(x)) +--R +--R +--R 3 +--R sin(x) +--R (44) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 47 + +--S 48 of 546 +r0408:= -1/2*(cos(x)^2*sin(x)-2*cos(x)^2-3*x*cos(x)-2+2*sin(x))/a/cos(x) +--R +--R +--R 2 2 +--R (- cos(x) - 2)sin(x) + 2cos(x) + 3x cos(x) + 2 +--R (45) ------------------------------------------------ +--R 2a cos(x) +--R Type: Expression(Integer) +--E 48 + +--S 49 of 546 +a0408:= integrate(t0408,x) +--R +--R +--R (46) +--R 2 3 2 +--R (- cos(x) + cos(x) + 3x + 2)sin(x) + cos(x) + 2cos(x) + (3x + 7)cos(x) +--R + +--R 3x + 6 +--R / +--R 2a sin(x) + 2a cos(x) + 2a +--R Type: Union(Expression(Integer),...) +--E 49 + +--S 50 of 546 +m0408:= a0408-r0408 +--R +--R +--R (47) +--R 2 2 4 2 +--R (cos(x) + 2)sin(x) + 4cos(x)sin(x) + cos(x) + 5cos(x) + 4cos(x) - 2 +--R ----------------------------------------------------------------------- +--R 2 +--R 2a cos(x)sin(x) + 2a cos(x) + 2a cos(x) +--R Type: Expression(Integer) +--E 50 + +--S 51 of 546 +d0408:= D(m0408,x) +--R +--R +--R (48) +--R 2 4 2 3 +--R (- cos(x) + 2)sin(x) + (- cos(x) + 4cos(x) + 2)sin(x) +--R + +--R 4 2 2 +--R (- 2cos(x) + cos(x) - 2)sin(x) +--R + +--R 4 3 2 6 4 +--R (- cos(x) + 4cos(x) + 3cos(x) - 4cos(x) - 2)sin(x) - cos(x) - cos(x) +--R + +--R 2 +--R 2cos(x) +--R / +--R 2 2 3 2 4 +--R 2a cos(x) sin(x) + (4a cos(x) + 4a cos(x) )sin(x) + 2a cos(x) +--R + +--R 3 2 +--R 4a cos(x) + 2a cos(x) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 546 +t0409:= sin(x)^4/(a+a*sin(x)) +--R +--R +--R 4 +--R sin(x) +--R (49) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 52 + +--S 53 of 546 +r0409:= 1/6*(2*cos(x)^4+3*cos(x)^2*sin(x)-12*cos(x)^2-9*x*cos(x)-_ + 6+6*sin(x))/a/cos(x) +--R +--R +--R 2 4 2 +--R (3cos(x) + 6)sin(x) + 2cos(x) - 12cos(x) - 9x cos(x) - 6 +--R (50) ----------------------------------------------------------- +--R 6a cos(x) +--R Type: Expression(Integer) +--E 53 + +--S 54 of 546 +a0409:= integrate(t0409,x) +--R +--R +--R (51) +--R 3 2 4 3 +--R (2cos(x) + 3cos(x) - 9cos(x) - 9x - 10)sin(x) + 2cos(x) - cos(x) +--R + +--R 2 +--R - 12cos(x) + (- 9x - 31)cos(x) - 9x - 22 +--R / +--R 6a sin(x) + 6a cos(x) + 6a +--R Type: Union(Expression(Integer),...) +--E 54 + +--S 55 of 546 +m0409:= a0409-r0409 +--R +--R +--R (52) +--R 2 2 4 2 +--R (- 3cos(x) - 6)sin(x) - 16cos(x)sin(x) - 3cos(x) - 19cos(x) +--R + +--R - 16cos(x) + 6 +--R / +--R 2 +--R 6a cos(x)sin(x) + 6a cos(x) + 6a cos(x) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 546 +d0409:= D(m0409,x) +--R +--R +--R (53) +--R 2 4 2 3 +--R (cos(x) - 2)sin(x) + (cos(x) - 4cos(x) - 2)sin(x) +--R + +--R 4 2 2 +--R (2cos(x) - cos(x) + 2)sin(x) +--R + +--R 4 3 2 6 4 +--R (cos(x) - 4cos(x) - 3cos(x) + 4cos(x) + 2)sin(x) + cos(x) + cos(x) +--R + +--R 2 +--R - 2cos(x) +--R / +--R 2 2 3 2 4 +--R 2a cos(x) sin(x) + (4a cos(x) + 4a cos(x) )sin(x) + 2a cos(x) +--R + +--R 3 2 +--R 4a cos(x) + 2a cos(x) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 546 +t0410:= cos(x)^2/(a+b*sin(x)) +--R +--R +--R 2 +--R cos(x) +--R (54) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 57 + +--S 58 of 546 +r0410:= a*x/b^2-2*(a^2-b^2)^(1/2)*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2+_ + cos(x)/b +--R +--R +--R x +--R +---------+ a tan(-) + b +--R | 2 2 2 +--R - 2\|- b + a atan(------------) + b cos(x) + a x +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (55) -------------------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 58 + +--S 59 of 546 +a0410:= integrate(t0410,x) +--R +--R +--R (56) +--R [ +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R b cos(x) + a x +--R / +--R 2 +--R b +--R , +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R 2\|- b + a atan(------------------------) + b cos(x) + a x +--R a sin(x) + b cos(x) + b +--R ------------------------------------------------------------] +--R 2 +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 59 + +--S 60 of 546 +m0410a:= a0410.1-r0410 +--R +--R +--R (57) +--R +-------+ +--R | 2 2 +--R \|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R x +--R +---------+ a tan(-) + b +--R | 2 2 2 +--R 2\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 +--R b +--R Type: Expression(Integer) +--E 60 + +--S 61 of 546 +d0410a:= D(m0410a,x) +--R +--R +--R (58) +--R 3 2 3 2 2 3 2 2 +--R ((- b + a b)cos(x) - b + a b)sin(x) + (a b - a )cos(x) - a b +--R + +--R 3 +--R a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 3 3 2 2 +--R (2b - 2a b)sin(x) + (2a b - 2a )sin(x) + (2b - 2a b)cos(x) +--R + +--R 3 2 +--R (2b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 2 2 3 2 2 3 +--R ((- b + a b)cos(x) - b + a b)sin(x) + (a b - a )cos(x) - a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 2 4 4 2 2 3 3 2 +--R ((b - 2a b + a )cos(x) + b - a b )sin(x) + (- a b + a b)cos(x) +--R + +--R 3 3 +--R a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 3 3 +--R (- 2b + 2a b )sin(x) + (- 2a b + 2a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 4 +--R (- 2b + 2a b )cos(x) + (- 2b + 4a b - 2a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 4 2 2 3 3 2 +--R ((b - 2a b + a )cos(x) + b - a b )sin(x) + (- a b + a b)cos(x) +--R + +--R 3 3 +--R a b - a b +--R / +--R 2 2 2 3 3 3 2 2 2 2 +--R (a b sin(x) + (a b cos(x) + a b + a b)sin(x) + a b cos(x) + a b ) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 2 2 3 +--R 2a b sin(x) + (2b cos(x) + 2b + 2a b )sin(x) + 2a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 3 2 2 2 2 +--R a b sin(x) + (a b cos(x) + a b + a b)sin(x) + a b cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 4 3 2 4 3 2 +--R - a b sin(x) + ((- a b + a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (- a b + a b)cos(x) - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 5 2 3 +--R - 2a b sin(x) + ((- 2b + 2a b )cos(x) - 2b - 2a b )sin(x) +--R + +--R 4 3 2 4 +--R (- 2a b + 2a b )cos(x) - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 3 2 4 3 2 +--R - a b sin(x) + ((- a b + a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (- a b + a b)cos(x) - a b +--R Type: Expression(Integer) +--E 61 + +--S 62 of 546 +m0410b:= a0410.2-r0410 +--R +--R +--R (59) +--R +---------+ x +--R +---------+ | 2 2 +---------+ a tan(-) + b +--R | 2 2 (cos(x) + 1)\|- b + a | 2 2 2 +--R 2\|- b + a atan(------------------------) + 2\|- b + a atan(------------) +--R a sin(x) + b cos(x) + b +---------+ +--R | 2 2 +--R \|- b + a +--R ----------------------------------------------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 62 + +--S 63 of 546 +d0410b:= D(m0410b,x) +--R +--R +--R (60) +--R 2 3 2 3 2 3 2 +--R (a b - a )sin(x) + ((- 2b + 2a b)cos(x) - 2b + 2a b)sin(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )cos(x) - a b + a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 2 3 2 x +--R ((4b - 4a b)sin(x) + (4b - 4a b)cos(x) + (4b - 4a b)cos(x))tan(-) +--R 2 +--R + +--R 2 3 2 3 2 3 2 +--R (a b - a )sin(x) + ((- 2b + 2a b)cos(x) - 2b + 2a b)sin(x) +--R + +--R 2 3 2 2 3 +--R (a b - a )cos(x) - a b + a +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R Type: Expression(Integer) +--E 63 + +--S 64 of 546 +t0411:= cos(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R cos(x) +--R (61) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 546 +r0411:= -a^3*x/b^4+3/2*a*x/b^2+2*(a^2-b^2)^(3/2)*_ + atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^4-_ + a^2*cos(x)/b^3+cos(x)/b+1/3*cos(x)^3/b+1/2*a*cos(x)*sin(x)/b^2 +--R +--R +--R (62) +--R x +--R +---------+ a tan(-) + b +--R 2 2 | 2 2 2 2 +--R (- 12b + 12a )\|- b + a atan(------------) + 3a b cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 3 2 2 3 +--R 2b cos(x) + (6b - 6a b)cos(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 65 + +--S 66 of 546 +a0411:= integrate(t0411,x) +--R +--R +--R (63) +--R [ +--R +-------+ +--R 2 2 | 2 2 +--R (6b - 6a )\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R 2 3 3 3 2 2 3 +--R 3a b cos(x)sin(x) + 2b cos(x) + (6b - 6a b)cos(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R , +--R +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 | 2 2 (cos(x) + 1)\|- b + a +--R (12b - 12a )\|- b + a atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R 2 3 3 3 2 2 3 +--R 3a b cos(x)sin(x) + 2b cos(x) + (6b - 6a b)cos(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 66 + +--S 67 of 546 +m0411a:= a0411.1-r0411 +--R +--R +--R (64) +--R +-------+ +--R 2 2 | 2 2 +--R (b - a )\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 2 | 2 2 2 +--R (2b - 2a )\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 +--R b +--R Type: Expression(Integer) +--E 67 + +--S 68 of 546 +d0411a:= D(m0411a,x) +--R +--R +--R (65) +--R 5 2 3 4 5 2 3 4 +--R ((- b + 2a b - a b)cos(x) - b + 2a b - a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (a b - 2a b + a )cos(x) - a b + 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 2 4 3 2 5 +--R (2b - 4a b + 2a b)sin(x) + (2a b - 4a b + 2a )sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (2b - 4a b + 2a b)cos(x) + (2b - 4a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 5 2 3 4 +--R ((- b + 2a b - a b)cos(x) - b + 2a b - a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (a b - 2a b + a )cos(x) - a b + 2a b - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 +--R ((b - 3a b + 3a b - a )cos(x) + b - 2a b + a b )sin(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- a b + 2a b - a b)cos(x) + a b - 2a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 +--R (- 2b + 4a b - 2a b )sin(x) + (- 2a b + 4a b - 2a b)sin(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 6 +--R (- 2b + 4a b - 2a b )cos(x) + (- 2b + 6a b - 6a b + 2a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 +--R ((b - 3a b + 3a b - a )cos(x) + b - 2a b + a b )sin(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- a b + 2a b - a b)cos(x) + a b - 2a b + a b +--R / +--R 2 4 2 5 5 3 3 2 4 +--R a b sin(x) + (a b cos(x) + a b + a b )sin(x) + a b cos(x) +--R + +--R 2 4 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 2 4 5 +--R 2a b sin(x) + (2b cos(x) + 2b + 2a b )sin(x) + 2a b cos(x) +--R + +--R 5 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 5 5 3 3 2 4 2 4 +--R a b sin(x) + (a b cos(x) + a b + a b )sin(x) + a b cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 2 6 3 4 6 3 4 +--R - a b sin(x) + ((- a b + a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 5 4 3 2 5 +--R (- a b + a b )cos(x) - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 7 2 5 7 2 5 +--R - 2a b sin(x) + ((- 2b + 2a b )cos(x) - 2b - 2a b )sin(x) +--R + +--R 6 3 4 6 +--R (- 2a b + 2a b )cos(x) - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 2 6 3 4 6 3 4 +--R - a b sin(x) + ((- a b + a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 5 4 3 2 5 +--R (- a b + a b )cos(x) - a b +--R Type: Expression(Integer) +--E 68 + +--S 69 of 546 +m0411b:= a0411.2-r0411 +--R +--R +--R (66) +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 | 2 2 (cos(x) + 1)\|- b + a +--R (2b - 2a )\|- b + a atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 2 | 2 2 2 +--R (2b - 2a )\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 +--R b +--R Type: Expression(Integer) +--E 69 + +--S 70 of 546 +d0411b:= D(m0411b,x) +--R +--R +--R (67) +--R 4 3 2 5 2 +--R (a b - 2a b + a )sin(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R ((- 2b + 4a b - 2a b)cos(x) - 2b + 4a b - 2a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (a b - 2a b + a )cos(x) - a b + 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 2 5 2 3 4 2 +--R (4b - 8a b + 4a b)sin(x) + (4b - 8a b + 4a b)cos(x) +--R + +--R 5 2 3 4 +--R (4b - 8a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 5 2 +--R (a b - 2a b + a )sin(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R ((- 2b + 4a b - 2a b)cos(x) - 2b + 4a b - 2a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (a b - 2a b + a )cos(x) - a b + 2a b - a +--R / +--R 2 4 2 5 5 2 4 2 2 4 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 4 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 5 2 5 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 5 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 5 5 2 4 2 2 4 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 4 +--R a b +--R Type: Expression(Integer) +--E 70 + +--S 71 of 546 +t0412:= cos(x)^2/(a+a*sin(x)) +--R +--R +--R 2 +--R cos(x) +--R (68) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 546 +r0412:= (x+cos(x))/a +--R +--R +--R cos(x) + x +--R (69) ---------- +--R a +--R Type: Expression(Integer) +--E 72 + +--S 73 of 546 +a0412:= integrate(t0412,x) +--R +--R +--R cos(x) + x +--R (70) ---------- +--R a +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 546 +m0412:= a0412-r0412 +--R +--R +--R (71) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 546 +d0412:= D(m0412,x) +--R +--R +--R (72) 0 +--R Type: Expression(Integer) +--E 75 + +--S 76 of 546 +t0413:= tan(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R tan(x) +--R (73) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 546 +r0413:= 2*a^4*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+_ + 1/12*cos(x)/(a+b)/(1-sin(x))^2+1/12*cos(x)/(a+b)/(1-sin(x))-_ + 1/4*(3*a+2*b)*cos(x)/(a+b)^2/(1-sin(x))-_ + 1/12*cos(x)/(a-b)/(1+sin(x))^2+_ + 1/4*(3*a-2*b)*cos(x)/(a-b)^2/(1+sin(x))-1/12*cos(x)/(a-b)/(1+sin(x)) +--R +--R +--R (74) +--R x +--R a tan(-) + b +--R 4 4 4 2 4 2 +--R (6a sin(x) - 12a sin(x) + 6a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 3 2 2 +--R (- a b + 4a )cos(x)sin(x) + (3b - 6a b)cos(x)sin(x) +--R + +--R 3 3 2 +--R - 3a cos(x)sin(x) + (- 2b + 5a b)cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 4 4 2 2 4 2 4 +--R (3b - 6a b + 3a )sin(x) + (- 6b + 12a b - 6a )sin(x) + 3b +--R + +--R 2 2 4 +--R - 6a b + 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 77 + +--S 78 of 546 +a0413:= integrate(t0413,x) +--R +--R +--R (75) +--R [ +--R 4 3 +--R 3a cos(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 2 3 2 2 3 3 2 3 +--R ((a b - 4a )cos(x) - a b + a )sin(x) + (- 2b + 5a b)cos(x) +--R + +--R 3 2 2 3 2 +--R (- 3b + 6a b)cos(x) + b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 4 3 (a sin(x) + b cos(x) + b)\|- b + a +--R - 6a cos(x) atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 2 2 3 3 2 3 +--R ((a b - 4a )cos(x) - a b + a )sin(x) + (- 2b + 5a b)cos(x) +--R + +--R 3 2 2 3 2 +--R (- 3b + 6a b)cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 78 + +--S 79 of 546 +m0413a:= a0413.1-r0413 +--R +--R +--R (76) +--R +---------+ +--R 4 3 4 4 3 2 4 3 | 2 2 +--R (3a cos(x) sin(x) - 6a cos(x) sin(x) + 3a cos(x) )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 4 3 4 4 3 2 4 3 | 2 2 +--R (- 6a cos(x) sin(x) + 12a cos(x) sin(x) - 6a cos(x) )\|b - a +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 5 +--R ((a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 3 2 2 3 2 4 +--R ((- 2b + 5a b)cos(x) + (- 3b + 6a b)cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((a b - 4a )cos(x) + (- 2a b + 8a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 2 4 3 2 3 +--R (- 3b + 6a b)cos(x) + (4b - 10a b)cos(x) +--R + +--R 3 2 2 3 2 +--R (6b - 12a b)cos(x) - 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 2 3 2 2 3 +--R (3a cos(x) + (a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2b - 5a b)cos(x) + (- 2b + 5a b)cos(x) + (- 3b + 6a b)cos(x) +--R + +--R 3 2 +--R b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 79 + +--S 80 of 546 +d0413a:= D(m0413a,x) +--R +--R +--R (77) +--R 3 4 5 2 2 3 4 5 2 10 +--R ((a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 +--R (a b - 5a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 2a b + 3a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 3a b + 10a b - 11a b + 4a )cos(x) +--R + +--R 6 5 2 2 +--R (- 3a b + 15a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (3a b - 9a b + 9a b - 3a )cos(x) + 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 6 5 2 5 4 3 4 +--R (- 3a b + 3a b)cos(x) + (3a b - 9a b )cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 7a b + 26a b - 19a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (2a b - 3a b + 13a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 5 +--R (- a b + 7a b )cos(x) + (3a b - 9a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (3a b - 5a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (9a b - 31a b + 35a b - 13a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (9a b - 7a b - 20a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- a b + 5a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (5a b - 9a b + 4a b)cos(x) + (a b + 7a b - 8a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 4a b + 17a b + 5a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (15a b - 48a b + 33a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (6a b - 9a b - 15a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (6a b - 19a b + 17a b - 4a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (6a b - 10a b - 14a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 5a b + 14a b - 4a b - 5a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 5a b + 7a b + 16a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 9a b + 33a b - 39a b + 15a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 9a b + 11a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (9a b - 27a b + 27a b - 9a )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (3a b - 12a b + 9a b)cos(x) + (a b - 4a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (- 2a b - 5a b + 7a b)cos(x) + (- 9a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 13a b + 38a b - 25a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 10a b + 15a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 2a b + 7a b - 2a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 2a b + 3a b + 17a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (2a b - 4a b - 7a b + 9a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (2a b - a b - 19a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (3a b - 13a b + 17a b - 7a )cos(x) +--R + +--R 6 3 4 2 +--R (3a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- 2a b + 7a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (- 2a b + 5a b - 3a b)cos(x) + (a b + a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (a b + a b + 4a b)cos(x) + (4a b - 11a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (4a b - 6a b - a b)cos(x) + (- 3a b + 6a b - 3a b)cos(x) +--R + +--R 2 5 4 3 +--R - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 5 2 7 7 5 2 6 +--R (- 3a b + 3a )cos(x) - 6a b cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (- a b + 5a b - 4a )cos(x) + (- a b + 7a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (a b - 2a b + a )cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 2 5 4 3 10 +--R ((2a b - 8a b )cos(x) - 6a b + 6a b )sin(x) +--R + +--R 6 3 4 5 2 3 +--R (2a b - 10a b + 8a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 4a b + 6a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (- 6a b + 12a b - 6a b )cos(x) - 6a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 4 7 2 5 4 3 6 3 +--R 6a b cos(x) + (- 6b + 20a b - 22a b + 8a b)cos(x) +--R + +--R 7 4 3 2 +--R (- 6b + 30a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (6b - 18a b + 18a b - 6a b)cos(x) + 6b + 12a b - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 14a b + 52a b - 38a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (4a b - 6a b + 26a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (24a b - 48a b + 24a b )cos(x) + 6a b + 12a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 4 3 6 +--R (- 2a b + 14a b )cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (6b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (6b - 10a b - 20a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (18b - 62a b + 70a b - 26a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (18b - 14a b - 40a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 4 3 +--R (- 18b + 54a b - 54a b + 18a b)cos(x) - 18b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (- 2a b + 10a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (10a b - 18a b + 8a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (30a b - 96a b + 66a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (12a b - 18a b - 30a b )cos(x) +--R + +--R 6 3 4 5 2 6 5 2 +--R (- 36a b + 72a b - 36a b )cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (12b - 38a b + 34a b - 8a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (12b - 20a b - 28a b )cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 10b + 28a b - 26a b + 8a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (- 10b + 14a b + 32a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 18b + 66a b - 78a b + 30a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (- 18b + 22a b + 20a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (18b - 54a b + 54a b - 18a b)cos(x) + 18b - 12a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (6a b - 24a b + 18a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (2a b - 8a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 26a b + 76a b - 50a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 20a b + 30a b + 14a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (24a b - 48a b + 24a b )cos(x) + 18a b - 12a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 4b + 14a b - 4a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (- 4b + 6a b + 34a b )cos(x) +--R + +--R 7 2 5 4 3 5 7 2 5 4 3 4 +--R (4b - 8a b + 4a b )cos(x) + (4b - 2a b - 26a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (6b - 26a b + 34a b - 14a b)cos(x) +--R + +--R 7 2 5 2 +--R (6b - 12a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 +--R (- 6b + 18a b - 18a b + 6a b)cos(x) - 6b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (- 4a b + 14a b - 10a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 4a b + 10a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (8a b - 22a b + 14a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (8a b - 12a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (- 6a b + 12a b - 6a b )cos(x) - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 4 3 6 7 4 3 6 +--R (- 6a b + 6a b)cos(x) - 12a b cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 4 +--R (- 2a b + 4a b - 2a b)cos(x) + (- 2a b + 8a b )cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 2 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 10 +--R ((a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (a b - 5a b + 4a b)cos(x) + (- 2a b + 3a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 3a b + 10a b - 11a b + 4a )cos(x) +--R + +--R 6 5 2 2 6 3 4 5 2 7 +--R (- 3a b + 15a b )cos(x) + (3a b - 9a b + 9a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 +--R 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 6 5 2 5 4 3 4 +--R (- 3a b + 3a b)cos(x) + (3a b - 9a b )cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 7a b + 26a b - 19a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (2a b - 3a b + 13a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 +--R 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 5 +--R (- a b + 7a b )cos(x) + (3a b - 9a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (3a b - 5a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (9a b - 31a b + 35a b - 13a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (9a b - 7a b - 20a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (- a b + 5a b - 4a b)cos(x) + (5a b - 9a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (a b + 7a b - 8a b)cos(x) + (- 4a b + 17a b + 5a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (15a b - 48a b + 33a b)cos(x) + (6a b - 9a b - 15a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (6a b - 19a b + 17a b - 4a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (6a b - 10a b - 14a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 5a b + 14a b - 4a b - 5a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 5a b + 7a b + 16a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 9a b + 33a b - 39a b + 15a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 9a b + 11a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (9a b - 27a b + 27a b - 9a )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (3a b - 12a b + 9a b)cos(x) + (a b - 4a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (- 2a b - 5a b + 7a b)cos(x) + (- 9a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 13a b + 38a b - 25a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 10a b + 15a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 2a b + 7a b - 2a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 2a b + 3a b + 17a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (2a b - 4a b - 7a b + 9a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (2a b - a b - 19a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 6 3 4 2 +--R (3a b - 13a b + 17a b - 7a )cos(x) + (3a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (- 2a b + 7a b - 5a b)cos(x) + (- 2a b + 5a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (a b + a b - 2a b)cos(x) + (a b + a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (4a b - 11a b + 7a b)cos(x) + (4a b - 6a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 5 2 7 7 5 2 6 3 4 5 2 7 5 +--R (- 3a b + 3a )cos(x) - 6a b cos(x) + (- a b + 5a b - 4a )cos(x) +--R + +--R 3 4 5 2 4 3 4 5 2 7 3 +--R (- a b + 7a b )cos(x) + (a b - 2a b + a )cos(x) +--R + +--R 3 4 5 2 2 +--R (a b - a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((- a b + 5a b - 4a b)cos(x) + 3a b - 6a b + 3a b)sin(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- a b + 5a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (2a b - 5a b + 7a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 8 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a +--R * +--R 9 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (3a b - 10a b + 11a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (3a b - 3a b - 15a b + 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) - 3a b - 3a b + 15a b +--R + +--R 7 +--R - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 4 6 2 5 2 6 4 4 6 2 4 +--R (3a b - 3a b )cos(x) + (- 3a b + 12a b - 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (7a b - 26a b + 19a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 2a b + 5a b - 16a b + 13a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 3a b - 3a b + 15a b - 9a +--R * +--R 7 +--R sin(x) +--R + +--R 3 5 5 3 7 6 7 3 5 5 3 5 +--R (a b - 8a b + 7a b)cos(x) + (- 3a b + 9a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 8a b - a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 9a b + 31a b - 35a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 9a b + 16a b + 13a b - 20a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (9a b - 27a b + 27a b - 9a b)cos(x) + 9a b - 9a b - 9a b +--R + +--R 7 +--R 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (a b - 5a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 5a b + 14a b - 13a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- a b - 7a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (4a b - 21a b + 12a b + 5a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 15a b + 48a b - 33a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 6a b + 15a b + 6a b - 15a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (18a b - 36a b + 18a b )cos(x) + 9a b - 9a b - 9a b + 9a +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 6a b + 19a b - 17a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 6a b + 16a b + 4a b - 14a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (5a b - 14a b + 4a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (5a b - 12a b - 9a b + 16a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (9a b - 33a b + 39a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (9a b - 20a b + a b + 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) - 9a b + 15a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 3a b + 12a b - 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- a b + 5a b - 7a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 5 4 4 8 4 +--R (2a b + 5a b - 7a b )cos(x) + (9a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (13a b - 38a b + 25a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (10a b - 25a b + 8a b + 7a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 9a b + 15a b - 3a b - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (2a b - 7a b + 2a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b - 5a b - 14a b + 17a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 2a b + 4a b + 7a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 2a b + 3a b + 18a b - 19a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b + 13a b - 17a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 3a b + 9a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (3a b - 9a b + 9a b - 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (2a b - 7a b + 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (2a b - 7a b + 8a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 5 2 6 6 2 8 4 +--R (- a b - a b + 2a b )cos(x) + (- a b - 3a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 4a b + 11a b - 7a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 4a b + 10a b - 5a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 5 3 7 7 5 3 7 6 +--R (3a b - 3a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (a b - 5a b + 4a b)cos(x) + (a b - 8a b + 7a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((- 2a b + 10a b - 8a b )cos(x) + 6a b - 12a b + 6a b )sin(x) +--R + +--R 7 3 5 5 3 3 +--R (- 2a b + 10a b - 8a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b - 10a b + 14a b - 8a b)cos(x) +--R + +--R 7 3 5 5 3 3 5 5 3 7 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 4 6 2 4 8 2 6 4 4 6 2 3 +--R (- 6a b + 6a b )cos(x) + (6b - 20a b + 22a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (6b - 6a b - 30a b + 30a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) - 6b - 6a b + 30a b +--R + +--R 6 2 +--R - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (14a b - 52a b + 38a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 4a b + 10a b - 32a b + 26a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (- 24a b + 48a b - 24a b )cos(x) - 6a b - 6a b + 30a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 6 +--R (2a b - 16a b + 14a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 6b + 16a b + 10a b - 20a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 18b + 62a b - 70a b + 26a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 18b + 32a b + 26a b - 40a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (18b - 54a b + 54a b - 18a b )cos(x) + 18b - 18a b - 18a b +--R + +--R 6 2 +--R 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (2a b - 10a b + 8a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 10a b + 28a b - 26a b + 8a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (8a b - 24a b + 24a b - 8a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 30a b + 96a b - 66a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 12a b + 30a b + 12a b - 30a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (36a b - 72a b + 36a b )cos(x) + 18a b - 18a b - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 7 +--R (- 12b + 38a b - 34a b + 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 12b + 32a b + 8a b - 28a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (10b - 28a b + 26a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (10b - 24a b - 18a b + 32a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (18b - 66a b + 78a b - 30a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (18b - 40a b + 2a b + 20a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) - 18b + 30a b - 6a b +--R + +--R 6 2 +--R - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (- 6a b + 24a b - 18a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 2a b + 10a b - 14a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (26a b - 76a b + 50a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (20a b - 50a b + 16a b + 14a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (- 24a b + 48a b - 24a b )cos(x) - 18a b + 30a b - 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 7 +--R (4b - 14a b + 4a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (4b - 10a b - 28a b + 34a b )cos(x) +--R + +--R 8 2 6 4 4 5 +--R (- 4b + 8a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 4b + 6a b + 24a b - 26a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 6b + 26a b - 34a b + 14a b )cos(x) +--R + +--R 8 2 6 4 4 2 +--R (- 6b + 18a b - 12a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (6b - 18a b + 18a b - 6a b )cos(x) + 6b - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (4a b - 14a b + 10a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (4a b - 14a b + 16a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 2a b + 6a b - 6a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 8a b + 22a b - 14a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 8a b + 20a b - 10a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R sin(x) +--R + +--R 4 4 6 2 7 4 4 6 2 6 +--R (6a b - 6a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 2 6 4 4 6 2 4 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 10a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((- a b + 5a b - 4a b)cos(x) + 3a b - 6a b + 3a b)sin(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- a b + 5a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 2 6 4 4 6 2 +--R (2a b - 5a b + 7a b - 4a )cos(x) + (3a b - 6a b + 3a b )cos(x) +--R + +--R 4 4 6 2 8 +--R 3a b - 6a b + 3a +--R * +--R 9 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (3a b - 10a b + 11a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (3a b - 3a b - 15a b + 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) - 3a b - 3a b + 15a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 4 6 2 5 2 6 4 4 6 2 4 +--R (3a b - 3a b )cos(x) + (- 3a b + 12a b - 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (7a b - 26a b + 19a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 2a b + 5a b - 16a b + 13a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 3a b - 3a b + 15a b - 9a +--R * +--R 7 +--R sin(x) +--R + +--R 3 5 5 3 7 6 7 3 5 5 3 5 +--R (a b - 8a b + 7a b)cos(x) + (- 3a b + 9a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 8a b - a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 9a b + 31a b - 35a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 9a b + 16a b + 13a b - 20a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 27a b + 27a b - 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (a b - 5a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 5a b + 14a b - 13a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- a b - 7a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (4a b - 21a b + 12a b + 5a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 15a b + 48a b - 33a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 6a b + 15a b + 6a b - 15a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (18a b - 36a b + 18a b )cos(x) + 9a b - 9a b - 9a b + 9a +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 6a b + 19a b - 17a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 6a b + 16a b + 4a b - 14a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (5a b - 14a b + 4a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (5a b - 12a b - 9a b + 16a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (9a b - 33a b + 39a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (9a b - 20a b + a b + 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) - 9a b + 15a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 3a b + 12a b - 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- a b + 5a b - 7a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 5 4 4 8 4 +--R (2a b + 5a b - 7a b )cos(x) + (9a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (13a b - 38a b + 25a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (10a b - 25a b + 8a b + 7a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 9a b + 15a b - 3a b - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (2a b - 7a b + 2a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b - 5a b - 14a b + 17a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 2a b + 4a b + 7a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 2a b + 3a b + 18a b - 19a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b + 13a b - 17a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 3a b + 9a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (3a b - 9a b + 9a b - 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 2 6 4 4 6 2 8 6 +--R (2a b - 7a b + 5a b )cos(x) + (2a b - 7a b + 8a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 5 2 6 6 2 8 4 +--R (- a b - a b + 2a b )cos(x) + (- a b - 3a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 4a b + 11a b - 7a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 4a b + 10a b - 5a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 5 3 7 7 5 3 7 6 +--R (3a b - 3a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (a b - 5a b + 4a b)cos(x) + (a b - 8a b + 7a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R / +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (3a b - 9a b + 9a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 4 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (9a b - 27a b + 27a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 4 8 +--R (6a b - 12a b + 6a b )cos(x) sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (6b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (6b - 6a b - 6a b + 6a b )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (- 12a b + 24a b - 12a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 18b + 18a b + 18a b - 18a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 4 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (18b - 54a b + 54a b - 18a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (18b - 18a b - 18a b + 18a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (18a b - 54a b + 54a b - 18a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (12a b - 24a b + 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 6b + 6a b + 6a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (3a b - 9a b + 9a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 4 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (9a b - 27a b + 27a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 3a b + 6a b - 6a b + 3a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (9a b - 27a b + 27a b - 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (9a b - 18a b + 18a b - 9a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (9a b - 27a b + 27a b - 9a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 9a b + 18a b - 18a b + 9a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (3a b - 6a b + 6a b - 3a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 6b + 12a b - 12a b + 6a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (12a b - 36a b + 36a b - 12a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (18b - 54a b + 54a b - 18a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (18b - 36a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (18a b - 54a b + 54a b - 18a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 18b + 36a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 18a b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 12a b + 36a b - 36a b + 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (6b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (6b - 12a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 3a b + 6a b - 6a b + 3a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (9a b - 27a b + 27a b - 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (9a b - 18a b + 18a b - 9a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (9a b - 27a b + 27a b - 9a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 9a b + 18a b - 18a b + 9a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (3a b - 6a b + 6a b - 3a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R Type: Expression(Integer) +--E 80 + +--S 81 of 546 +m0413b:= a0413.2-r0413 +--R +--R +--R (78) +--R 4 3 4 4 3 2 4 3 +--R (- 6a cos(x) sin(x) + 12a cos(x) sin(x) - 6a cos(x) ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +--R 4 3 4 4 3 2 4 3 2 +--R (- 6a cos(x) sin(x) + 12a cos(x) sin(x) - 6a cos(x) )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 5 +--R ((a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 3 2 2 3 2 4 +--R ((- 2b + 5a b)cos(x) + (- 3b + 6a b)cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((a b - 4a )cos(x) + (- 2a b + 8a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 2 4 3 2 3 +--R (- 3b + 6a b)cos(x) + (4b - 10a b)cos(x) +--R + +--R 3 2 2 3 2 +--R (6b - 12a b)cos(x) - 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 2 3 2 2 3 +--R (3a cos(x) + (a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (2b - 5a b)cos(x) + (- 2b + 5a b)cos(x) + (- 3b + 6a b)cos(x) +--R + +--R 3 2 +--R b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 546 +d0413b:= D(m0413b,x) +--R +--R +--R (79) +--R 3 2 5 2 3 2 5 10 +--R ((a b - 4a )cos(x) - 3a b + 3a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (2a b - 8a b)cos(x) + (- a b - 2a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (a b - a )cos(x) + (- 6a b + 14a b - 8a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 6a b + 6a b + 12a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 4 5 +--R 6a b - 6a +--R * +--R 8 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R - 6a b cos(x) - 6a b cos(x) + (- 14a b + 38a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (a b + 11a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 2 5 6 4 3 2 5 +--R (- a b + 7a )cos(x) + (6a b - 12a b )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (6a b - 18a b + 6a )cos(x) + (18a b - 44a b + 26a )cos(x) +--R + +--R 4 3 2 5 2 +--R (18a b - 25a b - 11a )cos(x) +--R + +--R 4 3 2 5 4 3 2 +--R (- 18a b + 36a b - 18a )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 2a b + 8a b)cos(x) + (7a b - 10a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (2a b + 16a b)cos(x) + (3a b + 15a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (30a b - 66a b)cos(x) + (3a b - 21a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 36a b + 36a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- a b + 4a )cos(x) + (12a b - 26a b + 8a )cos(x) +--R + +--R 4 3 2 5 6 +--R (12a b - 30a b + 3a )cos(x) +--R + +--R 4 3 2 5 5 +--R (- 10a b + 18a b + 10a )cos(x) +--R + +--R 4 3 2 5 4 +--R (- 10a b + 29a b - a )cos(x) +--R + +--R 4 3 2 5 3 +--R (- 18a b + 48a b - 30a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 18a b + 29a b + a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 4 3 2 5 +--R 18a b - 24a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (6a b - 12a b)cos(x) + (6a b - 18a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 7a b + 13a b)cos(x) + (- 4a b - 14a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 6a b - 12a b)cos(x) + (- 26a b + 50a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (- 5a b + 17a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- 3a b + 3a )cos(x) + (- 4a b + 10a b + 6a )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 4a b + 16a b )cos(x) + (4a b - 4a b - 18a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (4a b - 12a b - 10a )cos(x) + (6a b - 20a b + 14a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (6a b - 12a b + 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 4 3 2 5 +--R - 6a b + 9a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 4 6 +--R (- 2a b + 8a b)cos(x) + (- 4a b + 10a b)cos(x) - 3a b cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (2a b + 4a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (8a b - 14a b)cos(x) + (2a b - 5a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 5 8 5 7 3 2 5 6 +--R - 3a cos(x) - 6a cos(x) + (- a b - 2a )cos(x) +--R + +--R 3 2 5 5 5 4 3 2 5 3 +--R (- 2a b + 8a )cos(x) + 6a cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 2 5 2 +--R (a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 2 3 4 10 +--R ((2a b - 8a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (4a b - 16a b )cos(x) + (- 2a b - 4a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 12a b + 12a b )cos(x) - 6a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (2a b + 4a b)cos(x) + (- 12b + 28a b - 16a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 12b + 12a b + 24a b)cos(x) + (12b - 24a b + 12a b)cos(x) +--R + +--R 5 4 +--R 12b - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 28a b + 76a b )cos(x) + (2a b + 22a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (48a b - 48a b )cos(x) + 24a b - 24a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 3 4 6 5 2 3 4 5 +--R (- 2a b + 20a b)cos(x) + (12b - 24a b + 12a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 3 +--R (12b - 36a b )cos(x) + (36b - 88a b + 52a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (36b - 50a b - 22a b)cos(x) + (- 36b + 72a b - 36a b)cos(x) +--R + +--R 5 2 3 +--R - 36b + 36a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 4a b + 16a b )cos(x) + (14a b - 20a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (4a b - 4a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (60a b - 132a b )cos(x) + (6a b - 42a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 72a b + 72a b )cos(x) - 36a b + 36a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 8 5 2 3 4 7 +--R (- 2a b + 8a b)cos(x) + (24b - 52a b + 16a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (24b - 60a b - 12a b)cos(x) + (- 20b + 36a b - 16a b)cos(x) +--R + +--R 5 2 3 4 4 +--R (- 20b + 58a b - 2a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 36b + 96a b - 60a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 36b + 58a b + 2a b)cos(x) + (36b - 72a b + 36a b)cos(x) +--R + +--R 5 2 3 4 +--R 36b - 48a b + 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (12a b - 24a b )cos(x) + (12a b - 36a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 14a b + 26a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 12a b + 12a b )cos(x) + (- 52a b + 100a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 4 +--R (- 10a b + 34a b )cos(x) + (48a b - 48a b )cos(x) + 24a b +--R + +--R 3 2 +--R - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 8 5 2 3 4 7 +--R (- 6a b + 6a b)cos(x) + (- 8b + 20a b + 12a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 5 +--R (- 8b + 32a b + 18a b)cos(x) + (8b - 8a b )cos(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (8b - 24a b - 8a b)cos(x) + (12b - 40a b + 28a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (12b - 24a b + 6a b)cos(x) + (- 12b + 24a b - 12a b)cos(x) +--R + +--R 5 2 3 4 +--R - 12b + 18a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- 4a b + 16a b )cos(x) + (- 8a b + 20a b )cos(x) +--R + +--R 3 2 6 4 3 2 5 4 3 2 4 +--R - 6a b cos(x) + (4a b - 4a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (16a b - 28a b )cos(x) + (4a b - 10a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 12a b + 12a b )cos(x) - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 4 8 4 7 2 3 4 6 +--R - 6a b cos(x) - 12a b cos(x) + (- 2a b - 10a b)cos(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (- 4a b + 4a b)cos(x) + 6a b cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 3 4 2 +--R (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 5 2 3 2 5 10 +--R ((a b - 4a )cos(x) - 3a b + 3a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (2a b - 8a b)cos(x) + (- a b - 2a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (a b - a )cos(x) + (- 6a b + 14a b - 8a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 6a b + 6a b + 12a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 4 5 +--R 6a b - 6a +--R * +--R 8 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R - 6a b cos(x) - 6a b cos(x) + (- 14a b + 38a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (a b + 11a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 2 5 6 4 3 2 5 +--R (- a b + 7a )cos(x) + (6a b - 12a b )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (6a b - 18a b + 6a )cos(x) + (18a b - 44a b + 26a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (18a b - 25a b - 11a )cos(x) + (- 18a b + 36a b - 18a )cos(x) +--R + +--R 4 3 2 +--R - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 2a b + 8a b)cos(x) + (7a b - 10a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (2a b + 16a b)cos(x) + (3a b + 15a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (30a b - 66a b)cos(x) + (3a b - 21a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 36a b + 36a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- a b + 4a )cos(x) + (12a b - 26a b + 8a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (12a b - 30a b + 3a )cos(x) + (- 10a b + 18a b + 10a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 10a b + 29a b - a )cos(x) + (- 18a b + 48a b - 30a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 18a b + 29a b + a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 4 3 2 5 +--R 18a b - 24a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (6a b - 12a b)cos(x) + (6a b - 18a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 7a b + 13a b)cos(x) + (- 4a b - 14a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 6a b - 12a b)cos(x) + (- 26a b + 50a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (- 5a b + 17a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- 3a b + 3a )cos(x) + (- 4a b + 10a b + 6a )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 4a b + 16a b )cos(x) + (4a b - 4a b - 18a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (4a b - 12a b - 10a )cos(x) + (6a b - 20a b + 14a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (6a b - 12a b + 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 4 3 2 5 +--R - 6a b + 9a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 4 6 +--R (- 2a b + 8a b)cos(x) + (- 4a b + 10a b)cos(x) - 3a b cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (2a b + 4a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (8a b - 14a b)cos(x) + (2a b - 5a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 5 8 5 7 3 2 5 6 +--R - 3a cos(x) - 6a cos(x) + (- a b - 2a )cos(x) +--R + +--R 3 2 5 5 5 4 3 2 5 3 +--R (- 2a b + 8a )cos(x) + 6a cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 2 5 2 +--R (a b - a )cos(x) +--R / +--R 2 4 4 2 6 4 8 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (3a b - 6a b + 3a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 6a b + 12a b - 6a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 6 6 +--R (- 9a b + 18a b - 9a )cos(x) +--R + +--R 2 4 4 2 6 5 +--R (- 18a b + 36a b - 18a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (18a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (9a b - 18a b + 9a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (6a b - 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 3a b + 6a b - 3a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 4 +--R ((12b - 24a b + 12a b )cos(x) + (12b - 24a b + 12a b )cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (6a b - 12a b + 6a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 6 2 4 4 2 5 +--R (- 36b + 72a b - 36a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 36b + 72a b - 36a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 36a b + 72a b - 36a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 4 +--R ((36b - 72a b + 36a b )cos(x) + (36b - 72a b + 36a b )cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (36a b - 72a b + 36a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 4 2 5 +--R (- 12b + 24a b - 12a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 12b + 24a b - 12a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) + (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 6 4 8 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 7 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) )sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (3a b - 6a b + 3a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 6a b + 12a b - 6a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R ((- 9a b + 18a b - 9a )cos(x) + (- 18a b + 36a b - 18a )cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((18a b - 36a b + 18a b)cos(x) + (18a b - 36a b + 18a b)cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (9a b - 18a b + 9a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (6a b - 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((- 6a b + 12a b - 6a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) ) +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 3a b + 6a b - 3a )cos(x) +--R Type: Expression(Integer) +--E 82 + +--S 83 of 546 +t0414:= tan(x)/(a+a*sin(x)) +--R +--R +--R tan(x) +--R (80) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 83 + +--S 84 of 546 +r0414:= 1/2*atanh(sin(x))/a+1/2/a/(1+sin(x)) +--R +--R +--R (sin(x) + 1)atanh(sin(x)) + 1 +--R (81) ----------------------------- +--R 2a sin(x) + 2a +--R Type: Expression(Integer) +--E 84 + +--S 85 of 546 +a0414:= integrate(t0414,x) +--R +--R +--R (82) +--R sin(x) + cos(x) + 1 +--R (sin(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R sin(x) - cos(x) - 1 +--R (- sin(x) - 1)log(-------------------) - sin(x) +--R cos(x) + 1 +--R / +--R 2a sin(x) + 2a +--R Type: Union(Expression(Integer),...) +--E 85 + +--S 86 of 546 +m0414:= a0414-r0414 +--R +--R +--R (83) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) - 1 +--R cos(x) + 1 cos(x) + 1 +--R ----------------------------------------------------------------------- +--R 2a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 546 +d0414:= D(m0414,x) +--R +--R +--R (84) +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R / +--R 4 2 2 2 +--R 2a sin(x) + (- 2a cos(x) - 4a cos(x) - 4a)sin(x) + 2a cos(x) +--R + +--R 4a cos(x) + 2a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 546 +t0415:= tan(x)^2/(a+a*sin(x)) +--R +--R +--R 2 +--R tan(x) +--R (85) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 88 + +--S 89 of 546 +r0415:= 1/3*(1+2*sin(x)+cos(x)^2)/cos(x)/a/(1+sin(x)) +--R +--R +--R 2 +--R 2sin(x) + cos(x) + 1 +--R (86) --------------------------- +--R 3a cos(x)sin(x) + 3a cos(x) +--R Type: Expression(Integer) +--E 89 + +--S 90 of 546 +a0415:= integrate(t0415,x) +--R +--R +--R 2 +--R (2cos(x) + 2)sin(x) + cos(x) + 2cos(x) + 1 +--R (87) ------------------------------------------- +--R 3a cos(x)sin(x) + 3a cos(x) +--R Type: Union(Expression(Integer),...) +--E 90 + +--S 91 of 546 +m0415:= a0415-r0415 +--R +--R +--R 2 +--R (88) -- +--R 3a +--R Type: Expression(Integer) +--E 91 + +--S 92 of 546 +d0415:= D(m0415,x) +--R +--R +--R (89) 0 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 546 +t0416:= tan(x)^3/(a+a*sin(x)) +--R +--R +--R 3 +--R tan(x) +--R (90) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 93 + +--S 94 of 546 +r0416:= -1/8/cos(x)^4*(3*atanh(sin(x))*cos(x)^4+2*sin(x)-2-_ + 5*sin(x)*cos(x)^2+4*cos(x)^2)/a +--R +--R +--R 4 2 2 +--R - 3cos(x) atanh(sin(x)) + (5cos(x) - 2)sin(x) - 4cos(x) + 2 +--R (91) ------------------------------------------------------------- +--R 4 +--R 8a cos(x) +--R Type: Expression(Integer) +--E 94 + +--S 95 of 546 +a0416:= integrate(t0416,x) +--R +--R +--R (92) +--R 2 2 sin(x) + cos(x) + 1 +--R (- 3cos(x) sin(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 sin(x) - cos(x) - 1 +--R (3cos(x) sin(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2cos(x) + 1)sin(x) - 3cos(x) + 3 +--R / +--R 2 2 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Union(Expression(Integer),...) +--E 95 + +--S 96 of 546 +m0416:= a0416-r0416 +--R +--R +--R (93) +--R 4 4 sin(x) + cos(x) + 1 +--R (- 3cos(x) sin(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 sin(x) - cos(x) - 1 +--R (3cos(x) sin(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 2 2 +--R (3cos(x) sin(x) + 3cos(x) )atanh(sin(x)) + (- 5cos(x) + 2)sin(x) +--R + +--R 4 4 2 +--R 2cos(x) sin(x) - 3cos(x) + 7cos(x) - 2 +--R / +--R 4 4 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 546 +d0416:= D(m0416,x) +--R +--R +--R (94) +--R 2 7 +--R (- 10cos(x) + 8)sin(x) +--R + +--R 5 4 3 2 5 +--R (6cos(x) + 5cos(x) + 20cos(x) + 28cos(x) - 16cos(x) - 24)sin(x) +--R + +--R 5 4 2 4 +--R (6cos(x) - 5cos(x) + 2cos(x) )sin(x) +--R + +--R 7 6 5 4 3 2 +--R 6cos(x) + 13cos(x) + 4cos(x) - 18cos(x) - 52cos(x) - 26cos(x) +--R + +--R 32cos(x) + 24 +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 2 2 +--R (6cos(x) + 3cos(x) + 4cos(x) + 10cos(x) - 4cos(x) - 4cos(x) )sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 2cos(x) - 10cos(x) - 11cos(x) - 6cos(x) + 13cos(x) + 32cos(x) +--R + +--R 2 +--R 8cos(x) - 16cos(x) - 8 +--R * +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R 8cos(x) + 10cos(x) - 5cos(x) - 14cos(x) - 5cos(x) + 4cos(x) +--R + +--R 2 +--R 2cos(x) +--R / +--R 5 5 5 4 +--R 8a cos(x) sin(x) + 8a cos(x) sin(x) +--R + +--R 7 6 5 3 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 2 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 7 6 +--R (8a cos(x) + 16a cos(x) + 8a cos(x) )sin(x) + 8a cos(x) + 16a cos(x) +--R + +--R 5 +--R 8a cos(x) +--R Type: Expression(Integer) +--E 97 + +--S 98 of 546 +t0417:= tan(x)^4/(a+a*sin(x)) +--R +--R +--R 4 +--R tan(x) +--R (95) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 98 + +--S 99 of 546 +r0417:= -1/15*(-1-4*sin(x)+12*sin(x)*cos(x)^2+6*cos(x)^2+_ + 3*cos(x)^4)/cos(x)^3/a/(1+sin(x)) +--R +--R +--R 2 4 2 +--R (- 12cos(x) + 4)sin(x) - 3cos(x) - 6cos(x) + 1 +--R (96) ------------------------------------------------- +--R 3 3 +--R 15a cos(x) sin(x) + 15a cos(x) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 546 +a0417:= integrate(t0417,x) +--R +--R +--R (97) +--R 3 2 4 3 2 +--R (- 8cos(x) - 12cos(x) + 4)sin(x) - 3cos(x) - 8cos(x) - 6cos(x) + 1 +--R ----------------------------------------------------------------------- +--R 3 3 +--R 15a cos(x) sin(x) + 15a cos(x) +--R Type: Union(Expression(Integer),...) +--E 100 + +--S 101 of 546 +m0417:= a0417-r0417 +--R +--R +--R 8 +--R (98) - --- +--R 15a +--R Type: Expression(Integer) +--E 101 + +--S 102 of 546 +d0417:= D(m0417,x) +--R +--R +--R (99) 0 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 546 +t0418:= cot(x)^2/(a+b*sin(x)) +--R +--R +--R 2 +--R cot(x) +--R (100) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 103 + +--S 104 of 546 +r0418:= -2*(a^2-b^2)^(1/2)*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^2+_ + b*atanh(cos(x))/a^2-cot(x)/a +--R +--R +--R x +--R +---------+ a tan(-) + b +--R | 2 2 2 +--R b atanh(cos(x)) - 2\|- b + a atan(------------) - a cot(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (101) ------------------------------------------------------------ +--R 2 +--R a +--R Type: Expression(Integer) +--E 104 + +--S 105 of 546 +a0418:= integrate(t0418,x) +--R +--R +--R (102) +--R [ +--R sin(x) +--R - b sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R sin(x)\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R - a cos(x) +--R / +--R 2 +--R a sin(x) +--R , +--R +--R sin(x) +--R - b sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R 2sin(x)\|- b + a atan(------------------------) - a cos(x) +--R a sin(x) + b cos(x) + b +--R / +--R 2 +--R a sin(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 105 + +--S 106 of 546 +m0418a:= a0418.1-r0418 +--R +--R +--R (103) +--R sin(x) +--R - b sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R sin(x)\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R x +--R +---------+ a tan(-) + b +--R | 2 2 2 +--R - b sin(x)atanh(cos(x)) + 2sin(x)\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R a cot(x)sin(x) - a cos(x) +--R / +--R 2 +--R a sin(x) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 546 +d0418a:= D(m0418a,x) +--R +--R +--R (104) +--R 2 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 3 2 +--R (- a b cos(x) + a b)cot(x) - a b cos(x) +--R + +--R 3 3 +--R (- a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 2 2 4 2 2 2 2 2 +--R - a b cos(x) + (- a b - a )cos(x) + a b cos(x) + a b +--R + +--R 4 +--R a +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 4 2 4 2 2 4 2 2 +--R - b cos(x) - b cos(x) + (b - a b )cos(x) + b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 3 2 3 3 2 +--R (- a b cos(x) - a b cos(x) + a b cos(x) + a b)cot(x) +--R + +--R 3 3 3 3 3 2 +--R (- a b - a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 3 3 +--R (a b + a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 4 4 2 2 3 4 2 +--R a b cos(x) + a cos(x) - 2a b cos(x) - a cos(x) +--R + +--R 2 2 +--R a b cos(x) +--R * +--R sin(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R a b cos(x) + a b cos(x) - a b cos(x) - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 +--R - 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R (- 2a b cos(x) + 2a b )cot(x) - 2a b cos(x) +--R + +--R 4 2 2 4 2 2 +--R (- 2b - 2a b )cos(x) - 2b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 3 3 2 3 +--R - 2a b cos(x) + (- 2a b - 2a b)cos(x) + 2a b cos(x) +--R + +--R 3 3 +--R 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 3 2 3 3 +--R - 2a b cos(x) - 2a b cos(x) - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b )cot(x) +--R + +--R 2 2 3 2 2 +--R - 4a b cos(x) + 4a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R 2a b cos(x) + 2a b cos(x) - 4a b cos(x) - 2a b cos(x) +--R + +--R 3 +--R 2a b cos(x) +--R * +--R sin(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 3 2 3 3 +--R ((- a b cos(x) + a b)cot(x) - a b cos(x) + (- a b - a b)cos(x)) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 2 2 4 2 2 2 2 2 4 +--R (- a b cos(x) + (- a b - a )cos(x) + a b cos(x) + a b + a ) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 4 2 4 2 2 4 2 2 +--R - b cos(x) - b cos(x) + (b - a b )cos(x) + b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 3 2 3 3 2 +--R (- a b cos(x) - a b cos(x) + a b cos(x) + a b)cot(x) +--R + +--R 3 3 3 3 3 2 +--R (- a b - a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 3 3 +--R (a b + a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 4 4 2 2 3 4 2 2 2 +--R (a b cos(x) + a cos(x) - 2a b cos(x) - a cos(x) + a b cos(x)) +--R * +--R sin(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R a b cos(x) + a b cos(x) - a b cos(x) - a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 5 +--R a b cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 4 3 2 2 +--R (a b cos(x) - a b )cot(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 +--R (a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (a b - a b)cos(x) + (a b + a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- a b + a b)cos(x) - a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 3 5 4 2 +--R (b - a b + a b)cos(x) + (b - a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 +--R (- b + 2a b - a b)cos(x) - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 3 2 5 3 2 +--R ((a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) - a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 4 3 2 3 4 2 +--R - a b cos(x) + (a b + a b )cos(x) + a b cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- a b - a b )cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (- a b + a b)cos(x) - 2a b cos(x) + (2a b - a b)cos(x) +--R + +--R 4 2 2 3 +--R 2a b cos(x) - a b cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 5 3 2 4 3 2 5 3 3 2 2 +--R (- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) + a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 5 +--R 2a b cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 5 2 3 5 2 3 +--R ((2a b cos(x) - 2a b )cot(x) + (2b + 2a b )cos(x) + 2b - 2a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (2a b - 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 2a b + 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 4 3 2 +--R 2a b cos(x) + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 3 2 3 2 2 3 4 +--R (2a b - 2a b)cos(x) + 2a b cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 2 3 +--R - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 2 3 4 3 2 3 2 +--R - 2a b cos(x) + (6a b - 2a b)cos(x) + 2a b cos(x) +--R + +--R 2 3 4 +--R (- 6a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 3 2 4 4 3 2 3 +--R (- 2a b + 2a b )cos(x) - 4a b cos(x) + (4a b - 2a b )cos(x) +--R + +--R 3 2 2 4 +--R 4a b cos(x) - 2a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 2 3 4 3 +--R (- 2a b + 2a b)cos(x) - 2a b cos(x) + (2a b - 2a b)cos(x) +--R + +--R 2 3 2 +--R 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 5 +--R a b cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 4 3 2 2 +--R (a b cos(x) - a b )cot(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 +--R (a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 2 3 4 +--R (a b - a b)cos(x) + (a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 2 3 4 +--R - a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 3 5 4 2 +--R (b - a b + a b)cos(x) + (b - a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 +--R (- b + 2a b - a b)cos(x) - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 3 2 5 3 2 +--R ((a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) - a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 4 3 2 3 4 2 +--R - a b cos(x) + (a b + a b )cos(x) + a b cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- a b - a b )cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (- a b + a b)cos(x) - 2a b cos(x) + (2a b - a b)cos(x) +--R + +--R 4 2 2 3 +--R 2a b cos(x) - a b cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 5 3 2 4 3 2 5 3 3 2 2 +--R (- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) + a b cos(x) +--R / +--R 4 2 4 4 +--R (a b cos(x) - a b)sin(x) +--R + +--R 3 2 3 3 2 5 2 3 2 3 2 5 +--R (a b cos(x) + (a b + a )cos(x) - a b cos(x) - a b - a ) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 4 2 4 4 2 +--R (a b cos(x) + a b cos(x) - a b cos(x) - a b)sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 4 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 2 3 3 2 3 4 2 2 3 2 3 +--R 2a b cos(x) + (2a b + 2a b)cos(x) - 2a b cos(x) - 2a b +--R + +--R 4 +--R - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 2 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 4 4 +--R (a b cos(x) - a b)sin(x) +--R + +--R 3 2 3 3 2 5 2 3 2 3 2 5 3 +--R (a b cos(x) + (a b + a )cos(x) - a b cos(x) - a b - a )sin(x) +--R + +--R 4 3 4 2 4 4 2 +--R (a b cos(x) + a b cos(x) - a b cos(x) - a b)sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 2 4 2 4 +--R (- a b cos(x) + a b )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (a b - a b)cos(x) + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 6 3 4 2 2 4 2 6 4 2 2 +--R ((- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) + a b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 4 +--R (- 2a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 2 3 3 5 +--R (- 2a b + 2a b)cos(x) - 2a b cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 3 +--R 2a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 2 4 +--R (- a b cos(x) + a b )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 3 3 5 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 3 5 +--R a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 6 3 4 2 2 4 2 6 4 2 2 +--R ((- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) + a b )sin(x) +--R Type: Expression(Integer) +--E 107 + +--S 108 of 546 +m0418b:= a0418.2-r0418 +--R +--R +--R (105) +--R sin(x) +--R - b sin(x)log(----------) - b sin(x)atanh(cos(x)) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R 2sin(x)\|- b + a atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R x +--R +---------+ a tan(-) + b +--R | 2 2 2 +--R 2sin(x)\|- b + a atan(------------) + a cot(x)sin(x) - a cos(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 +--R a sin(x) +--R Type: Expression(Integer) +--E 108 + +--S 109 of 546 +d0418b:= D(m0418b,x) +--R +--R +--R (106) +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 3 2 2 +--R (- a cos(x) + a )cot(x) + (- a b - a )cos(x) - 2a b cos(x) +--R + +--R 2 3 +--R - a b + a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b)cot(x) +--R + +--R 3 3 3 2 3 2 3 2 +--R - 2b cos(x) - 2b cos(x) + (2b - 2a b)cos(x) + 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 2 4 +--R (- a cos(x) - 2a cos(x) + 2a cos(x) + a )cot(x) - a b cos(x) +--R + +--R 2 3 3 2 2 2 3 +--R - 2a b cos(x) + a cos(x) + 2a b cos(x) + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + a cos(x) +--R + +--R 3 5 3 3 3 2 +--R 2a cos(x) - 2a cos(x) - a cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 2 2 3 3 +--R (- 2a b cos(x) + 2a b)cot(x) - 4a b cos(x) - 4b cos(x) - 4b +--R + +--R 2 +--R 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 4a b cos(x) - 4a b cos(x) + 4a b cos(x) + 4a b )cot(x) +--R + +--R 2 3 2 2 +--R - 4a b cos(x) - 4a b cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R (- 2a b cos(x) - 4a b cos(x) + 4a b cos(x) + 2a b)cot(x) +--R + +--R 2 4 2 3 2 2 2 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) + 4a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 2 6 +--R (2a b cos(x) - 4a b cos(x) + 2a b cos(x))sin(x) + 2a b cos(x) +--R + +--R 2 5 2 3 2 2 +--R 4a b cos(x) - 4a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 3 2 2 2 +--R (- a cos(x) + a )cot(x) + (- a b - a )cos(x) - 2a b cos(x) - a b +--R + +--R 3 +--R a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b)cot(x) +--R + +--R 3 3 3 2 3 2 3 2 +--R - 2b cos(x) - 2b cos(x) + (2b - 2a b)cos(x) + 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 2 4 +--R (- a cos(x) - 2a cos(x) + 2a cos(x) + a )cot(x) - a b cos(x) +--R + +--R 2 3 3 2 2 2 3 +--R - 2a b cos(x) + a cos(x) + 2a b cos(x) + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 3 5 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + a cos(x) + 2a cos(x) +--R + +--R 3 3 3 2 +--R - 2a cos(x) - a cos(x) +--R / +--R 4 2 4 4 +--R (a cos(x) - a )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 3 4 +--R (2a b cos(x) - 2a b)sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 3 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b)sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 4 4 +--R (a cos(x) - a )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a )sin(x) +--R Type: Expression(Integer) +--E 109 + +--S 110 of 546 +t0419:= cot(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R cot(x) +--R (107) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 110 + +--S 111 of 546 +r0419:= 2*(a^2-b^2)^(3/2)*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^4-_ + 3/2*b*atanh(cos(x))/a^2+b^3*atanh(cos(x))/a^4+cot(x)/a-_ + b^2*cot(x)/a^3-1/3*cot(x)^3/a+1/2*b*cot(x)*csc(x)/a^2 +--R +--R +--R (108) +--R x +--R +---------+ a tan(-) + b +--R 3 2 2 2 | 2 2 2 +--R (6b - 9a b)atanh(cos(x)) + (- 12b + 12a )\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 3 +--R 3a b cot(x)csc(x) - 2a cot(x) + (- 6a b + 6a )cot(x) +--R / +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 111 + +--S 112 of 546 +a0419:= integrate(t0419,x) +--R +--R +--R (109) +--R [ +--R 3 2 2 3 2 sin(x) +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 2 2 2 2 | 2 2 +--R ((6b - 6a )cos(x) - 6b + 6a )sin(x)\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R 2 2 3 3 2 3 +--R - 3a b cos(x)sin(x) + (- 6a b + 8a )cos(x) + (6a b - 6a )cos(x) +--R / +--R 4 2 4 +--R (6a cos(x) - 6a )sin(x) +--R , +--R +--R 3 2 2 3 2 sin(x) +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((12b - 12a )cos(x) - 12b + 12a )sin(x)\|- b + a +--R * +--R +---------+ +--R | 2 2 +--R (cos(x) + 1)\|- b + a +--R atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R 2 2 3 3 2 3 +--R - 3a b cos(x)sin(x) + (- 6a b + 8a )cos(x) + (6a b - 6a )cos(x) +--R / +--R 4 2 4 +--R (6a cos(x) - 6a )sin(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 112 + +--S 113 of 546 +m0419a:= a0419.1-r0419 +--R +--R +--R (110) +--R 3 2 2 3 2 sin(x) +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 2 2 2 2 | 2 2 +--R ((6b - 6a )cos(x) - 6b + 6a )sin(x)\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R 3 2 2 3 2 +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)atanh(cos(x)) +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 2 2 2 2 | 2 2 2 +--R ((12b - 12a )cos(x) - 12b + 12a )sin(x)\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 3 2 3 3 +--R (- 3a b cos(x) + 3a b)cot(x)csc(x) + (2a cos(x) - 2a )cot(x) +--R + +--R 2 3 2 2 3 2 +--R ((6a b - 6a )cos(x) - 6a b + 6a )cot(x) - 3a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 3 2 3 +--R (- 6a b + 8a )cos(x) + (6a b - 6a )cos(x) +--R / +--R 4 2 4 +--R (6a cos(x) - 6a )sin(x) +--R Type: Expression(Integer) +--E 113 + +--S 114 of 546 +d0419a:= D(m0419a,x) +--R +--R +--R (111) +--R 2 4 4 2 3 4 2 2 +--R (- 6a b + 9a b )cos(x) - 3a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (6a b - 9a b )cos(x) - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 4 4 2 2 4 2 2 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 4 2 4 4 2 2 4 2 +--R 3a b cos(x) - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b)cot(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 5 3 3 5 4 5 5 3 +--R (- 6a b + 9a b - 2a b)cos(x) + (- 6a b + 9a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (6a b - 12a b + 3a b)cos(x) + (6a b - 6a b - 9a b)cos(x) +--R + +--R 3 3 5 +--R - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 3 3 5 4 3 3 3 +--R 6a b cos(x) + (6a b + 6a b)cos(x) - 12a b cos(x) +--R + +--R 3 3 5 2 3 3 3 3 5 +--R (- 12a b - 12a b)cos(x) + 6a b cos(x) + 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 5 4 3 3 3 +--R 3a b cos(x) + (3a b + 3a b)cos(x) - 6a b cos(x) +--R + +--R 3 3 5 2 3 3 3 3 5 +--R (- 6a b - 6a b)cos(x) + 3a b cos(x) + 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 2 5 4 2 6 4 4 2 3 +--R - 6a b cos(x) + (- 6a b - 6a )cos(x) + 12a b cos(x) +--R + +--R 4 2 6 2 4 2 4 2 6 +--R (12a b + 12a )cos(x) - 6a b cos(x) - 6a b - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 2 4 5 2 4 4 2 4 2 4 3 +--R - 6a b cos(x) + (- 6a b - 6a b )cos(x) + 12a b cos(x) +--R + +--R 2 4 4 2 2 2 4 2 4 4 2 +--R (12a b + 12a b )cos(x) - 6a b cos(x) - 6a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 4 2 5 +--R (- 6b + 6a b + a b )cos(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 6b + 6a b + a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 3 +--R (12b - 18a b + 6a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (12b - 18a b + 6a b + 6a )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (- 6b + 12a b - 9a b )cos(x) - 6b + 12a b - 9a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) +--R + +--R 4 2 2 4 2 4 2 +--R - 12a b cos(x) + 6a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 5 4 2 4 4 2 3 4 2 2 +--R 3a b cos(x) + 3a b cos(x) - 6a b cos(x) - 6a b cos(x) +--R + +--R 4 2 4 2 +--R 3a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 5 5 4 5 3 +--R - 6a b cos(x) - 6a b cos(x) + 12a b cos(x) +--R + +--R 5 2 5 5 +--R 12a b cos(x) - 6a b cos(x) - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 3 5 3 3 4 3 3 3 +--R - 6a b cos(x) - 6a b cos(x) + 12a b cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R 12a b cos(x) - 6a b cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (3a b - 2a b)cos(x) + (- 6a b + 3a b + 7a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 6a b - 6a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (12a b - 6a b - 12a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (12a b - 21a b + 18a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 6a b + 3a b + 9a b)cos(x) - 6a b + 12a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 4 2 6 6 +--R (6a b - 8a b )cos(x) + (7a b - 8a )cos(x) +--R + +--R 2 4 4 2 5 4 2 6 4 +--R (- 18a b + 23a b )cos(x) + (- 16a b + 14a )cos(x) +--R + +--R 2 4 4 2 3 4 2 6 2 +--R (18a b - 24a b )cos(x) + (9a b - 6a )cos(x) +--R + +--R 2 4 4 2 +--R (- 6a b + 9a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (6a b - 8a b)cos(x) + (6a b - 8a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 12a b + 14a b)cos(x) + (- 12a b + 14a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (6a b - 6a b)cos(x) + (6a b - 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 3 3 3 2 +--R (- 12a b + 18a b )cos(x) - 6a b cos(x) +--R + +--R 5 3 3 3 3 +--R (12a b - 18a b )cos(x) - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 3 3 4 3 3 2 3 3 +--R 6a b cos(x) - 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 2 4 4 2 2 4 2 4 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )cot(x) +--R + +--R 2 4 4 2 4 2 2 4 2 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )cot(x) +--R + +--R 2 4 4 2 4 6 4 2 3 +--R (- 6a b + 8a b )cos(x) + (- 12b + 18a b )cos(x) +--R + +--R 6 2 4 4 2 2 +--R (- 12b + 24a b - 18a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (12b - 12a b - 18a b )cos(x) + 12b - 30a b + 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 5 2 4 4 2 4 +--R 12a b cos(x) + (12a b + 12a b )cos(x) +--R + +--R 2 4 3 2 4 4 2 2 +--R - 24a b cos(x) + (- 24a b - 24a b )cos(x) +--R + +--R 2 4 2 4 4 2 +--R 12a b cos(x) + 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 5 2 4 4 2 4 2 4 3 +--R 6a b cos(x) + (6a b + 6a b )cos(x) - 12a b cos(x) +--R + +--R 2 4 4 2 2 2 4 2 4 4 2 +--R (- 12a b - 12a b )cos(x) + 6a b cos(x) + 6a b + 6a b +--R * +--R csc(x) +--R + +--R 3 3 5 3 3 5 4 +--R - 12a b cos(x) + (- 12a b - 12a b)cos(x) +--R + +--R 3 3 3 3 3 5 2 3 3 +--R 24a b cos(x) + (24a b + 24a b)cos(x) - 12a b cos(x) +--R + +--R 3 3 5 +--R - 12a b - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 5 5 5 3 3 4 +--R - 12a b cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 5 3 5 3 3 2 5 +--R 24a b cos(x) + (24a b + 24a b )cos(x) - 12a b cos(x) +--R + +--R 5 3 3 +--R - 12a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 3 3 5 4 +--R (- 12a b + 14a b )cos(x) + (- 10a b + 8a b)cos(x) +--R + +--R 5 3 3 3 5 3 3 5 2 +--R (12a b - 12a b )cos(x) + (- 12a b + 36a b - 12a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R - 6a b cos(x) + 12a b - 30a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 4 3 3 3 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R - 24a b cos(x) + 12a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 4 3 3 3 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R - 12a b cos(x) + 6a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 2 5 4 2 4 4 2 3 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) +--R + +--R 4 2 2 4 2 4 2 +--R 24a b cos(x) - 12a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 4 5 2 4 4 2 4 3 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) +--R + +--R 2 4 2 2 4 2 4 +--R 24a b cos(x) - 12a b cos(x) - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (6a b - 4a b )cos(x) + (- 18a b + 26a b )cos(x) +--R + +--R 2 4 4 2 4 4 2 3 +--R - 12a b cos(x) + (36a b - 48a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (6a b + 12a b )cos(x) + (- 18a b + 30a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 7 3 3 5 6 +--R (12a b - 16a b )cos(x) + (14a b - 16a b)cos(x) +--R + +--R 5 3 3 5 3 3 5 4 +--R (- 36a b + 46a b )cos(x) + (- 32a b + 28a b)cos(x) +--R + +--R 5 3 3 3 3 3 5 2 +--R (36a b - 48a b )cos(x) + (18a b - 12a b)cos(x) +--R + +--R 5 3 3 +--R (- 12a b + 18a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (12a b - 16a b )cos(x) + (12a b - 16a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 24a b + 28a b )cos(x) + (- 24a b + 28a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 3 4 2 2 2 4 4 2 +--R (- 6a b + 9a b )cos(x) - 3a b cos(x) + (6a b - 9a b )cos(x) +--R + +--R 4 2 +--R - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 4 4 2 2 4 2 2 4 2 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) + 3a b cos(x) +--R + +--R 4 2 2 4 2 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b)cot(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 5 3 3 5 4 5 5 3 +--R (- 6a b + 9a b - 2a b)cos(x) + (- 6a b + 9a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (6a b - 12a b + 3a b)cos(x) + (6a b - 6a b - 9a b)cos(x) +--R + +--R 3 3 5 +--R - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 3 3 5 4 3 3 3 +--R 6a b cos(x) + (6a b + 6a b)cos(x) - 12a b cos(x) +--R + +--R 3 3 5 2 3 3 3 3 5 +--R (- 12a b - 12a b)cos(x) + 6a b cos(x) + 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 5 4 3 3 3 +--R 3a b cos(x) + (3a b + 3a b)cos(x) - 6a b cos(x) +--R + +--R 3 3 5 2 3 3 3 3 5 +--R (- 6a b - 6a b)cos(x) + 3a b cos(x) + 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 2 5 4 2 6 4 4 2 3 +--R - 6a b cos(x) + (- 6a b - 6a )cos(x) + 12a b cos(x) +--R + +--R 4 2 6 2 4 2 4 2 6 +--R (12a b + 12a )cos(x) - 6a b cos(x) - 6a b - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 2 4 5 2 4 4 2 4 2 4 3 +--R - 6a b cos(x) + (- 6a b - 6a b )cos(x) + 12a b cos(x) +--R + +--R 2 4 4 2 2 2 4 2 4 4 2 +--R (12a b + 12a b )cos(x) - 6a b cos(x) - 6a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 4 2 5 +--R (- 6b + 6a b + a b )cos(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 6b + 6a b + a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 3 +--R (12b - 18a b + 6a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (12b - 18a b + 6a b + 6a )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (- 6b + 12a b - 9a b )cos(x) - 6b + 12a b - 9a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) +--R + +--R 4 2 2 4 2 4 2 +--R - 12a b cos(x) + 6a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 5 4 2 4 4 2 3 4 2 2 +--R 3a b cos(x) + 3a b cos(x) - 6a b cos(x) - 6a b cos(x) +--R + +--R 4 2 4 2 +--R 3a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R - 6a b cos(x) - 6a b cos(x) + 12a b cos(x) + 12a b cos(x) +--R + +--R 5 5 +--R - 6a b cos(x) - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 3 5 3 3 4 3 3 3 3 3 2 +--R - 6a b cos(x) - 6a b cos(x) + 12a b cos(x) + 12a b cos(x) +--R + +--R 3 3 3 3 +--R - 6a b cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (3a b - 2a b)cos(x) + (- 6a b + 3a b + 7a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 6a b + 6a b - 6a b)cos(x) + (12a b - 6a b - 12a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (12a b - 21a b + 18a b)cos(x) + (- 6a b + 3a b + 9a b)cos(x) +--R + +--R 5 3 3 5 +--R - 6a b + 12a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 4 2 6 6 +--R (6a b - 8a b )cos(x) + (7a b - 8a )cos(x) +--R + +--R 2 4 4 2 5 4 2 6 4 +--R (- 18a b + 23a b )cos(x) + (- 16a b + 14a )cos(x) +--R + +--R 2 4 4 2 3 4 2 6 2 +--R (18a b - 24a b )cos(x) + (9a b - 6a )cos(x) +--R + +--R 2 4 4 2 +--R (- 6a b + 9a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (6a b - 8a b)cos(x) + (6a b - 8a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 12a b + 14a b)cos(x) + (- 12a b + 14a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (6a b - 6a b)cos(x) + (6a b - 6a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 4 3 3 4 3 2 2 5 4 3 +--R (6a b - 9a b )cos(x) + 3a b cos(x) + (- 6a b + 9a b )cos(x) +--R + +--R 4 3 +--R 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 4 4 3 2 4 3 2 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 4 3 4 4 3 2 4 3 +--R - 3a b cos(x) + 6a b cos(x) - 3a b +--R * +--R csc(x) +--R + +--R 5 2 4 5 2 2 5 2 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 3 4 4 3 4 2 3 4 2 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 6 3 4 5 2 4 6 5 2 3 +--R (6a b - 15a b + 11a b )cos(x) + (6a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 6a b + 18a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (- 6a b + 6a b + 6a b )cos(x) + 3a b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 6a b + 6a b )cos(x) - 6a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b - 3a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 3a b + 3a b )cos(x) - 3a b - 3a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (6a b - 6a b)cos(x) + (6a b + 6a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b - 12a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (6a b - 6a b)cos(x) + 6a b + 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (6a b - 6a b )cos(x) + 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 5 4 3 6 5 +--R (6b - 12a b + 11a b - 8a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (6b - 6a b - 7a b + 11a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 12b + 30a b - 30a b + 15a b)cos(x) +--R + +--R 7 2 5 6 2 +--R (- 12b + 18a b - 15a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (6b - 18a b + 21a b - 9a b)cos(x) + 6b - 12a b + 9a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 5 4 3 4 +--R (- 6a b + 6a b)cos(x) - 6a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (12a b - 12a b)cos(x) + 12a b cos(x) +--R + +--R 4 3 6 4 3 +--R (- 6a b + 6a b)cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 4 +--R (- 3a b + 3a b)cos(x) - 3a b cos(x) +--R + +--R 4 3 6 3 4 3 2 4 3 6 +--R (6a b - 6a b)cos(x) + 6a b cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 4 3 +--R - 3a b +--R * +--R csc(x) +--R + +--R 5 2 7 5 5 2 4 +--R (6a b - 6a )cos(x) + 6a b cos(x) +--R + +--R 5 2 7 3 5 2 2 +--R (- 12a b + 12a )cos(x) - 12a b cos(x) +--R + +--R 5 2 7 5 2 +--R (6a b - 6a )cos(x) + 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (6a b - 6a b )cos(x) + 6a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (- 12a b + 12a b )cos(x) - 12a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (6a b - 6a b )cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 7 5 +--R (- 9a b + 11a b )cos(x) + (6a b - 3a b - 7a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b + 6a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 12a b + 6a b + 12a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 12a b + 15a b - 9a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (6a b - 3a b - 9a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 4 3 6 6 +--R (- 6a b + 14a b - 8a b)cos(x) + (- 13a b + 17a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (18a b - 35a b + 14a b)cos(x) + (28a b - 32a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (- 18a b + 30a b - 6a b)cos(x) + (- 15a b + 15a b)cos(x) +--R + +--R 2 5 4 3 +--R (6a b - 9a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 3 4 5 2 6 +--R (- 6a b + 14a b - 8a )cos(x) + (- 6a b + 8a b )cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (12a b - 26a b + 14a )cos(x) + (12a b - 14a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (- 6a b + 12a b - 6a )cos(x) + (- 6a b + 6a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 3 3 4 2 +--R (12a b - 18a b )cos(x) + 6a b cos(x) +--R + +--R 6 3 4 3 4 +--R (- 12a b + 18a b )cos(x) + 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 4 4 3 4 2 3 4 2 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )cot(x) +--R + +--R 3 4 4 3 4 2 3 4 +--R - 6a b cos(x) + 12a b cos(x) - 6a b +--R * +--R csc(x) +--R + +--R 4 3 4 4 3 2 4 3 4 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 2 5 4 2 5 2 2 5 2 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 2 5 4 3 4 7 4 3 3 +--R (- 6a b + 10a b )cos(x) + (12b - 24a b )cos(x) +--R + +--R 7 2 5 2 7 2 5 4 3 7 +--R (12b - 12a b )cos(x) + (- 12b + 12a b + 12a b )cos(x) - 12b +--R + +--R 2 5 4 3 +--R 30a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (24a b - 24a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 12a b + 12a b )cos(x) - 12a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 6a b + 6a b )cos(x) - 6a b - 6a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 24a b + 24a b )cos(x) + (- 24a b - 24a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (12a b - 12a b )cos(x) + 12a b + 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- 24a b + 24a b )cos(x) + (- 24a b - 24a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (12a b - 12a b )cos(x) + 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (12a b - 14a b - 4a b )cos(x) + (- 2a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 12a b + 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 2 3 4 5 2 6 +--R (12a b - 24a b - 6a b )cos(x) + (6a b - 6a b )cos(x) - 12a b +--R + +--R 3 4 5 2 +--R 30a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (- 12a b + 12a b )cos(x) - 12a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (24a b - 24a b )cos(x) + 24a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (- 12a b + 12a b )cos(x) - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (- 6a b + 6a b )cos(x) - 6a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (12a b - 12a b )cos(x) + 12a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (- 6a b + 6a b )cos(x) - 6a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 4 +--R (12a b - 12a b)cos(x) + 12a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (- 24a b + 24a b)cos(x) - 24a b cos(x) +--R + +--R 4 3 6 4 3 +--R (12a b - 12a b)cos(x) + 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 +--R (12a b - 12a b )cos(x) + 12a b cos(x) +--R + +--R 2 5 4 3 3 2 5 2 +--R (- 24a b + 24a b )cos(x) - 24a b cos(x) +--R + +--R 2 5 4 3 2 5 +--R (12a b - 12a b )cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 5 +--R (- 18a b + 22a b )cos(x) + (30a b - 50a b + 8a b)cos(x) +--R + +--R 2 5 4 3 4 2 5 4 3 6 3 +--R (36a b - 36a b )cos(x) + (- 60a b + 96a b - 12a b)cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 +--R (- 18a b + 6a b )cos(x) + (30a b - 54a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 6 +--R (- 12a b + 28a b - 16a b )cos(x) + (- 26a b + 34a b )cos(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (36a b - 70a b + 28a b )cos(x) + (56a b - 64a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- 36a b + 60a b - 12a b )cos(x) + (- 30a b + 30a b )cos(x) +--R + +--R 6 3 4 +--R (12a b - 18a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 +--R (- 12a b + 28a b - 16a b)cos(x) + (- 12a b + 16a b )cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 4 +--R (24a b - 52a b + 28a b)cos(x) + (24a b - 28a b )cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 2 +--R (- 12a b + 24a b - 12a b)cos(x) + (- 12a b + 12a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 3 4 3 2 2 5 4 3 +--R (6a b - 9a b )cos(x) + 3a b cos(x) + (- 6a b + 9a b )cos(x) +--R + +--R 4 3 +--R 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 4 4 3 2 4 3 2 4 3 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) - 3a b cos(x) +--R + +--R 4 3 2 4 3 +--R 6a b cos(x) - 3a b +--R * +--R csc(x) +--R + +--R 5 2 4 5 2 2 5 2 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 3 4 4 3 4 2 3 4 2 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 6 3 4 5 2 4 6 5 2 3 +--R (6a b - 15a b + 11a b )cos(x) + (6a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 6a b + 18a b - 12a b )cos(x) + (- 6a b + 6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 +--R 3a b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 6a b + 6a b )cos(x) - 6a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b - 3a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 3a b + 3a b )cos(x) - 3a b - 3a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (6a b - 6a b)cos(x) + (6a b + 6a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b - 12a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (6a b - 6a b)cos(x) + 6a b + 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (6a b - 6a b )cos(x) + 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 5 4 3 6 5 +--R (6b - 12a b + 11a b - 8a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (6b - 6a b - 7a b + 11a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 12b + 30a b - 30a b + 15a b)cos(x) +--R + +--R 7 2 5 6 2 +--R (- 12b + 18a b - 15a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (6b - 18a b + 21a b - 9a b)cos(x) + 6b - 12a b + 9a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 5 4 3 4 +--R (- 6a b + 6a b)cos(x) - 6a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (12a b - 12a b)cos(x) + 12a b cos(x) +--R + +--R 4 3 6 4 3 +--R (- 6a b + 6a b)cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 4 4 3 6 3 +--R (- 3a b + 3a b)cos(x) - 3a b cos(x) + (6a b - 6a b)cos(x) +--R + +--R 4 3 2 4 3 6 4 3 +--R 6a b cos(x) + (- 3a b + 3a b)cos(x) - 3a b +--R * +--R csc(x) +--R + +--R 5 2 7 5 5 2 4 5 2 7 3 +--R (6a b - 6a )cos(x) + 6a b cos(x) + (- 12a b + 12a )cos(x) +--R + +--R 5 2 2 5 2 7 5 2 +--R - 12a b cos(x) + (6a b - 6a )cos(x) + 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (6a b - 6a b )cos(x) + 6a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (- 12a b + 12a b )cos(x) - 12a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (6a b - 6a b )cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 7 5 +--R (- 9a b + 11a b )cos(x) + (6a b - 3a b - 7a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b + 6a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 12a b + 6a b + 12a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 12a b + 15a b - 9a b )cos(x) + (6a b - 3a b - 9a b )cos(x) +--R + +--R 6 3 4 5 2 +--R 6a b - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 4 3 6 6 +--R (- 6a b + 14a b - 8a b)cos(x) + (- 13a b + 17a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (18a b - 35a b + 14a b)cos(x) + (28a b - 32a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (- 18a b + 30a b - 6a b)cos(x) + (- 15a b + 15a b)cos(x) +--R + +--R 2 5 4 3 +--R (6a b - 9a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 3 4 5 2 6 +--R (- 6a b + 14a b - 8a )cos(x) + (- 6a b + 8a b )cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (12a b - 26a b + 14a )cos(x) + (12a b - 14a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (- 6a b + 12a b - 6a )cos(x) + (- 6a b + 6a b )cos(x) +--R / +--R 6 4 6 2 6 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)sin(x) +--R + +--R 5 2 5 5 2 7 4 5 2 3 +--R 6a b cos(x) + (6a b + 6a )cos(x) - 12a b cos(x) +--R + +--R 5 2 7 2 5 2 5 2 7 +--R (- 12a b - 12a )cos(x) + 6a b cos(x) + 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 6 4 6 3 6 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 6 6 +--R 6a b cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 5 2 2 5 2 4 +--R (12a b cos(x) - 24a b cos(x) + 12a b )sin(x) +--R + +--R 4 3 5 4 3 6 4 4 3 3 +--R 12a b cos(x) + (12a b + 12a b)cos(x) - 24a b cos(x) +--R + +--R 4 3 6 2 4 3 4 3 6 +--R (- 24a b - 24a b)cos(x) + 12a b cos(x) + 12a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 5 5 2 4 5 2 3 5 2 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 5 2 5 2 +--R 12a b cos(x) + 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 4 6 2 6 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)sin(x) +--R + +--R 5 2 5 5 2 7 4 5 2 3 +--R 6a b cos(x) + (6a b + 6a )cos(x) - 12a b cos(x) +--R + +--R 5 2 7 2 5 2 5 2 7 +--R (- 12a b - 12a )cos(x) + 6a b cos(x) + 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 6 4 6 3 6 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 6 6 +--R 6a b cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 2 4 6 2 2 6 2 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (12a b - 12a b)cos(x) + (12a b + 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (- 6a b + 6a b)cos(x) - 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 8 5 6 2 4 6 2 8 3 +--R (- 6a b + 6a )cos(x) - 6a b cos(x) + (12a b - 12a )cos(x) +--R + +--R 6 2 2 6 2 8 6 2 +--R 12a b cos(x) + (- 6a b + 6a )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 4 5 3 2 5 3 4 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (24a b - 24a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 12a b + 12a b )cos(x) - 12a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 7 5 5 3 4 +--R (- 12a b + 12a b)cos(x) - 12a b cos(x) +--R + +--R 5 3 7 3 5 3 2 +--R (24a b - 24a b)cos(x) + 24a b cos(x) +--R + +--R 5 3 7 5 3 +--R (- 12a b + 12a b)cos(x) - 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 6 2 2 6 2 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (12a b - 12a b)cos(x) + (12a b + 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (- 6a b + 6a b)cos(x) - 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 8 5 6 2 4 6 2 8 3 +--R (- 6a b + 6a )cos(x) - 6a b cos(x) + (12a b - 12a )cos(x) +--R + +--R 6 2 2 6 2 8 6 2 +--R 12a b cos(x) + (- 6a b + 6a )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R Type: Expression(Integer) +--E 114 + +--S 115 of 546 +m0419b:= a0419.2-r0419 +--R +--R +--R (112) +--R 3 2 2 3 2 sin(x) +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R 3 2 2 3 2 +--R ((- 6b + 9a b)cos(x) + 6b - 9a b)sin(x)atanh(cos(x)) +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((12b - 12a )cos(x) - 12b + 12a )sin(x)\|- b + a +--R * +--R +---------+ +--R | 2 2 +--R (cos(x) + 1)\|- b + a +--R atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 2 2 2 2 | 2 2 2 +--R ((12b - 12a )cos(x) - 12b + 12a )sin(x)\|- b + a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 3 2 3 3 +--R (- 3a b cos(x) + 3a b)cot(x)csc(x) + (2a cos(x) - 2a )cot(x) +--R + +--R 2 3 2 2 3 2 +--R ((6a b - 6a )cos(x) - 6a b + 6a )cot(x) - 3a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 3 2 3 +--R (- 6a b + 8a )cos(x) + (6a b - 6a )cos(x) +--R / +--R 4 2 4 +--R (6a cos(x) - 6a )sin(x) +--R Type: Expression(Integer) +--E 115 + +--S 116 of 546 +d0419b:= D(m0419b,x) +--R +--R +--R (113) +--R 2 3 4 3 4 2 2 3 4 +--R (- 6a b + 9a b)cos(x) - 3a b cos(x) + (6a b - 9a b)cos(x) +--R + +--R 4 +--R - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)cot(x) + 3a b cos(x) +--R + +--R 4 2 4 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a cos(x) + 12a cos(x) - 6a )cot(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 4 3 2 5 4 4 3 2 3 +--R (- 6a b + 6a b + 4a )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 5 2 4 3 2 4 3 2 5 +--R - 6a cos(x) + (12a b - 24a b )cos(x) + 6a b - 18a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R - 24a b cos(x) + 12a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 2 +--R 6a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 5 4 4 4 3 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) +--R + +--R 4 2 4 4 +--R 24a b cos(x) - 12a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 24a b cos(x) - 12a b cos(x) - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (- 12b + 12a b + 2a b)cos(x) + (- 12b + 12a b - a b)cos(x) +--R + +--R 5 2 3 4 3 5 2 3 4 2 +--R (24b - 36a b + 12a b)cos(x) + (24b - 36a b + 12a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R (- 12b + 24a b - 18a b)cos(x) - 12b + 24a b - 15a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 4 5 4 4 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) +--R + +--R 4 3 4 2 4 4 +--R - 24a b cos(x) - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 3a b cos(x) + 6a b cos(x) - 3a b cos(x) - 12a b cos(x) +--R + +--R 4 2 4 4 +--R - 3a b cos(x) + 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R - 6a cos(x) - 12a cos(x) + 6a cos(x) + 24a cos(x) +--R + +--R 5 2 5 5 +--R 6a cos(x) - 12a cos(x) - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 3 2 6 3 2 5 3 2 4 3 2 3 +--R - 6a b cos(x) - 12a b cos(x) + 6a b cos(x) + 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R 6a b cos(x) - 12a b cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 6 +--R (- 6a b + 12a b - 4a )cos(x) +--R + +--R 4 3 2 5 5 4 3 2 4 +--R (- 12a b + 18a b - 4a )cos(x) + (6a b - 12a b )cos(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (24a b - 36a b + 12a )cos(x) + (6a b - 12a b + 18a )cos(x) +--R + +--R 4 3 2 4 3 2 5 +--R (- 12a b + 18a b )cos(x) - 6a b + 12a b - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 4 6 2 3 4 5 +--R (6a b - 7a b)cos(x) + 2a b cos(x) + (- 18a b + 19a b)cos(x) +--R + +--R 4 4 2 3 4 3 4 2 +--R - 8a b cos(x) + (18a b - 21a b)cos(x) + 6a b cos(x) +--R + +--R 2 3 4 +--R (- 6a b + 9a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (6a b - 8a )cos(x) + (12a b - 16a )cos(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (- 6a b + 6a )cos(x) + (- 24a b + 28a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 3 2 5 2 +--R (- 6a b + 8a )cos(x) + (12a b - 12a )cos(x) + (6a b - 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 3 2 2 +--R (- 12a b + 18a b )cos(x) - 6a b cos(x) +--R + +--R 4 3 2 3 2 +--R (12a b - 18a b )cos(x) - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R 6a b cos(x) - 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 4 4 2 4 4 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b)cot(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )cot(x) +--R + +--R 2 3 4 4 5 2 3 3 +--R (- 12a b + 20a b)cos(x) + (- 24b + 24a b )cos(x) +--R + +--R 5 2 3 4 2 5 2 3 5 +--R (- 24b + 48a b - 36a b)cos(x) + (24b - 48a b )cos(x) + 24b +--R + +--R 2 3 4 +--R - 60a b + 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R 24a b cos(x) + 24a b cos(x) - 48a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R - 48a b cos(x) + 24a b cos(x) + 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 2 3 2 3 +--R 12a b cos(x) + 12a b +--R * +--R csc(x) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R - 24a b cos(x) - 24a b cos(x) + 48a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R 48a b cos(x) - 24a b cos(x) - 24a b +--R * +--R 4 +--R cot(x) +--R + +--R 4 5 4 4 4 3 +--R - 24a b cos(x) - 24a b cos(x) + 48a b cos(x) +--R + +--R 4 2 4 4 +--R 48a b cos(x) - 24a b cos(x) - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 24a b + 28a b )cos(x) + (- 24a b + 22a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (24a b - 24a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 2 3 2 +--R - 12a b cos(x) - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 6 3 2 5 3 2 4 +--R 12a b cos(x) + 24a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 +--R - 48a b cos(x) - 12a b cos(x) + 24a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 6 3 2 5 3 2 4 3 2 3 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) - 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 6 4 5 4 4 +--R - 12a b cos(x) - 24a b cos(x) + 12a b cos(x) +--R + +--R 4 3 4 2 4 4 +--R 48a b cos(x) + 12a b cos(x) - 24a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 6 2 3 5 2 3 4 +--R - 12a b cos(x) - 24a b cos(x) + 12a b cos(x) +--R + +--R 2 3 3 2 3 2 2 3 2 3 +--R 48a b cos(x) + 12a b cos(x) - 24a b cos(x) - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 2 3 4 5 4 4 +--R 4a b cos(x) + (- 12a b + 16a b)cos(x) - 12a b cos(x) +--R + +--R 2 3 4 3 4 2 2 3 4 +--R (24a b - 24a b)cos(x) + 24a b cos(x) + (- 12a b + 24a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 3 2 6 +--R (12a b - 14a b )cos(x) + 4a b cos(x) +--R + +--R 4 3 2 5 3 2 4 +--R (- 36a b + 38a b )cos(x) - 16a b cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (36a b - 42a b )cos(x) + 12a b cos(x) +--R + +--R 4 3 2 +--R (- 12a b + 18a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (12a b - 16a b)cos(x) + (24a b - 32a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 12a b + 12a b)cos(x) + (- 48a b + 56a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 12a b + 16a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 2 3 4 2 +--R (12a b - 12a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 3 4 2 2 3 4 4 +--R ((- 6a b + 9a b)cos(x) - 3a b cos(x) + (6a b - 9a b)cos(x) - 3a b) +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)cot(x) + 3a b cos(x) +--R + +--R 4 2 4 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a cos(x) + 12a cos(x) - 6a )cot(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 4 3 2 5 4 4 3 2 3 +--R (- 6a b + 6a b + 4a )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 5 2 4 3 2 4 3 2 5 +--R - 6a cos(x) + (12a b - 24a b )cos(x) + 6a b - 18a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 3 2 3 2 +--R 12a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 2 +--R 6a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) + 24a b cos(x) +--R + +--R 4 4 +--R - 12a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) + 24a b cos(x) +--R + +--R 2 3 2 3 +--R - 12a b cos(x) - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (- 12b + 12a b + 2a b)cos(x) + (- 12b + 12a b - a b)cos(x) +--R + +--R 5 2 3 4 3 5 2 3 4 2 +--R (24b - 36a b + 12a b)cos(x) + (24b - 36a b + 12a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R (- 12b + 24a b - 18a b)cos(x) - 12b + 24a b - 15a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) - 24a b cos(x) +--R + +--R 4 2 4 4 +--R - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 3a b cos(x) + 6a b cos(x) - 3a b cos(x) - 12a b cos(x) +--R + +--R 4 2 4 4 +--R - 3a b cos(x) + 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R - 6a cos(x) - 12a cos(x) + 6a cos(x) + 24a cos(x) +--R + +--R 5 2 5 5 +--R 6a cos(x) - 12a cos(x) - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 3 2 6 3 2 5 3 2 4 3 2 3 +--R - 6a b cos(x) - 12a b cos(x) + 6a b cos(x) + 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R 6a b cos(x) - 12a b cos(x) - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (- 6a b + 12a b - 4a )cos(x) + (- 12a b + 18a b - 4a )cos(x) +--R + +--R 4 3 2 4 4 3 2 5 3 +--R (6a b - 12a b )cos(x) + (24a b - 36a b + 12a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 4 +--R (6a b - 12a b + 18a )cos(x) + (- 12a b + 18a b )cos(x) - 6a b +--R + +--R 3 2 5 +--R 12a b - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 4 6 2 3 4 5 +--R (6a b - 7a b)cos(x) + 2a b cos(x) + (- 18a b + 19a b)cos(x) +--R + +--R 4 4 2 3 4 3 4 2 +--R - 8a b cos(x) + (18a b - 21a b)cos(x) + 6a b cos(x) +--R + +--R 2 3 4 +--R (- 6a b + 9a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 3 2 5 6 +--R (6a b - 8a )cos(x) + (12a b - 16a )cos(x) + (- 6a b + 6a )cos(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (- 24a b + 28a )cos(x) + (- 6a b + 8a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (12a b - 12a )cos(x) + (6a b - 6a )cos(x) +--R / +--R 6 4 6 2 6 4 +--R (6a cos(x) - 12a cos(x) + 6a )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 5 5 +--R 12a b cos(x) + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 6 5 6 4 6 3 6 2 +--R 6a cos(x) + 12a cos(x) - 6a cos(x) - 24a cos(x) - 6a cos(x) +--R + +--R 6 6 +--R 12a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 4 +--R (12a b cos(x) - 24a b cos(x) + 12a b)sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 4 2 2 +--R 24a b cos(x) + 24a b cos(x) - 48a b cos(x) - 48a b cos(x) +--R + +--R 4 2 4 2 +--R 24a b cos(x) + 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R 12a b cos(x) + 24a b cos(x) - 12a b cos(x) - 48a b cos(x) +--R + +--R 5 2 5 5 +--R - 12a b cos(x) + 24a b cos(x) + 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 4 6 2 6 4 +--R (6a cos(x) - 12a cos(x) + 6a )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 5 5 +--R 12a b cos(x) + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 6 5 6 4 6 3 6 2 +--R 6a cos(x) + 12a cos(x) - 6a cos(x) - 24a cos(x) - 6a cos(x) +--R + +--R 6 6 +--R 12a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R Type: Expression(Integer) +--E 116 + +--S 117 of 546 +t0420:= cot(x)/(a+a*sin(x)) +--R +--R +--R cot(x) +--R (114) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 117 + +--S 118 of 546 +r0420:= -2*atanh(1+2*sin(x))/a +--R +--R +--R 2atanh(2sin(x) + 1) +--R (115) - ------------------- +--R a +--R Type: Expression(Integer) +--E 118 + +--S 119 of 546 +a0420:= integrate(t0420,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) +--R - 2log(-------------------) + log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (116) --------------------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 119 + +--S 120 of 546 +m0420:= a0420-r0420 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) +--R - 2log(-------------------) + log(----------) + 2atanh(2sin(x) + 1) +--R cos(x) + 1 cos(x) + 1 +--R (117) ------------------------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 120 + +--S 121 of 546 +d0420:= D(m0420,x) +--R +--R +--R (118) +--R 3 2 2 3 +--R - sin(x) + cos(x)sin(x) + (- cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 2 2 +--R (a cos(x) + a)sin(x) + (a cos(x) + 3a cos(x) + 2a)sin(x) + a cos(x) +--R + +--R 2a cos(x) + a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 546 +t0421:= cot(x)^2/(a+a*sin(x)) +--R +--R +--R 2 +--R cot(x) +--R (119) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 122 + +--S 123 of 546 +r0421:= atanh(cos(x))/a-cot(x)/a +--R +--R +--R atanh(cos(x)) - cot(x) +--R (120) ---------------------- +--R a +--R Type: Expression(Integer) +--E 123 + +--S 124 of 546 +a0421:= integrate(t0421,x) +--R +--R +--R sin(x) +--R - sin(x)log(----------) - cos(x) +--R cos(x) + 1 +--R (121) -------------------------------- +--R a sin(x) +--R Type: Union(Expression(Integer),...) +--E 124 + +--S 125 of 546 +m0421:= a0421-r0421 +--R +--R +--R (122) +--R sin(x) +--R - sin(x)log(----------) - sin(x)atanh(cos(x)) + cot(x)sin(x) - cos(x) +--R cos(x) + 1 +--R --------------------------------------------------------------------- +--R a sin(x) +--R Type: Expression(Integer) +--E 125 + +--S 126 of 546 +d0421:= D(m0421,x) +--R +--R +--R (123) +--R 3 2 2 2 +--R - cos(x)sin(x) + (- cos(x) + 1)cot(x) sin(x) +--R + +--R 3 4 2 +--R (- cos(x) + cos(x))sin(x) + cos(x) - cos(x) +--R / +--R 2 2 +--R (a cos(x) - a)sin(x) +--R Type: Expression(Integer) +--E 126 + +--S 127 of 546 +t0422:= cot(x)^4/(a+a*sin(x)) +--R +--R +--R 4 +--R cot(x) +--R (124) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 127 + +--S 128 of 546 +r0422:= -1/2*atanh(cos(x))/a-1/3*cot(x)^3/a+1/2*cot(x)*csc(x)/a +--R +--R +--R 3 +--R - 3atanh(cos(x)) + 3cot(x)csc(x) - 2cot(x) +--R (125) ------------------------------------------- +--R 6a +--R Type: Expression(Integer) +--E 128 + +--S 129 of 546 +a0422:= integrate(t0422,x) +--R +--R +--R 2 sin(x) 3 +--R (3cos(x) - 3)sin(x)log(----------) - 3cos(x)sin(x) + 2cos(x) +--R cos(x) + 1 +--R (126) -------------------------------------------------------------- +--R 2 +--R (6a cos(x) - 6a)sin(x) +--R Type: Union(Expression(Integer),...) +--E 129 + +--S 130 of 546 +m0422:= a0422-r0422 +--R +--R +--R (127) +--R 2 sin(x) 2 +--R (3cos(x) - 3)sin(x)log(----------) + (3cos(x) - 3)sin(x)atanh(cos(x)) +--R cos(x) + 1 +--R + +--R 2 2 3 +--R ((- 3cos(x) + 3)cot(x)csc(x) + (2cos(x) - 2)cot(x) - 3cos(x))sin(x) +--R + +--R 3 +--R 2cos(x) +--R / +--R 2 +--R (6a cos(x) - 6a)sin(x) +--R Type: Expression(Integer) +--E 130 + +--S 131 of 546 +d0422:= D(m0422,x) +--R +--R +--R (128) +--R 3 2 3 +--R (3cos(x) - 3cos(x) - 3cos(x) - 3)sin(x) +--R + +--R 4 2 2 4 2 +--R ((6cos(x) - 12cos(x) + 6)cot(x) + 3cos(x) - 6cos(x) + 3)csc(x) +--R + +--R 4 2 4 +--R (- 6cos(x) + 12cos(x) - 6)cot(x) +--R + +--R 4 2 2 4 2 +--R (- 6cos(x) + 12cos(x) - 6)cot(x) - 2cos(x) + 6cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 6 4 +--R (3cos(x) - 6cos(x) + 3cos(x))sin(x) - 2cos(x) + 2cos(x) +--R / +--R 4 2 2 +--R (6a cos(x) - 12a cos(x) + 6a)sin(x) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 546 +t0423:= sec(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R sec(x) +--R (129) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 132 + +--S 133 of 546 +r0423:= 2*b^4*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+_ + 1/12*cos(x)/(a+b)/(1-sin(x))^2+1/12*cos(x)/(a+b)/(1-sin(x))+_ + 1/4*(a+2*b)*cos(x)/(a+b)^2/(1-sin(x))-1/12*cos(x)/(a-b)/(1+sin(x))^2-_ + 1/4*(a-2*b)*cos(x)/(a-b)^2/(1+sin(x))-1/12*cos(x)/(a-b)/(1+sin(x)) +--R +--R +--R (130) +--R x +--R a tan(-) + b +--R 4 4 4 2 4 2 +--R (6b sin(x) - 12b sin(x) + 6b )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 3 2 +--R (5a b - 2a )cos(x)sin(x) - 3b cos(x)sin(x) +--R + +--R 2 3 3 2 +--R (- 6a b + 3a )cos(x)sin(x) + (4b - a b)cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 4 4 2 2 4 2 4 +--R (3b - 6a b + 3a )sin(x) + (- 6b + 12a b - 6a )sin(x) + 3b +--R + +--R 2 2 4 +--R - 6a b + 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 133 + +--S 134 of 546 +a0423:= integrate(t0423,x) +--R +--R +--R (131) +--R [ +--R 4 3 +--R 3b cos(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 2 3 2 2 3 3 2 3 +--R ((- 5a b + 2a )cos(x) - a b + a )sin(x) + (4b - a b)cos(x) +--R + +--R 3 2 3 2 +--R 3b cos(x) + b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 4 3 (a sin(x) + b cos(x) + b)\|- b + a +--R - 6b cos(x) atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 2 2 3 3 2 3 +--R ((- 5a b + 2a )cos(x) - a b + a )sin(x) + (4b - a b)cos(x) +--R + +--R 3 2 3 2 +--R 3b cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 134 + +--S 135 of 546 +m0423a:= a0423.1-r0423 +--R +--R +--R (132) +--R +---------+ +--R 4 3 4 4 3 2 4 3 | 2 2 +--R (3b cos(x) sin(x) - 6b cos(x) sin(x) + 3b cos(x) )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 4 3 4 4 3 2 4 3 | 2 2 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) )\|b - a +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 5 +--R ((- 5a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 3 2 3 2 4 +--R ((4b - a b)cos(x) + 3b cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((- 5a b + 2a )cos(x) + (10a b - 4a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 4 3 2 3 3 2 3 2 2 +--R (3b cos(x) + (- 8b + 2a b)cos(x) - 6b cos(x) - 2b + 2a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R ((6a b - 3a )cos(x) + (- 5a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 3 2 3 2 +--R (- 4b + a b)cos(x) + (4b - a b)cos(x) + 3b cos(x) + b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 135 + +--S 136 of 546 +d0423a:= D(m0423a,x) +--R +--R +--R (133) +--R 3 4 5 2 2 3 4 5 2 10 +--R ((- 5a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 +--R (- 5a b + 7a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 2a b - 3a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (3a b - 8a b + 7a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (3a b + 12a b - 3a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (3a b - 9a b + 9a b - 3a )cos(x) + 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 2 5 5 7 2 5 4 +--R (- 3b + 3a b )cos(x) + (- 3b - 3a b )cos(x) +--R + +--R 2 5 4 3 6 3 +--R (17a b - 22a b + 5a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (8a b + 9a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 +--R (3a b + 5a b - 2a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 9a b + 23a b - 19a b + 5a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 9a b - 7a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (5a b - 7a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (- a b + 3a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (9b - 8a b - 2a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (9b + 8a b + 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 21a b + 24a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 12a b - 9a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 6a b + 11a b - 7a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 15a b - 4a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (7a b - 4a b - 4a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (16a b + a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (9a b - 21a b + 15a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (9a b - a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (9a b - 27a b + 27a b - 9a )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- 9a b + 12a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 9b + 7a b + 4a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (- 9b - 6a b - 6a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (11a b - 10a b - a b)cos(x) + (8a b + 3a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (10a b - 17a b + 10a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (19a b - 3a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 4a b - 4a b + 11a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 13a b - 7a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 6 2 +--R (- 3a b + 5a b - a b - a )cos(x) - 3a b cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (4a b - 5a b + a b)cos(x) + (4a b - 7a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (3b - 2a b - 2a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (3b + a b + 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 6 2 +--R (- 2a b + a b + a b)cos(x) + (- 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 6 3 4 5 2 6 +--R (- 6a b + 9a b - 3a )cos(x) + (- 3a b - 6a b + 3a b )cos(x) +--R + +--R 3 4 5 2 7 5 6 3 4 5 2 4 +--R (5a b - 7a b + 2a )cos(x) + (3a b + 5a b - 2a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (a b - 2a b + a )cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 2 5 4 3 10 +--R ((- 10a b + 4a b )cos(x) - 6a b + 6a b )sin(x) +--R + +--R 6 3 4 5 2 3 +--R (- 10a b + 14a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 4a b - 6a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (- 6a b + 12a b - 6a b )cos(x) - 6a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 7 4 7 2 5 4 3 6 3 +--R 6b cos(x) + (6b - 16a b + 14a b - 4a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (6b + 24a b - 6a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (6b - 18a b + 18a b - 6a b)cos(x) + 6b + 12a b - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 6 3 4 5 2 3 +--R (34a b - 44a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (16a b + 18a b - 10a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (24a b - 48a b + 24a b )cos(x) + 6a b + 12a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 7 2 5 4 3 6 +--R (6b + 10a b - 4a b )cos(x) +--R + +--R 7 2 5 4 3 4 +--R (- 24b + 2a b - 2a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 18b + 46a b - 38a b + 10a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (- 18b - 14a b - 4a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 4 3 +--R (- 18b + 54a b - 54a b + 18a b)cos(x) - 18b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (10a b - 14a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 2a b + 6a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 42a b + 48a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 24a b - 18a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 6 5 2 +--R (- 36a b + 72a b - 36a b )cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 12b + 22a b - 14a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (- 30b - 8a b + 2a b )cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 4b + 10a b - 8a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (32b + 2a b + 2a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (18b - 42a b + 30a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (18b - 2a b + 8a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (18b - 54a b + 54a b - 18a b)cos(x) + 18b - 12a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (- 18a b + 24a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (2a b - 8a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (22a b - 20a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (16a b + 6a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (24a b - 48a b + 24a b )cos(x) + 18a b - 12a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (20b - 34a b + 20a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (38b - 6a b + 4a b )cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (10b - 26a b + 22a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (- 14b - 14a b + 4a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 7 2 +--R (- 6b + 10a b - 2a b - 2a b)cos(x) - 6b cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 +--R (- 6b + 18a b - 18a b + 6a b)cos(x) - 6b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (8a b - 10a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (8a b - 14a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 3 6 5 2 2 +--R (- 4a b + 2a b + 2a b )cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (- 6a b + 12a b - 6a b )cos(x) - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- 12a b + 18a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (- 6b - 12a b + 6a b )cos(x) +--R + +--R 7 2 5 4 3 6 5 2 5 4 3 4 +--R (- 6b + 16a b - 14a b + 4a b)cos(x) + (10a b - 4a b )cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 2 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 10 +--R ((- 5a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (- 5a b + 7a b - 2a b)cos(x) + (- 2a b - 3a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (3a b - 8a b + 7a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (3a b + 12a b - 3a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (3a b - 9a b + 9a b - 3a )cos(x) + 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 2 5 5 7 2 5 4 +--R (- 3b + 3a b )cos(x) + (- 3b - 3a b )cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (17a b - 22a b + 5a b)cos(x) + (8a b + 9a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 +--R (3a b + 5a b - 2a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 9a b + 23a b - 19a b + 5a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 9a b - 7a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (5a b - 7a b + 2a b)cos(x) + (- a b + 3a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (9b - 8a b - 2a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (9b + 8a b + 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 21a b + 24a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 12a b - 9a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 6a b + 11a b - 7a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 15a b - 4a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (7a b - 4a b - 4a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (16a b + a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (9a b - 21a b + 15a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (9a b - a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (9a b - 27a b + 27a b - 9a )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (- 9a b + 12a b - 3a b)cos(x) + (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 9b + 7a b + 4a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (- 9b - 6a b - 6a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (11a b - 10a b - a b)cos(x) + (8a b + 3a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (12a b - 24a b + 12a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (10a b - 17a b + 10a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (19a b - 3a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 4a b - 4a b + 11a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 13a b - 7a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 6 2 +--R (- 3a b + 5a b - a b - a )cos(x) - 3a b cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (4a b - 5a b + a b)cos(x) + (4a b - 7a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (3b - 2a b - 2a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (3b + a b + 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 6 2 +--R (- 2a b + a b + a b)cos(x) + (- 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (- 3a b + 6a b - 3a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 6 3 4 5 2 6 +--R (- 6a b + 9a b - 3a )cos(x) + (- 3a b - 6a b + 3a b )cos(x) +--R + +--R 3 4 5 2 7 5 6 3 4 5 2 4 +--R (5a b - 7a b + 2a )cos(x) + (3a b + 5a b - 2a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (a b - 2a b + a )cos(x) + (a b - a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((5a b - 7a b + 2a b)cos(x) + 3a b - 6a b + 3a b)sin(x) +--R + +--R 2 6 4 4 6 2 3 +--R (5a b - 7a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (2a b + a b - 5a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 8 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a +--R * +--R 9 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b + 8a b - 7a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 3a b - 9a b + 15a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) - 3a b - 3a b + 15a b +--R + +--R 7 +--R - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 8 2 6 5 8 4 4 4 +--R (3b - 3a b )cos(x) + (3b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 17a b + 22a b - 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 8a b - a b + 14a b - 5a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 3a b - 3a b + 15a b - 9a +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 6 7 3 5 5 +--R (- 3a b - 2a b + 7a b - 2a b)cos(x) + (3a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b - 7a b + 2a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (9a b - 23a b + 19a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (9a b - 2a b - 5a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (9a b - 27a b + 27a b - 9a b)cos(x) + 9a b - 9a b - 9a b +--R + +--R 7 +--R 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 5a b + 7a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (a b - 4a b + 5a b - 2a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 8a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 9b + a b + 6a b + 3a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (21a b - 24a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (12a b - 3a b - 12a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (18a b - 36a b + 18a b )cos(x) + 9a b - 9a b - 9a b + 9a +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (6a b - 11a b + 7a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (15a b - 11a b - 5a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 7a b + 4a b + 4a b - a b)cos(x) +--R + +--R 7 3 5 7 4 +--R (- 16a b + 15a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 9a b + 21a b - 15a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 9a b + 10a b - 5a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) - 9a b + 15a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (9a b - 12a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- a b + 5a b - 7a b + 3a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (9b - 7a b - 4a b + 2a b )cos(x) +--R + +--R 8 2 6 6 2 8 4 +--R (9b - 3a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 11a b + 10a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 8a b + 5a b + 2a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 9a b + 15a b - 3a b - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 10a b + 17a b - 10a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 19a b + 22a b - 5a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (4a b + 4a b - 11a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (13a b - 6a b - 9a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 7 3 5 2 +--R (3a b - 5a b + a b + a b)cos(x) + (3a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (3a b - 9a b + 9a b - 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 4a b + 5a b - a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 4a b + 11a b - 10a b + 3a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 2a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 3b + 2a b - 3a b + 6a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 8 2 +--R (2a b - a b - a b )cos(x) + (2a b - 2a b + a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 7 3 5 5 3 7 6 +--R (6a b - 9a b + 3a b)cos(x) + (3a b + 3a b - 9a b + 3a b)cos(x) +--R + +--R 3 5 5 3 7 5 +--R (- 5a b + 7a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b - 2a b + 7a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((10a b - 14a b + 4a b )cos(x) + 6a b - 12a b + 6a b )sin(x) +--R + +--R 7 3 5 5 3 3 +--R (10a b - 14a b + 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b + 2a b - 10a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 3 5 5 3 7 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 8 2 6 4 8 2 6 4 4 6 2 3 +--R (- 6b + 6a b )cos(x) + (- 6b + 16a b - 14a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 6b - 18a b + 30a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) - 6b - 6a b + 30a b +--R + +--R 6 2 +--R - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 3 5 5 3 3 +--R (- 34a b + 44a b - 10a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 16a b - 2a b + 28a b - 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (- 24a b + 48a b - 24a b )cos(x) - 6a b - 6a b + 30a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 6b - 4a b + 14a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (24b - 26a b + 4a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (18b - 46a b + 38a b - 10a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (18b - 4a b - 10a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (18b - 54a b + 54a b - 18a b )cos(x) + 18b - 18a b - 18a b +--R + +--R 6 2 +--R 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (- 10a b + 14a b - 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b - 8a b + 10a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (42a b - 48a b + 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (24a b - 6a b - 24a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (36a b - 72a b + 36a b )cos(x) + 18a b - 18a b - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 7 +--R (12b - 22a b + 14a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (30b - 22a b - 10a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (4b - 10a b + 8a b - 2a b )cos(x) +--R + +--R 8 2 6 6 2 4 +--R (- 32b + 30a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 18b + 42a b - 30a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 18b + 20a b - 10a b + 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) - 18b + 30a b - 6a b +--R + +--R 6 2 +--R - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (18a b - 24a b + 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 2a b + 10a b - 14a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 22a b + 20a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 16a b + 10a b + 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (- 24a b + 48a b - 24a b )cos(x) - 18a b + 30a b - 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 7 +--R (- 20b + 34a b - 20a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 38b + 44a b - 10a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 10b + 26a b - 22a b + 6a b )cos(x) +--R + +--R 8 4 4 6 2 4 +--R (14b - 18a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 8 2 6 2 +--R (6b - 10a b + 2a b + 2a b )cos(x) + (6b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (6b - 18a b + 18a b - 6a b )cos(x) + 6b - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (- 8a b + 10a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 8a b + 22a b - 20a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (4a b - 12a b + 12a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (4a b - 2a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b - 4a b + 2a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (12a b - 18a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (6b + 6a b - 18a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (6b - 16a b + 14a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (- 10a b + 14a b - 4a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 2a b + 4a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((5a b - 7a b + 2a b)cos(x) + 3a b - 6a b + 3a b)sin(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 8 2 +--R (5a b - 7a b + 2a b )cos(x) + (2a b + a b - 5a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 8 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a +--R * +--R 9 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b + 8a b - 7a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 3a b - 9a b + 15a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) - 3a b - 3a b + 15a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 8 2 6 5 8 4 4 4 +--R (3b - 3a b )cos(x) + (3b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 17a b + 22a b - 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 8a b - a b + 14a b - 5a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 3a b - 3a b + 15a b - 9a +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 6 7 3 5 5 +--R (- 3a b - 2a b + 7a b - 2a b)cos(x) + (3a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b - 7a b + 2a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (9a b - 23a b + 19a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (9a b - 2a b - 5a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 27a b + 27a b - 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 5a b + 7a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (a b - 4a b + 5a b - 2a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 8a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 9b + a b + 6a b + 3a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (21a b - 24a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (12a b - 3a b - 12a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (18a b - 36a b + 18a b )cos(x) + 9a b - 9a b - 9a b + 9a +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (6a b - 11a b + 7a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (15a b - 11a b - 5a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 7a b + 4a b + 4a b - a b)cos(x) +--R + +--R 7 3 5 7 4 +--R (- 16a b + 15a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 9a b + 21a b - 15a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 9a b + 10a b - 5a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) - 9a b + 15a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (9a b - 12a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- a b + 5a b - 7a b + 3a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (9b - 7a b - 4a b + 2a b )cos(x) +--R + +--R 8 2 6 6 2 8 4 +--R (9b - 3a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 11a b + 10a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 8a b + 5a b + 2a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (- 12a b + 24a b - 12a b )cos(x) - 9a b + 15a b - 3a b - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 10a b + 17a b - 10a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 19a b + 22a b - 5a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (4a b + 4a b - 11a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (13a b - 6a b - 9a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 7 3 5 2 +--R (3a b - 5a b + a b + a b)cos(x) + (3a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (3a b - 9a b + 9a b - 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 4a b + 5a b - a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 4a b + 11a b - 10a b + 3a )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 2a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 3b + 2a b - 3a b + 6a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 8 2 +--R (2a b - a b - a b )cos(x) + (2a b - 2a b + a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 7 3 5 5 3 7 6 +--R (6a b - 9a b + 3a b)cos(x) + (3a b + 3a b - 9a b + 3a b)cos(x) +--R + +--R 3 5 5 3 7 5 7 3 5 5 3 7 4 +--R (- 5a b + 7a b - 2a b)cos(x) + (- 3a b - 2a b + 7a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R / +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (3a b - 9a b + 9a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 4 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (9a b - 27a b + 27a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 4 8 +--R (6a b - 12a b + 6a b )cos(x) sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (6b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (6b - 6a b - 6a b + 6a b )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (- 12a b + 24a b - 12a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 18b + 18a b + 18a b - 18a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 4 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (18b - 54a b + 54a b - 18a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (18b - 18a b - 18a b + 18a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (18a b - 54a b + 54a b - 18a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (12a b - 24a b + 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 6b + 6a b + 6a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (3a b - 9a b + 9a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 4 +--R (- 9a b + 27a b - 27a b + 9a )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (9a b - 27a b + 27a b - 9a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 3a b + 9a b - 9a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 3a b + 6a b - 6a b + 3a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (9a b - 27a b + 27a b - 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (9a b - 18a b + 18a b - 9a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (9a b - 27a b + 27a b - 9a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 9a b + 18a b - 18a b + 9a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (3a b - 6a b + 6a b - 3a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (- 6b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 6b + 12a b - 12a b + 6a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (12a b - 36a b + 36a b - 12a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (18b - 54a b + 54a b - 18a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (18b - 36a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (18a b - 54a b + 54a b - 18a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (- 18b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 18b + 36a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 18a b + 54a b - 54a b + 18a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 12a b + 36a b - 36a b + 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (6b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (6b - 12a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 3a b + 6a b - 6a b + 3a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (9a b - 27a b + 27a b - 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (9a b - 18a b + 18a b - 9a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (9a b - 27a b + 27a b - 9a b)cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 9a b + 18a b - 18a b + 9a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (3a b - 6a b + 6a b - 3a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 546 +m0423b:= a0423.2-r0423 +--R +--R +--R (134) +--R 4 3 4 4 3 2 4 3 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +--R 4 3 4 4 3 2 4 3 2 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 5 +--R ((- 5a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 3 2 3 2 4 +--R ((4b - a b)cos(x) + 3b cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((- 5a b + 2a )cos(x) + (10a b - 4a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 4 3 2 3 3 2 3 2 2 +--R (3b cos(x) + (- 8b + 2a b)cos(x) - 6b cos(x) - 2b + 2a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R ((6a b - 3a )cos(x) + (- 5a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 3 2 3 2 +--R (- 4b + a b)cos(x) + (4b - a b)cos(x) + 3b cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 137 + +--S 138 of 546 +d0423b:= D(m0423b,x) +--R +--R +--R (135) +--R 3 2 5 2 3 2 5 10 +--R ((- 5a b + 2a )cos(x) - 3a b + 3a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 10a b + 4a b)cos(x) + (- 7a b + 4a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (3a b - 5a b + 2a )cos(x) + (6a b - 10a b + 4a )cos(x) +--R + +--R 4 3 2 2 4 3 2 5 4 5 +--R (6a b + 6a b )cos(x) + (6a b - 12a b + 6a )cos(x) + 6a b - 6a +--R * +--R 8 +--R sin(x) +--R + +--R 5 5 5 4 2 3 4 3 +--R - 6b cos(x) - 6b cos(x) + (34a b - 10a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (25a b - 13a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 2 5 6 4 5 +--R (3a b + 5a b - 2a )cos(x) - 6a b cos(x) +--R + +--R 4 3 2 5 4 +--R (- 18a b + 18a b - 6a )cos(x) +--R + +--R 4 3 2 5 3 +--R (- 18a b + 28a b - 10a )cos(x) +--R + +--R 4 3 2 5 2 +--R (- 18a b + 11a b - 11a )cos(x) +--R + +--R 4 3 2 5 4 3 2 +--R (- 18a b + 36a b - 18a )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (10a b - 4a b)cos(x) + (a b - 4a b)cos(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (18b + 2a b - 2a b)cos(x) + (18b + 3a b - 3a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 42a b + 6a b)cos(x) + (- 33a b + 15a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 36a b + 36a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (5a b - 2a )cos(x) + (- 12a b + 10a b - 4a )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 21a b + 6a b )cos(x) + (14a b + 6a b - 2a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (32a b - 19a b + 5a )cos(x) + (18a b - 24a b + 6a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (18a b - 19a b + 13a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 4 3 2 5 +--R 18a b - 24a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 8 2 3 4 7 2 3 4 6 +--R - 6a b cos(x) + (- 18a b + 6a b)cos(x) + (5a b + a b)cos(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (- 18b - 4a b + 4a b)cos(x) + (- 18b - 6a b + 6a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (22a b + 2a b)cos(x) + (19a b - 7a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- 3a b + 3a )cos(x) + (20a b - 14a b + 6a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (29a b - 26a b + 9a )cos(x) + (- 8a b - 16a b + 6a )cos(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (- 20a b + 2a )cos(x) + (- 6a b + 4a b + 2a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 6a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 4 3 2 5 +--R - 6a b + 9a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (10a b - 4a b)cos(x) + (8a b - 2a b)cos(x) +--R + +--R 2 3 4 6 5 2 3 4 5 +--R (- 6a b + 3a b)cos(x) + (6b + 2a b - 2a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (6b + 3a b - 3a b)cos(x) + (- 4a b - 2a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (- 4a b + a b)cos(x) + (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 6a b + 3a )cos(x) + (- 12a b + 6a )cos(x) +--R + +--R 4 3 2 5 6 3 2 5 5 +--R (- 3a b - a b + a )cos(x) + (10a b - 4a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 3 +--R (3a b + 6a b - 3a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 2 5 2 +--R (a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 2 3 4 10 +--R ((- 10a b + 4a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 20a b + 8a b )cos(x) + (- 14a b + 8a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 12a b + 12a b )cos(x) - 6a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (12b - 10a b + 4a b)cos(x) + (12b - 20a b + 8a b)cos(x) +--R + +--R 5 2 3 2 5 2 3 4 5 +--R (12b + 12a b )cos(x) + (12b - 24a b + 12a b)cos(x) + 12b +--R + +--R 4 +--R - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (68a b - 20a b )cos(x) + (50a b - 26a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (48a b - 48a b )cos(x) + 24a b - 24a b +--R * +--R 7 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 4 +--R (12b + 10a b - 4a b)cos(x) + (- 48b + 36a b - 12a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 36b + 56a b - 20a b)cos(x) +--R + +--R 5 2 3 4 2 +--R (- 36b + 22a b - 22a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 +--R (- 36b + 72a b - 36a b)cos(x) - 36b + 36a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (20a b - 8a b )cos(x) + (2a b - 8a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (4a b - 4a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 84a b + 12a b )cos(x) + (- 66a b + 30a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 72a b + 72a b )cos(x) - 36a b + 36a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 8 5 2 3 4 7 +--R (10a b - 4a b)cos(x) + (- 24b + 20a b - 8a b)cos(x) +--R + +--R 5 2 3 6 5 2 3 4 5 +--R (- 60b + 12a b )cos(x) + (- 8b + 12a b - 4a b)cos(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (64b - 38a b + 10a b)cos(x) + (36b - 48a b + 12a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (36b - 38a b + 26a b)cos(x) + (36b - 72a b + 36a b)cos(x) +--R + +--R 5 2 3 4 +--R 36b - 48a b + 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 8 4 3 2 7 +--R - 12a b cos(x) + (- 36a b + 12a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (10a b + 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 12a b + 12a b )cos(x) + (44a b + 4a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 4 +--R (38a b - 14a b )cos(x) + (48a b - 48a b )cos(x) + 24a b +--R + +--R 3 2 +--R - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 8 5 2 3 4 7 +--R (- 6a b + 6a b)cos(x) + (40b - 28a b + 12a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (76b - 52a b + 18a b)cos(x) + (20b - 32a b + 12a b)cos(x) +--R + +--R 5 4 4 5 2 3 4 3 +--R (- 28b + 4a b)cos(x) + (- 12b + 8a b + 4a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 12b + 12a b - 6a b)cos(x) + (- 12b + 24a b - 12a b)cos(x) +--R + +--R 5 2 3 4 +--R - 12b + 18a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (20a b - 8a b )cos(x) + (16a b - 4a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 12a b + 6a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (6a b - 6a b )cos(x) + (- 8a b - 4a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 4 +--R (- 8a b + 2a b )cos(x) + (- 12a b + 12a b )cos(x) - 6a b +--R + +--R 3 2 +--R 6a b +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 12a b + 6a b)cos(x) + (- 24a b + 12a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (- 12b - 2a b + 2a b)cos(x) + (- 12b + 20a b - 8a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 2 3 4 2 +--R (12a b - 6a b)cos(x) + (4a b - 4a b)cos(x) + (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 5 2 3 2 5 10 +--R ((- 5a b + 2a )cos(x) - 3a b + 3a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 10a b + 4a b)cos(x) + (- 7a b + 4a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (3a b - 5a b + 2a )cos(x) + (6a b - 10a b + 4a )cos(x) +--R + +--R 4 3 2 2 4 3 2 5 4 5 +--R (6a b + 6a b )cos(x) + (6a b - 12a b + 6a )cos(x) + 6a b - 6a +--R * +--R 8 +--R sin(x) +--R + +--R 5 5 5 4 2 3 4 3 +--R - 6b cos(x) - 6b cos(x) + (34a b - 10a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (25a b - 13a b)cos(x) + (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 2 5 6 4 5 +--R (3a b + 5a b - 2a )cos(x) - 6a b cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 18a b + 18a b - 6a )cos(x) + (- 18a b + 28a b - 10a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 18a b + 11a b - 11a )cos(x) + (- 18a b + 36a b - 18a )cos(x) +--R + +--R 4 3 2 +--R - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (10a b - 4a b)cos(x) + (a b - 4a b)cos(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (18b + 2a b - 2a b)cos(x) + (18b + 3a b - 3a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 42a b + 6a b)cos(x) + (- 33a b + 15a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 36a b + 36a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (5a b - 2a )cos(x) + (- 12a b + 10a b - 4a )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 21a b + 6a b )cos(x) + (14a b + 6a b - 2a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (32a b - 19a b + 5a )cos(x) + (18a b - 24a b + 6a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (18a b - 19a b + 13a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 4 3 2 5 +--R 18a b - 24a b + 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 8 2 3 4 7 2 3 4 6 +--R - 6a b cos(x) + (- 18a b + 6a b)cos(x) + (5a b + a b)cos(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (- 18b - 4a b + 4a b)cos(x) + (- 18b - 6a b + 6a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (22a b + 2a b)cos(x) + (19a b - 7a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (24a b - 24a b)cos(x) + 12a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 8 4 3 2 5 7 +--R (- 3a b + 3a )cos(x) + (20a b - 14a b + 6a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (29a b - 26a b + 9a )cos(x) + (- 8a b - 16a b + 6a )cos(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (- 20a b + 2a )cos(x) + (- 6a b + 4a b + 2a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (- 6a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 4 3 2 5 +--R - 6a b + 9a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (10a b - 4a b)cos(x) + (8a b - 2a b)cos(x) +--R + +--R 2 3 4 6 5 2 3 4 5 +--R (- 6a b + 3a b)cos(x) + (6b + 2a b - 2a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (6b + 3a b - 3a b)cos(x) + (- 4a b - 2a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (- 4a b + a b)cos(x) + (- 6a b + 6a b)cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 6a b + 3a )cos(x) + (- 12a b + 6a )cos(x) +--R + +--R 4 3 2 5 6 3 2 5 5 +--R (- 3a b - a b + a )cos(x) + (10a b - 4a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 3 3 2 5 2 +--R (3a b + 6a b - 3a )cos(x) + (2a b - 2a )cos(x) + (a b - a )cos(x) +--R / +--R 2 4 4 2 6 4 8 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (3a b - 6a b + 3a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 6a b + 12a b - 6a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 6 6 +--R (- 9a b + 18a b - 9a )cos(x) +--R + +--R 2 4 4 2 6 5 +--R (- 18a b + 36a b - 18a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (18a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (9a b - 18a b + 9a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (6a b - 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 3a b + 6a b - 3a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 4 +--R ((12b - 24a b + 12a b )cos(x) + (12b - 24a b + 12a b )cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (6a b - 12a b + 6a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 6 2 4 4 2 5 +--R (- 36b + 72a b - 36a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 36b + 72a b - 36a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 36a b + 72a b - 36a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 4 +--R ((36b - 72a b + 36a b )cos(x) + (36b - 72a b + 36a b )cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (36a b - 72a b + 36a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 4 2 5 +--R (- 12b + 24a b - 12a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 12b + 24a b - 12a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) + (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 6 4 8 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 7 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) )sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (3a b - 6a b + 3a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 6a b + 12a b - 6a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R ((- 9a b + 18a b - 9a )cos(x) + (- 18a b + 36a b - 18a )cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((18a b - 36a b + 18a b)cos(x) + (18a b - 36a b + 18a b)cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (9a b - 18a b + 9a )cos(x) + (18a b - 36a b + 18a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (6a b - 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((- 6a b + 12a b - 6a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) ) +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 6a b - 3a )cos(x) + (- 6a b + 12a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 3a b + 6a b - 3a )cos(x) +--R Type: Expression(Integer) +--E 138 + +--S 139 of 546 +t0424:= sec(x)/(a+a*sin(x)) +--R +--R +--R sec(x) +--R (136) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 139 + +--S 140 of 546 +r0424:= 1/2/a*(atanh(sin(x))*cos(x)^2+sin(x)-1)/cos(x)^2 +--R +--R +--R 2 +--R cos(x) atanh(sin(x)) + sin(x) - 1 +--R (137) --------------------------------- +--R 2 +--R 2a cos(x) +--R Type: Expression(Integer) +--E 140 + +--S 141 of 546 +a0424:= integrate(t0424,x) +--R +--R +--R (138) +--R sin(x) + cos(x) + 1 +--R (sin(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R sin(x) - cos(x) - 1 +--R (- sin(x) - 1)log(-------------------) + sin(x) +--R cos(x) + 1 +--R / +--R 2a sin(x) + 2a +--R Type: Union(Expression(Integer),...) +--E 141 + +--S 142 of 546 +m0424:= a0424-r0424 +--R +--R +--R (139) +--R 2 2 sin(x) + cos(x) + 1 +--R (cos(x) sin(x) + cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 sin(x) - cos(x) - 1 +--R (- cos(x) sin(x) - cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 +--R (- cos(x) sin(x) - cos(x) )atanh(sin(x)) - sin(x) + cos(x) sin(x) + 1 +--R / +--R 2 2 +--R 2a cos(x) sin(x) + 2a cos(x) +--R Type: Expression(Integer) +--E 142 + +--S 143 of 546 +d0424:= D(m0424,x) +--R +--R +--R (140) +--R 7 3 2 5 +--R - 2sin(x) + (- 2cos(x) + cos(x) + 4cos(x) + 6)sin(x) +--R + +--R 3 2 4 +--R (- 2cos(x) - cos(x) )sin(x) +--R + +--R 5 4 3 2 3 +--R (- 2cos(x) + cos(x) + 4cos(x) - 2cos(x) - 8cos(x) - 6)sin(x) +--R + +--R 5 4 3 2 2 +--R (- 2cos(x) - cos(x) + 4cos(x) + 2cos(x) )sin(x) +--R + +--R 6 5 4 3 2 +--R (- 2cos(x) - 2cos(x) - cos(x) - 2cos(x) + cos(x) + 4cos(x) + 2) +--R * +--R sin(x) +--R + +--R 5 4 3 2 +--R 2cos(x) + cos(x) - 2cos(x) - cos(x) +--R / +--R 3 5 3 4 +--R 2a cos(x) sin(x) + 2a cos(x) sin(x) +--R + +--R 5 4 3 3 +--R (- 2a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 4 3 2 +--R (- 2a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 4 3 5 4 +--R (2a cos(x) + 4a cos(x) + 2a cos(x) )sin(x) + 2a cos(x) + 4a cos(x) +--R + +--R 3 +--R 2a cos(x) +--R Type: Expression(Integer) +--E 143 + +--S 144 of 546 +t0425:= sec(x)^3/(a+a*sin(x)) +--R +--R +--R 3 +--R sec(x) +--R (141) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 144 + +--S 145 of 546 +r0425:= 1/8/cos(x)^4*(3*atanh(sin(x))*cos(x)^4+2*sin(x)-2+3*sin(x)*cos(x)^2)/a +--R +--R +--R 4 2 +--R 3cos(x) atanh(sin(x)) + (3cos(x) + 2)sin(x) - 2 +--R (142) ------------------------------------------------ +--R 4 +--R 8a cos(x) +--R Type: Expression(Integer) +--E 145 + +--S 146 of 546 +a0425:= integrate(t0425,x) +--R +--R +--R (143) +--R 2 2 sin(x) + cos(x) + 1 +--R (3cos(x) sin(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 sin(x) - cos(x) - 1 +--R (- 3cos(x) sin(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2cos(x) + 3)sin(x) - cos(x) + 1 +--R / +--R 2 2 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Union(Expression(Integer),...) +--E 146 + +--S 147 of 546 +m0425:= a0425-r0425 +--R +--R +--R (144) +--R 4 4 sin(x) + cos(x) + 1 +--R (3cos(x) sin(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 sin(x) - cos(x) - 1 +--R (- 3cos(x) sin(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 2 2 +--R (- 3cos(x) sin(x) - 3cos(x) )atanh(sin(x)) + (- 3cos(x) - 2)sin(x) +--R + +--R 4 4 2 +--R 2cos(x) sin(x) - cos(x) + cos(x) + 2 +--R / +--R 4 4 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Expression(Integer) +--E 147 + +--S 148 of 546 +d0425:= D(m0425,x) +--R +--R +--R (145) +--R 2 7 +--R (- 6cos(x) - 8)sin(x) +--R + +--R 5 4 3 2 5 +--R (- 6cos(x) + 3cos(x) + 12cos(x) + 20cos(x) + 16cos(x) + 24)sin(x) +--R + +--R 5 4 2 4 +--R (- 6cos(x) - 3cos(x) - 2cos(x) )sin(x) +--R + +--R 7 6 5 4 3 2 +--R - 6cos(x) + 3cos(x) + 12cos(x) + 2cos(x) - 12cos(x) - 22cos(x) +--R + +--R - 32cos(x) - 24 +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R (- 6cos(x) - 3cos(x) + 12cos(x) + 6cos(x) + 4cos(x) + 4cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 8 7 6 5 4 2 +--R - 6cos(x) - 6cos(x) - 5cos(x) - 10cos(x) - 5cos(x) + 8cos(x) +--R + +--R 16cos(x) + 8 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R 6cos(x) + 5cos(x) - 2cos(x) - 3cos(x) - 4cos(x) - 2cos(x) +--R / +--R 5 5 5 4 +--R 8a cos(x) sin(x) + 8a cos(x) sin(x) +--R + +--R 7 6 5 3 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 2 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 7 6 +--R (8a cos(x) + 16a cos(x) + 8a cos(x) )sin(x) + 8a cos(x) + 16a cos(x) +--R + +--R 5 +--R 8a cos(x) +--R Type: Expression(Integer) +--E 148 + +--S 149 of 546 +t0426:= csc(x)^2/(a+b*sin(x)) +--R +--R +--R 2 +--R csc(x) +--R (146) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 149 + +--S 150 of 546 +r0426:= 2*b^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)+_ + b*atanh(cos(x))/a^2-cot(x)/a +--R +--R +--R (147) +--R x +--R +---------+ a tan(-) + b +---------+ +--R | 2 2 2 2 | 2 2 +--R b\|- b + a atanh(cos(x)) + 2b atan(------------) - a cot(x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ------------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 546 +a0426:= integrate(t0426,x) +--R +--R +--R (148) +--R [ +--R 2 +--R b sin(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) | 2 2 +--R - b sin(x)\|b - a log(----------) - a cos(x)\|b - a +--R cos(x) + 1 +--R / +--R +-------+ +--R 2 | 2 2 +--R a sin(x)\|b - a +--R , +--R +--R +---------+ +--R | 2 2 sin(x) +--R - b sin(x)\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 2 (a sin(x) + b cos(x) + b)\|- b + a +--R - 2b sin(x)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R | 2 2 +--R - a cos(x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a sin(x)\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 151 + +--S 152 of 546 +m0426a:= a0426.1-r0426 +--R +--R +--R (149) +--R +---------+ +--R 2 | 2 2 +--R b sin(x)\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) +--R - b sin(x)\|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R - b sin(x)\|- b + a \|b - a atanh(cos(x)) +--R + +--R x +--R +-------+ a tan(-) + b +--R 2 | 2 2 2 +--R - 2b sin(x)\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R (a cot(x)sin(x) - a cos(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a sin(x)\|- b + a \|b - a +--R Type: Expression(Integer) +--E 152 + +--S 153 of 546 +d0426a:= D(m0426a,x) +--R +--R +--R (150) +--R 2 3 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 4 3 2 2 +--R (- a b cos(x) + a b )cot(x) + (- a b + a b )cos(x) +--R + +--R 4 3 2 +--R (- a b - a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (a b - a b)cos(x) + a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 5 2 3 4 2 5 2 3 +--R - b cos(x) + (- b - a b + a b)cos(x) + (b - a b )cos(x) +--R + +--R 5 +--R b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 3 2 5 +--R (- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) +--R + +--R 3 2 +--R a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 4 3 2 3 +--R 2a b cos(x) + (- a b - a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 4 +--R (- a b - 2a b )cos(x) + (a b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (a b - a b)cos(x) + 2a b cos(x) + (- 2a b + a b)cos(x) +--R + +--R 4 2 2 3 +--R - 2a b cos(x) + a b cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 5 3 2 4 3 2 5 3 +--R (a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) +--R + +--R 3 2 2 +--R - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 5 +--R - 2a b cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 2 3 2 +--R (- 2a b cos(x) + 2a b )cot(x) + 2a b cos(x) +--R + +--R 5 2 3 5 +--R (- 2b - 2a b )cos(x) - 2b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (2a b - 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 3 2 2 4 +--R - 2a b cos(x) + 2a b cos(x) - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 2a b + 2a b)cos(x) - 2a b cos(x) +--R + +--R 2 3 4 2 3 +--R (2a b - 2a b)cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 2 3 3 2 3 2 2 3 +--R 4a b cos(x) - 4a b cos(x) - 4a b cos(x) + 4a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 3 2 4 +--R (2a b - 2a b )cos(x) + 4a b cos(x) +--R + +--R 4 3 2 3 3 2 2 4 +--R (- 4a b + 2a b )cos(x) - 4a b cos(x) + 2a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 2 3 4 3 +--R (2a b - 2a b)cos(x) + 2a b cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 2 3 2 +--R - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 4 3 2 2 +--R (- a b cos(x) + a b )cot(x) + (- a b + a b )cos(x) +--R + +--R 4 3 2 +--R (- a b - a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (a b - a b)cos(x) + a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 5 2 3 4 2 5 2 3 5 +--R - b cos(x) + (- b - a b + a b)cos(x) + (b - a b )cos(x) + b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 3 2 5 3 2 +--R ((- a b + a )cos(x) - a b cos(x) + (a b - a )cos(x) + a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 4 3 2 3 4 3 2 2 +--R 2a b cos(x) + (- a b - a b )cos(x) + (- a b - 2a b )cos(x) +--R + +--R 4 3 2 4 +--R (a b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (a b - a b)cos(x) + 2a b cos(x) + (- 2a b + a b)cos(x) +--R + +--R 4 2 2 3 +--R - 2a b cos(x) + a b cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 5 3 2 4 3 2 5 3 3 2 2 +--R (a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) - a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 5 +--R (a b - a b )cos(x)sin(x) +--R + +--R 3 3 5 2 3 3 5 2 5 3 3 2 +--R ((a b - a b)cos(x) - a b + a b)cot(x) + (a b - a b )cos(x) +--R + +--R 5 5 +--R (a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 6 2 +--R (a b - a b )cos(x) + (a b - a )cos(x) +--R + +--R 2 4 4 2 2 4 6 +--R (- a b + a b )cos(x) - a b + a +--R * +--R 2 +--R cot(x) +--R + +--R 6 4 2 3 6 4 2 2 6 2 4 +--R (b - a b )cos(x) + (b - a b )cos(x) + (- b + a b )cos(x) +--R + +--R 6 2 4 +--R - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (a b - a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 4 5 5 3 5 5 2 +--R (- a b + a b)cos(x) + (a b - a b)cos(x) + (a b - a b)cos(x) +--R + +--R 5 5 5 3 3 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 5 4 2 6 4 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) +--R + +--R 2 4 4 2 3 4 2 6 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + (a b - a )cos(x) + (- a b + a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 3 3 5 3 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 3 5 2 +--R (a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 +--R (2a b - 2a b )cos(x)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 +--R ((2a b - 2a b )cos(x) - 2a b + 2a b )cot(x) +--R + +--R 6 4 2 6 2 4 +--R (2b - 2a b )cos(x) + 2b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 3 5 5 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 3 5 3 3 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (- 2a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 3 3 5 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 5 3 3 3 3 3 5 2 +--R (4a b - 4a b )cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 5 +--R (a b - a b )cos(x)sin(x) +--R + +--R 3 3 5 2 3 3 5 2 5 3 3 2 +--R ((a b - a b)cos(x) - a b + a b)cot(x) + (a b - a b )cos(x) +--R + +--R 5 5 +--R (a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 6 2 2 4 4 2 +--R (a b - a b )cos(x) + (a b - a )cos(x) + (- a b + a b )cos(x) +--R + +--R 2 4 6 +--R - a b + a +--R * +--R 2 +--R cot(x) +--R + +--R 6 4 2 3 6 4 2 2 6 2 4 6 +--R (b - a b )cos(x) + (b - a b )cos(x) + (- b + a b )cos(x) - b +--R + +--R 2 4 +--R a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 5 2 3 3 5 +--R (a b - a b)cos(x) + (a b - a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 5 +--R - a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 4 5 5 3 5 5 2 +--R (- a b + a b)cos(x) + (a b - a b)cos(x) + (a b - a b)cos(x) +--R + +--R 5 5 5 3 3 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 5 4 2 6 4 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) +--R + +--R 2 4 4 2 3 4 2 6 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + (a b - a )cos(x) + (- a b + a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 3 3 5 3 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 3 5 2 +--R (a b - a b)cos(x) +--R / +--R 4 2 2 4 2 4 +--R (a b cos(x) - a b )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (a b - a b)cos(x) + (a b + a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- a b + a b)cos(x) - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 6 3 4 2 2 4 2 6 4 2 +--R ((a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) - a b ) +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 4 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (2a b - 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 2 3 3 5 +--R (2a b - 2a b)cos(x) + 2a b cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 3 3 +--R - 2a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 2 4 +--R (a b cos(x) - a b )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 3 3 5 +--R (a b - a b)cos(x) + (a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 5 +--R - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 6 3 4 2 2 4 2 6 4 2 2 +--R ((a b - a )cos(x) + a b cos(x) + (- a b + a )cos(x) - a b )sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 3 6 2 4 3 6 4 +--R ((- a b + a b)cos(x) + a b - a b)sin(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (a b - a b )cos(x) + a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (a b - a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 4 +--R ((- 2a b + 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 6 2 4 3 6 4 +--R ((- a b + a b)cos(x) + a b - a b)sin(x) +--R + +--R 3 4 5 2 3 3 4 7 2 3 4 5 2 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) + (a b - a b )cos(x) +--R + +--R 3 4 7 +--R a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 3 4 3 6 2 4 3 6 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 4 3 6 +--R a b - a b +--R * +--R 2 +--R sin(x) +--R Type: Expression(Integer) +--E 153 + +--S 154 of 546 +m0426b:= a0426.2-r0426 +--R +--R +--R (151) +--R +---------+ +---------+ +--R | 2 2 sin(x) | 2 2 +--R - b sin(x)\|- b + a log(----------) - b sin(x)\|- b + a atanh(cos(x)) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 2 (a sin(x) + b cos(x) + b)\|- b + a +--R - 2b sin(x)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +---------+ +--R 2 2 | 2 2 +--R - 2b sin(x)atan(------------) + (a cot(x)sin(x) - a cos(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a sin(x)\|- b + a +--R Type: Expression(Integer) +--E 154 + +--S 155 of 546 +d0426b:= D(m0426b,x) +--R +--R +--R (152) +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 2 2 2 4 +--R ((- a cos(x) + a )cot(x) - a b cos(x) - 2a b cos(x) - a b )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b)cot(x) +--R + +--R 3 2 3 3 2 2 3 3 +--R (- 2b - 2a b)cos(x) + (- 2b - 2a b)cos(x) + 2b cos(x) + 2b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (- a cos(x) - 2a cos(x) + 2a cos(x) + a )cot(x) +--R + +--R 2 3 4 2 3 3 2 2 +--R (- a b + a )cos(x) - 2a b cos(x) - a cos(x) + 2a b cos(x) +--R + +--R 2 +--R a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + a cos(x) +--R + +--R 3 5 3 3 3 2 +--R 2a cos(x) - 2a cos(x) - a cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 3 3 4 +--R ((- 2a b cos(x) + 2a b)cot(x) - 4b cos(x) - 4b )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 4a b cos(x) - 4a b cos(x) + 4a b cos(x) + 4a b )cot(x) +--R + +--R 2 3 2 2 +--R - 4a b cos(x) - 4a b cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R (- 2a b cos(x) - 4a b cos(x) + 4a b cos(x) + 2a b)cot(x) +--R + +--R 2 4 2 2 +--R 2a b cos(x) - 2a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 2 6 +--R (2a b cos(x) - 4a b cos(x) + 2a b cos(x))sin(x) + 2a b cos(x) +--R + +--R 2 5 2 3 2 2 +--R 4a b cos(x) - 4a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 2 2 2 4 +--R ((- a cos(x) + a )cot(x) - a b cos(x) - 2a b cos(x) - a b )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b)cot(x) +--R + +--R 3 2 3 3 2 2 3 3 +--R (- 2b - 2a b)cos(x) + (- 2b - 2a b)cos(x) + 2b cos(x) + 2b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (- a cos(x) - 2a cos(x) + 2a cos(x) + a )cot(x) +--R + +--R 2 3 4 2 3 3 2 2 2 +--R (- a b + a )cos(x) - 2a b cos(x) - a cos(x) + 2a b cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 3 5 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + a cos(x) + 2a cos(x) +--R + +--R 3 3 3 2 +--R - 2a cos(x) - a cos(x) +--R / +--R 4 2 4 4 +--R (a cos(x) - a )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 3 4 +--R (2a b cos(x) - 2a b)sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 3 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b)sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 4 4 +--R (a cos(x) - a )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a )sin(x) +--R Type: Expression(Integer) +--E 155 + +--S 156 of 546 +t0427:= csc(x)^3/(a+b*sin(x)) +--R +--R +--R 3 +--R csc(x) +--R (153) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 546 +r0427:= -2*b^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)-_ + 1/2*atanh(cos(x))/a-b^2*atanh(cos(x))/a^3+b*cot(x)/a^2-_ + 1/2*cot(x)*csc(x)/a +--R +--R +--R (154) +--R x +--R +---------+ a tan(-) + b +--R 2 2 | 2 2 3 2 +--R (- 2b - a )\|- b + a atanh(cos(x)) - 4b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (- a cot(x)csc(x) + 2a b cot(x))\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression(Integer) +--E 157 + +--S 158 of 546 +a0427:= integrate(t0427,x) +--R +--R +--R (155) +--R [ +--R 3 2 3 +--R (2b cos(x) - 2b ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((2b + a )cos(x) - 2b - a )\|b - a log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 | 2 2 +--R (- 2a b cos(x)sin(x) + a cos(x))\|b - a +--R / +--R +-------+ +--R 3 2 3 | 2 2 +--R (2a cos(x) - 2a )\|b - a +--R , +--R +--R +---------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((2b + a )cos(x) - 2b - a )\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 3 2 3 (a sin(x) + b cos(x) + b)\|- b + a +--R (4b cos(x) - 4b )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 2a b cos(x)sin(x) + a cos(x))\|- b + a +--R / +--R +---------+ +--R 3 2 3 | 2 2 +--R (2a cos(x) - 2a )\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 158 + +--S 159 of 546 +m0427a:= a0427.1-r0427 +--R +--R +--R (156) +--R +---------+ +--R 3 2 3 | 2 2 +--R (2b cos(x) - 2b )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R +---------+ +-------+ +--R 2 2 2 2 2 | 2 2 | 2 2 sin(x) +--R ((2b + a )cos(x) - 2b - a )\|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 2 2 2 | 2 2 | 2 2 +--R ((2b + a )cos(x) - 2b - a )\|- b + a \|b - a atanh(cos(x)) +--R + +--R x +--R +-------+ a tan(-) + b +--R 3 2 3 | 2 2 2 +--R (4b cos(x) - 4b )\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 +--R - 2a b cos(x)sin(x) + (a cos(x) - a )cot(x)csc(x) +--R + +--R 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + a cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 3 | 2 2 | 2 2 +--R (2a cos(x) - 2a )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 159 + +--S 160 of 546 +d0427a:= D(m0427a,x) +--R +--R +--R (157) +--R 3 3 2 3 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 2 3 2 4 4 2 2 +--R 3a b cos(x) + (- 2a b - a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 4a b + a b )cos(x) - 2a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 4 4 2 2 4 2 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 4 2 4 4 2 2 4 2 +--R - a b cos(x) + 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (2a b - a b - a b)cos(x) + (2a b + 2a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 +--R (- 2a b - 2a b + 2a b)cos(x) + (- 2a b - 4a b )cos(x) +--R + +--R 3 3 5 +--R a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (4a b - 4a b)cos(x) + (4a b + 4a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 2a b + 2a b)cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (2a b - 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- a b + a b)cos(x) - a b - a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 4 2 5 6 2 4 4 2 6 4 +--R (2b + a b )cos(x) + (2b + 2a b - a b - a )cos(x) +--R + +--R 6 4 2 6 3 6 2 4 6 2 +--R (- 4b + 2a b - a )cos(x) + (- 4b - 4a b + a )cos(x) +--R + +--R 6 4 2 6 6 2 4 4 2 +--R (2b - a b - a )cos(x) + 2b + 2a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 5 4 2 4 +--R (- 2a b + 2a )cos(x) - 2a b cos(x) +--R + +--R 4 2 6 3 4 2 2 +--R (4a b - 4a )cos(x) + 4a b cos(x) +--R + +--R 4 2 6 4 2 +--R (- 2a b + 2a )cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 6 5 4 2 4 4 2 6 3 +--R (- a b + a )cos(x) - a b cos(x) + (2a b - 2a )cos(x) +--R + +--R 4 2 2 4 2 6 4 2 +--R 2a b cos(x) + (- a b + a )cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 5 5 3 3 4 +--R (2a b - 2a b)cos(x) + 2a b cos(x) +--R + +--R 3 3 5 3 3 3 2 +--R (- 4a b + 4a b)cos(x) - 4a b cos(x) +--R + +--R 3 3 5 3 3 +--R (2a b - 2a b)cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (- a b - a b)cos(x) + (2a b + 3a b + a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 3 +--R (2a b + 2a b + 2a b)cos(x) + (- 4a b - 8a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 4a b - 3a b - a b)cos(x) + (2a b + 5a b - a b)cos(x) +--R + +--R 5 3 3 +--R 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (2a b - a b - a )cos(x) + (2a b + a b )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 3 +--R (- 4a b + 2a b + 2a )cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 +--R (2a b - a b - a )cos(x) + (2a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 4 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 3 3 5 3 3 2 +--R 6a b cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 8a b + 2a b )cos(x) - 4a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) +--R + +--R 3 3 4 3 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 4 2 2 4 2 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 2a b - 2a b )cos(x) + (4b + 4a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 6 +--R (4b - 4a b + 4a b )cos(x) + (- 4b - 8a b )cos(x) - 4b +--R + +--R 2 4 4 2 +--R 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (8a b - 8a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (4a b - 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) - 2a b - 2a b +--R * +--R csc(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (4a b - 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (4a b - 4a b )cos(x) + 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 3 3 5 4 +--R (4a b + 2a b )cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 3 5 2 +--R (- 8a b + 4a b - 2a b)cos(x) + 2a b cos(x) +--R + +--R 5 3 3 5 3 3 +--R (4a b - 2a b - 2a b)cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 5 3 3 4 +--R (- 4a b + 4a b)cos(x) - 4a b cos(x) +--R + +--R 3 3 5 3 3 3 2 +--R (8a b - 8a b)cos(x) + 8a b cos(x) +--R + +--R 3 3 5 3 3 +--R (- 4a b + 4a b)cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 5 3 3 4 +--R (- 2a b + 2a b)cos(x) - 2a b cos(x) +--R + +--R 3 3 5 3 3 3 2 +--R (4a b - 4a b)cos(x) + 4a b cos(x) +--R + +--R 3 3 5 3 3 +--R (- 2a b + 2a b)cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 +--R (4a b - 4a b )cos(x) + 4a b cos(x) +--R + +--R 2 4 4 2 3 2 4 2 +--R (- 8a b + 8a b )cos(x) - 8a b cos(x) +--R + +--R 2 4 4 2 2 4 +--R (4a b - 4a b )cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 2a b - 2a b )cos(x) + (10a b + 2a b )cos(x) +--R + +--R 2 4 4 2 4 2 4 3 +--R (4a b + 4a b )cos(x) - 24a b cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 +--R (- 6a b - 2a b )cos(x) + (14a b - 2a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 +--R (4a b - 2a b - 2a b)cos(x) + (4a b + 2a b )cos(x) +--R + +--R 5 3 3 5 4 5 3 3 3 +--R (- 8a b + 4a b + 4a b)cos(x) + (- 8a b - 4a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 +--R (4a b - 2a b - 2a b)cos(x) + (4a b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 2 3 2 4 4 2 2 2 4 4 2 +--R 3a b cos(x) + (- 2a b - a b )cos(x) + (- 4a b + a b )cos(x) +--R + +--R 2 4 4 2 +--R - 2a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 4 4 2 2 4 2 2 4 2 4 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) - a b cos(x) +--R + +--R 4 2 2 4 2 +--R 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (2a b - a b - a b)cos(x) + (2a b + 2a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 3 3 +--R (- 2a b - 2a b + 2a b)cos(x) + (- 2a b - 4a b )cos(x) + a b +--R + +--R 5 +--R a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (4a b - 4a b)cos(x) + (4a b + 4a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 2a b + 2a b)cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (2a b - 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- a b + a b)cos(x) - a b - a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 4 2 5 6 2 4 4 2 6 4 +--R (2b + a b )cos(x) + (2b + 2a b - a b - a )cos(x) +--R + +--R 6 4 2 6 3 6 2 4 6 2 +--R (- 4b + 2a b - a )cos(x) + (- 4b - 4a b + a )cos(x) +--R + +--R 6 4 2 6 6 2 4 4 2 +--R (2b - a b - a )cos(x) + 2b + 2a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 5 4 2 4 +--R (- 2a b + 2a )cos(x) - 2a b cos(x) +--R + +--R 4 2 6 3 4 2 2 +--R (4a b - 4a )cos(x) + 4a b cos(x) +--R + +--R 4 2 6 4 2 +--R (- 2a b + 2a )cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 6 5 4 2 4 4 2 6 3 +--R (- a b + a )cos(x) - a b cos(x) + (2a b - 2a )cos(x) +--R + +--R 4 2 2 4 2 6 4 2 +--R 2a b cos(x) + (- a b + a )cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 5 5 3 3 4 +--R (2a b - 2a b)cos(x) + 2a b cos(x) +--R + +--R 3 3 5 3 3 3 2 3 3 5 +--R (- 4a b + 4a b)cos(x) - 4a b cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 3 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (- a b - a b)cos(x) + (2a b + 3a b + a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 3 +--R (2a b + 2a b + 2a b)cos(x) + (- 4a b - 8a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 4a b - 3a b - a b)cos(x) + (2a b + 5a b - a b)cos(x) +--R + +--R 5 3 3 +--R 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (2a b - a b - a )cos(x) + (2a b + a b )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 3 +--R (- 4a b + 2a b + 2a )cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 +--R (2a b - a b - a )cos(x) + (2a b + a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 4 5 2 2 3 4 5 2 5 +--R ((- 2a b + 2a b )cos(x) - 2a b + 2a b )sin(x) +--R + +--R 4 3 6 3 2 5 4 3 6 2 +--R (a b - a b)cos(x) + (- 2a b + a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 4a b + 3a b + a b)cos(x) - 2a b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 6 4 4 3 6 2 4 3 +--R (- 2a b + 2a b)cos(x) + (4a b - 4a b)cos(x) - 2a b +--R + +--R 6 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 4 4 3 6 2 4 3 6 +--R (- a b + a b)cos(x) + (2a b - 2a b)cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 +--R (2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b +--R + +--R 5 2 +--R - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 4 6 5 2 7 3 +--R (2a b - a b - a b )cos(x) + (2a b - a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b - 2a b + 5a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 7 +--R (- 2a b - 2a b + 3a b + a )cos(x) + a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 7 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 7 4 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (- a b + a b )cos(x) - a b + a +--R * +--R csc(x) +--R + +--R 2 5 4 3 5 2 5 6 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 4 3 6 5 7 4 3 6 4 +--R (2b - a b - a b)cos(x) + (2b - a b - a b)cos(x) +--R + +--R 7 4 3 3 7 4 3 6 2 +--R (- 4b + 4a b )cos(x) + (- 4b + 2a b + 2a b)cos(x) +--R + +--R 7 4 3 6 7 4 3 6 +--R (2b - a b - a b)cos(x) + 2b + a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (4a b - 4a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 7 5 +--R (a b - a b )cos(x) + (2a b + a b - 2a b - a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 4a b - 4a b + 6a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 4a b + 3a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 +--R (2a b + 3a b - 4a b - a )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (2a b - a b - a b)cos(x) + (2a b - a b - a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 4a b + 2a b + 2a b)cos(x) + (- 4a b + 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (2a b - a b - a b)cos(x) + (2a b - a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 2 5 4 3 5 +--R ((- 4a b + 4a b )cos(x) - 4a b + 4a b )sin(x) +--R + +--R 3 4 5 2 3 6 3 4 5 2 2 +--R (2a b - 2a b )cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (- 8a b + 6a b + 2a b )cos(x) - 4a b + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 +--R (- 4a b + 4a b )cos(x) + (8a b - 8a b )cos(x) - 4a b +--R + +--R 5 2 +--R 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 +--R (- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b +--R + +--R 5 2 +--R 2a b +--R * +--R csc(x) +--R + +--R 2 5 4 3 4 2 5 4 3 2 2 5 +--R (4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b +--R + +--R 4 3 +--R - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 4 7 4 3 6 3 +--R (2a b - 2a b )cos(x) + (4b - 2a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (4b - 12a b + 10a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 6 +--R (- 4b - 4a b + 6a b + 2a b)cos(x) - 4b + 6a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 5 2 5 6 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 6 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R csc(x) +--R + +--R 6 3 4 5 6 5 2 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 6 3 4 3 6 5 2 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 6 3 4 6 5 2 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (4a b - 2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 6 3 4 3 3 4 5 2 2 +--R (- 8a b + 8a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (4a b - 2a b - 2a b )cos(x) + 6a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R csc(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 5 +--R (2a b - 2a b )cos(x) + (6a b - 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 4 2 5 4 3 6 3 +--R (- 4a b + 4a b )cos(x) + (- 16a b + 12a b + 4a b)cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 2 5 +--R (- 2a b + 2a b )cos(x) + (10a b - 8a b - 2a b)cos(x) + 4a b +--R + +--R 4 3 +--R - 4a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (4a b - 2a b - 2a b )cos(x) + (4a b - 2a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (- 8a b + 4a b + 4a b )cos(x) + (- 8a b + 4a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (4a b - 2a b - 2a b )cos(x) + (4a b - 2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 5 +--R ((- 2a b + 2a b )cos(x) - 2a b + 2a b )sin(x) +--R + +--R 4 3 6 3 2 5 4 3 6 2 +--R (a b - a b)cos(x) + (- 2a b + a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 4a b + 3a b + a b)cos(x) - 2a b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 6 4 4 3 6 2 4 3 +--R (- 2a b + 2a b)cos(x) + (4a b - 4a b)cos(x) - 2a b +--R + +--R 6 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 4 4 3 6 2 4 3 6 +--R (- a b + a b)cos(x) + (2a b - 2a b)cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 5 2 +--R ((2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b - 2a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 4 6 5 2 7 3 +--R (2a b - a b - a b )cos(x) + (2a b - a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b - 2a b + 5a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 7 +--R (- 2a b - 2a b + 3a b + a )cos(x) + a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 7 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 7 4 +--R (- a b + a b )cos(x) + (- a b + a )cos(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (- a b + a b )cos(x) - a b + a +--R * +--R csc(x) +--R + +--R 2 5 4 3 5 2 5 6 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 4 3 6 5 7 4 3 6 4 +--R (2b - a b - a b)cos(x) + (2b - a b - a b)cos(x) +--R + +--R 7 4 3 3 7 4 3 6 2 +--R (- 4b + 4a b )cos(x) + (- 4b + 2a b + 2a b)cos(x) +--R + +--R 7 4 3 6 7 4 3 6 +--R (2b - a b - a b)cos(x) + 2b + a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (4a b - 4a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 7 5 +--R (a b - a b )cos(x) + (2a b + a b - 2a b - a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 4a b - 4a b + 6a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 7 +--R (- 4a b + 3a b + a b )cos(x) + (2a b + 3a b - 4a b - a )cos(x) +--R + +--R 6 5 2 +--R 2a b - 2a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (2a b - a b - a b)cos(x) + (2a b - a b - a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 4a b + 2a b + 2a b)cos(x) + (- 4a b + 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (2a b - a b - a b)cos(x) + (2a b - a b - a b)cos(x) +--R / +--R 5 2 4 5 2 2 5 2 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (2a b - 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- 4a b + 4a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (2a b - 2a b)cos(x) + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 7 5 5 2 4 5 2 7 3 +--R (2a b - 2a )cos(x) + 2a b cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 5 2 2 5 2 7 5 2 +--R - 4a b cos(x) + (2a b - 2a )cos(x) + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 4 4 3 2 4 3 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (4a b - 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (4a b - 4a b )cos(x) + 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 6 5 4 3 4 +--R (4a b - 4a b)cos(x) + 4a b cos(x) +--R + +--R 4 3 6 3 4 3 2 4 3 6 +--R (- 8a b + 8a b)cos(x) - 8a b cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 3 +--R 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 4 5 2 2 5 2 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (2a b - 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- 4a b + 4a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (2a b - 2a b)cos(x) + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 7 5 5 2 4 5 2 7 3 +--R (2a b - 2a )cos(x) + 2a b cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 5 2 2 5 2 7 5 2 +--R - 4a b cos(x) + (2a b - 2a )cos(x) + 2a b +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 3 7 4 5 3 7 2 5 3 7 +--R ((2a b - 2a b)cos(x) + (- 4a b + 4a b)cos(x) + 2a b - 2a b) +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 8 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a )cos(x) +--R + +--R 4 4 6 2 3 4 4 8 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 4 4 6 2 4 4 8 +--R (2a b - 2a b )cos(x) + 2a b - 2a +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (2a b - 2a b)cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 6 2 +--R ((4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b - 4a b ) +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 3 7 4 5 3 7 2 5 3 7 3 +--R ((2a b - 2a b)cos(x) + (- 4a b + 4a b)cos(x) + 2a b - 2a b)sin(x) +--R + +--R 4 4 6 2 5 4 4 8 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a )cos(x) +--R + +--R 4 4 6 2 3 4 4 8 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 4 4 6 2 4 4 8 +--R (2a b - 2a b )cos(x) + 2a b - 2a +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (2a b - 2a b)cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 160 + +--S 161 of 546 +m0427b:= a0427.2-r0427 +--R +--R +--R (158) +--R +---------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((2b + a )cos(x) - 2b - a )\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((2b + a )cos(x) - 2b - a )\|- b + a atanh(cos(x)) +--R + +--R +---------+ +--R | 2 2 +--R 3 2 3 (a sin(x) + b cos(x) + b)\|- b + a +--R (4b cos(x) - 4b )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +--R 3 2 3 2 +--R (4b cos(x) - 4b )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 +--R - 2a b cos(x)sin(x) + (a cos(x) - a )cot(x)csc(x) +--R + +--R 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + a cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 3 | 2 2 +--R (2a cos(x) - 2a )\|- b + a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 546 +d0427b:= D(m0427b,x) +--R +--R +--R (159) +--R 3 2 3 5 +--R (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 2 2 4 3 2 2 4 2 +--R (- 2a b + a )cos(x) + (- 4a b + a )cos(x) +--R + +--R 2 2 4 2 2 4 +--R (- 6a b - a )cos(x) - 4a b + a +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (- 2a cos(x) + 4a cos(x) - 2a )cot(x) - a cos(x) +--R + +--R 4 2 4 +--R 2a cos(x) - a +--R * +--R csc(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b)cot(x) + 2a b cos(x) +--R + +--R 3 3 3 2 3 3 3 3 +--R 4a b cos(x) - 6a b cos(x) + (- 4a b - 4a b)cos(x) - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 3 4 3 3 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) +--R + +--R 3 2 3 3 +--R 8a b cos(x) - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 3 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 2 2 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 2 4 5 4 2 2 4 4 +--R (4b + 4a b + 2a )cos(x) + (4b + 4a b + 3a )cos(x) +--R + +--R 4 2 2 3 4 2 2 2 +--R (- 8b - 8a b )cos(x) + (- 8b - 8a b )cos(x) +--R + +--R 4 2 2 4 4 2 2 4 +--R (4b + 4a b + 2a )cos(x) + 4b + 4a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - 2a cos(x) - 4a cos(x) + 2a cos(x) + 8a cos(x) +--R + +--R 4 2 4 4 +--R 2a cos(x) - 4a cos(x) - 2a +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 4 2 +--R - a cos(x) - 2a cos(x) + a cos(x) + 4a cos(x) + a cos(x) +--R + +--R 4 4 +--R - 2a cos(x) - a +--R * +--R csc(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 6 3 3 5 +--R (2a b + 2a b)cos(x) + (4a b + 2a b)cos(x) +--R + +--R 3 3 4 3 3 3 +--R (- 2a b - 6a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (- 2a b + 2a b)cos(x) + (4a b + 6a b)cos(x) + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 2 2 4 5 +--R (2a b + a )cos(x) + (4a b + 2a )cos(x) + (- 2a b - a )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 2 2 4 2 +--R (- 8a b - 4a )cos(x) + (- 2a b - a )cos(x) + (4a b + 2a )cos(x) +--R + +--R 2 2 4 +--R (2a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 3 3 3 3 2 +--R (- 4a b + 2a b)cos(x) + (- 8a b + 2a b)cos(x) +--R + +--R 3 3 3 3 +--R (- 12a b - 2a b)cos(x) - 8a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b)cot(x) - 2a b cos(x) +--R + +--R 3 2 3 +--R 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 4 2 2 2 2 2 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) + 8b cos(x) +--R + +--R 4 2 2 2 4 2 2 4 2 2 +--R (8b - 12a b )cos(x) + (- 8b - 8a b )cos(x) - 8b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 5 2 2 4 2 2 3 +--R - 8a b cos(x) - 8a b cos(x) + 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R 16a b cos(x) - 8a b cos(x) - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 2 2 2 2 +--R - 4a b cos(x) - 4a b +--R * +--R csc(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 3 3 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 4 3 3 +--R (8a b + 4a b)cos(x) + (8a b + 6a b)cos(x) - 16a b cos(x) +--R + +--R 3 2 3 3 3 3 +--R - 16a b cos(x) + (8a b + 4a b)cos(x) + 8a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 3 5 3 4 +--R - 4a b cos(x) - 8a b cos(x) + 4a b cos(x) +--R + +--R 3 3 3 2 3 3 +--R 16a b cos(x) + 4a b cos(x) - 8a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) + 8a b cos(x) +--R + +--R 3 2 3 3 +--R 2a b cos(x) - 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 6 2 2 5 2 2 4 2 2 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 6 2 2 5 2 2 4 2 2 3 +--R 4a b cos(x) + 4a b cos(x) - 12a b cos(x) - 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R 4a b cos(x) + 12a b cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 3 7 3 3 6 +--R (4a b + 2a b)cos(x) + (8a b + 4a b)cos(x) +--R + +--R 3 3 5 3 3 4 +--R (- 4a b - 2a b)cos(x) + (- 16a b - 8a b)cos(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R (- 4a b - 2a b)cos(x) + (8a b + 4a b)cos(x) + (4a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 5 +--R (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 2 2 4 3 2 2 4 2 2 2 4 +--R (- 2a b + a )cos(x) + (- 4a b + a )cos(x) + (- 6a b - a )cos(x) +--R + +--R 2 2 4 +--R - 4a b + a +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 4 2 +--R (- 2a cos(x) + 4a cos(x) - 2a )cot(x) - a cos(x) + 2a cos(x) +--R + +--R 4 +--R - a +--R * +--R csc(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b)cot(x) + 2a b cos(x) +--R + +--R 3 3 3 2 3 3 3 3 +--R 4a b cos(x) - 6a b cos(x) + (- 4a b - 4a b)cos(x) - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 3 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 2 2 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 2 4 5 4 2 2 4 4 +--R (4b + 4a b + 2a )cos(x) + (4b + 4a b + 3a )cos(x) +--R + +--R 4 2 2 3 4 2 2 2 +--R (- 8b - 8a b )cos(x) + (- 8b - 8a b )cos(x) +--R + +--R 4 2 2 4 4 2 2 4 +--R (4b + 4a b + 2a )cos(x) + 4b + 4a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - 2a cos(x) - 4a cos(x) + 2a cos(x) + 8a cos(x) +--R + +--R 4 2 4 4 +--R 2a cos(x) - 4a cos(x) - 2a +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 4 2 +--R - a cos(x) - 2a cos(x) + a cos(x) + 4a cos(x) + a cos(x) +--R + +--R 4 4 +--R - 2a cos(x) - a +--R * +--R csc(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 6 3 3 5 +--R (2a b + 2a b)cos(x) + (4a b + 2a b)cos(x) +--R + +--R 3 3 4 3 3 3 +--R (- 2a b - 6a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (- 2a b + 2a b)cos(x) + (4a b + 6a b)cos(x) + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 2 2 4 5 +--R (2a b + a )cos(x) + (4a b + 2a )cos(x) + (- 2a b - a )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 2 2 4 2 +--R (- 8a b - 4a )cos(x) + (- 2a b - a )cos(x) + (4a b + 2a )cos(x) +--R + +--R 2 2 4 +--R (2a b + a )cos(x) +--R / +--R 5 4 5 2 5 3 +--R (2a cos(x) - 4a cos(x) + 2a )sin(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 4 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R 2a cos(x) + 4a cos(x) - 2a cos(x) - 8a cos(x) - 2a cos(x) +--R + +--R 5 5 +--R 4a cos(x) + 2a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 4 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b)sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 3 2 3 2 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 4 2 4 4 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 3 +--R (2a cos(x) - 4a cos(x) + 2a )sin(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 4 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R 2a cos(x) + 4a cos(x) - 2a cos(x) - 8a cos(x) - 2a cos(x) +--R + +--R 5 5 +--R 4a cos(x) + 2a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 162 + +--S 163 of 546 +t0428:= csc(x)^4/(a+b*sin(x)) +--R +--R +--R 4 +--R csc(x) +--R (160) ------------ +--R b sin(x) + a +--R Type: Expression(Integer) +--E 163 + +--S 164 of 546 +r0428:= 2*b^4*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)+_ + 1/2*b*atanh(cos(x))/a^2+b^3*atanh(cos(x))/a^4-cot(x)/a-_ + b^2*cot(x)/a^3-1/3*cot(x)^3/a+1/2*b*cot(x)*csc(x)/a^2 +--R +--R +--R (161) +--R x +--R +---------+ a tan(-) + b +--R 3 2 | 2 2 4 2 +--R (6b + 3a b)\|- b + a atanh(cos(x)) + 12b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 3 3 2 3 | 2 2 +--R (3a b cot(x)csc(x) - 2a cot(x) + (- 6a b - 6a )cot(x))\|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression(Integer) +--E 164 + +--S 165 of 546 +a0428:= integrate(t0428,x) +--R +--R +--R (162) +--R [ +--R 4 2 4 +--R (6b cos(x) - 6b )sin(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 3 2 2 3 2 | 2 2 sin(x) +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|b - a log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 3 2 3 +--R (- 3a b cos(x)sin(x) + (- 6a b - 4a )cos(x) + (6a b + 6a )cos(x)) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 2 4 | 2 2 +--R (6a cos(x) - 6a )sin(x)\|b - a +--R , +--R +--R +---------+ +--R 3 2 2 3 2 | 2 2 sin(x) +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 4 2 4 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 12b cos(x) + 12b )sin(x)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 3 3 2 3 +--R (- 3a b cos(x)sin(x) + (- 6a b - 4a )cos(x) + (6a b + 6a )cos(x)) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 4 | 2 2 +--R (6a cos(x) - 6a )sin(x)\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 165 + +--S 166 of 546 +m0428a:= a0428.1-r0428 +--R +--R +--R (163) +--R +---------+ +--R 4 2 4 | 2 2 +--R (6b cos(x) - 6b )sin(x)\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +---------+ +-------+ +--R 3 2 2 3 2 | 2 2 | 2 2 +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|- b + a \|b - a +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 3 2 2 3 2 | 2 2 | 2 2 +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|- b + a \|b - a +--R * +--R atanh(cos(x)) +--R + +--R x +--R +-------+ a tan(-) + b +--R 4 2 4 | 2 2 2 +--R (- 12b cos(x) + 12b )sin(x)\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 3 2 3 3 +--R (- 3a b cos(x) + 3a b)cot(x)csc(x) + (2a cos(x) - 2a )cot(x) +--R + +--R 2 3 2 2 3 2 +--R ((6a b + 6a )cos(x) - 6a b - 6a )cot(x) - 3a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 3 2 3 +--R (- 6a b - 4a )cos(x) + (6a b + 6a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 4 2 4 | 2 2 | 2 2 +--R (6a cos(x) - 6a )sin(x)\|- b + a \|b - a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 546 +d0428a:= D(m0428a,x) +--R +--R +--R (164) +--R 2 5 4 3 3 4 3 2 +--R (- 6a b - 3a b )cos(x) - 3a b cos(x) +--R + +--R 2 5 4 3 4 3 +--R (6a b + 3a b )cos(x) - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 4 4 3 2 4 3 2 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) +--R + +--R 4 3 4 4 3 2 4 3 +--R 3a b cos(x) - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 2 4 5 2 2 5 2 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 +--R (- 6a b - 12a b )cos(x) + (12a b + 24a b )cos(x) +--R + +--R 3 4 5 2 +--R - 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 4 6 3 4 3 +--R (- 6a b + 3a b + a b )cos(x) + (- 6a b - 12a b )cos(x) +--R + +--R 6 3 4 2 6 3 4 5 2 +--R (6a b - 6a b )cos(x) + (6a b + 6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 +--R - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 3 +--R (- 12a b + 12a b )cos(x) +--R + +--R 3 4 5 2 2 3 4 5 2 +--R (- 12a b - 12a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 3 4 5 2 +--R 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (3a b - 3a b )cos(x) + (3a b + 3a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 6a b + 6a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (3a b - 3a b )cos(x) + 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (12a b - 12a b)cos(x) + (12a b + 12a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- 6a b + 6a b)cos(x) - 6a b - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 6 5 +--R (- 6a b - 6a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 6a b - 18a b - 12a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (12a b + 12a b - 24a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (12a b + 36a b + 24a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 6a b - 6a b + 12a b)cos(x) - 6a b - 18a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 4 3 6 5 +--R (- 6b - 5a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (- 6b - 6a b + a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (12b - 6a b + 6a b - 3a b)cos(x) +--R + +--R 7 2 5 6 2 +--R (12b + 6a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 4 3 +--R (- 6b + 6a b - 3a b + 3a b)cos(x) - 6b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 5 4 3 4 +--R (6a b - 6a b)cos(x) + 6a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (- 12a b + 12a b)cos(x) - 12a b cos(x) +--R + +--R 4 3 6 4 3 +--R (6a b - 6a b)cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 4 +--R (3a b - 3a b)cos(x) + 3a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (- 6a b + 6a b)cos(x) - 6a b cos(x) +--R + +--R 4 3 6 4 3 +--R (3a b - 3a b)cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 2 7 5 5 2 4 +--R (- 6a b + 6a )cos(x) - 6a b cos(x) +--R + +--R 5 2 7 3 5 2 2 +--R (12a b - 12a )cos(x) + 12a b cos(x) +--R + +--R 5 2 7 5 2 +--R (- 6a b + 6a )cos(x) - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 4 5 2 7 5 +--R (- 6a b - 6a b + 12a )cos(x) +--R + +--R 3 4 5 2 4 +--R (- 6a b - 12a b )cos(x) +--R + +--R 3 4 5 2 7 3 +--R (12a b + 12a b - 24a )cos(x) +--R + +--R 3 4 5 2 2 3 4 5 2 7 +--R (12a b + 24a b )cos(x) + (- 6a b - 6a b + 12a )cos(x) +--R + +--R 3 4 5 2 +--R - 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 +--R (9a b + 7a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 6a b - 9a b - 5a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b - 18a b - 18a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (12a b + 18a b + 12a b - 6a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (12a b + 9a b + 15a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 6a b - 9a b - 3a b )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 4 3 6 6 +--R (6a b - 2a b - 4a b)cos(x) + (13a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (- 18a b - a b + 10a b)cos(x) + (- 28a b - 16a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (18a b + 6a b - 6a b)cos(x) + (15a b + 9a b)cos(x) +--R + +--R 2 5 4 3 +--R (- 6a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 3 4 5 2 6 +--R (6a b - 2a b - 4a )cos(x) + (6a b + 4a b )cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (- 12a b + 2a b + 10a )cos(x) + (- 12a b - 10a b )cos(x) +--R + +--R 3 4 7 3 3 4 5 2 2 +--R (6a b - 6a )cos(x) + (6a b + 6a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 3 3 4 2 +--R (- 12a b - 6a b )cos(x) - 6a b cos(x) +--R + +--R 6 3 4 3 4 +--R (12a b + 6a b )cos(x) - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 4 4 3 4 2 3 4 2 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 3 4 4 3 4 2 3 4 +--R 6a b cos(x) - 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 3 4 4 3 2 4 3 4 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b )cot(x) +--R + +--R 2 5 4 3 4 2 5 4 3 2 +--R (- 12a b - 24a b )cos(x) + (24a b + 48a b )cos(x) +--R + +--R 2 5 4 3 +--R - 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 4 7 2 5 3 +--R (6a b + 2a b )cos(x) + (- 12b - 24a b )cos(x) +--R + +--R 7 2 5 2 7 2 5 4 3 +--R (- 12b - 12a b )cos(x) + (12b + 12a b + 12a b )cos(x) +--R + +--R 7 2 5 4 3 +--R 12b - 6a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 2 5 4 3 3 +--R (- 24a b + 24a b )cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 +--R (- 24a b - 24a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 5 4 3 +--R 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (6a b - 6a b )cos(x) + 6a b + 6a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (24a b - 24a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 12a b + 12a b )cos(x) - 12a b - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 6 3 4 5 2 5 +--R (- 12a b - 12a b + 24a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 12a b - 36a b - 24a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (24a b + 24a b - 48a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (24a b + 72a b + 48a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (- 12a b - 12a b + 24a b )cos(x) - 12a b - 36a b +--R + +--R 5 2 +--R - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (- 12a b - 10a b + 4a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 6 5 2 2 +--R (12a b + 12a b - 6a b )cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 3 4 5 2 6 3 4 +--R (- 6a b + 6a b )cos(x) + 12a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (12a b - 12a b )cos(x) + 12a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (- 24a b + 24a b )cos(x) - 24a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (12a b - 12a b )cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 4 +--R (6a b - 6a b )cos(x) + 6a b cos(x) +--R + +--R 3 4 5 2 3 3 4 2 +--R (- 12a b + 12a b )cos(x) - 12a b cos(x) +--R + +--R 3 4 5 2 3 4 +--R (6a b - 6a b )cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 4 +--R (- 12a b + 12a b)cos(x) - 12a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (24a b - 24a b)cos(x) + 24a b cos(x) +--R + +--R 4 3 6 4 3 +--R (- 12a b + 12a b)cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 6 5 +--R (- 12a b - 12a b + 24a b)cos(x) +--R + +--R 2 5 4 3 4 +--R (- 12a b - 24a b )cos(x) +--R + +--R 2 5 4 3 6 3 +--R (24a b + 24a b - 48a b)cos(x) +--R + +--R 2 5 4 3 2 +--R (24a b + 48a b )cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (- 12a b - 12a b + 24a b)cos(x) - 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 5 +--R (18a b + 14a b )cos(x) + (- 30a b - 10a b + 4a b)cos(x) +--R + +--R 2 5 4 3 4 2 5 4 3 6 3 +--R (- 36a b - 36a b )cos(x) + (60a b + 24a b - 12a b)cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 +--R (18a b + 30a b )cos(x) + (- 30a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 6 +--R (12a b - 4a b - 8a b )cos(x) + (26a b + 14a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 36a b - 2a b + 20a b )cos(x) +--R + +--R 3 4 5 2 4 +--R (- 56a b - 32a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (36a b + 12a b - 12a b )cos(x) + (30a b + 18a b )cos(x) +--R + +--R 6 3 4 +--R (- 12a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 +--R (12a b - 4a b - 8a b)cos(x) + (12a b + 8a b )cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 4 +--R (- 24a b + 4a b + 20a b)cos(x) + (- 24a b - 20a b )cos(x) +--R + +--R 2 5 6 3 2 5 4 3 2 +--R (12a b - 12a b)cos(x) + (12a b + 12a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 3 4 3 2 2 5 4 3 +--R (- 6a b - 3a b )cos(x) - 3a b cos(x) + (6a b + 3a b )cos(x) +--R + +--R 4 3 +--R - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 4 4 3 2 4 3 2 4 3 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )cot(x) + 3a b cos(x) +--R + +--R 4 3 2 4 3 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 2 4 5 2 2 5 2 4 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b )cot(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 +--R (- 6a b - 12a b )cos(x) + (12a b + 24a b )cos(x) - 6a b +--R + +--R 5 2 +--R - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 2 4 6 3 4 3 +--R (- 6a b + 3a b + a b )cos(x) + (- 6a b - 12a b )cos(x) +--R + +--R 6 3 4 2 6 3 4 5 2 3 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b + 6a b )cos(x) - 3a b +--R + +--R 5 2 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (6a b - 6a b )cos(x) + (6a b + 6a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (6a b - 6a b )cos(x) + 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (3a b - 3a b )cos(x) + (3a b + 3a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 6a b + 6a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (3a b - 3a b )cos(x) + 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (12a b - 12a b)cos(x) + (12a b + 12a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (- 6a b + 6a b)cos(x) - 6a b - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 5 4 3 6 5 +--R (- 6a b - 6a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 6a b - 18a b - 12a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (12a b + 12a b - 24a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (12a b + 36a b + 24a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 6a b - 6a b + 12a b)cos(x) - 6a b - 18a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 4 3 6 5 +--R (- 6b - 5a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (- 6b - 6a b + a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (12b - 6a b + 6a b - 3a b)cos(x) +--R + +--R 7 2 5 6 2 +--R (12b + 6a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 4 3 +--R (- 6b + 6a b - 3a b + 3a b)cos(x) - 6b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 5 4 3 4 +--R (6a b - 6a b)cos(x) + 6a b cos(x) +--R + +--R 4 3 6 3 4 3 2 +--R (- 12a b + 12a b)cos(x) - 12a b cos(x) +--R + +--R 4 3 6 4 3 +--R (6a b - 6a b)cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 6 5 4 3 4 +--R (3a b - 3a b)cos(x) + 3a b cos(x) +--R + +--R 4 3 6 3 4 3 2 4 3 6 +--R (- 6a b + 6a b)cos(x) - 6a b cos(x) + (3a b - 3a b)cos(x) +--R + +--R 4 3 +--R 3a b +--R * +--R csc(x) +--R + +--R 5 2 7 5 5 2 4 +--R (- 6a b + 6a )cos(x) - 6a b cos(x) +--R + +--R 5 2 7 3 5 2 2 +--R (12a b - 12a )cos(x) + 12a b cos(x) +--R + +--R 5 2 7 5 2 +--R (- 6a b + 6a )cos(x) - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (- 6a b - 6a b + 12a )cos(x) + (- 6a b - 12a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (12a b + 12a b - 24a )cos(x) + (12a b + 24a b )cos(x) +--R + +--R 3 4 5 2 7 3 4 5 2 +--R (- 6a b - 6a b + 12a )cos(x) - 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 7 5 +--R (9a b + 7a b )cos(x) + (- 6a b - 9a b - 5a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b - 18a b - 18a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (12a b + 18a b + 12a b - 6a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (12a b + 9a b + 15a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 6a b - 9a b - 3a b )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 7 4 3 6 6 +--R (6a b - 2a b - 4a b)cos(x) + (13a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 5 4 3 6 4 +--R (- 18a b - a b + 10a b)cos(x) + (- 28a b - 16a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (18a b + 6a b - 6a b)cos(x) + (15a b + 9a b)cos(x) +--R + +--R 2 5 4 3 +--R (- 6a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 7 3 4 5 2 6 +--R (6a b - 2a b - 4a )cos(x) + (6a b + 4a b )cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (- 12a b + 2a b + 10a )cos(x) + (- 12a b - 10a b )cos(x) +--R + +--R 3 4 7 3 3 4 5 2 2 +--R (6a b - 6a )cos(x) + (6a b + 6a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 6 4 4 6 2 3 4 4 6 2 2 +--R (6a b - 3a b - 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 +--R (- 6a b + 3a b + 3a b )cos(x) + 3a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 +--R (- 6a b + 6a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 +--R - 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 +--R (- 3a b + 3a b )cos(x) + (6a b - 6a b )cos(x) - 3a b +--R + +--R 6 2 +--R 3a b +--R * +--R csc(x) +--R + +--R 5 3 7 4 5 3 7 2 5 3 +--R (6a b - 6a b)cos(x) + (- 12a b + 12a b)cos(x) + 6a b +--R + +--R 7 +--R - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 5 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 +--R (- 12a b - 12a b + 24a b)cos(x) + 6a b + 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b - 3a b - a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (6a b + 6a b - 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b + 6a b - 3a b + 3a b)cos(x) +--R + +--R 7 5 3 7 3 5 7 +--R (- 6a b + 3a b + 3a b)cos(x) + 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (6a b - 6a b )cos(x) + (6a b - 6a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 3a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 5 4 4 8 4 +--R (6a b - 6a b )cos(x) + (6a b - 6a )cos(x) +--R + +--R 4 4 6 2 3 4 4 8 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a )cos(x) +--R + +--R 4 4 6 2 4 4 8 +--R (6a b - 6a b )cos(x) + 6a b - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 2 6 4 4 6 2 5 +--R (6a b + 6a b - 12a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (6a b + 12a b - 6a b - 12a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 12a b - 12a b + 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 12a b - 24a b + 12a b + 24a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (6a b + 6a b - 12a b )cos(x) + 6a b + 12a b - 6a b - 12a +--R * +--R 2 +--R cot(x) +--R + +--R 8 4 4 6 2 5 8 4 4 6 2 8 4 +--R (6b - a b - 5a b )cos(x) + (6b - a b - 3a b - 2a )cos(x) +--R + +--R 8 2 6 6 2 3 8 2 6 8 2 +--R (- 12b + 6a b + 6a b )cos(x) + (- 12b + 6a b + 6a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (6b - 6a b + 3a b - 3a b )cos(x) + 6b - 6a b + 3a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (6a b - 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 3a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R csc(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (6a b - 6a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (6a b - 6a b)cos(x) + 6a b - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 5 5 3 7 5 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 12a b - 12a b + 24a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (- 12a b - 12a b + 24a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (6a b + 6a b - 12a b)cos(x) + 6a b + 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 7 6 +--R (- 3a b - a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b + 3a b - 4a b - 5a b)cos(x) +--R + +--R 7 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 12a b - 6a b + 6a b + 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 12a b + 9a b - 9a b + 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 +--R (6a b + 3a b - 6a b - 3a b)cos(x) + 6a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 4 4 6 2 8 6 +--R (- 6a b + 2a b + 4a b )cos(x) + (- 7a b + 3a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 5 4 4 6 2 8 4 +--R (18a b - 5a b - 13a b )cos(x) + (16a b - 6a b - 10a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 18a b + 6a b + 12a b )cos(x) +--R + +--R 4 4 6 2 8 2 2 6 4 4 6 2 +--R (- 9a b + 3a b + 6a )cos(x) + (6a b - 3a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 6 +--R (- 6a b + 2a b + 4a b)cos(x) + (- 6a b + 2a b + 4a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (12a b - 2a b - 10a b)cos(x) + (12a b - 2a b - 10a b)cos(x) +--R + +--R 3 5 7 3 3 5 7 2 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 3 3 5 5 3 2 +--R (12a b - 6a b - 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 3 5 5 3 +--R (- 12a b + 6a b + 6a b )cos(x) + 6a b - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 5 3 4 3 5 5 3 2 +--R (- 12a b + 12a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 5 5 3 +--R - 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 4 3 5 5 3 2 3 5 +--R (- 6a b + 6a b )cos(x) + (12a b - 12a b )cos(x) - 6a b +--R + +--R 5 3 +--R 6a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 +--R (12a b - 12a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 4 4 6 2 +--R 12a b - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 6 4 4 6 2 4 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 +--R (- 24a b - 24a b + 48a b )cos(x) + 12a b + 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 2a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (12b + 12a b - 18a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (12b - 12a b - 6a b + 6a b )cos(x) +--R + +--R 8 4 4 6 2 8 2 6 6 2 +--R (- 12b + 6a b + 6a b )cos(x) - 12b + 18a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 5 2 6 6 2 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 6 2 2 +--R (24a b - 24a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 2 6 4 4 2 6 6 2 +--R (- 12a b + 12a b )cos(x) - 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 5 2 6 6 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 6 2 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 6 4 4 2 6 6 2 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R csc(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (12a b - 12a b )cos(x) + (12a b - 12a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (- 24a b + 24a b )cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (12a b - 12a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 7 3 5 5 3 5 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (12a b + 24a b - 12a b - 24a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 24a b - 24a b + 48a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 24a b - 48a b + 24a b + 48a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (12a b + 12a b - 24a b )cos(x) + 12a b + 24a b - 12a b +--R + +--R 7 +--R - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 5 3 5 5 3 7 4 +--R (12a b - 2a b - 10a b )cos(x) + (10a b - 6a b - 4a b)cos(x) +--R + +--R 7 5 3 3 7 3 5 7 2 +--R (- 12a b + 12a b )cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 +--R (6a b - 6a b )cos(x) - 12a b + 18a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 5 3 5 5 3 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 3 5 5 3 3 3 5 5 3 2 +--R (24a b - 24a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 5 5 3 3 5 5 3 +--R (- 12a b + 12a b )cos(x) - 12a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 5 3 5 5 3 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 3 5 5 3 3 3 5 5 3 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 3 5 5 3 3 5 5 3 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (- 24a b + 24a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (12a b - 12a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 6 4 4 6 2 5 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 24a b - 24a b + 48a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 24a b - 24a b + 48a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (12a b + 12a b - 24a b )cos(x) + 12a b + 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 6 2 6 +--R (- 6a b - 2a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (18a b - 8a b - 10a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 36a b + 12a b + 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 6a b - 18a b + 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 +--R (18a b - 12a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 +--R (- 12a b + 4a b + 8a b )cos(x) +--R + +--R 3 5 5 3 7 6 +--R (- 14a b + 6a b + 8a b)cos(x) +--R + +--R 7 3 5 5 3 5 +--R (36a b - 10a b - 26a b )cos(x) +--R + +--R 3 5 5 3 7 4 +--R (32a b - 12a b - 20a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 36a b + 12a b + 24a b )cos(x) +--R + +--R 3 5 5 3 7 2 7 3 5 5 3 +--R (- 18a b + 6a b + 12a b)cos(x) + (12a b - 6a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 2 6 4 4 6 2 6 +--R (- 12a b + 4a b + 8a b )cos(x) + (- 12a b + 4a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 2 6 4 4 6 2 4 +--R (24a b - 4a b - 20a b )cos(x) + (24a b - 4a b - 20a b )cos(x) +--R + +--R 2 6 6 2 3 2 6 6 2 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 3 4 4 6 2 2 +--R (6a b - 3a b - 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 +--R (- 6a b + 3a b + 3a b )cos(x) + 3a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 +--R (- 6a b + 6a b )cos(x) + (12a b - 12a b )cos(x) - 6a b +--R + +--R 6 2 +--R 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 6 2 +--R (- 3a b + 3a b )cos(x) + (6a b - 6a b )cos(x) - 3a b + 3a b +--R * +--R csc(x) +--R + +--R 5 3 7 4 5 3 7 2 5 3 7 +--R ((6a b - 6a b)cos(x) + (- 12a b + 12a b)cos(x) + 6a b - 6a b) +--R * +--R 4 +--R cot(x) +--R + +--R 3 5 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 +--R (- 12a b - 12a b + 24a b)cos(x) + 6a b + 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b - 3a b - a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (6a b + 6a b - 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b + 6a b - 3a b + 3a b)cos(x) +--R + +--R 7 5 3 7 3 5 7 +--R (- 6a b + 3a b + 3a b)cos(x) + 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (6a b - 6a b )cos(x) + (6a b - 6a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 3a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 5 4 4 8 4 +--R (6a b - 6a b )cos(x) + (6a b - 6a )cos(x) +--R + +--R 4 4 6 2 3 4 4 8 2 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a )cos(x) +--R + +--R 4 4 6 2 4 4 8 +--R (6a b - 6a b )cos(x) + 6a b - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 2 6 4 4 6 2 5 +--R (6a b + 6a b - 12a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (6a b + 12a b - 6a b - 12a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 12a b - 12a b + 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 12a b - 24a b + 12a b + 24a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (6a b + 6a b - 12a b )cos(x) + 6a b + 12a b - 6a b - 12a +--R * +--R 2 +--R cot(x) +--R + +--R 8 4 4 6 2 5 8 4 4 6 2 8 4 +--R (6b - a b - 5a b )cos(x) + (6b - a b - 3a b - 2a )cos(x) +--R + +--R 8 2 6 6 2 3 8 2 6 8 2 +--R (- 12b + 6a b + 6a b )cos(x) + (- 12b + 6a b + 6a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (6b - 6a b + 3a b - 3a b )cos(x) + 6b - 6a b + 3a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (6a b - 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 3a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R csc(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (6a b - 6a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (6a b - 6a b)cos(x) + 6a b - 6a b +--R * +--R 4 +--R cot(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) + (6a b + 6a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 12a b - 12a b + 24a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (- 12a b - 12a b + 24a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (6a b + 6a b - 12a b)cos(x) + 6a b + 6a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 7 6 +--R (- 3a b - a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b + 3a b - 4a b - 5a b)cos(x) +--R + +--R 7 5 3 7 4 +--R (6a b + 6a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 12a b - 6a b + 6a b + 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 12a b + 9a b - 9a b + 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 +--R (6a b + 3a b - 6a b - 3a b)cos(x) + 6a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 4 4 6 2 8 6 +--R (- 6a b + 2a b + 4a b )cos(x) + (- 7a b + 3a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 5 4 4 6 2 8 4 +--R (18a b - 5a b - 13a b )cos(x) + (16a b - 6a b - 10a )cos(x) +--R + +--R 2 6 4 4 6 2 3 4 4 6 2 8 2 +--R (- 18a b + 6a b + 12a b )cos(x) + (- 9a b + 3a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 +--R (6a b - 3a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 6 +--R (- 6a b + 2a b + 4a b)cos(x) + (- 6a b + 2a b + 4a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (12a b - 2a b - 10a b)cos(x) + (12a b - 2a b - 10a b)cos(x) +--R + +--R 3 5 7 3 3 5 7 2 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b)cos(x) +--R / +--R 6 2 4 6 2 2 6 2 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (6a b - 6a b)cos(x) + (6a b + 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b - 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (6a b - 6a b)cos(x) + 6a b + 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 8 5 6 2 4 +--R (6a b - 6a )cos(x) + 6a b cos(x) +--R + +--R 6 2 8 3 6 2 2 +--R (- 12a b + 12a )cos(x) - 12a b cos(x) +--R + +--R 6 2 8 6 2 +--R (6a b - 6a )cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 4 5 3 2 5 3 4 +--R (12a b cos(x) - 24a b cos(x) + 12a b )sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (12a b - 12a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (- 24a b + 24a b )cos(x) + (- 24a b - 24a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (12a b - 12a b )cos(x) + 12a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 7 5 5 3 4 +--R (12a b - 12a b)cos(x) + 12a b cos(x) +--R + +--R 5 3 7 3 5 3 2 +--R (- 24a b + 24a b)cos(x) - 24a b cos(x) +--R + +--R 5 3 7 5 3 +--R (12a b - 12a b)cos(x) + 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 6 2 2 6 2 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b )sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (6a b - 6a b)cos(x) + (6a b + 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (- 12a b + 12a b)cos(x) + (- 12a b - 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (6a b - 6a b)cos(x) + 6a b + 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 8 5 6 2 4 6 2 8 3 +--R (6a b - 6a )cos(x) + 6a b cos(x) + (- 12a b + 12a )cos(x) +--R + +--R 6 2 2 6 2 8 6 2 +--R - 12a b cos(x) + (6a b - 6a )cos(x) + 6a b +--R * +--R 2 +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 3 8 4 6 3 8 2 6 3 8 +--R ((- 6a b + 6a b)cos(x) + (12a b - 12a b)cos(x) - 6a b + 6a b) +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 7 2 5 5 4 9 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a )cos(x) +--R + +--R 5 4 7 2 3 5 4 9 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a )cos(x) +--R + +--R 5 4 7 2 5 4 9 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 8 5 6 3 8 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 6 3 8 3 6 3 8 2 +--R (12a b - 12a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 6 3 8 6 3 8 +--R (- 6a b + 6a b)cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 7 2 4 5 4 7 2 2 5 4 +--R (- 12a b + 12a b )cos(x) + (24a b - 24a b )cos(x) - 12a b +--R + +--R 7 2 +--R 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 5 6 3 5 4 5 8 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 4 5 6 3 3 4 5 8 2 +--R (24a b - 24a b )cos(x) + (24a b - 24a b)cos(x) +--R + +--R 4 5 6 3 4 5 8 +--R (- 12a b + 12a b )cos(x) - 12a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 7 2 5 5 4 7 2 4 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 5 4 7 2 3 5 4 7 2 2 +--R (24a b - 24a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 5 4 7 2 5 4 7 2 +--R (- 12a b + 12a b )cos(x) - 12a b + 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 8 4 6 3 8 2 6 3 8 4 +--R ((- 6a b + 6a b)cos(x) + (12a b - 12a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 5 4 7 2 5 5 4 9 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a )cos(x) +--R + +--R 5 4 7 2 3 5 4 9 2 +--R (12a b - 12a b )cos(x) + (12a b - 12a )cos(x) +--R + +--R 5 4 7 2 5 4 9 +--R (- 6a b + 6a b )cos(x) - 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 8 5 6 3 8 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 6 3 8 3 6 3 8 2 +--R (12a b - 12a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 6 3 8 6 3 8 +--R (- 6a b + 6a b)cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R Type: Expression(Integer) +--E 167 + +--S 168 of 546 +m0428b:= a0428.2-r0428 +--R +--R +--R (165) +--R +---------+ +--R 3 2 2 3 2 | 2 2 sin(x) +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 3 2 2 3 2 | 2 2 +--R ((- 6b - 3a b)cos(x) + 6b + 3a b)sin(x)\|- b + a atanh(cos(x)) +--R + +--R +---------+ +--R | 2 2 +--R 4 2 4 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 12b cos(x) + 12b )sin(x)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +--R 4 2 4 2 +--R (- 12b cos(x) + 12b )sin(x)atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 3 2 3 3 +--R (- 3a b cos(x) + 3a b)cot(x)csc(x) + (2a cos(x) - 2a )cot(x) +--R + +--R 2 3 2 2 3 2 +--R ((6a b + 6a )cos(x) - 6a b - 6a )cot(x) - 3a b cos(x) +--R * +--R sin(x) +--R + +--R 2 3 3 2 3 +--R (- 6a b - 4a )cos(x) + (6a b + 6a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 4 | 2 2 +--R (6a cos(x) - 6a )sin(x)\|- b + a +--R Type: Expression(Integer) +--E 168 + +--S 169 of 546 +d0428b:= D(m0428b,x) +--R +--R +--R (166) +--R 2 3 4 3 4 2 2 3 4 +--R (- 6a b - 3a b)cos(x) - 3a b cos(x) + (6a b + 3a b)cos(x) +--R + +--R 4 +--R - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)cot(x) + 3a b cos(x) +--R + +--R 4 2 4 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a cos(x) + 12a cos(x) - 6a )cot(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 +--R (- 6a b - 12a )cos(x) + (12a b + 24a )cos(x) - 6a b +--R + +--R 5 +--R - 12a +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 4 4 3 2 3 +--R (- 6a b - 6a b - 2a )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 5 2 4 4 3 2 +--R 6a cos(x) + 12a b cos(x) + 6a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R - 24a b cos(x) + 12a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 2 +--R 6a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 5 4 4 4 3 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) +--R + +--R 4 2 4 4 +--R 24a b cos(x) - 12a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 12a b - 24a b)cos(x) + (- 12a b - 24a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (24a b + 48a b)cos(x) + (24a b + 48a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 12a b - 24a b)cos(x) - 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 5 +--R (- 12b - 12a b - 10a b)cos(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (- 12b - 12a b - 13a b)cos(x) + (24b + 12a b + 12a b)cos(x) +--R + +--R 5 2 3 4 2 5 4 5 +--R (24b + 12a b + 12a b)cos(x) + (- 12b - 6a b)cos(x) - 12b +--R + +--R 4 +--R - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 4 5 4 4 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) +--R + +--R 4 3 4 2 4 4 +--R - 24a b cos(x) - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 3a b cos(x) + 6a b cos(x) - 3a b cos(x) - 12a b cos(x) +--R + +--R 4 2 4 4 +--R - 3a b cos(x) + 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R - 6a cos(x) - 12a cos(x) + 6a cos(x) + 24a cos(x) +--R + +--R 5 2 5 5 +--R 6a cos(x) - 12a cos(x) - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (- 6a b - 12a )cos(x) + (- 12a b - 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (6a b + 12a )cos(x) + (24a b + 48a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (6a b + 12a )cos(x) + (- 12a b - 24a )cos(x) - 6a b - 12a +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 6 4 3 2 5 5 +--R (- 6a b + 2a )cos(x) + (- 12a b - 6a b - 4a )cos(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (6a b - 6a )cos(x) + (24a b + 12a b + 12a )cos(x) +--R + +--R 4 5 2 4 3 2 4 +--R (6a b + 12a )cos(x) + (- 12a b - 6a b )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 4 6 2 3 4 5 +--R (6a b + 5a b)cos(x) + 2a b cos(x) + (- 18a b - 17a b)cos(x) +--R + +--R 4 4 2 3 4 3 4 2 +--R - 8a b cos(x) + (18a b + 15a b)cos(x) + 6a b cos(x) +--R + +--R 2 3 4 +--R (- 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 3 2 5 6 +--R (6a b + 4a )cos(x) + (12a b + 8a )cos(x) + (- 6a b - 6a )cos(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (- 24a b - 20a )cos(x) + (- 6a b - 4a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (12a b + 12a )cos(x) + (6a b + 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 3 2 2 4 3 2 +--R (- 12a b - 6a b )cos(x) - 6a b cos(x) + (12a b + 6a b )cos(x) +--R + +--R 3 2 +--R - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R (12a b cos(x) - 24a b cos(x) + 12a b )cot(x) +--R + +--R 3 2 4 3 2 2 3 2 +--R 6a b cos(x) - 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 4 4 2 4 4 +--R (- 12a b cos(x) + 24a b cos(x) - 12a b)cot(x) +--R + +--R 2 3 4 4 2 3 4 2 2 3 +--R (- 12a b - 24a b)cos(x) + (24a b + 48a b)cos(x) - 12a b +--R + +--R 4 +--R - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 4 5 2 3 3 +--R (- 12a b - 4a b)cos(x) + (- 24b - 24a b )cos(x) +--R + +--R 5 4 2 5 5 2 3 +--R (- 24b + 12a b)cos(x) + 24b cos(x) + 24b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R 24a b cos(x) + 24a b cos(x) - 48a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R - 48a b cos(x) + 24a b cos(x) + 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 2 3 2 3 +--R 12a b cos(x) + 12a b +--R * +--R csc(x) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R - 24a b cos(x) - 24a b cos(x) + 48a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R 48a b cos(x) - 24a b cos(x) - 24a b +--R * +--R 4 +--R cot(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 24a b - 48a b )cos(x) + (- 24a b - 48a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (48a b + 96a b )cos(x) + (48a b + 96a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 24a b - 48a b )cos(x) - 24a b - 48a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 24a b - 20a b )cos(x) + (- 24a b - 26a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (24a b + 24a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 3 2 3 2 +--R - 12a b cos(x) - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 6 3 2 5 3 2 4 +--R 12a b cos(x) + 24a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 +--R - 48a b cos(x) - 12a b cos(x) + 24a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 6 3 2 5 3 2 4 3 2 3 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) - 24a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 6 4 5 4 4 +--R - 12a b cos(x) - 24a b cos(x) + 12a b cos(x) +--R + +--R 4 3 4 2 4 4 +--R 48a b cos(x) + 12a b cos(x) - 24a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 12a b - 24a b)cos(x) + (- 24a b - 48a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (12a b + 24a b)cos(x) + (48a b + 96a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (12a b + 24a b)cos(x) + (- 24a b - 48a b)cos(x) - 12a b +--R + +--R 4 +--R - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 2 3 4 5 4 4 +--R 4a b cos(x) + (- 12a b - 8a b)cos(x) - 12a b cos(x) +--R + +--R 2 3 4 3 4 2 2 3 +--R (24a b + 24a b)cos(x) + 24a b cos(x) - 12a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 3 2 6 +--R (12a b + 10a b )cos(x) + 4a b cos(x) +--R + +--R 4 3 2 5 3 2 4 +--R (- 36a b - 34a b )cos(x) - 16a b cos(x) +--R + +--R 4 3 2 3 3 2 2 4 3 2 +--R (36a b + 30a b )cos(x) + 12a b cos(x) + (- 12a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (12a b + 8a b)cos(x) + (24a b + 16a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 12a b - 12a b)cos(x) + (- 48a b - 40a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 12a b - 8a b)cos(x) + (24a b + 24a b)cos(x) +--R + +--R 2 3 4 2 +--R (12a b + 12a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 3 4 2 2 3 4 4 +--R ((- 6a b - 3a b)cos(x) - 3a b cos(x) + (6a b + 3a b)cos(x) - 3a b) +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (6a b cos(x) - 12a b cos(x) + 6a b)cot(x) + 3a b cos(x) +--R + +--R 4 2 4 +--R - 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 4 5 2 5 4 +--R (- 6a cos(x) + 12a cos(x) - 6a )cot(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R ((- 6a b - 12a )cos(x) + (12a b + 24a )cos(x) - 6a b - 12a ) +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 4 4 3 2 3 +--R (- 6a b - 6a b - 2a )cos(x) + (- 12a b - 12a b )cos(x) +--R + +--R 5 2 4 4 3 2 +--R 6a cos(x) + 12a b cos(x) + 6a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 3 2 3 2 +--R 12a b cos(x) + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 6a b cos(x) + 6a b cos(x) - 12a b cos(x) - 12a b cos(x) +--R + +--R 3 2 3 2 +--R 6a b cos(x) + 6a b +--R * +--R csc(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R - 12a b cos(x) - 12a b cos(x) + 24a b cos(x) + 24a b cos(x) +--R + +--R 4 4 +--R - 12a b cos(x) - 12a b +--R * +--R 4 +--R cot(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 12a b - 24a b)cos(x) + (- 12a b - 24a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (24a b + 48a b)cos(x) + (24a b + 48a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 12a b - 24a b)cos(x) - 12a b - 24a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 5 5 2 3 4 4 +--R (- 12b - 12a b - 10a b)cos(x) + (- 12b - 12a b - 13a b)cos(x) +--R + +--R 5 2 3 4 3 5 2 3 4 2 +--R (24b + 12a b + 12a b)cos(x) + (24b + 12a b + 12a b)cos(x) +--R + +--R 5 4 5 4 +--R (- 12b - 6a b)cos(x) - 12b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 6a b cos(x) + 12a b cos(x) - 6a b cos(x) - 24a b cos(x) +--R + +--R 4 2 4 4 +--R - 6a b cos(x) + 12a b cos(x) + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 3a b cos(x) + 6a b cos(x) - 3a b cos(x) - 12a b cos(x) +--R + +--R 4 2 4 4 +--R - 3a b cos(x) + 6a b cos(x) + 3a b +--R * +--R csc(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R - 6a cos(x) - 12a cos(x) + 6a cos(x) + 24a cos(x) +--R + +--R 5 2 5 5 +--R 6a cos(x) - 12a cos(x) - 6a +--R * +--R 4 +--R cot(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (- 6a b - 12a )cos(x) + (- 12a b - 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (6a b + 12a )cos(x) + (24a b + 48a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (6a b + 12a )cos(x) + (- 12a b - 24a )cos(x) - 6a b - 12a +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 6 4 3 2 5 5 +--R (- 6a b + 2a )cos(x) + (- 12a b - 6a b - 4a )cos(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (6a b - 6a )cos(x) + (24a b + 12a b + 12a )cos(x) +--R + +--R 4 5 2 4 3 2 4 +--R (6a b + 12a )cos(x) + (- 12a b - 6a b )cos(x) - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 4 6 2 3 4 5 +--R (6a b + 5a b)cos(x) + 2a b cos(x) + (- 18a b - 17a b)cos(x) +--R + +--R 4 4 2 3 4 3 4 2 +--R - 8a b cos(x) + (18a b + 15a b)cos(x) + 6a b cos(x) +--R + +--R 2 3 4 +--R (- 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 3 2 5 6 +--R (6a b + 4a )cos(x) + (12a b + 8a )cos(x) + (- 6a b - 6a )cos(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (- 24a b - 20a )cos(x) + (- 6a b - 4a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (12a b + 12a )cos(x) + (6a b + 6a )cos(x) +--R / +--R 6 4 6 2 6 4 +--R (6a cos(x) - 12a cos(x) + 6a )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 5 5 +--R 12a b cos(x) + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 6 5 6 4 6 3 6 2 +--R 6a cos(x) + 12a cos(x) - 6a cos(x) - 24a cos(x) - 6a cos(x) +--R + +--R 6 6 +--R 12a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 4 +--R (12a b cos(x) - 24a b cos(x) + 12a b)sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 4 2 2 +--R 24a b cos(x) + 24a b cos(x) - 48a b cos(x) - 48a b cos(x) +--R + +--R 4 2 4 2 +--R 24a b cos(x) + 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R 12a b cos(x) + 24a b cos(x) - 12a b cos(x) - 48a b cos(x) +--R + +--R 5 2 5 5 +--R - 12a b cos(x) + 24a b cos(x) + 12a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 4 6 2 6 4 +--R (6a cos(x) - 12a cos(x) + 6a )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 12a b cos(x) + 12a b cos(x) - 24a b cos(x) - 24a b cos(x) +--R + +--R 5 5 +--R 12a b cos(x) + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 6 5 6 4 6 3 6 2 +--R 6a cos(x) + 12a cos(x) - 6a cos(x) - 24a cos(x) - 6a cos(x) +--R + +--R 6 6 +--R 12a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R Type: Expression(Integer) +--E 169 + +--S 170 of 546 +t0429:= csc(x)/(a+a*sin(x)) +--R +--R +--R csc(x) +--R (167) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 170 + +--S 171 of 546 +r0429:= -1/a/cos(x)*(atanh(cos(x))*cos(x)+sin(x)-1) +--R +--R +--R - cos(x)atanh(cos(x)) - sin(x) + 1 +--R (168) ---------------------------------- +--R a cos(x) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 546 +a0429:= integrate(t0429,x) +--R +--R +--R sin(x) +--R (sin(x) + cos(x) + 1)log(----------) + 2cos(x) + 2 +--R cos(x) + 1 +--R (169) -------------------------------------------------- +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 172 + +--S 173 of 546 +m0429:= a0429-r0429 +--R +--R +--R (170) +--R 2 sin(x) +--R (cos(x)sin(x) + cos(x) + cos(x))log(----------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (cos(x)sin(x) + cos(x) + cos(x))atanh(cos(x)) + sin(x) + cos(x)sin(x) +--R + +--R 2 +--R 2cos(x) + cos(x) - 1 +--R / +--R 2 +--R a cos(x)sin(x) + a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 173 + +--S 174 of 546 +d0429:= D(m0429,x) +--R +--R +--R (171) +--R 2 5 3 2 4 +--R (cos(x) - 1)sin(x) + (3cos(x) + cos(x) - 2cos(x) - 1)sin(x) +--R + +--R 4 3 2 3 +--R (2cos(x) + 2cos(x) - cos(x) + 1)sin(x) +--R + +--R 5 4 3 2 2 +--R (4cos(x) + 3cos(x) - 4cos(x) - 2cos(x) + 2cos(x) + 1)sin(x) +--R + +--R 6 5 3 2 7 6 +--R (cos(x) + 2cos(x) - 2cos(x) - cos(x) )sin(x) + cos(x) + 2cos(x) +--R + +--R 4 3 +--R - 2cos(x) - cos(x) +--R / +--R 4 2 3 +--R (a cos(x) - a cos(x) )sin(x) +--R + +--R 5 4 3 2 2 +--R (2a cos(x) + 2a cos(x) - 2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 6 5 3 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a cos(x) )sin(x) +--R Type: Expression(Integer) +--E 174 + +--S 175 of 546 +t0430:= csc(x)^2/(a+a*sin(x)) +--R +--R +--R 2 +--R csc(x) +--R (172) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 175 + +--S 176 of 546 +r0430:= atanh(cos(x))/a-cot(x)/a-cos(x)/a/(1+sin(x)) +--R +--R +--R (sin(x) + 1)atanh(cos(x)) - cot(x)sin(x) - cot(x) - cos(x) +--R (173) ---------------------------------------------------------- +--R a sin(x) + a +--R Type: Expression(Integer) +--E 176 + +--S 177 of 546 +a0430:= integrate(t0430,x) +--R +--R +--R (174) +--R 2 sin(x) +--R ((- cos(x) - 1)sin(x) + cos(x) - 1)log(----------) +--R cos(x) + 1 +--R + +--R 2 +--R (- 3cos(x) - 2)sin(x) - cos(x) - cos(x) +--R / +--R 2 +--R (a cos(x) + a)sin(x) - a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 177 + +--S 178 of 546 +m0430:= a0430-r0430 +--R +--R +--R (175) +--R 2 2 2 +--R ((- cos(x) - 1)sin(x) + (cos(x) - cos(x) - 2)sin(x) + cos(x) - 1) +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R ((- cos(x) - 1)sin(x) + (cos(x) - cos(x) - 2)sin(x) + cos(x) - 1) +--R * +--R atanh(cos(x)) +--R + +--R 2 +--R ((cos(x) + 1)cot(x) - 3cos(x) - 2)sin(x) +--R + +--R 2 +--R ((- cos(x) + cos(x) + 2)cot(x) - 3cos(x) - 2)sin(x) +--R + +--R 2 3 2 +--R (- cos(x) + 1)cot(x) - cos(x) - cos(x) +--R / +--R 2 2 2 +--R (a cos(x) + a)sin(x) + (- a cos(x) + a cos(x) + 2a)sin(x) - a cos(x) + a +--R Type: Expression(Integer) +--E 178 + +--S 179 of 546 +d0430:= D(m0430,x) +--R +--R +--R (176) +--R 2 6 +--R (- cos(x) - 1)sin(x) +--R + +--R 3 2 2 3 2 +--R (- cos(x) - cos(x) + cos(x) + 1)cot(x) + 4cos(x) - 2cos(x) +--R + +--R - 2cos(x) - 4 +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (2cos(x) - 2cos(x) - 6cos(x) + 2cos(x) + 4)cot(x) + 2cos(x) +--R + +--R 3 2 +--R 10cos(x) - 5cos(x) - 6cos(x) - 3 +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 3 2 2 5 +--R (- cos(x) + 5cos(x) + cos(x) - 11cos(x) + 6)cot(x) + 3cos(x) +--R + +--R 4 3 2 +--R 3cos(x) + 2cos(x) - 8cos(x) - 3cos(x) + 3 +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (- 2cos(x) + 4cos(x) + 4cos(x) - 8cos(x) - 2cos(x) + 4)cot(x) +--R + +--R 6 5 4 3 2 +--R cos(x) + 10cos(x) + cos(x) - 15cos(x) - 6cos(x) + 5cos(x) + 4 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (- cos(x) + cos(x) + 2cos(x) - 2cos(x) - cos(x) + 1)cot(x) +--R + +--R 7 6 5 4 3 2 +--R - cos(x) - cos(x) + 9cos(x) + 3cos(x) - 13cos(x) - 3cos(x) +--R + +--R 5cos(x) + 1 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) + cos(x) + 2cos(x) - 2cos(x) - cos(x) + cos(x) +--R / +--R 3 2 5 +--R (a cos(x) + a cos(x) - a cos(x) - a)sin(x) +--R + +--R 4 3 2 4 +--R (- 2a cos(x) + 2a cos(x) + 6a cos(x) - 2a cos(x) - 4a)sin(x) +--R + +--R 5 4 3 2 3 +--R (a cos(x) - 5a cos(x) - a cos(x) + 11a cos(x) - 6a)sin(x) +--R + +--R 5 4 3 2 +--R (2a cos(x) - 4a cos(x) - 4a cos(x) + 8a cos(x) + 2a cos(x) - 4a) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R (a cos(x) - a cos(x) - 2a cos(x) + 2a cos(x) + a cos(x) - a)sin(x) +--R Type: Expression(Integer) +--E 179 + +--S 180 of 546 +t0431:= csc(x)^3/(a+a*sin(x)) +--R +--R +--R 3 +--R csc(x) +--R (177) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 180 + +--S 181 of 546 +r0431:= -3/2*atanh(cos(x))/a+cot(x)/a-1/2*cot(x)*csc(x)/a+cos(x)/a/(1+sin(x)) +--R +--R +--R (178) +--R (- 3sin(x) - 3)atanh(cos(x)) + (- cot(x)csc(x) + 2cot(x))sin(x) +--R + +--R - cot(x)csc(x) + 2cot(x) + 2cos(x) +--R / +--R 2a sin(x) + 2a +--R Type: Expression(Integer) +--E 181 + +--S 182 of 546 +a0431:= integrate(t0431,x) +--R +--R +--R (179) +--R 2 3 2 sin(x) +--R ((3cos(x) - 3)sin(x) + 3cos(x) + 3cos(x) - 3cos(x) - 3)log(----------) +--R cos(x) + 1 +--R + +--R 2 3 2 +--R (- 2cos(x) - cos(x))sin(x) + 6cos(x) + 5cos(x) - 5cos(x) - 4 +--R / +--R 2 3 2 +--R (2a cos(x) - 2a)sin(x) + 2a cos(x) + 2a cos(x) - 2a cos(x) - 2a +--R Type: Union(Expression(Integer),...) +--E 182 + +--S 183 of 546 +m0431:= a0431-r0431 +--R +--R +--R (180) +--R 2 2 3 2 +--R (3cos(x) - 3)sin(x) + (3cos(x) + 6cos(x) - 3cos(x) - 6)sin(x) +--R + +--R 3 2 +--R 3cos(x) + 3cos(x) - 3cos(x) - 3 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 2 +--R (3cos(x) - 3)sin(x) + (3cos(x) + 6cos(x) - 3cos(x) - 6)sin(x) +--R + +--R 3 2 +--R 3cos(x) + 3cos(x) - 3cos(x) - 3 +--R * +--R atanh(cos(x)) +--R + +--R 2 2 2 +--R (cos(x) - 1)cot(x)csc(x) + (- 2cos(x) + 2)cot(x) - 2cos(x) +--R + +--R - cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (cos(x) + 2cos(x) - cos(x) - 2)cot(x)csc(x) +--R + +--R 3 2 3 2 +--R (- 2cos(x) - 4cos(x) + 2cos(x) + 4)cot(x) + 4cos(x) + 3cos(x) +--R + +--R - 4cos(x) - 4 +--R * +--R sin(x) +--R + +--R 3 2 +--R (cos(x) + cos(x) - cos(x) - 1)cot(x)csc(x) +--R + +--R 3 2 4 3 +--R (- 2cos(x) - 2cos(x) + 2cos(x) + 2)cot(x) - 2cos(x) + 4cos(x) +--R + +--R 2 +--R 7cos(x) - 3cos(x) - 4 +--R / +--R 2 2 +--R (2a cos(x) - 2a)sin(x) +--R + +--R 3 2 3 +--R (2a cos(x) + 4a cos(x) - 2a cos(x) - 4a)sin(x) + 2a cos(x) +--R + +--R 2 +--R 2a cos(x) - 2a cos(x) - 2a +--R Type: Expression(Integer) +--E 183 + +--S 184 of 546 +d0431:= D(m0431,x) +--R +--R +--R (181) +--R 3 2 6 +--R (3cos(x) - cos(x) - 7cos(x) - 1)sin(x) +--R + +--R 4 2 2 4 2 +--R ((- 2cos(x) + 4cos(x) - 2)cot(x) - cos(x) + 2cos(x) - 1)csc(x) +--R + +--R 4 2 2 4 3 2 +--R (2cos(x) - 4cos(x) + 2)cot(x) + 2cos(x) + 10cos(x) - 6cos(x) +--R + +--R - 22cos(x) - 4 +--R * +--R 5 +--R sin(x) +--R + +--R 5 4 3 2 +--R (- 4cos(x) - 8cos(x) + 8cos(x) + 16cos(x) - 4cos(x) - 8) +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 3 2 +--R - 2cos(x) - 4cos(x) + 4cos(x) + 8cos(x) - 2cos(x) - 4 +--R * +--R csc(x) +--R + +--R 5 4 3 2 2 +--R (4cos(x) + 8cos(x) - 8cos(x) - 16cos(x) + 4cos(x) + 8)cot(x) +--R + +--R 5 4 3 2 +--R 14cos(x) + 15cos(x) - 9cos(x) - 21cos(x) - 13cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) - 12cos(x) - 8cos(x) + 24cos(x) + 22cos(x) +--R + +--R - 12cos(x) - 12 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) - 6cos(x) - 4cos(x) + 12cos(x) + 11cos(x) - 6cos(x) +--R + +--R - 6 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 12cos(x) + 8cos(x) - 24cos(x) - 22cos(x) +--R + +--R 12cos(x) + 12 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) + 30cos(x) + 14cos(x) - 44cos(x) - 24cos(x) + 18cos(x) +--R + +--R 10 +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 +--R (- 4cos(x) - 12cos(x) + 24cos(x) + 12cos(x) - 12cos(x) - 8) +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 3 2 +--R - 2cos(x) - 6cos(x) + 12cos(x) + 6cos(x) - 6cos(x) - 4 +--R * +--R csc(x) +--R + +--R 6 5 3 2 2 +--R (4cos(x) + 12cos(x) - 24cos(x) - 12cos(x) + 12cos(x) + 8)cot(x) +--R + +--R 7 6 5 4 3 +--R 7cos(x) + 12cos(x) + 7cos(x) - 17cos(x) - 35cos(x) + 25cos(x) + 9 +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) - 4cos(x) + 2cos(x) + 8cos(x) + 2cos(x) +--R + +--R - 4cos(x) - 2 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) - 2cos(x) + cos(x) + 4cos(x) + cos(x) - 2cos(x) - 1 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 4cos(x) - 2cos(x) - 8cos(x) - 2cos(x) + 4cos(x) +--R + +--R 2 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 3 +--R 2cos(x) + 10cos(x) + 10cos(x) - 12cos(x) - 28cos(x) - 10cos(x) +--R + +--R 2 +--R 14cos(x) + 12cos(x) + 2 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R 3cos(x) + 6cos(x) - 3cos(x) - 12cos(x) - 3cos(x) + 6cos(x) + 3cos(x) +--R / +--R 4 2 5 +--R (2a cos(x) - 4a cos(x) + 2a)sin(x) +--R + +--R 5 4 3 2 +--R (4a cos(x) + 8a cos(x) - 8a cos(x) - 16a cos(x) + 4a cos(x) + 8a) +--R * +--R 4 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2a cos(x) + 12a cos(x) + 8a cos(x) - 24a cos(x) - 22a cos(x) +--R + +--R 12a cos(x) + 12a +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 +--R 4a cos(x) + 12a cos(x) - 24a cos(x) - 12a cos(x) + 12a cos(x) +--R + +--R 8a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2a cos(x) + 4a cos(x) - 2a cos(x) - 8a cos(x) - 2a cos(x) +--R + +--R 4a cos(x) + 2a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 184 + +--S 185 of 546 +t0432:= csc(x)^4/(a+a*sin(x)) +--R +--R +--R 4 +--R csc(x) +--R (182) ------------ +--R a sin(x) + a +--R Type: Expression(Integer) +--E 185 + +--S 186 of 546 +r0432:= 3/2*atanh(cos(x))/a-2*cot(x)/a-1/3*cot(x)^3/a+1/2*cot(x)*csc(x)/a-_ + cos(x)/a/(1+sin(x)) +--R +--R +--R (183) +--R 3 +--R (9sin(x) + 9)atanh(cos(x)) + (3cot(x)csc(x) - 2cot(x) - 12cot(x))sin(x) +--R + +--R 3 +--R 3cot(x)csc(x) - 2cot(x) - 12cot(x) - 6cos(x) +--R / +--R 6a sin(x) + 6a +--R Type: Expression(Integer) +--E 186 + +--S 187 of 546 +a0432:= integrate(t0432,x) +--R +--R +--R (184) +--R 3 2 4 2 +--R (- 9cos(x) - 9cos(x) + 9cos(x) + 9)sin(x) + 9cos(x) - 18cos(x) +--R + +--R 9 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 2 4 3 +--R (- 22cos(x) - 15cos(x) + 21cos(x) + 12)sin(x) - 10cos(x) - 7cos(x) +--R + +--R 2 +--R 12cos(x) + 9cos(x) +--R / +--R 3 2 4 +--R (6a cos(x) + 6a cos(x) - 6a cos(x) - 6a)sin(x) - 6a cos(x) +--R + +--R 2 +--R 12a cos(x) - 6a +--R Type: Union(Expression(Integer),...) +--E 187 + +--S 188 of 546 +m0432:= a0432-r0432 +--R +--R +--R (185) +--R 3 2 2 +--R (- 9cos(x) - 9cos(x) + 9cos(x) + 9)sin(x) +--R + +--R 4 3 2 4 +--R (9cos(x) - 9cos(x) - 27cos(x) + 9cos(x) + 18)sin(x) + 9cos(x) +--R + +--R 2 +--R - 18cos(x) + 9 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 2 2 +--R (- 9cos(x) - 9cos(x) + 9cos(x) + 9)sin(x) +--R + +--R 4 3 2 4 +--R (9cos(x) - 9cos(x) - 27cos(x) + 9cos(x) + 18)sin(x) + 9cos(x) +--R + +--R 2 +--R - 18cos(x) + 9 +--R * +--R atanh(cos(x)) +--R + +--R 3 2 +--R (- 3cos(x) - 3cos(x) + 3cos(x) + 3)cot(x)csc(x) +--R + +--R 3 2 3 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2)cot(x) +--R + +--R 3 2 3 2 +--R (12cos(x) + 12cos(x) - 12cos(x) - 12)cot(x) - 22cos(x) - 15cos(x) +--R + +--R 21cos(x) + 12 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (3cos(x) - 3cos(x) - 9cos(x) + 3cos(x) + 6)cot(x)csc(x) +--R + +--R 4 3 2 3 +--R (- 2cos(x) + 2cos(x) + 6cos(x) - 2cos(x) - 4)cot(x) +--R + +--R 4 3 2 +--R (- 12cos(x) + 12cos(x) + 36cos(x) - 12cos(x) - 24)cot(x) +--R + +--R 4 3 2 +--R - 4cos(x) - 23cos(x) - 9cos(x) + 24cos(x) + 12 +--R * +--R sin(x) +--R + +--R 4 2 +--R (3cos(x) - 6cos(x) + 3)cot(x)csc(x) +--R + +--R 4 2 3 4 2 +--R (- 2cos(x) + 4cos(x) - 2)cot(x) + (- 12cos(x) + 24cos(x) - 12)cot(x) +--R + +--R 5 4 3 2 +--R - 6cos(x) - 10cos(x) + 5cos(x) + 12cos(x) + 3cos(x) +--R / +--R 3 2 2 +--R (6a cos(x) + 6a cos(x) - 6a cos(x) - 6a)sin(x) +--R + +--R 4 3 2 +--R (- 6a cos(x) + 6a cos(x) + 18a cos(x) - 6a cos(x) - 12a)sin(x) +--R + +--R 4 2 +--R - 6a cos(x) + 12a cos(x) - 6a +--R Type: Expression(Integer) +--E 188 + +--S 189 of 546 +d0432:= D(m0432,x) +--R +--R +--R (186) +--R 4 3 6 +--R (- 9cos(x) - 2cos(x) - 6cos(x) + 9)sin(x) +--R + +--R 5 4 3 2 +--R (6cos(x) + 6cos(x) - 12cos(x) - 12cos(x) + 6cos(x) + 6) +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 3 2 +--R 3cos(x) + 3cos(x) - 6cos(x) - 6cos(x) + 3cos(x) + 3 +--R * +--R csc(x) +--R + +--R 5 4 3 2 4 +--R (- 6cos(x) - 6cos(x) + 12cos(x) + 12cos(x) - 6cos(x) - 6)cot(x) +--R + +--R 5 4 3 2 +--R (- 18cos(x) - 18cos(x) + 36cos(x) + 36cos(x) - 18cos(x) - 18) +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 3 +--R 32cos(x) - 18cos(x) - 52cos(x) + 30 +--R * +--R 5 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 12cos(x) + 12cos(x) + 48cos(x) - 24cos(x) - 60cos(x) +--R + +--R 12cos(x) + 24 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - 6cos(x) + 6cos(x) + 24cos(x) - 12cos(x) - 30cos(x) +--R + +--R 6cos(x) + 12 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 12cos(x) - 12cos(x) - 48cos(x) + 24cos(x) + 60cos(x) +--R + +--R - 12cos(x) - 24 +--R * +--R 4 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R 36cos(x) - 36cos(x) - 144cos(x) + 72cos(x) + 180cos(x) +--R + +--R - 36cos(x) - 72 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R 18cos(x) + 77cos(x) - 66cos(x) - 132cos(x) + 60cos(x) + 39cos(x) +--R + +--R 12 +--R * +--R 4 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 6cos(x) - 30cos(x) - 12cos(x) + 96cos(x) + 6cos(x) +--R + +--R 2 +--R - 102cos(x) + 36 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R 3cos(x) - 15cos(x) - 6cos(x) + 48cos(x) + 3cos(x) +--R + +--R 2 +--R - 51cos(x) + 18 +--R * +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 6cos(x) + 30cos(x) + 12cos(x) - 96cos(x) - 6cos(x) +--R + +--R 2 +--R 102cos(x) - 36 +--R * +--R 4 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R - 18cos(x) + 90cos(x) + 36cos(x) - 288cos(x) - 18cos(x) +--R + +--R 2 +--R 306cos(x) - 108 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R 26cos(x) + 36cos(x) - 16cos(x) - 126cos(x) - 50cos(x) +--R + +--R 2 +--R 144cos(x) + 36cos(x) - 42 +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 12cos(x) - 24cos(x) - 36cos(x) + 72cos(x) + 36cos(x) +--R + +--R 2 +--R - 72cos(x) - 12cos(x) + 24 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R 6cos(x) - 12cos(x) - 18cos(x) + 36cos(x) + 18cos(x) +--R + +--R 2 +--R - 36cos(x) - 6cos(x) + 12 +--R * +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 12cos(x) + 24cos(x) + 36cos(x) - 72cos(x) - 36cos(x) +--R + +--R 2 +--R 72cos(x) + 12cos(x) - 24 +--R * +--R 4 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R - 36cos(x) + 72cos(x) + 108cos(x) - 216cos(x) - 108cos(x) +--R + +--R 2 +--R 216cos(x) + 36cos(x) - 72 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 +--R 3cos(x) + 79cos(x) + 27cos(x) - 198cos(x) - 108cos(x) +--R + +--R 3 2 +--R 143cos(x) + 123cos(x) - 24cos(x) - 45 +--R * +--R 2 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 6cos(x) - 6cos(x) - 18cos(x) + 18cos(x) + 18cos(x) +--R + +--R 2 +--R - 18cos(x) - 6cos(x) + 6 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 2 +--R 3cos(x) - 3cos(x) - 9cos(x) + 9cos(x) + 9cos(x) - 9cos(x) +--R + +--R - 3cos(x) + 3 +--R * +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 6cos(x) + 6cos(x) + 18cos(x) - 18cos(x) - 18cos(x) +--R + +--R 2 +--R 18cos(x) + 6cos(x) - 6 +--R * +--R 4 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R - 18cos(x) + 18cos(x) + 54cos(x) - 54cos(x) - 54cos(x) +--R + +--R 2 +--R 54cos(x) + 18cos(x) - 18 +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 7 6 5 +--R - 6cos(x) - 12cos(x) + 74cos(x) + 48cos(x) - 170cos(x) +--R + +--R 4 3 2 +--R - 72cos(x) + 138cos(x) + 48cos(x) - 36cos(x) - 12 +--R * +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 9cos(x) + 9cos(x) + 27cos(x) - 27cos(x) - 27cos(x) + 27cos(x) +--R + +--R 2 +--R 9cos(x) - 9cos(x) +--R / +--R 5 4 3 2 +--R (6a cos(x) + 6a cos(x) - 12a cos(x) - 12a cos(x) + 6a cos(x) + 6a) +--R * +--R 5 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 12a cos(x) + 12a cos(x) + 48a cos(x) - 24a cos(x) - 60a cos(x) +--R + +--R 12a cos(x) + 24a +--R * +--R 4 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 6a cos(x) - 30a cos(x) - 12a cos(x) + 96a cos(x) + 6a cos(x) +--R + +--R 2 +--R - 102a cos(x) + 36a +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 12a cos(x) - 24a cos(x) - 36a cos(x) + 72a cos(x) + 36a cos(x) +--R + +--R 2 +--R - 72a cos(x) - 12a cos(x) + 24a +--R * +--R 2 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 6a cos(x) - 6a cos(x) - 18a cos(x) + 18a cos(x) + 18a cos(x) +--R + +--R 2 +--R - 18a cos(x) - 6a cos(x) + 6a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 546 +t0433:= sin(x)^2/(a+b*cos(x)) +--R +--R +--R 2 +--R sin(x) +--R (187) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 546 +r0433:= 1/b^2*(a*x+2*(a^2-b^2)^(1/2)*_ + atan((a-b)/(a^2-b^2)^(1/2)*(-1+cos(x))/sin(x))-b*sin(x)) +--R +--R +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R - 2\|- b + a atan(---------------------) - b sin(x) + a x +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R (188) ----------------------------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 191 + +--S 192 of 546 +a0433:= integrate(t0433,x) +--R +--R +--R (189) +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 - sin(x)\|b - a - a cos(x) - b +--R \|b - a log(---------------------------------) - b sin(x) + a x +--R b cos(x) + a +--R [-----------------------------------------------------------------, +--R 2 +--R b +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R - 2\|- b + a atan(------------------------) - b sin(x) + a x +--R (b - a)sin(x) +--R --------------------------------------------------------------] +--R 2 +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 192 + +--S 193 of 546 +m0433a:= a0433.1-r0433 +--R +--R +--R (190) +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 - sin(x)\|b - a - a cos(x) - b +--R \|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2\|- b + a atan(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R / +--R 2 +--R b +--R Type: Expression(Integer) +--E 193 + +--S 194 of 546 +d0433a:= D(m0433a,x) +--R +--R +--R (191) +--R 3 2 3 2 2 3 3 +--R ((- 2b + 2a b)cos(x) + b - a b - a b + a )sin(x) +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 2b + 2a b)cos(x) + (b - a b - a b + a )cos(x) +--R + +--R 3 2 3 2 2 3 +--R (2b - 2a b)cos(x) - b + a b + a b - a +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 3 2 2 3 4 +--R (b + a b - a b - a b)sin(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 2 +--R ((- a b - a b + a b + a )cos(x) - b - a b + a b + a b)sin(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 4 3 +--R (- b - a b + a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 4 3 2 2 3 2 3 2 2 3 4 +--R (b + a b - a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R / +--R 4 3 3 2 2 3 +--R ((b + a b )cos(x) + a b + a b )sin(x) +--R + +--R 4 3 3 4 3 2 2 2 +--R (- b + a b )cos(x) + (2b - 3a b + a b )cos(x) +--R + +--R 4 3 2 2 3 2 2 +--R (- b + 3a b - 2a b )cos(x) - a b + a b +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 3 2 5 4 2 3 3 2 4 2 3 +--R ((a b + a b )cos(x) + (b + a b + a b + a b )cos(x) + a b + a b ) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 4 5 4 2 3 3 2 3 +--R (- a b + a b )cos(x) + (- b + 3a b - 3a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (2b - 4a b + 4a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 3 +--R (- b + 3a b - 3a b + a b )cos(x) - a b + a b +--R Type: Expression(Integer) +--E 194 + +--S 195 of 546 +m0433b:= a0433.2-r0433 +--R +--R +--R (192) +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R - 2\|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2\|- b + a atan(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R / +--R 2 +--R b +--R Type: Expression(Integer) +--E 195 + +--S 196 of 546 +d0433b:= D(m0433b,x) +--R +--R +--R (193) +--R 3 2 4 2 3 3 2 2 +--R (- 4b + 4a b)sin(x) + ((4a b - 4a )cos(x) + 4b - 4a b)sin(x) +--R + +--R 3 2 4 2 3 3 3 2 2 +--R (4b - 4a b)cos(x) + (4a b - 4a )cos(x) + (- 4b + 4a b)cos(x) +--R + +--R 2 3 +--R (- 4a b + 4a )cos(x) +--R / +--R 4 2 2 4 +--R (b - a b )sin(x) +--R + +--R 4 2 2 2 3 4 2 2 2 +--R ((- 2b - 2a b )cos(x) - 8a b cos(x) - 2b - 2a b )sin(x) +--R + +--R 4 2 2 4 4 2 2 2 4 2 2 +--R (b - a b )cos(x) + (- 2b + 2a b )cos(x) + b - a b +--R Type: Expression(Integer) +--E 196 + +--S 197 of 546 +t0434:= sin(x)^4/(a+b*cos(x)) +--R +--R +--R 4 +--R sin(x) +--R (194) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 197 + +--S 198 of 546 +r0434:= -a^3*x/b^4+3/2*a*x/b^2+2*(a^2-b^2)^(3/2)*_ + atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b^4+a^2*sin(x)/b^3-_ + sin(x)/b-1/2*a*cos(x)*sin(x)/b^2-1/3*sin(x)^3/b +--R +--R +--R (195) +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 2 3 3 +--R (12b - 12a )\|- b + a atan(-------------) - 2b sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 +--R (- 3a b cos(x) - 6b + 6a b)sin(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R Type: Expression(Integer) +--E 198 + +--S 199 of 546 +a0434:= integrate(t0434,x) +--R +--R +--R (196) +--R [ +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 | 2 2 - sin(x)\|b - a - a cos(x) - b +--R (6b - 6a )\|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R 3 2 2 3 2 2 3 +--R (2b cos(x) - 3a b cos(x) - 8b + 6a b)sin(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R , +--R +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 | 2 2 (cos(x) + 1)\|- b + a +--R (- 12b + 12a )\|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R 3 2 2 3 2 2 3 +--R (2b cos(x) - 3a b cos(x) - 8b + 6a b)sin(x) + (9a b - 6a )x +--R / +--R 4 +--R 6b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 199 + +--S 200 of 546 +m0434a:= a0434.1-r0434 +--R +--R +--R (197) +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 | 2 2 - sin(x)\|b - a - a cos(x) - b +--R (3b - 3a )\|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 2 3 3 +--R (- 6b + 6a )\|- b + a atan(-------------) + b sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 +--R (b cos(x) - b )sin(x) +--R / +--R 4 +--R 3b +--R Type: Expression(Integer) +--E 200 + +--S 201 of 546 +d0434a:= D(m0434a,x) +--R +--R +--R (198) +--R 4 3 2 3 2 2 3 +--R ((b - a b )cos(x) + (a b - a b )cos(x))sin(x) +--R + +--R 4 3 4 3 2 2 3 +--R (b - a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 2 4 4 +--R (- b + a b )cos(x) + (3b - a b - 5a b + 3a )cos(x) + 3b +--R + +--R 2 2 4 +--R - 6a b + 3a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 2 2 3 +--R ((- b - a b )cos(x) + (- a b - a b )cos(x))sin(x) +--R + +--R 4 3 4 3 2 2 3 +--R (- b - a b )cos(x) + (- a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 2 4 4 +--R (b + a b )cos(x) + (3b + a b - 5a b + 3a )cos(x) - 3b +--R + +--R 2 2 4 +--R 6a b - 3a +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 3 3 5 4 2 3 3 2 2 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) +--R + +--R 4 2 3 5 4 2 3 3 2 4 5 +--R (a b - a b )cos(x) + 3b - 3a b - 6a b + 6a b + 3a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (2b + a b - 7a b + a b + 3a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 3 2 5 +--R (3b + 2a b - 5a b - 6a b + 3a b + 3a )cos(x) + 3a b - 6a b + 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 5 4 2 3 3 2 2 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 4 2 3 5 4 2 3 3 2 4 5 +--R (- a b - a b )cos(x) - 3b - 3a b + 6a b + 6a b - 3a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 2b + a b + 7a b + a b - 3a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 3 2 5 +--R (3b - 2a b - 5a b + 6a b + 3a b - 3a )cos(x) + 3a b - 6a b + 3a +--R / +--R 5 4 4 2 3 x 2 +--R ((3b - 3a b )cos(x) + 3a b - 3a b )sin(x)tan(-) +--R 2 +--R + +--R 5 4 4 2 3 +--R ((- 3b - 3a b )cos(x) - 3a b - 3a b )sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 2 4 2 6 5 2 4 3 3 5 +--R (3a b - 3a b )cos(x) + (3b - 3a b + 3a b - 3a b )cos(x) + 3a b +--R + +--R 2 4 +--R - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 2 6 5 2 4 3 3 5 +--R (- 3a b - 3a b )cos(x) + (- 3b - 3a b - 3a b - 3a b )cos(x) - 3a b +--R + +--R 2 4 +--R - 3a b +--R Type: Expression(Integer) +--E 201 + +--S 202 of 546 +m0434b:= a0434.2-r0434 +--R +--R +--R (199) +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 | 2 2 (cos(x) + 1)\|- b + a +--R (- 6b + 6a )\|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 2 3 3 +--R (- 6b + 6a )\|- b + a atan(-------------) + b sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 +--R (b cos(x) - b )sin(x) +--R / +--R 4 +--R 3b +--R Type: Expression(Integer) +--E 202 + +--S 203 of 546 +d0434b:= D(m0434b,x) +--R +--R +--R (200) +--R 5 4 2 3 4 +--R (b - 2a b + a b )cos(x)sin(x) +--R + +--R 4 2 3 3 5 2 3 2 +--R (- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 5 4 5 4 2 3 3 2 4 5 +--R (- 2b + 2a b )cos(x) - 3b + 3a b + 6a b - 6a b - 3a b + 3a +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 5 5 2 3 4 +--R (- b + a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 7b + 3a b + 16a b - 6a b - 9a b + 3a )cos(x) +--R + +--R 5 2 3 4 5 4 2 3 3 2 4 +--R (- 11b + 23a b - 12a b)cos(x) - 3b - 3a b + 6a b + 6a b - 3a b +--R + +--R 5 +--R - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R (- b + a b )cos(x)sin(x) +--R + +--R 4 2 3 3 5 4 2 3 2 +--R (2a b + 2a b )cos(x) + (2b + 4a b + 2a b )cos(x) +--R + +--R 5 4 5 4 2 3 3 2 4 5 +--R (2b + 2a b )cos(x) + 9b + 3a b - 18a b - 6a b + 9a b + 3a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 5 5 4 2 3 4 +--R (b + 2a b + a b )cos(x) + (2b + 4a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (b - a b - 8a b - 6a b + 3a b + 3a )cos(x) +--R + +--R 5 4 2 3 5 4 2 3 3 2 4 5 +--R (- b - 2a b - a b )cos(x) - 3b - 3a b + 6a b + 6a b - 3a b - 3a +--R / +--R 6 5 2 4 2 6 2 4 2 +--R (3b - 6a b + 3a b )sin(x) + (- 3b + 3a b )cos(x) +--R + +--R 6 2 4 6 2 4 +--R (- 6b + 6a b )cos(x) - 3b + 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 4 2 6 5 2 4 2 +--R (- 3b + 3a b )sin(x) + (3b + 6a b + 3a b )cos(x) +--R + +--R 6 5 2 4 6 5 2 4 +--R (6b + 12a b + 6a b )cos(x) + 3b + 6a b + 3a b +--R Type: Expression(Integer) +--E 203 + +--S 204 of 546 +t0435:= sin(2*x)/(1+cos(2*x)) +--R +--R +--R sin(2x) +--R (201) ----------- +--R cos(2x) + 1 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 546 +r0435:= -log(cos(x)) +--R +--R +--R (202) - log(cos(x)) +--R Type: Expression(Integer) +--E 205 + +--S 206 of 546 +a0435:= integrate(t0435,x) +--R +--R +--R 2 +--R log(-----------) +--R cos(2x) + 1 +--R (203) ---------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 206 + +--S 207 of 546 +m0435:= a0435-r0435 +--R +--R +--R 2 +--R 2log(cos(x)) + log(-----------) +--R cos(2x) + 1 +--R (204) ------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 546 +d0435:= D(m0435,x) +--R +--R +--R cos(x)sin(2x) + (- cos(2x) - 1)sin(x) +--R (205) ------------------------------------- +--R cos(x)cos(2x) + cos(x) +--R Type: Expression(Integer) +--E 208 + +--S 209 of 546 +t0436:= sin(2*x)/(1-cos(2*x)) +--R +--R +--R sin(2x) +--R (206) - ----------- +--R cos(2x) - 1 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 546 +r0436:= log(sin(x)) +--R +--R +--R (207) log(sin(x)) +--R Type: Expression(Integer) +--E 210 + +--S 211 of 546 +a0436:= integrate(t0436,x) +--R +--R +--R sin(2x) 2 +--R 2log(-----------) - log(-----------) +--R cos(2x) + 1 cos(2x) + 1 +--R (208) ------------------------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 211 + +--S 212 of 546 +m0436:= a0436-r0436 +--R +--R +--R sin(2x) 2 +--R 2log(-----------) - 2log(sin(x)) - log(-----------) +--R cos(2x) + 1 cos(2x) + 1 +--R (209) --------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 546 +d0436:= D(m0436,x) +--R +--R +--R (210) +--R 2 +--R sin(x)sin(2x) + (- cos(x)cos(2x) - cos(x))sin(2x) +--R + +--R 2 +--R (2cos(2x) + 2cos(2x))sin(x) +--R / +--R (cos(2x) + 1)sin(x)sin(2x) +--R Type: Expression(Integer) +--E 213 + +--S 214 of 546 +t0437:= sin(x)^2/(a+a*cos(x)) +--R +--R +--R 2 +--R sin(x) +--R (211) ------------ +--R a cos(x) + a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 546 +r0437:= -(-x+sin(x))/a +--R +--R +--R - sin(x) + x +--R (212) ------------ +--R a +--R Type: Expression(Integer) +--E 215 + +--S 216 of 546 +a0437:= integrate(t0437,x) +--R +--R +--R - sin(x) + x +--R (213) ------------ +--R a +--R Type: Union(Expression(Integer),...) +--E 216 + +--S 217 of 546 +m0437:= a0437-r0437 +--R +--R +--R (214) 0 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 546 +d0437:= D(m0437,x) +--R +--R +--R (215) 0 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 546 +t0438:= cos(x)^2/(a+b*cos(x)) +--R +--R +--R 2 +--R cos(x) +--R (216) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 546 +r0438:= -a*x/b^2+2*a^2*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b^2/_ + (a^2-b^2)^(1/2)+sin(x)/b +--R +--R +--R x +--R (b - a)tan(-) +---------+ +--R 2 2 | 2 2 +--R - 2a atan(-------------) + (b sin(x) - a x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (217) ------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 220 + +--S 221 of 546 +a0438:= integrate(t0438,x) +--R +--R +--R (218) +--R [ +--R +-------+ +--R | 2 2 2 2 +--R 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R | 2 2 +--R (b sin(x) - a x)\|b - a +--R / +--R +-------+ +--R 2 | 2 2 +--R b \|b - a +--R , +--R +---------+ +--R | 2 2 +---------+ +--R 2 sin(x)\|- b + a | 2 2 +--R 2a atan(---------------------) + (b sin(x) - a x)\|- b + a +--R (b + a)cos(x) + b + a +--R -------------------------------------------------------------] +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Union(List(Expression(Integer)),...) +--E 221 + +--S 222 of 546 +m0438a:= a0438.1-r0438 +--R +--R +--R (219) +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 2 | 2 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R a \|- b + a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 2 | 2 2 2 +--R 2a \|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R b \|- b + a \|b - a +--R Type: Expression(Integer) +--E 222 + +--S 223 of 546 +d0438a:= D(m0438a,x) +--R +--R +--R (220) +--R 2 3 2 2 2 2 3 3 x 2 +--R ((a b - a )sin(x) + a b cos(x) + (a b + a )cos(x) + a )tan(-) +--R 2 +--R + +--R 2 3 2 2 2 2 3 3 +--R (- a b - a )sin(x) - a b cos(x) + (a b - a )cos(x) + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 4 2 2 4 x 2 +--R ((a b - a )cos(x) + a b - a )sin(x)tan(-) +--R 2 +--R + +--R 2 2 4 2 2 4 +--R ((a b - a )cos(x) - a b + a )sin(x) +--R / +--R 3 2 2 2 4 3 2 2 3 3 +--R (a b - a b )cos(x) + (b - a b + a b - a b)cos(x) + a b +--R + +--R 2 2 +--R - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 4 3 2 2 3 3 2 2 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b)cos(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 4 x 2 +--R ((b - a b - a b + a b )cos(x) + a b - a b - a b + a b)sin(x)tan(-) +--R 2 +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 4 +--R ((- b - a b + a b + a b )cos(x) - a b - a b + a b + a b)sin(x) +--R Type: Expression(Integer) +--E 223 + +--S 224 of 546 +m0438b:= a0438.2-r0438 +--R +--R +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R 2 sin(x)\|- b + a 2 2 +--R 2a atan(---------------------) + 2a atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R (221) ------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 546 +d0438b:= D(m0438b,x) +--R +--R +--R (222) +--R 2 3 2 2 3 2 2 2 3 +--R ((- a b + a )sin(x) + (- 3a b + a )cos(x) - 4a b cos(x) - a b - a ) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 3 2 2 3 +--R (3a b + a )sin(x) + (a b + a )cos(x) - a b - a +--R / +--R 4 3 2 2 2 4 2 2 2 +--R (b - 2a b + a b )sin(x) + (- b + a b )cos(x) +--R + +--R 4 2 2 4 2 2 +--R (- 2b + 2a b )cos(x) - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 4 3 2 2 2 +--R (- b + a b )sin(x) + (b + 2a b + a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R (2b + 4a b + 2a b )cos(x) + b + 2a b + a b +--R Type: Expression(Integer) +--E 225 + +--S 226 of 546 +t0439:= cos(x)^3/(a+b*cos(x)) +--R +--R +--R 3 +--R cos(x) +--R (223) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 546 +r0439:= a^2*x/b^3+1/2*x/b-2*a^3*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/_ + b^3/(a^2-b^2)^(1/2)-a*sin(x)/b^2+1/2*cos(x)*sin(x)/b +--R +--R +--R (224) +--R x +--R (b - a)tan(-) +---------+ +--R 3 2 2 2 2 | 2 2 +--R 4a atan(-------------) + ((b cos(x) - 2a b)sin(x) + (b + 2a )x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ---------------------------------------------------------------------------- +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression(Integer) +--E 227 + +--S 228 of 546 +a0439:= integrate(t0439,x) +--R +--R +--R (225) +--R [ +--R +-------+ +--R | 2 2 2 2 +--R 3 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R 2a log(--------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R ((b cos(x) - 2a b)sin(x) + (b + 2a )x)\|b - a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2b \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 3 sin(x)\|- b + a +--R - 4a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R ((b cos(x) - 2a b)sin(x) + (b + 2a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 228 + +--S 229 of 546 +m0439a:= a0439.1-r0439 +--R +--R +--R (226) +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 3 | 2 2 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R a \|- b + a log(--------------------------------------------) +--R b cos(x) + a +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 3 | 2 2 2 +--R - 2a \|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 3 | 2 2 | 2 2 +--R b \|- b + a \|b - a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 546 +d0439a:= D(m0439a,x) +--R +--R +--R (227) +--R 3 4 2 3 2 3 4 4 x 2 +--R ((- a b + a )sin(x) - a b cos(x) + (- a b - a )cos(x) - a )tan(-) +--R 2 +--R + +--R 3 4 2 3 2 3 4 4 +--R (a b + a )sin(x) + a b cos(x) + (- a b + a )cos(x) - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 2 5 3 2 5 x 2 +--R ((a b - a )cos(x) + a b - a )sin(x)tan(-) +--R 2 +--R + +--R 3 2 5 3 2 5 +--R ((a b - a )cos(x) - a b + a )sin(x) +--R / +--R 4 2 3 2 5 4 2 3 3 2 4 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) + a b +--R + +--R 2 3 +--R - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 2 5 4 2 3 3 2 4 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) - a b +--R + +--R 2 3 +--R - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 5 2 4 3 3 5 2 4 3 3 4 2 +--R ((- b + a b + a b - a b )cos(x) - a b + a b + a b - a b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 4 3 3 5 2 4 3 3 4 2 +--R ((b + a b - a b - a b )cos(x) + a b + a b - a b - a b )sin(x) +--R Type: Expression(Integer) +--E 230 + +--S 231 of 546 +m0439b:= a0439.2-r0439 +--R +--R +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R 3 sin(x)\|- b + a 3 2 +--R - 2a atan(---------------------) - 2a atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R (228) --------------------------------------------------------- +--R +---------+ +--R 3 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 546 +d0439b:= D(m0439b,x) +--R +--R +--R (229) +--R 3 4 2 3 4 2 3 3 4 x 2 +--R ((a b - a )sin(x) + (3a b - a )cos(x) + 4a b cos(x) + a b + a )tan(-) +--R 2 +--R + +--R 3 4 2 3 4 2 3 4 +--R (- 3a b - a )sin(x) + (- a b - a )cos(x) + a b + a +--R / +--R 5 4 2 3 2 5 2 3 2 +--R (b - 2a b + a b )sin(x) + (- b + a b )cos(x) +--R + +--R 5 2 3 5 2 3 +--R (- 2b + 2a b )cos(x) - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 2 5 4 2 3 2 +--R (- b + a b )sin(x) + (b + 2a b + a b )cos(x) +--R + +--R 5 4 2 3 5 4 2 3 +--R (2b + 4a b + 2a b )cos(x) + b + 2a b + a b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 546 +t0440:= cos(x)^4/(a+b*cos(x)) +--R +--R +--R 4 +--R cos(x) +--R (230) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 546 +r0440:= -a^3*x/b^4-1/2*a*x/b^2+2*a^4*atan((a-b)*tan(1/2*x)/_ + (a^2-b^2)^(1/2))/b^4/(a^2-b^2)^(1/2)+a^2*sin(x)/b^3+_ + sin(x)/b-1/2*a*cos(x)*sin(x)/b^2-1/3*sin(x)^3/b +--R +--R +--R (231) +--R x +--R (b - a)tan(-) +--R 4 2 +--R - 12a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 2 3 2 2 3 +--R (- 2b sin(x) + (- 3a b cos(x) + 6b + 6a b)sin(x) + (- 3a b - 6a )x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6b \|- b + a +--R Type: Expression(Integer) +--E 234 + +--S 235 of 546 +a0440:= integrate(t0440,x) +--R +--R +--R (232) +--R [ +--R +-------+ +--R | 2 2 2 2 +--R 4 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R 6a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R 3 2 2 3 2 2 3 +--R ((2b cos(x) - 3a b cos(x) + 4b + 6a b)sin(x) + (- 3a b - 6a )x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6b \|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 4 sin(x)\|- b + a +--R 12a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R 3 2 2 3 2 2 3 +--R ((2b cos(x) - 3a b cos(x) + 4b + 6a b)sin(x) + (- 3a b - 6a )x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6b \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 235 + +--S 236 of 546 +m0440a:= a0440.1-r0440 +--R +--R +--R (233) +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 4 | 2 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R 3a \|- b + a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 4 | 2 2 2 +--R 6a \|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 3 3 3 2 3 | 2 2 | 2 2 +--R (b sin(x) + (b cos(x) - b )sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 4 | 2 2 | 2 2 +--R 3b \|- b + a \|b - a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 546 +d0440a:= D(m0440a,x) +--R +--R +--R (234) +--R 4 2 3 3 5 4 2 3 3 2 2 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) +--R + +--R 4 2 3 4 5 +--R (a b - a b )cos(x) + 3a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- b + a b - a b + a b + 3a b)cos(x) +--R + +--R 4 2 3 4 5 5 +--R (- a b + a b + 3a b + 3a )cos(x) + 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 5 4 2 3 3 2 2 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 4 2 3 4 5 +--R (- a b - a b )cos(x) - 3a b - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (b + a b + a b + a b - 3a b)cos(x) +--R + +--R 4 2 3 4 5 5 +--R (a b + a b + 3a b - 3a )cos(x) + 3a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 5 2 4 3 3 2 +--R (b - a b - a b + a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 +--R (a b - a b - a b + a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 2 4 3 3 4 +--R (b - a b - a b + a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (a b - a b - a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (- b + a b + a b - a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 4 2 6 +--R (- a b + a b + a b + 2a b - 3a )cos(x) + 3a b - 3a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 +--R (- a b - a b + a b + a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- b - a b + a b + a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 4 2 6 +--R (a b + a b - a b + 2a b - 3a )cos(x) - 3a b + 3a +--R * +--R sin(x) +--R / +--R 5 2 4 2 6 5 2 4 3 3 +--R (3a b - 3a b )cos(x) + (3b - 3a b + 3a b - 3a b )cos(x) +--R + +--R 5 2 4 +--R 3a b - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 2 6 5 2 4 3 3 +--R (- 3a b - 3a b )cos(x) + (- 3b - 3a b - 3a b - 3a b )cos(x) +--R + +--R 5 2 4 +--R - 3a b - 3a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 7 6 2 5 3 4 6 2 5 3 4 4 3 +--R ((3b - 3a b - 3a b + 3a b )cos(x) + 3a b - 3a b - 3a b + 3a b ) +--R * +--R x 2 +--R sin(x)tan(-) +--R 2 +--R + +--R 7 6 2 5 3 4 6 2 5 3 4 4 3 +--R ((- 3b - 3a b + 3a b + 3a b )cos(x) - 3a b - 3a b + 3a b + 3a b ) +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 237 + +--S 238 of 546 +m0440b:= a0440.2-r0440 +--R +--R +--R (235) +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R 4 sin(x)\|- b + a 4 2 +--R 6a atan(---------------------) + 6a atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 3 3 2 3 | 2 2 +--R (b sin(x) + (b cos(x) - b )sin(x))\|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 3b \|- b + a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 546 +d0440b:= D(m0440b,x) +--R +--R +--R (236) +--R 5 4 2 3 4 +--R (b - 2a b + a b )cos(x)sin(x) +--R + +--R 4 2 3 3 5 2 3 2 +--R (- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 5 4 4 5 +--R (- 2b + 2a b )cos(x) - 3a b + 3a +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 5 5 2 3 4 +--R (- b + a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 5 2 3 4 5 2 5 2 3 4 4 +--R (2b - 2a b - 9a b + 3a )cos(x) + (b - a b - 12a b)cos(x) - 3a b +--R + +--R 5 +--R - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R (- b + a b )cos(x)sin(x) +--R + +--R 4 2 3 3 5 4 2 3 2 +--R (2a b + 2a b )cos(x) + (2b + 4a b + 2a b )cos(x) +--R + +--R 5 4 4 5 +--R (2b + 2a b )cos(x) + 9a b + 3a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 5 5 4 2 3 4 +--R (b + 2a b + a b )cos(x) + (2b + 4a b + 2a b )cos(x) +--R + +--R 5 4 2 3 4 5 2 5 4 2 3 +--R (- 2b - 4a b - 2a b + 3a b + 3a )cos(x) + (- b - 2a b - a b )cos(x) +--R + +--R 4 5 +--R - 3a b - 3a +--R / +--R 6 5 2 4 2 6 2 4 2 +--R (3b - 6a b + 3a b )sin(x) + (- 3b + 3a b )cos(x) +--R + +--R 6 2 4 6 2 4 +--R (- 6b + 6a b )cos(x) - 3b + 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 4 2 6 5 2 4 2 +--R (- 3b + 3a b )sin(x) + (3b + 6a b + 3a b )cos(x) +--R + +--R 6 5 2 4 6 5 2 4 +--R (6b + 12a b + 6a b )cos(x) + 3b + 6a b + 3a b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 546 +t0441:= tan(x)^2/(a+b*cos(x)) +--R +--R +--R 2 +--R tan(x) +--R (237) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 240 + +--S 241 of 546 +r0441:= -2*(a^2-b^2)^(1/2)*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^2-_ + b*atanh(sin(x))/a^2+tan(x)/a +--R +--R +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R - b atanh(sin(x)) + 2\|- b + a atan(-------------) + a tan(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (238) --------------------------------------------------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 546 +a0441:= integrate(t0441,x) +--R +--R +--R (239) +--R [ +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - b cos(x)log(-------------------) + b cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 - sin(x)\|b - a - a cos(x) - b +--R cos(x)\|b - a log(---------------------------------) + a sin(x) +--R b cos(x) + a +--R / +--R 2 +--R a cos(x) +--R , +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - b cos(x)log(-------------------) + b cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R - 2cos(x)\|- b + a atan(------------------------) + a sin(x) +--R (b - a)sin(x) +--R / +--R 2 +--R a cos(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 242 + +--S 243 of 546 +m0441a:= a0441.1-r0441 +--R +--R +--R (240) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - b cos(x)log(-------------------) + b cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 - sin(x)\|b - a - a cos(x) - b +--R cos(x)\|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R b cos(x)atanh(sin(x)) - 2cos(x)\|- b + a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R - a cos(x)tan(x) + a sin(x) +--R / +--R 2 +--R a cos(x) +--R Type: Expression(Integer) +--E 243 + +--S 244 of 546 +d0441a:= D(m0441a,x) +--R +--R +--R (241) +--R 2 2 3 2 3 2 5 +--R ((- a b + a b)cos(x) + (- a b + a )cos(x) )sin(x) +--R + +--R 2 2 5 2 2 3 4 +--R (a b - a b)cos(x) + (2a b - a b - a )cos(x) +--R + +--R 2 3 3 2 3 2 +--R (2a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- a b + a b)cos(x) + (- 2a b + a b + a )cos(x) +--R + +--R 2 2 3 3 2 3 2 +--R (- a b - a b + 2a )cos(x) + (- a b + a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 3 2 5 +--R ((a b + a b)cos(x) + (a b + a )cos(x) )sin(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- a b - a b)cos(x) + (- 2a b - 3a b - a )cos(x) +--R + +--R 2 2 3 3 2 3 2 +--R (- 2a b - 4a b - 2a )cos(x) + (- 2a b - 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 5 2 2 3 4 +--R (a b + a b)cos(x) + (2a b + 3a b + a )cos(x) +--R + +--R 2 2 3 3 2 3 2 +--R (a b + 3a b + 2a )cos(x) + (a b + a )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 2 3 7 +--R ((a b - a b)cos(x) + a b - a )sin(x) +--R + +--R 3 2 3 3 2 3 2 +--R (3b - 3a b )cos(x) + (b - 2a b + a )cos(x) +--R + +--R 2 3 2 3 +--R (- 2a b + 2a )cos(x) - 2a b + 2a +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (b - 2a b + a b)cos(x) + (- 2b + a b + a b)cos(x) +--R + +--R 3 2 2 3 3 2 3 2 +--R (- 6b + 4a b + 2a b)cos(x) + (- 2b + 3a b - a )cos(x) +--R + +--R 2 2 3 2 3 +--R (a b + a b - 2a )cos(x) + a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 6 3 2 2 5 +--R (b - a b )cos(x) + (b + a b - 2a b)cos(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (2b + a b - 3a b)cos(x) + (3b - a b - 2a b)cos(x) +--R + +--R 3 2 2 +--R (b - a b)cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 7 +--R ((- a b - a b)cos(x) - a b - a )sin(x) +--R + +--R 3 2 3 3 2 3 2 +--R (- b - a b )cos(x) + (- b + 2a b + a )cos(x) +--R + +--R 2 2 3 2 3 +--R (2a b + 4a b + 2a )cos(x) + 2a b + 2a +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 3b - 2a b + a b)cos(x) + (- 2b - 3a b - a b)cos(x) +--R + +--R 3 2 3 3 2 3 2 +--R (2b - 2a b)cos(x) + (2b - 3a b - a )cos(x) +--R + +--R 2 2 3 2 3 +--R (- a b - 3a b - 2a )cos(x) - a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 6 3 2 2 5 +--R (- b - a b )cos(x) + (b - a b - 2a b)cos(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (2b + a b - a b)cos(x) + (- b + a b + 2a b)cos(x) +--R + +--R 3 2 2 +--R (- b + a b)cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (- a b + a b)cos(x) + (- a b + a b - a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 3 2 2 3 4 4 3 4 3 +--R (2a b + a b - a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 2 2 3 2 +--R (2a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 3 4 4 3 2 2 3 4 3 +--R (- 2a b + 2a )cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b + a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 2a b - 5a b - 5a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (2a b + 4a b + 4a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (a b + 3a b + 3a b + a )cos(x) + (a b + a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 3 2 2 3 4 2 2 3 +--R ((b - a b )cos(x) + (a b - a b + a b - a )cos(x) + a b - a b) +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 4 4 2 2 3 4 3 +--R (3a b - 3a b )cos(x) + (b + 2a b - 4a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b + 3a b - a b - 2a b + 2a )cos(x) +--R + +--R 3 4 2 2 3 +--R (- 2a b + 2a )cos(x) - 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- b + 2a b - a b )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b - 2a b + 4a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - 5a b + 5a b + 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b - 2a b - 2a b + 7a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (b - 3a b + a b + 3a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (a b + a b - a b - a )cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 4 3 3 6 +--R (a b - a b )cos(x) + (2b - a b - a b)cos(x) +--R + +--R 4 3 2 2 3 5 +--R (3b + a b - 3a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 3 3 3 +--R (2b + 4a b - 4a b - 2a b)cos(x) + (b + 2a b - 3a b)cos(x) +--R + +--R 3 3 2 +--R (a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 2 2 3 4 2 2 3 +--R ((- b - a b )cos(x) + (- a b - a b - a b - a )cos(x) - a b - a b) +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 4 4 2 2 4 3 +--R (- a b - a b )cos(x) + (b - 2a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b + a b + 2a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (2a b + 4a b + 4a b + 2a )cos(x) + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 4 3 2 2 3 5 +--R (b - 2a b - 3a b )cos(x) + (- b - 2a b - 4a b - 3a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - a b - a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b - 2a b + 2a b + a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- b - 3a b - a b - a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- a b - 3a b - 3a b - a )cos(x) - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 4 3 3 6 +--R (- a b - a b )cos(x) + (- 2b - a b - a b)cos(x) +--R + +--R 4 3 2 2 3 5 4 3 4 +--R (- b - a b + a b + a b)cos(x) + (2b + 2a b)cos(x) +--R + +--R 4 3 3 3 3 3 2 +--R (b + 2a b - a b)cos(x) + (a b - a b)cos(x) +--R / +--R 2 2 3 3 3 4 2 5 +--R ((a b - a b)cos(x) + (a b - a )cos(x) )sin(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (- a b + a b)cos(x) + (- 2a b + a b + a )cos(x) +--R + +--R 2 2 4 3 3 4 2 +--R (- 2a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (a b - a b)cos(x) + (2a b - a b - a )cos(x) +--R + +--R 2 2 3 4 3 3 4 2 +--R (a b + a b - 2a )cos(x) + (a b - a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 3 3 4 2 5 +--R ((- a b - a b)cos(x) + (- a b - a )cos(x) )sin(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (a b + a b)cos(x) + (2a b + 3a b + a )cos(x) +--R + +--R 2 2 3 4 3 3 4 2 +--R (2a b + 4a b + 2a )cos(x) + (2a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (- a b - a b)cos(x) + (- 2a b - 3a b - a )cos(x) +--R + +--R 2 2 3 4 3 3 4 2 +--R (- a b - 3a b - 2a )cos(x) + (- a b - a )cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 2 4 4 2 3 3 2 4 5 3 +--R (a b - a b)cos(x) + (a b - a b + a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 2 3 3 2 4 5 4 2 3 5 3 +--R (- 2a b - a b + a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 3 2 4 2 +--R (- 2a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 2 3 5 4 2 3 3 2 4 5 3 +--R (2a b - 2a )cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 2 3 3 2 4 5 3 +--R (- a b - a b)cos(x) + (- a b - a b - a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (- a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (2a b + 5a b + 5a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (2a b + 4a b + 4a b + 2a )cos(x) + (2a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (- a b - 3a b - 3a b - a )cos(x) + (- a b - a b)cos(x) +--R Type: Expression(Integer) +--E 244 + +--S 245 of 546 +m0441b:= a0441.2-r0441 +--R +--R +--R (242) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - b cos(x)log(-------------------) + b cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|- b + a +--R b cos(x)atanh(sin(x)) - 2cos(x)\|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R - 2cos(x)\|- b + a atan(-------------) - a cos(x)tan(x) + a sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 +--R a cos(x) +--R Type: Expression(Integer) +--E 245 + +--S 246 of 546 +d0441b:= D(m0441b,x) +--R +--R +--R (243) +--R 2 2 3 2 6 +--R (- a b + 2a b - a )cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R (3a b - 4a b + a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 6 2 3 5 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 8a b + 2a b + 6a )cos(x) + (- 8a b + 4a b + 4a )cos(x) +--R + +--R 2 2 3 2 +--R (- 3a b + 2a b + a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 6 2 3 5 2 3 4 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) + (6a b - 6a )cos(x) +--R + +--R 2 3 3 2 3 2 +--R (4a b - 4a )cos(x) + (a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 6 +--R (a b - a )cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b - 2a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R (- 3a b - 2a b + a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (8a b + 14a b + 6a )cos(x) + (8a b + 12a b + 4a )cos(x) +--R + +--R 2 2 3 2 +--R (3a b + 4a b + a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 6a b - 12a b - 6a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b - 2a b - a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 8 +--R (a b - 2a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 2 2 +--R (b - 5a b + 5a b - a )cos(x) + (- 4a b + 4a b)cos(x) - 3a b +--R + +--R 2 3 +--R 4a b - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 3 2 3 3 +--R (- 2b - 3a b + 6a b - a )cos(x) + (- 5b + 7a b - 2a )cos(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 3b + 9a b - 3a b - 3a )cos(x) + (8a b - 4a b - 4a )cos(x) +--R + +--R 2 2 3 +--R 3a b - 2a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 6 3 2 2 3 5 +--R (b - a b - a b + a )cos(x) + (6b - 4a b - 4a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R (12b - a b - 12a b + a )cos(x) + (10b + 2a b - 12a b)cos(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (3b - 3a b - 3a b + 3a )cos(x) + (- 4a b + 4a )cos(x) - a b +--R + +--R 3 +--R a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 7 3 2 2 3 6 +--R (- b + a b)cos(x) + (- 5b + a b + 5a b - a )cos(x) +--R + +--R 3 2 2 3 5 3 2 4 +--R (- 10b + 2a b + 10a b - 2a )cos(x) + (- 10b + 10a b)cos(x) +--R + +--R 3 2 2 3 3 3 2 2 3 2 +--R (- 5b - 2a b + 5a b + 2a )cos(x) + (- b - a b + a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 8 +--R (- a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 2 2 2 +--R (b + 3a b + a b - a )cos(x) + (4a b + 4a b)cos(x) + 3a b + 2a b +--R + +--R 3 +--R - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- 2b + 3a b + 4a b - a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 3b + 2a b + 3a b - 2a )cos(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 3b - 7a b - 7a b - 3a )cos(x) + (- 8a b - 12a b - 4a )cos(x) +--R + +--R 2 2 3 +--R - 3a b - 4a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 6 3 2 2 3 5 +--R (b + 3a b + 3a b + a )cos(x) + (2b + 8a b + 8a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R (4b + 5a b + 2a b + a )cos(x) + (6b + 2a b - 4a b)cos(x) +--R + +--R 3 2 2 3 2 2 2 3 2 +--R (3b + 5a b + 5a b + 3a )cos(x) + (4a b + 8a b + 4a )cos(x) + a b +--R + +--R 2 3 +--R 2a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 3 2 2 3 6 +--R (b + 2a b + a b)cos(x) + (3b + 5a b + a b - a )cos(x) +--R + +--R 3 2 2 3 5 3 2 2 4 +--R (2b + 2a b - 2a b - 2a )cos(x) + (- 2b - 4a b - 2a b)cos(x) +--R + +--R 3 2 2 3 3 3 2 2 3 2 +--R (- 3b - 4a b + a b + 2a )cos(x) + (- b - a b + a b + a )cos(x) +--R / +--R 2 2 3 4 2 6 +--R (a b - 2a b + a )cos(x) sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 2 3 4 2 +--R (- 3a b + 4a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (8a b - 2a b - 6a )cos(x) + (8a b - 4a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (3a b - 2a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 2 2 4 2 +--R (- 6a b + 6a )cos(x) + (- 4a b + 4a )cos(x) + (- a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 6 +--R (- a b + a )cos(x) sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (2a b + 2a b)cos(x) + (4a b + 4a b)cos(x) +--R + +--R 2 2 3 4 2 +--R (3a b + 2a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 6 2 2 3 4 5 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (- 8a b - 14a b - 6a )cos(x) + (- 8a b - 12a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (- 3a b - 4a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 6 2 2 3 4 5 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (6a b + 12a b + 6a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (a b + 2a b + a )cos(x) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 546 +t0442:= tan(x)^4/(a+b*cos(x)) +--R +--R +--R 4 +--R tan(x) +--R (244) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 546 +r0442:= 2*(a^2-b^2)^(3/2)*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^4+_ + 3/2*b*atanh(sin(x))/a^2-b^3*atanh(sin(x))/a^4-tan(x)/a+_ + b^2*tan(x)/a^3-1/2*b*sec(x)*tan(x)/a^2+1/3*tan(x)^3/a +--R +--R +--R (245) +--R 3 2 +--R (- 6b + 9a b)atanh(sin(x)) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 2 3 3 +--R (12b - 12a )\|- b + a atan(-------------) + 2a tan(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 +--R (- 3a b sec(x) + 6a b - 6a )tan(x) +--R / +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 248 + +--S 249 of 546 +a0442:= integrate(t0442,x) +--R +--R +--R (246) +--R [ +--R 3 2 3 sin(x) + cos(x) + 1 +--R (- 6b + 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 sin(x) - cos(x) - 1 +--R (6b - 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 3 | 2 2 - sin(x)\|b - a - a cos(x) - b +--R (6b - 6a )cos(x) \|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R 2 3 2 2 3 +--R ((6a b - 8a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R / +--R 4 3 +--R 6a cos(x) +--R , +--R +--R 3 2 3 sin(x) + cos(x) + 1 +--R (- 6b + 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 sin(x) - cos(x) - 1 +--R (6b - 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 3 | 2 2 (cos(x) + 1)\|- b + a +--R (- 12b + 12a )cos(x) \|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R 2 3 2 2 3 +--R ((6a b - 8a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R / +--R 4 3 +--R 6a cos(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 249 + +--S 250 of 546 +m0442a:= a0442.1-r0442 +--R +--R +--R (247) +--R 3 2 3 sin(x) + cos(x) + 1 +--R (- 6b + 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 sin(x) - cos(x) - 1 +--R (6b - 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 3 | 2 2 - sin(x)\|b - a - a cos(x) - b +--R (6b - 6a )cos(x) \|b - a log(---------------------------------) +--R b cos(x) + a +--R + +--R 3 2 3 +--R (6b - 9a b)cos(x) atanh(sin(x)) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 3 | 2 2 2 3 3 3 +--R (- 12b + 12a )cos(x) \|- b + a atan(-------------) - 2a cos(x) tan(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 3 3 +--R (3a b cos(x) sec(x) + (- 6a b + 6a )cos(x) )tan(x) +--R + +--R 2 3 2 2 3 +--R ((6a b - 8a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R / +--R 4 3 +--R 6a cos(x) +--R Type: Expression(Integer) +--E 250 + +--S 251 of 546 +d0442a:= D(m0442a,x) +--R +--R +--R (248) +--R 3 2 4 5 4 5 4 5 +--R ((- 6a b + 6a b)cos(x) + (- 6a b + 6a )cos(x) )sin(x) +--R + +--R 3 2 4 7 3 2 4 5 6 +--R (6a b - 6a b)cos(x) + (12a b - 6a b - 6a )cos(x) +--R + +--R 3 2 5 5 4 5 4 +--R (12a b - 12a )cos(x) + (12a b - 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 7 3 2 4 5 6 +--R (- 6a b + 6a b)cos(x) + (- 12a b + 6a b + 6a )cos(x) +--R + +--R 3 2 4 5 5 4 5 4 +--R (- 6a b - 6a b + 12a )cos(x) + (- 6a b + 6a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 5 4 5 4 5 +--R ((6a b + 6a b)cos(x) + (6a b + 6a )cos(x) )sin(x) +--R + +--R 3 2 4 7 3 2 4 5 6 +--R (- 6a b - 6a b)cos(x) + (- 12a b - 18a b - 6a )cos(x) +--R + +--R 3 2 4 5 5 4 5 4 +--R (- 12a b - 24a b - 12a )cos(x) + (- 12a b - 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 7 3 2 4 5 6 +--R (6a b + 6a b)cos(x) + (12a b + 18a b + 6a )cos(x) +--R + +--R 3 2 4 5 5 4 5 4 +--R (6a b + 18a b + 12a )cos(x) + (6a b + 6a )cos(x) +--R * +--R sin(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R ((6a b - 6a b )cos(x) + (6a b - 6a b)cos(x) )sec(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 7 +--R (- 6a b + 6a b )cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 12a b + 6a b + 6a b)cos(x) +--R + +--R 2 3 4 5 3 2 4 4 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 12a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 7 4 2 3 3 2 6 +--R (6a b - 6a b )cos(x) + (12a b - 6a b - 6a b )cos(x) +--R + +--R 4 3 2 5 2 3 3 2 4 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 7 +--R (6a b - 6a b )cos(x) +--R + +--R 2 3 3 2 4 6 +--R (12a b - 6a b - 6a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (6a b + 6a b - 12a b)cos(x) + (6a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 7 +--R (- 6a b + 6a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (- 12a b + 6a b + 6a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (- 6a b - 6a b + 12a b )cos(x) +--R + +--R 2 3 3 2 4 +--R (- 6a b + 6a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 3 2 5 3 2 4 4 +--R ((- 6a b - 6a b )cos(x) + (- 6a b - 6a b)cos(x) )sec(x) +--R + +--R 4 2 3 5 2 3 3 2 4 +--R (6a b + 6a b )cos(x) + (6a b + 6a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 7 2 3 3 2 4 6 +--R (6a b + 6a b )cos(x) + (12a b + 18a b + 6a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (12a b + 24a b + 12a b)cos(x) + (12a b + 12a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 7 4 2 3 3 2 6 +--R (- 6a b - 6a b )cos(x) + (- 12a b - 18a b - 6a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (- 12a b - 24a b - 12a b )cos(x) +--R + +--R 2 3 3 2 4 +--R (- 12a b - 12a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 7 +--R (- 6a b - 6a b )cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 12a b - 18a b - 6a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (- 6a b - 18a b - 12a b)cos(x) + (- 6a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 7 4 2 3 3 2 6 +--R (6a b + 6a b )cos(x) + (12a b + 18a b + 6a b )cos(x) +--R + +--R 4 2 3 3 2 5 2 3 3 2 4 +--R (6a b + 18a b + 12a b )cos(x) + (6a b + 6a b )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 3 4 5 2 +--R (6a b - 6a b - 8a b + 8a b)cos(x) + (- 8a b + 8a )cos(x) +--R + +--R 4 5 +--R 6a b - 6a +--R * +--R 7 +--R sin(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R ((3a b - 3a b )cos(x) + (3a b - 3a b)cos(x) )sec(x) +--R + +--R 5 4 2 3 3 2 5 +--R (18b - 18a b - 24a b + 24a b )cos(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (6b - 15a b + a b + 14a b - 6a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 12a b + 12a b + 15a b + a b - 16a )cos(x) +--R + +--R 4 5 2 4 5 4 5 +--R (12a b - 12a )cos(x) + (- 12a b + 12a )cos(x) - 12a b + 12a +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 7 +--R (- 3a b + 3a b )cos(x) +--R + +--R 2 3 3 2 4 6 2 3 4 5 +--R (- 6a b + 3a b + 3a b)cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 3 2 4 4 +--R (- 6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (6b - 12a b - 6a b + 20a b - 8a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b + 6a b + 18a b - 8a b - 2a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 36b + 24a b + 60a b - 36a b - 8a b - 4a )cos(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (- 12b + 30a b - 2a b - 22a b + 6a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (6a b - 6a b - 6a b - 14a b + 20a )cos(x) +--R + +--R 4 5 2 4 5 4 5 +--R (- 6a b + 6a )cos(x) + (12a b - 12a )cos(x) + 6a b - 6a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 7 2 3 3 2 4 6 +--R (3a b - 3a b )cos(x) + (6a b - 3a b - 3a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (3a b + 3a b - 6a b)cos(x) + (3a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 8 +--R (6b - 6a b - 9a b + 9a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (6b + 6a b - 18a b - 11a b + 17a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (12b + 6a b - 30a b - 10a b + 20a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (18b - 6a b - 36a b + 12a b + 8a b + 4a )cos(x) +--R + +--R 5 2 3 3 2 4 4 +--R (6b - 15a b + a b + 8a b)cos(x) +--R + +--R 3 2 4 5 3 4 5 2 +--R (- a b + 5a b - 4a )cos(x) + (2a b - 2a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 3 4 5 2 +--R (- 6a b - 6a b + 8a b + 8a b)cos(x) + (8a b + 8a )cos(x) +--R + +--R 4 5 +--R - 6a b - 6a +--R * +--R 7 +--R sin(x) +--R + +--R 2 3 3 2 5 3 2 4 4 +--R ((- 3a b - 3a b )cos(x) + (- 3a b - 3a b)cos(x) )sec(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 6b - 6a b + 12a b + 12a b )cos(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (- 6b + 15a b + 5a b - 10a b - 6a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (12a b + 12a b - 15a b - 31a b - 16a )cos(x) +--R + +--R 4 5 2 4 5 4 5 +--R (- 12a b - 12a )cos(x) + (12a b + 12a )cos(x) + 12a b + 12a +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 7 2 3 3 2 4 6 +--R (3a b + 3a b )cos(x) + (6a b + 9a b + 3a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (6a b + 12a b + 6a b)cos(x) + (6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 18b - 12a b + 30a b + 16a b - 8a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b - 18a b + 6a b + 20a b + 6a b - 2a )cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (12b - 36a b - 12a b + 8a b - 4a )cos(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (12b - 30a b - 10a b + 14a b + 6a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 6a b - 6a b + 6a b + 26a b + 20a )cos(x) +--R + +--R 4 5 2 4 5 4 5 +--R (6a b + 6a )cos(x) + (- 12a b - 12a )cos(x) - 6a b - 6a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 7 2 3 3 2 4 6 +--R (- 3a b - 3a b )cos(x) + (- 6a b - 9a b - 3a b)cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 4 +--R (- 3a b - 9a b - 6a b)cos(x) + (- 3a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 8 +--R (- 6b - 6a b + 9a b + 9a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (6b - 6a b - 18a b + 11a b + 17a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (12b + 6a b - 18a b - 2a b + 12a b + 2a )cos(x) +--R + +--R 5 4 2 3 4 5 5 +--R (- 6b + 6a b + 24a b - 8a b + 4a )cos(x) +--R + +--R 5 2 3 3 2 4 4 +--R (- 6b + 15a b + 5a b - 4a b)cos(x) +--R + +--R 3 2 4 5 3 4 5 2 +--R (a b - 3a b - 4a )cos(x) + (- 2a b - 2a )cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 5 6 +--R (- 6a b + 6a b)cos(x) +--R + +--R 3 3 4 2 5 6 5 4 2 5 4 +--R (- 6a b + 6a b - 6a b + 6a )cos(x) + (- 6a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 8 3 3 4 2 5 6 7 +--R (6a b - 6a b)cos(x) + (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (12a b + 6a b - 6a b - 12a )cos(x) +--R + +--R 3 3 6 5 4 2 5 4 +--R (12a b - 12a )cos(x) + (12a b - 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 8 3 3 4 2 5 6 7 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 3 3 6 6 3 3 4 2 5 6 5 +--R (- 12a b + 12a )cos(x) + (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 4 2 5 4 +--R (- 6a b + 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 6 3 3 4 2 5 6 5 +--R (6a b + 6a b)cos(x) + (6a b + 6a b + 6a b + 6a )cos(x) +--R + +--R 4 2 5 4 +--R (6a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 8 3 3 4 2 5 6 7 +--R (- 6a b - 6a b)cos(x) + (- 6a b - 18a b - 18a b - 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (- 12a b - 30a b - 30a b - 12a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 12a b - 24a b - 24a b - 12a )cos(x) +--R + +--R 4 2 5 4 +--R (- 12a b - 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 8 3 3 4 2 5 6 7 +--R (6a b + 6a b)cos(x) + (6a b + 18a b + 18a b + 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (12a b + 24a b + 24a b + 12a )cos(x) +--R + +--R 3 3 4 2 5 6 5 4 2 5 4 +--R (6a b + 18a b + 18a b + 6a )cos(x) + (6a b + 6a b)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3 3 4 2 6 +--R (6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (6a b - 6a b + 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 6 +--R (- 6a b + 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 6a b + 6a b - 6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 +--R (- 6a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b - 6a b + 6a b + 12a b)cos(x) +--R + +--R 2 4 5 5 3 3 4 2 4 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 12a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 8 +--R (6a b - 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (6a b + 6a b - 6a b - 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (12a b + 6a b - 6a b - 12a b )cos(x) +--R + +--R 5 4 2 5 2 4 3 3 4 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (6a b + 6a b - 6a b - 6a b)cos(x) +--R + +--R 2 4 5 6 +--R (12a b - 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (6a b + 6a b - 6a b - 6a b)cos(x) + (6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 8 +--R (- 6a b + 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) +--R + +--R 5 4 2 6 +--R (- 12a b + 12a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 4 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 6 +--R (- 6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 6a b - 6a b - 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (- 6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 6 5 2 4 3 3 4 2 5 +--R (6a b + 6a b )cos(x) + (6a b + 6a b + 6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 +--R (6a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (6a b + 18a b + 18a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (12a b + 30a b + 30a b + 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (12a b + 24a b + 24a b + 12a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (12a b + 12a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 8 +--R (- 6a b - 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 6a b - 18a b - 18a b - 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 12a b - 30a b - 30a b - 12a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- 12a b - 24a b - 24a b - 12a b )cos(x) +--R + +--R 2 4 3 3 4 +--R (- 12a b - 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 6a b - 18a b - 18a b - 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b - 24a b - 24a b - 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 6a b - 18a b - 18a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (- 6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 8 5 2 4 3 3 4 2 7 +--R (6a b + 6a b )cos(x) + (6a b + 18a b + 18a b + 6a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (12a b + 24a b + 24a b + 12a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 4 3 3 4 +--R (6a b + 18a b + 18a b + 6a b )cos(x) + (6a b + 6a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (6b - 6a b - 6a b + 6a b - 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (6a b - 6a b - 8a b + 8a b - 8a b + 8a )cos(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (- 8a b + 8a b)cos(x) + (6a b - 6a )cos(x) + 6a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 4 2 6 +--R (3a b - 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (3a b - 3a b + 3a b - 3a b)cos(x) + (3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (18a b - 18a b - 24a b + 24a b )cos(x) +--R + +--R 6 3 3 4 2 5 6 5 +--R (6b - 15a b - 11a b + 26a b - 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b + 18a b + 9a b - 23a b + 11a b + 13a b - 16a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 12a b + 12a b + 15a b + a b - 4a b - 12a )cos(x) +--R + +--R 4 2 5 6 2 4 2 6 4 2 +--R (12a b - 24a b + 12a )cos(x) + (- 12a b + 12a )cos(x) - 12a b +--R + +--R 5 +--R 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 3a b + 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 3a b - 3a b + 3a b + 3a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 6a b - 3a b + 3a b + 6a b)cos(x) +--R + +--R 2 4 5 5 3 3 4 2 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 3 3 4 2 5 8 +--R (- 6b + 12a b - 18a b + 14a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 7 +--R (- 6b - 12a b + 24a b + 14a b - 28a b + 10a b - 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 12b - 30a b + 42a b + 52a b - 38a b - 10a b - 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 12b - 12a b + 12a b + 42a b + 14a b - 50a b + 6a )cos(x) +--R + +--R 6 5 3 3 4 2 5 6 4 +--R (6b - 18a b + 28a b - 10a b - 26a b + 20a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (6a b - 6a b - 6a b - 14a b + 14a b + 6a )cos(x) +--R + +--R 4 2 5 6 2 4 2 5 6 +--R (- 6a b + 18a b - 12a )cos(x) + (12a b - 6a b - 6a )cos(x) +--R + +--R 4 2 5 +--R 6a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 2 4 3 3 4 2 5 7 +--R (3a b - 3a b )cos(x) + (3a b + 3a b - 3a b - 3a b)cos(x) +--R + +--R 2 4 5 6 2 4 3 3 4 2 5 5 +--R (6a b - 6a b)cos(x) + (3a b + 3a b - 3a b - 3a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 9 +--R (6a b - 6a b - 9a b + 9a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (12b - 6a b - 15a b + 3a b - 5a b + 11a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 7 +--R (18b + 6a b - 36a b - 17a b + 19a b + 8a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (12b + 24a b - 36a b - 46a b + 32a b + 10a b + 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (6b + 12a b - 12a b - 27a b - 3a b + 24a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (6a b - 3a b - 11a b + a b + 11a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 4 2 5 2 +--R (- a b + 5a b - 2a b - 2a )cos(x) + (2a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (- 6b - 6a b + 6a b + 6a b + 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 6a b - 6a b + 8a b + 8a b + 8a b + 8a )cos(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (8a b + 8a b)cos(x) + (- 6a b - 6a )cos(x) - 6a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 4 2 6 +--R (- 3a b - 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (- 3a b - 3a b - 3a b - 3a b)cos(x) + (- 3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 6a b - 6a b + 12a b + 12a b )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 5 +--R (6b - 12a b + 3a b + 17a b + 2a b - 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (12b + 18a b - 9a b - 19a b - 7a b - 19a b - 16a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (12a b + 12a b - 15a b - 31a b - 28a b - 12a )cos(x) +--R + +--R 4 2 6 2 4 2 5 6 4 2 +--R (- 12a b + 12a )cos(x) + (12a b + 24a b + 12a )cos(x) + 12a b +--R + +--R 5 +--R 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 2 4 3 3 4 2 5 7 +--R (3a b + 3a b )cos(x) + (3a b + 9a b + 9a b + 3a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (6a b + 15a b + 15a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (6a b + 12a b + 12a b + 6a b)cos(x) + (6a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (6b - 12a b - 24a b + 18a b + 22a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 7 +--R (- 6b - 12a b - 12a b - 2a b + 24a b + 18a b - 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 12b - 6a b + 6a b - 16a b - 6a b + 6a b - 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 12b - 12a b + 12a b + 6a b - 26a b - 14a b + 6a )cos(x) +--R + +--R 6 5 3 3 4 2 5 6 4 +--R (- 6b - 18a b + 20a b + 2a b + 14a b + 20a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 6a b - 6a b + 6a b + 26a b + 26a b + 6a )cos(x) +--R + +--R 4 2 5 6 2 4 2 5 6 4 2 +--R (6a b - 6a b - 12a )cos(x) + (- 12a b - 18a b - 6a )cos(x) - 6a b +--R + +--R 5 +--R - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 2 4 3 3 4 2 5 7 +--R (- 3a b - 3a b )cos(x) + (- 3a b - 9a b - 9a b - 3a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 6a b - 12a b - 12a b - 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (- 3a b - 9a b - 9a b - 3a b)cos(x) + (- 3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 9 +--R (- 6a b - 6a b + 9a b + 9a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (- 12b - 6a b + 15a b + 3a b + 5a b + 11a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 7 +--R (- 6b - 6a b + 12a b + 17a b + 3a b + 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 6 +--R (12b - 12a b + 22a b + 12a b - 6a b + 4a )cos(x) +--R + +--R 6 5 3 3 4 2 5 5 +--R (6b + 12a b - 9a b + 9a b + 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (6a b + 3a b - 7a b + 3a b + 3a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 4 2 5 2 +--R (a b - 3a b - 6a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R / +--R 4 2 5 5 5 6 4 5 +--R ((6a b - 6a b)cos(x) + (6a b - 6a )cos(x) )sin(x) +--R + +--R 4 2 5 7 4 2 5 6 6 +--R (- 6a b + 6a b)cos(x) + (- 12a b + 6a b + 6a )cos(x) +--R + +--R 4 2 6 5 5 6 4 +--R (- 12a b + 12a )cos(x) + (- 12a b + 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 7 4 2 5 6 6 +--R (6a b - 6a b)cos(x) + (12a b - 6a b - 6a )cos(x) +--R + +--R 4 2 5 6 5 5 6 4 +--R (6a b + 6a b - 12a )cos(x) + (6a b - 6a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 5 5 6 4 5 +--R ((- 6a b - 6a b)cos(x) + (- 6a b - 6a )cos(x) )sin(x) +--R + +--R 4 2 5 7 4 2 5 6 6 +--R (6a b + 6a b)cos(x) + (12a b + 18a b + 6a )cos(x) +--R + +--R 4 2 5 6 5 5 6 4 +--R (12a b + 24a b + 12a )cos(x) + (12a b + 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 5 7 4 2 5 6 6 +--R (- 6a b - 6a b)cos(x) + (- 12a b - 18a b - 6a )cos(x) +--R + +--R 4 2 5 6 5 5 6 4 +--R (- 6a b - 18a b - 12a )cos(x) + (- 6a b - 6a )cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 2 6 6 4 3 5 2 6 7 5 +--R (6a b - 6a b)cos(x) + (6a b - 6a b + 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (6a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (- 6a b + 6a b)cos(x) + (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 12a b - 6a b + 6a b + 12a )cos(x) +--R + +--R 4 3 7 5 5 2 6 4 +--R (- 12a b + 12a )cos(x) + (- 12a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (6a b - 6a b)cos(x) + (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 4 3 7 6 4 3 5 2 6 7 5 +--R (12a b - 12a )cos(x) + (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (6a b - 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 4 3 5 2 6 7 5 +--R (- 6a b - 6a b)cos(x) + (- 6a b - 6a b - 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (- 6a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (6a b + 6a b)cos(x) + (6a b + 18a b + 18a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (12a b + 30a b + 30a b + 12a )cos(x) +--R + +--R 4 3 5 2 6 7 5 5 2 6 4 +--R (12a b + 24a b + 24a b + 12a )cos(x) + (12a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (- 6a b - 6a b)cos(x) + (- 6a b - 18a b - 18a b - 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 12a b - 24a b - 24a b - 12a )cos(x) +--R + +--R 4 3 5 2 6 7 5 5 2 6 4 +--R (- 6a b - 18a b - 18a b - 6a )cos(x) + (- 6a b - 6a b)cos(x) +--R Type: Expression(Integer) +--E 251 + +--S 252 of 546 +m0442b:= a0442.2-r0442 +--R +--R +--R (249) +--R 3 2 3 sin(x) + cos(x) + 1 +--R (- 6b + 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 sin(x) - cos(x) - 1 +--R (6b - 9a b)cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 +--R (6b - 9a b)cos(x) atanh(sin(x)) +--R + +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 3 | 2 2 (cos(x) + 1)\|- b + a +--R (- 12b + 12a )cos(x) \|- b + a atan(------------------------) +--R (b - a)sin(x) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 3 | 2 2 2 3 3 3 +--R (- 12b + 12a )cos(x) \|- b + a atan(-------------) - 2a cos(x) tan(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 3 3 +--R (3a b cos(x) sec(x) + (- 6a b + 6a )cos(x) )tan(x) +--R + +--R 2 3 2 2 3 +--R ((6a b - 8a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R / +--R 4 3 +--R 6a cos(x) +--R Type: Expression(Integer) +--E 252 + +--S 253 of 546 +d0442b:= D(m0442b,x) +--R +--R +--R (250) +--R 3 2 4 5 4 6 +--R (- 6a b + 12a b - 6a )cos(x) sin(x) +--R + +--R 3 2 4 6 3 2 4 5 +--R (12a b - 12a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 3 2 4 5 4 +--R (18a b - 24a b + 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 6a b + 6a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 3 2 4 5 6 +--R (- 48a b + 12a b + 36a )cos(x) +--R + +--R 3 2 4 5 5 +--R (- 48a b + 24a b + 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (- 18a b + 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (6a b - 6a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (36a b - 36a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 3 2 5 4 +--R (6a b - 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 4 6 +--R (6a b - 6a )cos(x) sin(x) +--R + +--R 3 2 4 6 3 2 4 5 +--R (- 12a b - 12a b)cos(x) + (- 24a b - 24a b)cos(x) +--R + +--R 3 2 4 5 4 +--R (- 18a b - 12a b + 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 5 8 3 2 4 5 7 +--R (6a b + 12a b + 6a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 3 2 4 5 6 3 2 4 5 5 +--R (48a b + 84a b + 36a )cos(x) + (48a b + 72a b + 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (18a b + 24a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 8 3 2 4 5 7 +--R (- 6a b - 12a b - 6a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 3 2 4 5 6 3 2 4 5 5 +--R (- 36a b - 72a b - 36a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (- 6a b - 12a b - 6a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 3 2 4 4 +--R (6a b - 12a b + 6a b)cos(x) sec(x) +--R + +--R 4 2 3 3 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 12a b + 12a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 18a b + 24a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 6 4 2 3 5 +--R (12a b - 12a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (18a b - 24a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (6a b - 6a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (48a b - 12a b - 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (48a b - 24a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (18a b - 12a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- 6a b + 6a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (- 48a b + 12a b + 36a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (- 48a b + 24a b + 24a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (- 18a b + 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 6a b + 6a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 36a b + 36a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (6a b - 6a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (36a b - 36a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 3 2 4 +--R (6a b - 6a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 4 4 3 2 4 6 +--R ((- 6a b + 6a b)cos(x) sec(x) + (6a b - 6a b )cos(x) )sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (12a b + 12a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (18a b + 12a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 6 4 2 3 5 +--R (- 12a b - 12a b )cos(x) + (- 24a b - 24a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (- 18a b - 12a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 4 8 +--R (- 6a b - 12a b - 6a b)cos(x) +--R + +--R 2 3 3 2 4 7 +--R (- 24a b - 48a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 48a b - 84a b - 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 48a b - 72a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 18a b - 24a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 8 +--R (6a b + 12a b + 6a b )cos(x) +--R + +--R 4 2 3 3 2 7 +--R (24a b + 48a b + 24a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (48a b + 84a b + 36a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (48a b + 72a b + 24a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (18a b + 24a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 8 2 3 3 2 4 7 +--R (6a b + 12a b + 6a b)cos(x) + (24a b + 48a b + 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (36a b + 72a b + 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 3 3 2 4 4 +--R (24a b + 48a b + 24a b)cos(x) + (6a b + 12a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 8 +--R (- 6a b - 12a b - 6a b )cos(x) +--R + +--R 4 2 3 3 2 7 +--R (- 24a b - 48a b - 24a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (- 36a b - 72a b - 36a b )cos(x) +--R + +--R 4 2 3 3 2 5 4 2 3 3 2 4 +--R (- 24a b - 48a b - 24a b )cos(x) + (- 6a b - 12a b - 6a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (6a b - 12a b - 2a b + 16a b - 8a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (- 6a b + 12a b - 6a b)cos(x) + 6a b - 12a b + 6a +--R * +--R 8 +--R sin(x) +--R + +--R 2 3 3 2 4 4 +--R (3a b - 6a b + 3a b)cos(x) sec(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (6b - 30a b + 18a b + 38a b - 36a b + 4a )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 24a b + 33a b + 26a b - 35a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 18a b + 48a b - 16a b - 24a b + 10a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (18a b - 48a b + 30a b)cos(x) - 18a b + 24a b - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 6a b + 6a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 9a b + 12a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b - 18a b + 48a b + 26a b - 52a b + 8a )cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (- 30b + 81a b - 12a b - 59a b + 20a )cos(x) +--R + +--R 5 4 3 2 4 5 4 +--R (- 18b + 54a b - 104a b + 42a b + 26a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (48a b - 63a b - 72a b + 79a b + 8a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (18a b - 60a b + 36a b + 36a b - 30a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (- 18a b + 60a b - 18a b - 24a )cos(x) + 18a b - 12a b - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (3a b - 3a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (24a b - 6a b - 18a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (24a b - 12a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (9a b - 6a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 5 8 +--R (6b - 6a b - 6a b + 10a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (36b - 24a b - 51a b + 34a b + 9a b - 4a )cos(x) +--R + +--R 5 4 2 3 4 5 6 +--R (72b - 6a b - 150a b + 82a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (60b + 12a b - 156a b - 12a b + 104a b - 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (18b - 18a b - 42a b + 64a b + 12a b - 34a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 24a b + 27a b + 54a b - 41a b - 16a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 6a b + 24a b - 16a b - 28a b + 26a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 5 +--R (6a b - 24a b - 6a b + 24a )cos(x) - 6a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 3a b + 3a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 18a b + 18a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 2 3 4 9 +--R (- 6b + 15a b - 9a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 30b + 6a b + 66a b - 10a b - 36a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 60b + 12a b + 123a b - 16a b - 63a b + 4a )cos(x) +--R + +--R 5 2 3 3 2 4 5 6 +--R (- 60b + 126a b + 10a b - 66a b - 10a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 30b - 12a b + 75a b + 24a b - 45a b - 12a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 6b - 6a b + 24a b + 2a b - 18a b + 4a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 5 2 +--R (3a b - 8a b - 3a b + 8a )cos(x) + (- 2a b + 2a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R ((- 6a b + 14a b - 8a )cos(x) + (6a b - 6a b)cos(x) - 6a b + 6a ) +--R * +--R 8 +--R sin(x) +--R + +--R 2 3 4 4 +--R (- 3a b + 3a b)cos(x) sec(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (6b + 18a b + 6a b - 26a b - 16a b + 4a )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (24a b + 15a b - 44a b - 35a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (18a b - 12a b - 44a b - 4a b + 10a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (- 18a b + 12a b + 30a b)cos(x) + 18a b + 12a b - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (6a b + 6a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (9a b + 6a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b + 18a b + 36a b - 38a b - 36a b + 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 18b + 12a b + 27a b - 42a b - 19a b + 20a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 18b - 42a b - 24a b + 56a b + 82a b + 26a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 48a b - 33a b + 102a b + 95a b + 8a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 18a b + 24a b + 48a b - 24a b - 30a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (18a b - 24a b - 66a b - 24a )cos(x) - 18a b - 24a b - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 4 8 +--R (- 3a b - 6a b - 3a b)cos(x) +--R + +--R 2 3 3 2 4 7 +--R (- 12a b - 24a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 24a b - 42a b - 18a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 24a b - 36a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 9a b - 12a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (6b + 18a b + 6a b - 22a b - 20a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (12b + 48a b + 27a b - 52a b - 47a b - 4a )cos(x) +--R + +--R 5 4 2 3 4 5 6 +--R (24b + 30a b - 6a b + 14a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (36b + 12a b - 36a b + 36a b + 40a b - 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (18b + 30a b + 18a b - 28a b - 68a b - 34a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (24a b + 21a b - 60a b - 73a b - 16a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (6a b - 12a b - 20a b + 24a b + 26a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (- 6a b + 12a b + 42a b + 24a )cos(x) + 6a b + 12a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 8 2 3 3 2 4 7 +--R (3a b + 6a b + 3a b)cos(x) + (12a b + 24a b + 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 2 3 3 2 4 5 +--R (18a b + 36a b + 18a b)cos(x) + (12a b + 24a b + 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (3a b + 6a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (6b + 12a b - 3a b - 18a b - 9a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (18b + 30a b - 18a b - 50a b - 16a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (12b + 12a b - 27a b - 38a b - 7a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b - 24a b - 6a b + 2a b - 14a b - 10a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 18b - 24a b + 9a b + 6a b - 21a b - 12a )cos(x) +--R + +--R 5 4 3 2 4 5 4 +--R (- 6b - 6a b - 2a b + 2a b + 4a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 5 2 +--R (- 3a b + 2a b + 13a b + 8a )cos(x) + (2a b + 4a b + 2a )cos(x) +--R / +--R 4 2 5 6 4 6 +--R (6a b - 12a b + 6a )cos(x) sin(x) +--R + +--R 4 2 5 6 4 2 5 5 +--R (- 12a b + 12a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 4 2 5 6 4 +--R (- 18a b + 24a b - 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 6 8 4 2 6 7 +--R (6a b - 6a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (48a b - 12a b - 36a )cos(x) + (48a b - 24a b - 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (18a b - 12a b - 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 8 4 2 6 7 +--R (- 6a b + 6a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (- 36a b + 36a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 4 2 6 4 +--R (- 6a b + 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 6 4 6 +--R (- 6a b + 6a )cos(x) sin(x) +--R + +--R 4 2 5 6 4 2 5 5 +--R (12a b + 12a b)cos(x) + (24a b + 24a b)cos(x) +--R + +--R 4 2 5 6 4 +--R (18a b + 12a b - 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 6 8 4 2 5 6 7 +--R (- 6a b - 12a b - 6a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (- 48a b - 84a b - 36a )cos(x) + (- 48a b - 72a b - 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (- 18a b - 24a b - 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 6 8 4 2 5 6 7 +--R (6a b + 12a b + 6a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (36a b + 72a b + 36a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (6a b + 12a b + 6a )cos(x) +--R Type: Expression(Integer) +--E 253 + +--S 254 of 546 +t0443:= tan(x)^2/(a+a*cos(x)) +--R +--R +--R 2 +--R tan(x) +--R (251) ------------ +--R a cos(x) + a +--R Type: Expression(Integer) +--E 254 + +--S 255 of 546 +r0443:= -atanh(sin(x))/a+tan(x)/a +--R +--R +--R - atanh(sin(x)) + tan(x) +--R (252) ------------------------ +--R a +--R Type: Expression(Integer) +--E 255 + +--S 256 of 546 +a0443:= integrate(t0443,x) +--R +--R +--R (253) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - cos(x)log(-------------------) + cos(x)log(-------------------) + sin(x) +--R cos(x) + 1 cos(x) + 1 +--R -------------------------------------------------------------------------- +--R a cos(x) +--R Type: Union(Expression(Integer),...) +--E 256 + +--S 257 of 546 +m0443:= a0443-r0443 +--R +--R +--R (254) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - cos(x)log(-------------------) + cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R cos(x)atanh(sin(x)) - cos(x)tan(x) + sin(x) +--R / +--R a cos(x) +--R Type: Expression(Integer) +--E 257 + +--S 258 of 546 +d0443:= D(m0443,x) +--R +--R +--R (255) +--R 2 4 4 3 2 2 4 +--R - cos(x) sin(x) + (cos(x) + 2cos(x) + 2cos(x) )sin(x) - cos(x) +--R + +--R 3 2 +--R - 2cos(x) - cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 2 4 +--R sin(x) + (cos(x) - 2cos(x) - 2)sin(x) +--R + +--R 4 3 2 2 5 3 +--R (2cos(x) + cos(x) - cos(x) + 2cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 4 4 3 2 2 +--R a cos(x) sin(x) + (- a cos(x) - 2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 4 3 2 +--R a cos(x) + 2a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 258 + +--S 259 of 546 +t0444:= tan(x)^4/(a+a*cos(x)) +--R +--R +--R 4 +--R tan(x) +--R (256) ------------ +--R a cos(x) + a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 546 +r0444:= 1/2*atanh(sin(x))/a-1/2*sec(x)*tan(x)/a+1/3*tan(x)^3/a +--R +--R +--R 3 +--R 3atanh(sin(x)) + 2tan(x) - 3sec(x)tan(x) +--R (257) ----------------------------------------- +--R 6a +--R Type: Expression(Integer) +--E 260 + +--S 261 of 546 +a0444:= integrate(t0444,x) +--R +--R +--R (258) +--R 3 sin(x) + cos(x) + 1 3 sin(x) - cos(x) - 1 +--R 3cos(x) log(-------------------) - 3cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 +--R (- 2cos(x) - 3cos(x) + 2)sin(x) +--R / +--R 3 +--R 6a cos(x) +--R Type: Union(Expression(Integer),...) +--E 261 + +--S 262 of 546 +m0444:= a0444-r0444 +--R +--R +--R (259) +--R 3 sin(x) + cos(x) + 1 3 sin(x) - cos(x) - 1 +--R 3cos(x) log(-------------------) - 3cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 3 3 3 3 +--R - 3cos(x) atanh(sin(x)) - 2cos(x) tan(x) + 3cos(x) sec(x)tan(x) +--R + +--R 2 +--R (- 2cos(x) - 3cos(x) + 2)sin(x) +--R / +--R 3 +--R 6a cos(x) +--R Type: Expression(Integer) +--E 262 + +--S 263 of 546 +d0444:= D(m0444,x) +--R +--R +--R (260) +--R 4 4 6 5 4 2 +--R - 6cos(x) sin(x) + (6cos(x) + 12cos(x) + 12cos(x) )sin(x) +--R + +--R 6 5 4 +--R - 6cos(x) - 12cos(x) - 6cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 4 4 4 +--R (6cos(x) sec(x) - 6cos(x) )sin(x) +--R + +--R 6 5 4 6 5 +--R (- 6cos(x) - 12cos(x) - 12cos(x) )sec(x) + 6cos(x) + 12cos(x) +--R + +--R 4 +--R 12cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 6 5 +--R (6cos(x) + 12cos(x) + 6cos(x) )sec(x) - 6cos(x) - 12cos(x) +--R + +--R 4 +--R - 6cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 6 +--R (- 2cos(x) - 6cos(x) + 6)sin(x) +--R + +--R 4 4 3 2 4 +--R (3cos(x) sec(x) - 6cos(x) + 7cos(x) + 12cos(x) - 12)sin(x) +--R + +--R 6 5 4 6 5 +--R (- 3cos(x) - 6cos(x) - 6cos(x) )sec(x) - 4cos(x) + 4cos(x) +--R + +--R 4 3 2 +--R 12cos(x) - 8cos(x) - 12cos(x) + 6cos(x) + 6 +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 7 6 5 +--R (3cos(x) + 6cos(x) + 3cos(x) )sec(x) - 3cos(x) - 2cos(x) - 4cos(x) +--R + +--R 4 3 2 +--R - 6cos(x) + cos(x) + 2cos(x) +--R / +--R 4 4 6 5 4 2 +--R 6a cos(x) sin(x) + (- 6a cos(x) - 12a cos(x) - 12a cos(x) )sin(x) +--R + +--R 6 5 4 +--R 6a cos(x) + 12a cos(x) + 6a cos(x) +--R Type: Expression(Integer) +--E 263 + +--S 264 of 546 +t0445:= cot(x)/(a+a*cos(x)) +--R +--R +--R cot(x) +--R (261) ------------ +--R a cos(x) + a +--R Type: Expression(Integer) +--E 264 + +--S 265 of 546 +r0445:= -1/2*atanh(cos(x))/a-1/2/a/(cos(x)+1) +--R +--R +--R (- cos(x) - 1)atanh(cos(x)) - 1 +--R (262) ------------------------------- +--R 2a cos(x) + 2a +--R Type: Expression(Integer) +--E 265 + +--S 266 of 546 +a0445:= integrate(t0445,x) +--R +--R +--R sin(x) +--R (2cos(x) + 2)log(----------) + cos(x) - 1 +--R cos(x) + 1 +--R (263) ----------------------------------------- +--R 4a cos(x) + 4a +--R Type: Union(Expression(Integer),...) +--E 266 + +--S 267 of 546 +m0445:= a0445-r0445 +--R +--R +--R sin(x) +--R 2log(----------) + 2atanh(cos(x)) + 1 +--R cos(x) + 1 +--R (264) ------------------------------------- +--R 4a +--R Type: Expression(Integer) +--E 267 + +--S 268 of 546 +d0445:= D(m0445,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (265) -------------------------------- +--R 2 +--R (2a cos(x) - 2a)sin(x) +--R Type: Expression(Integer) +--E 268 + +--S 269 of 546 +t0446:= sec(x)/(a+b*cos(x)) +--R +--R +--R sec(x) +--R (266) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 546 +r0446:= -2*b*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(1/2)+_ + atanh(sin(x))/a +--R +--R +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R \|- b + a atanh(sin(x)) + 2b atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (267) -------------------------------------------------- +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R Type: Expression(Integer) +--E 270 + +--S 271 of 546 +a0446:= integrate(t0446,x) +--R +--R +--R (268) +--R [ +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b - a log(-------------------) - \|b - a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 2 2 +--R (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R b log(--------------------------------------------) +--R b cos(x) + a +--R / +--R +-------+ +--R | 2 2 +--R a\|b - a +--R , +--R +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x) - cos(x) - 1 sin(x)\|- b + a +--R - \|- b + a log(-------------------) - 2b atan(---------------------) +--R cos(x) + 1 (b + a)cos(x) + b + a +--R / +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 271 + +--S 272 of 546 +m0446a:= a0446.1-r0446 +--R +--R +--R (269) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R - \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +---------+ | 2 2 2 2 +--R | 2 2 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R b\|- b + a log(--------------------------------------------) +--R b cos(x) + a +--R + +--R x +--R +---------+ +-------+ +-------+ (b - a)tan(-) +--R | 2 2 | 2 2 | 2 2 2 +--R - \|- b + a \|b - a atanh(sin(x)) - 2b\|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R a\|- b + a \|b - a +--R Type: Expression(Integer) +--E 272 + +--S 273 of 546 +d0446a:= D(m0446a,x) +--R +--R +--R (270) +--R 3 2 6 +--R (- b + a b )sin(x) +--R + +--R 2 2 2 3 2 2 3 +--R (- 3a b + 2a b)cos(x) + (- b - a b - 2a b + 2a )cos(x) +--R + +--R 3 2 2 +--R 2b - 5a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 4 3 2 2 3 3 +--R (b - 2a b + 2a b)cos(x) + (b + 2a b - a b + 2a )cos(x) +--R + +--R 3 2 2 3 2 +--R (2b + 5a b - a b + a )cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (2b + 3a b + 3a b - 2a )cos(x) - b + 5a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- a b + a b)cos(x) + (- 2b + a b - a b + a )cos(x) +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 3b - a b )cos(x) + (- 2b - 4a b + a b - a )cos(x) +--R + +--R 3 2 2 2 +--R (- b - 2a b - a b)cos(x) - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 6 +--R (b + a b )sin(x) +--R + +--R 2 2 2 3 2 2 3 3 +--R (a b + 2a b)cos(x) + (- b + a b + 2a b + 2a )cos(x) - 2b +--R + +--R 2 2 +--R - a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 4 3 2 2 3 3 +--R (- b + 2a b + 2a b)cos(x) + (b + 2a b + 3a b + 2a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (2b + a b + a b + a )cos(x) + (2b + a b - a b - 2a )cos(x) +--R + +--R 3 2 2 +--R b + a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (a b + a b)cos(x) + (2b + a b + a b + a )cos(x) +--R + +--R 3 2 3 3 2 3 2 +--R (b + a b )cos(x) + (- 2b - a b - a )cos(x) +--R + +--R 3 2 2 2 +--R (- b - 2a b - a b)cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (3b - 2a b - 3a b + 2a b)cos(x) + b + 2a b - 3a b - 2a b +--R + +--R 4 +--R 2a +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 3 3 +--R (b - 2a b - a b + 2a b)cos(x) +--R + +--R 4 3 3 4 2 +--R (- 2b + a b - a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 2 2 +--R (- 6b + 3a b + 5a b - 3a b + a )cos(x) - 2b - 2a b + 4a b +--R + +--R 3 4 +--R 2a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 3 4 +--R (b - a b - a b + a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b + a b - 2a b - a b + a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (2b + a b - 2a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 2 2 +--R (3b - a b - 2a b + a b - a )cos(x) + b - a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 3 4 3 2 2 3 4 +--R ((- b - 2a b + a b + 2a b)cos(x) - b - 2a b - a b + 2a b + 2a ) +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 3 3 +--R (- 3b - 2a b + 3a b + 2a b)cos(x) +--R + +--R 4 3 3 4 2 +--R (- 2b - 3a b + 3a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 3 4 +--R (2b + a b - 3a b - a b + a )cos(x) + 2b + 2a b - 2a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 3 4 +--R (- b - a b + a b + a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b - a b - 2a b + a b + a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (2b + a b - 2a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 2 2 +--R (- b + a b + 2a b - a b - a )cos(x) - b + a b +--R * +--R sin(x) +--R / +--R 2 2 3 2 3 2 2 3 4 2 2 +--R (a b - a b)cos(x) + (a b - a b + a b - a )cos(x) + a b +--R + +--R 3 +--R - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 3 2 2 3 4 2 3 4 +--R (- 2a b - a b + a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 2 2 3 +--R - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 3 4 2 3 2 2 3 4 2 2 3 +--R (2a b - 2a )cos(x) + (a b + a b - a b - a )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 3 2 2 3 4 2 2 +--R (- a b - a b)cos(x) + (- a b - a b - a b - a )cos(x) - a b +--R + +--R 3 +--R - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (2a b + 5a b + 5a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (2a b + 4a b + 4a b + 2a )cos(x) + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- a b - 3a b - 3a b - a )cos(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 5 +--R ((- a b + a b + a b - a b)cos(x) - a b + a b + a b - a )sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (2a b - a b - 3a b + a b + a )cos(x) +--R + +--R 4 3 2 5 2 3 3 2 4 5 +--R (2a b - 4a b + 2a )cos(x) + 2a b - 2a b - 2a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 2a b + a b + 3a b - a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 5 +--R (- a b - a b + 3a b + a b - 2a )cos(x) - a b + a b + a b - a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 5 +--R ((a b + a b - a b - a b)cos(x) + a b + a b - a b - a )sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 2a b - 3a b + a b + 3a b + a )cos(x) +--R + +--R 4 2 3 4 5 2 3 3 2 4 5 +--R (- 2a b - 4a b + 4a b + 2a )cos(x) - 2a b - 2a b + 2a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (2a b + 3a b - a b - 3a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 5 +--R (a b + 3a b + a b - 3a b - 2a )cos(x) + a b + a b - a b - a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 273 + +--S 274 of 546 +m0446b:= a0446.2-r0446 +--R +--R +--R (271) +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +---------+ +--R | 2 2 sin(x) - cos(x) - 1 | 2 2 +--R - \|- b + a log(-------------------) - \|- b + a atanh(sin(x)) +--R cos(x) + 1 +--R + +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R sin(x)\|- b + a 2 +--R - 2b atan(---------------------) - 2b atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R | 2 2 +--R a\|- b + a +--R Type: Expression(Integer) +--E 274 + +--S 275 of 546 +d0446b:= D(m0446b,x) +--R +--R +--R (272) +--R 2 2 6 +--R (- b + 3a b - 2a )sin(x) +--R + +--R 2 2 2 2 2 2 +--R ((2b + 4a b - 4a )cos(x) + (5b + 4a b - 5a )cos(x) + 3b - a b) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- b + a b - 2a )cos(x) + (- 6b + 4a b - 6a )cos(x) +--R + +--R 2 2 2 2 2 2 +--R (- 12b - 2a )cos(x) + (- 10b - 6a b + 4a )cos(x) - 3b - 3a b +--R + +--R 2 +--R 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 2 2 4 2 3 +--R (b - a )cos(x) + (5b - a b - 2a )cos(x) + (10b - 2a b)cos(x) +--R + +--R 2 2 2 2 2 2 +--R (10b + 2a )cos(x) + (5b + 2a b + a )cos(x) + b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 6 +--R (- b - a b - 2a )sin(x) +--R + +--R 2 2 2 2 2 2 4 +--R ((2b - 4a b - 4a )cos(x) + (3b - 6a b - 5a )cos(x) + 3b - a b)sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- b - 3a b - 2a )cos(x) + (- 2b - 8a b - 6a )cos(x) +--R + +--R 2 2 2 2 2 2 +--R (- 4b - 4a b - 2a )cos(x) + (- 6b + 2a b + 4a )cos(x) - 3b + a b +--R + +--R 2 +--R 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 2 2 4 +--R (- b - 2a b - a )cos(x) + (- 3b - 5a b - 2a )cos(x) +--R + +--R 2 3 2 2 2 +--R (- 2b - 2a b)cos(x) + (2b + 4a b + 2a )cos(x) +--R + +--R 2 2 2 +--R (3b + 4a b + a )cos(x) + b + a b +--R / +--R 2 2 3 6 +--R (a b - 2a b + a )sin(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 4a b)cos(x) - 3a b + 4a b +--R + +--R 3 +--R - a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 2 3 3 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) +--R + +--R 2 2 3 2 2 2 3 2 +--R (8a b - 2a b - 6a )cos(x) + (8a b - 4a b - 4a )cos(x) + 3a b +--R + +--R 2 3 +--R - 2a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 2 3 3 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 6a b + 6a )cos(x) + (- 4a b + 4a )cos(x) - a b + a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 6 +--R (- a b + a )sin(x) +--R + +--R 2 2 2 2 2 2 2 3 4 +--R ((2a b + 2a b)cos(x) + (4a b + 4a b)cos(x) + 3a b + 2a b - a )sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 8a b - 14a b - 6a )cos(x) + (- 8a b - 12a b - 4a )cos(x) +--R + +--R 2 2 3 +--R - 3a b - 4a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 2 2 2 3 2 2 +--R (6a b + 12a b + 6a )cos(x) + (4a b + 8a b + 4a )cos(x) + a b + 2a b +--R + +--R 3 +--R a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 546 +t0447:= sec(x)^2/(a+b*cos(x)) +--R +--R +--R 2 +--R sec(x) +--R (273) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 276 + +--S 277 of 546 +r0447:= 2*b^2*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)-_ + b*atanh(sin(x))/a^2+tan(x)/a +--R +--R +--R (274) +--R x +--R +---------+ (b - a)tan(-) +---------+ +--R | 2 2 2 2 | 2 2 +--R - b\|- b + a atanh(sin(x)) - 2b atan(-------------) + a tan(x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ---------------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 546 +a0447:= integrate(t0447,x) +--R +--R +--R (275) +--R [ +--R +-------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - b cos(x)\|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R b cos(x)\|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 2 2 +--R 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R b cos(x)log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R | 2 2 +--R a sin(x)\|b - a +--R / +--R +-------+ +--R 2 | 2 2 +--R a cos(x)\|b - a +--R , +--R +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - b cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R b cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +---------+ +--R 2 sin(x)\|- b + a | 2 2 +--R 2b cos(x)atan(---------------------) + a sin(x)\|- b + a +--R (b + a)cos(x) + b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a cos(x)\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 278 + +--S 279 of 546 +m0447a:= a0447.1-r0447 +--R +--R +--R (276) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R - b cos(x)\|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R b cos(x)\|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 2 | 2 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R b cos(x)\|- b + a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R b cos(x)\|- b + a \|b - a atanh(sin(x)) +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 2 | 2 2 2 +--R 2b cos(x)\|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R (- a cos(x)tan(x) + a sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a cos(x)\|- b + a \|b - a +--R Type: Expression(Integer) +--E 279 + +--S 280 of 546 +d0447a:= D(m0447a,x) +--R +--R +--R (277) +--R 2 2 3 4 3 2 2 3 4 3 +--R (- a b + a b)cos(x) + (- a b + a b - a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 3 2 2 3 4 4 3 4 3 +--R (2a b + a b - a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 2 2 3 2 +--R (2a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 3 4 4 3 2 2 3 4 3 +--R (- 2a b + 2a )cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b + a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) +--R + +--R 2 2 3 2 +--R (a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 2a b - 5a b - 5a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 3 2 2 3 4 5 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (2a b + 4a b + 4a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (a b + 3a b + 3a b + a )cos(x) + (a b + a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 2 3 2 +--R (b - a b + a b - a b)cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (a b - a b + a b - a )cos(x) + a b - a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 4 2 2 3 4 3 +--R (3a b - 3a b + a b)cos(x) + (b + a b - a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b + 3a b - 3a b + a b + 2a )cos(x) +--R + +--R 3 4 2 2 3 +--R (- 2a b + 2a )cos(x) - 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- b + 2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b - 2a b + a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - 5a b + 2a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b - 2a b - 2a b + a b - a )cos(x) +--R + +--R 4 3 2 2 4 2 +--R (b - 3a b + 2a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (a b + a b - a b - a )cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 4 3 2 2 3 6 +--R (a b - a b )cos(x) + (2b - a b + a b - a b)cos(x) +--R + +--R 4 3 5 4 3 2 2 3 4 +--R (3b + a b )cos(x) + (2b + 4a b - a b + a b)cos(x) +--R + +--R 4 3 2 2 3 3 2 +--R (b + 2a b + a b )cos(x) + a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (- b - a b - a b - a b)cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- a b - a b - a b - a )cos(x) - a b - a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 4 2 2 3 4 3 +--R (- a b - a b + a b)cos(x) + (b + a b + a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 3a b + 3a b + 5a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (2a b + 4a b + 4a b + 2a )cos(x) + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (b - 2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b - 2a b - 3a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - a b - 2a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b - 2a b - 2a b - a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- b - 3a b - 2a b - 4a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- a b - 3a b - 3a b - a )cos(x) - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 4 3 2 2 3 6 +--R (- a b - a b )cos(x) + (- 2b - a b - a b - a b)cos(x) +--R + +--R 4 3 5 4 2 2 3 4 +--R (- b - a b )cos(x) + (2b + a b + a b)cos(x) +--R + +--R 4 3 2 2 3 3 2 +--R (b + 2a b + a b )cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 2 3 3 2 4 3 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (- a b + a b + a b - a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (2a b - a b - 3a b + a b + a )cos(x) +--R + +--R 4 3 2 5 3 +--R (2a b - 4a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 2a b + a b + 3a b - a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- a b - a b + 3a b + a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (- a b + a b + a b - a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 3 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (a b + a b - a b - a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 2a b - 3a b + a b + 3a b + a )cos(x) +--R + +--R 4 2 3 4 5 3 +--R (- 2a b - 4a b + 4a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (2a b + 3a b - a b - 3a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (a b + 3a b + a b - 3a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (a b + a b - a b - a )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 7 +--R ((a b - a b - a b + a b)cos(x) + a b - a b - a b + a )sin(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (3b - 3a b - 2a b + 3a b - a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (b - 2a b + a b + a b - a )cos(x) +--R + +--R 4 3 2 5 2 3 3 2 4 5 +--R (- 2a b + 4a b - 2a )cos(x) - 2a b + 2a b + 2a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 4 2 3 3 2 5 +--R (b - 2a b - a b + 2a b )cos(x) +--R + +--R 5 4 3 2 4 4 +--R (- 2b + a b - a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- 6b + 4a b + 4a b - 4a b + 2a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (- 2b + 3a b - a b - a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 5 +--R (a b + a b - 3a b - a b + 2a )cos(x) + a b - a b - a b + a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 2 3 3 2 6 +--R (b - a b - a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (b + a b - 2a b - a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (2b + a b - 2a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 5 2 3 2 +--R (3b - a b - 2a b + a b - a b)cos(x) + (b - a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 7 +--R ((- a b - a b + a b + a b)cos(x) - a b - a b + a b + a )sin(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- b - a b + 2a b + a b - a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (- b + 2a b + a b - a b - a )cos(x) +--R + +--R 4 2 3 4 5 2 3 3 2 4 5 +--R (2a b + 4a b - 4a b - 2a )cos(x) + 2a b + 2a b - 2a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 3b - 2a b + 3a b + 2a b )cos(x) +--R + +--R 5 4 3 2 4 4 5 2 3 4 3 +--R (- 2b - 3a b + 3a b + 2a b)cos(x) + (2b - 4a b + 2a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (2b - 3a b - a b + a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 5 +--R (- a b - 3a b - a b + 3a b + 2a )cos(x) - a b - a b + a b + a +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- b - a b + a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - a b - 2a b + a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (2b + a b - 2a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 5 2 3 2 +--R (- b + a b + 2a b - a b - a b)cos(x) + (- b + a b )cos(x) +--R * +--R sin(x) +--R / +--R 3 2 4 4 2 3 3 2 4 5 3 +--R (a b - a b)cos(x) + (a b - a b + a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 2 3 3 2 4 5 4 2 3 5 3 +--R (- 2a b - a b + a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 3 2 4 2 +--R (- 2a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 2 3 5 4 2 3 3 2 4 5 3 +--R (2a b - 2a )cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 2 3 3 2 4 5 3 +--R (- a b - a b)cos(x) + (- a b - a b - a b - a )cos(x) +--R + +--R 3 2 4 2 +--R (- a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (2a b + 5a b + 5a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (2a b + 4a b + 4a b + 2a )cos(x) + (2a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (- a b - 3a b - 3a b - a )cos(x) + (- a b - a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 3 3 4 2 5 3 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (a b - a b - a b + a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 2a b + a b + 3a b - a b - a )cos(x) +--R + +--R 2 4 4 2 6 3 +--R (- 2a b + 4a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- 2a b + 2a b + 2a b - 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (2a b - a b - 3a b + a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (a b + a b - 3a b - a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (a b - a b - a b + a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 3 3 4 2 5 3 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- a b - a b + a b + a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (2a b + 3a b - a b - 3a b - a )cos(x) +--R + +--R 2 4 3 3 5 6 3 +--R (2a b + 4a b - 4a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (2a b + 2a b - 2a b - 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 2a b - 3a b + a b + 3a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- a b - 3a b - a b + 3a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- a b - a b + a b + a )cos(x) +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 280 + +--S 281 of 546 +m0447b:= a0447.2-r0447 +--R +--R +--R (278) +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - b cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R b cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 2 sin(x)\|- b + a +--R b cos(x)\|- b + a atanh(sin(x)) + 2b cos(x)atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R x +--R (b - a)tan(-) +---------+ +--R 2 2 | 2 2 +--R 2b cos(x)atan(-------------) + (- a cos(x)tan(x) + a sin(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a cos(x)\|- b + a +--R Type: Expression(Integer) +--E 281 + +--S 282 of 546 +d0447b:= D(m0447b,x) +--R +--R +--R (279) +--R 2 2 3 2 6 +--R (- a b + 2a b - a )cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R (3a b - 4a b + a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 6 2 3 5 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 8a b + 2a b + 6a )cos(x) + (- 8a b + 4a b + 4a )cos(x) +--R + +--R 2 2 3 2 +--R (- 3a b + 2a b + a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 6 2 3 5 2 3 4 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) + (6a b - 6a )cos(x) +--R + +--R 2 3 3 2 3 2 +--R (4a b - 4a )cos(x) + (a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 6 +--R (a b - a )cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b - 2a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R (- 3a b - 2a b + a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (8a b + 14a b + 6a )cos(x) + (8a b + 12a b + 4a )cos(x) +--R + +--R 2 2 3 2 +--R (3a b + 4a b + a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 6a b - 12a b - 6a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 2 +--R (- a b - 2a b - a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 8 +--R (a b - 2a b + a )sin(x) +--R + +--R 3 2 2 2 2 2 2 +--R (b - 5a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) - 3a b +--R + +--R 2 3 +--R 4a b - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 3 2 3 3 +--R (- 2b - 3a b + 4a b - a )cos(x) + (- 5b + 5a b - 4a )cos(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 3b + 9a b - 2a b - 6a )cos(x) + (8a b - 4a b - 4a )cos(x) +--R + +--R 2 2 3 +--R 3a b - 2a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (b - a b + 2a b)cos(x) + (6b - 4a b + 6a b)cos(x) +--R + +--R 3 2 2 3 4 +--R (12b - a b + 2a b + a )cos(x) +--R + +--R 3 2 2 3 3 +--R (10b + 2a b - 4a b + 4a )cos(x) +--R + +--R 3 2 2 3 2 2 3 2 +--R (3b - 3a b - 2a b + 6a )cos(x) + (- 4a b + 4a )cos(x) - a b +--R + +--R 3 +--R a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 7 3 2 2 6 +--R (- b + a b)cos(x) + (- 5b + a b + 2a b)cos(x) +--R + +--R 3 2 5 3 2 4 +--R (- 10b + 2a b )cos(x) + (- 10b - 2a b)cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 5b - 2a b - a b)cos(x) + (- b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 8 +--R (- a b + a )sin(x) +--R + +--R 3 2 2 2 2 2 2 2 3 +--R ((b + 3a b + 4a b)cos(x) + (4a b + 4a b)cos(x) + 3a b + 2a b - a ) +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- 2b + 3a b + 2a b - a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 3b + 2a b - 3a b - 4a )cos(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (- 3b - 7a b - 14a b - 6a )cos(x) + (- 8a b - 12a b - 4a )cos(x) +--R + +--R 2 2 3 +--R - 3a b - 4a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (b + 3a b + 2a b)cos(x) + (2b + 8a b + 6a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 3 +--R (4b + 5a b + 4a b + a )cos(x) + (6b + 2a b + 4a b + 4a )cos(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (3b + 5a b + 10a b + 6a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 +--R a b + 2a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 3 2 2 6 +--R (b + 2a b + a b)cos(x) + (3b + 5a b + 2a b)cos(x) +--R + +--R 3 2 5 3 2 2 4 +--R (2b + 2a b )cos(x) + (- 2b - 4a b - 2a b)cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 3b - 4a b - a b)cos(x) + (- b - a b )cos(x) +--R / +--R 2 2 3 4 2 6 +--R (a b - 2a b + a )cos(x) sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 2 3 4 2 +--R (- 3a b + 4a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (8a b - 2a b - 6a )cos(x) + (8a b - 4a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (3a b - 2a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 2 2 4 2 +--R (- 6a b + 6a )cos(x) + (- 4a b + 4a )cos(x) + (- a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 6 +--R (- a b + a )cos(x) sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (2a b + 2a b)cos(x) + (4a b + 4a b)cos(x) +--R + +--R 2 2 3 4 2 +--R (3a b + 2a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 6 2 2 3 4 5 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (- 8a b - 14a b - 6a )cos(x) + (- 8a b - 12a b - 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (- 3a b - 4a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 6 2 2 3 4 5 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (6a b + 12a b + 6a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 2 +--R (a b + 2a b + a )cos(x) +--R Type: Expression(Integer) +--E 282 + +--S 283 of 546 +t0448:= sec(x)^3/(a+b*cos(x)) +--R +--R +--R 3 +--R sec(x) +--R (280) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 546 +r0448:= -2*b^3*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)+_ + 1/2*atanh(sin(x))/a+b^2*atanh(sin(x))/a^3-b*tan(x)/a^2+_ + 1/2*sec(x)*tan(x)/a +--R +--R +--R (281) +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 3 2 +--R (2b + a )\|- b + a atanh(sin(x)) + 4b atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (a sec(x) - 2a b)tan(x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 546 +a0448:= integrate(t0448,x) +--R +--R +--R (282) +--R [ +--R +-------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (2b + a )cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- 2b - a )cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 2 2 +--R 3 2 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R 2b cos(x) log(--------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R 2 | 2 2 +--R (- 2a b cos(x) + a )sin(x)\|b - a +--R / +--R +-------+ +--R 3 2 | 2 2 +--R 2a cos(x) \|b - a +--R , +--R +--R +---------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (2b + a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- 2b - a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 3 2 sin(x)\|- b + a +--R - 4b cos(x) atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 2a b cos(x) + a )sin(x)\|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R 2a cos(x) \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 285 + +--S 286 of 546 +m0448a:= a0448.1-r0448 +--R +--R +--R (283) +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (2b + a )cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- 2b - a )cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 3 2 | 2 2 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R 2b cos(x) \|- b + a log(--------------------------------------------) +--R b cos(x) + a +--R + +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 +--R (- 2b - a )cos(x) \|- b + a \|b - a atanh(sin(x)) +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 3 2 | 2 2 2 +--R - 4b cos(x) \|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R ((- a cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + a )sin(x)) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 | 2 2 | 2 2 +--R 2a cos(x) \|- b + a \|b - a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 546 +d0448a:= D(m0448a,x) +--R +--R +--R (284) +--R 3 2 4 5 +--R (- 2a b + 2a b)cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 2a b + 2a b - 2a b + 2a )cos(x) +--R + +--R 3 2 4 3 +--R (- 2a b + 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 +--R (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (2a b - 2a b + 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 7 +--R (2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (2a b + 2a b - 2a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 5 +--R (4a b + 2a b - 2a b - 4a )cos(x) +--R + +--R 2 3 5 4 3 2 4 3 +--R (4a b - 4a )cos(x) + (4a b - 4a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 2a b + 2a b + 4a b)cos(x) +--R + +--R 4 4 4 2 3 3 2 3 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 7 +--R (- 2a b + 2a b)cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R + +--R 2 3 5 5 +--R (- 4a b + 4a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R + +--R 3 2 4 3 +--R (- 2a b + 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 4 4 5 +--R (2a b + 2a b - 2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b + 2a b - 2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 5 +--R (2a b + 2a b)cos(x) +--R + +--R 2 3 3 2 4 5 4 3 2 4 3 +--R (2a b + 2a b + 2a b + 2a )cos(x) + (2a b + 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 +--R (- 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 2a b - 2a b - 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (- 2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 7 +--R (- 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- 2a b - 6a b - 6a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 4a b - 10a b - 10a b - 4a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 4a b - 8a b - 8a b - 4a )cos(x) +--R + +--R 3 2 4 3 +--R (- 4a b - 4a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (2a b + 6a b + 6a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (4a b + 10a b + 10a b + 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (4a b + 8a b + 8a b + 4a b)cos(x) + (4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 6 +--R (2a b + 2a b)cos(x) + (2a b + 6a b + 6a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 5 +--R (4a b + 8a b + 8a b + 4a )cos(x) +--R + +--R 2 3 3 2 4 5 4 3 2 4 3 +--R (2a b + 6a b + 6a b + 2a )cos(x) + (2a b + 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 6a b - 6a b - 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 8a b - 8a b - 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (- 2a b - 6a b - 6a b - 2a b)cos(x) + (- 2a b - 2a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 2b + 2a b - 2a b + 2a b )cos(x) +--R + +--R 4 2 3 2 4 5 3 2 4 +--R (- 2a b + 2a b )cos(x) + (2a b - 2a )cos(x) + 2a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 4 5 2 3 3 2 4 5 4 +--R (- a b + a b)cos(x) + (- a b + a b - a b + a )cos(x) +--R + +--R 3 2 4 3 +--R (- a b + a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 6a b + 6a b - 4a b + 2a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 4 +--R (- 2b - 4a b + 3a b - 3a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (4b - 6a b + 5a b - 7a b + a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (4a b - 4a b - a b - 3a b + 4a )cos(x) +--R + +--R 3 2 5 3 2 4 +--R (- 4a b + 4a )cos(x) - 4a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 6 +--R (a b - a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 5 2 3 5 4 +--R (2a b + a b - a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 2 4 3 +--R (2a b - 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (2b - 4a b + 4a b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 5 6 +--R (2b + 4a b - 4a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 5 5 +--R (4b + 10a b - 6a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (4b + 4a b + 4a b - 4a b + 4a b)cos(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 2b + 6a b - 4a b + 4a b )cos(x) +--R + +--R 4 2 3 4 5 2 +--R (- 2a b + 2a b + 4a b - 4a )cos(x) +--R + +--R 3 2 4 5 3 2 4 +--R (4a b - 2a b - 2a )cos(x) + 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 6 +--R (- a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 2 3 5 5 2 3 3 2 4 5 4 +--R (- 2a b + 2a )cos(x) + (- a b - a b + a b + a )cos(x) +--R + +--R 3 2 4 3 +--R (- a b + a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (- 2a b + 2a b - a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 4b + 2a b - 3a b + 3a b - a b + a )cos(x) +--R + +--R 5 4 3 2 4 6 +--R (- 6b - 2a b + a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 5 5 +--R (- 4b - 8a b + 4a b - 2a b - 2a )cos(x) +--R + +--R 5 4 3 2 4 5 4 +--R (- 2b - 4a b + a b - a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 3 2 4 2 +--R (- 2a b + a b + a b - a b - a )cos(x) + (a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 3 3 2 3 4 2 3 2 +--R (2b + 2a b + 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 4 5 3 2 4 +--R (- 2a b - 2a )cos(x) - 2a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 4 5 2 3 3 2 4 5 4 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) +--R + +--R 3 2 4 3 +--R (a b + a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 4 5 5 3 2 4 5 4 +--R (2a b + 2a b + 2a b)cos(x) + (- 2b + a b + a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 4b - 6a b - 5a b - 3a b + 3a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 4a b - 4a b + a b + 5a b + 4a )cos(x) +--R + +--R 3 2 4 5 3 2 4 +--R (4a b + 8a b + 4a )cos(x) + 4a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 6 +--R (- a b - a b)cos(x) + (- a b - 3a b - 3a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 2a b - 5a b - 5a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 5 4 3 2 4 3 +--R (- 2a b - 4a b - 4a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 2b + 4a b + 4a b + 2a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (2b + 4a b + 8a b + 8a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (4b + 2a b + 6a b + 8a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (4b + 4a b + 4a b + 4a b + 4a b)cos(x) +--R + +--R 5 4 2 3 3 2 3 +--R (2b + 6a b + 4a b + 4a b )cos(x) +--R + +--R 4 2 3 4 5 2 +--R (2a b + 2a b - 4a b - 4a )cos(x) +--R + +--R 3 2 4 5 3 2 4 +--R (- 4a b - 6a b - 2a )cos(x) - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 7 2 3 3 2 4 5 6 +--R (a b + a b)cos(x) + (a b + 3a b + 3a b + a )cos(x) +--R + +--R 2 3 3 2 4 5 5 +--R (2a b + 4a b + 4a b + 2a )cos(x) +--R + +--R 2 3 3 2 4 5 4 3 2 4 3 +--R (a b + 3a b + 3a b + a )cos(x) + (a b + a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (2a b + 2a b + a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (4b + 2a b + 3a b + 3a b + a b + a )cos(x) +--R + +--R 5 4 3 2 4 6 +--R (2b + 2a b - a b - a b)cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (- 4b - 4a b - 6a b - 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 2b - 4a b - 4a b - 5a b - 5a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 3 2 4 2 +--R (- 2a b - a b - 3a b - 3a b - a )cos(x) + (- a b - a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 3 3 4 2 5 4 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 4a b + 2a b + 6a b - 2a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 4a b + 8a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- 4a b + 4a b + 4a b - 4a )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (4a b - 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2a b - 2a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (4a b + 6a b - 2a b - 6a b - 2a )cos(x) +--R + +--R 2 4 3 3 5 6 4 +--R (4a b + 8a b - 8a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (4a b + 4a b - 4a b - 4a )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 2a b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 4a b - 6a b + 2a b + 6a b + 2a b)cos(x) +--R + +--R 5 2 4 4 2 5 4 +--R (- 4a b - 8a b + 8a b + 4a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- 4a b - 4a b + 4a b + 4a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 4a b - 6a b + 2a b + 6a b + 2a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 2a b - 6a b - 2a b + 6a b + 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (2a b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (4a b + 6a b - 2a b - 6a b - 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (2a b + 6a b + 2a b - 6a b - 4a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 2 4 3 3 4 2 2 3 3 4 2 5 +--R (2a b - 2a b - 2a b + 2a b )cos(x) - 2a b + 2a b + 2a b +--R + +--R 6 +--R - 2a +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (a b - a b - a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (6b - 6a b - 2a b + 4a b - 4a b + 2a b)cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 3 +--R (2b - 3a b + 3a b - a b - 3a b + 2a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (- 4a b + 4a b + 5a b - 5a b - a b + a )cos(x) +--R + +--R 3 3 4 2 5 6 3 3 4 2 5 6 +--R (4a b - 4a b - 4a b + 4a )cos(x) + 4a b - 4a b - 4a b + 4a +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 2a b + a b + 3a b - a b - a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 2a b + 4a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- 2a b + 2a b + 2a b - 2a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 3 3 4 2 5 6 +--R (2b - 4a b + 2a b - 2a b + 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 6 5 +--R (- 4b + 2a b + 2a b - 2a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 12b + 8a b + 8a b - 6a b + 2a b - 2a b + 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 3 +--R (- 4b + 6a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 2 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R + +--R 3 3 4 2 5 6 3 3 4 2 5 6 +--R (- 4a b + 4a b + 4a b - 4a )cos(x) - 2a b + 2a b + 2a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (2a b - a b - 3a b + a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (a b + a b - 3a b - a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (a b - a b - a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (2b - 2a b - a b + a b - a b + a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (2b + 2a b - 4a b - a b + a b - a b + a )cos(x) +--R + +--R 6 5 2 4 4 2 5 5 +--R (4b + 2a b - 6a b + 2a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 4 +--R (6b - 2a b - 6a b + 2a b + 2a b - 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 3 +--R (2b - 3a b - a b + 3a b + a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- a b + a b + a b - a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 3 3 4 2 2 3 3 4 2 5 6 +--R ((- 2a b - 2a b + 2a b + 2a b )cos(x) + 2a b + 2a b - 2a b - 2a ) +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- a b - a b + a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 5 4 +--R (- 2b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 3 +--R (- 2b + 3a b - a b - 3a b + a b + 2a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 2 +--R (4a b + 4a b - 5a b - 5a b + a b + a )cos(x) +--R + +--R 3 3 4 2 5 6 3 3 4 2 5 6 +--R (- 4a b - 4a b + 4a b + 4a )cos(x) - 4a b - 4a b + 4a b + 4a +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (2a b + 3a b - a b - 3a b - a )cos(x) +--R + +--R 2 4 3 3 5 6 4 +--R (2a b + 4a b - 4a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (2a b + 2a b - 2a b - 2a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 6b - 4a b + 4a b + 2a b + 2a b + 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 4b - 6a b - 2a b + 2a b + 4a b + 4a b + 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b - 2a b + 2a b + 2a b + 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 3 +--R (4b - 6a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 2 +--R (- 2a b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 3 3 4 2 5 6 3 3 4 2 5 6 +--R (4a b + 4a b - 4a b - 4a )cos(x) + 2a b + 2a b - 2a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 5 +--R (- 2a b - 3a b + a b + 3a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- a b - 3a b - a b + 3a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 3 +--R (- a b - a b + a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 2b - 2a b + a b + a b + a b + a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (2b - 2a b - 4a b + a b + a b + a b + a )cos(x) +--R + +--R 6 5 2 4 4 2 5 5 +--R (4b + 2a b - 2a b - 2a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 2b + 2a b + 6a b + 2a b - 2a b - 4a b - 2a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 3 +--R (- 2b + 3a b + 3a b + a b - 3a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (a b + a b - a b - a )cos(x) +--R * +--R sin(x) +--R / +--R 4 2 5 5 3 3 4 2 5 6 4 +--R (2a b - 2a b)cos(x) + (2a b - 2a b + 2a b - 2a )cos(x) +--R + +--R 4 2 5 3 +--R (2a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 7 +--R (- 2a b + 2a b)cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 4a b - 2a b + 2a b + 4a )cos(x) +--R + +--R 3 3 6 4 4 2 5 3 +--R (- 4a b + 4a )cos(x) + (- 4a b + 4a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 7 3 3 4 2 5 6 6 +--R (2a b - 2a b)cos(x) + (2a b + 2a b - 2a b - 2a )cos(x) +--R + +--R 3 3 6 5 3 3 4 2 5 6 4 +--R (4a b - 4a )cos(x) + (2a b + 2a b - 2a b - 2a )cos(x) +--R + +--R 4 2 5 3 +--R (2a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 5 3 3 4 2 5 6 4 +--R (- 2a b - 2a b)cos(x) + (- 2a b - 2a b - 2a b - 2a )cos(x) +--R + +--R 4 2 5 3 +--R (- 2a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 7 3 3 4 2 5 6 6 +--R (2a b + 2a b)cos(x) + (2a b + 6a b + 6a b + 2a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (4a b + 10a b + 10a b + 4a )cos(x) +--R + +--R 3 3 4 2 5 6 4 4 2 5 3 +--R (4a b + 8a b + 8a b + 4a )cos(x) + (4a b + 4a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 7 3 3 4 2 5 6 6 +--R (- 2a b - 2a b)cos(x) + (- 2a b - 6a b - 6a b - 2a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 4a b - 8a b - 8a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 4 4 2 5 3 +--R (- 2a b - 6a b - 6a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R + +--R 4 3 5 2 6 7 3 +--R (- 2a b + 2a b + 2a b - 2a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 5 +--R (4a b - 2a b - 6a b + 2a b + 2a )cos(x) +--R + +--R 3 4 5 2 7 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 4a )cos(x) + (4a b - 4a b - 4a b + 4a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 5 +--R (- 4a b + 2a b + 6a b - 2a b - 2a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- 2a b - 2a b + 6a b + 2a b - 4a )cos(x) +--R + +--R 4 3 5 2 6 7 3 +--R (- 2a b + 2a b + 2a b - 2a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 4 3 5 2 6 4 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 4 3 5 2 6 7 3 +--R (2a b + 2a b - 2a b - 2a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 5 +--R (- 4a b - 6a b + 2a b + 6a b + 2a )cos(x) +--R + +--R 3 4 4 3 6 7 4 +--R (- 4a b - 8a b + 8a b + 4a )cos(x) +--R + +--R 4 3 5 2 6 7 3 +--R (- 4a b - 4a b + 4a b + 4a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 6 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 5 +--R (4a b + 6a b - 2a b - 6a b - 2a )cos(x) +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (2a b + 6a b + 2a b - 6a b - 4a )cos(x) +--R + +--R 4 3 5 2 6 7 3 +--R (2a b + 2a b - 2a b - 2a )cos(x) +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 287 + +--S 288 of 546 +m0448b:= a0448.2-r0448 +--R +--R +--R (285) +--R +---------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (2b + a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- 2b - a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- 2b - a )cos(x) \|- b + a atanh(sin(x)) +--R + +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R 3 2 sin(x)\|- b + a 3 2 2 +--R - 4b cos(x) atan(---------------------) - 4b cos(x) atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R ((- a cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + a )sin(x)) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R 2a cos(x) \|- b + a +--R Type: Expression(Integer) +--E 288 + +--S 289 of 546 +d0448b:= D(m0448b,x) +--R +--R +--R (286) +--R 2 2 3 4 3 +--R (- 2a b + 4a b - 2a )cos(x) sec(x) +--R + +--R 3 2 2 3 3 +--R (2a b - 4a b + 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (4a b - 4a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 2 3 4 3 +--R (6a b - 8a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 4a b + 4a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 6a b + 8a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 +--R (- 2a b + 2a )cos(x) + (- 8a b + 8a )cos(x) +--R + +--R 2 2 3 4 5 +--R (- 16a b + 4a b + 12a )cos(x) +--R + +--R 2 2 3 4 4 +--R (- 16a b + 8a b + 8a )cos(x) +--R + +--R 2 2 3 4 3 +--R (- 6a b + 4a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 3 7 3 3 6 +--R (2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 3 2 2 3 5 +--R (16a b - 4a b - 12a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 3 +--R (16a b - 8a b - 8a b)cos(x) + (6a b - 4a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 +--R (2a b - 2a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 2 2 4 5 2 2 4 4 +--R (12a b - 12a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 2 2 4 3 +--R (2a b - 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 3 7 3 3 6 +--R (- 2a b + 2a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 3 3 5 3 3 4 +--R (- 12a b + 12a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 3 3 3 +--R (- 2a b + 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 3 3 3 3 6 +--R ((2a b - 2a )cos(x) sec(x) + (- 2a b + 2a b)cos(x) )sin(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (- 4a b - 4a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 2 2 3 4 3 +--R (- 6a b - 4a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (4a b + 4a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 3 2 2 3 3 +--R (6a b + 4a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 7 2 2 3 4 6 +--R (2a b + 4a b + 2a )cos(x) + (8a b + 16a b + 8a )cos(x) +--R + +--R 2 2 3 4 5 +--R (16a b + 28a b + 12a )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (16a b + 24a b + 8a )cos(x) + (6a b + 8a b + 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 7 +--R (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8a b - 16a b - 8a b)cos(x) +--R + +--R 3 2 2 3 5 +--R (- 16a b - 28a b - 12a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 3 +--R (- 16a b - 24a b - 8a b)cos(x) + (- 6a b - 8a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 7 2 2 3 4 6 +--R (- 2a b - 4a b - 2a )cos(x) + (- 8a b - 16a b - 8a )cos(x) +--R + +--R 2 2 3 4 5 2 2 3 4 4 +--R (- 12a b - 24a b - 12a )cos(x) + (- 8a b - 16a b - 8a )cos(x) +--R + +--R 2 2 3 4 3 +--R (- 2a b - 4a b - 2a )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 7 3 2 2 3 6 +--R (2a b + 4a b + 2a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 3 2 2 3 5 3 2 2 3 4 +--R (12a b + 24a b + 12a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (2a b + 4a b + 2a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 2 2 3 4 8 +--R ((- 2a b + 4a b - 2a b)cos(x) + 2a b - 4a b + 2a )sin(x) +--R + +--R 2 2 3 4 3 +--R (- a b + 2a b - a )cos(x) sec(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b + 10a b - 10a b + 4a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (8a b - 11a b + 2a b + a )cos(x) +--R + +--R 3 2 2 3 2 2 3 4 +--R (6a b - 16a b + 10a b)cos(x) - 6a b + 8a b - 2a +--R * +--R 6 +--R sin(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 2 3 4 3 +--R (3a b - 4a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 5 +--R (4b + 6a b - 8a b + 6a b - 4a )cos(x) +--R + +--R 4 2 2 3 4 4 +--R (10b - 7a b + 12a b - 7a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (6b - 18a b + 12a b + 12a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (- 16a b + 21a b + 8a b - 13a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 4 +--R (- 6a b + 20a b - 6a b - 8a )cos(x) + 6a b - 4a b - 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 3 4 5 2 2 3 4 4 +--R (- 8a b + 2a b + 6a )cos(x) + (- 8a b + 4a b + 4a )cos(x) +--R + +--R 2 2 3 4 3 +--R (- 3a b + 2a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 4 7 +--R (- 2b + 2a b - 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 12b + 8a b - 7a b + 2a b - 7a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 24b + 2a b + 2a b - 2a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 20b - 4a b + 12a b - 12a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 6b + 6a b + 2a b - 16a b + 6a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (8a b - 9a b - 10a b + 11a )cos(x) +--R + +--R 3 2 2 3 4 2 2 4 +--R (2a b - 8a b - 2a b + 8a )cos(x) - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 7 2 2 4 6 2 2 4 5 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) + (6a b - 6a )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 +--R (4a b - 4a )cos(x) + (a b - a )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 2 4 8 4 3 2 2 4 7 +--R (2b - a b - a )cos(x) + (10b - 2a b - 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 4 6 4 2 2 4 5 +--R (20b - 4a b - a b + a )cos(x) + (20b - 2a b + 6a )cos(x) +--R + +--R 4 3 2 2 4 4 +--R (10b + 4a b - 5a b + 7a )cos(x) +--R + +--R 4 3 2 2 4 3 2 2 4 2 +--R (2b + 2a b - 4a b + 4a )cos(x) + (- a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 4 8 +--R ((2a b - 2a b)cos(x) - 2a b + 2a )sin(x) +--R + +--R 2 2 4 3 4 3 2 2 4 3 +--R (a b - a )cos(x) sec(x) + (- 2b - 6a b - 6a b - 2a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (- 8a b - 5a b + 4a b + a )cos(x) +--R + +--R 3 2 2 3 2 2 3 4 +--R (- 6a b + 4a b + 10a b)cos(x) + 6a b + 4a b - 2a +--R * +--R 6 +--R sin(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (- 2a b - 2a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 2 2 3 4 3 +--R (- 3a b - 2a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 5 +--R (4b - 6a b - 4a b - 2a b - 4a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (6b - 4a b + 3a b - 2a b - 7a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (6b + 14a b + 20a b - 4a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (16a b + 11a b - 18a b - 13a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 4 +--R (6a b - 8a b - 22a b - 8a )cos(x) - 6a b - 8a b - 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 7 2 2 3 4 6 +--R (a b + 2a b + a )cos(x) + (4a b + 8a b + 4a )cos(x) +--R + +--R 2 2 3 4 5 2 2 3 4 4 +--R (8a b + 14a b + 6a )cos(x) + (8a b + 12a b + 4a )cos(x) +--R + +--R 2 2 3 4 3 +--R (3a b + 4a b + a )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 2b - 6a b - 6a b - 4a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 16a b - 17a b - 12a b - 7a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 8b - 10a b - 14a b - 14a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 12b - 4a b - 12a b - 12a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 6b - 10a b - 18a b - 4a b + 6a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (- 8a b - 7a b + 12a b + 11a )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 4 +--R (- 2a b + 4a b + 14a b + 8a )cos(x) + 2a b + 4a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 7 2 2 3 4 6 +--R (- a b - 2a b - a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 5 2 2 3 4 4 +--R (- 6a b - 12a b - 6a )cos(x) + (- 4a b - 8a b - 4a )cos(x) +--R + +--R 2 2 3 4 3 +--R (- a b - 2a b - a )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- 2b - 4a b - 3a b - 2a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 6b - 10a b - 6a b - 4a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b - 4a b + a b + 2a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (4b + 8a b + 10a b + 12a b + 6a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (6b + 8a b + 9a b + 14a b + 7a )cos(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 4 2 +--R (2b + 2a b + 4a b + 8a b + 4a )cos(x) + (a b + 2a b + a )cos(x) +--R / +--R 3 2 4 5 3 6 +--R (2a b - 4a b + 2a )cos(x) sin(x) +--R + +--R 3 2 4 5 3 2 4 4 +--R (- 4a b + 4a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 3 2 4 5 3 +--R (- 6a b + 8a b - 2a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 7 3 2 5 6 +--R (2a b - 2a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 3 2 4 5 5 3 2 4 5 4 +--R (16a b - 4a b - 12a )cos(x) + (16a b - 8a b - 8a )cos(x) +--R + +--R 3 2 4 5 3 +--R (6a b - 4a b - 2a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 7 3 2 5 6 +--R (- 2a b + 2a )cos(x) + (- 8a b + 8a )cos(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (- 12a b + 12a )cos(x) + (- 8a b + 8a )cos(x) +--R + +--R 3 2 5 3 +--R (- 2a b + 2a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 3 6 +--R (- 2a b + 2a )cos(x) sin(x) +--R + +--R 3 2 4 5 3 2 4 4 +--R (4a b + 4a b)cos(x) + (8a b + 8a b)cos(x) +--R + +--R 3 2 4 5 3 +--R (6a b + 4a b - 2a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 5 7 3 2 4 5 6 +--R (- 2a b - 4a b - 2a )cos(x) + (- 8a b - 16a b - 8a )cos(x) +--R + +--R 3 2 4 5 5 3 2 4 5 4 +--R (- 16a b - 28a b - 12a )cos(x) + (- 16a b - 24a b - 8a )cos(x) +--R + +--R 3 2 4 5 3 +--R (- 6a b - 8a b - 2a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 7 3 2 4 5 6 +--R (2a b + 4a b + 2a )cos(x) + (8a b + 16a b + 8a )cos(x) +--R + +--R 3 2 4 5 5 3 2 4 5 4 +--R (12a b + 24a b + 12a )cos(x) + (8a b + 16a b + 8a )cos(x) +--R + +--R 3 2 4 5 3 +--R (2a b + 4a b + 2a )cos(x) +--R Type: Expression(Integer) +--E 289 + +--S 290 of 546 +t0449:= sec(x)^4/(a+b*cos(x)) +--R +--R +--R 4 +--R sec(x) +--R (287) ------------ +--R b cos(x) + a +--R Type: Expression(Integer) +--E 290 + +--S 291 of 546 +r0449:= 2*b^4*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)-_ + 1/2*b*atanh(sin(x))/a^2-b^3*atanh(sin(x))/a^4+tan(x)/a+_ + b^2*tan(x)/a^3-1/2*b*sec(x)*tan(x)/a^2+1/3*tan(x)^3/a +--R +--R +--R (288) +--R x +--R +---------+ (b - a)tan(-) +--R 3 2 | 2 2 4 2 +--R (- 6b - 3a b)\|- b + a atanh(sin(x)) - 12b atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 3 2 2 3 | 2 2 +--R (2a tan(x) + (- 3a b sec(x) + 6a b + 6a )tan(x))\|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 546 +a0449:= integrate(t0449,x) +--R +--R +--R (289) +--R [ +--R +-------+ +--R 3 2 3 | 2 2 sin(x) + cos(x) + 1 +--R (- 6b - 3a b)cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 3 2 3 | 2 2 sin(x) - cos(x) - 1 +--R (6b + 3a b)cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 2 2 +--R 4 3 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R 6b cos(x) log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R 2 3 2 2 3 | 2 2 +--R ((6a b + 4a )cos(x) - 3a b cos(x) + 2a )sin(x)\|b - a +--R / +--R +-------+ +--R 4 3 | 2 2 +--R 6a cos(x) \|b - a +--R , +--R +--R +---------+ +--R 3 2 3 | 2 2 sin(x) + cos(x) + 1 +--R (- 6b - 3a b)cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 3 2 3 | 2 2 sin(x) - cos(x) - 1 +--R (6b + 3a b)cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 4 3 sin(x)\|- b + a +--R 12b cos(x) atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +--R 2 3 2 2 3 | 2 2 +--R ((6a b + 4a )cos(x) - 3a b cos(x) + 2a )sin(x)\|- b + a +--R / +--R +---------+ +--R 4 3 | 2 2 +--R 6a cos(x) \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 292 + +--S 293 of 546 +m0449a:= a0449.1-r0449 +--R +--R +--R (290) +--R +---------+ +-------+ +--R 3 2 3 | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (- 6b - 3a b)cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 3 2 3 | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (6b + 3a b)cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +---------+ | 2 2 2 2 +--R 4 3 | 2 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R 6b cos(x) \|- b + a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +---------+ +-------+ +--R 3 2 3 | 2 2 | 2 2 +--R (6b + 3a b)cos(x) \|- b + a \|b - a atanh(sin(x)) +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 4 3 | 2 2 2 +--R 12b cos(x) \|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 3 +--R - 2a cos(x) tan(x) +--R + +--R 2 3 2 3 3 +--R (3a b cos(x) sec(x) + (- 6a b - 6a )cos(x) )tan(x) +--R + +--R 2 3 2 2 3 +--R ((6a b + 4a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 4 3 | 2 2 | 2 2 +--R 6a cos(x) \|- b + a \|b - a +--R Type: Expression(Integer) +--E 293 + +--S 294 of 546 +d0449a:= D(m0449a,x) +--R +--R +--R (291) +--R 4 2 5 6 +--R (- 6a b + 6a b)cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 6a b + 6a b - 6a b + 6a )cos(x) +--R + +--R 4 2 5 4 +--R (- 6a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 8 +--R (6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (12a b + 6a b - 6a b - 12a )cos(x) +--R + +--R 3 3 6 5 4 2 5 4 +--R (12a b - 12a )cos(x) + (12a b - 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 8 +--R (- 6a b + 6a b)cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 3 3 6 6 +--R (- 12a b + 12a )cos(x) +--R + +--R 3 3 4 2 5 6 5 4 2 5 4 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) + (- 6a b + 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 6 3 3 4 2 5 6 5 +--R (6a b + 6a b)cos(x) + (6a b + 6a b + 6a b + 6a )cos(x) +--R + +--R 4 2 5 4 +--R (6a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 8 +--R (- 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 5 6 7 +--R (- 6a b - 18a b - 18a b - 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (- 12a b - 30a b - 30a b - 12a )cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (- 12a b - 24a b - 24a b - 12a )cos(x) +--R + +--R 4 2 5 4 +--R (- 12a b - 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 8 3 3 4 2 5 6 7 +--R (6a b + 6a b)cos(x) + (6a b + 18a b + 18a b + 6a )cos(x) +--R + +--R 3 3 4 2 5 6 6 +--R (12a b + 24a b + 24a b + 12a )cos(x) +--R + +--R 3 3 4 2 5 6 5 4 2 5 4 +--R (6a b + 18a b + 18a b + 6a )cos(x) + (6a b + 6a b)cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 3 3 4 2 6 +--R (6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (6a b - 6a b + 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 6a b + 6a b - 12a b + 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b + 6a b - 18a b + 18a b - 12a b + 12a )cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 6a b + 6a b - 12a b + 12a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b - 6a b + 6a b + 12a b)cos(x) +--R + +--R 2 4 5 5 3 3 4 2 4 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 12a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (6a b - 6a b + 12a b - 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (6a b + 6a b + 6a b + 6a b - 12a b - 12a )cos(x) +--R + +--R 5 2 4 3 3 5 6 6 +--R (12a b + 6a b + 18a b - 12a b - 24a )cos(x) +--R + +--R 5 3 3 4 2 6 5 +--R (12a b + 24a b - 12a b - 24a )cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (12a b - 12a b + 24a b - 24a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (6a b + 6a b - 6a b - 6a b)cos(x) +--R + +--R 2 4 5 6 +--R (12a b - 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (6a b + 6a b - 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (- 6a b + 6a b - 12a b + 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (- 6a b - 6a b - 6a b - 6a b + 12a b + 12a )cos(x) +--R + +--R 5 3 3 4 2 6 6 +--R (- 12a b - 24a b + 12a b + 24a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 6a b - 6a b - 6a b - 6a b + 12a b + 12a )cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 6a b + 6a b - 12a b + 12a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 6 +--R (- 6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 6a b - 6a b - 6a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (- 6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (6a b + 6a b + 12a b + 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (6a b + 6a b + 18a b + 18a b + 12a b + 12a )cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (6a b + 6a b + 12a b + 12a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (6a b + 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (6a b + 18a b + 18a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (12a b + 30a b + 30a b + 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (12a b + 24a b + 24a b + 12a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (12a b + 12a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (- 6a b - 6a b - 12a b - 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (- 6a b - 18a b - 30a b - 42a b - 36a b - 12a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 12a b - 30a b - 54a b - 72a b - 60a b - 24a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 12a b - 24a b - 48a b - 60a b - 48a b - 24a )cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (- 12a b - 12a b - 24a b - 24a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 6a b - 6a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 6a b - 18a b - 18a b - 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 12a b - 24a b - 24a b - 12a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 6a b - 18a b - 18a b - 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (- 6a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 8 +--R (6a b + 6a b + 12a b + 12a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (6a b + 18a b + 30a b + 42a b + 36a b + 12a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (12a b + 24a b + 48a b + 60a b + 48a b + 24a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (6a b + 18a b + 30a b + 42a b + 36a b + 12a )cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (6a b + 6a b + 12a b + 12a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (6b - 6a b + 6a b - 6a b + 4a b - 4a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (6a b - 6a b + 4a b - 4a b + 4a b - 4a )cos(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (4a b - 4a b)cos(x) + (6a b - 6a )cos(x) + 6a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 4 2 6 +--R (3a b - 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (3a b - 3a b + 3a b - 3a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (18a b - 18a b + 12a b - 12a b + 6a b)cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 5 +--R (6b + 12a b - 15a b + 7a b - 4a b + 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b + 18a b - 15a b + 13a b - 13a b + 7a b + 8a ) +--R * +--R 4 +--R cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 12a b + 12a b - 9a b + a b - 4a b + 12a )cos(x) +--R + +--R 4 2 6 2 4 2 6 4 2 +--R (- 12a b + 12a )cos(x) + (- 12a b + 12a )cos(x) - 12a b +--R + +--R 5 +--R 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (- 3a b + 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (- 3a b - 3a b + 3a b + 3a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 6a b - 3a b + 3a b + 6a b)cos(x) +--R + +--R 2 4 5 5 3 3 4 2 4 +--R (- 6a b + 6a b)cos(x) + (- 6a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (- 6b + 12a b - 12a b + 6a b - 4a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 6b - 12a b + 12a b - 10a b + 2a b - 8a b - 2a ) +--R * +--R 7 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b - 30a b + 18a b - 8a b + 4a b - 10a b - 4a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 12b - 12a b - 12a b + 18a b - 10a b - 2a b - 6a ) +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (6b - 18a b + 12a b - 8a b + 8a b - 8a b - 4a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (6a b - 6a b + 6a b - 2a b + 2a b - 6a )cos(x) +--R + +--R 4 2 5 6 2 4 2 5 6 +--R (6a b + 6a b - 12a )cos(x) + (12a b - 6a b - 6a )cos(x) +--R + +--R 4 2 5 +--R 6a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (3a b - 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 2 4 5 6 +--R (3a b + 3a b - 3a b - 3a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 3 3 4 2 4 +--R (3a b + 3a b - 3a b - 3a b)cos(x) + (3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 9 +--R (6a b - 6a b + 3a b - 3a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (12b - 6a b + 9a b - 9a b + a b - a b)cos(x) +--R + +--R 6 5 3 3 4 2 5 6 7 +--R (18b + 6a b - 5a b + a b + 2a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (12b + 24a b - 12a b + 2a b + 2a b + 4a b + 4a )cos(x) +--R + +--R 6 5 3 3 4 2 5 5 +--R (6b + 12a b - 3a b + 3a b + 6a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (6a b - 3a b + a b + a b + 5a b - 4a )cos(x) +--R + +--R 3 3 4 2 5 6 3 4 2 5 2 +--R (- a b + 5a b - 2a b - 2a )cos(x) + (2a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (- 6b - 6a b - 6a b - 6a b - 4a b - 4a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (- 6a b - 6a b - 4a b - 4a b - 4a b - 4a )cos(x) +--R + +--R 4 2 5 2 5 6 4 2 5 +--R (- 4a b - 4a b)cos(x) + (- 6a b - 6a )cos(x) - 6a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 4 2 6 +--R (- 3a b - 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- 3a b - 3a b - 3a b - 3a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (- 3a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 5 6 +--R (- 6a b - 6a b + 6a b)cos(x) +--R + +--R 6 3 3 4 2 5 6 5 +--R (6b + 3a b + 11a b + 8a b + 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (12b + 18a b + 15a b + 17a b + 17a b + 23a b + 8a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 3 +--R (12a b + 12a b + 9a b + 17a b + 20a b + 12a )cos(x) +--R + +--R 4 2 5 6 2 4 2 5 6 +--R (12a b + 24a b + 12a )cos(x) + (12a b + 24a b + 12a )cos(x) +--R + +--R 4 2 5 +--R 12a b + 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 2 8 +--R (3a b + 3a b )cos(x) +--R + +--R 2 4 3 3 4 2 5 7 +--R (3a b + 9a b + 9a b + 3a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (6a b + 15a b + 15a b + 6a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (6a b + 12a b + 12a b + 6a b)cos(x) +--R + +--R 3 3 4 2 4 +--R (6a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 6 5 2 4 3 3 4 2 5 8 +--R (6b - 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6a b + 6a b + 6a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (- 12a b - 18a b + 6a b + 18a b + 6a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 5 +--R (- 6a b - 18a b - 6a b + 18a b + 12a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (6a b + 6a b + 6a b + 6a b - 12a b - 12a b)cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (12a b + 18a b + 18a b + 18a b - 18a b - 36a b - 12a ) +--R * +--R 6 +--R cos(x) +--R + +--R 6 2 5 3 4 4 3 6 7 5 +--R (6a b + 18a b + 18a b + 18a b - 36a b - 24a )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 7 4 +--R (6a b + 6a b + 6a b + 6a b - 12a b - 12a )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 3 +--R (6a b - 6a b - 2a b + 2a b - 4a b + 4a b)cos(x) +--R + +--R 4 3 5 2 6 7 2 4 3 5 2 6 7 +--R (4a b - 4a b - 4a b + 4a )cos(x) + 6a b - 6a b - 6a b + 6a +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 5 +--R (3a b - 3a b - 3a b + 3a b )cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 5 +--R (18b - 18a b - 6a b + 6a b - 6a b + 12a b - 6a b)cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 4 +--R (6b - 9a b + a b - a b + 5a b + 4a b - 6a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (- 12a b + 12a b + 3a b - 11a b + 17a b - a b - 8a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (- 12a b + 12a b + 12a b - 12a )cos(x) +--R + +--R 4 3 5 2 6 7 4 3 5 2 +--R (- 12a b + 12a b + 12a b - 12a )cos(x) - 12a b + 12a b +--R + +--R 6 7 +--R 12a b - 12a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (- 3a b + 3a b + 3a b - 3a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (- 6a b + 3a b + 9a b - 3a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 6a b + 6a b + 6a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 3 4 4 3 5 2 6 7 +--R (6b - 12a b + 8a b - 8a b + 4a b + 2a b)cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (- 12b + 6a b + 6a b - 2a b - 2a b - 6a b + 8a b + 2a ) +--R * +--R 6 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 36b + 24a b + 24a b - 12a b + 4a b - 16a b + 8a b +--R + +--R 7 +--R 4a +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 4 +--R (- 12b + 18a b - 2a b - 4a b - 4a b - 2a b + 6a )cos(x) +--R + +--R 6 2 5 4 3 5 2 6 7 3 +--R (6a b - 6a b + 4a b - 10a b + 2a b + 4a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (6a b - 6a b - 6a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 4 3 5 2 6 7 +--R (12a b - 12a b - 12a b + 12a )cos(x) + 6a b - 6a b - 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (3a b - 3a b - 3a b + 3a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (6a b - 3a b - 9a b + 3a b + 3a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 5 +--R (3a b + 3a b - 9a b - 3a b + 6a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 8 +--R (6b - 6a b - 3a b + 3a b - 3a b + 3a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (6b + 6a b - 12a b - 5a b + 5a b - a b + a b)cos(x) +--R + +--R 7 6 2 5 3 4 4 3 6 7 6 +--R (12b + 6a b - 18a b - 4a b + 8a b - 2a b - 2a )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (18b - 6a b - 18a b + 6a b + 2a b + 4a b - 2a b - 4a ) +--R * +--R 5 +--R cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 4 +--R (6b - 9a b + a b + 5a b - a b - 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (- a b + 5a b - 3a b - 5a b + 4a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 5 3 4 4 3 5 2 6 3 +--R (- 6a b - 6a b + 2a b + 2a b + 4a b + 4a b)cos(x) +--R + +--R 4 3 5 2 6 7 2 4 3 5 2 6 7 +--R (- 4a b - 4a b + 4a b + 4a )cos(x) - 6a b - 6a b + 6a b + 6a +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 5 +--R (- 3a b - 3a b + 3a b + 3a b )cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 3a b - 3a b + 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 2 5 3 4 4 3 6 5 +--R (- 6b - 6a b + 6a b + 6a b + 6a b - 6a b)cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 4 +--R (- 6b + 9a b + 5a b + 5a b + a b - 8a b - 6a )cos(x) +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (12a b + 12a b - 3a b + 5a b - a b - 17a b - 8a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (12a b + 12a b - 12a b - 12a )cos(x) +--R + +--R 4 3 5 2 6 7 4 3 5 2 6 7 +--R (12a b + 12a b - 12a b - 12a )cos(x) + 12a b + 12a b - 12a b - 12a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (3a b + 3a b - 3a b - 3a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (6a b + 9a b - 3a b - 9a b - 3a b)cos(x) +--R + +--R 2 5 3 4 5 2 6 5 +--R (6a b + 12a b - 12a b - 6a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (6a b + 6a b - 6a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (- 18b - 12a b + 12a b + 4a b + 4a b + 8a b + 2a b)cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (- 12b - 18a b - 6a b + 2a b + 6a b + 14a b + 12a b + 2a ) +--R * +--R 6 +--R cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (12b - 24a b - 12a b - 4a b + 8a b + 16a b + 4a )cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 4 +--R (12b - 18a b - 10a b - 4a b + 4a b + 10a b + 6a )cos(x) +--R + +--R 6 2 5 4 3 5 2 6 7 3 +--R (- 6a b - 6a b - 4a b + 2a b + 10a b + 4a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 4 3 5 2 6 7 +--R (- 12a b - 12a b + 12a b + 12a )cos(x) - 6a b - 6a b + 6a b + 6a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 3 4 4 3 5 2 7 +--R (- 3a b - 3a b + 3a b + 3a b )cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (- 6a b - 9a b + 3a b + 9a b + 3a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 6 5 +--R (- 3a b - 9a b - 3a b + 9a b + 6a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- 3a b - 3a b + 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 8 +--R (- 6b - 6a b + 3a b + 3a b + 3a b + 3a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 +--R (6b - 6a b - 12a b + 5a b + 5a b + a b + a b)cos(x) +--R + +--R 7 6 2 5 3 4 5 2 6 7 6 +--R (12b + 6a b - 6a b + 4a b - 8a b - 6a b - 2a )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 5 +--R (- 6b + 6a b + 18a b + 6a b - 2a b - 8a b - 10a b - 4a )cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 6 4 +--R (- 6b + 9a b + 5a b - a b - 5a b - 2a b)cos(x) +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (a b - 3a b - 5a b + 3a b + 4a )cos(x) +--R + +--R 4 3 5 2 6 7 2 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R * +--R sin(x) +--R / +--R 5 2 6 6 4 3 5 2 6 7 5 +--R (6a b - 6a b)cos(x) + (6a b - 6a b + 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (6a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 6 8 +--R (- 6a b + 6a b)cos(x) +--R + +--R 4 3 5 2 6 7 7 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 12a b - 6a b + 6a b + 12a )cos(x) +--R + +--R 4 3 7 5 5 2 6 4 +--R (- 12a b + 12a )cos(x) + (- 12a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (6a b - 6a b)cos(x) + (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 4 3 7 6 4 3 5 2 6 7 5 +--R (12a b - 12a )cos(x) + (6a b + 6a b - 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (6a b - 6a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 4 3 5 2 6 7 5 +--R (- 6a b - 6a b)cos(x) + (- 6a b - 6a b - 6a b - 6a )cos(x) +--R + +--R 5 2 6 4 +--R (- 6a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (6a b + 6a b)cos(x) + (6a b + 18a b + 18a b + 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (12a b + 30a b + 30a b + 12a )cos(x) +--R + +--R 4 3 5 2 6 7 5 5 2 6 4 +--R (12a b + 24a b + 24a b + 12a )cos(x) + (12a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 6 8 4 3 5 2 6 7 7 +--R (- 6a b - 6a b)cos(x) + (- 6a b - 18a b - 18a b - 6a )cos(x) +--R + +--R 4 3 5 2 6 7 6 +--R (- 12a b - 24a b - 24a b - 12a )cos(x) +--R + +--R 4 3 5 2 6 7 5 5 2 6 4 +--R (- 6a b - 18a b - 18a b - 6a )cos(x) + (- 6a b - 6a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 4 5 3 6 2 7 5 +--R (6a b - 6a b - 6a b + 6a b)cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (6a b - 6a b - 6a b + 6a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (- 6a b + 6a b + 6a b - 6a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 6 +--R (- 12a b + 6a b + 18a b - 6a b - 6a )cos(x) +--R + +--R 4 4 6 2 8 5 +--R (- 12a b + 24a b - 12a )cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (- 12a b + 12a b + 12a b - 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (6a b - 6a b - 6a b + 6a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 6 +--R (12a b - 6a b - 18a b + 6a b + 6a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 5 +--R (6a b + 6a b - 18a b - 6a b + 12a )cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (6a b - 6a b - 6a b + 6a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 5 3 6 2 7 5 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (6a b + 6a b - 6a b - 6a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 6 +--R (12a b + 18a b - 6a b - 18a b - 6a )cos(x) +--R + +--R 4 4 5 3 7 8 5 +--R (12a b + 24a b - 24a b - 12a )cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (12a b + 12a b - 12a b - 12a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 5 3 6 2 7 7 +--R (- 6a b - 6a b + 6a b + 6a b)cos(x) +--R + +--R 4 4 5 3 6 2 7 8 6 +--R (- 12a b - 18a b + 6a b + 18a b + 6a )cos(x) +--R + +--R 4 4 5 3 6 2 7 8 5 +--R (- 6a b - 18a b - 6a b + 18a b + 12a )cos(x) +--R + +--R 5 3 6 2 7 8 4 +--R (- 6a b - 6a b + 6a b + 6a )cos(x) +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 294 + +--S 295 of 546 +m0449b:= a0449.2-r0449 +--R +--R +--R (292) +--R +---------+ +--R 3 2 3 | 2 2 sin(x) + cos(x) + 1 +--R (- 6b - 3a b)cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 3 2 3 | 2 2 sin(x) - cos(x) - 1 +--R (6b + 3a b)cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 3 2 3 | 2 2 +--R (6b + 3a b)cos(x) \|- b + a atanh(sin(x)) +--R + +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R 4 3 sin(x)\|- b + a 4 3 2 +--R 12b cos(x) atan(---------------------) + 12b cos(x) atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 3 +--R - 2a cos(x) tan(x) +--R + +--R 2 3 2 3 3 +--R (3a b cos(x) sec(x) + (- 6a b - 6a )cos(x) )tan(x) +--R + +--R 2 3 2 2 3 +--R ((6a b + 4a )cos(x) - 3a b cos(x) + 2a )sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 3 | 2 2 +--R 6a cos(x) \|- b + a +--R Type: Expression(Integer) +--E 295 + +--S 296 of 546 +d0449b:= D(m0449b,x) +--R +--R +--R (293) +--R 3 2 4 5 4 6 +--R (- 6a b + 12a b - 6a )cos(x) sin(x) +--R + +--R 3 2 4 6 3 2 4 5 +--R (12a b - 12a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 3 2 4 5 4 +--R (18a b - 24a b + 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 6a b + 6a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 3 2 4 5 6 +--R (- 48a b + 12a b + 36a )cos(x) +--R + +--R 3 2 4 5 5 +--R (- 48a b + 24a b + 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (- 18a b + 12a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (6a b - 6a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (36a b - 36a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 3 2 5 4 +--R (6a b - 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 4 6 +--R (6a b - 6a )cos(x) sin(x) +--R + +--R 3 2 4 6 3 2 4 5 +--R (- 12a b - 12a b)cos(x) + (- 24a b - 24a b)cos(x) +--R + +--R 3 2 4 5 4 +--R (- 18a b - 12a b + 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 5 8 3 2 4 5 7 +--R (6a b + 12a b + 6a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 3 2 4 5 6 3 2 4 5 5 +--R (48a b + 84a b + 36a )cos(x) + (48a b + 72a b + 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (18a b + 24a b + 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 8 3 2 4 5 7 +--R (- 6a b - 12a b - 6a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 3 2 4 5 6 3 2 4 5 5 +--R (- 36a b - 72a b - 36a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 3 2 4 5 4 +--R (- 6a b - 12a b - 6a )cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 3 3 2 4 4 +--R (6a b - 12a b + 6a b)cos(x) sec(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 6a b + 12a b - 18a b + 24a b - 12a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 12a b + 12a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 18a b + 24a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 6 +--R (12a b - 12a b + 24a b - 24a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (24a b - 24a b + 48a b - 48a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (18a b - 24a b + 42a b - 48a b + 12a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (6a b - 6a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (48a b - 12a b - 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (48a b - 24a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (18a b - 12a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 5 8 +--R (- 6a b - 6a b + 12a )cos(x) +--R + +--R 4 3 2 5 7 +--R (- 24a b - 24a b + 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (- 48a b + 12a b - 60a b + 24a b + 72a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 48a b + 24a b - 72a b + 48a b + 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 18a b + 12a b - 30a b + 24a b + 12a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 6a b + 6a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 36a b + 36a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 6a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 5 8 4 3 2 5 7 +--R (6a b + 6a b - 12a )cos(x) + (24a b + 24a b - 48a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (36a b + 36a b - 72a )cos(x) + (24a b + 24a b - 48a )cos(x) +--R + +--R 4 3 2 5 4 +--R (6a b + 6a b - 12a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 4 4 3 2 5 4 +--R ((- 6a b + 6a b)cos(x) sec(x) + (6a b + 6a b - 12a )cos(x) ) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (12a b + 12a b )cos(x) + (24a b + 24a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (18a b + 12a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 12a b - 12a b - 24a b - 24a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 24a b - 24a b - 48a b - 48a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 18a b - 12a b - 30a b - 24a b + 12a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 4 8 +--R (- 6a b - 12a b - 6a b)cos(x) +--R + +--R 2 3 3 2 4 7 +--R (- 24a b - 48a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 48a b - 84a b - 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 48a b - 72a b - 24a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 18a b - 24a b - 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (6a b + 12a b + 18a b + 24a b + 12a )cos(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (24a b + 48a b + 72a b + 96a b + 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (48a b + 84a b + 132a b + 168a b + 72a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (48a b + 72a b + 120a b + 144a b + 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (18a b + 24a b + 42a b + 48a b + 12a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 8 2 3 3 2 4 7 +--R (6a b + 12a b + 6a b)cos(x) + (24a b + 48a b + 24a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (36a b + 72a b + 36a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 3 3 2 4 4 +--R (24a b + 48a b + 24a b)cos(x) + (6a b + 12a b + 6a b)cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (- 6a b - 12a b - 18a b - 24a b - 12a )cos(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (- 24a b - 48a b - 72a b - 96a b - 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 6 +--R (- 36a b - 72a b - 108a b - 144a b - 72a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 24a b - 48a b - 72a b - 96a b - 48a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 6a b - 12a b - 18a b - 24a b - 12a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (6a b - 12a b + 10a b - 8a b + 4a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (- 6a b + 12a b - 6a b)cos(x) + 6a b - 12a b + 6a +--R * +--R 8 +--R sin(x) +--R + +--R 2 3 3 2 4 4 +--R (3a b - 6a b + 3a b)cos(x) sec(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (6b - 30a b + 30a b - 22a b + 18a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 24a b + 33a b - 22a b + 13a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 18a b + 48a b - 52a b + 24a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (18a b - 48a b + 30a b)cos(x) - 18a b + 24a b - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (- 6a b + 6a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 9a b + 12a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b - 18a b + 24a b - 10a b + 8a b - 4a )cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (- 30b + 21a b - 12a b + 13a b - 16a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 18b + 54a b - 36a b + 4a b + 12a b - 28a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (48a b - 63a b + 24a b + 31a b - 40a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (18a b - 60a b + 72a b + 12a b - 42a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (- 18a b + 60a b - 18a b - 24a )cos(x) + 18a b - 12a b - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (3a b - 3a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (24a b - 6a b - 18a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (24a b - 12a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (9a b - 6a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (6b - 6a b + 6a b - 2a b + 6a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (36b - 24a b + 21a b - 14a b + 21a b + 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (72b - 6a b - 6a b - 12a b + 22a b + 14a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (60b + 12a b - 36a b + 12a b + 8a b + 16a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (18b - 18a b - 6a b + 28a b - 18a b + 20a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 24a b + 27a b + 6a b - 41a b + 32a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 6a b + 24a b - 28a b - 28a b + 38a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 5 +--R (6a b - 24a b - 6a b + 24a )cos(x) - 6a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 3a b + 3a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 18a b + 18a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 3a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 2 3 4 9 +--R (- 6b + 3a b + 3a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 30b + 6a b + 6a b + 2a b + 6a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 60b + 12a b + 3a b + 8a b - 3a b - 8a )cos(x) +--R + +--R 5 2 3 3 2 4 5 6 +--R (- 60b + 6a b + 10a b - 18a b - 10a )cos(x) +--R + +--R 5 4 2 3 4 5 +--R (- 30b - 12a b + 15a b - 21a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 6b - 6a b + 12a b - 10a b - 12a b + 10a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 5 2 +--R (3a b - 8a b - 3a b + 8a )cos(x) + (- 2a b + 2a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R ((- 6a b + 2a b + 4a )cos(x) + (6a b - 6a b)cos(x) - 6a b + 6a ) +--R * +--R 8 +--R sin(x) +--R + +--R 2 3 4 4 +--R (- 3a b + 3a b)cos(x) sec(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (6b + 18a b + 18a b + 10a b + 14a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (24a b + 15a b + 4a b + 13a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (18a b - 12a b - 8a b + 20a b - 2a )cos(x) +--R + +--R 2 3 3 2 4 3 2 4 5 +--R (- 18a b + 12a b + 30a b)cos(x) + 18a b + 12a b - 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 6 2 3 3 2 5 +--R (6a b + 6a b )cos(x) + (12a b + 12a b )cos(x) +--R + +--R 2 3 3 2 4 4 +--R (9a b + 6a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 5 6 +--R (- 12b + 18a b + 12a b - 2a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 18b + 12a b - 9a b - 18a b - 19a b - 16a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 18b - 42a b - 60a b - 28a b - 44a b - 28a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 48a b - 33a b + 6a b - 49a b - 40a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 18a b + 24a b + 12a b - 72a b - 42a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (18a b - 24a b - 66a b - 24a )cos(x) - 18a b - 24a b - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 4 8 +--R (- 3a b - 6a b - 3a b)cos(x) +--R + +--R 2 3 3 2 4 7 +--R (- 12a b - 24a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 24a b - 42a b - 18a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 24a b - 36a b - 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 9a b - 12a b - 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (6b + 18a b + 18a b + 14a b + 10a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (12b + 48a b + 51a b + 44a b + 37a b + 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (24b + 30a b + 42a b + 60a b + 50a b + 14a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (36b + 12a b + 36a b + 60a b + 40a b + 16a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (18b + 30a b + 54a b + 32a b + 22a b + 20a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (24a b + 21a b - 12a b + 23a b + 32a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (6a b - 12a b - 8a b + 48a b + 38a )cos(x) +--R + +--R 2 3 3 2 4 5 3 2 4 5 +--R (- 6a b + 12a b + 42a b + 24a )cos(x) + 6a b + 12a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 8 2 3 3 2 4 7 +--R (3a b + 6a b + 3a b)cos(x) + (12a b + 24a b + 12a b)cos(x) +--R + +--R 2 3 3 2 4 6 2 3 3 2 4 5 +--R (18a b + 36a b + 18a b)cos(x) + (12a b + 24a b + 12a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (3a b + 6a b + 3a b)cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 9 +--R (6b + 12a b + 9a b + 6a b + 3a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (18b + 30a b + 18a b + 10a b + 2a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (12b + 12a b - 3a b - 14a b - 19a b - 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 12b - 24a b - 30a b - 46a b - 38a b - 10a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 18b - 24a b - 27a b - 42a b - 21a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 6b - 6a b - 12a b - 14a b + 8a b + 10a )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 5 2 +--R (- 3a b + 2a b + 13a b + 8a )cos(x) + (2a b + 4a b + 2a )cos(x) +--R / +--R 4 2 5 6 4 6 +--R (6a b - 12a b + 6a )cos(x) sin(x) +--R + +--R 4 2 5 6 4 2 5 5 +--R (- 12a b + 12a b)cos(x) + (- 24a b + 24a b)cos(x) +--R + +--R 4 2 5 6 4 +--R (- 18a b + 24a b - 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 6 8 4 2 6 7 +--R (6a b - 6a )cos(x) + (24a b - 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (48a b - 12a b - 36a )cos(x) + (48a b - 24a b - 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (18a b - 12a b - 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 8 4 2 6 7 +--R (- 6a b + 6a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (- 36a b + 36a )cos(x) + (- 24a b + 24a )cos(x) +--R + +--R 4 2 6 4 +--R (- 6a b + 6a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 6 4 6 +--R (- 6a b + 6a )cos(x) sin(x) +--R + +--R 4 2 5 6 4 2 5 5 +--R (12a b + 12a b)cos(x) + (24a b + 24a b)cos(x) +--R + +--R 4 2 5 6 4 +--R (18a b + 12a b - 6a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 5 6 8 4 2 5 6 7 +--R (- 6a b - 12a b - 6a )cos(x) + (- 24a b - 48a b - 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (- 48a b - 84a b - 36a )cos(x) + (- 48a b - 72a b - 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (- 18a b - 24a b - 6a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 6 8 4 2 5 6 7 +--R (6a b + 12a b + 6a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 4 2 5 6 6 4 2 5 6 5 +--R (36a b + 72a b + 36a )cos(x) + (24a b + 48a b + 24a )cos(x) +--R + +--R 4 2 5 6 4 +--R (6a b + 12a b + 6a )cos(x) +--R Type: Expression(Integer) +--E 296 + +--S 297 of 546 +t0450:= sec(x)/(a+a*cos(x)) +--R +--R +--R sec(x) +--R (294) ------------ +--R a cos(x) + a +--R Type: Expression(Integer) +--E 297 + +--S 298 of 546 +r0450:= atanh(sin(x))/a-sin(x)/a/(cos(x)+1) +--R +--R +--R (cos(x) + 1)atanh(sin(x)) - sin(x) +--R (295) ---------------------------------- +--R a cos(x) + a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 546 +a0450:= integrate(t0450,x) +--R +--R +--R (296) +--R sin(x) + cos(x) + 1 +--R (cos(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R sin(x) - cos(x) - 1 +--R (- cos(x) - 1)log(-------------------) - sin(x) +--R cos(x) + 1 +--R / +--R a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 299 + +--S 300 of 546 +m0450:= a0450-r0450 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (297) ------------------------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 300 + +--S 301 of 546 +d0450:= D(m0450,x) +--R +--R +--R (298) +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R ----------------------------------------------------------------------------- +--R 4 2 2 2 +--R a sin(x) + (- a cos(x) - 2a cos(x) - 2a)sin(x) + a cos(x) + 2a cos(x) + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 546 +t0451:= sec(x)^2/(a+a*cos(x)) +--R +--R +--R 2 +--R sec(x) +--R (299) ------------ +--R a cos(x) + a +--R Type: Expression(Integer) +--E 302 + +--S 303 of 546 +r0451:= -atanh(sin(x))/a+sin(x)/a/(cos(x)+1)+tan(x)/a +--R +--R +--R (- cos(x) - 1)atanh(sin(x)) + (cos(x) + 1)tan(x) + sin(x) +--R (300) --------------------------------------------------------- +--R a cos(x) + a +--R Type: Expression(Integer) +--E 303 + +--S 304 of 546 +a0451:= integrate(t0451,x) +--R +--R +--R (301) +--R 2 sin(x) + cos(x) + 1 +--R (- cos(x) - cos(x))log(-------------------) +--R cos(x) + 1 +--R + +--R 2 sin(x) - cos(x) - 1 +--R (cos(x) + cos(x))log(-------------------) + (2cos(x) + 1)sin(x) +--R cos(x) + 1 +--R / +--R 2 +--R a cos(x) + a cos(x) +--R Type: Union(Expression(Integer),...) +--E 304 + +--S 305 of 546 +m0451:= a0451-r0451 +--R +--R +--R (302) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - cos(x)log(-------------------) + cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R cos(x)atanh(sin(x)) - cos(x)tan(x) + sin(x) +--R / +--R a cos(x) +--R Type: Expression(Integer) +--E 305 + +--S 306 of 546 +d0451:= D(m0451,x) +--R +--R +--R (303) +--R 2 4 4 3 2 2 4 +--R - cos(x) sin(x) + (cos(x) + 2cos(x) + 2cos(x) )sin(x) - cos(x) +--R + +--R 3 2 +--R - 2cos(x) - cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 2 4 +--R sin(x) + (cos(x) - 2cos(x) - 2)sin(x) +--R + +--R 4 3 2 2 5 3 +--R (2cos(x) + cos(x) - cos(x) + 2cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 4 4 3 2 2 +--R a cos(x) sin(x) + (- a cos(x) - 2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 4 3 2 +--R a cos(x) + 2a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 306 + +--S 307 of 546 +t0452:= sec(x)^3/(a+a*cos(x)) +--R +--R +--R 3 +--R sec(x) +--R (304) ------------ +--R a cos(x) + a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 546 +r0452:= 3/2*atanh(sin(x))/a-sin(x)/a/(cos(x)+1)-tan(x)/a+1/2*sec(x)*tan(x)/a +--R +--R +--R (305) +--R (3cos(x) + 3)atanh(sin(x)) + ((cos(x) + 1)sec(x) - 2cos(x) - 2)tan(x) +--R + +--R - 2sin(x) +--R / +--R 2a cos(x) + 2a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 546 +a0452:= integrate(t0452,x) +--R +--R +--R (306) +--R 3 2 sin(x) + cos(x) + 1 +--R (3cos(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 sin(x) - cos(x) - 1 +--R (- 3cos(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 +--R (- 4cos(x) - cos(x) + 1)sin(x) +--R / +--R 3 2 +--R 2a cos(x) + 2a cos(x) +--R Type: Union(Expression(Integer),...) +--E 309 + +--S 310 of 546 +m0452:= a0452-r0452 +--R +--R +--R (307) +--R 2 sin(x) + cos(x) + 1 2 sin(x) - cos(x) - 1 +--R 3cos(x) log(-------------------) - 3cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 2 2 +--R - 3cos(x) atanh(sin(x)) + (- cos(x) sec(x) + 2cos(x) )tan(x) +--R + +--R (- 2cos(x) + 1)sin(x) +--R / +--R 2 +--R 2a cos(x) +--R Type: Expression(Integer) +--E 310 + +--S 311 of 546 +d0452:= D(m0452,x) +--R +--R +--R (308) +--R 3 3 4 +--R (- 2cos(x) sec(x) + 2cos(x) )sin(x) +--R + +--R 5 4 3 5 4 +--R (2cos(x) + 4cos(x) + 4cos(x) )sec(x) - 2cos(x) - 4cos(x) +--R + +--R 3 +--R - 4cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 5 4 +--R (- 2cos(x) - 4cos(x) - 2cos(x) )sec(x) + 2cos(x) + 4cos(x) +--R + +--R 3 +--R 2cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 +--R (- 2cos(x) + 2)sin(x) +--R + +--R 3 3 2 4 +--R (- cos(x) sec(x) - 4cos(x) + 3cos(x) - 4)sin(x) +--R + +--R 5 4 3 5 4 +--R (cos(x) + 2cos(x) + 2cos(x) )sec(x) - 6cos(x) - 4cos(x) +--R + +--R 3 2 +--R 2cos(x) - 4cos(x) + 2cos(x) + 2 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 6 4 3 +--R (- cos(x) - 2cos(x) - cos(x) )sec(x) - 3cos(x) + 4cos(x) + 2cos(x) +--R + +--R 2 +--R cos(x) +--R / +--R 3 4 5 4 3 2 +--R 2a cos(x) sin(x) + (- 2a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 4 3 +--R 2a cos(x) + 4a cos(x) + 2a cos(x) +--R Type: Expression(Integer) +--E 311 + +--S 312 of 546 +t0453:= sec(x)^4/(a+a*cos(x)) +--R +--R +--R 4 +--R sec(x) +--R (309) ------------ +--R a cos(x) + a +--R Type: Expression(Integer) +--E 312 + +--S 313 of 546 +r0453:= -3/2*atanh(sin(x))/a+sin(x)/a/(cos(x)+1)+2*tan(x)/a-_ + 1/2*sec(x)*tan(x)/a+1/3*tan(x)^3/a +--R +--R +--R (310) +--R 3 +--R (- 9cos(x) - 9)atanh(sin(x)) + (2cos(x) + 2)tan(x) +--R + +--R ((- 3cos(x) - 3)sec(x) + 12cos(x) + 12)tan(x) + 6sin(x) +--R / +--R 6a cos(x) + 6a +--R Type: Expression(Integer) +--E 313 + +--S 314 of 546 +a0453:= integrate(t0453,x) +--R +--R +--R (311) +--R 4 3 sin(x) + cos(x) + 1 +--R (- 9cos(x) - 9cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 3 sin(x) - cos(x) - 1 +--R (9cos(x) + 9cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 +--R (16cos(x) + 7cos(x) - cos(x) + 2)sin(x) +--R / +--R 4 3 +--R 6a cos(x) + 6a cos(x) +--R Type: Union(Expression(Integer),...) +--E 314 + +--S 315 of 546 +m0453:= a0453-r0453 +--R +--R +--R (312) +--R 3 sin(x) + cos(x) + 1 3 sin(x) - cos(x) - 1 +--R - 9cos(x) log(-------------------) + 9cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 3 3 3 +--R 9cos(x) atanh(sin(x)) - 2cos(x) tan(x) +--R + +--R 3 3 2 +--R (3cos(x) sec(x) - 12cos(x) )tan(x) + (10cos(x) - 3cos(x) + 2)sin(x) +--R / +--R 3 +--R 6a cos(x) +--R Type: Expression(Integer) +--E 315 + +--S 316 of 546 +d0453:= D(m0453,x) +--R +--R +--R (313) +--R 4 4 6 5 4 2 +--R - 6cos(x) sin(x) + (6cos(x) + 12cos(x) + 12cos(x) )sin(x) +--R + +--R 6 5 4 +--R - 6cos(x) - 12cos(x) - 6cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 4 4 4 +--R (6cos(x) sec(x) - 18cos(x) )sin(x) +--R + +--R 6 5 4 6 +--R (- 6cos(x) - 12cos(x) - 12cos(x) )sec(x) + 18cos(x) +--R + +--R 5 4 +--R 36cos(x) + 36cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 6 5 +--R (6cos(x) + 12cos(x) + 6cos(x) )sec(x) - 18cos(x) - 36cos(x) +--R + +--R 4 +--R - 18cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 6 +--R (10cos(x) - 6cos(x) + 6)sin(x) +--R + +--R 4 4 3 2 4 +--R (3cos(x) sec(x) + 6cos(x) - 17cos(x) - 12cos(x) - 12)sin(x) +--R + +--R 6 5 4 6 5 +--R (- 3cos(x) - 6cos(x) - 6cos(x) )sec(x) + 20cos(x) + 16cos(x) +--R + +--R 3 +--R 16cos(x) + 6cos(x) + 6 +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 7 6 5 +--R (3cos(x) + 6cos(x) + 3cos(x) )sec(x) + 9cos(x) - 2cos(x) - 16cos(x) +--R + +--R 4 3 2 +--R - 6cos(x) + cos(x) + 2cos(x) +--R / +--R 4 4 6 5 4 2 +--R 6a cos(x) sin(x) + (- 6a cos(x) - 12a cos(x) - 12a cos(x) )sin(x) +--R + +--R 6 5 4 +--R 6a cos(x) + 12a cos(x) + 6a cos(x) +--R Type: Expression(Integer) +--E 316 + +--S 317 of 546 +t0454:= csc(x)/(a+a*cos(x)) +--R +--R +--R csc(x) +--R (314) ------------ +--R a cos(x) + a +--R Type: Expression(Integer) +--E 317 + +--S 318 of 546 +r0454:= -1/2*atanh(cos(x))/a+1/2/a/(cos(x)+1) +--R +--R +--R (- cos(x) - 1)atanh(cos(x)) + 1 +--R (315) ------------------------------- +--R 2a cos(x) + 2a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 546 +a0454:= integrate(t0454,x) +--R +--R +--R sin(x) +--R (2cos(x) + 2)log(----------) - cos(x) + 1 +--R cos(x) + 1 +--R (316) ----------------------------------------- +--R 4a cos(x) + 4a +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 546 +m0454:= a0454-r0454 +--R +--R +--R sin(x) +--R 2log(----------) + 2atanh(cos(x)) - 1 +--R cos(x) + 1 +--R (317) ------------------------------------- +--R 4a +--R Type: Expression(Integer) +--E 320 + +--S 321 of 546 +d0454:= D(m0454,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (318) -------------------------------- +--R 2 +--R (2a cos(x) - 2a)sin(x) +--R Type: Expression(Integer) +--E 321 + +--S 322 of 546 +t0455:= sin(x)/(a+b*tan(x)) +--R +--R +--R sin(x) +--R (319) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 546 +r0455:= a*b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ + a*cos(x)/(a^2+b^2)+b*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R a sin(x) - b cos(x) | 2 2 +--R - a b atanh(-------------------) + (b sin(x) - a cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (320) ------------------------------------------------------------------ +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 546 +a0455:= integrate(t0455,x) +--R +--R +--R (321) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (b sin(x) - a cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 324 + +--S 325 of 546 +m0455:= a0455-r0455 +--R +--R +--R (322) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R a sin(x) - b cos(x) +--R a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 546 +d0455:= D(m0455,x) +--R +--R +--R (323) +--R 2 3 2 2 2 2 2 +--R a b sin(x) - a b cos(x)sin(x) + (a b cos(x) - a b)sin(x) +--R + +--R 2 3 2 +--R - a b cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression(Integer) +--E 326 + +--S 327 of 546 +t0456:= sin(x)^2/(a+b*tan(x)) +--R +--R +--R 2 +--R sin(x) +--R (324) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 327 + +--S 328 of 546 +r0456:= -1/2*(-a^3*x+a*b^2*x-2*a^2*b*log(a*cos(x)+b*sin(x))+_ + sin(x)*a^3*cos(x)+sin(x)*a*b^2*cos(x)-a^2*b+a^2*b*cos(x)^2-_ + b^3+b^3*cos(x)^2)/(a^2+b^2)^2 +--R +--R +--R (325) +--R 2 2 3 +--R 2a b log(b sin(x) + a cos(x)) + (- a b - a )cos(x)sin(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- b - a b)cos(x) + (- a b + a )x + b + a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 546 +a0456:= integrate(t0456,x) +--R +--R +--R (326) +--R 2 2 2 - 2b sin(x) - 2a cos(x) +--R - 2a b log(----------) + 2a b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (- a b - a )cos(x)sin(x) + (- b - a b)cos(x) + (- a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression(Integer),...) +--E 329 + +--S 330 of 546 +m0456:= a0456-r0456 +--R +--R +--R (327) +--R 2 2 2 +--R - 2a b log(b sin(x) + a cos(x)) - 2a b log(----------) +--R cos(x) + 1 +--R + +--R 2 - 2b sin(x) - 2a cos(x) 3 2 +--R 2a b log(-----------------------) - b - a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 546 +d0456:= D(m0456,x) +--R +--R +--R (328) 0 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 546 +t0457:= sin(x)^3/(a+b*tan(x)) +--R +--R +--R 3 +--R sin(x) +--R (329) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 546 +r0457:= 2/3*(3*a^3*b*atanh(1/(a^2+b^2)^(1/2)*(a*cos(x)-a+b*sin(x))/sin(x))-_ + 6*a^3*cos(1/2*x)^4*(a^2+b^2)^(1/2)+4*a^3*cos(1/2*x)^6*(a^2+b^2)^(1/2)+_ + 4*b*cos(1/2*x)^3*sin(1/2*x)*(a^2+b^2)^(1/2)*a^2-4*b*cos(1/2*x)^5*_ + sin(1/2*x)*(a^2+b^2)^(1/2)*a^2+3*b*cos(1/2*x)*sin(1/2*x)*_ + (a^2+b^2)^(1/2)*a^2+3*a*cos(1/2*x)^2*(a^2+b^2)^(1/2)*b^2+_ + 4*a*cos(1/2*x)^6*(a^2+b^2)^(1/2)*b^2-6*a*cos(1/2*x)^4*_ + (a^2+b^2)^(1/2)*b^2+4*b^3*cos(1/2*x)^3*sin(1/2*x)*(a^2+b^2)^(1/2)-_ + 4*b^3*cos(1/2*x)^5*sin(1/2*x)*(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2) +--R +--R +--R (330) +--R 3 b sin(x) + a cos(x) - a +--R 6a b atanh(-----------------------) +--R +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R + +--R 3 2 x 5 3 2 x 3 2 x x +--R ((- 8b - 8a b)cos(-) + (8b + 8a b)cos(-) + 6a b cos(-))sin(-) +--R 2 2 2 2 +--R + +--R 2 3 x 6 2 3 x 4 2 x 2 +--R (8a b + 8a )cos(-) + (- 12a b - 12a )cos(-) + 6a b cos(-) +--R 2 2 2 +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 546 +a0457:= integrate(t0457,x) +--R +--R +--R (331) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 2 2 3 2 2 3 3 +--R ((- b - a b)cos(x) + b + 4a b)sin(x) + (a b + a )cos(x) +--R + +--R 3 +--R - 3a cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 334 + +--S 335 of 546 +m0457:= a0457-r0457 +--R +--R +--R (332) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 b sin(x) + a cos(x) - a +--R - 6a b atanh(-----------------------) +--R +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R + +--R 3 2 2 3 2 +--R ((- b - a b)cos(x) + b + 4a b)sin(x) +--R + +--R 3 2 x 5 3 2 x 3 2 x x +--R ((8b + 8a b)cos(-) + (- 8b - 8a b)cos(-) - 6a b cos(-))sin(-) +--R 2 2 2 2 +--R + +--R 2 3 3 3 2 3 x 6 +--R (a b + a )cos(x) - 3a cos(x) + (- 8a b - 8a )cos(-) +--R 2 +--R + +--R 2 3 x 4 2 x 2 +--R (12a b + 12a )cos(-) - 6a b cos(-) +--R 2 2 +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 546 +d0457:= D(m0457,x) +--R +--R +--R (333) +--R 2 5 4 3 6 +--R (2a b + 2a b )cos(x)sin(x) +--R + +--R 6 3 4 5 2 2 6 5 2 5 2 +--R ((- 6a b - 7a b - a b )cos(x) + (2a b - 2a b )cos(x) + 3a b ) +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 x 4 2 5 4 3 x 2 4 3 +--R ((- 20a b - 20a b )cos(-) + (12a b + 12a b )cos(-) + 3a b ) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 4 5 2 x 5 3 4 5 2 x 3 +--R (24a b + 24a b )cos(-) + (- 24a b - 24a b )cos(-) +--R 2 2 +--R + +--R 3 4 x +--R 6a b cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 2 5 4 3 6 3 +--R (4b + 4a b - 3a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (7a b + 8a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 x 6 +--R (- 4b - 9a b - 11a b + 3a b)cos(x) + (4a b + 4a b )cos(-) +--R 2 +--R + +--R 2 5 4 3 x 4 4 3 x 2 4 3 +--R (- 4a b - 4a b )cos(-) - 3a b cos(-) + 12a b +--R 2 2 +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 x 4 +--R (60a b + 40a b - 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 3 4 5 2 +--R (- 36a b - 24a b + 12a b )cos(-) - 9a b + 3a b +--R 2 +--R * +--R cos(x) +--R + +--R 6 5 2 x 4 6 5 2 x 2 3 4 +--R (- 20a b + 20a b )cos(-) + (12a b - 12a b )cos(-) + 3a b +--R 2 2 +--R + +--R 5 2 +--R - 3a b +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 x 5 +--R (- 72a b - 48a b + 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 2 5 4 3 x +--R (72a b + 48a b - 24a b)cos(-) + (- 18a b + 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R + +--R 2 5 6 x 5 2 5 6 x 3 +--R (24a b - 24a b)cos(-) + (- 24a b + 24a b)cos(-) +--R 2 2 +--R + +--R 2 5 4 3 x +--R (6a b - 6a b )cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 6 3 4 5 2 4 +--R (3a b + 12a b + 9a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 3a b - 7a b - a b + 3a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 3a b - 6a b - 9a b )cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (- 12a b - 8a b + 4a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 3 4 5 2 x 2 +--R (12a b + 8a b - 4a b )cos(-) + (9a b - 3a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 7 +--R 3a b - 5a b + 13a b - 3a +--R * +--R cos(x) +--R + +--R 6 5 2 x 6 6 5 2 x 4 +--R (4a b - 4a b )cos(-) + (- 4a b + 4a b )cos(-) +--R 2 2 +--R + +--R 3 4 5 2 x 2 3 4 5 2 +--R (- 3a b + 3a b )cos(-) - 6a b - 12a b +--R 2 +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 5 4 3 x 4 +--R (- 40b + 40a b + 80a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 2 2 5 4 3 +--R (24b - 24a b - 48a b )cos(-) + 6a b - 12a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 4 +--R (- 100a b - 80a b + 20a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 2 4 3 6 +--R (60a b + 48a b - 12a b)cos(-) + 15a b - 3a b +--R 2 +--R * +--R cos(x) +--R + +--R 7 2 5 4 3 x 4 +--R (40b + 100a b + 60a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 2 2 5 4 3 +--R (- 24b - 60a b - 36a b )cos(-) - 6a b - 9a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 6 3 4 5 2 x 5 +--R (48a b - 48a b - 96a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 3 +--R (- 48a b + 48a b + 96a b )cos(-) +--R 2 +--R + +--R 6 3 4 x +--R (12a b - 24a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 3 4 5 2 7 x 5 +--R (120a b + 96a b - 24a )cos(-) +--R 2 +--R + +--R 3 4 5 2 7 x 3 3 4 5 2 x +--R (- 120a b - 96a b + 24a )cos(-) + (30a b - 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R + +--R 6 3 4 5 2 x 5 +--R (- 48a b - 120a b - 72a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 3 6 3 4 x +--R (48a b + 120a b + 72a b )cos(-) + (- 12a b - 18a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 2 5 6 5 2 5 4 3 6 4 +--R (- 2b - 5a b + 3a b)cos(x) + (- 4a b - 16a b - 12a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (4b + 16a b + 14a b + 8a b)cos(x) +--R + +--R 7 2 5 4 3 x 6 +--R (8b - 8a b - 16a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 4 2 5 4 3 x 2 +--R (- 8b + 8a b + 16a b )cos(-) + (- 6a b + 12a b )cos(-) +--R 2 2 +--R + +--R 2 5 4 3 6 +--R 4a b + 14a b + 10a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 6 +--R (20a b + 16a b - 4a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 4 4 3 6 x 2 +--R (- 20a b - 16a b + 4a b)cos(-) + (- 15a b + 3a b)cos(-) +--R 2 2 +--R + +--R 7 2 5 4 3 6 +--R - 2b - 11a b - 18a b - 15a b +--R * +--R cos(x) +--R + +--R 7 2 5 4 3 x 6 7 2 5 4 3 x 4 +--R (- 8b - 20a b - 12a b )cos(-) + (8b + 20a b + 12a b )cos(-) +--R 2 2 +--R + +--R 2 5 4 3 x 2 4 3 +--R (6a b + 9a b )cos(-) - 6a b +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 x 4 +--R (- 60a b - 40a b + 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 3 4 5 2 +--R (36a b + 24a b - 12a b )cos(-) + 9a b - 3a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (20a b - 80a b - 100a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 3 4 5 2 +--R (- 12a b + 48a b + 60a b )cos(-) - 3a b + 15a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (60a b + 160a b + 100a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 3 4 5 2 +--R (- 36a b - 96a b - 60a b )cos(-) - 9a b - 15a b +--R 2 +--R * +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 3 4 5 2 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 x 5 +--R (72a b + 48a b - 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 2 5 4 3 x +--R (- 72a b - 48a b + 24a b)cos(-) + (18a b - 6a b )cos(-) +--R 2 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (- 24a b + 96a b + 120a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 +--R (24a b - 96a b - 120a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 x +--R (- 6a b + 30a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (- 72a b - 192a b - 120a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 +--R (72a b + 192a b + 120a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 x +--R (- 18a b - 30a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (24a b + 48a b + 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 2 5 4 3 x +--R (- 24a b - 48a b - 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 6 3 4 5 2 6 +--R (- 3a b - 5a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (a b - a b - 5a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 7 4 +--R (6a b + 22a b + 13a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (12a b + 8a b - 4a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 3 4 5 2 x 2 +--R (- 12a b - 8a b + 4a b )cos(-) + (- 9a b + 3a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 +--R - 2a b - 16a b + 10a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (- 4a b + 16a b + 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 3 4 5 2 x 2 +--R (4a b - 16a b - 20a b )cos(-) + (3a b - 15a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 7 +--R - 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40a b - 20a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 2 4 3 6 +--R (12a b + 24a b + 12a b)cos(-) + 3a b + 3a b +--R 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 4 5 2 x 5 3 4 5 2 x 3 +--R (24a b + 24a b )cos(-) + (- 24a b - 24a b )cos(-) +--R 2 2 +--R + +--R 3 4 x +--R 6a b cos(-) +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 3 4 7 x 5 3 4 7 x 3 +--R (- 24a b + 24a )cos(-) + (24a b - 24a )cos(-) +--R 2 2 +--R + +--R 3 4 5 2 x +--R (- 6a b + 6a b )cos(-) +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 3 4 5 2 7 x 5 +--R (- 24a b - 72a b - 48a )cos(-) +--R 2 +--R + +--R 3 4 5 2 7 x 3 3 4 5 2 x +--R (24a b + 72a b + 48a )cos(-) + (- 6a b - 12a b )cos(-) +--R 2 2 +--R * +--R 2 +--R cos(x) +--R + +--R 3 4 5 2 7 x 5 +--R (24a b + 48a b + 24a )cos(-) +--R 2 +--R + +--R 3 4 5 2 7 x 3 3 4 5 2 x +--R (- 24a b - 48a b - 24a )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 7 2 5 6 6 +--R (- a b - a b )cos(x) + (a b - a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (2a b + 7a b + 2a b)cos(x) +--R + +--R 2 5 4 3 x 6 2 5 4 3 x 4 4 3 x 2 +--R (4a b + 4a b )cos(-) + (- 4a b - 4a b )cos(-) - 3a b cos(-) +--R 2 2 2 +--R + +--R 2 5 4 3 +--R - 2a b - 14a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 5 6 x 6 2 5 6 x 4 +--R (- 4a b + 4a b)cos(-) + (4a b - 4a b)cos(-) +--R 2 2 +--R + +--R 4 3 6 x 2 2 5 4 3 6 +--R (3a b - 3a b)cos(-) - a b - 3a b - 8a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 4 3 6 x 6 2 5 4 3 6 x 4 +--R (- 4a b - 12a b - 8a b)cos(-) + (4a b + 12a b + 8a b)cos(-) +--R 2 2 +--R + +--R 4 3 6 x 2 2 5 4 3 6 +--R (3a b + 6a b)cos(-) + a b + 14a b + 7a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 6 2 5 4 3 6 x 4 +--R (4a b + 8a b + 4a b)cos(-) + (- 4a b - 8a b - 4a b)cos(-) +--R 2 2 +--R + +--R 4 3 6 x 2 4 3 +--R (- 3a b - 3a b)cos(-) - 3a b +--R 2 +--R * +--R cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 6 4 4 6 2 6 +--R (2a b + 4a b + 2a b )cos(x)sin(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b - 13a b - 8a b - a b)cos(x) +--R + +--R 7 3 5 5 3 5 3 7 +--R (2a b + 4a b + 2a b )cos(x) + 3a b + 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 5 5 3 7 x 5 +--R (24a b + 48a b + 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (- 24a b - 48a b - 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (4b + 8a b + a b - 6a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (3a b + 6a b + 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 +--R (- 4b - 9a b - 12a b - 4a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 4 4 6 2 x 2 4 4 6 2 +--R (- 3a b - 3a b )cos(-) + 12a b + 12a b +--R 2 +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 7 x 4 +--R (60a b + 100a b + 20a b - 20a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 2 3 5 5 3 +--R (- 36a b - 60a b - 12a b + 12a b)cos(-) - 9a b - 6a b +--R 2 +--R + +--R 7 +--R 3a b +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 3 5 5 3 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 5 +--R (- 72a b - 120a b - 24a b + 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 3 +--R (72a b + 120a b + 24a b - 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (- 18a b - 12a b + 6a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (24a b + 48a b + 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (- 24a b - 48a b - 24a b )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 4 +--R (3a b + 15a b + 21a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b - 11a b - 13a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 3a b - 7a b - 11a b - 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 x 6 +--R (- 12a b - 20a b - 4a b + 4a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 4 +--R (12a b + 20a b + 4a b - 4a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 2 7 3 5 5 3 7 +--R (9a b + 6a b - 3a b)cos(-) + 3a b - 3a b + 9a b + 15a b +--R 2 +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 3 5 5 3 x 2 3 5 5 3 7 +--R (- 3a b - 3a b )cos(-) - 6a b - 12a b - 6a b +--R 2 +--R * +--R 3 +--R sin(x) +--R + +--R 8 4 4 6 2 x 4 +--R (- 40b + 120a b + 80a b )cos(-) +--R 2 +--R + +--R 8 4 4 6 2 x 2 2 6 4 4 6 2 +--R (24b - 72a b - 48a b )cos(-) + 6a b - 6a b - 12a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 60a b - 120a b - 60a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (36a b + 72a b + 36a b )cos(-) + 9a b + 9a b +--R 2 +--R * +--R cos(x) +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (40b + 100a b + 80a b + 20a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 2 2 6 4 4 6 2 +--R (- 24b - 60a b - 48a b - 12a b )cos(-) - 6a b - 9a b - 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 7 5 3 7 x 5 +--R (48a b - 144a b - 96a b)cos(-) +--R 2 +--R + +--R 7 5 3 7 x 3 +--R (- 48a b + 144a b + 96a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (12a b - 12a b - 24a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (72a b + 144a b + 72a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (- 72a b - 144a b - 72a b)cos(-) + (18a b + 18a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 5 +--R (- 48a b - 120a b - 96a b - 24a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 3 +--R (48a b + 120a b + 96a b + 24a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (- 12a b - 18a b - 6a b )cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 8 5 +--R (- 2b - 7a b - 5a b + 3a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 2a b - 10a b - 14a b - 6a )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (4b + 18a b + 18a b + 4a b )cos(x) +--R + +--R 8 4 4 6 2 x 6 8 4 4 6 2 x 4 +--R (8b - 24a b - 16a b )cos(-) + (- 8b + 24a b + 16a b )cos(-) +--R 2 2 +--R + +--R 2 6 4 4 6 2 x 2 2 6 4 4 6 2 8 +--R (- 6a b + 6a b + 12a b )cos(-) + 2a b + 10a b + 14a b + 6a +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 +--R (12a b + 24a b + 12a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 4 4 4 6 2 x 2 +--R (- 12a b - 24a b - 12a b )cos(-) + (- 9a b - 9a b )cos(-) +--R 2 2 +--R + +--R 8 2 6 4 4 6 2 8 +--R - 2b - 11a b - 19a b - 13a b - 3a +--R * +--R cos(x) +--R + +--R 8 2 6 4 4 6 2 x 6 +--R (- 8b - 20a b - 16a b - 4a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (8b + 20a b + 16a b + 4a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (6a b + 9a b + 3a b )cos(-) - 6a b - 6a b +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 x 4 +--R (- 60a b - 100a b - 20a b + 20a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 2 3 5 5 3 +--R (36a b + 60a b + 12a b - 12a b)cos(-) + 9a b + 6a b +--R 2 +--R + +--R 7 +--R - 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 5 3 7 x 4 +--R (20a b - 60a b - 40a b)cos(-) +--R 2 +--R + +--R 7 5 3 7 x 2 3 5 5 3 7 +--R (- 12a b + 36a b + 24a b)cos(-) - 3a b + 3a b + 6a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 4 +--R (60a b + 140a b + 100a b + 20a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 2 3 5 5 3 +--R (- 36a b - 84a b - 60a b - 12a b)cos(-) - 9a b - 12a b +--R 2 +--R + +--R 7 +--R - 3a b +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 3 5 5 3 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 5 +--R (72a b + 120a b + 24a b - 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 3 +--R (- 72a b - 120a b - 24a b + 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (18a b + 12a b - 6a b )cos(-) +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 6 6 2 8 x 5 +--R (- 24a b + 72a b + 48a )cos(-) +--R 2 +--R + +--R 2 6 6 2 8 x 3 +--R (24a b - 72a b - 48a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (- 6a b + 6a b + 12a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 8 x 5 +--R (- 72a b - 168a b - 120a b - 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 3 +--R (72a b + 168a b + 120a b + 24a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (- 18a b - 24a b - 6a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (24a b + 48a b + 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (- 24a b - 48a b - 24a b )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 6 +--R (- 3a b - 8a b - 7a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (a b + 3a b + 3a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (6a b + 24a b + 21a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 x 6 +--R (12a b + 20a b + 4a b - 4a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 4 +--R (- 12a b - 20a b - 4a b + 4a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 2 7 3 5 5 3 7 +--R (- 9a b - 6a b + 3a b)cos(-) - 2a b - 20a b - 10a b + 8a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 7 5 3 7 x 6 7 5 3 7 x 4 +--R (- 4a b + 12a b + 8a b)cos(-) + (4a b - 12a b - 8a b)cos(-) +--R 2 2 +--R + +--R 3 5 5 3 7 x 2 7 3 5 5 3 7 +--R (3a b - 3a b - 6a b)cos(-) - 3a b - 16a b - 23a b - 10a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 6 +--R (- 12a b - 28a b - 20a b - 4a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 4 +--R (12a b + 28a b + 20a b + 4a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 2 7 3 5 5 3 7 +--R (9a b + 12a b + 3a b)cos(-) + a b + 17a b + 13a b - 3a b +--R 2 +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 3 5 5 3 x 2 5 3 7 +--R (- 3a b - 3a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (20a b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (- 12a b - 24a b - 12a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (20a b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (- 12a b - 24a b - 12a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 4 4 6 2 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 5 5 3 7 x 5 +--R (24a b + 48a b + 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (- 24a b - 48a b - 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R 4 +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (- 24a b - 48a b - 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (24a b + 48a b + 24a b)cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R 3 +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (- 24a b - 48a b - 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (24a b + 48a b + 24a b)cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R 2 +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (24a b + 48a b + 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (- 24a b - 48a b - 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 6 2 7 2 6 4 4 6 2 6 +--R (- a b - 2a b - a b )cos(x) + (a b + 2a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (2a b + 7a b + 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 4 4 6 2 x 2 2 6 4 4 6 2 +--R (- 3a b - 3a b )cos(-) - 2a b - 16a b - 14a b +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (- 4a b - 8a b - 4a b )cos(-) + (4a b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 4 4 6 2 x 2 2 6 4 4 6 2 +--R (3a b + 3a b )cos(-) - a b - 2a b - a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (- 4a b - 8a b - 4a b )cos(-) + (4a b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 4 4 6 2 x 2 2 6 4 4 6 2 +--R (3a b + 3a b )cos(-) + a b + 14a b + 13a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 4 4 6 2 x 2 4 4 6 2 +--R (- 3a b - 3a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R cos(x) +--R / +--R 2 6 4 4 6 2 4 +--R (3a b + 6a b + 3a b )sin(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b - 15a b - 3a b + 3a b)cos(x) + 3a b + 3a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 4 4 6 2 2 +--R (6b - 18a b - 12a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 8 2 6 4 4 +--R (15a b + 27a b + 9a b - 3a )cos(x) - 6b - 21a b - 24a b +--R + +--R 6 2 +--R - 9a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (9a b + 15a b + 3a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 3a b + 9a b + 27a b + 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b - 33a b - 39a b - 15a b)cos(x) + 3a b + 9a b + 9a b +--R + +--R 7 +--R 3a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (3a b + 6a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 3a b - 3a b + 3a b + 3a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 3a b - 12a b - 15a b - 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 +--R (3a b + 9a b + 9a b + 3a )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b + 9a b + 9a b + 3a b)sin(x) +--R + +--R 8 3 6 5 4 9 8 3 6 5 4 +--R (- 9a b - 24a b - 18a b + 3a )cos(x) + 3a b + 9a b + 9a b +--R + +--R 7 2 +--R 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (6b + 6a b - 18a b - 30a b - 12a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 9 2 7 4 5 +--R (9a b + 27a b + 27a b + 9a b)cos(x) - 6b - 21a b - 27a b +--R + +--R 6 3 8 +--R - 15a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 9 3 +--R (9a b + 24a b + 18a b - 3a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (- 3a b - 3a b + 9a b + 15a b + 6a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 8 3 6 +--R (- 9a b - 30a b - 36a b - 18a b - 3a )cos(x) + 3a b + 9a b +--R + +--R 5 4 7 2 +--R 9a b + 3a b +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b + 9a b + 9a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 3a b - 9a b - 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 3a b - 9a b - 9a b - 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 +--R (3a b + 9a b + 9a b + 3a b)cos(x) +--R Type: Expression(Integer) +--E 336 + +--S 337 of 546 +t0458:= cos(x)/(a+b*tan(x)) +--R +--R +--R cos(x) +--R (334) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 546 +r0458:= -b^2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+_ + b*cos(x)/(a^2+b^2)+a*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R b atanh(-------------------) + (a sin(x) + b cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (335) -------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 546 +a0458:= integrate(t0458,x) +--R +--R +--R (336) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (a sin(x) + b cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 339 + +--S 340 of 546 +m0458:= a0458-r0458 +--R +--R +--R (337) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 2 a sin(x) - b cos(x) +--R - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 546 +d0458:= D(m0458,x) +--R +--R +--R (338) +--R 2 3 3 2 2 2 2 3 3 +--R a b sin(x) - b cos(x)sin(x) + (a b cos(x) - a b )sin(x) - b cos(x) +--R + +--R 3 +--R b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 546 +t0459:= cos(x)^2/(a+b*tan(x)) +--R +--R +--R 2 +--R cos(x) +--R (339) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 342 + +--S 343 of 546 +r0459:= 1/2/(a^2+b^2)^2*(3*a*b^2*x+a^3*x+2*b^3*log(a*cos(x)+b*sin(x))+_ + a^3*cos(x)*sin(x)+a*cos(x)*sin(x)*b^2-a^2*b+a^2*b*cos(x)^2-_ + b^3+b^3*cos(x)^2) +--R +--R +--R (340) +--R 3 2 3 3 2 2 +--R 2b log(b sin(x) + a cos(x)) + (a b + a )cos(x)sin(x) + (b + a b)cos(x) +--R + +--R 2 3 3 2 +--R (3a b + a )x - b - a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 546 +a0459:= integrate(t0459,x) +--R +--R +--R (341) +--R 3 2 3 - 2b sin(x) - 2a cos(x) +--R - 2b log(----------) + 2b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (a b + a )cos(x)sin(x) + (b + a b)cos(x) + (3a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression(Integer),...) +--E 344 + +--S 345 of 546 +m0459:= a0459-r0459 +--R +--R +--R (342) +--R 3 3 2 +--R - 2b log(b sin(x) + a cos(x)) - 2b log(----------) +--R cos(x) + 1 +--R + +--R 3 - 2b sin(x) - 2a cos(x) 3 2 +--R 2b log(-----------------------) + b + a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 345 + +--S 346 of 546 +d0459:= D(m0459,x) +--R +--R +--R (343) 0 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 546 +t0460:= tan(x)/(a+b*tan(x)) +--R +--R +--R tan(x) +--R (344) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 546 +r0460:= -(-b*x+a*log(a*cos(x)+b*sin(x)))/(a^2+b^2) +--R +--R +--R - a log(b sin(x) + a cos(x)) + b x +--R (345) ---------------------------------- +--R 2 2 +--R b + a +--R Type: Expression(Integer) +--E 348 + +--S 349 of 546 +a0460:= integrate(t0460,x) +--R +--R +--R 2 +--R a log(tan(x) + 1) - 2a log(b tan(x) + a) + 2b x +--R (346) ------------------------------------------------ +--R 2 2 +--R 2b + 2a +--R Type: Union(Expression(Integer),...) +--E 349 + +--S 350 of 546 +m0460:= a0460-r0460 +--R +--R +--R (347) +--R 2 +--R a log(tan(x) + 1) - 2a log(b tan(x) + a) + 2a log(b sin(x) + a cos(x)) +--R ----------------------------------------------------------------------- +--R 2 2 +--R 2b + 2a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 546 +d0460:= D(m0460,x) +--R +--R +--R a cos(x)tan(x) - a sin(x) +--R (348) ----------------------------------------------------- +--R 2 2 +--R (b sin(x) + a b cos(x))tan(x) + a b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 351 + +--S 352 of 546 +t0461:= cot(x)/(a+b*tan(x)) +--R +--R +--R cot(x) +--R (349) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 546 +r0461:= -b*x/(a^2+b^2)+log(sin(x))/a-b^2*log(a*cos(x)+b*sin(x))/a/(a^2+b^2) +--R +--R +--R 2 2 2 +--R - b log(b sin(x) + a cos(x)) + (b + a )log(sin(x)) - a b x +--R (350) ----------------------------------------------------------- +--R 2 3 +--R a b + a +--R Type: Expression(Integer) +--E 353 + +--S 354 of 546 +a0461:= integrate(t0461,x) +--R +--R +--R (351) +--R 2 2 2 2 2 +--R - a log(tan(x) + 1) - 2b log(b tan(x) + a) + (2b + 2a )log(tan(x)) - 2a b x +--R ----------------------------------------------------------------------------- +--R 2 3 +--R 2a b + 2a +--R Type: Union(Expression(Integer),...) +--E 354 + +--S 355 of 546 +m0461:= a0461-r0461 +--R +--R +--R (352) +--R 2 2 2 2 2 +--R - a log(tan(x) + 1) - 2b log(b tan(x) + a) + (2b + 2a )log(tan(x)) +--R + +--R 2 2 2 +--R 2b log(b sin(x) + a cos(x)) + (- 2b - 2a )log(sin(x)) +--R / +--R 2 3 +--R 2a b + 2a +--R Type: Expression(Integer) +--E 355 + +--S 356 of 546 +d0461:= D(m0461,x) +--R +--R +--R (353) +--R 2 2 2 2 +--R - b cos(x) tan(x) - a cos(x) tan(x) + b sin(x) + a cos(x)sin(x) +--R ---------------------------------------------------------------------------- +--R 2 2 2 2 2 +--R (b sin(x) + a b cos(x)sin(x))tan(x) + (a b sin(x) + a cos(x)sin(x))tan(x) +--R Type: Expression(Integer) +--E 356 + +--S 357 of 546 +t0462:= sec(x)^3/(a+b*tan(x)) +--R +--R +--R 3 +--R sec(x) +--R (354) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 357 + +--S 358 of 546 +r0462:= 1/b^2*(-2*(a^2+b^2)^(1/2)*atanh(1/(a^2+b^2)^(1/2)*_ + (a*cos(x)-a+b*sin(x))/sin(x))*cos(x)+2*a*atanh((-1+cos(x))/sin(x))*_ + cos(x)+b*cos(x)+b)/cos(x) +--R +--R +--R (355) +--R cos(x) - 1 +--R 2a cos(x)atanh(----------) +--R sin(x) +--R + +--R +-------+ +--R | 2 2 b sin(x) + a cos(x) - a +--R - 2cos(x)\|b + a atanh(-----------------------) + b cos(x) + b +--R +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R / +--R 2 +--R b cos(x) +--R Type: Expression(Integer) +--E 358 + +--S 359 of 546 +a0462:= integrate(t0462,x) +--R +--R +--R (356) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - a cos(x)log(-------------------) + a cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R cos(x)\|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 +--R (- a sin(x) + b cos(x) + b)\|b + a + a b sin(x) - b cos(x) +--R + +--R 2 2 +--R - b - a +--R / +--R b sin(x) + a cos(x) +--R + +--R b cos(x) + b +--R / +--R 2 +--R b cos(x) +--R Type: Union(Expression(Integer),...) +--E 359 + +--S 360 of 546 +m0462:= a0462-r0462 +--R +--R +--R (357) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - a log(-------------------) + a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 +--R (- a sin(x) + b cos(x) + b)\|b + a + a b sin(x) - b cos(x) +--R + +--R 2 2 +--R - b - a +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R cos(x) - 1 | 2 2 b sin(x) + a cos(x) - a +--R - 2a atanh(----------) + 2\|b + a atanh(-----------------------) +--R sin(x) +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R / +--R 2 +--R b +--R Type: Expression(Integer) +--E 360 + +--S 361 of 546 +d0462:= D(m0462,x) +--R +--R +--R (358) +--R 3 3 8 +--R (- 3a b + a b)sin(x) +--R + +--R 4 2 2 4 2 2 4 7 +--R ((4b - 10a b + 2a )cos(x) + 5a b + a )sin(x) +--R + +--R 3 3 2 3 3 3 3 +--R ((14a b - 10a b)cos(x) + (- a b + 11a b)cos(x) + a b + a b) +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 2 4 3 2 2 4 2 +--R (- 4b + 10a b - 2a )cos(x) + (- 5a b + 7a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- 12b - 6a b - 2a )cos(x) - 3a b - 3a +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 3 3 3 2 +--R (a b - 3a b)cos(x) + (- 11a b + 13a b)cos(x) +--R + +--R 3 3 3 3 +--R (3a b - 5a b)cos(x) - a b - 5a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 4 5 2 2 4 4 +--R (- 4b + 10a b - 2a )cos(x) + (- 5a b - a )cos(x) +--R + +--R 4 2 2 4 3 2 2 4 2 +--R (- 8b - 28a b + 12a )cos(x) + (6a b - 10a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (12b + 18a b - 2a )cos(x) - a b + 3a +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 6 3 3 5 +--R (- 14a b + 10a b)cos(x) + (a b - 11a b)cos(x) +--R + +--R 3 3 4 3 3 3 3 2 +--R (19a b - 13a b)cos(x) + (2a b + 18a b)cos(x) - 8a b cos(x) +--R + +--R 3 3 3 3 +--R (- 3a b - 7a b)cos(x) + 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 2 4 7 2 2 4 6 +--R (4b - 10a b + 2a )cos(x) + (5a b - 7a )cos(x) +--R + +--R 4 2 2 4 5 2 2 4 4 +--R (- 12b + 18a b + 6a )cos(x) + (- 11a b + 5a )cos(x) +--R + +--R 4 2 2 4 3 2 2 4 2 +--R (12b - 6a b - 10a )cos(x) + (7a b + 3a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- 4b - 2a b + 2a )cos(x) - a b - a +--R * +--R sin(x) +--R + +--R 3 3 8 3 3 7 +--R (3a b - a b)cos(x) + (- a b + 3a b)cos(x) +--R + +--R 3 3 6 3 3 5 +--R (- 9a b - a b)cos(x) + (3a b - 5a b)cos(x) +--R + +--R 3 3 4 3 3 3 +--R (9a b + 5a b)cos(x) + (- 3a b + a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 3a b - 3a b)cos(x) + (a b + a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 5 8 +--R (3a b + a )sin(x) +--R + +--R 5 2 3 4 2 3 4 7 +--R ((- 4b + 8a b - 4a b)cos(x) - 5a b + 3a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R (- 14a b + 8a b - 2a )cos(x) + (a b - 19a b + 4a )cos(x) - a b +--R + +--R 3 2 5 +--R 4a b - 3a +--R * +--R 6 +--R sin(x) +--R + +--R 5 2 3 4 3 2 3 4 2 +--R (4b - 8a b + 4a b)cos(x) + (5a b - 19a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 +--R (12b + 12a b + 24a b)cos(x) + 3a b - 5a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (- a b + 3a b - 4a )cos(x) + (11a b - 12a b + 9a )cos(x) +--R + +--R 4 3 2 5 4 5 +--R (- 3a b + 13a b - 8a )cos(x) + a b + 3a +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (4b - 8a b + 4a b)cos(x) + (5a b - 3a b)cos(x) +--R + +--R 5 2 3 4 3 2 3 4 2 +--R (8b + 32a b - 8a b)cos(x) + (- 6a b + 26a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 +--R (- 12b - 24a b - 20a b)cos(x) + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (14a b - 8a b + 2a )cos(x) + (- a b + 19a b - 4a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 19a b + 4a b - a )cos(x) + (- 2a b - 26a b + 8a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R (8a b + 8a b - 8a )cos(x) + (3a b + 7a b + 4a )cos(x) - 3a b +--R + +--R 3 2 5 +--R - 4a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 7 2 3 4 6 +--R (- 4b + 8a b - 4a b)cos(x) + (- 5a b + 19a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (12b - 12a b - 16a b)cos(x) + (11a b - 13a b)cos(x) +--R + +--R 5 4 3 2 3 4 2 +--R (- 12b + 20a b)cos(x) + (- 7a b - 7a b)cos(x) +--R + +--R 5 2 3 2 3 4 +--R (4b + 4a b )cos(x) + a b + a b +--R * +--R sin(x) +--R + +--R 4 5 8 4 3 2 5 7 +--R (- 3a b - a )cos(x) + (a b - 3a b + 4a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 +--R (9a b + 4a b - 5a )cos(x) + (- 3a b + 5a b )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 9a b - 8a b + 5a )cos(x) + (3a b - a b - 4a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 +--R (3a b + 4a b + a )cos(x) + (- a b - a b )cos(x) +--R / +--R 2 3 8 4 3 2 4 7 +--R a b sin(x) + ((- 3a b + a b )cos(x) + a b )sin(x) +--R + +--R 5 2 3 2 2 3 5 2 3 6 +--R ((2b - 6a b )cos(x) + 3a b cos(x) - 2b - 3a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (9a b - 3a b )cos(x) + (- 3a b + 2a b )cos(x) +--R + +--R 4 3 2 4 +--R (3a b - 3a b )cos(x) - a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 3 4 2 3 3 2 3 2 +--R (- 4b + 10a b )cos(x) - 7a b cos(x) + 7a b cos(x) +--R + +--R 2 3 5 2 3 +--R - 5a b cos(x) + 4b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 9a b + 3a b )cos(x) + (3a b - 4a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (6a b + 2a b )cos(x) + (- 2a b - 4a b )cos(x) +--R + +--R 4 3 2 4 +--R (3a b + 3a b )cos(x) - a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 6 2 3 5 5 2 3 4 +--R (2b - 6a b )cos(x) + 5a b cos(x) + (- 6b + 7a b )cos(x) +--R + +--R 2 3 3 5 2 2 3 5 2 3 +--R - 6a b cos(x) + 6b cos(x) + a b cos(x) - 2b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (3a b - a b )cos(x) + (- a b + 2a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 9a b + a b )cos(x) + (3a b - 4a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (9a b + a b )cos(x) + (- 3a b + 2a b )cos(x) +--R + +--R 4 3 2 4 +--R (- 3a b - a b )cos(x) + a b +--R * +--R sin(x) +--R + +--R 2 3 8 2 3 7 2 3 6 2 3 5 +--R a b cos(x) - a b cos(x) - 3a b cos(x) + 3a b cos(x) +--R + +--R 2 3 4 2 3 3 2 3 2 2 3 +--R 3a b cos(x) - 3a b cos(x) - a b cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 8 5 3 3 5 3 3 7 +--R - a b sin(x) + ((3a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 6 2 4 2 2 4 4 2 6 2 4 6 +--R ((- 2b + 6a b )cos(x) + (- 5a b + a b )cos(x) + 2b + 5a b )sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 9a b + 3a b )cos(x) + (3a b - 7a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 3a b + 7a b )cos(x) + a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 2 4 4 2 4 4 2 3 +--R (4b - 10a b )cos(x) + (11a b - 3a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 6 2 4 +--R (- 11a b + 2a b )cos(x) + (9a b - 3a b )cos(x) - 4b - 7a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (9a b - 3a b )cos(x) + (- 3a b + 11a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 6a b - 10a b )cos(x) + (2a b + 10a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 3a b - 11a b )cos(x) + a b + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 6 2 4 4 2 5 +--R (- 2b + 6a b )cos(x) + (- 7a b + 3a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (6b - 5a b - 4a b )cos(x) + (10a b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 6 2 4 +--R (- 6b - 4a b - 4a b )cos(x) + (- 3a b + 3a b )cos(x) + 2b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 6 +--R (- 3a b + a b )cos(x) + (a b - 5a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (9a b + 3a b )cos(x) + (- 3a b + 9a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 9a b - 9a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (3a b + 5a b )cos(x) - a b - a b +--R * +--R sin(x) +--R + +--R 2 4 8 2 4 4 2 7 2 4 4 2 6 +--R - a b cos(x) + (a b - a b )cos(x) + (3a b + 2a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 3a b + a b )cos(x) + (- 3a b - 4a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 2 4 4 2 +--R (3a b + a b )cos(x) + (a b + 2a b )cos(x) + (- a b - a b )cos(x) +--R Type: Expression(Integer) +--E 361 + +--S 362 of 546 +t0463:= csc(x)^2/(a+b*tan(x)) +--R +--R +--R 2 +--R csc(x) +--R (359) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 362 + +--S 363 of 546 +r0463:= (-a*cot(x)+b*log(b+a*cot(x)))/a^2 +--R +--R +--R b log(a cot(x) + b) - a cot(x) +--R (360) ------------------------------ +--R 2 +--R a +--R Type: Expression(Integer) +--E 363 + +--S 364 of 546 +a0463:= integrate(t0463,x) +--R +--R +--R (361) +--R sin(x) - 2b sin(x) - 2a cos(x) +--R - b sin(x)log(----------) + b sin(x)log(-----------------------) - a cos(x) +--R cos(x) + 1 cos(x) + 1 +--R --------------------------------------------------------------------------- +--R 2 +--R a sin(x) +--R Type: Union(Expression(Integer),...) +--E 364 + +--S 365 of 546 +m0463:= a0463-r0463 +--R +--R +--R (362) +--R sin(x) +--R - b sin(x)log(----------) - b sin(x)log(a cot(x) + b) +--R cos(x) + 1 +--R + +--R - 2b sin(x) - 2a cos(x) +--R b sin(x)log(-----------------------) + a cot(x)sin(x) - a cos(x) +--R cos(x) + 1 +--R / +--R 2 +--R a sin(x) +--R Type: Expression(Integer) +--E 365 + +--S 366 of 546 +d0463:= D(m0463,x) +--R +--R +--R (363) +--R 3 3 3 2 +--R (- b cot(x) - b cot(x))sin(x) + (- a cos(x)cot(x) + b cos(x))sin(x) +--R + +--R 3 3 +--R a cos(x) cot(x) + b cos(x) +--R / +--R 2 3 2 2 +--R (a b cot(x) + b )sin(x) + (a cos(x)cot(x) + a b cos(x))sin(x) +--R Type: Expression(Integer) +--E 366 + +--S 367 of 546 +t0464:= csc(x)^4/(a+b*tan(x)) +--R +--R +--R 4 +--R csc(x) +--R (364) ------------ +--R b tan(x) + a +--R Type: Expression(Integer) +--E 367 + +--S 368 of 546 +r0464:= -(a^2+b^2)*cot(x)/a^3+1/2*b*cot(x)^2/a^2-1/3*cot(x)^3/a+_ + b*(a^2+b^2)*log(b+a*cot(x))/a^4 +--R +--R +--R (365) +--R 3 2 3 3 2 2 +--R (6b + 6a b)log(a cot(x) + b) - 2a cot(x) + 3a b cot(x) +--R + +--R 2 3 +--R (- 6a b - 6a )cot(x) +--R / +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 368 + +--S 369 of 546 +a0464:= integrate(t0464,x) +--R +--R +--R (366) +--R 3 2 2 3 2 sin(x) +--R ((- 12b - 12a b)cos(x) + 12b + 12a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R 3 2 2 3 2 - 2b sin(x) - 2a cos(x) +--R ((12b + 12a b)cos(x) - 12b - 12a b)sin(x)log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 3 3 +--R (- 3a b cos(x) - 3a b)sin(x) + (- 12a b - 8a )cos(x) +--R + +--R 2 3 +--R (12a b + 12a )cos(x) +--R / +--R 4 2 4 +--R (12a cos(x) - 12a )sin(x) +--R Type: Union(Expression(Integer),...) +--E 369 + +--S 370 of 546 +m0464:= a0464-r0464 +--R +--R +--R (367) +--R 3 2 2 3 2 sin(x) +--R ((- 12b - 12a b)cos(x) + 12b + 12a b)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R 3 2 2 3 2 +--R ((- 12b - 12a b)cos(x) + 12b + 12a b)sin(x)log(a cot(x) + b) +--R + +--R 3 2 2 3 2 - 2b sin(x) - 2a cos(x) +--R ((12b + 12a b)cos(x) - 12b - 12a b)sin(x)log(-----------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 3 2 2 2 2 +--R (4a cos(x) - 4a )cot(x) + (- 6a b cos(x) + 6a b)cot(x) +--R + +--R 2 3 2 2 3 2 2 2 +--R ((12a b + 12a )cos(x) - 12a b - 12a )cot(x) - 3a b cos(x) - 3a b +--R * +--R sin(x) +--R + +--R 2 3 3 2 3 +--R (- 12a b - 8a )cos(x) + (12a b + 12a )cos(x) +--R / +--R 4 2 4 +--R (12a cos(x) - 12a )sin(x) +--R Type: Expression(Integer) +--E 370 + +--S 371 of 546 +d0464:= D(m0464,x) +--R +--R +--R (368) +--R 2 3 4 +--R (- 3a b cos(x)cot(x) - 3b cos(x))sin(x) +--R + +--R 2 4 2 2 2 5 +--R (- 3a b cos(x) + 6a b cos(x) - 3a b)cot(x) +--R + +--R 2 4 2 2 2 3 +--R (- 6a b cos(x) + 12a b cos(x) - 6a b)cot(x) +--R + +--R 2 4 2 2 2 2 4 +--R (- 4a b cos(x) + 6a b cos(x) - 3a b)cot(x) - a b cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 3 3 3 5 +--R (- 3a cos(x) + 6a cos(x) - 3a cos(x))cot(x) +--R + +--R 3 5 3 3 3 3 +--R (- 6a cos(x) + 12a cos(x) - 6a cos(x))cot(x) +--R + +--R 2 3 5 2 3 3 2 +--R ((3a b - a )cos(x) + (- 6a b + 3a )cos(x) + 3a b cos(x))cot(x) +--R + +--R 3 2 5 3 2 3 3 2 +--R (3b + 2a b)cos(x) + (- 6b - 3a b)cos(x) + (3b + 3a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 4 2 6 2 4 +--R ((- a b cos(x) + a b cos(x) )cot(x) - a b cos(x) + a b cos(x) )sin(x) +--R + +--R 2 3 7 2 3 5 2 3 3 +--R ((3a b + 2a )cos(x) + (- 6a b - 5a )cos(x) + (3a b + 3a )cos(x) ) +--R * +--R cot(x) +--R + +--R 3 2 7 3 2 5 3 2 3 +--R (3b + 2a b)cos(x) + (- 6b - 5a b)cos(x) + (3b + 3a b)cos(x) +--R / +--R 3 4 3 2 3 2 2 4 +--R (3a b cos(x) - 6a b cos(x) + 3a b)cot(x) + 3a b cos(x) +--R + +--R 2 2 2 2 2 +--R - 6a b cos(x) + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 3 4 3 5 +--R (3a cos(x) - 6a cos(x) + 3a cos(x))cot(x) + 3a b cos(x) +--R + +--R 3 3 3 +--R - 6a b cos(x) + 3a b cos(x) +--R * +--R 2 +--R sin(x) +--R Type: Expression(Integer) +--E 371 + +--S 372 of 546 +t0465:= sin(x)/(%i+tan(x)) +--R +--R +--R sin(x) +--R (369) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 372 + +--S 373 of 546 +r0465:= 1/3*%i*cos(x)^3+1/3*sin(x)^3 +--R +--R +--R 1 3 1 3 +--R (370) - sin(x) + - %i cos(x) +--R 3 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 373 + +--S 374 of 546 +--a0465:= integrate(t0465,x) +--E 374 + +--S 375 of 546 +--m0465:= a0465-r0465 +--E 375 + +--S 376 of 546 +--d0465:= D(m0465,x) +--E 376 + +--S 377 of 546 +t0466:= sin(x)^2/(%i+tan(x)) +--R +--R +--R 2 +--R sin(x) +--R (371) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 377 + +--S 378 of 546 +r0466:= -1/8*%i*x-1/8*%i*cos(x)*sin(x)+1/4*%i*cos(x)^3*sin(x)+1/4*sin(x)^4 +--R +--R +--R 1 4 1 3 1 1 +--R (372) - sin(x) + (- %i cos(x) - - %i cos(x))sin(x) - - %i x +--R 4 4 8 8 +--R Type: Expression(Complex(Fraction(Integer))) +--E 378 + +--S 379 of 546 +--a0466:= integrate(t0466,x) +--E 379 + +--S 380 of 546 +--m0466:= a0466-r0466 +--E 380 + +--S 381 of 546 +--d0466:= D(m0466,x) +--E 381 + +--S 382 of 546 +t0467:= sin(x)^3/(%i+tan(x)) +--R +--R +--R 3 +--R sin(x) +--R (373) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 382 + +--S 383 of 546 +r0467:= 1/3*%i*cos(x)^3-1/5*%i*cos(x)^5+1/5*sin(x)^5 +--R +--R +--R 1 5 1 5 1 3 +--R (374) - sin(x) - - %i cos(x) + - %i cos(x) +--R 5 5 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 383 + +--S 384 of 546 +--a0467:= integrate(t0467,x) +--E 384 + +--S 385 of 546 +--m0467:= a0467-r0467 +--E 385 + +--S 386 of 546 +--d0467:= D(m0467,x) +--E 386 + +--S 387 of 546 +t0468:= sin(x)^4/(%i+tan(x)) +--R +--R +--R 4 +--R sin(x) +--R (375) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 387 + +--S 388 of 546 +r0468:= -1/16*%i*x-1/16*%i*cos(x)*sin(x)+1/8*%i*cos(x)^3*sin(x)+_ + 1/6*%i*cos(x)^3*sin(x)^3+1/6*sin(x)^6 +--R +--R +--R (376) +--R 1 6 1 3 3 1 3 1 +--R - sin(x) + - %i cos(x) sin(x) + (- %i cos(x) - -- %i cos(x))sin(x) +--R 6 6 8 16 +--R + +--R 1 +--R - -- %i x +--R 16 +--R Type: Expression(Complex(Fraction(Integer))) +--E 388 + +--S 389 of 546 +--a0468:= integrate(t0468,x) +--E 389 + +--S 390 of 546 +--m0468:= a0468-r0468 +--E 390 + +--S 391 of 546 +--d0468:= D(m0468,x) +--E 391 + +--S 392 of 546 +t0469:= cos(x)/(%i+tan(x)) +--R +--R +--R cos(x) +--R (377) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 392 + +--S 393 of 546 +r0469:= -1/3*cos(x)^3-%i*sin(x)+1/3*%i*sin(x)^3 +--R +--R +--R 1 3 1 3 +--R (378) - %i sin(x) - %i sin(x) - - cos(x) +--R 3 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 393 + +--S 394 of 546 +--a0469:= integrate(t0469,x) +--E 394 + +--S 395 of 546 +--m0469:= a0469-r0469 +--E 395 + +--S 396 of 546 +--d0469:= D(m0469,x) +--E 396 + +--S 397 of 546 +t0470:= cos(x)^2/(%i+tan(x)) +--R +--R +--R 2 +--R cos(x) +--R (379) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 397 + +--S 398 of 546 +r0470:= -3/8*%i*x-1/4*cos(x)^4-3/8*%i*cos(x)*sin(x)-1/4*%i*cos(x)^3*sin(x) +--R +--R +--R 1 3 3 1 4 3 +--R (380) (- - %i cos(x) - - %i cos(x))sin(x) - - cos(x) - - %i x +--R 4 8 4 8 +--R Type: Expression(Complex(Fraction(Integer))) +--E 398 + +--S 399 of 546 +--a0470:= integrate(t0470,x) +--E 399 + +--S 400 of 546 +--m0470:= a0470-r0470 +--E 400 + +--S 401 of 546 +--d0470:= D(m0470,x) +--E 401 + +--S 402 of 546 +t0471:= cos(x)^3/(%i+tan(x)) +--R +--R +--R 3 +--R cos(x) +--R (381) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 402 + +--S 403 of 546 +r0471:= -1/5*cos(x)^5-%i*sin(x)+2/3*%i*sin(x)^3-1/5*%i*sin(x)^5 +--R +--R +--R 1 5 2 3 1 5 +--R (382) - - %i sin(x) + - %i sin(x) - %i sin(x) - - cos(x) +--R 5 3 5 +--R Type: Expression(Complex(Fraction(Integer))) +--E 403 + +--S 404 of 546 +--a0471:= integrate(t0471,x) +--E 404 + +--S 405 of 546 +--m0471:= a0471-r0471 +--E 405 + +--S 406 of 546 +--d0471:= D(m0471,x) +--E 406 + +--S 407 of 546 +t0472:= cos(x)^4/(%i+tan(x)) +--R +--R +--R 4 +--R cos(x) +--R (383) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 407 + +--S 408 of 546 +r0472:= -5/16*%i*x-1/6*cos(x)^6-5/16*%i*cos(x)*sin(x)-_ + 5/24*%i*cos(x)^3*sin(x)-1/6*%i*cos(x)^5*sin(x) +--R +--R +--R (384) +--R 1 5 5 3 5 1 6 5 +--R (- - %i cos(x) - -- %i cos(x) - -- %i cos(x))sin(x) - - cos(x) - -- %i x +--R 6 24 16 6 16 +--R Type: Expression(Complex(Fraction(Integer))) +--E 408 + +--S 409 of 546 +--a0472:= integrate(t0472,x) +--E 409 + +--S 410 of 546 +--m0472:= a0472-r0472 +--E 410 + +--S 411 of 546 +--d0472:= D(m0472,x) +--E 411 + +--S 412 of 546 +t0473:= tan(x)/(%i+tan(x)) +--R +--R +--R tan(x) +--R (385) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 412 + +--S 413 of 546 +r0473:= 1/2*x-%i/(2+2*%i*cot(x)) +--R +--R +--R x cot(x) - %i x - 1 +--R (386) ------------------- +--R 2cot(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 413 + +--S 414 of 546 +a0473:= integrate(t0473,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 414 + +--S 415 of 546 +m0473:= a0473-r0473 +--R +--R +--R (- x + 2a0473)cot(x) + %i x - 2%i a0473 + 1 +--R (387) ------------------------------------------- +--R 2cot(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 415 + +--S 416 of 546 +d0473:= D(m0473,x) +--R +--R +--R %i +--R (388) ----------- +--R cot(x) - %i +--R Type: Expression(Complex(Integer)) +--E 416 + +--S 417 of 546 +t0474:= tan(x)^2/(%i+tan(x)) +--R +--R +--R 2 +--R tan(x) +--R (389) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 417 + +--S 418 of 546 +r0474:= -1/2*%i*x-log(cos(x))+%i/(2*%i+2*tan(x)) +--R +--R +--R %i (- 2tan(x) - 2%i)log(cos(x)) + %i +--R (390) - -- x + --------------------------------- +--R 2 2tan(x) + 2%i +--R Type: UnivariatePolynomial(x,Expression(Complex(Integer))) +--E 418 + +--S 419 of 546 +a0474:= integrate(t0474,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 419 + +--S 420 of 546 +m0474:= a0474-r0474 +--R +--R +--R %i (2tan(x) + 2%i)log(cos(x)) + 2a0474 tan(x) + 2%i a0474 - %i +--R (391) -- x + ----------------------------------------------------------- +--R 2 2tan(x) + 2%i +--R Type: UnivariatePolynomial(x,Expression(Complex(Integer))) +--E 420 + +--S 421 of 546 +d0474:= D(m0474,x) +--R +--R +--R (- sin(x) + %i cos(x))tan(x) - %i sin(x) +--R (392) ---------------------------------------- +--R cos(x)tan(x) + %i cos(x) +--R Type: UnivariatePolynomial(x,Expression(Complex(Integer))) +--E 421 + +--S 422 of 546 +t0475:= cot(x)/(%i+tan(x)) +--R +--R +--R cot(x) +--R (393) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 422 + +--S 423 of 546 +r0475:= 1/2*x-%i*log(sin(x))+1/(2*%i+2*tan(x)) +--R +--R +--R (- 2%i tan(x) + 2)log(sin(x)) + x tan(x) + %i x + 1 +--R (394) --------------------------------------------------- +--R 2tan(x) + 2%i +--R Type: Expression(Complex(Integer)) +--E 423 + +--S 424 of 546 +a0475:= integrate(t0475,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 424 + +--S 425 of 546 +m0475:= a0475-r0475 +--R +--R +--R (395) +--R (2%i tan(x) - 2)log(sin(x)) + (- x + 2a0475)tan(x) - %i x + 2%i a0475 - 1 +--R ------------------------------------------------------------------------- +--R 2tan(x) + 2%i +--R Type: Expression(Complex(Integer)) +--E 425 + +--S 426 of 546 +d0475:= D(m0475,x) +--R +--R +--R %i cos(x)tan(x) - %i sin(x) - cos(x) +--R (396) ------------------------------------ +--R sin(x)tan(x) + %i sin(x) +--R Type: Expression(Complex(Integer)) +--E 426 + +--S 427 of 546 +t0476:= cot(x)^2/(%i+tan(x)) +--R +--R +--R 2 +--R cot(x) +--R (397) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 427 + +--S 428 of 546 +r0476:= 3/2*%i*x+%i*cot(x)+log(sin(x))+%i/(2*%i+2*tan(x)) +--R +--R +--R (398) +--R (2tan(x) + 2%i)log(sin(x)) + (2%i cot(x) + 3%i x)tan(x) - 2cot(x) - 3x + %i +--R --------------------------------------------------------------------------- +--R 2tan(x) + 2%i +--R Type: Expression(Complex(Integer)) +--E 428 + +--S 429 of 546 +a0476:= integrate(t0476,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 429 + +--S 430 of 546 +m0476:= a0476-r0476 +--R +--R +--R (399) +--R (- 2tan(x) - 2%i)log(sin(x)) + (- 2%i cot(x) - 3%i x + 2a0476)tan(x) +--R + +--R 2cot(x) + 3x + 2%i a0476 - %i +--R / +--R 2tan(x) + 2%i +--R Type: Expression(Complex(Integer)) +--E 430 + +--S 431 of 546 +d0476:= D(m0476,x) +--R +--R +--R (400) +--R 2 2 +--R (%i cot(x) sin(x) - cos(x))tan(x) + (- cot(x) + 1)sin(x) - %i cos(x) +--R --------------------------------------------------------------------- +--R sin(x)tan(x) + %i sin(x) +--R Type: Expression(Complex(Integer)) +--E 431 + +--S 432 of 546 +t0477:= cot(x)^3/(%i+tan(x)) +--R +--R +--R 3 +--R cot(x) +--R (401) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 432 + +--S 433 of 546 +r0477:= -3/2*x-cot(x)+1/2*%i*cot(x)^2+2*%i*log(sin(x))-1/(2*%i+2*tan(x)) +--R +--R +--R (402) +--R 1 2 3 +--R (2%i tan(x) - 2)log(sin(x)) + (- %i cot(x) - cot(x) - - x)tan(x) +--R 2 2 +--R + +--R 1 2 3 1 +--R - - cot(x) - %i cot(x) - - %i x - - +--R 2 2 2 +--R / +--R tan(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 433 + +--S 434 of 546 +a0477:= integrate(t0477,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 434 + +--S 435 of 546 +m0477:= a0477-r0477 +--R +--R +--R (403) +--R (- 2%i tan(x) + 2)log(sin(x)) +--R + +--R 1 2 3 1 2 +--R (- - %i cot(x) + cot(x) + - x + a0477)tan(x) + - cot(x) + %i cot(x) +--R 2 2 2 +--R + +--R 3 1 +--R - %i x + %i a0477 + - +--R 2 2 +--R / +--R tan(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 435 + +--S 436 of 546 +d0477:= D(m0477,x) +--R +--R +--R (404) +--R 3 2 +--R ((%i cot(x) - cot(x) + %i cot(x))sin(x) - 2%i cos(x))tan(x) +--R + +--R 3 2 +--R (- cot(x) - %i cot(x) - cot(x) + %i)sin(x) + 2cos(x) +--R / +--R sin(x)tan(x) + %i sin(x) +--R Type: Expression(Complex(Fraction(Integer))) +--E 436 + +--S 437 of 546 +t0478:= cot(x)^4/(%i+tan(x)) +--R +--R +--R 4 +--R cot(x) +--R (405) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 437 + +--S 438 of 546 +r0478:= -5/2*%i*x-2*%i*cot(x)-1/2*cot(x)^2+1/3*%i*cot(x)^3-_ + 2*log(sin(x))-%i/(2*%i+2*tan(x)) +--R +--R +--R (406) +--R (- 2tan(x) - 2%i)log(sin(x)) +--R + +--R 1 3 1 2 5 1 3 +--R (- %i cot(x) - - cot(x) - 2%i cot(x) - - %i x)tan(x) - - cot(x) +--R 3 2 2 3 +--R + +--R 1 2 5 1 +--R - - %i cot(x) + 2cot(x) + - x - - %i +--R 2 2 2 +--R / +--R tan(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 438 + +--S 439 of 546 +a0478:= integrate(t0478,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 439 + +--S 440 of 546 +m0478:= a0478-r0478 +--R +--R +--R (407) +--R (2tan(x) + 2%i)log(sin(x)) +--R + +--R 1 3 1 2 5 +--R (- - %i cot(x) + - cot(x) + 2%i cot(x) + - %i x + a0478)tan(x) +--R 3 2 2 +--R + +--R 1 3 1 2 5 1 +--R - cot(x) + - %i cot(x) - 2cot(x) - - x + %i a0478 + - %i +--R 3 2 2 2 +--R / +--R tan(x) + %i +--R Type: Expression(Complex(Fraction(Integer))) +--E 440 + +--S 441 of 546 +d0478:= D(m0478,x) +--R +--R +--R (408) +--R 4 3 2 +--R ((%i cot(x) - cot(x) - %i cot(x) - cot(x))sin(x) + 2cos(x))tan(x) +--R + +--R 4 3 2 +--R (- cot(x) - %i cot(x) + cot(x) - %i cot(x) - 1)sin(x) + 2%i cos(x) +--R / +--R sin(x)tan(x) + %i sin(x) +--R Type: Expression(Complex(Fraction(Integer))) +--E 441 + +--S 442 of 546 +t0479:= sec(x)/(%i+tan(x)) +--R +--R +--R sec(x) +--R (409) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 442 + +--S 443 of 546 +r0479:= -cos(x)-%i*sin(x) +--R +--R +--R (410) - %i sin(x) - cos(x) +--R Type: Expression(Complex(Integer)) +--E 443 + +--S 444 of 546 +a0479:= integrate(t0479,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 444 + +--S 445 of 546 +m0479:= a0479-r0479 +--R +--R +--R (411) %i sin(x) + cos(x) + a0479 +--R Type: Expression(Complex(Integer)) +--E 445 + +--S 446 of 546 +d0479:= D(m0479,x) +--R +--R +--R (412) - sin(x) + %i cos(x) +--R Type: Expression(Complex(Integer)) +--E 446 + +--S 447 of 546 +t0480:= sec(x)^3/(%i+tan(x)) +--R +--R +--R 3 +--R sec(x) +--R (413) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 447 + +--S 448 of 546 +r0480:= -%i*atanh(sin(x))+sec(x) +--R +--R +--R (414) - %i atanh(sin(x)) + sec(x) +--R Type: Expression(Complex(Integer)) +--E 448 + +--S 449 of 546 +a0480:= integrate(t0480,x) +--R +--R +--R sin(x) - cos(x) - 1 +--R %i cos(x)log(-------------------) + cos(x) + 1 +--R sin(x) + cos(x) + 1 +--R (415) ---------------------------------------------- +--R cos(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 449 + +--S 450 of 546 +m0480:= a0480-r0480 +--R +--R +--R (416) +--R sin(x) - cos(x) - 1 +--R %i cos(x)log(-------------------) + %i cos(x)atanh(sin(x)) - cos(x)sec(x) +--R sin(x) + cos(x) + 1 +--R + +--R cos(x) + 1 +--R / +--R cos(x) +--R Type: Expression(Complex(Integer)) +--E 450 + +--S 451 of 546 +d0480:= D(m0480,x) +--R +--R +--R (417) +--R 2 4 4 3 2 2 +--R - cos(x) sec(x)sin(x) + (cos(x) + 2cos(x) + 2cos(x) )sec(x)sin(x) +--R + +--R 4 3 2 +--R (- cos(x) - 2cos(x) - cos(x) )sec(x) +--R * +--R tan(x) +--R + +--R 5 2 4 2 3 +--R sin(x) + 2%i cos(x) sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) +--R + +--R 4 3 2 2 +--R (2%i cos(x) + %i cos(x) - 2%i cos(x) )sin(x) +--R + +--R 2 5 3 +--R (cos(x) + 2cos(x) + 1)sin(x) + %i cos(x) - %i cos(x) +--R / +--R 2 4 4 3 2 2 4 +--R cos(x) sin(x) + (- cos(x) - 2cos(x) - 2cos(x) )sin(x) + cos(x) +--R + +--R 3 2 +--R 2cos(x) + cos(x) +--R Type: Expression(Complex(Integer)) +--E 451 + +--S 452 of 546 +t0481:= csc(x)/(%i+tan(x)) +--R +--R +--R csc(x) +--R (418) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 452 + +--S 453 of 546 +r0481:= %i*atanh(cos(x))-%i*cos(x)+sin(x) +--R +--R +--R (419) %i atanh(cos(x)) + sin(x) - %i cos(x) +--R Type: Expression(Complex(Integer)) +--E 453 + +--S 454 of 546 +a0481:= integrate(t0481,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 454 + +--S 455 of 546 +m0481:= a0481-r0481 +--R +--R +--R (420) - %i atanh(cos(x)) - sin(x) + %i cos(x) + a0481 +--R Type: Expression(Complex(Integer)) +--E 455 + +--S 456 of 546 +d0481:= D(m0481,x) +--R +--R +--R 2 3 +--R - %i cos(x) sin(x) - cos(x) + cos(x) +--R (421) ------------------------------------- +--R 2 +--R cos(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 456 + +--S 457 of 546 +t0482:= csc(x)^2/(%i+tan(x)) +--R +--R +--R 2 +--R csc(x) +--R (422) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 457 + +--S 458 of 546 +r0482:= %i*cot(x)-log(-%i+cot(x)) +--R +--R +--R (423) - log(cot(x) - %i) + %i cot(x) +--R Type: Expression(Complex(Integer)) +--E 458 + +--S 459 of 546 +a0482:= integrate(t0482,x) +--R +--R +--R (424) +--R sin(x) 2 +--R sin(x)log(----------) - sin(x)log(----------) + %i x sin(x) + %i cos(x) +--R cos(x) + 1 cos(x) + 1 +--R ----------------------------------------------------------------------- +--R sin(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 459 + +--S 460 of 546 +m0482:= a0482-r0482 +--R +--R +--R (425) +--R sin(x) 2 +--R sin(x)log(----------) + sin(x)log(cot(x) - %i) - sin(x)log(----------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R (- %i cot(x) + %i x)sin(x) + %i cos(x) +--R / +--R sin(x) +--R Type: Expression(Complex(Integer)) +--E 460 + +--S 461 of 546 +d0482:= D(m0482,x) +--R +--R +--R 2 2 2 +--R (%i cot(x) - cot(x))sin(x) + cos(x)sin(x) - %i cos(x) +--R (426) -------------------------------------------------------- +--R 2 +--R sin(x) +--R Type: Expression(Complex(Integer)) +--E 461 + +--S 462 of 546 +t0483:= csc(x)^3/(%i+tan(x)) +--R +--R +--R 3 +--R csc(x) +--R (427) ----------- +--R tan(x) + %i +--R Type: Expression(Complex(Integer)) +--E 462 + +--S 463 of 546 +r0483:= -1/2*%i*atanh(cos(x))-csc(x)+1/2*%i*cot(x)*csc(x) +--R +--R +--R 1 1 +--R (428) - - %i atanh(cos(x)) + (- %i cot(x) - 1)csc(x) +--R 2 2 +--R Type: Expression(Complex(Fraction(Integer))) +--E 463 + +--S 464 of 546 +a0483:= integrate(t0483,x) +--R +--R +--R 2 sin(x) +--R (%i cos(x) - %i)log(----------) + 2sin(x) - %i cos(x) +--R cos(x) + 1 +--R (429) ------------------------------------------------------ +--R 2 +--R 2cos(x) - 2 +--R Type: Union(Expression(Complex(Integer)),...) +--E 464 + +--S 465 of 546 +m0483:= a0483-r0483 +--R +--R +--R (430) +--R 1 2 1 sin(x) 1 2 1 +--R (- %i cos(x) - - %i)log(----------) + (- %i cos(x) - - %i)atanh(cos(x)) +--R 2 2 cos(x) + 1 2 2 +--R + +--R 1 2 1 2 1 +--R sin(x) + ((- - %i cos(x) + - %i)cot(x) + cos(x) - 1)csc(x) - - %i cos(x) +--R 2 2 2 +--R / +--R 2 +--R cos(x) - 1 +--R Type: Expression(Complex(Fraction(Integer))) +--E 465 + +--S 466 of 546 +d0483:= D(m0483,x) +--R +--R +--R (431) +--R 3 +--R 2cos(x)sin(x) +--R + +--R 1 3 1 2 1 1 2 +--R (- %i cos(x) - - %i cos(x) - - %i cos(x) - - %i)sin(x) +--R 2 2 2 2 +--R + +--R 4 2 2 +--R (%i cos(x) - 2%i cos(x) + %i)cot(x) +--R + +--R 4 2 1 4 2 1 +--R (- cos(x) + 2cos(x) - 1)cot(x) + - %i cos(x) - %i cos(x) + - %i +--R 2 2 +--R * +--R csc(x) +--R + +--R 3 +--R cos(x) - cos(x) +--R * +--R sin(x) +--R + +--R 1 5 3 1 +--R - %i cos(x) - %i cos(x) + - %i cos(x) +--R 2 2 +--R / +--R 4 2 +--R (cos(x) - 2cos(x) + 1)sin(x) +--R Type: Expression(Complex(Fraction(Integer))) +--E 466 + +--S 467 of 546 +t0484:= sin(x)/(a+b*cot(x)) +--R +--R +--R sin(x) +--R (432) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 546 +r0484:= -b^2*atanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ + a*cos(x)/(a^2+b^2)-b*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R 2 b sin(x) - a cos(x) | 2 2 +--R b atanh(-------------------) + (- b sin(x) - a cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (433) ---------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 468 + +--S 469 of 546 +a0484:= integrate(t0484,x) +--R +--R +--R (434) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (- b - a b)sin(x) +--R + +--R 2 3 2 3 +--R (a b + a )cos(x) + a b + a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (- b sin(x) - a cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 469 + +--S 470 of 546 +m0484:= a0484-r0484 +--R +--R +--R (435) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (- b - a b)sin(x) +--R + +--R 2 3 2 3 +--R (a b + a )cos(x) + a b + a +--R / +--R a sin(x) + b cos(x) +--R + +--R 2 b sin(x) - a cos(x) +--R - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 470 + +--S 471 of 546 +d0484:= D(m0484,x) +--R +--R +--R (436) +--R 3 3 2 2 3 2 3 2 3 +--R b sin(x) - a b cos(x)sin(x) + (b cos(x) - b )sin(x) - a b cos(x) +--R + +--R 2 +--R a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 2 3 5 2 3 4 2 +--R (a b + a b )sin(x) + (b - a b - 2a b)cos(x)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R ((- 2a b - a b + a )cos(x) - a b - 2a b - a )sin(x) +--R + +--R 2 3 4 3 5 2 3 4 +--R (a b + a b)cos(x) + (- b - 2a b - a b)cos(x) +--R Type: Expression(Integer) +--E 471 + +--S 472 of 546 +t0485:= sin(x)^2/(a+b*cot(x)) +--R +--R +--R 2 +--R sin(x) +--R (437) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 546 +r0485:= -1/2*(-a^3*x-3*a*b^2*x+2*b^3*log(b*cos(x)+a*sin(x))+_ + a^3*sin(x)*cos(x)+b^2*a*sin(x)*cos(x)+a^2*b-a^2*b*cos(x)^2+_ + b^3-b^3*cos(x)^2)/(a^2+b^2)^2 +--R +--R +--R (438) +--R 3 2 3 +--R - 2b log(a sin(x) + b cos(x)) + (- a b - a )cos(x)sin(x) +--R + +--R 3 2 2 2 3 3 2 +--R (b + a b)cos(x) + (3a b + a )x - b - a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 473 + +--S 474 of 546 +a0485:= integrate(t0485,x) +--R +--R +--R (439) +--R 3 2 3 - 2a sin(x) - 2b cos(x) +--R 2b log(----------) - 2b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (- a b - a )cos(x)sin(x) + (b + a b)cos(x) + (3a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression(Integer),...) +--E 474 + +--S 475 of 546 +m0485:= a0485-r0485 +--R +--R +--R (440) +--R 3 3 2 +--R 2b log(a sin(x) + b cos(x)) + 2b log(----------) +--R cos(x) + 1 +--R + +--R 3 - 2a sin(x) - 2b cos(x) 3 2 +--R - 2b log(-----------------------) + b + a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 475 + +--S 476 of 546 +d0485:= D(m0485,x) +--R +--R +--R (441) 0 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 546 +t0486:= sin(x)^3/(a+b*cot(x)) +--R +--R +--R 3 +--R sin(x) +--R (442) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 546 +r0486:= 2/3*(-6*a^3*cos(1/2*x)^4*(a^2+b^2)^(1/2)+4*a^3*cos(1/2*x)^6*_ + (a^2+b^2)^(1/2)+4*b*cos(1/2*x)^5*sin(1/2*x)*(a^2+b^2)^(1/2)*a^2-_ + 4*b*cos(1/2*x)^3*sin(1/2*x)*(a^2+b^2)^(1/2)*a^2-6*a*cos(1/2*x)^4*_ + (a^2+b^2)^(1/2)*b^2+4*a*cos(1/2*x)^6*(a^2+b^2)^(1/2)*b^2-_ + 3*a*cos(1/2*x)^2*(a^2+b^2)^(1/2)*b^2-3*b^4*atanh(1/(a^2+b^2)^(1/2)*_ + (b*cos(x)-b+a*sin(x))/sin(x))+4*b^3*cos(1/2*x)^5*sin(1/2*x)*_ + (a^2+b^2)^(1/2)-3*b^3*cos(1/2*x)*sin(1/2*x)*(a^2+b^2)^(1/2)-_ + 4*b^3*cos(1/2*x)^3*sin(1/2*x)*(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2) +--R +--R +--R (443) +--R 4 a sin(x) + b cos(x) - b +--R - 6b atanh(-----------------------) +--R +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R + +--R 3 2 x 5 3 2 x 3 3 x x +--R ((8b + 8a b)cos(-) + (- 8b - 8a b)cos(-) - 6b cos(-))sin(-) +--R 2 2 2 2 +--R + +--R 2 3 x 6 2 3 x 4 2 x 2 +--R (8a b + 8a )cos(-) + (- 12a b - 12a )cos(-) - 6a b cos(-) +--R 2 2 2 +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 478 + +--S 479 of 546 +a0486:= integrate(t0486,x) +--R +--R +--R (444) +--R 4 +--R 3b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (- b - a b)sin(x) +--R + +--R 2 3 2 3 +--R (a b + a )cos(x) + a b + a +--R / +--R a sin(x) + b cos(x) +--R + +--R 3 2 2 3 2 2 3 3 +--R ((b + a b)cos(x) - 4b - a b)sin(x) + (a b + a )cos(x) +--R + +--R 2 3 +--R (- 6a b - 3a )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 479 + +--S 480 of 546 +m0486:= a0486-r0486 +--R +--R +--R (445) +--R 4 +--R 3b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (- b - a b)sin(x) +--R + +--R 2 3 2 3 +--R (a b + a )cos(x) + a b + a +--R / +--R a sin(x) + b cos(x) +--R + +--R 4 a sin(x) + b cos(x) - b +--R 6b atanh(-----------------------) +--R +-------+ +--R | 2 2 +--R sin(x)\|b + a +--R + +--R 3 2 2 3 2 +--R ((b + a b)cos(x) - 4b - a b)sin(x) +--R + +--R 3 2 x 5 3 2 x 3 3 x x +--R ((- 8b - 8a b)cos(-) + (8b + 8a b)cos(-) + 6b cos(-))sin(-) +--R 2 2 2 2 +--R + +--R 2 3 3 2 3 2 3 x 6 +--R (a b + a )cos(x) + (- 6a b - 3a )cos(x) + (- 8a b - 8a )cos(-) +--R 2 +--R + +--R 2 3 x 4 2 x 2 +--R (12a b + 12a )cos(-) + 6a b cos(-) +--R 2 2 +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 480 + +--S 481 of 546 +d0486:= D(m0486,x) +--R +--R +--R (446) +--R 2 5 4 3 6 +--R (- 2a b - 2a b )cos(x)sin(x) +--R + +--R 6 3 4 5 2 2 6 5 2 3 4 +--R (- 2a b + a b + 3a b )cos(x) + (2a b - 2a b )cos(x) + 6a b +--R + +--R 5 2 +--R 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 x 4 2 5 4 3 x 2 2 5 +--R ((20a b + 20a b )cos(-) + (- 12a b - 12a b )cos(-) - 3a b ) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 4 5 2 x 5 3 4 5 2 x 3 +--R (24a b + 24a b )cos(-) + (- 24a b - 24a b )cos(-) +--R 2 2 +--R + +--R 3 4 x +--R - 6a b cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 3 +--R (6a b + 11a b + 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (2b - 5a b - 10a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 x 6 +--R (8a b - 6a b - 5a b)cos(x) + (- 4a b - 4a b )cos(-) +--R 2 +--R + +--R 2 5 4 3 x 4 2 5 x 2 7 2 5 4 3 6 +--R (4a b + 4a b )cos(-) + 3a b cos(-) - 3b - 15a b + 3a b + 3a b +--R 2 2 +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 x 4 +--R (20a b - 40a b - 60a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 6 3 4 +--R (- 12a b + 24a b + 36a b )cos(-) - 3a b + 9a b +--R 2 +--R * +--R cos(x) +--R + +--R 6 5 2 x 4 6 5 2 x 2 6 +--R (- 20a b + 20a b )cos(-) + (12a b - 12a b )cos(-) + 3a b +--R 2 2 +--R + +--R 3 4 +--R - 3a b +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 x 5 +--R (24a b - 48a b - 72a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 +--R (- 24a b + 48a b + 72a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 x +--R (- 6a b + 18a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 2 5 6 x 5 2 5 6 x 3 +--R (- 24a b + 24a b)cos(-) + (24a b - 24a b)cos(-) +--R 2 2 +--R + +--R 2 5 4 3 x +--R (6a b - 6a b )cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 6 3 4 5 2 7 4 +--R (3a b + 6a b - 3a b - 6a )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 8a b - 20a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (6a b + 12a b + 24a b + 12a )cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (- 4a b + 8a b + 12a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 6 3 4 x 2 +--R (4a b - 8a b - 12a b )cos(-) + (3a b - 9a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 +--R - 4a b + 32a b + 12a b +--R * +--R cos(x) +--R + +--R 6 5 2 x 6 6 5 2 x 4 +--R (4a b - 4a b )cos(-) + (- 4a b + 4a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 x 2 6 3 4 5 2 7 +--R (- 3a b + 3a b )cos(-) + 3a b - 18a b - 21a b - 6a +--R 2 +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 6 x 4 +--R (- 80a b - 40a b + 40a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 2 2 5 4 3 +--R (48a b + 24a b - 24a b)cos(-) + 12a b - 6a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 5 4 3 x 4 +--R (- 20b + 80a b + 100a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 2 7 2 5 +--R (12b - 48a b - 60a b )cos(-) + 3b - 15a b +--R 2 +--R * +--R cos(x) +--R + +--R 2 5 4 3 6 x 4 +--R (- 60a b - 100a b - 40a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 2 2 5 4 3 +--R (36a b + 60a b + 24a b)cos(-) + 9a b + 6a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 4 5 2 7 x 5 +--R (- 96a b - 48a b + 48a )cos(-) +--R 2 +--R + +--R 3 4 5 2 7 x 3 3 4 5 2 x +--R (96a b + 48a b - 48a )cos(-) + (24a b - 12a b )cos(-) +--R 2 2 +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 5 +--R (- 24a b + 96a b + 120a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 3 6 3 4 x +--R (24a b - 96a b - 120a b )cos(-) + (6a b - 30a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R + +--R 3 4 5 2 7 x 5 +--R (- 72a b - 120a b - 48a )cos(-) +--R 2 +--R + +--R 3 4 5 2 7 x 3 3 4 5 2 x +--R (72a b + 120a b + 48a )cos(-) + (18a b + 12a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 5 +--R (- 3a b - 10a b - 7a b)cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (- 3b - 11a b - 5a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (4b + 28a b + 32a b + 14a b)cos(x) +--R + +--R 2 5 4 3 6 x 6 +--R (16a b + 8a b - 8a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 4 2 5 4 3 x 2 +--R (- 16a b - 8a b + 8a b)cos(-) + (- 12a b + 6a b )cos(-) +--R 2 2 +--R + +--R 7 2 5 4 3 6 +--R 2b + 4a b - 4a b - 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 5 4 3 x 6 +--R (4b - 16a b - 20a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 4 7 2 5 x 2 +--R (- 4b + 16a b + 20a b )cos(-) + (- 3b + 15a b )cos(-) +--R 2 2 +--R + +--R 2 5 4 3 6 +--R - 21a b - 22a b - 7a b +--R * +--R cos(x) +--R + +--R 2 5 4 3 6 x 6 +--R (12a b + 20a b + 8a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 4 2 5 4 3 x 2 +--R (- 12a b - 20a b - 8a b)cos(-) + (- 9a b - 6a b )cos(-) +--R 2 2 +--R + +--R 7 2 5 4 3 6 +--R 3b + 15a b + 9a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 x 4 +--R (- 20a b + 40a b + 60a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 6 3 4 +--R (12a b - 24a b - 36a b )cos(-) + 3a b - 9a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (100a b + 80a b - 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 6 3 4 +--R (- 60a b - 48a b + 12a b )cos(-) - 15a b + 3a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (- 100a b - 160a b - 60a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 6 3 4 +--R (60a b + 96a b + 36a b )cos(-) + 15a b + 9a b +--R 2 +--R * +--R cos(x) +--R + +--R 6 3 4 5 2 x 4 +--R (20a b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 2 6 3 4 +--R (- 12a b - 24a b - 12a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 6 x 5 +--R (- 24a b + 48a b + 72a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 2 5 4 3 x +--R (24a b - 48a b - 72a b)cos(-) + (6a b - 18a b )cos(-) +--R 2 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (120a b + 96a b - 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 +--R (- 120a b - 96a b + 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 x +--R (- 30a b + 6a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (- 120a b - 192a b - 72a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 +--R (120a b + 192a b + 72a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 x +--R (30a b + 18a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 2 5 4 3 6 x 5 +--R (24a b + 48a b + 24a b)cos(-) +--R 2 +--R + +--R 2 5 4 3 6 x 3 2 5 4 3 x +--R (- 24a b - 48a b - 24a b)cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 6 3 4 6 6 3 4 5 2 5 +--R (- a b - a b )cos(x) + (2a b + 4a b + 2a b )cos(x) +--R + +--R 6 3 4 4 +--R (5a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (4a b - 8a b - 12a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 6 3 4 x 2 +--R (- 4a b + 8a b + 12a b )cos(-) + (- 3a b + 9a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 5 2 +--R - 16a b + 4a b - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (- 20a b - 16a b + 4a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 6 3 4 x 2 +--R (20a b + 16a b - 4a b )cos(-) + (15a b - 3a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 +--R 11a b + 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 6 +--R (20a b + 32a b + 12a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 4 +--R (- 20a b - 32a b - 12a b )cos(-) +--R 2 +--R + +--R 6 3 4 x 2 6 3 4 5 2 +--R (- 15a b - 9a b )cos(-) + 2a b - 8a b + 2a b +--R 2 +--R * +--R cos(x) +--R + +--R 6 3 4 5 2 x 6 6 3 4 5 2 x 4 +--R (- 4a b - 8a b - 4a b )cos(-) + (4a b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 x 2 6 +--R (3a b + 3a b )cos(-) - 3a b +--R 2 +--R * +--R sin(x) +--R + +--R 2 5 4 3 x 4 2 5 4 3 x 2 2 5 +--R ((20a b + 20a b )cos(-) + (- 12a b - 12a b )cos(-) - 3a b ) +--R 2 2 +--R * +--R 4 +--R cos(x) +--R + +--R 7 4 3 x 4 7 4 3 x 2 7 +--R (20b - 20a b )cos(-) + (- 12b + 12a b )cos(-) - 3b +--R 2 2 +--R + +--R 2 5 +--R 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 2 5 4 3 x 4 +--R (- 40b - 60a b - 20a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 2 7 2 5 +--R (24b + 36a b + 12a b )cos(-) + 6b + 3a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 5 4 3 x 4 +--R (20b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 7 2 5 4 3 x 2 7 2 5 +--R (- 12b - 24a b - 12a b )cos(-) - 3b - 3a b +--R 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 3 4 5 2 x 5 3 4 5 2 x 3 +--R (24a b + 24a b )cos(-) + (- 24a b - 24a b )cos(-) +--R 2 2 +--R + +--R 3 4 x +--R - 6a b cos(-) +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 x 5 6 5 2 x 3 +--R (24a b - 24a b )cos(-) + (- 24a b + 24a b )cos(-) +--R 2 2 +--R + +--R 6 3 4 x +--R (- 6a b + 6a b )cos(-) +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 4 5 2 x 5 +--R (- 48a b - 72a b - 24a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 3 6 3 4 x +--R (48a b + 72a b + 24a b )cos(-) + (12a b + 6a b )cos(-) +--R 2 2 +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 4 5 2 x 5 +--R (24a b + 48a b + 24a b )cos(-) +--R 2 +--R + +--R 6 3 4 5 2 x 3 6 3 4 x +--R (- 24a b - 48a b - 24a b )cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 2 5 4 3 7 7 4 3 6 +--R (a b + a b )cos(x) + (b - a b )cos(x) +--R + +--R 7 2 5 4 3 5 +--R (- 2b - 7a b - 2a b )cos(x) +--R + +--R 2 5 4 3 x 6 2 5 4 3 x 4 2 5 x 2 +--R (- 4a b - 4a b )cos(-) + (4a b + 4a b )cos(-) + 3a b cos(-) +--R 2 2 2 +--R + +--R 2 5 4 3 +--R 14a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 4 3 x 6 7 4 3 x 4 +--R (- 4b + 4a b )cos(-) + (4b - 4a b )cos(-) +--R 2 2 +--R + +--R 7 2 5 x 2 7 2 5 4 3 +--R (3b - 3a b )cos(-) + 8b + 3a b + a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 7 2 5 4 3 x 6 7 2 5 4 3 x 4 +--R (8b + 12a b + 4a b )cos(-) + (- 8b - 12a b - 4a b )cos(-) +--R 2 2 +--R + +--R 7 2 5 x 2 7 2 5 4 3 +--R (- 6b - 3a b )cos(-) - 7b - 14a b - a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 2 5 4 3 x 6 7 2 5 4 3 x 4 +--R (- 4b - 8a b - 4a b )cos(-) + (4b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 7 2 5 x 2 2 5 +--R (3b + 3a b )cos(-) + 3a b +--R 2 +--R * +--R cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 7 3 5 5 3 6 +--R (2a b + 4a b + 2a b )cos(x)sin(x) +--R + +--R 8 2 6 4 4 6 2 2 2 6 4 4 6 2 +--R (2b + a b - 4a b - 3a b )cos(x) + (2a b + 4a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 +--R - 6a b - 9a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 5 +--R (- 24a b - 48a b - 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (24a b + 48a b + 24a b )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 3 +--R (- 6a b - 17a b - 16a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (6a b + 15a b + 12a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 +--R (- 4a b + 6a b + 15a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 x 2 7 3 5 5 3 7 +--R (- 3a b - 3a b )cos(-) + 9a b + 3a b - 9a b - 3a b +--R 2 +--R * +--R 4 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (- 20b + 20a b + 100a b + 60a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 2 8 2 6 4 4 +--R (12b - 12a b - 60a b - 36a b )cos(-) + 3b - 6a b - 9a b +--R 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 2 6 4 4 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 5 +--R (- 24a b + 24a b + 120a b + 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 3 +--R (24a b - 24a b - 120a b - 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (6a b - 12a b - 18a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (- 24a b - 48a b - 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (24a b + 48a b + 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 3b - 9a b - 3a b + 9a b + 6a )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (4b + 14a b + 16a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (2b + 4a b - 16a b - 30a b - 12a )cos(x) +--R + +--R 8 2 6 4 4 6 2 x 6 +--R (4b - 4a b - 20a b - 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (- 4b + 4a b + 20a b + 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 x 2 8 2 6 4 4 6 2 +--R (- 3b + 6a b + 9a b )cos(-) + 6b - 18a b - 30a b - 6a b +--R 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 2 6 4 4 x 2 8 2 6 4 4 6 2 8 +--R (- 3a b - 3a b )cos(-) - 3b + 3a b + 21a b + 21a b + 6a +--R 2 +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 7 x 4 +--R (80a b + 120a b - 40a b)cos(-) +--R 2 +--R + +--R 7 3 5 7 x 2 7 3 5 5 3 +--R (- 48a b - 72a b + 24a b)cos(-) - 12a b - 6a b + 6a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 60a b - 120a b - 60a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (36a b + 72a b + 36a b )cos(-) + 9a b + 9a b +--R 2 +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 4 +--R (20a b + 80a b + 100a b + 40a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 2 7 3 5 5 3 +--R (- 12a b - 48a b - 60a b - 24a b)cos(-) - 3a b - 9a b - 6a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 8 x 5 +--R (96a b + 144a b - 48a )cos(-) +--R 2 +--R + +--R 2 6 4 4 8 x 3 +--R (- 96a b - 144a b + 48a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (- 24a b - 12a b + 12a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (- 72a b - 144a b - 72a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (72a b + 144a b + 72a b )cos(-) + (18a b + 18a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 8 x 5 +--R (24a b + 96a b + 120a b + 48a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 x 3 +--R (- 24a b - 96a b - 120a b - 48a )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x +--R (- 6a b - 18a b - 12a b )cos(-) +--R 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 5 +--R (3a b + 13a b + 17a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (a b - a b - 5a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 14a b - 36a b - 36a b - 14a b)cos(x) +--R + +--R 7 3 5 7 x 6 +--R (- 16a b - 24a b + 8a b)cos(-) +--R 2 +--R + +--R 7 3 5 7 x 4 7 3 5 5 3 x 2 +--R (16a b + 24a b - 8a b)cos(-) + (12a b + 6a b - 6a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 5 3 7 +--R 2a b + 10a b + 14a b + 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 +--R (12a b + 24a b + 12a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 4 7 3 5 x 2 +--R (- 12a b - 24a b - 12a b )cos(-) + (- 9a b - 9a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 5 3 7 +--R 5a b + 17a b + 19a b + 7a b +--R * +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 6 +--R (- 4a b - 16a b - 20a b - 8a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 4 +--R (4a b + 16a b + 20a b + 8a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 5 3 7 +--R (3a b + 9a b + 6a b )cos(-) - 9a b - 15a b - 9a b - 3a b +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (20b - 20a b - 100a b - 60a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 2 8 2 6 +--R (- 12b + 12a b + 60a b + 36a b )cos(-) - 3b + 6a b +--R 2 +--R + +--R 4 4 +--R 9a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 6 6 2 x 4 +--R (- 40b - 60a b + 20a b )cos(-) +--R 2 +--R + +--R 8 2 6 6 2 x 2 8 2 6 4 4 +--R (24b + 36a b - 12a b )cos(-) + 6b + 3a b - 3a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (20b + 100a b + 140a b + 60a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 2 8 2 6 +--R (- 12b - 60a b - 84a b - 36a b )cos(-) - 3b - 12a b +--R 2 +--R + +--R 4 4 +--R - 9a b +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 2 2 6 4 4 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 5 +--R (24a b - 24a b - 120a b - 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 3 +--R (- 24a b + 24a b + 120a b + 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (- 6a b + 12a b + 18a b )cos(-) +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 7 3 5 7 x 5 +--R (- 48a b - 72a b + 24a b)cos(-) +--R 2 +--R + +--R 7 3 5 7 x 3 +--R (48a b + 72a b - 24a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (12a b + 6a b - 6a b )cos(-) +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 7 x 5 +--R (24a b + 120a b + 168a b + 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 7 x 3 +--R (- 24a b - 120a b - 168a b - 72a b)cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x +--R (- 6a b - 24a b - 18a b )cos(-) +--R 2 +--R * +--R cos(x) +--R + +--R 3 5 5 3 7 x 5 +--R (- 24a b - 48a b - 24a b)cos(-) +--R 2 +--R + +--R 3 5 5 3 7 x 3 3 5 5 3 x +--R (24a b + 48a b + 24a b)cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 8 2 6 4 4 6 8 2 6 4 4 6 2 5 +--R (b + 2a b + a b )cos(x) + (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 4 +--R (- 3b + 3a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 x 6 +--R (- 4b + 4a b + 20a b + 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (4b - 4a b - 20a b - 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 x 2 8 2 6 4 4 6 2 +--R (3b - 6a b - 9a b )cos(-) + 14b + 8a b - 2a b + 4a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 8 2 6 6 2 x 6 8 2 6 6 2 x 4 +--R (8b + 12a b - 4a b )cos(-) + (- 8b - 12a b + 4a b )cos(-) +--R 2 2 +--R + +--R 8 2 6 4 4 x 2 8 2 6 4 4 +--R (- 6b - 3a b + 3a b )cos(-) - 7b - 14a b - 7a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 8 2 6 4 4 6 2 x 6 +--R (- 4b - 20a b - 28a b - 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 6 2 x 4 +--R (4b + 20a b + 28a b + 12a b )cos(-) +--R 2 +--R + +--R 8 2 6 4 4 x 2 8 2 6 4 4 6 2 +--R (3b + 12a b + 9a b )cos(-) - 6b + 4a b + 8a b - 2a b +--R 2 +--R * +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 6 2 6 4 4 6 2 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 2 6 4 4 x 2 8 2 6 +--R (- 3a b - 3a b )cos(-) + 3b + 3a b +--R 2 +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (20a b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (- 12a b - 24a b - 12a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (20a b + 40a b + 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (- 12a b - 24a b - 12a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 x 4 +--R (- 20a b - 40a b - 20a b )cos(-) +--R 2 +--R + +--R 7 3 5 5 3 x 2 7 3 5 +--R (12a b + 24a b + 12a b )cos(-) + 3a b + 3a b +--R 2 +--R * +--R cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 5 +--R (- 24a b - 48a b - 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (24a b + 48a b + 24a b )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R 4 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (24a b + 48a b + 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (- 24a b - 48a b - 24a b )cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R 3 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (24a b + 48a b + 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (- 24a b - 48a b - 24a b )cos(-) + (- 6a b - 6a b )cos(-) +--R 2 2 +--R * +--R 2 +--R cos(x) +--R + +--R 2 6 4 4 6 2 x 5 +--R (- 24a b - 48a b - 24a b )cos(-) +--R 2 +--R + +--R 2 6 4 4 6 2 x 3 2 6 4 4 x +--R (24a b + 48a b + 24a b )cos(-) + (6a b + 6a b )cos(-) +--R 2 2 +--R * +--R cos(x) +--R * +--R x +--R sin(-) +--R 2 +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 6 +--R (- a b - 2a b - a b )cos(x) + (a b + 2a b + a b )cos(x) +--R + +--R 7 3 5 5 3 5 +--R (5a b + 7a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 x 2 7 3 5 5 3 +--R (- 3a b - 3a b )cos(-) - 14a b - 16a b - 2a b +--R 2 +--R * +--R 4 +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (- 4a b - 8a b - 4a b )cos(-) + (4a b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 x 2 7 3 5 5 3 +--R (3a b + 3a b )cos(-) - a b - 2a b - a b +--R 2 +--R * +--R 3 +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (- 4a b - 8a b - 4a b )cos(-) + (4a b + 8a b + 4a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 x 2 7 3 5 5 3 +--R (3a b + 3a b )cos(-) + 13a b + 14a b + a b +--R 2 +--R * +--R 2 +--R cos(x) +--R + +--R 7 3 5 5 3 x 6 7 3 5 5 3 x 4 +--R (4a b + 8a b + 4a b )cos(-) + (- 4a b - 8a b - 4a b )cos(-) +--R 2 2 +--R + +--R 7 3 5 x 2 7 3 5 +--R (- 3a b - 3a b )cos(-) - 3a b - 3a b +--R 2 +--R * +--R cos(x) +--R / +--R 2 6 4 4 6 2 4 +--R (3a b + 6a b + 3a b )sin(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (3a b - 3a b - 15a b - 9a b)cos(x) - 3a b - 3a b + 3a b +--R + +--R 7 +--R 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 8 2 +--R (- 12a b - 18a b + 6a )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 6 4 4 6 2 +--R (- 3b + 9a b + 27a b + 15a b )cos(x) - 9a b - 24a b - 21a b +--R + +--R 8 +--R - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 3a b + 3a b + 15a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (15a b + 27a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 15a b - 39a b - 33a b - 9a b)cos(x) + 3a b + 9a b + 9a b +--R + +--R 7 +--R 3a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 8 2 6 4 4 6 2 3 +--R (3a b + 6a b + 3a b )cos(x) + (3b + 3a b - 3a b - 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 6b - 15a b - 12a b - 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 +--R (3b + 9a b + 9a b + 3a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 3a b - 9a b - 9a b - 3a b )sin(x) +--R + +--R 9 4 5 6 3 8 2 7 4 5 6 3 8 +--R ((- 3b + 18a b + 24a b + 9a b)cos(x) - 3a b - 9a b - 9a b - 3a b) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (12a b + 30a b + 18a b - 6a b - 6a )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (- 9a b - 27a b - 27a b - 9a b )cos(x) + 3a b + 15a b + 27a b +--R + +--R 7 2 9 +--R 21a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 9 4 5 6 3 8 3 +--R (3b - 18a b - 24a b - 9a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (- 6b - 15a b - 9a b + 3a b + 3a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 7 4 5 6 3 +--R (3b + 18a b + 36a b + 30a b + 9a b)cos(x) - 3a b - 9a b - 9a b +--R + +--R 8 +--R - 3a b +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 3a b - 9a b - 9a b - 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (3a b + 9a b + 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (3a b + 9a b + 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 +--R (- 3a b - 9a b - 9a b - 3a b )cos(x) +--R Type: Expression(Integer) +--E 481 + +--S 482 of 546 +t0487:= cos(x)/(a+b*cot(x)) +--R +--R +--R cos(x) +--R (447) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 546 +r0487:= a*b*atanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ + b*cos(x)/(a^2+b^2)+a*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R b sin(x) - a cos(x) | 2 2 +--R - a b atanh(-------------------) + (a sin(x) - b cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (448) ------------------------------------------------------------------ +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 483 + +--S 484 of 546 +a0487:= integrate(t0487,x) +--R +--R +--R (449) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (a sin(x) - b cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 484 + +--S 485 of 546 +m0487:= a0487-r0487 +--R +--R +--R (450) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R b sin(x) - a cos(x) +--R a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 485 + +--S 486 of 546 +d0487:= D(m0487,x) +--R +--R +--R (451) +--R 2 3 2 2 2 2 2 +--R a b sin(x) - a b cos(x)sin(x) + (a b cos(x) - a b )sin(x) +--R + +--R 2 3 2 +--R - a b cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 4 3 2 3 5 2 3 4 2 +--R (a b + a b )sin(x) + (b - a b - 2a b)cos(x)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R ((- 2a b - a b + a )cos(x) - a b - 2a b - a )sin(x) +--R + +--R 2 3 4 3 5 2 3 4 +--R (a b + a b)cos(x) + (- b - 2a b - a b)cos(x) +--R Type: Expression(Integer) +--E 486 + +--S 487 of 546 +t0488:= cos(x)^2/(a+b*cot(x)) +--R +--R +--R 2 +--R cos(x) +--R (452) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 546 +r0488:= -1/2*(a*b^2*x-a^3*x+2*a^2*b*log(b*cos(x)+a*sin(x))-_ + a^3*sin(x)*cos(x)-b^2*a*sin(x)*cos(x)-a^2*b+a^2*b*cos(x)^2-_ + b^3+b^3*cos(x)^2)/(a^2+b^2)^2 +--R +--R +--R (453) +--R 2 2 3 +--R - 2a b log(a sin(x) + b cos(x)) + (a b + a )cos(x)sin(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- b - a b)cos(x) + (- a b + a )x + b + a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 488 + +--S 489 of 546 +a0488:= integrate(t0488,x) +--R +--R +--R (454) +--R 2 2 2 - 2a sin(x) - 2b cos(x) +--R 2a b log(----------) - 2a b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (a b + a )cos(x)sin(x) + (- b - a b)cos(x) + (- a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression(Integer),...) +--E 489 + +--S 490 of 546 +m0488:= a0488-r0488 +--R +--R +--R (455) +--R 2 2 2 +--R 2a b log(a sin(x) + b cos(x)) + 2a b log(----------) +--R cos(x) + 1 +--R + +--R 2 - 2a sin(x) - 2b cos(x) 3 2 +--R - 2a b log(-----------------------) - b - a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 490 + +--S 491 of 546 +d0488:= D(m0488,x) +--R +--R +--R (456) 0 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 546 +t0489:= cot(x)/(a+b*cot(x)) +--R +--R +--R cot(x) +--R (457) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 492 + +--S 493 of 546 +r0489:= (b*x+a*log(b*cos(x)+a*sin(x)))/(a^2+b^2) +--R +--R +--R a log(a sin(x) + b cos(x)) + b x +--R (458) -------------------------------- +--R 2 2 +--R b + a +--R Type: Expression(Integer) +--E 493 + +--S 494 of 546 +a0489:= integrate(t0489,x) +--R +--R +--R a sin(2x) + b cos(2x) + b 2 +--R 2a log(-------------------------) - a log(-----------) + 2b x +--R cos(2x) + 1 cos(2x) + 1 +--R (459) ------------------------------------------------------------- +--R 2 2 +--R 2b + 2a +--R Type: Union(Expression(Integer),...) +--E 494 + +--S 495 of 546 +m0489:= a0489-r0489 +--R +--R +--R (460) +--R a sin(2x) + b cos(2x) + b +--R 2a log(-------------------------) - 2a log(a sin(x) + b cos(x)) +--R cos(2x) + 1 +--R + +--R 2 +--R - a log(-----------) +--R cos(2x) + 1 +--R / +--R 2 2 +--R 2b + 2a +--R Type: Expression(Integer) +--E 495 + +--S 496 of 546 +d0489:= D(m0489,x) +--R +--R +--R (461) +--R 3 2 2 +--R (a sin(x) + a b cos(x))sin(2x) +--R + +--R 2 3 2 3 +--R ((- a b - a )cos(x)cos(2x) + (- a b - a )cos(x))sin(2x) +--R + +--R 2 3 2 2 3 2 +--R ((a b + 2a )cos(2x) + (2a b + 2a )cos(2x) + a b )sin(x) +--R + +--R 2 2 2 +--R a b cos(x)cos(2x) - a b cos(x) +--R / +--R 2 2 4 2 2 4 3 3 +--R ((a b + a )cos(2x) + a b + a )sin(x) + (a b + a b)cos(x)cos(2x) +--R + +--R 3 3 +--R (a b + a b)cos(x) +--R * +--R sin(2x) +--R + +--R 3 3 2 3 3 3 3 +--R ((a b + a b)cos(2x) + (2a b + 2a b)cos(2x) + a b + a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 4 2 2 +--R (b + a b )cos(x)cos(2x) + (2b + 2a b )cos(x)cos(2x) + (b + a b )cos(x) +--R Type: Expression(Integer) +--E 496 + +--S 497 of 546 +t0490:= sec(x)/(a+b*cot(x)) +--R +--R +--R sec(x) +--R (462) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 497 + +--S 498 of 546 +r0490:= atanh(sin(x))/a+b*atanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/a/_ + (a^2+b^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 2 b sin(x) - a cos(x) +--R \|b + a atanh(sin(x)) - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R (463) ------------------------------------------------------ +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression(Integer) +--E 498 + +--S 499 of 546 +a0490:= integrate(t0490,x) +--R +--R +--R (464) +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b + a log(-------------------) - \|b + a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Union(Expression(Integer),...) +--E 499 + +--S 500 of 546 +m0490:= a0490-r0490 +--R +--R +--R (465) +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b + a log(-------------------) - \|b + a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 b sin(x) - a cos(x) +--R - \|b + a atanh(sin(x)) + b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression(Integer) +--E 500 + +--S 501 of 546 +d0490:= D(m0490,x) +--R +--R +--R (466) +--R 5 2 3 8 4 3 2 4 3 2 7 +--R (b - a b )sin(x) + ((- 4a b + 4a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 2 3 4 5 2 3 +--R (5a b - 5a b)cos(x) + (- 4a b - 3a b)cos(x) - 3b + a b +--R + +--R 4 +--R 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 5 3 4 3 2 5 2 +--R (- 2a b + 2a )cos(x) + (a b + 7a b + 2a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (13a b + 3a b - 2a )cos(x) - a b - 3a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- b + 5a b - 4a b)cos(x) + (- 2a b - 7a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 5 2 3 4 +--R (b - 12a b - a b)cos(x) + a b cos(x) + 3b + a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 5 3 2 5 4 +--R (2a b - 4a b + 2a )cos(x) + (3a b + 3a )cos(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (3a b + 8a b - 3a )cos(x) + (- 4a b - 13a b - 5a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (- 14a b - 13a b + a )cos(x) - a b + a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- a b + a b)cos(x) + (2a b - 3a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (2b - 3a b - 7a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 5 2 3 +--R (- 2b + 8a b + 10a b)cos(x) + (4a b + 4a b)cos(x) - b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 6 4 3 2 5 5 +--R (- 3a b + a )cos(x) + (- 4a b - 3a b + a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 4a b - 2a b - 2a )cos(x) + (- a b - 3a b - 2a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R (3a b + 4a b + a )cos(x) + (5a b + 6a b + a )cos(x) + a b +--R + +--R 3 2 +--R a b +--R * +--R sin(x) +--R + +--R 4 7 2 3 4 6 2 3 4 5 +--R a b cos(x) + (2a b + 2a b)cos(x) + (2a b + a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 3 +--R (- b - a b )cos(x) + (- a b - a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 +--R (b - a b - 2a b)cos(x) + (- a b - a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 5 3 3 8 +--R (- a b - a b )sin(x) +--R + +--R 6 2 4 4 2 6 4 2 7 +--R ((- 2b + 2a b + 4a b )cos(x) - b + a b )sin(x) +--R + +--R 5 3 3 5 2 3 3 5 5 3 3 +--R (4a b - a b - 5a b)cos(x) + (- 3a b - 3a b)cos(x) + a b + 3a b +--R + +--R 5 +--R 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 2 4 4 2 6 3 +--R (- 2b - 2a b + 2a b + 2a )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- b + 4a b + 7a b + 2a )cos(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 6 +--R (6b + 9a b + a b - 2a )cos(x) + 3b + 2a b - 3a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (5a b + a b - 4a b)cos(x) + (2a b - 5a b - 7a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 3 3 +--R (- 7a b - 8a b - a b)cos(x) + (- a b - a b )cos(x) + a b - a b +--R + +--R 5 +--R - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R (- 4a b - 2a b + 2a )cos(x) + (a b + 4a b + 3a )cos(x) +--R + +--R 6 2 4 4 2 6 3 +--R (4b + 11a b + 4a b - 3a )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (2b - 7a b - 14a b - 5a )cos(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 6 +--R (- 6b - 18a b - 11a b + a )cos(x) - 3b - 4a b + a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (a b + a b)cos(x) + (2a b - a b - 3a b)cos(x) +--R + +--R 5 3 3 5 4 5 5 3 +--R (- 2a b - 9a b - 7a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 5 +--R (4a b + 14a b + 10a b)cos(x) + (2a b + 6a b + 4a b)cos(x) - a b +--R + +--R 3 3 +--R - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b - 2a b + a )cos(x) + (- 4a b - 3a b + a )cos(x) +--R + +--R 2 4 4 2 6 4 6 2 4 4 2 6 3 +--R (- 2a b - 4a b - 2a )cos(x) + (- 2b - 3a b - 3a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (- b + 3a b + 5a b + a )cos(x) + (2b + 7a b + 6a b + a )cos(x) +--R + +--R 6 2 4 4 2 +--R b + 2a b + a b +--R * +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 3 3 5 5 +--R (a b + a b)cos(x) + (2a b + 2a b)cos(x) + (a b + a b)cos(x) +--R + +--R 5 3 3 4 5 5 3 +--R (a b + a b )cos(x) + (a b - a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- a b - 3a b - 2a b)cos(x) + (- a b - 2a b - a b)cos(x) +--R / +--R 3 3 8 2 4 4 2 2 4 4 2 7 +--R a b sin(x) + ((a b - 3a b )cos(x) - a b - a b )sin(x) +--R + +--R 3 3 5 2 5 3 3 5 3 3 +--R (- 4a b + 3a b)cos(x) + (- a b - a b + 2a b)cos(x) - 3a b +--R + +--R 5 +--R - a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (- a b + 6a b - a )cos(x) + (a b + 8a b - a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- a b + 8a b + a )cos(x) + 3a b + 4a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (3a b - 4a b)cos(x) + (a b + 4a b - 9a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (2a b + 7a b - 8a b)cos(x) + (3a b + 4a b - a b)cos(x) +--R + +--R 3 3 5 +--R 3a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 6 5 2 4 4 2 6 4 +--R (- 3a b + a )cos(x) + (- 2a b - 7a b + 3a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (- 2a b - 11a b + 3a )cos(x) + (- 2a b - 11a b - a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- a b - 9a b - 4a )cos(x) - 3a b - 5a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 3 3 5 5 3 3 5 4 +--R a b cos(x) + (a b + 3a b)cos(x) + (- 2a b + 6a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (- 2a b - 7a b + 7a b)cos(x) + (- 4a b - 8a b + 2a b)cos(x) +--R + +--R 5 3 3 5 3 3 5 +--R (- 3a b - 5a b - 2a b)cos(x) - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 5 2 4 4 2 6 4 +--R (3a b - a )cos(x) + (2a b + 7a b - 3a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (3a b + 5a b - 2a )cos(x) + (a b + 3a b + 2a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (a b + 4a b + 3a )cos(x) + a b + 2a b + a +--R * +--R sin(x) +--R + +--R 5 6 3 3 5 5 3 3 5 4 +--R - a b cos(x) + (- a b - 3a b)cos(x) + (- a b - 2a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (a b + 3a b + 2a b)cos(x) + (2a b + 5a b + 3a b)cos(x) +--R + +--R 5 3 3 5 +--R (a b + 2a b + a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 5 4 3 8 +--R (a b + a b )sin(x) +--R + +--R 6 3 4 5 2 3 4 5 2 7 +--R ((a b - 2a b - 3a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 4a b - a b + 3a b)cos(x) + (- 3a b - a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 +--R - 3a b - 4a b - a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- a b + 5a b + 5a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b + 7a b + 8a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- 3a b + 5a b + 9a b + a )cos(x) + 3a b + 4a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (3a b - a b - 4a b)cos(x) + (7a b - 2a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 2 5 +--R (11a b + 3a b - 8a b)cos(x) + (7a b + 6a b - a b)cos(x) + 3a b +--R + +--R 4 3 6 +--R 5a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R (- 3a b - 2a b + a )cos(x) + (- 8a b - 5a b + 3a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (2a b - 11a b - 10a b + 3a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (4a b - 8a b - 13a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (3a b - 4a b - 11a b - 4a )cos(x) - 3a b - 5a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (a b + a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 4a b + 2a b + 6a b)cos(x) + (- 10a b - 3a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 10a b - 8a b + 2a b)cos(x) + (- 5a b - 7a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 +--R - a b - 2a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R (3a b + 2a b - a )cos(x) + (8a b + 5a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- a b + 6a b + 5a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b + a b + 5a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- a b + a b + 5a b + 3a )cos(x) + a b + 2a b + a +--R * +--R sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (- a b - a b)cos(x) + (- 3a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (a b - a b - 2a b)cos(x) + (3a b + 5a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (3a b + 6a b + 3a b)cos(x) + (a b + 2a b + a b)cos(x) +--R Type: Expression(Integer) +--E 501 + +--S 502 of 546 +t0491:= sec(x)^3/(a+b*cot(x)) +--R +--R +--R 3 +--R sec(x) +--R (467) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 502 + +--S 503 of 546 +r0491:= (a^2+2*b^2)*atanh(tan(1/2*x))/a^3+2*b*(a^2+b^2)^(1/2)*_ + atanh((a-b*tan(1/2*x))/(a^2+b^2)^(1/2))/a^3+_ + 1/2/a/(1-tan(1/2*x))^2-1/2*(a+2*b)/a^2/(1-tan(1/2*x))-_ + 1/2/a/(1+tan(1/2*x))^2+1/2*(a-2*b)/a^2/(1+tan(1/2*x)) +--R +--R +--R (468) +--R 2 2 x 4 2 2 x 2 2 2 x +--R ((2b + a )tan(-) + (- 4b - 2a )tan(-) + 2b + a )atanh(tan(-)) +--R 2 2 2 +--R + +--R x +--R +-------+ b tan(-) - a +--R x 4 x 2 | 2 2 2 2 x 3 +--R (- 2b tan(-) + 4b tan(-) - 2b)\|b + a atanh(------------) + a tan(-) +--R 2 2 +-------+ 2 +--R | 2 2 +--R \|b + a +--R + +--R x 2 2 x +--R 2a b tan(-) + a tan(-) - 2a b +--R 2 2 +--R / +--R 3 x 4 3 x 2 3 +--R a tan(-) - 2a tan(-) + a +--R 2 2 +--R Type: Expression(Integer) +--E 503 + +--S 504 of 546 +a0491:= integrate(t0491,x) +--R +--R +--R (469) +--R +-------+ +--R 2 | 2 2 +--R 2b cos(x) \|b + a +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (b sin(x) - a cos(x) - a)\|b + a + a b sin(x) - a cos(x) - b +--R + +--R 2 +--R - a +--R / +--R a sin(x) + b cos(x) +--R + +--R 2 2 2 sin(x) + cos(x) + 1 +--R (2b + a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 sin(x) - cos(x) - 1 2 2 +--R (- 2b - a )cos(x) log(-------------------) + a sin(x) - 2a b cos(x) +--R cos(x) + 1 +--R + +--R - 2a b cos(x) +--R / +--R 3 2 +--R 2a cos(x) +--R Type: Union(Expression(Integer),...) +--E 504 + +--S 505 of 546 +m0491:= a0491-r0491 +--R +--R +--R (470) +--R +-------+ +--R 2 x 4 2 x 2 2 | 2 2 +--R (2b cos(x) tan(-) - 4b cos(x) tan(-) + 2b cos(x) )\|b + a +--R 2 2 +--R * +--R log +--R +-------+ +--R | 2 2 2 2 +--R (b sin(x) - a cos(x) - a)\|b + a + a b sin(x) - a cos(x) - b +--R + +--R 2 +--R - a +--R / +--R a sin(x) + b cos(x) +--R + +--R 2 2 2 x 4 2 2 2 x 2 +--R (2b + a )cos(x) tan(-) + (- 4b - 2a )cos(x) tan(-) +--R 2 2 +--R + +--R 2 2 2 +--R (2b + a )cos(x) +--R * +--R sin(x) + cos(x) + 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 x 4 2 2 2 x 2 +--R (- 2b - a )cos(x) tan(-) + (4b + 2a )cos(x) tan(-) +--R 2 2 +--R + +--R 2 2 2 +--R (- 2b - a )cos(x) +--R * +--R sin(x) - cos(x) - 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 x 4 2 2 2 x 2 +--R (- 4b - 2a )cos(x) tan(-) + (8b + 4a )cos(x) tan(-) +--R 2 2 +--R + +--R 2 2 2 +--R (- 4b - 2a )cos(x) +--R * +--R x +--R atanh(tan(-)) +--R 2 +--R + +--R +-------+ +--R 2 x 4 2 x 2 2 | 2 2 +--R (4b cos(x) tan(-) - 8b cos(x) tan(-) + 4b cos(x) )\|b + a +--R 2 2 +--R * +--R x +--R b tan(-) - a +--R 2 +--R atanh(------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 2 x 4 2 2 x 3 +--R (a sin(x) - 2a b cos(x) - 2a b cos(x))tan(-) - 2a cos(x) tan(-) +--R 2 2 +--R + +--R 2 x 2 2 2 x 2 +--R (- 2a sin(x) + 4a b cos(x))tan(-) - 2a cos(x) tan(-) + a sin(x) +--R 2 2 +--R + +--R 2 +--R 2a b cos(x) - 2a b cos(x) +--R / +--R 3 2 x 4 3 2 x 2 3 2 +--R 2a cos(x) tan(-) - 4a cos(x) tan(-) + 2a cos(x) +--R 2 2 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 546 +d0491:= D(m0491,x) +--R +--R +--R (471) +--R 3 2 6 4 4 5 +--R 2a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 3 4 3 2 2 3 2 +--R - 2a b cos(x) + (- 2a b - a b )cos(x) - 4a b cos(x) +--R + +--R 3 2 +--R - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (- 4b + 2a b + 2a b)cos(x) + (- 2b + 5a b + 3a b)cos(x) +--R + +--R 2 3 4 2 4 4 +--R (2a b + 5a b)cos(x) + 6a b cos(x) + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 4 3 2 3 +--R - 4a b cos(x) + (2a b - 5a b )cos(x) +--R + +--R 4 3 2 2 +--R (2a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (- 4b + 2a b + 2a b)cos(x) + (- 2b + 5a b + 5a b)cos(x) +--R + +--R 5 4 4 5 2 3 4 3 +--R (4b + 5a b)cos(x) + (2b - 5a b + 3a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 2a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 7 4 3 2 6 4 3 2 5 +--R 2a b cos(x) + (2a b - a b )cos(x) + (- 2a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 3 +--R (- 2a b + a b )cos(x) + a b cos(x) +--R * +--R x 8 +--R tan(-) +--R 2 +--R + +--R 4 6 5 5 5 +--R - 4a b sin(x) + (4a cos(x) + 4a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 4 +--R (4a b - 4a b)cos(x) + (4a b + 2a b)cos(x) + 8a b cos(x) +--R + +--R 4 +--R 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 5 3 +--R (8a b - 8a b )cos(x) + (4a b - 10a b - 2a )cos(x) +--R + +--R 3 2 5 2 5 5 +--R (- 4a b - 10a )cos(x) - 12a cos(x) - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 8a b cos(x) + 20a b cos(x) + (- 4a b + 14a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 4a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 4 3 2 5 5 +--R (8a b - 8a )cos(x) + (4a b - 2a b - 22a )cos(x) +--R + +--R 4 3 2 5 4 +--R (- 8a b + 4a b - 22a )cos(x) +--R + +--R 4 3 2 5 3 3 2 5 2 +--R (- 4a b + 10a b - 10a )cos(x) + (4a b - 2a )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 4a b - 4a b)cos(x) + (- 4a b - 10a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 4 3 +--R (4a b - 10a b)cos(x) + (4a b - 6a b)cos(x) - 2a b cos(x) +--R * +--R x 7 +--R tan(-) +--R 2 +--R + +--R 3 2 6 4 4 5 +--R - 8a b sin(x) + (8a b cos(x) + 8a b)sin(x) +--R + +--R 4 3 4 3 2 2 3 2 3 2 +--R (8a b cos(x) + (8a b + 4a b )cos(x) + 16a b cos(x) + 8a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (16b - 8a b - 8a b)cos(x) + (8b - 20a b - 12a b)cos(x) +--R + +--R 2 3 4 2 4 4 +--R (- 8a b - 20a b)cos(x) - 24a b cos(x) - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 4 3 2 3 +--R 16a b cos(x) + (- 8a b + 20a b )cos(x) +--R + +--R 4 3 2 2 +--R (- 8a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (16b - 8a b - 8a b)cos(x) + (8b - 20a b - 20a b)cos(x) +--R + +--R 5 4 4 5 2 3 4 3 +--R (- 16b - 20a b)cos(x) + (- 8b + 20a b - 12a b)cos(x) +--R + +--R 2 3 4 2 +--R (8a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 7 4 3 2 6 +--R - 8a b cos(x) + (- 8a b + 4a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 3 2 3 +--R (8a b + 4a b )cos(x) + (8a b - 4a b )cos(x) - 4a b cos(x) +--R * +--R x 6 +--R tan(-) +--R 2 +--R + +--R 4 6 5 5 5 +--R 12a b sin(x) + (- 12a cos(x) - 12a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 12a b - 12a b)cos(x) + (- 12a b - 6a b)cos(x) +--R + +--R 4 4 +--R - 24a b cos(x) - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (- 24a b + 24a )cos(x) + (- 12a b + 30a b + 30a )cos(x) +--R + +--R 3 2 5 2 5 5 +--R (12a b + 30a )cos(x) + 36a cos(x) + 12a +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 24a b cos(x) + 12a b cos(x) + (12a b - 18a b)cos(x) +--R + +--R 2 3 4 2 +--R (12a b - 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 24a b + 24a b )cos(x) + (- 12a b + 54a b - 6a )cos(x) +--R + +--R 4 3 2 5 4 +--R (24a b + 12a b - 6a )cos(x) +--R + +--R 4 3 2 5 3 3 2 5 2 +--R (12a b - 30a b + 6a )cos(x) + (- 12a b + 6a )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (12a b - 12a b)cos(x) + (12a b - 42a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 4 3 +--R (- 12a b - 42a b)cos(x) + (- 12a b - 6a b)cos(x) + 6a b cos(x) +--R * +--R x 5 +--R tan(-) +--R 2 +--R + +--R 3 2 6 4 4 5 +--R 12a b sin(x) + (- 12a b cos(x) - 12a b)sin(x) +--R + +--R 4 3 4 3 2 2 3 2 +--R - 12a b cos(x) + (- 12a b - 6a b )cos(x) - 24a b cos(x) +--R + +--R 3 2 +--R - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 4 +--R (- 24b + 12a b + 12a b)cos(x) +--R + +--R 5 2 3 4 3 2 3 4 2 +--R (- 12b + 30a b + 18a b)cos(x) + (12a b + 30a b)cos(x) +--R + +--R 4 4 +--R 36a b cos(x) + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 4 3 2 3 +--R - 24a b cos(x) + (12a b - 30a b )cos(x) +--R + +--R 4 3 2 2 +--R (12a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 6 +--R (- 24b + 12a b + 12a b)cos(x) +--R + +--R 5 2 3 4 5 5 4 4 +--R (- 12b + 30a b + 30a b)cos(x) + (24b + 30a b)cos(x) +--R + +--R 5 2 3 4 3 2 3 4 2 +--R (12b - 30a b + 18a b)cos(x) + (- 12a b + 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 7 4 3 2 6 +--R 12a b cos(x) + (12a b - 6a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 12a b - 6a b )cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 3 2 3 +--R 6a b cos(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 6 5 5 5 +--R - 12a b sin(x) + (12a cos(x) + 12a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (12a b - 12a b)cos(x) + (12a b + 6a b)cos(x) +--R + +--R 4 4 +--R 24a b cos(x) + 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 5 3 +--R (24a b - 24a b )cos(x) + (12a b - 30a b - 6a )cos(x) +--R + +--R 3 2 5 2 5 5 +--R (- 12a b - 30a )cos(x) - 36a cos(x) - 12a +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 24a b cos(x) + 60a b cos(x) + (- 12a b + 42a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 12a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 4 3 2 5 5 +--R (24a b - 24a )cos(x) + (12a b - 6a b - 66a )cos(x) +--R + +--R 4 3 2 5 4 +--R (- 24a b + 12a b - 66a )cos(x) +--R + +--R 4 3 2 5 3 3 2 5 2 +--R (- 12a b + 30a b - 30a )cos(x) + (12a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 12a b - 12a b)cos(x) + (- 12a b - 30a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 4 3 +--R (12a b - 30a b)cos(x) + (12a b - 18a b)cos(x) - 6a b cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 2 6 4 4 5 +--R - 8a b sin(x) + (8a b cos(x) + 8a b)sin(x) +--R + +--R 4 3 4 3 2 2 3 2 3 2 +--R (8a b cos(x) + (8a b + 4a b )cos(x) + 16a b cos(x) + 8a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (16b - 8a b - 8a b)cos(x) + (8b - 20a b - 12a b)cos(x) +--R + +--R 2 3 4 2 4 4 +--R (- 8a b - 20a b)cos(x) - 24a b cos(x) - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 4 3 2 3 +--R 16a b cos(x) + (- 8a b + 20a b )cos(x) +--R + +--R 4 3 2 2 +--R (- 8a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (16b - 8a b - 8a b)cos(x) + (8b - 20a b - 20a b)cos(x) +--R + +--R 5 4 4 5 2 3 4 3 +--R (- 16b - 20a b)cos(x) + (- 8b + 20a b - 12a b)cos(x) +--R + +--R 2 3 4 2 +--R (8a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 7 4 3 2 6 +--R - 8a b cos(x) + (- 8a b + 4a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 3 2 3 +--R (8a b + 4a b )cos(x) + (8a b - 4a b )cos(x) - 4a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 6 5 5 5 +--R 4a b sin(x) + (- 4a cos(x) - 4a )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 4a b - 4a b)cos(x) + (- 4a b - 2a b)cos(x) +--R + +--R 4 4 +--R - 8a b cos(x) - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 5 4 4 3 2 5 3 +--R (- 8a b + 8a )cos(x) + (- 4a b + 10a b + 10a )cos(x) +--R + +--R 3 2 5 2 5 5 +--R (4a b + 10a )cos(x) + 12a cos(x) + 4a +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 8a b cos(x) + 4a b cos(x) + (4a b - 6a b)cos(x) +--R + +--R 2 3 4 2 +--R (4a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 5 +--R (- 8a b + 8a b )cos(x) + (- 4a b + 18a b - 2a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (8a b + 4a b - 2a )cos(x) + (4a b - 10a b + 2a )cos(x) +--R + +--R 3 2 5 2 +--R (- 4a b + 2a )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (4a b - 4a b)cos(x) + (4a b - 14a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 4 3 +--R (- 4a b - 14a b)cos(x) + (- 4a b - 2a b)cos(x) + 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 6 4 4 5 +--R 2a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 3 4 3 2 2 3 2 3 2 +--R (- 2a b cos(x) + (- 2a b - a b )cos(x) - 4a b cos(x) - 2a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 3 +--R (- 4b + 2a b + 2a b)cos(x) + (- 2b + 5a b + 3a b)cos(x) +--R + +--R 2 3 4 2 4 4 +--R (2a b + 5a b)cos(x) + 6a b cos(x) + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 4 4 3 2 3 4 3 2 2 +--R (- 4a b cos(x) + (2a b - 5a b )cos(x) + (2a b - a b )cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (- 4b + 2a b + 2a b)cos(x) + (- 2b + 5a b + 5a b)cos(x) +--R + +--R 5 4 4 5 2 3 4 3 +--R (4b + 5a b)cos(x) + (2b - 5a b + 3a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 2a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 7 4 3 2 6 4 3 2 5 +--R 2a b cos(x) + (2a b - a b )cos(x) + (- 2a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 3 +--R (- 2a b + a b )cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 2 6 5 3 3 5 5 +--R 2a b sin(x) + (- 2a b cos(x) - 2a b - 2a b)sin(x) +--R + +--R 6 3 2 4 4 2 2 4 2 4 2 4 +--R (2b cos(x) + (- 2a b - a b )cos(x) - 4a b cos(x) - 2a b )sin(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 4a b + 2a b + 2a b)cos(x) + (2a b + 7a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 3 3 5 +--R (2a b + 3a b + 5a b)cos(x) + (4a b + 6a b)cos(x) + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 2a b - 4a b )cos(x) + (- 2b - a b - 5a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (2a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 4a b + 2a b + 2a b)cos(x) + (2a b + 7a b + 5a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (6a b + 3a b + 5a b)cos(x) + (- 2a b - 3a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- 2a b - a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 2 6 6 2 4 4 2 5 4 2 4 +--R - 2b cos(x) - a b cos(x) + (2b - a b - a b )cos(x) + a b cos(x) +--R + +--R 2 4 4 2 3 +--R (a b + a b )cos(x) +--R * +--R x 8 +--R tan(-) +--R 2 +--R + +--R 5 6 6 4 2 6 5 +--R - 4a b sin(x) + (4a cos(x) + 4a b + 4a )sin(x) +--R + +--R 5 5 3 3 3 5 2 5 +--R (- 4a b - 4a b)cos(x) + (4a b + 2a b)cos(x) + 8a b cos(x) +--R + +--R 5 +--R 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 4 4 2 6 3 +--R (8a b - 8a b )cos(x) + (- 4a b - 10a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 4 2 +--R (- 4a b - 6a b - 10a )cos(x) + (- 8a b - 12a )cos(x) - 4a b +--R + +--R 6 +--R - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 5 5 3 3 5 4 +--R 8a b cos(x) + (8a b + 20a b)cos(x) +--R + +--R 5 3 3 5 3 3 3 5 2 +--R (4a b + 2a b + 14a b)cos(x) + (- 4a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 6 6 2 4 4 2 6 5 +--R (8a b - 8a )cos(x) + (- 4a b - 10a b - 22a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (- 12a b - 10a b - 22a )cos(x) + (4a b + 2a b - 10a )cos(x) +--R + +--R 2 4 4 2 6 2 +--R (4a b + 2a b - 2a )cos(x) +--R * +--R sin(x) +--R + +--R 5 5 7 3 3 5 6 +--R (4a b - 4a b)cos(x) + (- 4a b - 10a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (- 4a b - 6a b - 10a b)cos(x) + (- 4a b - 6a b)cos(x) +--R + +--R 3 3 5 3 +--R (- 2a b - 2a b)cos(x) +--R * +--R x 7 +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 3 3 5 5 +--R - 8a b sin(x) + (8a b cos(x) + 8a b + 8a b)sin(x) +--R + +--R 6 3 2 4 4 2 2 4 2 4 2 4 +--R (- 8b cos(x) + (8a b + 4a b )cos(x) + 16a b cos(x) + 8a b )sin(x) +--R + +--R 5 3 3 5 4 +--R (16a b - 8a b - 8a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (- 8a b - 28a b - 12a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- 8a b - 12a b - 20a b)cos(x) + (- 16a b - 24a b)cos(x) +--R + +--R 3 3 5 +--R - 8a b - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (8a b + 16a b )cos(x) + (8b + 4a b + 20a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (- 8a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (16a b - 8a b - 8a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 8a b - 28a b - 20a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 24a b - 12a b - 20a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (8a b + 12a b - 12a b)cos(x) + (8a b + 4a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 2 6 6 2 4 4 2 5 +--R 8b cos(x) + 4a b cos(x) + (- 8b + 4a b + 4a b )cos(x) +--R + +--R 4 2 4 2 4 4 2 3 +--R - 4a b cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R x 6 +--R tan(-) +--R 2 +--R + +--R 5 6 6 4 2 6 5 +--R 12a b sin(x) + (- 12a cos(x) - 12a b - 12a )sin(x) +--R + +--R 5 5 3 3 3 5 2 5 +--R (12a b - 12a b)cos(x) + (- 12a b - 6a b)cos(x) - 24a b cos(x) +--R + +--R 5 +--R - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 6 4 2 4 4 2 6 3 +--R (- 24a b + 24a )cos(x) + (12a b + 54a b + 30a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 4 2 +--R (12a b + 18a b + 30a )cos(x) + (24a b + 36a )cos(x) + 12a b +--R + +--R 6 +--R 12a +--R * +--R 3 +--R sin(x) +--R + +--R 5 5 5 4 5 3 3 5 3 +--R 24a b cos(x) + 12a b cos(x) + (- 12a b - 6a b - 18a b)cos(x) +--R + +--R 3 3 5 2 +--R (12a b - 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 5 +--R (- 24a b + 24a b )cos(x) + (12a b + 54a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (36a b + 6a b - 6a )cos(x) + (- 12a b - 30a b + 6a )cos(x) +--R + +--R 2 4 4 2 6 2 +--R (- 12a b - 6a b + 6a )cos(x) +--R * +--R sin(x) +--R + +--R 5 5 7 3 3 5 6 +--R (- 12a b - 12a b)cos(x) + (- 12a b - 42a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (12a b - 30a b - 42a b)cos(x) + (- 12a b - 6a b)cos(x) +--R + +--R 3 3 5 3 +--R (6a b + 6a b)cos(x) +--R * +--R x 5 +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 3 3 5 5 +--R 12a b sin(x) + (- 12a b cos(x) - 12a b - 12a b)sin(x) +--R + +--R 6 3 2 4 4 2 2 4 2 4 2 +--R (12b cos(x) + (- 12a b - 6a b )cos(x) - 24a b cos(x) - 12a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 4 +--R (- 24a b + 12a b + 12a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (12a b + 42a b + 18a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (12a b + 18a b + 30a b)cos(x) + (24a b + 36a b)cos(x) +--R + +--R 3 3 5 +--R 12a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 12a b - 24a b )cos(x) + (- 12b - 6a b - 30a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (12a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 24a b + 12a b + 12a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (12a b + 42a b + 30a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (36a b + 18a b + 30a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (- 12a b - 18a b + 18a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- 12a b - 6a b + 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 2 6 6 2 4 4 2 5 +--R - 12b cos(x) - 6a b cos(x) + (12b - 6a b - 6a b )cos(x) +--R + +--R 4 2 4 2 4 4 2 3 +--R 6a b cos(x) + (6a b + 6a b )cos(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 5 6 6 4 2 6 5 +--R - 12a b sin(x) + (12a cos(x) + 12a b + 12a )sin(x) +--R + +--R 5 5 3 3 3 5 2 5 +--R (- 12a b - 12a b)cos(x) + (12a b + 6a b)cos(x) + 24a b cos(x) +--R + +--R 5 +--R 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 4 4 2 6 3 +--R (24a b - 24a b )cos(x) + (- 12a b - 30a b - 6a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (- 12a b - 18a b - 30a )cos(x) + (- 24a b - 36a )cos(x) +--R + +--R 4 2 6 +--R - 12a b - 12a +--R * +--R 3 +--R sin(x) +--R + +--R 5 5 3 3 5 4 +--R 24a b cos(x) + (24a b + 60a b)cos(x) +--R + +--R 5 3 3 5 3 3 3 5 2 +--R (12a b + 6a b + 42a b)cos(x) + (- 12a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 6 6 2 4 4 2 6 5 +--R (24a b - 24a )cos(x) + (- 12a b - 30a b - 66a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 36a b - 30a b - 66a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (12a b + 6a b - 30a )cos(x) + (12a b + 6a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 5 5 7 3 3 5 6 +--R (12a b - 12a b)cos(x) + (- 12a b - 30a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (- 12a b - 18a b - 30a b)cos(x) + (- 12a b - 18a b)cos(x) +--R + +--R 3 3 5 3 +--R (- 6a b - 6a b)cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 3 3 5 5 +--R - 8a b sin(x) + (8a b cos(x) + 8a b + 8a b)sin(x) +--R + +--R 6 3 2 4 4 2 2 4 2 4 2 4 +--R (- 8b cos(x) + (8a b + 4a b )cos(x) + 16a b cos(x) + 8a b )sin(x) +--R + +--R 5 3 3 5 4 +--R (16a b - 8a b - 8a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (- 8a b - 28a b - 12a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- 8a b - 12a b - 20a b)cos(x) + (- 16a b - 24a b)cos(x) +--R + +--R 3 3 5 +--R - 8a b - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (8a b + 16a b )cos(x) + (8b + 4a b + 20a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (- 8a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (16a b - 8a b - 8a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 8a b - 28a b - 20a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 24a b - 12a b - 20a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (8a b + 12a b - 12a b)cos(x) + (8a b + 4a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 2 6 6 2 4 4 2 5 +--R 8b cos(x) + 4a b cos(x) + (- 8b + 4a b + 4a b )cos(x) +--R + +--R 4 2 4 2 4 4 2 3 +--R - 4a b cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 6 4 2 6 5 +--R 4a b sin(x) + (- 4a cos(x) - 4a b - 4a )sin(x) +--R + +--R 5 5 3 3 3 5 2 5 +--R (4a b - 4a b)cos(x) + (- 4a b - 2a b)cos(x) - 8a b cos(x) +--R + +--R 5 +--R - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 6 4 2 4 4 2 6 3 +--R (- 8a b + 8a )cos(x) + (4a b + 18a b + 10a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 4 2 6 +--R (4a b + 6a b + 10a )cos(x) + (8a b + 12a )cos(x) + 4a b + 4a +--R * +--R 3 +--R sin(x) +--R + +--R 5 5 5 4 5 3 3 5 3 +--R 8a b cos(x) + 4a b cos(x) + (- 4a b - 2a b - 6a b)cos(x) +--R + +--R 3 3 5 2 +--R (4a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 5 +--R (- 8a b + 8a b )cos(x) + (4a b + 18a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (12a b + 2a b - 2a )cos(x) + (- 4a b - 10a b + 2a )cos(x) +--R + +--R 2 4 4 2 6 2 +--R (- 4a b - 2a b + 2a )cos(x) +--R * +--R sin(x) +--R + +--R 5 5 7 3 3 5 6 +--R (- 4a b - 4a b)cos(x) + (- 4a b - 14a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (4a b - 10a b - 14a b)cos(x) + (- 4a b - 2a b)cos(x) +--R + +--R 3 3 5 3 +--R (2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 3 3 5 5 +--R 2a b sin(x) + (- 2a b cos(x) - 2a b - 2a b)sin(x) +--R + +--R 6 3 2 4 4 2 2 4 2 4 2 4 +--R (2b cos(x) + (- 2a b - a b )cos(x) - 4a b cos(x) - 2a b )sin(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 4a b + 2a b + 2a b)cos(x) + (2a b + 7a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 3 3 5 +--R (2a b + 3a b + 5a b)cos(x) + (4a b + 6a b)cos(x) + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 2a b - 4a b )cos(x) + (- 2b - a b - 5a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (2a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 4a b + 2a b + 2a b)cos(x) + (2a b + 7a b + 5a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (6a b + 3a b + 5a b)cos(x) + (- 2a b - 3a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- 2a b - a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 2 6 6 2 4 4 2 5 4 2 4 +--R - 2b cos(x) - a b cos(x) + (2b - a b - a b )cos(x) + a b cos(x) +--R + +--R 2 4 4 2 3 +--R (a b + a b )cos(x) +--R / +--R 4 2 3 4 +--R 2a b cos(x) sin(x) +--R + +--R 3 3 5 4 5 3 3 +--R ((2a b - 2a b)cos(x) - 2a b cos(x) )sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 2 +--R (- 4a b cos(x) - 6a b cos(x) - 2a b cos(x) )sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 6a b)cos(x) +--R + +--R 3 3 5 4 5 3 +--R (- 2a b + 6a b)cos(x) + 2a b cos(x) +--R * +--R sin(x) +--R + +--R 4 2 7 4 2 6 4 2 5 4 2 4 +--R 2a b cos(x) + 6a b cos(x) + 6a b cos(x) + 2a b cos(x) +--R * +--R x 8 +--R tan(-) +--R 2 +--R + +--R 5 3 4 +--R - 4a b cos(x) sin(x) +--R + +--R 4 2 6 4 6 3 3 +--R ((- 4a b + 4a )cos(x) + 4a cos(x) )sin(x) +--R + +--R 5 5 5 4 5 3 2 +--R (8a b cos(x) + 12a b cos(x) + 4a b cos(x) )sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (4a b - 4a )cos(x) + (8a b - 12a )cos(x) +--R + +--R 4 2 6 4 6 3 +--R (4a b - 12a )cos(x) - 4a cos(x) +--R * +--R sin(x) +--R + +--R 5 7 5 6 5 5 5 4 +--R - 4a b cos(x) - 12a b cos(x) - 12a b cos(x) - 4a b cos(x) +--R * +--R x 7 +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 +--R - 8a b cos(x) sin(x) +--R + +--R 3 3 5 4 5 3 3 +--R ((- 8a b + 8a b)cos(x) + 8a b cos(x) )sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 2 +--R (16a b cos(x) + 24a b cos(x) + 8a b cos(x) )sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (8a b - 8a b)cos(x) + (16a b - 24a b)cos(x) +--R + +--R 3 3 5 4 5 3 +--R (8a b - 24a b)cos(x) - 8a b cos(x) +--R * +--R sin(x) +--R + +--R 4 2 7 4 2 6 4 2 5 4 2 4 +--R - 8a b cos(x) - 24a b cos(x) - 24a b cos(x) - 8a b cos(x) +--R * +--R x 6 +--R tan(-) +--R 2 +--R + +--R 5 3 4 +--R 12a b cos(x) sin(x) +--R + +--R 4 2 6 4 6 3 3 +--R ((12a b - 12a )cos(x) - 12a cos(x) )sin(x) +--R + +--R 5 5 5 4 5 3 2 +--R (- 24a b cos(x) - 36a b cos(x) - 12a b cos(x) )sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (- 12a b + 12a )cos(x) + (- 24a b + 36a )cos(x) +--R + +--R 4 2 6 4 6 3 +--R (- 12a b + 36a )cos(x) + 12a cos(x) +--R * +--R sin(x) +--R + +--R 5 7 5 6 5 5 5 4 +--R 12a b cos(x) + 36a b cos(x) + 36a b cos(x) + 12a b cos(x) +--R * +--R x 5 +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 +--R 12a b cos(x) sin(x) +--R + +--R 3 3 5 4 5 3 3 +--R ((12a b - 12a b)cos(x) - 12a b cos(x) )sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 2 +--R (- 24a b cos(x) - 36a b cos(x) - 12a b cos(x) )sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (- 12a b + 12a b)cos(x) + (- 24a b + 36a b)cos(x) +--R + +--R 3 3 5 4 5 3 +--R (- 12a b + 36a b)cos(x) + 12a b cos(x) +--R * +--R sin(x) +--R + +--R 4 2 7 4 2 6 4 2 5 4 2 4 +--R 12a b cos(x) + 36a b cos(x) + 36a b cos(x) + 12a b cos(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 5 3 4 +--R - 12a b cos(x) sin(x) +--R + +--R 4 2 6 4 6 3 3 +--R ((- 12a b + 12a )cos(x) + 12a cos(x) )sin(x) +--R + +--R 5 5 5 4 5 3 2 +--R (24a b cos(x) + 36a b cos(x) + 12a b cos(x) )sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (12a b - 12a )cos(x) + (24a b - 36a )cos(x) +--R + +--R 4 2 6 4 6 3 +--R (12a b - 36a )cos(x) - 12a cos(x) +--R * +--R sin(x) +--R + +--R 5 7 5 6 5 5 5 4 +--R - 12a b cos(x) - 36a b cos(x) - 36a b cos(x) - 12a b cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 +--R - 8a b cos(x) sin(x) +--R + +--R 3 3 5 4 5 3 3 +--R ((- 8a b + 8a b)cos(x) + 8a b cos(x) )sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 2 +--R (16a b cos(x) + 24a b cos(x) + 8a b cos(x) )sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (8a b - 8a b)cos(x) + (16a b - 24a b)cos(x) +--R + +--R 3 3 5 4 5 3 +--R (8a b - 24a b)cos(x) - 8a b cos(x) +--R * +--R sin(x) +--R + +--R 4 2 7 4 2 6 4 2 5 4 2 4 +--R - 8a b cos(x) - 24a b cos(x) - 24a b cos(x) - 8a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 4 4 2 6 4 6 3 3 +--R 4a b cos(x) sin(x) + ((4a b - 4a )cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 5 5 4 5 3 2 +--R (- 8a b cos(x) - 12a b cos(x) - 4a b cos(x) )sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (- 4a b + 4a )cos(x) + (- 8a b + 12a )cos(x) +--R + +--R 4 2 6 4 6 3 +--R (- 4a b + 12a )cos(x) + 4a cos(x) +--R * +--R sin(x) +--R + +--R 5 7 5 6 5 5 5 4 +--R 4a b cos(x) + 12a b cos(x) + 12a b cos(x) + 4a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 3 3 5 4 5 3 3 +--R 2a b cos(x) sin(x) + ((2a b - 2a b)cos(x) - 2a b cos(x) )sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 2 +--R (- 4a b cos(x) - 6a b cos(x) - 2a b cos(x) )sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 6a b)cos(x) +--R + +--R 3 3 5 4 5 3 +--R (- 2a b + 6a b)cos(x) + 2a b cos(x) +--R * +--R sin(x) +--R + +--R 4 2 7 4 2 6 4 2 5 4 2 4 +--R 2a b cos(x) + 6a b cos(x) + 6a b cos(x) + 2a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 5 2 3 4 +--R 2a b cos(x) sin(x) +--R + +--R 4 3 6 4 4 3 6 3 3 +--R ((2a b - 2a b)cos(x) + (- 2a b - 2a b)cos(x) )sin(x) +--R + +--R 5 2 5 3 4 5 2 4 5 2 3 2 +--R (- 4a b cos(x) + (- 2a b - 6a b )cos(x) - 2a b cos(x) )sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 6a b)cos(x) +--R + +--R 4 3 6 4 4 3 6 3 +--R (2a b + 6a b)cos(x) + (2a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 5 2 7 3 4 5 2 6 3 4 5 2 5 +--R 2a b cos(x) + (2a b + 6a b )cos(x) + (4a b + 6a b )cos(x) +--R + +--R 3 4 5 2 4 +--R (2a b + 2a b )cos(x) +--R * +--R x 8 +--R tan(-) +--R 2 +--R + +--R 6 3 4 +--R - 4a b cos(x) sin(x) +--R + +--R 5 2 7 4 5 2 7 3 3 +--R ((- 4a b + 4a )cos(x) + (4a b + 4a )cos(x) )sin(x) +--R + +--R 6 5 4 3 6 4 6 3 2 +--R (8a b cos(x) + (4a b + 12a b)cos(x) + 4a b cos(x) )sin(x) +--R + +--R 5 2 7 6 5 2 7 5 +--R (4a b - 4a )cos(x) + (4a b - 12a )cos(x) +--R + +--R 5 2 7 4 5 2 7 3 +--R (- 4a b - 12a )cos(x) + (- 4a b - 4a )cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 3 6 6 4 3 6 5 +--R - 4a b cos(x) + (- 4a b - 12a b)cos(x) + (- 8a b - 12a b)cos(x) +--R + +--R 4 3 6 4 +--R (- 4a b - 4a b)cos(x) +--R * +--R x 7 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R - 8a b cos(x) sin(x) +--R + +--R 4 3 6 4 4 3 6 3 3 +--R ((- 8a b + 8a b)cos(x) + (8a b + 8a b)cos(x) )sin(x) +--R + +--R 5 2 5 3 4 5 2 4 5 2 3 2 +--R (16a b cos(x) + (8a b + 24a b )cos(x) + 8a b cos(x) )sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (8a b - 8a b)cos(x) + (8a b - 24a b)cos(x) +--R + +--R 4 3 6 4 4 3 6 3 +--R (- 8a b - 24a b)cos(x) + (- 8a b - 8a b)cos(x) +--R * +--R sin(x) +--R + +--R 5 2 7 3 4 5 2 6 +--R - 8a b cos(x) + (- 8a b - 24a b )cos(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 16a b - 24a b )cos(x) + (- 8a b - 8a b )cos(x) +--R * +--R x 6 +--R tan(-) +--R 2 +--R + +--R 6 3 4 +--R 12a b cos(x) sin(x) +--R + +--R 5 2 7 4 5 2 7 3 3 +--R ((12a b - 12a )cos(x) + (- 12a b - 12a )cos(x) )sin(x) +--R + +--R 6 5 4 3 6 4 6 3 2 +--R (- 24a b cos(x) + (- 12a b - 36a b)cos(x) - 12a b cos(x) )sin(x) +--R + +--R 5 2 7 6 5 2 7 5 +--R (- 12a b + 12a )cos(x) + (- 12a b + 36a )cos(x) +--R + +--R 5 2 7 4 5 2 7 3 +--R (12a b + 36a )cos(x) + (12a b + 12a )cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 3 6 6 4 3 6 5 +--R 12a b cos(x) + (12a b + 36a b)cos(x) + (24a b + 36a b)cos(x) +--R + +--R 4 3 6 4 +--R (12a b + 12a b)cos(x) +--R * +--R x 5 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R 12a b cos(x) sin(x) +--R + +--R 4 3 6 4 4 3 6 3 3 +--R ((12a b - 12a b)cos(x) + (- 12a b - 12a b)cos(x) )sin(x) +--R + +--R 5 2 5 3 4 5 2 4 5 2 3 2 +--R (- 24a b cos(x) + (- 12a b - 36a b )cos(x) - 12a b cos(x) )sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (- 12a b + 12a b)cos(x) + (- 12a b + 36a b)cos(x) +--R + +--R 4 3 6 4 4 3 6 3 +--R (12a b + 36a b)cos(x) + (12a b + 12a b)cos(x) +--R * +--R sin(x) +--R + +--R 5 2 7 3 4 5 2 6 3 4 5 2 5 +--R 12a b cos(x) + (12a b + 36a b )cos(x) + (24a b + 36a b )cos(x) +--R + +--R 3 4 5 2 4 +--R (12a b + 12a b )cos(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 6 3 4 +--R - 12a b cos(x) sin(x) +--R + +--R 5 2 7 4 5 2 7 3 3 +--R ((- 12a b + 12a )cos(x) + (12a b + 12a )cos(x) )sin(x) +--R + +--R 6 5 4 3 6 4 6 3 2 +--R (24a b cos(x) + (12a b + 36a b)cos(x) + 12a b cos(x) )sin(x) +--R + +--R 5 2 7 6 5 2 7 5 +--R (12a b - 12a )cos(x) + (12a b - 36a )cos(x) +--R + +--R 5 2 7 4 5 2 7 3 +--R (- 12a b - 36a )cos(x) + (- 12a b - 12a )cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 3 6 6 +--R - 12a b cos(x) + (- 12a b - 36a b)cos(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 24a b - 36a b)cos(x) + (- 12a b - 12a b)cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R - 8a b cos(x) sin(x) +--R + +--R 4 3 6 4 4 3 6 3 3 +--R ((- 8a b + 8a b)cos(x) + (8a b + 8a b)cos(x) )sin(x) +--R + +--R 5 2 5 3 4 5 2 4 5 2 3 2 +--R (16a b cos(x) + (8a b + 24a b )cos(x) + 8a b cos(x) )sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (8a b - 8a b)cos(x) + (8a b - 24a b)cos(x) +--R + +--R 4 3 6 4 4 3 6 3 +--R (- 8a b - 24a b)cos(x) + (- 8a b - 8a b)cos(x) +--R * +--R sin(x) +--R + +--R 5 2 7 3 4 5 2 6 +--R - 8a b cos(x) + (- 8a b - 24a b )cos(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 16a b - 24a b )cos(x) + (- 8a b - 8a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 +--R 4a b cos(x) sin(x) +--R + +--R 5 2 7 4 5 2 7 3 3 +--R ((4a b - 4a )cos(x) + (- 4a b - 4a )cos(x) )sin(x) +--R + +--R 6 5 4 3 6 4 6 3 2 +--R (- 8a b cos(x) + (- 4a b - 12a b)cos(x) - 4a b cos(x) )sin(x) +--R + +--R 5 2 7 6 5 2 7 5 +--R (- 4a b + 4a )cos(x) + (- 4a b + 12a )cos(x) +--R + +--R 5 2 7 4 5 2 7 3 +--R (4a b + 12a )cos(x) + (4a b + 4a )cos(x) +--R * +--R sin(x) +--R + +--R 6 7 4 3 6 6 4 3 6 5 +--R 4a b cos(x) + (4a b + 12a b)cos(x) + (8a b + 12a b)cos(x) +--R + +--R 4 3 6 4 +--R (4a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 +--R 2a b cos(x) sin(x) +--R + +--R 4 3 6 4 4 3 6 3 3 +--R ((2a b - 2a b)cos(x) + (- 2a b - 2a b)cos(x) )sin(x) +--R + +--R 5 2 5 3 4 5 2 4 5 2 3 2 +--R (- 4a b cos(x) + (- 2a b - 6a b )cos(x) - 2a b cos(x) )sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 6a b)cos(x) +--R + +--R 4 3 6 4 4 3 6 3 +--R (2a b + 6a b)cos(x) + (2a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 5 2 7 3 4 5 2 6 3 4 5 2 5 +--R 2a b cos(x) + (2a b + 6a b )cos(x) + (4a b + 6a b )cos(x) +--R + +--R 3 4 5 2 4 +--R (2a b + 2a b )cos(x) +--R Type: Expression(Integer) +--E 506 + +--S 507 of 546 +t0492:= sec(x)/(1+2*cot(x)) +--R +--R +--R sec(x) +--R (472) ----------- +--R 2cot(x) + 1 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 546 +r0492:= 2/5*atanh(1/5*(cos(x)-2*sin(x))*5^(1/2))*5^(1/2)+atanh(sin(x)) +--R +--R +--R +-+ +-+ +--R +-+ 2\|5 sin(x) - \|5 cos(x) +--R - 2\|5 atanh(------------------------) + 5atanh(sin(x)) +--R 5 +--R (473) ------------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 508 + +--S 509 of 546 +a0492:= integrate(t0492,x) +--R +--R +--R (474) +--R +-+ sin(x) + cos(x) + 1 +-+ sin(x) - cos(x) - 1 +--R \|5 log(-------------------) - \|5 log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-+ +-+ +-+ +--R (2\|5 + 10)sin(x) + (- \|5 - 5)cos(x) - 5\|5 - 5 +--R 2log(---------------------------------------------------) +--R sin(x) + 2cos(x) +--R / +--R +-+ +--R \|5 +--R Type: Union(Expression(Integer),...) +--E 509 + +--S 510 of 546 +m0492:= a0492-r0492 +--R +--R +--R (475) +--R +-+ sin(x) + cos(x) + 1 +-+ sin(x) - cos(x) - 1 +--R \|5 log(-------------------) - \|5 log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-+ +-+ +-+ +--R (2\|5 + 10)sin(x) + (- \|5 - 5)cos(x) - 5\|5 - 5 +--R 2log(---------------------------------------------------) +--R sin(x) + 2cos(x) +--R + +--R +-+ +-+ +--R 2\|5 sin(x) - \|5 cos(x) +-+ +--R 2atanh(------------------------) - \|5 atanh(sin(x)) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 546 +d0492:= D(m0492,x) +--R +--R +--R (476) +--R +-+ 8 +-+ +-+ 7 +--R (24\|5 - 40)sin(x) + ((- 48\|5 - 80)cos(x) + 20\|5 - 60)sin(x) +--R + +--R +-+ 2 +-+ +-+ 6 +--R ((30\|5 + 110)cos(x) + (- 38\|5 - 30)cos(x) - 84\|5 + 60)sin(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 30\|5 - 150)cos(x) + (46\|5 + 30)cos(x) +--R + +--R +-+ +-+ +--R (218\|5 + 530)cos(x) - 30\|5 + 210 +--R * +--R 5 +--R sin(x) +--R + +--R 4 +-+ 3 +-+ 2 +--R 160cos(x) + (- 30\|5 + 10)cos(x) + (- 66\|5 - 290)cos(x) +--R + +--R +-+ +-+ +--R (8\|5 - 40)cos(x) + 100\|5 + 20 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R (18\|5 - 70)cos(x) + (15\|5 + 35)cos(x) + (77\|5 + 445)cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R (- 121\|5 - 45)cos(x) + (- 275\|5 - 715)cos(x) - 10\|5 - 250 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R (- 6\|5 + 10)cos(x) + (10\|5 + 50)cos(x) + (26\|5 - 150)cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (- 18\|5 - 90)cos(x) + (20\|5 + 260)cos(x) + (40\|5 + 120)cos(x) +--R + +--R +-+ +--R - 40\|5 - 40 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +--R (- 11\|5 - 55)cos(x) + (- 75\|5 - 75)cos(x) +--R + +--R +-+ 4 +-+ 3 +--R (- 74\|5 - 50)cos(x) + (- 30\|5 - 190)cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R (65\|5 + 5)cos(x) + (105\|5 + 265)cos(x) + 20\|5 + 100 +--R * +--R sin(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R (2\|5 + 10)cos(x) + (20\|5 + 20)cos(x) + (18\|5 + 10)cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R (- 40\|5 + 40)cos(x) + (- 10\|5 + 30)cos(x) + (20\|5 - 60)cos(x) +--R + +--R +-+ +--R (- 10\|5 - 50)cos(x) +--R / +--R +-+ 8 +-+ +-+ 7 +--R (8\|5 + 40)sin(x) + ((4\|5 + 20)cos(x) - 20\|5 - 20)sin(x) +--R + +--R +-+ 2 +-+ +-+ 6 +--R ((- 26\|5 - 130)cos(x) + (- 36\|5 - 100)cos(x) - 26\|5 - 130)sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (7\|5 + 35)cos(x) + (47\|5 + 15)cos(x) + (17\|5 - 75)cos(x) +--R + +--R +-+ +--R 65\|5 + 65 +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R (16\|5 + 80)cos(x) + (46\|5 + 190)cos(x) + (104\|5 + 360)cos(x) +--R + +--R +-+ +-+ +--R (126\|5 + 270)cos(x) + 28\|5 + 140 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +--R (- 11\|5 - 55)cos(x) + (- 57\|5 - 145)cos(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 73\|5 - 85)cos(x) + (- 77\|5 + 75)cos(x) +--R + +--R +-+ +-+ +--R (- 56\|5 + 80)cos(x) - 70\|5 - 70 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R (2\|5 + 10)cos(x) + (14\|5 + 30)cos(x) + (- 4\|5 - 100)cos(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 106\|5 - 330)cos(x) + (- 188\|5 - 380)cos(x) +--R + +--R +-+ +-+ +--R (- 140\|5 - 220)cos(x) - 10\|5 - 50 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R (11\|5 + 55)cos(x) + (57\|5 + 145)cos(x) + (66\|5 + 50)cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R (30\|5 - 90)cos(x) + (35\|5 - 25)cos(x) + 25\|5 + 25 +--R * +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R (- 2\|5 - 10)cos(x) + (- 14\|5 - 30)cos(x) + (- 12\|5 + 20)cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (60\|5 + 140)cos(x) + (110\|5 + 150)cos(x) + (50\|5 + 50)cos(x) +--R Type: Expression(Integer) +--E 511 + +--S 512 of 546 +t0493:= csc(x)^2/(a+b*cot(x)) +--R +--R +--R 2 +--R csc(x) +--R (477) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 512 + +--S 513 of 546 +r0493:= -log(a+b*cot(x))/b +--R +--R +--R log(b cot(x) + a) +--R (478) - ----------------- +--R b +--R Type: Expression(Integer) +--E 513 + +--S 514 of 546 +a0493:= integrate(t0493,x) +--R +--R +--R sin(x) - 2a sin(x) - 2b cos(x) +--R log(----------) - log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R (479) ---------------------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 514 + +--S 515 of 546 +m0493:= a0493-r0493 +--R +--R +--R sin(x) - 2a sin(x) - 2b cos(x) +--R log(----------) + log(b cot(x) + a) - log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R (480) ------------------------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 515 + +--S 516 of 546 +d0493:= D(m0493,x) +--R +--R +--R (481) +--R 2 2 2 +--R (- a cot(x) + b cot(x))sin(x) + (- b cos(x)cot(x) - b cos(x))sin(x) +--R + +--R 2 2 +--R b cos(x) cot(x) + a cos(x) +--R / +--R 2 2 2 +--R (a b cot(x) + a )sin(x) + (b cos(x)cot(x) + a b cos(x))sin(x) +--R Type: Expression(Integer) +--E 516 + +--S 517 of 546 +t0494:= csc(x)^4/(a+b*cot(x)) +--R +--R +--R 4 +--R csc(x) +--R (482) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 517 + +--S 518 of 546 +r0494:= a*cot(x)/b^2-1/2*cot(x)^2/b-(a^2+b^2)*log(a+b*cot(x))/b^3 +--R +--R +--R 2 2 2 2 +--R (- 2b - 2a )log(b cot(x) + a) - b cot(x) + 2a b cot(x) +--R (483) -------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 518 + +--S 519 of 546 +a0494:= integrate(t0494,x) +--R +--R +--R (484) +--R 2 2 2 2 2 sin(x) +--R ((4b + 4a )cos(x) - 4b - 4a )log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 - 2a sin(x) - 2b cos(x) +--R ((- 4b - 4a )cos(x) + 4b + 4a )log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R - 4a b cos(x)sin(x) + b cos(x) + b +--R / +--R 3 2 3 +--R 4b cos(x) - 4b +--R Type: Union(Expression(Integer),...) +--E 519 + +--S 520 of 546 +m0494:= a0494-r0494 +--R +--R +--R (485) +--R 2 2 2 2 2 sin(x) +--R ((4b + 4a )cos(x) - 4b - 4a )log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 +--R ((4b + 4a )cos(x) - 4b - 4a )log(b cot(x) + a) +--R + +--R 2 2 2 2 2 - 2a sin(x) - 2b cos(x) +--R ((- 4b - 4a )cos(x) + 4b + 4a )log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 +--R - 4a b cos(x)sin(x) + (2b cos(x) - 2b )cot(x) +--R + +--R 2 2 2 2 +--R (- 4a b cos(x) + 4a b)cot(x) + b cos(x) + b +--R / +--R 3 2 3 +--R 4b cos(x) - 4b +--R Type: Expression(Integer) +--E 520 + +--S 521 of 546 +d0494:= D(m0494,x) +--R +--R +--R (486) +--R 2 2 2 3 2 3 4 +--R ((- a b cos(x) - a b)cot(x) - a cos(x) - a )sin(x) +--R + +--R 2 3 2 3 3 +--R (- a b cos(x) cot(x) - a b cos(x) )sin(x) +--R + +--R 2 4 2 2 2 4 +--R (- a b cos(x) + 2a b cos(x) - a b )cot(x) +--R + +--R 2 4 2 2 2 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 3 4 3 2 2 3 2 +--R (b cos(x) + (- b - a b)cos(x) + b + a b)cot(x) +--R + +--R 2 3 2 3 +--R (a b - a )cos(x) + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 3 3 3 4 +--R (- b cos(x) + 2b cos(x) - b cos(x))cot(x) +--R + +--R 3 5 3 3 3 2 +--R (- 2b cos(x) + 4b cos(x) - 2b cos(x))cot(x) +--R + +--R 2 5 2 3 3 2 5 +--R (- a b cos(x) + a b cos(x) )cot(x) + (- b - a b)cos(x) +--R + +--R 3 2 3 3 +--R (2b + a b)cos(x) - b cos(x) +--R * +--R sin(x) +--R + +--R 3 2 6 3 2 4 3 2 2 +--R ((b + a b)cos(x) + (- 2b - 2a b)cos(x) + (b + a b)cos(x) )cot(x) +--R + +--R 2 3 6 2 3 4 2 3 2 +--R (a b + a )cos(x) + (- 2a b - 2a )cos(x) + (a b + a )cos(x) +--R / +--R 3 4 3 2 3 2 2 4 +--R (a b cos(x) - 2a b cos(x) + a b )cot(x) + a b cos(x) +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 4 3 4 3 5 +--R (b cos(x) - 2b cos(x) + b cos(x))cot(x) + a b cos(x) +--R + +--R 3 3 3 +--R - 2a b cos(x) + a b cos(x) +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 521 + +--S 522 of 546 +t0495:= sin(x)/(%i+cot(x)) +--R +--R +--R sin(x) +--R (487) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 522 + +--S 523 of 546 +r0495:= %i*cos(x)-1/3*%i*cos(x)^3+1/3*sin(x)^3 +--R +--R +--R 1 3 1 3 +--R (488) - sin(x) - - %i cos(x) + %i cos(x) +--R 3 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 523 + +--S 524 of 546 +--a0495:= integrate(t0495,x) +--E 524 + +--S 525 of 546 +--m0495:= a0495-r0495 +--E 525 + +--S 526 of 546 +--d0495:= D(m0495,x) +--E 526 + +--S 527 of 546 +t0496:= sin(x)^2/(%i+cot(x)) +--R +--R +--R 2 +--R sin(x) +--R (489) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 527 + +--S 528 of 546 +r0496:= -3/8*%i*x+3/8*%i*cos(x)*sin(x)+1/4*%i*cos(x)*sin(x)^3+1/4*sin(x)^4 +--R +--R +--R 1 4 1 3 3 3 +--R (490) - sin(x) + - %i cos(x)sin(x) + - %i cos(x)sin(x) - - %i x +--R 4 4 8 8 +--R Type: Expression(Complex(Fraction(Integer))) +--E 528 + +--S 529 of 546 +--a0496:= integrate(t0496,x) +--E 529 + +--S 530 of 546 +--m0496:= a0496-r0496 +--E 530 + +--S 531 of 546 +--d0496:= D(m0496,x) +--E 531 + +--S 532 of 546 +t0497:= sin(x)^3/(%i+cot(x)) +--R +--R +--R 3 +--R sin(x) +--R (491) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 532 + +--S 533 of 546 +r0497:= %i*cos(x)-2/3*%i*cos(x)^3+1/5*%i*cos(x)^5+1/5*sin(x)^5 +--R +--R +--R 1 5 1 5 2 3 +--R (492) - sin(x) + - %i cos(x) - - %i cos(x) + %i cos(x) +--R 5 5 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 533 + +--S 534 of 546 +--a0497:= integrate(t0497,x) +--E 534 + +--S 535 of 546 +--m0497:= a0497-r0497 +--E 535 + +--S 536 of 546 +--d0497:= D(m0497,x) +--E 536 + +--S 537 of 546 +t0498:= sin(x)^4/(%i+cot(x)) +--R +--R +--R 4 +--R sin(x) +--R (493) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 537 + +--S 538 of 546 +r0498:= -5/16*%i*x+5/16*%i*cos(x)*sin(x)+5/24*%i*cos(x)*sin(x)^3+_ + 1/6*%i*cos(x)*sin(x)^5+1/6*sin(x)^6 +--R +--R +--R (494) +--R 1 6 1 5 5 3 5 +--R - sin(x) + - %i cos(x)sin(x) + -- %i cos(x)sin(x) + -- %i cos(x)sin(x) +--R 6 6 24 16 +--R + +--R 5 +--R - -- %i x +--R 16 +--R Type: Expression(Complex(Fraction(Integer))) +--E 538 + +--S 539 of 546 +--a0498:= integrate(t0498,x) +--E 539 + +--S 540 of 546 +--m0498:= a0498-r0498 +--E 540 + +--S 541 of 546 +--d0498:= D(m0498,x) +--E 541 + +--S 542 of 546 +t0499:= cos(x)/(%i+cot(x)) +--R +--R +--R cos(x) +--R (495) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 542 + +--S 543 of 546 +r0499:= -1/3*cos(x)^3-1/3*%i*sin(x)^3 +--R +--R +--R 1 3 1 3 +--R (496) - - %i sin(x) - - cos(x) +--R 3 3 +--R Type: Expression(Complex(Fraction(Integer))) +--E 543 + +--S 544 of 546 +--a0499:= integrate(t0499,x) +--E 544 + +--S 545 of 546 +--m0499:= a0499-r0499 +--E 545 + +--S 546 of 546 +--d0499:= D(m0499,x) +--E 546 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richtrig400-499.input.pdf b/src/axiom-website/CATS/richtrig400-499.input.pdf new file mode 100644 index 0000000..69dea5f Binary files /dev/null and b/src/axiom-website/CATS/richtrig400-499.input.pdf differ diff --git a/src/axiom-website/CATS/richtrig500-599.input.pamphlet b/src/axiom-website/CATS/richtrig500-599.input.pamphlet new file mode 100644 index 0000000..271ad45 --- /dev/null +++ b/src/axiom-website/CATS/richtrig500-599.input.pamphlet @@ -0,0 +1,42910 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richtrig500-599.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig500-599.output +)spool richtrig500-599.output +)set message auto off +)clear all + +--S 1 of 586 +t0500:= cos(x)^2/(%i+cot(x)) +--R +--R +--R 2 +--R cos(x) +--R (1) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 1 + +--S 2 of 586 +r0500:= -1/8*%i*x-1/4*cos(x)^4-1/8*%i*cos(x)*sin(x)+1/4*%i*cos(x)^3*sin(x) +--R +--R +--R 1 3 1 1 4 1 +--R (2) (- %i cos(x) - - %i cos(x))sin(x) - - cos(x) - - %i x +--R 4 8 4 8 +--R Type: Expression(Complex(Fraction(Integer))) +--E 2 + +--S 3 of 586 +--a0500:= integrate(t0500,x) +--E 3 + +--S 4 of 586 +--m0500:= a0500-r0500 +--E 4 + +--S 5 of 586 +--d0500:= D(m0500,x) +--E 5 + +--S 6 of 586 +t0501:= cos(x)^3/(%i+cot(x)) +--R +--R +--R 3 +--R cos(x) +--R (3) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 6 + +--S 7 of 586 +r0501:= -1/5*cos(x)^5-1/3*%i*sin(x)^3+1/5*%i*sin(x)^5 +--R +--R +--R 1 5 1 3 1 5 +--R (4) - %i sin(x) - - %i sin(x) - - cos(x) +--R 5 3 5 +--R Type: Expression(Complex(Fraction(Integer))) +--E 7 + +--S 8 of 586 +--a0501:= integrate(t0501,x) +--E 8 + +--S 9 of 586 +--m0501:= a0501-r0501 +--E 9 + +--S 10 of 586 +--d0501:= D(m0501,x) +--E 10 + +--S 11 of 586 +t0502:= cos(x)^4/(%i+cot(x)) +--R +--R +--R 4 +--R cos(x) +--R (5) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 11 + +--S 12 of 586 +r0502:= -1/16*%i*x-1/6*cos(x)^6-1/16*%i*cos(x)*sin(x)-_ + 1/24*%i*cos(x)^3*sin(x)+1/6*%i*cos(x)^5*sin(x) +--R +--R +--R (6) +--R 1 5 1 3 1 1 6 1 +--R (- %i cos(x) - -- %i cos(x) - -- %i cos(x))sin(x) - - cos(x) - -- %i x +--R 6 24 16 6 16 +--R Type: Expression(Complex(Fraction(Integer))) +--E 12 + +--S 13 of 586 +--a0502:= integrate(t0502,x) +--E 13 + +--S 14 of 586 +--m0502:= a0502-r0502 +--E 14 + +--S 15 of 586 +--d0502:= D(m0502,x) +--E 15 + +--S 16 of 586 +t0503:= tan(x)/(%i+cot(x)) +--R +--R +--R tan(x) +--R (7) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 16 + +--S 17 of 586 +r0503:= 1/2*x+%i*log(cos(x))+1/(2*%i-2*tan(x)) +--R +--R +--R (2%i tan(x) + 2)log(cos(x)) + x tan(x) - %i x - 1 +--R (8) ------------------------------------------------- +--R 2tan(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 17 + +--S 18 of 586 +a0503:= integrate(t0503,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 18 + +--S 19 of 586 +m0503:= a0503-r0503 +--R +--R +--R (9) +--R (- 2%i tan(x) - 2)log(cos(x)) + (- x + 2a0503)tan(x) + %i x - 2%i a0503 + 1 +--R --------------------------------------------------------------------------- +--R 2tan(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 19 + +--S 20 of 586 +d0503:= D(m0503,x) +--R +--R +--R (%i sin(x) - cos(x))tan(x) + sin(x) +--R (10) ----------------------------------- +--R cos(x)tan(x) - %i cos(x) +--R Type: Expression(Complex(Integer)) +--E 20 + +--S 21 of 586 +t0504:= tan(x)^2/(%i+cot(x)) +--R +--R +--R 2 +--R tan(x) +--R (11) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 21 + +--S 22 of 586 +r0504:= 3/2*%i*x-log(cos(x))+%i/(2*%i-2*tan(x))-%i*tan(x) +--R +--R +--R 2 +--R 3%i (- 2tan(x) + 2%i)log(cos(x)) - 2%i tan(x) - 2tan(x) - %i +--R (12) --- x + --------------------------------------------------------- +--R 2 2tan(x) - 2%i +--R Type: UnivariatePolynomial(x,Expression(Complex(Integer))) +--E 22 + +--S 23 of 586 +a0504:= integrate(t0504,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 23 + +--S 24 of 586 +m0504:= a0504-r0504 +--R +--R +--R (13) +--R 3%i +--R - --- x +--R 2 +--R + +--R 2 +--R (2tan(x) - 2%i)log(cos(x)) + 2%i tan(x) + (2a0504 + 2)tan(x) +--R + +--R - 2%i a0504 + %i +--R / +--R 2tan(x) - 2%i +--R Type: UnivariatePolynomial(x,Expression(Complex(Integer))) +--E 24 + +--S 25 of 586 +d0504:= D(m0504,x) +--R +--R +--R (14) +--R 3 2 +--R %i cos(x)tan(x) + cos(x)tan(x) + (- sin(x) - %i cos(x))tan(x) + %i sin(x) +--R --------------------------------------------------------------------------- +--R cos(x)tan(x) - %i cos(x) +--R Type: UnivariatePolynomial(x,Expression(Complex(Integer))) +--E 25 + +--S 26 of 586 +t0505:= cot(x)/(%i+cot(x)) +--R +--R +--R cot(x) +--R (15) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 26 + +--S 27 of 586 +r0505:= 1/2*x+%i/(2+2*%i*tan(x)) +--R +--R +--R x tan(x) - %i x + 1 +--R (16) ------------------- +--R 2tan(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 27 + +--S 28 of 586 +a0505:= integrate(t0505,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 28 + +--S 29 of 586 +m0505:= a0505-r0505 +--R +--R +--R (- x + 2a0505)tan(x) + %i x - 2%i a0505 - 1 +--R (17) ------------------------------------------- +--R 2tan(x) - 2%i +--R Type: Expression(Complex(Integer)) +--E 29 + +--S 30 of 586 +d0505:= D(m0505,x) +--R +--R +--R %i +--R (18) ----------- +--R tan(x) - %i +--R Type: Expression(Complex(Integer)) +--E 30 + +--S 31 of 586 +t0506:= cot(x)^2/(%i+cot(x)) +--R +--R +--R 2 +--R cot(x) +--R (19) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 31 + +--S 32 of 586 +r0506:= -1/2*%i*x+log(sin(x))+%i/(2*%i-2*tan(x)) +--R +--R +--R %i (2tan(x) - 2%i)log(sin(x)) - %i +--R (20) - -- x + ------------------------------- +--R 2 2tan(x) - 2%i +--R Type: UnivariatePolynomial(x,Expression(Complex(Integer))) +--E 32 + +--S 33 of 586 +a0506:= integrate(t0506,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 33 + +--S 34 of 586 +m0506:= a0506-r0506 +--R +--R +--R %i (- 2tan(x) + 2%i)log(sin(x)) + 2a0506 tan(x) - 2%i a0506 + %i +--R (21) -- x + ------------------------------------------------------------- +--R 2 2tan(x) - 2%i +--R Type: UnivariatePolynomial(x,Expression(Complex(Integer))) +--E 34 + +--S 35 of 586 +d0506:= D(m0506,x) +--R +--R +--R - cos(x)tan(x) + sin(x) + %i cos(x) +--R (22) ----------------------------------- +--R sin(x)tan(x) - %i sin(x) +--R Type: UnivariatePolynomial(x,Expression(Complex(Integer))) +--E 35 + +--S 36 of 586 +t0507:= sec(x)/(%i+cot(x)) +--R +--R +--R sec(x) +--R (23) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 36 + +--S 37 of 586 +r0507:= -%i*atanh(sin(x))-cos(x)+%i*sin(x) +--R +--R +--R (24) - %i atanh(sin(x)) + %i sin(x) - cos(x) +--R Type: Expression(Complex(Integer)) +--E 37 + +--S 38 of 586 +a0507:= integrate(t0507,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 38 + +--S 39 of 586 +m0507:= a0507-r0507 +--R +--R +--R (25) %i atanh(sin(x)) - %i sin(x) + cos(x) + a0507 +--R Type: Expression(Complex(Integer)) +--E 39 + +--S 40 of 586 +d0507:= D(m0507,x) +--R +--R +--R 3 2 +--R - sin(x) - %i cos(x)sin(x) + sin(x) +--R (26) ------------------------------------- +--R 2 +--R sin(x) - 1 +--R Type: Expression(Complex(Integer)) +--E 40 + +--S 41 of 586 +t0508:= sec(x)^3/(%i+cot(x)) +--R +--R +--R 3 +--R sec(x) +--R (27) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 41 + +--S 42 of 586 +r0508:= 1/2*%i*atanh(sin(x))+sec(x)-1/2*%i*sec(x)*tan(x) +--R +--R +--R 1 1 +--R (28) - %i atanh(sin(x)) - - %i sec(x)tan(x) + sec(x) +--R 2 2 +--R Type: Expression(Complex(Fraction(Integer))) +--E 42 + +--S 43 of 586 +a0508:= integrate(t0508,x) +--R +--R +--R 2 sin(x) + cos(x) + 1 2 +--R %i cos(x) log(-------------------) - %i sin(x) + 2cos(x) + 2cos(x) +--R sin(x) - cos(x) - 1 +--R (29) ------------------------------------------------------------------- +--R 2 +--R 2cos(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 43 + +--S 44 of 586 +m0508:= a0508-r0508 +--R +--R +--R (30) +--R 1 2 sin(x) + cos(x) + 1 1 2 +--R - %i cos(x) log(-------------------) - - %i cos(x) atanh(sin(x)) +--R 2 sin(x) - cos(x) - 1 2 +--R + +--R 1 2 1 2 2 +--R - %i cos(x) sec(x)tan(x) - - %i sin(x) - cos(x) sec(x) + cos(x) + cos(x) +--R 2 2 +--R / +--R 2 +--R cos(x) +--R Type: Expression(Complex(Fraction(Integer))) +--E 44 + +--S 45 of 586 +d0508:= D(m0508,x) +--R +--R +--R (31) +--R 3 4 +--R %i cos(x) sec(x)sin(x) +--R + +--R 5 4 3 2 +--R (- %i cos(x) - 2%i cos(x) - 2%i cos(x) )sec(x)sin(x) +--R + +--R 5 4 3 +--R (%i cos(x) + 2%i cos(x) + %i cos(x) )sec(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 4 5 4 3 2 +--R - cos(x) sec(x)sin(x) + (cos(x) + 2cos(x) + 2cos(x) )sec(x)sin(x) +--R + +--R 5 4 3 +--R (- cos(x) - 2cos(x) - cos(x) )sec(x) +--R * +--R tan(x) +--R + +--R 6 5 +--R - %i sin(x) + cos(x)sin(x) +--R + +--R 1 3 3 1 2 +--R (- %i cos(x) sec(x) - %i cos(x) + - %i cos(x) + 2%i cos(x) + 2%i) +--R 2 2 +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 3 +--R (- cos(x) - 2cos(x) - 2cos(x))sin(x) +--R + +--R 1 5 4 3 5 +--R (- - %i cos(x) - %i cos(x) - %i cos(x) )sec(x) - %i cos(x) +--R 2 +--R + +--R 3 +--R 2%i cos(x) - 2%i cos(x) - %i +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (cos(x) + 2cos(x) + cos(x))sin(x) +--R + +--R 1 5 4 1 3 1 6 +--R (- %i cos(x) + %i cos(x) + - %i cos(x) )sec(x) - - %i cos(x) +--R 2 2 2 +--R + +--R 3 1 2 +--R - %i cos(x) - - %i cos(x) +--R 2 +--R / +--R 3 4 5 4 3 2 5 +--R cos(x) sin(x) + (- cos(x) - 2cos(x) - 2cos(x) )sin(x) + cos(x) +--R + +--R 4 3 +--R 2cos(x) + cos(x) +--R Type: Expression(Complex(Fraction(Integer))) +--E 45 + +--S 46 of 586 +t0509:= csc(x)/(%i+cot(x)) +--R +--R +--R csc(x) +--R (32) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 46 + +--S 47 of 586 +r0509:= %i*cos(x)+sin(x) +--R +--R +--R (33) sin(x) + %i cos(x) +--R Type: Expression(Complex(Integer)) +--E 47 + +--S 48 of 586 +a0509:= integrate(t0509,x) +--R +--R +--R >> Error detected within library code: +--R Denominator not equal to 1 +--R +--R Continuing to read the file... +--R +--E 48 + +--S 49 of 586 +m0509:= a0509-r0509 +--R +--R +--R (34) - sin(x) - %i cos(x) + a0509 +--R Type: Expression(Complex(Integer)) +--E 49 + +--S 50 of 586 +d0509:= D(m0509,x) +--R +--R +--R (35) %i sin(x) - cos(x) +--R Type: Expression(Complex(Integer)) +--E 50 + +--S 51 of 586 +t0510:= csc(x)^2/(%i+cot(x)) +--R +--R +--R 2 +--R csc(x) +--R (36) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 51 + +--S 52 of 586 +r0510:= -log(%i+cot(x)) +--R +--R +--R (37) - log(cot(x) + %i) +--R Type: Expression(Complex(Integer)) +--E 52 + +--S 53 of 586 +a0510:= integrate(t0510,x) +--R +--R +--R sin(x) 2 +--R (38) log(----------) - log(----------) - %i x +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Complex(Integer)),...) +--E 53 + +--S 54 of 586 +m0510:= a0510-r0510 +--R +--R +--R sin(x) 2 +--R (39) log(----------) + log(cot(x) + %i) - log(----------) - %i x +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Complex(Integer)) +--E 54 + +--S 55 of 586 +d0510:= D(m0510,x) +--R +--R +--R - cot(x)sin(x) + cos(x) +--R (40) ----------------------- +--R sin(x) +--R Type: Expression(Complex(Integer)) +--E 55 + +--S 56 of 586 +t0511:= csc(x)^3/(%i+cot(x)) +--R +--R +--R 3 +--R csc(x) +--R (41) ----------- +--R cot(x) + %i +--R Type: Expression(Complex(Integer)) +--E 56 + +--S 57 of 586 +r0511:= %i*atanh(cos(x))-csc(x) +--R +--R +--R (42) %i atanh(cos(x)) - csc(x) +--R Type: Expression(Complex(Integer)) +--E 57 + +--S 58 of 586 +a0511:= integrate(t0511,x) +--R +--R +--R sin(x) +--R - %i sin(x)log(----------) - 1 +--R cos(x) + 1 +--R (43) ------------------------------ +--R sin(x) +--R Type: Union(Expression(Complex(Integer)),...) +--E 58 + +--S 59 of 586 +m0511:= a0511-r0511 +--R +--R +--R (44) +--R sin(x) +--R - %i sin(x)log(----------) - %i sin(x)atanh(cos(x)) + csc(x)sin(x) - 1 +--R cos(x) + 1 +--R ---------------------------------------------------------------------- +--R sin(x) +--R Type: Expression(Complex(Integer)) +--E 59 + +--S 60 of 586 +d0511:= D(m0511,x) +--R +--R +--R (45) +--R 3 2 2 +--R - %i cos(x)sin(x) + (- cos(x) + 1)cot(x)csc(x)sin(x) +--R + +--R 3 3 +--R (- %i cos(x) + %i cos(x))sin(x) + cos(x) - cos(x) +--R / +--R 2 2 +--R (cos(x) - 1)sin(x) +--R Type: Expression(Complex(Integer)) +--E 60 + +--S 61 of 586 +t0512:= sin(x)^2/(a+b*sec(x)) +--R +--R +--R 2 +--R sin(x) +--R (46) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 586 +r0512:= 1/2/a^3*(a^2*x-2*b^2*x+4*b*(a^2-b^2)^(1/2)*_ + atanh((a-b)/(a^2-b^2)^(1/2)*(-1+cos(x))/sin(x))+_ + 2*a*b*sin(x)-cos(x)*sin(x)*a^2) +--R +--R +--R (47) +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a 2 +--R - 4b\|- b + a atanh(---------------------) + (- a cos(x) + 2a b)sin(x) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R + +--R 2 2 +--R (- 2b + a )x +--R / +--R 3 +--R 2a +--R Type: Expression(Integer) +--E 62 + +--S 63 of 586 +a0512:= integrate(t0512,x) +--R +--R +--R (48) +--R [ +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x)\|- b + a - b cos(x) - a +--R 2b\|- b + a log(---------------------------------) +--R a cos(x) + b +--R + +--R 2 2 2 +--R (- a cos(x) + 2a b)sin(x) + (- 2b + a )x +--R / +--R 3 +--R 2a +--R , +--R +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a 2 +--R - 4b\|b - a atan(----------------------) + (- a cos(x) + 2a b)sin(x) +--R (b - a)sin(x) +--R + +--R 2 2 +--R (- 2b + a )x +--R / +--R 3 +--R 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 63 + +--S 64 of 586 +m0512a:= a0512.1-r0512 +--R +--R +--R (49) +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x)\|- b + a - b cos(x) - a +--R b\|- b + a log(---------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2b\|- b + a atanh(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R / +--R 3 +--R a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 586 +d0512a:= D(m0512a,x) +--R +--R +--R (50) +--R 3 3 4 3 2 2 3 3 +--R ((- 2a b + 2a b)cos(x) - b + a b + a b - a b)sin(x) +--R + +--R 3 3 3 4 3 2 2 3 2 +--R (- 2a b + 2a b)cos(x) + (- b + a b + a b - a b)cos(x) +--R + +--R 3 3 4 3 2 2 3 +--R (2a b - 2a b)cos(x) + b - a b - a b + a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 3 3 2 4 4 +--R (- a b - a b + a b + a b)sin(x) +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 4 2 +--R ((b + a b - a b - a b )cos(x) + a b + a b - a b - a b)sin(x) +--R + +--R 4 2 3 3 2 4 4 5 4 2 3 3 2 3 +--R (a b + a b - a b - a b)cos(x) + (b + a b - a b - a b )cos(x) +--R + +--R 4 2 3 3 2 4 2 5 4 2 3 3 2 +--R (- a b - a b + a b + a b)cos(x) + (- b - a b + a b + a b )cos(x) +--R / +--R 4 5 3 2 4 3 +--R ((a b + a )cos(x) + a b + a b)sin(x) +--R + +--R 4 5 3 3 2 4 5 2 +--R (a b - a )cos(x) + (a b - 3a b + 2a )cos(x) +--R + +--R 3 2 4 5 3 2 4 +--R (- 2a b + 3a b - a )cos(x) + a b - a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 5 2 3 3 4 2 5 6 4 2 5 +--R ((- a b - a b)cos(x) + (- a b - a b - a b - a )cos(x) - a b - a b) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 5 4 3 3 4 2 5 6 3 +--R (- a b + a b)cos(x) + (- a b + 3a b - 3a b + a )cos(x) +--R + +--R 3 3 4 2 5 6 2 3 3 4 2 5 6 +--R (2a b - 4a b + 4a b - 2a )cos(x) + (- a b + 3a b - 3a b + a )cos(x) +--R + +--R 4 2 5 +--R - a b + a b +--R Type: Expression(Integer) +--E 65 + +--S 66 of 586 +m0512b:= a0512.2-r0512 +--R +--R +--R (51) +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2b\|- b + a atanh(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a +--R - 2b\|b - a atan(----------------------) +--R (b - a)sin(x) +--R / +--R 3 +--R a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 586 +d0512b:= D(m0512b,x) +--R +--R +--R (52) +--R 3 3 4 4 2 2 3 3 2 +--R (4a b - 4a b)sin(x) + ((- 4b + 4a b )cos(x) - 4a b + 4a b)sin(x) +--R + +--R 3 3 4 4 2 2 3 3 3 2 +--R (- 4a b + 4a b)cos(x) + (- 4b + 4a b )cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 2 2 +--R (4b - 4a b )cos(x) +--R / +--R 3 2 5 4 +--R (a b - a )sin(x) +--R + +--R 3 2 5 2 4 3 2 5 2 +--R ((2a b + 2a )cos(x) + 8a b cos(x) + 2a b + 2a )sin(x) +--R + +--R 3 2 5 4 3 2 5 2 3 2 5 +--R (a b - a )cos(x) + (- 2a b + 2a )cos(x) + a b - a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 586 +t0513:= sin(x)^4/(a+b*sec(x)) +--R +--R +--R 4 +--R sin(x) +--R (53) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 68 + +--S 69 of 586 +r0513:= -5/8*x/a+1/2*b^2*x/a^3+(a^2-b^2)^2*x/a^5-2*b*(a^2-b^2)^(3/2)*_ + atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^5+b*sin(x)/a^2-_ + b^3*sin(x)/a^4-5/8*cos(x)*sin(x)/a+1/2*b^2*cos(x)*sin(x)/a^3+_ + 1/4*cos(x)^3*sin(x)/a+1/3*b*sin(x)^3/a^2 +--R +--R +--R (54) +--R x +--R +---------+ (b - a)tan(-) +--R 3 2 | 2 2 2 3 3 +--R (- 48b + 48a b)\|- b + a atanh(-------------) + 8a b sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (12a b - 15a )cos(x) - 24a b + 24a b)sin(x) +--R + +--R 4 2 2 4 +--R (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R Type: Expression(Integer) +--E 69 + +--S 70 of 586 +a0513:= integrate(t0513,x) +--R +--R +--R (55) +--R [ +--R +---------+ +--R +---------+ | 2 2 +--R 3 2 | 2 2 - sin(x)\|- b + a - b cos(x) - a +--R (24b - 24a b)\|- b + a log(-----------------------------------) +--R a cos(x) + b +--R + +--R 4 3 3 2 2 2 4 3 3 +--R (6a cos(x) - 8a b cos(x) + (12a b - 15a )cos(x) - 24a b + 32a b) +--R * +--R sin(x) +--R + +--R 4 2 2 4 +--R (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R , +--R +--R +-------+ +--R +-------+ | 2 2 +--R 3 2 | 2 2 (cos(x) + 1)\|b - a +--R (48b - 48a b)\|b - a atan(----------------------) +--R (b - a)sin(x) +--R + +--R 4 3 3 2 2 2 4 3 3 +--R (6a cos(x) - 8a b cos(x) + (12a b - 15a )cos(x) - 24a b + 32a b) +--R * +--R sin(x) +--R + +--R 4 2 2 4 +--R (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 70 + +--S 71 of 586 +m0513a:= a0513.1-r0513 +--R +--R +--R (56) +--R +---------+ +--R +---------+ | 2 2 +--R 3 2 | 2 2 - sin(x)\|- b + a - b cos(x) - a +--R (3b - 3a b)\|- b + a log(-----------------------------------) +--R a cos(x) + b +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 3 2 | 2 2 2 3 3 +--R (6b - 6a b)\|- b + a atanh(-------------) - a b sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 +--R (- a b cos(x) + a b)sin(x) +--R / +--R 5 +--R 3a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 586 +d0513a:= D(m0513a,x) +--R +--R +--R (57) +--R 3 2 4 2 2 3 3 2 3 +--R ((- a b + a b)cos(x) + (- a b + a b )cos(x))sin(x) +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- a b + a b)cos(x) + (- a b + a b )cos(x) +--R + +--R 3 2 4 2 5 2 3 3 2 4 5 +--R (a b - a b)cos(x) + (3b - 5a b - a b + 3a b)cos(x) + 3b +--R + +--R 2 3 4 +--R - 6a b + 3a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 2 2 3 3 2 3 +--R ((- a b - a b)cos(x) + (- a b - a b )cos(x))sin(x) +--R + +--R 3 2 4 4 2 3 3 2 3 +--R (- a b - a b)cos(x) + (- a b - a b )cos(x) +--R + +--R 3 2 4 2 5 2 3 3 2 4 5 +--R (a b + a b)cos(x) + (3b - 5a b + a b + 3a b)cos(x) - 3b +--R + +--R 2 3 4 +--R 6a b - 3a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 4 2 3 2 4 3 3 4 2 5 2 +--R (- a b + a b )cos(x) + (- a b + a b - a b + a b)cos(x) +--R + +--R 3 3 4 2 6 5 2 4 3 3 4 2 5 +--R (- a b + a b )cos(x) - 3b + 3a b + 6a b - 6a b - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 2 4 3 3 4 2 5 4 +--R (- a b + a b )cos(x) + (- a b + a b - a b + a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (3a b + a b - 7a b + a b + 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 4 +--R (3b + 3a b - 6a b - 5a b + 2a b + 3a b)cos(x) + 3b - 6a b +--R + +--R 4 2 +--R 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 3 2 4 3 3 4 2 5 2 +--R (- a b - a b )cos(x) + (- a b - a b - a b - a b)cos(x) +--R + +--R 3 3 4 2 6 5 2 4 3 3 4 2 5 +--R (- a b - a b )cos(x) - 3b - 3a b + 6a b + 6a b - 3a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 2 4 3 3 4 2 5 4 +--R (- a b - a b )cos(x) + (- a b - a b - a b - a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 3a b + a b + 7a b + a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 4 4 2 +--R (- 3b + 3a b + 6a b - 5a b - 2a b + 3a b)cos(x) + 3b - 6a b + 3a b +--R / +--R 5 6 4 2 5 x 2 +--R ((3a b - 3a )cos(x) + 3a b - 3a b)sin(x)tan(-) +--R 2 +--R + +--R 5 6 4 2 5 +--R ((3a b + 3a )cos(x) + 3a b + 3a b)sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 6 2 4 3 5 2 6 7 5 2 +--R (3a b - 3a b)cos(x) + (3a b - 3a b + 3a b - 3a )cos(x) + 3a b +--R + +--R 6 +--R - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 2 4 3 5 2 6 7 5 2 6 +--R (3a b + 3a b)cos(x) + (3a b + 3a b + 3a b + 3a )cos(x) + 3a b + 3a b +--R Type: Expression(Integer) +--E 72 + +--S 73 of 586 +m0513b:= a0513.2-r0513 +--R +--R +--R (58) +--R x +--R +---------+ (b - a)tan(-) +--R 3 2 | 2 2 2 +--R (6b - 6a b)\|- b + a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 3 2 | 2 2 (cos(x) + 1)\|b - a 3 3 +--R (6b - 6a b)\|b - a atan(----------------------) - a b sin(x) +--R (b - a)sin(x) +--R + +--R 3 2 3 +--R (- a b cos(x) + a b)sin(x) +--R / +--R 5 +--R 3a +--R Type: Expression(Integer) +--E 73 + +--S 74 of 586 +d0513b:= D(m0513b,x) +--R +--R +--R (59) +--R 3 3 4 2 5 4 +--R (- a b + 2a b - a b)cos(x)sin(x) +--R + +--R 3 3 4 2 3 3 3 5 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 4 2 5 6 5 2 4 3 3 4 2 5 +--R (- 2a b + 2a b)cos(x) - 3b + 3a b + 6a b - 6a b - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- a b + a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 3b + 9a b + 6a b - 16a b - 3a b + 7a b)cos(x) +--R + +--R 5 3 3 5 6 5 2 4 3 3 4 2 +--R (12a b - 23a b + 11a b)cos(x) + 3b + 3a b - 6a b - 6a b + 3a b +--R + +--R 5 +--R 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 4 +--R (- a b + a b)cos(x)sin(x) +--R + +--R 3 3 4 2 3 3 3 4 2 5 2 +--R (- 2a b - 2a b )cos(x) + (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 4 2 5 6 5 2 4 3 3 4 2 5 +--R (- 2a b - 2a b)cos(x) - 3b - 9a b + 6a b + 18a b - 3a b - 9a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 5 3 3 4 2 5 4 +--R (- a b - 2a b - a b)cos(x) + (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 3b - 3a b + 6a b + 8a b + a b - a b)cos(x) +--R + +--R 3 3 4 2 5 6 5 2 4 3 3 4 2 5 +--R (a b + 2a b + a b)cos(x) + 3b + 3a b - 6a b - 6a b + 3a b + 3a b +--R / +--R 5 2 6 7 2 5 2 7 2 +--R (3a b - 6a b + 3a )sin(x) + (3a b - 3a )cos(x) +--R + +--R 5 2 7 5 2 7 +--R (6a b - 6a )cos(x) + 3a b - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 7 2 5 2 6 7 2 +--R (3a b - 3a )sin(x) + (3a b + 6a b + 3a )cos(x) +--R + +--R 5 2 6 7 5 2 6 7 +--R (6a b + 12a b + 6a )cos(x) + 3a b + 6a b + 3a +--R Type: Expression(Integer) +--E 74 + +--S 75 of 586 +t0514:= cos(x)/(a+b*sec(x)) +--R +--R +--R cos(x) +--R (60) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 75 + +--S 76 of 586 +r0514:= -b*x/a^2+2*b^2*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/_ + a^2/(a^2-b^2)^(1/2)+sin(x)/a +--R +--R +--R x +--R (b - a)tan(-) +---------+ +--R 2 2 | 2 2 +--R - 2b atanh(-------------) + (a sin(x) - b x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (61) -------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 586 +a0514:= integrate(t0514,x) +--R +--R +--R (62) +--R [ +--R +---------+ +--R | 2 2 2 2 +--R 2 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R b log(----------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - b x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R , +--R +-------+ +--R | 2 2 +-------+ +--R 2 sin(x)\|b - a | 2 2 +--R 2b atan(---------------------) + (a sin(x) - b x)\|b - a +--R (b + a)cos(x) + b + a +--R -----------------------------------------------------------] +--R +-------+ +--R 2 | 2 2 +--R a \|b - a +--R Type: Union(List(Expression(Integer)),...) +--E 77 + +--S 78 of 586 +m0514a:= a0514.1-r0514 +--R +--R +--R (63) +--R +---------+ +--R | 2 2 2 2 +--R 2 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R b log(----------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R (b - a)tan(-) +--R 2 2 +--R 2b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 78 + +--S 79 of 586 +d0514a:= D(m0514a,x) +--R +--R +--R (64) +--R 3 2 2 2 2 3 2 3 x 2 +--R ((b - a b )sin(x) - a b cos(x) + (- b - a b )cos(x) - b )tan(-) +--R 2 +--R + +--R 3 2 2 2 2 3 2 3 +--R (b + a b )sin(x) + a b cos(x) + (b - a b )cos(x) - b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 4 2 2 x 2 +--R ((b - a b )cos(x) + b - a b )sin(x)tan(-) +--R 2 +--R + +--R 4 2 2 4 2 2 +--R ((b - a b )cos(x) - b + a b )sin(x) +--R / +--R 2 2 3 2 3 2 2 3 4 2 2 3 +--R ((a b - a b)cos(x) + (a b - a b + a b - a )cos(x) + a b - a b) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 3 2 2 3 4 2 2 3 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) + a b + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R ((- a b + a b + a b - a )cos(x) - a b + a b + a b - a b)sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R ((- a b - a b + a b + a )cos(x) - a b - a b + a b + a b)sin(x) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 586 +m0514b:= a0514.2-r0514 +--R +--R +--R (65) +--R x +--R +-------+ (b - a)tan(-) +--R 2 | 2 2 2 +--R 2b \|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 2 | 2 2 sin(x)\|b - a +--R 2b \|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression(Integer) +--E 80 + +--S 81 of 586 +d0514b:= D(m0514b,x) +--R +--R +--R (66) +--R 3 2 2 3 2 2 2 3 2 +--R ((b - a b )sin(x) + (b - 3a b )cos(x) - 4a b cos(x) - b - a b ) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 2 3 2 +--R (b + 3a b )sin(x) + (b + a b )cos(x) - b - a b +--R / +--R 2 2 3 4 2 2 2 4 2 2 2 4 +--R (a b - 2a b + a )sin(x) + (a b - a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 2 2 4 +--R a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 2 2 3 4 2 +--R (a b - a )sin(x) + (a b + 2a b + a )cos(x) +--R + +--R 2 2 3 4 2 2 3 4 +--R (2a b + 4a b + 2a )cos(x) + a b + 2a b + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 586 +t0515:= cos(x)^2/(a+b*sec(x)) +--R +--R +--R 2 +--R cos(x) +--R (67) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 82 + +--S 83 of 586 +r0515:= 1/2*x/a+b^2*x/a^3-2*b^3*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/_ + a^3/(a^2-b^2)^(1/2)-b*sin(x)/a^2+1/2*cos(x)*sin(x)/a +--R +--R +--R (68) +--R x +--R (b - a)tan(-) +---------+ +--R 3 2 2 2 2 | 2 2 +--R 4b atanh(-------------) + ((a cos(x) - 2a b)sin(x) + (2b + a )x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ----------------------------------------------------------------------------- +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression(Integer) +--E 83 + +--S 84 of 586 +a0515:= integrate(t0515,x) +--R +--R +--R (69) +--R [ +--R +---------+ +--R | 2 2 2 2 +--R 3 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R 2b log(------------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R ((a cos(x) - 2a b)sin(x) + (2b + a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 3 sin(x)\|b - a +--R - 4b atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R ((a cos(x) - 2a b)sin(x) + (2b + a )x)\|b - a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2a \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 84 + +--S 85 of 586 +m0515a:= a0515.1-r0515 +--R +--R +--R (70) +--R +---------+ +--R | 2 2 2 2 +--R 3 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R b log(------------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R (b - a)tan(-) +--R 3 2 +--R - 2b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 85 + +--S 86 of 586 +d0515a:= D(m0515a,x) +--R +--R +--R (71) +--R 4 3 2 3 2 4 3 4 x 2 +--R ((- b + a b )sin(x) + a b cos(x) + (b + a b )cos(x) + b )tan(-) +--R 2 +--R + +--R 4 3 2 3 2 4 3 4 +--R (- b - a b )sin(x) - a b cos(x) + (- b + a b )cos(x) + b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 5 2 3 x 2 +--R ((b - a b )cos(x) + b - a b )sin(x)tan(-) +--R 2 +--R + +--R 5 2 3 5 2 3 +--R ((b - a b )cos(x) - b + a b )sin(x) +--R / +--R 3 2 4 2 2 3 3 2 4 5 3 2 4 +--R ((a b - a b)cos(x) + (a b - a b + a b - a )cos(x) + a b - a b) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 2 2 3 3 2 4 5 3 2 4 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) + a b + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 x 2 +--R ((a b - a b - a b + a )cos(x) + a b - a b - a b + a b)sin(x)tan(-) +--R 2 +--R + +--R 3 3 4 2 5 6 2 4 3 3 4 2 5 +--R ((a b + a b - a b - a )cos(x) + a b + a b - a b - a b)sin(x) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 586 +m0515b:= a0515.2-r0515 +--R +--R +--R (72) +--R x +--R +-------+ (b - a)tan(-) +--R 3 | 2 2 2 +--R - 2b \|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 | 2 2 sin(x)\|b - a +--R - 2b \|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R / +--R +---------+ +-------+ +--R 3 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 586 +d0515b:= D(m0515b,x) +--R +--R +--R (73) +--R 4 3 2 4 3 2 3 4 +--R (- b + a b )sin(x) + (- b + 3a b )cos(x) + 4a b cos(x) + b +--R + +--R 3 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 4 3 2 4 3 +--R (- b - 3a b )sin(x) + (- b - a b )cos(x) + b + a b +--R / +--R 3 2 4 5 2 3 2 5 2 3 2 5 +--R (a b - 2a b + a )sin(x) + (a b - a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 3 2 5 +--R a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 2 3 2 4 5 2 +--R (a b - a )sin(x) + (a b + 2a b + a )cos(x) +--R + +--R 3 2 4 5 3 2 4 5 +--R (2a b + 4a b + 2a )cos(x) + a b + 2a b + a +--R Type: Expression(Integer) +--E 88 + +--S 89 of 586 +t0516:= cos(x)^3/(a+b*sec(x)) +--R +--R +--R 3 +--R cos(x) +--R (74) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 89 + +--S 90 of 586 +r0516:= -1/2*b*x/a^2-b^3*x/a^4+2*b^4*atanh((a-b)*tan(1/2*x)/_ + (a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)+sin(x)/a+_ + b^2*sin(x)/a^3-1/2*b*cos(x)*sin(x)/a^2-1/3*sin(x)^3/a +--R +--R +--R (75) +--R x +--R (b - a)tan(-) +--R 4 2 +--R - 12b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 2 2 3 3 2 +--R (- 2a sin(x) + (- 3a b cos(x) + 6a b + 6a )sin(x) + (- 6b - 3a b)x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression(Integer) +--E 90 + +--S 91 of 586 +a0516:= integrate(t0516,x) +--R +--R +--R (76) +--R [ +--R +---------+ +--R | 2 2 2 2 +--R 4 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R 6b log(----------------------------------------------) +--R a cos(x) + b +--R + +--R 3 2 2 2 3 3 2 +--R ((2a cos(x) - 3a b cos(x) + 6a b + 4a )sin(x) + (- 6b - 3a b)x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 4 sin(x)\|b - a +--R 12b atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R 3 2 2 2 3 3 2 +--R ((2a cos(x) - 3a b cos(x) + 6a b + 4a )sin(x) + (- 6b - 3a b)x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6a \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 91 + +--S 92 of 586 +m0516a:= a0516.1-r0516 +--R +--R +--R (77) +--R +---------+ +--R | 2 2 2 2 +--R 4 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R 3b log(----------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R (b - a)tan(-) +---------+ +--R 4 2 3 3 3 2 3 | 2 2 +--R 6b atanh(-------------) + (a sin(x) + (a cos(x) - a )sin(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 3a \|- b + a +--R Type: Expression(Integer) +--E 92 + +--S 93 of 586 +d0516a:= D(m0516a,x) +--R +--R +--R (78) +--R 3 2 4 3 2 3 3 2 4 5 2 +--R (a b - a b)cos(x) + (a b - a b + a b - a )cos(x) +--R + +--R 3 2 4 5 4 +--R (a b - a b)cos(x) + 3b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 2 3 3 2 4 5 4 +--R (a b - a b)cos(x) + (a b - a b + a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 3a b - a b + a b - a b + a )cos(x) +--R + +--R 5 4 3 2 4 5 +--R (- 3b - 3a b - a b + a b)cos(x) - 3b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 3 2 3 3 2 4 5 2 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) +--R + +--R 3 2 4 5 4 +--R (a b + a b)cos(x) + 3b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 2 3 3 2 4 5 4 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (3a b - a b - a b - a b - a )cos(x) +--R + +--R 5 4 3 2 4 5 +--R (3b - 3a b - a b - a b)cos(x) - 3b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 4 2 5 6 2 +--R (- a b + a b + a b - a )cos(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- a b + a b + a b - a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 4 2 5 6 4 +--R (- a b + a b + a b - a )cos(x) +--R + +--R 2 4 3 3 4 2 5 3 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (a b - a b - a b + a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 4 +--R (3b - 2a b - a b - a b + a b)cos(x) + 3b - 3a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 5 6 2 +--R (- a b - a b + a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 +--R (- a b - a b + a b + a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 4 2 5 6 4 +--R (- a b - a b + a b + a )cos(x) +--R + +--R 2 4 3 3 4 2 5 3 3 3 4 2 5 6 2 +--R (- a b - a b + a b + a b)cos(x) + (a b + a b - a b - a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 2 4 +--R (3b - 2a b + a b - a b - a b)cos(x) - 3b + 3a b +--R * +--R sin(x) +--R / +--R 4 2 5 2 3 3 4 2 5 6 +--R (3a b - 3a b)cos(x) + (3a b - 3a b + 3a b - 3a )cos(x) +--R + +--R 4 2 5 +--R 3a b - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 3 4 2 5 6 4 2 +--R (3a b + 3a b)cos(x) + (3a b + 3a b + 3a b + 3a )cos(x) + 3a b +--R + +--R 5 +--R 3a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 5 2 6 7 3 4 4 3 5 2 6 +--R ((- 3a b + 3a b + 3a b - 3a )cos(x) - 3a b + 3a b + 3a b - 3a b) +--R * +--R x 2 +--R sin(x)tan(-) +--R 2 +--R + +--R 4 3 5 2 6 7 3 4 4 3 5 2 6 +--R ((- 3a b - 3a b + 3a b + 3a )cos(x) - 3a b - 3a b + 3a b + 3a b)sin(x) +--R Type: Expression(Integer) +--E 93 + +--S 94 of 586 +m0516b:= a0516.2-r0516 +--R +--R +--R (79) +--R x +--R +-------+ (b - a)tan(-) +--R 4 | 2 2 2 +--R 6b \|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 4 | 2 2 sin(x)\|b - a +--R 6b \|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +-------+ +--R 3 3 3 2 3 | 2 2 | 2 2 +--R (a sin(x) + (a cos(x) - a )sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 4 | 2 2 | 2 2 +--R 3a \|- b + a \|b - a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 586 +d0516b:= D(m0516b,x) +--R +--R +--R (80) +--R 3 2 4 5 4 +--R (a b - 2a b + a )cos(x)sin(x) +--R + +--R 3 2 4 3 3 2 5 2 4 5 +--R (2a b - 2a b)cos(x) + (2a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 5 4 +--R 3b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 5 4 3 2 5 2 4 3 2 5 +--R (3b - 9a b - 2a b + 2a )cos(x) + (- 12a b - a b + a )cos(x) +--R + +--R 5 4 +--R - 3b - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 4 +--R (a b - a )cos(x)sin(x) +--R + +--R 3 2 4 3 3 2 4 5 2 +--R (2a b + 2a b)cos(x) + (2a b + 4a b + 2a )cos(x) +--R + +--R 4 5 5 4 +--R (2a b + 2a )cos(x) + 3b + 9a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 5 5 3 2 4 5 4 +--R (a b + 2a b + a )cos(x) + (2a b + 4a b + 2a )cos(x) +--R + +--R 5 4 3 2 4 5 2 3 2 4 5 +--R (3b + 3a b - 2a b - 4a b - 2a )cos(x) + (- a b - 2a b - a )cos(x) +--R + +--R 5 4 +--R - 3b - 3a b +--R / +--R 4 2 5 6 2 4 2 6 2 +--R (3a b - 6a b + 3a )sin(x) + (3a b - 3a )cos(x) +--R + +--R 4 2 6 4 2 6 +--R (6a b - 6a )cos(x) + 3a b - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 6 2 4 2 5 6 2 +--R (3a b - 3a )sin(x) + (3a b + 6a b + 3a )cos(x) +--R + +--R 4 2 5 6 4 2 5 6 +--R (6a b + 12a b + 6a )cos(x) + 3a b + 6a b + 3a +--R Type: Expression(Integer) +--E 95 + +--S 96 of 586 +t0517:= cos(x)^4/(a+b*sec(x)) +--R +--R +--R 4 +--R cos(x) +--R (81) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 96 + +--S 97 of 586 +r0517:= 3/8*x/a+1/2*b^2*x/a^3+b^4*x/a^5-2*b^5*atanh((a-b)*tan(1/2*x)/_ + (a^2-b^2)^(1/2))/a^5/(a^2-b^2)^(1/2)-b*sin(x)/a^2-b^3*sin(x)/a^4+_ + 3/8*cos(x)*sin(x)/a+1/2*b^2*cos(x)*sin(x)/a^3+1/4*cos(x)^3*_ + sin(x)/a+1/3*b*sin(x)^3/a^2 +--R +--R +--R (82) +--R x +--R (b - a)tan(-) +--R 5 2 +--R 48b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 +--R 8a b sin(x) +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (12a b + 9a )cos(x) - 24a b - 24a b)sin(x) +--R + +--R 4 2 2 4 +--R (24b + 12a b + 9a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 24a \|- b + a +--R Type: Expression(Integer) +--E 97 + +--S 98 of 586 +a0517:= integrate(t0517,x) +--R +--R +--R (83) +--R [ +--R +---------+ +--R | 2 2 2 2 +--R 5 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R 24b log(------------------------------------------------) +--R a cos(x) + b +--R + +--R 4 3 3 2 2 2 4 3 +--R 6a cos(x) - 8a b cos(x) + (12a b + 9a )cos(x) - 24a b +--R + +--R 3 +--R - 16a b +--R * +--R sin(x) +--R + +--R 4 2 2 4 +--R (24b + 12a b + 9a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 24a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 5 sin(x)\|b - a +--R - 48b atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R 4 3 3 2 2 2 4 3 +--R 6a cos(x) - 8a b cos(x) + (12a b + 9a )cos(x) - 24a b +--R + +--R 3 +--R - 16a b +--R * +--R sin(x) +--R + +--R 4 2 2 4 +--R (24b + 12a b + 9a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 5 | 2 2 +--R 24a \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 98 + +--S 99 of 586 +m0517a:= a0517.1-r0517 +--R +--R +--R (84) +--R +---------+ +--R | 2 2 2 2 +--R 5 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R 3b log(------------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R (b - a)tan(-) +--R 5 2 +--R - 6b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 3 3 2 3 | 2 2 +--R (- a b sin(x) + (- a b cos(x) + a b)sin(x))\|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 3a \|- b + a +--R Type: Expression(Integer) +--E 99 + +--S 100 of 586 +d0517a:= D(m0517a,x) +--R +--R +--R (85) +--R 3 3 4 2 3 2 4 3 3 4 2 5 2 +--R (- a b + a b )cos(x) + (- a b + a b - a b + a b)cos(x) +--R + +--R 3 3 4 2 6 5 +--R (- a b + a b )cos(x) - 3b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 2 4 3 3 4 2 5 4 +--R (- a b + a b )cos(x) + (- a b + a b - a b + a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (3a b + a b - a b + a b - a b)cos(x) +--R + +--R 6 5 3 3 4 2 6 +--R (3b + 3a b + a b - a b )cos(x) + 3b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 3 2 4 3 3 4 2 5 2 +--R (- a b - a b )cos(x) + (- a b - a b - a b - a b)cos(x) +--R + +--R 3 3 4 2 6 5 +--R (- a b - a b )cos(x) - 3b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 2 4 3 3 4 2 5 4 +--R (- a b - a b )cos(x) + (- a b - a b - a b - a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (- 3a b + a b + a b + a b + a b)cos(x) +--R + +--R 6 5 3 3 4 2 6 +--R (- 3b + 3a b + a b + a b )cos(x) + 3b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 4 4 3 5 2 6 2 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- a b + a b + a b - a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (- a b + a b + a b - a b )cos(x) +--R + +--R 3 4 4 3 5 2 6 2 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 7 2 5 +--R (3b - 2a b - a b - a b + a b )cos(x) + 3b - 3a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 4 3 5 2 6 2 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 +--R (- a b - a b + a b + a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 4 3 5 2 6 4 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 3 4 4 3 5 2 6 2 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 7 2 5 3 4 4 3 5 2 7 2 5 +--R (3b - 2a b + a b - a b - a b )cos(x) - 3b + 3a b +--R * +--R sin(x) +--R / +--R 5 2 6 2 4 3 5 2 6 7 +--R (3a b - 3a b)cos(x) + (3a b - 3a b + 3a b - 3a )cos(x) +--R + +--R 5 2 6 +--R 3a b - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 2 4 3 5 2 6 7 5 2 +--R (3a b + 3a b)cos(x) + (3a b + 3a b + 3a b + 3a )cos(x) + 3a b +--R + +--R 6 +--R 3a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 3 6 2 7 8 4 4 5 3 6 2 7 +--R ((3a b - 3a b - 3a b + 3a )cos(x) + 3a b - 3a b - 3a b + 3a b) +--R * +--R x 2 +--R sin(x)tan(-) +--R 2 +--R + +--R 5 3 6 2 7 8 4 4 5 3 6 2 7 +--R ((3a b + 3a b - 3a b - 3a )cos(x) + 3a b + 3a b - 3a b - 3a b)sin(x) +--R Type: Expression(Integer) +--E 100 + +--S 101 of 586 +m0517b:= a0517.2-r0517 +--R +--R +--R (86) +--R x +--R +-------+ (b - a)tan(-) +--R 5 | 2 2 2 +--R - 6b \|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 5 | 2 2 sin(x)\|b - a +--R - 6b \|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +-------+ +--R 3 3 3 2 3 | 2 2 | 2 2 +--R (- a b sin(x) + (- a b cos(x) + a b)sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 5 | 2 2 | 2 2 +--R 3a \|- b + a \|b - a +--R Type: Expression(Integer) +--E 101 + +--S 102 of 586 +d0517b:= D(m0517b,x) +--R +--R +--R (87) +--R 3 3 4 2 5 4 +--R (- a b + 2a b - a b)cos(x)sin(x) +--R + +--R 3 3 4 2 3 3 3 5 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 4 2 5 6 5 +--R (- 2a b + 2a b)cos(x) - 3b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- a b + a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 6 5 3 3 5 2 5 3 3 5 +--R (- 3b + 9a b + 2a b - 2a b)cos(x) + (12a b + a b - a b)cos(x) +--R + +--R 6 5 +--R 3b + 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 4 +--R (- a b + a b)cos(x)sin(x) +--R + +--R 3 3 4 2 3 3 3 4 2 5 2 +--R (- 2a b - 2a b )cos(x) + (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 4 2 5 6 5 +--R (- 2a b - 2a b)cos(x) - 3b - 9a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 4 2 5 5 3 3 4 2 5 4 +--R (- a b - 2a b - a b)cos(x) + (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 6 5 3 3 4 2 5 2 +--R (- 3b - 3a b + 2a b + 4a b + 2a b)cos(x) +--R + +--R 3 3 4 2 5 6 5 +--R (a b + 2a b + a b)cos(x) + 3b + 3a b +--R / +--R 5 2 6 7 2 5 2 7 2 +--R (3a b - 6a b + 3a )sin(x) + (3a b - 3a )cos(x) +--R + +--R 5 2 7 5 2 7 +--R (6a b - 6a )cos(x) + 3a b - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 7 2 5 2 6 7 2 +--R (3a b - 3a )sin(x) + (3a b + 6a b + 3a )cos(x) +--R + +--R 5 2 6 7 5 2 6 7 +--R (6a b + 12a b + 6a )cos(x) + 3a b + 6a b + 3a +--R Type: Expression(Integer) +--E 102 + +--S 103 of 586 +t0518:= tan(x)/(a+b*sec(x)) +--R +--R +--R tan(x) +--R (88) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 103 + +--S 104 of 586 +r0518:= -log(b+a*cos(x))/a +--R +--R +--R log(a cos(x) + b) +--R (89) - ----------------- +--R a +--R Type: Expression(Integer) +--E 104 + +--S 105 of 586 +a0518:= integrate(t0518,x) +--R +--R +--R 2a cos(x) + 2b 2 +--R - log(--------------) + log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (90) --------------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 105 + +--S 106 of 586 +m0518:= a0518-r0518 +--R +--R +--R 2a cos(x) + 2b 2 +--R log(a cos(x) + b) - log(--------------) + log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (91) --------------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 106 + +--S 107 of 586 +d0518:= D(m0518,x) +--R +--R +--R (92) 0 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 586 +t0519:= tan(x)^2/(a+b*sec(x)) +--R +--R +--R 2 +--R tan(x) +--R (93) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 108 + +--S 109 of 586 +r0519:= 1/a/b*(-b*x+a*atanh(sin(x))+2*(a^2-b^2)^(1/2)*_ + atanh((a-b)/(a^2-b^2)^(1/2)*(-1+cos(x))/sin(x))) +--R +--R +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R a atanh(sin(x)) - 2\|- b + a atanh(---------------------) - b x +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R (94) ----------------------------------------------------------------- +--R a b +--R Type: Expression(Integer) +--E 109 + +--S 110 of 586 +a0519:= integrate(t0519,x) +--R +--R +--R (95) +--R [ +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x)\|- b + a - b cos(x) - a +--R \|- b + a log(---------------------------------) +--R a cos(x) + b +--R + +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R a log(-------------------) - a log(-------------------) - b x +--R cos(x) + 1 cos(x) + 1 +--R / +--R a b +--R , +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R a log(-------------------) - a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a +--R - 2\|b - a atan(----------------------) - b x +--R (b - a)sin(x) +--R / +--R a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 110 + +--S 111 of 586 +m0519a:= a0519.1-r0519 +--R +--R +--R (96) +--R +---------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x)\|- b + a - b cos(x) - a +--R \|- b + a log(---------------------------------) +--R a cos(x) + b +--R + +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R a log(-------------------) - a log(-------------------) - a atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2\|- b + a atanh(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R / +--R a b +--R Type: Expression(Integer) +--E 111 + +--S 112 of 586 +d0519a:= D(m0519a,x) +--R +--R +--R (97) +--R 2 2 3 2 2 3 7 +--R ((- 2a b - 2a b)cos(x) - b - a b - a b - a )sin(x) +--R + +--R 2 3 2 3 2 3 2 2 +--R - 4a b cos(x) + (3a b - 9a )cos(x) + (2b + 7a b - 7a b)cos(x) +--R + +--R 3 2 2 3 +--R 3b - 3a b + a b + 3a +--R * +--R 5 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (2a b - 2a b)cos(x) + (b + a b + 3a b - 7a )cos(x) +--R + +--R 3 2 3 2 2 3 2 +--R (2b - 4a b)cos(x) + (- 6a b - 6a b + 14a )cos(x) +--R + +--R 3 2 2 3 2 2 3 +--R (- 4b - 6a b + 12a b)cos(x) - 3b + 5a b + a b - 3a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 6 2 2 5 +--R (- a b + a )cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 3 +--R (- b - a b - a b + 3a )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 2 2 3 2 3 2 2 3 +--R (2a b + 3a b - 5a )cos(x) + (2b + a b - 3a b)cos(x) + b +--R + +--R 2 2 3 +--R - a b - a b + a +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 4 8 +--R (- a b - a b + a b + a )sin(x) +--R + +--R 3 2 2 3 4 2 4 3 2 2 3 +--R (a b + 3a b + a b - a )cos(x) + (b + 5a b + 3a b - a b)cos(x) +--R + +--R 3 2 2 3 4 +--R 3a b + 5a b - a b - 3a +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 4 3 2 2 3 3 +--R (a b + 5a b - a b - a )cos(x) + (4a b - 3a b + 9a b)cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b - 8a b + 8a b - 2a b + 8a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 3 4 +--R (- 3b - 7a b - 8a b + 12a b)cos(x) - 3a b - 3a b - a b + 3a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 4 6 +--R (- a b + a b - a b + a )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b - a b - 5a b + 9a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 2 2 3 3 +--R (- 2b - 5a b + 5a b + a b + 5a )cos(x) + (6a b - 6a b)cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (4b + 11a b - 11a b + a b - 9a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 3 4 +--R (3b + 3a b + 5a b - 13a b)cos(x) + a b - a b + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 7 3 2 2 3 4 6 +--R (a b - a b)cos(x) + (2a b - 2a b + 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 5 4 3 2 2 3 4 +--R (b + a b + 4a b - 6a b)cos(x) + (2b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 2 2 3 3 4 3 2 2 4 2 +--R (- 5a b + 5a b)cos(x) + (- 2b - 4a b + 4a b + 2a )cos(x) +--R + +--R 4 3 3 +--R (- b - a b + 2a b)cos(x) +--R / +--R 2 2 3 3 2 2 7 +--R ((a b + a b)cos(x) + a b + a b )sin(x) +--R + +--R 3 3 2 2 2 3 2 2 3 +--R - 2a b cos(x) - 6a b cos(x) + (- 4a b - a b - 3a b)cos(x) +--R + +--R 3 2 2 +--R - a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 2 3 5 3 2 2 4 2 2 3 +--R (- a b + a b)cos(x) + (- a b + a b )cos(x) + 2a b cos(x) +--R + +--R 3 2 2 2 3 2 2 3 3 2 2 +--R (2a b + 4a b )cos(x) + (4a b - a b + 3a b)cos(x) - a b + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 5 3 2 2 4 +--R (a b - a b)cos(x) + (a b - a b )cos(x) +--R + +--R 2 2 3 3 3 2 2 2 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 2 3 3 2 2 +--R (a b - a b)cos(x) + a b - a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 2 4 2 3 3 2 4 2 3 +--R (- a b - a b )cos(x) + (- a b - a b - a b - a b)cos(x) - a b +--R + +--R 3 2 +--R - a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 4 2 3 4 3 4 2 3 3 2 2 +--R 2a b cos(x) + (6a b + 2a b)cos(x) + (4a b + a b + 9a b )cos(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (a b + 7a b + a b + 3a b)cos(x) + a b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 6 4 2 3 3 2 4 5 +--R (a b - a b )cos(x) + (a b - a b + a b - a b)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 3 +--R (- a b - a b )cos(x) + (- 2a b - 4a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 2 4 2 3 3 2 4 +--R (- 4a b - a b - 7a b )cos(x) + (a b - 7a b + a b - 3a b)cos(x) +--R + +--R 2 3 3 2 +--R a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 6 4 2 3 3 2 4 5 +--R (- a b + a b )cos(x) + (- a b + a b - a b + a b)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 4 3 +--R (a b - a b )cos(x) + (2a b - 2a b + 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 2 4 2 3 3 2 4 2 3 3 2 +--R (a b - a b )cos(x) + (- a b + a b - a b + a b)cos(x) - a b + a b +--R Type: Expression(Integer) +--E 112 + +--S 113 of 586 +m0519b:= a0519.2-r0519 +--R +--R +--R (98) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R a log(-------------------) - a log(-------------------) - a atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 (b - a)cos(x) - b + a +--R 2\|- b + a atanh(---------------------) +--R +---------+ +--R | 2 2 +--R sin(x)\|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a +--R - 2\|b - a atan(----------------------) +--R (b - a)sin(x) +--R / +--R a b +--R Type: Expression(Integer) +--E 113 + +--S 114 of 586 +d0519b:= D(m0519b,x) +--R +--R +--R (99) +--R 2 3 8 +--R (2a b - 2a )sin(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- 10a b + 2a )cos(x) + (- 4b - 9a b - 12a b + 9a )cos(x) +--R + +--R 2 3 +--R - 14a b + 6a +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 2 2 3 3 +--R (- 10a b + 2a )cos(x) + (- 3a b - 16a b - a )cos(x) +--R + +--R 3 2 2 3 2 +--R (8b + 16a b - 16a b - 16a )cos(x) +--R + +--R 3 2 2 3 2 3 +--R (12b + 15a b + 4a b - 19a )cos(x) + 14a b - 6a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 6 3 2 2 3 5 +--R (2a b - 2a )cos(x) + (4b + 5a b - 4a b - 9a )cos(x) +--R + +--R 3 2 2 3 4 2 3 3 +--R (8b + 10a b - 16a b - 10a )cos(x) + (- 6a b + 6a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 16b - 18a b + 24a b + 18a )cos(x) +--R + +--R 3 2 2 3 2 3 +--R (- 12b - 7a b + 12a b + 11a )cos(x) - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 7 2 3 6 +--R (- a b + a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 3 2 2 3 5 3 2 4 +--R (- 4b - 5a b + 4a b + 5a )cos(x) + (- 8b + 8a b)cos(x) +--R + +--R 2 3 3 3 2 2 3 2 +--R (5a b - 5a )cos(x) + (8b + 4a b - 8a b - 4a )cos(x) +--R + +--R 3 2 2 3 +--R (4b + a b - 4a b - a )cos(x) +--R / +--R 3 3 8 +--R (a b - a b)sin(x) +--R + +--R 3 3 2 3 2 2 3 3 6 +--R ((a b + 3a b)cos(x) + (- 2a b + 8a b + 2a b)cos(x) + 4a b)sin(x) +--R + +--R 3 3 4 3 2 2 3 3 +--R (- a b - 3a b)cos(x) + (- 4a b - 8a b - 4a b)cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- 7a b - 16a b - 5a b)cos(x) + (- 2a b - 16a b - 6a b)cos(x) +--R + +--R 3 3 +--R - 2a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 6 3 3 5 +--R (- a b + a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 3 3 4 3 2 2 3 +--R (2a b + 2a b)cos(x) + (8a b + 8a b )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 3 +--R (7a b + 16a b + a b)cos(x) + (2a b + 8a b + 6a b)cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 6 3 3 5 3 3 4 +--R (a b - a b)cos(x) + (2a b - 2a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R (- 4a b + 4a b)cos(x) + (- a b + a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 3 +--R a b - a b +--R Type: Expression(Integer) +--E 114 + +--S 115 of 586 +t0520:= tan(x)^4/(a+b*sec(x)) +--R +--R +--R 4 +--R tan(x) +--R (100) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 115 + +--S 116 of 586 +r0520:= x/a+a^2*atanh(sin(x))/b^3-3/2*atanh(sin(x))/b-_ + 2*(a^2-b^2)^(3/2)*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a/b^3-_ + a*tan(x)/b^2+1/2*sec(x)*tan(x)/b +--R +--R +--R (101) +--R 2 3 +--R (- 3a b + 2a )atanh(sin(x)) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 2 2 2 +--R (- 4b + 4a )\|- b + a atanh(-------------) + (a b sec(x) - 2a b)tan(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 +--R 2b x +--R / +--R 3 +--R 2a b +--R Type: Expression(Integer) +--E 116 + +--S 117 of 586 +a0520:= integrate(t0520,x) +--R +--R +--R (102) +--R [ +--R 2 3 2 sin(x) + cos(x) + 1 +--R (- 3a b + 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 3 2 sin(x) - cos(x) - 1 +--R (3a b - 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 2 | 2 2 - sin(x)\|- b + a - b cos(x) - a +--R (2b - 2a )cos(x) \|- b + a log(-----------------------------------) +--R a cos(x) + b +--R + +--R 2 2 3 2 +--R (- 2a b cos(x) + a b )sin(x) + 2b x cos(x) +--R / +--R 3 2 +--R 2a b cos(x) +--R , +--R +--R 2 3 2 sin(x) + cos(x) + 1 +--R (- 3a b + 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 3 2 sin(x) - cos(x) - 1 +--R (3a b - 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 2 | 2 2 (cos(x) + 1)\|b - a +--R (4b - 4a )cos(x) \|b - a atan(----------------------) +--R (b - a)sin(x) +--R + +--R 2 2 3 2 +--R (- 2a b cos(x) + a b )sin(x) + 2b x cos(x) +--R / +--R 3 2 +--R 2a b cos(x) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 117 + +--S 118 of 586 +m0520a:= a0520.1-r0520 +--R +--R +--R (103) +--R 2 3 2 sin(x) + cos(x) + 1 +--R (- 3a b + 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 3 2 sin(x) - cos(x) - 1 +--R (3a b - 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R +---------+ | 2 2 +--R 2 2 2 | 2 2 - sin(x)\|- b + a - b cos(x) - a +--R (2b - 2a )cos(x) \|- b + a log(-----------------------------------) +--R a cos(x) + b +--R + +--R 2 3 2 +--R (3a b - 2a )cos(x) atanh(sin(x)) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 2 | 2 2 2 +--R (4b - 4a )cos(x) \|- b + a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 2 2 +--R (- a b cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + a b )sin(x) +--R / +--R 3 2 +--R 2a b cos(x) +--R Type: Expression(Integer) +--E 118 + +--S 119 of 586 +d0520a:= D(m0520a,x) +--R +--R +--R (104) +--R 3 2 2 4 4 3 3 +--R ((- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) )sec(x) +--R + +--R 2 2 3 4 3 2 2 3 +--R (2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (2a b - 2a b )cos(x) + (2b + 2a b - 4a b )cos(x) +--R + +--R 4 2 2 4 4 3 3 +--R (4b - 4a b )cos(x) + (4b - 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 6 3 2 2 3 5 +--R (- 2a b + 2a b)cos(x) + (- 2a b - 2a b + 4a b)cos(x) +--R + +--R 3 3 4 3 2 2 3 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 6 +--R (- 2a b + 2a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (- 2b - 2a b + 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (- 4b + 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 6 3 2 2 3 5 +--R (2a b - 2a b)cos(x) + (2a b + 2a b - 4a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R (4a b - 2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 4 3 3 +--R ((- 2a b - 2a b )cos(x) + (- 2b - 2a b )cos(x) )sec(x) +--R + +--R 2 2 3 4 3 2 2 3 +--R (2a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (2a b + 2a b )cos(x) + (2b + 6a b + 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (4b + 8a b + 4a b )cos(x) + (4b + 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 6 3 2 2 3 5 +--R (- 2a b - 2a b)cos(x) + (- 2a b - 6a b - 4a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R (- 4a b - 8a b - 4a b)cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (- 2a b - 2a b )cos(x) + (- 2b - 6a b - 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (- 4b - 6a b - 2a b )cos(x) + (- 2b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 6 3 2 2 3 5 +--R (2a b + 2a b)cos(x) + (2a b + 6a b + 4a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 +--R (4a b + 6a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 2 4 3 7 +--R ((- 2a b + 2a b)cos(x) + 2b - 2a b )sin(x) +--R + +--R 3 2 2 4 4 3 3 +--R ((- a b + a b )cos(x) + (- b + a b )cos(x) )sec(x) +--R + +--R 4 3 2 2 3 4 4 +--R (2b + 6a b - 8a b - 6a b + 6a )cos(x) +--R + +--R 4 3 2 2 4 3 +--R (8b - 5a b - 5a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- b + a b + 4a b - 4a b)cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 4 3 +--R - 4b + 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (a b - a b )cos(x) + (b + a b - 2a b )cos(x) +--R + +--R 4 2 2 4 4 3 3 +--R (2b - 2a b )cos(x) + (2b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 2b + 6a b - 2a b - 4a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 5 +--R (- 4a b + 6a b + 2a b - 4a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 6b - 10a b + 20a b + 8a b - 12a )cos(x) +--R + +--R 4 3 2 2 4 3 +--R (- 12b + 6a b + 10a b - 4a )cos(x) +--R + +--R 2 2 3 2 4 3 4 3 +--R (- 2a b + 2a b)cos(x) + (4b - 4a b )cos(x) + 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (- a b + a b )cos(x) + (- b - a b + 2a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (- 2b + a b + a b )cos(x) + (- b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 4 7 +--R (3a b - 3a b - 2a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (5b - 3a b - 6a b + 2a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (6b - 2a b - 10a b + 2a b + 4a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (4b + 4a b - 12a b - 2a b + 6a )cos(x) +--R + +--R 4 3 2 2 4 3 4 3 2 +--R (4b - a b - 5a b + 2a )cos(x) + (b - a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 4 3 7 +--R ((- 2a b - 2a b)cos(x) + 2b + 2a b )sin(x) +--R + +--R 3 2 2 4 4 3 3 +--R ((- a b - a b )cos(x) + (- b - a b )cos(x) )sec(x) +--R + +--R 4 3 2 2 3 4 4 +--R (2b + 6a b + 4a b - 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 4 3 +--R (4b + 7a b + 5a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 2 4 3 4 +--R (- b - a b + 4a b + 4a b)cos(x) + (- 4b - 4a b )cos(x) - 4b +--R + +--R 3 +--R - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (a b + a b )cos(x) + (b + 3a b + 2a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (2b + 4a b + 2a b )cos(x) + (2b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 2b + 6a b + 10a b - 4a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (4b + 8a b + 2a b - 6a b - 4a )cos(x) +--R + +--R 4 3 2 2 4 4 +--R (2b - 6a b - 12a b + 4a )cos(x) +--R + +--R 4 3 2 2 4 3 2 2 3 2 +--R (- 4b - 10a b - 10a b + 4a )cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 4 3 4 3 +--R (4b + 4a b )cos(x) + 2b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 5 +--R (- a b - a b )cos(x) + (- b - 3a b - 2a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 3 +--R (- 2b - 3a b - a b )cos(x) + (- b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 4 7 +--R (3a b + 3a b - 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (5b + 3a b - 6a b - 2a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (2b - 2a b - 6a b + 2a b + 4a )cos(x) +--R + +--R 4 2 2 3 4 4 +--R (- 4b + 8a b + 2a b - 2a )cos(x) +--R + +--R 3 2 2 4 3 4 3 2 +--R (3a b + 5a b - 2a )cos(x) + (b + a b )cos(x) +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 3 5 +--R (- 2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b + 2a b - 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 +--R (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b - 2a b + 2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 +--R (2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (4b + 2a b - 2a b - 4a b )cos(x) +--R + +--R 5 3 2 4 4 2 3 3 +--R (4b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 2a b + 2a b + 4a b)cos(x) +--R + +--R 4 4 4 2 3 3 2 3 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 5 3 2 5 +--R (- 4b + 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 4 2 3 3 2 4 6 +--R (2a b - 2a b )cos(x) + (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 4 4 5 4 2 3 3 2 4 4 +--R (4a b - 4a b)cos(x) + (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 5 +--R (- 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 2a b - 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 4 2 3 3 2 4 4 +--R (2a b + 2a b )cos(x) + (2a b + 2a b + 2a b + 2a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (2a b + 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (2a b + 2a b )cos(x) + (2b + 6a b + 6a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (4b + 10a b + 10a b + 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (4b + 8a b + 8a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 6a b - 6a b - 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 10a b - 10a b - 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (- 4a b - 8a b - 8a b - 4a b)cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (- 2a b - 2a b )cos(x) + (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 4b - 8a b - 8a b - 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (- 2b - 6a b - 6a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 4 2 3 3 2 4 6 +--R (2a b + 2a b )cos(x) + (2a b + 6a b + 6a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (4a b + 8a b + 8a b + 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b + 6a b + 6a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 2b + 2a b + 2a b - 2a b - 2a b + 2a )cos(x) +--R + +--R 3 2 4 2 5 4 4 2 3 +--R (- 2a b + 2a b)cos(x) + (2b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (- a b + a b )cos(x) + (- b + a b - a b + a b )cos(x) +--R + +--R 4 2 3 3 +--R (- a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b + 6a b - 8a b - 6a b + 6a b)cos(x) +--R + +--R 5 4 2 3 5 4 +--R (12b - 7a b - 7a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (5b + 3a b - 13a b + 3a b + 6a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 4b + 3a b + a b + 4a b - 4a b)cos(x) +--R + +--R 5 2 3 4 2 3 +--R (- 4b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (a b - a b )cos(x) + (b + a b - a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 5 3 2 4 +--R (2b + a b - a b - 2a b )cos(x) + (2b - 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 4 5 7 +--R (4a b - 6a b + 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (4b - 10a b + 4a b + 8a b - 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 6b - 10a b + 16a b + 14a b - 10a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 20b + 8a b + 16a b + 4a b - 4a b - 4a )cos(x) +--R + +--R 5 4 2 3 4 5 3 +--R (- 6b - 6a b + 16a b - 6a b + 2a )cos(x) +--R + +--R 5 4 3 2 4 2 5 4 2 3 +--R (4b - 4a b - 2a b + 2a b)cos(x) + (2b + 2a b - 4a b )cos(x) +--R + +--R 4 2 3 +--R 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (- a b + a b )cos(x) + (- b - a b + a b + a b )cos(x) +--R + +--R 5 3 2 5 5 4 2 3 3 2 4 +--R (- 2b + 2a b )cos(x) + (- b - a b + a b + a b )cos(x) +--R + +--R 4 2 3 3 +--R (- a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (3a b - 3a b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (3b - a b + a b - 5a b - 2a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (2b + 7a b - 5a b - 12a b + 2a b + 6a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (4b + 10a b - 14a b - 12a b + 8a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (8b - a b - 9a b - 4a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 4 2 3 2 +--R (3b + a b - 5a b - a b + 2a b)cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 2b - 2a b + 2a b + 2a b - 2a b - 2a )cos(x) +--R + +--R 3 2 4 2 5 4 4 2 3 +--R (- 2a b - 2a b)cos(x) + (2b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 4 2 3 3 +--R (- a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (2b + 6a b + 4a b - 2a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 5 4 +--R (8b + 13a b + 3a b - 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (5b + 9a b - a b - 3a b + 6a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 4b - 5a b - a b + 4a b + 4a b)cos(x) +--R + +--R 5 4 2 3 4 2 3 +--R (- 4b - 8a b - 4a b )cos(x) - 4a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (a b + a b )cos(x) + (b + 3a b + 3a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 5a b + 5a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (2b + 4a b + 4a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (8a b + 6a b - 8a b - 4a b + 2a )cos(x) +--R + +--R 5 4 3 2 4 5 6 +--R (8b + 10a b - 4a b - 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b - 2a b - 4a b + 2a b - 2a b - 4a )cos(x) +--R + +--R 5 4 3 2 4 5 4 +--R (- 12b - 16a b + 4a b - 4a b - 4a )cos(x) +--R + +--R 5 4 4 5 3 +--R (- 6b - 10a b - 6a b - 2a )cos(x) +--R + +--R 5 4 3 2 4 2 5 4 2 3 +--R (4b + 4a b - 2a b - 2a b)cos(x) + (2b + 6a b + 4a b )cos(x) +--R + +--R 4 2 3 +--R 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (- a b - a b )cos(x) + (- b - 3a b - 3a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 2b - 4a b - 4a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (- b - 3a b - 3a b - a b )cos(x) + (- a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (3a b + 3a b - 2a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (3b + a b + a b + 5a b - 2a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 2b - a b + 5a b + 4a b - 2a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 5 5 +--R (- 4b + 2a b + 6a b - 4a b + 4a )cos(x) +--R + +--R 5 4 2 3 4 5 4 +--R (4b + 3a b - 3a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 4 2 3 2 +--R (3b + 3a b - a b + a b + 2a b)cos(x) + (a b + a b )cos(x) +--R / +--R 4 2 3 4 5 4 3 5 +--R ((2a b - 2a b )cos(x) + (2b - 2a b )cos(x) )sin(x) +--R + +--R 4 2 3 6 5 4 2 3 5 +--R (- 2a b + 2a b )cos(x) + (- 2b - 2a b + 4a b )cos(x) +--R + +--R 5 2 3 4 5 4 3 +--R (- 4b + 4a b )cos(x) + (- 4b + 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 5 +--R (2a b - 2a b )cos(x) + (2b + 2a b - 4a b )cos(x) +--R + +--R 5 4 2 3 4 5 4 3 +--R (4b - 2a b - 2a b )cos(x) + (2b - 2a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 5 4 3 5 +--R ((2a b + 2a b )cos(x) + (2b + 2a b )cos(x) )sin(x) +--R + +--R 4 2 3 6 5 4 2 3 5 +--R (- 2a b - 2a b )cos(x) + (- 2b - 6a b - 4a b )cos(x) +--R + +--R 5 4 2 3 4 5 4 3 +--R (- 4b - 8a b - 4a b )cos(x) + (- 4b - 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 5 +--R (2a b + 2a b )cos(x) + (2b + 6a b + 4a b )cos(x) +--R + +--R 5 4 2 3 4 5 4 3 +--R (4b + 6a b + 2a b )cos(x) + (2b + 2a b )cos(x) +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 4 5 6 5 2 4 3 3 4 +--R (2a b - 2a b )cos(x) + (2b - 2a b + 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (- 2a b + 2a b )cos(x) + (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 6 3 3 4 +--R (- 4b - 2a b + 2a b + 4a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 5 2 4 3 +--R (- 4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (2a b - 2a b )cos(x) + (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 6 3 3 5 6 5 2 4 3 3 4 +--R (4b - 4a b )cos(x) + (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 5 6 5 2 4 3 3 4 +--R (2a b + 2a b )cos(x) + (2b + 2a b + 2a b + 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b + 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (- 2a b - 2a b )cos(x) + (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 4b - 10a b - 10a b - 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 5 2 4 3 +--R (- 4b - 8a b - 8a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (2a b + 2a b )cos(x) + (2b + 6a b + 6a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 8a b + 8a b + 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 5 2 4 3 +--R (2b + 6a b + 6a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R Type: Expression(Integer) +--E 119 + +--S 120 of 586 +m0520b:= a0520.2-r0520 +--R +--R +--R (105) +--R 2 3 2 sin(x) + cos(x) + 1 +--R (- 3a b + 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 3 2 sin(x) - cos(x) - 1 +--R (3a b - 2a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 2 3 2 +--R (3a b - 2a )cos(x) atanh(sin(x)) +--R + +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 2 | 2 2 2 +--R (4b - 4a )cos(x) \|- b + a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 2 | 2 2 (cos(x) + 1)\|b - a +--R (4b - 4a )cos(x) \|b - a atan(----------------------) +--R (b - a)sin(x) +--R + +--R 2 2 2 2 2 2 +--R (- a b cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + a b )sin(x) +--R / +--R 3 2 +--R 2a b cos(x) +--R Type: Expression(Integer) +--E 120 + +--S 121 of 586 +d0520b:= D(m0520b,x) +--R +--R +--R (106) +--R 4 2 3 3 2 3 +--R (- 2a b + 4a b - 2a b )cos(x) sec(x) +--R + +--R 2 3 3 2 4 3 +--R (2a b - 4a b + 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 5 2 3 3 2 4 +--R (- 4a b + 4a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (2a b - 8a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 4 5 3 2 4 4 +--R (4a b - 4a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 3 3 2 4 3 +--R (- 2a b + 8a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (2a b - 2a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (12a b + 4a b - 16a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (8a b + 8a b - 16a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (2a b + 4a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 2a b + 2a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 12a b - 4a b + 16a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (- 8a b - 8a b + 16a b)cos(x) +--R + +--R 2 3 3 2 4 3 +--R (- 2a b - 4a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 2a b + 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 12a b + 12a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (12a b - 12a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 3 4 3 +--R (2a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 2 3 4 3 6 +--R ((- 2a b + 2a b )cos(x) sec(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 2 3 3 2 5 2 3 3 2 4 +--R (- 4a b - 4a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (2a b - 4a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 4 5 3 2 4 4 +--R (4a b + 4a b)cos(x) + (8a b + 8a b)cos(x) +--R + +--R 2 3 3 2 4 3 +--R (- 2a b + 4a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 2 7 +--R (2a b + 4a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (8a b + 16a b + 8a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (12a b + 28a b + 16a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (8a b + 24a b + 16a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (2a b + 8a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 4 7 +--R (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 2 3 3 2 4 6 +--R (- 8a b - 16a b - 8a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R (- 12a b - 28a b - 16a b)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 4 3 +--R (- 8a b - 24a b - 16a b)cos(x) + (- 2a b - 8a b - 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 7 +--R (- 2a b - 4a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 6 +--R (- 8a b - 16a b - 8a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (- 12a b - 24a b - 12a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (- 8a b - 16a b - 8a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (- 2a b - 4a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 4 7 2 3 3 2 4 6 +--R (2a b + 4a b + 2a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 3 3 2 4 4 +--R (12a b + 24a b + 12a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 2 3 3 2 4 3 +--R (2a b + 4a b + 2a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 8 +--R ((- 2a b + 4a b - 2a b)cos(x) + 2a b - 4a b + 2a b )sin(x) +--R + +--R 4 2 3 3 2 3 +--R (- a b + 2a b - a b )cos(x) sec(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 2b + 8a b - 8a b - 6a b + 10a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (a b + 2a b - 11a b + 8a b)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 +--R (10a b - 16a b + 6a b)cos(x) - 2a b + 8a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 5 2 3 3 2 4 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (a b - 4a b + 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 10a b - 16a b + 6a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 5 4 +--R (4b + 17a b - 4a b - 27a b + 10a )cos(x) +--R + +--R 5 4 2 3 4 5 3 +--R (6b - 10a b + 16a b - 18a b + 6a )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (- 13a b + 8a b + 21a b - 16a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (- 8a b - 6a b + 20a b - 6a b)cos(x) - 2a b - 4a b + 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (a b - a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 2 3 3 2 5 +--R (6a b + 2a b - 8a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (4a b + 4a b - 8a b )cos(x) + (a b + 2a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 3 3 2 4 5 7 +--R (2b - 4a b + 2a b + 2a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (4b - 3a b - 14a b + 17a b + 8a b - 12a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 26a b - 2a b + 50a b + 2a b - 24a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 8b - 32a b + 12a b + 52a b - 4a b - 20a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 6b - 4a b - 4a b + 14a b + 6a b - 6a )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (11a b - 10a b - 9a b + 8a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 3 2 +--R (8a b - 2a b - 8a b + 2a b)cos(x) + 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- a b + a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 6a b + 6a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 3 2 3 +--R (- a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 5 8 +--R (3a b - 5a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 2b + 12a b + 4a b - 22a b - 2a b + 10a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 4b + 21a b + 8a b - 41a b - 4a b + 20a )cos(x) +--R + +--R 4 3 2 5 5 +--R (22a b - 42a b + 20a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (4b + 15a b - 8a b - 25a b + 4a b + 10a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (2b + 6a b - 4a b - 8a b + 2a b + 2a )cos(x) +--R + +--R 4 3 2 2 +--R (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 4 3 2 8 +--R ((- 2a b + 2a b)cos(x) + 2a b - 2a b )sin(x) +--R + +--R 4 3 2 3 +--R (- a b + a b )cos(x) sec(x) +--R + +--R 5 2 3 3 2 4 5 3 +--R (- 2b + 4a b - 2a b - 6a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 2 2 3 3 2 4 +--R (a b + 4a b - 5a b - 8a b)cos(x) + (10a b + 4a b - 6a b)cos(x) +--R + +--R 4 2 3 3 2 +--R - 2a b + 4a b + 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 3 2 5 2 3 3 2 4 +--R (- 2a b - 2a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (a b - 2a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b + 14a b - 12a b - 6a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (4b + 25a b + 22a b - 9a b - 4a b + 6a )cos(x) +--R + +--R 5 4 3 2 4 5 3 +--R (6b + 6a b + 8a b + 14a b + 6a )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (- 13a b - 18a b + 11a b + 16a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (- 8a b - 22a b - 8a b + 6a b)cos(x) - 2a b - 8a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 2 7 4 2 3 3 2 6 +--R (a b + 2a b + a b )cos(x) + (4a b + 8a b + 4a b )cos(x) +--R + +--R 4 2 3 3 2 5 4 2 3 3 2 4 +--R (6a b + 14a b + 8a b )cos(x) + (4a b + 12a b + 8a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (a b + 4a b + 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (2b + 8a b + 8a b - 2a b - 6a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (4b + 21a b + 20a b - 9a b - 16a b - 4a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 2a b + 2a b + 2a b - 10a b - 8a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 8b - 32a b - 20a b + 12a b - 4a b - 12a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 6b - 12a b - 8a b - 6a b - 10a b - 6a )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (11a b + 12a b - 7a b - 8a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (8a b + 14a b + 4a b - 2a b)cos(x) + 2a b + 4a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 7 4 2 3 3 2 6 +--R (- a b - 2a b - a b )cos(x) + (- 4a b - 8a b - 4a b )cos(x) +--R + +--R 4 2 3 3 2 5 4 2 3 3 2 4 +--R (- 6a b - 12a b - 6a b )cos(x) + (- 4a b - 8a b - 4a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (- a b - 2a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (3a b + 6a b + a b - 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 2b + 4a b + 16a b + 6a b - 10a b - 6a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 4b - 3a b + 10a b + 9a b - 4a b - 4a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 2a b - 4a b + 2a b + 8a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (4b + 7a b - 2a b - 3a b + 8a b + 6a )cos(x) +--R + +--R 5 4 2 3 4 5 3 4 2 3 3 2 2 +--R (2b + 6a b + 4a b + 2a b + 2a )cos(x) + (a b + 2a b + a b )cos(x) +--R / +--R 5 2 4 3 3 3 6 +--R (2a b - 4a b + 2a b )cos(x) sin(x) +--R + +--R 2 4 3 3 5 2 4 3 3 4 +--R (4a b - 4a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (- 2a b + 8a b - 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 6 +--R (- 2a b + 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 5 2 4 3 3 5 +--R (- 12a b - 4a b + 16a b )cos(x) +--R + +--R 5 2 4 3 3 4 +--R (- 8a b - 8a b + 16a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (- 2a b - 4a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 6 +--R (2a b - 2a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (12a b - 12a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 5 3 3 3 +--R (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 3 6 +--R (2a b - 2a b )cos(x) sin(x) +--R + +--R 2 4 3 3 5 2 4 3 3 4 +--R (4a b + 4a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (- 2a b + 4a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 4 3 3 7 5 2 4 3 3 6 +--R (- 2a b - 4a b - 2a b )cos(x) + (- 8a b - 16a b - 8a b )cos(x) +--R + +--R 5 2 4 3 3 5 +--R (- 12a b - 28a b - 16a b )cos(x) +--R + +--R 5 2 4 3 3 4 5 2 4 3 3 3 +--R (- 8a b - 24a b - 16a b )cos(x) + (- 2a b - 8a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 3 3 7 5 2 4 3 3 6 +--R (2a b + 4a b + 2a b )cos(x) + (8a b + 16a b + 8a b )cos(x) +--R + +--R 5 2 4 3 3 5 5 2 4 3 3 4 +--R (12a b + 24a b + 12a b )cos(x) + (8a b + 16a b + 8a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (2a b + 4a b + 2a b )cos(x) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 586 +t0521:= sec(x)^2/(a+b*sec(x)) +--R +--R +--R 2 +--R sec(x) +--R (107) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 122 + +--S 123 of 586 +r0521:= atanh(sin(x))/b-2*a*atanh((a-b)*_ + tan(1/2*x)/(a^2-b^2)^(1/2))/b/(a^2-b^2)^(1/2) +--R +--R +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R \|- b + a atanh(sin(x)) + 2a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (108) --------------------------------------------------- +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R Type: Expression(Integer) +--E 123 + +--S 124 of 586 +a0521:= integrate(t0521,x) +--R +--R +--R (109) +--R [ +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R - \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R a log(------------------------------------------------) +--R a cos(x) + b +--R / +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R , +--R +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b - a log(-------------------) - \|b - a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R sin(x)\|b - a +--R - 2a atan(---------------------) +--R (b + a)cos(x) + b + a +--R / +--R +-------+ +--R | 2 2 +--R b\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 124 + +--S 125 of 586 +m0521a:= a0521.1-r0521 +--R +--R +--R (110) +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R - \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R a log(------------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 +--R - \|- b + a atanh(sin(x)) - 2a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R Type: Expression(Integer) +--E 125 + +--S 126 of 586 +d0521a:= D(m0521a,x) +--R +--R +--R (111) +--R 2 3 6 +--R (- a b + a )sin(x) +--R + +--R 2 2 2 3 2 2 3 +--R (- 2a b + 3a b)cos(x) + (- 2b + 2a b + a b + a )cos(x) +--R + +--R 2 2 3 +--R - 2a b + 5a b - 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 +--R (- 2a b + 2a b - a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 2b + a b - 2a b - a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- b + a b - 5a b - 2a )cos(x) +--R + +--R 3 2 2 3 2 2 3 +--R (2b - 3a b - 3a b - 2a )cos(x) + 2a b - 5a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- a b + a b)cos(x) + (- b + a b - a b + 2a )cos(x) +--R + +--R 2 3 3 3 2 2 3 2 +--R (a b + 3a )cos(x) + (b - a b + 4a b + 2a )cos(x) +--R + +--R 2 2 3 2 +--R (a b + 2a b + a )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 6 +--R (- a b - a )sin(x) +--R + +--R 2 2 2 3 2 2 3 2 +--R (- 2a b - a b)cos(x) + (- 2b - 2a b - a b + a )cos(x) - 2a b +--R + +--R 2 3 +--R a b + 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 3 +--R (- 2a b - 2a b + a )cos(x) + (- 2b - 3a b - 2a b - a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (- b - a b - a b - 2a )cos(x) + (2b + a b - a b - 2a )cos(x) +--R + +--R 2 2 3 +--R 2a b - a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- a b - a b)cos(x) + (- b - a b - a b - 2a )cos(x) +--R + +--R 2 3 3 3 2 3 2 +--R (- a b - a )cos(x) + (b + a b + 2a )cos(x) +--R + +--R 2 2 3 2 +--R (a b + 2a b + a )cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 3 4 4 3 2 2 3 +--R (- 2a b + 3a b + 2a b - 3a )cos(x) - 2b + 2a b + 3a b - 2a b +--R + +--R 4 +--R - a +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 3 4 3 +--R (- 2a b + a b + 2a b - a )cos(x) +--R + +--R 4 3 3 4 2 +--R (- 2b + a b - a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 2 2 +--R (- b + 3a b - 5a b - 3a b + 6a )cos(x) + 2b - 2a b - 4a b +--R + +--R 3 4 +--R 2a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R (- a b + a b + a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- b + a b + 2a b - a b - a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (a b + 2a b - a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 2 2 4 +--R (b - a b + 2a b + a b - 3a )cos(x) + a b - a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 4 4 3 2 2 3 4 +--R ((- 2a b - a b + 2a b + a )cos(x) - 2b - 2a b + a b + 2a b + a ) +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 3 4 3 +--R (- 2a b - 3a b + 2a b + 3a )cos(x) +--R + +--R 4 3 3 4 2 +--R (- 2b - 3a b + 3a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 3 4 +--R (- b + a b + 3a b - a b - 2a )cos(x) + 2b + 2a b - 2a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R (- a b - a b + a b + a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- b - a b + 2a b + a b - a )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (a b + 2a b - a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 2 2 4 +--R (b + a b - 2a b - a b + a )cos(x) - a b + a +--R * +--R sin(x) +--R / +--R 3 2 2 2 4 3 2 2 3 3 +--R (a b - a b )cos(x) + (b - a b + a b - a b)cos(x) + a b +--R + +--R 2 2 +--R - a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 4 4 3 2 2 3 3 +--R (- a b + a b )cos(x) + (- b - a b + a b + a b)cos(x) +--R + +--R 4 3 2 2 3 2 4 3 +--R (- 2b - a b + a b + 2a b)cos(x) + (- 2b + 2a b)cos(x) +--R + +--R 3 2 2 +--R - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 4 4 3 2 2 3 3 +--R (a b - a b )cos(x) + (b + a b - a b - a b)cos(x) +--R + +--R 4 3 2 4 3 2 2 3 3 2 2 +--R (2b - 2a b)cos(x) + (b + a b - a b - a b)cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 4 3 2 2 3 3 +--R (a b + a b )cos(x) + (b + a b + a b + a b)cos(x) + a b +--R + +--R 2 2 +--R a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 4 4 3 2 2 3 3 +--R (- a b - a b )cos(x) + (- b - 3a b - 3a b - a b)cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 2b - 5a b - 5a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (- 2b - 4a b - 4a b - 2a b)cos(x) - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 4 4 3 2 2 3 3 +--R (a b + a b )cos(x) + (b + 3a b + 3a b + a b)cos(x) +--R + +--R 4 3 2 2 3 2 +--R (2b + 4a b + 4a b + 2a b)cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (b + 3a b + 3a b + a b)cos(x) + a b + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 3 3 2 4 5 4 2 3 3 2 5 +--R ((a b - a b - a b + a b)cos(x) + b - a b - a b + a b )sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- b - a b + 3a b + a b - 2a b)cos(x) +--R + +--R 5 2 3 4 5 4 2 3 3 2 +--R (- 2b + 4a b - 2a b)cos(x) - 2b + 2a b + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (b + a b - 3a b - a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 3 2 +--R (2b - a b - 3a b + a b + a b)cos(x) + b - a b - a b + a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 5 4 2 3 3 2 5 +--R ((a b + a b - a b - a b)cos(x) + b + a b - a b - a b )sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- b - 3a b - a b + 3a b + 2a b)cos(x) +--R + +--R 5 4 3 2 4 5 4 2 3 3 2 +--R (- 2b - 4a b + 4a b + 2a b)cos(x) - 2b - 2a b + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (b + 3a b + a b - 3a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 3 2 +--R (2b + 3a b - a b - 3a b - a b)cos(x) + b + a b - a b - a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 126 + +--S 127 of 586 +m0521b:= a0521.2-r0521 +--R +--R +--R (112) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R - \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R x +--R +---------+ +-------+ +-------+ (b - a)tan(-) +--R | 2 2 | 2 2 | 2 2 2 +--R - \|- b + a \|b - a atanh(sin(x)) - 2a\|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 sin(x)\|b - a +--R - 2a\|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R b\|- b + a \|b - a +--R Type: Expression(Integer) +--E 127 + +--S 128 of 586 +d0521b:= D(m0521b,x) +--R +--R +--R (113) +--R 2 2 6 +--R (- 2b + 3a b - a )sin(x) +--R + +--R 2 2 2 2 2 +--R (- 4b + 4a b + 2a )cos(x) + (- 5b + 4a b + 5a )cos(x) - a b +--R + +--R 2 +--R 3a +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2b + a b - a )cos(x) + (- 6b + 4a b - 6a )cos(x) +--R + +--R 2 2 2 2 2 2 +--R (- 2b - 12a )cos(x) + (4b - 6a b - 10a )cos(x) + 2b - 3a b +--R + +--R 2 +--R - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 2 2 4 +--R (- b + a )cos(x) + (- 2b - a b + 5a )cos(x) +--R + +--R 2 3 2 2 2 +--R (- 2a b + 10a )cos(x) + (2b + 10a )cos(x) +--R + +--R 2 2 2 +--R (b + 2a b + 5a )cos(x) + a b + a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 6 +--R (- 2b - a b - a )sin(x) +--R + +--R 2 2 2 2 2 2 +--R ((- 4b - 4a b + 2a )cos(x) + (- 5b - 6a b + 3a )cos(x) - a b + 3a ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2b - 3a b - a )cos(x) + (- 6b - 8a b - 2a )cos(x) +--R + +--R 2 2 2 2 2 2 +--R (- 2b - 4a b - 4a )cos(x) + (4b + 2a b - 6a )cos(x) + 2b + a b +--R + +--R 2 +--R - 3a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 2 2 4 +--R (- b - 2a b - a )cos(x) + (- 2b - 5a b - 3a )cos(x) +--R + +--R 2 3 2 2 2 +--R (- 2a b - 2a )cos(x) + (2b + 4a b + 2a )cos(x) +--R + +--R 2 2 2 +--R (b + 4a b + 3a )cos(x) + a b + a +--R / +--R 3 2 2 6 +--R (b - 2a b + a b)sin(x) +--R + +--R 2 2 2 2 2 3 2 2 +--R ((2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) - b + 4a b - 3a b) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 3 2 3 +--R (- b + a b)cos(x) + (- 4b + 4a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 3 +--R (- 6b - 2a b + 8a b)cos(x) + (- 4b - 4a b + 8a b)cos(x) - b +--R + +--R 2 2 +--R - 2a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (b - a b)cos(x) + (4b - 4a b)cos(x) + (6b - 6a b)cos(x) +--R + +--R 3 2 3 2 +--R (4b - 4a b)cos(x) + b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 6 +--R (b - a b)sin(x) +--R + +--R 2 2 2 2 2 3 2 2 4 +--R ((2a b + 2a b)cos(x) + (4a b + 4a b)cos(x) - b + 2a b + 3a b)sin(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (- b - 2a b - a b)cos(x) + (- 4b - 8a b - 4a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 3 +--R (- 6b - 14a b - 8a b)cos(x) + (- 4b - 12a b - 8a b)cos(x) - b +--R + +--R 2 2 +--R - 4a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (b + 2a b + a b)cos(x) + (4b + 8a b + 4a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 3 2 +--R (6b + 12a b + 6a b)cos(x) + (4b + 8a b + 4a b)cos(x) + b + 2a b +--R + +--R 2 +--R a b +--R Type: Expression(Integer) +--E 128 + +--S 129 of 586 +t0522:= sec(x)^3/(a+b*sec(x)) +--R +--R +--R 3 +--R sec(x) +--R (114) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 129 + +--S 130 of 586 +r0522:= -a*atanh(sin(x))/b^2+2*a^2*atanh((a-b)*tan(1/2*x)/_ + (a^2-b^2)^(1/2))/b^2/(a^2-b^2)^(1/2)+tan(x)/b +--R +--R +--R (115) +--R x +--R +---------+ (b - a)tan(-) +---------+ +--R | 2 2 2 2 | 2 2 +--R - a\|- b + a atanh(sin(x)) - 2a atanh(-------------) + b tan(x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ----------------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 130 + +--S 131 of 586 +a0522:= integrate(t0522,x) +--R +--R +--R (116) +--R [ +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - a cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R a cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R 2 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R a cos(x)log(----------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R | 2 2 +--R b sin(x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R b cos(x)\|- b + a +--R , +--R +--R +-------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - a cos(x)\|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R a cos(x)\|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +-------+ +--R 2 sin(x)\|b - a | 2 2 +--R 2a cos(x)atan(---------------------) + b sin(x)\|b - a +--R (b + a)cos(x) + b + a +--R / +--R +-------+ +--R 2 | 2 2 +--R b cos(x)\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 131 + +--S 132 of 586 +m0522a:= a0522.1-r0522 +--R +--R +--R (117) +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - a cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R a cos(x)\|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R 2 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R a cos(x)log(----------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R +---------+ (b - a)tan(-) +--R | 2 2 2 2 +--R a cos(x)\|- b + a atanh(sin(x)) + 2a cos(x)atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R (- b cos(x)tan(x) + b sin(x))\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R b cos(x)\|- b + a +--R Type: Expression(Integer) +--E 132 + +--S 133 of 586 +d0522a:= D(m0522a,x) +--R +--R +--R (118) +--R 3 2 2 4 +--R (- a b + a b )cos(x) +--R + +--R 4 3 2 2 3 3 3 2 2 2 +--R (- b + a b - a b + a b)cos(x) + (- a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 3 5 +--R (a b - a b )cos(x) + (b + a b - a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 3 3 +--R (2b + a b - a b - 2a b)cos(x) + (2b - 2a b)cos(x) +--R + +--R 3 2 2 2 +--R (2a b - 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 3 5 +--R (- a b + a b )cos(x) + (- b - a b + a b + a b)cos(x) +--R + +--R 4 3 4 4 3 2 2 3 3 +--R (- 2b + 2a b)cos(x) + (- b - a b + a b + a b)cos(x) +--R + +--R 3 2 2 2 +--R (- a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 4 3 2 2 3 3 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b)cos(x) +--R + +--R 3 2 2 2 +--R (- a b - a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 3 5 +--R (a b + a b )cos(x) + (b + 3a b + 3a b + a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (2b + 5a b + 5a b + 2a b)cos(x) +--R + +--R 4 3 2 2 3 3 3 2 2 2 +--R (2b + 4a b + 4a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 6 4 3 2 2 3 5 +--R (- a b - a b )cos(x) + (- b - 3a b - 3a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b - 4a b - 4a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 3 3 2 2 2 +--R (- b - 3a b - 3a b - a b)cos(x) + (- a b - a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 2 +--R (a b - a b + a b - a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (b - a b + a b - a b)cos(x) + a b - a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- a b + 3a b - 3a b)cos(x) +--R + +--R 4 3 2 2 4 3 +--R (- b + a b - a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b - a b + 3a b - 3a b + 2a )cos(x) +--R + +--R 4 3 3 2 2 +--R (- 2b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 6 +--R (2a b - 2a b + a )cos(x) +--R + +--R 3 2 2 3 4 5 +--R (2a b - a b + 2a b + a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (2a b - 2a b + 5a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b - a b + 2a b + 2a b + 2a )cos(x) +--R + +--R 4 2 2 3 4 2 +--R (2b - 2a b + 3a b - a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (b + a b - a b - a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 7 3 2 2 3 4 6 +--R (a b - a b)cos(x) + (a b - a b + a b - 2a )cos(x) +--R + +--R 3 4 5 3 2 2 3 4 4 +--R (- a b - 3a )cos(x) + (- a b + a b - 4a b - 2a )cos(x) +--R + +--R 2 2 3 4 3 3 2 +--R (- a b - 2a b - a )cos(x) - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 4 2 4 3 2 2 3 +--R (a b + a b + a b + a )cos(x) + (b + a b + a b + a b)cos(x) +--R + +--R 3 2 2 +--R a b + a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 4 3 2 2 4 3 +--R (- a b + a b + a b)cos(x) + (- b - a b - a b - a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (- 2b - 5a b - 3a b - 3a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (- 2b - 4a b - 4a b - 2a b)cos(x) - 2a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 6 3 2 2 3 4 5 +--R (2a b + 2a b - a )cos(x) + (2a b + 3a b + 2a b + a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (2a b + 2a b + a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b + a b + 2a b + 2a b + 2a )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b + 4a b + 2a b + 3a b + a )cos(x) +--R + +--R 4 3 2 2 3 3 2 2 +--R (b + 3a b + 3a b + a b)cos(x) + a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 7 3 2 2 3 4 6 +--R (a b + a b)cos(x) + (a b + a b + a b + 2a )cos(x) +--R + +--R 3 4 5 3 2 2 4 4 +--R (a b + a )cos(x) + (- a b - a b - 2a )cos(x) +--R + +--R 2 2 3 4 3 3 2 +--R (- a b - 2a b - a )cos(x) - a b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 3 3 2 4 3 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (b - a b - a b + a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- b - a b + 3a b + a b - 2a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 2b + 4a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (- 2b + 2a b + 2a b - 2a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (b + a b - 3a b - a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (2b - a b - 3a b + a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (b - a b - a b + a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 3 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (b + a b - a b - a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- a b - a b + a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- b - 3a b - a b + 3a b + 2a b)cos(x) +--R + +--R 5 4 3 2 4 3 +--R (- 2b - 4a b + 4a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (a b + a b - a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (b + 3a b + a b - 3a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (2b + 3a b - a b - 3a b - a b)cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (b + a b - a b - a b )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 5 4 2 3 3 2 7 +--R ((- a b + a b + a b - a b)cos(x) - b + a b + a b - a b )sin(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (a b - 3a b + 2a b + 3a b - 3a )cos(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (b - a b - a b + 2a b - a )cos(x) +--R + +--R 5 2 3 4 5 4 2 3 3 2 +--R (2b - 4a b + 2a b)cos(x) + 2b - 2a b - 2a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 2a b + a b + 2a b - a )cos(x) +--R + +--R 4 2 3 4 5 4 +--R (- 2a b + a b - a b + 2a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- 2a b + 4a b - 4a b - 4a b + 6a )cos(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (- b + a b + a b - 3a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 3 2 +--R (- 2b + a b + 3a b - a b - a b)cos(x) - b + a b + a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- a b + a b + a b - a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- a b + a b + 2a b - a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (a b + 2a b - a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 3 2 5 2 +--R (a b - a b + 2a b + a b - 3a )cos(x) + (a b - a )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 5 4 2 3 3 2 7 +--R ((- a b - a b + a b + a b)cos(x) - b - a b + a b + a b )sin(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (a b - a b - 2a b + a b + a )cos(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (b + a b - a b - 2a b + a )cos(x) +--R + +--R 5 4 3 2 4 5 4 2 3 3 2 +--R (2b + 4a b - 4a b - 2a b)cos(x) + 2b + 2a b - 2a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 3 2 4 5 5 +--R (- 2a b - 3a b + 2a b + 3a )cos(x) +--R + +--R 4 2 3 4 5 4 +--R (- 2a b - 3a b + 3a b + 2a )cos(x) +--R + +--R 4 3 2 5 3 +--R (- 2a b + 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 5 2 +--R (- b - a b + a b + 3a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 2 3 3 2 +--R (- 2b - 3a b + a b + 3a b + a b)cos(x) - b - a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 2 4 5 6 +--R (- a b - a b + a b + a )cos(x) +--R + +--R 4 2 3 3 2 4 5 5 +--R (- a b - a b + 2a b + a b - a )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (a b + 2a b - a b - 2a )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 3 2 5 2 +--R (a b + a b - 2a b - a b + a )cos(x) + (- a b + a )cos(x) +--R * +--R sin(x) +--R / +--R 4 2 3 4 5 4 2 3 3 2 3 +--R (a b - a b )cos(x) + (b - a b + a b - a b )cos(x) +--R + +--R 4 2 3 2 +--R (a b - a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 3 2 5 +--R (- a b + a b )cos(x) + (- b - a b + a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 2 3 +--R (- 2b - a b + a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 4 2 3 2 +--R (- 2a b + 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 3 2 5 +--R (a b - a b )cos(x) + (b + a b - a b - a b )cos(x) +--R + +--R 5 3 2 4 5 4 2 3 3 2 3 +--R (2b - 2a b )cos(x) + (b + a b - a b - a b )cos(x) +--R + +--R 4 2 3 2 +--R (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 4 5 4 2 3 3 2 3 +--R (a b + a b )cos(x) + (b + a b + a b + a b )cos(x) +--R + +--R 4 2 3 2 +--R (a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 3 2 5 +--R (- a b - a b )cos(x) + (- b - 3a b - 3a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 5a b - 5a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 3 4 2 3 2 +--R (- 2b - 4a b - 4a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 6 5 4 2 3 3 2 5 +--R (a b + a b )cos(x) + (b + 3a b + 3a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (2b + 4a b + 4a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 3 4 2 3 2 +--R (b + 3a b + 3a b + a b )cos(x) + (a b + a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 4 3 3 4 2 3 +--R (- a b + a b + a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (- b + a b + a b - a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (a b - a b - a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (b + a b - 3a b - a b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 3 6 5 2 4 3 3 2 +--R (2b - 4a b + 2a b )cos(x) + (2b - 2a b - 2a b + 2a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- a b + a b + a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- b - a b + 3a b + a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 2b + a b + 3a b - a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (- b + a b + a b - a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 3 3 4 2 3 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (a b + a b - a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (b + 3a b + a b - 3a b - 2a b )cos(x) +--R + +--R 6 5 3 3 4 2 3 +--R (2b + 4a b - 4a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- b - 3a b - a b + 3a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 2b - 3a b + a b + 3a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )cos(x) +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 133 + +--S 134 of 586 +m0522b:= a0522.2-r0522 +--R +--R +--R (119) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R - a cos(x)\|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R a cos(x)\|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R a cos(x)\|- b + a \|b - a atanh(sin(x)) +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 2 | 2 2 2 +--R 2a cos(x)\|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 2 | 2 2 sin(x)\|b - a +--R 2a cos(x)\|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R (- b cos(x)tan(x) + b sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R b cos(x)\|- b + a \|b - a +--R Type: Expression(Integer) +--E 134 + +--S 135 of 586 +d0522b:= D(m0522b,x) +--R +--R +--R (120) +--R 3 2 2 2 6 +--R (- b + 2a b - a b)cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 3 2 2 2 +--R (b - 4a b + 3a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 6 3 2 5 +--R (b - a b)cos(x) + (4b - 4a b)cos(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (6b + 2a b - 8a b)cos(x) + (4b + 4a b - 8a b)cos(x) +--R + +--R 3 2 2 2 +--R (b + 2a b - 3a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 6 3 2 5 +--R (- b + a b)cos(x) + (- 4b + 4a b)cos(x) +--R + +--R 3 2 4 3 2 3 3 2 2 +--R (- 6b + 6a b)cos(x) + (- 4b + 4a b)cos(x) + (- b + a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 6 +--R (- b + a b)cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2a b - 2a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 3 2 2 2 +--R (b - 2a b - 3a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (b + 2a b + a b)cos(x) + (4b + 8a b + 4a b)cos(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (6b + 14a b + 8a b)cos(x) + (4b + 12a b + 8a b)cos(x) +--R + +--R 3 2 2 2 +--R (b + 4a b + 3a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 6 3 2 2 5 +--R (- b - 2a b - a b)cos(x) + (- 4b - 8a b - 4a b)cos(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (- 6b - 12a b - 6a b)cos(x) + (- 4b - 8a b - 4a b)cos(x) +--R + +--R 3 2 2 2 +--R (- b - 2a b - a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 8 +--R (b - 2a b + a b)sin(x) +--R + +--R 2 2 3 2 2 2 3 2 +--R (4a b - 5a b + a )cos(x) + (4a b - 4a b)cos(x) - b + 4a b +--R + +--R 2 +--R - 3a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 3 2 3 3 +--R (- b + 4a b - 3a b - 2a )cos(x) + (- 4b + 5a b - 5a )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 6b - 2a b + 9a b - 3a )cos(x) +--R + +--R 3 2 2 3 2 2 +--R (- 4b - 4a b + 8a b)cos(x) - b - 2a b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (2a b - a b + a )cos(x) + (6a b - 4a b + 6a )cos(x) +--R + +--R 3 2 2 3 4 +--R (b + 2a b - a b + 12a )cos(x) +--R + +--R 3 2 2 3 3 +--R (4b - 4a b + 2a b + 10a )cos(x) +--R + +--R 3 2 2 3 2 3 2 3 2 +--R (6b - 2a b - 3a b + 3a )cos(x) + (4b - 4a b)cos(x) + b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 7 2 2 3 6 +--R (a b - a )cos(x) + (2a b + a b - 5a )cos(x) +--R + +--R 2 3 5 2 3 4 +--R (2a b - 10a )cos(x) + (- 2a b - 10a )cos(x) +--R + +--R 2 2 3 3 2 3 2 +--R (- a b - 2a b - 5a )cos(x) + (- a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 8 +--R (b - a b)sin(x) +--R + +--R 2 2 3 2 2 2 3 2 2 +--R ((4a b + 3a b + a )cos(x) + (4a b + 4a b)cos(x) - b + 2a b + 3a b) +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- b + 2a b + 3a b - 2a )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 4b - 3a b + 2a b - 3a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (- 6b - 14a b - 7a b - 3a )cos(x) + (- 4b - 12a b - 8a b)cos(x) +--R + +--R 3 2 2 +--R - b - 4a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 2 2 3 5 +--R (2a b + 3a b + a )cos(x) + (6a b + 8a b + 2a )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 3 +--R (b + 4a b + 5a b + 4a )cos(x) + (4b + 4a b + 2a b + 6a )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 3 +--R (6b + 10a b + 5a b + 3a )cos(x) + (4b + 8a b + 4a b)cos(x) + b +--R + +--R 2 2 +--R 2a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 7 2 2 3 6 +--R (a b + 2a b + a )cos(x) + (2a b + 5a b + 3a )cos(x) +--R + +--R 2 3 5 2 2 3 4 +--R (2a b + 2a )cos(x) + (- 2a b - 4a b - 2a )cos(x) +--R + +--R 2 2 3 3 2 3 2 +--R (- a b - 4a b - 3a )cos(x) + (- a b - a )cos(x) +--R / +--R 4 3 2 2 2 6 +--R (b - 2a b + a b )cos(x) sin(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 3 2 2 2 +--R (- b + 4a b - 3a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 6 4 2 2 5 +--R (- b + a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (- 6b - 2a b + 8a b )cos(x) + (- 4b - 4a b + 8a b )cos(x) +--R + +--R 4 3 2 2 2 +--R (- b - 2a b + 3a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 2 6 4 2 2 5 4 2 2 4 +--R (b - a b )cos(x) + (4b - 4a b )cos(x) + (6b - 6a b )cos(x) +--R + +--R 4 2 2 3 4 2 2 2 +--R (4b - 4a b )cos(x) + (b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 6 +--R (b - a b )cos(x) sin(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (2a b + 2a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 4 3 2 2 2 +--R (- b + 2a b + 3a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 4 3 2 2 5 +--R (- b - 2a b - a b )cos(x) + (- 4b - 8a b - 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (- 6b - 14a b - 8a b )cos(x) + (- 4b - 12a b - 8a b )cos(x) +--R + +--R 4 3 2 2 2 +--R (- b - 4a b - 3a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 6 4 3 2 2 5 +--R (b + 2a b + a b )cos(x) + (4b + 8a b + 4a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (6b + 12a b + 6a b )cos(x) + (4b + 8a b + 4a b )cos(x) +--R + +--R 4 3 2 2 2 +--R (b + 2a b + a b )cos(x) +--R Type: Expression(Integer) +--E 135 + +--S 136 of 586 +t0523:= sec(x)^4/(a+b*sec(x)) +--R +--R +--R 4 +--R sec(x) +--R (121) ------------ +--R b sec(x) + a +--R Type: Expression(Integer) +--E 136 + +--S 137 of 586 +r0523:= a^2*atanh(sin(x))/b^3+1/2*atanh(sin(x))/b-_ + 2*a^3*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(1/2)-_ + a*tan(x)/b^2+1/2*sec(x)*tan(x)/b +--R +--R +--R (122) +--R x +--R +---------+ (b - a)tan(-) +--R 2 2 | 2 2 3 2 +--R (b + 2a )\|- b + a atanh(sin(x)) + 4a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (b sec(x) - 2a b)tan(x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression(Integer) +--E 137 + +--S 138 of 586 +a0523:= integrate(t0523,x) +--R +--R +--R (123) +--R [ +--R +---------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (b + 2a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- b - 2a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R 3 2 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R 2a cos(x) log(------------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 2a b cos(x) + b )sin(x)\|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R 2b cos(x) \|- b + a +--R , +--R +--R +-------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (b + 2a )cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- b - 2a )cos(x) \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R 3 2 sin(x)\|b - a +--R - 4a cos(x) atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +-------+ +--R 2 | 2 2 +--R (- 2a b cos(x) + b )sin(x)\|b - a +--R / +--R +-------+ +--R 3 2 | 2 2 +--R 2b cos(x) \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 138 + +--S 139 of 586 +m0523a:= a0523.1-r0523 +--R +--R +--R (124) +--R +---------+ +--R 2 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (b + 2a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- b - 2a )cos(x) \|- b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 2 +--R 3 2 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R 2a cos(x) log(------------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- b - 2a )cos(x) \|- b + a atanh(sin(x)) +--R + +--R x +--R (b - a)tan(-) +--R 3 2 2 +--R - 4a cos(x) atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R ((- b cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + b )sin(x)) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R 2b cos(x) \|- b + a +--R Type: Expression(Integer) +--E 139 + +--S 140 of 586 +d0523a:= D(m0523a,x) +--R +--R +--R (125) +--R 4 2 3 5 +--R (- 2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b + 2a b - 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 +--R (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (2a b - 2a b + 2a b - 2a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 +--R (2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (4b + 2a b - 2a b - 4a b )cos(x) +--R + +--R 5 3 2 4 4 2 3 3 +--R (4b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 2a b + 2a b + 4a b)cos(x) +--R + +--R 4 4 4 2 3 3 2 3 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 5 3 2 5 +--R (- 4b + 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 4 4 5 +--R (2a b + 2a b - 2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b + 2a b - 2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 5 +--R (- 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 2a b - 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 5 +--R (2a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b + 2a b + 2a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 +--R (2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (2b + 6a b + 6a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (4b + 10a b + 10a b + 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (4b + 8a b + 8a b + 4a b )cos(x) +--R + +--R 4 2 3 3 +--R (4a b + 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 +--R (- 2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 2a b - 6a b - 6a b - 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 4a b - 10a b - 10a b - 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (- 4a b - 8a b - 8a b - 4a b)cos(x) +--R + +--R 2 3 3 2 3 +--R (- 4a b - 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 +--R (- 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 4b - 8a b - 8a b - 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (- 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 3 3 2 7 4 2 3 3 2 4 6 +--R (2a b + 2a b )cos(x) + (2a b + 6a b + 6a b + 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (4a b + 8a b + 8a b + 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 3 +--R (2a b + 6a b + 6a b + 2a b)cos(x) + (2a b + 2a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 2a b + 2a b - 2a b + 2a )cos(x) +--R + +--R 3 2 4 2 5 4 4 2 3 +--R (- 2a b + 2a b)cos(x) + (2b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 3 5 +--R (- a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (- b + a b - a b + a b )cos(x) + (- a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 2a b + 4a b - 6a b + 6a b)cos(x) +--R + +--R 5 4 2 3 3 2 5 4 +--R (- 2b + 3a b - 3a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- b - a b + 7a b - 5a b + 6a b - 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 4b + 3a b + a b + 4a b - 4a b)cos(x) +--R + +--R 5 2 3 4 2 3 +--R (- 4b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (a b - a b )cos(x) + (b + a b - a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 5 3 2 4 +--R (2b + a b - a b - 2a b )cos(x) + (2b - 2a b )cos(x) +--R + +--R 4 2 3 3 +--R (2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (- 2a b + 2a b - 4a b + 4a b - 2a )cos(x) +--R + +--R 5 2 3 3 2 4 5 6 +--R (- 2b - 4a b + 4a b - 4a b - 2a )cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (- 2b - 4a b + 6a b - 10a b - 4a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 4a b + 4a b - 4a b - 4a b - 4a )cos(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 4a b + 4a b - 6a b + 2a )cos(x) +--R + +--R 5 4 3 2 4 2 +--R (4b - 4a b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 3 4 2 3 +--R (2b + 2a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (- a b + a b )cos(x) + (- b - a b + a b + a b )cos(x) +--R + +--R 5 3 2 5 5 4 2 3 3 2 4 +--R (- 2b + 2a b )cos(x) + (- b - a b + a b + a b )cos(x) +--R + +--R 4 2 3 3 +--R (- a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (- a b + a b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- b + a b - 3a b + 3a b - 2a b + 4a )cos(x) +--R + +--R 4 2 3 4 5 6 +--R (a b - a b + 2a b + 6a )cos(x) +--R + +--R 5 2 3 3 2 4 5 5 +--R (2b + 2a b - 4a b + 8a b + 4a )cos(x) +--R + +--R 5 4 2 3 4 5 4 +--R (2b + a b - a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 4 2 3 2 +--R (b + a b - a b - a b + 2a b)cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (- 2a b - 2a b - 2a b - 2a )cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 5 4 4 2 3 +--R (2b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 3 5 5 4 2 3 3 2 4 +--R (- a b - a b )cos(x) + (- b - a b - a b - a b )cos(x) +--R + +--R 4 2 3 3 +--R (- a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 4 5 +--R (- 2a b - 2a b - 2a b)cos(x) +--R + +--R 5 4 2 3 5 4 +--R (- 2b - a b - a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- b - 3a b + 3a b + 5a b + 6a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 4b - 5a b - a b + 4a b + 4a b)cos(x) +--R + +--R 5 4 2 3 4 2 3 +--R (- 4b - 8a b - 4a b )cos(x) - 4a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (a b + a b )cos(x) + (b + 3a b + 3a b + a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (2b + 5a b + 5a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (2b + 4a b + 4a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 5 7 +--R (- 2a b - 2a b - 4a b - 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 2b - 4a b - 8a b - 8a b - 4a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 2b - 4a b - 8a b - 6a b - 2a b - 4a )cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 4a b - 4a b - 4a b - 4a b - 4a )cos(x) +--R + +--R 2 3 3 2 4 5 3 +--R (- 4a b - 4a b - 6a b - 2a )cos(x) +--R + +--R 5 4 3 2 4 2 5 4 2 3 +--R (4b + 4a b - 2a b - 2a b)cos(x) + (2b + 6a b + 4a b )cos(x) +--R + +--R 4 2 3 +--R 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 7 5 4 2 3 3 2 6 +--R (- a b - a b )cos(x) + (- b - 3a b - 3a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 2b - 4a b - 4a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 2 3 3 +--R (- b - 3a b - 3a b - a b )cos(x) + (- a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 3 3 2 4 8 +--R (- a b - a b - 2a b - 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- b - a b - 3a b - 3a b - 2a b - 4a )cos(x) +--R + +--R 4 2 3 4 5 6 +--R (a b + a b - 2a b - 2a )cos(x) +--R + +--R 5 4 2 3 3 2 5 5 +--R (2b + 4a b + 6a b + 4a b + 4a )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (2b + 5a b + 5a b + 4a b + 4a b + 2a )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 4 2 3 2 +--R (b + 3a b + 3a b + a b + 2a b)cos(x) + (a b + a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 2b + 2a b + 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b + 2a b - 6a b - 2a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (4b - 8a b + 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (4b - 4a b - 4a b + 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 2a b - 2a b + 6a b + 2a b - 4a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 2b - 2a b + 6a b + 2a b - 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 4b + 2a b + 6a b - 2a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 2b + 2a b + 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (2a b + 2a b - 6a b - 2a b + 4a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (4a b - 2a b - 6a b + 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 2a b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (2a b + 2a b - 2a b - 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (2a b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b + 6a b + 2a b - 6a b - 4a b )cos(x) +--R + +--R 6 5 3 3 4 2 4 +--R (4b + 8a b - 8a b - 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (4b + 4a b - 4a b - 4a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 2a b - 6a b - 2a b + 6a b + 4a b)cos(x) +--R + +--R 5 2 4 4 2 5 4 +--R (- 4a b - 8a b + 8a b + 4a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (- 4a b - 4a b + 4a b + 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- 2a b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 2b - 6a b - 2a b + 6a b + 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 4b - 6a b + 2a b + 6a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 4 3 3 4 2 5 6 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (2a b + 6a b + 2a b - 6a b - 4a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (4a b + 6a b - 2a b - 6a b - 2a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 3 +--R (2a b + 2a b - 2a b - 2a b )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 4 3 3 4 2 5 2 6 5 2 4 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) + 2b - 2a b - 2a b +--R + +--R 3 3 +--R 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- a b + a b + a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- b + a b + a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (- 2a b + 4a b - 4a b + 2a b + 6a b - 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 3 +--R (- 2b + 3a b + a b - 3a b + 3a b - 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- b + a b + 5a b - 5a b - 4a b + 4a b)cos(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 3 3 +--R (- 4b + 4a b + 4a b - 4a b )cos(x) - 4b + 4a b + 4a b - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (a b - a b - a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b + a b - 3a b - a b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (2b - 4a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (2b - 2a b - 2a b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 5 6 6 +--R (- 2a b + 2a b - 2a b + 4a b - 2a )cos(x) +--R + +--R 6 3 3 4 2 5 6 5 +--R (- 2b + 2a b - 2a b - 2a b + 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 2b + 2a b - 2a b + 6a b - 8a b - 8a b + 12a )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 3 +--R (- 2a b + 2a b + 2a b - 6a b + 4a )cos(x) +--R + +--R 2 4 3 3 4 2 5 2 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 3 3 +--R (4b - 4a b - 4a b + 4a b )cos(x) + 2b - 2a b - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- a b + a b + a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b - a b + 3a b + a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + a b + 3a b - a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- b + a b + a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (- a b + a b - a b + a b + 2a b - 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- b + a b - a b + a b + 4a b - 2a b - 2a )cos(x) +--R + +--R 5 2 4 4 2 5 6 5 +--R (2a b - 2a b + 6a b - 2a b - 4a )cos(x) +--R + +--R 6 2 4 3 3 4 2 5 6 4 +--R (2b - 2a b - 2a b + 6a b + 2a b - 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 3 +--R (2b - a b - 3a b + a b + 3a b - 2a )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (b - a b - a b + a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 3 3 4 2 5 2 6 5 2 4 3 3 +--R ((- 2a b - 2a b + 2a b + 2a b)cos(x) + 2b + 2a b - 2a b - 2a b ) +--R * +--R 7 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 4 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- b - a b + a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 4 2 5 6 4 +--R (- 2a b - 2a b + 2a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 3 +--R (- 2b - a b + 3a b + a b - 3a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- b - a b + 5a b + 5a b - 4a b - 4a b)cos(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 3 3 +--R (- 4b - 4a b + 4a b + 4a b )cos(x) - 4b - 4a b + 4a b + 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (a b + a b - a b - a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b + 3a b + a b - 3a b - 2a b )cos(x) +--R + +--R 6 5 3 3 4 2 4 +--R (2b + 4a b - 4a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 2a b - 2a b - 2a b - 4a b + 4a b + 6a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 2b - 4a b - 4a b - 2a b + 2a b + 6a b + 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 4 +--R (- 2b - 2a b - 2a b + 2a b + 8a b - 4a )cos(x) +--R + +--R 5 2 4 3 3 4 2 6 3 +--R (- 2a b - 2a b + 2a b + 6a b - 4a )cos(x) +--R + +--R 2 4 3 3 4 2 5 2 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 3 3 +--R (4b + 4a b - 4a b - 4a b )cos(x) + 2b + 2a b - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 6 +--R (- a b - a b + a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b - 3a b - a b + 3a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b - 3a b + a b + 3a b + a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (- b - a b + a b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 5 2 4 3 3 4 2 5 6 7 +--R (- a b - a b - a b - a b + 2a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- b - a b - a b - a b + 4a b + 2a b - 2a )cos(x) +--R + +--R 5 2 4 4 2 5 6 5 +--R (2a b + 2a b + 2a b - 2a b - 4a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b + 4a b + 2a b - 2a b - 6a b - 2a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 3 +--R (2b + 3a b - a b - 3a b - 3a b + 2a )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )cos(x) +--R * +--R sin(x) +--R / +--R 5 2 4 5 6 5 2 4 3 3 4 +--R (2a b - 2a b )cos(x) + (2b - 2a b + 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 4 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 6 +--R (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 4b - 2a b + 2a b + 4a b )cos(x) +--R + +--R 6 3 3 4 5 2 4 3 +--R (- 4b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (2a b - 2a b )cos(x) + (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 6 3 3 5 6 5 2 4 3 3 4 +--R (4b - 4a b )cos(x) + (2b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 5 6 5 2 4 3 3 4 +--R (2a b + 2a b )cos(x) + (2b + 2a b + 2a b + 2a b )cos(x) +--R + +--R 5 2 4 3 +--R (2a b + 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (- 2a b - 2a b )cos(x) + (- 2b - 6a b - 6a b - 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (- 4b - 10a b - 10a b - 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 5 2 4 3 +--R (- 4b - 8a b - 8a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 7 6 5 2 4 3 3 6 +--R (2a b + 2a b )cos(x) + (2b + 6a b + 6a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (4b + 8a b + 8a b + 4a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 5 2 4 3 +--R (2b + 6a b + 6a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 6 2 5 3 4 4 3 4 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (2b - 2a b - 2a b + 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 +--R (- 2b - 2a b + 6a b + 2a b - 4a b )cos(x) +--R + +--R 7 2 5 4 3 4 +--R (- 4b + 8a b - 4a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (- 4b + 4a b + 4a b - 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (2a b - 2a b - 2a b + 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 +--R (2b + 2a b - 6a b - 2a b + 4a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (4b - 2a b - 6a b + 2a b + 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (2b - 2a b - 2a b + 2a b )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 5 3 4 4 3 4 +--R (2a b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (- 2a b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 +--R (- 2b - 6a b - 2a b + 6a b + 4a b )cos(x) +--R + +--R 7 6 3 4 4 3 4 +--R (- 4b - 8a b + 8a b + 4a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (- 4b - 4a b + 4a b + 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 5 3 4 4 3 6 +--R (2a b + 2a b - 2a b - 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 5 +--R (2b + 6a b + 2a b - 6a b - 4a b )cos(x) +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (4b + 6a b - 2a b - 6a b - 2a b )cos(x) +--R + +--R 7 6 2 5 3 4 3 +--R (2b + 2a b - 2a b - 2a b )cos(x) +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 140 + +--S 141 of 586 +m0523b:= a0523.2-r0523 +--R +--R +--R (126) +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R (b + 2a )cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R (- b - 2a )cos(x) \|- b + a \|b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 2 | 2 2 | 2 2 +--R (- b - 2a )cos(x) \|- b + a \|b - a atanh(sin(x)) +--R + +--R x +--R +-------+ (b - a)tan(-) +--R 3 2 | 2 2 2 +--R - 4a cos(x) \|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 2 | 2 2 sin(x)\|b - a +--R - 4a cos(x) \|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R 2 2 2 2 +--R ((- b cos(x) sec(x) + 2a b cos(x) )tan(x) + (- 2a b cos(x) + b )sin(x)) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 | 2 2 | 2 2 +--R 2b cos(x) \|- b + a \|b - a +--R Type: Expression(Integer) +--E 141 + +--S 142 of 586 +d0523b:= D(m0523b,x) +--R +--R +--R (127) +--R 4 3 2 2 3 +--R (- 2b + 4a b - 2a b )cos(x) sec(x) +--R + +--R 3 2 2 3 3 +--R (2a b - 4a b + 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 4a b + 4a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (2b - 8a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (4a b - 4a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (- 2a b + 8a b - 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 +--R (2b - 2a b )cos(x) + (8b - 8a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (12b + 4a b - 16a b )cos(x) +--R + +--R 4 3 2 2 4 +--R (8b + 8a b - 16a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (2b + 4a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 3 7 3 3 6 +--R (- 2a b + 2a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 3 2 2 3 5 +--R (- 12a b - 4a b + 16a b)cos(x) +--R + +--R 3 2 2 3 4 +--R (- 8a b - 8a b + 16a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (- 2a b - 4a b + 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 +--R (- 2b + 2a b )cos(x) + (- 8b + 8a b )cos(x) +--R + +--R 4 2 2 5 4 2 2 4 +--R (- 12b + 12a b )cos(x) + (- 8b + 8a b )cos(x) +--R + +--R 4 2 2 3 +--R (- 2b + 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 3 7 3 3 6 +--R (2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 3 3 5 3 3 4 +--R (12a b - 12a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 3 3 3 +--R (2a b - 2a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 3 3 3 6 +--R ((- 2b + 2a b )cos(x) sec(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 4a b - 4a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (2b - 4a b - 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 2 2 3 5 2 2 3 4 +--R (4a b + 4a b)cos(x) + (8a b + 8a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (- 2a b + 4a b + 6a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 7 4 3 2 2 6 +--R (2b + 4a b + 2a b )cos(x) + (8b + 16a b + 8a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (12b + 28a b + 16a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (8b + 24a b + 16a b )cos(x) + (2b + 8a b + 6a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 7 +--R (- 2a b - 4a b - 2a b)cos(x) +--R + +--R 3 2 2 3 6 +--R (- 8a b - 16a b - 8a b)cos(x) +--R + +--R 3 2 2 3 5 +--R (- 12a b - 28a b - 16a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 3 +--R (- 8a b - 24a b - 16a b)cos(x) + (- 2a b - 8a b - 6a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 7 4 3 2 2 6 +--R (- 2b - 4a b - 2a b )cos(x) + (- 8b - 16a b - 8a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (- 12b - 24a b - 12a b )cos(x) +--R + +--R 4 3 2 2 4 4 3 2 2 3 +--R (- 8b - 16a b - 8a b )cos(x) + (- 2b - 4a b - 2a b )cos(x) +--R * +--R sec(x) +--R + +--R 3 2 2 3 7 3 2 2 3 6 +--R (2a b + 4a b + 2a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 3 2 2 3 5 3 2 2 3 4 +--R (12a b + 24a b + 12a b)cos(x) + (8a b + 16a b + 8a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (2a b + 4a b + 2a b)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 3 2 2 8 +--R ((- 2a b + 4a b - 2a b)cos(x) + 2b - 4a b + 2a b )sin(x) +--R + +--R 4 3 2 2 3 +--R (- b + 2a b - a b )cos(x) sec(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b + 4a b - 10a b + 10a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (b + 2a b - 11a b + 8a b)cos(x) +--R + +--R 3 2 2 3 4 3 2 2 +--R (10a b - 16a b + 6a b)cos(x) - 2b + 8a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (b - 4a b + 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 4b + 6a b - 8a b + 6a b + 4a )cos(x) +--R + +--R 4 3 2 2 4 4 +--R (- 7b + 12a b - 7a b + 10a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 8b + 12a b + 12a b - 18a b + 6a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 13b + 8a b + 21a b - 16a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b - 6a b + 20a b - 6a b)cos(x) - 2b - 4a b + 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 +--R (b - a b )cos(x) + (4b - 4a b )cos(x) +--R + +--R 4 3 2 2 5 4 3 2 2 4 +--R (6b + 2a b - 8a b )cos(x) + (4b + 4a b - 8a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (b + 2a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 2 3 4 7 +--R (- 2b - 2a b + 2a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 7b + 2a b - 7a b + 8a b - 12a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 6b - 2a b + 2a b + 2a b - 24a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 12a b + 12a b - 4a b - 20a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (6b - 16a b + 2a b + 6a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (11b - 10a b - 9a b + 8a b)cos(x) +--R + +--R 4 3 2 2 3 4 2 2 +--R (8b - 2a b - 8a b + 2a b)cos(x) + 2b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 +--R (- b + a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 4 2 2 5 4 2 2 4 +--R (- 6b + 6a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 4 2 2 3 +--R (- b + a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 2 2 4 8 4 2 2 3 4 7 +--R (- b - a b + 2a )cos(x) + (- 2b - 2a b - 2a b + 10a )cos(x) +--R + +--R 4 2 2 3 4 6 4 2 2 4 5 +--R (b - a b - 4a b + 20a )cos(x) + (6b - 2a b + 20a )cos(x) +--R + +--R 4 2 2 3 4 4 +--R (7b - 5a b + 4a b + 10a )cos(x) +--R + +--R 4 2 2 3 4 3 4 2 2 2 +--R (4b - 4a b + 2a b + 2a )cos(x) + (b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 2 2 8 +--R ((- 2a b + 2a b)cos(x) + 2b - 2a b )sin(x) +--R + +--R 4 2 2 3 4 2 2 3 4 3 +--R (- b + a b )cos(x) sec(x) + (- 2b - 6a b - 6a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 2 3 2 2 3 +--R (b + 4a b - 5a b - 8a b)cos(x) + (10a b + 4a b - 6a b)cos(x) +--R + +--R 4 3 2 2 +--R - 2b + 4a b + 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 5 3 2 2 4 +--R (- 2a b - 2a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (b - 2a b - 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 4b - 2a b - 4a b - 6a b + 4a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- 7b - 2a b + 3a b - 4a b + 6a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 8b - 4a b + 20a b + 14a b + 6a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 13b - 18a b + 11a b + 16a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 8b - 22a b - 8a b + 6a b)cos(x) - 2b - 8a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 7 4 3 2 2 6 +--R (b + 2a b + a b )cos(x) + (4b + 8a b + 4a b )cos(x) +--R + +--R 4 3 2 2 5 4 3 2 2 4 +--R (6b + 14a b + 8a b )cos(x) + (4b + 12a b + 8a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (b + 4a b + 3a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 2b - 4a b - 6a b - 6a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (- 7b - 12a b - 17a b - 16a b - 4a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (- 6b - 14a b - 14a b - 10a b - 8a )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 12a b - 12a b - 4a b - 12a )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (6b - 4a b - 18a b - 10a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (11b + 12a b - 7a b - 8a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (8b + 14a b + 4a b - 2a b)cos(x) + 2b + 4a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 7 4 3 2 2 6 +--R (- b - 2a b - a b )cos(x) + (- 4b - 8a b - 4a b )cos(x) +--R + +--R 4 3 2 2 5 4 3 2 2 4 +--R (- 6b - 12a b - 6a b )cos(x) + (- 4b - 8a b - 4a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (- b - 2a b - a b )cos(x) +--R * +--R sec(x) +--R + +--R 4 3 2 2 3 4 8 +--R (- b - 2a b - 3a b - 4a b - 2a )cos(x) +--R + +--R 4 3 2 2 3 4 7 +--R (- 2b - 4a b - 6a b - 10a b - 6a )cos(x) +--R + +--R 4 3 2 2 3 4 6 +--R (b + 2a b + a b - 4a b - 4a )cos(x) +--R + +--R 4 3 2 2 3 4 5 +--R (6b + 12a b + 10a b + 8a b + 4a )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (7b + 14a b + 9a b + 8a b + 6a )cos(x) +--R + +--R 4 3 2 2 3 4 3 4 3 2 2 2 +--R (4b + 8a b + 4a b + 2a b + 2a )cos(x) + (b + 2a b + a b )cos(x) +--R / +--R 5 4 2 3 3 6 +--R (2b - 4a b + 2a b )cos(x) sin(x) +--R + +--R 4 2 3 5 4 2 3 4 +--R (4a b - 4a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 5 4 2 3 3 +--R (- 2b + 8a b - 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 3 7 5 2 3 6 +--R (- 2b + 2a b )cos(x) + (- 8b + 8a b )cos(x) +--R + +--R 5 4 2 3 5 +--R (- 12b - 4a b + 16a b )cos(x) +--R + +--R 5 4 2 3 4 5 4 2 3 3 +--R (- 8b - 8a b + 16a b )cos(x) + (- 2b - 4a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 7 5 2 3 6 5 2 3 5 +--R (2b - 2a b )cos(x) + (8b - 8a b )cos(x) + (12b - 12a b )cos(x) +--R + +--R 5 2 3 4 5 2 3 3 +--R (8b - 8a b )cos(x) + (2b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 3 6 +--R (2b - 2a b )cos(x) sin(x) +--R + +--R 4 2 3 5 4 2 3 4 +--R (4a b + 4a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 5 4 2 3 3 +--R (- 2b + 4a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 2 3 7 5 4 2 3 6 +--R (- 2b - 4a b - 2a b )cos(x) + (- 8b - 16a b - 8a b )cos(x) +--R + +--R 5 4 2 3 5 5 4 2 3 4 +--R (- 12b - 28a b - 16a b )cos(x) + (- 8b - 24a b - 16a b )cos(x) +--R + +--R 5 4 2 3 3 +--R (- 2b - 8a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 7 5 4 2 3 6 +--R (2b + 4a b + 2a b )cos(x) + (8b + 16a b + 8a b )cos(x) +--R + +--R 5 4 2 3 5 5 4 2 3 4 +--R (12b + 24a b + 12a b )cos(x) + (8b + 16a b + 8a b )cos(x) +--R + +--R 5 4 2 3 3 +--R (2b + 4a b + 2a b )cos(x) +--R Type: Expression(Integer) +--E 142 + +--S 143 of 586 +t0524:= sin(x)^2/(a+a*sec(x)) +--R +--R +--R 2 +--R sin(x) +--R (128) ------------ +--R a sec(x) + a +--R Type: Expression(Integer) +--E 143 + +--S 144 of 586 +r0524:= -1/2*(x-2*sin(x)+cos(x)*sin(x))/a +--R +--R +--R (- cos(x) + 2)sin(x) - x +--R (129) ------------------------ +--R 2a +--R Type: Expression(Integer) +--E 144 + +--S 145 of 586 +a0524:= integrate(t0524,x) +--R +--R +--R (- cos(x) + 2)sin(x) - x +--R (130) ------------------------ +--R 2a +--R Type: Union(Expression(Integer),...) +--E 145 + +--S 146 of 586 +m0524:= a0524-r0524 +--R +--R +--R (131) 0 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 586 +d0524:= D(m0524,x) +--R +--R +--R (132) 0 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 586 +t0525:= cos(x)/(a+a*sec(x)) +--R +--R +--R cos(x) +--R (133) ------------ +--R a sec(x) + a +--R Type: Expression(Integer) +--E 148 + +--S 149 of 586 +r0525:= -x/a+sin(x)/a+sin(x)/a/(cos(x)+1) +--R +--R +--R (cos(x) + 2)sin(x) - x cos(x) - x +--R (134) --------------------------------- +--R a cos(x) + a +--R Type: Expression(Integer) +--E 149 + +--S 150 of 586 +a0525:= integrate(t0525,x) +--R +--R +--R (cos(x) + 2)sin(x) - x cos(x) - x +--R (135) --------------------------------- +--R a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 150 + +--S 151 of 586 +m0525:= a0525-r0525 +--R +--R +--R (136) 0 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 586 +d0525:= D(m0525,x) +--R +--R +--R (137) 0 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 586 +t0526:= tan(x)/(a+a*sec(x)) +--R +--R +--R tan(x) +--R (138) ------------ +--R a sec(x) + a +--R Type: Expression(Integer) +--E 153 + +--S 154 of 586 +r0526:= -log(cos(x)+1)/a +--R +--R +--R log(cos(x) + 1) +--R (139) - --------------- +--R a +--R Type: Expression(Integer) +--E 154 + +--S 155 of 586 +a0526:= integrate(t0526,x) +--R +--R +--R 2 +--R log(----------) +--R cos(x) + 1 +--R (140) --------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 155 + +--S 156 of 586 +m0526:= a0526-r0526 +--R +--R +--R 2 +--R log(cos(x) + 1) + log(----------) +--R cos(x) + 1 +--R (141) --------------------------------- +--R a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 586 +d0526:= D(m0526,x) +--R +--R +--R (142) 0 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 586 +t0527:= tan(x)^2/(a+a*sec(x)) +--R +--R +--R 2 +--R tan(x) +--R (143) ------------ +--R a sec(x) + a +--R Type: Expression(Integer) +--E 158 + +--S 159 of 586 +r0527:= (-x+atanh(sin(x)))/a +--R +--R +--R atanh(sin(x)) - x +--R (144) ----------------- +--R a +--R Type: Expression(Integer) +--E 159 + +--S 160 of 586 +a0527:= integrate(t0527,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - x +--R cos(x) + 1 cos(x) + 1 +--R (145) ------------------------------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 160 + +--S 161 of 586 +m0527:= a0527-r0527 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (146) ------------------------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 586 +d0527:= D(m0527,x) +--R +--R +--R (147) +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R ----------------------------------------------------------------------------- +--R 4 2 2 2 +--R a sin(x) + (- a cos(x) - 2a cos(x) - 2a)sin(x) + a cos(x) + 2a cos(x) + a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 586 +t0528:= tan(x)^4/(a+a*sec(x)) +--R +--R +--R 4 +--R tan(x) +--R (148) ------------ +--R a sec(x) + a +--R Type: Expression(Integer) +--E 163 + +--S 164 of 586 +r0528:= x/a-1/2*atanh(sin(x))/a-tan(x)/a+1/2*sec(x)*tan(x)/a +--R +--R +--R - atanh(sin(x)) + (sec(x) - 2)tan(x) + 2x +--R (149) ----------------------------------------- +--R 2a +--R Type: Expression(Integer) +--E 164 + +--S 165 of 586 +a0528:= integrate(t0528,x) +--R +--R +--R (150) +--R 2 sin(x) + cos(x) + 1 2 sin(x) - cos(x) - 1 +--R - cos(x) log(-------------------) + cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 +--R (- 2cos(x) + 1)sin(x) + 2x cos(x) +--R / +--R 2 +--R 2a cos(x) +--R Type: Union(Expression(Integer),...) +--E 165 + +--S 166 of 586 +m0528:= a0528-r0528 +--R +--R +--R (151) +--R 2 sin(x) + cos(x) + 1 2 sin(x) - cos(x) - 1 +--R - cos(x) log(-------------------) + cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 2 2 +--R cos(x) atanh(sin(x)) + (- cos(x) sec(x) + 2cos(x) )tan(x) +--R + +--R (- 2cos(x) + 1)sin(x) +--R / +--R 2 +--R 2a cos(x) +--R Type: Expression(Integer) +--E 166 + +--S 167 of 586 +d0528:= D(m0528,x) +--R +--R +--R (152) +--R 3 3 4 +--R (- 2cos(x) sec(x) + 2cos(x) )sin(x) +--R + +--R 5 4 3 5 4 +--R (2cos(x) + 4cos(x) + 4cos(x) )sec(x) - 2cos(x) - 4cos(x) +--R + +--R 3 +--R - 4cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 5 4 +--R (- 2cos(x) - 4cos(x) - 2cos(x) )sec(x) + 2cos(x) + 4cos(x) +--R + +--R 3 +--R 2cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 +--R (- 2cos(x) + 2)sin(x) +--R + +--R 3 3 2 4 +--R (- cos(x) sec(x) + 4cos(x) + 3cos(x) - 4)sin(x) +--R + +--R 5 4 3 5 3 +--R (cos(x) + 2cos(x) + 2cos(x) )sec(x) + 2cos(x) - 6cos(x) +--R + +--R 2 +--R - 4cos(x) + 2cos(x) + 2 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 6 3 2 +--R (- cos(x) - 2cos(x) - cos(x) )sec(x) + cos(x) + 2cos(x) + cos(x) +--R / +--R 3 4 5 4 3 2 +--R 2a cos(x) sin(x) + (- 2a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 4 3 +--R 2a cos(x) + 4a cos(x) + 2a cos(x) +--R Type: Expression(Integer) +--E 167 + +--S 168 of 586 +t0529:= sec(x)^2/(a+a*sec(x)) +--R +--R +--R 2 +--R sec(x) +--R (153) ------------ +--R a sec(x) + a +--R Type: Expression(Integer) +--E 168 + +--S 169 of 586 +r0529:= atanh(sin(x))/a-sin(x)/a/(cos(x)+1) +--R +--R +--R (cos(x) + 1)atanh(sin(x)) - sin(x) +--R (154) ---------------------------------- +--R a cos(x) + a +--R Type: Expression(Integer) +--E 169 + +--S 170 of 586 +a0529:= integrate(t0529,x) +--R +--R +--R (155) +--R sin(x) + cos(x) + 1 +--R (cos(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R sin(x) - cos(x) - 1 +--R (- cos(x) - 1)log(-------------------) - sin(x) +--R cos(x) + 1 +--R / +--R a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 170 + +--S 171 of 586 +m0529:= a0529-r0529 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (156) ------------------------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 586 +d0529:= D(m0529,x) +--R +--R +--R (157) +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R ----------------------------------------------------------------------------- +--R 4 2 2 2 +--R a sin(x) + (- a cos(x) - 2a cos(x) - 2a)sin(x) + a cos(x) + 2a cos(x) + a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 586 +t0530:= sec(x)^3/(a+a*sec(x)) +--R +--R +--R 3 +--R sec(x) +--R (158) ------------ +--R a sec(x) + a +--R Type: Expression(Integer) +--E 173 + +--S 174 of 586 +r0530:= -atanh(sin(x))/a+sin(x)/a/(cos(x)+1)+tan(x)/a +--R +--R +--R (- cos(x) - 1)atanh(sin(x)) + (cos(x) + 1)tan(x) + sin(x) +--R (159) --------------------------------------------------------- +--R a cos(x) + a +--R Type: Expression(Integer) +--E 174 + +--S 175 of 586 +a0530:= integrate(t0530,x) +--R +--R +--R (160) +--R 2 sin(x) + cos(x) + 1 +--R (- cos(x) - cos(x))log(-------------------) +--R cos(x) + 1 +--R + +--R 2 sin(x) - cos(x) - 1 +--R (cos(x) + cos(x))log(-------------------) + (2cos(x) + 1)sin(x) +--R cos(x) + 1 +--R / +--R 2 +--R a cos(x) + a cos(x) +--R Type: Union(Expression(Integer),...) +--E 175 + +--S 176 of 586 +m0530:= a0530-r0530 +--R +--R +--R (161) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - cos(x)log(-------------------) + cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R cos(x)atanh(sin(x)) - cos(x)tan(x) + sin(x) +--R / +--R a cos(x) +--R Type: Expression(Integer) +--E 176 + +--S 177 of 586 +d0530:= D(m0530,x) +--R +--R +--R (162) +--R 2 4 4 3 2 2 4 +--R - cos(x) sin(x) + (cos(x) + 2cos(x) + 2cos(x) )sin(x) - cos(x) +--R + +--R 3 2 +--R - 2cos(x) - cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 2 4 +--R sin(x) + (cos(x) - 2cos(x) - 2)sin(x) +--R + +--R 4 3 2 2 5 3 +--R (2cos(x) + cos(x) - cos(x) + 2cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 4 4 3 2 2 +--R a cos(x) sin(x) + (- a cos(x) - 2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 4 3 2 +--R a cos(x) + 2a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 177 + +--S 178 of 586 +t0531:= sec(x)^4/(a+a*sec(x)) +--R +--R +--R 4 +--R sec(x) +--R (163) ------------ +--R a sec(x) + a +--R Type: Expression(Integer) +--E 178 + +--S 179 of 586 +r0531:= 3/2*atanh(sin(x))/a-sin(x)/a/(cos(x)+1)-tan(x)/a+1/2*sec(x)*tan(x)/a +--R +--R +--R (164) +--R (3cos(x) + 3)atanh(sin(x)) + ((cos(x) + 1)sec(x) - 2cos(x) - 2)tan(x) +--R + +--R - 2sin(x) +--R / +--R 2a cos(x) + 2a +--R Type: Expression(Integer) +--E 179 + +--S 180 of 586 +a0531:= integrate(t0531,x) +--R +--R +--R (165) +--R 3 2 sin(x) + cos(x) + 1 +--R (3cos(x) + 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 sin(x) - cos(x) - 1 +--R (- 3cos(x) - 3cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 +--R (- 4cos(x) - cos(x) + 1)sin(x) +--R / +--R 3 2 +--R 2a cos(x) + 2a cos(x) +--R Type: Union(Expression(Integer),...) +--E 180 + +--S 181 of 586 +m0531:= a0531-r0531 +--R +--R +--R (166) +--R 2 sin(x) + cos(x) + 1 2 sin(x) - cos(x) - 1 +--R 3cos(x) log(-------------------) - 3cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 2 2 +--R - 3cos(x) atanh(sin(x)) + (- cos(x) sec(x) + 2cos(x) )tan(x) +--R + +--R (- 2cos(x) + 1)sin(x) +--R / +--R 2 +--R 2a cos(x) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 586 +d0531:= D(m0531,x) +--R +--R +--R (167) +--R 3 3 4 +--R (- 2cos(x) sec(x) + 2cos(x) )sin(x) +--R + +--R 5 4 3 5 4 +--R (2cos(x) + 4cos(x) + 4cos(x) )sec(x) - 2cos(x) - 4cos(x) +--R + +--R 3 +--R - 4cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 5 4 +--R (- 2cos(x) - 4cos(x) - 2cos(x) )sec(x) + 2cos(x) + 4cos(x) +--R + +--R 3 +--R 2cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 6 +--R (- 2cos(x) + 2)sin(x) +--R + +--R 3 3 2 4 +--R (- cos(x) sec(x) - 4cos(x) + 3cos(x) - 4)sin(x) +--R + +--R 5 4 3 5 4 +--R (cos(x) + 2cos(x) + 2cos(x) )sec(x) - 6cos(x) - 4cos(x) +--R + +--R 3 2 +--R 2cos(x) - 4cos(x) + 2cos(x) + 2 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 6 4 3 +--R (- cos(x) - 2cos(x) - cos(x) )sec(x) - 3cos(x) + 4cos(x) + 2cos(x) +--R + +--R 2 +--R cos(x) +--R / +--R 3 4 5 4 3 2 +--R 2a cos(x) sin(x) + (- 2a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 4 3 +--R 2a cos(x) + 4a cos(x) + 2a cos(x) +--R Type: Expression(Integer) +--E 182 + +--S 183 of 586 +t0532:= csc(x)/(a+a*sec(x)) +--R +--R +--R csc(x) +--R (168) ------------ +--R a sec(x) + a +--R Type: Expression(Integer) +--E 183 + +--S 184 of 586 +r0532:= -1/2*atanh(cos(x))/a-1/2/a/(cos(x)+1) +--R +--R +--R (- cos(x) - 1)atanh(cos(x)) - 1 +--R (169) ------------------------------- +--R 2a cos(x) + 2a +--R Type: Expression(Integer) +--E 184 + +--S 185 of 586 +a0532:= integrate(t0532,x) +--R +--R +--R sin(x) +--R (2cos(x) + 2)log(----------) + cos(x) - 1 +--R cos(x) + 1 +--R (170) ----------------------------------------- +--R 4a cos(x) + 4a +--R Type: Union(Expression(Integer),...) +--E 185 + +--S 186 of 586 +m0532:= a0532-r0532 +--R +--R +--R sin(x) +--R 2log(----------) + 2atanh(cos(x)) + 1 +--R cos(x) + 1 +--R (171) ------------------------------------- +--R 4a +--R Type: Expression(Integer) +--E 186 + +--S 187 of 586 +d0532:= D(m0532,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (172) -------------------------------- +--R 2 +--R (2a cos(x) - 2a)sin(x) +--R Type: Expression(Integer) +--E 187 + +--S 188 of 586 +t0533:= csc(x)^3/(a+a*sec(x)) +--R +--R +--R 3 +--R csc(x) +--R (173) ------------ +--R a sec(x) + a +--R Type: Expression(Integer) +--E 188 + +--S 189 of 586 +r0533:= -1/8*atanh(cos(x))/a-1/8/a/(1-cos(x))-1/8/a/(cos(x)+1)^2 +--R +--R +--R (174) +--R 3 2 2 +--R (- cos(x) - cos(x) + cos(x) + 1)atanh(cos(x)) + cos(x) + cos(x) + 2 +--R ---------------------------------------------------------------------- +--R 3 2 +--R 8a cos(x) + 8a cos(x) - 8a cos(x) - 8a +--R Type: Expression(Integer) +--E 189 + +--S 190 of 586 +a0533:= integrate(t0533,x) +--R +--R +--R (175) +--R 3 2 sin(x) 3 2 +--R (4cos(x) + 4cos(x) - 4cos(x) - 4)log(----------) + 3cos(x) + 7cos(x) +--R cos(x) + 1 +--R + +--R cos(x) + 5 +--R / +--R 3 2 +--R 32a cos(x) + 32a cos(x) - 32a cos(x) - 32a +--R Type: Union(Expression(Integer),...) +--E 190 + +--S 191 of 586 +m0533:= a0533-r0533 +--R +--R +--R sin(x) +--R 4log(----------) + 4atanh(cos(x)) + 3 +--R cos(x) + 1 +--R (176) ------------------------------------- +--R 32a +--R Type: Expression(Integer) +--E 191 + +--S 192 of 586 +d0533:= D(m0533,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (177) -------------------------------- +--R 2 +--R (8a cos(x) - 8a)sin(x) +--R Type: Expression(Integer) +--E 192 + +--S 193 of 586 +t0534:= sin(x)/(a+b*csc(x)) +--R +--R +--R sin(x) +--R (178) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 193 + +--S 194 of 586 +r0534:= -b*x/a^2-2*b^2*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/_ + a^2/(a^2-b^2)^(1/2)-cos(x)/a +--R +--R +--R x +--R b tan(-) + a +---------+ +--R 2 2 | 2 2 +--R - 2b atanh(------------) + (- a cos(x) - b x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (179) --------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 194 + +--S 195 of 586 +a0534:= integrate(t0534,x) +--R +--R +--R (180) +--R [ +--R 2 +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R +---------+ +--R | 2 2 +--R (- a cos(x) - b x)\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R , +--R +-------+ +--R | 2 2 +-------+ +--R 2 (b sin(x) + a cos(x) + a)\|b - a | 2 2 +--R 2b atan(-----------------------------------) + (- a cos(x) - b x)\|b - a +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R ---------------------------------------------------------------------------] +--R +-------+ +--R 2 | 2 2 +--R a \|b - a +--R Type: Union(List(Expression(Integer)),...) +--E 195 + +--S 196 of 586 +m0534a:= a0534.1-r0534 +--R +--R +--R (181) +--R 2 +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R x +--R b tan(-) + a +--R 2 2 +--R 2b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 196 + +--S 197 of 586 +d0534a:= D(m0534a,x) +--R +--R +--R (182) +--R 4 2 2 2 2 3 2 3 x 2 +--R (((b - a b )cos(x) - a b )sin(x) + a b cos(x) - a b )tan(-) +--R 2 +--R + +--R 2 2 2 3 2 2 2 4 2 2 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (- 2b + 2a b )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 2 3 2 3 +--R ((b - a b )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 2 4 3 2 5 2 3 2 5 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 3 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 5 2 3 4 3 2 2 +--R (2a b - 2a b )sin(x) + (2b - 2a b )sin(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 +--R (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 4 3 2 5 2 3 2 5 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 3 +--R a b +--R / +--R 3 2 2 2 3 4 2 3 4 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 4 3 2 3 2 +--R (- a b + a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 2 5 3 2 5 +--R 2a b sin(x) + ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 2 3 4 4 +--R (- 2a b + 2a b)cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 3 4 2 3 4 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 4 3 2 3 2 +--R (- a b + a b )cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 2 3 3 5 5 5 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 2 4 2 6 2 4 6 +--R (2a b - 2a b)sin(x) + ((2a b - 2a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 3 5 3 3 5 +--R (2a b - 2a b)cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 3 3 5 5 5 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(x) + a b - a b +--R Type: Expression(Integer) +--E 197 + +--S 198 of 586 +m0534b:= a0534.2-r0534 +--R +--R +--R (183) +--R x +--R +-------+ b tan(-) + a +--R 2 | 2 2 2 +--R 2b \|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 2 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R 2b \|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression(Integer) +--E 198 + +--S 199 of 586 +d0534b:= D(m0534b,x) +--R +--R +--R (184) +--R 3 2 2 2 3 2 3 x 2 +--R (b sin(x) + (- 2a b cos(x) - 2a b )sin(x) + b cos(x) - b )tan(-) +--R 2 +--R + +--R 2 2 2 2 2 x 3 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + b sin(x) +--R 2 +--R + +--R 2 2 3 2 3 +--R (- 2a b cos(x) - 2a b )sin(x) + b cos(x) - b +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2a b sin(x) + (4a cos(x) + 4a )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) + a b +--R Type: Expression(Integer) +--E 199 + +--S 200 of 586 +t0535:= sin(x)^2/(a+b*csc(x)) +--R +--R +--R 2 +--R sin(x) +--R (185) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 200 + +--S 201 of 586 +r0535:= 1/2*x/a+b^2*x/a^3+2*b^3*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/_ + a^3/(a^2-b^2)^(1/2)+b*cos(x)/a^2-1/2*cos(x)*sin(x)/a +--R +--R +--R (186) +--R x +--R b tan(-) + a +--R 3 2 +--R 4b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- a cos(x)sin(x) + 2a b cos(x) + (2b + a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R Type: Expression(Integer) +--E 201 + +--S 202 of 586 +a0535:= integrate(t0535,x) +--R +--R +--R (187) +--R [ +--R 3 +--R 2b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- a cos(x)sin(x) + 2a b cos(x) + (2b + a )x)\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 3 (b sin(x) + a cos(x) + a)\|b - a +--R - 4b atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (- a cos(x)sin(x) + 2a b cos(x) + (2b + a )x)\|b - a +--R / +--R +-------+ +--R 3 | 2 2 +--R 2a \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 202 + +--S 203 of 586 +m0535a:= a0535.1-r0535 +--R +--R +--R (188) +--R 3 +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R x +--R b tan(-) + a +--R 3 2 +--R - 2b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 203 + +--S 204 of 586 +d0535a:= D(m0535a,x) +--R +--R +--R (189) +--R 5 2 3 2 3 4 2 4 x 2 +--R (((- b + a b )cos(x) + a b )sin(x) - a b cos(x) + a b )tan(-) +--R 2 +--R + +--R 2 3 2 4 2 3 2 5 2 3 +--R (- 2a b sin(x) - 2a b sin(x) - 2a b cos(x) + (2b - 2a b )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 2 3 4 2 4 +--R ((- b + a b )cos(x) + a b )sin(x) - a b cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 3 3 5 3 3 6 2 4 2 6 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 4 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 6 2 4 5 3 3 2 +--R (2a b - 2a b )sin(x) + (2b - 2a b )sin(x) + (2a b - 2a b )cos(x) +--R + +--R 5 3 3 +--R (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 3 3 6 2 4 2 6 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 4 +--R a b +--R / +--R 4 2 2 3 3 5 3 3 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 2 4 4 2 4 2 +--R (- a b + a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 2 6 4 2 6 +--R 2a b sin(x) + ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 3 5 3 3 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 2 4 4 2 4 2 +--R (- a b + a b )cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 4 5 2 2 4 3 6 2 5 6 +--R (- a b + a b )sin(x) + ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 6 2 5 2 7 3 4 7 +--R (- 2a b + 2a b)sin(x) + ((- 2a b + 2a )cos(x) - 2a b + 2a )sin(x) +--R + +--R 4 3 6 4 3 6 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 4 3 6 2 5 6 +--R (- a b + a b )sin(x) + ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- a b + a b )cos(x) - a b + a b +--R Type: Expression(Integer) +--E 204 + +--S 205 of 586 +m0535b:= a0535.2-r0535 +--R +--R +--R (190) +--R x +--R +-------+ b tan(-) + a +--R 3 | 2 2 2 +--R - 2b \|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R - 2b \|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R / +--R +---------+ +-------+ +--R 3 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression(Integer) +--E 205 + +--S 206 of 586 +d0535b:= D(m0535b,x) +--R +--R +--R (191) +--R 4 2 3 3 4 2 4 x 2 +--R (- b sin(x) + (2a b cos(x) + 2a b )sin(x) - b cos(x) + b )tan(-) +--R 2 +--R + +--R 3 2 3 2 3 x 4 2 +--R (- 4a b sin(x) - 4a b cos(x) - 4a b cos(x))tan(-) - b sin(x) +--R 2 +--R + +--R 3 3 4 2 4 +--R (2a b cos(x) + 2a b )sin(x) - b cos(x) + b +--R / +--R 3 2 2 4 4 3 2 2 3 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 3 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 5 4 2 4 +--R 2a b sin(x) + (4a cos(x) + 4a )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 4 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 4 3 2 2 3 2 3 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) + a b +--R Type: Expression(Integer) +--E 206 + +--S 207 of 586 +t0536:= sin(x)^3/(a+b*csc(x)) +--R +--R +--R 3 +--R sin(x) +--R (192) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 207 + +--S 208 of 586 +r0536:= -1/2*b*x/a^2-b^3*x/a^4-2*b^4*atanh((a+b*tan(1/2*x))/_ + (a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)-cos(x)/a-b^2*cos(x)/a^3+_ + 1/3*cos(x)^3/a+1/2*b*cos(x)*sin(x)/a^2 +--R +--R +--R (193) +--R x +--R b tan(-) + a +--R 4 2 +--R - 12b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 3 +--R 3a b cos(x)sin(x) + 2a cos(x) + (- 6a b - 6a )cos(x) +--R + +--R 3 2 +--R (- 6b - 3a b)x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R Type: Expression(Integer) +--E 208 + +--S 209 of 586 +a0536:= integrate(t0536,x) +--R +--R +--R (194) +--R [ +--R 4 +--R 6b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R 2 3 3 2 3 +--R 3a b cos(x)sin(x) + 2a cos(x) + (- 6a b - 6a )cos(x) +--R + +--R 3 2 +--R (- 6b - 3a b)x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R 6a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 4 (b sin(x) + a cos(x) + a)\|b - a +--R 12b atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 3 2 3 +--R 3a b cos(x)sin(x) + 2a cos(x) + (- 6a b - 6a )cos(x) +--R + +--R 3 2 +--R (- 6b - 3a b)x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 | 2 2 +--R 6a \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 209 + +--S 210 of 586 +m0536a:= a0536.1-r0536 +--R +--R +--R (195) +--R 4 +--R b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R x +--R b tan(-) + a +--R 4 2 +--R 2b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 210 + +--S 211 of 586 +d0536a:= D(m0536a,x) +--R +--R +--R (196) +--R 6 2 4 2 4 5 2 5 x 2 +--R (((b - a b )cos(x) - a b )sin(x) + a b cos(x) - a b )tan(-) +--R 2 +--R + +--R 2 4 2 5 2 4 2 6 2 4 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (- 2b + 2a b )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 2 4 5 2 5 +--R ((b - a b )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 6 3 4 6 3 4 7 2 5 2 7 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 5 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 2 7 2 5 6 3 4 2 +--R (2a b - 2a b )sin(x) + (2b - 2a b )sin(x) + (2a b - 2a b )cos(x) +--R + +--R 6 3 4 +--R (2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 4 6 3 4 7 2 5 2 7 +--R ((- a b + a b )cos(x) - a b + a b )sin(x) + (b - a b )cos(x) - b +--R + +--R 2 5 +--R a b +--R / +--R 5 2 2 4 3 6 4 3 6 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 3 4 5 2 5 2 +--R (- a b + a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 5 2 7 5 2 7 +--R 2a b sin(x) + ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 4 3 6 6 +--R (- 2a b + 2a b)cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 2 4 3 6 4 3 6 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 3 4 5 2 5 2 +--R (- a b + a b )cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 6 2 2 5 3 7 3 5 7 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (a b - a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 7 2 6 2 8 4 4 8 +--R (2a b - 2a b)sin(x) + ((2a b - 2a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 5 3 7 5 3 7 +--R (2a b - 2a b)cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 4 6 2 2 5 3 7 3 5 7 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (a b - a b )cos(x) + a b - a b +--R Type: Expression(Integer) +--E 211 + +--S 212 of 586 +m0536b:= a0536.2-r0536 +--R +--R +--R (197) +--R x +--R +-------+ b tan(-) + a +--R 4 | 2 2 2 +--R 2b \|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 4 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R 2b \|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R / +--R +---------+ +-------+ +--R 4 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression(Integer) +--E 212 + +--S 213 of 586 +d0536b:= D(m0536b,x) +--R +--R +--R (198) +--R 5 2 4 4 5 2 5 x 2 +--R (b sin(x) + (- 2a b cos(x) - 2a b )sin(x) + b cos(x) - b )tan(-) +--R 2 +--R + +--R 4 2 4 2 4 x 5 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + b sin(x) +--R 2 +--R + +--R 4 4 5 2 5 +--R (- 2a b cos(x) - 2a b )sin(x) + b cos(x) - b +--R / +--R 4 2 2 5 5 4 2 2 4 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 4 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 6 6 5 2 5 +--R 2a b sin(x) + (4a cos(x) + 4a )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 5 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 5 5 4 2 2 4 2 4 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) + a b +--R Type: Expression(Integer) +--E 213 + +--S 214 of 586 +t0537:= sin(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R sin(x) +--R (199) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 586 +r0537:= 3/8*x/a+1/2*b^2*x/a^3+b^4*x/a^5+2*b^5*_ + atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a^5/(a^2-b^2)^(1/2)+_ + b*cos(x)/a^2+b^3*cos(x)/a^4-1/3*b*cos(x)^3/a^2-_ + 3/8*cos(x)*sin(x)/a-1/2*b^2*cos(x)*sin(x)/a^3-1/4*cos(x)*sin(x)^3/a +--R +--R +--R (200) +--R x +--R b tan(-) + a +--R 5 2 +--R 48b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 2 2 4 3 3 +--R - 6a cos(x)sin(x) + (- 12a b - 9a )cos(x)sin(x) - 8a b cos(x) +--R + +--R 3 3 4 2 2 4 +--R (24a b + 24a b)cos(x) + (24b + 12a b + 9a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 24a \|- b + a +--R Type: Expression(Integer) +--E 215 + +--S 216 of 586 +a0537:= integrate(t0537,x) +--R +--R +--R (201) +--R [ +--R 5 +--R 24b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (- 12a b - 15a )cos(x))sin(x) - 8a b cos(x) +--R + +--R 3 3 4 2 2 4 +--R (24a b + 24a b)cos(x) + (24b + 12a b + 9a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 24a \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 5 (b sin(x) + a cos(x) + a)\|b - a +--R - 48b atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (- 12a b - 15a )cos(x))sin(x) - 8a b cos(x) +--R + +--R 3 3 4 2 2 4 +--R (24a b + 24a b)cos(x) + (24b + 12a b + 9a )x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 5 | 2 2 +--R 24a \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 216 + +--S 217 of 586 +m0537a:= a0537.1-r0537 +--R +--R +--R (202) +--R 5 +--R 4b +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R x +--R b tan(-) + a +--R 5 2 +--R - 8b atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 4 3 4 3 4 | 2 2 +--R (a cos(x)sin(x) + (a cos(x) - a cos(x))sin(x))\|- b + a +--R / +--R +---------+ +--R 5 | 2 2 +--R 4a \|- b + a +--R Type: Expression(Integer) +--E 217 + +--S 218 of 586 +d0537a:= D(m0537a,x) +--R +--R +--R (203) +--R 5 2 6 4 3 6 4 3 6 5 +--R - a b sin(x) + ((a b - a b)cos(x) - a b - a b)sin(x) +--R + +--R 3 4 5 2 4 +--R (a b - a b )cos(x)sin(x) +--R + +--R 4 3 6 4 3 6 3 +--R ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 5 2 4 5 2 2 3 4 5 2 5 2 2 +--R (a b cos(x) - a b cos(x) + (- a b + a b )cos(x) + a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- a b + a b)cos(x) + (a b + a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (a b - a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 7 2 5 2 5 +--R (- 4b + 4a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 5 5 2 4 3 4 5 2 3 +--R (- a b + a b )cos(x) + a b cos(x) + (a b - a b )cos(x) +--R + +--R 6 5 2 2 6 +--R (- 4a b - a b )cos(x) + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 6 5 2 7 5 2 7 5 +--R - 2a b sin(x) + ((2a b - 2a )cos(x) - 2a b - 2a )sin(x) +--R + +--R 4 3 6 4 +--R (2a b - 2a b)cos(x)sin(x) +--R + +--R 5 2 7 5 2 7 3 +--R ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 6 4 6 2 4 3 6 2 5 +--R 2a b cos(x) - 2a b cos(x) + (- 2a b + 2a b)cos(x) - 8a b +--R + +--R 6 +--R 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 7 5 5 2 7 4 +--R (- 2a b + 2a )cos(x) + (2a b + 2a )cos(x) +--R + +--R 5 2 7 3 5 2 7 2 6 +--R (2a b - 2a )cos(x) + (- 2a b - 2a )cos(x) - 8a b +--R * +--R sin(x) +--R + +--R 4 3 6 5 6 4 4 3 6 3 +--R (- 2a b + 2a b)cos(x) + 2a b cos(x) + (2a b - 2a b)cos(x) +--R + +--R 2 5 6 2 7 2 5 +--R (- 8a b - 2a b)cos(x) + (8b - 8a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 6 4 3 6 4 3 6 5 +--R - a b sin(x) + ((a b - a b)cos(x) - a b - a b)sin(x) +--R + +--R 3 4 5 2 4 +--R (a b - a b )cos(x)sin(x) +--R + +--R 4 3 6 4 3 6 3 +--R ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 5 2 4 5 2 2 3 4 5 2 5 2 2 +--R (a b cos(x) - a b cos(x) + (- a b + a b )cos(x) + a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 4 3 6 3 +--R (- a b + a b)cos(x) + (a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 4 3 6 2 7 2 5 2 5 +--R (- a b - a b)cos(x) + (- 4b + 4a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 5 5 2 4 3 4 5 2 3 +--R (- a b + a b )cos(x) + a b cos(x) + (a b - a b )cos(x) +--R + +--R 6 5 2 2 6 +--R (- 4a b - a b )cos(x) + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 6 2 6 5 3 7 3 5 7 5 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 4 4 6 2 4 +--R (a b - a b )cos(x)sin(x) +--R + +--R 5 3 7 3 5 7 3 +--R ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 +--R (- a b + a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 7 5 3 5 7 4 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 5 3 7 3 3 5 7 2 +--R (a b - a b)cos(x) + (a b - a b)cos(x) +--R + +--R 7 3 5 7 3 5 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 +--R (- a b + a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 4 4 6 2 3 8 2 6 4 4 6 2 2 8 2 6 +--R (a b - a b )cos(x) + (4b - 4a b + a b - a b )cos(x) - 4b + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 7 6 6 2 8 4 4 8 5 +--R (2a b - 2a b)sin(x) + ((2a b - 2a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 5 3 7 4 +--R (2a b - 2a b)cos(x)sin(x) +--R + +--R 6 2 8 4 4 8 3 +--R ((- 2a b + 2a )cos(x) - 2a b + 2a )sin(x) +--R + +--R 5 3 7 4 5 3 7 2 +--R (- 2a b + 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 7 7 3 5 5 3 7 +--R (- 2a b + 2a b)cos(x) + 8a b - 8a b - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 8 5 4 4 8 4 +--R (- 2a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 6 2 8 3 4 4 8 2 8 2 6 +--R (2a b - 2a )cos(x) + (2a b - 2a )cos(x) + 8b - 8a b +--R * +--R sin(x) +--R + +--R 5 3 7 5 5 3 7 4 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 5 3 7 3 7 3 5 5 3 7 2 +--R (2a b - 2a b)cos(x) + (8a b - 8a b + 2a b - 2a b)cos(x) +--R + +--R 7 3 5 +--R (8a b - 8a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 4 6 2 6 5 3 7 3 5 7 5 +--R (a b - a b )sin(x) + ((a b - a b)cos(x) + a b - a b)sin(x) +--R + +--R 4 4 6 2 4 5 3 7 3 5 7 3 +--R (a b - a b )cos(x)sin(x) + ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 6 2 +--R (- a b + a b )cos(x) + (a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 4 4 6 2 +--R - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 7 5 3 5 7 4 5 3 7 3 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 5 7 2 7 3 5 7 3 5 +--R (a b - a b)cos(x) + (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R sin(x) +--R + +--R 4 4 6 2 5 4 4 6 2 4 4 4 6 2 3 +--R (- a b + a b )cos(x) + (- a b + a b )cos(x) + (a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 +--R (4b - 4a b + a b - a b )cos(x) - 4b + 4a b +--R / +--R 6 2 2 5 3 7 5 3 7 +--R 4a b sin(x) + ((- 4a b + 4a b)cos(x) + 4a b + 4a b)sin(x) +--R + +--R 4 4 6 2 6 2 +--R (- 4a b + 4a b )cos(x) + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 2 6 2 8 6 2 8 +--R 8a b sin(x) + ((- 8a b + 8a )cos(x) + 8a b + 8a )sin(x) +--R + +--R 5 3 7 7 +--R (- 8a b + 8a b)cos(x) + 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 2 5 3 7 5 3 7 +--R 4a b sin(x) + ((- 4a b + 4a b)cos(x) + 4a b + 4a b)sin(x) +--R + +--R 4 4 6 2 6 2 +--R (- 4a b + 4a b )cos(x) + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 4 7 2 2 +--R (- 4a b + 4a b )sin(x) +--R + +--R 6 3 8 4 5 8 +--R ((- 4a b + 4a b)cos(x) - 4a b + 4a b)sin(x) +--R + +--R 5 4 7 2 5 4 7 2 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 8 2 7 2 9 5 4 9 +--R (- 8a b + 8a b)sin(x) + ((- 8a b + 8a )cos(x) - 8a b + 8a )sin(x) +--R + +--R 6 3 8 6 3 8 +--R (- 8a b + 8a b)cos(x) - 8a b + 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 7 2 2 6 3 8 4 5 8 +--R (- 4a b + 4a b )sin(x) + ((- 4a b + 4a b)cos(x) - 4a b + 4a b)sin(x) +--R + +--R 5 4 7 2 5 4 7 2 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R Type: Expression(Integer) +--E 218 + +--S 219 of 586 +m0537b:= a0537.2-r0537 +--R +--R +--R (204) +--R x +--R +-------+ b tan(-) + a +--R 5 | 2 2 2 +--R - 8b \|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 5 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R - 8b \|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +-------+ +--R 4 3 4 3 4 | 2 2 | 2 2 +--R (a cos(x)sin(x) + (a cos(x) - a cos(x))sin(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 5 | 2 2 | 2 2 +--R 4a \|- b + a \|b - a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 586 +d0537b:= D(m0537b,x) +--R +--R +--R (205) +--R 4 2 6 5 5 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 2 2 4 2 4 5 5 3 +--R (- a b cos(x) - 2a b cos(x))sin(x) + (2a b cos(x) + 2a b)sin(x) +--R + +--R 4 2 4 4 2 6 4 2 2 +--R (a b cos(x) + 2a b cos(x) - 4b + a b )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R + +--R 5 5 +--R 8a b cos(x) + 8a b +--R * +--R sin(x) +--R + +--R 4 2 6 4 2 5 4 2 3 6 4 2 2 6 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) + (- 4b - a b )cos(x) + 4b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 6 6 5 +--R - 2a b sin(x) + (- 4a cos(x) - 4a )sin(x) +--R + +--R 5 2 5 4 6 6 3 +--R (- 2a b cos(x) - 4a b cos(x))sin(x) + (4a cos(x) + 4a )sin(x) +--R + +--R 5 4 5 5 5 2 +--R (2a b cos(x) + 4a b cos(x) - 16a b + 2a b)sin(x) +--R + +--R 6 5 6 4 6 3 6 2 +--R (4a cos(x) + 4a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 6 5 5 5 3 5 5 2 +--R 2a b cos(x) + 4a b cos(x) - 4a b cos(x) + (- 16a b - 2a b)cos(x) +--R + +--R 5 +--R - 16a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 5 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 2 2 4 2 4 5 5 3 +--R (- a b cos(x) - 2a b cos(x))sin(x) + (2a b cos(x) + 2a b)sin(x) +--R + +--R 4 2 4 4 2 6 4 2 2 +--R (a b cos(x) + 2a b cos(x) - 4b + a b )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R + +--R 5 5 +--R 8a b cos(x) + 8a b +--R * +--R sin(x) +--R + +--R 4 2 6 4 2 5 4 2 3 6 4 2 2 6 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) + (- 4b - a b )cos(x) + 4b +--R / +--R 5 2 2 6 6 5 2 2 +--R 4a b sin(x) + (8a b cos(x) + 8a b)sin(x) + 4a b cos(x) +--R + +--R 5 2 5 2 +--R 8a b cos(x) + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 7 7 6 2 +--R 8a b sin(x) + (16a cos(x) + 16a )sin(x) + 8a b cos(x) +--R + +--R 6 6 +--R 16a b cos(x) + 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 2 6 6 5 2 2 5 2 +--R 4a b sin(x) + (8a b cos(x) + 8a b)sin(x) + 4a b cos(x) + 8a b cos(x) +--R + +--R 5 2 +--R 4a b +--R Type: Expression(Integer) +--E 220 + +--S 221 of 586 +t0538:= cos(x)^2/(a+b*csc(x)) +--R +--R +--R 2 +--R cos(x) +--R (206) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 586 +r0538:= 1/2*x/a-b^2*x/a^3+2*b*(a^2-b^2)^(1/2)*_ + atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a^3-_ + b*cos(x)/a^2+1/2*cos(x)*sin(x)/a +--R +--R +--R (207) +--R x +--R +---------+ b tan(-) + a +--R | 2 2 2 2 +--R 4b\|- b + a atanh(------------) + a cos(x)sin(x) - 2a b cos(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 +--R (- 2b + a )x +--R / +--R 3 +--R 2a +--R Type: Expression(Integer) +--E 222 + +--S 223 of 586 +a0538:= integrate(t0538,x) +--R +--R +--R (208) +--R [ +--R +---------+ +--R | 2 2 +--R 2b\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R 2 2 2 +--R a cos(x)sin(x) - 2a b cos(x) + (- 2b + a )x +--R / +--R 3 +--R 2a +--R , +--R +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a 2 +--R - 4b\|b - a atan(-----------------------) + a cos(x)sin(x) +--R b sin(x) + a cos(x) + a +--R + +--R 2 2 +--R - 2a b cos(x) + (- 2b + a )x +--R / +--R 3 +--R 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 223 + +--S 224 of 586 +m0538a:= a0538.1-r0538 +--R +--R +--R (209) +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R x +--R +---------+ b tan(-) + a +--R | 2 2 2 +--R - 2b\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 +--R a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 586 +d0538a:= D(m0538a,x) +--R +--R +--R (210) +--R 3 3 3 3 4 2 2 2 +--R ((- a b + a b)cos(x) - a b + a b)sin(x) + (b - a b )cos(x) +--R + +--R 4 2 2 +--R - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 4 2 2 +--R (2a b - 2a b)sin(x) + (2b - 2a b )sin(x) +--R + +--R 3 3 2 3 3 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 3 3 4 2 2 2 4 +--R ((- a b + a b)cos(x) - a b + a b)sin(x) + (b - a b )cos(x) - b +--R + +--R 2 2 +--R a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 4 2 3 4 4 3 2 2 +--R ((b - 2a b + a b)cos(x) - a b + a b)sin(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 +--R - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 4 3 2 2 3 4 2 +--R (2a b - 2a b)sin(x) + (2a b - 2a b )sin(x) + (2a b - 2a b)cos(x) +--R + +--R 5 2 3 4 +--R (- 2b + 4a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 2 3 4 4 3 2 2 +--R ((b - 2a b + a b)cos(x) - a b + a b)sin(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 +--R - a b + a b +--R / +--R 3 2 2 4 2 3 4 3 2 3 2 +--R (a b sin(x) + (a b cos(x) + a b + a b)sin(x) + a b cos(x) + a b ) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 3 2 5 4 +--R 2a b sin(x) + (2a cos(x) + 2a b + 2a )sin(x) + 2a b cos(x) +--R + +--R 4 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 2 3 4 3 2 3 2 +--R a b sin(x) + (a b cos(x) + a b + a b)sin(x) + a b cos(x) + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 3 3 5 3 3 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 2 4 4 2 4 2 +--R (- a b + a b )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 4 2 6 4 2 6 +--R 2a b sin(x) + ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 3 5 3 3 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 2 4 4 2 4 2 +--R (- a b + a b )cos(x) + a b +--R Type: Expression(Integer) +--E 225 + +--S 226 of 586 +m0538b:= a0538.2-r0538 +--R +--R +--R (211) +--R x +--R +---------+ b tan(-) + a +--R | 2 2 2 +--R - 2b\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a +--R - 2b\|b - a atan(-----------------------) +--R b sin(x) + a cos(x) + a +--R / +--R 3 +--R a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 586 +d0538b:= D(m0538b,x) +--R +--R +--R (212) +--R 4 2 2 2 3 3 3 3 +--R (b - a b )sin(x) + ((- 2a b + 2a b)cos(x) - 2a b + 2a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 +--R (b - a b )cos(x) - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 2 3 3 +--R ((4a b - 4a b)sin(x) + (4a b - 4a b)cos(x) + (4a b - 4a b)cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 3 3 3 3 +--R (b - a b )sin(x) + ((- 2a b + 2a b)cos(x) - 2a b + 2a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 +--R (b - a b )cos(x) - b + a b +--R / +--R 3 2 2 4 4 3 2 2 3 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 3 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 5 4 2 4 +--R 2a b sin(x) + (4a cos(x) + 4a )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 4 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 4 3 2 2 3 2 3 2 +--R a b sin(x) + (2a b cos(x) + 2a b)sin(x) + a b cos(x) + 2a b cos(x) + a b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 586 +t0539:= cos(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R cos(x) +--R (213) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 228 + +--S 229 of 586 +r0539:= -5/8*x/a+1/2*b^2*x/a^3+(a^2-b^2)^2*x/a^5+2*b*(a^2-b^2)^(3/2)*_ + atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a^5-b*cos(x)/a^2+_ + b^3*cos(x)/a^4-1/3*b*cos(x)^3/a^2+5/8*cos(x)*sin(x)/a-_ + 1/2*b^2*cos(x)*sin(x)/a^3-1/4*cos(x)*sin(x)^3/a +--R +--R +--R (214) +--R x +--R +---------+ b tan(-) + a +--R 3 2 | 2 2 2 4 3 +--R (- 48b + 48a b)\|- b + a atanh(------------) - 6a cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 3 3 3 3 +--R (- 12a b + 15a )cos(x)sin(x) - 8a b cos(x) + (24a b - 24a b)cos(x) +--R + +--R 4 2 2 4 +--R (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 586 +a0539:= integrate(t0539,x) +--R +--R +--R (215) +--R [ +--R +---------+ +--R 3 2 | 2 2 +--R (24b - 24a b)\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (- b sin(x) - a cos(x) - a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (- 12a b + 9a )cos(x))sin(x) - 8a b cos(x) +--R + +--R 3 3 4 2 2 4 +--R (24a b - 24a b)cos(x) + (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R , +--R +--R +-------+ +--R +-------+ | 2 2 +--R 3 2 | 2 2 (cos(x) + 1)\|b - a +--R (48b - 48a b)\|b - a atan(-----------------------) +--R b sin(x) + a cos(x) + a +--R + +--R 4 3 2 2 4 3 3 +--R (6a cos(x) + (- 12a b + 9a )cos(x))sin(x) - 8a b cos(x) +--R + +--R 3 3 4 2 2 4 +--R (24a b - 24a b)cos(x) + (24b - 36a b + 9a )x +--R / +--R 5 +--R 24a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 230 + +--S 231 of 586 +m0539a:= a0539.1-r0539 +--R +--R +--R (216) +--R +---------+ +--R 3 2 | 2 2 +--R (4b - 4a b)\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (- b sin(x) - a cos(x) - a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R x +--R +---------+ b tan(-) + a +--R 3 2 | 2 2 2 4 3 +--R (8b - 8a b)\|- b + a atanh(------------) + a cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 3 4 +--R (a cos(x) - a cos(x))sin(x) +--R / +--R 5 +--R 4a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 586 +d0539a:= D(m0539a,x) +--R +--R +--R (217) +--R 4 2 6 5 3 3 5 5 +--R - a b sin(x) + (- a b cos(x) - a b - a b)sin(x) +--R + +--R 4 2 4 5 3 3 5 3 +--R - a b cos(x)sin(x) + (a b cos(x) + a b + a b)sin(x) +--R + +--R 4 2 4 4 2 2 4 2 4 2 2 +--R (a b cos(x) - a b cos(x) + a b cos(x) + a b )sin(x) +--R + +--R 5 5 3 3 5 4 5 3 +--R a b cos(x) + (a b + a b)cos(x) - a b cos(x) +--R + +--R 3 3 5 2 5 3 3 5 5 +--R (- a b - a b)cos(x) + (4a b - 8a b + 4a b)cos(x) + 4a b +--R + +--R 3 3 5 +--R - 8a b + 4a b +--R * +--R sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 +--R a b cos(x) + a b cos(x) - a b cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (- 4b + 8a b - 5a b )cos(x) + 4b - 8a b + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 6 4 2 6 5 +--R - 2a b sin(x) + (- 2a cos(x) - 2a b - 2a )sin(x) +--R + +--R 5 4 6 4 2 6 3 +--R - 2a b cos(x)sin(x) + (2a cos(x) + 2a b + 2a )sin(x) +--R + +--R 5 4 5 2 5 5 3 3 +--R 2a b cos(x) - 2a b cos(x) + 2a b cos(x) - 8a b + 16a b +--R + +--R 5 +--R - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 2 6 4 6 3 +--R 2a cos(x) + (2a b + 2a )cos(x) - 2a cos(x) +--R + +--R 4 2 6 2 6 2 4 4 2 +--R (- 2a b - 2a )cos(x) - 8b + 16a b - 8a b +--R * +--R sin(x) +--R + +--R 5 5 5 4 5 3 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 8a b + 16a b - 10a b)cos(x) + (- 8a b + 16a b - 8a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 3 3 5 5 +--R - a b sin(x) + (- a b cos(x) - a b - a b)sin(x) +--R + +--R 4 2 4 5 3 3 5 3 +--R - a b cos(x)sin(x) + (a b cos(x) + a b + a b)sin(x) +--R + +--R 4 2 4 4 2 2 4 2 4 2 2 +--R (a b cos(x) - a b cos(x) + a b cos(x) + a b )sin(x) +--R + +--R 5 5 3 3 5 4 5 3 +--R a b cos(x) + (a b + a b)cos(x) - a b cos(x) +--R + +--R 3 3 5 2 5 3 3 5 5 +--R (- a b - a b)cos(x) + (4a b - 8a b + 4a b)cos(x) + 4a b +--R + +--R 3 3 5 +--R - 8a b + 4a b +--R * +--R sin(x) +--R + +--R 4 2 5 4 2 4 4 2 3 +--R a b cos(x) + a b cos(x) - a b cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (- 4b + 8a b - 5a b )cos(x) + 4b - 8a b + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 6 4 3 6 4 3 6 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 3 4 5 2 4 +--R (- a b + a b )cos(x)sin(x) +--R + +--R 4 3 6 4 3 6 3 +--R ((a b - a b)cos(x) - a b - a b)sin(x) +--R + +--R 5 2 4 5 2 2 3 4 5 2 5 2 2 +--R (- a b cos(x) + a b cos(x) + (a b - a b )cos(x) - a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (a b - a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- a b + a b)cos(x) + (a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (4b - 12a b + 12a b - 4a b)cos(x) - 4a b + 8a b - 4a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 5 5 2 4 3 4 5 2 3 +--R (a b - a b )cos(x) - a b cos(x) + (- a b + a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (4a b - 8a b + 5a b )cos(x) - 4a b + 8a b - 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 6 5 2 7 5 2 7 5 +--R 2a b sin(x) + ((- 2a b + 2a )cos(x) + 2a b + 2a )sin(x) +--R + +--R 4 3 6 4 +--R (- 2a b + 2a b)cos(x)sin(x) +--R + +--R 5 2 7 5 2 7 3 +--R ((2a b - 2a )cos(x) - 2a b - 2a )sin(x) +--R + +--R 6 4 6 2 4 3 6 2 5 +--R - 2a b cos(x) + 2a b cos(x) + (2a b - 2a b)cos(x) + 8a b +--R + +--R 4 3 6 +--R - 16a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 7 5 5 2 7 4 +--R (2a b - 2a )cos(x) + (- 2a b - 2a )cos(x) +--R + +--R 5 2 7 3 5 2 7 2 6 3 4 +--R (- 2a b + 2a )cos(x) + (2a b + 2a )cos(x) + 8a b - 16a b +--R + +--R 5 2 +--R 8a b +--R * +--R sin(x) +--R + +--R 4 3 6 5 6 4 4 3 6 3 +--R (2a b - 2a b)cos(x) - 2a b cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (8a b - 16a b + 10a b)cos(x) +--R + +--R 7 2 5 4 3 6 +--R (- 8b + 24a b - 24a b + 8a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 6 4 3 6 4 3 6 5 +--R a b sin(x) + ((- a b + a b)cos(x) + a b + a b)sin(x) +--R + +--R 3 4 5 2 4 4 3 6 4 3 6 3 +--R (- a b + a b )cos(x)sin(x) + ((a b - a b)cos(x) - a b - a b)sin(x) +--R + +--R 5 2 4 5 2 2 3 4 5 2 5 2 2 +--R (- a b cos(x) + a b cos(x) + (a b - a b )cos(x) - a b )sin(x) +--R + +--R 4 3 6 5 4 3 6 4 4 3 6 3 +--R (a b - a b)cos(x) + (- a b - a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 4 3 6 2 7 2 5 4 3 6 2 5 +--R (a b + a b)cos(x) + (4b - 12a b + 12a b - 4a b)cos(x) - 4a b +--R + +--R 4 3 6 +--R 8a b - 4a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 5 5 2 4 3 4 5 2 3 +--R (a b - a b )cos(x) - a b cos(x) + (- a b + a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (4a b - 8a b + 5a b )cos(x) - 4a b + 8a b - 4a b +--R / +--R 5 2 2 6 4 3 6 5 2 +--R 4a b sin(x) + (4a b cos(x) + 4a b + 4a b)sin(x) + 4a b cos(x) +--R + +--R 5 2 +--R 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 7 5 2 7 6 +--R 8a b sin(x) + (8a cos(x) + 8a b + 8a )sin(x) + 8a b cos(x) +--R + +--R 6 +--R 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 2 6 4 3 6 5 2 5 2 +--R 4a b sin(x) + (4a b cos(x) + 4a b + 4a b)sin(x) + 4a b cos(x) + 4a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 6 2 2 5 3 7 5 3 7 +--R - 4a b sin(x) + ((4a b - 4a b)cos(x) - 4a b - 4a b)sin(x) +--R + +--R 4 4 6 2 6 2 +--R (4a b - 4a b )cos(x) - 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 2 6 2 8 6 2 8 +--R - 8a b sin(x) + ((8a b - 8a )cos(x) - 8a b - 8a )sin(x) +--R + +--R 5 3 7 7 +--R (8a b - 8a b)cos(x) - 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 2 5 3 7 5 3 7 +--R - 4a b sin(x) + ((4a b - 4a b)cos(x) - 4a b - 4a b)sin(x) +--R + +--R 4 4 6 2 6 2 +--R (4a b - 4a b )cos(x) - 4a b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 586 +m0539b:= a0539.2-r0539 +--R +--R +--R (218) +--R x +--R +---------+ b tan(-) + a +--R 3 2 | 2 2 2 +--R (8b - 8a b)\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 3 2 | 2 2 (cos(x) + 1)\|b - a 4 3 +--R (8b - 8a b)\|b - a atan(-----------------------) + a cos(x)sin(x) +--R b sin(x) + a cos(x) + a +--R + +--R 4 3 4 +--R (a cos(x) - a cos(x))sin(x) +--R / +--R 5 +--R 4a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 586 +d0539b:= D(m0539b,x) +--R +--R +--R (219) +--R 4 2 6 5 5 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 2 2 4 2 4 5 5 3 +--R (- a b cos(x) - 2a b cos(x))sin(x) + (2a b cos(x) + 2a b)sin(x) +--R + +--R 4 2 4 4 2 6 2 4 4 2 2 +--R (a b cos(x) + 2a b cos(x) - 4b + 8a b - 3a b )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (8a b - 16a b + 8a b)cos(x) + 8a b - 16a b + 8a b +--R * +--R sin(x) +--R + +--R 4 2 6 4 2 5 4 2 3 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (- 4b + 8a b - 5a b )cos(x) + 4b - 8a b + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 6 6 5 +--R - 2a b sin(x) + (- 4a cos(x) - 4a )sin(x) +--R + +--R 5 2 5 4 6 6 3 +--R (- 2a b cos(x) - 4a b cos(x))sin(x) + (4a cos(x) + 4a )sin(x) +--R + +--R 5 4 5 5 3 3 5 2 +--R (2a b cos(x) + 4a b cos(x) - 16a b + 32a b - 14a b)sin(x) +--R + +--R 6 5 6 4 6 3 6 2 +--R (4a cos(x) + 4a cos(x) - 4a cos(x) - 4a cos(x) )sin(x) +--R + +--R 5 6 5 5 5 3 +--R 2a b cos(x) + 4a b cos(x) - 4a b cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 16a b + 32a b - 18a b)cos(x) + (- 16a b + 32a b - 16a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 5 5 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 4 2 2 4 2 4 5 5 3 +--R (- a b cos(x) - 2a b cos(x))sin(x) + (2a b cos(x) + 2a b)sin(x) +--R + +--R 4 2 4 4 2 6 2 4 4 2 2 +--R (a b cos(x) + 2a b cos(x) - 4b + 8a b - 3a b )sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (8a b - 16a b + 8a b)cos(x) + 8a b - 16a b + 8a b +--R * +--R sin(x) +--R + +--R 4 2 6 4 2 5 4 2 3 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (- 4b + 8a b - 5a b )cos(x) + 4b - 8a b + 4a b +--R / +--R 5 2 2 6 6 5 2 2 +--R 4a b sin(x) + (8a b cos(x) + 8a b)sin(x) + 4a b cos(x) +--R + +--R 5 2 5 2 +--R 8a b cos(x) + 4a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 7 7 6 2 +--R 8a b sin(x) + (16a cos(x) + 16a )sin(x) + 8a b cos(x) +--R + +--R 6 6 +--R 16a b cos(x) + 8a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 2 6 6 5 2 2 5 2 +--R 4a b sin(x) + (8a b cos(x) + 8a b)sin(x) + 4a b cos(x) + 8a b cos(x) +--R + +--R 5 2 +--R 4a b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 586 +t0540:= tan(x)^2/(a+b*csc(x)) +--R +--R +--R 2 +--R tan(x) +--R (220) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 586 +r0540:= -x/a+2*b^3*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(3/2)+_ + 1/2*cos(x)/(a+b)/(1-sin(x))-1/2*cos(x)/(a-b)/(1+sin(x)) +--R +--R +--R (221) +--R x +--R b tan(-) + a +--R 3 2 3 2 +--R (- 2b sin(x) + 2b )atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 2 2 +--R ((- b + a )x sin(x) + a cos(x)sin(x) - a b cos(x) + (b - a )x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 3 2 2 3 | 2 2 +--R ((a b - a )sin(x) - a b + a )\|- b + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 586 +a0540:= integrate(t0540,x) +--R +--R +--R (222) +--R [ +--R 3 +--R b cos(x) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- a sin(x) + ((- b + a )x + a b)cos(x) + a b)\|- b + a +--R / +--R +---------+ +--R 2 3 | 2 2 +--R (a b - a )cos(x)\|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 3 (b sin(x) + a cos(x) + a)\|b - a +--R 2b cos(x)atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R (- a sin(x) + ((- b + a )x + a b)cos(x) + a b)\|b - a +--R / +--R +-------+ +--R 2 3 | 2 2 +--R (a b - a )cos(x)\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 237 + +--S 238 of 586 +m0540a:= a0540.1-r0540 +--R +--R +--R (223) +--R 3 2 3 +--R (b cos(x)sin(x) - b cos(x)) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R x +--R b tan(-) + a +--R 3 2 3 2 +--R (2b cos(x)sin(x) - 2b cos(x))atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 2 2 +--R - a sin(x) + (a b cos(x) + a b)sin(x) + (- a cos(x) + a )sin(x) +--R + +--R 2 +--R a b cos(x) - a b cos(x) - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 3 2 2 3 | 2 2 +--R ((a b - a )cos(x)sin(x) + (- a b + a )cos(x))\|- b + a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 586 +d0540a:= D(m0540a,x) +--R +--R +--R (224) +--R 3 2 8 2 3 4 4 7 +--R - a b sin(x) + ((a b - a b)cos(x) - a b)sin(x) +--R + +--R 4 3 2 6 +--R (a b + 2a b )sin(x) +--R + +--R 5 2 3 3 2 3 2 +--R (b - a b )cos(x) - 2a b cos(x) +--R + +--R 5 2 3 4 2 3 4 +--R (- b - a b + 2a b)cos(x) + a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 3 4 2 +--R (a b + a b )cos(x) + (a b - a b )cos(x) - 2a b cos(x) +--R + +--R 4 3 2 +--R - 2a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 5 4 3 2 3 4 2 +--R (- b + a b)cos(x) + (3a b + a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 +--R (2b - a b - a b)cos(x) - 2a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 5 4 4 +--R (a b - a b )cos(x) - 4a b cos(x) +--R + +--R 4 3 2 3 4 3 2 2 4 +--R (- 2a b + 2a b )cos(x) + (3a b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (2b - 3a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (a b - a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 5 2 3 2 3 +--R (- b + a b )cos(x) + a b +--R * +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (a b - a b )cos(x) + (- a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 8 3 2 5 5 7 +--R - 2a b sin(x) + ((2a b - 2a )cos(x) - 2a )sin(x) +--R + +--R 2 3 2 2 3 4 6 +--R (2a b cos(x) + 2a b + 4a b)sin(x) +--R + +--R 4 3 2 2 4 3 2 5 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b + 4a )cos(x) +--R + +--R 3 2 5 +--R 2a b + 4a +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (2a b + 2a b)cos(x) + (- 2b + 4a b - 2a b)cos(x) +--R + +--R 2 3 2 2 3 4 +--R - 6a b cos(x) - 4a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 5 3 2 5 4 +--R (- 2a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (2a b - 4a b + 2a )cos(x) + (- 4a b + 2a b + 2a )cos(x) +--R + +--R 4 3 2 5 3 2 5 +--R (4a b - 2a b - 2a )cos(x) - 4a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 +--R (2a b - 2a b)cos(x) - 8a b cos(x) +--R + +--R 5 2 3 4 3 2 3 4 2 2 3 +--R (4b - 8a b + 4a b)cos(x) + (4a b + 2a b)cos(x) + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 5 3 2 5 4 +--R (4a b - 6a b + 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 4 3 2 5 3 4 5 2 +--R (- 2a b + 4a b - 2a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 4 3 2 3 2 +--R (- 2a b + 2a b )cos(x) + 2a b +--R * +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 2a b + 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 5 2 3 4 3 4 2 +--R (- 2b + 4a b - 2a b)cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 8 2 3 4 4 7 +--R - a b sin(x) + ((a b - a b)cos(x) - a b)sin(x) +--R + +--R 4 3 2 6 +--R (a b + 2a b )sin(x) +--R + +--R 5 2 3 3 2 3 2 5 2 3 4 +--R (b - a b )cos(x) - 2a b cos(x) + (- b - a b + 2a b)cos(x) +--R + +--R 2 3 4 +--R a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 3 4 2 +--R (a b + a b )cos(x) + (a b - a b )cos(x) - 2a b cos(x) +--R + +--R 4 3 2 +--R - 2a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 5 4 3 2 3 4 2 +--R (- b + a b)cos(x) + (3a b + a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 +--R (2b - a b - a b)cos(x) - 2a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 5 4 4 4 3 2 3 +--R (a b - a b )cos(x) - 4a b cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 4 3 2 2 4 +--R (3a b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (2b - 3a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 5 2 3 +--R (a b - a b)cos(x) + (- a b - a b)cos(x) + (- b + a b )cos(x) +--R + +--R 2 3 +--R a b +--R * +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 4 3 2 3 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 2 +--R (- a b - a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 8 3 3 5 3 3 5 7 +--R (- a b + a b )sin(x) + ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 6 2 4 4 2 6 +--R (b + a b - 2a b )sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (a b + a b - 2a b)cos(x) + a b + a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 4 2 4 2 4 4 2 3 +--R (b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 2 4 2 6 2 4 4 2 +--R (- 2b + 2a b )cos(x) - 2b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 5 3 3 5 4 +--R (a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R + +--R 5 5 3 5 3 3 5 2 +--R (a b - a b)cos(x) + (3a b - 2a b - a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 2a b + a b + a b)cos(x) - 2a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 5 6 2 4 4 +--R (- a b + a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 2 4 4 2 3 6 2 4 4 2 2 6 2 4 +--R (2a b - 2a b )cos(x) + (3b - 2a b - a b )cos(x) + b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (- 2a b + 3a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R + +--R 3 3 5 3 5 5 2 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 5 6 4 2 4 2 4 4 2 3 +--R (a b - a b )cos(x) + (b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 4 2 2 +--R (- b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 8 +--R (- 2a b + 2a b)sin(x) +--R + +--R 4 2 6 4 2 6 7 +--R ((- 2a b + 2a )cos(x) - 2a b + 2a )sin(x) +--R + +--R 5 3 3 2 5 3 3 5 6 +--R ((2a b - 2a b )cos(x) + 2a b + 2a b - 4a b)sin(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 6 +--R (2b - 4a b + 2a b )cos(x) + (2a b + 2a b - 4a )cos(x) +--R + +--R 2 4 4 2 6 +--R 2a b + 2a b - 4a +--R * +--R 5 +--R sin(x) +--R + +--R 5 5 4 5 3 3 5 3 +--R (2a b - 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 5 3 3 2 5 3 3 5 +--R (- 6a b + 6a b )cos(x) - 4a b + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 6 5 2 4 4 2 6 4 +--R (2a b - 2a )cos(x) + (- 2a b + 4a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 3 6 2 4 6 2 +--R (- 2a b + 4a b - 2a )cos(x) + (- 4b + 6a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- 4a b + 2a b + 2a )cos(x) - 4a b + 2a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 5 5 3 3 4 +--R (- 2a b + 2a b)cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (- 4a b + 8a b - 4a b)cos(x) + (4a b - 2a b - 2a b)cos(x) +--R + +--R 5 3 3 +--R 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R (- 4a b + 6a b - 2a )cos(x) + (- 2a b + 4a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 3 6 2 4 4 2 6 2 +--R (2a b - 4a b + 2a )cos(x) + (2b - 2a b - 2a b + 2a )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 3 3 5 5 5 5 4 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 3 3 3 5 2 +--R (2a b - 4a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 8 3 3 5 3 3 5 7 +--R (- a b + a b )sin(x) + ((- a b + a b)cos(x) - a b + a b)sin(x) +--R + +--R 6 2 4 4 2 6 +--R (b + a b - 2a b )sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (a b + a b - 2a b)cos(x) + a b + a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 4 2 4 2 4 4 2 3 6 2 4 2 +--R (b - a b )cos(x) + (- a b + a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 +--R - 2b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 5 3 3 5 4 +--R (a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R + +--R 5 5 3 5 3 3 5 2 +--R (a b - a b)cos(x) + (3a b - 2a b - a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 2a b + a b + a b)cos(x) - 2a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 5 6 2 4 4 +--R (- a b + a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 2 4 4 2 3 6 2 4 4 2 2 6 2 4 +--R (2a b - 2a b )cos(x) + (3b - 2a b - a b )cos(x) + b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (- 2a b + 3a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R + +--R 3 3 5 3 5 5 2 5 3 3 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) + (a b - a b )cos(x) +--R + +--R 5 3 3 +--R a b - a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 5 6 4 2 4 2 4 4 2 3 +--R (a b - a b )cos(x) + (b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 4 2 2 +--R (- b + a b )cos(x) +--R / +--R 2 4 4 2 2 6 +--R (a b - a b )cos(x) sin(x) +--R + +--R 5 3 3 5 3 5 5 2 5 +--R ((- a b + 2a b - a b)cos(x) + (a b - a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 4 +--R ((- b + 2a b - a b )cos(x) + (- a b + a b )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 5 5 2 3 +--R ((2a b - 4a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 2 +--R ((2b - 4a b + 2a b )cos(x) + (- a b + a b )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 5 5 2 +--R ((- a b + 2a b - a b)cos(x) + (a b - a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 +--R (- b + 2a b - a b )cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 2 6 +--R (2a b - 2a b)cos(x) sin(x) +--R + +--R 2 4 4 2 6 3 2 4 6 2 5 +--R ((- 2a b + 4a b - 2a )cos(x) + (2a b - 2a )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 3 3 5 2 +--R ((- 2a b + 4a b - 2a b)cos(x) + (- 2a b + 2a b)cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 3 2 4 6 2 3 +--R ((4a b - 8a b + 4a )cos(x) + (- 4a b + 4a )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 3 3 5 2 2 +--R ((4a b - 8a b + 4a b)cos(x) + (- 2a b + 2a b)cos(x) )sin(x) +--R + +--R 2 4 4 2 6 3 2 4 6 2 +--R ((- 2a b + 4a b - 2a )cos(x) + (2a b - 2a )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 3 3 5 2 +--R (- 2a b + 4a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 6 +--R (a b - a b )cos(x) sin(x) +--R + +--R 5 3 3 5 3 5 5 2 5 +--R ((- a b + 2a b - a b)cos(x) + (a b - a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 4 +--R ((- b + 2a b - a b )cos(x) + (- a b + a b )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 5 5 2 3 +--R ((2a b - 4a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 2 +--R ((2b - 4a b + 2a b )cos(x) + (- a b + a b )cos(x) )sin(x) +--R + +--R 5 3 3 5 3 5 5 2 +--R ((- a b + 2a b - a b)cos(x) + (a b - a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 3 2 4 4 2 2 +--R (- b + 2a b - a b )cos(x) + (a b - a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 6 3 4 5 2 2 6 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 2 5 4 3 6 3 7 2 5 4 3 6 2 +--R ((a b - 2a b + a b)cos(x) + (b - a b - a b + a b)cos(x) ) +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R ((a b - 2a b + a b )cos(x) + (- a b + 2a b - a b )cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 3 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- 2b + 2a b + 2a b - 2a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R ((- 2a b + 4a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 3 7 2 5 4 3 6 2 +--R ((a b - 2a b + a b)cos(x) + (b - a b - a b + a b)cos(x) )sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R (a b - 2a b + a b )cos(x) + (a b - 2a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 2 6 +--R (2a b - 4a b + 2a b)cos(x) sin(x) +--R + +--R 3 4 5 2 7 3 +--R (2a b - 4a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R ((2a b - 4a b + 2a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 7 3 +--R (- 4a b + 8a b - 4a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 4a b + 4a b + 4a b - 4a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R ((- 4a b + 8a b - 4a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 7 3 +--R (2a b - 4a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (2a b - 2a b - 2a b + 2a )cos(x) +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 4 5 2 2 6 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 2 5 4 3 6 3 7 2 5 4 3 6 2 5 +--R ((a b - 2a b + a b)cos(x) + (b - a b - a b + a b)cos(x) )sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 4 +--R ((a b - 2a b + a b )cos(x) + (- a b + 2a b - a b )cos(x) )sin(x) +--R + +--R 2 5 4 3 6 3 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- 2b + 2a b + 2a b - 2a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R ((- 2a b + 4a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 3 7 2 5 4 3 6 2 +--R ((a b - 2a b + a b)cos(x) + (b - a b - a b + a b)cos(x) )sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R (a b - 2a b + a b )cos(x) + (a b - 2a b + a b )cos(x) +--R Type: Expression(Integer) +--E 239 + +--S 240 of 586 +m0540b:= a0540.2-r0540 +--R +--R +--R (225) +--R x +--R +-------+ b tan(-) + a +--R 3 2 3 | 2 2 2 +--R (2b cos(x)sin(x) - 2b cos(x))\|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 2 3 | 2 2 +--R (2b cos(x)sin(x) - 2b cos(x))\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|b - a +--R atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 2 2 2 2 +--R - a sin(x) + (a b cos(x) + a b)sin(x) + (- a cos(x) + a )sin(x) +--R + +--R 2 +--R a b cos(x) - a b cos(x) - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 3 2 2 3 | 2 2 | 2 2 +--R ((a b - a )cos(x)sin(x) + (- a b + a )cos(x))\|- b + a \|b - a +--R Type: Expression(Integer) +--E 240 + +--S 241 of 586 +d0540b:= D(m0540b,x) +--R +--R +--R (226) +--R 2 2 8 3 3 3 7 +--R - a b sin(x) + (- 2a b cos(x) + a b - 2a b)sin(x) +--R + +--R 4 2 2 2 2 2 6 +--R ((b - a b )cos(x) + 3a b )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R - 2a b cos(x) - 2a b cos(x) + (2a b + 4a b)cos(x) - a b +--R + +--R 3 +--R 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 2 4 2 2 3 4 2 2 2 2 2 +--R ((b + a b )cos(x) - 2a b cos(x) + (- 3b + a b )cos(x) - 3a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 3 3 4 3 3 3 +--R 2a b cos(x) + (- 3a b + 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b + 2a b)cos(x) + (- 4a b - 2a b)cos(x) - a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 2 2 5 4 2 2 4 2 2 3 +--R a b cos(x) - 2a b cos(x) + (- 2b - a b )cos(x) + 4a b cos(x) +--R + +--R 4 2 2 2 2 2 +--R (3b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 3 3 5 3 3 4 +--R - 2a b cos(x) + (- 4a b + 2a b)cos(x) + (- a b + 2a b)cos(x) +--R + +--R 3 3 3 2 3 3 +--R - 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + a b +--R * +--R sin(x) +--R + +--R 2 2 6 2 2 5 4 4 2 2 3 +--R a b cos(x) + 2a b cos(x) + b cos(x) - 2a b cos(x) +--R + +--R 4 2 2 2 +--R (- b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 8 4 2 2 4 7 +--R - 2a b sin(x) + (- 4a cos(x) + 2a b - 4a )sin(x) +--R + +--R 3 3 2 3 6 +--R ((4a b - 2a b)cos(x) + 6a b)sin(x) +--R + +--R 2 2 4 2 2 4 5 +--R ((4a b + 8a )cos(x) - 2a b + 8a )sin(x) +--R + +--R 3 3 4 3 3 3 +--R (4a b + 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 3 2 3 +--R (- 8a b + 2a b)cos(x) - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 5 2 2 4 4 2 2 4 3 +--R 4a cos(x) + (- 6a b + 4a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (- 4a b + 4a )cos(x) + (- 8a b - 4a )cos(x) - 2a b - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 3 6 3 5 3 3 4 +--R 2a b cos(x) - 4a b cos(x) + (- 8a b - 2a b)cos(x) +--R + +--R 3 3 3 3 3 2 3 +--R (- 8a b + 8a b)cos(x) + (4a b + 2a b)cos(x) + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 6 2 2 4 5 2 2 4 4 +--R - 4a b cos(x) + (- 8a b + 4a )cos(x) + (- 2a b + 4a )cos(x) +--R + +--R 2 2 4 3 2 2 4 2 2 2 2 2 +--R (4a b - 4a )cos(x) + (4a b - 4a )cos(x) + 4a b cos(x) + 2a b +--R * +--R sin(x) +--R + +--R 3 6 3 5 3 4 3 3 3 +--R 2a b cos(x) + 4a b cos(x) + 4a b cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 2 +--R - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 8 3 3 3 7 +--R - a b sin(x) + (- 2a b cos(x) + a b - 2a b)sin(x) +--R + +--R 4 2 2 2 2 2 6 +--R ((b - a b )cos(x) + 3a b )sin(x) +--R + +--R 3 3 3 2 3 3 3 3 +--R (- 2a b cos(x) - 2a b cos(x) + (2a b + 4a b)cos(x) - a b + 4a b) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 2 4 2 2 3 4 2 2 2 2 2 +--R ((b + a b )cos(x) - 2a b cos(x) + (- 3b + a b )cos(x) - 3a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 3 3 4 3 3 3 +--R 2a b cos(x) + (- 3a b + 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b + 2a b)cos(x) + (- 4a b - 2a b)cos(x) - a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 2 2 5 4 2 2 4 2 2 3 +--R a b cos(x) - 2a b cos(x) + (- 2b - a b )cos(x) + 4a b cos(x) +--R + +--R 4 2 2 2 2 2 +--R (3b + a b )cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 3 3 5 3 3 4 +--R - 2a b cos(x) + (- 4a b + 2a b)cos(x) + (- a b + 2a b)cos(x) +--R + +--R 3 3 3 2 3 3 +--R - 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + a b +--R * +--R sin(x) +--R + +--R 2 2 6 2 2 5 4 4 2 2 3 +--R a b cos(x) + 2a b cos(x) + b cos(x) - 2a b cos(x) +--R + +--R 4 2 2 2 +--R (- b - a b )cos(x) +--R / +--R 4 3 2 2 6 +--R (a b - a b )cos(x) sin(x) +--R + +--R 2 3 4 3 2 3 4 2 5 +--R ((2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 +--R (- a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 3 +--R ((- 4a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 3 2 2 +--R (- a b + a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R ((2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 4 3 2 2 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 6 +--R (2a b - 2a b)cos(x) sin(x) +--R + +--R 3 2 5 3 3 2 5 2 5 +--R ((4a b - 4a )cos(x) + (4a b - 4a )cos(x) )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 2a b + 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 5 3 3 2 5 2 3 +--R ((- 8a b + 8a )cos(x) + (- 8a b + 8a )cos(x) )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 4a b + 4a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 2 3 4 2 +--R (- 2a b + 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R ((4a b - 4a )cos(x) + (4a b - 4a )cos(x) )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 2 3 4 2 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) + (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 6 +--R (a b - a b )cos(x) sin(x) +--R + +--R 2 3 4 3 2 3 4 2 5 +--R ((2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 +--R (- a b + a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 3 +--R ((- 4a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 3 2 2 +--R (- a b + a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R ((2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 4 3 2 2 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + (a b - a b )cos(x) +--R Type: Expression(Integer) +--E 241 + +--S 242 of 586 +t0541:= tan(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R tan(x) +--R (227) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 242 + +--S 243 of 586 +r0541:= x/a+2*b^5*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(5/2)+_ + 1/12*cos(x)/(a+b)/(1-sin(x))^2+1/12*cos(x)/(a+b)/(1-sin(x))-_ + 1/4*(3*a+4*b)*cos(x)/(a+b)^2/(1-sin(x))-_ + 1/12*cos(x)/(a-b)/(1+sin(x))^2+1/4*(3*a-4*b)*cos(x)/(a-b)^2/_ + (1+sin(x))-1/12*cos(x)/(a-b)/(1+sin(x)) +--R +--R +--R (228) +--R x +--R b tan(-) + a +--R 5 4 5 2 5 2 +--R (6b sin(x) - 12b sin(x) + 6b )atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 4 4 2 2 4 3 +--R (3b - 6a b + 3a )x sin(x) + (- 7a b + 4a )cos(x)sin(x) +--R + +--R 3 3 4 2 2 4 2 +--R ((6a b - 3a b)cos(x) + (- 6b + 12a b - 6a )x)sin(x) +--R + +--R 2 2 4 3 3 +--R (6a b - 3a )cos(x)sin(x) + (- 5a b + 2a b)cos(x) +--R + +--R 4 2 2 4 +--R (3b - 6a b + 3a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 2 5 4 4 3 2 5 2 4 +--R (3a b - 6a b + 3a )sin(x) + (- 6a b + 12a b - 6a )sin(x) + 3a b +--R + +--R 3 2 5 +--R - 6a b + 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 243 + +--S 244 of 586 +a0541:= integrate(t0541,x) +--R +--R +--R (229) +--R [ +--R 5 3 +--R 3b cos(x) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R 2 2 4 2 2 2 4 +--R ((7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 4 2 2 4 3 3 3 +--R ((3b - 6a b + 3a )x - 5a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 6a b + 3a b)cos(x) + a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 3 2 5 3 | 2 2 +--R (3a b - 6a b + 3a )cos(x) \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 5 3 (b sin(x) + a cos(x) + a)\|b - a +--R - 6b cos(x) atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 4 2 2 2 4 +--R ((7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 4 2 2 4 3 3 3 +--R ((3b - 6a b + 3a )x - 5a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 6a b + 3a b)cos(x) + a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 3 2 5 3 | 2 2 +--R (3a b - 6a b + 3a )cos(x) \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 244 + +--S 245 of 586 +m0541a:= a0541.1-r0541 +--R +--R +--R (230) +--R 5 3 4 5 3 2 5 3 +--R (3b cos(x) sin(x) - 6b cos(x) sin(x) + 3b cos(x) ) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R 5 3 4 5 3 2 5 3 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) ) +--R * +--R x +--R b tan(-) + a +--R 2 +--R atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 2 2 2 4 5 +--R ((7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R ((- 5a b + 2a b)cos(x) + (- 6a b + 3a b)cos(x) + a b - a b) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 3 +--R ((7a b - 4a )cos(x) + (- 14a b + 8a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 3 4 3 3 3 +--R (- 6a b + 3a b)cos(x) + (10a b - 4a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (12a b - 6a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 +--R ((- 6a b + 3a )cos(x) + (7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 3 4 3 3 3 +--R (5a b - 2a b)cos(x) + (- 5a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 6a b + 3a b)cos(x) + a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 2 5 3 4 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 3 2 5 3 2 4 3 2 5 3 +--R (- 6a b + 12a b - 6a )cos(x) sin(x) + (3a b - 6a b + 3a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 245 + +--S 246 of 586 +d0541a:= D(m0541a,x) +--R +--R +--R (231) +--R 3 4 5 2 2 3 4 5 2 10 +--R ((7a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 +--R (- 7a b + 11a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (a b + 6a b - 4a b)cos(x) + (3a b - 6a b + 3a b)cos(x) +--R + +--R 4 3 6 +--R - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 3 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 6a b - 18a b + 12a b )cos(x) + 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 3 4 +--R (- 3b + 3a b )cos(x) + (9a b - 3a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (6b + 13a b - 32a b + 13a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 10a b - 15a b + 13a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 3b - 3a b + 15a b - 9a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 3 4 5 2 6 +--R (- 3a b - 7a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 6a b + 9a b - 3a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (9a b - 5a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 5 2 +--R (18a b + 11a b - 11a b )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (7a b - 11a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (5a b - 9a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (3b + 8a b - 16a b + 5a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 22a b - a b + 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 18b + 3a b + 30a b - 15a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (24a b + 9a b - 15a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 6 +--R (9b - 9a b - 9a b + 9a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (- 5a b + 7a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (21a b - 4a b + a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (19a b - 29a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 20a b + a b + a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 18a b + 5a b + a b )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 12b + 21a b - 12a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (2b - 22a b + 29a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (18a b + 9a b - 9a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (18b - 17a b - 8a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 22a b + 3a b + 7a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 9b + 15a b - 3a b - 3a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (11a b - 16a b + 5a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 17a b - 3a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 20a b + 31a b - 11a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (14a b + 11a b - 7a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 +--R (6a b - 6a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (8b - 16a b + 11a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (- 2a b + 5a b - 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 2b + 11a b - 13a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 5a b - 5a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 6b + 8a b - a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 +--R (7a b - 3a b - a b)cos(x) + (3b - 6a b + 3a b )cos(x) +--R + +--R 2 5 4 3 +--R - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 6 +--R (- 6a b + 9a b - 3a b )cos(x) + (3a b + 6a b - 3a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (7a b - 11a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (- 3a b - 7a b + 4a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 3 4 5 2 2 +--R (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 6 2 4 3 6 10 +--R ((14a b - 8a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 3 4 5 2 7 3 +--R (- 14a b + 22a b - 8a )cos(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 7 +--R (2a b + 12a b - 8a )cos(x) + (6a b - 12a b + 6a )cos(x) +--R + +--R 5 2 7 +--R - 6a b + 6a +--R * +--R 9 +--R sin(x) +--R + +--R 2 5 4 2 5 4 3 6 3 +--R - 6a b cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 12a b - 36a b + 24a b)cos(x) + 6a b + 12a b - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (12a b + 26a b - 64a b + 26a )cos(x) +--R + +--R 3 4 5 2 7 2 +--R (- 20a b - 30a b + 26a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- 6a b - 6a b + 30a b - 18a )cos(x) + 6a b + 12a b - 18a +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 4 3 6 6 +--R (- 6a b - 14a b + 8a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (6b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (30a b - 10a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 6 +--R (36a b + 22a b - 22a b)cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 4 5 2 7 7 +--R (14a b - 22a b + 8a )cos(x) +--R + +--R 3 4 5 2 7 6 +--R (10a b - 18a b + 8a )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 12a b + 34a b - 32a b + 10a )cos(x) +--R + +--R 6 3 4 5 2 7 4 +--R (18a b - 26a b - 2a b + 10a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 36a b + 6a b + 60a b - 30a )cos(x) +--R + +--R 3 4 5 2 7 2 +--R (48a b + 18a b - 30a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 7 +--R (18a b - 18a b - 18a b + 18a )cos(x) - 18a b + 18a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- 10a b + 14a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (42a b - 8a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 18b + 56a b - 58a b + 20a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 40a b + 2a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 36a b + 10a b + 2a b)cos(x) + 18a b - 12a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (- 24a b + 42a b - 24a b + 6a )cos(x) +--R + +--R 3 4 5 2 7 6 +--R (2a b - 8a b + 6a )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (22a b - 62a b + 58a b - 18a )cos(x) +--R + +--R 6 3 4 5 2 7 4 +--R (- 18a b + 18a b + 18a b - 18a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (36a b - 34a b - 16a b + 14a )cos(x) +--R + +--R 3 4 5 2 7 2 +--R (- 44a b + 6a b + 14a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- 18a b + 30a b - 6a b - 6a )cos(x) + 18a b - 12a b - 6a +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (22a b - 32a b + 10a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (- 34a b - 6a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (18b - 58a b + 62a b - 22a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (16a b + 22a b - 14a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 +--R (12a b - 12a b + 6a b)cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 7 +--R (16a b - 32a b + 22a b - 6a )cos(x) +--R + +--R 3 4 5 2 7 6 +--R (- 4a b + 10a b - 6a )cos(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 10a b + 28a b - 26a b + 8a )cos(x) +--R + +--R 6 3 4 5 2 7 4 +--R (6a b - 4a b - 10a b + 8a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- 12a b + 16a b - 2a b - 2a )cos(x) +--R + +--R 3 4 5 2 7 2 +--R (14a b - 6a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (6a b - 12a b + 6a b )cos(x) - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 7 +--R (- 12a b + 18a b - 6a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (6a b + 12a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 6b + 20a b - 22a b + 8a b)cos(x) +--R + +--R 4 3 6 4 2 5 4 3 6 3 +--R (- 14a b + 8a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 4 3 6 2 +--R (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 10 +--R ((7a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (- 7a b + 11a b - 4a b)cos(x) + (a b + 6a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (3a b - 6a b + 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 3 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 6a b - 18a b + 12a b )cos(x) + 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 3 4 +--R (- 3b + 3a b )cos(x) + (9a b - 3a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (6b + 13a b - 32a b + 13a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 10a b - 15a b + 13a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 3b - 3a b + 15a b - 9a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 3 4 5 2 6 +--R (- 3a b - 7a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 5 6 3 4 5 2 4 +--R (- 6a b + 9a b - 3a b )cos(x) + (9a b - 5a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 5 2 +--R (18a b + 11a b - 11a b )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (7a b - 11a b + 4a b)cos(x) + (5a b - 9a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (3b + 8a b - 16a b + 5a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 22a b - a b + 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 18b + 3a b + 30a b - 15a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (24a b + 9a b - 15a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 6 +--R (9b - 9a b - 9a b + 9a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 6 +--R (- 5a b + 7a b - 2a b )cos(x) + (21a b - 4a b + a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (19a b - 29a b + 10a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 20a b + a b + a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 18a b + 5a b + a b )cos(x) + 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 12b + 21a b - 12a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (2b - 22a b + 29a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (18a b + 9a b - 9a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (18b - 17a b - 8a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 22a b + 3a b + 7a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 9b + 15a b - 3a b - 3a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (11a b - 16a b + 5a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 17a b - 3a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 20a b + 31a b - 11a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (14a b + 11a b - 7a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 +--R (6a b - 6a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (8b - 16a b + 11a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (- 2a b + 5a b - 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 2b + 11a b - 13a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 5a b - 5a b + 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (- 6b + 8a b - a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 +--R (7a b - 3a b - a b)cos(x) + (3b - 6a b + 3a b )cos(x) +--R + +--R 2 5 4 3 +--R - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 6 +--R (- 6a b + 9a b - 3a b )cos(x) + (3a b + 6a b - 3a b )cos(x) +--R + +--R 6 3 4 5 2 5 6 3 4 5 2 4 +--R (7a b - 11a b + 4a b )cos(x) + (- 3a b - 7a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- a b + 2a b - a b )cos(x) + (a b - a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((- 7a b + 11a b - 4a b )cos(x) + 3a b - 6a b + 3a b )sin(x) +--R + +--R 3 5 5 3 7 3 +--R (- 7a b + 11a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- a b - 5a b + 10a b - 4a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (3a b - 6a b + 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (6b + 12a b - 30a b + 12a b )cos(x) - 3b - 3a b + 15a b +--R + +--R 6 2 +--R - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 5 3 4 +--R (- 3a b + 3a b )cos(x) + (- 9a b + 12a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (6a b + 13a b - 32a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (10a b + 5a b - 28a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 3a b - 3a b + 15a b - 9a b)cos(x) - 3a b - 3a b + 15a b +--R + +--R 7 +--R - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (3b + 4a b - 11a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 6a b + 9a b - 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 9b + 14a b - 7a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (- 18b + 7a b + 22a b - 11a b )cos(x) + 9b - 9a b - 9a b +--R + +--R 6 2 +--R 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (7a b - 11a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 5a b + 14a b - 13a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b + 8a b - 16a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (22a b - 21a b - 6a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 18a b + 3a b + 30a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 24a b + 15a b + 24a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 9a b - 9a b + 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 5a b + 7a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 21b + 25a b - 5a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 8 2 6 6 2 4 +--R (19a b - 29a b + 10a b )cos(x) + (20b - 21a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (18b - 23a b + 4a b + a b )cos(x) - 9b + 15a b - 3a b +--R + +--R 6 2 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 12a b + 21a b - 12a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- a b + 5a b - 7a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (2a b - 22a b + 29a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 18a b + 9a b + 18a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (18a b - 17a b - 8a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (22a b - 25a b - 4a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b + 15a b - 3a b - 3a b)cos(x) - 9a b + 15a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (11a b - 16a b + 5a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (17b - 14a b - 5a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 20a b + 31a b - 11a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 14b + 3a b + 18a b - 7a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (- 6b + 12a b - 9a b + 3a b )cos(x) + 3b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (8a b - 16a b + 11a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b - 7a b + 8a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 2a b + 11a b - 13a b + 4a b)cos(x) +--R + +--R 7 5 3 7 4 +--R (5a b - 9a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 6a b + 8a b - a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 7a b + 10a b - 2a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 6a b + 9a b - 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 3b - 3a b + 9a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (7a b - 11a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (3b + 4a b - 11a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((- 14a b + 22a b - 8a b)cos(x) + 6a b - 12a b + 6a b)sin(x) +--R + +--R 4 4 6 2 8 3 +--R (- 14a b + 22a b - 8a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 2a b - 10a b + 20a b - 8a )cos(x) +--R + +--R 4 4 6 2 8 4 4 6 2 8 +--R (6a b - 12a b + 6a )cos(x) + 6a b - 12a b + 6a +--R * +--R 9 +--R sin(x) +--R + +--R 7 3 5 4 3 5 5 3 7 3 +--R (6a b - 6a b )cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 7 3 5 +--R (12a b + 24a b - 60a b + 24a b)cos(x) - 6a b - 6a b +--R + +--R 5 3 7 +--R 30a b - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (6b - 18a b + 18a b - 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (12a b + 26a b - 64a b + 26a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (20a b + 10a b - 56a b + 26a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (- 6a b - 6a b + 30a b - 18a )cos(x) - 6a b - 6a b + 30a b +--R + +--R 8 +--R - 18a +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 6 +--R (6a b + 8a b - 22a b + 8a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 30a b + 40a b - 14a b + 4a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 7 3 5 +--R (- 36a b + 14a b + 44a b - 22a b)cos(x) + 18a b - 18a b +--R + +--R 5 3 7 +--R - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 4 6 2 8 7 +--R (14a b - 22a b + 8a )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 10a b + 28a b - 26a b + 8a )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 12a b + 34a b - 32a b + 10a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 18b + 44a b - 24a b - 12a b + 10a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 36a b + 6a b + 60a b - 30a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 48a b + 30a b + 48a b - 30a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 +--R (18a b - 18a b - 18a b + 18a )cos(x) + 18a b - 18a b +--R + +--R 6 2 8 +--R - 18a b + 18a +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (- 10a b + 14a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 42a b + 50a b - 10a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 18a b + 56a b - 58a b + 20a b)cos(x) +--R + +--R 7 3 5 7 4 +--R (40a b - 42a b + 2a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 7 3 5 5 3 +--R (36a b - 46a b + 8a b + 2a b)cos(x) - 18a b + 30a b - 6a b +--R + +--R 7 +--R - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 7 +--R (- 24a b + 42a b - 24a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 2a b + 10a b - 14a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (22a b - 62a b + 58a b - 18a )cos(x) +--R + +--R 8 2 6 6 2 8 4 +--R (18b - 36a b + 36a b - 18a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (36a b - 34a b - 16a b + 14a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (44a b - 50a b - 8a b + 14a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (- 18a b + 30a b - 6a b - 6a )cos(x) - 18a b + 30a b - 6a b +--R + +--R 8 +--R - 6a +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (22a b - 32a b + 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (34a b - 28a b - 10a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (18a b - 58a b + 62a b - 22a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 16a b - 6a b + 36a b - 14a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 7 3 5 5 3 +--R (- 12a b + 24a b - 18a b + 6a b)cos(x) + 6a b - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 7 +--R (16a b - 32a b + 22a b - 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (4a b - 14a b + 16a b - 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 10a b + 28a b - 26a b + 8a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 +--R (- 6b + 10a b + 6a b - 18a b + 8a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 12a b + 16a b - 2a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 14a b + 20a b - 4a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (- 12a b + 18a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 6a b - 6a b + 18a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 6a b + 20a b - 22a b + 8a b)cos(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (14a b - 22a b + 8a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (- 2a b + 4a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((- 7a b + 11a b - 4a b )cos(x) + 3a b - 6a b + 3a b )sin(x) +--R + +--R 3 5 5 3 7 3 +--R (- 7a b + 11a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- a b - 5a b + 10a b - 4a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (3a b - 6a b + 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (6b + 12a b - 30a b + 12a b )cos(x) - 3b - 3a b + 15a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 5 3 4 +--R (- 3a b + 3a b )cos(x) + (- 9a b + 12a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (6a b + 13a b - 32a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (10a b + 5a b - 28a b + 13a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 3a b - 3a b + 15a b - 9a b)cos(x) - 3a b - 3a b + 15a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (3b + 4a b - 11a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 6a b + 9a b - 3a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 9b + 14a b - 7a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (- 18b + 7a b + 22a b - 11a b )cos(x) + 9b - 9a b - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (7a b - 11a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 5a b + 14a b - 13a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b + 8a b - 16a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (22a b - 21a b - 6a b + 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 18a b + 3a b + 30a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 24a b + 15a b + 24a b - 15a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 9a b - 9a b + 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 5a b + 7a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 21b + 25a b - 5a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 8 2 6 6 2 4 +--R (19a b - 29a b + 10a b )cos(x) + (20b - 21a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (18b - 23a b + 4a b + a b )cos(x) - 9b + 15a b - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 12a b + 21a b - 12a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- a b + 5a b - 7a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (2a b - 22a b + 29a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 18a b + 9a b + 18a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (18a b - 17a b - 8a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (22a b - 25a b - 4a b + 7a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 9a b + 15a b - 3a b - 3a b)cos(x) - 9a b + 15a b - 3a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (11a b - 16a b + 5a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (17b - 14a b - 5a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 20a b + 31a b - 11a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 14b + 3a b + 18a b - 7a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (- 6b + 12a b - 9a b + 3a b )cos(x) + 3b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (8a b - 16a b + 11a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (2a b - 7a b + 8a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 2a b + 11a b - 13a b + 4a b)cos(x) +--R + +--R 7 5 3 7 4 7 3 5 5 3 7 3 +--R (5a b - 9a b + 4a b)cos(x) + (- 6a b + 8a b - a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 7a b + 10a b - 2a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (3a b - 6a b + 3a b )cos(x) + 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 8 2 6 4 4 6 2 6 +--R (- 6a b + 9a b - 3a b )cos(x) + (- 3b - 3a b + 9a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 8 2 6 4 4 6 2 4 +--R (7a b - 11a b + 4a b )cos(x) + (3b + 4a b - 11a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R / +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 4 +--R (9b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (3b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (6a b - 6a b - 6a b + 6a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (18a b - 54a b + 54a b - 18a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 18a b + 18a b + 18a b - 18a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 4 +--R (18a b - 54a b + 54a b - 18a b)cos(x) sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 18a b + 54a b - 54a b + 18a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (18a b - 18a b - 18a b + 18a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (6a b - 18a b + 18a b - 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 6a b + 6a b + 6a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 4 +--R (9b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 2 6 4 4 6 2 4 +--R (3b - 9a b + 9a b - 3a b )cos(x) + (- 3a b + 6a b - 3a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 3b + 6a b - 6a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (9b - 18a b + 18a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (9a b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 9b + 18a b - 18a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (3b - 6a b + 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 6a b + 12a b - 12a b + 6a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (12a b - 36a b + 36a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (18a b - 54a b + 54a b - 18a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (18a b - 36a b + 36a b - 18a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (18a b - 54a b + 54a b - 18a b)cos(x) sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (- 18a b + 54a b - 54a b + 18a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 18a b + 36a b - 36a b + 18a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 12a b + 36a b - 36a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (6a b - 18a b + 18a b - 6a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (6a b - 12a b + 12a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 3b + 6a b - 6a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (9b - 18a b + 18a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (9a b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 9b + 18a b - 18a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (3b - 6a b + 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 586 +m0541b:= a0541.2-r0541 +--R +--R +--R (232) +--R +-------+ +--R 5 3 4 5 3 2 5 3 | 2 2 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) )\|b - a +--R * +--R x +--R b tan(-) + a +--R 2 +--R atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 5 3 4 5 3 2 5 3 | 2 2 +--R (- 6b cos(x) sin(x) + 12b cos(x) sin(x) - 6b cos(x) )\|- b + a +--R * +--R +-------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|b - a +--R atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 4 2 2 2 4 5 +--R ((7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R ((- 5a b + 2a b)cos(x) + (- 6a b + 3a b)cos(x) + a b - a b) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 3 +--R ((7a b - 4a )cos(x) + (- 14a b + 8a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 3 4 3 3 3 +--R (- 6a b + 3a b)cos(x) + (10a b - 4a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (12a b - 6a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 4 2 2 4 2 2 2 4 +--R ((- 6a b + 3a )cos(x) + (7a b - 4a )cos(x) - a b + a )sin(x) +--R + +--R 3 3 4 3 3 3 +--R (5a b - 2a b)cos(x) + (- 5a b + 2a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 6a b + 3a b)cos(x) + a b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 3 2 5 3 4 +--R (3a b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 3 2 5 3 2 4 3 2 5 3 +--R (- 6a b + 12a b - 6a )cos(x) sin(x) + (3a b - 6a b + 3a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 586 +d0541b:= D(m0541b,x) +--R +--R +--R (233) +--R 2 4 4 2 2 2 4 4 2 10 +--R ((7a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 3 3 5 3 5 3 3 5 2 +--R (14a b - 8a b)cos(x) + (- 6a b + 17a b - 8a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 +--R (- 6a b + 6a b)cos(x) + 3a b - 9a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 3b + 7a b - 4a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 30a b + 18a b )cos(x) + 12a b - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 5 5 5 4 5 3 3 5 3 +--R 6a b cos(x) + 6a b cos(x) + (- 12a b - 38a b + 26a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (15a b - 53a b + 26a b)cos(x) + (6a b + 12a b - 18a b)cos(x) +--R + +--R 5 3 3 5 +--R - 6a b + 24a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 3b - 7a b + 4a b )cos(x) + (12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (12b - 18a b + 12a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (47a b - 29a b )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 5 7 5 3 3 5 6 +--R (- 14a b + 8a b)cos(x) + (18a b - 23a b + 8a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 6a b - 22a b + 10a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 5a b - 23a b + 10a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (36a b + 30a b - 30a b)cos(x) +--R + +--R 5 3 3 5 2 5 5 +--R (- 9a b + 57a b - 30a b)cos(x) + (- 18a b + 18a b)cos(x) +--R + +--R 3 3 5 +--R - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (- 7a b + 4a b )cos(x) + (10a b - 4a b )cos(x) +--R + +--R 6 2 4 6 2 4 4 2 5 +--R (9b + 6a b )cos(x) + (- 38a b + 20a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 18b + 9a b - 9a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 31a b + 19a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 8 5 3 3 5 7 +--R (12a b - 6a b )cos(x) + (24a b - 18a b + 6a b)cos(x) +--R + +--R 5 3 3 5 6 +--R (- 7a b - 5a b + 6a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 4a b + 40a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 42a b - 18a b)cos(x) +--R + +--R 5 3 3 5 3 +--R (- 36a b - 2a b + 14a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- 3a b - 23a b + 14a b)cos(x) +--R + +--R 5 3 3 5 5 5 +--R (18a b - 12a b - 6a b)cos(x) + 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (- 3a b + 3a b )cos(x) + (- 22a b + 10a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 9b + 2a b - 5a b )cos(x) + (40a b - 22a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (12b + 8a b - 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (6a b - 3a b )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 8 5 3 3 5 7 +--R (- 8a b + 2a b )cos(x) + (- 16a b + 16a b - 6a b)cos(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 3a b + 12a b - 6a b)cos(x) + (4a b - 18a b + 8a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (5a b - 19a b + 8a b)cos(x) + (12a b - 4a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (3a b + 2a b - 2a b)cos(x) + (- 6a b + 6a b )cos(x) - 3a b +--R + +--R 3 3 +--R 3a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (6a b - 3a b )cos(x) + (12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (3b - a b + a b )cos(x) + (- 14a b + 8a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 3b - 6a b + 3a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 2 3 3 5 10 +--R ((14a b - 8a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 4 2 6 3 2 4 4 2 6 2 +--R (28a b - 16a )cos(x) + (- 12a b + 34a b - 16a )cos(x) +--R + +--R 4 2 6 2 4 4 2 6 +--R (- 12a b + 12a )cos(x) + 6a b - 18a b + 12a +--R * +--R 9 +--R sin(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (- 12a b + 14a b - 8a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 60a b + 36a b)cos(x) + 24a b - 24a b +--R * +--R 8 +--R sin(x) +--R + +--R 2 4 4 2 6 3 +--R (- 24a b - 76a b + 52a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (30a b - 106a b + 52a )cos(x) + (12a b + 24a b - 36a )cos(x) +--R + +--R 2 4 4 2 6 +--R - 12a b + 48a b - 36a +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 12a b - 14a b + 8a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (36a b - 36a b + 24a b)cos(x) + (- 16a b + 16a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 +--R (94a b - 58a b)cos(x) - 36a b + 36a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 2 6 7 2 4 4 2 6 6 +--R (- 28a b + 16a )cos(x) + (36a b - 46a b + 16a )cos(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R (24a b - 44a b + 20a )cos(x) + (26a b - 46a b + 20a )cos(x) +--R + +--R 2 4 4 2 6 3 +--R (72a b + 60a b - 60a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 6 +--R (- 18a b + 114a b - 60a )cos(x) + (- 36a b + 36a )cos(x) +--R + +--R 4 2 6 +--R - 36a b + 36a +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 5 8 3 3 5 7 +--R (- 14a b + 8a b)cos(x) + (20a b - 8a b)cos(x) +--R + +--R 5 3 3 6 5 3 3 5 5 +--R (36a b + 12a b )cos(x) + (36a b - 76a b + 40a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (- 36a b + 18a b - 18a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 62a b + 38a b)cos(x) + 24a b - 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 6 7 +--R (24a b - 12a b )cos(x) + (48a b - 36a b + 12a )cos(x) +--R + +--R 2 4 4 2 6 6 +--R (- 14a b - 10a b + 12a )cos(x) +--R + +--R 2 4 4 2 6 5 +--R (- 44a b + 80a b - 36a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 48a b + 84a b - 36a )cos(x) +--R + +--R 2 4 4 2 6 3 +--R (- 72a b - 4a b + 28a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (- 6a b - 46a b + 28a )cos(x) + (36a b - 24a b - 12a )cos(x) +--R + +--R 2 4 6 +--R 12a b - 12a +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 8 3 3 5 7 +--R (- 6a b + 6a b)cos(x) + (- 44a b + 20a b)cos(x) +--R + +--R 5 3 3 5 6 +--R (- 36a b + 4a b - 10a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 36a b + 80a b - 44a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (12a b + 16a b - 4a b)cos(x) + (- 16a b + 16a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 +--R (12a b - 6a b)cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 6 7 +--R (- 16a b + 4a b )cos(x) + (- 32a b + 32a b - 12a )cos(x) +--R + +--R 2 4 4 2 6 6 +--R (- 6a b + 24a b - 12a )cos(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R (20a b - 36a b + 16a )cos(x) + (22a b - 38a b + 16a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (24a b - 8a b - 4a )cos(x) + (6a b + 4a b - 4a )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 12a b + 12a b )cos(x) - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 3 3 5 8 3 3 5 7 +--R (12a b - 6a b)cos(x) + (24a b - 12a b)cos(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (12a b - 2a b + 2a b)cos(x) + (12a b - 28a b + 16a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (- 12a b + 6a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 3 5 2 +--R (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 2 4 4 2 10 +--R ((7a b - 4a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 3 3 5 3 5 3 3 5 2 +--R (14a b - 8a b)cos(x) + (- 6a b + 17a b - 8a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 +--R (- 6a b + 6a b)cos(x) + 3a b - 9a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 3b + 7a b - 4a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 30a b + 18a b )cos(x) + 12a b - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 5 5 5 4 5 3 3 5 3 +--R 6a b cos(x) + 6a b cos(x) + (- 12a b - 38a b + 26a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (15a b - 53a b + 26a b)cos(x) + (6a b + 12a b - 18a b)cos(x) +--R + +--R 5 3 3 5 +--R - 6a b + 24a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 3b - 7a b + 4a b )cos(x) + (12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (12b - 18a b + 12a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (47a b - 29a b )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 5 7 5 3 3 5 6 +--R (- 14a b + 8a b)cos(x) + (18a b - 23a b + 8a b)cos(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (- 6a b - 22a b + 10a b)cos(x) + (- 5a b - 23a b + 10a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (36a b + 30a b - 30a b)cos(x) + (- 9a b + 57a b - 30a b)cos(x) +--R + +--R 5 5 3 3 5 +--R (- 18a b + 18a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (- 7a b + 4a b )cos(x) + (10a b - 4a b )cos(x) +--R + +--R 6 2 4 6 2 4 4 2 5 +--R (9b + 6a b )cos(x) + (- 38a b + 20a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 18b + 9a b - 9a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 31a b + 19a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 8 5 3 3 5 7 +--R (12a b - 6a b )cos(x) + (24a b - 18a b + 6a b)cos(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 7a b - 5a b + 6a b)cos(x) + (- 4a b + 40a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 6a b + 42a b - 18a b)cos(x) + (- 36a b - 2a b + 14a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 3a b - 23a b + 14a b)cos(x) + (18a b - 12a b - 6a b)cos(x) +--R + +--R 5 5 +--R 6a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (- 3a b + 3a b )cos(x) + (- 22a b + 10a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 9b + 2a b - 5a b )cos(x) + (40a b - 22a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (12b + 8a b - 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (6a b - 3a b )cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 8 5 3 3 5 7 +--R (- 8a b + 2a b )cos(x) + (- 16a b + 16a b - 6a b)cos(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 3a b + 12a b - 6a b)cos(x) + (4a b - 18a b + 8a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (5a b - 19a b + 8a b)cos(x) + (12a b - 4a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 3 3 +--R (3a b + 2a b - 2a b)cos(x) + (- 6a b + 6a b )cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 8 2 4 4 2 7 +--R (6a b - 3a b )cos(x) + (12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (3b - a b + a b )cos(x) + (- 14a b + 8a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (- 3b - 6a b + 3a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 2 +--R (a b - a b )cos(x) +--R / +--R 6 3 4 5 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (3a b - 6a b + 3a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 6 +--R (- 9a b + 18a b - 9a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 18a b + 36a b - 18a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (18a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 6 +--R (9a b - 18a b + 9a b )cos(x) +--R + +--R 6 3 4 5 2 5 6 3 4 5 2 4 +--R (18a b - 36a b + 18a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (- 3a b + 6a b - 3a b )cos(x) + (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R ((12a b - 24a b + 12a )cos(x) + (12a b - 24a b + 12a )cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (6a b - 12a b + 6a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 4 5 2 7 5 +--R (- 36a b + 72a b - 36a )cos(x) +--R + +--R 3 4 5 2 7 4 +--R (- 36a b + 72a b - 36a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 6 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (- 36a b + 72a b - 36a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R ((36a b - 72a b + 36a )cos(x) + (36a b - 72a b + 36a )cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 6 6 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (36a b - 72a b + 36a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 7 5 +--R (- 12a b + 24a b - 12a )cos(x) +--R + +--R 3 4 5 2 7 4 +--R (- 12a b + 24a b - 12a )cos(x) +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (- 6a b + 12a b - 6a b)cos(x) + (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 4 5 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 7 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) )sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (3a b - 6a b + 3a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 6 +--R (- 9a b + 18a b - 9a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 18a b + 36a b - 18a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R ((18a b - 36a b + 18a b)cos(x) + (18a b - 36a b + 18a b)cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (9a b - 18a b + 9a b )cos(x) + (18a b - 36a b + 18a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R ((- 6a b + 12a b - 6a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) ) +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (- 3a b + 6a b - 3a b )cos(x) + (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R Type: Expression(Integer) +--E 248 + +--S 249 of 586 +t0542:= cot(x)/(a+b*csc(x)) +--R +--R +--R cot(x) +--R (234) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 249 + +--S 250 of 586 +r0542:= log(b+a*sin(x))/a +--R +--R +--R log(a sin(x) + b) +--R (235) ----------------- +--R a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 586 +a0542:= integrate(t0542,x) +--R +--R +--R 2a sin(x) + 2b 2 +--R log(--------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (236) ------------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 251 + +--S 252 of 586 +m0542:= a0542-r0542 +--R +--R +--R 2a sin(x) + 2b 2 +--R - log(a sin(x) + b) + log(--------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (237) ----------------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 252 + +--S 253 of 586 +d0542:= D(m0542,x) +--R +--R +--R (238) 0 +--R Type: Expression(Integer) +--E 253 + +--S 254 of 586 +t0543:= cot(x)^2/(a+b*csc(x)) +--R +--R +--R 2 +--R cot(x) +--R (239) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 254 + +--S 255 of 586 +r0543:= -x/a-atanh(cos(x))/b+2*(a^2-b^2)^(1/2)*_ + atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a/b +--R +--R +--R x +--R +---------+ b tan(-) + a +--R | 2 2 2 +--R - a atanh(cos(x)) + 2\|- b + a atanh(------------) - b x +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (240) ---------------------------------------------------------- +--R a b +--R Type: Expression(Integer) +--E 255 + +--S 256 of 586 +a0543:= integrate(t0543,x) +--R +--R +--R (241) +--R [ +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R sin(x) +--R a log(----------) - b x +--R cos(x) + 1 +--R / +--R a b +--R , +--R +-------+ +--R +-------+ | 2 2 +--R sin(x) | 2 2 (cos(x) + 1)\|b - a +--R a log(----------) - 2\|b - a atan(-----------------------) - b x +--R cos(x) + 1 b sin(x) + a cos(x) + a +--R ------------------------------------------------------------------] +--R a b +--R Type: Union(List(Expression(Integer)),...) +--E 256 + +--S 257 of 586 +m0543a:= a0543.1-r0543 +--R +--R +--R (242) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R x +--R +---------+ b tan(-) + a +--R sin(x) | 2 2 2 +--R a log(----------) + a atanh(cos(x)) - 2\|- b + a atanh(------------) +--R cos(x) + 1 +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R a b +--R Type: Expression(Integer) +--E 257 + +--S 258 of 586 +d0543a:= D(m0543a,x) +--R +--R +--R (243) +--R 2 4 2 2 3 2 3 +--R a b cos(x)sin(x) + (a b cos(x) + (b + a b)cos(x))sin(x) +--R + +--R 3 3 3 2 2 3 2 3 2 +--R (a cos(x) + a cos(x) + (a b - a )cos(x) + a b - a )sin(x) +--R + +--R 3 4 3 2 3 3 2 2 +--R b cos(x) + (b + a b)cos(x) + (- 2b + a b)cos(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) + b - a b +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R a b cos(x) + a b cos(x) - a b cos(x) - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 +--R 2a b cos(x)sin(x) +--R + +--R 2 2 2 3 2 3 3 +--R (2a b cos(x) + (2a b + 2a )cos(x) - 2a b + 2a )sin(x) +--R + +--R 2 3 3 2 3 2 2 +--R (2a b cos(x) + 2b cos(x) - 2b + 2a b)sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R (2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 4a b cos(x))sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R 2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 3 2 3 +--R a b cos(x)sin(x) + (a b cos(x) + (b + a b)cos(x))sin(x) +--R + +--R 3 3 3 2 2 3 2 3 2 +--R (a cos(x) + a cos(x) + (a b - a )cos(x) + a b - a )sin(x) +--R + +--R 3 4 3 2 3 3 2 2 +--R b cos(x) + (b + a b)cos(x) + (- 2b + a b)cos(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) + b - a b +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R a b cos(x) + a b cos(x) - a b cos(x) - a b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 4 +--R a b cos(x)sin(x) +--R + +--R 3 3 2 3 3 3 +--R ((- a b + a b)cos(x) + (a b + a b)cos(x))sin(x) +--R + +--R 4 2 2 4 3 4 4 2 +--R (b - a b + a )cos(x) + (- b + a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- b + 2a b - a )cos(x) + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 3 3 2 +--R (a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 3 3 3 3 +--R (- a b - a b)cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 4 2 2 4 2 2 3 4 2 2 2 2 2 +--R (- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 2 2 4 2 2 4 3 +--R 2a b cos(x)sin(x) + ((2a b + 2a )cos(x) - 2a b + 2a )sin(x) +--R + +--R 3 3 3 3 2 +--R (2a b cos(x) - 2a b + 2a b)sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((- 2b + 6a b )cos(x) + (2b - 6a b )cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 2 +--R (- 2a b + 2a b)cos(x) + 2a b cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 +--R - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 3 3 2 3 3 3 +--R a b cos(x)sin(x) + ((- a b + a b)cos(x) + (a b + a b)cos(x))sin(x) +--R + +--R 4 2 2 4 3 4 4 2 +--R (b - a b + a )cos(x) + (- b + a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- b + 2a b - a )cos(x) + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R (a b + a b)cos(x) + (- a b + a b)cos(x) + (- a b - a b)cos(x) +--R + +--R 3 3 +--R a b - a b +--R * +--R sin(x) +--R + +--R 4 2 2 4 2 2 3 4 2 2 2 2 2 +--R (- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b cos(x) +--R / +--R 3 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 2 2 3 4 2 2 2 2 2 4 2 2 +--R (a b cos(x) + (b + a b )cos(x) - a b cos(x) - b - a b ) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 2 3 3 +--R (a b cos(x) + a b cos(x) - a b cos(x) - a b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 3 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 3 3 3 3 2 3 3 +--R 2a b cos(x) + (2a b + 2a b)cos(x) - 2a b cos(x) - 2a b +--R + +--R 3 +--R - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 2 2 3 4 2 2 2 2 2 4 2 2 2 +--R (a b cos(x) + (b + a b )cos(x) - a b cos(x) - b - a b )sin(x) +--R + +--R 3 3 3 2 3 3 +--R (a b cos(x) + a b cos(x) - a b cos(x) - a b )sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (a b - a b )cos(x) - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 3 2 3 2 5 2 3 2 3 +--R ((- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 3 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 2a b + 2a b)cos(x) + (2a b + 2a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (2a b - 2a b)cos(x) - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 3 3 2 2 4 3 2 +--R (- 2a b + 2a b )cos(x) + 2a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 2 +--R - 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 4 3 2 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 3 2 +--R - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 3 2 3 2 5 2 3 2 3 +--R ((- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b )sin(x) +--R Type: Expression(Integer) +--E 258 + +--S 259 of 586 +m0543b:= a0543.2-r0543 +--R +--R +--R (244) +--R x +--R +---------+ b tan(-) + a +--R sin(x) | 2 2 2 +--R a log(----------) + a atanh(cos(x)) - 2\|- b + a atanh(------------) +--R cos(x) + 1 +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R | 2 2 (cos(x) + 1)\|b - a +--R - 2\|b - a atan(-----------------------) +--R b sin(x) + a cos(x) + a +--R / +--R a b +--R Type: Expression(Integer) +--E 259 + +--S 260 of 586 +d0543b:= D(m0543b,x) +--R +--R +--R (245) +--R 2 4 +--R a b cos(x)sin(x) +--R + +--R 3 2 2 2 3 2 3 +--R ((b + a b)cos(x) + 2a b cos(x) - b + a b)sin(x) +--R + +--R 3 3 3 2 2 3 2 3 2 +--R (2a cos(x) + 2a cos(x) + (2a b - 2a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 2 4 2 3 3 2 2 3 +--R (b + a b)cos(x) + 2a b cos(x) - 2b cos(x) - 2a b cos(x) + b +--R + +--R 2 +--R - a b +--R * +--R sin(x) +--R + +--R 2 5 2 4 2 2 2 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 3 2 3 3 +--R 2a b cos(x)sin(x) + (4a b cos(x) + 4a cos(x) - 4a b + 4a )sin(x) +--R + +--R 2 3 2 2 2 +--R (4a b cos(x) + 4a b cos(x) )sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b cos(x))sin(x) +--R + +--R 2 5 2 4 2 2 2 +--R 2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 3 2 2 2 3 2 3 +--R a b cos(x)sin(x) + ((b + a b)cos(x) + 2a b cos(x) - b + a b)sin(x) +--R + +--R 3 3 3 2 2 3 2 3 2 +--R (2a cos(x) + 2a cos(x) + (2a b - 2a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 3 2 4 2 3 3 2 2 3 +--R (b + a b)cos(x) + 2a b cos(x) - 2b cos(x) - 2a b cos(x) + b +--R + +--R 2 +--R - a b +--R * +--R sin(x) +--R + +--R 2 5 2 4 2 2 2 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b cos(x) +--R / +--R 3 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 3 4 3 3 3 3 +--R (a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 3 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 3 3 3 2 3 3 2 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b)sin(x) +--R + +--R 2 2 4 2 2 3 2 2 2 2 +--R (2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b )sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 3 +--R (a b cos(x) - a b )sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 2 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 3 4 3 3 3 3 +--R (a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b )sin(x) +--R Type: Expression(Integer) +--E 260 + +--S 261 of 586 +t0544:= cot(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R cot(x) +--R (246) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 261 + +--S 262 of 586 +r0544:= x/a-a^2*atanh(cos(x))/b^3+3/2*atanh(cos(x))/b+2*(a^2-b^2)^(3/2)*_ + atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/a/b^3+a*cot(x)/b^2-_ + 1/2*cot(x)*csc(x)/b +--R +--R +--R (247) +--R x +--R +---------+ b tan(-) + a +--R 2 3 2 2 | 2 2 2 +--R (3a b - 2a )atanh(cos(x)) + (- 4b + 4a )\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 +--R - a b cot(x)csc(x) + 2a b cot(x) + 2b x +--R / +--R 3 +--R 2a b +--R Type: Expression(Integer) +--E 262 + +--S 263 of 586 +a0544:= integrate(t0544,x) +--R +--R +--R (248) +--R [ +--R 2 3 2 2 3 sin(x) +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((2b - 2a )cos(x) - 2b + 2a )\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (- b sin(x) - a cos(x) - a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R 2 3 2 2 3 +--R - 2a b cos(x)sin(x) + 2b x cos(x) + a b cos(x) - 2b x +--R / +--R 3 2 3 +--R 2a b cos(x) - 2a b +--R , +--R +--R 2 3 2 2 3 sin(x) +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 2 2 2 | 2 2 (cos(x) + 1)\|b - a +--R ((4b - 4a )cos(x) - 4b + 4a )\|b - a atan(-----------------------) +--R b sin(x) + a cos(x) + a +--R + +--R 2 3 2 2 3 +--R - 2a b cos(x)sin(x) + 2b x cos(x) + a b cos(x) - 2b x +--R / +--R 3 2 3 +--R 2a b cos(x) - 2a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 263 + +--S 264 of 586 +m0544a:= a0544.1-r0544 +--R +--R +--R (249) +--R 2 3 2 2 3 sin(x) +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((2b - 2a )cos(x) - 2b + 2a )\|- b + a +--R * +--R log +--R +---------+ +--R | 2 2 +--R (- b sin(x) - a cos(x) - a)\|- b + a + a b sin(x) +--R + +--R 2 2 2 +--R (- b + a )cos(x) + a +--R / +--R a sin(x) + b +--R + +--R 2 3 2 2 3 +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )atanh(cos(x)) +--R + +--R x +--R +---------+ b tan(-) + a +--R 2 2 2 2 2 | 2 2 2 +--R ((4b - 4a )cos(x) - 4b + 4a )\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R - 2a b cos(x)sin(x) + (a b cos(x) - a b )cot(x)csc(x) +--R + +--R 2 2 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + a b cos(x) +--R / +--R 3 2 3 +--R 2a b cos(x) - 2a b +--R Type: Expression(Integer) +--E 264 + +--S 265 of 586 +d0544a:= D(m0544a,x) +--R +--R +--R (250) +--R 2 3 2 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 3 4 3 2 2 +--R - 3a b cos(x) + (- a b - 2a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (3a b - 4a b )cos(x) - a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 4 4 4 2 4 +--R - a b cos(x) + 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (- 3a b + 2a b)cos(x) + (- 3b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 5 4 5 2 3 +--R (b - 2a b)cos(x) + (3b - 2a b)cos(x) + b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 5 5 2 3 4 +--R - 2a b cos(x) + (- 2b - 2a b )cos(x) +--R + +--R 2 3 3 5 2 3 2 2 3 +--R 4a b cos(x) + (4b + 4a b )cos(x) - 2a b cos(x) +--R + +--R 5 2 3 +--R - 2b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 5 2 3 4 2 3 3 +--R - a b cos(x) + (- b - a b )cos(x) + 2a b cos(x) +--R + +--R 5 2 3 2 2 3 5 2 3 +--R (2b + 2a b )cos(x) - a b cos(x) - b - a b +--R * +--R csc(x) +--R + +--R 3 2 5 4 3 2 4 3 2 3 +--R 2a b cos(x) + (2a b + 2a b )cos(x) - 4a b cos(x) +--R + +--R 4 3 2 2 3 2 4 3 2 +--R (- 4a b - 4a b )cos(x) + 2a b cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 5 4 3 2 5 4 +--R (- a b - 2a b + 2a )cos(x) + (- a b - 2a b + 2a )cos(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (4a b - 4a )cos(x) + (- 2a b + 4a b - 4a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (3a b - 2a b + 2a )cos(x) + 5a b - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 4 4 4 3 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) +--R + +--R 4 2 4 4 +--R 4a b cos(x) - 2a b cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R - a b cos(x) - a b cos(x) + 2a b cos(x) + 2a b cos(x) +--R + +--R 4 4 +--R - a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R 2a b cos(x) + 2a b cos(x) - 4a b cos(x) - 4a b cos(x) +--R + +--R 2 3 2 3 +--R 2a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 6 5 2 3 4 5 +--R (- 2b + a b )cos(x) + (- 3b - a b + 2a b)cos(x) +--R + +--R 5 2 3 4 4 5 4 3 +--R (6b - 6a b + 2a b)cos(x) + (6b - 4a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 6b + 7a b - 4a b)cos(x) + (- 3b + a b + 2a b)cos(x) +--R + +--R 5 2 3 4 +--R 2b - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 3a b + 2a b )cos(x) + (- 3a b + 2a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (6a b - 4a b )cos(x) + (6a b - 4a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 3a b + 2a b )cos(x) + (- 3a b + 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 2 3 3 2 3 4 2 +--R - 6a b cos(x) + (- 2a b - 4a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (6a b - 8a b)cos(x) - 2a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) +--R + +--R 2 3 4 2 3 2 2 3 +--R - 2a b cos(x) + 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 4 3 2 2 3 2 2 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) +--R + +--R 4 3 2 4 4 3 2 5 3 +--R (- 4a b + 2a b )cos(x) + (- 6a b - 4a b + 4a )cos(x) +--R + +--R 4 3 2 5 2 4 5 4 +--R (10a b - 16a b + 4a )cos(x) + (6a b - 4a )cos(x) - 2a b +--R + +--R 3 2 5 +--R 10a b - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 4 3 2 4 +--R - 4a b cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 3 2 3 4 3 2 2 3 2 +--R 8a b cos(x) + (8a b + 8a b )cos(x) - 4a b cos(x) +--R + +--R 4 3 2 +--R - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 4 3 2 4 3 2 3 +--R - 2a b cos(x) + (- 2a b - 2a b )cos(x) + 4a b cos(x) +--R + +--R 4 3 2 2 3 2 4 3 2 +--R (4a b + 4a b )cos(x) - 2a b cos(x) - 2a b - 2a b +--R * +--R csc(x) +--R + +--R 4 5 2 3 4 4 4 3 +--R 4a b cos(x) + (4a b + 4a b)cos(x) - 8a b cos(x) +--R + +--R 2 3 4 2 4 2 3 4 +--R (- 8a b - 8a b)cos(x) + 4a b cos(x) + 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 5 5 2 3 4 +--R (- 6a b + 4a b)cos(x) + (- 4b + 2a b )cos(x) +--R + +--R 2 3 4 3 5 2 3 2 +--R (8a b - 8a b)cos(x) + (8b - 12a b )cos(x) +--R + +--R 2 3 4 5 2 3 +--R (2a b + 4a b)cos(x) - 4b + 14a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 8a b cos(x) - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 4a b cos(x) - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 4a b + 2a b )cos(x) + (- 10a b + 6a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (8a b - 4a b )cos(x) + (20a b - 16a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 3 2 +--R (- 4a b - 2a b )cos(x) + (- 10a b + 10a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 6a b + 4a b)cos(x) + (- 6a b + 4a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (12a b - 8a b)cos(x) + (12a b - 8a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 6a b + 4a b)cos(x) + (- 6a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 3 4 3 2 2 4 3 2 +--R - 3a b cos(x) + (- a b - 2a b )cos(x) + (3a b - 4a b )cos(x) +--R + +--R 4 3 2 +--R - a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) - a b cos(x) +--R + +--R 4 2 4 +--R 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (- 3a b + 2a b)cos(x) + (- 3b - 2a b + 2a b)cos(x) +--R + +--R 5 4 2 5 4 5 2 3 +--R (b - 2a b)cos(x) + (3b - 2a b)cos(x) + b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 5 5 2 3 4 2 3 3 +--R - 2a b cos(x) + (- 2b - 2a b )cos(x) + 4a b cos(x) +--R + +--R 5 2 3 2 2 3 5 2 3 +--R (4b + 4a b )cos(x) - 2a b cos(x) - 2b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 5 2 3 4 2 3 3 +--R - a b cos(x) + (- b - a b )cos(x) + 2a b cos(x) +--R + +--R 5 2 3 2 2 3 5 2 3 +--R (2b + 2a b )cos(x) - a b cos(x) - b - a b +--R * +--R csc(x) +--R + +--R 3 2 5 4 3 2 4 3 2 3 +--R 2a b cos(x) + (2a b + 2a b )cos(x) - 4a b cos(x) +--R + +--R 4 3 2 2 3 2 4 3 2 +--R (- 4a b - 4a b )cos(x) + 2a b cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 5 4 3 2 5 4 +--R (- a b - 2a b + 2a )cos(x) + (- a b - 2a b + 2a )cos(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (4a b - 4a )cos(x) + (- 2a b + 4a b - 4a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (3a b - 2a b + 2a )cos(x) + 5a b - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 4 4 4 3 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) +--R + +--R 4 2 4 4 +--R 4a b cos(x) - 2a b cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R - a b cos(x) - a b cos(x) + 2a b cos(x) + 2a b cos(x) +--R + +--R 4 4 +--R - a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R 2a b cos(x) + 2a b cos(x) - 4a b cos(x) - 4a b cos(x) +--R + +--R 2 3 2 3 +--R 2a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 6 5 2 3 4 5 +--R (- 2b + a b )cos(x) + (- 3b - a b + 2a b)cos(x) +--R + +--R 5 2 3 4 4 5 4 3 +--R (6b - 6a b + 2a b)cos(x) + (6b - 4a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 5 +--R (- 6b + 7a b - 4a b)cos(x) + (- 3b + a b + 2a b)cos(x) + 2b +--R + +--R 2 3 4 +--R - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 3a b + 2a b )cos(x) + (- 3a b + 2a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (6a b - 4a b )cos(x) + (6a b - 4a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 3a b + 2a b )cos(x) + (- 3a b + 2a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 2 3 3 5 +--R (2a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 3 2 4 4 2 2 2 4 4 2 +--R a b cos(x) + (a b + 2a b )cos(x) + (- 5a b + 4a b )cos(x) +--R + +--R 2 4 4 2 +--R a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 2 4 2 2 4 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) + a b cos(x) +--R + +--R 2 4 2 2 4 +--R - 2a b cos(x) + a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 3a b + 5a b - 2a b)cos(x) + (2a b + 2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 5 5 +--R (2a b - 2a b + 2a b)cos(x) + (- 4a b + 2a b)cos(x) - a b +--R + +--R 3 3 +--R - a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- a b + a b )cos(x) + a b + a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 4 2 6 5 +--R (2b - 3a b + 4a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 3b + 3a b + 2a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 3 6 4 2 6 2 +--R (- 3b + 6a b - 8a b + 4a )cos(x) + (3b - 4a b + 4a )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 6 +--R (3b - 5a b + 4a b - 2a )cos(x) - 5a b + 2a b - 2a +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 5 2 4 4 +--R (- 2b + 2a b )cos(x) + 2a b cos(x) +--R + +--R 6 2 4 3 2 4 2 +--R (4b - 4a b )cos(x) - 4a b cos(x) +--R + +--R 6 2 4 2 4 +--R (- 2b + 2a b )cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 5 2 4 4 6 2 4 3 +--R (- b + a b )cos(x) + a b cos(x) + (2b - 2a b )cos(x) +--R + +--R 2 4 2 6 2 4 2 4 +--R - 2a b cos(x) + (- b + a b )cos(x) + a b +--R * +--R csc(x) +--R + +--R 5 3 3 5 3 3 4 +--R (2a b - 2a b )cos(x) - 2a b cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (- 4a b + 4a b )cos(x) + 4a b cos(x) +--R + +--R 5 3 3 3 3 +--R (2a b - 2a b )cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 6 5 3 3 5 5 +--R (- a b + a b )cos(x) + (3a b + a b - 2a b)cos(x) +--R + +--R 3 3 5 4 5 5 3 +--R (2a b - 2a b)cos(x) + (- 8a b + 4a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (3a b - 5a b + 4a b)cos(x) + (5a b - a b - 2a b)cos(x) +--R + +--R 5 3 3 5 +--R - 2a b + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 3b + 5a b - 2a b )cos(x) + (3a b - 2a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (6b - 10a b + 4a b )cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 +--R (- 3b + 5a b - 2a b )cos(x) + (3a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 2 5 +--R (4a b cos(x) + 4a b )sin(x) +--R + +--R 3 3 3 3 3 5 2 3 3 5 +--R 2a b cos(x) + (2a b + 4a b)cos(x) + (- 10a b + 8a b)cos(x) +--R + +--R 3 3 5 +--R 2a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 4 3 3 2 3 3 2 3 3 4 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) + 2a b cos(x) +--R + +--R 3 3 2 3 3 +--R - 4a b cos(x) + 2a b +--R * +--R csc(x) +--R + +--R 4 2 4 4 2 2 4 2 2 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) +--R + +--R 2 4 4 2 4 2 4 4 2 6 3 +--R (- 2a b + 2a b )cos(x) + (4a b + 4a b - 4a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 6 2 4 +--R (- 4a b + 12a b - 4a )cos(x) + (- 8a b + 4a )cos(x) + 2a b +--R + +--R 4 2 6 +--R - 10a b + 4a +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (8a b - 8a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R csc(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (4a b - 4a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- 8a b + 8a b)cos(x) + (8a b + 8a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (4a b - 4a b)cos(x) - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 5 5 3 3 4 +--R (6a b - 4a b)cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 5 3 5 3 3 2 +--R (2a b - 12a b + 8a b)cos(x) + (- 2a b + 8a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (2a b + 2a b - 4a b)cos(x) + 4a b - 14a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 3 3 4 +--R (- 4a b + 4a b )cos(x) + 4a b cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (8a b - 8a b )cos(x) - 8a b cos(x) +--R + +--R 5 3 3 3 3 +--R (- 4a b + 4a b )cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 3 3 4 +--R (- 2a b + 2a b )cos(x) + 2a b cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (4a b - 4a b )cos(x) - 4a b cos(x) +--R + +--R 5 3 3 3 3 +--R (- 2a b + 2a b )cos(x) + 2a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 4 2 4 +--R (4a b - 4a b )cos(x) - 4a b cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 8a b + 8a b )cos(x) + 8a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (4a b - 4a b )cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (- 2a b + 2a b )cos(x) + (- 4b + 18a b - 10a b )cos(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (4a b - 4a b )cos(x) + (8b - 40a b + 24a b )cos(x) +--R + +--R 2 4 4 2 2 6 2 4 4 2 4 2 +--R (- 2a b + 6a b )cos(x) + (- 4b + 22a b - 14a b )cos(x) - 4a b +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 3 3 5 5 +--R (- 6a b + 10a b - 4a b)cos(x) + (6a b - 4a b)cos(x) +--R + +--R 5 3 3 5 4 3 3 5 3 +--R (12a b - 20a b + 8a b)cos(x) + (- 12a b + 8a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- 6a b + 10a b - 4a b)cos(x) + (6a b - 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 5 +--R (2a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 3 2 4 4 2 2 2 4 4 2 2 4 +--R a b cos(x) + (a b + 2a b )cos(x) + (- 5a b + 4a b )cos(x) + a b +--R + +--R 4 2 +--R 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 2 4 2 2 4 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) + a b cos(x) +--R + +--R 2 4 2 2 4 +--R - 2a b cos(x) + a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 3a b + 5a b - 2a b)cos(x) + (2a b + 2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 5 5 3 3 +--R (2a b - 2a b + 2a b)cos(x) + (- 4a b + 2a b)cos(x) - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (- a b + a b )cos(x) + a b + a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 4 2 6 5 +--R (2b - 3a b + 4a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 3b + 3a b + 2a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 3 6 4 2 6 2 +--R (- 3b + 6a b - 8a b + 4a )cos(x) + (3b - 4a b + 4a )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 6 +--R (3b - 5a b + 4a b - 2a )cos(x) - 5a b + 2a b - 2a +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 5 2 4 4 6 2 4 3 +--R (- 2b + 2a b )cos(x) + 2a b cos(x) + (4b - 4a b )cos(x) +--R + +--R 2 4 2 6 2 4 2 4 +--R - 4a b cos(x) + (- 2b + 2a b )cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 5 2 4 4 6 2 4 3 +--R (- b + a b )cos(x) + a b cos(x) + (2b - 2a b )cos(x) +--R + +--R 2 4 2 6 2 4 2 4 +--R - 2a b cos(x) + (- b + a b )cos(x) + a b +--R * +--R csc(x) +--R + +--R 5 3 3 5 3 3 4 5 3 3 3 +--R (2a b - 2a b )cos(x) - 2a b cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 3 2 5 3 3 3 3 +--R 4a b cos(x) + (2a b - 2a b )cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 6 5 3 3 5 5 +--R (- a b + a b )cos(x) + (3a b + a b - 2a b)cos(x) +--R + +--R 3 3 5 4 5 5 3 +--R (2a b - 2a b)cos(x) + (- 8a b + 4a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 5 +--R (3a b - 5a b + 4a b)cos(x) + (5a b - a b - 2a b)cos(x) - 2a b +--R + +--R 3 3 5 +--R 2a b - 2a b +--R * +--R sin(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 5 +--R (- 3b + 5a b - 2a b )cos(x) + (3a b - 2a b )cos(x) +--R + +--R 6 2 4 4 2 4 2 4 4 2 3 +--R (6b - 10a b + 4a b )cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 +--R (- 3b + 5a b - 2a b )cos(x) + (3a b - 2a b )cos(x) +--R / +--R 5 4 5 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 5 6 2 4 4 2 4 3 +--R 2a b cos(x) + (2b + 2a b )cos(x) - 4a b cos(x) +--R + +--R 6 2 4 2 2 4 6 2 4 +--R (- 4b - 4a b )cos(x) + 2a b cos(x) + 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 4a b cos(x) - 4a b cos(x) +--R + +--R 5 5 +--R 2a b cos(x) + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 4 2 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )sin(x) +--R + +--R 3 3 5 5 3 3 4 3 3 3 +--R 4a b cos(x) + (4a b + 4a b )cos(x) - 8a b cos(x) +--R + +--R 5 3 3 2 3 3 5 3 3 +--R (- 8a b - 8a b )cos(x) + 4a b cos(x) + 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 5 2 4 4 2 4 3 2 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 4 2 4 +--R 4a b cos(x) + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 5 6 2 4 4 2 4 3 +--R 2a b cos(x) + (2b + 2a b )cos(x) - 4a b cos(x) +--R + +--R 6 2 4 2 2 4 6 2 4 +--R (- 4b - 4a b )cos(x) + 2a b cos(x) + 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 5 4 5 3 5 2 +--R 2a b cos(x) + 2a b cos(x) - 4a b cos(x) - 4a b cos(x) +--R + +--R 5 5 +--R 2a b cos(x) + 2a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 5 4 2 5 2 2 5 3 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )sin(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 7 2 5 3 +--R (2b - 2a b )cos(x) - 2a b cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 2 5 2 7 2 5 2 5 +--R 4a b cos(x) + (2b - 2a b )cos(x) - 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 4 3 4 2 3 4 3 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )sin(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 8a b + 8a b )cos(x) + (8a b + 8a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (4a b - 4a b )cos(x) - 4a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 3 4 4 6 3 4 3 +--R (4a b - 4a b )cos(x) - 4a b cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 3 4 2 6 3 4 3 4 +--R 8a b cos(x) + (4a b - 4a b )cos(x) - 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 2 5 2 2 5 3 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )sin(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 7 2 5 3 +--R (2b - 2a b )cos(x) - 2a b cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 2 5 2 7 2 5 2 5 +--R 4a b cos(x) + (2b - 2a b )cos(x) - 2a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 265 + +--S 266 of 586 +m0544b:= a0544.2-r0544 +--R +--R +--R (251) +--R 2 3 2 2 3 sin(x) +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )log(----------) +--R cos(x) + 1 +--R + +--R 2 3 2 2 3 +--R ((- 3a b + 2a )cos(x) + 3a b - 2a )atanh(cos(x)) +--R + +--R x +--R +---------+ b tan(-) + a +--R 2 2 2 2 2 | 2 2 2 +--R ((4b - 4a )cos(x) - 4b + 4a )\|- b + a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +-------+ | 2 2 +--R 2 2 2 2 2 | 2 2 (cos(x) + 1)\|b - a +--R ((4b - 4a )cos(x) - 4b + 4a )\|b - a atan(-----------------------) +--R b sin(x) + a cos(x) + a +--R + +--R 2 2 2 2 +--R - 2a b cos(x)sin(x) + (a b cos(x) - a b )cot(x)csc(x) +--R + +--R 2 2 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + a b cos(x) +--R / +--R 3 2 3 +--R 2a b cos(x) - 2a b +--R Type: Expression(Integer) +--E 266 + +--S 267 of 586 +d0544b:= D(m0544b,x) +--R +--R +--R (252) +--R 2 3 2 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 3a b - 2a b )cos(x) + (a b - 4a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (3a b - 6a b )cos(x) + a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) - a b cos(x) +--R + +--R 4 2 4 +--R 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- 2b - 4a b + 2a b)cos(x) + (- 8a b + 4a b)cos(x) +--R + +--R 5 2 3 2 2 3 4 5 2 3 4 +--R (4b - 6a b )cos(x) + (4a b - 4a b)cos(x) - 2b + 6a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 8a b cos(x) - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 2 3 2 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 5 4 3 2 5 4 +--R (- 2a b - 4a b + 4a )cos(x) + (- a b - 4a b + 4a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (8a b - 8a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (6a b - 4a b + 4a )cos(x) + 5a b - 4a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) +--R + +--R 4 3 4 2 4 4 +--R 8a b cos(x) + 2a b cos(x) - 4a b cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - a b cos(x) - 2a b cos(x) + a b cos(x) + 4a b cos(x) +--R + +--R 4 2 4 4 +--R a b cos(x) - 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 6 2 3 5 2 3 4 2 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 6 2 3 4 5 +--R (- 2b - 2a b + 2a b)cos(x) + (- 6a b + 4a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (6b - 2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 5 +--R (- 6b + 6a b - 2a b)cos(x) + (- 2a b + 4a b)cos(x) + 2b +--R + +--R 2 3 4 +--R - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 3a b + 2a b )cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (3a b - 2a b )cos(x) + (12a b - 8a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (3a b - 2a b )cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 4 3 2 +--R (- 3a b + 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 6a b - 4a b)cos(x) + (2a b - 8a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (6a b - 12a b)cos(x) + 2a b - 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 2 3 2 2 3 2 2 3 4 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) - 2a b cos(x) +--R + +--R 2 3 2 2 3 +--R 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 4 3 2 2 3 2 2 4 4 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) - 8a b cos(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (- 16a b + 8a )cos(x) + (16a b - 28a b + 8a )cos(x) +--R + +--R 3 2 5 4 3 2 5 +--R (8a b - 8a )cos(x) - 8a b + 20a b - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 2 4 3 2 3 +--R - 8a b cos(x) - 8a b cos(x) + 16a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R 16a b cos(x) - 8a b cos(x) - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 2 3 2 +--R - 4a b cos(x) - 4a b +--R * +--R csc(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 4 4 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 12a b + 8a b)cos(x) + (- 10a b + 8a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (16a b - 16a b)cos(x) + (16a b - 16a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (4a b + 8a b)cos(x) + 2a b + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 6 2 3 5 2 3 4 +--R - 4a b cos(x) - 8a b cos(x) + 4a b cos(x) +--R + +--R 2 3 3 2 3 2 2 3 2 3 +--R 16a b cos(x) + 4a b cos(x) - 8a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 6 2 3 5 2 3 4 2 3 3 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) + 8a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 2a b cos(x) - 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 6 3 2 5 3 2 4 3 2 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 8a b + 4a b )cos(x) + (- 8a b + 4a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (16a b - 12a b )cos(x) + (16a b - 16a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 3 2 +--R (- 8a b + 4a b )cos(x) + (- 8a b + 12a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 6a b + 4a b)cos(x) + (- 12a b + 8a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (6a b - 4a b)cos(x) + (24a b - 16a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (6a b - 4a b)cos(x) + (- 12a b + 8a b)cos(x) +--R + +--R 2 3 4 +--R (- 6a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 3a b - 2a b )cos(x) + (a b - 4a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (3a b - 6a b )cos(x) + a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) - a b cos(x) +--R + +--R 4 2 4 +--R 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 4 2 3 2 2 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- 2b - 4a b + 2a b)cos(x) + (- 8a b + 4a b)cos(x) +--R + +--R 5 2 3 2 2 3 4 5 2 3 4 +--R (4b - 6a b )cos(x) + (4a b - 4a b)cos(x) - 2b + 6a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 2 3 2 3 +--R - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 2 3 2 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 5 5 4 3 2 5 4 +--R (- 2a b - 4a b + 4a )cos(x) + (- a b - 4a b + 4a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (8a b - 8a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (6a b - 4a b + 4a )cos(x) + 5a b - 4a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) + 8a b cos(x) +--R + +--R 4 2 4 4 +--R 2a b cos(x) - 4a b cos(x) - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - a b cos(x) - 2a b cos(x) + a b cos(x) + 4a b cos(x) +--R + +--R 4 2 4 4 +--R a b cos(x) - 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 2 3 6 2 3 5 2 3 4 2 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 6 2 3 4 5 +--R (- 2b - 2a b + 2a b)cos(x) + (- 6a b + 4a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (6b - 2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 5 2 3 +--R (- 6b + 6a b - 2a b)cos(x) + (- 2a b + 4a b)cos(x) + 2b - 2a b +--R + +--R 4 +--R 2a b +--R * +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 3a b + 2a b )cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 4 3 2 3 +--R (3a b - 2a b )cos(x) + (12a b - 8a b )cos(x) + (3a b - 2a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 6a b + 4a b )cos(x) + (- 3a b + 2a b )cos(x) +--R / +--R 5 4 5 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 5 2 4 4 2 4 3 2 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 4 2 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 5 2 5 5 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 4 2 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )sin(x) +--R + +--R 3 3 5 3 3 4 3 3 3 3 3 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 3 3 3 3 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 6 2 4 5 2 4 4 2 4 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 2 4 2 2 4 2 4 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 2 4 5 2 4 4 2 4 3 2 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 4 2 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 5 2 5 5 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 267 + +--S 268 of 586 +t0545:= sec(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R sec(x) +--R (253) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 268 + +--S 269 of 586 +r0545:= 2*a^3*b*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+_ + 1/12*cos(x)/(a+b)/(1-sin(x))^2+1/4*a*cos(x)/(a+b)^2/(1-sin(x))+_ + 1/12*cos(x)/(a+b)/(1-sin(x))-1/12*cos(x)/(a-b)/(1+sin(x))^2-_ + 1/4*a*cos(x)/(a-b)^2/(1+sin(x))-1/12*cos(x)/(a-b)/(1+sin(x)) +--R +--R +--R (254) +--R x +--R b tan(-) + a +--R 3 4 3 2 3 2 +--R (6a b sin(x) - 12a b sin(x) + 6a b)atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 2 3 +--R (- a b - 2a )cos(x)sin(x) + 3a b cos(x)sin(x) + 3a cos(x)sin(x) +--R + +--R 3 2 +--R (b - 4a b)cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 4 4 2 2 4 2 4 +--R (3b - 6a b + 3a )sin(x) + (- 6b + 12a b - 6a )sin(x) + 3b +--R + +--R 2 2 4 +--R - 6a b + 3a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 586 +a0545:= integrate(t0545,x) +--R +--R +--R (255) +--R [ +--R 3 3 +--R 3a b cos(x) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R 2 3 2 2 3 3 2 3 +--R ((a b + 2a )cos(x) - a b + a )sin(x) + (b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R - 3a b cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 3 3 (b sin(x) + a cos(x) + a)\|b - a +--R - 6a b cos(x) atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 2 2 3 3 2 3 +--R ((a b + 2a )cos(x) - a b + a )sin(x) + (b - 4a b)cos(x) +--R + +--R 2 2 3 2 +--R - 3a b cos(x) + b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 2 2 4 3 | 2 2 +--R (3b - 6a b + 3a )cos(x) \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 270 + +--S 271 of 586 +m0545a:= a0545.1-r0545 +--R +--R +--R (256) +--R 3 3 4 3 3 2 3 3 +--R (3a b cos(x) sin(x) - 6a b cos(x) sin(x) + 3a b cos(x) ) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R 3 3 4 3 3 2 3 3 +--R (- 6a b cos(x) sin(x) + 12a b cos(x) sin(x) - 6a b cos(x) ) +--R * +--R x +--R b tan(-) + a +--R 2 +--R atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 2 3 5 +--R ((a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 2 2 3 2 4 +--R ((b - 4a b)cos(x) - 3a b cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((a b + 2a )cos(x) + (- 2a b - 4a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 2 4 3 2 3 2 2 3 +--R - 3a b cos(x) + (- 2b + 8a b)cos(x) + 6a b cos(x) - 2b +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 2 3 2 2 3 +--R (- 3a cos(x) + (a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 2 2 3 2 +--R (- b + 4a b)cos(x) + (b - 4a b)cos(x) - 3a b cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 586 +d0545a:= D(m0545a,x) +--R +--R +--R (257) +--R 3 4 5 2 2 3 4 5 2 10 +--R ((a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 6 2 +--R (- a b - a b + 2a b)cos(x) + (a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (3a b - 6a b + 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- a b + 2a b - a b )cos(x) + (- 6a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 +--R 3a b + 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 3a b + 3a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (7a b - 2a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 4a b - 3a b - 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 3b - 3a b + 15a b - 9a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 4 5 2 6 3 4 5 2 5 +--R (- a b - 5a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 3 4 5 2 4 6 3 4 5 2 3 +--R (a b + 5a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 4 5 2 2 6 5 2 +--R (11a b + 7a b )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (a b + a b - 2a b)cos(x) + (- a b + 3a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (- a b + 11a b - 10a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- a b - 7a b - 10a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 15a b + 12a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (6a b + 9a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 6 +--R (9b - 9a b - 9a b + 9a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 6 +--R (a b - 5a b + 4a b )cos(x) + (2a b + 16a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (a b + 7a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (a b - 5a b - 14a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- 6a b + 12a b - 6a b )cos(x) + (- 7a b - 5a b )cos(x) +--R + +--R 6 3 4 5 2 +--R 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 6 7 2 5 4 3 6 6 +--R (- 3a b + 3a b)cos(x) + (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- b + 5a b - 16a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (3a b + 3a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (13a b - 14a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 4a b - 9a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 9b + 15a b - 3a b - 3a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 +--R (- a b + 8a b - 7a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (4a b - 9a b - 13a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 2a b - 5a b + 7a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- a b + 5a b + 14a b )cos(x) +--R + +--R 6 3 4 5 2 3 5 2 2 6 3 4 +--R (4a b - 8a b + 4a b )cos(x) + 3a b cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 4b + 14a b - 13a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (4a b - 7a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (b - 4a b + 8a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 2a b + a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (- 4a b + 5a b - a b)cos(x) + (a b + 3a b - a b)cos(x) +--R + +--R 7 2 5 4 3 2 5 4 3 +--R (3b - 6a b + 3a b )cos(x) - 3a b + 3a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 5 2 6 +--R (- 3a b + 3a b )cos(x) + 6a b cos(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (a b + a b - 2a b )cos(x) + (- a b - 5a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- a b + 2a b - 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4a b + 2a b)cos(x) + (- 2a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 3 4 3 6 2 +--R (- 2a b + 4a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 10 +--R ((a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 6 2 +--R (- a b - a b + 2a b)cos(x) + (a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 3 6 +--R (3a b - 6a b + 3a b)cos(x) - 3a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 6 +--R (- a b + 2a b - a b )cos(x) + (- 6a b - 6a b )cos(x) + 3a b +--R + +--R 3 4 5 2 +--R 6a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (- 3a b + 3a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (7a b - 2a b - 5a b)cos(x) + (- 4a b - 3a b - 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 3b - 3a b + 15a b - 9a b)cos(x) + 3a b + 6a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 4 5 2 6 3 4 5 2 5 +--R (- a b - 5a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 3 4 5 2 4 6 3 4 5 2 3 +--R (a b + 5a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 4 5 2 2 6 5 2 +--R (11a b + 7a b )cos(x) - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 6 +--R (a b + a b - 2a b)cos(x) + (- a b + 3a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (- a b + 11a b - 10a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- a b - 7a b - 10a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (- 15a b + 12a b + 3a b)cos(x) + (6a b + 9a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 6 +--R (9b - 9a b - 9a b + 9a b)cos(x) - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 6 +--R (a b - 5a b + 4a b )cos(x) + (2a b + 16a b )cos(x) +--R + +--R 6 3 4 5 2 5 6 3 4 5 2 4 +--R (a b + 7a b - 8a b )cos(x) + (a b - 5a b - 14a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- 6a b + 12a b - 6a b )cos(x) + (- 7a b - 5a b )cos(x) +--R + +--R 6 3 4 5 2 +--R 9a b - 6a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 6 7 2 5 4 3 6 6 +--R (- 3a b + 3a b)cos(x) + (a b - 4a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- b + 5a b - 16a b + 12a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (3a b + 3a b + 12a b)cos(x) + (13a b - 14a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 4a b - 9a b + a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 4 3 6 +--R (- 9b + 15a b - 3a b - 3a b)cos(x) + 9a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 6 +--R (- a b + 8a b - 7a b )cos(x) + (4a b - 9a b - 13a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 2a b - 5a b + 7a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (- a b + 5a b + 14a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 5 2 2 6 3 4 +--R 3a b cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- 4b + 14a b - 13a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 6 +--R (4a b - 7a b + 3a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (b - 4a b + 8a b - 5a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 2a b + a b - 5a b)cos(x) + (- 4a b + 5a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 2 5 +--R (a b + 3a b - a b)cos(x) + (3b - 6a b + 3a b )cos(x) - 3a b +--R + +--R 4 3 +--R 3a b +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 5 2 6 +--R (- 3a b + 3a b )cos(x) + 6a b cos(x) +--R + +--R 6 3 4 5 2 5 3 4 5 2 4 +--R (a b + a b - 2a b )cos(x) + (- a b - 5a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- a b + 2a b - a b )cos(x) + (a b - a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((- a b - a b + 2a b )cos(x) + 3a b - 6a b + 3a b )sin(x) +--R + +--R 3 5 5 3 7 3 +--R (- a b - a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- a b + a b - 2a b + 2a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (3a b - 6a b + 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 2 6 4 4 6 2 3 2 6 6 2 2 8 +--R (- a b + 2a b - a b )cos(x) + (6a b - 6a b )cos(x) - 3b +--R + +--R 2 6 4 4 6 2 +--R - 3a b + 15a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 5 3 7 5 3 5 7 4 +--R (- 3a b + 3a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (7a b - 2a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b - a b + 2a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 3a b - 3a b + 15a b - 9a b)cos(x) - 3a b - 3a b + 15a b +--R + +--R 7 +--R - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 6 4 4 6 2 5 +--R (a b + 4a b - 5a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (- a b - 4a b + 5a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (- 11a b + 4a b + 7a b )cos(x) + 9b - 9a b - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (a b + a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (a b - 4a b + 5a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 5 +--R (- a b + 11a b - 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (a b + 6a b + 3a b - 10a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 15a b + 12a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b - 3a b + 6a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 9a b - 9a b + 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (a b - 5a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 6 +--R (- 2a b - 14a b + 16a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (a b + 7a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- b + 6a b + 9a b - 14a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (7a b - 2a b - 5a b )cos(x) - 9b + 15a b - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 7 7 7 3 5 5 3 7 6 +--R (- 3a b + 3a b)cos(x) + (- a b + 5a b - 7a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- a b + 5a b - 16a b + 12a b)cos(x) +--R + +--R 7 5 3 7 4 3 5 5 3 7 3 +--R (- 3a b - 9a b + 12a b)cos(x) + (13a b - 14a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b + 5a b - 10a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 9a b + 15a b - 3a b - 3a b)cos(x) - 9a b + 15a b - 3a b +--R + +--R 7 +--R - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- a b + 8a b - 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2a b )cos(x) + (a b + 4a b - 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 10 +--R ((- 2a b - 2a b + 4a b)cos(x) + 6a b - 12a b + 6a b)sin(x) +--R + +--R 4 4 6 2 8 3 +--R (- 2a b - 2a b + 4a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 2a b + 2a b - 4a b + 4a )cos(x) +--R + +--R 4 4 6 2 8 4 4 6 2 8 +--R (6a b - 12a b + 6a )cos(x) + 6a b - 12a b + 6a +--R * +--R 9 +--R sin(x) +--R + +--R 5 3 7 4 3 5 5 3 7 3 +--R (6a b - 6a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 3 5 7 2 7 3 5 5 3 7 +--R (12a b - 12a b)cos(x) - 6a b - 6a b + 30a b - 18a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 4 6 2 8 3 +--R (14a b - 4a b - 10a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (8a b - 2a b + 4a b - 10a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (- 6a b - 6a b + 30a b - 18a )cos(x) - 6a b - 6a b + 30a b +--R + +--R 8 +--R - 18a +--R * +--R 7 +--R sin(x) +--R + +--R 3 5 5 3 7 6 +--R (2a b + 8a b - 10a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 2a b - 20a b + 22a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 3 5 5 3 7 2 7 3 5 5 3 +--R (- 22a b + 8a b + 14a b)cos(x) + 18a b - 18a b - 18a b +--R + +--R 7 +--R 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 4 6 2 8 7 +--R (2a b + 2a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (2a b - 8a b + 10a b - 4a )cos(x) +--R + +--R 4 4 6 2 8 5 +--R (- 2a b + 4a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (2a b - 6a b + 6a b - 2a )cos(x) +--R + +--R 4 4 6 2 8 3 +--R (- 30a b + 24a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 12a b - 6a b + 12a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 +--R (18a b - 18a b - 18a b + 18a )cos(x) + 18a b - 18a b +--R + +--R 6 2 8 +--R - 18a b + 18a +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (2a b - 10a b + 8a b)cos(x) +--R + +--R 3 5 5 3 7 6 3 5 5 3 7 5 +--R (- 4a b - 28a b + 32a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 2a b + 12a b + 18a b - 28a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 2 7 3 5 5 3 7 +--R (14a b - 4a b - 10a b)cos(x) - 18a b + 30a b - 6a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 8 7 2 6 4 4 6 2 8 6 +--R (- 6a b + 6a )cos(x) + (- 2a b + 10a b - 14a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 2a b + 10a b - 14a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 4 4 6 2 8 3 +--R (26a b - 28a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (8a b + 10a b - 20a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (- 18a b + 30a b - 6a b - 6a )cos(x) - 18a b + 30a b - 6a b +--R + +--R 8 +--R - 6a +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 7 7 +--R (- 2a b + 16a b - 14a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 8a b + 26a b + 8a b - 26a b)cos(x) +--R + +--R 3 5 5 3 7 5 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b - 12a b - 6a b + 16a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 3 7 2 7 +--R (8a b - 16a b + 8a b)cos(x) + (- 6a b + 6a b)cos(x) + 6a b +--R + +--R 3 5 5 3 +--R - 12a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 7 +--R (- 8a b + 28a b - 26a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 6 +--R (- 8a b + 22a b - 20a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (2a b - 8a b + 10a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (4a b - 12a b + 12a b - 4a )cos(x) +--R + +--R 4 4 6 2 8 3 +--R (- 8a b + 10a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 2a b - 4a b + 8a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (6a b - 12a b + 6a b )cos(x) + 6a b - 12a b + 6a b +--R * +--R sin(x) +--R + +--R 5 3 7 7 5 3 7 6 +--R (- 6a b + 6a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (2a b - 4a b + 2a b)cos(x) + (2a b + 2a b - 4a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- 2a b + 4a b - 2a b)cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 10 +--R ((- a b - a b + 2a b )cos(x) + 3a b - 6a b + 3a b )sin(x) +--R + +--R 3 5 5 3 7 3 7 3 5 5 3 7 2 +--R (- a b - a b + 2a b)cos(x) + (- a b + a b - 2a b + 2a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (3a b - 6a b + 3a b)cos(x) + 3a b - 6a b + 3a b +--R * +--R 9 +--R sin(x) +--R + +--R 2 6 4 4 6 2 3 2 6 6 2 2 8 2 6 +--R (- a b + 2a b - a b )cos(x) + (6a b - 6a b )cos(x) - 3b - 3a b +--R + +--R 4 4 6 2 +--R 15a b - 9a b +--R * +--R 8 +--R sin(x) +--R + +--R 5 3 7 5 3 5 7 4 +--R (- 3a b + 3a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 3 5 5 3 7 3 7 3 5 5 3 7 2 +--R (7a b - 2a b - 5a b)cos(x) + (4a b - a b + 2a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 3a b - 3a b + 15a b - 9a b)cos(x) - 3a b - 3a b + 15a b - 9a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 6 4 4 6 2 5 +--R (a b + 4a b - 5a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (- a b - 4a b + 5a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 8 2 6 4 4 6 2 +--R (- 11a b + 4a b + 7a b )cos(x) + 9b - 9a b - 9a b + 9a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 7 7 3 5 5 3 7 6 +--R (a b + a b - 2a b)cos(x) + (a b - 4a b + 5a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 5 +--R (- a b + 11a b - 10a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (a b + 6a b + 3a b - 10a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 15a b + 12a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 6a b - 3a b + 6a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (9a b - 9a b - 9a b + 9a b)cos(x) + 9a b - 9a b - 9a b + 9a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 2 6 4 4 6 2 6 +--R (a b - 5a b + 4a b )cos(x) + (- 2a b - 14a b + 16a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (a b + 7a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- b + 6a b + 9a b - 14a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- 6a b + 12a b - 6a b )cos(x) + (7a b - 2a b - 5a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 +--R - 9b + 15a b - 3a b - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 7 7 7 3 5 5 3 7 6 +--R (- 3a b + 3a b)cos(x) + (- a b + 5a b - 7a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- a b + 5a b - 16a b + 12a b)cos(x) +--R + +--R 7 5 3 7 4 3 5 5 3 7 3 +--R (- 3a b - 9a b + 12a b)cos(x) + (13a b - 14a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (4a b + 5a b - 10a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 9a b + 15a b - 3a b - 3a b)cos(x) - 9a b + 15a b - 3a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- a b + 8a b - 7a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- 4b + 13a b + 4a b - 13a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 2a b - 5a b + 7a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (b - 6a b - 9a b + 14a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 4 6 2 2 8 2 6 4 4 +--R (- 3a b + 3a b )cos(x) + 3b - 6a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 4a b + 14a b - 13a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 6 +--R (- 4a b + 11a b - 10a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (a b - 4a b + 8a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b - 3a b + 6a b - 5a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 4a b + 5a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 7 3 5 5 3 +--R (- a b - 2a b + 4a b - a b)cos(x) + (3a b - 6a b + 3a b )cos(x) +--R + +--R 7 3 5 5 3 +--R 3a b - 6a b + 3a b +--R * +--R sin(x) +--R + +--R 4 4 6 2 7 4 4 6 2 6 +--R (- 3a b + 3a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 2 6 4 4 6 2 4 +--R (a b + a b - 2a b )cos(x) + (a b + 4a b - 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R / +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 4 +--R (9b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (3b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (6a b - 6a b - 6a b + 6a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (18a b - 54a b + 54a b - 18a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 18a b + 18a b + 18a b - 18a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 4 +--R (18a b - 54a b + 54a b - 18a b)cos(x) sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (- 18a b + 54a b - 54a b + 18a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (18a b - 18a b - 18a b + 18a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (6a b - 18a b + 18a b - 6a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 6a b + 6a b + 6a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 4 8 +--R (3a b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (3a b - 3a b - 3a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 3b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 9a b + 9a b + 9a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 4 +--R (9b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (9a b - 9a b - 9a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 9b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (6a b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 3a b + 3a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 2 6 4 4 6 2 4 +--R (3b - 9a b + 9a b - 3a b )cos(x) + (- 3a b + 6a b - 3a b )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 3b + 6a b - 6a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (9b - 18a b + 18a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (9a b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 9b + 18a b - 18a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (3b - 6a b + 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 8 4 8 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (- 6a b + 18a b - 18a b + 6a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 6a b + 12a b - 12a b + 6a )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 6a b + 18a b - 18a b + 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (12a b - 36a b + 36a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (18a b - 54a b + 54a b - 18a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (18a b - 36a b + 36a b - 18a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 4 +--R (18a b - 54a b + 54a b - 18a b)cos(x) sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (- 18a b + 54a b - 54a b + 18a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (- 18a b + 36a b - 36a b + 18a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 18a b + 54a b - 54a b + 18a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 12a b + 36a b - 36a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (6a b - 18a b + 18a b - 6a )cos(x) +--R + +--R 8 3 6 7 2 9 4 +--R (6a b - 12a b + 12a b - 6a )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (6a b - 18a b + 18a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 7 2 4 8 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 3a b + 9a b - 9a b + 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 3b + 6a b - 6a b + 3a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a b + 9a b - 9a b + 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 18a b + 18a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (9a b - 27a b + 27a b - 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (9b - 18a b + 18a b - 9a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 4 +--R (9a b - 27a b + 27a b - 9a b )cos(x) sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 9a b + 27a b - 27a b + 9a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (- 9b + 18a b - 18a b + 9a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 9a b + 27a b - 27a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 6a b + 18a b - 18a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (3a b - 9a b + 9a b - 3a b)cos(x) +--R + +--R 9 2 7 6 3 8 4 +--R (3b - 6a b + 6a b - 3a b)cos(x) +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (3a b - 9a b + 9a b - 3a b )cos(x) +--R Type: Expression(Integer) +--E 272 + +--S 273 of 586 +m0545b:= a0545.2-r0545 +--R +--R +--R (258) +--R +-------+ +--R 3 3 4 3 3 2 3 3 | 2 2 +--R (- 6a b cos(x) sin(x) + 12a b cos(x) sin(x) - 6a b cos(x) )\|b - a +--R * +--R x +--R b tan(-) + a +--R 2 +--R atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 3 4 3 3 2 3 3 +--R (- 6a b cos(x) sin(x) + 12a b cos(x) sin(x) - 6a b cos(x) ) +--R * +--R +-------+ +--R +---------+ | 2 2 +--R | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R \|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 2 2 3 5 +--R ((a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 3 2 2 3 2 4 +--R ((b - 4a b)cos(x) - 3a b cos(x) + b - a b)sin(x) +--R + +--R 2 3 4 2 3 2 2 3 3 +--R ((a b + 2a )cos(x) + (- 2a b - 4a )cos(x) + 2a b - 2a )sin(x) +--R + +--R 2 4 3 2 3 2 2 3 +--R - 3a b cos(x) + (- 2b + 8a b)cos(x) + 6a b cos(x) - 2b +--R + +--R 2 +--R 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 2 3 2 2 3 +--R (- 3a cos(x) + (a b + 2a )cos(x) - a b + a )sin(x) +--R + +--R 3 2 4 3 2 3 2 2 3 2 +--R (- b + 4a b)cos(x) + (b - 4a b)cos(x) - 3a b cos(x) + b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 2 4 3 4 +--R (3b - 6a b + 3a )cos(x) sin(x) +--R + +--R 4 2 2 4 3 2 4 2 2 4 3 +--R (- 6b + 12a b - 6a )cos(x) sin(x) + (3b - 6a b + 3a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 273 + +--S 274 of 586 +d0545b:= D(m0545b,x) +--R +--R +--R (259) +--R 4 3 2 2 4 3 2 10 +--R ((a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (2a b + 4a b)cos(x) + (- a b + 4a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 +--R (- 6a b + 6a b)cos(x) + 3b - 9a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 6a b - 6a b )cos(x) + 12a b - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 6a b cos(x) + 6a b cos(x) + (- 14a b - 10a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 5 +--R (3b - 5a b - 10a b)cos(x) + (6b + 12a b - 18a b)cos(x) - 6b +--R + +--R 2 3 4 +--R 24a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 2 6 3 2 5 +--R (- a b - 5a b )cos(x) + 6a b cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 6a b + 12a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (11a b + 7a b )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 2a b - 4a b)cos(x) + (7a b - 4a b)cos(x) +--R + +--R 2 3 4 5 5 2 3 4 4 +--R (2a b - 20a b)cos(x) + (b + a b - 20a b)cos(x) +--R + +--R 2 3 4 3 5 2 3 4 2 +--R (30a b + 6a b)cos(x) + (- 9b + 21a b + 6a b)cos(x) +--R + +--R 5 4 2 3 4 +--R (- 18b + 18a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- a b - 2a b )cos(x) + (- 2a b + 8a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 6a b + 21a b )cos(x) + (- 2a b - 16a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (9a b - 27a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 7a b - 5a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 8 2 3 4 7 +--R 6a b cos(x) + (6a b + 6a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (5b - 17a b + 6a b)cos(x) + (2b - 8a b + 24a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 6a b + 24a b)cos(x) + (- 26a b + 2a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 5 +--R (9b - 23a b + 2a b)cos(x) + (18b - 12a b - 6a b)cos(x) + 6b +--R + +--R 4 +--R - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- 3a b + 3a b )cos(x) + (2a b - 14a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (8a b - 20a b )cos(x) + (4a b + 14a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 4a b + 22a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 3 2 2 4 3 2 +--R 3a b cos(x) - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 8 5 2 3 4 7 +--R (4b - 10a b )cos(x) + (8b - 20a b + 6a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (3b - 6a b + 6a b)cos(x) + (- 2b + 6a b - 10a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- b + 5a b - 10a b)cos(x) + (8a b - 2a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 5 2 3 +--R (- 3b + 8a b - 2a b)cos(x) + (- 6b + 6a b )cos(x) - 3b + 3a b +--R * +--R sin(x) +--R + +--R 3 2 8 3 2 7 4 3 2 6 +--R 3a b cos(x) + 6a b cos(x) + (- a b + 4a b )cos(x) +--R + +--R 4 3 2 5 3 2 4 4 3 2 3 +--R (- 2a b - 4a b )cos(x) - 6a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 +--R (a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 2 3 4 10 +--R ((2a b + 4a b)cos(x) - 6a b + 6a b)sin(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (4a b + 8a )cos(x) + (- 2a b + 8a )cos(x) +--R + +--R 3 2 5 4 3 2 5 +--R (- 12a b + 12a )cos(x) + 6a b - 18a b + 12a +--R * +--R 9 +--R sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (2a b - 8a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 12a b - 12a b)cos(x) + 24a b - 24a b +--R * +--R 8 +--R sin(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (- 28a b - 20a )cos(x) + (6a b - 10a b - 20a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (12a b + 24a b - 36a )cos(x) - 12a b + 48a b - 36a +--R * +--R 7 +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 4 +--R (- 2a b - 16a b)cos(x) + (- 12a b + 36a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 2 3 +--R (- 16a b + 16a b)cos(x) + (22a b + 14a b)cos(x) - 36a b +--R + +--R 4 +--R 36a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 5 7 3 2 5 6 +--R (- 4a b - 8a )cos(x) + (14a b - 8a )cos(x) +--R + +--R 3 2 5 5 4 3 2 5 4 +--R (4a b - 4a )cos(x) + (2a b + 2a b - 4a )cos(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (60a b + 12a )cos(x) + (- 18a b + 42a b + 12a )cos(x) +--R + +--R 4 5 3 2 5 +--R (- 36a b + 36a )cos(x) - 36a b + 36a +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 2a b - 4a b)cos(x) + (- 4a b + 16a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 12a b + 60a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (18a b - 54a b)cos(x) + (24a b - 24a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 14a b - 10a b)cos(x) + 24a b - 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 8 3 2 5 7 +--R 12a b cos(x) + (12a b + 12a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (10a b - 34a b + 12a )cos(x) + (4a b - 16a b + 12a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (- 12a b + 12a )cos(x) + (- 52a b + 4a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (18a b - 46a b + 4a )cos(x) + (36a b - 24a b - 12a )cos(x) +--R + +--R 4 5 +--R 12a b - 12a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 6a b + 6a b)cos(x) + (4a b - 28a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (16a b - 58a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 8a b + 32a b)cos(x) + (- 16a b + 16a b)cos(x) +--R + +--R 4 2 2 3 4 +--R 6a b cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 5 7 +--R (8a b - 20a b )cos(x) + (16a b - 40a b + 12a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (6a b - 12a b + 12a )cos(x) + (- 4a b + 12a b - 8a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 3 +--R (- 2a b + 10a b - 8a )cos(x) + (16a b - 4a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 +--R (- 6a b + 16a b - 4a )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 4 3 2 +--R - 6a b + 6a b +--R * +--R sin(x) +--R + +--R 4 8 4 7 2 3 4 6 +--R 6a b cos(x) + 12a b cos(x) + (- 2a b + 14a b)cos(x) +--R + +--R 2 3 4 5 4 4 2 3 4 3 +--R (- 4a b + 4a b)cos(x) - 6a b cos(x) + (4a b - 4a b)cos(x) +--R + +--R 2 3 4 2 +--R (2a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 4 3 2 10 +--R ((a b + 2a b )cos(x) - 3a b + 3a b )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (2a b + 4a b)cos(x) + (- a b + 4a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 +--R (- 6a b + 6a b)cos(x) + 3b - 9a b + 6a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 6a b - 6a b )cos(x) + 12a b - 12a b +--R * +--R 8 +--R sin(x) +--R + +--R 4 5 4 4 2 3 4 3 +--R 6a b cos(x) + 6a b cos(x) + (- 14a b - 10a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 5 +--R (3b - 5a b - 10a b)cos(x) + (6b + 12a b - 18a b)cos(x) - 6b +--R + +--R 2 3 4 +--R 24a b - 18a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 2 6 3 2 5 4 3 2 4 +--R (- a b - 5a b )cos(x) + 6a b cos(x) + (- 6a b + 12a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 4 3 2 +--R (- 8a b + 8a b )cos(x) + (11a b + 7a b )cos(x) - 18a b + 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 2a b - 4a b)cos(x) + (7a b - 4a b)cos(x) +--R + +--R 2 3 4 5 5 2 3 4 4 +--R (2a b - 20a b)cos(x) + (b + a b - 20a b)cos(x) +--R + +--R 2 3 4 3 5 2 3 4 2 +--R (30a b + 6a b)cos(x) + (- 9b + 21a b + 6a b)cos(x) +--R + +--R 5 4 2 3 4 +--R (- 18b + 18a b)cos(x) - 18a b + 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- a b - 2a b )cos(x) + (- 2a b + 8a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 6a b + 21a b )cos(x) + (- 2a b - 16a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (9a b - 27a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 7a b - 5a b )cos(x) + 12a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 8 2 3 4 7 5 2 3 4 6 +--R 6a b cos(x) + (6a b + 6a b)cos(x) + (5b - 17a b + 6a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (2b - 8a b + 24a b)cos(x) + (- 6a b + 24a b)cos(x) +--R + +--R 2 3 4 3 5 2 3 4 2 +--R (- 26a b + 2a b)cos(x) + (9b - 23a b + 2a b)cos(x) +--R + +--R 5 2 3 4 5 4 +--R (18b - 12a b - 6a b)cos(x) + 6b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- 3a b + 3a b )cos(x) + (2a b - 14a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (8a b - 20a b )cos(x) + (4a b + 14a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 3 2 2 +--R (- 4a b + 22a b )cos(x) + (- 8a b + 8a b )cos(x) + 3a b cos(x) +--R + +--R 4 3 2 +--R - 3a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 8 5 2 3 4 7 +--R (4b - 10a b )cos(x) + (8b - 20a b + 6a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (3b - 6a b + 6a b)cos(x) + (- 2b + 6a b - 10a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- b + 5a b - 10a b)cos(x) + (8a b - 2a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 5 2 3 +--R (- 3b + 8a b - 2a b)cos(x) + (- 6b + 6a b )cos(x) - 3b + 3a b +--R * +--R sin(x) +--R + +--R 3 2 8 3 2 7 4 3 2 6 +--R 3a b cos(x) + 6a b cos(x) + (- a b + 4a b )cos(x) +--R + +--R 4 3 2 5 3 2 4 4 3 2 3 +--R (- 2a b - 4a b )cos(x) - 6a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 3 2 2 +--R (a b - a b )cos(x) +--R / +--R 6 2 4 4 2 4 8 +--R (3b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (3b - 6a b + 3a b )cos(x) + (6b - 12a b + 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 6b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 2 4 4 2 6 +--R (- 9b + 18a b - 9a b )cos(x) +--R + +--R 6 2 4 4 2 5 +--R (- 18b + 36a b - 18a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (18a b - 36a b + 18a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (9b - 18a b + 9a b )cos(x) + (18b - 36a b + 18a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (6b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (- 3b + 6a b - 3a b )cos(x) + (- 6b + 12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 3b + 6a b - 3a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 4 8 +--R (6a b - 12a b + 6a b)cos(x) sin(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R ((12a b - 24a b + 12a )cos(x) + (12a b - 24a b + 12a )cos(x) ) +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (6a b - 12a b + 6a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 12a b + 24a b - 12a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 4 4 2 6 5 +--R (- 36a b + 72a b - 36a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 36a b + 72a b - 36a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 36a b + 72a b - 36a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R ((36a b - 72a b + 36a )cos(x) + (36a b - 72a b + 36a )cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (18a b - 36a b + 18a b)cos(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R (36a b - 72a b + 36a b)cos(x) + (12a b - 24a b + 12a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 5 +--R (- 12a b + 24a b - 12a )cos(x) +--R + +--R 2 4 4 2 6 4 +--R (- 12a b + 24a b - 12a )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 5 +--R (- 6a b + 12a b - 6a b)cos(x) + (- 12a b + 24a b - 12a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 12a b - 6a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 4 2 4 8 +--R (3b - 6a b + 3a b )cos(x) sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 7 +--R ((6a b - 12a b + 6a b)cos(x) + (6a b - 12a b + 6a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (3b - 6a b + 3a b )cos(x) + (6b - 12a b + 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 6b + 12a b - 6a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18a b + 36a b - 18a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 18a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R ((- 9b + 18a b - 9a b )cos(x) + (- 18b + 36a b - 18a b )cos(x) ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((18a b - 36a b + 18a b)cos(x) + (18a b - 36a b + 18a b)cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (9b - 18a b + 9a b )cos(x) + (18b - 36a b + 18a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (6b - 12a b + 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 5 3 3 5 4 +--R ((- 6a b + 12a b - 6a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) ) +--R * +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 5 +--R (- 3b + 6a b - 3a b )cos(x) + (- 6b + 12a b - 6a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 3b + 6a b - 3a b )cos(x) +--R Type: Expression(Integer) +--E 274 + +--S 275 of 586 +t0546:= csc(x)^3/(a+b*csc(x)) +--R +--R +--R 3 +--R csc(x) +--R (260) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 586 +r0546:= a*atanh(cos(x))/b^2-2*a^2*atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/_ + b^2/(a^2-b^2)^(1/2)-cot(x)/b +--R +--R +--R (261) +--R x +--R +---------+ b tan(-) + a +---------+ +--R | 2 2 2 2 | 2 2 +--R a\|- b + a atanh(cos(x)) - 2a atanh(------------) - b cot(x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R -------------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R b \|- b + a +--R Type: Expression(Integer) +--E 276 + +--S 277 of 586 +a0546:= integrate(t0546,x) +--R +--R +--R (262) +--R [ +--R 2 +--R a sin(x) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R +---------+ +---------+ +--R | 2 2 sin(x) | 2 2 +--R - a sin(x)\|- b + a log(----------) - b cos(x)\|- b + a +--R cos(x) + 1 +--R / +--R +---------+ +--R 2 | 2 2 +--R b sin(x)\|- b + a +--R , +--R +--R +-------+ +--R | 2 2 sin(x) +--R - a sin(x)\|b - a log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +-------+ +--R 2 (b sin(x) + a cos(x) + a)\|b - a | 2 2 +--R 2a sin(x)atan(-----------------------------------) - b cos(x)\|b - a +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R / +--R +-------+ +--R 2 | 2 2 +--R b sin(x)\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 277 + +--S 278 of 586 +m0546a:= a0546.1-r0546 +--R +--R +--R (263) +--R 2 +--R a sin(x) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (b - a b)sin(x) + (a b - a )cos(x) + a b - a +--R / +--R a sin(x) + b +--R + +--R +---------+ +---------+ +--R | 2 2 sin(x) | 2 2 +--R - a sin(x)\|- b + a log(----------) - a sin(x)\|- b + a atanh(cos(x)) +--R cos(x) + 1 +--R + +--R x +--R b tan(-) + a +---------+ +--R 2 2 | 2 2 +--R 2a sin(x)atanh(------------) + (b cot(x)sin(x) - b cos(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R b sin(x)\|- b + a +--R Type: Expression(Integer) +--E 278 + +--S 279 of 586 +d0546a:= D(m0546a,x) +--R +--R +--R (264) +--R 3 2 5 +--R - a b cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 2 3 4 2 +--R (- a b cos(x) + a b )cot(x) + (a b - a b)cos(x) +--R + +--R 2 3 4 +--R (- a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (a b - a b )cos(x) + (- a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- a b + a b )cos(x) + a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 4 3 2 5 2 3 2 5 +--R - a cos(x) + (a b - a b - a )cos(x) + (- a b + a )cos(x) +--R + +--R 5 +--R a +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 3 2 3 2 5 2 3 +--R (b - a b )cos(x) - a b cos(x) + (- b + a b )cos(x) +--R + +--R 2 3 +--R a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 2 3 4 3 2 3 4 2 +--R 2a b cos(x) + (- a b - a b)cos(x) + (- 2a b - a b)cos(x) +--R + +--R 2 3 4 4 +--R (a b + a b)cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 4 4 4 3 2 3 +--R (- a b + a b )cos(x) + 2a b cos(x) + (a b - 2a b )cos(x) +--R + +--R 4 2 3 2 +--R - 2a b cos(x) + a b cos(x) +--R * +--R sin(x) +--R + +--R 5 2 3 5 2 3 4 5 2 3 3 +--R (- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) +--R + +--R 2 3 2 +--R - a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 5 +--R - 2a b cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 3 2 2 +--R (- 2a b cos(x) + 2a b )cot(x) + 2a b cos(x) +--R + +--R 3 2 5 5 +--R (- 2a b - 2a )cos(x) - 2a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (2a b - 2a b)cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 2a b + 2a b)cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 2 3 2 4 +--R - 2a b cos(x) + 2a b cos(x) - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 3 3 2 2 +--R (2a b - 2a b )cos(x) - 2a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 2a b + 2a b )cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 3 2 3 3 2 2 3 2 +--R 4a b cos(x) - 4a b cos(x) - 4a b cos(x) + 4a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 +--R (- 2a b + 2a b)cos(x) + 4a b cos(x) +--R + +--R 2 3 4 3 2 3 2 4 +--R (2a b - 4a b)cos(x) - 4a b cos(x) + 2a b cos(x) +--R * +--R sin(x) +--R + +--R 4 3 2 5 3 2 4 4 3 2 3 +--R (- 2a b + 2a b )cos(x) + 2a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 2 2 +--R - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 5 +--R - a b cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 2 3 4 2 +--R (- a b cos(x) + a b )cot(x) + (a b - a b)cos(x) +--R + +--R 2 3 4 +--R (- a b - a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (a b - a b )cos(x) + (- a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- a b + a b )cos(x) + a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 4 3 2 5 2 3 2 5 5 +--R - a cos(x) + (a b - a b - a )cos(x) + (- a b + a )cos(x) + a +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 3 2 3 2 5 2 3 2 3 +--R ((b - a b )cos(x) - a b cos(x) + (- b + a b )cos(x) + a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 2 3 4 3 2 3 4 2 +--R 2a b cos(x) + (- a b - a b)cos(x) + (- 2a b - a b)cos(x) +--R + +--R 2 3 4 4 +--R (a b + a b)cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 4 4 4 3 2 3 +--R (- a b + a b )cos(x) + 2a b cos(x) + (a b - 2a b )cos(x) +--R + +--R 4 2 3 2 +--R - 2a b cos(x) + a b cos(x) +--R * +--R sin(x) +--R + +--R 5 2 3 5 2 3 4 5 2 3 3 2 3 2 +--R (- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 4 4 2 5 +--R (- a b + a b )cos(x)sin(x) +--R + +--R 5 3 3 2 5 3 3 2 +--R ((- a b + a b )cos(x) + a b - a b )cot(x) +--R + +--R 3 3 5 2 5 5 +--R (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 3 6 4 2 2 +--R (- a b + a b )cos(x) + (- b + a b )cos(x) +--R + +--R 2 4 4 2 6 4 2 +--R (a b - a b )cos(x) + b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 6 3 2 4 6 2 4 2 6 +--R (- a b + a )cos(x) + (- a b + a )cos(x) + (a b - a )cos(x) +--R + +--R 4 2 6 +--R a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) + a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 4 5 5 3 +--R (a b - a b )cos(x) + (- a b + a b)cos(x) +--R + +--R 5 5 2 5 5 3 3 5 +--R (- a b + a b)cos(x) + (a b - a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 5 6 2 4 4 +--R (a b - a b )cos(x) + (b - a b )cos(x) +--R + +--R 2 4 4 2 3 6 2 4 2 +--R (- 2a b + 2a b )cos(x) + (- b + a b )cos(x) +--R + +--R 2 4 4 2 +--R (a b - a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 5 3 3 3 +--R (a b - a b )cos(x) + (a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 2 +--R (- a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 5 +--R (- 2a b + 2a b)cos(x)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 +--R ((- 2a b + 2a b )cos(x) + 2a b - 2a b )cot(x) +--R + +--R 2 4 6 4 2 6 +--R (- 2a b + 2a )cos(x) - 2a b + 2a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 3 5 5 2 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 3 3 5 5 5 +--R (2a b - 2a b)cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 3 5 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (2a b - 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 5 5 3 3 4 +--R (2a b - 2a b)cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 3 5 3 5 3 3 2 +--R (- 4a b + 4a b)cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 3 5 +--R (2a b - 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 5 +--R (- a b + a b )cos(x)sin(x) +--R + +--R 5 3 3 2 5 3 3 2 3 3 5 2 +--R ((- a b + a b )cos(x) + a b - a b )cot(x) + (- a b + a b)cos(x) +--R + +--R 5 5 +--R (- a b + a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 3 6 4 2 2 +--R (- a b + a b )cos(x) + (- b + a b )cos(x) +--R + +--R 2 4 4 2 6 4 2 +--R (a b - a b )cos(x) + b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 6 3 2 4 6 2 4 2 6 +--R (- a b + a )cos(x) + (- a b + a )cos(x) + (a b - a )cos(x) +--R + +--R 4 2 6 +--R a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) + a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 4 5 5 3 5 5 2 +--R (a b - a b )cos(x) + (- a b + a b)cos(x) + (- a b + a b)cos(x) +--R + +--R 5 5 3 3 5 +--R (a b - a b)cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 5 6 2 4 4 2 4 4 2 3 +--R (a b - a b )cos(x) + (b - a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 6 2 4 2 2 4 4 2 +--R (- b + a b )cos(x) + (a b - a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 5 3 3 3 +--R (a b - a b )cos(x) + (a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 2 +--R (- a b + a b )cos(x) +--R / +--R 2 4 2 2 4 4 +--R (a b cos(x) - a b )sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 3 2 4 2 6 2 4 2 4 +--R ((- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b ) +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 4 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 3 3 3 2 +--R (- 2a b + 2a b )cos(x) + 2a b cos(x) +--R + +--R 5 3 3 3 3 +--R (2a b - 2a b )cos(x) - 2a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 4 4 +--R (a b cos(x) - a b )sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- a b + a b )cos(x) + (a b + a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 3 2 4 2 6 2 4 2 4 2 +--R ((- b + a b )cos(x) + a b cos(x) + (b - a b )cos(x) - a b )sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 6 3 4 2 6 3 4 4 +--R ((a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 5 4 3 3 7 4 3 2 2 5 4 3 +--R (a b - a b )cos(x) + (b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 7 4 3 +--R - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (a b - a b )cos(x) + (a b - a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 2 5 4 3 4 +--R ((2a b - 2a b )cos(x) - 2a b + 2a b )sin(x) +--R + +--R 3 4 5 2 3 6 5 2 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 4 5 2 6 5 2 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 4 2 6 3 4 4 +--R ((a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 5 4 3 3 7 4 3 2 2 5 4 3 +--R (a b - a b )cos(x) + (b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 7 4 3 +--R - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 3 6 3 4 2 6 3 4 +--R (a b - a b )cos(x) + (a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 3 4 +--R - a b + a b +--R * +--R 2 +--R sin(x) +--R Type: Expression(Integer) +--E 279 + +--S 280 of 586 +m0546b:= a0546.2-r0546 +--R +--R +--R (265) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) +--R - a sin(x)\|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R - a sin(x)\|- b + a \|b - a atanh(cos(x)) +--R + +--R x +--R +-------+ b tan(-) + a +--R 2 | 2 2 2 +--R 2a sin(x)\|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 2 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R 2a sin(x)\|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R (b cot(x)sin(x) - b cos(x))\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R b sin(x)\|- b + a \|b - a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 586 +d0546b:= D(m0546b,x) +--R +--R +--R (266) +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 2 2 2 4 +--R ((- b cos(x) + b )cot(x) - a b cos(x) - 2a b cos(x) - a b)sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b )cot(x) +--R + +--R 2 3 3 2 3 2 3 3 +--R (- 2a b - 2a )cos(x) + (- 2a b - 2a )cos(x) + 2a cos(x) + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (- b cos(x) - 2b cos(x) + 2b cos(x) + b )cot(x) +--R + +--R 3 2 4 2 3 3 2 2 2 +--R (b - a b)cos(x) - 2a b cos(x) - b cos(x) + 2a b cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + b cos(x) +--R + +--R 3 5 3 3 3 2 +--R 2b cos(x) - 2b cos(x) - b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 3 3 4 +--R ((- 2a b cos(x) + 2a b )cot(x) - 4a cos(x) - 4a )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 4a b cos(x) - 4a b cos(x) + 4a b cos(x) + 4a b)cot(x) +--R + +--R 2 3 2 2 +--R - 4a b cos(x) - 4a b cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R (- 2a b cos(x) - 4a b cos(x) + 4a b cos(x) + 2a b )cot(x) +--R + +--R 2 4 2 2 +--R 2a b cos(x) - 2a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 2 6 +--R (2a b cos(x) - 4a b cos(x) + 2a b cos(x))sin(x) + 2a b cos(x) +--R + +--R 2 5 2 3 2 2 +--R 4a b cos(x) - 4a b cos(x) - 2a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - a b cos(x)sin(x) +--R + +--R 3 2 3 2 2 2 2 2 4 +--R ((- b cos(x) + b )cot(x) - a b cos(x) - 2a b cos(x) - a b)sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b )cot(x) +--R + +--R 2 3 3 2 3 2 3 3 +--R (- 2a b - 2a )cos(x) + (- 2a b - 2a )cos(x) + 2a cos(x) + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (- b cos(x) - 2b cos(x) + 2b cos(x) + b )cot(x) +--R + +--R 3 2 4 2 3 3 2 2 2 +--R (b - a b)cos(x) - 2a b cos(x) - b cos(x) + 2a b cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 3 5 +--R (a b cos(x) - 2a b cos(x) + a b cos(x))sin(x) + b cos(x) + 2b cos(x) +--R + +--R 3 3 3 2 +--R - 2b cos(x) - b cos(x) +--R / +--R 4 2 4 4 +--R (b cos(x) - b )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (b cos(x) + 2b cos(x) - 2b cos(x) - b )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 3 4 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 3 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b )sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 4 4 +--R (b cos(x) - b )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2a b cos(x) + 2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (b cos(x) + 2b cos(x) - 2b cos(x) - b )sin(x) +--R Type: Expression(Integer) +--E 281 + +--S 282 of 586 +t0547:= csc(x)^4/(a+b*csc(x)) +--R +--R +--R 4 +--R csc(x) +--R (267) ------------ +--R b csc(x) + a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 586 +r0547:= -a^2*atanh(cos(x))/b^3-1/2*atanh(cos(x))/b+2*a^3*_ + atanh((a+b*tan(1/2*x))/(a^2-b^2)^(1/2))/b^3/(a^2-b^2)^(1/2)+_ + a*cot(x)/b^2-1/2*cot(x)*csc(x)/b +--R +--R +--R (268) +--R x +--R +---------+ b tan(-) + a +--R 2 2 | 2 2 3 2 +--R (- b - 2a )\|- b + a atanh(cos(x)) + 4a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (- b cot(x)csc(x) + 2a b cot(x))\|- b + a +--R / +--R +---------+ +--R 3 | 2 2 +--R 2b \|- b + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 586 +a0547:= integrate(t0547,x) +--R +--R +--R (269) +--R [ +--R 3 2 3 +--R (2a cos(x) - 2a ) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((b + 2a )cos(x) - b - 2a )\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 2a b cos(x)sin(x) + b cos(x))\|- b + a +--R / +--R +---------+ +--R 3 2 3 | 2 2 +--R (2b cos(x) - 2b )\|- b + a +--R , +--R +--R +-------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((b + 2a )cos(x) - b - 2a )\|b - a log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 +--R 3 2 3 (b sin(x) + a cos(x) + a)\|b - a +--R (- 4a cos(x) + 4a )atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +-------+ +--R 2 | 2 2 +--R (- 2a b cos(x)sin(x) + b cos(x))\|b - a +--R / +--R +-------+ +--R 3 2 3 | 2 2 +--R (2b cos(x) - 2b )\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 284 + +--S 285 of 586 +m0547a:= a0547.1-r0547 +--R +--R +--R (270) +--R 3 2 3 +--R (2a cos(x) - 2a ) +--R * +--R log +--R +---------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (- b + a )cos(x) + a )\|- b + a +--R + +--R 3 2 2 3 2 3 +--R (- b + a b)sin(x) + (- a b + a )cos(x) - a b + a +--R / +--R a sin(x) + b +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 sin(x) +--R ((b + 2a )cos(x) - b - 2a )\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 2 2 2 | 2 2 +--R ((b + 2a )cos(x) - b - 2a )\|- b + a atanh(cos(x)) +--R + +--R x +--R b tan(-) + a +--R 3 2 3 2 +--R (- 4a cos(x) + 4a )atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 +--R - 2a b cos(x)sin(x) + (b cos(x) - b )cot(x)csc(x) +--R + +--R 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 3 2 3 | 2 2 +--R (2b cos(x) - 2b )\|- b + a +--R Type: Expression(Integer) +--E 285 + +--S 286 of 586 +d0547a:= D(m0547a,x) +--R +--R +--R (271) +--R 3 3 2 3 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 2 4 3 2 4 4 2 2 2 4 4 2 +--R 3a b cos(x) + (- a b - 2a b )cos(x) + (a b - 4a b )cos(x) +--R + +--R 2 4 4 2 +--R - a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 4 2 2 4 2 +--R (- 2a b cos(x) + 4a b cos(x) - 2a b )cot(x) +--R + +--R 2 4 4 2 4 2 2 4 +--R - a b cos(x) + 2a b cos(x) - a b +--R * +--R csc(x) +--R + +--R 3 3 4 3 3 2 3 3 2 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- a b - a b + 2a b)cos(x) + (2a b + 2a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 5 +--R (2a b - 2a b - 2a b)cos(x) + (- 4a b - 2a b)cos(x) + a b +--R + +--R 3 3 +--R a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (2a b - 2a b )cos(x) - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (a b - a b )cos(x) + (- a b - a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 +--R (a b - a b )cos(x) - a b - a b +--R * +--R csc(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 6 5 6 2 4 4 2 6 4 +--R (a b + 2a )cos(x) + (- b - a b + 2a b + 2a )cos(x) +--R + +--R 6 2 4 6 3 6 4 2 6 2 +--R (- b + 2a b - 4a )cos(x) + (b - 4a b - 4a )cos(x) +--R + +--R 6 2 4 6 2 4 4 2 6 +--R (- b - a b + 2a )cos(x) + 3a b + 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 5 2 4 4 +--R (2b - 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a b )cos(x) + a b - a b +--R * +--R csc(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 5 +--R (- a b + a b )cos(x) + (- b - 2a b + a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (2b + 6a b - 4a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (a b + 3a b - 4a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 5 6 +--R (- b - 4a b + 3a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (- a b - a b + 2a b )cos(x) + (- a b - a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (2a b + 2a b - 4a b )cos(x) + (2a b + 2a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- a b - a b + 2a b )cos(x) + (- a b - a b + 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 5 +--R ((4a b - 4a b )cos(x) + 4a b - 4a b )sin(x) +--R + +--R 2 5 4 3 3 2 5 4 3 6 2 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (2a b + 6a b - 8a b)cos(x) + 2a b + 2a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 4 2 5 4 3 2 2 5 +--R (4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b +--R + +--R 4 3 +--R - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 4 2 5 4 3 2 2 5 +--R (2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b +--R + +--R 4 3 +--R - 2a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 4 3 4 5 2 2 3 4 +--R (- 4a b + 4a b )cos(x) + (8a b - 8a b )cos(x) - 4a b +--R + +--R 5 2 +--R 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 4 6 3 4 7 3 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 2a b + 4a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b + 10a b - 12a b + 4a )cos(x) +--R + +--R 6 3 4 5 2 7 6 5 2 7 +--R (2a b + 6a b - 4a b - 4a )cos(x) - 2a b + 6a b - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 5 6 5 2 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 3 4 5 2 3 6 5 2 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 3 4 5 2 6 5 2 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 5 6 5 2 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 4 5 2 3 6 5 2 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 6 5 2 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R csc(x) +--R + +--R 4 3 6 5 2 5 6 4 +--R (- 4a b + 4a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 4 3 6 3 2 5 6 2 +--R (8a b - 8a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 4 3 6 2 5 6 +--R (- 4a b + 4a b)cos(x) - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 4 +--R (- 2a b - 2a b + 4a b)cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 4 3 6 3 2 5 4 3 2 +--R (8a b - 8a b)cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (- 2a b - 2a b + 4a b)cos(x) - 6a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 5 2 6 6 3 4 5 2 5 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 4a b + 6a b )cos(x) +--R + +--R 3 4 5 2 4 6 3 4 5 2 3 +--R (4a b - 4a b )cos(x) + (4a b + 12a b - 16a b )cos(x) +--R + +--R 3 4 5 2 2 6 3 4 5 2 3 4 +--R (2a b - 2a b )cos(x) + (- 2a b - 8a b + 10a b )cos(x) - 4a b +--R + +--R 5 2 +--R 4a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (- 2a b - 2a b + 4a b)cos(x) + (- 2a b - 2a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (4a b + 4a b - 8a b)cos(x) + (4a b + 4a b - 8a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 2a b - 2a b + 4a b)cos(x) + (- 2a b - 2a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 2 5 4 3 5 +--R ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 6 3 4 3 6 3 4 5 2 2 +--R (- a b + a b )cos(x) + (a b + a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (a b + 3a b - 4a b )cos(x) + a b + a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 4 6 3 4 2 6 +--R (2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b +--R + +--R 3 4 +--R - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 4 6 3 4 2 6 3 4 +--R (a b - a b )cos(x) + (- 2a b + 2a b )cos(x) + a b - a b +--R * +--R csc(x) +--R + +--R 2 5 4 3 4 2 5 4 3 2 2 5 4 3 +--R ((- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b + 2a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 4 7 2 5 6 3 +--R (- a b - a b + 2a b)cos(x) + (- b - a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- b + 5a b - 2a b - 2a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 4 3 +--R (b + 3a b - 2a b - 2a b)cos(x) - b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 4 3 5 7 4 3 4 +--R (2a b - 2a b )cos(x) + (2b - 2a b )cos(x) +--R + +--R 2 5 4 3 3 7 4 3 2 +--R (- 4a b + 4a b )cos(x) + (- 4b + 4a b )cos(x) +--R + +--R 2 5 4 3 7 4 3 +--R (2a b - 2a b )cos(x) + 2b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 5 7 4 3 4 +--R (a b - a b )cos(x) + (b - a b )cos(x) +--R + +--R 2 5 4 3 3 7 4 3 2 +--R (- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 2 5 4 3 7 4 3 +--R (a b - a b )cos(x) + b - a b +--R * +--R csc(x) +--R + +--R 3 4 5 2 5 6 5 2 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 4 5 2 3 6 5 2 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 3 4 5 2 6 5 2 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 7 5 6 3 4 7 4 +--R (- a b - a b + 2a )cos(x) + (- a b - a b + 2a )cos(x) +--R + +--R 3 4 7 3 6 3 4 7 2 +--R (4a b - 4a )cos(x) + (2a b + 2a b - 4a )cos(x) +--R + +--R 6 3 4 7 6 3 4 7 +--R (- a b - a b + 2a )cos(x) - 3a b + a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (a b - a b )cos(x) + (a b - a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (a b - a b )cos(x) + a b - a b +--R * +--R csc(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 4 3 6 7 2 5 4 3 6 5 +--R (- a b + a b )cos(x) + (- b - 2a b + a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 7 2 5 4 3 6 3 +--R (2a b - 4a b + 2a b)cos(x) + (2b + 6a b - 4a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 2 7 2 5 4 3 6 +--R (a b + 3a b - 4a b)cos(x) + (- b - 4a b + 3a b + 2a b)cos(x) +--R + +--R 2 5 6 +--R - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 6 6 3 4 5 2 5 +--R (- a b - a b + 2a b )cos(x) + (- a b - a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (2a b + 2a b - 4a b )cos(x) + (2a b + 2a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- a b - a b + 2a b )cos(x) + (- a b - a b + 2a b )cos(x) +--R / +--R 2 5 4 2 5 2 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 7 2 5 3 +--R (- 2b + 2a b )cos(x) + 2a b cos(x) + (4b - 4a b )cos(x) +--R + +--R 2 5 2 7 2 5 2 5 +--R - 4a b cos(x) + (- 2b + 2a b )cos(x) + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 4 3 4 2 3 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )sin(x) +--R + +--R 2 5 4 3 5 2 5 4 3 4 +--R (- 4a b + 4a b )cos(x) + (4a b + 4a b )cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 2 +--R (8a b - 8a b )cos(x) + (- 8a b - 8a b )cos(x) +--R + +--R 2 5 4 3 2 5 4 3 +--R (- 4a b + 4a b )cos(x) + 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 3 4 4 +--R (- 4a b + 4a b )cos(x) + 4a b cos(x) +--R + +--R 6 3 4 3 3 4 2 +--R (8a b - 8a b )cos(x) - 8a b cos(x) +--R + +--R 6 3 4 3 4 +--R (- 4a b + 4a b )cos(x) + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 2 5 2 2 5 3 +--R (2a b cos(x) - 4a b cos(x) + 2a b )sin(x) +--R + +--R 6 3 4 5 6 3 4 4 +--R (- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x) +--R + +--R 6 3 4 3 6 3 4 2 +--R (4a b - 4a b )cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 6 3 4 6 3 4 +--R (- 2a b + 2a b )cos(x) + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 5 5 2 5 4 7 2 5 3 +--R (- 2b + 2a b )cos(x) + 2a b cos(x) + (4b - 4a b )cos(x) +--R + +--R 2 5 2 7 2 5 2 5 +--R - 4a b cos(x) + (- 2b + 2a b )cos(x) + 2a b +--R * +--R sin(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 7 3 5 4 7 3 5 2 7 3 5 +--R ((- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b + 2a b ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 5 8 4 4 4 +--R (- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 2 6 4 4 3 8 4 4 2 +--R (4a b - 4a b )cos(x) + (4b - 4a b )cos(x) +--R + +--R 2 6 4 4 8 4 4 +--R (- 2a b + 2a b )cos(x) - 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 7 3 5 3 7 3 5 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 7 3 5 7 3 5 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 4 2 6 4 4 2 2 6 4 4 +--R ((- 4a b + 4a b )cos(x) + (8a b - 8a b )cos(x) - 4a b + 4a b ) +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 5 7 5 3 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 5 5 3 3 7 5 3 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 3 5 5 3 7 5 3 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 5 2 6 4 4 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 4 4 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 2 6 4 4 2 6 4 4 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 7 3 5 4 7 3 5 2 7 3 5 +--R ((- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b + 2a b ) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 5 8 4 4 4 +--R (- 2a b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 2 6 4 4 3 8 4 4 2 +--R (4a b - 4a b )cos(x) + (4b - 4a b )cos(x) +--R + +--R 2 6 4 4 8 4 4 +--R (- 2a b + 2a b )cos(x) - 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 7 3 5 3 7 3 5 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 7 3 5 7 3 5 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 286 + +--S 287 of 586 +m0547b:= a0547.2-r0547 +--R +--R +--R (272) +--R +---------+ +-------+ +--R 2 2 2 2 2 | 2 2 | 2 2 sin(x) +--R ((b + 2a )cos(x) - b - 2a )\|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 2 2 2 | 2 2 | 2 2 +--R ((b + 2a )cos(x) - b - 2a )\|- b + a \|b - a atanh(cos(x)) +--R + +--R x +--R +-------+ b tan(-) + a +--R 3 2 3 | 2 2 2 +--R (- 4a cos(x) + 4a )\|b - a atanh(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 2 3 | 2 2 (b sin(x) + a cos(x) + a)\|b - a +--R (- 4a cos(x) + 4a )\|- b + a atan(-----------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 2 +--R - 2a b cos(x)sin(x) + (b cos(x) - b )cot(x)csc(x) +--R + +--R 2 2 +--R (- 2a b cos(x) + 2a b)cot(x) + b cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 3 2 3 | 2 2 | 2 2 +--R (2b cos(x) - 2b )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 586 +d0547b:= D(m0547b,x) +--R +--R +--R (273) +--R 3 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 2 2 3 4 2 2 2 4 2 2 +--R (b - 2a b )cos(x) + (b - 4a b )cos(x) + (- b - 6a b )cos(x) +--R + +--R 4 2 2 +--R b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 +--R (- 2b cos(x) + 4b cos(x) - 2b )cot(x) - b cos(x) +--R + +--R 4 2 4 +--R 2b cos(x) - b +--R * +--R csc(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) + 2a b cos(x) +--R + +--R 3 3 3 2 3 3 3 3 +--R 4a b cos(x) - 6a b cos(x) + (- 4a b - 4a b)cos(x) + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 3 4 3 3 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) +--R + +--R 3 2 3 3 +--R 8a b cos(x) - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 3 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 2 2 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 2 4 5 4 2 2 4 4 +--R (2b + 4a b + 4a )cos(x) + (3b + 4a b + 4a )cos(x) +--R + +--R 2 2 4 3 2 2 4 2 +--R (- 8a b - 8a )cos(x) + (- 8a b - 8a )cos(x) +--R + +--R 4 2 2 4 4 2 2 4 +--R (2b + 4a b + 4a )cos(x) + b + 4a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - 2b cos(x) - 4b cos(x) + 2b cos(x) + 8b cos(x) +--R + +--R 4 2 4 4 +--R 2b cos(x) - 4b cos(x) - 2b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 4 2 +--R - b cos(x) - 2b cos(x) + b cos(x) + 4b cos(x) + b cos(x) +--R + +--R 4 4 +--R - 2b cos(x) - b +--R * +--R csc(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 6 3 3 5 +--R (2a b + 2a b)cos(x) + (2a b + 4a b)cos(x) +--R + +--R 3 3 4 3 3 3 +--R (- 6a b - 2a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b - 2a b)cos(x) + (6a b + 4a b)cos(x) + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 4 2 2 5 +--R (b + 2a b )cos(x) + (2b + 4a b )cos(x) + (- b - 2a b )cos(x) +--R + +--R 4 2 2 4 4 2 2 3 4 2 2 2 +--R (- 4b - 8a b )cos(x) + (- b - 2a b )cos(x) + (2b + 4a b )cos(x) +--R + +--R 4 2 2 +--R (b + 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 5 +--R (- 4a b cos(x) - 4a b )sin(x) +--R + +--R 3 3 3 3 3 2 +--R (2a b - 4a b)cos(x) + (2a b - 8a b)cos(x) +--R + +--R 3 3 3 3 +--R (- 2a b - 12a b)cos(x) + 2a b - 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (- 4a b cos(x) + 8a b cos(x) - 4a b )cot(x) - 2a b cos(x) +--R + +--R 3 2 3 +--R 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 4 2 2 2 2 2 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )cot(x) + 8a cos(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (- 12a b + 8a )cos(x) + (- 8a b - 8a )cos(x) + 4a b - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 5 2 2 4 2 2 3 +--R - 8a b cos(x) - 8a b cos(x) + 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R 16a b cos(x) - 8a b cos(x) - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 2 2 2 2 +--R - 4a b cos(x) - 4a b +--R * +--R csc(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 3 3 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 3 3 4 3 3 +--R (4a b + 8a b)cos(x) + (6a b + 8a b)cos(x) - 16a b cos(x) +--R + +--R 3 2 3 3 3 3 +--R - 16a b cos(x) + (4a b + 8a b)cos(x) + 2a b + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 3 5 3 4 +--R - 4a b cos(x) - 8a b cos(x) + 4a b cos(x) +--R + +--R 3 3 3 2 3 3 +--R 16a b cos(x) + 4a b cos(x) - 8a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R - 2a b cos(x) - 4a b cos(x) + 2a b cos(x) + 8a b cos(x) +--R + +--R 3 2 3 3 +--R 2a b cos(x) - 4a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 6 2 2 5 2 2 4 2 2 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 6 2 2 5 2 2 4 2 2 3 +--R 4a b cos(x) + 4a b cos(x) - 12a b cos(x) - 16a b cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R 4a b cos(x) + 12a b cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 3 7 3 3 6 +--R (2a b + 4a b)cos(x) + (4a b + 8a b)cos(x) +--R + +--R 3 3 5 3 3 4 +--R (- 2a b - 4a b)cos(x) + (- 8a b - 16a b)cos(x) +--R + +--R 3 3 3 3 3 2 3 3 +--R (- 2a b - 4a b)cos(x) + (4a b + 8a b)cos(x) + (2a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 5 +--R (- 2a b cos(x) - 2a b )sin(x) +--R + +--R 4 2 2 3 4 2 2 2 4 2 2 4 +--R (b - 2a b )cos(x) + (b - 4a b )cos(x) + (- b - 6a b )cos(x) + b +--R + +--R 2 2 +--R - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 4 2 4 2 4 4 4 2 +--R (- 2b cos(x) + 4b cos(x) - 2b )cot(x) - b cos(x) + 2b cos(x) +--R + +--R 4 +--R - b +--R * +--R csc(x) +--R + +--R 3 4 3 2 3 2 3 4 +--R (2a b cos(x) - 4a b cos(x) + 2a b )cot(x) + 2a b cos(x) +--R + +--R 3 3 3 2 3 3 3 3 +--R 4a b cos(x) - 6a b cos(x) + (- 4a b - 4a b)cos(x) + 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 4a b cos(x) - 4a b cos(x) + 8a b cos(x) + 8a b cos(x) +--R + +--R 3 3 +--R - 4a b cos(x) - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 3 4 3 3 3 2 +--R - 2a b cos(x) - 2a b cos(x) + 4a b cos(x) + 4a b cos(x) +--R + +--R 3 3 +--R - 2a b cos(x) - 2a b +--R * +--R csc(x) +--R + +--R 2 2 5 2 2 4 2 2 3 2 2 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 2 2 2 2 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 2 2 4 5 4 2 2 4 4 +--R (2b + 4a b + 4a )cos(x) + (3b + 4a b + 4a )cos(x) +--R + +--R 2 2 4 3 2 2 4 2 +--R (- 8a b - 8a )cos(x) + (- 8a b - 8a )cos(x) +--R + +--R 4 2 2 4 4 2 2 4 +--R (2b + 4a b + 4a )cos(x) + b + 4a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R - 2b cos(x) - 4b cos(x) + 2b cos(x) + 8b cos(x) +--R + +--R 4 2 4 4 +--R 2b cos(x) - 4b cos(x) - 2b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 4 5 4 4 4 3 4 2 +--R - b cos(x) - 2b cos(x) + b cos(x) + 4b cos(x) + b cos(x) +--R + +--R 4 4 +--R - 2b cos(x) - b +--R * +--R csc(x) +--R + +--R 3 6 3 5 3 4 3 3 +--R 2a b cos(x) + 4a b cos(x) - 2a b cos(x) - 8a b cos(x) +--R + +--R 3 2 3 3 +--R - 2a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 6 3 3 5 +--R (2a b + 2a b)cos(x) + (2a b + 4a b)cos(x) +--R + +--R 3 3 4 3 3 3 +--R (- 6a b - 2a b)cos(x) + (- 8a b - 8a b)cos(x) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b - 2a b)cos(x) + (6a b + 4a b)cos(x) + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 2 2 7 4 2 2 6 4 2 2 5 +--R (b + 2a b )cos(x) + (2b + 4a b )cos(x) + (- b - 2a b )cos(x) +--R + +--R 4 2 2 4 4 2 2 3 4 2 2 2 +--R (- 4b - 8a b )cos(x) + (- b - 2a b )cos(x) + (2b + 4a b )cos(x) +--R + +--R 4 2 2 +--R (b + 2a b )cos(x) +--R / +--R 5 4 5 2 5 3 +--R (2b cos(x) - 4b cos(x) + 2b )sin(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 4 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R 2b cos(x) + 4b cos(x) - 2b cos(x) - 8b cos(x) - 2b cos(x) +--R + +--R 5 5 +--R 4b cos(x) + 2b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 4 2 4 3 +--R (4a b cos(x) - 8a b cos(x) + 4a b )sin(x) +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 +--R 8a b cos(x) + 8a b cos(x) - 16a b cos(x) - 16a b cos(x) +--R + +--R 2 3 2 3 +--R 8a b cos(x) + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 4 5 4 4 4 3 +--R 4a b cos(x) + 8a b cos(x) - 4a b cos(x) - 16a b cos(x) +--R + +--R 4 2 4 4 +--R - 4a b cos(x) + 8a b cos(x) + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 5 2 5 3 +--R (2b cos(x) - 4b cos(x) + 2b )sin(x) +--R + +--R 4 5 4 4 4 3 4 2 +--R 4a b cos(x) + 4a b cos(x) - 8a b cos(x) - 8a b cos(x) +--R + +--R 4 4 +--R 4a b cos(x) + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 5 5 5 4 5 3 5 2 +--R 2b cos(x) + 4b cos(x) - 2b cos(x) - 8b cos(x) - 2b cos(x) +--R + +--R 5 5 +--R 4b cos(x) + 2b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 288 + +--S 289 of 586 +t0548:= sin(x)/(a+a*csc(x)) +--R +--R +--R sin(x) +--R (274) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 586 +r0548:= -(cos(x)^2+x*cos(x)-sin(x)+1)/a/cos(x) +--R +--R +--R 2 +--R sin(x) - cos(x) - x cos(x) - 1 +--R (275) ------------------------------- +--R a cos(x) +--R Type: Expression(Integer) +--E 290 + +--S 291 of 586 +a0548:= integrate(t0548,x) +--R +--R +--R 2 +--R (- cos(x) - x - 1)sin(x) - cos(x) + (- x - 4)cos(x) - x - 3 +--R (276) ------------------------------------------------------------ +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 291 + +--S 292 of 586 +m0548:= a0548-r0548 +--R +--R +--R 2 2 +--R - sin(x) - 2cos(x)sin(x) - 3cos(x) - 2cos(x) + 1 +--R (277) -------------------------------------------------- +--R 2 +--R a cos(x)sin(x) + a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 292 + +--S 293 of 586 +d0548:= D(m0548,x) +--R +--R +--R (278) +--R 4 3 2 +--R - sin(x) + (- 2cos(x) - 1)sin(x) + sin(x) +--R + +--R 3 2 4 2 +--R (- 2cos(x) - cos(x) + 2cos(x) + 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 2 3 2 4 +--R a cos(x) sin(x) + (2a cos(x) + 2a cos(x) )sin(x) + a cos(x) +--R + +--R 3 2 +--R 2a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 293 + +--S 294 of 586 +t0549:= sin(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R sin(x) +--R (279) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 586 +r0549:= -1/2*(sin(x)*cos(x)^2-2*cos(x)^2-3*x*cos(x)-2+2*sin(x))/a/cos(x) +--R +--R +--R 2 2 +--R (- cos(x) - 2)sin(x) + 2cos(x) + 3x cos(x) + 2 +--R (280) ------------------------------------------------ +--R 2a cos(x) +--R Type: Expression(Integer) +--E 295 + +--S 296 of 586 +a0549:= integrate(t0549,x) +--R +--R +--R (281) +--R 2 3 2 +--R (- cos(x) + cos(x) + 3x + 2)sin(x) + cos(x) + 2cos(x) + (3x + 7)cos(x) +--R + +--R 3x + 6 +--R / +--R 2a sin(x) + 2a cos(x) + 2a +--R Type: Union(Expression(Integer),...) +--E 296 + +--S 297 of 586 +m0549:= a0549-r0549 +--R +--R +--R (282) +--R 2 2 4 2 +--R (cos(x) + 2)sin(x) + 4cos(x)sin(x) + cos(x) + 5cos(x) + 4cos(x) - 2 +--R ----------------------------------------------------------------------- +--R 2 +--R 2a cos(x)sin(x) + 2a cos(x) + 2a cos(x) +--R Type: Expression(Integer) +--E 297 + +--S 298 of 586 +d0549:= D(m0549,x) +--R +--R +--R (283) +--R 2 4 2 3 +--R (- cos(x) + 2)sin(x) + (- cos(x) + 4cos(x) + 2)sin(x) +--R + +--R 4 2 2 +--R (- 2cos(x) + cos(x) - 2)sin(x) +--R + +--R 4 3 2 6 4 +--R (- cos(x) + 4cos(x) + 3cos(x) - 4cos(x) - 2)sin(x) - cos(x) - cos(x) +--R + +--R 2 +--R 2cos(x) +--R / +--R 2 2 3 2 4 +--R 2a cos(x) sin(x) + (4a cos(x) + 4a cos(x) )sin(x) + 2a cos(x) +--R + +--R 3 2 +--R 4a cos(x) + 2a cos(x) +--R Type: Expression(Integer) +--E 298 + +--S 299 of 586 +t0550:= sin(x)^3/(a+a*csc(x)) +--R +--R +--R 3 +--R sin(x) +--R (284) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 299 + +--S 300 of 586 +r0550:= 1/6*(2*cos(x)^4+3*sin(x)*cos(x)^2-12*cos(x)^2-_ + 9*x*cos(x)-6+6*sin(x))/a/cos(x) +--R +--R +--R 2 4 2 +--R (3cos(x) + 6)sin(x) + 2cos(x) - 12cos(x) - 9x cos(x) - 6 +--R (285) ----------------------------------------------------------- +--R 6a cos(x) +--R Type: Expression(Integer) +--E 300 + +--S 301 of 586 +a0550:= integrate(t0550,x) +--R +--R +--R (286) +--R 3 2 4 3 +--R (2cos(x) + 3cos(x) - 9cos(x) - 9x - 10)sin(x) + 2cos(x) - cos(x) +--R + +--R 2 +--R - 12cos(x) + (- 9x - 31)cos(x) - 9x - 22 +--R / +--R 6a sin(x) + 6a cos(x) + 6a +--R Type: Union(Expression(Integer),...) +--E 301 + +--S 302 of 586 +m0550:= a0550-r0550 +--R +--R +--R (287) +--R 2 2 4 2 +--R (- 3cos(x) - 6)sin(x) - 16cos(x)sin(x) - 3cos(x) - 19cos(x) +--R + +--R - 16cos(x) + 6 +--R / +--R 2 +--R 6a cos(x)sin(x) + 6a cos(x) + 6a cos(x) +--R Type: Expression(Integer) +--E 302 + +--S 303 of 586 +d0550:= D(m0550,x) +--R +--R +--R (288) +--R 2 4 2 3 +--R (cos(x) - 2)sin(x) + (cos(x) - 4cos(x) - 2)sin(x) +--R + +--R 4 2 2 +--R (2cos(x) - cos(x) + 2)sin(x) +--R + +--R 4 3 2 6 4 +--R (cos(x) - 4cos(x) - 3cos(x) + 4cos(x) + 2)sin(x) + cos(x) + cos(x) +--R + +--R 2 +--R - 2cos(x) +--R / +--R 2 2 3 2 4 +--R 2a cos(x) sin(x) + (4a cos(x) + 4a cos(x) )sin(x) + 2a cos(x) +--R + +--R 3 2 +--R 4a cos(x) + 2a cos(x) +--R Type: Expression(Integer) +--E 303 + +--S 304 of 586 +t0551:= cos(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R cos(x) +--R (289) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 304 + +--S 305 of 586 +r0551:= 1/2*(-x-2*cos(x)+cos(x)*sin(x))/a +--R +--R +--R cos(x)sin(x) - 2cos(x) - x +--R (290) -------------------------- +--R 2a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 586 +a0551:= integrate(t0551,x) +--R +--R +--R cos(x)sin(x) - 2cos(x) - x +--R (291) -------------------------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 306 + +--S 307 of 586 +m0551:= a0551-r0551 +--R +--R +--R (292) 0 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 586 +d0551:= D(m0551,x) +--R +--R +--R (293) 0 +--R Type: Expression(Integer) +--E 308 + +--S 309 of 586 +t0552:= cos(x)^4/(a+a*csc(x)) +--R +--R +--R 4 +--R cos(x) +--R (294) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 309 + +--S 310 of 586 +r0552:= 1/24/a*(-3*cos(x)*sin(x)+6*cos(x)^3*sin(x)-3*x-8*cos(x)^3) +--R +--R +--R 3 3 +--R (6cos(x) - 3cos(x))sin(x) - 8cos(x) - 3x +--R (295) ------------------------------------------ +--R 24a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 586 +a0552:= integrate(t0552,x) +--R +--R +--R 3 3 +--R (6cos(x) - 3cos(x))sin(x) - 8cos(x) - 3x +--R (296) ------------------------------------------ +--R 24a +--R Type: Union(Expression(Integer),...) +--E 311 + +--S 312 of 586 +m0552:= a0552-r0552 +--R +--R +--R (297) 0 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 586 +d0552:= D(m0552,x) +--R +--R +--R (298) 0 +--R Type: Expression(Integer) +--E 313 + +--S 314 of 586 +t0553:= tan(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R tan(x) +--R (299) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 314 + +--S 315 of 586 +r0553:= -1/3*(-4*sin(x)*cos(x)^2+3*cos(x)^2-1+sin(x)+3*x*cos(x)^3)/a/cos(x)^3 +--R +--R +--R 2 3 2 +--R (4cos(x) - 1)sin(x) - 3x cos(x) - 3cos(x) + 1 +--R (300) ------------------------------------------------ +--R 3 +--R 3a cos(x) +--R Type: Expression(Integer) +--E 315 + +--S 316 of 586 +a0553:= integrate(t0553,x) +--R +--R +--R 2 +--R ((- 3x - 2)cos(x) + 1)sin(x) - 4cos(x) + (- 3x - 2)cos(x) + 2 +--R (301) -------------------------------------------------------------- +--R 3a cos(x)sin(x) + 3a cos(x) +--R Type: Union(Expression(Integer),...) +--E 316 + +--S 317 of 586 +m0553:= a0553-r0553 +--R +--R +--R (302) +--R 2 2 3 4 3 2 +--R (- 4cos(x) + 1)sin(x) - 2cos(x) sin(x) - 4cos(x) - 2cos(x) + 5cos(x) - 1 +--R ----------------------------------------------------------------------------- +--R 3 3 +--R 3a cos(x) sin(x) + 3a cos(x) +--R Type: Expression(Integer) +--E 317 + +--S 318 of 586 +d0553:= D(m0553,x) +--R +--R +--R (303) +--R 2 4 2 3 2 2 +--R (- 4cos(x) + 3)sin(x) + (- 4cos(x) + 3)sin(x) + (6cos(x) - 3)sin(x) +--R + +--R 4 2 6 4 2 +--R (- 4cos(x) + 7cos(x) - 3)sin(x) + 4cos(x) - 5cos(x) + cos(x) +--R / +--R 4 2 4 4 +--R 3a cos(x) sin(x) + 6a cos(x) sin(x) + 3a cos(x) +--R Type: Expression(Integer) +--E 318 + +--S 319 of 586 +t0554:= cot(x)/(a+a*csc(x)) +--R +--R +--R cot(x) +--R (304) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 586 +r0554:= log(1+sin(x))/a +--R +--R +--R log(sin(x) + 1) +--R (305) --------------- +--R a +--R Type: Expression(Integer) +--E 320 + +--S 321 of 586 +a0554:= integrate(t0554,x) +--R +--R +--R sin(x) + cos(x) + 1 2 +--R 2log(-------------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (306) ------------------------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 321 + +--S 322 of 586 +m0554:= a0554-r0554 +--R +--R +--R sin(x) + cos(x) + 1 2 +--R - log(sin(x) + 1) + 2log(-------------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (307) --------------------------------------------------------------- +--R a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 586 +d0554:= D(m0554,x) +--R +--R +--R (308) +--R 3 2 2 3 +--R sin(x) - cos(x)sin(x) + (cos(x) - 1)sin(x) - cos(x) + cos(x) +--R / +--R 2 2 2 +--R (a cos(x) + a)sin(x) + (a cos(x) + 3a cos(x) + 2a)sin(x) + a cos(x) +--R + +--R 2a cos(x) + a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 586 +t0555:= cot(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R cot(x) +--R (309) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 324 + +--S 325 of 586 +r0555:= -(x+atanh(cos(x)))/a +--R +--R +--R - atanh(cos(x)) - x +--R (310) ------------------- +--R a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 586 +a0555:= integrate(t0555,x) +--R +--R +--R sin(x) +--R log(----------) - x +--R cos(x) + 1 +--R (311) ------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 326 + +--S 327 of 586 +m0555:= a0555-r0555 +--R +--R +--R sin(x) +--R log(----------) + atanh(cos(x)) +--R cos(x) + 1 +--R (312) ------------------------------- +--R a +--R Type: Expression(Integer) +--E 327 + +--S 328 of 586 +d0555:= D(m0555,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (313) -------------------------------- +--R 2 +--R (a cos(x) - a)sin(x) +--R Type: Expression(Integer) +--E 328 + +--S 329 of 586 +t0556:= cot(x)^4/(a+a*csc(x)) +--R +--R +--R 4 +--R cot(x) +--R (314) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 329 + +--S 330 of 586 +r0556:= x/a+1/2*atanh(cos(x))/a+cot(x)/a-1/2*cot(x)*csc(x)/a +--R +--R +--R atanh(cos(x)) - cot(x)csc(x) + 2cot(x) + 2x +--R (315) ------------------------------------------- +--R 2a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 586 +a0556:= integrate(t0556,x) +--R +--R +--R (316) +--R 2 sin(x) 2 +--R (- cos(x) + 1)log(----------) - 2cos(x)sin(x) + 2x cos(x) + cos(x) - 2x +--R cos(x) + 1 +--R ------------------------------------------------------------------------- +--R 2 +--R 2a cos(x) - 2a +--R Type: Union(Expression(Integer),...) +--E 331 + +--S 332 of 586 +m0556:= a0556-r0556 +--R +--R +--R (317) +--R 2 sin(x) 2 +--R (- cos(x) + 1)log(----------) + (- cos(x) + 1)atanh(cos(x)) +--R cos(x) + 1 +--R + +--R 2 2 +--R - 2cos(x)sin(x) + (cos(x) - 1)cot(x)csc(x) + (- 2cos(x) + 2)cot(x) +--R + +--R cos(x) +--R / +--R 2 +--R 2a cos(x) - 2a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 586 +d0556:= D(m0556,x) +--R +--R +--R (318) +--R 2 3 3 2 2 +--R (- 2cos(x) - 2)sin(x) + (- cos(x) + cos(x) + cos(x) + 1)sin(x) +--R + +--R 4 2 2 4 2 +--R ((- 2cos(x) + 4cos(x) - 2)cot(x) - cos(x) + 2cos(x) - 1)csc(x) +--R + +--R 4 2 2 2 +--R (2cos(x) - 4cos(x) + 2)cot(x) - 2cos(x) + 2 +--R * +--R sin(x) +--R + +--R 5 3 +--R - cos(x) + 2cos(x) - cos(x) +--R / +--R 4 2 +--R (2a cos(x) - 4a cos(x) + 2a)sin(x) +--R Type: Expression(Integer) +--E 333 + +--S 334 of 586 +t0557:= sec(x)/(a+a*csc(x)) +--R +--R +--R sec(x) +--R (319) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 586 +r0557:= 1/2*atanh(sin(x))/a+1/2/a/(1+sin(x)) +--R +--R +--R (sin(x) + 1)atanh(sin(x)) + 1 +--R (320) ----------------------------- +--R 2a sin(x) + 2a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 586 +a0557:= integrate(t0557,x) +--R +--R +--R (321) +--R sin(x) + cos(x) + 1 +--R (sin(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R sin(x) - cos(x) - 1 +--R (- sin(x) - 1)log(-------------------) - sin(x) +--R cos(x) + 1 +--R / +--R 2a sin(x) + 2a +--R Type: Union(Expression(Integer),...) +--E 336 + +--S 337 of 586 +m0557:= a0557-r0557 +--R +--R +--R (322) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) - 1 +--R cos(x) + 1 cos(x) + 1 +--R ----------------------------------------------------------------------- +--R 2a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 586 +d0557:= D(m0557,x) +--R +--R +--R (323) +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R / +--R 4 2 2 2 +--R 2a sin(x) + (- 2a cos(x) - 4a cos(x) - 4a)sin(x) + 2a cos(x) +--R + +--R 4a cos(x) + 2a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 586 +t0558:= sec(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R sec(x) +--R (324) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 586 +r0558:= 1/3/a/cos(x)^3*(-sin(x)+sin(x)*cos(x)^2+1) +--R +--R +--R 2 +--R (cos(x) - 1)sin(x) + 1 +--R (325) ----------------------- +--R 3 +--R 3a cos(x) +--R Type: Expression(Integer) +--E 340 + +--S 341 of 586 +a0558:= integrate(t0558,x) +--R +--R +--R 2 +--R (cos(x) + 1)sin(x) - cos(x) + cos(x) + 2 +--R (326) ----------------------------------------- +--R 3a cos(x)sin(x) + 3a cos(x) +--R Type: Union(Expression(Integer),...) +--E 341 + +--S 342 of 586 +m0558:= a0558-r0558 +--R +--R +--R (327) +--R 2 2 3 4 3 2 +--R (- cos(x) + 1)sin(x) + cos(x) sin(x) - cos(x) + cos(x) + 2cos(x) - 1 +--R ------------------------------------------------------------------------- +--R 3 3 +--R 3a cos(x) sin(x) + 3a cos(x) +--R Type: Expression(Integer) +--E 342 + +--S 343 of 586 +d0558:= D(m0558,x) +--R +--R +--R (328) +--R 2 4 2 3 2 2 +--R (- cos(x) + 3)sin(x) + (- cos(x) + 3)sin(x) + (3cos(x) - 3)sin(x) +--R + +--R 4 2 6 4 2 +--R (- cos(x) + 4cos(x) - 3)sin(x) + cos(x) - 2cos(x) + cos(x) +--R / +--R 4 2 4 4 +--R 3a cos(x) sin(x) + 6a cos(x) sin(x) + 3a cos(x) +--R Type: Expression(Integer) +--E 343 + +--S 344 of 586 +t0559:= sec(x)^3/(a+a*csc(x)) +--R +--R +--R 3 +--R sec(x) +--R (329) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 586 +r0559:= 1/8/cos(x)^4*(atanh(sin(x))*cos(x)^4-2*sin(x)+2+sin(x)*cos(x)^2)/a +--R +--R +--R 4 2 +--R cos(x) atanh(sin(x)) + (cos(x) - 2)sin(x) + 2 +--R (330) ---------------------------------------------- +--R 4 +--R 8a cos(x) +--R Type: Expression(Integer) +--E 345 + +--S 346 of 586 +a0559:= integrate(t0559,x) +--R +--R +--R (331) +--R 2 2 sin(x) + cos(x) + 1 +--R (cos(x) sin(x) + cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 sin(x) - cos(x) - 1 +--R (- cos(x) sin(x) - cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (- 2cos(x) + 1)sin(x) - 3cos(x) + 3 +--R / +--R 2 2 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Union(Expression(Integer),...) +--E 346 + +--S 347 of 586 +m0559:= a0559-r0559 +--R +--R +--R (332) +--R 4 4 sin(x) + cos(x) + 1 +--R (cos(x) sin(x) + cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 sin(x) - cos(x) - 1 +--R (- cos(x) sin(x) - cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 4 2 2 +--R (- cos(x) sin(x) - cos(x) )atanh(sin(x)) + (- cos(x) + 2)sin(x) +--R + +--R 4 4 2 +--R - 2cos(x) sin(x) - 3cos(x) + 3cos(x) - 2 +--R / +--R 4 4 +--R 8a cos(x) sin(x) + 8a cos(x) +--R Type: Expression(Integer) +--E 347 + +--S 348 of 586 +d0559:= D(m0559,x) +--R +--R +--R (333) +--R 2 7 +--R (- 2cos(x) + 8)sin(x) +--R + +--R 5 4 3 2 5 +--R (- 2cos(x) + cos(x) + 4cos(x) + 4cos(x) - 16cos(x) - 24)sin(x) +--R + +--R 5 4 2 4 +--R (- 2cos(x) - cos(x) + 2cos(x) )sin(x) +--R + +--R 7 6 5 4 3 2 +--R - 2cos(x) + cos(x) + 4cos(x) - 10cos(x) - 20cos(x) - 2cos(x) +--R + +--R 32cos(x) + 24 +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 2 2 +--R (- 2cos(x) - cos(x) + 4cos(x) + 2cos(x) - 4cos(x) - 4cos(x) )sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 2cos(x) - 2cos(x) + cos(x) + 2cos(x) + 9cos(x) + 16cos(x) +--R + +--R - 16cos(x) - 8 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R 2cos(x) - cos(x) - 6cos(x) - cos(x) + 4cos(x) + 2cos(x) +--R / +--R 5 5 5 4 +--R 8a cos(x) sin(x) + 8a cos(x) sin(x) +--R + +--R 7 6 5 3 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 2 +--R (- 8a cos(x) - 16a cos(x) - 16a cos(x) )sin(x) +--R + +--R 7 6 5 7 6 +--R (8a cos(x) + 16a cos(x) + 8a cos(x) )sin(x) + 8a cos(x) + 16a cos(x) +--R + +--R 5 +--R 8a cos(x) +--R Type: Expression(Integer) +--E 348 + +--S 349 of 586 +t0560:= sec(x)^4/(a+a*csc(x)) +--R +--R +--R 4 +--R sec(x) +--R (334) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 586 +r0560:= 1/15/a/cos(x)^5*(2*sin(x)*cos(x)^4+sin(x)*cos(x)^2-3*sin(x)+3) +--R +--R +--R 4 2 +--R (2cos(x) + cos(x) - 3)sin(x) + 3 +--R (335) ---------------------------------- +--R 5 +--R 15a cos(x) +--R Type: Expression(Integer) +--E 350 + +--S 351 of 586 +a0560:= integrate(t0560,x) +--R +--R +--R 3 2 4 3 2 +--R (3cos(x) + 2cos(x) + 1)sin(x) - 2cos(x) + 3cos(x) + cos(x) + 4 +--R (336) ------------------------------------------------------------------- +--R 3 3 +--R 15a cos(x) sin(x) + 15a cos(x) +--R Type: Union(Expression(Integer),...) +--E 351 + +--S 352 of 586 +m0560:= a0560-r0560 +--R +--R +--R (337) +--R 4 2 2 5 6 5 +--R (- 2cos(x) - cos(x) + 3)sin(x) + 3cos(x) sin(x) - 2cos(x) + 3cos(x) +--R + +--R 4 2 +--R cos(x) + 4cos(x) - 3 +--R / +--R 5 5 +--R 15a cos(x) sin(x) + 15a cos(x) +--R Type: Expression(Integer) +--E 352 + +--S 353 of 586 +d0560:= D(m0560,x) +--R +--R +--R (338) +--R 4 2 4 4 2 3 +--R (- 2cos(x) - 3cos(x) + 15)sin(x) + (- 2cos(x) - 3cos(x) + 15)sin(x) +--R + +--R 2 2 6 4 2 +--R (15cos(x) - 15)sin(x) + (- 2cos(x) - cos(x) + 18cos(x) - 15)sin(x) +--R + +--R 8 6 4 2 +--R 2cos(x) - cos(x) - 4cos(x) + 3cos(x) +--R / +--R 6 2 6 6 +--R 15a cos(x) sin(x) + 30a cos(x) sin(x) + 15a cos(x) +--R Type: Expression(Integer) +--E 353 + +--S 354 of 586 +t0561:= csc(x)^2/(a+a*csc(x)) +--R +--R +--R 2 +--R csc(x) +--R (339) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 354 + +--S 355 of 586 +r0561:= -1/a/cos(x)*(atanh(cos(x))*cos(x)+sin(x)-1) +--R +--R +--R - cos(x)atanh(cos(x)) - sin(x) + 1 +--R (340) ---------------------------------- +--R a cos(x) +--R Type: Expression(Integer) +--E 355 + +--S 356 of 586 +a0561:= integrate(t0561,x) +--R +--R +--R sin(x) +--R (sin(x) + cos(x) + 1)log(----------) + 2cos(x) + 2 +--R cos(x) + 1 +--R (341) -------------------------------------------------- +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 356 + +--S 357 of 586 +m0561:= a0561-r0561 +--R +--R +--R (342) +--R 2 sin(x) +--R (cos(x)sin(x) + cos(x) + cos(x))log(----------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (cos(x)sin(x) + cos(x) + cos(x))atanh(cos(x)) + sin(x) + cos(x)sin(x) +--R + +--R 2 +--R 2cos(x) + cos(x) - 1 +--R / +--R 2 +--R a cos(x)sin(x) + a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 357 + +--S 358 of 586 +d0561:= D(m0561,x) +--R +--R +--R (343) +--R 2 5 3 2 4 +--R (cos(x) - 1)sin(x) + (3cos(x) + cos(x) - 2cos(x) - 1)sin(x) +--R + +--R 4 3 2 3 +--R (2cos(x) + 2cos(x) - cos(x) + 1)sin(x) +--R + +--R 5 4 3 2 2 +--R (4cos(x) + 3cos(x) - 4cos(x) - 2cos(x) + 2cos(x) + 1)sin(x) +--R + +--R 6 5 3 2 7 6 +--R (cos(x) + 2cos(x) - 2cos(x) - cos(x) )sin(x) + cos(x) + 2cos(x) +--R + +--R 4 3 +--R - 2cos(x) - cos(x) +--R / +--R 4 2 3 +--R (a cos(x) - a cos(x) )sin(x) +--R + +--R 5 4 3 2 2 +--R (2a cos(x) + 2a cos(x) - 2a cos(x) - 2a cos(x) )sin(x) +--R + +--R 6 5 3 2 +--R (a cos(x) + 2a cos(x) - 2a cos(x) - a cos(x) )sin(x) +--R Type: Expression(Integer) +--E 358 + +--S 359 of 586 +t0562:= csc(x)^3/(a+a*csc(x)) +--R +--R +--R 3 +--R csc(x) +--R (344) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 359 + +--S 360 of 586 +r0562:= atanh(cos(x))/a-cot(x)/a-cos(x)/a/(1+sin(x)) +--R +--R +--R (sin(x) + 1)atanh(cos(x)) - cot(x)sin(x) - cot(x) - cos(x) +--R (345) ---------------------------------------------------------- +--R a sin(x) + a +--R Type: Expression(Integer) +--E 360 + +--S 361 of 586 +a0562:= integrate(t0562,x) +--R +--R +--R (346) +--R 2 sin(x) +--R ((- cos(x) - 1)sin(x) + cos(x) - 1)log(----------) +--R cos(x) + 1 +--R + +--R 2 +--R (- 3cos(x) - 2)sin(x) - cos(x) - cos(x) +--R / +--R 2 +--R (a cos(x) + a)sin(x) - a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 361 + +--S 362 of 586 +m0562:= a0562-r0562 +--R +--R +--R (347) +--R 2 2 2 +--R ((- cos(x) - 1)sin(x) + (cos(x) - cos(x) - 2)sin(x) + cos(x) - 1) +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R ((- cos(x) - 1)sin(x) + (cos(x) - cos(x) - 2)sin(x) + cos(x) - 1) +--R * +--R atanh(cos(x)) +--R + +--R 2 +--R ((cos(x) + 1)cot(x) - 3cos(x) - 2)sin(x) +--R + +--R 2 +--R ((- cos(x) + cos(x) + 2)cot(x) - 3cos(x) - 2)sin(x) +--R + +--R 2 3 2 +--R (- cos(x) + 1)cot(x) - cos(x) - cos(x) +--R / +--R 2 2 2 +--R (a cos(x) + a)sin(x) + (- a cos(x) + a cos(x) + 2a)sin(x) - a cos(x) + a +--R Type: Expression(Integer) +--E 362 + +--S 363 of 586 +d0562:= D(m0562,x) +--R +--R +--R (348) +--R 2 6 +--R (- cos(x) - 1)sin(x) +--R + +--R 3 2 2 3 2 +--R (- cos(x) - cos(x) + cos(x) + 1)cot(x) + 4cos(x) - 2cos(x) +--R + +--R - 2cos(x) - 4 +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (2cos(x) - 2cos(x) - 6cos(x) + 2cos(x) + 4)cot(x) + 2cos(x) +--R + +--R 3 2 +--R 10cos(x) - 5cos(x) - 6cos(x) - 3 +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 3 2 2 5 +--R (- cos(x) + 5cos(x) + cos(x) - 11cos(x) + 6)cot(x) + 3cos(x) +--R + +--R 4 3 2 +--R 3cos(x) + 2cos(x) - 8cos(x) - 3cos(x) + 3 +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (- 2cos(x) + 4cos(x) + 4cos(x) - 8cos(x) - 2cos(x) + 4)cot(x) +--R + +--R 6 5 4 3 2 +--R cos(x) + 10cos(x) + cos(x) - 15cos(x) - 6cos(x) + 5cos(x) + 4 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (- cos(x) + cos(x) + 2cos(x) - 2cos(x) - cos(x) + 1)cot(x) +--R + +--R 7 6 5 4 3 2 +--R - cos(x) - cos(x) + 9cos(x) + 3cos(x) - 13cos(x) - 3cos(x) +--R + +--R 5cos(x) + 1 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) + cos(x) + 2cos(x) - 2cos(x) - cos(x) + cos(x) +--R / +--R 3 2 5 +--R (a cos(x) + a cos(x) - a cos(x) - a)sin(x) +--R + +--R 4 3 2 4 +--R (- 2a cos(x) + 2a cos(x) + 6a cos(x) - 2a cos(x) - 4a)sin(x) +--R + +--R 5 4 3 2 3 +--R (a cos(x) - 5a cos(x) - a cos(x) + 11a cos(x) - 6a)sin(x) +--R + +--R 5 4 3 2 +--R (2a cos(x) - 4a cos(x) - 4a cos(x) + 8a cos(x) + 2a cos(x) - 4a) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R (a cos(x) - a cos(x) - 2a cos(x) + 2a cos(x) + a cos(x) - a)sin(x) +--R Type: Expression(Integer) +--E 363 + +--S 364 of 586 +t0563:= csc(x)^4/(a+a*csc(x)) +--R +--R +--R 4 +--R csc(x) +--R (349) ------------ +--R a csc(x) + a +--R Type: Expression(Integer) +--E 364 + +--S 365 of 586 +r0563:= -3/2*atanh(cos(x))/a+cot(x)/a-1/2*cot(x)*csc(x)/a+cos(x)/a/(1+sin(x)) +--R +--R +--R (350) +--R (- 3sin(x) - 3)atanh(cos(x)) + (- cot(x)csc(x) + 2cot(x))sin(x) +--R + +--R - cot(x)csc(x) + 2cot(x) + 2cos(x) +--R / +--R 2a sin(x) + 2a +--R Type: Expression(Integer) +--E 365 + +--S 366 of 586 +a0563:= integrate(t0563,x) +--R +--R +--R (351) +--R 2 3 2 sin(x) +--R ((3cos(x) - 3)sin(x) + 3cos(x) + 3cos(x) - 3cos(x) - 3)log(----------) +--R cos(x) + 1 +--R + +--R 2 3 2 +--R (- 2cos(x) - cos(x))sin(x) + 6cos(x) + 5cos(x) - 5cos(x) - 4 +--R / +--R 2 3 2 +--R (2a cos(x) - 2a)sin(x) + 2a cos(x) + 2a cos(x) - 2a cos(x) - 2a +--R Type: Union(Expression(Integer),...) +--E 366 + +--S 367 of 586 +m0563:= a0563-r0563 +--R +--R +--R (352) +--R 2 2 3 2 +--R (3cos(x) - 3)sin(x) + (3cos(x) + 6cos(x) - 3cos(x) - 6)sin(x) +--R + +--R 3 2 +--R 3cos(x) + 3cos(x) - 3cos(x) - 3 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 2 +--R (3cos(x) - 3)sin(x) + (3cos(x) + 6cos(x) - 3cos(x) - 6)sin(x) +--R + +--R 3 2 +--R 3cos(x) + 3cos(x) - 3cos(x) - 3 +--R * +--R atanh(cos(x)) +--R + +--R 2 2 2 +--R (cos(x) - 1)cot(x)csc(x) + (- 2cos(x) + 2)cot(x) - 2cos(x) +--R + +--R - cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (cos(x) + 2cos(x) - cos(x) - 2)cot(x)csc(x) +--R + +--R 3 2 3 2 +--R (- 2cos(x) - 4cos(x) + 2cos(x) + 4)cot(x) + 4cos(x) + 3cos(x) +--R + +--R - 4cos(x) - 4 +--R * +--R sin(x) +--R + +--R 3 2 +--R (cos(x) + cos(x) - cos(x) - 1)cot(x)csc(x) +--R + +--R 3 2 4 3 +--R (- 2cos(x) - 2cos(x) + 2cos(x) + 2)cot(x) - 2cos(x) + 4cos(x) +--R + +--R 2 +--R 7cos(x) - 3cos(x) - 4 +--R / +--R 2 2 +--R (2a cos(x) - 2a)sin(x) +--R + +--R 3 2 3 +--R (2a cos(x) + 4a cos(x) - 2a cos(x) - 4a)sin(x) + 2a cos(x) +--R + +--R 2 +--R 2a cos(x) - 2a cos(x) - 2a +--R Type: Expression(Integer) +--E 367 + +--S 368 of 586 +d0563:= D(m0563,x) +--R +--R +--R (353) +--R 3 2 6 +--R (3cos(x) - cos(x) - 7cos(x) - 1)sin(x) +--R + +--R 4 2 2 4 2 +--R ((- 2cos(x) + 4cos(x) - 2)cot(x) - cos(x) + 2cos(x) - 1)csc(x) +--R + +--R 4 2 2 4 3 2 +--R (2cos(x) - 4cos(x) + 2)cot(x) + 2cos(x) + 10cos(x) - 6cos(x) +--R + +--R - 22cos(x) - 4 +--R * +--R 5 +--R sin(x) +--R + +--R 5 4 3 2 +--R (- 4cos(x) - 8cos(x) + 8cos(x) + 16cos(x) - 4cos(x) - 8) +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 3 2 +--R - 2cos(x) - 4cos(x) + 4cos(x) + 8cos(x) - 2cos(x) - 4 +--R * +--R csc(x) +--R + +--R 5 4 3 2 2 +--R (4cos(x) + 8cos(x) - 8cos(x) - 16cos(x) + 4cos(x) + 8)cot(x) +--R + +--R 5 4 3 2 +--R 14cos(x) + 15cos(x) - 9cos(x) - 21cos(x) - 13cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) - 12cos(x) - 8cos(x) + 24cos(x) + 22cos(x) +--R + +--R - 12cos(x) - 12 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) - 6cos(x) - 4cos(x) + 12cos(x) + 11cos(x) - 6cos(x) +--R + +--R - 6 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 12cos(x) + 8cos(x) - 24cos(x) - 22cos(x) +--R + +--R 12cos(x) + 12 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) + 30cos(x) + 14cos(x) - 44cos(x) - 24cos(x) + 18cos(x) +--R + +--R 10 +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 +--R (- 4cos(x) - 12cos(x) + 24cos(x) + 12cos(x) - 12cos(x) - 8) +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 3 2 +--R - 2cos(x) - 6cos(x) + 12cos(x) + 6cos(x) - 6cos(x) - 4 +--R * +--R csc(x) +--R + +--R 6 5 3 2 2 +--R (4cos(x) + 12cos(x) - 24cos(x) - 12cos(x) + 12cos(x) + 8)cot(x) +--R + +--R 7 6 5 4 3 +--R 7cos(x) + 12cos(x) + 7cos(x) - 17cos(x) - 35cos(x) + 25cos(x) + 9 +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) - 4cos(x) + 2cos(x) + 8cos(x) + 2cos(x) +--R + +--R - 4cos(x) - 2 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) - 2cos(x) + cos(x) + 4cos(x) + cos(x) - 2cos(x) - 1 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 4cos(x) - 2cos(x) - 8cos(x) - 2cos(x) + 4cos(x) +--R + +--R 2 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 3 +--R 2cos(x) + 10cos(x) + 10cos(x) - 12cos(x) - 28cos(x) - 10cos(x) +--R + +--R 2 +--R 14cos(x) + 12cos(x) + 2 +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R 3cos(x) + 6cos(x) - 3cos(x) - 12cos(x) - 3cos(x) + 6cos(x) + 3cos(x) +--R / +--R 4 2 5 +--R (2a cos(x) - 4a cos(x) + 2a)sin(x) +--R + +--R 5 4 3 2 +--R (4a cos(x) + 8a cos(x) - 8a cos(x) - 16a cos(x) + 4a cos(x) + 8a) +--R * +--R 4 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2a cos(x) + 12a cos(x) + 8a cos(x) - 24a cos(x) - 22a cos(x) +--R + +--R 12a cos(x) + 12a +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 +--R 4a cos(x) + 12a cos(x) - 24a cos(x) - 12a cos(x) + 12a cos(x) +--R + +--R 8a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2a cos(x) + 4a cos(x) - 2a cos(x) - 8a cos(x) - 2a cos(x) +--R + +--R 4a cos(x) + 2a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 368 + +--S 369 of 586 +t0564:= sin(x)/(a+b*sin(x))^2 +--R +--R +--R sin(x) +--R (354) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 369 + +--S 370 of 586 +r0564:= -2*b*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ + a*cos(x)/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R x +--R a tan(-) + b +---------+ +--R 2 2 | 2 2 +--R (2b sin(x) + 2a b)atan(------------) + a cos(x)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (355) ----------------------------------------------------------- +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sin(x) + a b - a )\|- b + a +--R Type: Expression(Integer) +--E 370 + +--S 371 of 586 +a0564:= integrate(t0564,x) +--R +--R +--R (356) +--R [ +--R 2 +--R (b sin(x) + a b) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|b - a +--R / +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sin(x) + a b - a )\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 2b sin(x) - 2a b)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|- b + a +--R / +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sin(x) + a b - a )\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 371 + +--S 372 of 586 +m0564a:= a0564.1-r0564 +--R +--R +--R (357) +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +---------+ +-------+ +--R | 2 2 2 | 2 2 | 2 2 +--R - 2b\|b - a atan(------------) + \|- b + a \|b - a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (b - a )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 372 + +--S 373 of 586 +d0564a:= D(m0564a,x) +--R +--R +--R (358) +--R 4 2 2 4 3 2 3 x 2 +--R (((- b + a b )cos(x) - b )sin(x) + a b cos(x) - a b )tan(-) +--R 2 +--R + +--R 4 2 3 4 2 4 2 2 x +--R (2b sin(x) + 2a b sin(x) + 2b cos(x) + (2b - 2a b )cos(x))tan(-) +--R 2 +--R + +--R 4 2 2 4 3 2 3 +--R ((- b + a b )cos(x) - b )sin(x) + a b cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 2 3 5 2 3 4 3 2 2 4 +--R ((b - a b )cos(x) + b - a b )sin(x) + (- a b + a b )cos(x) + a b +--R + +--R 3 2 +--R - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 2 4 3 2 +--R (- 2b + 2a b )sin(x) + (- 2a b + 2a b )sin(x) +--R + +--R 5 2 3 2 5 2 3 +--R (- 2b + 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 5 2 3 4 3 2 2 4 +--R ((b - a b )cos(x) + b - a b )sin(x) + (- a b + a b )cos(x) + a b +--R + +--R 3 2 +--R - a b +--R / +--R 2 4 4 2 2 +--R (a b - a b )sin(x) +--R + +--R 5 3 3 5 5 5 +--R ((a b - 2a b + a b)cos(x) + a b - a b)sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (a b - 2a b + a )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 +--R (2a b - 2a b )sin(x) +--R + +--R 6 2 4 4 2 6 4 2 +--R ((2b - 4a b + 2a b )cos(x) + 2b - 2a b )sin(x) +--R + +--R 5 3 3 5 5 3 3 +--R (2a b - 4a b + 2a b)cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 +--R (a b - a b )sin(x) +--R + +--R 5 3 3 5 5 5 +--R ((a b - 2a b + a b)cos(x) + a b - a b)sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (a b - 2a b + a )cos(x) + a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 4 3 6 2 +--R (- a b + 2a b - a b)sin(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 7 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a )sin(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- a b + 2a b - a b)cos(x) - a b + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 5 2 2 +--R (- 2a b + 4a b - 2a b )sin(x) +--R + +--R 7 2 5 4 3 7 2 5 4 3 6 +--R ((- 2b + 4a b - 2a b )cos(x) - 2b + 2a b + 2a b - 2a b)sin(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 2 +--R (- a b + 2a b - a b)sin(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 7 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a )sin(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- a b + 2a b - a b)cos(x) - a b + 2a b - a b +--R Type: Expression(Integer) +--E 373 + +--S 374 of 586 +m0564b:= a0564.2-r0564 +--R +--R +--R (359) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R (a sin(x) + b cos(x) + b)\|- b + a 2 +--R - 2b atan(-------------------------------------) - 2b atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a +--R Type: Expression(Integer) +--E 374 + +--S 375 of 586 +d0564b:= D(m0564b,x) +--R +--R +--R (360) +--R 2 2 2 2 x 2 +--R (a b sin(x) + (- 2b cos(x) - 2b )sin(x) + a b cos(x) - a b)tan(-) +--R 2 +--R + +--R 2 2 2 2 2 x 2 +--R (4b sin(x) + 4b cos(x) + 4b cos(x))tan(-) + a b sin(x) +--R 2 +--R + +--R 2 2 2 +--R (- 2b cos(x) - 2b )sin(x) + a b cos(x) - a b +--R / +--R 2 2 4 2 3 3 3 3 +--R (a b - a )sin(x) + ((2a b - 2a b)cos(x) + 2a b - 2a b)sin(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 4 2 2 4 2 2 +--R (2a b - 2a b)sin(x) + ((4b - 4a b )cos(x) + 4b - 4a b )sin(x) +--R + +--R 3 3 2 3 3 3 3 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 3 3 3 3 +--R (a b - a )sin(x) + ((2a b - 2a b)cos(x) + 2a b - 2a b)sin(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + a b - a +--R Type: Expression(Integer) +--E 375 + +--S 376 of 586 +t0565:= sin(x)^2/(a+b*sin(x))^2 +--R +--R +--R 2 +--R sin(x) +--R (361) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 376 + +--S 377 of 586 +r0565:= x/b^2+2*a^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2/_ + (a^2-b^2)^(3/2)-4*a*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/_ + b^2/(a^2-b^2)^(1/2)+a^2*cos(x)/b/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (362) +--R x +--R a tan(-) + b +--R 3 3 2 2 4 2 +--R ((- 4a b + 2a b)sin(x) - 4a b + 2a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 2 2 2 3 | 2 2 +--R ((b - a b)x sin(x) - a b cos(x) + (a b - a )x)\|- b + a +--R / +--R +---------+ +--R 5 2 3 4 3 2 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|- b + a +--R Type: Expression(Integer) +--E 377 + +--S 378 of 586 +a0565:= integrate(t0565,x) +--R +--R +--R (363) +--R [ +--R 3 3 2 2 4 +--R ((2a b - a b)sin(x) + 2a b - a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 3 2 2 2 2 3 2 | 2 2 +--R (((b - a b)x - a b )sin(x) - a b cos(x) + (a b - a )x - a b)\|b - a +--R / +--R +-------+ +--R 5 2 3 4 3 2 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|b - a +--R , +--R +--R 3 3 2 2 4 +--R ((4a b - 2a b)sin(x) + 4a b - 2a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 3 2 2 2 2 3 2 +--R (((b - a b)x - a b )sin(x) - a b cos(x) + (a b - a )x - a b) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 2 3 4 3 2 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 378 + +--S 379 of 586 +m0565a:= a0565.1-r0565 +--R +--R +--R (364) +--R +---------+ +--R 2 3 | 2 2 +--R (2a b - a )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +---------+ +-------+ +--R 2 3 | 2 2 2 | 2 2 | 2 2 +--R (4a b - 2a )\|b - a atan(------------) - a b\|- b + a \|b - a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 4 2 2 | 2 2 | 2 2 +--R (b - a b )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 379 + +--S 380 of 586 +d0565a:= D(m0565a,x) +--R +--R +--R (365) +--R 4 3 2 5 4 3 2 +--R ((2a b - 3a b + a )cos(x) + 2a b - a b )sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 2a b + a b)cos(x) + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 2 3 4 +--R (- 4a b + 2a b )sin(x) + (- 4a b + 2a b)sin(x) +--R + +--R 4 3 2 2 4 3 2 5 +--R (- 4a b + 2a b )cos(x) + (- 4a b + 6a b - 2a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 5 4 3 2 +--R ((2a b - 3a b + a )cos(x) + 2a b - a b )sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 2a b + a b)cos(x) + 2a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 5 3 3 5 5 3 3 5 +--R ((2a b - 3a b + a b)cos(x) + 2a b - 3a b + a b)sin(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (- 2a b + 3a b - a )cos(x) + 2a b - 3a b + a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 2 2 4 4 2 6 +--R (- 4a b + 6a b - 2a b)sin(x) + (- 4a b + 6a b - 2a )sin(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 4a b + 6a b - 2a b)cos(x) + (- 4a b + 6a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 5 3 3 5 +--R ((2a b - 3a b + a b)cos(x) + 2a b - 3a b + a b)sin(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (- 2a b + 3a b - a )cos(x) + 2a b - 3a b + a +--R / +--R 2 5 4 3 2 +--R (a b - a b )sin(x) +--R + +--R 6 3 4 5 2 6 5 2 +--R ((a b - 2a b + a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (a b - 2a b + a b)cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 2 +--R (2a b - 2a b )sin(x) +--R + +--R 7 2 5 4 3 7 4 3 +--R ((2b - 4a b + 2a b )cos(x) + 2b - 2a b )sin(x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 +--R (a b - a b )sin(x) +--R + +--R 6 3 4 5 2 6 5 2 +--R ((a b - 2a b + a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (a b - 2a b + a b)cos(x) + a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 6 4 4 6 2 2 +--R (a b - 2a b + a b )sin(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R ((a b - 2a b + a b )cos(x) + a b - a b - a b + a b)sin(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (a b - 2a b + a b )cos(x) + a b - 2a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 2 +--R (2a b - 4a b + 2a b )sin(x) +--R + +--R 8 2 6 4 4 8 2 6 4 4 6 2 +--R ((2b - 4a b + 2a b )cos(x) + 2b - 2a b - 2a b + 2a b )sin(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 4a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 +--R (a b - 2a b + a b )sin(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R ((a b - 2a b + a b )cos(x) + a b - a b - a b + a b)sin(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (a b - 2a b + a b )cos(x) + a b - 2a b + a b +--R Type: Expression(Integer) +--E 380 + +--S 381 of 586 +m0565b:= a0565.2-r0565 +--R +--R +--R (366) +--R +---------+ +--R | 2 2 +--R 2 3 (a sin(x) + b cos(x) + b)\|- b + a +--R (4a b - 2a )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +---------+ +--R 2 3 2 | 2 2 +--R (4a b - 2a )atan(------------) - a b\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 2 | 2 2 +--R (b - a b )\|- b + a +--R Type: Expression(Integer) +--E 381 + +--S 382 of 586 +d0565b:= D(m0565b,x) +--R +--R +--R (367) +--R 2 2 4 2 3 3 3 3 +--R (- 2a b + a )sin(x) + ((4a b - 2a b)cos(x) + 4a b - 2a b)sin(x) +--R + +--R 2 2 4 2 2 2 4 +--R (- 2a b + a )cos(x) + 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 2 +--R (- 8a b + 4a b)sin(x) + (- 8a b + 4a b)cos(x) +--R + +--R 3 3 +--R (- 8a b + 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 3 3 3 3 +--R (- 2a b + a )sin(x) + ((4a b - 2a b)cos(x) + 4a b - 2a b)sin(x) +--R + +--R 2 2 4 2 2 2 4 +--R (- 2a b + a )cos(x) + 2a b - a +--R / +--R 2 4 4 2 2 5 3 3 5 3 3 +--R (a b - a b )sin(x) + ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 6 2 4 6 2 4 +--R (2a b - 2a b )sin(x) + ((4b - 4a b )cos(x) + 4b - 4a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 5 3 3 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 5 3 3 5 3 3 +--R (a b - a b )sin(x) + ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 4 2 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + a b - a b +--R Type: Expression(Integer) +--E 382 + +--S 383 of 586 +t0566:= sin(x)^3/(a+b*sin(x))^2 +--R +--R +--R 3 +--R sin(x) +--R (368) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 383 + +--S 384 of 586 +r0566:= -2*a*x/b^3-2*a^4*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^3/_ + (a^2-b^2)^(3/2)+6*a^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/_ + b^3/(a^2-b^2)^(1/2)-cos(x)/b^2-a^3*cos(x)/b^2/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (369) +--R x +--R a tan(-) + b +--R 2 3 4 3 2 5 2 +--R ((6a b - 4a b)sin(x) + 6a b - 4a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 3 3 +--R ((- b + a b )cos(x) + (- 2a b + 2a b)x)sin(x) +--R + +--R 3 3 2 2 4 +--R (- a b + 2a b)cos(x) + (- 2a b + 2a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 6 2 4 5 3 3 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|- b + a +--R Type: Expression(Integer) +--E 384 + +--S 385 of 586 +a0566:= integrate(t0566,x) +--R +--R +--R (370) +--R [ +--R 2 3 4 3 2 5 +--R ((3a b - 2a b)sin(x) + 3a b - 2a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 4 2 2 3 3 4 2 2 +--R ((- b + a b )cos(x) + (- 2a b + 2a b)x - b + 2a b )sin(x) +--R + +--R 3 3 2 2 4 3 3 +--R (- a b + 2a b)cos(x) + (- 2a b + 2a )x - a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 6 2 4 5 3 3 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|b - a +--R , +--R +--R 2 3 4 3 2 5 +--R ((- 6a b + 4a b)sin(x) - 6a b + 4a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 4 2 2 3 3 4 2 2 +--R ((- b + a b )cos(x) + (- 2a b + 2a b)x - b + 2a b )sin(x) +--R + +--R 3 3 2 2 4 3 3 +--R (- a b + 2a b)cos(x) + (- 2a b + 2a )x - a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 6 2 4 5 3 3 | 2 2 +--R ((b - a b )sin(x) + a b - a b )\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 385 + +--S 386 of 586 +m0566a:= a0566.1-r0566 +--R +--R +--R (371) +--R +---------+ +--R 2 2 4 | 2 2 +--R (3a b - 2a )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R 2 2 4 | 2 2 2 +--R (- 6a b + 4a )\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +-------+ +--R 3 2 | 2 2 | 2 2 +--R (- b + 2a b)\|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 5 2 3 | 2 2 | 2 2 +--R (b - a b )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 386 + +--S 387 of 586 +d0566a:= D(m0566a,x) +--R +--R +--R (372) +--R 2 4 4 2 6 2 4 4 2 +--R ((- 3a b + 5a b - 2a )cos(x) - 3a b + 2a b )sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (3a b - 2a b)cos(x) - 3a b + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 3 3 5 +--R (6a b - 4a b )sin(x) + (6a b - 4a b)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 6 +--R (6a b - 4a b )cos(x) + (6a b - 10a b + 4a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 6 2 4 4 2 +--R ((- 3a b + 5a b - 2a )cos(x) - 3a b + 2a b )sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (3a b - 2a b)cos(x) - 3a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R ((3a b - 5a b + 2a b)cos(x) + 3a b - 5a b + 2a b)sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 7 +--R (- 3a b + 5a b - 2a )cos(x) + 3a b - 5a b + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 2 3 4 5 2 7 +--R (- 6a b + 10a b - 4a b)sin(x) + (- 6a b + 10a b - 4a )sin(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 6a b + 10a b - 4a b)cos(x) + (- 6a b + 10a b - 4a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R ((3a b - 5a b + 2a b)cos(x) + 3a b - 5a b + 2a b)sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 7 +--R (- 3a b + 5a b - 2a )cos(x) + 3a b - 5a b + 2a +--R / +--R 2 6 4 4 2 +--R (a b - a b )sin(x) +--R + +--R 7 3 5 5 3 7 5 3 +--R ((a b - 2a b + a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 +--R (a b - 2a b + a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 2 +--R (2a b - 2a b )sin(x) +--R + +--R 8 2 6 4 4 8 4 4 +--R ((2b - 4a b + 2a b )cos(x) + 2b - 2a b )sin(x) +--R + +--R 7 3 5 5 3 7 3 5 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 2 +--R (a b - a b )sin(x) +--R + +--R 7 3 5 5 3 7 5 3 +--R ((a b - 2a b + a b )cos(x) + a b - a b )sin(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 +--R (a b - 2a b + a b )cos(x) + a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 7 4 5 6 3 2 +--R (- a b + 2a b - a b )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 7 2 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a b )sin(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (- a b + 2a b - a b )cos(x) - a b + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 2 +--R (- 2a b + 4a b - 2a b )sin(x) +--R + +--R 9 2 7 4 5 9 2 7 4 5 6 3 +--R ((- 2b + 4a b - 2a b )cos(x) - 2b + 2a b + 2a b - 2a b )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 2 +--R (- a b + 2a b - a b )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 7 2 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a b )sin(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (- a b + 2a b - a b )cos(x) - a b + 2a b - a b +--R Type: Expression(Integer) +--E 387 + +--S 388 of 586 +m0566b:= a0566.2-r0566 +--R +--R +--R (373) +--R +---------+ +--R | 2 2 +--R 2 2 4 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 6a b + 4a )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +---------+ +--R 2 2 4 2 3 2 | 2 2 +--R (- 6a b + 4a )atan(------------) + (- b + 2a b)\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 2 3 | 2 2 +--R (b - a b )\|- b + a +--R Type: Expression(Integer) +--E 388 + +--S 389 of 586 +d0566b:= D(m0566b,x) +--R +--R +--R (374) +--R 3 2 5 2 2 3 4 2 3 4 +--R (3a b - 2a )sin(x) + ((- 6a b + 4a b)cos(x) - 6a b + 4a b)sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (3a b - 2a )cos(x) - 3a b + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 2 3 4 2 +--R (12a b - 8a b)sin(x) + (12a b - 8a b)cos(x) +--R + +--R 2 3 4 +--R (12a b - 8a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 5 2 2 3 4 2 3 4 +--R (3a b - 2a )sin(x) + ((- 6a b + 4a b)cos(x) - 6a b + 4a b)sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (3a b - 2a )cos(x) - 3a b + 2a +--R / +--R 2 5 4 3 2 6 3 4 6 3 4 +--R (a b - a b )sin(x) + ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 2 5 4 3 2 2 5 4 3 2 5 4 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 2 7 2 5 7 2 5 +--R (2a b - 2a b )sin(x) + ((4b - 4a b )cos(x) + 4b - 4a b )sin(x) +--R + +--R 6 3 4 2 6 3 4 6 3 4 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 2 6 3 4 6 3 4 +--R (a b - a b )sin(x) + ((2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 2 5 4 3 2 2 5 4 3 2 5 4 3 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + a b - a b +--R Type: Expression(Integer) +--E 389 + +--S 390 of 586 +t0567:= sin(x)^4/(a+b*sin(x))^2 +--R +--R +--R 4 +--R sin(x) +--R (375) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 390 + +--S 391 of 586 +r0567:= 3*a^2*x/b^4+1/2*x/b^2+2*a^5*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/_ + b^4/(a^2-b^2)^(3/2)-8*a^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/_ + b^4/(a^2-b^2)^(1/2)+2*a*cos(x)/b^3-1/2*cos(x)*sin(x)/b^2+_ + a^4*cos(x)/b^3/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (376) +--R x +--R a tan(-) + b +--R 3 3 5 4 2 6 2 +--R ((- 16a b + 12a b)sin(x) - 16a b + 12a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 2 +--R (- b + a b )cos(x)sin(x) +--R + +--R 4 3 2 5 2 3 4 +--R ((3a b - 3a b )cos(x) + (b + 5a b - 6a b)x)sin(x) +--R + +--R 2 3 4 4 3 2 5 +--R (4a b - 6a b)cos(x) + (a b + 5a b - 6a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 7 2 5 6 3 4 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b )\|- b + a +--R Type: Expression(Integer) +--E 391 + +--S 392 of 586 +a0567:= integrate(t0567,x) +--R +--R +--R (377) +--R [ +--R 3 3 5 4 2 6 +--R ((8a b - 6a b)sin(x) + 8a b - 6a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 4 3 2 5 2 3 4 4 3 2 +--R ((3a b - 3a b )cos(x) + (b + 5a b - 6a b)x + 4a b - 6a b ) +--R * +--R sin(x) +--R + +--R 5 2 3 3 5 2 3 4 +--R (b - a b )cos(x) + (- b + 5a b - 6a b)cos(x) +--R + +--R 4 3 2 5 2 3 4 +--R (a b + 5a b - 6a )x + 4a b - 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 7 2 5 6 3 4 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b )\|b - a +--R , +--R +--R 3 3 5 4 2 6 +--R ((16a b - 12a b)sin(x) + 16a b - 12a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 4 3 2 5 2 3 4 4 3 2 +--R ((3a b - 3a b )cos(x) + (b + 5a b - 6a b)x + 4a b - 6a b ) +--R * +--R sin(x) +--R + +--R 5 2 3 3 5 2 3 4 +--R (b - a b )cos(x) + (- b + 5a b - 6a b)cos(x) +--R + +--R 4 3 2 5 2 3 4 +--R (a b + 5a b - 6a )x + 4a b - 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 7 2 5 6 3 4 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b )\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 392 + +--S 393 of 586 +m0567a:= a0567.1-r0567 +--R +--R +--R (378) +--R +---------+ +--R 3 3 5 4 2 6 | 2 2 +--R ((8a b - 6a b)sin(x) + 8a b - 6a )\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R 3 3 5 4 2 6 | 2 2 2 +--R ((16a b - 12a b)sin(x) + 16a b - 12a )\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 2 4 3 2 5 2 3 3 +--R (b - a b )cos(x)sin(x) + (4a b - 6a b )sin(x) + (b - a b )cos(x) +--R + +--R 5 2 3 2 3 4 +--R (- b + a b )cos(x) + 4a b - 6a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R +---------+ +-------+ +--R 7 2 5 6 3 4 | 2 2 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 393 + +--S 394 of 586 +d0567a:= D(m0567a,x) +--R +--R +--R (379) +--R 2 6 4 4 5 +--R (- a b + a b )sin(x) +--R + +--R 7 3 5 5 3 7 5 3 4 +--R ((- a b + 2a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 6 4 4 2 2 6 4 4 6 2 3 +--R ((- 2a b + 2a b )cos(x) + (- a b + 2a b - a b )cos(x))sin(x) +--R + +--R 7 3 5 5 3 3 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 2a b + a b + a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (a b + 6a b - 13a b + 6a b)cos(x) + a b + 8a b - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 4 2 6 4 4 6 2 3 +--R (- a b + a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 4 6 2 2 +--R (- 8a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (a b + 6a b - 13a b + 6a )cos(x) + a b + 15a b - 12a b +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 5 7 3 5 4 +--R (- a b + 2a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (a b - 2a b + a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 5 3 7 +--R (a b - a b - 8a b + 6a b)cos(x) + 8a b - 6a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 +--R (- 2a b + 2a b )sin(x) +--R + +--R 8 2 6 4 4 8 4 4 4 +--R ((- 2b + 4a b - 2a b )cos(x) - 2b + 2a b )sin(x) +--R + +--R 7 3 5 2 7 3 5 5 3 +--R (- 4a b + 4a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 5 5 3 +--R - 16a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 3 +--R (- 4b + 8a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 2 8 2 6 4 4 +--R (- 4b + 2a b + 2a b )cos(x) + (2b - 4a b + 2a b )cos(x) +--R + +--R 8 4 4 6 2 +--R 2b - 34a b + 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 4 7 3 5 5 3 3 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 5 5 3 2 +--R (- 16a b + 12a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 +--R (2a b - 20a b + 30a b - 12a b)cos(x) + 2a b - 2a b +--R + +--R 5 3 7 +--R - 16a b + 12a b +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 5 8 2 6 4 +--R (- 2b + 4a b - 2a b )cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 3 +--R (2b - 4a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (2b - 2a b - 16a b + 12a b )cos(x) +--R + +--R 4 4 6 2 8 +--R (- 16a b + 28a b - 12a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 5 +--R (- a b + a b )sin(x) +--R + +--R 7 3 5 5 3 7 5 3 4 +--R ((- a b + 2a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 2 6 4 4 2 2 6 4 4 6 2 3 +--R ((- 2a b + 2a b )cos(x) + (- a b + 2a b - a b )cos(x))sin(x) +--R + +--R 7 3 5 5 3 3 7 3 5 5 3 2 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + a b + a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (a b + 6a b - 13a b + 6a b)cos(x) + a b + 8a b - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 4 2 6 4 4 6 2 3 +--R (- a b + a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 4 6 2 2 2 6 4 4 6 2 8 +--R (- 8a b + 6a b )cos(x) + (a b + 6a b - 13a b + 6a )cos(x) +--R + +--R 2 6 4 4 6 2 +--R a b + 15a b - 12a b +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 5 7 3 5 4 +--R (- a b + 2a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 7 3 5 5 3 3 7 3 5 5 3 7 2 +--R (a b - 2a b + a b )cos(x) + (a b - a b - 8a b + 6a b)cos(x) +--R + +--R 5 3 7 +--R 8a b - 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 7 4 5 6 3 5 +--R (- a b + 2a b - a b )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 7 2 4 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a b )sin(x) +--R + +--R 2 7 4 5 6 3 2 2 7 4 5 6 3 +--R ((- 2a b + 4a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x)) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 3 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 8 3 6 7 2 2 +--R (- 2a b + 3a b - a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (a b + 6a b - 13a b + 6a b )cos(x) + a b + 7a b - 15a b +--R + +--R 7 2 +--R 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 4 2 7 4 5 6 3 3 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 5 6 3 8 2 +--R (- 8a b + 14a b - 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 +--R (a b + 6a b - 13a b + 6a b)cos(x) + a b + 14a b - 27a b +--R + +--R 8 +--R 12a b +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 5 8 3 6 5 4 4 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 8 3 6 5 4 3 +--R (a b - 2a b + a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 5 4 7 2 9 +--R (a b - 2a b - 7a b + 14a b - 6a )cos(x) + 8a b - 14a b + 6a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 5 +--R (- 2a b + 4a b - 2a b )sin(x) +--R + +--R 9 2 7 4 5 9 2 7 4 5 6 3 4 +--R ((- 2b + 4a b - 2a b )cos(x) - 2b + 2a b + 2a b - 2a b )sin(x) +--R + +--R 8 3 6 5 4 2 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 8 3 6 5 4 3 6 5 4 7 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 16a b + 28a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 9 2 7 4 5 3 9 2 7 6 3 2 +--R (- 4b + 8a b - 4a b )cos(x) + (- 4b + 6a b - 2a b )cos(x) +--R + +--R 9 2 7 4 5 9 2 7 4 5 6 3 8 +--R (2b - 4a b + 2a b )cos(x) + 2b - 2a b - 34a b + 58a b - 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 4 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 3 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 16a b + 28a b - 12a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (2a b - 20a b + 30a b - 12a b )cos(x) + 2a b - 4a b - 14a b +--R + +--R 7 2 9 +--R 28a b - 12a +--R * +--R sin(x) +--R + +--R 9 2 7 4 5 5 9 2 7 4 5 4 +--R (- 2b + 4a b - 2a b )cos(x) + (- 2b + 4a b - 2a b )cos(x) +--R + +--R 9 2 7 4 5 3 +--R (2b - 4a b + 2a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (2b - 4a b - 14a b + 28a b - 12a b)cos(x) +--R + +--R 4 5 6 3 8 +--R (- 16a b + 28a b - 12a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 5 +--R (- a b + 2a b - a b )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 7 2 4 +--R ((- a b + 2a b - a b )cos(x) - a b + a b + a b - a b )sin(x) +--R + +--R 2 7 4 5 6 3 2 2 7 4 5 6 3 3 +--R ((- 2a b + 4a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x))sin(x) +--R + +--R 8 3 6 5 4 3 8 3 6 7 2 2 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 3a b - a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 7 2 +--R (a b + 6a b - 13a b + 6a b )cos(x) + a b + 7a b - 15a b + 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 4 2 7 4 5 6 3 3 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 5 6 3 8 2 +--R (- 8a b + 14a b - 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 8 +--R (a b + 6a b - 13a b + 6a b)cos(x) + a b + 14a b - 27a b + 12a b +--R * +--R sin(x) +--R + +--R 8 3 6 5 4 5 8 3 6 5 4 4 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 8 3 6 5 4 3 +--R (a b - 2a b + a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 5 4 7 2 9 +--R (a b - 2a b - 7a b + 14a b - 6a )cos(x) + 8a b - 14a b + 6a +--R / +--R 2 8 4 6 3 +--R (2a b - 2a b )sin(x) +--R + +--R 9 3 7 5 5 9 3 7 5 5 2 +--R ((2a b - 4a b + 2a b )cos(x) + 2a b + 2a b - 4a b )sin(x) +--R + +--R 2 8 4 6 6 4 2 8 4 6 6 4 +--R ((4a b - 8a b + 4a b )cos(x) + 4a b - 2a b - 2a b )sin(x) +--R + +--R 3 7 5 5 7 3 3 7 5 5 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 9 3 7 3 +--R (4a b - 4a b )sin(x) +--R + +--R 10 2 8 4 6 10 2 8 4 6 2 +--R ((4b - 8a b + 4a b )cos(x) + 4b + 4a b - 8a b )sin(x) +--R + +--R 9 3 7 5 5 9 3 7 5 5 +--R ((8a b - 16a b + 8a b )cos(x) + 8a b - 4a b - 4a b )sin(x) +--R + +--R 2 8 4 6 6 4 2 8 4 6 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 8 4 6 3 +--R (2a b - 2a b )sin(x) +--R + +--R 9 3 7 5 5 9 3 7 5 5 2 +--R ((2a b - 4a b + 2a b )cos(x) + 2a b + 2a b - 4a b )sin(x) +--R + +--R 2 8 4 6 6 4 2 8 4 6 6 4 +--R ((4a b - 8a b + 4a b )cos(x) + 4a b - 2a b - 2a b )sin(x) +--R + +--R 3 7 5 5 7 3 3 7 5 5 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 9 4 7 6 5 3 +--R (2a b - 4a b + 2a b )sin(x) +--R + +--R 10 3 8 5 6 10 5 6 7 4 2 +--R ((2a b - 4a b + 2a b )cos(x) + 2a b - 6a b + 4a b )sin(x) +--R + +--R 2 9 4 7 6 5 2 9 4 7 8 3 +--R ((4a b - 8a b + 4a b )cos(x) + 4a b - 6a b + 2a b )sin(x) +--R + +--R 3 8 5 6 7 4 3 8 5 6 7 4 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 4a b + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 10 3 8 5 6 3 +--R (4a b - 8a b + 4a b )sin(x) +--R + +--R 11 2 9 4 7 11 4 7 6 5 2 +--R ((4b - 8a b + 4a b )cos(x) + 4b - 12a b + 8a b )sin(x) +--R + +--R 10 3 8 5 6 10 3 8 7 4 +--R ((8a b - 16a b + 8a b )cos(x) + 8a b - 12a b + 4a b )sin(x) +--R + +--R 2 9 4 7 6 5 2 9 4 7 6 5 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 8a b + 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 9 4 7 6 5 3 +--R (2a b - 4a b + 2a b )sin(x) +--R + +--R 10 3 8 5 6 10 5 6 7 4 2 +--R ((2a b - 4a b + 2a b )cos(x) + 2a b - 6a b + 4a b )sin(x) +--R + +--R 2 9 4 7 6 5 2 9 4 7 8 3 +--R ((4a b - 8a b + 4a b )cos(x) + 4a b - 6a b + 2a b )sin(x) +--R + +--R 3 8 5 6 7 4 3 8 5 6 7 4 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 4a b + 2a b +--R Type: Expression(Integer) +--E 394 + +--S 395 of 586 +m0567b:= a0567.2-r0567 +--R +--R +--R (380) +--R 3 3 5 4 2 6 +--R ((16a b - 12a b)sin(x) + 16a b - 12a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +--R 3 3 5 4 2 6 2 +--R ((16a b - 12a b)sin(x) + 16a b - 12a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 2 4 3 2 5 2 3 3 +--R (b - a b )cos(x)sin(x) + (4a b - 6a b )sin(x) + (b - a b )cos(x) +--R + +--R 5 2 3 2 3 4 +--R (- b + a b )cos(x) + 4a b - 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 7 2 5 6 3 4 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b )\|- b + a +--R Type: Expression(Integer) +--E 395 + +--S 396 of 586 +d0567b:= D(m0567b,x) +--R +--R +--R (381) +--R 2 6 4 4 6 +--R (- a b + a b )sin(x) +--R + +--R 7 3 5 7 3 5 5 3 5 +--R ((- 2a b + 2a b )cos(x) - 2a b + a b + a b )sin(x) +--R + +--R 2 6 4 4 2 2 6 4 4 2 6 +--R (- 3a b + 3a b )cos(x) + (- 4a b + 4a b )cos(x) - 2a b +--R + +--R 4 4 6 2 +--R - 6a b + 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 3 7 3 5 5 3 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (2a b + 12a b - 10a b )cos(x) + 2a b + 14a b - 28a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 4 2 6 4 4 3 +--R (- 3a b + 3a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 2a b - 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 8 +--R (4a b + 28a b - 24a b )cos(x) + 3a b + 37a b - 38a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 5 3 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + a b + a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 2a b - 16a b + 12a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (2a b + 14a b - 12a b)cos(x) + a b + 31a b - 24a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 6 4 4 5 +--R (- a b + a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 4 4 6 2 8 2 6 2 +--R (2a b - 2a b )cos(x) + (a b - a b - 8a b + 6a )cos(x) + 8a b +--R + +--R 8 +--R - 6a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 6 +--R (- 2a b + 2a b )sin(x) +--R + +--R 8 2 6 8 2 6 4 4 5 +--R ((- 4b + 4a b )cos(x) - 4b + 2a b + 2a b )sin(x) +--R + +--R 7 3 5 2 7 3 5 7 +--R (- 6a b + 6a b )cos(x) + (- 8a b + 8a b )cos(x) - 4a b +--R + +--R 3 5 5 3 +--R - 28a b + 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 8 2 6 3 8 2 6 4 4 2 +--R (- 8b + 8a b )cos(x) + (- 8b + 4a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 8 2 6 4 4 6 2 +--R (4b - 8a b + 4a b )cos(x) + 4b - 4a b - 64a b + 48a b +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 4 7 3 5 3 +--R (- 6a b + 6a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 4a b - 28a b + 24a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (8a b - 40a b + 24a b )cos(x) + 6a b - 6a b - 32a b + 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 6 5 8 2 6 4 4 4 +--R (- 4b + 4a b )cos(x) + (- 4b + 2a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 3 +--R (4b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (4b - 4a b - 64a b + 48a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 +--R (4a b - 68a b + 48a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 7 3 5 6 7 3 5 5 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 7 3 5 3 7 3 5 5 3 7 2 +--R (4a b - 4a b )cos(x) + (2a b - 2a b - 32a b + 24a b)cos(x) +--R + +--R 5 3 7 +--R (- 32a b + 24a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 +--R (- a b + a b )sin(x) +--R + +--R 7 3 5 7 3 5 5 3 5 +--R ((- 2a b + 2a b )cos(x) - 2a b + a b + a b )sin(x) +--R + +--R 2 6 4 4 2 2 6 4 4 2 6 4 4 +--R (- 3a b + 3a b )cos(x) + (- 4a b + 4a b )cos(x) - 2a b - 6a b +--R + +--R 6 2 +--R 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 3 7 3 5 5 3 2 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (2a b + 12a b - 10a b )cos(x) + 2a b + 14a b - 28a b + 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 4 2 6 4 4 3 +--R (- 3a b + 3a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 +--R (- 2a b - 6a b + 6a b )cos(x) + (4a b + 28a b - 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 +--R 3a b + 37a b - 38a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 7 3 5 5 3 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + a b + a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 2a b - 16a b + 12a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (2a b + 14a b - 12a b)cos(x) + a b + 31a b - 24a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 6 2 6 4 4 5 +--R (- a b + a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 4 4 6 2 8 2 6 2 8 +--R (2a b - 2a b )cos(x) + (a b - a b - 8a b + 6a )cos(x) + 8a b - 6a +--R / +--R 2 8 4 6 4 +--R (2a b - 2a b )sin(x) +--R + +--R 9 3 7 9 5 5 3 +--R ((4a b - 4a b )cos(x) + 4a b - 4a b )sin(x) +--R + +--R 2 8 4 6 2 2 8 4 6 2 8 4 6 +--R (2a b - 2a b )cos(x) + (12a b - 12a b )cos(x) + 10a b - 8a b +--R + +--R 6 4 +--R - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 7 5 5 2 3 7 5 5 3 7 5 5 +--R ((4a b - 4a b )cos(x) + (12a b - 12a b )cos(x) + 8a b - 8a b ) +--R * +--R sin(x) +--R + +--R 4 6 6 4 2 4 6 6 4 4 6 6 4 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 9 3 7 4 10 2 8 10 4 6 3 +--R (4a b - 4a b )sin(x) + ((8b - 8a b )cos(x) + 8b - 8a b )sin(x) +--R + +--R 9 3 7 2 9 3 7 9 +--R (4a b - 4a b )cos(x) + (24a b - 24a b )cos(x) + 20a b +--R + +--R 3 7 5 5 +--R - 16a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 8 4 6 2 2 8 4 6 2 8 +--R (8a b - 8a b )cos(x) + (24a b - 24a b )cos(x) + 16a b +--R + +--R 4 6 +--R - 16a b +--R * +--R sin(x) +--R + +--R 3 7 5 5 2 3 7 5 5 3 7 5 5 +--R (4a b - 4a b )cos(x) + (8a b - 8a b )cos(x) + 4a b - 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 8 4 6 4 9 3 7 9 5 5 3 +--R (2a b - 2a b )sin(x) + ((4a b - 4a b )cos(x) + 4a b - 4a b )sin(x) +--R + +--R 2 8 4 6 2 2 8 4 6 2 8 4 6 +--R (2a b - 2a b )cos(x) + (12a b - 12a b )cos(x) + 10a b - 8a b +--R + +--R 6 4 +--R - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 7 5 5 2 3 7 5 5 3 7 5 5 +--R ((4a b - 4a b )cos(x) + (12a b - 12a b )cos(x) + 8a b - 8a b )sin(x) +--R + +--R 4 6 6 4 2 4 6 6 4 4 6 6 4 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R Type: Expression(Integer) +--E 396 + +--S 397 of 586 +t0568:= sin(x)^2/(a+a*sin(x))^2 +--R +--R +--R 2 +--R sin(x) +--R (382) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 586 +r0568:= x/a^2-1/3*cos(x)/a^2/(1+sin(x))^2+5/3*cos(x)/a^2/(1+sin(x)) +--R +--R +--R 2 +--R 3x sin(x) + (5cos(x) + 6x)sin(x) + 4cos(x) + 3x +--R (383) ------------------------------------------------ +--R 2 2 2 2 +--R 3a sin(x) + 6a sin(x) + 3a +--R Type: Expression(Integer) +--E 398 + +--S 399 of 586 +a0568:= integrate(t0568,x) +--R +--R +--R (384) +--R 2 +--R ((3x + 9)cos(x) + 6x + 9)sin(x) + (- 3x + 1)cos(x) + (3x + 8)cos(x) + 6x + 7 +--R ----------------------------------------------------------------------------- +--R 2 2 2 2 2 2 +--R (3a cos(x) + 6a )sin(x) - 3a cos(x) + 3a cos(x) + 6a +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 586 +m0568:= a0568-r0568 +--R +--R +--R (385) +--R 3 2 2 +--R (9cos(x) + 9)sin(x) + (- 4cos(x) + 16cos(x) + 25)sin(x) +--R + +--R 3 2 3 2 +--R (5cos(x) - 7cos(x) + 7cos(x) + 23)sin(x) + 4cos(x) - 3cos(x) + 7 +--R / +--R 2 2 3 2 2 2 2 2 +--R (3a cos(x) + 6a )sin(x) + (- 3a cos(x) + 9a cos(x) + 18a )sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 6a cos(x) + 9a cos(x) + 18a )sin(x) - 3a cos(x) + 3a cos(x) + 6a +--R Type: Expression(Integer) +--E 400 + +--S 401 of 586 +d0568:= D(m0568,x) +--R +--R +--R (386) +--R 6 2 5 +--R - 9sin(x) + (- 5cos(x) - 2cos(x) - 25)sin(x) +--R + +--R 3 2 4 +--R (- 10cos(x) - 40cos(x) - 8cos(x) - 14)sin(x) +--R + +--R 3 2 3 +--R (- 18cos(x) - 62cos(x) - 8cos(x) + 18)sin(x) +--R + +--R 5 4 3 2 2 +--R (- 10cos(x) - 28cos(x) - 4cos(x) - 8cos(x) + 4cos(x) + 23)sin(x) +--R + +--R 6 5 4 3 2 +--R 5cos(x) - 16cos(x) - 47cos(x) + 6cos(x) + 35cos(x) + 10cos(x) +--R + +--R 7 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 3cos(x) - 6cos(x) - 19cos(x) + 2cos(x) + 16cos(x) + 4cos(x) +--R / +--R 2 2 2 2 5 +--R (3a cos(x) + 12a cos(x) + 12a )sin(x) +--R + +--R 2 3 2 2 2 2 4 +--R (- 6a cos(x) + 3a cos(x) + 60a cos(x) + 60a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 3 +--R (3a cos(x) - 24a cos(x) - 18a cos(x) + 120a cos(x) + 120a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (9a cos(x) - 36a cos(x) - 42a cos(x) + 120a cos(x) + 120a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (9a cos(x) - 24a cos(x) - 33a cos(x) + 60a cos(x) + 60a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R 3a cos(x) - 6a cos(x) - 9a cos(x) + 12a cos(x) + 12a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 586 +t0569:= sin(x)^3/(a+a*sin(x))^2 +--R +--R +--R 3 +--R sin(x) +--R (387) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 402 + +--S 403 of 586 +r0569:= -2*x/a^2-cos(x)/a^2+1/3*cos(x)/a^2/(1+sin(x))^2-_ + 8/3*cos(x)/a^2/(1+sin(x)) +--R +--R +--R 2 +--R (- 3cos(x) - 6x)sin(x) + (- 14cos(x) - 12x)sin(x) - 10cos(x) - 6x +--R (388) ------------------------------------------------------------------ +--R 2 2 2 2 +--R 3a sin(x) + 6a sin(x) + 3a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 586 +a0569:= integrate(t0569,x) +--R +--R +--R (389) +--R 2 3 +--R (- 3cos(x) + (- 6x - 24)cos(x) - 12x - 21)sin(x) + 3cos(x) +--R + +--R 2 +--R (6x - 1)cos(x) + (- 6x - 23)cos(x) - 12x - 19 +--R / +--R 2 2 2 2 2 2 +--R (3a cos(x) + 6a )sin(x) - 3a cos(x) + 3a cos(x) + 6a +--R Type: Union(Expression(Integer),...) +--E 404 + +--S 405 of 586 +m0569:= a0569-r0569 +--R +--R +--R (390) +--R 3 2 2 +--R (- 18cos(x) - 21)sin(x) + (10cos(x) - 37cos(x) - 61)sin(x) +--R + +--R 3 2 3 2 +--R (- 8cos(x) + 19cos(x) - 22cos(x) - 59)sin(x) - 7cos(x) + 9cos(x) +--R + +--R - 3cos(x) - 19 +--R / +--R 2 2 3 2 2 2 2 2 +--R (3a cos(x) + 6a )sin(x) + (- 3a cos(x) + 9a cos(x) + 18a )sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 6a cos(x) + 9a cos(x) + 18a )sin(x) - 3a cos(x) + 3a cos(x) + 6a +--R Type: Expression(Integer) +--E 405 + +--S 406 of 586 +d0569:= D(m0569,x) +--R +--R +--R (391) +--R 6 2 5 +--R 15sin(x) + (8cos(x) + 2cos(x) + 43)sin(x) +--R + +--R 3 2 4 +--R (16cos(x) + 64cos(x) + 8cos(x) + 26)sin(x) +--R + +--R 3 2 3 +--R (30cos(x) + 104cos(x) + 8cos(x) - 30)sin(x) +--R + +--R 5 4 3 2 2 +--R (16cos(x) + 43cos(x) + 4cos(x) + 20cos(x) - 4cos(x) - 41)sin(x) +--R + +--R 6 5 4 3 2 +--R - 8cos(x) + 28cos(x) + 77cos(x) - 18cos(x) - 56cos(x) - 10cos(x) +--R + +--R - 13 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 6cos(x) + 12cos(x) + 34cos(x) - 8cos(x) - 28cos(x) - 4cos(x) +--R / +--R 2 2 2 2 5 +--R (3a cos(x) + 12a cos(x) + 12a )sin(x) +--R + +--R 2 3 2 2 2 2 4 +--R (- 6a cos(x) + 3a cos(x) + 60a cos(x) + 60a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 3 +--R (3a cos(x) - 24a cos(x) - 18a cos(x) + 120a cos(x) + 120a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (9a cos(x) - 36a cos(x) - 42a cos(x) + 120a cos(x) + 120a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (9a cos(x) - 24a cos(x) - 33a cos(x) + 60a cos(x) + 60a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R 3a cos(x) - 6a cos(x) - 9a cos(x) + 12a cos(x) + 12a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 586 +t0570:= cos(x)^2/(a+b*sin(x))^2 +--R +--R +--R 2 +--R cos(x) +--R (392) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 407 + +--S 408 of 586 +r0570:= -x/b^2+2*a*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2/_ + (a^2-b^2)^(1/2)-cos(x)/b/(a+b*sin(x)) +--R +--R +--R (393) +--R x +--R a tan(-) + b +--R 2 2 +--R (2a b sin(x) + 2a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R (- b x sin(x) - b cos(x) - a x)\|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R (b sin(x) + a b )\|- b + a +--R Type: Expression(Integer) +--E 408 + +--S 409 of 586 +a0570:= integrate(t0570,x) +--R +--R +--R (394) +--R [ +--R 2 3 +--R (a b sin(x) + a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R ((- a b x - b )sin(x) - a b cos(x) - a x - a b)\|b - a +--R / +--R +-------+ +--R 3 2 2 | 2 2 +--R (a b sin(x) + a b )\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 3 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 2a b sin(x) - 2a )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((- a b x - b )sin(x) - a b cos(x) - a x - a b)\|- b + a +--R / +--R +---------+ +--R 3 2 2 | 2 2 +--R (a b sin(x) + a b )\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 409 + +--S 410 of 586 +m0570a:= a0570.1-r0570 +--R +--R +--R (395) +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +---------+ +-------+ +--R 2 | 2 2 2 | 2 2 | 2 2 +--R - 2a \|b - a atan(------------) - b\|- b + a \|b - a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a b \|- b + a \|b - a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 586 +d0570a:= D(m0570a,x) +--R +--R +--R (396) +--R 2 3 2 2 2 2 x 2 +--R (((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b)tan(-) +--R 2 +--R + +--R 2 2 2 2 2 2 3 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (2a b - 2a )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 2 2 +--R ((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 3 3 3 2 2 4 2 2 2 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b +--R + +--R 4 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 2 4 +--R (- 2a b + 2a b)sin(x) + (- 2a b + 2a )sin(x) +--R + +--R 3 3 2 3 3 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 3 3 2 2 4 2 2 2 4 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b - a +--R / +--R 2 3 2 4 3 2 4 3 2 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (a b - a b)cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 5 2 3 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 4 3 2 4 +--R (2a b - 2a b )cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 3 2 4 3 2 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (a b - a b)cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 +--R (- 2a b + 2a b )sin(x) +--R + +--R 6 2 4 6 4 2 5 3 3 +--R ((- 2b + 2a b )cos(x) - 2b + 2a b )sin(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 +--R - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- a b + a b )cos(x) - a b + a b +--R Type: Expression(Integer) +--E 411 + +--S 412 of 586 +m0570b:= a0570.2-r0570 +--R +--R +--R (397) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R 2 (a sin(x) + b cos(x) + b)\|- b + a 2 2 +--R - 2a atan(-------------------------------------) - 2a atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R - b\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a b \|- b + a +--R Type: Expression(Integer) +--E 412 + +--S 413 of 586 +d0570b:= D(m0570b,x) +--R +--R +--R (398) +--R 2 2 2 2 2 x 2 +--R (a sin(x) + (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a )tan(-) +--R 2 +--R + +--R 2 2 x 2 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + a sin(x) +--R 2 +--R + +--R 2 2 2 +--R (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R Type: Expression(Integer) +--E 413 + +--S 414 of 586 +t0571:= cos(x)^4/(a+b*sin(x))^2 +--R +--R +--R 4 +--R cos(x) +--R (399) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 414 + +--S 415 of 586 +r0571:= 3*a^2*x/b^4-3/2*x/b^2-6*a*(a^2-b^2)^(1/2)*_ + atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^4+_ + 2*a*cos(x)/b^3-1/2*cos(x)*sin(x)/b^2+(a^2-b^2)*cos(x)/b^3/(a+b*sin(x)) +--R +--R +--R (400) +--R x +--R +---------+ a tan(-) + b +--R 2 | 2 2 2 3 2 +--R (- 12a b sin(x) - 12a )\|- b + a atan(------------) - b cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 2 3 2 +--R (3a b cos(x) + (- 3b + 6a b)x)sin(x) + (- 2b + 6a b)cos(x) +--R + +--R 2 3 +--R (- 3a b + 6a )x +--R / +--R 5 4 +--R 2b sin(x) + 2a b +--R Type: Expression(Integer) +--E 415 + +--S 416 of 586 +a0571:= integrate(t0571,x) +--R +--R +--R (401) +--R [ +--R +-------+ +--R 2 3 | 2 2 +--R (6a b sin(x) + 6a )\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R 2 2 3 3 4 2 2 3 3 +--R (3a b cos(x) + (- 3a b + 6a b)x - 2b + 6a b )sin(x) + a b cos(x) +--R + +--R 3 3 2 2 4 3 3 +--R (- 3a b + 6a b)cos(x) + (- 3a b + 6a )x - 2a b + 6a b +--R / +--R 5 2 4 +--R 2a b sin(x) + 2a b +--R , +--R +--R +---------+ +--R +---------+ | 2 2 +--R 2 3 | 2 2 (cos(x) + 1)\|- b + a +--R (12a b sin(x) + 12a )\|- b + a atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R 2 2 3 3 4 2 2 3 3 +--R (3a b cos(x) + (- 3a b + 6a b)x - 2b + 6a b )sin(x) + a b cos(x) +--R + +--R 3 3 2 2 4 3 3 +--R (- 3a b + 6a b)cos(x) + (- 3a b + 6a )x - 2a b + 6a b +--R / +--R 5 2 4 +--R 2a b sin(x) + 2a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 416 + +--S 417 of 586 +m0571a:= a0571.1-r0571 +--R +--R +--R (402) +--R +-------+ +--R 2 3 | 2 2 +--R (6a b sin(x) + 6a )\|b - a +--R * +--R log +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x) - b)\|b - a + a b sin(x) +--R + +--R 2 2 2 +--R (b - a )cos(x) + b +--R / +--R b sin(x) + a +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 3 | 2 2 2 3 2 +--R (12a b sin(x) + 12a )\|- b + a atan(------------) + a b cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 3 3 3 3 3 +--R (- 2b + 6a b )sin(x) + a b cos(x) - a b cos(x) - 2a b + 6a b +--R / +--R 5 2 4 +--R 2a b sin(x) + 2a b +--R Type: Expression(Integer) +--E 417 + +--S 418 of 586 +d0571a:= D(m0571a,x) +--R +--R +--R (403) +--R 2 3 5 4 4 3 2 4 +--R - a b sin(x) + (- a b cos(x) - a b - a b )sin(x) +--R + +--R 2 3 2 2 3 3 +--R (- 2a b cos(x) - a b cos(x))sin(x) +--R + +--R 4 3 4 3 2 2 +--R - 2a b cos(x) + (- 2a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 5a b + 6a b )cos(x) - 5a b + 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 2 3 3 2 3 4 2 +--R - a b cos(x) - a b cos(x) + (6a b - 6a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 5a b + 6a b)cos(x) - 11a b + 12a b +--R * +--R sin(x) +--R + +--R 4 5 4 4 4 3 +--R - a b cos(x) - a b cos(x) + a b cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (a b + 6a b - 6a )cos(x) - 6a b + 6a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 5 5 5 2 3 4 +--R - 2a b sin(x) + (- 2b cos(x) - 2b - 2a b )sin(x) +--R + +--R 4 2 4 4 3 2 3 +--R (- 4a b cos(x) - 2a b cos(x) + 12a b - 12a b )sin(x) +--R + +--R 5 3 5 2 3 2 5 5 +--R - 4b cos(x) + (- 4b - 2a b )cos(x) + 2b cos(x) + 2b +--R + +--R 2 3 4 +--R 26a b - 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 4 3 4 3 2 2 +--R - 2a b cos(x) - 2a b cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 3 2 4 3 2 5 +--R (14a b - 12a b )cos(x) + 2a b + 12a b - 12a +--R * +--R sin(x) +--R + +--R 5 5 5 4 5 3 +--R - 2b cos(x) - 2b cos(x) + 2b cos(x) +--R + +--R 5 2 3 4 2 2 3 4 +--R (2b + 12a b - 12a b)cos(x) + (12a b - 12a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 5 4 4 3 2 4 +--R - a b sin(x) + (- a b cos(x) - a b - a b )sin(x) +--R + +--R 2 3 2 2 3 3 +--R (- 2a b cos(x) - a b cos(x))sin(x) +--R + +--R 4 3 4 3 2 2 +--R - 2a b cos(x) + (- 2a b - a b )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 5a b + 6a b )cos(x) - 5a b + 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 2 3 3 2 3 4 2 +--R - a b cos(x) - a b cos(x) + (6a b - 6a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 5a b + 6a b)cos(x) - 11a b + 12a b +--R * +--R sin(x) +--R + +--R 4 5 4 4 4 3 +--R - a b cos(x) - a b cos(x) + a b cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (a b + 6a b - 6a )cos(x) - 6a b + 6a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 5 5 3 3 5 3 3 4 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 4 2 2 4 4 2 3 +--R (2a b cos(x) + (a b - a b )cos(x))sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (2a b - 2a b )cos(x) + (2a b + a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (5a b - 11a b + 6a b)cos(x) + 5a b - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 4 4 2 3 2 4 4 2 2 +--R a b cos(x) + (a b - a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (5a b - 11a b + 6a )cos(x) + 11a b - 12a b +--R * +--R sin(x) +--R + +--R 5 3 3 5 5 4 5 3 3 3 +--R (a b - a b )cos(x) + a b cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- a b - 6a b + 6a b)cos(x) + 6a b - 6a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 5 6 2 4 6 2 4 4 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 5 2 5 3 3 5 3 3 3 +--R (4a b cos(x) + (2a b - 2a b )cos(x) - 12a b + 12a b )sin(x) +--R + +--R 6 2 4 3 6 2 4 2 +--R (4b - 4a b )cos(x) + (4b + 2a b )cos(x) +--R + +--R 6 2 4 6 2 4 4 2 +--R (- 2b + 2a b )cos(x) - 2b - 26a b + 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 5 3 3 3 +--R 2a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 3 3 2 5 3 3 5 +--R (- 12a b + 12a b )cos(x) + (- 14a b + 26a b - 12a b)cos(x) +--R + +--R 5 3 3 5 +--R - 2a b - 12a b + 12a b +--R * +--R sin(x) +--R + +--R 6 2 4 5 6 4 6 2 4 3 +--R (2b - 2a b )cos(x) + 2b cos(x) + (- 2b + 2a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 6 +--R (- 2b - 12a b + 12a b )cos(x) + (- 12a b + 24a b - 12a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 5 5 3 3 5 3 3 4 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 4 2 2 4 4 2 3 +--R (2a b cos(x) + (a b - a b )cos(x))sin(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (2a b - 2a b )cos(x) + (2a b + a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (5a b - 11a b + 6a b)cos(x) + 5a b - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 4 4 2 3 2 4 4 2 2 +--R a b cos(x) + (a b - a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 +--R (5a b - 11a b + 6a )cos(x) + 11a b - 12a b +--R * +--R sin(x) +--R + +--R 5 3 3 5 5 4 5 3 3 3 +--R (a b - a b )cos(x) + a b cos(x) + (- a b + a b )cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (- a b - 6a b + 6a b)cos(x) + 6a b - 6a b +--R / +--R 2 5 3 6 6 3 4 2 +--R 2a b sin(x) + (2a b cos(x) + 2a b + 4a b )sin(x) +--R + +--R 2 5 2 5 4 3 3 4 3 4 +--R (4a b cos(x) + 4a b + 2a b )sin(x) + 2a b cos(x) + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 7 7 2 5 2 +--R 4a b sin(x) + (4b cos(x) + 4b + 8a b )sin(x) +--R + +--R 6 6 3 4 2 5 2 5 +--R (8a b cos(x) + 8a b + 4a b )sin(x) + 4a b cos(x) + 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 3 6 6 3 4 2 +--R 2a b sin(x) + (2a b cos(x) + 2a b + 4a b )sin(x) +--R + +--R 2 5 2 5 4 3 3 4 3 4 +--R (4a b cos(x) + 4a b + 2a b )sin(x) + 2a b cos(x) + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 6 3 7 3 5 7 3 5 2 +--R - 2a b sin(x) + ((- 2a b + 2a b )cos(x) - 2a b - 4a b )sin(x) +--R + +--R 2 6 4 4 2 6 4 4 +--R ((- 4a b + 4a b )cos(x) - 4a b - 2a b )sin(x) +--R + +--R 3 5 5 3 3 5 +--R (- 2a b + 2a b )cos(x) - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 8 2 6 8 2 6 2 +--R - 4a b sin(x) + ((- 4b + 4a b )cos(x) - 4b - 8a b )sin(x) +--R + +--R 7 3 5 7 3 5 +--R ((- 8a b + 8a b )cos(x) - 8a b - 4a b )sin(x) +--R + +--R 2 6 4 4 2 6 +--R (- 4a b + 4a b )cos(x) - 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 3 7 3 5 7 3 5 2 +--R - 2a b sin(x) + ((- 2a b + 2a b )cos(x) - 2a b - 4a b )sin(x) +--R + +--R 2 6 4 4 2 6 4 4 3 5 5 3 +--R ((- 4a b + 4a b )cos(x) - 4a b - 2a b )sin(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 5 +--R - 2a b +--R Type: Expression(Integer) +--E 418 + +--S 419 of 586 +m0571b:= a0571.2-r0571 +--R +--R +--R (404) +--R +---------+ +--R +---------+ | 2 2 +--R 2 3 | 2 2 (cos(x) + 1)\|- b + a +--R (12a b sin(x) + 12a )\|- b + a atan(------------------------) +--R a sin(x) + b cos(x) + b +--R + +--R x +--R +---------+ a tan(-) + b +--R 2 3 | 2 2 2 3 2 +--R (12a b sin(x) + 12a )\|- b + a atan(------------) + a b cos(x)sin(x) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 3 3 3 3 3 +--R (- 2b + 6a b )sin(x) + a b cos(x) - a b cos(x) - 2a b + 6a b +--R / +--R 5 2 4 +--R 2a b sin(x) + 2a b +--R Type: Expression(Integer) +--E 419 + +--S 420 of 586 +d0571b:= D(m0571b,x) +--R +--R +--R (405) +--R 2 4 6 5 5 3 3 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b - a b )sin(x) +--R + +--R 2 4 2 2 4 2 4 4 2 4 +--R (- 3a b cos(x) - 4a b cos(x) + 4a b - 6a b )sin(x) +--R + +--R 5 3 5 3 3 2 +--R - 4a b cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 5 3 3 5 3 3 5 +--R (- 10a b + 10a b )cos(x) - 10a b + 24a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 3 2 4 4 2 2 +--R - 3a b cos(x) - 6a b cos(x) + (4a b - 6a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 6 +--R (- 20a b + 24a b )cos(x) - 27a b + 36a b - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 5 3 3 4 5 3 3 3 +--R - 2a b cos(x) + (- 2a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (2a b + 12a b - 12a b)cos(x) + (- 10a b + 12a b)cos(x) +--R + +--R 3 3 5 +--R - 23a b + 24a b +--R * +--R sin(x) +--R + +--R 2 4 6 2 4 5 2 4 3 +--R - a b cos(x) - 2a b cos(x) + 2a b cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (a b + 6a b - 6a )cos(x) - 6a b + 6a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 6 6 2 4 5 +--R - 2a b sin(x) + (- 4b cos(x) - 4b - 2a b )sin(x) +--R + +--R 5 2 5 5 3 3 4 +--R (- 6a b cos(x) - 8a b cos(x) + 20a b - 24a b )sin(x) +--R + +--R 6 3 6 2 4 2 6 2 4 6 +--R - 8b cos(x) + (- 8b - 4a b )cos(x) + (4b - 4a b )cos(x) + 4b +--R + +--R 2 4 4 2 +--R 48a b - 48a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 5 3 5 3 3 2 +--R - 6a b cos(x) - 12a b cos(x) + (20a b - 24a b )cos(x) +--R + +--R 5 3 3 5 3 3 5 +--R (32a b - 24a b )cos(x) + 6a b + 24a b - 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 6 2 4 4 6 2 4 3 +--R - 4b cos(x) + (- 4b - 2a b )cos(x) + (4b - 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 2 4 +--R (4b + 48a b - 48a b )cos(x) + (52a b - 48a b )cos(x) + 2a b +--R * +--R sin(x) +--R + +--R 5 6 5 5 5 3 +--R - 2a b cos(x) - 4a b cos(x) + 4a b cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (2a b + 24a b - 24a b)cos(x) + (24a b - 24a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 6 5 5 3 3 5 +--R - a b sin(x) + (- 2a b cos(x) - 2a b - a b )sin(x) +--R + +--R 2 4 2 2 4 2 4 4 2 4 +--R (- 3a b cos(x) - 4a b cos(x) + 4a b - 6a b )sin(x) +--R + +--R 5 3 5 3 3 2 5 3 3 +--R - 4a b cos(x) + (- 4a b - 2a b )cos(x) + (- 10a b + 10a b )cos(x) +--R + +--R 5 3 3 5 +--R - 10a b + 24a b - 12a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 4 3 2 4 4 2 2 +--R - 3a b cos(x) - 6a b cos(x) + (4a b - 6a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 6 +--R (- 20a b + 24a b )cos(x) - 27a b + 36a b - 6a +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 5 3 3 4 5 3 3 3 +--R - 2a b cos(x) + (- 2a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 3 3 5 2 3 3 5 3 3 +--R (2a b + 12a b - 12a b)cos(x) + (- 10a b + 12a b)cos(x) - 23a b +--R + +--R 5 +--R 24a b +--R * +--R sin(x) +--R + +--R 2 4 6 2 4 5 2 4 3 2 4 4 2 6 2 +--R - a b cos(x) - 2a b cos(x) + 2a b cos(x) + (a b + 6a b - 6a )cos(x) +--R + +--R 4 2 6 +--R - 6a b + 6a +--R / +--R 2 6 4 7 7 3 5 3 +--R 2a b sin(x) + (4a b cos(x) + 4a b + 4a b )sin(x) +--R + +--R 2 6 2 2 6 2 6 4 4 2 +--R (2a b cos(x) + 12a b cos(x) + 10a b + 2a b )sin(x) +--R + +--R 3 5 2 3 5 3 5 4 4 2 +--R (4a b cos(x) + 12a b cos(x) + 8a b )sin(x) + 2a b cos(x) +--R + +--R 4 4 4 4 +--R 4a b cos(x) + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 4 8 8 2 6 3 +--R 4a b sin(x) + (8b cos(x) + 8b + 8a b )sin(x) +--R + +--R 7 2 7 7 3 5 2 +--R (4a b cos(x) + 24a b cos(x) + 20a b + 4a b )sin(x) +--R + +--R 2 6 2 2 6 2 6 3 5 2 +--R (8a b cos(x) + 24a b cos(x) + 16a b )sin(x) + 4a b cos(x) +--R + +--R 3 5 3 5 +--R 8a b cos(x) + 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 7 7 3 5 3 +--R 2a b sin(x) + (4a b cos(x) + 4a b + 4a b )sin(x) +--R + +--R 2 6 2 2 6 2 6 4 4 2 +--R (2a b cos(x) + 12a b cos(x) + 10a b + 2a b )sin(x) +--R + +--R 3 5 2 3 5 3 5 4 4 2 4 4 +--R (4a b cos(x) + 12a b cos(x) + 8a b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 4 4 +--R 2a b +--R Type: Expression(Integer) +--E 420 + +--S 421 of 586 +t0572:= cos(x)^2/(a+a*sin(x))^2 +--R +--R +--R 2 +--R cos(x) +--R (406) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 586 +r0572:= -(x*cos(x)-2*sin(x)+2)/a^2/cos(x) +--R +--R +--R 2sin(x) - x cos(x) - 2 +--R (407) ---------------------- +--R 2 +--R a cos(x) +--R Type: Expression(Integer) +--E 422 + +--S 423 of 586 +a0572:= integrate(t0572,x) +--R +--R +--R - x sin(x) + (- x - 4)cos(x) - x - 4 +--R (408) ------------------------------------ +--R 2 2 2 +--R a sin(x) + a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 586 +m0572:= a0572-r0572 +--R +--R +--R 2 2 +--R - 2sin(x) - 2cos(x)sin(x) - 4cos(x) - 2cos(x) + 2 +--R (409) --------------------------------------------------- +--R 2 2 2 2 +--R a cos(x)sin(x) + a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 424 + +--S 425 of 586 +d0572:= D(m0572,x) +--R +--R +--R (410) +--R 4 3 2 +--R - 2sin(x) + (- 4cos(x) - 2)sin(x) + 2sin(x) +--R + +--R 3 2 4 2 +--R (- 4cos(x) - 2cos(x) + 4cos(x) + 2)sin(x) + 2cos(x) - 2cos(x) +--R / +--R 2 2 2 2 3 2 2 2 4 +--R a cos(x) sin(x) + (2a cos(x) + 2a cos(x) )sin(x) + a cos(x) +--R + +--R 2 3 2 2 +--R 2a cos(x) + a cos(x) +--R Type: Expression(Integer) +--E 425 + +--S 426 of 586 +t0573:= cos(x)^4/(a+a*sin(x))^2 +--R +--R +--R 4 +--R cos(x) +--R (411) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 426 + +--S 427 of 586 +r0573:= -1/2*(-3*x-4*cos(x)+cos(x)*sin(x))/a^2 +--R +--R +--R - cos(x)sin(x) + 4cos(x) + 3x +--R (412) ----------------------------- +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 586 +a0573:= integrate(t0573,x) +--R +--R +--R - cos(x)sin(x) + 4cos(x) + 3x +--R (413) ----------------------------- +--R 2 +--R 2a +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 586 +m0573:= a0573-r0573 +--R +--R +--R (414) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 586 +d0573:= D(m0573,x) +--R +--R +--R (415) 0 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 586 +t0574:= tan(x)^2/(a+b*sin(x))^2 +--R +--R +--R 2 +--R tan(x) +--R (416) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 586 +r0574:= -2*a^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)-_ + 4*a*b^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+_ + 1/2*cos(x)/(a+b)^2/(1-sin(x))-1/2*cos(x)/(a-b)^2/(1+sin(x))-_ + a^2*b*cos(x)/(a^2-b^2)^2/(a+b*sin(x)) +--R +--R +--R (417) +--R 3 3 3 2 2 4 2 +--R (- 4a b - 2a b)sin(x) + (- 4a b - 2a )sin(x) +--R + +--R 3 3 2 2 4 +--R (4a b + 2a b)sin(x) + 4a b + 2a +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 2 3 2 +--R ((- b - 2a b)cos(x)sin(x) + (a b - a )cos(x)sin(x) + 3a b cos(x)) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 2 3 4 3 4 3 2 5 2 +--R (b - 2a b + a b)sin(x) + (a b - 2a b + a )sin(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- b + 2a b - a b)sin(x) - a b + 2a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 586 +a0574:= integrate(t0574,x) +--R +--R +--R (418) +--R [ +--R 3 3 2 2 4 +--R ((2a b + a b)cos(x)sin(x) + (2a b + a )cos(x)) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 2 2 3 3 2 2 +--R (- 3a b cos(x) - a b + a )sin(x) + (- b - 2a b)cos(x) +--R + +--R 2 3 2 +--R - 3a b cos(x) + b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 5 2 3 4 4 3 2 5 | 2 2 +--R ((b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x))\|b - a +--R , +--R +--R 3 3 2 2 4 +--R ((4a b + 2a b)cos(x)sin(x) + (4a b + 2a )cos(x)) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 3 3 2 2 +--R (- 3a b cos(x) - a b + a )sin(x) + (- b - 2a b)cos(x) +--R + +--R 2 3 2 +--R - 3a b cos(x) + b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 5 2 3 4 4 3 2 5 | 2 2 +--R ((b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x))\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 433 + +--S 434 of 586 +m0574a:= a0574.1-r0574 +--R +--R +--R (419) +--R 3 3 3 2 2 4 2 +--R (2a b + a b)cos(x)sin(x) + (2a b + a )cos(x)sin(x) +--R + +--R 3 3 2 2 4 +--R (- 2a b - a b)cos(x)sin(x) + (- 2a b - a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 3 3 3 2 2 4 2 +--R (4a b + 2a b)cos(x)sin(x) + (4a b + 2a )cos(x)sin(x) +--R + +--R 3 3 2 2 4 +--R (- 4a b - 2a b)cos(x)sin(x) + (- 4a b - 2a )cos(x) +--R * +--R x +--R +-------+ a tan(-) + b +--R | 2 2 2 +--R \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 3 +--R (- 3a b cos(x) - a b + a )sin(x) +--R + +--R 2 3 2 2 +--R (- 3a b cos(x) + b - a b)sin(x) +--R + +--R 2 3 2 2 2 3 +--R ((- a b + a )cos(x) + 3a b cos(x) + a b - a )sin(x) +--R + +--R 3 2 2 2 3 2 +--R (b - a b)cos(x) + 3a b cos(x) - b + a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 5 2 3 4 3 4 3 2 5 2 +--R (b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- b + 2a b - a b)cos(x)sin(x) + (- a b + 2a b - a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 586 +d0574a:= D(m0574a,x) +--R +--R +--R (420) +--R 3 4 5 2 8 +--R (- a b + a b )sin(x) +--R + +--R 2 5 4 3 6 4 3 6 7 +--R ((- a b + 2a b - a b)cos(x) - a b + a b)sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 2 +--R (2a b - a b - a b )cos(x) + (2a b + 2a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (a b - 3a b + 3a b - a )cos(x) + a b + a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 3 4 2 5 4 3 3 +--R (- 2a b - a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 2 5 +--R (3a b + 3a b )cos(x) + (3a b - 6a b + 3a b)cos(x) + a b +--R + +--R 4 3 6 +--R a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 4 6 3 4 3 +--R - 3a b cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 6 5 2 2 +--R (- 6a b + 3a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (- 2a b + 6a b - 6a b + 2a )cos(x) - 2a b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (2a b - 4a b + 2a b)cos(x) + (3a b + 4a b - a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 6 2 +--R (- 6a b + 6a b )cos(x) + (- 7a b - 4a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 2a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 3a b + 7a b - 5a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 3a b + 6a b + 3a b )cos(x) +--R + +--R 6 3 4 7 3 6 3 4 5 2 2 +--R (5a b - 6a b + a )cos(x) + (5a b - 4a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (a b - 3a b + 3a b - a )cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 3 +--R (- 3a b + a b - a b)cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (4a b + a b + a b)cos(x) + (a b - 2a b + a b)cos(x) +--R + +--R 2 5 4 3 +--R a b - a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 6 3 4 5 2 4 +--R (a b - a b - a b + a )cos(x) + (a b - 2a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- a b + a b + a b - 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a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 6 2 +--R (- 6a b + 6a b )cos(x) + (- 7a b - 4a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 2a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 3a b + 7a b - 5a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 7 3 +--R (- 3a b + 6a b + 3a b )cos(x) + (5a b - 6a b + a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (5a b - 4a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (a b - 3a b + 3a b - a )cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (- 2a b + 4a b - 2a b)cos(x) + (- 3a b + a b - a b)cos(x) +--R + +--R 2 5 4 3 3 2 5 4 3 6 2 +--R (3a b - 3a b )cos(x) + (4a b + a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (a b - 2a b + a b)cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 6 3 4 5 2 4 +--R (a b - a b - a b + a )cos(x) + (a b - 2a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 6 3 4 5 2 2 +--R (- a b + a b + a b - a )cos(x) + (- a b + 2a b + 2a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - 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6a b + 2a b)cos(x) - 2a b + 3a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 5 2 6 4 4 6 2 8 4 +--R (2a b - 4a b + 2a b )cos(x) + (3a b + a b - 5a b + a )cos(x) +--R + +--R 2 6 4 4 3 2 6 4 4 6 2 8 2 +--R (- 6a b + 6a b )cos(x) + (- 7a b + 3a b + 3a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 8 +--R (- 3a b + 6a b - 3a b )cos(x) - 2a b + 3a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 7a b - 5a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 9a b - 3a b - 3a b)cos(x) +--R + +--R 7 3 5 7 3 7 3 5 7 2 +--R (5a b - 6a b + a b)cos(x) + (5a b - 9a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (a b - 3a b + 3a b - a b)cos(x) + a b - 2a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 2 6 4 4 3 +--R (- 3a b + 4a b - 2a b + a )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 2 6 4 4 8 2 2 6 4 4 6 2 2 6 +--R (4a b - 3a b - a )cos(x) + (a b - 2a b + a b )cos(x) + a b +--R + +--R 4 4 6 2 +--R - 2a b + a b +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 7 3 5 7 4 +--R (a b - a b - a b + a b)cos(x) + (a b - 3a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 7 3 5 7 2 +--R (- a b + a b + a b - a b)cos(x) + (- a b + 3a b - 2a b)cos(x) +--R / +--R 2 7 4 5 6 3 2 7 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 8 5 4 7 2 2 +--R (a b - 3a b + 2a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (a b - 2a b + a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 2a b + a b + 4a b - 3a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 4a b + 12a b - 12a b + 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 3a b + 4a b + a b - 2a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a )cos(x) +--R + +--R 8 3 6 5 4 2 +--R (a b - 2a b + a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 2 7 4 5 8 2 +--R (2a b - 3a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 3 3 6 5 4 7 2 2 +--R (a b - 3a b + 3a b - a )cos(x) + (a b - 2a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 2 7 +--R (2a b - 4a b + 2a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 3 +--R (2b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 9 4 5 6 3 2 +--R (2b - 6a b + 4a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (2a b - 4a b + 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (- 4b + 14a b - 18a b + 10a b - 2a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 2 +--R (- 4b + 2a b + 8a b - 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 8a b + 24a b - 24a b + 8a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 6a b + 8a b + 2a b - 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (2b - 10a b + 18a b - 14a b + 4a b)cos(x) +--R + +--R 9 2 7 4 5 2 +--R (2b - 4a b + 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 8 3 6 7 2 2 +--R (4a b - 6a b + 2a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (2a b - 4a b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 2 7 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 8 5 4 7 2 2 +--R (a b - 3a b + 2a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (a b - 2a b + a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 2a b + a b + 4a b - 3a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 4a b + 12a b - 12a b + 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 3a b + 4a b + a b - 2a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a )cos(x) +--R + +--R 8 3 6 5 4 2 +--R (a b - 2a b + a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 2 7 4 5 8 2 +--R (2a b - 3a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 3 3 6 5 4 7 2 2 +--R (a b - 3a b + 3a b - a )cos(x) + (a b - 2a b + a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 8 4 6 6 4 8 2 2 7 +--R (a b - 3a b + 3a b - a b )cos(x) sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (a b - a b - 3a b + 5a b - 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 10 2 +--R (a b - 3a b + 3a b - a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 2a b + 3a b + 3a b - 7a b + 3a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 4a b + 12a b - 12a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (- 3a b + 7a b - 3a b - 3a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (a b - 3a b + 3a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (2a b - 5a b + 3a b + a b - a )cos(x) +--R * +--R sin(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (a b - 3a b + 3a b - a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (a b - 3a b + 3a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 9 3 7 5 5 7 3 2 7 +--R (2a b - 6a b + 6a b - 2a b )cos(x) sin(x) +--R + +--R 10 2 8 4 6 6 4 3 +--R (2b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (2b - 2a b - 6a b + 10a b - 4a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 10 2 8 4 6 6 4 8 2 3 +--R (- 4b + 14a b - 18a b + 10a b - 2a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (- 4b + 6a b + 6a b - 14a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (- 8a b + 24a b - 24a b + 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 6a b + 14a b - 6a b - 6a b + 4a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 10 2 8 4 6 6 4 8 2 3 +--R (2b - 10a b + 18a b - 14a b + 4a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 2 +--R (2b - 6a b + 6a b - 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (4a b - 10a b + 6a b + 2a b - 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 8 4 6 6 4 8 2 2 7 +--R (a b - 3a b + 3a b - a b )cos(x) sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (a b - a b - 3a b + 5a b - 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 10 2 +--R (a b - 3a b + 3a b - a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 2a b + 3a b + 3a b - 7a b + 3a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 4a b + 12a b - 12a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (- 3a b + 7a b - 3a b - 3a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (a b - 3a b + 3a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (2a b - 5a b + 3a b + a b - a )cos(x) +--R * +--R sin(x) +--R + +--R 3 7 5 5 7 3 9 3 3 7 5 5 7 3 9 2 +--R (a b - 3a b + 3a b - a b)cos(x) + (a b - 3a b + 3a b - a b)cos(x) +--R Type: Expression(Integer) +--E 435 + +--S 436 of 586 +m0574b:= a0574.2-r0574 +--R +--R +--R (421) +--R 3 3 3 2 2 4 2 +--R (4a b + 2a b)cos(x)sin(x) + (4a b + 2a )cos(x)sin(x) +--R + +--R 3 3 2 2 4 +--R (- 4a b - 2a b)cos(x)sin(x) + (- 4a b - 2a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 3 3 3 2 2 4 2 +--R (4a b + 2a b)cos(x)sin(x) + (4a b + 2a )cos(x)sin(x) +--R + +--R 3 3 2 2 4 +--R (- 4a b - 2a b)cos(x)sin(x) + (- 4a b - 2a )cos(x) +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 3 3 +--R (- 3a b cos(x) - a b + a )sin(x) +--R + +--R 2 3 2 2 +--R (- 3a b cos(x) + b - a b)sin(x) +--R + +--R 2 3 2 2 2 3 +--R ((- a b + a )cos(x) + 3a b cos(x) + a b - a )sin(x) +--R + +--R 3 2 2 2 3 2 +--R (b - a b)cos(x) + 3a b cos(x) - b + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 2 3 4 3 4 3 2 5 2 +--R (b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- b + 2a b - a b)cos(x)sin(x) + (- a b + 2a b - a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 586 +d0574b:= D(m0574b,x) +--R +--R +--R (422) +--R 3 3 5 9 +--R (- a b + a b)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 6 +--R ((- 2a b - a b )cos(x) + (- 2a b + 2a b )cos(x) - a b + a ) +--R * +--R 8 +--R sin(x) +--R + +--R 5 3 3 3 5 3 3 5 2 +--R (4a b + 2a b )cos(x) + (4a b - 2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (2a b - 6a b + 4a b)cos(x) + 2a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (- 2a b - a b )cos(x) + (10a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 6 2 4 +--R (15a b + 3a b )cos(x) + (8a b - 10a b + 2a )cos(x) + 5a b +--R + +--R 4 2 6 +--R - 4a b - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 5 4 5 3 3 3 +--R (- a b - 5a b)cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 5 3 3 5 2 +--R (- 12a b + 18a b + 6a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 4a b + 14a b - 10a b)cos(x) - 4a b + 8a b - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 6 4 +--R (4a b - 4a b )cos(x) + (3a b + 2a b - 2a )cos(x) +--R + +--R 2 4 3 2 4 4 2 2 +--R - 24a b cos(x) + (- 27a b + 3a b )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- 10a b + 14a b - 4a )cos(x) - 7a b + 8a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (2a b - 2a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 6a b + 14a b + 4a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (10a b - 14a b - 2a b)cos(x) + (10a b - 26a b - 8a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (2a b - 10a b + 8a b)cos(x) + 2a b - 6a b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 4a b - a )cos(x) + (- 10a b + 12a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (- 5a b + 9a b - a )cos(x) + (16a b - 2a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (15a b - 7a b - 2a )cos(x) + (4a b - 6a b + 2a )cos(x) +--R + +--R 2 4 4 2 6 +--R 3a b - 4a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (2a b - 5a b - 3a b)cos(x) + (- 2a b + 6a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 3 3 +--R (- 2a b + 10a b + 4a b)cos(x) + (2a b - 2a b)cos(x) + a b +--R + +--R 5 +--R - a b +--R * +--R sin(x) +--R + +--R 2 4 6 6 2 4 6 5 4 2 6 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + (- 2a b - a )cos(x) +--R + +--R 2 4 6 3 2 4 4 2 6 2 +--R (- 2a b + 2a )cos(x) + (- a b + 2a b + 2a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 9 +--R (- 2a b + 2a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 5 5 +--R ((- 8a b - 4a b )cos(x) + (- 4a b + 4a b )cos(x) - 2a b + 2a b) +--R * +--R 8 +--R sin(x) +--R + +--R 2 4 4 2 2 6 2 4 4 2 6 +--R (- 16a b - 8a b )cos(x) + (4b - 12a b + 8a b )cos(x) + 4b +--R + +--R 2 4 +--R - 4a b +--R * +--R 7 +--R sin(x) +--R + +--R 5 3 3 4 5 3 3 3 +--R (- 8a b - 4a b )cos(x) + (- 4a b - 8a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (18a b - 4a b - 2a b)cos(x) + (16a b - 20a b + 4a b)cos(x) +--R + +--R 5 3 3 5 +--R 10a b - 8a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 10a b - 14a b )cos(x) + (- 8b - 4a b - 12a b )cos(x) +--R + +--R 6 2 4 4 2 2 +--R (- 8b + 44a b + 12a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (- 8b + 28a b - 20a b )cos(x) - 8b + 16a b - 8a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (8a b - 8a b )cos(x) + (14a b + 4a b - 6a b)cos(x) +--R + +--R 3 3 5 3 5 3 3 5 2 +--R (16a b - 4a b)cos(x) + (- 18a b + 28a b + 2a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 20a b + 28a b - 8a b)cos(x) - 14a b + 16a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (4a b - 4a b )cos(x) + (- 12b + 24a b - 12a b )cos(x) +--R + +--R 6 2 4 4 2 4 +--R (- 12b + 44a b + 16a b )cos(x) +--R + +--R 6 2 4 4 2 3 6 2 4 4 2 2 +--R (12b + 16a b + 20a b )cos(x) + (12b - 32a b - 4a b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (4b - 20a b + 16a b )cos(x) + 4b - 12a b + 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 6a b + 8a b - 2a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 20a b + 24a b - 4a b)cos(x) +--R + +--R 5 3 3 5 4 5 5 3 +--R (- 14a b + 24a b + 2a b)cos(x) + (8a b + 4a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (10a b - 20a b - 2a b)cos(x) + (8a b - 12a b + 4a b)cos(x) +--R + +--R 5 3 3 5 +--R 6a b - 8a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (- 4a b + 4a b )cos(x) + (4b - 8a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 4 6 2 4 4 2 3 +--R (4b - 18a b - 10a b )cos(x) + (- 4b - 12a b - 8a b )cos(x) +--R + +--R 6 2 4 2 2 4 4 2 2 4 4 2 +--R (- 4b + 4a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 5 5 6 5 5 5 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 3 5 4 5 3 3 3 +--R (- 8a b - 4a b)cos(x) + (- 4a b - 8a b )cos(x) +--R + +--R 5 5 2 +--R (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 5 9 +--R (- a b + a b)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 4 6 8 +--R ((- 2a b - a b )cos(x) + (- 2a b + 2a b )cos(x) - a b + a )sin(x) +--R + +--R 5 3 3 3 5 3 3 5 2 +--R (4a b + 2a b )cos(x) + (4a b - 2a b - 2a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (2a b - 6a b + 4a b)cos(x) + 2a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (- 2a b - a b )cos(x) + (10a b + 2a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 6 2 4 +--R (15a b + 3a b )cos(x) + (8a b - 10a b + 2a )cos(x) + 5a b +--R + +--R 4 2 6 +--R - 4a b - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 5 4 5 3 3 3 +--R (- a b - 5a b)cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 12a b + 18a b + 6a b)cos(x) + (- 4a b + 14a b - 10a b)cos(x) +--R + +--R 5 3 3 5 +--R - 4a b + 8a b - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 6 4 2 4 3 +--R (4a b - 4a b )cos(x) + (3a b + 2a b - 2a )cos(x) - 24a b cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 6 2 4 +--R (- 27a b + 3a b )cos(x) + (- 10a b + 14a b - 4a )cos(x) - 7a b +--R + +--R 4 2 6 +--R 8a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (2a b - 2a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (- 6a b + 14a b + 4a b)cos(x) + (10a b - 14a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (10a b - 26a b - 8a b)cos(x) + (2a b - 10a b + 8a b)cos(x) +--R + +--R 5 3 3 5 +--R 2a b - 6a b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 4a b - a )cos(x) + (- 10a b + 12a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (- 5a b + 9a b - a )cos(x) + (16a b - 2a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 2 4 +--R (15a b - 7a b - 2a )cos(x) + (4a b - 6a b + 2a )cos(x) + 3a b +--R + +--R 4 2 6 +--R - 4a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (2a b - 5a b - 3a b)cos(x) + (- 2a b + 6a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 3 3 5 +--R (- 2a b + 10a b + 4a b)cos(x) + (2a b - 2a b)cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 2 4 6 6 2 4 6 5 4 2 6 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + (- 2a b - a )cos(x) +--R + +--R 2 4 6 3 2 4 4 2 6 2 +--R (- 2a b + 2a )cos(x) + (- a b + 2a b + 2a )cos(x) +--R / +--R 2 6 4 4 6 2 2 8 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (a b - 2a b + a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (3a b - 5a b + a b + a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 4a b + 14a b - 16a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 4a b + 8a b - 4a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 2a b + 5a b - 4a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 12a b + 26a b - 16a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 9a b + 17a b - 7a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (2a b - 16a b + 26a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 10a b + 14a b - 6a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (a b - 4a b + 5a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (6a b - 16a b + 14a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (5a b - 11a b + 7a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (2a b - 4a b + 2a b)cos(x) + (6a b - 12a b + 6a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (4a b - 8a b + 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 8 3 +--R (a b - 2a b + a )cos(x) + (2a b - 4a b + 2a )cos(x) +--R + +--R 4 4 6 2 8 2 +--R (a b - 2a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 2 8 +--R (2a b - 4a b + 2a b )cos(x) sin(x) +--R + +--R 8 2 6 4 4 3 +--R (4b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (4b - 4a b - 4a b + 4a b )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (12a b - 24a b + 12a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (6a b - 10a b + 2a b + 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 8b + 28a b - 32a b + 12a b )cos(x) +--R + +--R 8 2 6 4 4 2 +--R (- 8b + 16a b - 8a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 4a b + 10a b - 8a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 24a b + 52a b - 32a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 18a b + 34a b - 14a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (4b - 32a b + 52a b - 24a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (4b - 20a b + 28a b - 12a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b - 8a b + 10a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (12a b - 32a b + 28a b - 8a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (10a b - 22a b + 14a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (12a b - 24a b + 12a b )cos(x) + (8a b - 16a b + 8a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (2a b - 4a b + 2a b)cos(x) + (4a b - 8a b + 4a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (2a b - 4a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 8 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (a b - 2a b + a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (3a b - 5a b + a b + a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 4a b + 14a b - 16a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 4a b + 8a b - 4a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 2a b + 5a b - 4a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 12a b + 26a b - 16a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 9a b + 17a b - 7a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (2a b - 16a b + 26a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 10a b + 14a b - 6a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (a b - 4a b + 5a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (6a b - 16a b + 14a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (5a b - 11a b + 7a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (2a b - 4a b + 2a b)cos(x) + (6a b - 12a b + 6a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (4a b - 8a b + 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 8 3 +--R (a b - 2a b + a )cos(x) + (2a b - 4a b + 2a )cos(x) +--R + +--R 4 4 6 2 8 2 +--R (a b - 2a b + a )cos(x) +--R Type: Expression(Integer) +--E 437 + +--S 438 of 586 +t0575:= tan(x)/(a+a*sin(x))^2 +--R +--R +--R tan(x) +--R (423) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 438 + +--S 439 of 586 +r0575:= 1/4*atanh(sin(x))/a^2+1/4/a^2/(1+sin(x))^2-1/4/a^2/(1+sin(x)) +--R +--R +--R 2 +--R (sin(x) + 2sin(x) + 1)atanh(sin(x)) - sin(x) +--R (424) --------------------------------------------- +--R 2 2 2 2 +--R 4a sin(x) + 8a sin(x) + 4a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 586 +a0575:= integrate(t0575,x) +--R +--R +--R (425) +--R 2 sin(x) + cos(x) + 1 +--R (2sin(x) - cos(x) + 2)log(-------------------) +--R cos(x) + 1 +--R + +--R 2 sin(x) - cos(x) - 1 +--R (- 2sin(x) + cos(x) - 2)log(-------------------) - sin(x) +--R cos(x) + 1 +--R / +--R 2 2 2 2 +--R 8a sin(x) - 4a cos(x) + 8a +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 586 +m0575:= a0575-r0575 +--R +--R +--R (426) +--R 3 2 2 2 2 +--R 2sin(x) + (- cos(x) + 6)sin(x) + (- 2cos(x) + 6)sin(x) - cos(x) +--R + +--R 2 +--R * +--R sin(x) + cos(x) + 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 2 2 2 +--R - 2sin(x) + (cos(x) - 6)sin(x) + (2cos(x) - 6)sin(x) + cos(x) +--R + +--R - 2 +--R * +--R sin(x) - cos(x) - 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 2 2 2 +--R - 2sin(x) + (cos(x) - 6)sin(x) + (2cos(x) - 6)sin(x) + cos(x) +--R + +--R - 2 +--R * +--R atanh(sin(x)) +--R + +--R 3 2 +--R - sin(x) + (- cos(x) + 1)sin(x) +--R / +--R 2 3 2 2 2 2 2 2 2 +--R 8a sin(x) + (- 4a cos(x) + 24a )sin(x) + (- 8a cos(x) + 24a )sin(x) +--R + +--R 2 2 2 +--R - 4a cos(x) + 8a +--R Type: Expression(Integer) +--E 441 + +--S 442 of 586 +d0575:= D(m0575,x) +--R +--R +--R (427) +--R 8 2 7 +--R (2cos(x) - 8)sin(x) + (8cos(x) + 4cos(x) - 32)sin(x) +--R + +--R 4 3 2 6 +--R (- 2cos(x) - cos(x) + 12cos(x) - 12cos(x) - 40)sin(x) +--R + +--R 4 3 2 5 +--R (4cos(x) + 6cos(x) - 24cos(x) - 28cos(x))sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) - 3cos(x) + 22cos(x) + 9cos(x) - 52cos(x) - 8cos(x) +--R + +--R 40 +--R * +--R 4 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 4cos(x) - 2cos(x) + 16cos(x) - 12cos(x) - 40cos(x) + 12cos(x) +--R + +--R 32 +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (16cos(x) + 18cos(x) - 31cos(x) - 28cos(x) + 12cos(x) + 8)sin(x) +--R + +--R 7 6 5 4 3 2 +--R - 4cos(x) - 4cos(x) + 18cos(x) + 12cos(x) - 26cos(x) - 8cos(x) +--R + +--R 12cos(x) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 3cos(x) - 6cos(x) - 9cos(x) + 4cos(x) + 6cos(x) +--R / +--R 2 8 2 2 2 7 +--R 16a sin(x) + (- 16a cos(x) + 64a )sin(x) +--R + +--R 2 4 2 2 2 2 6 +--R (4a cos(x) - 64a cos(x) - 32a cos(x) + 64a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 5 +--R (24a cos(x) + 32a cos(x) - 80a cos(x) - 128a cos(x) - 64a )sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 +--R - 4a cos(x) - 8a cos(x) + 44a cos(x) + 96a cos(x) - 160a cos(x) +--R + +--R 2 +--R - 160a +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R - 8a cos(x) - 16a cos(x) + 16a cos(x) + 64a cos(x) + 80a cos(x) +--R + +--R 2 +--R - 64a +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (- 36a cos(x) - 64a cos(x) + 64a cos(x) + 160a cos(x) + 64a )sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 8a cos(x) + 16a cos(x) - 40a cos(x) - 96a cos(x) + 16a cos(x) +--R + +--R 2 2 +--R 128a cos(x) + 64a +--R * +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 4a cos(x) + 8a cos(x) - 12a cos(x) - 32a cos(x) + 32a cos(x) + 16a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 586 +t0576:= tan(x)^2/(a+a*sin(x))^2 +--R +--R +--R 2 +--R tan(x) +--R (428) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 443 + +--S 444 of 586 +r0576:= 1/15/cos(x)^5/a^2*(cos(x)^4*sin(x)-_ + 7*sin(x)*cos(x)^2+6*sin(x)-6+10*cos(x)^2) +--R +--R +--R 4 2 2 +--R (cos(x) - 7cos(x) + 6)sin(x) + 10cos(x) - 6 +--R (429) ---------------------------------------------- +--R 2 5 +--R 15a cos(x) +--R Type: Expression(Integer) +--E 444 + +--S 445 of 586 +a0576:= integrate(t0576,x) +--R +--R +--R 2 3 2 +--R (- cos(x) + 8cos(x) + 9)sin(x) - 4cos(x) - 2cos(x) + 8cos(x) + 6 +--R (430) ------------------------------------------------------------------- +--R 2 2 3 2 +--R 30a cos(x)sin(x) - 15a cos(x) + 30a cos(x) +--R Type: Union(Expression(Integer),...) +--E 445 + +--S 446 of 586 +m0576:= a0576-r0576 +--R +--R +--R (431) +--R 4 2 2 5 7 +--R (- 2cos(x) + 14cos(x) - 12)sin(x) + 8cos(x) sin(x) - 4cos(x) +--R + +--R 6 5 4 2 +--R - 2cos(x) + 8cos(x) + 16cos(x) - 26cos(x) + 12 +--R / +--R 2 5 2 7 2 5 +--R 30a cos(x) sin(x) - 15a cos(x) + 30a cos(x) +--R Type: Expression(Integer) +--E 446 + +--S 447 of 586 +d0576:= D(m0576,x) +--R +--R +--R (432) +--R 4 2 4 +--R (- 4cos(x) + 84cos(x) - 120)sin(x) +--R + +--R 6 4 2 3 +--R (6cos(x) - 74cos(x) + 168cos(x) - 120)sin(x) +--R + +--R 4 2 2 +--R (60cos(x) - 180cos(x) + 120)sin(x) +--R + +--R 8 6 4 2 8 +--R (6cos(x) - 80cos(x) + 242cos(x) - 288cos(x) + 120)sin(x) + 4cos(x) +--R + +--R 6 4 2 +--R - 32cos(x) + 52cos(x) - 24cos(x) +--R / +--R 2 6 2 2 8 2 6 2 10 +--R 60a cos(x) sin(x) + (- 60a cos(x) + 120a cos(x) )sin(x) + 15a cos(x) +--R + +--R 2 8 2 6 +--R - 60a cos(x) + 60a cos(x) +--R Type: Expression(Integer) +--E 447 + +--S 448 of 586 +t0577:= cot(x)^2/(a+b*sin(x))^2 +--R +--R +--R 2 +--R cot(x) +--R (433) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 448 + +--S 449 of 586 +r0577:= -2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(1/2)+_ + 4*b^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)+_ + 2*b*atanh(cos(x))/a^3-cot(x)/a^2-b*cos(x)/a^2/(a+b*sin(x)) +--R +--R +--R (434) +--R +---------+ +--R 2 | 2 2 +--R (2b sin(x) + 2a b)\|- b + a atanh(cos(x)) +--R + +--R x +--R a tan(-) + b +--R 3 2 2 3 2 +--R ((4b - 2a b)sin(x) + 4a b - 2a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R (- a b cot(x)sin(x) - a cot(x) - a b cos(x))\|- b + a +--R / +--R +---------+ +--R 3 4 | 2 2 +--R (a b sin(x) + a )\|- b + a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 586 +a0577:= integrate(t0577,x) +--R +--R +--R (435) +--R [ +--R 2 3 3 2 2 3 2 +--R ((2a b - a )sin(x) + (- 2b + a b)cos(x) + 2b - a b) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 sin(x) +--R (- 2a b sin(x) + 2b cos(x) - 2b )\|b - a log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 2 2 2 2 | 2 2 +--R ((- 2a b cos(x) - a b)sin(x) + b cos(x) - a cos(x) - b )\|b - a +--R / +--R +-------+ +--R 4 3 2 3 | 2 2 +--R (a sin(x) - a b cos(x) + a b)\|b - a +--R , +--R +--R +---------+ +--R 2 2 2 | 2 2 sin(x) +--R (- 2a b sin(x) + 2b cos(x) - 2b )\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R 2 3 3 2 2 3 2 +--R ((- 4a b + 2a )sin(x) + (4b - 2a b)cos(x) - 4b + 2a b) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- 2a b cos(x) - a b)sin(x) + b cos(x) - a cos(x) - b )\|- b + a +--R / +--R +---------+ +--R 4 3 2 3 | 2 2 +--R (a sin(x) - a b cos(x) + a b)\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 450 + +--S 451 of 586 +m0577a:= a0577.1-r0577 +--R +--R +--R (436) +--R 3 3 2 +--R (2a b - a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 4 +--R ((- 2b + a b )cos(x) + 2b + a b - a )sin(x) +--R + +--R 3 3 2 3 3 +--R (- 2a b + a b)cos(x) + 2a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 2 2 3 2 3 2 2 2 +--R - 2a b sin(x) + (2b cos(x) - 2b - 2a b)sin(x) + 2a b cos(x) +--R + +--R 2 +--R - 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) +--R \|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 2 3 2 2 2 +--R - 2a b sin(x) + (2b cos(x) - 2b - 2a b)sin(x) + 2a b cos(x) +--R + +--R 2 +--R - 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atanh(cos(x)) +--R + +--R 3 3 2 +--R (- 4a b + 2a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 4 +--R ((4b - 2a b )cos(x) - 4b - 2a b + 2a )sin(x) +--R + +--R 3 3 2 3 3 +--R (4a b - 2a b)cos(x) - 4a b + 2a b +--R * +--R x +--R +-------+ a tan(-) + b +--R | 2 2 2 +--R \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R (a b cot(x) - 2a b cos(x) - a b )sin(x) +--R + +--R 2 2 2 3 3 2 2 3 +--R (- a b cos(x) + a b + a )cot(x) + b cos(x) - 2a b cos(x) - b +--R + +--R 2 +--R - a b +--R * +--R sin(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- a b cos(x) + a b)cot(x) - a b cos(x) + a b cos(x) +--R + +--R 2 3 2 +--R (a b - a )cos(x) - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 2 3 2 2 3 2 5 4 2 4 +--R (a b sin(x) + (- a b cos(x) + a b + a )sin(x) - a b cos(x) + a b) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 586 +d0577a:= D(m0577a,x) +--R +--R +--R (437) +--R 4 4 2 4 4 4 4 7 +--R (2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 5 3 2 5 3 2 3 5 4 +--R (- a b cos(x) + a b )cot(x) + 2a b cos(x) +--R + +--R 3 5 5 3 3 5 3 2 +--R (6a b - 2a b )cos(x) + 5a b cos(x) +--R + +--R 3 5 5 3 3 5 5 3 +--R (- 8a b - 2a b )cos(x) - 4a b - 3a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 4 4 4 4 6 2 3 +--R 2a b cos(x) + (- a b + a b )cos(x) +--R + +--R 4 4 6 2 2 4 4 6 2 4 4 +--R (- 5a b - 2a b )cos(x) + (a b - a b )cos(x) + 3a b +--R + +--R 6 2 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 5 2 6 4 4 4 +--R - 2a b cos(x) + (6a b + 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (6a b + 12a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 6a b - 4a b + 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 +--R (- 6a b - 14a b + 2a b )cos(x) - 5a b - a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 6 3 5 5 3 5 +--R - a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 5 5 3 4 3 5 5 3 7 3 +--R (5a b + 4a b )cos(x) + (- 4a b + 2a b + 2a b)cos(x) +--R + +--R 3 5 5 3 7 2 3 5 7 +--R (- 7a b - 10a b - a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 +--R 3a b + 6a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 6 7 3 5 5 3 5 +--R (- 2a b + 2a b )cos(x) + (2a b + 3a b - 7a b )cos(x) +--R + +--R 7 3 5 5 3 4 +--R (8a b + 13a b + 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 4a b + 8a b + 8a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 10a b - 18a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (2a b - 11a b - 3a b + 2a b)cos(x) + 4a b + 3a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 7 2 6 4 4 6 +--R (- a b + a b )cos(x) + (- a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (3a b + a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (3a b + 10a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 3a b - 5a b + 7a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 3a b - 14a b - 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (a b + 3a b - 3a b - a )cos(x) + a b + 6a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 2 6 4 4 7 8 2 6 4 4 6 +--R (- 2b + a b - a b )cos(x) + (- 2b - 3a b + 5a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (6b + 3a b + 11a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (6b + 15a b + a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 6b - 9a b - 11a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 6b - 21a b - 9a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (2b + 5a b + a b + 2a b )cos(x) + 2b + 9a b + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 7 3 5 5 3 6 +--R (- 2a b + 2a b )cos(x) + (- 2a b - a b )cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 4 +--R (6a b - 4a b - 2a b)cos(x) + (6a b + 5a b )cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 6a b + 2a b + 4a b)cos(x) +--R + +--R 3 5 5 3 2 3 5 7 3 5 +--R (- 6a b - 7a b )cos(x) + (2a b - 2a b)cos(x) + 2a b +--R + +--R 5 3 +--R 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 7 +--R (- 4a b + 2a b - 4a b )cos(x) +--R + +--R 7 3 5 5 3 6 +--R (- 4a b + 7a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (12a b + 6a b + 15a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (12a b - 9a b + 8a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 12a b - 18a b - 16a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 12a b - 3a b - 5a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 +--R (4a b + 10a b + 5a b - a b)cos(x) + 4a b + 5a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 6 2 7 4 4 6 +--R (- a b + a b )cos(x) - a b cos(x) +--R + +--R 4 4 6 2 5 4 4 4 +--R (3a b - 3a b )cos(x) + 3a b cos(x) +--R + +--R 4 4 6 2 3 4 4 2 +--R (- 3a b + 3a b )cos(x) - 3a b cos(x) +--R + +--R 4 4 6 2 4 4 +--R (a b - a b )cos(x) + a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 9 2 6 4 4 8 +--R (- a b + a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- a b - 4a b - a b )cos(x) +--R + +--R 2 6 4 4 6 2 6 +--R (7a b - 3a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (9a b + 12a b + 2a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b - 3a b + 9a b )cos(x) +--R + +--R 2 6 4 4 8 3 +--R (- 11a b - 16a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 3a b + 3a b - 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 +--R (4a b + 7a b - a b )cos(x) + 2a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 8 3 5 7 3 5 5 3 6 +--R (- 2a b + 2a b )cos(x) - 2a b cos(x) + (6a b - 6a b )cos(x) +--R + +--R 3 5 5 3 5 5 3 4 3 5 3 +--R 6a b cos(x) + (- 6a b + 6a b )cos(x) - 6a b cos(x) +--R + +--R 3 5 5 3 2 3 5 +--R (2a b - 2a b )cos(x) + 2a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 2 3 5 3 5 7 +--R (4a b cos(x) - 4a b cos(x) - 4a b )sin(x) +--R + +--R 4 4 2 4 4 2 2 6 4 +--R (- 2a b cos(x) + 2a b )cot(x) + 4a b cos(x) +--R + +--R 2 6 4 4 3 2 6 4 4 2 +--R (12a b - 4a b )cos(x) + (4a b + 8a b )cos(x) +--R + +--R 2 6 4 4 2 6 4 4 +--R (- 16a b - 4a b )cos(x) - 12a b - 4a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 4 3 5 5 3 3 +--R 4a b cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 5 5 3 2 3 5 5 3 3 5 +--R (- 10a b - 4a b )cos(x) + (2a b - 2a b )cos(x) + 6a b +--R + +--R 5 3 +--R 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 7 3 5 4 +--R - 4a b cos(x) + (4a b + 14a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (16a b + 18a b - 6a b )cos(x) +--R + +--R 7 3 5 5 3 2 +--R (8a b - 10a b + 6a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 +--R (- 16a b - 22a b + 2a b )cos(x) - 12a b - 12a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 6 2 6 4 4 5 +--R - 2a b cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 6 4 4 4 +--R (10a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 8a b + 4a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 14a b - 20a b - 2a b )cos(x) +--R + +--R 2 6 6 2 2 6 4 4 6 2 +--R (4a b - 4a b )cos(x) + 6a b + 12a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 6 8 2 6 4 4 5 +--R 2a b cos(x) + (- 4b + 18a b - 18a b )cos(x) +--R + +--R 8 2 6 4 4 4 8 4 4 3 +--R (- 4b + 20a b + 14a b )cos(x) + (8b + 12a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (8b - 10a b - 24a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 8 2 6 4 4 6 2 +--R (- 4b - 18a b + 2a b )cos(x) - 4b - 12a b + 6a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 7 7 3 5 6 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 4a b )cos(x) +--R + +--R 7 3 5 5 3 5 +--R (6a b + 2a b - 8a b )cos(x) +--R + +--R 7 3 5 5 3 4 +--R (6a b + 20a b + 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 6a b - 10a b + 14a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 6a b - 28a b - 10a b )cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 +--R (2a b + 6a b - 6a b - 2a b)cos(x) + 2a b + 12a b +--R + +--R 5 3 +--R 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 7 3 5 6 +--R - 4a b cos(x) + 6a b cos(x) +--R + +--R 7 3 5 5 3 5 +--R (8a b + 40a b - 24a b )cos(x) +--R + +--R 7 3 5 5 3 4 +--R (- 4a b + 14a b + 12a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 4a b - 60a b + 22a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (8a b - 26a b - 18a b )cos(x) +--R + +--R 3 5 5 3 7 7 3 5 5 3 +--R (20a b + 2a b - 2a b)cos(x) - 4a b + 6a b + 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 7 2 6 4 4 6 +--R (- 4a b + 4a b )cos(x) + (- 4a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (12a b - 8a b - 4a b )cos(x) +--R + +--R 2 6 4 4 4 +--R (12a b + 10a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 12a b + 4a b + 8a b )cos(x) +--R + +--R 2 6 4 4 2 2 6 6 2 +--R (- 12a b - 14a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 6 4 4 +--R 4a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 7 2 6 4 4 6 +--R (- 8a b - 4a b )cos(x) + (14a b - 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (40a b + 30a b - 14a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 26a b + 26a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 56a b - 44a b + 20a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (10a b - 24a b - 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 +--R (24a b + 18a b - 6a b )cos(x) + 2a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 5 3 7 3 5 6 +--R (- 2a b + 2a b )cos(x) - 2a b cos(x) +--R + +--R 3 5 5 3 5 3 5 4 +--R (6a b - 6a b )cos(x) + 6a b cos(x) +--R + +--R 3 5 5 3 3 3 5 2 +--R (- 6a b + 6a b )cos(x) - 6a b cos(x) +--R + +--R 3 5 5 3 3 5 +--R (2a b - 2a b )cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 9 7 3 5 8 +--R (- 2a b + 2a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 7 3 5 7 7 3 5 5 3 6 +--R (2a b - 14a b )cos(x) + (18a b - 8a b - 8a b )cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (6a b + 42a b - 2a b - 2a b)cos(x) +--R + +--R 7 5 3 4 +--R (- 18a b + 18a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 10a b - 50a b + 6a b + 2a b)cos(x) +--R + +--R 7 5 3 2 7 3 5 5 3 +--R (6a b - 10a b )cos(x) + (4a b + 20a b - 4a b )cos(x) +--R + +--R 3 5 +--R 2a b +--R * +--R sin(x) +--R + +--R 2 6 4 4 8 2 6 7 +--R (- 4a b + 4a b )cos(x) - 4a b cos(x) +--R + +--R 2 6 4 4 6 2 6 5 +--R (12a b - 12a b )cos(x) + 12a b cos(x) +--R + +--R 2 6 4 4 4 2 6 3 +--R (- 12a b + 12a b )cos(x) - 12a b cos(x) +--R + +--R 2 6 4 4 2 2 6 +--R (4a b - 4a b )cos(x) + 4a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 4 2 4 4 4 4 7 +--R (2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 5 3 2 5 3 2 3 5 4 +--R (- a b cos(x) + a b )cot(x) + 2a b cos(x) +--R + +--R 3 5 5 3 3 5 3 2 3 5 5 3 +--R (6a b - 2a b )cos(x) + 5a b cos(x) + (- 8a b - 2a b )cos(x) +--R + +--R 3 5 5 3 +--R - 4a b - 3a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 4 4 4 4 6 2 3 +--R 2a b cos(x) + (- a b + a b )cos(x) +--R + +--R 4 4 6 2 2 4 4 6 2 4 4 6 2 +--R (- 5a b - 2a b )cos(x) + (a b - a b )cos(x) + 3a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 5 2 6 4 4 4 +--R - 2a b cos(x) + (6a b + 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (6a b + 12a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 6a b - 4a b + 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 +--R (- 6a b - 14a b + 2a b )cos(x) - 5a b - a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 6 3 5 5 3 5 +--R - a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 5 5 3 4 3 5 5 3 7 3 +--R (5a b + 4a b )cos(x) + (- 4a b + 2a b + 2a b)cos(x) +--R + +--R 3 5 5 3 7 2 3 5 7 +--R (- 7a b - 10a b - a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 +--R 3a b + 6a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 6 7 3 5 5 3 5 +--R (- 2a b + 2a b )cos(x) + (2a b + 3a b - 7a b )cos(x) +--R + +--R 7 3 5 5 3 4 +--R (8a b + 13a b + 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 4a b + 8a b + 8a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 10a b - 18a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (2a b - 11a b - 3a b + 2a b)cos(x) + 4a b + 3a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 7 2 6 4 4 6 +--R (- a b + a b )cos(x) + (- a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 5 +--R (3a b + a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (3a b + 10a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 3a b - 5a b + 7a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 3a b - 14a b - 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (a b + 3a b - 3a b - a )cos(x) + a b + 6a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 2 6 4 4 7 8 2 6 4 4 6 +--R (- 2b + a b - a b )cos(x) + (- 2b - 3a b + 5a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (6b + 3a b + 11a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (6b + 15a b + a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 6b - 9a b - 11a b + 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 6b - 21a b - 9a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (2b + 5a b + a b + 2a b )cos(x) + 2b + 9a b + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 5 5 3 7 3 5 5 3 6 +--R (- 2a b + 2a b )cos(x) + (- 2a b - a b )cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 4 +--R (6a b - 4a b - 2a b)cos(x) + (6a b + 5a b )cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 2 +--R (- 6a b + 2a b + 4a b)cos(x) + (- 6a b - 7a b )cos(x) +--R + +--R 3 5 7 3 5 5 3 +--R (2a b - 2a b)cos(x) + 2a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 7 +--R (- 4a b + 2a b - 4a b )cos(x) +--R + +--R 7 3 5 5 3 6 +--R (- 4a b + 7a b - 3a b )cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (12a b + 6a b + 15a b - 5a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (12a b - 9a b + 8a b + 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 12a b - 18a b - 16a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 12a b - 3a b - 5a b - 3a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 +--R (4a b + 10a b + 5a b - a b)cos(x) + 4a b + 5a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 6 2 7 4 4 6 4 4 6 2 5 +--R (- a b + a b )cos(x) - a b cos(x) + (3a b - 3a b )cos(x) +--R + +--R 4 4 4 4 4 6 2 3 4 4 2 +--R 3a b cos(x) + (- 3a b + 3a b )cos(x) - 3a b cos(x) +--R + +--R 4 4 6 2 4 4 +--R (a b - a b )cos(x) + a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 9 2 6 4 4 8 +--R (- a b + a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 7 2 6 4 4 6 2 6 +--R (- a b - 4a b - a b )cos(x) + (7a b - 3a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (9a b + 12a b + 2a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 3a b - 3a b + 9a b )cos(x) +--R + +--R 2 6 4 4 8 3 +--R (- 11a b - 16a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 +--R (- 3a b + 3a b - 5a b )cos(x) + (4a b + 7a b - a b )cos(x) +--R + +--R 2 6 +--R 2a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 8 3 5 7 3 5 5 3 6 +--R (- 2a b + 2a b )cos(x) - 2a b cos(x) + (6a b - 6a b )cos(x) +--R + +--R 3 5 5 3 5 5 3 4 3 5 3 +--R 6a b cos(x) + (- 6a b + 6a b )cos(x) - 6a b cos(x) +--R + +--R 3 5 5 3 2 3 5 +--R (2a b - 2a b )cos(x) + 2a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 5 6 3 2 4 5 6 3 4 5 6 3 +--R ((- 2a b + 2a b )cos(x) + (2a b - 2a b )cos(x) + 2a b - 2a b ) +--R * +--R 7 +--R sin(x) +--R + +--R 5 4 7 2 2 5 4 7 2 2 +--R ((a b - a b )cos(x) - a b + a b )cot(x) +--R + +--R 3 6 5 4 4 3 6 5 4 3 +--R (- 2a b + 2a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 5 4 7 2 2 3 6 5 4 7 2 3 6 +--R (- 3a b + 3a b )cos(x) + (8a b - 4a b - 4a b )cos(x) + 4a b +--R + +--R 5 4 7 2 +--R - a b - 3a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 5 6 3 4 4 5 6 3 3 +--R (- 2a b + 2a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 5 6 3 8 2 4 5 6 3 4 5 +--R (5a b - 3a b - 2a b)cos(x) + (- a b + a b )cos(x) - 3a b +--R + +--R 6 3 8 +--R a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 6 3 4 +--R (- 6a b - 3a b + 9a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (- 6a b - 4a b + 10a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (6a b + 2a b - 9a b + a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 5 6 3 8 +--R (6a b + 8a b - 12a b - 2a b)cos(x) + 5a b - 4a b - a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 6 5 4 6 3 6 5 4 5 +--R (a b - a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 5a b + a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (4a b - 2a b - 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 2 3 6 7 2 +--R (7a b + 3a b - 9a b - a )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 +--R - 3a b - 3a b + 5a b + a +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 6 8 3 6 5 4 5 +--R (2a b - 2a b )cos(x) + (- 2a b - 5a b + 7a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 8a b - 9a b + 8a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (4a b - 4a b - 2a b + 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (10a b + 10a b - 10a b - 10a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (- 2a b + 9a b - 3a b - 4a b )cos(x) - 4a b + a b + 4a b +--R + +--R 7 2 +--R - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 7 2 7 4 5 6 3 6 +--R (a b - a b )cos(x) + (a b + a b - 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 5 +--R (- 3a b - a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 3a b - 7a b + 8a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (3a b + 5a b - 7a b - a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (3a b + 11a b - 9a b - 5a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 +--R (- a b - 3a b + 3a b + a b)cos(x) - a b - 5a b + 3a b +--R + +--R 8 +--R 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 2 7 4 5 7 9 2 7 4 5 6 3 6 +--R (2b - a b - a b )cos(x) + (2b + a b - 8a b + 5a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (- 6b - 3a b - 5a b + 14a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (- 6b - 9a b + 14a b - 3a b + 4a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (6b + 9a b + 5a b - 18a b - 2a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (6b + 15a b - 12a b - 5a b - 4a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 9 2 7 4 5 +--R (- 2b - 5a b + a b + 4a b + 2a b)cos(x) - 2b - 7a b + 6a b +--R + +--R 6 3 +--R 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 6 5 4 7 3 6 5 4 7 2 6 +--R (2a b - 2a b )cos(x) + (2a b - a b - a b )cos(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- 6a b + 4a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 6a b + a b + 5a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (6a b - 2a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 3 6 7 2 +--R (6a b + a b - 7a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 +--R - 2a b - a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 5 4 8 8 3 6 7 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 6 +--R (4a b - 17a b + 10a b + 3a b )cos(x) +--R + +--R 8 5 4 7 2 5 +--R (- 12a b + 3a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 4 +--R (- 12a b + 27a b - 11a b - 5a b + a )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (12a b + 12a b - 8a b - 16a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (12a b - 11a b - 2a b + 2a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (- 4a b - 8a b + 5a b + 7a b )cos(x) - 4a b - a b + 5a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 3 7 4 5 6 3 6 +--R (a b - a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 5 6 3 5 4 5 6 3 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 4 5 6 3 3 4 5 6 3 2 +--R (3a b - 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 4 5 6 3 4 5 6 3 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 9 2 7 4 5 6 3 8 +--R (a b - a b )cos(x) + (3a b - 2a b - a b )cos(x) +--R + +--R 2 7 6 3 7 2 7 4 5 6 3 6 +--R (a b - a b )cos(x) + (- 7a b - 2a b + 9a b )cos(x) +--R + +--R 2 7 6 3 8 5 +--R (- 9a b + 8a b + a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b + 12a b - 16a b + a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (11a b + 4a b - 14a b - a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (3a b - 10a b + 8a b - a b)cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 +--R (- 4a b - 3a b + 7a b )cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 3 6 5 4 8 3 6 5 4 7 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 6 5 4 6 3 6 5 4 5 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 3 6 5 4 4 3 6 5 4 3 +--R (6a b - 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 3 6 5 4 2 3 6 5 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 6 5 4 2 3 6 5 4 3 6 5 4 +--R ((- 4a b + 4a b )cos(x) + (4a b - 4a b )cos(x) + 4a b - 4a b ) +--R * +--R 7 +--R sin(x) +--R + +--R 4 5 6 3 2 4 5 6 3 2 +--R ((2a b - 2a b )cos(x) - 2a b + 2a b )cot(x) +--R + +--R 2 7 4 5 4 2 7 4 5 3 +--R (- 4a b + 4a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 2 7 6 3 2 2 7 4 5 6 3 +--R (- 4a b + 4a b )cos(x) + (16a b - 8a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 +--R 12a b - 8a b - 4a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 6 5 4 4 3 6 5 4 3 +--R (- 4a b + 4a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 3 6 5 4 +--R (10a b - 6a b - 4a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 +--R - 6a b + 2a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 5 4 4 +--R (- 4a b - 18a b + 22a b )cos(x) +--R + +--R 8 3 6 5 4 3 +--R (- 16a b - 2a b + 18a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 8a b + 26a b - 16a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 5 4 7 2 +--R (16a b + 10a b - 22a b - 4a b )cos(x) + 12a b - 14a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 6 2 7 4 5 5 +--R (2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 +--R (- 10a b + 2a b + 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (8a b - 4a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (14a b + 6a b - 18a b - 2a b)cos(x) +--R + +--R 2 7 6 3 2 7 4 5 6 3 8 +--R (- 4a b + 4a b )cos(x) - 6a b - 6a b + 10a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 6 9 2 7 4 5 5 +--R (2a b - 2a b )cos(x) + (4b - 22a b + 18a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 4 9 2 7 3 +--R (4b - 32a b + 2a b + 26a b )cos(x) + (- 8b + 8a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (- 8b + 22a b + 22a b - 34a b - 2a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 9 2 7 4 5 +--R (4b + 14a b - 14a b - 4a b )cos(x) + 4b + 8a b - 18a b +--R + +--R 6 3 8 +--R 4a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 8 3 6 7 8 3 6 5 4 6 +--R (2a b - 2a b )cos(x) + (2a b + 2a b - 4a b )cos(x) +--R + +--R 8 3 6 5 4 5 +--R (- 6a b - 2a b + 8a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 6a b - 14a b + 16a b + 4a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (6a b + 10a b - 14a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (6a b + 22a b - 18a b - 10a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 +--R (- 2a b - 6a b + 6a b + 2a b )cos(x) - 2a b - 10a b +--R + +--R 5 4 7 2 +--R 6a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 7 3 6 5 4 6 +--R (4a b - 4a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 5 +--R (- 8a b - 28a b + 36a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (4a b - 18a b + 2a b + 12a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (4a b + 48a b - 46a b - 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 8a b + 34a b - 8a b - 18a b )cos(x) +--R + +--R 3 6 5 4 7 2 8 3 6 7 2 +--R (- 16a b + 10a b + 6a b )cos(x) + 4a b - 10a b + 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 4 5 7 2 7 4 5 6 3 6 +--R (4a b - 4a b )cos(x) + (4a b - 2a b - 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 5 +--R (- 12a b + 8a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 +--R (- 12a b + 2a b + 10a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (12a b - 4a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 2 7 6 3 +--R (12a b + 2a b - 14a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 +--R - 4a b - 2a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 8 2 7 4 5 7 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 6 +--R (- 26a b + 22a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 5 +--R (- 28a b + 6a b + 22a b )cos(x) +--R + +--R 2 7 4 5 8 4 +--R (38a b - 40a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (44a b - 4a b - 40a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 14a b + 26a b - 10a b - 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (- 20a b + 2a b + 18a b )cos(x) - 2a b - 4a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 5 4 7 3 6 5 4 6 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 6 5 4 5 3 6 5 4 4 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 3 6 5 4 3 3 6 5 4 2 +--R (6a b - 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 3 6 5 4 3 6 5 4 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 9 8 3 6 5 4 8 +--R (2a b - 2a b )cos(x) + (6a b - 4a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 +--R (- 2a b + 6a b - 4a b )cos(x) +--R + +--R 8 3 6 5 4 6 +--R (- 18a b + 2a b + 16a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 6a b - 18a b + 22a b + 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (18a b + 6a b - 26a b + 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (10a b + 26a b - 34a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 6a b - 2a b + 10a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 3 6 5 4 +--R (- 4a b - 12a b + 16a b )cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 7 4 5 8 2 7 4 5 7 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 2 7 4 5 5 +--R (- 12a b + 12a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 2 7 4 5 4 2 7 4 5 3 +--R (12a b - 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 7 4 5 2 2 7 4 5 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 5 6 3 2 4 5 6 3 4 5 6 3 7 +--R ((- 2a b + 2a b )cos(x) + (2a b - 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 5 4 7 2 2 5 4 7 2 2 +--R ((a b - a b )cos(x) - a b + a b )cot(x) +--R + +--R 3 6 5 4 4 3 6 5 4 3 +--R (- 2a b + 2a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 5 4 7 2 2 3 6 5 4 7 2 3 6 +--R (- 3a b + 3a b )cos(x) + (8a b - 4a b - 4a b )cos(x) + 4a b +--R + +--R 5 4 7 2 +--R - a b - 3a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 5 6 3 4 4 5 6 3 3 +--R (- 2a b + 2a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 5 6 3 8 2 4 5 6 3 4 5 +--R (5a b - 3a b - 2a b)cos(x) + (- a b + a b )cos(x) - 3a b +--R + +--R 6 3 8 +--R a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 6 3 4 2 7 4 5 6 3 3 +--R (- 6a b - 3a b + 9a b )cos(x) + (- 6a b - 4a b + 10a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (6a b + 2a b - 9a b + a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 5 6 3 8 +--R (6a b + 8a b - 12a b - 2a b)cos(x) + 5a b - 4a b - a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 6 5 4 6 3 6 5 4 5 +--R (a b - a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 3 6 5 4 7 2 3 +--R (- 5a b + a b + 4a b )cos(x) + (4a b - 2a b - 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 2 3 6 7 2 +--R (7a b + 3a b - 9a b - a )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 +--R - 3a b - 3a b + 5a b + a +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 6 8 3 6 5 4 5 +--R (2a b - 2a b )cos(x) + (- 2a b - 5a b + 7a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 8a b - 9a b + 8a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (4a b - 4a b - 2a b + 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (10a b + 10a b - 10a b - 10a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 7 2 +--R (- 2a b + 9a b - 3a b - 4a b )cos(x) - 4a b + a b + 4a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 7 2 7 4 5 6 3 6 +--R (a b - a b )cos(x) + (a b + a b - 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 5 +--R (- 3a b - a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 3a b - 7a b + 8a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (3a b + 5a b - 7a b - a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (3a b + 11a b - 9a b - 5a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 8 +--R (- a b - 3a b + 3a b + a b)cos(x) - a b - 5a b + 3a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 2 7 4 5 7 9 2 7 4 5 6 3 6 +--R (2b - a b - a b )cos(x) + (2b + a b - 8a b + 5a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (- 6b - 3a b - 5a b + 14a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (- 6b - 9a b + 14a b - 3a b + 4a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (6b + 9a b + 5a b - 18a b - 2a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (6b + 15a b - 12a b - 5a b - 4a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 9 2 7 4 5 +--R (- 2b - 5a b + a b + 4a b + 2a b)cos(x) - 2b - 7a b + 6a b +--R + +--R 6 3 +--R 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 6 5 4 7 3 6 5 4 7 2 6 +--R (2a b - 2a b )cos(x) + (2a b - a b - a b )cos(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- 6a b + 4a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 3 6 5 4 7 2 3 +--R (- 6a b + a b + 5a b )cos(x) + (6a b - 2a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 3 6 7 2 3 6 +--R (6a b + a b - 7a b )cos(x) + (- 2a b + 2a b )cos(x) - 2a b +--R + +--R 5 4 7 2 +--R - a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 5 4 8 8 3 6 7 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 6 +--R (4a b - 17a b + 10a b + 3a b )cos(x) +--R + +--R 8 5 4 7 2 5 +--R (- 12a b + 3a b + 9a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 4 +--R (- 12a b + 27a b - 11a b - 5a b + a )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (12a b + 12a b - 8a b - 16a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (12a b - 11a b - 2a b + 2a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (- 4a b - 8a b + 5a b + 7a b )cos(x) - 4a b - a b + 5a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 3 7 4 5 6 3 6 +--R (a b - a b )cos(x) + (a b - a b )cos(x) +--R + +--R 4 5 6 3 5 4 5 6 3 4 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 4 5 6 3 3 4 5 6 3 2 +--R (3a b - 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 4 5 6 3 4 5 6 3 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 9 2 7 4 5 6 3 8 +--R (a b - a b )cos(x) + (3a b - 2a b - a b )cos(x) +--R + +--R 2 7 6 3 7 2 7 4 5 6 3 6 +--R (a b - a b )cos(x) + (- 7a b - 2a b + 9a b )cos(x) +--R + +--R 2 7 6 3 8 5 +--R (- 9a b + 8a b + a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a b + 12a b - 16a b + a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (11a b + 4a b - 14a b - a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (3a b - 10a b + 8a b - a b)cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 +--R (- 4a b - 3a b + 7a b )cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 3 6 5 4 8 3 6 5 4 7 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 6 5 4 6 3 6 5 4 5 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 3 6 5 4 4 3 6 5 4 3 +--R (6a b - 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 3 6 5 4 2 3 6 5 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R / +--R 7 3 2 7 3 6 +--R (a b cos(x) - a b )sin(x) +--R + +--R 6 4 4 6 4 8 2 3 +--R - 2a b cos(x) + (a b - a b )cos(x) +--R + +--R 6 4 8 2 2 6 4 8 2 6 4 8 2 +--R (5a b + 2a b )cos(x) + (- a b + a b )cos(x) - 3a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 5 6 5 5 7 3 5 +--R a b cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 5 7 3 4 5 5 7 3 9 3 +--R (- 5a b - 4a b )cos(x) + (4a b - 2a b - 2a b)cos(x) +--R + +--R 5 5 7 3 9 2 5 5 9 +--R (7a b + 10a b + a b)cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 5 5 7 3 9 +--R - 3a b - 6a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 6 6 4 7 4 6 6 4 6 +--R (a b - a b )cos(x) + (a b + 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 5 +--R (- 3a b - a b + 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 +--R (- 3a b - 10a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 10 3 +--R (3a b + 5a b - 7a b - a )cos(x) +--R + +--R 4 6 6 4 8 2 2 +--R (3a b + 14a b + 5a b )cos(x) +--R + +--R 4 6 6 4 8 2 10 4 6 6 4 8 2 +--R (- a b - 3a b + 3a b + a )cos(x) - a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 5 7 3 7 5 5 7 3 6 +--R (2a b - 2a b )cos(x) + (2a b + a b )cos(x) +--R + +--R 5 5 7 3 9 5 5 5 7 3 4 +--R (- 6a b + 4a b + 2a b)cos(x) + (- 6a b - 5a b )cos(x) +--R + +--R 5 5 7 3 9 3 5 5 7 3 2 +--R (6a b - 2a b - 4a b)cos(x) + (6a b + 7a b )cos(x) +--R + +--R 5 5 9 5 5 7 3 +--R (- 2a b + 2a b)cos(x) - 2a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 8 2 7 6 4 6 6 4 8 2 5 +--R (a b - a b )cos(x) + a b cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 6 4 4 6 4 8 2 3 6 4 2 +--R - 3a b cos(x) + (3a b - 3a b )cos(x) + 3a b cos(x) +--R + +--R 6 4 8 2 6 4 +--R (- a b + a b )cos(x) - a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 4 2 6 4 6 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 5 5 4 5 5 7 3 3 +--R - 4a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 5 7 3 2 5 5 7 3 5 5 +--R (10a b + 4a b )cos(x) + (- 2a b + 2a b )cos(x) - 6a b +--R + +--R 7 3 +--R - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 6 6 4 6 6 4 5 +--R 2a b cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 6 6 4 4 4 6 6 4 8 2 3 +--R (- 10a b - 8a b )cos(x) + (8a b - 4a b - 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 4 6 8 2 +--R (14a b + 20a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 +--R - 6a b - 12a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 7 5 5 7 3 7 5 5 6 +--R (2a b - 2a b )cos(x) + (2a b + 4a b )cos(x) +--R + +--R 3 7 5 5 7 3 5 +--R (- 6a b - 2a b + 8a b )cos(x) +--R + +--R 3 7 5 5 7 3 4 +--R (- 6a b - 20a b - 4a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (6a b + 10a b - 14a b - 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 2 +--R (6a b + 28a b + 10a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 3 7 5 5 7 3 +--R (- 2a b - 6a b + 6a b + 2a b)cos(x) - 2a b - 12a b - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 6 4 7 4 6 6 4 6 +--R (4a b - 4a b )cos(x) + (4a b + 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 5 +--R (- 12a b + 8a b + 4a b )cos(x) +--R + +--R 4 6 6 4 4 4 6 6 4 8 2 3 +--R (- 12a b - 10a b )cos(x) + (12a b - 4a b - 8a b )cos(x) +--R + +--R 4 6 6 4 2 4 6 8 2 4 6 +--R (12a b + 14a b )cos(x) + (- 4a b + 4a b )cos(x) - 4a b +--R + +--R 6 4 +--R - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 7 3 7 5 5 6 +--R (2a b - 2a b )cos(x) + 2a b cos(x) +--R + +--R 5 5 7 3 5 5 5 4 +--R (- 6a b + 6a b )cos(x) - 6a b cos(x) +--R + +--R 5 5 7 3 3 5 5 2 +--R (6a b - 6a b )cos(x) + 6a b cos(x) +--R + +--R 5 5 7 3 5 5 +--R (- 2a b + 2a b )cos(x) - 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 7 3 2 7 3 6 +--R (a b cos(x) - a b )sin(x) +--R + +--R 6 4 4 6 4 8 2 3 6 4 8 2 2 +--R - 2a b cos(x) + (a b - a b )cos(x) + (5a b + 2a b )cos(x) +--R + +--R 6 4 8 2 6 4 8 2 +--R (- a b + a b )cos(x) - 3a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 5 6 5 5 7 3 5 5 5 7 3 4 +--R a b cos(x) + (- 2a b + 2a b )cos(x) + (- 5a b - 4a b )cos(x) +--R + +--R 5 5 7 3 9 3 5 5 7 3 9 2 +--R (4a b - 2a b - 2a b)cos(x) + (7a b + 10a b + a b)cos(x) +--R + +--R 5 5 9 5 5 7 3 9 +--R (- 2a b + 2a b)cos(x) - 3a b - 6a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 6 6 4 7 4 6 6 4 6 +--R (a b - a b )cos(x) + (a b + 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 5 +--R (- 3a b - a b + 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 +--R (- 3a b - 10a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 10 3 +--R (3a b + 5a b - 7a b - a )cos(x) +--R + +--R 4 6 6 4 8 2 2 +--R (3a b + 14a b + 5a b )cos(x) +--R + +--R 4 6 6 4 8 2 10 4 6 6 4 8 2 +--R (- a b - 3a b + 3a b + a )cos(x) - a b - 6a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 5 7 3 7 5 5 7 3 6 +--R (2a b - 2a b )cos(x) + (2a b + a b )cos(x) +--R + +--R 5 5 7 3 9 5 5 5 7 3 4 +--R (- 6a b + 4a b + 2a b)cos(x) + (- 6a b - 5a b )cos(x) +--R + +--R 5 5 7 3 9 3 5 5 7 3 2 +--R (6a b - 2a b - 4a b)cos(x) + (6a b + 7a b )cos(x) +--R + +--R 5 5 9 5 5 7 3 +--R (- 2a b + 2a b)cos(x) - 2a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 8 2 7 6 4 6 6 4 8 2 5 +--R (a b - a b )cos(x) + a b cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 6 4 4 6 4 8 2 3 6 4 2 +--R - 3a b cos(x) + (3a b - 3a b )cos(x) + 3a b cos(x) +--R + +--R 6 4 8 2 6 4 +--R (- a b + a b )cos(x) - a b +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 7 4 9 2 2 7 4 9 2 6 +--R ((- a b + a b )cos(x) + a b - a b )sin(x) +--R + +--R 6 5 8 3 4 6 5 8 3 3 +--R (2a b - 2a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 5 8 3 10 2 6 5 8 3 6 5 +--R (- 5a b + 3a b + 2a b)cos(x) + (a b - a b )cos(x) + 3a b +--R + +--R 8 3 10 +--R - a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 6 7 4 6 5 6 7 4 5 +--R (- a b + a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 6 7 4 9 2 4 5 6 7 4 9 2 3 +--R (5a b - a b - 4a b )cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 5 6 7 4 9 2 11 2 5 6 9 2 +--R (- 7a b - 3a b + 9a b + a )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 6 7 4 9 2 11 +--R 3a b + 3a b - 5a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 4 7 6 5 7 4 7 6 5 8 3 6 +--R (- a b + a b )cos(x) + (- a b - a b + 2a b )cos(x) +--R + +--R 4 7 6 5 8 3 5 +--R (3a b + a b - 4a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 4 +--R (3a b + 7a b - 8a b - 2a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (- 3a b - 5a b + 7a b + a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (- 3a b - 11a b + 9a b + 5a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 4 7 6 5 8 3 10 +--R (a b + 3a b - 3a b - a b)cos(x) + a b + 5a b - 3a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 7 4 7 5 6 7 4 9 2 6 +--R (- 2a b + 2a b )cos(x) + (- 2a b + a b + a b )cos(x) +--R + +--R 5 6 7 4 9 2 5 5 6 7 4 9 2 4 +--R (6a b - 4a b - 2a b )cos(x) + (6a b - a b - 5a b )cos(x) +--R + +--R 5 6 7 4 9 2 3 +--R (- 6a b + 2a b + 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 5 6 9 2 5 6 +--R (- 6a b - a b + 7a b )cos(x) + (2a b - 2a b )cos(x) + 2a b +--R + +--R 7 4 9 2 +--R a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 8 3 7 6 5 8 3 6 +--R (- a b + a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 5 8 3 5 6 5 8 3 4 +--R (3a b - 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 6 5 8 3 3 6 5 8 3 2 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 6 5 8 3 6 5 8 3 +--R (a b - a b )cos(x) + a b - a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 8 3 2 6 5 8 3 6 +--R ((- 2a b + 2a b )cos(x) + 2a b - 2a b )sin(x) +--R + +--R 5 6 7 4 4 5 6 7 4 3 +--R (4a b - 4a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 5 6 7 4 5 6 +--R (- 10a b + 6a b + 4a b )cos(x) + (2a b - 2a b )cos(x) + 6a b +--R + +--R 7 4 9 2 +--R - 2a b - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 7 6 5 6 4 7 6 5 5 +--R (- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 +--R (10a b - 2a b - 8a b )cos(x) +--R + +--R 4 7 6 5 8 3 3 +--R (- 8a b + 4a b + 4a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (- 14a b - 6a b + 18a b + 2a b)cos(x) +--R + +--R 4 7 8 3 4 7 6 5 8 3 10 +--R (4a b - 4a b )cos(x) + 6a b + 6a b - 10a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 8 5 6 7 3 8 5 6 7 4 6 +--R (- 2a b + 2a b )cos(x) + (- 2a b - 2a b + 4a b )cos(x) +--R + +--R 3 8 5 6 7 4 5 +--R (6a b + 2a b - 8a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 4 +--R (6a b + 14a b - 16a b - 4a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (- 6a b - 10a b + 14a b + 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 2 +--R (- 6a b - 22a b + 18a b + 10a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 8 5 6 7 4 +--R (2a b + 6a b - 6a b - 2a b )cos(x) + 2a b + 10a b - 6a b +--R + +--R 9 2 +--R - 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 7 6 5 7 4 7 6 5 8 3 6 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 4 7 6 5 8 3 5 +--R (12a b - 8a b - 4a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 +--R (12a b - 2a b - 10a b )cos(x) +--R + +--R 4 7 6 5 8 3 3 +--R (- 12a b + 4a b + 8a b )cos(x) +--R + +--R 4 7 6 5 8 3 2 4 7 8 3 +--R (- 12a b - 2a b + 14a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 7 6 5 8 3 +--R 4a b + 2a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 6 7 4 7 5 6 7 4 6 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 6 7 4 5 5 6 7 4 4 +--R (6a b - 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 5 6 7 4 3 5 6 7 4 2 +--R (- 6a b + 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 5 6 7 4 5 6 7 4 +--R (2a b - 2a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 7 4 9 2 2 7 4 9 2 6 +--R ((- a b + a b )cos(x) + a b - a b )sin(x) +--R + +--R 6 5 8 3 4 6 5 8 3 3 +--R (2a b - 2a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 5 8 3 10 2 6 5 8 3 6 5 8 3 +--R (- 5a b + 3a b + 2a b)cos(x) + (a b - a b )cos(x) + 3a b - a b +--R + +--R 10 +--R - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 6 7 4 6 5 6 7 4 5 +--R (- a b + a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 6 7 4 9 2 4 5 6 7 4 9 2 3 +--R (5a b - a b - 4a b )cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 5 6 7 4 9 2 11 2 5 6 9 2 +--R (- 7a b - 3a b + 9a b + a )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 6 7 4 9 2 11 +--R 3a b + 3a b - 5a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 4 7 6 5 7 4 7 6 5 8 3 6 +--R (- a b + a b )cos(x) + (- a b - a b + 2a b )cos(x) +--R + +--R 4 7 6 5 8 3 5 +--R (3a b + a b - 4a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 4 +--R (3a b + 7a b - 8a b - 2a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (- 3a b - 5a b + 7a b + a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (- 3a b - 11a b + 9a b + 5a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 4 7 6 5 8 3 10 +--R (a b + 3a b - 3a b - a b)cos(x) + a b + 5a b - 3a b - 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 7 4 7 5 6 7 4 9 2 6 +--R (- 2a b + 2a b )cos(x) + (- 2a b + a b + a b )cos(x) +--R + +--R 5 6 7 4 9 2 5 5 6 7 4 9 2 4 +--R (6a b - 4a b - 2a b )cos(x) + (6a b - a b - 5a b )cos(x) +--R + +--R 5 6 7 4 9 2 3 5 6 7 4 9 2 2 +--R (- 6a b + 2a b + 4a b )cos(x) + (- 6a b - a b + 7a b )cos(x) +--R + +--R 5 6 9 2 5 6 7 4 9 2 +--R (2a b - 2a b )cos(x) + 2a b + a b - 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 8 3 7 6 5 8 3 6 +--R (- a b + a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 6 5 8 3 5 6 5 8 3 4 +--R (3a b - 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 6 5 8 3 3 6 5 8 3 2 +--R (- 3a b + 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 6 5 8 3 6 5 8 3 +--R (a b - a b )cos(x) + a b - a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 452 + +--S 453 of 586 +m0577b:= a0577.2-r0577 +--R +--R +--R (438) +--R 2 2 3 2 3 2 2 2 +--R - 2a b sin(x) + (2b cos(x) - 2b - 2a b)sin(x) + 2a b cos(x) +--R + +--R 2 +--R - 2a b +--R * +--R +---------+ +--R | 2 2 sin(x) +--R \|- b + a log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 2 3 2 2 2 +--R - 2a b sin(x) + (2b cos(x) - 2b - 2a b)sin(x) + 2a b cos(x) +--R + +--R 2 +--R - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atanh(cos(x)) +--R + +--R 3 3 2 +--R (- 4a b + 2a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 4 +--R ((4b - 2a b )cos(x) - 4b - 2a b + 2a )sin(x) +--R + +--R 3 3 2 3 3 +--R (4a b - 2a b)cos(x) - 4a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 3 3 2 +--R (- 4a b + 2a b)sin(x) +--R + +--R 4 2 2 2 4 2 2 4 +--R ((4b - 2a b )cos(x) - 4b - 2a b + 2a )sin(x) +--R + +--R 3 3 2 3 3 +--R (4a b - 2a b)cos(x) - 4a b + 2a b +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 2 2 2 +--R (a b cot(x) - 2a b cos(x) - a b )sin(x) +--R + +--R 2 2 2 3 3 2 2 3 +--R (- a b cos(x) + a b + a )cot(x) + b cos(x) - 2a b cos(x) - b +--R + +--R 2 +--R - a b +--R * +--R sin(x) +--R + +--R 2 2 2 2 3 2 2 +--R (- a b cos(x) + a b)cot(x) - a b cos(x) + a b cos(x) +--R + +--R 2 3 2 +--R (a b - a )cos(x) - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 2 3 2 2 3 2 5 4 2 4 +--R (a b sin(x) + (- a b cos(x) + a b + a )sin(x) - a b cos(x) + a b) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 453 + +--S 454 of 586 +d0577b:= D(m0577b,x) +--R +--R +--R (439) +--R 4 3 2 4 3 4 3 8 +--R (2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 5 2 2 5 2 2 3 4 4 3 4 3 +--R (- a b cos(x) + a b )cot(x) + 2a b cos(x) + 8a b cos(x) +--R + +--R 3 4 5 2 2 3 4 5 2 3 4 5 2 +--R (2a b + 2a b )cos(x) + (- 12a b - 4a b )cos(x) - 8a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 4 4 3 3 4 3 6 2 +--R 2a b cos(x) - 2a b cos(x) + (- 6a b - 2a b)cos(x) +--R + +--R 4 3 4 3 6 +--R 2a b cos(x) + 4a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 5 2 5 4 3 4 2 5 4 3 3 +--R 2a b cos(x) + (8a b + 13a b )cos(x) + (8a b + 16a b )cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 4a b - 12a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 10a b - 28a b - 2a b)cos(x) - 4a b - 13a b + a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 4 6 3 4 5 3 4 5 2 4 +--R - a b cos(x) + 4a b cos(x) + (7a b + 3a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 7 2 +--R (- 8a b - 6a b )cos(x) + (- 11a b - 12a b - a )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 7 +--R (4a b + 6a b )cos(x) + 5a b + 9a b + a +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 6 6 3 4 5 +--R (- 2a b + a b )cos(x) + (4a b + 22a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (10a b + 35a b + 16a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 8a b - 4a b + 8a b )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 14a b - 33a b - 22a b - a )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 7 +--R (4a b - 18a b - 20a b )cos(x) + 6a b - 3a b - 6a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 7 2 5 6 2 5 4 3 5 +--R - 2a b cos(x) - 2a b cos(x) + (6a b + 12a b )cos(x) +--R + +--R 2 5 4 3 4 2 5 4 3 6 3 +--R (6a b + 12a b )cos(x) + (- 6a b - 24a b - 6a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 6a b - 24a b - 6a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (2a b + 12a b + 6a b)cos(x) + 2a b + 12a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 5 7 7 2 5 4 3 6 +--R (- 4b - 2a b )cos(x) + (- 4b - 2a b + 12a b )cos(x) +--R + +--R 7 2 5 4 3 5 +--R (12b + 22a b + 42a b )cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (12b + 22a b + 22a b + 6a b)cos(x) +--R + +--R 7 2 5 4 3 3 +--R (- 12b - 38a b - 40a b )cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- 12b - 38a b - 36a b - 8a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 6 +--R (4b + 18a b - 2a b - 4a b)cos(x) + 4b + 18a b + 2a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 8 3 4 7 3 4 5 2 6 +--R - a b cos(x) - 6a b cos(x) + (- 2a b + 3a b )cos(x) +--R + +--R 3 4 5 2 5 3 4 5 2 7 4 +--R (18a b + 12a b )cos(x) + (12a b + 3a b - a )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (- 18a b - 24a b - 2a )cos(x) + (- 14a b - 15a b )cos(x) +--R + +--R 3 4 5 2 7 3 4 5 2 7 +--R (6a b + 12a b + 2a )cos(x) + 5a b + 9a b + a +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 8 6 3 4 7 +--R (- 2a b - 2a b )cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 4a b + 25a b + 14a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (36a b + 18a b + 30a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (24a b - 27a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 36a b - 54a b - 40a b )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 28a b - 13a b - 6a b + a )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 7 +--R (12a b + 30a b + 10a b )cos(x) + 10a b + 17a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 8 4 3 7 4 3 6 6 +--R - 2a b cos(x) - 6a b cos(x) + (2a b + 2a b)cos(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (18a b + 4a b)cos(x) + (6a b - 2a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- 18a b - 8a b)cos(x) + (- 10a b - 2a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (6a b + 4a b)cos(x) + 4a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 9 2 5 4 3 8 +--R - 4a b cos(x) + (- 10a b + a b )cos(x) +--R + +--R 2 5 4 3 7 2 5 4 3 6 6 +--R (- 2a b + 14a b )cos(x) + (22a b + 28a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 5 +--R (30a b - 6a b + 10a b)cos(x) +--R + +--R 2 5 4 3 6 4 +--R (- 6a b - 54a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 38a b - 30a b - 14a b)cos(x) +--R + +--R 2 5 4 3 6 2 +--R (- 14a b + 20a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (14a b + 22a b + 4a b)cos(x) + 8a b + 5a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 8 5 2 7 5 2 6 5 2 5 +--R - a b cos(x) - 2a b cos(x) + 2a b cos(x) + 6a b cos(x) +--R + +--R 5 2 3 5 2 2 5 2 5 2 +--R - 6a b cos(x) - 2a b cos(x) + 2a b cos(x) + a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 10 3 4 9 3 4 8 +--R - a b cos(x) - 6a b cos(x) - 8a b cos(x) +--R + +--R 3 4 5 2 7 3 4 5 2 7 6 +--R (10a b + 6a b )cos(x) + (28a b + 12a b + a )cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (6a b - 6a b + 2a )cos(x) + (- 26a b - 24a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 7 2 +--R (- 18a b - 6a b - 2a )cos(x) + (5a b + 12a b - a )cos(x) +--R + +--R 3 4 5 2 3 4 +--R (8a b + 6a b )cos(x) + 2a b +--R * +--R sin(x) +--R + +--R 4 3 9 4 3 8 4 3 7 4 3 6 +--R - 2a b cos(x) - 4a b cos(x) + 4a b cos(x) + 12a b cos(x) +--R + +--R 4 3 4 4 3 3 4 3 2 4 3 +--R - 12a b cos(x) - 4a b cos(x) + 4a b cos(x) + 2a b cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 2 3 4 3 4 8 +--R (4a b cos(x) - 4a b cos(x) - 4a b )sin(x) +--R + +--R 4 3 2 4 3 2 2 5 4 2 5 3 +--R (- 2a b cos(x) + 2a b )cot(x) + 4a b cos(x) + 16a b cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 2 5 4 3 +--R (8a b + 2a b )cos(x) + (- 24a b - 8a b )cos(x) - 20a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 4 4 3 4 3 3 4 5 2 2 +--R 4a b cos(x) - 4a b cos(x) + (- 12a b - 4a b )cos(x) +--R + +--R 3 4 3 4 5 2 +--R 4a b cos(x) + 8a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 6 3 4 4 6 3 4 3 +--R 4a b cos(x) + (8a b + 30a b )cos(x) + (24a b + 28a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (16a b - 28a b - 6a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (- 28a b - 52a b - 4a b )cos(x) - 24a b - 26a b + 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 6 2 5 5 2 5 4 3 4 +--R - 2a b cos(x) + 8a b cos(x) + (14a b + 6a b )cos(x) +--R + +--R 2 5 4 3 3 +--R (- 16a b - 12a b )cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 +--R (- 22a b - 24a b - 2a b)cos(x) + (8a b + 12a b )cos(x) +--R + +--R 2 5 4 3 6 +--R 10a b + 18a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 5 5 7 2 5 4 3 4 +--R (- 8b + 52a b )cos(x) + (- 8b + 72a b + 38a b )cos(x) +--R + +--R 7 4 3 3 7 2 5 4 3 6 2 +--R (16b + 4a b )cos(x) + (16b - 40a b - 64a b - 4a b)cos(x) +--R + +--R 7 2 5 4 3 7 2 5 4 3 6 +--R (- 8b - 52a b - 28a b )cos(x) - 8b - 32a b + 2a b + 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 6 7 6 6 6 3 4 5 +--R - 4a b cos(x) - 4a b cos(x) + (12a b + 24a b )cos(x) +--R + +--R 6 3 4 4 +--R (12a b + 24a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 12a b - 48a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 12a b - 48a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (4a b + 24a b + 12a b )cos(x) + 4a b + 24a b + 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 7 6 3 4 6 +--R - 8a b cos(x) + (- 8a b + 24a b )cos(x) +--R + +--R 6 3 4 5 6 3 4 5 2 4 +--R (8a b + 108a b )cos(x) + (8a b + 68a b + 12a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (8a b - 104a b - 12a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (8a b - 96a b - 28a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (- 8a b - 4a b + 4a b )cos(x) - 8a b + 4a b + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 8 2 5 7 2 5 4 3 6 +--R - 2a b cos(x) - 12a b cos(x) + (- 4a b + 6a b )cos(x) +--R + +--R 2 5 4 3 5 2 5 4 3 6 4 +--R (36a b + 24a b )cos(x) + (24a b + 6a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 36a b - 48a b - 4a b)cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 +--R (- 28a b - 30a b )cos(x) + (12a b + 24a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 +--R 10a b + 18a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 8 2 5 4 3 6 +--R - 6a b cos(x) + (34a b + 34a b )cos(x) +--R + +--R 2 5 4 3 5 2 5 4 3 6 4 +--R (24a b + 84a b )cos(x) + (- 42a b - 6a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 48a b - 120a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (6a b - 42a b + 2a b)cos(x) + (24a b + 36a b + 4a b)cos(x) +--R + +--R 2 5 4 3 +--R 8a b + 14a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 8 3 4 7 3 4 5 2 6 +--R - 4a b cos(x) - 12a b cos(x) + (4a b + 4a b )cos(x) +--R + +--R 3 4 5 2 5 3 4 5 2 4 +--R (36a b + 8a b )cos(x) + (12a b - 4a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 36a b - 16a b )cos(x) + (- 20a b - 4a b )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (12a b + 8a b )cos(x) + 8a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 6 9 6 3 4 8 +--R - 8a b cos(x) + (- 12a b - 2a b )cos(x) +--R + +--R 6 3 4 7 6 3 4 5 2 6 +--R (20a b + 16a b )cos(x) + (36a b + 52a b + 18a b )cos(x) +--R + +--R 6 3 4 5 2 5 +--R (- 12a b + 8a b + 28a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 36a b - 88a b - 22a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 4a b - 64a b - 44a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (12a b + 28a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 4 5 2 +--R (4a b + 40a b + 16a b )cos(x) + 10a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 8 4 3 7 4 3 6 4 3 5 +--R - 2a b cos(x) - 4a b cos(x) + 4a b cos(x) + 12a b cos(x) +--R + +--R 4 3 3 4 3 2 4 3 4 3 +--R - 12a b cos(x) - 4a b cos(x) + 4a b cos(x) + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 10 2 5 9 2 5 4 3 8 +--R - 2a b cos(x) - 12a b cos(x) + (- 12a b - 2a b )cos(x) +--R + +--R 2 5 4 3 7 2 5 4 3 6 6 +--R (28a b + 8a b )cos(x) + (48a b + 28a b + 2a b)cos(x) +--R + +--R 2 5 6 5 2 5 4 3 4 +--R (- 12a b + 4a b)cos(x) + (- 52a b - 48a b )cos(x) +--R + +--R 2 5 4 3 6 3 +--R (- 12a b - 24a b - 4a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 4 3 +--R (18a b + 20a b - 2a b)cos(x) + (8a b + 16a b )cos(x) + 2a b +--R * +--R sin(x) +--R + +--R 3 4 9 3 4 8 3 4 7 3 4 6 +--R - 4a b cos(x) - 8a b cos(x) + 8a b cos(x) + 24a b cos(x) +--R + +--R 3 4 4 3 4 3 3 4 2 3 4 +--R - 24a b cos(x) - 8a b cos(x) + 8a b cos(x) + 4a b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 4 3 4 3 8 +--R (2a b cos(x) - 2a b cos(x) - 2a b )sin(x) +--R + +--R 5 2 2 5 2 2 3 4 4 3 4 3 +--R (- a b cos(x) + a b )cot(x) + 2a b cos(x) + 8a b cos(x) +--R + +--R 3 4 5 2 2 3 4 5 2 3 4 5 2 +--R (2a b + 2a b )cos(x) + (- 12a b - 4a b )cos(x) - 8a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 4 4 3 3 4 3 6 2 +--R 2a b cos(x) - 2a b cos(x) + (- 6a b - 2a b)cos(x) +--R + +--R 4 3 4 3 6 +--R 2a b cos(x) + 4a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 5 2 5 4 3 4 2 5 4 3 3 +--R 2a b cos(x) + (8a b + 13a b )cos(x) + (8a b + 16a b )cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 4a b - 12a b - a b)cos(x) + (- 10a b - 28a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 +--R - 4a b - 13a b + a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 4 6 3 4 5 3 4 5 2 4 +--R - a b cos(x) + 4a b cos(x) + (7a b + 3a b )cos(x) +--R + +--R 3 4 5 2 3 3 4 5 2 7 2 +--R (- 8a b - 6a b )cos(x) + (- 11a b - 12a b - a )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 7 +--R (4a b + 6a b )cos(x) + 5a b + 9a b + a +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 6 6 3 4 5 +--R (- 2a b + a b )cos(x) + (4a b + 22a b )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (10a b + 35a b + 16a b )cos(x) + (- 8a b - 4a b + 8a b )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 14a b - 33a b - 22a b - a )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 7 +--R (4a b - 18a b - 20a b )cos(x) + 6a b - 3a b - 6a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 7 2 5 6 2 5 4 3 5 +--R - 2a b cos(x) - 2a b cos(x) + (6a b + 12a b )cos(x) +--R + +--R 2 5 4 3 4 2 5 4 3 6 3 +--R (6a b + 12a b )cos(x) + (- 6a b - 24a b - 6a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 6a b - 24a b - 6a b)cos(x) + (2a b + 12a b + 6a b)cos(x) +--R + +--R 2 5 4 3 6 +--R 2a b + 12a b + 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 2 5 7 7 2 5 4 3 6 +--R (- 4b - 2a b )cos(x) + (- 4b - 2a b + 12a b )cos(x) +--R + +--R 7 2 5 4 3 5 +--R (12b + 22a b + 42a b )cos(x) +--R + +--R 7 2 5 4 3 6 4 +--R (12b + 22a b + 22a b + 6a b)cos(x) +--R + +--R 7 2 5 4 3 3 +--R (- 12b - 38a b - 40a b )cos(x) +--R + +--R 7 2 5 4 3 6 2 +--R (- 12b - 38a b - 36a b - 8a b)cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 6 +--R (4b + 18a b - 2a b - 4a b)cos(x) + 4b + 18a b + 2a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 8 3 4 7 3 4 5 2 6 +--R - a b cos(x) - 6a b cos(x) + (- 2a b + 3a b )cos(x) +--R + +--R 3 4 5 2 5 3 4 5 2 7 4 +--R (18a b + 12a b )cos(x) + (12a b + 3a b - a )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 2 +--R (- 18a b - 24a b - 2a )cos(x) + (- 14a b - 15a b )cos(x) +--R + +--R 3 4 5 2 7 3 4 5 2 7 +--R (6a b + 12a b + 2a )cos(x) + 5a b + 9a b + a +--R * +--R 2 +--R cot(x) +--R + +--R 6 3 4 8 6 3 4 7 +--R (- 2a b - 2a b )cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 6 +--R (- 4a b + 25a b + 14a b )cos(x) +--R + +--R 6 3 4 5 2 5 6 3 4 5 2 4 +--R (36a b + 18a b + 30a b )cos(x) + (24a b - 27a b - 8a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (- 36a b - 54a b - 40a b )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 28a b - 13a b - 6a b + a )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 7 +--R (12a b + 30a b + 10a b )cos(x) + 10a b + 17a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 8 4 3 7 4 3 6 6 +--R - 2a b cos(x) - 6a b cos(x) + (2a b + 2a b)cos(x) +--R + +--R 4 3 6 5 4 3 6 4 +--R (18a b + 4a b)cos(x) + (6a b - 2a b)cos(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- 18a b - 8a b)cos(x) + (- 10a b - 2a b)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (6a b + 4a b)cos(x) + 4a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 5 9 2 5 4 3 8 2 5 4 3 7 +--R - 4a b cos(x) + (- 10a b + a b )cos(x) + (- 2a b + 14a b )cos(x) +--R + +--R 2 5 4 3 6 6 2 5 4 3 6 5 +--R (22a b + 28a b + 7a b)cos(x) + (30a b - 6a b + 10a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 6a b - 54a b - 9a b)cos(x) + (- 38a b - 30a b - 14a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 14a b + 20a b + 3a b)cos(x) + (14a b + 22a b + 4a b)cos(x) +--R + +--R 2 5 4 3 6 +--R 8a b + 5a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 8 5 2 7 5 2 6 5 2 5 +--R - a b cos(x) - 2a b cos(x) + 2a b cos(x) + 6a b cos(x) +--R + +--R 5 2 3 5 2 2 5 2 5 2 +--R - 6a b cos(x) - 2a b cos(x) + 2a b cos(x) + a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 4 10 3 4 9 3 4 8 +--R - a b cos(x) - 6a b cos(x) - 8a b cos(x) +--R + +--R 3 4 5 2 7 3 4 5 2 7 6 +--R (10a b + 6a b )cos(x) + (28a b + 12a b + a )cos(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 4 +--R (6a b - 6a b + 2a )cos(x) + (- 26a b - 24a b )cos(x) +--R + +--R 3 4 5 2 7 3 3 4 5 2 7 2 +--R (- 18a b - 6a b - 2a )cos(x) + (5a b + 12a b - a )cos(x) +--R + +--R 3 4 5 2 3 4 +--R (8a b + 6a b )cos(x) + 2a b +--R * +--R sin(x) +--R + +--R 4 3 9 4 3 8 4 3 7 4 3 6 +--R - 2a b cos(x) - 4a b cos(x) + 4a b cos(x) + 12a b cos(x) +--R + +--R 4 3 4 4 3 3 4 3 2 4 3 +--R - 12a b cos(x) - 4a b cos(x) + 4a b cos(x) + 2a b cos(x) +--R / +--R 7 2 2 7 2 7 +--R (a b cos(x) - a b )sin(x) +--R + +--R 6 3 4 6 3 3 6 3 8 2 +--R - 2a b cos(x) + 2a b cos(x) + (6a b + 2a b)cos(x) +--R + +--R 6 3 6 3 8 +--R - 2a b cos(x) - 4a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 5 4 6 5 4 5 5 4 7 2 4 +--R a b cos(x) - 4a b cos(x) + (- 7a b - 3a b )cos(x) +--R + +--R 5 4 7 2 3 5 4 7 2 9 2 +--R (8a b + 6a b )cos(x) + (11a b + 12a b + a )cos(x) +--R + +--R 5 4 7 2 5 4 7 2 9 +--R (- 4a b - 6a b )cos(x) - 5a b - 9a b - a +--R * +--R 5 +--R sin(x) +--R + +--R 4 5 7 4 5 6 4 5 6 3 5 +--R 2a b cos(x) + 2a b cos(x) + (- 6a b - 12a b )cos(x) +--R + +--R 4 5 6 3 4 4 5 6 3 8 3 +--R (- 6a b - 12a b )cos(x) + (6a b + 24a b + 6a b)cos(x) +--R + +--R 4 5 6 3 8 2 4 5 6 3 8 +--R (6a b + 24a b + 6a b)cos(x) + (- 2a b - 12a b - 6a b)cos(x) +--R + +--R 4 5 6 3 8 +--R - 2a b - 12a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 8 5 4 7 5 4 7 2 6 +--R a b cos(x) + 6a b cos(x) + (2a b - 3a b )cos(x) +--R + +--R 5 4 7 2 5 5 4 7 2 9 4 +--R (- 18a b - 12a b )cos(x) + (- 12a b - 3a b + a )cos(x) +--R + +--R 5 4 7 2 9 3 5 4 7 2 2 +--R (18a b + 24a b + 2a )cos(x) + (14a b + 15a b )cos(x) +--R + +--R 5 4 7 2 9 5 4 7 2 9 +--R (- 6a b - 12a b - 2a )cos(x) - 5a b - 9a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 8 6 3 7 6 3 8 6 +--R 2a b cos(x) + 6a b cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 6 3 8 5 6 3 8 4 +--R (- 18a b - 4a b)cos(x) + (- 6a b + 2a b)cos(x) +--R + +--R 6 3 8 3 6 3 8 2 +--R (18a b + 8a b)cos(x) + (10a b + 2a b)cos(x) +--R + +--R 6 3 8 6 3 8 +--R (- 6a b - 4a b)cos(x) - 4a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 8 7 2 7 7 2 6 7 2 5 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) - 6a b cos(x) +--R + +--R 7 2 3 7 2 2 7 2 7 2 +--R 6a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 6 3 7 +--R (2a b cos(x) - 2a b )sin(x) +--R + +--R 5 4 4 5 4 3 5 4 7 2 2 +--R - 4a b cos(x) + 4a b cos(x) + (12a b + 4a b )cos(x) +--R + +--R 5 4 5 4 7 2 +--R - 4a b cos(x) - 8a b - 4a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 5 6 4 5 5 4 5 6 3 4 +--R 2a b cos(x) - 8a b cos(x) + (- 14a b - 6a b )cos(x) +--R + +--R 4 5 6 3 3 4 5 6 3 8 2 +--R (16a b + 12a b )cos(x) + (22a b + 24a b + 2a b)cos(x) +--R + +--R 4 5 6 3 4 5 6 3 8 +--R (- 8a b - 12a b )cos(x) - 10a b - 18a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 6 7 3 6 6 3 6 5 4 5 +--R 4a b cos(x) + 4a b cos(x) + (- 12a b - 24a b )cos(x) +--R + +--R 3 6 5 4 4 3 6 5 4 7 2 3 +--R (- 12a b - 24a b )cos(x) + (12a b + 48a b + 12a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (12a b + 48a b + 12a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- 4a b - 24a b - 12a b )cos(x) - 4a b - 24a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 5 8 4 5 7 4 5 6 3 6 +--R 2a b cos(x) + 12a b cos(x) + (4a b - 6a b )cos(x) +--R + +--R 4 5 6 3 5 4 5 6 3 8 4 +--R (- 36a b - 24a b )cos(x) + (- 24a b - 6a b + 2a b)cos(x) +--R + +--R 4 5 6 3 8 3 4 5 6 3 2 +--R (36a b + 48a b + 4a b)cos(x) + (28a b + 30a b )cos(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (- 12a b - 24a b - 4a b)cos(x) - 10a b - 18a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 8 5 4 7 5 4 7 2 6 +--R 4a b cos(x) + 12a b cos(x) + (- 4a b - 4a b )cos(x) +--R + +--R 5 4 7 2 5 5 4 7 2 4 +--R (- 36a b - 8a b )cos(x) + (- 12a b + 4a b )cos(x) +--R + +--R 5 4 7 2 3 5 4 7 2 2 +--R (36a b + 16a b )cos(x) + (20a b + 4a b )cos(x) +--R + +--R 5 4 7 2 5 4 7 2 +--R (- 12a b - 8a b )cos(x) - 8a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 8 6 3 7 6 3 6 6 3 5 +--R 2a b cos(x) + 4a b cos(x) - 4a b cos(x) - 12a b cos(x) +--R + +--R 6 3 3 6 3 2 6 3 6 3 +--R 12a b cos(x) + 4a b cos(x) - 4a b cos(x) - 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 7 2 2 7 2 7 +--R (a b cos(x) - a b )sin(x) +--R + +--R 6 3 4 6 3 3 6 3 8 2 6 3 +--R - 2a b cos(x) + 2a b cos(x) + (6a b + 2a b)cos(x) - 2a b cos(x) +--R + +--R 6 3 8 +--R - 4a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 5 4 6 5 4 5 5 4 7 2 4 +--R a b cos(x) - 4a b cos(x) + (- 7a b - 3a b )cos(x) +--R + +--R 5 4 7 2 3 5 4 7 2 9 2 +--R (8a b + 6a b )cos(x) + (11a b + 12a b + a )cos(x) +--R + +--R 5 4 7 2 5 4 7 2 9 +--R (- 4a b - 6a b )cos(x) - 5a b - 9a b - a +--R * +--R 5 +--R sin(x) +--R + +--R 4 5 7 4 5 6 4 5 6 3 5 +--R 2a b cos(x) + 2a b cos(x) + (- 6a b - 12a b )cos(x) +--R + +--R 4 5 6 3 4 4 5 6 3 8 3 +--R (- 6a b - 12a b )cos(x) + (6a b + 24a b + 6a b)cos(x) +--R + +--R 4 5 6 3 8 2 4 5 6 3 8 +--R (6a b + 24a b + 6a b)cos(x) + (- 2a b - 12a b - 6a b)cos(x) +--R + +--R 4 5 6 3 8 +--R - 2a b - 12a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 8 5 4 7 5 4 7 2 6 +--R a b cos(x) + 6a b cos(x) + (2a b - 3a b )cos(x) +--R + +--R 5 4 7 2 5 5 4 7 2 9 4 +--R (- 18a b - 12a b )cos(x) + (- 12a b - 3a b + a )cos(x) +--R + +--R 5 4 7 2 9 3 5 4 7 2 2 +--R (18a b + 24a b + 2a )cos(x) + (14a b + 15a b )cos(x) +--R + +--R 5 4 7 2 9 5 4 7 2 9 +--R (- 6a b - 12a b - 2a )cos(x) - 5a b - 9a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 8 6 3 7 6 3 8 6 +--R 2a b cos(x) + 6a b cos(x) + (- 2a b - 2a b)cos(x) +--R + +--R 6 3 8 5 6 3 8 4 +--R (- 18a b - 4a b)cos(x) + (- 6a b + 2a b)cos(x) +--R + +--R 6 3 8 3 6 3 8 2 +--R (18a b + 8a b)cos(x) + (10a b + 2a b)cos(x) +--R + +--R 6 3 8 6 3 8 +--R (- 6a b - 4a b)cos(x) - 4a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 8 7 2 7 7 2 6 7 2 5 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) - 6a b cos(x) +--R + +--R 7 2 3 7 2 2 7 2 7 2 +--R 6a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 454 + +--S 455 of 586 +t0578:= cot(x)^2/(a+a*sin(x))^2 +--R +--R +--R 2 +--R cot(x) +--R (440) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 455 + +--S 456 of 586 +r0578:= 2*atanh(cos(x))/a^2-cot(x)/a^2-2*cos(x)/a^2/(1+sin(x)) +--R +--R +--R (2sin(x) + 2)atanh(cos(x)) - cot(x)sin(x) - cot(x) - 2cos(x) +--R (441) ------------------------------------------------------------ +--R 2 2 +--R a sin(x) + a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 586 +a0578:= integrate(t0578,x) +--R +--R +--R (442) +--R 2 sin(x) +--R ((- 2cos(x) - 2)sin(x) + 2cos(x) - 2)log(----------) +--R cos(x) + 1 +--R + +--R 2 +--R (- 5cos(x) - 4)sin(x) - cos(x) - cos(x) +--R / +--R 2 2 2 2 2 +--R (a cos(x) + a )sin(x) - a cos(x) + a +--R Type: Union(Expression(Integer),...) +--E 457 + +--S 458 of 586 +m0578:= a0578-r0578 +--R +--R +--R (443) +--R 2 2 2 +--R (- 2cos(x) - 2)sin(x) + (2cos(x) - 2cos(x) - 4)sin(x) + 2cos(x) +--R + +--R - 2 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R (- 2cos(x) - 2)sin(x) + (2cos(x) - 2cos(x) - 4)sin(x) + 2cos(x) +--R + +--R - 2 +--R * +--R atanh(cos(x)) +--R + +--R 2 +--R ((cos(x) + 1)cot(x) - 5cos(x) - 4)sin(x) +--R + +--R 2 2 +--R ((- cos(x) + cos(x) + 2)cot(x) + cos(x) - 4cos(x) - 4)sin(x) +--R + +--R 2 3 2 +--R (- cos(x) + 1)cot(x) - 2cos(x) - cos(x) + cos(x) +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (a cos(x) + a )sin(x) + (- a cos(x) + a cos(x) + 2a )sin(x) - a cos(x) +--R + +--R 2 +--R a +--R Type: Expression(Integer) +--E 458 + +--S 459 of 586 +d0578:= D(m0578,x) +--R +--R +--R (444) +--R 2 6 +--R (- 2cos(x) - cos(x) - 1)sin(x) +--R + +--R 3 2 2 3 2 +--R (- cos(x) - cos(x) + cos(x) + 1)cot(x) + 7cos(x) - 3cos(x) +--R + +--R - 7cos(x) - 5 +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (2cos(x) - 2cos(x) - 6cos(x) + 2cos(x) + 4)cot(x) + 2cos(x) +--R + +--R 3 2 +--R 17cos(x) - 5cos(x) - 14cos(x) - 4 +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 3 2 2 5 +--R (- cos(x) + 5cos(x) + cos(x) - 11cos(x) + 6)cot(x) + 5cos(x) +--R + +--R 4 3 2 +--R cos(x) + cos(x) - 7cos(x) - 4cos(x) + 4 +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (- 2cos(x) + 4cos(x) + 4cos(x) - 8cos(x) - 2cos(x) + 4)cot(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 18cos(x) - 2cos(x) - 31cos(x) - 5cos(x) + 13cos(x) + 5 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 2 +--R (- cos(x) + cos(x) + 2cos(x) - 2cos(x) - cos(x) + 1)cot(x) +--R + +--R 7 6 5 4 3 2 +--R - 2cos(x) - 2cos(x) + 17cos(x) + 5cos(x) - 26cos(x) - 4cos(x) +--R + +--R 11cos(x) + 1 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 2cos(x) + 2cos(x) + 4cos(x) - 4cos(x) - 2cos(x) + 2cos(x) +--R / +--R 2 3 2 2 2 2 5 +--R (a cos(x) + a cos(x) - a cos(x) - a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 4 +--R (- 2a cos(x) + 2a cos(x) + 6a cos(x) - 2a cos(x) - 4a )sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 3 +--R (a cos(x) - 5a cos(x) - a cos(x) + 11a cos(x) - 6a )sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (2a cos(x) - 4a cos(x) - 4a cos(x) + 8a cos(x) + 2a cos(x) - 4a ) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 2 +--R (a cos(x) - a cos(x) - 2a cos(x) + 2a cos(x) + a cos(x) - a )sin(x) +--R Type: Expression(Integer) +--E 459 + +--S 460 of 586 +t0579:= sec(x)^2/(a+b*sin(x))^2 +--R +--R +--R 2 +--R sec(x) +--R (445) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 460 + +--S 461 of 586 +r0579:= -6*a*b^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)+_ + 1/2*cos(x)/(a+b)^2/(1-sin(x))-1/2*cos(x)/(a-b)^2/(1+sin(x))-_ + b^3*cos(x)/(a^2-b^2)^2/(a+b*sin(x)) +--R +--R +--R (446) +--R x +--R a tan(-) + b +--R 3 3 2 2 2 3 2 2 2 +--R (- 6a b sin(x) - 6a b sin(x) + 6a b sin(x) + 6a b )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 2 2 3 +--R (- 2b - a b)cos(x)sin(x) + (a b - a )cos(x)sin(x) +--R + +--R 3 2 +--R (b + 2a b)cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 2 3 4 3 4 3 2 5 2 +--R (b - 2a b + a b)sin(x) + (a b - 2a b + a )sin(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- b + 2a b - a b)sin(x) - a b + 2a b - a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 586 +a0579:= integrate(t0579,x) +--R +--R +--R (447) +--R [ +--R 2 3 3 2 +--R (3a b cos(x)sin(x) + 3a b cos(x)) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 4 2 2 2 2 4 3 3 2 +--R ((- b - 2a b )cos(x) - a b + a )sin(x) + (- 2a b - a b)cos(x) +--R + +--R 3 3 3 3 +--R (- a b - 2a b)cos(x) + a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 5 3 3 5 2 4 4 2 6 | 2 2 +--R ((a b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x))\|b - a +--R , +--R +--R 2 3 3 2 +--R (6a b cos(x)sin(x) + 6a b cos(x)) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 4 2 2 2 2 4 3 3 2 +--R ((- b - 2a b )cos(x) - a b + a )sin(x) + (- 2a b - a b)cos(x) +--R + +--R 3 3 3 3 +--R (- a b - 2a b)cos(x) + a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 3 3 5 2 4 4 2 6 +--R ((a b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x)) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 462 + +--S 463 of 586 +m0579a:= a0579.1-r0579 +--R +--R +--R (448) +--R 2 3 3 3 2 2 2 3 +--R 3a b cos(x)sin(x) + 3a b cos(x)sin(x) - 3a b cos(x)sin(x) +--R + +--R 3 2 +--R - 3a b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 2 3 3 3 2 2 2 3 +--R 6a b cos(x)sin(x) + 6a b cos(x)sin(x) - 6a b cos(x)sin(x) +--R + +--R 3 2 +--R - 6a b cos(x) +--R * +--R x +--R +-------+ a tan(-) + b +--R | 2 2 2 +--R \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 2 2 4 3 +--R ((- b - 2a b )cos(x) - a b + a )sin(x) +--R + +--R 3 3 3 3 2 +--R ((- a b - 2a b)cos(x) + a b - a b)sin(x) +--R + +--R 2 2 4 2 4 2 2 2 2 4 +--R ((- a b + a )cos(x) + (b + 2a b )cos(x) + a b - a )sin(x) +--R + +--R 3 3 2 3 3 3 3 +--R (a b - a b)cos(x) + (a b + 2a b)cos(x) - a b + a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 5 3 3 5 3 2 4 4 2 6 2 +--R (a b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x)sin(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (- a b + 2a b - a b)cos(x)sin(x) + (- a b + 2a b - a )cos(x) +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 463 + +--S 464 of 586 +d0579a:= D(m0579a,x) +--R +--R +--R (449) +--R 3 4 5 2 8 +--R (- a b + a b )sin(x) +--R + +--R 2 5 4 3 6 4 3 6 7 +--R ((- a b + 2a b - a b)cos(x) - a b + a b)sin(x) +--R + +--R 6 3 4 3 6 3 4 5 2 2 +--R (3a b - 3a b )cos(x) + (3a b + a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (a b - 3a b + 3a b - a )cos(x) + a b + a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 2 5 4 3 6 3 +--R - 3a b cos(x) + (4a b - 5a b + a b)cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 2 5 +--R (5a b + a b )cos(x) + (3a b - 6a b + 3a b)cos(x) + a b +--R + +--R 4 3 6 +--R a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 4 5 2 4 6 3 4 5 2 3 +--R (- a b - 2a b )cos(x) + (- 8a b + 10a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 8a b + 3a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (- 2a b + 6a b - 6a b + 2a )cos(x) - 2a b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (2a b - 4a b + 2a b)cos(x) + (5a b + 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 6 2 +--R (- 8a b + 10a b - 2a b)cos(x) + (- 11a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 2a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 3a b + 7a b - 5a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 3a b + 8a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (6a b - 8a b + a b + a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (6a b - 7a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (a b - 3a b + 3a b - a )cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 5 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 4a b + 2a b - a b)cos(x) + (4a b - 5a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (6a b - a b + a b)cos(x) + (a b - 2a b + a b)cos(x) +--R + +--R 2 5 4 3 +--R a b - a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 6 3 4 5 2 4 +--R (a b - a b - a b + a )cos(x) + (a b - 3a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 6 3 4 5 2 2 +--R (- a b + a b + a b - a )cos(x) + (- a b + 3a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 8 +--R (- 2a b + 2a b )sin(x) +--R + +--R 6 2 6 3 4 5 2 3 4 +--R - 6a b cos(x) + (- 2a b + 4a b - 2a b )cos(x) - 2a b +--R + +--R 5 2 +--R 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 5 4 3 2 +--R (- 10a b - 2a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (2b - 6a b + 6a b - 2a b)cos(x) + 2b + 2a b - 4a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 4 6 3 4 5 2 3 +--R - 6a b cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 6 3 4 2 6 3 4 5 2 +--R (10a b - 4a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 6 3 4 5 2 +--R 2a b + 2a b - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 4 7 2 5 4 3 3 +--R (- 2a b - 4a b )cos(x) + (- 4b + 2a b + 2a b )cos(x) +--R + +--R 7 2 5 4 3 2 +--R (- 4b + 24a b + 4a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 4 3 +--R (- 4b + 12a b - 12a b + 4a b)cos(x) - 4b + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (10a b + 4a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 +--R (8a b - 4a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 4a b + 12a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 5 2 +--R (- 6a b + 12a b - 6a b )cos(x) - 4a b + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- 6b + 14a b - 10a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (- 6b + 16a b + 2a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 +--R (6b + 2a b - 10a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 2 +--R (6b - 14a b - 4a b )cos(x) +--R + +--R 7 2 5 4 3 6 7 2 5 +--R (2b - 6a b + 6a b - 2a b)cos(x) + 2b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 8a b + 4a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 +--R (- 4a b + 2a b + 2a b )cos(x) + (- 8a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 6 3 4 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 7 2 5 4 3 6 5 +--R (2b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 7 2 5 4 3 4 +--R (2b - 6a b - 2a b )cos(x) +--R + +--R 7 2 5 4 3 6 3 7 4 3 2 +--R (- 2b - 4a b + 8a b - 2a b)cos(x) + (- 2b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 8 +--R (- a b + a b )sin(x) +--R + +--R 2 5 4 3 6 4 3 6 7 +--R ((- a b + 2a b - a b)cos(x) - a b + a b)sin(x) +--R + +--R 6 3 4 3 6 3 4 5 2 2 +--R (3a b - 3a b )cos(x) + (3a b + a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (a b - 3a b + 3a b - a )cos(x) + a b + a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 5 4 2 5 4 3 6 3 +--R - 3a b cos(x) + (4a b - 5a b + a b)cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 2 5 +--R (5a b + a b )cos(x) + (3a b - 6a b + 3a b)cos(x) + a b +--R + +--R 4 3 6 +--R a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 4 5 2 4 6 3 4 5 2 3 +--R (- a b - 2a b )cos(x) + (- 8a b + 10a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (- 8a b + 3a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 5 2 +--R (- 2a b + 6a b - 6a b + 2a )cos(x) - 2a b + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (2a b - 4a b + 2a b)cos(x) + (5a b + 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 6 2 +--R (- 8a b + 10a b - 2a b)cos(x) + (- 11a b - a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 6 +--R (- 3a b + 6a b - 3a b)cos(x) - 2a b + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 +--R (- 3a b + 7a b - 5a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 +--R (- 3a b + 8a b + a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (6a b - 8a b + a b + a )cos(x) +--R + +--R 6 3 4 5 2 2 +--R (6a b - 7a b - 2a b )cos(x) +--R + +--R 6 3 4 5 2 7 6 3 4 +--R (a b - 3a b + 3a b - a )cos(x) + a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 6 5 2 5 4 3 6 4 +--R (- 2a b + 4a b - 2a b)cos(x) + (- 4a b + 2a b - a b)cos(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 6 2 +--R (4a b - 5a b + a b)cos(x) + (6a b - a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 5 4 3 +--R (a b - 2a b + a b)cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 7 5 6 3 4 5 2 4 +--R (a b - a b - a b + a )cos(x) + (a b - 3a b - a b )cos(x) +--R + +--R 6 3 4 5 2 7 3 6 3 4 5 2 2 +--R (- a b + a b + a b - a )cos(x) + (- a b + 3a b + a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 5 5 3 7 8 +--R (- a b + 2a b - a b)sin(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 8 7 +--R ((- a b + 2a b - a b )cos(x) - a b + 2a b - a )sin(x) +--R + +--R 7 3 5 3 7 3 5 5 3 7 2 +--R (3a b - 3a b )cos(x) + (3a b - 2a b - 2a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 5 3 7 +--R (a b - 3a b + 3a b - a b)cos(x) + a b - 3a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 4 2 6 4 4 6 2 3 +--R (- 3a b + 3a b )cos(x) + (4a b - 5a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 +--R (5a b - 4a b - a b )cos(x) + (3a b - 6a b + 3a b )cos(x) +--R + +--R 2 6 6 2 8 +--R a b - 3a b + 2a +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 5 3 7 4 7 3 5 5 3 3 +--R (- a b - a b + 2a b)cos(x) + (- 8a b + 10a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 8a b + 11a b - a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 7 +--R (- 2a b + 6a b - 6a b + 2a b)cos(x) - 2a b + 3a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (5a b - 3a b - 3a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 8a b + 10a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 11a b + 11a b - a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 8 +--R (- 3a b + 6a b - 3a b )cos(x) - 2a b + 3a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 7a b - 5a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 11a b - 7a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (6a b - 8a b + a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (6a b - 13a b + 5a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (a b - 3a b + 3a b - a b)cos(x) + a b - 2a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 4a b + 6a b - 3a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (4a b - 5a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 2 6 4 4 6 2 +--R (6a b - 7a b + 2a b - a )cos(x) + (a b - 2a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 +--R a b - 2a b + a b +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (a b - a b - a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (a b - 4a b + 2a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- a b + a b + a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- a b + 4a b - 2a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 8 +--R (- 2a b + 4a b - 2a b )sin(x) +--R + +--R 7 3 5 2 7 3 5 5 3 +--R (- 6a b + 6a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 5 5 3 7 +--R - 2a b + 4a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 10a b + 8a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 4 4 6 2 +--R (2b - 6a b + 6a b - 2a b )cos(x) + 2b - 6a b + 4a b +--R * +--R 6 +--R sin(x) +--R + +--R 7 3 5 4 7 3 5 5 3 3 +--R (- 6a b + 6a b )cos(x) + (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 2 7 3 5 5 3 +--R (10a b - 14a b + 4a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 7 5 3 7 +--R 2a b - 6a b + 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 8 2 6 4 4 3 +--R (- 2a b - 2a b + 4a b )cos(x) + (- 4b + 2a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 4b + 28a b - 20a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 6 2 +--R (- 4b + 12a b - 12a b + 4a b )cos(x) - 4b + 6a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (10a b - 6a b - 6a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (8a b - 4a b - 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 4a b + 16a b - 14a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 5 7 +--R (- 6a b + 12a b - 6a b )cos(x) - 4a b + 6a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (- 6b + 14a b - 10a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (- 6b + 22a b - 14a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (6b + 2a b - 10a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (6b - 20a b + 10a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (2b - 6a b + 6a b - 2a b )cos(x) + 2b - 4a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 8a b + 12a b - 6a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 3 5 5 3 7 2 7 3 5 5 3 +--R (- 8a b + 10a b - 2a b)cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 +--R 2a b - 4a b + 2a b +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (2b - 2a b - 2a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (2b - 8a b + 4a b + 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 2b - 4a b + 8a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (- 2b + 2a b + 2a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 7 8 +--R (- a b + 2a b - a b)sin(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 8 7 +--R ((- a b + 2a b - a b )cos(x) - a b + 2a b - a )sin(x) +--R + +--R 7 3 5 3 7 3 5 5 3 7 2 +--R (3a b - 3a b )cos(x) + (3a b - 2a b - 2a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 5 3 7 +--R (a b - 3a b + 3a b - a b)cos(x) + a b - 3a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 4 2 6 4 4 6 2 3 +--R (- 3a b + 3a b )cos(x) + (4a b - 5a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 2 2 6 +--R (5a b - 4a b - a b )cos(x) + (3a b - 6a b + 3a b )cos(x) + a b +--R + +--R 6 2 8 +--R - 3a b + 2a +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 5 3 7 4 7 3 5 5 3 3 +--R (- a b - a b + 2a b)cos(x) + (- 8a b + 10a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 8a b + 11a b - a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 7 +--R (- 2a b + 6a b - 6a b + 2a b)cos(x) - 2a b + 3a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 5 2 6 4 4 6 2 8 4 +--R (2a b - 4a b + 2a b )cos(x) + (5a b - 3a b - 3a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 8a b + 10a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 11a b + 11a b - a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 8 +--R (- 3a b + 6a b - 3a b )cos(x) - 2a b + 3a b - a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 +--R (- 3a b + 7a b - 5a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 3a b + 11a b - 7a b - a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (6a b - 8a b + a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (6a b - 13a b + 5a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (a b - 3a b + 3a b - a b)cos(x) + a b - 2a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 2 6 4 4 6 2 3 +--R (- 4a b + 6a b - 3a b + a )cos(x) + (4a b - 5a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 2 6 4 4 6 2 +--R (6a b - 7a b + 2a b - a )cos(x) + (a b - 2a b + a b )cos(x) +--R + +--R 2 6 4 4 6 2 +--R a b - 2a b + a b +--R * +--R sin(x) +--R + +--R 7 3 5 5 3 7 5 7 3 5 5 3 7 4 +--R (a b - a b - a b + a b)cos(x) + (a b - 4a b + 2a b + a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 7 3 5 5 3 7 2 +--R (- a b + a b + a b - a b)cos(x) + (- a b + 4a b - 2a b - a b)cos(x) +--R / +--R 2 7 4 5 6 3 2 7 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 8 5 4 7 2 2 +--R (a b - 3a b + 2a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (a b - 2a b + a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 2a b + a b + 4a b - 3a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 4a b + 12a b - 12a b + 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 3a b + 4a b + a b - 2a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a )cos(x) +--R + +--R 8 3 6 5 4 2 +--R (a b - 2a b + a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 2 7 4 5 8 2 +--R (2a b - 3a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 3 3 6 5 4 7 2 2 +--R (a b - 3a b + 3a b - a )cos(x) + (a b - 2a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 2 7 +--R (2a b - 4a b + 2a b )cos(x) sin(x) +--R + +--R 9 2 7 4 5 6 3 3 +--R (2b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 9 4 5 6 3 2 +--R (2b - 6a b + 4a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (2a b - 4a b + 2a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (- 4b + 14a b - 18a b + 10a b - 2a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 2 +--R (- 4b + 2a b + 8a b - 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 8a b + 24a b - 24a b + 8a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 6a b + 8a b + 2a b - 4a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (2b - 10a b + 18a b - 14a b + 4a b)cos(x) +--R + +--R 9 2 7 4 5 2 +--R (2b - 4a b + 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 8 3 6 7 2 2 +--R (4a b - 6a b + 2a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (2a b - 4a b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 2 7 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 8 5 4 7 2 2 +--R (a b - 3a b + 2a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (a b - 2a b + a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 2a b + a b + 4a b - 3a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 4a b + 12a b - 12a b + 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 3a b + 4a b + a b - 2a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a )cos(x) +--R + +--R 8 3 6 5 4 2 +--R (a b - 2a b + a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R + +--R 2 7 4 5 8 2 +--R (2a b - 3a b + a b)cos(x) +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 3 3 6 5 4 7 2 2 +--R (a b - 3a b + 3a b - a )cos(x) + (a b - 2a b + a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 8 4 6 6 4 8 2 2 7 +--R (a b - 3a b + 3a b - a b )cos(x) sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (a b - a b - 3a b + 5a b - 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 10 2 +--R (a b - 3a b + 3a b - a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 2a b + 3a b + 3a b - 7a b + 3a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 4a b + 12a b - 12a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (- 3a b + 7a b - 3a b - 3a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (a b - 3a b + 3a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (2a b - 5a b + 3a b + a b - a )cos(x) +--R * +--R sin(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (a b - 3a b + 3a b - a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (a b - 3a b + 3a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 9 3 7 5 5 7 3 2 7 +--R (2a b - 6a b + 6a b - 2a b )cos(x) sin(x) +--R + +--R 10 2 8 4 6 6 4 3 +--R (2b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (2b - 2a b - 6a b + 10a b - 4a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (2a b - 6a b + 6a b - 2a b)cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 10 2 8 4 6 6 4 8 2 3 +--R (- 4b + 14a b - 18a b + 10a b - 2a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (- 4b + 6a b + 6a b - 14a b + 6a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (- 8a b + 24a b - 24a b + 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 6a b + 14a b - 6a b - 6a b + 4a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 10 2 8 4 6 6 4 8 2 3 +--R (2b - 10a b + 18a b - 14a b + 4a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 2 +--R (2b - 6a b + 6a b - 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (4a b - 12a b + 12a b - 4a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (4a b - 10a b + 6a b + 2a b - 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 8 4 6 6 4 8 2 2 7 +--R (a b - 3a b + 3a b - a b )cos(x) sin(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (a b - 3a b + 3a b - a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (a b - a b - 3a b + 5a b - 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 10 2 +--R (a b - 3a b + 3a b - a )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 2a b + 7a b - 9a b + 5a b - a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 2a b + 3a b + 3a b - 7a b + 3a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 4a b + 12a b - 12a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (- 3a b + 7a b - 3a b - 3a b + 2a )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (a b - 5a b + 9a b - 7a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (a b - 3a b + 3a b - a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (2a b - 6a b + 6a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 +--R (2a b - 5a b + 3a b + a b - a )cos(x) +--R * +--R sin(x) +--R + +--R 3 7 5 5 7 3 9 3 3 7 5 5 7 3 9 2 +--R (a b - 3a b + 3a b - a b)cos(x) + (a b - 3a b + 3a b - a b)cos(x) +--R Type: Expression(Integer) +--E 464 + +--S 465 of 586 +m0579b:= a0579.2-r0579 +--R +--R +--R (450) +--R 2 3 3 3 2 2 2 3 +--R 6a b cos(x)sin(x) + 6a b cos(x)sin(x) - 6a b cos(x)sin(x) +--R + +--R 3 2 +--R - 6a b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 3 3 3 2 2 2 3 +--R 6a b cos(x)sin(x) + 6a b cos(x)sin(x) - 6a b cos(x)sin(x) +--R + +--R 3 2 +--R - 6a b cos(x) +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 2 2 2 2 4 3 +--R ((- b - 2a b )cos(x) - a b + a )sin(x) +--R + +--R 3 3 3 3 2 +--R ((- a b - 2a b)cos(x) + a b - a b)sin(x) +--R + +--R 2 2 4 2 4 2 2 2 2 4 +--R ((- a b + a )cos(x) + (b + 2a b )cos(x) + a b - a )sin(x) +--R + +--R 3 3 2 3 3 3 3 +--R (a b - a b)cos(x) + (a b + 2a b)cos(x) - a b + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 5 3 3 5 3 2 4 4 2 6 2 +--R (a b - 2a b + a b)cos(x)sin(x) + (a b - 2a b + a )cos(x)sin(x) +--R + +--R 5 3 3 5 2 4 4 2 6 +--R (- a b + 2a b - a b)cos(x)sin(x) + (- a b + 2a b - a )cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 465 + +--S 466 of 586 +d0579b:= D(m0579b,x) +--R +--R +--R (451) +--R 3 3 5 9 +--R (- a b + a b)sin(x) +--R + +--R 2 4 2 2 4 4 2 2 4 6 8 +--R (- 3a b cos(x) + (- 2a b + 2a b )cos(x) - a b + a )sin(x) +--R + +--R 5 3 5 3 3 2 +--R 6a b cos(x) + (6a b - 6a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 +--R (2a b - 6a b + 4a b)cos(x) + 2a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 4 2 4 4 2 3 +--R - 3a b cos(x) + (14a b - 2a b )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (22a b - 5a b + a )cos(x) + (8a b - 10a b + 2a )cos(x) +--R + +--R 2 4 4 2 6 +--R 5a b - 4a b - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (- 3a b - 3a b)cos(x) + (- 16a b + 12a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- 16a b + 30a b - 2a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 4a b + 14a b - 10a b)cos(x) - 4a b + 8a b - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 6 4 +--R (4a b - 4a b )cos(x) + (5a b - a b - a )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 6 2 +--R (- 32a b + 8a b )cos(x) + (- 38a b + 17a b - 3a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- 10a b + 14a b - 4a )cos(x) - 7a b + 8a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (2a b - 2a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 4 5 3 3 5 3 +--R (- 6a b + 18a b )cos(x) + (12a b - 20a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (12a b - 38a b + 2a b)cos(x) + (2a b - 10a b + 8a b)cos(x) +--R + +--R 5 3 3 5 +--R 2a b - 6a b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 4a b - a )cos(x) + (- 10a b + 12a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (- 6a b + 12a b - 3a )cos(x) + (20a b - 6a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 +--R (20a b - 15a b + a )cos(x) + (4a b - 6a b + 2a )cos(x) +--R + +--R 2 4 4 2 6 +--R 3a b - 4a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 3 +--R (2a b - 7a b - a b)cos(x) + (- 2a b + 8a b )cos(x) +--R + +--R 5 3 3 2 3 3 5 3 3 5 +--R (- 2a b + 14a b )cos(x) + (2a b - 2a b)cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 2 4 6 6 2 4 6 5 4 2 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) - 3a b cos(x) +--R + +--R 2 4 6 3 2 4 4 2 6 2 +--R (- 2a b + 2a )cos(x) + (- a b + 3a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 9 +--R (- 2a b + 2a b )sin(x) +--R + +--R 5 2 5 3 3 5 5 8 +--R (- 12a b cos(x) + (- 4a b + 4a b )cos(x) - 2a b + 2a b)sin(x) +--R + +--R 2 4 2 6 2 4 4 2 6 2 4 7 +--R (- 24a b cos(x) + (4b - 12a b + 8a b )cos(x) + 4b - 4a b )sin(x) +--R + +--R 5 4 5 3 3 3 +--R - 12a b cos(x) + (- 8a b - 4a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (26a b - 16a b + 2a b)cos(x) + (16a b - 20a b + 4a b)cos(x) +--R + +--R 5 3 3 5 +--R 10a b - 8a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 3 +--R (- 18a b - 6a b )cos(x) + (- 8b - 12a b - 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (- 8b + 60a b - 4a b )cos(x) + (- 8b + 28a b - 20a b )cos(x) +--R + +--R 6 2 4 4 2 +--R - 8b + 16a b - 8a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 5 4 +--R (8a b - 8a b )cos(x) + (22a b - 8a b - 2a b)cos(x) +--R + +--R 5 3 3 3 5 3 3 5 2 +--R (8a b + 4a b )cos(x) + (- 22a b + 40a b - 6a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 20a b + 28a b - 8a b)cos(x) - 14a b + 16a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (4a b - 4a b )cos(x) + (- 12b + 24a b - 12a b )cos(x) +--R + +--R 6 2 4 4 6 2 4 4 2 3 +--R (- 12b + 60a b )cos(x) + (12b + 32a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 +--R (12b - 40a b + 4a b )cos(x) + (4b - 20a b + 16a b )cos(x) +--R + +--R 6 2 4 4 2 +--R 4b - 12a b + 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 5 6 +--R (- 6a b + 8a b - 2a b)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 20a b + 24a b - 4a b)cos(x) +--R + +--R 5 3 3 5 4 +--R (- 18a b + 36a b - 6a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (4a b + 12a b - 4a b)cos(x) + (10a b - 24a b + 2a b)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (8a b - 12a b + 4a b)cos(x) + 6a b - 8a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 5 +--R (- 4a b + 4a b )cos(x) + (4b - 8a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 4 6 2 4 3 +--R (4b - 26a b - 2a b )cos(x) + (- 4b - 20a b )cos(x) +--R + +--R 6 2 4 2 2 4 4 2 2 4 4 2 +--R (- 4b + 4a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 5 5 6 5 5 5 3 3 4 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) - 12a b cos(x) +--R + +--R 5 3 3 5 3 5 5 2 +--R (- 4a b - 12a b + 4a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 5 9 +--R (- a b + a b)sin(x) +--R + +--R 2 4 2 2 4 4 2 2 4 6 8 +--R (- 3a b cos(x) + (- 2a b + 2a b )cos(x) - a b + a )sin(x) +--R + +--R 5 3 5 3 3 2 5 3 3 5 +--R 6a b cos(x) + (6a b - 6a b )cos(x) + (2a b - 6a b + 4a b)cos(x) +--R + +--R 5 3 3 +--R 2a b - 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 4 4 2 4 4 2 3 +--R - 3a b cos(x) + (14a b - 2a b )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 2 4 +--R (22a b - 5a b + a )cos(x) + (8a b - 10a b + 2a )cos(x) + 5a b +--R + +--R 4 2 6 +--R - 4a b - a +--R * +--R 6 +--R sin(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (- 3a b - 3a b)cos(x) + (- 16a b + 12a b - 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- 16a b + 30a b - 2a b)cos(x) + (- 4a b + 14a b - 10a b)cos(x) +--R + +--R 5 3 3 5 +--R - 4a b + 8a b - 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 6 4 +--R (4a b - 4a b )cos(x) + (5a b - a b - a )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 6 2 +--R (- 32a b + 8a b )cos(x) + (- 38a b + 17a b - 3a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- 10a b + 14a b - 4a )cos(x) - 7a b + 8a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (2a b - 2a b)cos(x) + (- 6a b + 12a b - 6a b)cos(x) +--R + +--R 5 3 3 4 5 3 3 5 3 +--R (- 6a b + 18a b )cos(x) + (12a b - 20a b + 2a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (12a b - 38a b + 2a b)cos(x) + (2a b - 10a b + 8a b)cos(x) +--R + +--R 5 3 3 5 +--R 2a b - 6a b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b + 4a b - a )cos(x) + (- 10a b + 12a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (- 6a b + 12a b - 3a )cos(x) + (20a b - 6a b - 2a )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 6 2 4 +--R (20a b - 15a b + a )cos(x) + (4a b - 6a b + 2a )cos(x) + 3a b +--R + +--R 4 2 6 +--R - 4a b + a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (- 2a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 5 3 3 5 4 5 3 3 3 +--R (2a b - 7a b - a b)cos(x) + (- 2a b + 8a b )cos(x) +--R + +--R 5 3 3 2 3 3 5 3 3 5 +--R (- 2a b + 14a b )cos(x) + (2a b - 2a b)cos(x) + a b - a b +--R * +--R sin(x) +--R + +--R 2 4 6 6 2 4 6 5 4 2 4 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) - 3a b cos(x) +--R + +--R 2 4 6 3 2 4 4 2 6 2 +--R (- 2a b + 2a )cos(x) + (- a b + 3a b + a )cos(x) +--R / +--R 2 6 4 4 6 2 2 8 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (a b - 2a b + a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (3a b - 5a b + a b + a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 4a b + 14a b - 16a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 4a b + 8a b - 4a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 2a b + 5a b - 4a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 12a b + 26a b - 16a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 9a b + 17a b - 7a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (2a b - 16a b + 26a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 10a b + 14a b - 6a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (a b - 4a b + 5a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (6a b - 16a b + 14a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (5a b - 11a b + 7a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (2a b - 4a b + 2a b)cos(x) + (6a b - 12a b + 6a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (4a b - 8a b + 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 8 3 +--R (a b - 2a b + a )cos(x) + (2a b - 4a b + 2a )cos(x) +--R + +--R 4 4 6 2 8 2 +--R (a b - 2a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 2 8 +--R (2a b - 4a b + 2a b )cos(x) sin(x) +--R + +--R 8 2 6 4 4 3 +--R (4b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (4b - 4a b - 4a b + 4a b )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 7 3 5 5 3 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 3 +--R (12a b - 24a b + 12a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (6a b - 10a b + 2a b + 2a b)cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (- 8b + 28a b - 32a b + 12a b )cos(x) +--R + +--R 8 2 6 4 4 2 +--R (- 8b + 16a b - 8a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 4a b + 10a b - 8a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 24a b + 52a b - 32a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 18a b + 34a b - 14a b - 2a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 3 +--R (4b - 32a b + 52a b - 24a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (4b - 20a b + 28a b - 12a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 5 5 3 7 4 +--R (2a b - 8a b + 10a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (12a b - 32a b + 28a b - 8a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (10a b - 22a b + 14a b - 2a b)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 2 6 4 4 6 2 2 +--R (12a b - 24a b + 12a b )cos(x) + (8a b - 16a b + 8a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (2a b - 4a b + 2a b)cos(x) + (4a b - 8a b + 4a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (2a b - 4a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 2 8 +--R (a b - 2a b + a b )cos(x) sin(x) +--R + +--R 7 3 5 5 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 6 2 3 +--R (a b - 2a b + a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (3a b - 5a b + a b + a )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 4a b + 14a b - 16a b + 6a b)cos(x) +--R + +--R 7 3 5 5 3 2 +--R (- 4a b + 8a b - 4a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 2a b + 5a b - 4a b + a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (- 12a b + 26a b - 16a b + 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 9a b + 17a b - 7a b - a )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 7 4 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (2a b - 16a b + 26a b - 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (2a b - 10a b + 14a b - 6a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (a b - 4a b + 5a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 3 +--R (6a b - 16a b + 14a b - 4a )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (5a b - 11a b + 7a b - a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 3 +--R (2a b - 4a b + 2a b)cos(x) + (6a b - 12a b + 6a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (4a b - 8a b + 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 8 3 +--R (a b - 2a b + a )cos(x) + (2a b - 4a b + 2a )cos(x) +--R + +--R 4 4 6 2 8 2 +--R (a b - 2a b + a )cos(x) +--R Type: Expression(Integer) +--E 466 + +--S 467 of 586 +t0580:= sec(x)/(a+a*sin(x))^2 +--R +--R +--R sec(x) +--R (452) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 586 +r0580:= 1/4/a^2*(atanh(sin(x))*cos(x)^4+2*sin(x)-2+sin(x)*cos(x)^2)/cos(x)^4 +--R +--R +--R 4 2 +--R cos(x) atanh(sin(x)) + (cos(x) + 2)sin(x) - 2 +--R (453) ---------------------------------------------- +--R 2 4 +--R 4a cos(x) +--R Type: Expression(Integer) +--E 468 + +--S 469 of 586 +a0580:= integrate(t0580,x) +--R +--R +--R (454) +--R 2 sin(x) + cos(x) + 1 +--R (2sin(x) - cos(x) + 2)log(-------------------) +--R cos(x) + 1 +--R + +--R 2 sin(x) - cos(x) - 1 2 +--R (- 2sin(x) + cos(x) - 2)log(-------------------) + 3sin(x) - 2cos(x) + 2 +--R cos(x) + 1 +--R / +--R 2 2 2 2 +--R 8a sin(x) - 4a cos(x) + 8a +--R Type: Union(Expression(Integer),...) +--E 469 + +--S 470 of 586 +m0580:= a0580-r0580 +--R +--R +--R (455) +--R 4 6 4 sin(x) + cos(x) + 1 +--R (2cos(x) sin(x) - cos(x) + 2cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 6 4 sin(x) - cos(x) - 1 +--R (- 2cos(x) sin(x) + cos(x) - 2cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 4 6 4 +--R (- 2cos(x) sin(x) + cos(x) - 2cos(x) )atanh(sin(x)) +--R + +--R 2 2 4 6 4 2 +--R (- 2cos(x) - 4)sin(x) + 4cos(x) sin(x) - 2cos(x) + 2cos(x) - 2cos(x) +--R + +--R 4 +--R / +--R 2 4 2 6 2 4 +--R 8a cos(x) sin(x) - 4a cos(x) + 8a cos(x) +--R Type: Expression(Integer) +--E 470 + +--S 471 of 586 +d0580:= D(m0580,x) +--R +--R +--R (456) +--R 2 8 4 2 7 +--R (- 8cos(x) - 32)sin(x) + (8cos(x) + 16cos(x) - 32)sin(x) +--R + +--R 5 4 3 2 6 +--R (- 8cos(x) + 4cos(x) + 16cos(x) + 32cos(x) + 64cos(x) + 96)sin(x) +--R + +--R 7 5 4 3 2 +--R 8cos(x) - 32cos(x) - 24cos(x) - 32cos(x) - 48cos(x) + 64cos(x) +--R + +--R 96 +--R * +--R 5 +--R sin(x) +--R + +--R 9 6 5 4 3 2 +--R - 2cos(x) + 4cos(x) + 8cos(x) + 20cos(x) + 16cos(x) - 48cos(x) +--R + +--R - 128cos(x) - 96 +--R * +--R 4 +--R sin(x) +--R + +--R 9 8 7 6 5 4 +--R 8cos(x) - 4cos(x) - 40cos(x) - 24cos(x) + 16cos(x) + 56cos(x) +--R + +--R 3 2 +--R 128cos(x) + 48cos(x) - 128cos(x) - 96 +--R * +--R 3 +--R sin(x) +--R + +--R 11 10 9 8 7 6 +--R - 2cos(x) - cos(x) + 10cos(x) - 4cos(x) - 24cos(x) - 16cos(x) +--R + +--R 5 4 3 2 +--R - 8cos(x) - 20cos(x) - 16cos(x) + 32cos(x) + 64cos(x) + 32 +--R * +--R 2 +--R sin(x) +--R + +--R 10 8 7 6 5 4 +--R 4cos(x) - 4cos(x) + 16cos(x) + 24cos(x) + 16cos(x) - 40cos(x) +--R + +--R 3 2 +--R - 96cos(x) - 16cos(x) + 64cos(x) + 32 +--R * +--R sin(x) +--R + +--R 12 10 8 7 6 5 +--R - cos(x) + 5cos(x) - 4cos(x) + 8cos(x) + 12cos(x) + 8cos(x) +--R + +--R 4 3 2 +--R - 4cos(x) - 16cos(x) - 8cos(x) +--R / +--R 2 5 6 2 7 2 5 5 +--R 16a cos(x) sin(x) + (- 16a cos(x) + 32a cos(x) )sin(x) +--R + +--R 2 9 2 7 2 6 2 5 4 +--R (4a cos(x) - 32a cos(x) - 32a cos(x) - 16a cos(x) )sin(x) +--R + +--R 2 9 2 8 2 6 2 5 3 +--R (16a cos(x) + 32a cos(x) - 64a cos(x) - 64a cos(x) )sin(x) +--R + +--R 2 11 2 10 2 9 2 8 2 7 +--R - 4a cos(x) - 8a cos(x) + 8a cos(x) + 32a cos(x) + 32a cos(x) +--R + +--R 2 5 +--R - 16a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 9 2 8 2 7 2 6 2 5 +--R (- 16a cos(x) - 32a cos(x) + 16a cos(x) + 64a cos(x) + 32a cos(x) ) +--R * +--R sin(x) +--R + +--R 2 11 2 10 2 9 2 8 2 6 +--R 4a cos(x) + 8a cos(x) - 12a cos(x) - 32a cos(x) + 32a cos(x) +--R + +--R 2 5 +--R 16a cos(x) +--R Type: Expression(Integer) +--E 471 + +--S 472 of 586 +t0581:= sec(x)^2/(a+a*sin(x))^2 +--R +--R +--R 2 +--R sec(x) +--R (457) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 586 +r0581:= 1/5/cos(x)^5/a^2*(2*cos(x)^4*sin(x)+sin(x)*cos(x)^2+2*sin(x)-2) +--R +--R +--R 4 2 +--R (2cos(x) + cos(x) + 2)sin(x) - 2 +--R (458) ---------------------------------- +--R 2 5 +--R 5a cos(x) +--R Type: Expression(Integer) +--E 473 + +--S 474 of 586 +a0581:= integrate(t0581,x) +--R +--R +--R 2 3 2 +--R (- 2cos(x) - 4cos(x) + 3)sin(x) + 2cos(x) - 4cos(x) - 4cos(x) + 2 +--R (459) -------------------------------------------------------------------- +--R 2 2 3 2 +--R 10a cos(x)sin(x) - 5a cos(x) + 10a cos(x) +--R Type: Union(Expression(Integer),...) +--E 474 + +--S 475 of 586 +m0581:= a0581-r0581 +--R +--R +--R (460) +--R 4 2 2 5 7 6 +--R (- 4cos(x) - 2cos(x) - 4)sin(x) - 4cos(x) sin(x) + 2cos(x) - 4cos(x) +--R + +--R 5 4 2 +--R - 4cos(x) + 2cos(x) - 2cos(x) + 4 +--R / +--R 2 5 2 7 2 5 +--R 10a cos(x) sin(x) - 5a cos(x) + 10a cos(x) +--R Type: Expression(Integer) +--E 475 + +--S 476 of 586 +d0581:= D(m0581,x) +--R +--R +--R (461) +--R 4 2 4 +--R (- 8cos(x) - 12cos(x) - 40)sin(x) +--R + +--R 6 4 2 3 +--R (12cos(x) + 2cos(x) + 16cos(x) - 40)sin(x) +--R + +--R 2 2 +--R (- 20cos(x) + 40)sin(x) +--R + +--R 8 6 4 2 8 +--R (12cos(x) - 10cos(x) + 14cos(x) - 56cos(x) + 40)sin(x) + 8cos(x) +--R + +--R 6 4 2 +--R - 4cos(x) + 4cos(x) - 8cos(x) +--R / +--R 2 6 2 2 8 2 6 2 10 +--R 20a cos(x) sin(x) + (- 20a cos(x) + 40a cos(x) )sin(x) + 5a cos(x) +--R + +--R 2 8 2 6 +--R - 20a cos(x) + 20a cos(x) +--R Type: Expression(Integer) +--E 476 + +--S 477 of 586 +t0582:= sec(x)^3/(a+a*sin(x))^2 +--R +--R +--R 3 +--R sec(x) +--R (462) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 586 +r0582:= 1/12/cos(x)^6*(3*cos(x)^6*atanh(sin(x))-_ + 4+4*sin(x)+2*sin(x)*cos(x)^2+3*cos(x)^4*sin(x))/a^2 +--R +--R +--R 6 4 2 +--R 3cos(x) atanh(sin(x)) + (3cos(x) + 2cos(x) + 4)sin(x) - 4 +--R (463) ----------------------------------------------------------- +--R 2 6 +--R 12a cos(x) +--R Type: Expression(Integer) +--E 478 + +--S 479 of 586 +a0582:= integrate(t0582,x) +--R +--R +--R (464) +--R 2 4 2 sin(x) + cos(x) + 1 +--R (6cos(x) sin(x) - 3cos(x) + 6cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 4 2 sin(x) - cos(x) - 1 +--R (- 6cos(x) sin(x) + 3cos(x) - 6cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 2 4 2 +--R (5cos(x) + 4)sin(x) - 4cos(x) + 2cos(x) + 2 +--R / +--R 2 2 2 4 2 2 +--R 24a cos(x) sin(x) - 12a cos(x) + 24a cos(x) +--R Type: Union(Expression(Integer),...) +--E 479 + +--S 480 of 586 +m0582:= a0582-r0582 +--R +--R +--R (465) +--R 6 8 6 sin(x) + cos(x) + 1 +--R (6cos(x) sin(x) - 3cos(x) + 6cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 6 8 6 sin(x) - cos(x) - 1 +--R (- 6cos(x) sin(x) + 3cos(x) - 6cos(x) )log(-------------------) +--R cos(x) + 1 +--R + +--R 6 8 6 +--R (- 6cos(x) sin(x) + 3cos(x) - 6cos(x) )atanh(sin(x)) +--R + +--R 4 2 2 6 8 6 +--R (- 6cos(x) - 4cos(x) - 8)sin(x) + 8cos(x) sin(x) - 4cos(x) + 2cos(x) +--R + +--R 4 2 +--R 2cos(x) - 4cos(x) + 8 +--R / +--R 2 6 2 8 2 6 +--R 24a cos(x) sin(x) - 12a cos(x) + 24a cos(x) +--R Type: Expression(Integer) +--E 480 + +--S 481 of 586 +d0582:= D(m0582,x) +--R +--R +--R (466) +--R 4 2 8 +--R (- 24cos(x) - 32cos(x) - 96)sin(x) +--R + +--R 6 2 7 +--R (24cos(x) + 32cos(x) - 96)sin(x) +--R + +--R 7 6 5 4 3 +--R - 24cos(x) + 12cos(x) + 48cos(x) + 80cos(x) + 64cos(x) +--R + +--R 2 +--R 112cos(x) + 192cos(x) + 288 +--R * +--R 6 +--R sin(x) +--R + +--R 9 7 6 3 2 +--R 24cos(x) - 96cos(x) - 72cos(x) - 64cos(x) - 96cos(x) + 192cos(x) +--R + +--R 288 +--R * +--R 5 +--R sin(x) +--R + +--R 11 8 7 6 5 +--R - 6cos(x) + 12cos(x) + 24cos(x) - 4cos(x) - 48cos(x) +--R + +--R 3 2 +--R 32cos(x) - 144cos(x) - 384cos(x) - 288 +--R * +--R 4 +--R sin(x) +--R + +--R 11 10 9 8 7 +--R 24cos(x) - 12cos(x) - 120cos(x) - 24cos(x) + 144cos(x) +--R + +--R 6 5 4 3 2 +--R 40cos(x) - 64cos(x) + 96cos(x) + 320cos(x) + 96cos(x) +--R + +--R - 384cos(x) - 288 +--R * +--R 3 +--R sin(x) +--R + +--R 13 12 11 10 9 +--R - 6cos(x) - 3cos(x) + 30cos(x) - 12cos(x) - 72cos(x) +--R + +--R 8 7 6 5 4 +--R - 32cos(x) + 8cos(x) - 12cos(x) - 16cos(x) - 48cos(x) +--R + +--R 3 2 +--R - 64cos(x) + 80cos(x) + 192cos(x) + 96 +--R * +--R 2 +--R sin(x) +--R + +--R 12 10 9 8 7 +--R 12cos(x) - 12cos(x) + 48cos(x) + 24cos(x) - 48cos(x) +--R + +--R 6 5 4 3 2 +--R 8cos(x) + 64cos(x) - 96cos(x) - 256cos(x) - 32cos(x) + 192cos(x) +--R + +--R 96 +--R * +--R sin(x) +--R + +--R 14 12 10 9 8 7 +--R - 3cos(x) + 15cos(x) - 12cos(x) + 24cos(x) + 20cos(x) - 8cos(x) +--R + +--R 6 5 4 3 2 +--R 4cos(x) + 16cos(x) - 8cos(x) - 32cos(x) - 16cos(x) +--R / +--R 2 7 6 2 9 2 7 5 +--R 48a cos(x) sin(x) + (- 48a cos(x) + 96a cos(x) )sin(x) +--R + +--R 2 11 2 9 2 8 2 7 4 +--R (12a cos(x) - 96a cos(x) - 96a cos(x) - 48a cos(x) )sin(x) +--R + +--R 2 11 2 10 2 8 2 7 3 +--R (48a cos(x) + 96a cos(x) - 192a cos(x) - 192a cos(x) )sin(x) +--R + +--R 2 13 2 12 2 11 2 10 +--R - 12a cos(x) - 24a cos(x) + 24a cos(x) + 96a cos(x) +--R + +--R 2 9 2 7 +--R 96a cos(x) - 48a cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 11 2 10 2 9 2 8 +--R - 48a cos(x) - 96a cos(x) + 48a cos(x) + 192a cos(x) +--R + +--R 2 7 +--R 96a cos(x) +--R * +--R sin(x) +--R + +--R 2 13 2 12 2 11 2 10 2 8 +--R 12a cos(x) + 24a cos(x) - 36a cos(x) - 96a cos(x) + 96a cos(x) +--R + +--R 2 7 +--R 48a cos(x) +--R Type: Expression(Integer) +--E 481 + +--S 482 of 586 +t0583:= csc(x)/(a+b*sin(x))^2 +--R +--R +--R csc(x) +--R (467) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 586 +r0583:= -2*b*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ + 2*b*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(1/2)-_ + atanh(cos(x))/a^2-b^2*cos(x)/a/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (468) +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((- b + a b)sin(x) - a b + a )\|- b + a atanh(cos(x)) +--R + +--R x +--R a tan(-) + b +--R 4 2 2 3 3 2 +--R ((- 2b + 4a b )sin(x) - 2a b + 4a b)atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 | 2 2 +--R a b cos(x)\|- b + a +--R / +--R +---------+ +--R 2 3 4 3 2 5 | 2 2 +--R ((a b - a b)sin(x) + a b - a )\|- b + a +--R Type: Expression(Integer) +--E 483 + +--S 484 of 586 +a0583:= integrate(t0583,x) +--R +--R +--R (469) +--R [ +--R 4 2 2 3 3 +--R ((b - 2a b )sin(x) + a b - 2a b) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 3 2 2 3 | 2 2 sin(x) +--R ((b - a b)sin(x) + a b - a )\|b - a log(----------) +--R cos(x) + 1 +--R + +--R +-------+ +--R 3 2 2 | 2 2 +--R (b sin(x) + a b cos(x) + a b )\|b - a +--R / +--R +-------+ +--R 2 3 4 3 2 5 | 2 2 +--R ((a b - a b)sin(x) + a b - a )\|b - a +--R , +--R +--R +---------+ +--R 3 2 2 3 | 2 2 sin(x) +--R ((b - a b)sin(x) + a b - a )\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R 4 2 2 3 3 +--R ((2b - 4a b )sin(x) + 2a b - 4a b) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R 3 2 2 | 2 2 +--R (b sin(x) + a b cos(x) + a b )\|- b + a +--R / +--R +---------+ +--R 2 3 4 3 2 5 | 2 2 +--R ((a b - a b)sin(x) + a b - a )\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 484 + +--S 485 of 586 +m0583a:= a0583.1-r0583 +--R +--R +--R (470) +--R +---------+ +--R 3 2 | 2 2 +--R (b - 2a b)\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 sin(x) +--R (b - a )\|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R 2 2 | 2 2 | 2 2 +--R (b - a )\|- b + a \|b - a atanh(cos(x)) +--R + +--R x +--R +-------+ a tan(-) + b +---------+ +-------+ +--R 3 2 | 2 2 2 2 | 2 2 | 2 2 +--R (2b - 4a b)\|b - a atan(------------) + b \|- b + a \|b - a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 2 4 | 2 2 | 2 2 +--R (a b - a )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 485 + +--S 486 of 586 +d0583a:= D(m0583a,x) +--R +--R +--R (471) +--R 2 4 4 2 4 +--R (a b - a b )cos(x)sin(x) +--R + +--R 5 3 3 5 2 5 5 3 +--R ((a b - 2a b + a b)cos(x) + (a b - a b)cos(x))sin(x) +--R + +--R 6 2 4 4 2 3 6 2 4 4 2 6 2 +--R (b - 2a b + a b )cos(x) + (b - a b - 2a b + a )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 +--R (- b + 3a b - 2a b )cos(x) - b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 5 5 3 +--R a b cos(x) + (a b - a b)cos(x) +--R + +--R 5 3 3 5 2 5 5 5 +--R (a b - 2a b - a b)cos(x) + (- a b + a b)cos(x) - a b +--R + +--R 3 3 +--R 2a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 3 +--R (a b - 2a b + a )cos(x) + (a b - a b )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 +--R (- a b + 2a b - a )cos(x) + (- a b + a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 4 +--R (2a b - 2a b )cos(x)sin(x) +--R + +--R 4 2 2 6 4 2 6 2 4 3 +--R (2a b cos(x) + (2b - 2a b )cos(x) + 2b - 4a b )sin(x) +--R + +--R 5 3 3 3 5 2 5 3 3 2 +--R ((2a b - 2a b )cos(x) + 2a b cos(x) + 2a b - 4a b )sin(x) +--R + +--R 4 2 4 2 4 4 2 3 4 2 2 +--R 2a b cos(x) + (6a b - 6a b )cos(x) - 2a b cos(x) +--R + +--R 2 4 4 2 +--R (- 6a b + 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 5 4 5 3 3 3 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 3 3 5 2 5 3 3 +--R (- 2a b + 4a b - 2a b)cos(x) + (- 2a b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 4 +--R (a b - a b )cos(x)sin(x) +--R + +--R 5 3 3 5 2 5 5 3 +--R ((a b - 2a b + a b)cos(x) + (a b - a b)cos(x))sin(x) +--R + +--R 6 2 4 4 2 3 6 2 4 4 2 6 2 +--R (b - 2a b + a b )cos(x) + (b - a b - 2a b + a )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 +--R (- b + 3a b - 2a b )cos(x) - b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 5 5 3 5 3 3 5 2 +--R a b cos(x) + (a b - a b)cos(x) + (a b - 2a b - a b)cos(x) +--R + +--R 5 5 5 3 3 +--R (- a b + a b)cos(x) - a b + 2a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 3 +--R (a b - 2a b + a )cos(x) + (a b - a b )cos(x) +--R + +--R 2 4 4 2 6 2 2 4 4 2 +--R (- a b + 2a b - a )cos(x) + (- a b + a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 5 4 3 6 4 +--R (a b - 2a b + a b)cos(x)sin(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 7 +--R ((a b - 2a b + a b )cos(x) + (a b - a b - a b + a )cos(x)) +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 5 6 3 7 2 5 6 2 +--R (b - 2a b + a b)cos(x) + (b - 2a b + a b)cos(x) +--R + +--R 7 2 5 4 3 7 2 5 4 3 +--R (- b + 3a b - 2a b )cos(x) - b + 3a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 4 6 3 4 5 2 7 3 +--R (a b - a b )cos(x) + (a b - a b - a b + a )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 7 +--R (a b - 4a b + 3a b )cos(x) + (- a b + a b + a b - a )cos(x) +--R + +--R 6 3 4 5 2 +--R - a b + 3a b - 2a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (a b - 2a b + a b)cos(x) + (a b - 2a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 4 5 2 4 +--R (2a b - 4a b + 2a b )cos(x)sin(x) +--R + +--R 2 5 4 3 2 7 2 5 4 3 6 7 +--R (2a b - 2a b )cos(x) + (2b - 2a b - 2a b + 2a b)cos(x) + 2b +--R + +--R 2 5 4 3 +--R - 6a b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 3 4 5 2 3 3 4 5 2 2 6 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 2a b )cos(x) + 2a b +--R + +--R 3 4 5 2 +--R - 6a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 4 3 4 2 5 4 3 6 3 +--R (2a b - 2a b )cos(x) + (4a b - 6a b + 2a b)cos(x) +--R + +--R 2 5 4 3 2 2 5 4 3 6 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 6a b - 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 6 3 4 5 2 4 6 3 4 5 2 3 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 4 3 6 4 +--R (a b - 2a b + a b)cos(x)sin(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 7 3 +--R ((a b - 2a b + a b )cos(x) + (a b - a b - a b + a )cos(x))sin(x) +--R + +--R 7 2 5 6 3 7 2 5 6 2 +--R (b - 2a b + a b)cos(x) + (b - 2a b + a b)cos(x) +--R + +--R 7 2 5 4 3 7 2 5 4 3 +--R (- b + 3a b - 2a b )cos(x) - b + 3a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 4 6 3 4 5 2 7 3 +--R (a b - a b )cos(x) + (a b - a b - a b + a )cos(x) +--R + +--R 6 3 4 5 2 2 6 3 4 5 2 7 +--R (a b - 4a b + 3a b )cos(x) + (- a b + a b + a b - a )cos(x) +--R + +--R 6 3 4 5 2 +--R - a b + 3a b - 2a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (a b - 2a b + a b)cos(x) + (a b - 2a b + a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R / +--R 4 4 6 2 2 4 4 6 2 3 +--R ((a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 3 5 5 3 7 3 3 5 7 2 +--R (a b - 2a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 7 +--R (- a b + 2a b - a b)cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 6 2 8 3 4 4 6 2 2 +--R (a b - 2a b + a )cos(x) + (a b - a b )cos(x) +--R + +--R 4 4 6 2 8 4 4 6 2 +--R (- a b + 2a b - a )cos(x) - a b + a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 5 5 3 2 3 5 5 3 3 +--R ((2a b - 2a b )cos(x) - 2a b + 2a b )sin(x) +--R + +--R 2 6 4 4 6 2 3 2 6 6 2 2 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 6 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 2 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 2a b )cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 +--R (- 2a b + 4a b - 2a b)cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 4 6 2 2 4 4 6 2 3 +--R ((a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 3 5 5 3 7 3 3 5 7 2 +--R (a b - 2a b + a b)cos(x) + (a b - a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 7 +--R (- a b + 2a b - a b)cos(x) - a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 6 2 8 3 4 4 6 2 2 +--R (a b - 2a b + a )cos(x) + (a b - a b )cos(x) +--R + +--R 4 4 6 2 8 4 4 6 2 +--R (- a b + 2a b - a )cos(x) - a b + a b +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 5 6 3 8 2 4 5 6 3 8 3 +--R ((a b - 2a b + a b)cos(x) - a b + 2a b - a b)sin(x) +--R + +--R 3 6 5 4 7 2 3 3 6 5 4 7 2 9 2 +--R (a b - 2a b + a b )cos(x) + (a b - a b - a b + a )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 9 +--R (- a b + 2a b - a b )cos(x) - a b + a b + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 3 8 3 4 5 6 3 8 2 +--R (a b - 2a b + a b)cos(x) + (a b - 2a b + a b)cos(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (- a b + 2a b - a b)cos(x) - a b + 2a b - a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 6 5 4 7 2 2 3 6 5 4 7 2 3 +--R ((2a b - 4a b + 2a b )cos(x) - 2a b + 4a b - 2a b )sin(x) +--R + +--R 2 7 4 5 6 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 8 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 2a b + 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 5 4 7 2 3 3 6 5 4 7 2 2 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 5 6 3 8 2 4 5 6 3 8 3 +--R ((a b - 2a b + a b)cos(x) - a b + 2a b - a b)sin(x) +--R + +--R 3 6 5 4 7 2 3 3 6 5 4 7 2 9 2 +--R (a b - 2a b + a b )cos(x) + (a b - a b - a b + a )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 9 +--R (- a b + 2a b - a b )cos(x) - a b + a b + a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 3 8 3 4 5 6 3 8 2 +--R (a b - 2a b + a b)cos(x) + (a b - 2a b + a b)cos(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (- a b + 2a b - a b)cos(x) - a b + 2a b - a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 486 + +--S 487 of 586 +m0583b:= a0583.2-r0583 +--R +--R +--R (472) +--R +---------+ +---------+ +--R 2 2 | 2 2 sin(x) 2 2 | 2 2 +--R (b - a )\|- b + a log(----------) + (b - a )\|- b + a atanh(cos(x)) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 3 2 (a sin(x) + b cos(x) + b)\|- b + a +--R (2b - 4a b)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R x +--R a tan(-) + b +---------+ +--R 3 2 2 2 | 2 2 +--R (2b - 4a b)atan(------------) + b \|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 2 4 | 2 2 +--R (a b - a )\|- b + a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 586 +d0583b:= D(m0583b,x) +--R +--R +--R (473) +--R 2 2 4 4 +--R (a b - a )cos(x)sin(x) +--R + +--R 3 2 3 3 3 3 3 +--R (a b cos(x) + (2a b - 2a b)cos(x) + a b - 2a b)sin(x) +--R + +--R 4 2 2 4 3 4 2 2 4 2 +--R (2b - 2a b - 2a )cos(x) + (2b - 2a b - 2a )cos(x) +--R + +--R 4 2 2 4 2 2 +--R (- 2b + 4a b )cos(x) - 2b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R a b cos(x) + (2a b - 2a b)cos(x) - 2a b cos(x) +--R + +--R 3 3 3 3 +--R (- 2a b + 2a b)cos(x) - a b + 2a b +--R * +--R sin(x) +--R + +--R 2 2 4 5 2 2 4 4 2 2 4 2 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 2 2 4 +--R (- a b + a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 4 +--R (2a b - 2a b)cos(x)sin(x) +--R + +--R 2 2 2 4 2 2 4 2 2 3 +--R (4a b cos(x) + (4b - 4a b )cos(x) + 4b - 8a b )sin(x) +--R + +--R 3 3 3 3 3 2 2 +--R ((4a b - 4a b)cos(x) + (4a b - 4a b)cos(x) )sin(x) +--R + +--R 2 2 4 2 2 3 2 2 2 2 2 +--R (4a b cos(x) + 4a b cos(x) - 4a b cos(x) - 4a b cos(x))sin(x) +--R + +--R 3 3 5 3 3 4 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 3 2 3 3 +--R (- 4a b + 4a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 +--R (a b - a )cos(x)sin(x) +--R + +--R 3 2 3 3 3 3 3 +--R (a b cos(x) + (2a b - 2a b)cos(x) + a b - 2a b)sin(x) +--R + +--R 4 2 2 4 3 4 2 2 4 2 +--R (2b - 2a b - 2a )cos(x) + (2b - 2a b - 2a )cos(x) +--R + +--R 4 2 2 4 2 2 +--R (- 2b + 4a b )cos(x) - 2b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R a b cos(x) + (2a b - 2a b)cos(x) - 2a b cos(x) +--R + +--R 3 3 3 3 +--R (- 2a b + 2a b)cos(x) - a b + 2a b +--R * +--R sin(x) +--R + +--R 2 2 4 5 2 2 4 4 2 2 4 2 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 2 2 4 +--R (- a b + a )cos(x) +--R / +--R 4 2 6 2 4 2 6 3 +--R ((a b - a )cos(x) - a b + a )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 4 4 2 6 3 4 2 6 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 4 2 6 +--R - a b + a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 5 2 3 3 5 3 +--R ((2a b - 2a b)cos(x) - 2a b + 2a b)sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (2a b - 2a b)cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 4a b + 4a b)cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 6 2 4 2 6 3 +--R ((a b - a )cos(x) - a b + a )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (2a b - 2a b)cos(x) + (2a b - 2a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 4 4 2 6 3 4 2 6 +--R (a b - a )cos(x) + (2a b - 2a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 4 2 6 +--R - a b + a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 488 + +--S 489 of 586 +t0584:= csc(x)^2/(a+b*sin(x))^2 +--R +--R +--R 2 +--R csc(x) +--R (474) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 489 + +--S 490 of 586 +r0584:= 2*b^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a/(a^2-b^2)^(3/2)+_ + 4*b^2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^3/(a^2-b^2)^(1/2)+_ + 2*b*atanh(cos(x))/a^3-cot(x)/a^2+b^3*cos(x)/a^2/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (475) +--R +---------+ +--R 4 2 2 3 3 | 2 2 +--R ((2b - 2a b )sin(x) + 2a b - 2a b)\|- b + a atanh(cos(x)) +--R + +--R x +--R a tan(-) + b +--R 5 2 3 4 3 2 2 +--R ((4b - 6a b )sin(x) + 4a b - 6a b )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 3 3 2 2 4 3 | 2 2 +--R ((- a b + a b)cot(x)sin(x) + (- a b + a )cot(x) - a b cos(x))\|- b + a +--R / +--R +---------+ +--R 3 3 5 4 2 6 | 2 2 +--R ((a b - a b)sin(x) + a b - a )\|- b + a +--R Type: Expression(Integer) +--E 490 + +--S 491 of 586 +a0584:= integrate(t0584,x) +--R +--R +--R (476) +--R [ +--R 4 3 2 5 2 3 2 5 2 3 +--R ((2a b - 3a b )sin(x) + (- 2b + 3a b )cos(x) + 2b - 3a b ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 3 3 4 2 2 2 4 2 2 +--R ((- 2a b + 2a b)sin(x) + (2b - 2a b )cos(x) - 2b + 2a b ) +--R * +--R +-------+ +--R | 2 2 sin(x) +--R \|b - a log(----------) +--R cos(x) + 1 +--R + +--R 3 3 3 4 2 +--R ((- 2a b + a b)cos(x) - a b )sin(x) + b cos(x) +--R + +--R 2 2 4 4 +--R (- a b + a )cos(x) - b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R +-------+ +--R 4 2 6 3 3 5 2 3 3 5 | 2 2 +--R ((a b - a )sin(x) + (- a b + a b)cos(x) + a b - a b)\|b - a +--R , +--R +--R 3 3 4 2 2 2 4 2 2 +--R ((- 2a b + 2a b)sin(x) + (2b - 2a b )cos(x) - 2b + 2a b ) +--R * +--R +---------+ +--R | 2 2 sin(x) +--R \|- b + a log(----------) +--R cos(x) + 1 +--R + +--R 4 3 2 5 2 3 2 5 2 3 +--R ((- 4a b + 6a b )sin(x) + (4b - 6a b )cos(x) - 4b + 6a b ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 3 3 3 4 2 +--R ((- 2a b + a b)cos(x) - a b )sin(x) + b cos(x) +--R + +--R 2 2 4 4 +--R (- a b + a )cos(x) - b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 6 3 3 5 2 3 3 5 | 2 2 +--R ((a b - a )sin(x) + (- a b + a b)cos(x) + a b - a b)\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 491 + +--S 492 of 586 +m0584a:= a0584.1-r0584 +--R +--R +--R (477) +--R 5 3 3 2 +--R (2a b - 3a b )sin(x) +--R + +--R 6 2 4 2 6 2 4 4 2 +--R ((- 2b + 3a b )cos(x) + 2b - a b - 3a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (- 2a b + 3a b )cos(x) + 2a b - 3a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R 4 3 2 2 5 2 3 2 5 4 +--R (- 2a b + 2a b )sin(x) + ((2b - 2a b )cos(x) - 2b + 2a b)sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (2a b - 2a b )cos(x) - 2a b + 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) +--R \|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R 4 3 2 2 5 2 3 2 5 4 +--R (- 2a b + 2a b )sin(x) + ((2b - 2a b )cos(x) - 2b + 2a b)sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (2a b - 2a b )cos(x) - 2a b + 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atanh(cos(x)) +--R + +--R 5 3 3 2 +--R (- 4a b + 6a b )sin(x) +--R + +--R 6 2 4 2 6 2 4 4 2 +--R ((4b - 6a b )cos(x) - 4b + 2a b + 6a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (4a b - 6a b )cos(x) - 4a b + 6a b +--R * +--R x +--R +-------+ a tan(-) + b +--R | 2 2 2 +--R \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 4 4 3 2 4 2 +--R ((a b - a b)cot(x) + (- 2a b + a b )cos(x) - a b )sin(x) +--R + +--R 4 3 2 2 4 5 5 2 +--R ((- a b + a b )cos(x) + a b - a )cot(x) + b cos(x) +--R + +--R 2 3 4 5 2 3 +--R (- 2a b + 2a b)cos(x) - b - a b +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 3 4 4 3 +--R ((- a b + a b)cos(x) + a b - a b)cot(x) - a b cos(x) +--R + +--R 4 2 4 3 2 5 4 +--R a b cos(x) + (a b - a b + a )cos(x) - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 3 6 2 3 4 5 2 2 3 4 7 +--R (a b - a b)sin(x) + ((- a b + a b )cos(x) + a b - a )sin(x) +--R + +--R 4 3 6 2 4 3 6 +--R (- a b + a b)cos(x) + a b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 492 + +--S 493 of 586 +d0584a:= D(m0584a,x) +--R +--R +--R (478) +--R 4 6 6 4 2 4 6 6 4 4 6 +--R (2a b - a b )cos(x) + (- 2a b + 2a b )cos(x) - 2a b +--R + +--R 6 4 +--R a b +--R * +--R 7 +--R sin(x) +--R + +--R 5 5 7 3 2 5 5 7 3 2 +--R ((- a b + a b )cos(x) + a b - a b )cot(x) +--R + +--R 3 7 5 5 4 3 7 5 5 7 3 3 +--R (2a b - a b )cos(x) + (6a b - 7a b + a b )cos(x) +--R + +--R 5 5 7 3 2 3 7 5 5 7 3 +--R (6a b - 4a b )cos(x) + (- 8a b + 5a b + 3a b )cos(x) +--R + +--R 3 7 5 5 7 3 +--R - 4a b - a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 6 6 4 4 4 6 6 4 8 2 3 +--R (2a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 +--R (- 5a b + 3a b + 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 6 6 4 8 2 +--R (a b - 2a b + a b )cos(x) + 3a b - a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 6 4 5 2 8 6 4 4 +--R (- a b + a b )cos(x) + (6a b - a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (6a b + 6a b - 14a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 6a b + 2a b + 7a b - 5a b )cos(x) +--R + +--R 2 8 4 6 6 4 4 6 6 4 8 2 +--R (- 6a b - 9a b + 15a b )cos(x) - 6a b + 2a b + a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 7 5 5 6 3 7 5 5 7 3 5 +--R (- a b + a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 4 +--R (5a b - a b - 4a b )cos(x) +--R + +--R 3 7 5 5 9 3 +--R (- 4a b + 6a b - 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (- 7a b - 3a b + 9a b + a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 3 7 5 5 +--R (2a b - 2a b - 2a b + 2a b)cos(x) + 3a b + 3a b +--R + +--R 7 3 9 +--R - 5a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 3 7 5 5 6 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 5 +--R (2a b + a b - 8a b + 5a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 4 +--R (8a b + 5a b - 7a b - 2a b )cos(x) +--R + +--R 9 3 7 7 3 9 3 +--R (- 4a b + 12a b - 9a b + a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 10a b - 8a b + 12a b + 6a b - 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 9 3 7 +--R (2a b - 13a b + 6a b + 6a b - a b)cos(x) + 4a b - a b +--R + +--R 5 5 +--R - 5a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 4 6 6 4 7 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 2 8 4 6 6 4 6 +--R (- a b - a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 5 +--R (3a b - 2a b - 5a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (3a b + 7a b - 8a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 3 +--R (- 3a b - 2a b + 12a b - 6a b - a )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 3a b - 11a b + 9a b + 5a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 8 4 6 +--R (a b + 2a b - 6a b + 2a b + a )cos(x) + a b + 5a b +--R + +--R 6 4 8 2 +--R - 3a b - 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 10 2 8 4 6 7 +--R (- 2b + 3a b - a b )cos(x) +--R + +--R 10 2 8 4 6 6 +--R (- 2b - a b + 9a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 5 +--R (6b - 3a b + 6a b - 17a b + 8a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 4 +--R (6b + 9a b - 16a b - 8a b - 5a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 3 +--R (- 6b - 3a b - a b + 17a b - 7a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (- 6b - 15a b + 13a b + 13a b + 6a b )cos(x) +--R + +--R 10 2 8 4 6 8 2 10 2 8 4 6 +--R (2b + 3a b - 4a b - a b )cos(x) + 2b + 7a b - 6a b +--R + +--R 6 4 8 2 +--R - 5a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 7 5 5 7 3 7 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 6 +--R (- 2a b + a b + a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 5 +--R (6a b - 10a b + 2a b + 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 4 +--R (6a b - a b - 5a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (- 6a b + 8a b + 2a b - 4a b)cos(x) +--R + +--R 3 7 5 5 7 3 2 +--R (- 6a b - a b + 7a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 3 7 5 5 7 3 +--R (2a b - 2a b - 2a b + 2a b)cos(x) + 2a b + a b - 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 5 8 9 3 7 5 5 7 +--R - 2a b cos(x) + (- 4a b + 6a b - 2a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 6 +--R (- 4a b + 11a b + a b + 6a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 5 +--R (12a b - 6a b + a b - 12a b + 5a b)cos(x) +--R + +--R 9 3 7 7 3 9 4 +--R (12a b - 21a b - 13a b - 3a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 12a b - 6a b + 6a b + 18a b - 6a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 12a b + 9a b + 7a b + 9a b + 3a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 9 3 7 +--R (4a b + 6a b - 5a b - 6a b + a b)cos(x) + 4a b + a b +--R + +--R 5 5 7 3 +--R - 6a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 6 4 8 2 7 4 6 6 4 6 +--R (- a b + 2a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 4 6 6 4 8 2 5 4 6 6 4 4 +--R (3a b - 6a b + 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 4 6 6 4 8 2 3 +--R (- 3a b + 6a b - 3a b )cos(x) +--R + +--R 4 6 6 4 2 4 6 6 4 8 2 +--R (- 3a b + 3a b )cos(x) + (a b - 2a b + a b )cos(x) +--R + +--R 4 6 6 4 +--R a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 8 4 6 9 2 8 4 6 6 4 8 +--R (- a b + a b )cos(x) + (- 3a b + 5a b - 4a b )cos(x) +--R + +--R 2 8 6 4 7 +--R (- a b + a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 6 +--R (7a b - 7a b + 4a b + 4a b )cos(x) +--R + +--R 2 8 6 4 8 2 10 5 +--R (9a b - 9a b - a b + a )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (- 3a b - 3a b + 4a b - 9a b )cos(x) +--R + +--R 2 8 4 6 6 4 10 3 +--R (- 11a b - 4a b + 16a b - a )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 3a b + 7a b - 3a b + 5a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 8 4 6 6 4 +--R (4a b + 3a b - 8a b + a b )cos(x) + 2a b - 2a b - a b +--R * +--R sin(x) +--R + +--R 3 7 5 5 7 3 8 3 7 5 5 7 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 6 3 7 5 5 5 +--R (6a b - 12a b + 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 3 7 5 5 7 3 4 3 7 5 5 3 +--R (- 6a b + 12a b - 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 3 7 5 5 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 7 5 5 2 3 7 5 5 3 7 +--R (4a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) - 4a b +--R + +--R 5 5 +--R 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 6 6 4 2 4 6 6 4 2 +--R ((- 2a b + 2a b )cos(x) + 2a b - 2a b )cot(x) +--R + +--R 2 8 4 6 4 2 8 4 6 6 4 3 +--R (4a b - 2a b )cos(x) + (12a b - 14a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 2 +--R (4a b + 6a b - 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 2 8 4 6 6 4 +--R (- 16a b + 10a b + 6a b )cos(x) - 12a b + 4a b + 4a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 7 5 5 4 3 7 5 5 7 3 3 +--R (4a b - 4a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 +--R (- 10a b + 6a b + 4a b )cos(x) +--R + +--R 3 7 5 5 7 3 3 7 5 5 7 3 +--R (2a b - 4a b + 2a b )cos(x) + 6a b - 2a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 7 5 5 5 9 3 7 5 5 4 +--R (- 2a b + 2a b )cos(x) + (4a b + 12a b - 2a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (16a b + 2a b - 22a b + 4a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (8a b - 18a b + 2a b - 10a b )cos(x) +--R + +--R 9 3 7 5 5 9 3 7 5 5 +--R (- 16a b - 8a b + 24a b )cos(x) - 12a b - 2a b + 16a b +--R + +--R 7 3 +--R 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 8 4 6 6 2 8 4 6 6 4 5 +--R (- 2a b + 2a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 4 +--R (10a b - 2a b - 8a b )cos(x) +--R + +--R 2 8 4 6 8 2 3 +--R (- 8a b + 12a b - 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 14a b - 6a b + 18a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 8 4 6 +--R (4a b - 4a b - 4a b + 4a b )cos(x) + 6a b + 6a b +--R + +--R 6 4 8 2 +--R - 10a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 8 4 6 6 +--R (2a b - 4a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 5 +--R (- 4b + 22a b - 28a b + 10a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 4 +--R (- 4b + 24a b + 10a b - 4a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 3 +--R (8b - 8a b + 4a b - 6a b + 2a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (8b - 18a b - 32a b + 6a b - 4a b )cos(x) +--R + +--R 10 2 8 4 6 8 2 10 2 8 +--R (- 4b - 14a b + 20a b - 2a b )cos(x) - 4b - 8a b +--R + +--R 4 6 6 4 +--R 22a b + 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 9 3 7 5 5 7 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 9 3 7 5 5 6 +--R (- 2a b - 2a b + 4a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 5 +--R (6a b - 4a b - 10a b + 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 4 +--R (6a b + 14a b - 16a b - 4a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 6a b - 4a b + 24a b - 12a b - 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (- 6a b - 22a b + 18a b + 10a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 9 +--R (2a b + 4a b - 12a b + 4a b + 2a b)cos(x) + 2a b +--R + +--R 3 7 5 5 7 3 +--R 10a b - 6a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 3 7 7 3 7 6 +--R (- 4a b + 4a b )cos(x) + 6a b cos(x) +--R + +--R 9 3 7 5 5 7 3 5 +--R (8a b + 34a b - 58a b + 16a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 4 +--R (- 4a b + 20a b - 4a b - 10a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 3 +--R (- 4a b - 60a b + 72a b - 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (8a b - 38a b - 4a b + 12a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 3 7 5 5 +--R (22a b - 14a b - 8a b )cos(x) - 4a b + 12a b + 8a b +--R + +--R 7 3 +--R - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 8 4 6 6 4 7 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 6 +--R (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 5 +--R (12a b - 20a b + 4a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 4 +--R (12a b - 2a b - 10a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 12a b + 16a b + 4a b - 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 2 +--R (- 12a b - 2a b + 14a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 8 4 6 +--R (4a b - 4a b - 4a b + 4a b )cos(x) + 4a b + 2a b +--R + +--R 6 4 +--R - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 8 2 8 4 6 7 +--R - 4a b cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 6 +--R (14a b - 4a b + 12a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 5 +--R (40a b - 14a b - 36a b + 10a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (- 26a b + 30a b - 26a b - 6a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 56a b + 8a b + 60a b - 12a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (10a b - 28a b + 18a b + 6a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 8 4 6 6 4 +--R (24a b - 2a b - 24a b + 2a b )cos(x) + 2a b + 6a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 7 5 5 7 3 7 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 7 5 5 6 +--R (- 2a b + 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 5 3 7 5 5 4 +--R (6a b - 12a b + 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 3 7 5 5 7 3 3 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 3 7 5 5 2 3 7 5 5 7 3 +--R (- 6a b + 6a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 7 5 5 +--R 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 3 7 9 9 3 7 5 5 8 +--R (- 2a b + 2a b )cos(x) + (- 6a b + 10a b - 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 +--R (2a b - 10a b + 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 6 +--R (18a b - 20a b + 8a b + 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 5 +--R (6a b + 30a b - 36a b - 2a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 4 +--R (- 18a b + 12a b + 8a b - 18a b )cos(x) +--R + +--R 9 3 7 5 5 9 3 +--R (- 10a b - 38a b + 50a b - 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (6a b - 4a b - 6a b + 10a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 3 7 5 5 +--R (4a b + 16a b - 22a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 8 4 6 7 +--R (- 4a b + 8a b - 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 6 2 8 4 6 5 +--R (12a b - 24a b + 12a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 2 8 4 6 6 4 4 2 8 4 6 3 +--R (- 12a b + 24a b - 12a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 2 8 4 6 6 4 2 2 8 4 6 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 4a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 6 6 4 2 4 6 6 4 4 6 6 4 +--R ((2a b - a b )cos(x) + (- 2a b + 2a b )cos(x) - 2a b + a b ) +--R * +--R 7 +--R sin(x) +--R + +--R 5 5 7 3 2 5 5 7 3 2 +--R ((- a b + a b )cos(x) + a b - a b )cot(x) +--R + +--R 3 7 5 5 4 3 7 5 5 7 3 3 +--R (2a b - a b )cos(x) + (6a b - 7a b + a b )cos(x) +--R + +--R 5 5 7 3 2 3 7 5 5 7 3 3 7 +--R (6a b - 4a b )cos(x) + (- 8a b + 5a b + 3a b )cos(x) - 4a b +--R + +--R 5 5 7 3 +--R - a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 6 6 4 4 4 6 6 4 8 2 3 +--R (2a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 +--R (- 5a b + 3a b + 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 6 6 4 8 2 +--R (a b - 2a b + a b )cos(x) + 3a b - a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 6 4 5 2 8 6 4 4 +--R (- a b + a b )cos(x) + (6a b - a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (6a b + 6a b - 14a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 6a b + 2a b + 7a b - 5a b )cos(x) +--R + +--R 2 8 4 6 6 4 4 6 6 4 8 2 +--R (- 6a b - 9a b + 15a b )cos(x) - 6a b + 2a b + a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 7 5 5 6 3 7 5 5 7 3 5 +--R (- a b + a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 4 +--R (5a b - a b - 4a b )cos(x) +--R + +--R 3 7 5 5 9 3 +--R (- 4a b + 6a b - 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (- 7a b - 3a b + 9a b + a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 3 7 5 5 7 3 +--R (2a b - 2a b - 2a b + 2a b)cos(x) + 3a b + 3a b - 5a b +--R + +--R 9 +--R - a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 3 7 5 5 6 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 5 +--R (2a b + a b - 8a b + 5a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 4 +--R (8a b + 5a b - 7a b - 2a b )cos(x) +--R + +--R 9 3 7 7 3 9 3 +--R (- 4a b + 12a b - 9a b + a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 10a b - 8a b + 12a b + 6a b - 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 9 3 7 5 5 +--R (2a b - 13a b + 6a b + 6a b - a b)cos(x) + 4a b - a b - 5a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 4 6 6 4 7 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 2 8 4 6 6 4 6 +--R (- a b - a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 5 +--R (3a b - 2a b - 5a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (3a b + 7a b - 8a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 3 +--R (- 3a b - 2a b + 12a b - 6a b - a )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 3a b - 11a b + 9a b + 5a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 8 4 6 +--R (a b + 2a b - 6a b + 2a b + a )cos(x) + a b + 5a b +--R + +--R 6 4 8 2 +--R - 3a b - 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 10 2 8 4 6 7 10 2 8 4 6 6 +--R (- 2b + 3a b - a b )cos(x) + (- 2b - a b + 9a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 5 +--R (6b - 3a b + 6a b - 17a b + 8a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 4 +--R (6b + 9a b - 16a b - 8a b - 5a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 3 +--R (- 6b - 3a b - a b + 17a b - 7a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 2 +--R (- 6b - 15a b + 13a b + 13a b + 6a b )cos(x) +--R + +--R 10 2 8 4 6 8 2 10 2 8 4 6 +--R (2b + 3a b - 4a b - a b )cos(x) + 2b + 7a b - 6a b +--R + +--R 6 4 8 2 +--R - 5a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 7 5 5 7 3 7 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 6 +--R (- 2a b + a b + a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 5 +--R (6a b - 10a b + 2a b + 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 4 +--R (6a b - a b - 5a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (- 6a b + 8a b + 2a b - 4a b)cos(x) +--R + +--R 3 7 5 5 7 3 2 +--R (- 6a b - a b + 7a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 3 7 5 5 7 3 +--R (2a b - 2a b - 2a b + 2a b)cos(x) + 2a b + a b - 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 5 8 9 3 7 5 5 7 +--R - 2a b cos(x) + (- 4a b + 6a b - 2a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 6 +--R (- 4a b + 11a b + a b + 6a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 5 +--R (12a b - 6a b + a b - 12a b + 5a b)cos(x) +--R + +--R 9 3 7 7 3 9 4 +--R (12a b - 21a b - 13a b - 3a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 12a b - 6a b + 6a b + 18a b - 6a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 12a b + 9a b + 7a b + 9a b + 3a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 9 3 7 +--R (4a b + 6a b - 5a b - 6a b + a b)cos(x) + 4a b + a b +--R + +--R 5 5 7 3 +--R - 6a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 6 4 8 2 7 4 6 6 4 6 +--R (- a b + 2a b - a b )cos(x) + (- a b + a b )cos(x) +--R + +--R 4 6 6 4 8 2 5 4 6 6 4 4 +--R (3a b - 6a b + 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 4 6 6 4 8 2 3 4 6 6 4 2 +--R (- 3a b + 6a b - 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 6 6 4 +--R (a b - 2a b + a b )cos(x) + a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 8 4 6 9 2 8 4 6 6 4 8 +--R (- a b + a b )cos(x) + (- 3a b + 5a b - 4a b )cos(x) +--R + +--R 2 8 6 4 7 2 8 4 6 6 4 8 2 6 +--R (- a b + a b )cos(x) + (7a b - 7a b + 4a b + 4a b )cos(x) +--R + +--R 2 8 6 4 8 2 10 5 +--R (9a b - 9a b - a b + a )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (- 3a b - 3a b + 4a b - 9a b )cos(x) +--R + +--R 2 8 4 6 6 4 10 3 +--R (- 11a b - 4a b + 16a b - a )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 3a b + 7a b - 3a b + 5a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 8 4 6 6 4 +--R (4a b + 3a b - 8a b + a b )cos(x) + 2a b - 2a b - a b +--R * +--R sin(x) +--R + +--R 3 7 5 5 7 3 8 3 7 5 5 7 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 6 3 7 5 5 5 +--R (6a b - 12a b + 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 3 7 5 5 7 3 4 3 7 5 5 3 +--R (- 6a b + 12a b - 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 3 7 5 5 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 7 6 5 8 3 2 4 7 6 5 8 3 +--R (- 2a b + 3a b - a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 4 7 6 5 8 3 +--R 2a b - 3a b + a b +--R * +--R 7 +--R sin(x) +--R + +--R 5 6 7 4 9 2 2 5 6 7 4 9 2 2 +--R ((a b - 2a b + a b )cos(x) - a b + 2a b - a b )cot(x) +--R + +--R 3 8 5 6 7 4 4 +--R (- 2a b + 3a b - a b )cos(x) +--R + +--R 3 8 5 6 7 4 3 +--R (- 6a b + 11a b - 5a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 +--R (- 4a b + 6a b - 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 8 5 6 7 4 +--R (8a b - 11a b - a b + 4a b )cos(x) + 4a b - 3a b - 3a b +--R + +--R 9 2 +--R 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 7 6 5 8 3 4 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 4 7 6 5 8 3 3 +--R (a b - 2a b + a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (5a b - 8a b + a b + 2a b)cos(x) +--R + +--R 4 7 6 5 8 3 4 7 6 5 8 3 10 +--R (- a b + 2a b - a b )cos(x) - 3a b + 4a b + a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 7 6 5 5 2 9 4 7 6 5 8 3 4 +--R (- a b + a b )cos(x) + (- 6a b + 2a b + 9a b - 5a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (- 6a b + 2a b + 12a b - 8a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (6a b - 4a b - 9a b + 8a b - a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 4 7 6 5 +--R (6a b + 3a b - 19a b + 8a b + 2a b)cos(x) + 6a b - 8a b +--R + +--R 8 3 10 +--R a b + a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 8 5 6 7 4 6 +--R (a b - 2a b + a b )cos(x) +--R + +--R 3 8 5 6 7 4 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 4 +--R (- 5a b + 6a b + 3a b - 4a b )cos(x) +--R + +--R 3 8 5 6 9 2 3 +--R (4a b - 6a b + 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 11 2 +--R (7a b - 4a b - 12a b + 8a b + a )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 8 7 4 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) - 3a b + 8a b +--R + +--R 9 2 11 +--R - 4a b - a +--R * +--R 2 +--R cot(x) +--R + +--R 10 3 8 5 6 6 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 5 +--R (- 2a b - 3a b + 10a b - 5a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 4 +--R (- 8a b - a b + 14a b + 3a b - 8a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 3 +--R (4a b - 8a b + 2a b + 3a b - a b )cos(x) +--R + +--R 10 5 6 7 4 9 2 2 +--R (10a b - 18a b - 2a b + 10a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 10 +--R (- 2a b + 11a b - 10a b - 2a b + 3a b )cos(x) - 4a b +--R + +--R 3 8 5 6 7 4 +--R 5a b + 4a b - 5a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 9 4 7 6 5 7 2 9 6 5 8 3 6 +--R (a b - 2a b + a b )cos(x) + (a b - 3a b + 2a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 5 +--R (- 3a b + 2a b + 5a b - 4a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 4 +--R (- 3a b - 4a b + 15a b - 6a b - 2a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 3 +--R (3a b + 2a b - 12a b + 6a b + a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (3a b + 8a b - 20a b + 4a b + 5a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 2 9 4 7 +--R (- a b - 2a b + 6a b - 2a b - a b)cos(x) - a b - 4a b +--R + +--R 6 5 10 +--R 8a b - 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 11 2 9 4 7 6 5 7 +--R (2b - 3a b - a b + 2a b )cos(x) +--R + +--R 11 2 9 4 7 6 5 6 +--R (2b - a b - 10a b + 9a b )cos(x) +--R + +--R 11 2 9 6 5 8 3 5 +--R (- 6b + 3a b + 17a b - 14a b )cos(x) +--R + +--R 11 2 9 4 7 6 5 8 3 10 4 +--R (- 6b - 3a b + 25a b - 8a b - 3a b - 5a b)cos(x) +--R + +--R 11 2 9 4 7 6 5 8 3 10 3 +--R (6b + 3a b - 5a b - 23a b + 17a b + 2a b)cos(x) +--R + +--R 11 2 9 4 7 8 3 10 2 +--R (6b + 9a b - 28a b + 7a b + 6a b)cos(x) +--R + +--R 11 2 9 4 7 6 5 8 3 10 11 +--R (- 2b - 3a b + 6a b + 4a b - 3a b - 2a b)cos(x) - 2b +--R + +--R 2 9 4 7 6 5 8 3 10 +--R - 5a b + 13a b - a b - 4a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 8 5 6 7 4 7 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 8 5 6 9 2 6 +--R (2a b - 3a b + a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 5 +--R (- 6a b + 10a b - 2a b - 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 4 +--R (- 6a b + 7a b + 4a b - 5a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (6a b - 8a b - 2a b + 4a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 2 +--R (6a b - 5a b - 8a b + 7a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 8 5 6 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) - 2a b + a b +--R + +--R 7 4 9 2 +--R 4a b - 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 8 5 6 8 10 3 8 7 4 7 +--R (2a b - 2a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 6 +--R (4a b - 21a b + 16a b + a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 5 +--R (- 12a b + 12a b + 11a b - 2a b - 9a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 11 4 +--R (- 12a b + 39a b - 21a b - 3a b - 2a b - a )cos(x) +--R + +--R 10 5 6 7 4 9 2 3 +--R (12a b - 24a b - 4a b + 16a b )cos(x) +--R + +--R 10 3 8 7 4 9 2 11 2 +--R (12a b - 23a b + 6a b + 4a b + a )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 10 +--R (- 4a b - 4a b + 13a b + 2a b - 7a b )cos(x) - 4a b +--R + +--R 3 8 5 6 7 4 9 2 +--R 3a b + 7a b - 4a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 7 6 5 8 3 7 4 7 6 5 8 3 6 +--R (a b - 2a b + a b )cos(x) + (a b - 2a b + a b )cos(x) +--R + +--R 4 7 6 5 8 3 5 +--R (- 3a b + 6a b - 3a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 +--R (- 3a b + 6a b - 3a b )cos(x) +--R + +--R 4 7 6 5 8 3 3 +--R (3a b - 6a b + 3a b )cos(x) +--R + +--R 4 7 6 5 8 3 2 +--R (3a b - 6a b + 3a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 7 6 5 8 3 +--R (- a b + 2a b - a b )cos(x) - a b + 2a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 9 4 7 9 2 9 4 7 6 5 8 +--R (a b - a b )cos(x) + (3a b - 4a b + a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 7 +--R (a b - 4a b + a b + 2a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 6 +--R (- 7a b + 2a b + 9a b - 4a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 5 +--R (- 9a b + 12a b + 7a b - 9a b - a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 4 +--R (3a b + 12a b - 23a b + 9a b - a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 3 +--R (11a b - 8a b - 18a b + 14a b + a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (3a b - 14a b + 14a b - 4a b + a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 9 4 7 6 5 +--R (- 4a b + a b + 10a b - 7a b )cos(x) - 2a b + 4a b - a b +--R + +--R 8 3 +--R - a b +--R * +--R sin(x) +--R + +--R 3 8 5 6 7 4 8 3 8 5 6 7 4 7 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 6 3 8 5 6 7 4 5 +--R (- 6a b + 12a b - 6a b )cos(x) + (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 3 8 5 6 7 4 4 3 8 5 6 7 4 3 +--R (6a b - 12a b + 6a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 3 8 5 6 7 4 2 3 8 5 6 7 4 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 8 5 6 7 4 2 3 8 5 6 7 4 +--R (- 4a b + 6a b - 2a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 8 5 6 7 4 +--R 4a b - 6a b + 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 7 6 5 8 3 2 4 7 6 5 8 3 2 +--R ((2a b - 4a b + 2a b )cos(x) - 2a b + 4a b - 2a b )cot(x) +--R + +--R 2 9 4 7 6 5 4 +--R (- 4a b + 6a b - 2a b )cos(x) +--R + +--R 2 9 4 7 6 5 3 +--R (- 12a b + 22a b - 10a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 +--R (- 4a b + 2a b + 6a b - 4a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 9 4 7 8 3 +--R (16a b - 22a b - 2a b + 8a b )cos(x) + 12a b - 16a b + 4a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 8 5 6 7 4 4 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 3 8 5 6 7 4 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 2 +--R (10a b - 16a b + 2a b + 4a b )cos(x) +--R + +--R 3 8 5 6 7 4 3 8 5 6 7 4 9 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 6a b + 8a b + 2a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 8 5 6 5 +--R (- 2a b + 2a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 4 +--R (- 4a b - 16a b + 30a b - 10a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 16a b + 14a b + 18a b - 16a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (- 8a b + 34a b - 28a b + 4a b - 2a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 10 +--R (16a b - 4a b - 32a b + 16a b + 4a b )cos(x) + 12a b +--R + +--R 3 8 5 6 7 4 9 2 +--R - 10a b - 18a b + 14a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 9 4 7 6 5 6 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 2 9 4 7 6 5 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 4 +--R (- 10a b + 12a b + 6a b - 8a b )cos(x) +--R + +--R 2 9 4 7 8 3 3 +--R (8a b - 12a b + 4a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (14a b - 8a b - 24a b + 16a b + 2a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 9 6 5 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) - 6a b + 16a b +--R + +--R 8 3 10 +--R - 8a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 9 4 7 6 11 2 9 4 7 6 5 5 +--R (2a b - 2a b )cos(x) + (4b - 26a b + 32a b - 10a b )cos(x) +--R + +--R 11 2 9 4 7 6 5 8 3 4 +--R (4b - 36a b + 18a b + 30a b - 16a b )cos(x) +--R + +--R 11 2 9 6 5 8 3 3 +--R (- 8b + 16a b - 6a b - 2a b )cos(x) +--R + +--R 11 2 9 4 7 6 5 8 3 2 +--R (- 8b + 30a b + 18a b - 54a b + 14a b )cos(x) +--R + +--R 11 2 9 4 7 6 5 8 3 11 2 9 +--R (4b + 10a b - 28a b + 8a b + 6a b )cos(x) + 4b + 4a b +--R + +--R 4 7 6 5 8 3 +--R - 30a b + 16a b + 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 10 3 8 5 6 7 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 10 5 6 7 4 6 +--R (2a b - 6a b + 4a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 5 +--R (- 6a b + 4a b + 10a b - 8a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 4 +--R (- 6a b - 8a b + 30a b - 12a b - 4a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 3 +--R (6a b + 4a b - 24a b + 12a b + 2a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (6a b + 16a b - 40a b + 8a b + 10a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 10 +--R (- 2a b - 4a b + 12a b - 4a b - 2a b )cos(x) - 2a b +--R + +--R 3 8 5 6 9 2 +--R - 8a b + 16a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 10 3 8 5 6 7 3 8 5 6 6 +--R (4a b - 8a b + 4a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 5 +--R (- 8a b - 22a b + 58a b - 28a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 4 +--R (4a b - 24a b + 24a b + 6a b - 10a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 3 +--R (4a b + 48a b - 84a b + 28a b + 4a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (- 8a b + 46a b - 34a b - 16a b + 12a b )cos(x) +--R + +--R 3 8 5 6 9 2 10 3 8 5 6 +--R (- 18a b + 22a b - 4a b )cos(x) + 4a b - 16a b + 4a b +--R + +--R 7 4 9 2 +--R 10a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 9 4 7 6 5 7 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 9 4 7 8 3 6 +--R (4a b - 6a b + 2a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 5 +--R (- 12a b + 20a b - 4a b - 4a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 4 +--R (- 12a b + 14a b + 8a b - 10a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (12a b - 16a b - 4a b + 8a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 +--R (12a b - 10a b - 16a b + 14a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 9 4 7 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) - 4a b + 2a b +--R + +--R 6 5 8 3 +--R 8a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 9 4 7 8 2 9 4 7 6 5 7 +--R (4a b - 4a b )cos(x) + (4a b - 12a b + 8a b )cos(x) +--R + +--R 2 9 4 7 6 5 6 +--R (- 26a b + 30a b - 4a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 5 +--R (- 28a b + 38a b + 8a b - 18a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 4 +--R (38a b - 56a b + 24a b - 4a b - 2a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (44a b - 44a b - 32a b + 32a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (- 14a b + 34a b - 30a b + 8a b + 2a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 9 4 7 +--R (- 20a b + 18a b + 16a b - 14a b )cos(x) - 2a b - 4a b +--R + +--R 6 5 8 3 +--R 10a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 8 5 6 7 4 7 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 6 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 5 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 3 8 5 6 7 4 4 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 3 8 5 6 7 4 3 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 3 8 5 6 7 4 2 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 3 8 5 6 7 4 3 8 5 6 7 4 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 10 3 8 9 10 3 8 5 6 8 +--R (2a b - 2a b )cos(x) + (6a b - 8a b + 2a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 7 +--R (- 2a b + 2a b - 4a b + 4a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 6 +--R (- 18a b + 14a b + 12a b - 8a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 5 +--R (- 6a b - 6a b + 32a b - 18a b - 2a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 4 +--R (18a b - 6a b - 28a b + 18a b - 2a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 3 +--R (10a b + 14a b - 54a b + 28a b + 2a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 2 +--R (- 6a b + 2a b + 10a b - 8a b + 2a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 3 8 5 6 7 4 +--R (- 4a b - 8a b + 26a b - 14a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R sin(x) +--R + +--R 2 9 4 7 6 5 8 2 9 4 7 6 5 7 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 9 4 7 6 5 6 +--R (- 12a b + 24a b - 12a b )cos(x) +--R + +--R 2 9 4 7 6 5 5 +--R (- 12a b + 24a b - 12a b )cos(x) +--R + +--R 2 9 4 7 6 5 4 2 9 4 7 6 5 3 +--R (12a b - 24a b + 12a b )cos(x) + (12a b - 24a b + 12a b )cos(x) +--R + +--R 2 9 4 7 6 5 2 2 9 4 7 6 5 +--R (- 4a b + 8a b - 4a b )cos(x) + (- 4a b + 8a b - 4a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 7 6 5 8 3 2 4 7 6 5 8 3 +--R (- 2a b + 3a b - a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 4 7 6 5 8 3 +--R 2a b - 3a b + a b +--R * +--R 7 +--R sin(x) +--R + +--R 5 6 7 4 9 2 2 5 6 7 4 9 2 2 +--R ((a b - 2a b + a b )cos(x) - a b + 2a b - a b )cot(x) +--R + +--R 3 8 5 6 7 4 4 3 8 5 6 7 4 3 +--R (- 2a b + 3a b - a b )cos(x) + (- 6a b + 11a b - 5a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 +--R (- 4a b + 6a b - 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 8 5 6 7 4 9 2 +--R (8a b - 11a b - a b + 4a b )cos(x) + 4a b - 3a b - 3a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 7 6 5 8 3 4 4 7 6 5 8 3 3 +--R (- 2a b + 4a b - 2a b )cos(x) + (a b - 2a b + a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (5a b - 8a b + a b + 2a b)cos(x) +--R + +--R 4 7 6 5 8 3 4 7 6 5 8 3 10 +--R (- a b + 2a b - a b )cos(x) - 3a b + 4a b + a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 7 6 5 5 2 9 4 7 6 5 8 3 4 +--R (- a b + a b )cos(x) + (- 6a b + 2a b + 9a b - 5a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (- 6a b + 2a b + 12a b - 8a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (6a b - 4a b - 9a b + 8a b - a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 4 7 6 5 8 3 +--R (6a b + 3a b - 19a b + 8a b + 2a b)cos(x) + 6a b - 8a b + a b +--R + +--R 10 +--R a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 8 5 6 7 4 6 3 8 5 6 7 4 5 +--R (a b - 2a b + a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 4 +--R (- 5a b + 6a b + 3a b - 4a b )cos(x) +--R + +--R 3 8 5 6 9 2 3 +--R (4a b - 6a b + 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 11 2 +--R (7a b - 4a b - 12a b + 8a b + a )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 8 7 4 9 2 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) - 3a b + 8a b - 4a b +--R + +--R 11 +--R - a +--R * +--R 2 +--R cot(x) +--R + +--R 10 3 8 5 6 6 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 5 +--R (- 2a b - 3a b + 10a b - 5a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 4 +--R (- 8a b - a b + 14a b + 3a b - 8a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 3 +--R (4a b - 8a b + 2a b + 3a b - a b )cos(x) +--R + +--R 10 5 6 7 4 9 2 2 +--R (10a b - 18a b - 2a b + 10a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 10 3 8 +--R (- 2a b + 11a b - 10a b - 2a b + 3a b )cos(x) - 4a b + 5a b +--R + +--R 5 6 7 4 +--R 4a b - 5a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 9 4 7 6 5 7 2 9 6 5 8 3 6 +--R (a b - 2a b + a b )cos(x) + (a b - 3a b + 2a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 5 +--R (- 3a b + 2a b + 5a b - 4a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 4 +--R (- 3a b - 4a b + 15a b - 6a b - 2a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 3 +--R (3a b + 2a b - 12a b + 6a b + a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (3a b + 8a b - 20a b + 4a b + 5a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 2 9 4 7 +--R (- a b - 2a b + 6a b - 2a b - a b)cos(x) - a b - 4a b +--R + +--R 6 5 10 +--R 8a b - 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 11 2 9 4 7 6 5 7 +--R (2b - 3a b - a b + 2a b )cos(x) +--R + +--R 11 2 9 4 7 6 5 6 +--R (2b - a b - 10a b + 9a b )cos(x) +--R + +--R 11 2 9 6 5 8 3 5 +--R (- 6b + 3a b + 17a b - 14a b )cos(x) +--R + +--R 11 2 9 4 7 6 5 8 3 10 4 +--R (- 6b - 3a b + 25a b - 8a b - 3a b - 5a b)cos(x) +--R + +--R 11 2 9 4 7 6 5 8 3 10 3 +--R (6b + 3a b - 5a b - 23a b + 17a b + 2a b)cos(x) +--R + +--R 11 2 9 4 7 8 3 10 2 +--R (6b + 9a b - 28a b + 7a b + 6a b)cos(x) +--R + +--R 11 2 9 4 7 6 5 8 3 10 11 2 9 +--R (- 2b - 3a b + 6a b + 4a b - 3a b - 2a b)cos(x) - 2b - 5a b +--R + +--R 4 7 6 5 8 3 10 +--R 13a b - a b - 4a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 8 5 6 7 4 7 3 8 5 6 9 2 6 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 3a b + a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 5 +--R (- 6a b + 10a b - 2a b - 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 4 +--R (- 6a b + 7a b + 4a b - 5a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (6a b - 8a b - 2a b + 4a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 2 +--R (6a b - 5a b - 8a b + 7a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 8 5 6 7 4 +--R (- 2a b + 2a b + 2a b - 2a b )cos(x) - 2a b + a b + 4a b +--R + +--R 9 2 +--R - 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 8 5 6 8 10 3 8 7 4 7 +--R (2a b - 2a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 6 +--R (4a b - 21a b + 16a b + a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 5 +--R (- 12a b + 12a b + 11a b - 2a b - 9a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 11 4 +--R (- 12a b + 39a b - 21a b - 3a b - 2a b - a )cos(x) +--R + +--R 10 5 6 7 4 9 2 3 +--R (12a b - 24a b - 4a b + 16a b )cos(x) +--R + +--R 10 3 8 7 4 9 2 11 2 +--R (12a b - 23a b + 6a b + 4a b + a )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 10 3 8 +--R (- 4a b - 4a b + 13a b + 2a b - 7a b )cos(x) - 4a b + 3a b +--R + +--R 5 6 7 4 9 2 +--R 7a b - 4a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 7 6 5 8 3 7 4 7 6 5 8 3 6 +--R (a b - 2a b + a b )cos(x) + (a b - 2a b + a b )cos(x) +--R + +--R 4 7 6 5 8 3 5 +--R (- 3a b + 6a b - 3a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 4 7 6 5 8 3 3 +--R (- 3a b + 6a b - 3a b )cos(x) + (3a b - 6a b + 3a b )cos(x) +--R + +--R 4 7 6 5 8 3 2 4 7 6 5 8 3 +--R (3a b - 6a b + 3a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 4 7 6 5 8 3 +--R - a b + 2a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 9 4 7 9 2 9 4 7 6 5 8 +--R (a b - a b )cos(x) + (3a b - 4a b + a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 7 +--R (a b - 4a b + a b + 2a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 6 +--R (- 7a b + 2a b + 9a b - 4a b )cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 5 +--R (- 9a b + 12a b + 7a b - 9a b - a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 4 +--R (3a b + 12a b - 23a b + 9a b - a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 3 +--R (11a b - 8a b - 18a b + 14a b + a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 2 +--R (3a b - 14a b + 14a b - 4a b + a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 9 4 7 6 5 8 3 +--R (- 4a b + a b + 10a b - 7a b )cos(x) - 2a b + 4a b - a b - a b +--R * +--R sin(x) +--R + +--R 3 8 5 6 7 4 8 3 8 5 6 7 4 7 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 6 3 8 5 6 7 4 5 +--R (- 6a b + 12a b - 6a b )cos(x) + (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 3 8 5 6 7 4 4 3 8 5 6 7 4 3 +--R (6a b - 12a b + 6a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 3 8 5 6 7 4 2 3 8 5 6 7 4 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R / +--R 7 5 9 3 2 7 5 9 3 6 +--R ((a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 6 6 8 4 4 6 6 8 4 10 2 3 +--R (- 2a b + 2a b )cos(x) + (a b - 2a b + a b )cos(x) +--R + +--R 6 6 8 4 10 2 2 +--R (5a b - 3a b - 2a b )cos(x) +--R + +--R 6 6 8 4 10 2 6 6 8 4 10 2 +--R (- a b + 2a b - a b )cos(x) - 3a b + a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 7 7 5 6 5 7 7 5 9 3 5 +--R (a b - a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 5 7 7 5 9 3 4 +--R (- 5a b + a b + 4a b )cos(x) +--R + +--R 5 7 7 5 11 3 +--R (4a b - 6a b + 2a b)cos(x) +--R + +--R 5 7 7 5 9 3 11 2 +--R (7a b + 3a b - 9a b - a b)cos(x) +--R + +--R 5 7 7 5 9 3 11 5 7 7 5 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) - 3a b - 3a b +--R + +--R 9 3 11 +--R 5a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 8 6 6 8 4 7 4 8 6 6 8 4 6 +--R (a b - 2a b + a b )cos(x) + (a b + a b - 2a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 5 +--R (- 3a b + 2a b + 5a b - 4a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 4 +--R (- 3a b - 7a b + 8a b + 2a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 12 3 +--R (3a b + 2a b - 12a b + 6a b + a )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 2 +--R (3a b + 11a b - 9a b - 5a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 12 4 8 6 6 +--R (- a b - 2a b + 6a b - 2a b - a )cos(x) - a b - 5a b +--R + +--R 8 4 10 2 +--R 3a b + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 7 7 5 9 3 7 5 7 7 5 9 3 6 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - a b - a b )cos(x) +--R + +--R 5 7 7 5 9 3 11 5 +--R (- 6a b + 10a b - 2a b - 2a b)cos(x) +--R + +--R 5 7 7 5 9 3 4 +--R (- 6a b + a b + 5a b )cos(x) +--R + +--R 5 7 7 5 9 3 11 3 +--R (6a b - 8a b - 2a b + 4a b)cos(x) +--R + +--R 5 7 7 5 9 3 2 +--R (6a b + a b - 7a b )cos(x) +--R + +--R 5 7 7 5 9 3 11 5 7 7 5 9 3 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) - 2a b - a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 6 8 4 10 2 7 6 6 8 4 6 +--R (a b - 2a b + a b )cos(x) + (a b - a b )cos(x) +--R + +--R 6 6 8 4 10 2 5 6 6 8 4 4 +--R (- 3a b + 6a b - 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 6 6 8 4 10 2 3 6 6 8 4 2 +--R (3a b - 6a b + 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 6 6 8 4 10 2 6 6 8 4 +--R (- a b + 2a b - a b )cos(x) - a b + a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 6 8 4 2 6 6 8 4 6 +--R ((2a b - 2a b )cos(x) - 2a b + 2a b )sin(x) +--R + +--R 5 7 7 5 4 5 7 7 5 9 3 3 +--R (- 4a b + 4a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 5 7 7 5 9 3 2 +--R (10a b - 6a b - 4a b )cos(x) +--R + +--R 5 7 7 5 9 3 5 7 7 5 9 3 +--R (- 2a b + 4a b - 2a b )cos(x) - 6a b + 2a b + 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 8 6 6 6 4 8 6 6 8 4 5 +--R (2a b - 2a b )cos(x) + (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 4 8 6 6 8 4 4 +--R (- 10a b + 2a b + 8a b )cos(x) +--R + +--R 4 8 6 6 10 2 3 +--R (8a b - 12a b + 4a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 2 +--R (14a b + 6a b - 18a b - 2a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 4 8 6 6 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) - 6a b - 6a b +--R + +--R 8 4 10 2 +--R 10a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 9 5 7 7 5 7 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 9 5 7 7 5 6 +--R (2a b + 2a b - 4a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 5 +--R (- 6a b + 4a b + 10a b - 8a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 4 +--R (- 6a b - 14a b + 16a b + 4a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 11 3 +--R (6a b + 4a b - 24a b + 12a b + 2a b)cos(x) +--R + +--R 3 9 5 7 7 5 9 3 2 +--R (6a b + 22a b - 18a b - 10a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 11 3 9 +--R (- 2a b - 4a b + 12a b - 4a b - 2a b)cos(x) - 2a b +--R + +--R 5 7 7 5 9 3 +--R - 10a b + 6a b + 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 8 6 6 8 4 7 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 8 6 6 8 4 6 +--R (4a b - 2a b - 2a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 5 +--R (- 12a b + 20a b - 4a b - 4a b )cos(x) +--R + +--R 4 8 6 6 8 4 4 +--R (- 12a b + 2a b + 10a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 3 +--R (12a b - 16a b - 4a b + 8a b )cos(x) +--R + +--R 4 8 6 6 8 4 2 +--R (12a b + 2a b - 14a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 4 8 6 6 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) - 4a b - 2a b +--R + +--R 8 4 +--R 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 7 7 5 9 3 7 5 7 7 5 6 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 7 7 5 9 3 5 5 7 7 5 4 +--R (- 6a b + 12a b - 6a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 5 7 7 5 9 3 3 5 7 7 5 2 +--R (6a b - 12a b + 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 5 7 7 5 9 3 5 7 7 5 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 7 5 9 3 2 7 5 9 3 6 +--R ((a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 6 6 8 4 4 6 6 8 4 10 2 3 +--R (- 2a b + 2a b )cos(x) + (a b - 2a b + a b )cos(x) +--R + +--R 6 6 8 4 10 2 2 6 6 8 4 10 2 +--R (5a b - 3a b - 2a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 6 6 8 4 10 2 +--R - 3a b + a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 7 7 5 6 5 7 7 5 9 3 5 +--R (a b - a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 5 7 7 5 9 3 4 5 7 7 5 11 3 +--R (- 5a b + a b + 4a b )cos(x) + (4a b - 6a b + 2a b)cos(x) +--R + +--R 5 7 7 5 9 3 11 2 +--R (7a b + 3a b - 9a b - a b)cos(x) +--R + +--R 5 7 7 5 9 3 11 5 7 7 5 9 3 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) - 3a b - 3a b + 5a b +--R + +--R 11 +--R a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 8 6 6 8 4 7 4 8 6 6 8 4 6 +--R (a b - 2a b + a b )cos(x) + (a b + a b - 2a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 5 +--R (- 3a b + 2a b + 5a b - 4a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 4 +--R (- 3a b - 7a b + 8a b + 2a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 12 3 +--R (3a b + 2a b - 12a b + 6a b + a )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 2 +--R (3a b + 11a b - 9a b - 5a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 12 4 8 6 6 +--R (- a b - 2a b + 6a b - 2a b - a )cos(x) - a b - 5a b +--R + +--R 8 4 10 2 +--R 3a b + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 7 7 5 9 3 7 5 7 7 5 9 3 6 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - a b - a b )cos(x) +--R + +--R 5 7 7 5 9 3 11 5 +--R (- 6a b + 10a b - 2a b - 2a b)cos(x) +--R + +--R 5 7 7 5 9 3 4 +--R (- 6a b + a b + 5a b )cos(x) +--R + +--R 5 7 7 5 9 3 11 3 +--R (6a b - 8a b - 2a b + 4a b)cos(x) +--R + +--R 5 7 7 5 9 3 2 +--R (6a b + a b - 7a b )cos(x) +--R + +--R 5 7 7 5 9 3 11 5 7 7 5 9 3 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) - 2a b - a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 6 8 4 10 2 7 6 6 8 4 6 +--R (a b - 2a b + a b )cos(x) + (a b - a b )cos(x) +--R + +--R 6 6 8 4 10 2 5 6 6 8 4 4 +--R (- 3a b + 6a b - 3a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 6 6 8 4 10 2 3 6 6 8 4 2 +--R (3a b - 6a b + 3a b )cos(x) + (3a b - 3a b )cos(x) +--R + +--R 6 6 8 4 10 2 6 6 8 4 +--R (- a b + 2a b - a b )cos(x) - a b + a b +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 7 6 9 4 11 2 2 7 6 9 4 11 2 6 +--R ((- a b + 2a b - a b )cos(x) + a b - 2a b + a b )sin(x) +--R + +--R 6 7 8 5 10 3 4 6 7 8 5 10 3 3 +--R (2a b - 4a b + 2a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 6 7 8 5 10 3 12 2 +--R (- 5a b + 8a b - a b - 2a b)cos(x) +--R + +--R 6 7 8 5 10 3 6 7 8 5 10 3 12 +--R (a b - 2a b + a b )cos(x) + 3a b - 4a b - a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 8 7 6 9 4 6 5 8 7 6 9 4 5 +--R (- a b + 2a b - a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (5a b - 6a b - 3a b + 4a b )cos(x) +--R + +--R 5 8 7 6 11 2 3 +--R (- 4a b + 6a b - 2a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 13 2 +--R (- 7a b + 4a b + 12a b - 8a b - a )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 5 8 9 4 11 2 +--R (2a b - 2a b - 2a b + 2a b )cos(x) + 3a b - 8a b + 4a b +--R + +--R 13 +--R a +--R * +--R 4 +--R sin(x) +--R + +--R 4 9 6 7 8 5 7 4 9 8 5 10 3 6 +--R (- a b + 2a b - a b )cos(x) + (- a b + 3a b - 2a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 5 +--R (3a b - 2a b - 5a b + 4a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 12 4 +--R (3a b + 4a b - 15a b + 6a b + 2a b)cos(x) +--R + +--R 4 9 6 7 8 5 10 3 12 3 +--R (- 3a b - 2a b + 12a b - 6a b - a b)cos(x) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 3a b - 8a b + 20a b - 4a b - 5a b)cos(x) +--R + +--R 4 9 6 7 8 5 10 3 12 4 9 6 7 +--R (a b + 2a b - 6a b + 2a b + a b)cos(x) + a b + 4a b +--R + +--R 8 5 12 +--R - 8a b + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 8 7 6 9 4 7 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 5 8 7 6 11 2 6 +--R (- 2a b + 3a b - a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 5 +--R (6a b - 10a b + 2a b + 2a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (6a b - 7a b - 4a b + 5a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (- 6a b + 8a b + 2a b - 4a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 6a b + 5a b + 8a b - 7a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 5 8 7 6 9 4 +--R (2a b - 2a b - 2a b + 2a b )cos(x) + 2a b - a b - 4a b +--R + +--R 11 2 +--R 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 7 8 5 10 3 7 6 7 8 5 10 3 6 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 6 7 8 5 10 3 5 6 7 8 5 10 3 4 +--R (3a b - 6a b + 3a b )cos(x) + (3a b - 6a b + 3a b )cos(x) +--R + +--R 6 7 8 5 10 3 3 +--R (- 3a b + 6a b - 3a b )cos(x) +--R + +--R 6 7 8 5 10 3 2 6 7 8 5 10 3 +--R (- 3a b + 6a b - 3a b )cos(x) + (a b - 2a b + a b )cos(x) +--R + +--R 6 7 8 5 10 3 +--R a b - 2a b + a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 7 8 5 10 3 2 6 7 8 5 10 3 6 +--R ((- 2a b + 4a b - 2a b )cos(x) + 2a b - 4a b + 2a b )sin(x) +--R + +--R 5 8 7 6 9 4 4 5 8 7 6 9 4 3 +--R (4a b - 8a b + 4a b )cos(x) + (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 10a b + 16a b - 2a b - 4a b )cos(x) +--R + +--R 5 8 7 6 9 4 5 8 7 6 9 4 11 2 +--R (2a b - 4a b + 2a b )cos(x) + 6a b - 8a b - 2a b + 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 9 6 7 8 5 6 4 9 6 7 8 5 5 +--R (- 2a b + 4a b - 2a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (10a b - 12a b - 6a b + 8a b )cos(x) +--R + +--R 4 9 6 7 10 3 3 +--R (- 8a b + 12a b - 4a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 14a b + 8a b + 24a b - 16a b - 2a b)cos(x) +--R + +--R 4 9 6 7 8 5 10 3 4 9 8 5 10 3 +--R (4a b - 4a b - 4a b + 4a b )cos(x) + 6a b - 16a b + 8a b +--R + +--R 12 +--R 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 10 5 8 7 6 7 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 10 7 6 9 4 6 +--R (- 2a b + 6a b - 4a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 5 +--R (6a b - 4a b - 10a b + 8a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 4 +--R (6a b + 8a b - 30a b + 12a b + 4a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 3 +--R (- 6a b - 4a b + 24a b - 12a b - 2a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (- 6a b - 16a b + 40a b - 8a b - 10a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 3 10 5 8 +--R (2a b + 4a b - 12a b + 4a b + 2a b )cos(x) + 2a b + 8a b +--R + +--R 7 6 11 2 +--R - 16a b + 6a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 9 6 7 8 5 7 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 4 9 6 7 10 3 6 +--R (- 4a b + 6a b - 2a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 5 +--R (12a b - 20a b + 4a b + 4a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 4 +--R (12a b - 14a b - 8a b + 10a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 12a b + 16a b + 4a b - 8a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 2 +--R (- 12a b + 10a b + 16a b - 14a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 4 9 6 7 8 5 +--R (4a b - 4a b - 4a b + 4a b )cos(x) + 4a b - 2a b - 8a b +--R + +--R 10 3 +--R 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 8 7 6 9 4 7 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 5 8 7 6 9 4 6 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 5 8 7 6 9 4 5 5 8 7 6 9 4 4 +--R (6a b - 12a b + 6a b )cos(x) + (6a b - 12a b + 6a b )cos(x) +--R + +--R 5 8 7 6 9 4 3 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 5 8 7 6 9 4 2 5 8 7 6 9 4 +--R (- 6a b + 12a b - 6a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 5 8 7 6 9 4 +--R 2a b - 4a b + 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 7 6 9 4 11 2 2 7 6 9 4 11 2 6 +--R ((- a b + 2a b - a b )cos(x) + a b - 2a b + a b )sin(x) +--R + +--R 6 7 8 5 10 3 4 6 7 8 5 10 3 3 +--R (2a b - 4a b + 2a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 6 7 8 5 10 3 12 2 +--R (- 5a b + 8a b - a b - 2a b)cos(x) +--R + +--R 6 7 8 5 10 3 6 7 8 5 10 3 12 +--R (a b - 2a b + a b )cos(x) + 3a b - 4a b - a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 5 8 7 6 9 4 6 5 8 7 6 9 4 5 +--R (- a b + 2a b - a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (5a b - 6a b - 3a b + 4a b )cos(x) +--R + +--R 5 8 7 6 11 2 3 +--R (- 4a b + 6a b - 2a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 13 2 +--R (- 7a b + 4a b + 12a b - 8a b - a )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 5 8 9 4 11 2 13 +--R (2a b - 2a b - 2a b + 2a b )cos(x) + 3a b - 8a b + 4a b + a +--R * +--R 4 +--R sin(x) +--R + +--R 4 9 6 7 8 5 7 4 9 8 5 10 3 6 +--R (- a b + 2a b - a b )cos(x) + (- a b + 3a b - 2a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 5 +--R (3a b - 2a b - 5a b + 4a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 12 4 +--R (3a b + 4a b - 15a b + 6a b + 2a b)cos(x) +--R + +--R 4 9 6 7 8 5 10 3 12 3 +--R (- 3a b - 2a b + 12a b - 6a b - a b)cos(x) +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (- 3a b - 8a b + 20a b - 4a b - 5a b)cos(x) +--R + +--R 4 9 6 7 8 5 10 3 12 4 9 6 7 8 5 +--R (a b + 2a b - 6a b + 2a b + a b)cos(x) + a b + 4a b - 8a b +--R + +--R 12 +--R 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 8 7 6 9 4 7 5 8 7 6 11 2 6 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 3a b - a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 5 +--R (6a b - 10a b + 2a b + 2a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 4 +--R (6a b - 7a b - 4a b + 5a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 3 +--R (- 6a b + 8a b + 2a b - 4a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 2 +--R (- 6a b + 5a b + 8a b - 7a b )cos(x) +--R + +--R 5 8 7 6 9 4 11 2 5 8 7 6 9 4 11 2 +--R (2a b - 2a b - 2a b + 2a b )cos(x) + 2a b - a b - 4a b + 3a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 7 8 5 10 3 7 6 7 8 5 10 3 6 +--R (- a b + 2a b - a b )cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 6 7 8 5 10 3 5 6 7 8 5 10 3 4 +--R (3a b - 6a b + 3a b )cos(x) + (3a b - 6a b + 3a b )cos(x) +--R + +--R 6 7 8 5 10 3 3 6 7 8 5 10 3 2 +--R (- 3a b + 6a b - 3a b )cos(x) + (- 3a b + 6a b - 3a b )cos(x) +--R + +--R 6 7 8 5 10 3 6 7 8 5 10 3 +--R (a b - 2a b + a b )cos(x) + a b - 2a b + a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 493 + +--S 494 of 586 +m0584b:= a0584.2-r0584 +--R +--R +--R (479) +--R 4 3 2 2 5 2 3 2 5 4 +--R (- 2a b + 2a b )sin(x) + ((2b - 2a b )cos(x) - 2b + 2a b)sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (2a b - 2a b )cos(x) - 2a b + 2a b +--R * +--R +---------+ +--R | 2 2 sin(x) +--R \|- b + a log(----------) +--R cos(x) + 1 +--R + +--R 4 3 2 2 5 2 3 2 5 4 +--R (- 2a b + 2a b )sin(x) + ((2b - 2a b )cos(x) - 2b + 2a b)sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (2a b - 2a b )cos(x) - 2a b + 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atanh(cos(x)) +--R + +--R 5 3 3 2 +--R (- 4a b + 6a b )sin(x) +--R + +--R 6 2 4 2 6 2 4 4 2 +--R ((4b - 6a b )cos(x) - 4b + 2a b + 6a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (4a b - 6a b )cos(x) - 4a b + 6a b +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 5 3 3 2 +--R (- 4a b + 6a b )sin(x) +--R + +--R 6 2 4 2 6 2 4 4 2 +--R ((4b - 6a b )cos(x) - 4b + 2a b + 6a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (4a b - 6a b )cos(x) - 4a b + 6a b +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 4 4 3 2 4 2 +--R ((a b - a b)cot(x) + (- 2a b + a b )cos(x) - a b )sin(x) +--R + +--R 4 3 2 2 4 5 5 2 +--R ((- a b + a b )cos(x) + a b - a )cot(x) + b cos(x) +--R + +--R 2 3 4 5 2 3 +--R (- 2a b + 2a b)cos(x) - b - a b +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 3 4 4 3 +--R ((- a b + a b)cos(x) + a b - a b)cot(x) - a b cos(x) +--R + +--R 4 2 4 3 2 5 4 +--R a b cos(x) + (a b - a b + a )cos(x) - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 6 2 3 4 5 2 2 3 4 7 +--R (a b - a b)sin(x) + ((- a b + a b )cos(x) + a b - a )sin(x) +--R + +--R 4 3 6 2 4 3 6 +--R (- a b + a b)cos(x) + a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 494 + +--S 495 of 586 +d0584b:= D(m0584b,x) +--R +--R +--R (480) +--R 4 5 6 3 2 4 5 6 3 4 5 6 3 +--R ((2a b - a b )cos(x) + (- 2a b + 2a b )cos(x) - 2a b + a b ) +--R * +--R 8 +--R sin(x) +--R + +--R 5 4 7 2 2 5 4 7 2 2 +--R ((- a b + a b )cos(x) + a b - a b )cot(x) +--R + +--R 3 6 5 4 4 3 6 5 4 3 +--R (2a b - a b )cos(x) + (8a b - 6a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 3 6 5 4 7 2 +--R (2a b + 2a b - 2a b )cos(x) + (- 12a b + 6a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 +--R - 8a b + 3a b + 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 5 6 3 4 4 5 6 3 3 +--R (2a b - 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 4 5 6 3 8 2 4 5 6 3 +--R (- 6a b + 4a b + 2a b)cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 5 6 3 8 +--R 4a b - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 5 2 7 4 5 6 3 4 +--R 2a b cos(x) + (8a b + 7a b - 6a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (8a b + 8a b - 10a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 4a b - 8a b + 7a b - a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 +--R (- 10a b - 20a b + 20a b + 2a b)cos(x) - 4a b - 11a b +--R + +--R 6 3 8 +--R 11a b + a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 6 5 4 6 3 6 5 4 5 +--R (- a b + a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (7a b - 4a b - 3a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 8a b + 2a b + 6a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 2 +--R (- 11a b - a b + 11a b + a )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 9 +--R (4a b + 2a b - 6a b )cos(x) + 5a b + 4a b - 8a b - a +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 5 4 6 +--R (- 2a b + 3a b - a b )cos(x) +--R + +--R 8 3 6 5 4 5 +--R (4a b + 18a b - 16a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (10a b + 25a b - 10a b - 10a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 8a b + 4a b + 12a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 14a b - 19a b + 5a b + 16a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (4a b - 22a b - 8a b + 14a b )cos(x) + 6a b - 9a b - 6a b +--R + +--R 7 2 +--R 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 7 2 7 4 5 6 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 5 +--R (6a b + 6a b - 12a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 +--R (6a b + 6a b - 12a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 6a b - 18a b + 18a b + 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 6a b - 18a b + 18a b + 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 +--R (2a b + 10a b - 6a b - 6a b)cos(x) + 2a b + 10a b +--R + +--R 6 3 8 +--R - 6a b - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 2 7 4 5 7 +--R (- 4b + 2a b + 4a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 6 +--R (- 4b + 2a b + 16a b - 5a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (12b + 10a b + 16a b - 38a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (12b + 10a b - 4a b - 25a b - 6a b)cos(x) +--R + +--R 9 2 7 6 3 8 3 +--R (- 12b - 26a b + 42a b + 2a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (- 12b - 26a b + 4a b + 35a b + 10a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 9 2 7 +--R (4b + 14a b - 20a b - 8a b + 2a b)cos(x) + 4b + 14a b +--R + +--R 4 5 6 3 +--R - 16a b - 9a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 6 5 4 8 3 6 5 4 7 +--R (- a b + a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 3 6 5 4 7 2 6 +--R (- 2a b + 5a b - 3a b )cos(x) +--R + +--R 3 6 5 4 7 2 5 +--R (18a b - 6a b - 12a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 4 +--R (12a b - 9a b - 4a b + a )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 +--R (- 18a b - 6a b + 22a b + 2a )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 14a b - a b + 15a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 6 5 4 7 2 +--R (6a b + 6a b - 10a b - 2a )cos(x) + 5a b + 4a b - 8a b +--R + +--R 9 +--R - a +--R * +--R 2 +--R cot(x) +--R + +--R 8 8 8 3 6 5 4 7 +--R - 2a b cos(x) + (- 12a b + 18a b + 4a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 6 +--R (- 4a b + 29a b + 7a b - 8a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (36a b - 18a b - 8a b - 30a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 4 +--R (24a b - 51a b - 13a b - 8a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 36a b - 18a b + 24a b + 42a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (- 28a b + 15a b + 25a b + 23a b + a )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 +--R (12a b + 18a b - 20a b - 12a b )cos(x) + 10a b + 7a b +--R + +--R 5 4 7 2 +--R - 19a b - 7a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 6 3 8 4 5 6 3 7 +--R (- 2a b + 2a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 4 5 8 6 4 5 6 3 8 5 +--R (2a b - 2a b)cos(x) + (18a b - 14a b - 4a b)cos(x) +--R + +--R 4 5 6 3 8 4 +--R (6a b - 8a b + 2a b)cos(x) +--R + +--R 4 5 6 3 8 3 +--R (- 18a b + 10a b + 8a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (- 10a b + 8a b + 2a b)cos(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (6a b - 2a b - 4a b)cos(x) + 4a b - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 9 2 7 4 5 8 +--R (- 4a b + 2a b )cos(x) + (- 10a b + 9a b )cos(x) +--R + +--R 2 7 4 5 6 3 7 +--R (- 2a b + 22a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (22a b + 12a b - 11a b - 5a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (30a b - 42a b - 4a b - 10a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 6a b - 54a b + 19a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 38a b + 10a b + 26a b + 14a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 14a b + 36a b + a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 +--R (14a b + 8a b - 18a b - 4a b)cos(x) + 8a b - 3a b - 9a b +--R + +--R 8 +--R - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 7 2 8 5 4 7 2 7 +--R (- a b + a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 4 7 2 6 5 4 7 2 5 +--R (2a b - 2a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 5 4 7 2 3 5 4 7 2 2 +--R (- 6a b + 6a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 4 7 2 5 4 7 2 +--R (2a b - 2a b )cos(x) + a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 10 3 6 5 4 9 +--R - a b cos(x) + (- 6a b + 4a b )cos(x) +--R + +--R 3 6 5 4 8 3 6 5 4 7 2 7 +--R (- 8a b + 10a b )cos(x) + (10a b + 2a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 6 +--R (28a b - 16a b - 8a b - a )cos(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (6a b - 18a b + 4a b - 2a )cos(x) +--R + +--R 3 6 7 2 4 +--R (- 26a b + 17a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 +--R (- 18a b + 14a b + 6a b + 2a )cos(x) +--R + +--R 3 6 5 4 7 2 9 2 +--R (5a b + 8a b - 8a b + a )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (8a b - 2a b - 6a b )cos(x) + 2a b - 2a b - a b +--R * +--R sin(x) +--R + +--R 4 5 6 3 9 4 5 6 3 8 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 5 6 3 7 4 5 6 3 6 +--R (4a b - 4a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 5 6 3 4 4 5 6 3 3 +--R (- 12a b + 12a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 5 6 3 2 4 5 6 3 +--R (4a b - 4a b )cos(x) + (2a b - 2a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 6 5 4 2 3 6 5 4 3 6 5 4 +--R ((4a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) - 4a b + 2a b ) +--R * +--R 8 +--R sin(x) +--R + +--R 4 5 6 3 2 4 5 6 3 2 +--R ((- 2a b + 2a b )cos(x) + 2a b - 2a b )cot(x) +--R + +--R 2 7 4 5 4 2 7 4 5 3 +--R (4a b - 2a b )cos(x) + (16a b - 12a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (8a b - 2a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (- 24a b + 12a b + 8a b )cos(x) - 20a b + 12a b + 4a b +--R * +--R 7 +--R sin(x) +--R + +--R 3 6 5 4 4 3 6 5 4 3 +--R (4a b - 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 3 6 5 4 +--R (- 12a b + 8a b + 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 +--R 8a b - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 5 8 3 6 5 4 4 +--R 4a b cos(x) + (8a b + 26a b - 12a b )cos(x) +--R + +--R 8 3 6 5 4 3 +--R (24a b + 4a b - 20a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (16a b - 44a b + 2a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 +--R (- 28a b - 28a b + 40a b + 4a b )cos(x) - 24a b - 6a b +--R + +--R 5 4 7 2 +--R 34a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 4 5 6 2 7 4 5 5 +--R (- 2a b + 2a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 +--R (14a b - 8a b - 6a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (- 16a b + 4a b + 12a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 22a b - 2a b + 22a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 8 +--R (8a b + 4a b - 12a b )cos(x) + 10a b + 8a b - 16a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 6 9 2 7 4 5 5 +--R - 2a b cos(x) + (- 8b + 60a b - 32a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 4 +--R (- 8b + 80a b - 2a b - 20a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 3 +--R (16b - 16a b - 12a b - 4a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 2 +--R (16b - 56a b - 58a b + 26a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 9 2 7 4 5 +--R (- 8b - 44a b + 20a b + 28a b )cos(x) - 8b - 24a b + 38a b +--R + +--R 6 3 +--R 18a b +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 7 8 3 6 6 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 8 3 6 5 4 5 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 8 3 6 5 4 4 +--R (12a b + 12a b - 24a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 12a b - 36a b + 36a b + 12a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 12a b - 36a b + 36a b + 12a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 +--R (4a b + 20a b - 12a b - 12a b )cos(x) + 4a b + 20a b +--R + +--R 5 4 7 2 +--R - 12a b - 12a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 7 8 3 6 5 4 6 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 32a b - 10a b )cos(x) +--R + +--R 8 3 6 5 4 5 +--R (8a b + 104a b - 76a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (8a b + 64a b - 50a b - 12a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (8a b - 120a b + 48a b + 4a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (8a b - 112a b + 34a b + 20a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (- 8a b + 8a b + 20a b + 4a b )cos(x) - 8a b + 16a b + 18a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 8 2 7 4 5 7 +--R (- 2a b + 2a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 2 7 4 5 6 3 6 +--R (- 4a b + 10a b - 6a b )cos(x) +--R + +--R 2 7 4 5 6 3 5 +--R (36a b - 12a b - 24a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (24a b - 18a b - 8a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 36a b - 12a b + 44a b + 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (- 28a b - 2a b + 30a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 +--R (12a b + 12a b - 20a b - 4a b)cos(x) + 10a b + 8a b +--R + +--R 6 3 8 +--R - 16a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 8 4 5 7 2 7 4 5 6 3 6 +--R - 6a b cos(x) + 8a b cos(x) + (34a b + 32a b - 16a b )cos(x) +--R + +--R 2 7 4 5 6 3 5 +--R (24a b + 56a b - 60a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 42a b - 4a b - 22a b - 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (- 48a b - 88a b + 72a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (6a b - 40a b + 46a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (24a b + 24a b - 12a b )cos(x) + 8a b + 12a b - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 6 5 4 8 3 6 5 4 7 +--R (- 4a b + 4a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 3 6 7 2 6 3 6 5 4 7 2 5 +--R (4a b - 4a b )cos(x) + (36a b - 28a b - 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (12a b - 16a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 36a b + 20a b + 16a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 20a b + 16a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (12a b - 4a b - 8a b )cos(x) + 8a b - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 9 8 3 6 8 +--R (- 8a b + 4a b )cos(x) + (- 12a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 +--R (20a b + 8a b - 8a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 6 +--R (36a b + 28a b - 10a b - 10a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 12a b + 8a b + 16a b - 20a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 36a b - 64a b + 26a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 4a b - 56a b + 4a b + 28a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (12a b + 20a b - 10a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 6 5 4 7 2 +--R (4a b + 36a b - 12a b - 8a b )cos(x) + 10a b - 6a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 3 8 4 5 6 3 7 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 5 6 3 6 4 5 6 3 5 +--R (4a b - 4a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 5 6 3 3 4 5 6 3 2 +--R (- 12a b + 12a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 5 6 3 4 5 6 3 +--R (4a b - 4a b )cos(x) + 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 10 2 7 4 5 9 +--R - 2a b cos(x) + (- 12a b + 8a b )cos(x) +--R + +--R 2 7 4 5 8 2 7 4 5 6 3 7 +--R (- 12a b + 14a b )cos(x) + (28a b - 8a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (48a b - 20a b - 16a b - 2a b)cos(x) +--R + +--R 2 7 6 3 8 5 2 7 6 3 4 +--R (- 12a b + 8a b - 4a b)cos(x) + (- 52a b + 34a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 12a b - 8a b + 12a b + 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (18a b + 4a b - 16a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 4 5 6 3 +--R (8a b + 8a b - 12a b )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 3 6 5 4 9 3 6 5 4 8 +--R (- 4a b + 4a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 3 6 5 4 7 3 6 5 4 6 +--R (8a b - 8a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 6 5 4 4 3 6 5 4 3 +--R (- 24a b + 24a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 3 6 5 4 2 3 6 5 4 +--R (8a b - 8a b )cos(x) + (4a b - 4a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 5 6 3 2 4 5 6 3 4 5 6 3 8 +--R ((2a b - a b )cos(x) + (- 2a b + 2a b )cos(x) - 2a b + a b )sin(x) +--R + +--R 5 4 7 2 2 5 4 7 2 2 3 6 5 4 4 +--R ((- a b + a b )cos(x) + a b - a b )cot(x) + (2a b - a b )cos(x) +--R + +--R 3 6 5 4 3 3 6 5 4 7 2 2 +--R (8a b - 6a b )cos(x) + (2a b + 2a b - 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- 12a b + 6a b + 4a b )cos(x) - 8a b + 3a b + 2a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 5 6 3 4 4 5 6 3 3 +--R (2a b - 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 4 5 6 3 8 2 4 5 6 3 4 5 +--R (- 6a b + 4a b + 2a b)cos(x) + (2a b - 2a b )cos(x) + 4a b +--R + +--R 6 3 8 +--R - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 5 2 7 4 5 6 3 4 +--R 2a b cos(x) + (8a b + 7a b - 6a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (8a b + 8a b - 10a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 4a b - 8a b + 7a b - a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 +--R (- 10a b - 20a b + 20a b + 2a b)cos(x) - 4a b - 11a b + 11a b +--R + +--R 8 +--R a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 6 5 4 6 3 6 5 4 5 +--R (- a b + a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 3 6 5 4 7 2 3 +--R (7a b - 4a b - 3a b )cos(x) + (- 8a b + 2a b + 6a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 2 +--R (- 11a b - a b + 11a b + a )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 9 +--R (4a b + 2a b - 6a b )cos(x) + 5a b + 4a b - 8a b - a +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 5 4 6 8 3 6 5 4 5 +--R (- 2a b + 3a b - a b )cos(x) + (4a b + 18a b - 16a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (10a b + 25a b - 10a b - 10a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 8a b + 4a b + 12a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 14a b - 19a b + 5a b + 16a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 7 2 +--R (4a b - 22a b - 8a b + 14a b )cos(x) + 6a b - 9a b - 6a b + 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 7 2 7 4 5 6 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 5 2 7 4 5 6 3 4 +--R (6a b + 6a b - 12a b )cos(x) + (6a b + 6a b - 12a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 6a b - 18a b + 18a b + 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 6a b - 18a b + 18a b + 6a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 +--R (2a b + 10a b - 6a b - 6a b)cos(x) + 2a b + 10a b - 6a b +--R + +--R 8 +--R - 6a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 2 7 4 5 7 +--R (- 4b + 2a b + 4a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 6 +--R (- 4b + 2a b + 16a b - 5a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (12b + 10a b + 16a b - 38a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (12b + 10a b - 4a b - 25a b - 6a b)cos(x) +--R + +--R 9 2 7 6 3 8 3 +--R (- 12b - 26a b + 42a b + 2a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (- 12b - 26a b + 4a b + 35a b + 10a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 9 2 7 4 5 +--R (4b + 14a b - 20a b - 8a b + 2a b)cos(x) + 4b + 14a b - 16a b +--R + +--R 6 3 +--R - 9a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 6 5 4 8 3 6 5 4 7 +--R (- a b + a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 3 6 5 4 7 2 6 +--R (- 2a b + 5a b - 3a b )cos(x) +--R + +--R 3 6 5 4 7 2 5 +--R (18a b - 6a b - 12a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 4 +--R (12a b - 9a b - 4a b + a )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 +--R (- 18a b - 6a b + 22a b + 2a )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 14a b - a b + 15a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 6 5 4 7 2 9 +--R (6a b + 6a b - 10a b - 2a )cos(x) + 5a b + 4a b - 8a b - a +--R * +--R 2 +--R cot(x) +--R + +--R 8 8 8 3 6 5 4 7 +--R - 2a b cos(x) + (- 12a b + 18a b + 4a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 6 +--R (- 4a b + 29a b + 7a b - 8a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (36a b - 18a b - 8a b - 30a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 4 +--R (24a b - 51a b - 13a b - 8a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 36a b - 18a b + 24a b + 42a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (- 28a b + 15a b + 25a b + 23a b + a )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (12a b + 18a b - 20a b - 12a b )cos(x) + 10a b + 7a b - 19a b +--R + +--R 7 2 +--R - 7a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 6 3 8 4 5 6 3 7 +--R (- 2a b + 2a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 4 5 8 6 4 5 6 3 8 5 +--R (2a b - 2a b)cos(x) + (18a b - 14a b - 4a b)cos(x) +--R + +--R 4 5 6 3 8 4 4 5 6 3 8 3 +--R (6a b - 8a b + 2a b)cos(x) + (- 18a b + 10a b + 8a b)cos(x) +--R + +--R 4 5 6 3 8 2 4 5 6 3 8 +--R (- 10a b + 8a b + 2a b)cos(x) + (6a b - 2a b - 4a b)cos(x) +--R + +--R 4 5 6 3 8 +--R 4a b - 2a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 9 2 7 4 5 8 +--R (- 4a b + 2a b )cos(x) + (- 10a b + 9a b )cos(x) +--R + +--R 2 7 4 5 6 3 7 +--R (- 2a b + 22a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (22a b + 12a b - 11a b - 5a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (30a b - 42a b - 4a b - 10a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 6a b - 54a b + 19a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 38a b + 10a b + 26a b + 14a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 14a b + 36a b + a b + 3a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 8 +--R (14a b + 8a b - 18a b - 4a b)cos(x) + 8a b - 3a b - 9a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 7 2 8 5 4 7 2 7 +--R (- a b + a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 4 7 2 6 5 4 7 2 5 +--R (2a b - 2a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 5 4 7 2 3 5 4 7 2 2 +--R (- 6a b + 6a b )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 4 7 2 5 4 7 2 +--R (2a b - 2a b )cos(x) + a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 10 3 6 5 4 9 3 6 5 4 8 +--R - a b cos(x) + (- 6a b + 4a b )cos(x) + (- 8a b + 10a b )cos(x) +--R + +--R 3 6 5 4 7 2 7 +--R (10a b + 2a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 6 +--R (28a b - 16a b - 8a b - a )cos(x) +--R + +--R 3 6 5 4 7 2 9 5 3 6 7 2 4 +--R (6a b - 18a b + 4a b - 2a )cos(x) + (- 26a b + 17a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 +--R (- 18a b + 14a b + 6a b + 2a )cos(x) +--R + +--R 3 6 5 4 7 2 9 2 3 6 5 4 7 2 +--R (5a b + 8a b - 8a b + a )cos(x) + (8a b - 2a b - 6a b )cos(x) +--R + +--R 3 6 5 4 7 2 +--R 2a b - 2a b - a b +--R * +--R sin(x) +--R + +--R 4 5 6 3 9 4 5 6 3 8 +--R (- 2a b + 2a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 5 6 3 7 4 5 6 3 6 +--R (4a b - 4a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 5 6 3 4 4 5 6 3 3 +--R (- 12a b + 12a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 5 6 3 2 4 5 6 3 +--R (4a b - 4a b )cos(x) + (2a b - 2a b )cos(x) +--R / +--R 7 4 9 2 2 7 4 9 2 7 +--R ((a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 6 5 8 3 4 6 5 8 3 3 +--R (- 2a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 6 5 8 3 10 2 6 5 8 3 6 5 +--R (6a b - 4a b - 2a b)cos(x) + (- 2a b + 2a b )cos(x) - 4a b +--R + +--R 8 3 10 +--R 2a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 5 6 7 4 6 5 6 7 4 5 +--R (a b - a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 4 5 6 7 4 9 2 3 +--R (- 7a b + 4a b + 3a b )cos(x) + (8a b - 2a b - 6a b )cos(x) +--R + +--R 5 6 7 4 9 2 11 2 +--R (11a b + a b - 11a b - a )cos(x) +--R + +--R 5 6 7 4 9 2 5 6 7 4 9 2 11 +--R (- 4a b - 2a b + 6a b )cos(x) - 5a b - 4a b + 8a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 4 7 6 5 7 4 7 6 5 6 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 7 6 5 8 3 5 +--R (- 6a b - 6a b + 12a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 +--R (- 6a b - 6a b + 12a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (6a b + 18a b - 18a b - 6a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (6a b + 18a b - 18a b - 6a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 4 7 6 5 8 3 +--R (- 2a b - 10a b + 6a b + 6a b)cos(x) - 2a b - 10a b + 6a b +--R + +--R 10 +--R 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 6 7 4 8 5 6 7 4 7 +--R (a b - a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 5 6 7 4 9 2 6 +--R (2a b - 5a b + 3a b )cos(x) +--R + +--R 5 6 7 4 9 2 5 +--R (- 18a b + 6a b + 12a b )cos(x) +--R + +--R 5 6 7 4 9 2 11 4 +--R (- 12a b + 9a b + 4a b - a )cos(x) +--R + +--R 5 6 7 4 9 2 11 3 +--R (18a b + 6a b - 22a b - 2a )cos(x) +--R + +--R 5 6 7 4 9 2 2 +--R (14a b + a b - 15a b )cos(x) +--R + +--R 5 6 7 4 9 2 11 5 6 7 4 9 2 +--R (- 6a b - 6a b + 10a b + 2a )cos(x) - 5a b - 4a b + 8a b +--R + +--R 11 +--R a +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 8 3 8 6 5 8 3 7 +--R (2a b - 2a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 6 5 10 6 6 5 8 3 10 5 +--R (- 2a b + 2a b)cos(x) + (- 18a b + 14a b + 4a b)cos(x) +--R + +--R 6 5 8 3 10 4 +--R (- 6a b + 8a b - 2a b)cos(x) +--R + +--R 6 5 8 3 10 3 +--R (18a b - 10a b - 8a b)cos(x) +--R + +--R 6 5 8 3 10 2 6 5 8 3 10 +--R (10a b - 8a b - 2a b)cos(x) + (- 6a b + 2a b + 4a b)cos(x) +--R + +--R 6 5 8 3 10 +--R - 4a b + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 4 9 2 8 7 4 9 2 7 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 7 4 9 2 6 7 4 9 2 5 +--R (- 2a b + 2a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 7 4 9 2 3 7 4 9 2 2 +--R (6a b - 6a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 7 4 9 2 7 4 9 2 +--R (- 2a b + 2a b )cos(x) - a b + a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 8 3 2 6 5 8 3 7 +--R ((2a b - 2a b )cos(x) - 2a b + 2a b )sin(x) +--R + +--R 5 6 7 4 4 5 6 7 4 3 +--R (- 4a b + 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 5 6 7 4 5 6 +--R (12a b - 8a b - 4a b )cos(x) + (- 4a b + 4a b )cos(x) - 8a b +--R + +--R 7 4 9 2 +--R 4a b + 4a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 7 6 5 6 4 7 6 5 5 +--R (2a b - 2a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 +--R (- 14a b + 8a b + 6a b )cos(x) +--R + +--R 4 7 6 5 8 3 3 +--R (16a b - 4a b - 12a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (22a b + 2a b - 22a b - 2a b)cos(x) +--R + +--R 4 7 6 5 8 3 4 7 6 5 8 3 10 +--R (- 8a b - 4a b + 12a b )cos(x) - 10a b - 8a b + 16a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 8 5 6 7 3 8 5 6 6 +--R (4a b - 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 3 8 5 6 7 4 5 +--R (- 12a b - 12a b + 24a b )cos(x) +--R + +--R 3 8 5 6 7 4 4 +--R (- 12a b - 12a b + 24a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (12a b + 36a b - 36a b - 12a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 2 +--R (12a b + 36a b - 36a b - 12a b )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 3 8 5 6 +--R (- 4a b - 20a b + 12a b + 12a b )cos(x) - 4a b - 20a b +--R + +--R 7 4 9 2 +--R 12a b + 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 7 6 5 8 4 7 6 5 7 +--R (2a b - 2a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 7 6 5 8 3 6 +--R (4a b - 10a b + 6a b )cos(x) +--R + +--R 4 7 6 5 8 3 5 +--R (- 36a b + 12a b + 24a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 4 +--R (- 24a b + 18a b + 8a b - 2a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (36a b + 12a b - 44a b - 4a b)cos(x) +--R + +--R 4 7 6 5 8 3 2 +--R (28a b + 2a b - 30a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 4 7 6 5 +--R (- 12a b - 12a b + 20a b + 4a b)cos(x) - 10a b - 8a b +--R + +--R 8 3 10 +--R 16a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 7 4 8 5 6 7 4 7 +--R (4a b - 4a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 5 6 9 2 6 5 6 7 4 9 2 5 +--R (- 4a b + 4a b )cos(x) + (- 36a b + 28a b + 8a b )cos(x) +--R + +--R 5 6 7 4 9 2 4 +--R (- 12a b + 16a b - 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 3 +--R (36a b - 20a b - 16a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 +--R (20a b - 16a b - 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 5 6 7 4 9 2 +--R (- 12a b + 4a b + 8a b )cos(x) - 8a b + 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 8 3 8 6 5 8 3 7 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 6 5 8 3 6 6 5 8 3 5 +--R (- 4a b + 4a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 6 5 8 3 3 6 5 8 3 2 +--R (12a b - 12a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 6 5 8 3 6 5 8 3 +--R (- 4a b + 4a b )cos(x) - 2a b + 2a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 7 4 9 2 2 7 4 9 2 7 +--R ((a b - a b )cos(x) - a b + a b )sin(x) +--R + +--R 6 5 8 3 4 6 5 8 3 3 +--R (- 2a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 6 5 8 3 10 2 6 5 8 3 6 5 +--R (6a b - 4a b - 2a b)cos(x) + (- 2a b + 2a b )cos(x) - 4a b +--R + +--R 8 3 10 +--R 2a b + 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 5 6 7 4 6 5 6 7 4 5 +--R (a b - a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 4 5 6 7 4 9 2 3 +--R (- 7a b + 4a b + 3a b )cos(x) + (8a b - 2a b - 6a b )cos(x) +--R + +--R 5 6 7 4 9 2 11 2 +--R (11a b + a b - 11a b - a )cos(x) +--R + +--R 5 6 7 4 9 2 5 6 7 4 9 2 11 +--R (- 4a b - 2a b + 6a b )cos(x) - 5a b - 4a b + 8a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 4 7 6 5 7 4 7 6 5 6 +--R (2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 7 6 5 8 3 5 4 7 6 5 8 3 4 +--R (- 6a b - 6a b + 12a b )cos(x) + (- 6a b - 6a b + 12a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (6a b + 18a b - 18a b - 6a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 2 +--R (6a b + 18a b - 18a b - 6a b)cos(x) +--R + +--R 4 7 6 5 8 3 10 4 7 6 5 8 3 +--R (- 2a b - 10a b + 6a b + 6a b)cos(x) - 2a b - 10a b + 6a b +--R + +--R 10 +--R 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 6 7 4 8 5 6 7 4 7 +--R (a b - a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 5 6 7 4 9 2 6 5 6 7 4 9 2 5 +--R (2a b - 5a b + 3a b )cos(x) + (- 18a b + 6a b + 12a b )cos(x) +--R + +--R 5 6 7 4 9 2 11 4 +--R (- 12a b + 9a b + 4a b - a )cos(x) +--R + +--R 5 6 7 4 9 2 11 3 +--R (18a b + 6a b - 22a b - 2a )cos(x) +--R + +--R 5 6 7 4 9 2 2 +--R (14a b + a b - 15a b )cos(x) +--R + +--R 5 6 7 4 9 2 11 5 6 7 4 9 2 11 +--R (- 6a b - 6a b + 10a b + 2a )cos(x) - 5a b - 4a b + 8a b + a +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 8 3 8 6 5 8 3 7 +--R (2a b - 2a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 6 5 10 6 6 5 8 3 10 5 +--R (- 2a b + 2a b)cos(x) + (- 18a b + 14a b + 4a b)cos(x) +--R + +--R 6 5 8 3 10 4 6 5 8 3 10 3 +--R (- 6a b + 8a b - 2a b)cos(x) + (18a b - 10a b - 8a b)cos(x) +--R + +--R 6 5 8 3 10 2 6 5 8 3 10 +--R (10a b - 8a b - 2a b)cos(x) + (- 6a b + 2a b + 4a b)cos(x) +--R + +--R 6 5 8 3 10 +--R - 4a b + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 4 9 2 8 7 4 9 2 7 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 7 4 9 2 6 7 4 9 2 5 +--R (- 2a b + 2a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 7 4 9 2 3 7 4 9 2 2 +--R (6a b - 6a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 7 4 9 2 7 4 9 2 +--R (- 2a b + 2a b )cos(x) - a b + a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 495 + +--S 496 of 586 +t0585:= csc(x)^3/(a+b*sin(x))^2 +--R +--R +--R 3 +--R csc(x) +--R (481) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 496 + +--S 497 of 586 +r0585:= -2*b^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^2/(a^2-b^2)^(3/2)-_ + 6*b^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/a^4/(a^2-b^2)^(1/2)-_ + 1/2*atanh(cos(x))/a^2-3*b^2*atanh(cos(x))/a^4+2*b*cot(x)/a^3-_ + 1/2*cot(x)*csc(x)/a^2-b^4*cos(x)/a^3/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (482) +--R +---------+ +--R 5 2 3 4 4 3 2 5 | 2 2 +--R ((- 6b + 5a b + a b)sin(x) - 6a b + 5a b + a )\|- b + a +--R * +--R atanh(cos(x)) +--R + +--R x +--R a tan(-) + b +--R 6 2 4 5 3 3 2 +--R ((- 12b + 16a b )sin(x) - 12a b + 16a b )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 4 4 3 2 +--R ((- a b + a b)cot(x)csc(x) + (4a b - 4a b )cot(x))sin(x) +--R + +--R 3 2 5 2 3 4 4 +--R (- a b + a )cot(x)csc(x) + (4a b - 4a b)cot(x) + 2a b cos(x) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 3 6 5 2 7 | 2 2 +--R ((2a b - 2a b)sin(x) + 2a b - 2a )\|- b + a +--R Type: Expression(Integer) +--E 497 + +--S 498 of 586 +a0585:= integrate(t0585,x) +--R +--R +--R (483) +--R [ +--R 6 2 4 2 6 2 4 5 3 3 2 +--R ((6b - 8a b )cos(x) - 6b + 8a b )sin(x) + (6a b - 8a b )cos(x) +--R + +--R 5 3 3 +--R - 6a b + 8a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((6b - 5a b - a b)cos(x) - 6b + 5a b + a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (6a b - 5a b - a )cos(x) - 6a b + 5a b + a +--R * +--R +-------+ +--R | 2 2 sin(x) +--R \|b - a log(----------) +--R cos(x) + 1 +--R + +--R 5 2 2 3 4 5 +--R (2b cos(x) + (- 3a b + 3a b)cos(x) - 2b )sin(x) +--R + +--R 4 3 2 3 4 2 +--R (6a b - 4a b )cos(x) + 2a b cos(x) +--R + +--R 4 3 2 5 4 +--R (- 6a b + 5a b - a )cos(x) - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 4 3 6 2 4 3 6 5 2 7 2 +--R ((2a b - 2a b)cos(x) - 2a b + 2a b)sin(x) + (2a b - 2a )cos(x) +--R + +--R 5 2 7 +--R - 2a b + 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 5 2 3 4 2 5 2 3 4 +--R ((6b - 5a b - a b)cos(x) - 6b + 5a b + a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (6a b - 5a b - a )cos(x) - 6a b + 5a b + a +--R * +--R +---------+ +--R | 2 2 sin(x) +--R \|- b + a log(----------) +--R cos(x) + 1 +--R + +--R 6 2 4 2 6 2 4 +--R ((12b - 16a b )cos(x) - 12b + 16a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (12a b - 16a b )cos(x) - 12a b + 16a b +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 5 2 2 3 4 5 +--R (2b cos(x) + (- 3a b + 3a b)cos(x) - 2b )sin(x) +--R + +--R 4 3 2 3 4 2 +--R (6a b - 4a b )cos(x) + 2a b cos(x) +--R + +--R 4 3 2 5 4 +--R (- 6a b + 5a b - a )cos(x) - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 6 2 4 3 6 5 2 7 2 +--R ((2a b - 2a b)cos(x) - 2a b + 2a b)sin(x) + (2a b - 2a )cos(x) +--R + +--R 5 2 7 +--R - 2a b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 498 + +--S 499 of 586 +m0585a:= a0585.1-r0585 +--R +--R +--R (484) +--R 6 2 4 2 6 2 4 5 3 3 2 +--R ((6b - 8a b )cos(x) - 6b + 8a b )sin(x) + (6a b - 8a b )cos(x) +--R + +--R 5 3 3 +--R - 6a b + 8a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((6b - 5a b - a b)cos(x) - 6b + 5a b + a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (6a b - 5a b - a )cos(x) - 6a b + 5a b + a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) +--R \|- b + a \|b - a log(----------) +--R cos(x) + 1 +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((6b - 5a b - a b)cos(x) - 6b + 5a b + a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (6a b - 5a b - a )cos(x) - 6a b + 5a b + a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a atanh(cos(x)) +--R + +--R 6 2 4 2 6 2 4 +--R ((12b - 16a b )cos(x) - 12b + 16a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (12a b - 16a b )cos(x) - 12a b + 16a b +--R * +--R x +--R +-------+ a tan(-) + b +--R | 2 2 2 +--R \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 4 2 2 3 4 +--R ((a b - a b)cos(x) - a b + a b)cot(x)csc(x) +--R + +--R 4 3 2 2 4 3 2 5 2 +--R ((- 4a b + 4a b )cos(x) + 4a b - 4a b )cot(x) + 2b cos(x) +--R + +--R 2 3 4 5 +--R (- 3a b + 3a b)cos(x) - 2b +--R * +--R sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R ((a b - a )cos(x) - a b + a )cot(x)csc(x) +--R + +--R 2 3 4 2 2 3 4 +--R ((- 4a b + 4a b)cos(x) + 4a b - 4a b)cot(x) +--R + +--R 4 3 2 3 4 2 4 3 2 5 +--R (4a b - 4a b )cos(x) + 2a b cos(x) + (- 4a b + 5a b - a )cos(x) +--R + +--R 4 +--R - 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 4 3 6 2 4 3 6 5 2 7 2 +--R ((2a b - 2a b)cos(x) - 2a b + 2a b)sin(x) + (2a b - 2a )cos(x) +--R + +--R 5 2 7 +--R - 2a b + 2a +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 499 + +--S 500 of 586 +d0585a:= D(m0585a,x) +--R +--R +--R (485) +--R 2 7 4 5 6 3 3 4 5 6 3 2 +--R (6a b - 5a b - a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 5 6 3 +--R (- 6a b + 5a b + a b )cos(x) - 3a b + 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 5 6 3 4 4 5 6 3 2 +--R (- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 5 6 3 +--R - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 6 3 4 4 5 6 3 2 4 5 +--R (- a b + a b )cos(x) + (2a b - 2a b )cos(x) - a b +--R + +--R 6 3 +--R a b +--R * +--R csc(x) +--R + +--R 3 6 5 4 4 3 6 5 4 2 3 6 +--R (4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b +--R + +--R 5 4 +--R - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 11a b + 4a b + a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (6a b + 4a b - 5a b - 5a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 6a b + 8a b - 3a b + a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- 6a b - 10a b + 17a b - a b )cos(x) - 3a b + a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 2a b - 2a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (4a b + 4a b - 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b - 2a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- a b - a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (2a b + 2a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- a b + 2a b - a b )cos(x) - a b - a b + 2a b +--R * +--R csc(x) +--R + +--R 2 7 4 5 6 3 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 +--R (4a b + 4a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (- 8a b - 8a b + 16a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (4a b - 8a b + 4a b )cos(x) + 4a b + 4a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (6b - 8a b + 3a b - a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (6b + 4a b - 18a b + 4a b + 2a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (- 12b + 28a b - 12a b - a b - 3a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (- 12b + 4a b + 12a b + 3a b - 3a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 9 2 7 +--R (6b - 20a b + 5a b + 10a b - a b)cos(x) + 6b - 8a b +--R + +--R 4 5 6 3 8 +--R 2a b - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 6 3 8 5 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 4 5 6 3 8 4 +--R (- 4a b + 2a b + 2a b)cos(x) +--R + +--R 4 5 6 3 8 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (8a b - 4a b - 4a b)cos(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (- 4a b + 8a b - 4a b)cos(x) - 4a b + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 6 3 8 5 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 4 5 6 3 8 4 +--R (- 2a b + a b + a b)cos(x) +--R + +--R 4 5 6 3 8 3 +--R (4a b - 8a b + 4a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (4a b - 2a b - 2a b)cos(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (- 2a b + 4a b - 2a b)cos(x) - 2a b + a b + a b +--R * +--R csc(x) +--R + +--R 3 6 5 4 7 2 5 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (8a b - 4a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 16a b + 8a b + 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (8a b - 16a b + 8a b )cos(x) + 8a b - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 5 4 7 2 6 +--R (- 7a b + 8a b + a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (12a b - 3a b - 11a b + 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 4 +--R (12a b + 8a b - 31a b + 2a b + a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 24a b + 12a b + 18a b - 7a b + a )cos(x) +--R + +--R 8 3 6 5 4 9 2 +--R (- 24a b + 11a b + 24a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 8 3 6 +--R (12a b - 9a b - 5a b + a b + a )cos(x) + 12a b - 12a b +--R + +--R 5 4 7 2 +--R a b - 5a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 7 2 9 5 +--R (- 2a b + 4a b - 2a )cos(x) +--R + +--R 5 4 7 2 4 +--R (- 2a b + 2a b )cos(x) +--R + +--R 5 4 7 2 9 3 5 4 7 2 2 +--R (4a b - 8a b + 4a )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 5 4 7 2 9 5 4 7 2 +--R (- 2a b + 4a b - 2a )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 7 2 9 5 5 4 7 2 4 +--R (- a b + 2a b - a )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 4 7 2 9 3 5 4 7 2 2 +--R (2a b - 4a b + 2a )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 4 7 2 9 5 4 7 2 +--R (- a b + 2a b - a )cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 4 5 6 3 8 5 4 5 6 3 4 +--R (4a b - 8a b + 4a b)cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 5 6 3 8 3 +--R (- 8a b + 16a b - 8a b)cos(x) +--R + +--R 4 5 6 3 2 4 5 6 3 8 +--R (- 8a b + 8a b )cos(x) + (4a b - 8a b + 4a b)cos(x) +--R + +--R 4 5 6 3 +--R 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 6 3 7 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (2a b - 10a b + 8a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (20a b - 20a b + a b - a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (2a b + 12a b - 16a b - 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 28a b + 12a b + 18a b - 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 10a b + 2a b + 12a b + 2a b)cos(x) +--R + +--R 2 7 6 3 8 2 7 4 5 6 3 +--R (12a b - 15a b + 3a b)cos(x) + 6a b - 4a b - 4a b +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 6 +--R (6a b - 11a b + 4a b + a )cos(x) +--R + +--R 3 6 5 4 7 2 5 +--R (6a b - 5a b - a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 4 +--R (- 12a b + 22a b - 8a b - 2a )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 12a b + 10a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 2 3 6 5 4 7 2 +--R (6a b - 11a b + 4a b + a )cos(x) + (6a b - 5a b - a b )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 8 3 6 5 4 3 3 6 5 4 2 +--R (12a b - 10a b - 2a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 3 6 5 4 +--R (- 12a b + 10a b + 2a b )cos(x) - 6a b + 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 6 5 4 4 3 6 5 4 2 +--R (- 4a b + 4a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 3 6 5 4 +--R - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 5 4 4 3 6 5 4 2 3 6 +--R (- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b +--R + +--R 5 4 +--R 2a b +--R * +--R csc(x) +--R + +--R 2 7 4 5 4 2 7 4 5 2 +--R (8a b - 8a b )cos(x) + (- 16a b + 16a b )cos(x) +--R + +--R 2 7 4 5 +--R 8a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 6 3 4 +--R (- 6a b + 8a b + 2a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 3 +--R (12b + 8a b - 10a b - 10a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 2 +--R (12b - 16a b - 6a b + 2a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 9 2 7 +--R (- 12b - 20a b + 34a b - 2a b )cos(x) - 12b + 10a b +--R + +--R 4 5 6 3 +--R 2a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 6 3 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 +--R (- 4a b - 4a b + 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (8a b + 8a b - 16a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (- 4a b + 8a b - 4a b )cos(x) - 4a b - 4a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 6 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 +--R (- 2a b - 2a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (4a b + 4a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b - 2a b + 4a b +--R * +--R csc(x) +--R + +--R 8 3 6 5 4 5 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 8 3 6 5 4 4 +--R (8a b + 8a b - 16a b )cos(x) +--R + +--R 8 3 6 5 4 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 8 3 6 5 4 2 +--R (- 16a b - 16a b + 32a b )cos(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 +--R (8a b - 16a b + 8a b )cos(x) + 8a b + 8a b - 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 5 4 5 +--R (12a b - 10a b - 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 4a b + 8a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (8a b - 2a b - 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (24a b - 40a b + 6a b - 6a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 +--R (- 12a b - 6a b + 20a b - 2a b )cos(x) - 24a b + 36a b +--R + +--R 5 4 7 2 +--R - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 8a b + 4a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (16a b - 32a b + 16a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (16a b - 8a b - 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 +--R (- 8a b + 16a b - 8a b )cos(x) - 8a b + 4a b +--R + +--R 7 2 +--R 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 4a b + 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (8a b - 4a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- 4a b + 8a b - 4a b )cos(x) - 4a b + 2a b + 2a b +--R * +--R csc(x) +--R + +--R 2 7 4 5 6 3 5 +--R (16a b - 32a b + 16a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 +--R (16a b - 8a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (- 32a b + 64a b - 32a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (- 32a b + 16a b + 16a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (16a b - 32a b + 16a b )cos(x) + 16a b - 8a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 6 3 6 +--R (- 14a b + 16a b + 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 5 +--R (50a b - 54a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (36a b - 46a b + 4a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 88a b + 100a b - 14a b + 2a b)cos(x) +--R + +--R 2 7 4 5 8 2 +--R (- 18a b + 16a b - 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 +--R (38a b - 42a b + 2a b + 2a b)cos(x) - 4a b + 18a b +--R + +--R 6 3 +--R - 10a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 3 8 5 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 4 5 6 3 4 +--R (- 4a b + 4a b )cos(x) +--R + +--R 4 5 6 3 8 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 4 5 6 3 2 +--R (8a b - 8a b )cos(x) +--R + +--R 4 5 6 3 8 4 5 6 3 +--R (- 4a b + 8a b - 4a b)cos(x) - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 6 3 8 5 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 4 5 6 3 4 4 5 6 3 8 3 +--R (- 2a b + 2a b )cos(x) + (4a b - 8a b + 4a b)cos(x) +--R + +--R 4 5 6 3 2 4 5 6 3 8 +--R (4a b - 4a b )cos(x) + (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 4 5 6 3 +--R - 2a b + 2a b +--R * +--R csc(x) +--R + +--R 3 6 5 4 7 2 5 3 6 5 4 4 +--R (8a b - 16a b + 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 3 6 5 4 2 +--R (- 16a b + 16a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 +--R (8a b - 16a b + 8a b )cos(x) + 8a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 5 4 7 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 6 +--R (4a b - 20a b + 16a b + 4a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (28a b - 12a b - 14a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 8a b + 40a b - 32a b - 8a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 32a b - 32a b + 68a b - 4a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (4a b - 28a b + 24a b + 4a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 6 5 4 +--R (12a b + 28a b - 46a b + 6a b )cos(x) + 8a b - 8a b +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (12a b - 22a b + 8a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 5 +--R (12a b - 10a b - 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 24a b + 44a b - 16a b - 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (- 24a b + 20a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (12a b - 22a b + 8a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 +--R (12a b - 10a b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 6 3 3 4 5 6 3 2 +--R (6a b - 5a b - a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 5 6 3 +--R (- 6a b + 5a b + a b )cos(x) - 3a b + 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 5 6 3 4 4 5 6 3 2 4 5 +--R (- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b +--R + +--R 6 3 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 6 3 4 4 5 6 3 2 4 5 6 3 +--R (- a b + a b )cos(x) + (2a b - 2a b )cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 6 5 4 4 3 6 5 4 2 3 6 +--R (4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b +--R + +--R 5 4 +--R - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (6a b - 11a b + 4a b + a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (6a b + 4a b - 5a b - 5a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 6a b + 8a b - 3a b + a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- 6a b - 10a b + 17a b - a b )cos(x) - 3a b + a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- 2a b - 2a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (4a b + 4a b - 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b - 2a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 5 4 7 2 5 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (- a b - a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (2a b + 2a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- a b + 2a b - a b )cos(x) - a b - a b + 2a b +--R * +--R csc(x) +--R + +--R 2 7 4 5 6 3 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 4 +--R (4a b + 4a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (- 8a b - 8a b + 16a b )cos(x) +--R + +--R 2 7 4 5 6 3 2 7 4 5 6 3 +--R (4a b - 8a b + 4a b )cos(x) + 4a b + 4a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 2 7 4 5 6 3 5 +--R (6b - 8a b + 3a b - a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (6b + 4a b - 18a b + 4a b + 2a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (- 12b + 28a b - 12a b - a b - 3a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (- 12b + 4a b + 12a b + 3a b - 3a b)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 9 2 7 4 5 +--R (6b - 20a b + 5a b + 10a b - a b)cos(x) + 6b - 8a b + 2a b +--R + +--R 6 3 8 +--R - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 6 3 8 5 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 4 5 6 3 8 4 +--R (- 4a b + 2a b + 2a b)cos(x) +--R + +--R 4 5 6 3 8 3 +--R (8a b - 16a b + 8a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (8a b - 4a b - 4a b)cos(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (- 4a b + 8a b - 4a b)cos(x) - 4a b + 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 5 6 3 8 5 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 4 5 6 3 8 4 4 5 6 3 8 3 +--R (- 2a b + a b + a b)cos(x) + (4a b - 8a b + 4a b)cos(x) +--R + +--R 4 5 6 3 8 2 +--R (4a b - 2a b - 2a b)cos(x) +--R + +--R 4 5 6 3 8 4 5 6 3 8 +--R (- 2a b + 4a b - 2a b)cos(x) - 2a b + a b + a b +--R * +--R csc(x) +--R + +--R 3 6 5 4 7 2 5 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 4 +--R (8a b - 4a b - 4a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (- 16a b + 8a b + 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 3 6 5 4 7 2 +--R (8a b - 16a b + 8a b )cos(x) + 8a b - 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 6 5 4 7 2 6 +--R (- 7a b + 8a b + a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (12a b - 3a b - 11a b + 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 4 +--R (12a b + 8a b - 31a b + 2a b + a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (- 24a b + 12a b + 18a b - 7a b + a )cos(x) +--R + +--R 8 3 6 5 4 9 2 +--R (- 24a b + 11a b + 24a b - a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 8 3 6 +--R (12a b - 9a b - 5a b + a b + a )cos(x) + 12a b - 12a b +--R + +--R 5 4 7 2 +--R a b - 5a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 7 2 9 5 5 4 7 2 4 +--R (- 2a b + 4a b - 2a )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 4 7 2 9 3 5 4 7 2 2 +--R (4a b - 8a b + 4a )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 5 4 7 2 9 5 4 7 2 +--R (- 2a b + 4a b - 2a )cos(x) - 2a b + 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 4 7 2 9 5 5 4 7 2 4 +--R (- a b + 2a b - a )cos(x) + (- a b + a b )cos(x) +--R + +--R 5 4 7 2 9 3 5 4 7 2 2 +--R (2a b - 4a b + 2a )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 5 4 7 2 9 5 4 7 2 +--R (- a b + 2a b - a )cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 4 5 6 3 8 5 4 5 6 3 4 +--R (4a b - 8a b + 4a b)cos(x) + (4a b - 4a b )cos(x) +--R + +--R 4 5 6 3 8 3 4 5 6 3 2 +--R (- 8a b + 16a b - 8a b)cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 4 5 6 3 8 4 5 6 3 +--R (4a b - 8a b + 4a b)cos(x) + 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 7 4 5 6 3 7 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (2a b - 10a b + 8a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (20a b - 20a b + a b - a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (2a b + 12a b - 16a b - 4a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 28a b + 12a b + 18a b - 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 10a b + 2a b + 12a b + 2a b)cos(x) +--R + +--R 2 7 6 3 8 2 7 4 5 6 3 +--R (12a b - 15a b + 3a b)cos(x) + 6a b - 4a b - 4a b +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 6 3 6 5 4 7 2 5 +--R (6a b - 11a b + 4a b + a )cos(x) + (6a b - 5a b - a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 4 +--R (- 12a b + 22a b - 8a b - 2a )cos(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 12a b + 10a b + 2a b )cos(x) +--R + +--R 3 6 5 4 7 2 9 2 3 6 5 4 7 2 +--R (6a b - 11a b + 4a b + a )cos(x) + (6a b - 5a b - a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (6a b - 11a b + 4a b + a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 +--R (- 3a b + 6a b - 3a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 6 6 4 8 2 +--R (- 6a b + 11a b - 4a b - a b )cos(x) - 3a b + 6a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 6 6 4 8 2 4 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 4 6 6 4 8 2 +--R (4a b - 8a b + 4a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 6 4 8 2 4 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 4 6 6 4 8 2 +--R (2a b - 4a b + 2a b )cos(x) - a b + 2a b - a b +--R * +--R csc(x) +--R + +--R 3 7 5 5 7 3 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 3 7 5 5 7 3 +--R (- 8a b + 16a b - 8a b )cos(x) + 4a b - 8a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 3 7 5 5 7 3 4 +--R (6a b - 11a b + 4a b + a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (6a b - 2a b - 12a b + 6a b + 2a b)cos(x) +--R + +--R 9 3 7 9 2 +--R (- 6a b + 8a b - 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 7 5 5 +--R (- 6a b - 4a b + 24a b - 12a b - 2a b)cos(x) - 3a b + 4a b +--R + +--R 7 3 9 +--R a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 7 5 5 7 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 7 7 3 9 4 +--R (- 2a b + 6a b - 4a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 7 7 3 9 2 +--R (4a b - 12a b + 8a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 7 7 3 9 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 6a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 7 5 5 7 3 5 +--R (- a b + 2a b - a b )cos(x) +--R + +--R 3 7 7 3 9 4 +--R (- a b + 3a b - 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 3 7 7 3 9 2 3 7 5 5 7 3 +--R (2a b - 6a b + 4a b)cos(x) + (- a b + 2a b - a b )cos(x) +--R + +--R 3 7 7 3 9 +--R - a b + 3a b - 2a b +--R * +--R csc(x) +--R + +--R 2 8 4 6 6 4 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 8 6 4 8 2 4 +--R (4a b - 12a b + 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 2 8 6 4 8 2 2 +--R (- 8a b + 24a b - 16a b )cos(x) +--R + +--R 2 8 4 6 6 4 2 8 6 4 8 2 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 12a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 10 2 8 4 6 6 4 8 2 5 +--R (6b - 8a b - 3a b + 4a b + a b )cos(x) +--R + +--R 10 2 8 4 6 8 2 4 +--R (6b - 2a b - 10a b + 6a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 10 3 +--R (- 12b + 28a b - 12a b - 7a b + 2a b + a )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 10 2 +--R (- 12b + 16a b - 4a b + 13a b - 14a b + a )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 10 10 +--R (6b - 20a b + 11a b + 11a b - 7a b - a )cos(x) + 6b +--R + +--R 2 8 4 6 6 4 10 +--R - 14a b + 10a b - 3a b + a +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 6 4 8 2 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 4 6 6 4 10 4 +--R (- 4a b + 6a b - 2a )cos(x) +--R + +--R 4 6 6 4 8 2 3 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 4 6 6 4 10 2 +--R (8a b - 12a b + 4a )cos(x) +--R + +--R 4 6 6 4 8 2 4 6 6 4 10 +--R (- 4a b + 8a b - 4a b )cos(x) - 4a b + 6a b - 2a +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 6 4 8 2 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 4 6 6 4 10 4 +--R (- 2a b + 3a b - a )cos(x) +--R + +--R 4 6 6 4 8 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 6 6 4 10 2 +--R (4a b - 6a b + 2a )cos(x) +--R + +--R 4 6 6 4 8 2 4 6 6 4 10 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 3a b - a +--R * +--R csc(x) +--R + +--R 3 7 5 5 7 3 5 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 3 7 5 5 9 4 +--R (8a b - 12a b + 4a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 3 7 5 5 9 2 +--R (- 16a b + 24a b - 8a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 7 5 5 9 +--R (8a b - 16a b + 8a b )cos(x) + 8a b - 12a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 7 5 5 7 3 6 +--R (- a b + 4a b - 3a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 5 +--R (12a b - 9a b - 18a b + 13a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 4 +--R (12a b - 16a b - 11a b + 14a b + a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 24a b + 24a b + 26a b - 24a b - 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 24a b + 41a b - 4a b - 9a b - 4a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 9 3 7 +--R (12a b - 15a b - 6a b + 7a b + 2a b)cos(x) + 12a b - 24a b +--R + +--R 5 5 7 3 9 +--R 13a b - 6a b + 5a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 7 3 9 5 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 5 5 7 3 9 4 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 5 5 7 3 9 3 +--R (4a b - 8a b + 4a b)cos(x) +--R + +--R 5 5 7 3 9 2 +--R (4a b - 8a b + 4a b)cos(x) +--R + +--R 5 5 7 3 9 5 5 7 3 9 +--R (- 2a b + 4a b - 2a b)cos(x) - 2a b + 4a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 5 7 3 9 5 5 5 7 3 9 4 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R + +--R 5 5 7 3 9 3 5 5 7 3 9 2 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 5 5 7 3 9 5 5 7 3 9 +--R (- a b + 2a b - a b)cos(x) - a b + 2a b - a b +--R * +--R csc(x) +--R + +--R 4 6 6 4 8 2 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 6 6 4 8 2 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 8a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 8 4 6 6 4 7 2 8 6 4 8 2 6 +--R (- 4a b + 8a b - 4a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 5 +--R (20a b - 32a b + 5a b + 6a b + a )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (2a b - 14a b + 16a b - 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 3 +--R (- 28a b + 36a b + 10a b - 16a b - 2a )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 10a b + 24a b - 12a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 8 4 6 +--R (12a b - 12a b - 11a b + 10a b + a )cos(x) + 6a b - 10a b +--R + +--R 8 2 +--R 4a b +--R * +--R sin(x) +--R + +--R 3 7 5 5 7 3 9 6 +--R (6a b - 11a b + 4a b + a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 5 +--R (6a b - 11a b + 4a b + a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 4 +--R (- 12a b + 22a b - 8a b - 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (- 12a b + 22a b - 8a b - 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (6a b - 11a b + 4a b + a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 +--R (6a b - 11a b + 4a b + a b)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 9 3 7 5 5 7 3 3 +--R (12a b - 22a b + 8a b + 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 +--R (- 6a b + 12a b - 6a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 3 7 5 5 7 3 +--R (- 12a b + 22a b - 8a b - 2a b )cos(x) - 6a b + 12a b - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 7 5 5 7 3 4 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 3 7 5 5 7 3 +--R (8a b - 16a b + 8a b )cos(x) - 4a b + 8a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 7 5 5 7 3 4 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 3 7 5 5 7 3 +--R (4a b - 8a b + 4a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R csc(x) +--R + +--R 2 8 4 6 6 4 4 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 2 2 8 4 6 6 4 +--R (- 16a b + 32a b - 16a b )cos(x) + 8a b - 16a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 8 4 6 6 4 4 +--R (6a b - 8a b + 2a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 3 +--R (12b - 4a b - 24a b + 12a b + 4a b )cos(x) +--R + +--R 10 2 8 4 6 8 2 2 +--R (12b - 40a b + 32a b - 4a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 10 +--R (- 12b - 8a b + 48a b - 24a b - 4a b )cos(x) - 12b +--R + +--R 2 8 4 6 6 4 8 2 +--R 22a b - 8a b + 2a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 4 6 6 4 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 2 8 6 4 8 2 4 +--R (- 4a b + 12a b - 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 3 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 2 8 6 4 8 2 2 +--R (8a b - 24a b + 16a b )cos(x) +--R + +--R 2 8 4 6 6 4 2 8 6 4 8 2 +--R (- 4a b + 8a b - 4a b )cos(x) - 4a b + 12a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 8 4 6 6 4 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 2 8 6 4 8 2 4 +--R (- 2a b + 6a b - 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 2 8 6 4 8 2 2 +--R (4a b - 12a b + 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 2 8 6 4 8 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 6a b - 4a b +--R * +--R csc(x) +--R + +--R 9 3 7 5 5 5 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 9 5 5 7 3 4 +--R (8a b - 24a b + 16a b )cos(x) +--R + +--R 9 3 7 5 5 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 9 5 5 7 3 2 +--R (- 16a b + 48a b - 32a b )cos(x) +--R + +--R 9 3 7 5 5 9 5 5 7 3 +--R (8a b - 16a b + 8a b )cos(x) + 8a b - 24a b + 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 3 7 5 5 7 3 5 +--R (12a b - 22a b + 8a b + 2a b )cos(x) +--R + +--R 3 7 5 5 7 3 4 +--R (20a b - 32a b + 12a b )cos(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (8a b - 14a b + 4a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (24a b - 88a b + 90a b - 28a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 9 +--R (- 12a b + 6a b + 22a b - 14a b - 2a b)cos(x) - 24a b +--R + +--R 3 7 5 5 9 +--R 60a b - 38a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 7 5 5 7 3 5 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 3 7 5 5 9 4 +--R (- 8a b + 12a b - 4a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 +--R (16a b - 32a b + 16a b )cos(x) +--R + +--R 3 7 5 5 9 2 +--R (16a b - 24a b + 8a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 7 5 5 9 +--R (- 8a b + 16a b - 8a b )cos(x) - 8a b + 12a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 7 5 5 7 3 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 3 7 5 5 9 4 +--R (- 4a b + 6a b - 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 3 7 5 5 9 2 +--R (8a b - 12a b + 4a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 7 5 5 9 +--R (- 4a b + 8a b - 4a b )cos(x) - 4a b + 6a b - 2a b +--R * +--R csc(x) +--R + +--R 2 8 4 6 6 4 5 +--R (16a b - 32a b + 16a b )cos(x) +--R + +--R 2 8 4 6 8 2 4 +--R (16a b - 24a b + 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 3 +--R (- 32a b + 64a b - 32a b )cos(x) +--R + +--R 2 8 4 6 8 2 2 +--R (- 32a b + 48a b - 16a b )cos(x) +--R + +--R 2 8 4 6 6 4 2 8 4 6 8 2 +--R (16a b - 32a b + 16a b )cos(x) + 16a b - 24a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 8 4 6 6 4 6 +--R (- 2a b + 8a b - 6a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 5 +--R (38a b - 68a b + 26a b + 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (12a b - 26a b + 12a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 64a b + 116a b - 48a b - 4a b )cos(x) +--R + +--R 2 8 6 4 8 2 2 +--R (- 6a b + 14a b - 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 8 4 6 +--R (26a b - 44a b + 14a b + 4a b )cos(x) - 4a b + 22a b +--R + +--R 6 4 8 2 +--R - 28a b + 10a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 6 6 4 8 2 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 3 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 6 6 4 8 2 +--R (- 4a b + 8a b - 4a b )cos(x) - 4a b + 8a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 6 4 8 2 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 4 6 6 4 8 2 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R csc(x) +--R + +--R 3 7 5 5 7 3 5 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 3 7 5 5 7 3 4 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 3 7 5 5 7 3 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 3 7 5 5 7 3 3 7 5 5 7 3 +--R (8a b - 16a b + 8a b )cos(x) + 8a b - 16a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 3 7 5 5 7 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 9 5 5 7 3 6 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 5 +--R (28a b - 36a b - 6a b + 12a b + 2a b)cos(x) +--R + +--R 9 5 5 7 3 4 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 32a b + 16a b + 52a b - 32a b - 4a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 2 +--R (4a b - 8a b + 8a b - 4a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 7 5 5 +--R (12a b + 4a b - 38a b + 20a b + 2a b)cos(x) + 8a b - 16a b +--R + +--R 7 3 +--R 8a b +--R * +--R sin(x) +--R + +--R 2 8 4 6 6 4 8 2 6 +--R (12a b - 22a b + 8a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 5 +--R (12a b - 22a b + 8a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (- 24a b + 44a b - 16a b - 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (- 24a b + 44a b - 16a b - 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (12a b - 22a b + 8a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 +--R (12a b - 22a b + 8a b + 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 8 4 6 6 4 8 2 3 +--R (6a b - 11a b + 4a b + a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 +--R (- 3a b + 6a b - 3a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 6 6 4 8 2 +--R (- 6a b + 11a b - 4a b - a b )cos(x) - 3a b + 6a b - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 6 6 4 8 2 4 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 4 6 6 4 8 2 +--R (4a b - 8a b + 4a b )cos(x) - 2a b + 4a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 6 4 8 2 4 4 6 6 4 8 2 2 +--R (- a b + 2a b - a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 4 6 6 4 8 2 +--R - a b + 2a b - a b +--R * +--R csc(x) +--R + +--R 3 7 5 5 7 3 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 3 7 5 5 7 3 +--R (- 8a b + 16a b - 8a b )cos(x) + 4a b - 8a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 3 7 5 5 7 3 4 +--R (6a b - 11a b + 4a b + a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (6a b - 2a b - 12a b + 6a b + 2a b)cos(x) +--R + +--R 9 3 7 9 2 +--R (- 6a b + 8a b - 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 7 5 5 +--R (- 6a b - 4a b + 24a b - 12a b - 2a b)cos(x) - 3a b + 4a b +--R + +--R 7 3 9 +--R a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 7 5 5 7 3 5 +--R (- 2a b + 4a b - 2a b )cos(x) +--R + +--R 3 7 7 3 9 4 +--R (- 2a b + 6a b - 4a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 7 7 3 9 2 +--R (4a b - 12a b + 8a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 7 7 3 9 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 6a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 7 5 5 7 3 5 3 7 7 3 9 4 +--R (- a b + 2a b - a b )cos(x) + (- a b + 3a b - 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 3 7 7 3 9 2 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 6a b + 4a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 7 7 3 9 +--R (- a b + 2a b - a b )cos(x) - a b + 3a b - 2a b +--R * +--R csc(x) +--R + +--R 2 8 4 6 6 4 5 2 8 6 4 8 2 4 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 12a b + 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 2 8 6 4 8 2 2 +--R (- 8a b + 24a b - 16a b )cos(x) +--R + +--R 2 8 4 6 6 4 2 8 6 4 8 2 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 12a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 10 2 8 4 6 6 4 8 2 5 +--R (6b - 8a b - 3a b + 4a b + a b )cos(x) +--R + +--R 10 2 8 4 6 8 2 4 +--R (6b - 2a b - 10a b + 6a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 10 3 +--R (- 12b + 28a b - 12a b - 7a b + 2a b + a )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 10 2 +--R (- 12b + 16a b - 4a b + 13a b - 14a b + a )cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 10 10 2 8 +--R (6b - 20a b + 11a b + 11a b - 7a b - a )cos(x) + 6b - 14a b +--R + +--R 4 6 6 4 10 +--R 10a b - 3a b + a +--R * +--R 3 +--R sin(x) +--R + +--R 4 6 6 4 8 2 5 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 4 6 6 4 10 4 +--R (- 4a b + 6a b - 2a )cos(x) +--R + +--R 4 6 6 4 8 2 3 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 4 6 6 4 10 2 +--R (8a b - 12a b + 4a )cos(x) +--R + +--R 4 6 6 4 8 2 4 6 6 4 10 +--R (- 4a b + 8a b - 4a b )cos(x) - 4a b + 6a b - 2a +--R * +--R 2 +--R cot(x) +--R + +--R 4 6 6 4 8 2 5 4 6 6 4 10 4 +--R (- 2a b + 4a b - 2a b )cos(x) + (- 2a b + 3a b - a )cos(x) +--R + +--R 4 6 6 4 8 2 3 4 6 6 4 10 2 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 6a b + 2a )cos(x) +--R + +--R 4 6 6 4 8 2 4 6 6 4 10 +--R (- 2a b + 4a b - 2a b )cos(x) - 2a b + 3a b - a +--R * +--R csc(x) +--R + +--R 3 7 5 5 7 3 5 3 7 5 5 9 4 +--R (8a b - 16a b + 8a b )cos(x) + (8a b - 12a b + 4a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 3 7 5 5 9 2 +--R (- 16a b + 24a b - 8a b)cos(x) +--R + +--R 3 7 5 5 7 3 3 7 5 5 9 +--R (8a b - 16a b + 8a b )cos(x) + 8a b - 12a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 7 5 5 7 3 6 +--R (- a b + 4a b - 3a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 5 +--R (12a b - 9a b - 18a b + 13a b + 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 4 +--R (12a b - 16a b - 11a b + 14a b + a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 3 +--R (- 24a b + 24a b + 26a b - 24a b - 2a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 2 +--R (- 24a b + 41a b - 4a b - 9a b - 4a b)cos(x) +--R + +--R 9 3 7 5 5 7 3 9 9 3 7 +--R (12a b - 15a b - 6a b + 7a b + 2a b)cos(x) + 12a b - 24a b +--R + +--R 5 5 7 3 9 +--R 13a b - 6a b + 5a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 5 7 3 9 5 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 5 5 7 3 9 4 +--R (- 2a b + 4a b - 2a b)cos(x) +--R + +--R 5 5 7 3 9 3 5 5 7 3 9 2 +--R (4a b - 8a b + 4a b)cos(x) + (4a b - 8a b + 4a b)cos(x) +--R + +--R 5 5 7 3 9 5 5 7 3 9 +--R (- 2a b + 4a b - 2a b)cos(x) - 2a b + 4a b - 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 5 7 3 9 5 5 5 7 3 9 4 +--R (- a b + 2a b - a b)cos(x) + (- a b + 2a b - a b)cos(x) +--R + +--R 5 5 7 3 9 3 5 5 7 3 9 2 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 5 5 7 3 9 5 5 7 3 9 +--R (- a b + 2a b - a b)cos(x) - a b + 2a b - a b +--R * +--R csc(x) +--R + +--R 4 6 6 4 8 2 5 4 6 6 4 8 2 4 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 4 6 6 4 8 2 2 4 6 6 4 8 2 +--R (- 8a b + 16a b - 8a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 6 6 4 8 2 +--R 4a b - 8a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 8 4 6 6 4 7 2 8 6 4 8 2 6 +--R (- 4a b + 8a b - 4a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 5 +--R (20a b - 32a b + 5a b + 6a b + a )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 4 +--R (2a b - 14a b + 16a b - 4a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 3 +--R (- 28a b + 36a b + 10a b - 16a b - 2a )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (- 10a b + 24a b - 12a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 10 2 8 4 6 +--R (12a b - 12a b - 11a b + 10a b + a )cos(x) + 6a b - 10a b +--R + +--R 8 2 +--R 4a b +--R * +--R sin(x) +--R + +--R 3 7 5 5 7 3 9 6 +--R (6a b - 11a b + 4a b + a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 5 +--R (6a b - 11a b + 4a b + a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 4 +--R (- 12a b + 22a b - 8a b - 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 3 +--R (- 12a b + 22a b - 8a b - 2a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 2 +--R (6a b - 11a b + 4a b + a b)cos(x) +--R + +--R 3 7 5 5 7 3 9 +--R (6a b - 11a b + 4a b + a b)cos(x) +--R / +--R 6 5 8 3 4 6 5 8 3 2 6 5 +--R (2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b +--R + +--R 8 3 +--R - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 6 7 4 9 2 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 5 6 7 4 9 2 4 +--R (2a b + 2a b - 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 3 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 +--R (- 4a b - 4a b + 8a b )cos(x) +--R + +--R 5 6 7 4 9 2 5 6 7 4 9 2 +--R (2a b - 4a b + 2a b )cos(x) + 2a b + 2a b - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 8 3 10 5 +--R (4a b - 8a b + 4a b)cos(x) +--R + +--R 6 5 8 3 10 4 +--R (4a b - 2a b - 2a b)cos(x) +--R + +--R 6 5 8 3 10 3 +--R (- 8a b + 16a b - 8a b)cos(x) +--R + +--R 6 5 8 3 10 2 +--R (- 8a b + 4a b + 4a b)cos(x) +--R + +--R 6 5 8 3 10 6 5 8 3 10 +--R (4a b - 8a b + 4a b)cos(x) + 4a b - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 4 9 2 11 5 7 4 9 2 4 +--R (2a b - 4a b + 2a )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 7 4 9 2 11 3 7 4 9 2 2 +--R (- 4a b + 8a b - 4a )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 7 4 9 2 11 7 4 9 2 +--R (2a b - 4a b + 2a )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 6 7 4 4 5 6 7 4 2 5 6 +--R (4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b +--R + +--R 7 4 +--R - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 7 6 5 8 3 5 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 +--R (4a b + 4a b - 8a b )cos(x) +--R + +--R 4 7 6 5 8 3 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 4 7 6 5 8 3 2 +--R (- 8a b - 8a b + 16a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 7 6 5 8 3 +--R (4a b - 8a b + 4a b )cos(x) + 4a b + 4a b - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 7 4 9 2 5 +--R (8a b - 16a b + 8a b )cos(x) +--R + +--R 5 6 7 4 9 2 4 +--R (8a b - 4a b - 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 +--R (- 16a b + 8a b + 8a b )cos(x) +--R + +--R 5 6 7 4 9 2 5 6 7 4 9 2 +--R (8a b - 16a b + 8a b )cos(x) + 8a b - 4a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 8 3 10 5 6 5 8 3 4 +--R (4a b - 8a b + 4a b)cos(x) + (4a b - 4a b )cos(x) +--R + +--R 6 5 8 3 10 3 6 5 8 3 2 +--R (- 8a b + 16a b - 8a b)cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 6 5 8 3 10 6 5 8 3 +--R (4a b - 8a b + 4a b)cos(x) + 4a b - 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 5 8 3 4 6 5 8 3 2 6 5 8 3 +--R ((2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b - 2a b ) +--R * +--R 4 +--R sin(x) +--R + +--R 5 6 7 4 9 2 5 5 6 7 4 9 2 4 +--R (2a b - 4a b + 2a b )cos(x) + (2a b + 2a b - 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 3 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 5 6 7 4 9 2 +--R (- 4a b - 4a b + 8a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 5 6 7 4 9 2 +--R 2a b + 2a b - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 8 3 10 5 6 5 8 3 10 4 +--R (4a b - 8a b + 4a b)cos(x) + (4a b - 2a b - 2a b)cos(x) +--R + +--R 6 5 8 3 10 3 +--R (- 8a b + 16a b - 8a b)cos(x) +--R + +--R 6 5 8 3 10 2 6 5 8 3 10 +--R (- 8a b + 4a b + 4a b)cos(x) + (4a b - 8a b + 4a b)cos(x) +--R + +--R 6 5 8 3 10 +--R 4a b - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 4 9 2 11 5 7 4 9 2 4 +--R (2a b - 4a b + 2a )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 7 4 9 2 11 3 7 4 9 2 2 +--R (- 4a b + 8a b - 4a )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 7 4 9 2 11 7 4 9 2 +--R (2a b - 4a b + 2a )cos(x) + 2a b - 2a b +--R * +--R sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 6 8 4 10 2 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 6 6 8 4 10 2 2 6 6 8 4 10 2 +--R (- 4a b + 8a b - 4a b )cos(x) + 2a b - 4a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 7 7 5 9 3 5 5 7 9 3 11 4 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 6a b + 4a b)cos(x) +--R + +--R 5 7 7 5 9 3 3 +--R (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 5 7 9 3 11 2 5 7 7 5 9 3 +--R (- 4a b + 12a b - 8a b)cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 5 7 9 3 11 +--R 2a b - 6a b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 8 4 10 2 5 6 6 8 4 12 4 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 6a b + 2a )cos(x) +--R + +--R 6 6 8 4 10 2 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 6 6 8 4 12 2 6 6 8 4 10 2 +--R (- 8a b + 12a b - 4a )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 6 8 4 12 +--R 4a b - 6a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 7 5 9 3 11 5 7 5 9 3 11 4 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 5 9 3 11 3 +--R (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 7 5 9 3 11 2 7 5 9 3 11 +--R (- 4a b + 8a b - 4a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 5 9 3 11 +--R 2a b - 4a b + 2a b +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 7 7 5 9 3 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 5 7 7 5 9 3 2 5 7 7 5 9 3 +--R (- 8a b + 16a b - 8a b )cos(x) + 4a b - 8a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 8 6 6 8 4 5 4 8 8 4 10 2 4 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 12a b + 8a b )cos(x) +--R + +--R 4 8 6 6 8 4 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 4 8 8 4 10 2 2 +--R (- 8a b + 24a b - 16a b )cos(x) +--R + +--R 4 8 6 6 8 4 4 8 8 4 10 2 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 12a b + 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 7 7 5 9 3 5 5 7 7 5 11 4 +--R (8a b - 16a b + 8a b )cos(x) + (8a b - 12a b + 4a b)cos(x) +--R + +--R 5 7 7 5 9 3 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 5 7 7 5 11 2 +--R (- 16a b + 24a b - 8a b)cos(x) +--R + +--R 5 7 7 5 9 3 5 7 7 5 11 +--R (8a b - 16a b + 8a b )cos(x) + 8a b - 12a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 6 8 4 10 2 5 6 6 8 4 10 2 4 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 6 6 8 4 10 2 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 6 6 8 4 10 2 2 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 6 6 8 4 10 2 6 6 8 4 10 2 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 8a b + 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 6 8 4 10 2 4 6 6 8 4 10 2 2 +--R (2a b - 4a b + 2a b )cos(x) + (- 4a b + 8a b - 4a b )cos(x) +--R + +--R 6 6 8 4 10 2 +--R 2a b - 4a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 7 7 5 9 3 5 5 7 9 3 11 4 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 6a b + 4a b)cos(x) +--R + +--R 5 7 7 5 9 3 3 5 7 9 3 11 2 +--R (- 4a b + 8a b - 4a b )cos(x) + (- 4a b + 12a b - 8a b)cos(x) +--R + +--R 5 7 7 5 9 3 5 7 9 3 11 +--R (2a b - 4a b + 2a b )cos(x) + 2a b - 6a b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 8 4 10 2 5 6 6 8 4 12 4 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 6a b + 2a )cos(x) +--R + +--R 6 6 8 4 10 2 3 6 6 8 4 12 2 +--R (- 8a b + 16a b - 8a b )cos(x) + (- 8a b + 12a b - 4a )cos(x) +--R + +--R 6 6 8 4 10 2 6 6 8 4 12 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 6a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 7 5 9 3 11 5 7 5 9 3 11 4 +--R (2a b - 4a b + 2a b)cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 7 5 9 3 11 3 7 5 9 3 11 2 +--R (- 4a b + 8a b - 4a b)cos(x) + (- 4a b + 8a b - 4a b)cos(x) +--R + +--R 7 5 9 3 11 7 5 9 3 11 +--R (2a b - 4a b + 2a b)cos(x) + 2a b - 4a b + 2a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 500 + +--S 501 of 586 +m0585b:= a0585.2-r0585 +--R +--R +--R (486) +--R 5 2 3 4 2 5 2 3 4 +--R ((6b - 5a b - a b)cos(x) - 6b + 5a b + a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (6a b - 5a b - a )cos(x) - 6a b + 5a b + a +--R * +--R +---------+ +--R | 2 2 sin(x) +--R \|- b + a log(----------) +--R cos(x) + 1 +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((6b - 5a b - a b)cos(x) - 6b + 5a b + a b)sin(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (6a b - 5a b - a )cos(x) - 6a b + 5a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a atanh(cos(x)) +--R + +--R 6 2 4 2 6 2 4 +--R ((12b - 16a b )cos(x) - 12b + 16a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (12a b - 16a b )cos(x) - 12a b + 16a b +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 6 2 4 2 6 2 4 +--R ((12b - 16a b )cos(x) - 12b + 16a b )sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (12a b - 16a b )cos(x) - 12a b + 16a b +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 4 2 2 3 4 +--R ((a b - a b)cos(x) - a b + a b)cot(x)csc(x) +--R + +--R 4 3 2 2 4 3 2 5 2 +--R ((- 4a b + 4a b )cos(x) + 4a b - 4a b )cot(x) + 2b cos(x) +--R + +--R 2 3 4 5 +--R (- 3a b + 3a b)cos(x) - 2b +--R * +--R sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R ((a b - a )cos(x) - a b + a )cot(x)csc(x) +--R + +--R 2 3 4 2 2 3 4 +--R ((- 4a b + 4a b)cos(x) + 4a b - 4a b)cot(x) +--R + +--R 4 3 2 3 4 2 4 3 2 5 +--R (4a b - 4a b )cos(x) + 2a b cos(x) + (- 4a b + 5a b - a )cos(x) +--R + +--R 4 +--R - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 4 3 6 2 4 3 6 5 2 7 2 +--R ((2a b - 2a b)cos(x) - 2a b + 2a b)sin(x) + (2a b - 2a )cos(x) +--R + +--R 5 2 7 +--R - 2a b + 2a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 501 + +--S 502 of 586 +d0585b:= D(m0585b,x) +--R +--R +--R (487) +--R 2 6 4 4 6 2 3 4 4 6 2 2 +--R (6a b - 5a b - a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 +--R (- 6a b + 5a b + a b )cos(x) - 3a b + 3a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 +--R (- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b +--R + +--R 6 2 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 6 2 +--R (- a b + a b )cos(x) + (2a b - 2a b )cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 5 5 3 4 3 5 5 3 2 3 5 +--R (4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b +--R + +--R 5 3 +--R - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 4 +--R (6a b - 2a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (12a b - 4a b - 6a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (- 12a b + 6a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (- 12a b - 8a b + 18a b + 2a b)cos(x) - 6a b + 2a b + 4a b +--R + +--R 7 +--R 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R csc(x) +--R + +--R 2 6 4 4 5 2 6 6 2 4 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 6 2 2 +--R (- 16a b + 16a b )cos(x) + (- 16a b + 16a b )cos(x) +--R + +--R 2 6 4 4 2 6 6 2 +--R (8a b - 8a b )cos(x) + 8a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (12b - 4a b - 10a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (12b + 8a b - 13a b - 7a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (- 24b + 44a b - 14a b + 3a b - a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- 24b + 20a b - 20a b + 25a b - a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 8 2 6 +--R (12b - 40a b + 4a b + 19a b + a )cos(x) + 12b - 28a b +--R + +--R 4 4 6 2 8 +--R 13a b + 4a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 6 2 6 4 4 6 2 5 +--R (- 2a b + 2a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 3 +--R (- 6a b + 4a b + 2a )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 4 6 2 8 2 +--R (18a b - 14a b - 4a )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 8 +--R (- 12a b + 12a b )cos(x) - 10a b + 8a b + 2a +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 6 4 4 6 2 5 +--R (- a b + a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 3 +--R (- 3a b + 2a b + a )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 8 2 4 4 6 2 +--R (9a b - 7a b - 2a )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 4 4 6 2 8 +--R - 5a b + 4a b + a +--R * +--R csc(x) +--R + +--R 3 5 5 3 6 3 5 5 3 5 +--R (4a b - 4a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 3 +--R (12a b - 8a b - 4a b)cos(x) + (- 48a b + 48a b )cos(x) +--R + +--R 3 5 5 3 7 2 3 5 5 3 +--R (- 36a b + 28a b + 8a b)cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 5 5 3 7 +--R 20a b - 16a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 6 +--R (6a b - 6a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (36a b - 10a b - 30a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (18a b + 10a b - 36a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 72a b + 56a b + 28a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 54a b + 34a b + 26a b + 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 +--R (36a b - 46a b - 2a b + 4a b)cos(x) + 30a b - 38a b + 4a b +--R + +--R 7 +--R - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 7 6 5 3 7 5 +--R (- 4a b + 4a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (24a b - 24a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (- 12a b + 12a b)cos(x) - 8a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 7 6 5 3 7 5 +--R (- 2a b + 2a b)cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (12a b - 12a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (- 6a b + 6a b)cos(x) - 4a b + 4a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 6 4 4 6 2 5 +--R (8a b - 8a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (- 48a b + 48a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (24a b - 24a b )cos(x) + 16a b - 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 6 2 7 +--R (- 2a b + 3a b - a b )cos(x) +--R + +--R 2 6 4 4 6 2 6 +--R (16a b - 2a b - 10a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (46a b - 27a b - 21a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 8a b - 12a b + 7a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 86a b + 49a b + 45a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 32a b + 34a b + 18a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 +--R (42a b - 25a b - 19a b - 2a )cos(x) + 24a b - 20a b - 11a b +--R + +--R 8 +--R - a +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 8 6 6 2 8 5 +--R (- 2a b + 2a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 6 2 8 4 6 2 8 3 +--R (2a b - 2a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 6 2 8 2 6 2 8 6 2 8 +--R (2a b - 2a )cos(x) + (- 4a b + 4a )cos(x) - 2a b + 2a +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 8 6 6 2 8 5 +--R (- a b + a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 6 2 8 4 6 2 8 3 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) +--R + +--R 6 2 8 2 6 2 8 6 2 8 +--R (a b - a )cos(x) + (- 2a b + 2a )cos(x) - a b + a +--R * +--R csc(x) +--R + +--R 5 3 7 6 5 3 7 5 +--R (4a b - 4a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 5 3 7 4 5 3 7 3 +--R (- 4a b + 4a b)cos(x) + (- 16a b + 16a b)cos(x) +--R + +--R 5 3 7 2 5 3 7 5 3 7 +--R (- 4a b + 4a b)cos(x) + (8a b - 8a b)cos(x) + 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 8 3 5 5 3 7 7 +--R (- 4a b + 4a b )cos(x) + (4a b - 2a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 6 3 5 5 3 5 +--R (34a b - 26a b - 6a b)cos(x) + (16a b - 16a b )cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 50a b + 28a b + 16a b)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 44a b + 30a b + 14a b)cos(x) +--R + +--R 3 5 5 3 7 2 3 5 5 3 7 +--R (14a b - 2a b - 6a b)cos(x) + (24a b - 12a b - 12a b)cos(x) +--R + +--R 3 5 5 3 7 +--R 6a b - 4a b - 4a b +--R * +--R sin(x) +--R + +--R 4 4 6 2 8 7 4 4 6 2 8 6 +--R (6a b - 5a b - a )cos(x) + (12a b - 10a b - 2a )cos(x) +--R + +--R 4 4 6 2 8 5 4 4 6 2 8 4 +--R (- 6a b + 5a b + a )cos(x) + (- 24a b + 20a b + 4a )cos(x) +--R + +--R 4 4 6 2 8 3 4 4 6 2 8 2 +--R (- 6a b + 5a b + a )cos(x) + (12a b - 10a b - 2a )cos(x) +--R + +--R 4 4 6 2 8 +--R (6a b - 5a b - a )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 7 3 5 5 3 3 3 5 5 3 2 +--R (12a b - 10a b - 2a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 7 3 5 5 3 3 5 5 3 +--R (- 12a b + 10a b + 2a b )cos(x) - 6a b + 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 5 5 3 4 3 5 5 3 2 3 5 +--R (- 4a b + 4a b )cos(x) + (8a b - 8a b )cos(x) - 4a b +--R + +--R 5 3 +--R 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 4 3 5 5 3 2 3 5 +--R (- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b +--R + +--R 5 3 +--R 2a b +--R * +--R csc(x) +--R + +--R 2 6 4 4 4 2 6 4 4 2 2 6 +--R (8a b - 8a b )cos(x) + (- 16a b + 16a b )cos(x) + 8a b +--R + +--R 4 4 +--R - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 4 8 2 6 4 4 6 2 3 +--R (12a b - 4a b )cos(x) + (24b - 8a b - 12a b - 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 +--R (24b - 56a b + 12a b + 4a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 6 4 4 +--R (- 24b - 16a b + 36a b + 4a b )cos(x) - 24b + 20a b + 8a b +--R + +--R 6 2 +--R 4a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 4 4 5 2 6 6 2 4 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 6 2 2 +--R (16a b - 16a b )cos(x) + (16a b - 16a b )cos(x) +--R + +--R 2 6 4 4 2 6 6 2 +--R (- 8a b + 8a b )cos(x) - 8a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 5 2 6 6 2 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 6 2 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 2 6 4 4 2 6 6 2 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R csc(x) +--R + +--R 7 3 5 5 7 5 3 4 +--R (16a b - 16a b )cos(x) + (16a b - 16a b )cos(x) +--R + +--R 7 3 5 3 7 5 3 2 +--R (- 32a b + 32a b )cos(x) + (- 32a b + 32a b )cos(x) +--R + +--R 7 3 5 7 5 3 +--R (16a b - 16a b )cos(x) + 16a b - 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 5 +--R (24a b - 20a b - 4a b )cos(x) +--R + +--R 7 3 5 5 3 4 +--R (24a b + 6a b - 14a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (24a b - 28a b + 6a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (24a b - 104a b + 50a b - 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 +--R (- 48a b + 8a b + 38a b + 2a b)cos(x) - 48a b + 58a b +--R + +--R 5 3 7 +--R 8a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 5 5 3 6 3 5 5 3 5 +--R (- 4a b + 4a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 12a b + 8a b + 4a b)cos(x) +--R + +--R 3 5 5 3 3 +--R (48a b - 48a b )cos(x) +--R + +--R 3 5 5 3 7 2 +--R (36a b - 28a b - 8a b)cos(x) +--R + +--R 3 5 5 3 3 5 5 3 7 +--R (- 24a b + 24a b )cos(x) - 20a b + 16a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 6 3 5 5 3 5 +--R (- 2a b + 2a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 3 +--R (- 6a b + 4a b + 2a b)cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 5 5 3 7 2 3 5 5 3 +--R (18a b - 14a b - 4a b)cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 3 5 5 3 7 +--R - 10a b + 8a b + 2a b +--R * +--R csc(x) +--R + +--R 2 6 4 4 6 2 6 4 4 5 +--R (8a b - 8a b )cos(x) + (48a b - 48a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 2 6 4 4 3 +--R (24a b - 16a b - 8a b )cos(x) + (- 96a b + 96a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 +--R (- 72a b + 56a b + 16a b )cos(x) + (48a b - 48a b )cos(x) +--R + +--R 2 6 4 4 6 2 +--R 40a b - 32a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 6 2 6 4 4 6 2 5 +--R (4a b + 4a b )cos(x) + (76a b - 60a b - 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (56a b - 56a b - 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 80a b + 56a b + 8a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 52a b + 20a b + 24a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 6 4 4 6 2 +--R (4a b - 4a b + 8a b )cos(x) - 8a b + 24a b - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 6 2 6 4 4 6 2 5 +--R (- 8a b + 8a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (48a b - 48a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 24a b + 24a b )cos(x) - 16a b + 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 6 4 4 6 2 5 +--R (- 4a b + 4a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (24a b - 24a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (- 12a b + 12a b )cos(x) - 8a b + 8a b +--R * +--R csc(x) +--R + +--R 3 5 5 3 6 3 5 5 3 5 +--R (16a b - 16a b )cos(x) + (48a b - 48a b )cos(x) +--R + +--R 3 5 5 3 3 3 5 5 3 2 +--R (- 96a b + 96a b )cos(x) + (- 48a b + 48a b )cos(x) +--R + +--R 3 5 5 3 3 5 5 3 +--R (48a b - 48a b )cos(x) + 32a b - 32a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 7 +--R (- 4a b + 6a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 6 +--R (8a b + 28a b - 20a b )cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (20a b + 42a b - 42a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (- 16a b - 24a b + 14a b - 6a b)cos(x) +--R + +--R 7 3 5 5 3 3 +--R (- 28a b - 94a b + 90a b )cos(x) +--R + +--R 7 3 5 5 3 2 +--R (8a b - 28a b + 36a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 5 5 3 7 +--R (12a b + 46a b - 38a b - 4a b)cos(x) + 24a b - 22a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 7 6 5 3 7 5 +--R (- 4a b + 4a b)cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 5 3 7 4 5 3 7 3 +--R (4a b - 4a b)cos(x) + (16a b - 16a b)cos(x) +--R + +--R 5 3 7 2 5 3 7 5 3 +--R (4a b - 4a b)cos(x) + (- 8a b + 8a b)cos(x) - 4a b +--R + +--R 7 +--R 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 7 6 5 3 7 5 +--R (- 2a b + 2a b)cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 5 3 7 4 5 3 7 3 +--R (2a b - 2a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 5 3 7 2 5 3 7 5 3 7 +--R (2a b - 2a b)cos(x) + (- 4a b + 4a b)cos(x) - 2a b + 2a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 6 4 4 6 2 5 +--R (8a b - 8a b )cos(x) + (16a b - 16a b )cos(x) +--R + +--R 4 4 6 2 4 4 4 6 2 3 +--R (- 8a b + 8a b )cos(x) + (- 32a b + 32a b )cos(x) +--R + +--R 4 4 6 2 2 4 4 6 2 4 4 +--R (- 8a b + 8a b )cos(x) + (16a b - 16a b )cos(x) + 8a b +--R + +--R 6 2 +--R - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 8 2 6 4 4 6 2 7 +--R (- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a b )cos(x) +--R + +--R 2 6 4 4 6 2 6 2 6 5 +--R (56a b - 36a b - 12a b )cos(x) + 8a b cos(x) +--R + +--R 2 6 4 4 6 2 4 +--R (- 88a b + 40a b + 32a b )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 40a b - 4a b + 28a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (40a b - 20a b - 12a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 +--R (24a b + 8a b - 24a b )cos(x) + 8a b - 8a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 7 3 5 5 3 7 6 +--R (12a b - 10a b - 2a b)cos(x) + (24a b - 20a b - 4a b)cos(x) +--R + +--R 3 5 5 3 7 5 3 5 5 3 7 4 +--R (- 12a b + 10a b + 2a b)cos(x) + (- 48a b + 40a b + 8a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- 12a b + 10a b + 2a b)cos(x) + (24a b - 20a b - 4a b)cos(x) +--R + +--R 3 5 5 3 7 +--R (12a b - 10a b - 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 6 4 4 6 2 3 4 4 6 2 2 +--R (6a b - 5a b - a b )cos(x) + (- 3a b + 3a b )cos(x) +--R + +--R 2 6 4 4 6 2 4 4 6 2 +--R (- 6a b + 5a b + a b )cos(x) - 3a b + 3a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 +--R (- 2a b + 2a b )cos(x) + (4a b - 4a b )cos(x) - 2a b +--R + +--R 6 2 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 4 4 4 6 2 2 4 4 6 2 +--R (- a b + a b )cos(x) + (2a b - 2a b )cos(x) - a b + a b +--R * +--R csc(x) +--R + +--R 3 5 5 3 4 3 5 5 3 2 3 5 5 3 +--R ((4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b - 4a b ) +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 4 +--R (6a b - 2a b - 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (12a b - 4a b - 6a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (- 12a b + 6a b + 2a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (- 12a b - 8a b + 18a b + 2a b)cos(x) - 6a b + 2a b + 4a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 4a b + 4a b )cos(x) + (- 4a b + 4a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (8a b - 8a b )cos(x) + (8a b - 8a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 4a b + 4a b )cos(x) - 4a b + 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 5 3 5 7 4 +--R (- 2a b + 2a b )cos(x) + (- 2a b + 2a b)cos(x) +--R + +--R 3 5 5 3 3 3 5 7 2 +--R (4a b - 4a b )cos(x) + (4a b - 4a b)cos(x) +--R + +--R 3 5 5 3 3 5 7 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R csc(x) +--R + +--R 2 6 4 4 5 2 6 6 2 4 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 2 6 4 4 3 2 6 6 2 2 +--R (- 16a b + 16a b )cos(x) + (- 16a b + 16a b )cos(x) +--R + +--R 2 6 4 4 2 6 6 2 +--R (8a b - 8a b )cos(x) + 8a b - 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 8 2 6 4 4 6 2 5 +--R (12b - 4a b - 10a b - 2a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (12b + 8a b - 13a b - 7a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 3 +--R (- 24b + 44a b - 14a b + 3a b - a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 2 +--R (- 24b + 20a b - 20a b + 25a b - a )cos(x) +--R + +--R 8 2 6 4 4 6 2 8 8 2 6 4 4 +--R (12b - 40a b + 4a b + 19a b + a )cos(x) + 12b - 28a b + 13a b +--R + +--R 6 2 8 +--R 4a b - a +--R * +--R 4 +--R sin(x) +--R + +--R 4 4 6 2 6 4 4 6 2 5 +--R (- 2a b + 2a b )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 3 +--R (- 6a b + 4a b + 2a )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 4 6 2 8 2 4 4 6 2 +--R (18a b - 14a b - 4a )cos(x) + (- 12a b + 12a b )cos(x) +--R + +--R 4 4 6 2 8 +--R - 10a b + 8a b + 2a +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 6 4 4 6 2 5 +--R (- a b + a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 3 +--R (- 3a b + 2a b + a )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 4 4 6 2 8 2 4 4 6 2 4 4 +--R (9a b - 7a b - 2a )cos(x) + (- 6a b + 6a b )cos(x) - 5a b +--R + +--R 6 2 8 +--R 4a b + a +--R * +--R csc(x) +--R + +--R 3 5 5 3 6 3 5 5 3 5 +--R (4a b - 4a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 3 +--R (12a b - 8a b - 4a b)cos(x) + (- 48a b + 48a b )cos(x) +--R + +--R 3 5 5 3 7 2 3 5 5 3 +--R (- 36a b + 28a b + 8a b)cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 5 5 3 7 +--R 20a b - 16a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 7 3 5 5 3 6 +--R (6a b - 6a b + 2a b )cos(x) +--R + +--R 7 3 5 5 3 7 5 +--R (36a b - 10a b - 30a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 4 +--R (18a b + 10a b - 36a b - 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 3 +--R (- 72a b + 56a b + 28a b + 4a b)cos(x) +--R + +--R 7 3 5 5 3 7 2 +--R (- 54a b + 34a b + 26a b + 12a b)cos(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 7 +--R (36a b - 46a b - 2a b + 4a b)cos(x) + 30a b - 38a b + 4a b - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 7 6 5 3 7 5 +--R (- 4a b + 4a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (24a b - 24a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (- 12a b + 12a b)cos(x) - 8a b + 8a b +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 7 6 5 3 7 5 +--R (- 2a b + 2a b)cos(x) + (- 6a b + 6a b)cos(x) +--R + +--R 5 3 7 3 5 3 7 2 +--R (12a b - 12a b)cos(x) + (6a b - 6a b)cos(x) +--R + +--R 5 3 7 5 3 7 +--R (- 6a b + 6a b)cos(x) - 4a b + 4a b +--R * +--R csc(x) +--R + +--R 4 4 6 2 6 4 4 6 2 5 +--R (8a b - 8a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 4 4 6 2 3 4 4 6 2 2 +--R (- 48a b + 48a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 4 4 6 2 4 4 6 2 +--R (24a b - 24a b )cos(x) + 16a b - 16a b +--R * +--R 2 +--R cot(x) +--R + +--R 2 6 4 4 6 2 7 2 6 4 4 6 2 6 +--R (- 2a b + 3a b - a b )cos(x) + (16a b - 2a b - 10a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 5 +--R (46a b - 27a b - 21a b - 2a )cos(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 8a b - 12a b + 7a b - 3a )cos(x) +--R + +--R 2 6 4 4 6 2 3 +--R (- 86a b + 49a b + 45a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 32a b + 34a b + 18a b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 4 4 6 2 8 +--R (42a b - 25a b - 19a b - 2a )cos(x) + 24a b - 20a b - 11a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 8 6 6 2 8 5 +--R (- 2a b + 2a )cos(x) + (- 4a b + 4a )cos(x) +--R + +--R 6 2 8 4 6 2 8 3 +--R (2a b - 2a )cos(x) + (8a b - 8a )cos(x) +--R + +--R 6 2 8 2 6 2 8 6 2 8 +--R (2a b - 2a )cos(x) + (- 4a b + 4a )cos(x) - 2a b + 2a +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 8 6 6 2 8 5 +--R (- a b + a )cos(x) + (- 2a b + 2a )cos(x) +--R + +--R 6 2 8 4 6 2 8 3 6 2 8 2 +--R (a b - a )cos(x) + (4a b - 4a )cos(x) + (a b - a )cos(x) +--R + +--R 6 2 8 6 2 8 +--R (- 2a b + 2a )cos(x) - a b + a +--R * +--R csc(x) +--R + +--R 5 3 7 6 5 3 7 5 +--R (4a b - 4a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 5 3 7 4 5 3 7 3 +--R (- 4a b + 4a b)cos(x) + (- 16a b + 16a b)cos(x) +--R + +--R 5 3 7 2 5 3 7 5 3 7 +--R (- 4a b + 4a b)cos(x) + (8a b - 8a b)cos(x) + 4a b - 4a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 8 3 5 5 3 7 7 +--R (- 4a b + 4a b )cos(x) + (4a b - 2a b - 2a b)cos(x) +--R + +--R 3 5 5 3 7 6 3 5 5 3 5 +--R (34a b - 26a b - 6a b)cos(x) + (16a b - 16a b )cos(x) +--R + +--R 3 5 5 3 7 4 +--R (- 50a b + 28a b + 16a b)cos(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 2 +--R (- 44a b + 30a b + 14a b)cos(x) + (14a b - 2a b - 6a b)cos(x) +--R + +--R 3 5 5 3 7 3 5 5 3 7 +--R (24a b - 12a b - 12a b)cos(x) + 6a b - 4a b - 4a b +--R * +--R sin(x) +--R + +--R 4 4 6 2 8 7 4 4 6 2 8 6 +--R (6a b - 5a b - a )cos(x) + (12a b - 10a b - 2a )cos(x) +--R + +--R 4 4 6 2 8 5 4 4 6 2 8 4 +--R (- 6a b + 5a b + a )cos(x) + (- 24a b + 20a b + 4a )cos(x) +--R + +--R 4 4 6 2 8 3 4 4 6 2 8 2 +--R (- 6a b + 5a b + a )cos(x) + (12a b - 10a b - 2a )cos(x) +--R + +--R 4 4 6 2 8 +--R (6a b - 5a b - a )cos(x) +--R / +--R 6 4 8 2 4 6 4 8 2 2 6 4 8 2 +--R ((2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b - 2a b ) +--R * +--R 5 +--R sin(x) +--R + +--R 5 5 7 3 5 5 5 9 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b)cos(x) +--R + +--R 5 5 7 3 3 5 5 9 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 5 5 7 3 5 5 9 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 4 8 2 6 6 4 8 2 5 +--R (2a b - 2a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 6 4 8 2 10 4 6 4 8 2 3 +--R (6a b - 4a b - 2a )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 6 4 8 2 10 2 6 4 8 2 +--R (- 18a b + 14a b + 4a )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 6 4 8 2 10 +--R 10a b - 8a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 9 6 7 3 9 5 +--R (4a b - 4a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 7 3 9 3 7 3 9 2 +--R (- 24a b + 24a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 7 3 9 7 3 9 +--R (12a b - 12a b)cos(x) + 8a b - 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 10 6 8 2 10 5 +--R (2a b - 2a )cos(x) + (4a b - 4a )cos(x) +--R + +--R 8 2 10 4 8 2 10 3 +--R (- 2a b + 2a )cos(x) + (- 8a b + 8a )cos(x) +--R + +--R 8 2 10 2 8 2 10 8 2 10 +--R (- 2a b + 2a )cos(x) + (4a b - 4a )cos(x) + 2a b - 2a +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 5 7 3 4 5 5 7 3 2 5 5 7 3 +--R ((4a b - 4a b )cos(x) + (- 8a b + 8a b )cos(x) + 4a b - 4a b ) +--R * +--R 5 +--R sin(x) +--R + +--R 4 6 6 4 5 4 6 8 2 4 +--R (8a b - 8a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 4 6 6 4 3 4 6 8 2 2 +--R (- 16a b + 16a b )cos(x) + (- 16a b + 16a b )cos(x) +--R + +--R 4 6 6 4 4 6 8 2 +--R (8a b - 8a b )cos(x) + 8a b - 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 5 7 3 6 5 5 7 3 5 +--R (4a b - 4a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 5 5 7 3 9 4 5 5 7 3 3 +--R (12a b - 8a b - 4a b)cos(x) + (- 48a b + 48a b )cos(x) +--R + +--R 5 5 7 3 9 2 5 5 7 3 +--R (- 36a b + 28a b + 8a b)cos(x) + (24a b - 24a b )cos(x) +--R + +--R 5 5 7 3 9 +--R 20a b - 16a b - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 4 8 2 6 6 4 8 2 5 +--R (8a b - 8a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 6 4 8 2 3 6 4 8 2 2 +--R (- 48a b + 48a b )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 6 4 8 2 6 4 8 2 +--R (24a b - 24a b )cos(x) + 16a b - 16a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 9 6 7 3 9 5 +--R (4a b - 4a b)cos(x) + (8a b - 8a b)cos(x) +--R + +--R 7 3 9 4 7 3 9 3 +--R (- 4a b + 4a b)cos(x) + (- 16a b + 16a b)cos(x) +--R + +--R 7 3 9 2 7 3 9 7 3 9 +--R (- 4a b + 4a b)cos(x) + (8a b - 8a b)cos(x) + 4a b - 4a b +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 4 8 2 4 6 4 8 2 2 6 4 8 2 +--R ((2a b - 2a b )cos(x) + (- 4a b + 4a b )cos(x) + 2a b - 2a b ) +--R * +--R 5 +--R sin(x) +--R + +--R 5 5 7 3 5 5 5 9 4 +--R (4a b - 4a b )cos(x) + (4a b - 4a b)cos(x) +--R + +--R 5 5 7 3 3 5 5 9 2 +--R (- 8a b + 8a b )cos(x) + (- 8a b + 8a b)cos(x) +--R + +--R 5 5 7 3 5 5 9 +--R (4a b - 4a b )cos(x) + 4a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 4 8 2 6 6 4 8 2 5 +--R (2a b - 2a b )cos(x) + (12a b - 12a b )cos(x) +--R + +--R 6 4 8 2 10 4 6 4 8 2 3 +--R (6a b - 4a b - 2a )cos(x) + (- 24a b + 24a b )cos(x) +--R + +--R 6 4 8 2 10 2 6 4 8 2 6 4 +--R (- 18a b + 14a b + 4a )cos(x) + (12a b - 12a b )cos(x) + 10a b +--R + +--R 8 2 10 +--R - 8a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 7 3 9 6 7 3 9 5 +--R (4a b - 4a b)cos(x) + (12a b - 12a b)cos(x) +--R + +--R 7 3 9 3 7 3 9 2 +--R (- 24a b + 24a b)cos(x) + (- 12a b + 12a b)cos(x) +--R + +--R 7 3 9 7 3 9 +--R (12a b - 12a b)cos(x) + 8a b - 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 2 10 6 8 2 10 5 +--R (2a b - 2a )cos(x) + (4a b - 4a )cos(x) +--R + +--R 8 2 10 4 8 2 10 3 +--R (- 2a b + 2a )cos(x) + (- 8a b + 8a )cos(x) +--R + +--R 8 2 10 2 8 2 10 8 2 10 +--R (- 2a b + 2a )cos(x) + (4a b - 4a )cos(x) + 2a b - 2a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 502 + +--S 503 of 586 +t0586:= csc(x)/(a+a*sin(x))^2 +--R +--R +--R csc(x) +--R (488) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 586 +r0586:= -atanh(cos(x))/a^2+1/3*cos(x)/a^2/(1+sin(x))^2+_ + 4/3*cos(x)/a^2/(1+sin(x)) +--R +--R +--R 2 +--R (- 3sin(x) - 6sin(x) - 3)atanh(cos(x)) + 4cos(x)sin(x) + 5cos(x) +--R (489) ----------------------------------------------------------------- +--R 2 2 2 2 +--R 3a sin(x) + 6a sin(x) + 3a +--R Type: Expression(Integer) +--E 504 + +--S 505 of 586 +a0586:= integrate(t0586,x) +--R +--R +--R (490) +--R 2 sin(x) +--R ((3cos(x) + 6)sin(x) - 3cos(x) + 3cos(x) + 6)log(----------) +--R cos(x) + 1 +--R + +--R 2 +--R (9cos(x) + 9)sin(x) - cos(x) + 10cos(x) + 11 +--R / +--R 2 2 2 2 2 2 +--R (3a cos(x) + 6a )sin(x) - 3a cos(x) + 3a cos(x) + 6a +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 586 +m0586:= a0586-r0586 +--R +--R +--R (491) +--R 3 2 2 +--R (3cos(x) + 6)sin(x) + (- 3cos(x) + 9cos(x) + 18)sin(x) +--R + +--R 2 2 +--R (- 6cos(x) + 9cos(x) + 18)sin(x) - 3cos(x) + 3cos(x) + 6 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 2 2 +--R (3cos(x) + 6)sin(x) + (- 3cos(x) + 9cos(x) + 18)sin(x) +--R + +--R 2 2 +--R (- 6cos(x) + 9cos(x) + 18)sin(x) - 3cos(x) + 3cos(x) + 6 +--R * +--R atanh(cos(x)) +--R + +--R 3 2 2 +--R (9cos(x) + 9)sin(x) + (- 5cos(x) + 20cos(x) + 29)sin(x) +--R + +--R 3 2 3 2 +--R (4cos(x) - 11cos(x) + 11cos(x) + 31)sin(x) + 5cos(x) - 6cos(x) + 11 +--R / +--R 2 2 3 2 2 2 2 2 +--R (3a cos(x) + 6a )sin(x) + (- 3a cos(x) + 9a cos(x) + 18a )sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (- 6a cos(x) + 9a cos(x) + 18a )sin(x) - 3a cos(x) + 3a cos(x) + 6a +--R Type: Expression(Integer) +--E 506 + +--S 507 of 586 +d0586:= D(m0586,x) +--R +--R +--R (492) +--R 3 2 7 +--R (3cos(x) + 3cos(x) + 12cos(x) + 9)sin(x) +--R + +--R 4 3 2 6 +--R (- 10cos(x) + 5cos(x) + 35cos(x) + 58cos(x) + 29)sin(x) +--R + +--R 5 4 3 2 5 +--R (- 2cos(x) - 44cos(x) + 7cos(x) + 118cos(x) + 100cos(x) + 22)sin(x) +--R + +--R 6 5 4 3 2 +--R - 6cos(x) - 6cos(x) - 34cos(x) + 41cos(x) + 142cos(x) + 52cos(x) +--R + +--R - 18 +--R * +--R 4 +--R sin(x) +--R + +--R 7 6 4 3 2 +--R - 5cos(x) - 41cos(x) + 109cos(x) + 97cos(x) - cos(x) - 56cos(x) +--R + +--R - 31 +--R * +--R 3 +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R 4cos(x) - 11cos(x) - 83cos(x) + 2cos(x) + 221cos(x) + 113cos(x) +--R + +--R 2 +--R - 125cos(x) - 98cos(x) - 11 +--R * +--R 2 +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R 6cos(x) - 3cos(x) - 56cos(x) - 14cos(x) + 130cos(x) + 73cos(x) +--R + +--R 2 +--R - 80cos(x) - 56cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R 3cos(x) - 6cos(x) - 12cos(x) + 18cos(x) + 21cos(x) - 12cos(x) +--R + +--R - 12cos(x) +--R / +--R 2 4 2 3 2 2 2 2 6 +--R (3a cos(x) + 12a cos(x) + 9a cos(x) - 12a cos(x) - 12a )sin(x) +--R + +--R 2 5 2 4 2 3 2 2 2 +--R - 6a cos(x) + 3a cos(x) + 66a cos(x) + 57a cos(x) - 60a cos(x) +--R + +--R 2 +--R - 60a +--R * +--R 5 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 3a cos(x) - 24a cos(x) - 21a cos(x) + 144a cos(x) + 138a cos(x) +--R + +--R 2 2 +--R - 120a cos(x) - 120a +--R * +--R 4 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 9a cos(x) - 36a cos(x) - 51a cos(x) + 156a cos(x) + 162a cos(x) +--R + +--R 2 2 +--R - 120a cos(x) - 120a +--R * +--R 3 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 9a cos(x) - 24a cos(x) - 42a cos(x) + 84a cos(x) + 93a cos(x) +--R + +--R 2 2 +--R - 60a cos(x) - 60a +--R * +--R 2 +--R sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 3a cos(x) - 6a cos(x) - 12a cos(x) + 18a cos(x) + 21a cos(x) +--R + +--R 2 2 +--R - 12a cos(x) - 12a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 507 + +--S 508 of 586 +t0587:= csc(x)^2/(a+a*sin(x))^2 +--R +--R +--R 2 +--R csc(x) +--R (493) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 508 + +--S 509 of 586 +r0587:= 2*atanh(cos(x))/a^2-cot(x)/a^2-1/3*cos(x)/a^2/(1+sin(x))^2-_ + 7/3*cos(x)/a^2/(1+sin(x)) +--R +--R +--R (494) +--R 2 2 +--R (6sin(x) + 12sin(x) + 6)atanh(cos(x)) - 3cot(x)sin(x) +--R + +--R (- 6cot(x) - 7cos(x))sin(x) - 3cot(x) - 8cos(x) +--R / +--R 2 2 2 2 +--R 3a sin(x) + 6a sin(x) + 3a +--R Type: Expression(Integer) +--E 509 + +--S 510 of 586 +a0587:= integrate(t0587,x) +--R +--R +--R (495) +--R 2 3 2 +--R (- 6cos(x) + 6cos(x) + 12)sin(x) - 6cos(x) - 12cos(x) + 6cos(x) +--R + +--R 12 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 3 2 +--R (2cos(x) + 22cos(x) + 17)sin(x) - 18cos(x) - 12cos(x) + 21cos(x) + 15 +--R / +--R 2 2 2 2 2 3 2 2 +--R (3a cos(x) - 3a cos(x) - 6a )sin(x) + 3a cos(x) + 6a cos(x) +--R + +--R 2 2 +--R - 3a cos(x) - 6a +--R Type: Union(Expression(Integer),...) +--E 510 + +--S 511 of 586 +m0587:= a0587-r0587 +--R +--R +--R (496) +--R 2 3 +--R (- 6cos(x) + 6cos(x) + 12)sin(x) +--R + +--R 3 2 2 +--R (- 6cos(x) - 24cos(x) + 18cos(x) + 36)sin(x) +--R + +--R 3 2 3 +--R (- 12cos(x) - 30cos(x) + 18cos(x) + 36)sin(x) - 6cos(x) +--R + +--R 2 +--R - 12cos(x) + 6cos(x) + 12 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 3 +--R (- 6cos(x) + 6cos(x) + 12)sin(x) +--R + +--R 3 2 2 +--R (- 6cos(x) - 24cos(x) + 18cos(x) + 36)sin(x) +--R + +--R 3 2 3 +--R (- 12cos(x) - 30cos(x) + 18cos(x) + 36)sin(x) - 6cos(x) +--R + +--R 2 +--R - 12cos(x) + 6cos(x) + 12 +--R * +--R atanh(cos(x)) +--R + +--R 2 2 3 +--R ((3cos(x) - 3cos(x) - 6)cot(x) + 2cos(x) + 22cos(x) + 17)sin(x) +--R + +--R 3 2 3 2 +--R (3cos(x) + 12cos(x) - 9cos(x) - 18)cot(x) - 11cos(x) - 15cos(x) +--R + +--R 51cos(x) + 49 +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 3 +--R (6cos(x) + 15cos(x) - 9cos(x) - 18)cot(x) + 7cos(x) - 14cos(x) +--R + +--R 2 +--R - 37cos(x) + 34cos(x) + 47 +--R * +--R sin(x) +--R + +--R 3 2 4 3 +--R (3cos(x) + 6cos(x) - 3cos(x) - 6)cot(x) + 8cos(x) - 2cos(x) +--R + +--R 2 +--R - 20cos(x) + 5cos(x) + 15 +--R / +--R 2 2 2 2 3 +--R (3a cos(x) - 3a cos(x) - 6a )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (3a cos(x) + 12a cos(x) - 9a cos(x) - 18a )sin(x) +--R + +--R 2 3 2 2 2 2 2 3 +--R (6a cos(x) + 15a cos(x) - 9a cos(x) - 18a )sin(x) + 3a cos(x) +--R + +--R 2 2 2 2 +--R 6a cos(x) - 3a cos(x) - 6a +--R Type: Expression(Integer) +--E 511 + +--S 512 of 586 +d0587:= D(m0587,x) +--R +--R +--R (497) +--R 4 3 2 7 +--R (- 6cos(x) + 42cos(x) + 18cos(x) - 39cos(x) - 27)sin(x) +--R + +--R 5 4 3 2 2 5 +--R (- 3cos(x) + 9cos(x) + 3cos(x) - 21cos(x) + 12)cot(x) - 2cos(x) +--R + +--R 3 2 +--R 186cos(x) + 44cos(x) - 169cos(x) - 95 +--R * +--R 6 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (- 6cos(x) - 9cos(x) + 63cos(x) + 9cos(x) - 117cos(x) + 60) +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - 32cos(x) + 24cos(x) + 132cos(x) + 261cos(x) - 69cos(x) +--R + +--R - 258cos(x) - 94 +--R * +--R 5 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 3cos(x) - 27cos(x) - 3cos(x) + 165cos(x) + 6cos(x) +--R + +--R 2 +--R - 258cos(x) + 120 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R - 9cos(x) - 93cos(x) + 148cos(x) + 330cos(x) - 20cos(x) +--R + +--R 2 +--R - 300cos(x) - 98cos(x) + 30 +--R * +--R 4 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 9cos(x) - 45cos(x) + 15cos(x) + 207cos(x) - 6cos(x) +--R + +--R 2 +--R - 282cos(x) + 120 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 +--R - 20cos(x) - 27cos(x) - 19cos(x) + 320cos(x) + 228cos(x) +--R + +--R 3 2 +--R - 460cos(x) - 304cos(x) + 173cos(x) + 109 +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 9cos(x) - 33cos(x) + 18cos(x) + 126cos(x) - 9cos(x) +--R + +--R 2 +--R - 153cos(x) + 60 +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 7 6 5 +--R - 7cos(x) - 57cos(x) - 33cos(x) + 145cos(x) + 357cos(x) +--R + +--R 4 3 2 +--R - 57cos(x) - 560cos(x) - 96cos(x) + 243cos(x) + 65 +--R * +--R 2 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 3cos(x) - 9cos(x) + 6cos(x) + 30cos(x) - 3cos(x) +--R + +--R 2 +--R - 33cos(x) + 12 +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 7 6 5 +--R - 9cos(x) - 45cos(x) - 31cos(x) + 117cos(x) + 219cos(x) +--R + +--R 4 3 2 +--R - 87cos(x) - 303cos(x) + 3cos(x) + 124cos(x) + 12 +--R * +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 6cos(x) - 18cos(x) + 12cos(x) + 60cos(x) - 6cos(x) - 66cos(x) +--R + +--R 24cos(x) +--R / +--R 2 5 2 4 2 3 2 2 2 6 +--R (3a cos(x) - 9a cos(x) - 3a cos(x) + 21a cos(x) - 12a )sin(x) +--R + +--R 2 6 2 5 2 4 2 3 2 2 +--R 6a cos(x) + 9a cos(x) - 63a cos(x) - 9a cos(x) + 117a cos(x) +--R + +--R 2 +--R - 60a +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 2 3 +--R 3a cos(x) + 27a cos(x) + 3a cos(x) - 165a cos(x) - 6a cos(x) +--R + +--R 2 2 2 +--R 258a cos(x) - 120a +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 2 3 +--R 9a cos(x) + 45a cos(x) - 15a cos(x) - 207a cos(x) + 6a cos(x) +--R + +--R 2 2 2 +--R 282a cos(x) - 120a +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 2 3 +--R 9a cos(x) + 33a cos(x) - 18a cos(x) - 126a cos(x) + 9a cos(x) +--R + +--R 2 2 2 +--R 153a cos(x) - 60a +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 2 3 +--R 3a cos(x) + 9a cos(x) - 6a cos(x) - 30a cos(x) + 3a cos(x) +--R + +--R 2 2 2 +--R 33a cos(x) - 12a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 512 + +--S 513 of 586 +t0588:= csc(x)^3/(a+a*sin(x))^2 +--R +--R +--R 3 +--R csc(x) +--R (498) -------------------------- +--R 2 2 2 2 +--R a sin(x) + 2a sin(x) + a +--R Type: Expression(Integer) +--E 513 + +--S 514 of 586 +r0588:= -7/2*atanh(cos(x))/a^2+2*cot(x)/a^2-1/2*cot(x)*csc(x)/a^2+_ + 1/3*cos(x)/a^2/(1+sin(x))^2+10/3*cos(x)/a^2/(1+sin(x)) +--R +--R +--R (499) +--R 2 +--R (- 21sin(x) - 42sin(x) - 21)atanh(cos(x)) +--R + +--R 2 +--R (- 3cot(x)csc(x) + 12cot(x))sin(x) +--R + +--R (- 6cot(x)csc(x) + 24cot(x) + 20cos(x))sin(x) - 3cot(x)csc(x) + 12cot(x) +--R + +--R 22cos(x) +--R / +--R 2 2 2 2 +--R 6a sin(x) + 12a sin(x) + 6a +--R Type: Expression(Integer) +--E 514 + +--S 515 of 586 +a0588:= integrate(t0588,x) +--R +--R +--R (500) +--R 3 2 4 3 +--R (21cos(x) + 42cos(x) - 21cos(x) - 42)sin(x) - 21cos(x) + 21cos(x) +--R + +--R 2 +--R 63cos(x) - 21cos(x) - 42 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 2 4 3 +--R (54cos(x) + 33cos(x) - 60cos(x) - 42)sin(x) + 10cos(x) + 65cos(x) +--R + +--R 2 +--R 39cos(x) - 62cos(x) - 46 +--R / +--R 2 3 2 2 2 2 2 4 +--R (6a cos(x) + 12a cos(x) - 6a cos(x) - 12a )sin(x) - 6a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 6a cos(x) + 18a cos(x) - 6a cos(x) - 12a +--R Type: Union(Expression(Integer),...) +--E 515 + +--S 516 of 586 +m0588:= a0588-r0588 +--R +--R +--R (501) +--R 3 2 3 +--R (21cos(x) + 42cos(x) - 21cos(x) - 42)sin(x) +--R + +--R 4 3 2 2 +--R (- 21cos(x) + 63cos(x) + 147cos(x) - 63cos(x) - 126)sin(x) +--R + +--R 4 3 2 +--R (- 42cos(x) + 63cos(x) + 168cos(x) - 63cos(x) - 126)sin(x) +--R + +--R 4 3 2 +--R - 21cos(x) + 21cos(x) + 63cos(x) - 21cos(x) - 42 +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 2 3 +--R (21cos(x) + 42cos(x) - 21cos(x) - 42)sin(x) +--R + +--R 4 3 2 2 +--R (- 21cos(x) + 63cos(x) + 147cos(x) - 63cos(x) - 126)sin(x) +--R + +--R 4 3 2 +--R (- 42cos(x) + 63cos(x) + 168cos(x) - 63cos(x) - 126)sin(x) +--R + +--R 4 3 2 +--R - 21cos(x) + 21cos(x) + 63cos(x) - 21cos(x) - 42 +--R * +--R atanh(cos(x)) +--R + +--R 3 2 +--R (3cos(x) + 6cos(x) - 3cos(x) - 6)cot(x)csc(x) +--R + +--R 3 2 3 +--R (- 12cos(x) - 24cos(x) + 12cos(x) + 24)cot(x) + 54cos(x) +--R + +--R 2 +--R 33cos(x) - 60cos(x) - 42 +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 +--R (- 3cos(x) + 9cos(x) + 21cos(x) - 9cos(x) - 18)cot(x)csc(x) +--R + +--R 4 3 2 4 +--R (12cos(x) - 36cos(x) - 84cos(x) + 36cos(x) + 72)cot(x) - 10cos(x) +--R + +--R 3 2 +--R 133cos(x) + 125cos(x) - 142cos(x) - 130 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (- 6cos(x) + 9cos(x) + 24cos(x) - 9cos(x) - 18)cot(x)csc(x) +--R + +--R 4 3 2 5 +--R (24cos(x) - 36cos(x) - 96cos(x) + 36cos(x) + 72)cot(x) + 20cos(x) +--R + +--R 4 3 2 +--R - 22cos(x) + 80cos(x) + 153cos(x) - 100cos(x) - 134 +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- 3cos(x) + 3cos(x) + 9cos(x) - 3cos(x) - 6)cot(x)csc(x) +--R + +--R 4 3 2 5 +--R (12cos(x) - 12cos(x) - 36cos(x) + 12cos(x) + 24)cot(x) + 22cos(x) +--R + +--R 4 3 2 +--R - 12cos(x) - cos(x) + 61cos(x) - 18cos(x) - 46 +--R / +--R 2 3 2 2 2 2 3 +--R (6a cos(x) + 12a cos(x) - 6a cos(x) - 12a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 2 +--R (- 6a cos(x) + 18a cos(x) + 42a cos(x) - 18a cos(x) - 36a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R (- 12a cos(x) + 18a cos(x) + 48a cos(x) - 18a cos(x) - 36a )sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R - 6a cos(x) + 6a cos(x) + 18a cos(x) - 6a cos(x) - 12a +--R Type: Expression(Integer) +--E 516 + +--S 517 of 586 +d0588:= D(m0588,x) +--R +--R +--R (502) +--R 5 4 3 2 7 +--R (21cos(x) + 9cos(x) + 51cos(x) + 27cos(x) - 120cos(x) - 78)sin(x) +--R + +--R 6 5 4 3 2 +--R - 6cos(x) - 24cos(x) - 12cos(x) + 48cos(x) + 42cos(x) +--R + +--R - 24cos(x) - 24 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - 3cos(x) - 12cos(x) - 6cos(x) + 24cos(x) + 21cos(x) +--R + +--R - 12cos(x) - 12 +--R * +--R csc(x) +--R + +--R 6 5 4 3 2 +--R 12cos(x) + 48cos(x) + 24cos(x) - 96cos(x) - 84cos(x) +--R + +--R 48cos(x) + 48 +--R * +--R 2 +--R cot(x) +--R + +--R 6 5 4 3 2 +--R - 74cos(x) + 43cos(x) + 291cos(x) + 349cos(x) - 93cos(x) +--R + +--R - 548cos(x) - 262 +--R * +--R 6 +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 12cos(x) - 6cos(x) - 144cos(x) - 108cos(x) + 252cos(x) +--R + +--R 2 +--R 234cos(x) - 120cos(x) - 120 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R 6cos(x) - 3cos(x) - 72cos(x) - 54cos(x) + 126cos(x) +--R + +--R 2 +--R 117cos(x) - 60cos(x) - 60 +--R * +--R csc(x) +--R + +--R 7 6 5 4 3 +--R - 24cos(x) + 12cos(x) + 288cos(x) + 216cos(x) - 504cos(x) +--R + +--R 2 +--R - 468cos(x) + 240cos(x) + 240 +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R - 22cos(x) - 337cos(x) + 135cos(x) + 1185cos(x) + 579cos(x) +--R + +--R 2 +--R - 786cos(x) - 860cos(x) - 212 +--R * +--R 5 +--R sin(x) +--R + +--R 8 7 6 5 4 +--R - 6cos(x) + 48cos(x) + 48cos(x) - 336cos(x) - 318cos(x) +--R + +--R 3 2 +--R 528cos(x) + 516cos(x) - 240cos(x) - 240 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 +--R - 3cos(x) + 24cos(x) + 24cos(x) - 168cos(x) - 159cos(x) +--R + +--R 3 2 +--R 264cos(x) + 258cos(x) - 120cos(x) - 120 +--R * +--R csc(x) +--R + +--R 8 7 6 5 4 +--R 12cos(x) - 96cos(x) - 96cos(x) + 672cos(x) + 636cos(x) +--R + +--R 3 2 +--R - 1056cos(x) - 1032cos(x) + 480cos(x) + 480 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 +--R - 54cos(x) - 120cos(x) - 287cos(x) + 649cos(x) + 1525cos(x) +--R + +--R 3 2 +--R - 293cos(x) - 1430cos(x) - 284cos(x) + 204 +--R * +--R 4 +--R sin(x) +--R + +--R 8 7 6 5 +--R - 18cos(x) + 72cos(x) + 120cos(x) - 384cos(x) +--R + +--R 4 3 2 +--R - 426cos(x) + 552cos(x) + 564cos(x) - 240cos(x) - 240 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 +--R - 9cos(x) + 36cos(x) + 60cos(x) - 192cos(x) - 213cos(x) +--R + +--R 3 2 +--R 276cos(x) + 282cos(x) - 120cos(x) - 120 +--R * +--R csc(x) +--R + +--R 8 7 6 5 4 +--R 36cos(x) - 144cos(x) - 240cos(x) + 768cos(x) + 852cos(x) +--R + +--R 3 2 +--R - 1104cos(x) - 1128cos(x) + 480cos(x) + 480 +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 7 6 5 +--R - 19cos(x) - 298cos(x) - 233cos(x) + 801cos(x) + 1403cos(x) +--R + +--R 4 3 2 +--R - 112cos(x) - 1839cos(x) - 801cos(x) + 712cos(x) + 434 +--R * +--R 3 +--R sin(x) +--R + +--R 8 7 6 5 +--R - 18cos(x) + 48cos(x) + 102cos(x) - 216cos(x) +--R + +--R 4 3 2 +--R - 270cos(x) + 288cos(x) + 306cos(x) - 120cos(x) - 120 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 +--R - 9cos(x) + 24cos(x) + 51cos(x) - 108cos(x) - 135cos(x) +--R + +--R 3 2 +--R 144cos(x) + 153cos(x) - 60cos(x) - 60 +--R * +--R csc(x) +--R + +--R 8 7 6 5 4 +--R 36cos(x) - 96cos(x) - 204cos(x) + 432cos(x) + 540cos(x) +--R + +--R 3 2 +--R - 576cos(x) - 612cos(x) + 240cos(x) + 240 +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 8 7 6 +--R 20cos(x) - 25cos(x) - 534cos(x) - 283cos(x) + 1709cos(x) +--R + +--R 5 4 3 2 +--R 1533cos(x) - 1688cos(x) - 2153cos(x) + 255cos(x) + 940cos(x) + 250 +--R * +--R 2 +--R sin(x) +--R + +--R 8 7 6 5 4 +--R - 6cos(x) + 12cos(x) + 30cos(x) - 48cos(x) - 66cos(x) +--R + +--R 3 2 +--R 60cos(x) + 66cos(x) - 24cos(x) - 24 +--R * +--R 2 +--R cot(x) +--R + +--R 8 7 6 5 4 +--R - 3cos(x) + 6cos(x) + 15cos(x) - 24cos(x) - 33cos(x) +--R + +--R 3 2 +--R 30cos(x) + 33cos(x) - 12cos(x) - 12 +--R * +--R csc(x) +--R + +--R 8 7 6 5 4 +--R 12cos(x) - 24cos(x) - 60cos(x) + 96cos(x) + 132cos(x) +--R + +--R 3 2 +--R - 120cos(x) - 132cos(x) + 48cos(x) + 48 +--R * +--R 2 +--R cot(x) +--R + +--R 10 9 8 7 6 +--R 24cos(x) + 15cos(x) - 340cos(x) - 253cos(x) + 1056cos(x) +--R + +--R 5 4 3 2 +--R 897cos(x) - 1164cos(x) - 1119cos(x) + 376cos(x) + 460cos(x) + 48 +--R * +--R sin(x) +--R + +--R 9 8 7 6 5 4 +--R 21cos(x) - 42cos(x) - 105cos(x) + 168cos(x) + 231cos(x) - 210cos(x) +--R + +--R 3 2 +--R - 231cos(x) + 84cos(x) + 84cos(x) +--R / +--R 2 6 2 5 2 4 2 3 2 2 +--R 6a cos(x) + 24a cos(x) + 12a cos(x) - 48a cos(x) - 42a cos(x) +--R + +--R 2 2 +--R 24a cos(x) + 24a +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 2 6 2 5 2 4 +--R - 12a cos(x) + 6a cos(x) + 144a cos(x) + 108a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 252a cos(x) - 234a cos(x) + 120a cos(x) + 120a +--R * +--R 5 +--R sin(x) +--R + +--R 2 8 2 7 2 6 2 5 2 4 +--R 6a cos(x) - 48a cos(x) - 48a cos(x) + 336a cos(x) + 318a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 528a cos(x) - 516a cos(x) + 240a cos(x) + 240a +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 2 7 2 6 2 5 +--R 18a cos(x) - 72a cos(x) - 120a cos(x) + 384a cos(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R 426a cos(x) - 552a cos(x) - 564a cos(x) + 240a cos(x) + 240a +--R * +--R 3 +--R sin(x) +--R + +--R 2 8 2 7 2 6 2 5 +--R 18a cos(x) - 48a cos(x) - 102a cos(x) + 216a cos(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R 270a cos(x) - 288a cos(x) - 306a cos(x) + 120a cos(x) + 120a +--R * +--R 2 +--R sin(x) +--R + +--R 2 8 2 7 2 6 2 5 2 4 +--R 6a cos(x) - 12a cos(x) - 30a cos(x) + 48a cos(x) + 66a cos(x) +--R + +--R 2 3 2 2 2 2 +--R - 60a cos(x) - 66a cos(x) + 24a cos(x) + 24a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 517 + +--S 518 of 586 +t0589:= tan(3*x)/(1+cos(3*x))^2 +--R +--R +--R tan(3x) +--R (503) ----------------------- +--R 2 +--R cos(3x) + 2cos(3x) + 1 +--R Type: Expression(Integer) +--E 518 + +--S 519 of 586 +r0589:= -1/(3+3*cos(3*x))+1/3*log(1+sec(3*x)) +--R +--R +--R (cos(3x) + 1)log(sec(3x) + 1) - 1 +--R (504) --------------------------------- +--R 3cos(3x) + 3 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 586 +a0589:= integrate(t0589,x) +--R +--R +--R 2cos(3x) +--R (- 2cos(3x) - 2)log(- -----------) + cos(3x) - 1 +--R cos(3x) + 1 +--R (505) ------------------------------------------------ +--R 6cos(3x) + 6 +--R Type: Union(Expression(Integer),...) +--E 520 + +--S 521 of 586 +m0589:= a0589-r0589 +--R +--R +--R 2cos(3x) +--R - 2log(sec(3x) + 1) - 2log(- -----------) + 1 +--R cos(3x) + 1 +--R (506) --------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 586 +d0589:= D(m0589,x) +--R +--R +--R 2 +--R (- cos(3x) - cos(3x))sec(3x)tan(3x) + (sec(3x) + 1)sin(3x) +--R (507) ----------------------------------------------------------- +--R 2 2 +--R (cos(3x) + cos(3x))sec(3x) + cos(3x) + cos(3x) +--R Type: Expression(Integer) +--E 522 + +--S 523 of 586 +t0590:= cos(x)^2/(a+b*sin(x)^2) +--R +--R +--R 2 +--R cos(x) +--R (508) ------------- +--R 2 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 523 + +--S 524 of 586 +r0590:= -x/b+(a+b)^(1/2)*atan((a+b)^(1/2)*tan(x)/a^(1/2))/a^(1/2)/b +--R +--R +--R +-----+ +--R +-----+ tan(x)\|b + a +-+ +--R \|b + a atan(--------------) - x\|a +--R +-+ +--R \|a +--R (509) ------------------------------------ +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 524 + +--S 525 of 586 +a0590:= integrate(t0590,x) +--R +--R +--R (510) +--R +-------+ +--R |- b - a 2 +--R +-------+ 2a cos(x)sin(x) |------- + (- b - 2a)cos(x) + b + a +--R |- b - a \| a +--R |------- log(-----------------------------------------------------) - 2x +--R \| a 2 +--R b cos(x) - b - a +--R [-------------------------------------------------------------------------, +--R 2b +--R +-----+ +--R |b + a +--R +-----+ sin(x) |----- +--R |b + a \| a +--R |----- atan(--------------) - x +--R \| a cos(x) +--R --------------------------------] +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 525 + +--S 526 of 586 +m0590a:= a0590.1-r0590 +--R +--R +--R (511) +--R +-------+ +--R |- b - a 2 +--R +-------+ 2a cos(x)sin(x) |------- + (- b - 2a)cos(x) + b + a +--R |- b - a +-+ \| a +--R |------- \|a log(-----------------------------------------------------) +--R \| a 2 +--R b cos(x) - b - a +--R + +--R +-----+ +--R +-----+ tan(x)\|b + a +--R - 2\|b + a atan(--------------) +--R +-+ +--R \|a +--R / +--R +-+ +--R 2b\|a +--R Type: Expression(Integer) +--E 526 + +--S 527 of 586 +d0590a:= D(m0590a,x) +--R +--R +--R (512) +--R 2 2 3 2 +--R (- 2a b - 2a b)cos(x) sin(x)tan(x) +--R + +--R 2 2 3 2 2 +--R ((- 2a b - 2a b)cos(x) + (2a b + 2a b)cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 3 2 2 2 3 2 2 3 2 +--R ((- b - 2a b - a b)cos(x) - b - 3a b - 3a b - a )sin(x) +--R + +--R 2 2 4 3 2 2 3 2 3 2 +--R (a b + a b)cos(x) + (- b - 3a b - 3a b - a )cos(x) + b + 3a b +--R + +--R 2 3 +--R 3a b + a +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 2 2 2 3 2 +--R ((- a b - a b)cos(x) - a b - 2a b - a )sin(x) +--R + +--R 3 2 2 4 3 2 2 3 2 3 +--R (b + 2a b + a b)cos(x) + (- 2b - 5a b - 4a b - a )cos(x) + b +--R + +--R 2 2 3 +--R 3a b + 3a b + a +--R / +--R 3 2 2 3 3 2 2 3 +--R ((2a b + 2a b )cos(x) + (- 2a b - 4a b - 2a b)cos(x))sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 2 2 3 +--R (2a b cos(x) + (- 2a b - 2a b)cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 4 3 2 2 4 4 3 2 2 3 2 +--R (- b - 3a b - 2a b )cos(x) + (2b + 6a b + 6a b + 2a b)cos(x) +--R + +--R 4 3 2 2 3 +--R - b - 3a b - 3a b - a b +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 4 3 2 2 3 2 3 2 2 +--R (- a b - 2a b )cos(x) + (2a b + 4a b + 2a b)cos(x) - a b - 2a b +--R + +--R 3 +--R - a b +--R Type: Expression(Integer) +--E 527 + +--S 528 of 586 +m0590b:= a0590.2-r0590 +--R +--R +--R +-----+ +--R |b + a +--R +-----+ +-----+ sin(x) |----- +--R +-----+ tan(x)\|b + a +-+ |b + a \| a +--R - \|b + a atan(--------------) + \|a |----- atan(--------------) +--R +-+ \| a cos(x) +--R \|a +--R (513) ----------------------------------------------------------------- +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 528 + +--S 529 of 586 +d0590b:= D(m0590b,x) +--R +--R +--R (514) +--R 2 2 2 +--R (b + a)cos(x) tan(x) + (- b - a)sin(x) +--R / +--R 2 2 2 2 2 2 2 2 +--R ((b + 2a b + a )sin(x) + (a b + a )cos(x) )tan(x) + (a b + a )sin(x) +--R + +--R 2 2 +--R a cos(x) +--R Type: Expression(Integer) +--E 529 + +--S 530 of 586 +t0591:= cos(x)^3/(a+b*sin(x)^2) +--R +--R +--R 3 +--R cos(x) +--R (515) ------------- +--R 2 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 530 + +--S 531 of 586 +r0591:= (a+b)*atan(b^(1/2)*sin(x)/a^(1/2))/a^(1/2)/b^(3/2)-sin(x)/b +--R +--R +--R +-+ +--R sin(x)\|b +-+ +-+ +--R (b + a)atan(----------) - sin(x)\|a \|b +--R +-+ +--R \|a +--R (516) ---------------------------------------- +--R +-+ +-+ +--R b\|a \|b +--R Type: Expression(Integer) +--E 531 + +--S 532 of 586 +a0591:= integrate(t0591,x) +--R +--R +--R (517) +--R 2 +-----+ +--R (- b cos(x) + b - a)\|- a b + 2a b sin(x) +-----+ +--R (b + a)log(-------------------------------------------) - 2sin(x)\|- a b +--R 2 +--R b cos(x) - b - a +--R [-------------------------------------------------------------------------, +--R +-----+ +--R 2b\|- a b +--R +--R +---+ +--R sin(x)\|a b +--R (- b - a)atan(--------------) +--R 2b cos(x) + 2b +--R + +--R (2b cos(x) + 2b + a)sin(x) +---+ +--R (b + a)atan(-----------------------------) - sin(x)\|a b +--R 2 +---+ +--R (cos(x) + 2cos(x) + 1)\|a b +--R / +--R +---+ +--R b\|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 532 + +--S 533 of 586 +m0591a:= a0591.1-r0591 +--R +--R +--R (518) +--R 2 +-----+ +--R +-+ +-+ (- b cos(x) + b - a)\|- a b + 2a b sin(x) +--R (b + a)\|a \|b log(-------------------------------------------) +--R 2 +--R b cos(x) - b - a +--R + +--R +-+ +--R +-----+ sin(x)\|b +--R (- 2b - 2a)\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 533 + +--S 534 of 586 +d0591a:= D(m0591a,x) +--R +--R +--R (519) +--R 2 4 +--R (2b + 2a b)cos(x)sin(x) +--R + +--R 2 3 2 2 2 2 5 +--R ((b + a b)cos(x) + (- b + a )cos(x))sin(x) + (- b - a b)cos(x) +--R + +--R 2 2 3 2 2 +--R (2b + 3a b + a )cos(x) + (- b - 2a b - a )cos(x) +--R * +--R +-----+ +--R \|- a b +--R + +--R 2 2 3 +--R (2a b + 2a b)cos(x)sin(x) +--R + +--R 2 2 3 2 2 +--R ((2a b + 2a b)cos(x) + (- 2a b - 2a b)cos(x))sin(x) +--R / +--R 3 4 3 2 3 2 2 2 4 +--R (b cos(x) - 2b cos(x) + b - a b)sin(x) + a b cos(x) +--R + +--R 2 2 2 3 +--R - 2a b cos(x) + a b - a +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 2 3 2 2 3 +--R (- 2a b cos(x) + 2a b + 2a b )sin(x) +--R + +--R 2 2 2 2 2 3 +--R (- 2a b cos(x) + 2a b + 2a b)sin(x) +--R Type: Expression(Integer) +--E 534 + +--S 535 of 586 +m0591b:= a0591.2-r0591 +--R +--R +--R (520) +--R +---+ +-+ +--R +-+ +-+ sin(x)\|a b +---+ sin(x)\|b +--R (- b - a)\|a \|b atan(--------------) + (- b - a)\|a b atan(----------) +--R 2b cos(x) + 2b +-+ +--R \|a +--R + +--R +-+ +-+ (2b cos(x) + 2b + a)sin(x) +--R (b + a)\|a \|b atan(-----------------------------) +--R 2 +---+ +--R (cos(x) + 2cos(x) + 1)\|a b +--R / +--R +-+ +-+ +---+ +--R b\|a \|b \|a b +--R Type: Expression(Integer) +--E 535 + +--S 536 of 586 +d0591b:= D(m0591b,x) +--R +--R +--R (521) +--R 4 3 2 2 2 +--R (- 8b - 6a b + 2a b )cos(x) +--R + +--R 4 3 2 2 3 4 3 2 2 +--R (- 16b - 20a b - 2a b + 2a b)cos(x) - 8b - 14a b - 6a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 3 2 2 3 3 +--R (8b + 2a b - 5a b + a b)cos(x) +--R + +--R 4 3 2 2 3 2 +--R (24b + 10a b - 16a b - 2a b)cos(x) +--R + +--R 4 3 2 2 3 4 4 3 2 2 3 +--R (24b + 14a b - 19a b - 8a b + a )cos(x) + 8b + 6a b - 8a b - 6a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 4 3 2 2 3 5 +--R (8b + 6a b - 2a b )cos(x) + (24b + 18a b - 7a b - a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (16b - 4a b - 24a b - 4a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 16b - 52a b - 48a b - 11a b + a )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 24b - 42a b - 28a b - 10a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 2 2 3 +--R (- 8b + 2a b + 15a b + 4a b - a )cos(x) + 8a b + 14a b + 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 3 2 2 3 6 +--R (- 4a b - 4a b )cos(x) + (- 16a b - 18a b - 2a b)cos(x) +--R + +--R 3 2 2 3 5 2 2 3 4 +--R (- 20a b - 26a b - 6a b)cos(x) + (- 4a b - 4a b)cos(x) +--R + +--R 3 2 2 3 3 3 2 2 3 2 +--R (20a b + 24a b + 4a b)cos(x) + (16a b + 22a b + 6a b)cos(x) +--R + +--R 3 2 2 3 +--R (4a b + 6a b + 2a b)cos(x) +--R / +--R 4 2 4 2 3 4 2 3 3 2 6 +--R (4a b cos(x) + (8a b + 4a b )cos(x) + 4a b + 4a b + a b )sin(x) +--R + +--R 5 2 3 4 5 4 2 3 3 +--R (16b + a b )cos(x) + (64b + 16a b + 4a b )cos(x) +--R + +--R 5 4 2 3 2 +--R (96b + 48a b + 14a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 4 2 3 +--R (64b + 48a b + 20a b + 4a b )cos(x) + 16b + 16a b + 9a b +--R + +--R 3 2 4 +--R 4a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 6 4 5 4 3 2 4 +--R 4a b cos(x) + 24a b cos(x) + (76a b + a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (144a b + 16a b + 4a b )cos(x) +--R + +--R 4 2 3 3 2 2 4 2 3 3 2 +--R (156a b + 48a b + 10a b )cos(x) + (88a b + 48a b + 12a b )cos(x) +--R + +--R 4 2 3 3 2 +--R 20a b + 16a b + 5a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 6 2 3 5 2 3 4 2 3 3 +--R 4a b cos(x) + 24a b cos(x) + 60a b cos(x) + 80a b cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R 60a b cos(x) + 24a b cos(x) + 4a b +--R Type: Expression(Integer) +--E 536 + +--S 537 of 586 +t0592:= cos(x)^4/(a+b*sin(x)^2) +--R +--R +--R 4 +--R cos(x) +--R (522) ------------- +--R 2 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 537 + +--S 538 of 586 +r0592:= -a*x/b^2-3/2*x/b+(a+b)^(3/2)*atan((a+b)^(1/2)*tan(x)/a^(1/2))/_ + a^(1/2)/b^2-1/2*cos(x)*sin(x)/b +--R +--R +--R (523) +--R +-----+ +--R +-----+ tan(x)\|b + a +-+ +--R (2b + 2a)\|b + a atan(--------------) + (- b cos(x)sin(x) + (- 3b - 2a)x)\|a +--R +-+ +--R \|a +--R ----------------------------------------------------------------------------- +--R 2 +-+ +--R 2b \|a +--R Type: Expression(Integer) +--E 538 + +--S 539 of 586 +a0592:= integrate(t0592,x) +--R +--R +--R (524) +--R [ +--R +-------+ +--R |- b - a +--R (b + a) |------- +--R \| a +--R * +--R +-------+ +--R |- b - a 2 +--R 2a cos(x)sin(x) |------- + (- b - 2a)cos(x) + b + a +--R \| a +--R log(-----------------------------------------------------) +--R 2 +--R b cos(x) - b - a +--R + +--R - b cos(x)sin(x) + (- 3b - 2a)x +--R / +--R 2 +--R 2b +--R , +--R +-----+ +--R |b + a +--R +-----+ sin(x) |----- +--R |b + a \| a +--R (2b + 2a) |----- atan(--------------) - b cos(x)sin(x) + (- 3b - 2a)x +--R \| a cos(x) +--R ---------------------------------------------------------------------] +--R 2 +--R 2b +--R Type: Union(List(Expression(Integer)),...) +--E 539 + +--S 540 of 586 +m0592a:= a0592.1-r0592 +--R +--R +--R (525) +--R +-------+ +--R |- b - a +-+ +--R (b + a) |------- \|a +--R \| a +--R * +--R +-------+ +--R |- b - a 2 +--R 2a cos(x)sin(x) |------- + (- b - 2a)cos(x) + b + a +--R \| a +--R log(-----------------------------------------------------) +--R 2 +--R b cos(x) - b - a +--R + +--R +-----+ +--R +-----+ tan(x)\|b + a +--R (- 2b - 2a)\|b + a atan(--------------) +--R +-+ +--R \|a +--R / +--R 2 +-+ +--R 2b \|a +--R Type: Expression(Integer) +--E 540 + +--S 541 of 586 +d0592a:= D(m0592a,x) +--R +--R +--R (526) +--R 3 2 2 3 3 2 +--R (- 2a b - 4a b - 2a b)cos(x) sin(x)tan(x) +--R + +--R 3 2 2 3 3 3 2 2 3 +--R ((- 2a b - 4a b - 2a b)cos(x) + (2a b + 4a b + 2a b)cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (- b - 3a b - 3a b - a b)cos(x) - b - 4a b - 6a b - 4a b +--R + +--R 4 +--R - a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (a b + 2a b + a b)cos(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 +--R (- b - 4a b - 6a b - 4a b - a )cos(x) + b + 4a b + 6a b + 4a b +--R + +--R 4 +--R a +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 2 3 2 2 3 4 2 +--R ((- a b - 2a b - a b)cos(x) - a b - 3a b - 3a b - a )sin(x) +--R + +--R 4 3 2 2 3 4 +--R (b + 3a b + 3a b + a b)cos(x) +--R + +--R 4 3 2 2 3 4 2 4 3 2 2 3 4 +--R (- 2b - 7a b - 9a b - 5a b - a )cos(x) + b + 4a b + 6a b + 4a b + a +--R / +--R 4 2 3 3 4 2 3 3 2 +--R ((2a b + 2a b )cos(x) + (- 2a b - 4a b - 2a b )cos(x))sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 3 2 3 3 2 +--R (2a b cos(x) + (- 2a b - 2a b )cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 5 4 2 3 4 5 4 2 3 3 2 2 +--R (- b - 3a b - 2a b )cos(x) + (2b + 6a b + 6a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 +--R - b - 3a b - 3a b - a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 4 4 2 3 3 2 2 4 2 3 +--R (- a b - 2a b )cos(x) + (2a b + 4a b + 2a b )cos(x) - a b - 2a b +--R + +--R 3 2 +--R - a b +--R Type: Expression(Integer) +--E 541 + +--S 542 of 586 +m0592b:= a0592.2-r0592 +--R +--R +--R (527) +--R +-----+ +--R +-----+ tan(x)\|b + a +--R (- b - a)\|b + a atan(--------------) +--R +-+ +--R \|a +--R + +--R +-----+ +--R |b + a +--R +-----+ sin(x) |----- +--R +-+ |b + a \| a +--R (b + a)\|a |----- atan(--------------) +--R \| a cos(x) +--R / +--R 2 +-+ +--R b \|a +--R Type: Expression(Integer) +--E 542 + +--S 543 of 586 +d0592b:= D(m0592b,x) +--R +--R +--R (528) +--R 2 2 2 2 2 2 2 +--R (b + 2a b + a )cos(x) tan(x) + (- b - 2a b - a )sin(x) +--R / +--R 3 2 2 2 2 2 2 2 +--R ((b + 2a b + a b)sin(x) + (a b + a b)cos(x) )tan(x) +--R + +--R 2 2 2 2 2 +--R (a b + a b)sin(x) + a b cos(x) +--R Type: Expression(Integer) +--E 543 + +--S 544 of 586 +t0593:= cos(x)^5/(a+b*sin(x)^2) +--R +--R +--R 5 +--R cos(x) +--R (529) ------------- +--R 2 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 544 + +--S 545 of 586 +r0593:= (a+b)^2*atan(b^(1/2)*sin(x)/a^(1/2))/a^(1/2)/b^(5/2)-_ + a*sin(x)/b^2-2*sin(x)/b+1/3*sin(x)^3/b +--R +--R +--R (530) +--R +-+ +--R 2 2 sin(x)\|b 3 +-+ +-+ +--R (3b + 6a b + 3a )atan(----------) + (b sin(x) + (- 6b - 3a)sin(x))\|a \|b +--R +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R 2 +-+ +-+ +--R 3b \|a \|b +--R Type: Expression(Integer) +--E 545 + +--S 546 of 586 +a0593:= integrate(t0593,x) +--R +--R +--R (531) +--R [ +--R 2 +-----+ +--R 2 2 (- b cos(x) + b - a)\|- a b + 2a b sin(x) +--R (3b + 6a b + 3a )log(-------------------------------------------) +--R 2 +--R b cos(x) - b - a +--R + +--R 2 +-----+ +--R (- 2b cos(x) - 10b - 6a)sin(x)\|- a b +--R / +--R 2 +-----+ +--R 6b \|- a b +--R , +--R +--R +---+ +--R 2 2 sin(x)\|a b +--R (- 3b - 6a b - 3a )atan(--------------) +--R 2b cos(x) + 2b +--R + +--R 2 2 (2b cos(x) + 2b + a)sin(x) +--R (3b + 6a b + 3a )atan(-----------------------------) +--R 2 +---+ +--R (cos(x) + 2cos(x) + 1)\|a b +--R + +--R 2 +---+ +--R (- b cos(x) - 5b - 3a)sin(x)\|a b +--R / +--R 2 +---+ +--R 3b \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 546 + +--S 547 of 586 +m0593a:= a0593.1-r0593 +--R +--R +--R (532) +--R 2 2 +-+ +-+ +--R (3b + 6a b + 3a )\|a \|b +--R * +--R 2 +-----+ +--R (- b cos(x) + b - a)\|- a b + 2a b sin(x) +--R log(-------------------------------------------) +--R 2 +--R b cos(x) - b - a +--R + +--R +-+ +--R 2 2 +-----+ sin(x)\|b +--R (- 6b - 12a b - 6a )\|- a b atan(----------) +--R +-+ +--R \|a +--R + +--R 3 2 +-----+ +-+ +-+ +--R (- 2b sin(x) + (- 2b cos(x) + 2b)sin(x))\|- a b \|a \|b +--R / +--R 2 +-----+ +-+ +-+ +--R 6b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 547 + +--S 548 of 586 +d0593a:= D(m0593a,x) +--R +--R +--R (533) +--R 3 5 3 3 3 2 2 4 +--R (- b cos(x) + 2b cos(x) + (5b + 12a b + 7a b)cos(x))sin(x) +--R + +--R 3 7 3 2 5 2 2 3 +--R - b cos(x) + (3b - a b )cos(x) + (8a b + 4a b)cos(x) +--R + +--R 3 2 2 3 +--R (- 2b - 4a b + 2a b + 4a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 3 2 2 5 +--R - a b cos(x) + (- 3b - 3a b - 3a b)cos(x) +--R + +--R 3 2 2 3 3 +--R (6b + 12a b + 12a b + 4a )cos(x) +--R + +--R 3 2 2 3 +--R (- 3b - 8a b - 9a b - 4a )cos(x) +--R * +--R +-----+ +--R \|- a b +--R + +--R 3 3 3 2 2 5 +--R (2a b cos(x) + (- 2a b - 2a b )cos(x))sin(x) +--R + +--R 3 5 3 3 3 2 2 3 3 +--R (2a b cos(x) - 4a b cos(x) + (8a b + 12a b + 4a b)cos(x))sin(x) +--R + +--R 2 2 5 3 2 2 3 3 +--R 2a b cos(x) + (6a b + 8a b + 4a b)cos(x) +--R + +--R 3 2 2 3 +--R (- 6a b - 10a b - 4a b)cos(x) +--R * +--R sin(x) +--R / +--R 4 4 4 2 4 2 2 2 3 4 +--R (3b cos(x) - 6b cos(x) + 3b - 3a b )sin(x) + 3a b cos(x) +--R + +--R 3 2 3 3 +--R - 6a b cos(x) + 3a b - 3a b +--R * +--R +-----+ +--R \|- a b +--R + +--R 4 2 4 2 3 3 +--R (- 6a b cos(x) + 6a b + 6a b )sin(x) +--R + +--R 2 3 2 2 3 3 2 +--R (- 6a b cos(x) + 6a b + 6a b )sin(x) +--R Type: Expression(Integer) +--E 548 + +--S 549 of 586 +m0593b:= a0593.2-r0593 +--R +--R +--R (534) +--R +---+ +--R 2 2 +-+ +-+ sin(x)\|a b +--R (- 3b - 6a b - 3a )\|a \|b atan(--------------) +--R 2b cos(x) + 2b +--R + +--R +-+ +--R 2 2 +---+ sin(x)\|b +--R (- 3b - 6a b - 3a )\|a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 2 +-+ +-+ (2b cos(x) + 2b + a)sin(x) +--R (3b + 6a b + 3a )\|a \|b atan(-----------------------------) +--R 2 +---+ +--R (cos(x) + 2cos(x) + 1)\|a b +--R + +--R 3 2 +-+ +-+ +---+ +--R (- b sin(x) + (- b cos(x) + b)sin(x))\|a \|b \|a b +--R / +--R 2 +-+ +-+ +---+ +--R 3b \|a \|b \|a b +--R Type: Expression(Integer) +--E 549 + +--S 550 of 586 +d0593b:= D(m0593b,x) +--R +--R +--R (535) +--R 4 3 4 2 3 2 +--R - 4a b cos(x) + (- 8a b - 4a b )cos(x) +--R + +--R 4 2 3 3 2 +--R (- 4a b - 4a b - a b )cos(x) +--R * +--R 8 +--R sin(x) +--R + +--R 5 4 2 3 5 5 4 2 3 4 +--R (- 16b - 4a b - a b )cos(x) + (- 64b - 24a b - 8a b )cos(x) +--R + +--R 5 4 2 3 3 2 3 +--R (- 96b - 48a b - 18a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 2 +--R (- 88b - 82a b - 28a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 64b - 120a b - 71a b - 3a b + 5a b)cos(x) - 24b - 66a b +--R + +--R 2 3 3 2 +--R - 60a b - 18a b +--R * +--R 6 +--R sin(x) +--R + +--R 5 4 2 3 7 5 4 2 3 6 +--R (- 16b - 4a b - a b )cos(x) + (- 64b - 40a b - 4a b )cos(x) +--R + +--R 5 4 2 3 3 2 5 +--R (- 80b - 124a b - 13a b - a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (- 176a b - 32a b - 8a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (104b - 94a b - 52a b - 26a b + 2a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (136b + 62a b - 46a b - 62a b - 6a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (88b + 110a b - 22a b - 82a b - 20a b + 3a )cos(x) + 24b +--R + +--R 4 2 3 3 2 4 +--R 42a b - 6a b - 42a b - 18a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 9 4 8 4 2 3 3 2 7 +--R - 4a b cos(x) - 24a b cos(x) + (- 72a b - 4a b - a b )cos(x) +--R + +--R 5 4 2 3 3 2 6 +--R (24b - 78a b - 28a b - 10a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (72b + 46a b - 75a b - 33a b - 3a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (48b + 92a b - 196a b - 92a b - 12a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 3 +--R (- 48b - 68a b - 328a b - 172a b - 30a b + 3a )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 72b - 110a b - 186a b - 102a b - 30a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 4 +--R (- 24b + 2a b + 63a b + 62a b + 9a b - 3a )cos(x) + 24a b +--R + +--R 2 3 3 2 4 +--R 66a b + 60a b + 18a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 9 2 3 8 4 2 3 3 2 7 +--R - 4a b cos(x) - 24a b cos(x) + (- 12a b - 80a b - 12a b )cos(x) +--R + +--R 4 2 3 3 2 4 6 +--R (- 48a b - 158a b - 60a b - 6a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- 60a b - 138a b - 96a b - 18a b)cos(x) +--R + +--R 2 3 3 2 4 4 +--R (44a b - 24a b - 12a b)cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (60a b + 188a b + 84a b + 12a b)cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (48a b + 138a b + 84a b + 18a b)cos(x) +--R + +--R 4 2 3 3 2 4 +--R (12a b + 34a b + 24a b + 6a b)cos(x) +--R / +--R 5 2 5 2 4 5 2 4 3 3 +--R (12a b cos(x) + (24a b + 12a b )cos(x) + 12a b + 12a b + 3a b ) +--R * +--R 6 +--R sin(x) +--R + +--R 6 2 4 4 6 5 2 4 3 +--R (48b + 3a b )cos(x) + (192b + 48a b + 12a b )cos(x) +--R + +--R 6 5 2 4 2 +--R (288b + 144a b + 42a b )cos(x) +--R + +--R 6 5 2 4 3 3 6 5 2 4 +--R (192b + 144a b + 60a b + 12a b )cos(x) + 48b + 48a b + 27a b +--R + +--R 3 3 4 2 +--R 12a b + 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 6 5 5 5 3 3 4 +--R 12a b cos(x) + 72a b cos(x) + (228a b + 3a b )cos(x) +--R + +--R 5 2 4 3 3 3 +--R (432a b + 48a b + 12a b )cos(x) +--R + +--R 5 2 4 3 3 2 +--R (468a b + 144a b + 30a b )cos(x) +--R + +--R 5 2 4 3 3 5 2 4 3 3 +--R (264a b + 144a b + 36a b )cos(x) + 60a b + 48a b + 15a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 6 2 4 5 2 4 4 2 4 3 +--R 12a b cos(x) + 72a b cos(x) + 180a b cos(x) + 240a b cos(x) +--R + +--R 2 4 2 2 4 2 4 +--R 180a b cos(x) + 72a b cos(x) + 12a b +--R Type: Expression(Integer) +--E 550 + +--S 551 of 586 +t0594:= cos(x)^6/(a+b*sin(x)^2) +--R +--R +--R 6 +--R cos(x) +--R (536) ------------- +--R 2 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 551 + +--S 552 of 586 +r0594:= -1/2*a*x/b^2-7/8*x/b-(a+b)^2*x/b^3+(a+b)^(5/2)*atan((a+b)^(1/2)*_ + tan(x)/a^(1/2))/a^(1/2)/b^3-1/2*a*cos(x)*sin(x)/b^2-_ + 7/8*cos(x)*sin(x)/b-1/4*cos(x)^3*sin(x)/b +--R +--R +--R (537) +--R +-----+ +--R 2 2 +-----+ tan(x)\|b + a +--R (8b + 16a b + 8a )\|b + a atan(--------------) +--R +-+ +--R \|a +--R + +--R 2 3 2 2 2 +-+ +--R ((- 2b cos(x) + (- 7b - 4a b)cos(x))sin(x) + (- 15b - 20a b - 8a )x)\|a +--R / +--R 3 +-+ +--R 8b \|a +--R Type: Expression(Integer) +--E 552 + +--S 553 of 586 +a0594:= integrate(t0594,x) +--R +--R +--R (538) +--R [ +--R +-------+ +--R 2 2 |- b - a +--R (4b + 8a b + 4a ) |------- +--R \| a +--R * +--R +-------+ +--R |- b - a 2 +--R 2a cos(x)sin(x) |------- + (- b - 2a)cos(x) + b + a +--R \| a +--R log(-----------------------------------------------------) +--R 2 +--R b cos(x) - b - a +--R + +--R 2 3 2 2 2 +--R (- 2b cos(x) + (- 7b - 4a b)cos(x))sin(x) + (- 15b - 20a b - 8a )x +--R / +--R 3 +--R 8b +--R , +--R +--R +-----+ +--R |b + a +--R +-----+ sin(x) |----- +--R 2 2 |b + a \| a +--R (8b + 16a b + 8a ) |----- atan(--------------) +--R \| a cos(x) +--R + +--R 2 3 2 2 2 +--R (- 2b cos(x) + (- 7b - 4a b)cos(x))sin(x) + (- 15b - 20a b - 8a )x +--R / +--R 3 +--R 8b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 553 + +--S 554 of 586 +m0594a:= a0594.1-r0594 +--R +--R +--R (539) +--R +-------+ +--R 2 2 |- b - a +-+ +--R (b + 2a b + a ) |------- \|a +--R \| a +--R * +--R +-------+ +--R |- b - a 2 +--R 2a cos(x)sin(x) |------- + (- b - 2a)cos(x) + b + a +--R \| a +--R log(-----------------------------------------------------) +--R 2 +--R b cos(x) - b - a +--R + +--R +-----+ +--R 2 2 +-----+ tan(x)\|b + a +--R (- 2b - 4a b - 2a )\|b + a atan(--------------) +--R +-+ +--R \|a +--R / +--R 3 +-+ +--R 2b \|a +--R Type: Expression(Integer) +--E 554 + +--S 555 of 586 +d0594a:= D(m0594a,x) +--R +--R +--R (540) +--R 4 2 3 3 2 4 3 2 +--R (- 2a b - 6a b - 6a b - 2a b)cos(x) sin(x)tan(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 2a b - 6a b - 6a b - 2a b)cos(x) +--R + +--R 4 2 3 3 2 4 +--R (2a b + 6a b + 6a b + 2a b)cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 5 4 2 3 3 2 4 2 5 4 2 3 +--R (- b - 4a b - 6a b - 4a b - a b)cos(x) - b - 5a b - 10a b +--R + +--R 3 2 4 5 +--R - 10a b - 5a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 4 4 +--R (a b + 3a b + 3a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- b - 5a b - 10a b - 10a b - 5a b - a )cos(x) + b + 5a b +--R + +--R 2 3 3 2 4 5 +--R 10a b + 10a b + 5a b + a +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 2 4 2 3 3 2 4 +--R (- a b - 3a b - 3a b - a b)cos(x) - a b - 4a b - 6a b - 4a b +--R + +--R 5 +--R - a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (b + 4a b + 6a b + 4a b + a b)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 2 5 4 +--R (- 2b - 9a b - 16a b - 14a b - 6a b - a )cos(x) + b + 5a b +--R + +--R 2 3 3 2 4 5 +--R 10a b + 10a b + 5a b + a +--R / +--R 5 2 4 3 5 2 4 3 3 +--R ((2a b + 2a b )cos(x) + (- 2a b - 4a b - 2a b )cos(x))sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 4 3 2 4 3 3 +--R (2a b cos(x) + (- 2a b - 2a b )cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 6 5 2 4 4 6 5 2 4 3 3 2 +--R (- b - 3a b - 2a b )cos(x) + (2b + 6a b + 6a b + 2a b )cos(x) +--R + +--R 6 5 2 4 3 3 +--R - b - 3a b - 3a b - a b +--R * +--R 2 +--R tan(x) +--R + +--R 5 2 4 4 5 2 4 3 3 2 5 2 4 +--R (- a b - 2a b )cos(x) + (2a b + 4a b + 2a b )cos(x) - a b - 2a b +--R + +--R 3 3 +--R - a b +--R Type: Expression(Integer) +--E 555 + +--S 556 of 586 +m0594b:= a0594.2-r0594 +--R +--R +--R (541) +--R +-----+ +--R 2 2 +-----+ tan(x)\|b + a +--R (- b - 2a b - a )\|b + a atan(--------------) +--R +-+ +--R \|a +--R + +--R +-----+ +--R |b + a +--R +-----+ sin(x) |----- +--R 2 2 +-+ |b + a \| a +--R (b + 2a b + a )\|a |----- atan(--------------) +--R \| a cos(x) +--R / +--R 3 +-+ +--R b \|a +--R Type: Expression(Integer) +--E 556 + +--S 557 of 586 +d0594b:= D(m0594b,x) +--R +--R +--R (542) +--R 3 2 2 3 2 2 3 2 2 3 2 +--R (b + 3a b + 3a b + a )cos(x) tan(x) + (- b - 3a b - 3a b - a )sin(x) +--R / +--R 4 3 2 2 2 3 2 2 2 2 +--R ((b + 2a b + a b )sin(x) + (a b + a b )cos(x) )tan(x) +--R + +--R 3 2 2 2 2 2 2 +--R (a b + a b )sin(x) + a b cos(x) +--R Type: Expression(Integer) +--E 557 + +--S 558 of 586 +t0595:= cos(x)^7/(a+b*sin(x)^2) +--R +--R +--R 7 +--R cos(x) +--R (543) ------------- +--R 2 +--R b sin(x) + a +--R Type: Expression(Integer) +--E 558 + +--S 559 of 586 +r0595:= (a+b)^3*atan(b^(1/2)*sin(x)/a^(1/2))/a^(1/2)/b^(7/2)-_ + a*sin(x)/b^2-2*sin(x)/b-(a+b)^2*sin(x)/b^3+_ + 1/3*a*sin(x)^3/b^2+sin(x)^3/b-1/5*sin(x)^5/b +--R +--R +--R (544) +--R +-+ +--R 3 2 2 3 sin(x)\|b +--R (15b + 45a b + 45a b + 15a )atan(----------) +--R +-+ +--R \|a +--R + +--R 2 5 2 3 2 2 +--R (- 3b sin(x) + (15b + 5a b)sin(x) + (- 45b - 45a b - 15a )sin(x)) +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 3 +-+ +-+ +--R 15b \|a \|b +--R Type: Expression(Integer) +--E 559 + +--S 560 of 586 +a0595:= integrate(t0595,x) +--R +--R +--R (545) +--R [ +--R 3 2 2 3 +--R (15b + 45a b + 45a b + 15a ) +--R * +--R 2 +-----+ +--R (- b cos(x) + b - a)\|- a b + 2a b sin(x) +--R log(-------------------------------------------) +--R 2 +--R b cos(x) - b - a +--R + +--R 2 4 2 2 2 2 +--R (- 6b cos(x) + (- 18b - 10a b)cos(x) - 66b - 80a b - 30a )sin(x) +--R * +--R +-----+ +--R \|- a b +--R / +--R 3 +-----+ +--R 30b \|- a b +--R , +--R +--R +---+ +--R 3 2 2 3 sin(x)\|a b +--R (- 15b - 45a b - 45a b - 15a )atan(--------------) +--R 2b cos(x) + 2b +--R + +--R 3 2 2 3 (2b cos(x) + 2b + a)sin(x) +--R (15b + 45a b + 45a b + 15a )atan(-----------------------------) +--R 2 +---+ +--R (cos(x) + 2cos(x) + 1)\|a b +--R + +--R 2 4 2 2 2 2 +---+ +--R (- 3b cos(x) + (- 9b - 5a b)cos(x) - 33b - 40a b - 15a )sin(x)\|a b +--R / +--R 3 +---+ +--R 15b \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 560 + +--S 561 of 586 +m0595a:= a0595.1-r0595 +--R +--R +--R (546) +--R 3 2 2 3 +-+ +-+ +--R (15b + 45a b + 45a b + 15a )\|a \|b +--R * +--R 2 +-----+ +--R (- b cos(x) + b - a)\|- a b + 2a b sin(x) +--R log(-------------------------------------------) +--R 2 +--R b cos(x) - b - a +--R + +--R +-+ +--R 3 2 2 3 +-----+ sin(x)\|b +--R (- 30b - 90a b - 90a b - 30a )\|- a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 5 2 3 +--R 6b sin(x) + (- 30b - 10a b)sin(x) +--R + +--R 2 4 2 2 2 +--R (- 6b cos(x) + (- 18b - 10a b)cos(x) + 24b + 10a b)sin(x) +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R / +--R 3 +-----+ +-+ +-+ +--R 30b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 561 + +--S 562 of 586 +d0595a:= D(m0595a,x) +--R +--R +--R (547) +--R 4 5 4 3 4 2 2 6 +--R (15b cos(x) - 30b cos(x) + (15b - 15a b )cos(x))sin(x) +--R + +--R 4 7 4 3 5 +--R 12b cos(x) + (- 51b + 10a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (66b - 20a b - 12a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (3b + 100a b + 117a b + 20a b)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 4 9 4 3 7 +--R - 3b cos(x) + (- 3b + 7a b )cos(x) +--R + +--R 4 3 2 2 5 +--R (27b - 36a b - 2a b )cos(x) +--R + +--R 4 3 2 2 3 3 +--R (- 18b + 96a b + 64a b + 8a b)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 3b - 52a b - 17a b + 52a b + 20a )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 9 3 2 2 7 +--R - 3a b cos(x) + (- 3a b - 5a b )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- 15b - 18a b - 30a b - 12a b)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (30b + 72a b + 120a b + 84a b + 20a )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 15b - 48a b - 85a b - 72a b - 20a )cos(x) +--R * +--R +-----+ +--R \|- a b +--R + +--R 4 3 4 2 3 7 +--R (- 30a b cos(x) + (30a b + 30a b )cos(x))sin(x) +--R + +--R 4 5 4 2 3 3 +--R - 24a b cos(x) + (78a b + 4a b )cos(x) +--R + +--R 4 2 3 3 2 +--R (- 54a b - 34a b + 20a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 7 4 2 3 5 +--R 6a b cos(x) + (12a b - 20a b )cos(x) +--R + +--R 4 2 3 3 2 3 +--R (- 42a b + 40a b + 24a b )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (54a b + 70a b + 36a b + 20a b)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 7 2 3 3 2 5 +--R 6a b cos(x) + (12a b + 4a b )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (30a b + 48a b + 52a b + 20a b)cos(x) +--R + +--R 4 2 3 3 2 4 +--R (- 30a b - 66a b - 56a b - 20a b)cos(x) +--R * +--R sin(x) +--R / +--R 5 4 5 2 5 2 3 2 4 4 +--R (15b cos(x) - 30b cos(x) + 15b - 15a b )sin(x) + 15a b cos(x) +--R + +--R 4 2 4 3 2 +--R - 30a b cos(x) + 15a b - 15a b +--R * +--R +-----+ +--R \|- a b +--R + +--R 5 2 5 2 4 3 +--R (- 30a b cos(x) + 30a b + 30a b )sin(x) +--R + +--R 2 4 2 2 4 3 3 +--R (- 30a b cos(x) + 30a b + 30a b )sin(x) +--R Type: Expression(Integer) +--E 562 + +--S 563 of 586 +m0595b:= a0595.2-r0595 +--R +--R +--R (548) +--R +---+ +--R 3 2 2 3 +-+ +-+ sin(x)\|a b +--R (- 15b - 45a b - 45a b - 15a )\|a \|b atan(--------------) +--R 2b cos(x) + 2b +--R + +--R +-+ +--R 3 2 2 3 +---+ sin(x)\|b +--R (- 15b - 45a b - 45a b - 15a )\|a b atan(----------) +--R +-+ +--R \|a +--R + +--R 3 2 2 3 +-+ +-+ (2b cos(x) + 2b + a)sin(x) +--R (15b + 45a b + 45a b + 15a )\|a \|b atan(-----------------------------) +--R 2 +---+ +--R (cos(x) + 2cos(x) + 1)\|a b +--R + +--R 2 5 2 3 +--R 3b sin(x) + (- 15b - 5a b)sin(x) +--R + +--R 2 4 2 2 2 +--R (- 3b cos(x) + (- 9b - 5a b)cos(x) + 12b + 5a b)sin(x) +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R / +--R 3 +-+ +-+ +---+ +--R 15b \|a \|b \|a b +--R Type: Expression(Integer) +--E 563 + +--S 564 of 586 +d0595b:= D(m0595b,x) +--R +--R +--R (549) +--R 5 3 5 2 4 2 +--R 60a b cos(x) + (120a b + 60a b )cos(x) +--R + +--R 5 2 4 3 3 +--R (60a b + 60a b + 15a b )cos(x) +--R * +--R 10 +--R sin(x) +--R + +--R 6 5 2 4 5 6 5 2 4 4 +--R (240b + 48a b + 15a b )cos(x) + (960b + 336a b + 108a b )cos(x) +--R + +--R 6 5 2 4 3 3 3 +--R (1440b + 660a b + 238a b + 12a b )cos(x) +--R + +--R 6 5 2 4 3 3 2 +--R (960b + 504a b + 152a b + 40a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R (240b + 132a b + 7a b + 13a b + 10a b )cos(x) +--R * +--R 8 +--R sin(x) +--R + +--R 6 5 2 4 7 6 5 2 4 6 +--R (192b + 48a b + 12a b )cos(x) + (768b + 528a b + 36a b )cos(x) +--R + +--R 6 5 2 4 3 3 5 +--R (720b + 1588a b + 109a b + 7a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 +--R (- 960b + 1912a b + 216a b + 68a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 3 +--R (- 2400b + 768a b + 174a b + 99a b + 7a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (- 1848b - 530a b - 242a b - 38a b + 10a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 672b - 944a b - 885a b - 376a b - 12a b + 25a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 +--R - 120b - 450a b - 630a b - 390a b - 90a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 5 2 4 9 +--R (- 48b + 48a b - 3a b )cos(x) +--R + +--R 6 5 2 4 8 +--R (- 192b + 240a b - 12a b )cos(x) +--R + +--R 6 5 2 4 3 3 7 +--R (- 432b + 580a b - 11a b + 7a b )cos(x) +--R + +--R 6 5 2 4 3 3 6 +--R (- 768b + 472a b + 256a b + 16a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 720b - 1060a b + 715a b + 16a b - 8a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (192b - 3072a b + 332a b - 160a b - 40a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 3 +--R (1128b - 2870a b - 632a b - 566a b - 124a b + 10a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (1128b - 610a b - 476a b - 776a b - 340a b - 30a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (552b + 662a b + 211a b - 602a b - 503a b - 85a b + 15a )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 120b + 330a b + 180a b - 240a b - 300a b - 90a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 11 5 10 +--R - 12a b cos(x) - 72a b cos(x) +--R + +--R 5 2 4 3 3 9 +--R (- 264a b + 28a b - 3a b )cos(x) +--R + +--R 5 2 4 3 3 8 +--R (- 648a b + 120a b - 12a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 1104a b + 108a b - 59a b - 5a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (120b - 942a b - 306a b - 242a b - 50a b )cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (360b + 438a b - 985a b - 588a b - 180a b - 15a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (240b + 1356a b - 2072a b - 1460a b - 520a b - 60a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 240b + 432a b - 2980a b - 2450a b - 1010a b - 135a b +--R + +--R 6 +--R 15a +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 2 +--R (- 360b - 294a b - 1672a b - 1356a b - 660a b - 150a b)cos(x) +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 120b + 30a b + 349a b + 660a b + 355a b + 30a b - 15a )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R 120a b + 450a b + 630a b + 390a b + 90a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 11 2 4 10 2 4 3 3 9 +--R - 12a b cos(x) - 72a b cos(x) + (- 216a b - 20a b )cos(x) +--R + +--R 2 4 3 3 8 +--R (- 456a b - 120a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 7 +--R (- 60a b - 852a b - 460a b - 60a b )cos(x) +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 240a b - 1254a b - 1090a b - 330a b - 30a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 5 +--R (- 300a b - 822a b - 1170a b - 570a b - 90a b)cos(x) +--R + +--R 2 4 3 3 4 2 5 4 +--R (684a b + 100a b - 180a b - 60a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 3 +--R (300a b + 1644a b + 1360a b + 480a b + 60a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (240a b + 1098a b + 1110a b + 510a b + 90a b)cos(x) +--R + +--R 5 2 4 3 3 4 2 5 +--R (60a b + 258a b + 290a b + 150a b + 30a b)cos(x) +--R / +--R 6 2 6 2 5 6 2 5 3 4 +--R (60a b cos(x) + (120a b + 60a b )cos(x) + 60a b + 60a b + 15a b ) +--R * +--R 6 +--R sin(x) +--R + +--R 7 2 5 4 7 6 2 5 3 +--R (240b + 15a b )cos(x) + (960b + 240a b + 60a b )cos(x) +--R + +--R 7 6 2 5 2 +--R (1440b + 720a b + 210a b )cos(x) +--R + +--R 7 6 2 5 3 4 7 6 +--R (960b + 720a b + 300a b + 60a b )cos(x) + 240b + 240a b +--R + +--R 2 5 3 4 4 3 +--R 135a b + 60a b + 15a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 6 6 5 6 3 4 4 +--R 60a b cos(x) + 360a b cos(x) + (1140a b + 15a b )cos(x) +--R + +--R 6 2 5 3 4 3 +--R (2160a b + 240a b + 60a b )cos(x) +--R + +--R 6 2 5 3 4 2 +--R (2340a b + 720a b + 150a b )cos(x) +--R + +--R 6 2 5 3 4 6 2 5 3 4 +--R (1320a b + 720a b + 180a b )cos(x) + 300a b + 240a b + 75a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 6 2 5 5 2 5 4 2 5 3 +--R 60a b cos(x) + 360a b cos(x) + 900a b cos(x) + 1200a b cos(x) +--R + +--R 2 5 2 2 5 2 5 +--R 900a b cos(x) + 360a b cos(x) + 60a b +--R Type: Expression(Integer) +--E 564 + +--S 565 of 586 +t0596:= cos(x)^2/(a-a*sin(x)^2) +--R +--R +--R 2 +--R cos(x) +--R (550) - ------------- +--R 2 +--R a sin(x) - a +--R Type: Expression(Integer) +--E 565 + +--S 566 of 586 +r0596:= x/a +--R +--R +--R x +--R (551) - +--R a +--R Type: Fraction(Polynomial(Integer)) +--E 566 + +--S 567 of 586 +a0596:= integrate(t0596,x) +--R +--R +--R x +--R (552) - +--R a +--R Type: Union(Expression(Integer),...) +--E 567 + +--S 568 of 586 +m0596:= a0596-r0596 +--R +--R +--R (553) 0 +--R Type: Expression(Integer) +--E 568 + +--S 569 of 586 +d0596:= D(m0596,x) +--R +--R +--R (554) 0 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 586 +t0597:= cos(x)^4/(a-a*sin(x)^2) +--R +--R +--R 4 +--R cos(x) +--R (555) - ------------- +--R 2 +--R a sin(x) - a +--R Type: Expression(Integer) +--E 570 + +--S 571 of 586 +r0597:= 1/2*(x+cos(x)*sin(x))/a +--R +--R +--R cos(x)sin(x) + x +--R (556) ---------------- +--R 2a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 586 +a0597:= integrate(t0597,x) +--R +--R +--R cos(x)sin(x) + x +--R (557) ---------------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 572 + +--S 573 of 586 +m0597:= a0597-r0597 +--R +--R +--R (558) 0 +--R Type: Expression(Integer) +--E 573 + +--S 574 of 586 +d0597:= D(m0597,x) +--R +--R +--R (559) 0 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 586 +t0598:= cot(x)/(1+sin(x)^2) +--R +--R +--R cot(x) +--R (560) ----------- +--R 2 +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 575 + +--S 576 of 586 +r0598:= -1/2*log(1+csc(x)^2) +--R +--R +--R 2 +--R log(csc(x) + 1) +--R (561) - ---------------- +--R 2 +--R Type: Expression(Integer) +--E 576 + +--S 577 of 586 +a0598:= integrate(t0598,x) +--R +--R +--R 2 +--R sin(x) - 4cos(x) + 8 +--R 2log(----------) - log(---------------------) +--R cos(x) + 1 2 +--R cos(x) + 2cos(x) + 1 +--R (562) --------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 577 + +--S 578 of 586 +m0598:= a0598-r0598 +--R +--R +--R 2 +--R sin(x) 2 - 4cos(x) + 8 +--R 2log(----------) + log(csc(x) + 1) - log(---------------------) +--R cos(x) + 1 2 +--R cos(x) + 2cos(x) + 1 +--R (563) ---------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 578 + +--S 579 of 586 +d0598:= D(m0598,x) +--R +--R +--R (564) +--R 2 2 2 2 +--R (cos(x)csc(x) + cos(x))sin(x) + (- cos(x) + 2)cot(x)csc(x) sin(x) +--R + +--R 3 2 3 +--R (cos(x) - 2cos(x))csc(x) + cos(x) - 2cos(x) +--R / +--R 2 2 2 +--R ((cos(x) - 2)csc(x) + cos(x) - 2)sin(x) +--R Type: Expression(Integer) +--E 579 + +--S 580 of 586 +t0599:= sin(x)^2/(a+b*cos(x)^2) +--R +--R +--R 2 +--R sin(x) +--R (565) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 580 + +--S 581 of 586 +r0599:= -x/b+(a+b)^(1/2)*atan(a^(1/2)*tan(x)/(a+b)^(1/2))/a^(1/2)/b +--R +--R +--R +-+ +--R +-----+ tan(x)\|a +-+ +--R \|b + a atan(----------) - x\|a +--R +-----+ +--R \|b + a +--R (566) -------------------------------- +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 581 + +--S 582 of 586 +a0599:= integrate(t0599,x) +--R +--R +--R (567) +--R +-------+ +--R |- b - a 2 +--R +-------+ - 2a cos(x)sin(x) |------- + (b + 2a)cos(x) - a +--R |- b - a \| a +--R |------- log(-------------------------------------------------) - 2x +--R \| a 2 +--R b cos(x) + a +--R [---------------------------------------------------------------------, +--R 2b +--R +-----+ +--R |b + a +--R +-----+ a sin(x) |----- +--R |b + a \| a +--R |----- atan(----------------) - x +--R \| a (b + a)cos(x) +--R ----------------------------------] +--R b +--R Type: Union(List(Expression(Integer)),...) +--E 582 + +--S 583 of 586 +m0599a:= a0599.1-r0599 +--R +--R +--R (568) +--R +-------+ +--R |- b - a 2 +--R +-------+ - 2a cos(x)sin(x) |------- + (b + 2a)cos(x) - a +--R |- b - a +-+ \| a +--R |------- \|a log(-------------------------------------------------) +--R \| a 2 +--R b cos(x) + a +--R + +--R +-+ +--R +-----+ tan(x)\|a +--R - 2\|b + a atan(----------) +--R +-----+ +--R \|b + a +--R / +--R +-+ +--R 2b\|a +--R Type: Expression(Integer) +--E 583 + +--S 584 of 586 +d0599a:= D(m0599a,x) +--R +--R +--R (569) +--R 2 2 3 2 +--R (- 2a b - 2a b)cos(x) sin(x)tan(x) +--R + +--R 2 2 3 2 2 +--R ((- 2a b - 2a b)cos(x) + (2a b + 2a b)cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 2 2 2 2 3 2 3 2 2 4 +--R ((- a b - a b)cos(x) + a b + a )sin(x) + (b + 2a b + a b)cos(x) +--R + +--R 2 3 2 2 3 +--R (a b + a )cos(x) - a b - a +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 2 2 2 3 2 +--R ((- b - 2a b - a b)cos(x) + a b + 2a b + a )sin(x) +--R + +--R 2 2 4 2 3 2 2 3 +--R (a b + a b)cos(x) + (- a b + a )cos(x) - a b - a +--R / +--R 2 2 3 3 2 +--R (2a b cos(x) + 2a b cos(x))sin(x)tan(x) +--R + +--R 3 2 2 3 2 2 3 +--R ((2a b + 2a b )cos(x) + (2a b + 2a b)cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 3 2 2 4 3 2 3 2 +--R ((- a b - 2a b )cos(x) - 2a b cos(x) + a b)tan(x) +--R + +--R 4 3 2 2 4 2 2 3 2 2 2 3 +--R (- b - 3a b - 2a b )cos(x) + (- 2a b - 2a b)cos(x) + a b + a b +--R Type: Expression(Integer) +--E 584 + +--S 585 of 586 +m0599b:= a0599.2-r0599 +--R +--R +--R +-----+ +--R |b + a +--R +-----+ a sin(x) |----- +-+ +--R +-+ |b + a \| a +-----+ tan(x)\|a +--R \|a |----- atan(----------------) - \|b + a atan(----------) +--R \| a (b + a)cos(x) +-----+ +--R \|b + a +--R (570) ------------------------------------------------------------- +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 585 + +--S 586 of 586 +d0599b:= D(m0599b,x) +--R +--R +--R (571) +--R 2 2 2 +--R (- b - a)cos(x) tan(x) + (b + a)sin(x) +--R / +--R 2 2 2 2 2 2 2 +--R (a sin(x) + (a b + a )cos(x) )tan(x) + (a b + a )sin(x) +--R + +--R 2 2 2 +--R (b + 2a b + a )cos(x) +--R Type: Expression(Integer) +--E 586 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richtrig500-599.input.pdf b/src/axiom-website/CATS/richtrig500-599.input.pdf new file mode 100644 index 0000000..2732654 Binary files /dev/null and b/src/axiom-website/CATS/richtrig500-599.input.pdf differ diff --git a/src/axiom-website/CATS/richtrig600-699.input.pamphlet b/src/axiom-website/CATS/richtrig600-699.input.pamphlet new file mode 100644 index 0000000..00d54c0 --- /dev/null +++ b/src/axiom-website/CATS/richtrig600-699.input.pamphlet @@ -0,0 +1,16079 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richtrig600-699.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig600-699.output +)spool richtrig600-699.output +)set message auto off +)clear all + +--S 1 of 534 +t0600:= sin(x)^3/(a+b*cos(x)^2) +--R +--R +--R 3 +--R sin(x) +--R (1) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 534 +r0600:= -(a+b)*atan(b^(1/2)*cos(x)/a^(1/2))/a^(1/2)/b^(3/2)+cos(x)/b +--R +--R +--R +-+ +--R cos(x)\|b +-+ +-+ +--R (- b - a)atan(----------) + cos(x)\|a \|b +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R +-+ +-+ +--R b\|a \|b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 534 +a0600:= integrate(t0600,x) +--R +--R +--R (3) +--R [ +--R (b + a) +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R +-----+ +--R 2cos(x)\|- a b +--R / +--R +-----+ +--R 2b\|- a b +--R , +--R +---+ +--R (b cos(x) - a)\|a b +---+ +--R (- b - a)atan(--------------------) + cos(x)\|a b +--R a b cos(x) + a b +--R --------------------------------------------------] +--R +---+ +--R b\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 3 + +--S 4 of 534 +m0600a:= a0600.1-r0600 +--R +--R +--R (4) +--R +-+ +-+ +--R (b + a)\|a \|b +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R +-+ +--R +-----+ cos(x)\|b +--R (2b + 2a)\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 4 + +--S 5 of 534 +d0600a:= D(m0600a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 534 +m0600b:= a0600.2-r0600 +--R +--R +--R (6) +--R +---+ +-+ +--R +-+ +-+ (b cos(x) - a)\|a b +---+ cos(x)\|b +--R (- b - a)\|a \|b atan(--------------------) + (b + a)\|a b atan(----------) +--R a b cos(x) + a b +-+ +--R \|a +--R --------------------------------------------------------------------------- +--R +-+ +-+ +---+ +--R b\|a \|b \|a b +--R Type: Expression(Integer) +--E 6 + +--S 7 of 534 +d0600b:= D(m0600b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 534 +t0601:= sin(x)^4/(a+b*cos(x)^2) +--R +--R +--R 4 +--R sin(x) +--R (8) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 8 + +--S 9 of 534 +r0601:= -a*x/b^2-3/2*x/b+(a+b)^(3/2)*atan(a^(1/2)*tan(x)/(a+b)^(1/2))/_ + a^(1/2)/b^2+1/2*cos(x)*sin(x)/b +--R +--R +--R (9) +--R +-+ +--R +-----+ tan(x)\|a +-+ +--R (2b + 2a)\|b + a atan(----------) + (b cos(x)sin(x) + (- 3b - 2a)x)\|a +--R +-----+ +--R \|b + a +--R ----------------------------------------------------------------------- +--R 2 +-+ +--R 2b \|a +--R Type: Expression(Integer) +--E 9 + +--S 10 of 534 +a0601:= integrate(t0601,x) +--R +--R +--R (10) +--R [ +--R +-------+ +--R |- b - a 2 +--R +-------+ - 2a cos(x)sin(x) |------- + (b + 2a)cos(x) - a +--R |- b - a \| a +--R (b + a) |------- log(-------------------------------------------------) +--R \| a 2 +--R b cos(x) + a +--R + +--R b cos(x)sin(x) + (- 3b - 2a)x +--R / +--R 2 +--R 2b +--R , +--R +-----+ +--R |b + a +--R +-----+ a sin(x) |----- +--R |b + a \| a +--R (2b + 2a) |----- atan(----------------) + b cos(x)sin(x) + (- 3b - 2a)x +--R \| a (b + a)cos(x) +--R -----------------------------------------------------------------------] +--R 2 +--R 2b +--R Type: Union(List(Expression(Integer)),...) +--E 10 + +--S 11 of 534 +m0601a:= a0601.1-r0601 +--R +--R +--R (11) +--R +-------+ +--R |- b - a +-+ +--R (b + a) |------- \|a +--R \| a +--R * +--R +-------+ +--R |- b - a 2 +--R - 2a cos(x)sin(x) |------- + (b + 2a)cos(x) - a +--R \| a +--R log(-------------------------------------------------) +--R 2 +--R b cos(x) + a +--R + +--R +-+ +--R +-----+ tan(x)\|a +--R (- 2b - 2a)\|b + a atan(----------) +--R +-----+ +--R \|b + a +--R / +--R 2 +-+ +--R 2b \|a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 534 +d0601a:= D(m0601a,x) +--R +--R +--R (12) +--R 3 2 2 3 3 2 +--R (- 2a b - 4a b - 2a b)cos(x) sin(x)tan(x) +--R + +--R 3 2 2 3 3 3 2 2 3 +--R ((- 2a b - 4a b - 2a b)cos(x) + (2a b + 4a b + 2a b)cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 3 2 2 3 2 2 2 3 4 2 +--R ((- a b - 2a b - a b)cos(x) + a b + 2a b + a )sin(x) +--R + +--R 4 3 2 2 3 4 2 2 3 4 2 2 2 +--R (b + 3a b + 3a b + a b)cos(x) + (a b + 2a b + a )cos(x) - a b +--R + +--R 3 4 +--R - 2a b - a +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 2 3 2 3 2 2 3 4 2 +--R ((- b - 3a b - 3a b - a b)cos(x) + a b + 3a b + 3a b + a )sin(x) +--R + +--R 3 2 2 3 4 3 2 2 3 4 2 2 2 +--R (a b + 2a b + a b)cos(x) + (- a b - a b + a b + a )cos(x) - a b +--R + +--R 3 4 +--R - 2a b - a +--R / +--R 2 3 3 3 2 2 +--R (2a b cos(x) + 2a b cos(x))sin(x)tan(x) +--R + +--R 4 2 3 3 2 3 3 2 +--R ((2a b + 2a b )cos(x) + (2a b + 2a b )cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 4 2 3 4 3 2 2 3 2 2 +--R ((- a b - 2a b )cos(x) - 2a b cos(x) + a b )tan(x) +--R + +--R 5 4 2 3 4 2 3 3 2 2 2 3 3 2 +--R (- b - 3a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) + a b + a b +--R Type: Expression(Integer) +--E 12 + +--S 13 of 534 +m0601b:= a0601.2-r0601 +--R +--R +--R (13) +--R +-----+ +--R |b + a +--R +-----+ a sin(x) |----- +-+ +--R +-+ |b + a \| a +-----+ tan(x)\|a +--R (b + a)\|a |----- atan(----------------) + (- b - a)\|b + a atan(----------) +--R \| a (b + a)cos(x) +-----+ +--R \|b + a +--R ----------------------------------------------------------------------------- +--R 2 +-+ +--R b \|a +--R Type: Expression(Integer) +--E 13 + +--S 14 of 534 +d0601b:= D(m0601b,x) +--R +--R +--R (14) +--R 2 2 2 2 2 2 2 +--R (- b - 2a b - a )cos(x) tan(x) + (b + 2a b + a )sin(x) +--R / +--R 2 2 2 2 2 2 2 2 2 +--R (a b sin(x) + (a b + a b)cos(x) )tan(x) + (a b + a b)sin(x) +--R + +--R 3 2 2 2 +--R (b + 2a b + a b)cos(x) +--R Type: Expression(Integer) +--E 14 + +--S 15 of 534 +t0602:= sin(x)^5/(a+b*cos(x)^2) +--R +--R +--R 5 +--R sin(x) +--R (15) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 15 + +--S 16 of 534 +r0602:= -(a+b)^2*atan(b^(1/2)*cos(x)/a^(1/2))/a^(1/2)/b^(5/2)+_ + a*cos(x)/b^2+2*cos(x)/b-1/3*cos(x)^3/b +--R +--R +--R (16) +--R +-+ +--R 2 2 cos(x)\|b +--R (- 3b - 6a b - 3a )atan(----------) +--R +-+ +--R \|a +--R + +--R 3 +-+ +-+ +--R (- b cos(x) + (6b + 3a)cos(x))\|a \|b +--R / +--R 2 +-+ +-+ +--R 3b \|a \|b +--R Type: Expression(Integer) +--E 16 + +--S 17 of 534 +a0602:= integrate(t0602,x) +--R +--R +--R (17) +--R [ +--R 2 2 +--R (3b + 6a b + 3a ) +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R 3 +-----+ +--R (- 2b cos(x) + (12b + 6a)cos(x))\|- a b +--R / +--R 2 +-----+ +--R 6b \|- a b +--R , +--R +--R +---+ +--R 2 2 (b cos(x) - a)\|a b +--R (- 3b - 6a b - 3a )atan(--------------------) +--R a b cos(x) + a b +--R + +--R 3 +---+ +--R (- b cos(x) + (6b + 3a)cos(x))\|a b +--R / +--R 2 +---+ +--R 3b \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 17 + +--S 18 of 534 +m0602a:= a0602.1-r0602 +--R +--R +--R (18) +--R 2 2 +-+ +-+ +--R (b + 2a b + a )\|a \|b +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R +-+ +--R 2 2 +-----+ cos(x)\|b +--R (2b + 4a b + 2a )\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R 2 +-----+ +-+ +-+ +--R 2b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 18 + +--S 19 of 534 +d0602a:= D(m0602a,x) +--R +--R +--R (19) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 534 +m0602b:= a0602.2-r0602 +--R +--R +--R (20) +--R +---+ +--R 2 2 +-+ +-+ (b cos(x) - a)\|a b +--R (- b - 2a b - a )\|a \|b atan(--------------------) +--R a b cos(x) + a b +--R + +--R +-+ +--R 2 2 +---+ cos(x)\|b +--R (b + 2a b + a )\|a b atan(----------) +--R +-+ +--R \|a +--R / +--R 2 +-+ +-+ +---+ +--R b \|a \|b \|a b +--R Type: Expression(Integer) +--E 20 + +--S 21 of 534 +d0602b:= D(m0602b,x) +--R +--R +--R (21) 0 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 534 +t0603:= sin(x)^6/(a+b*cos(x)^2) +--R +--R +--R 6 +--R sin(x) +--R (22) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 22 + +--S 23 of 534 +r0603:= -1/2*a*x/b^2-7/8*x/b-(a+b)^2*x/b^3+(a+b)^(5/2)*atan(a^(1/2)*_ + tan(x)/(a+b)^(1/2))/a^(1/2)/b^3+1/2*a*cos(x)*sin(x)/b^2+_ + 7/8*cos(x)*sin(x)/b+1/4*cos(x)*sin(x)^3/b +--R +--R +--R (23) +--R +-+ +--R 2 2 +-----+ tan(x)\|a +--R (8b + 16a b + 8a )\|b + a atan(----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 2 2 +-+ +--R (2b cos(x)sin(x) + (7b + 4a b)cos(x)sin(x) + (- 15b - 20a b - 8a )x)\|a +--R / +--R 3 +-+ +--R 8b \|a +--R Type: Expression(Integer) +--E 23 + +--S 24 of 534 +a0603:= integrate(t0603,x) +--R +--R +--R (24) +--R [ +--R +-------+ +--R 2 2 |- b - a +--R (4b + 8a b + 4a ) |------- +--R \| a +--R * +--R +-------+ +--R |- b - a 2 +--R - 2a cos(x)sin(x) |------- + (b + 2a)cos(x) - a +--R \| a +--R log(-------------------------------------------------) +--R 2 +--R b cos(x) + a +--R + +--R 2 3 2 2 2 +--R (- 2b cos(x) + (9b + 4a b)cos(x))sin(x) + (- 15b - 20a b - 8a )x +--R / +--R 3 +--R 8b +--R , +--R +--R +-----+ +--R |b + a +--R +-----+ a sin(x) |----- +--R 2 2 |b + a \| a +--R (8b + 16a b + 8a ) |----- atan(----------------) +--R \| a (b + a)cos(x) +--R + +--R 2 3 2 2 2 +--R (- 2b cos(x) + (9b + 4a b)cos(x))sin(x) + (- 15b - 20a b - 8a )x +--R / +--R 3 +--R 8b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 24 + +--S 25 of 534 +m0603a:= a0603.1-r0603 +--R +--R +--R (25) +--R +-------+ +--R 2 2 |- b - a +-+ +--R (2b + 4a b + 2a ) |------- \|a +--R \| a +--R * +--R +-------+ +--R |- b - a 2 +--R - 2a cos(x)sin(x) |------- + (b + 2a)cos(x) - a +--R \| a +--R log(-------------------------------------------------) +--R 2 +--R b cos(x) + a +--R + +--R +-+ +--R 2 2 +-----+ tan(x)\|a +--R (- 4b - 8a b - 4a )\|b + a atan(----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 3 2 +-+ +--R (- b cos(x)sin(x) + (- b cos(x) + b cos(x))sin(x))\|a +--R / +--R 3 +-+ +--R 4b \|a +--R Type: Expression(Integer) +--E 25 + +--S 26 of 534 +d0603a:= D(m0603a,x) +--R +--R +--R (26) +--R 2 3 3 3 2 5 +--R (2a b cos(x) + 2a b cos(x))sin(x) +--R + +--R 2 3 3 3 2 3 +--R (- 2a b cos(x) - 2a b cos(x))sin(x) +--R + +--R 2 3 7 2 3 3 2 5 +--R - 2a b cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 24a b - 22a b - 8a b)cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 3 3 2 5 +--R ((2a b + 2a b )cos(x) + (2a b + 2a b )cos(x))sin(x) +--R + +--R 4 2 3 3 2 3 3 2 3 +--R ((- 2a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x))sin(x) +--R + +--R 4 2 3 7 4 3 2 5 +--R (- 2a b - 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 22a b - 22a b - 8a b)cos(x) +--R + +--R 4 2 3 3 2 4 +--R (8a b + 24a b + 24a b + 8a b)cos(x) +--R * +--R sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 4 2 3 4 3 2 2 3 2 4 +--R ((- a b - 2a b )cos(x) - 2a b cos(x) + a b )sin(x) +--R + +--R 4 2 3 4 4 2 3 3 2 4 2 +--R (a b + 2a b )cos(x) + (- 4a b - 12a b - 10a b - 4a b)cos(x) +--R + +--R 2 3 3 2 4 5 +--R 4a b + 11a b + 12a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 8 4 2 3 3 2 6 +--R (a b + 2a b )cos(x) + (- a b - 2a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (4b + 16a b + 24a b + 13a b + 4a b)cos(x) +--R + +--R 2 3 3 2 4 5 2 2 3 3 2 4 5 +--R (4a b + 13a b + 12a b + 4a )cos(x) - 4a b - 12a b - 12a b - 4a +--R * +--R 2 +--R tan(x) +--R + +--R 5 4 2 3 4 2 3 3 2 2 2 3 +--R (- b - 3a b - 2a b )cos(x) + (- 2a b - 2a b )cos(x) + a b +--R + +--R 3 2 +--R a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 2 3 4 +--R (b + 3a b + 2a b )cos(x) +--R + +--R 5 4 2 3 3 2 4 2 4 2 3 +--R (- 4b - 16a b - 22a b - 14a b - 4a b)cos(x) + 4a b + 15a b +--R + +--R 3 2 4 5 +--R 23a b + 16a b + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 8 5 4 3 2 6 +--R (b + 3a b + 2a b )cos(x) + (- b - 3a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (4a b + 9a b + 9a b + 4a b)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 2 3 3 2 4 5 +--R (- 4a b - 7a b + a b + 8a b + 4a )cos(x) - 4a b - 12a b - 12a b - 4a +--R / +--R 2 4 3 3 3 2 +--R (8a b cos(x) + 8a b cos(x))sin(x)tan(x) +--R + +--R 5 2 4 3 2 4 3 3 +--R ((8a b + 8a b )cos(x) + (8a b + 8a b )cos(x))sin(x) +--R * +--R +-------+ +--R |- b - a +--R |------- +--R \| a +--R + +--R 5 2 4 4 3 3 2 3 3 2 +--R ((- 4a b - 8a b )cos(x) - 8a b cos(x) + 4a b )tan(x) +--R + +--R 6 5 2 4 4 2 4 3 3 2 2 4 3 3 +--R (- 4b - 12a b - 8a b )cos(x) + (- 8a b - 8a b )cos(x) + 4a b + 4a b +--R Type: Expression(Integer) +--E 26 + +--S 27 of 534 +m0603b:= a0603.2-r0603 +--R +--R +--R (27) +--R +-----+ +--R |b + a +--R +-----+ a sin(x) |----- +--R 2 2 +-+ |b + a \| a +--R (4b + 8a b + 4a )\|a |----- atan(----------------) +--R \| a (b + a)cos(x) +--R + +--R +-+ +--R 2 2 +-----+ tan(x)\|a +--R (- 4b - 8a b - 4a )\|b + a atan(----------) +--R +-----+ +--R \|b + a +--R + +--R 2 3 2 3 2 +-+ +--R (- b cos(x)sin(x) + (- b cos(x) + b cos(x))sin(x))\|a +--R / +--R 3 +-+ +--R 4b \|a +--R Type: Expression(Integer) +--E 27 + +--S 28 of 534 +d0603b:= D(m0603b,x) +--R +--R +--R (28) +--R 2 6 2 2 2 2 4 +--R a b sin(x) + ((a b + a b)cos(x) - a b)sin(x) +--R + +--R 2 4 2 2 2 2 2 6 +--R (- a b cos(x) - a b cos(x) )sin(x) + (- a b - a b)cos(x) +--R + +--R 2 2 4 3 2 2 3 2 +--R (a b + a b)cos(x) + (- 4b - 12a b - 12a b - 4a )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 6 3 2 2 2 2 2 4 +--R (a b + a b)sin(x) + ((b + 2a b + a b)cos(x) - a b - a b)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 +--R (- a b - a b)cos(x) + (- b - a b )cos(x) + 4b + 12a b + 12a b +--R + +--R 3 +--R 4a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 6 3 2 2 4 +--R (- b - 2a b - a b)cos(x) + (b + 2a b + a b)cos(x) +--R / +--R 2 2 2 3 2 2 2 2 3 2 2 2 +--R (4a b sin(x) + (4a b + 4a b )cos(x) )tan(x) + (4a b + 4a b )sin(x) +--R + +--R 4 3 2 2 2 +--R (4b + 8a b + 4a b )cos(x) +--R Type: Expression(Integer) +--E 28 + +--S 29 of 534 +t0604:= sin(x)^7/(a+b*cos(x)^2) +--R +--R +--R 7 +--R sin(x) +--R (29) ------------- +--R 2 +--R b cos(x) + a +--R Type: Expression(Integer) +--E 29 + +--S 30 of 534 +r0604:= -(a+b)^3*atan(b^(1/2)*cos(x)/a^(1/2))/a^(1/2)/b^(7/2)+_ + a*cos(x)/b^2+2*cos(x)/b+(a+b)^2*cos(x)/b^3-1/3*a*cos(x)^3/b^2-_ + cos(x)^3/b+1/5*cos(x)^5/b +--R +--R +--R (30) +--R +-+ +--R 3 2 2 3 cos(x)\|b +--R (- 15b - 45a b - 45a b - 15a )atan(----------) +--R +-+ +--R \|a +--R + +--R 2 5 2 3 2 2 +-+ +-+ +--R (3b cos(x) + (- 15b - 5a b)cos(x) + (45b + 45a b + 15a )cos(x))\|a \|b +--R / +--R 3 +-+ +-+ +--R 15b \|a \|b +--R Type: Expression(Integer) +--E 30 + +--S 31 of 534 +a0604:= integrate(t0604,x) +--R +--R +--R (31) +--R [ +--R 3 2 2 3 +--R (15b + 45a b + 45a b + 15a ) +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R 2 5 2 3 2 2 +--R (6b cos(x) + (- 30b - 10a b)cos(x) + (90b + 90a b + 30a )cos(x)) +--R * +--R +-----+ +--R \|- a b +--R / +--R 3 +-----+ +--R 30b \|- a b +--R , +--R +--R +---+ +--R 3 2 2 3 (b cos(x) - a)\|a b +--R (- 15b - 45a b - 45a b - 15a )atan(--------------------) +--R a b cos(x) + a b +--R + +--R 2 5 2 3 2 2 +---+ +--R (3b cos(x) + (- 15b - 5a b)cos(x) + (45b + 45a b + 15a )cos(x))\|a b +--R / +--R 3 +---+ +--R 15b \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 31 + +--S 32 of 534 +m0604a:= a0604.1-r0604 +--R +--R +--R (32) +--R 3 2 2 3 +-+ +-+ +--R (b + 3a b + 3a b + a )\|a \|b +--R * +--R log +--R 2 2 2 +-----+ +--R ((b - a b)cos(x) - 4a b cos(x) - a b + a )\|- a b +--R + +--R 2 2 2 2 2 +--R - 2a b cos(x) + (- 2a b + 2a b)cos(x) + 2a b +--R / +--R 2 +--R b cos(x) + a +--R + +--R +-+ +--R 3 2 2 3 +-----+ cos(x)\|b +--R (2b + 6a b + 6a b + 2a )\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R 3 +-----+ +-+ +-+ +--R 2b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 32 + +--S 33 of 534 +d0604a:= D(m0604a,x) +--R +--R +--R (33) 0 +--R Type: Expression(Integer) +--E 33 + +--S 34 of 534 +m0604b:= a0604.2-r0604 +--R +--R +--R (34) +--R +---+ +--R 3 2 2 3 +-+ +-+ (b cos(x) - a)\|a b +--R (- b - 3a b - 3a b - a )\|a \|b atan(--------------------) +--R a b cos(x) + a b +--R + +--R +-+ +--R 3 2 2 3 +---+ cos(x)\|b +--R (b + 3a b + 3a b + a )\|a b atan(----------) +--R +-+ +--R \|a +--R / +--R 3 +-+ +-+ +---+ +--R b \|a \|b \|a b +--R Type: Expression(Integer) +--E 34 + +--S 35 of 534 +d0604b:= D(m0604b,x) +--R +--R +--R (35) 0 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 534 +t0605:= sin(x)^2/(a-a*cos(x)^2) +--R +--R +--R 2 +--R sin(x) +--R (36) - ------------- +--R 2 +--R a cos(x) - a +--R Type: Expression(Integer) +--E 36 + +--S 37 of 534 +r0605:= x/a +--R +--R +--R x +--R (37) - +--R a +--R Type: Fraction(Polynomial(Integer)) +--E 37 + +--S 38 of 534 +a0605:= integrate(t0605,x) +--R +--R +--R x +--R (38) - +--R a +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 534 +m0605:= a0605-r0605 +--R +--R +--R (39) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 534 +d0605:= D(m0605,x) +--R +--R +--R (40) 0 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 534 +t0606:= sin(x)^4/(a-a*cos(x)^2) +--R +--R +--R 4 +--R sin(x) +--R (41) - ------------- +--R 2 +--R a cos(x) - a +--R Type: Expression(Integer) +--E 41 + +--S 42 of 534 +r0606:= -1/2*(-x+cos(x)*sin(x))/a +--R +--R +--R - cos(x)sin(x) + x +--R (42) ------------------ +--R 2a +--R Type: Expression(Integer) +--E 42 + +--S 43 of 534 +a0606:= integrate(t0606,x) +--R +--R +--R - cos(x)sin(x) + x +--R (43) ------------------ +--R 2a +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 534 +m0606:= a0606-r0606 +--R +--R +--R (44) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 534 +d0606:= D(m0606,x) +--R +--R +--R (45) 0 +--R Type: Expression(Integer) +--E 45 + +--S 46 of 534 +t0607:= tan(x)/(1+cos(x)^2) +--R +--R +--R tan(x) +--R (46) ----------- +--R 2 +--R cos(x) + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 534 +r0607:= atanh(1+2*cos(x)^2) +--R +--R +--R 2 +--R (47) atanh(2cos(x) + 1) +--R Type: Expression(Integer) +--E 47 + +--S 48 of 534 +a0607:= integrate(t0607,x) +--R +--R +--R 2 +--R 2cos(x) + 2 2cos(x) +--R log(---------------------) - 2log(- ----------) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R (48) ----------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 534 +m0607:= a0607-r0607 +--R +--R +--R (49) +--R 2 +--R 2cos(x) + 2 2cos(x) 2 +--R log(---------------------) - 2log(- ----------) - 2atanh(2cos(x) + 1) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R ---------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 534 +d0607:= D(m0607,x) +--R +--R +--R (50) 0 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 534 +t0608:= cos(a+b*x)^3*sin(a+b*x)^n +--R +--R +--R 3 n +--R (51) cos(b x + a) sin(b x + a) +--R Type: Expression(Integer) +--E 51 + +--S 52 of 534 +r0608:= sin(a+b*x)^(1+n)/b/(1+n)-sin(a+b*x)^(3+n)/b/(3+n) +--R +--R +--R n + 3 n + 1 +--R (- n - 1)sin(b x + a) + (n + 3)sin(b x + a) +--R (52) ----------------------------------------------------- +--R 2 +--R b n + 4b n + 3b +--R Type: Expression(Integer) +--E 52 + +--S 53 of 534 +a0608:= integrate(t0608,x) +--R +--R +--R 2 n log(sin(b x + a)) +--R ((n + 1)cos(b x + a) + 2)sin(b x + a)%e +--R (53) ----------------------------------------------------------- +--R 2 +--R b n + 4b n + 3b +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 534 +m0608:= a0608-r0608 +--R +--R +--R (54) +--R 2 n log(sin(b x + a)) +--R ((n + 1)cos(b x + a) + 2)sin(b x + a)%e +--R + +--R n + 3 n + 1 +--R (n + 1)sin(b x + a) + (- n - 3)sin(b x + a) +--R / +--R 2 +--R b n + 4b n + 3b +--R Type: Expression(Integer) +--E 54 + +--S 55 of 534 +d0608:= D(m0608,x) +--R +--R +--R (55) +--R 2 3 +--R (- 2cos(b x + a)sin(b x + a) + (n + 1)cos(b x + a) + 2cos(b x + a)) +--R * +--R n log(sin(b x + a)) +--R %e +--R + +--R n + 2 n +--R (n + 3)cos(b x + a)sin(b x + a) + (- n - 3)cos(b x + a)sin(b x + a) +--R / +--R n + 3 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 534 +t0609:= cos(a+b*x)^5*sin(a+b*x)^n +--R +--R +--R 5 n +--R (56) cos(b x + a) sin(b x + a) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 534 +r0609:= sin(a+b*x)^(1+n)/b/(1+n)-2*sin(a+b*x)^(3+n)/b/(3+n)+_ + sin(a+b*x)^(5+n)/b/(5+n) +--R +--R +--R (57) +--R 2 n + 5 2 n + 3 +--R (n + 4n + 3)sin(b x + a) + (- 2n - 12n - 10)sin(b x + a) +--R + +--R 2 n + 1 +--R (n + 8n + 15)sin(b x + a) +--R / +--R 3 2 +--R b n + 9b n + 23b n + 15b +--R Type: Expression(Integer) +--E 57 + +--S 58 of 534 +a0609:= integrate(t0609,x) +--R +--R +--R (58) +--R 2 4 2 +--R ((n + 4n + 3)cos(b x + a) + (4n + 4)cos(b x + a) + 8)sin(b x + a) +--R * +--R n log(sin(b x + a)) +--R %e +--R / +--R 3 2 +--R b n + 9b n + 23b n + 15b +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 534 +m0609:= a0609-r0609 +--R +--R +--R (59) +--R 2 4 2 +--R ((n + 4n + 3)cos(b x + a) + (4n + 4)cos(b x + a) + 8)sin(b x + a) +--R * +--R n log(sin(b x + a)) +--R %e +--R + +--R 2 n + 5 2 n + 3 +--R (- n - 4n - 3)sin(b x + a) + (2n + 12n + 10)sin(b x + a) +--R + +--R 2 n + 1 +--R (- n - 8n - 15)sin(b x + a) +--R / +--R 3 2 +--R b n + 9b n + 23b n + 15b +--R Type: Expression(Integer) +--E 59 + +--S 60 of 534 +d0609:= D(m0609,x) +--R +--R +--R (60) +--R 3 2 +--R ((- 4n - 12)cos(b x + a) - 8cos(b x + a))sin(b x + a) +--R + +--R 2 5 3 +--R (n + 4n + 3)cos(b x + a) + (4n + 4)cos(b x + a) + 8cos(b x + a) +--R * +--R n log(sin(b x + a)) +--R %e +--R + +--R 2 n + 4 +--R (- n - 8n - 15)cos(b x + a)sin(b x + a) +--R + +--R 2 n + 2 +--R (2n + 16n + 30)cos(b x + a)sin(b x + a) +--R + +--R 2 n +--R (- n - 8n - 15)cos(b x + a)sin(b x + a) +--R / +--R 2 +--R n + 8n + 15 +--R Type: Expression(Integer) +--E 60 + +--S 61 of 534 +t0610:= cos(a+b*x)^m*sin(a+b*x)^3 +--R +--R +--R 3 m +--R (61) sin(b x + a) cos(b x + a) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 534 +r0610:= -cos(a+b*x)^(1+m)/b/(1+m)+cos(a+b*x)^(3+m)/b/(3+m) +--R +--R +--R m + 3 m + 1 +--R (m + 1)cos(b x + a) + (- m - 3)cos(b x + a) +--R (62) ----------------------------------------------------- +--R 2 +--R b m + 4b m + 3b +--R Type: Expression(Integer) +--E 62 + +--S 63 of 534 +a0610:= integrate(t0610,x) +--R +--R +--R 3 m log(cos(b x + a)) +--R ((m + 1)cos(b x + a) + (- m - 3)cos(b x + a))%e +--R (63) ------------------------------------------------------------------- +--R 2 +--R b m + 4b m + 3b +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 534 +m0610:= a0610-r0610 +--R +--R +--R (64) +--R 3 m log(cos(b x + a)) +--R ((m + 1)cos(b x + a) + (- m - 3)cos(b x + a))%e +--R + +--R m + 3 m + 1 +--R (- m - 1)cos(b x + a) + (m + 3)cos(b x + a) +--R / +--R 2 +--R b m + 4b m + 3b +--R Type: Expression(Integer) +--E 64 + +--S 65 of 534 +d0610:= D(m0610,x) +--R +--R +--R (65) +--R 2 m log(cos(b x + a)) +--R (- cos(b x + a) + 1)sin(b x + a)%e +--R + +--R m + 2 m +--R sin(b x + a)cos(b x + a) - sin(b x + a)cos(b x + a) +--R Type: Expression(Integer) +--E 65 + +--S 66 of 534 +t0611:= cos(a+b*x)^m*sin(a+b*x)^5 +--R +--R +--R 5 m +--R (66) sin(b x + a) cos(b x + a) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 534 +r0611:= -cos(a+b*x)^(1+m)/b/(1+m)+2*cos(a+b*x)^(3+m)/b/(3+m)-_ + cos(a+b*x)^(5+m)/b/(5+m) +--R +--R +--R (67) +--R 2 m + 5 2 m + 3 +--R (- m - 4m - 3)cos(b x + a) + (2m + 12m + 10)cos(b x + a) +--R + +--R 2 m + 1 +--R (- m - 8m - 15)cos(b x + a) +--R / +--R 3 2 +--R b m + 9b m + 23b m + 15b +--R Type: Expression(Integer) +--E 67 + +--S 68 of 534 +a0611:= integrate(t0611,x) +--R +--R +--R (68) +--R 2 5 2 3 +--R (- m - 4m - 3)cos(b x + a) + (2m + 12m + 10)cos(b x + a) +--R + +--R 2 +--R (- m - 8m - 15)cos(b x + a) +--R * +--R m log(cos(b x + a)) +--R %e +--R / +--R 3 2 +--R b m + 9b m + 23b m + 15b +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 534 +m0611:= a0611-r0611 +--R +--R +--R (69) +--R 2 5 2 3 +--R (- m - 4m - 3)cos(b x + a) + (2m + 12m + 10)cos(b x + a) +--R + +--R 2 +--R (- m - 8m - 15)cos(b x + a) +--R * +--R m log(cos(b x + a)) +--R %e +--R + +--R 2 m + 5 2 m + 3 +--R (m + 4m + 3)cos(b x + a) + (- 2m - 12m - 10)cos(b x + a) +--R + +--R 2 m + 1 +--R (m + 8m + 15)cos(b x + a) +--R / +--R 3 2 +--R b m + 9b m + 23b m + 15b +--R Type: Expression(Integer) +--E 69 + +--S 70 of 534 +d0611:= D(m0611,x) +--R +--R +--R (70) +--R 4 2 m log(cos(b x + a)) +--R (cos(b x + a) - 2cos(b x + a) + 1)sin(b x + a)%e +--R + +--R m + 4 m + 2 +--R - sin(b x + a)cos(b x + a) + 2sin(b x + a)cos(b x + a) +--R + +--R m +--R - sin(b x + a)cos(b x + a) +--R Type: Expression(Integer) +--E 70 + +--S 71 of 534 +t0612:= csc(a+b*x)*sec(a+b*x)^2 +--R +--R +--R 2 +--R (71) csc(b x + a)sec(b x + a) +--R Type: Expression(Integer) +--E 71 + +--S 72 of 534 +r0612:= -atanh(cos(a+b*x))/b+sec(a+b*x)/b +--R +--R +--R - atanh(cos(b x + a)) + sec(b x + a) +--R (72) ------------------------------------ +--R b +--R Type: Expression(Integer) +--E 72 + +--S 73 of 534 +a0612:= integrate(t0612,x) +--R +--R +--R sin(b x + a) +--R cos(b x + a)log(----------------) + cos(b x + a) + 1 +--R cos(b x + a) + 1 +--R (73) ---------------------------------------------------- +--R b cos(b x + a) +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 534 +m0612:= a0612-r0612 +--R +--R +--R (74) +--R sin(b x + a) +--R cos(b x + a)log(----------------) + cos(b x + a)atanh(cos(b x + a)) +--R cos(b x + a) + 1 +--R + +--R - cos(b x + a)sec(b x + a) + cos(b x + a) + 1 +--R / +--R b cos(b x + a) +--R Type: Expression(Integer) +--E 74 + +--S 75 of 534 +d0612:= D(m0612,x) +--R +--R +--R (75) +--R 4 2 +--R (- cos(b x + a) + cos(b x + a) )sec(b x + a)sin(b x + a)tan(b x + a) +--R + +--R 3 2 2 5 +--R (cos(b x + a) + cos(b x + a) - 1)sin(b x + a) + cos(b x + a) +--R + +--R 3 +--R - cos(b x + a) +--R / +--R 4 2 +--R (cos(b x + a) - cos(b x + a) )sin(b x + a) +--R Type: Expression(Integer) +--E 75 + +--S 76 of 534 +t0613:= csc(a+b*x)^2*sec(a+b*x) +--R +--R +--R 2 +--R (76) csc(b x + a) sec(b x + a) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 534 +r0613:= atanh(sin(a+b*x))/b-csc(a+b*x)/b +--R +--R +--R atanh(sin(b x + a)) - csc(b x + a) +--R (77) ---------------------------------- +--R b +--R Type: Expression(Integer) +--E 77 + +--S 78 of 534 +a0613:= integrate(t0613,x) +--R +--R +--R (78) +--R sin(b x + a) + cos(b x + a) + 1 +--R sin(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R - sin(b x + a)log(-------------------------------) - 1 +--R cos(b x + a) + 1 +--R / +--R b sin(b x + a) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 534 +m0613:= a0613-r0613 +--R +--R +--R (79) +--R sin(b x + a) + cos(b x + a) + 1 +--R sin(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R - sin(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R - sin(b x + a)atanh(sin(b x + a)) + csc(b x + a)sin(b x + a) - 1 +--R / +--R b sin(b x + a) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 534 +d0613:= D(m0613,x) +--R +--R +--R (80) +--R 6 +--R (- cot(b x + a)csc(b x + a) - 2)sin(b x + a) +--R + +--R 2 +--R (cos(b x + a) + 2cos(b x + a) + 2)cot(b x + a)csc(b x + a) +--R + +--R 2 +--R - 2cos(b x + a) + 2 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - 2cos(b x + a) - 1)cot(b x + a)csc(b x + a) +--R + +--R 3 2 +--R - 2cos(b x + a) - 2cos(b x + a) - cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 +--R cos(b x + a) + 2cos(b x + a) + cos(b x + a) +--R / +--R 6 2 4 +--R sin(b x + a) + (- cos(b x + a) - 2cos(b x + a) - 2)sin(b x + a) +--R + +--R 2 2 +--R (cos(b x + a) + 2cos(b x + a) + 1)sin(b x + a) +--R Type: Expression(Integer) +--E 80 + +--S 81 of 534 +t0614:= cos(a+b*x)*cot(a+b*x) +--R +--R +--R (81) cos(b x + a)cot(b x + a) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 534 +r0614:= -(atanh(cos(a+b*x))-cos(a+b*x))/b +--R +--R +--R - atanh(cos(b x + a)) + cos(b x + a) +--R (82) ------------------------------------ +--R b +--R Type: Expression(Integer) +--E 82 + +--S 83 of 534 +a0614:= integrate(t0614,x) +--R +--R +--R sin(b x + a) +--R log(----------------) + cos(b x + a) +--R cos(b x + a) + 1 +--R (83) ------------------------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 534 +m0614:= a0614-r0614 +--R +--R +--R sin(b x + a) +--R log(----------------) + atanh(cos(b x + a)) +--R cos(b x + a) + 1 +--R (84) ------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 84 + +--S 85 of 534 +d0614:= D(m0614,x) +--R +--R +--R 2 3 +--R cos(b x + a)sin(b x + a) + cos(b x + a) - cos(b x + a) +--R (85) -------------------------------------------------------- +--R 2 +--R (cos(b x + a) - 1)sin(b x + a) +--R Type: Expression(Integer) +--E 85 + +--S 86 of 534 +t0615:= cos(a+b*x)*cot(a+b*x)^3 +--R +--R +--R 3 +--R (86) cos(b x + a)cot(b x + a) +--R Type: Expression(Integer) +--E 86 + +--S 87 of 534 +r0615:= 3/2*atanh(cos(a+b*x))/b-3/2*cos(a+b*x)/b-1/2*cos(a+b*x)*cot(a+b*x)^2/b +--R +--R +--R 2 +--R 3atanh(cos(b x + a)) - cos(b x + a)cot(b x + a) - 3cos(b x + a) +--R (87) ---------------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 87 + +--S 88 of 534 +a0615:= integrate(t0615,x) +--R +--R +--R (88) +--R 2 sin(b x + a) 3 +--R (- 3cos(b x + a) + 3)log(----------------) - 2cos(b x + a) +--R cos(b x + a) + 1 +--R + +--R 2 +--R - 2cos(b x + a) + 3cos(b x + a) + 2 +--R / +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 534 +m0615:= a0615-r0615 +--R +--R +--R (89) +--R 2 sin(b x + a) +--R (- 3cos(b x + a) + 3)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 2 +--R (- 3cos(b x + a) + 3)atanh(cos(b x + a)) +--R + +--R 3 2 3 +--R (cos(b x + a) - cos(b x + a))cot(b x + a) + cos(b x + a) +--R + +--R 2 +--R - 2cos(b x + a) + 2 +--R / +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Expression(Integer) +--E 89 + +--S 90 of 534 +d0615:= D(m0615,x) +--R +--R +--R (90) +--R 4 2 2 4 +--R (- cos(b x + a) + 2cos(b x + a) - 1)cot(b x + a) - cos(b x + a) +--R + +--R 3 2 +--R - 3cos(b x + a) + 3cos(b x + a) + 3cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 3 3 +--R (- 2cos(b x + a) + 4cos(b x + a) - 2cos(b x + a))cot(b x + a) +--R + +--R 5 3 +--R (- 2cos(b x + a) + 4cos(b x + a) - 2cos(b x + a))cot(b x + a) +--R * +--R sin(b x + a) +--R + +--R 5 3 +--R - 3cos(b x + a) + 6cos(b x + a) - 3cos(b x + a) +--R / +--R 4 2 +--R (2cos(b x + a) - 4cos(b x + a) + 2)sin(b x + a) +--R Type: Expression(Integer) +--E 90 + +--S 91 of 534 +t0616:= sin(a+b*x)*tan(a+b*x) +--R +--R +--R (91) sin(b x + a)tan(b x + a) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 534 +r0616:= (atanh(sin(a+b*x))-sin(a+b*x))/b +--R +--R +--R atanh(sin(b x + a)) - sin(b x + a) +--R (92) ---------------------------------- +--R b +--R Type: Expression(Integer) +--E 92 + +--S 93 of 534 +a0616:= integrate(t0616,x) +--R +--R +--R (93) +--R sin(b x + a) + cos(b x + a) + 1 +--R log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R - log(-------------------------------) - sin(b x + a) +--R cos(b x + a) + 1 +--R / +--R b +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 534 +m0616:= a0616-r0616 +--R +--R +--R (94) +--R sin(b x + a) + cos(b x + a) + 1 +--R log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R - log(-------------------------------) - atanh(sin(b x + a)) +--R cos(b x + a) + 1 +--R / +--R b +--R Type: Expression(Integer) +--E 94 + +--S 95 of 534 +d0616:= D(m0616,x) +--R +--R +--R (95) +--R 4 2 2 +--R - 2sin(b x + a) + (- 2cos(b x + a) - cos(b x + a) + 2)sin(b x + a) +--R + +--R 3 +--R - cos(b x + a) + cos(b x + a) +--R / +--R 4 2 2 +--R sin(b x + a) + (- cos(b x + a) - 2cos(b x + a) - 2)sin(b x + a) +--R + +--R 2 +--R cos(b x + a) + 2cos(b x + a) + 1 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 534 +t0617:= sin(a+b*x)*tan(a+b*x)^3 +--R +--R +--R 3 +--R (96) sin(b x + a)tan(b x + a) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 534 +r0617:= -3/2*atanh(sin(a+b*x))/b+3/2*sin(a+b*x)/b+1/2*sin(a+b*x)*tan(a+b*x)^2/b +--R +--R +--R 2 +--R - 3atanh(sin(b x + a)) + sin(b x + a)tan(b x + a) + 3sin(b x + a) +--R (97) ------------------------------------------------------------------ +--R 2b +--R Type: Expression(Integer) +--E 97 + +--S 98 of 534 +a0617:= integrate(t0617,x) +--R +--R +--R (98) +--R 2 sin(b x + a) + cos(b x + a) + 1 +--R - 3cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 sin(b x + a) - cos(b x + a) - 1 +--R 3cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 +--R (2cos(b x + a) + 1)sin(b x + a) +--R / +--R 2 +--R 2b cos(b x + a) +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 534 +m0617:= a0617-r0617 +--R +--R +--R (99) +--R 2 sin(b x + a) + cos(b x + a) + 1 +--R - 3cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 sin(b x + a) - cos(b x + a) - 1 +--R 3cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 +--R 3cos(b x + a) atanh(sin(b x + a)) +--R + +--R 2 2 +--R - cos(b x + a) sin(b x + a)tan(b x + a) +--R + +--R 2 +--R (- cos(b x + a) + 1)sin(b x + a) +--R / +--R 2 +--R 2b cos(b x + a) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 534 +d0617:= D(m0617,x) +--R +--R +--R (100) +--R 3 5 +--R - 2cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 3 +--R (2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R (- 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a) )sin(b x + a) +--R * +--R 3 +--R tan(b x + a) +--R + +--R 4 4 +--R - cos(b x + a) sin(b x + a) +--R + +--R 6 5 4 2 +--R (cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) )sin(b x + a) +--R + +--R 6 5 4 +--R - cos(b x + a) - 2cos(b x + a) - cos(b x + a) +--R * +--R 2 +--R tan(b x + a) +--R + +--R 3 5 +--R - 2cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 3 +--R (2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R (- 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a) )sin(b x + a) +--R * +--R tan(b x + a) +--R + +--R 6 +--R 2sin(b x + a) +--R + +--R 4 3 2 +--R (- cos(b x + a) + 6cos(b x + a) - cos(b x + a) - 4cos(b x + a) - 4) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R cos(b x + a) + 8cos(b x + a) + 4cos(b x + a) - 8cos(b x + a) +--R + +--R 4cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) - 2cos(b x + a) - 3cos(b x + a) + 2cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R / +--R 3 4 +--R 2cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 2 +--R (- 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R 2cos(b x + a) + 4cos(b x + a) + 2cos(b x + a) +--R Type: Expression(Integer) +--E 100 + +--S 101 of 534 +t0618:= sin(a+b*x)^2*tan(a+b*x)^2 +--R +--R +--R 2 2 +--R (101) sin(b x + a) tan(b x + a) +--R Type: Expression(Integer) +--E 101 + +--S 102 of 534 +r0618:= -3/2*x+3/2*tan(a+b*x)/b-1/2*sin(a+b*x)^2*tan(a+b*x)/b +--R +--R +--R 2 +--R (- sin(b x + a) + 3)tan(b x + a) - 3b x +--R (102) ---------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 102 + +--S 103 of 534 +a0618:= integrate(t0618,x) +--R +--R +--R 2 +--R (cos(b x + a) + 2)sin(b x + a) - 3b x cos(b x + a) +--R (103) --------------------------------------------------- +--R 2b cos(b x + a) +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 534 +m0618:= a0618-r0618 +--R +--R +--R (104) +--R 2 +--R (cos(b x + a)sin(b x + a) - 3cos(b x + a))tan(b x + a) +--R + +--R 2 +--R (cos(b x + a) + 2)sin(b x + a) +--R / +--R 2b cos(b x + a) +--R Type: Expression(Integer) +--E 104 + +--S 105 of 534 +d0618:= D(m0618,x) +--R +--R +--R (105) +--R 2 2 2 2 +--R (cos(b x + a) sin(b x + a) - 3cos(b x + a) )tan(b x + a) +--R + +--R 3 2 4 +--R 2cos(b x + a) sin(b x + a)tan(b x + a) + 2sin(b x + a) + cos(b x + a) +--R + +--R 2 +--R - cos(b x + a) +--R / +--R 2 +--R 2cos(b x + a) +--R Type: Expression(Integer) +--E 105 + +--S 106 of 534 +t0619:= sec(a+b*x)^2*tan(a+b*x)^n +--R +--R +--R 2 n +--R (106) sec(b x + a) tan(b x + a) +--R Type: Expression(Integer) +--E 106 + +--S 107 of 534 +r0619:= tan(a+b*x)^(1+n)/b/(1+n) +--R +--R +--R n + 1 +--R tan(b x + a) +--R (107) ----------------- +--R b n + b +--R Type: Expression(Integer) +--E 107 + +--S 108 of 534 +a0619:= integrate(t0619,x) +--R +--R +--R sin(b x + a) +--R n log(------------) +--R cos(b x + a) +--R sin(b x + a)%e +--R (108) --------------------------------- +--R (b n + b)cos(b x + a) +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 534 +m0619:= a0619-r0619 +--R +--R +--R sin(b x + a) +--R n log(------------) +--R cos(b x + a) n + 1 +--R sin(b x + a)%e - cos(b x + a)tan(b x + a) +--R (109) ----------------------------------------------------------------- +--R (b n + b)cos(b x + a) +--R Type: Expression(Integer) +--E 109 + +--S 110 of 534 +d0619:= D(m0619,x) +--R +--R +--R (110) +--R sin(b x + a) +--R n log(------------) +--R 2 2 cos(b x + a) +--R (sin(b x + a) + cos(b x + a) )%e +--R + +--R 2 2 2 n +--R (- cos(b x + a) tan(b x + a) - cos(b x + a) )tan(b x + a) +--R / +--R 2 +--R cos(b x + a) +--R Type: Expression(Integer) +--E 110 + +--S 111 of 534 +t0620:= sec(a+b*x)^n*tan(a+b*x)^3 +--R +--R +--R 3 n +--R (111) tan(b x + a) sec(b x + a) +--R Type: Expression(Integer) +--E 111 + +--S 112 of 534 +r0620:= -sec(a+b*x)^n/b/n+sec(a+b*x)^(2+n)/b/(2+n) +--R +--R +--R n + 2 n +--R n sec(b x + a) + (- n - 2)sec(b x + a) +--R (112) -------------------------------------------- +--R 2 +--R b n + 2b n +--R Type: Expression(Integer) +--E 112 + +--S 113 of 534 +a0620:= integrate(t0620,x) +--R +--R +--R 1 +--R n log(-------------) +--R 2 +--R cos(b x + a) +--R -------------------- +--R 2 2 +--R ((- n - 2)cos(b x + a) + n)%e +--R (113) -------------------------------------------------- +--R 2 2 +--R (b n + 2b n)cos(b x + a) +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 534 +m0620:= a0620-r0620 +--R +--R +--R (114) +--R 1 +--R n log(-------------) +--R 2 +--R cos(b x + a) +--R -------------------- +--R 2 2 +--R ((- n - 2)cos(b x + a) + n)%e +--R + +--R 2 n + 2 2 n +--R - n cos(b x + a) sec(b x + a) + (n + 2)cos(b x + a) sec(b x + a) +--R / +--R 2 2 +--R (b n + 2b n)cos(b x + a) +--R Type: Expression(Integer) +--E 114 + +--S 115 of 534 +d0620:= D(m0620,x) +--R +--R +--R (115) +--R 1 +--R n log(-------------) +--R 2 +--R cos(b x + a) +--R -------------------- +--R 2 2 +--R (- cos(b x + a) + 1)sin(b x + a)%e +--R + +--R 3 n + 1 +--R - cos(b x + a) sec(b x + a)tan(b x + a)sec(b x + a) +--R + +--R 3 n - 1 +--R cos(b x + a) sec(b x + a)tan(b x + a)sec(b x + a) +--R / +--R 3 +--R cos(b x + a) +--R Type: Expression(Integer) +--E 115 + +--S 116 of 534 +t0621:= sec(a+b*x)^4*tan(a+b*x)^n +--R +--R +--R 4 n +--R (116) sec(b x + a) tan(b x + a) +--R Type: Expression(Integer) +--E 116 + +--S 117 of 534 +r0621:= tan(a+b*x)^(1+n)/b/(1+n)+tan(a+b*x)^(3+n)/b/(3+n) +--R +--R +--R n + 3 n + 1 +--R (n + 1)tan(b x + a) + (n + 3)tan(b x + a) +--R (117) --------------------------------------------------- +--R 2 +--R b n + 4b n + 3b +--R Type: Expression(Integer) +--E 117 + +--S 118 of 534 +a0621:= integrate(t0621,x) +--R +--R +--R sin(b x + a) +--R n log(------------) +--R 2 cos(b x + a) +--R (2cos(b x + a) + n + 1)sin(b x + a)%e +--R (118) --------------------------------------------------------- +--R 2 3 +--R (b n + 4b n + 3b)cos(b x + a) +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 534 +m0621:= a0621-r0621 +--R +--R +--R (119) +--R sin(b x + a) +--R n log(------------) +--R 2 cos(b x + a) +--R (2cos(b x + a) + n + 1)sin(b x + a)%e +--R + +--R 3 n + 3 +--R (- n - 1)cos(b x + a) tan(b x + a) +--R + +--R 3 n + 1 +--R (- n - 3)cos(b x + a) tan(b x + a) +--R / +--R 2 3 +--R (b n + 4b n + 3b)cos(b x + a) +--R Type: Expression(Integer) +--E 119 + +--S 120 of 534 +d0621:= D(m0621,x) +--R +--R +--R (120) +--R 2 2 4 +--R (2cos(b x + a) + n + 3)sin(b x + a) + 2cos(b x + a) +--R + +--R 2 +--R (n + 1)cos(b x + a) +--R * +--R sin(b x + a) +--R n log(------------) +--R cos(b x + a) +--R %e +--R + +--R 4 2 4 +--R ((- n - 3)cos(b x + a) tan(b x + a) + (- n - 3)cos(b x + a) ) +--R * +--R n + 2 +--R tan(b x + a) +--R + +--R 4 2 4 n +--R ((- n - 3)cos(b x + a) tan(b x + a) + (- n - 3)cos(b x + a) )tan(b x + a) +--R / +--R 4 +--R (n + 3)cos(b x + a) +--R Type: Expression(Integer) +--E 120 + +--S 121 of 534 +t0622:= sec(a+b*x)*tan(a+b*x)^2 +--R +--R +--R 2 +--R (121) sec(b x + a)tan(b x + a) +--R Type: Expression(Integer) +--E 121 + +--S 122 of 534 +r0622:= -1/2*atanh(sin(a+b*x))/b+1/2*sec(a+b*x)*tan(a+b*x)/b +--R +--R +--R - atanh(sin(b x + a)) + sec(b x + a)tan(b x + a) +--R (122) ------------------------------------------------ +--R 2b +--R Type: Expression(Integer) +--E 122 + +--S 123 of 534 +a0622:= integrate(t0622,x) +--R +--R +--R (123) +--R 2 sin(b x + a) + cos(b x + a) + 1 +--R - cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 sin(b x + a) - cos(b x + a) - 1 +--R cos(b x + a) log(-------------------------------) + sin(b x + a) +--R cos(b x + a) + 1 +--R / +--R 2 +--R 2b cos(b x + a) +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 534 +m0622:= a0622-r0622 +--R +--R +--R (124) +--R 2 sin(b x + a) + cos(b x + a) + 1 +--R - cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 sin(b x + a) - cos(b x + a) - 1 +--R cos(b x + a) log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R 2 2 +--R cos(b x + a) atanh(sin(b x + a)) - cos(b x + a) sec(b x + a)tan(b x + a) +--R + +--R sin(b x + a) +--R / +--R 2 +--R 2b cos(b x + a) +--R Type: Expression(Integer) +--E 124 + +--S 125 of 534 +d0622:= D(m0622,x) +--R +--R +--R (125) +--R 3 4 +--R - 2cos(b x + a) sec(b x + a)sin(b x + a) +--R + +--R 5 4 3 +--R (2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) )sec(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R (- 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a) )sec(b x + a) +--R * +--R 2 +--R tan(b x + a) +--R + +--R 6 +--R 2sin(b x + a) +--R + +--R 3 3 2 +--R - cos(b x + a) sec(b x + a) + 2cos(b x + a) - cos(b x + a) +--R + +--R - 4cos(b x + a) - 4 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 5 4 3 +--R (cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) )sec(b x + a) +--R + +--R 5 3 +--R 2cos(b x + a) - 4cos(b x + a) + 4cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R (- cos(b x + a) - 2cos(b x + a) - cos(b x + a) )sec(b x + a) +--R + +--R 6 3 2 +--R cos(b x + a) + 2cos(b x + a) + cos(b x + a) +--R / +--R 3 4 +--R 2cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 2 +--R (- 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R 2cos(b x + a) + 4cos(b x + a) + 2cos(b x + a) +--R Type: Expression(Integer) +--E 125 + +--S 126 of 534 +t0623:= sec(1/2*x)^3*tan(1/2*x)^2 +--R +--R +--R x 3 x 2 +--R (126) sec(-) tan(-) +--R 2 2 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 534 +r0623:= -1/4*atanh(sin(1/2*x))+1/4*sec(1/2*x)*tan(1/2*x)+_ + 1/2*sec(1/2*x)*tan(1/2*x)^3 +--R +--R +--R x x x 3 x x +--R - atanh(sin(-)) + 2sec(-)tan(-) + sec(-)tan(-) +--R 2 2 2 2 2 +--R (127) ----------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 534 +a0623:= integrate(t0623,x) +--R +--R +--R (128) +--R x x x x +--R sin(-) + cos(-) + 1 sin(-) - cos(-) - 1 +--R x 4 2 2 x 4 2 2 +--R - cos(-) log(-------------------) + cos(-) log(-------------------) +--R 2 x 2 x +--R cos(-) + 1 cos(-) + 1 +--R 2 2 +--R + +--R x 2 x +--R (- cos(-) + 2)sin(-) +--R 2 2 +--R / +--R x 4 +--R 4cos(-) +--R 2 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 534 +m0623:= a0623-r0623 +--R +--R +--R (129) +--R x x x x +--R sin(-) + cos(-) + 1 sin(-) - cos(-) - 1 +--R x 4 2 2 x 4 2 2 +--R - cos(-) log(-------------------) + cos(-) log(-------------------) +--R 2 x 2 x +--R cos(-) + 1 cos(-) + 1 +--R 2 2 +--R + +--R x 4 x x 4 x x 3 x 4 x x +--R cos(-) atanh(sin(-)) - 2cos(-) sec(-)tan(-) - cos(-) sec(-)tan(-) +--R 2 2 2 2 2 2 2 2 +--R + +--R x 2 x +--R (- cos(-) + 2)sin(-) +--R 2 2 +--R / +--R x 4 +--R 4cos(-) +--R 2 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 534 +d0623:= D(m0623,x) +--R +--R +--R (130) +--R x 5 x x 4 +--R - 8cos(-) sec(-)sin(-) +--R 2 2 2 +--R + +--R x 7 x 6 x 5 x x 2 +--R (8cos(-) + 16cos(-) + 16cos(-) )sec(-)sin(-) +--R 2 2 2 2 2 +--R + +--R x 7 x 6 x 5 x +--R (- 8cos(-) - 16cos(-) - 8cos(-) )sec(-) +--R 2 2 2 2 +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R x 5 x x 4 +--R - 8cos(-) sec(-)sin(-) +--R 2 2 2 +--R + +--R x 7 x 6 x 5 x x 2 +--R (8cos(-) + 16cos(-) + 16cos(-) )sec(-)sin(-) +--R 2 2 2 2 2 +--R + +--R x 7 x 6 x 5 x +--R (- 8cos(-) - 16cos(-) - 8cos(-) )sec(-) +--R 2 2 2 2 +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R x 2 x 6 +--R (- 2cos(-) + 8)sin(-) +--R 2 2 +--R + +--R x 5 x x 5 x 4 x 3 x 2 x +--R - cos(-) sec(-) + 2cos(-) + cos(-) + 4cos(-) - 2cos(-) - 16cos(-) +--R 2 2 2 2 2 2 2 +--R + +--R - 16 +--R * +--R x 4 +--R sin(-) +--R 2 +--R + +--R x 7 x 6 x 5 x x 7 x 6 +--R (cos(-) + 2cos(-) + 2cos(-) )sec(-) + 2cos(-) + 2cos(-) +--R 2 2 2 2 2 2 +--R + +--R x 4 x 3 x 2 x +--R - 2cos(-) - 8cos(-) + 2cos(-) + 16cos(-) + 8 +--R 2 2 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 7 x 6 x 5 x x 8 x 6 x 5 +--R (- cos(-) - 2cos(-) - cos(-) )sec(-) + cos(-) - 2cos(-) - 2cos(-) +--R 2 2 2 2 2 2 2 +--R + +--R x 4 x 3 x 2 +--R cos(-) + 4cos(-) + 2cos(-) +--R 2 2 2 +--R / +--R x 5 x 4 x 7 x 6 x 5 x 2 x 7 +--R 8cos(-) sin(-) + (- 8cos(-) - 16cos(-) - 16cos(-) )sin(-) + 8cos(-) +--R 2 2 2 2 2 2 2 +--R + +--R x 6 x 5 +--R 16cos(-) + 8cos(-) +--R 2 2 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 534 +t0624:= cot(a+b*x)^n*csc(a+b*x)^2 +--R +--R +--R 2 n +--R (131) csc(b x + a) cot(b x + a) +--R Type: Expression(Integer) +--E 131 + +--S 132 of 534 +r0624:= -cot(a+b*x)^(1+n)/b/(1+n) +--R +--R +--R n + 1 +--R cot(b x + a) +--R (132) - ----------------- +--R b n + b +--R Type: Expression(Integer) +--E 132 + +--S 133 of 534 +a0624:= integrate(t0624,x) +--R +--R +--R cos(b x + a) +--R n log(------------) +--R sin(b x + a) +--R cos(b x + a)%e +--R (133) - --------------------------------- +--R (b n + b)sin(b x + a) +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 534 +m0624:= a0624-r0624 +--R +--R +--R cos(b x + a) +--R n log(------------) +--R sin(b x + a) n + 1 +--R - cos(b x + a)%e + sin(b x + a)cot(b x + a) +--R (134) ------------------------------------------------------------------- +--R (b n + b)sin(b x + a) +--R Type: Expression(Integer) +--E 134 + +--S 135 of 534 +d0624:= D(m0624,x) +--R +--R +--R (135) +--R cos(b x + a) +--R n log(------------) +--R 2 2 sin(b x + a) +--R (sin(b x + a) + cos(b x + a) )%e +--R + +--R 2 2 n +--R (- cot(b x + a) - 1)sin(b x + a) cot(b x + a) +--R / +--R 2 +--R sin(b x + a) +--R Type: Expression(Integer) +--E 135 + +--S 136 of 534 +t0625:= cot(a+b*x)^3*csc(a+b*x)^n +--R +--R +--R 3 n +--R (136) cot(b x + a) csc(b x + a) +--R Type: Expression(Integer) +--E 136 + +--S 137 of 534 +r0625:= csc(a+b*x)^n/b/n-csc(a+b*x)^(2+n)/b/(2+n) +--R +--R +--R n + 2 n +--R - n csc(b x + a) + (n + 2)csc(b x + a) +--R (137) -------------------------------------------- +--R 2 +--R b n + 2b n +--R Type: Expression(Integer) +--E 137 + +--S 138 of 534 +a0625:= integrate(t0625,x) +--R +--R +--R 1 +--R n log(- -----------------) +--R 2 +--R cos(b x + a) - 1 +--R -------------------------- +--R 2 2 +--R ((n + 2)cos(b x + a) - 2)%e +--R (138) ------------------------------------------------------ +--R 2 2 2 +--R (b n + 2b n)cos(b x + a) - b n - 2b n +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 534 +m0625:= a0625-r0625 +--R +--R +--R (139) +--R 1 +--R n log(- -----------------) +--R 2 +--R cos(b x + a) - 1 +--R -------------------------- +--R 2 2 +--R ((n + 2)cos(b x + a) - 2)%e +--R + +--R 2 n + 2 +--R (n cos(b x + a) - n)csc(b x + a) +--R + +--R 2 n +--R ((- n - 2)cos(b x + a) + n + 2)csc(b x + a) +--R / +--R 2 2 2 +--R (b n + 2b n)cos(b x + a) - b n - 2b n +--R Type: Expression(Integer) +--E 139 + +--S 140 of 534 +d0625:= D(m0625,x) +--R +--R +--R (140) +--R 1 +--R n log(- -----------------) +--R 2 +--R cos(b x + a) - 1 +--R -------------------------- +--R 3 2 +--R cos(b x + a) sin(b x + a)%e +--R + +--R 4 2 +--R (- cos(b x + a) + 2cos(b x + a) - 1)cot(b x + a)csc(b x + a) +--R * +--R n + 1 +--R csc(b x + a) +--R + +--R 4 2 +--R (cos(b x + a) - 2cos(b x + a) + 1)cot(b x + a)csc(b x + a) +--R * +--R n - 1 +--R csc(b x + a) +--R / +--R 4 2 +--R cos(b x + a) - 2cos(b x + a) + 1 +--R Type: Expression(Integer) +--E 140 + +--S 141 of 534 +t0626:= cot(a+b*x)^2*csc(a+b*x) +--R +--R +--R 2 +--R (141) cot(b x + a) csc(b x + a) +--R Type: Expression(Integer) +--E 141 + +--S 142 of 534 +r0626:= 1/2*atanh(cos(a+b*x))/b-1/2*cot(a+b*x)*csc(a+b*x)/b +--R +--R +--R atanh(cos(b x + a)) - cot(b x + a)csc(b x + a) +--R (142) ---------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 142 + +--S 143 of 534 +a0626:= integrate(t0626,x) +--R +--R +--R 2 sin(b x + a) +--R (- cos(b x + a) + 1)log(----------------) + cos(b x + a) +--R cos(b x + a) + 1 +--R (143) --------------------------------------------------------- +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 534 +m0626:= a0626-r0626 +--R +--R +--R (144) +--R 2 sin(b x + a) +--R (- cos(b x + a) + 1)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 2 +--R (- cos(b x + a) + 1)atanh(cos(b x + a)) +--R + +--R 2 +--R (cos(b x + a) - 1)cot(b x + a)csc(b x + a) + cos(b x + a) +--R / +--R 2 +--R 2b cos(b x + a) - 2b +--R Type: Expression(Integer) +--E 144 + +--S 145 of 534 +d0626:= D(m0626,x) +--R +--R +--R (145) +--R 3 2 2 +--R (- cos(b x + a) + cos(b x + a) + cos(b x + a) + 1)sin(b x + a) +--R + +--R 4 2 2 4 +--R (- 2cos(b x + a) + 4cos(b x + a) - 2)cot(b x + a) - cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) - 1 +--R * +--R csc(b x + a)sin(b x + a) +--R + +--R 5 3 +--R - cos(b x + a) + 2cos(b x + a) - cos(b x + a) +--R / +--R 4 2 +--R (2cos(b x + a) - 4cos(b x + a) + 2)sin(b x + a) +--R Type: Expression(Integer) +--E 145 + +--S 146 of 534 +t0627:= cot(a+b*x)^2*csc(a+b*x)^3 +--R +--R +--R 2 3 +--R (146) cot(b x + a) csc(b x + a) +--R Type: Expression(Integer) +--E 146 + +--S 147 of 534 +r0627:= 1/8*atanh(cos(a+b*x))/b-1/8*cot(a+b*x)*csc(a+b*x)/b-_ + 1/4*cot(a+b*x)^3*csc(a+b*x)/b +--R +--R +--R 3 +--R atanh(cos(b x + a)) + (- 2cot(b x + a) - cot(b x + a))csc(b x + a) +--R (147) ------------------------------------------------------------------- +--R 8b +--R Type: Expression(Integer) +--E 147 + +--S 148 of 534 +a0627:= integrate(t0627,x) +--R +--R +--R (148) +--R 4 2 sin(b x + a) +--R (- cos(b x + a) + 2cos(b x + a) - 1)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 3 +--R - cos(b x + a) - cos(b x + a) +--R / +--R 4 2 +--R 8b cos(b x + a) - 16b cos(b x + a) + 8b +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 534 +m0627:= a0627-r0627 +--R +--R +--R (149) +--R 4 2 sin(b x + a) +--R (- cos(b x + a) + 2cos(b x + a) - 1)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 4 2 +--R (- cos(b x + a) + 2cos(b x + a) - 1)atanh(cos(b x + a)) +--R + +--R 4 2 3 +--R (2cos(b x + a) - 4cos(b x + a) + 2)cot(b x + a) +--R + +--R 4 2 +--R (cos(b x + a) - 2cos(b x + a) + 1)cot(b x + a) +--R * +--R csc(b x + a) +--R + +--R 3 +--R - cos(b x + a) - cos(b x + a) +--R / +--R 4 2 +--R 8b cos(b x + a) - 16b cos(b x + a) + 8b +--R Type: Expression(Integer) +--E 149 + +--S 150 of 534 +d0627:= D(m0627,x) +--R +--R +--R (150) +--R 5 4 3 2 +--R - cos(b x + a) - cos(b x + a) + 2cos(b x + a) - 6cos(b x + a) +--R + +--R - cos(b x + a) - 1 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 4 2 +--R (- 8cos(b x + a) + 24cos(b x + a) - 24cos(b x + a) + 8) +--R * +--R 4 +--R cot(b x + a) +--R + +--R 6 4 2 +--R (- 8cos(b x + a) + 24cos(b x + a) - 24cos(b x + a) + 8) +--R * +--R 2 +--R cot(b x + a) +--R + +--R 6 4 2 +--R - cos(b x + a) + 3cos(b x + a) - 3cos(b x + a) + 1 +--R * +--R csc(b x + a)sin(b x + a) +--R + +--R 7 5 3 +--R - cos(b x + a) + 3cos(b x + a) - 3cos(b x + a) + cos(b x + a) +--R / +--R 6 4 2 +--R (8cos(b x + a) - 24cos(b x + a) + 24cos(b x + a) - 8)sin(b x + a) +--R Type: Expression(Integer) +--E 150 + +--S 151 of 534 +t0628:= cot(a+b*x)^4*csc(a+b*x) +--R +--R +--R 4 +--R (151) cot(b x + a) csc(b x + a) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 534 +r0628:= -3/8*atanh(cos(a+b*x))/b+3/8*cot(a+b*x)*csc(a+b*x)/b-_ + 1/4*cot(a+b*x)^3*csc(a+b*x)/b +--R +--R +--R (152) +--R 3 +--R - 3atanh(cos(b x + a)) + (- 2cot(b x + a) + 3cot(b x + a))csc(b x + a) +--R ----------------------------------------------------------------------- +--R 8b +--R Type: Expression(Integer) +--E 152 + +--S 153 of 534 +a0628:= integrate(t0628,x) +--R +--R +--R (153) +--R 4 2 sin(b x + a) +--R (3cos(b x + a) - 6cos(b x + a) + 3)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 3 +--R - 5cos(b x + a) + 3cos(b x + a) +--R / +--R 4 2 +--R 8b cos(b x + a) - 16b cos(b x + a) + 8b +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 534 +m0628:= a0628-r0628 +--R +--R +--R (154) +--R 4 2 sin(b x + a) +--R (3cos(b x + a) - 6cos(b x + a) + 3)log(----------------) +--R cos(b x + a) + 1 +--R + +--R 4 2 +--R (3cos(b x + a) - 6cos(b x + a) + 3)atanh(cos(b x + a)) +--R + +--R 4 2 3 +--R (2cos(b x + a) - 4cos(b x + a) + 2)cot(b x + a) +--R + +--R 4 2 +--R (- 3cos(b x + a) + 6cos(b x + a) - 3)cot(b x + a) +--R * +--R csc(b x + a) +--R + +--R 3 +--R - 5cos(b x + a) + 3cos(b x + a) +--R / +--R 4 2 +--R 8b cos(b x + a) - 16b cos(b x + a) + 8b +--R Type: Expression(Integer) +--E 154 + +--S 155 of 534 +d0628:= D(m0628,x) +--R +--R +--R (155) +--R 5 4 3 2 +--R 3cos(b x + a) - 5cos(b x + a) - 6cos(b x + a) - 6cos(b x + a) +--R + +--R 3cos(b x + a) + 3 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 4 2 +--R (- 8cos(b x + a) + 24cos(b x + a) - 24cos(b x + a) + 8) +--R * +--R 4 +--R cot(b x + a) +--R + +--R 6 4 2 +--R 3cos(b x + a) - 9cos(b x + a) + 9cos(b x + a) - 3 +--R * +--R csc(b x + a)sin(b x + a) +--R + +--R 7 5 3 +--R 3cos(b x + a) - 9cos(b x + a) + 9cos(b x + a) - 3cos(b x + a) +--R / +--R 6 4 2 +--R (8cos(b x + a) - 24cos(b x + a) + 24cos(b x + a) - 8)sin(b x + a) +--R Type: Expression(Integer) +--E 155 + +--S 156 of 534 +t0629:= cot(3*x)^4*csc(3*x) +--R +--R +--R 4 +--R (156) cot(3x) csc(3x) +--R Type: Expression(Integer) +--E 156 + +--S 157 of 534 +r0629:= -1/8*atanh(cos(3*x))+1/8*cot(3*x)*csc(3*x)-1/12*cot(3*x)^3*csc(3*x) +--R +--R +--R 3 +--R - 3atanh(cos(3x)) + (- 2cot(3x) + 3cot(3x))csc(3x) +--R (157) --------------------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 534 +a0629:= integrate(t0629,x) +--R +--R +--R 4 2 sin(3x) 3 +--R (3cos(3x) - 6cos(3x) + 3)log(-----------) - 5cos(3x) + 3cos(3x) +--R cos(3x) + 1 +--R (158) ------------------------------------------------------------------ +--R 4 2 +--R 24cos(3x) - 48cos(3x) + 24 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 534 +m0629:= a0629-r0629 +--R +--R +--R (159) +--R 4 2 sin(3x) +--R (3cos(3x) - 6cos(3x) + 3)log(-----------) +--R cos(3x) + 1 +--R + +--R 4 2 +--R (3cos(3x) - 6cos(3x) + 3)atanh(cos(3x)) +--R + +--R 4 2 3 +--R (2cos(3x) - 4cos(3x) + 2)cot(3x) +--R + +--R 4 2 +--R (- 3cos(3x) + 6cos(3x) - 3)cot(3x) +--R * +--R csc(3x) +--R + +--R 3 +--R - 5cos(3x) + 3cos(3x) +--R / +--R 4 2 +--R 24cos(3x) - 48cos(3x) + 24 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 534 +d0629:= D(m0629,x) +--R +--R +--R (160) +--R 5 4 3 2 2 +--R (3cos(3x) - 5cos(3x) - 6cos(3x) - 6cos(3x) + 3cos(3x) + 3)sin(3x) +--R + +--R 6 4 2 4 6 +--R (- 8cos(3x) + 24cos(3x) - 24cos(3x) + 8)cot(3x) + 3cos(3x) +--R + +--R 4 2 +--R - 9cos(3x) + 9cos(3x) - 3 +--R * +--R csc(3x)sin(3x) +--R + +--R 7 5 3 +--R 3cos(3x) - 9cos(3x) + 9cos(3x) - 3cos(3x) +--R / +--R 6 4 2 +--R (8cos(3x) - 24cos(3x) + 24cos(3x) - 8)sin(3x) +--R Type: Expression(Integer) +--E 160 + +--S 161 of 534 +t0630:= cot(x)^4*csc(x)^3 +--R +--R +--R 4 3 +--R (161) cot(x) csc(x) +--R Type: Expression(Integer) +--E 161 + +--S 162 of 534 +r0630:= -1/16*atanh(cos(x))+1/16*cot(x)*csc(x)-_ + 1/24*cot(x)^3*csc(x)-1/6*cot(x)^5*csc(x) +--R +--R +--R 5 3 +--R - 3atanh(cos(x)) + (- 8cot(x) - 2cot(x) + 3cot(x))csc(x) +--R (162) ---------------------------------------------------------- +--R 48 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 534 +a0630:= integrate(t0630,x) +--R +--R +--R (163) +--R 6 4 2 sin(x) 5 3 +--R (3cos(x) - 9cos(x) + 9cos(x) - 3)log(----------) + 3cos(x) + 8cos(x) +--R cos(x) + 1 +--R + +--R - 3cos(x) +--R / +--R 6 4 2 +--R 48cos(x) - 144cos(x) + 144cos(x) - 48 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 534 +m0630:= a0630-r0630 +--R +--R +--R (164) +--R 6 4 2 sin(x) +--R (3cos(x) - 9cos(x) + 9cos(x) - 3)log(----------) +--R cos(x) + 1 +--R + +--R 6 4 2 +--R (3cos(x) - 9cos(x) + 9cos(x) - 3)atanh(cos(x)) +--R + +--R 6 4 2 5 +--R (8cos(x) - 24cos(x) + 24cos(x) - 8)cot(x) +--R + +--R 6 4 2 3 +--R (2cos(x) - 6cos(x) + 6cos(x) - 2)cot(x) +--R + +--R 6 4 2 +--R (- 3cos(x) + 9cos(x) - 9cos(x) + 3)cot(x) +--R * +--R csc(x) +--R + +--R 5 3 +--R 3cos(x) + 8cos(x) - 3cos(x) +--R / +--R 6 4 2 +--R 48cos(x) - 144cos(x) + 144cos(x) - 48 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 534 +d0630:= D(m0630,x) +--R +--R +--R (165) +--R 7 6 5 4 3 2 +--R cos(x) + cos(x) - 3cos(x) + 13cos(x) + 3cos(x) + 3cos(x) +--R + +--R - cos(x) - 1 +--R * +--R 2 +--R sin(x) +--R + +--R 8 6 4 2 6 +--R (- 16cos(x) + 64cos(x) - 96cos(x) + 64cos(x) - 16)cot(x) +--R + +--R 8 6 4 2 4 +--R (- 16cos(x) + 64cos(x) - 96cos(x) + 64cos(x) - 16)cot(x) +--R + +--R 8 6 4 2 +--R cos(x) - 4cos(x) + 6cos(x) - 4cos(x) + 1 +--R * +--R csc(x)sin(x) +--R + +--R 9 7 5 3 +--R cos(x) - 4cos(x) + 6cos(x) - 4cos(x) + cos(x) +--R / +--R 8 6 4 2 +--R (16cos(x) - 64cos(x) + 96cos(x) - 64cos(x) + 16)sin(x) +--R Type: Expression(Integer) +--E 165 + +--S 166 of 534 +t0631:= cos(x)^(2/3)/sin(x)^(8/3) +--R +--R +--R 3+------+2 +--R \|cos(x) +--R (166) ----------------- +--R 2 3+------+2 +--R sin(x) \|sin(x) +--R Type: Expression(Integer) +--E 166 + +--S 167 of 534 +r0631:= -3/5*cos(x)^(5/3)/sin(x)^(5/3) +--R +--R +--R 3+------+2 +--R 3cos(x)\|cos(x) +--R (167) - ----------------- +--R 3+------+2 +--R 5sin(x)\|sin(x) +--R Type: Expression(Integer) +--E 167 + +--S 168 of 534 +--a0631:= integrate(t0631,x) +--E 168 + +--S 169 of 534 +--m0631:= a0631-r0631 +--E 169 + +--S 170 of 534 +--d0631:= D(m0631,x) +--E 170 + +--S 171 of 534 +t0632:= sin(x)^(2/3)/cos(x)^(8/3) +--R +--R +--R 3+------+2 +--R \|sin(x) +--R (168) ----------------- +--R 2 3+------+2 +--R cos(x) \|cos(x) +--R Type: Expression(Integer) +--E 171 + +--S 172 of 534 +r0632:= 3/5*sin(x)^(5/3)/cos(x)^(5/3) +--R +--R +--R 3+------+2 +--R 3sin(x)\|sin(x) +--R (169) ----------------- +--R 3+------+2 +--R 5cos(x)\|cos(x) +--R Type: Expression(Integer) +--E 172 + +--S 173 of 534 +--a0632:= integrate(t0632,x) +--E 173 + +--S 174 of 534 +--m0632:= a0632-r0632 +--E 174 + +--S 175 of 534 +--d0632:= D(m0632,x) +--E 175 + +--S 176 of 534 +t0633:= sin(x)^(1/2)/cos(x)^(1/2) +--R +--R +--R +------+ +--R \|sin(x) +--R (170) --------- +--R +------+ +--R \|cos(x) +--R Type: Expression(Integer) +--E 176 + +--S 177 of 534 +r0633:= -1/2*atan(1-2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2))*2^(1/2)+_ + 1/2*atan(1+2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2))*2^(1/2)+_ + 1/4*log(1-2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2)+tan(x))*2^(1/2)-_ + 1/4*log(1+2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2)+tan(x))*2^(1/2) +--R +--R +--R (171) +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R - \|2 log(-------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ - \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R \|2 log(---------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + \|cos(x) +-+ \|2 \|sin(x) - \|cos(x) +--R 2\|2 atan(-------------------------) + 2\|2 atan(-------------------------) +--R +------+ +------+ +--R \|cos(x) \|cos(x) +--R / +--R 4 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 534 +a0633:= integrate(t0633,x) +--R +--R +--R >> Error detected within library code: +--R Imaginary part is nonzero. Cannot retract. +--R +--R Continuing to read the file... +--R +--E 178 + +--S 179 of 534 +m0633:= a0633-r0633 +--R +--R +--R (172) +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R \|2 log(-------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ - \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R - \|2 log(---------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + \|cos(x) +--R - 2\|2 atan(-------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) - \|cos(x) +--R - 2\|2 atan(-------------------------) + 4a0633 +--R +------+ +--R \|cos(x) +--R / +--R 4 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 534 +d0633:= D(m0633,x) +--R +--R +--R (173) +--R 2 2 +--R (- 3cos(x)sin(x) - cos(x) )tan(x) +--R + +--R 2 2 2 +--R (sin(x) - 2cos(x)sin(x) - cos(x) )tan(x) + 3sin(x) - cos(x)sin(x) +--R * +--R +------+ +------+ +--R \|cos(x) \|sin(x) +--R / +--R 2 2 2 2 +--R 2cos(x) sin(x)tan(x) + 4cos(x) sin(x)tan(x) - 4cos(x)sin(x) +--R + +--R 2 +--R 2cos(x) sin(x) +--R Type: Expression(Integer) +--E 180 + +--S 181 of 534 +t0634:= sin(x)^(5/2)/cos(x)^(1/2) +--R +--R +--R 2 +------+ +--R sin(x) \|sin(x) +--R (174) ---------------- +--R +------+ +--R \|cos(x) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 534 +r0634:= -3/8*atan(1-2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2))*2^(1/2)+_ + 3/8*atan(1+2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2))*2^(1/2)+_ + 3/16*log(1-2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2)+tan(x))*2^(1/2)-_ + 3/16*log(1+2^(1/2)*sin(x)^(1/2)/cos(x)^(1/2)+tan(x))*2^(1/2)-_ + 1/2*cos(x)^(1/2)*sin(x)^(3/2) +--R +--R +--R (175) +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R - 3\|2 log(-------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ - \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R 3\|2 log(---------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + \|cos(x) +--R 6\|2 atan(-------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) - \|cos(x) +------+ +------+ +--R 6\|2 atan(-------------------------) - 8sin(x)\|cos(x) \|sin(x) +--R +------+ +--R \|cos(x) +--R / +--R 16 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 534 +a0634:= integrate(t0634,x) +--R +--R +--R >> Error detected within library code: +--R Imaginary part is nonzero. Cannot retract. +--R +--R Continuing to read the file... +--R +--E 183 + +--S 184 of 534 +m0634:= a0634-r0634 +--R +--R +--R (176) +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R 3\|2 log(-------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ - \|2 \|sin(x) + (tan(x) + 1)\|cos(x) +--R - 3\|2 log(---------------------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) + \|cos(x) +--R - 6\|2 atan(-------------------------) +--R +------+ +--R \|cos(x) +--R + +--R +-+ +------+ +------+ +--R +-+ \|2 \|sin(x) - \|cos(x) +------+ +------+ +--R - 6\|2 atan(-------------------------) + 8sin(x)\|cos(x) \|sin(x) +--R +------+ +--R \|cos(x) +--R + +--R 16a0634 +--R / +--R 16 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 534 +d0634:= D(m0634,x) +--R +--R +--R (177) +--R 3 3 2 2 +--R (- 2cos(x)sin(x) + (6cos(x) - 9cos(x))sin(x) - 3cos(x) )tan(x) +--R + +--R 3 2 3 2 +--R (- 4cos(x)sin(x) + 3sin(x) + (12cos(x) - 6cos(x))sin(x) - 3cos(x) ) +--R * +--R tan(x) +--R + +--R 4 3 2 2 +--R 4sin(x) - 2cos(x)sin(x) + (- 12cos(x) + 9)sin(x) +--R + +--R 3 +--R (6cos(x) - 3cos(x))sin(x) +--R / +--R 2 +------+ +------+ +--R (8cos(x)tan(x) + 16cos(x)tan(x) - 16sin(x) + 8cos(x))\|cos(x) \|sin(x) +--R Type: Expression(Integer) +--E 185 + +--S 186 of 534 +t0635:= sec(x)^(3/2)*sin(x) +--R +--R +--R +------+ +--R (178) sec(x)sin(x)\|sec(x) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 534 +r0635:= 2*sec(x)^(1/2) +--R +--R +--R +------+ +--R (179) 2\|sec(x) +--R Type: Expression(Integer) +--E 187 + +--S 188 of 534 +a0635:= integrate(t0635,x) +--R +--R +--R +-------+ +--R 2 | 1 +--R (2cos(x) - 1) |------- +--R 4| 2 +--R \|cos(x) +--R (180) ------------------------ +--R 2 +--R 2cos(x) +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 534 +m0635:= a0635-r0635 +--R +--R +--R +-------+ +--R 2 +------+ 2 | 1 +--R - 4cos(x) \|sec(x) + (2cos(x) - 1) |------- +--R 4| 2 +--R \|cos(x) +--R (181) ---------------------------------------------- +--R 2 +--R 2cos(x) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 534 +d0635:= D(m0635,x) +--R +--R +--R +-------+3 +--R 2 +------+ 5 | 1 +--R (2cos(x) - 5)sin(x)\|sec(x) - 4cos(x) sec(x)tan(x) |------- +--R 4| 2 +--R \|cos(x) +--R (182) --------------------------------------------------------------- +--R +-------+3 +--R 5 | 1 +------+ +--R 4cos(x) |------- \|sec(x) +--R 4| 2 +--R \|cos(x) +--R Type: Expression(Integer) +--E 190 + +--S 191 of 534 +t0636:= sec(x)^(5/2)*sin(x) +--R +--R +--R 2 +------+ +--R (183) sec(x) sin(x)\|sec(x) +--R Type: Expression(Integer) +--E 191 + +--S 192 of 534 +r0636:= 2/3*sec(x)^(3/2) +--R +--R +--R +------+ +--R 2sec(x)\|sec(x) +--R (184) ---------------- +--R 3 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 534 +a0636:= integrate(t0636,x) +--R +--R +--R +-------+ +--R 2 | 1 +--R (2cos(x) - 1) |------- +--R 4| 2 +--R \|cos(x) +--R (185) ------------------------ +--R 3 +--R 6cos(x) +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 534 +m0636:= a0636-r0636 +--R +--R +--R +-------+ +--R 3 +------+ 2 | 1 +--R - 4cos(x) sec(x)\|sec(x) + (2cos(x) - 1) |------- +--R 4| 2 +--R \|cos(x) +--R (186) ---------------------------------------------------- +--R 3 +--R 6cos(x) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 534 +d0636:= D(m0636,x) +--R +--R +--R +-------+3 +--R 2 +------+ 6 2 | 1 +--R (6cos(x) - 7)sin(x)\|sec(x) - 12cos(x) sec(x) tan(x) |------- +--R 4| 2 +--R \|cos(x) +--R (187) ----------------------------------------------------------------- +--R +-------+3 +--R 6 | 1 +------+ +--R 12cos(x) |------- \|sec(x) +--R 4| 2 +--R \|cos(x) +--R Type: Expression(Integer) +--E 195 + +--S 196 of 534 +t0637:= sec(x)^(5/2)*sin(x)^3 +--R +--R +--R 2 3 +------+ +--R (188) sec(x) sin(x) \|sec(x) +--R Type: Expression(Integer) +--E 196 + +--S 197 of 534 +r0637:= 2/sec(x)^(1/2)+2/3*sec(x)^(3/2) +--R +--R +--R 2 +--R 2sec(x) + 6 +--R (189) ------------ +--R +------+ +--R 3\|sec(x) +--R Type: Expression(Integer) +--E 197 + +--S 198 of 534 +a0637:= integrate(t0637,x) +--R +--R +--R +-------+ +--R 2 | 1 +--R (6cos(x) + 2) |------- +--R 4| 2 +--R \|cos(x) +--R (190) ------------------------ +--R 3cos(x) +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 534 +m0637:= a0637-r0637 +--R +--R +--R +-------+ +--R 2 | 1 +------+ 2 +--R (6cos(x) + 2) |------- \|sec(x) - 2cos(x)sec(x) - 6cos(x) +--R 4| 2 +--R \|cos(x) +--R (191) ------------------------------------------------------------ +--R +------+ +--R 3cos(x)\|sec(x) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 534 +d0637:= D(m0637,x) +--R +--R +--R (192) +--R 2 +------+ +--R (- cos(x) + 1)sin(x)\|sec(x) +--R + +--R +-------+3 +--R 4 2 4 | 1 +--R (- cos(x) sec(x) + cos(x) )tan(x) |------- +--R 4| 2 +--R \|cos(x) +--R / +--R +-------+3 +--R 4 | 1 +------+ +--R cos(x) |------- \|sec(x) +--R 4| 2 +--R \|cos(x) +--R Type: Expression(Integer) +--E 200 + +--S 201 of 534 +t0638:= sec(x)^(9/2)*sin(x)^3 +--R +--R +--R 4 3 +------+ +--R (193) sec(x) sin(x) \|sec(x) +--R Type: Expression(Integer) +--E 201 + +--S 202 of 534 +r0638:= -2/3*sec(x)^(3/2)+2/7*sec(x)^(7/2) +--R +--R +--R 3 +------+ +--R (6sec(x) - 14sec(x))\|sec(x) +--R (194) ------------------------------ +--R 21 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 534 +a0638:= integrate(t0638,x) +--R +--R +--R +-------+ +--R 4 2 | 1 +--R (- 14cos(x) + 13cos(x) - 3) |------- +--R 4| 2 +--R \|cos(x) +--R (195) --------------------------------------- +--R 5 +--R 42cos(x) +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 534 +m0638:= a0638-r0638 +--R +--R +--R (196) +--R 5 3 5 +------+ +--R (- 12cos(x) sec(x) + 28cos(x) sec(x))\|sec(x) +--R + +--R +-------+ +--R 4 2 | 1 +--R (- 14cos(x) + 13cos(x) - 3) |------- +--R 4| 2 +--R \|cos(x) +--R / +--R 5 +--R 42cos(x) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 534 +d0638:= D(m0638,x) +--R +--R +--R (197) +--R 4 2 +------+ +--R (- 42cos(x) + 91cos(x) - 33)sin(x)\|sec(x) +--R + +--R +-------+3 +--R 8 4 8 2 | 1 +--R (- 84cos(x) sec(x) + 84cos(x) sec(x) )tan(x) |------- +--R 4| 2 +--R \|cos(x) +--R / +--R +-------+3 +--R 8 | 1 +------+ +--R 84cos(x) |------- \|sec(x) +--R 4| 2 +--R \|cos(x) +--R Type: Expression(Integer) +--E 205 + +--S 206 of 534 +t0639:= x*sin(a+b*x)^2*cos(a+b*x)^2 +--R +--R +--R 2 2 +--R (198) x cos(b x + a) sin(b x + a) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 534 +r0639:= -1/128*(-8*b^2*x^2+cos(4*a+4*b*x)+4*x*sin(4*a+4*b*x)*b)/b^2 +--R +--R +--R 2 2 +--R - 4b x sin(4b x + 4a) - cos(4b x + 4a) + 8b x +--R (199) ---------------------------------------------- +--R 2 +--R 128b +--R Type: Expression(Integer) +--E 207 + +--S 208 of 534 +a0639:= integrate(t0639,x) +--R +--R +--R (200) +--R 3 4 +--R (- 4b x cos(b x + a) + 2b x cos(b x + a))sin(b x + a) - cos(b x + a) +--R + +--R 2 2 2 +--R cos(b x + a) + b x +--R / +--R 2 +--R 16b +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 534 +m0639:= a0639-r0639 +--R +--R +--R (201) +--R 4b x sin(4b x + 4a) +--R + +--R 3 +--R (- 32b x cos(b x + a) + 16b x cos(b x + a))sin(b x + a) + cos(4b x + 4a) +--R + +--R 4 2 +--R - 8cos(b x + a) + 8cos(b x + a) +--R / +--R 2 +--R 128b +--R Type: Expression(Integer) +--E 209 + +--S 210 of 534 +d0639:= D(m0639,x) +--R +--R +--R (202) +--R 2 2 4 +--R (6x cos(b x + a) - x)sin(b x + a) + x cos(4b x + 4a) - 2x cos(b x + a) +--R + +--R 2 +--R x cos(b x + a) +--R / +--R 8 +--R Type: Expression(Integer) +--E 210 + +--S 211 of 534 +t0640:= x^2*sin(a+b*x)^2*cos(a+b*x)^2 +--R +--R +--R 2 2 2 +--R (203) x cos(b x + a) sin(b x + a) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 534 +r0640:= -1/768*(-32*b^3*x^3+12*b*x*cos(4*a+4*b*x)-3*sin(4*a+4*b*x)+_ + 24*x^2*sin(4*a+4*b*x)*b^2)/b^3 +--R +--R +--R 2 2 3 3 +--R (- 24b x + 3)sin(4b x + 4a) - 12b x cos(4b x + 4a) + 32b x +--R (204) ------------------------------------------------------------ +--R 3 +--R 768b +--R Type: Expression(Integer) +--E 212 + +--S 213 of 534 +a0640:= integrate(t0640,x) +--R +--R +--R (205) +--R 2 2 3 2 2 +--R ((- 48b x + 6)cos(b x + a) + (24b x - 3)cos(b x + a))sin(b x + a) +--R + +--R 4 2 3 3 +--R - 24b x cos(b x + a) + 24b x cos(b x + a) + 8b x - 3b x +--R / +--R 3 +--R 192b +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 534 +m0640:= a0640-r0640 +--R +--R +--R (206) +--R 2 2 +--R (8b x - 1)sin(4b x + 4a) +--R + +--R 2 2 3 2 2 +--R ((- 64b x + 8)cos(b x + a) + (32b x - 4)cos(b x + a))sin(b x + a) +--R + +--R 4 2 +--R 4b x cos(4b x + 4a) - 32b x cos(b x + a) + 32b x cos(b x + a) - 4b x +--R / +--R 3 +--R 256b +--R Type: Expression(Integer) +--E 214 + +--S 215 of 534 +d0640:= D(m0640,x) +--R +--R +--R (207) +--R 2 2 2 2 2 2 +--R ((48b x - 6)cos(b x + a) - 8b x + 1)sin(b x + a) +--R + +--R 2 2 2 2 4 +--R 8b x cos(4b x + 4a) + (- 16b x - 6)cos(b x + a) +--R + +--R 2 2 2 +--R (8b x + 7)cos(b x + a) - 1 +--R / +--R 2 +--R 64b +--R Type: Expression(Integer) +--E 215 + +--S 216 of 534 +t0641:= x^3*sin(a+b*x)^2*cos(a+b*x)^2 +--R +--R +--R 3 2 2 +--R (208) x cos(b x + a) sin(b x + a) +--R Type: Expression(Integer) +--E 216 + +--S 217 of 534 +r0641:= -1/1024*(-32*x^4*b^4-3*cos(4*a+4*b*x)+24*b^2*x^2*cos(4*a+4*b*x)-_ + 12*x*sin(4*a+4*b*x)*b+32*x^3*sin(4*a+4*b*x)*b^3)/b^4 +--R +--R +--R (209) +--R 3 3 2 2 4 4 +--R (- 32b x + 12b x)sin(4b x + 4a) + (- 24b x + 3)cos(4b x + 4a) + 32b x +--R ------------------------------------------------------------------------ +--R 4 +--R 1024b +--R Type: Expression(Integer) +--E 217 + +--S 218 of 534 +a0641:= integrate(t0641,x) +--R +--R +--R (210) +--R 3 3 3 3 3 +--R ((- 32b x + 12b x)cos(b x + a) + (16b x - 6b x)cos(b x + a)) +--R * +--R sin(b x + a) +--R + +--R 2 2 4 2 2 2 4 4 2 2 +--R (- 24b x + 3)cos(b x + a) + (24b x - 3)cos(b x + a) + 4b x - 3b x +--R / +--R 4 +--R 128b +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 534 +m0641:= a0641-r0641 +--R +--R +--R (211) +--R 3 3 +--R (32b x - 12b x)sin(4b x + 4a) +--R + +--R 3 3 3 3 3 +--R ((- 256b x + 96b x)cos(b x + a) + (128b x - 48b x)cos(b x + a)) +--R * +--R sin(b x + a) +--R + +--R 2 2 2 2 4 +--R (24b x - 3)cos(4b x + 4a) + (- 192b x + 24)cos(b x + a) +--R + +--R 2 2 2 2 2 +--R (192b x - 24)cos(b x + a) - 24b x +--R / +--R 4 +--R 1024b +--R Type: Expression(Integer) +--E 219 + +--S 220 of 534 +d0641:= D(m0641,x) +--R +--R +--R (212) +--R 2 3 2 2 3 2 +--R ((48b x - 18x)cos(b x + a) - 8b x + 3x)sin(b x + a) +--R + +--R 2 3 2 3 4 +--R 8b x cos(4b x + 4a) + (- 16b x - 18x)cos(b x + a) +--R + +--R 2 3 2 +--R (8b x + 21x)cos(b x + a) - 3x +--R / +--R 2 +--R 64b +--R Type: Expression(Integer) +--E 220 + +--S 221 of 534 +t0642:= x*sec(a+b*x)*tan(a+b*x) +--R +--R +--R (213) x sec(b x + a)tan(b x + a) +--R Type: Expression(Integer) +--E 221 + +--S 222 of 534 +r0642:= -atanh(sin(a+b*x))/b^2+x*sec(a+b*x)/b +--R +--R +--R - atanh(sin(b x + a)) + b x sec(b x + a) +--R (214) ---------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 222 + +--S 223 of 534 +a0642:= integrate(t0642,x) +--R +--R +--R (215) +--R sin(b x + a) + cos(b x + a) + 1 +--R - cos(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R cos(b x + a)log(-------------------------------) + b x +--R cos(b x + a) + 1 +--R / +--R 2 +--R b cos(b x + a) +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 534 +m0642:= a0642-r0642 +--R +--R +--R (216) +--R sin(b x + a) + cos(b x + a) + 1 +--R - cos(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R sin(b x + a) - cos(b x + a) - 1 +--R cos(b x + a)log(-------------------------------) +--R cos(b x + a) + 1 +--R + +--R cos(b x + a)atanh(sin(b x + a)) - b x cos(b x + a)sec(b x + a) + b x +--R / +--R 2 +--R b cos(b x + a) +--R Type: Expression(Integer) +--E 224 + +--S 225 of 534 +d0642:= D(m0642,x) +--R +--R +--R (217) +--R 2 4 +--R - b x cos(b x + a) sec(b x + a)sin(b x + a) +--R + +--R 4 3 2 +--R (b x cos(b x + a) + 2b x cos(b x + a) + 2b x cos(b x + a) ) +--R * +--R 2 +--R sec(b x + a)sin(b x + a) +--R + +--R 4 3 2 +--R (- b x cos(b x + a) - 2b x cos(b x + a) - b x cos(b x + a) ) +--R * +--R sec(b x + a) +--R * +--R tan(b x + a) +--R + +--R 5 +--R b x sin(b x + a) +--R + +--R 2 2 +--R (- cos(b x + a) sec(b x + a) + 2cos(b x + a) + cos(b x + a)) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 2 3 +--R (- b x cos(b x + a) - 2b x cos(b x + a) - 2b x)sin(b x + a) +--R + +--R 4 3 2 +--R (cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) )sec(b x + a) +--R + +--R 4 2 +--R 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 2 +--R (b x cos(b x + a) + 2b x cos(b x + a) + b x)sin(b x + a) +--R + +--R 4 3 2 +--R (- cos(b x + a) - 2cos(b x + a) - cos(b x + a) )sec(b x + a) +--R + +--R 5 2 +--R cos(b x + a) + 2cos(b x + a) + cos(b x + a) +--R / +--R 2 4 +--R b cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 2 +--R (- b cos(b x + a) - 2b cos(b x + a) - 2b cos(b x + a) )sin(b x + a) +--R + +--R 4 3 2 +--R b cos(b x + a) + 2b cos(b x + a) + b cos(b x + a) +--R Type: Expression(Integer) +--E 225 + +--S 226 of 534 +t0643:= x^2*sec(a+b*x)*tan(a+b*x) +--R +--R +--R 2 +--R (218) x sec(b x + a)tan(b x + a) +--R Type: Expression(Integer) +--E 226 + +--S 227 of 534 +r0643:= 4*%i*x*atan(exp(1)^(%i*b*x+%i*a))/b^2-_ + 2*%i*polylog(2,-%i*exp(1)^(%i*b*x+%i*a))/b^3+_ + 2*%i*polylog(2,%i*exp(1)^(%i*b*x+%i*a))/b^3+x^2*sec(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 227 + +--S 228 of 534 +a0643:= integrate(t0643,x) +--R +--R +--R x +--R ++ 2 +--R (219) | %L sec(%L b + a)tan(%L b + a)d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 534 +m0643:= a0643-r0643 +--R +--R +--R x +--R ++ 2 +--R (220) | %L sec(%L b + a)tan(%L b + a)d%L - r0643 +--R ++ +--R Type: Expression(Integer) +--E 229 + +--S 230 of 534 +d0643:= D(m0643,x) +--R +--R +--R 2 +--R (221) x sec(b x + a)tan(b x + a) +--R Type: Expression(Integer) +--E 230 + +--S 231 of 534 +t0644:= x^3*sec(a+b*x)*tan(a+b*x) +--R +--R +--R 3 +--R (222) x sec(b x + a)tan(b x + a) +--R Type: Expression(Integer) +--E 231 + +--S 232 of 534 +r0644:= 6*%i*x^2*atan(exp(1)^(%i*b*x+%i*a))/b^2-_ + 6*%i*x*polylog(2,-%i*exp(1)^(%i*b*x+%i*a))/b^3+_ + 6*%i*x*polylog(2,%i*exp(1)^(%i*b*x+%i*a))/b^3+_ + 6*polylog(3,-%i*exp(1)^(%i*b*x+%i*a))/b^4-_ + 6*polylog(3,%i*exp(1)^(%i*b*x+%i*a))/b^4+x^3*sec(a+b*x)/b +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 232 + +--S 233 of 534 +a0644:= integrate(t0644,x) +--R +--R +--R x +--R ++ 3 +--R (223) | %L sec(%L b + a)tan(%L b + a)d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 534 +m0644:= a0644-r0644 +--R +--R +--R x +--R ++ 3 +--R (224) | %L sec(%L b + a)tan(%L b + a)d%L - r0644 +--R ++ +--R Type: Expression(Integer) +--E 234 + +--S 235 of 534 +d0644:= D(m0644,x) +--R +--R +--R 3 +--R (225) x sec(b x + a)tan(b x + a) +--R Type: Expression(Integer) +--E 235 + +--S 236 of 534 +t0645:= x^3*sec(a+b*x)^2*tan(a+b*x) +--R +--R +--R 3 2 +--R (226) x sec(b x + a) tan(b x + a) +--R Type: Expression(Integer) +--E 236 + +--S 237 of 534 +r0645:= 3/2*%i*x^2/b^2-3*x*log(1+exp(1)^(2*%i*a+2*%i*b*x))/b^3+_ + 3/2*%i*polylog(2,-exp(1)^(2*%i*a+2*%i*b*x))/b^4+_ + 1/2*x^3*sec(a+b*x)^2/b-3/2*x^2*tan(a+b*x)/b^2 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 237 + +--S 238 of 534 +a0645:= integrate(t0645,x) +--R +--R +--R x +--R ++ 3 2 +--R (227) | %L sec(%L b + a) tan(%L b + a)d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 534 +m0645:= a0645-r0645 +--R +--R +--R x +--R ++ 3 2 +--R (228) | %L sec(%L b + a) tan(%L b + a)d%L - r0645 +--R ++ +--R Type: Expression(Integer) +--E 239 + +--S 240 of 534 +d0645:= D(m0645,x) +--R +--R +--R 3 2 +--R (229) x sec(b x + a) tan(b x + a) +--R Type: Expression(Integer) +--E 240 + +--S 241 of 534 +t0646:= x*csc(a+b*x)*cot(a+b*x) +--R +--R +--R (230) x cot(b x + a)csc(b x + a) +--R Type: Expression(Integer) +--E 241 + +--S 242 of 534 +r0646:= -atanh(cos(a+b*x))/b^2-x*csc(a+b*x)/b +--R +--R +--R - atanh(cos(b x + a)) - b x csc(b x + a) +--R (231) ---------------------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 242 + +--S 243 of 534 +a0646:= integrate(t0646,x) +--R +--R +--R sin(b x + a) +--R sin(b x + a)log(----------------) - b x +--R cos(b x + a) + 1 +--R (232) --------------------------------------- +--R 2 +--R b sin(b x + a) +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 534 +m0646:= a0646-r0646 +--R +--R +--R (233) +--R sin(b x + a) +--R sin(b x + a)log(----------------) + sin(b x + a)atanh(cos(b x + a)) +--R cos(b x + a) + 1 +--R + +--R b x csc(b x + a)sin(b x + a) - b x +--R / +--R 2 +--R b sin(b x + a) +--R Type: Expression(Integer) +--E 244 + +--S 245 of 534 +d0646:= D(m0646,x) +--R +--R +--R (234) +--R 3 +--R cos(b x + a)sin(b x + a) +--R + +--R 2 2 +--R ((- b x cos(b x + a) + b x)cot(b x + a) + cos(b x + a) - 1) +--R * +--R 2 +--R csc(b x + a)sin(b x + a) +--R + +--R 3 2 +--R (cos(b x + a) - cos(b x + a) - cos(b x + a) + 1)sin(b x + a) +--R + +--R 3 +--R b x cos(b x + a) - b x cos(b x + a) +--R / +--R 2 2 +--R (b cos(b x + a) - b)sin(b x + a) +--R Type: Expression(Integer) +--E 245 + +--S 246 of 534 +t0647:= x^2*csc(a+b*x)*cot(a+b*x) +--R +--R +--R 2 +--R (235) x cot(b x + a)csc(b x + a) +--R Type: Expression(Integer) +--E 246 + +--S 247 of 534 +r0647:= -4*x*atanh(exp(1)^(%i*b*x+%i*a))/b^2-x^2*csc(a+b*x)/b+_ + 2*%i*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^3-_ + 2*%i*polylog(2,exp(1)^(%i*b*x+%i*a))/b^3 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 247 + +--S 248 of 534 +a0647:= integrate(t0647,x) +--R +--R +--R x +--R ++ 2 +--R (236) | %L cot(%L b + a)csc(%L b + a)d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 534 +m0647:= a0647-r0647 +--R +--R +--R x +--R ++ 2 +--R (237) | %L cot(%L b + a)csc(%L b + a)d%L - r0647 +--R ++ +--R Type: Expression(Integer) +--E 249 + +--S 250 of 534 +d0647:= D(m0647,x) +--R +--R +--R 2 +--R (238) x cot(b x + a)csc(b x + a) +--R Type: Expression(Integer) +--E 250 + +--S 251 of 534 +t0648:= x^3*csc(a+b*x)*cot(a+b*x) +--R +--R +--R 3 +--R (239) x cot(b x + a)csc(b x + a) +--R Type: Expression(Integer) +--E 251 + +--S 252 of 534 +r0648:= -6*x^2*atanh(exp(1)^(%i*b*x+%i*a))/b^2-x^3*csc(a+b*x)/b+_ + 6*%i*x*polylog(2,-exp(1)^(%i*b*x+%i*a))/b^3-_ + 6*%i*x*polylog(2,exp(1)^(%i*b*x+%i*a))/b^3-_ + 6*polylog(3,-exp(1)^(%i*b*x+%i*a))/b^4+_ + 6*polylog(3,exp(1)^(%i*b*x+%i*a))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 252 + +--S 253 of 534 +a0648:= integrate(t0648,x) +--R +--R +--R x +--R ++ 3 +--R (240) | %L cot(%L b + a)csc(%L b + a)d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 534 +m0648:= a0648-r0648 +--R +--R +--R x +--R ++ 3 +--R (241) | %L cot(%L b + a)csc(%L b + a)d%L - r0648 +--R ++ +--R Type: Expression(Integer) +--E 254 + +--S 255 of 534 +d0648:= D(m0648,x) +--R +--R +--R 3 +--R (242) x cot(b x + a)csc(b x + a) +--R Type: Expression(Integer) +--E 255 + +--S 256 of 534 +t0649:= x^3*csc(a+b*x)^2*cot(a+b*x) +--R +--R +--R 3 2 +--R (243) x cot(b x + a)csc(b x + a) +--R Type: Expression(Integer) +--E 256 + +--S 257 of 534 +r0649:= -3/2*%i*x^2/b^2-3/2*x^2*cot(a+b*x)/b^2-1/2*x^3*csc(a+b*x)^2/b+_ + 3*x*log(1-exp(1)^(2*%i*a+2*%i*b*x))/b^3-_ + 3/2*%i*polylog(2,exp(1)^(2*%i*a+2*%i*b*x))/b^4 +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 257 + +--S 258 of 534 +a0649:= integrate(t0649,x) +--R +--R +--R x +--R ++ 3 2 +--R (244) | %L cot(%L b + a)csc(%L b + a) d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 534 +m0649:= a0649-r0649 +--R +--R +--R x +--R ++ 3 2 +--R (245) | %L cot(%L b + a)csc(%L b + a) d%L - r0649 +--R ++ +--R Type: Expression(Integer) +--E 259 + +--S 260 of 534 +d0649:= D(m0649,x) +--R +--R +--R 3 2 +--R (246) x cot(b x + a)csc(b x + a) +--R Type: Expression(Integer) +--E 260 + +--S 261 of 534 +t0650:= x*csc(x)*sec(x) +--R +--R +--R (247) x csc(x)sec(x) +--R Type: Expression(Integer) +--E 261 + +--S 262 of 534 +r0650:= -2*x*atanh(exp(2*%i*x))+1/2*%i*polylog(2,-exp(2*%i*x))-_ + 1/2*%i*polylog(2,exp(2*%i*x)) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 262 + +--S 263 of 534 +a0650:= integrate(t0650,x) +--R +--R +--R x +--R ++ +--R (248) | %L csc(%L)sec(%L)d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 534 +m0650:= a0650-r0650 +--R +--R +--R x +--R ++ +--R (249) | %L csc(%L)sec(%L)d%L - r0650 +--R ++ +--R Type: Expression(Integer) +--E 264 + +--S 265 of 534 +d0650:= D(m0650,x) +--R +--R +--R (250) x csc(x)sec(x) +--R Type: Expression(Integer) +--E 265 + +--S 266 of 534 +t0651:= x*csc(x)*sec(x)^2 +--R +--R +--R 2 +--R (251) x csc(x)sec(x) +--R Type: Expression(Integer) +--E 266 + +--S 267 of 534 +r0651:= -2*atanh(tan(1/2*x))+x*log(1-exp(1)^(%i*x))-x*log(1+exp(1)^(%i*x))+_ + %i*polylog(2,-exp(1)^(%i*x))-%i*polylog(2,exp(1)^(%i*x))+x*sec(x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 267 + +--S 268 of 534 +a0651:= integrate(t0651,x) +--R +--R +--R x +--R ++ 2 +--R (252) | %L csc(%L)sec(%L) d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 534 +m0651:= a0651-r0651 +--R +--R +--R x +--R ++ 2 +--R (253) | %L csc(%L)sec(%L) d%L - r0651 +--R ++ +--R Type: Expression(Integer) +--E 269 + +--S 270 of 534 +d0651:= D(m0651,x) +--R +--R +--R 2 +--R (254) x csc(x)sec(x) +--R Type: Expression(Integer) +--E 270 + +--S 271 of 534 +t0652:= x*csc(x)*sec(x)^3 +--R +--R +--R 3 +--R (255) x csc(x)sec(x) +--R Type: Expression(Integer) +--E 271 + +--S 272 of 534 +r0652:= x*log(1-exp(1)^(2*%i*x))-x*log(1+exp(1)^(2*%i*x))+_ + 1/2*%i*polylog(2,-exp(1)^(2*%i*x))-_ + 1/2*%i*polylog(2,exp(1)^(2*%i*x))+_ + 1/2*x*sec(x)^2-1/2*tan(x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 272 + +--S 273 of 534 +a0652:= integrate(t0652,x) +--R +--R +--R x +--R ++ 3 +--R (256) | %L csc(%L)sec(%L) d%L +--R ++ +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 534 +m0652:= a0652-r0652 +--R +--R +--R x +--R ++ 3 +--R (257) | %L csc(%L)sec(%L) d%L - r0652 +--R ++ +--R Type: Expression(Integer) +--E 274 + +--S 275 of 534 +d0652:= D(m0652,x) +--R +--R +--R 3 +--R (258) x csc(x)sec(x) +--R Type: Expression(Integer) +--E 275 + +--S 276 of 534 +t0653:= x*sin(a+b*x)*cos(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (259) x cos(b x + a)sin(b x + a)\|cos(b x + a) +--R Type: Expression(Integer) +--E 276 + +--S 277 of 534 +r0653:= -2/25*(5*x*cos(a+b*x)^(5/2)*b-_ + 6*EllipticE(1/2*a+1/2*b*x,2)-2*cos(a+b*x)^(3/2)*sin(a+b*x))/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 277 + +--S 278 of 534 +a0653:= integrate(t0653,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 278 + +--S 279 of 534 +m0653:= a0653-r0653 +--R +--R +--R (260) - r0653 + a0653 +--R Type: Polynomial(Integer) +--E 279 + +--S 280 of 534 +d0653:= D(m0653,x) +--R +--R +--R (261) 0 +--R Type: Polynomial(Integer) +--E 280 + +--S 281 of 534 +t0654:= x*sin(a+b*x)*cos(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (262) x sin(b x + a)\|cos(b x + a) +--R Type: Expression(Integer) +--E 281 + +--S 282 of 534 +r0654:= -2/9*(3*x*cos(a+b*x)^(3/2)*b-_ + 2*EllipticF(1/2*a+1/2*b*x,2)-2*cos(a+b*x)^(1/2)*sin(a+b*x))/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 282 + +--S 283 of 534 +a0654:= integrate(t0654,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 283 + +--S 284 of 534 +m0654:= a0654-r0654 +--R +--R +--R (263) - r0654 + a0654 +--R Type: Polynomial(Integer) +--E 284 + +--S 285 of 534 +d0654:= D(m0654,x) +--R +--R +--R (264) 0 +--R Type: Polynomial(Integer) +--E 285 + +--S 286 of 534 +t0655:= x*sin(a+b*x)/cos(a+b*x)^(1/2) +--R +--R +--R x sin(b x + a) +--R (265) --------------- +--R +------------+ +--R \|cos(b x + a) +--R Type: Expression(Integer) +--E 286 + +--S 287 of 534 +r0655:= -2*(x*cos(a+b*x)^(1/2)*b-2*EllipticE(1/2*a+1/2*b*x,2))/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 287 + +--S 288 of 534 +a0655:= integrate(t0655,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 288 + +--S 289 of 534 +m0655:= a0655-r0655 +--R +--R +--R (266) - r0655 + a0655 +--R Type: Polynomial(Integer) +--E 289 + +--S 290 of 534 +d0655:= D(m0655,x) +--R +--R +--R (267) 0 +--R Type: Polynomial(Integer) +--E 290 + +--S 291 of 534 +t0656:= x*sin(a+b*x)/cos(a+b*x)^(3/2) +--R +--R +--R x sin(b x + a) +--R (268) --------------------------- +--R +------------+ +--R cos(b x + a)\|cos(b x + a) +--R Type: Expression(Integer) +--E 291 + +--S 292 of 534 +r0656:= 2*x/b/cos(a+b*x)^(1/2)-4*EllipticF(1/2*a+1/2*b*x,2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 292 + +--S 293 of 534 +a0656:= integrate(t0656,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 293 + +--S 294 of 534 +m0656:= a0656-r0656 +--R +--R +--R (269) - r0656 + a0656 +--R Type: Polynomial(Integer) +--E 294 + +--S 295 of 534 +d0656:= D(m0656,x) +--R +--R +--R (270) 0 +--R Type: Polynomial(Integer) +--E 295 + +--S 296 of 534 +t0657:= x*sin(a+b*x)/cos(a+b*x)^(5/2) +--R +--R +--R x sin(b x + a) +--R (271) ---------------------------- +--R 2 +------------+ +--R cos(b x + a) \|cos(b x + a) +--R Type: Expression(Integer) +--E 296 + +--S 297 of 534 +r0657:= 2/3*(b*x+2*EllipticE(1/2*a+1/2*b*x,2)*cos(a+b*x)^(3/2)-_ + 2*cos(a+b*x)*sin(a+b*x))/b^2/cos(a+b*x)^(3/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 297 + +--S 298 of 534 +a0657:= integrate(t0657,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 298 + +--S 299 of 534 +m0657:= a0657-r0657 +--R +--R +--R (272) - r0657 + a0657 +--R Type: Polynomial(Integer) +--E 299 + +--S 300 of 534 +d0657:= D(m0657,x) +--R +--R +--R (273) 0 +--R Type: Polynomial(Integer) +--E 300 + +--S 301 of 534 +t0658:= x*cos(a+b*x)*sin(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (274) x cos(b x + a)sin(b x + a)\|sin(b x + a) +--R Type: Expression(Integer) +--E 301 + +--S 302 of 534 +r0658:= -2/25*(6*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)-_ + 2*cos(a+b*x)*sin(a+b*x)^(3/2)-5*x*sin(a+b*x)^(5/2)*b)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 302 + +--S 303 of 534 +a0658:= integrate(t0658,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 303 + +--S 304 of 534 +m0658:= a0658-r0658 +--R +--R +--R (275) - r0658 + a0658 +--R Type: Polynomial(Integer) +--E 304 + +--S 305 of 534 +d0658:= D(m0658,x) +--R +--R +--R (276) 0 +--R Type: Polynomial(Integer) +--E 305 + +--S 306 of 534 +t0659:= x*cos(a+b*x)*sin(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (277) x cos(b x + a)\|sin(b x + a) +--R Type: Expression(Integer) +--E 306 + +--S 307 of 534 +r0659:= 2/9*(-2*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)+_ + 2*cos(a+b*x)*sin(a+b*x)^(1/2)+3*x*sin(a+b*x)^(3/2)*b)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 307 + +--S 308 of 534 +a0659:= integrate(t0659,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 308 + +--S 309 of 534 +m0659:= a0659-r0659 +--R +--R +--R (278) - r0659 + a0659 +--R Type: Polynomial(Integer) +--E 309 + +--S 310 of 534 +d0659:= D(m0659,x) +--R +--R +--R (279) 0 +--R Type: Polynomial(Integer) +--E 310 + +--S 311 of 534 +t0660:= x*cos(a+b*x)/sin(a+b*x)^(1/2) +--R +--R +--R x cos(b x + a) +--R (280) --------------- +--R +------------+ +--R \|sin(b x + a) +--R Type: Expression(Integer) +--E 311 + +--S 312 of 534 +r0660:= -4*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)/b^2+2*x*sin(a+b*x)^(1/2)/b +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 312 + +--S 313 of 534 +a0660:= integrate(t0660,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 313 + +--S 314 of 534 +m0660:= a0660-r0660 +--R +--R +--R (281) - r0660 + a0660 +--R Type: Polynomial(Integer) +--E 314 + +--S 315 of 534 +d0660:= D(m0660,x) +--R +--R +--R (282) 0 +--R Type: Polynomial(Integer) +--E 315 + +--S 316 of 534 +t0661:= x*cos(a+b*x)/sin(a+b*x)^(3/2) +--R +--R +--R x cos(b x + a) +--R (283) --------------------------- +--R +------------+ +--R sin(b x + a)\|sin(b x + a) +--R Type: Expression(Integer) +--E 316 + +--S 317 of 534 +r0661:= 4*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)/b^2-2*x/b/sin(a+b*x)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 317 + +--S 318 of 534 +a0661:= integrate(t0661,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 318 + +--S 319 of 534 +m0661:= a0661-r0661 +--R +--R +--R (284) - r0661 + a0661 +--R Type: Polynomial(Integer) +--E 319 + +--S 320 of 534 +d0661:= D(m0661,x) +--R +--R +--R (285) 0 +--R Type: Polynomial(Integer) +--E 320 + +--S 321 of 534 +t0662:= x*cos(a+b*x)/sin(a+b*x)^(5/2) +--R +--R +--R x cos(b x + a) +--R (286) ---------------------------- +--R 2 +------------+ +--R sin(b x + a) \|sin(b x + a) +--R Type: Expression(Integer) +--E 321 + +--S 322 of 534 +r0662:= -2/3*(2*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(3/2)+_ + b*x+2*cos(a+b*x)*sin(a+b*x))/b^2/sin(a+b*x)^(3/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 322 + +--S 323 of 534 +a0662:= integrate(t0662,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 323 + +--S 324 of 534 +m0662:= a0662-r0662 +--R +--R +--R (287) - r0662 + a0662 +--R Type: Polynomial(Integer) +--E 324 + +--S 325 of 534 +d0662:= D(m0662,x) +--R +--R +--R (288) 0 +--R Type: Polynomial(Integer) +--E 325 + +--S 326 of 534 +t0663:= x*sin(a+b*x)*sec(a+b*x)^(5/2) +--R +--R +--R 2 +------------+ +--R (289) x sec(b x + a) sin(b x + a)\|sec(b x + a) +--R Type: Expression(Integer) +--E 326 + +--S 327 of 534 +r0663:= 2/3*(1/cos(a+b*x))^(1/2)*(b*x+_ + 2*EllipticE(1/2*a+1/2*b*x,2)*cos(a+b*x)^(3/2)-_ + 2*cos(a+b*x)*sin(a+b*x))/cos(a+b*x)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 327 + +--S 328 of 534 +a0663:= integrate(t0663,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 328 + +--S 329 of 534 +m0663:= a0663-r0663 +--R +--R +--R (290) - r0663 + a0663 +--R Type: Polynomial(Integer) +--E 329 + +--S 330 of 534 +d0663:= D(m0663,x) +--R +--R +--R (291) 0 +--R Type: Polynomial(Integer) +--E 330 + +--S 331 of 534 +t0664:= x*sin(a+b*x)*sec(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (292) x sec(b x + a)sin(b x + a)\|sec(b x + a) +--R Type: Expression(Integer) +--E 331 + +--S 332 of 534 +r0664:= -2*(1/cos(a+b*x))^(1/2)*(-b*x+2*EllipticF(1/2*a+1/2*b*x,2)*_ + cos(a+b*x)^(1/2))/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 332 + +--S 333 of 534 +a0664:= integrate(t0664,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 333 + +--S 334 of 534 +m0664:= a0664-r0664 +--R +--R +--R (293) - r0664 + a0664 +--R Type: Polynomial(Integer) +--E 334 + +--S 335 of 534 +d0664:= D(m0664,x) +--R +--R +--R (294) 0 +--R Type: Polynomial(Integer) +--E 335 + +--S 336 of 534 +t0665:= x*sin(a+b*x)*sec(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (295) x sin(b x + a)\|sec(b x + a) +--R Type: Expression(Integer) +--E 336 + +--S 337 of 534 +r0665:= -2*x/b/sec(a+b*x)^(1/2)+4*cos(a+b*x)^(1/2)*_ + EllipticE(1/2*a+1/2*b*x,2)*sec(a+b*x)^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 337 + +--S 338 of 534 +a0665:= integrate(t0665,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 338 + +--S 339 of 534 +m0665:= a0665-r0665 +--R +--R +--R (296) - r0665 + a0665 +--R Type: Polynomial(Integer) +--E 339 + +--S 340 of 534 +d0665:= D(m0665,x) +--R +--R +--R (297) 0 +--R Type: Polynomial(Integer) +--E 340 + +--S 341 of 534 +t0666:= x*sin(a+b*x)/sec(a+b*x)^(1/2) +--R +--R +--R x sin(b x + a) +--R (298) --------------- +--R +------------+ +--R \|sec(b x + a) +--R Type: Expression(Integer) +--E 341 + +--S 342 of 534 +r0666:= -2/9*(3*b*x*cos(a+b*x)^(3/2)-2*EllipticF(1/2*a+1/2*b*x,2)-_ + 2*sin(a+b*x)*cos(a+b*x)^(1/2))/_ + cos(a+b*x)^(1/2)/(1/cos(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 342 + +--S 343 of 534 +a0666:= integrate(t0666,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 343 + +--S 344 of 534 +m0666:= a0666-r0666 +--R +--R +--R (299) - r0666 + a0666 +--R Type: Polynomial(Integer) +--E 344 + +--S 345 of 534 +d0666:= D(m0666,x) +--R +--R +--R (300) 0 +--R Type: Polynomial(Integer) +--E 345 + +--S 346 of 534 +t0667:= x*sin(a+b*x)/sec(a+b*x)^(3/2) +--R +--R +--R x sin(b x + a) +--R (301) --------------------------- +--R +------------+ +--R sec(b x + a)\|sec(b x + a) +--R Type: Expression(Integer) +--E 346 + +--S 347 of 534 +r0667:= 2/25*(-5*b*x*cos(a+b*x)^(5/2)+6*EllipticE(1/2*a+1/2*b*x,2)+_ + 2*sin(a+b*x)*cos(a+b*x)^(3/2))/cos(a+b*x)^(1/2)/_ + (1/cos(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 347 + +--S 348 of 534 +a0667:= integrate(t0667,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 348 + +--S 349 of 534 +m0667:= a0667-r0667 +--R +--R +--R (302) - r0667 + a0667 +--R Type: Polynomial(Integer) +--E 349 + +--S 350 of 534 +d0667:= D(m0667,x) +--R +--R +--R (303) 0 +--R Type: Polynomial(Integer) +--E 350 + +--S 351 of 534 +t0668:= x*cos(a+b*x)*csc(a+b*x)^(5/2) +--R +--R +--R 2 +------------+ +--R (304) x cos(b x + a)csc(b x + a) \|csc(b x + a) +--R Type: Expression(Integer) +--E 351 + +--S 352 of 534 +r0668:= -2/3*(1/sin(a+b*x))^(1/2)*(2*cos(a+b*x)*sin(a+b*x)+b*x+_ + 2*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(3/2))/sin(a+b*x)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 352 + +--S 353 of 534 +a0668:= integrate(t0668,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 353 + +--S 354 of 534 +m0668:= a0668-r0668 +--R +--R +--R (305) - r0668 + a0668 +--R Type: Polynomial(Integer) +--E 354 + +--S 355 of 534 +d0668:= D(m0668,x) +--R +--R +--R (306) 0 +--R Type: Polynomial(Integer) +--E 355 + +--S 356 of 534 +t0669:= x*cos(a+b*x)*csc(a+b*x)^(3/2) +--R +--R +--R +------------+ +--R (307) x cos(b x + a)csc(b x + a)\|csc(b x + a) +--R Type: Expression(Integer) +--E 356 + +--S 357 of 534 +r0669:= 2*(1/sin(a+b*x))^(1/2)*(-b*x+2*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2)*_ + sin(a+b*x)^(1/2))/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 357 + +--S 358 of 534 +a0669:= integrate(t0669,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 358 + +--S 359 of 534 +m0669:= a0669-r0669 +--R +--R +--R (308) - r0669 + a0669 +--R Type: Polynomial(Integer) +--E 359 + +--S 360 of 534 +d0669:= D(m0669,x) +--R +--R +--R (309) 0 +--R Type: Polynomial(Integer) +--E 360 + +--S 361 of 534 +t0670:= x*cos(a+b*x)*csc(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R (310) x cos(b x + a)\|csc(b x + a) +--R Type: Expression(Integer) +--E 361 + +--S 362 of 534 +r0670:= 2*x/b/csc(a+b*x)^(1/2)-4*csc(a+b*x)^(1/2)*_ + EllipticE(1/2*a-1/4*%pi+1/2*b*x,2)*sin(a+b*x)^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 362 + +--S 363 of 534 +a0670:= integrate(t0670,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 363 + +--S 364 of 534 +m0670:= a0670-r0670 +--R +--R +--R (311) - r0670 + a0670 +--R Type: Polynomial(Integer) +--E 364 + +--S 365 of 534 +d0670:= D(m0670,x) +--R +--R +--R (312) 0 +--R Type: Polynomial(Integer) +--E 365 + +--S 366 of 534 +t0671:= x*cos(a+b*x)/csc(a+b*x)^(1/2) +--R +--R +--R x cos(b x + a) +--R (313) --------------- +--R +------------+ +--R \|csc(b x + a) +--R Type: Expression(Integer) +--E 366 + +--S 367 of 534 +r0671:= -2/9*(-3*b*x*sin(a+b*x)^(3/2)-2*cos(a+b*x)*sin(a+b*x)^(1/2)+_ + 2*EllipticF(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/_ + (1/sin(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 367 + +--S 368 of 534 +a0671:= integrate(t0671,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 368 + +--S 369 of 534 +m0671:= a0671-r0671 +--R +--R +--R (314) - r0671 + a0671 +--R Type: Polynomial(Integer) +--E 369 + +--S 370 of 534 +d0671:= D(m0671,x) +--R +--R +--R (315) 0 +--R Type: Polynomial(Integer) +--E 370 + +--S 371 of 534 +t0672:= x*cos(a+b*x)/csc(a+b*x)^(3/2) +--R +--R +--R x cos(b x + a) +--R (316) --------------------------- +--R +------------+ +--R csc(b x + a)\|csc(b x + a) +--R Type: Expression(Integer) +--E 371 + +--S 372 of 534 +r0672:= -2/25*(-5*b*x*sin(a+b*x)^(5/2)-2*cos(a+b*x)*sin(a+b*x)^(3/2)+_ + 6*EllipticE(1/2*a-1/4*%pi+1/2*b*x,2))/sin(a+b*x)^(1/2)/_ + (1/sin(a+b*x))^(1/2)/b^2 +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 372 + +--S 373 of 534 +a0672:= integrate(t0672,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 373 + +--S 374 of 534 +m0672:= a0672-r0672 +--R +--R +--R (317) - r0672 + a0672 +--R Type: Polynomial(Integer) +--E 374 + +--S 375 of 534 +d0672:= D(m0672,x) +--R +--R +--R (318) 0 +--R Type: Polynomial(Integer) +--E 375 + +--S 376 of 534 +t0673:= x/(a+b*sin(x)*cos(x)) +--R +--R +--R x +--R (319) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression(Integer) +--E 376 + +--S 377 of 534 +r0673:= -1/2*(2*%i*x*log((-2*a+(4*a^2-b^2)^(1/2)+%i*b*exp(2*%i*x))/_ + (-2*a+(4*a^2-b^2)^(1/2)))-2*%i*x*log((2*a+(4*a^2-b^2)^(1/2)-_ + %i*b*exp(2*%i*x))/(2*a+(4*a^2-b^2)^(1/2)))+_ + polylog(2,-%i*b*exp(2*%i*x)/(-2*a+(4*a^2-b^2)^(1/2)))-_ + polylog(2,%i*b*exp(2*%i*x)/(2*a+(4*a^2-b^2)^(1/2))))/(4*a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 377 + +--S 378 of 534 +a0673:= integrate(t0673,x) +--R +--R +--R x +--R ++ %L +--R (320) | -------------------- d%L +--R ++ b cos(%L)sin(%L) + a +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 534 +m0673:= a0673-r0673 +--R +--R +--R x +--R ++ %L +--R (321) | -------------------- d%L - r0673 +--R ++ b cos(%L)sin(%L) + a +--R Type: Expression(Integer) +--E 379 + +--S 380 of 534 +d0673:= D(m0673,x) +--R +--R +--R x +--R (322) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression(Integer) +--E 380 + +--S 381 of 534 +t0674:= x^2/(a+b*sin(x)*cos(x)) +--R +--R +--R 2 +--R x +--R (323) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression(Integer) +--E 381 + +--S 382 of 534 +r0674:= 1/2*(-2*%i*x^2*log((-2*a+(4*a^2-b^2)^(1/2)+_ + %i*b*exp(2*%i*x))/(-2*a+(4*a^2-b^2)^(1/2)))+_ + 2*%i*x^2*log((2*a+(4*a^2-b^2)^(1/2)-%i*b*exp(2*%i*x))/_ + (2*a+(4*a^2-b^2)^(1/2)))-2*x*polylog(2,-%i*b*exp(2*%i*x)/_ + (-2*a+(4*a^2-b^2)^(1/2)))+2*x*polylog(2,%i*b*exp(2*%i*x)/_ + (2*a+(4*a^2-b^2)^(1/2)))-%i*polylog(3,-%i*b*exp(2*%i*x)/_ + (-2*a+(4*a^2-b^2)^(1/2)))+%i*polylog(3,%i*b*exp(2*%i*x)/_ + (2*a+(4*a^2-b^2)^(1/2))))/(4*a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 382 + +--S 383 of 534 +a0674:= integrate(t0674,x) +--R +--R +--R x 2 +--R ++ %L +--R (324) | -------------------- d%L +--R ++ b cos(%L)sin(%L) + a +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 534 +m0674:= a0674-r0674 +--R +--R +--R x 2 +--R ++ %L +--R (325) | -------------------- d%L - r0674 +--R ++ b cos(%L)sin(%L) + a +--R Type: Expression(Integer) +--E 384 + +--S 385 of 534 +d0674:= D(m0674,x) +--R +--R +--R 2 +--R x +--R (326) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression(Integer) +--E 385 + +--S 386 of 534 +t0675:= x^3/(a+b*sin(x)*cos(x)) +--R +--R +--R 3 +--R x +--R (327) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression(Integer) +--E 386 + +--S 387 of 534 +r0675:= 1/4*(-4*%i*x^3*log((-2*a+(4*a^2-b^2)^(1/2)+%i*b*exp(2*%i*x))/_ + (-2*a+(4*a^2-b^2)^(1/2)))+4*%i*x^3*log((2*a+(4*a^2-b^2)^(1/2)-_ + %i*b*exp(2*%i*x))/(2*a+(4*a^2-b^2)^(1/2)))-_ + 6*x^2*polylog(2,-%i*b*exp(2*%i*x)/(-2*a+(4*a^2-b^2)^(1/2)))+_ + 6*x^2*polylog(2,%i*b*exp(2*%i*x)/(2*a+(4*a^2-b^2)^(1/2)))-_ + 6*%i*x*polylog(3,-%i*b*exp(2*%i*x)/(-2*a+(4*a^2-b^2)^(1/2)))+_ + 6*%i*x*polylog(3,%i*b*exp(2*%i*x)/(2*a+(4*a^2-b^2)^(1/2)))+_ + 3*polylog(4,-%i*b*exp(2*%i*x)/(-2*a+(4*a^2-b^2)^(1/2)))-_ + 3*polylog(4,%i*b*exp(2*%i*x)/_ + (2*a+(4*a^2-b^2)^(1/2))))/(4*a^2-b^2)^(1/2) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 387 + +--S 388 of 534 +a0675:= integrate(t0675,x) +--R +--R +--R x 3 +--R ++ %L +--R (328) | -------------------- d%L +--R ++ b cos(%L)sin(%L) + a +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 534 +m0675:= a0675-r0675 +--R +--R +--R x 3 +--R ++ %L +--R (329) | -------------------- d%L - r0675 +--R ++ b cos(%L)sin(%L) + a +--R Type: Expression(Integer) +--E 389 + +--S 390 of 534 +d0675:= D(m0675,x) +--R +--R +--R 3 +--R x +--R (330) ------------------ +--R b cos(x)sin(x) + a +--R Type: Expression(Integer) +--E 390 + +--S 391 of 534 +t0676:= (a+b*sin(x))/(b+a*sin(x))^2 +--R +--R +--R b sin(x) + a +--R (331) ---------------------------- +--R 2 2 2 +--R a sin(x) + 2a b sin(x) + b +--R Type: Expression(Integer) +--E 391 + +--S 392 of 534 +r0676:= -cos(x)/(b+a*sin(x)) +--R +--R +--R cos(x) +--R (332) - ------------ +--R a sin(x) + b +--R Type: Expression(Integer) +--E 392 + +--S 393 of 534 +a0676:= integrate(t0676,x) +--R +--R +--R - a sin(x) - b cos(x) - b +--R (333) ------------------------- +--R 2 +--R a b sin(x) + b +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 534 +m0676:= a0676-r0676 +--R +--R +--R 1 +--R (334) - - +--R b +--R Type: Expression(Integer) +--E 394 + +--S 395 of 534 +d0676:= D(m0676,x) +--R +--R +--R (335) 0 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 534 +t0677:= x*(b+a*sin(x))/(a+b*sin(x))^2 +--R +--R +--R a x sin(x) + b x +--R (336) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 396 + +--S 397 of 534 +r0677:= log(a+b*sin(x))/b-x*cos(x)/(a+b*sin(x)) +--R +--R +--R (b sin(x) + a)log(b sin(x) + a) - b x cos(x) +--R (337) -------------------------------------------- +--R 2 +--R b sin(x) + a b +--R Type: Expression(Integer) +--E 397 + +--S 398 of 534 +a0677:= integrate(t0677,x) +--R +--R +--R (338) +--R 2b sin(x) + 2a 2 +--R (b sin(x) + a)log(--------------) + (- b sin(x) - a)log(----------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R - b x cos(x) +--R / +--R 2 +--R b sin(x) + a b +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 534 +m0677:= a0677-r0677 +--R +--R +--R 2b sin(x) + 2a 2 +--R - log(b sin(x) + a) + log(--------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (339) ----------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 399 + +--S 400 of 534 +d0677:= D(m0677,x) +--R +--R +--R (340) 0 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 534 +t0678:= x*(b+a*cos(x))/(a+b*cos(x))^2 +--R +--R +--R a x cos(x) + b x +--R (341) ---------------------------- +--R 2 2 2 +--R b cos(x) + 2a b cos(x) + a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 534 +r0678:= log(a+b*cos(x))/b+x*sin(x)/(a+b*cos(x)) +--R +--R +--R (b cos(x) + a)log(b cos(x) + a) + b x sin(x) +--R (342) -------------------------------------------- +--R 2 +--R b cos(x) + a b +--R Type: Expression(Integer) +--E 402 + +--S 403 of 534 +a0678:= integrate(t0678,x) +--R +--R +--R (343) +--R 2 - 2b cos(x) - 2a +--R (- b cos(x) - a)log(----------) + (b cos(x) + a)log(----------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R b x sin(x) +--R / +--R 2 +--R b cos(x) + a b +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 534 +m0678:= a0678-r0678 +--R +--R +--R 2 - 2b cos(x) - 2a +--R - log(b cos(x) + a) - log(----------) + log(----------------) +--R cos(x) + 1 cos(x) + 1 +--R (344) ------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 404 + +--S 405 of 534 +d0678:= D(m0678,x) +--R +--R +--R (345) 0 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 534 +t0679:= sin(x)/(a+a*sin(x))^(1/2) +--R +--R +--R sin(x) +--R (346) --------------- +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 534 +r0679:= 2*(-cos(x)+atanh(cos(1/4*%pi+1/2*x))*_ + sin(1/4*%pi+1/2*x))/(a*(1+sin(x)))^(1/2) +--R +--R +--R 2x + %pi 2x + %pi +--R 2sin(--------)atanh(cos(--------)) - 2cos(x) +--R 4 4 +--R (347) -------------------------------------------- +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression(Integer) +--E 407 + +--S 408 of 534 +a0679:= integrate(t0679,x) +--R +--R +--R (348) +--R [ +--R +-+ +--R |2 +--R (a cos(x) + a) |- +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (- \|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) + 3cos(x) + 3 +--R / +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2\|2 sin(x) - 2\|2 cos(x) - 2\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R (- a cos(x) - a) |- +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) - \|2 cos(x) - \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (cos(x) + 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2\|2 sin(x) - 2\|2 cos(x) - 2\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 408 + +--S 409 of 534 +m0679a:= a0679.1-r0679 +--R +--R +--R (349) +--R +-+ +--R |2 +------------+ +--R (a cos(x) + a) |- \|a sin(x) + a +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (- \|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) + 3cos(x) + 3 +--R / +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R + +--R +-+ +-+ +-+ +------------+ +------------+ +--R (2\|2 sin(x) - 2\|2 cos(x) - 2\|2 )\|a cos(x) + a \|a sin(x) + a +--R + +--R 2x + %pi 2x + %pi 2 +--R (- 4a cos(x) - 4a)sin(--------)atanh(cos(--------)) + 4a cos(x) +--R 4 4 +--R + +--R 4a cos(x) +--R / +--R +------------+ +--R (2a cos(x) + 2a)\|a sin(x) + a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 534 +d0679a:= D(m0679a,x) +--R +--R +--R (350) +--R +-+ 2x + %pi 2 +-+ 4 +--R (\|2 cos(--------) - \|2 )sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (\|2 cos(--------) - \|2 )cos(x)sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2\|2 cos(--------) - 2\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +-+ +--R (\|2 cos(--------) - \|2 )cos(x) - 3\|2 cos(--------) + 3\|2 +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 4\|2 cos(--------) + 4\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 6\|2 cos(--------) + 6\|2 )cos(x) - 2\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 2\|2 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (2\|2 cos(--------) - 2\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2\|2 cos(--------) + 2\|2 )cos(x) +--R 4 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (2a cos(--------) - 2a)sin(x) + (2a cos(--------) - 2a)sin(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 2 +--R ((2a cos(--------) - 2a)cos(x) - 2a cos(--------) + 2a)sin(x) +--R 4 4 +--R + +--R 2x + %pi 2 3 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 6a cos(--------) + 6a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 4a cos(--------) + 4a)cos(x) - 2a cos(--------) + 2a +--R 4 4 +--R * +--R sin(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a sin(x) + a +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (- 2a\|2 cos(--------) + 2a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R - 2a\|2 cos(--------) + 2a\|2 cos(--------) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (2a\|2 cos(--------) - 2a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (2a\|2 cos(--------) - 2a\|2 cos(--------))cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (2a\|2 cos(--------) - 2a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (4a\|2 cos(--------) - 4a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R 2a\|2 cos(--------) - 2a\|2 cos(--------) +--R 4 4 +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 4a\|2 cos(--------) + 4a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ +-+ 2x + %pi 2 +--R (- 2a\|2 cos(x) - 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2 +-+ 2x + %pi 2 +--R (2a\|2 cos(x) + 2a\|2 cos(x))sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) + 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 4a\|2 +--R * +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (2a\|2 cos(x) + 4a\|2 cos(x) + 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (- 2a cos(--------) + 2a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R (- 4a cos(--------) + 4a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R - 2a cos(--------) + 2a cos(--------) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (2a cos(--------) - 2a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (4a cos(--------) - 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (2a cos(--------) - 2a)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (4a cos(--------) - 4a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2x + %pi 3 +--R (8a cos(--------) - 8a cos(--------))cos(x) + 4a cos(--------) +--R 4 4 4 +--R + +--R 2x + %pi +--R - 4a cos(--------) +--R 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (- 6a cos(--------) + 6a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 12a cos(--------) + 12a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 6a cos(--------) + 6a)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (6a cos(--------) - 6a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2x + %pi 3 +--R (12a cos(--------) - 12a cos(--------))cos(x) + 6a cos(--------) +--R 4 4 4 +--R + +--R 2x + %pi +--R - 6a cos(--------) +--R 4 +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (- 4a cos(--------) + 4a)cos(x) + (- 8a cos(--------) + 8a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 4a cos(--------) + 4a +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2 2x + %pi 2 +--R (- 2a cos(x) - 4a cos(x) - 2a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (8a cos(--------) - 8a)cos(x) + (16a cos(--------) - 16a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 8a cos(--------) - 8a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2 2x + %pi 2 +--R (4a cos(x) + 8a cos(x) + 4a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (- 2a cos(--------) + 2a)cos(x) + (- 4a cos(--------) + 4a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (10a cos(--------) - 10a)cos(x) + (24a cos(--------) - 24a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 12a cos(--------) - 12a +--R 4 +--R * +--R sin(x) +--R + +--R 2 2x + %pi 2 +--R (6a cos(x) + 12a cos(x) + 6a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (6a cos(--------) - 6a)cos(x) + (12a cos(--------) - 12a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 +--R (6a cos(--------) - 6a)cos(x) +--R 4 +--R / +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) + 2a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 2a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) - 2a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 2a\|2 +--R * +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (2a cos(--------) - 2a)cos(x) + (4a cos(--------) - 4a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 2a cos(--------) - 2a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 2 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 8a cos(--------) + 8a)cos(x) - 4a cos(--------) + 4a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (- 6a cos(--------) + 6a)cos(x) + (- 12a cos(--------) + 12a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 6a cos(--------) + 6a +--R 4 +--R * +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 534 +m0679b:= a0679.2-r0679 +--R +--R +--R (351) +--R +-+ +--R |2 +------------+ +--R (- a cos(x) - a) |- \|a sin(x) + a +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) - \|2 cos(x) - \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (cos(x) + 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +------------+ +--R (2\|2 sin(x) - 2\|2 cos(x) - 2\|2 )\|a cos(x) + a \|a sin(x) + a +--R + +--R 2x + %pi 2x + %pi 2 +--R (- 4a cos(x) - 4a)sin(--------)atanh(cos(--------)) + 4a cos(x) +--R 4 4 +--R + +--R 4a cos(x) +--R / +--R +------------+ +--R (2a cos(x) + 2a)\|a sin(x) + a +--R Type: Expression(Integer) +--E 411 + +--S 412 of 534 +d0679b:= D(m0679b,x) +--R +--R +--R (352) +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (\|2 cos(--------) - \|2 )cos(x) + 5\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 5\|2 +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (\|2 cos(--------) - \|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 6\|2 cos(--------) + 6\|2 )cos(x) - 3\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 3\|2 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (2\|2 cos(--------) - 2\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (4\|2 cos(--------) - 4\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 9\|2 cos(--------) + 9\|2 )cos(x) - 11\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 11\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 22\|2 cos(--------) + 22\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 35\|2 cos(--------) + 35\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 6\|2 cos(--------) + 6\|2 )cos(x) + 7\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 7\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (10\|2 cos(--------) - 10\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (34\|2 cos(--------) - 34\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (48\|2 cos(--------) - 48\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (34\|2 cos(--------) - 34\|2 )cos(x) + 10\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 10\|2 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 6\|2 cos(--------) + 6\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 6\|2 cos(--------) + 6\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (6\|2 cos(--------) - 6\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (6\|2 cos(--------) - 6\|2 )cos(x) +--R 4 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 2x + %pi 2 5 +--R ((4a cos(--------) - 4a)cos(x) + 4a cos(--------) - 4a)sin(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R ((- 6a cos(--------) + 6a)cos(x) - 6a cos(--------) + 6a) +--R 4 4 +--R * +--R 4 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (4a cos(--------) - 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (4a cos(--------) - 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 14a cos(--------) + 14a)cos(x) - 14a cos(--------) + 14a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R (- 8a cos(--------) + 8a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 34a cos(--------) + 34a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 38a cos(--------) + 38a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 6a cos(--------) + 6a)cos(x) + 6a cos(--------) - 6a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R (24a cos(--------) - 24a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (62a cos(--------) - 62a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (62a cos(--------) - 62a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (34a cos(--------) - 34a)cos(x) + 10a cos(--------) - 10a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 5 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (- 8a cos(--------) + 8a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (8a cos(--------) - 8a)cos(x) + (4a cos(--------) - 4a)cos(x) +--R 4 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a sin(x) + a +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (- 4a\|2 cos(--------) + 4a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (- 8a\|2 cos(--------) + 8a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R - 4a\|2 cos(--------) + 4a\|2 cos(--------) +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 3 +--R (4a\|2 cos(--------) - 4a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (20a\|2 cos(--------) - 20a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (28a\|2 cos(--------) - 28a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R 12a\|2 cos(--------) - 12a\|2 cos(--------) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 24a\|2 cos(--------) + 24a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 36a\|2 cos(--------) + 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 16a\|2 cos(--------) + 16a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 3 +--R (- 8a\|2 cos(--------) + 8a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (- 12a\|2 cos(--------) + 12a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R 4a\|2 cos(--------) - 4a\|2 cos(--------) +--R 4 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 3 +--R (- 12a\|2 cos(--------) + 12a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R (- 36a\|2 cos(--------) + 36a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R (- 36a\|2 cos(--------) + 36a\|2 cos(--------))cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi +--R - 12a\|2 cos(--------) + 12a\|2 cos(--------) +--R 4 4 +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 8a\|2 cos(--------) + 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 16a\|2 cos(--------) + 16a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 8a\|2 cos(--------) + 8a\|2 +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (- 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (40a\|2 cos(--------) - 40a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (56a\|2 cos(--------) - 56a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R 24a\|2 cos(--------) - 24a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (4a\|2 cos(x) + 20a\|2 cos(x) + 28a\|2 cos(x) + 12a\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 24a\|2 cos(--------) + 24a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 28a\|2 cos(--------) + 28a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R 8a\|2 cos(--------) - 8a\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2x + %pi 2 +--R (- 8a\|2 cos(x) - 12a\|2 cos(x) + 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 5 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (24a\|2 cos(--------) - 24a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 56a\|2 cos(--------) + 56a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 72a\|2 cos(--------) + 72a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 24a\|2 cos(--------) + 24a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 12a\|2 cos(x) - 36a\|2 cos(x) - 36a\|2 cos(x) - 12a\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 5 +--R (- 12a\|2 cos(--------) + 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 36a\|2 cos(--------) + 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 36a\|2 cos(--------) + 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 12a\|2 cos(--------) + 12a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 3 2x + %pi 3 +--R (- 2a cos(--------) + 2a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (- 14a cos(--------) + 14a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R (- 22a cos(--------) + 22a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R - 10a cos(--------) + 10a cos(--------) +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R (2a cos(--------) - 2a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (14a cos(--------) - 14a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (22a cos(--------) - 22a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (10a cos(--------) - 10a)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 3 +--R (26a cos(--------) - 26a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (70a cos(--------) - 70a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R (62a cos(--------) - 62a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R 18a cos(--------) - 18a cos(--------) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R (- 28a cos(--------) + 28a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 84a cos(--------) + 84a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 84a cos(--------) + 84a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 28a cos(--------) + 28a)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 4 +--R (- 8a cos(--------) + 8a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 3 +--R (- 22a cos(--------) + 22a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (- 18a cos(--------) + 18a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R (- 2a cos(--------) + 2a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi +--R 2a cos(--------) - 2a cos(--------) +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 5 +--R (8a cos(--------) - 8a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (50a cos(--------) - 50a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (102a cos(--------) - 102a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (86a cos(--------) - 86a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (26a cos(--------) - 26a)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 4 +--R (- 8a cos(--------) + 8a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 3 +--R (- 50a cos(--------) + 50a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R (- 102a cos(--------) + 102a cos(--------))cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2x + %pi 3 +--R (- 86a cos(--------) + 86a cos(--------))cos(x) - 26a cos(--------) +--R 4 4 4 +--R + +--R 2x + %pi +--R 26a cos(--------) +--R 4 +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 28a cos(--------) + 28a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 44a cos(--------) + 44a)cos(x) - 20a cos(--------) + 20a +--R 4 4 +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2x + %pi 2 +--R (- 2a cos(x) - 14a cos(x) - 22a cos(x) - 10a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (52a cos(--------) - 52a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (140a cos(--------) - 140a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (124a cos(--------) - 124a)cos(x) + 36a cos(--------) - 36a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2x + %pi 2 +--R (26a cos(x) + 70a cos(x) + 62a cos(x) + 18a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 5 +--R (- 2a cos(--------) + 2a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (- 30a cos(--------) + 30a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 66a cos(--------) + 66a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 46a cos(--------) + 46a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 4a cos(--------) + 4a)cos(x) + 4a cos(--------) - 4a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (- 8a cos(x) - 22a cos(x) - 18a cos(x) - 2a cos(x) + 2a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 5 2x + %pi 2 4 +--R (28a cos(--------) - 28a)cos(x) + (68a cos(--------) - 68a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 3 +--R (- 16a cos(--------) + 16a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 176a cos(--------) + 176a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 172a cos(--------) + 172a)cos(x) - 52a cos(--------) + 52a +--R 4 4 +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- 8a cos(x) - 50a cos(x) - 102a cos(x) - 86a cos(x) - 26a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 6 2x + %pi 2 5 +--R (- 8a cos(--------) + 8a)cos(x) + (- 50a cos(--------) + 50a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 4 +--R (- 102a cos(--------) + 102a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 2x + %pi 2 2 +--R (- 86a cos(--------) + 86a)cos(x) + (- 26a cos(--------) + 26a)cos(x) +--R 4 4 +--R / +--R +-+ 2x + %pi 2 +-+ 2 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) + 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 4a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 20a\|2 cos(--------) + 20a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 28a\|2 cos(--------) + 28a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 12a\|2 cos(--------) + 12a\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +-+ 2x + %pi 2 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) - 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 4a\|2 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) + 12a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 12a\|2 +--R * +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R + +--R 2x + %pi 2 3 2x + %pi 2 2 +--R (2a cos(--------) - 2a)cos(x) + (14a cos(--------) - 14a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (22a cos(--------) - 22a)cos(x) + 10a cos(--------) - 10a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (- 26a cos(--------) + 26a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 70a cos(--------) + 70a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 62a cos(--------) + 62a)cos(x) - 18a cos(--------) + 18a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (8a cos(--------) - 8a)cos(x) + (22a cos(--------) - 22a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (18a cos(--------) - 18a)cos(x) + (2a cos(--------) - 2a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 2a cos(--------) + 2a +--R 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (8a cos(--------) - 8a)cos(x) + (50a cos(--------) - 50a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (102a cos(--------) - 102a)cos(x) + (86a cos(--------) - 86a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 26a cos(--------) - 26a +--R 4 +--R * +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression(Integer) +--E 412 + +--S 413 of 534 +t0680:= sin(x)/(a-a*sin(x))^(1/2) +--R +--R +--R sin(x) +--R (353) ----------------- +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 534 +r0680:= 2*(-cos(x)+atanh(sin(1/4*%pi+1/2*x))*_ + cos(1/4*%pi+1/2*x))/(-a*(sin(x)-1))^(1/2) +--R +--R +--R 2x + %pi 2x + %pi +--R 2cos(--------)atanh(sin(--------)) - 2cos(x) +--R 4 4 +--R (354) -------------------------------------------- +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression(Integer) +--E 414 + +--S 415 of 534 +a0680:= integrate(t0680,x) +--R +--R +--R (355) +--R [ +--R +-+ +--R |2 +--R (a cos(x) + a) |- +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R / +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2\|2 sin(x) + 2\|2 cos(x) + 2\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R (- a cos(x) - a) |- +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2\|2 sin(x) + 2\|2 cos(x) + 2\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 415 + +--S 416 of 534 +m0680a:= a0680.1-r0680 +--R +--R +--R (356) +--R +-+ +--R |2 +--------------+ +--R (a cos(x) + a) |- \|- a sin(x) + a +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R / +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R + +--R +-+ +-+ +-+ +--------------+ +------------+ +--R (2\|2 sin(x) + 2\|2 cos(x) + 2\|2 )\|- a sin(x) + a \|a cos(x) + a +--R + +--R 2x + %pi 2x + %pi 2x + %pi +--R (- 4a cos(--------)cos(x) - 4a cos(--------))atanh(sin(--------)) +--R 4 4 4 +--R + +--R 2 +--R 4a cos(x) + 4a cos(x) +--R / +--R +--------------+ +--R (2a cos(x) + 2a)\|- a sin(x) + a +--R Type: Expression(Integer) +--E 416 + +--S 417 of 534 +d0680a:= D(m0680a,x) +--R +--R +--R (357) +--R +-+ 2x + %pi 2 +-+ 4 +--R (- \|2 sin(--------) + \|2 )sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (\|2 cos(x)sin(--------) - \|2 cos(x))sin(x) +--R 4 +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (- 2\|2 cos(x) - \|2 cos(x) + 3\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R 2\|2 cos(x) + \|2 cos(x) - 3\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (- 4\|2 cos(x) - 6\|2 cos(x) - 2\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R 4\|2 cos(x) + 6\|2 cos(x) + 2\|2 +--R * +--R sin(x) +--R + +--R +-+ 3 +-+ 2x + %pi 2 +-+ 3 +--R (- 2\|2 cos(x) + 2\|2 cos(x))sin(--------) + 2\|2 cos(x) +--R 4 +--R + +--R +-+ +--R - 2\|2 cos(x) +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R + +--R +-+ +-+ 2x + %pi 3 +--R (2a\|2 cos(x) + 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ +-+ 2x + %pi +--R (- 2a\|2 cos(x) - 2a\|2 )sin(--------) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2 +-+ 2x + %pi 3 +--R (2a\|2 cos(x) + 2a\|2 cos(x))sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R (2a\|2 cos(--------)cos(x) + 2a\|2 cos(--------)cos(x)) +--R 4 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ 2x + %pi +--R (- 2a\|2 cos(x) - 2a\|2 cos(x))sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R - 2a\|2 cos(--------)cos(x) - 2a\|2 cos(--------)cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 3 +--R (- 2a\|2 cos(x) - 4a\|2 cos(x) - 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R 2a\|2 cos(--------)cos(x) + 4a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi +--R 2a\|2 cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ 2x + %pi +--R (2a\|2 cos(x) + 4a\|2 cos(x) + 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R - 2a\|2 cos(--------)cos(x) - 4a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi +--R - 2a\|2 cos(--------)cos(x) +--R 4 +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(sin(--------)) +--R \|a 4 +--R + +--R +-+ +-+ 2x + %pi 2 +-+ +--R (- 4a\|2 cos(x) - 4a\|2 )sin(--------) + 4a\|2 cos(x) +--R 4 +--R + +--R +-+ +--R 4a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2 +-+ 2x + %pi 2 +--R (- 4a\|2 cos(x) - 4a\|2 cos(x))sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ 2x + %pi 2 +-+ +--R 4a\|2 cos(x) + (2a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +--R 2a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 2a\|2 cos(x) + 2a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2x + %pi 2 +-+ 2 +--R 2a\|2 cos(x) + (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ +--R (2a\|2 cos(--------) - 8a\|2 )cos(x) - 4a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 2x + %pi 2 +--R (- 2a\|2 cos(x) - 4a\|2 cos(x) - 2a\|2 cos(x) )sin(--------) +--R 4 +--R + +--R +-+ 4 +-+ 3 +--R 2a\|2 cos(x) + 4a\|2 cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi 2 +--R - 4a\|2 cos(--------) cos(x) - 2a\|2 cos(--------) +--R 4 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (2a sin(--------) - 2a)sin(x) + (- 2a sin(--------) + 2a)sin(x) +--R 4 4 +--R + +--R 2 2x + %pi 2 2 2 +--R ((2a cos(x) - 2a)sin(--------) - 2a cos(x) + 2a)sin(x) +--R 4 +--R + +--R 3 2 2x + %pi 2 +--R (4a cos(x) + 6a cos(x) + 4a cos(x) + 2a)sin(--------) +--R 4 +--R + +--R 3 2 +--R - 4a cos(x) - 6a cos(x) - 4a cos(x) - 2a +--R * +--R sin(x) +--R * +--R +-+ +--R |2 +--------------+ +--R |- \|- a sin(x) + a +--R \|a +--R + +--R 2 2x + %pi 3 +--R (- 2a cos(x) - 4a cos(x) - 2a)sin(--------) +--R 4 +--R + +--R 2 2x + %pi +--R (2a cos(x) + 4a cos(x) + 2a)sin(--------) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2 2x + %pi 3 +--R (- 4a cos(x) - 8a cos(x) - 4a)sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R - 2a cos(--------)cos(x) - 4a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R - 2a cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 2 2x + %pi +--R (4a cos(x) + 8a cos(x) + 4a)sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R 2a cos(--------)cos(x) + 4a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R 2a cos(--------)cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R 2 2x + %pi 3 +--R (6a cos(x) + 12a cos(x) + 6a)sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R - 6a cos(--------)cos(x) - 12a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R - 6a cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 2 2x + %pi +--R (- 6a cos(x) - 12a cos(x) - 6a)sin(--------) +--R 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R 6a cos(--------)cos(x) + 12a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R 6a cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi +--R atanh(sin(--------)) +--R 4 +--R + +--R 2 2x + %pi 2 2 +--R (4a cos(x) + 8a cos(x) + 4a)sin(--------) - 4a cos(x) - 8a cos(x) +--R 4 +--R + +--R - 4a +--R * +--R 3 +--R sin(x) +--R + +--R 2 2x + %pi 2 +--R (8a cos(x) + 16a cos(x) + 8a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (- 2a cos(--------) - 8a)cos(x) + (- 4a cos(--------) - 16a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 2a cos(--------) - 8a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (2a cos(x) + 4a cos(x) - 10a cos(x) - 24a cos(x) - 12a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2x + %pi 2 2 +--R - 2a cos(x) - 4a cos(x) + (- 4a cos(--------) + 10a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 8a cos(--------) + 24a)cos(x) - 4a cos(--------) + 12a +--R 4 4 +--R * +--R sin(x) +--R + +--R 4 3 2 2x + %pi 2 4 +--R (6a cos(x) + 12a cos(x) + 6a cos(x) )sin(--------) - 6a cos(x) +--R 4 +--R + +--R 3 2x + %pi 2 2 +--R - 12a cos(x) + (6a cos(--------) - 6a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R 12a cos(--------) cos(x) + 6a cos(--------) +--R 4 4 +--R / +--R +-+ +-+ 2x + %pi 2 +-+ +-+ +--R ((2a\|2 cos(x) + 2a\|2 )sin(--------) - 2a\|2 cos(x) - 2a\|2 ) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2 +-+ 2x + %pi 2 +-+ 2 +--R (2a\|2 cos(x) + 2a\|2 cos(x))sin(--------) - 2a\|2 cos(x) +--R 4 +--R + +--R +-+ +--R - 2a\|2 cos(x) +--R * +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (- 2a\|2 cos(x) - 4a\|2 cos(x) - 2a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R 2a\|2 cos(x) + 4a\|2 cos(x) + 2a\|2 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a sin(x) + a \|a cos(x) + a +--R \|a +--R + +--R 2 2x + %pi 2 2 +--R (- 2a cos(x) - 4a cos(x) - 2a)sin(--------) + 2a cos(x) +--R 4 +--R + +--R 4a cos(x) + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2x + %pi 2 2 +--R (- 4a cos(x) - 8a cos(x) - 4a)sin(--------) + 4a cos(x) +--R 4 +--R + +--R 8a cos(x) + 4a +--R * +--R sin(x) +--R + +--R 2 2x + %pi 2 2 +--R (6a cos(x) + 12a cos(x) + 6a)sin(--------) - 6a cos(x) +--R 4 +--R + +--R - 12a cos(x) - 6a +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression(Integer) +--E 417 + +--S 418 of 534 +m0680b:= a0680.2-r0680 +--R +--R +--R (358) +--R +-+ +--R |2 +--------------+ +--R (- a cos(x) - a) |- \|- a sin(x) + a +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +--------------+ +------------+ +--R (2\|2 sin(x) + 2\|2 cos(x) + 2\|2 )\|- a sin(x) + a \|a cos(x) + a +--R + +--R 2x + %pi 2x + %pi 2x + %pi +--R (- 4a cos(--------)cos(x) - 4a cos(--------))atanh(sin(--------)) +--R 4 4 4 +--R + +--R 2 +--R 4a cos(x) + 4a cos(x) +--R / +--R +--------------+ +--R (2a cos(x) + 2a)\|- a sin(x) + a +--R Type: Expression(Integer) +--E 418 + +--S 419 of 534 +d0680b:= D(m0680b,x) +--R +--R +--R (359) +--R +-+ +-+ 2x + %pi 2 +-+ +-+ +--R ((- \|2 cos(x) - 5\|2 )sin(--------) + \|2 cos(x) + 5\|2 ) +--R 4 +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (\|2 cos(x) - 6\|2 cos(x) - 3\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R - \|2 cos(x) + 6\|2 cos(x) + 3\|2 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 2\|2 cos(x) - 4\|2 cos(x) + 9\|2 cos(x) + 11\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 2\|2 cos(x) + 4\|2 cos(x) - 9\|2 cos(x) - 11\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 22\|2 cos(x) - 35\|2 cos(x) - 6\|2 cos(x) + 7\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 22\|2 cos(x) + 35\|2 cos(x) + 6\|2 cos(x) - 7\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 10\|2 cos(x) - 34\|2 cos(x) - 48\|2 cos(x) +--R + +--R +-+ +-+ +--R - 34\|2 cos(x) - 10\|2 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 10\|2 cos(x) + 34\|2 cos(x) + 48\|2 cos(x) + 34\|2 cos(x) +--R + +--R +-+ +--R 10\|2 +--R * +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R (- 6\|2 cos(x) - 6\|2 cos(x) + 6\|2 cos(x) + 6\|2 cos(x)) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R 6\|2 cos(x) + 6\|2 cos(x) - 6\|2 cos(x) - 6\|2 cos(x) +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 3 +--R (4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ 2x + %pi +--R (- 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 )sin(--------) +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (4a\|2 cos(x) + 20a\|2 cos(x) + 28a\|2 cos(x) + 12a\|2 ) +--R * +--R 2x + %pi 3 +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R 4a\|2 cos(--------)cos(x) + 8a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi +--R 4a\|2 cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 4a\|2 cos(x) - 20a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +--R - 12a\|2 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 3 +-+ 2x + %pi 2 +--R - 4a\|2 cos(--------)cos(x) - 8a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi +--R - 4a\|2 cos(--------)cos(x) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2x + %pi 3 +--R (8a\|2 cos(x) + 12a\|2 cos(x) - 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 4 +-+ 2x + %pi 3 +--R 4a\|2 cos(--------)cos(x) + 24a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R 36a\|2 cos(--------)cos(x) + 16a\|2 cos(--------)cos(x) +--R 4 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ 2x + %pi +--R (- 8a\|2 cos(x) - 12a\|2 cos(x) + 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 4 +-+ 2x + %pi 3 +--R - 4a\|2 cos(--------)cos(x) - 24a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R - 36a\|2 cos(--------)cos(x) - 16a\|2 cos(--------)cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 12a\|2 cos(x) - 36a\|2 cos(x) - 36a\|2 cos(x) - 12a\|2 ) +--R * +--R 2x + %pi 3 +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 4 +-+ 2x + %pi 3 +--R 12a\|2 cos(--------)cos(x) + 36a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R 36a\|2 cos(--------)cos(x) + 12a\|2 cos(--------)cos(x) +--R 4 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (12a\|2 cos(x) + 36a\|2 cos(x) + 36a\|2 cos(x) + 12a\|2 ) +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 4 +-+ 2x + %pi 3 +--R - 12a\|2 cos(--------)cos(x) - 36a\|2 cos(--------)cos(x) +--R 4 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi +--R - 36a\|2 cos(--------)cos(x) - 12a\|2 cos(--------)cos(x) +--R 4 4 +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(sin(--------)) +--R \|a 4 +--R + +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (- 8a\|2 cos(x) - 16a\|2 cos(x) - 8a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R 8a\|2 cos(x) + 16a\|2 cos(x) + 8a\|2 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 40a\|2 cos(x) - 56a\|2 cos(x) +--R + +--R +-+ +--R - 24a\|2 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2x + %pi 2 +-+ 2 +--R 8a\|2 cos(x) + (4a\|2 cos(--------) + 40a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (8a\|2 cos(--------) + 56a\|2 )cos(x) + 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 24a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R - 4a\|2 cos(x) - 24a\|2 cos(x) - 28a\|2 cos(x) +--R + +--R +-+ +--R 8a\|2 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 4 +-+ 2x + %pi 2 +-+ 3 +--R 4a\|2 cos(x) + (4a\|2 cos(--------) + 24a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (20a\|2 cos(--------) + 28a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi 2 +-+ +--R 28a\|2 cos(--------) cos(x) + 12a\|2 cos(--------) - 8a\|2 +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 4a\|2 cos(x) - 24a\|2 cos(x) - 12a\|2 cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R 56a\|2 cos(x) + 72a\|2 cos(x) + 24a\|2 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 5 +-+ 4 +--R 4a\|2 cos(x) + 24a\|2 cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (8a\|2 cos(--------) + 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +-+ +--R (12a\|2 cos(--------) - 56a\|2 )cos(x) - 72a\|2 cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 4a\|2 cos(--------) - 24a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 12a\|2 cos(x) - 36a\|2 cos(x) - 36a\|2 cos(x) +--R + +--R +-+ 2 +--R - 12a\|2 cos(x) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 5 +-+ 4 +--R 12a\|2 cos(x) + 36a\|2 cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 12a\|2 cos(--------) + 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 36a\|2 cos(--------) + 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2x + %pi 2 +--R - 36a\|2 cos(--------) cos(x) - 12a\|2 cos(--------) +--R 4 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 5 +--R ((4a cos(x) + 4a)sin(--------) - 4a cos(x) - 4a)sin(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R ((6a cos(x) + 6a)sin(--------) - 6a cos(x) - 6a)sin(x) +--R 4 +--R + +--R 3 2 2x + %pi 2 +--R (4a cos(x) + 4a cos(x) - 14a cos(x) - 14a)sin(--------) +--R 4 +--R + +--R 3 2 +--R - 4a cos(x) - 4a cos(x) + 14a cos(x) + 14a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 +--R (8a cos(x) + 34a cos(x) + 38a cos(x) + 6a cos(x) - 6a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R - 8a cos(x) - 34a cos(x) - 38a cos(x) - 6a cos(x) + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (24a cos(x) + 62a cos(x) + 62a cos(x) + 34a cos(x) + 10a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R - 24a cos(x) - 62a cos(x) - 62a cos(x) - 34a cos(x) - 10a +--R * +--R sin(x) +--R + +--R 5 4 2 2x + %pi 2 +--R (4a cos(x) + 8a cos(x) - 8a cos(x) - 4a cos(x))sin(--------) +--R 4 +--R + +--R 5 4 2 +--R - 4a cos(x) - 8a cos(x) + 8a cos(x) + 4a cos(x) +--R * +--R +-+ +--R |2 +--------------+ +--R |- \|- a sin(x) + a +--R \|a +--R + +--R 3 2 2x + %pi 3 +--R (- 2a cos(x) - 14a cos(x) - 22a cos(x) - 10a)sin(--------) +--R 4 +--R + +--R 3 2 2x + %pi +--R (2a cos(x) + 14a cos(x) + 22a cos(x) + 10a)sin(--------) +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2x + %pi 3 +--R (- 26a cos(x) - 70a cos(x) - 62a cos(x) - 18a)sin(--------) +--R 4 +--R + +--R 2x + %pi 4 2x + %pi 3 +--R - 2a cos(--------)cos(x) - 14a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi +--R - 22a cos(--------)cos(x) - 10a cos(--------)cos(x) +--R 4 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 3 2 2x + %pi +--R (26a cos(x) + 70a cos(x) + 62a cos(x) + 18a)sin(--------) +--R 4 +--R + +--R 2x + %pi 4 2x + %pi 3 +--R 2a cos(--------)cos(x) + 14a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi +--R 22a cos(--------)cos(x) + 10a cos(--------)cos(x) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (- 8a cos(x) - 22a cos(x) - 18a cos(x) - 2a cos(x) + 2a) +--R * +--R 2x + %pi 3 +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 4 2x + %pi 3 +--R - 28a cos(--------)cos(x) - 84a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi +--R - 84a cos(--------)cos(x) - 28a cos(--------)cos(x) +--R 4 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R (8a cos(x) + 22a cos(x) + 18a cos(x) + 2a cos(x) - 2a) +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 4 2x + %pi 3 +--R 28a cos(--------)cos(x) + 84a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi +--R 84a cos(--------)cos(x) + 28a cos(--------)cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (8a cos(x) + 50a cos(x) + 102a cos(x) + 86a cos(x) + 26a) +--R * +--R 2x + %pi 3 +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 5 2x + %pi 4 +--R - 8a cos(--------)cos(x) - 50a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R - 102a cos(--------)cos(x) - 86a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R - 26a cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R (- 8a cos(x) - 50a cos(x) - 102a cos(x) - 86a cos(x) - 26a) +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 5 2x + %pi 4 +--R 8a cos(--------)cos(x) + 50a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 3 2x + %pi 2 +--R 102a cos(--------)cos(x) + 86a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R 26a cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi +--R atanh(sin(--------)) +--R 4 +--R + +--R 3 2 2x + %pi 2 +--R (4a cos(x) + 28a cos(x) + 44a cos(x) + 20a)sin(--------) +--R 4 +--R + +--R 3 2 +--R - 4a cos(x) - 28a cos(x) - 44a cos(x) - 20a +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2x + %pi 2 +--R (52a cos(x) + 140a cos(x) + 124a cos(x) + 36a)sin(--------) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 2a cos(--------) - 52a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 14a cos(--------) - 140a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 22a cos(--------) - 124a)cos(x) - 10a cos(--------) - 36a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 +--R 2a cos(x) + 30a cos(x) + 66a cos(x) + 46a cos(x) + 4a cos(x) +--R + +--R - 4a +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 5 4 2x + %pi 2 3 +--R - 2a cos(x) - 30a cos(x) + (- 26a cos(--------) - 66a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 70a cos(--------) - 46a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 62a cos(--------) - 4a)cos(x) - 18a cos(--------) + 4a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R 28a cos(x) + 68a cos(x) - 16a cos(x) - 176a cos(x) +--R + +--R - 172a cos(x) - 52a +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 5 2x + %pi 2 4 +--R - 28a cos(x) + (- 8a cos(--------) - 68a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 22a cos(--------) + 16a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 18a cos(--------) + 176a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 2a cos(--------) + 172a)cos(x) + 2a cos(--------) + 52a +--R 4 4 +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (8a cos(x) + 50a cos(x) + 102a cos(x) + 86a cos(x) + 26a cos(x) ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 6 5 2x + %pi 2 4 +--R - 8a cos(x) - 50a cos(x) + (8a cos(--------) - 102a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 2x + %pi 2 2 +--R (50a cos(--------) - 86a)cos(x) + (102a cos(--------) - 26a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R 86a cos(--------) cos(x) + 26a cos(--------) +--R 4 4 +--R / +--R +-+ 2 +-+ +-+ 2x + %pi 2 +--R (4a\|2 cos(x) + 8a\|2 cos(x) + 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 2 +-+ +-+ +--R - 4a\|2 cos(x) - 8a\|2 cos(x) - 4a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (4a\|2 cos(x) + 20a\|2 cos(x) + 28a\|2 cos(x) + 12a\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R - 4a\|2 cos(x) - 20a\|2 cos(x) - 28a\|2 cos(x) - 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ 2x + %pi 2 +--R (8a\|2 cos(x) + 12a\|2 cos(x) - 4a\|2 )sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +--R - 8a\|2 cos(x) - 12a\|2 cos(x) + 4a\|2 +--R * +--R sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 12a\|2 cos(x) - 36a\|2 cos(x) - 36a\|2 cos(x) - 12a\|2 ) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R +-+ 3 +-+ 2 +-+ +-+ +--R 12a\|2 cos(x) + 36a\|2 cos(x) + 36a\|2 cos(x) + 12a\|2 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a sin(x) + a \|a cos(x) + a +--R \|a +--R + +--R 3 2 2x + %pi 2 +--R (- 2a cos(x) - 14a cos(x) - 22a cos(x) - 10a)sin(--------) +--R 4 +--R + +--R 3 2 +--R 2a cos(x) + 14a cos(x) + 22a cos(x) + 10a +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2x + %pi 2 +--R (- 26a cos(x) - 70a cos(x) - 62a cos(x) - 18a)sin(--------) +--R 4 +--R + +--R 3 2 +--R 26a cos(x) + 70a cos(x) + 62a cos(x) + 18a +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (- 8a cos(x) - 22a cos(x) - 18a cos(x) - 2a cos(x) + 2a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R 8a cos(x) + 22a cos(x) + 18a cos(x) + 2a cos(x) - 2a +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (8a cos(x) + 50a cos(x) + 102a cos(x) + 86a cos(x) + 26a) +--R * +--R 2x + %pi 2 +--R sin(--------) +--R 4 +--R + +--R 4 3 2 +--R - 8a cos(x) - 50a cos(x) - 102a cos(x) - 86a cos(x) - 26a +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 534 +t0681:= sin(x)/(a+b*sin(x))^(1/2) +--R +--R +--R sin(x) +--R (360) --------------- +--R +------------+ +--R \|b sin(x) + a +--R Type: Expression(Integer) +--E 420 + +--S 421 of 534 +r0681:= 2*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))*_ + (a+b*sin(x))^(1/2)/b/((a+b*sin(x))/(a+b))^(1/2)-_ + 2*a*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))*((a+b*sin(x))/(a+b))^(1/2)/_ + b/(a+b*sin(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 421 + +--S 422 of 534 +a0681:= integrate(t0681,x) +--R +--R +--R x +--R ++ sin(%L) +--R (361) | ---------------- d%L +--R ++ +-------------+ +--R \|b sin(%L) + a +--R Type: Union(Expression(Integer),...) +--E 422 + +--S 423 of 534 +m0681:= a0681-r0681 +--R +--R +--R x +--R ++ sin(%L) +--R (362) | ---------------- d%L - r0681 +--R ++ +-------------+ +--R \|b sin(%L) + a +--R Type: Expression(Integer) +--E 423 + +--S 424 of 534 +d0681:= D(m0681,x) +--R +--R +--R sin(x) +--R (363) --------------- +--R +------------+ +--R \|b sin(x) + a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 534 +t0682:= (A+B*sin(x))/(a+a*sin(x))^(1/2) +--R +--R +--R B sin(x) + A +--R (364) --------------- +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression(Integer) +--E 425 + +--S 426 of 534 +r0682:= -2*B*cos(x)/(a+a*sin(x))^(1/2)-2*(A-B)*atanh(cos(1/4*%pi+1/2*x))*_ + cos(-1/4*%pi+1/2*x)/(a+a*sin(x))^(1/2) +--R +--R +--R 2x - %pi 2x + %pi +--R (2B - 2A)cos(--------)atanh(cos(--------)) - 2B cos(x) +--R 4 4 +--R (365) ------------------------------------------------------ +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression(Integer) +--E 426 + +--S 427 of 534 +a0682:= integrate(t0682,x) +--R +--R +--R (366) +--R [ +--R +-+ +--R |2 +--R ((B - A)a cos(x) + (B - A)a) |- +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (- \|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) + 3cos(x) + 3 +--R / +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2B\|2 sin(x) - 2B\|2 cos(x) - 2B\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R ((- B + A)a cos(x) + (- B + A)a) |- +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) - \|2 cos(x) - \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (cos(x) + 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2B\|2 sin(x) - 2B\|2 cos(x) - 2B\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 427 + +--S 428 of 534 +m0682a:= a0682.1-r0682 +--R +--R +--R (367) +--R +-+ +--R |2 +------------+ +--R ((B - A)a cos(x) + (B - A)a) |- \|a sin(x) + a +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (- \|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) + 3cos(x) + 3 +--R / +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R + +--R +-+ +-+ +-+ +------------+ +------------+ +--R (2B\|2 sin(x) - 2B\|2 cos(x) - 2B\|2 )\|a cos(x) + a \|a sin(x) + a +--R + +--R 2x - %pi 2x - %pi +--R ((- 4B + 4A)a cos(--------)cos(x) + (- 4B + 4A)a cos(--------)) +--R 4 4 +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2 +--R 4B a cos(x) + 4B a cos(x) +--R / +--R +------------+ +--R (2a cos(x) + 2a)\|a sin(x) + a +--R Type: Expression(Integer) +--E 428 + +--S 429 of 534 +d0682a:= D(m0682a,x) +--R +--R +--R (368) +--R +-+ 2x + %pi 2 +-+ 4 +--R (B\|2 cos(--------) - B\|2 )sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (B\|2 cos(--------) - B\|2 )cos(x) - A\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R A\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2B\|2 cos(--------) - 2B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((B - A)\|2 cos(--------) + (- B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 3B - 2A)\|2 cos(--------) + (3B + 2A)\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 4B\|2 cos(--------) + 4B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 6B - A)\|2 cos(--------) + (6B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2B - A)\|2 cos(--------) + (2B + A)\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((2B - 2A)\|2 cos(--------) + (- 2B + 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 6A\|2 cos(--------) + 6A\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 2B - 4A)\|2 cos(--------) + (2B + 4A)\|2 )cos(x) +--R 4 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 4 +--R (2B a cos(--------) - 2B a)sin(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (2B a cos(--------) - 2B a)sin(x) +--R 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (2B a cos(--------) - 2B a)cos(x) - 2B a cos(--------) +--R 4 4 +--R + +--R 2B a +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (- 4B a cos(--------) + 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 6B a cos(--------) + 6B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 4B a cos(--------) + 4B a)cos(x) - 2B a cos(--------) +--R 4 4 +--R + +--R 2B a +--R * +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (- 4A a cos(--------) + 4A a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 8A a cos(--------) + 8A a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 4A a cos(--------) + 4A a)cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a sin(x) + a +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((2B - 2A)a\|2 cos(--------) + (- 2B + 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (2B - 2A)a\|2 cos(--------) + (- 2B + 2A)a\|2 +--R 4 +--R * +--R 2x - %pi 2 +--R sin(--------)sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((- 2B + 2A)a\|2 cos(--------) + (2B - 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 2B + 2A)a\|2 cos(--------) + (2B - 2A)a\|2 )cos(x) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (2B - 2A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 2B + 2A)a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (2B - 2A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 2B + 2A)a\|2 cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((- 2B + 2A)a\|2 cos(--------) + (2B - 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 4B + 4A)a\|2 cos(--------) + (4B - 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2B + 2A)a\|2 cos(--------) + (2B - 2A)a\|2 +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 2B + 2A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (2B - 2A)a\|2 cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 4B + 4A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (4B - 4A)a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 2B + 2A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (2B - 2A)a\|2 cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 4B a\|2 cos(--------) + 4B a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x - %pi +--R (- 2B + 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (- 2B + 2A)a\|2 cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (4B a\|2 cos(--------) - 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (4B a\|2 cos(--------) - 4B a\|2 )cos(x) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +--R (2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 2B a\|2 cos(--------) + 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2B a\|2 cos(--------) - 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (8B a\|2 cos(--------) - 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R 4B a\|2 cos(--------) - 4B a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +--R (2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +-+ 2x - %pi +--R (4B - 4A)a\|2 cos(--------)cos(x) + (2B - 2A)a\|2 cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (2B a\|2 cos(--------) - 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (4B a\|2 cos(--------) - 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (2B a\|2 cos(--------) - 2B a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 2 +--R ((2B - 2A)a cos(--------) + (- 2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((4B - 4A)a cos(--------) + (- 4B + 4A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (2B - 2A)a cos(--------) + (- 2B + 2A)a +--R 4 +--R * +--R 2x - %pi 2 +--R sin(--------)sin(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((- 4B + 4A)a cos(--------) + (4B - 4A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((- 8B + 8A)a cos(--------) + (8B - 8A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 4B + 4A)a cos(--------) + (4B - 4A)a +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2x + %pi 2 +--R (2B - 2A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 2B + 2A)a cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (4B - 4A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 4B + 4A)a cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (2B - 2A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 2B + 2A)a cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R sin(x) +--R + +--R 2x + %pi 2 2 +--R ((- 6B + 6A)a cos(--------) + (6B - 6A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((- 12B + 12A)a cos(--------) + (12B - 12A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 6B + 6A)a cos(--------) + (6B - 6A)a +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 6B + 6A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (6B - 6A)a cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 12B + 12A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (12B - 12A)a cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 6B + 6A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (6B - 6A)a cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 4B a cos(--------) + 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 8B a cos(--------) + 8B a)cos(x) - 4B a cos(--------) + 4B a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x - %pi 2 +--R (- 2B + 2A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2x - %pi +--R (- 4B + 4A)a cos(--------)cos(x) + (- 2B + 2A)a cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (8B a cos(--------) - 8B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (16B a cos(--------) - 16B a)cos(x) + 8B a cos(--------) - 8B a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 2x - %pi +--R (4B - 4A)a cos(--------)cos(x) + (8B - 8A)a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi +--R (4B - 4A)a cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (- 2B a cos(--------) + 2B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 4B a cos(--------) + 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (10B a cos(--------) - 10B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (24B a cos(--------) - 24B a)cos(x) + 12B a cos(--------) - 12B a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 2x - %pi +--R (6B - 6A)a cos(--------)cos(x) + (12B - 12A)a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi +--R (6B - 6A)a cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (6B a cos(--------) - 6B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 2x + %pi 2 2 +--R (12B a cos(--------) - 12B a)cos(x) + (6B a cos(--------) - 6B a)cos(x) +--R 4 4 +--R / +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) + 2a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 2a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) - 2a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 2a\|2 +--R * +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (2a cos(--------) - 2a)cos(x) + (4a cos(--------) - 4a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 2a cos(--------) - 2a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 2 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 8a cos(--------) + 8a)cos(x) - 4a cos(--------) + 4a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (- 6a cos(--------) + 6a)cos(x) + (- 12a cos(--------) + 12a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 6a cos(--------) + 6a +--R 4 +--R * +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression(Integer) +--E 429 + +--S 430 of 534 +m0682b:= a0682.2-r0682 +--R +--R +--R (369) +--R +-+ +--R |2 +------------+ +--R ((- B + A)a cos(x) + (- B + A)a) |- \|a sin(x) + a +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) + cos(x) + 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) - \|2 cos(x) - \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (cos(x) + 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +------------+ +--R (2B\|2 sin(x) - 2B\|2 cos(x) - 2B\|2 )\|a cos(x) + a \|a sin(x) + a +--R + +--R 2x - %pi 2x - %pi +--R ((- 4B + 4A)a cos(--------)cos(x) + (- 4B + 4A)a cos(--------)) +--R 4 4 +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2 +--R 4B a cos(x) + 4B a cos(x) +--R / +--R +------------+ +--R (2a cos(x) + 2a)\|a sin(x) + a +--R Type: Expression(Integer) +--E 430 + +--S 431 of 534 +d0682b:= D(m0682b,x) +--R +--R +--R (370) +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (B\|2 cos(--------) - B\|2 )cos(x) + 5B\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 5B\|2 +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (B\|2 cos(--------) - B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 6B - A)\|2 cos(--------) + (6B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 3B - A)\|2 cos(--------) + (3B + A)\|2 +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (2B\|2 cos(--------) - 2B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((4B - A)\|2 cos(--------) + (- 4B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 9B\|2 cos(--------) + 9B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 11B + A)\|2 cos(--------) + (11B - A)\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 22B\|2 cos(--------) + 22B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((- 35B + 2A)\|2 cos(--------) + (35B - 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 6B + 7A)\|2 cos(--------) + (6B - 7A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (7B + 5A)\|2 cos(--------) + (- 7B - 5A)\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R ((10B - 2A)\|2 cos(--------) + (- 10B + 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((34B - 16A)\|2 cos(--------) + (- 34B + 16A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((48B - 23A)\|2 cos(--------) + (- 48B + 23A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((34B - 6A)\|2 cos(--------) + (- 34B + 6A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (10B + 3A)\|2 cos(--------) + (- 10B - 3A)\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R ((- 6B + 14A)\|2 cos(--------) + (6B - 14A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((- 6B + 48A)\|2 cos(--------) + (6B - 48A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((6B + 54A)\|2 cos(--------) + (- 6B - 54A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((6B + 20A)\|2 cos(--------) + (- 6B - 20A)\|2 )cos(x) +--R 4 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (4B a cos(--------) - 4B a)cos(x) + 4B a cos(--------) +--R 4 4 +--R + +--R - 4B a +--R * +--R 5 +--R sin(x) +--R + +--R 2x + %pi 2 +--R ((- 6B - 2A)a cos(--------) + (6B + 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 6B - 2A)a cos(--------) + (6B + 2A)a +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((- 14B - 2A)a cos(--------) + (14B + 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 14B - 2A)a cos(--------) + (14B + 2A)a +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R (- 8B a cos(--------) + 8B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R ((- 34B + 2A)a cos(--------) + (34B - 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((- 38B + 6A)a cos(--------) + (38B - 6A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((- 6B + 6A)a cos(--------) + (6B - 6A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (6B + 2A)a cos(--------) + (- 6B - 2A)a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R ((24B - 8A)a cos(--------) + (- 24B + 8A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R ((62B - 26A)a cos(--------) + (- 62B + 26A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((62B - 26A)a cos(--------) + (- 62B + 26A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((34B - 6A)a cos(--------) + (- 34B + 6A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (10B + 2A)a cos(--------) + (- 10B - 2A)a +--R 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 5 +--R ((- 4B + 4A)a cos(--------) + (4B - 4A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R ((- 8B + 32A)a cos(--------) + (8B - 32A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (72A a cos(--------) - 72A a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((8B + 64A)a cos(--------) + (- 8B - 64A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((4B + 20A)a cos(--------) + (- 4B - 20A)a)cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a sin(x) + a +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((4B - 4A)a\|2 cos(--------) + (- 4B + 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((8B - 8A)a\|2 cos(--------) + (- 8B + 8A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (4B - 4A)a\|2 cos(--------) + (- 4B + 4A)a\|2 +--R 4 +--R * +--R 2x - %pi 3 +--R sin(--------)sin(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((- 4B + 4A)a\|2 cos(--------) + (4B - 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 20B + 20A)a\|2 cos(--------) + (20B - 20A)a\|2 ) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((- 28B + 28A)a\|2 cos(--------) + (28B - 28A)a\|2 ) +--R 4 +--R * +--R cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 12B + 12A)a\|2 cos(--------) + (12B - 12A)a\|2 +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (4B - 4A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 4B + 4A)a\|2 cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (8B - 8A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 8B + 8A)a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (4B - 4A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 4B + 4A)a\|2 cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((8B - 8A)a\|2 cos(--------) + (- 8B + 8A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((12B - 12A)a\|2 cos(--------) + (- 12B + 12A)a\|2 ) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 4B + 4A)a\|2 cos(--------) + (4B - 4A)a\|2 +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 4B + 4A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (4B - 4A)a\|2 cos(--------) +--R 4 +--R * +--R 4 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 24B + 24A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (24B - 24A)a\|2 cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 36B + 36A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (36B - 36A)a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (- 16B + 16A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (16B - 16A)a\|2 cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R ((12B - 12A)a\|2 cos(--------) + (- 12B + 12A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R ((36B - 36A)a\|2 cos(--------) + (- 36B + 36A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R ((36B - 36A)a\|2 cos(--------) + (- 36B + 36A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (12B - 12A)a\|2 cos(--------) + (- 12B + 12A)a\|2 +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (12B - 12A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 12B + 12A)a\|2 cos(--------) +--R 4 +--R * +--R 4 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (36B - 36A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 36B + 36A)a\|2 cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (36B - 36A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 36B + 36A)a\|2 cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2x + %pi 2 +--R (12B - 12A)a\|2 cos(--------)cos(--------) +--R 4 4 +--R + +--R +-+ 2x - %pi +--R (- 12B + 12A)a\|2 cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R +-+ +--R |2 2x + %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 8B a\|2 cos(--------) + 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 16B a\|2 cos(--------) + 16B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 8B a\|2 cos(--------) + 8B a\|2 +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +--R (- 4B + 4A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (- 8B + 8A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (- 4B + 4A)a\|2 cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (8B a\|2 cos(--------) - 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (40B a\|2 cos(--------) - 40B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (56B a\|2 cos(--------) - 56B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R 24B a\|2 cos(--------) - 24B a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x - %pi 3 +--R (4B - 4A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +--R (20B - 20A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (28B - 28A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (12B - 12A)a\|2 cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 24B a\|2 cos(--------) + 24B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 28B a\|2 cos(--------) + 28B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R 8B a\|2 cos(--------) - 8B a\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 3 +--R (- 8B + 8A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +--R (- 12B + 12A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (4B - 4A)a\|2 cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 5 +--R (4B a\|2 cos(--------) - 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (24B a\|2 cos(--------) - 24B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (12B a\|2 cos(--------) - 12B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 56B a\|2 cos(--------) + 56B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 72B a\|2 cos(--------) + 72B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 24B a\|2 cos(--------) + 24B a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 3 +--R (- 12B + 12A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +--R (- 36B + 36A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (- 36B + 36A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi +--R (- 12B + 12A)a\|2 cos(--------) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 5 +--R (- 12B a\|2 cos(--------) + 12B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 4 +--R (- 36B a\|2 cos(--------) + 36B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 36B a\|2 cos(--------) + 36B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 12B a\|2 cos(--------) + 12B a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x + %pi 2 3 +--R ((2B - 2A)a cos(--------) + (- 2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((14B - 14A)a cos(--------) + (- 14B + 14A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((22B - 22A)a cos(--------) + (- 22B + 22A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (10B - 10A)a cos(--------) + (- 10B + 10A)a +--R 4 +--R * +--R 2x - %pi 3 +--R sin(--------)sin(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R ((- 26B + 26A)a cos(--------) + (26B - 26A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((- 70B + 70A)a cos(--------) + (70B - 70A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((- 62B + 62A)a cos(--------) + (62B - 62A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 18B + 18A)a cos(--------) + (18B - 18A)a +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2x + %pi 2 +--R (2B - 2A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 2B + 2A)a cos(--------) +--R 4 +--R * +--R 4 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (14B - 14A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 14B + 14A)a cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (22B - 22A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 22B + 22A)a cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (10B - 10A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 10B + 10A)a cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R ((8B - 8A)a cos(--------) + (- 8B + 8A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R ((22B - 22A)a cos(--------) + (- 22B + 22A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((18B - 18A)a cos(--------) + (- 18B + 18A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((2B - 2A)a cos(--------) + (- 2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 2B + 2A)a cos(--------) + (2B - 2A)a +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 28B + 28A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (28B - 28A)a cos(--------) +--R 4 +--R * +--R 4 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 84B + 84A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (84B - 84A)a cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 84B + 84A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (84B - 84A)a cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (- 28B + 28A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (28B - 28A)a cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R sin(x) +--R + +--R 2x + %pi 2 4 +--R ((8B - 8A)a cos(--------) + (- 8B + 8A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R ((50B - 50A)a cos(--------) + (- 50B + 50A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R ((102B - 102A)a cos(--------) + (- 102B + 102A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R ((86B - 86A)a cos(--------) + (- 86B + 86A)a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (26B - 26A)a cos(--------) + (- 26B + 26A)a +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2x + %pi 2 +--R (8B - 8A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 8B + 8A)a cos(--------) +--R 4 +--R * +--R 5 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (50B - 50A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 50B + 50A)a cos(--------) +--R 4 +--R * +--R 4 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (102B - 102A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 102B + 102A)a cos(--------) +--R 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (86B - 86A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 86B + 86A)a cos(--------) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2x + %pi 2 +--R (26B - 26A)a cos(--------)cos(--------) +--R 4 4 +--R + +--R 2x - %pi +--R (- 26B + 26A)a cos(--------) +--R 4 +--R * +--R cos(x) +--R * +--R 2x + %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 4B a cos(--------) + 4B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 28B a cos(--------) + 28B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 44B a cos(--------) + 44B a)cos(x) - 20B a cos(--------) + 20B a +--R 4 4 +--R * +--R 4 +--R sin(x) +--R + +--R 2x - %pi 3 +--R (- 2B + 2A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 14B + 14A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2x - %pi +--R (- 22B + 22A)a cos(--------)cos(x) + (- 10B + 10A)a cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (52B a cos(--------) - 52B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (140B a cos(--------) - 140B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (124B a cos(--------) - 124B a)cos(x) + 36B a cos(--------) - 36B a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x - %pi 3 +--R (26B - 26A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (70B - 70A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2x - %pi +--R (62B - 62A)a cos(--------)cos(x) + (18B - 18A)a cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 5 +--R (- 2B a cos(--------) + 2B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (- 30B a cos(--------) + 30B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 66B a cos(--------) + 66B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 46B a cos(--------) + 46B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 4B a cos(--------) + 4B a)cos(x) + 4B a cos(--------) - 4B a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 4 +--R (- 8B + 8A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 3 +--R (- 22B + 22A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 18B + 18A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2x - %pi +--R (- 2B + 2A)a cos(--------)cos(x) + (2B - 2A)a cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 5 +--R (28B a cos(--------) - 28B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (68B a cos(--------) - 68B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 16B a cos(--------) + 16B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 176B a cos(--------) + 176B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 172B a cos(--------) + 172B a)cos(x) - 52B a cos(--------) + 52B a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 4 +--R (- 8B + 8A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 3 +--R (- 50B + 50A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 102B + 102A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x - %pi 2x - %pi +--R (- 86B + 86A)a cos(--------)cos(x) + (- 26B + 26A)a cos(--------) +--R 4 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x + %pi 2 6 +--R (- 8B a cos(--------) + 8B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 5 +--R (- 50B a cos(--------) + 50B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 4 +--R (- 102B a cos(--------) + 102B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 3 +--R (- 86B a cos(--------) + 86B a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 26B a cos(--------) + 26B a)cos(x) +--R 4 +--R / +--R +-+ 2x + %pi 2 +-+ 2 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) + 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 4a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (- 20a\|2 cos(--------) + 20a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R (- 28a\|2 cos(--------) + 28a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +--R - 12a\|2 cos(--------) + 12a\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +-+ 2x + %pi 2 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) - 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 4a\|2 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +-+ 3 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ 2 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +-+ +-+ 2x + %pi 2 +--R (36a\|2 cos(--------) - 36a\|2 )cos(x) + 12a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 12a\|2 +--R * +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R + +--R 2x + %pi 2 3 2x + %pi 2 2 +--R (2a cos(--------) - 2a)cos(x) + (14a cos(--------) - 14a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (22a cos(--------) - 22a)cos(x) + 10a cos(--------) - 10a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 3 +--R (- 26a cos(--------) + 26a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2 +--R (- 70a cos(--------) + 70a)cos(x) +--R 4 +--R + +--R 2x + %pi 2 2x + %pi 2 +--R (- 62a cos(--------) + 62a)cos(x) - 18a cos(--------) + 18a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (8a cos(--------) - 8a)cos(x) + (22a cos(--------) - 22a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (18a cos(--------) - 18a)cos(x) + (2a cos(--------) - 2a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R - 2a cos(--------) + 2a +--R 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 4 2x + %pi 2 3 +--R (8a cos(--------) - 8a)cos(x) + (50a cos(--------) - 50a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 2 2x + %pi 2 +--R (102a cos(--------) - 102a)cos(x) + (86a cos(--------) - 86a)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2 +--R 26a cos(--------) - 26a +--R 4 +--R * +--R +------------+ +--R \|a sin(x) + a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 534 +t0683:= (A+B*sin(x))/(a-a*sin(x))^(1/2) +--R +--R +--R B sin(x) + A +--R (371) ----------------- +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 534 +r0683:= -2*B*cos(x)/(a-a*sin(x))^(1/2)+2*(A+B)*atanh(cos(-1/4*%pi+1/2*x))*_ + cos(1/4*%pi+1/2*x)/(a-a*sin(x))^(1/2) +--R +--R +--R 2x + %pi 2x - %pi +--R (2B + 2A)cos(--------)atanh(cos(--------)) - 2B cos(x) +--R 4 4 +--R (372) ------------------------------------------------------ +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression(Integer) +--E 433 + +--S 434 of 534 +a0683:= integrate(t0683,x) +--R +--R +--R (373) +--R [ +--R +-+ +--R |2 +--R ((B + A)a cos(x) + (B + A)a) |- +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R / +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2B\|2 sin(x) + 2B\|2 cos(x) + 2B\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R ((- B - A)a cos(x) + (- B - A)a) |- +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +------------+ +--R (2B\|2 sin(x) + 2B\|2 cos(x) + 2B\|2 )\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 434 + +--S 435 of 534 +m0683a:= a0683.1-r0683 +--R +--R +--R (374) +--R +-+ +--R |2 +--------------+ +--R ((B + A)a cos(x) + (B + A)a) |- \|- a sin(x) + a +--R \|a +--R * +--R log +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R / +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R + +--R +-+ +-+ +-+ +--------------+ +------------+ +--R (2B\|2 sin(x) + 2B\|2 cos(x) + 2B\|2 )\|- a sin(x) + a \|a cos(x) + a +--R + +--R 2x + %pi 2x + %pi +--R ((- 4B - 4A)a cos(--------)cos(x) + (- 4B - 4A)a cos(--------)) +--R 4 4 +--R * +--R 2x - %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2 +--R 4B a cos(x) + 4B a cos(x) +--R / +--R +--------------+ +--R (2a cos(x) + 2a)\|- a sin(x) + a +--R Type: Expression(Integer) +--E 435 + +--S 436 of 534 +d0683a:= D(m0683a,x) +--R +--R +--R (375) +--R +-+ 2x - %pi 2 +-+ 4 +--R (- B\|2 cos(--------) + B\|2 )sin(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (B\|2 cos(--------) - B\|2 )cos(x) + A\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - A\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 2B\|2 cos(--------) + 2B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- B - A)\|2 cos(--------) + (B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (3B - 2A)\|2 cos(--------) + (- 3B + 2A)\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 4B\|2 cos(--------) + 4B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 6B + A)\|2 cos(--------) + (6B - A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 2B + A)\|2 cos(--------) + (2B - A)\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((- 2B - 2A)\|2 cos(--------) + (2B + 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 6A\|2 cos(--------) + 6A\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((2B - 4A)\|2 cos(--------) + (- 2B + 4A)\|2 )cos(x) +--R 4 +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------)sin(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 )cos(x) +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 2 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 ) +--R 4 +--R * +--R 2x + %pi +--R cos(--------)cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((- 2B - 2A)a\|2 cos(--------) + (2B + 2A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 4B - 4A)a\|2 cos(--------) + (4B + 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 2B - 2A)a\|2 cos(--------) + (2B + 2A)a\|2 +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2x + %pi +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 )cos(--------) +--R 4 4 +--R * +--R 3 +--R cos(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2x + %pi +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 )cos(--------) +--R 4 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2x + %pi +--R ((2B + 2A)a\|2 cos(--------) + (- 2B - 2A)a\|2 )cos(--------) +--R 4 4 +--R * +--R cos(x) +--R * +--R +-+ +--R |2 2x - %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R - 4B a\|2 cos(--------) + 4B a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi +--R (- 2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 2B - 2A)a\|2 cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +--R (- 2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 2B - 2A)a\|2 cos(--------)cos(x) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 2B a\|2 cos(--------) + 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (2B a\|2 cos(--------) - 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (8B a\|2 cos(--------) - 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R 4B a\|2 cos(--------) - 4B a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +--R (2B + 2A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +-+ 2x + %pi +--R (4B + 4A)a\|2 cos(--------)cos(x) + (2B + 2A)a\|2 cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R (- 2B a\|2 cos(--------) + 2B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 2B a\|2 cos(--------) + 2B a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x - %pi 2 4 +--R (2B a cos(--------) - 2B a)sin(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (- 2B a cos(--------) + 2B a)sin(x) +--R 4 +--R + +--R 2x - %pi 2 2 2x - %pi 2 +--R ((2B a cos(--------) - 2B a)cos(x) - 2B a cos(--------) + 2B a) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 3 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (6B a cos(--------) - 6B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (4B a cos(--------) - 4B a)cos(x) + 2B a cos(--------) - 2B a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 3 +--R (4A a cos(--------) - 4A a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (8A a cos(--------) - 8A a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (4A a cos(--------) - 4A a)cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--------------+ +--R |- \|- a sin(x) + a +--R \|a +--R + +--R 2x - %pi 2 2 +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 4B - 4A)a cos(--------) + (4B + 4A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 2B - 2A)a cos(--------) + (2B + 2A)a +--R 4 +--R * +--R 2x + %pi 2 +--R sin(--------)sin(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((- 4B - 4A)a cos(--------) + (4B + 4A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 8B - 8A)a cos(--------) + (8B + 8A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 4B - 4A)a cos(--------) + (4B + 4A)a +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x + %pi 3 +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi 2 +--R ((- 4B - 4A)a cos(--------) + (4B + 4A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(--------)cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 2 +--R ((6B + 6A)a cos(--------) + (- 6B - 6A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((12B + 12A)a cos(--------) + (- 12B - 12A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (6B + 6A)a cos(--------) + (- 6B - 6A)a +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x + %pi 3 +--R ((- 6B - 6A)a cos(--------) + (6B + 6A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi 2 +--R ((- 12B - 12A)a cos(--------) + (12B + 12A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 6B - 6A)a cos(--------) + (6B + 6A)a)cos(--------)cos(x) +--R 4 4 +--R * +--R 2x - %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (8B a cos(--------) - 8B a)cos(x) + 4B a cos(--------) - 4B a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 2 2x + %pi +--R (2B + 2A)a cos(--------)cos(x) + (4B + 4A)a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R (2B + 2A)a cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (8B a cos(--------) - 8B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (16B a cos(--------) - 16B a)cos(x) + 8B a cos(--------) - 8B a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 2 2x + %pi +--R (4B + 4A)a cos(--------)cos(x) + (8B + 8A)a cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi +--R (4B + 4A)a cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 4 +--R (2B a cos(--------) - 2B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (- 10B a cos(--------) + 10B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 24B a cos(--------) + 24B a)cos(x) - 12B a cos(--------) + 12B a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 2 +--R (- 6B - 6A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (- 12B - 12A)a cos(--------)cos(x) + (- 6B - 6A)a cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 4 +--R (6B a cos(--------) - 6B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 2x - %pi 2 2 +--R (12B a cos(--------) - 12B a)cos(x) + (6B a cos(--------) - 6B a)cos(x) +--R 4 4 +--R / +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) + 2a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 2a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (2a\|2 cos(--------) - 2a\|2 )cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 2a\|2 cos(--------) + 2a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +-+ +--R (- 4a\|2 cos(--------) + 4a\|2 )cos(x) - 2a\|2 cos(--------) + 2a\|2 +--R 4 4 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a sin(x) + a \|a cos(x) + a +--R \|a +--R + +--R 2x - %pi 2 2 +--R (- 2a cos(--------) + 2a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 4a cos(--------) + 4a)cos(x) - 2a cos(--------) + 2a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 2 +--R (- 4a cos(--------) + 4a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 8a cos(--------) + 8a)cos(x) - 4a cos(--------) + 4a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 2 2x - %pi 2 +--R (6a cos(--------) - 6a)cos(x) + (12a cos(--------) - 12a)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 +--R 6a cos(--------) - 6a +--R 4 +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 534 +m0683b:= a0683.2-r0683 +--R +--R +--R (376) +--R +-+ +--R |2 +--------------+ +--R ((- B - A)a cos(x) + (- B - A)a) |- \|- a sin(x) + a +--R \|a +--R * +--R log +--R (cos(x) + 1)sin(x) - cos(x) - 1 +--R / +--R +-+ +--R +-+ +-+ +-+ |2 +------------+ +--R (\|2 sin(x) + \|2 cos(x) + \|2 ) |- \|a cos(x) + a +--R \|a +--R + +--R (- cos(x) - 1)sin(x) - 3cos(x) - 3 +--R + +--R +-+ +-+ +-+ +--------------+ +------------+ +--R (2B\|2 sin(x) + 2B\|2 cos(x) + 2B\|2 )\|- a sin(x) + a \|a cos(x) + a +--R + +--R 2x + %pi 2x + %pi +--R ((- 4B - 4A)a cos(--------)cos(x) + (- 4B - 4A)a cos(--------)) +--R 4 4 +--R * +--R 2x - %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2 +--R 4B a cos(x) + 4B a cos(x) +--R / +--R +--------------+ +--R (2a cos(x) + 2a)\|- a sin(x) + a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 534 +d0683b:= D(m0683b,x) +--R +--R +--R (377) +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (- B\|2 cos(--------) + B\|2 )cos(x) - 5B\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 5B\|2 +--R * +--R 5 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (B\|2 cos(--------) - B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 6B + A)\|2 cos(--------) + (6B - A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 3B + A)\|2 cos(--------) + (3B - A)\|2 +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 2B\|2 cos(--------) + 2B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((- 4B - A)\|2 cos(--------) + (4B + A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (9B\|2 cos(--------) - 9B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (11B + A)\|2 cos(--------) + (- 11B - A)\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 22B\|2 cos(--------) + 22B\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((- 35B - 2A)\|2 cos(--------) + (35B + 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 6B - 7A)\|2 cos(--------) + (6B + 7A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (7B - 5A)\|2 cos(--------) + (- 7B + 5A)\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R ((- 10B - 2A)\|2 cos(--------) + (10B + 2A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((- 34B - 16A)\|2 cos(--------) + (34B + 16A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((- 48B - 23A)\|2 cos(--------) + (48B + 23A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 34B - 6A)\|2 cos(--------) + (34B + 6A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 10B + 3A)\|2 cos(--------) + (10B - 3A)\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R ((- 6B - 14A)\|2 cos(--------) + (6B + 14A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((- 6B - 48A)\|2 cos(--------) + (6B + 48A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((6B - 54A)\|2 cos(--------) + (- 6B + 54A)\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((6B - 20A)\|2 cos(--------) + (- 6B + 20A)\|2 )cos(x) +--R 4 +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((8B + 8A)a\|2 cos(--------) + (- 8B - 8A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 +--R 4 +--R * +--R 2x + %pi 3 +--R sin(--------)sin(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((20B + 20A)a\|2 cos(--------) + (- 20B - 20A)a\|2 ) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((28B + 28A)a\|2 cos(--------) + (- 28B - 28A)a\|2 ) +--R 4 +--R * +--R cos(x) +--R + +--R +-+ 2x - %pi 2 +-+ +--R (12B + 12A)a\|2 cos(--------) + (- 12B - 12A)a\|2 +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 3 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((8B + 8A)a\|2 cos(--------) + (- 8B - 8A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 2 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 ) +--R 4 +--R * +--R 2x + %pi +--R cos(--------)cos(x) +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((8B + 8A)a\|2 cos(--------) + (- 8B - 8A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((12B + 12A)a\|2 cos(--------) + (- 12B - 12A)a\|2 ) +--R 4 +--R * +--R 2 +--R cos(x) +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 4B - 4A)a\|2 cos(--------) + (4B + 4A)a\|2 +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((4B + 4A)a\|2 cos(--------) + (- 4B - 4A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 4 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((24B + 24A)a\|2 cos(--------) + (- 24B - 24A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 3 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((36B + 36A)a\|2 cos(--------) + (- 36B - 36A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 2 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((16B + 16A)a\|2 cos(--------) + (- 16B - 16A)a\|2 ) +--R 4 +--R * +--R 2x + %pi +--R cos(--------)cos(x) +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R ((- 12B - 12A)a\|2 cos(--------) + (12B + 12A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R ((- 36B - 36A)a\|2 cos(--------) + (36B + 36A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((- 36B - 36A)a\|2 cos(--------) + (36B + 36A)a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 12B - 12A)a\|2 cos(--------) + (12B + 12A)a\|2 +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((12B + 12A)a\|2 cos(--------) + (- 12B - 12A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 4 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((36B + 36A)a\|2 cos(--------) + (- 36B - 36A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 3 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((36B + 36A)a\|2 cos(--------) + (- 36B - 36A)a\|2 ) +--R 4 +--R * +--R 2x + %pi 2 +--R cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R ((12B + 12A)a\|2 cos(--------) + (- 12B - 12A)a\|2 ) +--R 4 +--R * +--R 2x + %pi +--R cos(--------)cos(x) +--R 4 +--R * +--R +-+ +--R |2 2x - %pi +--R |- atanh(cos(--------)) +--R \|a 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 8B a\|2 cos(--------) + 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 16B a\|2 cos(--------) + 16B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R - 8B a\|2 cos(--------) + 8B a\|2 +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 2x + %pi 2 +--R (- 4B - 4A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 8B - 8A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 4B - 4A)a\|2 cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 8B a\|2 cos(--------) + 8B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 40B a\|2 cos(--------) + 40B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (- 56B a\|2 cos(--------) + 56B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R - 24B a\|2 cos(--------) + 24B a\|2 +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x + %pi 3 +--R (- 4B - 4A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +--R (- 20B - 20A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 28B - 28A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (- 12B - 12A)a\|2 cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 24B a\|2 cos(--------) + 24B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 28B a\|2 cos(--------) + 28B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R 8B a\|2 cos(--------) - 8B a\|2 +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x + %pi 3 +--R (- 8B - 8A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +--R (- 12B - 12A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (4B + 4A)a\|2 cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 5 +--R (- 4B a\|2 cos(--------) + 4B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R (- 24B a\|2 cos(--------) + 24B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 12B a\|2 cos(--------) + 12B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (56B a\|2 cos(--------) - 56B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R (72B a\|2 cos(--------) - 72B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +--R 24B a\|2 cos(--------) - 24B a\|2 +--R 4 +--R * +--R sin(x) +--R + +--R +-+ 2x + %pi 3 +--R (12B + 12A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi 2 +--R (36B + 36A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (36B + 36A)a\|2 cos(--------)cos(x) +--R 4 +--R + +--R +-+ 2x + %pi +--R (12B + 12A)a\|2 cos(--------) +--R 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 5 +--R (- 12B a\|2 cos(--------) + 12B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 4 +--R (- 36B a\|2 cos(--------) + 36B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 36B a\|2 cos(--------) + 36B a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 12B a\|2 cos(--------) + 12B a\|2 )cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2x - %pi 2 2x - %pi 2 +--R ((4B a cos(--------) - 4B a)cos(x) + 4B a cos(--------) - 4B a) +--R 4 4 +--R * +--R 5 +--R sin(x) +--R + +--R 2x - %pi 2 +--R ((6B - 2A)a cos(--------) + (- 6B + 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (6B - 2A)a cos(--------) + (- 6B + 2A)a +--R 4 +--R * +--R 4 +--R sin(x) +--R + +--R 2x - %pi 2 3 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 14B + 2A)a cos(--------) + (14B - 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 14B + 2A)a cos(--------) + (14B - 2A)a +--R 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x - %pi 2 4 +--R (8B a cos(--------) - 8B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R ((34B + 2A)a cos(--------) + (- 34B - 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((38B + 6A)a cos(--------) + (- 38B - 6A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((6B + 6A)a cos(--------) + (- 6B - 6A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 6B + 2A)a cos(--------) + (6B - 2A)a +--R 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 4 +--R ((24B + 8A)a cos(--------) + (- 24B - 8A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R ((62B + 26A)a cos(--------) + (- 62B - 26A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((62B + 26A)a cos(--------) + (- 62B - 26A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((34B + 6A)a cos(--------) + (- 34B - 6A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (10B - 2A)a cos(--------) + (- 10B + 2A)a +--R 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 5 +--R ((4B + 4A)a cos(--------) + (- 4B - 4A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 4 +--R ((8B + 32A)a cos(--------) + (- 8B - 32A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (72A a cos(--------) - 72A a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((- 8B + 64A)a cos(--------) + (8B - 64A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 4B + 20A)a cos(--------) + (4B - 20A)a)cos(x) +--R 4 +--R * +--R +-+ +--R |2 +--------------+ +--R |- \|- a sin(x) + a +--R \|a +--R + +--R 2x - %pi 2 3 +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((- 14B - 14A)a cos(--------) + (14B + 14A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 22B - 22A)a cos(--------) + (22B + 22A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 10B - 10A)a cos(--------) + (10B + 10A)a +--R 4 +--R * +--R 2x + %pi 3 +--R sin(--------)sin(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R ((- 26B - 26A)a cos(--------) + (26B + 26A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((- 70B - 70A)a cos(--------) + (70B + 70A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 62B - 62A)a cos(--------) + (62B + 62A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (- 18B - 18A)a cos(--------) + (18B + 18A)a +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x + %pi 4 +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 14B - 14A)a cos(--------) + (14B + 14A)a)cos(--------) +--R 4 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 22B - 22A)a cos(--------) + (22B + 22A)a)cos(--------) +--R 4 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 10B - 10A)a cos(--------) + (10B + 10A)a)cos(--------)cos(x) +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 4 +--R ((- 8B - 8A)a cos(--------) + (8B + 8A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R ((- 22B - 22A)a cos(--------) + (22B + 22A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((- 18B - 18A)a cos(--------) + (18B + 18A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((- 2B - 2A)a cos(--------) + (2B + 2A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (2B + 2A)a cos(--------) + (- 2B - 2A)a +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 28B - 28A)a cos(--------) + (28B + 28A)a)cos(--------) +--R 4 4 +--R * +--R 4 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 84B - 84A)a cos(--------) + (84B + 84A)a)cos(--------) +--R 4 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 84B - 84A)a cos(--------) + (84B + 84A)a)cos(--------) +--R 4 4 +--R * +--R 2 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 28B - 28A)a cos(--------) + (28B + 28A)a)cos(--------)cos(x) +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 4 +--R ((8B + 8A)a cos(--------) + (- 8B - 8A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R ((50B + 50A)a cos(--------) + (- 50B - 50A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R ((102B + 102A)a cos(--------) + (- 102B - 102A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R ((86B + 86A)a cos(--------) + (- 86B - 86A)a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 +--R (26B + 26A)a cos(--------) + (- 26B - 26A)a +--R 4 +--R * +--R 2x + %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 2x + %pi 5 +--R ((- 8B - 8A)a cos(--------) + (8B + 8A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi 4 +--R ((- 50B - 50A)a cos(--------) + (50B + 50A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 102B - 102A)a cos(--------) + (102B + 102A)a)cos(--------) +--R 4 4 +--R * +--R 3 +--R cos(x) +--R + +--R 2x - %pi 2 2x + %pi 2 +--R ((- 86B - 86A)a cos(--------) + (86B + 86A)a)cos(--------)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2x + %pi +--R ((- 26B - 26A)a cos(--------) + (26B + 26A)a)cos(--------)cos(x) +--R 4 4 +--R * +--R 2x - %pi +--R atanh(cos(--------)) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (4B a cos(--------) - 4B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (28B a cos(--------) - 28B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (44B a cos(--------) - 44B a)cos(x) + 20B a cos(--------) - 20B a +--R 4 4 +--R * +--R 4 +--R sin(x) +--R + +--R 2x + %pi 3 +--R (2B + 2A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (14B + 14A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (22B + 22A)a cos(--------)cos(x) + (10B + 10A)a cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (52B a cos(--------) - 52B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (140B a cos(--------) - 140B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (124B a cos(--------) - 124B a)cos(x) + 36B a cos(--------) - 36B a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x + %pi 3 +--R (26B + 26A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (70B + 70A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (62B + 62A)a cos(--------)cos(x) + (18B + 18A)a cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 5 +--R (2B a cos(--------) - 2B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 4 +--R (30B a cos(--------) - 30B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (66B a cos(--------) - 66B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (46B a cos(--------) - 46B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (4B a cos(--------) - 4B a)cos(x) - 4B a cos(--------) + 4B a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x + %pi 4 +--R (8B + 8A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 3 +--R (22B + 22A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (18B + 18A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (2B + 2A)a cos(--------)cos(x) + (- 2B - 2A)a cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 5 +--R (28B a cos(--------) - 28B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 4 +--R (68B a cos(--------) - 68B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (- 16B a cos(--------) + 16B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (- 176B a cos(--------) + 176B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 172B a cos(--------) + 172B a)cos(x) - 52B a cos(--------) + 52B a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x + %pi 4 +--R (- 8B - 8A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 3 +--R (- 50B - 50A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2 +--R (- 102B - 102A)a cos(--------)cos(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi +--R (- 86B - 86A)a cos(--------)cos(x) + (- 26B - 26A)a cos(--------) +--R 4 4 +--R * +--R 2x - %pi +--R sin(--------) +--R 4 +--R + +--R 2x - %pi 2 6 +--R (8B a cos(--------) - 8B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 5 +--R (50B a cos(--------) - 50B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 4 +--R (102B a cos(--------) - 102B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (86B a cos(--------) - 86B a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (26B a cos(--------) - 26B a)cos(x) +--R 4 +--R / +--R +-+ 2x - %pi 2 +-+ 2 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) + 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 4a\|2 +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (4a\|2 cos(--------) - 4a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (20a\|2 cos(--------) - 20a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (28a\|2 cos(--------) - 28a\|2 )cos(x) + 12a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R - 12a\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (8a\|2 cos(--------) - 8a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +-+ 2x - %pi 2 +--R (12a\|2 cos(--------) - 12a\|2 )cos(x) - 4a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 4a\|2 +--R * +--R sin(x) +--R + +--R +-+ 2x - %pi 2 +-+ 3 +--R (- 12a\|2 cos(--------) + 12a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ 2 +--R (- 36a\|2 cos(--------) + 36a\|2 )cos(x) +--R 4 +--R + +--R +-+ 2x - %pi 2 +-+ +-+ 2x - %pi 2 +--R (- 36a\|2 cos(--------) + 36a\|2 )cos(x) - 12a\|2 cos(--------) +--R 4 4 +--R + +--R +-+ +--R 12a\|2 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a sin(x) + a \|a cos(x) + a +--R \|a +--R + +--R 2x - %pi 2 3 +--R (- 2a cos(--------) + 2a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (- 14a cos(--------) + 14a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 22a cos(--------) + 22a)cos(x) - 10a cos(--------) + 10a +--R 4 4 +--R * +--R 3 +--R sin(x) +--R + +--R 2x - %pi 2 3 +--R (- 26a cos(--------) + 26a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (- 70a cos(--------) + 70a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 62a cos(--------) + 62a)cos(x) - 18a cos(--------) + 18a +--R 4 4 +--R * +--R 2 +--R sin(x) +--R + +--R 2x - %pi 2 4 +--R (- 8a cos(--------) + 8a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 3 +--R (- 22a cos(--------) + 22a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2 +--R (- 18a cos(--------) + 18a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (- 2a cos(--------) + 2a)cos(x) + 2a cos(--------) - 2a +--R 4 4 +--R * +--R sin(x) +--R + +--R 2x - %pi 2 4 2x - %pi 2 3 +--R (8a cos(--------) - 8a)cos(x) + (50a cos(--------) - 50a)cos(x) +--R 4 4 +--R + +--R 2x - %pi 2 2 +--R (102a cos(--------) - 102a)cos(x) +--R 4 +--R + +--R 2x - %pi 2 2x - %pi 2 +--R (86a cos(--------) - 86a)cos(x) + 26a cos(--------) - 26a +--R 4 4 +--R * +--R +--------------+ +--R \|- a sin(x) + a +--R Type: Expression(Integer) +--E 438 + +--S 439 of 534 +t0684:= (A+B*sin(x))/(a+b*sin(x))^(1/2) +--R +--R +--R B sin(x) + A +--R (378) --------------- +--R +------------+ +--R \|b sin(x) + a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 534 +r0684:= 2*B*EllipticE(-1/4*%pi+1/2*x,2*b/(a+b))*_ + (a+b*sin(x))^(1/2)/b/((a+b*sin(x))/(a+b))^(1/2)+_ + 2*(A*b-a*B)*EllipticF(-1/4*%pi+1/2*x,2*b/(a+b))*_ + ((a+b*sin(x))/(a+b))^(1/2)/b/(a+b*sin(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 440 + +--S 441 of 534 +a0684:= integrate(t0684,x) +--R +--R +--R x +--R ++ B sin(%L) + A +--R (379) | ---------------- d%L +--R ++ +-------------+ +--R \|b sin(%L) + a +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 534 +m0684:= a0684-r0684 +--R +--R +--R x +--R ++ B sin(%L) + A +--R (380) | ---------------- d%L - r0684 +--R ++ +-------------+ +--R \|b sin(%L) + a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 534 +d0684:= D(m0684,x) +--R +--R +--R B sin(x) + A +--R (381) --------------- +--R +------------+ +--R \|b sin(x) + a +--R Type: Expression(Integer) +--E 443 + +--S 444 of 534 +t0685:= cos(x)/(a+a*cos(x))^(1/2) +--R +--R +--R cos(x) +--R (382) --------------- +--R +------------+ +--R \|a cos(x) + a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 534 +r0685:= -2*(atanh(sin(1/2*x))*cos(1/2*x)-sin(x))/(a*(cos(x)+1))^(1/2) +--R +--R +--R x x +--R - 2cos(-)atanh(sin(-)) + 2sin(x) +--R 2 2 +--R (383) -------------------------------- +--R +------------+ +--R \|a cos(x) + a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 534 +a0685:= integrate(t0685,x) +--R +--R +--R (384) +--R [ +--R +-+ +--R |2 +--R (a cos(x) + a) |- +--R \|a +--R * +--R +-+ +--R |2 +------------+ 2 +--R - 2sin(x) |- \|a cos(x) + a - cos(x) + 2cos(x) + 3 +--R \|a +--R log(----------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +------------+ +--R 4sin(x)\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R (- a cos(x) - a) |- +--R \|a +--R * +--R 2 +--R cos(x) + 2cos(x) + 1 +--R log(--------------------------------------------------) +--R +-+ +--R |2 +------------+ 2 +--R 2sin(x) |- \|a cos(x) + a + cos(x) - 2cos(x) - 3 +--R \|a +--R + +--R +------------+ +--R 4sin(x)\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 446 + +--S 447 of 534 +m0685a:= a0685.1-r0685 +--R +--R +--R (385) +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R * +--R +-+ +--R |2 +------------+ 2 +--R - 2sin(x) |- \|a cos(x) + a - cos(x) + 2cos(x) + 3 +--R \|a +--R log(----------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R x x +--R 4cos(-)atanh(sin(-)) +--R 2 2 +--R / +--R +------------+ +--R 2\|a cos(x) + a +--R Type: Expression(Integer) +--E 447 + +--S 448 of 534 +d0685a:= D(m0685a,x) +--R +--R +--R (386) +--R x x 2 x 2 +--R (2cos(-)sin(-) - 2cos(-))sin(x) +--R 2 2 2 +--R + +--R x 3 x +--R ((- 2cos(x) - 2)sin(-) + (2cos(x) + 2)sin(-))sin(x) +--R 2 2 +--R * +--R +-+ +--R |2 x +--R |- atanh(sin(-)) +--R \|a 2 +--R + +--R x 2 x 2 x 2 +--R ((- 2cos(x) - 2)sin(-) + (- 2cos(-) + 2)cos(x) - 2cos(-) + 2) +--R 2 2 2 +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 x x x 2 x 2 +--R (cos(-)cos(x) - 2cos(-)cos(x) - 3cos(-))sin(-) - cos(-)cos(x) +--R 2 2 2 2 2 +--R + +--R x x +--R 2cos(-)cos(x) + 3cos(-) +--R 2 2 +--R * +--R sin(x) +--R + +--R 3 2 x 3 +--R (- cos(x) + cos(x) + 5cos(x) + 3)sin(-) +--R 2 +--R + +--R 3 2 x +--R (cos(x) - cos(x) - 5cos(x) - 3)sin(-) +--R 2 +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R x 2 2 +--R ((3cos(x) + 3)sin(-) - 3cos(x) - 3)sin(x) +--R 2 +--R + +--R 3 2 x 2 x 2 3 +--R (2cos(x) + 4cos(x) + 2cos(x))sin(-) + (- cos(-) - 2)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 x 2 +--R (cos(-) - 4)cos(x) + (5cos(-) - 2)cos(x) + 3cos(-) +--R 2 2 2 +--R / +--R 3 2 x 2 3 2 +--R (cos(x) - cos(x) - 5cos(x) - 3)sin(-) - cos(x) + cos(x) +--R 2 +--R + +--R 5cos(x) + 3 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2 x 2 2 +--R ((2a cos(x) + 4a cos(x) + 2a)sin(-) - 2a cos(x) - 4a cos(x) - 2a) +--R 2 +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R Type: Expression(Integer) +--E 448 + +--S 449 of 534 +m0685b:= a0685.2-r0685 +--R +--R +--R (387) +--R - +--R +-+ +--R |2 +------------+ +--R |- \|a cos(x) + a +--R \|a +--R * +--R 2 +--R cos(x) + 2cos(x) + 1 +--R log(--------------------------------------------------) +--R +-+ +--R |2 +------------+ 2 +--R 2sin(x) |- \|a cos(x) + a + cos(x) - 2cos(x) - 3 +--R \|a +--R + +--R x x +--R 4cos(-)atanh(sin(-)) +--R 2 2 +--R / +--R +------------+ +--R 2\|a cos(x) + a +--R Type: Expression(Integer) +--E 449 + +--S 450 of 534 +d0685b:= D(m0685b,x) +--R +--R +--R (388) +--R x x x 2 x x +--R ((4cos(-)cos(x) - 12cos(-))sin(-) - 4cos(-)cos(x) + 12cos(-)) +--R 2 2 2 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 x 3 +--R (- 4cos(x) + 8cos(x) + 12)sin(-) +--R 2 +--R + +--R 2 x +--R (4cos(x) - 8cos(x) - 12)sin(-) +--R 2 +--R * +--R sin(x) +--R * +--R +-+ +--R |2 x +--R |- atanh(sin(-)) +--R \|a 2 +--R + +--R x 2 3 +--R (6sin(-) - 6)sin(x) +--R 2 +--R + +--R 2 x 2 x 2 2 +--R (2cos(x) + 8cos(x) + 6)sin(-) + (- 4cos(-) - 2)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (8cos(-) - 8)cos(x) + 12cos(-) - 6 +--R 2 2 +--R * +--R sin(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x x 2 x 3 +--R (8cos(-)sin(-) - 8cos(-))sin(x) +--R 2 2 2 +--R + +--R x 3 x 2 +--R ((- 8cos(x) - 8)sin(-) + (8cos(x) + 8)sin(-))sin(x) +--R 2 2 +--R + +--R x 3 x 2 x x x 2 +--R (cos(-)cos(x) - 5cos(-)cos(x) + 3cos(-)cos(x) + 9cos(-))sin(-) +--R 2 2 2 2 2 +--R + +--R x 3 x 2 x x +--R - cos(-)cos(x) + 5cos(-)cos(x) - 3cos(-)cos(x) - 9cos(-) +--R 2 2 2 2 +--R * +--R sin(x) +--R + +--R 4 3 2 x 3 +--R (- cos(x) + 4cos(x) + 2cos(x) - 12cos(x) - 9)sin(-) +--R 2 +--R + +--R 4 3 2 x +--R (cos(x) - 4cos(x) - 2cos(x) + 12cos(x) + 9)sin(-) +--R 2 +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R 2 x 2 2 +--R (3cos(x) - 14cos(x) - 17)sin(-) - 3cos(x) +--R 2 +--R + +--R x 2 x 2 +--R (- 8cos(-) + 14)cos(x) - 8cos(-) + 17 +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 x 2 +--R (2cos(x) - 2cos(x) - 10cos(x) - 6cos(x))sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 x 2 2 +--R (- cos(-) - 2)cos(x) + (4cos(-) + 2)cos(x) + (2cos(-) + 10)cos(x) +--R 2 2 2 +--R + +--R x 2 x 2 +--R (- 12cos(-) + 6)cos(x) - 9cos(-) +--R 2 2 +--R / +--R x 2 2 +--R ((8cos(x) + 8)sin(-) - 8cos(x) - 8)sin(x) +--R 2 +--R + +--R 4 3 2 x 2 4 +--R (cos(x) - 4cos(x) - 2cos(x) + 12cos(x) + 9)sin(-) - cos(x) +--R 2 +--R + +--R 3 2 +--R 4cos(x) + 2cos(x) - 12cos(x) - 9 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 3 2 x 2 3 +--R (4a cos(x) - 4a cos(x) - 20a cos(x) - 12a)sin(-) - 4a cos(x) +--R 2 +--R + +--R 2 +--R 4a cos(x) + 20a cos(x) + 12a +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R Type: Expression(Integer) +--E 450 + +--S 451 of 534 +t0686:= cos(x)/(a-a*cos(x))^(1/2) +--R +--R +--R cos(x) +--R (389) ----------------- +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 534 +r0686:= -2*(atanh(cos(1/2*x))*sin(1/2*x)-sin(x))/(-(-1+cos(x))*a)^(1/2) +--R +--R +--R x x +--R - 2sin(-)atanh(cos(-)) + 2sin(x) +--R 2 2 +--R (390) -------------------------------- +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 534 +a0686:= integrate(t0686,x) +--R +--R +--R (391) +--R +-+ +--R |2 +------------+ +--R +-+ 2 |- \|a cos(x) + a - cos(x) - 3 +--R |2 \|a +------------+ +--R a |- log(---------------------------------) + 4\|a cos(x) + a +--R \|a cos(x) - 1 +--R [--------------------------------------------------------------, +--R 2a +--R +-+ +--R |2 cos(x) - 1 +------------+ +--R - a |- log(---------------------------------) + 4\|a cos(x) + a +--R \|a +-+ +--R |2 +------------+ +--R 2 |- \|a cos(x) + a - cos(x) - 3 +--R \|a +--R ----------------------------------------------------------------] +--R 2a +--R Type: Union(List(Expression(Integer)),...) +--E 453 + +--S 454 of 534 +m0686a:= a0686.1-r0686 +--R +--R +--R (392) +--R +-+ +--R |2 +------------+ +--R +-+ 2 |- \|a cos(x) + a - cos(x) - 3 +--R |2 +--------------+ \|a +--R a |- \|- a cos(x) + a log(---------------------------------) +--R \|a cos(x) - 1 +--R + +--R +--------------+ +------------+ x x +--R 4\|- a cos(x) + a \|a cos(x) + a + 4a sin(-)atanh(cos(-)) - 4a sin(x) +--R 2 2 +--R / +--R +--------------+ +--R 2a\|- a cos(x) + a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 534 +d0686a:= D(m0686a,x) +--R +--R +--R (393) +--R x 2 2 x 2 +--------------+ +--R ((cos(-) - 1)cos(x) + (3cos(-) - 3)cos(x))sin(x)\|- a cos(x) + a +--R 2 2 +--R + +--R x 2 x 2 x +--R ((2a cos(-) - 2a)cos(x) + 2a cos(-) - 2a)sin(-)sin(x) +--R 2 2 2 +--R + +--R x 3 x 2 x 3 x +--R (2a cos(-) - 2a cos(-))cos(x) - 2a cos(-) + 2a cos(-) +--R 2 2 2 2 +--R * +--R +-+ +--R |2 x +--R |- atanh(cos(-)) +--R \|a 2 +--R + +--R x 2 x 2 2 +--R ((- 2a cos(-) + 2a)cos(x) - 2a cos(-) + 2a)sin(x) +--R 2 2 +--R + +--R 2 x 2 x 2 3 +--R (2a cos(x) - 2a)sin(-) + (- 4a cos(-) + 4a)cos(x) +--R 2 2 +--R + +--R x 2 +--R (4a cos(-) - 4a)cos(x) +--R 2 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R +-+ +--R x 2 2 x 2 |2 +--R ((- 2a cos(-) + 2a)cos(x) + (- 2a cos(-) + 2a)cos(x))sin(x) |- +--R 2 2 \|a +--R * +--R +--------------+ +--R \|- a cos(x) + a +--R + +--R x 2 2 x 2 x 2 +--R (- a cos(-) + a)cos(x) + (- 4a cos(-) + 4a)cos(x) - 3a cos(-) +--R 2 2 2 +--R + +--R 3a +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 3 x 3 x 2 +--R (- a cos(-) + a cos(-))cos(x) + (- 3a cos(-) + 3a cos(-))cos(x) +--R 2 2 2 2 +--R + +--R x 3 x x 3 x +--R (a cos(-) - a cos(-))cos(x) + 3a cos(-) - 3a cos(-) +--R 2 2 2 2 +--R * +--R x +--R atanh(cos(-)) +--R 2 +--R + +--R x 2 2 x 2 x 2 +--R ((a cos(-) - a)cos(x) + (4a cos(-) - 4a)cos(x) + 3a cos(-) - 3a) +--R 2 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 x 2 +--R (- a cos(x) - 3a cos(x) + a cos(x) + 3a)sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (2a cos(-) - 2a)cos(x) + (6a cos(-) - 6a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (- 2a cos(-) + 2a)cos(x) + (- 6a cos(-) + 6a)cos(x) +--R 2 2 +--R / +--R +-+ +--R x 2 2 x 2 |2 +--------------+ +--R ((2a cos(-) - 2a)cos(x) - 2a cos(-) + 2a) |- \|- a cos(x) + a +--R 2 2 \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 3 x 2 2 +--R (- a cos(-) + a)cos(x) + (- 3a cos(-) + 3a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (a cos(-) - a)cos(x) + 3a cos(-) - 3a +--R 2 2 +--R * +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression(Integer) +--E 455 + +--S 456 of 534 +m0686b:= a0686.2-r0686 +--R +--R +--R (394) +--R +-+ +--R |2 +--------------+ cos(x) - 1 +--R - a |- \|- a cos(x) + a log(---------------------------------) +--R \|a +-+ +--R |2 +------------+ +--R 2 |- \|a cos(x) + a - cos(x) - 3 +--R \|a +--R + +--R +--------------+ +------------+ x x +--R 4\|- a cos(x) + a \|a cos(x) + a + 4a sin(-)atanh(cos(-)) - 4a sin(x) +--R 2 2 +--R / +--R +--------------+ +--R 2a\|- a cos(x) + a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 534 +d0686b:= D(m0686b,x) +--R +--R +--R (395) +--R x 2 3 x 2 2 +--R (cos(-) - 1)cos(x) + (14cos(-) - 14)cos(x) +--R 2 2 +--R + +--R x 2 +--R (17cos(-) - 17)cos(x) +--R 2 +--R * +--R +--------------+ +--R sin(x)\|- a cos(x) + a +--R + +--R x 2 2 x 2 +--R (4a cos(-) - 4a)cos(x) + (16a cos(-) - 16a)cos(x) +--R 2 2 +--R + +--R x 2 +--R 12a cos(-) - 12a +--R 2 +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 3 +--R (4a cos(-) - 4a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x 2 +--R (12a cos(-) - 12a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x x 3 x +--R (- 4a cos(-) + 4a cos(-))cos(x) - 12a cos(-) + 12a cos(-) +--R 2 2 2 2 +--R * +--R +-+ +--R |2 x +--R |- atanh(cos(-)) +--R \|a 2 +--R + +--R x 2 2 x 2 +--R (- 4a cos(-) + 4a)cos(x) + (- 16a cos(-) + 16a)cos(x) +--R 2 2 +--R + +--R x 2 +--R - 12a cos(-) + 12a +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 x 2 +--R (4a cos(x) + 12a cos(x) - 4a cos(x) - 12a)sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (- 8a cos(-) + 8a)cos(x) + (- 24a cos(-) + 24a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (8a cos(-) - 8a)cos(x) + (24a cos(-) - 24a)cos(x) +--R 2 2 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 3 x 2 2 +--R (- 4a cos(-) + 4a)cos(x) + (- 16a cos(-) + 16a)cos(x) +--R 2 2 +--R + +--R x 2 +--R (- 12a cos(-) + 12a)cos(x) +--R 2 +--R * +--R +-+ +--R |2 +--------------+ +--R sin(x) |- \|- a cos(x) + a +--R \|a +--R + +--R x 2 3 x 2 2 +--R (- a cos(-) + a)cos(x) + (- 15a cos(-) + 15a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (- 31a cos(-) + 31a)cos(x) - 17a cos(-) + 17a +--R 2 2 +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 4 x 3 x 3 +--R (- a cos(-) + a cos(-))cos(x) + (- 14a cos(-) + 14a cos(-))cos(x) +--R 2 2 2 2 +--R + +--R x 3 x 2 +--R (- 16a cos(-) + 16a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x x 3 x +--R (14a cos(-) - 14a cos(-))cos(x) + 17a cos(-) - 17a cos(-) +--R 2 2 2 2 +--R * +--R x +--R atanh(cos(-)) +--R 2 +--R + +--R x 2 3 x 2 2 +--R (a cos(-) - a)cos(x) + (15a cos(-) - 15a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (31a cos(-) - 31a)cos(x) + 17a cos(-) - 17a +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 x 2 +--R (- a cos(x) - 14a cos(x) - 16a cos(x) + 14a cos(x) + 17a)sin(-) +--R 2 +--R + +--R x 2 5 x 2 4 +--R (2a cos(-) - 2a)cos(x) + (28a cos(-) - 28a)cos(x) +--R 2 2 +--R + +--R x 2 3 x 2 2 +--R (32a cos(-) - 32a)cos(x) + (- 28a cos(-) + 28a)cos(x) +--R 2 2 +--R + +--R x 2 +--R (- 34a cos(-) + 34a)cos(x) +--R 2 +--R / +--R x 2 3 x 2 2 +--R (4a cos(-) - 4a)cos(x) + (12a cos(-) - 12a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (- 4a cos(-) + 4a)cos(x) - 12a cos(-) + 12a +--R 2 2 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a cos(x) + a \|a cos(x) + a +--R \|a +--R + +--R x 2 4 x 2 3 +--R (- a cos(-) + a)cos(x) + (- 14a cos(-) + 14a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (- 16a cos(-) + 16a)cos(x) + (14a cos(-) - 14a)cos(x) +--R 2 2 +--R + +--R x 2 +--R 17a cos(-) - 17a +--R 2 +--R * +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 534 +t0687:= cos(x)/(a+b*cos(x))^(1/2) +--R +--R +--R cos(x) +--R (396) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression(Integer) +--E 458 + +--S 459 of 534 +r0687:= 2*(a+b*cos(x))^(1/2)*(EllipticE(1/2*x,2*b/(a+b))*a+_ + EllipticE(1/2*x,2*b/(a+b))*b-_ + a*EllipticF(1/2*x,2*b/(a+b)))/(a+b)/b/((a+b*cos(x))/(a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 459 + +--S 460 of 534 +a0687:= integrate(t0687,x) +--R +--R +--R x +--R ++ cos(%L) +--R (397) | ---------------- d%L +--R ++ +-------------+ +--R \|b cos(%L) + a +--R Type: Union(Expression(Integer),...) +--E 460 + +--S 461 of 534 +m0687:= a0687-r0687 +--R +--R +--R x +--R ++ cos(%L) +--R (398) | ---------------- d%L - r0687 +--R ++ +-------------+ +--R \|b cos(%L) + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 534 +d0687:= D(m0687,x) +--R +--R +--R cos(x) +--R (399) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression(Integer) +--E 462 + +--S 463 of 534 +t0688:= (A+B*cos(x))/(a+a*cos(x))^(1/2) +--R +--R +--R B cos(x) + A +--R (400) --------------- +--R +------------+ +--R \|a cos(x) + a +--R Type: Expression(Integer) +--E 463 + +--S 464 of 534 +r0688:= 2*(A-B)*atanh(sin(1/2*x))*cos(1/2*x)/(a+a*cos(x))^(1/2)+_ + 2*B*sin(x)/(a+a*cos(x))^(1/2) +--R +--R +--R x x +--R (- 2B + 2A)cos(-)atanh(sin(-)) + 2B sin(x) +--R 2 2 +--R (401) ------------------------------------------ +--R +------------+ +--R \|a cos(x) + a +--R Type: Expression(Integer) +--E 464 + +--S 465 of 534 +a0688:= integrate(t0688,x) +--R +--R +--R (402) +--R [ +--R +-+ +--R |2 +--R ((B - A)a cos(x) + (B - A)a) |- +--R \|a +--R * +--R +-+ +--R |2 +------------+ 2 +--R - 2sin(x) |- \|a cos(x) + a - cos(x) + 2cos(x) + 3 +--R \|a +--R log(----------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +------------+ +--R 4B sin(x)\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R , +--R +--R +-+ +--R |2 +--R ((- B + A)a cos(x) + (- B + A)a) |- +--R \|a +--R * +--R 2 +--R cos(x) + 2cos(x) + 1 +--R log(--------------------------------------------------) +--R +-+ +--R |2 +------------+ 2 +--R 2sin(x) |- \|a cos(x) + a + cos(x) - 2cos(x) - 3 +--R \|a +--R + +--R +------------+ +--R 4B sin(x)\|a cos(x) + a +--R / +--R 2a cos(x) + 2a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 465 + +--S 466 of 534 +m0688a:= a0688.1-r0688 +--R +--R +--R (403) +--R +-+ +--R |2 +------------+ +--R (B - A) |- \|a cos(x) + a +--R \|a +--R * +--R +-+ +--R |2 +------------+ 2 +--R - 2sin(x) |- \|a cos(x) + a - cos(x) + 2cos(x) + 3 +--R \|a +--R log(----------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R x x +--R (4B - 4A)cos(-)atanh(sin(-)) +--R 2 2 +--R / +--R +------------+ +--R 2\|a cos(x) + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 534 +d0688a:= D(m0688a,x) +--R +--R +--R (404) +--R x x 2 x 2 +--R ((2B - 2A)cos(-)sin(-) + (- 2B + 2A)cos(-))sin(x) +--R 2 2 2 +--R + +--R x 3 +--R ((- 2B + 2A)cos(x) - 2B + 2A)sin(-) +--R 2 +--R + +--R x +--R ((2B - 2A)cos(x) + 2B - 2A)sin(-) +--R 2 +--R * +--R sin(x) +--R * +--R +-+ +--R |2 x +--R |- atanh(sin(-)) +--R \|a 2 +--R + +--R x 2 +--R ((- 2B + 2A)cos(x) - 2B + 2A)sin(-) +--R 2 +--R + +--R x 2 x 2 +--R ((- 2B + 2A)cos(-) + 2B - 2A)cos(x) + (- 2B + 2A)cos(-) + 2B - 2A +--R 2 2 +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 x +--R (B - A)cos(-)cos(x) + (- 2B + 2A)cos(-)cos(x) +--R 2 2 +--R + +--R x +--R (- 3B + 3A)cos(-) +--R 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 2 x x +--R (- B + A)cos(-)cos(x) + (2B - 2A)cos(-)cos(x) + (3B - 3A)cos(-) +--R 2 2 2 +--R * +--R sin(x) +--R + +--R 3 2 +--R ((- B + A)cos(x) + (B - A)cos(x) + (5B - 5A)cos(x) + 3B - 3A) +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R 3 2 x +--R ((B - A)cos(x) + (- B + A)cos(x) + (- 5B + 5A)cos(x) - 3B + 3A)sin(-) +--R 2 +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R x 2 2 +--R (((3B - 3A)cos(x) + 3B - 3A)sin(-) + (- 3B + 3A)cos(x) - 3B + 3A)sin(x) +--R 2 +--R + +--R 3 2 x 2 +--R ((2B - 2A)cos(x) + (4B - 4A)cos(x) + (2B - 2A)cos(x))sin(-) +--R 2 +--R + +--R x 2 3 x 2 2 +--R ((- B + A)cos(-) - 2B + 2A)cos(x) + ((B - A)cos(-) - 4B + 4A)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R ((5B - 5A)cos(-) - 2B + 2A)cos(x) + (3B - 3A)cos(-) +--R 2 2 +--R / +--R 3 2 x 2 3 2 +--R (cos(x) - cos(x) - 5cos(x) - 3)sin(-) - cos(x) + cos(x) +--R 2 +--R + +--R 5cos(x) + 3 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 2 x 2 2 +--R ((2a cos(x) + 4a cos(x) + 2a)sin(-) - 2a cos(x) - 4a cos(x) - 2a) +--R 2 +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 534 +m0688b:= a0688.2-r0688 +--R +--R +--R (405) +--R +-+ +--R |2 +------------+ +--R (- B + A) |- \|a cos(x) + a +--R \|a +--R * +--R 2 +--R cos(x) + 2cos(x) + 1 +--R log(--------------------------------------------------) +--R +-+ +--R |2 +------------+ 2 +--R 2sin(x) |- \|a cos(x) + a + cos(x) - 2cos(x) - 3 +--R \|a +--R + +--R x x +--R (4B - 4A)cos(-)atanh(sin(-)) +--R 2 2 +--R / +--R +------------+ +--R 2\|a cos(x) + a +--R Type: Expression(Integer) +--E 468 + +--S 469 of 534 +d0688b:= D(m0688b,x) +--R +--R +--R (406) +--R x x x 2 +--R ((4B - 4A)cos(-)cos(x) + (- 12B + 12A)cos(-))sin(-) +--R 2 2 2 +--R + +--R x x +--R (- 4B + 4A)cos(-)cos(x) + (12B - 12A)cos(-) +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 2 x 3 +--R ((- 4B + 4A)cos(x) + (8B - 8A)cos(x) + 12B - 12A)sin(-) +--R 2 +--R + +--R 2 x +--R ((4B - 4A)cos(x) + (- 8B + 8A)cos(x) - 12B + 12A)sin(-) +--R 2 +--R * +--R sin(x) +--R * +--R +-+ +--R |2 x +--R |- atanh(sin(-)) +--R \|a 2 +--R + +--R x 2 3 +--R ((6B - 6A)sin(-) - 6B + 6A)sin(x) +--R 2 +--R + +--R 2 x 2 +--R ((2B - 2A)cos(x) + (8B - 8A)cos(x) + 6B - 6A)sin(-) +--R 2 +--R + +--R x 2 2 +--R ((- 4B + 4A)cos(-) - 2B + 2A)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R ((8B - 8A)cos(-) - 8B + 8A)cos(x) + (12B - 12A)cos(-) - 6B +--R 2 2 +--R + +--R 6A +--R * +--R sin(x) +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x x 2 x 3 +--R ((8B - 8A)cos(-)sin(-) + (- 8B + 8A)cos(-))sin(x) +--R 2 2 2 +--R + +--R x 3 +--R ((- 8B + 8A)cos(x) - 8B + 8A)sin(-) +--R 2 +--R + +--R x +--R ((8B - 8A)cos(x) + 8B - 8A)sin(-) +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R x 3 x 2 +--R (B - A)cos(-)cos(x) + (- 5B + 5A)cos(-)cos(x) +--R 2 2 +--R + +--R x x +--R (3B - 3A)cos(-)cos(x) + (9B - 9A)cos(-) +--R 2 2 +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 3 x 2 +--R (- B + A)cos(-)cos(x) + (5B - 5A)cos(-)cos(x) +--R 2 2 +--R + +--R x x +--R (- 3B + 3A)cos(-)cos(x) + (- 9B + 9A)cos(-) +--R 2 2 +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (- B + A)cos(x) + (4B - 4A)cos(x) + (2B - 2A)cos(x) +--R + +--R (- 12B + 12A)cos(x) - 9B + 9A +--R * +--R x 3 +--R sin(-) +--R 2 +--R + +--R 4 3 2 +--R (B - A)cos(x) + (- 4B + 4A)cos(x) + (- 2B + 2A)cos(x) +--R + +--R (12B - 12A)cos(x) + 9B - 9A +--R * +--R x +--R sin(-) +--R 2 +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R 2 x 2 +--R ((3B - 3A)cos(x) + (- 14B + 14A)cos(x) - 17B + 17A)sin(-) +--R 2 +--R + +--R 2 x 2 +--R (- 3B + 3A)cos(x) + ((- 8B + 8A)cos(-) + 14B - 14A)cos(x) +--R 2 +--R + +--R x 2 +--R (- 8B + 8A)cos(-) + 17B - 17A +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (2B - 2A)cos(x) + (- 2B + 2A)cos(x) + (- 10B + 10A)cos(x) +--R + +--R (- 6B + 6A)cos(x) +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R ((- B + A)cos(-) - 2B + 2A)cos(x) + ((4B - 4A)cos(-) + 2B - 2A)cos(x) +--R 2 2 +--R + +--R x 2 2 +--R ((2B - 2A)cos(-) + 10B - 10A)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R ((- 12B + 12A)cos(-) + 6B - 6A)cos(x) + (- 9B + 9A)cos(-) +--R 2 2 +--R / +--R x 2 2 +--R ((8cos(x) + 8)sin(-) - 8cos(x) - 8)sin(x) +--R 2 +--R + +--R 4 3 2 x 2 4 +--R (cos(x) - 4cos(x) - 2cos(x) + 12cos(x) + 9)sin(-) - cos(x) +--R 2 +--R + +--R 3 2 +--R 4cos(x) + 2cos(x) - 12cos(x) - 9 +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R 3 2 x 2 3 +--R (4a cos(x) - 4a cos(x) - 20a cos(x) - 12a)sin(-) - 4a cos(x) +--R 2 +--R + +--R 2 +--R 4a cos(x) + 20a cos(x) + 12a +--R * +--R +-+ +--R |2 +--R sin(x) |- +--R \|a +--R Type: Expression(Integer) +--E 469 + +--S 470 of 534 +t0689:= (A+B*cos(x))/(a-a*cos(x))^(1/2) +--R +--R +--R B cos(x) + A +--R (407) ----------------- +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression(Integer) +--E 470 + +--S 471 of 534 +r0689:= -2*(A+B)*atanh(cos(1/2*x))*sin(1/2*x)/(a-a*cos(x))^(1/2)+_ + 2*B*sin(x)/(a-a*cos(x))^(1/2) +--R +--R +--R x x +--R (- 2B - 2A)sin(-)atanh(cos(-)) + 2B sin(x) +--R 2 2 +--R (408) ------------------------------------------ +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression(Integer) +--E 471 + +--S 472 of 534 +a0689:= integrate(t0689,x) +--R +--R +--R (409) +--R +-+ +--R |2 +------------+ +--R +-+ 2 |- \|a cos(x) + a - cos(x) - 3 +--R |2 \|a +------------+ +--R (B + A)a |- log(---------------------------------) + 4B\|a cos(x) + a +--R \|a cos(x) - 1 +--R [----------------------------------------------------------------------, +--R 2a +--R +-+ +--R |2 cos(x) - 1 +------------+ +--R (- B - A)a |- log(---------------------------------) + 4B\|a cos(x) + a +--R \|a +-+ +--R |2 +------------+ +--R 2 |- \|a cos(x) + a - cos(x) - 3 +--R \|a +--R ------------------------------------------------------------------------] +--R 2a +--R Type: Union(List(Expression(Integer)),...) +--E 472 + +--S 473 of 534 +m0689a:= a0689.1-r0689 +--R +--R +--R (410) +--R +-+ +--R |2 +------------+ +--R +-+ 2 |- \|a cos(x) + a - cos(x) - 3 +--R |2 +--------------+ \|a +--R (B + A)a |- \|- a cos(x) + a log(---------------------------------) +--R \|a cos(x) - 1 +--R + +--R +--------------+ +------------+ x x +--R 4B\|- a cos(x) + a \|a cos(x) + a + (4B + 4A)a sin(-)atanh(cos(-)) +--R 2 2 +--R + +--R - 4B a sin(x) +--R / +--R +--------------+ +--R 2a\|- a cos(x) + a +--R Type: Expression(Integer) +--E 473 + +--S 474 of 534 +d0689a:= D(m0689a,x) +--R +--R +--R (411) +--R x 2 2 x 2 +--R (B cos(-) - B)cos(x) + ((3B + A)cos(-) - 3B - A)cos(x) +--R 2 2 +--R + +--R x 2 +--R 3A cos(-) - 3A +--R 2 +--R * +--R +--------------+ +--R sin(x)\|- a cos(x) + a +--R + +--R x 2 +--R ((2B + 2A)a cos(-) + (- 2B - 2A)a)cos(x) +--R 2 +--R + +--R x 2 +--R (2B + 2A)a cos(-) + (- 2B - 2A)a +--R 2 +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 2 +--R ((2B + 2A)a cos(-) + (- 2B - 2A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x +--R (- 2B - 2A)a cos(-) + (2B + 2A)a cos(-) +--R 2 2 +--R * +--R +-+ +--R |2 x +--R |- atanh(cos(-)) +--R \|a 2 +--R + +--R x 2 x 2 2 +--R ((- 2B a cos(-) + 2B a)cos(x) - 2B a cos(-) + 2B a)sin(x) +--R 2 2 +--R + +--R 2 x 2 +--R ((2B + 2A)a cos(x) + (- 2B - 2A)a)sin(-) +--R 2 +--R + +--R x 2 3 x 2 +--R (- 4B a cos(-) + 4B a)cos(x) + (4B a cos(-) - 4B a)cos(x) +--R 2 2 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 2 +--R (- 2B a cos(-) + 2B a)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R ((- 2B - 2A)a cos(-) + (2B + 2A)a)cos(x) - 2A a cos(-) + 2A a +--R 2 2 +--R * +--R +-+ +--R |2 +--------------+ +--R sin(x) |- \|- a cos(x) + a +--R \|a +--R + +--R x 2 2 +--R ((- B - A)a cos(-) + (B + A)a)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R ((- 4B - 4A)a cos(-) + (4B + 4A)a)cos(x) + (- 3B - 3A)a cos(-) +--R 2 2 +--R + +--R (3B + 3A)a +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 3 +--R ((- B - A)a cos(-) + (B + A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x 2 +--R ((- 3B - 3A)a cos(-) + (3B + 3A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x x 3 +--R ((B + A)a cos(-) + (- B - A)a cos(-))cos(x) + (3B + 3A)a cos(-) +--R 2 2 2 +--R + +--R x +--R (- 3B - 3A)a cos(-) +--R 2 +--R * +--R x +--R atanh(cos(-)) +--R 2 +--R + +--R x 2 2 x 2 +--R (B a cos(-) - B a)cos(x) + (4B a cos(-) - 4B a)cos(x) +--R 2 2 +--R + +--R x 2 +--R 3B a cos(-) - 3B a +--R 2 +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (- B - A)a cos(x) + (- 3B - 3A)a cos(x) + (B + A)a cos(x) +--R + +--R (3B + 3A)a +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (2B a cos(-) - 2B a)cos(x) + (6B a cos(-) - 6B a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (- 2B a cos(-) + 2B a)cos(x) + (- 6B a cos(-) + 6B a)cos(x) +--R 2 2 +--R / +--R +-+ +--R x 2 2 x 2 |2 +--------------+ +--R ((2a cos(-) - 2a)cos(x) - 2a cos(-) + 2a) |- \|- a cos(x) + a +--R 2 2 \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 3 x 2 2 +--R (- a cos(-) + a)cos(x) + (- 3a cos(-) + 3a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (a cos(-) - a)cos(x) + 3a cos(-) - 3a +--R 2 2 +--R * +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression(Integer) +--E 474 + +--S 475 of 534 +m0689b:= a0689.2-r0689 +--R +--R +--R (412) +--R +-+ +--R |2 +--------------+ cos(x) - 1 +--R (- B - A)a |- \|- a cos(x) + a log(---------------------------------) +--R \|a +-+ +--R |2 +------------+ +--R 2 |- \|a cos(x) + a - cos(x) - 3 +--R \|a +--R + +--R +--------------+ +------------+ x x +--R 4B\|- a cos(x) + a \|a cos(x) + a + (4B + 4A)a sin(-)atanh(cos(-)) +--R 2 2 +--R + +--R - 4B a sin(x) +--R / +--R +--------------+ +--R 2a\|- a cos(x) + a +--R Type: Expression(Integer) +--E 475 + +--S 476 of 534 +d0689b:= D(m0689b,x) +--R +--R +--R (413) +--R x 2 3 x 2 2 +--R (B cos(-) - B)cos(x) + ((14B + A)cos(-) - 14B - A)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R ((17B + 14A)cos(-) - 17B - 14A)cos(x) + 17A cos(-) - 17A +--R 2 2 +--R * +--R +--------------+ +--R sin(x)\|- a cos(x) + a +--R + +--R x 2 2 +--R ((4B + 4A)a cos(-) + (- 4B - 4A)a)cos(x) +--R 2 +--R + +--R x 2 +--R ((16B + 16A)a cos(-) + (- 16B - 16A)a)cos(x) +--R 2 +--R + +--R x 2 +--R (12B + 12A)a cos(-) + (- 12B - 12A)a +--R 2 +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 3 +--R ((4B + 4A)a cos(-) + (- 4B - 4A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x 2 +--R ((12B + 12A)a cos(-) + (- 12B - 12A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x +--R ((- 4B - 4A)a cos(-) + (4B + 4A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x +--R (- 12B - 12A)a cos(-) + (12B + 12A)a cos(-) +--R 2 2 +--R * +--R +-+ +--R |2 x +--R |- atanh(cos(-)) +--R \|a 2 +--R + +--R x 2 2 +--R (- 4B a cos(-) + 4B a)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R (- 16B a cos(-) + 16B a)cos(x) - 12B a cos(-) + 12B a +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (4B + 4A)a cos(x) + (12B + 12A)a cos(x) +--R + +--R (- 4B - 4A)a cos(x) + (- 12B - 12A)a +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 2 4 x 2 3 +--R (- 8B a cos(-) + 8B a)cos(x) + (- 24B a cos(-) + 24B a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (8B a cos(-) - 8B a)cos(x) + (24B a cos(-) - 24B a)cos(x) +--R 2 2 +--R * +--R +-+ +--R |2 +--R |- +--R \|a +--R * +--R +------------+ +--R \|a cos(x) + a +--R + +--R x 2 3 +--R (- 4B a cos(-) + 4B a)cos(x) +--R 2 +--R + +--R x 2 2 +--R ((- 16B - 4A)a cos(-) + (16B + 4A)a)cos(x) +--R 2 +--R + +--R x 2 x 2 +--R ((- 12B - 16A)a cos(-) + (12B + 16A)a)cos(x) - 12A a cos(-) + 12A a +--R 2 2 +--R * +--R +-+ +--R |2 +--------------+ +--R sin(x) |- \|- a cos(x) + a +--R \|a +--R + +--R x 2 3 +--R ((- B - A)a cos(-) + (B + A)a)cos(x) +--R 2 +--R + +--R x 2 2 +--R ((- 15B - 15A)a cos(-) + (15B + 15A)a)cos(x) +--R 2 +--R + +--R x 2 +--R ((- 31B - 31A)a cos(-) + (31B + 31A)a)cos(x) +--R 2 +--R + +--R x 2 +--R (- 17B - 17A)a cos(-) + (17B + 17A)a +--R 2 +--R * +--R x +--R sin(-)sin(x) +--R 2 +--R + +--R x 3 x 4 +--R ((- B - A)a cos(-) + (B + A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x 3 +--R ((- 14B - 14A)a cos(-) + (14B + 14A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x 2 +--R ((- 16B - 16A)a cos(-) + (16B + 16A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x +--R ((14B + 14A)a cos(-) + (- 14B - 14A)a cos(-))cos(x) +--R 2 2 +--R + +--R x 3 x +--R (17B + 17A)a cos(-) + (- 17B - 17A)a cos(-) +--R 2 2 +--R * +--R x +--R atanh(cos(-)) +--R 2 +--R + +--R x 2 3 x 2 2 +--R (B a cos(-) - B a)cos(x) + (15B a cos(-) - 15B a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (31B a cos(-) - 31B a)cos(x) + 17B a cos(-) - 17B a +--R 2 2 +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 +--R (- B - A)a cos(x) + (- 14B - 14A)a cos(x) + (- 16B - 16A)a cos(x) +--R + +--R (14B + 14A)a cos(x) + (17B + 17A)a +--R * +--R x 2 +--R sin(-) +--R 2 +--R + +--R x 2 5 x 2 4 +--R (2B a cos(-) - 2B a)cos(x) + (28B a cos(-) - 28B a)cos(x) +--R 2 2 +--R + +--R x 2 3 x 2 2 +--R (32B a cos(-) - 32B a)cos(x) + (- 28B a cos(-) + 28B a)cos(x) +--R 2 2 +--R + +--R x 2 +--R (- 34B a cos(-) + 34B a)cos(x) +--R 2 +--R / +--R x 2 3 x 2 2 +--R (4a cos(-) - 4a)cos(x) + (12a cos(-) - 12a)cos(x) +--R 2 2 +--R + +--R x 2 x 2 +--R (- 4a cos(-) + 4a)cos(x) - 12a cos(-) + 12a +--R 2 2 +--R * +--R +-+ +--R |2 +--------------+ +------------+ +--R |- \|- a cos(x) + a \|a cos(x) + a +--R \|a +--R + +--R x 2 4 x 2 3 +--R (- a cos(-) + a)cos(x) + (- 14a cos(-) + 14a)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 +--R (- 16a cos(-) + 16a)cos(x) + (14a cos(-) - 14a)cos(x) +--R 2 2 +--R + +--R x 2 +--R 17a cos(-) - 17a +--R 2 +--R * +--R +--------------+ +--R \|- a cos(x) + a +--R Type: Expression(Integer) +--E 476 + +--S 477 of 534 +t0690:= (A+B*cos(x))/(a+b*cos(x))^(1/2) +--R +--R +--R B cos(x) + A +--R (414) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 534 +r0690:= 2*B*(a+b*cos(x))^(1/2)*_ + EllipticE(1/2*x,2*b/(a+b))/b/((a+b*cos(x))/(a+b))^(1/2)+_ + 2*(A*b-a*B)*((a+b*cos(x))/(a+b))^(1/2)*_ + EllipticF(1/2*x,2*b/(a+b))/b/(a+b*cos(x))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 478 + +--S 479 of 534 +a0690:= integrate(t0690,x) +--R +--R +--R x +--R ++ B cos(%L) + A +--R (415) | ---------------- d%L +--R ++ +-------------+ +--R \|b cos(%L) + a +--R Type: Union(Expression(Integer),...) +--E 479 + +--S 480 of 534 +m0690:= a0690-r0690 +--R +--R +--R x +--R ++ B cos(%L) + A +--R (416) | ---------------- d%L - r0690 +--R ++ +-------------+ +--R \|b cos(%L) + a +--R Type: Expression(Integer) +--E 480 + +--S 481 of 534 +d0690:= D(m0690,x) +--R +--R +--R B cos(x) + A +--R (417) --------------- +--R +------------+ +--R \|b cos(x) + a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 534 +t0691:= (-1+1/d^2*c^2+sin(x)^2)/(c+d*cos(x)) +--R +--R +--R 2 2 2 2 +--R d sin(x) - d + c +--R (418) ------------------- +--R 3 2 +--R d cos(x) + c d +--R Type: Expression(Integer) +--E 482 + +--S 483 of 534 +r0691:= c*x/d^2-sin(x)/d +--R +--R +--R - d sin(x) + c x +--R (419) ---------------- +--R 2 +--R d +--R Type: Expression(Integer) +--E 483 + +--S 484 of 534 +a0691:= integrate(t0691,x) +--R +--R +--R - d sin(x) + c x +--R (420) ---------------- +--R 2 +--R d +--R Type: Union(Expression(Integer),...) +--E 484 + +--S 485 of 534 +m0691:= a0691-r0691 +--R +--R +--R (421) 0 +--R Type: Expression(Integer) +--E 485 + +--S 486 of 534 +d0691:= D(m0691,x) +--R +--R +--R (422) 0 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 534 +t0692:= (a+b*sin(x)^2)/(c+d*cos(x)) +--R +--R +--R 2 +--R b sin(x) + a +--R (423) ------------- +--R d cos(x) + c +--R Type: Expression(Integer) +--E 487 + +--S 488 of 534 +r0692:= b*c*x/d^2+2*(a*d^2-b*(c^2-d^2))*atan((c-d)*_ + tan(1/2*x)/(c^2-d^2)^(1/2))/d^2/(c^2-d^2)^(1/2)-b*sin(x)/d +--R +--R +--R (424) +--R x +--R (d - c)tan(-) +--R 2 2 2 +--R ((- 2b - 2a)d + 2b c )atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +---------+ +--R | 2 2 +--R (- b d sin(x) + b c x)\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R Type: Expression(Integer) +--E 488 + +--S 489 of 534 +a0692:= integrate(t0692,x) +--R +--R +--R (425) +--R [ +--R +-------+ +--R | 2 2 2 2 +--R 2 2 (- c cos(x) - d)\|d - c + (- d + c )sin(x) +--R ((b + a)d - b c )log(----------------------------------------------) +--R d cos(x) + c +--R + +--R +-------+ +--R | 2 2 +--R (- b d sin(x) + b c x)\|d - c +--R / +--R +-------+ +--R 2 | 2 2 +--R d \|d - c +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 2 sin(x)\|- d + c +--R ((2b + 2a)d - 2b c )atan(---------------------) +--R (d + c)cos(x) + d + c +--R + +--R +---------+ +--R | 2 2 +--R (- b d sin(x) + b c x)\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 489 + +--S 490 of 534 +m0692a:= a0692.1-r0692 +--R +--R +--R (426) +--R +---------+ +--R 2 2 | 2 2 +--R ((b + a)d - b c )\|- d + c +--R * +--R +-------+ +--R | 2 2 2 2 +--R (- c cos(x) - d)\|d - c + (- d + c )sin(x) +--R log(----------------------------------------------) +--R d cos(x) + c +--R + +--R x +--R +-------+ (d - c)tan(-) +--R 2 2 | 2 2 2 +--R ((2b + 2a)d - 2b c )\|d - c atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R d \|- d + c \|d - c +--R Type: Expression(Integer) +--E 490 + +--S 491 of 534 +d0692a:= D(m0692a,x) +--R +--R +--R (427) +--R 3 2 2 3 2 +--R ((b + a)d + (- b - a)c d - b c d + b c )sin(x) +--R + +--R 3 2 2 +--R ((b + a)d - b c d)cos(x) +--R + +--R 3 2 2 3 2 3 +--R ((b + a)d + (b + a)c d - b c d - b c )cos(x) + (b + a)c d - b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 +--R ((- b - a)d + (- b - a)c d + b c d + b c )sin(x) +--R + +--R 3 2 2 +--R ((- b - a)d + b c d)cos(x) +--R + +--R 3 2 2 3 2 3 +--R ((b + a)d + (- b - a)c d - b c d + b c )cos(x) + (b + a)c d - b c +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 4 2 2 4 4 +--R ((b + a)d + (- 2b - a)c d + b c )cos(x) + (b + a)d +--R + +--R 2 2 4 +--R (- 2b - a)c d + b c +--R * +--R x 2 +--R sin(x)tan(-) +--R 2 +--R + +--R 4 2 2 4 4 +--R ((b + a)d + (- 2b - a)c d + b c )cos(x) + (- b - a)d +--R + +--R 2 2 4 +--R (2b + a)c d - b c +--R * +--R sin(x) +--R / +--R 3 2 2 2 4 3 2 2 3 3 +--R (c d - c d )cos(x) + (d - c d + c d - c d)cos(x) + c d +--R + +--R 2 2 +--R - c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 4 3 2 2 3 3 2 2 +--R (- c d - c d )cos(x) + (- d - c d - c d - c d)cos(x) - c d - c d +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 4 x 2 +--R ((d - c d - c d + c d )cos(x) + c d - c d - c d + c d)sin(x)tan(-) +--R 2 +--R + +--R 5 4 2 3 3 2 4 2 3 3 2 4 +--R ((- d - c d + c d + c d )cos(x) - c d - c d + c d + c d)sin(x) +--R Type: Expression(Integer) +--E 491 + +--S 492 of 534 +m0692b:= a0692.2-r0692 +--R +--R +--R (428) +--R +---------+ +--R | 2 2 +--R 2 2 sin(x)\|- d + c +--R ((2b + 2a)d - 2b c )atan(---------------------) +--R (d + c)cos(x) + d + c +--R + +--R x +--R (d - c)tan(-) +--R 2 2 2 +--R ((2b + 2a)d - 2b c )atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R Type: Expression(Integer) +--E 492 + +--S 493 of 534 +d0692b:= D(m0692b,x) +--R +--R +--R (429) +--R 3 2 2 3 2 +--R ((- b - a)d + (b + a)c d + b c d - b c )sin(x) +--R + +--R 3 2 2 3 2 +--R ((- 3b - 3a)d + (b + a)c d + 3b c d - b c )cos(x) +--R + +--R 3 2 3 2 2 +--R ((- 4b - 4a)d + 4b c d)cos(x) + (- b - a)d + (- b - a)c d + b c d +--R + +--R 3 +--R b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 +--R ((3b + 3a)d + (b + a)c d - 3b c d - b c )sin(x) +--R + +--R 3 2 2 3 2 3 +--R ((b + a)d + (b + a)c d - b c d - b c )cos(x) + (- b - a)d +--R + +--R 2 2 3 +--R (- b - a)c d + b c d + b c +--R / +--R 4 3 2 2 2 4 2 2 2 +--R (d - 2c d + c d )sin(x) + (- d + c d )cos(x) +--R + +--R 4 2 2 4 2 2 +--R (- 2d + 2c d )cos(x) - d + c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 4 3 2 2 2 +--R (- d + c d )sin(x) + (d + 2c d + c d )cos(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R (2d + 4c d + 2c d )cos(x) + d + 2c d + c d +--R Type: Expression(Integer) +--E 493 + +--S 494 of 534 +t0693:= (a+b*sin(x)^2)/(c+c*cos(x)^2) +--R +--R +--R 2 +--R b sin(x) + a +--R (430) ------------- +--R 2 +--R c cos(x) + c +--R Type: Expression(Integer) +--E 494 + +--S 495 of 534 +r0693:= -b*x/c+1/2*(a+2*b)*atan(1/2*2^(1/2)*tan(x))*2^(1/2)/c +--R +--R +--R +-+ +--R +-+ \|2 tan(x) +--R (2b + a)\|2 atan(----------) - 2b x +--R 2 +--R (431) ----------------------------------- +--R 2c +--R Type: Expression(Integer) +--E 495 + +--S 496 of 534 +a0693:= integrate(t0693,x) +--R +--R +--R (432) +--R +-+ +--R \|2 sin(x) +--R (2b + a)atan(-----------) +--R 2cos(x) + 2 +--R + +--R 2sin(x) +-+ +--R (2b + a)atan(--------------------------------) - b x\|2 +--R +-+ 2 +-+ +-+ +--R \|2 cos(x) + 2\|2 cos(x) + \|2 +--R / +--R +-+ +--R c\|2 +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 534 +m0693:= a0693-r0693 +--R +--R +--R (433) +--R +-+ +-+ +--R \|2 tan(x) \|2 sin(x) +--R (- 2b - a)atan(----------) + (2b + a)atan(-----------) +--R 2 2cos(x) + 2 +--R + +--R 2sin(x) +--R (2b + a)atan(--------------------------------) +--R +-+ 2 +-+ +-+ +--R \|2 cos(x) + 2\|2 cos(x) + \|2 +--R / +--R +-+ +--R c\|2 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 534 +d0693:= D(m0693,x) +--R +--R +--R (434) +--R 4 +--R ((4b + 2a)cos(x) + 4b + 2a)sin(x) +--R + +--R 3 2 2 +--R ((10b + 5a)cos(x) + (24b + 12a)cos(x) + (14b + 7a)cos(x))sin(x) +--R + +--R 6 5 4 +--R (- 2b - a)cos(x) + (- 10b - 5a)cos(x) + (- 24b - 12a)cos(x) +--R + +--R 3 2 +--R (- 36b - 18a)cos(x) + (- 34b - 17a)cos(x) + (- 18b - 9a)cos(x) - 4b +--R + +--R - 2a +--R * +--R 2 +--R tan(x) +--R + +--R 4 +--R ((8b + 4a)cos(x) + 12b + 6a)sin(x) +--R + +--R 4 3 2 +--R (2b + a)cos(x) + (28b + 14a)cos(x) + (68b + 34a)cos(x) +--R + +--R (52b + 26a)cos(x) + 10b + 5a +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 +--R (4b + 2a)cos(x) + (12b + 6a)cos(x) + (8b + 4a)cos(x) +--R + +--R 2 +--R (- 8b - 4a)cos(x) + (- 12b - 6a)cos(x) - 4b - 2a +--R / +--R 4 +--R 2c sin(x) +--R + +--R 4 3 2 2 +--R (c cos(x) + 4c cos(x) + 10c cos(x) + 12c cos(x) + 5c)sin(x) +--R + +--R 6 5 4 3 2 +--R 2c cos(x) + 12c cos(x) + 30c cos(x) + 40c cos(x) + 30c cos(x) +--R + +--R 12c cos(x) + 2c +--R * +--R 2 +--R tan(x) +--R + +--R 4 +--R 4c sin(x) +--R + +--R 4 3 2 2 +--R (2c cos(x) + 8c cos(x) + 20c cos(x) + 24c cos(x) + 10c)sin(x) +--R + +--R 6 5 4 3 2 +--R 4c cos(x) + 24c cos(x) + 60c cos(x) + 80c cos(x) + 60c cos(x) +--R + +--R 24c cos(x) + 4c +--R Type: Expression(Integer) +--E 498 + +--S 499 of 534 +t0694:= (a+b*sin(x)^2)/(c-c*cos(x)^2) +--R +--R +--R 2 +--R - b sin(x) - a +--R (435) --------------- +--R 2 +--R c cos(x) - c +--R Type: Expression(Integer) +--E 499 + +--S 500 of 534 +r0694:= -(-b*x+a*cot(x))/c +--R +--R +--R - a cot(x) + b x +--R (436) ---------------- +--R c +--R Type: Expression(Integer) +--E 500 + +--S 501 of 534 +a0694:= integrate(t0694,x) +--R +--R +--R b x sin(x) - a cos(x) +--R (437) --------------------- +--R c sin(x) +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 534 +m0694:= a0694-r0694 +--R +--R +--R a cot(x)sin(x) - a cos(x) +--R (438) ------------------------- +--R c sin(x) +--R Type: Expression(Integer) +--E 502 + +--S 503 of 534 +d0694:= D(m0694,x) +--R +--R +--R 2 2 2 +--R - a cot(x) sin(x) + a cos(x) +--R (439) ------------------------------ +--R 2 +--R c sin(x) +--R Type: Expression(Integer) +--E 503 + +--S 504 of 534 +t0695:= (a+b*sin(x)^2)/(c+d*cos(x)^2) +--R +--R +--R 2 +--R b sin(x) + a +--R (440) ------------- +--R 2 +--R d cos(x) + c +--R Type: Expression(Integer) +--E 504 + +--S 505 of 534 +r0695:= -b*x/d+(b*c+(a+b)*d)*atan(c^(1/2)*tan(x)/(c+d)^(1/2))/_ + c^(1/2)/d/(c+d)^(1/2) +--R +--R +--R +-+ +--R tan(x)\|c +-+ +-----+ +--R ((b + a)d + b c)atan(----------) - b x\|c \|d + c +--R +-----+ +--R \|d + c +--R (441) -------------------------------------------------- +--R +-+ +-----+ +--R d\|c \|d + c +--R Type: Expression(Integer) +--E 505 + +--S 506 of 534 +a0695:= integrate(t0695,x) +--R +--R +--R (442) +--R [ +--R ((b + a)d + b c) +--R * +--R +----------+ +--R 2 | 2 2 +--R ((d + 2c)cos(x) - c)\|- c d - c + (- 2c d - 2c )cos(x)sin(x) +--R log(---------------------------------------------------------------) +--R 2 +--R d cos(x) + c +--R + +--R +----------+ +--R | 2 +--R - 2b x\|- c d - c +--R / +--R +----------+ +--R | 2 +--R 2d\|- c d - c +--R , +--R +--R +--------+ +--R | 2 +--R sin(x)\|c d + c +--R ((b + a)d + b c)atan(-----------------) +--R 2c cos(x) + 2c +--R + +--R ((d - c)cos(x) - 2c)sin(x) +--R ((- b - a)d - b c)atan(----------------------------------) +--R +--------+ +--R 2 | 2 +--R (cos(x) + 2cos(x) + 1)\|c d + c +--R + +--R +--------+ +--R | 2 +--R - b x\|c d + c +--R / +--R +--------+ +--R | 2 +--R d\|c d + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 506 + +--S 507 of 534 +m0695a:= a0695.1-r0695 +--R +--R +--R (443) +--R +-+ +-----+ +--R ((b + a)d + b c)\|c \|d + c +--R * +--R +----------+ +--R 2 | 2 2 +--R ((d + 2c)cos(x) - c)\|- c d - c + (- 2c d - 2c )cos(x)sin(x) +--R log(---------------------------------------------------------------) +--R 2 +--R d cos(x) + c +--R + +--R +----------+ +-+ +--R | 2 tan(x)\|c +--R ((- 2b - 2a)d - 2b c)\|- c d - c atan(----------) +--R +-----+ +--R \|d + c +--R / +--R +----------+ +--R | 2 +-+ +-----+ +--R 2d\|- c d - c \|c \|d + c +--R Type: Expression(Integer) +--E 507 + +--S 508 of 534 +d0695a:= D(m0695a,x) +--R +--R +--R (444) +--R 2 2 2 2 3 2 +--R (((b + a)c d + b c d)cos(x) + (- b - a)c d - b c )sin(x) +--R + +--R 3 2 2 4 +--R ((- b - a)d + (- 2b - a)c d - b c d)cos(x) +--R + +--R 2 3 2 2 3 +--R ((- b - a)c d - b c )cos(x) + (b + a)c d + b c +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 2 2 +--R ((b + a)d + (2b + a)c d + b c d)cos(x) + (- b - a)c d +--R + +--R 2 3 +--R (- 2b - a)c d - b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 2 2 3 2 +--R ((- b - a)c d - b c d)cos(x) + ((b + a)c d - a c d - b c )cos(x) +--R + +--R 2 3 +--R (b + a)c d + b c +--R * +--R +----------+ +--R | 2 +--R \|- c d - c +--R + +--R 3 2 2 3 3 2 +--R ((2b + 2a)c d + (4b + 2a)c d + 2b c d)cos(x) sin(x)tan(x) +--R + +--R 3 2 2 3 3 +--R ((2b + 2a)c d + (4b + 2a)c d + 2b c d)cos(x) +--R + +--R 3 2 2 3 +--R ((- 2b - 2a)c d + (- 4b - 2a)c d - 2b c d)cos(x) +--R * +--R sin(x) +--R / +--R 3 2 2 4 3 2 3 2 +--R ((c d + 2c d )cos(x) + 2c d cos(x) - c d)tan(x) +--R + +--R 4 3 2 2 4 2 2 3 2 2 2 3 +--R (d + 3c d + 2c d )cos(x) + (2c d + 2c d)cos(x) - c d - c d +--R * +--R +----------+ +--R | 2 +--R \|- c d - c +--R + +--R 2 3 3 2 3 3 2 4 2 +--R ((- 2c d - 2c d )cos(x) + (- 2c d - 2c d)cos(x))sin(x)tan(x) +--R + +--R 4 2 3 3 2 3 2 3 3 2 4 +--R ((- 2c d - 4c d - 2c d )cos(x) + (- 2c d - 4c d - 2c d)cos(x))sin(x) +--R Type: Expression(Integer) +--E 508 + +--S 509 of 534 +m0695b:= a0695.2-r0695 +--R +--R +--R (445) +--R +--------+ +--R | 2 +--R +-+ +-----+ sin(x)\|c d + c +--R ((b + a)d + b c)\|c \|d + c atan(-----------------) +--R 2c cos(x) + 2c +--R + +--R +--------+ +-+ +--R | 2 tan(x)\|c +--R ((- b - a)d - b c)\|c d + c atan(----------) +--R +-----+ +--R \|d + c +--R + +--R +-+ +-----+ ((d - c)cos(x) - 2c)sin(x) +--R ((- b - a)d - b c)\|c \|d + c atan(----------------------------------) +--R +--------+ +--R 2 | 2 +--R (cos(x) + 2cos(x) + 1)\|c d + c +--R / +--R +--------+ +--R +-+ +-----+ | 2 +--R d\|c \|d + c \|c d + c +--R Type: Expression(Integer) +--E 509 + +--S 510 of 534 +d0695b:= D(m0695b,x) +--R +--R +--R (446) +--R 4 3 2 2 3 +--R (- b - a)d + (b + 2a)c d + (- b - 3a)c d + (- b + 2a)c d +--R + +--R 4 +--R 2b c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((4b + 4a)c d - 4a c d + (4b + 8a)c d + 8b c )cos(x) +--R + +--R 3 2 2 3 4 +--R (b + a)c d + b c d + (7b + 7a)c d + 7b c +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R ((- 4b - 4a)c d - 4b c d + (4b + 4a)c d + 4b c )cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 12b - 12a)c d + (2b + 14a)c d + (32b + 18a)c d + 18b c ) +--R * +--R 3 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 11b - 11a)c d + (25b + 36a)c d + (59b + 23a)c d + 23b c ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 4b - 4a)c d + (22b + 26a)c d + (32b + 6a)c d + 6b c )cos(x) +--R + +--R 3 2 2 3 4 +--R (- b - a)c d + (3b + 4a)c d + (b - 3a)c d - 3b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 6 +--R ((- 6b - 6a)c d + (- 4b + 2a)c d + 2b c )cos(x) +--R + +--R 2 2 3 4 5 +--R ((- 30b - 30a)c d + (- 20b + 10a)c d + 10b c )cos(x) +--R + +--R 2 2 3 4 4 +--R ((- 64b - 64a)c d + (- 48b + 16a)c d + 16b c )cos(x) +--R + +--R 2 2 3 4 3 +--R ((- 76b - 76a)c d + (- 72b + 4a)c d + 4b c )cos(x) +--R + +--R 2 2 3 4 2 +--R ((- 54b - 54a)c d + (- 68b - 14a)c d - 14b c )cos(x) +--R + +--R 2 2 3 4 +--R ((- 22b - 22a)c d + (- 36b - 14a)c d - 14b c )cos(x) +--R + +--R 2 2 3 4 +--R (- 4b - 4a)c d + (- 8b - 4a)c d - 4b c +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 2 +--R ((- 2b - 2a)c d - 2b c d + (2b + 2a)c d + 2b c )cos(x) +--R + +--R 2 2 3 4 4 +--R ((8b + 8a)c d + (16b + 8a)c d + 8b c )cos(x) + (b + a)d +--R + +--R 3 2 2 3 4 +--R (6b + 5a)c d + (16b + 11a)c d + (18b + 7a)c d + 7b c +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 3 +--R (b + a)d + (- 9b - 10a)c d + (- b + 9a)c d + (13b + 4a)c d +--R + +--R 4 +--R 4b c +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 22b - 22a)c d + (38b + 60a)c d + (78b + 18a)c d + 18b c ) +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- b - a)d + (- 4b - 3a)c d + (114b + 117a)c d +--R + +--R 3 4 +--R (140b + 23a)c d + 23b c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((14b + 14a)c d + (98b + 84a)c d + (90b + 6a)c d + 6b c )cos(x) +--R + +--R 3 2 2 3 4 +--R (5b + 5a)c d + (23b + 18a)c d + (15b - 3a)c d - 3b c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 6 +--R ((- 2b - 2a)c d - 2b c d + (2b + 2a)c d + 2b c )cos(x) +--R + +--R 3 2 2 3 4 5 +--R ((- 6b - 6a)c d + (- 2b + 4a)c d + (14b + 10a)c d + 10b c )cos(x) +--R + +--R 3 2 2 3 4 4 +--R ((- 4b - 4a)c d + (8b + 12a)c d + (28b + 16a)c d + 16b c )cos(x) +--R + +--R 3 2 2 3 4 3 +--R ((4b + 4a)c d + (12b + 8a)c d + (12b + 4a)c d + 4b c )cos(x) +--R + +--R 3 2 2 3 4 2 +--R ((6b + 6a)c d + (- 2b - 8a)c d + (- 22b - 14a)c d - 14b c )cos(x) +--R + +--R 3 2 2 3 4 +--R ((2b + 2a)c d + (- 10b - 12a)c d + (- 26b - 14a)c d - 14b c )cos(x) +--R + +--R 2 2 3 4 +--R (- 4b - 4a)c d + (- 8b - 4a)c d - 4b c +--R / +--R 4 2 3 3 2 4 2 2 3 4 +--R (c d - c d - c d + c d)cos(x) + (- 4c d + 4c d)cos(x) +--R + +--R 3 2 4 +--R 4c d + 4c d +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 4 3 +--R (5c d - 6c d + 5c d)cos(x) + (12c d - 24c d + 28c d)cos(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 +--R (10c d - 28c d + 58c d)cos(x) + (4c d - 8c d + 52c d)cos(x) +--R + +--R 2 3 3 2 4 +--R c d + 2c d + 17c d +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 3 2 4 5 +--R (4c d + 4c d)cos(x) + (24c d + 24c d)cos(x) +--R + +--R 3 2 4 4 3 2 4 3 +--R (60c d + 60c d)cos(x) + (80c d + 80c d)cos(x) +--R + +--R 3 2 4 2 3 2 4 3 2 4 +--R (60c d + 60c d)cos(x) + (24c d + 24c d)cos(x) + 4c d + 4c d +--R * +--R 2 +--R tan(x) +--R + +--R 5 2 3 4 2 4 2 3 3 2 4 +--R (d - 2c d + c d)cos(x) + (- 4c d - 4c d + 4c d + 4c d)cos(x) +--R + +--R 2 3 3 2 4 +--R 4c d + 8c d + 4c d +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 2 4 4 +--R (5c d - c d - c d + 5c d)cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (12c d - 12c d + 4c d + 28c d)cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (10c d - 18c d + 30c d + 58c d)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 4 +--R (4c d - 4c d + 44c d + 52c d)cos(x) + c d + 3c d + 19c d + 17c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 6 2 3 3 2 4 5 +--R (4c d + 8c d + 4c d)cos(x) + (24c d + 48c d + 24c d)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 4 3 +--R (60c d + 120c d + 60c d)cos(x) + (80c d + 160c d + 80c d)cos(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 +--R (60c d + 120c d + 60c d)cos(x) + (24c d + 48c d + 24c d)cos(x) +--R + +--R 2 3 3 2 4 +--R 4c d + 8c d + 4c d +--R Type: Expression(Integer) +--E 510 + +--S 511 of 534 +t0696:= (-1+1/d^2*c^2+cos(x)^2)/(c+d*sin(x)) +--R +--R +--R 2 2 2 2 +--R d cos(x) - d + c +--R (447) ------------------- +--R 3 2 +--R d sin(x) + c d +--R Type: Expression(Integer) +--E 511 + +--S 512 of 534 +r0696:= (c*x+d*cos(x))/d^2 +--R +--R +--R d cos(x) + c x +--R (448) -------------- +--R 2 +--R d +--R Type: Expression(Integer) +--E 512 + +--S 513 of 534 +a0696:= integrate(t0696,x) +--R +--R +--R d cos(x) + c x +--R (449) -------------- +--R 2 +--R d +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 534 +m0696:= a0696-r0696 +--R +--R +--R (450) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 534 +d0696:= D(m0696,x) +--R +--R +--R (451) 0 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 534 +t0697:= (a+b*cos(x)^2)/(c+d*sin(x)) +--R +--R +--R 2 +--R b cos(x) + a +--R (452) ------------- +--R d sin(x) + c +--R Type: Expression(Integer) +--E 516 + +--S 517 of 534 +r0697:= b*c*x/d^2+2*(a*d^2-b*(c^2-d^2))*atan((d+c*tan(1/2*x))/_ + (c^2-d^2)^(1/2))/d^2/(c^2-d^2)^(1/2)+b*cos(x)/d +--R +--R +--R (453) +--R x +--R c tan(-) + d +---------+ +--R 2 2 2 | 2 2 +--R ((2b + 2a)d - 2b c )atan(------------) + (b d cos(x) + b c x)\|- d + c +--R +---------+ +--R | 2 2 +--R \|- d + c +--R -------------------------------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R Type: Expression(Integer) +--E 517 + +--S 518 of 534 +a0697:= integrate(t0697,x) +--R +--R +--R (454) +--R [ +--R 2 2 +--R ((b + a)d - b c ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (c d sin(x) + (d - c )cos(x) + d )\|d - c +--R + +--R 2 3 3 2 3 2 +--R (- c d + c )sin(x) + (- d + c d)cos(x) - d + c d +--R / +--R d sin(x) + c +--R + +--R +-------+ +--R | 2 2 +--R (b d cos(x) + b c x)\|d - c +--R / +--R +-------+ +--R 2 | 2 2 +--R d \|d - c +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 2 (c sin(x) + d cos(x) + d)\|- d + c +--R ((- 2b - 2a)d + 2b c )atan(-------------------------------------) +--R 2 2 2 2 +--R (d - c )cos(x) + d - c +--R + +--R +---------+ +--R | 2 2 +--R (b d cos(x) + b c x)\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 518 + +--S 519 of 534 +m0697a:= a0697.1-r0697 +--R +--R +--R (455) +--R +---------+ +--R 2 2 | 2 2 +--R ((b + a)d - b c )\|- d + c +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (c d sin(x) + (d - c )cos(x) + d )\|d - c +--R + +--R 2 3 3 2 3 2 +--R (- c d + c )sin(x) + (- d + c d)cos(x) - d + c d +--R / +--R d sin(x) + c +--R + +--R x +--R +-------+ c tan(-) + d +--R 2 2 | 2 2 2 +--R ((- 2b - 2a)d + 2b c )\|d - c atan(------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R d \|- d + c \|d - c +--R Type: Expression(Integer) +--E 519 + +--S 520 of 534 +d0697a:= D(m0697a,x) +--R +--R +--R (456) +--R 4 2 2 4 4 +--R ((- b - a)d + (2b + a)c d - b c )cos(x) + (- b - a)d +--R + +--R 2 2 +--R b c d +--R * +--R sin(x) +--R + +--R 3 3 2 3 3 +--R ((b + a)c d - b c d)cos(x) + (- b - a)c d + b c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 3 3 +--R ((2b + 2a)d - 2b c d )sin(x) + ((2b + 2a)c d - 2b c d)sin(x) +--R + +--R 4 2 2 2 +--R ((2b + 2a)d - 2b c d )cos(x) +--R + +--R 4 2 2 4 +--R ((2b + 2a)d + (- 4b - 2a)c d + 2b c )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 4 2 2 +--R (((- b - a)d + (2b + a)c d - b c )cos(x) + (- b - a)d + b c d ) +--R * +--R sin(x) +--R + +--R 3 3 2 3 3 +--R ((b + a)c d - b c d)cos(x) + (- b - a)c d + b c d +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 5 2 3 4 5 +--R ((b + a)d + (- 2b - a)c d + b c d)cos(x) + (b + a)d +--R + +--R 2 3 4 +--R (- 2b - a)c d + b c d +--R * +--R sin(x) +--R + +--R 4 3 2 5 2 4 +--R ((- b - a)c d + (2b + a)c d - b c )cos(x) + (b + a)c d +--R + +--R 3 2 5 +--R (- 2b - a)c d + b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 2 +--R ((- 2b - 2a)d + (4b + 2a)c d - 2b c d)sin(x) +--R + +--R 4 3 2 5 +--R ((- 2b - 2a)c d + (4b + 2a)c d - 2b c )sin(x) +--R + +--R 5 2 3 4 2 +--R ((- 2b - 2a)d + (4b + 2a)c d - 2b c d)cos(x) +--R + +--R 5 2 3 4 +--R ((- 2b - 2a)d + (4b + 2a)c d - 2b c d)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 5 +--R ((b + a)d + (- 2b - a)c d + b c d)cos(x) + (b + a)d +--R + +--R 2 3 4 +--R (- 2b - a)c d + b c d +--R * +--R sin(x) +--R + +--R 4 3 2 5 2 4 +--R ((- b - a)c d + (2b + a)c d - b c )cos(x) + (b + a)c d +--R + +--R 3 2 5 +--R (- 2b - a)c d + b c +--R / +--R 2 3 2 4 3 2 4 3 2 +--R c d sin(x) + ((c d - c d )cos(x) + c d + c d )sin(x) +--R + +--R 2 3 4 2 3 +--R (c d - c d)cos(x) + c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 5 2 3 +--R 2c d sin(x) + ((2d - 2c d )cos(x) + 2d + 2c d )sin(x) +--R + +--R 4 3 2 4 +--R (2c d - 2c d )cos(x) + 2c d +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 3 2 4 3 2 +--R c d sin(x) + ((c d - c d )cos(x) + c d + c d )sin(x) +--R + +--R 2 3 4 2 3 +--R (c d - c d)cos(x) + c d +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- c d + c d )sin(x) + ((- c d + c d )cos(x) - c d + c d)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- c d + c d )cos(x) - c d + c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 +--R (- 2c d + 2c d )sin(x) +--R + +--R 6 2 4 6 4 2 5 3 3 +--R ((- 2d + 2c d )cos(x) - 2d + 2c d )sin(x) + (- 2c d + 2c d )cos(x) +--R + +--R 5 3 3 +--R - 2c d + 2c d +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- c d + c d )sin(x) + ((- c d + c d )cos(x) - c d + c d)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- c d + c d )cos(x) - c d + c d +--R Type: Expression(Integer) +--E 520 + +--S 521 of 534 +m0697b:= a0697.2-r0697 +--R +--R +--R (457) +--R +---------+ +--R | 2 2 +--R 2 2 (c sin(x) + d cos(x) + d)\|- d + c +--R ((- 2b - 2a)d + 2b c )atan(-------------------------------------) +--R 2 2 2 2 +--R (d - c )cos(x) + d - c +--R + +--R x +--R c tan(-) + d +--R 2 2 2 +--R ((- 2b - 2a)d + 2b c )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R d \|- d + c +--R Type: Expression(Integer) +--E 521 + +--S 522 of 534 +d0697b:= D(m0697b,x) +--R +--R +--R (458) +--R 2 3 2 +--R ((b + a)c d - b c )sin(x) +--R + +--R 3 2 3 2 +--R (((- 2b - 2a)d + 2b c d)cos(x) + (- 2b - 2a)d + 2b c d)sin(x) +--R + +--R 2 3 2 2 3 +--R ((b + a)c d - b c )cos(x) + (- b - a)c d + b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 2 +--R ((4b + 4a)d - 4b c d)sin(x) + ((4b + 4a)d - 4b c d)cos(x) +--R + +--R 3 2 +--R ((4b + 4a)d - 4b c d)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 +--R ((b + a)c d - b c )sin(x) +--R + +--R 3 2 3 2 +--R (((- 2b - 2a)d + 2b c d)cos(x) + (- 2b - 2a)d + 2b c d)sin(x) +--R + +--R 2 3 2 2 3 +--R ((b + a)c d - b c )cos(x) + (- b - a)c d + b c +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R c d sin(x) + (2c d cos(x) + 2c d )sin(x) + c d cos(x) + 2c d cos(x) +--R + +--R 2 2 +--R c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2c d sin(x) + (4d cos(x) + 4d )sin(x) + 2c d cos(x) + 4c d cos(x) +--R + +--R 3 +--R 2c d +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 +--R c d sin(x) + (2c d cos(x) + 2c d )sin(x) + c d cos(x) + 2c d cos(x) +--R + +--R 2 2 +--R c d +--R Type: Expression(Integer) +--E 522 + +--S 523 of 534 +t0698:= (a+b*cos(x)^2)/(c+c*sin(x)^2) +--R +--R +--R 2 +--R b cos(x) + a +--R (459) ------------- +--R 2 +--R c sin(x) + c +--R Type: Expression(Integer) +--E 523 + +--S 524 of 534 +r0698:= -b*x/c+1/2*(a+2*b)*atan(2^(1/2)*tan(x))*2^(1/2)/c +--R +--R +--R +-+ +-+ +--R (2b + a)\|2 atan(\|2 tan(x)) - 2b x +--R (460) ----------------------------------- +--R 2c +--R Type: Expression(Integer) +--E 524 + +--S 525 of 534 +a0698:= integrate(t0698,x) +--R +--R +--R (461) +--R +-+ +--R \|2 sin(x) +--R (2b + a)atan(-----------) +--R 4cos(x) + 4 +--R + +--R (3cos(x) + 4)sin(x) +-+ +--R (2b + a)atan(--------------------------------) - b x\|2 +--R +-+ 2 +-+ +-+ +--R \|2 cos(x) + 2\|2 cos(x) + \|2 +--R / +--R +-+ +--R c\|2 +--R Type: Union(Expression(Integer),...) +--E 525 + +--S 526 of 534 +m0698:= a0698-r0698 +--R +--R +--R (462) +--R +-+ +--R +-+ \|2 sin(x) +--R (- 2b - a)atan(\|2 tan(x)) + (2b + a)atan(-----------) +--R 4cos(x) + 4 +--R + +--R (3cos(x) + 4)sin(x) +--R (2b + a)atan(--------------------------------) +--R +-+ 2 +-+ +-+ +--R \|2 cos(x) + 2\|2 cos(x) + \|2 +--R / +--R +-+ +--R c\|2 +--R Type: Expression(Integer) +--E 526 + +--S 527 of 534 +d0698:= D(m0698,x) +--R +--R +--R (463) +--R 2 4 +--R ((66b + 33a)cos(x) + (176b + 88a)cos(x) + 116b + 58a)sin(x) +--R + +--R 4 3 2 +--R (48b + 24a)cos(x) + (128b + 64a)cos(x) + (36b + 18a)cos(x) +--R + +--R (- 128b - 64a)cos(x) - 84b - 42a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R (80b + 40a)cos(x) + (400b + 200a)cos(x) + (768b + 384a)cos(x) +--R + +--R 3 2 +--R (672b + 336a)cos(x) + (208b + 104a)cos(x) + (- 48b - 24a)cos(x) +--R + +--R - 32b - 16a +--R * +--R 2 +--R tan(x) +--R + +--R 2 4 +--R ((24b + 12a)cos(x) + (64b + 32a)cos(x) + 42b + 21a)sin(x) +--R + +--R 4 3 +--R (- 50b - 25a)cos(x) + (- 280b - 140a)cos(x) +--R + +--R 2 +--R (- 578b - 289a)cos(x) + (- 520b - 260a)cos(x) - 172b - 86a +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 +--R (24b + 12a)cos(x) + (104b + 52a)cos(x) + (144b + 72a)cos(x) +--R + +--R 3 2 +--R (16b + 8a)cos(x) + (- 136b - 68a)cos(x) + (- 120b - 60a)cos(x) - 32b +--R + +--R - 16a +--R / +--R 2 4 +--R (18c cos(x) + 48c cos(x) + 32c)sin(x) +--R + +--R 4 3 2 +--R (148c cos(x) + 688c cos(x) + 1192c cos(x) + 912c cos(x) + 260c) +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 4 3 +--R 32c cos(x) + 192c cos(x) + 480c cos(x) + 640c cos(x) +--R + +--R 2 +--R 480c cos(x) + 192c cos(x) + 32c +--R * +--R 2 +--R tan(x) +--R + +--R 2 4 +--R (9c cos(x) + 24c cos(x) + 16c)sin(x) +--R + +--R 4 3 2 2 +--R (74c cos(x) + 344c cos(x) + 596c cos(x) + 456c cos(x) + 130c)sin(x) +--R + +--R 6 5 4 3 2 +--R 16c cos(x) + 96c cos(x) + 240c cos(x) + 320c cos(x) + 240c cos(x) +--R + +--R 96c cos(x) + 16c +--R Type: Expression(Integer) +--E 527 + +--S 528 of 534 +t0699:= (a+b*cos(x)^2)/(c+d*sin(x)^2) +--R +--R +--R 2 +--R b cos(x) + a +--R (464) ------------- +--R 2 +--R d sin(x) + c +--R Type: Expression(Integer) +--E 528 + +--S 529 of 534 +r0699:= -b*x/d+(b*c+(a+b)*d)*atan((c+d)^(1/2)*tan(x)/c^(1/2))/_ + c^(1/2)/d/(c+d)^(1/2) +--R +--R +--R +-----+ +--R tan(x)\|d + c +-+ +-----+ +--R ((b + a)d + b c)atan(--------------) - b x\|c \|d + c +--R +-+ +--R \|c +--R (465) ------------------------------------------------------ +--R +-+ +-----+ +--R d\|c \|d + c +--R Type: Expression(Integer) +--E 529 + +--S 530 of 534 +a0699:= integrate(t0699,x) +--R +--R +--R (466) +--R [ +--R ((b + a)d + b c) +--R * +--R log +--R +----------+ +--R 2 | 2 +--R ((- d - 2c)cos(x) + d + c)\|- c d - c +--R + +--R 2 +--R (2c d + 2c )cos(x)sin(x) +--R / +--R 2 +--R d cos(x) - d - c +--R + +--R +----------+ +--R | 2 +--R - 2b x\|- c d - c +--R / +--R +----------+ +--R | 2 +--R 2d\|- c d - c +--R , +--R +--R +--------+ +--R | 2 +--R sin(x)\|c d + c +--R ((b + a)d + b c)atan(-------------------------) +--R (2d + 2c)cos(x) + 2d + 2c +--R + +--R +--------+ +--R ((2d + c)cos(x) + 2d + 2c)sin(x) | 2 +--R ((b + a)d + b c)atan(----------------------------------) - b x\|c d + c +--R +--------+ +--R 2 | 2 +--R (cos(x) + 2cos(x) + 1)\|c d + c +--R / +--R +--------+ +--R | 2 +--R d\|c d + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 530 + +--S 531 of 534 +m0699a:= a0699.1-r0699 +--R +--R +--R (467) +--R +-+ +-----+ +--R ((b + a)d + b c)\|c \|d + c +--R * +--R +----------+ +--R 2 | 2 2 +--R ((- d - 2c)cos(x) + d + c)\|- c d - c + (2c d + 2c )cos(x)sin(x) +--R log(-------------------------------------------------------------------) +--R 2 +--R d cos(x) - d - c +--R + +--R +----------+ +-----+ +--R | 2 tan(x)\|d + c +--R ((- 2b - 2a)d - 2b c)\|- c d - c atan(--------------) +--R +-+ +--R \|c +--R / +--R +----------+ +--R | 2 +-+ +-----+ +--R 2d\|- c d - c \|c \|d + c +--R Type: Expression(Integer) +--E 531 + +--S 532 of 534 +d0699a:= D(m0699a,x) +--R +--R +--R (468) +--R 3 2 2 2 3 +--R ((b + a)d + (2b + a)c d + b c d)cos(x) + (b + a)d +--R + +--R 2 2 3 +--R (3b + 2a)c d + (3b + a)c d + b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 +--R ((- b - a)c d - b c d)cos(x) +--R + +--R 3 2 2 3 2 +--R ((b + a)d + (3b + 2a)c d + (3b + a)c d + b c )cos(x) +--R + +--R 3 2 2 3 +--R (- b - a)d + (- 3b - 2a)c d + (- 3b - a)c d - b c +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 2 2 2 3 +--R (((b + a)c d + b c d)cos(x) + (b + a)c d + (2b + a)c d + b c ) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 4 +--R ((- b - a)d + (- 2b - a)c d - b c d)cos(x) +--R + +--R 3 2 2 3 2 +--R ((2b + 2a)d + (5b + 3a)c d + (4b + a)c d + b c )cos(x) +--R + +--R 3 2 2 3 +--R (- b - a)d + (- 3b - 2a)c d + (- 3b - a)c d - b c +--R * +--R +----------+ +--R | 2 +--R \|- c d - c +--R + +--R 3 2 2 3 3 2 +--R ((2b + 2a)c d + (4b + 2a)c d + 2b c d)cos(x) sin(x)tan(x) +--R + +--R 3 2 2 3 3 +--R ((2b + 2a)c d + (4b + 2a)c d + 2b c d)cos(x) +--R + +--R 3 2 2 3 +--R ((- 2b - 2a)c d + (- 4b - 2a)c d - 2b c d)cos(x) +--R * +--R sin(x) +--R / +--R 4 3 2 2 4 +--R (d + 3c d + 2c d )cos(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (- 2d - 6c d - 6c d - 2c d)cos(x) + d + 3c d + 3c d + c d +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 4 3 2 2 3 2 3 +--R (c d + 2c d )cos(x) + (- 2c d - 4c d - 2c d)cos(x) + c d +--R + +--R 2 2 3 +--R 2c d + c d +--R * +--R +----------+ +--R | 2 +--R \|- c d - c +--R + +--R 4 2 3 3 2 3 +--R (- 2c d - 4c d - 2c d )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (2c d + 6c d + 6c d + 2c d)cos(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 2 3 3 2 3 2 3 3 2 4 +--R ((- 2c d - 2c d )cos(x) + (2c d + 4c d + 2c d)cos(x))sin(x) +--R Type: Expression(Integer) +--E 532 + +--S 533 of 534 +m0699b:= a0699.2-r0699 +--R +--R +--R (469) +--R +--------+ +--R | 2 +--R +-+ +-----+ sin(x)\|c d + c +--R ((b + a)d + b c)\|c \|d + c atan(-------------------------) +--R (2d + 2c)cos(x) + 2d + 2c +--R + +--R +--------+ +-----+ +--R | 2 tan(x)\|d + c +--R ((- b - a)d - b c)\|c d + c atan(--------------) +--R +-+ +--R \|c +--R + +--R +-+ +-----+ ((2d + c)cos(x) + 2d + 2c)sin(x) +--R ((b + a)d + b c)\|c \|d + c atan(----------------------------------) +--R +--------+ +--R 2 | 2 +--R (cos(x) + 2cos(x) + 1)\|c d + c +--R / +--R +--------+ +--R +-+ +-----+ | 2 +--R d\|c \|d + c \|c d + c +--R Type: Expression(Integer) +--E 533 + +--S 534 of 534 +d0699b:= D(m0699b,x) +--R +--R +--R (470) +--R 4 3 2 2 +--R (8b + 8a)d + (22b + 14a)c d + (23b + 9a)c d +--R + +--R 3 4 +--R (11b + 2a)c d + 2b c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 +--R (16b + 16a)d + (52b + 36a)c d + (64b + 28a)c d +--R + +--R 3 4 +--R (36b + 8a)c d + 8b c +--R * +--R cos(x) +--R + +--R 4 3 2 2 3 +--R (8b + 8a)d + (30b + 22a)c d + (43b + 21a)c d + (28b + 7a)c d +--R + +--R 4 +--R 7b c +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R ((8b + 8a)c d + (20b + 12a)c d + (16b + 4a)c d + 4b c )cos(x) +--R + +--R 4 3 2 2 +--R (- 8b - 8a)d + (6b + 14a)c d + (54b + 40a)c d +--R + +--R 3 4 +--R (58b + 18a)c d + 18b c +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 24b - 24a)d + (- 38b - 14a)c d + (19b + 33a)c d +--R + +--R 3 4 +--R (56b + 23a)c d + 23b c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 24b - 24a)d + (- 62b - 38a)c d + (- 46b - 8a)c d +--R + +--R 3 4 +--R (- 2b + 6a)c d + 6b c +--R * +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 8b - 8a)d + (- 26b - 18a)c d + (- 31b - 13a)c d +--R + +--R 3 4 +--R (- 16b - 3a)c d - 3b c +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 3 +--R (8b + 8a)d + (26b + 18a)c d + (30b + 12a)c d + (14b + 2a)c d +--R + +--R 4 +--R 2b c +--R * +--R 6 +--R cos(x) +--R + +--R 4 3 2 2 +--R (40b + 40a)d + (130b + 90a)c d + (150b + 60a)c d +--R + +--R 3 4 +--R (70b + 10a)c d + 10b c +--R * +--R 5 +--R cos(x) +--R + +--R 4 3 2 2 +--R (80b + 80a)d + (256b + 176a)c d + (288b + 112a)c d +--R + +--R 3 4 +--R (128b + 16a)c d + 16b c +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 2 2 +--R (80b + 80a)d + (244b + 164a)c d + (252b + 88a)c d +--R + +--R 3 4 +--R (92b + 4a)c d + 4b c +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 2 +--R (40b + 40a)d + (106b + 66a)c d + (78b + 12a)c d +--R + +--R 3 4 +--R (- 2b - 14a)c d - 14b c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 +--R (8b + 8a)d + (10b + 2a)c d + (- 18b - 20a)c d +--R + +--R 3 4 +--R (- 34b - 14a)c d - 14b c +--R * +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4b - 4a)c d + (- 12b - 8a)c d + (- 12b - 4a)c d - 4b c +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 4 2 +--R ((4b + 4a)c d + (10b + 6a)c d + (8b + 2a)c d + 2b c )cos(x) +--R + +--R 3 2 2 3 4 +--R ((8b + 8a)c d + (24b + 16a)c d + (24b + 8a)c d + 8b c )cos(x) +--R + +--R 3 2 2 3 4 +--R (4b + 4a)c d + (14b + 10a)c d + (17b + 7a)c d + 7b c +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 +--R (- 16b - 16a)d + (- 32b - 16a)c d + (- 13b + 3a)c d +--R + +--R 3 4 +--R (7b + 4a)c d + 4b c +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 64b - 64a)d + (- 152b - 88a)c d + (- 94b - 6a)c d +--R + +--R 3 4 +--R (12b + 18a)c d + 18b c +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 96b - 96a)d + (- 264b - 168a)c d + (- 216b - 48a)c d +--R + +--R 3 4 +--R (- 25b + 23a)c d + 23b c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 64b - 64a)d + (- 200b - 136a)c d + (- 202b - 66a)c d +--R + +--R 3 4 +--R (- 60b + 6a)c d + 6b c +--R * +--R cos(x) +--R + +--R 4 3 2 2 +--R (- 16b - 16a)d + (- 56b - 40a)c d + (- 67b - 27a)c d +--R + +--R 3 4 +--R (- 30b - 3a)c d - 3b c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 6 +--R ((4b + 4a)c d + (10b + 6a)c d + (8b + 2a)c d + 2b c )cos(x) +--R + +--R 3 2 2 3 4 5 +--R ((16b + 16a)c d + (42b + 26a)c d + (36b + 10a)c d + 10b c )cos(x) +--R + +--R 3 2 2 3 4 4 +--R ((20b + 20a)c d + (56b + 36a)c d + (52b + 16a)c d + 16b c )cos(x) +--R + +--R 2 2 3 4 3 +--R ((4b + 4a)c d + (8b + 4a)c d + 4b c )cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 20b - 20a)c d + (- 54b - 34a)c d + (- 48b - 14a)c d - 14b c ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R ((- 16b - 16a)c d + (- 46b - 30a)c d + (- 44b - 14a)c d - 14b c )cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4b - 4a)c d + (- 12b - 8a)c d + (- 12b - 4a)c d - 4b c +--R / +--R 4 2 3 3 2 4 2 +--R (4c d + 8c d + 5c d + c d)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (8c d + 20c d + 16c d + 4c d)cos(x) + 4c d + 12c d + 12c d +--R + +--R 4 +--R 4c d +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (16d + 48c d + 53c d + 26c d + 5c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (64d + 208c d + 252c d + 136c d + 28c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 2 +--R (96d + 336c d + 442c d + 260c d + 58c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (64d + 240c d + 340c d + 216c d + 52c d)cos(x) + 16d +--R + +--R 4 2 3 3 2 4 +--R 64c d + 97c d + 66c d + 17c d +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 4 6 +--R (4c d + 12c d + 12c d + 4c d)cos(x) +--R + +--R 4 2 3 3 2 4 5 +--R (24c d + 72c d + 72c d + 24c d)cos(x) +--R + +--R 4 2 3 3 2 4 4 +--R (60c d + 180c d + 180c d + 60c d)cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (80c d + 240c d + 240c d + 80c d)cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (60c d + 180c d + 180c d + 60c d)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (24c d + 72c d + 72c d + 24c d)cos(x) + 4c d + 12c d + 12c d +--R + +--R 4 +--R 4c d +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 2 3 +--R (4c d + 4c d + c d)cos(x) + (8c d + 12c d + 4c d)cos(x) + 4c d +--R + +--R 3 2 4 +--R 8c d + 4c d +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 2 4 4 +--R (16c d + 32c d + 21c d + 5c d)cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (64c d + 144c d + 108c d + 28c d)cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (96c d + 240c d + 202c d + 58c d)cos(x) +--R + +--R 4 2 3 3 2 4 4 2 3 3 2 +--R (64c d + 176c d + 164c d + 52c d)cos(x) + 16c d + 48c d + 49c d +--R + +--R 4 +--R 17c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 3 2 4 6 2 3 3 2 4 5 +--R (4c d + 8c d + 4c d)cos(x) + (24c d + 48c d + 24c d)cos(x) +--R + +--R 2 3 3 2 4 4 2 3 3 2 4 3 +--R (60c d + 120c d + 60c d)cos(x) + (80c d + 160c d + 80c d)cos(x) +--R + +--R 2 3 3 2 4 2 2 3 3 2 4 +--R (60c d + 120c d + 60c d)cos(x) + (24c d + 48c d + 24c d)cos(x) +--R + +--R 2 3 3 2 4 +--R 4c d + 8c d + 4c d +--R Type: Expression(Integer) +--E 534 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richtrig600-699.input.pdf b/src/axiom-website/CATS/richtrig600-699.input.pdf new file mode 100644 index 0000000..2a971f6 Binary files /dev/null and b/src/axiom-website/CATS/richtrig600-699.input.pdf differ diff --git a/src/axiom-website/CATS/richtrig700-799.input.pamphlet b/src/axiom-website/CATS/richtrig700-799.input.pamphlet new file mode 100644 index 0000000..6285029 --- /dev/null +++ b/src/axiom-website/CATS/richtrig700-799.input.pamphlet @@ -0,0 +1,56692 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richtrig700-799.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig700-799.output +)spool richtrig700-799.output +)set message auto off +)clear all + +--S 1 of 532 +t0700:= (1-cos(x))/(1+sin(x)) +--R +--R +--R - cos(x) + 1 +--R (1) ------------ +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 532 +r0700:= -log(1+sin(x))-cos(x)/(1+sin(x)) +--R +--R +--R (- sin(x) - 1)log(sin(x) + 1) - cos(x) +--R (2) -------------------------------------- +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 532 +a0700:= integrate(t0700,x) +--R +--R +--R (3) +--R sin(x) + cos(x) + 1 +--R (- 2sin(x) - 2cos(x) - 2)log(-------------------) +--R cos(x) + 1 +--R + +--R 2 +--R (sin(x) + cos(x) + 1)log(----------) - 2cos(x) - 2 +--R cos(x) + 1 +--R / +--R sin(x) + cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 532 +m0700:= a0700-r0700 +--R +--R +--R (4) +--R 2 +--R (sin(x) + (cos(x) + 2)sin(x) + cos(x) + 1)log(sin(x) + 1) +--R + +--R 2 +--R (- 2sin(x) + (- 2cos(x) - 4)sin(x) - 2cos(x) - 2) +--R * +--R sin(x) + cos(x) + 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (sin(x) + (cos(x) + 2)sin(x) + cos(x) + 1)log(----------) +--R cos(x) + 1 +--R + +--R 2 +--R (- cos(x) - 2)sin(x) + cos(x) - cos(x) - 2 +--R / +--R 2 +--R sin(x) + (cos(x) + 2)sin(x) + cos(x) + 1 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 532 +d0700:= D(m0700,x) +--R +--R +--R (5) +--R 5 4 2 3 +--R - sin(x) + (cos(x) - 1)sin(x) + (- 2cos(x) + 1)sin(x) +--R + +--R 2 2 4 2 5 +--R (- 3cos(x) - 2cos(x) + 1)sin(x) + (- cos(x) + cos(x) )sin(x) - cos(x) +--R + +--R 4 2 +--R - 2cos(x) + 2cos(x) + cos(x) +--R / +--R 4 2 3 +--R (cos(x) + 1)sin(x) + (2cos(x) + 6cos(x) + 4)sin(x) +--R + +--R 3 2 2 +--R (cos(x) + 7cos(x) + 12cos(x) + 6)sin(x) +--R + +--R 3 2 3 2 +--R (2cos(x) + 8cos(x) + 10cos(x) + 4)sin(x) + cos(x) + 3cos(x) + 3cos(x) +--R + +--R 1 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 532 +t0701:= (a+b*sec(x))/(c+d*cos(x)) +--R +--R +--R b sec(x) + a +--R (6) ------------ +--R d cos(x) + c +--R Type: Expression(Integer) +--E 6 + +--S 7 of 532 +r0701:= 2*(a*c-b*d)*atan((c-d)*tan(1/2*x)/(c^2-d^2)^(1/2))/c/(c^2-d^2)^(1/2)+_ + b*atanh(sin(x))/c +--R +--R +--R x +--R +---------+ (d - c)tan(-) +--R | 2 2 2 +--R b\|- d + c atanh(sin(x)) + (2b d - 2a c)atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R (7) ------------------------------------------------------------- +--R +---------+ +--R | 2 2 +--R c\|- d + c +--R Type: Expression(Integer) +--E 7 + +--S 8 of 532 +a0701:= integrate(t0701,x) +--R +--R +--R (8) +--R [ +--R +-------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R b\|d - c log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R - b\|d - c log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 2 2 +--R (- c cos(x) - d)\|d - c + (d - c )sin(x) +--R (b d - a c)log(--------------------------------------------) +--R d cos(x) + c +--R / +--R +-------+ +--R | 2 2 +--R c\|d - c +--R , +--R +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R b\|- d + c log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R - b\|- d + c log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R sin(x)\|- d + c +--R (- 2b d + 2a c)atan(---------------------) +--R (d + c)cos(x) + d + c +--R / +--R +---------+ +--R | 2 2 +--R c\|- d + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 8 + +--S 9 of 532 +m0701a:= a0701.1-r0701 +--R +--R +--R (9) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R b\|- d + c \|d - c log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R - b\|- d + c \|d - c log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R +---------+ | 2 2 2 2 +--R | 2 2 (- c cos(x) - d)\|d - c + (d - c )sin(x) +--R (b d - a c)\|- d + c log(--------------------------------------------) +--R d cos(x) + c +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R - b\|- d + c \|d - c atanh(sin(x)) +--R + +--R x +--R +-------+ (d - c)tan(-) +--R | 2 2 2 +--R (- 2b d + 2a c)\|d - c atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R c\|- d + c \|d - c +--R Type: Expression(Integer) +--E 9 + +--S 10 of 532 +d0701a:= D(m0701a,x) +--R +--R +--R (10) +--R 3 2 2 6 +--R (- b d + (b + a)c d - a c d)sin(x) +--R + +--R 2 2 2 +--R (- 3b c d + (2b + a)c d)cos(x) +--R + +--R 3 2 2 3 +--R (- b d + (- b - a)c d + (- 2b + 3a)c d + 2b c )cos(x) +--R + +--R 3 2 2 +--R 2b d + (- 5b - 2a)c d + (2b + 3a)c d +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 4 +--R (b d + (- 2b - a)c d + 2b c d)cos(x) +--R + +--R 3 2 2 3 3 +--R (b d + (2b - 3a)c d + (- b - a)c d + 2b c )cos(x) +--R + +--R 3 2 2 3 2 +--R (2b d + (5b - 3a)c d + (- b - 4a)c d + b c )cos(x) +--R + +--R 3 2 2 3 3 +--R (2b d + 3b c d + (3b - 6a)c d - 2b c )cos(x) - b d +--R + +--R 2 2 +--R (5b + a)c d + (- 2b - 3a)c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 +--R (- b c d + b c d)cos(x) +--R + +--R 3 2 2 3 4 +--R (- 2b d + (b + a)c d - b c d + b c )cos(x) +--R + +--R 3 2 2 3 +--R (- 3b d + (- b + 3a)c d + a c d)cos(x) +--R + +--R 3 2 2 3 2 +--R (- 2b d + (- 4b + 3a)c d + (b + 3a)c d - b c )cos(x) +--R + +--R 3 2 2 2 2 +--R (- b d + (- 2b + a)c d + (- b + 3a)c d)cos(x) - b c d + a c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 6 +--R (b d + (b - a)c d - a c d)sin(x) +--R + +--R 2 2 2 +--R (b c d + (2b + a)c d)cos(x) +--R + +--R 3 2 2 3 3 +--R (- b d + (b + 3a)c d + (2b + a)c d + 2b c )cos(x) - 2b d +--R + +--R 2 2 +--R (- b + 2a)c d + (2b + 3a)c d +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 4 +--R (- b d + (2b + a)c d + 2b c d)cos(x) +--R + +--R 3 2 2 3 3 +--R (b d + (2b + a)c d + (3b + a)c d + 2b c )cos(x) +--R + +--R 3 2 2 3 2 +--R (2b d + (b - a)c d + b c d + b c )cos(x) +--R + +--R 3 2 2 3 3 +--R (2b d + (b - 4a)c d + (- b - 2a)c d - 2b c )cos(x) + b d +--R + +--R 2 2 +--R (b - a)c d + (- 2b - 3a)c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (b c d + b c d)cos(x) + (2b d + (b - a)c d + b c d + b c )cos(x) +--R + +--R 3 2 2 3 +--R (b d + (b - a)c d - a c d)cos(x) +--R + +--R 3 2 2 3 2 +--R (- 2b d + a c d + (- b - a)c d - b c )cos(x) +--R + +--R 3 2 2 2 2 +--R (- b d + (- 2b + a)c d + (- b + a)c d)cos(x) - b c d + a c d +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 4 3 2 2 3 4 +--R (3b d + (- 2b - a)c d - 3b c d + (2b + a)c d)cos(x) + b d +--R + +--R 3 2 2 3 4 +--R (2b - a)c d - 3b c d + (- 2b + a)c d + 2b c +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 3 3 +--R (b d + (- 2b + a)c d - b c d + (2b - a)c d)cos(x) +--R + +--R 4 3 3 4 2 +--R (- 2b d + (b + 3a)c d + (- b - 3a)c d + 2b c )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 6b d + (3b + 4a)c d + 5b c d + (- 3b - 4a)c d + b c )cos(x) +--R + +--R 4 3 2 2 3 4 +--R - 2b d + (- 2b + 2a)c d + 4b c d + (2b - 2a)c d - 2b c +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 3 4 +--R (b d - b c d - b c d + b c d)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b d + (b - a)c d - 2b c d + (- b + a)c d + b c )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (2b d + (b - 3a)c d - 2b c d + (- b + 3a)c d)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (3b d + (- b - 3a)c d - 2b c d + (b + 3a)c d - b c )cos(x) +--R + +--R 4 3 2 2 3 +--R b d - a c d - b c d + a c d +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 3 4 +--R (- b d + (- 2b - a)c d + b c d + (2b + a)c d)cos(x) - b d +--R + +--R 3 2 2 3 4 +--R (- 2b + a)c d - b c d + (2b - a)c d + 2b c +--R * +--R 5 +--R sin(x) +--R + +--R 4 3 2 2 3 3 +--R (- 3b d + (- 2b + a)c d + 3b c d + (2b - a)c d)cos(x) +--R + +--R 4 3 3 4 2 +--R (- 2b d + (- 3b + a)c d + (3b - a)c d + 2b c )cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (2b d + b c d - 3b c d - b c d + b c )cos(x) + 2b d +--R + +--R 3 3 4 +--R (2b - 2a)c d + (- 2b + 2a)c d - 2b c +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 2 3 4 +--R (- b d - b c d + b c d + b c d)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (b d + (- b - a)c d - 2b c d + (b + a)c d + b c )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (2b d + (b - a)c d - 2b c d + (- b + a)c d)cos(x) +--R + +--R 4 3 2 2 3 4 4 +--R (- b d + (b + a)c d + 2b c d + (- b - a)c d - b c )cos(x) - b d +--R + +--R 3 2 2 3 +--R a c d + b c d - a c d +--R * +--R sin(x) +--R / +--R 2 2 3 2 3 2 2 3 4 2 2 +--R (c d - c d)cos(x) + (c d - c d + c d - c )cos(x) + c d +--R + +--R 3 +--R - c d +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (- c d + c d)cos(x) + (- c d - c d + c d + c )cos(x) +--R + +--R 3 2 2 3 4 2 3 4 +--R (- 2c d - c d + c d + 2c )cos(x) + (- 2c d + 2c )cos(x) +--R + +--R 2 2 3 +--R - 2c d + 2c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (c d - c d)cos(x) + (c d + c d - c d - c )cos(x) +--R + +--R 3 4 2 3 2 2 3 4 2 2 3 +--R (2c d - 2c )cos(x) + (c d + c d - c d - c )cos(x) + c d - c d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 3 2 2 3 4 2 2 +--R (- c d - c d)cos(x) + (- c d - c d - c d - c )cos(x) - c d +--R + +--R 3 +--R - c d +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (c d + c d)cos(x) + (c d + 3c d + 3c d + c )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (2c d + 5c d + 5c d + 2c )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (2c d + 4c d + 4c d + 2c )cos(x) + 2c d + 2c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 4 3 +--R (- c d - c d)cos(x) + (- c d - 3c d - 3c d - c )cos(x) +--R + +--R 3 2 2 3 4 2 +--R (- 2c d - 4c d - 4c d - 2c )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- c d - 3c d - 3c d - c )cos(x) - c d - c d +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 5 +--R ((- c d + c d + c d - c d)cos(x) - c d + c d + c d - c )sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (c d - c d - c d + c d)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (2c d - c d - 3c d + c d + c )cos(x) +--R + +--R 4 3 2 5 2 3 3 2 4 5 +--R (2c d - 4c d + 2c )cos(x) + 2c d - 2c d - 2c d + 2c +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- c d + c d + c d - c d)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 2c d + c d + 3c d - c d - c )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 5 +--R (- c d - c d + 3c d + c d - 2c )cos(x) - c d + c d + c d - c +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 5 5 +--R ((c d + c d - c d - c d)cos(x) + c d + c d - c d - c )sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (- c d - c d + c d + c d)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 2c d - 3c d + c d + 3c d + c )cos(x) +--R + +--R 4 2 3 4 5 2 3 3 2 4 5 +--R (- 2c d - 4c d + 4c d + 2c )cos(x) - 2c d - 2c d + 2c d + 2c +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 +--R (c d + c d - c d - c d)cos(x) +--R + +--R 4 2 3 3 2 4 5 2 +--R (2c d + 3c d - c d - 3c d - c )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 3 2 4 5 +--R (c d + 3c d + c d - 3c d - 2c )cos(x) + c d + c d - c d - c +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 10 + +--S 11 of 532 +m0701b:= a0701.2-r0701 +--R +--R +--R (11) +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R b\|- d + c log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +---------+ +--R | 2 2 sin(x) - cos(x) - 1 | 2 2 +--R - b\|- d + c log(-------------------) - b\|- d + c atanh(sin(x)) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R sin(x)\|- d + c +--R (- 2b d + 2a c)atan(---------------------) +--R (d + c)cos(x) + d + c +--R + +--R x +--R (d - c)tan(-) +--R 2 +--R (- 2b d + 2a c)atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +--R | 2 2 +--R c\|- d + c +--R Type: Expression(Integer) +--E 11 + +--S 12 of 532 +d0701b:= D(m0701b,x) +--R +--R +--R (12) +--R 2 2 6 +--R (- b d + (3b - a)c d + (- 2b + a)c )sin(x) +--R + +--R 2 2 2 +--R (2b d + (4b - 2a)c d - 4b c )cos(x) +--R + +--R 2 2 2 +--R (5b d + (4b - 2a)c d + (- 5b - 2a)c )cos(x) + 3b d +--R + +--R 2 +--R (- b + a)c d - 3a c +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 +--R (- b d + (b + 3a)c d + (- 2b - a)c )cos(x) +--R + +--R 2 2 3 +--R (- 6b d + (4b + 10a)c d + (- 6b - 2a)c )cos(x) +--R + +--R 2 2 2 +--R (- 12b d + 14a c d - 2b c )cos(x) +--R + +--R 2 2 2 +--R (- 10b d + (- 6b + 8a)c d + (4b + 4a)c )cos(x) - 3b d +--R + +--R 2 +--R (- 3b + a)c d + (2b + 3a)c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 2 2 4 +--R (b d - b c )cos(x) + (5b d + (- b - 3a)c d + (- 2b + a)c )cos(x) +--R + +--R 2 2 3 +--R (10b d + (- 2b - 10a)c d + 2a c )cos(x) +--R + +--R 2 2 2 +--R (10b d - 12a c d + 2b c )cos(x) +--R + +--R 2 2 2 2 +--R (5b d + (2b - 6a)c d + (b - 2a)c )cos(x) + b d + (b - a)c d - a c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 6 +--R (- b d + (- b + 3a)c d + (- 2b + a)c )sin(x) +--R + +--R 2 2 2 +--R (2b d + (- 4b - 2a)c d - 4b c )cos(x) +--R + +--R 2 2 2 +--R (3b d + (- 6b - 6a)c d + (- 5b - 2a)c )cos(x) + 3b d +--R + +--R 2 +--R (- b - 7a)c d - 3a c +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 +--R (- b d + (- 3b - a)c d + (- 2b - a)c )cos(x) +--R + +--R 2 2 3 +--R (- 2b d + (- 8b - 2a)c d + (- 6b - 2a)c )cos(x) +--R + +--R 2 2 2 +--R (- 4b d + (- 4b + 2a)c d - 2b c )cos(x) +--R + +--R 2 2 2 +--R (- 6b d + (2b + 8a)c d + (4b + 4a)c )cos(x) - 3b d + (b + 5a)c d +--R + +--R 2 +--R (2b + 3a)c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 5 +--R (- b d - 2b c d - b c )cos(x) +--R + +--R 2 2 4 +--R (- 3b d + (- 5b + a)c d + (- 2b + a)c )cos(x) +--R + +--R 2 2 3 +--R (- 2b d + (- 2b + 2a)c d + 2a c )cos(x) +--R + +--R 2 2 2 +--R (2b d + 4b c d + 2b c )cos(x) +--R + +--R 2 2 2 2 +--R (3b d + (4b - 2a)c d + (b - 2a)c )cos(x) + b d + (b - a)c d - a c +--R / +--R 2 2 3 6 +--R (c d - 2c d + c )sin(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 2c d + 2c d)cos(x) + (- 4c d + 4c d)cos(x) - 3c d + 4c d +--R + +--R 3 +--R - c +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 2 3 3 +--R (c d - c )cos(x) + (4c d - 4c )cos(x) +--R + +--R 2 2 3 2 2 2 3 2 +--R (8c d - 2c d - 6c )cos(x) + (8c d - 4c d - 4c )cos(x) + 3c d +--R + +--R 2 3 +--R - 2c d - c +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 2 3 3 +--R (- c d + c )cos(x) + (- 4c d + 4c )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 6c d + 6c )cos(x) + (- 4c d + 4c )cos(x) - c d + c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 6 +--R (- c d + c )sin(x) +--R + +--R 2 2 2 2 2 2 2 3 4 +--R ((2c d + 2c d)cos(x) + (4c d + 4c d)cos(x) + 3c d + 2c d - c )sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- c d - 2c d - c )cos(x) + (- 4c d - 8c d - 4c )cos(x) +--R + +--R 2 2 3 2 2 2 3 +--R (- 8c d - 14c d - 6c )cos(x) + (- 8c d - 12c d - 4c )cos(x) +--R + +--R 2 2 3 +--R - 3c d - 4c d - c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (c d + 2c d + c )cos(x) + (4c d + 8c d + 4c )cos(x) +--R + +--R 2 2 3 2 2 2 3 2 2 +--R (6c d + 12c d + 6c )cos(x) + (4c d + 8c d + 4c )cos(x) + c d + 2c d +--R + +--R 3 +--R c +--R Type: Expression(Integer) +--E 12 + +--S 13 of 532 +t0702:= (a+b*csc(x))/(c+d*sin(x)) +--R +--R +--R b csc(x) + a +--R (13) ------------ +--R d sin(x) + c +--R Type: Expression(Integer) +--E 13 + +--S 14 of 532 +r0702:= 2*(a*c-b*d)*atan((d+c*tan(1/2*x))/(c^2-d^2)^(1/2))/c/(c^2-d^2)^(1/2)-_ + b*atanh(cos(x))/c +--R +--R +--R x +--R +---------+ c tan(-) + d +--R | 2 2 2 +--R - b\|- d + c atanh(cos(x)) + (- 2b d + 2a c)atan(------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R (14) ---------------------------------------------------------------- +--R +---------+ +--R | 2 2 +--R c\|- d + c +--R Type: Expression(Integer) +--E 14 + +--S 15 of 532 +a0702:= integrate(t0702,x) +--R +--R +--R (15) +--R [ +--R (b d - a c) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (c d sin(x) + (d - c )cos(x) + d )\|d - c +--R + +--R 2 3 3 2 3 2 +--R (c d - c )sin(x) + (d - c d)cos(x) + d - c d +--R / +--R d sin(x) + c +--R + +--R +-------+ +--R | 2 2 sin(x) +--R b\|d - c log(----------) +--R cos(x) + 1 +--R / +--R +-------+ +--R | 2 2 +--R c\|d - c +--R , +--R +--R +---------+ +--R | 2 2 sin(x) +--R b\|- d + c log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R (c sin(x) + d cos(x) + d)\|- d + c +--R (2b d - 2a c)atan(-------------------------------------) +--R 2 2 2 2 +--R (d - c )cos(x) + d - c +--R / +--R +---------+ +--R | 2 2 +--R c\|- d + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 15 + +--S 16 of 532 +m0702a:= a0702.1-r0702 +--R +--R +--R (16) +--R +---------+ +--R | 2 2 +--R (b d - a c)\|- d + c +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (c d sin(x) + (d - c )cos(x) + d )\|d - c +--R + +--R 2 3 3 2 3 2 +--R (c d - c )sin(x) + (d - c d)cos(x) + d - c d +--R / +--R d sin(x) + c +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) +--R b\|- d + c \|d - c log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R b\|- d + c \|d - c atanh(cos(x)) +--R + +--R x +--R +-------+ c tan(-) + d +--R | 2 2 2 +--R (2b d - 2a c)\|d - c atan(------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R c\|- d + c \|d - c +--R Type: Expression(Integer) +--E 16 + +--S 17 of 532 +d0702a:= D(m0702a,x) +--R +--R +--R (17) +--R 2 2 4 +--R b c d cos(x)sin(x) +--R + +--R 3 3 2 3 3 3 +--R ((b c d - b c d)cos(x) + (b c d + b c d)cos(x))sin(x) +--R + +--R 4 3 3 3 +--R (b d - a c d + a c d)cos(x) +--R + +--R 4 3 2 2 4 2 +--R (b d - a c d + b c d - b c )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- b d + a c d + b c d - a c d)cos(x) - b d + a c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 3 3 +--R (a c d - b c d)cos(x) + (b c d + b c d)cos(x) +--R + +--R 3 2 2 3 2 3 3 +--R (b c d - 2a c d + b c d)cos(x) + (- b c d - b c d)cos(x) +--R + +--R 3 2 2 +--R - b c d + a c d +--R * +--R sin(x) +--R + +--R 2 2 4 4 2 2 3 2 2 4 2 +--R (b c d - b c )cos(x) + b c d cos(x) + (- b c d + b c )cos(x) +--R + +--R 2 2 +--R - b c d cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 +--R 2b c d cos(x)sin(x) +--R + +--R 3 2 2 2 4 2 2 4 +--R (2a c d - 2b c d )cos(x) + (2b d + 2b c d )cos(x) + 2b d +--R + +--R 3 +--R - 2a c d +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 2 2 3 2 3 +--R 2b c d cos(x) + (2a c d - 2b c d)cos(x) + 2b c d +--R + +--R 2 2 +--R - 2a c d +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 4 +--R (2a c d - 2b c d )cos(x) +--R + +--R 3 2 2 3 3 +--R (2a c d + 4b c d - 2a c d)cos(x) +--R + +--R 3 2 2 2 +--R (- 2a c d + 2b c d )cos(x) +--R + +--R 3 2 2 3 +--R (- 2a c d - 4b c d + 2a c d)cos(x) +--R * +--R sin(x) +--R + +--R 3 3 4 3 3 +--R (2b c d - 2b c d)cos(x) + 2b c d cos(x) +--R + +--R 3 3 2 3 +--R (- 2b c d + 2b c d)cos(x) - 2b c d cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 +--R b c d cos(x)sin(x) +--R + +--R 3 3 2 3 3 3 +--R ((b c d - b c d)cos(x) + (b c d + b c d)cos(x))sin(x) +--R + +--R 4 3 3 3 +--R (b d - a c d + a c d)cos(x) +--R + +--R 4 3 2 2 4 2 +--R (b d - a c d + b c d - b c )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- b d + a c d + b c d - a c d)cos(x) - b d + a c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 3 3 +--R (a c d - b c d)cos(x) + (b c d + b c d)cos(x) +--R + +--R 3 2 2 3 2 3 3 +--R (b c d - 2a c d + b c d)cos(x) + (- b c d - b c d)cos(x) +--R + +--R 3 2 2 +--R - b c d + a c d +--R * +--R sin(x) +--R + +--R 2 2 4 4 2 2 3 2 2 4 2 +--R (b c d - b c )cos(x) + b c d cos(x) + (- b c d + b c )cos(x) +--R + +--R 2 2 +--R - b c d cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 2 3 4 4 +--R (b c d - b c d)cos(x)sin(x) +--R + +--R 4 3 2 2 4 5 3 +--R ((b c d - b c d )cos(x) + (b c d - b c )cos(x))sin(x) +--R + +--R 5 4 3 2 4 3 +--R (b d - a c d + a c d - b c d)cos(x) +--R + +--R 5 4 3 2 4 2 +--R (b d - a c d + a c d - b c d)cos(x) +--R + +--R 5 4 2 3 3 2 5 4 +--R (- b d + a c d + b c d - a c d )cos(x) - b d + a c d +--R + +--R 2 3 3 2 +--R b c d - a c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 4 4 5 3 +--R (a c d - a c d)cos(x) + (b c d - b c )cos(x) +--R + +--R 4 2 3 3 2 4 2 +--R (b c d - 2a c d - b c d + 2a c d)cos(x) +--R + +--R 4 5 4 2 3 3 2 4 +--R (- b c d + b c )cos(x) - b c d + a c d + b c d - a c d +--R * +--R sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (b c d - b c d)cos(x) + (b c d - b c d)cos(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- b c d + b c d)cos(x) + (- b c d + b c d)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 4 +--R (2b c d - 2b c d )cos(x)sin(x) +--R + +--R 4 3 2 2 5 4 5 +--R (2a c d - 2a c d )cos(x) + (2b d - 2b c d)cos(x) + 2b d +--R + +--R 4 2 3 3 2 +--R - 2a c d - 2b c d + 2a c d +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 3 2 3 4 2 4 +--R (2b c d - 2b c d )cos(x) + (2a c d - 2a c d)cos(x) + 2b c d +--R + +--R 2 3 3 2 4 +--R - 2a c d - 2b c d + 2a c d +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 4 +--R (2a c d - 2a c d )cos(x) +--R + +--R 4 2 3 3 2 4 3 +--R (2a c d + 2b c d - 2a c d - 2b c d)cos(x) +--R + +--R 4 3 2 2 +--R (- 2a c d + 2a c d )cos(x) +--R + +--R 4 2 3 3 2 4 +--R (- 2a c d - 2b c d + 2a c d + 2b c d)cos(x) +--R * +--R sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (2b c d - 2b c d )cos(x) + (2b c d - 2b c d )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 2b c d + 2b c d )cos(x) + (- 2b c d + 2b c d )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 4 +--R (b c d - b c d)cos(x)sin(x) +--R + +--R 4 3 2 2 4 5 3 +--R ((b c d - b c d )cos(x) + (b c d - b c )cos(x))sin(x) +--R + +--R 5 4 3 2 4 3 +--R (b d - a c d + a c d - b c d)cos(x) +--R + +--R 5 4 3 2 4 2 +--R (b d - a c d + a c d - b c d)cos(x) +--R + +--R 5 4 2 3 3 2 5 4 2 3 +--R (- b d + a c d + b c d - a c d )cos(x) - b d + a c d + b c d +--R + +--R 3 2 +--R - a c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 4 4 5 3 +--R (a c d - a c d)cos(x) + (b c d - b c )cos(x) +--R + +--R 4 2 3 3 2 4 2 4 5 +--R (b c d - 2a c d - b c d + 2a c d)cos(x) + (- b c d + b c )cos(x) +--R + +--R 4 2 3 3 2 4 +--R - b c d + a c d + b c d - a c d +--R * +--R sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (b c d - b c d)cos(x) + (b c d - b c d)cos(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- b c d + b c d)cos(x) + (- b c d + b c d)cos(x) +--R / +--R 3 2 2 3 2 3 +--R (c d cos(x) - c d )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (c d - c d)cos(x) + (c d + c d)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- c d + c d)cos(x) - c d - c d +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 3 2 5 3 2 +--R ((c d - c )cos(x) + c d cos(x) + (- c d + c )cos(x) - c d ) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 3 3 +--R (2c d cos(x) - 2c d )sin(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (2c d - 2c d )cos(x) + (2c d + 2c d )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (- 2c d + 2c d )cos(x) - 2c d - 2c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 3 2 3 2 2 3 4 +--R (2c d - 2c d)cos(x) + 2c d cos(x) + (- 2c d + 2c d)cos(x) +--R + +--R 2 3 +--R - 2c d +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 3 +--R (c d cos(x) - c d )sin(x) +--R + +--R 2 3 4 3 2 3 4 2 2 3 4 +--R (c d - c d)cos(x) + (c d + c d)cos(x) + (- c d + c d)cos(x) +--R + +--R 2 3 4 +--R - c d - c d +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 3 2 5 3 2 +--R ((c d - c )cos(x) + c d cos(x) + (- c d + c )cos(x) - c d )sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 3 3 5 2 3 3 5 3 +--R ((c d - c d)cos(x) - c d + c d)sin(x) +--R + +--R 2 4 4 2 3 2 4 6 2 2 4 4 2 +--R (c d - c d )cos(x) + (c d - c )cos(x) + (- c d + c d )cos(x) +--R + +--R 2 4 6 +--R - c d + c +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 3 3 3 5 2 3 3 5 +--R (c d - c d)cos(x) + (c d - c d)cos(x) + (- c d + c d)cos(x) +--R + +--R 3 3 5 +--R - c d + c d +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 2 4 4 2 3 +--R ((2c d - 2c d )cos(x) - 2c d + 2c d )sin(x) +--R + +--R 5 3 3 3 5 5 2 +--R (2c d - 2c d )cos(x) + (2c d - 2c d)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 2c d + 2c d )cos(x) - 2c d + 2c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (2c d - 2c d )cos(x) + (2c d - 2c d )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2c d + 2c d )cos(x) - 2c d + 2c d +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 5 2 3 3 5 3 +--R ((c d - c d)cos(x) - c d + c d)sin(x) +--R + +--R 2 4 4 2 3 2 4 6 2 2 4 4 2 +--R (c d - c d )cos(x) + (c d - c )cos(x) + (- c d + c d )cos(x) +--R + +--R 2 4 6 +--R - c d + c +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 3 3 3 5 2 3 3 5 +--R (c d - c d)cos(x) + (c d - c d)cos(x) + (- c d + c d)cos(x) +--R + +--R 3 3 5 +--R - c d + c d +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 17 + +--S 18 of 532 +m0702b:= a0702.2-r0702 +--R +--R +--R (18) +--R +---------+ +---------+ +--R | 2 2 sin(x) | 2 2 +--R b\|- d + c log(----------) + b\|- d + c atanh(cos(x)) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R (c sin(x) + d cos(x) + d)\|- d + c +--R (2b d - 2a c)atan(-------------------------------------) +--R 2 2 2 2 +--R (d - c )cos(x) + d - c +--R + +--R x +--R c tan(-) + d +--R 2 +--R (2b d - 2a c)atan(------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R / +--R +---------+ +--R | 2 2 +--R c\|- d + c +--R Type: Expression(Integer) +--E 18 + +--S 19 of 532 +d0702b:= D(m0702b,x) +--R +--R +--R (19) +--R 2 4 +--R b c cos(x)sin(x) +--R + +--R 2 2 2 3 +--R ((b c d + a c )cos(x) + 2b c d cos(x) + b c d - a c )sin(x) +--R + +--R 2 2 3 2 2 2 +--R (2b d - 2a c d + 2b c )cos(x) + (2b d - 2a c d + 2b c )cos(x) +--R + +--R 2 2 +--R (- 2b d + 2a c d)cos(x) - 2b d + 2a c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 3 2 2 +--R (b c d + a c )cos(x) + 2b c d cos(x) - 2a c cos(x) +--R + +--R 2 +--R - 2b c d cos(x) - b c d + a c +--R * +--R sin(x) +--R + +--R 2 5 2 4 2 2 2 +--R b c cos(x) + 2b c cos(x) - 2b c cos(x) - b c cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 +--R 2b c d cos(x)sin(x) +--R + +--R 2 2 2 3 +--R (4a c d cos(x) + 4b d cos(x) + 4b d - 4a c d)sin(x) +--R + +--R 3 2 2 +--R (4b c d cos(x) + 4b c d cos(x) )sin(x) +--R + +--R 4 3 2 +--R (4a c d cos(x) + 4a c d cos(x) - 4a c d cos(x) - 4a c d cos(x)) +--R * +--R sin(x) +--R + +--R 5 4 2 +--R 2b c d cos(x) + 4b c d cos(x) - 4b c d cos(x) - 2b c d cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 +--R b c cos(x)sin(x) +--R + +--R 2 2 2 3 +--R ((b c d + a c )cos(x) + 2b c d cos(x) + b c d - a c )sin(x) +--R + +--R 2 2 3 2 2 2 +--R (2b d - 2a c d + 2b c )cos(x) + (2b d - 2a c d + 2b c )cos(x) +--R + +--R 2 2 +--R (- 2b d + 2a c d)cos(x) - 2b d + 2a c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 3 2 2 +--R (b c d + a c )cos(x) + 2b c d cos(x) - 2a c cos(x) - 2b c d cos(x) +--R + +--R 2 +--R - b c d + a c +--R * +--R sin(x) +--R + +--R 2 5 2 4 2 2 2 +--R b c cos(x) + 2b c cos(x) - 2b c cos(x) - b c cos(x) +--R / +--R 3 2 3 3 +--R (c cos(x) - c )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (2c d cos(x) + 2c d cos(x) - 2c d cos(x) - 2c d)sin(x) +--R + +--R 3 4 3 3 3 3 +--R (c cos(x) + 2c cos(x) - 2c cos(x) - c )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 +--R (2c d cos(x) - 2c d)sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (4c d cos(x) + 4c d cos(x) - 4c d cos(x) - 4c d )sin(x) +--R + +--R 2 4 2 3 2 2 +--R (2c d cos(x) + 4c d cos(x) - 4c d cos(x) - 2c d)sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 3 +--R (c cos(x) - c )sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (2c d cos(x) + 2c d cos(x) - 2c d cos(x) - 2c d)sin(x) +--R + +--R 3 4 3 3 3 3 +--R (c cos(x) + 2c cos(x) - 2c cos(x) - c )sin(x) +--R Type: Expression(Integer) +--E 19 + +--S 20 of 532 +t0703:= (a+b*sec(x)^2)/(c+d*cos(x)) +--R +--R +--R 2 +--R b sec(x) + a +--R (20) ------------- +--R d cos(x) + c +--R Type: Expression(Integer) +--E 20 + +--S 21 of 532 +r0703:= 2*(a*c^2+b*d^2)*atan((c-d)*tan(1/2*x)/(c^2-d^2)^(1/2))/c^2/_ + (c^2-d^2)^(1/2)-b*d*atanh(sin(x))/c^2+b*tan(x)/c +--R +--R +--R (21) +--R x +--R +---------+ (d - c)tan(-) +--R | 2 2 2 2 2 +--R - b d\|- d + c atanh(sin(x)) + (- 2b d - 2a c )atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +---------+ +--R | 2 2 +--R b c tan(x)\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R c \|- d + c +--R Type: Expression(Integer) +--E 21 + +--S 22 of 532 +a0703:= integrate(t0703,x) +--R +--R +--R (22) +--R [ +--R +-------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - b d cos(x)\|d - c log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R b d cos(x)\|d - c log(-------------------) +--R cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 2 2 +--R 2 2 (- c cos(x) - d)\|d - c + (- d + c )sin(x) +--R (b d + a c )cos(x)log(----------------------------------------------) +--R d cos(x) + c +--R + +--R +-------+ +--R | 2 2 +--R b c sin(x)\|d - c +--R / +--R +-------+ +--R 2 | 2 2 +--R c cos(x)\|d - c +--R , +--R +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - b d cos(x)\|- d + c log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R b d cos(x)\|- d + c log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +---------+ +--R 2 2 sin(x)\|- d + c | 2 2 +--R (2b d + 2a c )cos(x)atan(---------------------) + b c sin(x)\|- d + c +--R (d + c)cos(x) + d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R c cos(x)\|- d + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 22 + +--S 23 of 532 +m0703a:= a0703.1-r0703 +--R +--R +--R (23) +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) + cos(x) + 1 +--R - b d cos(x)\|- d + c \|d - c log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) - cos(x) - 1 +--R b d cos(x)\|- d + c \|d - c log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R 2 2 | 2 2 +--R (b d + a c )cos(x)\|- d + c +--R * +--R +-------+ +--R | 2 2 2 2 +--R (- c cos(x) - d)\|d - c + (- d + c )sin(x) +--R log(----------------------------------------------) +--R d cos(x) + c +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R b d cos(x)\|- d + c \|d - c atanh(sin(x)) +--R + +--R x +--R +-------+ (d - c)tan(-) +--R 2 2 | 2 2 2 +--R (2b d + 2a c )cos(x)\|d - c atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R (- b c cos(x)tan(x) + b c sin(x))\|- d + c \|d - c +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R c cos(x)\|- d + c \|d - c +--R Type: Expression(Integer) +--E 23 + +--S 24 of 532 +d0703a:= D(m0703a,x) +--R +--R +--R (24) +--R 2 2 3 4 +--R (- b c d + b c d)cos(x) +--R + +--R 3 2 2 3 4 3 +--R (- b c d + b c d - b c d + b c )cos(x) +--R + +--R 2 2 3 2 +--R (- b c d + b c d)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 +--R (b c d - b c d)cos(x) +--R + +--R 3 2 2 3 4 5 +--R (b c d + b c d - b c d - b c )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (2b c d + b c d - b c d - 2b c )cos(x) +--R + +--R 3 4 3 2 2 3 2 +--R (2b c d - 2b c )cos(x) + (2b c d - 2b c d)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 +--R (- b c d + b c d)cos(x) +--R + +--R 3 2 2 3 4 5 +--R (- b c d - b c d + b c d + b c )cos(x) +--R + +--R 3 4 4 +--R (- 2b c d + 2b c )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (- b c d - b c d + b c d + b c )cos(x) +--R + +--R 2 2 3 2 +--R (- b c d + b c d)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 4 +--R (b c d + b c d)cos(x) +--R + +--R 3 2 2 3 4 3 +--R (b c d + b c d + b c d + b c )cos(x) +--R + +--R 2 2 3 2 +--R (b c d + b c d)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 +--R (- b c d - b c d)cos(x) +--R + +--R 3 2 2 3 4 5 +--R (- b c d - 3b c d - 3b c d - b c )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (- 2b c d - 5b c d - 5b c d - 2b c )cos(x) +--R + +--R 3 2 2 3 4 3 +--R (- 2b c d - 4b c d - 4b c d - 2b c )cos(x) +--R + +--R 2 2 3 2 +--R (- 2b c d - 2b c d)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 +--R (b c d + b c d)cos(x) +--R + +--R 3 2 2 3 4 5 +--R (b c d + 3b c d + 3b c d + b c )cos(x) +--R + +--R 3 2 2 3 4 4 +--R (2b c d + 4b c d + 4b c d + 2b c )cos(x) +--R + +--R 3 2 2 3 4 3 2 2 3 2 +--R (b c d + 3b c d + 3b c d + b c )cos(x) + (b c d + b c d)cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 2 3 2 +--R (b d - b c d + (b + a)c d + (- b - a)c d)cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (b c d - b c d + b c d - b c )cos(x) + b c d - b c d +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (3b c d - 3b c d + (b + a)c d)cos(x) +--R + +--R 4 2 2 3 4 3 +--R (b d + (b - a)c d + (- b + 3a)c d + b c )cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b d + 3b c d + (- 3b - 2a)c d + (b + 3a)c d + 2b c ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 4 2 2 3 +--R (- 2b c d + 2b c )cos(x) - 2b c d + 2b c d +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- b d + 2b c d + (- 2b - a)c d )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b d - 2b c d + (b - 3a)c d + (- 2b - a)c d)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b d - 5b c d + (2b - 3a)c d + (- 2b - 4a)c d)cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (- 2b d - 2b c d - 2b c d + (b - 6a)c d - b c )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (b d - 3b c d + (2b + a)c d - 3a c d - 2b c )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (b c d + b c d - b c d - b c )cos(x) + b c d - b c d +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 +--R (b c d - b c d )cos(x) +--R + +--R 4 3 2 2 3 6 +--R (2b d - b c d + (b + a)c d - b c d)cos(x) +--R + +--R 4 3 2 2 3 5 +--R (3b d + b c d + 3a c d + a c d)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (2b d + 4b c d + (- b + 3a)c d + (b + 3a)c d)cos(x) +--R + +--R 4 3 2 2 3 3 +--R (b d + 2b c d + (b + a)c d + 3a c d)cos(x) +--R + +--R 3 3 2 +--R (b c d + a c d)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (- b d - b c d + (- b - a)c d + (- b - a)c d)cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- b c d - b c d - b c d - b c )cos(x) - b c d - b c d +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- b c d - b c d + (b + a)c d)cos(x) +--R + +--R 4 2 2 3 4 3 +--R (b d + (b + 3a)c d + (b + a)c d + b c )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (2b d + 3b c d + (3b + 2a)c d + (5b + 3a)c d + 2b c )cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (2b c d + 4b c d + 4b c d + 2b c )cos(x) + 2b c d + 2b c d +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (b d - 2b c d + (- 2b + a)c d )cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b d - 2b c d + (- 3b + a)c d + (- 2b + a)c d)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b d - b c d + (- 2b - a)c d - 2b c d)cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- 2b d - 2b c d + (- 2b - 4a)c d + (- b - 2a)c d - b c ) +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 2 3 4 +--R (- b d - 3b c d + (- 2b - a)c d + (- 4b - 3a)c d - 2b c ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 2 2 3 +--R (- b c d - 3b c d - 3b c d - b c )cos(x) - b c d - b c d +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 +--R (- b c d - b c d )cos(x) +--R + +--R 4 3 2 2 3 6 +--R (- 2b d - b c d + (- b - a)c d - b c d)cos(x) +--R + +--R 4 3 2 2 3 5 +--R (- b d - b c d - a c d - a c d)cos(x) +--R + +--R 4 2 2 3 4 +--R (2b d + (b + a)c d + (b - a)c d)cos(x) +--R + +--R 4 3 2 2 3 3 3 3 2 +--R (b d + 2b c d + (b + a)c d + a c d)cos(x) + (b c d + a c d)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 4 2 3 3 2 4 3 +--R (- b c d + b c d + b c d - b c d)cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (- b c d + b c d + b c d - b c )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (b c d - b c d - b c d + b c d)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (2b c d - b c d - 3b c d + b c d + b c )cos(x) +--R + +--R 4 3 2 5 3 +--R (2b c d - 4b c d + 2b c )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (2b c d - 2b c d - 2b c d + 2b c )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- b c d + b c d + b c d - b c d)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 2b c d + b c d + 3b c d - b c d - b c )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (- b c d - b c d + 3b c d + b c d - 2b c )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (- b c d + b c d + b c d - b c )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 3 +--R (b c d + b c d - b c d - b c d)cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (b c d + b c d - b c d - b c )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (- b c d - b c d + b c d + b c d)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (- 2b c d - 3b c d + b c d + 3b c d + b c )cos(x) +--R + +--R 4 2 3 4 5 3 +--R (- 2b c d - 4b c d + 4b c d + 2b c )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (- 2b c d - 2b c d + 2b c d + 2b c )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 4 5 +--R (b c d + b c d - b c d - b c d)cos(x) +--R + +--R 4 2 3 3 2 4 5 4 +--R (2b c d + 3b c d - b c d - 3b c d - b c )cos(x) +--R + +--R 4 2 3 3 2 4 5 3 +--R (b c d + 3b c d + b c d - 3b c d - 2b c )cos(x) +--R + +--R 2 3 3 2 4 5 2 +--R (b c d + b c d - b c d - b c )cos(x) +--R * +--R sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 3 3 2 4 2 3 3 2 +--R (b c d - b c d - b c d + b c d)cos(x) + b c d - b c d +--R + +--R 4 5 +--R - b c d + b c +--R * +--R 7 +--R sin(x) +--R + +--R 5 4 2 3 3 2 4 +--R (3b d - 3b c d + (- 2b + a)c d + 3b c d + (- b - a)c d) +--R * +--R 3 +--R cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (b d + (- 2b + a)c d + b c d + (b - a)c d - b c )cos(x) +--R + +--R 4 3 2 5 2 3 3 2 4 +--R (- 2b c d + 4b c d - 2b c )cos(x) - 2b c d + 2b c d + 2b c d +--R + +--R 5 +--R - 2b c +--R * +--R 5 +--R sin(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (b d - 2b c d + (- b - a)c d + 2b c d + a c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 2b d + b c d - 3a c d - b c d + (2b + 3a)c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (- 6b d + 4b c d + (4b - 4a)c d - 4b c d + (2b + 4a)c d) +--R * +--R 3 +--R cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (- 2b d + (3b - 2a)c d - b c d + (- b + 2a)c d + b c )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 +--R (b c d + b c d - 3b c d - b c d + 2b c )cos(x) + b c d +--R + +--R 3 2 4 5 +--R - b c d - b c d + b c +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 2 3 3 2 6 +--R (b d - b c d - b c d + b c d )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (b d + b c d + (- 2b + a)c d - b c d + (b - a)c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (2b d + b c d + (- 2b + 3a)c d - b c d - 3a c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 +--R (3b d - b c d + (- 2b + 3a)c d + b c d + (- b - 3a)c d) +--R * +--R 3 +--R cos(x) +--R + +--R 5 2 3 4 2 +--R (b d + (- b + a)c d - a c d)cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 2 3 3 2 4 +--R (- b c d - b c d + b c d + b c d)cos(x) - b c d - b c d + b c d +--R + +--R 5 +--R b c +--R * +--R 7 +--R sin(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- b d - b c d + (2b + a)c d + b c d + (- b - a)c d)cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (- b d + (2b - a)c d + b c d + (- b + a)c d - b c )cos(x) +--R + +--R 4 2 3 4 5 2 3 3 2 +--R (2b c d + 4b c d - 4b c d - 2b c )cos(x) + 2b c d + 2b c d +--R + +--R 4 5 +--R - 2b c d - 2b c +--R * +--R 5 +--R sin(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 3b d - 2b c d + (3b - a)c d + 2b c d + a c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (- 2b d - 3b c d - a c d + 3b c d + (2b + a)c d)cos(x) +--R + +--R 5 2 3 4 3 +--R (2b d - 4b c d + 2b c d)cos(x) +--R + +--R 5 2 3 3 2 4 5 2 +--R (2b d + (- 3b + 2a)c d - b c d + (b - 2a)c d + b c )cos(x) +--R + +--R 4 2 3 3 2 4 5 2 3 +--R (- b c d - 3b c d - b c d + 3b c d + 2b c )cos(x) - b c d +--R + +--R 3 2 4 5 +--R - b c d + b c d + b c +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 2 3 3 2 6 +--R (- b d - b c d + b c d + b c d )cos(x) +--R + +--R 5 4 2 3 3 2 4 5 +--R (b d - b c d + (- 2b + a)c d + b c d + (b - a)c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 4 +--R (2b d + b c d + (- 2b + a)c d - b c d - a c d)cos(x) +--R + +--R 5 4 2 3 3 2 4 3 +--R (- b d + b c d + (2b - a)c d - b c d + (- b + a)c d)cos(x) +--R + +--R 5 2 3 4 2 +--R (- b d + (b - a)c d + a c d)cos(x) +--R * +--R sin(x) +--R / +--R 3 2 4 4 2 3 3 2 4 5 3 +--R (c d - c d)cos(x) + (c d - c d + c d - c )cos(x) +--R + +--R 3 2 4 2 +--R (c d - c d)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (- c d + c d)cos(x) + (- c d - c d + c d + c )cos(x) +--R + +--R 2 3 3 2 4 5 4 2 3 5 3 +--R (- 2c d - c d + c d + 2c )cos(x) + (- 2c d + 2c )cos(x) +--R + +--R 3 2 4 2 +--R (- 2c d + 2c d)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (c d - c d)cos(x) + (c d + c d - c d - c )cos(x) +--R + +--R 2 3 5 4 2 3 3 2 4 5 3 +--R (2c d - 2c )cos(x) + (c d + c d - c d - c )cos(x) +--R + +--R 3 2 4 2 +--R (c d - c d)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 2 3 3 2 4 5 3 +--R (- c d - c d)cos(x) + (- c d - c d - c d - c )cos(x) +--R + +--R 3 2 4 2 +--R (- c d - c d)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (c d + c d)cos(x) + (c d + 3c d + 3c d + c )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (2c d + 5c d + 5c d + 2c )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (2c d + 4c d + 4c d + 2c )cos(x) + (2c d + 2c d)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 6 2 3 3 2 4 5 5 +--R (- c d - c d)cos(x) + (- c d - 3c d - 3c d - c )cos(x) +--R + +--R 2 3 3 2 4 5 4 +--R (- 2c d - 4c d - 4c d - 2c )cos(x) +--R + +--R 2 3 3 2 4 5 3 3 2 4 2 +--R (- c d - 3c d - 3c d - c )cos(x) + (- c d - c d)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 2 4 3 3 4 2 5 3 +--R (c d - c d - c d + c d)cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (c d - c d - c d + c )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- c d + c d + c d - c d)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 2c d + c d + 3c d - c d - c )cos(x) +--R + +--R 2 4 4 2 6 3 +--R (- 2c d + 4c d - 2c )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- 2c d + 2c d + 2c d - 2c )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (c d - c d - c d + c d)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (2c d - c d - 3c d + c d + c )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (c d + c d - 3c d - c d + 2c )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (c d - c d - c d + c )cos(x) +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 3 3 4 2 5 3 +--R (- c d - c d + c d + c d)cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- c d - c d + c d + c )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (c d + c d - c d - c d)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (2c d + 3c d - c d - 3c d - c )cos(x) +--R + +--R 2 4 3 3 5 6 3 +--R (2c d + 4c d - 4c d - 2c )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (2c d + 2c d - 2c d - 2c )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 3 3 4 2 5 5 +--R (- c d - c d + c d + c d)cos(x) +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (- 2c d - 3c d + c d + 3c d + c )cos(x) +--R + +--R 2 4 3 3 4 2 5 6 3 +--R (- c d - 3c d - c d + 3c d + 2c )cos(x) +--R + +--R 3 3 4 2 5 6 2 +--R (- c d - c d + c d + c )cos(x) +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 24 + +--S 25 of 532 +m0703b:= a0703.2-r0703 +--R +--R +--R (25) +--R +---------+ +--R | 2 2 sin(x) + cos(x) + 1 +--R - b d cos(x)\|- d + c log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 sin(x) - cos(x) - 1 +--R b d cos(x)\|- d + c log(-------------------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R b d cos(x)\|- d + c atanh(sin(x)) +--R + +--R +---------+ +--R | 2 2 +--R 2 2 sin(x)\|- d + c +--R (2b d + 2a c )cos(x)atan(---------------------) +--R (d + c)cos(x) + d + c +--R + +--R x +--R (d - c)tan(-) +--R 2 2 2 +--R (2b d + 2a c )cos(x)atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +---------+ +--R | 2 2 +--R (- b c cos(x)tan(x) + b c sin(x))\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R c cos(x)\|- d + c +--R Type: Expression(Integer) +--E 25 + +--S 26 of 532 +d0703b:= D(m0703b,x) +--R +--R +--R (26) +--R 2 2 3 2 6 +--R (- b c d + 2b c d - b c )cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (2b c d - 2b c d)cos(x) + (4b c d - 4b c d)cos(x) +--R + +--R 2 2 3 2 +--R (3b c d - 4b c d + b c )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 6 2 3 5 +--R (- b c d + b c )cos(x) + (- 4b c d + 4b c )cos(x) +--R + +--R 2 2 3 4 +--R (- 8b c d + 2b c d + 6b c )cos(x) +--R + +--R 2 2 3 3 +--R (- 8b c d + 4b c d + 4b c )cos(x) +--R + +--R 2 2 3 2 +--R (- 3b c d + 2b c d + b c )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 6 2 3 5 +--R (b c d - b c )cos(x) + (4b c d - 4b c )cos(x) +--R + +--R 2 3 4 2 3 3 +--R (6b c d - 6b c )cos(x) + (4b c d - 4b c )cos(x) +--R + +--R 2 3 2 +--R (b c d - b c )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 6 +--R (b c d - b c )cos(x) sin(x) +--R + +--R 2 2 4 2 2 3 +--R (- 2b c d - 2b c d)cos(x) + (- 4b c d - 4b c d)cos(x) +--R + +--R 2 2 3 2 +--R (- 3b c d - 2b c d + b c )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 6 +--R (b c d + 2b c d + b c )cos(x) +--R + +--R 2 2 3 5 +--R (4b c d + 8b c d + 4b c )cos(x) +--R + +--R 2 2 3 4 +--R (8b c d + 14b c d + 6b c )cos(x) +--R + +--R 2 2 3 3 +--R (8b c d + 12b c d + 4b c )cos(x) +--R + +--R 2 2 3 2 +--R (3b c d + 4b c d + b c )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 6 +--R (- b c d - 2b c d - b c )cos(x) +--R + +--R 2 2 3 5 +--R (- 4b c d - 8b c d - 4b c )cos(x) +--R + +--R 2 2 3 4 +--R (- 6b c d - 12b c d - 6b c )cos(x) +--R + +--R 2 2 3 3 2 2 3 2 +--R (- 4b c d - 8b c d - 4b c )cos(x) + (- b c d - 2b c d - b c )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 3 8 +--R (b c d - 2b c d + b c )sin(x) +--R + +--R 3 2 2 3 2 +--R (b d - 5b c d + (4b - a)c d + a c )cos(x) +--R + +--R 2 2 2 2 3 +--R (- 4b c d + 4b c d)cos(x) - 3b c d + 4b c d - b c +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- 2b d - 3b c d + (4b - 2a)c d - b c )cos(x) +--R + +--R 3 2 3 3 +--R (- 5b d + (5b - 2a)c d + (- 4b - 2a)c )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 3b d + 9b c d + (- 2b + a)c d + (- 6b - 3a)c )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (8b c d - 4b c d - 4b c )cos(x) + 3b c d - 2b c d - b c +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 6 +--R (b d - b c d + (2b + 3a)c d - a c )cos(x) +--R + +--R 3 2 2 3 5 +--R (6b d - 4b c d + (6b + 10a)c d - 2a c )cos(x) +--R + +--R 3 2 2 3 4 +--R (12b d - b c d + (2b + 14a)c d + b c )cos(x) +--R + +--R 3 2 2 3 3 +--R (10b d + 2b c d + (- 4b + 8a)c d + (4b + 4a)c )cos(x) +--R + +--R 3 2 2 3 2 +--R (3b d - 3b c d + (- 2b + a)c d + (6b + 3a)c )cos(x) +--R + +--R 2 3 2 3 +--R (- 4b c d + 4b c )cos(x) - b c d + b c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 7 +--R (- b d + b c d)cos(x) +--R + +--R 3 2 2 3 6 +--R (- 5b d + b c d + (2b - 3a)c d + a c )cos(x) +--R + +--R 3 2 2 3 5 +--R (- 10b d + 2b c d - 10a c d + 2a c )cos(x) +--R + +--R 3 2 4 +--R (- 10b d + (- 2b - 12a)c d)cos(x) +--R + +--R 3 2 2 3 3 +--R (- 5b d - 2b c d + (- b - 6a)c d - 2a c )cos(x) +--R + +--R 3 2 2 3 2 +--R (- b d - b c d - a c d - a c )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 8 +--R (- b c d + b c )sin(x) +--R + +--R 3 2 2 3 2 +--R (b d + 3b c d + (4b + 3a)c d + a c )cos(x) +--R + +--R 2 2 2 2 3 +--R (4b c d + 4b c d)cos(x) + 3b c d + 2b c d - b c +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 3 4 +--R (- 2b d + 3b c d + (2b - 2a)c d - b c )cos(x) +--R + +--R 3 2 2 3 3 +--R (- 3b d + 2b c d + (- 3b - 6a)c d + (- 4b - 2a)c )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 3b d - 7b c d + (- 14b - 7a)c d + (- 6b - 3a)c )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 8b c d - 12b c d - 4b c )cos(x) - 3b c d - 4b c d - b c +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 6 +--R (b d + 3b c d + (2b - a)c d - a c )cos(x) +--R + +--R 3 2 2 3 5 +--R (2b d + 8b c d + (6b - 2a)c d - 2a c )cos(x) +--R + +--R 3 2 2 3 4 +--R (4b d + 5b c d + (4b + 2a)c d + b c )cos(x) +--R + +--R 3 2 2 3 3 +--R (6b d + 2b c d + (4b + 8a)c d + (4b + 4a)c )cos(x) +--R + +--R 3 2 2 3 2 +--R (3b d + 5b c d + (10b + 5a)c d + (6b + 3a)c )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (4b c d + 8b c d + 4b c )cos(x) + b c d + 2b c d + b c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 +--R (b d + 2b c d + b c d)cos(x) +--R + +--R 3 2 2 3 6 +--R (3b d + 5b c d + (2b + a)c d + a c )cos(x) +--R + +--R 3 2 2 3 5 +--R (2b d + 2b c d + 2a c d + 2a c )cos(x) +--R + +--R 3 2 2 4 +--R (- 2b d - 4b c d - 2b c d)cos(x) +--R + +--R 3 2 2 3 3 +--R (- 3b d - 4b c d + (- b - 2a)c d - 2a c )cos(x) +--R + +--R 3 2 2 3 2 +--R (- b d - b c d - a c d - a c )cos(x) +--R / +--R 2 2 3 4 2 6 +--R (c d - 2c d + c )cos(x) sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (- 2c d + 2c d)cos(x) + (- 4c d + 4c d)cos(x) +--R + +--R 2 2 3 4 2 +--R (- 3c d + 4c d - c )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (c d - c )cos(x) + (4c d - 4c )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (8c d - 2c d - 6c )cos(x) + (8c d - 4c d - 4c )cos(x) +--R + +--R 2 2 3 4 2 +--R (3c d - 2c d - c )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 6 2 2 4 5 +--R (- c d + c )cos(x) + (- 4c d + 4c )cos(x) +--R + +--R 2 2 4 4 2 2 4 3 2 2 4 2 +--R (- 6c d + 6c )cos(x) + (- 4c d + 4c )cos(x) + (- c d + c )cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 6 +--R (- c d + c )cos(x) sin(x) +--R + +--R 2 2 3 4 2 2 3 3 +--R (2c d + 2c d)cos(x) + (4c d + 4c d)cos(x) +--R + +--R 2 2 3 4 2 +--R (3c d + 2c d - c )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 3 4 6 2 2 3 4 5 +--R (- c d - 2c d - c )cos(x) + (- 4c d - 8c d - 4c )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (- 8c d - 14c d - 6c )cos(x) + (- 8c d - 12c d - 4c )cos(x) +--R + +--R 2 2 3 4 2 +--R (- 3c d - 4c d - c )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 6 2 2 3 4 5 +--R (c d + 2c d + c )cos(x) + (4c d + 8c d + 4c )cos(x) +--R + +--R 2 2 3 4 4 2 2 3 4 3 +--R (6c d + 12c d + 6c )cos(x) + (4c d + 8c d + 4c )cos(x) +--R + +--R 2 2 3 4 2 +--R (c d + 2c d + c )cos(x) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 532 +t0704:= (a+b*csc(x)^2)/(c+d*sin(x)) +--R +--R +--R 2 +--R b csc(x) + a +--R (27) ------------- +--R d sin(x) + c +--R Type: Expression(Integer) +--E 27 + +--S 28 of 532 +r0704:= 2*(a*c^2+b*d^2)*atan((d+c*tan(1/2*x))/(c^2-d^2)^(1/2))/c^2/_ + (c^2-d^2)^(1/2)+b*d*atanh(cos(x))/c^2-b*cot(x)/c +--R +--R +--R (28) +--R x +--R +---------+ c tan(-) + d +--R | 2 2 2 2 2 +--R b d\|- d + c atanh(cos(x)) + (2b d + 2a c )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +---------+ +--R | 2 2 +--R - b c cot(x)\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R c \|- d + c +--R Type: Expression(Integer) +--E 28 + +--S 29 of 532 +a0704:= integrate(t0704,x) +--R +--R +--R (29) +--R [ +--R 2 2 +--R (b d + a c )sin(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (c d sin(x) + (d - c )cos(x) + d )\|d - c +--R + +--R 2 3 3 2 3 2 +--R (- c d + c )sin(x) + (- d + c d)cos(x) - d + c d +--R / +--R d sin(x) + c +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) | 2 2 +--R - b d sin(x)\|d - c log(----------) - b c cos(x)\|d - c +--R cos(x) + 1 +--R / +--R +-------+ +--R 2 | 2 2 +--R c sin(x)\|d - c +--R , +--R +--R +---------+ +--R | 2 2 sin(x) +--R - b d sin(x)\|- d + c log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R 2 2 (c sin(x) + d cos(x) + d)\|- d + c +--R (- 2b d - 2a c )sin(x)atan(-------------------------------------) +--R 2 2 2 2 +--R (d - c )cos(x) + d - c +--R + +--R +---------+ +--R | 2 2 +--R - b c cos(x)\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R c sin(x)\|- d + c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 29 + +--S 30 of 532 +m0704a:= a0704.1-r0704 +--R +--R +--R (30) +--R +---------+ +--R 2 2 | 2 2 +--R (b d + a c )sin(x)\|- d + c +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (c d sin(x) + (d - c )cos(x) + d )\|d - c +--R + +--R 2 3 3 2 3 2 +--R (- c d + c )sin(x) + (- d + c d)cos(x) - d + c d +--R / +--R d sin(x) + c +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 sin(x) +--R - b d sin(x)\|- d + c \|d - c log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R - b d sin(x)\|- d + c \|d - c atanh(cos(x)) +--R + +--R x +--R +-------+ c tan(-) + d +--R 2 2 | 2 2 2 +--R (- 2b d - 2a c )sin(x)\|d - c atan(------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R (b c cot(x)sin(x) - b c cos(x))\|- d + c \|d - c +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R c sin(x)\|- d + c \|d - c +--R Type: Expression(Integer) +--E 30 + +--S 31 of 532 +d0704a:= D(m0704a,x) +--R +--R +--R (31) +--R 2 3 5 +--R - b c d cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- b c d cos(x) + b c d )cot(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- b c d + b c d )cos(x) + (- b c d - b c d )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- b c d + b c d)cos(x) + (- b c d - b c d)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (b c d - b c d)cos(x) + b c d + b c d +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 3 +--R (- b d - a c d + a c d)cos(x) +--R + +--R 5 2 3 4 2 +--R (- b d + (- b - a)c d + b c d)cos(x) +--R + +--R 5 2 3 4 5 2 3 +--R (b d + (- b + a)c d - a c d)cos(x) + b d + a c d +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 +--R (- b c d + b c )cos(x) - b c d cos(x) +--R + +--R 3 2 5 3 2 +--R (b c d - b c )cos(x) + b c d +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 4 3 2 3 +--R (2b + a)c d cos(x) + (- b c d - b c d )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- b c d + (- 2b - 2a)c d )cos(x) + (b c d + b c d )cos(x) +--R + +--R 4 3 2 +--R b c d + a c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 4 4 +--R (b c d - b c d)cos(x) + 2b c d cos(x) +--R + +--R 2 3 4 3 4 2 2 3 +--R (- 2b c d + b c d)cos(x) - 2b c d cos(x) + b c d cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 5 3 2 4 3 2 5 3 +--R (b c d - b c )cos(x) + b c d cos(x) + (- b c d + b c )cos(x) +--R + +--R 3 2 2 +--R - b c d cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 5 +--R - 2b c d cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 2 3 2 +--R (- 2b c d cos(x) + 2b c d )cot(x) + (2b + 2a)c d cos(x) +--R + +--R 5 2 3 5 2 3 +--R (- 2b d - 2b c d )cos(x) - 2b d - 2a c d +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 3 +--R (- 2b c d + 2b c d )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 2b c d - 2b c d )cos(x) + (2b c d - 2b c d )cos(x) +--R + +--R 4 3 2 +--R 2b c d + 2b c d +--R * +--R 2 +--R cot(x) +--R + +--R 4 3 3 2 2 4 3 2 +--R - 2b c d cos(x) + (2b + 2a)c d cos(x) - 2b c d - 2a c d +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 2b c d + 2b c d)cos(x) - 2b c d cos(x) +--R + +--R 2 3 4 2 3 +--R (2b c d - 2b c d)cos(x) + 2b c d +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 4 2 3 4 3 +--R (4b + 2a)c d cos(x) + ((- 4b + 2a)c d - 2a c d)cos(x) +--R + +--R 2 3 2 2 3 4 +--R (- 4b - 2a)c d cos(x) + ((4b - 2a)c d + 2a c d)cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 3 2 4 +--R (2b c d - 2b c d )cos(x) + 4b c d cos(x) +--R + +--R 4 3 2 3 3 2 2 4 +--R (- 4b c d + 2b c d )cos(x) - 4b c d cos(x) + 2b c d cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 +--R (2b c d - 2b c d)cos(x) + 2b c d cos(x) +--R + +--R 2 3 4 3 2 3 2 +--R (- 2b c d + 2b c d)cos(x) - 2b c d cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 5 +--R - b c d cos(x)sin(x) +--R + +--R 3 2 2 3 2 2 4 3 2 2 +--R (- b c d cos(x) + b c d )cot(x) + (- b c d + b c d )cos(x) +--R + +--R 4 3 2 +--R (- b c d - b c d )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- b c d + b c d)cos(x) + (- b c d - b c d)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (b c d - b c d)cos(x) + b c d + b c d +--R * +--R 2 +--R cot(x) +--R + +--R 5 2 3 4 3 +--R (- b d - a c d + a c d)cos(x) +--R + +--R 5 2 3 4 2 +--R (- b d + (- b - a)c d + b c d)cos(x) +--R + +--R 5 2 3 4 5 2 3 +--R (b d + (- b + a)c d - a c d)cos(x) + b d + a c d +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 5 3 3 2 2 +--R (- b c d + b c )cos(x) - b c d cos(x) +--R + +--R 3 2 5 3 2 +--R (b c d - b c )cos(x) + b c d +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 4 4 3 2 3 +--R (2b + a)c d cos(x) + (- b c d - b c d )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- b c d + (- 2b - 2a)c d )cos(x) + (b c d + b c d )cos(x) +--R + +--R 4 3 2 +--R b c d + a c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 5 4 4 +--R (b c d - b c d)cos(x) + 2b c d cos(x) +--R + +--R 2 3 4 3 4 2 2 3 +--R (- 2b c d + b c d)cos(x) - 2b c d cos(x) + b c d cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 5 3 2 4 3 2 5 3 +--R (b c d - b c )cos(x) + b c d cos(x) + (- b c d + b c )cos(x) +--R + +--R 3 2 2 +--R - b c d cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 2 4 4 2 5 +--R (b c d - b c d )cos(x)sin(x) +--R + +--R 3 3 5 2 3 3 5 2 +--R ((b c d - b c d)cos(x) - b c d + b c d)cot(x) +--R + +--R 5 3 3 2 5 5 +--R (b c d - b c d )cos(x) + (b c d - b c d)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 6 2 +--R (b c d - b c d )cos(x) + (b c d - b c )cos(x) +--R + +--R 2 4 4 2 2 4 6 +--R (- b c d + b c d )cos(x) - b c d + b c +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 4 2 3 +--R (b d + a c d + (- b - a)c d )cos(x) +--R + +--R 6 2 4 4 2 2 +--R (b d + a c d + (- b - a)c d )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (- b d + (b - a)c d + a c d )cos(x) - b d + (b - a)c d + a c d +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (b c d - b c d)cos(x) + (b c d - b c d)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- b c d + b c d)cos(x) - b c d + b c d +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 4 5 5 3 +--R ((- b - a)c d + (b + a)c d)cos(x) + (b c d - b c d)cos(x) +--R + +--R 5 3 3 5 2 +--R (b c d + 2a c d + (- b - 2a)c d)cos(x) +--R + +--R 5 5 5 3 3 5 +--R (- b c d + b c d)cos(x) - b c d + (b - a)c d + a c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 5 4 2 6 4 +--R (- b c d + b c d )cos(x) + (- b c d + b c )cos(x) +--R + +--R 2 4 4 2 3 4 2 6 2 +--R (2b c d - 2b c d )cos(x) + (b c d - b c )cos(x) +--R + +--R 2 4 4 2 +--R (- b c d + b c d )cos(x) +--R * +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- b c d + b c d)cos(x) + (- b c d + b c d)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (b c d - b c d)cos(x) + (b c d - b c d)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 5 +--R (2b c d - 2b c d )cos(x)sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 2 +--R ((2b c d - 2b c d )cos(x) - 2b c d + 2b c d )cot(x) +--R + +--R 2 4 4 2 2 6 4 2 6 +--R (- 2a c d + 2a c d )cos(x) + (2b d - 2b c d )cos(x) + 2b d +--R + +--R 2 4 4 2 +--R (- 2b + 2a)c d - 2a c d +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 3 5 5 2 +--R (2b c d - 2b c d )cos(x) + (2b c d - 2b c d)cos(x) +--R + +--R 5 3 3 5 5 +--R (- 2b c d + 2b c d )cos(x) - 2b c d + 2b c d +--R * +--R 2 +--R cot(x) +--R + +--R 5 3 3 3 3 3 5 2 +--R (2b c d - 2b c d )cos(x) + (- 2a c d + 2a c d)cos(x) +--R + +--R 5 3 3 5 +--R 2b c d + (- 2b + 2a)c d - 2a c d +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (2b c d - 2b c d )cos(x) + (2b c d - 2b c d )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2b c d + 2b c d )cos(x) - 2b c d + 2b c d +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 4 2 4 +--R ((- 2b - 2a)c d + (2b + 2a)c d )cos(x) +--R + +--R 2 4 4 2 3 +--R ((2b - 2a)c d + (- 2b + 2a)c d )cos(x) +--R + +--R 2 4 4 2 2 +--R ((2b + 2a)c d + (- 2b - 2a)c d )cos(x) +--R + +--R 2 4 4 2 +--R ((- 2b + 2a)c d + (2b - 2a)c d )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 3 3 5 4 +--R (- 2b c d + 2b c d )cos(x) + (- 2b c d + 2b c d)cos(x) +--R + +--R 5 3 3 3 3 3 5 2 +--R (4b c d - 4b c d )cos(x) + (2b c d - 2b c d)cos(x) +--R + +--R 5 3 3 +--R (- 2b c d + 2b c d )cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 2b c d + 2b c d )cos(x) + (- 2b c d + 2b c d )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (2b c d - 2b c d )cos(x) + (2b c d - 2b c d )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 5 +--R (b c d - b c d )cos(x)sin(x) +--R + +--R 3 3 5 2 3 3 5 2 +--R ((b c d - b c d)cos(x) - b c d + b c d)cot(x) +--R + +--R 5 3 3 2 5 5 +--R (b c d - b c d )cos(x) + (b c d - b c d)cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 3 2 4 6 2 +--R (b c d - b c d )cos(x) + (b c d - b c )cos(x) +--R + +--R 2 4 4 2 2 4 6 +--R (- b c d + b c d )cos(x) - b c d + b c +--R * +--R 2 +--R cot(x) +--R + +--R 6 2 4 4 2 3 +--R (b d + a c d + (- b - a)c d )cos(x) +--R + +--R 6 2 4 4 2 2 +--R (b d + a c d + (- b - a)c d )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 +--R (- b d + (b - a)c d + a c d )cos(x) - b d + (b - a)c d + a c d +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (b c d - b c d)cos(x) + (b c d - b c d)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- b c d + b c d)cos(x) - b c d + b c d +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 5 4 5 5 3 +--R ((- b - a)c d + (b + a)c d)cos(x) + (b c d - b c d)cos(x) +--R + +--R 5 3 3 5 2 5 5 +--R (b c d + 2a c d + (- b - 2a)c d)cos(x) + (- b c d + b c d)cos(x) +--R + +--R 5 3 3 5 +--R - b c d + (b - a)c d + a c d +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 5 4 2 6 4 +--R (- b c d + b c d )cos(x) + (- b c d + b c )cos(x) +--R + +--R 2 4 4 2 3 4 2 6 2 +--R (2b c d - 2b c d )cos(x) + (b c d - b c )cos(x) +--R + +--R 2 4 4 2 +--R (- b c d + b c d )cos(x) +--R * +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- b c d + b c d)cos(x) + (- b c d + b c d)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (b c d - b c d)cos(x) + (b c d - b c d)cos(x) +--R / +--R 4 2 2 4 2 4 +--R (c d cos(x) - c d )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (c d - c d)cos(x) + (c d + c d)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- c d + c d)cos(x) - c d - c d +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 6 3 4 2 2 4 2 6 4 2 +--R ((c d - c )cos(x) + c d cos(x) + (- c d + c )cos(x) - c d ) +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 3 3 4 +--R (2c d cos(x) - 2c d )sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (2c d - 2c d )cos(x) + (2c d + 2c d )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 2c d + 2c d )cos(x) - 2c d - 2c d +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 2 3 3 5 +--R (2c d - 2c d)cos(x) + 2c d cos(x) + (- 2c d + 2c d)cos(x) +--R + +--R 3 3 +--R - 2c d +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 2 4 +--R (c d cos(x) - c d )sin(x) +--R + +--R 3 3 5 3 3 3 5 2 3 3 5 +--R (c d - c d)cos(x) + (c d + c d)cos(x) + (- c d + c d)cos(x) +--R + +--R 3 3 5 +--R - c d - c d +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 6 3 4 2 2 4 2 6 4 2 2 +--R ((c d - c )cos(x) + c d cos(x) + (- c d + c )cos(x) - c d )sin(x) +--R * +--R +-------+ +--R | 2 2 +--R \|d - c +--R + +--R 4 3 6 2 4 3 6 4 +--R ((- c d + c d)cos(x) + c d - c d)sin(x) +--R + +--R 3 4 5 2 3 3 4 7 2 +--R (- c d + c d )cos(x) + (- c d + c )cos(x) +--R + +--R 3 4 5 2 3 4 7 +--R (c d - c d )cos(x) + c d - c +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 3 4 3 6 2 +--R (- c d + c d)cos(x) + (- c d + c d)cos(x) +--R + +--R 4 3 6 4 3 6 +--R (c d - c d)cos(x) + c d - c d +--R * +--R 2 +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 4 5 2 2 3 4 5 2 4 +--R ((- 2c d + 2c d )cos(x) + 2c d - 2c d )sin(x) +--R + +--R 2 5 4 3 3 2 5 6 2 +--R (- 2c d + 2c d )cos(x) + (- 2c d + 2c d)cos(x) +--R + +--R 2 5 4 3 2 5 6 +--R (2c d - 2c d )cos(x) + 2c d - 2c d +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 5 2 3 3 4 5 2 2 +--R (- 2c d + 2c d )cos(x) + (- 2c d + 2c d )cos(x) +--R + +--R 3 4 5 2 3 4 5 2 +--R (2c d - 2c d )cos(x) + 2c d - 2c d +--R * +--R 2 +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 6 2 4 3 6 4 +--R ((- c d + c d)cos(x) + c d - c d)sin(x) +--R + +--R 3 4 5 2 3 3 4 7 2 3 4 5 2 +--R (- c d + c d )cos(x) + (- c d + c )cos(x) + (c d - c d )cos(x) +--R + +--R 3 4 7 +--R c d - c +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 3 4 3 6 2 4 3 6 +--R (- c d + c d)cos(x) + (- c d + c d)cos(x) + (c d - c d)cos(x) +--R + +--R 4 3 6 +--R c d - c d +--R * +--R 2 +--R sin(x) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 532 +m0704b:= a0704.2-r0704 +--R +--R +--R (32) +--R +---------+ +--R | 2 2 sin(x) +--R - b d sin(x)\|- d + c log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R - b d sin(x)\|- d + c atanh(cos(x)) +--R + +--R +---------+ +--R | 2 2 +--R 2 2 (c sin(x) + d cos(x) + d)\|- d + c +--R (- 2b d - 2a c )sin(x)atan(-------------------------------------) +--R 2 2 2 2 +--R (d - c )cos(x) + d - c +--R + +--R x +--R c tan(-) + d +--R 2 2 2 +--R (- 2b d - 2a c )sin(x)atan(------------) +--R +---------+ +--R | 2 2 +--R \|- d + c +--R + +--R +---------+ +--R | 2 2 +--R (b c cot(x)sin(x) - b c cos(x))\|- d + c +--R / +--R +---------+ +--R 2 | 2 2 +--R c sin(x)\|- d + c +--R Type: Expression(Integer) +--E 32 + +--S 33 of 532 +d0704b:= D(m0704b,x) +--R +--R +--R (33) +--R 2 5 +--R - b c d cos(x)sin(x) +--R + +--R 3 2 3 2 2 3 2 +--R (- b c cos(x) + b c )cot(x) + (- b c d + a c )cos(x) +--R + +--R 2 2 3 +--R - 2b c d cos(x) - b c d - a c +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 +--R (- 2b c d cos(x) - 2b c d cos(x) + 2b c d cos(x) + 2b c d) +--R * +--R 2 +--R cot(x) +--R + +--R 3 2 3 +--R (- 2b d + (- 2b - 2a)c d)cos(x) +--R + +--R 3 2 2 3 2 +--R (- 2b d + (- 2b - 2a)c d)cos(x) + (2b d + 2a c d)cos(x) +--R + +--R 3 2 +--R 2b d + 2a c d +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (- b c cos(x) - 2b c cos(x) + 2b c cos(x) + b c )cot(x) +--R + +--R 2 3 4 2 3 +--R (- b c d + (b + a)c )cos(x) - 2b c d cos(x) +--R + +--R 3 2 2 2 3 +--R (- b - 2a)c cos(x) + 2b c d cos(x) + b c d + a c +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 +--R (b c d cos(x) - 2b c d cos(x) + b c d cos(x))sin(x) + b c cos(x) +--R + +--R 3 5 3 3 3 2 +--R 2b c cos(x) - 2b c cos(x) - b c cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - 2b c d cos(x)sin(x) +--R + +--R 2 2 2 2 2 2 3 +--R (- 2b c d cos(x) + 2b c d)cot(x) + 4a c d cos(x) - 4b d cos(x) +--R + +--R 3 2 +--R - 4b d - 4a c d +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 +--R (- 4b c d cos(x) - 4b c d cos(x) + 4b c d cos(x) + 4b c d ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 2 2 +--R - 4b c d cos(x) - 4b c d cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 2 2 +--R (- 2b c d cos(x) - 4b c d cos(x) + 4b c d cos(x) + 2b c d) +--R * +--R 2 +--R cot(x) +--R + +--R 2 4 2 3 2 2 +--R (2b + 4a)c d cos(x) + 4a c d cos(x) + (- 2b - 4a)c d cos(x) +--R + +--R 2 +--R - 4a c d cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 +--R (2b c d cos(x) - 4b c d cos(x) + 2b c d cos(x))sin(x) +--R + +--R 2 6 2 5 2 3 2 2 +--R 2b c d cos(x) + 4b c d cos(x) - 4b c d cos(x) - 2b c d cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 5 +--R - b c d cos(x)sin(x) +--R + +--R 3 2 3 2 2 3 2 +--R (- b c cos(x) + b c )cot(x) + (- b c d + a c )cos(x) +--R + +--R 2 2 3 +--R - 2b c d cos(x) - b c d - a c +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 2b c d cos(x) - 2b c d cos(x) + 2b c d cos(x) + 2b c d)cot(x) +--R + +--R 3 2 3 3 2 2 +--R (- 2b d + (- 2b - 2a)c d)cos(x) + (- 2b d + (- 2b - 2a)c d)cos(x) +--R + +--R 3 2 3 2 +--R (2b d + 2a c d)cos(x) + 2b d + 2a c d +--R * +--R 3 +--R sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (- b c cos(x) - 2b c cos(x) + 2b c cos(x) + b c )cot(x) +--R + +--R 2 3 4 2 3 3 2 +--R (- b c d + (b + a)c )cos(x) - 2b c d cos(x) + (- b - 2a)c cos(x) +--R + +--R 2 2 3 +--R 2b c d cos(x) + b c d + a c +--R * +--R 2 +--R sin(x) +--R + +--R 2 5 2 3 2 3 6 +--R (b c d cos(x) - 2b c d cos(x) + b c d cos(x))sin(x) + b c cos(x) +--R + +--R 3 5 3 3 3 2 +--R 2b c cos(x) - 2b c cos(x) - b c cos(x) +--R / +--R 4 2 4 4 +--R (c cos(x) - c )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2c d cos(x) + 2c d cos(x) - 2c d cos(x) - 2c d)sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (c cos(x) + 2c cos(x) - 2c cos(x) - c )sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 3 4 +--R (2c d cos(x) - 2c d)sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 3 +--R (4c d cos(x) + 4c d cos(x) - 4c d cos(x) - 4c d )sin(x) +--R + +--R 3 4 3 3 3 3 2 +--R (2c d cos(x) + 4c d cos(x) - 4c d cos(x) - 2c d)sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 4 4 +--R (c cos(x) - c )sin(x) +--R + +--R 3 3 3 2 3 3 3 +--R (2c d cos(x) + 2c d cos(x) - 2c d cos(x) - 2c d)sin(x) +--R + +--R 4 4 4 3 4 4 2 +--R (c cos(x) + 2c cos(x) - 2c cos(x) - c )sin(x) +--R Type: Expression(Integer) +--E 33 + +--S 34 of 532 +t0705:= (tan(x)*sin(x))^(1/2) +--R +--R +--R +------------+ +--R (34) \|sin(x)tan(x) +--R Type: Expression(Integer) +--E 34 + +--S 35 of 532 +r0705:= -2*cot(x)*(tan(x)*sin(x))^(1/2) +--R +--R +--R +------------+ +--R (35) - 2cot(x)\|sin(x)tan(x) +--R Type: Expression(Integer) +--E 35 + +--S 36 of 532 +a0705:= integrate(t0705,x) +--R +--R +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R (36) (- cos(x) - 1) |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 36 + +--S 37 of 532 +m0705:= a0705-r0705 +--R +--R +--R (37) +--R +------------+ +--R 2cot(x)\|sin(x)tan(x) +--R + +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R (- cos(x) - 1) |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 532 +d0705:= D(m0705,x) +--R +--R +--R (38) +--R +------------+ +--R 8cos(x)sin(x)\|sin(x)tan(x) +--R + +--R 3 2 2 +--R (cos(x) + 3cos(x) + 3cos(x) + 1)cot(x)sin(x)tan(x) +--R + +--R 3 2 2 3 +--R (- 2cos(x) - 6cos(x) - 6cos(x) - 2)cot(x) - 2cos(x) +--R + +--R 2 +--R - 6cos(x) - 6cos(x) - 2 +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (cos(x) + 3cos(x) + 3cos(x) + cos(x))cot(x) +--R * +--R tan(x) +--R + +--R 3 2 +--R (cos(x) + 3cos(x) + 3cos(x) + 1)cot(x)sin(x) +--R * +--R +-------------------------------------------+3 +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 3 2 +--R (cos(x) + 3cos(x) + 3cos(x) + 1) +--R * +--R +-------------------------------------------+3 +--R | 2 +--R | 16cos(x) +------------+ +--R |------------------------------------------- \|sin(x)tan(x) +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R Type: Expression(Integer) +--E 38 + +--S 39 of 532 +t0706:= (tan(x)*sin(x))^(3/2) +--R +--R +--R +------------+ +--R (39) sin(x)tan(x)\|sin(x)tan(x) +--R Type: Expression(Integer) +--E 39 + +--S 40 of 532 +r0706:= 2/3*csc(x)*(4-sin(x)^2)*(tan(x)*sin(x))^(1/2) +--R +--R +--R 2 +------------+ +--R (- 2csc(x)sin(x) + 8csc(x))\|sin(x)tan(x) +--R (40) ------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 532 +a0706:= integrate(t0706,x) +--R +--R +--R (41) +--R 3 2 +--R (cos(x) + cos(x) + 3cos(x) + 3) +--R * +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 3cos(x) +--R Type: Union(Expression(Integer),...) +--E 41 + +--S 42 of 532 +m0706:= a0706-r0706 +--R +--R +--R (42) +--R 2 +------------+ +--R (2cos(x)csc(x)sin(x) - 8cos(x)csc(x))\|sin(x)tan(x) +--R + +--R 3 2 +--R (cos(x) + cos(x) + 3cos(x) + 3) +--R * +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 3cos(x) +--R Type: Expression(Integer) +--E 42 + +--S 43 of 532 +d0706:= D(m0706,x) +--R +--R +--R (43) +--R +------------+ +--R (- 24cos(x) + 24)sin(x)\|sin(x)tan(x) +--R + +--R 2 3 +--R (cos(x) + 2cos(x) + 1)csc(x)sin(x) +--R + +--R 2 +--R (- 4cos(x) - 8cos(x) - 4)csc(x)sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 +--R (- 2cos(x) - 4cos(x) - 2)cot(x)csc(x)sin(x) +--R + +--R 3 2 2 +--R (5cos(x) + 10cos(x) + 5cos(x))csc(x)sin(x) +--R + +--R 2 +--R (8cos(x) + 16cos(x) + 8)cot(x)csc(x)sin(x) +--R + +--R 3 2 +--R (- 4cos(x) - 8cos(x) - 4cos(x))csc(x) +--R * +--R tan(x) +--R + +--R 2 3 +--R (cos(x) + 2cos(x) + 1)csc(x)sin(x) +--R + +--R 2 +--R (- 4cos(x) - 8cos(x) - 4)csc(x)sin(x) +--R * +--R +-------------------------------------------+3 +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R +-------------------------------------------+3 +--R | 2 +--R 2 | 16cos(x) +--R (3cos(x) + 6cos(x) + 3) |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R * +--R +------------+ +--R \|sin(x)tan(x) +--R Type: Expression(Integer) +--E 43 + +--S 44 of 532 +t0707:= (tan(x)*sin(x))^(5/2) +--R +--R +--R 2 2 +------------+ +--R (44) sin(x) tan(x) \|sin(x)tan(x) +--R Type: Expression(Integer) +--E 44 + +--S 45 of 532 +r0707:= 2/15*cot(x)*(tan(x)*sin(x))^(1/2)*(32+(8-3*sin(x)^2)*tan(x)^2) +--R +--R +--R 2 2 +------------+ +--R ((- 6cot(x)sin(x) + 16cot(x))tan(x) + 64cot(x))\|sin(x)tan(x) +--R (45) ---------------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 45 + +--S 46 of 532 +a0707:= integrate(t0707,x) +--R +--R +--R (46) +--R 5 4 3 2 +--R (- 3cos(x) - 3cos(x) + 30cos(x) + 30cos(x) + 5cos(x) + 5) +--R * +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 2 +--R 15cos(x) +--R Type: Union(Expression(Integer),...) +--E 46 + +--S 47 of 532 +m0707:= a0707-r0707 +--R +--R +--R (47) +--R 2 2 2 2 2 +--R ((6cos(x) cot(x)sin(x) - 16cos(x) cot(x))tan(x) - 64cos(x) cot(x)) +--R * +--R +------------+ +--R \|sin(x)tan(x) +--R + +--R 5 4 3 2 +--R (- 3cos(x) - 3cos(x) + 30cos(x) + 30cos(x) + 5cos(x) + 5) +--R * +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 2 +--R 15cos(x) +--R Type: Expression(Integer) +--E 47 + +--S 48 of 532 +d0707:= D(m0707,x) +--R +--R +--R (48) +--R 2 +------------+ +--R (120cos(x) - 240cos(x) + 120)sin(x)\|sin(x)tan(x) +--R + +--R 2 3 +--R (15cos(x) + 15cos(x))cot(x)sin(x) +--R + +--R 2 +--R (- 40cos(x) - 40cos(x))cot(x)sin(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 2 3 +--R ((- 6cos(x) - 6cos(x))cot(x) - 6cos(x) - 6cos(x))sin(x) +--R + +--R 3 2 2 +--R (15cos(x) + 15cos(x) )cot(x)sin(x) +--R + +--R 2 2 2 +--R ((16cos(x) + 16cos(x))cot(x) + 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 +--R (- 8cos(x) - 8cos(x) )cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R 2 3 +--R (15cos(x) + 15cos(x))cot(x)sin(x) +--R + +--R 2 +--R (- 72cos(x) - 72cos(x))cot(x)sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 2 +--R ((64cos(x) + 64cos(x))cot(x) + 64cos(x) + 64cos(x))sin(x) +--R + +--R 3 2 +--R (- 32cos(x) - 32cos(x) )cot(x) +--R * +--R tan(x) +--R + +--R 2 +--R (- 32cos(x) - 32cos(x))cot(x)sin(x) +--R * +--R +-------------------------------------------+3 +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R +-------------------------------------------+3 +--R | 2 +--R 2 | 16cos(x) +--R (15cos(x) + 15cos(x)) |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R * +--R +------------+ +--R \|sin(x)tan(x) +--R Type: Expression(Integer) +--E 48 + +--S 49 of 532 +t0708:= (a+b*sin(x)*cos(x))^(1/2) +--R +--R +--R +------------------+ +--R (49) \|b cos(x)sin(x) + a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 532 +r0708:= 1/2*EllipticE(-1/4*%pi+x,2*b/(2*a+b))*(2*a+b*sin(2*x))^(1/2)*_ + 2^(1/2)/((2*a+b*sin(2*x))/(2*a+b))^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 50 + +--S 51 of 532 +a0708:= integrate(t0708,x) +--R +--R +--R x +--R ++ +--------------------+ +--R (50) | \|b cos(%P)sin(%P) + a d%P +--R ++ +--R Type: Union(Expression(Integer),...) +--E 51 + +--S 52 of 532 +m0708:= a0708-r0708 +--R +--R +--R x +--R ++ +--------------------+ +--R (51) | \|b cos(%P)sin(%P) + a d%P - r0708 +--R ++ +--R Type: Expression(Integer) +--E 52 + +--S 53 of 532 +d0708:= D(m0708,x) +--R +--R +--R +------------------+ +--R (52) \|b cos(x)sin(x) + a +--R Type: Expression(Integer) +--E 53 + +--S 54 of 532 +t0709:= 1/(a+b*sin(x)*cos(x))^(1/2) +--R +--R +--R 1 +--R (53) --------------------- +--R +------------------+ +--R \|b cos(x)sin(x) + a +--R Type: Expression(Integer) +--E 54 + +--S 55 of 532 +r0709:= 2^(1/2)*EllipticF(-1/4*%pi+x,2*b/(2*a+b))*((2*a+b*sin(2*x))/_ + (2*a+b))^(1/2)/(2*a+b*sin(2*x))^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 55 + +--S 56 of 532 +a0709:= integrate(t0709,x) +--R +--R +--R x +--R ++ 1 +--R (54) | ----------------------- d%P +--R ++ +--------------------+ +--R \|b cos(%P)sin(%P) + a +--R Type: Union(Expression(Integer),...) +--E 56 + +--S 57 of 532 +m0709:= a0709-r0709 +--R +--R +--R x +--R ++ 1 +--R (55) | ----------------------- d%P - r0709 +--R ++ +--------------------+ +--R \|b cos(%P)sin(%P) + a +--R Type: Expression(Integer) +--E 57 + +--S 58 of 532 +d0709:= D(m0709,x) +--R +--R +--R 1 +--R (56) --------------------- +--R +------------------+ +--R \|b cos(x)sin(x) + a +--R Type: Expression(Integer) +--E 58 + +--S 59 of 532 +t0710:= (a*cos(x)+b*sin(x))^4 +--R +--R +--R (57) +--R 4 4 3 3 2 2 2 2 3 3 +--R b sin(x) + 4a b cos(x)sin(x) + 6a b cos(x) sin(x) + 4a b cos(x) sin(x) +--R + +--R 4 4 +--R a cos(x) +--R Type: Expression(Integer) +--E 59 + +--S 60 of 532 +r0710:= 3/8*(a^2+b^2)^2*x-3/8*(a^2+b^2)*(b*cos(x)-a*sin(x))*_ + (a*cos(x)+b*sin(x))-1/4*(b*cos(x)-a*sin(x))*(a*cos(x)+b*sin(x))^3 +--R +--R +--R (58) +--R 3 4 4 2 2 3 +--R 2a b sin(x) + (- 2b + 6a b )cos(x)sin(x) +--R + +--R 3 3 2 3 3 2 +--R ((- 6a b + 6a b)cos(x) + 3a b + 3a b)sin(x) +--R + +--R 2 2 4 3 4 4 3 4 +--R ((- 6a b + 2a )cos(x) + (- 3b + 3a )cos(x))sin(x) - 2a b cos(x) +--R + +--R 3 3 2 4 2 2 4 +--R (- 3a b - 3a b)cos(x) + (3b + 6a b + 3a )x +--R / +--R 8 +--R Type: Expression(Integer) +--E 60 + +--S 61 of 532 +a0710:= integrate(t0710,x) +--R +--R +--R (59) +--R 4 2 2 4 3 4 2 2 4 +--R ((2b - 12a b + 2a )cos(x) + (- 5b + 6a b + 3a )cos(x))sin(x) +--R + +--R 3 3 4 3 2 4 2 2 4 +--R (8a b - 8a b)cos(x) - 16a b cos(x) + (3b + 6a b + 3a )x +--R / +--R 8 +--R Type: Union(Expression(Integer),...) +--E 61 + +--S 62 of 532 +m0710:= a0710-r0710 +--R +--R +--R (60) +--R 3 4 4 2 2 3 +--R - 2a b sin(x) + (2b - 6a b )cos(x)sin(x) +--R + +--R 3 3 2 3 3 2 +--R ((6a b - 6a b)cos(x) - 3a b - 3a b)sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((2b - 6a b )cos(x) + (- 2b + 6a b )cos(x))sin(x) +--R + +--R 3 3 4 3 3 2 +--R (8a b - 6a b)cos(x) + (- 13a b + 3a b)cos(x) +--R / +--R 8 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 532 +d0710:= D(m0710,x) +--R +--R +--R (61) +--R 4 2 2 4 3 3 3 +--R (- b + 3a b )sin(x) + (- 10a b + 6a b)cos(x)sin(x) +--R + +--R 4 2 2 2 +--R (b - 3a b )sin(x) +--R + +--R 3 3 3 3 3 +--R ((- 10a b + 6a b)cos(x) + (10a b - 6a b)cos(x))sin(x) +--R + +--R 4 2 2 4 4 2 2 2 +--R (b - 3a b )cos(x) + (- b + 3a b )cos(x) +--R / +--R 4 +--R Type: Expression(Integer) +--E 63 + +--S 64 of 532 +t0711:= 1/(a*cos(x)+b*sin(x))^3 +--R +--R +--R 1 +--R (62) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 64 + +--S 65 of 532 +r0711:= -1/2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ + 1/2*(b*cos(x)-a*sin(x))/(a^2+b^2)/(a*cos(x)+b*sin(x))^2 +--R +--R +--R (63) +--R 2 2 2 2 a sin(x) - b cos(x) +--R (b sin(x) + 2a b cos(x)sin(x) + a cos(x) )atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R | 2 2 +--R (a sin(x) - b cos(x))\|b + a +--R / +--R 4 2 2 2 3 3 +--R (2b + 2a b )sin(x) + (4a b + 4a b)cos(x)sin(x) +--R + +--R 2 2 4 2 +--R (2a b + 2a )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 65 + +--S 66 of 532 +a0711:= integrate(t0711,x) +--R +--R +--R (64) +--R 3 2 2 4 2 2 2 +--R (2a b cos(x)sin(x) + (- a b + a )cos(x) + a b ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 2 3 3 2 2 2 3 +--R ((- 2a b cos(x) + a )sin(x) + (b - a b)cos(x) - a b cos(x) - b ) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 3 5 2 4 6 2 2 4 4 2 +--R ((4a b + 4a b)cos(x)sin(x) + (- 2a b + 2a )cos(x) + 2a b + 2a b ) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 66 + +--S 67 of 532 +m0711:= a0711-r0711 +--R +--R +--R (65) +--R 3 3 3 2 4 4 2 2 2 4 2 +--R 2a b cos(x)sin(x) + ((- a b + 5a b )cos(x) + a b )sin(x) +--R + +--R 3 3 5 3 3 3 4 2 6 4 +--R ((- 2a b + 4a b)cos(x) + 2a b cos(x))sin(x) + (- a b + a )cos(x) +--R + +--R 4 2 2 +--R a b cos(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 3 3 2 4 4 2 2 2 4 2 +--R - 2a b cos(x)sin(x) + ((a b - 5a b )cos(x) - a b )sin(x) +--R + +--R 3 3 5 3 3 3 4 2 6 4 +--R ((2a b - 4a b)cos(x) - 2a b cos(x))sin(x) + (a b - a )cos(x) +--R + +--R 4 2 2 +--R - a b cos(x) +--R * +--R a sin(x) - b cos(x) +--R atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 3 2 3 +--R (- 2a b cos(x) + a b )sin(x) +--R + +--R 5 2 3 2 2 3 5 2 +--R ((b - 5a b )cos(x) - a b cos(x) - b )sin(x) +--R + +--R 4 3 2 3 3 2 2 4 3 2 +--R ((2a b - 4a b )cos(x) + a b cos(x) - 2a b cos(x) - a b )sin(x) +--R + +--R 2 3 4 4 2 3 3 2 3 2 2 3 +--R (a b - a b)cos(x) - a b cos(x) - a b cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 3 5 5 3 3 +--R (4a b + 4a b )cos(x)sin(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 2 +--R ((- 2a b + 8a b + 10a b )cos(x) + 2a b + 2a b )sin(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 +--R ((- 4a b + 4a b + 8a b)cos(x) + (4a b + 4a b )cos(x))sin(x) +--R + +--R 4 4 8 4 4 4 6 2 2 +--R (- 2a b + 2a )cos(x) + (2a b + 2a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 532 +d0711:= D(m0711,x) +--R +--R +--R (66) +--R 3 4 2 7 +--R 4a b cos(x) sin(x) +--R + +--R 2 5 4 3 3 2 5 6 +--R ((- 8a b + 12a b )cos(x) + 4a b cos(x))sin(x) +--R + +--R 6 3 4 5 2 4 6 3 4 2 +--R (5a b - 18a b + 13a b )cos(x) + (- 6a b + 6a b )cos(x) +--R + +--R 6 +--R a b +--R * +--R 5 +--R sin(x) +--R + +--R 7 2 5 4 3 6 5 +--R (- b + 4a b - 9a b + 6a b)cos(x) +--R + +--R 7 2 5 4 3 3 7 2 5 +--R (2b - 2a b - 4a b )cos(x) + (- b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 6 3 4 5 2 7 6 +--R (3a b - 13a b + 5a b + a )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 2 6 +--R (- 7a b + 22a b - 11a b )cos(x) + (5a b - 9a b )cos(x) - a b +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 5 4 3 6 7 +--R (- b + 11a b - 19a b + 5a b)cos(x) +--R + +--R 7 2 5 4 3 6 5 +--R (3b - 24a b + 27a b - 6a b)cos(x) +--R + +--R 7 2 5 4 3 3 7 2 5 +--R (- 3b + 15a b - 8a b )cos(x) + (b - 2a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 4 5 2 7 8 +--R (- 2a b + 9a b - 8a b + a )cos(x) +--R + +--R 6 3 4 5 2 7 6 +--R (6a b - 19a b + 10a b - a )cos(x) +--R + +--R 6 3 4 5 2 4 6 3 4 2 +--R (- 6a b + 11a b - 2a b )cos(x) + (2a b - a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 5 4 3 6 9 2 5 4 3 6 7 +--R (- a b + 2a b - a b)cos(x) + (3a b - 4a b + a b)cos(x) +--R + +--R 2 5 4 3 5 2 5 3 +--R (- 3a b + 2a b )cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 4 8 3 5 5 3 7 +--R 2a b sin(x) + (- 6a b + 8a b )cos(x)sin(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 6 +--R ((7a b - 27a b + 4a b )cos(x) - a b - 2a b )sin(x) +--R + +--R 7 3 5 5 3 3 3 5 5 3 5 +--R ((- 4a b + 38a b - 4a b )cos(x) + (- 6a b - 16a b )cos(x))sin(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (b - 28a b - 14a b + 5a b )cos(x) +--R + +--R 2 6 4 4 6 2 2 8 2 6 4 4 +--R (12a b + 39a b - 8a b )cos(x) - b - 2a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 7 3 5 5 3 5 +--R (10a b + 34a b - 14a b )cos(x) +--R + +--R 7 3 5 5 3 3 7 3 5 5 3 +--R (- 12a b - 64a b + 8a b )cos(x) + (2a b + 14a b + 8a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 8 2 6 4 4 6 2 6 +--R (- b - 32a b + 16a b + a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 +--R (3b + 55a b - 9a b - 6a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 2 8 2 6 4 4 +--R (- 3b - 26a b - 13a b + 4a b )cos(x) + b + 3a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 3 5 5 3 7 7 3 5 5 3 5 +--R (14a b - 10a b - 2a b )cos(x) + (- 30a b + 2a b + 6a b )cos(x) +--R + +--R 7 3 5 5 3 3 7 3 5 +--R (18a b + 10a b - 4a b )cos(x) + (- 2a b - 2a b )cos(x) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 8 8 2 6 4 4 6 2 6 +--R (- 2b + 3a b + a b )cos(x) + (6b - 3a b - 5a b - a b )cos(x) +--R + +--R 8 2 6 4 4 6 2 4 8 2 6 4 4 2 +--R (- 6b - 3a b + 3a b + a b )cos(x) + (2b + 3a b + a b )cos(x) +--R / +--R 4 7 6 5 2 7 +--R (8a b + 8a b )cos(x) sin(x) +--R + +--R 3 8 5 6 7 4 3 3 8 5 6 6 +--R ((- 24a b + 8a b + 32a b )cos(x) + (8a b + 8a b )cos(x))sin(x) +--R + +--R 2 9 4 7 6 5 8 3 4 +--R (26a b - 66a b - 42a b + 50a b )cos(x) +--R + +--R 2 9 4 7 6 5 2 2 9 4 7 +--R (- 28a b - 8a b + 20a b )cos(x) + 2a b + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 10 3 8 5 6 7 4 9 2 5 +--R (- 12a b + 82a b - 42a b - 98a b + 38a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 3 +--R (24a b - 68a b - 88a b + 4a b )cos(x) +--R + +--R 10 3 8 5 6 +--R (- 12a b - 14a b - 2a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 11 2 9 4 7 6 5 8 3 10 6 +--R (2b - 38a b + 88a b + 32a b - 82a b + 14a b)cos(x) +--R + +--R 11 2 9 4 7 6 5 8 3 4 +--R (- 6b + 72a b - 28a b - 136a b - 30a b )cos(x) +--R + +--R 11 2 9 4 7 6 5 2 11 2 9 4 7 +--R (6b - 30a b - 58a b - 22a b )cos(x) - 2b - 4a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 10 3 8 5 6 7 4 9 2 11 7 +--R (6a b - 42a b + 32a b + 48a b - 30a b + 2a )cos(x) +--R + +--R 10 3 8 5 6 7 4 9 2 5 +--R (- 18a b + 72a b + 44a b - 80a b - 34a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 3 +--R (18a b - 18a b - 70a b - 34a b )cos(x) +--R + +--R 10 3 8 5 6 +--R (- 6a b - 12a b - 6a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 9 4 7 6 5 8 3 10 8 +--R (6a b - 18a b - 2a b + 18a b - 4a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 10 6 +--R (- 18a b + 24a b + 40a b - 16a b - 14a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 4 +--R (18a b + 6a b - 32a b - 20a b )cos(x) +--R + +--R 2 9 4 7 6 5 2 +--R (- 6a b - 12a b - 6a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 8 5 6 7 4 9 2 9 3 8 7 4 11 7 +--R (2a b - 2a b - 2a b + 2a b )cos(x) + (- 6a b + 8a b - 2a )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 5 3 8 5 6 7 4 3 +--R (6a b + 6a b - 4a b - 4a b )cos(x) + (- 2a b - 4a b - 2a b )cos(x) +--R Type: Expression(Integer) +--E 68 + +--S 69 of 532 +t0712:= 1/(a*cos(x)+b*sin(x))^5 +--R +--R +--R (67) +--R 1 +--R / +--R 5 5 4 4 2 3 2 3 +--R b sin(x) + 5a b cos(x)sin(x) + 10a b cos(x) sin(x) +--R + +--R 3 2 3 2 4 4 5 5 +--R 10a b cos(x) sin(x) + 5a b cos(x) sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 69 + +--S 70 of 532 +r0712:= -3/8*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ + 1/4*(b*cos(x)-a*sin(x))/(a^2+b^2)/(a*cos(x)+b*sin(x))^4-_ + 3/8*(b*cos(x)-a*sin(x))/(a^2+b^2)^2/(a*cos(x)+b*sin(x))^2 +--R +--R +--R (68) +--R 4 4 3 3 2 2 2 2 +--R 3b sin(x) + 12a b cos(x)sin(x) + 18a b cos(x) sin(x) +--R + +--R 3 3 4 4 +--R 12a b cos(x) sin(x) + 3a cos(x) +--R * +--R a sin(x) - b cos(x) +--R atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 3 3 2 2 +--R 3a b sin(x) + (- 3b + 6a b)cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 3 +--R ((- 6a b + 3a )cos(x) + 2a b + 2a )sin(x) - 3a b cos(x) +--R + +--R 3 2 +--R (- 2b - 2a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 8 2 6 4 4 4 7 3 5 5 3 3 +--R (8b + 16a b + 8a b )sin(x) + (32a b + 64a b + 32a b )cos(x)sin(x) +--R + +--R 2 6 4 4 6 2 2 2 +--R (48a b + 96a b + 48a b )cos(x) sin(x) +--R + +--R 3 5 5 3 7 3 4 4 6 2 8 4 +--R (32a b + 64a b + 32a b)cos(x) sin(x) + (8a b + 16a b + 8a )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 70 + +--S 71 of 532 +a0712:= integrate(t0712,x) +--R +--R +--R (69) +--R 5 3 7 3 5 3 +--R ((12a b - 12a b)cos(x) - 12a b cos(x))sin(x) +--R + +--R 4 4 6 2 8 4 4 4 6 2 2 4 4 +--R (- 3a b + 18a b - 3a )cos(x) + (6a b - 18a b )cos(x) - 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 6 3 4 5 2 3 5 2 7 2 +--R (- 8a b - 12a b + 20a b )cos(x) + (9a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 7 +--R (8a b + 20a b )cos(x) - 5a b - 2a +--R * +--R sin(x) +--R + +--R 7 2 5 4 3 6 4 4 3 6 3 +--R (2b - 7a b - 28a b + 5a b)cos(x) + (- 3a b + 9a b)cos(x) +--R + +--R 7 2 5 4 3 2 4 3 6 7 2 5 +--R (- 4b + 2a b + 30a b )cos(x) + (5a b - 4a b)cos(x) + 2b + 5a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 7 7 5 9 3 11 3 +--R (32a b + 32a b - 32a b - 32a b)cos(x) +--R + +--R 5 7 7 5 9 3 +--R (- 32a b - 64a b - 32a b )cos(x) +--R * +--R sin(x) +--R + +--R 4 8 6 6 8 4 10 2 12 4 +--R (- 8a b + 32a b + 80a b + 32a b - 8a )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 2 4 8 6 6 8 4 +--R (16a b - 16a b - 80a b - 48a b )cos(x) - 8a b - 16a b - 8a b +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Union(Expression(Integer),...) +--E 71 + +--S 72 of 532 +m0712:= a0712-r0712 +--R +--R +--R (70) +--R 5 7 7 5 3 5 7 5 +--R ((12a b - 12a b )cos(x) - 12a b cos(x))sin(x) +--R + +--R 4 8 6 6 8 4 4 4 8 6 6 2 +--R (- 3a b + 66a b - 51a b )cos(x) + (6a b - 66a b )cos(x) +--R + +--R 4 8 +--R - 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 7 7 5 9 3 5 5 7 7 5 3 +--R (- 12a b + 144a b - 84a b )cos(x) + (24a b - 144a b )cos(x) +--R + +--R 5 7 +--R - 12a b cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 8 4 10 2 6 6 6 8 4 4 +--R (- 18a b + 156a b - 66a b )cos(x) + (36a b - 156a b )cos(x) +--R + +--R 6 6 2 +--R - 18a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 5 9 3 11 7 7 5 9 3 5 +--R (- 12a b + 84a b - 24a b)cos(x) + (24a b - 84a b )cos(x) +--R + +--R 7 5 3 +--R - 12a b cos(x) +--R * +--R sin(x) +--R + +--R 8 4 10 2 12 8 8 4 10 2 6 +--R (- 3a b + 18a b - 3a )cos(x) + (6a b - 18a b )cos(x) +--R + +--R 8 4 4 +--R - 3a b cos(x) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 5 7 7 5 3 5 7 5 +--R ((- 12a b + 12a b )cos(x) + 12a b cos(x))sin(x) +--R + +--R 4 8 6 6 8 4 4 4 8 6 6 2 +--R (3a b - 66a b + 51a b )cos(x) + (- 6a b + 66a b )cos(x) +--R + +--R 4 8 +--R 3a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 7 7 5 9 3 5 5 7 7 5 3 +--R (12a b - 144a b + 84a b )cos(x) + (- 24a b + 144a b )cos(x) +--R + +--R 5 7 +--R 12a b cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 6 8 4 10 2 6 6 6 8 4 4 +--R (18a b - 156a b + 66a b )cos(x) + (- 36a b + 156a b )cos(x) +--R + +--R 6 6 2 +--R 18a b cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 5 9 3 11 7 7 5 9 3 5 +--R (12a b - 84a b + 24a b)cos(x) + (- 24a b + 84a b )cos(x) +--R + +--R 7 5 3 +--R 12a b cos(x) +--R * +--R sin(x) +--R + +--R 8 4 10 2 12 8 8 4 10 2 6 +--R (3a b - 18a b + 3a )cos(x) + (- 6a b + 18a b )cos(x) +--R + +--R 8 4 4 +--R 3a b cos(x) +--R * +--R a sin(x) - b cos(x) +--R atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 10 3 8 5 6 3 5 6 7 4 2 +--R (- 8a b - 12a b + 20a b )cos(x) + (9a b - 3a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 +--R (8a b + 20a b )cos(x) - 5a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 11 2 9 4 7 6 5 4 +--R (2b - 39a b - 76a b + 85a b )cos(x) +--R + +--R 4 7 6 5 3 11 2 9 4 7 2 +--R (- 3a b + 33a b )cos(x) + (- 4b + 34a b + 110a b )cos(x) +--R + +--R 4 7 6 5 8 3 11 2 9 +--R (5a b - 12a b - 8a b )cos(x) + 2b + 5a b +--R * +--R 4 +--R sin(x) +--R + +--R 10 3 8 5 6 7 4 5 +--R (8a b - 76a b - 184a b + 140a b )cos(x) +--R + +--R 5 6 7 4 9 2 4 +--R (3a b + 36a b + 9a b )cos(x) +--R + +--R 10 3 8 5 6 3 +--R (- 16a b + 56a b + 240a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 10 3 8 5 6 +--R (2a b - 4a b - 12a b )cos(x) + (8a b + 20a b )cos(x) + 3a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 9 4 7 6 5 8 3 6 +--R (12a b - 74a b - 216a b + 110a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 5 +--R (- 3a b + 30a b + 15a b + 6a b)cos(x) +--R + +--R 2 9 4 7 6 5 4 +--R (- 24a b + 44a b + 260a b )cos(x) +--R + +--R 4 7 6 5 8 3 3 2 9 4 7 2 +--R (6a b - 32a b + 4a b )cos(x) + (12a b + 30a b )cos(x) +--R + +--R 4 7 6 5 8 3 +--R (- 3a b + 14a b + 8a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 8 5 6 7 4 9 2 7 +--R (8a b - 36a b - 124a b + 40a b )cos(x) +--R + +--R 5 6 7 4 9 2 6 +--R (- 6a b + 39a b + 9a b )cos(x) +--R + +--R 3 8 5 6 7 4 5 +--R (- 16a b + 16a b + 140a b )cos(x) +--R + +--R 5 6 7 4 9 2 4 3 8 5 6 3 +--R (22a b - 44a b - 21a b )cos(x) + (8a b + 20a b )cos(x) +--R + +--R 5 6 7 4 9 2 2 5 6 7 4 +--R (- 18a b + 3a b + 12a b )cos(x) + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 4 7 6 5 8 3 10 8 +--R (2a b - 7a b - 28a b + 5a b)cos(x) +--R + +--R 6 5 8 3 10 7 4 7 6 5 8 3 6 +--R (- 3a b + 15a b + 6a b)cos(x) + (- 4a b + 2a b + 30a b )cos(x) +--R + +--R 4 7 6 5 8 3 10 5 4 7 6 5 4 +--R (- 2a b + 16a b - 3a b - 6a b)cos(x) + (2a b + 5a b )cos(x) +--R + +--R 4 7 6 5 8 3 3 4 7 6 5 +--R (4a b - 11a b - 12a b )cos(x) + (- 2a b - 2a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 5 11 7 9 9 7 11 5 3 +--R (32a b + 32a b - 32a b - 32a b )cos(x) +--R + +--R 5 11 7 9 9 7 +--R (- 32a b - 64a b - 32a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 4 12 6 10 8 8 10 6 12 4 4 +--R (- 8a b + 160a b + 208a b - 96a b - 136a b )cos(x) +--R + +--R 4 12 6 10 8 8 10 6 2 4 12 6 10 +--R (16a b - 144a b - 336a b - 176a b )cos(x) - 8a b - 16a b +--R + +--R 8 8 +--R - 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 11 7 9 9 7 11 5 13 3 5 +--R (- 32a b + 320a b + 512a b - 64a b - 224a b )cos(x) +--R + +--R 5 11 7 9 9 7 11 5 3 +--R (64a b - 256a b - 704a b - 384a b )cos(x) +--R + +--R 5 11 7 9 9 7 +--R (- 32a b - 64a b - 32a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 10 8 8 10 6 12 4 14 2 6 +--R (- 48a b + 320a b + 608a b + 64a b - 176a b )cos(x) +--R + +--R 6 10 8 8 10 6 12 4 4 +--R (96a b - 224a b - 736a b - 416a b )cos(x) +--R + +--R 6 10 8 8 10 6 2 +--R (- 48a b - 96a b - 48a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 7 9 9 7 11 5 13 3 15 7 +--R (- 32a b + 160a b + 352a b + 96a b - 64a b)cos(x) +--R + +--R 7 9 9 7 11 5 13 3 5 +--R (64a b - 96a b - 384a b - 224a b )cos(x) +--R + +--R 7 9 9 7 11 5 3 +--R (- 32a b - 64a b - 32a b )cos(x) +--R * +--R sin(x) +--R + +--R 8 8 10 6 12 4 14 2 16 8 +--R (- 8a b + 32a b + 80a b + 32a b - 8a )cos(x) +--R + +--R 8 8 10 6 12 4 14 2 6 +--R (16a b - 16a b - 80a b - 48a b )cos(x) +--R + +--R 8 8 10 6 12 4 4 +--R (- 8a b - 16a b - 8a b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R Type: Expression(Integer) +--E 72 + +--S 73 of 532 +d0712:= D(m0712,x) +--R +--R +--R (71) +--R 3 10 5 8 7 6 6 3 10 5 8 4 +--R (48a b - 96a b + 48a b )cos(x) + (- 96a b + 96a b )cos(x) +--R + +--R 3 10 2 +--R 48a b cos(x) +--R * +--R 9 +--R sin(x) +--R + +--R 2 11 4 9 6 7 8 5 7 +--R (- 72a b + 456a b - 600a b + 216a b )cos(x) +--R + +--R 2 11 4 9 6 7 5 +--R (168a b - 816a b + 552a b )cos(x) +--R + +--R 2 11 4 9 3 2 11 +--R (- 120a b + 360a b )cos(x) + 24a b cos(x) +--R * +--R 8 +--R sin(x) +--R + +--R 12 3 10 5 8 7 6 9 4 8 +--R (27a b - 444a b + 1530a b - 1452a b + 387a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 6 +--R (- 84a b + 972a b - 2508a b + 1236a b )cos(x) +--R + +--R 12 3 10 5 8 4 +--R (90a b - 612a b + 978a b )cos(x) +--R + +--R 12 3 10 2 12 +--R (- 36a b + 84a b )cos(x) + 3a b +--R * +--R 7 +--R sin(x) +--R + +--R 13 2 11 4 9 6 7 8 5 10 3 +--R (- 3b + 72a b - 906a b + 2340a b - 1707a b + 348a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 13 2 11 4 9 6 7 8 5 7 +--R (12b - 204a b + 1740a b - 3444a b + 1320a b )cos(x) +--R + +--R 13 2 11 4 9 6 7 5 +--R (- 18b + 180a b - 762a b + 1104a b )cos(x) +--R + +--R 13 2 11 4 9 3 13 2 11 +--R (12b - 36a b - 72a b )cos(x) + (- 3b - 12a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 12 3 10 5 8 7 6 9 4 11 2 +--R (15a b - 186a b - 342a b + 1440a b - 945a b + 162a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 12 3 10 5 8 7 6 9 4 8 +--R (- 63a b + 672a b - 78a b - 1560a b + 597a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 6 +--R (102a b - 900a b + 1182a b + 120a b )cos(x) +--R + +--R 12 3 10 5 8 4 +--R (- 78a b + 528a b - 762a b )cos(x) +--R + +--R 12 3 10 2 12 +--R (27a b - 114a b )cos(x) - 3a b +--R * +--R 5 +--R sin(x) +--R + +--R 13 2 11 4 9 6 7 8 5 10 3 +--R - 3b + 126a b - 1038a b + 1368a b - 315a b - 126a b +--R + +--R 12 +--R 36a b +--R * +--R 11 +--R cos(x) +--R + +--R 13 2 11 4 9 6 7 8 5 10 3 +--R (15b - 516a b + 3390a b - 4224a b + 1227a b - 36a b ) +--R * +--R 9 +--R cos(x) +--R + +--R 13 2 11 4 9 6 7 8 5 7 +--R (- 30b + 804a b - 3942a b + 4344a b - 912a b )cos(x) +--R + +--R 13 2 11 4 9 6 7 5 +--R (30b - 576a b + 1866a b - 1488a b )cos(x) +--R + +--R 13 2 11 4 9 3 13 2 11 +--R (- 15b + 174a b - 276a b )cos(x) + (3b - 12a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 12 3 10 5 8 7 6 9 4 +--R - 12a b + 294a b - 1797a b + 2280a b - 906a b +--R + +--R 11 2 13 +--R 90a b + 3a +--R * +--R 12 +--R cos(x) +--R + +--R 12 3 10 5 8 7 6 9 4 +--R 60a b - 1194a b + 5700a b - 5928a b + 1776a b +--R + +--R 11 2 +--R - 126a b +--R * +--R 10 +--R cos(x) +--R + +--R 12 3 10 5 8 7 6 9 4 8 +--R (- 120a b + 1836a b - 6318a b + 5016a b - 870a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 6 +--R (120a b - 1284a b + 2724a b - 1368a b )cos(x) +--R + +--R 12 3 10 5 8 4 +--R (- 60a b + 366a b - 309a b )cos(x) +--R + +--R 12 3 10 2 +--R (12a b - 18a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R (- 18a b + 321a b - 1536a b + 1494a b - 438a b + 33a b) +--R * +--R 13 +--R cos(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 12 +--R (90a b - 1296a b + 4776a b - 3612a b + 750a b - 36a b) +--R * +--R 11 +--R cos(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 9 +--R (- 180a b + 1974a b - 5112a b + 2742a b - 312a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 7 +--R (180a b - 1356a b + 2040a b - 624a b )cos(x) +--R + +--R 2 11 4 9 6 7 5 2 11 4 9 3 +--R (- 90a b + 369a b - 168a b )cos(x) + (18a b - 12a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 13 +--R (- 12a b + 171a b - 660a b + 426a b - 72a b + 3a ) +--R * +--R 14 +--R cos(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 13 +--R (60a b - 687a b + 2016a b - 966a b + 108a b - 3a ) +--R * +--R 12 +--R cos(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 10 +--R (- 120a b + 1038a b - 2088a b + 654a b - 36a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 8 +--R (120a b - 702a b + 768a b - 114a b )cos(x) +--R + +--R 3 10 5 8 7 6 6 3 10 5 8 4 +--R (- 60a b + 183a b - 36a b )cos(x) + (12a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 4 9 6 7 8 5 10 3 12 15 +--R (- 3a b + 36a b - 114a b + 36a b - 3a b)cos(x) +--R + +--R 4 9 6 7 8 5 10 3 12 13 +--R (15a b - 144a b + 342a b - 72a b + 3a b)cos(x) +--R + +--R 4 9 6 7 8 5 10 3 11 +--R (- 30a b + 216a b - 342a b + 36a b )cos(x) +--R + +--R 4 9 6 7 8 5 9 4 9 6 7 7 +--R (30a b - 144a b + 114a b )cos(x) + (- 15a b + 36a b )cos(x) +--R + +--R 4 9 5 +--R 3a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 4 10 6 8 8 6 4 +--R (36a b - 48a b + 12a b )cos(x) +--R + +--R 4 10 6 8 8 6 2 4 10 6 8 +--R (- 24a b + 24a b + 24a b )cos(x) + 20a b + 8a b +--R * +--R 10 +--R sin(x) +--R + +--R 3 11 5 9 7 7 9 5 5 +--R (- 90a b + 390a b - 318a b + 66a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 3 +--R (84a b - 280a b + 76a b + 128a b )cos(x) +--R + +--R 3 11 5 9 7 7 +--R (- 42a b + 130a b + 64a b )cos(x) +--R * +--R 9 +--R sin(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 6 +--R (75a b - 801a b + 1587a b - 747a b + 54a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 4 +--R (- 141a b + 842a b - 925a b - 188a b + 280a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 2 2 12 4 10 +--R (49a b - 353a b + 182a b + 176a b )cos(x) - 15a b - 32a b +--R + +--R 6 8 +--R - 8a b +--R * +--R 8 +--R sin(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 24a b + 666a b - 2694a b + 2730a b - 474a b - 60a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (72a b - 1318a b + 2464a b - 446a b - 1004a b + 320a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (- 40a b + 558a b - 630a b - 388a b + 192a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 +--R (- 8a b - 130a b - 276a b - 64a b )cos(x) +--R * +--R 7 +--R sin(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R 3b - 252a b + 1818a b - 3546a b + 1473a b + 294a b +--R + +--R 12 2 +--R - 78a b +--R * +--R 8 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R - 12b + 768a b - 3350a b + 1176a b + 2310a b - 1244a b +--R + +--R 12 2 +--R 72a b +--R * +--R 6 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 4 +--R (10b - 576a b + 980a b + 1006a b - 1200a b - 256a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 2 14 +--R (4b + 64a b - 126a b - 916a b - 328a b )cos(x) - 5b +--R + +--R 2 12 4 10 +--R - 4a b - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R 48a b - 336a b + 1032a b - 762a b - 510a b + 306a b +--R + +--R 13 +--R - 18a b +--R * +--R 9 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 192a b + 1240a b - 790a b - 4736a b + 2706a b + 180a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (240a b - 840a b - 2438a b + 3478a b + 548a b - 640a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (- 96a b - 120a b + 1054a b - 716a b - 768a b )cos(x) +--R + +--R 3 11 5 9 7 7 +--R (56a b - 26a b - 64a b )cos(x) +--R * +--R 5 +--R sin(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R - 3b - 123a b + 1167a b - 2298a b + 1503a b - 291a b +--R + +--R 12 2 +--R - 3a b +--R * +--R 10 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R 15b + 243a b - 2926a b + 6622a b - 4537a b - 1305a b +--R + +--R 12 2 +--R 240a b +--R * +--R 8 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R - 30b - 118a b + 3852a b - 6974a b - 1226a b + 2272a b +--R + +--R 12 2 +--R - 144a b +--R * +--R 6 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 4 +--R (30b + 6a b - 2718a b + 802a b + 1548a b - 328a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 2 14 +--R (- 15b - 15a b + 629a b + 616a b + 32a b )cos(x) + 3b +--R + +--R 2 12 4 10 6 8 +--R 7a b - 4a b - 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R 60a b - 888a b + 3228a b - 3102a b + 306a b + 270a b +--R + +--R 13 +--R - 18a b +--R * +--R 11 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 220a b + 3308a b - 9000a b + 4470a b + 2260a b +--R + +--R 11 3 13 +--R - 782a b + 36a b +--R * +--R 9 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (280a b - 4640a b + 8792a b + 994a b - 4970a b - 4a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 120a b + 3048a b - 3024a b - 4158a b + 740a b + 320a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (- 20a b - 968a b - 180a b + 1156a b + 448a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 +--R (20a b + 140a b + 184a b + 64a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R - 6b + 198a b - 1419a b + 2694a b - 762a b - 492a b +--R + +--R 12 2 +--R 75a b +--R * +--R 12 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R 28b - 1162a b + 5922a b - 5240a b - 2962a b + 942a b +--R + +--R 12 2 +--R - 24a b +--R * +--R 10 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R - 50b + 2424a b - 7984a b + 184a b + 6222a b + 218a b +--R + +--R 12 2 +--R - 174a b +--R * +--R 8 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R 40b - 2292a b + 3752a b + 3836a b - 2486a b - 1156a b +--R + +--R 12 2 +--R 72a b +--R * +--R 6 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R (- 10b + 982a b - 127a b - 1574a b - 196a b + 304a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 2 14 +--R (- 4b - 162a b - 162a b + 92a b + 96a b )cos(x) + 2b +--R + +--R 2 12 4 10 6 8 +--R 12a b + 18a b + 8a b +--R * +--R 2 +--R sin(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 12a b + 204a b - 888a b + 708a b + 276a b - 96a b ) +--R * +--R 13 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R 152a b - 1476a b + 3012a b + 800a b - 1218a b - 120a b +--R + +--R 13 +--R 18a b +--R * +--R 11 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 500a b + 3136a b - 2076a b - 4376a b + 42a b + 332a b +--R + +--R 13 +--R - 18a b +--R * +--R 9 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (720a b - 2568a b - 1496a b + 2816a b + 1250a b - 116a b ) +--R * +--R 7 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 5 +--R (- 500a b + 588a b + 1600a b + 180a b - 350a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 3 +--R (152a b + 140a b - 140a b - 128a b )cos(x) +--R + +--R 13 3 11 5 9 +--R (- 12a b - 24a b - 12a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 14 +--R (- 6a b + 69a b - 189a b - 33a b + 39a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 8b + 116a b - 453a b + 199a b + 398a b - 33a b - 39a b ) +--R * +--R 12 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 12 2 +--R (40b - 386a b + 734a b + 784a b - 324a b - 161a b + 27a b ) +--R * +--R 10 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R - 80b + 504a b - 186a b - 1266a b - 478a b + 81a b +--R + +--R 12 2 +--R 12a b +--R * +--R 8 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 6 +--R (80b - 266a b - 351a b + 331a b + 413a b + 74a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 4 +--R (- 40b + 20a b + 175a b + 139a b + 24a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 2 +--R (8b + 18a b + 12a b + 2a b )cos(x) +--R / +--R 4 15 8 11 12 7 6 +--R (128a b - 256a b + 128a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 4 +--R (- 256a b - 256a b + 256a b + 256a b )cos(x) +--R + +--R 4 15 6 13 8 11 2 +--R (128a b + 256a b + 128a b )cos(x) +--R * +--R 9 +--R sin(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R - 320a b + 960a b + 896a b - 1664a b - 576a b +--R + +--R 13 6 +--R 704a b +--R * +--R 7 +--R cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 5 +--R (704a b - 1280a b - 2944a b + 768a b + 1728a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 3 +--R (- 448a b + 192a b + 1728a b + 1088a b )cos(x) +--R + +--R 3 16 5 14 7 12 +--R (64a b + 128a b + 64a b )cos(x) +--R * +--R 8 +--R sin(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 +--R 264a b - 2320a b + 1976a b + 5664a b - 3592a b +--R + +--R 12 7 14 5 +--R - 3088a b + 1608a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 +--R - 800a b + 4384a b + 192a b - 11200a b - 1440a b +--R + +--R 12 7 +--R 4768a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 4 +--R (816a b - 1792a b - 2464a b + 3712a b + 3568a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 2 2 17 +--R (- 288a b - 288a b + 288a b + 288a b )cos(x) + 8a b +--R + +--R 4 15 6 13 +--R 16a b + 8a b +--R * +--R 7 +--R sin(x) +--R + +--R 18 3 16 5 14 7 12 9 10 +--R - 80a b + 1800a b - 6656a b - 1256a b + 14320a b +--R + +--R 11 8 13 6 15 4 +--R - 1736a b - 6816a b + 1960a b +--R * +--R 9 +--R cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 +--R 320a b - 5216a b + 9632a b + 12864a b - 18816a b +--R + +--R 11 8 13 6 +--R - 9696a b + 6816a b +--R * +--R 7 +--R cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 +--R - 480a b + 4848a b + 576a b - 9760a b + 544a b +--R + +--R 11 8 +--R 5552a b +--R * +--R 5 +--R cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 3 +--R (320a b - 1248a b - 3424a b - 1824a b + 32a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 +--R (- 80a b - 184a b - 128a b - 24a b )cos(x) +--R * +--R 6 +--R sin(x) +--R + +--R 19 2 17 4 15 6 13 8 11 10 9 +--R 8b - 480a b + 5160a b - 9264a b - 11160a b + 17920a b +--R + +--R 12 7 14 5 16 3 +--R 4888a b - 7920a b + 1360a b +--R * +--R 10 +--R cos(x) +--R + +--R 19 2 17 4 15 6 13 8 11 +--R - 40b + 1896a b - 14184a b + 5672a b + 33608a b +--R + +--R 10 9 12 7 14 5 +--R - 11144a b - 17848a b + 5112a b +--R * +--R 8 +--R cos(x) +--R + +--R 19 2 17 4 15 6 13 8 11 +--R 80b - 2784a b + 11616a b + 15296a b - 12528a b +--R + +--R 10 9 12 7 +--R - 10080a b + 3264a b +--R * +--R 6 +--R cos(x) +--R + +--R 19 2 17 4 15 6 13 8 11 +--R - 80b + 1776a b - 1344a b - 10560a b - 9584a b +--R + +--R 10 9 +--R - 2224a b +--R * +--R 4 +--R cos(x) +--R + +--R 19 2 17 4 15 6 13 8 11 2 19 +--R (40b - 384a b - 1224a b - 1136a b - 336a b )cos(x) - 8b +--R + +--R 2 17 4 15 6 13 +--R - 24a b - 24a b - 8a b +--R * +--R 5 +--R sin(x) +--R + +--R 18 3 16 5 14 7 12 9 10 +--R 40a b - 1200a b + 8040a b - 5280a b - 18872a b +--R + +--R 11 8 13 6 15 4 17 2 +--R 10320a b + 8984a b - 5120a b + 528a b +--R * +--R 11 +--R cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 +--R - 200a b + 4680a b - 20680a b - 11960a b + 39144a b +--R + +--R 11 8 13 6 15 4 +--R 8344a b - 15704a b + 1496a b +--R * +--R 9 +--R cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 +--R 400a b - 6720a b + 13920a b + 36480a b + 208a b +--R + +--R 11 8 13 6 +--R - 17344a b - 2112a b +--R * +--R 7 +--R cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 +--R - 400a b + 4080a b + 1920a b - 16000a b - 19440a b +--R + +--R 11 8 +--R - 6000a b +--R * +--R 5 +--R cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 3 +--R (200a b - 720a b - 3080a b - 3200a b - 1040a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 +--R (- 40a b - 120a b - 120a b - 40a b )cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 +--R 80a b - 1600a b + 7320a b + 1680a b - 15160a b +--R + +--R 12 7 14 5 16 3 18 +--R 416a b + 6376a b - 1776a b + 104a b +--R * +--R 12 +--R cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 +--R - 400a b + 6160a b - 17200a b - 25936a b + 20880a b +--R + +--R 12 7 14 5 16 3 +--R 17136a b - 6352a b - 432a b +--R * +--R 10 +--R cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 +--R 800a b - 8640a b + 7920a b + 42112a b + 17152a b +--R + +--R 12 7 14 5 +--R - 12352a b - 4752a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 +--R - 800a b + 4960a b + 6240a b - 13216a b - 21312a b +--R + +--R 12 7 +--R - 7616a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 4 +--R (400a b - 640a b - 4040a b - 4560a b - 1560a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 2 +--R (- 80a b - 240a b - 240a b - 80a b )cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R 80a b - 1200a b + 3864a b + 4160a b - 5784a b +--R + +--R 13 6 15 4 17 2 19 +--R - 2416a b + 2088a b - 288a b + 8a +--R * +--R 13 +--R cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R - 400a b + 4560a b - 7920a b - 21456a b + 1552a b +--R + +--R 13 6 15 4 17 2 +--R 10160a b - 400a b - 432a b +--R * +--R 11 +--R cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R 800a b - 6240a b + 816a b + 26688a b + 18816a b +--R + +--R 13 6 15 4 +--R - 3168a b - 3152a b +--R * +--R 9 +--R cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R - 800a b + 3360a b + 6432a b - 5728a b - 13312a b +--R + +--R 13 6 +--R - 5312a b +--R * +--R 7 +--R cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 5 +--R (400a b - 240a b - 2952a b - 3584a b - 1272a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 3 +--R (- 80a b - 240a b - 240a b - 80a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 14 5 +--R 40a b - 480a b + 1080a b + 2224a b - 616a b - 960a b +--R + +--R 16 3 18 +--R 264a b - 16a b +--R * +--R 14 +--R cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 +--R - 200a b + 1800a b - 1736a b - 8568a b - 3096a b +--R + +--R 14 5 16 3 18 +--R 2264a b + 424a b - 104a b +--R * +--R 12 +--R cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 +--R 400a b - 2400a b - 1152a b + 8896a b + 8720a b +--R + +--R 14 5 16 3 +--R 544a b - 928a b +--R * +--R 10 +--R cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 +--R - 400a b + 1200a b + 3072a b - 1024a b - 4464a b +--R + +--R 14 5 +--R - 1968a b +--R * +--R 8 +--R cos(x) +--R + +--R 4 15 8 11 10 9 12 7 6 +--R (200a b - 1144a b - 1488a b - 544a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 4 +--R (- 40a b - 120a b - 120a b - 40a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 15 4 17 2 +--R (8a b - 80a b + 120a b + 416a b + 120a b - 80a b + 8a b ) +--R * +--R 15 +--R cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 15 4 +--R - 40a b + 296a b - 104a b - 1368a b - 952a b + 56a b +--R + +--R 17 2 19 +--R 72a b - 8a +--R * +--R 13 +--R cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 15 4 +--R 80a b - 384a b - 384a b + 1216a b + 1552a b + 320a b +--R + +--R 17 2 +--R - 96a b +--R * +--R 11 +--R cos(x) +--R + +--R 5 14 7 12 9 10 13 6 15 4 9 +--R (- 80a b + 176a b + 576a b - 624a b - 304a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 7 +--R (40a b + 16a b - 184a b - 256a b - 96a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 5 +--R (- 8a b - 24a b - 24a b - 8a b )cos(x) +--R Type: Expression(Integer) +--E 73 + +--S 74 of 532 +t0713:= (a*cos(x)+b*sin(x))^(1/2) +--R +--R +--R +-------------------+ +--R (72) \|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 74 + +--S 75 of 532 +r0713:= 2*EllipticE(1/2*x-1/2*atan(a,b),2)*(a*cos(x)+_ + b*sin(x))^(1/2)/((a*cos(x)+b*sin(x))/(a^2+b^2)^(1/2))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Variable(a) +--R Variable(b) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 75 + +--S 76 of 532 +a0713:= integrate(t0713,x) +--R +--R +--R x +--R ++ +---------------------+ +--R (73) | \|b sin(%P) + a cos(%P) d%P +--R ++ +--R Type: Union(Expression(Integer),...) +--E 76 + +--S 77 of 532 +m0713:= a0713-r0713 +--R +--R +--R x +--R ++ +---------------------+ +--R (74) | \|b sin(%P) + a cos(%P) d%P - r0713 +--R ++ +--R Type: Expression(Integer) +--E 77 + +--S 78 of 532 +d0713:= D(m0713,x) +--R +--R +--R +-------------------+ +--R (75) \|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 78 + +--S 79 of 532 +t0714:= (a*cos(x)+b*sin(x))^(3/2) +--R +--R +--R +-------------------+ +--R (76) (b sin(x) + a cos(x))\|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 532 +r0714:= -2/3*(b*cos(x)-a*sin(x))*(a*cos(x)+b*sin(x))^(1/2)+_ + 2/3*(a^2+b^2)*EllipticF(1/2*x-1/2*atan(a,b),2)*_ + ((a*cos(x)+b*sin(x))/(a^2+b^2)^(1/2))^(1/2)/(a*cos(x)+b*sin(x))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Variable(a) +--R Variable(b) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 80 + +--S 81 of 532 +a0714:= integrate(t0714,x) +--R +--R +--R x +--R ++ +---------------------+ +--R (77) | (b sin(%P) + a cos(%P))\|b sin(%P) + a cos(%P) d%P +--R ++ +--R Type: Union(Expression(Integer),...) +--E 81 + +--S 82 of 532 +m0714:= a0714-r0714 +--R +--R +--R x +--R ++ +---------------------+ +--R (78) | (b sin(%P) + a cos(%P))\|b sin(%P) + a cos(%P) d%P - r0714 +--R ++ +--R Type: Expression(Integer) +--E 82 + +--S 83 of 532 +d0714:= D(m0714,x) +--R +--R +--R +-------------------+ +--R (79) (b sin(x) + a cos(x))\|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 83 + +--S 84 of 532 +t0715:= (a*cos(x)+b*sin(x))^(5/2) +--R +--R +--R 2 2 2 2 +-------------------+ +--R (80) (b sin(x) + 2a b cos(x)sin(x) + a cos(x) )\|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 84 + +--S 85 of 532 +r0715:= -2/5*(b*cos(x)-a*sin(x))*(a*cos(x)+b*sin(x))^(3/2)+_ + 6/5*(a^2+b^2)*EllipticE(1/2*x-1/2*atan(a,b),2)*_ + (a*cos(x)+b*sin(x))^(1/2)/((a*cos(x)+b*sin(x))/(a^2+b^2)^(1/2))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Variable(a) +--R Variable(b) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 85 + +--S 86 of 532 +a0715:= integrate(t0715,x) +--R +--R +--R (81) +--R INTSIGN +--R , +--R x +--R , +--R 2 2 2 2 +---------------------+ +--R (b sin(%P) + 2a b cos(%P)sin(%P) + a cos(%P) )\|b sin(%P) + a cos(%P) d%P +--R Type: Union(Expression(Integer),...) +--E 86 + +--S 87 of 532 +m0715:= a0715-r0715 +--R +--R +--R (82) +--R INTSIGN +--R , +--R x +--R , +--R 2 2 2 2 +--R (b sin(%P) + 2a b cos(%P)sin(%P) + a cos(%P) ) +--R * +--R +---------------------+ +--R \|b sin(%P) + a cos(%P) d%P +--R + +--R - r0715 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 532 +d0715:= D(m0715,x) +--R +--R +--R 2 2 2 2 +-------------------+ +--R (83) (b sin(x) + 2a b cos(x)sin(x) + a cos(x) )\|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 88 + +--S 89 of 532 +t0716:= 1/(a*cos(x)+b*sin(x))^(1/2) +--R +--R +--R 1 +--R (84) ---------------------- +--R +-------------------+ +--R \|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 89 + +--S 90 of 532 +r0716:= 2*EllipticF(1/2*x-1/2*atan(a,b),2)*_ + ((a*cos(x)+b*sin(x))/(a^2+b^2)^(1/2))^(1/2)/(a*cos(x)+b*sin(x))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Variable(a) +--R Variable(b) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 90 + +--S 91 of 532 +a0716:= integrate(t0716,x) +--R +--R +--R x +--R ++ 1 +--R (85) | ------------------------ d%P +--R ++ +---------------------+ +--R \|b sin(%P) + a cos(%P) +--R Type: Union(Expression(Integer),...) +--E 91 + +--S 92 of 532 +m0716:= a0716-r0716 +--R +--R +--R x +--R ++ 1 +--R (86) | ------------------------ d%P - r0716 +--R ++ +---------------------+ +--R \|b sin(%P) + a cos(%P) +--R Type: Expression(Integer) +--E 92 + +--S 93 of 532 +d0716:= D(m0716,x) +--R +--R +--R 1 +--R (87) ---------------------- +--R +-------------------+ +--R \|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 93 + +--S 94 of 532 +t0717:= 1/(a*cos(x)+b*sin(x))^(3/2) +--R +--R +--R 1 +--R (88) ------------------------------------------- +--R +-------------------+ +--R (b sin(x) + a cos(x))\|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 94 + +--S 95 of 532 +r0717:= -2*(b*cos(x)-a*sin(x))/(a^2+b^2)/(a*cos(x)+b*sin(x))^(1/2)-_ + 2*EllipticE(1/2*x-1/2*atan(a,b),2)*(a*cos(x)+b*sin(x))^(1/2)/_ + (a^2+b^2)/((a*cos(x)+b*sin(x))/(a^2+b^2)^(1/2))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Variable(a) +--R Variable(b) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 95 + +--S 96 of 532 +a0717:= integrate(t0717,x) +--R +--R +--R x +--R ++ 1 +--R (89) | ----------------------------------------------- d%P +--R ++ +---------------------+ +--R (b sin(%P) + a cos(%P))\|b sin(%P) + a cos(%P) +--R Type: Union(Expression(Integer),...) +--E 96 + +--S 97 of 532 +m0717:= a0717-r0717 +--R +--R +--R x +--R ++ 1 +--R (90) | ----------------------------------------------- d%P - r0717 +--R ++ +---------------------+ +--R (b sin(%P) + a cos(%P))\|b sin(%P) + a cos(%P) +--R Type: Expression(Integer) +--E 97 + +--S 98 of 532 +d0717:= D(m0717,x) +--R +--R +--R 1 +--R (91) ------------------------------------------- +--R +-------------------+ +--R (b sin(x) + a cos(x))\|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 98 + +--S 99 of 532 +t0718:= 1/(a*cos(x)+b*sin(x))^(5/2) +--R +--R +--R 1 +--R (92) ----------------------------------------------------------------- +--R 2 2 2 2 +-------------------+ +--R (b sin(x) + 2a b cos(x)sin(x) + a cos(x) )\|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 532 +r0718:= -2/3*(b*cos(x)-a*sin(x))/(a^2+b^2)/(a*cos(x)+b*sin(x))^(3/2)+_ + 2/3*EllipticF(1/2*x-1/2*atan(a,b),2)*((a*cos(x)+b*sin(x))/_ + (a^2+b^2)^(1/2))^(1/2)/(a^2+b^2)/(a*cos(x)+b*sin(x))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Variable(a) +--R Variable(b) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 100 + +--S 101 of 532 +a0718:= integrate(t0718,x) +--R +--R +--R (93) +--R INTSIGN +--R , +--R x +--R , +--R 1 +--R ----------------------------------------------------------------------- +--R 2 2 2 2 +---------------------+ +--R (b sin(%P) + 2a b cos(%P)sin(%P) + a cos(%P) )\|b sin(%P) + a cos(%P) +--R * +--R d%P +--R Type: Union(Expression(Integer),...) +--E 101 + +--S 102 of 532 +m0718:= a0718-r0718 +--R +--R +--R (94) +--R INTSIGN +--R , +--R x +--R , +--R 1 +--R / +--R 2 2 2 2 +--R (b sin(%P) + 2a b cos(%P)sin(%P) + a cos(%P) ) +--R * +--R +---------------------+ +--R \|b sin(%P) + a cos(%P) +--R * +--R d%P +--R + +--R - r0718 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 532 +d0718:= D(m0718,x) +--R +--R +--R 1 +--R (95) ----------------------------------------------------------------- +--R 2 2 2 2 +-------------------+ +--R (b sin(x) + 2a b cos(x)sin(x) + a cos(x) )\|b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 103 + +--S 104 of 532 +t0719:= (a*sec(x)+b*tan(x))^5 +--R +--R +--R (96) +--R 5 5 4 4 2 3 2 3 +--R b tan(x) + 5a b sec(x)tan(x) + 10a b sec(x) tan(x) +--R + +--R 3 2 3 2 4 4 5 5 +--R 10a b sec(x) tan(x) + 5a b sec(x) tan(x) + a sec(x) +--R Type: Expression(Integer) +--E 104 + +--S 105 of 532 +r0719:= -1/16*(a+b)^3*(3*a^2-9*a*b+8*b^2)*log(1-sin(x))+1/16*(a-b)^3*_ + (3*a^2+9*a*b+8*b^2)*log(1+sin(x))+1/16*(a+b)^5/(1-sin(x))^2+_ + (3*a-7*b)*(a+b)^4/(16-16*sin(x))-1/16*(a-b)^5/(1+sin(x))^2-_ + (a-b)^4*(3*a+7*b)/(16+16*sin(x)) +--R +--R +--R (97) +--R 5 4 3 2 5 4 +--R (- 8b + 15a b - 10a b + 3a )sin(x) +--R + +--R 5 4 3 2 5 2 5 4 3 2 5 +--R (16b - 30a b + 20a b - 6a )sin(x) - 8b + 15a b - 10a b + 3a +--R * +--R log(sin(x) + 1) +--R + +--R 5 4 3 2 5 4 +--R (- 8b - 15a b + 10a b - 3a )sin(x) +--R + +--R 5 4 3 2 5 2 5 4 3 2 5 +--R (16b + 30a b - 20a b + 6a )sin(x) - 8b - 15a b + 10a b - 3a +--R * +--R log(- sin(x) + 1) +--R + +--R 4 3 2 5 3 5 2 3 2 +--R (50a b + 20a b - 6a )sin(x) + (16b + 80a b )sin(x) +--R + +--R 4 3 2 5 5 2 3 4 +--R (- 30a b + 20a b + 10a )sin(x) - 12b - 40a b + 20a b +--R / +--R 4 2 +--R 16sin(x) - 32sin(x) + 16 +--R Type: Expression(Integer) +--E 105 + +--S 106 of 532 +a0719:= integrate(t0719,x) +--R +--R +--R (98) +--R 5 4 3 2 5 4 sin(x) + cos(x) + 1 +--R (- 8b + 15a b - 10a b + 3a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 5 4 3 2 5 4 sin(x) - cos(x) - 1 +--R (- 8b - 15a b + 10a b - 3a )cos(x) log(-------------------) +--R cos(x) + 1 +--R + +--R 5 4 2 +--R 8b cos(x) log(----------) +--R cos(x) + 1 +--R + +--R 4 3 2 5 2 4 3 2 5 +--R ((- 25a b - 10a b + 3a )cos(x) + 10a b + 20a b + 2a )sin(x) +--R + +--R 5 2 3 4 4 5 2 3 2 5 2 3 +--R (6b + 20a b - 10a b)cos(x) + (- 8b - 40a b )cos(x) + 2b + 20a b +--R + +--R 4 +--R 10a b +--R / +--R 4 +--R 8cos(x) +--R Type: Union(Expression(Integer),...) +--E 106 + +--S 107 of 532 +m0719:= a0719-r0719 +--R +--R +--R (99) +--R 5 4 3 2 5 4 4 +--R (8b - 15a b + 10a b - 3a )cos(x) sin(x) +--R + +--R 5 4 3 2 5 4 2 +--R (- 16b + 30a b - 20a b + 6a )cos(x) sin(x) +--R + +--R 5 4 3 2 5 4 +--R (8b - 15a b + 10a b - 3a )cos(x) +--R * +--R log(sin(x) + 1) +--R + +--R 5 4 3 2 5 4 4 +--R (- 16b + 30a b - 20a b + 6a )cos(x) sin(x) +--R + +--R 5 4 3 2 5 4 2 +--R (32b - 60a b + 40a b - 12a )cos(x) sin(x) +--R + +--R 5 4 3 2 5 4 +--R (- 16b + 30a b - 20a b + 6a )cos(x) +--R * +--R sin(x) + cos(x) + 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 5 4 3 2 5 4 4 +--R (- 16b - 30a b + 20a b - 6a )cos(x) sin(x) +--R + +--R 5 4 3 2 5 4 2 +--R (32b + 60a b - 40a b + 12a )cos(x) sin(x) +--R + +--R 5 4 3 2 5 4 +--R (- 16b - 30a b + 20a b - 6a )cos(x) +--R * +--R sin(x) - cos(x) - 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 5 4 4 5 4 2 5 4 2 +--R (16b cos(x) sin(x) - 32b cos(x) sin(x) + 16b cos(x) )log(----------) +--R cos(x) + 1 +--R + +--R 5 4 3 2 5 4 4 +--R (8b + 15a b - 10a b + 3a )cos(x) sin(x) +--R + +--R 5 4 3 2 5 4 2 +--R (- 16b - 30a b + 20a b - 6a )cos(x) sin(x) +--R + +--R 5 4 3 2 5 4 +--R (8b + 15a b - 10a b + 3a )cos(x) +--R * +--R log(- sin(x) + 1) +--R + +--R 4 3 2 5 2 4 3 2 5 5 +--R ((- 50a b - 20a b + 6a )cos(x) + 20a b + 40a b + 4a )sin(x) +--R + +--R 5 2 3 4 4 5 2 3 2 5 +--R (12b + 40a b - 20a b)cos(x) + (- 16b - 80a b )cos(x) + 4b +--R + +--R 2 3 4 +--R 40a b + 20a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 4 3 2 5 2 +--R (- 50a b - 20a b + 6a )cos(x) + (100a b + 40a b - 12a )cos(x) +--R + +--R 4 3 2 5 +--R - 40a b - 80a b - 8a +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 2 5 +--R (- 40b - 160a b + 40a b)cos(x) + (32b + 160a b )cos(x) - 8b +--R + +--R 2 3 4 +--R - 80a b - 40a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 5 4 4 3 2 5 2 +--R (30a b - 20a b - 10a )cos(x) + (- 50a b - 20a b + 6a )cos(x) +--R + +--R 4 3 2 5 +--R 20a b + 40a b + 4a +--R * +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 2 5 2 3 +--R (24b + 80a b - 40a b)cos(x) + (- 16b - 80a b )cos(x) + 4b + 40a b +--R + +--R 4 +--R 20a b +--R / +--R 4 4 4 2 4 +--R 16cos(x) sin(x) - 32cos(x) sin(x) + 16cos(x) +--R Type: Expression(Integer) +--E 107 + +--S 108 of 532 +d0719:= D(m0719,x) +--R +--R +--R (100) +--R 4 3 2 5 3 4 3 2 5 2 +--R (- 50a b - 20a b + 6a )cos(x) + (- 50a b - 20a b + 6a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (40a b + 80a b + 8a )cos(x) + 40a b + 80a b + 8a +--R * +--R 10 +--R sin(x) +--R + +--R 5 5 5 2 3 3 5 2 3 2 +--R - 8b cos(x) + (- 16b - 80a b )cos(x) + (- 16b - 80a b )cos(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R (8b + 80a b + 40a b)cos(x) + 8b + 80a b + 40a b +--R * +--R 9 +--R sin(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (- 30a b + 20a b - 6a )cos(x) + (- 5a b + 30a b - 9a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (125a b + 50a b - 15a )cos(x) + (270a b + 60a b - 42a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (90a b - 140a b - 46a )cos(x) + (- 240a b - 480a b - 48a )cos(x) +--R + +--R 4 3 2 5 +--R - 160a b - 320a b - 32a +--R * +--R 8 +--R sin(x) +--R + +--R 5 7 5 6 5 2 3 5 +--R - 16b cos(x) - 24b cos(x) + (32b + 80a b )cos(x) +--R + +--R 5 2 3 4 5 2 3 4 3 +--R (48b + 240a b )cos(x) + (88b + 400a b - 40a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (40b + 80a b - 120a b)cos(x) + (- 48b - 480a b - 240a b)cos(x) +--R + +--R 5 2 3 4 +--R - 32b - 320a b - 160a b +--R * +--R 7 +--R sin(x) +--R + +--R 4 3 2 5 8 4 3 2 5 7 +--R (- 30a b + 20a b - 6a )cos(x) + (5a b + 50a b - 15a )cos(x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (175a b - 10a b + 3a )cos(x) + (80a b - 80a b + 16a )cos(x) +--R + +--R 4 3 2 5 4 +--R (- 380a b - 200a b + 36a )cos(x) +--R + +--R 4 3 2 5 3 +--R (- 540a b - 120a b + 84a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 +--R (20a b + 520a b + 100a )cos(x) + (480a b + 960a b + 96a )cos(x) +--R + +--R 4 3 2 5 +--R 240a b + 480a b + 48a +--R * +--R 6 +--R sin(x) +--R + +--R 5 9 5 8 5 2 3 7 +--R - 8b cos(x) - 24b cos(x) + (48b + 80a b )cos(x) +--R + +--R 5 2 3 6 5 2 3 5 +--R (88b + 80a b )cos(x) + (- 48b - 240a b )cos(x) +--R + +--R 5 2 3 4 5 2 3 4 3 +--R (- 144b - 720a b )cos(x) + (- 168b - 720a b + 120a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 24b + 240a b + 360a b)cos(x) + (96b + 960a b + 480a b)cos(x) +--R + +--R 5 2 3 4 +--R 48b + 480a b + 240a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 9 4 3 2 5 8 +--R - 40a b cos(x) + (- 30a b - 60a b + 18a )cos(x) +--R + +--R 4 3 2 5 7 +--R (- 15a b - 70a b + 45a )cos(x) +--R + +--R 4 3 2 5 6 +--R (- 265a b - 10a b + 27a )cos(x) +--R + +--R 4 3 2 5 5 4 3 2 5 4 +--R (- 210a b + 60a b + 6a )cos(x) + (390a b + 300a b - 18a )cos(x) +--R + +--R 4 3 2 5 3 +--R (500a b + 200a b - 60a )cos(x) +--R + +--R 4 3 2 5 2 +--R (- 100a b - 520a b - 84a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (- 400a b - 800a b - 80a )cos(x) - 160a b - 320a b - 32a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 9 2 3 8 5 2 3 4 7 +--R - 80a b cos(x) - 240a b cos(x) + (- 72b - 240a b + 40a b)cos(x) +--R + +--R 5 2 3 4 6 5 2 3 5 +--R (- 96b - 80a b + 40a b)cos(x) + (32b + 240a b )cos(x) +--R + +--R 5 2 3 4 5 2 3 4 3 +--R (144b + 720a b )cos(x) + (136b + 560a b - 120a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 8b - 400a b - 360a b)cos(x) + (- 80b - 800a b - 400a b)cos(x) +--R + +--R 5 2 3 4 +--R - 32b - 320a b - 160a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 9 4 3 2 5 8 +--R - 80a b cos(x) + (- 90a b - 180a b - 18a )cos(x) +--R + +--R 4 3 2 5 7 4 3 2 5 6 +--R (- 105a b - 90a b - 37a )cos(x) + (165a b + 50a b - 31a )cos(x) +--R + +--R 4 5 5 4 3 2 5 4 +--R (200a b - 24a )cos(x) + (- 140a b - 200a b - 12a )cos(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (- 210a b - 180a b + 6a )cos(x) + (30a b + 140a b + 22a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (120a b + 240a b + 24a )cos(x) + 40a b + 80a b + 8a +--R * +--R 2 +--R sin(x) +--R + +--R 4 9 4 8 5 4 7 +--R - 40a b cos(x) - 120a b cos(x) + (24b - 120a b)cos(x) +--R + +--R 5 4 6 5 2 3 5 +--R (32b - 40a b)cos(x) + (- 8b - 80a b )cos(x) +--R + +--R 5 2 3 4 5 2 3 4 3 +--R (- 48b - 240a b )cos(x) + (- 40b - 160a b + 40a b)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (8b + 160a b + 120a b)cos(x) + (24b + 240a b + 120a b)cos(x) +--R + +--R 5 2 3 4 +--R 8b + 80a b + 40a b +--R * +--R sin(x) +--R + +--R 5 9 4 3 2 5 8 +--R - 8a cos(x) + (30a b - 20a b - 18a )cos(x) +--R + +--R 4 3 2 5 7 4 3 2 5 6 +--R (35a b - 50a b - 9a )cos(x) + (- 45a b - 50a b + 7a )cos(x) +--R + +--R 4 3 2 5 5 4 3 2 5 4 +--R (- 65a b - 10a b + 11a )cos(x) + (5a b + 50a b + 9a )cos(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (30a b + 60a b + 6a )cos(x) + (10a b + 20a b + 2a )cos(x) +--R / +--R 6 5 8 +--R (8cos(x) + 8cos(x) )sin(x) +--R + +--R 8 7 6 5 6 +--R (- 8cos(x) - 24cos(x) - 48cos(x) - 32cos(x) )sin(x) +--R + +--R 8 7 6 5 4 +--R (24cos(x) + 72cos(x) + 96cos(x) + 48cos(x) )sin(x) +--R + +--R 8 7 6 5 2 8 +--R (- 24cos(x) - 72cos(x) - 80cos(x) - 32cos(x) )sin(x) + 8cos(x) +--R + +--R 7 6 5 +--R 24cos(x) + 24cos(x) + 8cos(x) +--R Type: Expression(Integer) +--E 108 + +--S 109 of 532 +t0720:= 1/(a*sec(x)+b*tan(x))^2 +--R +--R +--R 1 +--R (101) ----------------------------------------- +--R 2 2 2 2 +--R b tan(x) + 2a b sec(x)tan(x) + a sec(x) +--R Type: Expression(Integer) +--E 109 + +--S 110 of 532 +r0720:= -x/b^2+2*a*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2/_ + (a^2-b^2)^(1/2)-cos(x)/b/(a+b*sin(x)) +--R +--R +--R (102) +--R x +--R a tan(-) + b +--R 2 2 +--R (2a b sin(x) + 2a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R (- b x sin(x) - b cos(x) - a x)\|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R (b sin(x) + a b )\|- b + a +--R Type: Expression(Integer) +--E 110 + +--S 111 of 532 +a0720:= integrate(t0720,x) +--R +--R +--R (103) +--R [ +--R 2 3 +--R (a b sin(x) + a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R 2 2 | 2 2 +--R ((- a b x - b )sin(x) - a b cos(x) - a x - a b)\|b - a +--R / +--R +-------+ +--R 3 2 2 | 2 2 +--R (a b sin(x) + a b )\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 3 (a sin(x) + b cos(x) + b)\|- b + a +--R (- 2a b sin(x) - 2a )atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R 2 2 | 2 2 +--R ((- a b x - b )sin(x) - a b cos(x) - a x - a b)\|- b + a +--R / +--R +---------+ +--R 3 2 2 | 2 2 +--R (a b sin(x) + a b )\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 111 + +--S 112 of 532 +m0720a:= a0720.1-r0720 +--R +--R +--R (104) +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +---------+ +-------+ +--R 2 | 2 2 2 | 2 2 | 2 2 +--R - 2a \|b - a atan(------------) - b\|- b + a \|b - a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a b \|- b + a \|b - a +--R Type: Expression(Integer) +--E 112 + +--S 113 of 532 +d0720a:= D(m0720a,x) +--R +--R +--R (105) +--R 2 3 2 2 2 2 x 2 +--R (((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b)tan(-) +--R 2 +--R + +--R 2 2 2 2 2 2 3 +--R (2a b sin(x) + 2a b sin(x) + 2a b cos(x) + (2a b - 2a )cos(x)) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 2 2 +--R ((- a b + a )cos(x) - a b )sin(x) + a b cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 3 3 3 2 2 4 2 2 2 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b +--R + +--R 4 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 2 4 +--R (- 2a b + 2a b)sin(x) + (- 2a b + 2a )sin(x) +--R + +--R 3 3 2 3 3 +--R (- 2a b + 2a b)cos(x) + (- 2a b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 3 3 2 2 4 2 2 2 4 +--R ((a b - a b)cos(x) + a b - a b)sin(x) + (- a b + a )cos(x) + a b - a +--R / +--R 2 3 2 4 3 2 4 3 2 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (a b - a b)cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 5 2 3 5 2 3 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 4 3 2 4 +--R (2a b - 2a b )cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 4 3 2 4 3 2 +--R a b sin(x) + ((a b - a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 3 +--R (a b - a b)cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- a b + a b )cos(x) - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 3 2 +--R (- 2a b + 2a b )sin(x) +--R + +--R 6 2 4 6 4 2 5 3 3 +--R ((- 2b + 2a b )cos(x) - 2b + 2a b )sin(x) + (- 2a b + 2a b )cos(x) +--R + +--R 5 3 3 +--R - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 5 3 3 5 5 +--R (- a b + a b )sin(x) + ((- a b + a b )cos(x) - a b + a b)sin(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- a b + a b )cos(x) - a b + a b +--R Type: Expression(Integer) +--E 113 + +--S 114 of 532 +m0720b:= a0720.2-r0720 +--R +--R +--R (106) +--R +---------+ x +--R | 2 2 a tan(-) + b +--R 2 (a sin(x) + b cos(x) + b)\|- b + a 2 2 +--R - 2a atan(-------------------------------------) - 2a atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R - b\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a b \|- b + a +--R Type: Expression(Integer) +--E 114 + +--S 115 of 532 +d0720b:= D(m0720b,x) +--R +--R +--R (107) +--R 2 2 2 2 2 x 2 +--R (a sin(x) + (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a )tan(-) +--R 2 +--R + +--R 2 2 x 2 2 +--R (4a b sin(x) + 4a b cos(x) + 4a b cos(x))tan(-) + a sin(x) +--R 2 +--R + +--R 2 2 2 +--R (- 2a b cos(x) - 2a b)sin(x) + a cos(x) - a +--R / +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 4 3 2 3 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 3 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 2 +--R a b +--R Type: Expression(Integer) +--E 115 + +--S 116 of 532 +t0721:= 1/(a*sec(x)+b*tan(x))^4 +--R +--R +--R (108) +--R 1 +--R / +--R 4 4 3 3 2 2 2 2 3 3 +--R b tan(x) + 4a b sec(x)tan(x) + 6a b sec(x) tan(x) + 4a b sec(x) tan(x) +--R + +--R 4 4 +--R a sec(x) +--R Type: Expression(Integer) +--E 116 + +--S 117 of 532 +r0721:= x/b^4+2*a^3*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^4/_ + (a^2-b^2)^(3/2)-a*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^2/_ + (a^2-b^2)^(3/2)-4*a*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b^4/_ + (a^2-b^2)^(1/2)+1/3*(a^2-b^2)*cos(x)/b^3/(a+b*sin(x))^3-_ + 7/6*a*cos(x)/b^3/(a+b*sin(x))^2+11/6*a^2*cos(x)/b^3/(a^2-b^2)/_ + (a+b*sin(x))-4/3*cos(x)/b/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (109) +--R 5 3 3 3 2 4 4 2 2 +--R (- 18a b + 12a b )sin(x) + (- 54a b + 36a b )sin(x) +--R + +--R 3 3 5 4 2 6 +--R (- 54a b + 36a b)sin(x) - 18a b + 12a +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 3 +--R (6b - 6a b )x sin(x) +--R + +--R 5 2 3 4 3 2 2 +--R ((8b - 11a b )cos(x) + (18a b - 18a b )x)sin(x) +--R + +--R 4 3 2 2 3 4 +--R ((9a b - 15a b )cos(x) + (18a b - 18a b)x)sin(x) +--R + +--R 5 2 3 4 3 2 5 +--R (- 2b + 5a b - 6a b)cos(x) + (6a b - 6a )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 9 2 7 3 8 3 6 2 +--R (6b - 6a b )sin(x) + (18a b - 18a b )sin(x) +--R + +--R 2 7 4 5 3 6 5 4 +--R (18a b - 18a b )sin(x) + 6a b - 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 117 + +--S 118 of 532 +a0721:= integrate(t0721,x) +--R +--R +--R (110) +--R [ +--R 4 5 6 3 2 4 5 6 3 8 +--R ((9a b - 6a b )cos(x) - 9a b - 21a b + 18a b)sin(x) +--R + +--R 5 4 7 2 2 5 4 7 2 9 +--R (27a b - 18a b )cos(x) - 27a b + 9a b + 6a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 3 5 5 3 8 2 6 4 4 2 +--R ((6a b - 6a b )x - 2b + 5a b - 6a b )cos(x) +--R + +--R 4 4 6 2 3 5 5 3 7 8 +--R (- 9a b + 15a b )cos(x) + (- 6a b - 12a b + 18a b)x + 2b +--R + +--R 2 6 4 4 6 2 +--R a b - 9a b + 18a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 3 +--R (8a b - 11a b )cos(x) +--R + +--R 4 4 6 2 7 3 5 5 3 2 +--R ((18a b - 18a b )x - 6a b + 15a b - 18a b )cos(x) +--R + +--R 3 5 5 3 7 4 4 6 2 8 7 +--R (- 6a b + 6a b + 6a b)cos(x) + (- 18a b + 12a b + 6a )x + 6a b +--R + +--R 3 5 5 3 7 +--R - 13a b + 13a b + 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 3 9 5 7 2 3 9 5 7 7 5 +--R ((6a b - 6a b )cos(x) - 6a b - 12a b + 18a b )sin(x) +--R + +--R 4 8 6 6 2 4 8 6 6 8 4 +--R (18a b - 18a b )cos(x) - 18a b + 12a b + 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 4 5 6 3 2 4 5 6 3 8 +--R ((18a b - 12a b )cos(x) - 18a b - 42a b + 36a b)sin(x) +--R + +--R 5 4 7 2 2 5 4 7 2 9 +--R (54a b - 36a b )cos(x) - 54a b + 18a b + 12a +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 3 5 5 3 8 2 6 4 4 2 +--R ((6a b - 6a b )x - 2b + 5a b - 6a b )cos(x) +--R + +--R 4 4 6 2 3 5 5 3 7 8 +--R (- 9a b + 15a b )cos(x) + (- 6a b - 12a b + 18a b)x + 2b +--R + +--R 2 6 4 4 6 2 +--R a b - 9a b + 18a b +--R * +--R sin(x) +--R + +--R 3 5 5 3 3 +--R (8a b - 11a b )cos(x) +--R + +--R 4 4 6 2 7 3 5 5 3 2 +--R ((18a b - 18a b )x - 6a b + 15a b - 18a b )cos(x) +--R + +--R 3 5 5 3 7 4 4 6 2 8 7 +--R (- 6a b + 6a b + 6a b)cos(x) + (- 18a b + 12a b + 6a )x + 6a b +--R + +--R 3 5 5 3 7 +--R - 13a b + 13a b + 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 9 5 7 2 3 9 5 7 7 5 +--R ((6a b - 6a b )cos(x) - 6a b - 12a b + 18a b )sin(x) +--R + +--R 4 8 6 6 2 4 8 6 6 8 4 +--R (18a b - 18a b )cos(x) - 18a b + 12a b + 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 118 + +--S 119 of 532 +m0721a:= a0721.1-r0721 +--R +--R +--R (111) +--R 4 8 6 6 2 4 8 6 6 8 4 4 +--R ((9a b - 6a b )cos(x) - 9a b - 21a b + 18a b )sin(x) +--R + +--R 5 7 7 5 2 5 7 7 5 9 3 3 +--R ((54a b - 36a b )cos(x) - 54a b - 54a b + 60a b )sin(x) +--R + +--R 6 6 8 4 2 6 6 8 4 10 2 2 +--R ((108a b - 72a b )cos(x) - 108a b - 36a b + 72a b )sin(x) +--R + +--R 7 5 9 3 2 7 5 9 3 11 +--R ((90a b - 60a b )cos(x) - 90a b + 6a b + 36a b)sin(x) +--R + +--R 8 4 10 2 2 8 4 10 2 12 +--R (27a b - 18a b )cos(x) - 27a b + 9a b + 6a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 4 8 6 6 2 4 8 6 6 8 4 4 +--R ((18a b - 12a b )cos(x) - 18a b - 42a b + 36a b )sin(x) +--R + +--R 5 7 7 5 2 5 7 7 5 9 3 3 +--R ((108a b - 72a b )cos(x) - 108a b - 108a b + 120a b )sin(x) +--R + +--R 6 6 8 4 2 6 6 8 4 10 2 2 +--R ((216a b - 144a b )cos(x) - 216a b - 72a b + 144a b )sin(x) +--R + +--R 7 5 9 3 2 7 5 9 3 11 +--R ((180a b - 120a b )cos(x) - 180a b + 12a b + 72a b)sin(x) +--R + +--R 8 4 10 2 2 8 4 10 2 12 +--R (54a b - 36a b )cos(x) - 54a b + 18a b + 12a +--R * +--R x +--R +-------+ a tan(-) + b +--R | 2 2 2 +--R \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 11 2 9 4 7 2 4 7 6 5 11 +--R (- 2b + 5a b - 6a b )cos(x) + (- 9a b + 15a b )cos(x) + 2b +--R + +--R 2 9 4 7 6 5 +--R a b - 9a b + 18a b +--R * +--R 4 +--R sin(x) +--R + +--R 10 3 8 5 6 2 +--R (- 12a b + 30a b - 36a b )cos(x) +--R + +--R 3 8 5 6 7 4 10 3 8 5 6 7 4 +--R (2a b - 8a b + 18a b )cos(x) + 12a b - 10a b - 14a b + 60a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 7 6 5 3 2 9 4 7 6 5 2 +--R (- 9a b + 15a b )cos(x) + (- 24a b + 60a b - 72a b )cos(x) +--R + +--R 4 7 6 5 8 3 2 9 4 7 6 5 8 3 +--R (15a b - 22a b + 7a b )cos(x) + 24a b - 36a b + 12a b + 72a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 8 5 6 7 4 3 +--R (2a b - 8a b + 18a b )cos(x) +--R + +--R 3 8 5 6 7 4 2 +--R (- 20a b + 50a b - 60a b )cos(x) +--R + +--R 3 8 5 6 7 4 3 8 5 6 7 4 +--R (- 2a b + 8a b - 18a b )cos(x) + 20a b - 38a b + 30a b +--R + +--R 9 2 +--R 36a b +--R * +--R sin(x) +--R + +--R 4 7 6 5 8 3 3 4 7 6 5 8 3 2 +--R (6a b - 7a b + 7a b )cos(x) + (- 6a b + 15a b - 18a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 7 6 5 8 3 10 +--R (- 6a b + 7a b - 7a b )cos(x) + 6a b - 13a b + 13a b + 6a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 3 12 5 10 2 3 12 5 10 7 8 4 +--R ((6a b - 6a b )cos(x) - 6a b - 12a b + 18a b )sin(x) +--R + +--R 4 11 6 9 2 4 11 6 9 8 7 3 +--R ((36a b - 36a b )cos(x) - 36a b - 24a b + 60a b )sin(x) +--R + +--R 5 10 7 8 2 5 10 9 6 2 +--R ((72a b - 72a b )cos(x) - 72a b + 72a b )sin(x) +--R + +--R 6 9 8 7 2 6 9 8 7 10 5 +--R ((60a b - 60a b )cos(x) - 60a b + 24a b + 36a b )sin(x) +--R + +--R 7 8 9 6 2 7 8 9 6 11 4 +--R (18a b - 18a b )cos(x) - 18a b + 12a b + 6a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 119 + +--S 120 of 532 +d0721a:= D(m0721a,x) +--R +--R +--R (112) +--R 3 11 5 9 2 3 11 5 9 7 7 8 +--R ((- 9a b + 15a b )cos(x) - 9a b - 12a b + 45a b )sin(x) +--R + +--R 2 12 4 10 6 8 3 +--R (- 9a b + 24a b - 15a b )cos(x) +--R + +--R 2 12 4 10 6 8 2 +--R (- 7a b - 29a b + 78a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 2 12 +--R (- 9a b - 3a b + 57a b - 45a b )cos(x) - 7a b +--R + +--R 4 10 6 8 8 6 +--R - 50a b + 63a b + 114a b +--R * +--R 7 +--R sin(x) +--R + +--R 13 3 11 5 9 5 +--R (9a b - 15a b + 6a b )cos(x) +--R + +--R 13 3 11 5 9 4 +--R (9a b + 3a b - 15a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 3 +--R (- 16a b - 70a b + 200a b - 114a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 2 +--R (- 16a b - 90a b - 3a b + 259a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 13 +--R (11a b - a b + 53a b - 3a b - 60a b )cos(x) + 11a b +--R + +--R 3 11 5 9 7 7 9 5 +--R 33a b + 35a b + 77a b + 108a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 12 4 10 6 +--R (- 9a b + 6a b )cos(x) +--R + +--R 2 12 4 10 6 8 5 +--R (90a b - 159a b + 69a b )cos(x) +--R + +--R 2 12 4 10 6 8 4 +--R (113a b - 35a b - 42a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 3 +--R (- 166a b - 185a b + 838a b - 487a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 2 +--R (- 187a b - 429a b + 396a b + 382a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (104a b + 156a b - 174a b - 176a b + 90a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R 111a b + 376a b + 87a b - 212a b + 46a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 11 5 9 6 +--R (- 63a b + 24a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 5 +--R (- 4a b + 272a b - 454a b + 186a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 4 +--R (- 4a b + 453a b - 44a b - 60a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (6a b - 534a b + 50a b + 1310a b - 832a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 2 +--R (6a b - 717a b - 878a b + 782a b + 417a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 2a b + 340a b + 194a b - 690a b - 72a b +--R + +--R 11 3 +--R 230a b +--R * +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 2a b + 405a b + 878a b - 166a b - 522a b + 7a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 12 4 10 6 8 7 +--R (18a b - 48a b + 30a b )cos(x) +--R + +--R 2 12 4 10 6 8 6 +--R (12a b - 258a b + 96a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (- 58a b + 434a b - 484a b + 108a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 4 +--R (- 46a b + 1096a b + 216a b - 306a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 3 +--R (54a b - 760a b + 293a b + 1136a b - 723a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 2 +--R (48a b - 1438a b - 1401a b + 1131a b + 346a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R - 14a b + 486a b - 69a b - 731a b + 155a b +--R + +--R 12 2 +--R 173a b +--R * +--R cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R - 14a b + 712a b + 1005a b - 464a b - 495a b +--R * +--R 3 +--R sin(x) +--R + +--R 13 3 11 5 9 7 7 7 +--R (- 6a b + 48a b - 126a b + 84a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 6 +--R (- 6a b + 6a b - 476a b + 230a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 5 +--R (12a b - 102a b + 495a b - 405a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 4 +--R (12a b - 18a b + 1697a b - 83a b - 393a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 6a b + 84a b - 688a b + 478a b + 430a b +--R + +--R 11 3 +--R - 298a b +--R * +--R 3 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 6a b + 42a b - 1906a b - 774a b + 939a b +--R + +--R 11 3 +--R 187a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R - 30a b + 353a b - 225a b - 291a b + 139a b +--R + +--R 13 +--R 54a b +--R * +--R cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R - 30a b + 719a b + 593a b - 441a b - 241a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 12 4 10 6 8 8 6 7 +--R (- 36a b + 58a b - 68a b + 46a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 6 +--R (- 36a b - 32a b - 297a b + 182a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 5 +--R (72a b - 22a b + 20a b - 13a b - 57a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 4 +--R (72a b + 158a b + 903a b - 197a b - 204a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 36a b - 18a b - 66a b + 77a b + 86a b - 43a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R - 36a b - 108a b - 999a b - 115a b + 394a b +--R + +--R 12 2 +--R 54a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 +--R (- 18a b + 114a b - 110a b - 20a b + 28a b + 6a ) +--R * +--R cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R - 18a b + 393a b + 130a b - 181a b - 60a b +--R * +--R sin(x) +--R + +--R 3 11 5 9 7 7 9 5 7 +--R (- 54a b + 100a b - 62a b + 16a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 6 +--R (- 54a b + 46a b - 97a b + 54a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 5 +--R (108a b - 166a b + 56a b + 26a b - 24a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 4 +--R (108a b - 58a b + 241a b - 84a b - 36a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (- 54a b + 66a b + 6a b - 42a b + 24a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 2 +--R (- 54a b + 12a b - 225a b + 30a b + 63a b + 6a b)cos(x) +--R + +--R 7 7 11 3 13 +--R 81a b - 27a b - 6a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 12 4 10 2 2 12 4 10 6 8 +--R ((- 18a b + 30a b )cos(x) - 18a b - 24a b + 90a b ) +--R * +--R 8 +--R sin(x) +--R + +--R 13 3 11 4 +--R (- 18a b + 12a b )cos(x) +--R + +--R 13 3 11 5 9 3 +--R (- 18a b + 48a b - 30a b )cos(x) +--R + +--R 13 3 11 5 9 2 +--R (22a b + 26a b + 84a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 13 +--R (- 18a b - 6a b + 114a b - 90a b )cos(x) - 32a b +--R + +--R 3 11 5 9 7 7 +--R - 196a b + 36a b + 336a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 12 4 10 4 +--R (- 162a b + 90a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 3 +--R (4b - 92a b + 244a b - 156a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 2 +--R (4b + 264a b + 474a b - 10a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 14 +--R (4b - 80a b + 112a b + 192a b - 228a b )cos(x) + 4b +--R + +--R 2 12 4 10 6 8 8 6 +--R - 210a b - 692a b + 34a b + 720a b +--R * +--R 6 +--R sin(x) +--R + +--R 13 3 11 6 3 11 5 9 5 +--R (- 18a b + 12a b )cos(x) + (- 18a b + 18a b )cos(x) +--R + +--R 13 3 11 5 9 4 +--R (46a b - 652a b + 384a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 3 +--R (28a b - 178a b + 596a b - 446a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 2 +--R (- 14a b + 1098a b + 1524a b - 700a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (28a b - 180a b + 96a b + 380a b - 324a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R 42a b - 622a b - 1782a b + 122a b + 1040a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 12 4 10 6 +--R (- 126a b + 48a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 5 +--R (- 8b - 158a b + 262a b - 96a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 4 +--R (- 8b + 204a b - 988a b + 792a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 3 +--R (12b + 336a b - 44a b - 104a b - 200a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 2 +--R (12b - 30a b + 2240a b + 1300a b - 1182a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 +--R - 4b - 22a b - 638a b + 390a b + 762a b +--R + +--R 10 4 +--R - 488a b +--R * +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 10 4 +--R - 4b + 108a b - 1340a b - 2402a b + 552a b + 926a b +--R * +--R 4 +--R sin(x) +--R + +--R 13 3 11 5 9 7 +--R (36a b - 96a b + 60a b )cos(x) +--R + +--R 13 3 11 5 9 6 +--R (24a b - 516a b + 192a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 5 +--R (- 116a b - 500a b + 1312a b - 696a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 4 +--R (- 92a b + 824a b - 78a b + 336a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (108a b + 1216a b - 950a b - 944a b + 570a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 2 +--R (96a b - 140a b + 1242a b + 546a b - 772a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 28a b - 396a b - 882a b + 1298a b + 574a b +--R + +--R 11 3 +--R - 566a b +--R * +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 28a b + 56a b - 1524a b - 1528a b + 684a b + 468a b +--R * +--R 3 +--R sin(x) +--R + +--R 14 2 12 4 10 6 8 7 +--R (- 12b + 96a b - 252a b + 168a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 6 +--R (- 12b + 12a b - 952a b + 460a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 5 +--R (24b - 204a b - 432a b + 1560a b - 948a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 4 +--R (24b - 36a b + 1972a b + 26a b - 282a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 +--R - 12b + 168a b + 1468a b - 1588a b - 904a b +--R + +--R 10 4 +--R 868a b +--R * +--R 3 +--R cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 +--R - 12b + 84a b - 968a b + 264a b + 198a b +--R + +--R 10 4 +--R - 154a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R - 60a b - 716a b - 276a b + 1428a b - 16a b +--R + +--R 12 2 +--R - 360a b +--R * +--R cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R - 60a b + 16a b - 818a b - 408a b + 334a b + 120a b +--R * +--R 2 +--R sin(x) +--R + +--R 13 3 11 5 9 7 7 7 +--R (- 72a b + 116a b - 136a b + 92a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 6 +--R (- 72a b - 64a b - 594a b + 364a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 5 +--R (144a b - 44a b - 716a b + 1234a b - 618a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 4 +--R (144a b + 316a b + 1050a b - 52a b - 300a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 72a b - 36a b + 1380a b - 1574a b - 140a b +--R + +--R 11 3 +--R 442a b +--R * +--R 3 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 72a b - 216a b - 486a b - 122a b + 152a b +--R + +--R 11 3 +--R 36a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R - 36a b - 528a b + 248a b + 596a b - 172a b +--R + +--R 13 +--R - 108a b +--R * +--R cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R - 36a b + 30a b - 190a b - 14a b + 54a b + 12a b +--R * +--R sin(x) +--R + +--R 2 12 4 10 6 8 8 6 7 +--R (- 108a b + 200a b - 124a b + 32a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 6 +--R (- 108a b + 92a b - 194a b + 108a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 5 +--R (216a b - 332a b - 50a b + 322a b - 156a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 4 +--R (216a b - 116a b + 320a b - 60a b - 72a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 108a b + 132a b + 336a b - 516a b + 84a b + 72a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 108a b + 24a b - 126a b - 48a b + 54a b + 12a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 6 8 8 6 10 4 12 2 14 +--R (- 162a b + 162a b + 54a b - 42a b - 12a )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 11 5 9 2 3 11 5 9 7 7 8 +--R ((- 9a b + 15a b )cos(x) - 9a b - 12a b + 45a b )sin(x) +--R + +--R 2 12 4 10 6 8 3 +--R (- 9a b + 24a b - 15a b )cos(x) +--R + +--R 2 12 4 10 6 8 2 +--R (- 7a b - 29a b + 78a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 2 12 4 10 +--R (- 9a b - 3a b + 57a b - 45a b )cos(x) - 7a b - 50a b +--R + +--R 6 8 8 6 +--R 63a b + 114a b +--R * +--R 7 +--R sin(x) +--R + +--R 13 3 11 5 9 5 +--R (9a b - 15a b + 6a b )cos(x) +--R + +--R 13 3 11 5 9 4 +--R (9a b + 3a b - 15a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 3 +--R (- 16a b - 70a b + 200a b - 114a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 2 +--R (- 16a b - 90a b - 3a b + 259a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 13 +--R (11a b - a b + 53a b - 3a b - 60a b )cos(x) + 11a b +--R + +--R 3 11 5 9 7 7 9 5 +--R 33a b + 35a b + 77a b + 108a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 12 4 10 6 2 12 4 10 6 8 5 +--R (- 9a b + 6a b )cos(x) + (90a b - 159a b + 69a b )cos(x) +--R + +--R 2 12 4 10 6 8 4 +--R (113a b - 35a b - 42a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 3 +--R (- 166a b - 185a b + 838a b - 487a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 2 +--R (- 187a b - 429a b + 396a b + 382a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (104a b + 156a b - 174a b - 176a b + 90a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R 111a b + 376a b + 87a b - 212a b + 46a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 11 5 9 6 +--R (- 63a b + 24a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 5 +--R (- 4a b + 272a b - 454a b + 186a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 4 +--R (- 4a b + 453a b - 44a b - 60a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (6a b - 534a b + 50a b + 1310a b - 832a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 2 +--R (6a b - 717a b - 878a b + 782a b + 417a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 2a b + 340a b + 194a b - 690a b - 72a b + 230a b ) +--R * +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 2a b + 405a b + 878a b - 166a b - 522a b + 7a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 12 4 10 6 8 7 +--R (18a b - 48a b + 30a b )cos(x) +--R + +--R 2 12 4 10 6 8 6 +--R (12a b - 258a b + 96a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (- 58a b + 434a b - 484a b + 108a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 4 +--R (- 46a b + 1096a b + 216a b - 306a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 3 +--R (54a b - 760a b + 293a b + 1136a b - 723a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 2 +--R (48a b - 1438a b - 1401a b + 1131a b + 346a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 14a b + 486a b - 69a b - 731a b + 155a b + 173a b ) +--R * +--R cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R - 14a b + 712a b + 1005a b - 464a b - 495a b +--R * +--R 3 +--R sin(x) +--R + +--R 13 3 11 5 9 7 7 7 +--R (- 6a b + 48a b - 126a b + 84a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 6 +--R (- 6a b + 6a b - 476a b + 230a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 5 +--R (12a b - 102a b + 495a b - 405a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 4 +--R (12a b - 18a b + 1697a b - 83a b - 393a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 6a b + 84a b - 688a b + 478a b + 430a b - 298a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 6a b + 42a b - 1906a b - 774a b + 939a b + 187a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (- 30a b + 353a b - 225a b - 291a b + 139a b + 54a b) +--R * +--R cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R - 30a b + 719a b + 593a b - 441a b - 241a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 12 4 10 6 8 8 6 7 +--R (- 36a b + 58a b - 68a b + 46a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 6 +--R (- 36a b - 32a b - 297a b + 182a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 5 +--R (72a b - 22a b + 20a b - 13a b - 57a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 4 +--R (72a b + 158a b + 903a b - 197a b - 204a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 36a b - 18a b - 66a b + 77a b + 86a b - 43a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 36a b - 108a b - 999a b - 115a b + 394a b + 54a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 +--R (- 18a b + 114a b - 110a b - 20a b + 28a b + 6a )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R - 18a b + 393a b + 130a b - 181a b - 60a b +--R * +--R sin(x) +--R + +--R 3 11 5 9 7 7 9 5 7 +--R (- 54a b + 100a b - 62a b + 16a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 6 +--R (- 54a b + 46a b - 97a b + 54a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 5 +--R (108a b - 166a b + 56a b + 26a b - 24a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 4 +--R (108a b - 58a b + 241a b - 84a b - 36a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (- 54a b + 66a b + 6a b - 42a b + 24a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 2 +--R (- 54a b + 12a b - 225a b + 30a b + 63a b + 6a b)cos(x) +--R + +--R 7 7 11 3 13 +--R 81a b - 27a b - 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 12 5 10 7 8 2 3 12 5 10 7 8 +--R (- 9a b + 24a b - 15a b )cos(x) - 9a b - 3a b + 57a b +--R + +--R 9 6 +--R - 45a b +--R * +--R 8 +--R sin(x) +--R + +--R 2 13 4 11 6 9 3 +--R (- 9a b + 24a b - 15a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 2 +--R (- 7a b - 22a b + 107a b - 78a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 2 13 4 11 +--R (- 9a b - 3a b + 57a b - 45a b )cos(x) - 7a b - 43a b +--R + +--R 6 9 8 7 10 5 +--R 113a b + 51a b - 114a b +--R * +--R 7 +--R sin(x) +--R + +--R 14 3 12 5 10 5 +--R (9a b - 15a b + 6a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 4 +--R (9a b - 6a b - 18a b + 15a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 3 +--R (- 16a b - 70a b + 200a b - 114a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 2 +--R (- 16a b - 74a b + 87a b + 262a b - 259a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 14 +--R (11a b - a b + 53a b - 3a b - 60a b )cos(x) + 11a b +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R 22a b + 2a b + 42a b + 31a b - 108a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 13 4 11 6 9 6 +--R (- 9a b + 15a b - 6a b )cos(x) +--R + +--R 2 13 4 11 6 9 5 +--R (90a b - 159a b + 69a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 4 +--R (113a b - 148a b - 7a b + 42a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 3 +--R (- 166a b - 185a b + 838a b - 487a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 2 +--R (- 187a b - 242a b + 825a b - 14a b - 382a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R (104a b + 156a b - 174a b - 176a b + 90a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R 111a b + 265a b - 289a b - 299a b + 258a b - 46a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 12 5 10 7 8 6 +--R (- 63a b + 87a b - 24a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 5 +--R (- 4a b + 272a b - 454a b + 186a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 4 +--R (- 4a b + 457a b - 497a b - 16a b + 60a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 3 +--R (6a b - 534a b + 50a b + 1310a b - 832a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (6a b - 723a b - 161a b + 1660a b - 365a b - 417a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (- 2a b + 340a b + 194a b - 690a b - 72a b + 230a b ) +--R * +--R cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 2a b + 407a b + 473a b - 1044a b - 356a b + 529a b +--R + +--R 13 2 +--R - 7a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 13 4 11 6 9 7 +--R (18a b - 48a b + 30a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 6 +--R (12a b - 270a b + 354a b - 96a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 5 +--R (- 58a b + 434a b - 484a b + 108a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 4 +--R (- 46a b + 1142a b - 880a b - 522a b + 306a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 3 +--R (54a b - 760a b + 293a b + 1136a b - 723a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (48a b - 1486a b + 37a b + 2532a b - 785a b - 346a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (- 14a b + 486a b - 69a b - 731a b + 155a b + 173a b ) +--R * +--R cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 14a b + 726a b + 293a b - 1469a b - 31a b + 495a b +--R * +--R 3 +--R sin(x) +--R + +--R 14 3 12 5 10 7 8 7 +--R (- 6a b + 48a b - 126a b + 84a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 6 +--R (- 6a b + 12a b - 482a b + 706a b - 230a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 5 +--R (12a b - 102a b + 495a b - 405a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (12a b - 30a b + 1715a b - 1780a b - 310a b + 393a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (- 6a b + 84a b - 688a b + 478a b + 430a b - 298a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 6a b + 48a b - 1948a b + 1132a b + 1713a b +--R + +--R 11 4 13 2 +--R - 752a b - 187a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (- 30a b + 353a b - 225a b - 291a b + 139a b + 54a b ) +--R * +--R cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R - 30a b + 749a b - 126a b - 1034a b + 200a b + 241a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 13 4 11 6 9 8 7 7 +--R (- 36a b + 58a b - 68a b + 46a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 6 +--R (- 36a b + 4a b - 265a b + 479a b - 182a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 5 +--R (72a b - 22a b + 20a b - 13a b - 57a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (72a b + 86a b + 745a b - 1100a b - 7a b + 204a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (- 36a b - 18a b - 66a b + 77a b + 86a b - 43a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 36a b - 72a b - 891a b + 884a b + 509a b - 340a b +--R + +--R 14 +--R - 54a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R (- 18a b + 114a b - 110a b - 20a b + 28a b + 6a b)cos(x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R - 18a b + 411a b - 263a b - 311a b + 121a b + 60a b +--R * +--R sin(x) +--R + +--R 3 12 5 10 7 8 9 6 7 +--R (- 54a b + 100a b - 62a b + 16a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 6 +--R (- 54a b + 100a b - 143a b + 151a b - 54a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 5 +--R (108a b - 166a b + 56a b + 26a b - 24a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 4 +--R (108a b - 166a b + 299a b - 325a b + 48a b + 36a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 3 +--R (- 54a b + 66a b + 6a b - 42a b + 24a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R - 54a b + 66a b - 237a b + 255a b + 33a b - 57a b +--R + +--R 15 +--R - 6a +--R * +--R 2 +--R cos(x) +--R + +--R 7 8 9 6 11 4 13 2 15 +--R 81a b - 81a b - 27a b + 21a b + 6a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 13 4 11 6 9 2 2 13 4 11 +--R (- 18a b + 48a b - 30a b )cos(x) - 18a b - 6a b +--R + +--R 6 9 8 7 +--R 114a b - 90a b +--R * +--R 8 +--R sin(x) +--R + +--R 14 3 12 5 10 4 +--R (- 18a b + 30a b - 12a b )cos(x) +--R + +--R 14 3 12 5 10 3 +--R (- 18a b + 48a b - 30a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 2 +--R (22a b + 4a b + 58a b - 84a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 14 +--R (- 18a b - 6a b + 114a b - 90a b )cos(x) - 32a b +--R + +--R 3 12 5 10 7 8 9 6 +--R - 164a b + 232a b + 300a b - 336a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 13 4 11 6 9 4 +--R (- 162a b + 252a b - 90a b )cos(x) +--R + +--R 15 2 13 4 11 6 9 3 +--R (4b - 92a b + 244a b - 156a b )cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 2 +--R (4b + 260a b + 210a b - 484a b + 10a b )cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 15 +--R (4b - 80a b + 112a b + 192a b - 228a b )cos(x) + 4b +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 214a b - 482a b + 726a b + 686a b - 720a b +--R * +--R 6 +--R sin(x) +--R + +--R 14 3 12 5 10 6 +--R (- 18a b + 30a b - 12a b )cos(x) +--R + +--R 3 12 5 10 5 +--R (- 18a b + 18a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 4 +--R (46a b - 698a b + 1036a b - 384a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 3 +--R (28a b - 178a b + 596a b - 446a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 2 +--R (- 14a b + 1112a b + 426a b - 2224a b + 700a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R (28a b - 180a b + 96a b + 380a b - 324a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R 42a b - 664a b - 1160a b + 1904a b + 918a b - 1040a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 13 4 11 6 9 6 +--R (- 126a b + 174a b - 48a b )cos(x) +--R + +--R 15 2 13 4 11 6 9 5 +--R (- 8b - 158a b + 262a b - 96a b )cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 4 +--R (- 8b + 212a b - 1192a b + 1780a b - 792a b )cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 3 +--R (12b + 336a b - 44a b - 104a b - 200a b )cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R (12b - 42a b + 2270a b - 940a b - 2482a b + 1182a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R (- 4b - 22a b - 638a b + 390a b + 762a b - 488a b ) +--R * +--R cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R - 4b + 112a b - 1448a b - 1062a b + 2954a b + 374a b +--R + +--R 12 3 +--R - 926a b +--R * +--R 4 +--R sin(x) +--R + +--R 14 3 12 5 10 7 +--R (36a b - 96a b + 60a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 6 +--R (24a b - 540a b + 708a b - 192a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 5 +--R (- 116a b - 500a b + 1312a b - 696a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 4 +--R (- 92a b + 916a b - 902a b + 414a b - 336a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 3 +--R (108a b + 1216a b - 950a b - 944a b + 570a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 96a b - 236a b + 1382a b - 696a b - 1318a b +--R + +--R 11 4 +--R 772a b +--R * +--R 2 +--R cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 28a b - 396a b - 882a b + 1298a b + 574a b +--R + +--R 11 4 +--R - 566a b +--R * +--R cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 28a b + 84a b - 1580a b - 4a b + 2212a b - 216a b +--R + +--R 13 2 +--R - 468a b +--R * +--R 3 +--R sin(x) +--R + +--R 15 2 13 4 11 6 9 7 +--R (- 12b + 96a b - 252a b + 168a b )cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 6 +--R (- 12b + 24a b - 964a b + 1412a b - 460a b )cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 5 +--R (24b - 204a b - 432a b + 1560a b - 948a b )cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R (24b - 60a b + 2008a b - 1946a b - 308a b + 282a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 +--R - 12b + 168a b + 1468a b - 1588a b - 904a b +--R + +--R 10 5 +--R 868a b +--R * +--R 3 +--R cos(x) +--R + +--R 15 2 13 4 11 6 9 8 7 10 5 +--R - 12b + 96a b - 1052a b + 1232a b - 66a b - 352a b +--R + +--R 12 3 +--R 154a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R - 60a b - 716a b - 276a b + 1428a b - 16a b +--R + +--R 12 3 +--R - 360a b +--R * +--R cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 60a b + 76a b - 834a b + 410a b + 742a b - 214a b +--R + +--R 14 +--R - 120a b +--R * +--R 2 +--R sin(x) +--R + +--R 14 3 12 5 10 7 8 7 +--R (- 72a b + 116a b - 136a b + 92a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 6 +--R (- 72a b + 8a b - 530a b + 958a b - 364a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 5 +--R (144a b - 44a b - 716a b + 1234a b - 618a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 144a b + 172a b + 734a b - 1102a b - 248a b +--R + +--R 11 4 +--R 300a b +--R * +--R 4 +--R cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 72a b - 36a b + 1380a b - 1574a b - 140a b +--R + +--R 11 4 +--R 442a b +--R * +--R 3 +--R cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 +--R - 72a b - 144a b - 270a b + 364a b + 274a b +--R + +--R 11 4 13 2 +--R - 116a b - 36a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R - 36a b - 528a b + 248a b + 596a b - 172a b +--R + +--R 13 2 +--R - 108a b +--R * +--R cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 15 +--R - 36a b + 66a b - 220a b + 176a b + 68a b - 42a b - 12a +--R * +--R sin(x) +--R + +--R 2 13 4 11 6 9 8 7 7 +--R (- 108a b + 200a b - 124a b + 32a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 6 +--R (- 108a b + 200a b - 286a b + 302a b - 108a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 5 +--R (216a b - 332a b - 50a b + 322a b - 156a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 4 +--R (216a b - 332a b + 436a b - 380a b - 12a b + 72a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (- 108a b + 132a b + 336a b - 516a b + 84a b + 72a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 108a b + 132a b - 150a b + 78a b + 102a b - 42a b +--R + +--R 14 +--R - 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 9 8 7 10 5 12 3 14 +--R (- 162a b + 162a b + 54a b - 42a b - 12a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 12 5 10 7 8 2 3 12 5 10 7 8 +--R (- 9a b + 24a b - 15a b )cos(x) - 9a b - 3a b + 57a b +--R + +--R 9 6 +--R - 45a b +--R * +--R 8 +--R sin(x) +--R + +--R 2 13 4 11 6 9 3 +--R (- 9a b + 24a b - 15a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 2 +--R (- 7a b - 22a b + 107a b - 78a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 2 13 4 11 +--R (- 9a b - 3a b + 57a b - 45a b )cos(x) - 7a b - 43a b +--R + +--R 6 9 8 7 10 5 +--R 113a b + 51a b - 114a b +--R * +--R 7 +--R sin(x) +--R + +--R 14 3 12 5 10 5 +--R (9a b - 15a b + 6a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 4 +--R (9a b - 6a b - 18a b + 15a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 3 +--R (- 16a b - 70a b + 200a b - 114a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 2 +--R (- 16a b - 74a b + 87a b + 262a b - 259a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 14 +--R (11a b - a b + 53a b - 3a b - 60a b )cos(x) + 11a b +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R 22a b + 2a b + 42a b + 31a b - 108a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 13 4 11 6 9 6 +--R (- 9a b + 15a b - 6a b )cos(x) +--R + +--R 2 13 4 11 6 9 5 +--R (90a b - 159a b + 69a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 4 +--R (113a b - 148a b - 7a b + 42a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 3 +--R (- 166a b - 185a b + 838a b - 487a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 2 +--R (- 187a b - 242a b + 825a b - 14a b - 382a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 2 13 +--R (104a b + 156a b - 174a b - 176a b + 90a b )cos(x) + 111a b +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R 265a b - 289a b - 299a b + 258a b - 46a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 12 5 10 7 8 6 +--R (- 63a b + 87a b - 24a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 5 +--R (- 4a b + 272a b - 454a b + 186a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 4 +--R (- 4a b + 457a b - 497a b - 16a b + 60a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 3 +--R (6a b - 534a b + 50a b + 1310a b - 832a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 2 +--R (6a b - 723a b - 161a b + 1660a b - 365a b - 417a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (- 2a b + 340a b + 194a b - 690a b - 72a b + 230a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 13 2 +--R - 2a b + 407a b + 473a b - 1044a b - 356a b + 529a b - 7a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 13 4 11 6 9 7 +--R (18a b - 48a b + 30a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 6 +--R (12a b - 270a b + 354a b - 96a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 5 +--R (- 58a b + 434a b - 484a b + 108a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 4 +--R (- 46a b + 1142a b - 880a b - 522a b + 306a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 3 +--R (54a b - 760a b + 293a b + 1136a b - 723a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (48a b - 1486a b + 37a b + 2532a b - 785a b - 346a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R (- 14a b + 486a b - 69a b - 731a b + 155a b + 173a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 14a b + 726a b + 293a b - 1469a b - 31a b + 495a b +--R * +--R 3 +--R sin(x) +--R + +--R 14 3 12 5 10 7 8 7 +--R (- 6a b + 48a b - 126a b + 84a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 6 +--R (- 6a b + 12a b - 482a b + 706a b - 230a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 5 +--R (12a b - 102a b + 495a b - 405a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R (12a b - 30a b + 1715a b - 1780a b - 310a b + 393a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 3 +--R (- 6a b + 84a b - 688a b + 478a b + 430a b - 298a b )cos(x) +--R + +--R 14 3 12 5 10 7 8 9 6 11 4 +--R - 6a b + 48a b - 1948a b + 1132a b + 1713a b - 752a b +--R + +--R 13 2 +--R - 187a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R (- 30a b + 353a b - 225a b - 291a b + 139a b + 54a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 +--R - 30a b + 749a b - 126a b - 1034a b + 200a b + 241a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 13 4 11 6 9 8 7 7 +--R (- 36a b + 58a b - 68a b + 46a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 6 +--R (- 36a b + 4a b - 265a b + 479a b - 182a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 5 +--R (72a b - 22a b + 20a b - 13a b - 57a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 4 +--R (72a b + 86a b + 745a b - 1100a b - 7a b + 204a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 3 +--R (- 36a b - 18a b - 66a b + 77a b + 86a b - 43a b )cos(x) +--R + +--R 2 13 4 11 6 9 8 7 10 5 12 3 +--R - 36a b - 72a b - 891a b + 884a b + 509a b - 340a b +--R + +--R 14 +--R - 54a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R (- 18a b + 114a b - 110a b - 20a b + 28a b + 6a b)cos(x) +--R + +--R 4 11 6 9 8 7 10 5 12 3 14 +--R - 18a b + 411a b - 263a b - 311a b + 121a b + 60a b +--R * +--R sin(x) +--R + +--R 3 12 5 10 7 8 9 6 7 +--R (- 54a b + 100a b - 62a b + 16a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 6 +--R (- 54a b + 100a b - 143a b + 151a b - 54a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 5 +--R (108a b - 166a b + 56a b + 26a b - 24a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 4 +--R (108a b - 166a b + 299a b - 325a b + 48a b + 36a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 3 +--R (- 54a b + 66a b + 6a b - 42a b + 24a b )cos(x) +--R + +--R 3 12 5 10 7 8 9 6 11 4 13 2 15 +--R (- 54a b + 66a b - 237a b + 255a b + 33a b - 57a b - 6a ) +--R * +--R 2 +--R cos(x) +--R + +--R 7 8 9 6 11 4 13 2 15 +--R 81a b - 81a b - 27a b + 21a b + 6a +--R / +--R 2 16 4 14 4 +--R (6a b - 6a b )cos(x) +--R + +--R 2 16 4 14 6 12 2 2 16 4 14 +--R (- 12a b - 24a b + 36a b )cos(x) + 6a b + 30a b +--R + +--R 6 12 8 10 +--R 18a b - 54a b +--R * +--R 7 +--R sin(x) +--R + +--R 17 3 15 5 13 5 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 17 3 15 5 13 4 +--R (6a b + 54a b - 60a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 3 +--R (- 12a b - 12a b + 60a b - 36a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 2 +--R (- 12a b - 144a b - 108a b + 264a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 9 9 +--R (6a b + 24a b - 12a b - 72a b + 54a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 9 9 +--R 6a b + 90a b + 222a b - 66a b - 252a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 16 4 14 6 12 5 +--R (60a b - 120a b + 60a b )cos(x) +--R + +--R 2 16 4 14 6 12 4 +--R (60a b + 174a b - 234a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 3 +--R (- 120a b - 24a b + 408a b - 264a b )cos(x) +--R + +--R 2 16 4 14 8 10 2 +--R (- 120a b - 612a b + 732a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R (60a b + 144a b - 216a b - 240a b + 252a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R 60a b + 438a b + 486a b - 510a b - 474a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 15 5 13 7 11 5 +--R (234a b - 468a b + 234a b )cos(x) +--R + +--R 3 15 5 13 7 11 4 +--R (234a b + 222a b - 456a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 3 +--R (- 468a b + 204a b + 996a b - 732a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 2 +--R (- 468a b - 1176a b + 636a b + 1008a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R (234a b + 264a b - 756a b - 216a b + 474a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R 234a b + 954a b + 294a b - 1026a b - 456a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 14 6 12 8 10 5 +--R (456a b - 912a b + 456a b )cos(x) +--R + +--R 4 14 6 12 8 10 4 +--R (456a b + 18a b - 474a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 3 +--R (- 912a b + 816a b + 1104a b - 1008a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 2 +--R (- 912a b - 1044a b + 1224a b + 732a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R (456a b + 96a b - 1104a b + 96a b + 456a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R 456a b + 1026a b - 294a b - 954a b - 234a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 13 7 11 9 9 5 +--R (474a b - 948a b + 474a b )cos(x) +--R + +--R 5 13 7 11 9 9 4 +--R (474a b - 222a b - 252a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 3 +--R (- 948a b + 1164a b + 516a b - 732a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 2 +--R (- 948a b - 288a b + 972a b + 264a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R (474a b - 216a b - 756a b + 264a b + 234a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R 474a b + 510a b - 486a b - 438a b - 60a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 12 8 10 10 8 5 +--R (252a b - 504a b + 252a b )cos(x) +--R + +--R 6 12 8 10 10 8 4 +--R (252a b - 198a b - 54a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 3 +--R (- 504a b + 744a b + 24a b - 264a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 2 +--R (- 504a b + 132a b + 336a b + 36a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R (252a b - 240a b - 216a b + 144a b + 60a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R 252a b + 66a b - 222a b - 90a b - 6a b +--R * +--R sin(x) +--R + +--R 7 11 9 9 11 7 5 7 11 9 9 4 +--R (54a b - 108a b + 54a b )cos(x) + (54a b - 54a b )cos(x) +--R + +--R 7 11 9 9 11 7 13 5 3 +--R (- 108a b + 180a b - 36a b - 36a b )cos(x) +--R + +--R 7 11 9 9 11 7 2 +--R (- 108a b + 72a b + 36a b )cos(x) +--R + +--R 7 11 9 9 11 7 13 5 15 3 7 11 +--R (54a b - 72a b - 12a b + 24a b + 6a b )cos(x) + 54a b +--R + +--R 9 9 11 7 13 5 +--R - 18a b - 30a b - 6a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 17 3 15 4 +--R (12a b - 12a b )cos(x) +--R + +--R 17 3 15 5 13 2 17 3 15 +--R (- 24a b - 48a b + 72a b )cos(x) + 12a b + 60a b +--R + +--R 5 13 7 11 +--R 36a b - 108a b +--R * +--R 7 +--R sin(x) +--R + +--R 18 2 16 4 14 5 +--R (12b - 24a b + 12a b )cos(x) +--R + +--R 18 2 16 4 14 4 +--R (12b + 108a b - 120a b )cos(x) +--R + +--R 18 2 16 4 14 6 12 3 +--R (- 24b - 24a b + 120a b - 72a b )cos(x) +--R + +--R 18 2 16 4 14 6 12 2 +--R (- 24b - 288a b - 216a b + 528a b )cos(x) +--R + +--R 18 2 16 4 14 6 12 8 10 +--R (12b + 48a b - 24a b - 144a b + 108a b )cos(x) +--R + +--R 18 2 16 4 14 6 12 8 10 +--R 12b + 180a b + 444a b - 132a b - 504a b +--R * +--R 6 +--R sin(x) +--R + +--R 17 3 15 5 13 5 +--R (120a b - 240a b + 120a b )cos(x) +--R + +--R 17 3 15 5 13 4 +--R (120a b + 348a b - 468a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 3 +--R (- 240a b - 48a b + 816a b - 528a b )cos(x) +--R + +--R 17 3 15 7 11 2 +--R (- 240a b - 1224a b + 1464a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 9 9 +--R (120a b + 288a b - 432a b - 480a b + 504a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 9 9 +--R 120a b + 876a b + 972a b - 1020a b - 948a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 16 4 14 6 12 5 +--R (468a b - 936a b + 468a b )cos(x) +--R + +--R 2 16 4 14 6 12 4 +--R (468a b + 444a b - 912a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 3 +--R (- 936a b + 408a b + 1992a b - 1464a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 2 +--R (- 936a b - 2352a b + 1272a b + 2016a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R (468a b + 528a b - 1512a b - 432a b + 948a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R 468a b + 1908a b + 588a b - 2052a b - 912a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 15 5 13 7 11 5 +--R (912a b - 1824a b + 912a b )cos(x) +--R + +--R 3 15 5 13 7 11 4 +--R (912a b + 36a b - 948a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 3 +--R (- 1824a b + 1632a b + 2208a b - 2016a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 2 +--R (- 1824a b - 2088a b + 2448a b + 1464a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R (912a b + 192a b - 2208a b + 192a b + 912a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R 912a b + 2052a b - 588a b - 1908a b - 468a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 14 6 12 8 10 5 +--R (948a b - 1896a b + 948a b )cos(x) +--R + +--R 4 14 6 12 8 10 4 +--R (948a b - 444a b - 504a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 3 +--R (- 1896a b + 2328a b + 1032a b - 1464a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 2 +--R (- 1896a b - 576a b + 1944a b + 528a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R (948a b - 432a b - 1512a b + 528a b + 468a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R 948a b + 1020a b - 972a b - 876a b - 120a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 13 7 11 9 9 5 +--R (504a b - 1008a b + 504a b )cos(x) +--R + +--R 5 13 7 11 9 9 4 +--R (504a b - 396a b - 108a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 3 +--R (- 1008a b + 1488a b + 48a b - 528a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 2 +--R (- 1008a b + 264a b + 672a b + 72a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R (504a b - 480a b - 432a b + 288a b + 120a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R 504a b + 132a b - 444a b - 180a b - 12a b +--R * +--R sin(x) +--R + +--R 6 12 8 10 10 8 5 +--R (108a b - 216a b + 108a b )cos(x) +--R + +--R 6 12 8 10 4 +--R (108a b - 108a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 3 +--R (- 216a b + 360a b - 72a b - 72a b )cos(x) +--R + +--R 6 12 8 10 10 8 2 +--R (- 216a b + 144a b + 72a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R (108a b - 144a b - 24a b + 48a b + 12a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 +--R 108a b - 36a b - 60a b - 12a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 16 4 14 4 2 16 4 14 6 12 2 +--R (6a b - 6a b )cos(x) + (- 12a b - 24a b + 36a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 +--R 6a b + 30a b + 18a b - 54a b +--R * +--R 7 +--R sin(x) +--R + +--R 17 3 15 5 13 5 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 17 3 15 5 13 4 +--R (6a b + 54a b - 60a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 3 +--R (- 12a b - 12a b + 60a b - 36a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 2 +--R (- 12a b - 144a b - 108a b + 264a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 9 9 17 +--R (6a b + 24a b - 12a b - 72a b + 54a b )cos(x) + 6a b +--R + +--R 3 15 5 13 7 11 9 9 +--R 90a b + 222a b - 66a b - 252a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 16 4 14 6 12 5 +--R (60a b - 120a b + 60a b )cos(x) +--R + +--R 2 16 4 14 6 12 4 +--R (60a b + 174a b - 234a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 3 +--R (- 120a b - 24a b + 408a b - 264a b )cos(x) +--R + +--R 2 16 4 14 8 10 2 +--R (- 120a b - 612a b + 732a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R (60a b + 144a b - 216a b - 240a b + 252a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 10 8 +--R 60a b + 438a b + 486a b - 510a b - 474a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 15 5 13 7 11 5 +--R (234a b - 468a b + 234a b )cos(x) +--R + +--R 3 15 5 13 7 11 4 +--R (234a b + 222a b - 456a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 3 +--R (- 468a b + 204a b + 996a b - 732a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 2 +--R (- 468a b - 1176a b + 636a b + 1008a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R (234a b + 264a b - 756a b - 216a b + 474a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 11 7 +--R 234a b + 954a b + 294a b - 1026a b - 456a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 14 6 12 8 10 5 +--R (456a b - 912a b + 456a b )cos(x) +--R + +--R 4 14 6 12 8 10 4 +--R (456a b + 18a b - 474a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 3 +--R (- 912a b + 816a b + 1104a b - 1008a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 2 +--R (- 912a b - 1044a b + 1224a b + 732a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R (456a b + 96a b - 1104a b + 96a b + 456a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 12 6 +--R 456a b + 1026a b - 294a b - 954a b - 234a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 13 7 11 9 9 5 +--R (474a b - 948a b + 474a b )cos(x) +--R + +--R 5 13 7 11 9 9 4 +--R (474a b - 222a b - 252a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 3 +--R (- 948a b + 1164a b + 516a b - 732a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 2 +--R (- 948a b - 288a b + 972a b + 264a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R (474a b - 216a b - 756a b + 264a b + 234a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 13 5 +--R 474a b + 510a b - 486a b - 438a b - 60a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 12 8 10 10 8 5 +--R (252a b - 504a b + 252a b )cos(x) +--R + +--R 6 12 8 10 10 8 4 +--R (252a b - 198a b - 54a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 3 +--R (- 504a b + 744a b + 24a b - 264a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 2 +--R (- 504a b + 132a b + 336a b + 36a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R (252a b - 240a b - 216a b + 144a b + 60a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 14 4 +--R 252a b + 66a b - 222a b - 90a b - 6a b +--R * +--R sin(x) +--R + +--R 7 11 9 9 11 7 5 7 11 9 9 4 +--R (54a b - 108a b + 54a b )cos(x) + (54a b - 54a b )cos(x) +--R + +--R 7 11 9 9 11 7 13 5 3 +--R (- 108a b + 180a b - 36a b - 36a b )cos(x) +--R + +--R 7 11 9 9 11 7 2 +--R (- 108a b + 72a b + 36a b )cos(x) +--R + +--R 7 11 9 9 11 7 13 5 15 3 7 11 +--R (54a b - 72a b - 12a b + 24a b + 6a b )cos(x) + 54a b +--R + +--R 9 9 11 7 13 5 +--R - 18a b - 30a b - 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 17 4 15 6 13 4 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 2 2 17 +--R (- 12a b - 12a b + 60a b - 36a b )cos(x) + 6a b +--R + +--R 4 15 6 13 8 11 10 9 +--R 24a b - 12a b - 72a b + 54a b +--R * +--R 7 +--R sin(x) +--R + +--R 18 3 16 5 14 5 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 4 +--R (6a b + 48a b - 114a b + 60a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 3 +--R (- 12a b - 12a b + 60a b - 36a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 2 +--R (- 12a b - 132a b + 36a b + 372a b - 264a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 18 +--R (6a b + 24a b - 12a b - 72a b + 54a b )cos(x) + 6a b +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R 84a b + 132a b - 288a b - 186a b + 252a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 17 4 15 6 13 5 +--R (60a b - 120a b + 60a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 4 +--R (60a b + 114a b - 408a b + 234a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 3 +--R (- 120a b - 24a b + 408a b - 264a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 2 +--R (- 120a b - 492a b + 612a b + 732a b - 732a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 +--R (60a b + 144a b - 216a b - 240a b + 252a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 12 7 +--R 60a b + 378a b + 48a b - 996a b + 36a b + 474a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 16 5 14 7 12 5 +--R (234a b - 468a b + 234a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 4 +--R (234a b - 12a b - 678a b + 456a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 3 +--R (- 468a b + 204a b + 996a b - 732a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 2 +--R (- 468a b - 708a b + 1812a b + 372a b - 1008a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R (234a b + 264a b - 756a b - 216a b + 474a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 13 6 +--R 234a b + 720a b - 660a b - 1320a b + 570a b + 456a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 15 6 13 8 11 5 +--R (456a b - 912a b + 456a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 4 +--R (456a b - 438a b - 492a b + 474a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 3 +--R (- 912a b + 816a b + 1104a b - 1008a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 2 +--R (- 912a b - 132a b + 2268a b - 492a b - 732a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 +--R (456a b + 96a b - 1104a b + 96a b + 456a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 14 5 +--R 456a b + 570a b - 1320a b - 660a b + 720a b + 234a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 14 7 12 9 10 5 +--R (474a b - 948a b + 474a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 4 +--R (474a b - 696a b - 30a b + 252a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 3 +--R (- 948a b + 1164a b + 516a b - 732a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 2 +--R (- 948a b + 660a b + 1260a b - 708a b - 264a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 +--R (474a b - 216a b - 756a b + 264a b + 234a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 15 4 +--R 474a b + 36a b - 996a b + 48a b + 378a b + 60a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 13 8 11 10 9 5 +--R (252a b - 504a b + 252a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 4 +--R (252a b - 450a b + 144a b + 54a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 3 +--R (- 504a b + 744a b + 24a b - 264a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 14 5 2 +--R (- 504a b + 636a b + 204a b - 300a b - 36a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 14 5 +--R (252a b - 240a b - 216a b + 144a b + 60a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 14 5 16 3 +--R 252a b - 186a b - 288a b + 132a b + 84a b + 6a b +--R * +--R sin(x) +--R + +--R 7 12 9 10 11 8 5 +--R (54a b - 108a b + 54a b )cos(x) +--R + +--R 7 12 9 10 11 8 4 +--R (54a b - 108a b + 54a b )cos(x) +--R + +--R 7 12 9 10 11 8 13 6 3 +--R (- 108a b + 180a b - 36a b - 36a b )cos(x) +--R + +--R 7 12 9 10 11 8 13 6 2 +--R (- 108a b + 180a b - 36a b - 36a b )cos(x) +--R + +--R 7 12 9 10 11 8 13 6 15 4 7 12 +--R (54a b - 72a b - 12a b + 24a b + 6a b )cos(x) + 54a b +--R + +--R 9 10 11 8 13 6 15 4 +--R - 72a b - 12a b + 24a b + 6a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 18 3 16 5 14 4 +--R (12a b - 24a b + 12a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 2 18 +--R (- 24a b - 24a b + 120a b - 72a b )cos(x) + 12a b +--R + +--R 3 16 5 14 7 12 9 10 +--R 48a b - 24a b - 144a b + 108a b +--R * +--R 7 +--R sin(x) +--R + +--R 19 2 17 4 15 5 +--R (12b - 24a b + 12a b )cos(x) +--R + +--R 19 2 17 4 15 6 13 4 +--R (12b + 96a b - 228a b + 120a b )cos(x) +--R + +--R 19 2 17 4 15 6 13 3 +--R (- 24b - 24a b + 120a b - 72a b )cos(x) +--R + +--R 19 2 17 4 15 6 13 8 11 2 +--R (- 24b - 264a b + 72a b + 744a b - 528a b )cos(x) +--R + +--R 19 2 17 4 15 6 13 8 11 19 +--R (12b + 48a b - 24a b - 144a b + 108a b )cos(x) + 12b +--R + +--R 2 17 4 15 6 13 8 11 10 9 +--R 168a b + 264a b - 576a b - 372a b + 504a b +--R * +--R 6 +--R sin(x) +--R + +--R 18 3 16 5 14 5 +--R (120a b - 240a b + 120a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 4 +--R (120a b + 228a b - 816a b + 468a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 3 +--R (- 240a b - 48a b + 816a b - 528a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 +--R (- 240a b - 984a b + 1224a b + 1464a b - 1464a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 +--R (120a b + 288a b - 432a b - 480a b + 504a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 11 8 +--R 120a b + 756a b + 96a b - 1992a b + 72a b + 948a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 17 4 15 6 13 5 +--R (468a b - 936a b + 468a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 4 +--R (468a b - 24a b - 1356a b + 912a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 3 +--R (- 936a b + 408a b + 1992a b - 1464a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 +--R (- 936a b - 1416a b + 3624a b + 744a b - 2016a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 +--R (468a b + 528a b - 1512a b - 432a b + 948a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 12 7 +--R 468a b + 1440a b - 1320a b - 2640a b + 1140a b + 912a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 16 5 14 7 12 5 +--R (912a b - 1824a b + 912a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 4 +--R (912a b - 876a b - 984a b + 948a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 3 +--R (- 1824a b + 1632a b + 2208a b - 2016a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R (- 1824a b - 264a b + 4536a b - 984a b - 1464a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R (912a b + 192a b - 2208a b + 192a b + 912a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 13 6 +--R 912a b + 1140a b - 2640a b - 1320a b + 1440a b + 468a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 15 6 13 8 11 5 +--R (948a b - 1896a b + 948a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 4 +--R (948a b - 1392a b - 60a b + 504a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 3 +--R (- 1896a b + 2328a b + 1032a b - 1464a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 +--R (- 1896a b + 1320a b + 2520a b - 1416a b - 528a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 +--R (948a b - 432a b - 1512a b + 528a b + 468a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 14 5 +--R 948a b + 72a b - 1992a b + 96a b + 756a b + 120a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 14 7 12 9 10 5 +--R (504a b - 1008a b + 504a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 4 +--R (504a b - 900a b + 288a b + 108a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 3 +--R (- 1008a b + 1488a b + 48a b - 528a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 2 +--R (- 1008a b + 1272a b + 408a b - 600a b - 72a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 +--R (504a b - 480a b - 432a b + 288a b + 120a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 15 4 +--R 504a b - 372a b - 576a b + 264a b + 168a b + 12a b +--R * +--R sin(x) +--R + +--R 6 13 8 11 10 9 5 +--R (108a b - 216a b + 108a b )cos(x) +--R + +--R 6 13 8 11 10 9 4 +--R (108a b - 216a b + 108a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 3 +--R (- 216a b + 360a b - 72a b - 72a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 2 +--R (- 216a b + 360a b - 72a b - 72a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 14 5 6 13 +--R (108a b - 144a b - 24a b + 48a b + 12a b )cos(x) + 108a b +--R + +--R 8 11 10 9 12 7 14 5 +--R - 144a b - 24a b + 48a b + 12a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 17 4 15 6 13 4 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 2 2 17 4 15 +--R (- 12a b - 12a b + 60a b - 36a b )cos(x) + 6a b + 24a b +--R + +--R 6 13 8 11 10 9 +--R - 12a b - 72a b + 54a b +--R * +--R 7 +--R sin(x) +--R + +--R 18 3 16 5 14 5 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 4 +--R (6a b + 48a b - 114a b + 60a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 3 +--R (- 12a b - 12a b + 60a b - 36a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 2 +--R (- 12a b - 132a b + 36a b + 372a b - 264a b )cos(x) +--R + +--R 18 3 16 5 14 7 12 9 10 18 +--R (6a b + 24a b - 12a b - 72a b + 54a b )cos(x) + 6a b +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R 84a b + 132a b - 288a b - 186a b + 252a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 17 4 15 6 13 5 +--R (60a b - 120a b + 60a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 4 +--R (60a b + 114a b - 408a b + 234a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 3 +--R (- 120a b - 24a b + 408a b - 264a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 2 +--R (- 120a b - 492a b + 612a b + 732a b - 732a b )cos(x) +--R + +--R 2 17 4 15 6 13 8 11 10 9 2 17 +--R (60a b + 144a b - 216a b - 240a b + 252a b )cos(x) + 60a b +--R + +--R 4 15 6 13 8 11 10 9 12 7 +--R 378a b + 48a b - 996a b + 36a b + 474a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 16 5 14 7 12 5 +--R (234a b - 468a b + 234a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 4 +--R (234a b - 12a b - 678a b + 456a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 3 +--R (- 468a b + 204a b + 996a b - 732a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 2 +--R (- 468a b - 708a b + 1812a b + 372a b - 1008a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 +--R (234a b + 264a b - 756a b - 216a b + 474a b )cos(x) +--R + +--R 3 16 5 14 7 12 9 10 11 8 13 6 +--R 234a b + 720a b - 660a b - 1320a b + 570a b + 456a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 15 6 13 8 11 5 +--R (456a b - 912a b + 456a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 4 +--R (456a b - 438a b - 492a b + 474a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 3 +--R (- 912a b + 816a b + 1104a b - 1008a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 2 +--R (- 912a b - 132a b + 2268a b - 492a b - 732a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 +--R (456a b + 96a b - 1104a b + 96a b + 456a b )cos(x) +--R + +--R 4 15 6 13 8 11 10 9 12 7 14 5 +--R 456a b + 570a b - 1320a b - 660a b + 720a b + 234a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 14 7 12 9 10 5 +--R (474a b - 948a b + 474a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 4 +--R (474a b - 696a b - 30a b + 252a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 3 +--R (- 948a b + 1164a b + 516a b - 732a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 2 +--R (- 948a b + 660a b + 1260a b - 708a b - 264a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 +--R (474a b - 216a b - 756a b + 264a b + 234a b )cos(x) +--R + +--R 5 14 7 12 9 10 11 8 13 6 15 4 +--R 474a b + 36a b - 996a b + 48a b + 378a b + 60a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 13 8 11 10 9 5 +--R (252a b - 504a b + 252a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 4 +--R (252a b - 450a b + 144a b + 54a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 3 +--R (- 504a b + 744a b + 24a b - 264a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 14 5 2 +--R (- 504a b + 636a b + 204a b - 300a b - 36a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 14 5 +--R (252a b - 240a b - 216a b + 144a b + 60a b )cos(x) +--R + +--R 6 13 8 11 10 9 12 7 14 5 16 3 +--R 252a b - 186a b - 288a b + 132a b + 84a b + 6a b +--R * +--R sin(x) +--R + +--R 7 12 9 10 11 8 5 +--R (54a b - 108a b + 54a b )cos(x) +--R + +--R 7 12 9 10 11 8 4 +--R (54a b - 108a b + 54a b )cos(x) +--R + +--R 7 12 9 10 11 8 13 6 3 +--R (- 108a b + 180a b - 36a b - 36a b )cos(x) +--R + +--R 7 12 9 10 11 8 13 6 2 +--R (- 108a b + 180a b - 36a b - 36a b )cos(x) +--R + +--R 7 12 9 10 11 8 13 6 15 4 7 12 +--R (54a b - 72a b - 12a b + 24a b + 6a b )cos(x) + 54a b +--R + +--R 9 10 11 8 13 6 15 4 +--R - 72a b - 12a b + 24a b + 6a b +--R Type: Expression(Integer) +--E 120 + +--S 121 of 532 +m0721b:= a0721.2-r0721 +--R +--R +--R (113) +--R 4 8 6 6 2 4 8 6 6 8 4 4 +--R ((18a b - 12a b )cos(x) - 18a b - 42a b + 36a b )sin(x) +--R + +--R 5 7 7 5 2 5 7 7 5 9 3 3 +--R ((108a b - 72a b )cos(x) - 108a b - 108a b + 120a b )sin(x) +--R + +--R 6 6 8 4 2 6 6 8 4 10 2 2 +--R ((216a b - 144a b )cos(x) - 216a b - 72a b + 144a b )sin(x) +--R + +--R 7 5 9 3 2 7 5 9 3 11 +--R ((180a b - 120a b )cos(x) - 180a b + 12a b + 72a b)sin(x) +--R + +--R 8 4 10 2 2 8 4 10 2 12 +--R (54a b - 36a b )cos(x) - 54a b + 18a b + 12a +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 4 8 6 6 2 4 8 6 6 8 4 4 +--R ((18a b - 12a b )cos(x) - 18a b - 42a b + 36a b )sin(x) +--R + +--R 5 7 7 5 2 5 7 7 5 9 3 3 +--R ((108a b - 72a b )cos(x) - 108a b - 108a b + 120a b )sin(x) +--R + +--R 6 6 8 4 2 6 6 8 4 10 2 2 +--R ((216a b - 144a b )cos(x) - 216a b - 72a b + 144a b )sin(x) +--R + +--R 7 5 9 3 2 7 5 9 3 11 +--R ((180a b - 120a b )cos(x) - 180a b + 12a b + 72a b)sin(x) +--R + +--R 8 4 10 2 2 8 4 10 2 12 +--R (54a b - 36a b )cos(x) - 54a b + 18a b + 12a +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 11 2 9 4 7 2 4 7 6 5 11 +--R (- 2b + 5a b - 6a b )cos(x) + (- 9a b + 15a b )cos(x) + 2b +--R + +--R 2 9 4 7 6 5 +--R a b - 9a b + 18a b +--R * +--R 4 +--R sin(x) +--R + +--R 10 3 8 5 6 2 +--R (- 12a b + 30a b - 36a b )cos(x) +--R + +--R 3 8 5 6 7 4 10 3 8 5 6 7 4 +--R (2a b - 8a b + 18a b )cos(x) + 12a b - 10a b - 14a b + 60a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 7 6 5 3 2 9 4 7 6 5 2 +--R (- 9a b + 15a b )cos(x) + (- 24a b + 60a b - 72a b )cos(x) +--R + +--R 4 7 6 5 8 3 2 9 4 7 6 5 8 3 +--R (15a b - 22a b + 7a b )cos(x) + 24a b - 36a b + 12a b + 72a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 8 5 6 7 4 3 +--R (2a b - 8a b + 18a b )cos(x) +--R + +--R 3 8 5 6 7 4 2 +--R (- 20a b + 50a b - 60a b )cos(x) +--R + +--R 3 8 5 6 7 4 3 8 5 6 7 4 +--R (- 2a b + 8a b - 18a b )cos(x) + 20a b - 38a b + 30a b +--R + +--R 9 2 +--R 36a b +--R * +--R sin(x) +--R + +--R 4 7 6 5 8 3 3 4 7 6 5 8 3 2 +--R (6a b - 7a b + 7a b )cos(x) + (- 6a b + 15a b - 18a b )cos(x) +--R + +--R 4 7 6 5 8 3 4 7 6 5 8 3 10 +--R (- 6a b + 7a b - 7a b )cos(x) + 6a b - 13a b + 13a b + 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 3 12 5 10 2 3 12 5 10 7 8 4 +--R ((6a b - 6a b )cos(x) - 6a b - 12a b + 18a b )sin(x) +--R + +--R 4 11 6 9 2 4 11 6 9 8 7 3 +--R ((36a b - 36a b )cos(x) - 36a b - 24a b + 60a b )sin(x) +--R + +--R 5 10 7 8 2 5 10 9 6 2 +--R ((72a b - 72a b )cos(x) - 72a b + 72a b )sin(x) +--R + +--R 6 9 8 7 2 6 9 8 7 10 5 +--R ((60a b - 60a b )cos(x) - 60a b + 24a b + 36a b )sin(x) +--R + +--R 7 8 9 6 2 7 8 9 6 11 4 +--R (18a b - 18a b )cos(x) - 18a b + 12a b + 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 532 +d0721b:= D(m0721b,x) +--R +--R +--R (114) +--R 3 11 5 9 2 3 11 5 9 7 7 9 +--R ((- 9a b + 15a b )cos(x) - 9a b - 12a b + 45a b )sin(x) +--R + +--R 2 12 4 10 4 2 12 4 10 3 +--R (- 9a b + 6a b )cos(x) + (- 18a b + 30a b )cos(x) +--R + +--R 2 12 4 10 6 8 2 +--R (2a b + 28a b + 42a b )cos(x) +--R + +--R 2 12 4 10 6 8 2 12 4 10 +--R (- 18a b - 24a b + 90a b )cos(x) - 25a b - 110a b +--R + +--R 6 8 8 6 +--R 63a b + 168a b +--R * +--R 8 +--R sin(x) +--R + +--R 13 3 11 5 13 3 11 5 9 4 +--R (18a b - 12a b )cos(x) + (18a b - 102a b + 60a b )cos(x) +--R + +--R 13 3 11 5 9 3 +--R (- 32a b - 190a b + 258a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 2 +--R (- 32a b - 14a b + 390a b + 40a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 13 3 11 +--R (22a b + 2a b + 102a b + 210a b )cos(x) + 22a b - 56a b +--R + +--R 5 9 7 7 9 5 +--R - 250a b + 68a b + 360a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 12 4 10 6 2 12 4 10 5 +--R (- 9a b + 6a b )cos(x) + (198a b - 150a b )cos(x) +--R + +--R 2 12 4 10 6 8 4 +--R (223a b - 511a b + 270a b )cos(x) +--R + +--R 2 12 4 10 6 8 3 +--R (- 364a b - 874a b + 1202a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 2 +--R (- 385a b - 244a b + 1681a b - 236a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 2 12 +--R (230a b + 540a b + 298a b - 60a b )cos(x) + 235a b +--R + +--R 4 10 6 8 8 6 10 4 +--R 343a b - 583a b - 275a b + 520a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 11 5 9 6 +--R (- 63a b + 15a b )cos(x) +--R + +--R 13 3 11 5 9 5 +--R (- 8a b + 716a b - 510a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 4 +--R (- 8a b + 915a b - 1118a b + 619a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 3 +--R (12a b - 1388a b - 1658a b + 2638a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 2 +--R (12a b - 1577a b - 691a b + 2937a b - 429a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (- 4a b + 884a b + 1584a b - 144a b - 640a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 4a b + 937a b + 1322a b - 1180a b - 770a b + 463a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 12 4 10 7 +--R (36a b - 60a b )cos(x) +--R + +--R 2 12 4 10 6 8 6 +--R (26a b - 371a b + 144a b )cos(x) +--R + +--R 2 12 4 10 6 8 5 +--R (- 124a b + 1288a b - 588a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 4 +--R (- 102a b + 2265a b - 871a b + 268a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 3 +--R (120a b - 2468a b - 1782a b + 3110a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 2 +--R (106a b - 3387a b - 1832a b + 3431a b - 142a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (- 32a b + 1620a b + 1870a b - 972a b - 806a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R - 30a b + 1873a b + 2093a b - 1595a b - 991a b + 234a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 11 5 9 8 +--R (18a b - 30a b )cos(x) +--R + +--R 13 3 11 5 9 7 +--R (- 12a b + 120a b - 228a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 6 +--R (- 12a b + 8a b - 898a b + 578a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 5 +--R (24a b - 296a b + 1562a b - 216a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 4 +--R (24a b - 112a b + 3824a b - 838a b - 426a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (- 12a b + 264a b - 2632a b - 1090a b + 2042a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 12a b + 160a b - 4802a b - 1816a b + 2856a b +--R + +--R 11 3 +--R 206a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R (- 88a b + 1590a b + 1002a b - 1042a b - 454a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R - 74a b + 2198a b + 1772a b - 1430a b - 750a b + 60a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 12 4 10 6 8 8 +--R (- 6a b + 42a b - 84a b )cos(x) +--R + +--R 2 12 4 10 6 8 7 +--R (- 84a b + 128a b - 260a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 6 +--R (- 66a b - 58a b - 733a b + 656a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (168a b - 80a b + 950a b + 114a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 4 +--R (150a b + 196a b + 2901a b - 677a b - 584a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 3 +--R (- 84a b + 48a b - 1460a b - 350a b + 682a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R - 78a b - 114a b - 3539a b - 804a b + 1601a b +--R + +--R 12 2 +--R 198a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R (- 96a b + 838a b + 168a b - 454a b - 120a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 +--R - 66a b + 1523a b + 757a b - 789a b - 327a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 3 11 5 9 7 7 8 +--R (- 36a b + 22a b - 46a b )cos(x) +--R + +--R 3 11 5 9 7 7 7 +--R (- 180a b + 136a b - 124a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 6 +--R (- 72a b + 164a b - 467a b + 363a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 5 +--R (360a b - 16a b + 136a b + 162a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 4 +--R (252a b - 120a b + 1323a b - 406a b - 257a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (- 180a b - 84a b - 204a b - 134a b + 86a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R (- 144a b - 48a b - 1365a b - 87a b + 510a b + 60a b) +--R * +--R 2 +--R cos(x) +--R + +--R 5 9 7 7 9 5 11 3 13 5 9 +--R (- 36a b + 192a b - 28a b - 68a b - 12a b)cos(x) - 18a b +--R + +--R 7 7 9 5 11 3 13 +--R 555a b + 130a b - 235a b - 72a b +--R * +--R sin(x) +--R + +--R 4 10 6 8 8 6 8 +--R (- 54a b + 46a b - 16a b )cos(x) +--R + +--R 4 10 6 8 8 6 7 +--R (- 108a b + 92a b - 32a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 6 +--R (54a b - 12a b - 99a b + 78a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 5 +--R (216a b - 116a b - 4a b + 48a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 4 +--R (54a b - 46a b + 259a b - 108a b - 36a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 3 +--R (- 108a b + 24a b + 36a b - 48a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 2 +--R (- 54a b + 12a b - 225a b + 30a b + 63a b + 6a )cos(x) +--R + +--R 8 6 12 2 14 +--R 81a b - 27a b - 6a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 12 4 10 2 2 12 4 10 6 8 9 +--R ((- 18a b + 30a b )cos(x) - 18a b - 24a b + 90a b )sin(x) +--R + +--R 13 3 11 4 13 3 11 3 +--R (- 36a b + 24a b )cos(x) + (- 36a b + 60a b )cos(x) +--R + +--R 13 3 11 5 9 2 +--R (40a b + 140a b + 12a b )cos(x) +--R + +--R 13 3 11 5 9 13 3 11 +--R (- 36a b - 48a b + 180a b )cos(x) - 68a b - 316a b +--R + +--R 5 9 7 7 +--R 36a b + 444a b +--R * +--R 8 +--R sin(x) +--R + +--R 2 12 4 10 4 +--R (- 360a b + 240a b )cos(x) +--R + +--R 14 2 12 4 10 3 +--R (8b - 212a b + 372a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 2 +--R (8b + 500a b + 1188a b - 448a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 14 2 12 +--R (8b - 188a b + 24a b + 636a b )cos(x) + 8b - 484a b +--R + +--R 4 10 6 8 8 6 +--R - 1352a b + 124a b + 1224a b +--R * +--R 7 +--R sin(x) +--R + +--R 13 3 11 6 3 11 5 +--R (- 36a b + 24a b )cos(x) - 36a b cos(x) +--R + +--R 13 3 11 5 9 4 +--R (104a b - 1388a b + 936a b )cos(x) +--R + +--R 13 3 11 5 9 3 +--R (64a b - 476a b + 1204a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 2 +--R (- 32a b + 2008a b + 3404a b - 1828a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 13 +--R (64a b - 456a b - 40a b + 1104a b )cos(x) + 92a b +--R + +--R 3 11 5 9 7 7 9 5 +--R - 1456a b - 3440a b + 608a b + 1988a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 12 4 10 6 +--R (- 306a b + 150a b )cos(x) +--R + +--R 14 2 12 4 10 5 +--R (- 16b - 332a b + 156a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 4 +--R (- 16b + 606a b - 1996a b + 1622a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 3 +--R (24b + 752a b + 308a b + 1292a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 2 +--R (24b - 166a b + 3754a b + 3390a b - 2370a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 14 +--R (- 8b + 4a b - 1632a b - 660a b + 1624a b )cos(x) - 8b +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R 290a b - 2852a b - 4616a b + 1508a b + 1838a b +--R * +--R 5 +--R sin(x) +--R + +--R 13 3 11 7 +--R (72a b - 120a b )cos(x) +--R + +--R 13 3 11 5 9 6 +--R (52a b - 1444a b + 756a b )cos(x) +--R + +--R 13 3 11 5 9 5 +--R (- 248a b - 1564a b + 1584a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 4 +--R (- 204a b + 2496a b + 388a b + 20a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 3 +--R (240a b + 3344a b + 1356a b - 740a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 2 +--R (212a b - 600a b + 1112a b + 1708a b - 800a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (- 64a b - 900a b - 3940a b - 564a b + 2108a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R - 60a b + 308a b - 3188a b - 3100a b + 1552a b + 936a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 12 4 10 8 +--R (36a b - 60a b )cos(x) +--R + +--R 14 2 12 4 10 7 +--R (- 24b + 240a b - 456a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 6 +--R (- 24b + 16a b - 3164a b + 2068a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 5 +--R (48b - 592a b - 2456a b + 3288a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 4 +--R (48b - 224a b + 6172a b + 1576a b - 2364a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 3 +--R (- 24b + 528a b + 5896a b + 820a b - 2876a b )cos(x) +--R + +--R 14 2 12 4 10 6 8 8 6 +--R - 24b + 320a b - 2548a b - 2432a b + 1200a b +--R + +--R 10 4 +--R 796a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (- 176a b - 2400a b - 4716a b + 736a b + 1852a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R - 148a b + 184a b - 1820a b - 976a b + 696a b + 240a b +--R * +--R 3 +--R sin(x) +--R + +--R 13 3 11 5 9 8 +--R (- 12a b + 84a b - 168a b )cos(x) +--R + +--R 13 3 11 5 9 7 +--R (- 168a b + 256a b - 520a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 6 +--R (- 132a b - 116a b - 2888a b + 2260a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 5 +--R (336a b - 160a b - 2456a b + 3132a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 4 +--R (300a b + 392a b + 5712a b + 740a b - 2524a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (- 168a b + 96a b + 5792a b - 532a b - 2620a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 +--R - 156a b - 228a b - 2632a b - 2664a b + 1336a b +--R + +--R 11 3 +--R 792a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R (- 192a b - 2680a b - 2736a b + 1312a b + 936a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R - 132a b + 112a b - 472a b - 120a b + 108a b + 24a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 12 4 10 6 8 8 +--R (- 72a b + 44a b - 92a b )cos(x) +--R + +--R 2 12 4 10 6 8 7 +--R (- 360a b + 272a b - 248a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 6 +--R (- 144a b + 328a b - 1690a b + 1230a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (720a b - 32a b - 1564a b + 1548a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 4 +--R (504a b - 240a b + 3078a b - 308a b - 1042a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 3 +--R (- 360a b - 168a b + 3264a b - 916a b - 1028a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R - 288a b - 96a b - 1326a b - 894a b + 696a b +--R + +--R 12 2 +--R 240a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R (- 72a b - 1452a b - 632a b + 668a b + 240a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 +--R - 36a b + 30a b - 28a b - 14a b +--R * +--R sin(x) +--R + +--R 3 11 5 9 7 7 8 +--R (- 108a b + 92a b - 32a b )cos(x) +--R + +--R 3 11 5 9 7 7 7 +--R (- 216a b + 184a b - 64a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 6 +--R (108a b - 24a b - 360a b + 264a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 5 +--R (432a b - 232a b - 332a b + 312a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 4 +--R (108a b - 92a b + 680a b - 216a b - 144a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (- 216a b + 48a b + 720a b - 312a b - 144a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 2 +--R (- 108a b + 24a b - 288a b - 48a b + 108a b + 24a b)cos(x) +--R + +--R 7 7 11 3 13 +--R (- 324a b + 108a b + 24a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 11 5 9 2 3 11 5 9 7 7 9 +--R ((- 9a b + 15a b )cos(x) - 9a b - 12a b + 45a b )sin(x) +--R + +--R 2 12 4 10 4 2 12 4 10 3 +--R (- 9a b + 6a b )cos(x) + (- 18a b + 30a b )cos(x) +--R + +--R 2 12 4 10 6 8 2 +--R (2a b + 28a b + 42a b )cos(x) +--R + +--R 2 12 4 10 6 8 2 12 4 10 6 8 +--R (- 18a b - 24a b + 90a b )cos(x) - 25a b - 110a b + 63a b +--R + +--R 8 6 +--R 168a b +--R * +--R 8 +--R sin(x) +--R + +--R 13 3 11 5 13 3 11 5 9 4 +--R (18a b - 12a b )cos(x) + (18a b - 102a b + 60a b )cos(x) +--R + +--R 13 3 11 5 9 3 +--R (- 32a b - 190a b + 258a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 2 +--R (- 32a b - 14a b + 390a b + 40a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 13 3 11 +--R (22a b + 2a b + 102a b + 210a b )cos(x) + 22a b - 56a b +--R + +--R 5 9 7 7 9 5 +--R - 250a b + 68a b + 360a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 12 4 10 6 2 12 4 10 5 +--R (- 9a b + 6a b )cos(x) + (198a b - 150a b )cos(x) +--R + +--R 2 12 4 10 6 8 4 +--R (223a b - 511a b + 270a b )cos(x) +--R + +--R 2 12 4 10 6 8 3 +--R (- 364a b - 874a b + 1202a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 2 +--R (- 385a b - 244a b + 1681a b - 236a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 2 12 4 10 +--R (230a b + 540a b + 298a b - 60a b )cos(x) + 235a b + 343a b +--R + +--R 6 8 8 6 10 4 +--R - 583a b - 275a b + 520a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 11 5 9 6 13 3 11 5 9 5 +--R (- 63a b + 15a b )cos(x) + (- 8a b + 716a b - 510a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 4 +--R (- 8a b + 915a b - 1118a b + 619a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 3 +--R (12a b - 1388a b - 1658a b + 2638a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 2 +--R (12a b - 1577a b - 691a b + 2937a b - 429a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 13 +--R (- 4a b + 884a b + 1584a b - 144a b - 640a b )cos(x) - 4a b +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R 937a b + 1322a b - 1180a b - 770a b + 463a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 12 4 10 7 2 12 4 10 6 8 6 +--R (36a b - 60a b )cos(x) + (26a b - 371a b + 144a b )cos(x) +--R + +--R 2 12 4 10 6 8 5 +--R (- 124a b + 1288a b - 588a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 4 +--R (- 102a b + 2265a b - 871a b + 268a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 3 +--R (120a b - 2468a b - 1782a b + 3110a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 2 +--R (106a b - 3387a b - 1832a b + 3431a b - 142a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (- 32a b + 1620a b + 1870a b - 972a b - 806a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R - 30a b + 1873a b + 2093a b - 1595a b - 991a b + 234a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 11 5 9 8 13 3 11 5 9 7 +--R (18a b - 30a b )cos(x) + (- 12a b + 120a b - 228a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 6 +--R (- 12a b + 8a b - 898a b + 578a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 5 +--R (24a b - 296a b + 1562a b - 216a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 4 +--R (24a b - 112a b + 3824a b - 838a b - 426a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 3 +--R (- 12a b + 264a b - 2632a b - 1090a b + 2042a b )cos(x) +--R + +--R 13 3 11 5 9 7 7 9 5 11 3 +--R (- 12a b + 160a b - 4802a b - 1816a b + 2856a b + 206a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R (- 88a b + 1590a b + 1002a b - 1042a b - 454a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 +--R - 74a b + 2198a b + 1772a b - 1430a b - 750a b + 60a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 12 4 10 6 8 8 +--R (- 6a b + 42a b - 84a b )cos(x) +--R + +--R 2 12 4 10 6 8 7 +--R (- 84a b + 128a b - 260a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 6 +--R (- 66a b - 58a b - 733a b + 656a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 5 +--R (168a b - 80a b + 950a b + 114a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 4 +--R (150a b + 196a b + 2901a b - 677a b - 584a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 3 +--R (- 84a b + 48a b - 1460a b - 350a b + 682a b )cos(x) +--R + +--R 2 12 4 10 6 8 8 6 10 4 12 2 +--R (- 78a b - 114a b - 3539a b - 804a b + 1601a b + 198a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 4 10 +--R (- 96a b + 838a b + 168a b - 454a b - 120a b )cos(x) - 66a b +--R + +--R 6 8 8 6 10 4 12 2 14 +--R 1523a b + 757a b - 789a b - 327a b + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 3 11 5 9 7 7 8 +--R (- 36a b + 22a b - 46a b )cos(x) +--R + +--R 3 11 5 9 7 7 7 +--R (- 180a b + 136a b - 124a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 6 +--R (- 72a b + 164a b - 467a b + 363a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 5 +--R (360a b - 16a b + 136a b + 162a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 4 +--R (252a b - 120a b + 1323a b - 406a b - 257a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 3 +--R (- 180a b - 84a b - 204a b - 134a b + 86a b )cos(x) +--R + +--R 3 11 5 9 7 7 9 5 11 3 13 2 +--R (- 144a b - 48a b - 1365a b - 87a b + 510a b + 60a b)cos(x) +--R + +--R 5 9 7 7 9 5 11 3 13 5 9 +--R (- 36a b + 192a b - 28a b - 68a b - 12a b)cos(x) - 18a b +--R + +--R 7 7 9 5 11 3 13 +--R 555a b + 130a b - 235a b - 72a b +--R * +--R sin(x) +--R + +--R 4 10 6 8 8 6 8 +--R (- 54a b + 46a b - 16a b )cos(x) +--R + +--R 4 10 6 8 8 6 7 +--R (- 108a b + 92a b - 32a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 6 +--R (54a b - 12a b - 99a b + 78a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 5 +--R (216a b - 116a b - 4a b + 48a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 4 +--R (54a b - 46a b + 259a b - 108a b - 36a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 3 +--R (- 108a b + 24a b + 36a b - 48a b )cos(x) +--R + +--R 4 10 6 8 8 6 10 4 12 2 14 2 8 6 +--R (- 54a b + 12a b - 225a b + 30a b + 63a b + 6a )cos(x) + 81a b +--R + +--R 12 2 14 +--R - 27a b - 6a +--R / +--R 2 16 4 14 4 2 16 4 14 6 12 2 +--R (6a b - 6a b )cos(x) + (- 12a b - 24a b + 36a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 +--R 6a b + 30a b + 18a b - 54a b +--R * +--R 8 +--R sin(x) +--R + +--R 17 3 15 5 17 3 15 5 13 4 +--R (12a b - 12a b )cos(x) + (12a b + 48a b - 60a b )cos(x) +--R + +--R 17 3 15 5 13 3 +--R (- 24a b - 48a b + 72a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 2 +--R (- 24a b - 168a b - 72a b + 264a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 17 +--R (12a b + 60a b + 36a b - 108a b )cos(x) + 12a b +--R + +--R 3 15 5 13 7 11 9 9 +--R 120a b + 240a b - 120a b - 252a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 16 4 14 6 2 16 4 14 5 +--R (6a b - 6a b )cos(x) + (132a b - 132a b )cos(x) +--R + +--R 2 16 4 14 6 12 4 +--R (114a b + 84a b - 198a b )cos(x) +--R + +--R 2 16 4 14 6 12 3 +--R (- 264a b - 336a b + 600a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 2 +--R (- 246a b - 750a b + 318a b + 678a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 2 16 +--R (132a b + 468a b + 12a b - 612a b )cos(x) + 126a b +--R + +--R 4 14 6 12 8 10 10 8 +--R 672a b + 492a b - 816a b - 474a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 15 5 13 6 3 15 5 13 5 +--R (60a b - 60a b )cos(x) + (588a b - 588a b )cos(x) +--R + +--R 3 15 5 13 7 11 4 +--R (408a b - 216a b - 192a b )cos(x) +--R + +--R 3 15 5 13 7 11 3 +--R (- 1176a b - 816a b + 1992a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 2 +--R (- 996a b - 1380a b + 1620a b + 756a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 3 15 +--R (588a b + 1404a b - 540a b - 1452a b )cos(x) + 528a b +--R + +--R 5 13 7 11 9 9 11 7 +--R 1656a b + 24a b - 1752a b - 456a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 14 6 12 6 4 14 6 12 5 +--R (234a b - 234a b )cos(x) + (1380a b - 1380a b )cos(x) +--R + +--R 4 14 6 12 8 10 4 +--R (678a b - 936a b + 258a b )cos(x) +--R + +--R 4 14 6 12 8 10 3 +--R (- 2760a b - 720a b + 3480a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 2 +--R (- 2058a b - 906a b + 2706a b + 258a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 4 14 +--R (1380a b + 2100a b - 1620a b - 1860a b )cos(x) + 1146a b +--R + +--R 6 12 8 10 10 8 12 6 +--R 2076a b - 1104a b - 1884a b - 234a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 13 7 11 6 5 13 7 11 5 +--R (456a b - 456a b )cos(x) + (1860a b - 1860a b )cos(x) +--R + +--R 5 13 7 11 9 9 4 +--R (492a b - 1248a b + 756a b )cos(x) +--R + +--R 5 13 7 11 9 9 3 +--R (- 3720a b + 240a b + 3480a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 2 +--R (- 2352a b + 384a b + 2160a b - 192a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 5 13 +--R (1860a b + 1620a b - 2100a b - 1380a b )cos(x) + 1404a b +--R + +--R 7 11 9 9 11 7 13 5 +--R 1320a b - 1536a b - 1128a b - 60a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 12 8 10 6 6 12 8 10 5 +--R (474a b - 474a b )cos(x) + (1452a b - 1452a b )cos(x) +--R + +--R 6 12 8 10 10 8 4 +--R (30a b - 708a b + 678a b )cos(x) +--R + +--R 6 12 8 10 10 8 3 +--R (- 2904a b + 912a b + 1992a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 2 +--R (- 1482a b + 846a b + 834a b - 198a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 6 12 +--R (1452a b + 540a b - 1404a b - 588a b )cos(x) + 978a b +--R + +--R 8 10 10 8 12 6 14 4 +--R 336a b - 924a b - 384a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 11 9 9 6 7 11 9 9 5 +--R (252a b - 252a b )cos(x) + (612a b - 612a b )cos(x) +--R + +--R 7 11 9 9 11 7 4 +--R (- 144a b - 120a b + 264a b )cos(x) +--R + +--R 7 11 9 9 11 7 3 +--R (- 1224a b + 624a b + 600a b )cos(x) +--R + +--R 7 11 9 9 11 7 13 5 2 +--R (- 468a b + 396a b + 132a b - 60a b )cos(x) +--R + +--R 7 11 9 9 11 7 13 5 7 11 +--R (612a b - 12a b - 468a b - 132a b )cos(x) + 360a b +--R + +--R 9 9 11 7 13 5 +--R - 24a b - 264a b - 72a b +--R * +--R sin(x) +--R + +--R 8 10 10 8 6 8 10 10 8 5 +--R (54a b - 54a b )cos(x) + (108a b - 108a b )cos(x) +--R + +--R 8 10 10 8 12 6 4 +--R (- 54a b + 18a b + 36a b )cos(x) +--R + +--R 8 10 10 8 12 6 3 +--R (- 216a b + 144a b + 72a b )cos(x) +--R + +--R 8 10 10 8 12 6 14 4 2 +--R (- 54a b + 54a b + 6a b - 6a b )cos(x) +--R + +--R 8 10 10 8 12 6 14 4 8 10 10 8 +--R (108a b - 36a b - 60a b - 12a b )cos(x) + 54a b - 18a b +--R + +--R 12 6 14 4 +--R - 30a b - 6a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 17 3 15 4 +--R (12a b - 12a b )cos(x) +--R + +--R 17 3 15 5 13 2 17 3 15 +--R (- 24a b - 48a b + 72a b )cos(x) + 12a b + 60a b +--R + +--R 5 13 7 11 +--R 36a b - 108a b +--R * +--R 8 +--R sin(x) +--R + +--R 18 2 16 5 18 2 16 4 14 4 +--R (24b - 24a b )cos(x) + (24b + 96a b - 120a b )cos(x) +--R + +--R 18 2 16 4 14 3 +--R (- 48b - 96a b + 144a b )cos(x) +--R + +--R 18 2 16 4 14 6 12 2 +--R (- 48b - 336a b - 144a b + 528a b )cos(x) +--R + +--R 18 2 16 4 14 6 12 18 2 16 +--R (24b + 120a b + 72a b - 216a b )cos(x) + 24b + 240a b +--R + +--R 4 14 6 12 8 10 +--R 480a b - 240a b - 504a b +--R * +--R 7 +--R sin(x) +--R + +--R 17 3 15 6 17 3 15 5 +--R (12a b - 12a b )cos(x) + (264a b - 264a b )cos(x) +--R + +--R 17 3 15 5 13 4 +--R (228a b + 168a b - 396a b )cos(x) +--R + +--R 17 3 15 5 13 3 +--R (- 528a b - 672a b + 1200a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 2 +--R (- 492a b - 1500a b + 636a b + 1356a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 17 +--R (264a b + 936a b + 24a b - 1224a b )cos(x) + 252a b +--R + +--R 3 15 5 13 7 11 9 9 +--R 1344a b + 984a b - 1632a b - 948a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 16 4 14 6 2 16 4 14 5 +--R (120a b - 120a b )cos(x) + (1176a b - 1176a b )cos(x) +--R + +--R 2 16 4 14 6 12 4 +--R (816a b - 432a b - 384a b )cos(x) +--R + +--R 2 16 4 14 6 12 3 +--R (- 2352a b - 1632a b + 3984a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 2 +--R (- 1992a b - 2760a b + 3240a b + 1512a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 2 16 +--R (1176a b + 2808a b - 1080a b - 2904a b )cos(x) + 1056a b +--R + +--R 4 14 6 12 8 10 10 8 +--R 3312a b + 48a b - 3504a b - 912a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 15 5 13 6 3 15 5 13 5 +--R (468a b - 468a b )cos(x) + (2760a b - 2760a b )cos(x) +--R + +--R 3 15 5 13 7 11 4 +--R (1356a b - 1872a b + 516a b )cos(x) +--R + +--R 3 15 5 13 7 11 3 +--R (- 5520a b - 1440a b + 6960a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 2 +--R (- 4116a b - 1812a b + 5412a b + 516a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 3 15 +--R (2760a b + 4200a b - 3240a b - 3720a b )cos(x) + 2292a b +--R + +--R 5 13 7 11 9 9 11 7 +--R 4152a b - 2208a b - 3768a b - 468a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 14 6 12 6 4 14 6 12 5 +--R (912a b - 912a b )cos(x) + (3720a b - 3720a b )cos(x) +--R + +--R 4 14 6 12 8 10 4 +--R (984a b - 2496a b + 1512a b )cos(x) +--R + +--R 4 14 6 12 8 10 3 +--R (- 7440a b + 480a b + 6960a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 2 +--R (- 4704a b + 768a b + 4320a b - 384a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 4 14 +--R (3720a b + 3240a b - 4200a b - 2760a b )cos(x) + 2808a b +--R + +--R 6 12 8 10 10 8 12 6 +--R 2640a b - 3072a b - 2256a b - 120a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 13 7 11 6 5 13 7 11 5 +--R (948a b - 948a b )cos(x) + (2904a b - 2904a b )cos(x) +--R + +--R 5 13 7 11 9 9 4 +--R (60a b - 1416a b + 1356a b )cos(x) +--R + +--R 5 13 7 11 9 9 3 +--R (- 5808a b + 1824a b + 3984a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 2 +--R (- 2964a b + 1692a b + 1668a b - 396a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 5 13 +--R (2904a b + 1080a b - 2808a b - 1176a b )cos(x) + 1956a b +--R + +--R 7 11 9 9 11 7 13 5 +--R 672a b - 1848a b - 768a b - 12a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 12 8 10 6 6 12 8 10 5 +--R (504a b - 504a b )cos(x) + (1224a b - 1224a b )cos(x) +--R + +--R 6 12 8 10 10 8 4 +--R (- 288a b - 240a b + 528a b )cos(x) +--R + +--R 6 12 8 10 10 8 3 +--R (- 2448a b + 1248a b + 1200a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 2 +--R (- 936a b + 792a b + 264a b - 120a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 6 12 +--R (1224a b - 24a b - 936a b - 264a b )cos(x) + 720a b +--R + +--R 8 10 10 8 12 6 +--R - 48a b - 528a b - 144a b +--R * +--R sin(x) +--R + +--R 7 11 9 9 6 7 11 9 9 5 +--R (108a b - 108a b )cos(x) + (216a b - 216a b )cos(x) +--R + +--R 7 11 9 9 11 7 4 +--R (- 108a b + 36a b + 72a b )cos(x) +--R + +--R 7 11 9 9 11 7 3 +--R (- 432a b + 288a b + 144a b )cos(x) +--R + +--R 7 11 9 9 11 7 13 5 2 +--R (- 108a b + 108a b + 12a b - 12a b )cos(x) +--R + +--R 7 11 9 9 11 7 13 5 7 11 9 9 +--R (216a b - 72a b - 120a b - 24a b )cos(x) + 108a b - 36a b +--R + +--R 11 7 13 5 +--R - 60a b - 12a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 16 4 14 4 2 16 4 14 6 12 2 +--R (6a b - 6a b )cos(x) + (- 12a b - 24a b + 36a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 +--R 6a b + 30a b + 18a b - 54a b +--R * +--R 8 +--R sin(x) +--R + +--R 17 3 15 5 17 3 15 5 13 4 +--R (12a b - 12a b )cos(x) + (12a b + 48a b - 60a b )cos(x) +--R + +--R 17 3 15 5 13 3 +--R (- 24a b - 48a b + 72a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 2 +--R (- 24a b - 168a b - 72a b + 264a b )cos(x) +--R + +--R 17 3 15 5 13 7 11 17 3 15 +--R (12a b + 60a b + 36a b - 108a b )cos(x) + 12a b + 120a b +--R + +--R 5 13 7 11 9 9 +--R 240a b - 120a b - 252a b +--R * +--R 7 +--R sin(x) +--R + +--R 2 16 4 14 6 2 16 4 14 5 +--R (6a b - 6a b )cos(x) + (132a b - 132a b )cos(x) +--R + +--R 2 16 4 14 6 12 4 +--R (114a b + 84a b - 198a b )cos(x) +--R + +--R 2 16 4 14 6 12 3 +--R (- 264a b - 336a b + 600a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 2 +--R (- 246a b - 750a b + 318a b + 678a b )cos(x) +--R + +--R 2 16 4 14 6 12 8 10 2 16 +--R (132a b + 468a b + 12a b - 612a b )cos(x) + 126a b +--R + +--R 4 14 6 12 8 10 10 8 +--R 672a b + 492a b - 816a b - 474a b +--R * +--R 6 +--R sin(x) +--R + +--R 3 15 5 13 6 3 15 5 13 5 +--R (60a b - 60a b )cos(x) + (588a b - 588a b )cos(x) +--R + +--R 3 15 5 13 7 11 4 +--R (408a b - 216a b - 192a b )cos(x) +--R + +--R 3 15 5 13 7 11 3 +--R (- 1176a b - 816a b + 1992a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 2 +--R (- 996a b - 1380a b + 1620a b + 756a b )cos(x) +--R + +--R 3 15 5 13 7 11 9 9 3 15 +--R (588a b + 1404a b - 540a b - 1452a b )cos(x) + 528a b +--R + +--R 5 13 7 11 9 9 11 7 +--R 1656a b + 24a b - 1752a b - 456a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 14 6 12 6 4 14 6 12 5 +--R (234a b - 234a b )cos(x) + (1380a b - 1380a b )cos(x) +--R + +--R 4 14 6 12 8 10 4 +--R (678a b - 936a b + 258a b )cos(x) +--R + +--R 4 14 6 12 8 10 3 +--R (- 2760a b - 720a b + 3480a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 2 +--R (- 2058a b - 906a b + 2706a b + 258a b )cos(x) +--R + +--R 4 14 6 12 8 10 10 8 4 14 +--R (1380a b + 2100a b - 1620a b - 1860a b )cos(x) + 1146a b +--R + +--R 6 12 8 10 10 8 12 6 +--R 2076a b - 1104a b - 1884a b - 234a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 13 7 11 6 5 13 7 11 5 +--R (456a b - 456a b )cos(x) + (1860a b - 1860a b )cos(x) +--R + +--R 5 13 7 11 9 9 4 +--R (492a b - 1248a b + 756a b )cos(x) +--R + +--R 5 13 7 11 9 9 3 +--R (- 3720a b + 240a b + 3480a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 2 +--R (- 2352a b + 384a b + 2160a b - 192a b )cos(x) +--R + +--R 5 13 7 11 9 9 11 7 5 13 +--R (1860a b + 1620a b - 2100a b - 1380a b )cos(x) + 1404a b +--R + +--R 7 11 9 9 11 7 13 5 +--R 1320a b - 1536a b - 1128a b - 60a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 12 8 10 6 6 12 8 10 5 +--R (474a b - 474a b )cos(x) + (1452a b - 1452a b )cos(x) +--R + +--R 6 12 8 10 10 8 4 +--R (30a b - 708a b + 678a b )cos(x) +--R + +--R 6 12 8 10 10 8 3 +--R (- 2904a b + 912a b + 1992a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 2 +--R (- 1482a b + 846a b + 834a b - 198a b )cos(x) +--R + +--R 6 12 8 10 10 8 12 6 6 12 +--R (1452a b + 540a b - 1404a b - 588a b )cos(x) + 978a b +--R + +--R 8 10 10 8 12 6 14 4 +--R 336a b - 924a b - 384a b - 6a b +--R * +--R 2 +--R sin(x) +--R + +--R 7 11 9 9 6 7 11 9 9 5 +--R (252a b - 252a b )cos(x) + (612a b - 612a b )cos(x) +--R + +--R 7 11 9 9 11 7 4 +--R (- 144a b - 120a b + 264a b )cos(x) +--R + +--R 7 11 9 9 11 7 3 +--R (- 1224a b + 624a b + 600a b )cos(x) +--R + +--R 7 11 9 9 11 7 13 5 2 +--R (- 468a b + 396a b + 132a b - 60a b )cos(x) +--R + +--R 7 11 9 9 11 7 13 5 7 11 9 9 +--R (612a b - 12a b - 468a b - 132a b )cos(x) + 360a b - 24a b +--R + +--R 11 7 13 5 +--R - 264a b - 72a b +--R * +--R sin(x) +--R + +--R 8 10 10 8 6 8 10 10 8 5 +--R (54a b - 54a b )cos(x) + (108a b - 108a b )cos(x) +--R + +--R 8 10 10 8 12 6 4 +--R (- 54a b + 18a b + 36a b )cos(x) +--R + +--R 8 10 10 8 12 6 3 +--R (- 216a b + 144a b + 72a b )cos(x) +--R + +--R 8 10 10 8 12 6 14 4 2 +--R (- 54a b + 54a b + 6a b - 6a b )cos(x) +--R + +--R 8 10 10 8 12 6 14 4 8 10 10 8 +--R (108a b - 36a b - 60a b - 12a b )cos(x) + 54a b - 18a b +--R + +--R 12 6 14 4 +--R - 30a b - 6a b +--R Type: Expression(Integer) +--E 122 + +--S 123 of 532 +t0722:= (a*cot(x)+b*csc(x))^3 +--R +--R +--R 3 3 2 2 2 2 3 3 +--R (115) b csc(x) + 3a b cot(x)csc(x) + 3a b cot(x) csc(x) + a cot(x) +--R Type: Expression(Integer) +--E 123 + +--S 124 of 532 +r0722:= -(a+b)^3/(4-4*cos(x))-(a-b)^3/(4*cos(x)+4)-_ + 1/4*(2*a-b)*(a+b)^2*log(1-cos(x))-1/4*(a-b)^2*(2*a+b)*log(cos(x)+1) +--R +--R +--R (116) +--R 3 2 3 2 3 2 3 +--R ((- b + 3a b - 2a )cos(x) + b - 3a b + 2a )log(cos(x) + 1) +--R + +--R 3 2 3 2 3 2 3 +--R ((b - 3a b - 2a )cos(x) - b + 3a b + 2a )log(- cos(x) + 1) +--R + +--R 3 2 2 3 +--R (2b + 6a b)cos(x) + 6a b + 2a +--R / +--R 2 +--R 4cos(x) - 4 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 532 +a0722:= integrate(t0722,x) +--R +--R +--R (117) +--R 3 2 3 2 3 2 3 sin(x) +--R ((2b - 6a b - 4a )cos(x) - 2b + 6a b + 4a )log(----------) +--R cos(x) + 1 +--R + +--R 3 2 3 2 2 3 2 +--R (4a cos(x) - 4a )log(----------) + (3a b + a )cos(x) +--R cos(x) + 1 +--R + +--R 3 2 2 3 +--R (2b + 6a b)cos(x) + 3a b + a +--R / +--R 2 +--R 4cos(x) - 4 +--R Type: Union(Expression(Integer),...) +--E 125 + +--S 126 of 532 +m0722:= a0722-r0722 +--R +--R +--R (118) +--R 3 2 3 sin(x) 3 2 3 +--R (2b - 6a b - 4a )log(----------) + (b - 3a b + 2a )log(cos(x) + 1) +--R cos(x) + 1 +--R + +--R 3 2 3 2 3 2 3 +--R 4a log(----------) + (- b + 3a b + 2a )log(- cos(x) + 1) + 3a b + a +--R cos(x) + 1 +--R / +--R 4 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 532 +d0722:= D(m0722,x) +--R +--R +--R (119) +--R 3 2 3 2 3 2 3 3 +--R (b - 3a b - 2a )cos(x)sin(x) + (b - 3a b - 2a )cos(x) +--R + +--R 3 2 3 +--R (- b + 3a b + 2a )cos(x) +--R / +--R 2 +--R (2cos(x) - 2)sin(x) +--R Type: Expression(Integer) +--E 127 + +--S 128 of 532 +t0723:= (a*cot(x)+b*csc(x))^5 +--R +--R +--R (120) +--R 5 5 4 4 2 3 2 3 +--R b csc(x) + 5a b cot(x)csc(x) + 10a b cot(x) csc(x) +--R + +--R 3 2 3 2 4 4 5 5 +--R 10a b cot(x) csc(x) + 5a b cot(x) csc(x) + a cot(x) +--R Type: Expression(Integer) +--E 128 + +--S 129 of 532 +r0723:= -1/16*(a+b)^5/(1-cos(x))^2+(7*a-3*b)*(a+b)^4/(16-16*cos(x))-_ + 1/16*(a-b)^5/(cos(x)+1)^2+(a-b)^4*(7*a+3*b)/(16*cos(x)+16)+_ + 1/16*(a+b)^3*(8*a^2-9*a*b+3*b^2)*log(1-cos(x))+1/16*(a-b)^3*_ + (8*a^2+9*a*b+3*b^2)*log(cos(x)+1) +--R +--R +--R (121) +--R 5 2 3 4 5 4 +--R (- 3b + 10a b - 15a b + 8a )cos(x) +--R + +--R 5 2 3 4 5 2 5 2 3 4 5 +--R (6b - 20a b + 30a b - 16a )cos(x) - 3b + 10a b - 15a b + 8a +--R * +--R log(cos(x) + 1) +--R + +--R 5 2 3 4 5 4 +--R (3b - 10a b + 15a b + 8a )cos(x) +--R + +--R 5 2 3 4 5 2 5 2 3 4 5 +--R (- 6b + 20a b - 30a b - 16a )cos(x) + 3b - 10a b + 15a b + 8a +--R * +--R log(- cos(x) + 1) +--R + +--R 5 2 3 4 3 3 2 5 2 +--R (6b - 20a b - 50a b)cos(x) + (- 80a b - 16a )cos(x) +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 10b - 20a b + 30a b)cos(x) - 20a b + 40a b + 12a +--R / +--R 4 2 +--R 16cos(x) - 32cos(x) + 16 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 532 +a0723:= integrate(t0723,x) +--R +--R +--R (122) +--R 5 2 3 4 5 4 +--R (12b - 40a b + 60a b + 32a )cos(x) +--R + +--R 5 2 3 4 5 2 5 2 3 4 5 +--R (- 24b + 80a b - 120a b - 64a )cos(x) + 12b - 40a b + 60a b + 32a +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 5 4 5 2 5 2 +--R (- 32a cos(x) + 64a cos(x) - 32a )log(----------) +--R cos(x) + 1 +--R + +--R 4 3 2 5 4 5 2 3 4 3 +--R (15a b - 50a b - 13a )cos(x) + (12b - 40a b - 100a b)cos(x) +--R + +--R 4 3 2 5 2 5 2 3 4 +--R (- 30a b - 60a b - 6a )cos(x) + (- 20b - 40a b + 60a b)cos(x) +--R + +--R 4 3 2 5 +--R - 25a b + 30a b + 11a +--R / +--R 4 2 +--R 32cos(x) - 64cos(x) + 32 +--R Type: Union(Expression(Integer),...) +--E 130 + +--S 131 of 532 +m0723:= a0723-r0723 +--R +--R +--R (123) +--R 5 2 3 4 5 sin(x) +--R (12b - 40a b + 60a b + 32a )log(----------) +--R cos(x) + 1 +--R + +--R 5 2 3 4 5 5 2 +--R (6b - 20a b + 30a b - 16a )log(cos(x) + 1) - 32a log(----------) +--R cos(x) + 1 +--R + +--R 5 2 3 4 5 4 3 2 5 +--R (- 6b + 20a b - 30a b - 16a )log(- cos(x) + 1) + 15a b - 50a b - 13a +--R / +--R 32 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 532 +d0723:= D(m0723,x) +--R +--R +--R (124) +--R 5 2 3 4 5 2 +--R (3b - 10a b + 15a b + 8a )cos(x)sin(x) +--R + +--R 5 2 3 4 5 3 5 2 3 4 5 +--R (3b - 10a b + 15a b + 8a )cos(x) + (- 3b + 10a b - 15a b - 8a )cos(x) +--R / +--R 2 +--R (8cos(x) - 8)sin(x) +--R Type: Expression(Integer) +--E 132 + +--S 133 of 532 +t0724:= 1/(a*cot(x)+b*csc(x))^2 +--R +--R +--R 1 +--R (125) ----------------------------------------- +--R 2 2 2 2 +--R b csc(x) + 2a b cot(x)csc(x) + a cot(x) +--R Type: Expression(Integer) +--E 133 + +--S 134 of 532 +r0724:= -x/a^2+2*b*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^2/_ + (a^2-b^2)^(1/2)+sin(x)/a/(b+a*cos(x)) +--R +--R +--R (126) +--R x +--R (b - a)tan(-) +--R 2 2 +--R (- 2a b cos(x) - 2b )atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - a x cos(x) - b x)\|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R (a cos(x) + a b)\|- b + a +--R Type: Expression(Integer) +--E 134 + +--S 135 of 532 +a0724:= integrate(t0724,x) +--R +--R +--R (127) +--R [ +--R +---------+ +--R | 2 2 2 2 +--R 2 (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R (a b cos(x) + b )log(----------------------------------------------) +--R a cos(x) + b +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - a x cos(x) - b x)\|- b + a +--R / +--R +---------+ +--R 3 2 | 2 2 +--R (a cos(x) + a b)\|- b + a +--R , +--R +--R +-------+ +--R | 2 2 +--R 2 sin(x)\|b - a +--R (2a b cos(x) + 2b )atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +-------+ +--R | 2 2 +--R (a sin(x) - a x cos(x) - b x)\|b - a +--R / +--R +-------+ +--R 3 2 | 2 2 +--R (a cos(x) + a b)\|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 135 + +--S 136 of 532 +m0724a:= a0724.1-r0724 +--R +--R +--R (128) +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(x) - a)\|- b + a + (b - a )sin(x) +--R b log(----------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R (b - a)tan(-) +--R 2 +--R 2b atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R a \|- b + a +--R Type: Expression(Integer) +--E 136 + +--S 137 of 532 +d0724a:= D(m0724a,x) +--R +--R +--R (129) +--R 2 2 2 2 2 x 2 +--R ((b - a b)sin(x) - a b cos(x) + (- b - a b)cos(x) - b )tan(-) +--R 2 +--R + +--R 2 2 2 2 2 +--R (b + a b)sin(x) + a b cos(x) + (b - a b)cos(x) - b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 3 2 x 2 +--R ((b - a b)cos(x) + b - a b)sin(x)tan(-) +--R 2 +--R + +--R 3 2 3 2 +--R ((b - a b)cos(x) - b + a b)sin(x) +--R / +--R 2 2 3 2 3 2 2 3 4 2 2 3 +--R ((a b - a b)cos(x) + (a b - a b + a b - a )cos(x) + a b - a b) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 3 2 2 3 4 2 2 3 +--R (a b + a b)cos(x) + (a b + a b + a b + a )cos(x) + a b + a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R ((- a b + a b + a b - a )cos(x) - a b + a b + a b - a b)sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 3 2 4 5 4 2 3 3 2 4 +--R ((- a b - a b + a b + a )cos(x) - a b - a b + a b + a b)sin(x) +--R Type: Expression(Integer) +--E 137 + +--S 138 of 532 +m0724b:= a0724.2-r0724 +--R +--R +--R (130) +--R x +-------+ +--R +-------+ (b - a)tan(-) +---------+ | 2 2 +--R | 2 2 2 | 2 2 sin(x)\|b - a +--R 2b\|b - a atanh(-------------) + 2b\|- b + a atan(---------------------) +--R +---------+ (b + a)cos(x) + b + a +--R | 2 2 +--R \|- b + a +--R ---------------------------------------------------------------------------- +--R +---------+ +-------+ +--R 2 | 2 2 | 2 2 +--R a \|- b + a \|b - a +--R Type: Expression(Integer) +--E 138 + +--S 139 of 532 +d0724b:= D(m0724b,x) +--R +--R +--R (131) +--R 2 2 2 2 2 x 2 +--R ((b - a b)sin(x) + (b - 3a b)cos(x) - 4a b cos(x) - b - a b)tan(-) +--R 2 +--R + +--R 2 2 2 2 2 +--R (b + 3a b)sin(x) + (b + a b)cos(x) - b - a b +--R / +--R 2 2 3 4 2 2 2 4 2 2 2 4 +--R (a b - 2a b + a )sin(x) + (a b - a )cos(x) + (2a b - 2a )cos(x) +--R + +--R 2 2 4 +--R a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 2 2 3 4 2 +--R (a b - a )sin(x) + (a b + 2a b + a )cos(x) +--R + +--R 2 2 3 4 2 2 3 4 +--R (2a b + 4a b + 2a )cos(x) + a b + 2a b + a +--R Type: Expression(Integer) +--E 139 + +--S 140 of 532 +t0725:= 1/(a*cot(x)+b*csc(x))^4 +--R +--R +--R (132) +--R 1 +--R / +--R 4 4 3 3 2 2 2 2 3 3 +--R b csc(x) + 4a b cot(x)csc(x) + 6a b cot(x) csc(x) + 4a b cot(x) csc(x) +--R + +--R 4 4 +--R a cot(x) +--R Type: Expression(Integer) +--E 140 + +--S 141 of 532 +r0725:= x/a^4+5*b*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/a^2/_ + (a^2-b^2)^(3/2)-6*b^3*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/_ + a^4/(a^2-b^2)^(3/2)-8*b*atanh((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/_ + a^4/(a^2-b^2)^(1/2)+1/3*(a^2-b^2)*sin(x)/a^3/(b+a*cos(x))^3+_ + 7/6*b*sin(x)/a^3/(b+a*cos(x))^2-4/3*sin(x)/a/(a^2-b^2)/_ + (b+a*cos(x))+11/6*b^2*sin(x)/a^3/(a^2-b^2)/(b+a*cos(x)) +--R +--R +--R (133) +--R 3 3 5 3 2 4 4 2 2 +--R (12a b - 18a b)cos(x) + (36a b - 54a b )cos(x) +--R + +--R 5 3 3 6 2 4 +--R (36a b - 54a b )cos(x) + 12b - 18a b +--R * +--R x +--R (b - a)tan(-) +--R 2 +--R atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 3 2 5 2 2 3 4 4 3 2 +--R (- 11a b + 8a )cos(x) + (- 15a b + 9a b)cos(x) - 6a b + 5a b +--R + +--R 5 +--R - 2a +--R * +--R sin(x) +--R + +--R 3 2 5 3 2 3 4 2 +--R (6a b - 6a )x cos(x) + (18a b - 18a b)x cos(x) +--R + +--R 4 3 2 5 2 3 +--R (18a b - 18a b )x cos(x) + (6b - 6a b )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 7 2 9 3 6 3 8 2 +--R (6a b - 6a )cos(x) + (18a b - 18a b)cos(x) +--R + +--R 5 4 7 2 4 5 6 3 +--R (18a b - 18a b )cos(x) + 6a b - 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 141 + +--S 142 of 532 +a0725:= integrate(t0725,x) +--R +--R +--R (134) +--R [ +--R 3 3 5 3 2 4 4 2 2 +--R (6a b - 9a b)cos(x) + (18a b - 27a b )cos(x) +--R + +--R 5 3 3 6 2 4 +--R (18a b - 27a b )cos(x) + 6b - 9a b +--R * +--R +---------+ +--R | 2 2 2 2 +--R (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R log(------------------------------------------------) +--R a cos(x) + b +--R + +--R 3 2 5 2 2 3 4 4 +--R (- 11a b + 8a )cos(x) + (- 15a b + 9a b)cos(x) - 6a b +--R + +--R 3 2 5 +--R 5a b - 2a +--R * +--R sin(x) +--R + +--R 3 2 5 3 2 3 4 2 +--R (6a b - 6a )x cos(x) + (18a b - 18a b)x cos(x) +--R + +--R 4 3 2 5 2 3 +--R (18a b - 18a b )x cos(x) + (6b - 6a b )x +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 7 2 9 3 6 3 8 2 +--R (6a b - 6a )cos(x) + (18a b - 18a b)cos(x) +--R + +--R 5 4 7 2 4 5 6 3 +--R (18a b - 18a b )cos(x) + 6a b - 6a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R , +--R +--R 3 3 5 3 2 4 4 2 2 +--R (- 12a b + 18a b)cos(x) + (- 36a b + 54a b )cos(x) +--R + +--R 5 3 3 6 2 4 +--R (- 36a b + 54a b )cos(x) - 12b + 18a b +--R * +--R +-------+ +--R | 2 2 +--R sin(x)\|b - a +--R atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R 3 2 5 2 2 3 4 4 +--R (- 11a b + 8a )cos(x) + (- 15a b + 9a b)cos(x) - 6a b +--R + +--R 3 2 5 +--R 5a b - 2a +--R * +--R sin(x) +--R + +--R 3 2 5 3 2 3 4 2 +--R (6a b - 6a )x cos(x) + (18a b - 18a b)x cos(x) +--R + +--R 4 3 2 5 2 3 +--R (18a b - 18a b )x cos(x) + (6b - 6a b )x +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 7 2 9 3 6 3 8 2 +--R (6a b - 6a )cos(x) + (18a b - 18a b)cos(x) +--R + +--R 5 4 7 2 4 5 6 3 +--R (18a b - 18a b )cos(x) + 6a b - 6a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 142 + +--S 143 of 532 +m0725a:= a0725.1-r0725 +--R +--R +--R (135) +--R +---------+ +--R | 2 2 2 2 +--R 3 2 (- b cos(x) - a)\|- b + a + (- b + a )sin(x) +--R (2b - 3a b)log(------------------------------------------------) +--R a cos(x) + b +--R + +--R x +--R (b - a)tan(-) +--R 3 2 2 +--R (- 4b + 6a b)atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +--R 4 2 6 | 2 2 +--R (2a b - 2a )\|- b + a +--R Type: Expression(Integer) +--E 143 + +--S 144 of 532 +d0725a:= D(m0725a,x) +--R +--R +--R (136) +--R 4 3 2 2 3 2 3 3 2 +--R (- 2b + 2a b + 3a b - 3a b)sin(x) + (2a b - 3a b)cos(x) +--R + +--R 4 3 2 2 3 4 2 2 +--R (2b + 2a b - 3a b - 3a b)cos(x) + 2b - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 3 2 3 3 2 +--R (- 2b - 2a b + 3a b + 3a b)sin(x) + (- 2a b + 3a b)cos(x) +--R + +--R 4 3 2 2 3 4 2 2 +--R (- 2b + 2a b + 3a b - 3a b)cos(x) + 2b - 3a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 5 2 3 4 5 2 3 4 x 2 +--R ((2b - 5a b + 3a b)cos(x) + 2b - 5a b + 3a b)sin(x)tan(-) +--R 2 +--R + +--R 5 2 3 4 5 2 3 4 +--R ((2b - 5a b + 3a b)cos(x) - 2b + 5a b - 3a b)sin(x) +--R / +--R 4 4 5 3 6 2 7 2 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 3 5 4 4 7 8 4 4 5 3 6 2 7 +--R (2a b - 2a b - 2a b + 2a )cos(x) + 2a b - 2a b - 2a b + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 5 3 6 2 7 2 +--R (2a b + 2a b - 2a b - 2a b)cos(x) +--R + +--R 3 5 4 4 7 8 4 4 5 3 6 2 7 +--R (2a b + 2a b - 2a b - 2a )cos(x) + 2a b + 2a b - 2a b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 5 5 4 6 3 7 2 8 9 3 6 4 5 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )cos(x) + 2a b - 2a b +--R + +--R 5 4 6 3 7 2 8 +--R - 4a b + 4a b + 2a b - 2a b +--R * +--R x 2 +--R sin(x)tan(-) +--R 2 +--R + +--R 4 5 5 4 6 3 7 2 8 9 3 6 4 5 +--R (2a b + 2a b - 4a b - 4a b + 2a b + 2a )cos(x) + 2a b + 2a b +--R + +--R 5 4 6 3 7 2 8 +--R - 4a b - 4a b + 2a b + 2a b +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 144 + +--S 145 of 532 +m0725b:= a0725.2-r0725 +--R +--R +--R (137) +--R x +--R +-------+ (b - a)tan(-) +--R 3 2 | 2 2 2 +--R (- 2b + 3a b)\|b - a atanh(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +-------+ +--R +---------+ | 2 2 +--R 3 2 | 2 2 sin(x)\|b - a +--R (- 2b + 3a b)\|- b + a atan(---------------------) +--R (b + a)cos(x) + b + a +--R / +--R +---------+ +-------+ +--R 4 2 6 | 2 2 | 2 2 +--R (a b - a )\|- b + a \|b - a +--R Type: Expression(Integer) +--E 145 + +--S 146 of 532 +d0725b:= D(m0725b,x) +--R +--R +--R (138) +--R 4 3 2 2 3 2 +--R (- 2b + 2a b + 3a b - 3a b)sin(x) +--R + +--R 4 3 2 2 3 2 3 3 4 +--R (- 2b + 6a b + 3a b - 9a b)cos(x) + (8a b - 12a b)cos(x) + 2b +--R + +--R 3 2 2 3 +--R 2a b - 3a b - 3a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 3 2 +--R (- 2b - 6a b + 3a b + 9a b)sin(x) +--R + +--R 4 3 2 2 3 2 4 3 2 2 3 +--R (- 2b - 2a b + 3a b + 3a b)cos(x) + 2b + 2a b - 3a b - 3a b +--R / +--R 4 4 5 3 7 8 2 4 4 6 2 8 2 +--R (2a b - 4a b + 4a b - 2a )sin(x) + (2a b - 4a b + 2a )cos(x) +--R + +--R 4 4 6 2 8 4 4 6 2 8 +--R (4a b - 8a b + 4a )cos(x) + 2a b - 4a b + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 6 2 8 2 4 4 5 3 7 8 2 +--R (2a b - 4a b + 2a )sin(x) + (2a b + 4a b - 4a b - 2a )cos(x) +--R + +--R 4 4 5 3 7 8 4 4 5 3 7 8 +--R (4a b + 8a b - 8a b - 4a )cos(x) + 2a b + 4a b - 4a b - 2a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 532 +t0726:= 1/(a*cos(c+d*x)+%i*a*sin(c+d*x))^3 +--R +--R +--R (139) +--R %i +--R / +--R 3 3 3 2 +--R a sin(d x + c) - 3%i a cos(d x + c)sin(d x + c) +--R + +--R 3 2 3 3 +--R - 3a cos(d x + c) sin(d x + c) + %i a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 147 + +--S 148 of 532 +r0726:= 1/3*%i*(cos(c+d*x)-%i*sin(c+d*x))^3/a^3/d +--R +--R +--R (140) +--R 1 3 2 +--R - - sin(d x + c) - %i cos(d x + c)sin(d x + c) +--R 3 +--R + +--R 2 1 3 +--R cos(d x + c) sin(d x + c) + - %i cos(d x + c) +--R 3 +--R / +--R 3 +--R a d +--R Type: Expression(Complex(Fraction(Integer))) +--E 148 + +--S 149 of 532 +--a0726:= integrate(t0726,x) +--E 149 + +--S 150 of 532 +--m0726:= a0726-r0726 +--E 150 + +--S 151 of 532 +--d0726:= D(m0726,x) +--E 151 + +--S 152 of 532 +t0727:= (a*cos(c+d*x)+%i*a*sin(c+d*x))^(1/2) +--R +--R +--R +----------------------------------+ +--R (141) \|%i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 152 + +--S 153 of 532 +r0727:= -2*%i*(a*(cos(c+d*x)+%i*sin(c+d*x)))^(1/2)/d +--R +--R +--R +----------------------------------+ +--R 2%i\|%i a sin(d x + c) + a cos(d x + c) +--R (142) - ---------------------------------------- +--R d +--R Type: Expression(Complex(Integer)) +--E 153 + +--S 154 of 532 +a0727:= integrate(t0727,x) +--R +--R +--R >> System error: +--R Zero divisor. +--R +--R Continuing to read the file... +--R +--E 154 + +--S 155 of 532 +m0727:= a0727-r0727 +--R +--R +--R +----------------------------------+ +--R 2%i\|%i a sin(d x + c) + a cos(d x + c) + a0727 d +--R (143) -------------------------------------------------- +--R d +--R Type: Expression(Complex(Integer)) +--E 155 + +--S 156 of 532 +d0727:= D(m0727,x) +--R +--R +--R - %i a sin(d x + c) - a cos(d x + c) +--R (144) ------------------------------------- +--R +----------------------------------+ +--R \|%i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 156 + +--S 157 of 532 +t0728:= 1/(a*cos(c+d*x)+%i*a*sin(c+d*x))^(1/2) +--R +--R +--R 1 +--R (145) ------------------------------------- +--R +----------------------------------+ +--R \|%i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 157 + +--S 158 of 532 +r0728:= 2*%i/(a*(cos(c+d*x)+%i*sin(c+d*x)))^(1/2)/d +--R +--R +--R 2%i +--R (146) -------------------------------------- +--R +----------------------------------+ +--R d\|%i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 158 + +--S 159 of 532 +a0728:= integrate(t0728,x) +--R +--R +--R >> System error: +--R Zero divisor. +--R +--R Continuing to read the file... +--R +--E 159 + +--S 160 of 532 +m0728:= a0728-r0728 +--R +--R +--R +----------------------------------+ +--R a0728 d\|%i a sin(d x + c) + a cos(d x + c) - 2%i +--R (147) -------------------------------------------------- +--R +----------------------------------+ +--R d\|%i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 160 + +--S 161 of 532 +d0728:= D(m0728,x) +--R +--R +--R 1 +--R (148) - ------------------------------------- +--R +----------------------------------+ +--R \|%i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 161 + +--S 162 of 532 +t0729:= 1/(a*cos(c+d*x)-%i*a*sin(c+d*x))^3 +--R +--R +--R (149) +--R - +--R %i +--R / +--R 3 3 3 2 +--R a sin(d x + c) + 3%i a cos(d x + c)sin(d x + c) +--R + +--R 3 2 3 3 +--R - 3a cos(d x + c) sin(d x + c) - %i a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 162 + +--S 163 of 532 +r0729:= -1/3*%i*(cos(c+d*x)+%i*sin(c+d*x))^3/a^3/d +--R +--R +--R (150) +--R 1 3 2 +--R - - sin(d x + c) + %i cos(d x + c)sin(d x + c) +--R 3 +--R + +--R 2 1 3 +--R cos(d x + c) sin(d x + c) - - %i cos(d x + c) +--R 3 +--R / +--R 3 +--R a d +--R Type: Expression(Complex(Fraction(Integer))) +--E 163 + +--S 164 of 532 +--a0729:= integrate(t0729,x) +--E 164 + +--S 165 of 532 +--m0729:= a0729-r0729 +--E 165 + +--S 166 of 532 +--d0729:= D(m0729,x) +--E 166 + +--S 167 of 532 +t0730:= (a*cos(c+d*x)-%i*a*sin(c+d*x))^(1/2) +--R +--R +--R +------------------------------------+ +--R (151) \|- %i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 167 + +--S 168 of 532 +r0730:= 2*%i*(a*cos(c+d*x)-%i*a*sin(c+d*x))^(1/2)/d +--R +--R +--R +------------------------------------+ +--R 2%i\|- %i a sin(d x + c) + a cos(d x + c) +--R (152) ------------------------------------------ +--R d +--R Type: Expression(Complex(Integer)) +--E 168 + +--S 169 of 532 +a0730:= integrate(t0730,x) +--R +--R +--R >> System error: +--R Zero divisor. +--R +--R Continuing to read the file... +--R +--E 169 + +--S 170 of 532 +m0730:= a0730-r0730 +--R +--R +--R +------------------------------------+ +--R - 2%i\|- %i a sin(d x + c) + a cos(d x + c) + a0730 d +--R (153) ------------------------------------------------------ +--R d +--R Type: Expression(Complex(Integer)) +--E 170 + +--S 171 of 532 +d0730:= D(m0730,x) +--R +--R +--R %i a sin(d x + c) - a cos(d x + c) +--R (154) --------------------------------------- +--R +------------------------------------+ +--R \|- %i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 171 + +--S 172 of 532 +t0731:= 1/(a*cos(c+d*x)-%i*a*sin(c+d*x))^(1/2) +--R +--R +--R 1 +--R (155) --------------------------------------- +--R +------------------------------------+ +--R \|- %i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 172 + +--S 173 of 532 +r0731:= -2*%i/d/(a*cos(c+d*x)-%i*a*sin(c+d*x))^(1/2) +--R +--R +--R 2%i +--R (156) - ---------------------------------------- +--R +------------------------------------+ +--R d\|- %i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 173 + +--S 174 of 532 +a0731:= integrate(t0731,x) +--R +--R +--R >> System error: +--R Zero divisor. +--R +--R Continuing to read the file... +--R +--E 174 + +--S 175 of 532 +m0731:= a0731-r0731 +--R +--R +--R +------------------------------------+ +--R a0731 d\|- %i a sin(d x + c) + a cos(d x + c) + 2%i +--R (157) ---------------------------------------------------- +--R +------------------------------------+ +--R d\|- %i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 175 + +--S 176 of 532 +d0731:= D(m0731,x) +--R +--R +--R 1 +--R (158) - --------------------------------------- +--R +------------------------------------+ +--R \|- %i a sin(d x + c) + a cos(d x + c) +--R Type: Expression(Complex(Integer)) +--E 176 + +--S 177 of 532 +t0732:= sec(x)-tan(x) +--R +--R +--R (159) - tan(x) + sec(x) +--R Type: Expression(Integer) +--E 177 + +--S 178 of 532 +r0732:= 2*log(sin(1/4*%pi+1/2*x)) +--R +--R +--R 2x + %pi +--R (160) 2log(sin(--------)) +--R 4 +--R Type: Expression(Integer) +--E 178 + +--S 179 of 532 +a0732:= integrate(t0732,x) +--R +--R +--R sin(x) + cos(x) + 1 2 +--R (161) 2log(-------------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 179 + +--S 180 of 532 +m0732:= a0732-r0732 +--R +--R +--R sin(x) + cos(x) + 1 2x + %pi 2 +--R (162) 2log(-------------------) - 2log(sin(--------)) - log(----------) +--R cos(x) + 1 4 cos(x) + 1 +--R Type: Expression(Integer) +--E 180 + +--S 181 of 532 +d0732:= D(m0732,x) +--R +--R +--R (163) +--R 2x + %pi 2 +--R sin(--------)sin(x) +--R 4 +--R + +--R 2x + %pi 2x + %pi 2x + %pi +--R ((- cos(x) - 1)sin(--------) - cos(--------)cos(x) - cos(--------))sin(x) +--R 4 4 4 +--R + +--R 2 2x + %pi 2x + %pi 2 +--R (2cos(x) + 2cos(x))sin(--------) - cos(--------)cos(x) +--R 4 4 +--R + +--R 2x + %pi 2x + %pi +--R - 2cos(--------)cos(x) - cos(--------) +--R 4 4 +--R / +--R 2x + %pi 2 2x + %pi +--R (cos(x) + 1)sin(--------)sin(x) + (cos(x) + 2cos(x) + 1)sin(--------) +--R 4 4 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 532 +t0733:= (sec(x)+tan(x))^3 +--R +--R +--R 3 2 2 3 +--R (164) tan(x) + 3sec(x)tan(x) + 3sec(x) tan(x) + sec(x) +--R Type: Expression(Integer) +--E 182 + +--S 183 of 532 +r0733:= log(1-sin(x))+2/(1-sin(x)) +--R +--R +--R (sin(x) - 1)log(- sin(x) + 1) - 2 +--R (165) --------------------------------- +--R sin(x) - 1 +--R Type: Expression(Integer) +--E 183 + +--S 184 of 532 +a0733:= integrate(t0733,x) +--R +--R +--R (166) +--R sin(x) - cos(x) - 1 2 +--R (2sin(x) - 2)log(-------------------) + (- sin(x) + 1)log(----------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R - 2sin(x) +--R / +--R sin(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 184 + +--S 185 of 532 +m0733:= a0733-r0733 +--R +--R +--R sin(x) - cos(x) - 1 2 +--R (167) 2log(-------------------) - log(----------) - log(- sin(x) + 1) - 2 +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 185 + +--S 186 of 532 +d0733:= D(m0733,x) +--R +--R +--R (168) +--R 3 2 2 3 +--R sin(x) + cos(x)sin(x) + (cos(x) - 1)sin(x) + cos(x) - cos(x) +--R ----------------------------------------------------------------------------- +--R 2 2 2 +--R (cos(x) + 1)sin(x) + (- cos(x) - 3cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 532 +t0734:= (sec(x)-tan(x))^3 +--R +--R +--R 3 2 2 3 +--R (169) - tan(x) + 3sec(x)tan(x) - 3sec(x) tan(x) + sec(x) +--R Type: Expression(Integer) +--E 187 + +--S 188 of 532 +r0734:= -log(1+sin(x))-2/(1+sin(x)) +--R +--R +--R (- sin(x) - 1)log(sin(x) + 1) - 2 +--R (170) --------------------------------- +--R sin(x) + 1 +--R Type: Expression(Integer) +--E 188 + +--S 189 of 532 +a0734:= integrate(t0734,x) +--R +--R +--R (171) +--R sin(x) + cos(x) + 1 2 +--R (- 2sin(x) - 2)log(-------------------) + (sin(x) + 1)log(----------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2sin(x) +--R / +--R sin(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 189 + +--S 190 of 532 +m0734:= a0734-r0734 +--R +--R +--R sin(x) + cos(x) + 1 2 +--R (172) log(sin(x) + 1) - 2log(-------------------) + log(----------) + 2 +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 190 + +--S 191 of 532 +d0734:= D(m0734,x) +--R +--R +--R (173) +--R 3 2 2 3 +--R - sin(x) + cos(x)sin(x) + (- cos(x) + 1)sin(x) + cos(x) - cos(x) +--R --------------------------------------------------------------------------- +--R 2 2 2 +--R (cos(x) + 1)sin(x) + (cos(x) + 3cos(x) + 2)sin(x) + cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 532 +t0735:= (sec(x)+tan(x))^5 +--R +--R +--R (174) +--R 5 4 2 3 3 2 +--R tan(x) + 5sec(x)tan(x) + 10sec(x) tan(x) + 10sec(x) tan(x) +--R + +--R 4 5 +--R 5sec(x) tan(x) + sec(x) +--R Type: Expression(Integer) +--E 192 + +--S 193 of 532 +r0735:= -log(1-sin(x))+2/(1-sin(x))^2-4/(1-sin(x)) +--R +--R +--R 2 +--R (- sin(x) + 2sin(x) - 1)log(- sin(x) + 1) + 4sin(x) - 2 +--R (175) -------------------------------------------------------- +--R 2 +--R sin(x) - 2sin(x) + 1 +--R Type: Expression(Integer) +--E 193 + +--S 194 of 532 +a0735:= integrate(t0735,x) +--R +--R +--R (176) +--R 2 sin(x) - cos(x) - 1 +--R (- 4sin(x) - 2cos(x) + 4)log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R (2sin(x) + cos(x) - 2)log(----------) + 2cos(x) - 2 +--R cos(x) + 1 +--R / +--R 2 +--R 2sin(x) + cos(x) - 2 +--R Type: Union(Expression(Integer),...) +--E 194 + +--S 195 of 532 +m0735:= a0735-r0735 +--R +--R +--R (177) +--R 3 2 2 2 +--R - 4sin(x) + (- 2cos(x) + 12)sin(x) + (4cos(x) - 12)sin(x) +--R + +--R 2 +--R - 2cos(x) + 4 +--R * +--R sin(x) - cos(x) - 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 2 2 2 +--R 2sin(x) + (cos(x) - 6)sin(x) + (- 2cos(x) + 6)sin(x) + cos(x) +--R + +--R - 2 +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 2 2 2 2 +--R 2sin(x) + (cos(x) - 6)sin(x) + (- 2cos(x) + 6)sin(x) + cos(x) +--R + +--R - 2 +--R * +--R log(- sin(x) + 1) +--R + +--R 2 2 2 2 +--R (2cos(x) - 10)sin(x) + (- 8cos(x) + 16)sin(x) + 4cos(x) - 6 +--R / +--R 3 2 2 2 2 +--R 2sin(x) + (cos(x) - 6)sin(x) + (- 2cos(x) + 6)sin(x) + cos(x) - 2 +--R Type: Expression(Integer) +--E 195 + +--S 196 of 532 +d0735:= D(m0735,x) +--R +--R +--R (178) +--R 7 2 6 +--R - 4sin(x) + (- 12cos(x) - 12cos(x) + 16)sin(x) +--R + +--R 4 3 2 5 +--R (- cos(x) + 4cos(x) + 52cos(x) + 52cos(x) - 20)sin(x) +--R + +--R 5 4 3 2 4 +--R (- cos(x) - 6cos(x) - 24cos(x) - 64cos(x) - 64cos(x))sin(x) +--R + +--R 6 5 4 3 2 +--R - cos(x) + 2cos(x) + 48cos(x) + 56cos(x) - 24cos(x) - 8cos(x) +--R + +--R 20 +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R - cos(x) + 6cos(x) - 12cos(x) - 98cos(x) - 64cos(x) + 100cos(x) +--R + +--R 68cos(x) - 16 +--R * +--R 2 +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R - 2cos(x) - 9cos(x) + 10cos(x) + 65cos(x) + 36cos(x) - 60cos(x) +--R + +--R - 44cos(x) + 4 +--R * +--R sin(x) +--R + +--R 7 5 4 3 2 +--R - cos(x) + cos(x) - 8cos(x) - 8cos(x) + 8cos(x) + 8cos(x) +--R / +--R 6 3 5 +--R (4cos(x) + 4)sin(x) + (4cos(x) - 28cos(x) - 24)sin(x) +--R + +--R 5 4 3 4 +--R (cos(x) - 3cos(x) - 24cos(x) + 80cos(x) + 60)sin(x) +--R + +--R 6 5 4 3 3 +--R (- cos(x) - 5cos(x) + 12cos(x) + 56cos(x) - 120cos(x) - 80)sin(x) +--R + +--R 6 5 4 3 2 +--R (3cos(x) + 9cos(x) - 18cos(x) - 64cos(x) + 100cos(x) + 60)sin(x) +--R + +--R 6 5 4 3 +--R (- 3cos(x) - 7cos(x) + 12cos(x) + 36cos(x) - 44cos(x) - 24)sin(x) +--R + +--R 6 5 4 3 +--R cos(x) + 2cos(x) - 3cos(x) - 8cos(x) + 8cos(x) + 4 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 532 +t0736:= (sec(x)-tan(x))^5 +--R +--R +--R (179) +--R 5 4 2 3 3 2 +--R - tan(x) + 5sec(x)tan(x) - 10sec(x) tan(x) + 10sec(x) tan(x) +--R + +--R 4 5 +--R - 5sec(x) tan(x) + sec(x) +--R Type: Expression(Integer) +--E 197 + +--S 198 of 532 +r0736:= log(1+sin(x))-2/(1+sin(x))^2+4/(1+sin(x)) +--R +--R +--R 2 +--R (sin(x) + 2sin(x) + 1)log(sin(x) + 1) + 4sin(x) + 2 +--R (180) ---------------------------------------------------- +--R 2 +--R sin(x) + 2sin(x) + 1 +--R Type: Expression(Integer) +--E 198 + +--S 199 of 532 +a0736:= integrate(t0736,x) +--R +--R +--R (181) +--R 2 sin(x) + cos(x) + 1 +--R (4sin(x) - 2cos(x) + 4)log(-------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R (- 2sin(x) + cos(x) - 2)log(----------) + 2cos(x) - 2 +--R cos(x) + 1 +--R / +--R 2 +--R 2sin(x) - cos(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 199 + +--S 200 of 532 +m0736:= a0736-r0736 +--R +--R +--R (182) +--R 3 2 2 2 2 +--R - 2sin(x) + (cos(x) - 6)sin(x) + (2cos(x) - 6)sin(x) + cos(x) +--R + +--R - 2 +--R * +--R log(sin(x) + 1) +--R + +--R 3 2 2 2 +--R 4sin(x) + (- 2cos(x) + 12)sin(x) + (- 4cos(x) + 12)sin(x) +--R + +--R 2 +--R - 2cos(x) + 4 +--R * +--R sin(x) + cos(x) + 1 +--R log(-------------------) +--R cos(x) + 1 +--R + +--R 3 2 2 2 2 +--R - 2sin(x) + (cos(x) - 6)sin(x) + (2cos(x) - 6)sin(x) + cos(x) +--R + +--R - 2 +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 +--R (2cos(x) - 10)sin(x) + (8cos(x) - 16)sin(x) + 4cos(x) - 6 +--R / +--R 3 2 2 2 2 +--R 2sin(x) + (- cos(x) + 6)sin(x) + (- 2cos(x) + 6)sin(x) - cos(x) + 2 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 532 +d0736:= D(m0736,x) +--R +--R +--R (183) +--R 7 2 6 +--R 4sin(x) + (- 12cos(x) - 12cos(x) + 16)sin(x) +--R + +--R 4 3 2 5 +--R (cos(x) - 4cos(x) - 52cos(x) - 52cos(x) + 20)sin(x) +--R + +--R 5 4 3 2 4 +--R (- cos(x) - 6cos(x) - 24cos(x) - 64cos(x) - 64cos(x))sin(x) +--R + +--R 6 5 4 3 2 +--R (cos(x) - 2cos(x) - 48cos(x) - 56cos(x) + 24cos(x) + 8cos(x) - 20) +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R - cos(x) + 6cos(x) - 12cos(x) - 98cos(x) - 64cos(x) + 100cos(x) +--R + +--R 68cos(x) - 16 +--R * +--R 2 +--R sin(x) +--R + +--R 7 6 5 4 3 2 +--R 2cos(x) + 9cos(x) - 10cos(x) - 65cos(x) - 36cos(x) + 60cos(x) +--R + +--R 44cos(x) - 4 +--R * +--R sin(x) +--R + +--R 7 5 4 3 2 +--R - cos(x) + cos(x) - 8cos(x) - 8cos(x) + 8cos(x) + 8cos(x) +--R / +--R 6 3 5 +--R (4cos(x) + 4)sin(x) + (- 4cos(x) + 28cos(x) + 24)sin(x) +--R + +--R 5 4 3 4 +--R (cos(x) - 3cos(x) - 24cos(x) + 80cos(x) + 60)sin(x) +--R + +--R 6 5 4 3 3 +--R (cos(x) + 5cos(x) - 12cos(x) - 56cos(x) + 120cos(x) + 80)sin(x) +--R + +--R 6 5 4 3 2 +--R (3cos(x) + 9cos(x) - 18cos(x) - 64cos(x) + 100cos(x) + 60)sin(x) +--R + +--R 6 5 4 3 +--R (3cos(x) + 7cos(x) - 12cos(x) - 36cos(x) + 44cos(x) + 24)sin(x) +--R + +--R 6 5 4 3 +--R cos(x) + 2cos(x) - 3cos(x) - 8cos(x) + 8cos(x) + 4 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 532 +t0737:= csc(x)+cot(x) +--R +--R +--R (184) csc(x) + cot(x) +--R Type: Expression(Integer) +--E 202 + +--S 203 of 532 +r0737:= -atanh(cos(x))+log(sin(x)) +--R +--R +--R (185) log(sin(x)) - atanh(cos(x)) +--R Type: Expression(Integer) +--E 203 + +--S 204 of 532 +a0737:= integrate(t0737,x) +--R +--R +--R sin(x) 2 +--R (186) 2log(----------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 204 + +--S 205 of 532 +m0737:= a0737-r0737 +--R +--R +--R sin(x) 2 +--R (187) - log(sin(x)) + 2log(----------) - log(----------) + atanh(cos(x)) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 205 + +--S 206 of 532 +d0737:= D(m0737,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (188) -------------------------------- +--R 2 +--R (cos(x) - 1)sin(x) +--R Type: Expression(Integer) +--E 206 + +--S 207 of 532 +t0738:= (csc(x)+cot(x))^3 +--R +--R +--R 3 2 2 3 +--R (189) csc(x) + 3cot(x)csc(x) + 3cot(x) csc(x) + cot(x) +--R Type: Expression(Integer) +--E 207 + +--S 208 of 532 +r0738:= -2/(1-cos(x))-log(1-cos(x)) +--R +--R +--R (- cos(x) + 1)log(- cos(x) + 1) + 2 +--R (190) ----------------------------------- +--R cos(x) - 1 +--R Type: Expression(Integer) +--E 208 + +--S 209 of 532 +a0738:= integrate(t0738,x) +--R +--R +--R (191) +--R sin(x) 2 +--R (- 2cos(x) + 2)log(----------) + (cos(x) - 1)log(----------) + cos(x) + 1 +--R cos(x) + 1 cos(x) + 1 +--R ------------------------------------------------------------------------- +--R cos(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 209 + +--S 210 of 532 +m0738:= a0738-r0738 +--R +--R +--R sin(x) 2 +--R (192) - 2log(----------) + log(----------) + log(- cos(x) + 1) + 1 +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 210 + +--S 211 of 532 +d0738:= D(m0738,x) +--R +--R +--R 2 3 +--R - 2cos(x)sin(x) - 2cos(x) + 2cos(x) +--R (193) ------------------------------------- +--R 2 +--R (cos(x) - 1)sin(x) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 532 +t0739:= (csc(x)-cot(x))^3 +--R +--R +--R 3 2 2 3 +--R (194) csc(x) - 3cot(x)csc(x) + 3cot(x) csc(x) - cot(x) +--R Type: Expression(Integer) +--E 212 + +--S 213 of 532 +r0739:= 2/(cos(x)+1)+log(cos(x)+1) +--R +--R +--R (cos(x) + 1)log(cos(x) + 1) + 2 +--R (195) ------------------------------- +--R cos(x) + 1 +--R Type: Expression(Integer) +--E 213 + +--S 214 of 532 +a0739:= integrate(t0739,x) +--R +--R +--R 2 +--R (- cos(x) - 1)log(----------) - cos(x) + 1 +--R cos(x) + 1 +--R (196) ------------------------------------------ +--R cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 214 + +--S 215 of 532 +m0739:= a0739-r0739 +--R +--R +--R 2 +--R (197) - log(cos(x) + 1) - log(----------) - 1 +--R cos(x) + 1 +--R Type: Expression(Integer) +--E 215 + +--S 216 of 532 +d0739:= D(m0739,x) +--R +--R +--R (198) 0 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 532 +t0740:= (csc(x)+cot(x))^5 +--R +--R +--R (199) +--R 5 4 2 3 3 2 +--R csc(x) + 5cot(x)csc(x) + 10cot(x) csc(x) + 10cot(x) csc(x) +--R + +--R 4 5 +--R 5cot(x) csc(x) + cot(x) +--R Type: Expression(Integer) +--E 217 + +--S 218 of 532 +r0740:= -2/(1-cos(x))^2+4/(1-cos(x))+log(1-cos(x)) +--R +--R +--R 2 +--R (cos(x) - 2cos(x) + 1)log(- cos(x) + 1) - 4cos(x) + 2 +--R (200) ------------------------------------------------------ +--R 2 +--R cos(x) - 2cos(x) + 1 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 532 +a0740:= integrate(t0740,x) +--R +--R +--R (201) +--R 2 sin(x) +--R (4cos(x) - 8cos(x) + 4)log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R (- 2cos(x) + 4cos(x) - 2)log(----------) - 3cos(x) - 2cos(x) + 1 +--R cos(x) + 1 +--R / +--R 2 +--R 2cos(x) - 4cos(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 219 + +--S 220 of 532 +m0740:= a0740-r0740 +--R +--R +--R sin(x) 2 +--R 4log(----------) - 2log(----------) - 2log(- cos(x) + 1) - 3 +--R cos(x) + 1 cos(x) + 1 +--R (202) ------------------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 220 + +--S 221 of 532 +d0740:= D(m0740,x) +--R +--R +--R 2 3 +--R 2cos(x)sin(x) + 2cos(x) - 2cos(x) +--R (203) ----------------------------------- +--R 2 +--R (cos(x) - 1)sin(x) +--R Type: Expression(Integer) +--E 221 + +--S 222 of 532 +t0741:= (csc(x)-cot(x))^5 +--R +--R +--R (204) +--R 5 4 2 3 3 2 +--R csc(x) - 5cot(x)csc(x) + 10cot(x) csc(x) - 10cot(x) csc(x) +--R + +--R 4 5 +--R 5cot(x) csc(x) - cot(x) +--R Type: Expression(Integer) +--E 222 + +--S 223 of 532 +r0741:= 2/(cos(x)+1)^2-4/(cos(x)+1)-log(cos(x)+1) +--R +--R +--R 2 +--R (- cos(x) - 2cos(x) - 1)log(cos(x) + 1) - 4cos(x) - 2 +--R (205) ------------------------------------------------------ +--R 2 +--R cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 223 + +--S 224 of 532 +a0741:= integrate(t0741,x) +--R +--R +--R 2 2 2 +--R (2cos(x) + 4cos(x) + 2)log(----------) + 3cos(x) - 2cos(x) - 1 +--R cos(x) + 1 +--R (206) ---------------------------------------------------------------- +--R 2 +--R 2cos(x) + 4cos(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 224 + +--S 225 of 532 +m0741:= a0741-r0741 +--R +--R +--R 2 +--R 2log(cos(x) + 1) + 2log(----------) + 3 +--R cos(x) + 1 +--R (207) --------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 225 + +--S 226 of 532 +d0741:= D(m0741,x) +--R +--R +--R (208) 0 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 532 +t0742:= 1/(csc(x)-cot(x)) +--R +--R +--R 1 +--R (209) --------------- +--R csc(x) - cot(x) +--R Type: Expression(Integer) +--E 227 + +--S 228 of 532 +r0742:= log(1-cos(x)) +--R +--R +--R (210) log(- cos(x) + 1) +--R Type: Expression(Integer) +--E 228 + +--S 229 of 532 +a0742:= integrate(t0742,x) +--R +--R +--R sin(x) 2 +--R (211) 2log(----------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 229 + +--S 230 of 532 +m0742:= a0742-r0742 +--R +--R +--R sin(x) 2 +--R (212) 2log(----------) - log(----------) - log(- cos(x) + 1) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 230 + +--S 231 of 532 +d0742:= D(m0742,x) +--R +--R +--R 2 3 +--R 2cos(x)sin(x) + 2cos(x) - 2cos(x) +--R (213) ----------------------------------- +--R 2 +--R (cos(x) - 1)sin(x) +--R Type: Expression(Integer) +--E 231 + +--S 232 of 532 +t0743:= csc(x)-sin(x) +--R +--R +--R (214) - sin(x) + csc(x) +--R Type: Expression(Integer) +--E 232 + +--S 233 of 532 +r0743:= -atanh(cos(x))+cos(x) +--R +--R +--R (215) - atanh(cos(x)) + cos(x) +--R Type: Expression(Integer) +--E 233 + +--S 234 of 532 +a0743:= integrate(t0743,x) +--R +--R +--R sin(x) +--R (216) log(----------) + cos(x) +--R cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 234 + +--S 235 of 532 +m0743:= a0743-r0743 +--R +--R +--R sin(x) +--R (217) log(----------) + atanh(cos(x)) +--R cos(x) + 1 +--R Type: Expression(Integer) +--E 235 + +--S 236 of 532 +d0743:= D(m0743,x) +--R +--R +--R 2 3 +--R cos(x)sin(x) + cos(x) - cos(x) +--R (218) -------------------------------- +--R 2 +--R (cos(x) - 1)sin(x) +--R Type: Expression(Integer) +--E 236 + +--S 237 of 532 +t0744:= sec(x)-cos(x) +--R +--R +--R (219) sec(x) - cos(x) +--R Type: Expression(Integer) +--E 237 + +--S 238 of 532 +r0744:= atanh(sin(x))-sin(x) +--R +--R +--R (220) atanh(sin(x)) - sin(x) +--R Type: Expression(Integer) +--E 238 + +--S 239 of 532 +a0744:= integrate(t0744,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (221) log(-------------------) - log(-------------------) - sin(x) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 239 + +--S 240 of 532 +m0744:= a0744-r0744 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (222) log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 240 + +--S 241 of 532 +d0744:= D(m0744,x) +--R +--R +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R (223) ------------------------------------------------------------------ +--R 4 2 2 2 +--R sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 532 +t0745:= (sec(x)-cos(x))^(1/2) +--R +--R +--R +---------------+ +--R (224) \|sec(x) - cos(x) +--R Type: Expression(Integer) +--E 242 + +--S 243 of 532 +r0745:= -2*cot(x)*(tan(x)*sin(x))^(1/2) +--R +--R +--R +------------+ +--R (225) - 2cot(x)\|sin(x)tan(x) +--R Type: Expression(Integer) +--E 243 + +--S 244 of 532 +a0745:= integrate(t0745,x) +--R +--R +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R (226) (- cos(x) - 1) |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 244 + +--S 245 of 532 +m0745:= a0745-r0745 +--R +--R +--R (227) +--R +------------+ +--R 2cot(x)\|sin(x)tan(x) +--R + +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R (- cos(x) - 1) |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R Type: Expression(Integer) +--E 245 + +--S 246 of 532 +d0745:= D(m0745,x) +--R +--R +--R (228) +--R +------------+ +--R 8cos(x)sin(x)\|sin(x)tan(x) +--R + +--R 3 2 2 +--R (cos(x) + 3cos(x) + 3cos(x) + 1)cot(x)sin(x)tan(x) +--R + +--R 3 2 2 3 +--R (- 2cos(x) - 6cos(x) - 6cos(x) - 2)cot(x) - 2cos(x) +--R + +--R 2 +--R - 6cos(x) - 6cos(x) - 2 +--R * +--R sin(x) +--R + +--R 4 3 2 +--R (cos(x) + 3cos(x) + 3cos(x) + cos(x))cot(x) +--R * +--R tan(x) +--R + +--R 3 2 +--R (cos(x) + 3cos(x) + 3cos(x) + 1)cot(x)sin(x) +--R * +--R +-------------------------------------------+3 +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 3 2 +--R (cos(x) + 3cos(x) + 3cos(x) + 1) +--R * +--R +-------------------------------------------+3 +--R | 2 +--R | 16cos(x) +------------+ +--R |------------------------------------------- \|sin(x)tan(x) +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 532 +t0746:= (sec(x)-cos(x))^(3/2) +--R +--R +--R +---------------+ +--R (229) (sec(x) - cos(x))\|sec(x) - cos(x) +--R Type: Expression(Integer) +--E 247 + +--S 248 of 532 +r0746:= 2/3*csc(x)*(4-sin(x)^2)*(tan(x)*sin(x))^(1/2) +--R +--R +--R 2 +------------+ +--R (- 2csc(x)sin(x) + 8csc(x))\|sin(x)tan(x) +--R (230) ------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 248 + +--S 249 of 532 +a0746:= integrate(t0746,x) +--R +--R +--R (231) +--R 3 2 +--R (cos(x) + cos(x) + 3cos(x) + 3) +--R * +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 3cos(x) +--R Type: Union(Expression(Integer),...) +--E 249 + +--S 250 of 532 +m0746:= a0746-r0746 +--R +--R +--R (232) +--R 2 +------------+ +--R (2cos(x)csc(x)sin(x) - 8cos(x)csc(x))\|sin(x)tan(x) +--R + +--R 3 2 +--R (cos(x) + cos(x) + 3cos(x) + 3) +--R * +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 3cos(x) +--R Type: Expression(Integer) +--E 250 + +--S 251 of 532 +d0746:= D(m0746,x) +--R +--R +--R (233) +--R +------------+ +--R (- 24cos(x) + 24)sin(x)\|sin(x)tan(x) +--R + +--R 2 3 +--R (cos(x) + 2cos(x) + 1)csc(x)sin(x) +--R + +--R 2 +--R (- 4cos(x) - 8cos(x) - 4)csc(x)sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 3 +--R (- 2cos(x) - 4cos(x) - 2)cot(x)csc(x)sin(x) +--R + +--R 3 2 2 +--R (5cos(x) + 10cos(x) + 5cos(x))csc(x)sin(x) +--R + +--R 2 +--R (8cos(x) + 16cos(x) + 8)cot(x)csc(x)sin(x) +--R + +--R 3 2 +--R (- 4cos(x) - 8cos(x) - 4cos(x))csc(x) +--R * +--R tan(x) +--R + +--R 2 3 +--R (cos(x) + 2cos(x) + 1)csc(x)sin(x) +--R + +--R 2 +--R (- 4cos(x) - 8cos(x) - 4)csc(x)sin(x) +--R * +--R +-------------------------------------------+3 +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R +-------------------------------------------+3 +--R | 2 +--R 2 | 16cos(x) +--R (3cos(x) + 6cos(x) + 3) |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R * +--R +------------+ +--R \|sin(x)tan(x) +--R Type: Expression(Integer) +--E 251 + +--S 252 of 532 +t0747:= (sec(x)-cos(x))^(5/2) +--R +--R +--R 2 2 +---------------+ +--R (234) (sec(x) - 2cos(x)sec(x) + cos(x) )\|sec(x) - cos(x) +--R Type: Expression(Integer) +--E 252 + +--S 253 of 532 +r0747:= 2/15*cot(x)*(tan(x)*sin(x))^(1/2)*(32+(8-3*sin(x)^2)*tan(x)^2) +--R +--R +--R 2 2 +------------+ +--R ((- 6cot(x)sin(x) + 16cot(x))tan(x) + 64cot(x))\|sin(x)tan(x) +--R (235) ---------------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 253 + +--S 254 of 532 +a0747:= integrate(t0747,x) +--R +--R +--R (236) +--R 5 4 3 2 +--R (- 3cos(x) - 3cos(x) + 30cos(x) + 30cos(x) + 5cos(x) + 5) +--R * +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 2 +--R 15cos(x) +--R Type: Union(Expression(Integer),...) +--E 254 + +--S 255 of 532 +m0747:= a0747-r0747 +--R +--R +--R (237) +--R 2 2 2 2 2 +--R ((6cos(x) cot(x)sin(x) - 16cos(x) cot(x))tan(x) - 64cos(x) cot(x)) +--R * +--R +------------+ +--R \|sin(x)tan(x) +--R + +--R 5 4 3 2 +--R (- 3cos(x) - 3cos(x) + 30cos(x) + 30cos(x) + 5cos(x) + 5) +--R * +--R +-------------------------------------------+ +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R 2 +--R 15cos(x) +--R Type: Expression(Integer) +--E 255 + +--S 256 of 532 +d0747:= D(m0747,x) +--R +--R +--R (238) +--R 2 +------------+ +--R (120cos(x) - 240cos(x) + 120)sin(x)\|sin(x)tan(x) +--R + +--R 2 3 +--R (15cos(x) + 15cos(x))cot(x)sin(x) +--R + +--R 2 +--R (- 40cos(x) - 40cos(x))cot(x)sin(x) +--R * +--R 4 +--R tan(x) +--R + +--R 2 2 2 3 +--R ((- 6cos(x) - 6cos(x))cot(x) - 6cos(x) - 6cos(x))sin(x) +--R + +--R 3 2 2 +--R (15cos(x) + 15cos(x) )cot(x)sin(x) +--R + +--R 2 2 2 +--R ((16cos(x) + 16cos(x))cot(x) + 16cos(x) + 16cos(x))sin(x) +--R + +--R 3 2 +--R (- 8cos(x) - 8cos(x) )cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R 2 3 +--R (15cos(x) + 15cos(x))cot(x)sin(x) +--R + +--R 2 +--R (- 72cos(x) - 72cos(x))cot(x)sin(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 2 +--R ((64cos(x) + 64cos(x))cot(x) + 64cos(x) + 64cos(x))sin(x) +--R + +--R 3 2 +--R (- 32cos(x) - 32cos(x) )cot(x) +--R * +--R tan(x) +--R + +--R 2 +--R (- 32cos(x) - 32cos(x))cot(x)sin(x) +--R * +--R +-------------------------------------------+3 +--R | 2 +--R | 16cos(x) +--R |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R / +--R +-------------------------------------------+3 +--R | 2 +--R 2 | 16cos(x) +--R (15cos(x) + 15cos(x)) |------------------------------------------- +--R 4| 4 3 2 +--R \|cos(x) + 4cos(x) + 6cos(x) + 4cos(x) + 1 +--R * +--R +------------+ +--R \|sin(x)tan(x) +--R Type: Expression(Integer) +--E 256 + +--S 257 of 532 +t0748:= 1/(cos(x)^2-sin(x)^2) +--R +--R +--R 1 +--R (239) - ----------------- +--R 2 2 +--R sin(x) - cos(x) +--R Type: Expression(Integer) +--E 257 + +--S 258 of 532 +r0748:= 1/2*atanh(sin(2*x)) +--R +--R +--R atanh(sin(2x)) +--R (240) -------------- +--R 2 +--R Type: Expression(Integer) +--E 258 + +--S 259 of 532 +a0748:= integrate(t0748,x) +--R +--R +--R 2sin(x) - 2cos(x) - 2sin(x) - 2cos(x) +--R - log(-----------------) + log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R (241) --------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 259 + +--S 260 of 532 +m0748:= a0748-r0748 +--R +--R +--R 2sin(x) - 2cos(x) - 2sin(x) - 2cos(x) +--R - log(-----------------) + log(-------------------) - atanh(sin(2x)) +--R cos(x) + 1 cos(x) + 1 +--R (242) -------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 532 +d0748:= D(m0748,x) +--R +--R +--R (243) +--R 2 2 2 2 2 +--R (- sin(x) - cos(x) )sin(2x) + (cos(2x) + 1)sin(x) - cos(x) cos(2x) +--R + +--R 2 +--R cos(x) +--R / +--R 2 2 2 2 2 +--R (sin(x) - cos(x) )sin(2x) - sin(x) + cos(x) +--R Type: Expression(Integer) +--E 261 + +--S 262 of 532 +t0749:= 1/(cos(x)^2-sin(x)^2)^3 +--R +--R +--R 1 +--R (244) - ----------------------------------------------------- +--R 6 2 4 4 2 6 +--R sin(x) - 3cos(x) sin(x) + 3cos(x) sin(x) - cos(x) +--R Type: Expression(Integer) +--E 262 + +--S 263 of 532 +r0749:= 1/4*atanh(sin(2*x))+1/4*sec(2*x)*tan(2*x) +--R +--R +--R atanh(sin(2x)) + sec(2x)tan(2x) +--R (245) ------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 263 + +--S 264 of 532 +a0749:= integrate(t0749,x) +--R +--R +--R (246) +--R 4 2 2sin(x) - 2cos(x) +--R (- 4cos(x) + 4cos(x) - 1)log(-----------------) +--R cos(x) + 1 +--R + +--R 4 2 - 2sin(x) - 2cos(x) +--R (4cos(x) - 4cos(x) + 1)log(-------------------) + 2cos(x)sin(x) +--R cos(x) + 1 +--R / +--R 4 2 +--R 16cos(x) - 16cos(x) + 4 +--R Type: Union(Expression(Integer),...) +--E 264 + +--S 265 of 532 +m0749:= a0749-r0749 +--R +--R +--R (247) +--R 4 2 2sin(x) - 2cos(x) +--R (- 4cos(x) + 4cos(x) - 1)log(-----------------) +--R cos(x) + 1 +--R + +--R 4 2 - 2sin(x) - 2cos(x) +--R (4cos(x) - 4cos(x) + 1)log(-------------------) +--R cos(x) + 1 +--R + +--R 4 2 +--R (- 4cos(x) + 4cos(x) - 1)atanh(sin(2x)) +--R + +--R 4 2 +--R (- 4cos(x) + 4cos(x) - 1)sec(2x)tan(2x) + 2cos(x)sin(x) +--R / +--R 4 2 +--R 16cos(x) - 16cos(x) + 4 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 532 +d0749:= D(m0749,x) +--R +--R +--R (248) +--R 6 4 2 2 +--R (- 16cos(x) + 24cos(x) - 12cos(x) + 2)sec(2x)sin(x) +--R + +--R 8 6 4 2 +--R (16cos(x) - 24cos(x) + 12cos(x) - 2cos(x) )sec(2x) +--R * +--R 2 +--R sin(2x) +--R + +--R 6 4 2 2 +--R (16cos(x) - 24cos(x) + 12cos(x) - 2)sec(2x)sin(x) +--R + +--R 8 6 4 2 +--R (- 16cos(x) + 24cos(x) - 12cos(x) + 2cos(x) )sec(2x) +--R * +--R 2 +--R tan(2x) +--R + +--R 2 4 +--R (6cos(x) + 1)sin(x) +--R + +--R 6 4 2 6 +--R (- 8cos(x) + 12cos(x) - 6cos(x) + 1)sec(2x) - 8cos(x) +--R + +--R 4 2 +--R 8cos(x) - 8cos(x) + 1 +--R * +--R 2 +--R sin(x) +--R + +--R 8 6 4 2 8 +--R (8cos(x) - 12cos(x) + 6cos(x) - cos(x) )sec(2x) - 8cos(x) +--R + +--R 6 4 2 +--R 10cos(x) - 5cos(x) + cos(x) +--R * +--R 2 +--R sin(2x) +--R + +--R 2 4 +--R (- 6cos(x) - 1)sin(x) +--R + +--R 6 4 2 +--R (8cos(x) - 12cos(x) + 6cos(x) - 1)sec(2x) +--R + +--R 6 4 2 6 4 +--R (8cos(x) - 12cos(x) + 6cos(x) - 1)cos(2x) + 8cos(x) - 8cos(x) +--R + +--R 2 +--R 8cos(x) - 1 +--R * +--R 2 +--R sin(x) +--R + +--R 8 6 4 2 +--R (- 8cos(x) + 12cos(x) - 6cos(x) + cos(x) )sec(2x) +--R + +--R 8 6 4 2 8 +--R (- 8cos(x) + 12cos(x) - 6cos(x) + cos(x) )cos(2x) + 8cos(x) +--R + +--R 6 4 2 +--R - 10cos(x) + 5cos(x) - cos(x) +--R / +--R 6 4 2 2 8 +--R (16cos(x) - 24cos(x) + 12cos(x) - 2)sin(x) - 16cos(x) +--R + +--R 6 4 2 +--R 24cos(x) - 12cos(x) + 2cos(x) +--R * +--R 2 +--R sin(2x) +--R + +--R 6 4 2 2 8 6 +--R (- 16cos(x) + 24cos(x) - 12cos(x) + 2)sin(x) + 16cos(x) - 24cos(x) +--R + +--R 4 2 +--R 12cos(x) - 2cos(x) +--R Type: Expression(Integer) +--E 266 + +--S 267 of 532 +t0750:= 1/(sec(x)^2-tan(x)^2) +--R +--R +--R 1 +--R (249) - ----------------- +--R 2 2 +--R tan(x) - sec(x) +--R Type: Expression(Integer) +--E 267 + +--S 268 of 532 +r0750:= x +--R +--R +--R (250) x +--R Type: Variable(x) +--E 268 + +--S 269 of 532 +a0750:= integrate(t0750,x) +--R +--R +--R (251) x +--R Type: Union(Expression(Integer),...) +--E 269 + +--S 270 of 532 +m0750:= a0750-r0750 +--R +--R +--R (252) 0 +--R Type: Expression(Integer) +--E 270 + +--S 271 of 532 +d0750:= D(m0750,x) +--R +--R +--R (253) 0 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 532 +t0751:= 1/(sec(x)^2-tan(x)^2)^2 +--R +--R +--R 1 +--R (254) ----------------------------------- +--R 4 2 2 4 +--R tan(x) - 2sec(x) tan(x) + sec(x) +--R Type: Expression(Integer) +--E 272 + +--S 273 of 532 +r0751:= x +--R +--R +--R (255) x +--R Type: Variable(x) +--E 273 + +--S 274 of 532 +a0751:= integrate(t0751,x) +--R +--R +--R (256) x +--R Type: Union(Expression(Integer),...) +--E 274 + +--S 275 of 532 +m0751:= a0751-r0751 +--R +--R +--R (257) 0 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 532 +d0751:= D(m0751,x) +--R +--R +--R (258) 0 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 532 +t0752:= 1/(sec(x)^2-tan(x)^2)^3 +--R +--R +--R 1 +--R (259) - ----------------------------------------------------- +--R 6 2 4 4 2 6 +--R tan(x) - 3sec(x) tan(x) + 3sec(x) tan(x) - sec(x) +--R Type: Expression(Integer) +--E 277 + +--S 278 of 532 +r0752:= x +--R +--R +--R (260) x +--R Type: Variable(x) +--E 278 + +--S 279 of 532 +a0752:= integrate(t0752,x) +--R +--R +--R (261) x +--R Type: Union(Expression(Integer),...) +--E 279 + +--S 280 of 532 +m0752:= a0752-r0752 +--R +--R +--R (262) 0 +--R Type: Expression(Integer) +--E 280 + +--S 281 of 532 +d0752:= D(m0752,x) +--R +--R +--R (263) 0 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 532 +t0753:= 1/(cot(x)^2-csc(x)^2) +--R +--R +--R 1 +--R (264) - ----------------- +--R 2 2 +--R csc(x) - cot(x) +--R Type: Expression(Integer) +--E 282 + +--S 283 of 532 +r0753:= -x +--R +--R +--R (265) - x +--R Type: Polynomial(Integer) +--E 283 + +--S 284 of 532 +a0753:= integrate(t0753,x) +--R +--R +--R (266) - x +--R Type: Union(Expression(Integer),...) +--E 284 + +--S 285 of 532 +m0753:= a0753-r0753 +--R +--R +--R (267) 0 +--R Type: Expression(Integer) +--E 285 + +--S 286 of 532 +d0753:= D(m0753,x) +--R +--R +--R (268) 0 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 532 +t0754:= 1/(cot(x)^2-csc(x)^2)^2 +--R +--R +--R 1 +--R (269) ----------------------------------- +--R 4 2 2 4 +--R csc(x) - 2cot(x) csc(x) + cot(x) +--R Type: Expression(Integer) +--E 287 + +--S 288 of 532 +r0754:= x +--R +--R +--R (270) x +--R Type: Variable(x) +--E 288 + +--S 289 of 532 +a0754:= integrate(t0754,x) +--R +--R +--R (271) x +--R Type: Union(Expression(Integer),...) +--E 289 + +--S 290 of 532 +m0754:= a0754-r0754 +--R +--R +--R (272) 0 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 532 +d0754:= D(m0754,x) +--R +--R +--R (273) 0 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 532 +t0755:= 1/(cot(x)^2-csc(x)^2)^3 +--R +--R +--R 1 +--R (274) - ----------------------------------------------------- +--R 6 2 4 4 2 6 +--R csc(x) - 3cot(x) csc(x) + 3cot(x) csc(x) - cot(x) +--R Type: Expression(Integer) +--E 292 + +--S 293 of 532 +r0755:= -x +--R +--R +--R (275) - x +--R Type: Polynomial(Integer) +--E 293 + +--S 294 of 532 +a0755:= integrate(t0755,x) +--R +--R +--R (276) - x +--R Type: Union(Expression(Integer),...) +--E 294 + +--S 295 of 532 +m0755:= a0755-r0755 +--R +--R +--R (277) 0 +--R Type: Expression(Integer) +--E 295 + +--S 296 of 532 +d0755:= D(m0755,x) +--R +--R +--R (278) 0 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 532 +t0756:= ((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^3 +--R +--R +--R (279) +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (3c sin(x) + 6b c cos(x)sin(x) + 3b cos(x) + c + b )\|c + b +--R + +--R 3 3 2 2 2 2 3 2 +--R c sin(x) + 3b c cos(x)sin(x) + (3b c cos(x) + 3c + 3b c)sin(x) +--R + +--R 3 3 2 3 +--R b cos(x) + (3b c + 3b )cos(x) +--R Type: Expression(Integer) +--E 297 + +--S 298 of 532 +r0756:= 5/2*(b^2+c^2)^(3/2)*x-5/2*c*(b^2+c^2)*cos(x)+_ + 5/2*b*(b^2+c^2)*sin(x)-5/6*(b^2+c^2)^(1/2)*(c*cos(x)-b*sin(x))*_ + ((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))-1/3*(c*cos(x)-b*sin(x))*_ + ((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^2 +--R +--R +--R (280) +--R 2 2 2 2 +--R 9b c sin(x) + (- 9c + 9b )cos(x)sin(x) - 9b c cos(x) +--R + +--R 2 2 +--R (15c + 15b )x +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 2 3 3 2 2 +--R 2b c sin(x) + (- 2c + 4b c)cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 3 +--R ((- 4b c + 2b )cos(x) + 22b c + 22b )sin(x) - 2b c cos(x) +--R + +--R 3 2 +--R (- 22c - 22b c)cos(x) +--R / +--R 6 +--R Type: Expression(Integer) +--E 298 + +--S 299 of 532 +--a0756:= integrate(t0756,x) +--E 299 + +--S 300 of 532 +--m0756:= a0756-r0756 +--E 300 + +--S 301 of 532 +--d0756:= D(m0756,x) +--E 301 + +--S 302 of 532 +t0757:= 1/((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^2 +--R +--R +--R (281) +--R 1 +--R / +--R +-------+ +--R | 2 2 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + c sin(x) + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 +--R b cos(x) + c + b +--R Type: Expression(Integer) +--E 302 + +--S 303 of 532 +r0757:= -1/3*(c*cos(x)-b*sin(x))/(b^2+c^2)^(1/2)/((b^2+c^2)^(1/2)+_ + b*cos(x)+c*sin(x))^2-2/3/(b^2+c^2)^(1/2)/(c-(b-(b^2+c^2)^(1/2))*_ + tan(1/2*x)) +--R +--R +--R (282) +--R 2 x 2 2 +--R (- b sin(x) + b c cos(x))tan(-) - 2c sin(x) +--R 2 +--R + +--R 2 2 2 2 2 +--R (- 4b c cos(x) + b c)sin(x) - 2b cos(x) - c cos(x) - 2c - 2b +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 2 3 3 2 x 3 2 +--R ((b c + b )sin(x) + (- c - b c)cos(x))tan(-) + (- 4c - 4b c)sin(x) +--R 2 +--R + +--R 2 3 +--R (- 4b c - 4b )cos(x) +--R / +--R 4 2 2 2 +--R (3c + 3b c )sin(x) +--R + +--R 3 3 3 3 +--R ((6b c + 6b c)cos(x) - 6b c - 6b c)sin(x) +--R + +--R 2 2 4 2 2 2 4 4 2 2 4 +--R (3b c + 3b )cos(x) + (- 6b c - 6b )cos(x) + 3c + 6b c + 3b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 3 +--R (6c + 6b c )sin(x) + (6b c + 6b c)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 4 3 2 2 +--R (- 3b c - 3b c )sin(x) +--R + +--R 2 3 4 5 2 3 4 +--R ((- 6b c - 6b c)cos(x) + 6c + 12b c + 6b c)sin(x) +--R + +--R 3 2 5 2 4 3 2 5 4 3 2 +--R (- 3b c - 3b )cos(x) + (6b c + 12b c + 6b )cos(x) - 3b c - 6b c +--R + +--R 5 +--R - 3b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 2 3 2 4 3 2 +--R (3c + 3b c )sin(x) + (6b c + 6b c )cos(x)sin(x) +--R + +--R 2 3 4 2 5 2 3 4 +--R (3b c + 3b c)cos(x) + 3c + 6b c + 3b c +--R Type: Expression(Integer) +--E 303 + +--S 304 of 532 +--a0757:= integrate(t0757,x) +--E 304 + +--S 305 of 532 +--m0757:= a0757-r0757 +--E 305 + +--S 306 of 532 +--d0757:= D(m0757,x) +--E 306 + +--S 307 of 532 +t0758:= 1/((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^3 +--R +--R +--R (283) +--R 1 +--R / +--R +-------+ +--R 2 2 2 2 2 2 | 2 2 +--R (3c sin(x) + 6b c cos(x)sin(x) + 3b cos(x) + c + b )\|c + b +--R + +--R 3 3 2 2 2 2 3 2 +--R c sin(x) + 3b c cos(x)sin(x) + (3b c cos(x) + 3c + 3b c)sin(x) +--R + +--R 3 3 2 3 +--R b cos(x) + (3b c + 3b )cos(x) +--R Type: Expression(Integer) +--E 307 + +--S 308 of 532 +r0758:= -1/5*(c*cos(x)-b*sin(x))/(b^2+c^2)^(1/2)/((b^2+c^2)^(1/2)+_ + b*cos(x)+c*sin(x))^3-2/15*(c*cos(x)-b*sin(x))/(b^2+c^2)/_ + ((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^2-4/15/(b^2+c^2)/_ + (c-(b-(b^2+c^2)^(1/2))*tan(1/2*x)) +--R +--R +--R (284) +--R 2 3 4 4 3 2 4 3 2 3 +--R 2b c sin(x) + ((- 2b c + 6b c )cos(x) - 9b c - 9b c )sin(x) +--R + +--R 2 3 4 2 5 2 3 4 +--R (- 6b c + 6b c)cos(x) + (9c - 9b c - 18b c)cos(x) +--R + +--R 2 3 4 +--R 12b c + 12b c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 3 4 3 2 5 2 +--R (- 6b c + 2b )cos(x) + (18b c + 9b c - 9b )cos(x) +--R + +--R 4 5 4 3 2 5 +--R (- 12b c + 12b )cos(x) - 5b c - 10b c - 5b +--R * +--R sin(x) +--R + +--R 4 4 2 3 4 3 +--R - 2b c cos(x) + (9b c + 9b c)cos(x) +--R + +--R 2 3 4 2 5 2 3 4 +--R (- 12b c - 12b c)cos(x) + (5c + 10b c + 5b c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 5 4 4 4 +--R 4c sin(x) + (20b c cos(x) - 2b c )sin(x) +--R + +--R 2 3 2 5 2 3 5 2 3 3 +--R (40b c cos(x) + (2c - 6b c )cos(x) + 40c + 40b c )sin(x) +--R + +--R 3 2 3 4 3 2 2 +--R 40b c cos(x) + (6b c - 6b c )cos(x) +--R + +--R 4 3 2 4 3 2 +--R (120b c + 120b c )cos(x) - 12b c - 12b c +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 2 3 4 3 2 3 4 2 +--R 20b c cos(x) + (6b c - 2b c)cos(x) + (120b c + 120b c)cos(x) +--R + +--R 5 4 5 2 3 4 +--R (12c - 12b c)cos(x) + 20c + 40b c + 20b c +--R * +--R sin(x) +--R + +--R 5 5 3 2 4 3 2 5 3 +--R 4b cos(x) + 2b c cos(x) + (40b c + 40b )cos(x) +--R + +--R 4 3 2 2 4 3 2 5 +--R (12b c + 12b c )cos(x) + (20b c + 40b c + 20b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 5 3 3 4 +--R (- 2b c - 2b c )sin(x) +--R + +--R 6 2 4 4 2 2 4 4 2 3 +--R ((2c - 4b c - 6b c )cos(x) + 9b c + 9b c )sin(x) +--R + +--R 5 5 2 5 3 3 5 5 +--R (6b c - 6b c)cos(x) + (- 9b c + 9b c + 18b c)cos(x) - 12b c +--R + +--R 3 3 5 +--R - 24b c - 12b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (6b c + 4b c - 2b )cos(x) + (- 18b c - 9b c + 9b )cos(x) +--R + +--R 6 2 4 4 2 6 2 4 4 2 6 +--R (12c + 12b c - 12b c - 12b )cos(x) + 5b c + 10b c + 5b +--R * +--R sin(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (2b c + 2b c)cos(x) + (- 9b c - 9b c)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (12b c + 24b c + 12b c)cos(x) + (- 5b c - 10b c - 5b c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 2 4 4 5 3 3 5 3 3 3 +--R (20c + 20b c )sin(x) + ((80b c + 80b c )cos(x) - 9b c - 9b c )sin(x) +--R + +--R 2 4 4 2 2 6 2 4 4 2 6 +--R (120b c + 120b c )cos(x) + (9c - 9b c - 18b c )cos(x) + 40c +--R + +--R 2 4 4 2 +--R 80b c + 40b c +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 3 5 3 3 5 2 +--R (80b c + 80b c)cos(x) + (18b c + 9b c - 9b c)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (80b c + 160b c + 80b c)cos(x) - 5b c - 10b c - 5b c +--R * +--R sin(x) +--R + +--R 4 2 6 4 2 4 4 2 3 +--R (20b c + 20b )cos(x) + (9b c + 9b c )cos(x) +--R + +--R 2 4 4 2 6 2 6 2 4 4 2 6 +--R (40b c + 80b c + 40b )cos(x) + (5c + 10b c + 5b c )cos(x) + 4c +--R + +--R 2 4 4 2 6 +--R 12b c + 12b c + 4b +--R / +--R 7 3 5 5 +--R (15b c + 15b c )sin(x) +--R + +--R 2 6 4 4 8 2 6 4 4 4 +--R ((75b c + 75b c )cos(x) - 75c - 150b c - 75b c )sin(x) +--R + +--R 3 5 5 3 2 +--R (150b c + 150b c )cos(x) +--R + +--R 7 3 5 5 3 7 3 5 +--R (- 300b c - 600b c - 300b c )cos(x) + 150b c + 300b c +--R + +--R 5 3 +--R 150b c +--R * +--R 3 +--R sin(x) +--R + +--R 4 4 6 2 3 +--R (150b c + 150b c )cos(x) +--R + +--R 2 6 4 4 6 2 2 +--R (- 450b c - 900b c - 450b c )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 6 +--R (450b c + 900b c + 450b c )cos(x) - 150c - 450b c +--R + +--R 4 4 6 2 +--R - 450b c - 150b c +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 7 4 +--R (75b c + 75b c)cos(x) +--R + +--R 3 5 5 3 7 3 +--R (- 300b c - 600b c - 300b c)cos(x) +--R + +--R 3 5 5 3 7 2 +--R (450b c + 900b c + 450b c)cos(x) +--R + +--R 7 3 5 5 3 7 7 +--R (- 300b c - 900b c - 900b c - 300b c)cos(x) + 75b c +--R + +--R 3 5 5 3 7 +--R 225b c + 225b c + 75b c +--R * +--R sin(x) +--R + +--R 6 2 8 5 4 4 6 2 8 4 +--R (15b c + 15b )cos(x) + (- 75b c - 150b c - 75b )cos(x) +--R + +--R 4 4 6 2 8 3 +--R (150b c + 300b c + 150b )cos(x) +--R + +--R 2 6 4 4 6 2 8 2 +--R (- 150b c - 450b c - 450b c - 150b )cos(x) +--R + +--R 2 6 4 4 6 2 8 8 2 6 +--R (75b c + 225b c + 225b c + 75b )cos(x) - 15c - 60b c +--R + +--R 4 4 6 2 8 +--R - 90b c - 60b c - 15b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 8 2 6 5 7 3 5 4 +--R (- 15c - 15b c )sin(x) + (- 75b c - 75b c )cos(x)sin(x) +--R + +--R 2 6 4 4 2 8 2 6 4 4 3 +--R ((- 150b c - 150b c )cos(x) - 150c - 300b c - 150b c )sin(x) +--R + +--R 3 5 5 3 3 +--R (- 150b c - 150b c )cos(x) +--R + +--R 7 3 5 5 3 +--R (- 450b c - 900b c - 450b c )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 6 2 4 +--R (- 75b c - 75b c )cos(x) +--R + +--R 2 6 4 4 6 2 2 8 2 6 4 4 +--R (- 450b c - 900b c - 450b c )cos(x) - 75c - 225b c - 225b c +--R + +--R 6 2 +--R - 75b c +--R * +--R sin(x) +--R + +--R 5 3 7 5 3 5 5 3 7 3 +--R (- 15b c - 15b c)cos(x) + (- 150b c - 300b c - 150b c)cos(x) +--R + +--R 7 3 5 5 3 7 +--R (- 75b c - 225b c - 225b c - 75b c)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 9 2 7 4 5 5 +--R (- 15c - 30b c - 15b c )sin(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 +--R ((- 75b c - 150b c - 75b c )cos(x) + 75b c + 150b c + 75b c ) +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 5 6 3 2 +--R (- 150b c - 300b c - 150b c )cos(x) +--R + +--R 2 7 4 5 6 3 9 2 7 4 5 +--R (300b c + 600b c + 300b c )cos(x) - 150c - 450b c - 450b c +--R + +--R 6 3 +--R - 150b c +--R * +--R 3 +--R sin(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 150b c - 300b c - 150b c )cos(x) +--R + +--R 3 6 5 4 7 2 2 +--R (450b c + 900b c + 450b c )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 +--R (- 450b c - 1350b c - 1350b c - 450b c )cos(x) + 150b c +--R + +--R 3 6 5 4 7 2 +--R 450b c + 450b c + 150b c +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 6 3 8 4 +--R (- 75b c - 150b c - 75b c)cos(x) +--R + +--R 4 5 6 3 8 3 +--R (300b c + 600b c + 300b c)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (- 450b c - 1350b c - 1350b c - 450b c)cos(x) +--R + +--R 2 7 4 5 6 3 8 9 2 7 +--R (300b c + 900b c + 900b c + 300b c)cos(x) - 75c - 300b c +--R + +--R 4 5 6 3 8 +--R - 450b c - 300b c - 75b c +--R * +--R sin(x) +--R + +--R 5 4 7 2 9 5 5 4 7 2 9 4 +--R (- 15b c - 30b c - 15b )cos(x) + (75b c + 150b c + 75b )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 +--R (- 150b c - 450b c - 450b c - 150b )cos(x) +--R + +--R 3 6 5 4 7 2 9 2 +--R (150b c + 450b c + 450b c + 150b )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 8 +--R (- 75b c - 300b c - 450b c - 300b c - 75b )cos(x) + 15b c +--R + +--R 3 6 5 4 7 2 9 +--R 60b c + 90b c + 60b c + 15b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 9 2 7 4 5 4 +--R (- 75c - 150b c - 75b c )sin(x) +--R + +--R 8 3 6 5 4 3 +--R (- 300b c - 600b c - 300b c )cos(x)sin(x) +--R + +--R 2 7 4 5 6 3 2 9 2 7 4 5 +--R (- 450b c - 900b c - 450b c )cos(x) - 150c - 450b c - 450b c +--R + +--R 6 3 +--R - 150b c +--R * +--R 2 +--R sin(x) +--R + +--R 3 6 5 4 7 2 3 +--R (- 300b c - 600b c - 300b c )cos(x) +--R + +--R 8 3 6 5 4 7 2 +--R (- 300b c - 900b c - 900b c - 300b c )cos(x) +--R * +--R sin(x) +--R + +--R 4 5 6 3 8 4 +--R (- 75b c - 150b c - 75b c)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 9 2 7 4 5 +--R (- 150b c - 450b c - 450b c - 150b c)cos(x) - 15c - 60b c - 90b c +--R + +--R 6 3 8 +--R - 60b c - 15b c +--R Type: Expression(Integer) +--E 308 + +--S 309 of 532 +--a0758:= integrate(t0758,x) +--E 309 + +--S 310 of 532 +--m0758:= a0758-r0758 +--E 310 + +--S 311 of 532 +--d0758:= D(m0758,x) +--E 311 + +--S 312 of 532 +t0759:= ((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^(1/2) +--R +--R +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R (285) \|\|c + b + c sin(x) + b cos(x) +--R Type: Expression(Integer) +--E 312 + +--S 313 of 532 +r0759:= -2*(c*cos(x)-b*sin(x))/((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^(1/2) +--R +--R +--R 2b sin(x) - 2c cos(x) +--R (286) ----------------------------------- +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R Type: Expression(Integer) +--E 313 + +--S 314 of 532 +a0759:= integrate(t0759,x) +--R +--R +--R (287) +--R 2b sin(x) - 2c cos(x) +--R / +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R Type: Union(Expression(Integer),...) +--E 314 + +--S 315 of 532 +m0759:= a0759-r0759 +--R +--R +--R (288) +--R (- 2b sin(x) + 2c cos(x)) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R + +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R (2b sin(x) - 2c cos(x))\|\|c + b + c sin(x) + b cos(x) +--R / +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 532 +d0759:= D(m0759,x) +--R +--R +--R (289) +--R 3 2 3 2 3 2 +--R (- 4c - 2b c)sin(x) + (- 12b c - 2b )cos(x)sin(x) +--R + +--R 2 2 3 2 3 3 +--R (- 14b c cos(x) - 4c - 2b c)sin(x) - 6b cos(x) +--R + +--R 2 3 +--R (- 4b c - 2b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 3 3 3 +--R (- 4b c - 2b c)cos(x)sin(x) +--R + +--R 4 2 2 4 2 4 2 2 4 2 +--R ((2c - 5b c - b )cos(x) - 8c - 8b c - b )sin(x) +--R + +--R 3 3 3 3 +--R (- 6b c cos(x) + (- 12b c - 10b c)cos(x))sin(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (c + b c - 2b )cos(x) + (- 2c - 9b c - 6b )cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R + +--R 3 2 3 2 3 2 +--R (4c + 2b c)sin(x) + (12b c + 2b )cos(x)sin(x) +--R + +--R 2 2 3 2 3 3 +--R (14b c cos(x) + 4c + 2b c)sin(x) + 6b cos(x) +--R + +--R 2 3 +--R (4b c + 2b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 2 2 4 3 3 3 +--R b c sin(x) + (2b c + 2b c)cos(x)sin(x) +--R + +--R 4 2 2 4 2 4 2 2 4 2 +--R ((- c + 6b c + b )cos(x) + 8c + 7b c + b )sin(x) +--R + +--R 3 3 3 3 3 +--R ((- 2b c + 6b c)cos(x) + (14b c + 10b c)cos(x))sin(x) +--R + +--R 2 2 4 4 4 2 2 4 2 +--R (- b c + 2b )cos(x) + (c + 9b c + 6b )cos(x) +--R * +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R / +--R 2 2 2 2 2 2 2 +--R (2c sin(x) + 6b c cos(x)sin(x) + (- c + 3b )cos(x) + 2c + b ) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 2 2 3 2 2 3 2 +--R 2b c cos(x)sin(x) + ((- c + 3b c)cos(x) + 4c + 3b c)sin(x) +--R + +--R 2 3 3 2 3 +--R (- b c + b )cos(x) + (4b c + 3b )cos(x) +--R * +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 532 +t0760:= ((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^(3/2) +--R +--R +--R (290) +--R +--------------------------------+ +--R +-------+ | +-------+ +--R | 2 2 | | 2 2 +--R (\|c + b + c sin(x) + b cos(x))\|\|c + b + c sin(x) + b cos(x) +--R Type: Expression(Integer) +--E 317 + +--S 318 of 532 +r0760:= -8/3*(b^2+c^2)^(1/2)*(c*cos(x)-b*sin(x))/((b^2+c^2)^(1/2)+_ + b*cos(x)+c*sin(x))^(1/2)-2/3*(c*cos(x)-b*sin(x))*((b^2+c^2)^(1/2)+_ + b*cos(x)+c*sin(x))^(1/2) +--R +--R +--R (291) +--R +-------+ +--R | 2 2 2 +--R (10b sin(x) - 10c cos(x))\|c + b + 2b c sin(x) +--R + +--R 2 2 2 +--R (- 2c + 2b )cos(x)sin(x) - 2b c cos(x) +--R / +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R 3\|\|c + b + c sin(x) + b cos(x) +--R Type: Expression(Integer) +--E 318 + +--S 319 of 532 +a0760:= integrate(t0760,x) +--R +--R +--R (292) +--R +-------+ +--R | 2 2 2 2 +--R (10b sin(x) - 10c cos(x))\|c + b + (- 2c + 2b )cos(x)sin(x) +--R + +--R 2 +--R - 4b c cos(x) + 2b c +--R / +--R 3 +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 532 +m0760:= a0760-r0760 +--R +--R +--R (293) +--R +-------+ +--R | 2 2 2 +--R (- 10b sin(x) + 10c cos(x))\|c + b - 2b c sin(x) +--R + +--R 2 2 2 +--R (2c - 2b )cos(x)sin(x) + 2b c cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R + +--R +-------+ +--R | 2 2 2 2 +--R (10b sin(x) - 10c cos(x))\|c + b + (- 2c + 2b )cos(x)sin(x) +--R + +--R 2 +--R - 4b c cos(x) + 2b c +--R * +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R / +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R 3\|\|c + b + c sin(x) + b cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 532 +d0760:= D(m0760,x) +--R +--R +--R (294) +--R 4 2 2 4 3 3 3 +--R (- 4c + 2b c )sin(x) + (- 44b c - 2b c)cos(x)sin(x) +--R + +--R 4 2 2 4 2 4 2 2 4 2 +--R ((14c - 77b c - b )cos(x) - 44c - 38b c - 3b )sin(x) +--R + +--R 3 3 3 3 3 +--R ((16b c - 62b c)cos(x) + (- 76b c - 58b c)cos(x))sin(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (3c + 11b c - 16b )cos(x) + (- 6c - 47b c - 32b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 4 3 2 4 +--R (- 4b c + 2b c )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 3 +--R ((2c - 19b c + 3b c)cos(x) - 28c - 30b c - 5b c)sin(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((10b c - 25b c + b )cos(x) + (- 96b c - 92b c - 5b )cos(x)) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 2 +--R (- c + 11b c - 12b c)cos(x) + (6c - 101b c - 98b c)cos(x) +--R + +--R 5 2 3 4 +--R - 20c - 30b c - 10b c +--R * +--R sin(x) +--R + +--R 4 3 2 5 5 4 3 2 5 3 +--R (- b c + 3b c - 2b )cos(x) + (6b c - 33b c - 36b )cos(x) +--R + +--R 4 3 2 5 +--R (- 20b c - 30b c - 10b )cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R + +--R 4 2 2 4 3 3 +--R (4c + b c )sin(x) + 36b c cos(x)sin(x) +--R + +--R 4 2 2 4 2 4 2 2 4 2 +--R ((- 9c + 82b c + b )cos(x) + 44c + 35b c + 3b )sin(x) +--R + +--R 3 3 3 3 3 +--R ((- 24b c + 60b c)cos(x) + (84b c + 60b c)cos(x))sin(x) +--R + +--R 4 2 2 4 4 4 2 2 4 2 +--R (2c - 9b c + 16b )cos(x) + (c + 45b c + 32b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 4 3 2 4 +--R (3b c - 3b c )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 3 +--R ((- c + 19b c - 4b c)cos(x) + 28c + 29b c + 4b c)sin(x) +--R + +--R 4 3 2 5 3 4 3 2 5 +--R ((- 10b c + 25b c - b )cos(x) + (98b c + 94b c + 5b )cos(x)) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 4 5 2 3 4 2 +--R (2c - 11b c + 11b c)cos(x) + (- 7c + 100b c + 98b c)cos(x) +--R + +--R 5 2 3 4 +--R 20c + 31b c + 11b c +--R * +--R sin(x) +--R + +--R 4 3 2 5 5 4 3 2 5 3 +--R (2b c - 2b c + 2b )cos(x) + (- 6b c + 33b c + 36b )cos(x) +--R + +--R 4 3 2 5 +--R (19b c + 29b c + 10b )cos(x) +--R * +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R / +--R 2 2 2 2 2 2 2 +--R (6c sin(x) + 18b c cos(x)sin(x) + (- 3c + 9b )cos(x) + 6c + 3b ) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 2 2 3 2 2 3 2 +--R 6b c cos(x)sin(x) + ((- 3c + 9b c)cos(x) + 12c + 9b c)sin(x) +--R + +--R 2 3 3 2 3 +--R (- 3b c + 3b )cos(x) + (12b c + 9b )cos(x) +--R * +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 532 +t0761:= ((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^(5/2) +--R +--R +--R (295) +--R +-------+ +--R | 2 2 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + c sin(x) + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 +--R b cos(x) + c + b +--R * +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R Type: Expression(Integer) +--E 322 + +--S 323 of 532 +r0761:= -64/15*(b^2+c^2)*(c*cos(x)-b*sin(x))/((b^2+c^2)^(1/2)+_ + b*cos(x)+c*sin(x))^(1/2)-16/15*(b^2+c^2)^(1/2)*(c*cos(x)-b*sin(x))*_ + ((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^(1/2)-_ + 2/5*(c*cos(x)-b*sin(x))*((b^2+c^2)^(1/2)+b*cos(x)+c*sin(x))^(3/2) +--R +--R +--R (296) +--R +-------+ +--R 2 2 2 2 | 2 2 +--R (28b c sin(x) + (- 28c + 28b )cos(x)sin(x) - 28b c cos(x) )\|c + b +--R + +--R 2 3 3 2 2 +--R 6b c sin(x) + (- 6c + 12b c)cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 3 +--R ((- 12b c + 6b )cos(x) + 86b c + 86b )sin(x) - 6b c cos(x) +--R + +--R 3 2 +--R (- 86c - 86b c)cos(x) +--R / +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R 15\|\|c + b + c sin(x) + b cos(x) +--R Type: Expression(Integer) +--E 323 + +--S 324 of 532 +a0761:= integrate(t0761,x) +--R +--R +--R (297) +--R +-------+ +--R 2 2 2 | 2 2 +--R ((- 28c + 28b )cos(x)sin(x) - 56b c cos(x) + 28b c)\|c + b +--R + +--R 2 3 2 2 3 3 2 3 +--R ((- 18b c + 6b )cos(x) + 92b c + 86b )sin(x) + (6c - 18b c)cos(x) +--R + +--R 3 2 +--R (- 92c - 74b c)cos(x) +--R / +--R 15 +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R Type: Union(Expression(Integer),...) +--E 324 + +--S 325 of 532 +m0761:= a0761-r0761 +--R +--R +--R (298) +--R 2 2 2 2 +--R (- 28b c sin(x) + (28c - 28b )cos(x)sin(x) + 28b c cos(x) ) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 2 3 3 2 2 +--R - 6b c sin(x) + (6c - 12b c)cos(x)sin(x) +--R + +--R 2 3 2 2 3 2 3 +--R ((12b c - 6b )cos(x) - 86b c - 86b )sin(x) + 6b c cos(x) +--R + +--R 3 2 +--R (86c + 86b c)cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R ((- 28c + 28b )cos(x)sin(x) - 56b c cos(x) + 28b c)\|c + b +--R + +--R 2 3 2 2 3 +--R ((- 18b c + 6b )cos(x) + 92b c + 86b )sin(x) +--R + +--R 3 2 3 3 2 +--R (6c - 18b c)cos(x) + (- 92c - 74b c)cos(x) +--R * +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R / +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R 15\|\|c + b + c sin(x) + b cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 532 +d0761:= D(m0761,x) +--R +--R +--R (299) +--R 5 2 3 5 4 3 2 4 +--R (- 12c + 18b c )sin(x) + (- 164b c + 106b c )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((52c - 596b c + 132b c)cos(x) - 296c - 240b c - 4b c) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 5 3 +--R (260b c - 716b c + 44b )cos(x) +--R + +--R 4 3 2 5 +--R (- 1104b c - 928b c - 4b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 4 +--R (- 26c + 286b c - 318b c)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (108c - 1108b c - 1036b c)cos(x) - 172c - 258b c - 86b c +--R * +--R sin(x) +--R + +--R 4 3 2 5 5 +--R (- 26b c + 78b c - 46b )cos(x) +--R + +--R 4 3 2 5 3 +--R (108b c - 300b c - 348b )cos(x) +--R + +--R 4 3 2 5 +--R (- 172b c - 258b c - 86b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 5 3 3 5 +--R (- 12b c + 18b c )cos(x)sin(x) +--R + +--R 6 2 4 4 2 2 6 2 4 4 2 4 +--R ((6c - 99b c + 45b c )cos(x) - 80c - 4b c + 61b c )sin(x) +--R + +--R 5 3 3 5 3 +--R (60b c - 204b c + 36b c)cos(x) +--R + +--R 5 3 3 5 +--R (- 688b c - 536b c + 92b c)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 4 2 6 4 +--R (- 9c + 117b c - 165b c + 9b )cos(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 +--R (184c - 1080b c - 1128b c + 46b )cos(x) - 400c - 716b c +--R + +--R 4 2 6 +--R - 331b c - 15b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (- 18b c + 78b c - 54b c)cos(x) +--R + +--R 5 3 3 5 3 +--R (308b c - 596b c - 844b c)cos(x) +--R + +--R 5 3 3 5 +--R (- 740b c - 1282b c - 542b c)cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 +--R (- 9b c + 15b c - 6b )cos(x) +--R + +--R 6 2 4 4 2 6 4 +--R (15c + 184b c - 34b c - 188b )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- 30c - 445b c - 701b c - 286b )cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R + +--R 4 3 2 4 +--R (114b c - 66b c )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((- 50c + 572b c - 122b c)cos(x) + 296c + 226b c + 2b c) +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 5 3 +--R (- 296b c + 764b c - 44b )cos(x) +--R + +--R 4 3 2 5 +--R (1156b c + 896b c + 4b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 4 4 +--R (40c - 328b c + 328b c)cos(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R (- 134c + 1154b c + 1024b c)cos(x) + 184c + 254b c + 88b c +--R * +--R sin(x) +--R + +--R 4 3 2 5 5 +--R (40b c - 70b c + 46b )cos(x) +--R + +--R 4 3 2 5 3 +--R (- 120b c + 300b c + 348b )cos(x) +--R + +--R 4 3 2 5 +--R (170b c + 250b c + 86b )cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 2 4 4 2 2 6 2 4 4 2 4 +--R ((63b c - 21b c )cos(x) + 56c + 46b c - 13b c )sin(x) +--R + +--R 5 3 3 5 3 +--R (- 60b c + 198b c - 30b c)cos(x) +--R + +--R 5 3 3 5 +--R (600b c + 444b c - 90b c)cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 4 2 6 4 +--R (15c - 147b c + 189b c - 9b )cos(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 +--R (- 174c + 1208b c + 1168b c - 46b )cos(x) + 424c + 674b c +--R + +--R 4 2 6 +--R 283b c + 15b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 5 +--R (30b c - 102b c + 60b c)cos(x) +--R + +--R 5 3 3 5 3 +--R (- 420b c + 546b c + 840b c)cos(x) +--R + +--R 5 3 3 5 +--R (840b c + 1356b c + 540b c)cos(x) +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 6 +--R (15b c - 15b c + 6b )cos(x) +--R + +--R 6 2 4 4 2 6 4 +--R (25c - 140b c + 50b c + 188b )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- 10c + 395b c + 685b c + 286b )cos(x) +--R * +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R / +--R 2 2 2 2 2 2 +--R 30c sin(x) + 90b c cos(x)sin(x) + (- 15c + 45b )cos(x) + 30c +--R + +--R 2 +--R 15b +--R * +--R +-------+ +--R | 2 2 +--R \|c + b +--R + +--R 2 2 3 2 2 3 2 +--R 30b c cos(x)sin(x) + ((- 15c + 45b c)cos(x) + 60c + 45b c)sin(x) +--R + +--R 2 3 3 2 3 +--R (- 15b c + 15b )cos(x) + (60b c + 45b )cos(x) +--R * +--R +--------------------------------+ +--R | +-------+ +--R | | 2 2 +--R \|\|c + b + c sin(x) + b cos(x) +--R * +--R ROOT +--R +-------+ +--R | 2 2 +--R (2c sin(x) + 2b cos(x))\|c + b + 2b c cos(x)sin(x) +--R + +--R 2 2 2 2 2 +--R (- c + b )cos(x) + 2c + b +--R , +--R 4 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 532 +t0762:= 1/(a+b*cos(x)+c*sin(x))^2 +--R +--R +--R (300) +--R 1 +--R --------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a +--R Type: Expression(Integer) +--E 327 + +--S 328 of 532 +r0762:= 2*a*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ + (a^2-b^2-c^2)^(3/2)+(c*cos(x)-b*sin(x))/(a^2-b^2-c^2)/_ + (a+b*cos(x)+c*sin(x)) +--R +--R +--R (301) +--R x +--R (b - a)tan(-) - c +--R 2 2 +--R (2a c sin(x) + 2a b cos(x) + 2a )atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (b sin(x) - c cos(x))\|- c - b + a +--R / +--R 3 2 2 2 3 2 2 2 3 +--R ((c + (b - a )c)sin(x) + (b c + b - a b)cos(x) + a c + a b - a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 532 +a0762:= integrate(t0762,x) +--R +--R +--R (302) +--R [ +--R 2 2 2 2 3 +--R ((a b - a )c sin(x) + (a b - a b)cos(x) + a b - a ) +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +------------+ +--R 2 2 | 2 2 2 +--R ((c + b - a b)sin(x) + a c cos(x) + a c)\|c + b - a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 2 2 2 2 3 +--R ((- 2a b + 2a )c sin(x) + (- 2a b + 2a b)cos(x) - 2a b + 2a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R +--------------+ +--R 2 2 | 2 2 2 +--R ((c + b - a b)sin(x) + a c cos(x) + a c)\|- c - b + a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 329 + +--S 330 of 532 +m0762a:= a0762.1-r0762 +--R +--R +--R (303) +--R +--------------+ +--R 2 | 2 2 2 +--R (a b - a )\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 | 2 2 2 2 +--R (- 2a b + 2a )\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R c\|- c - b + a \|c + b - a +--R / +--R +--------------+ +------------+ +--R 2 3 2 2 3 | 2 2 2 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 532 +d0762a:= D(m0762a,x) +--R +--R +--R (304) +--R 3 2 2 3 2 +--R (a b - 2a b + a b)sin(x) +--R + +--R 3 2 2 3 3 +--R ((a c + (- a b + 2a b - a )c)cos(x) + a c )sin(x) +--R + +--R 2 2 3 2 2 2 +--R ((2a b - a )c + a b - a b )cos(x) +--R + +--R 2 3 3 2 2 2 2 3 +--R (2a b c + a b - a b)cos(x) + a c + a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 2 2 +--R (- 2a c + (- 2a b + 2a b)c)sin(x) + (2a b - 2a )c sin(x) +--R + +--R 3 2 2 2 +--R (- 2a c + (- 2a b + 2a b)c)cos(x) +--R + +--R 3 2 3 +--R (- 2a c + (- 2a b + 2a )c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 3 2 +--R (- 2a b c - a b + a b)sin(x) +--R + +--R 3 2 2 3 3 2 2 +--R ((a c + (- a b + 2a b - a )c)cos(x) + a c + (2a b - 2a b)c)sin(x) +--R + +--R 2 2 3 2 2 2 3 2 2 3 2 2 +--R (- a c - a b + a b )cos(x) + (a b - 2a b + a b)cos(x) + a c +--R + +--R 2 2 3 +--R a b - a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 4 2 3 2 4 2 3 3 2 4 4 +--R (a c + (a b - a )c - a b + a b + a b - a b)cos(x) + a c +--R + +--R 2 3 2 4 2 3 3 2 4 +--R (a b - a )c - a b + a b + a b - a b +--R * +--R sin(x) +--R + +--R 2 3 3 2 2 3 4 2 +--R ((2a b - a )c + (2a b - a b - 2a b + a )c)cos(x) +--R + +--R 3 3 3 2 3 2 2 4 +--R (2a b c + (2a b - 2a b)c)cos(x) + a c + (a b - a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 2 2 +--R (- 2a c + (- 2a b + 2a )c )sin(x) +--R + +--R 2 3 3 2 2 3 4 +--R ((2a b - 2a )c + (2a b - 2a b - 2a b + 2a )c)sin(x) +--R + +--R 4 2 3 2 2 +--R (- 2a c + (- 2a b + 2a )c )cos(x) +--R + +--R 4 2 3 2 +--R (- 2a c + (- 2a b + 2a )c )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 +--R (- 2a b c + (- 2a b + 2a b)c)sin(x) +--R + +--R 4 2 3 2 4 2 3 3 2 4 4 +--R (a c + (a b - a )c - a b + a b + a b - a b)cos(x) + a c +--R + +--R 2 2 3 2 4 2 3 3 2 4 +--R (2a b - a b - a )c + a b - a b - a b + a b +--R * +--R sin(x) +--R + +--R 2 3 2 2 4 2 2 3 2 2 4 +--R (- a c + (- a b + a )c)cos(x) + a c + (a b - a )c +--R / +--R 2 2 4 4 3 3 4 2 2 +--R ((b - 2a b + a )c + (b - 2a b + 2a b - a )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 4a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 +--R (- b + a)c + (- 2b + 4a b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 +--R (- b + a b)c + (- b + 3a b - 2a b)c - a b + 2a b +--R + +--R 4 2 5 +--R - 2a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 5 +--R (- b + a )c + (- 2b + 2a b + 2a b - 2a )c - b + 2a b +--R + +--R 2 4 4 2 5 6 +--R - a b + a b - 2a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 4 2 5 2 4 4 2 +--R (- a b + a )c + (- 2a b + 3a b - a )c - a b + 2a b - 2a b +--R + +--R 5 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 2 3 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c )sin(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R (2c + (4a b - 4a )c + (- 2b + 4a b - 4a b + 2a )c )cos(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R 2c + (4b - 4a b)c + (2b - 4a b + 4a b - 2a )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 +--R 2b c + (2b + 2a b - 4a b)c +--R + +--R 4 2 3 3 2 4 +--R (2a b - 2a b - 2a b + 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 3 5 4 4 5 +--R ((2b + 2a)c + (4b - 4a )c + (2b - 2a b - 2a b + 2a )c)cos(x) +--R + +--R 5 2 2 3 3 4 2 3 3 2 4 +--R 2a c + (4a b - 2a b - 2a )c + (2a b - 2a b - 2a b + 2a b)c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((- b + a )c + (- b + 2a b - a )c )sin(x) +--R + +--R 5 2 3 3 +--R (b + a)c + (2a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + a b + 2a b - 2a b - a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 +--R (b + a)c + (2b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - a b - 2a b + 2a b + a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 2 2 3 2 5 3 3 5 +--R ((b + a b)c + (b + 2a b - a b - 2a b)c + a b - 2a b + a b) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 2 4 +--R (b + 2a b + a )c + (2b + 2a b - 2a b - 2a )c + b - a b +--R + +--R 4 2 6 +--R - a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 4 2 5 3 3 5 +--R (a b + a )c + (2a b + a b - 2a b - a )c + a b - 2a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 3 4 3 +--R (b - 2a b + a )c + (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (b - 2a b - a b + 4a b - a b - 2a b + a )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (- b + a)c + (- b + 3a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 6 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c + b - 2a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R - a b + 4a b - a b - 2a b + a b +--R * +--R cos(x) +--R + +--R 6 3 2 3 4 +--R (- b + a)c + (- 2b + 3a b - a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 2 5 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c + a b - 2a b +--R + +--R 3 4 4 3 5 2 6 7 +--R - a b + 4a b - a b - 2a b + a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b + a b)c + (- 2b + 2a b + 2a b - 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b + a b + 2a b - 2a b - a b + a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 +--R (- b + a )c + (- 2b + 4a b - 2a )c +--R + +--R 6 2 4 4 2 6 +--R (- b + 3a b - 3a b + a )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b + a )c + (- 2a b + 2a b + 2a b - 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- a b + a b + 2a b - 2a b - a b + a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (- 2b + 2a)c + (- 4b + 4a b + 4a b - 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 2b + 2a b + 4a b - 4a b - 2a b + 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R 2c + (2b + 2a b - 4a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 2b + 2a b + 4a b - 4a b - 2a b + 2a b)c +--R * +--R cos(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R 2c + (4b - 2a b - 2a )c + (2b - 4a b + 4a b - 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- 2a b + 2a b + 4a b - 4a b - 2a b + 2a )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 4 2 2 +--R (2b c + (4b - 4a b)c + (2b - 4a b + 2a b)c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (2b + 2a)c + (4b + 4a b - 4a b - 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2b + 2a b - 4a b - 4a b + 2a b + 2a )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 5 2 +--R 2a c + (4a b - 4a )c + (2a b - 4a b + 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 +--R (- b + a )c + (- 2b + 4a b - 2a )c +--R + +--R 6 2 4 4 2 6 +--R (- b + 3a b - 3a b + a )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 2 3 4 +--R (b + a)c + (b + 2a b - a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 2 5 4 3 +--R (- b + a b + 2a b - 2a b - a b + a )c - b + 3a b - 3a b +--R + +--R 6 +--R a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R (b + a)c + (2b + a b - 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 3 4 5 2 7 +--R (b - a b - 2a b + 2a b + a b - a )c - a b + 3a b - 3a b + a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b + a b)c + (2b + 2a b - 2a b - 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b + a b - 2a b - 2a b + a b + a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 3 4 3 +--R (b + 2a b + a )c + (2b + 4a b - 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (b + 2a b - a b - 4a b - a b + 2a b + a )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (a b + a )c + (2a b + 2a b - 2a b - 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (a b + a b - 2a b - 2a b + a b + a )c +--R Type: Expression(Integer) +--E 331 + +--S 332 of 532 +m0762b:= a0762.2-r0762 +--R +--R +--R (305) +--R +--------------+ +--R | 2 2 2 +--R 2 ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R (- 2a b + 2a )atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--------------+ +--R 2 2 | 2 2 2 +--R (- 2a b + 2a )atan(-----------------) + c\|- c - b + a +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 3 2 2 3 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 532 +d0762b:= D(m0762b,x) +--R +--R +--R (306) +--R 2 2 2 2 +--R (a b - a )sin(x) + (2a c cos(x) + 2a c)sin(x) + (3a b - a )cos(x) +--R + +--R 2 +--R 4a b cos(x) + a b + a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 x +--R (- 4a c sin(x) - 4a c cos(x) - 4a c cos(x))tan(-) +--R 2 +--R + +--R 2 2 2 2 +--R (- 3a b - a )sin(x) + (2a c cos(x) + 2a c)sin(x) + (- a b - a )cos(x) +--R + +--R 2 +--R a b + a +--R / +--R 2 2 2 4 3 3 4 2 +--R ((b - 2a b + a )c + b - 2a b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 +--R (- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )cos(x) +--R + +--R 2 2 2 4 2 2 4 2 2 2 4 +--R ((- 2b + 2a )c - 2b + 4a b - 2a )cos(x) + (- b + a )c - b +--R + +--R 2 2 4 +--R 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)sin(x) +--R + +--R 4 2 2 2 4 2 2 2 +--R ((4c + (4b - 4a )c )cos(x) + 4c + (4b - 4a )c )sin(x) +--R + +--R 3 3 2 2 3 2 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 3 +--R ((4b + 4a)c + (4b + 4a b - 4a b - 4a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 3 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 3 4 2 +--R ((b + 2a b + a )c + b + 2a b - 2a b - a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R ((2b + 4a b + 2a )c + 2b + 4a b - 4a b - 2a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R (b + 2a b + a )c + b + 2a b - 2a b - a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 532 +t0763:= 1/(a+b*cos(x)+c*sin(x))^3 +--R +--R +--R (307) +--R 1 +--R / +--R 3 3 2 2 2 +--R c sin(x) + (3b c cos(x) + 3a c )sin(x) +--R + +--R 2 2 2 3 3 2 2 +--R (3b c cos(x) + 6a b c cos(x) + 3a c)sin(x) + b cos(x) + 3a b cos(x) +--R + +--R 2 3 +--R 3a b cos(x) + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 532 +r0763:= (2*a^2+b^2+c^2)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ + (a^2-b^2-c^2)^(5/2)+1/2*(c*cos(x)-b*sin(x))/(a^2-b^2-c^2)/_ + (a+b*cos(x)+c*sin(x))^2+_ + 3/2*a*(c*cos(x)-b*sin(x))/(a^2-b^2-c^2)^2/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (308) +--R 4 2 2 2 2 +--R (- 2c + (- 2b - 4a )c )sin(x) +--R + +--R 3 3 2 3 2 3 +--R ((- 4b c + (- 4b - 8a b)c)cos(x) - 4a c + (- 4a b - 8a )c)sin(x) +--R + +--R 2 2 4 2 2 2 2 3 3 +--R (- 2b c - 2b - 4a b )cos(x) + (- 4a b c - 4a b - 8a b)cos(x) +--R + +--R 2 2 2 2 4 +--R - 2a c - 2a b - 4a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 2 2 2 2 3 2 +--R - 3a b c sin(x) + ((3a c - 3a b )cos(x) + b c + b - 4a b)sin(x) +--R + +--R 2 3 2 2 +--R 3a b c cos(x) + (- c + (- b + 4a )c)cos(x) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (4b - 4a )c + (2b - 4a b + 2a )c )sin(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (8b - 8a b)c + (4b - 8a b + 4a b)c)cos(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (8a b - 8a )c + (4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (4b - 4a b )c + 2b - 4a b + 2a b )cos(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (8a b - 8a b)c + 4a b - 8a b + 4a b)cos(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (4a b - 4a )c + 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 532 +a0763:= integrate(t0763,x) +--R +--R +--R (309) +--R [ +--R 3 2 2 3 +--R (2b - 4a b + 2a b)c +--R + +--R 5 4 2 3 3 2 4 +--R (2b - 4a b + 6a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 3 4 2 3 3 2 4 5 +--R (2a b - 4a b + 2a )c + (2a b - 4a b + 6a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 4 2 6 5 +--R (- b + 2a b - a )c + (- 2a b + 4a b - 2a )c + b - 2a b +--R + +--R 2 4 3 3 4 2 +--R 3a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 5 2 4 3 3 4 2 5 +--R ((2a b - 4a b + 2a b)c + 2a b - 4a b + 6a b - 8a b + 4a b) +--R * +--R cos(x) +--R + +--R 2 2 4 4 3 2 2 3 4 2 2 4 +--R (b - 2a b + a )c + (b - 2a b + 4a b - 6a b + 3a )c + a b +--R + +--R 3 3 4 2 5 6 +--R - 2a b + 3a b - 4a b + 2a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 4 3 2 2 3 2 4 2 3 +--R - 2b c + (- 2b - 3a b + 2a b + 3a )c - 3a b + 6a b +--R + +--R 3 2 +--R - 3a b +--R * +--R cos(x) +--R + +--R 4 3 2 2 3 2 5 4 2 3 +--R - 2a c + (b - 4a b - 5a b + 8a )c + b - 2a b - 3a b +--R + +--R 3 2 4 +--R 8a b - 4a b +--R * +--R sin(x) +--R + +--R 5 2 3 4 3 2 2 3 2 +--R (c + (3a b - 4a )c + (- b + 3a b - 8a b + 6a b)c)cos(x) +--R + +--R 2 2 3 4 2 2 4 5 +--R ((- b - a )c + (- b - 3a b + 4a )c)cos(x) - c +--R + +--R 2 2 3 3 2 2 3 4 +--R (- b - 3a b + 3a )c + (- 3a b + 5a b - 6a b + 4a )c +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 2 2 5 5 4 3 2 4 3 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 3 2 2 3 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 +--R (4b - 8a b + 12a b - 16a b + 8a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 3 4 2 3 3 2 4 5 +--R (4a b - 8a b + 4a )c + (4a b - 8a b + 12a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 4 2 6 5 +--R (- 2b + 4a b - 2a )c + (- 4a b + 8a b - 4a )c + 2b - 4a b +--R + +--R 2 4 3 3 4 2 +--R 6a b - 8a b + 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 5 2 4 3 3 4 2 +--R (4a b - 8a b + 4a b)c + 4a b - 8a b + 12a b - 16a b +--R + +--R 5 +--R 8a b +--R * +--R cos(x) +--R + +--R 2 2 4 4 3 2 2 3 4 2 +--R (2b - 4a b + 2a )c + (2b - 4a b + 8a b - 12a b + 6a )c +--R + +--R 2 4 3 3 4 2 5 6 +--R 2a b - 4a b + 6a b - 8a b + 4a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 4 3 2 2 3 2 4 2 3 +--R - 2b c + (- 2b - 3a b + 2a b + 3a )c - 3a b + 6a b +--R + +--R 3 2 +--R - 3a b +--R * +--R cos(x) +--R + +--R 4 3 2 2 3 2 5 4 2 3 +--R - 2a c + (b - 4a b - 5a b + 8a )c + b - 2a b - 3a b +--R + +--R 3 2 4 +--R 8a b - 4a b +--R * +--R sin(x) +--R + +--R 5 2 3 4 3 2 2 3 2 +--R (c + (3a b - 4a )c + (- b + 3a b - 8a b + 6a b)c)cos(x) +--R + +--R 2 2 3 4 2 2 4 5 +--R ((- b - a )c + (- b - 3a b + 4a )c)cos(x) - c +--R + +--R 2 2 3 3 2 2 3 4 +--R (- b - 3a b + 3a )c + (- 3a b + 5a b - 6a b + 4a )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 5 5 4 3 2 4 3 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 336 + +--S 337 of 532 +m0763a:= a0763.1-r0763 +--R +--R +--R (310) +--R 3 2 2 5 +--R (2b - 4a b + 2a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (2b - 4a b + 6a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 3 2 4 5 3 +--R (2a b - 4a b + 2a )c + (2a b - 4a b + 6a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- b + 2a b - a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (5b - 10a b + 15a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (10a b - 20a b + 10a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (10a b - 20a b + 30a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (b - 2a b + a )c + (b - 2a b + 8a b - 14a b + 7a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (5a b - 10a b + 15a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 2b + 4a b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (2b - 4a b - 2a b + 8a b - 4a b)c +--R + +--R 7 6 2 5 3 4 4 3 +--R (4b - 8a b + 12a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 2a b + 4a b - 2a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (10a b - 20a b + 6a b + 8a b - 4a )c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (12a b - 24a b + 36a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 5 +--R (2b - 4a b + 2a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (2b - 4a b + 18a b - 32a b + 16a b)c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (12a b - 24a b + 36a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 3 2 4 5 3 +--R (2a b - 4a b + 2a )c + (2a b - 4a b + 10a b - 16a b + 8a )c +--R + +--R 3 4 4 3 5 2 6 7 +--R (4a b - 8a b + 12a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 2 4 3 3 4 2 2 8 +--R (- b + 2a b - a b )c + (- 2a b + 4a b - 2a b )c + b +--R + +--R 7 2 6 3 5 4 4 +--R - 2a b + 3a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 2a b + 4a b - 2a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 7 2 6 3 5 +--R (2a b - 4a b - 2a b + 8a b - 4a b)c + 4a b - 8a b + 12a b +--R + +--R 4 4 5 3 +--R - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 4 +--R (b - 2a b + 2a b - a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 2 6 +--R (b - 2a b + 8a b - 14a b + 5a b + 4a b - 2a )c + 6a b +--R + +--R 3 5 4 4 5 3 6 2 +--R - 12a b + 18a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (2a b - 4a b + 2a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 3 5 4 4 +--R (2a b - 4a b + 10a b - 16a b + 8a b)c + 4a b - 8a b +--R + +--R 5 3 6 2 7 +--R 12a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 2 4 3 3 4 2 5 6 2 4 4 +--R (a b - 2a b + a )c + (a b - 2a b + 4a b - 6a b + 3a )c + a b +--R + +--R 5 3 6 2 7 8 +--R - 2a b + 3a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 3 2 2 5 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b - 8a b + 12a b - 16a b + 8a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 3 2 4 5 3 +--R (4a b - 8a b + 4a )c + (4a b - 8a b + 12a b - 16a b + 8a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 +--R (- 2b + 4a b - 2a )c +--R + +--R 4 3 2 2 3 4 4 +--R (8b - 16a b + 4a b + 8a b - 4a )c +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (10b - 20a b + 30a b - 40a b + 20a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (20a b - 40a b + 60a b - 80a b + 40a b)c +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 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2a b )c + (- 4a b + 8a b - 4a b )c + 2b +--R + +--R 7 2 6 3 5 4 4 +--R - 4a b + 6a b - 8a b + 4a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4a b + 8a b - 4a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 7 2 6 +--R (4a b - 8a b - 4a b + 16a b - 8a b)c + 8a b - 16a b +--R + +--R 3 5 4 4 5 3 +--R 24a b - 32a b + 16a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 4 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 2 6 +--R (2b - 4a b + 16a b - 28a b + 10a b + 8a b - 4a )c + 12a b +--R + +--R 3 5 4 4 5 3 6 2 +--R - 24a b + 36a b - 48a b + 24a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4a b - 8a b + 4a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 3 5 4 4 +--R (4a b - 8a b + 20a b - 32a b + 16a b)c + 8a b - 16a b +--R + +--R 5 3 6 2 7 +--R 24a b - 32a b + 16a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 2 4 3 3 4 2 5 6 2 +--R (2a b - 4a b + 2a )c + (2a b - 4a b + 8a b - 12a b + 6a )c +--R + +--R 4 4 5 3 6 2 7 8 +--R 2a b - 4a b + 6a b - 8a b + 4a +--R * +--R x +--R +------------+ (b - a)tan(-) - c +--R | 2 2 2 2 +--R \|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 6 3 2 2 3 4 +--R - 2b c + (- 2b - 3a b + 2a b + 3a )c +--R + +--R 4 2 3 3 2 2 +--R (3a b - 6a b + 3a b )c +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R - 2a c + (b - 4a b - 5a b + 8a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (b - 2a b + 3a b - 4a b + 2a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 2 5 +--R c + (- 4b + 3a b - 4a )c +--R + +--R 4 3 2 2 3 3 5 2 4 3 3 +--R (- 5b - 12a b + 14a b + 3a b)c + (3a b - 6a b + 3a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 +--R (- b - 8a b - a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- b - 8a b - 27a b + 32a b + 4a )c +--R + +--R 2 4 3 3 4 2 +--R (6a b - 12a b + 6a b )c +--R * +--R cos(x) +--R + +--R 7 2 2 5 2 2 3 4 3 +--R - c + (- b - 3a b - a )c + (- 5a b - 15a b + 20a )c +--R + +--R 3 3 4 2 5 +--R (3a b - 6a b + 3a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 2 3 4 +--R 2b c + (- 2b + 9a b - 14a b + 3a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 4b - 9a b + 10a b + 3a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R 2a c + (b - 12a b + 7a b - 8a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (b - 14a b - 33a b + 44a b + 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R - 2b c + (- 2b - 9a b + 2a b - 3a )c +--R + +--R 4 2 3 3 2 4 2 +--R (- 3a b - 6a b - 39a b + 48a b)c +--R * +--R cos(x) +--R + +--R 6 3 2 3 4 +--R - 2a c + (- b - 7a b + 4a )c +--R + +--R 5 4 2 3 4 5 2 +--R (- b + 2a b - 3a b - 14a b + 16a )c +--R * +--R sin(x) +--R + +--R 2 5 3 2 2 3 3 6 2 4 3 3 4 +--R (b c + (6a b - 10a b + 3a b)c + (- b - 2a b + 3a b )c)cos(x) +--R + +--R 2 2 5 4 2 2 3 4 3 +--R (- b + 4a b - a )c + (- b + 9a b - 16a b + 4a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- 4a b - 6a b + 4a b + 6a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 4 3 2 2 4 3 +--R (- b + a )c + (- b - 6a b + 5a b - 4a )c +--R + +--R 5 3 3 4 2 5 +--R (- 3a b - 18a b + 18a b + 3a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b - 4a b + a )c + (b - 4a b - 9a b + 12a b - 4a )c +--R + +--R 2 4 3 3 4 2 5 +--R (- 6a b + 8a b - 18a b + 16a b)c +--R * +--R cos(x) +--R + +--R 2 5 2 2 3 4 3 3 3 4 2 5 6 +--R - a c + (- a b - 3a b + 3a )c + (- 3a b + 5a b - 6a b + 4a )c +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 532 +d0763a:= D(m0763a,x) +--R +--R +--R (311) +--R 4 3 2 2 3 4 7 +--R (2b - 4a b - 4a b + 12a b - 6a )c +--R + +--R 6 5 3 3 4 2 5 +--R (2b - 4a b + 4a b - 2a b )c +--R * +--R 7 +--R sin(x) +--R + +--R 2 2 3 8 +--R (- 3a b + 6a b - 3a )c +--R + +--R 5 4 2 3 3 2 6 +--R (- 4b + 14a b - 16a b + 6a b )c +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 4b + 17a b - 30a b + 25a b - 8a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 8 +--R (- 4b + 6a b + 4a b - 6a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (4b - 20a b + 18a b + 14a b - 22a b + 6a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (8b - 26a b + 38a b - 44a b + 38a b - 14a b )c +--R * +--R cos(x) +--R + +--R 3 2 2 3 8 +--R (- 2b + a b + 8a b - 7a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 4b + 13a b - 12a b - 16a b + 36a b - 17a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 4 +--R (- 2b + 12a b - 20a b + 13a b - 12a b + 17a b - 8a b)c +--R * +--R 6 +--R sin(x) +--R + +--R 2 2 9 +--R (- 4b + 3a b - 3a )c +--R + +--R 4 3 2 2 3 4 7 +--R (4b - 43a b + 51a b - 27a b + 3a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 4b - 7a b + 27a b - 26a b + 10a b )c +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (- 12b + 39a b - 75a b + 81a b - 33a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 9 +--R (- b - 9a b - 2a )c +--R + +--R 4 3 2 2 3 4 7 +--R (- 20b + 29a b - 61a b + 41a b - 25a )c +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (- 15b - 23a b + 48a b + 40a b - 84a b + 34a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 3 +--R (4b - 61a b + 151a b - 217a b + 205a b - 82a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 9 +--R (2b - 9a b - 5a )c +--R + +--R 4 3 2 2 3 4 7 +--R (- 8b - 16a b + 38a b - 30a b - 20a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 18b + 17a b - 43a b + 55a b + 39a b - 75a b +--R + +--R 6 +--R 25a +--R * +--R 5 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 8b + 24a b - 78a b + 153a b - 201a b + 183a b +--R + +--R 6 2 +--R - 73a b +--R * +--R 3 +--R c +--R * +--R cos(x) +--R + +--R 2 2 9 4 3 2 2 3 4 7 +--R (b - a b - 4a )c + (b - 12a b + 12a b + 10a b - 23a )c +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 19a b + 34a b - 23a b - 4a b + 27a b - 15a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 8a b + 20a b - 29a b + 41a b - 59a b + 59a b +--R + +--R 7 +--R - 24a b +--R * +--R 3 +--R c +--R * +--R 5 +--R sin(x) +--R + +--R 10 3 2 2 8 +--R 4b c + (- 21b + 35a b - 18a b)c +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 7b - 38a b + 18a b - 32a b + 11a b)c +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (5b - 41a b + 90a b - 104a b + 50a b )c +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (- 13b + 32a b - 66a b + 88a b - 41a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (3b + 5a)c + (2b - 58a b + 38a b - 22a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 5b - 2a b - 232a b + 116a b - 86a b + 17a )c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 4b - 10a b - 104a b + 274a b - 284a b +--R + +--R 5 2 +--R 128a b +--R * +--R 4 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 2 +--R (- 71a b + 166a b - 264a b + 314a b - 145a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 5b + 5a)c + (11b - 55a b - 45a b - 7a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (13b - 86a b + 73a b - 325a b + 77a b - 40a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 7b - 18a b - 53a b - 14a b + 249a b - 274a b +--R + +--R 6 +--R 117a b +--R * +--R 4 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 4b + 8a b - 131a b + 290a b - 392a b + 422a b +--R + +--R 6 3 +--R - 193a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 5b - 3a)c + (- 5b + 11a b - 79a b - 15a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 8b + 13a b - 63a b + 29a b - 142a b - 21a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 8b - 9a b + 6a b - 77a b + 84a b + 63a b +--R + +--R 6 7 +--R - 98a b + 39a +--R * +--R 4 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 8a b + 16a b - 101a b + 210a b - 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4b - 94a b + 76a b - 202a b + 304a b - 228a b +--R + +--R 7 +--R 148a b +--R * +--R 3 +--R c +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R (- 96a b + 192a b - 240a b + 288a b - 144a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 11 2 9 +--R - c + (- 36a b - 9a )c +--R + +--R 4 3 2 2 3 4 7 +--R (7b - 28a b - 31a b - 190a b - 9a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 14b - 16a b - 10a b - 126a b + 18a b - 244a b +--R + +--R 6 +--R - 11a +--R * +--R 5 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 8b - 24a b + 20a b - 84a b + 43a b - 38a b +--R + +--R 6 2 7 8 +--R 91a b - 46a b + 30a +--R * +--R 3 +--R c +--R + +--R 4 6 5 5 6 4 7 3 8 2 +--R (- 54a b + 108a b - 120a b + 132a b - 66a b )c +--R * +--R cos(x) +--R + +--R 11 2 2 9 +--R - c + (- 2b - 15a )c +--R + +--R 4 3 2 2 3 4 7 +--R (- 3b + 8a b - 15a b - 22a b - 35a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 2b + 16a b - 24a b - 14a b + 20a b - 32a b - 39a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 3 +--R (8a b - 20a b + 8a b - 11a b + 2a b + 7a b + 6a b)c +--R + +--R 5 5 6 4 7 3 8 2 9 +--R (- 12a b + 24a b - 24a b + 24a b - 12a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 10 3 2 2 3 8 +--R (- 4b + a)c + (25b + 9a b - 30a b + 5a )c +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 2b - 4a b + 105a b - 86a b + 22a b)c +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 36b - 9a b - 3a b - 3a b - 6a b )c +--R + +--R 9 8 2 7 3 6 4 5 2 11 +--R (- 6b + 5a b - 21a b + 12a b + 10a b )c - b +--R + +--R 10 2 9 3 8 4 7 +--R 2a b - 3a b + 4a b - 2a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 3b - 3a)c + (44b + 52a b - 27a b - 15a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (16b - 50a b + 21a b + 229a b - 132a b + 18a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (- 44b - 130a b - 79a b - 85a b + 10a b - 14a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 2 +--R (- 13b - 31a b + 21a b - 59a b + 10a b + 72a b )c +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 6a b + 12a b - 18a b + 24a b - 12a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (9b - 6a)c + (- 10b + 58a b + 84a b - 33a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 14b - 54a b - 233a b + 274a b + 63a b - 51a )c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2b - 175a b - 229a b - 253a b - 221a b +--R + +--R 5 2 6 +--R 19a b + 6a b +--R * +--R 4 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 7b - 57a b - 7a b - 76a b + 15a b - 32a b +--R + +--R 6 3 +--R 164a b +--R * +--R 2 +--R c +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R - 15a b + 30a b - 45a b + 60a b - 30a b +--R * +--R 4 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (6b + 6a)c + (- 48b - 38a b + 98a b + 24a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 56b - 74a b - 124a b - 374a b + 290a b - 42a )c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 2b - 30a b - 260a b - 204a b - 516a b +--R + +--R 5 2 6 7 +--R - 172a b + 32a b + 12a +--R * +--R 4 +--R c +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 154a b + 134a b - 302a b + 202a b - 44a b +--R + +--R 7 2 +--R 164a b +--R * +--R 2 +--R c +--R + +--R 3 8 4 7 5 6 6 5 7 4 +--R - 20a b + 40a b - 60a b + 80a b - 40a b +--R * +--R 3 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 6b + 9a)c + (- 23b - 61a b - 50a b + 53a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 30b - 55a b - 81a b - 298a b - 160a b + 69a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 9b + 7a b - 9a b - 301a b - 59a b - 462a b +--R + +--R 6 7 +--R - 44a b + 22a +--R * +--R 4 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 4b - 8a b + 34a b - 226a b + 224a b - 339a b +--R + +--R 6 3 7 2 8 +--R 249a b - 12a b + 74a b +--R * +--R 2 +--R c +--R + +--R 4 7 5 6 6 5 7 4 8 3 +--R - 15a b + 30a b - 45a b + 60a b - 30a b +--R * +--R 2 +--R cos(x) +--R + +--R 10 2 2 3 8 +--R (- 3b - 3a)c + (- 18a b - 67a b - 5a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (3b - 19a b - 63a b - 25a b - 227a b + a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 4a b - 24a b + 20a b - 170a b + 12a b - 179a b +--R + +--R 7 +--R - 5a +--R * +--R 4 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 8a b - 16a b + 40a b - 153a b + 137a b - 151a b +--R + +--R 7 2 8 9 +--R 121a b + 2a b + 12a +--R * +--R 2 +--R c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R - 6a b + 12a b - 18a b + 24a b - 12a b +--R * +--R cos(x) +--R + +--R 10 3 2 3 8 +--R (b - 4a)c + (4b - 10a b - 21a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (5b - 10a b + 3a b - 20a b - 14a b - 37a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 2b - 4a b + 7a b - 17a b + 5a b - 22a b + 6a b +--R + +--R 7 +--R - 34a +--R * +--R 4 +--R c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 2 +--R (4a b - 8a b + 13a b - 37a b + 29a b - 22a b + 21a b)c +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - a b + 2a b - 3a b + 4a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 9 +--R (- 5b - a b + 3a )c +--R + +--R 4 3 2 2 3 4 7 +--R (12b + 21a b - 42a b + 13a b - 3a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (10b + 9a b + 48a b - 70a b + 26a b )c +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (- 12b - 9a b + 30a b - 47a b + 17a b )c +--R + +--R 10 9 2 8 3 7 4 6 +--R (- 5b + 4a b - 15a b + 20a b - 4a b )c +--R * +--R 7 +--R cos(x) +--R + +--R 2 2 9 +--R (- 17b + 5a b + 3a )c +--R + +--R 4 3 2 2 3 4 7 +--R (6b + 65a b + 34a b - 91a b + 9a )c +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (19b + 33a b + 7a b + 168a b - 188a b + 62a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 3 +--R (- 10b - 57a b - 76a b + 83a b - 133a b + 46a b )c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R (- 6b - 30a b + 24a b - 72a b + 96a b - 12a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 9 4 3 2 2 3 4 7 +--R - 3a b c + (- 22b + 62a b + 146a b - 72a b - 33a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 24b + 39a b - 19a b + 59a b + 176a b - 141a b +--R + +--R 6 +--R 33a +--R * +--R 5 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 2b - 62a b - 182a b - 129a b + 8a b - 115a b +--R + +--R 6 2 +--R 41a b +--R * +--R 3 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R (- 36a b - 57a b + 24a b - 117a b + 192a b - 6a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 2 2 9 +--R (26b - 9a b - 2a )c +--R + +--R 4 3 2 2 3 4 7 +--R (6b - 66a b + 62a b + 152a b - 59a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 29b - 89a b - 22a b - 203a b + 264a b + 13a b +--R + +--R 6 +--R - 29a +--R * +--R 5 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 9b - 26a b - 114a b - 351a b - 75a b - 165a b +--R + +--R 6 2 7 +--R - 7a b + 12a b +--R * +--R 3 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 6a b - 102a b - 16a b - 76a b - 36a b + 208a b +--R + +--R 7 3 +--R 16a b +--R * +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 9 +--R (7b + 9a b - a )c +--R + +--R 4 3 2 2 3 4 7 +--R (14b - 77a b - 100a b + 123a b + 35a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 3b - 113a b - 160a b - 56a b - 265a b + 230a b +--R + +--R 6 +--R - 34a +--R * +--R 5 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 4b - 27a b - 45a b - 127a b - 333a b - 60a b +--R + +--R 6 2 7 +--R - 173a b + 34a b +--R * +--R 3 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R 24a b - 168a b + 81a b - 204a b + 111a b +--R + +--R 7 3 8 2 +--R 132a b + 24a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 9 +--R (- 9b + 3a b + 3a )c +--R + +--R 4 3 2 2 3 4 7 +--R (- 12b - a b - 88a b - 61a b + 63a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 3b - 11a b - 116a b - 106a b - 134a b - 98a b +--R + +--R 6 +--R 51a +--R * +--R 5 +--R c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 7a b - 37a b - 9a b - 137a b - 110a b - 99a b +--R + +--R 7 8 +--R - 54a b + 12a +--R * +--R 3 +--R c +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R 36a b - 162a b + 114a b - 192a b + 144a b +--R + +--R 8 2 9 +--R 48a b + 12a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 9 +--R (- 2b - 5a b - 2a )c +--R + +--R 4 3 2 2 3 4 7 +--R (- 4b - 6a b - 4a b - 64a b + a )c +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (- 2b - a b - 4a b - 73a b - 12a b - 107a b)c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 2a b - 29a b + 23a b - 99a b + 27a b - 66a b +--R + +--R 8 +--R - a +--R * +--R 3 +--R c +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 10 +--R (24a b - 84a b + 61a b - 80a b + 69a b + 8a b + 2a )c +--R * +--R cos(x) +--R + +--R 2 9 3 2 2 4 7 +--R (a b - 4a )c + (2a b - 8a b - 13a )c +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (a b - 4a b + a b - 17a b + 5a b - 23a )c +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (a b - 10a b + 11a b - 27a b + 18a b - 14a )c +--R + +--R 5 5 6 4 7 3 8 2 9 +--R (6a b - 18a b + 12a b - 12a b + 12a b)c +--R * +--R sin(x) +--R + +--R 3 2 2 8 +--R (- 2b - 2a b + 3a b)c +--R + +--R 5 4 2 3 3 2 4 6 +--R (b + 6a b - 13a b + 8a b - 3a b)c +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (3b + 7a b + 3a b - 14a b + 6a b )c +--R + +--R 9 2 7 3 6 4 5 2 11 10 2 9 3 8 +--R (- b + 9a b - 20a b + 9a b )c - b + a b - 2a b + 2a b +--R * +--R 8 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (2b - 2a)c + (- 3b - 4a b - 4a b + 7a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 3b + 16a b + 19a b - 41a b + 14a b - 5a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (2b + 22a b + 21a b + 17a b - 58a b + 24a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 2 11 +--R (- b - 2a b - 13a b + 37a b - 82a b + 37a b )c - b +--R + +--R 10 2 9 3 8 4 7 +--R - 6a b + 5a b - 12a b + 14a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (2b - 2a)c + (5b - 11a b - 4a b + 6a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 3b + a b + 60a b - 3a b - 41a b + 2a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 9b + 11a b + 56a b + 14a b + 33a b - 80a b +--R + +--R 6 +--R 31a b +--R * +--R 4 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 3b - 6a b - 14a b - 36a b + 42a b - 124a b +--R + +--R 6 3 +--R 57a b +--R * +--R 2 +--R c +--R + +--R 10 2 9 3 8 4 7 5 6 +--R - 7a b - 14a b + 7a b - 28a b + 42a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 4b + 4a)c + (2b + 5a b + 7a b - 10a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (5b - 23a b + 26a b + 92a b - 53a b - 7a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 3b - 43a b + 13a b + 48a b + 23a b + 17a b +--R + +--R 6 7 +--R - 40a b + 13a +--R * +--R 4 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 2b - 19a b - 9a b - 64a b - 11a b - 24a b +--R + +--R 6 3 7 2 +--R - 78a b + 39a b +--R * +--R 2 +--R c +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R - 21a b - 14a b - 7a b - 28a b + 70a b +--R * +--R 5 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 4b + 4a)c + (- 8b + 24a b + 3a b - 9a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 2b + 7a b - 47a b + 30a b + 63a b - 21a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 3b - 25a b - 94a b + 14a b - 19a b + 70a b - 15a b +--R + +--R 7 +--R - 4a +--R * +--R 4 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R b - 12a b - 46a b + 4a b - 116a b + 48a b - 89a b +--R + +--R 7 2 8 +--R - 10a b + 10a b +--R * +--R 2 +--R c +--R + +--R 3 8 5 6 7 4 +--R - 35a b - 35a b + 70a b +--R * +--R 4 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (2b - 2a)c + (b - 2a b + 2a b + 3a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 2b + 5a b - 35a b - 51a b + 55a b + 12a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - b + 8a b - 59a b - 106a b + 27a b - 52a b + 56a b +--R + +--R 7 +--R - 13a +--R * +--R 4 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 3a b - 26a b - 52a b + 15a b - 90a b + 43a b +--R + +--R 7 2 8 +--R - 69a b + 8a b +--R * +--R 2 +--R c +--R + +--R 4 7 5 6 6 5 7 4 8 3 +--R - 35a b + 14a b - 49a b + 28a b + 42a b +--R * +--R 3 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (2b - 2a)c + (5b - 11a b - 2a b + 4a )c +--R + +--R 5 4 3 2 4 5 6 +--R (4b - 14a b - 33a b - 20a b + 23a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R b - 5a b + 5a b - 53a b - 51a b + 4a b - 22a b +--R + +--R 7 +--R 9a +--R * +--R 4 +--R c +--R + +--R 2 7 3 6 4 5 6 3 7 2 8 9 2 +--R (3a b - 26a b - 25a b - 18a b - 2a b - 18a b + 2a )c +--R + +--R 5 6 6 5 7 4 8 3 9 2 +--R - 21a b + 14a b - 35a b + 28a b + 14a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 8 4 2 3 4 6 +--R (a b - 5a b)c + (2a b - 10a b - 16a b)c +--R + +--R 6 2 5 3 4 4 3 5 2 6 4 +--R (a b - 5a b + a b - 22a b - a b - 18a b)c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 2 6 5 +--R (a b - 12a b - a b - 13a b + 12a b - 11a b)c - 7a b +--R + +--R 7 4 8 3 9 2 10 +--R 6a b - 13a b + 12a b + 2a b +--R * +--R cos(x) +--R + +--R 3 8 3 2 4 5 6 +--R - a c + (- 2a b + a b - 4a )c +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- a b + a b - 6a b + 4a b - 5a )c +--R + +--R 5 4 6 3 7 2 8 9 2 7 4 8 3 9 2 +--R (- 2a b + 2a b - 6a b + 5a b - 2a )c - a b + a b - 2a b +--R + +--R 10 +--R 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 8 +--R (- 4b + 4a b + 12a b - 12a )c +--R + +--R 5 4 2 3 3 2 6 +--R (- 4b + 4a b + 4a b - 4a b )c +--R * +--R 7 +--R sin(x) +--R + +--R 2 2 9 4 3 2 2 7 +--R (8b + 6a b - 6a )c + (16b - 20a b + 28a b )c +--R + +--R 6 5 2 4 3 3 5 +--R (8b - 26a b + 34a b - 16a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 9 +--R (8b + 12a b - 12a )c +--R + +--R 4 3 2 2 4 7 +--R (- 8b + 48a b - 4a b + 12a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 16b + 36a b - 40a b + 48a b - 28a b )c +--R * +--R cos(x) +--R + +--R 2 2 9 +--R (4b + 2a b - 6a )c +--R + +--R 4 3 2 2 3 4 7 +--R (8b - 18a b + 14a b + 38a b - 18a )c +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (4b - 20a b + 20a b - 6a b + 18a b - 16a b)c +--R * +--R 6 +--R sin(x) +--R + +--R 10 3 2 2 3 8 +--R (- 8b - 6a)c + (8b + 62a b - 64a b + 6a )c +--R + +--R 5 4 2 3 3 2 6 +--R (40b + 14a b + 32a b + 4a b )c +--R + +--R 7 6 2 5 3 4 4 +--R (24b - 54a b + 96a b - 66a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 6b - 12a)c + (24b + 46a b + 48a b - 66a )c +--R + +--R 5 4 2 3 3 2 4 6 +--R (22b + 172a b - 52a b + 92a b + 36a b)c +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 8b + 114a b - 188a b + 246a b - 164a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (4b - 2a)c + (24b + 16a b + 60a b - 32a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (36b - 14a b + 184a b - 62a b + 92a b + 34a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (16b - 32a b + 124a b - 182a b + 220a b - 146a b )c +--R * +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 2b + 8a)c + (- 2b + 30a b - 18a b + 18a )c +--R + +--R 4 2 3 3 2 4 5 6 +--R (38a b - 38a b + 48a b + 8a b + 34a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 4 +--R (16a b - 24a b + 34a b - 48a b + 70a b - 48a b)c +--R * +--R 5 +--R sin(x) +--R + +--R 11 2 2 9 +--R 2c + (- 8b - 44a b + 4a )c +--R + +--R 4 3 2 2 3 7 +--R (4b + 34a b - 98a b + 38a b)c +--R + +--R 6 5 2 4 3 3 5 +--R (40b + 40a b - 8a b + 36a b )c +--R + +--R 8 7 2 6 3 5 3 +--R (26b - 38a b + 94a b - 82a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 11 2 2 9 +--R 2c + (- 20b - 56a b - 52a )c +--R + +--R 4 3 2 2 3 4 7 +--R (- 46b + 30a b + 214a b - 250a b + 50a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- 24b + 228a b + 76a b + 88a b + 64a b )c +--R + +--R 7 2 6 3 5 4 4 3 +--R (142a b - 190a b + 338a b - 290a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 11 2 2 9 +--R - 2c + (- 6b - 8a b - 66a )c +--R + +--R 4 3 2 2 3 4 7 +--R (2b - 46a b + 136a b + 170a b - 136a )c +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (14b - 46a b + 456a b - 104a b + 286a b + 42a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 3 +--R (8b - 8a b + 254a b - 326a b + 458a b - 386a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 11 2 2 9 +--R 2c + (- 6b + 28a b + 10a )c +--R + +--R 4 3 2 2 3 4 7 +--R (8b + 46a b - 100a b + 242a b - 26a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 16b + 34a b - 74a b + 376a b - 216a b + 282a b +--R + +--R 6 +--R 14a +--R * +--R 5 +--R c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 3 +--R (16a b - 16a b + 186a b - 234a b + 278a b - 230a b )c +--R * +--R cos(x) +--R + +--R 11 2 2 9 +--R 4c + (8b - 16a b + 40a )c +--R + +--R 4 2 2 3 4 7 +--R (4b + 52a b - 96a b + 104a )c +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (16a b + 20a b - 52a b + 108a b - 76a b + 92a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 3 +--R (8a b - 8a b + 48a b - 60a b + 64a b - 52a b)c +--R * +--R 4 +--R sin(x) +--R + +--R 10 2 2 8 +--R - 4b c + (4a b - 44a b)c +--R + +--R 5 4 2 3 3 2 6 +--R (24b - 4a b - 52a b + 44a b )c +--R + +--R 7 6 2 5 3 4 4 +--R (32b - 20a b + 28a b + 8a b )c +--R + +--R 9 8 2 7 3 6 2 +--R (12b - 12a b + 36a b - 36a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (8b - 4a)c + (80b - 52a b - 132a b - 32a )c +--R + +--R 5 4 2 3 3 2 4 6 +--R (36b + 80a b + 36a b - 228a b + 160a b)c +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 36b + 200a b - 104a b + 172a b + 8a b )c +--R + +--R 8 2 7 3 6 4 5 2 +--R (72a b - 72a b + 168a b - 168a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (16b + 4a)c + (56b + 56a b - 120a b - 116a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (64b - 68a b + 104a b + 260a b - 256a b + 112a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (24b - 120a b + 392a b - 224a b + 472a b - 64a b )c +--R + +--R 2 7 3 6 4 5 5 4 2 +--R (168a b - 168a b + 312a b - 312a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (8b + 12a)c + (- 60b + 116a b + 76a b - 88a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 60b + 112a b - 196a b + 312a b + 176a b - 80a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 8b + 8a b - 104a b + 424a b - 352a b + 600a b +--R + +--R 6 +--R - 104a b +--R * +--R 4 +--R c +--R + +--R 3 6 4 5 5 4 6 3 2 +--R (192a b - 192a b + 288a b - 288a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (4b + 12a)c + (- 8b - 72a b + 140a b + 56a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 28b - 52a b + 132a b - 264a b + 396a b - 28a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 16b + 32a b - 8a b - 40a b + 264a b - 300a b +--R + +--R 6 7 +--R 348a b - 40a +--R * +--R 4 +--R c +--R + +--R 4 5 5 4 6 3 7 2 2 +--R (108a b - 108a b + 132a b - 132a b )c +--R * +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R 8a c + (4b - 4a b - 40a b + 84a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (4b - 28a b - 8a b + 84a b - 148a b + 132a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 16a b + 24a b + 8a b - 20a b + 64a b - 88a b +--R + +--R 7 +--R 76a +--R * +--R 4 +--R c +--R + +--R 5 4 6 3 7 2 8 2 +--R (24a b - 24a b + 24a b - 24a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 11 2 2 9 +--R 2c + (- 14b - 44a b + 10a )c +--R + +--R 4 3 2 2 3 7 +--R (- 12b + 40a b - 116a b + 32a b)c +--R + +--R 6 5 2 4 3 3 5 +--R (28b + 50a b - 58a b + 60a b )c +--R + +--R 8 7 2 6 3 5 3 +--R (26b - 36a b + 72a b - 56a b )c +--R + +--R 10 9 2 8 3 7 +--R (2b - 2a b + 4a b - 4a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 2 2 9 +--R (- 64b - 48a b - 24a )c +--R + +--R 4 3 2 2 3 4 7 +--R (- 4b - 84a b + 104a b - 204a b + 24a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (48b + 124a b + 192a b - 168a b + 188a b )c +--R + +--R 8 7 2 6 3 5 4 4 3 +--R (- 12b + 172a b - 220a b + 332a b - 236a b )c +--R + +--R 9 2 8 3 7 4 6 +--R (12a b - 12a b + 24a b - 24a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 11 2 2 9 +--R - 6c + (- 16b - 12a b - 48a )c +--R + +--R 3 2 2 3 4 7 +--R (96a b + 2a b - 72a b - 90a )c +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (24b + 46a b + 372a b + 240a b - 190a b + 228a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 3 +--R (14b - 62a b + 352a b - 466a b + 684a b - 432a b )c +--R + +--R 2 8 3 7 4 6 5 5 +--R (30a b - 30a b + 60a b - 60a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 2 9 +--R (84b + 28a b)c +--R + +--R 4 3 2 2 3 4 7 +--R (52b + 172a b + 56a b + 80a b - 96a )c +--R + +--R 6 5 2 4 3 3 4 2 +--R - 32b + 144a b - 248a b + 592a b + 160a b +--R + +--R 5 6 +--R - 72a b + 96a +--R * +--R 5 +--R c +--R + +--R 2 6 3 5 4 4 5 3 6 2 3 +--R (- 72a b + 320a b - 496a b + 800a b - 432a b )c +--R + +--R 3 7 4 6 5 5 6 4 +--R (40a b - 40a b + 80a b - 80a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 11 2 2 9 +--R 6c + (46b + 72a b + 34a )c +--R + +--R 4 3 2 2 3 4 7 +--R (66b - 40a b + 236a b + 92a b + 22a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 18b - 104a b + 142a b - 424a b + 602a b + 2a b +--R + +--R 6 +--R 4a +--R * +--R 5 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 8b + 8a b - 60a b + 12a b + 154a b - 328a b +--R + +--R 6 2 7 +--R 544a b - 232a b +--R * +--R 3 +--R c +--R + +--R 4 6 5 5 6 4 7 3 +--R (30a b - 30a b + 60a b - 60a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 9 +--R (- 12b + 36a b + 32a )c +--R + +--R 4 3 2 2 3 4 7 +--R (- 12b + 44a b - 76a b + 168a b + 64a )c +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- 8a b - 68a b + 80a b - 292a b + 332a b - 44a )c +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 16a b + 16a b - 64a b + 52a b + 52a b +--R + +--R 6 2 7 8 +--R - 148a b + 196a b - 52a +--R * +--R 3 +--R c +--R + +--R 5 5 6 4 7 3 8 2 +--R (12a b - 12a b + 24a b - 24a b )c +--R * +--R cos(x) +--R + +--R 11 2 2 9 +--R - 2c + (- 8b + 12a )c +--R + +--R 4 3 2 2 3 4 7 +--R (- 10b + 4a b + 10a b - 40a b + 68a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (- 4b + 4a b - 10a b - 12a b + 34a b - 90a b + 62a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 3 +--R (- 8a b + 8a b - 18a b + 18a b + 12a b - 34a b + 28a )c +--R + +--R 6 4 7 3 8 2 9 +--R (2a b - 2a b + 4a b - 4a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 10 3 2 2 3 8 +--R (4b + 6a)c + (- 8b - 58a b + 20a b - 6a )c +--R + +--R 5 4 2 3 3 2 6 +--R (- 16b - 18a b - 84a b + 40a b )c +--R + +--R 7 6 2 5 3 4 4 +--R (8b + 34a b - 68a b + 74a b )c +--R + +--R 9 8 2 7 3 6 2 +--R (12b - 12a b + 36a b - 36a b )c +--R * +--R 7 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (28b + 6a)c + (- 4b - 54a b - 152a b + 18a )c +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 18b - 116a b - 20a b - 240a b + 100a b)c +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (12b + 30a b + 196a b - 214a b + 252a b )c +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (- 2b + 86a b - 88a b + 196a b - 192a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (12b + 6a)c + (32b - 20a b - 168a b - 60a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (28b + 6a b - 188a b + 10a b - 204a b + 54a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (8b + 20a b + 208a b + 318a b - 228a b + 322a b )c +--R + +--R 8 2 7 3 6 4 5 5 4 2 +--R (- 12a b + 228a b - 240a b + 456a b - 432a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 40b + 2a)c + (- 8b + 44a b + 88a b - 104a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (30b + 144a b + 132a b + 34a b - 76a b - 54a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 2b + 90a b - 122a b + 580a b + 120a b - 70a b +--R + +--R 6 +--R 184a b +--R * +--R 4 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 12a b - 18a b + 294a b - 324a b + 588a b +--R + +--R 6 3 +--R - 528a b +--R * +--R 2 +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 20b - 14a)c + (- 32b + 82a b + 132a b + 38a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 4b + 78a b + 372a b + 100a b + 148a b - 64a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 8b - 18a b + 192a b - 354a b + 712a b - 128a b +--R + +--R 6 7 +--R 28a b + 40a +--R * +--R 4 +--R c +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R - 48a b + 8a b + 196a b - 236a b + 452a b +--R + +--R 7 2 +--R - 372a b +--R * +--R 2 +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (12b - 6a)c + (12b + 14a b + 64a b + 78a )c +--R + +--R 4 2 3 3 2 4 5 6 +--R (34a b + 8a b + 320a b + 50a b + 50a )c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R 14a b - 32a b + 146a b - 340a b + 424a b +--R + +--R 6 7 +--R - 120a b + 16a +--R * +--R 4 +--R c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 2 +--R (- 72a b + 42a b + 66a b - 96a b + 204a b - 144a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (4b + 2a)c + (8b - 4a b + 16a b + 28a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (4b - 6a b + 20a b - 30a b + 116a b + 22a )c +--R + +--R 2 5 3 4 4 3 5 2 6 7 4 +--R (4a b - 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4a b + 25a b + 4a b + 61a b - 15a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 3 +--R (8a b - 4a b + 5a b - 7a b + 11a b + 11a b - 24a b)c +--R * +--R 5 +--R sin(x) +--R + +--R 10 3 2 2 8 +--R 6b c + (- 29b - 9a b - 14a b)c +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 3b - 4a b - 80a b + 6a b + 11a b)c +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (45b - a b + 82a b - 68a b + 50a b )c +--R + +--R 9 8 2 7 3 6 4 5 2 +--R (13b - 6a b + 28a b + 6a b - 41a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (5b + 5a)c + (- 18b - 114a b - 14a b - 22a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 51b + 28a b - 18a b - 134a b - 36a b + 17a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (- 28b + 218a b - 28a b + 362a b - 220a b + 128a b )c +--R + +--R 8 2 7 3 6 4 5 5 4 2 +--R (71a b - 24a b + 74a b + 24a b - 145a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 7b + 5a)c + (5b - 63a b - 111a b - 7a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (15b - 132a b + 209a b - 155a b - 59a b - 40a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 7b - 64a b + 403a b - 118a b + 535a b - 232a b +--R + +--R 6 +--R 117a b +--R * +--R 4 +--R c +--R + +--R 9 2 7 3 6 4 5 5 4 6 3 2 +--R (4b + 123a b - 36a b + 66a b + 36a b - 193a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 3b - 3a)c + (- 11b + 39a b - 69a b - 15a )c +--R + +--R 4 2 3 3 2 4 5 6 +--R (59a b - 163a b + 271a b - 168a b - 21a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 8b + 25a b - 68a b + 299a b - 132a b + 345a b +--R + +--R 6 7 +--R - 84a b + 39a +--R * +--R 4 +--R c +--R + +--R 8 3 6 4 5 5 4 6 3 7 2 2 +--R (8a b + 85a b - 24a b + 22a b + 24a b - 115a b )c +--R * +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (3b - 3a)c + (5b - 13a b + 32a b - 20a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (2b - 2a b + 44a b - 76a b + 81a b - 33a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 4 +--R (8a b + 18a b - 32a b + 69a b - 41a b + 90a b - 4a )c +--R + +--R 2 7 4 5 5 4 6 3 7 2 8 2 +--R (4a b + 20a b - 6a b + 2a b + 6a b - 26a b)c +--R * +--R 4 +--R sin(x) +--R + +--R 11 2 2 9 +--R - c + (14b - 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86a b + 30a +--R * +--R 3 +--R c +--R + +--R 4 6 6 4 8 2 +--R (54a b + 12a b - 66a b )c +--R * +--R cos(x) +--R + +--R 11 2 2 9 +--R - c + (- 2b + 8a b - 15a )c +--R + +--R 4 3 2 2 3 4 7 +--R (b + 4a b - 55a b + 62a b - 35a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 5 +--R (2b - 12a b - 32a b + 70a b - 128a b + 100a b - 39a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 3 +--R (- 8a b + 4a b + 16a b - 31a b + 66a b - 81a b + 82a b)c +--R + +--R 5 5 9 +--R (12a b - 12a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 10 3 2 2 3 8 +--R (- 2b + a)c + (11b - 35a b - 20a b + 5a )c +--R + +--R 5 4 2 3 3 2 4 6 +--R (- 14b + 36a b - 11a b - 54a b + 22a b)c +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- 8b + 41a b - 61a b + 57a b - 6a b )c +--R + +--R 9 8 2 7 3 6 4 5 2 11 2 9 +--R (20b - 31a b + 51a b - 44a b + 10a b )c + b + a b +--R + +--R 4 7 +--R - 2a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 3b - 3a)c + (- 20b + 4a b - 51a b - 15a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (12b - 134a b + 125a b + 25a b - 108a b + 18a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (4b - 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226a b + 454a b - 798a b + 1002a b - 476a b +--R + +--R 7 2 +--R 164a b +--R * +--R 2 +--R c +--R + +--R 3 8 5 6 7 4 +--R 20a b + 20a b - 40a b +--R * +--R 3 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R 9a c + (23b + 11a b - 16a b + 53a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (36b - 95a b + 155a b - 206a b - 138a b + 69a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 9b - 97a b + 133a b - 725a b + 543a b - 460a b +--R + +--R 6 7 +--R - 40a b + 22a +--R * +--R 4 +--R c +--R + +--R 9 2 7 3 6 4 5 5 4 6 3 +--R - 4b - 26a b - 214a b + 378a b - 667a b + 793a b +--R + +--R 7 2 8 +--R - 244a b + 74a b +--R * +--R 2 +--R c +--R + +--R 4 7 6 5 8 3 +--R 15a b + 15a b - 30a b +--R * +--R 2 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 3b - 3a)c + (- 12b + 18a b - 35a b - 5a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (- 9b + 25a b - 139a b + 143a b - 163a b + a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 4a b - 92a b + 100a b - 462a b + 344a b - 223a b +--R + +--R 7 +--R - 5a +--R * +--R 4 +--R c +--R + +--R 8 3 6 4 5 5 4 6 3 7 2 +--R - 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236a b + 229a b + 45a b - 235a b +--R + +--R 6 2 7 +--R 177a b + 12a b +--R * +--R 3 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 6a b - 120a b + 278a b - 400a b + 552a b - 320a b +--R + +--R 7 3 +--R 16a b +--R * +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 9 +--R (- 13b - 5a b - a )c +--R + +--R 4 3 2 2 3 4 7 +--R (- 18b + 5a b + 32a b + 161a b + 35a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - b - 35a b + 212a b + 44a b - 117a b + 166a b +--R + +--R 6 +--R - 34a +--R * +--R 5 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 4b - 45a b + 147a b - 481a b + 379a b - 188a b +--R + +--R 6 2 7 +--R - 145a b + 74a b +--R * +--R 3 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 24a b - 160a b + 277a b - 440a b + 563a b +--R + +--R 7 3 8 2 +--R - 240a b + 24a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 9 3 2 2 3 4 7 +--R (3b - 3a b + 3a )c + (13a b - 24a b + 17a b + 63a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 3b + 23a b - 108a b + 214a b - 84a b - 48a b +--R + +--R 6 +--R 51a +--R * +--R 5 +--R c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 7a b - 69a b + 137a b - 477a b + 314a b - 219a b +--R + +--R 7 8 +--R - 38a b + 12a +--R * +--R 3 +--R c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 36a b - 120a b + 180a b - 288a b + 348a b - 96a b +--R + +--R 9 +--R 12a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 9 4 3 2 2 3 4 7 +--R (2b - 3a b - 2a )c + (4b - 10a b + 12a b - 36a b + a )c +--R + +--R 6 5 2 4 3 3 4 2 5 5 +--R (2b - 7a b + 16a b - 103a b + 104a b - 85a b)c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 3 +--R (2a b - 47a b + 59a b - 233a b + 143a b - 94a b - a )c +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R - 24a b - 48a b + 73a b - 104a b + 117a b - 16a b +--R + +--R 10 +--R 2a +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 9 3 2 2 3 4 7 +--R (- a b - 4a )c + (- 2a b - 8a b + 8a b - 13a )c +--R + +--R 5 2 4 3 3 4 2 5 6 5 +--R (- a b - 4a b + 7a b - 31a b + 21a b - 23a )c +--R + +--R 3 5 4 4 5 3 6 2 7 8 3 +--R (- a b - 12a b + 11a b - 45a b + 28a b - 14a )c +--R + +--R 5 5 6 4 7 3 8 2 9 +--R (- 6a b - 8a b + 14a b - 16a b + 16a b)c +--R * +--R sin(x) +--R + +--R 2 2 8 5 4 2 3 3 2 4 6 +--R (4a b + 3a b)c + (b - 8a b - 3a b + 2a b - 3a b)c +--R + +--R 7 6 2 5 3 4 4 3 4 +--R (- b - 9a b - 13a b - 6a b + 6a b )c +--R + +--R 9 8 2 7 3 6 4 5 2 11 10 2 9 +--R (- b + 2a b - 13a b + 6a b + 9a b )c + b - a b + 2a b +--R + +--R 3 8 +--R - 2a b +--R * +--R 8 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 2b - 2a)c + (b + 2a b + 10a b + 7a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (3b + 6a b - 39a b - 23a b + 4a b - 5a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 4 +--R (2b - 18a b - 43a b - 51a b - 22a b + 24a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 2 11 +--R (b - 12a b + 13a b - 53a b + 32a b + 37a b )c - b +--R + +--R 10 2 9 3 8 4 7 +--R 8a b - 9a b + 16a b - 14a b +--R * +--R 7 +--R cos(x) +--R + +--R 10 3 2 2 3 8 +--R (- 2b - 2a)c + (- b - a b + 8a b + 6a )c +--R + +--R 5 4 3 2 4 5 6 +--R (3b + 17a b - 75a b - 37a b + 2a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 4 +--R (5b + 23a b - 68a b - 68a b - 65a b - 30a b + 31a b)c +--R + +--R 9 2 7 3 6 4 5 5 4 6 3 2 10 +--R (3b - 24a b + 28a b - 92a b + 70a b + 57a b )c - 7a b +--R + +--R 2 9 3 8 4 7 5 6 +--R 28a b - 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21a b + 28a b - 49a b + 56a b - 14a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 8 4 2 3 3 2 4 6 +--R (- a b - 3a b)c + (- 2a b - 6a b + 8a b - 10a b)c +--R + +--R 6 2 5 3 4 4 3 5 2 6 4 +--R (- a b - 3a b + 7a b - 26a b + 27a b - 16a b)c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 2 6 5 +--R (- a b - 10a b + 23a b - 35a b + 22a b - 17a b)c - 7a b +--R + +--R 7 4 8 3 9 2 10 +--R 8a b - 15a b + 16a b - 2a b +--R * +--R cos(x) +--R + +--R 3 8 3 2 4 5 6 +--R - a c + (- 2a b + a b - 4a )c +--R + +--R 3 4 4 3 5 2 6 7 4 +--R (- a b + a b - 6a b + 4a b - 5a )c +--R + +--R 5 4 6 3 7 2 8 9 2 7 4 8 3 9 2 10 +--R (- 2a b + 2a b - 6a b + 5a b - 2a )c - a b + a b - 2a b + 2a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 4 3 2 2 3 4 8 +--R (- 2b + 4a b + 4a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 4b + 8a b + 6a b - 20a b + 4a b + 12a b - 6a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 2a b + 4a b - 2a b )c +--R * +--R 7 +--R sin(x) +--R + +--R 2 2 3 9 +--R (3a b - 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10a b - 13a b - 6a b + 7a b )c - b +--R + +--R 11 2 10 3 9 4 8 5 7 +--R a b - a b + a b + 2a b - 2a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 2 10 +--R (17b - 5a b - 3a )c +--R + +--R 4 3 2 2 3 4 8 +--R (8b - 84a b - 26a b + 85a b - 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 21b - 73a b - 68a b + 59a b + 73a b - 80a b + 9a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 4 +--R (b + 81a b - 7a b - 60a b + 108a b + 100a b - 76a b )c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 12b + 70a b + 43a b - 39a b - 79a b - 46a b +--R + +--R 6 4 +--R 39a b +--R * +--R 2 +--R c +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R - b - 5a b + 5a b - 5a b + 8a b + 10a b - 12a b +--R * +--R 6 +--R cos(x) +--R + +--R 10 4 3 2 2 3 4 8 +--R 3a b c + (16b - 47a b - 155a b + 72a b + 33a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (30b - 39a b - 101a b - 59a b + 73a b + 6a b - 33a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 12b + 69a b + 236a b - 31a b - 57a b + 178a b +--R + +--R 6 2 7 +--R 115a b - 81a b +--R * +--R 4 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R - 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2a b +--R * +--R sin(x) +--R + +--R 3 2 2 9 4 2 3 3 2 4 7 +--R (2b + 2a b - 3a b)c + (- 3a b + 5a b - 4a b + 3a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 5 +--R (- 4b - 13a b + 13a b + 7a b - 10a b + 2a b )c +--R + +--R 8 2 7 3 6 4 5 5 4 3 +--R (- 9a b + 7a b + 10a b - a b - 4a b )c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R (2b - a b + 2a b - a b - 4a b + 2a b )c +--R * +--R 8 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 2b + 2a)c + (b + 8a b + 2a b - 7a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (5b - 16a b - 11a b + 21a b - 4a b + 5a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 5 +--R (b - 36a b - 44a b + 59a b + 20a b - 32a b + 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 3 +--R (b - 2a b - 35a b + 43a b + 38a b - 5a b - 16a b )c +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R (2b + 12a b - 4a b + 12a b - 10a b - 24a b + 12a b )c +--R * +--R 7 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 2b + 2a)c + (- 5b + 9a b + 8a b - 8a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (b + 3a b - 58a b + 5a b + 29a b + 4a )c +--R + +--R 7 2 5 3 4 4 3 5 2 6 7 5 +--R (9b - 106a b - 41a b + 111a b + 4a b - 35a b + 2a )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 5b + 17a b - 10a b - 56a b + 104a b + 57a b - 9a b +--R + +--R 7 2 +--R - 24a b +--R * +--R 3 +--R c +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 7 4 +--R (13a b + 30a b - 2a b + 30a b - 41a b - 60a b + 30a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (4b - 4a)c + (2b - 13a b - 3a b + 10a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 5b + 15a b - 26a b - 72a b + 41a b + 7a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 5 +--R (53a b + 6a b - 152a b - 3a b + 107a b - 26a b - 13a )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 3b + 29a b + 65a b - 30a b - 54a b + 128a b + 50a b +--R + +--R 7 2 8 +--R - 7a b - 16a b +--R * +--R 3 +--R c +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 8 3 +--R (36a b + 40a b + 16a b + 40a b - 92a b - 80a b + 40a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (4b - 4a)c + (8b - 20a b - 11a b + 13a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (3b - 12a b + 43a b - 30a b - 46a b + 12a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 2b + 20a b + 122a b + 10a b - 130a b + 12a b + 55a b +--R + +--R 7 +--R - 17a +--R * +--R 5 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - b + 16a b + 68a b + 108a b - 60a b - 38a b + 85a b +--R + +--R 7 2 8 9 +--R 38a b - 2a b - 4a +--R * +--R 3 +--R c +--R + +--R 3 8 4 7 5 6 6 5 7 4 8 3 9 2 +--R (55a b + 30a b + 40a b + 30a b - 125a b - 60a b + 30a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 2b + 2a)c + (- 3b + 6a b - 4a b - 3a )c +--R + +--R 4 2 3 3 2 4 5 7 +--R (3a b + 27a b + 47a b - 49a b - 12a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R b - 4a b + 63a b + 130a b - 12a b - 70a b + 19a b +--R + +--R 7 +--R 13a +--R * +--R 5 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 3a b + 32a b + 80a b + 93a b - 70a b - 17a b + 29a b +--R + +--R 8 +--R 24a b +--R * +--R 3 +--R c +--R + +--R 4 7 5 6 6 5 7 4 8 3 9 2 10 +--R (50a b + 12a b + 44a b + 12a b - 106a b - 24a b + 12a b)c +--R * +--R 3 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 2b + 2a)c + (- 5b + 9a b + 6a b - 6a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 4b + 12a b + 10a b + 27a b + 14a b - 19a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 5 +--R (- b + 5a b + a b + 63a b + 59a b - 11a b - 18a b + 14a )c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R - 3a b + 30a b + 47a b + 47a b - 42a b - 6a b + 4a b +--R + +--R 9 +--R 7a +--R * +--R 3 +--R c +--R + +--R 5 6 6 5 7 4 8 3 9 2 10 11 +--R (27a b + 2a b + 26a b + 2a b - 55a b - 4a b + 2a )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 9 4 2 3 3 2 4 7 +--R (- a b + 5a b)c + (- 2a b + 10a b + 4a b + 12a b)c +--R + +--R 6 2 5 3 4 4 3 5 2 6 5 +--R (- a b + 5a b + 3a b + 25a b + 7a b + 5a b)c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 3 +--R (- a b + 13a b + 11a b + 17a b - 10a b - 6a b)c +--R + +--R 6 5 8 3 10 +--R (8a b + 8a b - 16a b)c +--R * +--R cos(x) +--R + +--R 3 9 3 2 5 7 3 4 5 2 7 5 +--R a c + (2a b + 3a )c + (a b + 5a b + a )c +--R + +--R 5 4 7 2 9 3 7 4 9 2 11 +--R (2a b + 4a b - 3a )c + (a b + a b - 2a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 9 +--R (4b - 4a b - 12a b + 12a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (8b - 8a b - 20a b + 20a b + 12a b - 12a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 5 +--R (4b - 4a b - 8a b + 8a b + 4a b - 4a b )c +--R * +--R 7 +--R sin(x) +--R + +--R 2 2 10 +--R (- 8b - 6a b + 6a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 16b + 6a b - 14a b + 6a b - 6a )c +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 8b + 30a b - 38a b - 12a b + 28a b )c +--R + +--R 7 2 6 3 5 4 4 4 +--R (18a b - 18a b - 18a b + 18a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 10 3 2 2 4 8 +--R (- 8b - 12a b + 12a )c + (- 40a b + 4a b - 12a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (24b - 44a b - 4a b - 4a b + 16a b + 12a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 4 +--R (16b - 16a b + 4a b - 4a b - 20a b + 20a b )c +--R * +--R cos(x) +--R + +--R 2 2 10 +--R (- 4b - 2a b + 6a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 8b + 12a b - 8a b - 32a b + 12a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 4b + 30a b - 30a b - 46a b + 34a b + 34a b - 18a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 4 +--R (16a b - 16a b - 14a b + 14a b - 2a b + 2a b )c +--R * +--R 6 +--R sin(x) +--R + +--R 11 3 2 2 3 9 +--R (8b + 6a)c + (- 8b - 48a b + 50a b - 6a )c +--R + +--R 5 4 2 3 3 2 4 7 +--R (- 40b - 84a b + 38a b + 54a b - 58a b)c +--R + +--R 7 2 5 3 4 4 3 5 +--R (- 24b - 42a b + 30a b + 36a b )c +--R + +--R 8 2 7 3 6 4 5 3 +--R (30a b - 30a b - 30a b + 30a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (6b + 12a)c + (- 18b - 52a b - 36a b + 54a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 46b - 148a b - 42a b + 2a b + 30a b - 66a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 5 +--R (- 14b - 92a b + 68a b - 126a b + 36a b + 128a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 3 +--R (8b - 8a b + 74a b - 74a b - 82a b + 82a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 4b + 2a)c + (- 24b - 18a b - 58a b + 32a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 36b - 26a b - 144a b + 34a b - 64a b - 34a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 16b + 10a b - 102a b + 60a b - 98a b + 20a b +--R + +--R 6 +--R 126a b +--R * +--R 5 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 3 +--R (16a b - 16a b + 58a b - 58a b - 74a b + 74a b )c +--R * +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (2b - 8a)c + (4b - 32a b + 10a b - 10a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (2b - 40a b + 26a b - 36a b - 26a b - 16a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 5 +--R (- 16a b + 24a b - 34a b - 8a b - 14a b + 14a b + 34a )c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 3 +--R (8a b - 8a b + 14a b - 14a b - 22a b + 22a b )c +--R * +--R 5 +--R sin(x) +--R + +--R 12 2 2 10 +--R - 2c + (8b + 42a b - 2a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 4b + 18a b + 46a b - 42a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (- 40b - 78a b + 46a b + 24a b - 60a b )c +--R + +--R 8 7 2 6 3 5 4 4 4 +--R (- 26b - 42a b - 14a b + 54a b + 28a b )c +--R + +--R 9 2 8 3 7 4 6 2 +--R (12a b - 12a b - 12a b + 12a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 12 2 2 10 +--R - 2c + (18b + 58a b + 52a )c +--R + +--R 4 3 2 2 3 4 8 +--R (66b - 50a b - 106a b + 142a b - 50a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (70b - 274a b - 320a b + 156a b + 136a b - 200a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 4 +--R (24b - 166a b - 114a b - 34a b + 138a b + 152a b )c +--R + +--R 2 8 3 7 4 6 5 5 2 +--R (48a b - 48a b - 48a b + 48a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 12 2 2 10 +--R 2c + (6b + 10a b + 64a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 2b + 60a b - 150a b - 104a b + 70a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 14b + 90a b - 500a b - 202a b + 20a b + 94a b +--R + +--R 6 +--R - 136a +--R * +--R 6 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 8b + 40a b - 286a b - 26a b - 106a b + 58a b +--R + +--R 6 2 +--R 328a b +--R * +--R 4 +--R c +--R + +--R 3 7 4 6 5 5 6 4 2 +--R (72a b - 72a b - 72a b + 72a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 12 2 2 10 +--R - 2c + (4b - 26a b - 10a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 2b - 52a b + 62a b - 204a b + 26a )c +--R + +--R 6 5 2 4 3 3 5 6 6 +--R (- 24b - 26a b + 128a b - 430a b - 66a b - 14a )c +--R + +--R 8 2 6 3 5 4 4 5 3 6 2 +--R - 16b + 56a b - 226a b + 74a b - 118a b - 66a b +--R + +--R 7 +--R 296a b +--R * +--R 4 +--R c +--R + +--R 4 6 5 5 6 4 7 3 2 +--R (48a b - 48a b - 48a b + 48a b )c +--R * +--R cos(x) +--R + +--R 12 2 2 10 +--R - 4c + (- 8b + 12a b - 36a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 4b + 8a b - 60a b + 56a b - 64a )c +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (- 20a b - 16a b + 96a b - 152a b - 28a b + 12a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R - 16a b + 8a b + 40a b - 80a b + 28a b - 32a b - 40a b +--R + +--R 8 +--R 92a +--R * +--R 4 +--R c +--R + +--R 5 5 6 4 7 3 8 2 2 +--R (12a b - 12a b - 12a b + 12a b )c +--R * +--R 4 +--R sin(x) +--R + +--R 11 2 9 5 2 3 4 7 +--R 4b c + 40a b c + (- 24b + 56a b - 44a b)c +--R + +--R 7 2 5 4 3 5 9 2 7 4 5 3 +--R (- 32b - 8a b - 8a b )c + (- 12b - 24a b + 36a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 8b + 4a)c + (- 88b + 60a b + 136a b + 28a )c +--R + +--R 5 2 3 3 2 4 5 7 +--R (- 116b + 148a b + 44a b - 128a b - 32a )c +--R + +--R 6 2 5 3 4 4 3 5 2 5 +--R (- 164a b - 12a b - 56a b + 60a b - 68a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 3 +--R (36b - 108a b - 24a b - 72a b - 12a b + 180a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 16b - 4a)c + (- 56b - 76a b + 140a b + 116a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 64b - 44a b + 8a b - 24a b + 20a b - 112a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 24b + 124a b - 396a b - 140a b - 108a b + 208a b +--R + +--R 6 +--R - 144a b +--R * +--R 5 +--R c +--R + +--R 8 2 7 4 5 5 4 6 3 3 +--R (96a b - 264a b - 144a b - 96a b + 408a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 8b - 12a)c + (52b - 108a b - 88a b + 100a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (120b - 172a b + 4a b - 120a b - 88a b - 8a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 52b - 68a b + 188a b - 508a b - 136a b - 112a b +--R + +--R 6 7 +--R 184a b - 80a +--R * +--R 5 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 8b + 8a b + 96a b - 288a b + 120a b - 216a b +--R + +--R 6 3 7 2 +--R - 208a b + 496a b +--R * +--R 3 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 4b - 12a)c + (8b + 56a b - 124a b - 56a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (28b + 132a b - 212a b + 68a b - 200a b + 28a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 16b + 48a b - 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14a b - 12a b + 16a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 2 2 10 +--R (64b + 48a b + 24a )c +--R + +--R 4 3 2 2 3 4 8 +--R (68b + 20a b - 32a b + 132a b - 24a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 44b - 128a b - 212a b + 188a b - 8a b - 180a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 4 +--R (- 36b - 124a b - 96a b - 16a b + 216a b + 20a b )c +--R + +--R 10 9 2 8 3 7 4 6 5 5 2 +--R (12b - 24a b + 60a b - 72a b - 72a b + 96a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 12 2 2 10 +--R 6c + (16b + 18a b + 42a )c +--R + +--R 3 2 2 3 4 8 +--R (- 68a b - 30a b + 120a b + 42a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 24b - 142a b - 276a b - 170a b + 120a b - 138a b +--R + +--R 6 +--R - 90a +--R * +--R 6 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 14b - 8a b - 282a b - 146a b - 72a b + 394a b +--R + +--R 6 2 +--R 38a b +--R * +--R 4 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 2 +--R (48a b - 78a b + 144a b - 174a b - 192a b + 252a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 2 10 +--R (- 84b - 28a b)c +--R + +--R 4 3 2 2 3 4 8 +--R (- 136b - 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56a b + 8a b - 100a b - 64a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (12b - 4a b + 100a b - 112a b + 60a b - 100a b + 44a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 16a b + 60a b - 12a b + 160a b - 264a b - 140a b +--R + +--R 7 8 +--R 92a b + 52a +--R * +--R 4 +--R c +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 2 +--R (12a b - 24a b + 108a b - 120a b - 120a b + 144a b)c +--R * +--R cos(x) +--R + +--R 12 2 2 10 +--R 2c + (8b + 2a b - 14a )c +--R + +--R 4 3 2 2 3 4 8 +--R (10b + 4a b - 18a b + 28a b - 56a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (4b + 2a b + 4a b + 42a b - 64a b + 22a b + 6a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 4 +--R (8a b + 14a b - 4a b + 38a b - 68a b - 28a b + 34a )c +--R + +--R 6 4 7 3 8 2 9 10 2 +--R (- 2a b + 24a b - 26a b - 24a b + 28a )c +--R * +--R 2 +--R sin(x) +--R + +--R 11 3 2 2 3 9 +--R (- 4b - 6a)c + (8b + 48a b - 10a b + 6a )c +--R + +--R 5 4 2 3 3 2 4 7 +--R (16b + 84a b + 18a b - 54a b + 14a b)c +--R + +--R 7 2 5 3 4 4 3 5 +--R (- 8b + 34a b - 30a b - 44a b )c +--R + +--R 9 8 2 7 3 6 4 5 3 +--R (- 12b - 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40a b + 40a b - 40a b - 80a b + 80a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 12b + 6a)c + (- 24b - 2a b - 58a b - 84a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 12b - 22a b - 86a b - 242a b - 128a b + 28a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 14a b - 10a b - 104a b - 30a b - 54a b + 70a b +--R + +--R 7 +--R 34a +--R * +--R 5 +--R c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R 18a b + 54a b + 152a b - 260a b - 208a b + 100a b +--R + +--R 8 9 +--R 128a b + 16a +--R * +--R 3 +--R c +--R + +--R 4 7 5 6 6 5 7 4 8 3 9 2 +--R (30a b - 30a b + 30a b - 30a b - 60a b + 60a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 4b - 2a)c + (- 8b - 2a b - 10a b - 28a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 4b + 2a b - 16a b - 14a b - 72a b - 22a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 5 +--R (2a b - 6a b + 28a b - 46a b - 4a b + 22a b + 28a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 +--R 14a b + 34a b + 62a b - 110a b - 64a b + 40a b +--R + +--R 9 +--R 24a +--R * +--R 3 +--R c +--R + +--R 5 6 6 5 7 4 8 3 9 2 10 +--R (12a b - 12a b + 12a b - 12a b - 24a b + 24a b)c +--R * +--R cos(x) +--R + +--R 11 2 2 3 9 +--R 2a c + (4a b + 2a b - 10a )c +--R + +--R 4 2 3 3 2 4 5 7 +--R (2a b + 4a b - 10a b + 6a b - 8a )c +--R + +--R 2 5 4 3 5 2 6 7 5 +--R (2a b + 10a b - 8a b + 2a b + 6a )c +--R + +--R 4 5 5 4 6 3 7 2 8 9 3 +--R (4a b + 8a b + 8a b - 20a b - 6a b + 6a )c +--R + +--R 6 5 7 4 8 3 9 2 10 11 +--R (2a b - 2a b + 2a b - 2a b - 4a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 10 3 2 2 3 8 +--R (- 2b - 6a b)c + (6a b - 2a b + 6a b)c +--R + +--R 6 5 2 4 3 3 4 2 6 +--R (4b + 30a b + 2a b - 12a b + 4a b )c +--R + +--R 7 2 6 3 5 4 4 4 10 2 8 4 6 2 +--R (18a b + 2a b - 18a b - 8a b )c + (- 2b - 2a b + 4a b )c +--R * +--R 8 +--R cos(x) +--R + +--R 12 2 10 +--R 4c + (- 10a b - 14a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 10b + 14a b + 38a b + 2a b + 10a )c +--R + +--R 6 5 2 4 4 2 5 6 +--R (- 6b + 46a b + 132a b - 44a b + 8a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 4 +--R (- 2b + 10a b + 78a b - 14a b - 82a b - 32a b )c +--R + +--R 10 9 2 8 3 7 4 6 5 5 2 +--R (- 2b - 12a b - 2a b - 12a b + 4a b + 24a b )c +--R * +--R 7 +--R cos(x) +--R + +--R 12 2 2 10 +--R 4c + (6b - 6a b - 16a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 6b - 20a b + 64a b + 60a b + 8a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 14b - 34a b + 146a b + 214a b - 34a b - 54a b + 4a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 4 +--R (- 6b - 32a b + 36a b + 142a b - 72a b - 146a b - 48a b )c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 2 +--R (- 12a b - 30a b - 12a b - 30a b + 24a b + 60a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 12 2 2 10 +--R - 8c + (- 8b + 6a b + 18a )c +--R + +--R 4 3 2 2 3 4 8 +--R (6b - 28a b - 8a b + 88a b + 12a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (4b - 74a b - 118a b + 186a b + 166a b - 62a b - 22a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 2b - 40a b - 122a b + 58a b + 160a b - 106a b +--R + +--R 6 2 7 +--R - 126a b - 32a b +--R * +--R 4 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 2 +--R (- 30a b - 40a b - 30a b - 40a b + 60a b + 80a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 12 2 2 10 +--R - 8c + (- 14b + 14a b + 24a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 2b + 18a b - 50a b - 38a b + 22a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (6b - 6a b - 180a b - 200a b + 114a b + 76a b - 30a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 2b - 10a b - 106a b - 202a b + 78a b + 144a b - 56a b +--R + +--R 7 8 +--R - 52a b - 8a +--R * +--R 4 +--R c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 2 +--R (- 40a b - 30a b - 40a b - 30a b + 80a b + 60a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 12 2 2 10 +--R 4c + (8b + 2a b - 2a )c +--R + +--R 4 3 2 2 3 4 8 +--R (4b + 10a b - 26a b - 82a b - 16a )c +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (14a b - 42a b - 220a b - 142a b + 56a b + 22a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 8 4 +--R (6a b - 18a b - 138a b - 164a b + 96a b + 100a b - 8a )c +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 2 +--R (- 30a b - 12a b - 30a b - 12a b + 60a b + 24a b)c +--R * +--R 3 +--R cos(x) +--R + +--R 12 2 2 10 +--R 4c + (10b - 2a b - 8a )c +--R + +--R 4 3 2 2 3 4 8 +--R (8b - 4a b - 12a b - 28a b - 30a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (2b - 2a b + 2a b - 42a b - 114a b - 34a b + 24a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 4 +--R (6a b - 14a b - 88a b - 62a b + 70a b + 40a b + 6a )c +--R + +--R 5 5 6 4 7 3 8 2 9 10 2 +--R (- 12a b - 2a b - 12a b - 2a b + 24a b + 4a )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 10 3 2 2 3 4 8 +--R (2a b - 2a )c + (4a b - 4a b - 8a b - 6a )c +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (2a b - 2a b - 6a b - 10a b - 14a b - 2a )c +--R + +--R 3 5 4 4 5 3 6 2 7 8 4 +--R (2a b - 4a b - 22a b - 8a b + 20a b + 6a )c +--R + +--R 6 4 8 2 10 2 +--R (- 2a b - 2a b + 4a )c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 8 6 2 4 4 2 6 6 +--R (2b - 8a b + 6a )c + (4b - 14a b + 16a b - 6a )c +--R + +--R 8 2 6 4 4 6 2 4 +--R (2b - 6a b + 6a b - 2a b )c +--R * +--R 7 +--R sin(x) +--R + +--R 3 2 3 9 5 4 2 3 5 7 +--R (- 8b - 3a b + 3a )c + (- 16b + 3a b - 8a b - 3a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 5 +--R (- 8b + 15a b - 8a b - 21a b + 16a b + 6a b )c +--R + +--R 8 3 6 5 4 3 +--R (9a b - 18a b + 9a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 9 +--R (- 4b - 18a b + 8a b + 6a )c +--R + +--R 4 2 3 3 2 4 5 7 +--R (- 36a b - 2a b - 6a b + 2a b - 6a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 5 +--R (12b - 18a b - 16a b - 12a b + 14a b + 30a b - 10a b)c +--R + +--R 9 2 7 4 5 6 3 3 +--R (8b - 6a b - 12a b + 10a b )c +--R * +--R cos(x) +--R + +--R 3 2 2 3 9 +--R (- 2b - 3a b - 2a b + 7a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 4b + 2a b - 6a b - 12a b - 14a b + 10a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 5 +--R (- 2b + 13a b - 4a b - 34a b - 10a b + 38a b + 16a b - 17a )c +--R + +--R 8 3 6 5 4 7 2 3 +--R (8a b - 15a b + 6a b + a b )c +--R * +--R 6 +--R sin(x) +--R + +--R 2 2 10 4 3 2 2 3 4 8 +--R (12b + 3a b + 3a )c + (- 4b - 20a b + 9a b + 18a b - 3a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 44b - 34a b - 31a b + 58a b - 18a b - 21a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 4 +--R (- 28b + 4a b - 37a b + 10a b + 65a b - 14a b )c +--R + +--R 9 3 7 5 5 2 +--R (15a b - 30a b + 15a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 10 4 3 3 4 8 +--R (7b + 21a b + 2a )c + (- b - 59a b + 21a b + 23a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 19b - 181a b + a b - 56a b + 52a b - 42a b - 25a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 4 +--R (- 7b - 101a b + 36a b - 77a b + 3a b + 178a b - 32a b )c +--R + +--R 10 2 8 4 6 6 4 2 +--R (4b + 33a b - 78a b + 41a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 10 +--R (- 6b + 11a b + 5a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 20b + 3a b - 82a b + 47a b + 20a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 22b - 19a b - 181a b + 53a b - 51a b - 25a b - 25a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 8b - 3a b - 94a b + 27a b - 67a b + 9a b + 169a b +--R + +--R 7 +--R - 33a b +--R * +--R 4 +--R c +--R + +--R 9 3 7 5 5 7 3 2 +--R (8a b + 21a b - 66a b + 37a b )c +--R * +--R cos(x) +--R + +--R 2 2 10 4 3 2 2 3 4 8 +--R (b - 7a b + 4a )c + (2b - 22a b + 5a b - 20a b + 19a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (b - 23a b + a b - 41a b + 9a b - 29a b - 8a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 4 +--R (- 8a b + 4a b - 21a b - 5a b - 27a b + 16a b + 56a b - 15a )c +--R + +--R 2 8 4 6 6 4 8 2 2 +--R (4a b + 3a b - 18a b + 11a b )c +--R * +--R 5 +--R sin(x) +--R + +--R 11 3 2 2 9 +--R - 6b c + (24b + 13a b + 15a b)c +--R + +--R 5 4 2 3 3 2 4 7 +--R (28b + 5a b + 57a b - 11a b - 9a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 5 +--R (- 40b - 23a b - 11a b + 46a b - 78a b - 2a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 3 +--R (- 38b - 9a b - 53a b + 45a b + 91a b - 36a b )c +--R + +--R 10 3 8 5 6 +--R (6a b - 12a b + 6a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 5b - 5a)c + (17b + 106a b + 23a b + 22a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (61b + 56a b - 22a b + 90a b + 26a b - 17a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 51b - 226a b - 109a b - 106a b + 186a b - 184a b +--R + +--R 6 +--R - 44a b +--R * +--R 5 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 12b - 171a b - 40a b - 174a b + 152a b + 345a b +--R + +--R 6 3 +--R - 124a b +--R * +--R 3 +--R c +--R + +--R 2 9 4 7 6 5 +--R (24a b - 48a b + 24a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (7b - 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65a b - 18a b - 22a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 4 +--R (25b - 118a b + 73a b + 25a b - 7a b - 312a b + 74a b )c +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 2 +--R (18b - 131a b + 29a b - 143a b + 53a b + 274a b - 100a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 12 2 2 10 +--R - 2c + (8b - 44a b - 18a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 8b - 16a b + 226a b + 40a b + 48a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 48b + 148a b + 188a b + 158a b + 148a b - 32a b - 28a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 30b + 168a b - 330a b + 176a b - 74a b - 50a b +--R + +--R 6 2 7 +--R - 376a b + 36a b +--R * +--R 4 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 48a b - 274a b + 58a b - 262a b + 70a b + 536a b +--R + +--R 7 3 +--R - 176a b +--R * +--R 2 +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 12 2 2 10 +--R - 2c + (6b + 24a b - 28a )c +--R + +--R 4 3 2 2 3 4 8 +--R (52b - 14a b + 78a b + 158a b + 16a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (74b - 100a b + 318a b - 32a b + 206a b + 2a b + 18a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 26b - 62a b + 264a b - 476a b + 244a b - 88a b +--R + +--R 6 2 7 8 +--R - 200a b - 184a b - 4a +--R * +--R 4 +--R c +--R + +--R 10 2 8 3 7 4 6 5 5 6 4 +--R - 4b + 52a b - 286a b + 106a b - 238a b - 22a b +--R + +--R 7 3 8 2 +--R 524a b - 132a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 12 2 2 10 +--R c + (- 3b + 23a b + 9a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- b + 94a b - 62a b + 95a b + 9a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (11b + 111a b - 137a b + 267a b - 145a b + 101a b + 11a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 8b + 32a b - 66a b + 204a b - 331a b + 112a b + 14a b +--R + +--R 7 8 +--R - 183a b - 30a +--R * +--R 4 +--R c +--R + +--R 9 3 7 4 6 5 5 6 4 7 3 +--R - 8a b + 32a b - 149a b + 89a b - 107a b - 77a b +--R + +--R 8 2 9 +--R 256a b - 36a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 12 2 2 10 +--R c + (2b - 7a b + 14a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- b - 6a b + 53a b - 43a b + 20a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 4b + 9a b + 59a b - 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29a b - 47a b + 37a b + 64a b - 152a b + 90a b )c +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R (6b - 48a b + 60a b - 48a b - 30a b + 96a b - 36a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 3b + 6a)c + (20b - 37a b - 33a b + 27a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (32b - 46a b + 105a b - 66a b + 36a b + 18a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 7 5 +--R (- 8b + 67a b + 143a b - 190a b + 120a b + 54a b - 51a )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 17b + 94a b - 115a b + 41a b + 56a b - 4a b - 284a b +--R + +--R 7 2 +--R 139a b +--R * +--R 3 +--R c +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 24a b - 120a b + 138a b - 120a b - 78a b + 240a b +--R + +--R 7 4 +--R - 84a b +--R * +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (- 6b - 6a)c + (- 36b - 2a b - 86a b - 24a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 38b - 26a b + 24a b + 186a b - 72a b + 42a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 8b - 70a b + 376a b + 156a b - 66a b + 36a b + 72a b +--R + +--R 7 +--R - 12a +--R * +--R 5 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 16b - 40a b + 302a b - 214a b + 130a b + 18a b +--R + +--R 6 3 7 2 8 +--R - 180a b - 244a b + 92a b +--R * +--R 3 +--R c +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 +--R 36a b - 160a b + 192a b - 160a b - 132a b + 320a b +--R + +--R 8 3 +--R - 96a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R - 9a c + (- 20b - 17a b + 10a b - 44a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 36b + 36a b - 38a b + 131a b + 102a b - 16a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 12b + 87a b - 82a b + 523a b + 22a b + 48a b - 18a b +--R + +--R 7 +--R 47a +--R * +--R 5 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 4b + 43a b - 34a b + 372a b - 248a b + 94a b + 12a b +--R + +--R 7 2 8 9 +--R - 261a b - 94a b + 22a +--R * +--R 3 +--R c +--R + +--R 3 8 4 7 5 6 6 5 7 4 8 3 +--R 24a b - 120a b + 168a b - 120a b - 138a b + 240a b +--R + +--R 9 2 +--R - 54a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (3b + 3a)c + (12b - 12a b + 29a b + 5a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (15b - 25a b + 99a b - 53a b + 107a b - a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R 6b - 2a b + 108a b - 74a b + 304a b - 34a b + 29a b +--R + +--R 7 +--R 5a +--R * +--R 5 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 8a b + 38a b - 16a b + 209a b - 157a b + 17a b + 33a b +--R + +--R 8 9 +--R - 156a b - 12a +--R * +--R 3 +--R c +--R + +--R 4 7 5 6 6 5 7 4 8 3 9 2 10 +--R (6a b - 48a b + 84a b - 48a b - 78a b + 96a b - 12a b)c +--R * +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (b + 4a)c + (4b + 11a b - 9a b + 17a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (5b + 10a b - 13a b + 50a b - 27a b + 16a )c +--R + +--R 7 6 3 4 4 3 5 2 6 7 5 +--R (2b + 3a b + 44a b - 34a b + 58a b + 3a b - 3a )c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 3 +--R (4a b + 11a b - 5a b + 46a b - 39a b - 5a b + 16a b - 34a )c +--R + +--R 6 5 7 4 8 3 9 2 10 +--R (- 8a b + 18a b - 8a b - 18a b + 16a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 10 4 3 2 2 3 4 8 +--R (b - 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57a b + 99a b + 159a b + 49a b - 48a b - 33a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 4b + 15a b + 62a b - 171a b - 7a b + 6a b - 35a b +--R + +--R 7 +--R - 81a b +--R * +--R 4 +--R c +--R + +--R 10 9 2 8 3 7 5 5 6 4 +--R - 2b + 36a b - 27a b - 177a b + 117a b - 34a b +--R + +--R 7 3 +--R 87a b +--R * +--R 2 +--R c +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 7 5 +--R 6a b - 21a b + 21a b - 21a b + 3a b + 42a b - 30a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 2 10 +--R (14b + 7a b + 2a )c +--R + +--R 4 3 2 2 3 4 8 +--R (22b + 4a b - 153a b - 45a b + 57a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (3b - 17a b - 218a b + 29a b + 70a b + 48a b - 30a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 4b - 18a b + 67a b + 51a b - 166a b + 2a b + 62a b +--R + +--R 7 8 +--R - 10a b - 29a +--R * +--R 4 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R b - 4a b + 145a b - 58a b - 186a b + 13a b + 48a b +--R + +--R 7 3 8 2 +--R - 56a b + 97a b +--R * +--R 2 +--R c +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 8 4 +--R 15a b - 35a b + 35a b - 35a b - 10a b + 70a b - 40a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 10 4 3 2 2 3 4 8 +--R (13b + 5a b + a )c + (21b + 9a b - 50a b - 160a b - 35a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (3b + 8a b - 117a b - 199a b + 25a b + 11a b + 34a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 5b + 9a b - 62a b + 197a b + 54a b - 51a b + 23a b +--R + +--R 7 +--R 90a b +--R * +--R 4 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 5a b + 4a b + 256a b - 77a b - 133a b + 12a b - 77a b +--R + +--R 8 2 9 +--R - 44a b + 54a b +--R * +--R 2 +--R c +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 9 3 +--R 20a b - 35a b + 35a b - 35a b - 25a b + 70a b - 30a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 10 +--R (- 3b + 3a b - 3a )c +--R + +--R 4 3 2 2 3 4 8 +--R (- 6b - 4a b + 24a b - 23a b - 60a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 6 +--R (- 3b - 17a b + 69a b - 97a b - 33a b + 24a b + 12a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 10a b + 51a b - 58a b + 234a b + 53a b + 12a b +--R + +--R 7 8 +--R 12a b + 39a +--R * +--R 4 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 9a b + 16a b + 228a b - 72a b - 69a b + 9a b - 117a b +--R + +--R 9 10 +--R - 16a b + 12a +--R * +--R 2 +--R c +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 15a b - 21a b + 21a b - 21a b - 24a b + 42a b - 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 10 4 3 2 2 3 4 8 +--R (- 2b + 3a b + 2a )c + (- 4b + 7a b - 3a b + 30a b - a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- 2b + 5a b - 10a b + 77a b - 33a b + 36a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 8 4 +--R (a b - 5a b + 54a b - 22a b + 122a b + 22a b - 2a b + a )c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 7a b + 14a b + 100a b - 41a b - 21a b + 8a b - 65a b +--R + +--R 10 +--R - 2a +--R * +--R 2 +--R c +--R + +--R 5 7 6 6 7 5 8 4 9 3 10 2 11 +--R 6a b - 7a b + 7a b - 7a b - 11a b + 14a b - 2a b +--R * +--R cos(x) +--R + +--R 2 10 3 2 2 3 4 8 +--R (a b + 4a )c + (2a b + 9a b - 5a b + 9a )c +--R + +--R 5 2 4 3 3 4 2 5 6 6 +--R (a b + 6a b - 5a b + 23a b - 4a b + 10a )c +--R + +--R 2 6 4 4 5 3 6 2 7 8 4 +--R (a b + 16a b - 4a b + 26a b + 3a b - 9a )c +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 10 2 6 6 +--R (2a b + 4a b + 17a b - 10a b - 2a b + 3a b - 14a )c + a b +--R + +--R 7 5 8 4 9 3 10 2 11 +--R - a b + a b - a b - 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 2 9 4 2 3 3 2 4 7 +--R (- 4a b - 3a b)c + (3a b + 3a b + 2a b + 3a b)c +--R + +--R 6 2 5 3 4 4 3 5 2 5 +--R (17a b + 15a b - 5a b - 6a b + 2a b )c +--R + +--R 8 2 7 3 6 4 5 5 4 3 10 3 8 5 6 +--R (9a b + 9a b - 8a b - 9a b - 4a b )c + (- a b - a b + 2a b )c +--R * +--R 8 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (2b + 2a)c + (b - 2a b - 12a b - 7a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 5b - 2a b + 27a b + 23a b + 6a b + 5a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 5 +--R (- 5b + 10a b + 88a b + 59a b - 24a b - 24a b + 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 3 +--R (- b + 8a b + 43a b + 29a b - 44a b - 37a b - 16a b )c +--R + +--R 2 9 4 7 6 5 +--R (- 6a b - 6a b + 12a b )c +--R * +--R 7 +--R cos(x) +--R + +--R 11 3 2 2 3 9 +--R (2b + 2a)c + (b + 3a b - 8a b - 8a )c +--R + +--R 5 4 2 3 3 2 4 5 7 +--R (- 5b - 17a b + 6a b + 65a b + 37a b + 4a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 5 +--R (- 5b - 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41a b - 15a b + 28a b + 34a b + 10a b + 7a )c +--R + +--R 5 6 7 4 9 2 11 +--R (15a b + 14a b - 31a b + 2a )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 9 4 2 3 3 2 4 7 +--R (a b + 3a b)c + (2a b + 6a b - 4a b + 6a b)c +--R + +--R 6 2 5 3 4 4 3 5 2 6 5 +--R (a b + 3a b - 3a b + 15a b - 7a b + 3a b)c +--R + +--R 3 6 4 5 5 4 6 3 7 2 3 6 5 8 3 10 +--R (a b + 9a b - 11a b + 9a b + 10a b )c + (6a b + 6a b - 12a b)c +--R * +--R cos(x) +--R + +--R 3 9 3 2 5 7 3 4 5 2 7 5 5 4 7 2 9 3 +--R a c + (2a b + 3a )c + (a b + 5a b + a )c + (2a b + 4a b - 3a )c +--R + +--R 7 4 9 2 11 +--R (a b + a b - 2a )c +--R / +--R 4 3 2 2 10 +--R (8b - 16a b + 8a b )c +--R + +--R 6 5 3 3 4 2 8 +--R (16b - 32a b + 32a b - 16a b )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 6 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 10 +--R (16a b - 32a b + 16a b)c +--R + +--R 5 2 4 4 2 5 8 +--R (32a b - 64a b + 64a b - 32a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 16a b - 32a b - 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8b + 112a b - 200a b - 96a b + 408a b +--R + +--R 5 4 6 3 7 2 8 +--R - 144a b - 184a b + 128a b - 16a b +--R * +--R 5 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 11 +--R (8b - 32a b + 16a b + 8a )c +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (16b - 80a b + 144a b - 136a b + 80a b - 24a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 8b - 64a b + 256a b - 328a b - 56a b + 368a b +--R + +--R 6 7 +--R - 208a b + 24a +--R * +--R 7 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 16a b + 128a b - 184a b - 144a b + 408a b +--R + +--R 6 3 7 2 8 9 +--R - 96a b - 200a b + 112a b - 8a +--R * +--R 5 +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 11 +--R (8a b - 24a b + 16a )c +--R + +--R 4 2 3 3 2 4 9 +--R (16a b - 56a b + 64a b - 24a b)c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 7 +--R (8a b - 40a b + 96a b - 80a b - 56a b + 120a b - 48a )c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 8a b + 48a b - 56a b - 64a b + 136a b - 16a b +--R + +--R 8 9 +--R - 72a b + 32a +--R * +--R 5 +--R c +--R * +--R 5 +--R sin(x) +--R + +--R 2 2 12 +--R (10b - 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520a b - 336a b + 392a b - 96a b +--R * +--R 4 +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 12 +--R (- 12b + 24a b - 12a )c +--R + +--R 4 3 3 4 10 +--R (4b - 104a b + 104a b - 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 44b - 376a b + 448a b - 232a b + 448a b - 376a b +--R + +--R 6 +--R 44a +--R * +--R 8 +--R c +--R + +--R 8 7 2 6 3 5 5 3 +--R 28b - 344a b + 928a b - 936a b + 936a b +--R + +--R 6 2 7 8 +--R - 928a b + 344a b - 28a +--R * +--R 6 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 96a b + 492a b - 600a b - 492a b + 1392a b +--R + +--R 6 4 7 3 8 2 9 +--R - 492a b - 600a b + 492a b - 96a b +--R * +--R 4 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 12 +--R (- 8b + 8a )c +--R + +--R 4 3 2 2 3 4 10 +--R (- 24b + 72a b - 192a b + 136a b + 8a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 24b + 144a b - 504a b + 520a b - 56a b - 8a b +--R + +--R 6 +--R - 72a +--R * +--R 8 +--R c +--R + +--R 8 7 2 6 3 5 4 4 +--R - 8b + 72a b - 400a b + 776a b - 400a b +--R + +--R 5 3 6 2 7 8 +--R - 456a b + 720a b - 392a b + 88a +--R * +--R 6 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 96a b + 392a b - 336a b - 520a b + 928a b +--R + +--R 7 3 8 2 9 10 +--R - 136a b - 464a b + 264a b - 32a +--R * +--R 4 +--R c +--R * +--R cos(x) +--R + +--R 2 2 12 +--R (2b - 12a b + 10a )c +--R + +--R 4 3 2 2 3 4 10 +--R (4b - 32a b + 60a b - 72a b + 40a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 8 +--R (2b - 28a b + 94a b - 184a b + 128a b + 48a b - 60a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 8a b + 44a b - 144a b + 200a b - 16a b - 204a b +--R + +--R 7 8 +--R 168a b - 40a +--R * +--R 6 +--R c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 32a b + 114a b - 68a b - 178a b + 232a b + 14a b +--R + +--R 9 10 +--R - 132a b + 50a +--R * +--R 4 +--R c +--R * +--R 4 +--R sin(x) +--R + +--R 13 3 2 2 3 11 +--R (- 2b + 2a)c + (30b - 38a b + 14a b - 6a )c +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (- 20b + 68a b - 136a b + 104a b - 22a b + 6a )c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 100b + 132a b + 68a b - 212a b + 198a b +--R + +--R 5 2 6 7 +--R - 94a b + 10a b - 2a +--R * +--R 7 +--R c +--R + +--R 9 8 2 7 3 6 4 5 +--R - 10b - 102a b + 280a b - 120a b - 178a b +--R + +--R 5 4 6 3 7 2 +--R 194a b - 92a b + 28a b +--R * +--R 5 +--R c +--R + +--R 11 10 2 9 3 8 4 7 +--R 38b - 126a b + 62a b + 202a b - 238a b +--R + +--R 5 6 6 5 7 4 +--R - 26a b + 138a b - 50a b +--R * +--R 3 +--R c +--R * +--R 5 +--R cos(x) +--R + +--R 13 3 2 2 3 11 +--R (- 2b + 2a)c + (22b + 42a b - 66a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 9 +--R (28b - 236a b + 312a b - 288a b + 194a b - 10a )c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 68b - 300a b + 292a b + 708a b - 922a b +--R + +--R 5 2 6 7 +--R 466a b - 182a b + 6a +--R * +--R 7 +--R c +--R + +--R 9 8 2 7 3 6 4 5 +--R - 122b + 266a b - 616a b + 1008a b - 106a b +--R + +--R 5 4 6 3 7 2 8 +--R - 1054a b + 788a b - 220a b + 56a b +--R * +--R 5 +--R c +--R + +--R 11 10 2 9 3 8 4 7 +--R - 50b + 290a b - 530a b + 10a b + 1010a b +--R + +--R 5 6 6 5 7 4 8 3 +--R - 890a b - 230a b + 590a b - 200a b +--R * +--R 3 +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 13 3 2 2 3 11 +--R (4b - 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230a b - 120a b +--R + +--R 6 6 7 5 8 4 10 2 +--R 242a b + 68a b - 30a b - 40a b +--R * +--R 3 +--R c +--R + +--R 2 12 3 11 4 10 5 9 6 8 7 7 +--R 42a b + 28a b - 196a b - 84a b + 336a b + 84a b +--R + +--R 8 6 9 5 10 4 +--R - 252a b - 28a b + 70a b +--R * +--R c +--R * +--R 5 +--R cos(x) +--R + +--R 4 3 3 4 11 +--R (2b - 14a b + 14a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 9 +--R (6b - 22a b + 14a b + 4a b + 14a b - 22a b + 6a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 +--R 6b + 18a b + 48a b - 104a b + 104a b - 48a b - 18a b +--R + +--R 8 +--R - 6a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 2b + 46a b + 54a b - 94a b - 56a b + 96a b - 56a b +--R + +--R 7 3 8 2 9 10 +--R - 94a b + 54a b + 46a b + 2a +--R * +--R 5 +--R c +--R + +--R 11 2 10 3 9 4 8 5 7 7 5 +--R 20a b + 20a b + 70a b - 40a b - 310a b + 310a b +--R + +--R 8 4 9 3 10 2 11 +--R 40a b - 70a b - 20a b - 20a b +--R * +--R 3 +--R c +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R (70a b - 280a b + 420a b - 280a b + 70a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 2 2 3 4 11 +--R (2b + 4a b - 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138a b + 36a b + 60a b + 12a b +--R + +--R 9 10 +--R - 20a b + 8a +--R * +--R 5 +--R c +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 9 3 +--R 40a b - 20a b - 18a b - 20a b - 102a b + 96a b + 98a b +--R + +--R 10 2 11 12 +--R - 52a b - 18a b - 4a +--R * +--R 3 +--R c +--R + +--R 5 9 6 8 7 7 8 6 9 5 10 4 +--R 42a b - 28a b - 140a b + 84a b + 168a b - 84a b +--R + +--R 11 3 12 2 13 +--R - 84a b + 28a b + 14a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 4 11 +--R (6a b - 4a b - 2a )c +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (18a b - 12a b - 4a b - 4a b + 2a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 7 +--R (18a b - 12a b + 18a b - 24a b - 28a b + 24a b + 4a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 6a b - 4a b + 40a b - 36a b - 66a b + 48a b + 24a b +--R + +--R 9 10 +--R - 8a b - 4a +--R * +--R 5 +--R c +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 20a b - 16a b - 22a b + 12a b - 18a b + 24a b + 22a b +--R + +--R 11 12 +--R - 20a b - 2a +--R * +--R 3 +--R c +--R + +--R 6 8 7 7 8 6 9 5 10 4 11 3 +--R 14a b - 12a b - 44a b + 36a b + 48a b - 36a b +--R + +--R 12 2 13 14 +--R - 20a b + 12a b + 2a +--R * +--R c +--R * +--R cos(x) +--R + +--R 3 4 11 3 3 4 2 5 6 9 +--R (2a b - 2a )c + (6a b - 6a b - 2a b + 2a )c +--R + +--R 3 5 4 4 7 8 7 +--R (6a b - 6a b - 4a b + 4a )c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 5 +--R (2a b - 2a b + 6a b - 6a b - 12a b + 12a b + 4a b - 4a )c +--R + +--R 5 7 6 6 7 5 8 4 11 12 3 +--R (4a b - 4a b - 6a b + 6a b + 2a b - 2a )c +--R + +--R 7 7 8 6 9 5 10 4 11 3 12 2 13 14 +--R (2a b - 2a b - 6a b + 6a b + 6a b - 6a b - 2a b + 2a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 12 5 4 2 3 3 2 10 +--R (16b - 16a b )c + (48b - 48a b - 48a b + 48a b )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 8 +--R (48b - 48a b - 96a b + 96a b + 48a b - 48a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 16b - 16a b - 48a b + 48a b + 48a b - 48a b +--R + +--R 6 3 7 2 +--R - 16a b + 16a b +--R * +--R 6 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 12 4 2 3 3 2 4 10 +--R (32a b - 32a b)c + (96a b - 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192a b +--R + +--R 6 4 7 3 +--R - 64a b + 64a b +--R * +--R 5 +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 13 +--R (- 16b - 48a b + 16a )c +--R + +--R 4 3 2 2 3 4 11 +--R (- 48b + 48a b - 96a b + 144a b - 48a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 48b + 432a b - 432a b - 288a b + 432a b - 144a b +--R + +--R 6 +--R 48a +--R * +--R 9 +--R c +--R + +--R 8 7 2 6 3 5 4 4 +--R - 16b + 528a b - 512a b - 1008a b + 1056a b +--R + +--R 5 3 6 2 7 8 +--R 432a b - 512a b + 48a b - 16a +--R * +--R 7 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 192a b - 192a b - 576a b + 576a b + 576a b - 576a b +--R + +--R 7 3 8 2 +--R - 192a b + 192a b +--R * +--R 5 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 13 +--R (16b - 48a b - 16a )c +--R + +--R 4 3 2 2 3 4 11 +--R (48b - 144a b + 96a b - 48a b + 48a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 48b - 144a b + 432a b - 288a b - 432a b + 432a b +--R + +--R 6 +--R - 48a +--R * +--R 9 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 16b - 48a b + 512a b - 432a b - 1056a b + 1008a b +--R + +--R 6 2 7 8 +--R 512a b - 528a b + 16a +--R * +--R 7 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 192a b - 192a b - 576a b + 576a b + 576a b - 576a b +--R + +--R 8 2 9 +--R - 192a b + 192a b +--R * +--R 5 +--R c +--R * +--R cos(x) +--R + +--R 2 13 3 2 2 3 4 11 +--R (16a b - 32a )c + (48a b - 96a b + 16a b + 32a )c +--R + +--R 5 2 4 3 3 5 6 9 +--R (48a b - 96a b + 96a b - 144a b + 96a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 16a b - 32a b + 144a b - 96a b - 336a b + 288a b +--R + +--R 7 8 +--R 176a b - 160a +--R * +--R 7 +--R c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R 64a b - 64a b - 192a b + 192a b + 192a b - 192a b +--R + +--R 9 10 +--R - 64a b + 64a +--R * +--R 5 +--R c +--R * +--R 5 +--R sin(x) +--R + +--R 14 3 2 2 3 12 +--R (20b - 4a)c + (- 60b + 44a b - 60a b + 12a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (- 200b + 56a b + 240a b - 144a b + 60a b - 12a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 40b - 136a b + 360a b - 24a b - 300a b + 156a b +--R + +--R 6 7 +--R - 20a b + 4a +--R * +--R 8 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 180b - 244a b - 240a b + 432a b - 60a b - 132a b +--R + +--R 6 3 7 2 +--R 120a b - 56a b +--R * +--R 6 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 100b - 100a b - 300a b + 300a b + 300a b - 300a b +--R + +--R 6 5 7 4 +--R - 100a b + 100a b +--R * +--R 4 +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 14 3 2 2 3 12 +--R (16b + 16a)c + (- 16b - 256a b + 64a b - 48a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (- 144b - 464a b + 32a b + 816a b - 288a b + 48a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 176b + 304a b - 528a b + 576a b + 384a b - 864a b +--R + +--R 6 7 +--R 320a b - 16a +--R * +--R 8 +--R c +--R + +--R 9 8 2 7 3 6 4 5 +--R - 64b + 896a b - 896a b - 1488a b + 1872a b +--R + +--R 5 4 6 3 7 2 8 +--R 288a b - 800a b + 304a b - 112a b +--R * +--R 6 +--R c +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 400a b - 400a b - 1200a b + 1200a b + 1200a b +--R + +--R 6 5 7 4 8 3 +--R - 1200a b - 400a b + 400a b +--R * +--R 4 +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 14 3 2 2 3 12 +--R (- 24b + 24a)c + (- 16b - 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28a b - 84a b + 84a b + 84a b - 84a b +--R + +--R 7 7 8 6 +--R - 28a b + 28a b +--R * +--R c +--R * +--R 6 +--R cos(x) +--R + +--R 2 2 13 +--R (24b - 24a b - 12a )c +--R + +--R 4 3 2 2 3 4 11 +--R (24b + 96a b + 144a b + 60a b + 36a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 64b + 256a b + 220a b - 316a b - 612a b - 36a b +--R + +--R 6 +--R - 36a +--R * +--R 9 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 96b - 48a b - 480a b - 288a b - 48a b + 264a b +--R + +--R 6 2 7 8 +--R 696a b - 12a b + 12a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 +--R - 24b - 360a b - 900a b + 528a b + 1872a b +--R + +--R 5 5 6 4 7 3 8 2 9 +--R - 216a b - 696a b + 36a b - 252a b + 12a b +--R * +--R 5 +--R c +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 8b - 176a b - 272a b + 356a b + 1020a b - 264a b +--R + +--R 6 6 7 5 8 4 9 3 +--R - 1256a b + 164a b + 500a b - 80a b +--R * +--R 3 +--R c +--R + +--R 2 12 3 11 4 10 5 9 6 8 +--R 84a b - 84a b - 252a b + 252a b + 252a b +--R + +--R 7 7 8 6 9 5 +--R - 252a b - 84a b + 84a b +--R * +--R c +--R * +--R 5 +--R cos(x) +--R + +--R 2 2 13 +--R (24b + 48a b - 12a )c +--R + +--R 4 3 2 2 3 4 11 +--R (32b - 40a b + 156a b + 20a b + 32a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 48b - 368a b + 272a b + 116a b - 580a b - 348a b +--R + +--R 6 +--R - 24a +--R * +--R 9 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 96b - 384a b - 432a b - 448a b - 128a b + 528a b +--R + +--R 6 2 7 +--R 516a b + 444a b +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 +--R - 40b - 64a b - 996a b - 1024a b + 1664a b +--R + +--R 5 5 6 4 7 3 8 2 9 10 +--R 2496a b - 596a b - 1244a b - 36a b - 164a b + 4a +--R * +--R 5 +--R c +--R + +--R 11 2 10 3 9 4 8 5 7 +--R 40a b - 460a b - 340a b + 1040a b + 1200a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R - 780a b - 1540a b + 280a b + 640a b - 80a b +--R * +--R 3 +--R c +--R + +--R 3 11 4 10 5 9 6 8 7 7 +--R 140a b - 140a b - 420a b + 420a b + 420a b +--R + +--R 8 6 9 5 10 4 +--R - 420a b - 140a b + 140a b +--R * +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 13 +--R (- 12b + 48a b + 24a )c +--R + +--R 4 3 2 2 3 4 11 +--R (- 32b - 20a b - 156a b + 40a b - 32a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 24b - 348a b - 580a b + 116a b + 272a b - 368a b +--R + +--R 6 +--R - 48a +--R * +--R 9 +--R c +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 444a b - 516a b - 528a b + 128a b + 448a b +--R + +--R 6 2 7 8 +--R 432a b + 384a b + 96a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 4b - 164a b - 36a b - 1244a b - 596a b + 2496a b +--R + +--R 6 4 7 3 8 2 9 10 +--R 1664a b - 1024a b - 996a b - 64a b - 40a +--R * +--R 5 +--R c +--R + +--R 2 10 3 9 4 8 5 7 6 6 +--R 80a b - 640a b - 280a b + 1540a b + 780a b +--R + +--R 7 5 8 4 9 3 10 2 11 +--R - 1200a b - 1040a b + 340a b + 460a b - 40a b +--R * +--R 3 +--R c +--R + +--R 4 10 5 9 6 8 7 7 8 6 +--R 140a b - 140a b - 420a b + 420a b + 420a b +--R + +--R 9 5 10 4 11 3 +--R - 420a b - 140a b + 140a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 13 +--R (- 12b - 24a b + 24a )c +--R + +--R 4 3 2 2 3 4 11 +--R (- 36b - 60a b - 144a b - 96a b - 24a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 36b - 36a b - 612a b - 316a b + 220a b + 256a b +--R + +--R 6 +--R - 64a +--R * +--R 9 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 12b + 12a b - 696a b - 264a b + 48a b + 288a b +--R + +--R 6 2 7 8 +--R 480a b + 48a b + 96a +--R * +--R 7 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 12a b - 252a b + 36a b - 696a b - 216a b + 1872a b +--R + +--R 7 3 8 2 9 10 +--R 528a b - 900a b - 360a b - 24a +--R * +--R 5 +--R c +--R + +--R 3 9 4 8 5 7 6 6 7 5 +--R 80a b - 500a b - 164a b + 1256a b + 264a b +--R + +--R 8 4 9 3 10 2 11 12 +--R - 1020a b - 356a b + 272a b + 176a b - 8a +--R * +--R 3 +--R c +--R + +--R 5 9 6 8 7 7 8 6 9 5 10 4 +--R 84a b - 84a b - 252a b + 252a b + 252a b - 252a b +--R + +--R 11 3 12 2 +--R - 84a b + 84a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 13 3 2 2 3 4 11 +--R (- 24a b - 12a )c + (- 72a b - 24a b - 100a b - 4a )c +--R + +--R 5 3 3 4 2 5 6 9 +--R (- 72a b - 372a b - 44a b + 236a b + 56a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 24a b + 24a b - 444a b - 36a b + 336a b + 64a b +--R + +--R 7 8 +--R 104a b - 24a +--R * +--R 7 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R 12a b - 172a b + 44a b - 108a b - 84a b + 648a b +--R + +--R 8 2 9 10 +--R 72a b - 368a b - 44a +--R * +--R 5 +--R c +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 +--R 40a b - 208a b - 64a b + 540a b + 36a b - 456a b +--R + +--R 10 2 11 12 +--R - 40a b + 124a b + 28a +--R * +--R 3 +--R c +--R + +--R 6 8 7 7 8 6 9 5 10 4 11 3 +--R 28a b - 28a b - 84a b + 84a b + 84a b - 84a b +--R + +--R 12 2 13 +--R - 28a b + 28a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 13 2 2 3 4 11 +--R - 12a c + (- 36a b + 4a b - 8a )c +--R + +--R 2 4 3 3 4 2 5 6 9 +--R (- 36a b + 12a b - 60a b - 4a b + 60a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 7 +--R (- 12a b + 12a b - 96a b + 120a b - 8a b - 16a )c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 4a b - 44a b + 12a b + 24a b - 24a b + 72a b + 8a b +--R + +--R 10 +--R - 52a +--R * +--R 5 +--R c +--R + +--R 5 7 6 6 7 5 8 4 10 2 11 12 3 +--R (8a b - 36a b - 12a b + 96a b - 84a b + 4a b + 24a )c +--R + +--R 7 7 8 6 9 5 10 4 11 3 12 2 13 +--R 4a b - 4a b - 12a b + 12a b + 12a b - 12a b - 4a b +--R + +--R 14 +--R 4a +--R * +--R c +--R * +--R sin(x) +--R + +--R 3 12 5 2 3 10 7 4 3 8 +--R - 4b c + (- 4b + 12a b )c + (8b - 12a b )c +--R + +--R 9 2 7 4 5 6 3 6 11 4 7 6 5 4 +--R (8b - 24a b + 12a b + 4a b )c + (- 4b + 12a b - 8a b )c +--R + +--R 13 2 11 4 9 6 7 2 +--R (- 4b + 12a b - 12a b + 4a b )c +--R * +--R 8 +--R cos(x) +--R + +--R 3 2 12 5 4 2 3 3 2 10 +--R (- 4b - 12a b )c + (- 4b + 4a b + 12a b + 36a b )c +--R + +--R 7 6 3 4 4 3 5 2 8 +--R (8b + 56a b - 48a b - 12a b - 36a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 8b + 24a b - 24a b - 120a b + 12a b + 84a b + 4a b +--R + +--R 7 2 +--R 12a b +--R * +--R 6 +--R c +--R + +--R 11 10 3 8 4 7 5 6 6 5 7 4 4 +--R (- 4b - 44a b + 48a b + 12a b + 36a b - 8a b - 40a b )c +--R + +--R 13 12 2 11 3 10 4 9 5 8 +--R - 4b - 28a b + 12a b + 84a b - 12a b - 84a b +--R + +--R 6 7 7 6 +--R 4a b + 28a b +--R * +--R 2 +--R c +--R * +--R 7 +--R cos(x) +--R + +--R 3 2 2 12 +--R (8b - 12a b - 12a b)c +--R + +--R 5 4 2 3 3 2 4 10 +--R (16b + 4a b + 20a b + 36a b + 36a b)c +--R + +--R 6 2 5 3 4 4 3 5 2 6 8 +--R (56a b + 96a b - 48a b - 144a b - 36a b - 36a b)c +--R + +--R 9 8 3 6 4 5 5 4 6 3 +--R - 16b + 24a b - 120a b - 192a b + 84a b + 196a b +--R + +--R 7 2 8 +--R 12a b + 12a b +--R * +--R 6 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 8b - 44a b - 148a b + 48a b + 240a b + 36a b +--R + +--R 6 5 7 4 8 3 +--R - 4a b - 40a b - 80a b +--R * +--R 4 +--R c +--R + +--R 12 2 11 3 10 4 9 5 8 6 7 +--R - 28a b - 84a b + 84a b + 252a b - 84a b - 252a b +--R + +--R 7 6 8 5 +--R 28a b + 84a b +--R * +--R 2 +--R c +--R * +--R 6 +--R cos(x) +--R + +--R 3 2 2 3 12 +--R (8b + 24a b - 12a b - 4a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (16b + 32a b + 20a b - 4a b + 36a b + 12a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 8 +--R (- 48a b + 96a b + 64a b - 144a b - 144a b - 36a b - 12a )c +--R + +--R 9 8 3 6 4 5 5 4 6 3 +--R - 16b - 96a b - 16a b - 192a b - 96a b + 196a b +--R + +--R 7 2 8 9 +--R 204a b + 12a b + 4a +--R * +--R 6 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 8b - 40a b - 148a b - 220a b + 240a b + 480a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 4a b - 140a b - 80a b - 80a b +--R * +--R 4 +--R c +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R - 84a b - 140a b + 252a b + 420a b - 252a b - 420a b +--R + +--R 8 5 9 4 +--R 84a b + 140a b +--R * +--R 2 +--R c +--R * +--R 5 +--R cos(x) +--R + +--R 3 2 2 3 12 +--R (- 4b + 24a b + 24a b - 4a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (- 12b + 32a b + 4a b - 4a b - 32a b + 12a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 12b - 48a b - 144a b + 64a b + 64a b - 144a b - 48a b +--R + +--R 7 +--R - 12a +--R * +--R 8 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 4b - 96a b - 204a b - 16a b + 96a b - 96a b + 16a b +--R + +--R 7 2 8 9 +--R 204a b + 96a b + 4a +--R * +--R 6 +--R c +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R - 40a b - 80a b - 220a b - 140a b + 480a b + 480a b +--R + +--R 7 4 8 3 9 2 10 +--R - 140a b - 220a b - 80a b - 40a b +--R * +--R 4 +--R c +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 +--R - 140a b - 140a b + 420a b + 420a b - 420a b - 420a b +--R + +--R 9 4 10 3 +--R 140a b + 140a b +--R * +--R 2 +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 12 +--R (- 4b - 12a b + 24a b + 8a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (- 12b - 36a b + 4a b - 20a b - 32a b - 16a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 8 +--R (- 12b - 36a b - 144a b - 144a b + 64a b + 96a b - 48a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 4b - 12a b - 204a b - 196a b + 96a b + 192a b +--R + +--R 6 3 8 9 +--R 16a b + 96a b + 16a +--R * +--R 6 +--R c +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 +--R - 80a b - 80a b - 140a b - 4a b + 480a b + 240a b +--R + +--R 8 3 9 2 10 11 +--R - 220a b - 148a b - 40a b - 8a +--R * +--R 4 +--R c +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R - 140a b - 84a b + 420a b + 252a b - 420a b - 252a b +--R + +--R 10 3 11 2 +--R 140a b + 84a b +--R * +--R 2 +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 12 +--R (- 12a b - 12a b + 8a )c +--R + +--R 4 2 3 3 2 4 5 10 +--R (- 36a b - 36a b - 20a b - 4a b - 16a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 8 +--R (- 36a b - 36a b - 144a b - 48a b + 96a b + 56a b)c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 12a b - 12a b - 196a b - 84a b + 192a b + 120a b +--R + +--R 8 9 +--R - 24a b + 16a +--R * +--R 6 +--R c +--R + +--R 3 8 4 7 5 6 6 5 7 4 8 3 +--R - 80a b - 40a b - 4a b + 36a b + 240a b + 48a b +--R + +--R 9 2 10 11 +--R - 148a b - 44a b - 8a +--R * +--R 4 +--R c +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 +--R - 84a b - 28a b + 252a b + 84a b - 252a b - 84a b +--R + +--R 11 2 12 +--R 84a b + 28a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 12 2 3 3 2 4 5 10 +--R (- 12a b - 4a )c + (- 36a b - 12a b - 4a b + 4a )c +--R + +--R 2 5 3 4 4 3 6 7 8 +--R (- 36a b - 12a b - 48a b + 56a b + 8a )c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R - 12a b - 4a b - 84a b - 12a b + 120a b + 24a b - 24a b +--R + +--R 9 +--R - 8a +--R * +--R 6 +--R c +--R + +--R 4 7 5 6 6 5 7 4 8 3 10 11 4 +--R (- 40a b - 8a b + 36a b + 12a b + 48a b - 44a b - 4a )c +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 +--R - 28a b - 4a b + 84a b + 12a b - 84a b - 12a b +--R + +--R 12 13 +--R 28a b + 4a +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 3 12 3 2 5 10 3 4 7 8 +--R - 4a c + (- 12a b + 4a )c + (- 12a b + 8a )c +--R + +--R 3 6 5 4 7 2 9 6 5 6 7 4 11 4 +--R (- 4a b - 12a b + 24a b - 8a )c + (- 8a b + 12a b - 4a )c +--R + +--R 7 6 9 4 11 2 13 2 +--R (- 4a b + 12a b - 12a b + 4a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 11 6 2 4 4 2 9 +--R (8b - 8a b )c + (24b - 48a b + 24a b )c +--R + +--R 8 2 6 4 4 6 2 7 +--R (24b - 72a b + 72a b - 24a b )c +--R + +--R 10 2 8 4 6 6 4 8 2 5 +--R (8b - 32a b + 48a b - 32a b + 8a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 3 11 5 3 3 5 9 +--R (16a b - 16a b)c + (48a b - 96a b + 48a b)c +--R + +--R 7 3 5 5 3 7 7 +--R (48a b - 144a b + 144a b - 48a b)c +--R + +--R 9 3 7 5 5 7 3 9 5 +--R (16a b - 64a b + 96a b - 64a b + 16a b)c +--R * +--R cos(x) +--R + +--R 2 2 4 11 2 4 4 2 6 9 +--R (8a b - 8a )c + (24a b - 48a b + 24a )c +--R + +--R 2 6 4 4 6 2 8 7 +--R (24a b - 72a b + 72a b - 24a )c +--R + +--R 2 8 4 6 6 4 8 2 10 5 +--R (8a b - 32a b + 48a b - 32a b + 8a )c +--R * +--R 6 +--R sin(x) +--R + +--R 3 2 2 12 +--R (- 16b - 8a b + 8a b)c +--R + +--R 5 4 2 3 3 2 4 10 +--R (- 16b - 24a b + 40a b + 24a b - 24a b)c +--R + +--R 7 6 2 5 3 4 5 2 6 8 +--R (48b - 24a b - 72a b + 48a b - 24a b + 24a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 80b - 8a b - 232a b + 24a b + 216a b - 24a b - 56a b +--R + +--R 7 2 8 +--R 8a b - 8a b +--R * +--R 6 +--R c +--R + +--R 11 2 9 4 7 6 5 8 3 4 +--R (32b - 128a b + 192a b - 128a b + 32a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 3 2 2 3 12 +--R (- 8b - 32a b - 16a b + 8a )c +--R + +--R 5 2 3 3 2 4 5 10 +--R (- 24b - 24a b + 24a b + 48a b - 24a )c +--R + +--R 7 6 3 4 4 3 5 2 6 7 8 +--R (- 24b + 192a b - 360a b + 72a b + 144a b - 48a b + 24a )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R - 8b + 256a b + 8a b - 760a b + 24a b + 744a b - 40a b +--R + +--R 7 2 8 9 +--R - 232a b + 16a b - 8a +--R * +--R 6 +--R c +--R + +--R 10 3 8 5 6 7 4 9 2 4 +--R (96a b - 384a b + 576a b - 384a b + 96a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 12 +--R (8b - 16a b - 32a b - 8a )c +--R + +--R 5 4 2 3 3 2 5 10 +--R (24b - 48a b - 24a b + 24a b + 24a )c +--R + +--R 7 6 2 5 3 4 4 3 6 7 8 +--R (24b - 48a b + 144a b + 72a b - 360a b + 192a b - 24a )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 8b - 16a b + 232a b + 40a b - 744a b - 24a b + 760a b +--R + +--R 7 2 8 9 +--R - 8a b - 256a b + 8a +--R * +--R 6 +--R c +--R + +--R 2 9 4 7 6 5 8 3 10 4 +--R (96a b - 384a b + 576a b - 384a b + 96a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 12 +--R (8a b - 8a b - 16a )c +--R + +--R 4 2 3 3 2 4 5 10 +--R (24a b - 24a b - 40a b + 24a b + 16a )c +--R + +--R 6 2 5 4 3 5 2 6 7 8 +--R (24a b - 24a b + 48a b - 72a b - 24a b + 48a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 8a b - 8a b + 56a b + 24a b - 216a b - 24a b + 232a b +--R + +--R 8 9 +--R 8a b - 80a +--R * +--R 6 +--R c +--R + +--R 3 8 5 6 7 4 9 2 11 4 +--R (32a b - 128a b + 192a b - 128a b + 32a )c +--R * +--R 5 +--R sin(x) +--R + +--R 2 2 13 +--R (10b + 8a b - 2a )c +--R + +--R 4 3 2 2 3 4 11 +--R (- 30b - 8a b - 8a b - 24a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 9 +--R (- 100b - 72a b + 148a b + 48a b - 42a b + 24a b - 6a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 20b - 88a b + 112a b + 168a b - 162a b - 72a b +--R + +--R 6 2 7 8 +--R 68a b - 8a b + 2a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R 90b - 32a b - 242a b + 96a b + 186a b - 96a b - 6a b +--R + +--R 7 3 8 2 +--R 32a b - 28a b +--R * +--R 5 +--R c +--R + +--R 12 2 10 4 8 6 6 8 4 3 +--R (50b - 200a b + 300a b - 200a b + 50a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 13 +--R (8b + 16a b + 8a )c +--R + +--R 4 3 2 2 3 4 11 +--R (- 8b - 136a b - 96a b + 8a b - 24a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 72b - 304a b - 216a b + 424a b + 264a b - 120a b +--R + +--R 6 +--R 24a +--R * +--R 9 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 88b + 64a b - 112a b + 24a b + 480a b - 240a b +--R + +--R 6 2 7 8 +--R - 272a b + 152a b - 8a +--R * +--R 7 +--R c +--R + +--R 10 9 3 7 4 6 5 5 6 4 +--R - 32b + 416a b - 1192a b + 192a b + 1080a b - 256a b +--R + +--R 7 3 8 2 9 +--R - 248a b + 96a b - 56a b +--R * +--R 5 +--R c +--R + +--R 11 3 9 5 7 7 5 9 3 3 +--R (200a b - 800a b + 1200a b - 800a b + 200a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 13 4 3 2 2 3 4 11 +--R (- 12b + 12a )c + (- 8b - 96a b - 176a b - 96a b - 8a )c +--R + +--R 6 5 2 4 4 2 5 6 9 +--R (48b - 288a b - 420a b + 420a b + 288a b - 48a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 72b - 288a b + 36a b + 288a b - 216a b + 288a b +--R + +--R 6 2 7 8 +--R 36a b - 288a b + 72a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 6 4 +--R 28b - 96a b + 568a b + 192a b - 1844a b + 1844a b +--R + +--R 7 3 8 2 9 10 +--R - 192a b - 568a b + 96a b - 28a +--R * +--R 5 +--R c +--R + +--R 2 10 4 8 6 6 8 4 10 2 3 +--R (300a b - 1200a b + 1800a b - 1200a b + 300a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 13 +--R (- 8b - 16a b - 8a )c +--R + +--R 4 3 2 2 3 4 11 +--R (- 24b + 8a b - 96a b - 136a b - 8a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 24b + 120a b - 264a b - 424a b + 216a b + 304a b +--R + +--R 6 +--R 72a +--R * +--R 9 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 8b + 152a b - 272a b - 240a b + 480a b + 24a b +--R + +--R 6 2 7 8 +--R - 112a b + 64a b - 88a +--R * +--R 7 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 56a b - 96a b + 248a b + 256a b - 1080a b - 192a b +--R + +--R 7 3 9 10 +--R 1192a b - 416a b + 32a +--R * +--R 5 +--R c +--R + +--R 3 9 5 7 7 5 9 3 11 3 +--R (200a b - 800a b + 1200a b - 800a b + 200a b)c +--R * +--R cos(x) +--R + +--R 2 2 13 4 3 2 2 3 4 11 +--R (2b - 8a b - 10a )c + (6b - 24a b - 8a b - 8a b - 30a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 9 +--R (6b - 24a b + 42a b - 48a b - 148a b + 72a b + 100a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R 2b - 8a b + 68a b - 72a b - 162a b + 168a b + 112a b +--R + +--R 7 8 +--R - 88a b - 20a +--R * +--R 7 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 28a b - 32a b + 6a b + 96a b - 186a b - 96a b + 242a b +--R + +--R 9 10 +--R 32a b - 90a +--R * +--R 5 +--R c +--R + +--R 4 8 6 6 8 4 10 2 12 3 +--R (50a b - 200a b + 300a b - 200a b + 50a )c +--R * +--R 4 +--R sin(x) +--R + +--R 14 3 2 3 12 +--R (- 2b - 2a)c + (28b + 22a b + 6a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (10b + 28a b - 72a b - 72a b + 12a b - 6a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 120b - 68a b + 112a b - 12a b + 24a b + 78a b - 16a b +--R + +--R 7 +--R 2a +--R * +--R 8 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 110b - 122a b + 288a b + 216a b - 240a b - 66a b +--R + +--R 6 3 7 2 8 +--R 56a b - 28a b + 6a b +--R * +--R 6 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 28b - 50a b - 48a b + 150a b - 24a b - 150a b +--R + +--R 6 5 7 4 8 3 +--R 80a b + 50a b - 36a b +--R * +--R 4 +--R c +--R + +--R 13 2 11 4 9 6 7 8 5 2 +--R (38b - 152a b + 228a b - 152a b + 38a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 14 3 2 2 12 +--R (- 2b - 2a)c + (22b + 84a b + 62a b)c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (28b - 94a b - 104a b - 168a b - 174a b + 12a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 68b - 616a b - 444a b + 656a b + 342a b - 24a b +--R + +--R 6 7 +--R 170a b - 16a +--R * +--R 8 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 122b - 414a b - 328a b + 1056a b + 966a b - 864a b +--R + +--R 6 3 7 2 8 9 +--R - 460a b + 216a b - 56a b + 6a +--R * +--R 6 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 50b + 212a b - 50a b - 528a b + 450a b + 312a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 550a b + 112a b + 200a b - 108a b +--R * +--R 4 +--R c +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (190a b - 760a b + 1140a b - 760a b + 190a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 14 3 2 2 3 12 +--R (4b + 4a)c + (- 28b + 40a b + 84a b + 16a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (- 72b - 104a b - 260a b - 324a b - 168a b - 72a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 8b - 512a b - 1144a b - 396a b + 1192a b + 828a b +--R + +--R 6 7 +--R - 40a b + 80a +--R * +--R 8 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 68b - 572a b - 792a b + 244a b + 1608a b + 1200a b +--R + +--R 6 3 7 2 8 9 +--R - 1112a b - 844a b + 228a b - 28a +--R * +--R 6 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 36b - 200a b + 388a b + 300a b - 1272a b + 300a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R 1128a b - 700a b - 172a b + 300a b - 108a b +--R * +--R 4 +--R c +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (380a b - 1520a b + 2280a b - 1520a b + 380a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 14 3 2 2 3 12 +--R (4b + 4a)c + (- 16b - 84a b - 40a b + 28a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (- 72b - 168a b - 324a b - 260a b - 104a b - 72a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 80b + 40a b - 828a b - 1192a b + 396a b + 1144a b +--R + +--R 6 7 +--R 512a b + 8a +--R * +--R 8 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 28b + 228a b - 844a b - 1112a b + 1200a b + 1608a b +--R + +--R 6 3 7 2 8 9 +--R 244a b - 792a b - 572a b + 68a +--R * +--R 6 +--R c +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 108a b - 300a b + 172a b + 700a b - 1128a b - 300a b +--R + +--R 7 4 8 3 9 2 10 11 +--R 1272a b - 300a b - 388a b + 200a b - 36a +--R * +--R 4 +--R c +--R + +--R 3 10 5 8 7 6 9 4 11 2 2 +--R (380a b - 1520a b + 2280a b - 1520a b + 380a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 14 2 2 3 12 +--R (- 2b - 2a)c + (- 62a b - 84a b - 22a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (12b - 174a b - 168a b - 104a b - 94a b + 28a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 16b - 170a b + 24a b - 342a b - 656a b + 444a b +--R + +--R 6 7 +--R 616a b + 68a +--R * +--R 8 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 6b - 56a b + 216a b - 460a b - 864a b + 966a b +--R + +--R 6 3 7 2 8 9 +--R 1056a b - 328a b - 414a b - 122a +--R * +--R 6 +--R c +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 +--R 108a b - 200a b - 112a b + 550a b - 312a b - 450a b +--R + +--R 8 3 9 2 10 11 +--R 528a b + 50a b - 212a b + 50a +--R * +--R 4 +--R c +--R + +--R 4 9 6 7 8 5 10 3 12 2 +--R (190a b - 760a b + 1140a b - 760a b + 190a b)c +--R * +--R cos(x) +--R + +--R 14 3 2 3 12 +--R (- 2b - 2a)c + (- 6b - 22a b - 28a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (- 6b + 12a b - 72a b - 72a b + 28a b + 10a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 2b + 16a b - 78a b - 24a b + 12a b - 112a b + 68a b +--R + +--R 7 +--R 120a +--R * +--R 8 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 6a b - 28a b + 56a b - 66a b - 240a b + 216a b + 288a b +--R + +--R 8 9 +--R - 122a b - 110a +--R * +--R 6 +--R c +--R + +--R 3 8 4 7 5 6 6 5 7 4 8 3 9 2 +--R 36a b - 50a b - 80a b + 150a b + 24a b - 150a b + 48a b +--R + +--R 10 11 +--R 50a b - 28a +--R * +--R 4 +--R c +--R + +--R 5 8 7 6 9 4 11 2 13 2 +--R (38a b - 152a b + 228a b - 152a b + 38a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 13 4 3 2 2 3 11 +--R (- 6b - 6a b)c + (24b + 18a b + 12a b + 18a b)c +--R + +--R 6 5 2 4 3 3 5 9 +--R (50b + 52a b - 88a b - 72a b - 18a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 40b - 12a b - 32a b - 84a b + 84a b + 90a b - 12a b +--R + +--R 7 +--R 6a b +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R - 90b - 78a b + 192a b + 120a b - 108a b - 6a b +--R + +--R 7 3 8 2 +--R - 36a b + 6a b +--R * +--R 5 +--R c +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R - 16b - 38a b + 68a b + 114a b - 108a b - 114a b +--R + +--R 6 6 7 5 8 4 +--R 76a b + 38a b - 20a b +--R * +--R 3 +--R c +--R + +--R 14 2 12 4 10 6 8 8 6 +--R (14b - 56a b + 84a b - 56a b + 14a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 2 2 13 +--R (- 6b - 12a b - 6a )c +--R + +--R 4 3 2 2 3 4 11 +--R (18b + 120a b + 108a b + 24a b + 18a )c +--R + +--R 6 5 2 4 3 3 4 2 6 9 +--R (52b + 124a b + 44a b - 352a b - 306a b - 18a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 12b - 384a b - 336a b + 144a b + 30a b + 264a b +--R + +--R 6 2 7 8 +--R 312a b - 24a b + 6a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R - 78b - 516a b - 342a b + 1104a b + 810a b - 648a b +--R + +--R 6 4 7 3 8 2 9 +--R - 282a b + 48a b - 108a b + 12a b +--R * +--R 5 +--R c +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R - 38b - 56a b - 76a b + 248a b + 456a b - 408a b +--R + +--R 6 6 7 5 8 4 9 3 +--R - 532a b + 296a b + 190a b - 80a b +--R * +--R 3 +--R c +--R + +--R 13 3 11 5 9 7 7 9 5 +--R (84a b - 336a b + 504a b - 336a b + 84a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 2 2 13 +--R (12b + 6a b - 6a )c +--R + +--R 4 3 2 2 3 4 11 +--R (- 12b + 90a b + 180a b + 90a b + 12a )c +--R + +--R 6 5 2 4 3 3 4 2 5 9 +--R (- 88b + 44a b + 46a b - 308a b - 528a b - 306a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 72b - 348a b - 1032a b - 696a b + 768a b + 726a b +--R + +--R 6 2 7 8 +--R 348a b + 318a b - 12a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 12b - 498a b - 1242a b - 108a b + 2568a b + 1602a b +--R + +--R 6 4 7 3 8 2 9 10 +--R - 1452a b - 888a b + 108a b - 108a b + 6a +--R * +--R 5 +--R c +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 20b - 190a b - 140a b + 190a b + 420a b + 570a b +--R + +--R 6 6 7 5 8 4 9 3 10 2 +--R - 620a b - 950a b + 440a b + 380a b - 120a b +--R * +--R 3 +--R c +--R + +--R 2 12 4 10 6 8 8 6 10 4 +--R (210a b - 840a b + 1260a b - 840a b + 210a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 13 3 3 11 +--R (12b + 24a b + 12a )c + (- 96a b + 96a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 6 9 +--R (- 72b - 352a b - 308a b - 56a b - 308a b - 352a b - 72a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R - 96b - 240a b - 948a b - 1280a b + 1280a b + 948a b +--R + +--R 7 8 +--R 240a b + 96a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R - 36b + 72a b - 1032a b - 1728a b + 1068a b + 3312a b +--R + +--R 6 4 7 3 8 2 9 10 +--R 1068a b - 1728a b - 1032a b + 72a b - 36a +--R * +--R 5 +--R c +--R + +--R 11 2 10 3 9 4 8 5 7 7 5 +--R 80a b - 380a b - 320a b + 760a b + 560a b - 560a b +--R + +--R 8 4 9 3 10 2 11 +--R - 760a b + 320a b + 380a b - 80a b +--R * +--R 3 +--R c +--R + +--R 3 11 5 9 7 7 9 5 11 3 +--R (280a b - 1120a b + 1680a b - 1120a b + 280a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 13 +--R (- 6b + 6a b + 12a )c +--R + +--R 4 3 2 2 3 4 11 +--R (- 12b - 90a b - 180a b - 90a b + 12a )c +--R + +--R 5 2 4 3 3 4 2 5 6 9 +--R (- 306a b - 528a b - 308a b + 46a b + 44a b - 88a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 12b - 318a b - 348a b - 726a b - 768a b + 696a b +--R + +--R 6 2 7 8 +--R 1032a b + 348a b + 72a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 6b - 108a b + 108a b - 888a b - 1452a b + 1602a b +--R + +--R 6 4 7 3 8 2 9 10 +--R 2568a b - 108a b - 1242a b - 498a b + 12a +--R * +--R 5 +--R c +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R 120a b - 380a b - 440a b + 950a b + 620a b - 570a b +--R + +--R 8 4 9 3 10 2 11 12 +--R - 420a b - 190a b + 140a b + 190a b - 20a +--R * +--R 3 +--R c +--R + +--R 4 10 6 8 8 6 10 4 12 2 +--R (210a b - 840a b + 1260a b - 840a b + 210a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 13 +--R (- 6b - 12a b - 6a )c +--R + +--R 4 3 2 2 3 4 11 +--R (- 18b - 24a b - 108a b - 120a b - 18a )c +--R + +--R 6 2 4 3 3 4 2 5 6 9 +--R (- 18b - 306a b - 352a b + 44a b + 124a b + 52a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 6b + 24a b - 312a b - 264a b - 30a b - 144a b +--R + +--R 6 2 7 8 +--R 336a b + 384a b + 12a +--R * +--R 7 +--R c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R 12a b - 108a b + 48a b - 282a b - 648a b + 810a b +--R + +--R 7 3 8 2 9 10 +--R 1104a b - 342a b - 516a b - 78a +--R * +--R 5 +--R c +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 +--R 80a b - 190a b - 296a b + 532a b + 408a b - 456a b +--R + +--R 9 3 10 2 11 12 +--R - 248a b + 76a b + 56a b + 38a +--R * +--R 3 +--R c +--R + +--R 5 9 7 7 9 5 11 3 13 +--R (84a b - 336a b + 504a b - 336a b + 84a b)c +--R * +--R cos(x) +--R + +--R 2 13 3 2 2 3 4 11 +--R (- 6a b - 6a )c + (- 18a b - 12a b - 18a b - 24a )c +--R + +--R 5 3 3 4 2 5 6 9 +--R (- 18a b - 72a b - 88a b + 52a b + 50a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R - 6a b + 12a b - 90a b - 84a b + 84a b + 32a b + 12a b +--R + +--R 8 +--R 40a +--R * +--R 7 +--R c +--R + +--R 2 8 3 7 5 5 6 4 7 3 8 2 9 +--R 6a b - 36a b - 6a b - 108a b + 120a b + 192a b - 78a b +--R + +--R 10 +--R - 90a +--R * +--R 5 +--R c +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R 20a b - 38a b - 76a b + 114a b + 108a b - 114a b - 68a b +--R + +--R 11 12 +--R 38a b + 16a +--R * +--R 3 +--R c +--R + +--R 6 8 8 6 10 4 12 2 14 +--R (14a b - 56a b + 84a b - 56a b + 14a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 12 5 4 2 3 3 2 10 +--R (- 6b - 6a b )c + (4b + 2a b + 16a b + 18a b )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 8 +--R (30b + 28a b - 32a b - 24a b - 12a b - 18a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 7 2 6 +--R (8b + 12a b - 56a b - 60a b + 48a b + 42a b + 6a b )c +--R + +--R 11 10 2 9 3 8 5 6 6 5 +--R - 26b - 22a b + 40a b + 24a b + 18a b - 16a b +--R + +--R 7 4 8 3 +--R - 20a b + 2a b +--R * +--R 4 +--R c +--R + +--R 13 12 2 11 3 10 4 9 5 8 +--R - 12b - 14a b + 40a b + 42a b - 48a b - 42a b +--R + +--R 6 7 7 6 8 5 +--R 24a b + 14a b - 4a b +--R * +--R 2 +--R c +--R + +--R 15 2 13 4 11 6 9 8 7 +--R 2b - 8a b + 12a b - 8a b + 2a b +--R * +--R 7 +--R cos(x) +--R + +--R 3 2 2 12 +--R (- 6b - 18a b - 12a b)c +--R + +--R 5 4 2 3 3 2 4 10 +--R (2b + 52a b + 62a b + 48a b + 36a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 8 +--R (28b + 146a b + 96a b - 208a b - 186a b - 36a b - 36a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 12b - 40a b - 84a b - 200a b - 150a b + 240a b +--R + +--R 6 3 8 +--R 210a b + 12a b +--R * +--R 6 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 22b - 206a b - 148a b + 360a b + 282a b - 96a b +--R + +--R 6 5 7 4 8 3 9 2 +--R - 32a b - 64a b - 80a b + 6a b +--R * +--R 4 +--R c +--R + +--R 13 12 2 11 3 10 4 9 5 8 +--R - 14b - 76a b - 42a b + 248a b + 210a b - 288a b +--R + +--R 6 7 7 6 8 5 9 4 +--R - 238a b + 136a b + 84a b - 20a b +--R * +--R 2 +--R c +--R + +--R 14 3 12 5 10 7 8 9 6 +--R 14a b - 56a b + 84a b - 56a b + 14a b +--R * +--R 6 +--R cos(x) +--R + +--R 3 2 3 12 +--R (12b - 18a b - 6a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (12b + 60a b + 120a b + 102a b + 48a b + 18a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 32b + 96a b + 238a b - 48a b - 464a b - 324a b +--R + +--R 6 7 +--R - 36a b - 18a +--R * +--R 8 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 48b - 72a b - 264a b - 384a b - 168a b + 108a b +--R + +--R 6 3 7 2 9 +--R 480a b + 342a b + 6a +--R * +--R 6 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 12b - 192a b - 630a b - 186a b + 1200a b + 828a b +--R + +--R 6 5 7 4 8 3 9 2 10 +--R - 456a b - 330a b - 108a b - 120a b + 6a b +--R * +--R 4 +--R c +--R + +--R 13 12 2 11 3 10 4 9 5 8 +--R 4b - 84a b - 224a b + 42a b + 688a b + 378a b +--R + +--R 6 7 7 6 8 5 9 4 10 3 +--R - 760a b - 546a b + 332a b + 210a b - 40a b +--R * +--R 2 +--R c +--R + +--R 2 13 4 11 6 9 8 7 10 5 +--R 42a b - 168a b + 252a b - 168a b + 42a b +--R * +--R 5 +--R cos(x) +--R + +--R 3 2 2 3 12 +--R (12b + 36a b + 18a b - 6a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (16b - 4a b + 58a b + 88a b + 26a b + 16a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 24b - 208a b - 48a b + 194a b - 232a b - 464a b +--R + +--R 6 7 +--R - 186a b - 12a +--R * +--R 8 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 48b - 240a b - 408a b - 440a b - 288a b + 200a b +--R + +--R 6 3 7 2 8 +--R 522a b + 480a b + 222a b +--R * +--R 6 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 20b - 52a b - 530a b - 1010a b + 320a b + 2080a b +--R + +--R 6 5 7 4 8 3 9 2 10 11 +--R 950a b - 920a b - 640a b - 100a b - 80a b + 2a +--R * +--R 4 +--R c +--R + +--R 12 2 11 3 10 4 9 5 8 6 7 +--R 20a b - 210a b - 400a b + 350a b + 1120a b + 210a b +--R + +--R 7 6 8 5 9 4 10 3 11 2 +--R - 1160a b - 630a b + 460a b + 280a b - 40a b +--R * +--R 2 +--R c +--R + +--R 3 12 5 10 7 8 9 6 11 4 +--R 70a b - 280a b + 420a b - 280a b + 70a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 12 +--R (- 6b + 18a b + 36a b + 12a )c +--R + +--R 5 4 2 3 3 2 4 5 10 +--R (- 16b - 26a b - 88a b - 58a b + 4a b - 16a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 12b - 186a b - 464a b - 232a b + 194a b - 48a b +--R + +--R 6 7 +--R - 208a b - 24a +--R * +--R 8 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 222a b - 480a b - 522a b - 200a b + 288a b + 440a b +--R + +--R 7 2 8 9 +--R 408a b + 240a b + 48a +--R * +--R 6 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 2b - 80a b - 100a b - 640a b - 920a b + 950a b +--R + +--R 6 5 7 4 8 3 9 2 10 11 +--R 2080a b + 320a b - 1010a b - 530a b - 52a b - 20a +--R * +--R 4 +--R c +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 +--R 40a b - 280a b - 460a b + 630a b + 1160a b - 210a b +--R + +--R 8 5 9 4 10 3 11 2 12 +--R - 1120a b - 350a b + 400a b + 210a b - 20a b +--R * +--R 2 +--R c +--R + +--R 4 11 6 9 8 7 10 5 12 3 +--R 70a b - 280a b + 420a b - 280a b + 70a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 2 3 12 +--R (- 6b - 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2a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 36a b - 36a b - 186a b - 208a b + 96a b + 146a b +--R + +--R 7 +--R 28a +--R * +--R 8 +--R c +--R + +--R 8 3 6 4 5 5 4 6 3 7 2 +--R - 12a b - 210a b - 240a b + 150a b + 200a b + 84a b +--R + +--R 8 9 +--R 40a b - 12a +--R * +--R 6 +--R c +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 8 3 +--R 6a b - 80a b - 64a b - 32a b - 96a b + 282a b + 360a b +--R + +--R 9 2 10 11 +--R - 148a b - 206a b - 22a +--R * +--R 4 +--R c +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 20a b - 84a b - 136a b + 238a b + 288a b - 210a b +--R + +--R 10 3 11 2 12 13 +--R - 248a b + 42a b + 76a b + 14a +--R * +--R 2 +--R c +--R + +--R 6 9 8 7 10 5 12 3 14 +--R 14a b - 56a b + 84a b - 56a b + 14a b +--R * +--R cos(x) +--R + +--R 2 3 12 2 3 3 2 4 5 10 +--R (- 6a b - 6a )c + (- 18a b - 16a b - 2a b - 4a )c +--R + +--R 2 5 3 4 4 3 5 2 6 7 8 +--R (- 18a b - 12a b - 24a b - 32a b + 28a b + 30a )c +--R + +--R 2 7 4 5 5 4 6 3 7 2 8 9 6 +--R (- 6a b - 42a b - 48a b + 60a b + 56a b - 12a b - 8a )c +--R + +--R 3 8 4 7 5 6 6 5 8 3 9 2 10 +--R 2a b - 20a b - 16a b + 18a b + 24a b + 40a b - 22a b +--R + +--R 11 +--R - 26a +--R * +--R 4 +--R c +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 11 2 +--R 4a b - 14a b - 24a b + 42a b + 48a b - 42a b - 40a b +--R + +--R 12 13 +--R 14a b + 12a +--R * +--R 2 +--R c +--R + +--R 7 8 9 6 11 4 13 2 15 +--R 2a b - 8a b + 12a b - 8a b + 2a +--R * +--R sin(x) +--R + +--R 4 3 11 6 5 2 4 3 3 9 +--R (- 2b - 2a b )c + (- 2b - 2a b + 6a b + 6a b )c +--R + +--R 8 7 4 4 5 3 7 +--R (4b + 4a b - 6a b - 6a b )c +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 7 3 5 +--R (4b + 4a b - 12a b - 12a b + 6a b + 6a b + 2a b + 2a b )c +--R + +--R 12 11 4 8 5 7 6 6 7 5 3 +--R (- 2b - 2a b + 6a b + 6a b - 4a b - 4a b )c +--R + +--R 14 13 2 12 3 11 4 10 5 9 6 8 7 7 +--R (- 2b - 2a b + 6a b + 6a b - 6a b - 6a b + 2a b + 2a b )c +--R * +--R 8 +--R cos(x) +--R + +--R 4 3 2 2 11 6 2 4 3 3 4 2 9 +--R (- 2b - 8a b - 6a b )c + (- 2b + 8a b + 24a b + 18a b )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 7 +--R (4b + 32a b + 28a b - 24a b - 30a b - 24a b - 18a b )c +--R + +--R 10 9 3 7 4 6 5 5 6 4 7 3 8 2 5 +--R (4b + 16a b - 72a b - 54a b + 48a b + 44a b + 8a b + 6a b )c +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R - 2b - 24a b - 22a b + 24a b + 30a b + 24a b + 14a b +--R + +--R 7 5 8 4 +--R - 24a b - 20a b +--R * +--R 3 +--R c +--R + +--R 14 13 2 12 3 11 4 10 5 9 6 8 +--R - 2b - 16a b - 8a b + 48a b + 36a b - 48a b - 40a b +--R + +--R 7 7 8 6 +--R 16a b + 14a b +--R * +--R c +--R * +--R 7 +--R cos(x) +--R + +--R 4 3 2 2 3 11 +--R (4b - 2a b - 12a b - 6a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 9 +--R (8b + 10a b + 12a b + 28a b + 36a b + 18a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 7 +--R (28a b + 76a b + 24a b - 96a b - 90a b - 36a b - 18a b)c +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 8b + 4a b + 12a b - 60a b - 156a b - 54a b + 140a b +--R + +--R 7 3 8 2 9 +--R 104a b + 12a b + 6a b +--R * +--R 5 +--R c +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R - 4b - 26a b - 96a b - 50a b + 144a b + 138a b + 16a b +--R + +--R 7 5 8 4 9 3 +--R - 22a b - 60a b - 40a b +--R * +--R 3 +--R c +--R + +--R 13 2 12 4 10 5 9 6 8 7 7 +--R - 14a b - 56a b + 168a b + 84a b - 168a b - 112a b +--R + +--R 8 6 9 5 +--R 56a b + 42a b +--R * +--R c +--R * +--R 6 +--R cos(x) +--R + +--R 4 3 2 2 3 4 11 +--R (4b + 16a b + 6a b - 8a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 9 +--R (8b + 24a b + 26a b + 8a b + 16a b + 24a b + 6a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R - 24a b + 24a b + 80a b - 40a b - 144a b - 90a b - 24a b +--R + +--R 8 +--R - 6a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 8b - 56a b - 48a b - 8a b - 104a b - 144a b + 50a b +--R + +--R 7 3 8 2 9 10 +--R 200a b + 108a b + 8a b + 2a +--R * +--R 5 +--R c +--R + +--R 12 11 2 10 3 9 4 8 5 7 6 6 +--R - 4b - 24a b - 94a b - 184a b + 10a b + 360a b + 238a b +--R + +--R 7 5 8 4 9 3 10 2 +--R - 72a b - 110a b - 80a b - 40a b +--R * +--R 3 +--R c +--R + +--R 2 12 3 11 4 10 5 9 6 8 7 7 +--R - 42a b - 112a b + 56a b + 336a b + 84a b - 336a b +--R + +--R 8 6 9 5 10 4 +--R - 168a b + 112a b + 70a b +--R * +--R c +--R * +--R 5 +--R cos(x) +--R + +--R 4 3 2 2 3 4 11 +--R (- 2b + 10a b + 24a b + 10a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 9 +--R (- 6b + 10a b + 18a b - 18a b - 10a b + 6a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 6b - 30a b - 96a b - 40a b + 64a b - 40a b - 96a b +--R + +--R 7 8 +--R - 30a b - 6a +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 6 4 7 3 +--R - 2b - 50a b - 150a b - 110a b + 40a b - 40a b + 110a b +--R + +--R 8 2 9 10 +--R 150a b + 50a b + 2a +--R * +--R 5 +--R c +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R - 20a b - 60a b - 150a b - 180a b + 170a b + 480a b +--R + +--R 7 5 8 4 9 3 10 2 11 +--R 170a b - 180a b - 150a b - 60a b - 20a b +--R * +--R 3 +--R c +--R + +--R 3 11 4 10 5 9 6 8 8 6 9 5 +--R - 70a b - 140a b + 140a b + 420a b - 420a b - 140a b +--R + +--R 10 4 11 3 +--R 140a b + 70a b +--R * +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 2 2 3 4 11 +--R (- 2b - 8a b + 6a b + 16a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 9 +--R (- 6b - 24a b - 16a b - 8a b - 26a b - 24a b - 8a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 6b - 24a b - 90a b - 144a b - 40a b + 80a b + 24a b +--R + +--R 7 +--R - 24a b +--R * +--R 7 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 6 4 +--R - 2b - 8a b - 108a b - 200a b - 50a b + 144a b + 104a b +--R + +--R 7 3 8 2 9 10 +--R 8a b + 48a b + 56a b + 8a +--R * +--R 5 +--R c +--R + +--R 2 10 3 9 4 8 5 7 6 6 7 5 +--R - 40a b - 80a b - 110a b - 72a b + 238a b + 360a b +--R + +--R 8 4 9 3 10 2 11 12 +--R 10a b - 184a b - 94a b - 24a b - 4a +--R * +--R 3 +--R c +--R + +--R 4 10 5 9 6 8 7 7 8 6 9 5 +--R - 70a b - 112a b + 168a b + 336a b - 84a b - 336a b +--R + +--R 10 4 11 3 12 2 +--R - 56a b + 112a b + 42a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 3 2 2 3 4 11 +--R (- 6a b - 12a b - 2a b + 4a )c +--R + +--R 5 2 4 3 3 4 2 5 6 9 +--R (- 18a b - 36a b - 28a b - 12a b - 10a b - 8a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 7 +--R (- 18a b - 36a b - 90a b - 96a b + 24a b + 76a b + 28a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 6a b - 12a b - 104a b - 140a b + 54a b + 156a b + 60a b +--R + +--R 8 2 9 10 +--R - 12a b - 4a b + 8a +--R * +--R 5 +--R c +--R + +--R 3 9 4 8 5 7 6 6 7 5 8 4 9 3 +--R - 40a b - 60a b - 22a b + 16a b + 138a b + 144a b - 50a b +--R + +--R 10 2 11 12 +--R - 96a b - 26a b - 4a +--R * +--R 3 +--R c +--R + +--R 5 9 6 8 7 7 8 6 9 5 10 4 +--R - 42a b - 56a b + 112a b + 168a b - 84a b - 168a b +--R + +--R 12 2 13 +--R 56a b + 14a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 4 11 2 4 3 3 4 2 6 9 +--R (- 6a b - 8a b - 2a )c + (- 18a b - 24a b - 8a b + 2a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 7 +--R (- 18a b - 24a b - 30a b - 24a b + 28a b + 32a b + 4a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 9 +--R - 6a b - 8a b - 44a b - 48a b + 54a b + 72a b - 16a b +--R + +--R 10 +--R - 4a +--R * +--R 5 +--R c +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 10 2 +--R - 20a b - 24a b + 14a b + 24a b + 30a b + 24a b - 22a b +--R + +--R 11 12 +--R - 24a b - 2a +--R * +--R 3 +--R c +--R + +--R 6 8 7 7 8 6 9 5 10 4 11 3 12 2 +--R - 14a b - 16a b + 40a b + 48a b - 36a b - 48a b + 8a b +--R + +--R 13 14 +--R 16a b + 2a +--R * +--R c +--R * +--R cos(x) +--R + +--R 3 4 11 3 3 4 2 5 6 9 +--R (- 2a b - 2a )c + (- 6a b - 6a b + 2a b + 2a )c +--R + +--R 3 5 4 4 7 8 7 +--R (- 6a b - 6a b + 4a b + 4a )c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 10 5 +--R (- 2a b - 2a b - 6a b - 6a b + 12a b + 12a b - 4a b - 4a )c +--R + +--R 5 7 6 6 7 5 8 4 11 12 3 +--R (- 4a b - 4a b + 6a b + 6a b - 2a b - 2a )c +--R + +--R 7 7 8 6 9 5 10 4 11 3 12 2 13 14 +--R (- 2a b - 2a b + 6a b + 6a b - 6a b - 6a b + 2a b + 2a )c +--R Type: Expression(Integer) +--E 338 + +--S 339 of 532 +m0763b:= a0763.2-r0763 +--R +--R +--R (312) +--R 3 2 2 5 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b - 8a b + 12a b - 16a b + 8a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 3 2 4 5 3 +--R (4a b - 8a b + 4a )c + (4a b - 8a b + 12a b - 16a b + 8a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 +--R (- 2b + 4a b - 2a )c +--R + +--R 4 3 2 2 3 4 4 +--R (8b - 16a b + 4a b + 8a b - 4a )c +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (10b - 20a b + 30a b - 40a b + 20a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (20a b - 40a b + 60a b - 80a b + 40a b)c +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (2b - 4a b + 16a b - 28a b + 14a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (10a b - 20a b + 30a b - 40a b + 20a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 4b + 8a b - 4a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b - 8a b - 4a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 +--R (8b - 16a b + 24a b - 32a b + 16a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (20a b - 40a b + 12a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (24a b - 48a b + 72a b - 96a b + 48a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 5 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b - 8a b + 36a b - 64a b + 32a b)c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (24a b - 48a b + 72a b - 96a b + 48a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 +--R (4a b - 8a b + 4a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (4a b - 8a b + 20a b - 32a b + 16a )c +--R + +--R 3 4 4 3 5 2 6 7 +--R (8a b - 16a b + 24a b - 32a b + 16a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 2 4 3 3 4 2 2 8 +--R (- 2b + 4a b - 2a b )c + (- 4a b + 8a b - 4a b )c + 2b +--R + +--R 7 2 6 3 5 4 4 +--R - 4a b + 6a b - 8a b + 4a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4a b + 8a b - 4a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 7 2 6 +--R (4a b - 8a b - 4a b + 16a b - 8a b)c + 8a b - 16a b +--R + +--R 3 5 4 4 5 3 +--R 24a b - 32a b + 16a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 4 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 2 6 +--R (2b - 4a b + 16a b - 28a b + 10a b + 8a b - 4a )c + 12a b +--R + +--R 3 5 4 4 5 3 6 2 +--R - 24a b + 36a b - 48a b + 24a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4a b - 8a b + 4a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 3 5 4 4 +--R (4a b - 8a b + 20a b - 32a b + 16a b)c + 8a b - 16a b +--R + +--R 5 3 6 2 7 +--R 24a b - 32a b + 16a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 2 4 3 3 4 2 5 6 2 +--R (2a b - 4a b + 2a )c + (2a b - 4a b + 8a b - 12a b + 6a )c +--R + +--R 4 4 5 3 6 2 7 8 +--R 2a b - 4a b + 6a b - 8a b + 4a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 3 2 2 5 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b - 8a b + 12a b - 16a b + 8a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 3 2 4 5 3 +--R (4a b - 8a b + 4a )c + (4a b - 8a b + 12a b - 16a b + 8a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 +--R (- 2b + 4a b - 2a )c +--R + +--R 4 3 2 2 3 4 4 +--R (8b - 16a b + 4a b + 8a b - 4a )c +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (10b - 20a b + 30a b - 40a b + 20a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (20a b - 40a b + 60a b - 80a b + 40a b)c +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (2b - 4a b + 16a b - 28a b + 14a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (10a b - 20a b + 30a b - 40a b + 20a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 4b + 8a b - 4a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b - 8a b - 4a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 +--R (8b - 16a b + 24a b - 32a b + 16a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (20a b - 40a b + 12a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (24a b - 48a b + 72a b - 96a b + 48a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 5 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4b - 8a b + 36a b - 64a b + 32a b)c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (24a b - 48a b + 72a b - 96a b + 48a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 +--R (4a b - 8a b + 4a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (4a b - 8a b + 20a b - 32a b + 16a )c +--R + +--R 3 4 4 3 5 2 6 7 +--R (8a b - 16a b + 24a b - 32a b + 16a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 2 4 3 3 4 2 2 8 +--R (- 2b + 4a b - 2a b )c + (- 4a b + 8a b - 4a b )c + 2b +--R + +--R 7 2 6 3 5 4 4 +--R - 4a b + 6a b - 8a b + 4a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4a b + 8a b - 4a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 7 2 6 +--R (4a b - 8a b - 4a b + 16a b - 8a b)c + 8a b - 16a b +--R + +--R 3 5 4 4 5 3 +--R 24a b - 32a b + 16a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 4 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 2 2 6 +--R (2b - 4a b + 16a b - 28a b + 10a b + 8a b - 4a )c + 12a b +--R + +--R 3 5 4 4 5 3 6 2 +--R - 24a b + 36a b - 48a b + 24a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4a b - 8a b + 4a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 3 5 4 4 +--R (4a b - 8a b + 20a b - 32a b + 16a b)c + 8a b - 16a b +--R + +--R 5 3 6 2 7 +--R 24a b - 32a b + 16a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 2 4 3 3 4 2 5 6 2 +--R (2a b - 4a b + 2a )c + (2a b - 4a b + 8a b - 12a b + 6a )c +--R + +--R 4 4 5 3 6 2 7 8 +--R 2a b - 4a b + 6a b - 8a b + 4a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 6 3 2 2 3 4 +--R - 2b c + (- 2b - 3a b + 2a b + 3a )c +--R + +--R 4 2 3 3 2 2 +--R (3a b - 6a b + 3a b )c +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R - 2a c + (b - 4a b - 5a b + 8a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (b - 2a b + 3a b - 4a b + 2a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 2 5 +--R c + (- 4b + 3a b - 4a )c +--R + +--R 4 3 2 2 3 3 5 2 4 3 3 +--R (- 5b - 12a b + 14a b + 3a b)c + (3a b - 6a b + 3a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 +--R (- b - 8a b - a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- b - 8a b - 27a b + 32a b + 4a )c +--R + +--R 2 4 3 3 4 2 +--R (6a b - 12a b + 6a b )c +--R * +--R cos(x) +--R + +--R 7 2 2 5 2 2 3 4 3 +--R - c + (- b - 3a b - a )c + (- 5a b - 15a b + 20a )c +--R + +--R 3 3 4 2 5 +--R (3a b - 6a b + 3a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 2 3 4 +--R 2b c + (- 2b + 9a b - 14a b + 3a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 4b - 9a b + 10a b + 3a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R 2a c + (b - 12a b + 7a b - 8a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (b - 14a b - 33a b + 44a b + 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R - 2b c + (- 2b - 9a b + 2a b - 3a )c +--R + +--R 4 2 3 3 2 4 2 +--R (- 3a b - 6a b - 39a b + 48a b)c +--R * +--R cos(x) +--R + +--R 6 3 2 3 4 +--R - 2a c + (- b - 7a b + 4a )c +--R + +--R 5 4 2 3 4 5 2 +--R (- b + 2a b - 3a b - 14a b + 16a )c +--R * +--R sin(x) +--R + +--R 2 5 3 2 2 3 3 6 2 4 3 3 4 +--R (b c + (6a b - 10a b + 3a b)c + (- b - 2a b + 3a b )c)cos(x) +--R + +--R 2 2 5 4 2 2 3 4 3 +--R (- b + 4a b - a )c + (- b + 9a b - 16a b + 4a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- 4a b - 6a b + 4a b + 6a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 4 3 2 2 4 3 +--R (- b + a )c + (- b - 6a b + 5a b - 4a )c +--R + +--R 5 3 3 4 2 5 +--R (- 3a b - 18a b + 18a b + 3a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b - 4a b + a )c + (b - 4a b - 9a b + 12a b - 4a )c +--R + +--R 2 4 3 3 4 2 5 +--R (- 6a b + 8a b - 18a b + 16a b)c +--R * +--R cos(x) +--R + +--R 2 5 2 2 3 4 3 3 3 4 2 5 6 +--R - a c + (- a b - 3a b + 3a )c + (- 3a b + 5a b - 6a b + 4a )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 532 +d0763b:= D(m0763b,x) +--R +--R +--R (313) +--R 4 3 2 2 3 4 6 +--R (2b - 4a b - 4a b + 12a b - 6a )c +--R + +--R 6 5 3 3 4 2 4 +--R (2b - 4a b + 4a b - 2a b )c +--R * +--R 8 +--R sin(x) +--R + +--R 3 2 2 3 7 +--R (- 4b + a b + 6a b - 3a )c +--R + +--R 5 4 2 3 3 2 5 +--R (- 4b + 10a b - 20a b + 14a b )c +--R + +--R 6 2 5 3 4 3 +--R (9a b - 18a b + 9a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 3 7 5 4 2 3 4 5 +--R (- 6b + 18a b - 12a )c + (2b - 16a b + 8a b + 6a b)c +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (8b - 16a b + 18a b - 20a b + 10a b )c +--R * +--R cos(x) +--R + +--R 3 2 2 3 7 +--R (- 4b + 3a b + 10a b - 9a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 4b + 11a b - 14a b - 10a b + 26a b - 9a )c +--R + +--R 6 2 5 3 4 4 3 5 2 3 +--R (8a b - 16a b + 9a b - 2a b + a b )c +--R * +--R 7 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 6 +--R (- 4b + 2a b - 6a )c + (- 20b - 21a b + 46a b - 29a b)c +--R + +--R 6 5 2 4 3 3 4 +--R (- 16b - 8a b - 2a b + 26a b )c +--R + +--R 7 2 6 3 5 2 +--R (15a b - 30a b + 15a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 8 +--R (- 3b - 12a b - 9a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 32b - 40a b + 33a b + 6a b - 39a )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 25b - 36a b + 27a b - 44a b + 78a b )c +--R + +--R 8 7 2 6 3 5 4 4 2 +--R (4b - 8a b + 45a b - 82a b + 41a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 8 +--R (- 14a b - 10a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 20b - 25a b + 8a b + 27a b - 62a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (- 20b - 3a b - 38a b + 38a b - 48a b + 71a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 2 +--R (8a b - 16a b + 45a b - 74a b + 37a b )c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (b - 4a b - 5a )c + (- b - 20a b + 21a b + 6a b - 30a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 2b - 16a b + 24a b - 26a b + 5a b - 2a b + 17a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 2 +--R (4a b - 8a b + 15a b - 22a b + 11a b )c +--R * +--R 6 +--R sin(x) +--R + +--R 9 3 2 2 3 7 +--R (7b + a)c + (- 23b + 36a b - 28a b - a )c +--R + +--R 5 4 2 3 3 2 5 +--R (- 55b + 3a b - 36a b - 32a b )c +--R + +--R 7 6 2 5 3 4 3 +--R (- 25b - 26a b + 4a b + 47a b )c +--R + +--R 8 2 7 3 6 +--R (6a b - 12a b + 6a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (6b + 10a)c + (- 10b - 72a b + 10a b - 40a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 28b - 230a b - 36a b - 68a b - 118a b)c +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 12b - 148a b - 2a b + 4a b + 158a b )c +--R + +--R 2 7 3 6 4 5 +--R (24a b - 48a b + 24a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 9 2 2 3 7 +--R (- 8b + 8a)c + (- 100a b - 94a b - 46a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 16b - 141a b - 218a b - 98a b - 162a b - 85a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (- 24b - 33a b - 204a b + 102a b - 78a b + 237a b )c +--R + +--R 3 6 4 5 5 4 +--R (36a b - 72a b + 36a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 10b - 6a)c + (- 8b - 18a b - 136a b - 46a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 14b - 28a b - 94a b - 106a b - 110a b - 128a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 16b - 16a b - 14a b - 128a b + 122a b - 120a b +--R + +--R 6 +--R 172a b +--R * +--R 3 +--R c +--R + +--R 4 5 5 4 6 3 +--R (24a b - 48a b + 24a b )c +--R * +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 3b - 5a)c + (- 3b - 2a b - 28a b - 31a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 13a b - 14a b + 18a b - 59a b - 52a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (- 16a b + 8a b + 7a b - 47a b + 44a b - 42a b + 46a )c +--R + +--R 5 4 6 3 7 2 +--R (6a b - 12a b + 6a b )c +--R * +--R 5 +--R sin(x) +--R + +--R 10 2 2 8 +--R - 2c + (35b - a b - 4a )c +--R + +--R 4 3 2 2 3 6 +--R (- 43b + 36a b + 74a b - 41a b)c +--R + +--R 6 5 2 4 3 3 4 +--R (- 99b + 35a b - 160a b - 22a b )c +--R + +--R 8 7 2 6 3 5 2 +--R (- 19b - 2a b - 38a b + 59a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 10 2 2 8 +--R - 2c + (24b + 83a b - 5a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 95b - 101a b + 171a b - 20a b - 41a )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 120b - 331a b - 93a b - 620a b - 66a b )c +--R + +--R 8 7 2 6 3 5 4 4 2 +--R (b - 147a b + 31a b - 120a b + 235a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 10 2 2 8 +--R 4c + (- 44b + 78a b + 50a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 68b - 242a b - 288a b + 84a b - 90a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (- 28b - 347a b - 562a b - 602a b - 828a b - 93a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 2 +--R (- 8b - 27a b - 304a b + 128a b - 186a b + 397a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 10 2 2 8 +--R 4c + (- 40b - 74a b + 54a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- b - 186a b - 510a b - 292a b - 47a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 35b - 120a b - 445a b - 508a b - 865a b - 510a b +--R + +--R 6 +--R - 47a +--R * +--R 4 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 8b - 8a b - 79a b - 252a b + 186a b - 202a b +--R + +--R 6 2 +--R 363a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 10 2 2 8 +--R - 2c + (- 11b - 77a b - 26a )c +--R + +--R 4 3 2 2 3 4 6 +--R (7b - 54a b - 190a b - 423a b - 74a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 16b + 7a b - 110a b - 234a b - 299a b - 472a b +--R + +--R 6 +--R - 138a +--R * +--R 4 +--R c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 16a b + 8a b - 73a b - 85a b + 122a b - 136a b +--R + +--R 7 +--R 180a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 10 2 2 8 +--R - 2c + (- 4b - 9a b - 29a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b + 11a b - 41a b - 84a b - 72a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 2b + 20a b - 24a b - 30a b - 16a b - 109a b - 85a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (- 8a b + 8a b - 22a b - 9a b + 31a b - 38a b + 38a )c +--R * +--R 4 +--R sin(x) +--R + +--R 9 3 2 2 3 7 +--R (- 9b + a)c + (66b + 29a b - 60a b + 5a )c +--R + +--R 5 4 2 3 3 2 5 +--R (- 28b + 22a b + 174a b - 64a b )c +--R + +--R 7 6 2 5 3 4 3 +--R (- 110b + a b - 152a b - 3a b )c +--R + +--R 9 8 2 7 3 6 +--R (- 7b + 7a b - 26a b + 26a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 8b - 8a)c + (106b + 174a b - 32a b - 40a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 42b - 226a b + 302a b + 376a b - 170a b)c +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 156b - 462a b - 180a b - 792a b + 6a b )c +--R + +--R 8 2 7 3 6 4 5 +--R (- 54a b + 42a b - 120a b + 132a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (19b - 11a)c + (- 35b + 178a b + 251a b - 50a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 107b - 352a b - 525a b + 617a b + 108a b - 101a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (- 53b - 553a b - 877a b - 974a b - 1554a b + 51a b )c +--R + +--R 8 2 7 3 6 4 5 5 4 +--R (- 12a b - 141a b + 105a b - 234a b + 282a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (16b + 16a)c + (- 128b - 120a b + 244a b + 100a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 128b - 268a b - 916a b - 776a b + 408a b - 80a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 16b - 132a b - 856a b - 1096a b - 1868a b - 1408a b +--R + +--R 6 +--R 64a b +--R * +--R 3 +--R c +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R (- 48a b - 164a b + 140a b - 256a b + 328a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 11b + 19a)c + (- 60b - 215a b - 142a b + 121a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 25b - 203a b - 430a b - 1228a b - 463a b + 69a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 24b + 31a b - 164a b - 745a b - 896a b - 1654a b +--R + +--R 6 7 +--R - 578a b + 22a +--R * +--R 3 +--R c +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (- 72a b - 81a b + 105a b - 174a b + 222a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 8b - 8a)c + (- 2b - 78a b - 188a b - 36a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (14b - 38a b - 178a b - 344a b - 698a b - 52a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 8b + 32a b - 2a b - 96a b - 354a b - 410a b +--R + +--R 6 7 +--R - 678a b - 84a +--R * +--R 3 +--R c +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (- 48a b - 6a b + 42a b - 72a b + 84a b)c +--R * +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (b - 9a)c + (5b - 16a b - 25a b - 52a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (4b + a b - 11a b - 69a b - 105a b - 100a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (8a b + 8a b - 17a b - 11a b - 68a b - 85a b - 99a )c +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 12a b + 5a b + 7a b - 14a b + 14a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 6 +--R (- 15b - 3a b + 6a )c + (58b + 55a b - 84a b - 9a b)c +--R + +--R 6 5 2 4 3 3 4 +--R (4b + 48a b + 116a b - 52a b )c +--R + +--R 8 7 2 6 3 5 2 10 9 2 8 +--R (- 70b - 9a b - 108a b + 31a b )c - b + a b - 2a b +--R + +--R 3 7 +--R 2a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 2 8 +--R (- 39b - 3a b + 6a )c +--R + +--R 4 3 2 2 3 4 6 +--R (74b + 312a b - 7a b - 204a b - 3a )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (19b - 70a b + 313a b + 378a b - 164a b )c +--R + +--R 8 7 2 6 3 5 4 4 2 9 +--R (- 94b - 392a b - 159a b - 584a b + 137a b )c - 7a b +--R + +--R 2 8 3 7 4 6 +--R 7a b - 14a b + 14a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 2 8 +--R (9b - 15a b - 6a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 17b + 272a b + 489a b - 174a b - 102a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (- 57b - 172a b - 397a b + 821a b + 414a b - 189a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 2 +--R (- 31b - 459a b - 905a b - 818a b - 1326a b + 263a b )c +--R + +--R 2 8 3 7 4 6 5 5 +--R - 21a b + 21a b - 42a b + 42a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 2 8 +--R (63b + 5a b - 8a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 45b - 233a b + 436a b + 417a b - 115a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 110b - 321a b - 843a b - 727a b + 972a b + 124a b +--R + +--R 6 +--R - 75a +--R * +--R 4 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 2b - 83a b - 949a b - 1243a b - 1882a b - 1574a b +--R + +--R 6 2 +--R 273a b +--R * +--R 2 +--R c +--R + +--R 3 7 4 6 5 5 6 4 +--R - 35a b + 35a b - 70a b + 70a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 8 +--R (11b + 39a b + 10a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 48b - 309a b - 310a b + 439a b + 128a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 51b - 339a b - 572a b - 1524a b - 689a b + 539a b +--R + +--R 6 +--R - 24a +--R * +--R 4 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 8b + 9a b - 96a b - 1087a b - 1188a b - 2262a b +--R + +--R 6 2 7 +--R - 994a b + 150a b +--R * +--R 2 +--R c +--R + +--R 4 6 5 5 6 4 7 3 +--R - 35a b + 35a b - 70a b + 70a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 8 +--R (- 25b - a b + 14a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 40b - 94a b - 411a b - 166a b + 171a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 11b - 77a b - 382a b - 602a b - 1364a b - 285a b +--R + +--R 6 +--R 117a +--R * +--R 4 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 4b + 16a b + 31a b - 76a b - 747a b - 770a b +--R + +--R 6 2 7 8 +--R - 1470a b - 298a b + 34a +--R * +--R 2 +--R c +--R + +--R 5 5 6 4 7 3 8 2 +--R - 21a b + 21a b - 42a b + 42a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 8 +--R (- 5b - 21a b - 10a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- b - 34a b - 95a b - 240a b - 18a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 5a b - 59a b - 213a b - 337a b - 578a b - 16a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R 8a b + 8a b + 27a b - 41a b - 298a b - 285a b +--R + +--R 7 8 +--R - 483a b - 28a +--R * +--R 2 +--R c +--R + +--R 6 4 7 3 8 2 9 +--R - 7a b + 7a b - 14a b + 14a b +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (b - a b - 12a )c + (3b - a b - 18a b - 31a b - 45a )c +--R + +--R 6 3 3 4 2 5 6 4 +--R (2b - 17a b - 56a b - 67a b - 82a )c +--R + +--R 2 6 4 4 5 3 6 2 7 8 2 7 3 8 2 +--R (4a b + 7a b - 9a b - 54a b - 43a b - 61a )c - a b + a b +--R + +--R 9 10 +--R - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 7 +--R (- 11b - 6a b + 6a b + 3a )c +--R + +--R 5 4 2 3 3 2 5 +--R (23b + 29a b - 34a b - 18a b )c +--R + +--R 7 6 2 5 3 4 3 +--R (11b + 36a b + 50a b - 41a b )c +--R + +--R 9 8 2 7 3 6 +--R (- 23b + a b - 46a b + 20a b )c +--R * +--R 8 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (4b - 4a)c + (- 26b - 34a b + 12a b + 16a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (16b + 184a b + 38a b - 144a b - 46a b)c +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (16b + 62a b + 204a b + 164a b - 142a b )c +--R + +--R 9 8 2 7 3 6 4 5 +--R (- 30b - 152a b - 42a b - 268a b + 108a b )c +--R * +--R 7 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (4b - 4a)c + (- 3b - 43a b - 3a b + 17a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 25b + 146a b + 445a b - 93a b - 208a b - 25a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (- 25b - 4a b + 29a b + 543a b + 202a b - 185a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R (- 7b - 189a b - 419a b - 309a b - 666a b + 246a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 8b + 8a)c + (26b + 42a b - 24a b - 12a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 8b - 132a b + 362a b + 456a b - 154a b - 92a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 42b - 196a b - 286a b - 178a b + 810a b + 112a b +--R + +--R 6 +--R - 108a b +--R * +--R 3 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R (- 30a b - 504a b - 658a b - 892a b - 908a b + 304a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 8b + 8a)c + (15b + 81a b + 9a b - 25a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (7b - 140a b - 323a b + 467a b + 290a b - 61a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 16b - 207a b - 483a b - 811a b - 285a b + 682a b +--R + +--R 6 7 +--R 24a b - 24a +--R * +--R 3 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 6a b - 57a b - 741a b - 691a b - 1371a b - 722a b +--R + +--R 7 2 +--R 216a b +--R * +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 2 2 7 +--R (4b - 4a)c + (2b - 6a b + 36a b)c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 6b - 50a b - 370a b - 244a b + 336a b + 94a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 4b - 48a b - 378a b - 580a b - 1030a b - 166a b +--R + +--R 6 +--R 302a b +--R * +--R 3 +--R c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R 24a b - 68a b - 654a b - 532a b - 1218a b - 324a b +--R + +--R 8 +--R 84a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (4b - 4a)c + (- b - 33a b - 9a b + 11a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 5b - 36a b - 85a b - 347a b - 66a b + 107a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 7a b - 58a b - 322a b - 397a b - 688a b - 39a b +--R + +--R 7 +--R 55a +--R * +--R 3 +--R c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (36a b - 57a b - 351a b - 293a b - 623a b - 70a b + 14a )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 7 +--R (- 2b - 2a b - 24a b - 4a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 2b - 2a b - 30a b - 68a b - 136a b - 2a )c +--R + +--R 2 5 3 4 4 3 5 2 6 7 3 +--R (- 2a b - 36a b - 128a b - 156a b - 236a b - 2a )c +--R + +--R 4 5 5 4 6 3 7 2 8 9 +--R (24a b - 30a b - 108a b - 98a b - 168a b - 4a )c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 4 5 5 +--R (a b - 3a b - 6a )c + (a b - 3a b - 9a b - 16a b - 21a )c +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (a b - 10a b - 19a b - 27a b - 33a )c +--R + +--R 5 4 6 3 7 2 8 9 +--R (6a b - 7a b - 15a b - 14a b - 18a )c +--R * +--R sin(x) +--R + +--R 4 3 3 6 6 5 2 4 3 3 4 +--R (- 3b - 2a b + 3a b)c + (3b + 5a b - 6a b - 4a b )c +--R + +--R 8 7 2 6 3 5 2 10 9 2 8 3 7 +--R (3b + 8a b + 12a b - 13a b )c - 3b + a b - 6a b + 2a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 2a )c + (- 5b - 15a b - a b + 6a b + 5a )c +--R + +--R 5 2 4 3 3 4 2 4 +--R (33a b + 13a b - 30a b - 18a b )c +--R + +--R 8 7 2 6 3 5 4 4 2 10 9 +--R (3b + 27a b + 51a b + 42a b - 57a b )c - 4b - 21a b +--R + +--R 2 8 3 7 4 6 +--R - a b - 42a b + 14a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (4b - 4a )c + (3b - 19a b - 17a b + 7a b + 10a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (- 7b + 22a b + 117a b - 9a b - 66a b - 25a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 2 10 +--R (- 7b + 12a b + 65a b + 149a b + 46a b - 97a b )c - b +--R + +--R 9 2 8 3 7 4 6 5 5 +--R - 29a b - 65a b - 37a b - 126a b + 42a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 6 +--R (- 2b + 2a )c + (5b + 13a b - 17a b - a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- b - 31a b + 96a b + 175a b - 48a b - 68a b - 11a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (- 8b - 51a b - 10a b + 53a b + 257a b + 6a b - 79a b )c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 +--R - 7a b - 91a b - 119a b - 147a b - 210a b + 70a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 8b + 8a )c + (- 5b + 29a b + 31a b - 15a b - 12a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (3b - 22a b - 81a b + 171a b + 134a b - 39a b - 26a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 51a b - 147a b - 117a b + 3a b + 276a b - 18a b +--R + +--R 7 +--R - 30a b +--R * +--R 2 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 21a b - 161a b - 147a b - 287a b - 210a b + 70a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 2a )c + (- 3b + 3a b + 37a b - a b - 8a )c +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (- a b - 93a b - 109a b + 167a b + 72a b - 8a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R b - 4a b - 128a b - 217a b - 238a b - a b + 179a b +--R + +--R 7 8 +--R - 8a b - 4a +--R * +--R 2 +--R c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 35a b - 175a b - 133a b - 329a b - 126a b + 42a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (4b - 4a )c + (5b - 9a b - 11a b + 13a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (b - 6a b - 27a b - 147a b - 52a b + 93a b + 26a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (3a b - 14a b - 160a b - 179a b - 234a b + 17a b + 63a b)c +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R - 35a b - 119a b - 91a b - 231a b - 42a b + 14a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 2a )c + (3b - a b - 19a b - 3a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 6 4 +--R (b - a b - 16a b - 35a b - 100a b + 23a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (3a b - 18a b - 102a b - 87a b - 126a b + 9a b + 9a )c +--R + +--R 5 5 6 4 7 3 8 2 9 10 +--R - 21a b - 49a b - 45a b - 97a b - 6a b + 2a +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (a b - 3a b - 8a b)c +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (a b - 3a b - 11a b - 16a b - 29a b)c +--R + +--R 3 5 4 4 5 3 6 2 7 2 6 4 7 3 +--R (a b - 10a b - 29a b - 27a b - 37a b)c - 7a b - 11a b +--R + +--R 8 2 9 +--R - 14a b - 22a b +--R * +--R cos(x) +--R + +--R 3 4 6 3 3 4 2 5 6 4 +--R (- a b - a )c + (- a b - a b - 4a b - 4a )c +--R + +--R 5 3 6 2 7 8 2 7 3 8 2 9 10 +--R (- 2a b - 2a b - 5a b - 5a )c - a b - a b - 2a b - 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 7 +--R (- 4b + 4a b + 12a b - 12a )c +--R + +--R 5 4 2 3 3 2 5 +--R (- 4b + 4a b + 4a b - 4a b )c +--R * +--R 8 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 6 +--R (16b + 6a b - 6a )c + (16b - 12a b + 44a b )c +--R + +--R 5 2 4 4 +--R (- 18a b + 18a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 6 +--R (12b + 28a b - 24a )c + (- 4b + 44a b + 12a b + 44a b)c +--R + +--R 6 5 2 4 3 3 4 +--R (- 16b + 16a b - 20a b + 20a b )c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (8b + 2a b - 10a )c + (8b - 14a b + 22a b + 34a b - 2a )c +--R + +--R 5 2 4 3 3 4 2 4 +--R (- 16a b + 16a b - 2a b + 2a b )c +--R * +--R 7 +--R sin(x) +--R + +--R 9 3 2 2 7 +--R (- 16b - 12a)c + (48b + 66a b - 74a b)c +--R + +--R 5 4 2 3 5 6 2 5 3 +--R (64b + 48a b + 116a b )c + (- 30a b + 30a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 10b - 26a)c + (48b + 184a b - 2a b - 94a )c +--R + +--R 5 4 2 3 3 2 5 +--R (50b + 218a b + 68a b + 348a b )c +--R + +--R 7 6 2 5 3 4 3 +--R (- 8b + 8a b - 82a b + 82a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (8b - 4a)c + (48b + 58a b + 138a b - 92a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (40b + 46a b + 218a b + 46a b + 334a b)c +--R + +--R 6 2 5 3 4 4 3 3 +--R (- 16a b + 16a b - 74a b + 74a b )c +--R * +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 2b + 14a)c + (2b + 50a b - 16a b + 20a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (4b + 36a b - 12a b + 72a b + 30a b + 98a )c +--R + +--R 2 5 3 4 4 3 5 2 3 +--R (- 8a b + 8a b - 22a b + 22a b )c +--R * +--R 6 +--R sin(x) +--R + +--R 10 2 2 8 4 3 2 2 6 +--R 4c + (- 36b - 90a b + 2a )c + (60b + 24a b - 104a b )c +--R + +--R 6 5 2 4 4 7 2 6 2 +--R (100b + 102a b + 194a b )c + (- 12a b + 12a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 10 2 2 8 +--R 4c + (- 44b - 164a b - 112a )c +--R + +--R 4 3 2 2 3 6 +--R (- 24b + 356a b + 108a b - 316a b)c +--R + +--R 6 5 2 4 3 3 4 2 6 3 5 2 +--R (24b + 520a b + 324a b + 716a b )c + (- 48a b + 48a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 10 2 8 +--R - 4c + (- 40a b - 152a )c +--R + +--R 4 3 2 2 3 4 6 +--R (52b + 74a b + 590a b - 14a b - 210a )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (48b + 114a b + 822a b + 318a b + 1074a b )c +--R + +--R 3 5 4 4 2 +--R (- 72a b + 72a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 10 2 8 +--R 4c + (60a b + 20a )c +--R + +--R 4 3 2 2 3 4 6 +--R (28b + 124a b + 32a b + 444a b - 96a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (32b + 64a b + 92a b + 548a b + 104a b + 744a b)c +--R + +--R 4 4 5 3 2 +--R (- 48a b + 48a b )c +--R * +--R cos(x) +--R + +--R 10 2 2 8 +--R 8c + (8b - 6a b + 74a )c +--R + +--R 3 2 2 3 4 6 +--R (26a b + 74a b - 62a b + 146a )c +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (32a b + 16a b + 2a b + 146a b + 8a b + 192a )c +--R + +--R 5 3 6 2 2 +--R (- 12a b + 12a b )c +--R * +--R 5 +--R sin(x) +--R + +--R 9 3 2 2 7 +--R - 4b c + (- 12b - 78a b - 86a b)c +--R + +--R 5 4 2 3 5 7 6 2 5 3 +--R (68b - 36a b - 52a b )c + (76b + 42a b + 194a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (20b - 4a)c + (98b - 226a b - 410a b - 86a )c +--R + +--R 5 4 2 3 3 2 5 +--R (76b + 260a b - 60a b - 156a b )c +--R + +--R 7 6 2 5 3 4 3 +--R (- 2b + 482a b + 230a b + 850a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (28b + 12a)c + (72b + 36a b - 448a b - 324a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (60b + 94a b + 610a b + 126a b - 210a b)c +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (16b + 70a b + 1058a b + 422a b + 1554a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (16b + 24a)c + (- 70b + 174a b + 122a b - 234a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 70b + 182a b + 76a b + 836a b + 198a b - 102a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (16b + 32a b + 190a b + 1074a b + 322a b + 1486a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (16b + 28a)c + (- 16b - 50a b + 266a b + 160a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 32b - 46a b + 186a b - 14a b + 634a b + 52a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 3 +--R (32a b + 16a b + 162a b + 522a b + 88a b + 740a b)c +--R * +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (4b + 20a)c + (8b - 16a b - 4a b + 164a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (4b - 36a b + 12a b + 76a b - 60a b + 204a )c +--R + +--R 2 5 4 3 5 2 7 3 +--R (16a b + 44a b + 100a b + 152a )c +--R * +--R 4 +--R sin(x) +--R + +--R 10 2 2 8 +--R 4c + (- 40b - 78a b + 14a )c +--R + +--R 4 3 2 2 6 6 5 2 4 4 +--R (16b - 36a b - 172a b )c + (88b + 42a b + 54a b )c +--R + +--R 8 2 6 2 +--R (28b + 80a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 2 2 8 +--R (- 100b - 124a b - 48a )c +--R + +--R 4 3 2 2 3 6 +--R (36b + 68a b - 356a b - 428a b)c +--R + +--R 6 5 2 4 3 3 4 +--R (136b + 384a b + 188a b + 252a b )c +--R + +--R 7 2 6 3 5 2 +--R (192a b + 24a b + 432a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 10 2 2 8 +--R - 12c + (12b - 14a b - 102a )c +--R + +--R 4 3 2 2 3 4 6 +--R (100b + 294a b - 42a b - 754a b - 246a )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (76b + 332a b + 656a b + 514a b + 462a b )c +--R + +--R 7 2 6 3 5 4 4 2 +--R (24a b + 516a b + 96a b + 984a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 8 +--R (160b + 136a b + 8a )c +--R + +--R 4 3 2 2 3 4 6 +--R (128b + 248a b + 480a b - 72a b - 416a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (- 32b + 112a b + 184a b + 776a b + 832a b + 368a b)c +--R + +--R 2 6 3 5 4 4 5 3 2 +--R (96a b + 704a b + 144a b + 1216a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 10 2 2 8 +--R 12c + (88b + 182a b + 106a )c +--R + +--R 4 3 2 2 3 6 +--R (28b + 72a b + 368a b + 604a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 48b - 110a b + 38a b - 52a b + 740a b + 648a b +--R + +--R 6 +--R 104a +--R * +--R 4 +--R c +--R + +--R 3 5 4 4 5 3 6 2 2 +--R (144a b + 516a b + 96a b + 864a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 8 +--R (- 12b + 84a b + 88a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 28b + 4a b + 20a b + 372a b + 328a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 16b - 80a b - 76a b - 4a b - 56a b + 432a b +--R + +--R 6 +--R 184a +--R * +--R 4 +--R c +--R + +--R 4 4 5 3 6 2 7 2 +--R (96a b + 192a b + 24a b + 336a b)c +--R * +--R cos(x) +--R + +--R 10 2 2 8 +--R - 4c + (- 12b + 6a b + 30a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 8b - 10a b - 10a b + 22a b + 158a )c +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (- 16a b - 32a b + 2a b - 6a b - 16a b + 108a )c +--R + +--R 5 3 6 2 8 2 +--R (24a b + 28a b + 56a )c +--R * +--R 3 +--R sin(x) +--R + +--R 9 3 2 2 7 +--R (12b + 12a)c + (- 56b - 138a b - 6a b)c +--R + +--R 4 2 3 5 7 6 2 5 3 +--R (- 96a b - 172a b )c + (72b + 54a b + 130a b )c +--R + +--R 9 2 7 +--R (4b + 8a b )c +--R * +--R 7 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (54b + 18a)c + (- 60b - 380a b - 318a b + 6a )c +--R + +--R 5 4 2 3 3 2 5 +--R (- 30b + 2a b - 468a b - 532a b )c +--R + +--R 7 6 2 5 3 4 3 8 3 6 +--R (84b + 428a b + 354a b + 614a b )c + (28a b + 56a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (12b + 12a)c + (20b - 174a b - 546a b - 156a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (36b + 170a b + 226a b - 894a b - 582a b)c +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (28b + 356a b + 920a b + 994a b + 1206a b )c +--R + +--R 2 7 4 5 +--R (84a b + 168a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 78b - 10a)c + (26b + 326a b + 12a b - 252a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (108b + 336a b + 876a b + 516a b - 798a b - 218a )c +--R + +--R 7 2 5 3 4 4 3 5 2 3 +--R (4b + 508a b + 984a b + 1558a b + 1226a b )c +--R + +--R 3 6 5 4 +--R (140a b + 280a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 28b - 28a)c + (56b + 338a b + 526a b + 48a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (68b + 332a b + 600a b + 1324a b + 488a b - 272a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 16b - 34a b - 182a b + 252a b + 628a b + 1432a b +--R + +--R 6 +--R 640a b +--R * +--R 3 +--R c +--R + +--R 4 5 6 3 +--R (140a b + 280a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (26b - 2a)c + (56b + 112a b + 346a b + 238a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (22b + 74a b + 268a b + 548a b + 960a b + 180a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 8b - 40a b - 102a b - 290a b - 16a b + 296a b +--R + +--R 6 7 +--R 720a b + 136a +--R * +--R 3 +--R c +--R + +--R 5 4 7 2 +--R (84a b + 168a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (4b + 4a)c + (- 4b + 22a b + 74a b + 124a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 8b + 2a b + 18a b + 98a b + 286a b + 296a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 16a b - 32a b - 86a b - 174a b - 32a b + 108a b +--R + +--R 7 +--R 152a +--R * +--R 3 +--R c +--R + +--R 6 3 8 +--R (28a b + 56a b)c +--R * +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 2b - 6a)c + (- 6b - 10a b + 8a b + 24a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 4b - 4a b - 4a b - 4a b + 30a b + 62a )c +--R + +--R 2 5 3 4 4 3 5 2 7 3 7 2 9 +--R (- 8a b - 8a b - 22a b - 38a b + 20a )c + (4a b + 8a )c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 6 +--R (12b + 18a b + 6a )c + (- 28b - 72a b - 24a b )c +--R + +--R 6 5 2 4 4 8 7 2 6 2 +--R (- 12b - 78a b - 122a b )c + (28b + 12a b + 68a b )c +--R * +--R 8 +--R cos(x) +--R + +--R 10 2 2 8 +--R - 8c + (36b + 68a b + 32a )c +--R + +--R 3 2 2 3 6 +--R (- 244a b - 284a b - 68a b)c +--R + +--R 6 5 2 4 3 3 4 +--R (- 16b - 120a b - 436a b - 444a b )c +--R + +--R 8 7 2 6 3 5 2 +--R (28b + 192a b + 128a b + 384a b )c +--R * +--R 7 +--R cos(x) +--R + +--R 10 2 2 8 +--R - 8c + (20b + 76a b + 40a )c +--R + +--R 4 3 2 2 3 4 6 +--R (56b - 66a b - 610a b - 370a b - 38a )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (28b + 26a b - 150a b - 926a b - 610a b )c +--R + +--R 7 2 6 3 5 4 4 2 +--R (168a b + 516a b + 504a b + 912a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 10 2 2 8 +--R 16c + (- 20b - 44a b - 8a )c +--R + +--R 3 2 2 3 4 6 +--R (244a b - 108a b - 516a b - 152a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (36b + 264a b + 472a b + 228a b - 952a b - 376a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 2 +--R (- 24a b + 396a b + 704a b + 1032a b + 1168a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 10 2 2 8 +--R 16c + (- 28b - 112a b - 52a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 32b + 106a b + 594a b + 58a b - 146a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 12b + 206a b + 682a b + 1194a b + 594a b - 480a b +--R + +--R 6 +--R - 88a +--R * +--R 4 +--R c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 +--R (- 12a b - 108a b + 464a b + 516a b + 1228a b + 852a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 10 2 2 8 +--R - 8c + (- 20b - 20a b - 32a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 4b + 4a b + 372a b + 548a b + 76a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 8b + 24a b + 380a b + 780a b + 1280a b + 432a b +--R + +--R 6 +--R - 96a +--R * +--R 4 +--R c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 2 +--R (- 48a b - 192a b + 276a b + 192a b + 864a b + 336a b)c +--R * +--R 3 +--R cos(x) +--R + +--R 10 2 2 8 +--R - 8c + (- 4b + 20a b + 8a )c +--R + +--R 4 3 2 2 3 4 6 +--R (4b + 34a b + 42a b + 306a b + 178a )c +--R + +--R 5 2 4 3 3 4 2 5 6 4 +--R (14a b + 10a b + 294a b + 438a b + 640a b + 108a )c +--R + +--R 3 5 4 4 5 3 6 2 7 8 2 +--R (- 72a b - 168a b + 72a b + 28a b + 336a b + 56a )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 8 +--R (4b - 4a b + 8a )c +--R + +--R 4 3 2 2 3 4 6 +--R (4b - 4a b + 20a b + 36a b + 76a )c +--R + +--R 2 4 3 3 4 2 5 6 4 +--R (4a b - 4a b + 92a b + 112a b + 124a )c +--R + +--R 4 4 5 3 6 2 8 2 +--R (- 48a b - 72a b + 4a b + 56a )c +--R * +--R cos(x) +--R + +--R 2 8 3 2 2 3 4 6 +--R (- 2a b - 2a )c + (- 2a b - 2a b + 6a b + 6a )c +--R + +--R 3 3 4 2 5 6 4 5 3 6 2 2 +--R (- 2a b - 2a b + 8a b + 8a )c + (- 12a b - 12a b )c +--R * +--R sin(x) +--R + +--R 3 2 2 7 5 4 2 3 5 +--R (4b + 6a b + 6a b)c + (- 4b - 12a b - 4a b )c +--R + +--R 7 6 2 5 3 9 2 7 +--R (- 4b - 18a b - 34a b )c + (4b + 8a b )c +--R * +--R 9 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 4b - 4a)c + (6b + 26a b + 22a b + 10a )c +--R + +--R 5 4 2 3 3 2 5 +--R (4b - 44a b - 64a b - 24a b )c +--R + +--R 7 6 2 5 3 4 3 +--R (- 2b - 46a b - 126a b - 154a b )c +--R + +--R 9 8 2 7 3 6 +--R (4b + 28a b + 8a b + 56a b )c +--R * +--R 8 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 8b - 8a)c + (- 4b + 24a b + 40a b + 20a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (16b + 2a b - 166a b - 134a b - 38a b)c +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (12b - 2a b - 122a b - 342a b - 274a b )c +--R + +--R 8 2 7 3 6 4 5 +--R (28a b + 84a b + 56a b + 168a b )c +--R * +--R 7 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (4b + 4a)c + (- 2b - 14a b + 14a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b + 70a b - 32a b - 248a b - 126a b - 18a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (8b + 88a b + 74a b - 82a b - 466a b - 238a b )c +--R + +--R 2 7 3 6 4 5 5 4 +--R (84a b + 140a b + 168a b + 280a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (16b + 16a)c + (12b - 20a b - 52a b - 20a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 8b + 18a b + 174a b - 34a b - 146a b - 44a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 4b + 54a b + 258a b + 302a b + 106a b - 336a b +--R + +--R 6 +--R - 100a b +--R * +--R 3 +--R c +--R + +--R 3 6 4 5 5 4 6 3 +--R (140a b + 140a b + 280a b + 280a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (4b + 4a)c + (2b - 2a b - 46a b - 18a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 4b - 20a b + 88a b + 256a b + 24a b - 24a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 2b - 14a b + 142a b + 386a b + 492a b + 196a b +--R + +--R 6 7 +--R - 120a b - 16a +--R * +--R 3 +--R c +--R + +--R 4 5 5 4 6 3 7 2 +--R (140a b + 84a b + 280a b + 168a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 8b - 8a)c + (- 12b - 8a b + 8a b - 4a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 4b - 6a b - 2a b + 158a b + 178a b + 28a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 6a b - 18a b + 182a b + 310a b + 392a b + 108a b +--R + +--R 7 +--R - 16a +--R * +--R 3 +--R c +--R + +--R 5 4 6 3 7 2 8 +--R (84a b + 28a b + 168a b + 56a b)c +--R * +--R 3 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 4b - 4a)c + (- 6b - 10a b + 10a b + 6a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 2b - 6a b + 8a b + 16a b + 102a b + 42a )c +--R + +--R 2 5 3 4 4 3 5 2 6 7 3 +--R (- 6a b - 10a b + 114a b + 126a b + 148a b + 20a )c +--R + +--R 6 3 7 2 8 9 +--R (28a b + 4a b + 56a b + 8a )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 2a b - 2a b + 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 2a b - 2a b + 10a b + 6a b + 16a )c +--R + +--R 3 4 4 3 5 2 6 7 3 7 2 9 +--R (- 2a b - 2a b + 28a b + 20a b + 20a )c + (4a b + 8a )c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 6 6 2 4 4 2 4 8 +--R ((- 2b + 8a b - 6a )c + (- 2b + 4a b - 2a b )c )sin(x) +--R + +--R 3 2 3 7 5 4 2 3 3 2 5 +--R (12b + 7a b - 3a )c + (12b - 2a b + 24a b + 14a b )c +--R + +--R 6 3 4 3 +--R (- 9a b + 9a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 7 +--R (6b + 28a b - 6a b - 12a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 2b + 28a b + 20a b + 44a b + 6a b)c +--R + +--R 7 2 5 4 3 3 +--R (- 8b - 2a b + 10a b )c +--R * +--R cos(x) +--R + +--R 3 2 3 7 +--R (4b + 5a b - 9a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (4b - 3a b + 8a b + 24a b + 24a b - 9a )c +--R + +--R 6 3 4 5 2 3 +--R (- 8a b + 7a b + a b )c +--R * +--R 7 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 6 +--R (- 20b - 10a b - 6a )c + (28b + 45a b - 28a b - 29a b)c +--R + +--R 6 5 2 4 3 3 4 7 3 5 2 +--R (48b + 40a b + 114a b + 26a b )c + (- 15a b + 15a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 8 +--R (- 13b - 38a b - 9a )c +--R + +--R 4 3 2 2 3 4 6 +--R (16b + 144a b + 31a b - 88a b - 39a )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (25b + 182a b + 95a b + 304a b + 78a b )c +--R + +--R 8 2 6 4 4 2 +--R (- 4b - 37a b + 41a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 8 +--R (8b - 18a b - 10a )c +--R + +--R 4 3 2 2 3 4 6 +--R (28b + 33a b + 146a b - 65a b - 62a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (20b + 43a b + 180a b + 84a b + 286a b + 71a b)c +--R + +--R 7 3 5 5 3 2 +--R (- 8a b - 29a b + 37a b )c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- b + 10a b - 5a )c + (b + 30a b + 5a b + 26a b - 30a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b + 20a b + 12a b + 46a b + 35a b + 96a b + 17a )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 4a b - 7a b + 11a b )c +--R * +--R 6 +--R sin(x) +--R + +--R 9 3 2 2 3 7 +--R (11b + a)c + (- 59b - 54a b - 26a b - a )c +--R + +--R 5 4 2 3 3 2 5 +--R (5b + 27a b - 140a b - 32a b )c +--R + +--R 7 6 2 5 3 4 3 8 3 6 +--R (75b + 76a b + 198a b + 47a b )c + (- 6a b + 6a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (10b + 10a)c + (- 54b - 236a b - 102a b - 40a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 52b + 126a b + 72a b - 384a b - 118a b)c +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (12b + 372a b + 322a b + 720a b + 158a b )c +--R + +--R 2 7 4 5 +--R (- 24a b + 24a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 9 2 2 3 7 +--R (- 12b + 8a)c + (- 140a b - 246a b - 46a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (36b - 67a b + 372a b - 112a b - 372a b - 85a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (24b + 81a b + 618a b + 420a b + 996a b + 237a b )c +--R + +--R 3 6 5 4 +--R (- 36a b + 36a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 6b - 6a)c + (- 8b + 42a b - 116a b - 46a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (14b + 96a b - 62a b + 338a b - 206a b - 128a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (16b + 48a b + 78a b + 420a b + 226a b + 624a b + 172a b)c +--R + +--R 4 5 6 3 +--R (- 24a b + 24a b )c +--R * +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (5b - 5a)c + (5b - 8a b + 46a b - 31a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (13a b + 60a b - 44a b + 87a b - 52a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (16a b + 24a b + 9a b + 99a b + 52a b + 150a b + 46a )c +--R + +--R 5 4 7 2 +--R (- 6a b + 6a b )c +--R * +--R 5 +--R sin(x) +--R + +--R 10 2 2 8 +--R - 2c + (31b - a b - 4a )c +--R + +--R 4 3 2 2 3 6 +--R (- 55b - 42a b - 12a b - 41a b)c +--R + +--R 6 5 2 4 3 3 4 +--R (- 31b - a b - 212a b - 22a b )c +--R + +--R 8 7 2 6 3 5 2 +--R (57b + 40a b + 156a b + 59a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 10 2 2 8 +--R - 2c + (44b + 79a b - 5a )c +--R + +--R 4 3 2 2 3 4 6 +--R (3b - 327a b - 239a b - 106a b - 41a )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 44b - 71a b - 153a b - 776a b - 66a b )c +--R + +--R 8 7 2 6 3 5 4 4 2 +--R (- b + 335a b + 261a b + 730a b + 235a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 10 2 2 8 +--R 4c + (- 16b + 90a b + 50a )c +--R + +--R 4 3 2 2 3 4 6 +--R (4b - 206a b - 736a b - 240a b - 90a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (32b - 253a b + 48a b - 476a b - 1038a b - 93a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 2 +--R (8b + 43a b + 754a b + 550a b + 1368a b + 397a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 10 2 2 8 +--R 4c + (- 24b - 50a b + 54a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 71b - 12a b - 388a b - 526a b - 47a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 35b + 62a b - 369a b + 328a b - 667a b - 612a b - 47a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (8b + 24a b + 111a b + 822a b + 508a b + 1284a b + 363a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 10 2 2 8 +--R - 2c + (5b - 49a b - 26a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 9b - 104a b + 76a b - 263a b - 74a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 16b - 39a b + 76a b - 248a b + 335a b - 420a b - 138a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (16a b + 24a b + 89a b + 437a b + 210a b + 604a b + 180a b)c +--R * +--R cos(x) +--R + +--R 10 2 8 4 3 2 2 3 4 6 +--R - 2c + (11a b - 29a )c + (4b - 5a b - 45a b + 80a b - 72a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 16a b - 12a b + 46a b - 76a b + 95a b - 85a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (8a b + 8a b + 22a b + 91a b + 31a b + 114a b + 38a )c +--R * +--R 4 +--R sin(x) +--R + +--R 9 3 2 2 3 7 +--R (- 5b + a)c + (26b - 49a b - 46a b + 5a )c +--R + +--R 5 4 2 3 3 2 5 +--R (- 12b - 14a b + 2a b - 64a b )c +--R + +--R 7 6 2 5 3 4 3 +--R (- 22b + 43a b - 98a b - 3a b )c +--R + +--R 9 8 2 7 3 6 +--R (21b + 7a b + 54a b + 26a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 8b - 8a)c + (6b + 50a b - 80a b - 40a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- 6b - 158a b - 54a b - 52a b - 170a b)c +--R + +--R 7 6 2 5 3 4 4 3 3 +--R (- 20b - 78a b + 8a b - 540a b + 6a b )c +--R + +--R 8 2 7 3 6 4 5 +--R (138a b + 66a b + 312a b + 132a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (7b - 11a)c + (- 23b + 164a b + 149a b - 50a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 7b - 58a b - 567a b - 137a b - 138a b - 101a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (23b - 221a b - 221a b - 460a b - 1092a b + 51a b )c +--R + +--R 8 2 7 3 6 4 5 5 4 +--R (12a b + 375a b + 201a b + 750a b + 282a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (16b + 16a)c + (32b + 16a b + 252a b + 100a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (- 20a b - 436a b - 848a b - 8a b - 80a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 16b - 20a b - 672a b - 320a b - 1036a b - 1040a b +--R + +--R 6 +--R 64a b +--R * +--R 3 +--R c +--R + +--R 2 7 3 6 4 5 5 4 6 3 +--R (48a b + 540a b + 284a b + 960a b + 328a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (b + 19a)c + (28b - 33a b - 36a b + 121a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (3b - 131a b - 62a b - 624a b - 463a b + 69a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 24b - 79a b - 126a b - 797a b - 156a b - 1006a b +--R + +--R 6 7 +--R - 474a b + 22a +--R * +--R 3 +--R c +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R (72a b + 435a b + 201a b + 690a b + 222a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 8b - 8a)c + (- 14b + 6a b - 100a b - 36a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 14b - 34a b - 158a b + 28a b - 370a b - 52a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 8b - 48a b - 78a b - 100a b - 410a b + 22a b - 494a b +--R + +--R 7 +--R - 84a +--R * +--R 3 +--R c +--R + +--R 4 5 5 4 6 3 7 2 8 +--R (48a b + 186a b + 66a b + 264a b + 84a b)c +--R * +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 3b - 9a)c + (- 7b - 10a b + 5a b - 52a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 4b - 9a b - 21a b - 47a b + 53a b - 100a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (- 8a b - 24a b - 15a b - 17a b - 84a b + 23a b - 99a )c +--R + +--R 5 4 6 3 7 2 8 9 +--R (12a b + 33a b + 7a b + 42a b + 14a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 6 +--R (- 3b + 9a b + 6a )c + (2b - 83a b - 90a b - 9a b)c +--R + +--R 6 5 2 4 3 3 4 +--R (4b - 48a b - 56a b - 52a b )c +--R + +--R 8 7 2 6 3 5 2 10 9 2 8 3 7 +--R (2b + 45a b + 22a b + 31a b )c + 3b + a b + 6a b + 2a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 2 8 +--R (15b + 15a b + 6a )c +--R + +--R 4 3 2 2 3 4 6 +--R (14b - 68a b - 325a b - 198a b - 3a )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 11b - 68a b - 155a b - 154a b - 164a b )c +--R + +--R 8 7 2 6 3 5 4 4 2 9 2 8 +--R (- 10b + 36a b + 195a b + 30a b + 137a b )c + 21a b + 7a b +--R + +--R 3 7 4 6 +--R 42a b + 14a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 2 8 +--R (21b - 3a b - 6a )c +--R + +--R 4 3 2 2 3 4 6 +--R (3b + 98a b - 57a b - 330a b - 102a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (- 21b - 2a b - 171a b - 73a b - 168a b - 189a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 2 +--R (- 3b - 103a b + 15a b + 176a b - 120a b + 263a b )c +--R + +--R 2 8 3 7 4 6 5 5 +--R 63a b + 21a b + 126a b + 42a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 2 8 +--R (- 15b - 5a b - 8a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 19b + 93a b + 448a b + 165a b - 115a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 2b + 15a b + 33a b - 211a b + 174a b - 94a b - 75a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 2b - 83a b - 441a b - 259a b - 324a b - 348a b +--R + +--R 6 2 +--R 273a b +--R * +--R 2 +--R c +--R + +--R 3 7 4 6 5 5 6 4 +--R 105a b + 35a b + 210a b + 70a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 8 +--R (- 17b + 11a b + 10a )c +--R + +--R 4 3 2 2 3 4 6 +--R (8b + 29a b + 216a b + 487a b + 128a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (17b - 7a b + 28a b - 200a b - 201a b + 267a b - 24a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 8b - 25a b - 278a b - 835a b - 560a b - 830a b +--R + +--R 6 2 7 +--R - 354a b + 150a b +--R * +--R 2 +--R c +--R + +--R 4 6 5 5 6 4 7 3 +--R 105a b + 35a b + 210a b + 70a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (b - 3a b + 14a )c + (16b + 18a b - 65a b + 72a b + 171a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (11b - 3a b - 114a b - 54a b - 404a b - 105a b + 117a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 4b - 24a b - 71a b - 366a b - 763a b - 474a b +--R + +--R 6 2 7 8 +--R - 750a b - 162a b + 34a +--R * +--R 2 +--R c +--R + +--R 5 5 6 4 7 3 8 2 +--R 63a b + 21a b + 126a b + 42a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 8 +--R (- b - 17a b - 10a )c +--R + +--R 4 3 2 2 3 4 6 +--R (- 5b - 12a b - 21a b - 116a b - 18a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 4b - 3a b - 41a b - 115a b - 51a b - 282a b - 16a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 +--R - 8a b - 24a b - 59a b - 215a b - 330a b - 177a b +--R + +--R 7 8 +--R - 331a b - 28a +--R * +--R 2 +--R c +--R + +--R 6 4 7 3 8 2 9 +--R 21a b + 7a b + 42a b + 14a b +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- b - 7a b - 12a )c + (- 3b - 11a b - 10a b - 7a b - 45a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 2b - 4a b - 4a b - 21a b - 26a b - 5a b - 82a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 7 3 +--R (- 4a b - 8a b - 15a b - 47a b - 54a b - 23a b - 61a )c + 3a b +--R + +--R 8 2 9 10 +--R a b + 6a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 7 +--R (b + 12a b + 12a b + 3a )c +--R + +--R 5 4 2 3 3 2 5 +--R (- 5b - 43a b - 58a b - 18a b )c +--R + +--R 7 6 2 5 3 4 3 +--R (- b - 42a b - 72a b - 41a b )c +--R + +--R 9 8 2 7 3 6 +--R (5b + 13a b + 22a b + 20a b )c +--R * +--R 8 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 4b - 4a)c + (10b + 34a b + 44a b + 16a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (16b - 60a b - 246a b - 212a b - 46a b)c +--R + +--R 6 2 5 3 4 4 3 3 +--R (- 58a b - 232a b - 280a b - 142a b )c +--R + +--R 9 8 2 7 3 6 4 5 +--R (- 2b + 40a b + 86a b + 116a b + 108a b )c +--R * +--R 7 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 4b - 4a)c + (17b + 33a b + 37a b + 17a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (31b + 80a b - 165a b - 463a b - 246a b - 25a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 3 +--R (3b + 22a b - 121a b - 383a b - 408a b - 185a b )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R (- 7b - 21a b + 97a b + 195a b + 246a b + 246a b )c +--R * +--R 6 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (8b + 8a)c + (6b - 2a b - 32a b - 12a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 8b + 112a b + 254a b - 60a b - 306a b - 92a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 6b + 68a b + 186a b + 50a b - 142a b - 264a b +--R + +--R 6 +--R - 108a b +--R * +--R 3 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R (- 54a b - 108a b + 46a b + 140a b + 260a b + 304a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (8b + 8a)c + (- 13b - 31a b - 43a b - 25a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 25b - 34a b + 271a b + 525a b + 144a b - 61a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 4b - a b + 199a b + 383a b + 309a b + 202a b - 64a b +--R + +--R 7 +--R - 24a +--R * +--R 3 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R - 6a b - 165a b - 277a b - 175a b - 143a b + 130a b +--R + +--R 7 2 +--R 216a b +--R * +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 2 2 7 +--R (- 4b - 4a)c + (- 18b - 26a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- 10b - 46a b + 2a b + 304a b + 412a b + 94a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 24a b + 2a b + 200a b + 250a b + 266a b + 206a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 24a b - 260a b - 378a b - 340a b - 354a b + 12a b +--R + +--R 8 +--R 84a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 9 3 2 2 3 7 +--R (- 4b - 4a)c + (- 5b - 13a b - a b + 11a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (- b - 2a b - 43a b - 41a b + 112a b + 107a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (7a b - 48a b - 28a b + 41a b - 48a b + 69a b + 55a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (- 36a b - 225a b - 279a b - 265a b - 287a b - 14a b + 14a )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 7 +--R (2b - 6a b - 16a b - 4a )c +--R + +--R 5 4 2 3 3 2 4 5 5 +--R (2b - 6a b - 10a b - 32a b - 60a b - 2a )c +--R + +--R 2 5 3 4 4 3 5 2 6 7 3 +--R (2a b - 40a b - 36a b - 44a b - 112a b - 2a )c +--R + +--R 4 5 5 4 6 3 7 2 8 9 +--R (- 24a b - 102a b - 104a b - 98a b - 112a b - 4a )c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 4 5 5 +--R (- a b - 5a b - 6a )c + (- a b - 5a b - 3a b - 10a b - 21a )c +--R + +--R 3 4 4 3 5 2 6 7 3 +--R (- a b - 12a b - 11a b - 19a b - 33a )c +--R + +--R 5 4 6 3 7 2 8 9 +--R (- 6a b - 19a b - 15a b - 14a b - 18a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 3 6 6 5 2 4 3 3 4 +--R (b + 4a b + 6a b + 3a b)c + (- b - 7a b - 10a b - 4a b )c +--R + +--R 8 7 2 6 3 5 2 10 9 2 8 3 7 +--R (- b - 10a b - 22a b - 13a b )c + b + a b + 2a b + 2a b +--R * +--R 9 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b - 4a b - 2a )c + (b + 11a b + 21a b + 16a b + 5a )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (4b - 11a b - 51a b - 54a b - 18a b )c +--R + +--R 8 7 2 6 3 5 4 4 2 9 2 8 3 7 +--R (b - 19a b - 75a b - 112a b - 57a b )c + 7a b + 7a b + 14a b +--R + +--R 4 6 +--R 14a b +--R * +--R 8 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 4b - 8a b - 4a )c + (- b + 5a b + 23a b + 27a b + 10a )c +--R + +--R 6 5 2 4 3 3 4 2 5 4 +--R (9b + 24a b - 49a b - 143a b - 104a b - 25a b)c +--R + +--R 8 7 2 6 3 5 4 4 5 3 2 10 9 +--R (5b + 10a b - 57a b - 193a b - 228a b - 97a b )c - b - a b +--R + +--R 2 8 3 7 4 6 5 5 +--R 19a b + 19a b + 42a b + 42a b +--R * +--R 7 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 6 +--R (2b + 4a b + 2a )c + (3b - a b - 3a b + a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (b + 39a b + 64a b - 73a b - 174a b - 86a b - 11a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 2 9 +--R (37a b + 64a b - 29a b - 209a b - 232a b - 79a b )c - 7a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 7a b + 21a b + 21a b + 70a b + 70a b +--R * +--R 6 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (8b + 16a b + 8a )c + (7b + 9a b - 21a b - 35a b - 12a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 5b - 4a b + 93a b + 137a b - 12a b - 83a b - 26a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - 4b + 3a b + 111a b + 185a b + 109a b - 60a b - 118a b +--R + +--R 7 +--R - 30a b +--R * +--R 2 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 +--R - 21a b - 21a b - 7a b - 7a b + 70a b + 70a b +--R * +--R 5 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b + 4a b + 2a )c + (- b + a b - 9a b - 19a b - 8a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 4b - 21a b - 5a b + 147a b + 191a b + 48a b - 8a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 +--R - b - 18a b + 14a b + 169a b + 254a b + 195a b + 59a b +--R + +--R 7 8 +--R - 24a b - 4a +--R * +--R 2 +--R c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 +--R - 35a b - 35a b - 49a b - 49a b + 42a b + 42a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 4b - 8a b - 4a )c + (- 7b - 17a b - 3a b + 9a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- 3b - 12a b - 29a b + 11a b + 126a b + 121a b + 26a )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (- 3a b - 32a b + 22a b + 131a b + 158a b + 125a b + 47a b)c +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R - 35a b - 35a b - 63a b - 63a b + 14a b + 14a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b - 4a b - 2a )c + (- 3b - 11a b - 9a b + 3a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (- b - 7a b - 8a b - 19a b + 2a b + 42a b + 23a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (- 3a b - 28a b + 12a b + 39a b + 22a b + 29a b + 9a )c +--R + +--R 5 5 6 4 7 3 8 2 9 10 +--R - 21a b - 21a b - 41a b - 41a b + 2a b + 2a +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (- a b - 5a b - 4a b)c +--R + +--R 5 2 4 3 3 4 2 5 4 +--R (- a b - 5a b - a b - 10a b - 13a b)c +--R + +--R 3 5 4 4 5 3 6 2 7 2 6 4 7 3 8 2 +--R (- a b - 12a b - a b - 7a b - 17a b)c - 7a b - 7a b - 14a b +--R + +--R 9 +--R - 14a b +--R * +--R cos(x) +--R + +--R 3 4 6 3 3 4 2 5 6 4 +--R (- a b - a )c + (- a b - a b - 4a b - 4a )c +--R + +--R 5 3 6 2 7 8 2 7 3 8 2 9 10 +--R (- 2a b - 2a b - 5a b - 5a )c - a b - a b - 2a b - 2a +--R / +--R 4 3 2 2 9 +--R (8b - 16a b + 8a b )c +--R + +--R 6 5 3 3 4 2 7 +--R (16b - 32a b + 32a b - 16a b )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 5 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 9 +--R (16a b - 32a b + 16a b)c +--R + +--R 5 2 4 4 2 5 7 +--R (32a b - 64a b + 64a b - 32a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 5 +--R (16a b - 32a b - 16a b + 64a b - 16a b - 32a b + 16a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 4 9 2 4 3 3 5 6 7 +--R (8a b - 16a b + 8a )c + (16a b - 32a b + 32a b - 16a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 5 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R 7 +--R sin(x) +--R + +--R 3 2 2 10 +--R (- 24b + 32a b - 8a b)c +--R + +--R 5 2 3 3 2 4 8 +--R (- 16b + 64a b - 64a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (40b - 96a b + 40a b + 64a b - 72a b + 32a b - 8a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 4 +--R (32b - 64a b - 32a b + 128a b - 32a b - 64a b + 32a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 3 2 2 3 10 +--R (- 16b - 24a b + 48a b - 8a )c +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 32b + 48a b - 64a b + 128a b - 96a b + 16a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 16b + 168a b - 304a b + 40a b + 272a b - 200a b +--R + +--R 6 7 +--R 48a b - 8a +--R * +--R 6 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 +--R 96a b - 192a b - 96a b + 384a b - 96a b - 192a b +--R + +--R 7 2 +--R 96a b +--R * +--R 4 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 10 +--R (8b - 48a b + 24a b + 16a )c +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (16b - 96a b + 128a b - 64a b + 48a b - 32a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 8b - 48a b + 200a b - 272a b - 40a b + 304a b +--R + +--R 6 7 +--R - 168a b + 16a +--R * +--R 6 +--R c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R 96a b - 192a b - 96a b + 384a b - 96a b - 192a b +--R + +--R 8 +--R 96a b +--R * +--R 4 +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 10 4 2 3 3 2 5 8 +--R (8a b - 32a b + 24a )c + (16a b - 64a b + 64a b - 16a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 6 +--R (8a b - 32a b + 72a b - 64a b - 40a b + 96a b - 40a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 4 +--R (32a b - 64a b - 32a b + 128a b - 32a b - 64a b + 32a )c +--R * +--R 6 +--R sin(x) +--R + +--R 2 2 11 +--R (18b - 20a b + 2a )c +--R + +--R 4 3 2 2 3 4 9 +--R (- 64b + 80a b - 52a b + 40a b - 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 132b + 120a b + 176a b - 200a b + 54a b - 20a b +--R + +--R 6 +--R 2a +--R * +--R 7 +--R c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 5 +--R (- 80a b + 180a b - 40a b - 160a b + 120a b - 20a b )c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R 50b - 100a b - 50a b + 200a b - 50a b - 100a b +--R + +--R 6 4 +--R 50a b +--R * +--R 3 +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 11 +--R (16b - 16a )c +--R + +--R 4 3 2 2 3 4 9 +--R (- 48b - 200a b + 256a b - 40a b + 32a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 144b - 200a b + 352a b + 520a b - 592a b + 80a b +--R + +--R 6 +--R - 16a +--R * +--R 7 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 80b + 200a b - 320a b + 360a b + 80a b - 520a b +--R + +--R 6 2 7 +--R 320a b - 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92b + 20a b + 332a b - 192a b - 236a b + 172a b +--R + +--R 6 3 +--R - 4a b +--R * +--R 4 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R 38b - 76a b - 38a b + 152a b - 38a b - 76a b +--R + +--R 6 5 +--R 38a b +--R * +--R 2 +--R c +--R * +--R 5 +--R cos(x) +--R + +--R 12 3 2 2 3 10 +--R (- 4b + 4a)c + (64b + 78a b - 132a b - 10a )c +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 24b - 360a b + 264a b - 164a b + 276a b + 8a )c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 256b - 748a b + 1024a b + 1032a b - 1008a b +--R + +--R 5 2 6 7 +--R 98a b - 140a b - 2a +--R * +--R 6 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 164b - 124a b + 248a b + 996a b - 764a b - 860a b +--R + +--R 6 3 7 2 +--R 680a b - 12a b +--R * +--R 4 +--R c +--R + +--R 10 2 9 3 8 4 7 5 6 +--R 190a b - 380a b - 190a b + 760a b - 190a b +--R + +--R 6 5 7 4 +--R - 380a b + 190a b +--R * +--R 2 +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 12 3 2 2 3 10 +--R (8b - 8a)c + (- 52b + 192a b - 84a b - 56a )c +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 124b - 256a b - 352a b + 464a b + 132a b + 136a )c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 60b - 1120a b - 232a b + 2096a b + 1096a b +--R + +--R 5 2 6 7 +--R - 1664a b - 44a b - 72a +--R * +--R 6 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R 4b - 664a b + 416a b + 816a b + 664a b - 1160a b +--R + +--R 6 3 7 2 8 +--R - 1072a b + 1008a b - 12a b +--R * +--R 4 +--R c +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R 380a b - 760a b - 380a b + 1520a b - 380a b +--R + +--R 7 4 8 3 +--R - 760a b + 380a b +--R * +--R 2 +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 12 3 2 2 3 10 +--R (8b - 8a)c + (- 56b - 84a b + 192a b - 52a )c +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 136b - 132a b - 464a b + 352a b + 256a b + 124a )c +--R + +--R 7 6 2 5 3 4 4 3 +--R - 72b - 44a b - 1664a b + 1096a b + 2096a b +--R + +--R 5 2 6 7 +--R - 232a b - 1120a b - 60a +--R * +--R 6 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 +--R 12a b - 1008a b + 1072a b + 1160a b - 664a b +--R + +--R 6 3 7 2 8 9 +--R - 816a b - 416a b + 664a b - 4a +--R * +--R 4 +--R c +--R + +--R 3 8 4 7 5 6 6 5 7 4 +--R 380a b - 760a b - 380a b + 1520a b - 380a b +--R + +--R 8 3 9 2 +--R - 760a b + 380a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 12 3 2 2 3 10 +--R (- 4b + 4a)c + (- 10b - 132a b + 78a b + 64a )c +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 8b - 276a b + 164a b - 264a b + 360a b + 24a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 2b - 140a b + 98a b - 1008a b + 1032a b + 1024a b +--R + +--R 6 7 +--R - 748a b - 256a +--R * +--R 6 +--R c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 +--R 12a b - 680a b + 860a b + 764a b - 996a b - 248a b +--R + +--R 8 9 +--R 124a b + 164a +--R * +--R 4 +--R c +--R + +--R 4 7 5 6 6 5 7 4 8 3 9 2 +--R 190a b - 380a b - 190a b + 760a b - 190a b - 380a b +--R + +--R 10 +--R 190a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 12 3 2 2 3 10 +--R (- 4b + 4a)c + (- 8b + 6a b - 60a b + 62a )c +--R + +--R 5 2 3 3 2 4 5 8 +--R (- 4b - 128a b + 140a b - 40a b + 32a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R - 2a b - 68a b + 82a b - 208a b + 224a b + 200a b +--R + +--R 7 +--R - 228a +--R * +--R 6 +--R c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 4 +--R (4a b - 172a b + 236a b + 192a b - 332a b - 20a b + 92a )c +--R + +--R 5 6 6 5 7 4 8 3 9 2 10 11 2 +--R (38a b - 76a b - 38a b + 152a b - 38a b - 76a b + 38a )c +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 11 +--R (- 14b + 12a b + 2a )c +--R + +--R 4 3 2 2 3 4 9 +--R (78b - 60a b + 10a b - 24a b - 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 7 +--R (52b - 40a b - 196a b + 144a b + 26a b + 12a b + 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 172b + 120a b + 132a b - 64a b + 90a b - 84a b +--R + +--R 6 2 +--R - 22a b +--R * +--R 5 +--R c +--R + +--R 10 9 2 8 3 7 4 6 5 5 +--R - 118b + 60a b + 322a b - 176a b - 234a b + 116a b +--R + +--R 6 4 +--R 30a b +--R * +--R 3 +--R c +--R + +--R 12 11 2 10 3 9 4 8 5 7 +--R 14b - 28a b - 14a b + 56a b - 14a b - 28a b +--R + +--R 6 6 +--R 14a b +--R * +--R c +--R * +--R 6 +--R cos(x) +--R + +--R 2 2 11 +--R (- 16b + 16a )c +--R + +--R 4 3 2 2 3 4 9 +--R (96b + 212a b - 232a b - 44a b - 32a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 64b - 160a b - 160a b - 392a b + 544a b + 88a b +--R + +--R 6 +--R 16a +--R * +--R 7 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R - 224b - 872a b + 912a b + 1024a b - 560a b + 60a b +--R + +--R 6 2 7 +--R - 296a b - 44a b +--R * +--R 5 +--R c +--R + +--R 10 9 2 8 3 7 4 6 +--R - 176b - 416a b + 656a b + 1288a b - 1120a b +--R + +--R 5 5 6 4 7 3 +--R - 992a b + 640a b + 120a b +--R * +--R 3 +--R c +--R + +--R 11 2 10 3 9 4 8 5 7 6 6 +--R 84a b - 168a b - 84a b + 336a b - 84a b - 168a b +--R + +--R 7 5 +--R 84a b +--R * +--R c +--R * +--R 5 +--R cos(x) +--R + +--R 2 2 11 +--R (26b - 36a b + 10a )c +--R + +--R 4 3 2 2 3 4 9 +--R (- 32b + 352a b - 10a b - 268a b - 42a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 172b - 8a b - 560a b - 56a b + 98a b + 644a b +--R + +--R 6 +--R 54a +--R * +--R 7 +--R c +--R + +--R 8 7 2 6 3 5 4 4 +--R - 144b - 1216a b - 1000a b + 2832a b + 1880a b +--R + +--R 5 3 6 2 7 8 +--R - 1696a b - 294a b - 340a b - 22a +--R * +--R 5 +--R c +--R + +--R 10 9 2 8 3 7 4 6 +--R - 30b - 820a b - 250a b + 2200a b + 1610a b +--R + +--R 5 5 6 4 7 3 8 2 +--R - 2780a b - 1510a b + 1400a b + 180a b +--R * +--R 3 +--R c +--R + +--R 2 10 3 9 4 8 5 7 6 6 +--R 210a b - 420a b - 210a b + 840a b - 210a b +--R + +--R 7 5 8 4 +--R - 420a b + 210a b +--R * +--R c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 11 +--R (32b - 32a )c +--R + +--R 4 3 2 2 3 4 9 +--R (- 64b - 168a b + 464a b - 168a b - 64a )c +--R + +--R 6 5 2 4 4 2 5 6 7 +--R (- 224b - 456a b - 176a b + 176a b + 456a b + 224a )c +--R + +--R 8 7 2 6 3 5 4 4 +--R - 128b - 408a b - 2192a b + 688a b + 4080a b +--R + +--R 5 3 6 2 7 8 +--R 688a b - 2192a b - 408a b - 128a +--R * +--R 5 +--R c +--R + +--R 9 2 8 3 7 4 6 6 4 +--R - 120a b - 1520a b + 800a b + 3440a b - 3440a b +--R + +--R 7 3 8 2 9 +--R - 800a b + 1520a b + 120a b +--R * +--R 3 +--R c +--R + +--R 3 9 4 8 5 7 6 6 7 5 +--R 280a b - 560a b - 280a b + 1120a b - 280a b +--R + +--R 8 4 9 3 +--R - 560a b + 280a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 11 +--R (- 10b + 36a b - 26a )c +--R + +--R 4 3 2 2 3 4 9 +--R (- 42b - 268a b - 10a b + 352a b - 32a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 54b - 644a b - 98a b + 56a b + 560a b + 8a b +--R + +--R 6 +--R 172a +--R * +--R 7 +--R c +--R + +--R 8 7 2 6 3 5 4 4 +--R - 22b - 340a b - 294a b - 1696a b + 1880a b +--R + +--R 5 3 6 2 7 8 +--R 2832a b - 1000a b - 1216a b - 144a +--R * +--R 5 +--R c +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 180a b - 1400a b + 1510a b + 2780a b - 1610a b +--R + +--R 7 3 8 2 9 10 +--R - 2200a b + 250a b + 820a b + 30a +--R * +--R 3 +--R c +--R + +--R 4 8 5 7 6 6 7 5 8 4 9 3 +--R 210a b - 420a b - 210a b + 840a b - 210a b - 420a b +--R + +--R 10 2 +--R 210a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 11 +--R (- 16b + 16a )c +--R + +--R 4 3 2 2 3 4 9 +--R (- 32b - 44a b - 232a b + 212a b + 96a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R - 16b - 88a b - 544a b + 392a b + 160a b + 160a b +--R + +--R 6 +--R - 64a +--R * +--R 7 +--R c +--R + +--R 7 2 6 3 5 4 4 5 3 +--R - 44a b - 296a b + 60a b - 560a b + 1024a b +--R + +--R 6 2 7 8 +--R 912a b - 872a b - 224a +--R * +--R 5 +--R c +--R + +--R 3 7 4 6 5 5 6 4 7 3 +--R - 120a b - 640a b + 992a b + 1120a b - 1288a b +--R + +--R 8 2 9 10 +--R - 656a b + 416a b + 176a +--R * +--R 3 +--R c +--R + +--R 5 7 6 6 7 5 8 4 9 3 10 2 +--R 84a b - 168a b - 84a b + 336a b - 84a b - 168a b +--R + +--R 11 +--R 84a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 11 +--R (- 2b - 12a b + 14a )c +--R + +--R 4 3 2 2 3 4 9 +--R (- 4b - 24a b + 10a b - 60a b + 78a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 7 +--R (- 2b - 12a b - 26a b - 144a b + 196a b + 40a b - 52a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 +--R - 22a b - 84a b + 90a b - 64a b + 132a b + 120a b +--R + +--R 8 +--R - 172a +--R * +--R 5 +--R c +--R + +--R 4 6 5 5 6 4 7 3 8 2 9 +--R - 30a b - 116a b + 234a b + 176a b - 322a b - 60a b +--R + +--R 10 +--R 118a +--R * +--R 3 +--R c +--R + +--R 6 6 7 5 8 4 9 3 10 2 11 12 +--R (14a b - 28a b - 14a b + 56a b - 14a b - 28a b + 14a )c +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 10 +--R (- 18b + 12a b + 6a b)c +--R + +--R 5 4 2 3 3 2 4 8 +--R (42b - 20a b + 14a b - 24a b - 12a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (68b - 40a b - 148a b + 64a b + 38a b + 12a b + 6a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 60b + 24a b + 20a b + 16a b + 78a b - 44a b +--R + +--R 6 3 +--R - 34a b +--R * +--R 4 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 +--R - 66b + 28a b + 174a b - 64a b - 142a b + 36a b +--R + +--R 6 5 +--R 34a b +--R * +--R 2 +--R c +--R + +--R 13 12 2 11 3 10 4 9 5 8 6 7 +--R 2b - 4a b - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 7 +--R cos(x) +--R + +--R 3 2 2 3 10 +--R (- 24b - 18a b + 36a b + 6a )c +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (64b + 198a b - 124a b - 54a b - 72a b - 12a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R 96b + 100a b - 344a b - 460a b + 392a b + 174a b +--R + +--R 6 7 +--R 36a b + 6a +--R * +--R 6 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 +--R - 96b - 452a b + 280a b + 484a b + 32a b + 98a b +--R + +--R 6 3 7 2 +--R - 244a b - 102a b +--R * +--R 4 +--R c +--R + +--R 11 10 2 9 3 8 4 7 +--R - 104b - 322a b + 436a b + 870a b - 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34b - 380a b - 666a b - 1328a b + 1392a b +--R + +--R 5 4 6 3 7 2 8 9 +--R 3184a b - 80a b - 1504a b - 472a b - 112a +--R * +--R 4 +--R c +--R + +--R 2 9 3 8 4 7 5 6 6 5 +--R - 340a b - 1400a b + 1170a b + 3740a b - 870a b +--R + +--R 7 4 8 3 9 2 10 +--R - 3560a b - 130a b + 1220a b + 170a b +--R * +--R 2 +--R c +--R + +--R 4 9 5 8 6 7 7 6 8 5 9 4 +--R 70a b - 140a b - 70a b + 280a b - 70a b - 140a b +--R + +--R 10 3 +--R 70a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 2 2 3 10 +--R (- 24b - 6a b + 60a b - 30a )c +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 48b - 114a b - 300a b + 142a b + 304a b + 16a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 +--R - 24b - 210a b - 828a b + 226a b + 760a b + 216a b +--R + +--R 6 7 +--R - 232a b + 92a +--R * +--R 6 +--R c +--R + +--R 8 2 7 3 6 4 5 5 4 +--R - 102a b - 468a b - 286a b - 400a b + 1456a b +--R + +--R 6 3 7 2 8 9 +--R 1472a b - 872a b - 688a b - 112a +--R * +--R 4 +--R c +--R + +--R 3 8 4 7 5 6 6 5 7 4 +--R - 340a b - 880a b + 1394a b + 2148a b - 1566a b +--R + +--R 8 3 9 2 10 11 +--R - 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128a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 +--R 88a b + 680a b + 560a b + 1680a b - 368a b - 2192a b +--R + +--R 7 +--R - 448a +--R * +--R 6 +--R c +--R + +--R 3 6 4 5 5 4 6 3 7 2 +--R 240a b + 1520a b - 464a b - 2704a b - 128a b +--R + +--R 8 9 +--R 1184a b + 352a +--R * +--R 4 +--R c +--R + +--R 5 6 6 5 7 4 8 3 9 2 10 2 +--R (- 168a b + 168a b + 336a b - 336a b - 168a b + 168a b)c +--R * +--R cos(x) +--R + +--R 12 3 2 2 3 10 +--R (4b + 28a)c + (8b + 56a b + 36a b + 156a )c +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (4b + 28a b + 80a b + 368a b - 24a b - 104a )c +--R + +--R 2 5 3 4 4 3 5 2 6 7 6 +--R (44a b + 212a b + 32a b + 160a b - 104a b - 344a )c +--R + +--R 4 5 5 4 6 3 7 2 8 9 4 +--R (60a b + 292a b - 176a b - 528a b + 116a b + 236a )c +--R + +--R 6 5 7 4 8 3 9 2 10 11 2 +--R (- 28a b + 28a b + 56a b - 56a b - 28a b + 28a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 11 4 3 2 2 3 9 +--R (36b + 12a b)c + (- 84b - 44a b - 72a b - 24a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 7 +--R (- 136b - 56a b + 240a b + 112a b + 36a b + 12a b)c +--R + +--R 8 7 2 6 4 4 5 3 5 +--R (120b + 72a b + 32a b - 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1416a b - 1584a b + 528a b +--R + +--R 6 4 7 3 +--R 880a b + 120a b +--R * +--R 3 +--R c +--R + +--R 11 3 9 5 7 7 5 +--R (- 84a b + 252a b - 252a b + 84a b )c +--R * +--R 5 +--R cos(x) +--R + +--R 2 2 11 +--R (- 26b - 16a b + 10a )c +--R + +--R 4 3 2 2 3 4 9 +--R (32b - 288a b - 630a b - 352a b - 42a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 172b + 352a b + 920a b + 1536a b + 1494a b + 752a b +--R + +--R 6 +--R 54a +--R * +--R 7 +--R c +--R + +--R 8 7 2 6 3 5 4 4 5 3 +--R 144b + 1504a b + 3720a b + 1888a b - 2824a b - 3008a b +--R + +--R 6 2 7 8 +--R - 1018a b - 384a b - 22a +--R * +--R 5 +--R c +--R + +--R 10 9 2 8 4 6 5 5 6 4 +--R 30b + 880a b + 1950a b - 3810a b - 2640a b + 1650a b +--R + +--R 7 3 8 2 +--R 1760a b + 180a b +--R * +--R 3 +--R c +--R + +--R 2 10 4 8 6 6 8 4 +--R (- 210a b + 630a b - 630a b + 210a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 11 4 3 3 4 9 +--R (- 32b - 64a b - 32a )c + (64b + 296a b - 296a b - 64a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 224b + 904a b + 1536a b + 1712a b + 1536a b + 904a b +--R + +--R 6 +--R 224a +--R * +--R 7 +--R c +--R + +--R 8 7 2 6 3 5 5 3 6 2 +--R 128b + 664a b + 3264a b + 4768a b - 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24a b - 60a b - 88a b - 84a b - 48a b - 12a b)c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R - 40a b - 108a b - 40a b + 150a b + 200a b + 96a b + 24a b +--R + +--R 8 +--R 6a b +--R * +--R 4 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R 4b + 24a b + 76a b + 120a b + 84a b - 24a b - 124a b +--R + +--R 7 4 8 3 +--R - 120a b - 40a b +--R * +--R 2 +--R c +--R + +--R 13 12 2 11 3 10 4 9 5 8 6 7 +--R 2b + 32a b + 96a b + 48a b - 156a b - 192a b + 16a b +--R + +--R 7 6 8 5 +--R 112a b + 42a b +--R * +--R 7 +--R cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 8b - 22a b - 8a b + 20a b + 16a b + 2a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R - 8b - 28a b - 72a b - 116a b - 112a b - 76a b - 32a b +--R + +--R 7 +--R - 4a +--R * +--R 6 +--R c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 8b + 24a b - 40a b - 116a b + 72a b + 330a b + 280a b +--R + +--R 7 2 8 9 +--R 96a b + 16a b + 2a +--R * +--R 4 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R 8b + 44a b + 136a b + 244a b + 216a b + 12a b - 200a b +--R + +--R 7 4 8 3 9 2 +--R - 260a b - 160a b - 40a b +--R * +--R 2 +--R c +--R + +--R 12 2 11 3 10 5 8 6 7 7 6 8 5 +--R 14a b + 112a b + 224a b - 420a b - 336a b + 112a b + 224a b +--R + +--R 9 4 +--R 70a b +--R * +--R 6 +--R cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (- 2b - 28a b - 56a b - 32a b + 2a b + 4a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 6 +--R (- 8a b - 24a b - 48a b - 64a b - 48a b - 24a b - 8a )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 6b + 68a b + 150a b + 72a b - 24a b + 160a b + 330a b +--R + +--R 7 2 8 9 +--R 200a b + 42a b + 4a +--R * +--R 4 +--R c +--R + +--R 11 10 2 9 3 8 4 7 5 6 6 5 +--R 4b + 48a b + 160a b + 312a b + 356a b + 120a b - 220a b +--R + +--R 7 4 8 3 9 2 10 +--R - 360a b - 280a b - 120a b - 20a b +--R * +--R 2 +--R c +--R + +--R 2 11 3 10 4 9 5 8 6 7 7 6 8 5 +--R 42a b + 224a b + 308a b - 168a b - 672a b - 336a b + 252a b +--R + +--R 9 4 10 3 +--R 280a b + 70a b +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (4b + 2a b - 32a b - 56a b - 28a b - 2a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 6 +--R (8b + 24a b + 48a b + 64a b + 48a b + 24a b + 8a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 4b + 42a b + 200a b + 330a b + 160a b - 24a b + 72a b +--R + +--R 7 2 8 9 +--R 150a b + 68a b + 6a +--R * +--R 4 +--R c +--R + +--R 10 2 9 3 8 4 7 5 6 6 5 +--R 20a b + 120a b + 280a b + 360a b + 220a b - 120a b +--R + +--R 7 4 8 3 9 2 10 11 +--R - 356a b - 312a b - 160a b - 48a b - 4a +--R * +--R 2 +--R c +--R + +--R 3 10 4 9 5 8 6 7 7 6 8 5 9 4 +--R 70a b + 280a b + 252a b - 336a b - 672a b - 168a b + 308a b +--R + +--R 10 3 11 2 +--R 224a b + 42a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 2 3 3 2 4 5 8 +--R (2b + 16a b + 20a b - 8a b - 22a b - 8a )c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 7 6 +--R (4b + 32a b + 76a b + 112a b + 116a b + 72a b + 28a b + 8a )c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R 2b + 16a b + 96a b + 280a b + 330a b + 72a b - 116a b +--R + +--R 7 2 8 9 +--R - 40a b + 24a b + 8a +--R * +--R 4 +--R c +--R + +--R 2 9 3 8 4 7 5 6 6 5 7 4 8 3 +--R 40a b + 160a b + 260a b + 200a b - 12a b - 216a b - 244a b +--R + +--R 9 2 10 11 +--R - 136a b - 44a b - 8a +--R * +--R 2 +--R c +--R + +--R 4 9 5 8 6 7 7 6 8 5 10 3 11 2 +--R 70a b + 224a b + 112a b - 336a b - 420a b + 224a b + 112a b +--R + +--R 12 +--R 14a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 2 3 3 2 4 5 8 +--R (6a b + 24a b + 28a b + 8a b - 2a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 6 +--R (12a b + 48a b + 84a b + 88a b + 60a b + 24a b + 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R 6a b + 24a b + 96a b + 200a b + 150a b - 40a b - 108a b +--R + +--R 8 +--R - 40a b +--R * +--R 4 +--R c +--R + +--R 3 8 4 7 5 6 6 5 7 4 8 3 9 2 +--R 40a b + 120a b + 124a b + 24a b - 84a b - 120a b - 76a b +--R + +--R 10 11 +--R - 24a b - 4a +--R * +--R 2 +--R c +--R + +--R 5 8 6 7 7 6 8 5 9 4 10 3 11 2 +--R 42a b + 112a b + 16a b - 192a b - 156a b + 48a b + 96a b +--R + +--R 12 13 +--R 32a b + 2a +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 3 2 4 5 8 +--R (6a b + 16a b + 14a b + 4a )c +--R + +--R 2 5 3 4 4 3 5 2 6 6 +--R (12a b + 32a b + 36a b + 24a b + 8a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 9 4 +--R (6a b + 16a b + 42a b + 68a b + 24a b - 40a b - 36a b - 8a )c +--R + +--R 4 7 5 6 6 5 7 4 8 3 9 2 10 2 +--R (20a b + 48a b + 24a b - 24a b - 36a b - 24a b - 8a b)c +--R + +--R 6 7 7 6 8 5 9 4 10 3 11 2 12 13 +--R 14a b + 32a b - 6a b - 60a b - 30a b + 24a b + 22a b + 4a +--R * +--R cos(x) +--R + +--R 3 2 4 5 8 3 4 4 3 5 2 6 +--R (2a b + 4a b + 2a )c + (4a b + 8a b + 4a b )c +--R + +--R 3 6 4 5 5 4 6 3 8 9 4 +--R (2a b + 4a b + 6a b + 8a b - 8a b - 4a )c +--R + +--R 5 6 6 5 8 3 9 2 2 7 6 8 5 9 4 10 3 +--R (4a b + 8a b - 8a b - 4a b )c + 2a b + 4a b - 2a b - 8a b +--R + +--R 11 2 12 13 +--R - 2a b + 4a b + 2a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 532 +t0764:= 1/(2+cos(x)+2*sin(x)) +--R +--R +--R 1 +--R (314) -------------------- +--R 2sin(x) + cos(x) + 2 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 532 +r0764:= -2*atanh(2+tan(1/2*x)) +--R +--R +--R x +--R (315) - 2atanh(tan(-) + 2) +--R 2 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 532 +a0764:= integrate(t0764,x) +--R +--R +--R sin(x) + 3cos(x) + 3 sin(x) + cos(x) + 1 +--R (316) - log(--------------------) + log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 532 +m0764:= a0764-r0764 +--R +--R +--R (317) +--R sin(x) + 3cos(x) + 3 sin(x) + cos(x) + 1 x +--R - log(--------------------) + log(-------------------) + 2atanh(tan(-) + 2) +--R cos(x) + 1 cos(x) + 1 2 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 532 +d0764:= D(m0764,x) +--R +--R +--R (318) +--R 2 2 x 2 +--R (sin(x) + (- 4cos(x) - 4)sin(x) - cos(x) - 4cos(x) - 3)tan(-) +--R 2 +--R + +--R 2 2 x 2 +--R (8sin(x) + 8cos(x) + 8cos(x))tan(-) + 5sin(x) + (- 4cos(x) - 4)sin(x) +--R 2 +--R + +--R 2 +--R 3cos(x) - 3 +--R / +--R 2 2 x 2 +--R (sin(x) + (4cos(x) + 4)sin(x) + 3cos(x) + 6cos(x) + 3)tan(-) +--R 2 +--R + +--R 2 2 x +--R (4sin(x) + (16cos(x) + 16)sin(x) + 12cos(x) + 24cos(x) + 12)tan(-) +--R 2 +--R + +--R 2 2 +--R 3sin(x) + (12cos(x) + 12)sin(x) + 9cos(x) + 18cos(x) + 9 +--R Type: Expression(Integer) +--E 345 + +--S 346 of 532 +t0765:= 1/(a+a*cos(x)+c*sin(x))^2 +--R +--R +--R 1 +--R (319) ------------------------------------------------------------------- +--R 2 2 2 2 2 2 +--R c sin(x) + (2a c cos(x) + 2a c)sin(x) + a cos(x) + 2a cos(x) + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 532 +r0765:= -a*log(a+c*tan(1/2*x))/c^3-(c*cos(x)-a*sin(x))/c^2/_ + (a+a*cos(x)+c*sin(x)) +--R +--R +--R (320) +--R 2 2 x 2 +--R (- a c sin(x) - a cos(x) - a )log(c tan(-) + a) + a c sin(x) - c cos(x) +--R 2 +--R ----------------------------------------------------------------------- +--R 4 3 3 +--R c sin(x) + a c cos(x) + a c +--R Type: Expression(Integer) +--E 347 + +--S 348 of 532 +a0765:= integrate(t0765,x) +--R +--R +--R (321) +--R 2 2 c sin(x) + a cos(x) + a +--R (- 2a c sin(x) - 2a cos(x) - 2a )log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 +--R a c sin(x) + (- 2c - a )cos(x) - a +--R / +--R 4 3 3 +--R 2c sin(x) + 2a c cos(x) + 2a c +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 532 +m0765:= a0765-r0765 +--R +--R +--R x c sin(x) + a cos(x) + a +--R 2a log(c tan(-) + a) - 2a log(-----------------------) - a +--R 2 cos(x) + 1 +--R (322) ---------------------------------------------------------- +--R 3 +--R 2c +--R Type: Expression(Integer) +--E 349 + +--S 350 of 532 +d0765:= D(m0765,x) +--R +--R +--R (323) +--R 2 2 2 2 x 2 +--R ((a c cos(x) + a c)sin(x) + a cos(x) + 2a cos(x) + a )tan(-) +--R 2 +--R + +--R 2 2 x 2 2 +--R (- 2a c sin(x) - 2a c cos(x) - 2a c cos(x))tan(-) - 2a sin(x) +--R 2 +--R + +--R 2 2 2 +--R (a c cos(x) + a c)sin(x) - a cos(x) + a +--R / +--R 4 4 3 2 3 3 x +--R ((2c cos(x) + 2c )sin(x) + 2a c cos(x) + 4a c cos(x) + 2a c )tan(-) +--R 2 +--R + +--R 3 3 2 2 2 2 2 2 2 +--R (2a c cos(x) + 2a c )sin(x) + 2a c cos(x) + 4a c cos(x) + 2a c +--R Type: Expression(Integer) +--E 350 + +--S 351 of 532 +t0766:= 1/(a+a*cos(x)+c*sin(x))^3 +--R +--R +--R (324) +--R 1 +--R / +--R 3 3 2 2 2 +--R c sin(x) + (3a c cos(x) + 3a c )sin(x) +--R + +--R 2 2 2 2 3 3 3 2 +--R (3a c cos(x) + 6a c cos(x) + 3a c)sin(x) + a cos(x) + 3a cos(x) +--R + +--R 3 3 +--R 3a cos(x) + a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 532 +r0766:= 1/2*(3*a^2+c^2)*log(a+c*tan(1/2*x))/c^5-1/2*(c*cos(x)-a*sin(x))/_ + c^2/(a+a*cos(x)+c*sin(x))^2+3/2*a*(c*cos(x)-a*sin(x))/c^4/_ + (a+a*cos(x)+c*sin(x)) +--R +--R +--R (325) +--R 4 2 2 2 3 3 3 3 +--R (c + 3a c )sin(x) + ((2a c + 6a c)cos(x) + 2a c + 6a c)sin(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 +--R (a c + 3a )cos(x) + (2a c + 6a )cos(x) + a c + 3a +--R * +--R x +--R log(c tan(-) + a) +--R 2 +--R + +--R 2 2 2 3 3 3 3 +--R - 3a c sin(x) + ((3a c - 3a c)cos(x) + a c - 3a c)sin(x) +--R + +--R 2 2 2 4 2 2 +--R 3a c cos(x) + (- c + 3a c )cos(x) +--R / +--R 7 2 6 6 2 5 2 2 5 +--R 2c sin(x) + (4a c cos(x) + 4a c )sin(x) + 2a c cos(x) + 4a c cos(x) +--R + +--R 2 5 +--R 2a c +--R Type: Expression(Integer) +--E 352 + +--S 353 of 532 +a0766:= integrate(t0766,x) +--R +--R +--R (326) +--R 3 3 3 3 +--R ((8a c + 24a c)cos(x) + 8a c + 24a c)sin(x) +--R + +--R 4 2 2 4 2 2 2 4 4 2 2 +--R (- 4c - 8a c + 12a )cos(x) + (8a c + 24a )cos(x) + 4c + 16a c +--R + +--R 4 +--R 12a +--R * +--R c sin(x) + a cos(x) + a +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 3 3 3 3 2 2 4 2 +--R ((12a c + 2a c)cos(x) + 4a c + 2a c)sin(x) + (17a c + 7a )cos(x) +--R + +--R 4 2 2 4 2 2 4 +--R (- 4c + 12a c + 14a )cos(x) - 5a c + 7a +--R / +--R 6 6 7 2 5 2 2 5 +--R (16a c cos(x) + 16a c )sin(x) + (- 8c + 8a c )cos(x) + 16a c cos(x) +--R + +--R 7 2 5 +--R 8c + 8a c +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 532 +m0766:= a0766-r0766 +--R +--R +--R (327) +--R 5 3 3 5 3 3 3 +--R ((- 8a c - 24a c )cos(x) - 8a c - 24a c )sin(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 6 +--R (4c - 8a c - 60a c )cos(x) + (- 40a c - 120a c )cos(x) - 4c +--R + +--R 2 4 4 2 +--R - 32a c - 60a c +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (8a c + 8a c - 48a c)cos(x) + (8a c - 24a c - 144a c)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 8a c - 72a c - 144a c)cos(x) - 8a c - 40a c - 48a c +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (4a c + 8a c - 12a )cos(x) + (8a c + 8a c - 48a )cos(x) +--R + +--R 4 2 6 2 2 4 4 2 6 2 4 +--R (- 24a c - 72a )cos(x) + (- 8a c - 40a c - 48a )cos(x) - 4a c +--R + +--R 4 2 6 +--R - 16a c - 12a +--R * +--R x +--R log(c tan(-) + a) +--R 2 +--R + +--R 5 3 3 5 3 3 3 +--R ((8a c + 24a c )cos(x) + 8a c + 24a c )sin(x) +--R + +--R 6 2 4 4 2 2 2 4 4 2 6 +--R (- 4c + 8a c + 60a c )cos(x) + (40a c + 120a c )cos(x) + 4c +--R + +--R 2 4 4 2 +--R 32a c + 60a c +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 3 +--R (- 8a c - 8a c + 48a c)cos(x) +--R + +--R 5 3 3 5 2 +--R (- 8a c + 24a c + 144a c)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (8a c + 72a c + 144a c)cos(x) + 8a c + 40a c + 48a c +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 4 2 4 4 2 6 3 +--R (- 4a c - 8a c + 12a )cos(x) + (- 8a c - 8a c + 48a )cos(x) +--R + +--R 4 2 6 2 2 4 4 2 6 2 4 +--R (24a c + 72a )cos(x) + (8a c + 40a c + 48a )cos(x) + 4a c +--R + +--R 4 2 6 +--R 16a c + 12a +--R * +--R c sin(x) + a cos(x) + a +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 5 3 3 5 3 3 3 +--R ((12a c + 26a c )cos(x) + 4a c + 26a c )sin(x) +--R + +--R 2 4 4 2 2 6 2 4 4 2 2 4 +--R (5a c + 47a c )cos(x) + (- 4c + 12a c + 94a c )cos(x) + 7a c +--R + +--R 4 2 +--R 47a c +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (12a c - 2a c + 28a c)cos(x) + (4a c - 2a c + 84a c)cos(x) +--R + +--R 5 3 3 5 5 3 3 5 +--R (- 12a c + 2a c + 84a c)cos(x) - 4a c + 2a c + 28a c +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 4 6 2 4 4 2 6 3 +--R (12a c + 5a c + 7a )cos(x) + (- 4c + 12a c + 10a c + 28a )cos(x) +--R + +--R 2 4 6 2 6 2 4 4 2 6 4 2 +--R (- 12a c + 42a )cos(x) + (4c - 12a c - 10a c + 28a )cos(x) - 5a c +--R + +--R 6 +--R 7a +--R / +--R 8 8 3 +--R (16a c cos(x) + 16a c )sin(x) +--R + +--R 9 2 7 2 2 7 9 2 7 2 +--R ((- 8c + 40a c )cos(x) + 80a c cos(x) + 8c + 40a c )sin(x) +--R + +--R 8 3 6 3 8 3 6 2 +--R (- 16a c + 32a c )cos(x) + (- 16a c + 96a c )cos(x) +--R + +--R 8 3 6 8 3 6 +--R (16a c + 96a c )cos(x) + 16a c + 32a c +--R * +--R sin(x) +--R + +--R 2 7 4 5 4 2 7 4 5 3 4 5 2 +--R (- 8a c + 8a c )cos(x) + (- 16a c + 32a c )cos(x) + 48a c cos(x) +--R + +--R 2 7 4 5 2 7 4 5 +--R (16a c + 32a c )cos(x) + 8a c + 8a c +--R Type: Expression(Integer) +--E 354 + +--S 355 of 532 +d0766:= D(m0766,x) +--R +--R +--R (328) +--R 2 7 4 5 2 2 7 4 5 2 7 +--R (- 4a c - 12a c )cos(x) + (- 8a c - 24a c )cos(x) - 4a c +--R + +--R 4 5 +--R - 12a c +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 3 +--R (4a c - 4a c - 48a c )cos(x) +--R + +--R 8 3 6 5 4 2 +--R (4a c - 36a c - 144a c )cos(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 +--R (- 4a c - 60a c - 144a c )cos(x) - 4a c - 28a c - 48a c +--R * +--R 4 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 4 +--R (- c + 11a c + 17a c - 75a c )cos(x) +--R + +--R 2 7 4 5 6 3 3 +--R (28a c - 16a c - 300a c )cos(x) +--R + +--R 9 2 7 4 5 6 3 2 +--R (2c + 6a c - 150a c - 450a c )cos(x) +--R + +--R 2 7 4 5 6 3 9 2 7 4 5 +--R (- 28a c - 184a c - 300a c )cos(x) - c - 17a c - 67a c +--R + +--R 6 3 +--R - 75a c +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (- 3a c + 9a c + 35a c - 57a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 3a c + 45a c + 67a c - 285a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (6a c + 54a c - 82a c - 570a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (6a c - 18a c - 298a c - 570a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 +--R (- 3a c - 63a c - 257a c - 285a c )cos(x) - 3a c - 27a c +--R + +--R 5 4 7 2 +--R - 73a c - 57a c +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (- 3a c + a c + 23a c - 21a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (- 6a c + 22a c + 78a c - 126a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (3a c + 59a c + 45a c - 315a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (12a c + 36a c - 140a c - 420a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (3a c - 41a c - 255a c - 315a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 +--R (- 6a c - 58a c - 162a c - 126a c)cos(x) - 3a c - 19a c +--R + +--R 6 3 8 +--R - 37a c - 21a c +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 7 +--R (- a c - a c + 5a c - 3a )cos(x) +--R + +--R 3 6 5 4 7 2 9 6 +--R (- 3a c + a c + 23a c - 21a )cos(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (- a c + 15a c + 33a c - 63a )cos(x) +--R + +--R 3 6 5 4 7 2 9 4 +--R (5a c + 25a c - 5a c - 105a )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 +--R (5a c + 5a c - 65a c - 105a )cos(x) +--R + +--R 3 6 5 4 7 2 9 2 +--R (- a c - 21a c - 75a c - 63a )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 6 5 4 7 2 9 +--R (- 3a c - 19a c - 37a c - 21a )cos(x) - a c - 5a c - 7a c - 3a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 7 4 5 4 5 6 +--R ((8a c + 24a c )cos(x) + 24a c )sin(x) +--R + +--R 8 3 6 5 4 2 +--R (- 14a c + 12a c + 90a c )cos(x) +--R + +--R 8 3 6 5 4 8 3 6 5 4 +--R (- 4a c + 40a c + 180a c )cos(x) + 6a c + 28a c + 90a c +--R * +--R 5 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 3 +--R (2c - 48a c - 22a c + 108a c )cos(x) +--R + +--R 2 7 4 5 6 3 2 +--R (- 80a c + 20a c + 324a c )cos(x) +--R + +--R 9 4 5 6 3 9 2 7 4 5 6 3 +--R (- 2c + 106a c + 324a c )cos(x) + 4c + 32a c + 64a c + 108a c +--R * +--R 4 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 4a c - 40a c + 12a c + 48a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (8a c - 96a c + 72a c + 192a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (12a c - 28a c + 144a c + 288a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 +--R (8a c + 72a c + 120a c + 192a c )cos(x) + 8a c + 44a c +--R + +--R 5 4 7 2 +--R 36a c + 48a c +--R * +--R 3 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 8 5 +--R (2c - 48a c - 56a c + 80a c + 6a c)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (- 2c - 88a c - 108a c + 304a c + 30a c)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 3 +--R (- 4c + 12a c + 44a c + 416a c + 60a c)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (4c + 100a c + 220a c + 224a c + 60a c)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 9 2 7 +--R (2c + 52a c + 156a c + 16a c + 30a c)cos(x) - 2c + 4a c +--R + +--R 4 5 6 3 8 +--R 32a c - 16a c + 6a c +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 6 +--R (10a c - 52a c - 78a c + 48a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (24a c - 140a c - 216a c + 228a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 4 +--R (- 6a c - 76a c - 78a c + 420a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (- 32a c + 96a c + 288a c + 360a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (- 2a c + 124a c + 342a c + 120a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 8 3 6 5 4 +--R (8a c + 44a c + 120a c - 12a c )cos(x) - 2a c + 4a c + 6a c +--R + +--R 7 2 +--R - 12a c +--R * +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 7 +--R (8a c - 10a c - 28a c + 6a c)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 6 +--R (- 4c + 16a c - 44a c - 108a c + 36a c)cos(x) +--R + +--R 4 5 6 3 8 5 +--R (- 62a c - 120a c + 90a c)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (8c - 16a c - 8a c + 40a c + 120a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 8a c + 58a c + 180a c + 90a c)cos(x) +--R + +--R 9 4 5 6 3 8 2 +--R (- 4c + 52a c + 132a c + 36a c)cos(x) +--R + +--R 4 5 6 3 8 +--R (14a c + 32a c + 6a c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 6 5 4 5 4 6 +--R ((8a c + 24a c )cos(x) + 24a c )sin(x) +--R + +--R 2 7 6 3 2 2 7 4 5 6 3 +--R (- 18a c + 90a c )cos(x) + (- 12a c + 16a c + 180a c )cos(x) +--R + +--R 2 7 4 5 6 3 +--R 2a c + 16a c + 90a c +--R * +--R 5 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 3 +--R (6a c - 52a c - 70a c + 108a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 +--R (4a c - 116a c - 124a c + 324a c )cos(x) +--R + +--R 8 3 6 5 4 7 2 3 6 5 4 7 2 +--R (- 6a c - 60a c - 38a c + 324a c )cos(x) + 4a c + 16a c + 108a c +--R * +--R 4 +--R sin(x) +--R + +--R 9 2 7 4 5 6 3 8 4 +--R (- c + 7a c - 23a c - 63a c + 48a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (36a c - 112a c - 228a c + 192a c)cos(x) +--R + +--R 9 2 7 4 5 6 3 8 2 +--R (2c + 18a c - 178a c - 306a c + 288a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 9 2 7 4 5 +--R (- 20a c - 112a c - 180a c + 192a c)cos(x) - c - 9a c - 23a c +--R + +--R 6 3 8 +--R - 39a c + 48a c +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 9 5 +--R (- a c - 39a c - 21a c + 23a c + 6a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 4 +--R (- 5a c - 43a c - 41a c + 19a c + 30a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 3 +--R (2a c + 66a c - 38a c - 154a c + 60a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (10a c + 82a c - 78a c - 346a c + 60a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 8 3 6 +--R (- a c - 11a c - 101a c - 269a c + 30a )cos(x) - 5a c - 23a c +--R + +--R 5 4 7 2 9 +--R - 41a c - 73a c + 6a +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (7a c - 51a c - 55a c + 27a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 5 +--R (18a c - 118a c - 138a c + 102a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 4 +--R (- 3a c - 17a c - 33a c + 105a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 3 +--R (- 20a c + 132a c + 148a c - 60a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 +--R (a c + 83a c + 87a c - 195a c)cos(x) +--R + +--R 2 7 4 5 6 3 8 2 7 4 5 6 3 +--R (2a c - 14a c - 42a c - 138a c)cos(x) - 5a c - 15a c - 31a c +--R + +--R 8 +--R - 33a c +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 7 +--R (7a c - 11a c - 23a c + 3a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 6 +--R (- 4a c + 13a c - 43a c - 85a c + 15a )cos(x) +--R + +--R 3 6 5 4 7 2 9 5 +--R (- a c - 47a c - 87a c + 27a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 4 +--R (8a c - 11a c + 17a c + 35a c + 15a )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 +--R (- 3a c + 63a c + 115a c - 15a )cos(x) +--R + +--R 8 3 6 5 4 7 2 9 2 +--R (- 4a c - a c + 31a c + 57a c - 27a )cos(x) +--R + +--R 3 6 5 4 7 2 9 3 6 5 4 7 2 9 +--R (- 3a c - 5a c - 5a c - 15a )cos(x) - a c - 5a c - 7a c - 3a +--R / +--R 2 10 2 2 10 2 10 5 +--R (16a c cos(x) + 32a c cos(x) + 16a c )sin(x) +--R + +--R 11 3 9 3 11 3 9 2 +--R (- 16a c + 64a c )cos(x) + (- 16a c + 192a c )cos(x) +--R + +--R 11 3 9 11 3 9 +--R (16a c + 192a c )cos(x) + 16a c + 64a c +--R * +--R 4 +--R sin(x) +--R + +--R 12 2 10 4 8 4 2 10 4 8 3 +--R (4c - 56a c + 100a c )cos(x) + (- 112a c + 400a c )cos(x) +--R + +--R 12 4 8 2 2 10 4 8 12 +--R (- 8c + 600a c )cos(x) + (112a c + 400a c )cos(x) + 4c +--R + +--R 2 10 4 8 +--R 56a c + 100a c +--R * +--R 3 +--R sin(x) +--R + +--R 11 3 9 5 7 5 +--R (12a c - 72a c + 76a c )cos(x) +--R + +--R 11 3 9 5 7 4 +--R (12a c - 216a c + 380a c )cos(x) +--R + +--R 11 3 9 5 7 3 +--R (- 24a c - 144a c + 760a c )cos(x) +--R + +--R 11 3 9 5 7 2 +--R (- 24a c + 144a c + 760a c )cos(x) +--R + +--R 11 3 9 5 7 11 3 9 5 7 +--R (12a c + 216a c + 380a c )cos(x) + 12a c + 72a c + 76a c +--R * +--R 2 +--R sin(x) +--R + +--R 2 10 4 8 6 6 6 +--R (12a c - 40a c + 28a c )cos(x) +--R + +--R 2 10 4 8 6 6 5 +--R (24a c - 160a c + 168a c )cos(x) +--R + +--R 2 10 4 8 6 6 4 +--R (- 12a c - 200a c + 420a c )cos(x) +--R + +--R 2 10 6 6 3 +--R (- 48a c + 560a c )cos(x) +--R + +--R 2 10 4 8 6 6 2 +--R (- 12a c + 200a c + 420a c )cos(x) +--R + +--R 2 10 4 8 6 6 2 10 4 8 6 6 +--R (24a c + 160a c + 168a c )cos(x) + 12a c + 40a c + 28a c +--R * +--R sin(x) +--R + +--R 3 9 5 7 7 5 7 3 9 5 7 7 5 6 +--R (4a c - 8a c + 4a c )cos(x) + (12a c - 40a c + 28a c )cos(x) +--R + +--R 3 9 5 7 7 5 5 +--R (4a c - 72a c + 84a c )cos(x) +--R + +--R 3 9 5 7 7 5 4 +--R (- 20a c - 40a c + 140a c )cos(x) +--R + +--R 3 9 5 7 7 5 3 +--R (- 20a c + 40a c + 140a c )cos(x) +--R + +--R 3 9 5 7 7 5 2 3 9 5 7 7 5 +--R (4a c + 72a c + 84a c )cos(x) + (12a c + 40a c + 28a c )cos(x) +--R + +--R 3 9 5 7 7 5 +--R 4a c + 8a c + 4a c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 9 2 3 9 3 9 5 +--R (16a c cos(x) + 32a c cos(x) + 16a c )sin(x) +--R + +--R 2 10 4 8 3 2 10 4 8 2 +--R (- 16a c + 64a c )cos(x) + (- 16a c + 192a c )cos(x) +--R + +--R 2 10 4 8 2 10 4 8 +--R (16a c + 192a c )cos(x) + 16a c + 64a c +--R * +--R 4 +--R sin(x) +--R + +--R 11 3 9 5 7 4 3 9 5 7 3 +--R (4a c - 56a c + 100a c )cos(x) + (- 112a c + 400a c )cos(x) +--R + +--R 11 5 7 2 3 9 5 7 11 +--R (- 8a c + 600a c )cos(x) + (112a c + 400a c )cos(x) + 4a c +--R + +--R 3 9 5 7 +--R 56a c + 100a c +--R * +--R 3 +--R sin(x) +--R + +--R 2 10 4 8 6 6 5 +--R (12a c - 72a c + 76a c )cos(x) +--R + +--R 2 10 4 8 6 6 4 +--R (12a c - 216a c + 380a c )cos(x) +--R + +--R 2 10 4 8 6 6 3 +--R (- 24a c - 144a c + 760a c )cos(x) +--R + +--R 2 10 4 8 6 6 2 +--R (- 24a c + 144a c + 760a c )cos(x) +--R + +--R 2 10 4 8 6 6 2 10 4 8 6 6 +--R (12a c + 216a c + 380a c )cos(x) + 12a c + 72a c + 76a c +--R * +--R 2 +--R sin(x) +--R + +--R 3 9 5 7 7 5 6 +--R (12a c - 40a c + 28a c )cos(x) +--R + +--R 3 9 5 7 7 5 5 +--R (24a c - 160a c + 168a c )cos(x) +--R + +--R 3 9 5 7 7 5 4 3 9 7 5 3 +--R (- 12a c - 200a c + 420a c )cos(x) + (- 48a c + 560a c )cos(x) +--R + +--R 3 9 5 7 7 5 2 +--R (- 12a c + 200a c + 420a c )cos(x) +--R + +--R 3 9 5 7 7 5 3 9 5 7 7 5 +--R (24a c + 160a c + 168a c )cos(x) + 12a c + 40a c + 28a c +--R * +--R sin(x) +--R + +--R 4 8 6 6 8 4 7 4 8 6 6 8 4 6 +--R (4a c - 8a c + 4a c )cos(x) + (12a c - 40a c + 28a c )cos(x) +--R + +--R 4 8 6 6 8 4 5 4 8 6 6 8 4 4 +--R (4a c - 72a c + 84a c )cos(x) + (- 20a c - 40a c + 140a c )cos(x) +--R + +--R 4 8 6 6 8 4 3 4 8 6 6 8 4 2 +--R (- 20a c + 40a c + 140a c )cos(x) + (4a c + 72a c + 84a c )cos(x) +--R + +--R 4 8 6 6 8 4 4 8 6 6 8 4 +--R (12a c + 40a c + 28a c )cos(x) + 4a c + 8a c + 4a c +--R Type: Expression(Integer) +--E 355 + +--S 356 of 532 +t0767:= 1/(a+b*cos(x)+c*sin(x))^(1/2) +--R +--R +--R 1 +--R (329) -------------------------- +--R +-----------------------+ +--R \|c sin(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 532 +r0767:= 2*EllipticF(1/2*x-1/2*atan(b,c),2/(1+a/(b^2+c^2)^(1/2)))*_ + ((a+b*cos(x)+c*sin(x))/(a+(b^2+c^2)^(1/2)))^(1/2)/_ + (a+b*cos(x)+c*sin(x))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Variable(b) +--R Variable(c) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 357 + +--S 358 of 532 +a0767:= integrate(t0767,x) +--R +--R +--R x +--R ++ 1 +--R (330) | ---------------------------- d%P +--R ++ +-------------------------+ +--R \|c sin(%P) + b cos(%P) + a +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 532 +m0767:= a0767-r0767 +--R +--R +--R x +--R ++ 1 +--R (331) | ---------------------------- d%P - r0767 +--R ++ +-------------------------+ +--R \|c sin(%P) + b cos(%P) + a +--R Type: Expression(Integer) +--E 359 + +--S 360 of 532 +d0767:= D(m0767,x) +--R +--R +--R 1 +--R (332) -------------------------- +--R +-----------------------+ +--R \|c sin(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 360 + +--S 361 of 532 +t0768:= 1/(a+b*cos(x)+c*sin(x))^(3/2) +--R +--R +--R 1 +--R (333) --------------------------------------------------- +--R +-----------------------+ +--R (c sin(x) + b cos(x) + a)\|c sin(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 532 +r0768:= 2*(c*cos(x)-b*sin(x))/(a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x))^(1/2)+_ + 2*EllipticE(1/2*x-1/2*atan(b,c),2/(1+a/(b^2+c^2)^(1/2)))*_ + (a+b*cos(x)+c*sin(x))^(1/2)/(a^2-b^2-c^2)/_ + ((a+b*cos(x)+c*sin(x))/(a+(b^2+c^2)^(1/2)))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Variable(b) +--R Variable(c) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 362 + +--S 363 of 532 +a0768:= integrate(t0768,x) +--R +--R +--R x +--R ++ 1 +--R (334) | ------------------------------------------------------- d%P +--R ++ +-------------------------+ +--R (c sin(%P) + b cos(%P) + a)\|c sin(%P) + b cos(%P) + a +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 532 +m0768:= a0768-r0768 +--R +--R +--R (335) +--R x +--R ++ 1 +--R | ------------------------------------------------------- d%P - r0768 +--R ++ +-------------------------+ +--R (c sin(%P) + b cos(%P) + a)\|c sin(%P) + b cos(%P) + a +--R Type: Expression(Integer) +--E 364 + +--S 365 of 532 +d0768:= D(m0768,x) +--R +--R +--R 1 +--R (336) --------------------------------------------------- +--R +-----------------------+ +--R (c sin(x) + b cos(x) + a)\|c sin(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 365 + +--S 366 of 532 +t0769:= (a+b*cos(x)+c*sin(x))^(1/2) +--R +--R +--R +-----------------------+ +--R (337) \|c sin(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 366 + +--S 367 of 532 +r0769:= 2*EllipticE(1/2*x-1/2*atan(b,c),2/(1+a/(b^2+c^2)^(1/2)))*_ + (a+b*cos(x)+c*sin(x))^(1/2)/((a+b*cos(x)+c*sin(x))/_ + (a+(b^2+c^2)^(1/2)))^(1/2) +--R +--R There are 2 exposed and 0 unexposed library operations named atan +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op atan +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--R Cannot find a definition or applicable library operation named atan +--R with argument type(s) +--R Variable(b) +--R Variable(c) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 367 + +--S 368 of 532 +a0769:= integrate(t0769,x) +--R +--R +--R x +--R ++ +-------------------------+ +--R (338) | \|c sin(%P) + b cos(%P) + a d%P +--R ++ +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 532 +m0769:= a0769-r0769 +--R +--R +--R x +--R ++ +-------------------------+ +--R (339) | \|c sin(%P) + b cos(%P) + a d%P - r0769 +--R ++ +--R Type: Expression(Integer) +--E 369 + +--S 370 of 532 +d0769:= D(m0769,x) +--R +--R +--R +-----------------------+ +--R (340) \|c sin(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 370 + +--S 371 of 532 +t0770:= 1/(a+b*tan(x)+c*sec(x)) +--R +--R +--R 1 +--R (341) ----------------------- +--R b tan(x) + c sec(x) + a +--R Type: Expression(Integer) +--E 371 + +--S 372 of 532 +r0770:= a*x/(a^2+b^2)+2*a*c*atanh((b+(-a+c)*tan(1/2*x))/_ + (a^2+b^2-c^2)^(1/2))/(a^2+b^2)/(a^2+b^2-c^2)^(1/2)+_ + b*log(c+a*cos(x)+b*sin(x))/(a^2+b^2) +--R +--R +--R (342) +--R +--------------+ +--R | 2 2 2 +--R b\|- c + b + a log(b sin(x) + a cos(x) + c) +--R + +--R x +--R (c - a)tan(-) + b +--------------+ +--R 2 | 2 2 2 +--R 2a c atanh(-----------------) + a x\|- c + b + a +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b + a )\|- c + b + a +--R Type: Expression(Integer) +--E 372 + +--S 373 of 532 +a0770:= integrate(t0770,x) +--R +--R +--R (343) +--R [ +--R a c +--R * +--R log +--R 2 2 2 +--R (b c - a b)sin(x) + (- c + a c + b )cos(x) - a c + b +--R + +--R 2 +--R a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 2 3 +--R (- c + a c + (b + a )c - a b - a )sin(x) +--R + +--R 2 3 2 2 3 2 +--R (- b c + b + a b)cos(x) - b c + b + a b +--R / +--R b sin(x) + a cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--------------+ +--R | 2 2 2 2 | 2 2 2 +--R - b\|- c + b + a log(----------) + a x\|- c + b + a +--R cos(x) + 1 +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b + a )\|- c + b + a +--R , +--R +--R +------------+ +--R | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R b\|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 2 +--R - b\|c - b - a log(----------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R ((c - a)sin(x) + b cos(x) + b)\|c - b - a +--R - 2a c atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R + +--R +------------+ +--R | 2 2 2 +--R a x\|c - b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (b + a )\|c - b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 373 + +--S 374 of 532 +m0770a:= a0770.1-r0770 +--R +--R +--R (344) +--R a c +--R * +--R log +--R 2 2 2 2 +--R ((b c - a b)sin(x) + (- c + a c + b )cos(x) - a c + b + a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 2 3 +--R (- c + a c + (b + a )c - a b - a )sin(x) +--R + +--R 2 3 2 2 3 2 +--R (- b c + b + a b)cos(x) - b c + b + a b +--R / +--R b sin(x) + a cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 +--R - b\|- c + b + a log(b sin(x) + a cos(x) + c) +--R + +--R +--------------+ +--R | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R x +--R +--------------+ (c - a)tan(-) + b +--R | 2 2 2 2 2 +--R - b\|- c + b + a log(----------) - 2a c atanh(-----------------) +--R cos(x) + 1 +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b + a )\|- c + b + a +--R Type: Expression(Integer) +--E 374 + +--S 375 of 532 +d0770a:= D(m0770a,x) +--R +--R +--R (345) +--R 2 3 3 2 4 2 +--R (a c - 2a c + a c)sin(x) +--R + +--R 3 2 2 3 3 3 +--R ((- a b c + 2a b c + (a b - a b)c)cos(x) + a b c)sin(x) +--R + +--R 2 3 2 2 2 4 2 +--R ((- a b - a )c + (2a b + a )c)cos(x) +--R + +--R 2 3 2 2 4 2 3 2 3 2 +--R (- a c + (2a b + a )c)cos(x) - a c + (a b + a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 3 2 2 2 2 2 +--R (2a b c + (- 2a b - 2a b)c)sin(x) + (- 2a b c + 2a b c)sin(x) +--R + +--R 2 2 3 3 2 +--R (2a b c + (- 2a b - 2a b)c)cos(x) +--R + +--R 3 2 2 3 +--R (2a b c - 2a b c - 2a b c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 4 2 +--R (a c + (- 2a b - a )c)sin(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- a b c + 2a b c + (a b - a b)c)cos(x) - 2a b c +--R + +--R 3 3 +--R (a b + 2a b)c +--R * +--R sin(x) +--R + +--R 2 3 2 4 2 2 3 3 2 4 2 3 +--R ((- a b + a )c - a c)cos(x) + (a c - 2a c + a c)cos(x) - a c +--R + +--R 2 3 2 +--R (a b + a )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 2 4 2 3 3 2 2 4 2 4 5 +--R (- a c + (- a b + a )c + (a b + a )c + (a b - a )c)cos(x) +--R + +--R 2 4 2 3 3 2 2 4 2 4 5 +--R - a c + (- a b + a )c + (a b + a )c + (a b - a )c +--R * +--R sin(x) +--R + +--R 4 2 3 3 3 2 2 3 4 2 +--R (a b c - 2a b c + (- a b - a b)c + (2a b + 2a b)c)cos(x) +--R + +--R 2 3 2 3 4 4 3 3 2 +--R (- 2a b c + (2a b + 2a b)c)cos(x) - a b c + (a b + a b)c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 4 3 2 2 +--R (2a b c + (- 2a b - 2a b )c)sin(x) +--R + +--R 4 2 3 3 3 2 2 3 4 +--R (2a b c - 2a b c + (- 2a b - 2a b)c + (2a b + 2a b)c)sin(x) +--R + +--R 2 3 4 3 2 2 +--R (2a b c + (- 2a b - 2a b )c)cos(x) +--R + +--R 2 3 4 3 2 +--R (2a b c + (- 2a b - 2a b )c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 3 4 2 +--R (2a b c + (- 2a b - 2a b)c)sin(x) +--R + +--R 2 4 2 3 3 2 2 4 2 4 5 +--R (- a c + (- a b + a )c + (a b + a )c + (a b - a )c)cos(x) +--R + +--R 2 4 2 3 3 2 2 4 2 4 3 2 5 +--R a c + (- a b - a )c + (- a b - a )c + (a b + 2a b + a )c +--R * +--R sin(x) +--R + +--R 4 3 3 2 2 4 3 3 2 +--R (a b c + (- a b - a b)c )cos(x) - a b c + (a b + a b)c +--R / +--R 4 2 2 2 4 3 2 2 4 4 2 2 +--R ((b + a b )c + (- 2a b - 2a b )c + a b + a b )sin(x) +--R + +--R 3 2 3 3 3 2 5 2 3 4 +--R (- b - a b)c + (3a b + 3a b)c + (b - 2a b - 3a b)c +--R + +--R 5 5 +--R - a b + a b +--R * +--R cos(x) +--R + +--R 3 2 3 3 3 2 5 2 3 4 +--R (b + a b)c + (- 3a b - 3a b)c + (b + 4a b + 3a b)c +--R + +--R 5 3 3 5 +--R - a b - 2a b - a b +--R * +--R sin(x) +--R + +--R 2 3 3 2 2 4 2 4 5 2 4 +--R (- a b - a )c + (2a b + 2a )c + (a b - a )c - a b +--R + +--R 4 2 +--R - a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 2 3 3 4 2 2 4 2 +--R (- b - a )c + (2a b + 2a )c + (b - a b - 2a )c +--R + +--R 3 2 5 2 4 4 2 6 +--R (2a b + 2a )c - a b - 2a b - a +--R * +--R cos(x) +--R + +--R 2 3 3 4 2 2 4 2 4 3 2 5 +--R (- a b - a )c + (b + 3a b + 2a )c + (- a b - 2a b - a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 5 3 3 2 +--R ((2b + 2a b )c - 2a b - 2a b )sin(x) +--R + +--R 4 2 2 2 4 3 2 6 4 2 +--R ((- 2b - 2a b )c + (4a b + 4a b )c + 2b - 2a b )cos(x) +--R + +--R 4 2 2 2 4 3 2 6 2 4 4 2 +--R (2b + 2a b )c + (- 4a b - 4a b )c + 2b + 4a b + 2a b +--R * +--R sin(x) +--R + +--R 3 3 2 2 3 4 5 3 3 2 +--R ((- 2a b - 2a b)c + (2a b + 2a b)c + 2a b + 2a b )cos(x) +--R + +--R 3 2 3 3 3 2 5 4 5 +--R (- 2b - 2a b)c + (2a b + 2a b)c + (2b - 2a b)c + 2a b +--R + +--R 3 3 5 +--R 4a b + 2a b +--R * +--R cos(x) +--R + +--R 3 3 2 5 2 3 4 +--R (- 2a b - 2a b)c + (2b + 4a b + 2a b)c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 2 2 2 4 4 2 2 +--R ((b + a b )c - a b - a b )sin(x) +--R + +--R 3 2 3 3 3 2 5 2 3 4 5 +--R (- b - a b)c + (a b + a b)c + (b + 2a b + a b)c + a b +--R + +--R 5 +--R - a b +--R * +--R cos(x) +--R + +--R 3 2 3 3 3 2 5 4 5 3 3 5 +--R (b + a b)c + (- a b - a b)c + (b - a b)c + a b + 2a b + a b +--R * +--R sin(x) +--R + +--R 2 3 3 4 3 2 5 2 4 4 2 2 +--R ((- a b - a )c + (a b + 2a b + a )c + a b + a b )cos(x) +--R + +--R 2 2 4 4 2 2 2 4 3 2 2 4 4 2 +--R (- b - a )c + (b + a b )c + (2a b + 2a b )c + a b + 2a b +--R + +--R 6 +--R a +--R * +--R cos(x) +--R + +--R 2 3 3 4 2 2 2 4 3 2 5 +--R (- a b - a )c + (b + a b )c + (a b + 2a b + a )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 4 3 3 3 5 2 3 2 +--R (- b - a b)c + (2a b + 2a b)c + (b + a b )c +--R + +--R 5 3 3 5 2 5 4 3 6 +--R (- 2a b - 4a b - 2a b)c + a b + 2a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 4 2 2 4 3 4 3 2 2 +--R (- a b - a )c + (- b + a b + 2a )c + (2a b + 2a b )c +--R + +--R 6 4 2 6 6 3 4 5 2 7 +--R (b - 3a b - 2a )c - a b - a b + a b + a +--R * +--R cos(x) +--R + +--R 2 2 5 2 3 4 4 3 2 5 2 +--R (- b - a )c + (2a b + 2a )c + (- a b - 3a b - 2a )c +--R + +--R 6 2 4 4 2 6 6 3 4 5 2 +--R (b + 3a b + 3a b + a )c - a b - 2a b - a b +--R * +--R sin(x) +--R + +--R 3 3 3 2 3 4 2 5 3 3 5 2 5 +--R (- a b - a b)c + (a b + a b)c + (a b + 2a b + a b)c - a b +--R + +--R 4 3 6 +--R - 2a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 4 5 2 3 4 2 2 5 4 3 6 +--R ((- b - a b)c + (b + 3a b + 2a b)c - a b - 2a b - a b)cos(x) +--R + +--R 3 2 4 3 3 3 5 2 3 4 2 +--R (- b - a b)c + (a b + a b)c + (b + 2a b + a b)c +--R + +--R 5 3 3 5 +--R (- a b - 2a b - a b)c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 4 3 2 2 6 2 4 4 2 +--R (- 2b - 2a b )c + (2a b + 2a b )c + (2b + 4a b + 2a b )c +--R + +--R 6 3 4 5 2 +--R - 2a b - 4a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 5 4 2 +--R (- 2a b - 2a b)c + (- 2b + 2a b)c +--R + +--R 5 3 3 5 7 2 5 4 3 6 +--R (2a b + 4a b + 2a b)c + 2b + 2a b - 2a b - 2a b +--R * +--R cos(x) +--R + +--R 3 2 4 3 3 3 2 3 4 2 +--R (- 2b - 2a b)c + (2a b + 2a b)c + (2a b + 2a b)c +--R + +--R 5 3 3 5 7 2 5 4 3 +--R (- 2a b - 4a b - 2a b)c + 2b + 4a b + 2a b +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 3 4 5 2 2 +--R ((- 2a b - 2a b )c + 2a b + 4a b + 2a b )cos(x) +--R + +--R 4 2 2 3 4 3 2 2 6 2 4 4 2 +--R (- 2b - 2a b )c + (- 2a b - 2a b )c + (2b + 4a b + 2a b )c +--R + +--R 6 3 4 5 2 +--R 2a b + 4a b + 2a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 6 2 4 4 2 +--R (- 2b - 2a b )c + (2b + 4a b + 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 4 5 2 3 4 2 2 5 4 3 6 2 +--R ((- b - a b)c + (b + 3a b + 2a b)c - a b - 2a b - a b)sin(x) +--R + +--R 2 3 4 4 2 2 3 3 2 5 2 +--R (- a b - a )c + (- b - a b )c + (2a b + 2a )c +--R + +--R 6 2 4 4 2 6 3 4 5 2 7 +--R (b + 2a b + a b )c + a b + a b - a b - a +--R * +--R cos(x) +--R + +--R 2 2 5 2 2 4 3 4 3 2 2 +--R (- b - a )c + (2a b + 2a )c + (- a b - a b )c +--R + +--R 6 2 4 4 2 6 6 3 4 5 2 +--R (b + a b - a b - a )c + a b + 2a b + a b +--R * +--R sin(x) +--R + +--R 3 3 3 2 3 4 2 5 3 3 5 2 5 +--R (- a b - a b)c + (- a b - a b)c + (a b + 2a b + a b)c + a b +--R + +--R 4 3 6 +--R 2a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 4 3 3 3 5 2 3 2 +--R (- b - a b)c + (- 2a b - 2a b)c + (b + a b )c +--R + +--R 5 3 3 5 2 5 4 3 6 +--R (2a b + 4a b + 2a b)c + a b + 2a b + a b +--R * +--R cos(x) +--R + +--R 3 2 4 3 3 3 5 2 3 4 2 +--R (- b - a b)c + (- a b - a b)c + (b + 2a b + a b)c +--R + +--R 5 3 3 5 +--R (a b + 2a b + a b)c +--R Type: Expression(Integer) +--E 375 + +--S 376 of 532 +m0770b:= a0770.2-r0770 +--R +--R +--R (346) +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - b\|- c + b + a \|c - b - a log(b sin(x) + a cos(x) + c) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R b\|- c + b + a \|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2 +--R - b\|- c + b + a \|c - b - a log(----------) +--R cos(x) + 1 +--R + +--R x +--R +------------+ (c - a)tan(-) + b +--R | 2 2 2 2 +--R - 2a c\|c - b - a atanh(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R +------------+ +--R +--------------+ | 2 2 2 +--R | 2 2 2 ((c - a)sin(x) + b cos(x) + b)\|c - b - a +--R - 2a c\|- c + b + a atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (b + a )\|- c + b + a \|c - b - a +--R Type: Expression(Integer) +--E 376 + +--S 377 of 532 +d0770b:= D(m0770b,x) +--R +--R +--R (347) +--R 2 2 2 +--R (- a c + a c)sin(x) + (2a b c cos(x) + 2a b c)sin(x) +--R + +--R 2 2 2 2 2 2 +--R (- a c + 3a c)cos(x) + 4a c cos(x) + a c + a c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 x +--R (- 4a b c sin(x) - 4a b c cos(x) - 4a b c cos(x))tan(-) +--R 2 +--R + +--R 2 2 2 +--R (- a c - 3a c)sin(x) + (2a b c cos(x) + 2a b c)sin(x) +--R + +--R 2 2 2 2 2 +--R (- a c - a c)cos(x) + a c + a c +--R / +--R 2 2 2 2 3 2 2 4 2 +--R ((b + a )c + (- 2a b - 2a )c + a b + a )sin(x) +--R + +--R 3 2 3 3 3 2 3 +--R ((2b + 2a b)c - 2a b - 2a b)cos(x) + (2b + 2a b)c - 2a b +--R + +--R 3 +--R - 2a b +--R * +--R sin(x) +--R + +--R 2 2 2 2 2 4 2 +--R ((b + a )c - a b - a )cos(x) +--R + +--R 2 2 2 2 2 4 2 2 2 2 2 4 +--R ((2b + 2a )c - 2a b - 2a )cos(x) + (b + a )c - a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 3 3 2 +--R ((2b + 2a b)c - 2a b - 2a b)sin(x) +--R + +--R 4 2 2 4 2 2 +--R ((4b + 4a b )cos(x) + 4b + 4a b )sin(x) +--R + +--R 3 2 3 3 2 +--R ((2b + 2a b)c + 2a b + 2a b)cos(x) +--R + +--R 3 2 3 3 3 2 3 3 +--R ((4b + 4a b)c + 4a b + 4a b)cos(x) + (2b + 2a b)c + 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 4 2 +--R ((b + a )c - a b - a )sin(x) +--R + +--R 3 2 3 3 3 2 3 3 +--R (((2b + 2a b)c + 2a b + 2a b)cos(x) + (2b + 2a b)c + 2a b + 2a b) +--R * +--R sin(x) +--R + +--R 2 2 2 2 3 2 2 4 2 +--R ((b + a )c + (2a b + 2a )c + a b + a )cos(x) +--R + +--R 2 2 2 2 3 2 2 4 2 2 2 +--R ((2b + 2a )c + (4a b + 4a )c + 2a b + 2a )cos(x) + (b + a )c +--R + +--R 2 3 2 2 4 +--R (2a b + 2a )c + a b + a +--R Type: Expression(Integer) +--E 377 + +--S 378 of 532 +t0771:= 1/(a+b*cot(x)+c*csc(x)) +--R +--R +--R 1 +--R (348) ----------------------- +--R c csc(x) + b cot(x) + a +--R Type: Expression(Integer) +--E 378 + +--S 379 of 532 +r0771:= a*x/(a^2+b^2)+2*a*c*atanh((a+(-b+c)*tan(1/2*x))/_ + (a^2+b^2-c^2)^(1/2))/(a^2+b^2)/(a^2+b^2-c^2)^(1/2)-_ + b*log(c+b*cos(x)+a*sin(x))/(a^2+b^2) +--R +--R +--R (349) +--R +--------------+ +--R | 2 2 2 +--R - b\|- c + b + a log(a sin(x) + b cos(x) + c) +--R + +--R x +--R (c - b)tan(-) + a +--------------+ +--R 2 | 2 2 2 +--R 2a c atanh(-----------------) + a x\|- c + b + a +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b + a )\|- c + b + a +--R Type: Expression(Integer) +--E 379 + +--S 380 of 532 +a0771:= integrate(t0771,x) +--R +--R +--R (350) +--R [ +--R a c +--R * +--R log +--R 2 2 2 +--R (a c - a b)sin(x) + (- c + b c + a )cos(x) - b c + b +--R + +--R 2 +--R a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 3 2 +--R (- c + b c + (b + a )c - b - a b)sin(x) +--R + +--R 2 2 3 2 2 3 +--R (- a c + a b + a )cos(x) - a c + a b + a +--R / +--R a sin(x) + b cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R - b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--------------+ +--R | 2 2 2 2 | 2 2 2 +--R b\|- c + b + a log(----------) + a x\|- c + b + a +--R cos(x) + 1 +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b + a )\|- c + b + a +--R , +--R +--R +------------+ +--R | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R - b\|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 2 +--R b\|c - b - a log(----------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R ((c - b)sin(x) + a cos(x) + a)\|c - b - a +--R - 2a c atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R + +--R +------------+ +--R | 2 2 2 +--R a x\|c - b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (b + a )\|c - b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 380 + +--S 381 of 532 +m0771a:= a0771.1-r0771 +--R +--R +--R (351) +--R a c +--R * +--R log +--R 2 2 2 2 +--R ((a c - a b)sin(x) + (- c + b c + a )cos(x) - b c + b + a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 3 2 +--R (- c + b c + (b + a )c - b - a b)sin(x) +--R + +--R 2 2 3 2 2 3 +--R (- a c + a b + a )cos(x) - a c + a b + a +--R / +--R a sin(x) + b cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 +--R b\|- c + b + a log(a sin(x) + b cos(x) + c) +--R + +--R +--------------+ +--R | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R - b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R x +--R +--------------+ (c - b)tan(-) + a +--R | 2 2 2 2 2 +--R b\|- c + b + a log(----------) - 2a c atanh(-----------------) +--R cos(x) + 1 +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (b + a )\|- c + b + a +--R Type: Expression(Integer) +--E 381 + +--S 382 of 532 +d0771a:= D(m0771a,x) +--R +--R +--R (352) +--R 3 2 2 3 2 +--R (a b c - 2a b c + a b c)sin(x) +--R + +--R 2 3 2 2 2 2 4 4 +--R ((- a c + 2a b c + (- a b + a )c)cos(x) + a c)sin(x) +--R + +--R 2 3 2 3 3 2 +--R ((- a b - a )c + (a b + 2a b)c)cos(x) +--R + +--R 3 3 3 3 2 3 2 +--R (- a b c + (a b + 2a b)c)cos(x) - a b c + (a b + a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 4 2 3 2 3 +--R (2a b c + (- 2a b - 2a )c)sin(x) + (- 2a c + 2a b c)sin(x) +--R + +--R 2 2 2 2 4 2 +--R (2a b c + (- 2a b - 2a )c)cos(x) +--R + +--R 2 3 2 2 4 +--R (2a c - 2a b c - 2a c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 +--R (a b c + (- a b - 2a b)c)sin(x) +--R + +--R 2 3 2 2 2 2 4 2 2 +--R (- a c + 2a b c + (- a b + a )c)cos(x) - 2a b c +--R + +--R 2 2 4 +--R (2a b + a )c +--R * +--R sin(x) +--R + +--R 2 3 2 3 2 3 2 2 3 +--R ((a b - a )c - a b c)cos(x) + (a b c - 2a b c + a b c)cos(x) +--R + +--R 3 2 3 2 +--R - a b c + (a b + a )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 4 2 3 3 3 3 2 4 5 +--R (- a b c + (a b - a )c + (a b + a b)c + (- a b + a )c) +--R * +--R cos(x) +--R + +--R 4 2 3 3 3 3 2 4 5 +--R - a b c + (a b - a )c + (a b + a b)c + (- a b + a )c +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 4 2 2 3 4 2 +--R (a c - 2a b c + (- a b - a )c + (2a b + 2a b)c)cos(x) +--R + +--R 2 3 2 3 4 2 4 2 2 4 2 +--R (- 2a b c + (2a b + 2a b)c)cos(x) - a c + (a b + a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 5 2 +--R (2a c + (- 2a b - 2a )c)sin(x) +--R + +--R 2 4 2 3 2 2 4 2 2 3 4 +--R (2a c - 2a b c + (- 2a b - 2a )c + (2a b + 2a b)c)sin(x) +--R + +--R 3 3 3 2 5 2 3 3 3 2 5 +--R (2a c + (- 2a b - 2a )c)cos(x) + (2a c + (- 2a b - 2a )c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 3 4 2 +--R (2a b c + (- 2a b - 2a b)c)sin(x) +--R + +--R 4 2 3 3 3 3 2 4 5 +--R (- a b c + (a b - a )c + (a b + a b)c + (- a b + a )c)cos(x) +--R + +--R 4 2 3 3 3 3 2 4 3 2 5 +--R a b c + (- a b - a )c + (- a b - a b)c + (a b + 2a b + a )c +--R * +--R sin(x) +--R + +--R 2 4 2 2 4 2 2 2 4 2 2 4 2 +--R (a c + (- a b - a )c )cos(x) - a c + (a b + a )c +--R / +--R 2 2 4 2 2 3 4 2 4 4 2 2 +--R ((a b + a )c + (- 2a b - 2a b)c + a b + a b )sin(x) +--R + +--R 2 3 3 3 3 2 +--R (- a b - a )c + (3a b + 3a b)c +--R + +--R 4 3 2 5 5 5 +--R (- 3a b - 2a b + a )c + a b - a b +--R * +--R cos(x) +--R + +--R 2 3 3 3 3 2 4 3 2 5 +--R (a b + a )c + (- 3a b - 3a b)c + (3a b + 4a b + a )c +--R + +--R 5 3 3 5 +--R - a b - 2a b - a b +--R * +--R sin(x) +--R + +--R 3 2 3 4 2 2 2 5 4 2 4 +--R (- b - a b)c + (2b + 2a b )c + (- b + a b)c - a b +--R + +--R 4 2 +--R - a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 3 2 3 4 2 2 4 2 +--R (- b - a )c + (2b + 2a b)c + (- 2b - a b + a )c +--R + +--R 5 2 3 6 2 4 4 2 +--R (2b + 2a b )c - b - 2a b - a b +--R * +--R cos(x) +--R + +--R 3 2 3 4 2 2 4 2 5 2 3 4 +--R (- b - a b)c + (2b + 3a b + a )c + (- b - 2a b - a b)c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 5 3 3 5 2 +--R ((2a b + 2a )c - 2a b - 2a b)sin(x) +--R + +--R 2 2 4 2 2 3 4 2 4 6 +--R ((- 2a b - 2a )c + (4a b + 4a b)c - 2a b + 2a )cos(x) +--R + +--R 2 2 4 2 2 3 4 2 4 4 2 6 +--R (2a b + 2a )c + (- 4a b - 4a b)c + 2a b + 4a b + 2a +--R * +--R sin(x) +--R + +--R 3 3 2 4 3 2 3 3 5 2 +--R ((- 2a b - 2a b)c + (2a b + 2a b )c + 2a b + 2a b)cos(x) +--R + +--R 2 3 3 3 3 2 4 5 +--R (- 2a b - 2a )c + (2a b + 2a b)c + (- 2a b + 2a )c +--R + +--R 5 3 3 5 +--R 2a b + 4a b + 2a b +--R * +--R cos(x) +--R + +--R 3 3 2 4 3 2 5 +--R (- 2a b - 2a b)c + (2a b + 4a b + 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 2 4 4 2 2 +--R ((a b + a )c - a b - a b )sin(x) +--R + +--R 2 3 3 3 3 2 4 3 2 5 +--R (- a b - a )c + (a b + a b)c + (a b + 2a b + a )c +--R + +--R 5 5 +--R - a b + a b +--R * +--R cos(x) +--R + +--R 2 3 3 3 3 2 4 5 5 3 3 +--R (a b + a )c + (- a b - a b)c + (- a b + a )c + a b + 2a b +--R + +--R 5 +--R a b +--R * +--R sin(x) +--R + +--R 3 2 3 5 2 3 4 2 4 4 2 2 +--R ((- b - a b)c + (b + 2a b + a b)c + a b + a b )cos(x) +--R + +--R 2 2 4 2 2 4 2 2 3 4 6 2 4 +--R (- b - a )c + (a b + a )c + (2a b + 2a b)c + b + 2a b +--R + +--R 4 2 +--R a b +--R * +--R cos(x) +--R + +--R 3 2 3 2 2 4 2 5 2 3 4 +--R (- b - a b)c + (a b + a )c + (b + 2a b + a b)c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 2 3 4 3 3 3 3 2 5 2 +--R (- a b - a )c + (2a b + 2a b)c + (a b + a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (- 2a b - 4a b - 2a b)c + a b + 2a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 4 4 2 2 4 3 2 3 4 2 +--R (- b - a b)c + (2b + a b - a )c + (2a b + 2a b)c +--R + +--R 6 2 4 6 7 2 5 4 3 6 +--R (- 2b - 3a b + a )c + b + a b - a b - a b +--R * +--R cos(x) +--R + +--R 2 2 5 3 2 4 5 2 3 4 2 +--R (- b - a )c + (2b + 2a b)c + (- 2b - 3a b - a b)c +--R + +--R 6 2 4 4 2 6 2 5 4 3 6 +--R (b + 3a b + 3a b + a )c - a b - 2a b - a b +--R * +--R sin(x) +--R + +--R 3 3 3 4 3 2 2 5 3 3 5 6 +--R (- a b - a b)c + (a b + a b )c + (a b + 2a b + a b)c - a b +--R + +--R 3 4 5 2 +--R - 2a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 4 4 3 2 5 2 6 3 4 5 2 +--R ((- a b - a )c + (2a b + 3a b + a )c - a b - 2a b - a b ) +--R * +--R cos(x) +--R + +--R 2 3 4 3 3 3 4 3 2 5 2 +--R (- a b - a )c + (a b + a b)c + (a b + 2a b + a )c +--R + +--R 5 3 3 5 +--R (- a b - 2a b - a b)c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 3 2 3 4 2 2 4 4 2 6 +--R (- 2a b - 2a )c + (2a b + 2a b)c + (2a b + 4a b + 2a )c +--R + +--R 2 5 4 3 6 +--R - 2a b - 4a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 4 5 2 +--R (- 2a b - 2a b)c + (2a b - 2a )c +--R + +--R 5 3 3 5 6 3 4 5 2 7 +--R (2a b + 4a b + 2a b)c - 2a b - 2a b + 2a b + 2a +--R * +--R cos(x) +--R + +--R 2 3 4 3 3 3 4 3 2 2 +--R (- 2a b - 2a )c + (2a b + 2a b)c + (2a b + 2a b )c +--R + +--R 5 3 3 5 3 4 5 2 7 +--R (- 2a b - 4a b - 2a b)c + 2a b + 4a b + 2a +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 5 4 3 6 2 +--R ((- 2a b - 2a b)c + 2a b + 4a b + 2a b)cos(x) +--R + +--R 2 2 4 3 2 3 4 2 2 4 4 2 6 +--R (- 2a b - 2a )c + (- 2a b - 2a b)c + (2a b + 4a b + 2a )c +--R + +--R 2 5 4 3 6 +--R 2a b + 4a b + 2a b +--R * +--R cos(x) +--R + +--R 2 2 4 3 2 4 4 2 6 +--R (- 2a b - 2a )c + (2a b + 4a b + 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 4 3 2 5 2 6 3 4 5 2 2 +--R ((- a b - a )c + (2a b + 3a b + a )c - a b - 2a b - a b )sin(x) +--R + +--R 3 2 4 2 2 4 3 5 2 3 2 +--R (- b - a b)c + (- a b - a )c + (2b + 2a b )c +--R + +--R 2 4 4 2 6 7 2 5 4 3 6 +--R (a b + 2a b + a )c - b - a b + a b + a b +--R * +--R cos(x) +--R + +--R 2 2 5 4 2 2 3 2 3 4 2 +--R (- b - a )c + (2b + 2a b )c + (- a b - a b)c +--R + +--R 6 2 4 4 2 6 2 5 4 3 6 +--R (- b - a b + a b + a )c + a b + 2a b + a b +--R * +--R sin(x) +--R + +--R 3 3 3 4 3 2 2 5 3 3 5 6 +--R (- a b - a b)c + (- a b - a b )c + (a b + 2a b + a b)c + a b +--R + +--R 3 4 5 2 +--R 2a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 4 3 3 3 3 2 5 2 +--R (- a b - a )c + (- 2a b - 2a b)c + (a b + a )c +--R + +--R 5 3 3 5 6 3 4 5 2 +--R (2a b + 4a b + 2a b)c + a b + 2a b + a b +--R * +--R cos(x) +--R + +--R 2 3 4 3 3 3 4 3 2 5 2 +--R (- a b - a )c + (- a b - a b)c + (a b + 2a b + a )c +--R + +--R 5 3 3 5 +--R (a b + 2a b + a b)c +--R Type: Expression(Integer) +--E 382 + +--S 383 of 532 +m0771b:= a0771.2-r0771 +--R +--R +--R (353) +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R b\|- c + b + a \|c - b - a log(a sin(x) + b cos(x) + c) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R - b\|- c + b + a \|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2 +--R b\|- c + b + a \|c - b - a log(----------) +--R cos(x) + 1 +--R + +--R x +--R +------------+ (c - b)tan(-) + a +--R | 2 2 2 2 +--R - 2a c\|c - b - a atanh(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R +------------+ +--R +--------------+ | 2 2 2 +--R | 2 2 2 ((c - b)sin(x) + a cos(x) + a)\|c - b - a +--R - 2a c\|- c + b + a atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (b + a )\|- c + b + a \|c - b - a +--R Type: Expression(Integer) +--E 383 + +--S 384 of 532 +d0771b:= D(m0771b,x) +--R +--R +--R (354) +--R 2 2 2 2 +--R (- a c + a b c)sin(x) + (2a c cos(x) + 2a c)sin(x) +--R + +--R 2 2 2 +--R (- a c + 3a b c)cos(x) + 4a b c cos(x) + a c + a b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 x +--R (- 4a c sin(x) - 4a c cos(x) - 4a c cos(x))tan(-) +--R 2 +--R + +--R 2 2 2 2 +--R (- a c - 3a b c)sin(x) + (2a c cos(x) + 2a c)sin(x) +--R + +--R 2 2 2 +--R (- a c - a b c)cos(x) + a c + a b c +--R / +--R 2 2 2 3 2 4 2 2 2 +--R ((b + a )c + (- 2b - 2a b)c + b + a b )sin(x) +--R + +--R 2 3 3 3 2 3 3 +--R ((2a b + 2a )c - 2a b - 2a b)cos(x) + (2a b + 2a )c - 2a b +--R + +--R 3 +--R - 2a b +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 +--R ((b + a )c - b - a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 2 4 2 2 +--R ((2b + 2a )c - 2b - 2a b )cos(x) + (b + a )c - b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 3 3 2 +--R ((2a b + 2a )c - 2a b - 2a b)sin(x) +--R + +--R 2 2 4 2 2 4 +--R ((4a b + 4a )cos(x) + 4a b + 4a )sin(x) +--R + +--R 2 3 3 3 2 +--R ((2a b + 2a )c + 2a b + 2a b)cos(x) +--R + +--R 2 3 3 3 2 3 3 3 +--R ((4a b + 4a )c + 4a b + 4a b)cos(x) + (2a b + 2a )c + 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 2 +--R ((b + a )c - b - a b )sin(x) +--R + +--R 2 3 3 3 2 3 3 3 +--R (((2a b + 2a )c + 2a b + 2a b)cos(x) + (2a b + 2a )c + 2a b + 2a b) +--R * +--R sin(x) +--R + +--R 2 2 2 3 2 4 2 2 2 +--R ((b + a )c + (2b + 2a b)c + b + a b )cos(x) +--R + +--R 2 2 2 3 2 4 2 2 2 2 2 +--R ((2b + 2a )c + (4b + 4a b)c + 2b + 2a b )cos(x) + (b + a )c +--R + +--R 3 2 4 2 2 +--R (2b + 2a b)c + b + a b +--R Type: Expression(Integer) +--E 384 + +--S 385 of 532 +t0772:= x*cos(x)/(a+b*sin(x))^2 +--R +--R +--R x cos(x) +--R (355) ---------------------------- +--R 2 2 2 +--R b sin(x) + 2a b sin(x) + a +--R Type: Expression(Integer) +--E 385 + +--S 386 of 532 +r0772:= 2*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b/(a^2-b^2)^(1/2)-_ + x/b/(a+b*sin(x)) +--R +--R +--R x +--R a tan(-) + b +---------+ +--R 2 | 2 2 +--R (2b sin(x) + 2a)atan(------------) - x\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (356) -------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R (b sin(x) + a b)\|- b + a +--R Type: Expression(Integer) +--E 386 + +--S 387 of 532 +a0772:= integrate(t0772,x) +--R +--R +--R (357) +--R [ +--R (b sin(x) + a) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R +-------+ +--R | 2 2 +--R - x\|b - a +--R / +--R +-------+ +--R 2 | 2 2 +--R (b sin(x) + a b)\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R (- 2b sin(x) - 2a)atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R +---------+ +--R | 2 2 +--R - x\|- b + a +--R / +--R +---------+ +--R 2 | 2 2 +--R (b sin(x) + a b)\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 387 + +--S 388 of 532 +m0772a:= a0772.1-r0772 +--R +--R +--R (358) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (- a b + a )sin(x) + (- b + a b)cos(x) - b + a b +--R / +--R b sin(x) + a +--R + +--R x +--R +-------+ a tan(-) + b +--R | 2 2 2 +--R - 2\|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R b\|- b + a \|b - a +--R Type: Expression(Integer) +--E 388 + +--S 389 of 532 +d0772a:= D(m0772a,x) +--R +--R +--R (359) +--R 2 2 2 2 x 2 +--R (((- b + a )cos(x) - b )sin(x) + a b cos(x) - a b)tan(-) +--R 2 +--R + +--R 2 2 2 2 2 2 x +--R (2b sin(x) + 2a b sin(x) + 2b cos(x) + (2b - 2a )cos(x))tan(-) +--R 2 +--R + +--R 2 2 2 2 +--R ((- b + a )cos(x) - b )sin(x) + a b cos(x) - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 2 3 2 2 3 2 2 +--R ((b - a b)cos(x) + b - a b)sin(x) + (- a b + a )cos(x) + a b +--R + +--R 3 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 3 3 2 2 +--R (- 2b + 2a b)sin(x) + (- 2a b + 2a )sin(x) + (- 2b + 2a b)cos(x) +--R + +--R 3 2 +--R (- 2b + 2a b)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 2 2 3 2 2 3 +--R ((b - a b)cos(x) + b - a b)sin(x) + (- a b + a )cos(x) + a b - a +--R / +--R 2 2 2 3 3 3 3 +--R a b sin(x) + ((a b - a b)cos(x) + a b + a b)sin(x) +--R + +--R 2 2 4 2 2 +--R (a b - a )cos(x) + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 4 2 2 4 2 2 +--R 2a b sin(x) + ((2b - 2a b )cos(x) + 2b + 2a b )sin(x) +--R + +--R 3 3 3 +--R (2a b - 2a b)cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 3 3 3 +--R a b sin(x) + ((a b - a b)cos(x) + a b + a b)sin(x) +--R + +--R 2 2 4 2 2 +--R (a b - a )cos(x) + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 4 2 4 3 2 4 5 +--R (- a b + a b)sin(x) + ((- a b + a b )cos(x) - a b + a )sin(x) +--R + +--R 2 3 4 2 3 4 +--R (- a b + a b)cos(x) - a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 5 2 3 5 4 +--R (- 2a b + 2a b )sin(x) + ((- 2b + 2a b )cos(x) - 2b + 2a b)sin(x) +--R + +--R 4 3 2 4 3 2 +--R (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 2 4 3 2 4 5 +--R (- a b + a b)sin(x) + ((- a b + a b )cos(x) - a b + a )sin(x) +--R + +--R 2 3 4 2 3 4 +--R (- a b + a b)cos(x) - a b + a b +--R Type: Expression(Integer) +--E 389 + +--S 390 of 532 +m0772b:= a0772.2-r0772 +--R +--R +--R +---------+ x +--R | 2 2 a tan(-) + b +--R (a sin(x) + b cos(x) + b)\|- b + a 2 +--R - 2atan(-------------------------------------) - 2atan(------------) +--R 2 2 2 2 +---------+ +--R (b - a )cos(x) + b - a | 2 2 +--R \|- b + a +--R (360) -------------------------------------------------------------------- +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R Type: Expression(Integer) +--E 390 + +--S 391 of 532 +d0772b:= D(m0772b,x) +--R +--R +--R (361) +--R 2 2 x 2 +--R (a sin(x) + (- 2b cos(x) - 2b)sin(x) + a cos(x) - a)tan(-) +--R 2 +--R + +--R 2 2 x 2 +--R (4b sin(x) + 4b cos(x) + 4b cos(x))tan(-) + a sin(x) +--R 2 +--R + +--R 2 +--R (- 2b cos(x) - 2b)sin(x) + a cos(x) - a +--R / +--R 2 2 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) +--R + +--R 2 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 3 3 2 2 2 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) + 2a b cos(x) + 4a b cos(x) +--R + +--R 2 +--R 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 2 2 2 +--R a b sin(x) + (2a b cos(x) + 2a b )sin(x) + a b cos(x) + 2a b cos(x) + a b +--R Type: Expression(Integer) +--E 391 + +--S 392 of 532 +t0773:= x*cos(x)/(a+b*sin(x))^3 +--R +--R +--R x cos(x) +--R (362) ------------------------------------------- +--R 3 3 2 2 2 3 +--R b sin(x) + 3a b sin(x) + 3a b sin(x) + a +--R Type: Expression(Integer) +--E 392 + +--S 393 of 532 +r0773:= a*atan((b+a*tan(1/2*x))/(a^2-b^2)^(1/2))/b/(a^2-b^2)^(3/2)-_ + 1/2*x/b/(a+b*sin(x))^2+1/2*cos(x)/(a^2-b^2)/(a+b*sin(x)) +--R +--R +--R (363) +--R x +--R a tan(-) + b +--R 2 2 2 3 2 +--R (- 2a b sin(x) - 4a b sin(x) - 2a )atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R (- b cos(x)sin(x) - a b cos(x) + (- b + a )x)\|- b + a +--R / +--R +---------+ +--R 5 2 3 2 4 3 2 2 3 4 | 2 2 +--R ((2b - 2a b )sin(x) + (4a b - 4a b )sin(x) + 2a b - 2a b)\|- b + a +--R Type: Expression(Integer) +--E 393 + +--S 394 of 532 +a0773:= integrate(t0773,x) +--R +--R +--R (364) +--R [ +--R 3 2 2 2 2 2 4 +--R (2a b sin(x) - a b cos(x) + a b + a ) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 2 2 3 2 2 +--R (- a b cos(x) - 2a b )sin(x) + b cos(x) - a b cos(x) +--R + +--R 2 3 3 2 +--R (- a b + a )x - b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R / +--R 2 4 4 2 5 3 3 2 5 5 +--R ((4a b - 4a b )sin(x) + (- 2a b + 2a b )cos(x) + 2a b - 2a b) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R , +--R +--R 3 2 2 2 2 2 4 +--R (4a b sin(x) - 2a b cos(x) + 2a b + 2a ) +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 2 2 3 2 2 +--R (- a b cos(x) - 2a b )sin(x) + b cos(x) - a b cos(x) +--R + +--R 2 3 3 2 +--R (- a b + a )x - b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 4 4 2 5 3 3 2 5 5 +--R ((4a b - 4a b )sin(x) + (- 2a b + 2a b )cos(x) + 2a b - 2a b) +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 394 + +--S 395 of 532 +m0773a:= a0773.1-r0773 +--R +--R +--R (365) +--R 3 3 3 2 4 2 2 4 4 2 2 +--R 2a b sin(x) + (- a b cos(x) + a b + 5a b )sin(x) +--R + +--R 3 3 2 3 3 5 4 2 2 4 2 6 +--R (- 2a b cos(x) + 2a b + 4a b)sin(x) - a b cos(x) + a b + a +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) + (b - a )cos(x) + b )\|b - a +--R + +--R 2 3 3 2 3 2 +--R (a b - a )sin(x) + (b - a b)cos(x) + b - a b +--R / +--R b sin(x) + a +--R + +--R 3 3 3 2 4 2 2 4 4 2 2 +--R 4a b sin(x) + (- 2a b cos(x) + 2a b + 10a b )sin(x) +--R + +--R 3 3 2 3 3 5 4 2 2 4 2 6 +--R (- 4a b cos(x) + 4a b + 8a b)sin(x) - 2a b cos(x) + 2a b + 2a +--R * +--R x +--R +-------+ a tan(-) + b +--R | 2 2 2 +--R \|b - a atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 3 +--R (- a b cos(x) - 2a b )sin(x) +--R + +--R 5 2 2 3 4 3 2 5 2 3 2 +--R (b cos(x) - a b cos(x) + (- a b + a b )x - b - 5a b )sin(x) +--R + +--R 4 3 4 2 4 4 3 2 +--R (- a b cos(x) + 2a b cos(x) + a b cos(x) - 2a b - 4a b )sin(x) +--R + +--R 2 3 3 4 3 2 2 3 2 2 3 +--R - a b cos(x) + ((- a b + a b )x + a b )cos(x) + a b cos(x) +--R + +--R 4 3 2 2 3 4 +--R (a b - a b )x - a b - a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R / +--R 2 6 4 4 3 +--R (4a b - 4a b )sin(x) +--R + +--R 7 3 5 2 7 3 5 5 3 2 +--R ((- 2a b + 2a b )cos(x) + 2a b + 8a b - 10a b )sin(x) +--R + +--R 2 6 4 4 2 2 6 4 4 6 2 +--R ((- 4a b + 4a b )cos(x) + 4a b + 4a b - 8a b )sin(x) +--R + +--R 3 5 5 3 2 3 5 7 +--R (- 2a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a +--R Type: Expression(Integer) +--E 395 + +--S 396 of 532 +d0773a:= D(m0773a,x) +--R +--R +--R (366) +--R 3 6 7 +--R 2a b sin(x) +--R + +--R 2 7 2 2 7 4 5 2 7 4 5 6 +--R (a b cos(x) + (2a b - 2a b )cos(x) + 3a b + 5a b )sin(x) +--R + +--R 8 3 6 3 8 3 6 2 +--R (a b - a b )cos(x) + (a b + 8a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 4 8 +--R ((2a b - 2a b )x + a b + 8a b - 9a b )cos(x) + a b +--R + +--R 3 6 5 4 +--R 7a b + 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 3 +--R (4a b - 4a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 2 +--R ((2a b - 4a b + 2a b )x + 6a b + 8a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 +--R ((2a b + 6a b - 8a b )x + 2a b + 16a b - 18a b )cos(x) +--R + +--R 4 5 6 3 +--R 16a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 8 3 6 5 8 3 6 4 +--R (a b - a b )cos(x) + (a b + 9a b )cos(x) +--R + +--R 3 6 5 4 3 +--R (2a b - 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 6 5 4 2 +--R ((8a b - 16a b + 8a b )x - 10a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 7 2 +--R ((8a b - 4a b - 4a b )x - a b + 5a b + 13a b - 17a b ) +--R * +--R cos(x) +--R + +--R 8 3 6 5 4 7 2 +--R - a b + 7a b + 23a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 6 2 7 4 5 5 +--R - 2a b cos(x) + (7a b - 7a b )cos(x) +--R + +--R 2 7 4 5 4 +--R (13a b + 17a b )cos(x) +--R + +--R 3 6 5 4 2 7 4 5 3 +--R ((8a b - 8a b )x - 8a b + 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 2 +--R ((4a b - 8a b + 4a b )x - 14a b - 28a b - 9a b )cos(x) +--R + +--R 3 6 5 4 2 7 4 5 6 3 8 +--R ((- 4a b + 4a b )x + a b + a b + 5a b - 7a b)cos(x) +--R + +--R 2 7 4 5 6 3 +--R 3a b + 13a b + 16a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 7 8 3 6 6 +--R (- a b + a b )cos(x) + (- a b - 3a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 4 5 +--R ((- 2a b + 2a b )x + 3a b + 5a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 4 +--R ((8a b - 16a b + 8a b )x + 3a b + 17a b + 10a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (12a b - 8a b - 4a b )x - 3a b - 7a b + 12a b +--R + +--R 7 2 +--R - 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (- 8a b + 16a b - 8a b )x - 3a b - 19a b - 16a b +--R + +--R 7 2 +--R - 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 7 2 +--R (- 10a b + 6a b + 4a b )x + a b + a b - 4a b + 3a b +--R + +--R 9 +--R - a +--R * +--R cos(x) +--R + +--R 8 3 6 5 4 7 2 +--R a b + 5a b + 6a b + 6a b +--R * +--R sin(x) +--R + +--R 2 7 4 5 7 +--R (- a b + a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 +--R ((- 2a b + 4a b - 2a b )x - a b - a b )cos(x) +--R + +--R 8 3 6 2 7 4 5 6 3 5 +--R ((- 2a b + 2a b )x + 3a b - a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 4 +--R ((4a b - 4a b - 4a b + 4a b )x + 3a b + 5a b + 2a b )cos(x) +--R + +--R 8 5 4 2 7 4 5 6 3 8 3 +--R ((4a b - 4a b )x - 3a b + a b + 3a b - a b)cos(x) +--R + +--R 8 5 4 7 2 2 7 4 5 6 3 8 2 +--R ((- 2a b + 6a b - 4a b )x - 3a b - 5a b - 3a b - a b)cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 8 +--R ((- 2a b - 2a b + 4a b )x + a b - a b - a b + a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 +--R a b + a b + a b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 7 7 +--R 4a b sin(x) +--R + +--R 8 2 8 3 6 8 3 6 6 +--R (2a b cos(x) + (4a b - 4a b )cos(x) + 6a b + 2a b )sin(x) +--R + +--R 9 2 7 3 9 2 7 2 +--R (2b - 2a b )cos(x) + (2b + 24a b )cos(x) +--R + +--R 8 3 6 9 2 7 4 5 9 2 7 +--R ((4a b - 4a b )x + 2b + 8a b - 10a b )cos(x) + 2b - 2a b +--R + +--R 4 5 +--R - 20a b +--R * +--R 5 +--R sin(x) +--R + +--R 8 4 8 3 6 3 +--R - 2a b cos(x) + (16a b - 16a b )cos(x) +--R + +--R 9 2 7 4 5 8 3 6 2 +--R ((4b - 8a b + 4a b )x + 24a b + 44a b )cos(x) +--R + +--R 9 2 7 4 5 8 3 6 5 4 +--R ((4b + 12a b - 16a b )x - 4a b + 8a b - 4a b )cos(x) +--R + +--R 8 3 6 5 4 +--R - 10a b - 28a b - 42a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 4 9 2 7 4 5 3 +--R 12a b cos(x) + (4b + 28a b - 32a b )cos(x) +--R + +--R 8 3 6 5 4 9 2 7 4 5 2 +--R ((16a b - 32a b + 16a b )x + 4b + 20a b + 28a b )cos(x) +--R + +--R 8 3 6 5 4 9 2 7 4 5 6 3 +--R ((16a b - 8a b - 8a b )x - 4b - 16a b + 4a b + 16a b ) +--R * +--R cos(x) +--R + +--R 9 2 7 4 5 6 3 +--R - 4b - 20a b - 40a b - 36a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 6 8 3 6 5 +--R - 4a b cos(x) + (8a b - 8a b )cos(x) +--R + +--R 8 3 6 4 +--R (20a b + 28a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 4 3 +--R ((16a b - 16a b )x - 4a b + 40a b - 36a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 2 +--R ((8a b - 16a b + 8a b )x - 16a b - 8a b + 2a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 4 7 2 +--R ((- 8a b + 8a b )x - 4a b - 28a b + 8a b + 24a b )cos(x) +--R + +--R 3 6 5 4 7 2 +--R - 16a b - 26a b - 14a b +--R * +--R 2 +--R sin(x) +--R + +--R 9 2 7 7 9 2 7 6 +--R (- 2b + 2a b )cos(x) + (- 2b - 6a b )cos(x) +--R + +--R 8 3 6 9 2 7 4 5 5 +--R ((- 4a b + 4a b )x + 6b + 4a b - 10a b )cos(x) +--R + +--R 8 3 6 5 4 9 2 7 4 5 4 +--R ((16a b - 32a b + 16a b )x + 6b + 28a b + 18a b )cos(x) +--R + +--R 8 3 6 5 4 9 2 7 4 5 +--R (24a b - 16a b - 8a b )x - 6b - 2a b + 32a b +--R + +--R 6 3 +--R - 24a b +--R * +--R 3 +--R cos(x) +--R + +--R 8 3 6 5 4 9 2 7 4 5 +--R (- 16a b + 32a b - 16a b )x - 6b - 26a b - 8a b +--R + +--R 6 3 +--R - 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 3 6 5 4 9 2 7 4 5 +--R (- 20a b + 12a b + 8a b )x + 2b - 4a b - 22a b +--R + +--R 6 3 8 +--R 12a b + 12a b +--R * +--R cos(x) +--R + +--R 9 2 7 4 5 6 3 8 +--R 2b + 4a b - 10a b - 6a b - 2a b +--R * +--R sin(x) +--R + +--R 8 3 6 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 9 2 7 4 5 8 3 6 6 +--R ((- 4b + 8a b - 4a b )x - 2a b - 2a b )cos(x) +--R + +--R 9 2 7 8 3 6 5 4 5 +--R ((- 4b + 4a b )x + 6a b - 4a b - 2a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 3 6 5 4 4 +--R ((8b - 8a b - 8a b + 8a b )x + 6a b + 8a b + 4a b )cos(x) +--R + +--R 9 4 5 8 3 6 5 4 7 2 3 +--R ((8b - 8a b )x - 6a b + 6a b + 6a b - 6a b )cos(x) +--R + +--R 9 4 5 6 3 8 3 6 5 4 7 2 +--R ((- 4b + 12a b - 8a b )x - 6a b - 6a b - 2a b - 2a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 9 2 7 4 5 8 3 6 5 4 7 2 +--R (- 4b - 4a b + 8a b )x + 2a b - 4a b - 4a b + 4a b +--R + +--R 9 +--R 2a +--R * +--R cos(x) +--R + +--R 8 5 4 +--R 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 6 7 +--R 2a b sin(x) +--R + +--R 2 7 2 2 7 4 5 2 7 4 5 6 +--R (a b cos(x) + (2a b - 2a b )cos(x) + 3a b + 5a b )sin(x) +--R + +--R 8 3 6 3 8 3 6 2 +--R (a b - a b )cos(x) + (a b + 8a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 4 8 3 6 +--R ((2a b - 2a b )x + a b + 8a b - 9a b )cos(x) + a b + 7a b +--R + +--R 5 4 +--R 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 5 3 +--R (4a b - 4a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 2 +--R ((2a b - 4a b + 2a b )x + 6a b + 8a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 +--R ((2a b + 6a b - 8a b )x + 2a b + 16a b - 18a b )cos(x) +--R + +--R 4 5 6 3 +--R 16a b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 8 3 6 5 8 3 6 4 +--R (a b - a b )cos(x) + (a b + 9a b )cos(x) +--R + +--R 3 6 5 4 3 +--R (2a b - 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 6 5 4 2 +--R ((8a b - 16a b + 8a b )x - 10a b - 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 7 2 +--R ((8a b - 4a b - 4a b )x - a b + 5a b + 13a b - 17a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 +--R - a b + 7a b + 23a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 7 6 2 7 4 5 5 +--R - 2a b cos(x) + (7a b - 7a b )cos(x) +--R + +--R 2 7 4 5 4 +--R (13a b + 17a b )cos(x) +--R + +--R 3 6 5 4 2 7 4 5 3 +--R ((8a b - 8a b )x - 8a b + 8a b )cos(x) +--R + +--R 3 6 5 4 7 2 2 7 4 5 6 3 2 +--R ((4a b - 8a b + 4a b )x - 14a b - 28a b - 9a b )cos(x) +--R + +--R 3 6 5 4 2 7 4 5 6 3 8 2 7 +--R ((- 4a b + 4a b )x + a b + a b + 5a b - 7a b)cos(x) + 3a b +--R + +--R 4 5 6 3 +--R 13a b + 16a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 3 6 7 8 3 6 6 +--R (- a b + a b )cos(x) + (- a b - 3a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 4 5 +--R ((- 2a b + 2a b )x + 3a b + 5a b - 8a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 4 +--R ((8a b - 16a b + 8a b )x + 3a b + 17a b + 10a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 7 2 +--R ((12a b - 8a b - 4a b )x - 3a b - 7a b + 12a b - 2a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 7 2 +--R ((- 8a b + 16a b - 8a b )x - 3a b - 19a b - 16a b - 5a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 7 2 +--R (- 10a b + 6a b + 4a b )x + a b + a b - 4a b + 3a b +--R + +--R 9 +--R - a +--R * +--R cos(x) +--R + +--R 8 3 6 5 4 7 2 +--R a b + 5a b + 6a b + 6a b +--R * +--R sin(x) +--R + +--R 2 7 4 5 7 +--R (- a b + a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 +--R ((- 2a b + 4a b - 2a b )x - a b - a b )cos(x) +--R + +--R 8 3 6 2 7 4 5 6 3 5 +--R ((- 2a b + 2a b )x + 3a b - a b - 2a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 2 7 4 5 6 3 4 +--R ((4a b - 4a b - 4a b + 4a b )x + 3a b + 5a b + 2a b )cos(x) +--R + +--R 8 5 4 2 7 4 5 6 3 8 3 +--R ((4a b - 4a b )x - 3a b + a b + 3a b - a b)cos(x) +--R + +--R 8 5 4 7 2 2 7 4 5 6 3 8 2 +--R ((- 2a b + 6a b - 4a b )x - 3a b - 5a b - 3a b - a b)cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 8 2 7 +--R ((- 2a b - 2a b + 4a b )x + a b - a b - a b + a b)cos(x) + a b +--R + +--R 4 5 6 3 8 +--R a b + a b + a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 3 7 5 5 7 +--R (2a b - 2a b )sin(x) +--R + +--R 2 8 4 6 2 2 8 4 6 2 8 4 6 +--R (a b - a b )cos(x) + (2a b - 2a b )cos(x) + 3a b + 2a b +--R + +--R 6 4 +--R - 5a b +--R * +--R 6 +--R sin(x) +--R + +--R 9 3 7 3 9 3 7 5 5 2 +--R (a b - a b )cos(x) + (a b + 7a b - 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 9 +--R ((2a b - 4a b + 2a b )x + a b + 8a b - 9a b )cos(x) + a b +--R + +--R 3 7 5 5 7 3 +--R 6a b - a b - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 8 4 6 3 +--R (4a b - 4a b )cos(x) +--R + +--R 9 3 7 5 5 2 8 4 6 6 4 2 +--R ((2a b - 4a b + 2a b )x + 6a b + 2a b - 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 6 4 +--R ((2a b + 4a b - 14a b + 8a b )x + 2a b + 16a b - 18a b ) +--R * +--R cos(x) +--R + +--R 4 6 6 4 8 2 +--R 16a b - 12a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 9 3 7 5 9 3 7 5 5 4 +--R (a b - a b )cos(x) + (a b + 8a b - 9a b )cos(x) +--R + +--R 3 7 5 5 3 +--R (2a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 3 7 5 5 7 3 2 +--R ((8a b - 16a b + 8a b )x - 10a b + 6a b + 4a b )cos(x) +--R + +--R 2 8 4 6 8 2 9 3 7 5 5 7 3 +--R ((8a b - 12a b + 4a b )x - a b + 5a b + 13a b - 17a b ) +--R * +--R cos(x) +--R + +--R 9 3 7 5 5 7 3 9 +--R - a b + 8a b + 16a b - 22a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 8 4 6 6 2 8 4 6 5 +--R (- 2a b + 2a b )cos(x) + (7a b - 7a b )cos(x) +--R + +--R 2 8 4 6 6 4 4 +--R (13a b + 4a b - 17a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 8 4 6 3 +--R ((8a b - 16a b + 8a b )x - 8a b + 8a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 8 4 6 6 4 8 2 +--R ((4a b - 8a b + 4a b )x - 14a b - 14a b + 19a b + 9a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 7 5 5 7 3 2 8 4 6 6 4 8 2 +--R ((- 4a b + 8a b - 4a b )x + a b + a b + 5a b - 7a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 +--R 3a b + 10a b + 3a b - 16a b +--R * +--R 2 +--R sin(x) +--R + +--R 9 3 7 7 9 3 7 5 5 6 +--R (- a b + a b )cos(x) + (- a b - 2a b + 3a b )cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 5 +--R ((- 2a b + 4a b - 2a b )x + 3a b + 5a b - 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 7 3 +--R ((8a b - 16a b + 8a b )x + 3a b + 14a b - 7a b - 10a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 2 8 4 6 6 4 8 2 9 3 7 5 5 +--R (12a b - 20a b + 4a b + 4a b )x - 3a b - 7a b + 12a b +--R + +--R 7 3 +--R - 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 7 3 +--R (- 8a b + 16a b - 8a b )x - 3a b - 16a b + 3a b + 11a b +--R + +--R 9 +--R 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 8 4 6 6 4 8 2 9 3 7 5 5 +--R (- 10a b + 16a b - 2a b - 4a b )x + a b + a b - 4a b +--R + +--R 7 3 9 +--R 3a b - a b +--R * +--R cos(x) +--R + +--R 9 3 7 5 5 9 +--R a b + 4a b + a b - 6a b +--R * +--R sin(x) +--R + +--R 2 8 4 6 7 +--R (- a b + a b )cos(x) +--R + +--R 9 3 7 5 5 2 8 6 4 6 +--R ((- 2a b + 4a b - 2a b )x - a b + a b )cos(x) +--R + +--R 9 3 7 5 5 2 8 4 6 6 4 5 +--R ((- 2a b + 4a b - 2a b )x + 3a b - a b - 2a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 6 4 8 2 +--R ((4a b - 4a b - 4a b + 4a b )x + 3a b + 2a b - 3a b - 2a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 6 4 8 2 +--R ((4a b - 4a b - 4a b + 4a b )x - 3a b + a b + 3a b - a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 9 5 5 7 3 2 8 4 6 6 4 8 2 10 +--R ((- 2a b + 6a b - 4a b )x - 3a b - 2a b + 2a b + 2a b + a ) +--R * +--R 2 +--R cos(x) +--R + +--R 9 5 5 7 3 2 8 4 6 6 4 8 2 2 8 +--R ((- 2a b + 6a b - 4a b )x + a b - a b - a b + a b )cos(x) + a b +--R + +--R 10 +--R - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 8 4 6 7 +--R (4a b - 4a b )sin(x) +--R + +--R 9 3 7 2 9 3 7 9 3 7 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 6a b - 4a b +--R + +--R 5 5 +--R - 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 10 2 8 3 10 2 8 4 6 2 +--R (2b - 2a b )cos(x) + (2b + 22a b - 24a b )cos(x) +--R + +--R 9 3 7 5 5 10 2 8 4 6 10 +--R ((4a b - 8a b + 4a b )x + 2b + 8a b - 10a b )cos(x) + 2b +--R + +--R 2 8 4 6 6 4 +--R - 4a b - 18a b + 20a b +--R * +--R 5 +--R sin(x) +--R + +--R 9 3 7 4 9 3 7 3 +--R (- 2a b + 2a b )cos(x) + (16a b - 16a b )cos(x) +--R + +--R 10 2 8 4 6 9 3 7 5 5 2 +--R ((4b - 8a b + 4a b )x + 24a b + 20a b - 44a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 9 3 7 5 5 +--R ((4b + 8a b - 28a b + 16a b )x - 4a b + 8a b - 4a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 +--R - 10a b - 18a b - 14a b + 42a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 8 4 6 4 10 2 8 4 6 3 +--R (12a b - 12a b )cos(x) + (4b + 28a b - 32a b )cos(x) +--R + +--R 9 3 7 5 5 10 2 8 4 6 6 4 +--R ((16a b - 32a b + 16a b )x + 4b + 16a b + 8a b - 28a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 9 3 7 7 3 10 2 8 4 6 6 4 +--R ((16a b - 24a b + 8a b )x - 4b - 16a b + 4a b + 16a b ) +--R * +--R cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 +--R - 4b - 16a b - 20a b + 4a b + 36a b +--R * +--R 3 +--R sin(x) +--R + +--R 9 3 7 6 9 3 7 5 +--R (- 4a b + 4a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 9 3 7 5 5 4 +--R (20a b + 8a b - 28a b )cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 3 +--R ((16a b - 32a b + 16a b )x - 4a b + 40a b - 36a b )cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 7 3 +--R ((8a b - 16a b + 8a b )x - 16a b + 8a b + 10a b - 2a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 7 3 +--R ((- 8a b + 16a b - 8a b )x - 4a b - 28a b + 8a b + 24a b ) +--R * +--R cos(x) +--R + +--R 3 7 5 5 7 3 9 +--R - 16a b - 10a b + 12a b + 14a b +--R * +--R 2 +--R sin(x) +--R + +--R 10 2 8 7 10 2 8 4 6 6 +--R (- 2b + 2a b )cos(x) + (- 2b - 4a b + 6a b )cos(x) +--R + +--R 9 3 7 5 5 10 2 8 4 6 5 +--R ((- 4a b + 8a b - 4a b )x + 6b + 4a b - 10a b )cos(x) +--R + +--R 9 3 7 5 5 10 2 8 4 6 6 4 +--R ((16a b - 32a b + 16a b )x + 6b + 22a b - 10a b - 18a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 9 3 7 5 5 7 3 10 2 8 4 6 +--R (24a b - 40a b + 8a b + 8a b )x - 6b - 2a b + 32a b +--R + +--R 6 4 +--R - 24a b +--R * +--R 3 +--R cos(x) +--R + +--R 9 3 7 5 5 10 2 8 4 6 +--R (- 16a b + 32a b - 16a b )x - 6b - 20a b + 18a b +--R + +--R 6 4 8 2 +--R 2a b + 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 9 3 7 5 5 7 3 10 2 8 4 6 +--R (- 20a b + 32a b - 4a b - 8a b )x + 2b - 4a b - 22a b +--R + +--R 6 4 8 2 +--R 12a b + 12a b +--R * +--R cos(x) +--R + +--R 10 2 8 4 6 6 4 8 2 10 +--R 2b + 2a b - 14a b + 4a b + 4a b + 2a +--R * +--R sin(x) +--R + +--R 9 3 7 7 +--R (- 2a b + 2a b )cos(x) +--R + +--R 10 2 8 4 6 9 5 5 6 +--R ((- 4b + 8a b - 4a b )x - 2a b + 2a b )cos(x) +--R + +--R 10 2 8 4 6 9 3 7 5 5 5 +--R ((- 4b + 8a b - 4a b )x + 6a b - 4a b - 2a b )cos(x) +--R + +--R 10 2 8 4 6 6 4 9 3 7 5 5 7 3 +--R ((8b - 8a b - 8a b + 8a b )x + 6a b + 2a b - 4a b - 4a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 10 2 8 4 6 6 4 9 3 7 5 5 7 3 +--R ((8b - 8a b - 8a b + 8a b )x - 6a b + 6a b + 6a b - 6a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 10 4 6 6 4 9 5 5 9 2 +--R ((- 4b + 12a b - 8a b )x - 6a b + 4a b + 2a b)cos(x) +--R + +--R 10 4 6 6 4 9 3 7 5 5 7 3 9 +--R ((- 4b + 12a b - 8a b )x + 2a b - 4a b - 4a b + 4a b + 2a b) +--R * +--R cos(x) +--R + +--R 9 3 7 5 5 7 3 +--R 2a b - 2a b - 2a b + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 7 5 5 7 +--R (2a b - 2a b )sin(x) +--R + +--R 2 8 4 6 2 2 8 4 6 2 8 4 6 6 4 +--R ((a b - a b )cos(x) + (2a b - 2a b )cos(x) + 3a b + 2a b - 5a b ) +--R * +--R 6 +--R sin(x) +--R + +--R 9 3 7 3 9 3 7 5 5 2 +--R (a b - a b )cos(x) + (a b + 7a b - 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 9 +--R ((2a b - 4a b + 2a b )x + a b + 8a b - 9a b )cos(x) + a b +--R + +--R 3 7 5 5 7 3 +--R 6a b - a b - 6a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 8 4 6 3 +--R (4a b - 4a b )cos(x) +--R + +--R 9 3 7 5 5 2 8 4 6 6 4 2 +--R ((2a b - 4a b + 2a b )x + 6a b + 2a b - 8a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 6 4 +--R ((2a b + 4a b - 14a b + 8a b )x + 2a b + 16a b - 18a b )cos(x) +--R + +--R 4 6 6 4 8 2 +--R 16a b - 12a b - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 9 3 7 5 9 3 7 5 5 4 +--R (a b - a b )cos(x) + (a b + 8a b - 9a b )cos(x) +--R + +--R 3 7 5 5 3 +--R (2a b - 2a b )cos(x) +--R + +--R 2 8 4 6 6 4 3 7 5 5 7 3 2 +--R ((8a b - 16a b + 8a b )x - 10a b + 6a b + 4a b )cos(x) +--R + +--R 2 8 4 6 8 2 9 3 7 5 5 7 3 +--R ((8a b - 12a b + 4a b )x - a b + 5a b + 13a b - 17a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 9 +--R - a b + 8a b + 16a b - 22a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 8 4 6 6 2 8 4 6 5 +--R (- 2a b + 2a b )cos(x) + (7a b - 7a b )cos(x) +--R + +--R 2 8 4 6 6 4 4 +--R (13a b + 4a b - 17a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 8 4 6 3 +--R ((8a b - 16a b + 8a b )x - 8a b + 8a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 8 4 6 6 4 8 2 2 +--R ((4a b - 8a b + 4a b )x - 14a b - 14a b + 19a b + 9a b )cos(x) +--R + +--R 3 7 5 5 7 3 2 8 4 6 6 4 8 2 +--R ((- 4a b + 8a b - 4a b )x + a b + a b + 5a b - 7a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 +--R 3a b + 10a b + 3a b - 16a b +--R * +--R 2 +--R sin(x) +--R + +--R 9 3 7 7 9 3 7 5 5 6 +--R (- a b + a b )cos(x) + (- a b - 2a b + 3a b )cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 5 +--R ((- 2a b + 4a b - 2a b )x + 3a b + 5a b - 8a b )cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 7 3 4 +--R ((8a b - 16a b + 8a b )x + 3a b + 14a b - 7a b - 10a b )cos(x) +--R + +--R 2 8 4 6 6 4 8 2 9 3 7 5 5 +--R (12a b - 20a b + 4a b + 4a b )x - 3a b - 7a b + 12a b +--R + +--R 7 3 +--R - 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 8 4 6 6 4 9 3 7 5 5 7 3 +--R (- 8a b + 16a b - 8a b )x - 3a b - 16a b + 3a b + 11a b +--R + +--R 9 +--R 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 8 4 6 6 4 8 2 9 3 7 5 5 +--R (- 10a b + 16a b - 2a b - 4a b )x + a b + a b - 4a b +--R + +--R 7 3 9 +--R 3a b - a b +--R * +--R cos(x) +--R + +--R 9 3 7 5 5 9 +--R a b + 4a b + a b - 6a b +--R * +--R sin(x) +--R + +--R 2 8 4 6 7 +--R (- a b + a b )cos(x) +--R + +--R 9 3 7 5 5 2 8 6 4 6 +--R ((- 2a b + 4a b - 2a b )x - a b + a b )cos(x) +--R + +--R 9 3 7 5 5 2 8 4 6 6 4 5 +--R ((- 2a b + 4a b - 2a b )x + 3a b - a b - 2a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 6 4 8 2 4 +--R ((4a b - 4a b - 4a b + 4a b )x + 3a b + 2a b - 3a b - 2a b )cos(x) +--R + +--R 9 3 7 5 5 7 3 2 8 4 6 6 4 8 2 3 +--R ((4a b - 4a b - 4a b + 4a b )x - 3a b + a b + 3a b - a b )cos(x) +--R + +--R 9 5 5 7 3 2 8 4 6 6 4 8 2 10 2 +--R ((- 2a b + 6a b - 4a b )x - 3a b - 2a b + 2a b + 2a b + a )cos(x) +--R + +--R 9 5 5 7 3 2 8 4 6 6 4 8 2 2 8 10 +--R ((- 2a b + 6a b - 4a b )x + a b - a b - a b + a b )cos(x) + a b - a +--R / +--R 4 8 6 6 6 +--R (8a b - 8a b )sin(x) +--R + +--R 3 9 5 7 2 3 9 5 7 7 5 +--R (- 8a b + 8a b )cos(x) + (8a b - 16a b + 8a b )cos(x) +--R + +--R 3 9 5 7 7 5 +--R 16a b + 16a b - 32a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 10 4 8 4 2 10 4 8 6 6 3 +--R (2a b - 2a b )cos(x) + (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 2 10 4 8 6 6 2 +--R (- 12a b - 16a b + 28a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 10 4 8 +--R (8a b + 16a b - 56a b + 32a b )cos(x) + 10a b + 50a b +--R + +--R 6 6 8 4 +--R - 10a b - 50a b +--R * +--R 4 +--R sin(x) +--R + +--R 11 3 9 5 7 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 11 3 9 5 7 4 +--R (2a b + 4a b - 6a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 3 +--R (- 4a b - 20a b + 52a b - 28a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 4a b - 36a b + 4a b + 36a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (2a b + 24a b - 4a b - 72a b + 50a b )cos(x) + 2a b +--R + +--R 3 9 5 7 7 5 9 3 +--R 32a b + 52a b - 48a b - 38a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 10 4 8 6 6 5 2 10 6 6 4 +--R (6a b - 12a b + 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 3 +--R (- 12a b - 12a b + 60a b - 36a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 +--R (- 12a b - 36a b + 28a b + 20a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 10 +--R (6a b + 24a b - 28a b - 40a b + 38a b )cos(x) + 6a b +--R + +--R 4 8 6 6 8 4 10 2 +--R 36a b + 16a b - 44a b - 14a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 9 5 7 7 5 5 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 3 9 5 7 7 5 4 +--R (6a b - 4a b - 2a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 3 +--R (- 12a b + 4a b + 28a b - 20a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 2 +--R (- 12a b - 12a b + 20a b + 4a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 11 3 9 +--R (6a b + 8a b - 20a b - 8a b + 14a b)cos(x) + 6a b +--R + +--R 5 7 7 5 9 3 11 +--R 16a b - 4a b - 16a b - 2a b +--R * +--R sin(x) +--R + +--R 4 8 6 6 8 4 5 4 8 6 6 4 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 3 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) +--R + +--R 4 8 8 4 2 4 8 8 4 12 4 8 +--R (- 4a b + 4a b )cos(x) + (2a b - 4a b + 2a )cos(x) + 2a b +--R + +--R 6 6 8 4 10 2 +--R 2a b - 2a b - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 9 5 7 6 +--R (16a b - 16a b )sin(x) +--R + +--R 2 10 4 8 2 +--R (- 16a b + 16a b )cos(x) +--R + +--R 2 10 4 8 6 6 2 10 4 8 6 6 +--R (16a b - 32a b + 16a b )cos(x) + 32a b + 32a b - 64a b +--R * +--R 5 +--R sin(x) +--R + +--R 11 3 9 4 +--R (4a b - 4a b )cos(x) +--R + +--R 11 3 9 5 7 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 11 3 9 5 7 2 +--R (- 24a b - 32a b + 56a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 11 +--R (16a b + 32a b - 112a b + 64a b )cos(x) + 20a b +--R + +--R 3 9 5 7 7 5 +--R 100a b - 20a b - 100a b +--R * +--R 4 +--R sin(x) +--R + +--R 12 2 10 4 8 5 +--R (4b - 8a b + 4a b )cos(x) +--R + +--R 12 2 10 4 8 4 +--R (4b + 8a b - 12a b )cos(x) +--R + +--R 12 2 10 4 8 6 6 3 +--R (- 8b - 40a b + 104a b - 56a b )cos(x) +--R + +--R 12 2 10 4 8 6 6 2 +--R (- 8b - 72a b + 8a b + 72a b )cos(x) +--R + +--R 12 2 10 4 8 6 6 8 4 12 +--R (4b + 48a b - 8a b - 144a b + 100a b )cos(x) + 4b +--R + +--R 2 10 4 8 6 6 8 4 +--R 64a b + 104a b - 96a b - 76a b +--R * +--R 3 +--R sin(x) +--R + +--R 11 3 9 5 7 5 +--R (12a b - 24a b + 12a b )cos(x) +--R + +--R 11 5 7 4 +--R (12a b - 12a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 3 +--R (- 24a b - 24a b + 120a b - 72a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 24a b - 72a b + 56a b + 40a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (12a b + 48a b - 56a b - 80a b + 76a b )cos(x) + 12a b +--R + +--R 3 9 5 7 7 5 9 3 +--R 72a b + 32a b - 88a b - 28a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 10 4 8 6 6 5 +--R (12a b - 24a b + 12a b )cos(x) +--R + +--R 2 10 4 8 6 6 4 +--R (12a b - 8a b - 4a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 3 +--R (- 24a b + 8a b + 56a b - 40a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 +--R (- 24a b - 24a b + 40a b + 8a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R (12a b + 16a b - 40a b - 16a b + 28a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 +--R 12a b + 32a b - 8a b - 32a b - 4a b +--R * +--R sin(x) +--R + +--R 3 9 5 7 7 5 5 3 9 5 7 4 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 3 +--R (- 8a b + 8a b + 8a b - 8a b )cos(x) +--R + +--R 3 9 7 5 2 3 9 7 5 11 3 9 +--R (- 8a b + 8a b )cos(x) + (4a b - 8a b + 4a b)cos(x) + 4a b +--R + +--R 5 7 7 5 9 3 +--R 4a b - 4a b - 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 8 6 6 6 +--R (8a b - 8a b )sin(x) +--R + +--R 3 9 5 7 2 3 9 5 7 7 5 +--R (- 8a b + 8a b )cos(x) + (8a b - 16a b + 8a b )cos(x) +--R + +--R 3 9 5 7 7 5 +--R 16a b + 16a b - 32a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 10 4 8 4 2 10 4 8 6 6 3 +--R (2a b - 2a b )cos(x) + (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 2 10 4 8 6 6 2 +--R (- 12a b - 16a b + 28a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 10 4 8 +--R (8a b + 16a b - 56a b + 32a b )cos(x) + 10a b + 50a b +--R + +--R 6 6 8 4 +--R - 10a b - 50a b +--R * +--R 4 +--R sin(x) +--R + +--R 11 3 9 5 7 5 11 3 9 5 7 4 +--R (2a b - 4a b + 2a b )cos(x) + (2a b + 4a b - 6a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 3 +--R (- 4a b - 20a b + 52a b - 28a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 4a b - 36a b + 4a b + 36a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 9 3 11 +--R (2a b + 24a b - 4a b - 72a b + 50a b )cos(x) + 2a b +--R + +--R 3 9 5 7 7 5 9 3 +--R 32a b + 52a b - 48a b - 38a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 10 4 8 6 6 5 2 10 6 6 4 +--R (6a b - 12a b + 6a b )cos(x) + (6a b - 6a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 3 +--R (- 12a b - 12a b + 60a b - 36a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 +--R (- 12a b - 36a b + 28a b + 20a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 10 2 2 10 +--R (6a b + 24a b - 28a b - 40a b + 38a b )cos(x) + 6a b +--R + +--R 4 8 6 6 8 4 10 2 +--R 36a b + 16a b - 44a b - 14a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 9 5 7 7 5 5 3 9 5 7 7 5 4 +--R (6a b - 12a b + 6a b )cos(x) + (6a b - 4a b - 2a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 3 +--R (- 12a b + 4a b + 28a b - 20a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 2 +--R (- 12a b - 12a b + 20a b + 4a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 11 3 9 5 7 +--R (6a b + 8a b - 20a b - 8a b + 14a b)cos(x) + 6a b + 16a b +--R + +--R 7 5 9 3 11 +--R - 4a b - 16a b - 2a b +--R * +--R sin(x) +--R + +--R 4 8 6 6 8 4 5 4 8 6 6 4 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 2a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 3 4 8 8 4 2 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) + (- 4a b + 4a b )cos(x) +--R + +--R 4 8 8 4 12 4 8 6 6 8 4 10 2 +--R (2a b - 4a b + 2a )cos(x) + 2a b + 2a b - 2a b - 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 9 6 7 8 5 6 +--R (8a b - 16a b + 8a b )sin(x) +--R + +--R 3 10 5 8 7 6 2 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 3 10 5 8 7 6 3 10 7 6 9 4 +--R (8a b - 16a b + 8a b )cos(x) + 16a b - 48a b + 32a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 11 4 9 6 7 4 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 2 11 4 9 6 7 3 +--R (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 2 +--R (- 12a b - 4a b + 44a b - 28a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 2 11 4 9 +--R (8a b + 16a b - 56a b + 32a b )cos(x) + 10a b + 40a b +--R + +--R 6 7 8 5 10 3 +--R - 60a b - 40a b + 50a b +--R * +--R 4 +--R sin(x) +--R + +--R 12 3 10 5 8 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 4 +--R (2a b + 2a b - 10a b + 6a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 3 +--R (- 4a b - 20a b + 52a b - 28a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 4a b - 32a b + 40a b + 32a b - 36a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 9 4 12 +--R (2a b + 24a b - 4a b - 72a b + 50a b )cos(x) + 2a b +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R 30a b + 20a b - 100a b + 10a b + 38a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 11 4 9 6 7 5 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 4 +--R (6a b - 6a b - 6a b + 6a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 3 +--R (- 12a b - 12a b + 60a b - 36a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 12a b - 24a b + 64a b - 8a b - 20a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 11 +--R (6a b + 24a b - 28a b - 40a b + 38a b )cos(x) + 6a b +--R + +--R 4 9 6 7 8 5 10 3 12 +--R 30a b - 20a b - 60a b + 30a b + 14a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 10 5 8 7 6 5 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (6a b - 10a b + 2a b + 2a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 12a b + 4a b + 28a b - 20a b )cos(x) +--R + +--R 3 10 7 6 9 4 11 2 2 +--R (- 12a b + 32a b - 16a b - 4a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 3 10 +--R (6a b + 8a b - 20a b - 8a b + 14a b )cos(x) + 6a b +--R + +--R 5 8 7 6 9 4 11 2 13 +--R 10a b - 20a b - 12a b + 14a b + 2a +--R * +--R sin(x) +--R + +--R 4 9 6 7 8 5 5 4 9 6 7 8 5 4 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 2 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) +--R + +--R 4 9 8 5 12 4 9 8 5 12 +--R (2a b - 4a b + 2a b)cos(x) + 2a b - 4a b + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 10 5 8 7 6 6 +--R (16a b - 32a b + 16a b )sin(x) +--R + +--R 2 11 4 9 6 7 2 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 2 11 4 9 6 7 2 11 6 7 8 5 +--R (16a b - 32a b + 16a b )cos(x) + 32a b - 96a b + 64a b +--R * +--R 5 +--R sin(x) +--R + +--R 12 3 10 5 8 4 +--R (4a b - 8a b + 4a b )cos(x) +--R + +--R 12 3 10 5 8 3 +--R (- 16a b + 32a b - 16a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 2 +--R (- 24a b - 8a b + 88a b - 56a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 12 3 10 +--R (16a b + 32a b - 112a b + 64a b )cos(x) + 20a b + 80a b +--R + +--R 5 8 7 6 9 4 +--R - 120a b - 80a b + 100a b +--R * +--R 4 +--R sin(x) +--R + +--R 13 2 11 4 9 5 +--R (4b - 8a b + 4a b )cos(x) +--R + +--R 13 2 11 4 9 6 7 4 +--R (4b + 4a b - 20a b + 12a b )cos(x) +--R + +--R 13 2 11 4 9 6 7 3 +--R (- 8b - 40a b + 104a b - 56a b )cos(x) +--R + +--R 13 2 11 4 9 6 7 8 5 2 +--R (- 8b - 64a b + 80a b + 64a b - 72a b )cos(x) +--R + +--R 13 2 11 4 9 6 7 8 5 13 +--R (4b + 48a b - 8a b - 144a b + 100a b )cos(x) + 4b +--R + +--R 2 11 4 9 6 7 8 5 10 3 +--R 60a b + 40a b - 200a b + 20a b + 76a b +--R * +--R 3 +--R sin(x) +--R + +--R 12 3 10 5 8 5 +--R (12a b - 24a b + 12a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 4 +--R (12a b - 12a b - 12a b + 12a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 3 +--R (- 24a b - 24a b + 120a b - 72a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 24a b - 48a b + 128a b - 16a b - 40a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 9 4 12 +--R (12a b + 48a b - 56a b - 80a b + 76a b )cos(x) + 12a b +--R + +--R 3 10 5 8 7 6 9 4 11 2 +--R 60a b - 40a b - 120a b + 60a b + 28a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 11 4 9 6 7 5 +--R (12a b - 24a b + 12a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 4 +--R (12a b - 20a b + 4a b + 4a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 3 +--R (- 24a b + 8a b + 56a b - 40a b )cos(x) +--R + +--R 2 11 6 7 8 5 10 3 2 +--R (- 24a b + 64a b - 32a b - 8a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 11 +--R (12a b + 16a b - 40a b - 16a b + 28a b )cos(x) + 12a b +--R + +--R 4 9 6 7 8 5 10 3 12 +--R 20a b - 40a b - 24a b + 28a b + 4a b +--R * +--R sin(x) +--R + +--R 3 10 5 8 7 6 5 3 10 5 8 7 6 4 +--R (4a b - 8a b + 4a b )cos(x) + (4a b - 8a b + 4a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 8a b + 8a b + 8a b - 8a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 2 +--R (- 8a b + 8a b + 8a b - 8a b )cos(x) +--R + +--R 3 10 7 6 11 2 3 10 7 6 11 2 +--R (4a b - 8a b + 4a b )cos(x) + 4a b - 8a b + 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 9 6 7 8 5 6 +--R (8a b - 16a b + 8a b )sin(x) +--R + +--R 3 10 5 8 7 6 2 3 10 5 8 7 6 +--R (- 8a b + 16a b - 8a b )cos(x) + (8a b - 16a b + 8a b )cos(x) +--R + +--R 3 10 7 6 9 4 +--R 16a b - 48a b + 32a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 11 4 9 6 7 4 2 11 4 9 6 7 3 +--R (2a b - 4a b + 2a b )cos(x) + (- 8a b + 16a b - 8a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 2 +--R (- 12a b - 4a b + 44a b - 28a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 2 11 4 9 6 7 +--R (8a b + 16a b - 56a b + 32a b )cos(x) + 10a b + 40a b - 60a b +--R + +--R 8 5 10 3 +--R - 40a b + 50a b +--R * +--R 4 +--R sin(x) +--R + +--R 12 3 10 5 8 5 +--R (2a b - 4a b + 2a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 4 +--R (2a b + 2a b - 10a b + 6a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 3 +--R (- 4a b - 20a b + 52a b - 28a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 9 4 2 +--R (- 4a b - 32a b + 40a b + 32a b - 36a b )cos(x) +--R + +--R 12 3 10 5 8 7 6 9 4 12 3 10 +--R (2a b + 24a b - 4a b - 72a b + 50a b )cos(x) + 2a b + 30a b +--R + +--R 5 8 7 6 9 4 11 2 +--R 20a b - 100a b + 10a b + 38a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 11 4 9 6 7 5 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 4 +--R (6a b - 6a b - 6a b + 6a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 3 +--R (- 12a b - 12a b + 60a b - 36a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 +--R (- 12a b - 24a b + 64a b - 8a b - 20a b )cos(x) +--R + +--R 2 11 4 9 6 7 8 5 10 3 2 11 4 9 +--R (6a b + 24a b - 28a b - 40a b + 38a b )cos(x) + 6a b + 30a b +--R + +--R 6 7 8 5 10 3 12 +--R - 20a b - 60a b + 30a b + 14a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 10 5 8 7 6 5 +--R (6a b - 12a b + 6a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 4 +--R (6a b - 10a b + 2a b + 2a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 3 +--R (- 12a b + 4a b + 28a b - 20a b )cos(x) +--R + +--R 3 10 7 6 9 4 11 2 2 +--R (- 12a b + 32a b - 16a b - 4a b )cos(x) +--R + +--R 3 10 5 8 7 6 9 4 11 2 3 10 5 8 +--R (6a b + 8a b - 20a b - 8a b + 14a b )cos(x) + 6a b + 10a b +--R + +--R 7 6 9 4 11 2 13 +--R - 20a b - 12a b + 14a b + 2a +--R * +--R sin(x) +--R + +--R 4 9 6 7 8 5 5 4 9 6 7 8 5 4 +--R (2a b - 4a b + 2a b )cos(x) + (2a b - 4a b + 2a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 3 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) +--R + +--R 4 9 6 7 8 5 10 3 2 4 9 8 5 12 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) + (2a b - 4a b + 2a b)cos(x) +--R + +--R 4 9 8 5 12 +--R 2a b - 4a b + 2a b +--R Type: Expression(Integer) +--E 396 + +--S 397 of 532 +m0773b:= a0773.2-r0773 +--R +--R +--R (367) +--R 3 3 3 2 4 2 2 4 4 2 2 +--R 4a b sin(x) + (- 2a b cos(x) + 2a b + 10a b )sin(x) +--R + +--R 3 3 2 3 3 5 4 2 2 4 2 6 +--R (- 4a b cos(x) + 4a b + 8a b)sin(x) - 2a b cos(x) + 2a b + 2a +--R * +--R +---------+ +--R | 2 2 +--R (a sin(x) + b cos(x) + b)\|- b + a +--R atan(-------------------------------------) +--R 2 2 2 2 +--R (b - a )cos(x) + b - a +--R + +--R 3 3 3 2 4 2 2 4 4 2 2 +--R 4a b sin(x) + (- 2a b cos(x) + 2a b + 10a b )sin(x) +--R + +--R 3 3 2 3 3 5 4 2 2 4 2 6 +--R (- 4a b cos(x) + 4a b + 8a b)sin(x) - 2a b cos(x) + 2a b + 2a +--R * +--R x +--R a tan(-) + b +--R 2 +--R atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 4 4 3 +--R (- a b cos(x) - 2a b )sin(x) +--R + +--R 5 2 2 3 4 3 2 5 2 3 2 +--R (b cos(x) - a b cos(x) + (- a b + a b )x - b - 5a b )sin(x) +--R + +--R 4 3 4 2 4 4 3 2 +--R (- a b cos(x) + 2a b cos(x) + a b cos(x) - 2a b - 4a b )sin(x) +--R + +--R 2 3 3 4 3 2 2 3 2 2 3 +--R - a b cos(x) + ((- a b + a b )x + a b )cos(x) + a b cos(x) +--R + +--R 4 3 2 2 3 4 +--R (a b - a b )x - a b - a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R 2 6 4 4 3 +--R (4a b - 4a b )sin(x) +--R + +--R 7 3 5 2 7 3 5 5 3 2 +--R ((- 2a b + 2a b )cos(x) + 2a b + 8a b - 10a b )sin(x) +--R + +--R 2 6 4 4 2 2 6 4 4 6 2 +--R ((- 4a b + 4a b )cos(x) + 4a b + 4a b - 8a b )sin(x) +--R + +--R 3 5 5 3 2 3 5 7 +--R (- 2a b + 2a b )cos(x) + 2a b - 2a b +--R * +--R +---------+ +--R | 2 2 +--R \|- b + a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 532 +d0773b:= D(m0773b,x) +--R +--R +--R (368) +--R 3 6 8 2 7 2 2 7 2 7 4 5 7 +--R 2a b sin(x) + (a b cos(x) + 4a b cos(x) + 5a b + a b )sin(x) +--R + +--R 8 3 8 3 6 2 +--R 2a b cos(x) + (2a b + 14a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 8 3 6 5 4 +--R ((2a b - 2a b )x + 2a b + 22a b )cos(x) + 2a b + 14a b - 10a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 3 8 3 6 2 7 4 5 2 +--R 10a b cos(x) + ((4a b - 4a b )x + 14a b + 27a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 2 7 +--R ((4a b + 4a b - 8a b )x + 6a b + 54a b )cos(x) + 2a b +--R + +--R 4 5 6 3 +--R 33a b - 21a b +--R * +--R 5 +--R sin(x) +--R + +--R 8 5 8 3 6 4 +--R 2a b cos(x) + (2a b + 14a b )cos(x) +--R + +--R 2 7 4 5 3 6 3 +--R ((2a b - 2a b )x + 12a b )cos(x) +--R + +--R 2 7 4 5 3 6 5 4 2 +--R ((20a b - 20a b )x - 4a b + 16a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R ((18a b - 14a b - 4a b )x - 2a b + 12a b + 70a b )cos(x) +--R + +--R 8 3 6 5 4 7 2 +--R - 2a b + 14a b + 56a b - 18a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 6 2 7 5 2 7 4 5 4 +--R - 2a b cos(x) + 16a b cos(x) + (24a b + 30a b )cos(x) +--R + +--R 3 6 5 4 2 7 4 5 3 +--R ((16a b - 16a b )x - 16a b + 4a b )cos(x) +--R + +--R 3 6 5 4 2 7 4 5 6 3 2 +--R ((24a b - 24a b )x - 26a b - 44a b - 7a b )cos(x) +--R + +--R 3 6 5 4 4 5 6 3 2 7 4 5 +--R ((8a b - 8a b )x + 12a b + 48a b )cos(x) + 4a b + 30a b +--R + +--R 6 3 8 +--R 55a b - 7a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 7 8 3 6 6 +--R - 2a b cos(x) + (- 2a b + a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 +--R ((- 2a b + 2a b )x + 6a b + 30a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 4 4 +--R ((16a b - 16a b )x + 6a b + 33a b + 27a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 3 +--R ((20a b - 12a b - 8a b )x - 6a b - 36a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 +--R (- 16a b + 24a b - 8a b )x - 6a b - 45a b - 46a b +--R + +--R 7 2 +--R - 15a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 7 4 5 8 3 6 7 2 8 +--R ((- 18a b + 18a b )x + 2a b + 6a b + 16a b )cos(x) + 2a b +--R + +--R 3 6 5 4 7 2 9 +--R 11a b + 23a b + 31a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 8 2 7 7 +--R - a b cos(x) - 4a b cos(x) +--R + +--R 8 3 6 4 5 6 +--R ((- 4a b + 4a b )x + 4a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 5 +--R ((- 4a b + 12a b - 8a b )x + 12a b + 20a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 4 +--R ((8a b + 16a b - 24a b )x + 6a b + 14a b + 14a b )cos(x) +--R + +--R 8 5 4 2 7 4 5 6 3 3 +--R ((8a b - 8a b )x - 12a b - 24a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 8 +--R ((- 4a b - 20a b + 24a b )x - 8a b - 24a b - 22a b - 7a b) +--R * +--R 2 +--R cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 8 +--R ((- 4a b - 12a b + 16a b )x + 4a b + 4a b - 6a b + 2a b) +--R * +--R cos(x) +--R + +--R 2 7 4 5 6 3 8 +--R 3a b + 6a b + 8a b + 9a b +--R * +--R sin(x) +--R + +--R 3 6 8 2 7 4 5 3 6 7 +--R - a b cos(x) + ((- 2a b + 2a b )x - 2a b )cos(x) +--R + +--R 2 7 4 5 3 6 5 4 6 +--R ((- 4a b + 4a b )x + 2a b + a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 6 5 4 5 +--R ((2a b + 2a b - 4a b )x + 6a b + 4a b )cos(x) +--R + +--R 2 7 6 3 5 4 7 2 4 +--R ((8a b - 8a b )x + 3a b + 3a b )cos(x) +--R + +--R 2 7 4 5 3 6 5 4 7 2 3 +--R ((2a b - 2a b )x - 6a b - 4a b + 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 6 5 4 7 2 9 2 +--R ((- 4a b - 4a b + 8a b )x - 2a b - 5a b - 4a b - a )cos(x) +--R + +--R 2 7 4 5 6 3 3 6 7 2 3 6 5 4 +--R ((- 2a b - 2a b + 4a b )x + 2a b - 2a b )cos(x) + a b + a b +--R + +--R 7 2 9 +--R a b + a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 7 8 8 2 8 8 3 6 7 +--R 4a b sin(x) + (2a b cos(x) + 8a b cos(x) + 10a b - 6a b )sin(x) +--R + +--R 9 3 9 2 7 2 +--R 4b cos(x) + (4b + 36a b )cos(x) +--R + +--R 8 3 6 9 2 7 9 2 7 4 5 +--R ((4a b - 4a b )x + 4b + 28a b )cos(x) + 4b + 4a b - 52a b +--R * +--R 6 +--R sin(x) +--R + +--R 8 4 8 3 +--R - 2a b cos(x) + 36a b cos(x) +--R + +--R 9 2 7 8 3 6 2 +--R ((8b - 8a b )x + 48a b + 74a b )cos(x) +--R + +--R 9 2 7 4 5 8 3 6 8 +--R ((8b + 8a b - 16a b )x - 4a b + 28a b )cos(x) - 14a b +--R + +--R 3 6 5 4 +--R - 34a b - 92a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 7 4 8 3 6 9 2 7 3 +--R 30a b cos(x) + ((4a b - 4a b )x + 8b + 96a b )cos(x) +--R + +--R 8 3 6 9 2 7 4 5 2 +--R ((40a b - 40a b )x + 8b + 60a b + 36a b )cos(x) +--R + +--R 8 3 6 5 4 9 2 7 4 5 9 +--R ((36a b - 28a b - 8a b )x - 8b - 48a b - 24a b )cos(x) - 8b +--R + +--R 2 7 4 5 6 3 +--R - 42a b - 56a b - 74a b +--R * +--R 4 +--R sin(x) +--R + +--R 8 6 8 5 8 3 6 4 +--R - 6a b cos(x) + 16a b cos(x) + (38a b + 82a b )cos(x) +--R + +--R 2 7 4 5 3 6 3 +--R ((32a b - 32a b )x + 136a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 4 2 +--R ((48a b - 48a b )x - 26a b - 4a b - 44a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 4 8 +--R ((16a b - 16a b )x - 16a b - 104a b - 80a b )cos(x) - 6a b +--R + +--R 3 6 5 4 7 2 +--R - 46a b - 36a b - 28a b +--R * +--R 3 +--R sin(x) +--R + +--R 9 7 9 2 7 6 +--R - 4b cos(x) + (- 4b - 4a b )cos(x) +--R + +--R 8 3 6 9 2 7 5 +--R ((- 4a b + 4a b )x + 12b + 36a b )cos(x) +--R + +--R 8 3 6 9 2 7 4 5 4 +--R ((32a b - 32a b )x + 12b + 60a b + 88a b )cos(x) +--R + +--R 8 3 6 5 4 9 2 7 4 5 3 +--R ((40a b - 24a b - 16a b )x - 12b - 24a b + 120a b )cos(x) +--R + +--R 8 3 6 5 4 9 2 7 4 5 +--R (- 32a b + 48a b - 16a b )x - 12b - 60a b - 48a b +--R + +--R 6 3 +--R - 64a b +--R * +--R 2 +--R cos(x) +--R + +--R 8 3 6 9 2 7 4 5 6 3 +--R ((- 36a b + 36a b )x + 4b - 12a b - 112a b - 72a b )cos(x) +--R + +--R 9 2 7 4 5 6 3 8 +--R 4b + 4a b - 32a b - 8a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 8 8 8 7 9 2 7 3 6 6 +--R - 2a b cos(x) - 8a b cos(x) + ((- 8b + 8a b )x + 2a b )cos(x) +--R + +--R 9 2 7 4 5 8 3 6 5 +--R ((- 8b + 24a b - 16a b )x + 24a b + 24a b )cos(x) +--R + +--R 9 2 7 4 5 8 3 6 5 4 4 +--R ((16b + 32a b - 48a b )x + 12a b + 30a b + 48a b )cos(x) +--R + +--R 9 4 5 8 3 6 5 4 3 +--R ((16b - 16a b )x - 24a b - 16a b + 60a b )cos(x) +--R + +--R 9 2 7 4 5 8 3 6 5 4 +--R (- 8b - 40a b + 48a b )x - 16a b - 34a b - 36a b +--R + +--R 7 2 +--R - 28a b +--R * +--R 2 +--R cos(x) +--R + +--R 9 2 7 4 5 8 3 6 5 4 7 2 +--R ((- 8b - 24a b + 32a b )x + 8a b - 8a b - 60a b - 28a b ) +--R * +--R cos(x) +--R + +--R 8 3 6 5 4 +--R 6a b + 2a b - 12a b +--R * +--R sin(x) +--R + +--R 2 7 8 8 3 6 2 7 7 +--R - 2a b cos(x) + ((- 4a b + 4a b )x - 4a b )cos(x) +--R + +--R 8 3 6 2 7 6 +--R ((- 8a b + 8a b )x + 4a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 5 +--R ((4a b + 4a b - 8a b )x + 12a b + 4a b )cos(x) +--R + +--R 8 5 4 4 5 6 3 4 +--R ((16a b - 16a b )x + 8a b + 10a b )cos(x) +--R + +--R 8 3 6 2 7 6 3 3 +--R ((4a b - 4a b )x - 12a b + 12a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 8 2 +--R ((- 8a b - 8a b + 16a b )x - 4a b - 8a b - 8a b - 4a b)cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 8 +--R ((- 4a b - 4a b + 8a b )x + 4a b - 4a b - 12a b - 4a b)cos(x) +--R + +--R 2 7 6 3 +--R 2a b - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 6 8 2 7 2 2 7 2 7 4 5 7 +--R 2a b sin(x) + (a b cos(x) + 4a b cos(x) + 5a b + a b )sin(x) +--R + +--R 8 3 8 3 6 2 +--R 2a b cos(x) + (2a b + 14a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 8 3 6 5 4 +--R ((2a b - 2a b )x + 2a b + 22a b )cos(x) + 2a b + 14a b - 10a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 7 3 8 3 6 2 7 4 5 2 +--R 10a b cos(x) + ((4a b - 4a b )x + 14a b + 27a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 2 7 4 5 +--R ((4a b + 4a b - 8a b )x + 6a b + 54a b )cos(x) + 2a b + 33a b +--R + +--R 6 3 +--R - 21a b +--R * +--R 5 +--R sin(x) +--R + +--R 8 5 8 3 6 4 +--R 2a b cos(x) + (2a b + 14a b )cos(x) +--R + +--R 2 7 4 5 3 6 3 +--R ((2a b - 2a b )x + 12a b )cos(x) +--R + +--R 2 7 4 5 3 6 5 4 2 +--R ((20a b - 20a b )x - 4a b + 16a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 8 +--R ((18a b - 14a b - 4a b )x - 2a b + 12a b + 70a b )cos(x) - 2a b +--R + +--R 3 6 5 4 7 2 +--R 14a b + 56a b - 18a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 7 6 2 7 5 2 7 4 5 4 +--R - 2a b cos(x) + 16a b cos(x) + (24a b + 30a b )cos(x) +--R + +--R 3 6 5 4 2 7 4 5 3 +--R ((16a b - 16a b )x - 16a b + 4a b )cos(x) +--R + +--R 3 6 5 4 2 7 4 5 6 3 2 +--R ((24a b - 24a b )x - 26a b - 44a b - 7a b )cos(x) +--R + +--R 3 6 5 4 4 5 6 3 2 7 4 5 6 3 +--R ((8a b - 8a b )x + 12a b + 48a b )cos(x) + 4a b + 30a b + 55a b +--R + +--R 8 +--R - 7a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 7 8 3 6 6 +--R - 2a b cos(x) + (- 2a b + a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 +--R ((- 2a b + 2a b )x + 6a b + 30a b )cos(x) +--R + +--R 2 7 4 5 8 3 6 5 4 4 +--R ((16a b - 16a b )x + 6a b + 33a b + 27a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 3 +--R ((20a b - 12a b - 8a b )x - 6a b - 36a b + 4a b )cos(x) +--R + +--R 2 7 4 5 6 3 8 3 6 5 4 7 2 +--R ((- 16a b + 24a b - 8a b )x - 6a b - 45a b - 46a b - 15a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 7 4 5 8 3 6 7 2 8 +--R ((- 18a b + 18a b )x + 2a b + 6a b + 16a b )cos(x) + 2a b +--R + +--R 3 6 5 4 7 2 9 +--R 11a b + 23a b + 31a b - a +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 8 2 7 7 8 3 6 4 5 6 +--R - a b cos(x) - 4a b cos(x) + ((- 4a b + 4a b )x + 4a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 5 +--R ((- 4a b + 12a b - 8a b )x + 12a b + 20a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 4 +--R ((8a b + 16a b - 24a b )x + 6a b + 14a b + 14a b )cos(x) +--R + +--R 8 5 4 2 7 4 5 6 3 3 +--R ((8a b - 8a b )x - 12a b - 24a b + 6a b )cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 8 +--R ((- 4a b - 20a b + 24a b )x - 8a b - 24a b - 22a b - 7a b) +--R * +--R 2 +--R cos(x) +--R + +--R 8 3 6 5 4 2 7 4 5 6 3 8 +--R ((- 4a b - 12a b + 16a b )x + 4a b + 4a b - 6a b + 2a b)cos(x) +--R + +--R 2 7 4 5 6 3 8 +--R 3a b + 6a b + 8a b + 9a b +--R * +--R sin(x) +--R + +--R 3 6 8 2 7 4 5 3 6 7 +--R - a b cos(x) + ((- 2a b + 2a b )x - 2a b )cos(x) +--R + +--R 2 7 4 5 3 6 5 4 6 +--R ((- 4a b + 4a b )x + 2a b + a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 6 5 4 5 +--R ((2a b + 2a b - 4a b )x + 6a b + 4a b )cos(x) +--R + +--R 2 7 6 3 5 4 7 2 4 +--R ((8a b - 8a b )x + 3a b + 3a b )cos(x) +--R + +--R 2 7 4 5 3 6 5 4 7 2 3 +--R ((2a b - 2a b )x - 6a b - 4a b + 2a b )cos(x) +--R + +--R 2 7 4 5 6 3 3 6 5 4 7 2 9 2 +--R ((- 4a b - 4a b + 8a b )x - 2a b - 5a b - 4a b - a )cos(x) +--R + +--R 2 7 4 5 6 3 3 6 7 2 3 6 5 4 7 2 +--R ((- 2a b - 2a b + 4a b )x + 2a b - 2a b )cos(x) + a b + a b + a b +--R + +--R 9 +--R a +--R / +--R 4 8 6 6 7 +--R (8a b - 8a b )sin(x) +--R + +--R 3 9 5 7 2 3 9 5 7 3 9 +--R (- 8a b + 8a b )cos(x) + (16a b - 16a b )cos(x) + 24a b +--R + +--R 5 7 7 5 +--R 8a b - 32a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 10 4 8 4 2 10 4 8 3 +--R (2a b - 2a b )cos(x) + (- 16a b + 16a b )cos(x) +--R + +--R 2 10 6 6 2 2 10 4 8 6 6 +--R (- 20a b + 20a b )cos(x) + (16a b + 64a b - 80a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 +--R 18a b + 82a b - 50a b - 50a b +--R * +--R 5 +--R sin(x) +--R + +--R 11 3 9 5 11 3 9 5 7 4 +--R (4a b - 4a b )cos(x) + (4a b - 6a b + 2a b )cos(x) +--R + +--R 11 3 9 5 7 3 +--R (- 8a b - 64a b + 72a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 8a b - 60a b + 64a b + 4a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 11 3 9 +--R (4a b + 68a b + 92a b - 164a b )cos(x) + 4a b + 66a b +--R + +--R 5 7 7 5 9 3 +--R 98a b - 130a b - 38a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 10 4 8 6 2 10 4 8 5 +--R (2a b - 2a b )cos(x) + (16a b - 16a b )cos(x) +--R + +--R 2 10 4 8 6 6 4 +--R (10a b - 32a b + 22a b )cos(x) +--R + +--R 2 10 4 8 6 6 3 +--R (- 32a b - 96a b + 128a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 +--R (- 26a b - 58a b + 114a b - 30a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 10 4 8 +--R (16a b + 112a b + 48a b - 176a b )cos(x) + 14a b + 92a b +--R + +--R 6 6 8 4 10 2 +--R 40a b - 132a b - 14a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 9 5 7 6 3 9 5 7 5 +--R (6a b - 6a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 9 5 7 7 5 4 +--R (6a b - 40a b + 34a b )cos(x) +--R + +--R 3 9 5 7 7 5 3 +--R (- 48a b - 64a b + 112a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 2 +--R (- 30a b - 14a b + 78a b - 34a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 3 9 5 7 +--R (24a b + 88a b - 8a b - 104a b )cos(x) + 18a b + 60a b +--R + +--R 7 5 9 3 11 +--R - 8a b - 68a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 8 6 6 6 4 8 6 6 5 +--R (6a b - 6a b )cos(x) + (16a b - 16a b )cos(x) +--R + +--R 4 8 6 6 8 4 4 +--R (- 2a b - 18a b + 20a b )cos(x) +--R + +--R 4 8 6 6 8 4 3 +--R (- 32a b - 16a b + 48a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 2 +--R (- 14a b + 6a b + 22a b - 14a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 4 8 6 6 +--R (16a b + 32a b - 16a b - 32a b )cos(x) + 10a b + 18a b +--R + +--R 8 4 10 2 +--R - 10a b - 18a b +--R * +--R sin(x) +--R + +--R 5 7 7 5 6 5 7 7 5 5 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 5 7 7 5 9 3 4 5 7 9 3 3 +--R (- 2a b - 2a b + 4a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 5 7 7 5 9 3 11 2 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R + +--R 5 7 7 5 9 3 11 5 7 7 5 9 3 11 +--R (4a b + 4a b - 4a b - 4a b)cos(x) + 2a b + 2a b - 2a b - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 9 5 7 7 +--R (16a b - 16a b )sin(x) +--R + +--R 2 10 4 8 2 2 10 4 8 2 10 +--R (- 16a b + 16a b )cos(x) + (32a b - 32a b )cos(x) + 48a b +--R + +--R 4 8 6 6 +--R 16a b - 64a b +--R * +--R 6 +--R sin(x) +--R + +--R 11 3 9 4 11 3 9 3 +--R (4a b - 4a b )cos(x) + (- 32a b + 32a b )cos(x) +--R + +--R 11 5 7 2 11 3 9 5 7 +--R (- 40a b + 40a b )cos(x) + (32a b + 128a b - 160a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 +--R 36a b + 164a b - 100a b - 100a b +--R * +--R 5 +--R sin(x) +--R + +--R 12 2 10 5 12 2 10 4 8 4 +--R (8b - 8a b )cos(x) + (8b - 12a b + 4a b )cos(x) +--R + +--R 12 2 10 4 8 3 +--R (- 16b - 128a b + 144a b )cos(x) +--R + +--R 12 2 10 4 8 6 6 2 +--R (- 16b - 120a b + 128a b + 8a b )cos(x) +--R + +--R 12 2 10 4 8 6 6 12 2 10 +--R (8b + 136a b + 184a b - 328a b )cos(x) + 8b + 132a b +--R + +--R 4 8 6 6 8 4 +--R 196a b - 260a b - 76a b +--R * +--R 4 +--R sin(x) +--R + +--R 11 3 9 6 11 3 9 5 +--R (4a b - 4a b )cos(x) + (32a b - 32a b )cos(x) +--R + +--R 11 3 9 5 7 4 +--R (20a b - 64a b + 44a b )cos(x) +--R + +--R 11 3 9 5 7 3 +--R (- 64a b - 192a b + 256a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 52a b - 116a b + 228a b - 60a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 11 3 9 +--R (32a b + 224a b + 96a b - 352a b )cos(x) + 28a b + 184a b +--R + +--R 5 7 7 5 9 3 +--R 80a b - 264a b - 28a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 10 4 8 6 2 10 4 8 5 +--R (12a b - 12a b )cos(x) + (48a b - 48a b )cos(x) +--R + +--R 2 10 4 8 6 6 4 +--R (12a b - 80a b + 68a b )cos(x) +--R + +--R 2 10 4 8 6 6 3 +--R (- 96a b - 128a b + 224a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 +--R (- 60a b - 28a b + 156a b - 68a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 10 4 8 +--R (48a b + 176a b - 16a b - 208a b )cos(x) + 36a b + 120a b +--R + +--R 6 6 8 4 10 2 +--R - 16a b - 136a b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 9 5 7 6 3 9 5 7 5 +--R (12a b - 12a b )cos(x) + (32a b - 32a b )cos(x) +--R + +--R 3 9 5 7 7 5 4 +--R (- 4a b - 36a b + 40a b )cos(x) +--R + +--R 3 9 5 7 7 5 3 +--R (- 64a b - 32a b + 96a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 2 +--R (- 28a b + 12a b + 44a b - 28a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 3 9 5 7 +--R (32a b + 64a b - 32a b - 64a b )cos(x) + 20a b + 36a b +--R + +--R 7 5 9 3 +--R - 20a b - 36a b +--R * +--R sin(x) +--R + +--R 4 8 6 6 6 4 8 6 6 5 +--R (4a b - 4a b )cos(x) + (8a b - 8a b )cos(x) +--R + +--R 4 8 6 6 8 4 4 4 8 8 4 3 +--R (- 4a b - 4a b + 8a b )cos(x) + (- 16a b + 16a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 2 +--R (- 4a b + 4a b + 4a b - 4a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 4 8 6 6 8 4 10 2 +--R (8a b + 8a b - 8a b - 8a b )cos(x) + 4a b + 4a b - 4a b - 4a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 8 6 6 7 +--R (8a b - 8a b )sin(x) +--R + +--R 3 9 5 7 2 3 9 5 7 3 9 5 7 +--R (- 8a b + 8a b )cos(x) + (16a b - 16a b )cos(x) + 24a b + 8a b +--R + +--R 7 5 +--R - 32a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 10 4 8 4 2 10 4 8 3 +--R (2a b - 2a b )cos(x) + (- 16a b + 16a b )cos(x) +--R + +--R 2 10 6 6 2 2 10 4 8 6 6 +--R (- 20a b + 20a b )cos(x) + (16a b + 64a b - 80a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 +--R 18a b + 82a b - 50a b - 50a b +--R * +--R 5 +--R sin(x) +--R + +--R 11 3 9 5 11 3 9 5 7 4 +--R (4a b - 4a b )cos(x) + (4a b - 6a b + 2a b )cos(x) +--R + +--R 11 3 9 5 7 3 +--R (- 8a b - 64a b + 72a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 2 +--R (- 8a b - 60a b + 64a b + 4a b )cos(x) +--R + +--R 11 3 9 5 7 7 5 11 3 9 5 7 +--R (4a b + 68a b + 92a b - 164a b )cos(x) + 4a b + 66a b + 98a b +--R + +--R 7 5 9 3 +--R - 130a b - 38a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 10 4 8 6 2 10 4 8 5 +--R (2a b - 2a b )cos(x) + (16a b - 16a b )cos(x) +--R + +--R 2 10 4 8 6 6 4 +--R (10a b - 32a b + 22a b )cos(x) +--R + +--R 2 10 4 8 6 6 3 +--R (- 32a b - 96a b + 128a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 +--R (- 26a b - 58a b + 114a b - 30a b )cos(x) +--R + +--R 2 10 4 8 6 6 8 4 2 10 4 8 +--R (16a b + 112a b + 48a b - 176a b )cos(x) + 14a b + 92a b +--R + +--R 6 6 8 4 10 2 +--R 40a b - 132a b - 14a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 9 5 7 6 3 9 5 7 5 +--R (6a b - 6a b )cos(x) + (24a b - 24a b )cos(x) +--R + +--R 3 9 5 7 7 5 4 +--R (6a b - 40a b + 34a b )cos(x) +--R + +--R 3 9 5 7 7 5 3 +--R (- 48a b - 64a b + 112a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 2 +--R (- 30a b - 14a b + 78a b - 34a b )cos(x) +--R + +--R 3 9 5 7 7 5 9 3 3 9 5 7 7 5 +--R (24a b + 88a b - 8a b - 104a b )cos(x) + 18a b + 60a b - 8a b +--R + +--R 9 3 11 +--R - 68a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 8 6 6 6 4 8 6 6 5 +--R (6a b - 6a b )cos(x) + (16a b - 16a b )cos(x) +--R + +--R 4 8 6 6 8 4 4 +--R (- 2a b - 18a b + 20a b )cos(x) +--R + +--R 4 8 6 6 8 4 3 +--R (- 32a b - 16a b + 48a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 2 +--R (- 14a b + 6a b + 22a b - 14a b )cos(x) +--R + +--R 4 8 6 6 8 4 10 2 4 8 6 6 8 4 +--R (16a b + 32a b - 16a b - 32a b )cos(x) + 10a b + 18a b - 10a b +--R + +--R 10 2 +--R - 18a b +--R * +--R sin(x) +--R + +--R 5 7 7 5 6 5 7 7 5 5 +--R (2a b - 2a b )cos(x) + (4a b - 4a b )cos(x) +--R + +--R 5 7 7 5 9 3 4 5 7 9 3 3 +--R (- 2a b - 2a b + 4a b )cos(x) + (- 8a b + 8a b )cos(x) +--R + +--R 5 7 7 5 9 3 11 2 +--R (- 2a b + 2a b + 2a b - 2a b)cos(x) +--R + +--R 5 7 7 5 9 3 11 5 7 7 5 9 3 11 +--R (4a b + 4a b - 4a b - 4a b)cos(x) + 2a b + 2a b - 2a b - 2a b +--R Type: Expression(Integer) +--E 398 + +--S 399 of 532 +t0774:= x*sin(x)/(a+b*cos(x))^2 +--R +--R +--R x sin(x) +--R (369) ---------------------------- +--R 2 2 2 +--R b cos(x) + 2a b cos(x) + a +--R Type: Expression(Integer) +--E 399 + +--S 400 of 532 +r0774:= -2*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b/(a^2-b^2)^(1/2)+_ + x/b/(a+b*cos(x)) +--R +--R +--R x +--R (b - a)tan(-) +---------+ +--R 2 | 2 2 +--R (2b cos(x) + 2a)atan(-------------) + x\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (370) --------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R (b cos(x) + a b)\|- b + a +--R Type: Expression(Integer) +--E 400 + +--S 401 of 532 +a0774:= integrate(t0774,x) +--R +--R +--R (371) +--R [ +--R +-------+ +--R | 2 2 2 2 +--R (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R (b cos(x) + a)log(--------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R | 2 2 +--R x\|b - a +--R / +--R +-------+ +--R 2 | 2 2 +--R (b cos(x) + a b)\|b - a +--R , +--R +---------+ +--R | 2 2 +---------+ +--R sin(x)\|- b + a | 2 2 +--R (- 2b cos(x) - 2a)atan(---------------------) + x\|- b + a +--R (b + a)cos(x) + b + a +--R -------------------------------------------------------------] +--R +---------+ +--R 2 | 2 2 +--R (b cos(x) + a b)\|- b + a +--R Type: Union(List(Expression(Integer)),...) +--E 401 + +--S 402 of 532 +m0774a:= a0774.1-r0774 +--R +--R +--R (372) +--R +-------+ +--R +---------+ | 2 2 2 2 +--R | 2 2 (- a cos(x) - b)\|b - a + (b - a )sin(x) +--R \|- b + a log(--------------------------------------------) +--R b cos(x) + a +--R + +--R x +--R +-------+ (b - a)tan(-) +--R | 2 2 2 +--R - 2\|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R b\|- b + a \|b - a +--R Type: Expression(Integer) +--E 402 + +--S 403 of 532 +d0774a:= D(m0774a,x) +--R +--R +--R (373) +--R 2 2 x 2 +--R ((- b + a)sin(x) - b cos(x) + (- b - a)cos(x) - a)tan(-) +--R 2 +--R + +--R 2 2 +--R (b + a)sin(x) + b cos(x) + (- b + a)cos(x) - a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 2 2 2 x 2 +--R ((b - a )cos(x) + b - a )sin(x)tan(-) +--R 2 +--R + +--R 2 2 2 2 +--R ((b - a )cos(x) - b + a )sin(x) +--R / +--R 2 2 2 3 2 2 3 2 2 +--R ((a b - a b)cos(x) + (b - a b + a b - a )cos(x) + a b - a b) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 2 2 3 2 2 +--R (- a b - a b)cos(x) + (- b - a b - a b - a )cos(x) - a b - a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 4 3 2 2 3 3 2 2 3 4 x 2 +--R ((- b + a b + a b - a b)cos(x) - a b + a b + a b - a )sin(x)tan(-) +--R 2 +--R + +--R 4 3 2 2 3 3 2 2 3 4 +--R ((b + a b - a b - a b)cos(x) + a b + a b - a b - a )sin(x) +--R Type: Expression(Integer) +--E 403 + +--S 404 of 532 +m0774b:= a0774.2-r0774 +--R +--R +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R sin(x)\|- b + a 2 +--R - 2atan(---------------------) - 2atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R (374) ----------------------------------------------------- +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R Type: Expression(Integer) +--E 404 + +--S 405 of 532 +d0774b:= D(m0774b,x) +--R +--R +--R (375) +--R 2 2 x 2 +--R ((b - a)sin(x) + (3b - a)cos(x) + 4b cos(x) + b + a)tan(-) +--R 2 +--R + +--R 2 2 +--R (- 3b - a)sin(x) + (- b - a)cos(x) + b + a +--R / +--R 3 2 2 2 3 2 2 +--R (b - 2a b + a b)sin(x) + (- b + a b)cos(x) +--R + +--R 3 2 3 2 +--R (- 2b + 2a b)cos(x) - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 2 2 +--R (- b + a b)sin(x) + (b + 2a b + a b)cos(x) +--R + +--R 3 2 2 3 2 2 +--R (2b + 4a b + 2a b)cos(x) + b + 2a b + a b +--R Type: Expression(Integer) +--E 405 + +--S 406 of 532 +t0775:= x*sin(x)/(a+b*cos(x))^3 +--R +--R +--R x sin(x) +--R (376) ------------------------------------------- +--R 3 3 2 2 2 3 +--R b cos(x) + 3a b cos(x) + 3a b cos(x) + a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 532 +r0775:= -a*atan((a-b)*tan(1/2*x)/(a^2-b^2)^(1/2))/b/(a^2-b^2)^(3/2)+_ + 1/2*x/b/(a+b*cos(x))^2+1/2*sin(x)/(a^2-b^2)/(a+b*cos(x)) +--R +--R +--R (377) +--R x +--R (b - a)tan(-) +--R 2 2 2 3 2 +--R (- 2a b cos(x) - 4a b cos(x) - 2a )atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R ((- b cos(x) - a b)sin(x) + (b - a )x)\|- b + a +--R / +--R +---------+ +--R 5 2 3 2 4 3 2 2 3 4 | 2 2 +--R ((2b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b)\|- b + a +--R Type: Expression(Integer) +--E 407 + +--S 408 of 532 +a0775:= integrate(t0775,x) +--R +--R +--R (378) +--R [ +--R 2 2 2 3 +--R (a b cos(x) + 2a b cos(x) + a ) +--R * +--R +-------+ +--R | 2 2 2 2 +--R (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R log(----------------------------------------------) +--R b cos(x) + a +--R + +--R +-------+ +--R 2 2 2 | 2 2 +--R ((- b cos(x) - a b)sin(x) + (b - a )x)\|b - a +--R / +--R +-------+ +--R 5 2 3 2 4 3 2 2 3 4 | 2 2 +--R ((2b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b)\|b - a +--R , +--R +--R +---------+ +--R | 2 2 +--R 2 2 2 3 sin(x)\|- b + a +--R (2a b cos(x) + 4a b cos(x) + 2a )atan(---------------------) +--R (b + a)cos(x) + b + a +--R + +--R +---------+ +--R 2 2 2 | 2 2 +--R ((- b cos(x) - a b)sin(x) + (b - a )x)\|- b + a +--R / +--R +---------+ +--R 5 2 3 2 4 3 2 2 3 4 | 2 2 +--R ((2b - 2a b )cos(x) + (4a b - 4a b )cos(x) + 2a b - 2a b)\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 408 + +--S 409 of 532 +m0775a:= a0775.1-r0775 +--R +--R +--R (379) +--R +-------+ +--R +---------+ | 2 2 2 2 +--R | 2 2 (- a cos(x) - b)\|b - a + (- b + a )sin(x) +--R a\|- b + a log(----------------------------------------------) +--R b cos(x) + a +--R + +--R x +--R +-------+ (b - a)tan(-) +--R | 2 2 2 +--R 2a\|b - a atan(-------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R 3 2 | 2 2 | 2 2 +--R (2b - 2a b)\|- b + a \|b - a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 532 +d0775a:= D(m0775a,x) +--R +--R +--R (380) +--R 2 2 2 2 2 x 2 +--R ((a b - a )sin(x) + a b cos(x) + (a b + a )cos(x) + a )tan(-) +--R 2 +--R + +--R 2 2 2 2 2 +--R (- a b - a )sin(x) - a b cos(x) + (a b - a )cos(x) + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 2 3 x 2 +--R ((a b - a )cos(x) + a b - a )sin(x)tan(-) +--R 2 +--R + +--R 2 3 2 3 +--R ((a b - a )cos(x) - a b + a )sin(x) +--R / +--R 4 2 3 3 2 4 2 +--R (2a b - 2a b - 2a b + 2a b)cos(x) +--R + +--R 5 4 4 5 4 2 3 3 2 4 +--R (2b - 2a b - 2a b + 2a )cos(x) + 2a b - 2a b - 2a b + 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 4 2 +--R (- 2a b - 2a b + 2a b + 2a b)cos(x) +--R + +--R 5 4 4 5 4 2 3 3 2 4 +--R (- 2b - 2a b + 2a b + 2a )cos(x) - 2a b - 2a b + 2a b + 2a b +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 6 5 2 4 3 3 4 2 5 5 2 4 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a b)cos(x) + 2a b - 2a b +--R + +--R 3 3 4 2 5 6 +--R - 4a b + 4a b + 2a b - 2a +--R * +--R x 2 +--R sin(x)tan(-) +--R 2 +--R + +--R 6 5 2 4 3 3 4 2 5 5 2 4 +--R (- 2b - 2a b + 4a b + 4a b - 2a b - 2a b)cos(x) - 2a b - 2a b +--R + +--R 3 3 4 2 5 6 +--R 4a b + 4a b - 2a b - 2a +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 410 + +--S 411 of 532 +m0775b:= a0775.2-r0775 +--R +--R +--R +---------+ x +--R | 2 2 (b - a)tan(-) +--R sin(x)\|- b + a 2 +--R a atan(---------------------) + a atan(-------------) +--R (b + a)cos(x) + b + a +---------+ +--R | 2 2 +--R \|- b + a +--R (381) ----------------------------------------------------- +--R +---------+ +--R 3 2 | 2 2 +--R (b - a b)\|- b + a +--R Type: Expression(Integer) +--E 411 + +--S 412 of 532 +d0775b:= D(m0775b,x) +--R +--R +--R (382) +--R 2 2 2 2 2 +--R ((- a b + a )sin(x) + (- 3a b + a )cos(x) - 4a b cos(x) - a b - a ) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 +--R (3a b + a )sin(x) + (a b + a )cos(x) - a b - a +--R / +--R 5 4 3 2 4 2 5 2 3 4 2 +--R (2b - 4a b + 4a b - 2a b)sin(x) + (- 2b + 4a b - 2a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 +--R (- 4b + 8a b - 4a b)cos(x) - 2b + 4a b - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 4 2 5 4 3 2 4 2 +--R (- 2b + 4a b - 2a b)sin(x) + (2b + 4a b - 4a b - 2a b)cos(x) +--R + +--R 5 4 3 2 4 5 4 3 2 4 +--R (4b + 8a b - 8a b - 4a b)cos(x) + 2b + 4a b - 4a b - 2a b +--R Type: Expression(Integer) +--E 412 + +--S 413 of 532 +t0776:= x*sec(x)^2/(a+b*tan(x))^2 +--R +--R +--R 2 +--R x sec(x) +--R (383) ---------------------------- +--R 2 2 2 +--R b tan(x) + 2a b tan(x) + a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 532 +r0776:= a*x/b/(a^2+b^2)+log(a*cos(x)+b*sin(x))/(a^2+b^2)-x/b/(a+b*tan(x)) +--R +--R +--R (b tan(x) + a)log(b sin(x) + a cos(x)) + a x tan(x) - b x +--R (384) --------------------------------------------------------- +--R 3 2 2 3 +--R (b + a b)tan(x) + a b + a +--R Type: Expression(Integer) +--E 414 + +--S 415 of 532 +a0776:= integrate(t0776,x) +--R +--R +--R (385) +--R 2 +--R (- b sin(x) - a cos(x))log(----------) +--R cos(x) + 1 +--R + +--R - 2b sin(x) - 2a cos(x) +--R (b sin(x) + a cos(x))log(-----------------------) + a x sin(x) - b x cos(x) +--R cos(x) + 1 +--R / +--R 3 2 2 3 +--R (b + a b)sin(x) + (a b + a )cos(x) +--R Type: Union(Expression(Integer),...) +--E 415 + +--S 416 of 532 +m0776:= a0776-r0776 +--R +--R +--R (386) +--R 2 2 +--R ((- b sin(x) - a b cos(x))tan(x) - a b sin(x) - a cos(x)) +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 2 2 2 +--R ((- b sin(x) - a b cos(x))tan(x) - a b sin(x) - a cos(x))log(----------) +--R cos(x) + 1 +--R + +--R 2 2 +--R ((b sin(x) + a b cos(x))tan(x) + a b sin(x) + a cos(x)) +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 +--R (- b - a )x cos(x)tan(x) + (b + a )x sin(x) +--R / +--R 4 2 2 3 3 3 3 +--R ((b + a b )sin(x) + (a b + a b)cos(x))tan(x) + (a b + a b)sin(x) +--R + +--R 2 2 4 +--R (a b + a )cos(x) +--R Type: Expression(Integer) +--E 416 + +--S 417 of 532 +d0776:= D(m0776,x) +--R +--R +--R (387) +--R 2 2 2 2 2 +--R ((- 2a b x - b )cos(x)sin(x) + ((b - a )x - a b)cos(x) )tan(x) +--R + +--R 2 2 2 2 +--R ((2a b x + b )sin(x) + (2a b x - a )cos(x) )tan(x) +--R + +--R 2 2 2 2 +--R ((- b + a )x + a b)sin(x) + (- 2a b x + a )cos(x)sin(x) +--R / +--R 4 2 3 2 2 2 2 +--R (b sin(x) + 2a b cos(x)sin(x) + a b cos(x) )tan(x) +--R + +--R 3 2 2 2 3 2 2 2 2 +--R (2a b sin(x) + 4a b cos(x)sin(x) + 2a b cos(x) )tan(x) + a b sin(x) +--R + +--R 3 4 2 +--R 2a b cos(x)sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 417 + +--S 418 of 532 +t0777:= x*csc(x)^2/(a+b*cot(x))^2 +--R +--R +--R 2 +--R x csc(x) +--R (388) ---------------------------- +--R 2 2 2 +--R b cot(x) + 2a b cot(x) + a +--R Type: Expression(Integer) +--E 418 + +--S 419 of 532 +r0777:= -a*x/b/(a^2+b^2)+x/b/(a+b*cot(x))+log(b*cos(x)+a*sin(x))/(a^2+b^2) +--R +--R +--R (b cot(x) + a)log(a sin(x) + b cos(x)) - a x cot(x) + b x +--R (389) --------------------------------------------------------- +--R 3 2 2 3 +--R (b + a b)cot(x) + a b + a +--R Type: Expression(Integer) +--E 419 + +--S 420 of 532 +a0777:= integrate(t0777,x) +--R +--R +--R (390) +--R 2 +--R (- a sin(x) - b cos(x))log(----------) +--R cos(x) + 1 +--R + +--R - 2a sin(x) - 2b cos(x) +--R (a sin(x) + b cos(x))log(-----------------------) + b x sin(x) - a x cos(x) +--R cos(x) + 1 +--R / +--R 2 3 3 2 +--R (a b + a )sin(x) + (b + a b)cos(x) +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 532 +m0777:= a0777-r0777 +--R +--R +--R (391) +--R 2 2 +--R ((- a b cot(x) - a )sin(x) - b cos(x)cot(x) - a b cos(x)) +--R * +--R log(a sin(x) + b cos(x)) +--R + +--R 2 2 2 +--R ((- a b cot(x) - a )sin(x) - b cos(x)cot(x) - a b cos(x))log(----------) +--R cos(x) + 1 +--R + +--R 2 2 +--R ((a b cot(x) + a )sin(x) + b cos(x)cot(x) + a b cos(x)) +--R * +--R - 2a sin(x) - 2b cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 +--R (b + a )x cot(x)sin(x) + (- b - a )x cos(x) +--R / +--R 3 3 2 2 4 4 2 2 +--R ((a b + a b)cot(x) + a b + a )sin(x) + (b + a b )cos(x)cot(x) +--R + +--R 3 3 +--R (a b + a b)cos(x) +--R Type: Expression(Integer) +--E 421 + +--S 422 of 532 +d0777:= D(m0777,x) +--R +--R +--R (392) +--R 2 2 2 2 2 +--R (((b - a )x + a b)cot(x) + (2a b x + a )cot(x))sin(x) +--R + +--R 2 2 2 +--R ((- 2a b x + b )cos(x)cot(x) + (- 2a b x - a )cos(x))sin(x) +--R + +--R 2 2 2 2 2 +--R (2a b x - b )cos(x) cot(x) + ((- b + a )x - a b)cos(x) +--R / +--R 2 2 2 3 4 2 +--R (a b cot(x) + 2a b cot(x) + a )sin(x) +--R + +--R 3 2 2 2 3 +--R (2a b cos(x)cot(x) + 4a b cos(x)cot(x) + 2a b cos(x))sin(x) +--R + +--R 4 2 2 3 2 2 2 2 +--R b cos(x) cot(x) + 2a b cos(x) cot(x) + a b cos(x) +--R Type: Expression(Integer) +--E 422 + +--S 423 of 532 +t0778:= sin(a+b*x)*tan(c+b*x) +--R +--R +--R (393) sin(b x + a)tan(b x + c) +--R Type: Expression(Integer) +--E 423 + +--S 424 of 532 +r0778:= (atanh(sin(c+b*x))*cos(a-c)-sin(a+b*x))/b +--R +--R +--R cos(c - a)atanh(sin(b x + c)) - sin(b x + a) +--R (394) -------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 424 + +--S 425 of 532 +a0778:= integrate(t0778,x) +--R +--R +--R (395) +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) +--R + +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R +---------------+ +--R | 2 +--R - sin(b x + a)\|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R b\|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 425 + +--S 426 of 532 +m0778:= a0778-r0778 +--R +--R +--R (396) +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) +--R + +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R +---------------+ +--R | 2 +--R - cos(c - a)atanh(sin(b x + c))\|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R b\|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 532 +d0778:= D(m0778,x) +--R +--R +--R (397) +--R (cos(c - a)cos(b x + a) + cos(c - a))cos(b x + c)sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 2 +--R (- sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 +--R (cos(c - a)cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a))cos(b x + c) +--R + +--R 2 +--R cos(b x + a) + cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R - sin(b x + a)sin(b x + c) +--R + +--R ((- cos(c - a)cos(b x + a) + cos(c - a))cos(b x + c) + 1) +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 2 2 +--R (- sin(b x + a) - cos(b x + a) )sin(b x + c) + sin(b x + a) +--R + +--R 2 +--R - cos(c - a)cos(b x + a)cos(b x + c) + cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 4 +--R (cos(c - a)cos(b x + a) + cos(c - a))cos(b x + c)sin(b x + a)tan(c - a) +--R + +--R 2 2 2 +--R (- sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 +--R (cos(c - a)cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a))cos(b x + c) +--R + +--R 2 +--R cos(b x + a) + cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 +--R - sin(b x + a)sin(b x + c) +--R + +--R (cos(c - a)cos(b x + c) + 1)sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 2 2 +--R (- sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 +--R (cos(c - a)cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a))cos(b x + c) +--R + +--R 2 +--R cos(b x + a) + cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R - sin(b x + a)sin(b x + c) +--R + +--R (- cos(c - a)cos(b x + a)cos(b x + c) + 1)sin(b x + a) +--R / +--R 2 +--R (cos(b x + a) + 1)sin(b x + a)sin(b x + c) +--R + +--R (- cos(b x + a) - 1)sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 2 +--R (sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 2 +--R - sin(b x + a) + cos(b x + a) + cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R (- cos(b x + a) + 1)sin(b x + a)sin(b x + c) +--R + +--R (cos(b x + a) - 1)sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R - cos(b x + a)sin(b x + c) + cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 +--R (cos(b x + a) + 1)sin(b x + a)sin(b x + c) +--R + +--R (- cos(b x + a) - 1)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 2 2 +--R (sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 2 +--R - sin(b x + a) + cos(b x + a) + cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 +--R (sin(b x + a)sin(b x + c) - sin(b x + a))tan(c - a) +--R + +--R 2 2 2 +--R (sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 2 +--R - sin(b x + a) + cos(b x + a) + cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R - cos(b x + a)sin(b x + a)sin(b x + c) + cos(b x + a)sin(b x + a) +--R Type: Expression(Integer) +--E 427 + +--S 428 of 532 +t0779:= sin(a+b*x)*tan(c+b*x)^2 +--R +--R +--R 2 +--R (398) sin(b x + a)tan(b x + c) +--R Type: Expression(Integer) +--E 428 + +--S 429 of 532 +r0779:= cos(a+b*x)/b+cos(a-c)*sec(c+b*x)/b+atanh(sin(c+b*x))*sin(a-c)/b +--R +--R +--R (399) +--R - sin(c - a)atanh(sin(b x + c)) + cos(c - a)sec(b x + c) + cos(b x + a) +--R ----------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 429 + +--S 430 of 532 +a0779:= integrate(t0779,x) +--R +--R +--R (400) +--R 2 +--R (sin(b x + a)tan(c - a) - cos(b x + a)tan(c - a)) +--R * +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a)tan(c - a) +--R + +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R 2 +--R (cos(b x + a) + 2)sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R - 2cos(b x + a) - 1 +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R (b sin(b x + a)tan(c - a) - b cos(b x + a))\|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 430 + +--S 431 of 532 +m0779:= a0779-r0779 +--R +--R +--R (401) +--R 2 +--R (sin(b x + a)tan(c - a) - cos(b x + a)tan(c - a)) +--R * +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a)tan(c - a) +--R + +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R (sin(c - a)sin(b x + a)tan(c - a) - cos(b x + a)sin(c - a)) +--R * +--R atanh(sin(b x + c)) +--R + +--R (- cos(c - a)sec(b x + c) + 2)sin(b x + a)tan(c - a) +--R + +--R cos(c - a)cos(b x + a)sec(b x + c) - 2cos(b x + a) - 1 +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R (b sin(b x + a)tan(c - a) - b cos(b x + a))\|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 532 +d0779:= D(m0779,x) +--R +--R +--R (402) +--R (- cos(c - a)cos(b x + a) - cos(c - a))sec(b x + c) +--R * +--R 2 2 +--R sin(b x + a) sin(b x + c) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) + cos(c - a))sec(b x + c)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 +--R - cos(c - a)sec(b x + c)sin(b x + a) +--R + +--R 2 +--R (2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a)) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R cos(c - a)sec(b x + c)sin(b x + a) +--R + +--R 2 +--R (- 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a)) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R (2cos(c - a)cos(b x + a) - cos(c - a))sec(b x + c) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 +--R (- cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R (- 2cos(c - a)cos(b x + a) + cos(c - a))sec(b x + c) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 +--R (cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) )sec(b x + c) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a)) +--R * +--R 2 +--R sec(b x + c)sin(b x + a)sin(b x + c) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a)) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 +--R - cos(c - a)cos(b x + a) sec(b x + c)sin(b x + c) +--R + +--R 2 +--R cos(c - a)cos(b x + a) sec(b x + c) +--R * +--R tan(b x + c) +--R + +--R 3 2 +--R (sin(b x + a) + (cos(b x + a) + cos(b x + a))sin(b x + a)) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R - sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - 1)cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - cos(b x + a))sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 3 +--R (- cos(b x + a) + 1)sin(b x + a) - cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R - cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (cos(b x + a) - 1)sin(b x + a) +--R + +--R 2 +--R (2cos(b x + a) + 2cos(b x + a))cos(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R + +--R 3 +--R cos(b x + a) - cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 +--R sin(b x + a) +--R + +--R 2 +--R (cos(b x + a) + cos(b x + a) + 1)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R - sin(b x + a) +--R + +--R 2 +--R (2cos(b x + a) - 1)cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - cos(b x + a) - 1)sin(b x + a) +--R + +--R 3 2 +--R (- cos(b x + a) - cos(b x + a) )cos(b x + c)sin(c - a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 3 +--R (- cos(b x + a) + 1)sin(b x + a) - cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (cos(b x + a) - 1)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) + 2cos(b x + a))cos(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R + +--R 3 +--R cos(b x + a) - cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R sin(b x + a)sin(b x + c) - sin(b x + a) +--R + +--R 2 +--R - cos(b x + a) cos(b x + c)sin(c - a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 +--R (cos(c - a)cos(b x + a) + cos(c - a))sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) - cos(c - a))sec(b x + c)sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 3 +--R cos(c - a)sec(b x + c)sin(b x + a) +--R + +--R 2 +--R (- 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a)) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R - cos(c - a)sec(b x + c)sin(b x + a) +--R + +--R 2 +--R (2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a)) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R (- cos(c - a)cos(b x + a) + cos(c - a))sec(b x + c) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 +--R (cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) )sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) - cos(c - a))sec(b x + c)sin(b x + a) +--R + +--R 3 2 +--R (- cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) )sec(b x + c) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 +--R cos(c - a)sec(b x + c)sin(b x + a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a)) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R - cos(c - a)sec(b x + c)sin(b x + a) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a))sec(b x + c) +--R * +--R sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a)sec(b x + c)sin(b x + a) +--R + +--R 3 2 +--R (cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) )sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a)sec(b x + c)sin(b x + a) +--R + +--R 3 2 +--R (- cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) )sec(b x + c) +--R * +--R tan(c - a) +--R + +--R 2 2 +--R cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a)sin(b x + c) +--R + +--R 2 +--R - cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R * +--R tan(b x + c) +--R + +--R 3 2 +--R (- sin(b x + a) + (- cos(b x + a) - cos(b x + a))sin(b x + a)) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R sin(b x + a) + (cos(b x + a) + 1)cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (cos(b x + a) + cos(b x + a))sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 3 +--R ((cos(b x + a) - 1)sin(b x + a) + cos(b x + a) - cos(b x + a)) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) + 1)sin(b x + a) +--R + +--R 2 +--R (- 2cos(b x + a) - 2cos(b x + a))cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 +--R - cos(b x + a) + cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 +--R - sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - 2cos(b x + a) - 1)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) + 1)cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (cos(b x + a) + 2cos(b x + a) + 1)sin(b x + a) +--R + +--R 3 2 +--R (cos(b x + a) + cos(b x + a) )cos(b x + c)sin(c - a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 3 +--R ((cos(b x + a) - 2)sin(b x + a) + cos(b x + a) - cos(b x + a)) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) + 2)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - 2cos(b x + a))cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 +--R - cos(b x + a) + cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R (- cos(b x + a) - 1)sin(b x + a)sin(b x + c) +--R + +--R 2 +--R - 2cos(b x + a)cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R (cos(b x + a) + 1)sin(b x + a) +--R + +--R 3 2 +--R (cos(b x + a) + cos(b x + a) )cos(b x + c)sin(c - a) +--R * +--R tan(c - a) +--R + +--R 2 2 2 +--R - sin(b x + a) sin(b x + c) + sin(b x + a) +--R + +--R 2 +--R cos(b x + a) cos(b x + c)sin(c - a)sin(b x + a) +--R / +--R 2 2 +--R (cos(b x + a) + 1)sin(b x + a) sin(b x + c) +--R + +--R 2 +--R (- cos(b x + a) - 1)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 +--R sin(b x + a) +--R + +--R 2 +--R (- 2cos(b x + a) - 2cos(b x + a))sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R - sin(b x + a) + (2cos(b x + a) + 2cos(b x + a))sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 3 +--R (- 2cos(b x + a) + 1)sin(b x + a) + cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 2 +--R (2cos(b x + a) - 1)sin(b x + a) - cos(b x + a) - cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 2 +--R (cos(b x + a) - 2cos(b x + a))sin(b x + a)sin(b x + c) +--R + +--R 2 +--R (- cos(b x + a) + 2cos(b x + a))sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 2 +--R cos(b x + a) sin(b x + c) - cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 2 +--R (- cos(b x + a) - 1)sin(b x + a) sin(b x + c) +--R + +--R 2 +--R (cos(b x + a) + 1)sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 3 2 +--R (- sin(b x + a) + (2cos(b x + a) + 2cos(b x + a))sin(b x + a)) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R sin(b x + a) + (- 2cos(b x + a) - 2cos(b x + a))sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 3 2 +--R ((cos(b x + a) - 1)sin(b x + a) - cos(b x + a) - cos(b x + a) ) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 2 +--R (- cos(b x + a) + 1)sin(b x + a) + cos(b x + a) + cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 2 +--R (- sin(b x + a) + (cos(b x + a) + 2cos(b x + a))sin(b x + a)) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R sin(b x + a) + (- cos(b x + a) - 2cos(b x + a))sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 3 2 +--R (2cos(b x + a)sin(b x + a) - cos(b x + a) - cos(b x + a) ) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 2 +--R - 2cos(b x + a)sin(b x + a) + cos(b x + a) + cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 2 +--R - cos(b x + a) sin(b x + a)sin(b x + c) + cos(b x + a) sin(b x + a) +--R Type: Expression(Integer) +--E 432 + +--S 433 of 532 +t0780:= sin(a+b*x)*tan(c+b*x)^3 +--R +--R +--R 3 +--R (403) sin(b x + a)tan(b x + c) +--R Type: Expression(Integer) +--E 433 + +--S 434 of 532 +r0780:= -3/2*atanh(sin(c+b*x))*cos(a-c)/b+sec(c+b*x)*sin(a-c)/b+sin(a+b*x)/b+_ + 1/2*cos(a-c)*sec(c+b*x)*tan(c+b*x)/b +--R +--R +--R (404) +--R - 3cos(c - a)atanh(sin(b x + c)) + cos(c - a)sec(b x + c)tan(b x + c) +--R + +--R 2sin(b x + a) - 2sec(b x + c)sin(c - a) +--R / +--R 2b +--R Type: Expression(Integer) +--E 434 + +--S 435 of 532 +a0780:= integrate(t0780,x) +--R +--R +--R (405) +--R 2 2 +--R (3cos(b x + a) - 3)tan(c - a) + 6cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 +--R - 3cos(b x + a) +--R * +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a)tan(c - a) +--R + +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R 2 3 +--R (- cos(b x + a) + 1)tan(c - a) +--R + +--R 2 2 +--R (2cos(b x + a) - 2cos(b x + a) - 4)sin(b x + a)tan(c - a) +--R + +--R 3 2 +--R (- 4cos(b x + a) + cos(b x + a) + 5cos(b x + a))tan(c - a) +--R + +--R 2 +--R (- 2cos(b x + a) - 1)sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R 2 2 +--R (2b cos(b x + a) - 2b)tan(c - a) +--R + +--R 2 +--R 4b cos(b x + a)sin(b x + a)tan(c - a) - 2b cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 435 + +--S 436 of 532 +m0780:= a0780-r0780 +--R +--R +--R (406) +--R 2 2 +--R (3cos(b x + a) - 3)tan(c - a) + 6cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 +--R - 3cos(b x + a) +--R * +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a)tan(c - a) +--R + +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R 2 2 +--R (3cos(c - a)cos(b x + a) - 3cos(c - a))tan(c - a) +--R + +--R 6cos(c - a)cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 +--R - 3cos(c - a)cos(b x + a) +--R * +--R atanh(sin(b x + c)) +--R + +--R 2 2 +--R (- cos(c - a)cos(b x + a) + cos(c - a))sec(b x + c)tan(c - a) +--R + +--R - 2cos(c - a)cos(b x + a)sec(b x + c)sin(b x + a)tan(c - a) +--R + +--R 2 +--R cos(c - a)cos(b x + a) sec(b x + c) +--R * +--R tan(b x + c) +--R + +--R 2 3 +--R (- cos(b x + a) + 1)tan(c - a) +--R + +--R (- 2cos(b x + a) - 2)sin(b x + a) +--R + +--R 2 +--R (2cos(b x + a) - 2)sec(b x + c)sin(c - a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R - 4cos(b x + a)sin(b x + a) +--R + +--R 3 +--R 4cos(b x + a)sec(b x + c)sin(c - a)sin(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R cos(b x + a) + 5cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R - sin(b x + a) - 2cos(b x + a) sec(b x + c)sin(c - a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R 2 2 +--R (2b cos(b x + a) - 2b)tan(c - a) +--R + +--R 2 +--R 4b cos(b x + a)sin(b x + a)tan(c - a) - 2b cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 532 +d0780:= D(m0780,x) +--R +--R +--R (407) +--R 5 4 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a)sin(b x + c) +--R + +--R 5 4 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 4 +--R - 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 +--R 10cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 6 +--R tan(c - a) +--R + +--R 3 +--R - 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R 14cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 8cos(c - a)cos(b x + a) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R - 14cos(c - a)cos(b x + a) - 10cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 4 +--R - 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R 28cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 4cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 +--R 4cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R - 28cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 4cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 +--R - 4cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 2 +--R (16cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) ) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 +--R - 14cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (- 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) ) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R 14cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 4cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 4 +--R - 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R 16cos(c - a)cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 +--R 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 +--R (10cos(c - a)cos(b x + a) - 16cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R tan(c - a) +--R + +--R 5 4 +--R (2cos(c - a)cos(b x + a) - 10cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R sec(b x + c)sin(b x + a)sin(b x + c) +--R + +--R 5 4 +--R (- 2cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 5 2 +--R 2cos(c - a)cos(b x + a) sec(b x + c)sin(b x + c) +--R + +--R 5 +--R - 2cos(c - a)cos(b x + a) sec(b x + c) +--R * +--R 2 +--R tan(b x + c) +--R + +--R 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 3 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 3 2 +--R (16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R - 14cos(b x + a) - 10cos(b x + a) + 16cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) - 2cos(b x + a) + 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (- 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R 14cos(b x + a) + 10cos(b x + a) - 16cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) + 2cos(b x + a) - 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 4 +--R 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R - 28cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R - 8cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R 4cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R - 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R 28cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R 8cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 4cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 2 +--R (- 16cos(b x + a) + 8cos(b x + a) )sec(b x + c) +--R * +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R 14cos(b x + a) - 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 12cos(b x + a) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (16cos(b x + a) - 8cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 14cos(b x + a) + 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R - 12cos(b x + a) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 4 3 +--R (10cos(b x + a) - 16cos(b x + a) )sec(b x + c) +--R * +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 6 5 3 +--R (- 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) ) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 +--R (- 10cos(b x + a) + 16cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 3 +--R (2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) ) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 5 4 +--R (- 2cos(b x + a) + 10cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + a)sin(b x + c) +--R + +--R 5 4 +--R (2cos(b x + a) - 10cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 5 2 +--R - 2cos(b x + a) sec(b x + c)sin(c - a)sin(b x + c) +--R + +--R 5 +--R 2cos(b x + a) sec(b x + c)sin(c - a) +--R * +--R tan(b x + c) +--R + +--R 2 3 +--R (- 4cos(b x + a) - 4cos(b x + a))sin(b x + a) +--R + +--R 5 4 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R - cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 4 3 2 +--R - 2cos(b x + a) - 2cos(b x + a) + 2cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 +--R (4cos(b x + a) + 4cos(b x + a))sin(b x + a) +--R + +--R 5 4 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R cos(c - a)cos(b x + a) + cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 5 4 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 6cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R + +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a) +--R * +--R cos(b x + c) +--R + +--R 4 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 2cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 3 2 +--R (- 4cos(b x + a) - 4cos(b x + a) - 12cos(b x + a) - 8) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R - 5cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 6cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R - 4cos(b x + a) - cos(b x + a) + 3cos(b x + a) +--R + +--R 2 +--R - cos(b x + a) + 7cos(b x + a) + 8 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R 3cos(b x + a) + 5cos(b x + a) - 4cos(b x + a) +--R + +--R 3 2 +--R - 8cos(b x + a) + cos(b x + a) + 3cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (4cos(b x + a) + 4cos(b x + a) + 12cos(b x + a) + 8) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R 5cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 6cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 4 3 +--R - 15cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R 18cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R + +--R - 3cos(c - a) +--R * +--R cos(b x + c) +--R + +--R 5 4 3 +--R 4cos(b x + a) + cos(b x + a) - 3cos(b x + a) +--R + +--R 2 +--R cos(b x + a) - 7cos(b x + a) - 8 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 +--R 3cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 6cos(c - a)cos(b x + a) - 6cos(c - a)cos(b x + a) +--R + +--R 2 +--R 3cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 6 5 4 +--R - 3cos(b x + a) - 5cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 8cos(b x + a) - cos(b x + a) - 3cos(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 5 +--R (- 4cos(b x + a) - 8)sin(b x + a) +--R + +--R 3 2 +--R - 8cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 4 3 2 +--R 8cos(b x + a) + 24cos(b x + a) + 15cos(b x + a) +--R + +--R - 6cos(b x + a) + 5 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R 7cos(c - a)cos(b x + a) + 5cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 8cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R 12cos(b x + a) + 24cos(b x + a) + 7cos(b x + a) +--R + +--R 3 2 +--R - 24cos(b x + a) - 24cos(b x + a) - 2cos(b x + a) + 3 +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 5 +--R (4cos(b x + a) + 8)sin(b x + a) +--R + +--R 3 2 +--R 8cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 3 2 +--R - 24cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 12cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 4 3 2 +--R - 8cos(b x + a) - 24cos(b x + a) - 15cos(b x + a) +--R + +--R 6cos(b x + a) - 5 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R - 7cos(c - a)cos(b x + a) - 5cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 8cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - cos(c - a)cos(b x + a) + cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 5 4 +--R 21cos(c - a)cos(b x + a) + 15cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 24cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 3cos(c - a)cos(b x + a) - 3cos(c - a) +--R * +--R cos(b x + c) +--R + +--R 6 5 4 +--R - 12cos(b x + a) - 24cos(b x + a) - 7cos(b x + a) +--R + +--R 3 2 +--R 24cos(b x + a) + 24cos(b x + a) + 2cos(b x + a) - 3 +--R * +--R sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 3 +--R - 4cos(c - a)cos(b x + a) sec(b x + c) + 16cos(b x + a) +--R + +--R 2 +--R 12cos(b x + a) + 8cos(b x + a) - 10 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R 14cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 6cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R 8cos(b x + a) + cos(b x + a) + 7cos(b x + a) +--R + +--R 2 +--R - 2cos(b x + a) - 16cos(b x + a) + 8 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 4 +--R 2cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 7 6 5 +--R - 8cos(b x + a) - 11cos(b x + a) + 3cos(b x + a) +--R + +--R 4 3 +--R 11cos(b x + a) + 5cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R 4cos(c - a)cos(b x + a) sec(b x + c) +--R + +--R 2 3 +--R - 12cos(c - a)cos(b x + a) cos(b x + c) - 16cos(b x + a) +--R + +--R 2 +--R - 12cos(b x + a) - 8cos(b x + a) + 10 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R - 14cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 6cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 4 3 +--R 42cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 18cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 5 4 3 +--R - 8cos(b x + a) - cos(b x + a) - 7cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) + 16cos(b x + a) - 8 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 4 +--R - 2cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 +--R - 6cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R + +--R 4 +--R 6cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 7 6 5 +--R 8cos(b x + a) + 11cos(b x + a) - 3cos(b x + a) +--R + +--R 4 3 +--R - 11cos(b x + a) - 5cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 5 +--R (4cos(b x + a) - 2)sin(b x + a) +--R + +--R 3 2 +--R (8cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c) +--R + +--R 4 3 2 +--R - 8cos(b x + a) + 8cos(b x + a) + 9cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R - 7cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 2cos(c - a)cos(b x + a) - 6cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R - 12cos(b x + a) + 8cos(b x + a) - 3cos(b x + a) +--R + +--R 3 2 +--R - 16cos(b x + a) + 5cos(b x + a) - 4cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 5 +--R (- 4cos(b x + a) + 2)sin(b x + a) +--R + +--R 3 2 +--R (- 8cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c) +--R + +--R 3 2 +--R (24cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) ) +--R * +--R cos(b x + c) +--R + +--R 4 3 2 +--R 8cos(b x + a) - 8cos(b x + a) - 9cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R 7cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 2cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 5 4 +--R - 21cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 6cos(c - a)cos(b x + a) - 18cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 6 5 4 +--R 12cos(b x + a) - 8cos(b x + a) + 3cos(b x + a) +--R + +--R 3 2 +--R 16cos(b x + a) - 5cos(b x + a) + 4cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 2 +--R (- 4cos(b x + a) + 16cos(b x + a) + 4cos(b x + a) - 2) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R (- 5cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R - 4cos(b x + a) + 5cos(b x + a) - 8cos(b x + a) +--R + +--R 2 +--R - 3cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 3 +--R 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R - 11cos(b x + a) + 2cos(b x + a) + 14cos(b x + a) +--R + +--R 2 +--R - cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (4cos(b x + a) - 16cos(b x + a) - 4cos(b x + a) + 2) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R (5cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c) +--R + +--R 4 3 +--R (- 15cos(c - a)cos(b x + a) + 24cos(c - a)cos(b x + a) ) +--R * +--R cos(b x + c) +--R + +--R 5 4 3 +--R 4cos(b x + a) - 5cos(b x + a) + 8cos(b x + a) +--R + +--R 2 +--R 3cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R - cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 +--R 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R + +--R 3 +--R 6cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 6 5 4 2 +--R 11cos(b x + a) - 2cos(b x + a) - 14cos(b x + a) + cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 3 2 +--R (- 16cos(b x + a) - 2cos(b x + a) + 4cos(b x + a)) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R (cos(c - a)cos(b x + a) - 5cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R - 16cos(b x + a) + 2cos(b x + a) + 6cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 3 +--R (16cos(b x + a) + 2cos(b x + a) - 4cos(b x + a))sin(b x + a) +--R + +--R 5 4 +--R (- cos(c - a)cos(b x + a) + 5cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c) +--R + +--R 5 4 +--R (3cos(c - a)cos(b x + a) - 15cos(c - a)cos(b x + a) ) +--R * +--R cos(b x + c) +--R + +--R 5 4 3 +--R 16cos(b x + a) - 2cos(b x + a) - 6cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 4 2 2 +--R (3cos(b x + a) - 2cos(b x + a) )sin(b x + a) +--R + +--R 5 6 +--R cos(c - a)cos(b x + a) sec(b x + c) + 3cos(b x + a) +--R + +--R 4 +--R - cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 2 2 +--R (- 3cos(b x + a) + 2cos(b x + a) )sin(b x + a) +--R + +--R 5 +--R - cos(c - a)cos(b x + a) sec(b x + c) +--R + +--R 5 6 4 +--R 3cos(c - a)cos(b x + a) cos(b x + c) - 3cos(b x + a) + cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 5 4 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a)sin(b x + c) +--R + +--R 5 4 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 8 +--R tan(c - a) +--R + +--R 4 3 +--R 10cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 +--R - 10cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 7 +--R tan(c - a) +--R + +--R 3 2 +--R 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 8cos(c - a)cos(b x + a) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R - 12cos(c - a)cos(b x + a) - 10cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R - 16cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 8cos(c - a)cos(b x + a) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R 12cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 12cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 4 +--R 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R - 18cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R - 8cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R - 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R 18cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 8cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 +--R (8cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R - 2cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (- 8cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 4 +--R 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R - 18cos(c - a)cos(b x + a) - 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R - 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R 18cos(c - a)cos(b x + a) + 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 3 +--R - 16cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R 12cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 3 +--R 16cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R - 12cos(c - a)cos(b x + a) - 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 2 +--R 10cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R (- 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 2 +--R - 10cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R (2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) )sec(b x + c) +--R * +--R tan(c - a) +--R + +--R 5 2 +--R - 2cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a)sin(b x + c) +--R + +--R 5 +--R 2cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R * +--R 2 +--R tan(b x + c) +--R + +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 8 +--R tan(c - a) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 3 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 3 2 +--R (- 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 10cos(b x + a) - 12cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) - 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a))sec(b x + c) +--R * +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 10cos(b x + a) + 12cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) + 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 4 +--R - 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 +--R (18cos(b x + a) + 8cos(b x + a) + 8cos(b x + a) - 2) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 2 +--R - 2cos(b x + a) - 2cos(b x + a) + 2cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 +--R (- 18cos(b x + a) - 8cos(b x + a) - 8cos(b x + a) + 2) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 2 +--R 2cos(b x + a) + 2cos(b x + a) - 2cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 +--R (- 8cos(b x + a) + 8cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R 2cos(b x + a) - 12cos(b x + a) - 12cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (8cos(b x + a) - 8cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 2cos(b x + a) + 12cos(b x + a) + 12cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 4 +--R - 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R (18cos(b x + a) + 16cos(b x + a) - 12cos(b x + a) ) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 +--R 4cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R (- 18cos(b x + a) - 16cos(b x + a) + 12cos(b x + a) ) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 3 +--R - 4cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 3 +--R 16cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R (- 12cos(b x + a) - 10cos(b x + a) + 4cos(b x + a) ) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 3 +--R - 16cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R (12cos(b x + a) + 10cos(b x + a) - 4cos(b x + a) ) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 2 +--R - 10cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 +--R (2cos(b x + a) + 2cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 2 +--R 10cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 +--R (- 2cos(b x + a) - 2cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R tan(c - a) +--R + +--R 5 2 +--R 2cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 5 +--R - 2cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R tan(b x + c) +--R + +--R 2 3 +--R (4cos(b x + a) + 4cos(b x + a))sin(b x + a) +--R + +--R 5 4 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R cos(c - a)cos(b x + a) + cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 4 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 2cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 +--R (- 4cos(b x + a) - 4cos(b x + a))sin(b x + a) +--R + +--R 5 4 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R - cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 5 4 +--R 3cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 6cos(c - a)cos(b x + a) - 6cos(c - a)cos(b x + a) +--R + +--R 3cos(c - a)cos(b x + a) + 3cos(c - a) +--R * +--R cos(b x + c) +--R + +--R 4 3 2 +--R - 2cos(b x + a) - 2cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 8 +--R tan(c - a) +--R + +--R 3 2 +--R (4cos(b x + a) + 4cos(b x + a) + 12cos(b x + a) + 8) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R 5cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 6cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R 4cos(b x + a) + cos(b x + a) - 3cos(b x + a) +--R + +--R 2 +--R cos(b x + a) - 7cos(b x + a) - 8 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R - 3cos(b x + a) - 5cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 8cos(b x + a) - cos(b x + a) - 3cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 4 +--R (- 4cos(b x + a) - 4cos(b x + a) - 12cos(b x + a) - 8)sin(b x + a) +--R + +--R 4 3 +--R - 5cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 6cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 4 3 +--R 15cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 18cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 3cos(c - a) +--R * +--R cos(b x + c) +--R + +--R 5 4 3 2 +--R - 4cos(b x + a) - cos(b x + a) + 3cos(b x + a) - cos(b x + a) +--R + +--R 7cos(b x + a) + 8 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 6cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 6 5 4 3 +--R 3cos(b x + a) + 5cos(b x + a) - 4cos(b x + a) - 8cos(b x + a) +--R + +--R 2 +--R cos(b x + a) + 3cos(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 2 5 +--R (4cos(b x + a) + 8)sin(b x + a) +--R + +--R 3 2 +--R 8cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 4 3 2 +--R - 8cos(b x + a) - 24cos(b x + a) - 11cos(b x + a) +--R + +--R 6cos(b x + a) - 5 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R - 6cos(c - a)cos(b x + a) - 5cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 6cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R - 12cos(b x + a) - 24cos(b x + a) - 5cos(b x + a) +--R + +--R 3 2 +--R 24cos(b x + a) + 22cos(b x + a) + 2cos(b x + a) - 3 +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 5 +--R (- 4cos(b x + a) - 8)sin(b x + a) +--R + +--R 3 2 +--R - 8cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 3 2 +--R 24cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R + +--R - 12cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 4 3 2 +--R 8cos(b x + a) + 24cos(b x + a) + 11cos(b x + a) +--R + +--R - 6cos(b x + a) + 5 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R 6cos(c - a)cos(b x + a) + 5cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 6cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R - cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 5 4 +--R - 18cos(c - a)cos(b x + a) - 15cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 18cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R + +--R 3cos(c - a) +--R * +--R cos(b x + c) +--R + +--R 6 5 4 +--R 12cos(b x + a) + 24cos(b x + a) + 5cos(b x + a) +--R + +--R 3 2 +--R - 24cos(b x + a) - 22cos(b x + a) - 2cos(b x + a) + 3 +--R * +--R sin(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 3 +--R 4cos(c - a)cos(b x + a) sec(b x + c) - 12cos(b x + a) +--R + +--R 2 +--R - 12cos(b x + a) + 4cos(b x + a) + 10 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R - 9cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R - 4cos(c - a)cos(b x + a) + cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R - 4cos(b x + a) - cos(b x + a) - 10cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) + 9cos(b x + a) - 8 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 2 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 7 6 5 +--R 8cos(b x + a) + 11cos(b x + a) - 8cos(b x + a) +--R + +--R 4 3 +--R - 11cos(b x + a) + 3cos(b x + a) - 3cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R - 4cos(c - a)cos(b x + a) sec(b x + c) +--R + +--R 2 3 +--R 12cos(c - a)cos(b x + a) cos(b x + c) + 12cos(b x + a) +--R + +--R 2 +--R 12cos(b x + a) - 4cos(b x + a) - 10 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R 9cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 4cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R sec(b x + c) +--R + +--R 4 3 +--R - 27cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R - 12cos(c - a)cos(b x + a) + 3cos(c - a) +--R * +--R cos(b x + c) +--R + +--R 5 4 3 2 +--R 4cos(b x + a) + cos(b x + a) + 10cos(b x + a) - 2cos(b x + a) +--R + +--R - 9cos(b x + a) + 8 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 2 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 +--R 3cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 7 6 5 4 +--R - 8cos(b x + a) - 11cos(b x + a) + 8cos(b x + a) + 11cos(b x + a) +--R + +--R 3 +--R - 3cos(b x + a) + 3cos(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 5 +--R 10sin(b x + a) +--R + +--R 2 +--R (4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a)) +--R * +--R sec(b x + c) +--R + +--R 3 2 +--R - 8cos(b x + a) - 24cos(b x + a) - 2cos(b x + a) - 5 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 +--R - cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R + +--R 2 +--R 6cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R - 8cos(b x + a) - 4cos(b x + a) + 16cos(b x + a) +--R + +--R 2 +--R 19cos(b x + a) + 4cos(b x + a) - 3 +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 5 +--R - 10sin(b x + a) +--R + +--R 2 +--R (- 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a)) +--R * +--R sec(b x + c) +--R + +--R 2 +--R (12cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a)) +--R * +--R cos(b x + c) +--R + +--R 3 2 +--R 8cos(b x + a) + 24cos(b x + a) + 2cos(b x + a) + 5 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 +--R cos(c - a)cos(b x + a) - 6cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 6cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 4 3 +--R - 3cos(c - a)cos(b x + a) + 18cos(c - a)cos(b x + a) +--R + +--R 2 +--R 18cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 5 4 3 +--R 8cos(b x + a) + 4cos(b x + a) - 16cos(b x + a) +--R + +--R 2 +--R - 19cos(b x + a) - 4cos(b x + a) + 3 +--R * +--R sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 3 +--R 4cos(c - a)cos(b x + a) sec(b x + c) - 12cos(b x + a) +--R + +--R 2 +--R - 16cos(b x + a) - 12cos(b x + a) + 2 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R - 9cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 6cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R - 4cos(b x + a) - 5cos(b x + a) + cos(b x + a) +--R + +--R 2 +--R 3cos(b x + a) + 16cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 7 6 5 +--R 8cos(b x + a) + 11cos(b x + a) - 5cos(b x + a) +--R + +--R 4 3 2 +--R - 14cos(b x + a) - 5cos(b x + a) + cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R - 4cos(c - a)cos(b x + a) sec(b x + c) +--R + +--R 2 3 +--R 12cos(c - a)cos(b x + a) cos(b x + c) + 12cos(b x + a) +--R + +--R 2 +--R 16cos(b x + a) + 12cos(b x + a) - 2 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 4 3 +--R 9cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 6cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 4 3 +--R - 27cos(c - a)cos(b x + a) - 24cos(c - a)cos(b x + a) +--R + +--R 2 +--R 18cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 5 4 3 2 +--R 4cos(b x + a) + 5cos(b x + a) - cos(b x + a) - 3cos(b x + a) +--R + +--R - 16cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 +--R 3cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 6cos(c - a)cos(b x + a) - 6cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 7 6 5 4 +--R - 8cos(b x + a) - 11cos(b x + a) + 5cos(b x + a) + 14cos(b x + a) +--R + +--R 3 2 +--R 5cos(b x + a) - cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 5 +--R (- 4cos(b x + a) + 2)sin(b x + a) +--R + +--R 3 4 +--R - 8cos(c - a)cos(b x + a) sec(b x + c) + 8cos(b x + a) +--R + +--R 3 2 +--R 16cos(b x + a) - 7cos(b x + a) - 4cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R 6cos(c - a)cos(b x + a) + 5cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R 12cos(b x + a) + 16cos(b x + a) + cos(b x + a) +--R + +--R 3 2 +--R - 6cos(b x + a) - 5cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 5 +--R (4cos(b x + a) - 2)sin(b x + a) +--R + +--R 3 +--R 8cos(c - a)cos(b x + a) sec(b x + c) +--R + +--R 3 4 +--R - 24cos(c - a)cos(b x + a) cos(b x + c) - 8cos(b x + a) +--R + +--R 3 2 +--R - 16cos(b x + a) + 7cos(b x + a) + 4cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R - 6cos(c - a)cos(b x + a) - 5cos(c - a)cos(b x + a) +--R + +--R 3 +--R 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 5 4 +--R 18cos(c - a)cos(b x + a) + 15cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 6cos(c - a)cos(b x + a) +--R * +--R cos(b x + c) +--R + +--R 6 5 4 +--R - 12cos(b x + a) - 16cos(b x + a) - cos(b x + a) +--R + +--R 3 2 +--R 6cos(b x + a) + 5cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 3 4 +--R (4cos(b x + a) - 4cos(b x + a))sin(b x + a) +--R + +--R 4 5 +--R 5cos(c - a)cos(b x + a) sec(b x + c) + 4cos(b x + a) +--R + +--R 4 3 2 +--R - 3cos(b x + a) + 8cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R (- cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) )sec(b x + c) +--R + +--R 6 5 4 +--R - 3cos(b x + a) - 2cos(b x + a) + cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 4 +--R (- 4cos(b x + a) + 4cos(b x + a))sin(b x + a) +--R + +--R 4 +--R - 5cos(c - a)cos(b x + a) sec(b x + c) +--R + +--R 4 5 +--R 15cos(c - a)cos(b x + a) cos(b x + c) - 4cos(b x + a) +--R + +--R 4 3 2 +--R 3cos(b x + a) - 8cos(b x + a) - 2cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R (cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) )sec(b x + c) +--R + +--R 6 5 +--R (- 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) )cos(b x + c) +--R + +--R 6 5 4 +--R 3cos(b x + a) + 2cos(b x + a) - cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 3 +--R 2cos(b x + a) sin(b x + a) +--R + +--R 5 4 +--R (- cos(c - a)cos(b x + a) sec(b x + c) - 2cos(b x + a) )sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 +--R - 2cos(b x + a) sin(b x + a) +--R + +--R 5 +--R cos(c - a)cos(b x + a) sec(b x + c) +--R + +--R 5 4 +--R - 3cos(c - a)cos(b x + a) cos(b x + c) + 2cos(b x + a) +--R * +--R sin(b x + a) +--R / +--R 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a)sin(b x + c) +--R + +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) + 2cos(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 3 2 +--R (16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a)) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 14cos(b x + a) - 10cos(b x + a) + 16cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) - 2cos(b x + a) + 2 +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 3 +--R (- 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a))sin(b x + a) +--R + +--R 5 4 3 +--R 14cos(b x + a) + 10cos(b x + a) - 16cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) + 2cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 4 +--R 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 +--R - 28cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R - 8cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 +--R 4cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R - 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 +--R 28cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R 8cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 +--R - 4cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 2cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 2 3 +--R (- 16cos(b x + a) + 8cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R 14cos(b x + a) - 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 12cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 3 +--R (16cos(b x + a) - 8cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R - 14cos(b x + a) + 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R - 12cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 4 3 2 +--R (10cos(b x + a) - 16cos(b x + a) )sin(b x + a) +--R + +--R 6 5 3 +--R - 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R (- 10cos(b x + a) + 16cos(b x + a) )sin(b x + a) +--R + +--R 6 5 3 +--R 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 5 4 2 +--R (- 2cos(b x + a) + 10cos(b x + a) )sin(b x + a)sin(b x + c) +--R + +--R 5 4 +--R (2cos(b x + a) - 10cos(b x + a) )sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 5 2 5 +--R - 2cos(b x + a) sin(b x + c) + 2cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a)sin(b x + c) +--R + +--R 5 4 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R + +--R 2cos(b x + a) + 2 +--R * +--R sin(b x + a) +--R * +--R 8 +--R tan(c - a) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 3 2 3 +--R (- 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a))sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 10cos(b x + a) - 12cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 3 +--R (16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a))sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 10cos(b x + a) + 12cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) + 2 +--R * +--R sin(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 4 +--R - 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 +--R (18cos(b x + a) + 8cos(b x + a) + 8cos(b x + a) - 2) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 2 +--R - 2cos(b x + a) - 2cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 +--R (- 18cos(b x + a) - 8cos(b x + a) - 8cos(b x + a) + 2)sin(b x + a) +--R + +--R 6 5 2 +--R 2cos(b x + a) + 2cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 3 +--R (- 8cos(b x + a) + 8cos(b x + a))sin(b x + a) +--R + +--R 4 3 2 +--R 2cos(b x + a) - 12cos(b x + a) - 12cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 +--R (8cos(b x + a) - 8cos(b x + a))sin(b x + a) +--R + +--R 4 3 2 +--R - 2cos(b x + a) + 12cos(b x + a) + 12cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 4 +--R - 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 +--R (18cos(b x + a) + 16cos(b x + a) - 12cos(b x + a) ) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 2 +--R (- 18cos(b x + a) - 16cos(b x + a) + 12cos(b x + a) )sin(b x + a) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 3 +--R 16cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 +--R (- 12cos(b x + a) - 10cos(b x + a) + 4cos(b x + a) )sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 3 +--R - 16cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 +--R (12cos(b x + a) + 10cos(b x + a) - 4cos(b x + a) )sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 2 6 5 +--R (- 10cos(b x + a) sin(b x + a) + 2cos(b x + a) + 2cos(b x + a) ) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 2 6 5 +--R 10cos(b x + a) sin(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 5 2 5 +--R 2cos(b x + a) sin(b x + a)sin(b x + c) - 2cos(b x + a) sin(b x + a) +--R Type: Expression(Integer) +--E 437 + +--S 438 of 532 +t0781:= sin(a+b*x)*cot(c+b*x) +--R +--R +--R (408) cot(b x + c)sin(b x + a) +--R Type: Expression(Integer) +--E 438 + +--S 439 of 532 +r0781:= -(atanh(cos(c+b*x))*sin(a-c)-sin(a+b*x))/b +--R +--R +--R sin(c - a)atanh(cos(b x + c)) + sin(b x + a) +--R (409) -------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 439 + +--S 440 of 532 +a0781:= integrate(t0781,x) +--R +--R +--R (410) +--R tan(c - a) +--R * +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R sin(b x + a)tan(c - a) + (- cos(b x + a) - 1)tan(c - a) +--R + +--R sin(b x + a)tan(c - a) - cos(b x + a) - 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R +---------------+ +--R | 2 +--R sin(b x + a)\|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R b\|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 532 +m0781:= a0781-r0781 +--R +--R +--R (411) +--R tan(c - a) +--R * +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R sin(b x + a)tan(c - a) + (- cos(b x + a) - 1)tan(c - a) +--R + +--R sin(b x + a)tan(c - a) - cos(b x + a) - 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R +---------------+ +--R | 2 +--R - sin(c - a)atanh(cos(b x + c))\|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R b\|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 532 +d0781:= D(m0781,x) +--R +--R +--R (412) +--R - cos(b x + a)sin(c - a)sin(b x + c) +--R + +--R 2 2 2 2 +--R (- cos(b x + c) + 1)sin(b x + a) - cos(b x + a) cos(b x + c) +--R + +--R 2 +--R cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R (cos(b x + a) - 1)sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 2 +--R (cos(b x + c) - 1)sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - cos(b x + a))sin(c - a) +--R * +--R sin(b x + c) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R tan(c - a) +--R + +--R (- cos(b x + a) - 1)sin(c - a)sin(b x + a)sin(b x + c) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R cos(b x + a)sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 2 +--R (cos(b x + c) - 1)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - cos(b x + a))sin(c - a) +--R * +--R sin(b x + c) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R - sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 2 +--R (cos(b x + c) - 1)sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - cos(b x + a))sin(c - a) +--R * +--R sin(b x + c) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R tan(c - a) +--R + +--R (- cos(b x + a) - 1)sin(c - a)sin(b x + a)sin(b x + c) +--R / +--R 2 3 +--R (cos(b x + a)cos(b x + c) - cos(b x + a))tan(c - a) +--R + +--R 2 +--R ((- cos(b x + a) + 1)cos(b x + c) + cos(b x + a) - 1)sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 2 +--R (cos(b x + a) + cos(b x + a))cos(b x + c) - cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R ((cos(b x + a) + 1)cos(b x + c) - cos(b x + a) - 1)sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 4 +--R (- cos(b x + a)cos(b x + c) + cos(b x + a))sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 2 +--R (cos(b x + a) + cos(b x + a))cos(b x + c) - cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 +--R (cos(b x + c) - 1)sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 2 +--R (cos(b x + a) + cos(b x + a))cos(b x + c) - cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R ((cos(b x + a) + 1)cos(b x + c) - cos(b x + a) - 1)sin(b x + a) +--R Type: Expression(Integer) +--E 442 + +--S 443 of 532 +t0782:= sin(a+b*x)*cot(c+b*x)^2 +--R +--R +--R 2 +--R (413) cot(b x + c) sin(b x + a) +--R Type: Expression(Integer) +--E 443 + +--S 444 of 532 +r0782:= -atanh(cos(c+b*x))*cos(a-c)/b+cos(a+b*x)/b-csc(c+b*x)*sin(a-c)/b +--R +--R +--R (414) +--R - cos(c - a)atanh(cos(b x + c)) + csc(b x + c)sin(c - a) + cos(b x + a) +--R ----------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 444 + +--S 445 of 532 +a0782:= integrate(t0782,x) +--R +--R +--R (415) +--R (cos(b x + a)tan(c - a) + sin(b x + a)) +--R * +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R - sin(b x + a)tan(c - a) + (cos(b x + a) + 1)tan(c - a) +--R + +--R - sin(b x + a)tan(c - a) + cos(b x + a) + 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R 2 +--R (cos(b x + a) + 2cos(b x + a) + 1)tan(c - a) +--R + +--R (cos(b x + a) + 2)sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R (b cos(b x + a)tan(c - a) + b sin(b x + a))\|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 445 + +--S 446 of 532 +m0782:= a0782-r0782 +--R +--R +--R (416) +--R (cos(b x + a)tan(c - a) + sin(b x + a)) +--R * +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R - sin(b x + a)tan(c - a) + (cos(b x + a) + 1)tan(c - a) +--R + +--R - sin(b x + a)tan(c - a) + cos(b x + a) + 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R (cos(c - a)cos(b x + a)tan(c - a) + cos(c - a)sin(b x + a)) +--R * +--R atanh(cos(b x + c)) +--R + +--R (- cos(b x + a)csc(b x + c)sin(c - a) + 2cos(b x + a) + 1)tan(c - a) +--R + +--R (- csc(b x + c)sin(c - a) + 2)sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R (b cos(b x + a)tan(c - a) + b sin(b x + a))\|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 532 +d0782:= D(m0782,x) +--R +--R +--R (417) +--R 2 +--R cos(c - a)cos(b x + a) sin(b x + c) +--R + +--R 2 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 2 2 +--R (cos(b x + a) cos(b x + c) - cos(b x + a) )cot(b x + c) +--R * +--R csc(b x + c)sin(c - a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a)) +--R * +--R sin(b x + a)sin(b x + c) +--R + +--R 2 2 +--R ((cos(b x + a) - 1)cos(b x + c) - cos(b x + a) + 1)sin(b x + a) +--R + +--R 2 2 +--R (- cos(b x + a) + 2cos(b x + a))cos(b x + c) +--R + +--R 2 +--R cos(b x + a) - 2cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 3 +--R (cos(b x + a) - cos(b x + a))cos(b x + c) - cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 +--R (- 2cos(c - a)cos(b x + a) + cos(c - a))sin(b x + a) +--R + +--R 3 2 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 3 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 +--R ((- 2cos(b x + a) + 1)cos(b x + c) + 2cos(b x + a) - 1) +--R * +--R 2 +--R cot(b x + c)csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 2 +--R (cos(b x + a) + cos(b x + a) + 1)cos(b x + c) +--R + +--R 2 +--R - cos(b x + a) - cos(b x + a) - 1 +--R * +--R sin(b x + a) +--R + +--R 3 2 2 3 +--R (cos(b x + a) + cos(b x + a) )cos(b x + c) - cos(b x + a) +--R + +--R 2 +--R - cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 3 +--R - cos(c - a)sin(b x + a) +--R + +--R 2 +--R (2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a)) +--R * +--R sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 +--R (- cos(b x + c) + 1)cot(b x + c)csc(b x + c)sin(c - a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 2 2 +--R ((cos(b x + a) - 1)cos(b x + c) - cos(b x + a) + 1)sin(b x + a) +--R + +--R 2 2 +--R (2cos(b x + a) + 2cos(b x + a))cos(b x + c) +--R + +--R 2 +--R - 2cos(b x + a) - 2cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 3 +--R (cos(b x + a) - cos(b x + a))cos(b x + c) - cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) + cos(c - a))sin(b x + a) sin(b x + c) +--R + +--R 2 3 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 +--R ((cos(b x + a) + 1)cos(b x + c) - cos(b x + a) - 1)cot(b x + c) +--R * +--R 2 +--R csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 2 2 +--R (cos(b x + a) + cos(b x + a))cos(b x + c) - cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 +--R cos(c - a)cos(b x + a) sin(b x + a)sin(b x + c) +--R + +--R 2 2 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 2 2 +--R (cos(b x + a) cos(b x + c) - cos(b x + a) )cot(b x + c) +--R * +--R csc(b x + c)sin(c - a)sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 3 +--R 2cos(c - a)cos(b x + a)sin(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 2 +--R - cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 +--R (2cos(b x + a)cos(b x + c) - 2cos(b x + a))cot(b x + c) +--R * +--R 2 +--R csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R ((- cos(b x + a) - 1)cos(b x + c) + cos(b x + a) + 1)sin(b x + a) +--R + +--R 3 2 2 3 +--R (- cos(b x + a) - cos(b x + a) )cos(b x + c) + cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 +--R cos(c - a)sin(b x + a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a))sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 3 +--R (cos(b x + c) - 1)cot(b x + c)csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 2 +--R ((- cos(b x + a) + 2)cos(b x + c) + cos(b x + a) - 2)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - 2cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 3 +--R (- cos(b x + a) + cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) - cos(c - a))sin(b x + a) +--R + +--R 3 2 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 3 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 +--R ((cos(b x + a) - 1)cos(b x + c) - cos(b x + a) + 1)cot(b x + c) +--R * +--R 2 +--R csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 2 +--R (- cos(b x + a) - 2cos(b x + a) - 1)cos(b x + c) +--R + +--R 2 +--R cos(b x + a) + 2cos(b x + a) + 1 +--R * +--R sin(b x + a) +--R + +--R 3 2 2 3 +--R (- cos(b x + a) - cos(b x + a) )cos(b x + c) + cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 3 +--R cos(c - a)sin(b x + a) +--R + +--R 2 +--R (- 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a))sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 3 +--R (cos(b x + c) - 1)cot(b x + c)csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 2 +--R ((- cos(b x + a) + 1)cos(b x + c) + cos(b x + a) - 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- 2cos(b x + a) - 2cos(b x + a))cos(b x + c) + 2cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 3 +--R (- cos(b x + a) + cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) - cos(c - a))sin(b x + a) sin(b x + c) +--R + +--R 2 3 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 +--R ((- cos(b x + a) - 1)cos(b x + c) + cos(b x + a) + 1)cot(b x + c) +--R * +--R 2 +--R csc(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R sin(b x + a) +--R / +--R 2 2 2 4 +--R (cos(b x + a) cos(b x + c) - cos(b x + a) )tan(c - a) +--R + +--R 2 2 2 +--R (- cos(b x + a) + 2cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 3 +--R sin(b x + a)tan(c - a) +--R + +--R 2 +--R ((- 2cos(b x + a) + 1)cos(b x + c) + 2cos(b x + a) - 1) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 2 3 +--R (cos(b x + a) + cos(b x + a) )cos(b x + c) - cos(b x + a) +--R + +--R 2 +--R - cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 3 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 +--R (2cos(b x + a) + 2cos(b x + a))cos(b x + c) +--R + +--R 2 +--R - 2cos(b x + a) - 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 +--R ((cos(b x + a) + 1)cos(b x + c) - cos(b x + a) - 1)sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 2 2 5 +--R (cos(b x + a) cos(b x + c) - cos(b x + a) )sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (2cos(b x + a)cos(b x + c) - 2cos(b x + a))sin(b x + a) +--R + +--R 3 2 2 3 +--R (- cos(b x + a) - cos(b x + a) )cos(b x + c) + cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 3 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - 2cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 +--R ((cos(b x + a) - 1)cos(b x + c) - cos(b x + a) + 1)sin(b x + a) +--R + +--R 3 2 2 3 +--R (- cos(b x + a) - cos(b x + a) )cos(b x + c) + cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 3 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- 2cos(b x + a) - 2cos(b x + a))cos(b x + c) + 2cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 +--R ((- cos(b x + a) - 1)cos(b x + c) + cos(b x + a) + 1)sin(b x + a) +--R Type: Expression(Integer) +--E 447 + +--S 448 of 532 +t0783:= sin(a+b*x)*cot(c+b*x)^3 +--R +--R +--R 3 +--R (418) cot(b x + c) sin(b x + a) +--R Type: Expression(Integer) +--E 448 + +--S 449 of 532 +r0783:= -cos(a-c)*csc(c+b*x)/b+3/2*atanh(cos(c+b*x))*sin(a-c)/b-_ + 1/2*cot(c+b*x)*csc(c+b*x)*sin(a-c)/b-sin(a+b*x)/b +--R +--R +--R (419) +--R - 3sin(c - a)atanh(cos(b x + c)) - 2sin(b x + a) +--R + +--R cot(b x + c)csc(b x + c)sin(c - a) - 2cos(c - a)csc(b x + c) +--R / +--R 2b +--R Type: Expression(Integer) +--E 449 + +--S 450 of 532 +a0783:= integrate(t0783,x) +--R +--R +--R (420) +--R 2 4 3 +--R 3cos(b x + a) tan(c - a) + 6cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (- 3cos(b x + a) + 3)tan(c - a) +--R * +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R - sin(b x + a)tan(c - a) + (cos(b x + a) + 1)tan(c - a) +--R + +--R - sin(b x + a)tan(c - a) + cos(b x + a) + 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R 2 3 +--R (- 2cos(b x + a) - 1)sin(b x + a)tan(c - a) +--R + +--R 3 2 2 +--R (4cos(b x + a) - cos(b x + a) - 5cos(b x + a))tan(c - a) +--R + +--R 2 +--R (2cos(b x + a) - 2cos(b x + a) - 4)sin(b x + a)tan(c - a) +--R + +--R 2 +--R cos(b x + a) - 1 +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R 2 3 2 +--R 2b cos(b x + a) tan(c - a) + 4b cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 +--R (- 2b cos(b x + a) + 2b)tan(c - a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 450 + +--S 451 of 532 +m0783:= a0783-r0783 +--R +--R +--R (421) +--R 2 4 3 +--R 3cos(b x + a) tan(c - a) + 6cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (- 3cos(b x + a) + 3)tan(c - a) +--R * +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R - sin(b x + a)tan(c - a) + (cos(b x + a) + 1)tan(c - a) +--R + +--R - sin(b x + a)tan(c - a) + cos(b x + a) + 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R 2 3 +--R 3cos(b x + a) sin(c - a)tan(c - a) +--R + +--R 2 +--R 6cos(b x + a)sin(c - a)sin(b x + a)tan(c - a) +--R + +--R 2 +--R (- 3cos(b x + a) + 3)sin(c - a)tan(c - a) +--R * +--R atanh(cos(b x + c)) +--R + +--R 2 +--R - sin(b x + a) - cos(b x + a) cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) csc(b x + c) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 +--R 4cos(b x + a)sin(b x + a) +--R + +--R - 2cos(b x + a)cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 4cos(c - a)cos(b x + a)csc(b x + c) +--R * +--R sin(b x + a) +--R + +--R 3 2 +--R 4cos(b x + a) - cos(b x + a) - 5cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R (- 2cos(b x + a) - 2)sin(b x + a) +--R + +--R 2 +--R (cos(b x + a) - 1)cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 2 +--R (- 2cos(c - a)cos(b x + a) + 2cos(c - a))csc(b x + c) +--R * +--R tan(c - a) +--R + +--R 2 +--R cos(b x + a) - 1 +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R 2 3 2 +--R 2b cos(b x + a) tan(c - a) + 4b cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 +--R (- 2b cos(b x + a) + 2b)tan(c - a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 532 +--d0783:= D(m0783,x) +--E 452 + +--S 453 of 532 +t0784:= sin(a+b*x)*sec(c+b*x) +--R +--R +--R (422) sec(b x + c)sin(b x + a) +--R Type: Expression(Integer) +--E 453 + +--S 454 of 532 +r0784:= -cos(a-c)*log(cos(c+b*x))/b+x*sin(a-c) +--R +--R +--R - cos(c - a)log(cos(b x + c)) - b x sin(c - a) +--R (423) ---------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 454 + +--S 455 of 532 +a0784:= integrate(t0784,x) +--R +--R +--R (424) +--R c - a 2 2 +--R (- tan(-----) + 1)log(----------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a 2 2cos(b x + c) c - a +--R (tan(-----) - 1)log(- ----------------) - 2b x tan(-----) +--R 2 cos(b x + c) + 1 2 +--R / +--R c - a 2 +--R b tan(-----) + b +--R 2 +--R Type: Union(Expression(Integer),...) +--E 455 + +--S 456 of 532 +m0784:= a0784-r0784 +--R +--R +--R (425) +--R c - a 2 +--R (cos(c - a)tan(-----) + cos(c - a))log(cos(b x + c)) +--R 2 +--R + +--R c - a 2 2 +--R (- tan(-----) + 1)log(----------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a 2 2cos(b x + c) c - a 2 +--R (tan(-----) - 1)log(- ----------------) + b x sin(c - a)tan(-----) +--R 2 cos(b x + c) + 1 2 +--R + +--R c - a +--R - 2b x tan(-----) + b x sin(c - a) +--R 2 +--R / +--R c - a 2 +--R b tan(-----) + b +--R 2 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 532 +d0784:= D(m0784,x) +--R +--R +--R (426) +--R c - a 2 +--R ((- cos(c - a) - 1)sin(b x + c) + cos(b x + c)sin(c - a))tan(-----) +--R 2 +--R + +--R c - a +--R - 2cos(b x + c)tan(-----) + (- cos(c - a) + 1)sin(b x + c) +--R 2 +--R + +--R cos(b x + c)sin(c - a) +--R / +--R c - a 2 +--R cos(b x + c)tan(-----) + cos(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 532 +t0785:= sin(a+b*x)*sec(c+b*x)^2 +--R +--R +--R 2 +--R (427) sec(b x + c) sin(b x + a) +--R Type: Expression(Integer) +--E 458 + +--S 459 of 532 +r0785:= cos(a-c)*sec(c+b*x)/b+atanh(sin(c+b*x))*sin(a-c)/b +--R +--R +--R - sin(c - a)atanh(sin(b x + c)) + cos(c - a)sec(b x + c) +--R (428) -------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 459 + +--S 460 of 532 +a0785:= integrate(t0785,x) +--R +--R +--R (429) +--R c - a sin(b x + c) + cos(b x + c) + 1 +--R - 2cos(b x + c)tan(-----)log(-------------------------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a sin(b x + c) - cos(b x + c) - 1 +--R 2cos(b x + c)tan(-----)log(-------------------------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a 2 +--R (- cos(b x + c) - 1)tan(-----) + cos(b x + c) + 1 +--R 2 +--R / +--R c - a 2 +--R b cos(b x + c)tan(-----) + b cos(b x + c) +--R 2 +--R Type: Union(Expression(Integer),...) +--E 460 + +--S 461 of 532 +m0785:= a0785-r0785 +--R +--R +--R (430) +--R c - a sin(b x + c) + cos(b x + c) + 1 +--R - 2cos(b x + c)tan(-----)log(-------------------------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a sin(b x + c) - cos(b x + c) - 1 +--R 2cos(b x + c)tan(-----)log(-------------------------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a 2 +--R (cos(b x + c)sin(c - a)tan(-----) + cos(b x + c)sin(c - a)) +--R 2 +--R * +--R atanh(sin(b x + c)) +--R + +--R c - a 2 +--R (- cos(c - a)cos(b x + c)sec(b x + c) - cos(b x + c) - 1)tan(-----) +--R 2 +--R + +--R - cos(c - a)cos(b x + c)sec(b x + c) + cos(b x + c) + 1 +--R / +--R c - a 2 +--R b cos(b x + c)tan(-----) + b cos(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 532 +d0785:= D(m0785,x) +--R +--R +--R (431) +--R 2 4 +--R - cos(c - a)cos(b x + c) sec(b x + c)sin(b x + c) +--R + +--R 4 3 +--R cos(c - a)cos(b x + c) + 2cos(c - a)cos(b x + c) +--R + +--R 2 +--R 2cos(c - a)cos(b x + c) +--R * +--R 2 +--R sec(b x + c)sin(b x + c) +--R + +--R 4 3 +--R - cos(c - a)cos(b x + c) - 2cos(c - a)cos(b x + c) +--R + +--R 2 +--R - cos(c - a)cos(b x + c) +--R * +--R sec(b x + c) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 2 4 +--R - cos(c - a)cos(b x + c) sec(b x + c)sin(b x + c) +--R + +--R 4 3 +--R cos(c - a)cos(b x + c) + 2cos(c - a)cos(b x + c) +--R + +--R 2 +--R 2cos(c - a)cos(b x + c) +--R * +--R 2 +--R sec(b x + c)sin(b x + c) +--R + +--R 4 3 +--R - cos(c - a)cos(b x + c) - 2cos(c - a)cos(b x + c) +--R + +--R 2 +--R - cos(c - a)cos(b x + c) +--R * +--R sec(b x + c) +--R * +--R tan(b x + c) +--R + +--R 5 2 3 +--R - sin(b x + c) + (cos(b x + c) + 2cos(b x + c) + 2)sin(b x + c) +--R + +--R 3 2 +--R - cos(b x + c) sin(c - a)sin(b x + c) +--R + +--R 2 +--R (- cos(b x + c) - 2cos(b x + c) - 1)sin(b x + c) +--R + +--R 5 4 3 +--R (cos(b x + c) + 2cos(b x + c) + cos(b x + c) )sin(c - a) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 2 4 +--R 4cos(b x + c) sin(b x + c) +--R + +--R 4 3 2 2 +--R (4cos(b x + c) + 4cos(b x + c) - 4cos(b x + c) )sin(b x + c) +--R + +--R 4 3 +--R - 4cos(b x + c) - 4cos(b x + c) +--R * +--R c - a +--R tan(-----) +--R 2 +--R + +--R 5 2 3 +--R sin(b x + c) + (- cos(b x + c) - 2cos(b x + c) - 2)sin(b x + c) +--R + +--R 3 2 +--R - cos(b x + c) sin(c - a)sin(b x + c) +--R + +--R 2 +--R (cos(b x + c) + 2cos(b x + c) + 1)sin(b x + c) +--R + +--R 5 4 3 +--R (cos(b x + c) + 2cos(b x + c) + cos(b x + c) )sin(c - a) +--R / +--R 2 4 +--R cos(b x + c) sin(b x + c) +--R + +--R 4 3 2 2 +--R (- cos(b x + c) - 2cos(b x + c) - 2cos(b x + c) )sin(b x + c) +--R + +--R 4 3 2 +--R cos(b x + c) + 2cos(b x + c) + cos(b x + c) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 2 4 +--R cos(b x + c) sin(b x + c) +--R + +--R 4 3 2 2 +--R (- cos(b x + c) - 2cos(b x + c) - 2cos(b x + c) )sin(b x + c) +--R + +--R 4 3 2 +--R cos(b x + c) + 2cos(b x + c) + cos(b x + c) +--R Type: Expression(Integer) +--E 462 + +--S 463 of 532 +t0786:= sin(a+b*x)*sec(c+b*x)^3 +--R +--R +--R 3 +--R (432) sec(b x + c) sin(b x + a) +--R Type: Expression(Integer) +--E 463 + +--S 464 of 532 +r0786:= 1/2*cos(a-c)*sec(c+b*x)^2/b+sin(a-c)*tan(c+b*x)/b +--R +--R +--R 2 +--R - 2sin(c - a)tan(b x + c) + cos(c - a)sec(b x + c) +--R (433) --------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 464 + +--S 465 of 532 +a0786:= integrate(t0786,x) +--R +--R +--R (434) +--R 2 c - a 2 c - a +--R (cos(b x + c) - 1)tan(-----) - 4cos(b x + c)sin(b x + c)tan(-----) +--R 2 2 +--R + +--R 2 +--R - cos(b x + c) + 1 +--R / +--R 2 c - a 2 2 +--R 2b cos(b x + c) tan(-----) + 2b cos(b x + c) +--R 2 +--R Type: Union(Expression(Integer),...) +--E 465 + +--S 466 of 532 +m0786:= a0786-r0786 +--R +--R +--R (435) +--R 2 c - a 2 2 +--R (2cos(b x + c) sin(c - a)tan(-----) + 2cos(b x + c) sin(c - a)) +--R 2 +--R * +--R tan(b x + c) +--R + +--R 2 2 2 c - a 2 +--R (- cos(c - a)cos(b x + c) sec(b x + c) + cos(b x + c) - 1)tan(-----) +--R 2 +--R + +--R c - a +--R - 4cos(b x + c)sin(b x + c)tan(-----) +--R 2 +--R + +--R 2 2 2 +--R - cos(c - a)cos(b x + c) sec(b x + c) - cos(b x + c) + 1 +--R / +--R 2 c - a 2 2 +--R 2b cos(b x + c) tan(-----) + 2b cos(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 532 +d0786:= D(m0786,x) +--R +--R +--R (436) +--R 3 c - a 2 3 +--R (cos(b x + c) sin(c - a)tan(-----) + cos(b x + c) sin(c - a)) +--R 2 +--R * +--R 2 +--R tan(b x + c) +--R + +--R 3 2 c - a 2 +--R - cos(c - a)cos(b x + c) sec(b x + c) tan(-----) +--R 2 +--R + +--R 3 2 +--R - cos(c - a)cos(b x + c) sec(b x + c) +--R * +--R tan(b x + c) +--R + +--R 3 c - a 2 +--R (- sin(b x + c) + cos(b x + c) sin(c - a))tan(-----) +--R 2 +--R + +--R 2 3 c - a +--R (- 2cos(b x + c)sin(b x + c) - 2cos(b x + c) )tan(-----) + sin(b x + c) +--R 2 +--R + +--R 3 +--R cos(b x + c) sin(c - a) +--R / +--R 3 c - a 2 3 +--R cos(b x + c) tan(-----) + cos(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 532 +t0787:= sin(a+b*x)*csc(c+b*x) +--R +--R +--R (437) csc(b x + c)sin(b x + a) +--R Type: Expression(Integer) +--E 468 + +--S 469 of 532 +r0787:= x*cos(a-c)+log(sin(c+b*x))*sin(a-c)/b +--R +--R +--R - sin(c - a)log(sin(b x + c)) + b x cos(c - a) +--R (438) ---------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 469 + +--S 470 of 532 +a0787:= integrate(t0787,x) +--R +--R +--R (439) +--R c - a sin(b x + c) c - a 2 +--R - 2tan(-----)log(----------------) + 2tan(-----)log(----------------) +--R 2 cos(b x + c) + 1 2 cos(b x + c) + 1 +--R + +--R c - a 2 +--R - b x tan(-----) + b x +--R 2 +--R / +--R c - a 2 +--R b tan(-----) + b +--R 2 +--R Type: Union(Expression(Integer),...) +--E 470 + +--S 471 of 532 +m0787:= a0787-r0787 +--R +--R +--R (440) +--R c - a 2 +--R (sin(c - a)tan(-----) + sin(c - a))log(sin(b x + c)) +--R 2 +--R + +--R c - a sin(b x + c) c - a 2 +--R - 2tan(-----)log(----------------) + 2tan(-----)log(----------------) +--R 2 cos(b x + c) + 1 2 cos(b x + c) + 1 +--R + +--R c - a 2 +--R (- b x cos(c - a) - b x)tan(-----) - b x cos(c - a) + b x +--R 2 +--R / +--R c - a 2 +--R b tan(-----) + b +--R 2 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 532 +d0787:= D(m0787,x) +--R +--R +--R (441) +--R c - a 2 +--R ((- cos(c - a) - 1)sin(b x + c) + cos(b x + c)sin(c - a))tan(-----) +--R 2 +--R + +--R c - a +--R - 2cos(b x + c)tan(-----) + (- cos(c - a) + 1)sin(b x + c) +--R 2 +--R + +--R cos(b x + c)sin(c - a) +--R / +--R c - a 2 +--R sin(b x + c)tan(-----) + sin(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 532 +t0788:= sin(a+b*x)*csc(c+b*x)^2 +--R +--R +--R 2 +--R (442) csc(b x + c) sin(b x + a) +--R Type: Expression(Integer) +--E 473 + +--S 474 of 532 +r0788:= -atanh(cos(c+b*x))*cos(a-c)/b-csc(c+b*x)*sin(a-c)/b +--R +--R +--R - cos(c - a)atanh(cos(b x + c)) + csc(b x + c)sin(c - a) +--R (443) -------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 474 + +--S 475 of 532 +a0788:= integrate(t0788,x) +--R +--R +--R (444) +--R c - a 2 sin(b x + c) c - a +--R (- sin(b x + c)tan(-----) + sin(b x + c))log(----------------) + 2tan(-----) +--R 2 cos(b x + c) + 1 2 +--R ----------------------------------------------------------------------------- +--R c - a 2 +--R b sin(b x + c)tan(-----) + b sin(b x + c) +--R 2 +--R Type: Union(Expression(Integer),...) +--E 475 + +--S 476 of 532 +m0788:= a0788-r0788 +--R +--R +--R (445) +--R c - a 2 sin(b x + c) +--R (- sin(b x + c)tan(-----) + sin(b x + c))log(----------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a 2 +--R (cos(c - a)sin(b x + c)tan(-----) + cos(c - a)sin(b x + c)) +--R 2 +--R * +--R atanh(cos(b x + c)) +--R + +--R c - a 2 c - a +--R - csc(b x + c)sin(c - a)sin(b x + c)tan(-----) + 2tan(-----) +--R 2 2 +--R + +--R - csc(b x + c)sin(c - a)sin(b x + c) +--R / +--R c - a 2 +--R b sin(b x + c)tan(-----) + b sin(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 532 +d0788:= D(m0788,x) +--R +--R +--R (446) +--R 3 +--R (- cos(b x + c) + cos(c - a) + 1)sin(b x + c) +--R + +--R 2 2 +--R (cos(b x + c) - 1)cot(b x + c)csc(b x + c)sin(c - a)sin(b x + c) +--R + +--R 3 +--R (- cos(b x + c) + cos(b x + c))sin(b x + c) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 3 c - a +--R (- 2cos(b x + c) + 2cos(b x + c))tan(-----) +--R 2 +--R + +--R 3 +--R (cos(b x + c) + cos(c - a) - 1)sin(b x + c) +--R + +--R 2 2 +--R (cos(b x + c) - 1)cot(b x + c)csc(b x + c)sin(c - a)sin(b x + c) +--R + +--R 3 +--R (cos(b x + c) - cos(b x + c))sin(b x + c) +--R / +--R 2 2 c - a 2 +--R (cos(b x + c) - 1)sin(b x + c) tan(-----) +--R 2 +--R + +--R 2 2 +--R (cos(b x + c) - 1)sin(b x + c) +--R Type: Expression(Integer) +--E 477 + +--S 478 of 532 +t0789:= sin(a+b*x)*csc(c+b*x)^3 +--R +--R +--R 3 +--R (447) csc(b x + c) sin(b x + a) +--R Type: Expression(Integer) +--E 478 + +--S 479 of 532 +r0789:= -cos(a-c)*cot(c+b*x)/b-1/2*csc(c+b*x)^2*sin(a-c)/b +--R +--R +--R 2 +--R csc(b x + c) sin(c - a) - 2cos(c - a)cot(b x + c) +--R (448) ------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 479 + +--S 480 of 532 +a0789:= integrate(t0789,x) +--R +--R +--R (449) +--R c - a 2 2 c - a +--R - 2cos(b x + c)sin(b x + c)tan(-----) + (- cos(b x + c) - 1)tan(-----) +--R 2 2 +--R + +--R 2cos(b x + c)sin(b x + c) +--R / +--R 2 c - a 2 2 +--R (2b cos(b x + c) - 2b)tan(-----) + 2b cos(b x + c) - 2b +--R 2 +--R Type: Union(Expression(Integer),...) +--E 480 + +--S 481 of 532 +m0789:= a0789-r0789 +--R +--R +--R (450) +--R - 2cos(b x + c)sin(b x + c) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)csc(b x + c) sin(c - a) +--R + +--R 2 +--R (2cos(c - a)cos(b x + c) - 2cos(c - a))cot(b x + c) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 2 c - a +--R (- cos(b x + c) - 1)tan(-----) + 2cos(b x + c)sin(b x + c) +--R 2 +--R + +--R 2 2 +--R (- cos(b x + c) + 1)csc(b x + c) sin(c - a) +--R + +--R 2 +--R (2cos(c - a)cos(b x + c) - 2cos(c - a))cot(b x + c) +--R / +--R 2 c - a 2 2 +--R (2b cos(b x + c) - 2b)tan(-----) + 2b cos(b x + c) - 2b +--R 2 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 532 +d0789:= D(m0789,x) +--R +--R +--R (451) +--R 2 2 +--R (- cos(b x + c) - 1)sin(b x + c) +--R + +--R 4 2 2 +--R (cos(b x + c) - 2cos(b x + c) + 1)cot(b x + c)csc(b x + c) +--R * +--R sin(c - a) +--R + +--R 4 2 +--R (- cos(c - a)cos(b x + c) + 2cos(c - a)cos(b x + c) - cos(c - a)) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 4 2 +--R (- cos(c - a) - 1)cos(b x + c) + (2cos(c - a) + 1)cos(b x + c) +--R + +--R - cos(c - a) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R c - a 2 2 +--R - 2cos(b x + c)sin(b x + c)tan(-----) + (cos(b x + c) + 1)sin(b x + c) +--R 2 +--R + +--R 4 2 2 +--R (cos(b x + c) - 2cos(b x + c) + 1)cot(b x + c)csc(b x + c) sin(c - a) +--R + +--R 4 2 +--R (- cos(c - a)cos(b x + c) + 2cos(c - a)cos(b x + c) - cos(c - a)) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 4 2 +--R (- cos(c - a) + 1)cos(b x + c) + (2cos(c - a) - 1)cos(b x + c) +--R + +--R - cos(c - a) +--R / +--R 4 2 c - a 2 4 +--R (cos(b x + c) - 2cos(b x + c) + 1)tan(-----) + cos(b x + c) +--R 2 +--R + +--R 2 +--R - 2cos(b x + c) + 1 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 532 +t0790:= cos(a+b*x)*tan(c+b*x) +--R +--R +--R (452) cos(b x + a)tan(b x + c) +--R Type: Expression(Integer) +--E 483 + +--S 484 of 532 +r0790:= -(cos(a+b*x)+atanh(sin(c+b*x))*sin(a-c))/b +--R +--R +--R sin(c - a)atanh(sin(b x + c)) - cos(b x + a) +--R (453) -------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 484 + +--S 485 of 532 +a0790:= integrate(t0790,x) +--R +--R +--R (454) +--R tan(c - a) +--R * +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) +--R + +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R +---------------+ +--R | 2 +--R - cos(b x + a)\|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R b\|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 532 +m0790:= a0790-r0790 +--R +--R +--R (455) +--R tan(c - a) +--R * +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) +--R + +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R +---------------+ +--R | 2 +--R - sin(c - a)atanh(sin(b x + c))\|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R b\|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 532 +d0790:= D(m0790,x) +--R +--R +--R (456) +--R 2 2 2 +--R (- sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 +--R sin(b x + a) +--R + +--R (cos(b x + a) + 1)cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R cos(b x + a) + cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 +--R - sin(b x + a)sin(b x + c) + cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - cos(b x + a))cos(b x + c)sin(c - a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 2 2 2 +--R (- sin(b x + a) - cos(b x + a) )sin(b x + c) + sin(b x + a) +--R + +--R (- cos(b x + a) + 1)cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R tan(c - a) +--R + +--R - cos(b x + a)cos(b x + c)sin(c - a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 2 2 +--R (- sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 +--R sin(b x + a) + (cos(b x + a) + 1)cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R cos(b x + a) + cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 2 +--R - sin(b x + a)sin(b x + c) + cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R sin(b x + a) + (- cos(b x + a) - cos(b x + a))cos(b x + c)sin(c - a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 2 +--R (- sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 2 +--R sin(b x + a) + cos(b x + c)sin(c - a)sin(b x + a) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 2 +--R - sin(b x + a)sin(b x + c) + cos(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R sin(b x + a) + (- cos(b x + a) - cos(b x + a))cos(b x + c)sin(c - a) +--R * +--R tan(c - a) +--R + +--R - cos(b x + a)cos(b x + c)sin(c - a)sin(b x + a) +--R / +--R 2 +--R (cos(b x + a) + 1)sin(b x + a)sin(b x + c) +--R + +--R (- cos(b x + a) - 1)sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 2 +--R (sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 2 +--R - sin(b x + a) + cos(b x + a) + cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R (- cos(b x + a) + 1)sin(b x + a)sin(b x + c) +--R + +--R (cos(b x + a) - 1)sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R - cos(b x + a)sin(b x + c) + cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 +--R (cos(b x + a) + 1)sin(b x + a)sin(b x + c) +--R + +--R (- cos(b x + a) - 1)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 2 2 +--R (sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 2 +--R - sin(b x + a) + cos(b x + a) + cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 +--R (sin(b x + a)sin(b x + c) - sin(b x + a))tan(c - a) +--R + +--R 2 2 2 +--R (sin(b x + a) - cos(b x + a) - cos(b x + a))sin(b x + c) +--R + +--R 2 2 +--R - sin(b x + a) + cos(b x + a) + cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R - cos(b x + a)sin(b x + a)sin(b x + c) + cos(b x + a)sin(b x + a) +--R Type: Expression(Integer) +--E 487 + +--S 488 of 532 +t0791:= cos(a+b*x)*tan(c+b*x)^2 +--R +--R +--R 2 +--R (457) cos(b x + a)tan(b x + c) +--R Type: Expression(Integer) +--E 488 + +--S 489 of 532 +r0791:= atanh(sin(c+b*x))*cos(a-c)/b-sec(c+b*x)*sin(a-c)/b-sin(a+b*x)/b +--R +--R +--R (458) +--R cos(c - a)atanh(sin(b x + c)) - sin(b x + a) + sec(b x + c)sin(c - a) +--R --------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 489 + +--S 490 of 532 +a0791:= integrate(t0791,x) +--R +--R +--R (459) +--R (sin(b x + a)tan(c - a) - cos(b x + a)) +--R * +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) +--R + +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R 2 +--R sin(b x + a)tan(c - a) +--R + +--R 2 +--R (cos(b x + a) - cos(b x + a) - 2)tan(c - a) + cos(b x + a)sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R (b sin(b x + a)tan(c - a) - b cos(b x + a))\|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 490 + +--S 491 of 532 +m0791:= a0791-r0791 +--R +--R +--R (460) +--R (sin(b x + a)tan(c - a) - cos(b x + a)) +--R * +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) +--R + +--R (cos(b x + a) + 1)tan(c - a) + sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R (- cos(c - a)sin(b x + a)tan(c - a) + cos(c - a)cos(b x + a)) +--R * +--R atanh(sin(b x + c)) +--R + +--R 2 +--R sin(b x + a)tan(c - a) +--R + +--R 2 +--R sin(b x + a) - sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R cos(b x + a) - cos(b x + a) - 2 +--R * +--R tan(c - a) +--R + +--R cos(b x + a)sec(b x + c)sin(c - a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R (b sin(b x + a)tan(c - a) - b cos(b x + a))\|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 532 +d0791:= D(m0791,x) +--R +--R +--R (461) +--R 2 +--R (- cos(b x + a) - 1)sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (cos(b x + a) + 1)sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 +--R - sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (2cos(b x + a) + 2cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- 2cos(b x + a) - 2cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 +--R (2cos(b x + a) - 1)sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 +--R (- cos(b x + a) - cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (- 2cos(b x + a) + 1)sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 +--R (cos(b x + a) + cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R (- cos(b x + a) + 2cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + a)sin(b x + c) +--R + +--R 2 +--R (cos(b x + a) - 2cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 +--R - cos(b x + a) sec(b x + c)sin(c - a)sin(b x + c) +--R + +--R 2 +--R cos(b x + a) sec(b x + c)sin(c - a) +--R * +--R tan(b x + c) +--R + +--R 2 2 4 +--R (- cos(b x + a) - cos(b x + a))sin(b x + a) - cos(b x + a) +--R + +--R 3 2 +--R - cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R (cos(c - a)cos(b x + a) + cos(c - a))cos(b x + c) +--R + +--R 2 +--R cos(b x + a) + cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 4 3 2 +--R cos(b x + a) + cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 +--R (- 2cos(b x + a) - 2)sin(b x + a) +--R + +--R 3 2 +--R (- 2cos(b x + a) - 2cos(b x + a) + 3cos(b x + a) + 2) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R (cos(c - a)cos(b x + c) + 2cos(b x + a) + 2)sin(b x + a) +--R + +--R 2 +--R (- 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a)) +--R * +--R cos(b x + c) +--R + +--R 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 3cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 4 2 2 +--R - sin(b x + a) + (- cos(b x + a) + 1)sin(b x + a) +--R + +--R 2 +--R cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 +--R sin(b x + a) +--R + +--R (- 2cos(c - a)cos(b x + a) + cos(c - a))cos(b x + c) +--R + +--R 2 +--R cos(b x + a) - 1 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 +--R (cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) )cos(b x + c) +--R + +--R 2 +--R - cos(b x + a) - 2cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 3 +--R - 2sin(b x + a) +--R + +--R 2 +--R (- 2cos(b x + a) + cos(b x + a) + 2)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R 2sin(b x + a) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a)) +--R * +--R cos(b x + c) +--R + +--R 2 +--R 2cos(b x + a) - cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 3 2 +--R (cos(b x + a)sin(b x + a) + cos(b x + a) )sin(b x + c) +--R + +--R 2 2 +--R - cos(b x + a)sin(b x + a) + cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 3 +--R - cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 +--R (- cos(b x + a) - 1)sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (cos(b x + a) + 1)sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 3 +--R - sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (2cos(b x + a) + 2cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- 2cos(b x + a) - 2cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 +--R (cos(b x + a) - 1)sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 +--R (- cos(b x + a) - cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (- cos(b x + a) + 1)sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 +--R (cos(b x + a) + cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 +--R - sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (cos(b x + a) + 2cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - 2cos(b x + a))sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R 2cos(b x + a)sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 +--R (- cos(b x + a) - cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R - 2cos(b x + a)sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 +--R (cos(b x + a) + cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R tan(c - a) +--R + +--R 2 2 +--R - cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 2 +--R cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R tan(b x + c) +--R + +--R 2 2 4 +--R (- cos(b x + a) - cos(b x + a))sin(b x + a) - cos(b x + a) +--R + +--R 3 2 +--R - cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) + cos(c - a))cos(b x + c) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 4 3 2 +--R cos(b x + a) + cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 3 +--R (- 2cos(b x + a) - 2)sin(b x + a) +--R + +--R 3 2 +--R (- 2cos(b x + a) - 2cos(b x + a) + 3cos(b x + a) + 2)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R (cos(c - a)cos(b x + c) + 2cos(b x + a) + 2)sin(b x + a) +--R + +--R 2 +--R (- 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a)) +--R * +--R cos(b x + c) +--R + +--R 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 3cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 4 2 2 +--R - sin(b x + a) + (- 2cos(b x + a) + 1)sin(b x + a) +--R + +--R 4 2 +--R - cos(b x + a) + 3cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 +--R sin(b x + a) +--R + +--R (- cos(c - a)cos(b x + a) + cos(c - a))cos(b x + c) +--R + +--R 2 +--R 2cos(b x + a) - 1 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 +--R (cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) )cos(b x + c) +--R + +--R 4 2 +--R cos(b x + a) - 3cos(b x + a) - 2cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 +--R (- 2cos(b x + a) - 2)sin(b x + a) +--R + +--R 3 2 +--R (- 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 2)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R (cos(c - a)cos(b x + c) + 2cos(b x + a) + 2)sin(b x + a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a))cos(b x + c) +--R + +--R 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 +--R - sin(b x + a) +--R + +--R 2 2 3 +--R (- cos(b x + a) + cos(b x + a) + 1)sin(b x + a) + cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 +--R sin(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a)cos(b x + c) + cos(b x + a) +--R + +--R - cos(b x + a) - 1 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 +--R (cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) )cos(b x + c) +--R + +--R 3 2 +--R - cos(b x + a) - cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R cos(b x + a)sin(b x + a)sin(b x + c) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) cos(b x + c) - cos(b x + a))sin(b x + a) +--R / +--R 2 2 +--R (cos(b x + a) + 1)sin(b x + a) sin(b x + c) +--R + +--R 2 +--R (- cos(b x + a) - 1)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 +--R sin(b x + a) +--R + +--R 2 +--R (- 2cos(b x + a) - 2cos(b x + a))sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R - sin(b x + a) + (2cos(b x + a) + 2cos(b x + a))sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 3 +--R (- 2cos(b x + a) + 1)sin(b x + a) + cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 2 +--R (2cos(b x + a) - 1)sin(b x + a) - cos(b x + a) - cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 2 +--R (cos(b x + a) - 2cos(b x + a))sin(b x + a)sin(b x + c) +--R + +--R 2 +--R (- cos(b x + a) + 2cos(b x + a))sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 2 +--R cos(b x + a) sin(b x + c) - cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 2 +--R (cos(b x + a) + 1)sin(b x + a) sin(b x + c) +--R + +--R 2 +--R (- cos(b x + a) - 1)sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 3 2 +--R (sin(b x + a) + (- 2cos(b x + a) - 2cos(b x + a))sin(b x + a)) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R - sin(b x + a) + (2cos(b x + a) + 2cos(b x + a))sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 3 2 +--R ((- cos(b x + a) + 1)sin(b x + a) + cos(b x + a) + cos(b x + a) ) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 2 +--R (cos(b x + a) - 1)sin(b x + a) - cos(b x + a) - cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 2 +--R (sin(b x + a) + (- cos(b x + a) - 2cos(b x + a))sin(b x + a)) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R - sin(b x + a) + (cos(b x + a) + 2cos(b x + a))sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 3 2 +--R (- 2cos(b x + a)sin(b x + a) + cos(b x + a) + cos(b x + a) ) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 2 +--R 2cos(b x + a)sin(b x + a) - cos(b x + a) - cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 2 +--R cos(b x + a) sin(b x + a)sin(b x + c) - cos(b x + a) sin(b x + a) +--R Type: Expression(Integer) +--E 492 + +--S 493 of 532 +t0792:= cos(a+b*x)*tan(c+b*x)^3 +--R +--R +--R 3 +--R (462) cos(b x + a)tan(b x + c) +--R Type: Expression(Integer) +--E 493 + +--S 494 of 532 +r0792:= cos(a+b*x)/b+cos(a-c)*sec(c+b*x)/b+3/2*atanh(sin(c+b*x))*_ + sin(a-c)/b-1/2*sec(c+b*x)*sin(a-c)*tan(c+b*x)/b +--R +--R +--R (463) +--R - 3sin(c - a)atanh(sin(b x + c)) + sec(b x + c)sin(c - a)tan(b x + c) +--R + +--R 2cos(c - a)sec(b x + c) + 2cos(b x + a) +--R / +--R 2b +--R Type: Expression(Integer) +--E 494 + +--S 495 of 532 +a0792:= integrate(t0792,x) +--R +--R +--R (464) +--R 2 3 +--R (3cos(b x + a) - 3)tan(c - a) +--R + +--R 2 2 +--R 6cos(b x + a)sin(b x + a)tan(c - a) - 3cos(b x + a) tan(c - a) +--R * +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a)tan(c - a) +--R + +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R 2 4 3 +--R (cos(b x + a) - 1)tan(c - a) + 2cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 3 2 2 +--R (2cos(b x + a) + 3cos(b x + a) - 3cos(b x + a) - 4)tan(c - a) +--R + +--R 2 +--R (4cos(b x + a) + 8cos(b x + a) + 1)sin(b x + a)tan(c - a) +--R + +--R 3 2 +--R - 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R 2 2 +--R (2b cos(b x + a) - 2b)tan(c - a) +--R + +--R 2 +--R 4b cos(b x + a)sin(b x + a)tan(c - a) - 2b cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 532 +m0792:= a0792-r0792 +--R +--R +--R (465) +--R 2 3 +--R (3cos(b x + a) - 3)tan(c - a) +--R + +--R 2 2 +--R 6cos(b x + a)sin(b x + a)tan(c - a) - 3cos(b x + a) tan(c - a) +--R * +--R log +--R 2 +--R ((cos(b x + a) + 1)tan(c - a) + sin(b x + a)tan(c - a) + 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a)tan(c - a) +--R + +--R (- cos(b x + a) - 1)tan(c - a) - sin(b x + a) +--R / +--R sin(b x + a)tan(c - a) - cos(b x + a) +--R + +--R 2 2 +--R (3cos(b x + a) - 3)sin(c - a)tan(c - a) +--R + +--R 6cos(b x + a)sin(c - a)sin(b x + a)tan(c - a) +--R + +--R 2 +--R - 3cos(b x + a) sin(c - a) +--R * +--R atanh(sin(b x + c)) +--R + +--R 2 2 +--R (- cos(b x + a) + 1)sec(b x + c)sin(c - a)tan(c - a) +--R + +--R - 2cos(b x + a)sec(b x + c)sin(c - a)sin(b x + a)tan(c - a) +--R + +--R 2 +--R cos(b x + a) sec(b x + c)sin(c - a) +--R * +--R tan(b x + c) +--R + +--R 2 4 3 +--R (cos(b x + a) - 1)tan(c - a) + 2cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 +--R (- 2cos(c - a)cos(b x + a) + 2cos(c - a))sec(b x + c) +--R + +--R 2 +--R 3cos(b x + a) - cos(b x + a) - 4 +--R * +--R 2 +--R tan(c - a) +--R + +--R (- 4cos(c - a)cos(b x + a)sec(b x + c) + 8cos(b x + a) + 1) +--R * +--R sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R 2cos(c - a)cos(b x + a) sec(b x + c) - 4cos(b x + a) - 2cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R 2 2 +--R (2b cos(b x + a) - 2b)tan(c - a) +--R + +--R 2 +--R 4b cos(b x + a)sin(b x + a)tan(c - a) - 2b cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 532 +d0792:= D(m0792,x) +--R +--R +--R (466) +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 3 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 3 2 +--R (- 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R 14cos(b x + a) + 10cos(b x + a) - 16cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) + 2cos(b x + a) - 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R - 14cos(b x + a) - 10cos(b x + a) + 16cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) - 2cos(b x + a) + 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 4 +--R - 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R 28cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R 8cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 4cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R - 28cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R - 8cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R 4cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 2 +--R (16cos(b x + a) - 8cos(b x + a) )sec(b x + c) +--R * +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R - 14cos(b x + a) + 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R - 12cos(b x + a) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (- 16cos(b x + a) + 8cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 3 +--R 14cos(b x + a) - 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 12cos(b x + a) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 4 3 +--R (- 10cos(b x + a) + 16cos(b x + a) )sec(b x + c) +--R * +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 6 5 3 +--R (2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) ) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 +--R (10cos(b x + a) - 16cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 3 +--R (- 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) ) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 5 4 +--R (2cos(b x + a) - 10cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + a)sin(b x + c) +--R + +--R 5 4 +--R (- 2cos(b x + a) + 10cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 5 2 +--R 2cos(b x + a) sec(b x + c)sin(c - a)sin(b x + c) +--R + +--R 5 +--R - 2cos(b x + a) sec(b x + c)sin(c - a) +--R * +--R 2 +--R tan(b x + c) +--R + +--R 5 4 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a)sin(b x + c) +--R + +--R 5 4 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 4 +--R - 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 +--R 10cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 6 +--R tan(c - a) +--R + +--R 3 +--R - 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R 14cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 8cos(c - a)cos(b x + a) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R - 14cos(c - a)cos(b x + a) - 10cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 4 +--R - 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R 28cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 4cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 +--R 4cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R - 28cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 4cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 +--R - 4cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 2 +--R (16cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) ) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 +--R - 14cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (- 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) ) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R 14cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 4cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 4 +--R - 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R 16cos(c - a)cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 +--R 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 +--R (10cos(c - a)cos(b x + a) - 16cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R tan(c - a) +--R + +--R 5 4 +--R (2cos(c - a)cos(b x + a) - 10cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R sec(b x + c)sin(b x + a)sin(b x + c) +--R + +--R 5 4 +--R (- 2cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 5 2 +--R 2cos(c - a)cos(b x + a) sec(b x + c)sin(b x + c) +--R + +--R 5 +--R - 2cos(c - a)cos(b x + a) sec(b x + c) +--R * +--R tan(b x + c) +--R + +--R 4 3 2 +--R 3cos(b x + a) - cos(b x + a) - 7cos(b x + a) +--R + +--R - cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - cos(b x + a) - cos(b x + a) + 2cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) - cos(b x + a) - 1 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R 3cos(b x + a) + 3cos(b x + a) - 6cos(b x + a) +--R + +--R 3 2 +--R - 6cos(b x + a) + 3cos(b x + a) + 3cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R - 3cos(b x + a) + cos(b x + a) + 7cos(b x + a) +--R + +--R cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R cos(b x + a) + cos(b x + a) - 2cos(b x + a) +--R + +--R 2 +--R - 2cos(b x + a) + cos(b x + a) + 1 +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R - 3cos(b x + a) - 3cos(b x + a) + 6cos(b x + a) +--R + +--R 2 +--R 6cos(b x + a) - 3cos(b x + a) - 3 +--R * +--R cos(b x + c) +--R * +--R sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 3cos(b x + a) - 3cos(b x + a) + 6cos(b x + a) +--R + +--R 3 2 +--R 6cos(b x + a) - 3cos(b x + a) - 3cos(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 3 2 +--R (12cos(b x + a) + cos(b x + a) - 10cos(b x + a) - 1) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 5cos(b x + a) - 4cos(b x + a) + 6cos(b x + a) +--R + +--R 4cos(b x + a) - 1 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 19cos(b x + a) - 8cos(b x + a) +--R + +--R 2 +--R - 18cos(b x + a) + 3 +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R cos(b x + a) + cos(b x + a) - 2cos(b x + a) +--R + +--R 3 2 +--R - 2cos(b x + a) + cos(b x + a) + cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (- 12cos(b x + a) - cos(b x + a) + 10cos(b x + a) + 1) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R 5cos(b x + a) + 4cos(b x + a) - 6cos(b x + a) +--R + +--R - 4cos(b x + a) + 1 +--R * +--R sec(b x + c) +--R + +--R 4 3 2 +--R - 15cos(b x + a) - 12cos(b x + a) + 18cos(b x + a) +--R + +--R 12cos(b x + a) - 3 +--R * +--R cos(b x + c) +--R * +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 19cos(b x + a) + 8cos(b x + a) +--R + +--R 2 +--R 18cos(b x + a) - 3 +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R - cos(b x + a) - cos(b x + a) + 2cos(b x + a) +--R + +--R 3 2 +--R 2cos(b x + a) - cos(b x + a) - cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R 3cos(b x + a) + 3cos(b x + a) - 6cos(b x + a) +--R + +--R 3 2 +--R - 6cos(b x + a) + 3cos(b x + a) + 3cos(b x + a) +--R * +--R cos(b x + c) +--R * +--R sin(c - a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 4 +--R (12cos(b x + a) + 4cos(b x + a) + 2)sin(b x + a) +--R + +--R 3 2 +--R (- 8cos(b x + a) - 4cos(b x + a) + 4cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R 9cos(b x + a) + 25cos(b x + a) - 4cos(b x + a) +--R + +--R - 14cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R 7cos(b x + a) + 5cos(b x + a) - 8cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) + cos(b x + a) - 1 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 3cos(b x + a) - 9cos(b x + a) - 3cos(b x + a) +--R + +--R 3 2 +--R 7cos(b x + a) + 4cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R (- 12cos(b x + a) - 4cos(b x + a) - 2)sin(b x + a) +--R + +--R 3 2 +--R (8cos(b x + a) + 4cos(b x + a) - 4cos(b x + a))sec(b x + c) +--R + +--R 3 2 +--R (- 24cos(b x + a) - 12cos(b x + a) + 12cos(b x + a)) +--R * +--R cos(b x + c) +--R * +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R - 9cos(b x + a) - 25cos(b x + a) + 4cos(b x + a) +--R + +--R 14cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 7cos(b x + a) - 5cos(b x + a) + 8cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - cos(b x + a) + 1 +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R 21cos(b x + a) + 15cos(b x + a) - 24cos(b x + a) +--R + +--R 2 +--R - 12cos(b x + a) + 3cos(b x + a) - 3 +--R * +--R cos(b x + c) +--R * +--R sin(c - a)sin(b x + a) +--R + +--R 6 5 4 3 +--R 3cos(b x + a) + 9cos(b x + a) + 3cos(b x + a) - 7cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 5 +--R 2sin(b x + a) +--R + +--R 2 4 +--R - 4cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 3 +--R (5cos(b x + a) - 14cos(b x + a) - 2)sin(b x + a) +--R + +--R 4 3 2 +--R 14cos(b x + a) + 4cos(b x + a) - 6cos(b x + a) +--R + +--R 4cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R - 17cos(b x + a) - 4cos(b x + a) + 9cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - cos(b x + a) + 2cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 5 +--R - 2sin(b x + a) +--R + +--R 2 2 +--R (4cos(b x + a) sec(b x + c) - 12cos(b x + a) cos(b x + c)) +--R * +--R 4 +--R sin(c - a)sin(b x + a) +--R + +--R 2 3 +--R (- 5cos(b x + a) + 14cos(b x + a) + 2)sin(b x + a) +--R + +--R 4 3 2 +--R - 14cos(b x + a) - 4cos(b x + a) + 6cos(b x + a) +--R + +--R - 4cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 4 3 2 +--R 42cos(b x + a) + 12cos(b x + a) - 18cos(b x + a) +--R + +--R 12cos(b x + a) +--R * +--R cos(b x + c) +--R * +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R 17cos(b x + a) + 4cos(b x + a) - 9cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R 2cos(b x + a) + cos(b x + a) - 2cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R - 6cos(b x + a) - 3cos(b x + a) + 6cos(b x + a) +--R + +--R 3cos(b x + a) +--R * +--R cos(b x + c) +--R * +--R sin(c - a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 4 +--R (12cos(b x + a) - 4cos(b x + a) + 2)sin(b x + a) +--R + +--R 3 2 +--R (8cos(b x + a) - 4cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R 9cos(b x + a) - 4cos(b x + a) + 7cos(b x + a) +--R + +--R 2cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 7cos(b x + a) + cos(b x + a) + 2cos(b x + a) +--R + +--R 2 +--R - 6cos(b x + a) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 2 +--R - 3cos(b x + a) + cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R (- 12cos(b x + a) + 4cos(b x + a) - 2)sin(b x + a) +--R + +--R 3 2 +--R (- 8cos(b x + a) + 4cos(b x + a) )sec(b x + c) +--R + +--R 3 2 +--R (24cos(b x + a) - 12cos(b x + a) )cos(b x + c) +--R * +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R - 9cos(b x + a) + 4cos(b x + a) - 7cos(b x + a) +--R + +--R - 2cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R 7cos(b x + a) - cos(b x + a) - 2cos(b x + a) +--R + +--R 2 +--R 6cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R - 21cos(b x + a) + 3cos(b x + a) + 6cos(b x + a) +--R + +--R 2 +--R - 18cos(b x + a) +--R * +--R cos(b x + c) +--R * +--R sin(c - a)sin(b x + a) +--R + +--R 6 2 +--R 3cos(b x + a) - cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 2 +--R (- 12cos(b x + a) + 4cos(b x + a) - 4cos(b x + a)) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 +--R (- 5cos(b x + a) + 8cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 2cos(b x + a) + 2cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 6 5 3 +--R (cos(b x + a) - cos(b x + a) + 2cos(b x + a) ) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 3 +--R (12cos(b x + a) - 4cos(b x + a) + 4cos(b x + a))sin(b x + a) +--R + +--R 4 3 +--R (5cos(b x + a) - 8cos(b x + a) )sec(b x + c) +--R + +--R 4 3 +--R (- 15cos(b x + a) + 24cos(b x + a) )cos(b x + c) +--R * +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 2cos(b x + a) - 2cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 6 5 3 +--R (- cos(b x + a) + cos(b x + a) - 2cos(b x + a) ) +--R * +--R sec(b x + c) +--R + +--R 6 5 3 +--R (3cos(b x + a) - 3cos(b x + a) + 6cos(b x + a) )cos(b x + c) +--R * +--R sin(c - a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 3 2 +--R (3cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) ) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 +--R (cos(b x + a) - 5cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R sin(b x + a) +--R + +--R 6 4 +--R 3cos(b x + a) - 3cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 2 +--R (- 3cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) )sin(b x + a) +--R + +--R 5 4 +--R (- cos(b x + a) + 5cos(b x + a) )sec(b x + c) +--R + +--R 5 4 +--R (3cos(b x + a) - 15cos(b x + a) )cos(b x + c) +--R * +--R sin(c - a)sin(b x + a) +--R + +--R 6 4 +--R - 3cos(b x + a) + 3cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 3 +--R - 2cos(b x + a) sin(b x + a) +--R + +--R 5 +--R cos(b x + a) sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R 2cos(b x + a) sin(b x + a) +--R + +--R 5 5 +--R (- cos(b x + a) sec(b x + c) + 3cos(b x + a) cos(b x + c))sin(c - a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 8 +--R tan(c - a) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 3 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 3 2 +--R (16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 10cos(b x + a) + 12cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) + 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R (- 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 10cos(b x + a) - 12cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) - 2 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 4 +--R 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 +--R (- 18cos(b x + a) - 8cos(b x + a) - 8cos(b x + a) + 2) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 2 +--R 2cos(b x + a) + 2cos(b x + a) - 2cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R - 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 +--R (18cos(b x + a) + 8cos(b x + a) + 8cos(b x + a) - 2) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 2 +--R - 2cos(b x + a) - 2cos(b x + a) + 2cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 +--R (8cos(b x + a) - 8cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 2cos(b x + a) + 12cos(b x + a) + 12cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (- 8cos(b x + a) + 8cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R 2cos(b x + a) - 12cos(b x + a) - 12cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 4 +--R 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R (- 18cos(b x + a) - 16cos(b x + a) + 12cos(b x + a) ) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 3 +--R - 4cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R - 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R (18cos(b x + a) + 16cos(b x + a) - 12cos(b x + a) ) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 +--R 4cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 3 +--R - 16cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R (12cos(b x + a) + 10cos(b x + a) - 4cos(b x + a) ) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 3 +--R 16cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R (- 12cos(b x + a) - 10cos(b x + a) + 4cos(b x + a) ) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 2 +--R 10cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 +--R (- 2cos(b x + a) - 2cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 2 +--R - 10cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 +--R (2cos(b x + a) + 2cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R tan(c - a) +--R + +--R 5 2 +--R - 2cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 5 +--R 2cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R tan(b x + c) +--R + +--R 5 4 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a)sin(b x + c) +--R + +--R 5 4 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 8 +--R tan(c - a) +--R + +--R 4 3 +--R 10cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 +--R - 10cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 7 +--R tan(c - a) +--R + +--R 3 2 +--R 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 8cos(c - a)cos(b x + a) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R - 12cos(c - a)cos(b x + a) - 10cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R - 16cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 8cos(c - a)cos(b x + a) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R 12cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 12cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 4 +--R 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R - 18cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R - 8cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R - 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R 18cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 8cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 +--R (8cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R - 2cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 +--R (- 8cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a)) +--R * +--R 3 +--R sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 4 +--R 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R - 18cos(c - a)cos(b x + a) - 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R - 8cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 4 3 +--R 18cos(c - a)cos(b x + a) + 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) +--R * +--R 2 +--R sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 3 +--R - 16cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R 12cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 3 +--R 16cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 5 4 +--R - 12cos(c - a)cos(b x + a) - 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R 4cos(c - a)cos(b x + a) +--R * +--R sec(b x + c)sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 2 +--R 10cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R (- 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) ) +--R * +--R sec(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 2 +--R - 10cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R + +--R 6 5 +--R (2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) )sec(b x + c) +--R * +--R tan(c - a) +--R + +--R 5 2 +--R - 2cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a)sin(b x + c) +--R + +--R 5 +--R 2cos(c - a)cos(b x + a) sec(b x + c)sin(b x + a) +--R * +--R tan(b x + c) +--R + +--R 4 3 2 +--R - 3cos(b x + a) + cos(b x + a) + 7cos(b x + a) +--R + +--R cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R cos(b x + a) + cos(b x + a) - 2cos(b x + a) +--R + +--R 2 +--R - 2cos(b x + a) + cos(b x + a) + 1 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 +--R - 3cos(b x + a) - 3cos(b x + a) + 6cos(b x + a) +--R + +--R 3 2 +--R 6cos(b x + a) - 3cos(b x + a) - 3cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R 3cos(b x + a) - cos(b x + a) - 7cos(b x + a) - cos(b x + a) +--R + +--R 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - cos(b x + a) - cos(b x + a) + 2cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) - cos(b x + a) - 1 +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R 3cos(b x + a) + 3cos(b x + a) - 6cos(b x + a) +--R + +--R 2 +--R - 6cos(b x + a) + 3cos(b x + a) + 3 +--R * +--R cos(b x + c) +--R * +--R sin(c - a)sin(b x + a) +--R + +--R 6 5 4 3 +--R 3cos(b x + a) + 3cos(b x + a) - 6cos(b x + a) - 6cos(b x + a) +--R + +--R 2 +--R 3cos(b x + a) + 3cos(b x + a) +--R * +--R 8 +--R tan(c - a) +--R + +--R 3 2 +--R (- 12cos(b x + a) - cos(b x + a) + 10cos(b x + a) + 1) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R 5cos(b x + a) + 4cos(b x + a) - 6cos(b x + a) +--R + +--R - 4cos(b x + a) + 1 +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 19cos(b x + a) + 8cos(b x + a) +--R + +--R 2 +--R 18cos(b x + a) - 3 +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R - cos(b x + a) - cos(b x + a) + 2cos(b x + a) +--R + +--R 3 2 +--R 2cos(b x + a) - cos(b x + a) - cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 3 +--R (12cos(b x + a) + cos(b x + a) - 10cos(b x + a) - 1)sin(b x + a) +--R + +--R 4 3 2 +--R - 5cos(b x + a) - 4cos(b x + a) + 6cos(b x + a) +--R + +--R 4cos(b x + a) - 1 +--R * +--R sec(b x + c) +--R + +--R 4 3 2 +--R 15cos(b x + a) + 12cos(b x + a) - 18cos(b x + a) +--R + +--R - 12cos(b x + a) + 3 +--R * +--R cos(b x + c) +--R * +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 19cos(b x + a) - 8cos(b x + a) +--R + +--R 2 +--R - 18cos(b x + a) + 3 +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R cos(b x + a) + cos(b x + a) - 2cos(b x + a) +--R + +--R 3 2 +--R - 2cos(b x + a) + cos(b x + a) + cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R - 3cos(b x + a) - 3cos(b x + a) + 6cos(b x + a) +--R + +--R 3 2 +--R 6cos(b x + a) - 3cos(b x + a) - 3cos(b x + a) +--R * +--R cos(b x + c) +--R * +--R sin(c - a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 2 4 +--R (- 12cos(b x + a) - 4cos(b x + a) - 2)sin(b x + a) +--R + +--R 3 2 +--R (8cos(b x + a) + 4cos(b x + a) - 4cos(b x + a))sec(b x + c) +--R * +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R - 9cos(b x + a) - 24cos(b x + a) + 4cos(b x + a) +--R + +--R 15cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 6cos(b x + a) - 5cos(b x + a) + 6cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) + 1 +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 4 3 +--R 3cos(b x + a) + 6cos(b x + a) + 3cos(b x + a) - cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) - 3cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R (12cos(b x + a) + 4cos(b x + a) + 2)sin(b x + a) +--R + +--R 3 2 +--R (- 8cos(b x + a) - 4cos(b x + a) + 4cos(b x + a))sec(b x + c) +--R + +--R 3 2 +--R (24cos(b x + a) + 12cos(b x + a) - 12cos(b x + a))cos(b x + c) +--R * +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R 9cos(b x + a) + 24cos(b x + a) - 4cos(b x + a) +--R + +--R - 15cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R 6cos(b x + a) + 5cos(b x + a) - 6cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) - 1 +--R * +--R sec(b x + c) +--R + +--R 5 4 3 +--R - 18cos(b x + a) - 15cos(b x + a) + 18cos(b x + a) +--R + +--R 2 +--R 12cos(b x + a) + 3 +--R * +--R cos(b x + c) +--R * +--R sin(c - a)sin(b x + a) +--R + +--R 6 5 4 3 +--R - 3cos(b x + a) - 6cos(b x + a) - 3cos(b x + a) + cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) + 3cos(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 5 +--R - 2sin(b x + a) +--R + +--R 2 4 +--R 4cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 2 3 +--R (- 6cos(b x + a) + 14cos(b x + a) + 3)sin(b x + a) +--R + +--R 4 3 +--R (- 9cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) + 1) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R - 2cos(b x + a) + 4cos(b x + a) + 9cos(b x + a) +--R + +--R - 2cos(b x + a) - 3 +--R * +--R sin(b x + a) +--R + +--R 6 5 2 +--R (cos(b x + a) + cos(b x + a) - cos(b x + a) - cos(b x + a)) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 5 +--R 2sin(b x + a) +--R + +--R 2 2 +--R (- 4cos(b x + a) sec(b x + c) + 12cos(b x + a) cos(b x + c)) +--R * +--R 4 +--R sin(c - a)sin(b x + a) +--R + +--R 2 3 +--R (6cos(b x + a) - 14cos(b x + a) - 3)sin(b x + a) +--R + +--R 4 3 +--R (9cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) - 1)sec(b x + c) +--R + +--R 4 3 +--R (- 27cos(b x + a) - 12cos(b x + a) - 12cos(b x + a) + 3) +--R * +--R cos(b x + c) +--R * +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R 2cos(b x + a) - 4cos(b x + a) - 9cos(b x + a) + 2cos(b x + a) +--R + +--R 3 +--R * +--R sin(b x + a) +--R + +--R 6 5 2 +--R - cos(b x + a) - cos(b x + a) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 2 +--R 3cos(b x + a) + 3cos(b x + a) - 3cos(b x + a) +--R + +--R - 3cos(b x + a) +--R * +--R cos(b x + c) +--R * +--R sin(c - a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 4 +--R (- 12cos(b x + a) - 2)sin(b x + a) +--R + +--R 2 +--R (4cos(b x + a) - 4cos(b x + a))sec(b x + c)sin(c - a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 9cos(b x + a) - 21cos(b x + a) - 7cos(b x + a) +--R + +--R 12cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - cos(b x + a) + 6cos(b x + a) + 6cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 6 5 3 2 +--R 3cos(b x + a) + 9cos(b x + a) - 7cos(b x + a) - cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R (12cos(b x + a) + 2)sin(b x + a) +--R + +--R 2 +--R (- 4cos(b x + a) + 4cos(b x + a))sec(b x + c) +--R + +--R 2 +--R (12cos(b x + a) - 12cos(b x + a))cos(b x + c) +--R * +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R 9cos(b x + a) + 21cos(b x + a) + 7cos(b x + a) +--R + +--R - 12cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 4 3 2 +--R cos(b x + a) - 6cos(b x + a) - 6cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 4 3 2 +--R - 3cos(b x + a) + 18cos(b x + a) + 18cos(b x + a) +--R + +--R - 3cos(b x + a) +--R * +--R cos(b x + c) +--R * +--R sin(c - a)sin(b x + a) +--R + +--R 6 5 3 2 +--R - 3cos(b x + a) - 9cos(b x + a) + 7cos(b x + a) + cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 5 +--R - 2sin(b x + a) +--R + +--R 2 4 +--R 4cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 3 2 +--R (12cos(b x + a) - 9cos(b x + a) + 4cos(b x + a) + 2) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R (- 9cos(b x + a) - 8cos(b x + a) + 6cos(b x + a) ) +--R * +--R 2 +--R sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 19cos(b x + a) - 2cos(b x + a) +--R + +--R 2 +--R - 9cos(b x + a) - 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R cos(b x + a) + cos(b x + a) - 2cos(b x + a) +--R + +--R 3 +--R - 2cos(b x + a) +--R * +--R sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 5 +--R 2sin(b x + a) +--R + +--R 2 2 +--R (- 4cos(b x + a) sec(b x + c) + 12cos(b x + a) cos(b x + c)) +--R * +--R 4 +--R sin(c - a)sin(b x + a) +--R + +--R 3 2 3 +--R (- 12cos(b x + a) + 9cos(b x + a) - 4cos(b x + a) - 2)sin(b x + a) +--R + +--R 4 3 2 +--R (9cos(b x + a) + 8cos(b x + a) - 6cos(b x + a) )sec(b x + c) +--R + +--R 4 3 2 +--R (- 27cos(b x + a) - 24cos(b x + a) + 18cos(b x + a) )cos(b x + c) +--R * +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 19cos(b x + a) + 2cos(b x + a) +--R + +--R 2 +--R 9cos(b x + a) + 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R - cos(b x + a) - cos(b x + a) + 2cos(b x + a) +--R + +--R 3 +--R 2cos(b x + a) +--R * +--R sec(b x + c) +--R + +--R 6 5 4 +--R 3cos(b x + a) + 3cos(b x + a) - 6cos(b x + a) +--R + +--R 3 +--R - 6cos(b x + a) +--R * +--R cos(b x + c) +--R * +--R sin(c - a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 4 +--R 4cos(b x + a)sin(b x + a) +--R + +--R 3 3 +--R - 8cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R - 3cos(b x + a) + 6cos(b x + a) - 4cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R (6cos(b x + a) + 5cos(b x + a) - 2cos(b x + a) )sec(b x + c) +--R * +--R sin(c - a)sin(b x + a) +--R + +--R 6 4 +--R - 3cos(b x + a) + 3cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 +--R - 4cos(b x + a)sin(b x + a) +--R + +--R 3 3 +--R (8cos(b x + a) sec(b x + c) - 24cos(b x + a) cos(b x + c)) +--R * +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 4 3 2 +--R (3cos(b x + a) - 6cos(b x + a) + 4cos(b x + a) + 2cos(b x + a)) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R (- 6cos(b x + a) - 5cos(b x + a) + 2cos(b x + a) )sec(b x + c) +--R + +--R 5 4 3 +--R (18cos(b x + a) + 15cos(b x + a) - 6cos(b x + a) )cos(b x + c) +--R * +--R sin(c - a)sin(b x + a) +--R + +--R 6 4 +--R 3cos(b x + a) - 3cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 3 +--R - 4cos(b x + a) sin(b x + a) +--R + +--R 4 2 +--R 5cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R + +--R 4 3 +--R (2cos(b x + a) + 2cos(b x + a) )sin(b x + a) +--R + +--R 6 5 +--R (- cos(b x + a) - cos(b x + a) )sec(b x + c)sin(c - a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 +--R 4cos(b x + a) sin(b x + a) +--R + +--R 4 4 +--R (- 5cos(b x + a) sec(b x + c) + 15cos(b x + a) cos(b x + c)) +--R * +--R 2 +--R sin(c - a)sin(b x + a) +--R + +--R 4 3 +--R (- 2cos(b x + a) - 2cos(b x + a) )sin(b x + a) +--R + +--R 6 5 +--R (cos(b x + a) + cos(b x + a) )sec(b x + c) +--R + +--R 6 5 +--R (- 3cos(b x + a) - 3cos(b x + a) )cos(b x + c) +--R * +--R sin(c - a) +--R * +--R tan(c - a) +--R + +--R 3 2 +--R 2cos(b x + a) sin(b x + a) +--R + +--R 5 +--R - cos(b x + a) sec(b x + c)sin(c - a)sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 +--R - 2cos(b x + a) sin(b x + a) +--R + +--R 5 5 +--R (cos(b x + a) sec(b x + c) - 3cos(b x + a) cos(b x + c))sin(c - a) +--R * +--R sin(b x + a) +--R / +--R 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a)sin(b x + c) +--R + +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) + 2cos(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 3 2 +--R (16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a)) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 14cos(b x + a) - 10cos(b x + a) + 16cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) - 2cos(b x + a) + 2 +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 3 +--R (- 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a))sin(b x + a) +--R + +--R 5 4 3 +--R 14cos(b x + a) + 10cos(b x + a) - 16cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) + 2cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 4 +--R 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 +--R - 28cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R - 8cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 +--R 4cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R - 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 +--R 28cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R 8cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 +--R - 4cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 2cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 2 3 +--R (- 16cos(b x + a) + 8cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R 14cos(b x + a) - 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 12cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 3 +--R (16cos(b x + a) - 8cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 +--R - 14cos(b x + a) + 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R - 12cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 4 3 2 +--R (10cos(b x + a) - 16cos(b x + a) )sin(b x + a) +--R + +--R 6 5 3 +--R - 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R (- 10cos(b x + a) + 16cos(b x + a) )sin(b x + a) +--R + +--R 6 5 3 +--R 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 5 4 2 +--R (- 2cos(b x + a) + 10cos(b x + a) )sin(b x + a)sin(b x + c) +--R + +--R 5 4 +--R (2cos(b x + a) - 10cos(b x + a) )sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 5 2 5 +--R - 2cos(b x + a) sin(b x + c) + 2cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a)sin(b x + c) +--R + +--R 5 4 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R + +--R 2cos(b x + a) + 2 +--R * +--R sin(b x + a) +--R * +--R 8 +--R tan(c - a) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 3 2 3 +--R (- 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a))sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 10cos(b x + a) - 12cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 2 3 +--R (16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a))sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 10cos(b x + a) + 12cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) + 2 +--R * +--R sin(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 4 +--R - 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 +--R (18cos(b x + a) + 8cos(b x + a) + 8cos(b x + a) - 2) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 2 +--R - 2cos(b x + a) - 2cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 +--R (- 18cos(b x + a) - 8cos(b x + a) - 8cos(b x + a) + 2)sin(b x + a) +--R + +--R 6 5 2 +--R 2cos(b x + a) + 2cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 3 +--R (- 8cos(b x + a) + 8cos(b x + a))sin(b x + a) +--R + +--R 4 3 2 +--R 2cos(b x + a) - 12cos(b x + a) - 12cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 3 +--R (8cos(b x + a) - 8cos(b x + a))sin(b x + a) +--R + +--R 4 3 2 +--R - 2cos(b x + a) + 12cos(b x + a) + 12cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 4 +--R - 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 +--R (18cos(b x + a) + 16cos(b x + a) - 12cos(b x + a) ) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 2 4 +--R 8cos(b x + a) sin(b x + a) +--R + +--R 4 3 2 2 +--R (- 18cos(b x + a) - 16cos(b x + a) + 12cos(b x + a) )sin(b x + a) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 3 +--R 16cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 +--R (- 12cos(b x + a) - 10cos(b x + a) + 4cos(b x + a) )sin(b x + a) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 3 +--R - 16cos(b x + a) sin(b x + a) +--R + +--R 5 4 3 +--R (12cos(b x + a) + 10cos(b x + a) - 4cos(b x + a) )sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 2 6 5 +--R (- 10cos(b x + a) sin(b x + a) + 2cos(b x + a) + 2cos(b x + a) ) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 4 2 6 5 +--R 10cos(b x + a) sin(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 5 2 5 +--R 2cos(b x + a) sin(b x + a)sin(b x + c) - 2cos(b x + a) sin(b x + a) +--R Type: Expression(Integer) +--E 497 + +--S 498 of 532 +t0793:= cos(a+b*x)*cot(c+b*x) +--R +--R +--R (467) cos(b x + a)cot(b x + c) +--R Type: Expression(Integer) +--E 498 + +--S 499 of 532 +r0793:= -(atanh(cos(c+b*x))*cos(a-c)-cos(a+b*x))/b +--R +--R +--R - cos(c - a)atanh(cos(b x + c)) + cos(b x + a) +--R (468) ---------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 499 + +--S 500 of 532 +a0793:= integrate(t0793,x) +--R +--R +--R (469) +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R - sin(b x + a)tan(c - a) + (cos(b x + a) + 1)tan(c - a) +--R + +--R - sin(b x + a)tan(c - a) + cos(b x + a) + 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R +---------------+ +--R | 2 +--R cos(b x + a)\|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R b\|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 500 + +--S 501 of 532 +m0793:= a0793-r0793 +--R +--R +--R (470) +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R - sin(b x + a)tan(c - a) + (cos(b x + a) + 1)tan(c - a) +--R + +--R - sin(b x + a)tan(c - a) + cos(b x + a) + 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R +---------------+ +--R | 2 +--R cos(c - a)atanh(cos(b x + c))\|tan(c - a) + 1 +--R / +--R +---------------+ +--R | 2 +--R b\|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 501 + +--S 502 of 532 +d0793:= D(m0793,x) +--R +--R +--R (471) +--R 3 +--R cos(c - a)cos(b x + a)sin(b x + c)tan(c - a) +--R + +--R (- cos(c - a)cos(b x + a) + cos(c - a))sin(b x + a)sin(b x + c) +--R + +--R 2 2 2 2 +--R (cos(b x + c) - 1)sin(b x + a) + cos(b x + a) cos(b x + c) +--R + +--R 2 +--R - cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 2 +--R - cos(c - a)sin(b x + a) + cos(c - a)cos(b x + a) +--R + +--R cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 +--R (- cos(b x + c) + 1)sin(b x + a) +--R * +--R tan(c - a) +--R + +--R (cos(c - a)cos(b x + a) + cos(c - a))sin(b x + a)sin(b x + c) +--R + +--R 2 2 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 2 2 +--R (cos(b x + a) + cos(b x + a))cos(b x + c) - cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 4 +--R cos(c - a)cos(b x + a)sin(b x + a)sin(b x + c)tan(c - a) +--R + +--R 2 2 +--R cos(c - a)sin(b x + a) - cos(c - a)cos(b x + a) +--R + +--R - cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 +--R (cos(b x + c) - 1)sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R - cos(c - a)sin(b x + a)sin(b x + c) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 2 +--R cos(c - a)sin(b x + a) - cos(c - a)cos(b x + a) +--R + +--R - cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 +--R (cos(b x + c) - 1)sin(b x + a) +--R * +--R tan(c - a) +--R + +--R (- cos(c - a)cos(b x + a) - cos(c - a))sin(b x + a)sin(b x + c) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R cos(b x + a) +--R / +--R 2 3 +--R (cos(b x + a)cos(b x + c) - cos(b x + a))tan(c - a) +--R + +--R 2 +--R ((- cos(b x + a) + 1)cos(b x + c) + cos(b x + a) - 1)sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 2 +--R (cos(b x + a) + cos(b x + a))cos(b x + c) - cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R ((cos(b x + a) + 1)cos(b x + c) - cos(b x + a) - 1)sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 4 +--R (cos(b x + a)cos(b x + c) - cos(b x + a))sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 +--R (- cos(b x + c) + 1)sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R ((- cos(b x + a) - 1)cos(b x + c) + cos(b x + a) + 1)sin(b x + a) +--R Type: Expression(Integer) +--E 502 + +--S 503 of 532 +t0794:= cos(a+b*x)*cot(c+b*x)^2 +--R +--R +--R 2 +--R (472) cos(b x + a)cot(b x + c) +--R Type: Expression(Integer) +--E 503 + +--S 504 of 532 +r0794:= -cos(a-c)*csc(c+b*x)/b+atanh(cos(c+b*x))*sin(a-c)/b-sin(a+b*x)/b +--R +--R +--R (473) +--R - sin(c - a)atanh(cos(b x + c)) - sin(b x + a) - cos(c - a)csc(b x + c) +--R ----------------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 504 + +--S 505 of 532 +a0794:= integrate(t0794,x) +--R +--R +--R (474) +--R 3 2 +--R (cos(b x + a)tan(c - a) + sin(b x + a)tan(c - a) ) +--R * +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R - sin(b x + a)tan(c - a) + (cos(b x + a) + 1)tan(c - a) +--R + +--R - sin(b x + a)tan(c - a) + cos(b x + a) + 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R 2 +--R - cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 +--R (cos(b x + a) - cos(b x + a) - 2)tan(c - a) - sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R +---------------+ +--R 2 | 2 +--R (b cos(b x + a)tan(c - a) + b sin(b x + a)tan(c - a))\|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 532 +m0794:= a0794-r0794 +--R +--R +--R (475) +--R 3 2 +--R (cos(b x + a)tan(c - a) + sin(b x + a)tan(c - a) ) +--R * +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R - sin(b x + a)tan(c - a) + (cos(b x + a) + 1)tan(c - a) +--R + +--R - sin(b x + a)tan(c - a) + cos(b x + a) + 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R 2 +--R cos(b x + a)sin(c - a)tan(c - a) +--R + +--R sin(c - a)sin(b x + a)tan(c - a) +--R * +--R atanh(cos(b x + c)) +--R + +--R 2 +--R cos(c - a)cos(b x + a)csc(b x + c)tan(c - a) +--R + +--R 2 +--R sin(b x + a) + cos(c - a)csc(b x + c)sin(b x + a) +--R + +--R 2 +--R cos(b x + a) - cos(b x + a) - 2 +--R * +--R tan(c - a) +--R + +--R - sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R +---------------+ +--R 2 | 2 +--R (b cos(b x + a)tan(c - a) + b sin(b x + a)tan(c - a))\|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 506 + +--S 507 of 532 +d0794:= D(m0794,x) +--R +--R +--R (476) +--R 2 +--R cos(b x + a) sin(c - a)sin(b x + c) +--R + +--R 2 2 +--R (cos(b x + a)cos(b x + c) - cos(b x + a))sin(b x + a) +--R + +--R 2 2 +--R - cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 2 +--R cos(c - a)cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 3 2 3 +--R cos(b x + a) cos(b x + c) - cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 +--R (- cos(b x + a) + 2cos(b x + a))sin(c - a)sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 3 +--R (2cos(b x + c) - 2)sin(b x + a) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 2 +--R - cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 2 2 +--R (2cos(b x + a) - cos(b x + a) - 2)cos(b x + c) +--R + +--R 2 +--R - 2cos(b x + a) + cos(b x + a) + 2 +--R * +--R sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 +--R (- 2cos(b x + a) + 1)sin(c - a)sin(b x + a) +--R + +--R 3 2 +--R (cos(b x + a) + cos(b x + a) )sin(c - a) +--R * +--R sin(b x + c) +--R + +--R 2 4 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 +--R (2cos(c - a)cos(b x + a) - cos(c - a))cos(b x + c) +--R + +--R - 2cos(c - a)cos(b x + a) + cos(c - a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 2 2 2 +--R (- cos(b x + a) + 1)cos(b x + c) + cos(b x + a) - 1 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 +--R (- cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 2 2 2 +--R (cos(b x + a) + 2cos(b x + a))cos(b x + c) - cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 3 +--R - sin(c - a)sin(b x + a) +--R + +--R 2 +--R (2cos(b x + a) + 2cos(b x + a))sin(c - a)sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 +--R (cos(c - a)cos(b x + c) - cos(c - a))cot(b x + c) +--R * +--R csc(b x + c) +--R + +--R 2 +--R (2cos(b x + a) + 2)cos(b x + c) - 2cos(b x + a) - 2 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 2 +--R (- 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 3 2 +--R (2cos(b x + a) + 2cos(b x + a) - 3cos(b x + a) - 2) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R - 2cos(b x + a) - 2cos(b x + a) + 3cos(b x + a) + 2 +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R (cos(b x + a) + 1)sin(c - a)sin(b x + a) sin(b x + c) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) - cos(c - a))cos(b x + c) +--R + +--R cos(c - a)cos(b x + a) + cos(c - a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 2 2 2 +--R (- cos(b x + a) - cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 4 3 2 +--R (- cos(b x + a) - cos(b x + a) + 2cos(b x + a) + 2cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R cos(b x + a) + cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 +--R cos(b x + a) sin(c - a)sin(b x + a)sin(b x + c) +--R + +--R 2 2 +--R - cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 2 +--R cos(c - a)cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 2 +--R cos(b x + a)cos(b x + c) - cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 +--R 2cos(b x + a)sin(c - a)sin(b x + a) +--R + +--R 3 2 +--R (- cos(b x + a) - cos(b x + a) )sin(c - a) +--R * +--R sin(b x + c) +--R + +--R 2 4 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a)cos(b x + c) +--R + +--R 2cos(c - a)cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 2 2 2 +--R (cos(b x + a) - cos(b x + a) - 1)cos(b x + c) - cos(b x + a) +--R + +--R cos(b x + a) + 1 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 2 +--R (cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) )cos(b x + c) +--R + +--R 3 2 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 3 2 2 3 +--R (- cos(b x + a) - cos(b x + a) )cos(b x + c) + cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- cos(b x + a) - 2cos(b x + a))sin(c - a)sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 +--R (- cos(c - a)cos(b x + c) + cos(c - a))cot(b x + c)csc(b x + c) +--R + +--R 2 +--R (- 2cos(b x + a) - 2)cos(b x + c) + 2cos(b x + a) + 2 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 2 +--R - cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 3 2 +--R (- 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 2) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 +--R (cos(b x + a) - 1)sin(c - a)sin(b x + a) +--R + +--R 3 2 +--R (- cos(b x + a) - cos(b x + a) )sin(c - a) +--R * +--R sin(b x + c) +--R + +--R 2 4 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) + cos(c - a))cos(b x + c) +--R + +--R cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 2 2 2 +--R (2cos(b x + a) - 1)cos(b x + c) - 2cos(b x + a) + 1 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 2 +--R (cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) )cos(b x + c) +--R + +--R 3 2 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 4 2 2 +--R (cos(b x + a) - 3cos(b x + a) - 2cos(b x + a))cos(b x + c) +--R + +--R 4 2 +--R - cos(b x + a) + 3cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 3 +--R sin(c - a)sin(b x + a) +--R + +--R 2 +--R (- 2cos(b x + a) - 2cos(b x + a))sin(c - a)sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 +--R (- cos(c - a)cos(b x + c) + cos(c - a))cot(b x + c)csc(b x + c) +--R + +--R 2 +--R (- 2cos(b x + a) - 2)cos(b x + c) + 2cos(b x + a) + 2 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 2 +--R (2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 3 2 +--R (- 2cos(b x + a) - 2cos(b x + a) + 3cos(b x + a) + 2) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 3cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 +--R (- cos(b x + a) - 1)sin(c - a)sin(b x + a) sin(b x + c) +--R + +--R 2 +--R (cos(c - a)cos(b x + a) + cos(c - a))cos(b x + c) +--R + +--R - cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R cot(b x + c)csc(b x + c) +--R + +--R 2 2 2 +--R (cos(b x + a) + cos(b x + a))cos(b x + c) - cos(b x + a) +--R + +--R - cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 4 3 2 +--R (cos(b x + a) + cos(b x + a) - 2cos(b x + a) - 2cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R - cos(b x + a) - cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R / +--R 2 2 2 4 +--R (cos(b x + a) cos(b x + c) - cos(b x + a) )tan(c - a) +--R + +--R 2 2 2 +--R (- cos(b x + a) + 2cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 3 +--R sin(b x + a)tan(c - a) +--R + +--R 2 +--R ((- 2cos(b x + a) + 1)cos(b x + c) + 2cos(b x + a) - 1) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 3 2 2 3 +--R (cos(b x + a) + cos(b x + a) )cos(b x + c) - cos(b x + a) +--R + +--R 2 +--R - cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 3 +--R (- cos(b x + c) + 1)sin(b x + a) +--R + +--R 2 2 +--R (2cos(b x + a) + 2cos(b x + a))cos(b x + c) +--R + +--R 2 +--R - 2cos(b x + a) - 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 +--R ((cos(b x + a) + 1)cos(b x + c) - cos(b x + a) - 1)sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 2 2 2 5 +--R (cos(b x + a) cos(b x + c) - cos(b x + a) )sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (2cos(b x + a)cos(b x + c) - 2cos(b x + a))sin(b x + a) +--R + +--R 3 2 2 3 +--R (- cos(b x + a) - cos(b x + a) )cos(b x + c) + cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 3 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- cos(b x + a) - 2cos(b x + a))cos(b x + c) + cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 2 2 +--R ((cos(b x + a) - 1)cos(b x + c) - cos(b x + a) + 1)sin(b x + a) +--R + +--R 3 2 2 3 +--R (- cos(b x + a) - cos(b x + a) )cos(b x + c) + cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 3 +--R (cos(b x + c) - 1)sin(b x + a) +--R + +--R 2 2 2 +--R (- 2cos(b x + a) - 2cos(b x + a))cos(b x + c) + 2cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R tan(c - a) +--R + +--R 2 2 +--R ((- cos(b x + a) - 1)cos(b x + c) + cos(b x + a) + 1)sin(b x + a) +--R Type: Expression(Integer) +--E 507 + +--S 508 of 532 +t0795:= cos(a+b*x)*cot(c+b*x)^3 +--R +--R +--R 3 +--R (477) cos(b x + a)cot(b x + c) +--R Type: Expression(Integer) +--E 508 + +--S 509 of 532 +r0795:= 3/2*atanh(cos(c+b*x))*cos(a-c)/b-cos(a+b*x)/b-_ + 1/2*cos(a-c)*cot(c+b*x)*csc(c+b*x)/b+csc(c+b*x)*sin(a-c)/b +--R +--R +--R (478) +--R 3cos(c - a)atanh(cos(b x + c)) - 2csc(b x + c)sin(c - a) +--R + +--R - cos(c - a)cot(b x + c)csc(b x + c) - 2cos(b x + a) +--R / +--R 2b +--R Type: Expression(Integer) +--E 509 + +--S 510 of 532 +a0795:= integrate(t0795,x) +--R +--R +--R (479) +--R 2 4 3 +--R 3cos(b x + a) tan(c - a) + 6cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (- 3cos(b x + a) + 3)tan(c - a) +--R * +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R sin(b x + a)tan(c - a) + (- cos(b x + a) - 1)tan(c - a) +--R + +--R sin(b x + a)tan(c - a) - cos(b x + a) - 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R 3 2 4 +--R (- 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a))tan(c - a) +--R + +--R 2 3 +--R (- 4cos(b x + a) - 8cos(b x + a) - 1)sin(b x + a)tan(c - a) +--R + +--R 3 2 2 +--R (2cos(b x + a) + 3cos(b x + a) - 3cos(b x + a) - 4)tan(c - a) +--R + +--R 2 +--R - 2cos(b x + a)sin(b x + a)tan(c - a) + cos(b x + a) - 1 +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R 2 4 3 +--R 2b cos(b x + a) tan(c - a) + 4b cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (- 2b cos(b x + a) + 2b)tan(c - a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R Type: Union(Expression(Integer),...) +--E 510 + +--S 511 of 532 +m0795:= a0795-r0795 +--R +--R +--R (480) +--R 2 4 3 +--R 3cos(b x + a) tan(c - a) + 6cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (- 3cos(b x + a) + 3)tan(c - a) +--R * +--R log +--R 2 +--R (- tan(c - a) + sin(b x + a)tan(c - a) - cos(b x + a) - 1) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 3 2 +--R sin(b x + a)tan(c - a) + (- cos(b x + a) - 1)tan(c - a) +--R + +--R sin(b x + a)tan(c - a) - cos(b x + a) - 1 +--R / +--R cos(b x + a)tan(c - a) + sin(b x + a) +--R + +--R 2 4 +--R - 3cos(c - a)cos(b x + a) tan(c - a) +--R + +--R 3 +--R - 6cos(c - a)cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (3cos(c - a)cos(b x + a) - 3cos(c - a))tan(c - a) +--R * +--R atanh(cos(b x + c)) +--R + +--R 2 +--R 2cos(b x + a) csc(b x + c)sin(c - a) +--R + +--R 2 2 +--R cos(c - a)cos(b x + a) cot(b x + c)csc(b x + c) - 4cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 4cos(b x + a)csc(b x + c)sin(c - a) +--R + +--R 2cos(c - a)cos(b x + a)cot(b x + c)csc(b x + c) - 8cos(b x + a) - 1 +--R * +--R 3 +--R sin(b x + a)tan(c - a) +--R + +--R 2 +--R (- 2cos(b x + a) + 2)csc(b x + c)sin(c - a) +--R + +--R 2 +--R (- cos(c - a)cos(b x + a) + cos(c - a))cot(b x + c)csc(b x + c) +--R + +--R 2 +--R 3cos(b x + a) - cos(b x + a) - 4 +--R * +--R 2 +--R tan(c - a) +--R + +--R 2 +--R - 2cos(b x + a)sin(b x + a)tan(c - a) + cos(b x + a) - 1 +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R / +--R 2 4 3 +--R 2b cos(b x + a) tan(c - a) + 4b cos(b x + a)sin(b x + a)tan(c - a) +--R + +--R 2 2 +--R (- 2b cos(b x + a) + 2b)tan(c - a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R Type: Expression(Integer) +--E 511 + +--S 512 of 532 +d0795:= D(m0795,x) +--R +--R +--R (481) +--R 5 +--R - 3cos(c - a)cos(b x + a) sin(b x + c) +--R + +--R 3 2 3 +--R (- 2cos(b x + a) cos(b x + c) + 2cos(b x + a) )sin(b x + a) +--R + +--R 5 2 5 +--R (- 2cos(b x + a) cos(b x + c) + 2cos(b x + a) )cot(b x + c) +--R * +--R csc(b x + c)sin(c - a) +--R + +--R 5 2 +--R - 2cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 5 +--R 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 5 2 +--R - cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 5 +--R cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 7 +--R tan(c - a) +--R + +--R 5 4 +--R (3cos(c - a)cos(b x + a) - 15cos(c - a)cos(b x + a) ) +--R * +--R sin(b x + a)sin(b x + c) +--R + +--R 4 3 2 +--R (- 3cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 3cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 2 +--R (2cos(b x + a) - 10cos(b x + a) )cos(b x + c) +--R + +--R 5 4 +--R - 2cos(b x + a) + 10cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 5 +--R 2cos(c - a)cos(b x + a) +--R + +--R 4 +--R - 10cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R - 2cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 5 4 +--R (cos(c - a)cos(b x + a) - 5cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R - cos(c - a)cos(b x + a) + 5cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R sin(b x + a) +--R + +--R 6 4 2 6 +--R (- 3cos(b x + a) + 3cos(b x + a) )cos(b x + c) + 3cos(b x + a) +--R + +--R 4 +--R - 3cos(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 4 3 +--R (15cos(c - a)cos(b x + a) - 24cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R - 3cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 6cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 3 2 +--R (- 12cos(b x + a) + 4cos(b x + a) - 4cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R 12cos(b x + a) - 4cos(b x + a) + 4cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R (10cos(b x + a) - 16cos(b x + a) )cos(b x + c) +--R + +--R 4 3 +--R - 10cos(b x + a) + 16cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 4 +--R 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 16cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R - 10cos(c - a)cos(b x + a) + 16cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 4 3 +--R (5cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R - 5cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 2cos(b x + a) + 2cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 2cos(b x + a) - 2cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 6 5 3 +--R (- 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 3 +--R 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 4cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 +--R 4cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 6 5 +--R - cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 3 +--R 2cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 5 +--R tan(c - a) +--R + +--R 3 2 +--R (24cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) ) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R - 21cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 6cos(c - a)cos(b x + a) - 18cos(c - a)cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 2 +--R (- 12cos(b x + a) + 4cos(b x + a) - 2)cos(b x + c) +--R + +--R 2 +--R 12cos(b x + a) - 4cos(b x + a) + 2 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 3 2 2 +--R (16cos(b x + a) - 8cos(b x + a) )cos(b x + c) +--R + +--R 3 2 +--R - 16cos(b x + a) + 8cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 3 +--R 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R - 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 3 2 +--R (8cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R - 8cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 9cos(b x + a) + 4cos(b x + a) - 7cos(b x + a) +--R + +--R - 2cos(b x + a) + 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 9cos(b x + a) - 4cos(b x + a) + 7cos(b x + a) +--R + +--R 2cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 14cos(b x + a) + 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R - 12cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R 14cos(b x + a) - 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 12cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 5 +--R - 14cos(c - a)cos(b x + a) +--R + +--R 4 +--R 2cos(c - a)cos(b x + a) +--R + +--R 3 +--R 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R 14cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 4cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 5 4 +--R - 7cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 2cos(c - a)cos(b x + a) - 6cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R 7cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 2cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R sin(b x + a) +--R + +--R 6 2 2 6 +--R (3cos(b x + a) - cos(b x + a) )cos(b x + c) - 3cos(b x + a) +--R + +--R 2 +--R cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 4 +--R 12cos(c - a)cos(b x + a) sin(b x + a) +--R + +--R 4 3 +--R - 42cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R 18cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R 6cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R + +--R 4 +--R - 6cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 5 +--R (2cos(b x + c) - 2)sin(b x + a) +--R + +--R 2 2 2 +--R (8cos(b x + a) cos(b x + c) - 8cos(b x + a) )cot(b x + c) +--R * +--R csc(b x + c)sin(c - a) +--R + +--R 2 2 +--R 8cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 2 2 +--R 4cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 2 +--R - 4cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 2 2 +--R (5cos(b x + a) - 14cos(b x + a) - 2)cos(b x + c) +--R + +--R 2 +--R - 5cos(b x + a) + 14cos(b x + a) + 2 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 28cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R - 8cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 28cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R 8cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 4 +--R - 28cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R 28cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 4 +--R - 14cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 4cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R + +--R - 4cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R 14cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 6cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 17cos(b x + a) - 4cos(b x + a) + 9cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 17cos(b x + a) + 4cos(b x + a) - 9cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R 4cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 +--R - 4cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 6 5 +--R 4cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 +--R - 4cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R - 4cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 +--R 4cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 4 +--R - 2cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 4 +--R 2cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 2 +--R - 24cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 12cos(c - a)cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R 21cos(c - a)cos(b x + a) + 15cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 24cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 3cos(c - a)cos(b x + a) - 3cos(c - a) +--R * +--R sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 2 +--R (- 12cos(b x + a) - 4cos(b x + a) - 2)cos(b x + c) +--R + +--R 2 +--R 12cos(b x + a) + 4cos(b x + a) + 2 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 3 2 +--R (- 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R 16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 3 +--R - 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) +--R + +--R 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 3 2 +--R - 8cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 4cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R 8cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - 4cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 9cos(b x + a) - 25cos(b x + a) + 4cos(b x + a) +--R + +--R 14cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 9cos(b x + a) + 25cos(b x + a) - 4cos(b x + a) +--R + +--R - 14cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R 14cos(b x + a) + 10cos(b x + a) - 16cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) + 2cos(b x + a) - 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R - 14cos(b x + a) - 10cos(b x + a) + 16cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) - 2cos(b x + a) + 2 +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 5 +--R 14cos(c - a)cos(b x + a) +--R + +--R 4 +--R 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 +--R - 14cos(c - a)cos(b x + a) +--R + +--R 4 +--R - 10cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 5 4 +--R 7cos(c - a)cos(b x + a) + 5cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 8cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R - 7cos(c - a)cos(b x + a) - 5cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 8cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - cos(c - a)cos(b x + a) + cos(c - a) +--R * +--R csc(b x + c) +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R 3cos(b x + a) + 9cos(b x + a) + 3cos(b x + a) +--R + +--R 3 2 +--R - 7cos(b x + a) - 4cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 +--R - 3cos(b x + a) - 9cos(b x + a) - 3cos(b x + a) +--R + +--R 3 2 +--R 7cos(b x + a) + 4cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 3 +--R 15cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 18cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 3cos(c - a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 6cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 3 2 +--R (12cos(b x + a) + cos(b x + a) - 10cos(b x + a) - 1) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R - 12cos(b x + a) - cos(b x + a) + 10cos(b x + a) + 1 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 4 +--R 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) +--R + +--R - 8cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 +--R - 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 4 3 +--R 5cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 6cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R - 5cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 6cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - cos(c - a) +--R * +--R csc(b x + c) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 19cos(b x + a) - 8cos(b x + a) +--R + +--R 2 +--R - 18cos(b x + a) + 3 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 19cos(b x + a) + 8cos(b x + a) +--R + +--R 2 +--R 18cos(b x + a) - 3 +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 3 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 6 5 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R tan(c - a) +--R + +--R 5 4 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 6cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R + +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a) +--R * +--R sin(b x + a)sin(b x + c) +--R + +--R 4 3 2 +--R - 3cos(b x + a) + cos(b x + a) + 7cos(b x + a) +--R + +--R cos(b x + a) - 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 3cos(b x + a) - cos(b x + a) - 7cos(b x + a) - cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2 +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 5 4 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 5 4 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R - cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R cos(c - a)cos(b x + a) + cos(c - a) +--R * +--R csc(b x + c) +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R - 3cos(b x + a) - 3cos(b x + a) + 6cos(b x + a) +--R + +--R 3 2 +--R 6cos(b x + a) - 3cos(b x + a) - 3cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 3 +--R 3cos(b x + a) + 3cos(b x + a) - 6cos(b x + a) - 6cos(b x + a) +--R + +--R 2 +--R 3cos(b x + a) + 3cos(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 5 +--R 3cos(c - a)cos(b x + a) sin(b x + a)sin(b x + c) +--R + +--R 3 2 3 2 +--R (2cos(b x + a) cos(b x + c) - 2cos(b x + a) )sin(b x + a) +--R + +--R 5 2 5 +--R (2cos(b x + a) cos(b x + c) - 2cos(b x + a) )cot(b x + c) +--R * +--R csc(b x + c)sin(c - a) +--R + +--R 5 2 +--R 2cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 5 +--R - 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 5 2 5 +--R cos(c - a)cos(b x + a) cos(b x + c) - cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R sin(b x + a) +--R * +--R 8 +--R tan(c - a) +--R + +--R 4 2 6 +--R 15cos(c - a)cos(b x + a) sin(b x + a) - 3cos(c - a)cos(b x + a) +--R + +--R 5 +--R - 3cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 2 2 3 +--R (4cos(b x + a) cos(b x + c) - 4cos(b x + a) )sin(b x + a) +--R + +--R 4 2 4 +--R (10cos(b x + a) cos(b x + c) - 10cos(b x + a) )cot(b x + c) +--R * +--R csc(b x + c)sin(c - a) +--R + +--R 4 2 +--R 10cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 4 +--R - 10cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 4 2 +--R 5cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 4 +--R - 5cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 4 3 2 4 +--R (- 2cos(b x + a) - 2cos(b x + a) )cos(b x + c) + 2cos(b x + a) +--R + +--R 3 +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 6 5 2 6 +--R (- 2cos(b x + a) - 2cos(b x + a) )cos(b x + c) + 2cos(b x + a) +--R + +--R 5 +--R 2cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 6 5 +--R (- 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 6 5 +--R (- cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 7 +--R tan(c - a) +--R + +--R 3 3 +--R 24cos(c - a)cos(b x + a) sin(b x + a) +--R + +--R 5 4 +--R - 18cos(c - a)cos(b x + a) - 15cos(c - a)cos(b x + a) +--R + +--R 3 +--R 6cos(c - a)cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 4 +--R (4cos(b x + a)cos(b x + c) - 4cos(b x + a))sin(b x + a) +--R + +--R 3 2 3 +--R (16cos(b x + a) cos(b x + c) - 16cos(b x + a) )cot(b x + c) +--R * +--R csc(b x + c)sin(c - a) +--R + +--R 3 2 +--R 16cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 3 +--R - 16cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 3 2 +--R 8cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 3 +--R - 8cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 3cos(b x + a) + 6cos(b x + a) - 4cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 3cos(b x + a) - 6cos(b x + a) + 4cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R (- 12cos(b x + a) - 10cos(b x + a) + 4cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 10cos(b x + a) - 4cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 5 +--R - 12cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 10cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R 12cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 4cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 5 4 +--R - 6cos(c - a)cos(b x + a) - 5cos(c - a)cos(b x + a) +--R + +--R 3 +--R 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R 6cos(c - a)cos(b x + a) + 5cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 2cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R sin(b x + a) +--R + +--R 6 4 2 6 +--R (- 3cos(b x + a) + 3cos(b x + a) )cos(b x + c) + 3cos(b x + a) +--R + +--R 4 +--R - 3cos(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 4 +--R 12cos(c - a)cos(b x + a) sin(b x + a) +--R + +--R 4 3 +--R - 27cos(c - a)cos(b x + a) - 24cos(c - a)cos(b x + a) +--R + +--R 2 +--R 18cos(c - a)cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R 3cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 6cos(c - a)cos(b x + a) - 6cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 5 +--R (2cos(b x + c) - 2)sin(b x + a) +--R + +--R 2 2 2 +--R (8cos(b x + a) cos(b x + c) - 8cos(b x + a) )cot(b x + c) +--R * +--R csc(b x + c)sin(c - a) +--R + +--R 2 2 +--R 8cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 2 2 +--R 4cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 2 +--R - 4cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 3 2 +--R (- 12cos(b x + a) + 9cos(b x + a) - 4cos(b x + a) - 2) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R 12cos(b x + a) - 9cos(b x + a) + 4cos(b x + a) + 2 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R (- 18cos(b x + a) - 16cos(b x + a) + 12cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 18cos(b x + a) + 16cos(b x + a) - 12cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 4 +--R - 18cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 16cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R 18cos(c - a)cos(b x + a) + 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 4 3 +--R - 9cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 6cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R 9cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 6cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 19cos(b x + a) + 2cos(b x + a) +--R + +--R 2 +--R 9cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 19cos(b x + a) - 2cos(b x + a) +--R + +--R 2 +--R - 9cos(b x + a) - 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 3 +--R - 4cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 +--R (- 12cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a)) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 +--R 3cos(c - a)cos(b x + a) - 18cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 18cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 2 2 +--R ((- 12cos(b x + a) - 2)cos(b x + c) + 12cos(b x + a) + 2) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 2 2 +--R (- 8cos(b x + a) + 8cos(b x + a))cos(b x + c) +--R + +--R 2 +--R 8cos(b x + a) - 8cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 2 +--R (- 8cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 2 +--R 8cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 2 +--R (- 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 2 +--R 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 9cos(b x + a) - 21cos(b x + a) - 7cos(b x + a) +--R + +--R 12cos(b x + a) + 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 9cos(b x + a) + 21cos(b x + a) + 7cos(b x + a) +--R + +--R - 12cos(b x + a) - 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 4 3 2 +--R 2cos(b x + a) - 12cos(b x + a) - 12cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R - 2cos(b x + a) + 12cos(b x + a) + 12cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R - 2cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 4 3 +--R cos(c - a)cos(b x + a) - 6cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 6cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R - cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R + +--R 2 +--R 6cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R sin(b x + a) +--R + +--R 6 5 3 2 +--R (3cos(b x + a) + 9cos(b x + a) - 7cos(b x + a) - cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 3 2 +--R - 3cos(b x + a) - 9cos(b x + a) + 7cos(b x + a) + cos(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 4 +--R 12cos(c - a)cos(b x + a) sin(b x + a) +--R + +--R 4 3 +--R - 27cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R - 12cos(c - a)cos(b x + a) + 3cos(c - a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R 3cos(c - a)cos(b x + a) + 3cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 5 +--R (2cos(b x + c) - 2)sin(b x + a) +--R + +--R 2 2 2 +--R (8cos(b x + a) cos(b x + c) - 8cos(b x + a) )cot(b x + c) +--R * +--R csc(b x + c)sin(c - a) +--R + +--R 2 2 +--R 8cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 2 2 +--R 4cos(c - a)cos(b x + a) cos(b x + c) +--R + +--R 2 +--R - 4cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 4 +--R sin(b x + a) +--R + +--R 2 2 +--R (6cos(b x + a) - 14cos(b x + a) - 3)cos(b x + c) +--R + +--R 2 +--R - 6cos(b x + a) + 14cos(b x + a) + 3 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 +--R (- 18cos(b x + a) - 8cos(b x + a) - 8cos(b x + a) + 2) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R 18cos(b x + a) + 8cos(b x + a) + 8cos(b x + a) - 2 +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 4 +--R - 18cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 8cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R 18cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 8cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 4 3 +--R - 9cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R - 4cos(c - a)cos(b x + a) + cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R 9cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 4cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R csc(b x + c) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 4 3 2 +--R 2cos(b x + a) - 4cos(b x + a) - 9cos(b x + a) +--R + +--R 2cos(b x + a) + 3 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R - 2cos(b x + a) + 4cos(b x + a) + 9cos(b x + a) +--R + +--R - 2cos(b x + a) - 3 +--R * +--R sin(b x + a) +--R + +--R 6 5 2 +--R 2cos(b x + a) + 2cos(b x + a) - 2cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 2 +--R - 2cos(b x + a) - 2cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 2 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 2 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 2 +--R - 24cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 12cos(c - a)cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 +--R 18cos(c - a)cos(b x + a) + 15cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 18cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R - 3cos(c - a) +--R * +--R sin(b x + a) +--R * +--R sin(b x + c) +--R + +--R 2 2 +--R (- 12cos(b x + a) - 4cos(b x + a) - 2)cos(b x + c) +--R + +--R 2 +--R 12cos(b x + a) + 4cos(b x + a) + 2 +--R * +--R 4 +--R sin(b x + a) +--R + +--R 3 2 +--R (- 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R 16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 3 +--R - 16cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R 16cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 8cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 3 2 +--R - 8cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 4cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R 8cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - 4cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 9cos(b x + a) - 24cos(b x + a) + 4cos(b x + a) +--R + +--R 15cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 9cos(b x + a) + 24cos(b x + a) - 4cos(b x + a) - 15cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 10cos(b x + a) - 12cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) - 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 10cos(b x + a) + 12cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) + 2 +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 5 4 +--R 12cos(c - a)cos(b x + a) + 10cos(c - a)cos(b x + a) +--R + +--R 3 +--R - 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 8cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R - 12cos(c - a)cos(b x + a) - 10cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 5 4 +--R 6cos(c - a)cos(b x + a) + 5cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 6cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R - cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R - 6cos(c - a)cos(b x + a) - 5cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 6cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R cos(c - a) +--R * +--R csc(b x + c) +--R * +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R 3cos(b x + a) + 6cos(b x + a) + 3cos(b x + a) - cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) - 3cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 3 +--R - 3cos(b x + a) - 6cos(b x + a) - 3cos(b x + a) + cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) + 3cos(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 3 +--R 15cos(c - a)cos(b x + a) + 12cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 18cos(c - a)cos(b x + a) - 12cos(c - a)cos(b x + a) +--R + +--R 3cos(c - a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 6cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R * +--R sin(b x + c) +--R + +--R 3 2 +--R (12cos(b x + a) + cos(b x + a) - 10cos(b x + a) - 1) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R - 12cos(b x + a) - cos(b x + a) + 10cos(b x + a) + 1 +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 4 3 +--R 10cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 12cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R - 10cos(c - a)cos(b x + a) - 8cos(c - a)cos(b x + a) +--R + +--R 2 +--R 12cos(c - a)cos(b x + a) + 8cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 4 3 +--R 5cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 6cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R - 5cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 6cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R csc(b x + c) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 19cos(b x + a) - 8cos(b x + a) +--R + +--R 2 +--R - 18cos(b x + a) + 3 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 19cos(b x + a) + 8cos(b x + a) +--R + +--R 2 +--R 18cos(b x + a) - 3 +--R * +--R sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) + 2cos(b x + a) +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 6 5 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 6 5 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 4 3 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 2 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R * +--R csc(b x + c) +--R * +--R tan(c - a) +--R + +--R 5 4 +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 6cos(c - a)cos(b x + a) + 6cos(c - a)cos(b x + a) +--R + +--R - 3cos(c - a)cos(b x + a) - 3cos(c - a) +--R * +--R sin(b x + a)sin(b x + c) +--R + +--R 4 3 2 +--R - 3cos(b x + a) + cos(b x + a) + 7cos(b x + a) + cos(b x + a) +--R + +--R - 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 3cos(b x + a) - cos(b x + a) - 7cos(b x + a) - cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R + +--R 2cos(b x + a) + 2 +--R * +--R cot(b x + c)csc(b x + c)sin(c - a) +--R + +--R 5 4 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 4cos(c - a)cos(b x + a) + 4cos(c - a)cos(b x + a) +--R + +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 4cos(c - a)cos(b x + a) - 4cos(c - a)cos(b x + a) +--R + +--R 2cos(c - a)cos(b x + a) + 2cos(c - a) +--R * +--R 2 +--R cot(b x + c) +--R + +--R 5 4 +--R - cos(c - a)cos(b x + a) - cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R 2cos(c - a)cos(b x + a) + 2cos(c - a)cos(b x + a) +--R + +--R - cos(c - a)cos(b x + a) - cos(c - a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 +--R cos(c - a)cos(b x + a) + cos(c - a)cos(b x + a) +--R + +--R 3 2 +--R - 2cos(c - a)cos(b x + a) - 2cos(c - a)cos(b x + a) +--R + +--R cos(c - a)cos(b x + a) + cos(c - a) +--R * +--R csc(b x + c) +--R * +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R - 3cos(b x + a) - 3cos(b x + a) + 6cos(b x + a) + 6cos(b x + a) +--R + +--R 2 +--R - 3cos(b x + a) - 3cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 3 +--R 3cos(b x + a) + 3cos(b x + a) - 6cos(b x + a) - 6cos(b x + a) +--R + +--R 2 +--R 3cos(b x + a) + 3cos(b x + a) +--R / +--R 5 2 5 7 +--R (2cos(b x + a) cos(b x + c) - 2cos(b x + a) )tan(c - a) +--R + +--R 5 4 2 +--R (- 2cos(b x + a) + 10cos(b x + a) )cos(b x + c) +--R + +--R 5 4 +--R 2cos(b x + a) - 10cos(b x + a) +--R * +--R 6 +--R sin(b x + a)tan(c - a) +--R + +--R 4 3 2 +--R (- 10cos(b x + a) + 16cos(b x + a) )cos(b x + c) +--R + +--R 4 3 +--R 10cos(b x + a) - 16cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 3 2 +--R (2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) )cos(b x + c) +--R + +--R 6 5 3 +--R - 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 3 2 2 +--R (- 16cos(b x + a) + 8cos(b x + a) )cos(b x + c) +--R + +--R 3 2 +--R 16cos(b x + a) - 8cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 3 +--R 14cos(b x + a) - 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 12cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R - 14cos(b x + a) + 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R - 12cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 2 2 4 +--R (- 8cos(b x + a) cos(b x + c) + 8cos(b x + a) )sin(b x + a) +--R + +--R 4 3 2 +--R 28cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R 8cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R - 28cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R - 8cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 +--R - 4cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 +--R 4cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 2cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 2 +--R (16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a)) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 3 2 +--R - 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 14cos(b x + a) - 10cos(b x + a) + 16cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) - 2cos(b x + a) + 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R 14cos(b x + a) + 10cos(b x + a) - 16cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) + 2cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 3 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) + 2cos(b x + a) + 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R 4cos(b x + a) - 2cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R +---------------+ +--R | 2 +--R \|tan(c - a) + 1 +--R + +--R 5 2 5 8 +--R (- 2cos(b x + a) cos(b x + c) + 2cos(b x + a) )sin(b x + a)tan(c - a) +--R + +--R 4 2 4 2 +--R (- 10cos(b x + a) cos(b x + c) + 10cos(b x + a) )sin(b x + a) +--R + +--R 6 5 2 6 +--R (2cos(b x + a) + 2cos(b x + a) )cos(b x + c) - 2cos(b x + a) +--R + +--R 5 +--R - 2cos(b x + a) +--R * +--R 7 +--R tan(c - a) +--R + +--R 3 2 3 3 +--R (- 16cos(b x + a) cos(b x + c) + 16cos(b x + a) )sin(b x + a) +--R + +--R 5 4 3 2 +--R (12cos(b x + a) + 10cos(b x + a) - 4cos(b x + a) )cos(b x + c) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 10cos(b x + a) + 4cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 6 +--R tan(c - a) +--R + +--R 2 2 2 4 +--R (- 8cos(b x + a) cos(b x + c) + 8cos(b x + a) )sin(b x + a) +--R + +--R 4 3 2 +--R (18cos(b x + a) + 16cos(b x + a) - 12cos(b x + a) ) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R - 18cos(b x + a) - 16cos(b x + a) + 12cos(b x + a) +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) +--R + +--R 3 +--R 4cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R * +--R 5 +--R tan(c - a) +--R + +--R 2 2 2 +--R (8cos(b x + a) - 8cos(b x + a))cos(b x + c) - 8cos(b x + a) +--R + +--R 8cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 4 3 2 +--R - 2cos(b x + a) + 12cos(b x + a) + 12cos(b x + a) +--R + +--R - 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 2cos(b x + a) - 12cos(b x + a) - 12cos(b x + a) + 2cos(b x + a) +--R * +--R sin(b x + a) +--R * +--R 4 +--R tan(c - a) +--R + +--R 2 2 2 4 +--R (- 8cos(b x + a) cos(b x + c) + 8cos(b x + a) )sin(b x + a) +--R + +--R 4 3 +--R (18cos(b x + a) + 8cos(b x + a) + 8cos(b x + a) - 2) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 +--R - 18cos(b x + a) - 8cos(b x + a) - 8cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 2 +--R - 2cos(b x + a) - 2cos(b x + a) + 2cos(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 2 +--R 2cos(b x + a) + 2cos(b x + a) - 2cos(b x + a) - 2cos(b x + a) +--R * +--R 3 +--R tan(c - a) +--R + +--R 3 2 2 +--R (16cos(b x + a) + 8cos(b x + a) - 8cos(b x + a))cos(b x + c) +--R + +--R 3 2 +--R - 16cos(b x + a) - 8cos(b x + a) + 8cos(b x + a) +--R * +--R 3 +--R sin(b x + a) +--R + +--R 5 4 3 +--R - 12cos(b x + a) - 10cos(b x + a) + 12cos(b x + a) +--R + +--R 2 +--R 8cos(b x + a) + 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 +--R 12cos(b x + a) + 10cos(b x + a) - 12cos(b x + a) +--R + +--R 2 +--R - 8cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R * +--R 2 +--R tan(c - a) +--R + +--R 4 3 2 +--R - 10cos(b x + a) - 8cos(b x + a) + 12cos(b x + a) +--R + +--R 8cos(b x + a) - 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 4 3 2 +--R 10cos(b x + a) + 8cos(b x + a) - 12cos(b x + a) +--R + +--R - 8cos(b x + a) + 2 +--R * +--R 2 +--R sin(b x + a) +--R + +--R 6 5 4 3 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R + +--R 2 +--R 2cos(b x + a) + 2cos(b x + a) +--R * +--R 2 +--R cos(b x + c) +--R + +--R 6 5 4 3 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) +--R + +--R 2 +--R - 2cos(b x + a) - 2cos(b x + a) +--R * +--R tan(c - a) +--R + +--R 5 4 3 2 +--R 2cos(b x + a) + 2cos(b x + a) - 4cos(b x + a) - 4cos(b x + a) +--R + +--R 2cos(b x + a) + 2 +--R * +--R 2 +--R cos(b x + c) +--R + +--R 5 4 3 2 +--R - 2cos(b x + a) - 2cos(b x + a) + 4cos(b x + a) + 4cos(b x + a) +--R + +--R - 2cos(b x + a) - 2 +--R * +--R sin(b x + a) +--R Type: Expression(Integer) +--E 512 + +--S 513 of 532 +t0796:= cos(a+b*x)*sec(c+b*x) +--R +--R +--R (482) cos(b x + a)sec(b x + c) +--R Type: Expression(Integer) +--E 513 + +--S 514 of 532 +r0796:= x*cos(a-c)+log(cos(c+b*x))*sin(a-c)/b +--R +--R +--R - sin(c - a)log(cos(b x + c)) + b x cos(c - a) +--R (483) ---------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 514 + +--S 515 of 532 +a0796:= integrate(t0796,x) +--R +--R +--R (484) +--R c - a 2 c - a 2cos(b x + c) +--R 2tan(-----)log(----------------) - 2tan(-----)log(- ----------------) +--R 2 cos(b x + c) + 1 2 cos(b x + c) + 1 +--R + +--R c - a 2 +--R - b x tan(-----) + b x +--R 2 +--R / +--R c - a 2 +--R b tan(-----) + b +--R 2 +--R Type: Union(Expression(Integer),...) +--E 515 + +--S 516 of 532 +m0796:= a0796-r0796 +--R +--R +--R (485) +--R c - a 2 +--R (sin(c - a)tan(-----) + sin(c - a))log(cos(b x + c)) +--R 2 +--R + +--R c - a 2 c - a 2cos(b x + c) +--R 2tan(-----)log(----------------) - 2tan(-----)log(- ----------------) +--R 2 cos(b x + c) + 1 2 cos(b x + c) + 1 +--R + +--R c - a 2 +--R (- b x cos(c - a) - b x)tan(-----) - b x cos(c - a) + b x +--R 2 +--R / +--R c - a 2 +--R b tan(-----) + b +--R 2 +--R Type: Expression(Integer) +--E 516 + +--S 517 of 532 +d0796:= D(m0796,x) +--R +--R +--R (486) +--R c - a 2 +--R (- sin(c - a)sin(b x + c) + (- cos(c - a) - 1)cos(b x + c))tan(-----) +--R 2 +--R + +--R c - a +--R 2sin(b x + c)tan(-----) - sin(c - a)sin(b x + c) +--R 2 +--R + +--R (- cos(c - a) + 1)cos(b x + c) +--R / +--R c - a 2 +--R cos(b x + c)tan(-----) + cos(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 532 +t0797:= cos(a+b*x)*sec(c+b*x)^2 +--R +--R +--R 2 +--R (487) cos(b x + a)sec(b x + c) +--R Type: Expression(Integer) +--E 518 + +--S 519 of 532 +r0797:= atanh(sin(c+b*x))*cos(a-c)/b-sec(c+b*x)*sin(a-c)/b +--R +--R +--R cos(c - a)atanh(sin(b x + c)) + sec(b x + c)sin(c - a) +--R (488) ------------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 519 + +--S 520 of 532 +a0797:= integrate(t0797,x) +--R +--R +--R (489) +--R c - a 2 +--R (- cos(b x + c)tan(-----) + cos(b x + c)) +--R 2 +--R * +--R sin(b x + c) + cos(b x + c) + 1 +--R log(-------------------------------) +--R cos(b x + c) + 1 +--R + +--R c - a 2 +--R (cos(b x + c)tan(-----) - cos(b x + c)) +--R 2 +--R * +--R sin(b x + c) - cos(b x + c) - 1 +--R log(-------------------------------) +--R cos(b x + c) + 1 +--R + +--R c - a +--R (2cos(b x + c) + 2)tan(-----) +--R 2 +--R / +--R c - a 2 +--R b cos(b x + c)tan(-----) + b cos(b x + c) +--R 2 +--R Type: Union(Expression(Integer),...) +--E 520 + +--S 521 of 532 +m0797:= a0797-r0797 +--R +--R +--R (490) +--R c - a 2 +--R (- cos(b x + c)tan(-----) + cos(b x + c)) +--R 2 +--R * +--R sin(b x + c) + cos(b x + c) + 1 +--R log(-------------------------------) +--R cos(b x + c) + 1 +--R + +--R c - a 2 +--R (cos(b x + c)tan(-----) - cos(b x + c)) +--R 2 +--R * +--R sin(b x + c) - cos(b x + c) - 1 +--R log(-------------------------------) +--R cos(b x + c) + 1 +--R + +--R c - a 2 +--R (- cos(c - a)cos(b x + c)tan(-----) - cos(c - a)cos(b x + c)) +--R 2 +--R * +--R atanh(sin(b x + c)) +--R + +--R c - a 2 +--R - cos(b x + c)sec(b x + c)sin(c - a)tan(-----) +--R 2 +--R + +--R c - a +--R (2cos(b x + c) + 2)tan(-----) - cos(b x + c)sec(b x + c)sin(c - a) +--R 2 +--R / +--R c - a 2 +--R b cos(b x + c)tan(-----) + b cos(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 532 +d0797:= D(m0797,x) +--R +--R +--R (491) +--R 2 4 +--R - cos(b x + c) sec(b x + c)sin(c - a)sin(b x + c) +--R + +--R 4 3 2 +--R (cos(b x + c) + 2cos(b x + c) + 2cos(b x + c) )sec(b x + c) +--R * +--R 2 +--R sin(c - a)sin(b x + c) +--R + +--R 4 3 2 +--R (- cos(b x + c) - 2cos(b x + c) - cos(b x + c) )sec(b x + c) +--R * +--R sin(c - a) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 2 4 +--R - cos(b x + c) sec(b x + c)sin(c - a)sin(b x + c) +--R + +--R 4 3 2 +--R (cos(b x + c) + 2cos(b x + c) + 2cos(b x + c) )sec(b x + c) +--R * +--R 2 +--R sin(c - a)sin(b x + c) +--R + +--R 4 3 2 +--R (- cos(b x + c) - 2cos(b x + c) - cos(b x + c) )sec(b x + c) +--R * +--R sin(c - a) +--R * +--R tan(b x + c) +--R + +--R 2 4 +--R 2cos(b x + c) sin(b x + c) +--R + +--R 4 3 2 +--R (2cos(b x + c) + (cos(c - a) + 2)cos(b x + c) - 2cos(b x + c) ) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 5 4 +--R - cos(c - a)cos(b x + c) + (- 2cos(c - a) - 2)cos(b x + c) +--R + +--R 3 +--R (- cos(c - a) - 2)cos(b x + c) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 5 2 3 +--R 2sin(b x + c) + (- 2cos(b x + c) - 4cos(b x + c) - 4)sin(b x + c) +--R + +--R 2 +--R (2cos(b x + c) + 4cos(b x + c) + 2)sin(b x + c) +--R * +--R c - a +--R tan(-----) +--R 2 +--R + +--R 2 4 +--R - 2cos(b x + c) sin(b x + c) +--R + +--R 4 3 2 +--R (- 2cos(b x + c) + (cos(c - a) - 2)cos(b x + c) + 2cos(b x + c) ) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 5 4 +--R - cos(c - a)cos(b x + c) + (- 2cos(c - a) + 2)cos(b x + c) +--R + +--R 3 +--R (- cos(c - a) + 2)cos(b x + c) +--R / +--R 2 4 +--R cos(b x + c) sin(b x + c) +--R + +--R 4 3 2 2 +--R (- cos(b x + c) - 2cos(b x + c) - 2cos(b x + c) )sin(b x + c) +--R + +--R 4 3 2 +--R cos(b x + c) + 2cos(b x + c) + cos(b x + c) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 2 4 +--R cos(b x + c) sin(b x + c) +--R + +--R 4 3 2 2 +--R (- cos(b x + c) - 2cos(b x + c) - 2cos(b x + c) )sin(b x + c) +--R + +--R 4 3 2 +--R cos(b x + c) + 2cos(b x + c) + cos(b x + c) +--R Type: Expression(Integer) +--E 522 + +--S 523 of 532 +t0798:= cos(a+b*x)*sec(c+b*x)^3 +--R +--R +--R 3 +--R (492) cos(b x + a)sec(b x + c) +--R Type: Expression(Integer) +--E 523 + +--S 524 of 532 +r0798:= -1/2*sec(c+b*x)^2*sin(a-c)/b+cos(a-c)*tan(c+b*x)/b +--R +--R +--R 2 +--R 2cos(c - a)tan(b x + c) + sec(b x + c) sin(c - a) +--R (493) ------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 524 + +--S 525 of 532 +a0798:= integrate(t0798,x) +--R +--R +--R (494) +--R c - a 2 2 c - a +--R - cos(b x + c)sin(b x + c)tan(-----) + (- cos(b x + c) + 1)tan(-----) +--R 2 2 +--R + +--R cos(b x + c)sin(b x + c) +--R / +--R 2 c - a 2 2 +--R b cos(b x + c) tan(-----) + b cos(b x + c) +--R 2 +--R Type: Union(Expression(Integer),...) +--E 525 + +--S 526 of 532 +m0798:= a0798-r0798 +--R +--R +--R (495) +--R 2 c - a 2 2 +--R (- 2cos(c - a)cos(b x + c) tan(-----) - 2cos(c - a)cos(b x + c) ) +--R 2 +--R * +--R tan(b x + c) +--R + +--R 2 2 +--R (- 2cos(b x + c)sin(b x + c) - cos(b x + c) sec(b x + c) sin(c - a)) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 2 c - a +--R (- 2cos(b x + c) + 2)tan(-----) + 2cos(b x + c)sin(b x + c) +--R 2 +--R + +--R 2 2 +--R - cos(b x + c) sec(b x + c) sin(c - a) +--R / +--R 2 c - a 2 2 +--R 2b cos(b x + c) tan(-----) + 2b cos(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 526 + +--S 527 of 532 +d0798:= D(m0798,x) +--R +--R +--R (496) +--R 3 c - a 2 3 +--R (- cos(c - a)cos(b x + c) tan(-----) - cos(c - a)cos(b x + c) ) +--R 2 +--R * +--R 2 +--R tan(b x + c) +--R + +--R 3 2 c - a 2 +--R - cos(b x + c) sec(b x + c) sin(c - a)tan(-----) +--R 2 +--R + +--R 3 2 +--R - cos(b x + c) sec(b x + c) sin(c - a) +--R * +--R tan(b x + c) +--R + +--R 2 3 +--R (- cos(b x + c)sin(b x + c) + (- cos(c - a) - 1)cos(b x + c) ) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R c - a 2 +--R 2sin(b x + c)tan(-----) + cos(b x + c)sin(b x + c) +--R 2 +--R + +--R 3 +--R (- cos(c - a) + 1)cos(b x + c) +--R / +--R 3 c - a 2 3 +--R cos(b x + c) tan(-----) + cos(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 532 +t0799:= cos(a+b*x)*csc(c+b*x) +--R +--R +--R (497) cos(b x + a)csc(b x + c) +--R Type: Expression(Integer) +--E 528 + +--S 529 of 532 +r0799:= cos(a-c)*log(sin(c+b*x))/b-x*sin(a-c) +--R +--R +--R cos(c - a)log(sin(b x + c)) + b x sin(c - a) +--R (498) -------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 529 + +--S 530 of 532 +a0799:= integrate(t0799,x) +--R +--R +--R (499) +--R c - a 2 sin(b x + c) +--R (- tan(-----) + 1)log(----------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a 2 2 c - a +--R (tan(-----) - 1)log(----------------) + 2b x tan(-----) +--R 2 cos(b x + c) + 1 2 +--R / +--R c - a 2 +--R b tan(-----) + b +--R 2 +--R Type: Union(Expression(Integer),...) +--E 530 + +--S 531 of 532 +m0799:= a0799-r0799 +--R +--R +--R (500) +--R c - a 2 +--R (- cos(c - a)tan(-----) - cos(c - a))log(sin(b x + c)) +--R 2 +--R + +--R c - a 2 sin(b x + c) +--R (- tan(-----) + 1)log(----------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a 2 2 c - a 2 +--R (tan(-----) - 1)log(----------------) - b x sin(c - a)tan(-----) +--R 2 cos(b x + c) + 1 2 +--R + +--R c - a +--R 2b x tan(-----) - b x sin(c - a) +--R 2 +--R / +--R c - a 2 +--R b tan(-----) + b +--R 2 +--R Type: Expression(Integer) +--E 531 + +--S 532 of 532 +d0799:= D(m0799,x) +--R +--R +--R (501) +--R c - a 2 +--R (- sin(c - a)sin(b x + c) + (- cos(c - a) - 1)cos(b x + c))tan(-----) +--R 2 +--R + +--R c - a +--R 2sin(b x + c)tan(-----) - sin(c - a)sin(b x + c) +--R 2 +--R + +--R (- cos(c - a) + 1)cos(b x + c) +--R / +--R c - a 2 +--R sin(b x + c)tan(-----) + sin(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 532 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richtrig700-799.input.pdf b/src/axiom-website/CATS/richtrig700-799.input.pdf new file mode 100644 index 0000000..1769ecb Binary files /dev/null and b/src/axiom-website/CATS/richtrig700-799.input.pdf differ diff --git a/src/axiom-website/CATS/richtrig800-899.input.pamphlet b/src/axiom-website/CATS/richtrig800-899.input.pamphlet new file mode 100644 index 0000000..e9d0244 --- /dev/null +++ b/src/axiom-website/CATS/richtrig800-899.input.pamphlet @@ -0,0 +1,45329 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richtrig800-899.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig800-899.output +)spool richtrig800-899.output +)set message auto off +)clear all + +--S 1 of 526 +t0800:= cos(a+b*x)*csc(c+b*x)^2 +--R +--R +--R 2 +--R (1) cos(b x + a)csc(b x + c) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 526 +r0800:= -cos(a-c)*csc(c+b*x)/b+atanh(cos(c+b*x))*sin(a-c)/b +--R +--R +--R - sin(c - a)atanh(cos(b x + c)) - cos(c - a)csc(b x + c) +--R (2) -------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 526 +a0800:= integrate(t0800,x) +--R +--R +--R c - a sin(b x + c) c - a 2 +--R 2sin(b x + c)tan(-----)log(----------------) + tan(-----) - 1 +--R 2 cos(b x + c) + 1 2 +--R (3) -------------------------------------------------------------- +--R c - a 2 +--R b sin(b x + c)tan(-----) + b sin(b x + c) +--R 2 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 526 +m0800:= a0800-r0800 +--R +--R +--R (4) +--R c - a sin(b x + c) +--R 2sin(b x + c)tan(-----)log(----------------) +--R 2 cos(b x + c) + 1 +--R + +--R c - a 2 +--R (sin(c - a)sin(b x + c)tan(-----) + sin(c - a)sin(b x + c)) +--R 2 +--R * +--R atanh(cos(b x + c)) +--R + +--R c - a 2 +--R (cos(c - a)csc(b x + c)sin(b x + c) + 1)tan(-----) +--R 2 +--R + +--R cos(c - a)csc(b x + c)sin(b x + c) - 1 +--R / +--R c - a 2 +--R b sin(b x + c)tan(-----) + b sin(b x + c) +--R 2 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 526 +d0800:= D(m0800,x) +--R +--R +--R (5) +--R 3 +--R sin(c - a)sin(b x + c) +--R + +--R 2 +--R (- cos(c - a)cos(b x + c) + cos(c - a))cot(b x + c)csc(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R - cos(b x + c) + cos(b x + c) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 3 +--R (2cos(b x + c) - 2)sin(b x + c) +--R + +--R 3 +--R (2cos(b x + c) - 2cos(b x + c))sin(b x + c) +--R * +--R c - a +--R tan(-----) +--R 2 +--R + +--R 3 +--R sin(c - a)sin(b x + c) +--R + +--R 2 +--R (- cos(c - a)cos(b x + c) + cos(c - a))cot(b x + c)csc(b x + c) +--R * +--R 2 +--R sin(b x + c) +--R + +--R 3 +--R cos(b x + c) - cos(b x + c) +--R / +--R 2 2 c - a 2 +--R (cos(b x + c) - 1)sin(b x + c) tan(-----) +--R 2 +--R + +--R 2 2 +--R (cos(b x + c) - 1)sin(b x + c) +--R Type: Expression(Integer) +--E 5 + +)clear all + + +--S 6 of 526 +t0801:= cos(a+b*x)*csc(c+b*x)^3 +--R +--R +--R 3 +--R (1) cos(b x + a)csc(b x + c) +--R Type: Expression(Integer) +--E 6 + +--S 7 of 526 +r0801:= -1/2*cos(a-c)*csc(c+b*x)^2/b+cot(c+b*x)*sin(a-c)/b +--R +--R +--R 2 +--R - 2cot(b x + c)sin(c - a) - cos(c - a)csc(b x + c) +--R (2) --------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 7 + +--S 8 of 526 +a0801:= integrate(t0801,x) +--R +--R +--R (3) +--R 2 c - a 2 c - a +--R (- cos(b x + c) - 1)tan(-----) + 8cos(b x + c)sin(b x + c)tan(-----) +--R 2 2 +--R + +--R 2 +--R cos(b x + c) + 1 +--R / +--R 2 c - a 2 2 +--R (4b cos(b x + c) - 4b)tan(-----) + 4b cos(b x + c) - 4b +--R 2 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 526 +m0801:= a0801-r0801 +--R +--R +--R (4) +--R 2 +--R (4cos(b x + c) - 4)cot(b x + c)sin(c - a) +--R + +--R 2 2 2 +--R (2cos(c - a)cos(b x + c) - 2cos(c - a))csc(b x + c) - cos(b x + c) +--R + +--R - 1 +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R c - a +--R 8cos(b x + c)sin(b x + c)tan(-----) +--R 2 +--R + +--R 2 +--R (4cos(b x + c) - 4)cot(b x + c)sin(c - a) +--R + +--R 2 2 2 +--R (2cos(c - a)cos(b x + c) - 2cos(c - a))csc(b x + c) + cos(b x + c) + 1 +--R / +--R 2 c - a 2 2 +--R (4b cos(b x + c) - 4b)tan(-----) + 4b cos(b x + c) - 4b +--R 2 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 526 +d0801:= D(m0801,x) +--R +--R +--R (5) +--R - cos(b x + c)sin(b x + c) +--R + +--R 4 2 2 +--R (- cos(b x + c) + 2cos(b x + c) - 1)cot(b x + c) +--R + +--R 4 2 +--R - cos(b x + c) + 2cos(b x + c) - 1 +--R * +--R sin(c - a) +--R + +--R 4 2 +--R (- cos(c - a)cos(b x + c) + 2cos(c - a)cos(b x + c) - cos(c - a)) +--R * +--R 2 +--R cot(b x + c)csc(b x + c) +--R * +--R c - a 2 +--R tan(-----) +--R 2 +--R + +--R 2 2 4 2 +--R ((2cos(b x + c) + 2)sin(b x + c) + 2cos(b x + c) - 2cos(b x + c) ) +--R * +--R c - a +--R tan(-----) +--R 2 +--R + +--R cos(b x + c)sin(b x + c) +--R + +--R 4 2 2 4 +--R (- cos(b x + c) + 2cos(b x + c) - 1)cot(b x + c) - cos(b x + c) +--R + +--R 2 +--R 2cos(b x + c) - 1 +--R * +--R sin(c - a) +--R + +--R 4 2 +--R (- cos(c - a)cos(b x + c) + 2cos(c - a)cos(b x + c) - cos(c - a)) +--R * +--R 2 +--R cot(b x + c)csc(b x + c) +--R / +--R 4 2 c - a 2 4 +--R (cos(b x + c) - 2cos(b x + c) + 1)tan(-----) + cos(b x + c) +--R 2 +--R + +--R 2 +--R - 2cos(b x + c) + 1 +--R Type: Expression(Integer) +--E 10 + +)clear all + + +--S 11 of 526 +t0802:= sin(x)^2/(a+b*sin(2*x)) +--R +--R +--R 2 +--R sin(x) +--R (1) ------------- +--R b sin(2x) + a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 526 +r0802:= 1/2*atan((b+a*tan(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(1/2)-_ + 1/4*log(a+b*sin(2*x))/b +--R +--R +--R +---------+ +--R | 2 2 a tan(x) + b +--R - \|- b + a log(b sin(2x) + a) + 2b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) -------------------------------------------------------- +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R Type: Expression(Integer) +--E 12 + +--S 13 of 526 +a0802:= integrate(t0802,x) +--R +--R +--R (3) +--R [ +--R b +--R * +--R log +--R 2 2 2 2 2 +--R (2a b cos(x)sin(x) + (- 2b + 2a )cos(x) + 2b - a ) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 3 2 2 3 2 +--R (2a b - 2a )cos(x)sin(x) + (- 2b + 2a b)cos(x) + 2b - 2a b +--R / +--R 2b cos(x)sin(x) + a +--R + +--R +-------+ +-------+ +--R | 2 2 8b cos(x)sin(x) + 4a | 2 2 2 +--R - \|b - a log(---------------------) + 2\|b - a log(----------) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R / +--R +-------+ +--R | 2 2 +--R 4b\|b - a +--R , +--R +--R +---------+ +---------+ +--R | 2 2 8b cos(x)sin(x) + 4a | 2 2 2 +--R - \|- b + a log(---------------------) + 2\|- b + a log(----------) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - 2b cos(x) - 2b)\|- b + a +--R - 2b atan(---------------------------------------) +--R 2 2 2 2 +--R (2b - 2a )cos(x) + 2b - 2a +--R + +--R 2 +--R (a cos(x) + 2a)sin(x) + 3b cos(x) + 2b cos(x) - b +--R 2b atan(--------------------------------------------------) +--R +---------+ +--R 2 | 2 2 +--R (cos(x) + 2cos(x) + 1)\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 13 + +--S 14 of 526 +m0802a:= a0802.1-r0802 +--R +--R +--R (4) +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 2 2 | 2 2 +--R (2a b cos(x)sin(x) + (- 2b + 2a )cos(x) + 2b - a )\|b - a +--R + +--R 2 3 3 2 2 3 2 +--R (2a b - 2a )cos(x)sin(x) + (- 2b + 2a b)cos(x) + 2b - 2a b +--R / +--R 2b cos(x)sin(x) + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R \|- b + a \|b - a log(b sin(2x) + a) +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 8b cos(x)sin(x) + 4a +--R - \|- b + a \|b - a log(---------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +-------+ +-------+ +--R | 2 2 | 2 2 2 | 2 2 a tan(x) + b +--R 2\|- b + a \|b - a log(----------) - 2b\|b - a atan(------------) +--R cos(x) + 1 +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R 4b\|- b + a \|b - a +--R Type: Expression(Integer) +--E 14 + +--S 15 of 526 +d0802a:= D(m0802a,x) +--R +--R +--R (5) +--R 2 2 3 +--R 2a b cos(x)sin(x) +--R + +--R 3 3 2 3 3 2 +--R ((- 4a b + 2a b)cos(x) + 4a b - 2a b)sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((4b - 6a b )cos(x) + (- 4b + 2a b )cos(x))sin(x) +--R + +--R 3 3 4 3 2 3 3 +--R (4a b - 2a b)cos(x) - 2a b cos(x) - 2a b + a b +--R * +--R sin(2x) +--R + +--R 3 3 +--R 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 2 4 2 2 2 4 +--R (4a b cos(x) cos(2x) + (- 4a b + 2a )cos(x) + 4a b - 2a ) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 3 +--R ((- 4a b + 4a b)cos(x) + 4a b cos(x))cos(2x) +--R + +--R 3 3 3 3 3 +--R (4a b - 6a b)cos(x) + (- 4a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 2 4 +--R ((- 2a b + 2a )cos(x) + 2a b - a )cos(2x) +--R + +--R 2 2 4 4 2 2 2 2 2 4 +--R (4a b - 2a )cos(x) - 2a b cos(x) - 2a b + a +--R * +--R 2 +--R tan(x) +--R + +--R 3 3 2 2 2 4 2 2 2 +--R 4a b cos(x)sin(x) + (4a b cos(x) + 8b - 4a b )sin(x) +--R + +--R 3 3 3 4 2 2 4 +--R (- 4a b cos(x) + 4a b cos(x))sin(x) + (8b - 4a b )cos(x) +--R + +--R 4 2 2 2 +--R (- 8b + 4a b )cos(x) +--R * +--R sin(2x) +--R + +--R 2 2 3 +--R 4a b cos(x)sin(x) +--R + +--R 3 2 3 2 3 3 2 +--R (8a b cos(x) cos(2x) + 4a b cos(x) + 8a b - 4a b)sin(x) +--R + +--R 4 2 2 3 4 2 2 3 +--R ((- 8b + 8a b )cos(x) + 8b cos(x))cos(2x) - 4a b cos(x) +--R + +--R 2 2 +--R 4a b cos(x) +--R * +--R sin(x) +--R + +--R 3 3 2 3 3 +--R ((- 4a b + 4a b)cos(x) + 4a b - 2a b)cos(2x) +--R + +--R 3 3 4 3 3 2 +--R (8a b - 4a b)cos(x) + (- 8a b + 4a b)cos(x) +--R * +--R tan(x) +--R + +--R 2 2 3 +--R 2a b cos(x)sin(x) +--R + +--R 3 3 2 3 3 2 +--R ((- 4a b + 2a b)cos(x) + 4a b - 2a b)sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((4b - 6a b )cos(x) + (- 4b + 2a b )cos(x))sin(x) +--R + +--R 3 3 4 3 2 3 3 +--R (4a b - 2a b)cos(x) - 2a b cos(x) - 2a b + a b +--R * +--R sin(2x) +--R + +--R 3 3 +--R 2a b cos(x)sin(x) +--R + +--R 2 2 2 2 2 4 2 2 2 4 2 +--R (4a b cos(x) cos(2x) + (- 4a b + 2a )cos(x) + 4a b - 2a )sin(x) +--R + +--R 3 3 3 3 +--R ((- 4a b + 4a b)cos(x) + 4a b cos(x))cos(2x) +--R + +--R 3 3 3 3 3 +--R (4a b - 6a b)cos(x) + (- 4a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 2 4 2 2 4 4 +--R ((- 2a b + 2a )cos(x) + 2a b - a )cos(2x) + (4a b - 2a )cos(x) +--R + +--R 2 2 2 2 2 4 +--R - 2a b cos(x) - 2a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 4 3 +--R (2a b - 2a b)cos(x)sin(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R ((- 4a b + 4a b )cos(x) + 4a b - 4a b )sin(x) +--R + +--R 5 2 3 4 3 5 2 3 +--R ((4b - 6a b + 2a b)cos(x) + (- 4b + 4a b )cos(x))sin(x) +--R + +--R 4 3 2 4 4 3 2 2 4 3 2 +--R (4a b - 4a b )cos(x) + (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(2x) +--R + +--R 3 2 5 3 +--R (2a b - 2a )cos(x)sin(x) +--R + +--R 2 3 4 2 2 3 4 2 2 3 +--R (4a b - 4a b)cos(x) cos(2x) + (- 4a b + 4a b)cos(x) + 4a b +--R + +--R 4 +--R - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R ((- 4a b + 4a b )cos(x) + (4a b - 2a b - 2a )cos(x))cos(2x) +--R + +--R 4 3 2 5 3 4 3 2 +--R (4a b - 6a b + 2a )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R ((- 2a b + 2a b)cos(x) + 2a b - 2a b)cos(2x) +--R + +--R 2 3 4 4 2 3 4 2 2 3 4 +--R (4a b - 4a b)cos(x) + (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 3 5 2 3 2 +--R (4a b - 4a b )cos(x)sin(x) + (8b - 8a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 +--R ((- 4a b + 4a b )cos(x) + (4a b - 4a b )cos(x))sin(x) +--R + +--R 5 2 3 4 5 2 3 2 +--R (8b - 8a b )cos(x) + (- 8b + 8a b )cos(x) +--R * +--R sin(2x) +--R + +--R 2 3 4 3 +--R (4a b - 4a b)cos(x)sin(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R ((8a b - 8a b )cos(x) cos(2x) + 8a b - 8a b )sin(x) +--R + +--R 5 2 3 3 5 2 3 4 +--R ((- 8b + 8a b )cos(x) + (8b - 4a b - 4a b)cos(x))cos(2x) +--R + +--R 2 3 4 3 2 3 4 +--R (- 4a b + 4a b)cos(x) + (4a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R ((- 4a b + 4a b )cos(x) + 4a b - 4a b )cos(2x) +--R + +--R 4 3 2 4 4 3 2 2 +--R (8a b - 8a b )cos(x) + (- 8a b + 8a b )cos(x) +--R * +--R tan(x) +--R + +--R 2 3 4 3 +--R (2a b - 2a b)cos(x)sin(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R ((- 4a b + 4a b )cos(x) + 4a b - 4a b )sin(x) +--R + +--R 5 2 3 4 3 5 2 3 +--R ((4b - 6a b + 2a b)cos(x) + (- 4b + 4a b )cos(x))sin(x) +--R + +--R 4 3 2 4 4 3 2 2 4 3 2 +--R (4a b - 4a b )cos(x) + (- 2a b + 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(2x) +--R + +--R 3 2 5 3 +--R (2a b - 2a )cos(x)sin(x) +--R + +--R 2 3 4 2 2 3 4 2 2 3 4 +--R ((4a b - 4a b)cos(x) cos(2x) + (- 4a b + 4a b)cos(x) + 4a b - 4a b) +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R ((- 4a b + 4a b )cos(x) + (4a b - 2a b - 2a )cos(x))cos(2x) +--R + +--R 4 3 2 5 3 4 3 2 +--R (4a b - 6a b + 2a )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 4 +--R ((- 2a b + 2a b)cos(x) + 2a b - 2a b)cos(2x) + (4a b - 4a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 2a b + 2a b)cos(x) - 2a b + 2a b +--R / +--R 2 3 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 8a b + 8a b )cos(x) + 8a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 4a b + 4a b)cos(x) + 4a b - 2a b +--R * +--R sin(2x) +--R + +--R 3 2 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 2 3 4 3 2 3 +--R ((- 8a b + 8a b)cos(x) + 8a b cos(x))sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (- 4a b + 4a )cos(x) + 4a b - 2a +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 2 +--R 16a b cos(x) sin(x) +--R + +--R 5 2 3 3 5 +--R ((- 16b + 16a b )cos(x) + 16b cos(x))sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 8a b + 8a b )cos(x) + 8a b - 4a b +--R * +--R sin(2x) +--R + +--R 2 3 2 2 +--R 16a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 16a b + 16a b )cos(x) + 16a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 8a b + 8a b)cos(x) + 8a b - 4a b +--R * +--R tan(x) +--R + +--R 2 3 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 8a b + 8a b )cos(x) + 8a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 4a b + 4a b)cos(x) + 4a b - 2a b +--R * +--R sin(2x) +--R + +--R 3 2 2 2 2 3 4 3 2 3 +--R 8a b cos(x) sin(x) + ((- 8a b + 8a b)cos(x) + 8a b cos(x))sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (- 4a b + 4a )cos(x) + 4a b - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 2 2 +--R (8a b - 8a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b - 4a b +--R * +--R sin(2x) +--R + +--R 3 3 5 2 2 +--R (8a b - 8a b)cos(x) sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 6 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a )cos(x))sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 4a b + 4a b)cos(x) + 4a b - 4a b +--R * +--R 2 +--R tan(x) +--R + +--R 5 3 3 2 2 +--R (16a b - 16a b )cos(x) sin(x) +--R + +--R 6 2 4 3 6 2 4 4 2 +--R ((- 16b + 16a b )cos(x) + (16b - 8a b - 8a b )cos(x))sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (- 8a b + 8a b )cos(x) + 8a b - 8a b +--R * +--R sin(2x) +--R + +--R 2 4 4 2 2 2 +--R (16a b - 16a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 16a b + 16a b )cos(x) + (16a b - 8a b - 8a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 8a b + 8a b )cos(x) + 8a b - 8a b +--R * +--R tan(x) +--R + +--R 2 4 4 2 2 2 +--R (8a b - 8a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b - 4a b +--R * +--R sin(2x) +--R + +--R 3 3 5 2 2 +--R (8a b - 8a b)cos(x) sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 6 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a )cos(x))sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 4a b + 4a b)cos(x) + 4a b - 4a b +--R Type: Expression(Integer) +--E 15 + +--S 16 of 526 +m0802b:= a0802.2-r0802 +--R +--R +--R (6) +--R +---------+ +---------+ +--R | 2 2 | 2 2 8b cos(x)sin(x) + 4a +--R \|- b + a log(b sin(2x) + a) - \|- b + a log(---------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 +--R 2\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - 2b cos(x) - 2b)\|- b + a +--R - 2b atan(---------------------------------------) +--R 2 2 2 2 +--R (2b - 2a )cos(x) + 2b - 2a +--R + +--R a tan(x) + b +--R - 2b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 +--R (a cos(x) + 2a)sin(x) + 3b cos(x) + 2b cos(x) - b +--R 2b atan(--------------------------------------------------) +--R +---------+ +--R 2 | 2 2 +--R (cos(x) + 2cos(x) + 1)\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 526 +d0802b:= D(m0802b,x) +--R +--R +--R (7) +--R 4 2 4 4 6 +--R (a b cos(x) + 4a b cos(x) + 4a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 5 +--R (6a b cos(x) + 12a b cos(x) - 12a b cos(x) - 20a b )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 4a b + 4a b)cos(x) + (- 56a b + 24a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (- 92a b + 56a b)cos(x) + (- 24a b + 60a b)cos(x) + 16a b +--R + +--R 4 +--R 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (32a b + 26a b )cos(x) + (160a b + 132a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (256a b + 214a b )cos(x) + (160a b + 100a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (32a b - 32a b )cos(x) - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (64b + 24a b - a b)cos(x) + (128b + 8a b - 4a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 192a b + 6a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 128b - 288a b + 46a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 4 +--R (- 64b - 88a b + 66a b)cos(x) + (24a b + 30a b)cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 7 4 3 2 6 +--R - 16a b cos(x) + (- 64a b - 72a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 96a b - 116a b )cos(x) + (64a b - 132a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (128a b - 192a b )cos(x) - 184a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b - 60a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 32a b - 4a b)cos(x) + (- 96a b - 24a b)cos(x) +--R + +--R 2 3 4 6 4 5 +--R (- 80a b - 58a b)cos(x) - 70a b cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (32a b - 44a b)cos(x) + (64a b - 20a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R (80a b - 18a b)cos(x) + (32a b - 14a b)cos(x) - 4a b +--R * +--R sin(2x) +--R + +--R 5 2 5 5 6 +--R (a cos(x) + 4a cos(x) + 4a )sin(x) +--R + +--R 4 3 4 2 4 4 3 +--R (2a b cos(x) + 8a b cos(x) + 8a b cos(x))cos(2x) + 6a b cos(x) +--R + +--R 4 2 4 4 +--R 12a b cos(x) - 12a b cos(x) - 20a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 3 3 2 5 2 +--R 4a b cos(x) - 8a b cos(x) + (- 52a b + a )cos(x) +--R + +--R 3 2 5 5 +--R (- 40a b + 4a )cos(x) + 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (- 4a b + 4a )cos(x) + (- 56a b + 24a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (- 92a b + 56a )cos(x) + (- 24a b + 60a )cos(x) + 16a b + 24a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 32a b + 10a b)cos(x) + (- 160a b + 56a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 192a b + 118a b)cos(x) + (- 32a b + 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b + 8a b)cos(x) - 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (32a b + 26a b)cos(x) + (160a b + 132a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (256a b + 214a b)cos(x) + (160a b + 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 32a b)cos(x) - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 64a b + 40a b )cos(x) + (- 128a b + 184a b )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (256a b + 5a )cos(x) + (128a b + 32a b + 28a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (64a b - 152a b + 58a )cos(x) + (- 56a b + 52a )cos(x) +--R + +--R 3 2 5 +--R 16a b + 17a +--R * +--R cos(2x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (64a b + 24a b - a )cos(x) + (128a b + 8a b - 4a )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 192a b + 6a )cos(x) + (- 128a b - 288a b + 46a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 5 +--R (- 64a b - 88a b + 66a )cos(x) + (24a b + 30a )cos(x) + a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (96a b + 140a b)cos(x) + (- 192a b + 252a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (- 192a b + 256a b)cos(x) + 104a b cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 20a b)cos(x) - 20a b +--R * +--R cos(2x) +--R + +--R 4 7 2 3 4 6 +--R - 16a b cos(x) + (- 64a b - 72a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b - 116a b)cos(x) + (64a b - 132a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (128a b - 192a b)cos(x) - 184a b cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b - 60a b)cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (32a b + 4a )cos(x) + (96a b + 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (64a b + 60a )cos(x) + (- 64a b + 80a )cos(x) +--R + +--R 3 2 5 2 3 2 5 5 +--R (- 96a b + 60a )cos(x) + (- 32a b + 24a )cos(x) + 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 32a b - 4a )cos(x) + (- 96a b - 24a )cos(x) +--R + +--R 3 2 5 6 5 5 3 2 5 4 +--R (- 80a b - 58a )cos(x) - 70a cos(x) + (32a b - 44a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 +--R (64a b - 20a )cos(x) + (80a b - 18a )cos(x) +--R + +--R 3 2 5 5 +--R (32a b - 14a )cos(x) - 4a +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 2 3 2 6 +--R (2a b cos(x) + 8a b cos(x) + 8a b )sin(x) +--R + +--R 2 3 3 2 3 2 2 3 2 3 5 +--R (16a b cos(x) + 40a b cos(x) - 8a b cos(x) - 40a b )sin(x) +--R + +--R 3 2 4 4 3 2 3 +--R 8a b cos(x) + (- 128a b + 48a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 288a b + 114a b )cos(x) + (- 128a b + 128a b )cos(x) +--R + +--R 4 3 2 +--R 32a b + 56a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 5 2 3 4 5 2 3 3 +--R 72a b cos(x) + 376a b cos(x) + (128b + 664a b )cos(x) +--R + +--R 5 2 3 2 5 2 3 2 3 +--R (256b + 400a b )cos(x) + (128b - 48a b )cos(x) - 88a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (128a b - 2a b )cos(x) + (384a b - 8a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (128a b + 22a b )cos(x) + (- 512a b + 148a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 480a b + 248a b )cos(x) + (- 64a b + 164a b )cos(x) +--R + +--R 4 3 2 +--R 32a b + 36a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 7 5 2 3 6 +--R (128b - 16a b )cos(x) + (256b - 48a b )cos(x) +--R + +--R 2 3 5 5 2 3 4 +--R 48a b cos(x) + (- 256b + 240a b )cos(x) +--R + +--R 5 2 3 3 2 3 2 2 3 +--R (- 128b + 128a b )cos(x) - 160a b cos(x) - 160a b cos(x) +--R + +--R 2 3 +--R - 32a b +--R * +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (- 64a b - 8a b )cos(x) + (- 192a b - 48a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 96a b - 108a b )cos(x) + (192a b - 92a b )cos(x) +--R + +--R 4 3 2 4 3 2 3 +--R (192a b + 32a b )cos(x) + 120a b cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 32a b + 84a b )cos(x) + 20a b cos(x) +--R * +--R sin(2x) +--R + +--R 4 2 4 4 6 +--R (2a b cos(x) + 8a b cos(x) + 8a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))cos(2x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 +--R 16a b cos(x) + 40a b cos(x) - 8a b cos(x) - 40a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 2 3 3 2 3 4 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 80a b + 8a b)cos(x) + 8a b +--R * +--R cos(2x) +--R + +--R 4 4 2 3 4 3 +--R 8a b cos(x) + (- 128a b + 48a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (- 288a b + 114a b)cos(x) + (- 128a b + 128a b)cos(x) + 32a b +--R + +--R 4 +--R 56a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 64a b + 20a b )cos(x) + (- 320a b + 112a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (- 384a b + 236a b )cos(x) + (- 64a b + 200a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (64a b + 16a b )cos(x) - 40a b +--R * +--R cos(2x) +--R + +--R 3 2 5 3 2 4 4 3 2 3 +--R 72a b cos(x) + 376a b cos(x) + (128a b + 664a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 3 2 +--R (256a b + 400a b )cos(x) + (128a b - 48a b )cos(x) - 88a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 6 5 2 3 5 +--R (- 128b + 80a b )cos(x) + (- 256b + 368a b )cos(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (512a b + 10a b)cos(x) + (256b + 64a b + 56a b)cos(x) +--R + +--R 5 2 3 4 2 +--R (128b - 304a b + 116a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (- 112a b + 104a b)cos(x) + 32a b + 34a b +--R * +--R cos(2x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (128a b - 2a b)cos(x) + (384a b - 8a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (128a b + 22a b)cos(x) + (- 512a b + 148a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (- 480a b + 248a b)cos(x) + (- 64a b + 164a b)cos(x) + 32a b +--R + +--R 4 +--R 36a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (192a b + 280a b )cos(x) + (- 384a b + 504a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (- 384a b + 512a b )cos(x) + 208a b cos(x) +--R + +--R 4 3 2 3 2 +--R (64a b - 40a b )cos(x) - 40a b +--R * +--R cos(2x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (128a b - 16a b )cos(x) + (256a b - 48a b )cos(x) +--R + +--R 3 2 5 4 3 2 4 +--R 48a b cos(x) + (- 256a b + 240a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 3 2 +--R (- 128a b + 128a b )cos(x) - 160a b cos(x) - 160a b cos(x) +--R + +--R 3 2 +--R - 32a b +--R * +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (128a b + 120a b)cos(x) + (- 128a b + 160a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R (- 192a b + 120a b)cos(x) + (- 64a b + 48a b)cos(x) + 8a b +--R * +--R cos(2x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 64a b - 8a b)cos(x) + (- 192a b - 48a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 96a b - 108a b)cos(x) + (192a b - 92a b)cos(x) +--R + +--R 2 3 4 4 4 3 2 3 4 2 +--R (192a b + 32a b)cos(x) + 120a b cos(x) + (- 32a b + 84a b)cos(x) +--R + +--R 4 +--R 20a b cos(x) +--R * +--R tan(x) +--R + +--R 4 2 4 4 6 +--R (a b cos(x) + 4a b cos(x) + 4a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 5 +--R (6a b cos(x) + 12a b cos(x) - 12a b cos(x) - 20a b )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 4a b + 4a b)cos(x) + (- 56a b + 24a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (- 92a b + 56a b)cos(x) + (- 24a b + 60a b)cos(x) + 16a b +--R + +--R 4 +--R 24a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (32a b + 26a b )cos(x) + (160a b + 132a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (256a b + 214a b )cos(x) + (160a b + 100a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (32a b - 32a b )cos(x) - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (64b + 24a b - a b)cos(x) + (128b + 8a b - 4a b)cos(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (- 192a b + 6a b)cos(x) + (- 128b - 288a b + 46a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 4 +--R (- 64b - 88a b + 66a b)cos(x) + (24a b + 30a b)cos(x) + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 7 4 3 2 6 +--R - 16a b cos(x) + (- 64a b - 72a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 96a b - 116a b )cos(x) + (64a b - 132a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (128a b - 192a b )cos(x) - 184a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b - 60a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (- 32a b - 4a b)cos(x) + (- 96a b - 24a b)cos(x) +--R + +--R 2 3 4 6 4 5 2 3 4 4 +--R (- 80a b - 58a b)cos(x) - 70a b cos(x) + (32a b - 44a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (64a b - 20a b)cos(x) + (80a b - 18a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 14a b)cos(x) - 4a b +--R * +--R sin(2x) +--R + +--R 5 2 5 5 6 +--R (a cos(x) + 4a cos(x) + 4a )sin(x) +--R + +--R 4 3 4 2 4 4 3 +--R (2a b cos(x) + 8a b cos(x) + 8a b cos(x))cos(2x) + 6a b cos(x) +--R + +--R 4 2 4 4 +--R 12a b cos(x) - 12a b cos(x) - 20a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 3 3 2 5 2 +--R 4a b cos(x) - 8a b cos(x) + (- 52a b + a )cos(x) +--R + +--R 3 2 5 5 +--R (- 40a b + 4a )cos(x) + 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (- 4a b + 4a )cos(x) + (- 56a b + 24a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (- 92a b + 56a )cos(x) + (- 24a b + 60a )cos(x) + 16a b + 24a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 32a b + 10a b)cos(x) + (- 160a b + 56a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (- 192a b + 118a b)cos(x) + (- 32a b + 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b + 8a b)cos(x) - 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (32a b + 26a b)cos(x) + (160a b + 132a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (256a b + 214a b)cos(x) + (160a b + 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 32a b)cos(x) - 24a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 64a b + 40a b )cos(x) + (- 128a b + 184a b )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (256a b + 5a )cos(x) + (128a b + 32a b + 28a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (64a b - 152a b + 58a )cos(x) + (- 56a b + 52a )cos(x) +--R + +--R 3 2 5 +--R 16a b + 17a +--R * +--R cos(2x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (64a b + 24a b - a )cos(x) + (128a b + 8a b - 4a )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 192a b + 6a )cos(x) + (- 128a b - 288a b + 46a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 5 +--R (- 64a b - 88a b + 66a )cos(x) + (24a b + 30a )cos(x) + a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (96a b + 140a b)cos(x) + (- 192a b + 252a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (- 192a b + 256a b)cos(x) + 104a b cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 20a b)cos(x) - 20a b +--R * +--R cos(2x) +--R + +--R 4 7 2 3 4 6 +--R - 16a b cos(x) + (- 64a b - 72a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b - 116a b)cos(x) + (64a b - 132a b)cos(x) +--R + +--R 2 3 4 3 4 2 2 3 4 +--R (128a b - 192a b)cos(x) - 184a b cos(x) + (- 32a b - 60a b)cos(x) +--R + +--R 4 +--R 4a b +--R * +--R sin(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (32a b + 4a )cos(x) + (96a b + 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (64a b + 60a )cos(x) + (- 64a b + 80a )cos(x) +--R + +--R 3 2 5 2 3 2 5 5 +--R (- 96a b + 60a )cos(x) + (- 32a b + 24a )cos(x) + 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (- 32a b - 4a )cos(x) + (- 96a b - 24a )cos(x) +--R + +--R 3 2 5 6 5 5 3 2 5 4 +--R (- 80a b - 58a )cos(x) - 70a cos(x) + (32a b - 44a )cos(x) +--R + +--R 3 2 5 3 3 2 5 2 3 2 5 +--R (64a b - 20a )cos(x) + (80a b - 18a )cos(x) + (32a b - 14a )cos(x) +--R + +--R 5 +--R - 4a +--R / +--R 4 2 3 4 2 2 4 2 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 80a b + 8a b)cos(x) + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 64a b + 20a b )cos(x) + (- 320a b + 112a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 384a b + 236a b )cos(x) + (- 64a b + 200a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b + 16a b )cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (512a b + 10a b)cos(x) + (256a b + 64a b + 56a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (128a b - 304a b + 116a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 112a b + 104a b)cos(x) + 32a b + 34a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (192a b + 280a b )cos(x) + (- 384a b + 504a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 384a b + 512a b )cos(x) + 208a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b - 40a b )cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (128a b + 120a b)cos(x) + (- 128a b + 160a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 192a b + 120a b)cos(x) + (- 64a b + 48a b)cos(x) + 8a b +--R * +--R sin(2x) +--R + +--R 5 3 5 2 5 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 4 2 4 4 2 3 4 2 6 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a )cos(x) +--R + +--R 4 2 6 6 +--R (- 80a b + 8a )cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 64a b + 20a b)cos(x) + (- 320a b + 112a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- 384a b + 236a b)cos(x) + (- 64a b + 200a b)cos(x) +--R + +--R 3 3 5 5 +--R (64a b + 16a b)cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 4 2 6 4 2 4 4 2 6 3 +--R (512a b + 10a )cos(x) + (256a b + 64a b + 56a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (128a b - 304a b + 116a )cos(x) + (- 112a b + 104a )cos(x) +--R + +--R 4 2 6 +--R 32a b + 34a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (192a b + 280a b)cos(x) + (- 384a b + 504a b)cos(x) +--R + +--R 3 3 5 3 5 2 +--R (- 384a b + 512a b)cos(x) + 208a b cos(x) +--R + +--R 3 3 5 5 +--R (64a b - 40a b)cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (64a b + 8a )cos(x) + (192a b + 48a )cos(x) +--R + +--R 4 2 6 4 4 2 6 3 +--R (128a b + 120a )cos(x) + (- 128a b + 160a )cos(x) +--R + +--R 4 2 6 2 4 2 6 6 +--R (- 192a b + 120a )cos(x) + (- 64a b + 48a )cos(x) + 8a +--R * +--R 2 +--R tan(x) +--R + +--R 3 3 3 3 3 2 3 3 5 +--R (8a b cos(x) + 32a b cos(x) + 32a b cos(x))sin(x) +--R + +--R 2 4 4 2 4 3 2 4 4 2 2 +--R 16a b cos(x) - 32a b cos(x) + (- 208a b + 4a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (- 160a b + 16a b )cos(x) + 16a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- 128a b + 40a b )cos(x) + (- 640a b + 224a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 768a b + 472a b )cos(x) + (- 128a b + 400a b )cos(x) +--R + +--R 5 3 3 3 3 +--R (128a b + 32a b )cos(x) - 80a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 6 6 2 4 5 +--R (- 256b + 160a b )cos(x) + (- 512b + 736a b )cos(x) +--R + +--R 2 4 4 2 4 +--R (1024a b + 20a b )cos(x) +--R + +--R 6 2 4 4 2 3 +--R (512b + 128a b + 112a b )cos(x) +--R + +--R 6 2 4 4 2 2 +--R (256b - 608a b + 232a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 224a b + 208a b )cos(x) + 64a b + 68a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 6 +--R (256a b + 32a b )cos(x) + (768a b + 192a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (384a b + 560a b )cos(x) + (- 768a b + 1008a b )cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (- 768a b + 1024a b )cos(x) + 416a b cos(x) +--R + +--R 5 3 3 3 3 +--R (128a b - 80a b )cos(x) - 80a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (256a b + 240a b )cos(x) + (- 256a b + 320a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 4 2 +--R (- 384a b + 240a b )cos(x) + (- 128a b + 96a b )cos(x) + 16a b +--R * +--R sin(2x) +--R + +--R 4 2 3 4 2 2 4 2 5 +--R (8a b cos(x) + 32a b cos(x) + 32a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 16a b cos(x) - 32a b cos(x) + (- 208a b + 4a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 160a b + 16a b)cos(x) + 16a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 128a b + 40a b )cos(x) + (- 640a b + 224a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 768a b + 472a b )cos(x) + (- 128a b + 400a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (128a b + 32a b )cos(x) - 80a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 256a b + 160a b )cos(x) + (- 512a b + 736a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (1024a b + 20a b)cos(x) + (512a b + 128a b + 112a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (256a b - 608a b + 232a b)cos(x) + (- 224a b + 208a b)cos(x) +--R + +--R 3 3 5 +--R 64a b + 68a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (256a b + 32a b )cos(x) + (768a b + 192a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (384a b + 560a b )cos(x) + (- 768a b + 1008a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 768a b + 1024a b )cos(x) + 416a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (128a b - 80a b )cos(x) - 80a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (256a b + 240a b)cos(x) + (- 256a b + 320a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 384a b + 240a b)cos(x) + (- 128a b + 96a b)cos(x) + 16a b +--R * +--R tan(x) +--R + +--R 4 2 3 4 2 2 4 2 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 80a b + 8a b)cos(x) + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 64a b + 20a b )cos(x) + (- 320a b + 112a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 384a b + 236a b )cos(x) + (- 64a b + 200a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b + 16a b )cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (512a b + 10a b)cos(x) + (256a b + 64a b + 56a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (128a b - 304a b + 116a b)cos(x) + (- 112a b + 104a b)cos(x) +--R + +--R 3 3 5 +--R 32a b + 34a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (192a b + 280a b )cos(x) + (- 384a b + 504a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 384a b + 512a b )cos(x) + 208a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b - 40a b )cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (128a b + 120a b)cos(x) + (- 128a b + 160a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 192a b + 120a b)cos(x) + (- 64a b + 48a b)cos(x) + 8a b +--R * +--R sin(2x) +--R + +--R 5 3 5 2 5 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 4 2 4 4 2 3 4 2 6 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a )cos(x) +--R + +--R 4 2 6 6 +--R (- 80a b + 8a )cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 64a b + 20a b)cos(x) + (- 320a b + 112a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- 384a b + 236a b)cos(x) + (- 64a b + 200a b)cos(x) +--R + +--R 3 3 5 5 +--R (64a b + 16a b)cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 4 2 6 4 2 4 4 2 6 3 +--R (512a b + 10a )cos(x) + (256a b + 64a b + 56a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (128a b - 304a b + 116a )cos(x) + (- 112a b + 104a )cos(x) +--R + +--R 4 2 6 +--R 32a b + 34a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (192a b + 280a b)cos(x) + (- 384a b + 504a b)cos(x) +--R + +--R 3 3 5 3 5 2 3 3 5 +--R (- 384a b + 512a b)cos(x) + 208a b cos(x) + (64a b - 40a b)cos(x) +--R + +--R 5 +--R - 40a b +--R * +--R sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (64a b + 8a )cos(x) + (192a b + 48a )cos(x) +--R + +--R 4 2 6 4 4 2 6 3 +--R (128a b + 120a )cos(x) + (- 128a b + 160a )cos(x) +--R + +--R 4 2 6 2 4 2 6 6 +--R (- 192a b + 120a )cos(x) + (- 64a b + 48a )cos(x) + 8a +--R Type: Expression(Integer) +--E 17 + +)clear all + + +--S 18 of 526 +t0803:= cos(x)^2/(a+b*sin(2*x)) +--R +--R +--R 2 +--R cos(x) +--R (1) ------------- +--R b sin(2x) + a +--R Type: Expression(Integer) +--E 18 + +--S 19 of 526 +r0803:= 1/2*atan((b+a*tan(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(1/2)+_ + 1/4*log(a+b*sin(2*x))/b +--R +--R +--R +---------+ +--R | 2 2 a tan(x) + b +--R \|- b + a log(b sin(2x) + a) + 2b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) ------------------------------------------------------ +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 526 +a0803:= integrate(t0803,x) +--R +--R +--R (3) +--R [ +--R b +--R * +--R log +--R 2 2 2 2 2 +--R (2a b cos(x)sin(x) + (- 2b + 2a )cos(x) + 2b - a ) +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 3 2 2 3 2 +--R (2a b - 2a )cos(x)sin(x) + (- 2b + 2a b)cos(x) + 2b - 2a b +--R / +--R 2b cos(x)sin(x) + a +--R + +--R +-------+ +-------+ +--R | 2 2 8b cos(x)sin(x) + 4a | 2 2 2 +--R \|b - a log(---------------------) - 2\|b - a log(----------) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R / +--R +-------+ +--R | 2 2 +--R 4b\|b - a +--R , +--R +--R +---------+ +---------+ +--R | 2 2 8b cos(x)sin(x) + 4a | 2 2 2 +--R \|- b + a log(---------------------) - 2\|- b + a log(----------) +--R 2 cos(x) + 1 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - 2b cos(x) - 2b)\|- b + a +--R - 2b atan(---------------------------------------) +--R 2 2 2 2 +--R (2b - 2a )cos(x) + 2b - 2a +--R + +--R 2 +--R (a cos(x) + 2a)sin(x) + 3b cos(x) + 2b cos(x) - b +--R 2b atan(--------------------------------------------------) +--R +---------+ +--R 2 | 2 2 +--R (cos(x) + 2cos(x) + 1)\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 20 + +--S 21 of 526 +m0803a:= a0803.1-r0803 +--R +--R +--R (4) +--R +---------+ +--R | 2 2 +--R b\|- b + a +--R * +--R log +--R +-------+ +--R 2 2 2 2 2 | 2 2 +--R (2a b cos(x)sin(x) + (- 2b + 2a )cos(x) + 2b - a )\|b - a +--R + +--R 2 3 3 2 2 3 2 +--R (2a b - 2a )cos(x)sin(x) + (- 2b + 2a b)cos(x) + 2b - 2a b +--R / +--R 2b cos(x)sin(x) + a +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R - \|- b + a \|b - a log(b sin(2x) + a) +--R + +--R +---------+ +-------+ +--R | 2 2 | 2 2 8b cos(x)sin(x) + 4a +--R \|- b + a \|b - a log(---------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +-------+ +-------+ +--R | 2 2 | 2 2 2 | 2 2 a tan(x) + b +--R - 2\|- b + a \|b - a log(----------) - 2b\|b - a atan(------------) +--R cos(x) + 1 +---------+ +--R | 2 2 +--R \|- b + a +--R / +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R 4b\|- b + a \|b - a +--R Type: Expression(Integer) +--E 21 + +--S 22 of 526 +d0803a:= D(m0803a,x) +--R +--R +--R (5) +--R 2 2 3 3 2 2 +--R - 2a b cos(x)sin(x) - 2a b cos(x) sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((4b - 2a b )cos(x) + (- 4b + 2a b )cos(x))sin(x) +--R + +--R 3 4 3 3 2 3 3 +--R 2a b cos(x) + (2a b - 2a b)cos(x) - 2a b + a b +--R * +--R sin(2x) +--R + +--R 3 3 +--R - 2a b cos(x)sin(x) +--R + +--R 2 2 2 4 2 2 +--R (- 4a b cos(x) cos(2x) - 2a cos(x) )sin(x) +--R + +--R 3 3 3 3 +--R ((4a b - 4a b)cos(x) - 4a b cos(x))cos(2x) +--R + +--R 3 3 3 3 3 +--R (4a b - 2a b)cos(x) + (- 4a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 2 4 4 4 +--R ((2a b - 2a )cos(x) - 2a b + a )cos(2x) + 2a cos(x) +--R + +--R 2 2 4 2 2 2 4 +--R (2a b - 2a )cos(x) - 2a b + a +--R * +--R 2 +--R tan(x) +--R + +--R 3 3 4 2 2 2 2 +--R - 4a b cos(x)sin(x) + (8b - 4a b )cos(x) sin(x) +--R + +--R 3 3 3 2 2 4 +--R (4a b cos(x) + 4a b cos(x))sin(x) + 4a b cos(x) +--R * +--R sin(2x) +--R + +--R 2 2 3 +--R - 4a b cos(x)sin(x) +--R + +--R 3 2 3 3 2 2 +--R (- 8a b cos(x) cos(2x) + (8a b - 4a b)cos(x) )sin(x) +--R + +--R 4 2 2 3 4 2 2 3 +--R ((8b - 8a b )cos(x) - 8b cos(x))cos(2x) + 4a b cos(x) +--R + +--R 2 2 +--R 4a b cos(x) +--R * +--R sin(x) +--R + +--R 3 3 2 3 3 3 4 +--R ((4a b - 4a b)cos(x) - 4a b + 2a b)cos(2x) + 4a b cos(x) +--R * +--R tan(x) +--R + +--R 2 2 3 3 2 2 +--R - 2a b cos(x)sin(x) - 2a b cos(x) sin(x) +--R + +--R 4 2 2 3 4 2 2 +--R ((4b - 2a b )cos(x) + (- 4b + 2a b )cos(x))sin(x) +--R + +--R 3 4 3 3 2 3 3 +--R 2a b cos(x) + (2a b - 2a b)cos(x) - 2a b + a b +--R * +--R sin(2x) +--R + +--R 3 3 2 2 2 4 2 2 +--R - 2a b cos(x)sin(x) + (- 4a b cos(x) cos(2x) - 2a cos(x) )sin(x) +--R + +--R 3 3 3 3 +--R ((4a b - 4a b)cos(x) - 4a b cos(x))cos(2x) +--R + +--R 3 3 3 3 3 +--R (4a b - 2a b)cos(x) + (- 4a b + 2a b)cos(x) +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 2 4 4 4 +--R ((2a b - 2a )cos(x) - 2a b + a )cos(2x) + 2a cos(x) +--R + +--R 2 2 4 2 2 2 4 +--R (2a b - 2a )cos(x) - 2a b + a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 3 4 3 +--R (- 2a b + 2a b)cos(x)sin(x) +--R + +--R 5 2 3 4 3 5 2 3 +--R ((4b - 2a b - 2a b)cos(x) + (- 4b + 4a b )cos(x))sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (2a b - 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(2x) +--R + +--R 3 2 5 3 2 3 4 2 2 +--R (- 2a b + 2a )cos(x)sin(x) + (- 4a b + 4a b)cos(x) cos(2x)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R ((4a b - 4a b )cos(x) + (- 4a b + 2a b + 2a )cos(x))cos(2x) +--R + +--R 4 3 2 5 3 4 3 2 +--R (4a b - 2a b - 2a )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 2 +--R ((2a b - 2a b)cos(x) - 2a b + 2a b)cos(2x) + (2a b - 2a b)cos(x) +--R + +--R 2 3 4 +--R - 2a b + 2a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 3 2 3 5 2 3 2 2 +--R (- 4a b + 4a b )cos(x)sin(x) + (8b - 8a b )cos(x) sin(x) +--R + +--R 4 3 2 3 4 3 2 +--R ((4a b - 4a b )cos(x) + (4a b - 4a b )cos(x))sin(x) +--R * +--R sin(2x) +--R + +--R 2 3 4 3 +--R (- 4a b + 4a b)cos(x)sin(x) +--R + +--R 4 3 2 2 4 3 2 2 2 +--R ((- 8a b + 8a b )cos(x) cos(2x) + (8a b - 8a b )cos(x) )sin(x) +--R + +--R 5 2 3 3 5 2 3 4 +--R ((8b - 8a b )cos(x) + (- 8b + 4a b + 4a b)cos(x))cos(2x) +--R + +--R 2 3 4 3 2 3 4 +--R (4a b - 4a b)cos(x) + (4a b - 4a b)cos(x) +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R ((4a b - 4a b )cos(x) - 4a b + 4a b )cos(2x) +--R * +--R tan(x) +--R + +--R 2 3 4 3 +--R (- 2a b + 2a b)cos(x)sin(x) +--R + +--R 5 2 3 4 3 5 2 3 +--R ((4b - 2a b - 2a b)cos(x) + (- 4b + 4a b )cos(x))sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (2a b - 2a b )cos(x) - 2a b + 2a b +--R * +--R sin(2x) +--R + +--R 3 2 5 3 2 3 4 2 2 +--R (- 2a b + 2a )cos(x)sin(x) + (- 4a b + 4a b)cos(x) cos(2x)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R ((4a b - 4a b )cos(x) + (- 4a b + 2a b + 2a )cos(x))cos(2x) +--R + +--R 4 3 2 5 3 4 3 2 +--R (4a b - 2a b - 2a )cos(x) + (- 4a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 2 +--R ((2a b - 2a b)cos(x) - 2a b + 2a b)cos(2x) + (2a b - 2a b)cos(x) +--R + +--R 2 3 4 +--R - 2a b + 2a b +--R / +--R 2 3 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 8a b + 8a b )cos(x) + 8a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 4a b + 4a b)cos(x) + 4a b - 2a b +--R * +--R sin(2x) +--R + +--R 3 2 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 2 3 4 3 2 3 +--R ((- 8a b + 8a b)cos(x) + 8a b cos(x))sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (- 4a b + 4a )cos(x) + 4a b - 2a +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 2 +--R 16a b cos(x) sin(x) +--R + +--R 5 2 3 3 5 +--R ((- 16b + 16a b )cos(x) + 16b cos(x))sin(x) +--R + +--R 4 3 2 2 4 3 2 +--R (- 8a b + 8a b )cos(x) + 8a b - 4a b +--R * +--R sin(2x) +--R + +--R 2 3 2 2 +--R 16a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 16a b + 16a b )cos(x) + 16a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 8a b + 8a b)cos(x) + 8a b - 4a b +--R * +--R tan(x) +--R + +--R 2 3 2 2 +--R 8a b cos(x) sin(x) +--R + +--R 4 3 2 3 4 +--R ((- 8a b + 8a b )cos(x) + 8a b cos(x))sin(x) +--R + +--R 2 3 4 2 2 3 4 +--R (- 4a b + 4a b)cos(x) + 4a b - 2a b +--R * +--R sin(2x) +--R + +--R 3 2 2 2 2 3 4 3 2 3 +--R 8a b cos(x) sin(x) + ((- 8a b + 8a b)cos(x) + 8a b cos(x))sin(x) +--R + +--R 3 2 5 2 3 2 5 +--R (- 4a b + 4a )cos(x) + 4a b - 2a +--R * +--R +-------+ +--R | 2 2 +--R \|b - a +--R + +--R 2 4 4 2 2 2 +--R (8a b - 8a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b - 4a b +--R * +--R sin(2x) +--R + +--R 3 3 5 2 2 +--R (8a b - 8a b)cos(x) sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 6 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a )cos(x))sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 4a b + 4a b)cos(x) + 4a b - 4a b +--R * +--R 2 +--R tan(x) +--R + +--R 5 3 3 2 2 +--R (16a b - 16a b )cos(x) sin(x) +--R + +--R 6 2 4 3 6 2 4 4 2 +--R ((- 16b + 16a b )cos(x) + (16b - 8a b - 8a b )cos(x))sin(x) +--R + +--R 5 3 3 2 5 3 3 +--R (- 8a b + 8a b )cos(x) + 8a b - 8a b +--R * +--R sin(2x) +--R + +--R 2 4 4 2 2 2 +--R (16a b - 16a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 16a b + 16a b )cos(x) + (16a b - 8a b - 8a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 8a b + 8a b )cos(x) + 8a b - 8a b +--R * +--R tan(x) +--R + +--R 2 4 4 2 2 2 +--R (8a b - 8a b )cos(x) sin(x) +--R + +--R 5 3 3 3 5 3 3 5 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a b)cos(x))sin(x) +--R + +--R 2 4 4 2 2 2 4 4 2 +--R (- 4a b + 4a b )cos(x) + 4a b - 4a b +--R * +--R sin(2x) +--R + +--R 3 3 5 2 2 +--R (8a b - 8a b)cos(x) sin(x) +--R + +--R 2 4 4 2 3 2 4 4 2 6 +--R ((- 8a b + 8a b )cos(x) + (8a b - 4a b - 4a )cos(x))sin(x) +--R + +--R 3 3 5 2 3 3 5 +--R (- 4a b + 4a b)cos(x) + 4a b - 4a b +--R Type: Expression(Integer) +--E 22 + +--S 23 of 526 +m0803b:= a0803.2-r0803 +--R +--R +--R (6) +--R +---------+ +---------+ +--R | 2 2 | 2 2 8b cos(x)sin(x) + 4a +--R - \|- b + a log(b sin(2x) + a) + \|- b + a log(---------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 2 +--R - 2\|- b + a log(----------) +--R cos(x) + 1 +--R + +--R +---------+ +--R | 2 2 +--R (a sin(x) - 2b cos(x) - 2b)\|- b + a +--R - 2b atan(---------------------------------------) +--R 2 2 2 2 +--R (2b - 2a )cos(x) + 2b - 2a +--R + +--R a tan(x) + b +--R - 2b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R + +--R 2 +--R (a cos(x) + 2a)sin(x) + 3b cos(x) + 2b cos(x) - b +--R 2b atan(--------------------------------------------------) +--R +---------+ +--R 2 | 2 2 +--R (cos(x) + 2cos(x) + 1)\|- b + a +--R / +--R +---------+ +--R | 2 2 +--R 4b\|- b + a +--R Type: Expression(Integer) +--E 23 + +--S 24 of 526 +d0803b:= D(m0803b,x) +--R +--R +--R (7) +--R 4 2 4 4 6 +--R (- a b cos(x) - 4a b cos(x) - 4a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 5 +--R (2a b cos(x) + 20a b cos(x) + 40a b cos(x) + 20a b )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (28a b - 4a b)cos(x) + (104a b - 24a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (100a b - 52a b)cos(x) + (8a b - 44a b)cos(x) - 16a b +--R + +--R 4 +--R - 10a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (96a b - 10a b )cos(x) + (288a b - 60a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (256a b - 110a b )cos(x) + (32a b - 52a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b + 24a b )cos(x) + 16a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 4 6 +--R (64b - 72a b + a b)cos(x) +--R + +--R 5 2 3 4 5 2 3 4 4 +--R (128b - 344a b + 4a b)cos(x) + (- 512a b + 2a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 128b - 192a b - 10a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 +--R (- 64b + 136a b - 20a b)cos(x) + (88a b - 18a b)cos(x) +--R + +--R 4 +--R - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 64a b + 24a b )cos(x) + (- 192a b + 112a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 96a b + 156a b )cos(x) + (192a b - 20a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (192a b - 248a b )cos(x) - 224a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b - 60a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (32a b + 4a b)cos(x) + (96a b + 24a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (48a b + 62a b)cos(x) + (- 128a b + 90a b)cos(x) +--R + +--R 2 3 4 4 4 3 +--R (- 160a b + 76a b)cos(x) + 28a b cos(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R (80a b - 10a b)cos(x) + (32a b - 14a b)cos(x) - 4a b +--R * +--R sin(2x) +--R + +--R 5 2 5 5 6 +--R (- a cos(x) - 4a cos(x) - 4a )sin(x) +--R + +--R 4 3 4 2 4 +--R (- 2a b cos(x) - 8a b cos(x) - 8a b cos(x))cos(2x) +--R + +--R 4 3 4 2 4 4 +--R 2a b cos(x) + 20a b cos(x) + 40a b cos(x) + 20a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 3 3 2 5 2 +--R - 4a b cos(x) + 8a b cos(x) + (52a b - a )cos(x) +--R + +--R 3 2 5 5 +--R (40a b - 4a )cos(x) - 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (28a b - 4a )cos(x) + (104a b - 24a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (100a b - 52a )cos(x) + (8a b - 44a )cos(x) - 16a b - 10a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (32a b - 10a b)cos(x) + (160a b - 56a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (192a b - 118a b)cos(x) + (32a b - 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b - 8a b)cos(x) + 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (96a b - 10a b)cos(x) + (288a b - 60a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (256a b - 110a b)cos(x) + (32a b - 52a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b + 24a b)cos(x) + 16a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (64a b - 40a b )cos(x) + (128a b - 184a b )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 256a b - 5a )cos(x) + (- 128a b - 32a b - 28a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (- 64a b + 152a b - 58a )cos(x) + (56a b - 52a )cos(x) +--R + +--R 3 2 5 +--R - 16a b - 17a +--R * +--R cos(2x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (64a b - 72a b + a )cos(x) + (128a b - 344a b + 4a )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 512a b + 2a )cos(x) + (- 128a b - 192a b - 10a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 5 +--R (- 64a b + 136a b - 20a )cos(x) + (88a b - 18a )cos(x) - 7a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 64a b - 8a b)cos(x) + (- 192a b - 48a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b - 140a b)cos(x) + (192a b - 252a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (192a b - 256a b)cos(x) - 104a b cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b + 20a b)cos(x) + 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 64a b + 24a b)cos(x) + (- 192a b + 112a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b + 156a b)cos(x) + (192a b - 20a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (192a b - 248a b)cos(x) - 224a b cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b - 60a b)cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (- 32a b - 4a )cos(x) + (- 96a b - 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (- 64a b - 60a )cos(x) + (64a b - 80a )cos(x) +--R + +--R 3 2 5 2 3 2 5 5 +--R (96a b - 60a )cos(x) + (32a b - 24a )cos(x) - 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 8 3 2 5 7 +--R (32a b + 4a )cos(x) + (96a b + 24a )cos(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (48a b + 62a )cos(x) + (- 128a b + 90a )cos(x) +--R + +--R 3 2 5 4 5 3 3 2 5 2 +--R (- 160a b + 76a )cos(x) + 28a cos(x) + (80a b - 10a )cos(x) +--R + +--R 3 2 5 5 +--R (32a b - 14a )cos(x) - 4a +--R * +--R 2 +--R tan(x) +--R + +--R 3 2 2 3 2 3 2 6 +--R (- 2a b cos(x) - 8a b cos(x) - 8a b )sin(x) +--R + +--R 2 3 3 2 3 2 2 3 2 3 5 +--R (8a b cos(x) + 56a b cos(x) + 96a b cos(x) + 40a b )sin(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (64a b - 8a b )cos(x) + (192a b - 48a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 +--R (96a b - 102a b )cos(x) + (- 64a b - 80a b )cos(x) +--R + +--R 4 3 2 +--R - 32a b - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 5 5 2 3 4 +--R 128b cos(x) + (256b - 8a b )cos(x) +--R + +--R 5 2 3 3 2 3 2 2 3 2 3 +--R (128b + 16a b )cos(x) + 96a b cos(x) + 64a b cos(x) - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (- 64a b + 2a b )cos(x) + (- 320a b + 8a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 512a b + 14a b )cos(x) + (- 320a b + 36a b )cos(x) +--R + +--R 4 3 2 2 4 3 2 4 +--R (- 32a b + 76a b )cos(x) + (64a b + 68a b )cos(x) + 32a b +--R + +--R 3 2 +--R 20a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 7 2 3 6 2 3 5 +--R 64a b cos(x) + 320a b cos(x) + 592a b cos(x) +--R + +--R 2 3 4 2 3 3 2 3 2 +--R 464a b cos(x) + 16a b cos(x) - 240a b cos(x) +--R + +--R 2 3 2 3 +--R - 160a b cos(x) - 32a b +--R * +--R sin(x) +--R + +--R 4 3 2 8 4 3 2 7 +--R (64a b + 8a b )cos(x) + (192a b + 48a b )cos(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (160a b + 132a b )cos(x) + (- 64a b + 228a b )cos(x) +--R + +--R 4 3 2 4 4 3 2 3 +--R (- 192a b + 272a b )cos(x) + (- 128a b + 216a b )cos(x) +--R + +--R 4 3 2 2 3 2 +--R (- 32a b + 100a b )cos(x) + 20a b cos(x) +--R * +--R sin(2x) +--R + +--R 4 2 4 4 6 +--R (- 2a b cos(x) - 8a b cos(x) - 8a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 +--R (- 4a b cos(x) - 16a b cos(x) - 16a b cos(x))cos(2x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 +--R 8a b cos(x) + 56a b cos(x) + 96a b cos(x) + 40a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 4 2 3 3 2 3 4 2 +--R - 8a b cos(x) + 16a b cos(x) + (104a b - 2a b)cos(x) +--R + +--R 2 3 4 4 +--R (80a b - 8a b)cos(x) - 8a b +--R * +--R cos(2x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (64a b - 8a b)cos(x) + (192a b - 48a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 +--R (96a b - 102a b)cos(x) + (- 64a b - 80a b)cos(x) - 32a b +--R + +--R 4 +--R - 12a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (64a b - 20a b )cos(x) + (320a b - 112a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (384a b - 236a b )cos(x) + (64a b - 200a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (- 64a b - 16a b )cos(x) + 40a b +--R * +--R cos(2x) +--R + +--R 4 5 4 3 2 4 +--R 128a b cos(x) + (256a b - 8a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 3 2 3 2 +--R (128a b + 16a b )cos(x) + 96a b cos(x) + 64a b cos(x) - 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 6 5 2 3 5 +--R (128b - 80a b )cos(x) + (256b - 368a b )cos(x) +--R + +--R 2 3 4 4 +--R (- 512a b - 10a b)cos(x) +--R + +--R 5 2 3 4 3 +--R (- 256b - 64a b - 56a b)cos(x) +--R + +--R 5 2 3 4 2 +--R (- 128b + 304a b - 116a b)cos(x) +--R + +--R 2 3 4 2 3 4 +--R (112a b - 104a b)cos(x) - 32a b - 34a b +--R * +--R cos(2x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 64a b + 2a b)cos(x) + (- 320a b + 8a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 512a b + 14a b)cos(x) + (- 320a b + 36a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (- 32a b + 76a b)cos(x) + (64a b + 68a b)cos(x) + 32a b + 20a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 128a b - 16a b )cos(x) + (- 384a b - 96a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 192a b - 280a b )cos(x) + (384a b - 504a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (384a b - 512a b )cos(x) - 208a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 64a b + 40a b )cos(x) + 40a b +--R * +--R cos(2x) +--R + +--R 3 2 7 3 2 6 3 2 5 3 2 4 +--R 64a b cos(x) + 320a b cos(x) + 592a b cos(x) + 464a b cos(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 +--R 16a b cos(x) - 240a b cos(x) - 160a b cos(x) - 32a b +--R * +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- 64a b - 8a b)cos(x) + (- 192a b - 48a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 128a b - 120a b)cos(x) + (128a b - 160a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 4 +--R (192a b - 120a b)cos(x) + (64a b - 48a b)cos(x) - 8a b +--R * +--R cos(2x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (160a b + 132a b)cos(x) + (- 64a b + 228a b)cos(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (- 192a b + 272a b)cos(x) + (- 128a b + 216a b)cos(x) +--R + +--R 2 3 4 2 4 +--R (- 32a b + 100a b)cos(x) + 20a b cos(x) +--R * +--R tan(x) +--R + +--R 4 2 4 4 6 +--R (- a b cos(x) - 4a b cos(x) - 4a b)sin(x) +--R + +--R 3 2 3 3 2 2 3 2 3 2 5 +--R (2a b cos(x) + 20a b cos(x) + 40a b cos(x) + 20a b )sin(x) +--R + +--R 2 3 4 4 2 3 4 3 +--R (28a b - 4a b)cos(x) + (104a b - 24a b)cos(x) +--R + +--R 2 3 4 2 2 3 4 2 3 4 +--R (100a b - 52a b)cos(x) + (8a b - 44a b)cos(x) - 16a b - 10a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (96a b - 10a b )cos(x) + (288a b - 60a b )cos(x) +--R + +--R 4 3 2 3 4 3 2 2 +--R (256a b - 110a b )cos(x) + (32a b - 52a b )cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b + 24a b )cos(x) + 16a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 3 4 6 5 2 3 4 5 +--R (64b - 72a b + a b)cos(x) + (128b - 344a b + 4a b)cos(x) +--R + +--R 2 3 4 4 5 2 3 4 3 +--R (- 512a b + 2a b)cos(x) + (- 128b - 192a b - 10a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 4 +--R (- 64b + 136a b - 20a b)cos(x) + (88a b - 18a b)cos(x) - 7a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 7 4 3 2 6 +--R (- 64a b + 24a b )cos(x) + (- 192a b + 112a b )cos(x) +--R + +--R 4 3 2 5 4 3 2 4 +--R (- 96a b + 156a b )cos(x) + (192a b - 20a b )cos(x) +--R + +--R 4 3 2 3 3 2 2 +--R (192a b - 248a b )cos(x) - 224a b cos(x) +--R + +--R 4 3 2 3 2 +--R (- 32a b - 60a b )cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 3 4 8 2 3 4 7 +--R (32a b + 4a b)cos(x) + (96a b + 24a b)cos(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (48a b + 62a b)cos(x) + (- 128a b + 90a b)cos(x) +--R + +--R 2 3 4 4 4 3 2 3 4 2 +--R (- 160a b + 76a b)cos(x) + 28a b cos(x) + (80a b - 10a b)cos(x) +--R + +--R 2 3 4 4 +--R (32a b - 14a b)cos(x) - 4a b +--R * +--R sin(2x) +--R + +--R 5 2 5 5 6 +--R (- a cos(x) - 4a cos(x) - 4a )sin(x) +--R + +--R 4 3 4 2 4 4 3 +--R (- 2a b cos(x) - 8a b cos(x) - 8a b cos(x))cos(2x) + 2a b cos(x) +--R + +--R 4 2 4 4 +--R 20a b cos(x) + 40a b cos(x) + 20a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 4 3 2 3 3 2 5 2 +--R - 4a b cos(x) + 8a b cos(x) + (52a b - a )cos(x) +--R + +--R 3 2 5 5 +--R (40a b - 4a )cos(x) - 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (28a b - 4a )cos(x) + (104a b - 24a )cos(x) +--R + +--R 3 2 5 2 3 2 5 3 2 5 +--R (100a b - 52a )cos(x) + (8a b - 44a )cos(x) - 16a b - 10a +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (32a b - 10a b)cos(x) + (160a b - 56a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (192a b - 118a b)cos(x) + (32a b - 100a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b - 8a b)cos(x) + 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (96a b - 10a b)cos(x) + (288a b - 60a b)cos(x) +--R + +--R 2 3 4 3 2 3 4 2 +--R (256a b - 110a b)cos(x) + (32a b - 52a b)cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b + 24a b)cos(x) + 16a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 6 4 3 2 5 +--R (64a b - 40a b )cos(x) + (128a b - 184a b )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 256a b - 5a )cos(x) + (- 128a b - 32a b - 28a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 +--R (- 64a b + 152a b - 58a )cos(x) + (56a b - 52a )cos(x) +--R + +--R 3 2 5 +--R - 16a b - 17a +--R * +--R cos(2x) +--R + +--R 4 3 2 5 6 4 3 2 5 5 +--R (64a b - 72a b + a )cos(x) + (128a b - 344a b + 4a )cos(x) +--R + +--R 3 2 5 4 4 3 2 5 3 +--R (- 512a b + 2a )cos(x) + (- 128a b - 192a b - 10a )cos(x) +--R + +--R 4 3 2 5 2 3 2 5 5 +--R (- 64a b + 136a b - 20a )cos(x) + (88a b - 18a )cos(x) - 7a +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 64a b - 8a b)cos(x) + (- 192a b - 48a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b - 140a b)cos(x) + (192a b - 252a b)cos(x) +--R + +--R 2 3 4 3 4 2 +--R (192a b - 256a b)cos(x) - 104a b cos(x) +--R + +--R 2 3 4 4 +--R (- 32a b + 20a b)cos(x) + 20a b +--R * +--R cos(2x) +--R + +--R 2 3 4 7 2 3 4 6 +--R (- 64a b + 24a b)cos(x) + (- 192a b + 112a b)cos(x) +--R + +--R 2 3 4 5 2 3 4 4 +--R (- 96a b + 156a b)cos(x) + (192a b - 20a b)cos(x) +--R + +--R 2 3 4 3 4 2 2 3 4 +--R (192a b - 248a b)cos(x) - 224a b cos(x) + (- 32a b - 60a b)cos(x) +--R + +--R 4 +--R 4a b +--R * +--R sin(x) +--R + +--R 3 2 5 6 3 2 5 5 +--R (- 32a b - 4a )cos(x) + (- 96a b - 24a )cos(x) +--R + +--R 3 2 5 4 3 2 5 3 +--R (- 64a b - 60a )cos(x) + (64a b - 80a )cos(x) +--R + +--R 3 2 5 2 3 2 5 5 +--R (96a b - 60a )cos(x) + (32a b - 24a )cos(x) - 4a +--R * +--R cos(2x) +--R + +--R 3 2 5 8 3 2 5 7 3 2 5 6 +--R (32a b + 4a )cos(x) + (96a b + 24a )cos(x) + (48a b + 62a )cos(x) +--R + +--R 3 2 5 5 3 2 5 4 5 3 +--R (- 128a b + 90a )cos(x) + (- 160a b + 76a )cos(x) + 28a cos(x) +--R + +--R 3 2 5 2 3 2 5 5 +--R (80a b - 10a )cos(x) + (32a b - 14a )cos(x) - 4a +--R / +--R 4 2 3 4 2 2 4 2 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 80a b + 8a b)cos(x) + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 64a b + 20a b )cos(x) + (- 320a b + 112a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 384a b + 236a b )cos(x) + (- 64a b + 200a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b + 16a b )cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (512a b + 10a b)cos(x) + (256a b + 64a b + 56a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (128a b - 304a b + 116a b)cos(x) +--R + +--R 3 3 5 3 3 5 +--R (- 112a b + 104a b)cos(x) + 32a b + 34a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (192a b + 280a b )cos(x) + (- 384a b + 504a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 384a b + 512a b )cos(x) + 208a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b - 40a b )cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (128a b + 120a b)cos(x) + (- 128a b + 160a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 192a b + 120a b)cos(x) + (- 64a b + 48a b)cos(x) + 8a b +--R * +--R sin(2x) +--R + +--R 5 3 5 2 5 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 4 2 4 4 2 3 4 2 6 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a )cos(x) +--R + +--R 4 2 6 6 +--R (- 80a b + 8a )cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 64a b + 20a b)cos(x) + (- 320a b + 112a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- 384a b + 236a b)cos(x) + (- 64a b + 200a b)cos(x) +--R + +--R 3 3 5 5 +--R (64a b + 16a b)cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 4 2 6 4 2 4 4 2 6 3 +--R (512a b + 10a )cos(x) + (256a b + 64a b + 56a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (128a b - 304a b + 116a )cos(x) + (- 112a b + 104a )cos(x) +--R + +--R 4 2 6 +--R 32a b + 34a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (192a b + 280a b)cos(x) + (- 384a b + 504a b)cos(x) +--R + +--R 3 3 5 3 5 2 +--R (- 384a b + 512a b)cos(x) + 208a b cos(x) +--R + +--R 3 3 5 5 +--R (64a b - 40a b)cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (64a b + 8a )cos(x) + (192a b + 48a )cos(x) +--R + +--R 4 2 6 4 4 2 6 3 +--R (128a b + 120a )cos(x) + (- 128a b + 160a )cos(x) +--R + +--R 4 2 6 2 4 2 6 6 +--R (- 192a b + 120a )cos(x) + (- 64a b + 48a )cos(x) + 8a +--R * +--R 2 +--R tan(x) +--R + +--R 3 3 3 3 3 2 3 3 5 +--R (8a b cos(x) + 32a b cos(x) + 32a b cos(x))sin(x) +--R + +--R 2 4 4 2 4 3 2 4 4 2 2 +--R 16a b cos(x) - 32a b cos(x) + (- 208a b + 4a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (- 160a b + 16a b )cos(x) + 16a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (- 128a b + 40a b )cos(x) + (- 640a b + 224a b )cos(x) +--R + +--R 5 3 3 3 5 3 3 2 +--R (- 768a b + 472a b )cos(x) + (- 128a b + 400a b )cos(x) +--R + +--R 5 3 3 3 3 +--R (128a b + 32a b )cos(x) - 80a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 2 4 6 6 2 4 5 +--R (- 256b + 160a b )cos(x) + (- 512b + 736a b )cos(x) +--R + +--R 2 4 4 2 4 +--R (1024a b + 20a b )cos(x) +--R + +--R 6 2 4 4 2 3 +--R (512b + 128a b + 112a b )cos(x) +--R + +--R 6 2 4 4 2 2 +--R (256b - 608a b + 232a b )cos(x) +--R + +--R 2 4 4 2 2 4 4 2 +--R (- 224a b + 208a b )cos(x) + 64a b + 68a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 6 +--R (256a b + 32a b )cos(x) + (768a b + 192a b )cos(x) +--R + +--R 5 3 3 5 5 3 3 4 +--R (384a b + 560a b )cos(x) + (- 768a b + 1008a b )cos(x) +--R + +--R 5 3 3 3 3 3 2 +--R (- 768a b + 1024a b )cos(x) + 416a b cos(x) +--R + +--R 5 3 3 3 3 +--R (128a b - 80a b )cos(x) - 80a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 4 2 4 4 2 3 +--R (256a b + 240a b )cos(x) + (- 256a b + 320a b )cos(x) +--R + +--R 2 4 4 2 2 2 4 4 2 4 2 +--R (- 384a b + 240a b )cos(x) + (- 128a b + 96a b )cos(x) + 16a b +--R * +--R sin(2x) +--R + +--R 4 2 3 4 2 2 4 2 5 +--R (8a b cos(x) + 32a b cos(x) + 32a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 16a b cos(x) - 32a b cos(x) + (- 208a b + 4a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 160a b + 16a b)cos(x) + 16a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 128a b + 40a b )cos(x) + (- 640a b + 224a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 768a b + 472a b )cos(x) + (- 128a b + 400a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (128a b + 32a b )cos(x) - 80a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 256a b + 160a b )cos(x) + (- 512a b + 736a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (1024a b + 20a b)cos(x) + (512a b + 128a b + 112a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (256a b - 608a b + 232a b)cos(x) + (- 224a b + 208a b)cos(x) +--R + +--R 3 3 5 +--R 64a b + 68a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (256a b + 32a b )cos(x) + (768a b + 192a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (384a b + 560a b )cos(x) + (- 768a b + 1008a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 768a b + 1024a b )cos(x) + 416a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (128a b - 80a b )cos(x) - 80a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (256a b + 240a b)cos(x) + (- 256a b + 320a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 384a b + 240a b)cos(x) + (- 128a b + 96a b)cos(x) + 16a b +--R * +--R tan(x) +--R + +--R 4 2 3 4 2 2 4 2 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 3 3 4 3 3 3 3 3 5 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a b)cos(x) +--R + +--R 3 3 5 5 +--R (- 80a b + 8a b)cos(x) + 8a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (- 64a b + 20a b )cos(x) + (- 320a b + 112a b )cos(x) +--R + +--R 2 4 4 2 3 2 4 4 2 2 +--R (- 384a b + 236a b )cos(x) + (- 64a b + 200a b )cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b + 16a b )cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (512a b + 10a b)cos(x) + (256a b + 64a b + 56a b)cos(x) +--R + +--R 5 3 3 5 2 3 3 5 +--R (128a b - 304a b + 116a b)cos(x) + (- 112a b + 104a b)cos(x) +--R + +--R 3 3 5 +--R 32a b + 34a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 7 2 4 4 2 6 +--R (128a b + 16a b )cos(x) + (384a b + 96a b )cos(x) +--R + +--R 2 4 4 2 5 2 4 4 2 4 +--R (192a b + 280a b )cos(x) + (- 384a b + 504a b )cos(x) +--R + +--R 2 4 4 2 3 4 2 2 +--R (- 384a b + 512a b )cos(x) + 208a b cos(x) +--R + +--R 2 4 4 2 4 2 +--R (64a b - 40a b )cos(x) - 40a b +--R * +--R sin(x) +--R + +--R 3 3 5 6 3 3 5 5 +--R (64a b + 8a b)cos(x) + (192a b + 48a b)cos(x) +--R + +--R 3 3 5 4 3 3 5 3 +--R (128a b + 120a b)cos(x) + (- 128a b + 160a b)cos(x) +--R + +--R 3 3 5 2 3 3 5 5 +--R (- 192a b + 120a b)cos(x) + (- 64a b + 48a b)cos(x) + 8a b +--R * +--R sin(2x) +--R + +--R 5 3 5 2 5 5 +--R (4a b cos(x) + 16a b cos(x) + 16a b cos(x))sin(x) +--R + +--R 4 2 4 4 2 3 4 2 6 2 +--R 8a b cos(x) - 16a b cos(x) + (- 104a b + 2a )cos(x) +--R + +--R 4 2 6 6 +--R (- 80a b + 8a )cos(x) + 8a +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (- 64a b + 20a b)cos(x) + (- 320a b + 112a b)cos(x) +--R + +--R 3 3 5 3 3 3 5 2 +--R (- 384a b + 236a b)cos(x) + (- 64a b + 200a b)cos(x) +--R + +--R 3 3 5 5 +--R (64a b + 16a b)cos(x) - 40a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 4 2 6 2 4 4 2 5 +--R (- 128a b + 80a b )cos(x) + (- 256a b + 368a b )cos(x) +--R + +--R 4 2 6 4 2 4 4 2 6 3 +--R (512a b + 10a )cos(x) + (256a b + 64a b + 56a )cos(x) +--R + +--R 2 4 4 2 6 2 4 2 6 +--R (128a b - 304a b + 116a )cos(x) + (- 112a b + 104a )cos(x) +--R + +--R 4 2 6 +--R 32a b + 34a +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 +--R (128a b + 16a b)cos(x) + (384a b + 96a b)cos(x) +--R + +--R 3 3 5 5 3 3 5 4 +--R (192a b + 280a b)cos(x) + (- 384a b + 504a b)cos(x) +--R + +--R 3 3 5 3 5 2 3 3 5 +--R (- 384a b + 512a b)cos(x) + 208a b cos(x) + (64a b - 40a b)cos(x) +--R + +--R 5 +--R - 40a b +--R * +--R sin(x) +--R + +--R 4 2 6 6 4 2 6 5 +--R (64a b + 8a )cos(x) + (192a b + 48a )cos(x) +--R + +--R 4 2 6 4 4 2 6 3 +--R (128a b + 120a )cos(x) + (- 128a b + 160a )cos(x) +--R + +--R 4 2 6 2 4 2 6 6 +--R (- 192a b + 120a )cos(x) + (- 64a b + 48a )cos(x) + 8a +--R Type: Expression(Integer) +--E 24 + +)clear all + + +--S 25 of 526 +t0804:= csc(2*x)*sin(x) +--R +--R +--R (1) csc(2x)sin(x) +--R Type: Expression(Integer) +--E 25 + +--S 26 of 526 +r0804:= 1/2*atanh(sin(x)) +--R +--R +--R atanh(sin(x)) +--R (2) ------------- +--R 2 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 526 +a0804:= integrate(t0804,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R (3) --------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 27 + +--S 28 of 526 +m0804:= a0804-r0804 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (4) ------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 28 + +--S 29 of 526 +d0804:= D(m0804,x) +--R +--R +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R (5) --------------------------------------------------------------------- +--R 4 2 2 2 +--R 2sin(x) + (- 2cos(x) - 4cos(x) - 4)sin(x) + 2cos(x) + 4cos(x) + 2 +--R Type: Expression(Integer) +--E 29 + +)clear all + + +--S 30 of 526 +t0805:= cos(4*x)*sec(2*x) +--R +--R +--R (1) cos(4x)sec(2x) +--R Type: Expression(Integer) +--E 30 + +--S 31 of 526 +r0805:= -1/2*atanh(sin(2*x))+sin(2*x) +--R +--R +--R - atanh(sin(2x)) + 2sin(2x) +--R (2) --------------------------- +--R 2 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 526 +a0805:= integrate(t0805,x) +--R +--R +--R sin(2x) + cos(2x) + 1 sin(2x) - cos(2x) - 1 +--R - log(---------------------) + log(---------------------) + 2sin(2x) +--R cos(2x) + 1 cos(2x) + 1 +--R (3) -------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 32 + +--S 33 of 526 +m0805:= a0805-r0805 +--R +--R +--R (4) +--R sin(2x) + cos(2x) + 1 sin(2x) - cos(2x) - 1 +--R - log(---------------------) + log(---------------------) + atanh(sin(2x)) +--R cos(2x) + 1 cos(2x) + 1 +--R -------------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 33 + +--S 34 of 526 +d0805:= D(m0805,x) +--R +--R +--R (5) +--R 4 2 2 3 +--R 2sin(2x) + (2cos(2x) + cos(2x) - 2)sin(2x) + cos(2x) - cos(2x) +--R ------------------------------------------------------------------------ +--R 4 2 2 2 +--R sin(2x) + (- cos(2x) - 2cos(2x) - 2)sin(2x) + cos(2x) + 2cos(2x) + 1 +--R Type: Expression(Integer) +--E 34 + +)clear all + + +--S 35 of 526 +t0806:= x*cos(2*x)*sec(x)^3 +--R +--R +--R 3 +--R (1) x cos(2x)sec(x) +--R Type: Expression(Integer) +--E 35 + +--S 36 of 526 +r0806:= -3*%i*x*atan(exp(1)^(%i*x))+3/2*%i*polylog(2,-%i*exp(1)^(%i*x))-_ + 3/2*%i*polylog(2,%i*exp(1)^(%i*x))+1/2*sec(x)-1/2*x*sec(x)*tan(x) +--R +--R There are no library operations named polylog +--R Use HyperDoc Browse or issue +--R )what op polylog +--R to learn if there is any operation containing " polylog " in its +--R name. +--R +--R Cannot find a definition or applicable library operation named +--R polylog with argument type(s) +--R PositiveInteger +--R Expression(Complex(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 36 + +--S 37 of 526 +a0806:= integrate(t0806,x) +--R +--R +--R x +--R ++ 3 +--R (2) | %J cos(2%J)sec(%J) d%J +--R ++ +--R Type: Union(Expression(Integer),...) +--E 37 + +--S 38 of 526 +m0806:= a0806-r0806 +--R +--R +--R x +--R ++ 3 +--R (3) | %J cos(2%J)sec(%J) d%J - r0806 +--R ++ +--R Type: Expression(Integer) +--E 38 + +--S 39 of 526 +d0806:= D(m0806,x) +--R +--R +--R 3 +--R (4) x cos(2x)sec(x) +--R Type: Expression(Integer) +--E 39 + +)clear all + + +--S 40 of 526 +t0807:= sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R \|sin(b x + a) +--R (1) --------------- +--R +------------+ +--R \|cos(b x + a) +--R Type: Expression(Integer) +--E 40 + +--S 41 of 526 +r0807:= -1/2*atan(1-2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2))*2^(1/2)/b+_ + 1/2*atan(1+2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2))*2^(1/2)/b+_ + 1/4*log(1-2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2)+_ + tan(a+b*x))*2^(1/2)/b-1/4*_ + log(1+2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2)+tan(a+b*x))*2^(1/2)/b +--R +--R +--R (2) +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) + (tan(b x + a) + 1)\|cos(b x + a) +--R - \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ - \|2 \|sin(b x + a) + (tan(b x + a) + 1)\|cos(b x + a) +--R \|2 log(---------------------------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) + \|cos(b x + a) +--R 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) - \|cos(b x + a) +--R 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R / +--R 4b +--R Type: Expression(Integer) +--E 41 + +--S 42 of 526 +a0807:= integrate(t0807,x) +--R +--R +--R x +-------------+ +--R ++ \|sin(%J b + a) +--R (3) | ---------------- d%J +--R ++ +-------------+ +--R \|cos(%J b + a) +--R Type: Union(Expression(Integer),...) +--E 42 + +--S 43 of 526 +m0807:= a0807-r0807 +--R +--R +--R (4) +--R x +-------------+ +--R ++ \|sin(%J b + a) +--R 4b | ---------------- d%J +--R ++ +-------------+ +--R \|cos(%J b + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) + (tan(b x + a) + 1)\|cos(b x + a) +--R \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ - \|2 \|sin(b x + a) + (tan(b x + a) + 1)\|cos(b x + a) +--R - \|2 log(---------------------------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) + \|cos(b x + a) +--R - 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|sin(b x + a) - \|cos(b x + a) +--R - 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|cos(b x + a) +--R / +--R 4b +--R Type: Expression(Integer) +--E 43 + +--S 44 of 526 +d0807:= D(m0807,x) +--R +--R +--R (5) +--R 2 2 +--R (- cos(b x + a)sin(b x + a) - cos(b x + a) )tan(b x + a) +--R + +--R 2 2 +--R (sin(b x + a) + 2cos(b x + a)sin(b x + a) - cos(b x + a) )tan(b x + a) +--R + +--R 2 +--R - sin(b x + a) + cos(b x + a)sin(b x + a) +--R * +--R +------------+ +--R \|sin(b x + a) +--R / +--R 2 +--R 2cos(b x + a)sin(b x + a)tan(b x + a) +--R + +--R 2 +--R 4cos(b x + a)sin(b x + a)tan(b x + a) - 4sin(b x + a) +--R + +--R 2cos(b x + a)sin(b x + a) +--R * +--R +------------+ +--R \|cos(b x + a) +--R Type: Expression(Integer) +--E 44 + +)clear all + + +--S 45 of 526 +t0808:= cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2) +--R +--R +--R +------------+ +--R \|cos(b x + a) +--R (1) --------------- +--R +------------+ +--R \|sin(b x + a) +--R Type: Expression(Integer) +--E 45 + +--S 46 of 526 +r0808:= -1/2*atan(-1+2^(1/2)*cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*2^(1/2)/b-_ + 1/2*atan(1+2^(1/2)*cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*2^(1/2)/b-_ + 1/4*log(1+cot(a+b*x)-2^(1/2)*cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*_ + 2^(1/2)/b+1/4*log(1+cot(a+b*x)+2^(1/2)*_ + cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*2^(1/2)/b +--R +--R +--R (2) +--R +------------+ +-+ +------------+ +--R +-+ (cot(b x + a) + 1)\|sin(b x + a) + \|2 \|cos(b x + a) +--R \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ (cot(b x + a) + 1)\|sin(b x + a) - \|2 \|cos(b x + a) +--R - \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ \|sin(b x + a) + \|2 \|cos(b x + a) +--R - 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ \|sin(b x + a) - \|2 \|cos(b x + a) +--R 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R / +--R 4b +--R Type: Expression(Integer) +--E 46 + +--S 47 of 526 +a0808:= integrate(t0808,x) +--R +--R +--R x +-------------+ +--R ++ \|cos(%J b + a) +--R (3) | ---------------- d%J +--R ++ +-------------+ +--R \|sin(%J b + a) +--R Type: Union(Expression(Integer),...) +--E 47 + +--S 48 of 526 +m0808:= a0808-r0808 +--R +--R +--R (4) +--R x +-------------+ +--R ++ \|cos(%J b + a) +--R 4b | ---------------- d%J +--R ++ +-------------+ +--R \|sin(%J b + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ (cot(b x + a) + 1)\|sin(b x + a) + \|2 \|cos(b x + a) +--R - \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ (cot(b x + a) + 1)\|sin(b x + a) - \|2 \|cos(b x + a) +--R \|2 log(-------------------------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ \|sin(b x + a) + \|2 \|cos(b x + a) +--R 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R + +--R +------------+ +-+ +------------+ +--R +-+ \|sin(b x + a) - \|2 \|cos(b x + a) +--R - 2\|2 atan(-------------------------------------) +--R +------------+ +--R \|sin(b x + a) +--R / +--R 4b +--R Type: Expression(Integer) +--E 48 + +--S 49 of 526 +d0808:= D(m0808,x) +--R +--R +--R (5) +--R 2 2 +--R (- cot(b x + a) - cot(b x + a))sin(b x + a) +--R + +--R 2 +--R - cos(b x + a)cot(b x + a) + 2cos(b x + a)cot(b x + a) +--R + +--R cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 2 2 +--R cos(b x + a) cot(b x + a) - cos(b x + a) +--R * +--R +------------+ +--R \|cos(b x + a) +--R / +--R 2 +--R 2cos(b x + a)cot(b x + a) + 4cos(b x + a)cot(b x + a) +--R + +--R 2cos(b x + a) +--R * +--R sin(b x + a) +--R + +--R 2 +--R - 4cos(b x + a) +--R * +--R +------------+ +--R \|sin(b x + a) +--R Type: Expression(Integer) +--E 49 + +)clear all + + +--S 50 of 526 +t0809:= sin(a+b*x)^(1/3)/cos(a+b*x)^(1/3) +--R +--R +--R 3+------------+ +--R \|sin(b x + a) +--R (1) --------------- +--R 3+------------+ +--R \|cos(b x + a) +--R Type: Expression(Integer) +--E 50 + +--S 51 of 526 +r0809:= -1/2*3^(1/2)*atan(1/3*(1-2*sin(a+b*x)^(2/3)/cos(a+b*x)^(2/3))*_ + 3^(1/2))/b-1/2*log(1+sin(a+b*x)^(2/3)/cos(a+b*x)^(2/3))/b+_ + 1/4*log(1-sin(a+b*x)^(2/3)/cos(a+b*x)^(2/3)+_ + sin(a+b*x)^(4/3)/cos(a+b*x)^(4/3))/b +--R +--R +--R (2) +--R 3+------------+2 3+------------+2 +--R \|sin(b x + a) + \|cos(b x + a) +--R - 2log(-----------------------------------) +--R 3+------------+2 +--R \|cos(b x + a) +--R + +--R log +--R 3+------------+2 +--R - cos(b x + a)\|sin(b x + a) +--R + +--R 3+------------+3+------------+ +--R sin(b x + a)\|cos(b x + a) \|sin(b x + a) +--R + +--R 3+------------+2 +--R cos(b x + a)\|cos(b x + a) +--R / +--R 3+------------+2 +--R cos(b x + a)\|cos(b x + a) +--R + +--R +-+3+------------+2 +-+3+------------+2 +--R +-+ 2\|3 \|sin(b x + a) - \|3 \|cos(b x + a) +--R 2\|3 atan(--------------------------------------------) +--R 3+------------+2 +--R 3\|cos(b x + a) +--R / +--R 4b +--R Type: Expression(Integer) +--E 51 + +--S 52 of 526 +--a0809:= integrate(t0809,x) +--E 52 + +--S 53 of 526 +--m0809:= a0809-r0809 +--E 53 + +--S 54 of 526 +--d0809:= D(m0809,x) +--E 54 + +)clear all + + +--S 55 of 526 +t0810:= cos(a+b*x)^(1/3)/sin(a+b*x)^(1/3) +--R +--R +--R 3+------------+ +--R \|cos(b x + a) +--R (1) --------------- +--R 3+------------+ +--R \|sin(b x + a) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 526 +r0810:= 1/2*3^(1/2)*atan(1/3*(1-2*cos(a+b*x)^(2/3)/sin(a+b*x)^(2/3))*_ + 3^(1/2))/b-1/4*log(1+cos(a+b*x)^(4/3)/sin(a+b*x)^(4/3)-_ + cos(a+b*x)^(2/3)/sin(a+b*x)^(2/3))/b+_ + 1/2*log(1+cos(a+b*x)^(2/3)/sin(a+b*x)^(2/3))/b +--R +--R +--R (2) +--R - +--R log +--R 3+------------+2 +--R sin(b x + a)\|sin(b x + a) +--R + +--R 3+------------+3+------------+ +--R cos(b x + a)\|cos(b x + a) \|sin(b x + a) +--R + +--R 3+------------+2 +--R - sin(b x + a)\|cos(b x + a) +--R / +--R 3+------------+2 +--R sin(b x + a)\|sin(b x + a) +--R + +--R 3+------------+2 3+------------+2 +--R \|sin(b x + a) + \|cos(b x + a) +--R 2log(-----------------------------------) +--R 3+------------+2 +--R \|sin(b x + a) +--R + +--R +-+3+------------+2 +-+3+------------+2 +--R +-+ \|3 \|sin(b x + a) - 2\|3 \|cos(b x + a) +--R 2\|3 atan(--------------------------------------------) +--R 3+------------+2 +--R 3\|sin(b x + a) +--R / +--R 4b +--R Type: Expression(Integer) +--E 56 + +--S 57 of 526 +--a0810:= integrate(t0810,x) +--E 57 + +--S 58 of 526 +--m0810:= a0810-r0810 +--E 58 + +--S 59 of 526 +--d0810:= D(m0810,x) +--E 59 + +)clear all + + +--S 60 of 526 +t0811:= x*sin(x)*sec(x)^(1/2) +--R +--R +--R +------+ +--R (1) x sin(x)\|sec(x) +--R Type: Expression(Integer) +--E 60 + +--S 61 of 526 +r0811:= -2*x/sec(x)^(1/2)+4*cos(x)^(1/2)*EllipticE(1/2*x,2)*sec(x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Polynomial(Fraction(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 61 + +--S 62 of 526 +a0811:= integrate(t0811,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 62 + +--S 63 of 526 +m0811:= a0811-r0811 +--R +--R +--R (2) - r0811 + a0811 +--R Type: Polynomial(Integer) +--E 63 + +--S 64 of 526 +d0811:= D(m0811,x) +--R +--R +--R (3) 0 +--R Type: Polynomial(Integer) +--E 64 + +)clear all + + +--S 65 of 526 +t0812:= x*cos(x)*csc(x)^(1/2) +--R +--R +--R +------+ +--R (1) x cos(x)\|csc(x) +--R Type: Expression(Integer) +--E 65 + +--S 66 of 526 +r0812:= 2*x/csc(x)^(1/2)-4*csc(x)^(1/2)*_ + EllipticE(-1/4*%pi+1/2*x,2)*sin(x)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 66 + +--S 67 of 526 +a0812:= integrate(t0812,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 67 + +--S 68 of 526 +m0812:= a0812-r0812 +--R +--R +--R (2) - r0812 + a0812 +--R Type: Polynomial(Integer) +--E 68 + +--S 69 of 526 +d0812:= D(m0812,x) +--R +--R +--R (3) 0 +--R Type: Polynomial(Integer) +--E 69 + +)clear all + + +--S 70 of 526 +t0813:= cos(x)/(cos(x)+1)^(1/2) +--R +--R +--R cos(x) +--R (1) ------------- +--R +----------+ +--R \|cos(x) + 1 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 526 +r0813:= -2*(atanh(sin(1/2*x))*cos(1/2*x)-sin(x))/(cos(x)+1)^(1/2) +--R +--R +--R x x +--R - 2cos(-)atanh(sin(-)) + 2sin(x) +--R 2 2 +--R (2) -------------------------------- +--R +----------+ +--R \|cos(x) + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 526 +a0813:= integrate(t0813,x) +--R +--R +--R (3) +--R +-+ +-+ +--R (\|2 cos(x) + \|2 ) +--R * +--R +-+ +----------+ 2 +--R - 2\|2 sin(x)\|cos(x) + 1 - cos(x) + 2cos(x) + 3 +--R log(--------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R +----------+ +--R 4sin(x)\|cos(x) + 1 +--R / +--R 2cos(x) + 2 +--R Type: Union(Expression(Integer),...) +--E 72 + +--S 73 of 526 +m0813:= a0813-r0813 +--R +--R +--R (4) +--R +-+ +----------+ 2 +--R +-+ +----------+ - 2\|2 sin(x)\|cos(x) + 1 - cos(x) + 2cos(x) + 3 +--R \|2 \|cos(x) + 1 log(--------------------------------------------------) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R x x +--R 4cos(-)atanh(sin(-)) +--R 2 2 +--R / +--R +----------+ +--R 2\|cos(x) + 1 +--R Type: Expression(Integer) +--E 73 + +--S 74 of 526 +d0813:= D(m0813,x) +--R +--R +--R (5) +--R +-+ x x 2 +-+ x 2 +--R (2\|2 cos(-)sin(-) - 2\|2 cos(-))sin(x) +--R 2 2 2 +--R + +--R +-+ +-+ x 3 +-+ +-+ x +--R ((- 2\|2 cos(x) - 2\|2 )sin(-) + (2\|2 cos(x) + 2\|2 )sin(-)) +--R 2 2 +--R * +--R sin(x) +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R +-+ +-+ x 2 +-+ x 2 +-+ +--R (- 2\|2 cos(x) - 2\|2 )sin(-) + (- 2\|2 cos(-) + 2\|2 )cos(x) +--R 2 2 +--R + +--R +-+ x 2 +-+ +--R - 2\|2 cos(-) + 2\|2 +--R 2 +--R * +--R sin(x) +--R * +--R +----------+ +--R \|cos(x) + 1 +--R + +--R x 2 x x x 2 x 2 +--R (cos(-)cos(x) - 2cos(-)cos(x) - 3cos(-))sin(-) - cos(-)cos(x) +--R 2 2 2 2 2 +--R + +--R x x +--R 2cos(-)cos(x) + 3cos(-) +--R 2 2 +--R * +--R sin(x) +--R + +--R 3 2 x 3 +--R (- cos(x) + cos(x) + 5cos(x) + 3)sin(-) +--R 2 +--R + +--R 3 2 x +--R (cos(x) - cos(x) - 5cos(x) - 3)sin(-) +--R 2 +--R * +--R x +--R atanh(sin(-)) +--R 2 +--R + +--R x 2 2 +--R ((3cos(x) + 3)sin(-) - 3cos(x) - 3)sin(x) +--R 2 +--R + +--R 3 2 x 2 x 2 3 +--R (2cos(x) + 4cos(x) + 2cos(x))sin(-) + (- cos(-) - 2)cos(x) +--R 2 2 +--R + +--R x 2 2 x 2 x 2 +--R (cos(-) - 4)cos(x) + (5cos(-) - 2)cos(x) + 3cos(-) +--R 2 2 2 +--R / +--R 3 2 x 2 3 2 +--R (cos(x) - cos(x) - 5cos(x) - 3)sin(-) - cos(x) + cos(x) +--R 2 +--R + +--R 5cos(x) + 3 +--R * +--R +----------+ +--R \|cos(x) + 1 +--R + +--R +-+ 2 +-+ +-+ x 2 +-+ 2 +--R (2\|2 cos(x) + 4\|2 cos(x) + 2\|2 )sin(-) - 2\|2 cos(x) +--R 2 +--R + +--R +-+ +-+ +--R - 4\|2 cos(x) - 2\|2 +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 74 + +)clear all + + +--S 75 of 526 +t0814:= cos(x)/(1-cos(2*x))^(1/2) +--R +--R +--R cos(x) +--R (1) ---------------- +--R +-------------+ +--R \|- cos(2x) + 1 +--R Type: Expression(Integer) +--E 75 + +--S 76 of 526 +r0814:= 1/2*log(sin(x))*2^(1/2)*cos(sin(x)) +--R +--R +--R +-+ +--R \|2 cos(sin(x))log(sin(x)) +--R (2) -------------------------- +--R 2 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 526 +a0814:= integrate(t0814,x) +--R +--R +--R +-+ sin(x) +-+ 2 +--R \|2 log(----------) - \|2 log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (3) ----------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 77 + +--S 78 of 526 +m0814:= a0814-r0814 +--R +--R +--R (4) +--R +-+ +-+ sin(x) +-+ 2 +--R - \|2 cos(sin(x))log(sin(x)) + \|2 log(----------) - \|2 log(----------) +--R cos(x) + 1 cos(x) + 1 +--R ------------------------------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 78 + +--S 79 of 526 +d0814:= D(m0814,x) +--R +--R +--R (5) +--R +-+ +-+ +-+ +--R \|2 cos(x)sin(x)log(sin(x))sin(sin(x)) - \|2 cos(x)cos(sin(x)) + \|2 cos(x) +--R --------------------------------------------------------------------------- +--R 2sin(x) +--R Type: Expression(Integer) +--E 79 + +)clear all + + +--S 80 of 526 +t0815:= tan(x)*(2+3*cos(x))^(1/2) +--R +--R +--R +-----------+ +--R (1) tan(x)\|3cos(x) + 2 +--R Type: Expression(Integer) +--E 80 + +--S 81 of 526 +r0815:= 2*2^(1/2)*atanh(1/2*(2+3*cos(x))^(1/2)*2^(1/2))-2*(2+3*cos(x))^(1/2) +--R +--R +--R +-+ +-----------+ +--R +-+ \|2 \|3cos(x) + 2 +-----------+ +--R (2) 2\|2 atanh(------------------) - 2\|3cos(x) + 2 +--R 2 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 526 +a0815:= integrate(t0815,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ +-+ +-----------+ 2 +--R (- 12\|2 cos(x) - 16\|2 )\|3cos(x) + 2 + 9cos(x) + 48cos(x) +--R + +--R 32 +--R / +--R 2 +--R cos(x) +--R + +--R +-----------+ +--R - 4\|3cos(x) + 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 82 + +--S 83 of 526 +m0815:= a0815-r0815 +--R +--R +--R (4) +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ +-+ +-----------+ 2 +--R (- 12\|2 cos(x) - 16\|2 )\|3cos(x) + 2 + 9cos(x) + 48cos(x) +--R + +--R 32 +--R / +--R 2 +--R cos(x) +--R + +--R +-+ +-----------+ +--R +-+ \|2 \|3cos(x) + 2 +--R - 4\|2 atanh(------------------) +--R 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 83 + +--S 84 of 526 +d0815:= D(m0815,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + + +--S 85 of 526 +t0816:= cot(x)*(1+sin(x))^(1/2) +--R +--R +--R +----------+ +--R (1) cot(x)\|sin(x) + 1 +--R Type: Expression(Integer) +--E 85 + +--S 86 of 526 +r0816:= -2*atanh((1+sin(x))^(1/2))+2*(1+sin(x))^(1/2) +--R +--R +--R +----------+ +----------+ +--R (2) - 2atanh(\|sin(x) + 1 ) + 2\|sin(x) + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 526 +a0816:= integrate(t0816,x) +--R +--R +--R (3) +--R +---------------------+ +--R | 4 +--R (- cos(x) - 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R * +--R log +--R +---------------------+2 +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (2sin(x) + 2cos(x) + 2) |--------------------- + 2sin(x) + 2 +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R * +--R log +--R +---------------------+2 +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (- 2sin(x) - 2cos(x) - 2) |--------------------- + 2sin(x) + 2 +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4sin(x) + 4cos(x) + 4 +--R / +--R +---------------------+ +--R | 4 +--R (2cos(x) + 2) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 87 + +--S 88 of 526 +m0816:= a0816-r0816 +--R +--R +--R (4) +--R +---------------------+ +--R | 4 +--R (- cos(x) - 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R * +--R log +--R +---------------------+2 +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (2sin(x) + 2cos(x) + 2) |--------------------- + 2sin(x) + 2 +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R * +--R log +--R +---------------------+2 +--R | 4 +--R (cos(x) + 1) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +--R (- 2sin(x) - 2cos(x) - 2) |--------------------- + 2sin(x) + 2 +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +----------+ +--R (4cos(x) + 4) |--------------------- atanh(\|sin(x) + 1 ) +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 4 +----------+ +--R (- 4cos(x) - 4) |--------------------- \|sin(x) + 1 + 4sin(x) + 4cos(x) +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R / +--R +---------------------+ +--R | 4 +--R (2cos(x) + 2) |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 88 + +--S 89 of 526 +d0816:= D(m0816,x) +--R +--R +--R (5) +--R 5 4 2 3 +--R 2sin(x) + (cos(x) + 1)sin(x) + (3cos(x) + cos(x) - 2)sin(x) +--R + +--R 3 2 2 +--R (2cos(x) + 3cos(x) - 1)sin(x) +--R + +--R 4 3 2 +--R (2cos(x) + 4cos(x) + 2cos(x) )sin(x) +--R * +--R +---------------------+2 +--R | 4 +--R |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 5 4 2 3 +--R - 2sin(x) + (2cos(x) - 2)sin(x) + (- 4cos(x) + 2)sin(x) +--R + +--R 2 2 2 +--R (- 8cos(x) - 6cos(x) + 2)sin(x) + (- 4cos(x) - 4cos(x))sin(x) +--R * +--R +----------+ +--R \|sin(x) + 1 +--R + +--R 3 2 3 +--R (- 2cos(x) - 4cos(x) - 2cos(x))sin(x) +--R + +--R 4 3 2 2 +--R (- 2cos(x) - 8cos(x) - 10cos(x) - 4cos(x))sin(x) +--R + +--R 5 4 3 2 +--R (- 2cos(x) - 8cos(x) - 12cos(x) - 8cos(x) - 2cos(x))sin(x) +--R + +--R 5 4 3 2 +--R - 2cos(x) - 6cos(x) - 6cos(x) - 2cos(x) +--R * +--R +---------------------+3 +--R | 4 +--R |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 2 3 +--R (2cos(x) + 4cos(x) + 2cos(x))sin(x) +--R + +--R 3 2 2 +--R (6cos(x) + 12cos(x) + 6cos(x))sin(x) +--R + +--R 3 2 3 2 +--R (8cos(x) + 16cos(x) + 8cos(x))sin(x) + 4cos(x) + 8cos(x) + 4cos(x) +--R * +--R +---------------------+ +--R | 4 +--R |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R / +--R 2 3 +--R (2cos(x) + 4cos(x) + 2)sin(x) +--R + +--R 3 2 2 +--R (2cos(x) + 6cos(x) + 6cos(x) + 2)sin(x) +--R + +--R 4 3 2 +--R (2cos(x) + 6cos(x) + 6cos(x) + 2cos(x))sin(x) +--R * +--R +---------------------+3 +--R | 4 +--R |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 2 3 +--R (- 2cos(x) - 4cos(x) - 2)sin(x) +--R + +--R 2 2 2 +--R (- 4cos(x) - 8cos(x) - 4)sin(x) + (- 4cos(x) - 8cos(x) - 4)sin(x) +--R * +--R +---------------------+ +--R | 4 +--R |--------------------- +--R 4| 2 +--R \|cos(x) + 2cos(x) + 1 +--R * +--R +----------+ +--R \|sin(x) + 1 +--R Type: Expression(Integer) +--E 89 + +)clear all + + +--S 90 of 526 +t0817:= cot(x)/(3-cos(x))^(1/2) +--R +--R +--R cot(x) +--R (1) --------------- +--R +------------+ +--R \|- cos(x) + 3 +--R Type: Expression(Integer) +--E 90 + +--S 91 of 526 +r0817:= -1/2*atanh(1/2*(3-cos(x))^(1/2))-_ + 1/2*atanh(1/2*(3-cos(x))^(1/2)*2^(1/2))*2^(1/2) +--R +--R +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|- cos(x) + 3 \|- cos(x) + 3 +--R - \|2 atanh(-------------------) - atanh(---------------) +--R 2 2 +--R (2) --------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 526 +a0817:= integrate(t0817,x) +--R +--R +--R (3) +--R log +--R 3 2 +------------+ 2 +--R (16cos(x) - 112cos(x) - 8cos(x) + 56)\|- cos(x) + 3 + cos(x) +--R + +--R - 30cos(x) + 97 +--R / +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 8\|2 cos(x) + 40\|2 cos(x) + 4\|2 cos(x) - 20\|2 ) +--R * +--R +------------+ +--R \|- cos(x) + 3 +--R + +--R 2 +--R cos(x) - 18cos(x) + 49 +--R / +--R 2 +--R cos(x) - 2cos(x) + 1 +--R / +--R 8 +--R Type: Union(Expression(Integer),...) +--E 92 + +--S 93 of 526 +m0817:= a0817-r0817 +--R +--R +--R (4) +--R log +--R 3 2 +------------+ 2 +--R (16cos(x) - 112cos(x) - 8cos(x) + 56)\|- cos(x) + 3 + cos(x) +--R + +--R - 30cos(x) + 97 +--R / +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R - +--R +-+ +--R \|2 +--R * +--R log +--R +-+ 3 +-+ 2 +-+ +-+ +--R (- 8\|2 cos(x) + 40\|2 cos(x) + 4\|2 cos(x) - 20\|2 ) +--R * +--R +------------+ +--R \|- cos(x) + 3 +--R + +--R 2 +--R cos(x) - 18cos(x) + 49 +--R / +--R 2 +--R cos(x) - 2cos(x) + 1 +--R + +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|- cos(x) + 3 \|- cos(x) + 3 +--R 4\|2 atanh(-------------------) + 4atanh(---------------) +--R 2 2 +--R / +--R 8 +--R Type: Expression(Integer) +--E 93 + +--S 94 of 526 +d0817:= D(m0817,x) +--R +--R +--R (5) +--R +-+ 6 +-+ 5 +-+ 4 +--R 128\|2 cos(x) + (- 1920\|2 + 6)cos(x) + (9024\|2 - 168)cos(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 12480\|2 + 1036)cos(x) + (- 4544\|2 - 1944)cos(x) +--R + +--R +-+ +--R (6720\|2 + 430)cos(x) +--R * +--R +------------+ +--R sin(x)\|- cos(x) + 3 +--R + +--R +-+ 7 +-+ 6 +--R (24\|2 - 48)cos(x) + (- 264\|2 + 720)cos(x) +--R + +--R +-+ 5 +-+ 4 +--R (584\|2 - 3856)cos(x) + (2432\|2 + 10336)cos(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 10408\|2 - 17872)cos(x) + (6920\|2 + 20176)cos(x) +--R + +--R +-+ +--R (6600\|2 - 6384)cos(x) +--R * +--R sin(x) +--R / +--R +-+ 6 +-+ 5 +--R (8\|2 - 16)cos(x) + (- 304\|2 + 448)cos(x) +--R + +--R +-+ 4 +-+ 3 +--R (2812\|2 - 3992)cos(x) + (- 9656\|2 + 13664)cos(x) +--R + +--R +-+ 2 +-+ +-+ +--R (10232\|2 - 14464)cos(x) + (4904\|2 - 6944)cos(x) - 5820\|2 + 8232 +--R * +--R +------------+ +--R \|- cos(x) + 3 +--R + +--R +-+ 8 +-+ 7 +-+ 6 +--R - 128\|2 cos(x) + 2304\|2 cos(x) - 14720\|2 cos(x) +--R + +--R +-+ 5 +-+ 4 +--R (38400\|2 - 1)cos(x) + (- 25504\|2 + 51)cos(x) +--R + +--R +-+ 3 +-+ 2 +--R (- 40128\|2 - 830)cos(x) + (36608\|2 + 5274)cos(x) +--R + +--R +-+ +-+ +--R (10176\|2 - 14401)cos(x) - 10080\|2 + 14259 +--R Type: Expression(Integer) +--E 94 + +)clear all + + +--S 95 of 526 +t0818:= sin(x)/(1+sin(x)^2)^(1/2) +--R +--R +--R sin(x) +--R (1) -------------- +--R +-----------+ +--R | 2 +--R \|sin(x) + 1 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 526 +r0818:= -asin(1/2*cos(x)*2^(1/2)) +--R +--R +--R +-+ +--R \|2 cos(x) +--R (2) - asin(----------) +--R 2 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 526 +a0818:= integrate(t0818,x) +--R +--R +--R (3) +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R - atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 97 + +--S 98 of 526 +m0818:= a0818-r0818 +--R +--R +--R (4) +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R - atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R + +--R +-+ +--R \|2 cos(x) +--R 2asin(----------) +--R 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 98 + +--S 99 of 526 +d0818:= D(m0818,x) +--R +--R +--R (5) +--R 7 6 5 4 3 +--R - 16cos(x) - 16cos(x) + 48cos(x) + 48cos(x) - 36cos(x) +--R + +--R 2 +--R - 36cos(x) + 8cos(x) + 8 +--R * +--R 9 +--R sin(x) +--R + +--R 9 8 7 6 +--R 240cos(x) + 240cos(x) - 1136cos(x) - 1136cos(x) +--R + +--R 5 4 3 2 +--R 1752cos(x) + 1752cos(x) - 964cos(x) - 964cos(x) +--R + +--R 172cos(x) + 172 +--R * +--R 7 +--R sin(x) +--R + +--R 11 10 9 8 +--R - 240cos(x) - 240cos(x) + 1680cos(x) + 1680cos(x) +--R + +--R 7 6 5 4 +--R - 4264cos(x) - 4264cos(x) + 4688cos(x) + 4688cos(x) +--R + +--R 3 2 +--R - 2073cos(x) - 2073cos(x) + 310cos(x) + 310 +--R * +--R 5 +--R sin(x) +--R + +--R 13 12 11 10 +--R 16cos(x) + 16cos(x) - 208cos(x) - 208cos(x) +--R + +--R 9 8 7 6 +--R 920cos(x) + 920cos(x) - 1836cos(x) - 1836cos(x) +--R + +--R 5 4 3 2 +--R 1705cos(x) + 1705cos(x) - 652cos(x) - 652cos(x) +--R + +--R 85cos(x) + 85 +--R * +--R 3 +--R sin(x) +--R + +--R 11 10 9 8 7 +--R - 4cos(x) - 4cos(x) + 24cos(x) + 24cos(x) - 52cos(x) +--R + +--R 6 5 4 3 2 +--R - 52cos(x) + 48cos(x) + 48cos(x) - 17cos(x) - 17cos(x) +--R + +--R 2cos(x) + 2 +--R * +--R sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R + +--R 9 8 7 6 5 +--R - 96cos(x) - 96cos(x) + 464cos(x) + 464cos(x) - 736cos(x) +--R + +--R 4 3 2 +--R - 736cos(x) + 424cos(x) + 424cos(x) - 80cos(x) - 80 +--R * +--R 8 +--R sin(x) +--R + +--R 11 10 9 8 +--R 320cos(x) + 320cos(x) - 2160cos(x) - 2160cos(x) +--R + +--R 7 6 5 4 +--R 5360cos(x) + 5360cos(x) - 5868cos(x) - 5868cos(x) +--R + +--R 3 2 +--R 2664cos(x) + 2664cos(x) - 416cos(x) - 416 +--R * +--R 6 +--R sin(x) +--R + +--R 13 12 11 10 +--R - 96cos(x) - 96cos(x) + 944cos(x) + 944cos(x) +--R + +--R 9 8 7 6 +--R - 3552cos(x) - 3552cos(x) + 6424cos(x) + 6424cos(x) +--R + +--R 5 4 3 2 +--R - 5670cos(x) - 5670cos(x) + 2174cos(x) + 2174cos(x) +--R + +--R - 292cos(x) - 292 +--R * +--R 4 +--R sin(x) +--R + +--R 13 12 11 10 +--R - 16cos(x) - 16cos(x) + 144cos(x) + 144cos(x) +--R + +--R 9 8 7 6 5 +--R - 500cos(x) - 500cos(x) + 836cos(x) + 836cos(x) - 678cos(x) +--R + +--R 4 3 2 +--R - 678cos(x) + 234cos(x) + 234cos(x) - 28cos(x) - 28 +--R * +--R 2 +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 8 6 4 2 8 +--R (192cos(x) - 928cos(x) + 1472cos(x) - 848cos(x) + 160)sin(x) +--R + +--R 10 8 6 4 +--R - 640cos(x) + 4320cos(x) - 10720cos(x) + 11736cos(x) +--R + +--R 2 +--R - 5328cos(x) + 832 +--R * +--R 6 +--R sin(x) +--R + +--R 12 10 8 6 +--R 192cos(x) - 1888cos(x) + 7104cos(x) - 12848cos(x) +--R + +--R 4 2 +--R 11340cos(x) - 4348cos(x) + 584 +--R * +--R 4 +--R sin(x) +--R + +--R 12 10 8 6 +--R 32cos(x) - 288cos(x) + 1000cos(x) - 1672cos(x) +--R + +--R 4 2 +--R 1356cos(x) - 468cos(x) + 56 +--R * +--R 2 +--R sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R + +--R 8 6 4 2 9 +--R (- 32cos(x) + 160cos(x) - 264cos(x) + 160cos(x) - 32)sin(x) +--R + +--R 10 8 6 4 2 +--R 480cos(x) - 3232cos(x) + 8048cos(x) - 8936cos(x) + 4200cos(x) +--R + +--R - 688 +--R * +--R 7 +--R sin(x) +--R + +--R 12 10 8 6 +--R - 480cos(x) + 4320cos(x) - 15248cos(x) + 26432cos(x) +--R + +--R 4 2 +--R - 22898cos(x) + 8912cos(x) - 1240 +--R * +--R 5 +--R sin(x) +--R + +--R 14 12 10 8 6 +--R 32cos(x) - 480cos(x) + 2672cos(x) - 7352cos(x) + 10754cos(x) +--R + +--R 4 2 +--R - 8124cos(x) + 2778cos(x) - 340 +--R * +--R 3 +--R sin(x) +--R + +--R 12 10 8 6 4 +--R - 8cos(x) + 64cos(x) - 200cos(x) + 304cos(x) - 226cos(x) +--R + +--R 2 +--R 72cos(x) - 8 +--R * +--R sin(x) +--R / +--R 9 8 7 6 5 +--R 96cos(x) + 96cos(x) - 464cos(x) - 464cos(x) + 736cos(x) +--R + +--R 4 3 2 +--R 736cos(x) - 424cos(x) - 424cos(x) + 80cos(x) + 80 +--R * +--R 7 +--R sin(x) +--R + +--R 11 10 9 8 +--R - 320cos(x) - 320cos(x) + 2160cos(x) + 2160cos(x) +--R + +--R 7 6 5 4 +--R - 5360cos(x) - 5360cos(x) + 5868cos(x) + 5868cos(x) +--R + +--R 3 2 +--R - 2664cos(x) - 2664cos(x) + 416cos(x) + 416 +--R * +--R 5 +--R sin(x) +--R + +--R 13 12 11 10 9 +--R 96cos(x) + 96cos(x) - 944cos(x) - 944cos(x) + 3552cos(x) +--R + +--R 8 7 6 5 +--R 3552cos(x) - 6424cos(x) - 6424cos(x) + 5670cos(x) +--R + +--R 4 3 2 +--R 5670cos(x) - 2174cos(x) - 2174cos(x) + 292cos(x) + 292 +--R * +--R 3 +--R sin(x) +--R + +--R 13 12 11 10 9 +--R 16cos(x) + 16cos(x) - 144cos(x) - 144cos(x) + 500cos(x) +--R + +--R 8 7 6 5 4 +--R 500cos(x) - 836cos(x) - 836cos(x) + 678cos(x) + 678cos(x) +--R + +--R 3 2 +--R - 234cos(x) - 234cos(x) + 28cos(x) + 28 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R +-------------+ | 2 +--R | 2 | - 4cos(x) + 8 +--R \|- cos(x) + 2 |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 8 6 4 2 8 +--R (32cos(x) - 160cos(x) + 264cos(x) - 160cos(x) + 32)sin(x) +--R + +--R 10 8 6 4 +--R - 480cos(x) + 3232cos(x) - 8048cos(x) + 8936cos(x) +--R + +--R 2 +--R - 4200cos(x) + 688 +--R * +--R 6 +--R sin(x) +--R + +--R 12 10 8 6 +--R 480cos(x) - 4320cos(x) + 15248cos(x) - 26432cos(x) +--R + +--R 4 2 +--R 22898cos(x) - 8912cos(x) + 1240 +--R * +--R 4 +--R sin(x) +--R + +--R 14 12 10 8 +--R - 32cos(x) + 480cos(x) - 2672cos(x) + 7352cos(x) +--R + +--R 6 4 2 +--R - 10754cos(x) + 8124cos(x) - 2778cos(x) + 340 +--R * +--R 2 +--R sin(x) +--R + +--R 12 10 8 6 4 +--R 8cos(x) - 64cos(x) + 200cos(x) - 304cos(x) + 226cos(x) +--R + +--R 2 +--R - 72cos(x) + 8 +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R Type: Expression(Integer) +--E 99 + +)clear all + + +--S 100 of 526 +t0819:= sin(x)*(1+sin(x)^2)^(1/2) +--R +--R +--R +-----------+ +--R | 2 +--R (1) sin(x)\|sin(x) + 1 +--R Type: Expression(Integer) +--E 100 + +--S 101 of 526 +r0819:= -asin(1/2*cos(x)*2^(1/2))-1/2*cos(x)*(2-cos(x)^2)^(1/2) +--R +--R +--R +-------------+ +-+ +--R | 2 \|2 cos(x) +--R - cos(x)\|- cos(x) + 2 - 2asin(----------) +--R 2 +--R (2) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 526 +a0819:= integrate(t0819,x) +--R +--R +--R (3) +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (- 8cos(x) - 8cos(x) + 12cos(x) + 12)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 16cos(x) - 48cos(x) + 34 +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (- 8cos(x) - 8cos(x) + 12cos(x) + 12)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 16cos(x) - 48cos(x) + 34 +--R * +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R + +--R 6 5 4 3 2 +--R (8cos(x) + 8cos(x) - 24cos(x) - 24cos(x) + 17cos(x) + 17cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 5 3 +--R (16cos(x) - 56cos(x) + 48cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (16cos(x) + 16cos(x) - 24cos(x) - 24)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 32cos(x) + 96cos(x) - 68 +--R Type: Union(Expression(Integer),...) +--E 102 + +--S 103 of 526 +m0819:= a0819-r0819 +--R +--R +--R (4) +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (- 8cos(x) - 8cos(x) + 12cos(x) + 12)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 16cos(x) - 48cos(x) + 34 +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 2 +--R (cos(x) + 1)sin(x) |--------------------- - 2cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | - 4cos(x) + 8 +--R (cos(x) + cos(x)) |--------------------- + 2cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (- 8cos(x) - 8cos(x) + 12cos(x) + 12)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 16cos(x) - 48cos(x) + 34 +--R * +--R atan +--R 4 3 2 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (4cos(x) - 6cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (2cos(x) + 2cos(x) - cos(x) - 1)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 4cos(x) + 8cos(x) - 2 +--R + +--R +-------------+ +--R 4 3 2 | 2 +--R (8cos(x) + 8cos(x) - 12cos(x) - 12cos(x))sin(x)\|- cos(x) + 2 +--R + +--R +-+ +--R 3 2 \|2 cos(x) +--R (16cos(x) + 16cos(x) - 24cos(x) - 24)sin(x)asin(----------) +--R 2 +--R + +--R 6 5 4 3 2 +--R 8cos(x) + 8cos(x) - 24cos(x) - 24cos(x) + 17cos(x) + 17cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-------------+ +--R 5 3 | 2 +--R (- 16cos(x) + 48cos(x) - 34cos(x))\|- cos(x) + 2 +--R + +--R +-+ +--R 4 2 \|2 cos(x) +--R (- 32cos(x) + 96cos(x) - 68)asin(----------) +--R 2 +--R + +--R 5 3 +--R (16cos(x) - 56cos(x) + 48cos(x))sin(x) +--R / +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 8 +--R (16cos(x) + 16cos(x) - 24cos(x) - 24)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R - 32cos(x) + 96cos(x) - 68 +--R Type: Expression(Integer) +--E 103 + +--S 104 of 526 +d0819:= D(m0819,x) +--R +--R +--R (5) +--R 13 12 11 10 +--R 1024cos(x) + 1024cos(x) - 8192cos(x) - 8192cos(x) +--R + +--R 9 8 7 6 +--R 26112cos(x) + 26112cos(x) - 41984cos(x) - 41984cos(x) +--R + +--R 5 4 3 2 +--R 35392cos(x) + 35392cos(x) - 14592cos(x) - 14592cos(x) +--R + +--R 2304cos(x) + 2304 +--R * +--R 11 +--R sin(x) +--R + +--R 15 14 13 +--R - 28672cos(x) - 28672cos(x) + 273408cos(x) +--R + +--R 12 11 10 +--R 273408cos(x) - 1079552cos(x) - 1079552cos(x) +--R + +--R 9 8 7 +--R 2270208cos(x) + 2270208cos(x) - 2717008cos(x) +--R + +--R 6 5 4 +--R - 2717008cos(x) + 1824560cos(x) + 1824560cos(x) +--R + +--R 3 2 +--R - 626212cos(x) - 626212cos(x) + 84488cos(x) + 84488 +--R * +--R 9 +--R sin(x) +--R + +--R 17 16 15 +--R 71680cos(x) + 71680cos(x) - 809984cos(x) +--R + +--R 14 13 12 +--R - 809984cos(x) + 3890688cos(x) + 3890688cos(x) +--R + +--R 11 10 9 +--R - 10315008cos(x) - 10315008cos(x) + 16378800cos(x) +--R + +--R 8 7 6 +--R 16378800cos(x) - 15778608cos(x) - 15778608cos(x) +--R + +--R 5 4 3 +--R 8875528cos(x) + 8875528cos(x) - 2619332cos(x) +--R + +--R 2 +--R - 2619332cos(x) + 308716cos(x) + 308716 +--R * +--R 7 +--R sin(x) +--R + +--R 19 18 17 +--R - 28672cos(x) - 28672cos(x) + 394240cos(x) +--R + +--R 16 15 14 +--R 394240cos(x) - 2335232cos(x) - 2335232cos(x) +--R + +--R 13 12 11 +--R 7792128cos(x) + 7792128cos(x) - 16054512cos(x) +--R + +--R 10 9 8 +--R - 16054512cos(x) + 21018896cos(x) + 21018896cos(x) +--R + +--R 7 6 5 +--R - 17296488cos(x) - 17296488cos(x) + 8496880cos(x) +--R + +--R 4 3 2 +--R 8496880cos(x) - 2219321cos(x) - 2219321cos(x) +--R + +--R 233206cos(x) + 233206 +--R * +--R 5 +--R sin(x) +--R + +--R 21 20 19 18 +--R 1024cos(x) + 1024cos(x) - 21504cos(x) - 21504cos(x) +--R + +--R 17 16 15 +--R 180224cos(x) + 180224cos(x) - 823552cos(x) +--R + +--R 14 13 12 +--R - 823552cos(x) + 2305424cos(x) + 2305424cos(x) +--R + +--R 11 10 9 +--R - 4148816cos(x) - 4148816cos(x) + 4849928cos(x) +--R + +--R 8 7 6 +--R 4849928cos(x) - 3607708cos(x) - 3607708cos(x) +--R + +--R 5 4 3 +--R 1611481cos(x) + 1611481cos(x) - 382956cos(x) +--R + +--R 2 +--R - 382956cos(x) + 36565cos(x) + 36565 +--R * +--R 3 +--R sin(x) +--R + +--R 19 18 17 16 +--R - 256cos(x) - 256cos(x) + 3072cos(x) + 3072cos(x) +--R + +--R 15 14 13 +--R - 15936cos(x) - 15936cos(x) + 46656cos(x) +--R + +--R 12 11 10 9 +--R 46656cos(x) - 84356cos(x) - 84356cos(x) + 96728cos(x) +--R + +--R 8 7 6 5 +--R 96728cos(x) - 69380cos(x) - 69380cos(x) + 29440cos(x) +--R + +--R 4 3 2 +--R 29440cos(x) - 6545cos(x) - 6545cos(x) + 578cos(x) + 578 +--R * +--R sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R + +--R 15 14 13 12 +--R 8192cos(x) + 8192cos(x) - 79872cos(x) - 79872cos(x) +--R + +--R 11 10 9 8 +--R 322816cos(x) + 322816cos(x) - 695936cos(x) - 695936cos(x) +--R + +--R 7 6 5 4 +--R 855744cos(x) + 855744cos(x) - 592352cos(x) - 592352cos(x) +--R + +--R 3 2 +--R 210560cos(x) + 210560cos(x) - 29568cos(x) - 29568 +--R * +--R 10 +--R sin(x) +--R + +--R 17 16 15 14 +--R - 57344cos(x) - 57344cos(x) + 652288cos(x) + 652288cos(x) +--R + +--R 13 12 11 +--R - 3159296cos(x) - 3159296cos(x) + 8462976cos(x) +--R + +--R 10 9 8 +--R 8462976cos(x) - 13612896cos(x) - 13612896cos(x) +--R + +--R 7 6 5 +--R 13330320cos(x) + 13330320cos(x) - 7658112cos(x) +--R + +--R 4 3 2 +--R - 7658112cos(x) + 2323208cos(x) + 2323208cos(x) - 283280cos(x) +--R + +--R - 283280 +--R * +--R 8 +--R sin(x) +--R + +--R 19 18 17 16 +--R 57344cos(x) + 57344cos(x) - 766976cos(x) - 766976cos(x) +--R + +--R 15 14 13 +--R 4447488cos(x) + 4447488cos(x) - 14613120cos(x) +--R + +--R 12 11 10 +--R - 14613120cos(x) + 29814336cos(x) + 29814336cos(x) +--R + +--R 9 8 7 +--R - 38874800cos(x) - 38874800cos(x) + 32061280cos(x) +--R + +--R 6 5 4 +--R 32061280cos(x) - 15903716cos(x) - 15903716cos(x) +--R + +--R 3 2 +--R 4233448cos(x) + 4233448cos(x) - 457280cos(x) - 457280 +--R * +--R 6 +--R sin(x) +--R + +--R 21 20 19 18 +--R - 8192cos(x) - 8192cos(x) + 138240cos(x) + 138240cos(x) +--R + +--R 17 16 15 +--R - 1008384cos(x) - 1008384cos(x) + 4190592cos(x) +--R + +--R 14 13 12 +--R 4190592cos(x) - 10970464cos(x) - 10970464cos(x) +--R + +--R 11 10 9 +--R 18831024cos(x) + 18831024cos(x) - 21324528cos(x) +--R + +--R 8 7 6 +--R - 21324528cos(x) + 15574576cos(x) + 15574576cos(x) +--R + +--R 5 4 3 +--R - 6921094cos(x) - 6921094cos(x) + 1659606cos(x) +--R + +--R 2 +--R 1659606cos(x) - 161812cos(x) - 161812 +--R * +--R 4 +--R sin(x) +--R + +--R 21 20 19 18 +--R - 1024cos(x) - 1024cos(x) + 15872cos(x) + 15872cos(x) +--R + +--R 17 16 15 +--R - 107264cos(x) - 107264cos(x) + 415296cos(x) +--R + +--R 14 13 12 +--R 415296cos(x) - 1016368cos(x) - 1016368cos(x) +--R + +--R 11 10 9 +--R 1633744cos(x) + 1633744cos(x) - 1732660cos(x) +--R + +--R 8 7 6 +--R - 1732660cos(x) + 1183124cos(x) + 1183124cos(x) +--R + +--R 5 4 3 2 +--R - 489566cos(x) - 489566cos(x) + 108554cos(x) + 108554cos(x) +--R + +--R - 9724cos(x) - 9724 +--R * +--R 2 +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 8 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 14 12 10 +--R - 16384cos(x) + 159744cos(x) - 645632cos(x) +--R + +--R 8 6 4 2 +--R 1391872cos(x) - 1711488cos(x) + 1184704cos(x) - 421120cos(x) +--R + +--R 59136 +--R * +--R 10 +--R sin(x) +--R + +--R 16 14 12 +--R 114688cos(x) - 1304576cos(x) + 6318592cos(x) +--R + +--R 10 8 6 +--R - 16925952cos(x) + 27225792cos(x) - 26660640cos(x) +--R + +--R 4 2 +--R 15316224cos(x) - 4646416cos(x) + 566560 +--R * +--R 8 +--R sin(x) +--R + +--R 18 16 14 +--R - 114688cos(x) + 1533952cos(x) - 8894976cos(x) +--R + +--R 12 10 8 +--R 29226240cos(x) - 59628672cos(x) + 77749600cos(x) +--R + +--R 6 4 2 +--R - 64122560cos(x) + 31807432cos(x) - 8466896cos(x) + 914560 +--R * +--R 6 +--R sin(x) +--R + +--R 20 18 16 +--R 16384cos(x) - 276480cos(x) + 2016768cos(x) +--R + +--R 14 12 10 +--R - 8381184cos(x) + 21940928cos(x) - 37662048cos(x) +--R + +--R 8 6 4 +--R 42649056cos(x) - 31149152cos(x) + 13842188cos(x) +--R + +--R 2 +--R - 3319212cos(x) + 323624 +--R * +--R 4 +--R sin(x) +--R + +--R 20 18 16 14 +--R 2048cos(x) - 31744cos(x) + 214528cos(x) - 830592cos(x) +--R + +--R 12 10 8 +--R 2032736cos(x) - 3267488cos(x) + 3465320cos(x) +--R + +--R 6 4 2 +--R - 2366248cos(x) + 979132cos(x) - 217108cos(x) + 19448 +--R * +--R 2 +--R sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R + +--R 14 12 10 8 +--R 2048cos(x) - 20480cos(x) + 84992cos(x) - 188416cos(x) +--R + +--R 6 4 2 +--R 238720cos(x) - 170752cos(x) + 62976cos(x) - 9216 +--R * +--R 11 +--R sin(x) +--R + +--R 16 14 12 10 +--R - 57344cos(x) + 661504cos(x) - 3252736cos(x) + 8858624cos(x) +--R + +--R 8 6 4 2 +--R - 14514848cos(x) + 14517152cos(x) - 8550664cos(x) + 2673824cos(x) +--R + +--R - 337952 +--R * +--R 9 +--R sin(x) +--R + +--R 18 16 14 +--R 143360cos(x) - 1906688cos(x) + 11021312cos(x) +--R + +--R 12 10 8 +--R - 36192768cos(x) + 74017632cos(x) - 97072416cos(x) +--R + +--R 6 4 2 +--R 80865488cos(x) - 40740776cos(x) + 11094760cos(x) - 1234864 +--R * +--R 7 +--R sin(x) +--R + +--R 20 18 16 14 +--R - 57344cos(x) + 903168cos(x) - 6247424cos(x) + 24925184cos(x) +--R + +--R 12 10 8 +--R - 63277536cos(x) + 106255840cos(x) - 118668560cos(x) +--R + +--R 6 4 2 +--R 86179712cos(x) - 38426162cos(x) + 9343696cos(x) - 932824 +--R * +--R 5 +--R sin(x) +--R + +--R 22 20 18 16 +--R 2048cos(x) - 47104cos(x) + 446464cos(x) - 2368000cos(x) +--R + +--R 14 12 10 +--R 7905056cos(x) - 17519328cos(x) + 26295120cos(x) +--R + +--R 8 6 4 2 +--R - 26615128cos(x) + 17653794cos(x) - 7211836cos(x) + 1604954cos(x) +--R + +--R - 146260 +--R * +--R 3 +--R sin(x) +--R + +--R 20 18 16 14 +--R - 512cos(x) + 7168cos(x) - 44160cos(x) + 157056cos(x) +--R + +--R 12 10 8 6 +--R - 355336cos(x) + 530880cos(x) - 525672cos(x) + 336400cos(x) +--R + +--R 4 2 +--R - 130850cos(x) + 27336cos(x) - 2312 +--R * +--R sin(x) +--R / +--R 13 12 11 10 +--R 8192cos(x) + 8192cos(x) - 63488cos(x) - 63488cos(x) +--R + +--R 9 8 7 6 +--R 195840cos(x) + 195840cos(x) - 304256cos(x) - 304256cos(x) +--R + +--R 5 4 3 2 +--R 247232cos(x) + 247232cos(x) - 97888cos(x) - 97888cos(x) +--R + +--R 14784cos(x) + 14784 +--R * +--R 9 +--R sin(x) +--R + +--R 15 14 13 12 +--R - 57344cos(x) - 57344cos(x) + 537600cos(x) + 537600cos(x) +--R + +--R 11 10 9 +--R - 2084096cos(x) - 2084096cos(x) + 4294784cos(x) +--R + +--R 8 7 6 5 +--R 4294784cos(x) - 5023328cos(x) - 5023328cos(x) + 3283664cos(x) +--R + +--R 4 3 2 +--R 3283664cos(x) - 1090784cos(x) - 1090784cos(x) + 141640cos(x) +--R + +--R 141640 +--R * +--R 7 +--R sin(x) +--R + +--R 17 16 15 14 +--R 57344cos(x) + 57344cos(x) - 652288cos(x) - 652288cos(x) +--R + +--R 13 12 11 +--R 3142912cos(x) + 3142912cos(x) - 8327296cos(x) +--R + +--R 10 9 8 +--R - 8327296cos(x) + 13159744cos(x) + 13159744cos(x) +--R + +--R 7 6 5 +--R - 12555312cos(x) - 12555312cos(x) + 6950656cos(x) +--R + +--R 4 3 2 +--R 6950656cos(x) - 2002404cos(x) - 2002404cos(x) + 228640cos(x) +--R + +--R 228640 +--R * +--R 5 +--R sin(x) +--R + +--R 19 18 17 16 +--R - 8192cos(x) - 8192cos(x) + 121856cos(x) + 121856cos(x) +--R + +--R 15 14 13 +--R - 764672cos(x) - 764672cos(x) + 2661248cos(x) +--R + +--R 12 11 10 +--R 2661248cos(x) - 5647968cos(x) - 5647968cos(x) +--R + +--R 9 8 7 6 +--R 7535088cos(x) + 7535088cos(x) - 6254352cos(x) - 6254352cos(x) +--R + +--R 5 4 3 2 +--R 3065872cos(x) + 3065872cos(x) - 789350cos(x) - 789350cos(x) +--R + +--R 80906cos(x) + 80906 +--R * +--R 3 +--R sin(x) +--R + +--R 19 18 17 16 +--R - 1024cos(x) - 1024cos(x) + 13824cos(x) + 13824cos(x) +--R + +--R 15 14 13 12 +--R - 79616cos(x) - 79616cos(x) + 256064cos(x) + 256064cos(x) +--R + +--R 11 10 9 8 +--R - 504240cos(x) - 504240cos(x) + 625264cos(x) + 625264cos(x) +--R + +--R 7 6 5 4 +--R - 482132cos(x) - 482132cos(x) + 218860cos(x) + 218860cos(x) +--R + +--R 3 2 +--R - 51846cos(x) - 51846cos(x) + 4862cos(x) + 4862 +--R * +--R sin(x) +--R * +--R +---------------------+ +--R +-------------+ | 2 +--R | 2 | - 4cos(x) + 8 +--R \|- cos(x) + 2 |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 12 10 8 6 +--R 2048cos(x) - 16384cos(x) + 52224cos(x) - 83968cos(x) +--R + +--R 4 2 +--R 70784cos(x) - 29184cos(x) + 4608 +--R * +--R 10 +--R sin(x) +--R + +--R 14 12 10 +--R - 57344cos(x) + 546816cos(x) - 2159104cos(x) +--R + +--R 8 6 4 2 +--R 4540416cos(x) - 5434016cos(x) + 3649120cos(x) - 1252424cos(x) +--R + +--R 168976 +--R * +--R 8 +--R sin(x) +--R + +--R 16 14 12 +--R 143360cos(x) - 1619968cos(x) + 7781376cos(x) +--R + +--R 10 8 6 +--R - 20630016cos(x) + 32757600cos(x) - 31557216cos(x) +--R + +--R 4 2 +--R 17751056cos(x) - 5238664cos(x) + 617432 +--R * +--R 6 +--R sin(x) +--R + +--R 18 16 14 +--R - 57344cos(x) + 788480cos(x) - 4670464cos(x) +--R + +--R 12 10 8 +--R 15584256cos(x) - 32109024cos(x) + 42037792cos(x) +--R + +--R 6 4 2 +--R - 34592976cos(x) + 16993760cos(x) - 4438642cos(x) + 466412 +--R * +--R 4 +--R sin(x) +--R + +--R 20 18 16 14 +--R 2048cos(x) - 43008cos(x) + 360448cos(x) - 1647104cos(x) +--R + +--R 12 10 8 +--R 4610848cos(x) - 8297632cos(x) + 9699856cos(x) +--R + +--R 6 4 2 +--R - 7215416cos(x) + 3222962cos(x) - 765912cos(x) + 73130 +--R * +--R 2 +--R sin(x) +--R + +--R 18 16 14 12 +--R - 512cos(x) + 6144cos(x) - 31872cos(x) + 93312cos(x) +--R + +--R 10 8 6 4 +--R - 168712cos(x) + 193456cos(x) - 138760cos(x) + 58880cos(x) +--R + +--R 2 +--R - 13090cos(x) + 1156 +--R * +--R +-------------+ +--R | 2 +--R \|- cos(x) + 2 +--R Type: Expression(Integer) +--E 104 + +)clear all + + +--S 105 of 526 +t0820:= sin(7+3*x)/(3+sin(7+3*x)^2)^(1/2) +--R +--R +--R sin(3x + 7) +--R (1) ------------------- +--R +----------------+ +--R | 2 +--R \|sin(3x + 7) + 3 +--R Type: Expression(Integer) +--E 105 + +--S 106 of 526 +r0820:= -1/3*asin(1/2*cos(7+3*x)) +--R +--R +--R cos(3x + 7) +--R asin(-----------) +--R 2 +--R (2) - ----------------- +--R 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 526 +a0820:= integrate(t0820,x) +--R +--R +--R (3) +--R - +--R atan +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R (cos(3x + 7) + 1)sin(3x + 7) |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 2 +--R - 2cos(3x + 7) + 2 +--R / +--R +-------------------------------+ +--R | 2 +--R 2 | - 4cos(3x + 7) + 16 +--R (cos(3x + 7) + cos(3x + 7)) |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 2cos(3x + 7)sin(3x + 7) +--R + +--R - +--R atan +--R 4 3 2 +--R 2cos(3x + 7) + 2cos(3x + 7) - 3cos(3x + 7) +--R + +--R - 3cos(3x + 7) +--R * +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 3 +--R (4cos(3x + 7) - 12cos(3x + 7))sin(3x + 7) +--R / +--R 3 2 +--R (2cos(3x + 7) + 2cos(3x + 7) - 2cos(3x + 7) - 2)sin(3x + 7) +--R * +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 4 2 +--R - 4cos(3x + 7) + 14cos(3x + 7) - 4 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 107 + +--S 108 of 526 +m0820:= a0820-r0820 +--R +--R +--R (4) +--R - +--R atan +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R (cos(3x + 7) + 1)sin(3x + 7) |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 2 +--R - 2cos(3x + 7) + 2 +--R / +--R +-------------------------------+ +--R | 2 +--R 2 | - 4cos(3x + 7) + 16 +--R (cos(3x + 7) + cos(3x + 7)) |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 2cos(3x + 7)sin(3x + 7) +--R + +--R - +--R atan +--R 4 3 2 +--R 2cos(3x + 7) + 2cos(3x + 7) - 3cos(3x + 7) +--R + +--R - 3cos(3x + 7) +--R * +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 3 +--R (4cos(3x + 7) - 12cos(3x + 7))sin(3x + 7) +--R / +--R 3 2 +--R (2cos(3x + 7) + 2cos(3x + 7) - 2cos(3x + 7) - 2)sin(3x + 7) +--R * +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 4 2 +--R - 4cos(3x + 7) + 14cos(3x + 7) - 4 +--R + +--R cos(3x + 7) +--R 2asin(-----------) +--R 2 +--R / +--R 6 +--R Type: Expression(Integer) +--E 108 + +--S 109 of 526 +d0820:= D(m0820,x) +--R +--R +--R (5) +--R 7 6 5 +--R - 64cos(3x + 7) - 64cos(3x + 7) + 384cos(3x + 7) +--R + +--R 4 3 2 +--R 384cos(3x + 7) - 576cos(3x + 7) - 576cos(3x + 7) +--R + +--R 256cos(3x + 7) + 256 +--R * +--R 9 +--R sin(3x + 7) +--R + +--R 9 8 7 +--R 592cos(3x + 7) + 592cos(3x + 7) - 5440cos(3x + 7) +--R + +--R 6 5 4 +--R - 5440cos(3x + 7) + 16032cos(3x + 7) + 16032cos(3x + 7) +--R + +--R 3 2 +--R - 16096cos(3x + 7) - 16096cos(3x + 7) + 5056cos(3x + 7) +--R + +--R 5056 +--R * +--R 7 +--R sin(3x + 7) +--R + +--R 11 10 9 +--R 80cos(3x + 7) + 80cos(3x + 7) + 800cos(3x + 7) +--R + +--R 8 7 6 +--R 800cos(3x + 7) - 10744cos(3x + 7) - 10744cos(3x + 7) +--R + +--R 5 4 3 +--R 31456cos(3x + 7) + 31456cos(3x + 7) - 26612cos(3x + 7) +--R + +--R 2 +--R - 26612cos(3x + 7) + 6640cos(3x + 7) + 6640 +--R * +--R 5 +--R sin(3x + 7) +--R + +--R 13 12 11 +--R - 80cos(3x + 7) - 80cos(3x + 7) + 1152cos(3x + 7) +--R + +--R 10 9 8 +--R 1152cos(3x + 7) - 5136cos(3x + 7) - 5136cos(3x + 7) +--R + +--R 7 6 5 +--R 6952cos(3x + 7) + 6952cos(3x + 7) + 2421cos(3x + 7) +--R + +--R 4 3 2 +--R 2421cos(3x + 7) - 4764cos(3x + 7) - 4764cos(3x + 7) +--R + +--R 1156cos(3x + 7) + 1156 +--R * +--R 3 +--R sin(3x + 7) +--R + +--R 15 14 13 +--R - 16cos(3x + 7) - 16cos(3x + 7) + 160cos(3x + 7) +--R + +--R 12 11 10 +--R 160cos(3x + 7) - 504cos(3x + 7) - 504cos(3x + 7) +--R + +--R 9 8 7 +--R 392cos(3x + 7) + 392cos(3x + 7) + 391cos(3x + 7) +--R + +--R 6 5 4 +--R 391cos(3x + 7) - 144cos(3x + 7) - 144cos(3x + 7) +--R + +--R 3 2 +--R - 52cos(3x + 7) - 52cos(3x + 7) + 16cos(3x + 7) + 16 +--R * +--R sin(3x + 7) +--R * +--R +------------------+ +--R | 2 +--R \|- cos(3x + 7) + 4 +--R + +--R 9 8 7 +--R - 320cos(3x + 7) - 320cos(3x + 7) + 3008cos(3x + 7) +--R + +--R 6 5 4 +--R 3008cos(3x + 7) - 9216cos(3x + 7) - 9216cos(3x + 7) +--R + +--R 3 2 +--R 10112cos(3x + 7) + 10112cos(3x + 7) - 3584cos(3x + 7) - 3584 +--R * +--R 8 +--R sin(3x + 7) +--R + +--R 11 10 9 +--R 416cos(3x + 7) + 416cos(3x + 7) - 6112cos(3x + 7) +--R + +--R 8 7 6 +--R - 6112cos(3x + 7) + 31808cos(3x + 7) + 31808cos(3x + 7) +--R + +--R 5 4 3 +--R - 69392cos(3x + 7) - 69392cos(3x + 7) + 57088cos(3x + 7) +--R + +--R 2 +--R 57088cos(3x + 7) - 15104cos(3x + 7) - 15104 +--R * +--R 6 +--R sin(3x + 7) +--R + +--R 13 12 11 +--R 256cos(3x + 7) + 256cos(3x + 7) - 2688cos(3x + 7) +--R + +--R 10 9 8 +--R - 2688cos(3x + 7) + 7968cos(3x + 7) + 7968cos(3x + 7) +--R + +--R 7 6 5 +--R 1480cos(3x + 7) + 1480cos(3x + 7) - 34140cos(3x + 7) +--R + +--R 4 3 2 +--R - 34140cos(3x + 7) + 30696cos(3x + 7) + 30696cos(3x + 7) +--R + +--R - 7136cos(3x + 7) - 7136 +--R * +--R 4 +--R sin(3x + 7) +--R + +--R 15 14 13 +--R 32cos(3x + 7) + 32cos(3x + 7) - 224cos(3x + 7) +--R + +--R 12 11 10 +--R - 224cos(3x + 7) - 96cos(3x + 7) - 96cos(3x + 7) +--R + +--R 9 8 7 +--R 3512cos(3x + 7) + 3512cos(3x + 7) - 6650cos(3x + 7) +--R + +--R 6 5 4 +--R - 6650cos(3x + 7) + 744cos(3x + 7) + 744cos(3x + 7) +--R + +--R 3 2 +--R 1640cos(3x + 7) + 1640cos(3x + 7) - 416cos(3x + 7) - 416 +--R * +--R 2 +--R sin(3x + 7) +--R * +--R +-------------------------------+ +--R | 2 +--R | - 4cos(3x + 7) + 16 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 8 6 4 +--R 640cos(3x + 7) - 6016cos(3x + 7) + 18432cos(3x + 7) +--R + +--R 2 +--R - 20224cos(3x + 7) + 7168 +--R * +--R 8 +--R sin(3x + 7) +--R + +--R 10 8 6 +--R - 832cos(3x + 7) + 12224cos(3x + 7) - 63616cos(3x + 7) +--R + +--R 4 2 +--R 138784cos(3x + 7) - 114176cos(3x + 7) + 30208 +--R * +--R 6 +--R sin(3x + 7) +--R + +--R 12 10 8 +--R - 512cos(3x + 7) + 5376cos(3x + 7) - 15936cos(3x + 7) +--R + +--R 6 4 2 +--R - 2960cos(3x + 7) + 68280cos(3x + 7) - 61392cos(3x + 7) + 14272 +--R * +--R 4 +--R sin(3x + 7) +--R + +--R 14 12 10 +--R - 64cos(3x + 7) + 448cos(3x + 7) + 192cos(3x + 7) +--R + +--R 8 6 4 +--R - 7024cos(3x + 7) + 13300cos(3x + 7) - 1488cos(3x + 7) +--R + +--R 2 +--R - 3280cos(3x + 7) + 832 +--R * +--R 2 +--R sin(3x + 7) +--R * +--R +------------------+ +--R | 2 +--R \|- cos(3x + 7) + 4 +--R + +--R 8 6 4 +--R - 128cos(3x + 7) + 1280cos(3x + 7) - 4224cos(3x + 7) +--R + +--R 2 +--R 5120cos(3x + 7) - 2048 +--R * +--R 9 +--R sin(3x + 7) +--R + +--R 10 8 6 +--R 1184cos(3x + 7) - 15616cos(3x + 7) + 75584cos(3x + 7) +--R + +--R 4 2 +--R - 160448cos(3x + 7) + 138880cos(3x + 7) - 40448 +--R * +--R 7 +--R sin(3x + 7) +--R + +--R 12 10 8 +--R 160cos(3x + 7) + 960cos(3x + 7) - 27888cos(3x + 7) +--R + +--R 6 4 2 +--R 148864cos(3x + 7) - 304872cos(3x + 7) + 226176cos(3x + 7) - 53120 +--R * +--R 5 +--R sin(3x + 7) +--R + +--R 14 12 10 +--R - 160cos(3x + 7) + 2944cos(3x + 7) - 19488cos(3x + 7) +--R + +--R 8 6 4 +--R 54992cos(3x + 7) - 50774cos(3x + 7) - 28896cos(3x + 7) +--R + +--R 2 +--R 40424cos(3x + 7) - 9248 +--R * +--R 3 +--R sin(3x + 7) +--R + +--R 16 14 12 +--R - 32cos(3x + 7) + 448cos(3x + 7) - 2288cos(3x + 7) +--R + +--R 10 8 6 +--R 4816cos(3x + 7) - 2354cos(3x + 7) - 3416cos(3x + 7) +--R + +--R 4 2 +--R 1048cos(3x + 7) + 448cos(3x + 7) - 128 +--R * +--R sin(3x + 7) +--R / +--R 9 8 7 +--R 320cos(3x + 7) + 320cos(3x + 7) - 3008cos(3x + 7) +--R + +--R 6 5 4 +--R - 3008cos(3x + 7) + 9216cos(3x + 7) + 9216cos(3x + 7) +--R + +--R 3 2 +--R - 10112cos(3x + 7) - 10112cos(3x + 7) + 3584cos(3x + 7) + 3584 +--R * +--R 7 +--R sin(3x + 7) +--R + +--R 11 10 9 +--R - 416cos(3x + 7) - 416cos(3x + 7) + 6112cos(3x + 7) +--R + +--R 8 7 6 +--R 6112cos(3x + 7) - 31808cos(3x + 7) - 31808cos(3x + 7) +--R + +--R 5 4 3 +--R 69392cos(3x + 7) + 69392cos(3x + 7) - 57088cos(3x + 7) +--R + +--R 2 +--R - 57088cos(3x + 7) + 15104cos(3x + 7) + 15104 +--R * +--R 5 +--R sin(3x + 7) +--R + +--R 13 12 11 +--R - 256cos(3x + 7) - 256cos(3x + 7) + 2688cos(3x + 7) +--R + +--R 10 9 8 +--R 2688cos(3x + 7) - 7968cos(3x + 7) - 7968cos(3x + 7) +--R + +--R 7 6 5 +--R - 1480cos(3x + 7) - 1480cos(3x + 7) + 34140cos(3x + 7) +--R + +--R 4 3 2 +--R 34140cos(3x + 7) - 30696cos(3x + 7) - 30696cos(3x + 7) +--R + +--R 7136cos(3x + 7) + 7136 +--R * +--R 3 +--R sin(3x + 7) +--R + +--R 15 14 13 +--R - 32cos(3x + 7) - 32cos(3x + 7) + 224cos(3x + 7) +--R + +--R 12 11 10 +--R 224cos(3x + 7) + 96cos(3x + 7) + 96cos(3x + 7) +--R + +--R 9 8 7 +--R - 3512cos(3x + 7) - 3512cos(3x + 7) + 6650cos(3x + 7) +--R + +--R 6 5 4 +--R 6650cos(3x + 7) - 744cos(3x + 7) - 744cos(3x + 7) +--R + +--R 3 2 +--R - 1640cos(3x + 7) - 1640cos(3x + 7) + 416cos(3x + 7) + 416 +--R * +--R sin(3x + 7) +--R * +--R +-------------------------------+ +--R +------------------+ | 2 +--R | 2 | - 4cos(3x + 7) + 16 +--R \|- cos(3x + 7) + 4 |------------------------------- +--R | 2 +--R \|cos(3x + 7) + 2cos(3x + 7) + 1 +--R + +--R 8 6 4 +--R 128cos(3x + 7) - 1280cos(3x + 7) + 4224cos(3x + 7) +--R + +--R 2 +--R - 5120cos(3x + 7) + 2048 +--R * +--R 8 +--R sin(3x + 7) +--R + +--R 10 8 6 +--R - 1184cos(3x + 7) + 15616cos(3x + 7) - 75584cos(3x + 7) +--R + +--R 4 2 +--R 160448cos(3x + 7) - 138880cos(3x + 7) + 40448 +--R * +--R 6 +--R sin(3x + 7) +--R + +--R 12 10 8 +--R - 160cos(3x + 7) - 960cos(3x + 7) + 27888cos(3x + 7) +--R + +--R 6 4 2 +--R - 148864cos(3x + 7) + 304872cos(3x + 7) - 226176cos(3x + 7) +--R + +--R 53120 +--R * +--R 4 +--R sin(3x + 7) +--R + +--R 14 12 10 +--R 160cos(3x + 7) - 2944cos(3x + 7) + 19488cos(3x + 7) +--R + +--R 8 6 4 +--R - 54992cos(3x + 7) + 50774cos(3x + 7) + 28896cos(3x + 7) +--R + +--R 2 +--R - 40424cos(3x + 7) + 9248 +--R * +--R 2 +--R sin(3x + 7) +--R + +--R 16 14 12 +--R 32cos(3x + 7) - 448cos(3x + 7) + 2288cos(3x + 7) +--R + +--R 10 8 6 +--R - 4816cos(3x + 7) + 2354cos(3x + 7) + 3416cos(3x + 7) +--R + +--R 4 2 +--R - 1048cos(3x + 7) - 448cos(3x + 7) + 128 +--R * +--R +------------------+ +--R | 2 +--R \|- cos(3x + 7) + 4 +--R Type: Expression(Integer) +--E 109 + +)clear all + + +--S 110 of 526 +t0821:= cos(x)/(1+cos(x)^2)^(1/2) +--R +--R +--R cos(x) +--R (1) -------------- +--R +-----------+ +--R | 2 +--R \|cos(x) + 1 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 526 +r0821:= asin(1/2*sin(x)*2^(1/2)) +--R +--R +--R +-+ +--R \|2 sin(x) +--R (2) asin(----------) +--R 2 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 526 +a0821:= integrate(t0821,x) +--R +--R +--R (3) +--R - +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R 4 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R sin(x) +--R atan(------) +--R cos(x) +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 112 + +--S 113 of 526 +m0821:= a0821-r0821 +--R +--R +--R (4) +--R - +--R atan +--R +---------------------+ +--R | 2 +--R 3 2 | 4cos(x) + 4 +--R (2cos(x) + 2cos(x) )sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R (- 4cos(x) - 2cos(x))sin(x) +--R / +--R 4 3 2 +--R (2cos(x) + 2cos(x) - cos(x) - cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 +--R - 4cos(x) + 2 +--R + +--R +-+ +--R sin(x) \|2 sin(x) +--R atan(------) - 2asin(----------) +--R cos(x) 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 113 + +--S 114 of 526 +d0821:= D(m0821,x) +--R +--R +--R (5) +--R 13 12 11 10 +--R - 64cos(x) - 64cos(x) - 112cos(x) - 112cos(x) +--R + +--R 9 8 7 6 5 +--R 40cos(x) + 40cos(x) + 89cos(x) + 89cos(x) - 6cos(x) +--R + +--R 4 3 2 +--R - 6cos(x) - 16cos(x) - 16cos(x) - cos(x) - 1 +--R * +--R 2 +--R sin(x) +--R + +--R 15 14 13 12 11 +--R - 64cos(x) - 64cos(x) - 48cos(x) - 48cos(x) + 88cos(x) +--R + +--R 10 9 8 7 6 +--R 88cos(x) + 49cos(x) + 49cos(x) - 43cos(x) - 43cos(x) +--R + +--R 5 4 3 2 +--R - 14cos(x) - 14cos(x) + 7cos(x) + 7cos(x) + cos(x) + 1 +--R * +--R +-------------+ +--R | 2 +--R \|- sin(x) + 2 +--R + +--R 16 15 14 13 +--R - 256cos(x) - 256cos(x) - 256cos(x) - 256cos(x) +--R + +--R 12 11 10 9 8 +--R 192cos(x) + 192cos(x) + 192cos(x) + 192cos(x) - 34cos(x) +--R + +--R 7 6 5 4 3 +--R - 34cos(x) - 34cos(x) - 34cos(x) - 2cos(x) - 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 18 17 14 13 12 +--R - 256cos(x) - 256cos(x) + 448cos(x) + 448cos(x) - 64cos(x) +--R + +--R 11 10 9 8 7 +--R - 64cos(x) - 258cos(x) - 258cos(x) + 60cos(x) + 60cos(x) +--R + +--R 6 5 4 3 2 +--R 50cos(x) + 50cos(x) - 12cos(x) - 12cos(x) - 2cos(x) - 2cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 4cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 13 11 9 7 5 +--R 128cos(x) + 288cos(x) + 16cos(x) - 238cos(x) - 58cos(x) +--R + +--R 3 +--R 50cos(x) + 12cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 15 13 11 9 7 +--R 128cos(x) + 160cos(x) - 144cos(x) - 190cos(x) + 60cos(x) +--R + +--R 5 3 +--R 72cos(x) - 10cos(x) - 8cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|- sin(x) + 2 +--R + +--R 16 14 12 10 8 +--R 512cos(x) + 768cos(x) - 192cos(x) - 608cos(x) - 64cos(x) +--R + +--R 6 4 +--R 120cos(x) + 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 18 16 14 12 10 +--R 512cos(x) + 256cos(x) - 960cos(x) - 288cos(x) + 672cos(x) +--R + +--R 8 6 2 +--R 80cos(x) - 192cos(x) + 16cos(x) +--R / +--R 15 14 13 12 +--R 256cos(x) + 256cos(x) + 256cos(x) + 256cos(x) +--R + +--R 11 10 9 8 7 +--R - 192cos(x) - 192cos(x) - 192cos(x) - 192cos(x) + 34cos(x) +--R + +--R 6 5 4 3 2 +--R 34cos(x) + 34cos(x) + 34cos(x) + 2cos(x) + 2cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 16 13 12 11 +--R 256cos(x) + 256cos(x) - 448cos(x) - 448cos(x) + 64cos(x) +--R + +--R 10 9 8 7 6 +--R 64cos(x) + 258cos(x) + 258cos(x) - 60cos(x) - 60cos(x) +--R + +--R 5 4 3 2 +--R - 50cos(x) - 50cos(x) + 12cos(x) + 12cos(x) + 2cos(x) + 2 +--R * +--R +---------------------+ +--R +-------------+ | 2 +--R | 2 | 4cos(x) + 4 +--R \|- sin(x) + 2 |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 15 13 11 9 +--R - 512cos(x) - 768cos(x) + 192cos(x) + 608cos(x) +--R + +--R 7 5 3 +--R 64cos(x) - 120cos(x) - 24cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 17 15 13 11 9 +--R - 512cos(x) - 256cos(x) + 960cos(x) + 288cos(x) - 672cos(x) +--R + +--R 7 5 +--R - 80cos(x) + 192cos(x) - 16cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|- sin(x) + 2 +--R Type: Expression(Integer) +--E 114 + +)clear all + + +--S 115 of 526 +t0822:= cos(5+3*x)/(3+cos(5+3*x)^2)^(1/2) +--R +--R +--R cos(3x + 5) +--R (1) ------------------- +--R +----------------+ +--R | 2 +--R \|cos(3x + 5) + 3 +--R Type: Expression(Integer) +--E 115 + +--S 116 of 526 +r0822:= 1/3*asin(1/2*sin(5+3*x)) +--R +--R +--R sin(3x + 5) +--R asin(-----------) +--R 2 +--R (2) ----------------- +--R 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 526 +a0822:= integrate(t0822,x) +--R +--R +--R (3) +--R - +--R atan +--R 3 2 +--R (2cos(3x + 5) + 2cos(3x + 5) + cos(3x + 5) + 1)sin(3x + 5) +--R * +--R +-------------------------------+ +--R | 2 +--R | cos(3x + 5) + 3 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 3 +--R (- 2cos(3x + 5) - 4cos(3x + 5))sin(3x + 5) +--R / +--R 4 3 +--R (2cos(3x + 5) + 2cos(3x + 5) ) +--R * +--R +-------------------------------+ +--R | 2 +--R | cos(3x + 5) + 3 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 4 2 +--R - 2cos(3x + 5) - 3cos(3x + 5) + 3 +--R + +--R sin(3x + 5) +--R atan(-----------) +--R cos(3x + 5) +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 117 + +--S 118 of 526 +m0822:= a0822-r0822 +--R +--R +--R (4) +--R - +--R atan +--R 3 2 +--R (2cos(3x + 5) + 2cos(3x + 5) + cos(3x + 5) + 1)sin(3x + 5) +--R * +--R +-------------------------------+ +--R | 2 +--R | cos(3x + 5) + 3 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 3 +--R (- 2cos(3x + 5) - 4cos(3x + 5))sin(3x + 5) +--R / +--R 4 3 +--R (2cos(3x + 5) + 2cos(3x + 5) ) +--R * +--R +-------------------------------+ +--R | 2 +--R | cos(3x + 5) + 3 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 4 2 +--R - 2cos(3x + 5) - 3cos(3x + 5) + 3 +--R + +--R sin(3x + 5) sin(3x + 5) +--R atan(-----------) - 2asin(-----------) +--R cos(3x + 5) 2 +--R / +--R 6 +--R Type: Expression(Integer) +--E 118 + +--S 119 of 526 +d0822:= D(m0822,x) +--R +--R +--R (5) +--R 13 12 11 +--R - 64cos(3x + 5) - 64cos(3x + 5) - 496cos(3x + 5) +--R + +--R 10 9 8 +--R - 496cos(3x + 5) - 1032cos(3x + 5) - 1032cos(3x + 5) +--R + +--R 7 6 5 +--R - 183cos(3x + 5) - 183cos(3x + 5) + 729cos(3x + 5) +--R + +--R 4 3 2 +--R 729cos(3x + 5) - 9cos(3x + 5) - 9cos(3x + 5) +--R + +--R - 81cos(3x + 5) - 81 +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 15 14 13 +--R - 64cos(3x + 5) - 64cos(3x + 5) - 432cos(3x + 5) +--R + +--R 12 11 10 +--R - 432cos(3x + 5) - 792cos(3x + 5) - 792cos(3x + 5) +--R + +--R 9 8 7 +--R 81cos(3x + 5) + 81cos(3x + 5) + 864cos(3x + 5) +--R + +--R 6 5 4 +--R 864cos(3x + 5) - 162cos(3x + 5) - 162cos(3x + 5) +--R + +--R 3 2 +--R - 216cos(3x + 5) - 216cos(3x + 5) + 81cos(3x + 5) + 81 +--R * +--R +------------------+ +--R | 2 +--R \|- sin(3x + 5) + 4 +--R + +--R 16 15 14 +--R - 256cos(3x + 5) - 256cos(3x + 5) - 1792cos(3x + 5) +--R + +--R 13 12 11 +--R - 1792cos(3x + 5) - 3904cos(3x + 5) - 3904cos(3x + 5) +--R + +--R 10 9 8 +--R - 1920cos(3x + 5) - 1920cos(3x + 5) + 2094cos(3x + 5) +--R + +--R 7 6 5 +--R 2094cos(3x + 5) + 1062cos(3x + 5) + 1062cos(3x + 5) +--R + +--R 4 3 2 +--R - 414cos(3x + 5) - 414cos(3x + 5) - 54cos(3x + 5) +--R + +--R - 54cos(3x + 5) +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 18 17 16 +--R - 256cos(3x + 5) - 256cos(3x + 5) - 1536cos(3x + 5) +--R + +--R 15 14 13 +--R - 1536cos(3x + 5) - 2112cos(3x + 5) - 2112cos(3x + 5) +--R + +--R 12 11 10 +--R 1728cos(3x + 5) + 1728cos(3x + 5) + 2862cos(3x + 5) +--R + +--R 9 8 7 +--R 2862cos(3x + 5) - 1944cos(3x + 5) - 1944cos(3x + 5) +--R + +--R 6 5 4 +--R - 540cos(3x + 5) - 540cos(3x + 5) + 648cos(3x + 5) +--R + +--R 3 2 +--R 648cos(3x + 5) - 162cos(3x + 5) - 162cos(3x + 5) +--R * +--R +-------------------------------+ +--R | 2 +--R | cos(3x + 5) + 3 +--R |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 13 11 9 +--R 64cos(3x + 5) + 592cos(3x + 5) + 1704cos(3x + 5) +--R + +--R 7 5 3 +--R 1281cos(3x + 5) - 981cos(3x + 5) - 693cos(3x + 5) +--R + +--R 297cos(3x + 5) +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 15 13 11 +--R 64cos(3x + 5) + 528cos(3x + 5) + 1368cos(3x + 5) +--R + +--R 9 7 5 +--R 729cos(3x + 5) - 1350cos(3x + 5) - 648cos(3x + 5) +--R + +--R 3 +--R 702cos(3x + 5) - 81cos(3x + 5) +--R * +--R +------------------+ +--R | 2 +--R \|- sin(3x + 5) + 4 +--R + +--R 16 14 12 +--R 256cos(3x + 5) + 2176cos(3x + 5) + 6304cos(3x + 5) +--R + +--R 10 8 6 +--R 6192cos(3x + 5) - 1392cos(3x + 5) - 3744cos(3x + 5) +--R + +--R 4 2 +--R 144cos(3x + 5) + 432cos(3x + 5) +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 18 16 14 +--R 256cos(3x + 5) + 1920cos(3x + 5) + 4128cos(3x + 5) +--R + +--R 12 10 6 4 +--R 144cos(3x + 5) - 6048cos(3x + 5) + 3456cos(3x + 5) - 1296cos(3x + 5) +--R / +--R 15 14 13 +--R 256cos(3x + 5) + 256cos(3x + 5) + 1792cos(3x + 5) +--R + +--R 12 11 10 +--R 1792cos(3x + 5) + 3904cos(3x + 5) + 3904cos(3x + 5) +--R + +--R 9 8 7 +--R 1920cos(3x + 5) + 1920cos(3x + 5) - 2094cos(3x + 5) +--R + +--R 6 5 4 +--R - 2094cos(3x + 5) - 1062cos(3x + 5) - 1062cos(3x + 5) +--R + +--R 3 2 +--R 414cos(3x + 5) + 414cos(3x + 5) + 54cos(3x + 5) + 54 +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 17 16 15 +--R 256cos(3x + 5) + 256cos(3x + 5) + 1536cos(3x + 5) +--R + +--R 14 13 12 +--R 1536cos(3x + 5) + 2112cos(3x + 5) + 2112cos(3x + 5) +--R + +--R 11 10 9 +--R - 1728cos(3x + 5) - 1728cos(3x + 5) - 2862cos(3x + 5) +--R + +--R 8 7 6 +--R - 2862cos(3x + 5) + 1944cos(3x + 5) + 1944cos(3x + 5) +--R + +--R 5 4 3 2 +--R 540cos(3x + 5) + 540cos(3x + 5) - 648cos(3x + 5) - 648cos(3x + 5) +--R + +--R 162cos(3x + 5) + 162 +--R * +--R +-------------------------------+ +--R +------------------+ | 2 +--R | 2 | cos(3x + 5) + 3 +--R \|- sin(3x + 5) + 4 |------------------------------- +--R | 2 +--R \|cos(3x + 5) + 2cos(3x + 5) + 1 +--R + +--R 15 13 11 +--R - 256cos(3x + 5) - 2176cos(3x + 5) - 6304cos(3x + 5) +--R + +--R 9 7 5 +--R - 6192cos(3x + 5) + 1392cos(3x + 5) + 3744cos(3x + 5) +--R + +--R 3 +--R - 144cos(3x + 5) - 432cos(3x + 5) +--R * +--R 2 +--R sin(3x + 5) +--R + +--R 17 15 13 +--R - 256cos(3x + 5) - 1920cos(3x + 5) - 4128cos(3x + 5) +--R + +--R 11 9 5 +--R - 144cos(3x + 5) + 6048cos(3x + 5) - 3456cos(3x + 5) +--R + +--R 3 +--R 1296cos(3x + 5) +--R * +--R +------------------+ +--R | 2 +--R \|- sin(3x + 5) + 4 +--R Type: Expression(Integer) +--E 119 + +)clear all + + +--S 120 of 526 +t0823:= cos(x)/(4-cos(x)^2)^(1/2) +--R +--R +--R cos(x) +--R (1) ---------------- +--R +-------------+ +--R | 2 +--R \|- cos(x) + 4 +--R Type: Expression(Integer) +--E 120 + +--S 121 of 526 +r0823:= asinh(1/3*sin(x)*3^(1/2)) +--R +--R +--R +-+ +--R \|3 sin(x) +--R (2) asinh(----------) +--R 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 526 +a0823:= integrate(t0823,x) +--R +--R +--R (3) +--R log +--R +---------------------+ +--R | 2 +--R 3 2 | - 4cos(x) + 16 +--R (- 4cos(x) - 4cos(x) + 10cos(x) + 10)sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 8cos(x) - 40cos(x) + 41 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 122 + +--S 123 of 526 +m0823:= a0823-r0823 +--R +--R +--R (4) +--R log +--R 3 2 +--R (- 4cos(x) - 4cos(x) + 10cos(x) + 10)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 16 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R 8cos(x) - 40cos(x) + 41 +--R + +--R +-+ +--R \|3 sin(x) +--R - 4asinh(----------) +--R 3 +--R / +--R 4 +--R Type: Expression(Integer) +--E 123 + +--S 124 of 526 +d0823:= D(m0823,x) +--R +--R +--R (5) +--R 4 3 2 +--R (- 8cos(x) - 8cos(x) + 20cos(x) + 20cos(x))sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 16 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 2 5 3 +--R (- 12cos(x) + 42cos(x))sin(x) + 4cos(x) - 26cos(x) + 40cos(x) +--R * +--R +-----------+ +--R | 2 +--R \|sin(x) + 3 +--R + +--R 6 5 4 3 2 +--R (- 8cos(x) - 8cos(x) + 40cos(x) + 40cos(x) - 41cos(x) - 41cos(x)) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 16 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 5 3 +--R (- 16cos(x) + 104cos(x) - 160cos(x))sin(x) +--R / +--R 5 4 3 2 +--R (8cos(x) + 8cos(x) - 40cos(x) - 40cos(x) + 41cos(x) + 41) +--R * +--R +---------------------+ +--R | 2 +--R | - 4cos(x) + 16 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 +--R (16cos(x) - 104cos(x) + 160)sin(x) +--R * +--R +-----------+ +--R | 2 +--R \|sin(x) + 3 +--R Type: Expression(Integer) +--E 124 + +)clear all + + +--S 125 of 526 +t0824:= sin(x)/(a*cos(x)+b*sin(x)) +--R +--R +--R sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 125 + +--S 126 of 526 +r0824:= -(-b*x+a*log(a*cos(x)+b*sin(x)))/(a^2+b^2) +--R +--R +--R - a log(b sin(x) + a cos(x)) + b x +--R (2) ---------------------------------- +--R 2 2 +--R b + a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 526 +a0824:= integrate(t0824,x) +--R +--R +--R 2 - 2b sin(x) - 2a cos(x) +--R a log(----------) - a log(-----------------------) + b x +--R cos(x) + 1 cos(x) + 1 +--R (3) -------------------------------------------------------- +--R 2 2 +--R b + a +--R Type: Union(Expression(Integer),...) +--E 127 + +--S 128 of 526 +m0824:= a0824-r0824 +--R +--R +--R (4) +--R 2 +--R a log(b sin(x) + a cos(x)) + a log(----------) +--R cos(x) + 1 +--R + +--R - 2b sin(x) - 2a cos(x) +--R - a log(-----------------------) +--R cos(x) + 1 +--R / +--R 2 2 +--R b + a +--R Type: Expression(Integer) +--E 128 + +--S 129 of 526 +d0824:= D(m0824,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + + +--S 130 of 526 +t0825:= sin(x)^2/(a*cos(x)+b*sin(x)) +--R +--R +--R 2 +--R sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 130 + +--S 131 of 526 +r0825:= -a^2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ + b*cos(x)/(a^2+b^2)-a*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R a atanh(-------------------) + (- a sin(x) - b cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) ---------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 131 + +--S 132 of 526 +a0825:= integrate(t0825,x) +--R +--R +--R (3) +--R 2 +--R a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (- a sin(x) - b cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 132 + +--S 133 of 526 +m0825:= a0825-r0825 +--R +--R +--R (4) +--R 2 +--R a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 2 a sin(x) - b cos(x) +--R - a atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 133 + +--S 134 of 526 +d0825:= D(m0825,x) +--R +--R +--R (5) +--R 3 3 2 2 3 2 3 2 3 +--R a sin(x) - a b cos(x)sin(x) + (a cos(x) - a )sin(x) - a b cos(x) +--R + +--R 2 +--R a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression(Integer) +--E 134 + +)clear all + + +--S 135 of 526 +t0826:= sin(x)^3/(a*cos(x)+b*sin(x)) +--R +--R +--R 3 +--R sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 135 + +--S 136 of 526 +r0826:= 1/2/(a^2+b^2)^2*(3*a^2*b*x+b^3*x-2*a^3*log(a*cos(x)+b*sin(x))-_ + a^2*b*sin(x)*cos(x)-b^3*sin(x)*cos(x)-a^3+a^3*cos(x)^2-_ + b^2*a+b^2*a*cos(x)^2) +--R +--R +--R (2) +--R 3 3 2 +--R - 2a log(b sin(x) + a cos(x)) + (- b - a b)cos(x)sin(x) +--R + +--R 2 3 2 3 2 2 3 +--R (a b + a )cos(x) + (b + 3a b)x - a b - a +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 136 + +--S 137 of 526 +a0826:= integrate(t0826,x) +--R +--R +--R (3) +--R 3 2 3 - 2b sin(x) - 2a cos(x) +--R 2a log(----------) - 2a log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 3 2 2 3 2 3 2 +--R (- b - a b)cos(x)sin(x) + (a b + a )cos(x) + (b + 3a b)x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression(Integer),...) +--E 137 + +--S 138 of 526 +m0826:= a0826-r0826 +--R +--R +--R (4) +--R 3 3 2 +--R 2a log(b sin(x) + a cos(x)) + 2a log(----------) +--R cos(x) + 1 +--R + +--R 3 - 2b sin(x) - 2a cos(x) 2 3 +--R - 2a log(-----------------------) + a b + a +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 138 + +--S 139 of 526 +d0826:= D(m0826,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 139 + +)clear all + + +--S 140 of 526 +t0827:= sin(x)/(a*cos(x)+b*sin(x))^2 +--R +--R +--R sin(x) +--R (1) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 140 + +--S 141 of 526 +r0827:= -b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+_ + a/(a^2+b^2)/(a*cos(x)+b*sin(x)) +--R +--R +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R (b sin(x) + a b cos(x))atanh(-------------------) + a\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) --------------------------------------------------------------- +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b + a b)sin(x) + (a b + a )cos(x))\|b + a +--R Type: Expression(Integer) +--E 141 + +--S 142 of 526 +a0827:= integrate(t0827,x) +--R +--R +--R (3) +--R 2 +--R (b sin(x) + a b cos(x)) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (b sin(x) + a cos(x) + a)\|b + a +--R / +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b + a b)sin(x) + (a b + a )cos(x))\|b + a +--R Type: Union(Expression(Integer),...) +--E 142 + +--S 143 of 526 +m0827:= a0827-r0827 +--R +--R +--R (4) +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R a sin(x) - b cos(x) | 2 2 +--R - b atanh(-------------------) + \|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 143 + +--S 144 of 526 +d0827:= D(m0827,x) +--R +--R +--R (5) +--R 3 2 2 2 2 3 +--R a b sin(x) - b cos(x)sin(x) + (a b cos(x) - a b)sin(x) - b cos(x) +--R + +--R 2 +--R b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression(Integer) +--E 144 + +)clear all + + +--S 145 of 526 +t0828:= sin(x)^2/(a*cos(x)+b*sin(x))^2 +--R +--R +--R 2 +--R sin(x) +--R (1) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 145 + +--S 146 of 526 +r0828:= -(a^2-b^2)*x/(a^2+b^2)^2+a/(a^2+b^2)/(b+a*cot(x))-_ + 2*a*b*log(a*cos(x)+b*sin(x))/(a^2+b^2)^2 +--R +--R +--R (2) +--R 2 2 2 3 +--R (- 2a b cot(x) - 2a b )log(b sin(x) + a cos(x)) + (a b - a )x cot(x) +--R + +--R 3 2 2 3 +--R (b - a b)x + a b + a +--R / +--R 4 3 2 5 5 2 3 4 +--R (a b + 2a b + a )cot(x) + b + 2a b + a b +--R Type: Expression(Integer) +--E 146 + +--S 147 of 526 +a0828:= integrate(t0828,x) +--R +--R +--R (3) +--R 2 2 2 +--R (2a b sin(x) + 2a b cos(x))log(----------) +--R cos(x) + 1 +--R + +--R 2 2 - 2b sin(x) - 2a cos(x) +--R (- 2a b sin(x) - 2a b cos(x))log(-----------------------) +--R cos(x) + 1 +--R + +--R 3 2 2 3 2 3 +--R ((b - a b)x + a b + a )sin(x) + (a b - a )x cos(x) +--R / +--R 5 2 3 4 4 3 2 5 +--R (b + 2a b + a b)sin(x) + (a b + 2a b + a )cos(x) +--R Type: Union(Expression(Integer),...) +--E 147 + +--S 148 of 526 +m0828:= a0828-r0828 +--R +--R +--R (4) +--R 2 2 3 3 2 2 +--R ((2a b cot(x) + 2a b )sin(x) + 2a b cos(x)cot(x) + 2a b cos(x)) +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 2 2 3 3 2 2 +--R ((2a b cot(x) + 2a b )sin(x) + 2a b cos(x)cot(x) + 2a b cos(x)) +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 3 2 2 +--R ((- 2a b cot(x) - 2a b )sin(x) - 2a b cos(x)cot(x) - 2a b cos(x)) +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 4 2 2 4 +--R (a b + a )cot(x)sin(x) + (- a b - a )cos(x) +--R / +--R 5 3 3 5 6 2 4 4 2 +--R ((a b + 2a b + a b)cot(x) + b + 2a b + a b )sin(x) +--R + +--R 2 4 4 2 6 5 3 3 5 +--R (a b + 2a b + a )cos(x)cot(x) + (a b + 2a b + a b)cos(x) +--R Type: Expression(Integer) +--E 148 + +--S 149 of 526 +d0828:= D(m0828,x) +--R +--R +--R (5) +--R 2 2 4 2 3 2 +--R ((- a b + a )cot(x) + 2a b cot(x))sin(x) +--R + +--R 3 2 3 3 2 +--R (- 2a b cos(x)cot(x) - 2a b cos(x))sin(x) + 2a b cos(x) cot(x) +--R + +--R 2 2 4 2 +--R (a b - a )cos(x) +--R / +--R 2 4 4 2 2 5 3 3 6 2 4 2 +--R ((a b + a b )cot(x) + (2a b + 2a b )cot(x) + b + a b )sin(x) +--R + +--R 3 3 5 2 2 4 4 2 +--R (2a b + 2a b)cos(x)cot(x) + (4a b + 4a b )cos(x)cot(x) +--R + +--R 5 3 3 +--R (2a b + 2a b )cos(x) +--R * +--R sin(x) +--R + +--R 4 2 6 2 2 3 3 5 2 +--R (a b + a )cos(x) cot(x) + (2a b + 2a b)cos(x) cot(x) +--R + +--R 2 4 4 2 2 +--R (a b + a b )cos(x) +--R Type: Expression(Integer) +--E 149 + +)clear all + + +--S 150 of 526 +t0829:= sin(x)/(a*cos(x)+b*sin(x))^3 +--R +--R +--R sin(x) +--R (1) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 150 + +--S 151 of 526 +r0829:= 1/2*a/(a^2+b^2)/(a*cos(x)+b*sin(x))^2+_ + b*sin(x)/a/(a^2+b^2)/(a*cos(x)+b*sin(x)) +--R +--R +--R (2) +--R 2 2 2 +--R 2b sin(x) + 2a b cos(x)sin(x) + a +--R -------------------------------------------------------------------------- +--R 4 3 2 2 2 3 4 3 2 5 2 +--R (2a b + 2a b )sin(x) + (4a b + 4a b)cos(x)sin(x) + (2a b + 2a )cos(x) +--R Type: Expression(Integer) +--E 151 + +--S 152 of 526 +a0829:= integrate(t0829,x) +--R +--R +--R 2 +--R - cos(x) + 1 +--R (3) -------------------------------------------------- +--R 2 2 3 2 2 +--R 4a b cos(x)sin(x) + (- 2a b + 2a )cos(x) + 2a b +--R Type: Union(Expression(Integer),...) +--E 152 + +--S 153 of 526 +m0829:= a0829-r0829 +--R +--R +--R (4) +--R 3 3 4 2 2 2 4 2 2 2 +--R - 4a b cos(x)sin(x) + ((b - 7a b )cos(x) - b + a b )sin(x) +--R + +--R 3 3 2 2 4 4 2 2 2 2 2 +--R - 4a b cos(x) sin(x) + (- a b - a )cos(x) + 2a b cos(x) - a b +--R / +--R 2 5 4 3 3 +--R (4a b + 4a b )cos(x)sin(x) +--R + +--R 6 3 4 5 2 2 6 3 4 2 +--R ((- 2a b + 8a b + 10a b )cos(x) + 2a b + 2a b )sin(x) +--R + +--R 2 5 4 3 6 3 2 5 4 3 +--R ((- 4a b + 4a b + 8a b)cos(x) + (4a b + 4a b )cos(x))sin(x) +--R + +--R 3 4 7 4 3 4 5 2 2 +--R (- 2a b + 2a )cos(x) + (2a b + 2a b )cos(x) +--R Type: Expression(Integer) +--E 153 + +--S 154 of 526 +d0829:= D(m0829,x) +--R +--R +--R (5) +--R 6 2 4 2 6 2 4 5 +--R ((b - 3a b )cos(x) + b + a b )sin(x) +--R + +--R 5 3 3 3 3 3 4 +--R ((7a b - 5a b )cos(x) + 4a b cos(x))sin(x) +--R + +--R 2 4 4 2 4 6 2 4 4 2 2 6 3 +--R ((6a b - 2a b )cos(x) + (b - a b + 2a b )cos(x) - b )sin(x) +--R + +--R 5 3 3 5 5 3 3 3 +--R (6a b - 2a b )cos(x) + (- 5a b + 7a b )cos(x) +--R + +--R 5 3 3 +--R (- a b - 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 4 +--R (- b + 9a b - 2a b )cos(x) + (2b - 14a b + 4a b )cos(x) +--R + +--R 6 2 4 4 2 2 2 4 +--R (- b + 6a b - 2a b )cos(x) - a b +--R * +--R sin(x) +--R + +--R 5 3 3 7 5 3 3 5 +--R (- a b + 3a b )cos(x) + (3a b - 5a b )cos(x) +--R + +--R 5 3 3 3 5 +--R (- 3a b + 2a b )cos(x) + a b cos(x) +--R / +--R 2 7 4 5 2 5 +--R (4a b + 4a b )cos(x) sin(x) +--R + +--R 8 3 6 5 4 3 8 3 6 4 +--R ((- 4a b + 12a b + 16a b )cos(x) + (4a b + 4a b )cos(x))sin(x) +--R + +--R 9 2 7 4 5 6 3 4 +--R (b - 13a b + 11a b + 25a b )cos(x) +--R + +--R 9 2 7 4 5 2 9 2 7 +--R (- 2b + 12a b + 14a b )cos(x) + b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 15a b + a b + 19a b )cos(x) +--R + +--R 8 3 6 5 4 3 8 3 6 +--R (- 6a b + 12a b + 18a b )cos(x) + (3a b + 3a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (3a b - 7a b - 3a b + 7a b)cos(x) +--R + +--R 2 7 4 5 6 3 4 2 7 4 5 2 +--R (- 6a b + 4a b + 10a b )cos(x) + (3a b + 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 7 3 6 7 2 5 +--R (a b - a b - a b + a )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 3 +--R (a b + a b )cos(x) +--R Type: Expression(Integer) +--E 154 + +)clear all + + +--S 155 of 526 +t0830:= sin(x)^3/(a*cos(x)+b*sin(x))^3 +--R +--R +--R 3 +--R sin(x) +--R (1) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 155 + +--S 156 of 526 +r0830:= -b*(3*a^2-b^2)*x/(a^2+b^2)^3+1/2*a/(a^2+b^2)/(b+a*cot(x))^2+_ + 2*a*b/(a^2+b^2)^2/(b+a*cot(x))+a*(a^2-3*b^2)*_ + log(a*cos(x)+b*sin(x))/(a^2+b^2)^3 +--R +--R +--R (2) +--R 3 2 5 2 2 3 4 4 3 2 +--R ((- 6a b + 2a )cot(x) + (- 12a b + 4a b)cot(x) - 6a b + 2a b ) +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 2 3 4 2 4 3 2 2 3 4 +--R (2a b - 6a b)x cot(x) + ((4a b - 12a b )x + 4a b + 4a b)cot(x) +--R + +--R 5 2 3 4 3 2 5 +--R (2b - 6a b )x + 5a b + 6a b + a +--R / +--R 2 6 4 4 6 2 8 2 +--R (2a b + 6a b + 6a b + 2a )cot(x) +--R + +--R 7 3 5 5 3 7 8 2 6 4 4 6 2 +--R (4a b + 12a b + 12a b + 4a b)cot(x) + 2b + 6a b + 6a b + 2a b +--R Type: Expression(Integer) +--E 156 + +--S 157 of 526 +a0830:= integrate(t0830,x) +--R +--R +--R (3) +--R 2 3 4 4 3 2 5 2 4 +--R (12a b - 4a b)cos(x)sin(x) + (- 6a b + 8a b - 2a )cos(x) + 6a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 3 4 4 3 2 5 2 4 +--R (- 12a b + 4a b)cos(x)sin(x) + (6a b - 8a b + 2a )cos(x) - 6a b +--R + +--R 3 2 +--R 2a b +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 4 3 2 2 3 4 +--R ((4a b - 12a b )x + 4a b + 4a b)cos(x)sin(x) +--R + +--R 5 2 3 4 4 3 2 5 2 5 2 3 +--R ((- 2b + 8a b - 6a b)x - 5a b - 6a b - a )cos(x) + (2b - 6a b )x +--R + +--R 4 3 2 5 +--R 5a b + 6a b + a +--R / +--R 7 3 5 5 3 7 +--R (4a b + 12a b + 12a b + 4a b)cos(x)sin(x) +--R + +--R 8 2 6 6 2 8 2 8 2 6 4 4 6 2 +--R (- 2b - 4a b + 4a b + 2a )cos(x) + 2b + 6a b + 6a b + 2a b +--R Type: Union(Expression(Integer),...) +--E 157 + +--S 158 of 526 +m0830:= a0830-r0830 +--R +--R +--R (4) +--R 4 3 6 2 3 4 5 2 +--R (12a b - 4a b)cos(x)cot(x) + (24a b - 8a b )cos(x)cot(x) +--R + +--R 2 5 4 3 +--R (12a b - 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 2 +--R ((- 6a b + 8a b - 2a )cos(x) + 6a b - 2a b )cot(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 +--R ((- 12a b + 16a b - 4a b)cos(x) + 12a b - 4a b )cot(x) +--R + +--R 6 3 4 5 2 2 6 3 4 +--R (- 6a b + 8a b - 2a b )cos(x) + 6a b - 2a b +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 4 3 6 2 3 4 5 2 +--R (12a b - 4a b)cos(x)cot(x) + (24a b - 8a b )cos(x)cot(x) +--R + +--R 2 5 4 3 +--R (12a b - 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 2 +--R ((- 6a b + 8a b - 2a )cos(x) + 6a b - 2a b )cot(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 +--R ((- 12a b + 16a b - 4a b)cos(x) + 12a b - 4a b )cot(x) +--R + +--R 6 3 4 5 2 2 6 3 4 +--R (- 6a b + 8a b - 2a b )cos(x) + 6a b - 2a b +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 4 3 6 2 3 4 5 2 +--R (- 12a b + 4a b)cos(x)cot(x) + (- 24a b + 8a b )cos(x)cot(x) +--R + +--R 2 5 4 3 +--R (- 12a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 2 +--R ((6a b - 8a b + 2a )cos(x) - 6a b + 2a b )cot(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 +--R ((12a b - 16a b + 4a b)cos(x) - 12a b + 4a b )cot(x) +--R + +--R 6 3 4 5 2 2 6 3 4 +--R (6a b - 8a b + 2a b )cos(x) - 6a b + 2a b +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 4 3 6 2 2 5 4 3 6 +--R ((4a b + 4a b)cos(x)cot(x) + (- 6a b - 8a b - 2a b)cos(x))sin(x) +--R + +--R 3 4 5 2 7 2 3 4 5 2 7 2 +--R ((- 5a b - 6a b - a )cos(x) + 5a b + 6a b + a )cot(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R ((- 6a b - 12a b - 6a b)cos(x) + 6a b + 8a b + 2a b)cot(x) +--R + +--R 3 4 5 2 7 2 +--R (- 5a b - 6a b - a )cos(x) +--R / +--R 3 7 5 5 7 3 9 2 +--R (4a b + 12a b + 12a b + 4a b)cos(x)cot(x) +--R + +--R 2 8 4 6 6 4 8 2 +--R (8a b + 24a b + 24a b + 8a b )cos(x)cot(x) +--R + +--R 9 3 7 5 5 7 3 +--R (4a b + 12a b + 12a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 8 4 6 8 2 10 2 2 8 4 6 6 4 +--R (- 2a b - 4a b + 4a b + 2a )cos(x) + 2a b + 6a b + 6a b +--R + +--R 8 2 +--R 2a b +--R * +--R 2 +--R cot(x) +--R + +--R 9 3 7 7 3 9 2 9 3 7 5 5 +--R (- 4a b - 8a b + 8a b + 4a b)cos(x) + 4a b + 12a b + 12a b +--R + +--R 7 3 +--R 4a b +--R * +--R cot(x) +--R + +--R 10 2 8 6 4 8 2 2 10 2 8 4 6 6 4 +--R (- 2b - 4a b + 4a b + 2a b )cos(x) + 2b + 6a b + 6a b + 2a b +--R Type: Expression(Integer) +--E 158 + +--S 159 of 526 +d0830:= D(m0830,x) +--R +--R +--R (5) +--R 5 3 7 2 5 3 7 3 +--R ((- 5a b + 3a b)cos(x) + 3a b + a b)cot(x) +--R + +--R 4 4 6 2 2 4 4 6 2 2 +--R ((- 3a b + 5a b )cos(x) + 9a b + 3a b )cot(x) +--R + +--R 3 5 5 3 2 3 5 5 3 +--R ((9a b + a b )cos(x) + 9a b + 3a b )cot(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 +--R (3a b - 9a b - 4a b )cos(x) + 3a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 4 6 2 3 4 4 6 2 8 3 +--R ((8a b - 8a b )cos(x) + (- 8a b + 5a b + a )cos(x))cot(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 7 +--R ((12a b - 8a b - 4a b)cos(x) + (- 12a b + 11a b + 3a b)cos(x)) +--R * +--R 2 +--R cot(x) +--R + +--R 4 4 6 2 3 4 4 6 2 +--R ((8a b - 8a b )cos(x) + (7a b + 3a b )cos(x))cot(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 +--R (12a b - 8a b - 4a b)cos(x) + (- 7a b - 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 7 2 3 5 +--R ((- 2a b + 7a b + a b)cos(x) + (4a b - 7a b - a b)cos(x) - 2a b ) +--R * +--R 3 +--R cot(x) +--R + +--R 2 6 4 4 6 2 8 4 +--R (- 3a b + 14a b + 8a b - a )cos(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 +--R (6a b - 13a b - 5a b )cos(x) - 3a b - a b +--R * +--R 2 +--R cot(x) +--R + +--R 3 5 5 3 7 4 3 5 5 3 2 3 5 +--R ((7a b + 13a b - 2a b)cos(x) + (- 5a b - 7a b )cos(x) - 2a b )cot(x) +--R + +--R 4 4 6 2 8 4 2 6 4 4 6 2 2 2 6 4 4 +--R (8a b - a b - a )cos(x) + (3a b - 5a b - 2a b )cos(x) - 3a b - a b +--R / +--R 5 6 7 4 9 2 2 3 +--R (4a b + 8a b + 4a b )cos(x) cot(x) +--R + +--R 4 7 6 5 8 3 2 2 +--R (12a b + 24a b + 12a b )cos(x) cot(x) +--R + +--R 3 8 5 6 7 4 2 +--R (12a b + 24a b + 12a b )cos(x) cot(x) +--R + +--R 2 9 4 7 6 5 2 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (- 4a b - 4a b + 4a b + 4a b)cos(x) +--R + +--R 4 7 6 5 8 3 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (- 12a b - 12a b + 12a b + 12a b )cos(x) +--R + +--R 3 8 5 6 7 4 +--R (12a b + 24a b + 12a b )cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (- 12a b - 12a b + 12a b + 12a b )cos(x) +--R + +--R 2 9 4 7 6 5 +--R (12a b + 24a b + 12a b )cos(x) +--R * +--R cot(x) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 4a b - 4a b + 4a b + 4a b )cos(x) +--R + +--R 10 3 8 5 6 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 8 7 4 11 4 +--R (a b - 2a b + a )cos(x) +--R + +--R 3 8 5 6 7 4 9 2 2 3 8 5 6 7 4 +--R (- 2a b - 2a b + 2a b + 2a b )cos(x) + a b + 2a b + a b +--R * +--R 3 +--R cot(x) +--R + +--R 2 9 6 5 10 4 +--R (3a b - 6a b + 3a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 2 9 4 7 6 5 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) + 3a b + 6a b + 3a b +--R * +--R 2 +--R cot(x) +--R + +--R 10 5 6 9 2 4 +--R (3a b - 6a b + 3a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 2 10 3 8 5 6 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) + 3a b + 6a b + 3a b +--R * +--R cot(x) +--R + +--R 11 4 7 8 3 4 11 2 9 4 7 6 5 2 +--R (b - 2a b + a b )cos(x) + (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 11 2 9 4 7 +--R b + 2a b + a b +--R Type: Expression(Integer) +--E 159 + +)clear all + + +--S 160 of 526 +t0831:= cos(x)/(a*cos(x)+b*sin(x)) +--R +--R +--R cos(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 160 + +--S 161 of 526 +r0831:= (a*x+b*log(a*cos(x)+b*sin(x)))/(a^2+b^2) +--R +--R +--R b log(b sin(x) + a cos(x)) + a x +--R (2) -------------------------------- +--R 2 2 +--R b + a +--R Type: Expression(Integer) +--E 161 + +--S 162 of 526 +a0831:= integrate(t0831,x) +--R +--R +--R 2 - 2b sin(x) - 2a cos(x) +--R - b log(----------) + b log(-----------------------) + a x +--R cos(x) + 1 cos(x) + 1 +--R (3) ---------------------------------------------------------- +--R 2 2 +--R b + a +--R Type: Union(Expression(Integer),...) +--E 162 + +--S 163 of 526 +m0831:= a0831-r0831 +--R +--R +--R (4) +--R 2 +--R - b log(b sin(x) + a cos(x)) - b log(----------) +--R cos(x) + 1 +--R + +--R - 2b sin(x) - 2a cos(x) +--R b log(-----------------------) +--R cos(x) + 1 +--R / +--R 2 2 +--R b + a +--R Type: Expression(Integer) +--E 163 + +--S 164 of 526 +d0831:= D(m0831,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 164 + +)clear all + + +--S 165 of 526 +t0832:= cos(x)^2/(a*cos(x)+b*sin(x)) +--R +--R +--R 2 +--R cos(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 165 + +--S 166 of 526 +r0832:= -b^2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+_ + b*cos(x)/(a^2+b^2)+a*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R b atanh(-------------------) + (a sin(x) + b cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) -------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 526 +a0832:= integrate(t0832,x) +--R +--R +--R (3) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (a sin(x) + b cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 167 + +--S 168 of 526 +m0832:= a0832-r0832 +--R +--R +--R (4) +--R 2 +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 2 a sin(x) - b cos(x) +--R - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 168 + +--S 169 of 526 +d0832:= D(m0832,x) +--R +--R +--R (5) +--R 2 3 3 2 2 2 2 3 3 +--R a b sin(x) - b cos(x)sin(x) + (a b cos(x) - a b )sin(x) - b cos(x) +--R + +--R 3 +--R b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression(Integer) +--E 169 + +)clear all + + +--S 170 of 526 +t0833:= cos(x)^3/(a*cos(x)+b*sin(x)) +--R +--R +--R 3 +--R cos(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 170 + +--S 171 of 526 +r0833:= 1/2/(a^2+b^2)^2*(3*a*b^2*x+a^3*x+2*b^3*log(a*cos(x)+_ + b*sin(x))+sin(x)*a^3*cos(x)+sin(x)*a*cos(x)*b^2-_ + a^2*b+b*cos(x)^2*a^2-b^3+b^3*cos(x)^2) +--R +--R +--R (2) +--R 3 2 3 3 2 2 +--R 2b log(b sin(x) + a cos(x)) + (a b + a )cos(x)sin(x) + (b + a b)cos(x) +--R + +--R 2 3 3 2 +--R (3a b + a )x - b - a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 526 +a0833:= integrate(t0833,x) +--R +--R +--R (3) +--R 3 2 3 - 2b sin(x) - 2a cos(x) +--R - 2b log(----------) + 2b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (a b + a )cos(x)sin(x) + (b + a b)cos(x) + (3a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression(Integer),...) +--E 172 + +--S 173 of 526 +m0833:= a0833-r0833 +--R +--R +--R (4) +--R 3 3 2 +--R - 2b log(b sin(x) + a cos(x)) - 2b log(----------) +--R cos(x) + 1 +--R + +--R 3 - 2b sin(x) - 2a cos(x) 3 2 +--R 2b log(-----------------------) + b + a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 173 + +--S 174 of 526 +d0833:= D(m0833,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + + +--S 175 of 526 +t0834:= cos(x)/(a*cos(x)+b*sin(x))^2 +--R +--R +--R cos(x) +--R (1) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 175 + +--S 176 of 526 +r0834:= -a*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ + b/(a^2+b^2)/(a*cos(x)+b*sin(x)) +--R +--R +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R (a b sin(x) + a cos(x))atanh(-------------------) - b\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) --------------------------------------------------------------- +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b + a b)sin(x) + (a b + a )cos(x))\|b + a +--R Type: Expression(Integer) +--E 176 + +--S 177 of 526 +a0834:= integrate(t0834,x) +--R +--R +--R (3) +--R 2 3 +--R (a b sin(x) + a cos(x)) +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R 2 | 2 2 +--R (- b sin(x) - a b cos(x) - a b)\|b + a +--R / +--R +-------+ +--R 3 3 2 2 4 | 2 2 +--R ((a b + a b)sin(x) + (a b + a )cos(x))\|b + a +--R Type: Union(Expression(Integer),...) +--E 177 + +--S 178 of 526 +m0834:= a0834-r0834 +--R +--R +--R (4) +--R 2 +--R a +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 +--R (a b sin(x) - b cos(x) - b - a )\|b + a +--R + +--R 2 3 3 2 3 2 +--R (- a b - a )sin(x) + (b + a b)cos(x) + b + a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R - a atanh(-------------------) - b\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 3 | 2 2 +--R (a b + a )\|b + a +--R Type: Expression(Integer) +--E 178 + +--S 179 of 526 +d0834:= D(m0834,x) +--R +--R +--R (5) +--R 2 3 2 2 2 2 3 +--R a sin(x) - a b cos(x)sin(x) + (a cos(x) - a )sin(x) - a b cos(x) +--R + +--R a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression(Integer) +--E 179 + +)clear all + + +--S 180 of 526 +t0835:= cos(x)^2/(a*cos(x)+b*sin(x))^2 +--R +--R +--R 2 +--R cos(x) +--R (1) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 180 + +--S 181 of 526 +r0835:= (a^2-b^2)*x/(a^2+b^2)^2+2*a*b*log(a*cos(x)+b*sin(x))/(a^2+b^2)^2-_ + b/(a^2+b^2)/(a+b*tan(x)) +--R +--R +--R (2) +--R 2 2 3 2 +--R (2a b tan(x) + 2a b)log(b sin(x) + a cos(x)) + (- b + a b)x tan(x) +--R + +--R 2 3 3 2 +--R (- a b + a )x - b - a b +--R / +--R 5 2 3 4 4 3 2 5 +--R (b + 2a b + a b)tan(x) + a b + 2a b + a +--R Type: Expression(Integer) +--E 181 + +--S 182 of 526 +a0835:= integrate(t0835,x) +--R +--R +--R (3) +--R 2 2 3 2 +--R (- 2a b sin(x) - 2a b cos(x))log(----------) +--R cos(x) + 1 +--R + +--R 2 2 3 - 2b sin(x) - 2a cos(x) +--R (2a b sin(x) + 2a b cos(x))log(-----------------------) +--R cos(x) + 1 +--R + +--R 3 3 4 2 2 2 2 4 +--R ((- a b + a b)x + b + a b )sin(x) + (- a b + a )x cos(x) +--R / +--R 5 3 3 5 2 4 4 2 6 +--R (a b + 2a b + a b)sin(x) + (a b + 2a b + a )cos(x) +--R Type: Union(Expression(Integer),...) +--E 182 + +--S 183 of 526 +m0835:= a0835-r0835 +--R +--R +--R (4) +--R 2 3 3 2 3 2 4 +--R ((- 2a b sin(x) - 2a b cos(x))tan(x) - 2a b sin(x) - 2a b cos(x)) +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 2 3 3 2 3 2 4 +--R ((- 2a b sin(x) - 2a b cos(x))tan(x) - 2a b sin(x) - 2a b cos(x)) +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 3 3 2 3 2 4 +--R ((2a b sin(x) + 2a b cos(x))tan(x) + 2a b sin(x) + 2a b cos(x)) +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 5 2 3 4 3 2 2 3 4 +--R (b + a b )sin(x)tan(x) + (2a b + 2a b )sin(x) + (a b + a b)cos(x) +--R / +--R 6 3 4 5 2 2 5 4 3 6 +--R ((a b + 2a b + a b )sin(x) + (a b + 2a b + a b)cos(x))tan(x) +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (a b + 2a b + a b)sin(x) + (a b + 2a b + a )cos(x) +--R Type: Expression(Integer) +--E 183 + +--S 184 of 526 +d0835:= D(m0835,x) +--R +--R +--R (5) +--R 3 4 2 2 2 2 +--R (- 2a b cos(x)sin(x) + (b - a b )cos(x) )tan(x) +--R + +--R 3 2 3 2 4 2 2 2 +--R (2a b sin(x) + 2a b cos(x) )tan(x) + (- b + a b )sin(x) +--R + +--R 3 +--R - 2a b cos(x)sin(x) +--R / +--R 6 2 4 2 5 3 3 +--R (b + a b )sin(x) + (2a b + 2a b )cos(x)sin(x) +--R + +--R 2 4 4 2 2 +--R (a b + a b )cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 3 3 2 2 4 4 2 +--R (2a b + 2a b )sin(x) + (4a b + 4a b )cos(x)sin(x) +--R + +--R 3 3 5 2 +--R (2a b + 2a b)cos(x) +--R * +--R tan(x) +--R + +--R 2 4 4 2 2 3 3 5 4 2 6 2 +--R (a b + a b )sin(x) + (2a b + 2a b)cos(x)sin(x) + (a b + a )cos(x) +--R Type: Expression(Integer) +--E 184 + +)clear all + + +--S 185 of 526 +t0836:= cos(x)/(a*cos(x)+b*sin(x))^3 +--R +--R +--R cos(x) +--R (1) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 185 + +--S 186 of 526 +r0836:= -1/2*b/(a^2+b^2)/(a*cos(x)+b*sin(x))^2+_ + sin(x)/(a^2+b^2)/(a*cos(x)+b*sin(x)) +--R +--R +--R (2) +--R 2 +--R 2b sin(x) + 2a cos(x)sin(x) - b +--R ------------------------------------------------------------------------ +--R 4 2 2 2 3 3 2 2 4 2 +--R (2b + 2a b )sin(x) + (4a b + 4a b)cos(x)sin(x) + (2a b + 2a )cos(x) +--R Type: Expression(Integer) +--E 186 + +--S 187 of 526 +a0836:= integrate(t0836,x) +--R +--R +--R 2 +--R 2a cos(x)sin(x) - b cos(x) + b +--R (3) -------------------------------------------------- +--R 3 2 2 4 2 2 2 +--R 4a b cos(x)sin(x) + (- 2a b + 2a )cos(x) + 2a b +--R Type: Union(Expression(Integer),...) +--E 187 + +--S 188 of 526 +m0836:= a0836-r0836 +--R +--R +--R (4) +--R 4 3 2 3 +--R (2a b - 2a b )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 2 +--R ((- b + 5a b - 2a b)cos(x) + b - a b )sin(x) +--R + +--R 4 3 2 3 4 3 2 +--R ((- 2a b + 2a b )cos(x) + (2a b + 2a b )cos(x))sin(x) +--R + +--R 2 3 4 4 4 2 2 3 +--R (- a b - a b)cos(x) + 2a b cos(x) + a b +--R / +--R 3 5 5 3 3 +--R (4a b + 4a b )cos(x)sin(x) +--R + +--R 2 6 4 4 6 2 2 2 6 4 4 2 +--R ((- 2a b + 8a b + 10a b )cos(x) + 2a b + 2a b )sin(x) +--R + +--R 3 5 5 3 7 3 3 5 5 3 +--R ((- 4a b + 4a b + 8a b)cos(x) + (4a b + 4a b )cos(x))sin(x) +--R + +--R 4 4 8 4 4 4 6 2 2 +--R (- 2a b + 2a )cos(x) + (2a b + 2a b )cos(x) +--R Type: Expression(Integer) +--E 188 + +--S 189 of 526 +d0836:= D(m0836,x) +--R +--R +--R (5) +--R 5 3 3 2 5 +--R (a b - 3a b )cos(x) sin(x) +--R + +--R 2 4 4 2 3 6 2 4 4 +--R ((7a b - 5a b )cos(x) + (b - 3a b )cos(x))sin(x) +--R + +--R 3 3 5 4 5 3 3 2 5 3 +--R ((6a b - 2a b)cos(x) + (5a b + a b )cos(x) - a b )sin(x) +--R + +--R 2 4 4 2 5 2 4 4 2 3 2 4 2 +--R ((6a b - 2a b )cos(x) + (- 7a b + 5a b )cos(x) + 3a b cos(x))sin(x) +--R + +--R 5 3 3 5 6 5 3 3 5 4 +--R (- a b + 9a b - 2a b)cos(x) + (7a b - 11a b + 2a b)cos(x) +--R + +--R 5 3 3 2 5 +--R (- 7a b + 2a b )cos(x) + a b +--R * +--R sin(x) +--R + +--R 2 4 4 2 7 6 2 4 4 2 5 +--R (- a b + 3a b )cos(x) + (- b + 4a b - 3a b )cos(x) +--R + +--R 6 2 4 3 6 +--R (2b - 3a b )cos(x) - b cos(x) +--R / +--R 2 7 4 5 2 5 +--R (4a b + 4a b )cos(x) sin(x) +--R + +--R 8 3 6 5 4 3 8 3 6 4 +--R ((- 4a b + 12a b + 16a b )cos(x) + (4a b + 4a b )cos(x))sin(x) +--R + +--R 9 2 7 4 5 6 3 4 +--R (b - 13a b + 11a b + 25a b )cos(x) +--R + +--R 9 2 7 4 5 2 9 2 7 +--R (- 2b + 12a b + 14a b )cos(x) + b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 8 3 6 5 4 7 2 5 +--R (3a b - 15a b + a b + 19a b )cos(x) +--R + +--R 8 3 6 5 4 3 8 3 6 +--R (- 6a b + 12a b + 18a b )cos(x) + (3a b + 3a b )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 2 7 4 5 6 3 8 6 +--R (3a b - 7a b - 3a b + 7a b)cos(x) +--R + +--R 2 7 4 5 6 3 4 2 7 4 5 2 +--R (- 6a b + 4a b + 10a b )cos(x) + (3a b + 3a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 6 5 4 7 2 9 7 3 6 7 2 5 +--R (a b - a b - a b + a )cos(x) + (- 2a b + 2a b )cos(x) +--R + +--R 3 6 5 4 3 +--R (a b + a b )cos(x) +--R Type: Expression(Integer) +--E 189 + +)clear all + + +--S 190 of 526 +t0837:= cos(x)^3/(a*cos(x)+b*sin(x))^3 +--R +--R +--R 3 +--R cos(x) +--R (1) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 190 + +--S 191 of 526 +r0837:= (a^3*x-3*a*b^2*x)/(a^2+b^2)^3+b*(3*a^2-b^2)*_ + log(a*cos(x)+b*sin(x))/(a^2+b^2)^3-1/2*b/(a^2+b^2)/(a+b*tan(x))^2-_ + 2*a*b/(a^2+b^2)^2/(a+b*tan(x)) +--R +--R +--R (2) +--R 5 2 3 2 4 3 2 2 3 4 +--R ((- 2b + 6a b )tan(x) + (- 4a b + 12a b )tan(x) - 2a b + 6a b) +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 4 3 2 2 2 3 4 4 3 2 +--R (- 6a b + 2a b )x tan(x) + ((- 12a b + 4a b)x - 4a b - 4a b )tan(x) +--R + +--R 3 2 5 5 2 3 4 +--R (- 6a b + 2a )x - b - 6a b - 5a b +--R / +--R 8 2 6 4 4 6 2 2 +--R (2b + 6a b + 6a b + 2a b )tan(x) +--R + +--R 7 3 5 5 3 7 2 6 4 4 6 2 8 +--R (4a b + 12a b + 12a b + 4a b)tan(x) + 2a b + 6a b + 6a b + 2a +--R Type: Expression(Integer) +--E 191 + +--S 192 of 526 +a0837:= integrate(t0837,x) +--R +--R +--R (3) +--R 3 4 5 2 2 5 4 3 6 2 +--R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b)cos(x) +--R + +--R 2 5 4 3 +--R 2a b - 6a b +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 4 5 2 2 5 4 3 6 2 +--R (- 4a b + 12a b )cos(x)sin(x) + (2a b - 8a b + 6a b)cos(x) +--R + +--R 2 5 4 3 +--R - 2a b + 6a b +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 4 3 6 6 3 4 5 2 +--R ((- 12a b + 4a b)x + 2a b + 8a b + 6a b )cos(x)sin(x) +--R + +--R 3 4 5 2 7 7 2 5 4 3 2 3 4 5 2 +--R ((6a b - 8a b + 2a )x - b - 6a b - 5a b )cos(x) + (- 6a b + 2a b )x +--R + +--R 7 2 5 4 3 +--R b + 6a b + 5a b +--R / +--R 3 7 5 5 7 3 9 +--R (4a b + 12a b + 12a b + 4a b)cos(x)sin(x) +--R + +--R 2 8 4 6 8 2 10 2 2 8 4 6 6 4 8 2 +--R (- 2a b - 4a b + 4a b + 2a )cos(x) + 2a b + 6a b + 6a b + 2a b +--R Type: Union(Expression(Integer),...) +--E 192 + +--S 193 of 526 +m0837:= a0837-r0837 +--R +--R +--R (4) +--R 3 6 5 4 2 7 4 5 6 3 2 +--R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b )cos(x) +--R + +--R 2 7 4 5 +--R 2a b - 6a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 5 6 3 3 6 5 4 7 2 2 +--R (8a b - 24a b )cos(x)sin(x) + (- 4a b + 16a b - 12a b )cos(x) +--R + +--R 3 6 5 4 +--R 4a b - 12a b +--R * +--R tan(x) +--R + +--R 5 4 7 2 4 5 6 3 8 2 +--R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b)cos(x) +--R + +--R 4 5 6 3 +--R 2a b - 6a b +--R * +--R log(b sin(x) + a cos(x)) +--R + +--R 3 6 5 4 2 7 4 5 6 3 2 +--R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b )cos(x) +--R + +--R 2 7 4 5 +--R 2a b - 6a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 5 6 3 3 6 5 4 7 2 2 +--R (8a b - 24a b )cos(x)sin(x) + (- 4a b + 16a b - 12a b )cos(x) +--R + +--R 3 6 5 4 +--R 4a b - 12a b +--R * +--R tan(x) +--R + +--R 5 4 7 2 4 5 6 3 8 2 +--R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b)cos(x) +--R + +--R 4 5 6 3 +--R 2a b - 6a b +--R * +--R 2 +--R log(----------) +--R cos(x) + 1 +--R + +--R 3 6 5 4 2 7 4 5 6 3 2 +--R (- 4a b + 12a b )cos(x)sin(x) + (2a b - 8a b + 6a b )cos(x) +--R + +--R 2 7 4 5 +--R - 2a b + 6a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 5 6 3 3 6 5 4 7 2 2 +--R (- 8a b + 24a b )cos(x)sin(x) + (4a b - 16a b + 12a b )cos(x) +--R + +--R 3 6 5 4 +--R - 4a b + 12a b +--R * +--R tan(x) +--R + +--R 5 4 7 2 4 5 6 3 8 2 +--R (- 4a b + 12a b )cos(x)sin(x) + (2a b - 8a b + 6a b)cos(x) +--R + +--R 4 5 6 3 +--R - 2a b + 6a b +--R * +--R - 2b sin(x) - 2a cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 8 3 6 5 4 9 2 7 4 5 2 +--R (2a b + 8a b + 6a b )cos(x)sin(x) + (- b - 6a b - 5a b )cos(x) +--R + +--R 9 2 7 4 5 +--R b + 6a b + 5a b +--R * +--R 2 +--R tan(x) +--R + +--R 2 7 4 5 6 3 +--R (4a b + 24a b + 20a b )cos(x)sin(x) +--R + +--R 8 3 6 5 4 7 2 2 8 3 6 5 4 +--R (- 2a b - 16a b - 10a b + 4a b )cos(x) + 2a b + 16a b + 14a b +--R * +--R tan(x) +--R + +--R 3 6 5 4 7 2 +--R (4a b + 20a b + 16a b )cos(x)sin(x) +--R + +--R 2 7 4 5 6 3 8 2 2 7 4 5 6 3 +--R (- 2a b - 11a b - 4a b + 5a b)cos(x) + 2a b + 12a b + 10a b +--R / +--R 3 9 5 7 7 5 9 3 +--R (4a b + 12a b + 12a b + 4a b )cos(x)sin(x) +--R + +--R 2 10 4 8 8 4 10 2 2 2 10 4 8 6 6 +--R (- 2a b - 4a b + 4a b + 2a b )cos(x) + 2a b + 6a b + 6a b +--R + +--R 8 4 +--R 2a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 8 6 6 8 4 10 2 +--R (8a b + 24a b + 24a b + 8a b )cos(x)sin(x) +--R + +--R 3 9 5 7 9 3 11 2 3 9 5 7 7 5 +--R (- 4a b - 8a b + 8a b + 4a b)cos(x) + 4a b + 12a b + 12a b +--R + +--R 9 3 +--R 4a b +--R * +--R tan(x) +--R + +--R 5 7 7 5 9 3 11 +--R (4a b + 12a b + 12a b + 4a b)cos(x)sin(x) +--R + +--R 4 8 6 6 10 2 12 2 4 8 6 6 8 4 10 2 +--R (- 2a b - 4a b + 4a b + 2a )cos(x) + 2a b + 6a b + 6a b + 2a b +--R Type: Expression(Integer) +--E 193 + +--S 194 of 526 +d0837:= D(m0837,x) +--R +--R +--R (5) +--R 7 3 5 2 7 2 +--R ((3a b - 5a b )cos(x) + 2a b )sin(x) +--R + +--R 2 6 4 4 3 8 2 6 +--R ((8a b - 8a b )cos(x) + (b - 3a b )cos(x))sin(x) +--R + +--R 7 3 5 5 3 4 7 3 5 2 7 +--R (a b + 7a b - 2a b )cos(x) + (2a b - 4a b )cos(x) - 2a b +--R * +--R 3 +--R tan(x) +--R + +--R 2 6 4 4 2 2 6 2 +--R ((5a b - 3a b )cos(x) + 6a b )sin(x) +--R + +--R 7 3 5 5 3 3 7 3 5 +--R ((4a b + 8a b - 12a b )cos(x) + (- a b + 3a b )cos(x))sin(x) +--R + +--R 8 2 6 4 4 6 2 4 8 2 6 4 4 2 +--R (- b + 8a b + 14a b - 3a b )cos(x) + (2b - 2a b - 6a b )cos(x) +--R + +--R 8 2 6 +--R - b - 3a b +--R * +--R 2 +--R tan(x) +--R + +--R 3 5 5 3 2 3 5 2 +--R ((a b + 9a b )cos(x) + 6a b )sin(x) +--R + +--R 2 6 4 4 3 2 6 4 4 +--R ((8a b - 8a b )cos(x) + (- 5a b + 15a b )cos(x))sin(x) +--R + +--R 7 3 5 5 3 4 7 3 5 2 7 +--R (- 2a b + 13a b + 7a b )cos(x) + (4a b - 10a b )cos(x) - 2a b +--R * +--R tan(x) +--R + +--R 2 6 4 4 6 2 2 4 4 2 +--R ((- 4a b - 9a b + 3a b )cos(x) + 2a b )sin(x) +--R + +--R 7 3 5 5 3 3 7 3 5 5 3 +--R ((4a b + 8a b - 12a b )cos(x) + (- 4a b - 11a b + 5a b )cos(x)) +--R * +--R sin(x) +--R + +--R 8 2 6 4 4 4 8 2 6 4 4 2 8 2 6 +--R (- b - a b + 8a b )cos(x) + (2b + 4a b - 8a b )cos(x) - b - 3a b +--R / +--R 2 9 4 7 6 5 2 2 +--R (4a b + 8a b + 4a b )cos(x) sin(x) +--R + +--R 10 3 8 5 6 7 4 3 +--R (- 4a b - 4a b + 4a b + 4a b )cos(x) +--R + +--R 10 3 8 5 6 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 11 4 7 8 3 4 11 2 9 4 7 6 5 2 +--R (b - 2a b + a b )cos(x) + (- 2b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 11 2 9 4 7 +--R b + 2a b + a b +--R * +--R 3 +--R tan(x) +--R + +--R 3 8 5 6 7 4 2 2 +--R (12a b + 24a b + 12a b )cos(x) sin(x) +--R + +--R 2 9 4 7 6 5 8 3 3 +--R (- 12a b - 12a b + 12a b + 12a b )cos(x) +--R + +--R 2 9 4 7 6 5 +--R (12a b + 24a b + 12a b )cos(x) +--R * +--R sin(x) +--R + +--R 10 5 6 9 2 4 +--R (3a b - 6a b + 3a b )cos(x) +--R + +--R 10 3 8 5 6 7 4 2 10 3 8 5 6 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) + 3a b + 6a b + 3a b +--R * +--R 2 +--R tan(x) +--R + +--R 4 7 6 5 8 3 2 2 +--R (12a b + 24a b + 12a b )cos(x) sin(x) +--R + +--R 3 8 5 6 7 4 9 2 3 +--R (- 12a b - 12a b + 12a b + 12a b )cos(x) +--R + +--R 3 8 5 6 7 4 +--R (12a b + 24a b + 12a b )cos(x) +--R * +--R sin(x) +--R + +--R 2 9 6 5 10 4 +--R (3a b - 6a b + 3a b)cos(x) +--R + +--R 2 9 4 7 6 5 8 3 2 2 9 4 7 6 5 +--R (- 6a b - 6a b + 6a b + 6a b )cos(x) + 3a b + 6a b + 3a b +--R * +--R tan(x) +--R + +--R 5 6 7 4 9 2 2 2 +--R (4a b + 8a b + 4a b )cos(x) sin(x) +--R + +--R 4 7 6 5 8 3 10 3 +--R (- 4a b - 4a b + 4a b + 4a b)cos(x) +--R + +--R 4 7 6 5 8 3 +--R (4a b + 8a b + 4a b )cos(x) +--R * +--R sin(x) +--R + +--R 3 8 7 4 11 4 3 8 5 6 7 4 9 2 2 +--R (a b - 2a b + a )cos(x) + (- 2a b - 2a b + 2a b + 2a b )cos(x) +--R + +--R 3 8 5 6 7 4 +--R a b + 2a b + a b +--R Type: Expression(Integer) +--E 194 + +)clear all + + +--S 195 of 526 +t0838:= tan(x)/(b*cos(x)+a*sin(x)) +--R +--R +--R tan(x) +--R (1) ------------------- +--R a sin(x) + b cos(x) +--R Type: Expression(Integer) +--E 195 + +--S 196 of 526 +r0838:= atanh(sin(x))/a+b*atanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/_ + a/(a^2+b^2)^(1/2) +--R +--R +--R +-------+ +--R | 2 2 b sin(x) - a cos(x) +--R \|b + a atanh(sin(x)) - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) ------------------------------------------------------ +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression(Integer) +--E 196 + +--S 197 of 526 +a0838:= integrate(t0838,x) +--R +--R +--R (3) +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b + a log(-------------------) - \|b + a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Union(Expression(Integer),...) +--E 197 + +--S 198 of 526 +m0838:= a0838-r0838 +--R +--R +--R (4) +--R b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 3 2 +--R (a b sin(x) - a cos(x) - b - a )\|b + a + (b + a b)sin(x) +--R + +--R 2 3 2 3 +--R (- a b - a )cos(x) - a b - a +--R / +--R a sin(x) + b cos(x) +--R + +--R +-------+ +-------+ +--R | 2 2 sin(x) + cos(x) + 1 | 2 2 sin(x) - cos(x) - 1 +--R \|b + a log(-------------------) - \|b + a log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-------+ +--R | 2 2 b sin(x) - a cos(x) +--R - \|b + a atanh(sin(x)) + b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R | 2 2 +--R a\|b + a +--R Type: Expression(Integer) +--E 198 + +--S 199 of 526 +d0838:= D(m0838,x) +--R +--R +--R (5) +--R 5 2 3 8 4 3 2 4 3 2 7 +--R (b - a b )sin(x) + ((- 4a b + 4a b )cos(x) + a b + a b )sin(x) +--R + +--R 2 3 4 2 2 3 4 5 2 3 +--R (5a b - 5a b)cos(x) + (- 4a b - 3a b)cos(x) - 3b + a b +--R + +--R 4 +--R 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 4 5 3 4 3 2 5 2 +--R (- 2a b + 2a )cos(x) + (a b + 7a b + 2a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (13a b + 3a b - 2a )cos(x) - a b - 3a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (- b + 5a b - 4a b)cos(x) + (- 2a b - 7a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 5 2 3 4 +--R (b - 12a b - a b)cos(x) + a b cos(x) + 3b + a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 2 5 5 3 2 5 4 +--R (2a b - 4a b + 2a )cos(x) + (3a b + 3a )cos(x) +--R + +--R 4 3 2 5 3 4 3 2 5 2 +--R (3a b + 8a b - 3a )cos(x) + (- 4a b - 13a b - 5a )cos(x) +--R + +--R 4 3 2 5 4 3 2 5 +--R (- 14a b - 13a b + a )cos(x) - a b + a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 4 6 2 3 4 5 +--R (- a b + a b)cos(x) + (2a b - 3a b)cos(x) +--R + +--R 5 2 3 4 4 2 3 4 3 +--R (2b - 3a b - 7a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 5 2 3 +--R (- 2b + 8a b + 10a b)cos(x) + (4a b + 4a b)cos(x) - b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 5 6 4 3 2 5 5 +--R (- 3a b + a )cos(x) + (- 4a b - 3a b + a )cos(x) +--R + +--R 4 3 2 5 4 4 3 2 5 3 +--R (- 4a b - 2a b - 2a )cos(x) + (- a b - 3a b - 2a )cos(x) +--R + +--R 4 3 2 5 2 4 3 2 5 4 +--R (3a b + 4a b + a )cos(x) + (5a b + 6a b + a )cos(x) + a b +--R + +--R 3 2 +--R a b +--R * +--R sin(x) +--R + +--R 4 7 2 3 4 6 2 3 4 5 +--R a b cos(x) + (2a b + 2a b)cos(x) + (2a b + a b)cos(x) +--R + +--R 5 2 3 4 2 3 4 3 +--R (- b - a b )cos(x) + (- a b - a b)cos(x) +--R + +--R 5 2 3 4 2 2 3 4 +--R (b - a b - 2a b)cos(x) + (- a b - a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 5 3 3 8 +--R (- a b - a b )sin(x) +--R + +--R 6 2 4 4 2 6 4 2 7 +--R ((- 2b + 2a b + 4a b )cos(x) - b + a b )sin(x) +--R + +--R 5 3 3 5 2 3 3 5 5 3 3 +--R (4a b - a b - 5a b)cos(x) + (- 3a b - 3a b)cos(x) + a b + 3a b +--R + +--R 5 +--R 2a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 2 4 4 2 6 3 +--R (- 2b - 2a b + 2a b + 2a )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (- b + 4a b + 7a b + 2a )cos(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 6 +--R (6b + 9a b + a b - 2a )cos(x) + 3b + 2a b - 3a b - 2a +--R * +--R 5 +--R sin(x) +--R + +--R 5 3 3 5 4 5 3 3 5 3 +--R (5a b + a b - 4a b)cos(x) + (2a b - 5a b - 7a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 3 3 +--R (- 7a b - 8a b - a b)cos(x) + (- a b - a b )cos(x) + a b - a b +--R + +--R 5 +--R - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 4 2 6 5 2 4 4 2 6 4 +--R (- 4a b - 2a b + 2a )cos(x) + (a b + 4a b + 3a )cos(x) +--R + +--R 6 2 4 4 2 6 3 +--R (4b + 11a b + 4a b - 3a )cos(x) +--R + +--R 6 2 4 4 2 6 2 +--R (2b - 7a b - 14a b - 5a )cos(x) +--R + +--R 6 2 4 4 2 6 6 2 4 4 2 6 +--R (- 6b - 18a b - 11a b + a )cos(x) - 3b - 4a b + a b + 2a +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 6 5 3 3 5 5 +--R (a b + a b)cos(x) + (2a b - a b - 3a b)cos(x) +--R + +--R 5 3 3 5 4 5 5 3 +--R (- 2a b - 9a b - 7a b)cos(x) + (- 3a b + 3a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 5 +--R (4a b + 14a b + 10a b)cos(x) + (2a b + 6a b + 4a b)cos(x) - a b +--R + +--R 3 3 +--R - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 4 2 6 6 2 4 4 2 6 5 +--R (- 3a b - 2a b + a )cos(x) + (- 4a b - 3a b + a )cos(x) +--R + +--R 2 4 4 2 6 4 6 2 4 4 2 6 3 +--R (- 2a b - 4a b - 2a )cos(x) + (- 2b - 3a b - 3a b - 2a )cos(x) +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R (- b + 3a b + 5a b + a )cos(x) + (2b + 7a b + 6a b + a )cos(x) +--R + +--R 6 2 4 4 2 +--R b + 2a b + a b +--R * +--R sin(x) +--R + +--R 3 3 5 7 3 3 5 6 3 3 5 5 +--R (a b + a b)cos(x) + (2a b + 2a b)cos(x) + (a b + a b)cos(x) +--R + +--R 5 3 3 4 5 5 3 +--R (a b + a b )cos(x) + (a b - a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (- a b - 3a b - 2a b)cos(x) + (- a b - 2a b - a b)cos(x) +--R / +--R 3 3 8 2 4 4 2 2 4 4 2 7 +--R a b sin(x) + ((a b - 3a b )cos(x) - a b - a b )sin(x) +--R + +--R 3 3 5 2 5 3 3 5 3 3 +--R (- 4a b + 3a b)cos(x) + (- a b - a b + 2a b)cos(x) - 3a b +--R + +--R 5 +--R - a b +--R * +--R 6 +--R sin(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (- a b + 6a b - a )cos(x) + (a b + 8a b - a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- a b + 8a b + a )cos(x) + 3a b + 4a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 5 4 5 3 3 5 3 +--R (3a b - 4a b)cos(x) + (a b + 4a b - 9a b)cos(x) +--R + +--R 5 3 3 5 2 5 3 3 5 +--R (2a b + 7a b - 8a b)cos(x) + (3a b + 4a b - a b)cos(x) +--R + +--R 3 3 5 +--R 3a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 6 5 2 4 4 2 6 4 +--R (- 3a b + a )cos(x) + (- 2a b - 7a b + 3a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (- 2a b - 11a b + 3a )cos(x) + (- 2a b - 11a b - a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (- a b - 9a b - 4a )cos(x) - 3a b - 5a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 5 6 3 3 5 5 3 3 5 4 +--R a b cos(x) + (a b + 3a b)cos(x) + (- 2a b + 6a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (- 2a b - 7a b + 7a b)cos(x) + (- 4a b - 8a b + 2a b)cos(x) +--R + +--R 5 3 3 5 3 3 5 +--R (- 3a b - 5a b - 2a b)cos(x) - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 6 5 2 4 4 2 6 4 +--R (3a b - a )cos(x) + (2a b + 7a b - 3a )cos(x) +--R + +--R 2 4 4 2 6 3 2 4 4 2 6 2 +--R (3a b + 5a b - 2a )cos(x) + (a b + 3a b + 2a )cos(x) +--R + +--R 2 4 4 2 6 2 4 4 2 6 +--R (a b + 4a b + 3a )cos(x) + a b + 2a b + a +--R * +--R sin(x) +--R + +--R 5 6 3 3 5 5 3 3 5 4 +--R - a b cos(x) + (- a b - 3a b)cos(x) + (- a b - 2a b)cos(x) +--R + +--R 5 3 3 5 3 5 3 3 5 2 +--R (a b + 3a b + 2a b)cos(x) + (2a b + 5a b + 3a b)cos(x) +--R + +--R 5 3 3 5 +--R (a b + 2a b + a b)cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 5 4 3 8 +--R (a b + a b )sin(x) +--R + +--R 6 3 4 5 2 3 4 5 2 7 +--R ((a b - 2a b - 3a b )cos(x) - a b - a b )sin(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 4a b - a b + 3a b)cos(x) + (- 3a b - a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 +--R - 3a b - 4a b - a b +--R * +--R 6 +--R sin(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- a b + 5a b + 5a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b + 7a b + 8a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- 3a b + 5a b + 9a b + a )cos(x) + 3a b + 4a b + a +--R * +--R 5 +--R sin(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (3a b - a b - 4a b)cos(x) + (7a b - 2a b - 9a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 2 5 +--R (11a b + 3a b - 8a b)cos(x) + (7a b + 6a b - a b)cos(x) + 3a b +--R + +--R 4 3 6 +--R 5a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R (- 3a b - 2a b + a )cos(x) + (- 8a b - 5a b + 3a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (2a b - 11a b - 10a b + 3a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (4a b - 8a b - 13a b - a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (3a b - 4a b - 11a b - 4a )cos(x) - 3a b - 5a b - 2a +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (a b + a b)cos(x) + (3a b + 3a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (- 4a b + 2a b + 6a b)cos(x) + (- 10a b - 3a b + 7a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (- 10a b - 8a b + 2a b)cos(x) + (- 5a b - 7a b - 2a b)cos(x) +--R + +--R 2 5 4 3 6 +--R - a b - 2a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 4 5 2 7 5 3 4 5 2 7 4 +--R (3a b + 2a b - a )cos(x) + (8a b + 5a b - 3a )cos(x) +--R + +--R 6 3 4 5 2 7 3 +--R (- a b + 6a b + 5a b - 2a )cos(x) +--R + +--R 6 3 4 5 2 7 2 +--R (- 2a b + a b + 5a b + 2a )cos(x) +--R + +--R 6 3 4 5 2 7 3 4 5 2 7 +--R (- a b + a b + 5a b + 3a )cos(x) + a b + 2a b + a +--R * +--R sin(x) +--R + +--R 4 3 6 6 4 3 6 5 +--R (- a b - a b)cos(x) + (- 3a b - 3a b)cos(x) +--R + +--R 2 5 4 3 6 4 2 5 4 3 6 3 +--R (a b - a b - 2a b)cos(x) + (3a b + 5a b + 2a b)cos(x) +--R + +--R 2 5 4 3 6 2 2 5 4 3 6 +--R (3a b + 6a b + 3a b)cos(x) + (a b + 2a b + a b)cos(x) +--R Type: Expression(Integer) +--E 199 + +)clear all + + +--S 200 of 526 +t0839:= sec(x)/(sec(x)-tan(x)) +--R +--R +--R sec(x) +--R (1) - --------------- +--R tan(x) - sec(x) +--R Type: Expression(Integer) +--E 200 + +--S 201 of 526 +r0839:= (1+sin(x))/cos(x) +--R +--R +--R sin(x) + 1 +--R (2) ---------- +--R cos(x) +--R Type: Expression(Integer) +--E 201 + +--S 202 of 526 +a0839:= integrate(t0839,x) +--R +--R +--R - 2cos(x) - 2 +--R (3) ------------------- +--R sin(x) - cos(x) - 1 +--R Type: Union(Expression(Integer),...) +--E 202 + +--S 203 of 526 +m0839:= a0839-r0839 +--R +--R +--R 2 2 +--R - sin(x) + cos(x)sin(x) - 2cos(x) - cos(x) + 1 +--R (4) ------------------------------------------------ +--R 2 +--R cos(x)sin(x) - cos(x) - cos(x) +--R Type: Expression(Integer) +--E 203 + +--S 204 of 526 +d0839:= D(m0839,x) +--R +--R +--R (5) +--R 4 3 2 +--R - sin(x) + (2cos(x) + 1)sin(x) + sin(x) +--R + +--R 3 2 4 2 +--R (2cos(x) + cos(x) - 2cos(x) - 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 2 3 2 4 3 +--R cos(x) sin(x) + (- 2cos(x) - 2cos(x) )sin(x) + cos(x) + 2cos(x) +--R + +--R 2 +--R cos(x) +--R Type: Expression(Integer) +--E 204 + +)clear all + + +--S 205 of 526 +t0840:= tan(x)/(csc(x)+cot(x)) +--R +--R +--R tan(x) +--R (1) --------------- +--R csc(x) + cot(x) +--R Type: Expression(Integer) +--E 205 + +--S 206 of 526 +r0840:= -x+atanh(sin(x)) +--R +--R +--R (2) atanh(sin(x)) - x +--R Type: Expression(Integer) +--E 206 + +--S 207 of 526 +a0840:= integrate(t0840,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (3) log(-------------------) - log(-------------------) - x +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 207 + +--S 208 of 526 +m0840:= a0840-r0840 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (4) log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 208 + +--S 209 of 526 +d0840:= D(m0840,x) +--R +--R +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R (5) ------------------------------------------------------------------ +--R 4 2 2 2 +--R sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 209 + +)clear all + + +--S 210 of 526 +t0841:= tan(x)/(csc(x)-cot(x)) +--R +--R +--R tan(x) +--R (1) --------------- +--R csc(x) - cot(x) +--R Type: Expression(Integer) +--E 210 + +--S 211 of 526 +r0841:= x+atanh(sin(x)) +--R +--R +--R (2) atanh(sin(x)) + x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 526 +a0841:= integrate(t0841,x) +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (3) log(-------------------) - log(-------------------) + x +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 212 + +--S 213 of 526 +m0841:= a0841-r0841 +--R +--R +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (4) log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 213 + +--S 214 of 526 +d0841:= D(m0841,x) +--R +--R +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R (5) ------------------------------------------------------------------ +--R 4 2 2 2 +--R sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 214 + +)clear all + + +--S 215 of 526 +t0842:= cos(x)*sin(x)/(a*cos(x)+b*sin(x)) +--R +--R +--R cos(x)sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 215 + +--S 216 of 526 +r0842:= a*b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ + a*cos(x)/(a^2+b^2)+b*sin(x)/(a^2+b^2) +--R +--R +--R +-------+ +--R a sin(x) - b cos(x) | 2 2 +--R - a b atanh(-------------------) + (b sin(x) - a cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) ------------------------------------------------------------------ +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 216 + +--S 217 of 526 +a0842:= integrate(t0842,x) +--R +--R +--R (3) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R +-------+ +--R | 2 2 +--R (b sin(x) - a cos(x))\|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 217 + +--S 218 of 526 +m0842:= a0842-r0842 +--R +--R +--R (4) +--R a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R a sin(x) - b cos(x) +--R a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a +--R Type: Expression(Integer) +--E 218 + +--S 291 of 526 +d0842:= D(m0842,x) +--R +--R +--R (5) +--R 2 3 2 2 2 2 2 +--R a b sin(x) - a b cos(x)sin(x) + (a b cos(x) - a b)sin(x) +--R + +--R 2 3 2 +--R - a b cos(x) + a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R 2 3 4 3 4 3 2 5 2 +--R (a b + a b)sin(x) + (- 2a b - a b + a )cos(x)sin(x) +--R + +--R 5 2 3 4 2 5 2 3 4 +--R ((b - a b - 2a b)cos(x) - b - 2a b - a b)sin(x) +--R + +--R 4 3 2 3 4 3 2 5 +--R (a b + a b )cos(x) + (- a b - 2a b - a )cos(x) +--R Type: Expression(Integer) +--E 291 + +)clear all + + +--S 220 of 526 +t0843:= cos(x)*sin(x)^2/(a*cos(x)+b*sin(x)) +--R +--R +--R 2 +--R cos(x)sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 220 + +--S 221 of 526 +r0843:= 1/2/(a^2+b^2)^2*(a^3*x-a*b^2*x+2*a^2*b*_ + log(a*cos(x)+b*sin(x))-cos(x)*sin(x)*a^3-_ + cos(x)*sin(x)*b^2*a-b*cos(x)^2*a^2+a^2*b-b^3*cos(x)^2+b^3) +--R +--R +--R (2) +--R 2 2 3 +--R 2a b log(b sin(x) + a cos(x)) + (- a b - a )cos(x)sin(x) +--R + +--R 3 2 2 2 3 3 2 +--R (- b - a b)cos(x) + (- a b + a )x + b + a b +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 526 +a0843:= integrate(t0843,x) +--R +--R +--R (3) +--R 2 2 2 - 2b sin(x) - 2a cos(x) +--R - 2a b log(----------) + 2a b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 +--R (- a b - a )cos(x)sin(x) + (- b - a b)cos(x) + (- a b + a )x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression(Integer),...) +--E 222 + +--S 223 of 526 +m0843:= a0843-r0843 +--R +--R +--R (4) +--R 2 2 2 +--R - 2a b log(b sin(x) + a cos(x)) - 2a b log(----------) +--R cos(x) + 1 +--R + +--R 2 - 2b sin(x) - 2a cos(x) 3 2 +--R 2a b log(-----------------------) - b - a b +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 223 + +--S 224 of 526 +d0843:= D(m0843,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 224 + +)clear all + + +--S 225 of 526 +t0844:= cos(x)*sin(x)^3/(a*cos(x)+b*sin(x)) +--R +--R +--R 3 +--R cos(x)sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 225 + +--S 226 of 526 +r0844:= a^3*b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ + a^3*cos(x)/(a^2+b^2)^2+a*cos(x)^3/(3*a^2+3*b^2)-_ + a^4*sin(x)/b/(a^2+b^2)^2+a^2*sin(x)/b/(a^2+b^2)+_ + b*sin(x)^3/(3*a^2+3*b^2) +--R +--R +--R (2) +--R 3 a sin(x) - b cos(x) +--R - 3a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 2 2 3 3 3 +--R ((b + a b)sin(x) + 3a b sin(x) + (a b + a )cos(x) - 3a cos(x)) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 526 +a0844:= integrate(t0844,x) +--R +--R +--R (3) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 2 2 3 2 2 3 3 +--R ((- b - a b)cos(x) + b + 4a b)sin(x) + (a b + a )cos(x) +--R + +--R 3 +--R - 3a cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 227 + +--S 228 of 526 +m0844:= a0844-r0844 +--R +--R +--R (4) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 a sin(x) - b cos(x) +--R 3a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 3 2 3 3 2 2 3 2 | 2 2 +--R ((- b - a b)sin(x) + ((- b - a b)cos(x) + b + a b)sin(x))\|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 228 + +--S 229 of 526 +d0844:= D(m0844,x) +--R +--R +--R (5) +--R 4 3 3 2 2 4 2 4 +--R 3a b sin(x) - 3a b cos(x)sin(x) + (3a b cos(x) - 3a b)sin(x) +--R + +--R 3 2 3 3 2 +--R - 3a b cos(x) + 3a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 4 2 5 5 3 3 5 2 4 +--R (- a b - a b )cos(x)sin(x) + (2a b + a b - a b)cos(x) sin(x) +--R + +--R 6 4 2 3 6 2 4 4 2 3 +--R ((- b + a b )cos(x) + (b + 3a b + 2a b )cos(x))sin(x) +--R + +--R 5 5 4 5 3 3 5 2 2 +--R ((a b - a b)cos(x) + (- a b + a b + 2a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 3 +--R (- b + a b + 2a b )cos(x) + (2b + a b - a b )cos(x) +--R + +--R 6 2 4 4 2 +--R (- b - 2a b - a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 4 +--R (- a b - a b )cos(x) + (2a b + 3a b + a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (- a b - 2a b - a b)cos(x) +--R / +--R 2 5 4 3 6 3 6 3 4 7 2 +--R (3a b + 6a b + 3a b)sin(x) + (- 6a b - 9a b + 3a )cos(x)sin(x) +--R + +--R 7 4 3 6 2 7 2 5 4 3 6 +--R ((3b - 9a b - 6a b)cos(x) - 3b - 9a b - 9a b - 3a b)sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 7 +--R (3a b + 6a b + 3a b )cos(x) + (- 3a b - 9a b - 9a b - 3a )cos(x) +--R Type: Expression(Integer) +--E 229 + +)clear all + + +--S 230 of 526 +t0845:= sin(x)*cos(x)^2/(a*cos(x)+b*sin(x)) +--R +--R +--R 2 +--R cos(x) sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 230 + +--S 231 of 526 +r0845:= -1/2*(-b^3*x+a^2*b*x+2*a*b^2*log(a*cos(x)+b*sin(x))-_ + a^2*b*sin(x)*cos(x)-b^3*sin(x)*cos(x)+cos(x)^2*a^3-_ + a^3+b^2*a*cos(x)^2-b^2*a)/(a^2+b^2)^2 +--R +--R +--R (2) +--R 2 3 2 +--R - 2a b log(b sin(x) + a cos(x)) + (b + a b)cos(x)sin(x) +--R + +--R 2 3 2 3 2 2 3 +--R (- a b - a )cos(x) + (b - a b)x + a b + a +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 526 +a0845:= integrate(t0845,x) +--R +--R +--R (3) +--R 2 2 2 - 2b sin(x) - 2a cos(x) +--R 2a b log(----------) - 2a b log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 3 2 2 3 2 3 2 +--R (b + a b)cos(x)sin(x) + (- a b - a )cos(x) + (b - a b)x +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Union(Expression(Integer),...) +--E 232 + +--S 233 of 526 +m0845:= a0845-r0845 +--R +--R +--R (4) +--R 2 2 2 +--R 2a b log(b sin(x) + a cos(x)) + 2a b log(----------) +--R cos(x) + 1 +--R + +--R 2 - 2b sin(x) - 2a cos(x) 2 3 +--R - 2a b log(-----------------------) - a b - a +--R cos(x) + 1 +--R / +--R 4 2 2 4 +--R 2b + 4a b + 2a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 526 +d0845:= D(m0845,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + + +--S 235 of 526 +t0846:= sin(x)*cos(x)^3/(a*cos(x)+b*sin(x)) +--R +--R +--R 3 +--R cos(x) sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) +--R Type: Expression(Integer) +--E 235 + +--S 236 of 526 +r0846:= a*b^3*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ + a*b^2*cos(x)/(a^2+b^2)^2-a*cos(x)^3/(3*a^2+3*b^2)-_ + a^2*b*sin(x)/(a^2+b^2)^2+b*sin(x)/(a^2+b^2)-b*sin(x)^3/(3*a^2+3*b^2) +--R +--R +--R (2) +--R 3 a sin(x) - b cos(x) +--R - 3a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 3 2 3 3 2 3 3 2 +--R ((- b - a b)sin(x) + 3b sin(x) + (- a b - a )cos(x) - 3a b cos(x)) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 526 +a0846:= integrate(t0846,x) +--R +--R +--R (3) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 2 2 3 2 2 3 3 +--R ((b + a b)cos(x) + 2b - a b)sin(x) + (- a b - a )cos(x) +--R + +--R 2 +--R - 3a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Union(Expression(Integer),...) +--E 237 + +--S 238 of 526 +m0846:= a0846-r0846 +--R +--R +--R (4) +--R 3 +--R 3a b +--R * +--R log +--R +-------+ +--R 2 2 2 | 2 2 2 3 +--R (a b sin(x) - b cos(x) - b - a )\|b + a + (a b + a )sin(x) +--R + +--R 3 2 3 2 +--R (- b - a b)cos(x) - b - a b +--R / +--R b sin(x) + a cos(x) +--R + +--R 3 a sin(x) - b cos(x) +--R 3a b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R +-------+ +--R 3 2 3 3 2 2 3 2 | 2 2 +--R ((b + a b)sin(x) + ((b + a b)cos(x) - b - a b)sin(x))\|b + a +--R / +--R +-------+ +--R 4 2 2 4 | 2 2 +--R (3b + 6a b + 3a )\|b + a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 526 +d0846:= D(m0846,x) +--R +--R +--R (5) +--R 2 3 3 4 2 2 3 2 2 3 +--R 3a b sin(x) - 3a b cos(x)sin(x) + (3a b cos(x) - 3a b )sin(x) +--R + +--R 4 3 4 +--R - 3a b cos(x) + 3a b cos(x) +--R * +--R +-------+ +--R | 2 2 +--R \|b + a +--R + +--R 2 4 4 2 5 5 3 3 5 2 4 +--R (a b + a b )cos(x)sin(x) + (- 2a b - a b + a b)cos(x) sin(x) +--R + +--R 6 4 2 3 6 2 4 4 2 3 +--R ((b - a b )cos(x) + (- b - 3a b - 2a b )cos(x))sin(x) +--R + +--R 5 5 4 5 3 3 5 2 2 +--R ((- a b + a b)cos(x) + (a b - a b - 2a b)cos(x) )sin(x) +--R + +--R 6 2 4 4 2 5 6 2 4 4 2 3 +--R (b - a b - 2a b )cos(x) + (- 2b - a b + a b )cos(x) +--R + +--R 6 2 4 4 2 +--R (b + 2a b + a b )cos(x) +--R * +--R sin(x) +--R + +--R 5 3 3 6 5 3 3 5 4 +--R (a b + a b )cos(x) + (- 2a b - 3a b - a b)cos(x) +--R + +--R 5 3 3 5 2 +--R (a b + 2a b + a b)cos(x) +--R / +--R 2 5 4 3 6 3 6 3 4 7 2 +--R (3a b + 6a b + 3a b)sin(x) + (- 6a b - 9a b + 3a )cos(x)sin(x) +--R + +--R 7 4 3 6 2 7 2 5 4 3 6 +--R ((3b - 9a b - 6a b)cos(x) - 3b - 9a b - 9a b - 3a b)sin(x) +--R + +--R 6 3 4 5 2 3 6 3 4 5 2 7 +--R (3a b + 6a b + 3a b )cos(x) + (- 3a b - 9a b - 9a b - 3a )cos(x) +--R Type: Expression(Integer) +--E 239 + +)clear all + + +--S 240 of 526 +t0847:= sec(x)^2/(a+b*tan(x)+c*sec(x)) +--R +--R +--R 2 +--R sec(x) +--R (1) ----------------------- +--R b tan(x) + c sec(x) + a +--R Type: Expression(Integer) +--E 240 + +--S 241 of 526 +r0847:= -2*a*c*atanh((b-(a-c)*tan(1/2*x))/(a^2+b^2-c^2)^(1/2))/_ + (b^2-c^2)/(a^2+b^2-c^2)^(1/2)-log(1-tan(1/2*x))/(b+c)-_ + log(1+tan(1/2*x))/(b-c)+b*log(a+c+2*b*tan(1/2*x)-(a-c)*_ + tan(1/2*x)^2)/(b^2-c^2) +--R +--R +--R (2) +--R +--------------+ +--R | 2 2 2 x 2 x +--R - b\|- c + b + a log((c - a)tan(-) + 2b tan(-) + c + a) +--R 2 2 +--R + +--R +--------------+ +--R | 2 2 2 x +--R (c + b)\|- c + b + a log(tan(-) + 1) +--R 2 +--R + +--R x +--R +--------------+ (c - a)tan(-) + b +--R | 2 2 2 x 2 +--R (- c + b)\|- c + b + a log(- tan(-) + 1) + 2a c atanh(-----------------) +--R 2 +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 526 +a0847:= integrate(t0847,x) +--R +--R +--R (3) +--R [ +--R a c +--R * +--R log +--R 2 2 2 +--R (b c - a b)sin(x) + (- c + a c + b )cos(x) - a c + b +--R + +--R 2 +--R a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 2 3 +--R (- c + a c + (b + a )c - a b - a )sin(x) +--R + +--R 2 3 2 2 3 2 +--R (- b c + b + a b)cos(x) - b c + b + a b +--R / +--R b sin(x) + a cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R - b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 sin(x) + cos(x) + 1 +--R (c + b)\|- c + b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 sin(x) - cos(x) - 1 +--R (- c + b)\|- c + b + a log(-------------------) +--R cos(x) + 1 +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R , +--R +--R +------------+ +--R | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R - b\|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 sin(x) + cos(x) + 1 +--R (c + b)\|c - b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 sin(x) - cos(x) - 1 +--R (- c + b)\|c - b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R ((c - a)sin(x) + b cos(x) + b)\|c - b - a +--R - 2a c atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 242 + +--S 243 of 526 +m0847a:= a0847.1-r0847 +--R +--R +--R (4) +--R a c +--R * +--R log +--R 2 2 2 2 +--R ((b c - a b)sin(x) + (- c + a c + b )cos(x) - a c + b + a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 2 3 +--R (- c + a c + (b + a )c - a b - a )sin(x) +--R + +--R 2 3 2 2 3 2 +--R (- b c + b + a b)cos(x) - b c + b + a b +--R / +--R b sin(x) + a cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 x 2 x +--R b\|- c + b + a log((c - a)tan(-) + 2b tan(-) + c + a) +--R 2 2 +--R + +--R +--------------+ +--R | 2 2 2 x +--R (- c - b)\|- c + b + a log(tan(-) + 1) +--R 2 +--R + +--R +--------------+ +--R | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R - b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 sin(x) + cos(x) + 1 +--R (c + b)\|- c + b + a log(-------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 sin(x) - cos(x) - 1 +--R (- c + b)\|- c + b + a log(-------------------) +--R cos(x) + 1 +--R + +--R x +--R +--------------+ (c - a)tan(-) + b +--R | 2 2 2 x 2 +--R (c - b)\|- c + b + a log(- tan(-) + 1) - 2a c atanh(-----------------) +--R 2 +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R Type: Expression(Integer) +--E 243 + +--S 244 of 526 +d0847a:= D(m0847a,x) +--R +--R +--R (5) +--R 3 2 3 2 3 5 +--R (b c - 2a b c + a b )sin(x) +--R + +--R 2 2 3 2 3 2 2 2 4 +--R (- 2b + a )c + (6a b - 2a )c + (- 6a b + a )c +--R + +--R 3 2 +--R 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 4 +--R a c - 2a c + a c +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R b c - 6a b c + (2b + 9a b)c + (- 2a b - 4a b)c - b +--R + +--R 2 3 +--R a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 3 5 4 4 +--R (- b c + (2b + a b)c + 2a b c - 2b - 2a b)cos(x) - b c +--R + +--R 3 2 2 3 3 5 2 3 4 +--R 2a b c - 2a b c + (2a b + 2a b)c - b - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 2 3 2 3 2 +--R a c + (- 5b - 3a )c + (11a b + 2a )c +--R + +--R 4 2 2 4 3 2 +--R (3b - 7a b )c - 4a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R c - a c + (- 7b - 4a )c + (11a b + 4a )c +--R + +--R 4 2 2 4 3 2 +--R (7b + a b )c - 10a b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R c - a c + (- 3b - 5a )c + (a b + 6a )c +--R + +--R 4 2 2 4 4 3 2 +--R (5b + 11a b - a )c - 8a b - 6a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 4 +--R a c + (- b - 4a )c + (a b + 4a )c + (b + 3a b - a )c +--R + +--R 4 3 2 +--R - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 3 2 2 3 3 +--R 3b c - 10a b c + (- 3b + 11a b)c + (4a b - 4a b)c +--R + +--R 5 2 3 +--R b - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R b c - 4a b c + (- 6b + 3a b)c + (4a b + 2a b)c + 4b +--R + +--R 2 3 4 +--R - 2a b - 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 2 2 +--R - 6b c + 16a b c + (- 2b - 15a b)c +--R + +--R 3 3 5 2 3 4 +--R (- 8a b + 6a b)c + 6b + 4a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 3 3 +--R - 5b c + 12a b c + (2b - 7a b)c + (- 12a b - 2a b)c +--R + +--R 5 2 3 4 +--R 4b + 6a b + 2a b +--R * +--R cos(x) +--R + +--R 4 3 3 2 3 3 5 2 3 4 +--R - b c + 2a b c + b c + (- 4a b - 2a b)c + b + 2a b + a b +--R * +--R sin(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 4 +--R (3a c + (- b - 6a )c + (- a b + 4a )c + (b + a b - a )c) +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 3c + a c + (- 7b - 7a )c + (- a b + 4a )c +--R + +--R 4 2 2 4 +--R (5b + 3a b - a )c +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 7c - 6a c + (- 16b + 2a )c + (2a b - 4a )c +--R + +--R 4 2 2 4 +--R (10b + 4a b + a )c +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 3 2 3 2 4 2 2 4 +--R (5c - 2a c - 16b c + (2a b - 4a )c + (10b + 4a b + a )c) +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 2 4 2 2 +--R (c + 3a c + (- 7b - 4a )c - a b c + (5b + 3a b )c)cos(x) +--R + +--R 4 2 2 3 2 2 4 2 2 +--R a c + (- b - a )c - a b c + (b + a b )c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 4 5 +--R (2b c - 2a b )sin(x) +--R + +--R 3 2 2 3 3 5 2 3 +--R ((- 6b + 2a b)c + (8a b - 2a b)c + 2b - 4a b )cos(x) +--R + +--R 3 2 2 3 5 +--R (- 2b + 2a b)c - 2a b c + 2b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (4b c - 12a b c + 8a b c)cos(x) +--R + +--R 2 3 2 2 3 2 2 3 2 2 2 2 +--R (- 2b c - 2a b c + 4a b )cos(x) - 4b c + 4a b c - 2a b c +--R + +--R 3 2 +--R 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 2 2 3 5 2 3 3 +--R (4a b c + (- 8b - 4a b)c + 8a b c + 4b - 4a b )cos(x) +--R + +--R 4 3 3 2 2 5 2 3 2 +--R (4b c + 2a b c + (- 12b - 6a b)c + 10b + 2a b )cos(x) +--R + +--R 4 3 3 2 2 3 3 +--R 4b c + 2a b c + (- 6b - 8a b)c + (- 12a b + 2a b)c +--R + +--R 5 2 3 +--R 8b + 10a b +--R * +--R cos(x) +--R + +--R 3 3 2 2 3 3 5 2 3 +--R 4a b c + (- 2b - 6a b)c + (- 4a b + 2a b)c + 2b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 4 2 2 4 4 +--R (4b c - 12a b c + (- 2b + 8a b )c + 2a b )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 2b c - 2a b c + 4a b )cos(x) +--R + +--R 2 3 2 2 4 2 2 4 3 2 +--R (- 12b c + 20a b c + (8b - 10a b )c - 8a b + 2a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 2 2 4 4 3 2 +--R (- 6b c + 10a b c + 8b c - 8a b - 4a b )cos(x) +--R + +--R 4 2 2 4 3 2 +--R (2b + 2a b )c - 2a b - 2a b +--R * +--R sin(x) +--R + +--R 3 3 2 2 3 5 5 +--R (4a b c + (- 2b - 6a b)c + 2a b c + 2b )cos(x) +--R + +--R 4 3 3 2 2 3 5 2 3 +--R (4b c + 2a b c + (- 10b - 8a b)c + 2a b c + 8b + 2a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 3 2 3 5 2 3 3 +--R (8b c - 6a b c - 18b c - 2a b c + 12b + 6a b )cos(x) +--R + +--R 4 3 3 2 3 5 2 3 2 +--R (4b c - 2a b c - 14b c - 2a b c + 8b + 6a b )cos(x) +--R + +--R 3 3 2 2 5 2 3 +--R (2a b c + (- 4b - 2a b)c + 2b + 2a b )cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 2 3 5 +--R (2a b c - 2a b )sin(x) +--R + +--R 2 3 2 3 2 4 2 2 4 +--R 2b c + (- 8a b + 2a )c + (- 2b + 8a b - 2a )c +--R + +--R 4 3 2 +--R 4a b - 4a b +--R * +--R cos(x) +--R + +--R 2 3 2 3 2 4 4 4 +--R 2b c + (- 4a b + 2a )c + (- 2b - 2a )c + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 3 2 2 3 3 +--R - 2b c + 8a b c + (4b - 14a b)c + (- 4a b + 8a b)c +--R + +--R 5 2 3 +--R - 2b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 3 2 2 5 4 4 +--R (- 2a b c + (4b - 2a b)c - 4b + 4a b)cos(x) + 2b c +--R + +--R 3 2 2 3 3 5 2 3 4 +--R - 8a b c + 6a b c + (4a b - 2a b)c - 2b - 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 2 3 2 3 2 +--R - 2a c + (- 2b + 6a )c + (- 2a b - 4a )c +--R + +--R 4 2 2 3 2 +--R (2b + 6a b )c - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R - 2c + 4a c + (- 2b + 2a )c + (- 2a b - 4a )c +--R + +--R 4 +--R 4b c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 3 2 3 2 +--R - 2c + 4a c + 2a c + (2a b - 6a )c +--R + +--R 4 2 2 4 3 2 +--R (2b - 12a b + 2a )c + 8a b +--R * +--R cos(x) +--R + +--R 4 2 3 2 3 2 2 2 4 3 2 +--R - 2a c + 6a c + (2a b - 6a )c + (- 6a b + 2a )c + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 3 3 5 4 +--R (2b c + (- 4b - 10a b)c + (2a b + 8a b)c + 2b )cos(x) +--R + +--R 4 3 3 2 2 3 5 +--R 4b c - 10a b c + (- 12b + 2a b)c + 8a b c + 8b +--R + +--R 2 3 4 +--R - 4a b + 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 3 2 2 3 3 5 +--R - 12a b c + (- 12b + 20a b)c + (8a b - 10a b)c + 12b +--R + +--R 2 3 4 +--R - 8a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 5 2 3 4 +--R (- 4b c + 2a b c + (- 4b + 6a b)c + 8b - 4a b - 4a b) +--R * +--R cos(x) +--R + +--R 4 3 2 2 3 3 5 4 +--R - 2b c + 4a b c - 2a b c + (- 2a b + 2a b)c + 2b - 2a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 2 2 4 4 +--R (2a c + 2a c + (- 6a b - 6a )c + (2a b + 2a )c + 4a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 2c + 8a c + (- 4b - 2a )c + (- 22a b - 10a )c +--R + +--R 4 2 2 4 4 3 2 +--R (2b + 4a b + 2a )c + 16a b + 4a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 6c + 10a c + (- 14b - 8a )c + (- 32a b - 6a )c +--R + +--R 4 2 2 4 4 3 2 +--R (8b + 2a b - 2a )c + 24a b + 12a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 6c + 6a c + (- 18b - 4a )c + (- 24a b - 6a )c +--R + +--R 4 2 2 4 4 3 2 +--R (12b + 2a b - 2a )c + 16a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R 2c + 4a c + (- 10b - 2a )c + (- 10a b - 4a )c +--R + +--R 4 2 2 4 3 2 +--R (8b + 4a b )c + 4a b + 4a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 2 4 2 2 +--R 2a c + (- 2b - 2a )c - 2a b c + (2b + 2a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 4 5 +--R (- 2b c + 2a b )sin(x) +--R + +--R 3 2 2 3 3 5 2 3 +--R ((6b - 2a b)c + (- 8a b + 2a b)c - 2b + 4a b )cos(x) +--R + +--R 3 2 2 3 5 +--R (2b - 2a b)c + 2a b c - 2b +--R * +--R 4 +--R sin(x) +--R + +--R 2 3 2 2 2 2 2 +--R (- 4b c + 12a b c - 8a b c)cos(x) +--R + +--R 2 3 2 2 3 2 2 3 2 2 2 2 +--R (2b c + 2a b c - 4a b )cos(x) + 4b c - 4a b c + 2a b c +--R + +--R 3 2 +--R - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 2 2 3 5 2 3 3 +--R (- 4a b c + (8b + 4a b)c - 8a b c - 4b + 4a b )cos(x) +--R + +--R 4 3 3 2 2 5 2 3 2 +--R (- 4b c - 2a b c + (12b + 6a b)c - 10b - 2a b )cos(x) +--R + +--R 4 3 3 2 2 3 3 +--R - 4b c - 2a b c + (6b + 8a b)c + (12a b - 2a b)c +--R + +--R 5 2 3 +--R - 8b - 10a b +--R * +--R cos(x) +--R + +--R 3 3 2 2 3 3 5 2 3 +--R - 4a b c + (2b + 6a b)c + (4a b - 2a b)c - 2b - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 4 2 2 4 4 +--R (- 4b c + 12a b c + (2b - 8a b )c - 2a b )cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (2b c + 2a b c - 4a b )cos(x) +--R + +--R 2 3 2 2 4 2 2 4 3 2 +--R (12b c - 20a b c + (- 8b + 10a b )c + 8a b - 2a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 2 2 4 4 3 2 +--R (6b c - 10a b c - 8b c + 8a b + 4a b )cos(x) +--R + +--R 4 2 2 4 3 2 +--R (- 2b - 2a b )c + 2a b + 2a b +--R * +--R sin(x) +--R + +--R 3 3 2 2 3 5 5 +--R (- 4a b c + (2b + 6a b)c - 2a b c - 2b )cos(x) +--R + +--R 4 3 3 2 2 3 5 2 3 +--R (- 4b c - 2a b c + (10b + 8a b)c - 2a b c - 8b - 2a b ) +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 3 2 3 5 2 3 3 +--R (- 8b c + 6a b c + 18b c + 2a b c - 12b - 6a b )cos(x) +--R + +--R 4 3 3 2 3 5 2 3 2 +--R (- 4b c + 2a b c + 14b c + 2a b c - 8b - 6a b )cos(x) +--R + +--R 3 3 2 2 5 2 3 +--R (- 2a b c + (4b + 2a b)c - 2b - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 5 +--R (- b c + a b )sin(x) +--R + +--R 2 2 3 2 2 4 2 2 4 3 2 +--R ((4b - a )c - 2a b c + (- 2b - 2a b + a )c + 2a b )cos(x) +--R + +--R 2 2 3 4 4 +--R (2b - a )c + (- 2b + a )c +--R * +--R 4 +--R sin(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R - 3b c + 6a b c + (2b + a b)c + (- 2a b - 4a b)c - b +--R + +--R 2 3 +--R a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 3 5 4 +--R (b c + 2a b c + (2b + a b)c - 2a b c - 2b - 2a b)cos(x) +--R + +--R 4 3 3 5 2 3 4 +--R 3b c - 2a b c + 2a b c - b - a b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R - 3a c + (3b + a )c + (3a b + 2a )c + (- b - 3a b )c +--R + +--R 4 3 2 +--R - 4a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R - 3c - 3a c + (5b + 2a )c + (11a b + 4a )c +--R + +--R 4 2 2 4 3 2 +--R (- 3b - a b )c - 10a b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R - 3c - 3a c + (3b + 3a )c + (13a b + 4a )c +--R + +--R 4 2 2 4 4 3 2 +--R (- 3b + a b - a )c - 8a b - 6a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 4 +--R - 3a c + (b + 2a )c + (5a b + 2a )c + (- b - a b - a )c +--R + +--R 4 3 2 +--R - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R - b c + 2a b c + (- b + 3a b)c + (2a b - 4a b)c + b +--R + +--R 2 3 +--R - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R 3b c - 2a b c + (- 6b + 3a b)c + (4a b - 2a b)c + 4b +--R + +--R 2 3 4 +--R - 2a b - 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 2 2 3 5 2 3 +--R 6b c - 4a b c + (- 10b - 5a b)c + 4a b c + 6b + 4a b +--R + +--R 4 +--R - a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 3 3 5 +--R b c + 2a b c + (- 6b - 7a b)c + (- 4a b + 2a b)c + 4b +--R + +--R 2 3 4 +--R 6a b + 2a b +--R * +--R cos(x) +--R + +--R 4 3 3 2 2 3 5 2 3 4 +--R - b c + 2a b c + (- b - 2a b)c - 2a b c + b + 2a b + a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 4 2 2 4 5 +--R (- a c + b c + (- a b + 2a )c + (- b + a b - a )c)cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R - c - a c + (3b + a )c + (- a b + 2a )c +--R + +--R 4 2 2 4 +--R (- 3b + a b - a )c +--R * +--R 4 +--R cos(x) +--R + +--R 5 2 2 3 2 3 2 4 2 2 4 +--R (- c + (2b + 2a )c + (2a b - 2a )c + (- 2b - 2a b + a )c) +--R * +--R 3 +--R cos(x) +--R + +--R 5 2 3 2 3 2 4 2 2 4 2 +--R (c - 2b c + (2a b - 2a )c + (2b - 2a b + a )c)cos(x) +--R + +--R 5 4 2 2 3 2 2 4 2 2 4 +--R (c + a c + (- 3b - 2a )c - a b c + (3b + a b )c)cos(x) + a c +--R + +--R 2 2 3 2 2 4 2 2 +--R (- b - a )c - a b c + (b + a b )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 2 4 2 3 4 2 4 3 2 2 4 4 2 5 +--R (- b c + 2a b c + b c + (- 2a b - 2a b )c + a b + a b )sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R b c - 4a b c + (- b + 4a b)c + (4a b + 2a b)c +--R + +--R 2 3 4 3 3 5 +--R (- 5a b - 5a b)c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 4 2 3 3 2 2 3 4 3 3 5 +--R - a b c + 2a b c + a b c + (- 2a b - 2a b)c + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 2 4 3 3 4 2 2 4 2 +--R a c + (- b - 3a )c + a c + (2b + 3a b + 3a )c +--R + +--R 4 3 2 5 6 4 2 +--R (- a b - 3a b - 2a )c - b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R c - a c + (- 2b - 4a )c + (a b + 4a )c +--R + +--R 4 2 2 4 2 3 2 5 6 2 4 4 2 +--R (3b + 3a b + 3a )c + (- 3a b - 3a )c - 2b - a b + a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 4 2 4 5 +--R c - 2a c + (- b - a )c + (a b + 3a )c + b c + (a b - a )c +--R + +--R 6 2 4 +--R - b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 3b c - 6a b c + (- 6b + a b)c + (10a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 5 +--R (3b - a b - 4a b)c - 4a b - 2a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 5b c - 7a b c + (- 12b - 5a b)c + (17a b + 6a b)c +--R + +--R 5 2 3 5 3 3 5 +--R (7b + 7a b )c - 10a b - 9a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 3b c - 2a b c + (- 8b - 9a b)c + (10a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 5 +--R (5b + 11a b + 6a b)c - 8a b - 10a b - 2a b +--R * +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R b c - a b c + (- 2b - 3a b)c + (3a b + 2a b)c +--R + +--R 5 2 3 4 5 3 3 5 +--R (b + 3a b + 2a b)c - 2a b - 3a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 2 4 2 3 3 +--R 3a c + (2b - 5a )c + (- 6a b - a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 2 4 +--R (- 3b + 5a b + 5a )c + (3a b + a b - 2a )c + b - a b +--R + +--R 4 2 +--R - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R 3c + a c - 10a c + (- 3a b + 2a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 2 4 +--R (- 7b + 7a b + 7a )c + (2a b - a b - 3a )c + 4b + a b +--R + +--R 4 2 +--R - 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 7c - 9a c + (- 8b - 4a )c + (17a b + 8a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- 5b - 3a b - 3a )c + (- 8a b - 7a b + a )c + 6b +--R + +--R 2 4 4 2 +--R 7a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 5c - 9a c + (- 8b + 2a )c + (19a b + 6a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- b - 7a b - 7a )c + (- 10a b - 7a b + 3a )c + 4b +--R + +--R 2 4 4 2 +--R 7a b + 3a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 2 2 4 2 +--R c - 2a c + (- 2b + a )c + (5a b + a )c + (- 2a b - 2a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (- 3a b - 2a b + a )c + b + 2a b + a b +--R * +--R sin(x) +--R + +--R 4 3 2 3 3 3 2 +--R 2a b c + (- b - a b)c + (- 2a b - 2a b)c +--R + +--R 5 2 3 4 +--R (b + 2a b + a b)c +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 3b c + 4a b c + (- 8b - 5a b)c + (- 4a b - 4a b)c +--R + +--R 5 2 3 4 +--R (5b + 7a b + 2a b)c +--R * +--R 4 +--R cos(x) +--R + +--R 5 3 2 3 5 2 3 3 +--R (10b c + (- 20b - 10a b)c + (10b + 10a b )c)cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 12b c - 4a b c + (- 22b - 10a b)c + (4a b + 4a b)c +--R + +--R 5 2 3 4 +--R (10b + 8a b - 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 6b c - 2a b c + (- 11b - 5a b)c + (2a b + 2a b)c +--R + +--R 5 2 3 4 +--R (5b + 4a b - a b)c +--R * +--R cos(x) +--R + +--R 5 3 2 3 5 2 3 +--R b c + (- 2b - a b)c + (b + a b )c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 5 2 3 5 3 3 5 +--R (- 2b c + 2a b c + (2b + 2a b )c - 2a b - 2a b )sin(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 2 4 +--R 4b c - 6a b c - 6b c + (6a b + 6a b )c + 2b - 2a b +--R + +--R 4 2 +--R - 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 4 2 +--R 2b c - 2a b c - 4b c + (2a b + 2a b )c + 2b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 3 2 2 3 4 2 +--R (4a b c - 4a b c + (- 4a b - 4a b)c + (4a b + 4a b)c)cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 4b c + 2a b c + (- 4b - 10a b)c + (- 2a b - 2a b)c +--R + +--R 2 3 4 +--R (6a b + 6a b)c +--R * +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 4b c - 2a b c + (- 4b - 6a b)c + (2a b + 2a b)c +--R + +--R 2 3 4 +--R (2a b + 2a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 4 2 3 +--R (4b c - 4a b c - 8b c + (4a b + 4a b )c + 4b - 4a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 +--R 6b c + 2a b c + (- 16b - 4a b )c + (- 2a b - 2a b )c +--R + +--R 6 2 4 4 2 +--R 10b + 8a b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 +--R 4b c + 8a b c + (- 12b - 8a b )c + (- 8a b - 8a b )c +--R + +--R 6 2 4 4 2 +--R 8b + 12a b + 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R 2b c + 2a b c + (- 4b - 4a b )c + (- 2a b - 2a b )c + 2b +--R + +--R 2 4 4 2 +--R 4a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 3 3 3 2 +--R 4a b c + (2b - 4a b)c + (- 6a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- 2b + 2a b + 4a b)c + 2a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 4b c + 2a b c + (- 4b - 10a b)c + (- 2a b - 2a b)c +--R + +--R 2 3 4 +--R (6a b + 6a b)c +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 8b c - 10a b c + (- 16b - 6a b)c + (18a b + 10a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (8b + 6a b - 2a b)c - 8a b - 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 4b c - 10a b c + (- 12b + 2a b)c + (18a b + 10a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (8b + 2a b - 6a b)c - 8a b - 8a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 5 4 +--R - 2a b c + (- 2b + 2a b)c + (4a b + 2a b)c + (2b - 2a b)c +--R + +--R 5 3 3 +--R - 2a b - 2a b +--R * +--R sin(x) +--R + +--R 2 3 4 2 4 3 2 6 2 4 5 +--R (2a b c - 2b c + (- 2a b - 2a b )c + 2b + 2a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R 4b c + 4a b c + (- 12b - 4a b )c + (- 4a b - 4a b )c + 8b +--R + +--R 2 4 +--R 8a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 4 4 2 2 2 6 2 4 3 +--R (12b c + (- 24b - 12a b )c + 12b + 12a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R 12b c - 4a b c + (- 20b - 12a b )c + (4a b + 4a b )c + 8b +--R + +--R 2 4 +--R 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R 4b c - 2a b c + (- 6b - 4a b )c + (2a b + 2a b )c + 2b +--R + +--R 2 4 +--R 2a b +--R * +--R cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 2 4 3 2 2 4 4 2 5 +--R (- 2a b c + 2a b c + (2a b + 2a b )c - 2a b - 2a b )sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c + 6a b c + (4b - 4a b)c + (- 10a b - 2a b)c +--R + +--R 5 2 3 4 5 5 +--R (- 2b + 4a b + 6a b)c + 4a b - 4a b +--R * +--R cos(x) +--R + +--R 5 4 3 3 3 3 2 5 4 +--R - 2b c + 4a b c + 4b c + (- 8a b - 2a b)c + (- 2b + 2a b)c +--R + +--R 5 3 3 5 +--R 4a b + 2a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 2 4 2 3 3 +--R - 2a c + (- 2b + 6a )c + (4a b - 2a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 4 2 +--R (4b - 6a b - 6a )c + (- 2a b + 2a b + 4a )c - 2b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R - 2c + 4a c + 6a c + (- 4a b - 10a )c +--R + +--R 4 2 2 4 2 3 2 5 6 2 4 4 2 +--R (6b - 4a b - 4a )c + (6a b + 6a )c - 4b - 2a b + 2a b +--R * +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R - 2c + 6a c + 2b c + (- 8a b - 8a )c + (2b + 2a b + 2a )c +--R + +--R 4 3 2 5 6 2 4 +--R (2a b + 4a b + 2a )c - 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 3 2 3 3 2 5 2 3 4 +--R 2b c + (- 4b - 6a b)c + 4a b c + (2b + 6a b + 4a b)c +--R + +--R 3 3 5 +--R - 4a b - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 4b c - 4a b c + (- 8b - 2a b)c + (4a b + 6a b)c +--R + +--R 5 2 3 4 3 3 5 +--R (4b + 2a b - 2a b)c - 2a b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 2 +--R 2b c - 4a b c + (- 4b + 6a b)c + 4a b c +--R + +--R 5 2 3 4 3 3 5 +--R (2b - 6a b - 8a b)c + 4a b + 4a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 4 3 3 5 +--R 2a b c - 2a b c + (- 2a b - 2a b)c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 2 4 2 3 3 +--R 2a c + (2b + 2a )c + (- 2a b - 6a )c +--R + +--R 4 2 2 4 2 3 2 5 6 2 4 +--R (- 4b - 4a b - 2a )c + (4a b + 4a )c + 2b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 2c + 8a c + (4b - 6a )c + (- 12a b - 14a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- 14b + 4a b + 4a )c + (4a b + 10a b + 6a )c + 8b +--R + +--R 2 4 4 2 +--R 2a b - 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R 6c + 8a c - 22a c + (- 16a b - 6a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- 18b + 24a b + 16a )c + (8a b + 6a b - 2a )c + 12b +--R + +--R 2 4 4 2 +--R - 2a b - 14a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 4 2 3 3 +--R 6c + (- 4b - 18a )c + (- 4a b + 6a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (- 10b + 20a b + 12a )c + (4a b - 2a b - 6a )c + 8b +--R + +--R 2 4 4 2 +--R - 2a b - 10a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 2c - 2a c + (- 2b - 4a )c + (2a b + 4a )c +--R + +--R 4 2 2 4 2 3 2 5 6 4 2 +--R (- 2b + 4a b + 2a )c + (- 2a b - 2a )c + 2b - 2a b +--R * +--R sin(x) +--R + +--R 4 2 3 3 3 2 2 3 4 +--R 2a b c + 2a b c + (- 6a b - 2a b)c + (- 2a b - 2a b)c +--R + +--R 5 3 3 +--R 4a b + 4a b +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 2b c + 12a b c + (- 4b + 2a b)c + (- 28a b - 12a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (2b - 2a b - 4a b)c + 16a b + 16a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 8b c + 24a b c + (- 16b - 8a b)c + (- 48a b - 24a b)c +--R + +--R 5 2 3 5 3 3 +--R (8b + 8a b )c + 24a b + 24a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 12b c + 20a b c + (- 24b - 16a b)c + (- 36a b - 20a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (12b + 16a b + 4a b)c + 16a b + 16a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 8b c + 6a b c + (- 16b - 10a b)c + (- 10a b - 6a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (8b + 10a b + 2a b)c + 4a b + 4a b +--R * +--R cos(x) +--R + +--R 5 3 2 3 5 2 3 +--R 2b c + (- 4b - 2a b)c + (2b + 2a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 5 2 3 5 3 3 5 +--R (2b c - 2a b c + (- 2b - 2a b )c + 2a b + 2a b )sin(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 2 4 +--R - 4b c + 6a b c + 6b c + (- 6a b - 6a b )c - 2b + 2a b +--R + +--R 4 2 +--R 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 4 2 +--R - 2b c + 2a b c + 4b c + (- 2a b - 2a b )c - 2b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 4 2 3 3 3 2 2 3 4 +--R (- 4a b c + 4a b c + (4a b + 4a b)c + (- 4a b - 4a b)c) +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 4b c - 2a b c + (4b + 10a b)c + (2a b + 2a b)c +--R + +--R 2 3 4 +--R (- 6a b - 6a b)c +--R * +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 4b c + 2a b c + (4b + 6a b)c + (- 2a b - 2a b)c +--R + +--R 2 3 4 +--R (- 2a b - 2a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 2 4 2 3 4 2 4 3 2 6 4 2 +--R (- 4b c + 4a b c + 8b c + (- 4a b - 4a b )c - 4b + 4a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 +--R - 6b c - 2a b c + (16b + 4a b )c + (2a b + 2a b )c +--R + +--R 6 2 4 4 2 +--R - 10b - 8a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R - 4b c - 8a b c + (12b + 8a b )c + (8a b + 8a b )c - 8b +--R + +--R 2 4 4 2 +--R - 12a b - 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R - 2b c - 2a b c + (4b + 4a b )c + (2a b + 2a b )c - 2b +--R + +--R 2 4 4 2 +--R - 4a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 3 3 3 2 +--R - 4a b c + (- 2b + 4a b)c + (6a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (2b - 2a b - 4a b)c - 2a b - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 4b c - 2a b c + (4b + 10a b)c + (2a b + 2a b)c +--R + +--R 2 3 4 +--R (- 6a b - 6a b)c +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 8b c + 10a b c + (16b + 6a b)c + (- 18a b - 10a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- 8b - 6a b + 2a b)c + 8a b + 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 4b c + 10a b c + (12b - 2a b)c + (- 18a b - 10a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- 8b - 2a b + 6a b)c + 8a b + 8a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 5 4 +--R 2a b c + (2b - 2a b)c + (- 4a b - 2a b)c + (- 2b + 2a b)c +--R + +--R 5 3 3 +--R 2a b + 2a b +--R * +--R sin(x) +--R + +--R 2 3 4 2 4 3 2 6 2 4 5 +--R (- 2a b c + 2b c + (2a b + 2a b )c - 2b - 2a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R - 4b c - 4a b c + (12b + 4a b )c + (4a b + 4a b )c - 8b +--R + +--R 2 4 +--R - 8a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 4 4 2 2 2 6 2 4 3 +--R (- 12b c + (24b + 12a b )c - 12b - 12a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R - 12b c + 4a b c + (20b + 12a b )c + (- 4a b - 4a b )c - 8b +--R + +--R 2 4 +--R - 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 3 2 6 +--R - 4b c + 2a b c + (6b + 4a b )c + (- 2a b - 2a b )c - 2b +--R + +--R 2 4 +--R - 2a b +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 2 2 4 4 2 5 +--R (b c + (- b - 2a b )c + a b + a b )sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 3b c + 2a b c + (5b + 4a b)c + (- 2a b - 4a b)c +--R + +--R 5 2 3 4 3 3 5 +--R (- 2b - 3a b - a b)c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c + a b c + (4b + 2a b)c + (- a b - 2a b)c +--R + +--R 5 2 3 3 3 5 +--R (- 2b - 2a b )c + a b + a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 2 2 4 2 3 3 4 2 2 4 2 +--R - 3a c + (- b + a )c + (4a b + 5a )c + (2b - a b - a )c +--R + +--R 4 3 2 5 6 4 2 +--R (- a b - 3a b - 2a )c - b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R - 3c - 3a c + (2b + 6a )c + (3a b + 6a )c +--R + +--R 4 2 2 4 2 3 2 5 6 2 4 4 2 +--R (3b - 3a b - 3a )c + (- 3a b - 3a )c - 2b - a b + a b +--R * +--R cos(x) +--R + +--R 6 2 2 4 2 3 3 4 2 2 4 2 +--R - 3c + (3b + 5a )c + (- a b + a )c + (b - 2a b - 2a )c +--R + +--R 4 5 6 2 4 +--R (a b - a )c - b - a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 4 3 2 3 3 2 5 2 3 +--R - b c - 2a b c + (2b + a b)c + 6a b c + (- b - a b )c +--R + +--R 5 3 3 5 +--R - 4a b - 2a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - b c - 9a b c + (4b - a b)c + (19a b + 8a b)c +--R + +--R 5 2 3 4 5 3 3 5 +--R (- 3b - a b + 2a b)c - 10a b - 9a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - b c - 10a b c + (4b - a b)c + (18a b + 12a b)c +--R + +--R 5 2 3 4 5 3 3 5 +--R (- 3b - a b + 2a b)c - 8a b - 10a b - 2a b +--R * +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 5 2 3 +--R - b c - 3a b c + (2b + a b)c + (5a b + 4a b)c + (- b - a b )c +--R + +--R 5 3 3 5 +--R - 2a b - 3a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 3 3 4 2 2 4 2 +--R - a c - a c + 3a c + (- b + 3a b + a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (a b - a b - 2a )c + b - a b - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R - c - a c + 4b c + (- a b + 4a )c + (- 7b + a b + a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (2a b - a b - 3a )c + 4b + a b - 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R - c + a c + (8b + 2a )c + (- a b - 2a )c +--R + +--R 4 2 2 4 2 3 2 5 6 2 4 4 2 +--R (- 13b - 9a b - a )c + (a b + a )c + 6b + 7a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R c + a c + 4b c + (a b - 4a )c + (- 9b - 9a b - a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (- 2a b + a b + 3a )c + 4b + 7a b + 3a b +--R * +--R cos(x) +--R + +--R 6 2 4 2 3 3 4 2 2 2 4 5 6 +--R c - a c + (a b - a )c + (- 2b - 2a b )c + (- a b + a )c + b +--R + +--R 2 4 4 2 +--R 2a b + a b +--R * +--R sin(x) +--R + +--R 3 2 3 5 4 5 +--R ((b - a b)c + (- b + a b)c)cos(x) +--R + +--R 5 3 2 3 5 2 3 4 4 +--R (- b c + (4b - a b)c + (- 3b - a b + 2a b)c)cos(x) +--R + +--R 5 3 2 3 5 2 3 3 +--R (- 2b c + (4b + 2a b)c + (- 2b - 2a b )c)cos(x) +--R + +--R 3 2 3 5 4 2 +--R ((- 2b + 2a b)c + (2b - 2a b)c)cos(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (2b c + (- 5b - a b)c + (3b + 2a b - a b)c)cos(x) + b c +--R + +--R 3 2 3 5 2 3 +--R (- 2b - a b)c + (b + a b )c +--R / +--R 2 4 2 3 4 2 2 2 4 2 4 +--R (b c - 2a b c + (- b + a b )c + 2a b c - a b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 2 4 +--R b c - 2a b c + (- b + a b )c + 2a b c - a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - b c + 3a b c + (2b - 3a b)c + (- 4a b + a b)c +--R + +--R 5 2 3 5 3 3 +--R (- b + 3a b )c + a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 3 3 2 5 5 5 4 +--R (2b c - 2a b c - 2b c + 2a b )cos(x) + b c - 3a b c +--R + +--R 2 3 3 3 2 5 2 3 5 3 3 +--R 3a b c + (2a b - a b)c + (- b - 3a b )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 2 4 2 3 3 4 2 2 2 +--R - a c + (- b + 2a )c + (4a b - a )c + (b - 4a b )c +--R + +--R 4 3 2 2 4 +--R (- 3a b + a b )c + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R - c + a c - b c + (6a b + a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (2b - 5a b - a )c + (- 7a b - a b )c + 5a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 3 3 4 2 2 4 2 +--R - c + a c + (4a b + a )c + (b - 4a b - a )c +--R + +--R 4 3 2 2 4 4 2 +--R (- 5a b - a b )c + 4a b + a b +--R * +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 2 4 3 2 +--R - a c + 2a c + (2a b - a )c - 3a b c + (- a b + a b )c +--R + +--R 2 4 +--R a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R b c - 3a b c + (- 2b + 3a b)c + (4a b - a b)c +--R + +--R 5 2 3 5 3 3 +--R (b - 3a b )c - a b + a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 2b c - 6a b c + (- 6b + 6a b)c + (10a b - 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (4b - 6a b )c - 4a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 3 3 2 5 5 2 +--R (- 6b c + 6a b c + 6b c - 6a b )cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c + 6a b c + (- 2b - 6a b)c + (- 2a b + 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (4b + 6a b )c - 4a b - 2a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 3 3 2 +--R - b c + 3a b c - 3a b c + (- 2a b + a b)c +--R + +--R 5 2 3 5 3 3 +--R (b + 3a b )c - a b - a b +--R * +--R sin(x) +--R + +--R 5 2 4 2 3 3 2 2 2 4 3 2 +--R a c - 2a c + (- 2a b + a )c + 3a b c + (a b - a b )c +--R + +--R 2 4 +--R - a b +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R c + a c + (- 2b - 4a )c + (- 4a b + a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (b + 8a b + a )c + (3a b - a b )c - 4a b - a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 2 4 3 3 4 2 2 4 2 +--R 3c - 2a c + (- 7b - 2a )c - 2a c + (4b + 8a b + 3a )c +--R + +--R 4 3 2 2 4 4 2 +--R (2a b + 2a b )c - 6a b - 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 3c - 2a c + (- 9b - 2a )c + (4a b - 2a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (6b + 6a b + 3a )c + (- 2a b + 2a b )c - 4a b - 3a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R c + a c + (- 5b - 4a )c + (2a b + a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (4b + 5a b + a )c + (- 3a b - a b )c - a b - a b +--R * +--R cos(x) +--R + +--R 5 2 2 4 3 3 4 2 2 2 4 3 2 +--R a c + (- b - 2a )c + a c + (b + 2a b )c + (- a b - a b )c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 5 5 3 3 3 2 +--R (2b c - 2a b c - 2b c + 2a b )cos(x) + 2b c - 2a b c +--R + +--R 5 5 +--R - 2b c + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R - 2b c + 4a b c + (4b - 2a b )c - 4a b c - 2b +--R + +--R 2 4 +--R 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 6 2 4 2 3 2 2 2 4 +--R (4b c - 4b )cos(x) + 2b c - 4a b c + 2a b c + 4a b c +--R + +--R 6 2 4 +--R - 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 3 3 2 5 2 3 +--R - 2a b c + (- 2b + 2a b)c + 6a b c + (2b - 2a b )c +--R + +--R 5 +--R - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 3 3 3 3 2 5 5 +--R - 2b c - 2b c + (10a b + 2a b)c + 4b c - 10a b +--R + +--R 3 3 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 2 5 5 3 3 +--R (- 2b c + (8a b + 2a b)c + 2b c - 8a b - 2a b )cos(x) +--R + +--R 4 2 3 3 2 2 3 5 +--R - 2a b c + 2a b c + 4a b c - 2a b c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R 2b c - 4a b c + (- 4b + 2a b )c + 4a b c + 2b +--R + +--R 2 4 +--R - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R 4b c - 8a b c + (- 12b + 4a b )c + 8a b c + 8b +--R + +--R 2 4 +--R - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 2 6 2 +--R (- 12b c + 12b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R - 4b c + 8a b c + (- 4b - 4a b )c - 8a b c + 8b +--R + +--R 2 4 +--R 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 2 2 2 4 6 2 4 +--R - 2b c + 4a b c - 2a b c - 4a b c + 2b + 2a b +--R * +--R sin(x) +--R + +--R 4 2 3 3 2 2 3 5 5 +--R (2a b c - 2a b c - 4a b c + 2a b c + 2a b )cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 2b c + 4a b c + (- 4b - 4a b)c + (- 12a b - 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (2b + 4a b )c + 8a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 6b c + 2a b c + (- 14b - 2a b)c + (- 14a b - 6a b)c +--R + +--R 5 2 3 5 3 3 +--R (8b + 2a b )c + 12a b + 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 6b c + 2a b c + (- 18b - 2a b)c + (- 10a b - 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4a )c + (- 12a b - 2a )c +--R + +--R 4 3 2 2 4 4 2 +--R (2a b + 4a b )c + 8a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R 6a c + 2a c + (- 14a b - 2a )c + (- 14a b - 6a )c +--R + +--R 4 3 2 2 4 4 2 +--R (8a b + 2a b )c + 12a b + 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R 6a c + 2a c + (- 18a b - 2a )c + (- 10a b - 6a )c +--R + +--R 4 3 2 2 4 4 2 +--R (12a b + 2a b )c + 8a b + 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R 2a c + 4a c + (- 10a b - 4a )c + (- 6a b - 2a )c +--R + +--R 4 3 2 2 4 4 2 +--R (8a b + 4a b )c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 3 2 2 2 4 3 2 +--R 2a c + (- 2a b - 2a )c - 2a b c + (2a b + 2a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 3 2 5 5 3 3 3 2 +--R (- 2b c + 2a b c + 2b c - 2a b )cos(x) - 2b c + 2a b c +--R + +--R 5 5 +--R 2b c - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R 2b c - 4a b c + (- 4b + 2a b )c + 4a b c + 2b +--R + +--R 2 4 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 6 2 4 2 3 2 2 2 4 +--R (- 4b c + 4b )cos(x) - 2b c + 4a b c - 2a b c - 4a b c +--R + +--R 6 2 4 +--R 2b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 2 3 3 2 5 2 3 +--R 2a b c + (2b - 2a b)c - 6a b c + (- 2b + 2a b )c +--R + +--R 5 +--R 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 3 3 3 3 2 5 5 +--R 2b c + 2b c + (- 10a b - 2a b)c - 4b c + 10a b +--R + +--R 3 3 +--R 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 2 5 5 3 3 +--R (2b c + (- 8a b - 2a b)c - 2b c + 8a b + 2a b )cos(x) +--R + +--R 4 2 3 3 2 2 3 5 +--R 2a b c - 2a b c - 4a b c + 2a b c + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R - 2b c + 4a b c + (4b - 2a b )c - 4a b c - 2b +--R + +--R 2 4 +--R 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 +--R - 4b c + 8a b c + (12b - 4a b )c - 8a b c - 8b +--R + +--R 2 4 +--R 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 2 6 2 +--R (12b c - 12b )cos(x) +--R + +--R 2 4 2 3 4 2 2 2 4 6 2 4 +--R (4b c - 8a b c + (4b + 4a b )c + 8a b c - 8b - 4a b ) +--R * +--R cos(x) +--R + +--R 2 4 2 3 2 2 2 4 6 2 4 +--R 2b c - 4a b c + 2a b c + 4a b c - 2b - 2a b +--R * +--R sin(x) +--R + +--R 4 2 3 3 2 2 3 5 5 +--R (- 2a b c + 2a b c + 4a b c - 2a b c - 2a b )cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c - 4a b c + (4b + 4a b)c + (12a b + 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 2b - 4a b )c - 8a b - 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 6b c - 2a b c + (14b + 2a b)c + (14a b + 6a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 8b - 2a b )c - 12a b - 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 6b c - 2a b c + (18b + 2a b)c + (10a b + 6a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 12b - 2a b )c - 8a b - 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c - 4a b c + (10b + 4a b)c + (6a b + 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 8b - 4a b )c - 2a b - 2a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 2 5 2 3 +--R - 2a b c + (2b + 2a b)c + 2a b c + (- 2b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 4 2 2 2 2 4 2 4 4 2 2 2 +--R (- b c + (b + a b )c - a b )cos(x) - b c + (b + a b )c +--R + +--R 2 4 +--R - a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 4 3 2 3 3 2 5 2 3 +--R b c - a b c + (- 2b - a b)c + a b c + (b + a b )c +--R + +--R 5 3 3 +--R a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 3 3 2 5 5 5 4 2 3 +--R (- 2b c - 2a b c + 2b c + 2a b )cos(x) - b c + a b c + a b c +--R + +--R 3 3 2 5 2 3 5 3 3 +--R (- 2a b - a b)c + (b - a b )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 4 2 3 3 4 2 2 2 +--R a c + b c + (- 2a b - a )c + (- b - 2a b )c +--R + +--R 4 3 2 2 4 +--R (a b + a b )c + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R c + a c + b c + (- 4a b - a )c + (- 2b - 5a b - a )c +--R + +--R 4 3 2 2 4 4 2 +--R (3a b + a b )c + 5a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 3 3 4 2 2 4 2 +--R c + a c + (- 4a b - a )c + (- b - 4a b - a )c +--R + +--R 4 3 2 2 4 4 2 +--R (3a b + a b )c + 4a b + a b +--R * +--R cos(x) +--R + +--R 5 2 3 3 2 2 2 4 3 2 2 4 +--R a c + (- 2a b - a )c - a b c + (a b + a b )c + a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 3 3 2 5 2 3 +--R - b c + a b c + (2b + a b)c - a b c + (- b - a b )c +--R + +--R 5 3 3 +--R - a b + a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R - 2b c + 2a b c + (6b + 2a b)c + (2a b - 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 4b - 2a b )c - 4a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 3 3 3 2 5 5 2 +--R (6b c + 6a b c - 6b c - 6a b )cos(x) +--R + +--R 5 4 3 2 3 3 3 2 +--R 2b c - 2a b c + (2b - 2a b)c + (6a b + 2a b)c +--R + +--R 5 2 3 5 3 3 +--R (- 4b + 2a b )c - 4a b - 2a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 3 3 2 5 2 3 5 +--R b c - a b c - a b c + (2a b + a b)c + (- b + a b )c - a b +--R + +--R 3 3 +--R - a b +--R * +--R sin(x) +--R + +--R 5 2 3 3 2 2 2 4 3 2 2 4 5 +--R (- a c + (2a b + a )c + a b c + (- a b - a b )c - a b )cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R - c - 3a c + 2b c + (8a b + 3a )c + (- b + 4a b + a )c +--R + +--R 4 3 2 2 4 4 2 +--R (- 5a b - 3a b )c - 4a b - a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R - 3c - 4a c + 7b c + (14a b + 4a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (- 4b + 6a b + 3a )c + (- 10a b - 4a b )c - 6a b - 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 +--R - 3c - 4a c + 9b c + (14a b + 4a )c +--R + +--R 4 2 2 4 2 4 3 2 2 4 4 2 +--R (- 6b + 4a b + 3a )c + (- 10a b - 4a b )c - 4a b - 3a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 4 2 3 3 4 2 2 4 2 +--R - c - 3a c + 5b c + (8a b + 3a )c + (- 4b + a b + a )c +--R + +--R 4 3 2 2 4 4 2 +--R (- 5a b - 3a b )c - a b - a b +--R * +--R cos(x) +--R + +--R 5 2 4 2 3 3 4 2 4 3 2 +--R - a c + b c + (2a b + a )c - b c + (- a b - a b )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 6 5 3 4 3 3 3 +--R - b c + 2a b c + 2b c + (- 4a b - 2a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- b + a b + a b)c + (2a b + 2a b )c - a b - a b +--R * +--R cos(x) +--R + +--R 6 5 3 4 3 3 3 +--R - b c + 2a b c + 2b c + (- 4a b - 2a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- b + a b + a b)c + (2a b + 2a b )c - a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 2 2 5 2 4 4 2 2 4 3 +--R - a c + (- b + 2a )c + 3a b c + (2b - 3a b - 2a )c +--R + +--R 4 5 2 6 2 4 4 2 6 5 2 +--R (- 3a b + a )c + (- b + a b + 2a b )c + a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 2 2 4 3 +--R - c + a c + 2a c - 2a c + (3b - a b - a )c +--R + +--R 4 3 2 5 2 6 2 4 4 2 6 +--R (- 3a b + a b + a )c + (- 2b - a b + a b )c + 2a b +--R + +--R 3 4 5 2 +--R a b - a b +--R * +--R cos(x) +--R + +--R 7 6 2 5 2 3 4 4 2 2 4 3 +--R - c + 2a c + b c + (- 3a b - 2a )c + (b + 2a b + a )c +--R + +--R 3 2 2 6 2 4 4 2 6 3 4 +--R a b c + (- b - 2a b - a b )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R b c - 3a b c + (- 2b + a b)c + (6a b + 3a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (b - 3a b - 2a b)c + (- 3a b - 3a b )c + 2a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R 2b c - 7a b c + (- 4b + 3a b)c + (14a b + 7a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (2b - 8a b - 5a b)c + (- 7a b - 7a b )c + 5a b + 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R b c - 5a b c + (- 2b + 3a b)c + (10a b + 5a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (b - 7a b - 4a b)c + (- 5a b - 5a b )c + 4a b + 4a b +--R * +--R cos(x) +--R + +--R 5 2 4 3 3 3 2 3 4 2 +--R - a b c + a b c + (2a b + a b)c + (- 2a b - a b)c +--R + +--R 5 3 3 2 5 4 3 +--R (- a b - a b )c + a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 2 5 2 4 4 2 2 4 3 +--R a c + (b - 2a )c - 3a b c + (- 2b + 3a b + 2a )c +--R + +--R 4 5 2 6 2 4 4 2 6 5 2 +--R (3a b - a )c + (b - a b - 2a b )c - a b + a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 2 5 2 3 4 +--R c + a c + (2b - 6a )c + (- 6a b + 2a )c +--R + +--R 4 2 2 4 3 4 3 2 5 2 +--R (- 7b + 7a b + 5a )c + (9a b - a b - 3a )c +--R + +--R 6 2 4 4 2 6 3 4 5 2 +--R (4b - a b - 5a b )c - 4a b - a b + 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 2 2 4 3 +--R 3c - 3a c - 6a c + 6a c + (- 9b + 3a b + 3a )c +--R + +--R 4 3 2 5 2 6 2 4 4 2 6 +--R (9a b - 3a b - 3a )c + (6b + 3a b - 3a b )c - 6a b +--R + +--R 3 4 5 2 +--R - 3a b + 3a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 2 5 2 3 4 +--R 3c - 5a c + (- 2b - 2a )c + (6a b + 6a )c +--R + +--R 4 2 2 4 3 4 3 2 5 2 +--R (- 5b - 3a b - a )c + (3a b - 3a b - a )c +--R + +--R 6 2 4 4 2 6 3 4 5 2 +--R (4b + 5a b + a b )c - 4a b - 3a b + a b +--R * +--R cos(x) +--R + +--R 7 6 2 5 2 3 4 4 2 2 4 3 +--R c - 2a c - b c + (3a b + 2a )c + (- b - 2a b - a )c +--R + +--R 3 2 2 6 2 4 4 2 6 3 4 +--R - a b c + (b + 2a b + a b )c - a b - a b +--R * +--R sin(x) +--R + +--R 5 2 4 3 3 3 2 3 4 2 +--R a b c - a b c + (- 2a b - a b)c + (2a b + a b)c +--R + +--R 5 3 3 2 5 4 3 +--R (a b + a b )c - a b - a b +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R b c + 3a b c + (- 2b - 5a b)c + (- 6a b - 3a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (b + 9a b + 4a b)c + (3a b + 3a b )c - 4a b - 4a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R 4b c + 2a b c + (- 8b - 10a b)c + (- 4a b - 2a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (4b + 16a b + 6a b)c + (2a b + 2a b )c - 6a b - 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R 6b c - 2a b c + (- 12b - 10a b)c + (4a b + 2a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (6b + 14a b + 4a b)c + (- 2a b - 2a b )c - 4a b - 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R 4b c - 3a b c + (- 8b - 5a b)c + (6a b + 3a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (4b + 6a b + a b)c + (- 3a b - 3a b )c - a b - a b +--R * +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 5 2 3 2 +--R b c - a b c + (- 2b - a b)c + (2a b + a b)c + (b + a b )c +--R + +--R 5 3 3 +--R (- a b - a b )c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 2b c + 2a b c + (4b + 2a b )c + (- 4a b - 2a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 2b - 2a b )c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 2b c + 2a b c + (4b + 2a b )c + (- 4a b - 2a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 2b - 2a b )c + 2a b + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 2 4 3 3 3 +--R - 2a b c + (- 2b + 2a b)c + (4a b + 2a b)c +--R + +--R 5 2 3 4 2 5 3 3 7 4 3 +--R (4b - 2a b - 2a b)c + (- 2a b - 2a b )c - 2b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 4 5 2 3 4 2 7 2 5 +--R - 2b c + 4a b c + (6b - 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2a b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 5 3 2 4 3 3 3 +--R 2a b c + (2b - 2a b)c + (- 4a b - 2a b)c +--R + +--R 5 2 3 4 2 5 3 3 7 4 3 +--R (- 4b + 2a b + 2a b)c + (2a b + 2a b )c + 2b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 4 5 2 3 4 2 7 2 5 +--R 2b c - 4a b c + (- 6b + 2a b + 2a b)c + 4b + 2a b +--R + +--R 4 3 +--R - 2a b +--R * +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 5 2 +--R 2b c - 2a b c + (- 2b - 2a b)c + (4a b + 2a b)c - 2b c +--R + +--R 5 3 3 7 2 5 +--R (- 2a b - 2a b )c + 2b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 2b c + 4a b c + (4b + 2a b )c + (- 8a b - 4a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 2b - 2a b )c + 4a b + 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 4b c + 10a b c + (8b + 4a b )c + (- 20a b - 10a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 4b - 4a b )c + 10a b + 10a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 2b c + 8a b c + (4b + 2a b )c + (- 16a b - 8a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 2b - 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2a b)c + 2b c +--R + +--R 5 3 3 7 2 5 +--R (2a b + 2a b )c - 2b - 2a b +--R * +--R sin(x) +--R + +--R 2 4 4 3 2 2 6 3 4 5 +--R (- 2a b c + (4a b + 2a b )c - 2a b - 2a b )cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 2b c - 8a b c + (4b + 2a b )c + (16a b + 8a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 2b - 2a b )c - 8a b - 8a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 8b c - 12a b c + (16b + 8a b )c + (24a b + 12a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 8b - 8a b )c - 12a b - 12a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 12b c - 8a b c + (24b + 12a b )c + (16a b + 8a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 12b - 12a b )c - 8a b - 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 5 2 4 4 2 2 3 4 3 2 2 +--R - 8b c - 2a b c + (16b + 8a b )c + (4a b + 2a b )c +--R + +--R 6 2 4 6 3 4 +--R (- 8b - 8a b )c - 2a b - 2a b +--R * +--R cos(x) +--R + +--R 2 5 4 2 2 3 6 2 4 +--R - 2b c + (4b + 2a b )c + (- 2b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 6 3 2 4 5 2 3 4 2 2 5 4 3 +--R (b c + (- 2b - 2a b)c + (b + 3a b + a b)c - a b - a b )cos(x) +--R + +--R 6 3 2 4 5 2 3 4 2 2 5 4 3 +--R b c + (- 2b - 2a b)c + (b + 3a b + a b)c - a b - a b +--R * +--R 4 +--R sin(x) +--R + +--R 6 2 5 2 3 4 4 2 2 3 +--R a c + b c + (- a b - 2a )c + (- 2b - a b )c +--R + +--R 4 3 2 5 2 6 2 4 6 5 2 +--R (- a b + 2a b + a )c + (b + a b )c + a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 2 2 4 3 +--R c + a c - 2a c - 2a c + (- 3b + a b + a )c +--R + +--R 4 3 2 5 2 6 2 4 4 2 6 3 4 +--R (- 3a b + a b + a )c + (2b + a b - a b )c + 2a b + a b +--R + +--R 5 2 +--R - a b +--R * +--R cos(x) +--R + +--R 7 2 2 5 2 4 4 2 2 4 3 +--R c + (- b - 2a )c + a b c + (- b + 2a b + a )c +--R + +--R 4 3 2 2 6 4 2 6 3 4 +--R (- 2a b - a b )c + (b - a b )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - b c + a b c + (2b + 3a b)c + (- 2a b - a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- b - 5a b - 2a b)c + (a b + a b )c + 2a b + 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - 2b c + 3a b c + (4b + 7a b)c + (- 6a b - 3a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- 2b - 12a b - 5a b)c + (3a b + 3a b )c + 5a b + 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - b c + 3a b c + (2b + 5a b)c + (- 6a b - 3a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- b - 9a b - 4a b)c + (3a b + 3a b )c + 4a b + 4a b +--R * +--R cos(x) +--R + +--R 5 2 4 3 3 3 2 3 4 2 +--R a b c + a b c + (- 2a b - a b)c + (- 2a b - a b)c +--R + +--R 5 3 3 2 5 4 3 +--R (a b + a b )c + a b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 5 2 3 4 4 2 2 3 +--R - a c - b c + (a b + 2a )c + (2b + a b )c +--R + +--R 4 3 2 5 2 6 2 4 6 5 2 +--R (a b - 2a b - a )c + (- b - a b )c - a b + a b +--R * +--R 4 +--R cos(x) +--R + +--R 7 6 2 2 5 2 3 4 +--R - c - 3a c + (- 2b + 2a )c + (2a b + 6a )c +--R + +--R 4 2 2 4 3 4 3 2 5 2 +--R (7b + a b - a )c + (5a b - 5a b - 3a )c +--R + +--R 6 2 4 4 2 6 3 4 5 2 +--R (- 4b - 3a b + a b )c - 4a b - a b + 3a b +--R * +--R 3 +--R cos(x) +--R + +--R 7 6 2 5 3 4 4 2 2 4 3 +--R - 3c - 3a c + 6a c + 6a c + (9b - 3a b - 3a )c +--R + +--R 4 3 2 5 2 6 2 4 4 2 6 +--R (9a b - 3a b - 3a )c + (- 6b - 3a b + 3a b )c - 6a b +--R + +--R 3 4 5 2 +--R - 3a b + 3a b +--R * +--R 2 +--R cos(x) +--R + +--R 7 6 2 2 5 2 3 4 +--R - 3c - a c + (2b + 6a )c + (- 2a b + 2a )c +--R + +--R 4 2 2 4 3 4 3 2 5 2 +--R (5b - 5a b - 3a )c + (7a b + a b - a )c +--R + +--R 6 2 4 4 2 6 3 4 5 2 +--R (- 4b - a b + 3a b )c - 4a b - 3a b + a b +--R * +--R cos(x) +--R + +--R 7 2 2 5 2 4 4 2 2 4 3 4 3 2 2 +--R - c + (b + 2a )c - a b c + (b - 2a b - a )c + (2a b + a b )c +--R + +--R 6 4 2 6 3 4 +--R (- b + a b )c - a b - a b +--R * +--R sin(x) +--R + +--R 5 2 4 3 3 3 2 3 4 2 +--R - a b c - a b c + (2a b + a b)c + (2a b + a b)c +--R + +--R 5 3 3 2 5 4 3 +--R (- a b - a b )c - a b - a b +--R * +--R 5 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - b c - 5a b c + (2b - 3a b)c + (10a b + 5a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- b + 7a b + 4a b)c + (- 5a b - 5a b )c - 4a b - 4a b +--R * +--R 4 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - 4b c - 10a b c + (8b - 2a b)c + (20a b + 10a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- 4b + 8a b + 6a b)c + (- 10a b - 10a b )c - 6a b - 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - 6b c - 10a b c + (12b + 2a b)c + (20a b + 10a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- 6b + 2a b + 4a b)c + (- 10a b - 10a b )c - 4a b - 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 +--R - 4b c - 5a b c + (8b + 3a b)c + (10a b + 5a b)c +--R + +--R 5 2 3 4 2 5 3 3 2 5 4 3 +--R (- 4b - 2a b + a b)c + (- 5a b - 5a b )c - a b - a b +--R * +--R cos(x) +--R + +--R 6 5 3 2 4 3 3 3 5 2 3 2 +--R - b c - a b c + (2b + a b)c + (2a b + a b)c + (- b - a b )c +--R + +--R 5 3 3 +--R (- a b - a b )c +--R Type: Expression(Integer) +--E 244 + +--S 245 of 526 +m0847b:= a0847.2-r0847 +--R +--R +--R (6) +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 x 2 x +--R b\|- c + b + a \|c - b - a log((c - a)tan(-) + 2b tan(-) + c + a) +--R 2 2 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 x +--R (- c - b)\|- c + b + a \|c - b - a log(tan(-) + 1) +--R 2 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2b sin(x) + 2a cos(x) + 2c +--R - b\|- c + b + a \|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 sin(x) + cos(x) + 1 +--R (c + b)\|- c + b + a \|c - b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 sin(x) - cos(x) - 1 +--R (- c + b)\|- c + b + a \|c - b - a log(-------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 x +--R (c - b)\|- c + b + a \|c - b - a log(- tan(-) + 1) +--R 2 +--R + +--R x +--R +------------+ (c - a)tan(-) + b +--R | 2 2 2 2 +--R - 2a c\|c - b - a atanh(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R +------------+ +--R +--------------+ | 2 2 2 +--R | 2 2 2 ((c - a)sin(x) + b cos(x) + b)\|c - b - a +--R - 2a c\|- c + b + a atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c - b )\|- c + b + a \|c - b - a +--R Type: Expression(Integer) +--E 245 + +--S 246 of 526 +d0847b:= D(m0847b,x) +--R +--R +--R (7) +--R 2 2 2 2 2 6 +--R (b c - 2a b c + a b )sin(x) +--R + +--R 3 2 3 2 3 3 +--R (- b c + 3a b c + (b - 4a b)c - a b + 2a b)cos(x) +--R + +--R 3 2 3 3 +--R (b - a b)c - a b + a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 2 2 4 2 2 2 +--R (- a c + (b + a )c + 3a b c - 2b - 2a b )cos(x) +--R + +--R 4 2 2 2 2 4 2 2 4 3 +--R (- c + (2b + a )c + 6a b c - 4b - 4a b )cos(x) - c + a c +--R + +--R 2 2 2 4 2 2 +--R b c + 3a b c - 2b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 3 3 3 +--R (- 4b c + 8a b c + 4b c - 8a b )cos(x) +--R + +--R 3 2 3 2 3 3 2 +--R (- 8b c + 16a b c + (8b + 8a b)c - 20a b - 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 +--R (- 6b c + 14a b c + (4b + 10a b)c - 16a b - 6a b)cos(x) +--R + +--R 3 2 2 3 3 +--R - 2b c + 6a b c + 2a b c - 4a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 2 2 4 2 2 4 +--R (- 4a c + (- 3b + 6a )c + 6a b c + 2b - 7a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 3 +--R (- 4c - 4a c + (- 4b + 16a )c + 4a b c + 8b - 16a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 +--R (- 10c + 8a c + (2b + 14a )c - 16a b c + 12b - 10a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 2 2 4 4 +--R (- 8c + 12a c + (4b + 4a )c - 20a b c + 8b )cos(x) - 2c +--R + +--R 3 2 2 2 4 2 2 +--R 4a c + b c - 6a b c + 2b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 3 2 3 3 5 +--R (- 3b c - 3a b c + (3b + 4a b)c + a b - 2a b)cos(x) +--R + +--R 3 2 3 2 3 3 4 +--R (- 16b c - 8a b c + (15b + 9a b)c + 5a b - 5a b)cos(x) +--R + +--R 3 2 3 2 3 3 3 +--R (- 32b c - 8a b c + (30b + 2a b)c + 10a b - 2a b)cos(x) +--R + +--R 3 2 3 2 3 3 2 +--R (- 30b c - 6a b c + (30b - 8a b)c + 10a b + 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 +--R (- 13b c - 5a b c + (15b - 6a b)c + 5a b + 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 +--R - 2b c - 2a b c + (3b - a b)c + a b + a b +--R * +--R sin(x) +--R + +--R 3 2 2 2 2 6 +--R (- 3a c + (b + a )c + a b c)cos(x) +--R + +--R 4 3 2 2 2 2 5 +--R (- 3c - 12a c + (6b + 3a )c + 6a b c)cos(x) +--R + +--R 4 3 2 2 2 2 4 +--R (- 13c - 19a c + (15b + 2a )c + 15a b c)cos(x) +--R + +--R 4 3 2 2 2 2 3 +--R (- 22c - 16a c + (20b - 2a )c + 20a b c)cos(x) +--R + +--R 4 3 2 2 2 2 2 +--R (- 18c - 9a c + (15b - 3a )c + 15a b c)cos(x) +--R + +--R 4 3 2 2 2 2 4 3 2 2 +--R (- 7c - 4a c + (6b - a )c + 6a b c)cos(x) - c - a c + b c +--R + +--R 2 +--R a b c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 3 3 6 +--R (2b c - 2a b )sin(x) +--R + +--R 2 2 2 4 2 2 2 2 4 2 2 5 +--R ((- 4b c + 4a b c + 4b - 4a b )cos(x) - 2b c + 4b - 2a b )sin(x) +--R + +--R 2 3 3 2 +--R (- 4a b c - 2b c + 6a b )cos(x) +--R + +--R 3 2 3 3 3 3 +--R (- 4b c - 4a b c - 2b c + 10a b )cos(x) - 4b c + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 3 +--R (- 8b c + 8b )cos(x) +--R + +--R 2 2 2 4 2 2 2 +--R (- 20b c - 8a b c + 20b + 8a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 4 2 2 +--R (- 20b c - 8a b c + 16b + 12a b )cos(x) - 8b c + 4b + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 4 +--R (- 8a b c - 2b c + 10a b )cos(x) +--R + +--R 3 2 3 3 3 +--R (- 8b c - 20a b c + 8b c + 20a b )cos(x) +--R + +--R 3 2 3 3 2 +--R (- 20b c - 16a b c + 28b c + 8a b )cos(x) +--R + +--R 3 2 3 3 3 3 3 +--R (- 16b c - 4a b c + 24b c - 4a b )cos(x) - 4b c + 6b c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 2 2 5 +--R (- 4b c - 4a b c + 4b + 4a b )cos(x) +--R + +--R 2 2 2 4 2 2 4 +--R (- 18b c - 8a b c + 16b + 10a b )cos(x) +--R + +--R 2 2 4 2 2 3 +--R (- 28b c + 24b + 4a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 +--R (- 16b c + 8a b c + 16b - 8a b )cos(x) +--R + +--R 2 4 2 2 2 2 2 2 +--R (4a b c + 4b - 8a b )cos(x) + 2b c - 2a b +--R * +--R sin(x) +--R + +--R 2 3 3 6 +--R (- 4a b c + 2b c + 2a b )cos(x) +--R + +--R 3 2 3 3 5 +--R (- 4b c - 16a b c + 10b c + 10a b )cos(x) +--R + +--R 3 2 3 3 4 +--R (- 16b c - 24a b c + 20b c + 20a b )cos(x) +--R + +--R 3 2 3 3 3 +--R (- 24b c - 16a b c + 20b c + 20a b )cos(x) +--R + +--R 3 2 3 3 2 +--R (- 16b c - 4a b c + 10b c + 10a b )cos(x) +--R + +--R 3 3 3 +--R (- 4b c + 2b c + 2a b )cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 2 2 6 +--R (2a b c - 2a b )sin(x) +--R + +--R 3 2 3 2 3 3 3 +--R (2b c - 6a b c + (- 2b + 4a b)c + 6a b - 4a b)cos(x) + 2b c +--R + +--R 2 3 3 3 +--R - 4a b c - 2b c + 6a b - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 2 2 4 2 2 2 +--R (2a c + (4b - 6a )c - 4a b c - 4b + 8a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 4 +--R (2c - 4a c + (6b - 6a )c - 2a b c - 8b + 12a b )cos(x) + 2c +--R + +--R 3 2 2 2 4 2 2 +--R - 6a c + 2b c + 2a b c - 4b + 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 3 2 3 2 +--R (4b c + (- 4b - 8a b)c + 8a b)cos(x) +--R + +--R 3 2 3 2 3 3 +--R (8b c - 4a b c + (- 8b - 8a b)c + 12a b)cos(x) + 4b c +--R + +--R 2 3 3 +--R - 4a b c - 4b c + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 4 2 2 4 +--R ((- 4b - 4a )c - 2a b c + 4b + 6a b )cos(x) +--R + +--R 3 2 2 2 2 4 2 2 3 +--R (- 4a c + (- 16b - 8a )c + 4a b c + 16b + 8a b )cos(x) +--R + +--R 3 2 2 2 2 4 2 2 2 +--R (- 8a c + (- 24b - 4a )c + 16a b c + 24b - 4a b )cos(x) +--R + +--R 3 2 2 2 4 2 2 2 2 +--R (- 4a c - 16b c + 12a b c + 16b - 8a b )cos(x) - 4b c +--R + +--R 2 4 2 2 +--R 2a b c + 4b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 3 2 3 3 5 +--R (- 2b c - 10a b c + (2b - 4a b)c + 10a b + 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 4 +--R (- 14b c - 44a b c + (14b - 8a b)c + 42a b + 10a b)cos(x) +--R + +--R 3 2 3 3 3 3 +--R (- 36b c - 72a b c + 36b c + 68a b + 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 2 +--R (- 44b c - 52a b c + (44b + 8a b)c + 52a b - 8a b)cos(x) +--R + +--R 3 2 3 2 3 3 +--R (- 26b c - 14a b c + (26b + 4a b)c + 18a b - 8a b)cos(x) +--R + +--R 3 3 3 3 +--R - 6b c + 6b c + 2a b - 2a b +--R * +--R sin(x) +--R + +--R 3 2 2 2 2 2 6 +--R (- 2a c - 6a c + 4a b c + 4a b )cos(x) +--R + +--R 4 3 2 2 2 2 2 2 5 +--R (- 2c - 16a c + (2b - 26a )c + 22a b c + 20a b )cos(x) +--R + +--R 4 3 2 2 2 2 2 2 4 +--R (- 10c - 46a c + (10b - 44a )c + 50a b c + 40a b )cos(x) +--R + +--R 4 3 2 2 2 2 2 2 3 +--R (- 20c - 64a c + (20b - 36a )c + 60a b c + 40a b )cos(x) +--R + +--R 4 3 2 2 2 2 2 2 2 +--R (- 20c - 46a c + (20b - 14a )c + 40a b c + 20a b )cos(x) +--R + +--R 4 3 2 2 2 2 2 2 4 +--R (- 10c - 16a c + (10b - 2a )c + 14a b c + 4a b )cos(x) - 2c +--R + +--R 3 2 2 2 +--R - 2a c + 2b c + 2a b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 6 +--R (- 2b c + 2a b )sin(x) +--R + +--R 2 2 2 4 2 2 2 2 4 2 2 5 +--R ((4b c - 4a b c - 4b + 4a b )cos(x) + 2b c - 4b + 2a b )sin(x) +--R + +--R 2 3 3 2 +--R (4a b c + 2b c - 6a b )cos(x) +--R + +--R 3 2 3 3 3 3 +--R (4b c + 4a b c + 2b c - 10a b )cos(x) + 4b c - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 3 2 2 2 4 2 2 2 +--R (8b c - 8b )cos(x) + (20b c + 8a b c - 20b - 8a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 4 2 2 +--R (20b c + 8a b c - 16b - 12a b )cos(x) + 8b c - 4b - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 3 4 +--R (8a b c + 2b c - 10a b )cos(x) +--R + +--R 3 2 3 3 3 +--R (8b c + 20a b c - 8b c - 20a b )cos(x) +--R + +--R 3 2 3 3 2 +--R (20b c + 16a b c - 28b c - 8a b )cos(x) +--R + +--R 3 2 3 3 3 3 3 +--R (16b c + 4a b c - 24b c + 4a b )cos(x) + 4b c - 6b c + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 2 2 5 +--R (4b c + 4a b c - 4b - 4a b )cos(x) +--R + +--R 2 2 2 4 2 2 4 +--R (18b c + 8a b c - 16b - 10a b )cos(x) +--R + +--R 2 2 4 2 2 3 +--R (28b c - 24b - 4a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 +--R (16b c - 8a b c - 16b + 8a b )cos(x) +--R + +--R 2 4 2 2 2 2 2 2 +--R (- 4a b c - 4b + 8a b )cos(x) - 2b c + 2a b +--R * +--R sin(x) +--R + +--R 2 3 3 6 +--R (4a b c - 2b c - 2a b )cos(x) +--R + +--R 3 2 3 3 5 +--R (4b c + 16a b c - 10b c - 10a b )cos(x) +--R + +--R 3 2 3 3 4 +--R (16b c + 24a b c - 20b c - 20a b )cos(x) +--R + +--R 3 2 3 3 3 +--R (24b c + 16a b c - 20b c - 20a b )cos(x) +--R + +--R 3 2 3 3 2 +--R (16b c + 4a b c - 10b c - 10a b )cos(x) +--R + +--R 3 3 3 +--R (4b c - 2b c - 2a b )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 6 +--R (- b c + a b )sin(x) +--R + +--R 3 2 3 3 3 3 3 2 +--R (3b c - a b c - 3b c - a b + 2a b)cos(x) + 2b c + (- 3b + a b)c +--R + +--R 3 3 +--R - a b + a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 2 2 2 2 4 2 2 2 +--R (3a c + (3b + a )c - 3a b c - 2b - 2a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 4 +--R (3c + 4a c + (4b + a )c - 4a b c - 4b - 4a b )cos(x) + 3c +--R + +--R 3 2 2 2 4 2 2 +--R a c + b c - a b c - 2b - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 3 3 3 +--R (4b c + 8a b c - 4b c - 8a b )cos(x) +--R + +--R 3 2 3 3 3 2 +--R (12b c + 24a b c - 12b c - 20a b - 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 3 +--R (14b c + 22a b c + (- 12b - 2a b)c - 16a b - 6a b)cos(x) + 6b c +--R + +--R 2 3 2 3 3 +--R 6a b c + (- 4b - 2a b)c - 4a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 2 2 4 2 2 4 +--R (4a c + (- b + 6a )c - 4a b c + 2b - 7a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 3 +--R (4c + 16a c + (- 12b + 16a )c - 16a b c + 8b - 16a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 2 2 2 +--R (10c + 24a c + (- 26b + 14a )c - 24a b c + 12b - 10a b )cos(x) +--R + +--R 4 3 2 2 2 2 4 4 3 +--R (8c + 16a c + (- 20b + 4a )c - 16a b c + 8b )cos(x) + 2c + 4a c +--R + +--R 2 2 2 4 2 2 +--R - 5b c - 4a b c + 2b + a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 3 3 3 5 +--R (b c + a b c - b c + a b - 2a b)cos(x) +--R + +--R 3 3 2 3 3 4 +--R (2b c + (- b - a b)c + 5a b - 5a b)cos(x) +--R + +--R 3 2 3 2 3 3 3 +--R (- 4b c - 8a b c + (6b - 2a b)c + 10a b - 2a b)cos(x) +--R + +--R 3 2 3 3 3 2 +--R (- 14b c - 14a b c + 14b c + 10a b + 4a b)cos(x) +--R + +--R 3 2 3 2 3 3 3 +--R (- 13b c - 9a b c + (11b + 2a b)c + 5a b + 4a b)cos(x) - 4b c +--R + +--R 2 3 2 3 3 +--R - 2a b c + (3b + a b)c + a b + a b +--R * +--R sin(x) +--R + +--R 3 2 2 2 2 6 +--R (a c + (- b + a )c - a b c)cos(x) +--R + +--R 4 3 2 2 2 2 5 +--R (c + 4a c + (- 4b + 3a )c - 4a b c)cos(x) +--R + +--R 4 3 2 2 2 2 4 4 2 2 3 +--R (3c + 5a c + (- 5b + 2a )c - 5a b c)cos(x) + (2c - 2a c )cos(x) +--R + +--R 4 3 2 2 2 2 2 +--R (- 2c - 5a c + (5b - 3a )c + 5a b c)cos(x) +--R + +--R 4 3 2 2 2 2 4 3 2 2 2 +--R (- 3c - 4a c + (4b - a )c + 4a b c)cos(x) - c - a c + b c + a b c +--R / +--R 4 3 3 2 2 3 2 3 4 +--R (b c - 2a b c + (- b + a b)c + 2a b c - a b )cos(x) + b c +--R + +--R 3 3 2 2 3 2 3 +--R - 2a b c + (- b + a b)c + 2a b c - a b +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R a c + (2b - 2a )c + (- 3a b + a )c + (- 2b + 2a b )c +--R + +--R 4 3 2 +--R 2a b - a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 4 2 2 +--R c - a c + (3b - a )c + (- 3a b + a )c + (- 4b + a b )c +--R + +--R 4 3 2 +--R 4a b - a b +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 4 2 2 4 +--R c - 2a c + (b + a )c + (- 2b - a b )c + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 2 3 3 +--R (4a b c - 4a b c - 4a b c + 4a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (2b c + 8a b c + (- 2b - 10a b)c - 8a b c + 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R (4b c + 4a b c + (- 4b - 8a b)c - 4a b c + 8a b )cos(x) +--R + +--R 4 3 2 2 2 3 +--R 2b c + (- 2b - 2a b)c + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 2 3 2 4 2 2 4 +--R (- 2b + 2a )c + (2a b - 2a )c + (2b - 2a b )c - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R 2a c + (- 8b + 4a )c + (6a b - 6a )c + (8b - 4a b )c +--R + +--R 4 3 2 +--R - 8a b + 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 2 3 2 3 2 4 4 3 2 +--R (6a c - 12b c + (6a b - 6a )c + 12b c - 12a b + 6a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R 6a c + (- 8b - 4a )c + (2a b - 2a )c + (8b + 4a b )c +--R + +--R 4 3 2 +--R - 8a b + 2a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 4 2 2 4 +--R 2a c + (- 2b - 2a )c + (2b + 2a b )c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 3 2 2 3 2 3 5 +--R (- b c - 2a b c + (b + 3a b)c + 2a b c - 3a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 4 +--R (- 7b c - 6a b c + (7b + 13a b)c + 6a b c - 13a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 3 +--R (- 18b c - 4a b c + (18b + 22a b)c + 4a b c - 22a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (- 22b c + 4a b c + (22b + 18a b)c - 4a b c - 18a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R (- 13b c + 6a b c + (13b + 7a b)c - 6a b c - 7a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R - 3b c + 2a b c + (3b + a b)c - 2a b c - a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 6 +--R (- a c + (a b + a )c - a b )cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 3 2 5 +--R (- c - 5a c + (b + a )c + (5a b + 5a )c - a b c - 5a b )cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R - 5c - 10a c + (5b + 5a )c + (10a b + 10a )c - 5a b c +--R + +--R 3 2 +--R - 10a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R - 10c - 10a c + (10b + 10a )c + (10a b + 10a )c - 10a b c +--R + +--R 3 2 +--R - 10a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R - 10c - 5a c + (10b + 10a )c + (5a b + 5a )c - 10a b c +--R + +--R 3 2 +--R - 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 3 2 +--R (- 5c - a c + (5b + 5a )c + (a b + a )c - 5a b c - a b )cos(x) +--R + +--R 5 2 2 3 2 2 +--R - c + (b + a )c - a b c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 4 4 2 3 2 2 4 +--R (2b c - 2a b c - 2b c + 2a b )cos(x) + 2b c - 2a b c - 2b c +--R + +--R 4 +--R 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 2 2 3 5 2 3 2 +--R (2a b c + (4b - 2a b)c - 2a b c - 4b + 2a b )cos(x) +--R + +--R 4 3 2 2 5 2 3 4 3 +--R (2b c + (6b - 2a b)c - 8b + 2a b )cos(x) + 2b c - 2a b c +--R + +--R 3 2 3 5 +--R 2b c + 2a b c - 4b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 3 +--R (8a b c - 8a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 +--R (4b c + 20a b c - 4b c - 20a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 3 2 2 4 +--R (8b c + 16a b c - 8b c - 16a b )cos(x) + 4b c + 4a b c - 4b c +--R + +--R 4 +--R - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 5 2 3 4 +--R ((- 4b + 4a b)c + 4b - 4a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 3 +--R (4a b c + (- 16b + 12a b)c - 4a b c + 16b - 12a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 2 +--R (12a b c + (- 24b + 12a b)c - 12a b c + 24b - 12a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 +--R (12a b c + (- 16b + 4a b)c - 12a b c + 16b - 4a b )cos(x) +--R + +--R 3 3 2 3 5 +--R 4a b c - 4b c - 4a b c + 4b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 4 4 5 +--R (- 2b c - 6a b c + 2b c + 6a b )cos(x) +--R + +--R 2 3 2 2 4 4 4 +--R (- 14b c - 26a b c + 14b c + 26a b )cos(x) +--R + +--R 2 3 2 2 4 4 3 +--R (- 36b c - 44a b c + 36b c + 44a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 +--R (- 44b c - 36a b c + 44b c + 36a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 3 2 2 +--R (- 26b c - 14a b c + 26b c + 14a b )cos(x) - 6b c - 2a b c +--R + +--R 4 4 +--R 6b c + 2a b +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 3 6 +--R (- 2a b c - 2a b c + 2a b c + 2a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 5 +--R (- 2b c - 12a b c + (2b - 10a b)c + 12a b c + 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 4 +--R (- 10b c - 30a b c + (10b - 20a b)c + 30a b c + 20a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 3 +--R (- 20b c - 40a b c + (20b - 20a b)c + 40a b c + 20a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (- 20b c - 30a b c + (20b - 10a b)c + 30a b c + 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R (- 10b c - 12a b c + (10b - 2a b)c + 12a b c + 2a b )cos(x) +--R + +--R 4 3 3 2 3 +--R - 2b c - 2a b c + 2b c + 2a b c +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 3 3 2 2 +--R (2a b c - 2a b c - 2a b c + 2a b )cos(x) + 2a b c - 2a b c +--R + +--R 3 2 3 +--R - 2a b c + 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 2 3 2 3 2 2 2 4 3 2 2 +--R (2a c + (4a b - 2a )c - 2a b c - 4a b + 2a b )cos(x) +--R + +--R 4 2 3 2 4 3 2 4 2 3 +--R (2a c + (6a b - 2a )c - 8a b + 2a b )cos(x) + 2a c - 2a c +--R + +--R 2 2 2 2 4 +--R 2a b c + 2a b c - 4a b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 2 3 3 +--R (8a b c - 8a b )cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R (4a b c + 20a b c - 4a b c - 20a b )cos(x) +--R + +--R 3 2 2 3 2 3 3 2 2 +--R (8a b c + 16a b c - 8a b c - 16a b )cos(x) + 4a b c + 4a b c +--R + +--R 3 2 3 +--R - 4a b c - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 3 2 4 3 2 4 +--R ((- 4a b + 4a )c + 4a b - 4a b )cos(x) +--R + +--R 2 3 2 3 2 2 2 4 3 2 3 +--R (4a c + (- 16a b + 12a )c - 4a b c + 16a b - 12a b )cos(x) +--R + +--R 2 3 2 3 2 2 2 4 3 2 2 +--R (12a c + (- 24a b + 12a )c - 12a b c + 24a b - 12a b )cos(x) +--R + +--R 2 3 2 3 2 2 2 4 3 2 +--R (12a c + (- 16a b + 4a )c - 12a b c + 16a b - 4a b )cos(x) +--R + +--R 2 3 2 2 2 2 4 +--R 4a c - 4a b c - 4a b c + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 2 3 5 +--R (- 2a b c - 6a b c + 2a b c + 6a b )cos(x) +--R + +--R 3 2 2 3 2 3 4 +--R (- 14a b c - 26a b c + 14a b c + 26a b )cos(x) +--R + +--R 3 2 2 3 2 3 3 +--R (- 36a b c - 44a b c + 36a b c + 44a b )cos(x) +--R + +--R 3 2 2 3 2 3 2 +--R (- 44a b c - 36a b c + 44a b c + 36a b )cos(x) +--R + +--R 3 2 2 3 2 3 3 +--R (- 26a b c - 14a b c + 26a b c + 14a b )cos(x) - 6a b c +--R + +--R 2 2 3 2 3 +--R - 2a b c + 6a b c + 2a b +--R * +--R sin(x) +--R + +--R 2 3 3 2 2 2 3 2 6 +--R (- 2a c - 2a c + 2a b c + 2a b )cos(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 5 +--R (- 2a c - 12a c + (2a b - 10a )c + 12a b c + 10a b )cos(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 4 +--R (- 10a c - 30a c + (10a b - 20a )c + 30a b c + 20a b )cos(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 3 +--R (- 20a c - 40a c + (20a b - 20a )c + 40a b c + 20a b )cos(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 2 +--R (- 20a c - 30a c + (20a b - 10a )c + 30a b c + 10a b )cos(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 +--R (- 10a c - 12a c + (10a b - 2a )c + 12a b c + 2a b )cos(x) +--R + +--R 4 2 3 2 2 2 2 +--R - 2a c - 2a c + 2a b c + 2a b c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 4 4 2 3 2 2 4 +--R (- 2b c + 2a b c + 2b c - 2a b )cos(x) - 2b c + 2a b c + 2b c +--R + +--R 4 +--R - 2a b +--R * +--R 5 +--R sin(x) +--R + +--R 3 3 2 2 3 5 2 3 2 +--R (- 2a b c + (- 4b + 2a b)c + 2a b c + 4b - 2a b )cos(x) +--R + +--R 4 3 2 2 5 2 3 4 +--R (- 2b c + (- 6b + 2a b)c + 8b - 2a b )cos(x) - 2b c +--R + +--R 3 3 2 3 5 +--R 2a b c - 2b c - 2a b c + 4b +--R * +--R 4 +--R sin(x) +--R + +--R 2 2 4 3 +--R (- 8a b c + 8a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 +--R (- 4b c - 20a b c + 4b c + 20a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 3 2 2 +--R (- 8b c - 16a b c + 8b c + 16a b )cos(x) - 4b c - 4a b c +--R + +--R 4 4 +--R 4b c + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 5 2 3 4 +--R ((4b - 4a b)c - 4b + 4a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 3 +--R (- 4a b c + (16b - 12a b)c + 4a b c - 16b + 12a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 2 +--R (- 12a b c + (24b - 12a b)c + 12a b c - 24b + 12a b )cos(x) +--R + +--R 3 3 2 2 3 5 2 3 +--R (- 12a b c + (16b - 4a b)c + 12a b c - 16b + 4a b )cos(x) +--R + +--R 3 3 2 3 5 +--R - 4a b c + 4b c + 4a b c - 4b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 4 4 5 +--R (2b c + 6a b c - 2b c - 6a b )cos(x) +--R + +--R 2 3 2 2 4 4 4 +--R (14b c + 26a b c - 14b c - 26a b )cos(x) +--R + +--R 2 3 2 2 4 4 3 +--R (36b c + 44a b c - 36b c - 44a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 +--R (44b c + 36a b c - 44b c - 36a b )cos(x) +--R + +--R 2 3 2 2 4 4 2 3 2 2 +--R (26b c + 14a b c - 26b c - 14a b )cos(x) + 6b c + 2a b c +--R + +--R 4 4 +--R - 6b c - 2a b +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 3 6 +--R (2a b c + 2a b c - 2a b c - 2a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 5 +--R (2b c + 12a b c + (- 2b + 10a b)c - 12a b c - 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 4 +--R (10b c + 30a b c + (- 10b + 20a b)c - 30a b c - 20a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 3 +--R (20b c + 40a b c + (- 20b + 20a b)c - 40a b c - 20a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (20b c + 30a b c + (- 20b + 10a b)c - 30a b c - 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R (10b c + 12a b c + (- 10b + 2a b)c - 12a b c - 2a b )cos(x) +--R + +--R 4 3 3 2 3 +--R 2b c + 2a b c - 2b c - 2a b c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 2 3 4 3 2 2 2 3 +--R ((- b c + (b + a b)c - a b )cos(x) - b c + (b + a b)c - a b ) +--R * +--R 5 +--R sin(x) +--R + +--R 4 2 3 2 3 2 4 4 3 2 2 +--R (- a c - 2b c + (- a b + a )c + 2b c + 2a b - a b )cos(x) +--R + +--R 5 4 2 2 3 2 3 2 4 2 2 +--R - c - a c + (- 3b + a )c + (- 3a b + a )c + (4b - a b )c +--R + +--R 4 3 2 +--R 4a b - a b +--R * +--R cos(x) +--R + +--R 5 2 2 3 2 2 4 2 2 4 +--R - c + (- b + a )c - 2a b c + (2b - a b )c + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 2 3 3 +--R (- 4a b c - 4a b c + 4a b c + 4a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (- 2b c - 12a b c + (2b - 10a b)c + 12a b c + 10a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 4 +--R (- 4b c - 12a b c + (4b - 8a b)c + 12a b c + 8a b )cos(x) - 2b c +--R + +--R 3 3 2 2 3 2 3 +--R - 4a b c + (2b - 2a b)c + 4a b c + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 2 3 2 4 2 2 4 +--R (2b - 2a )c + (2a b - 2a )c + (- 2b + 2a b )c - 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R - 2a c + (8b - 8a )c + (10a b - 6a )c + (- 8b + 8a b )c +--R + +--R 4 3 2 +--R - 8a b + 6a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R - 6a c + (12b - 12a )c + (18a b - 6a )c + (- 12b + 12a b )c +--R + +--R 4 3 2 +--R - 12a b + 6a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R - 6a c + (8b - 8a )c + (14a b - 2a )c + (- 8b + 8a b )c +--R + +--R 4 3 2 +--R - 8a b + 2a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 2 4 2 2 4 +--R - 2a c + (2b - 2a )c + 4a b c + (- 2b + 2a b )c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 3 2 2 3 2 3 5 +--R (b c + 4a b c + (- b + 3a b)c - 4a b c - 3a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 4 +--R (7b c + 20a b c + (- 7b + 13a b)c - 20a b c - 13a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 3 +--R (18b c + 40a b c + (- 18b + 22a b)c - 40a b c - 22a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 2 +--R (22b c + 40a b c + (- 22b + 18a b)c - 40a b c - 18a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R (13b c + 20a b c + (- 13b + 7a b)c - 20a b c - 7a b )cos(x) +--R + +--R 4 3 3 2 2 3 2 3 +--R 3b c + 4a b c + (- 3b + a b)c - 4a b c - a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 2 2 3 2 6 +--R (a c + 2a c + (- a b + a )c - 2a b c - a b )cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 3 2 +--R (c + 7a c + (- b + 11a )c + (- 7a b + 5a )c - 11a b c - 5a b ) +--R * +--R 5 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R 5c + 20a c + (- 5b + 25a )c + (- 20a b + 10a )c - 25a b c +--R + +--R 3 2 +--R - 10a b +--R * +--R 4 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R 10c + 30a c + (- 10b + 30a )c + (- 30a b + 10a )c - 30a b c +--R + +--R 3 2 +--R - 10a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 +--R 10c + 25a c + (- 10b + 20a )c + (- 25a b + 5a )c - 20a b c +--R + +--R 3 2 +--R - 5a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 2 2 3 2 +--R (5c + 11a c + (- 5b + 7a )c + (- 11a b + a )c - 7a b c - a b ) +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 2 2 2 2 +--R c + 2a c + (- b + a )c - 2a b c - a b c +--R Type: Expression(Integer) +--E 246 + +)clear all + + +--S 247 of 526 +t0848:= csc(x)^2/(a+b*cot(x)+c*csc(x)) +--R +--R +--R 2 +--R csc(x) +--R (1) ----------------------- +--R c csc(x) + b cot(x) + a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 526 +r0848:= -2*a*c*atanh((a-(b-c)*tan(1/2*x))/(a^2+b^2-c^2)^(1/2))/_ + (b^2-c^2)/(a^2+b^2-c^2)^(1/2)+log(tan(1/2*x))/(b+c)-_ + b*log(b+c+2*a*tan(1/2*x)-(b-c)*tan(1/2*x)^2)/(b^2-c^2) +--R +--R +--R (2) +--R +--------------+ +--R | 2 2 2 x 2 x +--R b\|- c + b + a log((c - b)tan(-) + 2a tan(-) + c + b) +--R 2 2 +--R + +--R x +--R +--------------+ (c - b)tan(-) + a +--R | 2 2 2 x 2 +--R (c - b)\|- c + b + a log(tan(-)) + 2a c atanh(-----------------) +--R 2 +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R Type: Expression(Integer) +--E 248 + +--S 249 of 526 +a0848:= integrate(t0848,x) +--R +--R +--R (3) +--R [ +--R a c +--R * +--R log +--R 2 2 2 +--R (a c - a b)sin(x) + (- c + b c + a )cos(x) - b c + b +--R + +--R 2 +--R a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 3 2 +--R (- c + b c + (b + a )c - b - a b)sin(x) +--R + +--R 2 2 3 2 2 3 +--R (- a c + a b + a )cos(x) - a c + a b + a +--R / +--R a sin(x) + b cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 sin(x) +--R (c - b)\|- c + b + a log(----------) +--R cos(x) + 1 +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R , +--R +--R +------------+ +--R | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R b\|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 sin(x) +--R (c - b)\|c - b - a log(----------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R ((c - b)sin(x) + a cos(x) + a)\|c - b - a +--R - 2a c atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|c - b - a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 249 + +--S 250 of 526 +m0848a:= a0848.1-r0848 +--R +--R +--R (4) +--R a c +--R * +--R log +--R 2 2 2 2 +--R ((a c - a b)sin(x) + (- c + b c + a )cos(x) - b c + b + a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 3 2 2 2 3 2 +--R (- c + b c + (b + a )c - b - a b)sin(x) +--R + +--R 2 2 3 2 2 3 +--R (- a c + a b + a )cos(x) - a c + a b + a +--R / +--R a sin(x) + b cos(x) + c +--R + +--R +--------------+ +--R | 2 2 2 x 2 x +--R - b\|- c + b + a log((c - b)tan(-) + 2a tan(-) + c + b) +--R 2 2 +--R + +--R +--------------+ +--R | 2 2 2 x +--R (- c + b)\|- c + b + a log(tan(-)) +--R 2 +--R + +--R +--------------+ +--R | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R b\|- c + b + a log(--------------------------) +--R cos(x) + 1 +--R + +--R x +--R +--------------+ (c - b)tan(-) + a +--R | 2 2 2 sin(x) 2 +--R (c - b)\|- c + b + a log(----------) - 2a c atanh(-----------------) +--R cos(x) + 1 +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c - b )\|- c + b + a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 526 +d0848a:= D(m0848a,x) +--R +--R +--R (5) +--R 2 2 2 2 2 2 2 2 3 +--R ((- a c + a b )cos(x) - a c + a b )sin(x) +--R + +--R 3 2 2 3 3 3 2 +--R (a c - a b c + (- a b - a )c + a b - a b)cos(x) +--R + +--R 3 3 3 2 2 3 3 +--R (- 2a c - 2a b)cos(x) - a c + a b c + (a b - a )c - a b +--R + +--R 3 +--R - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 2 2 2 3 +--R (b c + (- b - a b)c - a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + b c - a c + (- b - 3a b)c - b - 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 +--R (c + b c - 2a c + (- b - 3a b)c - b - a b )cos(x) + b c +--R + +--R 2 2 3 2 +--R - a c + (- b - a b)c +--R * +--R sin(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 +--R (2a c - 2a b c)sin(x) +--R + +--R 3 2 2 3 3 2 +--R (- 2a c + 6a b c - 6a b c + 2a b )cos(x) + 2a c - 2a b c +--R + +--R 2 3 +--R - 2a b c + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 2 3 2 2 2 +--R (- 2b c + (4b + 2a )c - 2b c - 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (- 2c + 2b c + 2a c + (2b + 2a b)c - 2b - 4a b )cos(x) +--R + +--R 3 2 2 3 2 4 2 2 +--R - 2b c + 2b c + (2b + 2a b)c - 2b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 3 +--R (- 2a c + 6a b c - 6a b c + 2a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (2a c - 2a b c - 2a b c + 2a b )cos(x) +--R + +--R 3 2 2 +--R (4a c - 8a b c + 4a b c)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 2 2 4 +--R (- 2b c + 4b c + (- 2b + 2a b)c - 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 +--R (- 2c + 2b c + 2a c + (2b + 2a b)c - 2b - 4a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (- 2c + 2b c + 4a c + (2b - 2a b)c - 2b - 2a b )cos(x) +--R + +--R 3 2 2 2 3 2 +--R (- 2b c + (4b + 2a )c + (- 2b - 2a b)c)cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 4 +--R 4a c sin(x) +--R + +--R 2 2 2 2 2 2 2 2 2 3 +--R ((- 6a c + 8a b c - 2a b )cos(x) + 2a c - 2a b )sin(x) +--R + +--R 3 2 2 3 3 3 2 +--R (2a c - 6a b c + (2a b + 2a )c + 2a b + 2a b)cos(x) +--R + +--R 3 3 3 3 2 +--R (- 4a c + 4a b + 4a b)cos(x) - 2a c - 2a b c +--R + +--R 2 3 3 3 +--R (2a b - 2a )c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 2 2 2 3 +--R (2b c - 4a c + (- 2b + 6a b)c - 6a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (2c + 2b c + 2a c + (- 2b - 6a b)c - 2b - 8a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 2b c + 4a c + (- 2b - 14a b)c - 2b - 2a b )cos(x) +--R + +--R 3 2 2 3 2 +--R 2b c - 2a c + (- 2b - 2a b)c +--R * +--R sin(x) +--R + +--R 2 2 3 4 +--R (- 4a b c + 4a b c + 4a b)cos(x) +--R + +--R 3 3 3 3 3 +--R (- 4a c + 4a c + 4a b + 8a b)cos(x) +--R + +--R 3 3 3 3 2 +--R (- 4a c + 8a c + 4a b + 4a b)cos(x) +--R + +--R 2 2 3 +--R (- 4a b c + (4a b + 4a )c)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 +--R (2a c + 2a b c)sin(x) +--R + +--R 3 2 2 3 3 2 +--R (- 2a c + 2a b c + 2a b c - 2a b )cos(x) + 2a c + 2a b c +--R + +--R 2 3 +--R - 2a b c - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 2 2 2 2 +--R (- 2b c + 2a c + (2b + 4a b)c + 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (- 2c - 2b c + 2a c + (2b + 6a b)c + 2b + 4a b )cos(x) +--R + +--R 3 2 2 3 2 4 2 2 +--R - 2b c - 2b c + (2b + 2a b)c + 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 3 +--R (- 2a c + 2a b c + 2a b c - 2a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (2a c + 2a b c - 2a b c - 2a b )cos(x) +--R + +--R 3 2 +--R (4a c - 4a b c)cos(x) +--R * +--R sin(x) +--R + +--R 3 3 2 2 2 4 +--R (- 2b c + (2b + 2a b)c + 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 +--R (- 2c - 2b c + 2a c + (2b + 6a b)c + 2b + 4a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (- 2c - 2b c + 4a c + (2b + 6a b)c + 2b + 2a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 2b c + 2a c + (2b + 2a b)c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 2 2 2 3 +--R ((- a c + a b )cos(x) - a c + a b )sin(x) +--R + +--R 3 2 2 3 3 3 2 +--R (a c - a b c + (- a b - a )c + a b - a b)cos(x) +--R + +--R 3 3 3 2 2 3 3 3 +--R (- 2a c - 2a b)cos(x) - a c + a b c + (a b - a )c - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 2 2 2 3 +--R (b c + (- b - a b)c - a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 2 +--R (c + b c - a c + (- b - 3a b)c - b - 2a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 3 +--R (c + b c - 2a c + (- b - 3a b)c - b - a b )cos(x) + b c +--R + +--R 2 2 3 2 +--R - a c + (- b - a b)c +--R * +--R sin(x) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 4 2 3 2 4 3 2 4 +--R (a c + (- 2a b - a )c + a b + a b )cos(x) + a c +--R + +--R 2 3 2 4 3 2 +--R (- 2a b - a )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 2 2 4 5 4 2 +--R (b c + a c - 2b c + (- a b - a )c + b - a b)cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R c + b c + (- 2b + a )c + (- 2b + a b)c +--R + +--R 4 2 2 4 5 2 3 4 +--R (b - a b - 2a )c + b - a b - 2a b +--R * +--R cos(x) +--R + +--R 5 2 3 2 2 4 4 2 3 4 +--R c - 2b c + a b c + (b - a )c - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 3 4 3 2 3 +--R (a b c + a b c + (- a b - a b)c - a b - a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R a c + 3a b c + (a b - a )c + (- 3a b - 3a b)c - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R 2a c + 3a b c + (- a b - 2a )c + (- 3a b - 3a b)c - a b +--R + +--R 3 2 +--R - a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R a c + a b c + (- a b - a )c + (- a b - a b)c +--R * +--R sin(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 2 3 3 4 +--R (- 2a c + 2a b c + (2a b + 2a )c + (- 2a b - 2a b)c)sin(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 +--R (- 2b c + 4b c + 2a b c + (- 4b - 4a b )c + 2b + 2a b ) +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c + 2b c + (4b + 2a )c + (- 4b - 2a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 2b - 2a b )c + 2b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 2 4 3 2 2 +--R (- 2a c + (4a b + 2a )c - 2a b - 2a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 2a c - 2a b c + (6a b + 2a )c + (2a b + 2a b)c - 4a b +--R + +--R 3 2 +--R - 4a b +--R * +--R cos(x) +--R + +--R 3 2 2 3 3 4 3 2 +--R - 2a b c + 2a b c + (2a b + 2a b)c - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 2 2 4 2 2 5 2 3 +--R (- 2b c + 4b c + 2a b c + (- 4b - 4a b )c + 2b + 2a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c + 2b c + (4b + 2a )c + (- 4b - 2a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 2b - 2a b )c + 2b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 3 3 2 2 4 2 2 +--R (- 2c + 4b c + 2a c + (- 4b - 4a b)c + (2b + 2a b )c)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 2 3 3 4 3 2 4 +--R (- 2a b c + 2a b c + (2a b + 2a b)c - 2a b - 2a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 2a c - 2a b c + (6a b + 2a )c + (2a b + 2a b)c - 4a b +--R + +--R 3 2 +--R - 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 4a c + 2a b c + (6a b + 4a )c + (- 2a b - 2a b)c - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R (- 2a c + 2a b c + (2a b + 2a )c + (- 2a b - 2a b)c)cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 4 4 +--R (- 4a c + (4a b + 4a )c)sin(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (2a c - 4a b c - 2a c + (4a b + 4a b)c - 2a b - 2a b )cos(x) +--R + +--R 4 2 3 2 4 3 2 +--R - 2a c + (4a b + 2a )c - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 2 2 2 4 5 +--R 2b c - 2a c + (- 4b - 4a b)c + (2a b + 2a )c + 2b +--R + +--R 2 3 4 +--R 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R 2c + 2b c + (- 4b - 2a )c + (- 4b - 6a b)c +--R + +--R 4 2 2 5 2 3 4 +--R (2b + 2a b )c + 2b + 6a b + 4a b +--R * +--R cos(x) +--R + +--R 5 2 3 2 2 4 4 2 3 4 +--R 2c - 4b c - 2a b c + (2b - 2a )c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 3 4 3 2 3 +--R (- 2a b c + 6a b c + (2a b + 2a b)c - 6a b - 6a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R - 2a c + 6a b c + (10a b + 2a )c + (- 6a b - 6a b)c +--R + +--R 4 3 2 +--R - 8a b - 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 3 4 3 2 +--R (10a b c + 2a b c + (- 10a b - 10a b)c - 2a b - 2a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R 2a c + 2a b c + (- 2a b - 2a )c + (- 2a b - 2a b)c +--R * +--R sin(x) +--R + +--R 2 2 2 3 4 4 +--R (- 4a b c + 4a b + 4a b)cos(x) +--R + +--R 2 3 2 2 2 2 4 2 3 4 3 +--R (- 4a c - 8a b c + (4a b + 4a )c + 8a b + 8a b)cos(x) +--R + +--R 2 3 2 2 2 2 4 2 3 4 2 +--R (- 8a c - 4a b c + (8a b + 8a )c + 4a b + 4a b)cos(x) +--R + +--R 2 3 2 2 4 +--R (- 4a c + (4a b + 4a )c)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 3 2 3 3 4 +--R (- 2a c - 2a b c + (2a b + 2a )c + (2a b + 2a b)c)sin(x) +--R + +--R 4 3 2 2 5 2 3 5 4 +--R (- 2b c + (4b + 2a b)c - 2b - 2a b )cos(x) - 2c - 2b c +--R + +--R 2 2 3 3 2 2 4 2 2 5 2 3 +--R (4b + 2a )c + (4b + 2a b)c + (- 2b - 2a b )c - 2b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 3 2 3 3 4 3 2 +--R (- 2a c - 4a b c + 2a c + (4a b + 4a b)c + 2a b + 2a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R - 2a c - 6a b c + (- 2a b + 2a )c + (6a b + 6a b)c +--R + +--R 4 3 2 +--R 4a b + 4a b +--R * +--R cos(x) +--R + +--R 3 2 2 3 3 4 3 2 +--R - 2a b c - 2a b c + (2a b + 2a b)c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 5 2 3 3 +--R (- 2b c + (4b + 2a b)c - 2b - 2a b )cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c - 2b c + (4b + 2a )c + (4b + 2a b)c +--R + +--R 4 2 2 5 2 3 +--R (- 2b - 2a b )c - 2b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 2 3 4 2 2 +--R (- 2c + (4b + 2a )c + (- 2b - 2a b )c)cos(x) +--R * +--R sin(x) +--R + +--R 3 2 2 3 3 4 3 2 4 +--R (- 2a b c - 2a b c + (2a b + 2a b)c + 2a b + 2a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 2a c - 6a b c + (- 2a b + 2a )c + (6a b + 6a b)c + 4a b +--R + +--R 3 2 +--R 4a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R - 4a c - 6a b c + (2a b + 4a )c + (6a b + 6a b)c + 2a b +--R + +--R 3 2 +--R 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R (- 2a c - 2a b c + (2a b + 2a )c + (2a b + 2a b)c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 3 2 4 3 2 4 +--R (a c + (- 2a b - a )c + a b + a b )cos(x) + a c +--R + +--R 2 3 2 4 3 2 +--R (- 2a b - a )c + a b + a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 3 2 2 2 4 5 4 2 +--R (b c + a c - 2b c + (- a b - a )c + b - a b)cos(x) +--R + +--R 5 4 2 2 3 3 2 2 4 2 2 4 +--R c + b c + (- 2b + a )c + (- 2b + a b)c + (b - a b - 2a )c +--R + +--R 5 2 3 4 +--R b - a b - 2a b +--R * +--R cos(x) +--R + +--R 5 2 3 2 2 4 4 2 3 4 +--R c - 2b c + a b c + (b - a )c - a b - a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 3 4 3 2 3 +--R (a b c + a b c + (- a b - a b)c - a b - a b )cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R a c + 3a b c + (a b - a )c + (- 3a b - 3a b)c - 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 4 +--R 2a c + 3a b c + (- a b - 2a )c + (- 3a b - 3a b)c - a b +--R + +--R 3 2 +--R - a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 2 3 3 +--R a c + a b c + (- a b - a )c + (- a b - a b)c +--R * +--R sin(x) +--R / +--R 2 3 2 2 2 2 2 3 2 3 2 2 +--R (2a c - 2a b c - 2a b c + 2a b )cos(x) + 2a c - 2a b c +--R + +--R 2 2 2 3 +--R - 2a b c + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 3 2 3 4 3 2 2 +--R (- 2a c + 4a b c + 2a c - 4a b c + 2a b - 2a b )cos(x) +--R + +--R 3 2 3 2 4 3 3 2 3 +--R (4a c - 4a b )cos(x) + 2a c - 4a b c + 2a c + 4a b c +--R + +--R 4 3 2 +--R - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 2 4 2 3 3 +--R (- 2b c + 2b c + (2b + 2a b)c - 2b c - 2a b )cos(x) +--R + +--R 5 2 2 3 3 2 2 2 2 5 +--R - 2c + (2b + 2a )c + (2b + 4a b)c - 2a b c - 2b +--R + +--R 2 3 +--R - 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 2 3 3 2 2 2 2 5 +--R - 2c + (2b + 4a )c + (2b + 2a b)c - 4a b c - 2b +--R + +--R 2 3 +--R - 2a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 3 2 4 2 2 +--R - 2b c + (2b + 2a )c + 2b c + (- 2b - 2a b )c +--R * +--R sin(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 2 3 2 3 2 3 2 3 +--R ((4a c - 4a b )cos(x) + 4a c - 4a b )sin(x) +--R + +--R 2 3 2 2 2 2 4 2 3 4 2 +--R (- 4a c + 4a b c + (4a b + 4a )c - 4a b + 4a b)cos(x) +--R + +--R 4 4 2 3 2 2 2 2 4 +--R (8a c + 8a b)cos(x) + 4a c - 4a b c + (- 4a b + 4a )c +--R + +--R 2 3 4 +--R 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 3 2 3 +--R (- 4a b c + (4a b + 4a b)c + 4a b )cos(x) +--R + +--R 4 3 3 2 3 3 4 +--R - 4a c - 4a b c + 4a c + (4a b + 12a b)c + 4a b +--R + +--R 3 2 +--R 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 3 3 4 +--R - 4a c - 4a b c + 8a c + (4a b + 12a b)c + 4a b +--R + +--R 3 2 +--R 4a b +--R * +--R cos(x) +--R + +--R 3 3 2 3 3 +--R - 4a b c + 4a c + (4a b + 4a b)c +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 2 2 2 3 2 3 2 2 +--R (2a c + 2a b c - 2a b c - 2a b )cos(x) + 2a c + 2a b c +--R + +--R 2 2 2 3 +--R - 2a b c - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 2 3 2 3 4 3 2 2 +--R (- 2a c + (4a b + 2a )c + 4a b c - 2a b + 2a b )cos(x) +--R + +--R 3 2 3 3 2 4 2 3 2 +--R (4a c + 8a b c + 4a b )cos(x) + 2a c + (- 4a b + 2a )c +--R + +--R 3 4 3 2 +--R 4a b c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 2 4 2 2 2 3 +--R (- 2b c - 2b c + (2b + 2a b)c + (2b + 4a b )c + 2a b ) +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c - 4b c + (- 2b + 2a )c + (2b + 8a b)c +--R + +--R 4 2 2 5 2 3 +--R (4b + 10a b )c + 2b + 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 3 2 2 +--R - 2c - 4b c + (- 2b + 4a )c + (2b + 10a b)c +--R + +--R 4 2 2 5 2 3 +--R (4b + 8a b )c + 2b + 2a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 3 2 2 4 2 2 +--R - 2b c + (- 2b + 2a )c + (2b + 4a b)c + (2b + 2a b )c +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c + 2a b c + (4a b + 2a )c + (- 4a b - 2a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 2a b - 2a b )c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c + 2a b c + (4a b + 2a )c + (- 4a b - 2a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 2a b - 2a b )c + 2a b + 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 2 4 3 2 3 +--R - 2b c + (2b - 2a )c + (4b + 2a b)c +--R + +--R 4 2 2 4 2 5 2 3 6 4 2 +--R (- 4b + 2a b + 2a )c + (- 2b - 2a b )c + 2b - 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 4 4 2 2 4 2 6 2 4 +--R - 2c + (6b - 2a )c + (- 6b + 4a b + 4a )c + 2b - 2a b +--R + +--R 4 2 +--R - 4a b +--R * +--R cos(x) +--R + +--R 6 5 2 4 3 2 3 +--R - 2c + 2b c + 4b c + (- 4b - 2a b)c +--R + +--R 4 2 2 4 2 5 2 3 2 4 4 2 +--R (- 2b + 2a b + 2a )c + (2b + 2a b )c - 2a b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 3 2 5 3 3 3 +--R (- 2a b c + (4a b + 2a b)c - 2a b - 2a b )cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c - 4a b c + (4a b + 2a )c + (8a b + 4a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 2a b - 2a b )c - 4a b - 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 4a c - 2a b c + (8a b + 4a )c + (4a b + 2a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 4a b - 4a b )c - 2a b - 2a b +--R * +--R cos(x) +--R + +--R 5 2 3 3 4 3 2 +--R - 2a c + (4a b + 2a )c + (- 2a b - 2a b )c +--R * +--R sin(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 4 2 2 4 4 2 2 4 +--R (- 4a c + (8a b + 4a )c - 4a b - 4a b )cos(x) - 4a c +--R + +--R 2 2 4 2 2 4 4 2 +--R (8a b + 4a )c - 4a b - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 4 3 3 3 2 3 2 5 5 5 +--R (- 4a b c - 4a c + 8a b c + (4a b + 4a )c - 4a b + 4a b) +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 4a c - 4a b c + (8a b - 4a )c + (8a b - 4a b)c +--R + +--R 4 3 2 5 5 3 3 5 +--R (- 4a b + 4a b + 8a )c - 4a b + 4a b + 8a b +--R * +--R cos(x) +--R + +--R 5 2 3 3 2 4 5 3 3 5 +--R - 4a c + 8a b c - 4a b c + (- 4a b + 4a )c + 4a b + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 2 2 3 4 2 4 4 2 3 +--R (- 4a b c - 4a b c + (4a b + 4a b)c + 4a b + 4a b )cos(x) +--R + +--R 2 4 2 3 2 2 4 2 2 3 4 +--R - 4a c - 12a b c + (- 4a b + 4a )c + (12a b + 12a b)c +--R + +--R 2 4 4 2 +--R 8a b + 8a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 4 2 3 2 2 4 2 2 3 4 +--R - 8a c - 12a b c + (4a b + 8a )c + (12a b + 12a b)c +--R + +--R 2 4 4 2 +--R 4a b + 4a b +--R * +--R cos(x) +--R + +--R 2 4 2 3 2 2 4 2 2 3 4 +--R - 4a c - 4a b c + (4a b + 4a )c + (4a b + 4a b)c +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c - 2a b c + (4a b + 2a )c + (4a b + 2a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 2a b - 2a b )c - 2a b - 2a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c - 2a b c + (4a b + 2a )c + (4a b + 2a b)c +--R + +--R 4 3 2 5 3 3 +--R (- 2a b - 2a b )c - 2a b - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 5 2 2 4 3 2 3 +--R - 2b c + (- 2b - 2a )c + (4b - 2a b)c +--R + +--R 4 2 2 4 2 5 2 3 4 6 4 2 +--R (4b + 2a b + 2a )c + (- 2b + 2a b + 4a b)c - 2b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 3 2 3 +--R - 2c - 4b c + (2b - 2a )c + (8b - 4a b)c +--R + +--R 4 4 2 5 2 3 4 6 2 4 4 2 +--R (2b + 4a )c + (- 4b + 4a b + 8a b)c - 2b + 2a b + 4a b +--R * +--R cos(x) +--R + +--R 6 5 2 4 3 2 3 4 2 2 4 2 +--R - 2c - 2b c + 4b c + (4b - 2a b)c + (- 2b - 2a b + 2a )c +--R + +--R 5 2 3 4 2 4 4 2 +--R (- 2b + 2a b + 4a b)c + 2a b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 3 2 4 3 2 5 +--R - 2a b c - 4a b c + 2a b c + (4a b + 4a b )c + 2a b +--R + +--R 3 3 +--R 2a b +--R * +--R 3 +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 2a c - 8a b c + (- 8a b + 2a )c + (4a b + 8a b)c +--R + +--R 4 3 2 5 3 3 +--R (10a b + 10a b )c + 4a b + 4a b +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 3 3 3 3 2 +--R - 4a c - 10a b c + (- 4a b + 4a )c + (8a b + 10a b)c +--R + +--R 4 3 2 5 3 3 +--R (8a b + 8a b )c + 2a b + 2a b +--R * +--R cos(x) +--R + +--R 5 4 3 3 3 3 2 4 3 2 +--R - 2a c - 4a b c + 2a c + (4a b + 4a b)c + (2a b + 2a b )c +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 526 +m0848b:= a0848.2-r0848 +--R +--R +--R (6) +--R - +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R b\|- c + b + a \|c - b - a +--R * +--R x 2 x +--R log((c - b)tan(-) + 2a tan(-) + c + b) +--R 2 2 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 x +--R (- c + b)\|- c + b + a \|c - b - a log(tan(-)) +--R 2 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2a sin(x) + 2b cos(x) + 2c +--R b\|- c + b + a \|c - b - a log(--------------------------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 sin(x) +--R (c - b)\|- c + b + a \|c - b - a log(----------) +--R cos(x) + 1 +--R + +--R x +--R +------------+ (c - b)tan(-) + a +--R | 2 2 2 2 +--R - 2a c\|c - b - a atanh(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c + b + a +--R + +--R +------------+ +--R +--------------+ | 2 2 2 +--R | 2 2 2 ((c - b)sin(x) + a cos(x) + a)\|c - b - a +--R - 2a c\|- c + b + a atan(---------------------------------------------) +--R 2 2 2 2 2 2 +--R (c - b - a )cos(x) + c - b - a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c - b )\|- c + b + a \|c - b - a +--R Type: Expression(Integer) +--E 252 + +--S 253 of 526 +d0848b:= D(m0848b,x) +--R +--R +--R (7) +--R 2 2 2 2 4 +--R ((- a c + a b )cos(x) - a c + a b )sin(x) +--R + +--R 2 2 3 2 2 +--R (- b c - 2a c + b - 2a b)cos(x) +--R + +--R 3 2 2 2 3 2 3 2 2 +--R (- c - b c + (b - 4a )c + b - 4a b)cos(x) - c + (b - 2a )c +--R + +--R 2 +--R - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 +--R (- a c - 4a b c - 3a b )cos(x) +--R + +--R 2 2 2 +--R (- 5a c - 12a b c - 7a b )cos(x) +--R + +--R 2 2 2 2 +--R (- 7a c - 12a b c - 5a b )cos(x) - 3a c - 4a b c - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 3 +--R (- b c - 2b c - b )cos(x) + (- c - 5b c - 7b c - 3b )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 3c - 9b c - 9b c - 3b )cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 3c - 7b c - 5b c - b )cos(x) - c - 2b c - b c +--R * +--R sin(x) +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R (2a c - 2a b c)sin(x) +--R + +--R 2 2 3 3 2 2 3 4 +--R ((2b c - 4b c + 2b )cos(x) + 2c - 2b c - 2b c + 2b )sin(x) +--R + +--R 2 2 2 2 2 2 +--R (4a c - 4a b )cos(x) + (6a c + 2a b c - 8a b )cos(x) + 2a c +--R + +--R 2 +--R 2a b c - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 3 2 2 3 2 +--R (4b c - 4b c)cos(x) + (4c + 4b c - 4b c - 4b )cos(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R (6c + 2b c - 2b c - 6b )cos(x) + 2c + 2b c - 2b c - 2b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 2 2 3 +--R (2a c + 2a b c - 4a b )cos(x) + (6a c + 2a b c - 8a b )cos(x) +--R + +--R 2 2 2 2 +--R (6a c - 2a b c - 4a b )cos(x) + (2a c - 2a b c)cos(x) +--R * +--R sin(x) +--R + +--R 2 3 5 3 2 2 3 4 +--R (2b c - 2b )cos(x) + (2c + 6b c - 2b c - 6b )cos(x) +--R + +--R 3 2 2 3 3 3 2 2 3 2 +--R (6c + 6b c - 6b c - 6b )cos(x) + (6c + 2b c - 6b c - 2b )cos(x) +--R + +--R 3 2 +--R (2c - 2b c)cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R 4a c sin(x) +--R + +--R 2 2 2 2 4 +--R ((- 2a c + 4a b c - 2a b )cos(x) + 2a c - 2a b )sin(x) +--R + +--R 2 2 3 2 2 +--R (- 2b c + 4a c + 2b + 4a b)cos(x) +--R + +--R 3 2 2 2 3 2 3 2 +--R (- 2c - 2b c + (2b + 4a )c + 2b + 8a b)cos(x) - 2c + 2b c +--R + +--R 2 +--R 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 2 2 2 +--R (- 2a c - 6a b )cos(x) + (- 2a c - 8a b c - 6a b )cos(x) +--R + +--R 2 2 2 2 +--R (- 2a c - 8a b c + 2a b )cos(x) - 2a c + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 3 2 4 +--R (- 2b c + (- 4b + 4a )c - 2b + 8a b)cos(x) +--R + +--R 3 2 2 2 3 2 3 +--R (- 2c - 10b c + (- 14b + 12a )c - 6b + 16a b)cos(x) +--R + +--R 3 2 2 2 3 2 2 +--R (- 6c - 18b c + (- 18b + 12a )c - 6b + 8a b)cos(x) +--R + +--R 3 2 2 2 3 3 2 2 +--R (- 6c - 14b c + (- 10b + 4a )c - 2b )cos(x) - 2c - 4b c - 2b c +--R * +--R sin(x) +--R + +--R 2 5 2 2 4 +--R (4a b c + 4a b )cos(x) + (4a c + 16a b c + 12a b )cos(x) +--R + +--R 2 2 3 +--R (12a c + 24a b c + 12a b )cos(x) +--R + +--R 2 2 2 2 +--R (12a c + 16a b c + 4a b )cos(x) + (4a c + 4a b c)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 5 +--R (2a c + 2a b c)sin(x) +--R + +--R 2 3 3 2 2 3 4 +--R ((2b c - 2b )cos(x) + 2c + 2b c - 2b c - 2b )sin(x) +--R + +--R 2 2 2 2 2 +--R (4a c + 8a b c + 4a b )cos(x) + (6a c + 14a b c + 8a b )cos(x) +--R + +--R 2 2 +--R 2a c + 6a b c + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 3 2 2 3 2 +--R (4b c + 4b c)cos(x) + (4c + 12b c + 12b c + 4b )cos(x) +--R + +--R 3 2 2 3 3 2 2 3 +--R (6c + 14b c + 14b c + 6b )cos(x) + 2c + 6b c + 6b c + 2b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 +--R (2a c + 6a b c + 4a b )cos(x) +--R + +--R 2 2 3 +--R (6a c + 14a b c + 8a b )cos(x) +--R + +--R 2 2 2 2 +--R (6a c + 10a b c + 4a b )cos(x) + (2a c + 2a b c)cos(x) +--R * +--R sin(x) +--R + +--R 2 2 3 5 3 2 2 3 4 +--R (2b c + 4b c + 2b )cos(x) + (2c + 10b c + 14b c + 6b )cos(x) +--R + +--R 3 2 2 3 3 +--R (6c + 18b c + 18b c + 6b )cos(x) +--R + +--R 3 2 2 3 2 3 2 2 +--R (6c + 14b c + 10b c + 2b )cos(x) + (2c + 4b c + 2b c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 4 +--R ((- a c + a b )cos(x) - a c + a b )sin(x) +--R + +--R 2 2 3 2 2 +--R (- b c - 2a c + b - 2a b)cos(x) +--R + +--R 3 2 2 2 3 2 3 2 2 2 +--R (- c - b c + (b - 4a )c + b - 4a b)cos(x) - c + (b - 2a )c - 2a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 3 2 2 2 +--R (- a c - 4a b c - 3a b )cos(x) + (- 5a c - 12a b c - 7a b )cos(x) +--R + +--R 2 2 2 2 +--R (- 7a c - 12a b c - 5a b )cos(x) - 3a c - 4a b c - a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 3 2 2 3 3 +--R (- b c - 2b c - b )cos(x) + (- c - 5b c - 7b c - 3b )cos(x) +--R + +--R 3 2 2 3 2 +--R (- 3c - 9b c - 9b c - 3b )cos(x) +--R + +--R 3 2 2 3 3 2 2 +--R (- 3c - 7b c - 5b c - b )cos(x) - c - 2b c - b c +--R * +--R sin(x) +--R / +--R 3 2 2 3 3 2 +--R (2a c - 2a b c - 2a b c + 2a b )cos(x) + 2a c - 2a b c +--R + +--R 2 3 +--R - 2a b c + 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (2b c + (- 2b + 4a )c - 2b c + 2b - 4a b )cos(x) +--R + +--R 4 2 2 2 4 2 2 4 3 +--R (2c + (- 4b + 8a )c + 2b - 8a b )cos(x) + 2c - 2b c +--R + +--R 2 2 2 3 2 2 +--R (- 2b + 4a )c + 2b c - 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 3 +--R (2a c + 6a b c - 2a b c - 6a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (10a c + 14a b c - 10a b c - 14a b )cos(x) +--R + +--R 3 2 2 3 3 2 +--R (14a c + 10a b c - 14a b c - 10a b )cos(x) + 6a c + 2a b c +--R + +--R 2 3 +--R - 6a b c - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R (2b c + 2b c - 2b c - 2b )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2c + 8b c + 4b c - 8b c - 6b )cos(x) +--R + +--R 4 3 3 4 2 +--R (6c + 12b c - 12b c - 6b )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 2 2 +--R (6c + 8b c - 4b c - 8b c - 2b )cos(x) + 2c + 2b c - 2b c +--R + +--R 3 +--R - 2b c +--R * +--R sin(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 2 2 2 4 +--R ((4a c - 4a b )cos(x) + 4a c - 4a b )sin(x) +--R + +--R 2 3 3 3 2 +--R (4a b c + 8a c - 4a b + 8a b)cos(x) +--R + +--R 3 2 2 3 3 3 +--R (4a c + 4a b c + (- 4a b + 16a )c - 4a b + 16a b)cos(x) +--R + +--R 3 2 3 3 +--R 4a c + (- 4a b + 8a )c + 8a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 2 3 +--R (4a c + 16a b c + 12a b )cos(x) +--R + +--R 2 2 2 2 2 2 +--R (20a c + 48a b c + 28a b )cos(x) +--R + +--R 2 2 2 2 2 2 2 2 2 2 +--R (28a c + 48a b c + 20a b )cos(x) + 12a c + 16a b c + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 4 +--R (4a b c + 8a b c + 4a b )cos(x) +--R + +--R 3 2 2 3 3 +--R (4a c + 20a b c + 28a b c + 12a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (12a c + 36a b c + 36a b c + 12a b )cos(x) +--R + +--R 3 2 2 3 3 2 +--R (12a c + 28a b c + 20a b c + 4a b )cos(x) + 4a c + 8a b c +--R + +--R 2 +--R 4a b c +--R * +--R sin(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 3 2 +--R (2a c + 2a b c - 2a b c - 2a b )cos(x) + 2a c + 2a b c +--R + +--R 2 3 +--R - 2a b c - 2a b +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 2 3 2 4 2 2 2 +--R (2b c + (2b + 4a )c + (- 2b + 8a b)c - 2b + 4a b )cos(x) +--R + +--R 4 3 2 2 3 2 4 2 2 +--R (2c + 4b c + 8a c + (- 4b + 16a b)c - 2b + 8a b )cos(x) +--R + +--R 4 3 2 2 2 3 2 2 2 +--R 2c + 2b c + (- 2b + 4a )c + (- 2b + 8a b)c + 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 3 2 2 3 3 +--R (2a c + 10a b c + 14a b c + 6a b )cos(x) +--R + +--R 3 2 2 3 2 +--R (10a c + 34a b c + 38a b c + 14a b )cos(x) +--R + +--R 3 2 2 3 3 2 +--R (14a c + 38a b c + 34a b c + 10a b )cos(x) + 6a c + 14a b c +--R + +--R 2 3 +--R 10a b c + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 4 4 +--R (2b c + 6b c + 6b c + 2b )cos(x) +--R + +--R 4 3 2 2 3 4 3 +--R (2c + 12b c + 24b c + 20b c + 6b )cos(x) +--R + +--R 4 3 2 2 3 4 2 +--R (6c + 24b c + 36b c + 24b c + 6b )cos(x) +--R + +--R 4 3 2 2 3 4 4 3 2 2 +--R (6c + 20b c + 24b c + 12b c + 2b )cos(x) + 2c + 6b c + 6b c +--R + +--R 3 +--R 2b c +--R * +--R sin(x) +--R * +--R x +--R tan(-) +--R 2 +--R Type: Expression(Integer) +--E 253 + +)clear all + + +--S 254 of 526 +t0849:= (A+C*sin(x))/(a+b*cos(x)+c*sin(x)) +--R +--R +--R C sin(x) + A +--R (1) ----------------------- +--R c sin(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 254 + +--S 255 of 526 +r0849:= c*C*x/(b^2+c^2)+2*(A-a*c*C/(b^2+c^2))*_ + atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(1/2)-_ + b*C*log(a+b*cos(x)+c*sin(x))/(b^2+c^2) +--R +--R +--R (2) +--R +--------------+ +--R | 2 2 2 +--R - C b\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R x +--R (b - a)tan(-) - c +--------------+ +--R 2 2 2 | 2 2 2 +--R (- 2A c + 2C a c - 2A b )atan(-----------------) + C c x\|- c - b + a +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression(Integer) +--E 255 + +--S 256 of 526 +a0849:= integrate(t0849,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (- A c + C a c - A b ) +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +------------+ +--R | 2 2 2 2 +--R C b\|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R - C b\|c + b - a log(----------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R C c x\|c + b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|c + b - a +--R , +--R +--R +--------------+ +--R | 2 2 2 2 +--R C b\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R - C b\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c - 2C a c + 2A b ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R +--------------+ +--R | 2 2 2 +--R C c x\|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 256 + +--S 257 of 526 +m0849a:= a0849.1-r0849 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 | 2 2 2 +--R (- A c + C a c - A b )\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R C b\|- c - b + a \|c + b - a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2 +--R C b\|- c - b + a \|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R - C b\|- c - b + a \|c + b - a log(----------------------------) +--R cos(x) + 1 +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 2 | 2 2 2 2 +--R (2A c - 2C a c + 2A b )\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c + b )\|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 257 + +--S 258 of 526 +d0849a:= D(m0849a,x) +--R +--R +--R (5) +--R 3 2 2 2 3 2 2 3 +--R (- A b + 2A a b - A a b)c + (C a b - 2C a b + C a b)c +--R + +--R 5 4 2 3 +--R - A b + 2A a b - A a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + (- 2A a b + A a )c +--R + +--R 2 2 3 2 4 3 2 2 +--R (- C a b + 2C a b - C a )c + (A b - 2A a b + A a b )c +--R * +--R cos(x) +--R + +--R 5 4 2 3 +--R - A c + C a c - A b c +--R * +--R sin(x) +--R + +--R 4 2 3 3 2 2 +--R (- 2A b + A a)c + (2C a b - C a )c + (- 3A b + 2A a b )c +--R + +--R 3 2 2 5 4 +--R (C a b - C a b )c - A b + A a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 +--R - 2A b c + 2C a b c + (- 3A b + A a b)c +--R + +--R 3 3 5 2 3 +--R (C a b - C a b)c - A b + A a b +--R * +--R cos(x) +--R + +--R 4 2 3 2 2 2 2 2 3 +--R - A a c + C a c + (- 2A a b + A a b)c + (C a b - C a b)c +--R + +--R 4 2 3 +--R - A a b + A a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 3 2 2 2 +--R 2A c - 2C a c + (4A b - 2A a b)c + (- 2C a b + 2C a b)c +--R + +--R 4 3 +--R (2A b - 2A a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 +--R (- 2A b + 2A a)c + (2C a b - 2C a )c +--R + +--R 3 2 2 +--R (- 2A b + 2A a b )c +--R * +--R sin(x) +--R + +--R 5 4 2 3 2 2 2 +--R 2A c - 2C a c + (4A b - 2A a b)c + (- 2C a b + 2C a b)c +--R + +--R 4 3 +--R (2A b - 2A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 +--R 2A c - 2C a c + (2A b + 2A a b - 2A a )c +--R + +--R 2 3 2 3 2 2 +--R (- 2C a b + 2C a )c + (2A a b - 2A a b )c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 3 2 2 3 3 +--R 2A b c - 2C a b c + (3A b - A a b)c + (- C a b + C a b)c +--R + +--R 5 2 3 +--R A b - A a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + (- 2A a b + A a )c +--R + +--R 2 2 3 2 4 3 2 2 +--R (- C a b + 2C a b - C a )c + (A b - 2A a b + A a b )c +--R * +--R cos(x) +--R + +--R 5 4 2 3 2 2 2 +--R - A c + C a c + (- 3A b + 2A a b)c + (2C a b - 2C a b)c +--R + +--R 4 3 +--R (- 2A b + 2A a b )c +--R * +--R sin(x) +--R + +--R 4 2 3 3 2 3 2 2 5 4 +--R (A a c - C a c + A b c + (- C a b + C a b )c + A b - A a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 2 3 2 2 3 5 +--R (- A b + 2A a b - A a b)c + (C a b - 2C a b + C a b)c - A b +--R + +--R 4 2 3 +--R 2A a b - A a b +--R * +--R cos(x) +--R + +--R 4 2 3 2 2 2 2 2 3 +--R - A a c + C a c + (- 2A a b + A a b)c + (C a b - C a b)c +--R + +--R 4 2 3 +--R - A a b + A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- A b - A a b + A a )c +--R + +--R 2 3 3 4 3 3 2 +--R (C a b - C a )c + (A b - 2A a b + A a b)c +--R + +--R 4 2 3 3 2 4 6 5 +--R (- C a b + C a b + C a b - C a b)c + A b - A a b +--R + +--R 2 4 3 3 +--R - A a b + A a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R - A c + C a c + (- A b - A a b + A a )c + (C a b - C a )c +--R + +--R 4 3 3 2 +--R (A b - 2A a b + A a b)c +--R + +--R 4 2 3 3 2 4 6 5 2 4 +--R (- C a b + C a b + C a b - C a b)c + A b - A a b - A a b +--R + +--R 3 3 +--R A a b +--R * +--R sin(x) +--R + +--R 5 2 4 +--R (- 2A b + A a)c + (2C a b - C a )c +--R + +--R 3 2 2 3 3 +--R (- 4A b + 2A a b + 2A a b - A a )c +--R + +--R 3 2 2 3 4 2 +--R (2C a b - C a b - 2C a b + C a )c +--R + +--R 5 4 2 3 3 2 +--R (- 2A b + A a b + 2A a b - A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 3 +--R - 2A b c + 2C a b c + (- 4A b + 2A a b)c +--R + +--R 3 3 2 5 2 3 +--R (2C a b - 2C a b)c + (- 2A b + 2A a b )c +--R * +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R - A a c + C a c + (- 2A a b + A a )c + (C a b - C a )c +--R + +--R 4 3 2 +--R (- A a b + A a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 2 4 2 3 3 +--R 2A c - 2C a c + (4A b - 2A a )c + (- 2C a b + 2C a )c +--R + +--R 4 2 2 2 +--R (2A b - 2A a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 +--R (- 2A b + 2A a)c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 3 +--R (- 4A b + 4A a b + 2A a b - 2A a )c +--R + +--R 3 2 2 3 4 2 +--R (2C a b - 2C a b - 2C a b + 2C a )c +--R + +--R 5 4 2 3 3 2 +--R (- 2A b + 2A a b + 2A a b - 2A a b )c +--R * +--R sin(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 2A c - 2C a c + (4A b - 2A a )c + (- 2C a b + 2C a )c +--R + +--R 4 2 2 2 +--R (2A b - 2A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R 2A c - 2C a c + (4A b - 2A a )c + (- 2C a b + 2C a )c +--R + +--R 4 2 2 2 +--R (2A b - 2A a b )c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 3 2 3 3 3 2 +--R 2A b c - 2C a b c + (4A b - 2A a b)c + (- 2C a b + 2C a b)c +--R + +--R 5 2 3 +--R (2A b - 2A a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 2 2 4 2 3 3 +--R - A c + C a c + (- A b - A a b + A a )c + (C a b - C a )c +--R + +--R 4 3 3 2 +--R (A b - 2A a b + A a b)c +--R + +--R 4 2 3 3 2 4 6 5 2 4 +--R (- C a b + C a b + C a b - C a b)c + A b - A a b - A a b +--R + +--R 3 3 +--R A a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- 3A b + A a b + A a )c +--R + +--R 2 2 3 3 4 3 2 2 3 2 +--R (2C a b - C a b - C a )c + (- 3A b + 2A a b + 2A a b - A a b)c +--R + +--R 4 2 3 3 2 4 6 5 2 4 3 3 +--R (C a b - C a b - C a b + C a b)c - A b + A a b + A a b - A a b +--R * +--R sin(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R A a c - C a c + (2A a b - A a )c + (- C a b + C a )c +--R + +--R 4 3 2 +--R (A a b - A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 4 2 3 3 2 2 4 2 +--R - A a c + C a c + (- 2A a b + A a )c + (C a b - C a )c +--R + +--R 4 3 2 +--R (- A a b + A a b )c +--R / +--R 2 2 4 4 3 2 2 2 2 +--R ((b - 2a b + a )c + (b - 2a b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 3a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (b - 3a b + 3a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 3 +--R (- b + a)c + (- 2b + 4a b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + 3a b - 3a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 3 3 +--R ((- b + a b)c + (- b + 2a b - a b)c - a b + 2a b - a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 2 2 3 4 2 6 +--R (- b + a )c + (- 2b + 2a b - a b + 2a b - a )c - b +--R + +--R 5 2 4 3 3 4 2 +--R 2a b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 2 5 2 4 3 3 +--R (- a b + a )c + (- 2a b + 3a b - a b)c - a b + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c )sin(x) +--R + +--R 6 2 4 4 3 2 2 2 +--R (2c + (4a b - 2a )c + (- 2b + 4a b - 2a b )c )cos(x) +--R + +--R 6 2 2 4 4 3 2 2 2 +--R 2c + (4b - 4a b + 2a )c + (2b - 4a b + 2a b )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 4 2 3 2 +--R (2b c + (2b + 2a b - 2a b)c + (2a b - 2a b )c)cos(x) +--R + +--R 5 3 2 3 3 +--R (2b + 2a)c + (4b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 +--R (2b - 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 5 2 2 3 4 2 3 +--R 2a c + (4a b - 2a b)c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 2 2 +--R ((- b + a )c + (- b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (b + a)c + (2a b + a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + a b + a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 3 5 4 2 3 3 2 +--R (b + a)c + (2b - a b + a )c + (b - a b - a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 3 2 5 3 3 2 +--R ((b + a b)c + (b + 2a b - a b)c + a b - a b )cos(x) +--R + +--R 2 2 4 4 3 2 2 4 2 6 4 2 +--R ((b + 2a b + a )c + (2b + 2a b + a b - a )c + b - a b )cos(x) +--R + +--R 2 4 3 2 2 3 2 5 3 3 +--R (a b + a )c + (2a b + a b - a b)c + a b - a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b - 2a b + a )c + (2b - 4a b + a b + 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b - 2a b + 2a b - a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (- b + a)c + (- b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 6 3 4 4 3 +--R (b - 3a b + 2a b + a b - a b)c + b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 +--R (- b + a)c + (- 2b + 3a b - a b)c +--R + +--R 5 4 2 3 4 5 2 6 2 5 4 3 5 2 +--R (- b + 3a b - 3a b + 2a b - a )c + a b - 2a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b + a b)c + (- 2b + 2a b + a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (- b + a b + a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b + a )c + (- 2a b + 2a b + a b - a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- a b + a b + a b - a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (- 2b + 2a)c + (- 4b + 4a b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 3 +--R 2c + (2b + 2a b - 2a )c + (- 2b + 4a b - 2a b)c +--R + +--R 6 5 2 4 3 3 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 7 2 5 4 3 2 2 3 4 3 +--R 2c + (4b - 2a b)c + (2b - 4a b + 2a b + 2a b - 2a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- 2a b + 2a b + 2a b - 2a b )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 2 2 +--R (2b c + (4b - 2a b)c + (2b - 2a b )c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (2b + 2a)c + (4b + 4a b - 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (2b + 2a b - 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 2 +--R 2a c + (4a b - 2a )c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c)sin(x) +--R + +--R 6 3 2 3 4 +--R (b + a)c + (b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 2 5 4 3 +--R (- b + a b + 2a b - a b - a b)c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 5 4 2 3 3 2 5 2 +--R (b + a)c + (2b + a b - a b)c + (b - a b - a b + 2a b - a )c +--R + +--R 6 3 4 5 2 +--R - a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b + a b)c + (2b + 2a b - a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (b + a b - a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b + 2a b + a )c + (2b + 4a b + a b - 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b + 2a b - 2a b - a b )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 5 2 4 3 3 4 2 +--R (a b + a )c + (2a b + 2a b - a b - a )c + (a b + a b - a b - a b )c +--R Type: Expression(Integer) +--E 258 + +--S 259 of 526 +m0849b:= a0849.2-r0849 +--R +--R +--R (6) +--R +--------------+ +--R | 2 2 2 +--R C b\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +--R | 2 2 2 2 +--R C b\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R - C b\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c - 2C a c + 2A b ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R (2A c - 2C a c + 2A b )atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 526 +d0849b:= D(m0849b,x) +--R +--R +--R (7) +--R 2 2 3 2 2 +--R ((- A b + A a)c + (C a b - C a )c - A b + A a b )sin(x) +--R + +--R 3 2 2 3 2 2 +--R ((- 2A c + 2C a c - 2A b c)cos(x) - 2A c + 2C a c - 2A b c)sin(x) +--R + +--R 2 2 3 2 2 +--R ((- 3A b + A a)c + (3C a b - C a )c - 3A b + A a b )cos(x) +--R + +--R 2 3 2 +--R (- 4A b c + 4C a b c - 4A b )cos(x) + (- A b - A a)c +--R + +--R 2 3 2 +--R (C a b + C a )c - A b - A a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 3 2 2 2 +--R (4A c - 4C a c + 4A b c)sin(x) + (4A c - 4C a c + 4A b c)cos(x) +--R + +--R 3 2 2 +--R (4A c - 4C a c + 4A b c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 2 +--R ((3A b + A a)c + (- 3C a b - C a )c + 3A b + A a b )sin(x) +--R + +--R 3 2 2 3 2 2 +--R ((- 2A c + 2C a c - 2A b c)cos(x) - 2A c + 2C a c - 2A b c)sin(x) +--R + +--R 2 2 3 2 2 +--R ((A b + A a)c + (- C a b - C a )c + A b + A a b )cos(x) +--R + +--R 2 2 3 2 +--R (- A b - A a)c + (C a b + C a )c - A b - A a b +--R / +--R 2 2 2 4 3 2 2 2 +--R ((b - 2a b + a )c + b - 2a b + a b )sin(x) +--R + +--R 3 3 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)cos(x) + (- 2b + 2a)c +--R + +--R 3 2 +--R (- 2b + 2a b )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 2 4 2 2 +--R ((- 2b + 2a )c - 2b + 2a b )cos(x) + (- b + a )c - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)sin(x) +--R + +--R 4 2 2 4 2 2 +--R ((4c + 4b c )cos(x) + 4c + 4b c )sin(x) +--R + +--R 3 3 2 2 +--R ((2b + 2a)c + (2b + 2a b )c)cos(x) +--R + +--R 3 3 2 3 3 2 +--R ((4b + 4a)c + (4b + 4a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )sin(x) +--R + +--R 3 3 2 3 3 2 +--R (((2b + 2a)c + (2b + 2a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c) +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 2 2 2 +--R ((b + 2a b + a )c + b + 2a b + a b )cos(x) +--R + +--R 2 2 2 4 3 2 2 2 2 2 +--R ((2b + 4a b + 2a )c + 2b + 4a b + 2a b )cos(x) + (b + 2a b + a )c +--R + +--R 4 3 2 2 +--R b + 2a b + a b +--R Type: Expression(Integer) +--E 260 + +)clear all + + +--S 261 of 526 +t0850:= (A+C*sin(x))/(a+b*cos(x)+c*sin(x))^2 +--R +--R +--R C sin(x) + A +--R (1) --------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a +--R Type: Expression(Integer) +--E 261 + +--S 262 of 526 +r0850:= 2*(a*A-c*C)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ + (a^2-b^2-c^2)^(3/2)-(b*C-(A*c-a*C)*cos(x)+A*b*sin(x))/_ + (a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (2) +--R 2 2 +--R ((- 2C c + 2A a c)sin(x) + (- 2C b c + 2A a b)cos(x) - 2C a c + 2A a ) +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (A b sin(x) + (- A c + C a)cos(x) + C b)\|- c - b + a +--R / +--R 3 2 2 2 3 2 2 2 3 +--R ((c + (b - a )c)sin(x) + (b c + b - a b)cos(x) + a c + a b - a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 262 + +--S 263 of 526 +a0850:= integrate(t0850,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R ((C b - C a)c + (- A a b + A a )c)sin(x) +--R + +--R 2 2 2 2 2 +--R ((C b - C a b)c - A a b + A a b)cos(x) + (C a b - C a )c - A a b +--R + +--R 3 +--R A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 2 2 +--R (A c + (C b - C a)c + A b - A a b)sin(x) +--R + +--R 2 2 2 2 +--R (A a c + C b - C a )cos(x) + A a c + C b - C a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 2 2 +--R ((2C b - 2C a)c + (- 2A a b + 2A a )c)sin(x) +--R + +--R 2 2 2 2 +--R ((2C b - 2C a b)c - 2A a b + 2A a b)cos(x) + (2C a b - 2C a )c +--R + +--R 2 3 +--R - 2A a b + 2A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 2 2 +--R (A c + (C b - C a)c + A b - A a b)sin(x) +--R + +--R 2 2 2 2 +--R (A a c + C b - C a )cos(x) + A a c + C b - C a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 263 + +--S 264 of 526 +m0850a:= a0850.1-r0850 +--R +--R +--R (4) +--R +--------------+ +--R 2 | 2 2 2 +--R ((C b - C a)c - A a b + A a )\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 | 2 2 2 2 +--R ((2C b - 2C a)c - 2A a b + 2A a )\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (A c + C b - C a)\|- c - b + a \|c + b - a +--R / +--R +--------------+ +------------+ +--R 2 3 2 2 3 | 2 2 2 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 264 + +--S 265 of 526 +d0850a:= D(m0850a,x) +--R +--R +--R (5) +--R 3 2 2 3 2 2 3 2 +--R ((- C b + 2C a b - C a b)c + A a b - 2A a b + A a b)sin(x) +--R + +--R 4 3 2 2 2 +--R - C c + A a c + (C b - 2C a b + C a )c +--R + +--R 2 2 3 +--R (- A a b + 2A a b - A a )c +--R * +--R cos(x) +--R + +--R 4 3 +--R - C c + A a c +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (- 2C b + C a)c + (2A a b - A a )c + (- C b + C a b )c +--R + +--R 3 2 2 +--R A a b - A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 3 2 3 3 +--R (- 2C b c + 2A a b c + (- C b + C a b)c + A a b - A a b) +--R * +--R cos(x) +--R + +--R 3 2 2 2 2 2 2 3 +--R - C a c + A a c + (- C a b + C a b)c + A a b - A a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 2 2 +--R (2C c - 2A a c + (2C b - 2C a b)c + (- 2A a b + 2A a b)c) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 +--R ((- 2C b + 2C a)c + (2A a b - 2A a )c )sin(x) +--R + +--R 4 3 2 2 2 2 +--R (2C c - 2A a c + (2C b - 2C a b)c + (- 2A a b + 2A a b)c) +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 2 3 +--R (2C c - 2A a c + (2C a b - 2C a )c + (- 2A a b + 2A a )c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 3 2 3 3 2 +--R (2C b c - 2A a b c + (C b - C a b)c - A a b + A a b)sin(x) +--R + +--R 4 3 2 2 2 +--R - C c + A a c + (C b - 2C a b + C a )c +--R + +--R 2 2 3 +--R (- A a b + 2A a b - A a )c +--R * +--R cos(x) +--R + +--R 4 3 2 2 2 2 +--R - C c + A a c + (- 2C b + 2C a b)c + (2A a b - 2A a b)c +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 3 2 2 2 +--R (C a c - A a c + (C b - C a b )c - A a b + A a b )cos(x) +--R + +--R 3 2 2 3 2 2 3 +--R ((- C b + 2C a b - C a b)c + A a b - 2A a b + A a b)cos(x) +--R + +--R 3 2 2 2 2 2 2 3 +--R - C a c + A a c + (- C a b + C a b)c + A a b - A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 5 4 2 3 2 3 2 +--R C c - A a c + (C a b - C a )c + (- A a b + A a )c +--R + +--R 4 3 2 2 3 4 2 3 +--R (- C b + C a b + C a b - C a b)c + A a b - A a b +--R + +--R 3 2 4 +--R - A a b + A a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 2 3 2 +--R C c - A a c + (C a b - C a )c + (- A a b + A a )c +--R + +--R 4 3 2 2 3 4 2 3 3 2 +--R (- C b + C a b + C a b - C a b)c + A a b - A a b - A a b +--R + +--R 4 +--R A a b +--R * +--R sin(x) +--R + +--R 4 2 3 +--R (2C b - C a)c + (- 2A a b + A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - C a b - 2C a b + C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A a b + A a b + 2A a b - A a )c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 3 3 +--R (2C b c - 2A a b c + (2C b - 2C a b)c + (- 2A a b + 2A a b)c) +--R * +--R cos(x) +--R + +--R 4 2 3 2 3 2 2 2 4 +--R C a c - A a c + (C a b - C a )c + (- A a b + A a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 2 3 2 3 2 +--R (- 2C c + 2A a c + (- 2C b + 2C a )c + (2A a b - 2A a )c ) +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 +--R (2C b - 2C a)c + (- 2A a b + 2A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - 2C a b - 2C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A a b + 2A a b + 2A a b - 2A a )c +--R * +--R sin(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R (- 2C c + 2A a c + (- 2C b + 2C a )c + (2A a b - 2A a )c ) +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 2 3 2 +--R (- 2C c + 2A a c + (- 2C b + 2C a )c + (2A a b - 2A a )c )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 3 2 2 3 3 +--R (- 2C b c + 2A a b c + (- 2C b + 2C a b)c + (2A a b - 2A a b)c) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 2 3 2 +--R C c - A a c + (C a b - C a )c + (- A a b + A a )c +--R + +--R 4 3 2 2 3 4 2 3 3 2 +--R (- C b + C a b + C a b - C a b)c + A a b - A a b - A a b +--R + +--R 4 +--R A a b +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 +--R C c - A a c + (2C b - C a b - C a )c +--R + +--R 2 2 3 2 4 3 2 2 3 +--R (- 2A a b + A a b + A a )c + (C b - C a b - C a b + C a b)c +--R + +--R 4 2 3 3 2 4 +--R - A a b + A a b + A a b - A a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 2 2 4 2 +--R (- C a c + A a c + (- C a b + C a )c + (A a b - A a )c)cos(x) +--R + +--R 4 2 3 2 3 2 2 2 4 +--R C a c - A a c + (C a b - C a )c + (- A a b + A a )c +--R / +--R 2 2 4 4 3 3 4 2 2 +--R ((b - 2a b + a )c + (b - 2a b + 2a b - a )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 4a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 +--R (- b + a)c + (- 2b + 4a b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 +--R (- b + a b)c + (- b + 3a b - 2a b)c - a b + 2a b +--R + +--R 4 2 5 +--R - 2a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 5 +--R (- b + a )c + (- 2b + 2a b + 2a b - 2a )c - b + 2a b +--R + +--R 2 4 4 2 5 6 +--R - a b + a b - 2a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 4 2 5 2 4 4 2 +--R (- a b + a )c + (- 2a b + 3a b - a )c - a b + 2a b - 2a b +--R + +--R 5 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 2 3 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c )sin(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R (2c + (4a b - 4a )c + (- 2b + 4a b - 4a b + 2a )c )cos(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R 2c + (4b - 4a b)c + (2b - 4a b + 4a b - 2a )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 +--R 2b c + (2b + 2a b - 4a b)c +--R + +--R 4 2 3 3 2 4 +--R (2a b - 2a b - 2a b + 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 3 5 4 4 5 +--R ((2b + 2a)c + (4b - 4a )c + (2b - 2a b - 2a b + 2a )c)cos(x) +--R + +--R 5 2 2 3 3 4 2 3 3 2 4 +--R 2a c + (4a b - 2a b - 2a )c + (2a b - 2a b - 2a b + 2a b)c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((- b + a )c + (- b + 2a b - a )c )sin(x) +--R + +--R 5 2 3 3 +--R (b + a)c + (2a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + a b + 2a b - 2a b - a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 +--R (b + a)c + (2b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - a b - 2a b + 2a b + a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 2 2 3 2 5 3 3 5 +--R ((b + a b)c + (b + 2a b - a b - 2a b)c + a b - 2a b + a b) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 2 4 +--R (b + 2a b + a )c + (2b + 2a b - 2a b - 2a )c + b - a b +--R + +--R 4 2 6 +--R - a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 4 2 5 3 3 5 +--R (a b + a )c + (2a b + a b - 2a b - a )c + a b - 2a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b + 2a b - a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b + 2a b + a b - 4a b + a b + 2a b - a )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (b - 3a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 6 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c - b + 2a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R a b - 4a b + a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (2b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 2 5 3 4 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c - a b + 2a b + a b +--R + +--R 4 3 5 2 6 7 +--R - 4a b + a b + 2a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b - a b)c + (2b - 2a b - 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b - a b - 2a b + 2a b + a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (a b - a )c + (2a b - 2a b - 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (a b - a b - 2a b + 2a b + a b - a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (2b - 2a)c + (4b - 4a b - 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 2b - 2a b + 4a )c + (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a b)c +--R * +--R cos(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 4b + 2a b + 2a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 4 2 2 +--R (- 2b c + (- 4b + 4a b)c + (- 2b + 4a b - 2a b)c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- 2b - 2a)c + (- 4b - 4a b + 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 2b - 2a b + 4a b + 4a b - 2a b - 2a )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 5 2 +--R - 2a c + (- 4a b + 4a )c + (- 2a b + 4a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 2 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c)sin(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- b - 2a b + a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 2 5 4 3 6 +--R (b - a b - 2a b + 2a b + a b - a )c + b - 3a b + 3a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- 2b - a b + 2a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 3 4 5 2 7 +--R (- b + a b + 2a b - 2a b - a b + a )c + a b - 3a b + 3a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b - a b)c + (- 2b - 2a b + 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b - a b + 2a b + 2a b - a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b - 2a b - a )c + (- 2b - 4a b + 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b - 2a b + a b + 4a b + a b - 2a b - a )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b - a )c + (- 2a b - 2a b + 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- a b - a b + 2a b + 2a b - a b - a )c +--R Type: Expression(Integer) +--E 265 + +--S 266 of 526 +m0850b:= a0850.2-r0850 +--R +--R +--R (6) +--R 2 +--R ((2C b - 2C a)c - 2A a b + 2A a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 +--R ((2C b - 2C a)c - 2A a b + 2A a )atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (A c + C b - C a)\|- c - b + a +--R / +--R +--------------+ +--R 2 3 2 2 3 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a +--R Type: Expression(Integer) +--E 266 + +--S 267 of 526 +d0850b:= D(m0850b,x) +--R +--R +--R (7) +--R 2 2 +--R ((- C b + C a)c + A a b - A a )sin(x) +--R + +--R 2 2 +--R ((- 2C c + 2A a c)cos(x) - 2C c + 2A a c)sin(x) +--R + +--R 2 2 +--R ((- 3C b + C a)c + 3A a b - A a )cos(x) + (- 4C b c + 4A a b)cos(x) +--R + +--R 2 +--R (- C b - C a)c + A a b + A a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 +--R (4C c - 4A a c)sin(x) + (4C c - 4A a c)cos(x) +--R + +--R 2 +--R (4C c - 4A a c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 +--R ((3C b + C a)c - 3A a b - A a )sin(x) +--R + +--R 2 2 +--R ((- 2C c + 2A a c)cos(x) - 2C c + 2A a c)sin(x) +--R + +--R 2 2 2 +--R ((C b + C a)c - A a b - A a )cos(x) + (- C b - C a)c + A a b + A a +--R / +--R 2 2 2 4 3 3 4 2 +--R ((b - 2a b + a )c + b - 2a b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 +--R (- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )cos(x) +--R + +--R 2 2 2 4 2 2 4 2 2 2 4 +--R ((- 2b + 2a )c - 2b + 4a b - 2a )cos(x) + (- b + a )c - b +--R + +--R 2 2 4 +--R 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)sin(x) +--R + +--R 4 2 2 2 4 2 2 2 +--R ((4c + (4b - 4a )c )cos(x) + 4c + (4b - 4a )c )sin(x) +--R + +--R 3 3 2 2 3 2 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 3 +--R ((4b + 4a)c + (4b + 4a b - 4a b - 4a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 3 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 3 4 2 +--R ((b + 2a b + a )c + b + 2a b - 2a b - a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R ((2b + 4a b + 2a )c + 2b + 4a b - 4a b - 2a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R (b + 2a b + a )c + b + 2a b - 2a b - a +--R Type: Expression(Integer) +--E 267 + +)clear all + + +--S 268 of 526 +t0851:= (A+C*sin(x))/(a+b*cos(x)+c*sin(x))^3 +--R +--R +--R (1) +--R C sin(x) + A +--R / +--R 3 3 2 2 2 +--R c sin(x) + (3b c cos(x) + 3a c )sin(x) +--R + +--R 2 2 2 3 3 2 2 +--R (3b c cos(x) + 6a b c cos(x) + 3a c)sin(x) + b cos(x) + 3a b cos(x) +--R + +--R 2 3 +--R 3a b cos(x) + a +--R Type: Expression(Integer) +--E 268 + +--S 269 of 526 +r0851:= (2*a^2*A+A*b^2+c*(A*c-3*a*C))*atan((c+(a-b)*tan(1/2*x))/_ + (a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(5/2)-1/2*(b*C-(A*c-a*C)*_ + cos(x)+A*b*sin(x))/(a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x))^2-_ + 1/2*(a*b*C+(2*c^2*C-a*(3*A*c-a*C))*cos(x)+b*(3*a*A-2*c*C)*_ + sin(x))/(a^2-b^2-c^2)^2/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (2) +--R 4 3 2 2 2 2 +--R (- 2A c + 6C a c + (- 2A b - 4A a )c )sin(x) +--R + +--R 3 2 3 2 3 +--R (- 4A b c + 12C a b c + (- 4A b - 8A a b)c)cos(x) - 4A a c +--R + +--R 2 2 2 3 +--R 12C a c + (- 4A a b - 8A a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 +--R (- 2A b c + 6C a b c - 2A b - 4A a b )cos(x) +--R + +--R 2 2 3 3 2 2 3 +--R (- 4A a b c + 12C a b c - 4A a b - 8A a b)cos(x) - 2A a c + 6C a c +--R + +--R 2 2 4 +--R - 2A a b - 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 2 2 +--R (2C b c - 3A a b c)sin(x) +--R + +--R 3 2 2 2 2 2 +--R (- 2C c + 3A a c + (2C b - C a )c - 3A a b )cos(x) + A b c +--R + +--R 3 2 +--R C a b c + A b - 4A a b +--R * +--R sin(x) +--R + +--R 2 2 2 +--R (- 2C b c + 3A a b c - C a b)cos(x) +--R + +--R 3 2 2 2 3 2 3 +--R (- A c - C a c + (- A b + 4A a )c - 2C a )cos(x) + C b c + C b +--R + +--R 2 +--R - 2C a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (4b - 4a )c + (2b - 4a b + 2a )c )sin(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (8b - 8a b)c + (4b - 8a b + 4a b)c)cos(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (8a b - 8a )c + (4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (4b - 4a b )c + 2b - 4a b + 2a b )cos(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (8a b - 8a b)c + 4a b - 8a b + 4a b)cos(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (4a b - 4a )c + 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 526 +a0851:= integrate(t0851,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 +--R (2A b - 4A a b + 2A a b)c +--R + +--R 3 2 2 3 2 +--R (- 6C a b + 12C a b - 6C a b)c +--R + +--R 5 4 2 3 3 2 4 +--R (2A b - 4A a b + 6A a b - 8A a b + 4A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 3 2 2 3 4 2 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 2 3 3 2 4 5 +--R (2A a b - 4A a b + 6A a b - 8A a b + 4A a )c +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 3 +--R (- A b + 2A a b - A a )c + (3C a b - 6C a b + 3C a )c +--R + +--R 2 2 3 4 2 +--R (- 2A a b + 4A a b - 2A a )c +--R + +--R 4 2 3 3 2 6 5 2 4 +--R (- 3C a b + 6C a b - 3C a b )c + A b - 2A a b + 3A a b +--R + +--R 3 3 4 2 +--R - 4A a b + 2A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 +--R (2A a b - 4A a b + 2A a b)c +--R + +--R 2 3 3 2 4 5 2 4 3 3 +--R (- 6C a b + 12C a b - 6C a b)c + 2A a b - 4A a b + 6A a b +--R + +--R 4 2 5 +--R - 8A a b + 4A a b +--R * +--R cos(x) +--R + +--R 2 2 4 2 2 3 3 +--R (A b - 2A a b + A a )c + (- 3C a b + 6C a b - 3C a )c +--R + +--R 4 3 2 2 3 4 2 +--R (A b - 2A a b + 4A a b - 6A a b + 3A a )c +--R + +--R 3 2 4 5 2 4 3 3 4 2 5 +--R (- 3C a b + 6C a b - 3C a )c + A a b - 2A a b + 3A a b - 4A a b +--R + +--R 6 +--R 2A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 4 2 3 +--R - 2A b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (- 2A b - 3A a b + 2A a b + 3A a )c +--R + +--R 3 2 2 3 4 4 2 3 +--R (- 4C a b + 7C a b - 2C a b - C a )c - 3A a b + 6A a b +--R + +--R 3 2 +--R - 3A a b +--R * +--R cos(x) +--R + +--R 4 2 3 +--R - 2A a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (A b - 4A a b - 5A a b + 8A a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- C a b - 2C a b + 7C a b - 4C a )c + A b - 2A a b +--R + +--R 2 3 3 2 4 +--R - 3A a b + 8A a b - 4A a b +--R * +--R sin(x) +--R + +--R 5 4 2 3 +--R A c + (- C b + C a)c + (3A a b - 4A a )c +--R + +--R 3 2 2 3 2 +--R (- 2C b + 7C a b - 7C a b + 2C a )c +--R + +--R 4 3 2 2 3 5 2 3 4 +--R (- A b + 3A a b - 8A a b + 6A a b)c - C b + 2C a b - C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 2 3 2 +--R (- A b - A a )c + (C a b - C a )c +--R + +--R 4 2 2 4 4 3 2 5 +--R (- A b - 3A a b + 4A a )c - 2C a b + 4C a b - 2C a +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 +--R - A c + (C b - C a)c + (- A b - 3A a b + 3A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - 6C a b + 7C a b - 3C a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 3A a b + 5A a b - 6A a b + 4A a )c + C b - 2C a b - 2C a b +--R + +--R 3 2 4 5 +--R 4C a b + C a b - 2C a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 2 2 5 5 4 3 2 4 3 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 3 2 2 3 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 2 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 3 2 4 +--R (4A b - 8A a b + 12A a b - 16A a b + 8A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 3 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 2 2 3 4 2 +--R (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 4 5 +--R (4A a b - 8A a b + 12A a b - 16A a b + 8A a )c +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 3 +--R (- 2A b + 4A a b - 2A a )c + (6C a b - 12C a b + 6C a )c +--R + +--R 2 2 3 4 2 +--R (- 4A a b + 8A a b - 4A a )c +--R + +--R 4 2 3 3 2 6 5 2 4 +--R (- 6C a b + 12C a b - 6C a b )c + 2A b - 4A a b + 6A a b +--R + +--R 3 3 4 2 +--R - 8A a b + 4A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 2 3 3 2 4 5 2 4 +--R (- 12C a b + 24C a b - 12C a b)c + 4A a b - 8A a b +--R + +--R 3 3 4 2 5 +--R 12A a b - 16A a b + 8A a b +--R * +--R cos(x) +--R + +--R 2 2 4 2 2 3 3 +--R (2A b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 3 2 2 3 4 2 +--R (2A b - 4A a b + 8A a b - 12A a b + 6A a )c +--R + +--R 3 2 4 5 2 4 3 3 4 2 +--R (- 6C a b + 12C a b - 6C a )c + 2A a b - 4A a b + 6A a b +--R + +--R 5 6 +--R - 8A a b + 4A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 4 2 3 +--R - 2A b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (- 2A b - 3A a b + 2A a b + 3A a )c +--R + +--R 3 2 2 3 4 4 2 3 +--R (- 4C a b + 7C a b - 2C a b - C a )c - 3A a b + 6A a b +--R + +--R 3 2 +--R - 3A a b +--R * +--R cos(x) +--R + +--R 4 2 3 +--R - 2A a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (A b - 4A a b - 5A a b + 8A a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- C a b - 2C a b + 7C a b - 4C a )c + A b - 2A a b +--R + +--R 2 3 3 2 4 +--R - 3A a b + 8A a b - 4A a b +--R * +--R sin(x) +--R + +--R 5 4 2 3 +--R A c + (- C b + C a)c + (3A a b - 4A a )c +--R + +--R 3 2 2 3 2 +--R (- 2C b + 7C a b - 7C a b + 2C a )c +--R + +--R 4 3 2 2 3 5 2 3 4 +--R (- A b + 3A a b - 8A a b + 6A a b)c - C b + 2C a b - C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 2 3 2 +--R (- A b - A a )c + (C a b - C a )c +--R + +--R 4 2 2 4 4 3 2 5 +--R (- A b - 3A a b + 4A a )c - 2C a b + 4C a b - 2C a +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 +--R - A c + (C b - C a)c + (- A b - 3A a b + 3A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - 6C a b + 7C a b - 3C a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 3A a b + 5A a b - 6A a b + 4A a )c + C b - 2C a b - 2C a b +--R + +--R 3 2 4 5 +--R 4C a b + C a b - 2C a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 5 5 4 3 2 4 3 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 270 + +--S 271 of 526 +m0851a:= a0851.1-r0851 +--R +--R +--R (4) +--R 3 2 2 5 +--R (2A b - 4A a b + 2A a b)c +--R + +--R 3 2 2 3 4 +--R (- 6C a b + 12C a b - 6C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (2A b - 4A a b + 6A a b - 8A a b + 4A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (2A a b - 4A a b + 6A a b - 8A a b + 4A a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 2 2 3 5 +--R (- A b + 2A a b - A a )c + (3C a b - 6C a b + 3C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (4A b - 8A a b + 2A a b + 4A a b - 2A a )c +--R + +--R 4 2 3 3 2 3 +--R (- 15C a b + 30C a b - 15C a b )c +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (5A b - 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24C a b)c + 8A a b - 16A a b +--R + +--R 5 3 6 2 7 +--R 24A a b - 32A a b + 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 3 2 4 5 3 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (2A a b - 4A a b + 8A a b - 12A a b + 6A a )c +--R + +--R 5 2 6 7 4 4 5 3 6 2 7 +--R (- 6C a b + 12C a b - 6C a )c + 2A a b - 4A a b + 6A a b - 8A a b +--R + +--R 8 +--R 4A a +--R * +--R x +--R +------------+ (b - a)tan(-) - c +--R | 2 2 2 2 +--R \|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 6 2 5 +--R - 2A b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b - 3A a b + 2A a b + 3A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- 4C b + 4C a b + 3C a b - 2C a b - C a )c +--R + +--R 4 2 3 3 2 2 +--R (3A a b - 6A a b + 3A a b )c +--R * +--R cos(x) +--R + +--R 6 2 5 +--R - 2A a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (A b - 4A a b - 5A a b + 8A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 5C a b + 6C a b + 3C a b - 4C a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (A b - 2A a b + 3A a b - 4A a b + 2A a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 2 2 5 +--R A c + (- C b + C a)c + (- 4A b + 3A a b - 4A a )c +--R + +--R 3 2 2 3 4 +--R (4C b - C a b - 5C a b + 2C a )c +--R + +--R 4 3 2 2 3 3 +--R (- 5A b - 12A a b + 14A a b + 3A a b)c +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 7C b + 4C a b + 12C a b - 8C a b - C a b)c +--R + +--R 5 2 4 3 3 +--R (3A a b - 6A a b + 3A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- A b - 8A a b - A a )c + (9C a b - 8C a b - C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- A b - 8A a b - 27A a b + 32A a b + 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 14C a b + 8C a b + 24C a b - 16C a b - 2C a )c +--R + +--R 2 4 3 3 4 2 +--R (6A a b - 12A a b + 6A a b )c +--R * +--R cos(x) +--R + +--R 7 6 2 2 5 +--R - A c + (C b - C a)c + (- A b - 3A a b - A a )c +--R + +--R 2 2 3 4 2 2 3 4 3 +--R (- 2C a b + 9C a b - 7C a )c + (- 5A a b - 15A a b + 20A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (C b - 2C a b - 8C a b + 8C a b + 11C a b - 10C a )c +--R + +--R 3 3 4 2 5 +--R (3A a b - 6A a b + 3A a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 2 5 +--R 2A b c + (- 4C b + 6C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b + 9A a b - 14A a b + 3A a )c +--R + +--R 4 2 2 3 4 3 +--R (4C b - 9C a b + 6C a b - C a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 4A b - 9A a b + 10A a b + 3A a b )c +--R + +--R 6 2 4 3 3 +--R (- 4C b + 12C a b - 8C a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 +--R 2A a c + (- 2C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (A b - 12A a b + 7A a b - 8A a )c +--R + +--R 3 2 2 3 4 3 +--R (11C a b - 6C a b - 9C a b + 4C a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (A b - 14A a b - 33A a b + 44A a b + 2A a b)c +--R + +--R 5 3 3 4 2 +--R (- 12C a b + 36C a b - 24C a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 5 +--R - 2A b c + (4C b - 6C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b - 9A a b + 2A a b - 3A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 4C a b + 21C a b - 18C a b + C a )c +--R + +--R 4 2 3 3 2 4 2 +--R (- 3A a b - 6A a b - 39A a b + 48A a b)c +--R + +--R 2 4 4 2 5 +--R (- 12C a b + 36C a b - 24C a b)c +--R * +--R cos(x) +--R + +--R 6 2 5 3 2 3 4 +--R - 2A a c + (2C a b - 2C a )c + (- A b - 7A a b + 4A a )c +--R + +--R 3 2 2 3 4 3 +--R (C a b - 6C a b + 13C a b - 8C a )c +--R + +--R 5 4 2 3 4 5 2 +--R (- A b + 2A a b - 3A a b - 14A a b + 16A a )c +--R + +--R 3 3 5 6 +--R (- 4C a b + 12C a b - 8C a )c +--R * +--R sin(x) +--R + +--R 2 5 3 2 2 4 +--R A b c + (- 3C b + 5C a b - 2C a b)c +--R + +--R 3 2 2 3 3 +--R (6A a b - 10A a b + 3A a b)c +--R + +--R 4 2 3 3 2 4 2 +--R (3C a b - 6C a b + 4C a b - C a b)c +--R + +--R 6 2 4 3 3 7 2 5 3 4 +--R (- A b - 2A a b + 3A a b )c - C b + 3C a b - 2C a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- A b + 4A a b - A a )c + (- 3C a b + 4C a b - C a )c +--R + +--R 4 2 2 3 4 3 +--R (- A b + 9A a b - 16A a b + 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b + 4C a b - 12C a b + 8C a b - 2C a )c +--R + +--R 5 2 4 3 3 4 2 6 3 4 +--R (- 4A a b - 6A a b + 4A a b + 6A a b )c - 4C a b + 12C a b +--R + +--R 4 3 +--R - 8C a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- A b + A a )c + (4C b - 7C a b + 2C a b + C a )c +--R + +--R 4 3 2 2 4 3 +--R (- A b - 6A a b + 5A a b - 4A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2C b - 6C a b + 10C a b - 2C a b - 6C a b + 2C a )c +--R + +--R 5 3 3 4 2 5 2 5 4 3 +--R (- 3A a b - 18A a b + 18A a b + 3A a b)c - 6C a b + 18C a b +--R + +--R 5 2 +--R - 12C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (A b - 4A a b + A a )c + (3C a b - 4C a b + C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (A b - 4A a b - 9A a b + 12A a b - 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b - 8C a b + 16C a b - 12C a b + 2C a )c +--R + +--R 2 4 3 3 4 2 5 3 4 5 2 +--R (- 6A a b + 8A a b - 18A a b + 16A a b)c - 4C a b + 12C a b +--R + +--R 6 +--R - 8C a b +--R * +--R cos(x) +--R + +--R 2 5 3 2 3 4 +--R - A a c + (- C b + 2C a b - C a )c +--R + +--R 2 2 3 4 3 +--R (- A a b - 3A a b + 3A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- C b + 2C a b + 2C a b - 8C a b + 8C a b - 3C a )c +--R + +--R 3 3 4 2 5 6 4 3 6 7 +--R (- 3A a b + 5A a b - 6A a b + 4A a )c - C a b + 3C a b - 2C a +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 526 +--d0851a:= D(m0851a,x) +--E 272 + +--S 273 of 526 +m0851b:= a0851.2-r0851 +--R +--R +--R (5) +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 4 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b + 12A a b - 16A a b + 8A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (4A a b - 8A a b + 4A a )c + (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (4A a b - 8A a b + 12A a b - 16A a b + 8A a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 2 2 3 5 +--R (- 2A b + 4A a b - 2A a )c + (6C a b - 12C a b + 6C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (8A b - 16A a b + 4A a b + 8A a b - 4A a )c +--R + +--R 4 2 3 3 2 3 +--R (- 30C a b + 60C a b - 30C a b )c +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (10A b - 20A a b + 30A a b - 40A a b + 20A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20A a b - 40A a b + 20A a b)c +--R + +--R 2 3 3 2 4 3 +--R (- 60C a b + 120C a b - 60C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (20A a b - 40A a b + 60A a b - 80A a b + 40A a b)c +--R * +--R cos(x) +--R + +--R 2 2 6 2 2 3 5 +--R (2A b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (2A b - 4A a b + 16A a b - 28A a b + 14A a )c +--R + +--R 3 2 4 5 3 +--R (- 30C a b + 60C a b - 30C a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (10A a b - 20A a b + 30A a b - 40A a b + 20A a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 4A b + 8A a b - 4A a b)c +--R + +--R 3 2 2 3 4 +--R (12C a b - 24C a b + 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b - 4A a b + 16A a b - 8A a b)c +--R + +--R 5 2 4 3 3 2 +--R (- 24C a b + 48C a b - 24C a b )c +--R + +--R 7 6 2 5 3 4 4 3 +--R (8A b - 16A a b + 24A a b - 32A a b + 16A a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 4A a b + 8A a b - 4A a )c +--R + +--R 2 2 3 4 4 +--R (12C a b - 24C a b + 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (20A a b - 40A a b + 12A a b + 16A a b - 8A a )c +--R + +--R 2 4 3 3 4 2 2 +--R (- 72C a b + 144C a b - 72C a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (24A a b - 48A a b + 72A a b - 96A a b + 48A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 4 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b + 36A a b - 64A a b + 32A a b)c +--R + +--R 3 3 4 2 5 2 +--R (- 72C a b + 144C a b - 72C a b)c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (24A a b - 48A a b + 72A a b - 96A a b + 48A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (4A a b - 8A a b + 4A a )c + (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (4A a b - 8A a b + 20A a b - 32A a b + 16A a )c +--R + +--R 4 2 5 6 2 +--R (- 24C a b + 48C a b - 24C a )c +--R + +--R 3 4 4 3 5 2 6 7 +--R (8A a b - 16A a b + 24A a b - 32A a b + 16A a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (- 2A b + 4A a b - 2A a b )c +--R + +--R 4 2 3 3 2 3 +--R (6C a b - 12C a b + 6C a b )c +--R + +--R 2 4 3 3 4 2 2 +--R (- 4A a b + 8A a b - 4A a b )c +--R + +--R 6 2 5 3 4 8 7 2 6 +--R (- 6C a b + 12C a b - 6C a b )c + 2A b - 4A a b + 6A a b +--R + +--R 3 5 4 4 +--R - 8A a b + 4A a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4A a b + 8A a b - 4A a b)c +--R + +--R 2 3 3 2 4 3 +--R (12C a b - 24C a b + 12C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (4A a b - 8A a b - 4A a b + 16A a b - 8A a b)c +--R + +--R 2 5 3 4 4 3 7 2 6 +--R (- 24C a b + 48C a b - 24C a b )c + 8A a b - 16A a b +--R + +--R 3 5 4 4 5 3 +--R 24A a b - 32A a b + 16A a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 4 +--R (2A b - 4A a b + 4A a b - 2A a )c +--R + +--R 4 2 3 4 5 3 +--R (- 6C a b + 12C a b - 12C a b + 6C a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 2A b - 4A a b + 16A a b - 28A a b + 10A a b + 8A a b +--R + +--R 6 +--R - 4A a +--R * +--R 2 +--R c +--R + +--R 3 4 4 3 5 2 2 6 3 5 +--R (- 36C a b + 72C a b - 36C a b )c + 12A a b - 24A a b +--R + +--R 4 4 5 3 6 2 +--R 36A a b - 48A a b + 24A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 2 3 3 2 4 3 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (4A a b - 8A a b + 20A a b - 32A a b + 16A a b)c +--R + +--R 4 3 5 2 6 3 5 4 4 +--R (- 24C a b + 48C a b - 24C a b)c + 8A a b - 16A a b +--R + +--R 5 3 6 2 7 +--R 24A a b - 32A a b + 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 3 2 4 5 3 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (2A a b - 4A a b + 8A a b - 12A a b + 6A a )c +--R + +--R 5 2 6 7 4 4 5 3 6 2 7 +--R (- 6C a b + 12C a b - 6C a )c + 2A a b - 4A a b + 6A a b - 8A a b +--R + +--R 8 +--R 4A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 4 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b + 12A a b - 16A a b + 8A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (4A a b - 8A a b + 4A a )c + (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (4A a b - 8A a b + 12A a b - 16A a b + 8A a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 2 2 3 5 +--R (- 2A b + 4A a b - 2A a )c + (6C a b - 12C a b + 6C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (8A b - 16A a b + 4A a b + 8A a b - 4A a )c +--R + +--R 4 2 3 3 2 3 +--R (- 30C a b + 60C a b - 30C a b )c +--R + +--R 6 5 2 4 3 3 4 2 2 +--R (10A b - 20A a b + 30A a b - 40A a b + 20A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20A a b - 40A a b + 20A a b)c +--R + +--R 2 3 3 2 4 3 +--R (- 60C a b + 120C a b - 60C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (20A a b - 40A a b + 60A a b - 80A a b + 40A a b)c +--R * +--R cos(x) +--R + +--R 2 2 6 2 2 3 5 +--R (2A b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (2A b - 4A a b + 16A a b - 28A a b + 14A a )c +--R + +--R 3 2 4 5 3 +--R (- 30C a b + 60C a b - 30C a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (10A a b - 20A a b + 30A a b - 40A a b + 20A a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 4A b + 8A a b - 4A a b)c +--R + +--R 3 2 2 3 4 +--R (12C a b - 24C a b + 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b - 4A a b + 16A a b - 8A a b)c +--R + +--R 5 2 4 3 3 2 +--R (- 24C a b + 48C a b - 24C a b )c +--R + +--R 7 6 2 5 3 4 4 3 +--R (8A b - 16A a b + 24A a b - 32A a b + 16A a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 4A a b + 8A a b - 4A a )c +--R + +--R 2 2 3 4 4 +--R (12C a b - 24C a b + 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (20A a b - 40A a b + 12A a b + 16A a b - 8A a )c +--R + +--R 2 4 3 3 4 2 2 +--R (- 72C a b + 144C a b - 72C a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 +--R (24A a b - 48A a b + 72A a b - 96A a b + 48A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 4 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 3 2 4 3 +--R (4A b - 8A a b + 36A a b - 64A a b + 32A a b)c +--R + +--R 3 3 4 2 5 2 +--R (- 72C a b + 144C a b - 72C a b)c +--R + +--R 2 5 3 4 4 3 5 2 6 +--R (24A a b - 48A a b + 72A a b - 96A a b + 48A a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (4A a b - 8A a b + 4A a )c + (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 4 5 3 +--R (4A a b - 8A a b + 20A a b - 32A a b + 16A a )c +--R + +--R 4 2 5 6 2 +--R (- 24C a b + 48C a b - 24C a )c +--R + +--R 3 4 4 3 5 2 6 7 +--R (8A a b - 16A a b + 24A a b - 32A a b + 16A a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (- 2A b + 4A a b - 2A a b )c +--R + +--R 4 2 3 3 2 3 +--R (6C a b - 12C a b + 6C a b )c +--R + +--R 2 4 3 3 4 2 2 +--R (- 4A a b + 8A a b - 4A a b )c +--R + +--R 6 2 5 3 4 8 7 2 6 +--R (- 6C a b + 12C a b - 6C a b )c + 2A b - 4A a b + 6A a b +--R + +--R 3 5 4 4 +--R - 8A a b + 4A a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4A a b + 8A a b - 4A a b)c +--R + +--R 2 3 3 2 4 3 +--R (12C a b - 24C a b + 12C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (4A a b - 8A a b - 4A a b + 16A a b - 8A a b)c +--R + +--R 2 5 3 4 4 3 7 2 6 +--R (- 24C a b + 48C a b - 24C a b )c + 8A a b - 16A a b +--R + +--R 3 5 4 4 5 3 +--R 24A a b - 32A a b + 16A a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 4 +--R (2A b - 4A a b + 4A a b - 2A a )c +--R + +--R 4 2 3 4 5 3 +--R (- 6C a b + 12C a b - 12C a b + 6C a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R 2A b - 4A a b + 16A a b - 28A a b + 10A a b + 8A a b +--R + +--R 6 +--R - 4A a +--R * +--R 2 +--R c +--R + +--R 3 4 4 3 5 2 2 6 3 5 +--R (- 36C a b + 72C a b - 36C a b )c + 12A a b - 24A a b +--R + +--R 4 4 5 3 6 2 +--R 36A a b - 48A a b + 24A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 2 3 3 2 4 3 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 2 4 3 3 4 2 5 2 +--R (4A a b - 8A a b + 20A a b - 32A a b + 16A a b)c +--R + +--R 4 3 5 2 6 3 5 4 4 +--R (- 24C a b + 48C a b - 24C a b)c + 8A a b - 16A a b +--R + +--R 5 3 6 2 7 +--R 24A a b - 32A a b + 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 3 2 4 5 3 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 2 4 3 3 4 2 5 6 2 +--R (2A a b - 4A a b + 8A a b - 12A a b + 6A a )c +--R + +--R 5 2 6 7 4 4 5 3 6 2 7 +--R (- 6C a b + 12C a b - 6C a )c + 2A a b - 4A a b + 6A a b - 8A a b +--R + +--R 8 +--R 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 6 2 5 +--R - 2A b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b - 3A a b + 2A a b + 3A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- 4C b + 4C a b + 3C a b - 2C a b - C a )c +--R + +--R 4 2 3 3 2 2 +--R (3A a b - 6A a b + 3A a b )c +--R * +--R cos(x) +--R + +--R 6 2 5 +--R - 2A a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (A b - 4A a b - 5A a b + 8A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 5C a b + 6C a b + 3C a b - 4C a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (A b - 2A a b + 3A a b - 4A a b + 2A a b)c +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 2 2 5 +--R A c + (- C b + C a)c + (- 4A b + 3A a b - 4A a )c +--R + +--R 3 2 2 3 4 +--R (4C b - C a b - 5C a b + 2C a )c +--R + +--R 4 3 2 2 3 3 +--R (- 5A b - 12A a b + 14A a b + 3A a b)c +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 7C b + 4C a b + 12C a b - 8C a b - C a b)c +--R + +--R 5 2 4 3 3 +--R (3A a b - 6A a b + 3A a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- A b - 8A a b - A a )c + (9C a b - 8C a b - C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- A b - 8A a b - 27A a b + 32A a b + 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 14C a b + 8C a b + 24C a b - 16C a b - 2C a )c +--R + +--R 2 4 3 3 4 2 +--R (6A a b - 12A a b + 6A a b )c +--R * +--R cos(x) +--R + +--R 7 6 2 2 5 +--R - A c + (C b - C a)c + (- A b - 3A a b - A a )c +--R + +--R 2 2 3 4 2 2 3 4 3 +--R (- 2C a b + 9C a b - 7C a )c + (- 5A a b - 15A a b + 20A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (C b - 2C a b - 8C a b + 8C a b + 11C a b - 10C a )c +--R + +--R 3 3 4 2 5 +--R (3A a b - 6A a b + 3A a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 2 5 +--R 2A b c + (- 4C b + 6C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b + 9A a b - 14A a b + 3A a )c +--R + +--R 4 2 2 3 4 3 +--R (4C b - 9C a b + 6C a b - C a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 4A b - 9A a b + 10A a b + 3A a b )c +--R + +--R 6 2 4 3 3 +--R (- 4C b + 12C a b - 8C a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 +--R 2A a c + (- 2C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (A b - 12A a b + 7A a b - 8A a )c +--R + +--R 3 2 2 3 4 3 +--R (11C a b - 6C a b - 9C a b + 4C a )c +--R + +--R 5 4 2 3 3 2 4 2 +--R (A b - 14A a b - 33A a b + 44A a b + 2A a b)c +--R + +--R 5 3 3 4 2 +--R (- 12C a b + 36C a b - 24C a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 5 +--R - 2A b c + (4C b - 6C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (- 2A b - 9A a b + 2A a b - 3A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 4C a b + 21C a b - 18C a b + C a )c +--R + +--R 4 2 3 3 2 4 2 +--R (- 3A a b - 6A a b - 39A a b + 48A a b)c +--R + +--R 2 4 4 2 5 +--R (- 12C a b + 36C a b - 24C a b)c +--R * +--R cos(x) +--R + +--R 6 2 5 3 2 3 4 +--R - 2A a c + (2C a b - 2C a )c + (- A b - 7A a b + 4A a )c +--R + +--R 3 2 2 3 4 3 +--R (C a b - 6C a b + 13C a b - 8C a )c +--R + +--R 5 4 2 3 4 5 2 +--R (- A b + 2A a b - 3A a b - 14A a b + 16A a )c +--R + +--R 3 3 5 6 +--R (- 4C a b + 12C a b - 8C a )c +--R * +--R sin(x) +--R + +--R 2 5 3 2 2 4 +--R A b c + (- 3C b + 5C a b - 2C a b)c +--R + +--R 3 2 2 3 3 +--R (6A a b - 10A a b + 3A a b)c +--R + +--R 4 2 3 3 2 4 2 +--R (3C a b - 6C a b + 4C a b - C a b)c +--R + +--R 6 2 4 3 3 7 2 5 3 4 +--R (- A b - 2A a b + 3A a b )c - C b + 3C a b - 2C a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (- A b + 4A a b - A a )c + (- 3C a b + 4C a b - C a )c +--R + +--R 4 2 2 3 4 3 +--R (- A b + 9A a b - 16A a b + 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b + 4C a b - 12C a b + 8C a b - 2C a )c +--R + +--R 5 2 4 3 3 4 2 6 3 4 +--R (- 4A a b - 6A a b + 4A a b + 6A a b )c - 4C a b + 12C a b +--R + +--R 4 3 +--R - 8C a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 3 2 2 3 4 +--R (- A b + A a )c + (4C b - 7C a b + 2C a b + C a )c +--R + +--R 4 3 2 2 4 3 +--R (- A b - 6A a b + 5A a b - 4A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2C b - 6C a b + 10C a b - 2C a b - 6C a b + 2C a )c +--R + +--R 5 3 3 4 2 5 2 5 4 3 +--R (- 3A a b - 18A a b + 18A a b + 3A a b)c - 6C a b + 18C a b +--R + +--R 5 2 +--R - 12C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (A b - 4A a b + A a )c + (3C a b - 4C a b + C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (A b - 4A a b - 9A a b + 12A a b - 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b - 8C a b + 16C a b - 12C a b + 2C a )c +--R + +--R 2 4 3 3 4 2 5 3 4 5 2 +--R (- 6A a b + 8A a b - 18A a b + 16A a b)c - 4C a b + 12C a b +--R + +--R 6 +--R - 8C a b +--R * +--R cos(x) +--R + +--R 2 5 3 2 3 4 +--R - A a c + (- C b + 2C a b - C a )c +--R + +--R 2 2 3 4 3 +--R (- A a b - 3A a b + 3A a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- C b + 2C a b + 2C a b - 8C a b + 8C a b - 3C a )c +--R + +--R 3 3 4 2 5 6 4 3 6 7 +--R (- 3A a b + 5A a b - 6A a b + 4A a )c - C a b + 3C a b - 2C a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 273 + +--S 274 of 526 +--d0851b:= D(m0851b,x) +--E 274 + +)clear all + + +--S 275 of 526 +t0852:= (A+B*cos(x))/(a+b*cos(x)+c*sin(x)) +--R +--R +--R B cos(x) + A +--R (1) ----------------------- +--R c sin(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 526 +r0852:= b*B*x/(b^2+c^2)+2*(A-a*b*B/(b^2+c^2))*atan((c+(a-b)*_ + tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(1/2)+_ + B*c*log(a+b*cos(x)+c*sin(x))/(b^2+c^2) +--R +--R +--R (2) +--R +--------------+ +--R | 2 2 2 +--R B c\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R x +--R (b - a)tan(-) - c +--------------+ +--R 2 2 2 | 2 2 2 +--R (- 2A c - 2A b + 2B a b)atan(-----------------) + B b x\|- c - b + a +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression(Integer) +--E 276 + +--S 277 of 526 +a0852:= integrate(t0852,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (- A c - A b + B a b) +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +------------+ +--R | 2 2 2 2 +--R - B c\|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R B c\|c + b - a log(----------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R B b x\|c + b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|c + b - a +--R , +--R +--R +--------------+ +--R | 2 2 2 2 +--R - B c\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R B c\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R +--------------+ +--R | 2 2 2 +--R B b x\|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 277 + +--S 278 of 526 +m0852a:= a0852.1-r0852 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 | 2 2 2 +--R (- A c - A b + B a b)\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R - B c\|- c - b + a \|c + b - a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2 +--R - B c\|- c - b + a \|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R B c\|- c - b + a \|c + b - a log(----------------------------) +--R cos(x) + 1 +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 2 | 2 2 2 2 +--R (2A c + 2A b - 2B a b)\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c + b )\|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 278 + +--S 279 of 526 +d0852a:= D(m0852a,x) +--R +--R +--R (5) +--R 3 2 2 2 5 4 +--R (- A b + 2A a b - A a b)c - A b + (B + 2A)a b +--R + +--R 2 3 3 2 +--R (- 2B - A)a b + B a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 +--R - A c + ((B - 2A)a b + A a )c +--R + +--R 4 3 2 2 3 +--R (A b + (- B - 2A)a b + (2B + A)a b - B a b)c +--R * +--R cos(x) +--R + +--R 5 2 3 +--R - A c + (- A b + B a b)c +--R * +--R sin(x) +--R + +--R 4 3 2 2 2 5 +--R (- 2A b + A a)c + (- 3A b + (2B + 2A)a b - B a b)c - A b +--R + +--R 4 2 3 +--R (B + A)a b - B a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 2 5 4 +--R - 2A b c + (- 3A b + 2B a b + A a b)c - A b + B a b +--R + +--R 2 3 3 2 +--R A a b - B a b +--R * +--R cos(x) +--R + +--R 4 2 2 2 4 2 3 +--R - A a c + (- 2A a b + (B + A)a b)c - A a b + (B + A)a b +--R + +--R 3 2 +--R - B a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 2 3 +--R 2A c + (4A b + (- 2B - 2A)a b)c +--R + +--R 4 3 2 2 +--R (2A b + (- 2B - 2A)a b + 2B a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 2 +--R ((- 2A b + 2A a)c + (- 2A b + (2B + 2A)a b - 2B a b)c )sin(x) +--R + +--R 5 2 3 +--R 2A c + (4A b + (- 2B - 2A)a b)c +--R + +--R 4 3 2 2 +--R (2A b + (- 2B - 2A)a b + 2B a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 2 3 +--R 2A c + (2A b + (- 2B + 2A)a b - 2A a )c +--R + +--R 3 2 2 3 +--R (2A a b + (- 2B - 2A)a b + 2B a b)c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 2 5 4 2 3 +--R 2A b c + (3A b - 2B a b - A a b)c + A b - B a b - A a b +--R + +--R 3 2 +--R B a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 3 +--R - A c + ((B - 2A)a b + A a )c +--R + +--R 4 3 2 2 3 +--R (A b + (- B - 2A)a b + (2B + A)a b - B a b)c +--R * +--R cos(x) +--R + +--R 5 2 3 +--R - A c + (- 3A b + (B + 2A)a b)c +--R + +--R 4 3 2 2 +--R (- 2A b + (2B + 2A)a b - 2B a b )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 5 4 2 3 2 +--R (A a c + (A b - B a b)c + A b + (- B - A)a b + B a b )cos(x) +--R + +--R 3 2 2 2 5 4 +--R (- A b + 2A a b - A a b)c - A b + (B + 2A)a b +--R + +--R 2 3 3 2 +--R (- 2B - A)a b + B a b +--R * +--R cos(x) +--R + +--R 4 2 2 2 4 2 3 3 2 +--R - A a c + (- 2A a b + (B + A)a b)c - A a b + (B + A)a b - B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 6 2 2 4 +--R - A c + (- A b + (B - A)a b + A a )c +--R + +--R 4 3 2 2 3 2 6 +--R (A b - 2A a b + B a b + (- B + A)a b)c + A b +--R + +--R 5 2 4 3 3 4 2 +--R (- B - A)a b + (B - A)a b + (B + A)a b - B a b +--R * +--R cos(x) +--R + +--R 6 2 2 4 +--R - A c + (- A b + (B - A)a b + A a )c +--R + +--R 4 3 2 2 3 2 6 5 +--R (A b - 2A a b + B a b + (- B + A)a b)c + A b + (- B - A)a b +--R + +--R 2 4 3 3 4 2 +--R (B - A)a b + (B + A)a b - B a b +--R * +--R sin(x) +--R + +--R 5 +--R (- 2A b + A a)c +--R + +--R 3 2 2 3 3 +--R (- 4A b + (2B + 2A)a b + (- B + 2A)a b - A a )c +--R + +--R 5 4 2 3 3 2 4 +--R (- 2A b + (2B + A)a b + (- B + 2A)a b + (- 2B - A)a b + B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 2 2 3 +--R - 2A b c + (- 4A b + 2B a b + 2A a b)c +--R + +--R 5 4 2 3 3 2 +--R (- 2A b + 2B a b + 2A a b - 2B a b )c +--R * +--R cos(x) +--R + +--R 5 2 2 3 3 +--R - A a c + (- 2A a b + B a b + A a )c +--R + +--R 4 2 3 3 2 4 +--R (- A a b + B a b + A a b - B a b)c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 2 2 4 +--R 2A c + (4A b - 2B a b - 2A a )c +--R + +--R 4 3 2 2 3 2 +--R (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 5 +--R (- 2A b + 2A a)c +--R + +--R 3 2 2 3 3 +--R (- 4A b + (2B + 4A)a b + (- 2B + 2A)a b - 2A a )c +--R + +--R 5 4 2 3 3 2 +--R - 2A b + (2B + 2A)a b + (- 2B + 2A)a b + (- 2B - 2A)a b +--R + +--R 4 +--R 2B a b +--R * +--R c +--R * +--R sin(x) +--R + +--R 6 2 2 4 +--R 2A c + (4A b - 2B a b - 2A a )c +--R + +--R 4 3 2 2 3 2 +--R (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 4 +--R 2A c + (4A b - 2B a b - 2A a )c +--R + +--R 4 3 2 2 3 2 +--R (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 3 2 2 3 +--R 2A b c + (4A b - 2B a b - 2A a b)c +--R + +--R 5 4 2 3 3 2 +--R (2A b - 2B a b - 2A a b + 2B a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 2 4 +--R - A c + (- A b + (B - A)a b + A a )c +--R + +--R 4 3 2 2 3 2 6 5 +--R (A b - 2A a b + B a b + (- B + A)a b)c + A b + (- B - A)a b +--R + +--R 2 4 3 3 4 2 +--R (B - A)a b + (B + A)a b - B a b +--R * +--R cos(x) +--R + +--R 6 2 2 4 +--R - A c + (- 3A b + (B + A)a b + A a )c +--R + +--R 4 3 2 2 3 2 6 +--R (- 3A b + (2B + 2A)a b + (- B + 2A)a b + (- B - A)a b)c - A b +--R + +--R 5 2 4 3 3 4 2 +--R (B + A)a b + (- B + A)a b + (- B - A)a b + B a b +--R * +--R sin(x) +--R + +--R 5 2 2 3 3 +--R A a c + (2A a b - B a b - A a )c +--R + +--R 4 2 3 3 2 4 +--R (A a b - B a b - A a b + B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 2 3 3 +--R - A a c + (- 2A a b + B a b + A a )c +--R + +--R 4 2 3 3 2 4 +--R (- A a b + B a b + A a b - B a b)c +--R / +--R 2 2 4 4 3 2 2 2 2 +--R ((b - 2a b + a )c + (b - 2a b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 3a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (b - 3a b + 3a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 3 +--R (- b + a)c + (- 2b + 4a b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + 3a b - 3a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 3 3 +--R ((- b + a b)c + (- b + 2a b - a b)c - a b + 2a b - a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 2 2 3 4 2 6 +--R (- b + a )c + (- 2b + 2a b - a b + 2a b - a )c - b +--R + +--R 5 2 4 3 3 4 2 +--R 2a b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 2 5 2 4 3 3 +--R (- a b + a )c + (- 2a b + 3a b - a b)c - a b + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c )sin(x) +--R + +--R 6 2 4 4 3 2 2 2 +--R (2c + (4a b - 2a )c + (- 2b + 4a b - 2a b )c )cos(x) +--R + +--R 6 2 2 4 4 3 2 2 2 +--R 2c + (4b - 4a b + 2a )c + (2b - 4a b + 2a b )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 4 2 3 2 +--R (2b c + (2b + 2a b - 2a b)c + (2a b - 2a b )c)cos(x) +--R + +--R 5 3 2 3 3 +--R (2b + 2a)c + (4b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 +--R (2b - 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 5 2 2 3 4 2 3 +--R 2a c + (4a b - 2a b)c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 2 2 +--R ((- b + a )c + (- b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (b + a)c + (2a b + a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + a b + a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 3 5 4 2 3 3 2 +--R (b + a)c + (2b - a b + a )c + (b - a b - a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 3 2 5 3 3 2 +--R ((b + a b)c + (b + 2a b - a b)c + a b - a b )cos(x) +--R + +--R 2 2 4 4 3 2 2 4 2 6 4 2 +--R ((b + 2a b + a )c + (2b + 2a b + a b - a )c + b - a b )cos(x) +--R + +--R 2 4 3 2 2 3 2 5 3 3 +--R (a b + a )c + (2a b + a b - a b)c + a b - a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b - 2a b + a )c + (2b - 4a b + a b + 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b - 2a b + 2a b - a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (- b + a)c + (- b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 6 3 4 4 3 +--R (b - 3a b + 2a b + a b - a b)c + b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 +--R (- b + a)c + (- 2b + 3a b - a b)c +--R + +--R 5 4 2 3 4 5 2 6 2 5 4 3 5 2 +--R (- b + 3a b - 3a b + 2a b - a )c + a b - 2a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b + a b)c + (- 2b + 2a b + a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (- b + a b + a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b + a )c + (- 2a b + 2a b + a b - a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- a b + a b + a b - a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (- 2b + 2a)c + (- 4b + 4a b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 3 +--R 2c + (2b + 2a b - 2a )c + (- 2b + 4a b - 2a b)c +--R + +--R 6 5 2 4 3 3 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 7 2 5 4 3 2 2 3 4 3 +--R 2c + (4b - 2a b)c + (2b - 4a b + 2a b + 2a b - 2a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- 2a b + 2a b + 2a b - 2a b )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 2 2 +--R (2b c + (4b - 2a b)c + (2b - 2a b )c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (2b + 2a)c + (4b + 4a b - 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (2b + 2a b - 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 2 +--R 2a c + (4a b - 2a )c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c)sin(x) +--R + +--R 6 3 2 3 4 +--R (b + a)c + (b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 2 5 4 3 +--R (- b + a b + 2a b - a b - a b)c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 5 4 2 3 3 2 5 2 +--R (b + a)c + (2b + a b - a b)c + (b - a b - a b + 2a b - a )c +--R + +--R 6 3 4 5 2 +--R - a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b + a b)c + (2b + 2a b - a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (b + a b - a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b + 2a b + a )c + (2b + 4a b + a b - 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b + 2a b - 2a b - a b )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 5 2 4 3 3 4 2 +--R (a b + a )c + (2a b + 2a b - a b - a )c + (a b + a b - a b - a b )c +--R Type: Expression(Integer) +--E 279 + +--S 280 of 526 +m0852b:= a0852.2-r0852 +--R +--R +--R (6) +--R +--------------+ +--R | 2 2 2 +--R - B c\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +--R | 2 2 2 2 +--R - B c\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R B c\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R (2A c + 2A b - 2B a b)atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 526 +d0852b:= D(m0852b,x) +--R +--R +--R (7) +--R 2 3 2 2 2 +--R ((- A b + A a)c - A b + (B + A)a b - B a b)sin(x) +--R + +--R 3 2 3 +--R (- 2A c + (- 2A b + 2B a b)c)cos(x) - 2A c +--R + +--R 2 +--R (- 2A b + 2B a b)c +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 +--R ((- 3A b + A a)c - 3A b + (3B + A)a b - B a b)cos(x) +--R + +--R 2 3 2 2 3 +--R (- 4A b c - 4A b + 4B a b )cos(x) + (- A b - A a)c - A b +--R + +--R 2 2 +--R (B - A)a b + B a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 +--R (4A c + (4A b - 4B a b)c)sin(x) +--R + +--R 3 2 2 3 2 +--R (4A c + (4A b - 4B a b)c)cos(x) + (4A c + (4A b - 4B a b)c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 2 2 2 +--R ((3A b + A a)c + 3A b + (- 3B + A)a b - B a b)sin(x) +--R + +--R 3 2 3 2 +--R ((- 2A c + (- 2A b + 2B a b)c)cos(x) - 2A c + (- 2A b + 2B a b)c) +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 2 +--R ((A b + A a)c + A b + (- B + A)a b - B a b)cos(x) + (- A b - A a)c +--R + +--R 3 2 2 +--R - A b + (B - A)a b + B a b +--R / +--R 2 2 2 4 3 2 2 2 +--R ((b - 2a b + a )c + b - 2a b + a b )sin(x) +--R + +--R 3 3 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)cos(x) + (- 2b + 2a)c +--R + +--R 3 2 +--R (- 2b + 2a b )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 2 4 2 2 +--R ((- 2b + 2a )c - 2b + 2a b )cos(x) + (- b + a )c - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)sin(x) +--R + +--R 4 2 2 4 2 2 +--R ((4c + 4b c )cos(x) + 4c + 4b c )sin(x) +--R + +--R 3 3 2 2 +--R ((2b + 2a)c + (2b + 2a b )c)cos(x) +--R + +--R 3 3 2 3 3 2 +--R ((4b + 4a)c + (4b + 4a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )sin(x) +--R + +--R 3 3 2 3 3 2 +--R (((2b + 2a)c + (2b + 2a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c) +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 2 2 2 +--R ((b + 2a b + a )c + b + 2a b + a b )cos(x) +--R + +--R 2 2 2 4 3 2 2 2 2 2 +--R ((2b + 4a b + 2a )c + 2b + 4a b + 2a b )cos(x) + (b + 2a b + a )c +--R + +--R 4 3 2 2 +--R b + 2a b + a b +--R Type: Expression(Integer) +--E 281 + +)clear all + + +--S 282 of 526 +t0853:= (A+B*cos(x))/(a+b*cos(x)+c*sin(x))^2 +--R +--R +--R B cos(x) + A +--R (1) --------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 526 +r0853:= 2*(a*A-b*B)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ + (a^2-b^2-c^2)^(3/2)+(B*c+A*c*cos(x)-_ + (A*b-a*B)*sin(x))/(a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (2) +--R 2 2 +--R ((- 2B b + 2A a)c sin(x) + (- 2B b + 2A a b)cos(x) - 2B a b + 2A a ) +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R ((A b - B a)sin(x) - A c cos(x) - B c)\|- c - b + a +--R / +--R 3 2 2 2 3 2 2 2 3 +--R ((c + (b - a )c)sin(x) + (b c + b - a b)cos(x) + a c + a b - a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 526 +a0853:= integrate(t0853,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (B b + (- B - A)a b + A a )c sin(x) +--R + +--R 3 2 2 2 2 3 +--R (B b + (- B - A)a b + A a b)cos(x) + B a b + (- B - A)a b + A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 2 2 2 +--R ((- B + A)c + A b + (- B - A)a b + B a )sin(x) +--R + +--R (- B b + A a)c cos(x) + (- B b + A a)c +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a )c sin(x) +--R + +--R 3 2 2 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a b)cos(x) + 2B a b + (- 2B - 2A)a b +--R + +--R 3 +--R 2A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 2 2 2 +--R ((- B + A)c + A b + (- B - A)a b + B a )sin(x) +--R + +--R (- B b + A a)c cos(x) + (- B b + A a)c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 284 + +--S 285 of 526 +m0853a:= a0853.1-r0853 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 | 2 2 2 +--R (B b + (- B - A)a b + A a )\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 2 | 2 2 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a )\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (- B + A)c\|- c - b + a \|c + b - a +--R / +--R +--------------+ +------------+ +--R 2 3 2 2 3 | 2 2 2 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 285 + +--S 286 of 526 +d0853a:= D(m0853a,x) +--R +--R +--R (5) +--R 4 3 2 2 3 2 +--R (- B b + (2B + A)a b + (- B - 2A)a b + A a b)sin(x) +--R + +--R 3 +--R (- B b + A a)c +--R + +--R 3 2 2 3 +--R (B b + (- 2B - A)a b + (B + 2A)a b - A a )c +--R * +--R cos(x) +--R + +--R 3 +--R (- B b + A a)c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 +--R (- 2B b + (B + 2A)a b - A a )c - B b + (B + A)a b +--R + +--R 2 2 +--R - A a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 3 2 2 3 +--R ((- 2B b + 2A a b)c - B b + A a b + B a b - A a b)cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- B a b + A a )c - B a b + (B + A)a b - A a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 2 +--R ((2B b - 2A a)c + (2B b + (- 2B - 2A)a b + 2A a b)c)sin(x) +--R + +--R 2 2 2 +--R (- 2B b + (2B + 2A)a b - 2A a )c sin(x) +--R + +--R 3 3 2 2 2 +--R ((2B b - 2A a)c + (2B b + (- 2B - 2A)a b + 2A a b)c)cos(x) +--R + +--R 3 2 2 3 +--R ((2B b - 2A a)c + (2B a b + (- 2B - 2A)a b + 2A a )c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 3 2 2 3 2 +--R ((2B b - 2A a b)c + B b - A a b - B a b + A a b)sin(x) +--R + +--R 3 +--R (- B b + A a)c +--R + +--R 3 2 2 3 +--R (B b + (- 2B - A)a b + (B + 2A)a b - A a )c +--R * +--R cos(x) +--R + +--R 3 3 2 2 +--R (- B b + A a)c + (- 2B b + (2B + 2A)a b - 2A a b)c +--R * +--R sin(x) +--R + +--R 2 2 4 3 2 2 2 +--R ((B a b - A a )c + B b + (- B - A)a b + A a b )cos(x) +--R + +--R 4 3 2 2 3 +--R (- B b + (2B + A)a b + (- B - 2A)a b + A a b)cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- B a b + A a )c - B a b + (B + A)a b - A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 4 2 2 3 2 5 +--R (B b - A a)c + (B a b + (- B - A)a b + A a )c - B b +--R + +--R 4 2 3 3 2 4 +--R (B + A)a b + (B - A)a b + (- B - A)a b + A a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 5 +--R (B b - A a)c + (B a b + (- B - A)a b + A a )c - B b +--R + +--R 4 2 3 3 2 4 +--R (B + A)a b + (B - A)a b + (- B - A)a b + A a b +--R * +--R sin(x) +--R + +--R 2 2 3 +--R (2B b + (- B - 2A)a b + A a )c +--R + +--R 4 3 2 2 3 4 +--R (2B b + (- B - 2A)a b + (- 2B + A)a b + (B + 2A)a b - A a )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 4 3 2 2 3 +--R ((2B b - 2A a b)c + (2B b - 2A a b - 2B a b + 2A a b)c)cos(x) +--R + +--R 2 3 3 2 2 3 4 +--R (B a b - A a )c + (B a b - A a b - B a b + A a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 3 2 2 +--R ((- 2B b + 2A a)c + (- 2B b + 2A a b + 2B a b - 2A a )c )sin(x) +--R + +--R 2 2 3 +--R (2B b + (- 2B - 2A)a b + 2A a )c +--R + +--R 4 3 2 2 3 4 +--R (2B b + (- 2B - 2A)a b + (- 2B + 2A)a b + (2B + 2A)a b - 2A a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 3 2 2 +--R ((- 2B b + 2A a)c + (- 2B b + 2A a b + 2B a b - 2A a )c )cos(x) +--R + +--R 4 3 2 2 3 2 +--R ((- 2B b + 2A a)c + (- 2B b + 2A a b + 2B a b - 2A a )c )cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 3 4 3 2 2 3 2 +--R ((- 2B b + 2A a b)c + (- 2B b + 2A a b + 2B a b - 2A a b)c)sin(x) +--R + +--R 4 2 2 3 2 5 +--R (B b - A a)c + (B a b + (- B - A)a b + A a )c - B b +--R + +--R 4 2 3 3 2 4 +--R (B + A)a b + (B - A)a b + (- B - A)a b + A a b +--R * +--R cos(x) +--R + +--R 4 3 2 2 3 2 +--R (B b - A a)c + (2B b + (- B - 2A)a b + (- B + A)a b + A a )c +--R + +--R 5 4 2 3 3 2 4 +--R B b + (- B - A)a b + (- B + A)a b + (B + A)a b - A a b +--R * +--R sin(x) +--R + +--R 2 3 3 2 2 3 4 2 +--R ((- B a b + A a )c + (- B a b + A a b + B a b - A a )c)cos(x) +--R + +--R 2 3 3 2 2 3 4 +--R (B a b - A a )c + (B a b - A a b - B a b + A a )c +--R / +--R 2 2 4 4 3 3 4 2 2 +--R ((b - 2a b + a )c + (b - 2a b + 2a b - a )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 4a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 +--R (- b + a)c + (- 2b + 4a b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 +--R (- b + a b)c + (- b + 3a b - 2a b)c - a b + 2a b +--R + +--R 4 2 5 +--R - 2a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 5 +--R (- b + a )c + (- 2b + 2a b + 2a b - 2a )c - b + 2a b +--R + +--R 2 4 4 2 5 6 +--R - a b + a b - 2a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 4 2 5 2 4 4 2 +--R (- a b + a )c + (- 2a b + 3a b - a )c - a b + 2a b - 2a b +--R + +--R 5 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 2 3 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c )sin(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R (2c + (4a b - 4a )c + (- 2b + 4a b - 4a b + 2a )c )cos(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R 2c + (4b - 4a b)c + (2b - 4a b + 4a b - 2a )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 +--R 2b c + (2b + 2a b - 4a b)c +--R + +--R 4 2 3 3 2 4 +--R (2a b - 2a b - 2a b + 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 3 5 4 4 5 +--R ((2b + 2a)c + (4b - 4a )c + (2b - 2a b - 2a b + 2a )c)cos(x) +--R + +--R 5 2 2 3 3 4 2 3 3 2 4 +--R 2a c + (4a b - 2a b - 2a )c + (2a b - 2a b - 2a b + 2a b)c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((- b + a )c + (- b + 2a b - a )c )sin(x) +--R + +--R 5 2 3 3 +--R (b + a)c + (2a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + a b + 2a b - 2a b - a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 +--R (b + a)c + (2b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - a b - 2a b + 2a b + a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 2 2 3 2 5 3 3 5 +--R ((b + a b)c + (b + 2a b - a b - 2a b)c + a b - 2a b + a b) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 2 4 +--R (b + 2a b + a )c + (2b + 2a b - 2a b - 2a )c + b - a b +--R + +--R 4 2 6 +--R - a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 4 2 5 3 3 5 +--R (a b + a )c + (2a b + a b - 2a b - a )c + a b - 2a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b + 2a b - a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b + 2a b + a b - 4a b + a b + 2a b - a )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (b - 3a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 6 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c - b + 2a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R a b - 4a b + a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (2b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 2 5 3 4 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c - a b + 2a b + a b +--R + +--R 4 3 5 2 6 7 +--R - 4a b + a b + 2a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b - a b)c + (2b - 2a b - 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b - a b - 2a b + 2a b + a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (a b - a )c + (2a b - 2a b - 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (a b - a b - 2a b + 2a b + a b - a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (2b - 2a)c + (4b - 4a b - 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 2b - 2a b + 4a )c + (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a b)c +--R * +--R cos(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 4b + 2a b + 2a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 4 2 2 +--R (- 2b c + (- 4b + 4a b)c + (- 2b + 4a b - 2a b)c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- 2b - 2a)c + (- 4b - 4a b + 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 2b - 2a b + 4a b + 4a b - 2a b - 2a )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 5 2 +--R - 2a c + (- 4a b + 4a )c + (- 2a b + 4a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 2 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c)sin(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- b - 2a b + a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 2 5 4 3 6 +--R (b - a b - 2a b + 2a b + a b - a )c + b - 3a b + 3a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- 2b - a b + 2a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 3 4 5 2 7 +--R (- b + a b + 2a b - 2a b - a b + a )c + a b - 3a b + 3a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b - a b)c + (- 2b - 2a b + 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b - a b + 2a b + 2a b - a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b - 2a b - a )c + (- 2b - 4a b + 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b - 2a b + a b + 4a b + a b - 2a b - a )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b - a )c + (- 2a b - 2a b + 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- a b - a b + 2a b + 2a b - a b - a )c +--R Type: Expression(Integer) +--E 286 + +--S 287 of 526 +m0853b:= a0853.2-r0853 +--R +--R +--R (6) +--R 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a )atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (- B + A)c\|- c - b + a +--R / +--R +--------------+ +--R 2 3 2 2 3 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 526 +d0853b:= D(m0853b,x) +--R +--R +--R (7) +--R 2 2 2 +--R (- B b + (B + A)a b - A a )sin(x) +--R + +--R ((- 2B b + 2A a)c cos(x) + (- 2B b + 2A a)c)sin(x) +--R + +--R 2 2 2 2 +--R (- 3B b + (B + 3A)a b - A a )cos(x) + (- 4B b + 4A a b)cos(x) +--R + +--R 2 2 +--R - B b + (- B + A)a b + A a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 +--R (4B b - 4A a)c sin(x) + (4B b - 4A a)c cos(x) +--R + +--R (4B b - 4A a)c cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 +--R (3B b + (B - 3A)a b - A a )sin(x) +--R + +--R ((- 2B b + 2A a)c cos(x) + (- 2B b + 2A a)c)sin(x) +--R + +--R 2 2 2 2 2 +--R (B b + (B - A)a b - A a )cos(x) - B b + (- B + A)a b + A a +--R / +--R 2 2 2 4 3 3 4 2 +--R ((b - 2a b + a )c + b - 2a b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 +--R (- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )cos(x) +--R + +--R 2 2 2 4 2 2 4 2 2 2 4 +--R ((- 2b + 2a )c - 2b + 4a b - 2a )cos(x) + (- b + a )c - b +--R + +--R 2 2 4 +--R 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)sin(x) +--R + +--R 4 2 2 2 4 2 2 2 +--R ((4c + (4b - 4a )c )cos(x) + 4c + (4b - 4a )c )sin(x) +--R + +--R 3 3 2 2 3 2 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 3 +--R ((4b + 4a)c + (4b + 4a b - 4a b - 4a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 3 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 3 4 2 +--R ((b + 2a b + a )c + b + 2a b - 2a b - a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R ((2b + 4a b + 2a )c + 2b + 4a b - 4a b - 2a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R (b + 2a b + a )c + b + 2a b - 2a b - a +--R Type: Expression(Integer) +--E 288 + +)clear all + + +--S 289 of 526 +t0854:= (A+B*cos(x))/(a+b*cos(x)+c*sin(x))^3 +--R +--R +--R (1) +--R B cos(x) + A +--R / +--R 3 3 2 2 2 +--R c sin(x) + (3b c cos(x) + 3a c )sin(x) +--R + +--R 2 2 2 3 3 2 2 +--R (3b c cos(x) + 6a b c cos(x) + 3a c)sin(x) + b cos(x) + 3a b cos(x) +--R + +--R 2 3 +--R 3a b cos(x) + a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 526 +r0854:= (2*a^2*A+b*(A*b-3*a*B)+A*c^2)*atan((c+(a-b)*tan(1/2*x))/_ + (a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(5/2)+_ + 1/2*(B*c+A*c*cos(x)-(A*b-a*B)*sin(x))/(a^2-b^2-c^2)/_ + (a+b*cos(x)+c*sin(x))^2+1/2*(a*B*c+(3*a*A-2*b*B)*c*cos(x)+_ + (2*b^2*B-a*(3*A*b-a*B))*sin(x))/(a^2-b^2-c^2)^2/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (2) +--R 4 2 2 2 2 +--R (- 2A c + (- 2A b + 6B a b - 4A a )c )sin(x) +--R + +--R 3 3 2 2 3 +--R (- 4A b c + (- 4A b + 12B a b - 8A a b)c)cos(x) - 4A a c +--R + +--R 2 2 3 +--R (- 4A a b + 12B a b - 8A a )c +--R * +--R sin(x) +--R + +--R 2 2 4 3 2 2 2 +--R (- 2A b c - 2A b + 6B a b - 4A a b )cos(x) +--R + +--R 2 3 2 2 3 2 2 2 2 +--R (- 4A a b c - 4A a b + 12B a b - 8A a b)cos(x) - 2A a c - 2A a b +--R + +--R 3 4 +--R 6B a b - 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 2 2 2 +--R (2B b - 3A a b + B a )c sin(x) +--R + +--R 2 3 2 2 2 +--R ((- 2B b + 3A a)c + 2B b - 3A a b + B a b)cos(x) + A b c +--R + +--R 3 2 2 3 +--R A b + B a b - 4A a b + 2B a +--R * +--R sin(x) +--R + +--R 2 2 +--R (- 2B b + 3A a b)c cos(x) +--R + +--R 3 2 2 3 2 2 +--R (- A c + (- A b - B a b + 4A a )c)cos(x) - B c + (- B b + 2B a )c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (4b - 4a )c + (2b - 4a b + 2a )c )sin(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (8b - 8a b)c + (4b - 8a b + 4a b)c)cos(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (8a b - 8a )c + (4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (4b - 4a b )c + 2b - 4a b + 2a b )cos(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (8a b - 8a b)c + 4a b - 8a b + 4a b)cos(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (4a b - 4a )c + 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 290 + +--S 291 of 526 +a0854:= integrate(t0854,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 +--R (2A b - 4A a b + 2A a b)c +--R + +--R 5 4 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 6A)a b +--R + +--R 3 2 4 +--R (- 6B - 8A)a b + 4A a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 3 +--R (2A a b - 4A a b + 2A a )c +--R + +--R 4 2 3 3 2 4 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b +--R + +--R 5 +--R 4A a +--R * +--R c +--R * +--R sin(x) +--R + +--R 2 2 4 +--R (- A b + 2A a b - A a )c +--R + +--R 3 2 2 3 4 2 6 +--R (3B a b + (- 6B - 2A)a b + (3B + 4A)a b - 2A a )c + A b +--R + +--R 5 2 4 3 3 4 2 +--R (- 3B - 2A)a b + (6B + 3A)a b + (- 3B - 4A)a b + 2A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 5 2 4 +--R (2A a b - 4A a b + 2A a b)c + 2A a b + (- 6B - 4A)a b +--R + +--R 3 3 4 2 5 +--R (12B + 6A)a b + (- 6B - 8A)a b + 4A a b +--R * +--R cos(x) +--R + +--R 2 2 4 +--R (A b - 2A a b + A a )c +--R + +--R 4 3 2 2 3 4 2 +--R (A b + (- 3B - 2A)a b + (6B + 4A)a b + (- 3B - 6A)a b + 3A a )c +--R + +--R 2 4 3 3 4 2 5 6 +--R A a b + (- 3B - 2A)a b + (6B + 3A)a b + (- 3B - 4A)a b + 2A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 4 +--R (2B - 2A)b c +--R + +--R 3 2 2 3 2 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 5 4 2 3 3 2 +--R 2B b + (- 4B - 3A)a b + (3B + 6A)a b + (- 2B - 3A)a b +--R + +--R 4 +--R B a b +--R * +--R cos(x) +--R + +--R 4 +--R (2B - 2A)a c +--R + +--R 3 2 2 3 2 +--R (A b + (6B - 4A)a b + (- 2B - 5A)a b + (- 4B + 8A)a )c +--R + +--R 5 4 2 3 3 2 +--R A b + (B - 2A)a b + (- 2B - 3A)a b + (3B + 8A)a b +--R + +--R 4 5 +--R (- 4B - 4A)a b + 2B a +--R * +--R sin(x) +--R + +--R 5 2 2 3 +--R (- B + A)c + (- 2B b + (B + 3A)a b + (2B - 4A)a )c +--R + +--R 4 3 2 2 +--R (- B - A)b + (7B + 3A)a b + (- 7B - 8A)a b +--R + +--R 3 4 +--R (2B + 6A)a b - B a +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 +--R (- A b + 2B a b - A a )c +--R + +--R 4 3 2 2 3 4 +--R (- A b + 5B a b - 3A a b - 5B a b + 4A a )c +--R * +--R cos(x) +--R + +--R 5 2 2 3 +--R (B - A)c + ((2B - A)b + (B - 3A)a b + (- 2B + 3A)a )c +--R + +--R 4 3 2 2 3 +--R B b + (- 2B - 3A)a b + (7B + 5A)a b + (- 7B - 6A)a b +--R + +--R 4 +--R (B + 4A)a +--R * +--R c +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 2 2 5 5 4 3 2 4 3 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 3 2 2 3 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 3 2 4 +--R (- 12B - 16A)a b + 8A a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 3 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 4 2 3 3 2 +--R 4A a b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 4 5 +--R (- 12B - 16A)a b + 8A a +--R * +--R c +--R * +--R sin(x) +--R + +--R 2 2 4 +--R (- 2A b + 4A a b - 2A a )c +--R + +--R 3 2 2 3 4 2 6 +--R (6B a b + (- 12B - 4A)a b + (6B + 8A)a b - 4A a )c + 2A b +--R + +--R 5 2 4 3 3 4 2 +--R (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 5 2 4 +--R (4A a b - 8A a b + 4A a b)c + 4A a b + (- 12B - 8A)a b +--R + +--R 3 3 4 2 5 +--R (24B + 12A)a b + (- 12B - 16A)a b + 8A a b +--R * +--R cos(x) +--R + +--R 2 2 4 +--R (2A b - 4A a b + 2A a )c +--R + +--R 4 3 2 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 8A)a b + (- 6B - 12A)a b +--R + +--R 4 +--R 6A a +--R * +--R 2 +--R c +--R + +--R 2 4 3 3 4 2 5 6 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 4 +--R (2B - 2A)b c +--R + +--R 3 2 2 3 2 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 5 4 2 3 3 2 +--R 2B b + (- 4B - 3A)a b + (3B + 6A)a b + (- 2B - 3A)a b +--R + +--R 4 +--R B a b +--R * +--R cos(x) +--R + +--R 4 +--R (2B - 2A)a c +--R + +--R 3 2 2 3 2 +--R (A b + (6B - 4A)a b + (- 2B - 5A)a b + (- 4B + 8A)a )c +--R + +--R 5 4 2 3 3 2 +--R A b + (B - 2A)a b + (- 2B - 3A)a b + (3B + 8A)a b +--R + +--R 4 5 +--R (- 4B - 4A)a b + 2B a +--R * +--R sin(x) +--R + +--R 5 2 2 3 +--R (- B + A)c + (- 2B b + (B + 3A)a b + (2B - 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12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 526 +--d0854a:= D(m0854a,x) +--E 293 + +--S 294 of 526 +m0854b:= a0854.2-r0854 +--R +--R +--R (5) +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 3 2 4 +--R (- 12B - 16A)a b + 8A a b +--R * +--R 3 +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 5 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 4 2 3 3 2 +--R 4A a b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 4 5 +--R (- 12B - 16A)a b + 8A a +--R * +--R 3 +--R c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 +--R (- 2A b + 4A a b - 2A a )c +--R + +--R 4 3 2 2 3 +--R 8A b + (6B - 16A)a b + (- 12B + 4A)a b + (6B + 8A)a b +--R + +--R 4 +--R - 4A a +--R * +--R 4 +--R c +--R + +--R 6 5 2 4 +--R 10A b + (- 30B - 20A)a b + (60B + 30A)a b +--R + +--R 3 3 4 2 +--R (- 30B - 40A)a b + 20A a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20A a b - 40A a b + 20A a b)c +--R + +--R 5 2 4 3 3 +--R 20A a b + (- 60B - 40A)a b + (120B + 60A)a b +--R + +--R 4 2 5 +--R (- 60B - 80A)a b + 40A a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 2 2 6 +--R (2A b - 4A a b + 2A a )c +--R + +--R 4 3 2 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 16A)a b + (- 6B - 28A)a b +--R + +--R 4 +--R 14A a +--R * +--R 4 +--R c +--R + +--R 2 4 3 3 4 2 +--R 10A a b + (- 30B - 20A)a b + (60B + 30A)a b +--R + +--R 5 6 +--R (- 30B - 40A)a b + 20A a +--R * +--R 2 +--R c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 4A b + 8A a b - 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (12B - 8A)a b + (- 24B - 4A)a b +--R + +--R 3 2 4 +--R (12B + 16A)a b - 8A a b +--R * +--R 3 +--R c +--R + +--R 7 6 2 5 +--R 8A b + (- 24B - 16A)a b + (48B + 24A)a b +--R + +--R 3 4 4 3 +--R (- 24B - 32A)a b + 16A a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 4A a b + 8A a b - 4A a )c +--R + +--R 4 2 3 3 2 +--R 20A a b + (12B - 40A)a b + (- 24B + 12A)a b +--R + +--R 4 5 +--R (12B + 16A)a b - 8A a +--R * +--R 3 +--R c +--R + +--R 6 2 5 3 4 +--R 24A a b + (- 72B - 48A)a b + (144B + 72A)a b +--R + +--R 4 3 5 2 +--R (- 72B - 96A)a b + 48A a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 36A)a b +--R + +--R 3 2 4 +--R (- 12B - 64A)a b + 32A a b +--R * +--R 3 +--R c +--R + +--R 2 5 3 4 4 3 +--R 24A a b + (- 72B - 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4A a b + 4A a b - 2A a )c +--R + +--R 6 5 2 4 3 3 +--R 2A b + (- 6B - 4A)a b + (12B + 16A)a b - 28A a b +--R + +--R 4 2 5 6 +--R (- 12B + 10A)a b + (6B + 8A)a b - 4A a +--R * +--R 2 +--R c +--R + +--R 2 6 3 5 4 4 +--R 12A a b + (- 36B - 24A)a b + (72B + 36A)a b +--R + +--R 5 3 6 2 +--R (- 36B - 48A)a b + 24A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 5 2 4 3 3 +--R 4A a b + (- 12B - 8A)a b + (24B + 20A)a b +--R + +--R 4 2 5 +--R (- 12B - 32A)a b + 16A a b +--R * +--R 2 +--R c +--R + +--R 3 5 4 4 5 3 6 2 +--R 8A a b + (- 24B - 16A)a b + (48B + 24A)a b + (- 24B - 32A)a b +--R + +--R 7 +--R 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 +--R (2A a b - 4A a b + 2A a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2A a b + (- 6B - 4A)a b + (12B + 8A)a b + (- 6B - 12A)a b +--R + +--R 6 +--R 6A a +--R * +--R 2 +--R c +--R + +--R 4 4 5 3 6 2 7 8 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 3 2 4 +--R (- 12B - 16A)a b + 8A a b +--R * +--R 3 +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 5 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 4 2 3 3 2 +--R 4A a b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 4 5 +--R (- 12B - 16A)a b + 8A a +--R * +--R 3 +--R c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 6 +--R (- 2A b + 4A a b - 2A a )c +--R + +--R 4 3 2 2 3 +--R 8A b + (6B - 16A)a b + (- 12B + 4A)a b + (6B + 8A)a b +--R + +--R 4 +--R - 4A a +--R * +--R 4 +--R c +--R + +--R 6 5 2 4 +--R 10A b + (- 30B - 20A)a b + (60B + 30A)a b +--R + +--R 3 3 4 2 +--R (- 30B - 40A)a b + 20A a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (20A a b - 40A a b + 20A a b)c +--R + +--R 5 2 4 3 3 +--R 20A a b + (- 60B - 40A)a b + (120B + 60A)a b +--R + +--R 4 2 5 +--R (- 60B - 80A)a b + 40A a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 2 2 6 +--R (2A b - 4A a b + 2A a )c +--R + +--R 4 3 2 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 16A)a b + (- 6B - 28A)a b +--R + +--R 4 +--R 14A a +--R * +--R 4 +--R c +--R + +--R 2 4 3 3 4 2 +--R 10A a b + (- 30B - 20A)a b + (60B + 30A)a b +--R + +--R 5 6 +--R (- 30B - 40A)a b + 20A a +--R * +--R 2 +--R c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 5 +--R (- 4A b + 8A a b - 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (12B - 8A)a b + (- 24B - 4A)a b +--R + +--R 3 2 4 +--R (12B + 16A)a b - 8A a b +--R * +--R 3 +--R c +--R + +--R 7 6 2 5 +--R 8A b + (- 24B - 16A)a b + (48B + 24A)a b +--R + +--R 3 4 4 3 +--R (- 24B - 32A)a b + 16A a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 5 +--R (- 4A a b + 8A a b - 4A a )c +--R + +--R 4 2 3 3 2 +--R 20A a b + (12B - 40A)a b + (- 24B + 12A)a b +--R + +--R 4 5 +--R (12B + 16A)a b - 8A a +--R * +--R 3 +--R c +--R + +--R 6 2 5 3 4 +--R 24A a b + (- 72B - 48A)a b + (144B + 72A)a b +--R + +--R 4 3 5 2 +--R (- 72B - 96A)a b + 48A a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 36A)a b +--R + +--R 3 2 4 +--R (- 12B - 64A)a b + 32A a b +--R * +--R 3 +--R c +--R + +--R 2 5 3 4 4 3 +--R 24A a b + (- 72B - 48A)a b + (144B + 72A)a b +--R + +--R 5 2 6 +--R (- 72B - 96A)a b + 48A a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 5 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 4 2 3 3 2 +--R 4A a b + (- 12B - 8A)a b + (24B + 20A)a b +--R + +--R 4 5 +--R (- 12B - 32A)a b + 16A a +--R * +--R 3 +--R c +--R + +--R 3 4 4 3 5 2 +--R 8A a b + (- 24B - 16A)a b + (48B + 24A)a b +--R + +--R 6 7 +--R (- 24B - 32A)a b + 16A a +--R * +--R c +--R * +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (- 2A b + 4A a b - 2A a b )c +--R + +--R 5 2 4 3 3 4 2 2 8 +--R (6B a b + (- 12B - 4A)a b + (6B + 8A)a b - 4A a b )c + 2A b +--R + +--R 7 2 6 3 5 4 4 +--R (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (- 4A a b + 8A a b - 4A a b)c +--R + +--R 5 2 4 3 3 4 2 +--R 4A a b + (12B - 8A)a b + (- 24B - 4A)a b + (12B + 16A)a b +--R + +--R 5 +--R - 8A a b +--R * +--R 2 +--R c +--R + +--R 7 2 6 3 5 4 4 +--R 8A a b + (- 24B - 16A)a b + (48B + 24A)a b + (- 24B - 32A)a b +--R + +--R 5 3 +--R 16A a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 4 +--R (2A b - 4A a b + 4A a b - 2A a )c +--R + +--R 6 5 2 4 3 3 +--R 2A b + (- 6B - 4A)a b + (12B + 16A)a b - 28A a b +--R + +--R 4 2 5 6 +--R (- 12B + 10A)a b + (6B + 8A)a b - 4A a +--R * +--R 2 +--R c +--R + +--R 2 6 3 5 4 4 +--R 12A a b + (- 36B - 24A)a b + (72B + 36A)a b +--R + +--R 5 3 6 2 +--R (- 36B - 48A)a b + 24A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 5 2 4 3 3 +--R 4A a b + (- 12B - 8A)a b + (24B + 20A)a b +--R + +--R 4 2 5 +--R (- 12B - 32A)a b + 16A a b +--R * +--R 2 +--R c +--R + +--R 3 5 4 4 5 3 6 2 +--R 8A a b + (- 24B - 16A)a b + (48B + 24A)a b + (- 24B - 32A)a b +--R + +--R 7 +--R 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 +--R (2A a b - 4A a b + 2A a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2A a b + (- 6B - 4A)a b + (12B + 8A)a b + (- 6B - 12A)a b +--R + +--R 6 +--R 6A a +--R * +--R 2 +--R c +--R + +--R 4 4 5 3 6 2 7 8 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b + 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 6 +--R (2B - 2A)b c +--R + +--R 3 2 2 3 4 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 5 4 2 3 3 2 +--R - 2B b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 4 +--R - B a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 6 +--R (2B - 2A)a c +--R + +--R 3 2 2 3 4 +--R (A b + (6B - 4A)a b + (- 2B - 5A)a b + (- 4B + 8A)a )c +--R + +--R 5 4 2 3 3 2 +--R A b + (- 3B - 2A)a b + (6B + 3A)a b + (- 3B - 4A)a b +--R + +--R 4 +--R 2A a b +--R * +--R 2 +--R c +--R * +--R 3 +--R sin(x) +--R + +--R 7 2 2 5 +--R (- B + A)c + ((2B - 4A)b + (B + 3A)a b + (2B - 4A)a )c +--R + +--R 4 3 2 2 +--R (13B - 5A)b + (- B - 12A)a b + (- 12B + 14A)a b +--R + +--R 3 +--R 3A a b +--R * +--R 3 +--R c +--R + +--R 6 5 2 4 3 3 +--R - 2B b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 4 2 +--R - B a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + (10B - 8A)a b - A a )c +--R + +--R 4 3 2 2 +--R - A b + (29B - 8A)a b + (- 8B - 27A)a b +--R + +--R 3 4 +--R (- 21B + 32A)a b + 4A a +--R * +--R 3 +--R c +--R + +--R 5 2 4 3 3 +--R - 4B a b + (8B + 6A)a b + (- 6B - 12A)a b +--R + +--R 4 2 5 +--R (4B + 6A)a b - 2B a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 7 2 2 5 +--R (B - A)c + ((2B - A)b + (B - 3A)a b + (2B - A)a )c +--R + +--R 4 3 2 2 3 +--R - B b + 2B a b + (16B - 5A)a b + (- 9B - 15A)a b +--R + +--R 4 +--R (- 8B + 20A)a +--R * +--R 3 +--R c +--R + +--R 2 4 3 3 4 2 5 +--R - 2B a b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 6 +--R - B a +--R * +--R c +--R * +--R 2 +--R sin(x) +--R + +--R 6 +--R (- 2B + 2A)b c +--R + +--R 3 2 2 3 4 +--R ((- 4B - 2A)b + (6B + 9A)a b + (2B - 14A)a b + 3A a )c +--R + +--R 5 4 2 3 +--R (10B - 4A)b - 9A a b + (- 11B + 10A)a b +--R + +--R 3 2 4 +--R (2B + 3A)a b - B a b +--R * +--R 2 +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 6 +--R (- 2B + 2A)a c +--R + +--R 3 2 2 3 4 +--R (A b + (6B - 12A)a b + (2B + 7A)a b + (4B - 8A)a )c +--R + +--R 5 4 2 3 +--R A b + (33B - 14A)a b + (- 6B - 33A)a b +--R + +--R 3 2 4 +--R (- 27B + 44A)a b + 2A a b +--R * +--R 2 +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 6 +--R (2B - 2A)b c +--R + +--R 3 2 2 3 4 +--R ((8B - 2A)b + (- 6B - 9A)a b + (10B + 2A)a b - 3A a )c +--R + +--R 5 4 2 3 +--R 2B b + (- 4B - 3A)a b + (39B - 6A)a b +--R + +--R 3 2 4 +--R (- 14B - 39A)a b + (- 23B + 48A)a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R (2B - 2A)a c + (- A b + 6B a b + (- 2B - 7A)a b + 4A a )c +--R + +--R 5 4 2 3 3 2 +--R - A b + (3B + 2A)a b + (- 6B - 3A)a b + 15B a b +--R + +--R 4 5 +--R (- 4B - 14A)a b + (- 8B + 16A)a +--R * +--R 2 +--R c +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- B + A)b c + (- 4B b + (5B + 6A)a b - 10A a b + 3A a b)c +--R + +--R 6 5 2 4 3 3 4 2 +--R ((B - A)b + 3B a b + (- 5B - 2A)a b + (2B + 3A)a b - B a b )c +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + (- 2B + 4A)a b - A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- A b - 3B a b + (4B + 9A)a b + (3B - 16A)a b + 4A a )c +--R + +--R 5 2 4 3 3 +--R (8B - 4A)a b + (4B - 6A)a b + (- 14B + 4A)a b +--R + +--R 4 2 5 +--R (4B + 6A)a b - 2B a b +--R * +--R c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + 2B a b + (- 2B + A)a )c +--R + +--R 4 3 2 2 3 +--R (4B - A)b + (- 3B - 6A)a b + (4B + 5A)a b - 3B a b +--R + +--R 4 +--R (4B - 4A)a +--R * +--R 3 +--R c +--R + +--R 6 5 2 4 3 3 +--R 2B b + (- 4B - 3A)a b + 19B a b + (- 4B - 18A)a b +--R + +--R 4 2 5 6 +--R (- 14B + 18A)a b + (2B + 3A)a b - B a +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 +--R (A b + (2B - 4A)a b + A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (A b + (7B - 4A)a b + (- 4B - 9A)a b + (B + 12A)a b - 4A a )c +--R + +--R 5 2 4 3 3 4 2 +--R 4B a b + (- 8B - 6A)a b + (18B + 8A)a b + (- 8B - 18A)a b +--R + +--R 5 +--R (- 6B + 16A)a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 5 +--R (B b - 2B a b + (2B - A)a )c +--R + +--R 4 3 2 2 3 4 3 +--R (B b - 2B a b + (2B - A)a b + (3B - 3A)a b + (- 3B + 3A)a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2B a b + (- 4B - 3A)a b + (6B + 5A)a b + (- 3B - 6A)a b +--R + +--R 6 +--R (- B + 4A)a +--R * +--R c +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 526 +--d0854b:= D(m0854b,x) +--E 295 + +)clear all + + +--S 296 of 526 +t0855:= (A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)) +--R +--R +--R C sin(x) + B cos(x) + A +--R (1) ----------------------- +--R c sin(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 526 +r0855:= (b*B+c*C)*x/(b^2+c^2)+2*(A-a*(b*B+c*C)/(b^2+c^2))*_ + atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(1/2)+_ + (B*c-b*C)*log(a+b*cos(x)+c*sin(x))/(b^2+c^2) +--R +--R +--R (2) +--R +--------------+ +--R | 2 2 2 +--R (B c - C b)\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R (- 2A c + 2C a c - 2A b + 2B a b)atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R (C c + B b)x\|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression(Integer) +--E 297 + +--S 298 of 526 +a0855:= integrate(t0855,x) +--R +--R +--R (3) +--R [ +--R 2 2 +--R (- A c + C a c - A b + B a b) +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +------------+ +--R | 2 2 2 2 +--R (- B c + C b)\|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R (B c - C b)\|c + b - a log(----------------------------) +--R cos(x) + 1 +--R + +--R +------------+ +--R | 2 2 2 +--R (C c + B b)x\|c + b - a +--R / +--R +------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|c + b - a +--R , +--R +--R +--------------+ +--R | 2 2 2 2 +--R (- B c + C b)\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R (B c - C b)\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c - 2C a c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R +--------------+ +--R | 2 2 2 +--R (C c + B b)x\|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 298 + +--S 299 of 526 +m0855a:= a0855.1-r0855 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 | 2 2 2 +--R (- A c + C a c - A b + B a b)\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((b - a)c + b - a b - a b + a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (- c + (- b + a )c)cos(x) - c + (- b + a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (- B c + C b)\|- c - b + a \|c + b - a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 2 +--R (- B c + C b)\|- c - b + a \|c + b - a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R (B c - C b)\|- c - b + a \|c + b - a +--R * +--R - 2c sin(x) - 2b cos(x) - 2a +--R log(----------------------------) +--R cos(x) + 1 +--R + +--R x +--R +------------+ (b - a)tan(-) - c +--R 2 2 | 2 2 2 2 +--R (2A c - 2C a c + 2A b - 2B a b)\|c + b - a atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +------------+ +--R 2 2 | 2 2 2 | 2 2 2 +--R (c + b )\|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 299 + +--S 300 of 526 +d0855a:= D(m0855a,x) +--R +--R +--R (5) +--R 3 2 2 2 3 2 2 3 +--R (- A b + 2A a b - A a b)c + (C a b - 2C a b + C a b)c +--R + +--R 5 4 2 3 3 2 +--R - A b + (B + 2A)a b + (- 2B - A)a b + B a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + ((B - 2A)a b + A a )c +--R + +--R 2 2 3 2 +--R (- C a b + 2C a b - C a )c +--R + +--R 4 3 2 2 3 +--R (A b + (- B - 2A)a b + (2B + A)a b - B a b)c +--R * +--R cos(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + (- A b + B a b)c +--R * +--R sin(x) +--R + +--R 4 2 3 +--R (- 2A b + A a)c + (2C a b - C a )c +--R + +--R 3 2 2 2 3 2 2 +--R (- 3A b + (2B + 2A)a b - B a b)c + (C a b - C a b )c +--R + +--R 5 4 2 3 +--R - A b + (B + A)a b - B a b +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 3 2 2 2 +--R - 2A b c + 2C a b c + (- 3A b + 2B a b + A a b)c +--R + +--R 3 3 5 4 2 3 3 2 +--R (C a b - C a b)c - A b + B a b + A a b - B a b +--R * +--R cos(x) +--R + +--R 4 2 3 2 2 2 +--R - A a c + C a c + (- 2A a b + (B + A)a b)c +--R + +--R 2 2 3 4 2 3 3 2 +--R (C a b - C a b)c - A a b + (B + A)a b - B a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 3 +--R 2A c - 2C a c + (4A b + (- 2B - 2A)a b)c +--R + +--R 2 2 2 4 3 2 2 +--R (- 2C a b + 2C a b)c + (2A b + (- 2B - 2A)a b + 2B a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 3 +--R (- 2A b + 2A a)c + (2C a b - 2C a )c +--R + +--R 3 2 2 2 +--R (- 2A b + (2B + 2A)a b - 2B a b)c +--R * +--R sin(x) +--R + +--R 5 4 2 3 +--R 2A c - 2C a c + (4A b + (- 2B - 2A)a b)c +--R + +--R 2 2 2 4 3 2 2 +--R (- 2C a b + 2C a b)c + (2A b + (- 2B - 2A)a b + 2B a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 +--R 2A c - 2C a c + (2A b + (- 2B + 2A)a b - 2A a )c +--R + +--R 2 3 2 3 2 2 3 +--R (- 2C a b + 2C a )c + (2A a b + (- 2B - 2A)a b + 2B a b)c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 3 2 2 2 +--R 2A b c - 2C a b c + (3A b - 2B a b - A a b)c +--R + +--R 3 3 5 4 2 3 3 2 +--R (- C a b + C a b)c + A b - B a b - A a b + B a b +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + ((B - 2A)a b + A a )c +--R + +--R 2 2 3 2 +--R (- C a b + 2C a b - C a )c +--R + +--R 4 3 2 2 3 +--R (A b + (- B - 2A)a b + (2B + A)a b - B a b)c +--R * +--R cos(x) +--R + +--R 5 4 2 3 +--R - A c + C a c + (- 3A b + (B + 2A)a b)c +--R + +--R 2 2 2 4 3 2 2 +--R (2C a b - 2C a b)c + (- 2A b + (2B + 2A)a b - 2B a b )c +--R * +--R sin(x) +--R + +--R 4 2 3 3 2 2 3 2 2 5 +--R A a c - C a c + (A b - B a b)c + (- C a b + C a b )c + A b +--R + +--R 4 2 3 +--R (- B - A)a b + B a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 2 3 2 2 3 5 +--R (- A b + 2A a b - A a b)c + (C a b - 2C a b + C a b)c - A b +--R + +--R 4 2 3 3 2 +--R (B + 2A)a b + (- 2B - A)a b + B a b +--R * +--R cos(x) +--R + +--R 4 2 3 2 2 2 2 2 3 +--R - A a c + C a c + (- 2A a b + (B + A)a b)c + (C a b - C a b)c +--R + +--R 4 2 3 3 2 +--R - A a b + (B + A)a b - B a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- A b + (B - A)a b + A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (C a b - C a )c + (A b - 2A a b + B a b + (- B + A)a b)c +--R + +--R 4 2 3 3 2 4 6 5 +--R (- C a b + C a b + C a b - C a b)c + A b + (- B - A)a b +--R + +--R 2 4 3 3 4 2 +--R (B - A)a b + (B + A)a b - B a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- A b + (B - A)a b + A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (C a b - C a )c + (A b - 2A a b + B a b + (- B + A)a b)c +--R + +--R 4 2 3 3 2 4 6 5 +--R (- C a b + C a b + C a b - C a b)c + A b + (- B - A)a b +--R + +--R 2 4 3 3 4 2 +--R (B - A)a b + (B + A)a b - B a b +--R * +--R sin(x) +--R + +--R 5 2 4 +--R (- 2A b + A a)c + (2C a b - C a )c +--R + +--R 3 2 2 3 3 +--R (- 4A b + (2B + 2A)a b + (- B + 2A)a b - A a )c +--R + +--R 3 2 2 3 4 2 +--R (2C a b - C a b - 2C a b + C a )c +--R + +--R 5 4 2 3 3 2 4 +--R (- 2A b + (2B + A)a b + (- B + 2A)a b + (- 2B - A)a b + B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 3 2 2 3 +--R - 2A b c + 2C a b c + (- 4A b + 2B a b + 2A a b)c +--R + +--R 3 3 2 5 4 2 3 3 2 +--R (2C a b - 2C a b)c + (- 2A b + 2B a b + 2A a b - 2B a b )c +--R * +--R cos(x) +--R + +--R 5 2 4 2 2 3 3 2 2 4 2 +--R - A a c + C a c + (- 2A a b + B a b + A a )c + (C a b - C a )c +--R + +--R 4 2 3 3 2 4 +--R (- A a b + B a b + A a b - B a b)c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 5 2 2 4 +--R 2A c - 2C a c + (4A b - 2B a b - 2A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (- 2C a b + 2C a )c + (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 5 2 4 +--R (- 2A b + 2A a)c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 3 +--R (- 4A b + (2B + 4A)a b + (- 2B + 2A)a b - 2A a )c +--R + +--R 3 2 2 3 4 2 +--R (2C a b - 2C a b - 2C a b + 2C a )c +--R + +--R 5 4 2 3 3 2 +--R - 2A b + (2B + 2A)a b + (- 2B + 2A)a b + (- 2B - 2A)a b +--R + +--R 4 +--R 2B a b +--R * +--R c +--R * +--R sin(x) +--R + +--R 6 5 2 2 4 +--R 2A c - 2C a c + (4A b - 2B a b - 2A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (- 2C a b + 2C a )c + (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 6 5 2 2 4 +--R 2A c - 2C a c + (4A b - 2B a b - 2A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (- 2C a b + 2C a )c + (2A b - 2B a b - 2A a b + 2B a b)c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 5 4 3 2 2 3 +--R 2A b c - 2C a b c + (4A b - 2B a b - 2A a b)c +--R + +--R 3 3 2 5 4 2 3 3 2 +--R (- 2C a b + 2C a b)c + (2A b - 2B a b - 2A a b + 2B a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- A b + (B - A)a b + A a )c +--R + +--R 2 3 3 4 3 2 2 3 2 +--R (C a b - C a )c + (A b - 2A a b + B a b + (- B + A)a b)c +--R + +--R 4 2 3 3 2 4 6 5 +--R (- C a b + C a b + C a b - C a b)c + A b + (- B - A)a b +--R + +--R 2 4 3 3 4 2 +--R (B - A)a b + (B + A)a b - B a b +--R * +--R cos(x) +--R + +--R 6 5 2 2 4 +--R - A c + C a c + (- 3A b + (B + A)a b + A a )c +--R + +--R 2 2 3 3 +--R (2C a b - C a b - C a )c +--R + +--R 4 3 2 2 3 2 +--R (- 3A b + (2B + 2A)a b + (- B + 2A)a b + (- B - A)a b)c +--R + +--R 4 2 3 3 2 4 6 5 +--R (C a b - C a b - C a b + C a b)c - A b + (B + A)a b +--R + +--R 2 4 3 3 4 2 +--R (- B + A)a b + (- B - A)a b + B a b +--R * +--R sin(x) +--R + +--R 5 2 4 2 2 3 3 2 2 4 2 +--R A a c - C a c + (2A a b - B a b - A a )c + (- C a b + C a )c +--R + +--R 4 2 3 3 2 4 +--R (A a b - B a b - A a b + B a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 2 4 2 2 3 3 2 2 4 2 +--R - A a c + C a c + (- 2A a b + B a b + A a )c + (C a b - C a )c +--R + +--R 4 2 3 3 2 4 +--R (- A a b + B a b + A a b - B a b)c +--R / +--R 2 2 4 4 3 2 2 2 2 +--R ((b - 2a b + a )c + (b - 2a b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 3a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (b - 3a b + 3a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 3 +--R (- b + a)c + (- 2b + 4a b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + 3a b - 3a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 3 3 +--R ((- b + a b)c + (- b + 2a b - a b)c - a b + 2a b - a b ) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 2 2 3 4 2 6 +--R (- b + a )c + (- 2b + 2a b - a b + 2a b - a )c - b +--R + +--R 5 2 4 3 3 4 2 +--R 2a b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 2 5 2 4 3 3 +--R (- a b + a )c + (- 2a b + 3a b - a b)c - a b + 2a b - a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c )sin(x) +--R + +--R 6 2 4 4 3 2 2 2 +--R (2c + (4a b - 2a )c + (- 2b + 4a b - 2a b )c )cos(x) +--R + +--R 6 2 2 4 4 3 2 2 2 +--R 2c + (4b - 4a b + 2a )c + (2b - 4a b + 2a b )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 4 2 3 2 +--R (2b c + (2b + 2a b - 2a b)c + (2a b - 2a b )c)cos(x) +--R + +--R 5 3 2 3 3 +--R (2b + 2a)c + (4b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 +--R (2b - 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 5 2 2 3 4 2 3 +--R 2a c + (4a b - 2a b)c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 2 2 +--R ((- b + a )c + (- b + a b )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (b + a)c + (2a b + a b - a )c +--R + +--R 5 4 2 3 3 2 +--R (- b + a b + a b - a b )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 3 5 4 2 3 3 2 +--R (b + a)c + (2b - a b + a )c + (b - a b - a b + a b )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 3 2 5 3 3 2 +--R ((b + a b)c + (b + 2a b - a b)c + a b - a b )cos(x) +--R + +--R 2 2 4 4 3 2 2 4 2 6 4 2 +--R ((b + 2a b + a )c + (2b + 2a b + a b - a )c + b - a b )cos(x) +--R + +--R 2 4 3 2 2 3 2 5 3 3 +--R (a b + a )c + (2a b + a b - a b)c + a b - a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b - 2a b + a )c + (2b - 4a b + a b + 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b - 2a b + 2a b - a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (- b + a)c + (- b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 6 3 4 4 3 +--R (b - 3a b + 2a b + a b - a b)c + b - 2a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 +--R (- b + a)c + (- 2b + 3a b - a b)c +--R + +--R 5 4 2 3 4 5 2 6 2 5 4 3 5 2 +--R (- b + 3a b - 3a b + 2a b - a )c + a b - 2a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b + a b)c + (- 2b + 2a b + a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (- b + a b + a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b + a )c + (- 2a b + 2a b + a b - a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- a b + a b + a b - a b )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (- 2b + 2a)c + (- 4b + 4a b + 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 3 +--R 2c + (2b + 2a b - 2a )c + (- 2b + 4a b - 2a b)c +--R + +--R 6 5 2 4 3 3 +--R (- 2b + 2a b + 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 7 2 5 4 3 2 2 3 4 3 +--R 2c + (4b - 2a b)c + (2b - 4a b + 2a b + 2a b - 2a )c +--R + +--R 5 2 4 3 3 4 2 +--R (- 2a b + 2a b + 2a b - 2a b )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 2 2 +--R (2b c + (4b - 2a b)c + (2b - 2a b )c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (2b + 2a)c + (4b + 4a b - 2a b - 2a )c +--R + +--R 5 4 2 3 3 2 2 +--R (2b + 2a b - 2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 2 +--R 2a c + (4a b - 2a )c + (2a b - 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 2 +--R ((- b + a )c + (- 2b + 3a b - a )c + (- b + 2a b - a b )c)sin(x) +--R + +--R 6 3 2 3 4 +--R (b + a)c + (b + 2a b - a )c +--R + +--R 5 4 2 3 3 2 4 2 7 2 5 4 3 +--R (- b + a b + 2a b - a b - a b)c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 4 5 4 2 3 3 2 5 2 +--R (b + a)c + (2b + a b - a b)c + (b - a b - a b + 2a b - a )c +--R + +--R 6 3 4 5 2 +--R - a b + 2a b - a b +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b + a b)c + (2b + 2a b - a b - a b)c +--R + +--R 6 5 2 4 3 3 +--R (b + a b - a b - a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 2 2 3 4 3 +--R (b + 2a b + a )c + (2b + 4a b + a b - 2a b - a )c +--R + +--R 6 5 3 3 4 2 +--R (b + 2a b - 2a b - a b )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 5 2 4 3 3 4 2 +--R (a b + a )c + (2a b + 2a b - a b - a )c + (a b + a b - a b - a b )c +--R Type: Expression(Integer) +--E 300 + +--S 301 of 526 +m0855b:= a0855.2-r0855 +--R +--R +--R (6) +--R +--------------+ +--R | 2 2 2 +--R (- B c + C b)\|- c - b + a log(c sin(x) + b cos(x) + a) +--R + +--R +--------------+ +--R | 2 2 2 2 +--R (- B c + C b)\|- c - b + a log(----------) +--R cos(x) + 1 +--R + +--R +--------------+ +--R | 2 2 2 - 2c sin(x) - 2b cos(x) - 2a +--R (B c - C b)\|- c - b + a log(----------------------------) +--R cos(x) + 1 +--R + +--R 2 2 +--R (2A c - 2C a c + 2A b - 2B a b) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R (2A c - 2C a c + 2A b - 2B a b)atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R +--------------+ +--R 2 2 | 2 2 2 +--R (c + b )\|- c - b + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 526 +d0855b:= D(m0855b,x) +--R +--R +--R (7) +--R 2 2 3 2 2 +--R ((- A b + A a)c + (C a b - C a )c - A b + (B + A)a b - B a b) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (- 2A c + 2C a c + (- 2A b + 2B a b)c)cos(x) - 2A c + 2C a c +--R + +--R 2 +--R (- 2A b + 2B a b)c +--R * +--R sin(x) +--R + +--R 2 2 3 2 +--R (- 3A b + A a)c + (3C a b - C a )c - 3A b + (3B + A)a b +--R + +--R 2 +--R - B a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 3 2 2 +--R (- 4A b c + 4C a b c - 4A b + 4B a b )cos(x) + (- A b - A a)c +--R + +--R 2 3 2 2 +--R (C a b + C a )c - A b + (B - A)a b + B a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 +--R (4A c - 4C a c + (4A b - 4B a b)c)sin(x) +--R + +--R 3 2 2 2 +--R (4A c - 4C a c + (4A b - 4B a b)c)cos(x) +--R + +--R 3 2 2 +--R (4A c - 4C a c + (4A b - 4B a b)c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 3 2 2 +--R ((3A b + A a)c + (- 3C a b - C a )c + 3A b + (- 3B + A)a b - B a b) +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 3 2 +--R (- 2A c + 2C a c + (- 2A b + 2B a b)c)cos(x) - 2A c + 2C a c +--R + +--R 2 +--R (- 2A b + 2B a b)c +--R * +--R sin(x) +--R + +--R 2 2 3 2 2 2 +--R ((A b + A a)c + (- C a b - C a )c + A b + (- B + A)a b - B a b)cos(x) +--R + +--R 2 2 3 2 2 +--R (- A b - A a)c + (C a b + C a )c - A b + (B - A)a b + B a b +--R / +--R 2 2 2 4 3 2 2 2 +--R ((b - 2a b + a )c + b - 2a b + a b )sin(x) +--R + +--R 3 3 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)cos(x) + (- 2b + 2a)c +--R + +--R 3 2 +--R (- 2b + 2a b )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )cos(x) +--R + +--R 2 2 2 4 2 2 2 2 2 4 2 2 +--R ((- 2b + 2a )c - 2b + 2a b )cos(x) + (- b + a )c - b + a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 +--R ((- 2b + 2a)c + (- 2b + 2a b )c)sin(x) +--R + +--R 4 2 2 4 2 2 +--R ((4c + 4b c )cos(x) + 4c + 4b c )sin(x) +--R + +--R 3 3 2 2 +--R ((2b + 2a)c + (2b + 2a b )c)cos(x) +--R + +--R 3 3 2 3 3 2 +--R ((4b + 4a)c + (4b + 4a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 2 +--R ((- b + a )c - b + a b )sin(x) +--R + +--R 3 3 2 3 3 2 +--R (((2b + 2a)c + (2b + 2a b )c)cos(x) + (2b + 2a)c + (2b + 2a b )c) +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 2 2 2 +--R ((b + 2a b + a )c + b + 2a b + a b )cos(x) +--R + +--R 2 2 2 4 3 2 2 2 2 2 +--R ((2b + 4a b + 2a )c + 2b + 4a b + 2a b )cos(x) + (b + 2a b + a )c +--R + +--R 4 3 2 2 +--R b + 2a b + a b +--R Type: Expression(Integer) +--E 302 + +)clear all + + +--S 303 of 526 +t0856:= (A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2 +--R +--R +--R C sin(x) + B cos(x) + A +--R (1) --------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a +--R Type: Expression(Integer) +--E 303 + +--S 304 of 526 +r0856:= 2*(a*A-b*B-c*C)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ + (a^2-b^2-c^2)^(3/2)+(B*c-b*C+(A*c-a*C)*cos(x)-(A*b-a*B)*sin(x))/_ + (a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (2) +--R 2 +--R (- 2C c + (- 2B b + 2A a)c)sin(x) +--R + +--R 2 2 +--R (- 2C b c - 2B b + 2A a b)cos(x) - 2C a c - 2B a b + 2A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R ((A b - B a)sin(x) + (- A c + C a)cos(x) - B c + C b)\|- c - b + a +--R / +--R 3 2 2 2 3 2 2 2 3 +--R ((c + (b - a )c)sin(x) + (b c + b - a b)cos(x) + a c + a b - a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 304 + +--S 305 of 526 +a0856:= integrate(t0856,x) +--R +--R +--R (3) +--R [ +--R 2 2 2 +--R ((C b - C a)c + (B b + (- B - A)a b + A a )c)sin(x) +--R + +--R 2 3 2 2 +--R ((C b - C a b)c + B b + (- B - A)a b + A a b)cos(x) +--R + +--R 2 2 2 3 +--R (C a b - C a )c + B a b + (- B - A)a b + A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 2 2 2 +--R ((- B + A)c + (C b - C a)c + A b + (- B - A)a b + B a )sin(x) +--R + +--R 2 2 2 2 +--R ((- B b + A a)c + C b - C a )cos(x) + (- B b + A a)c + C b - C a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 2 2 2 +--R ((2C b - 2C a)c + (2B b + (- 2B - 2A)a b + 2A a )c)sin(x) +--R + +--R 2 3 2 2 +--R ((2C b - 2C a b)c + 2B b + (- 2B - 2A)a b + 2A a b)cos(x) +--R + +--R 2 2 2 3 +--R (2C a b - 2C a )c + 2B a b + (- 2B - 2A)a b + 2A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 2 2 2 +--R ((- B + A)c + (C b - C a)c + A b + (- B - A)a b + B a )sin(x) +--R + +--R 2 2 2 2 +--R ((- B b + A a)c + C b - C a )cos(x) + (- B b + A a)c + C b - C a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 3 2 2 3 +--R ((b - a)c + (b - a b - a b + a )c)sin(x) +--R + +--R 2 2 4 3 2 2 3 2 2 3 +--R ((b - a b)c + b - a b - a b + a b)cos(x) + (a b - a )c + a b +--R + +--R 2 2 3 4 +--R - a b - a b + a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 305 + +--S 306 of 526 +m0856a:= a0856.1-r0856 +--R +--R +--R (4) +--R +--------------+ +--R 2 2 | 2 2 2 +--R ((C b - C a)c + B b + (- B - A)a b + A a )\|- c - b + a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R +------------+ +--R 2 2 | 2 2 2 +--R ((2C b - 2C a)c + 2B b + (- 2B - 2A)a b + 2A a )\|c + b - a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R ((- B + A)c + C b - C a)\|- c - b + a \|c + b - a +--R / +--R +--------------+ +------------+ +--R 2 3 2 2 3 | 2 2 2 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 526 +d0856a:= D(m0856a,x) +--R +--R +--R (5) +--R 3 2 2 4 3 +--R (- C b + 2C a b - C a b)c - B b + (2B + A)a b +--R + +--R 2 2 3 +--R (- B - 2A)a b + A a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 2 +--R - C c + (- B b + A a)c + (C b - 2C a b + C a )c +--R + +--R 3 2 2 3 +--R (B b + (- 2B - A)a b + (B + 2A)a b - A a )c +--R * +--R cos(x) +--R + +--R 4 3 +--R - C c + (- B b + A a)c +--R * +--R sin(x) +--R + +--R 3 2 2 2 +--R (- 2C b + C a)c + (- 2B b + (B + 2A)a b - A a )c +--R + +--R 3 2 4 3 2 2 +--R (- C b + C a b )c - B b + (B + A)a b - A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 4 +--R - 2C b c + (- 2B b + 2A a b)c + (- C b + C a b)c - B b +--R + +--R 3 2 2 3 +--R A a b + B a b - A a b +--R * +--R cos(x) +--R + +--R 3 2 2 2 2 3 +--R - C a c + (- B a b + A a )c + (- C a b + C a b)c - B a b +--R + +--R 2 2 3 +--R (B + A)a b - A a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 +--R 2C c + (2B b - 2A a)c + (2C b - 2C a b)c +--R + +--R 3 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 2 +--R ((- 2C b + 2C a)c + (- 2B b + (2B + 2A)a b - 2A a )c )sin(x) +--R + +--R 4 3 2 2 +--R 2C c + (2B b - 2A a)c + (2C b - 2C a b)c +--R + +--R 3 2 2 +--R (2B b + (- 2B - 2A)a b + 2A a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 4 3 2 2 +--R 2C c + (2B b - 2A a)c + (2C a b - 2C a )c +--R + +--R 2 2 3 +--R (2B a b + (- 2B - 2A)a b + 2A a )c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 3 2 2 3 2 4 3 +--R 2C b c + (2B b - 2A a b)c + (C b - C a b)c + B b - A a b +--R + +--R 2 2 3 +--R - B a b + A a b +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 2 +--R - C c + (- B b + A a)c + (C b - 2C a b + C a )c +--R + +--R 3 2 2 3 +--R (B b + (- 2B - A)a b + (B + 2A)a b - A a )c +--R * +--R cos(x) +--R + +--R 4 3 2 2 +--R - C c + (- B b + A a)c + (- 2C b + 2C a b)c +--R + +--R 3 2 2 +--R (- 2B b + (2B + 2A)a b - 2A a b)c +--R * +--R sin(x) +--R + +--R 3 2 2 3 2 4 +--R C a c + (B a b - A a )c + (C b - C a b )c + B b +--R + +--R 3 2 2 +--R (- B - A)a b + A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 4 3 +--R (- C b + 2C a b - C a b)c - B b + (2B + A)a b +--R + +--R 2 2 3 +--R (- B - 2A)a b + A a b +--R * +--R cos(x) +--R + +--R 3 2 2 2 2 3 +--R - C a c + (- B a b + A a )c + (- C a b + C a b)c - B a b +--R + +--R 2 2 3 +--R (B + A)a b - A a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 5 4 2 3 +--R C c + (B b - A a)c + (C a b - C a )c +--R + +--R 2 2 3 2 +--R (B a b + (- B - A)a b + A a )c +--R + +--R 4 3 2 2 3 5 4 +--R (- C b + C a b + C a b - C a b)c - B b + (B + A)a b +--R + +--R 2 3 3 2 4 +--R (B - A)a b + (- B - A)a b + A a b +--R * +--R cos(x) +--R + +--R 5 4 2 3 +--R C c + (B b - A a)c + (C a b - C a )c +--R + +--R 2 2 3 2 +--R (B a b + (- B - A)a b + A a )c +--R + +--R 4 3 2 2 3 5 4 +--R (- C b + C a b + C a b - C a b)c - B b + (B + A)a b +--R + +--R 2 3 3 2 4 +--R (B - A)a b + (- B - A)a b + A a b +--R * +--R sin(x) +--R + +--R 4 2 2 3 +--R (2C b - C a)c + (2B b + (- B - 2A)a b + A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - C a b - 2C a b + C a )c +--R + +--R 4 3 2 2 3 4 +--R (2B b + (- B - 2A)a b + (- 2B + A)a b + (B + 2A)a b - A a )c +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 3 3 2 2 +--R 2C b c + (2B b - 2A a b)c + (2C b - 2C a b)c +--R + +--R 4 3 2 2 3 +--R (2B b - 2A a b - 2B a b + 2A a b)c +--R * +--R cos(x) +--R + +--R 4 2 3 2 3 2 +--R C a c + (B a b - A a )c + (C a b - C a )c +--R + +--R 3 2 2 3 4 +--R (B a b - A a b - B a b + A a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 4 2 2 3 +--R - 2C c + (- 2B b + 2A a)c + (- 2C b + 2C a )c +--R + +--R 3 2 2 3 2 +--R (- 2B b + 2A a b + 2B a b - 2A a )c +--R * +--R 2 +--R sin(x) +--R + +--R 4 2 2 3 +--R (2C b - 2C a)c + (2B b + (- 2B - 2A)a b + 2A a )c +--R + +--R 3 2 2 3 2 +--R (2C b - 2C a b - 2C a b + 2C a )c +--R + +--R 4 3 2 2 3 4 +--R (2B b + (- 2B - 2A)a b + (- 2B + 2A)a b + (2B + 2A)a b - 2A a )c +--R * +--R sin(x) +--R + +--R 5 4 2 2 3 +--R - 2C c + (- 2B b + 2A a)c + (- 2C b + 2C a )c +--R + +--R 3 2 2 3 2 +--R (- 2B b + 2A a b + 2B a b - 2A a )c +--R * +--R 2 +--R cos(x) +--R + +--R 5 4 2 2 3 +--R - 2C c + (- 2B b + 2A a)c + (- 2C b + 2C a )c +--R + +--R 3 2 2 3 2 +--R (- 2B b + 2A a b + 2B a b - 2A a )c +--R * +--R cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 2 3 3 2 2 +--R - 2C b c + (- 2B b + 2A a b)c + (- 2C b + 2C a b)c +--R + +--R 4 3 2 2 3 +--R (- 2B b + 2A a b + 2B a b - 2A a b)c +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 3 +--R C c + (B b - A a)c + (C a b - C a )c +--R + +--R 2 2 3 2 +--R (B a b + (- B - A)a b + A a )c +--R + +--R 4 3 2 2 3 5 4 +--R (- C b + C a b + C a b - C a b)c - B b + (B + A)a b +--R + +--R 2 3 3 2 4 +--R (B - A)a b + (- B - A)a b + A a b +--R * +--R cos(x) +--R + +--R 5 4 2 2 3 +--R C c + (B b - A a)c + (2C b - C a b - C a )c +--R + +--R 3 2 2 3 2 +--R (2B b + (- B - 2A)a b + (- B + A)a b + A a )c +--R + +--R 4 3 2 2 3 5 4 +--R (C b - C a b - C a b + C a b)c + B b + (- B - A)a b +--R + +--R 2 3 3 2 4 +--R (- B + A)a b + (B + A)a b - A a b +--R * +--R sin(x) +--R + +--R 4 2 3 2 3 2 +--R - C a c + (- B a b + A a )c + (- C a b + C a )c +--R + +--R 3 2 2 3 4 +--R (- B a b + A a b + B a b - A a )c +--R * +--R 2 +--R cos(x) +--R + +--R 4 2 3 2 3 2 +--R C a c + (B a b - A a )c + (C a b - C a )c +--R + +--R 3 2 2 3 4 +--R (B a b - A a b - B a b + A a )c +--R / +--R 2 2 4 4 3 3 4 2 2 +--R ((b - 2a b + a )c + (b - 2a b + 2a b - a )c )sin(x) +--R + +--R 5 2 2 3 3 +--R (- b + a)c + (- 2a b + 4a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 2 3 +--R (- b + a)c + (- 2b + 4a b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 3 2 5 2 4 +--R (- b + a b)c + (- b + 3a b - 2a b)c - a b + 2a b +--R + +--R 4 2 5 +--R - 2a b + a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 5 +--R (- b + a )c + (- 2b + 2a b + 2a b - 2a )c - b + 2a b +--R + +--R 2 4 4 2 5 6 +--R - a b + a b - 2a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 4 2 5 2 4 4 2 +--R (- a b + a )c + (- 2a b + 3a b - a )c - a b + 2a b - 2a b +--R + +--R 5 +--R a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 5 3 2 2 3 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c )sin(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R (2c + (4a b - 4a )c + (- 2b + 4a b - 4a b + 2a )c )cos(x) +--R + +--R 6 2 4 4 3 3 4 2 +--R 2c + (4b - 4a b)c + (2b - 4a b + 4a b - 2a )c +--R * +--R sin(x) +--R + +--R 5 3 2 2 3 +--R 2b c + (2b + 2a b - 4a b)c +--R + +--R 4 2 3 3 2 4 +--R (2a b - 2a b - 2a b + 2a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 5 3 3 3 5 4 4 5 +--R ((2b + 2a)c + (4b - 4a )c + (2b - 2a b - 2a b + 2a )c)cos(x) +--R + +--R 5 2 2 3 3 4 2 3 3 2 4 +--R 2a c + (4a b - 2a b - 2a )c + (2a b - 2a b - 2a b + 2a b)c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 4 2 2 4 2 2 +--R ((- b + a )c + (- b + 2a b - a )c )sin(x) +--R + +--R 5 2 3 3 +--R (b + a)c + (2a b - 2a )c +--R + +--R 5 4 2 3 3 2 4 5 +--R (- b + a b + 2a b - 2a b - a b + a )c +--R * +--R cos(x) +--R + +--R 5 3 2 3 +--R (b + a)c + (2b - 2a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (b - a b - 2a b + 2a b + a b - a )c +--R * +--R sin(x) +--R + +--R 2 4 4 3 2 2 3 2 5 3 3 5 +--R ((b + a b)c + (b + 2a b - a b - 2a b)c + a b - 2a b + a b) +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 4 4 3 3 4 2 6 2 4 +--R (b + 2a b + a )c + (2b + 2a b - 2a b - 2a )c + b - a b +--R + +--R 4 2 6 +--R - a b + a +--R * +--R cos(x) +--R + +--R 2 4 3 2 2 3 4 2 5 3 3 5 +--R (a b + a )c + (2a b + a b - 2a b - a )c + a b - 2a b + a b +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b + 2a b - a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b + 2a b + a b - 4a b + a b + 2a b - a )c +--R * +--R 2 +--R sin(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (b - 3a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 6 +--R (- b + 3a b - 2a b - 2a b + 3a b - a )c - b + 2a b +--R + +--R 2 5 3 4 4 3 5 2 6 +--R a b - 4a b + a b + 2a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 3 4 +--R (b - a)c + (2b - 3a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 2 5 3 4 +--R (b - 3a b + 2a b + 2a b - 3a b + a )c - a b + 2a b + a b +--R + +--R 4 3 5 2 6 7 +--R - 4a b + a b + 2a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (b - a b)c + (2b - 2a b - 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (b - a b - 2a b + 2a b + a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c) +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (a b - a )c + (2a b - 2a b - 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (a b - a b - 2a b + 2a b + a b - a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 6 3 2 2 3 4 +--R (2b - 2a)c + (4b - 4a b - 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 2b - 2a b + 4a )c + (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (2b - 2a b - 4a b + 4a b + 2a b - 2a b)c +--R * +--R cos(x) +--R + +--R 7 2 2 5 4 3 3 4 3 +--R - 2c + (- 4b + 2a b + 2a )c + (- 2b + 4a b - 4a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (2a b - 2a b - 4a b + 4a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 6 3 2 4 5 2 3 4 2 2 +--R (- 2b c + (- 4b + 4a b)c + (- 2b + 4a b - 2a b)c )cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- 2b - 2a)c + (- 4b - 4a b + 4a b + 4a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- 2b - 2a b + 4a b + 4a b - 2a b - 2a )c +--R * +--R cos(x) +--R + +--R 6 2 3 4 4 3 2 5 2 +--R - 2a c + (- 4a b + 4a )c + (- 2a b + 4a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 5 4 2 2 4 3 6 2 4 4 2 6 2 +--R ((b - a )c + (2b - 4a b + 2a )c + (b - 3a b + 3a b - a )c)sin(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- b - 2a b + a b + 2a )c +--R + +--R 5 4 2 3 3 2 4 5 2 7 2 5 4 3 6 +--R (b - a b - 2a b + 2a b + a b - a )c + b - 3a b + 3a b - a b +--R * +--R cos(x) +--R + +--R 6 3 2 2 3 4 +--R (- b - a)c + (- 2b - a b + 2a b + a )c +--R + +--R 5 4 2 3 3 2 4 5 2 6 3 4 5 2 7 +--R (- b + a b + 2a b - 2a b - a b + a )c + a b - 3a b + 3a b - a +--R * +--R sin(x) +--R + +--R 2 5 4 3 2 2 3 3 +--R (- b - a b)c + (- 2b - 2a b + 2a b + 2a b)c +--R + +--R 6 5 2 4 3 3 4 2 5 +--R (- b - a b + 2a b + 2a b - a b - a b)c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 4 3 3 4 3 +--R (- b - 2a b - a )c + (- 2b - 4a b + 4a b + 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 +--R (- b - 2a b + a b + 4a b + a b - 2a b - a )c +--R * +--R cos(x) +--R + +--R 2 5 3 2 2 3 4 3 +--R (- a b - a )c + (- 2a b - 2a b + 2a b + 2a )c +--R + +--R 5 2 4 3 3 4 2 5 6 +--R (- a b - a b + 2a b + 2a b - a b - a )c +--R Type: Expression(Integer) +--E 307 + +--S 308 of 526 +m0856b:= a0856.2-r0856 +--R +--R +--R (6) +--R 2 2 +--R ((2C b - 2C a)c + 2B b + (- 2B - 2A)a b + 2A a ) +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R x +--R (b - a)tan(-) - c +--R 2 2 2 +--R ((2C b - 2C a)c + 2B b + (- 2B - 2A)a b + 2A a )atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R +--------------+ +--R | 2 2 2 +--R ((- B + A)c + C b - C a)\|- c - b + a +--R / +--R +--------------+ +--R 2 3 2 2 3 | 2 2 2 +--R ((b - a)c + b - a b - a b + a )\|- c - b + a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 526 +d0856b:= D(m0856b,x) +--R +--R +--R (7) +--R 2 2 2 +--R ((- C b + C a)c - B b + (B + A)a b - A a )sin(x) +--R + +--R 2 2 +--R ((- 2C c + (- 2B b + 2A a)c)cos(x) - 2C c + (- 2B b + 2A a)c)sin(x) +--R + +--R 2 2 2 +--R ((- 3C b + C a)c - 3B b + (B + 3A)a b - A a )cos(x) +--R + +--R 2 2 +--R (- 4C b c - 4B b + 4A a b)cos(x) + (- C b - C a)c - B b +--R + +--R 2 +--R (- B + A)a b + A a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 +--R (4C c + (4B b - 4A a)c)sin(x) + (4C c + (4B b - 4A a)c)cos(x) +--R + +--R 2 +--R (4C c + (4B b - 4A a)c)cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 +--R ((3C b + C a)c + 3B b + (B - 3A)a b - A a )sin(x) +--R + +--R 2 2 +--R ((- 2C c + (- 2B b + 2A a)c)cos(x) - 2C c + (- 2B b + 2A a)c)sin(x) +--R + +--R 2 2 2 2 +--R ((C b + C a)c + B b + (B - A)a b - A a )cos(x) + (- C b - C a)c - B b +--R + +--R 2 +--R (- B + A)a b + A a +--R / +--R 2 2 2 4 3 3 4 2 +--R ((b - 2a b + a )c + b - 2a b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 +--R (- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )cos(x) +--R + +--R 2 2 2 4 2 2 4 2 2 2 4 +--R ((- 2b + 2a )c - 2b + 4a b - 2a )cos(x) + (- b + a )c - b +--R + +--R 2 2 4 +--R 2a b - a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 3 2 2 3 2 +--R ((- 2b + 2a)c + (- 2b + 2a b + 2a b - 2a )c)sin(x) +--R + +--R 4 2 2 2 4 2 2 2 +--R ((4c + (4b - 4a )c )cos(x) + 4c + (4b - 4a )c )sin(x) +--R + +--R 3 3 2 2 3 2 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) +--R + +--R 3 3 2 2 3 3 +--R ((4b + 4a)c + (4b + 4a b - 4a b - 4a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 2 2 4 2 +--R ((- b + a )c - b + 2a b - a )sin(x) +--R + +--R 3 3 2 2 3 3 +--R ((2b + 2a)c + (2b + 2a b - 2a b - 2a )c)cos(x) + (2b + 2a)c +--R + +--R 3 2 2 3 +--R (2b + 2a b - 2a b - 2a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 3 4 2 +--R ((b + 2a b + a )c + b + 2a b - 2a b - a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R ((2b + 4a b + 2a )c + 2b + 4a b - 4a b - 2a )cos(x) +--R + +--R 2 2 2 4 3 3 4 +--R (b + 2a b + a )c + b + 2a b - 2a b - a +--R Type: Expression(Integer) +--E 309 + +)clear all + + +--S 310 of 526 +t0857:= (A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3 +--R +--R +--R (1) +--R C sin(x) + B cos(x) + A +--R / +--R 3 3 2 2 2 +--R c sin(x) + (3b c cos(x) + 3a c )sin(x) +--R + +--R 2 2 2 3 3 2 2 +--R (3b c cos(x) + 6a b c cos(x) + 3a c)sin(x) + b cos(x) + 3a b cos(x) +--R + +--R 2 3 +--R 3a b cos(x) + a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 526 +r0857:= -(b*(A*b-a*B)+c*(A*c-a*C)+2*a*(a*A-b*B-c*C))*_ + atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/(a^2-b^2-c^2)^(3/2)/_ + (-a^2+b^2+c^2)+1/2*(B*c-b*C-(-A*c+a*C)*cos(x)+(-A*b+a*B)*sin(x))/_ + (a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x))^2+_ + 1/2*((A*b-a*B)*c-b*(A*c-a*C)-(a*(A*c-a*C)+2*c*(a*A-b*B-c*C))*cos(x)+_ + (a*(A*b-a*B)+2*b*(a*A-b*B-c*C))*sin(x))/(a^2-b^2-c^2)/_ + (-a^2+b^2+c^2)/(a+b*cos(x)+c*sin(x)) +--R +--R +--R (2) +--R 4 3 2 2 2 2 +--R (- 2A c + 6C a c + (- 2A b + 6B a b - 4A a )c )sin(x) +--R + +--R 3 2 3 2 2 +--R (- 4A b c + 12C a b c + (- 4A b + 12B a b - 8A a b)c)cos(x) +--R + +--R 3 2 2 2 2 3 +--R - 4A a c + 12C a c + (- 4A a b + 12B a b - 8A a )c +--R * +--R sin(x) +--R + +--R 2 2 2 4 3 2 2 2 +--R (- 2A b c + 6C a b c - 2A b + 6B a b - 4A a b )cos(x) +--R + +--R 2 2 3 2 2 3 +--R (- 4A a b c + 12C a b c - 4A a b + 12B a b - 8A a b)cos(x) +--R + +--R 2 2 3 2 2 3 4 +--R - 2A a c + 6C a c - 2A a b + 6B a b - 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 2 2 2 2 +--R (2C b c + (2B b - 3A a b + B a )c)sin(x) +--R + +--R 3 2 2 2 3 +--R - 2C c + (- 2B b + 3A a)c + (2C b - C a )c + 2B b +--R + +--R 2 2 +--R - 3A a b + B a b +--R * +--R cos(x) +--R + +--R 2 3 2 2 3 +--R A b c + C a b c + A b + B a b - 4A a b + 2B a +--R * +--R sin(x) +--R + +--R 2 2 2 2 +--R (- 2C b c + (- 2B b + 3A a b)c - C a b)cos(x) +--R + +--R 3 2 2 2 3 3 +--R (- A c - C a c + (- A b - B a b + 4A a )c - 2C a )cos(x) - B c +--R + +--R 2 2 2 3 2 +--R C b c + (- B b + 2B a )c + C b - 2C a b +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 6 2 2 4 4 2 2 4 2 2 +--R (2c + (4b - 4a )c + (2b - 4a b + 2a )c )sin(x) +--R + +--R 5 3 2 3 5 2 3 4 5 +--R (4b c + (8b - 8a b)c + (4b - 8a b + 4a b)c)cos(x) + 4a c +--R + +--R 2 3 3 4 3 2 5 +--R (8a b - 8a )c + (4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 4 4 2 2 2 6 2 4 4 2 2 +--R (2b c + (4b - 4a b )c + 2b - 4a b + 2a b )cos(x) +--R + +--R 4 3 3 2 5 3 3 5 2 4 +--R (4a b c + (8a b - 8a b)c + 4a b - 8a b + 4a b)cos(x) + 2a c +--R + +--R 2 2 4 2 2 4 4 2 6 +--R (4a b - 4a )c + 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 526 +a0857:= integrate(t0857,x) +--R +--R +--R (3) +--R [ +--R 3 2 2 3 +--R (2A b - 4A a b + 2A a b)c +--R + +--R 3 2 2 3 2 +--R (- 6C a b + 12C a b - 6C a b)c +--R + +--R 5 4 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 6A)a b +--R + +--R 3 2 4 +--R (- 6B - 8A)a b + 4A a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 3 2 2 3 4 2 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 2 3 3 2 4 +--R 2A a b + (- 6B - 4A)a b + (12B + 6A)a b + (- 6B - 8A)a b +--R + +--R 5 +--R 4A a +--R * +--R c +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 3 +--R (- A b + 2A a b - A a )c + (3C a b - 6C a b + 3C a )c +--R + +--R 3 2 2 3 4 2 +--R (3B a b + (- 6B - 2A)a b + (3B + 4A)a b - 2A a )c +--R + +--R 4 2 3 3 2 6 5 +--R (- 3C a b + 6C a b - 3C a b )c + A b + (- 3B - 2A)a b +--R + +--R 2 4 3 3 4 2 +--R (6B + 3A)a b + (- 3B - 4A)a b + 2A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 +--R (2A a b - 4A a b + 2A a b)c +--R + +--R 2 3 3 2 4 5 2 4 +--R (- 6C a b + 12C a b - 6C a b)c + 2A a b + (- 6B - 4A)a b +--R + +--R 3 3 4 2 5 +--R (12B + 6A)a b + (- 6B - 8A)a b + 4A a b +--R * +--R cos(x) +--R + +--R 2 2 4 2 2 3 3 +--R (A b - 2A a b + A a )c + (- 3C a b + 6C a b - 3C a )c +--R + +--R 4 3 2 2 3 4 2 +--R (A b + (- 3B - 2A)a b + (6B + 4A)a b + (- 3B - 6A)a b + 3A a )c +--R + +--R 3 2 4 5 2 4 3 3 +--R (- 3C a b + 6C a b - 3C a )c + A a b + (- 3B - 2A)a b +--R + +--R 4 2 5 6 +--R (6B + 3A)a b + (- 3B - 4A)a b + 2A a +--R * +--R log +--R 2 2 2 2 +--R ((b - a)c sin(x) + (- c - a b + a )cos(x) - c - b + a b) +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R + +--R 2 3 2 2 3 +--R ((- b + a)c - b + a b + a b - a )sin(x) +--R + +--R 3 2 2 3 2 2 +--R (c + (b - a )c)cos(x) + c + (b - a )c +--R / +--R c sin(x) + b cos(x) + a +--R + +--R 4 2 3 +--R (2B - 2A)b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 3 2 2 3 4 5 +--R (- 4C a b + 7C a b - 2C a b - C a )c + 2B b +--R + +--R 4 2 3 3 2 4 +--R (- 4B - 3A)a b + (3B + 6A)a b + (- 2B - 3A)a b + B a b +--R * +--R cos(x) +--R + +--R 4 2 3 +--R (2B - 2A)a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (A b + (6B - 4A)a b + (- 2B - 5A)a b + (- 4B + 8A)a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- C a b - 2C a b + 7C a b - 4C a )c + A b + (B - 2A)a b +--R + +--R 2 3 3 2 4 5 +--R (- 2B - 3A)a b + (3B + 8A)a b + (- 4B - 4A)a b + 2B a +--R * +--R sin(x) +--R + +--R 5 4 +--R (- B + A)c + (- C b + C a)c +--R + +--R 2 2 3 +--R (- 2B b + (B + 3A)a b + (2B - 4A)a )c +--R + +--R 3 2 2 3 2 +--R (- 2C b + 7C a b - 7C a b + 2C a )c +--R + +--R 4 3 2 2 +--R (- B - A)b + (7B + 3A)a b + (- 7B - 8A)a b +--R + +--R 3 4 +--R (2B + 6A)a b - B a +--R * +--R c +--R + +--R 5 2 3 4 +--R - C b + 2C a b - C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 2 3 2 +--R (- A b + 2B a b - A a )c + (C a b - C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (- A b + 5B a b - 3A a b - 5B a b + 4A a )c - 2C a b +--R + +--R 3 2 5 +--R 4C a b - 2C a +--R * +--R cos(x) +--R + +--R 5 4 +--R (B - A)c + (C b - C a)c +--R + +--R 2 2 3 +--R ((2B - A)b + (B - 3A)a b + (- 2B + 3A)a )c +--R + +--R 3 2 2 3 2 +--R (2C b - 6C a b + 7C a b - 3C a )c +--R + +--R 4 3 2 2 3 +--R B b + (- 2B - 3A)a b + (7B + 5A)a b + (- 7B - 6A)a b +--R + +--R 4 +--R (B + 4A)a +--R * +--R c +--R + +--R 5 4 2 3 3 2 4 5 +--R C b - 2C a b - 2C a b + 4C a b + C a b - 2C a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R / +--R 3 2 2 5 5 4 3 2 4 3 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +------------+ +--R | 2 2 2 +--R \|c + b - a +--R , +--R +--R 3 2 2 3 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 2 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 3 2 4 +--R (- 12B - 16A)a b + 8A a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 3 +--R (4A a b - 8A a b + 4A a )c +--R + +--R 2 2 3 4 2 +--R (- 12C a b + 24C a b - 12C a )c +--R + +--R 4 2 3 3 2 +--R 4A a b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 4 5 +--R (- 12B - 16A)a b + 8A a +--R * +--R c +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 3 +--R (- 2A b + 4A a b - 2A a )c + (6C a b - 12C a b + 6C a )c +--R + +--R 3 2 2 3 4 2 +--R (6B a b + (- 12B - 4A)a b + (6B + 8A)a b - 4A a )c +--R + +--R 4 2 3 3 2 6 5 +--R (- 6C a b + 12C a b - 6C a b )c + 2A b + (- 6B - 4A)a b +--R + +--R 2 4 3 3 4 2 +--R (12B + 6A)a b + (- 6B - 8A)a b + 4A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 2 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 2 3 3 2 4 5 2 4 +--R (- 12C a b + 24C a b - 12C a b)c + 4A a b + (- 12B - 8A)a b +--R + +--R 3 3 4 2 5 +--R (24B + 12A)a b + (- 12B - 16A)a b + 8A a b +--R * +--R cos(x) +--R + +--R 2 2 4 2 2 3 3 +--R (2A b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 4 3 2 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 8A)a b + (- 6B - 12A)a b +--R + +--R 4 +--R 6A a +--R * +--R 2 +--R c +--R + +--R 3 2 4 5 2 4 3 3 +--R (- 6C a b + 12C a b - 6C a )c + 2A a b + (- 6B - 4A)a b +--R + +--R 4 2 5 6 +--R (12B + 6A)a b + (- 6B - 8A)a b + 4A a +--R * +--R +--------------+ +--R | 2 2 2 +--R ((b - a)sin(x) - c cos(x) - c)\|- c - b + a +--R atan(-----------------------------------------------) +--R 2 2 2 2 2 2 +--R (c + b - a )cos(x) + c + b - a +--R + +--R 4 2 3 +--R (2B - 2A)b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 3 2 2 3 4 5 +--R (- 4C a b + 7C a b - 2C a b - C a )c + 2B b +--R + +--R 4 2 3 3 2 4 +--R (- 4B - 3A)a b + (3B + 6A)a b + (- 2B - 3A)a b + B a b +--R * +--R cos(x) +--R + +--R 4 2 3 +--R (2B - 2A)a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 2 +--R (A b + (6B - 4A)a b + (- 2B - 5A)a b + (- 4B + 8A)a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- C a b - 2C a b + 7C a b - 4C a )c + A b + (B - 2A)a b +--R + +--R 2 3 3 2 4 5 +--R (- 2B - 3A)a b + (3B + 8A)a b + (- 4B - 4A)a b + 2B a +--R * +--R sin(x) +--R + +--R 5 4 +--R (- B + A)c + (- C b + C a)c +--R + +--R 2 2 3 +--R (- 2B b + (B + 3A)a b + (2B - 4A)a )c +--R + +--R 3 2 2 3 2 +--R (- 2C b + 7C a b - 7C a b + 2C a )c +--R + +--R 4 3 2 2 +--R (- B - A)b + (7B + 3A)a b + (- 7B - 8A)a b +--R + +--R 3 4 +--R (2B + 6A)a b - B a +--R * +--R c +--R + +--R 5 2 3 4 +--R - C b + 2C a b - C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 3 2 3 2 +--R (- A b + 2B a b - A a )c + (C a b - C a )c +--R + +--R 4 3 2 2 3 4 4 +--R (- A b + 5B a b - 3A a b - 5B a b + 4A a )c - 2C a b +--R + +--R 3 2 5 +--R 4C a b - 2C a +--R * +--R cos(x) +--R + +--R 5 4 +--R (B - A)c + (C b - C a)c +--R + +--R 2 2 3 +--R ((2B - A)b + (B - 3A)a b + (- 2B + 3A)a )c +--R + +--R 3 2 2 3 2 +--R (2C b - 6C a b + 7C a b - 3C a )c +--R + +--R 4 3 2 2 3 +--R B b + (- 2B - 3A)a b + (7B + 5A)a b + (- 7B - 6A)a b +--R + +--R 4 +--R (B + 4A)a +--R * +--R c +--R + +--R 5 4 2 3 3 2 4 5 +--R C b - 2C a b - 2C a b + 4C a b + C a b - 2C a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 5 5 4 3 2 4 3 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 5 4 2 3 4 5 3 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R sin(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (- 2b + 4a b - 2a )c + (- 2b + 4a b + 2a b - 8a b + 4a )c +--R + +--R 6 5 2 4 4 2 5 6 2 8 7 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2b - 4a b +--R + +--R 2 6 3 5 4 4 5 3 6 2 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 5 2 4 4 2 5 2 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 16a b - 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 +--R 4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b +--R * +--R cos(x) +--R + +--R 2 2 6 4 3 2 2 3 4 4 +--R (2b - 4a b + 2a )c + (4b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 6 5 2 4 4 2 5 6 2 2 6 3 5 4 4 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 5 3 6 2 7 8 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 312 + +--S 313 of 526 +m0857a:= a0857.1-r0857 +--R +--R +--R (4) +--R 3 2 2 5 +--R (2A b - 4A a b + 2A a b)c +--R + +--R 3 2 2 3 4 +--R (- 6C a b + 12C a b - 6C a b)c +--R + +--R 5 4 2 3 +--R 2A b + (- 6B - 4A)a b + (12B + 6A)a b +--R + +--R 3 2 4 +--R (- 6B - 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4A)a )c +--R + +--R 3 2 2 3 4 +--R (4C b - C a b - 5C a b + 2C a )c +--R + +--R 4 3 2 2 +--R (13B - 5A)b + (- B - 12A)a b + (- 12B + 14A)a b +--R + +--R 3 +--R 3A a b +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 7C b + 4C a b + 12C a b - 8C a b - C a b)c +--R + +--R 6 5 2 4 3 3 +--R - 2B b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 4 2 +--R - B a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + (10B - 8A)a b - A a )c +--R + +--R 2 2 3 4 +--R (9C a b - 8C a b - C a )c +--R + +--R 4 3 2 2 +--R - A b + (29B - 8A)a b + (- 8B - 27A)a b +--R + +--R 3 4 +--R (- 21B + 32A)a b + 4A a +--R * +--R 3 +--R c +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 14C a b + 8C a b + 24C a b - 16C a b - 2C a )c +--R + +--R 5 2 4 3 3 +--R - 4B a b + (8B + 6A)a b + (- 6B - 12A)a b +--R + +--R 4 2 5 +--R (4B + 6A)a b - 2B a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 7 6 +--R (B - A)c + (C b - C a)c +--R + +--R 2 2 5 +--R ((2B - A)b + (B - 3A)a b + (2B - A)a )c +--R + +--R 2 2 3 4 +--R (- 2C a b + 9C a b - 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14A)a b + (- 6B - 33A)a b +--R + +--R 3 2 4 +--R (- 27B + 44A)a b + 2A a b +--R * +--R 2 +--R c +--R + +--R 5 3 3 4 2 +--R (- 12C a b + 36C a b - 24C a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 5 +--R (2B - 2A)b c + (4C b - 6C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R ((8B - 2A)b + (- 6B - 9A)a b + (10B + 2A)a b - 3A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 4C a b + 21C a b - 18C a b + C a )c +--R + +--R 5 4 2 3 +--R 2B b + (- 4B - 3A)a b + (39B - 6A)a b +--R + +--R 3 2 4 +--R (- 14B - 39A)a b + (- 23B + 48A)a b +--R * +--R 2 +--R c +--R + +--R 2 4 4 2 5 +--R (- 12C a b + 36C a b - 24C a b)c +--R * +--R cos(x) +--R + +--R 6 2 5 +--R (2B - 2A)a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (- A b + 6B a b + (- 2B - 7A)a b + 4A a )c +--R + +--R 3 2 2 3 4 3 +--R (C a b - 6C a b + 13C a b - 8C a )c +--R + +--R 5 4 2 3 3 2 +--R - A b + (3B + 2A)a b + (- 6B - 3A)a b + 15B a b +--R + +--R 4 5 +--R (- 4B - 14A)a b + (- 8B + 16A)a +--R * +--R 2 +--R c +--R + +--R 3 3 5 6 +--R (- 4C a b + 12C a b - 8C a )c +--R * +--R sin(x) +--R + +--R 2 5 3 2 2 4 +--R (- B + A)b c + (- 3C b + 5C a b - 2C a b)c +--R + +--R 4 3 2 2 3 3 +--R (- 4B b + (5B + 6A)a b - 10A a b + 3A a b)c +--R + +--R 4 2 3 3 2 4 2 +--R (3C a b - 6C a b + 4C a b - C a b)c +--R + +--R 6 5 2 4 3 3 4 2 +--R ((B - A)b + 3B a b + (- 5B - 2A)a b + (2B + 3A)a b - B a b )c +--R + +--R 7 2 5 3 4 +--R - C b + 3C a b - 2C a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + (- 2B + 4A)a b - A a )c +--R + +--R 2 2 3 4 +--R (- 3C a b + 4C a b - C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- A b - 3B a b + (4B + 9A)a b + (3B - 16A)a b + 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b + 4C a b - 12C a b + 8C a b - 2C a )c +--R + +--R 5 2 4 3 3 +--R (8B - 4A)a b + (4B - 6A)a b + (- 14B + 4A)a b +--R + +--R 4 2 5 +--R (4B + 6A)a b - 2B a b +--R * +--R c +--R + +--R 6 3 4 4 3 +--R - 4C a b + 12C a b - 8C a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + 2B a b + (- 2B + A)a )c +--R + +--R 3 2 2 3 4 +--R (4C b - 7C a b + 2C a b + C a )c +--R + +--R 4 3 2 2 3 +--R (4B - A)b + (- 3B - 6A)a b + (4B + 5A)a b - 3B a b +--R + +--R 4 +--R (4B - 4A)a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2C b - 6C a b + 10C a b - 2C a b - 6C a b + 2C a )c +--R + +--R 6 5 2 4 3 3 +--R 2B b + (- 4B - 3A)a b + 19B a b + (- 4B - 18A)a b +--R + +--R 4 2 5 6 +--R (- 14B + 18A)a b + (2B + 3A)a b - B a +--R * +--R c +--R + +--R 2 5 4 3 5 2 +--R - 6C a b + 18C a b - 12C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (A b + (2B - 4A)a b + A a )c + (3C a b - 4C a b + C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (A b + (7B - 4A)a b + (- 4B - 9A)a b + (B + 12A)a b - 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b - 8C a b + 16C a b - 12C a b + 2C a )c +--R + +--R 5 2 4 3 3 4 2 +--R 4B a b + (- 8B - 6A)a b + (18B + 8A)a b + (- 8B - 18A)a b +--R + +--R 5 +--R (- 6B + 16A)a b +--R * +--R c +--R + +--R 3 4 5 2 6 +--R - 4C a b + 12C a b - 8C a b +--R * +--R cos(x) +--R + +--R 2 2 5 3 2 3 4 +--R (B b - 2B a b + (2B - A)a )c + (- C b + 2C a b - C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (B b - 2B a b + (2B - A)a b + (3B - 3A)a b + (- 3B + 3A)a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- C b + 2C a b + 2C a b - 8C a b + 8C a b - 3C a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2B a b + (- 4B - 3A)a b + (6B + 5A)a b + (- 3B - 6A)a b +--R + +--R 6 +--R (- B + 4A)a +--R * +--R c +--R + +--R 4 3 6 7 +--R - C a b + 3C a b - 2C a +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +------------+ +--R | 2 2 2 | 2 2 2 +--R \|- c - b + a \|c + b - a +--R Type: Expression(Integer) +--E 313 + +--S 314 of 526 +--d0857a:= D(m0857a,x) +--E 314 + +--S 315 of 526 +m0857b:= a0857.2-r0857 +--R +--R +--R (5) +--R 3 2 2 5 +--R (4A b - 8A a b + 4A a b)c +--R + +--R 3 2 2 3 4 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 4 2 3 +--R 4A b + (- 12B - 8A)a b + (24B + 12A)a b +--R + +--R 3 2 4 +--R (- 12B - 16A)a b + 8A a b +--R * +--R 3 +--R c +--R * +--R cos(x) +--R + +--R 2 2 3 5 2 2 3 4 4 +--R (4A a b - 8A a b + 4A a )c + (- 12C a b + 24C a b - 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48A)a b + 24A a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 4 +--R (4A a b - 8A a b + 4A a b)c +--R + +--R 2 3 3 2 4 3 +--R (- 12C a b + 24C a b - 12C a b)c +--R + +--R 5 2 4 3 3 +--R 4A a b + (- 12B - 8A)a b + (24B + 20A)a b +--R + +--R 4 2 5 +--R (- 12B - 32A)a b + 16A a b +--R * +--R 2 +--R c +--R + +--R 4 3 5 2 6 3 5 4 4 +--R (- 24C a b + 48C a b - 24C a b)c + 8A a b + (- 24B - 16A)a b +--R + +--R 5 3 6 2 7 +--R (48B + 24A)a b + (- 24B - 32A)a b + 16A a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 4 3 2 4 5 3 +--R (2A a b - 4A a b + 2A a )c + (- 6C a b + 12C a b - 6C a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2A a b + (- 6B - 4A)a b + (12B + 8A)a b + (- 6B - 12A)a b +--R + +--R 6 +--R 6A a +--R * +--R 2 +--R c +--R + +--R 5 2 6 7 4 4 5 3 +--R (- 6C a b + 12C a b - 6C a )c + 2A a b + (- 6B - 4A)a b +--R + +--R 6 2 7 8 +--R (12B + 6A)a b + (- 6B - 8A)a b + 4A a +--R * +--R x +--R (b - a)tan(-) - c +--R 2 +--R atan(-----------------) +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R + +--R 6 2 5 +--R (2B - 2A)b c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R ((4B - 2A)b + (2B - 3A)a b + (- 6B + 2A)a b + 3A a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- 4C b + 4C a b + 3C a b - 2C a b - C a )c +--R + +--R 5 4 2 3 3 2 +--R - 2B b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 4 +--R - B a b +--R * +--R 2 +--R c +--R * +--R cos(x) +--R + +--R 6 2 5 +--R (2B - 2A)a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (A b + (6B - 4A)a b + (- 2B - 5A)a b + (- 4B + 8A)a )c +--R + +--R 3 2 2 3 4 3 +--R (- 5C a b + 6C a b + 3C a b - 4C a )c +--R + +--R 5 4 2 3 3 2 +--R A b + (- 3B - 2A)a b + (6B + 3A)a b + (- 3B - 4A)a b +--R + +--R 4 +--R 2A a b +--R * +--R 2 +--R c +--R * +--R 3 +--R sin(x) +--R + +--R 7 6 +--R (- B + A)c + (- C b + C a)c +--R + +--R 2 2 5 +--R ((2B - 4A)b + (B + 3A)a b + (2B - 4A)a )c +--R + +--R 3 2 2 3 4 +--R (4C b - C a b - 5C a b + 2C a )c +--R + +--R 4 3 2 2 +--R (13B - 5A)b + (- B - 12A)a b + (- 12B + 14A)a b +--R + +--R 3 +--R 3A a b +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 4 2 +--R (- 7C b + 4C a b + 12C a b - 8C a b - C a b)c +--R + +--R 6 5 2 4 3 3 +--R - 2B b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 4 2 +--R - B a b +--R * +--R c +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + (10B - 8A)a b - A a )c +--R + +--R 2 2 3 4 +--R (9C a b - 8C a b - C a )c +--R + +--R 4 3 2 2 +--R - A b + (29B - 8A)a b + (- 8B - 27A)a b +--R + +--R 3 4 +--R (- 21B + 32A)a b + 4A a +--R * +--R 3 +--R c +--R + +--R 4 2 3 3 2 4 5 2 +--R (- 14C a b + 8C a b + 24C a b - 16C a b - 2C a )c +--R + +--R 5 2 4 3 3 +--R - 4B a b + (8B + 6A)a b + (- 6B - 12A)a b +--R + +--R 4 2 5 +--R (4B + 6A)a b - 2B a b +--R * +--R c +--R * +--R cos(x) +--R + +--R 7 6 +--R (B - A)c + (C b - C a)c +--R + +--R 2 2 5 +--R ((2B - A)b + (B - 3A)a b + (2B - A)a )c +--R + +--R 2 2 3 4 +--R (- 2C a b + 9C a b - 7C a )c +--R + +--R 4 3 2 2 3 +--R - B b + 2B a b + (16B - 5A)a b + (- 9B - 15A)a b +--R + +--R 4 +--R (- 8B + 20A)a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (C b - 2C a b - 8C a b + 8C a b + 11C a b - 10C a )c +--R + +--R 2 4 3 3 4 2 5 +--R - 2B a b + (4B + 3A)a b + (- 3B - 6A)a b + (2B + 3A)a b +--R + +--R 6 +--R - B a +--R * +--R c +--R * +--R 2 +--R sin(x) +--R + +--R 6 2 2 5 +--R (- 2B + 2A)b c + (- 4C b + 6C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R ((- 4B - 2A)b + (6B + 9A)a b + (2B - 14A)a b + 3A a )c +--R + +--R 4 2 2 3 4 3 +--R (4C b - 9C a b + 6C a b - C a )c +--R + +--R 5 4 2 3 +--R (10B - 4A)b - 9A a b + (- 11B + 10A)a b +--R + +--R 3 2 4 +--R (2B + 3A)a b - B a b +--R * +--R 2 +--R c +--R + +--R 6 2 4 3 3 +--R (- 4C b + 12C a b - 8C a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 6 2 5 +--R (- 2B + 2A)a c + (- 2C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R (A b + (6B - 12A)a b + (2B + 7A)a b + (4B - 8A)a )c +--R + +--R 3 2 2 3 4 3 +--R (11C a b - 6C a b - 9C a b + 4C a )c +--R + +--R 5 4 2 3 +--R A b + (33B - 14A)a b + (- 6B - 33A)a b +--R + +--R 3 2 4 +--R (- 27B + 44A)a b + 2A a b +--R * +--R 2 +--R c +--R + +--R 5 3 3 4 2 +--R (- 12C a b + 36C a b - 24C a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 6 2 2 5 +--R (2B - 2A)b c + (4C b - 6C a b + 2C a )c +--R + +--R 3 2 2 3 4 +--R ((8B - 2A)b + (- 6B - 9A)a b + (10B + 2A)a b - 3A a )c +--R + +--R 3 2 2 3 4 3 +--R (- 4C a b + 21C a b - 18C a b + C a )c +--R + +--R 5 4 2 3 +--R 2B b + (- 4B - 3A)a b + (39B - 6A)a b +--R + +--R 3 2 4 +--R (- 14B - 39A)a b + (- 23B + 48A)a b +--R * +--R 2 +--R c +--R + +--R 2 4 4 2 5 +--R (- 12C a b + 36C a b - 24C a b)c +--R * +--R cos(x) +--R + +--R 6 2 5 +--R (2B - 2A)a c + (2C a b - 2C a )c +--R + +--R 3 2 2 3 4 +--R (- A b + 6B a b + (- 2B - 7A)a b + 4A a )c +--R + +--R 3 2 2 3 4 3 +--R (C a b - 6C a b + 13C a b - 8C a )c +--R + +--R 5 4 2 3 3 2 +--R - A b + (3B + 2A)a b + (- 6B - 3A)a b + 15B a b +--R + +--R 4 5 +--R (- 4B - 14A)a b + (- 8B + 16A)a +--R * +--R 2 +--R c +--R + +--R 3 3 5 6 +--R (- 4C a b + 12C a b - 8C a )c +--R * +--R sin(x) +--R + +--R 2 5 3 2 2 4 +--R (- B + A)b c + (- 3C b + 5C a b - 2C a b)c +--R + +--R 4 3 2 2 3 3 +--R (- 4B b + (5B + 6A)a b - 10A a b + 3A a b)c +--R + +--R 4 2 3 3 2 4 2 +--R (3C a b - 6C a b + 4C a b - C a b)c +--R + +--R 6 5 2 4 3 3 4 2 +--R ((B - A)b + 3B a b + (- 5B - 2A)a b + (2B + 3A)a b - B a b )c +--R + +--R 7 2 5 3 4 +--R - C b + 3C a b - 2C a b +--R * +--R 4 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + (- 2B + 4A)a b - A a )c +--R + +--R 2 2 3 4 +--R (- 3C a b + 4C a b - C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (- A b - 3B a b + (4B + 9A)a b + (3B - 16A)a b + 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b + 4C a b - 12C a b + 8C a b - 2C a )c +--R + +--R 5 2 4 3 3 +--R (8B - 4A)a b + (4B - 6A)a b + (- 14B + 4A)a b +--R + +--R 4 2 5 +--R (4B + 6A)a b - 2B a b +--R * +--R c +--R + +--R 6 3 4 4 3 +--R - 4C a b + 12C a b - 8C a b +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 5 +--R (- A b + 2B a b + (- 2B + A)a )c +--R + +--R 3 2 2 3 4 +--R (4C b - 7C a b + 2C a b + C a )c +--R + +--R 4 3 2 2 3 +--R (4B - A)b + (- 3B - 6A)a b + (4B + 5A)a b - 3B a b +--R + +--R 4 +--R (4B - 4A)a +--R * +--R 3 +--R c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (2C b - 6C a b + 10C a b - 2C a b - 6C a b + 2C a )c +--R + +--R 6 5 2 4 3 3 +--R 2B b + (- 4B - 3A)a b + 19B a b + (- 4B - 18A)a b +--R + +--R 4 2 5 6 +--R (- 14B + 18A)a b + (2B + 3A)a b - B a +--R * +--R c +--R + +--R 2 5 4 3 5 2 +--R - 6C a b + 18C a b - 12C a b +--R * +--R 2 +--R cos(x) +--R + +--R 2 2 5 2 2 3 4 +--R (A b + (2B - 4A)a b + A a )c + (3C a b - 4C a b + C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (A b + (7B - 4A)a b + (- 4B - 9A)a b + (B + 12A)a b - 4A a )c +--R + +--R 4 2 3 3 2 4 5 2 +--R (2C a b - 8C a b + 16C a b - 12C a b + 2C a )c +--R + +--R 5 2 4 3 3 4 2 +--R 4B a b + (- 8B - 6A)a b + (18B + 8A)a b + (- 8B - 18A)a b +--R + +--R 5 +--R (- 6B + 16A)a b +--R * +--R c +--R + +--R 3 4 5 2 6 +--R - 4C a b + 12C a b - 8C a b +--R * +--R cos(x) +--R + +--R 2 2 5 3 2 3 4 +--R (B b - 2B a b + (2B - A)a )c + (- C b + 2C a b - C a )c +--R + +--R 4 3 2 2 3 4 3 +--R (B b - 2B a b + (2B - A)a b + (3B - 3A)a b + (- 3B + 3A)a )c +--R + +--R 5 4 2 3 3 2 4 5 2 +--R (- C b + 2C a b + 2C a b - 8C a b + 8C a b - 3C a )c +--R + +--R 2 4 3 3 4 2 5 +--R 2B a b + (- 4B - 3A)a b + (6B + 5A)a b + (- 3B - 6A)a b +--R + +--R 6 +--R (- B + 4A)a +--R * +--R c +--R + +--R 4 3 6 7 +--R - C a b + 3C a b - 2C a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R / +--R 3 2 2 7 5 4 3 2 4 5 +--R (4b - 8a b + 4a b)c + (8b - 16a b + 16a b - 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 4 5 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 16a b - 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b - 4a b + 16a b - 4a b - 8a b + 4a )c +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (- 2b + 4a b - 2a )c + (6b - 12a b + 10a b - 8a b + 4a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (18b - 36a b + 2a b + 32a b - 18a b + 4a b - 2a )c +--R + +--R 8 7 2 6 3 5 4 4 5 3 6 2 2 +--R (10b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 +--R (20a b - 40a b + 20a b)c +--R + +--R 5 2 4 4 2 5 4 +--R (40a b - 80a b + 80a b - 40a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (20a b - 40a b - 20a b + 80a b - 20a b - 40a b + 20a b)c +--R * +--R cos(x) +--R + +--R 2 2 8 4 3 2 2 3 4 6 +--R (2b - 4a b + 2a )c + (4b - 8a b + 10a b - 12a b + 6a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (2b - 4a b + 18a b - 32a b - 2a b + 36a b - 18a )c +--R + +--R 2 6 3 5 4 4 5 3 6 2 7 8 2 +--R (10a b - 20a b - 10a b + 40a b - 10a b - 20a b + 10a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 7 2 3 3 2 4 5 +--R (- 4b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (12b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 8 2 7 3 6 4 5 5 4 6 3 +--R (8b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b )c +--R * +--R 3 +--R cos(x) +--R + +--R 2 2 3 7 +--R (- 4a b + 8a b - 4a )c +--R + +--R 4 2 3 3 2 4 5 5 +--R (16a b - 32a b + 24a b - 16a b + 8a )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (44a b - 88a b + 4a b + 80a b - 44a b + 8a b - 4a )c +--R + +--R 8 2 7 3 6 4 5 5 4 6 3 7 2 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b )c +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 7 +--R (4b - 8a b + 4a b)c +--R + +--R 5 4 2 3 3 2 4 5 +--R (8b - 16a b + 24a b - 32a b + 16a b)c +--R + +--R 7 6 2 5 3 4 4 3 5 2 6 3 +--R (4b - 8a b + 44a b - 80a b - 4a b + 88a b - 44a b)c +--R + +--R 2 7 3 6 4 5 5 4 6 3 7 2 8 +--R (24a b - 48a b - 24a b + 96a b - 24a b - 48a b + 24a b)c +--R * +--R cos(x) +--R + +--R 2 2 3 7 4 2 3 3 2 5 +--R (4a b - 8a b + 4a )c + (8a b - 16a b + 8a b )c +--R + +--R 6 2 5 3 4 4 3 5 2 6 7 3 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a )c +--R + +--R 3 6 4 5 5 4 6 3 7 2 8 9 +--R (8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a )c +--R * +--R sin(x) +--R + +--R 4 3 2 2 6 +--R (- 2b + 4a b - 2a b )c +--R + +--R 6 5 2 4 3 3 4 2 4 +--R (- 2b + 4a b + 2a b - 8a b + 4a b )c +--R + +--R 8 7 2 6 4 4 5 3 6 2 2 10 9 +--R (2b - 4a b + 2a b - 2a b + 4a b - 2a b )c + 2b - 4a b +--R + +--R 2 8 3 7 4 6 5 5 6 4 +--R - 2a b + 8a b - 2a b - 4a b + 2a b +--R * +--R 4 +--R cos(x) +--R + +--R 3 2 2 3 6 3 3 4 2 5 4 +--R (- 4a b + 8a b - 4a b)c + (8a b - 16a b + 8a b)c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (12a b - 24a b + 4a b + 16a b - 12a b + 8a b - 4a b)c +--R + +--R 9 2 8 3 7 4 6 5 5 6 4 7 3 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R 3 +--R cos(x) +--R + +--R 4 3 3 4 6 +--R (2b - 4a b + 4a b - 2a )c +--R + +--R 6 5 2 4 3 3 4 2 5 6 4 +--R (4b - 8a b + 8a b - 8a b + 8a b - 8a b + 4a )c +--R + +--R 8 7 2 6 3 5 5 3 6 2 7 8 2 +--R (2b - 4a b + 20a b - 36a b + 36a b - 20a b + 4a b - 2a )c +--R + +--R 2 8 3 7 4 6 5 5 6 4 7 3 8 2 +--R 12a b - 24a b - 12a b + 48a b - 12a b - 24a b + 12a b +--R * +--R 2 +--R cos(x) +--R + +--R 3 2 2 3 6 5 2 4 3 3 4 +--R (4a b - 8a b + 4a b)c + (8a b - 16a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 5 3 6 2 7 2 +--R (4a b - 8a b + 12a b - 16a b - 4a b + 24a b - 12a b)c +--R + +--R 3 7 4 6 5 5 6 4 7 3 8 2 9 +--R 8a b - 16a b - 8a b + 32a b - 8a b - 16a b + 8a b +--R * +--R cos(x) +--R + +--R 2 2 3 4 6 2 4 3 3 4 2 5 6 4 +--R (2a b - 4a b + 2a )c + (4a b - 8a b + 2a b + 4a b - 2a )c +--R + +--R 2 6 3 5 4 4 6 2 7 8 2 4 6 5 5 6 4 +--R (2a b - 4a b + 2a b - 2a b + 4a b - 2a )c + 2a b - 4a b - 2a b +--R + +--R 7 3 8 2 9 10 +--R 8a b - 2a b - 4a b + 2a +--R * +--R +--------------+ +--R | 2 2 2 +--R \|- c - b + a +--R Type: Expression(Integer) +--E 315 + +--S 316 of 526 +--d0857b:= D(m0857b,x) +--E 316 + +)clear all + + +--S 317 of 526 +t0858:= sin(x)^3/(cos(x)^3+sin(x)^3) +--R +--R +--R 3 +--R sin(x) +--R (1) ----------------- +--R 3 3 +--R sin(x) + cos(x) +--R Type: Expression(Integer) +--E 317 + +--S 318 of 526 +r0858:= 1/2*x-1/6*log(cos(x)+sin(x))+1/3*log(1-cos(x)*sin(x)) +--R +--R +--R - log(sin(x) + cos(x)) + 2log(- cos(x)sin(x) + 1) + 3x +--R (2) ------------------------------------------------------ +--R 6 +--R Type: Expression(Integer) +--E 318 + +--S 319 of 526 +a0858:= integrate(t0858,x) +--R +--R +--R (3) +--R 2 - 2sin(x) - 2cos(x) +--R - 3log(----------) - log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R - 4cos(x)sin(x) + 4 +--R 2log(---------------------) + 3x +--R 2 +--R cos(x) + 2cos(x) + 1 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 526 +m0858:= a0858-r0858 +--R +--R +--R (4) +--R 2 - 2sin(x) - 2cos(x) +--R log(sin(x) + cos(x)) - 3log(----------) - log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R - 4cos(x)sin(x) + 4 +--R 2log(---------------------) - 2log(- cos(x)sin(x) + 1) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R / +--R 6 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 526 +d0858:= D(m0858,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + + +--S 322 of 526 +t0859:= cos(x)^3/(cos(x)^3+sin(x)^3) +--R +--R +--R 3 +--R cos(x) +--R (1) ----------------- +--R 3 3 +--R sin(x) + cos(x) +--R Type: Expression(Integer) +--E 322 + +--S 323 of 526 +r0859:= 1/2*x+1/6*log(cos(x)+sin(x))-1/3*log(1-cos(x)*sin(x)) +--R +--R +--R log(sin(x) + cos(x)) - 2log(- cos(x)sin(x) + 1) + 3x +--R (2) ---------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 526 +a0859:= integrate(t0859,x) +--R +--R +--R (3) +--R 2 - 2sin(x) - 2cos(x) - 4cos(x)sin(x) + 4 +--R 3log(----------) + log(-------------------) - 2log(---------------------) +--R cos(x) + 1 cos(x) + 1 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R 3x +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 324 + +--S 325 of 526 +m0859:= a0859-r0859 +--R +--R +--R (4) +--R 2 - 2sin(x) - 2cos(x) +--R - log(sin(x) + cos(x)) + 3log(----------) + log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R - 4cos(x)sin(x) + 4 +--R - 2log(---------------------) + 2log(- cos(x)sin(x) + 1) +--R 2 +--R cos(x) + 2cos(x) + 1 +--R / +--R 6 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 526 +d0859:= D(m0859,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 326 + +)clear all + + +--S 327 of 526 +t0860:= 1/(a+b*sin(x)+c*sin(x)^2) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 +--R c sin(x) + b sin(x) + a +--R Type: Expression(Integer) +--E 327 + +--S 328 of 526 +r0860:= -2*2^(1/2)*c*atanh(1/2*(2*c+(b-(b^2-4*a*c)^(1/2))*_ + tan(1/2*x))*2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ + (b^2-4*a*c)^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)+_ + 4*c*atanh((2*c+(b+(b^2-4*a*c)^(1/2))*tan(1/2*x))/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/(b^2-4*a*c)^(1/2)/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 4c\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + b tan(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-------------------------------------+ +--R | +-----------+ +--R +-+ | | 2 2 2 +--R 2c\|2 \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +-+ +--R \|2 tan(-)\|- 4a c + b - b\|2 tan(-) - 2c\|2 +--R 2 2 +--R atanh(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 328 + +--S 329 of 526 +a0860:= integrate(t0860,x) +--R +--R +--R (3) +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 2 +--R (- 4a b c + (b - 4a b)c + a b )cos(x) - 4a b c +--R + +--R 3 2 3 +--R (b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R 2b - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a b c sin(x) + 2b c cos(x) + 2b c +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 2 +--R (4a b c + (- b + 4a b)c - a b )cos(x) + 4a b c +--R + +--R 3 2 3 +--R (- b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c + (- 2b + 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a b c sin(x) + 2b c cos(x) + 2b c +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 2 +--R (- 4a b c + (b - 4a b)c + a b )cos(x) - 4a b c +--R + +--R 3 2 3 +--R (b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a b c sin(x) + 2b c cos(x) + 2b c +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 2 +--R (4a b c + (- b + 4a b)c - a b )cos(x) + 4a b c +--R + +--R 3 2 3 +--R (- b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + (2b - 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a b c sin(x) + 2b c cos(x) + 2b c +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 329 + +--S 330 of 526 +m0860:= a0860-r0860 +--R +--R +--R (4) +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 2 +--R (- 4a b c + (b - 4a b)c + a b )cos(x) - 4a b c +--R + +--R 3 2 3 +--R (b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R 2b - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a b c sin(x) + 2b c cos(x) + 2b c +--R / +--R cos(x) + 1 +--R + +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 2 +--R (4a b c + (- b + 4a b)c - a b )cos(x) + 4a b c +--R + +--R 3 2 3 +--R (- b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c + (- 2b + 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a b c sin(x) + 2b c cos(x) + 2b c +--R / +--R cos(x) + 1 +--R + +--R - +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 2 +--R (- 4a b c + (b - 4a b)c + a b )cos(x) - 4a b c +--R + +--R 3 2 3 +--R (b - 4a b)c + a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a b c sin(x) + 2b c cos(x) + 2b c +--R / +--R cos(x) + 1 +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R cos(x) +--R + +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 3 2 3 2 +--R (4a b c + (- b + 4a b)c - a b )cos(x) + 4a b c +--R + +--R 3 2 3 +--R (- b + 4a b)c - a b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R cos(x) +--R + +--R 4 2 2 3 2 3 2 4 2 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + (2b - 2a b )c +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a b c sin(x) + 2b c cos(x) + 2b c +--R / +--R cos(x) + 1 +--R + +--R - +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 8c\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + b tan(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R - +--R +-------------------------------------+ +--R | +-----------+ +--R +-+ | | 2 2 2 +--R 4c\|2 \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +-+ +--R \|2 tan(-)\|- 4a c + b - b\|2 tan(-) - 2c\|2 +--R 2 2 +--R atanh(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 330 + +--S 331 of 526 +d0860:= D(m0860,x) +--R +--R +--R (5) +--R 4 3 +--R a sin(x) + (- 2b cos(x) - 2b)sin(x) +--R + +--R 2 2 +--R ((- 4c + 2a)cos(x) + (- 8c + 2a)cos(x) - 4c)sin(x) +--R + +--R 3 2 4 +--R (- 2b cos(x) - 6b cos(x) - 6b cos(x) - 2b)sin(x) + a cos(x) +--R + +--R 3 +--R 2a cos(x) - 2a cos(x) - a +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 +--R 4b sin(x) + (8b cos(x) + 12b cos(x) + 4b)sin(x) + 4b cos(x) +--R + +--R 3 2 +--R 12b cos(x) + 12b cos(x) + 4b cos(x) +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 4 3 +--R (8c + 2a)sin(x) + (- 4b cos(x) - 4b)sin(x) +--R + +--R 2 2 +--R ((8c + 4a)cos(x) + (8c + 4a)cos(x))sin(x) +--R + +--R 3 2 +--R (- 4b cos(x) - 12b cos(x) - 12b cos(x) - 4b)sin(x) +--R + +--R 4 3 2 +--R (8c + 2a)cos(x) + (24c + 4a)cos(x) + 24c cos(x) + (8c - 4a)cos(x) +--R + +--R - 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 4 +--R 4b sin(x) + (8b cos(x) + 12b cos(x) + 4b)sin(x) + 4b cos(x) +--R + +--R 3 2 +--R 12b cos(x) + 12b cos(x) + 4b cos(x) +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 4 3 +--R a sin(x) + (- 2b cos(x) - 2b)sin(x) +--R + +--R 2 2 +--R ((- 4c + 2a)cos(x) + (- 8c + 2a)cos(x) - 4c)sin(x) +--R + +--R 3 2 4 +--R (- 2b cos(x) - 6b cos(x) - 6b cos(x) - 2b)sin(x) + a cos(x) +--R + +--R 3 +--R 2a cos(x) - 2a cos(x) - a +--R / +--R 2 4 3 +--R a sin(x) + (2a b cos(x) + 2a b)sin(x) +--R + +--R 2 2 2 2 2 +--R ((4a c + 2a )cos(x) + (8a c + 4a )cos(x) + 4a c + 2a )sin(x) +--R + +--R 3 2 2 4 +--R (2a b cos(x) + 6a b cos(x) + 6a b cos(x) + 2a b)sin(x) + a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 4a cos(x) + 6a cos(x) + 4a cos(x) + a +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) +--R + +--R 2 2 +--R ((8b c + 4a b)cos(x) + (16b c + 8a b)cos(x) + 8b c + 4a b)sin(x) +--R + +--R 2 3 2 2 2 2 4 +--R (4b cos(x) + 12b cos(x) + 12b cos(x) + 4b )sin(x) + 2a b cos(x) +--R + +--R 3 2 +--R 8a b cos(x) + 12a b cos(x) + 8a b cos(x) + 2a b +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 4 3 +--R (4a c + 2a )sin(x) + ((8b c + 4a b)cos(x) + 8b c + 4a b)sin(x) +--R + +--R 2 2 2 2 2 2 +--R (16c + 16a c + 4a )cos(x) + (32c + 32a c + 8a )cos(x) + 16c +--R + +--R 2 +--R 16a c + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 +--R (8b c + 4a b)cos(x) + (24b c + 12a b)cos(x) +--R + +--R (24b c + 12a b)cos(x) + 8b c + 4a b +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 +--R (4a c + 2a )cos(x) + (16a c + 8a )cos(x) + (24a c + 12a )cos(x) +--R + +--R 2 2 +--R (16a c + 8a )cos(x) + 4a c + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 +--R 2a b sin(x) + (4b cos(x) + 4b )sin(x) +--R + +--R 2 2 +--R ((8b c + 4a b)cos(x) + (16b c + 8a b)cos(x) + 8b c + 4a b)sin(x) +--R + +--R 2 3 2 2 2 2 4 +--R (4b cos(x) + 12b cos(x) + 12b cos(x) + 4b )sin(x) + 2a b cos(x) +--R + +--R 3 2 +--R 8a b cos(x) + 12a b cos(x) + 8a b cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 3 +--R a sin(x) + (2a b cos(x) + 2a b)sin(x) +--R + +--R 2 2 2 2 2 +--R ((4a c + 2a )cos(x) + (8a c + 4a )cos(x) + 4a c + 2a )sin(x) +--R + +--R 3 2 2 4 +--R (2a b cos(x) + 6a b cos(x) + 6a b cos(x) + 2a b)sin(x) + a cos(x) +--R + +--R 2 3 2 2 2 2 +--R 4a cos(x) + 6a cos(x) + 4a cos(x) + a +--R Type: Expression(Integer) +--E 331 + +)clear all + + +--S 332 of 526 +t0861:= sin(x)^2/(a+b*sin(x)+c*sin(x)^2) +--R +--R +--R 2 +--R sin(x) +--R (1) ------------------------ +--R 2 +--R c sin(x) + b sin(x) + a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 526 +r0861:= x/c+2^(1/2)*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ + atanh(1/2*(2*c+(b-(b^2-4*a*c)^(1/2))*tan(1/2*x))*_ + 2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/c/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)+2*(b+(b^2-2*a*c)/_ + (b^2-4*a*c)^(1/2))*atanh((2*c+(b+(b^2-4*a*c)^(1/2))*tan(1/2*x))/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/c/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 2 | | 2 2 2 +--R (2b\|- 4a c + b - 4a c + 2b )\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + b tan(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +--R (- b\|2 \|- 4a c + b + (- 2a c + b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +-+ +--R \|2 tan(-)\|- 4a c + b - b\|2 tan(-) - 2c\|2 +--R 2 2 +--R atanh(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R x\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 333 + +--S 334 of 526 +a0861:= integrate(t0861,x) +--R +--R +--R (3) +--R - +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 6 3 3 5 +--R 12a b c + (- 7a b + 28a b)c +--R + +--R 5 2 3 4 4 +--R (b - 27a b + 20a b)c +--R + +--R 5 3 3 5 3 7 2 5 4 3 2 +--R (9a b - 13a b + 4a b)c + (- b + 2a b - a b )c +--R * +--R cos(x) +--R + +--R 2 6 3 3 5 +--R 12a b c + (- 7a b + 28a b)c +--R + +--R 5 2 3 4 4 5 3 3 5 3 +--R (b - 27a b + 20a b)c + (9a b - 13a b + 4a b)c +--R + +--R 7 2 5 4 3 2 +--R (- b + 2a b - a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 3 4 2 +--R 8a b c + (- 14a b + 12a b)c +--R + +--R 5 3 3 5 7 2 5 4 3 +--R (7a b - 11a b + 4a b)c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 3 3 2 3 4 2 5 3 3 5 +--R 8a b c + (- 14a b + 12a b)c + (7a b - 11a b + 4a b)c +--R + +--R 7 2 5 4 3 +--R - b + 2a b - a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 7 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R cos(x) +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 4 3 3 5 +--R (8a b c - 4a b + 4a b)sin(x) +--R + +--R 3 2 2 4 4 2 3 2 2 4 4 2 +--R (4a b c - 2a b + 2a b )cos(x) + 4a b c - 2a b + 2a b +--R / +--R cos(x) + 1 +--R + +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 6 3 3 5 +--R 12a b c + (- 7a b + 28a b)c +--R + +--R 5 2 3 4 4 5 3 3 5 3 +--R (b - 27a b + 20a b)c + (9a b - 13a b + 4a b)c +--R + +--R 7 2 5 4 3 2 +--R (- b + 2a b - a b )c +--R * +--R cos(x) +--R + +--R 2 6 3 3 5 5 2 3 4 4 +--R 12a b c + (- 7a b + 28a b)c + (b - 27a b + 20a b)c +--R + +--R 5 3 3 5 3 7 2 5 4 3 2 +--R (9a b - 13a b + 4a b)c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 3 4 2 +--R - 8a b c + (14a b - 12a b)c +--R + +--R 5 3 3 5 7 2 5 4 3 +--R (- 7a b + 11a b - 4a b)c + b - 2a b + a b +--R * +--R cos(x) +--R + +--R 3 3 2 3 4 2 5 3 3 5 +--R - 8a b c + (14a b - 12a b)c + (- 7a b + 11a b - 4a b)c +--R + +--R 7 2 5 4 3 +--R b - 2a b + a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 4 3 3 5 3 2 2 4 4 2 +--R (8a b c - 4a b + 4a b)sin(x) + (4a b c - 2a b + 2a b )cos(x) +--R + +--R 3 2 2 4 4 2 +--R 4a b c - 2a b + 2a b +--R / +--R cos(x) + 1 +--R + +--R - 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4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 3 4 2 +--R 8a b c + (- 14a b + 12a b)c +--R + +--R 5 3 3 5 7 2 5 4 3 +--R (7a b - 11a b + 4a b)c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 3 3 2 3 4 2 5 3 3 5 +--R 8a b c + (- 14a b + 12a b)c + (7a b - 11a b + 4a b)c +--R + +--R 7 2 5 4 3 +--R - b + 2a b - a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 7 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 4 3 3 5 +--R (8a b c - 4a b + 4a b)sin(x) +--R + +--R 3 2 2 4 4 2 3 2 2 4 4 2 +--R (4a b c - 2a b + 2a b )cos(x) + 4a b c - 2a b + 2a b +--R / +--R cos(x) + 1 +--R + +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 6 3 3 5 +--R - 12a b c + (7a b - 28a b)c +--R + +--R 5 2 3 4 4 +--R (- b + 27a b - 20a b)c +--R + +--R 5 3 3 5 3 7 2 5 4 3 2 +--R (- 9a b + 13a b - 4a b)c + (b - 2a b + a b )c +--R * +--R cos(x) +--R + +--R 2 6 3 3 5 +--R - 12a b c + (7a b - 28a b)c +--R + +--R 5 2 3 4 4 5 3 3 5 3 +--R (- b + 27a b - 20a b)c + (- 9a b + 13a b - 4a b)c +--R + +--R 7 2 5 4 3 2 +--R (b - 2a b + a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 3 4 2 +--R - 8a b c + (14a b - 12a b)c +--R + +--R 5 3 3 5 7 2 5 4 3 +--R (- 7a b + 11a b - 4a b)c + b - 2a b + a b +--R * +--R cos(x) +--R + +--R 3 3 2 3 4 2 5 3 3 5 +--R - 8a b c + (14a b - 12a b)c + (- 7a b + 11a b - 4a b)c +--R + +--R 7 2 5 4 3 +--R b - 2a b + a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R cos(x) +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 4 3 3 5 3 2 2 4 4 2 +--R (8a b c - 4a b + 4a b)sin(x) + (4a b c - 2a b + 2a b )cos(x) +--R + +--R 3 2 2 4 4 2 +--R 4a b c - 2a b + 2a b +--R / +--R cos(x) + 1 +--R + +--R 2x +--R / +--R 2c +--R Type: Union(Expression(Integer),...) +--E 334 + +--S 335 of 526 +m0861:= a0861-r0861 +--R +--R +--R (4) +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 6 3 3 5 +--R 12a b c + (- 7a b + 28a b)c +--R + +--R 5 2 3 4 4 +--R (b - 27a b + 20a b)c +--R + +--R 5 3 3 5 3 7 2 5 4 3 2 +--R (9a b - 13a b + 4a b)c + (- b + 2a b - a b )c +--R * +--R cos(x) +--R + +--R 2 6 3 3 5 +--R 12a b c + (- 7a b + 28a b)c +--R + +--R 5 2 3 4 4 5 3 3 5 3 +--R (b - 27a b + 20a b)c + (9a b - 13a b + 4a b)c +--R + +--R 7 2 5 4 3 2 +--R (- b + 2a b - a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 3 4 2 +--R 8a b c + (- 14a b + 12a b)c +--R + +--R 5 3 3 5 7 2 5 4 3 +--R (7a b - 11a b + 4a b)c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 3 3 2 3 4 2 5 3 3 5 +--R 8a b c + (- 14a b + 12a b)c + (7a b - 11a b + 4a b)c +--R + +--R 7 2 5 4 3 +--R - b + 2a b - a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 7 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R cos(x) +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 4 3 3 5 +--R (8a b c - 4a b + 4a b)sin(x) +--R + +--R 3 2 2 4 4 2 3 2 2 4 4 2 +--R (4a b c - 2a b + 2a b )cos(x) + 4a b c - 2a b + 2a b +--R / +--R cos(x) + 1 +--R + +--R +-----------+ +--R | 2 +--R c\|- 4a c + b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 6 3 3 5 +--R 12a b c + (- 7a b + 28a b)c +--R + +--R 5 2 3 4 4 5 3 3 5 3 +--R (b - 27a b + 20a b)c + (9a b - 13a b + 4a b)c +--R + +--R 7 2 5 4 3 2 +--R (- b + 2a b - a b )c +--R * +--R cos(x) +--R + +--R 2 6 3 3 5 5 2 3 4 4 +--R 12a b c + (- 7a b + 28a b)c + (b - 27a b + 20a b)c +--R + +--R 5 3 3 5 3 7 2 5 4 3 2 +--R (9a b - 13a b + 4a b)c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 3 4 2 +--R - 8a b c + (14a b - 12a b)c +--R + +--R 5 3 3 5 7 2 5 4 3 +--R (- 7a b + 11a b - 4a b)c + b - 2a b + a b +--R * +--R cos(x) +--R + +--R 3 3 2 3 4 2 5 3 3 5 +--R - 8a b c + (14a b - 12a b)c + (- 7a b + 11a b - 4a b)c +--R + +--R 7 2 5 4 3 +--R b - 2a b + a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 4 3 3 5 3 2 2 4 4 2 +--R (8a b c - 4a b + 4a b)sin(x) + (4a b c - 2a b + 2a b )cos(x) +--R + +--R 3 2 2 4 4 2 +--R 4a b c - 2a b + 2a b +--R / +--R cos(x) + 1 +--R + +--R - +--R +-----------+ +--R | 2 +--R c\|- 4a c + b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 6 3 3 5 +--R - 12a b c + (7a b - 28a b)c +--R + +--R 5 2 3 4 4 +--R (- b + 27a b - 20a b)c +--R + +--R 5 3 3 5 3 7 2 5 4 3 2 +--R (- 9a b + 13a b - 4a b)c + (b - 2a b + a b )c +--R * +--R cos(x) +--R + +--R 2 6 3 3 5 +--R - 12a b c + (7a b - 28a b)c +--R + +--R 5 2 3 4 4 +--R (- b + 27a b - 20a b)c +--R + +--R 5 3 3 5 3 7 2 5 4 3 2 +--R (- 9a b + 13a b - 4a b)c + (b - 2a b + a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 3 3 2 3 4 2 +--R 8a b c + (- 14a b + 12a b)c +--R + +--R 5 3 3 5 7 2 5 4 3 +--R (7a b - 11a b + 4a b)c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 3 3 2 3 4 2 5 3 3 5 +--R 8a b c + (- 14a b + 12a b)c + (7a b - 11a b + 4a b)c +--R + +--R 7 2 5 4 3 +--R - b + 2a b - a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 7 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 2 4 4 2 2 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 4 3 3 5 +--R (8a b c - 4a b + 4a b)sin(x) +--R + +--R 3 2 2 4 4 2 3 2 2 4 4 2 +--R (4a b c - 2a b + 2a b )cos(x) + 4a b c - 2a b + 2a b +--R / +--R cos(x) + 1 +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 6 3 3 5 +--R - 12a b c + (7a b - 28a b)c +--R + +--R 5 2 3 4 4 +--R (- b + 27a b - 20a b)c +--R + +--R 5 3 3 5 3 7 2 5 4 3 2 +--R (- 9a b + 13a b - 4a b)c + (b - 2a b + a b )c +--R * +--R cos(x) +--R + +--R 2 6 3 3 5 +--R - 12a b c + (7a b - 28a b)c +--R + +--R 5 2 3 4 4 5 3 3 5 3 +--R (- b + 27a b - 20a b)c + (- 9a b + 13a b - 4a b)c +--R + +--R 7 2 5 4 3 2 +--R (b - 2a b + a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 3 4 2 +--R - 8a b c + (14a b - 12a b)c +--R + +--R 5 3 3 5 7 2 5 4 3 +--R (- 7a b + 11a b - 4a b)c + b - 2a b + a b +--R * +--R cos(x) +--R + +--R 3 3 2 3 4 2 5 3 3 5 +--R - 8a b c + (14a b - 12a b)c + (- 7a b + 11a b - 4a b)c +--R + +--R 7 2 5 4 3 +--R b - 2a b + a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R cos(x) +--R + +--R 3 5 2 2 4 4 3 2 5 3 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 2 4 4 2 2 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 4 3 3 5 3 2 2 4 4 2 +--R (8a b c - 4a b + 4a b)sin(x) + (4a b c - 2a b + 2a b )cos(x) +--R + +--R 3 2 2 4 4 2 +--R 4a b c - 2a b + 2a b +--R / +--R cos(x) + 1 +--R + +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 2 | | 2 2 2 +--R (- 4b\|- 4a c + b + 8a c - 4b )\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + b tan(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +--R (2b\|2 \|- 4a c + b + (4a c - 2b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +-+ +--R \|2 tan(-)\|- 4a c + b - b\|2 tan(-) - 2c\|2 +--R 2 2 +--R atanh(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 335 + +--S 336 of 526 +d0861:= D(m0861,x) +--R +--R +--R (5) +--R 2 4 3 +--R - a sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 2 2 2 2 +--R ((4a c - 2a )cos(x) + (8a c - 2a )cos(x) + 4a c)sin(x) +--R + +--R 3 2 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b)sin(x) +--R + +--R 2 4 2 3 2 2 +--R - a cos(x) - 2a cos(x) + 2a cos(x) + a +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 +--R - 2a b sin(x) + (- 4b cos(x) - 4b )sin(x) +--R + +--R 2 2 +--R ((8b c - 4a b)cos(x) + (16b c - 4a b)cos(x) + 8b c)sin(x) +--R + +--R 2 3 2 2 2 2 4 +--R (- 4b cos(x) - 4b cos(x) + 4b cos(x) + 4b )sin(x) - 2a b cos(x) +--R + +--R 3 +--R - 4a b cos(x) + 4a b cos(x) + 2a b +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 4 +--R (- 8a c - 2a )sin(x) +--R + +--R 3 +--R ((- 16b c - 4a b)cos(x) - 16b c - 4a b)sin(x) +--R + +--R 2 2 2 2 +--R ((- 8a c - 4a )cos(x) + (- 8a c - 4a )cos(x))sin(x) +--R + +--R 3 2 +--R (- 16b c - 4a b)cos(x) + (- 32b c - 4a b)cos(x) +--R + +--R (- 16b c + 4a b)cos(x) + 4a b +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 +--R (- 8a c - 2a )cos(x) + (- 24a c - 4a )cos(x) - 24a c cos(x) +--R + +--R 2 2 +--R (- 8a c + 4a )cos(x) + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 +--R - 2a b sin(x) + (- 4b cos(x) - 4b )sin(x) +--R + +--R 2 2 +--R ((8b c - 4a b)cos(x) + (16b c - 4a b)cos(x) + 8b c)sin(x) +--R + +--R 2 3 2 2 2 2 4 +--R (- 4b cos(x) - 4b cos(x) + 4b cos(x) + 4b )sin(x) - 2a b cos(x) +--R + +--R 3 +--R - 4a b cos(x) + 4a b cos(x) + 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 3 +--R - a sin(x) + (- 2a b cos(x) - 2a b)sin(x) +--R + +--R 2 2 2 2 +--R ((4a c - 2a )cos(x) + (8a c - 2a )cos(x) + 4a c)sin(x) +--R + +--R 3 2 2 4 +--R (- 2a b cos(x) - 2a b cos(x) + 2a b cos(x) + 2a b)sin(x) - a cos(x) +--R + +--R 2 3 2 2 +--R - 2a cos(x) + 2a cos(x) + a +--R / +--R 2 4 3 +--R a c sin(x) + (2a b c cos(x) + 2a b c)sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((4a c + 2a c)cos(x) + (8a c + 4a c)cos(x) + 4a c + 2a c)sin(x) +--R + +--R 3 2 +--R (2a b c cos(x) + 6a b c cos(x) + 6a b c cos(x) + 2a b c)sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R a c cos(x) + 4a c cos(x) + 6a c cos(x) + 4a c cos(x) + a c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 +--R 2a b c sin(x) + (4b c cos(x) + 4b c)sin(x) +--R + +--R 2 2 2 2 +--R (8b c + 4a b c)cos(x) + (16b c + 8a b c)cos(x) + 8b c +--R + +--R 4a b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 2 2 +--R (4b c cos(x) + 12b c cos(x) + 12b c cos(x) + 4b c)sin(x) +--R + +--R 4 3 2 +--R 2a b c cos(x) + 8a b c cos(x) + 12a b c cos(x) + 8a b c cos(x) +--R + +--R 2a b c +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 2 4 +--R (4a c + 2a c)sin(x) +--R + +--R 2 2 3 +--R ((8b c + 4a b c)cos(x) + 8b c + 4a b c)sin(x) +--R + +--R 3 2 2 2 3 2 2 +--R (16c + 16a c + 4a c)cos(x) + (32c + 32a c + 8a c)cos(x) +--R + +--R 3 2 2 +--R 16c + 16a c + 4a c +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 +--R (8b c + 4a b c)cos(x) + (24b c + 12a b c)cos(x) +--R + +--R 2 2 +--R (24b c + 12a b c)cos(x) + 8b c + 4a b c +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 +--R (4a c + 2a c)cos(x) + (16a c + 8a c)cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R (24a c + 12a c)cos(x) + (16a c + 8a c)cos(x) + 4a c + 2a c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 2 2 3 +--R 2a b c sin(x) + (4b c cos(x) + 4b c)sin(x) +--R + +--R 2 2 2 2 +--R (8b c + 4a b c)cos(x) + (16b c + 8a b c)cos(x) + 8b c +--R + +--R 4a b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 2 2 +--R (4b c cos(x) + 12b c cos(x) + 12b c cos(x) + 4b c)sin(x) +--R + +--R 4 3 2 +--R 2a b c cos(x) + 8a b c cos(x) + 12a b c cos(x) + 8a b c cos(x) +--R + +--R 2a b c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 3 +--R a c sin(x) + (2a b c cos(x) + 2a b c)sin(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R ((4a c + 2a c)cos(x) + (8a c + 4a c)cos(x) + 4a c + 2a c)sin(x) +--R + +--R 3 2 +--R (2a b c cos(x) + 6a b c cos(x) + 6a b c cos(x) + 2a b c)sin(x) +--R + +--R 2 4 2 3 2 2 2 2 +--R a c cos(x) + 4a c cos(x) + 6a c cos(x) + 4a c cos(x) + a c +--R Type: Expression(Integer) +--E 336 + +)clear all + + +--S 337 of 526 +t0862:= sin(x)^3/(a+b*sin(x)+c*sin(x)^2) +--R +--R +--R 3 +--R sin(x) +--R (1) ------------------------ +--R 2 +--R c sin(x) + b sin(x) + a +--R Type: Expression(Integer) +--E 337 + +--S 338 of 526 +r0862:= -b*x/c^2-2^(1/2)*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ + atanh(1/2*(2*c+(b-(b^2-4*a*c)^(1/2))*tan(1/2*x))*_ + 2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/c^2/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)-2*(b^2-a*c+b*(b^2-3*a*c)/_ + (b^2-4*a*c)^(1/2))*atanh((2*c+(b+(b^2-4*a*c)^(1/2))*tan(1/2*x))/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/c^2/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2)-cos(x)/c +--R +--R +--R (2) +--R +-----------+ +--R 2 | 2 3 +--R ((2a c - 2b )\|- 4a c + b + 6a b c - 2b ) +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + b tan(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R 2 +-+ | 2 3 +-+ +--R ((- a c + b )\|2 \|- 4a c + b + (3a b c - b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +-+ +--R \|2 tan(-)\|- 4a c + b - b\|2 tan(-) - 2c\|2 +--R 2 2 +--R atanh(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R + +--R +-----------+ +--R | 2 +--R (- c cos(x) - b x)\|- 4a c + b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 2 2 +--R c \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 338 + +--S 339 of 526 +a0862:= integrate(t0862,x) +--R +--R +--R (3) +--R 2 +--R c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b + 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 3 9 2 2 4 8 +--R 8a c + (- 18a b + 24a )c +--R + +--R 4 3 2 5 7 +--R (8a b - 50a b + 24a )c +--R + +--R 6 2 4 4 2 6 6 +--R (- b + 35a b - 38a b + 8a )c +--R + +--R 6 3 4 5 2 5 8 2 6 4 4 4 +--R (- 10a b + 16a b - 6a b )c + (b - 2a b + a b )c +--R * +--R cos(x) +--R + +--R 3 9 2 2 4 8 4 3 2 5 7 +--R 8a c + (- 18a b + 24a )c + (8a b - 50a b + 24a )c +--R + +--R 6 2 4 4 2 6 6 +--R (- b + 35a b - 38a b + 8a )c +--R + +--R 6 3 4 5 2 5 8 2 6 4 4 4 +--R (- 10a b + 16a b - 6a b )c + (b - 2a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 4 2 4 3 4 5 2 3 +--R 24a b c + (- 50a b + 28a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (35a b - 39a b + 8a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (- 10a b + 16a b - 6a b )c + b - 2a b + a b +--R * +--R cos(x) +--R + +--R 4 2 4 3 4 5 2 3 +--R 24a b c + (- 50a b + 28a b )c +--R + +--R 2 6 4 4 6 2 2 8 3 6 5 4 +--R (35a b - 39a b + 8a b )c + (- 10a b + 16a b - 6a b )c +--R + +--R 10 2 8 4 6 +--R b - 2a b + a b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 11 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b +--R + +--R 2 4 +--R 2a b +--R / +--R 7 2 2 6 2 3 5 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 4 +--R (b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 6 2 5 3 7 4 5 6 3 +--R (12a b c + (- 16a b + 8a b)c + 4a b - 4a b )sin(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 5 2 2 +--R (6a b c + (- 8a b + 4a b )c + 2a b - 2a b )cos(x) + 6a b c +--R + +--R 4 4 6 2 3 6 5 4 +--R (- 8a b + 4a b )c + 2a b - 2a b +--R / +--R cos(x) + 1 +--R + +--R - +--R 2 +--R c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b + 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 3 9 2 2 4 8 +--R 8a c + (- 18a b + 24a )c +--R + +--R 4 3 2 5 7 +--R (8a b - 50a b + 24a )c +--R + +--R 6 2 4 4 2 6 6 +--R (- b + 35a b - 38a b + 8a )c +--R + +--R 6 3 4 5 2 5 +--R (- 10a b + 16a b - 6a b )c +--R + +--R 8 2 6 4 4 4 +--R (b - 2a b + a b )c +--R * +--R cos(x) +--R + +--R 3 9 2 2 4 8 +--R 8a c + (- 18a b + 24a )c +--R + +--R 4 3 2 5 7 +--R (8a b - 50a b + 24a )c +--R + +--R 6 2 4 4 2 6 6 +--R (- b + 35a b - 38a b + 8a )c +--R + +--R 6 3 4 5 2 5 8 2 6 4 4 4 +--R (- 10a b + 16a b - 6a b )c + (b - 2a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 4 2 4 3 4 5 2 3 +--R - 24a b c + (50a b - 28a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 35a b + 39a b - 8a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (10a b - 16a b + 6a b )c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 4 2 4 3 4 5 2 3 +--R - 24a b c + (50a b - 28a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 35a b + 39a b - 8a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (10a b - 16a b + 6a b )c - b + 2a b - a b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 +--R (8a b - 12a b + 4a b )c - b + 2a b +--R + +--R 4 6 +--R - a b +--R / +--R 13 2 2 12 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 11 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b +--R + +--R 2 4 +--R 2a b +--R / +--R 7 2 2 6 2 3 5 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 4 +--R (b - 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8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b + 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 3 9 2 2 4 8 +--R - 8a c + (18a b - 24a )c +--R + +--R 4 3 2 5 7 +--R (- 8a b + 50a b - 24a )c +--R + +--R 6 2 4 4 2 6 6 +--R (b - 35a b + 38a b - 8a )c +--R + +--R 6 3 4 5 2 5 8 2 6 4 4 4 +--R (10a b - 16a b + 6a b )c + (- b + 2a b - a b )c +--R * +--R cos(x) +--R + +--R 3 9 2 2 4 8 +--R - 8a c + (18a b - 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2a b + a b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 4 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 11 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b +--R + +--R 2 4 +--R 2a b +--R / +--R 7 2 2 6 2 3 5 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 4 +--R (b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 3 4 5 2 4 +--R (- 2a b + 2a b )c +--R * +--R cos(x) +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R - 8a c + (2a b - 16a )c + (12a b - 8a )c +--R + +--R 3 4 5 2 4 +--R (- 2a b + 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 6 2 5 3 7 4 5 6 3 +--R (12a b c + (- 16a b + 8a b)c + 4a b - 4a b )sin(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 5 2 2 +--R (6a b c + (- 8a b + 4a b )c + 2a b - 2a b )cos(x) + 6a b c +--R + +--R 4 4 6 2 3 6 5 4 +--R (- 8a b + 4a b )c + 2a b - 2a b +--R / +--R cos(x) + 1 +--R + +--R - +--R 2 +--R c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b + 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 3 9 2 2 4 8 +--R - 8a c + (18a b - 24a )c +--R + +--R 4 3 2 5 7 +--R (- 8a b + 50a b - 24a )c +--R + +--R 6 2 4 4 2 6 6 +--R (b - 35a b + 38a b - 8a )c +--R + +--R 6 3 4 5 2 5 +--R (10a b - 16a b + 6a b )c +--R + +--R 8 2 6 4 4 4 +--R (- b + 2a b - a b )c +--R * +--R cos(x) +--R + +--R 3 9 2 2 4 8 +--R - 8a c + (18a b - 24a )c +--R + +--R 4 3 2 5 7 +--R (- 8a b + 50a b - 24a )c +--R + +--R 6 2 4 4 2 6 6 +--R (b - 35a b + 38a b - 8a )c +--R + +--R 6 3 4 5 2 5 8 2 6 4 4 4 +--R (10a b - 16a b + 6a b )c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 4 2 4 3 4 5 2 3 +--R - 24a b c + (50a b - 28a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 35a b + 39a b - 8a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (10a b - 16a b + 6a b )c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 4 2 4 3 4 5 2 3 +--R - 24a b c + (50a b - 28a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 35a b + 39a b - 8a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (10a b - 16a b + 6a b )c - b + 2a b - a b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 +--R (8a b - 12a b + 4a b )c - b + 2a b +--R + +--R 4 6 +--R - a b +--R / +--R 13 2 2 12 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 11 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b +--R + +--R 2 4 +--R 2a b +--R / +--R 7 2 2 6 2 3 5 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 4 +--R (b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 6 2 5 3 7 4 5 6 3 +--R (12a b c + (- 16a b + 8a b)c + 4a b - 4a b )sin(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R (6a b c + (- 8a b + 4a b )c + 2a b - 2a b )cos(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b + 4a b )c + 2a b - 2a b +--R / +--R cos(x) + 1 +--R + +--R - 2c cos(x) - 2b x +--R / +--R 2 +--R 2c +--R Type: Union(Expression(Integer),...) +--E 339 + +--S 340 of 526 +m0862:= a0862-r0862 +--R +--R +--R (4) +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 2 2 +--R c \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b + 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 3 9 2 2 4 8 +--R 8a c + (- 18a b + 24a )c +--R + +--R 4 3 2 5 7 +--R (8a b - 50a b + 24a )c +--R + +--R 6 2 4 4 2 6 6 +--R (- b + 35a b - 38a b + 8a )c +--R + +--R 6 3 4 5 2 5 8 2 6 4 4 4 +--R (- 10a b + 16a b - 6a b )c + (b - 2a b + a b )c +--R * +--R cos(x) +--R + +--R 3 9 2 2 4 8 4 3 2 5 7 +--R 8a c + (- 18a b + 24a )c + (8a b - 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8a c + (18a b - 24a )c +--R + +--R 4 3 2 5 7 +--R (- 8a b + 50a b - 24a )c +--R + +--R 6 2 4 4 2 6 6 +--R (b - 35a b + 38a b - 8a )c +--R + +--R 6 3 4 5 2 5 8 2 6 4 4 4 +--R (10a b - 16a b + 6a b )c + (- b + 2a b - a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 6 2 4 4 2 8 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 4 2 4 3 4 5 2 3 +--R - 24a b c + (50a b - 28a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 35a b + 39a b - 8a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (10a b - 16a b + 6a b )c - b + 2a b - a b +--R * +--R cos(x) +--R + +--R 4 2 4 3 4 5 2 3 +--R - 24a b c + (50a b - 28a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 35a b + 39a b - 8a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (10a b - 16a b + 6a b )c - b + 2a b - a b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 +--R (8a b - 12a b + 4a b )c - b + 2a b +--R + +--R 4 6 +--R - a b +--R / +--R 13 2 2 12 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 11 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b +--R + +--R 2 4 +--R 2a b +--R / +--R 7 2 2 6 2 3 5 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 4 +--R (b - a b )c +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b - 2a b )c +--R * +--R cos(x) +--R + +--R 4 7 3 2 5 6 4 2 6 5 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 3 4 5 2 4 +--R (2a b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 6 2 5 3 7 4 5 6 3 +--R (12a b c + (- 16a b + 8a b)c + 4a b - 4a b )sin(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R (6a b c + (- 8a b + 4a b )c + 2a b - 2a b )cos(x) +--R + +--R 5 2 2 4 4 6 2 3 6 5 4 +--R 6a b c + (- 8a b + 4a b )c + 2a b - 2a b +--R / +--R cos(x) + 1 +--R + +--R +-----------+ +--R 2 | 2 3 +--R ((- 4a c + 4b )\|- 4a c + b - 12a b c + 4b ) +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + b tan(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R 2 +-+ | 2 3 +-+ +--R ((2a c - 2b )\|2 \|- 4a c + b + (- 6a b c + 2b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +-+ +--R \|2 tan(-)\|- 4a c + b - b\|2 tan(-) - 2c\|2 +--R 2 2 +--R atanh(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 2 2 +--R 2c \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 340 + +--S 341 of 526 +d0862:= D(m0862,x) +--R +--R +--R (5) +--R 2 4 2 2 2 2 3 +--R a b sin(x) + ((- 4a c + 2a b )cos(x) - 4a c + 2a b )sin(x) +--R + +--R 2 2 2 2 +--R ((- 4a b c + 2a b)cos(x) + (- 8a b c + 2a b)cos(x) - 4a b c)sin(x) +--R + +--R 2 2 3 2 2 2 +--R (- 4a c + 2a b )cos(x) + (- 8a c + 2a b )cos(x) +--R + +--R 2 2 2 +--R (- 4a c - 2a b )cos(x) - 2a b +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 2 4 +--R (2a c + 2a b )sin(x) +--R + +--R 3 3 3 +--R ((- 4a b c + 4b )cos(x) - 4a b c + 4b )sin(x) +--R + +--R 2 2 2 2 2 +--R (8a c + (- 8b + 4a )c + 4a b )cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R (16a c + (- 16b + 8a )c + 4a b )cos(x) + 8a c + (- 8b + 4a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 2 +--R (- 4a b c + 4b )cos(x) + (- 4a b c + 4b )cos(x) +--R + +--R 3 3 +--R (4a b c - 4b )cos(x) + 4a b c - 4b +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 2 2 +--R (2a c + 2a b )cos(x) + (8a c + 4a b )cos(x) + 12a c cos(x) +--R + +--R 2 2 2 2 +--R (8a c - 4a b )cos(x) + 2a c - 2a b +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 2 4 +--R (8a b c + 2a b)sin(x) +--R + +--R 2 2 2 2 2 2 2 +--R (- 16a c + (16b - 8a )c + 4a b )cos(x) - 16a c + (16b - 8a )c +--R + +--R 2 +--R 4a b +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 2 2 +--R ((8a b c + 4a b)cos(x) + (8a b c + 4a b)cos(x))sin(x) +--R + +--R 2 2 2 2 3 +--R (- 16a c + (16b - 8a )c + 4a b )cos(x) +--R + +--R 2 2 2 2 2 +--R (- 32a c + (32b - 16a )c + 4a b )cos(x) +--R + +--R 2 2 2 2 2 +--R (- 16a c + (16b - 8a )c - 4a b )cos(x) - 4a b +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 +--R (8a b c + 2a b)cos(x) + (24a b c + 4a b)cos(x) + 24a b c cos(x) +--R + +--R 2 2 +--R (8a b c - 4a b)cos(x) - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 +--R (2a c + 2a b )sin(x) +--R + +--R 3 3 3 +--R ((- 4a b c + 4b )cos(x) - 4a b c + 4b )sin(x) +--R + +--R 2 2 2 2 2 +--R (8a c + (- 8b + 4a )c + 4a b )cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R (16a c + (- 16b + 8a )c + 4a b )cos(x) + 8a c + (- 8b + 4a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 2 +--R (- 4a b c + 4b )cos(x) + (- 4a b c + 4b )cos(x) +--R + +--R 3 3 +--R (4a b c - 4b )cos(x) + 4a b c - 4b +--R * +--R sin(x) +--R + +--R 2 2 4 2 2 3 2 2 +--R (2a c + 2a b )cos(x) + (8a c + 4a b )cos(x) + 12a c cos(x) +--R + +--R 2 2 2 2 +--R (8a c - 4a b )cos(x) + 2a c - 2a b +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 2 2 3 +--R a b sin(x) + ((- 4a c + 2a b )cos(x) - 4a c + 2a b )sin(x) +--R + +--R 2 2 2 2 +--R ((- 4a b c + 2a b)cos(x) + (- 8a b c + 2a b)cos(x) - 4a b c)sin(x) +--R + +--R 2 2 3 2 2 2 +--R (- 4a c + 2a b )cos(x) + (- 8a c + 2a b )cos(x) +--R + +--R 2 2 2 +--R (- 4a c - 2a b )cos(x) - 2a b +--R * +--R sin(x) +--R + +--R 2 4 2 3 2 2 +--R a b cos(x) + 2a b cos(x) - 2a b cos(x) - a b +--R / +--R 2 2 4 2 2 3 +--R a c sin(x) + (2a b c cos(x) + 2a b c )sin(x) +--R + +--R 3 2 2 2 3 2 2 3 2 2 +--R ((4a c + 2a c )cos(x) + (8a c + 4a c )cos(x) + 4a c + 2a c ) +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 2 2 2 2 +--R (2a b c cos(x) + 6a b c cos(x) + 6a b c cos(x) + 2a b c )sin(x) +--R + +--R 2 2 4 2 2 3 2 2 2 2 2 2 2 +--R a c cos(x) + 4a c cos(x) + 6a c cos(x) + 4a c cos(x) + a c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 2 2 3 +--R 2a b c sin(x) + (4b c cos(x) + 4b c )sin(x) +--R + +--R 3 2 2 3 2 3 +--R (8b c + 4a b c )cos(x) + (16b c + 8a b c )cos(x) + 8b c +--R + +--R 2 +--R 4a b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 +--R (4b c cos(x) + 12b c cos(x) + 12b c cos(x) + 4b c )sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R 2a b c cos(x) + 8a b c cos(x) + 12a b c cos(x) + 8a b c cos(x) +--R + +--R 2 +--R 2a b c +--R * +--R x 3 +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 +--R (4a c + 2a c )sin(x) +--R + +--R 3 2 3 2 3 +--R ((8b c + 4a b c )cos(x) + 8b c + 4a b c )sin(x) +--R + +--R 4 3 2 2 2 4 3 2 2 +--R (16c + 16a c + 4a c )cos(x) + (32c + 32a c + 8a c )cos(x) +--R + +--R 4 3 2 2 +--R 16c + 16a c + 4a c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 3 3 2 2 +--R (8b c + 4a b c )cos(x) + (24b c + 12a b c )cos(x) +--R + +--R 3 2 3 2 +--R (24b c + 12a b c )cos(x) + 8b c + 4a b c +--R * +--R sin(x) +--R + +--R 3 2 2 4 3 2 2 3 +--R (4a c + 2a c )cos(x) + (16a c + 8a c )cos(x) +--R + +--R 3 2 2 2 3 2 2 3 2 2 +--R (24a c + 12a c )cos(x) + (16a c + 8a c )cos(x) + 4a c + 2a c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 4 2 2 2 2 3 +--R 2a b c sin(x) + (4b c cos(x) + 4b c )sin(x) +--R + +--R 3 2 2 3 2 3 +--R (8b c + 4a b c )cos(x) + (16b c + 8a b c )cos(x) + 8b c +--R + +--R 2 +--R 4a b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 3 2 2 2 2 2 2 2 +--R (4b c cos(x) + 12b c cos(x) + 12b c cos(x) + 4b c )sin(x) +--R + +--R 2 4 2 3 2 2 2 +--R 2a b c cos(x) + 8a b c cos(x) + 12a b c cos(x) + 8a b c cos(x) +--R + +--R 2 +--R 2a b c +--R * +--R x +--R tan(-) +--R 2 +--R + +--R 2 2 4 2 2 3 +--R a c sin(x) + (2a b c cos(x) + 2a b c )sin(x) +--R + +--R 3 2 2 2 3 2 2 3 2 2 2 +--R ((4a c + 2a c )cos(x) + (8a c + 4a c )cos(x) + 4a c + 2a c )sin(x) +--R + +--R 2 3 2 2 2 2 +--R (2a b c cos(x) + 6a b c cos(x) + 6a b c cos(x) + 2a b c )sin(x) +--R + +--R 2 2 4 2 2 3 2 2 2 2 2 2 2 +--R a c cos(x) + 4a c cos(x) + 6a c cos(x) + 4a c cos(x) + a c +--R Type: Expression(Integer) +--E 341 + +)clear all + + +--S 342 of 526 +t0863:= (a+b*sin(x))/(b^2+2*a*b*sin(x)+a^2*sin(x)^2) +--R +--R +--R b sin(x) + a +--R (1) ---------------------------- +--R 2 2 2 +--R a sin(x) + 2a b sin(x) + b +--R Type: Expression(Integer) +--E 342 + +--S 343 of 526 +r0863:= -cos(x)/(b+a*sin(x)) +--R +--R +--R cos(x) +--R (2) - ------------ +--R a sin(x) + b +--R Type: Expression(Integer) +--E 343 + +--S 344 of 526 +a0863:= integrate(t0863,x) +--R +--R +--R - a sin(x) - b cos(x) - b +--R (3) ------------------------- +--R 2 +--R a b sin(x) + b +--R Type: Union(Expression(Integer),...) +--E 344 + +--S 345 of 526 +m0863:= a0863-r0863 +--R +--R +--R 1 +--R (4) - - +--R b +--R Type: Expression(Integer) +--E 345 + +--S 346 of 526 +d0863:= D(m0863,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 346 + +)clear all + + +--S 347 of 526 +t0864:= (d+e*sin(x))/(a+b*sin(x)+c*sin(x)^2) +--R +--R +--R e sin(x) + d +--R (1) ------------------------ +--R 2 +--R c sin(x) + b sin(x) + a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 526 +r0864:= -2^(1/2)*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atanh(1/2*(2*c+(b-(b^2-4*a*c)^(1/2))*tan(1/2*x))*2^(1/2)/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)-_ + 2*(e-(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atanh((2*c+(b+(b^2-4*a*c)^(1/2))*tan(1/2*x))/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (- 2e\|- 4a c + b - 2b e + 4c d)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + b tan(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (e\|2 \|- 4a c + b + (- b e + 2c d)\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +-+ +--R \|2 tan(-)\|- 4a c + b - b\|2 tan(-) - 2c\|2 +--R 2 2 +--R atanh(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 348 + +--S 349 of 526 ok to fail. known bug #7240 in buglist +a0864:= integrate(t0864,x) +--R +--R +--R (3) +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 2 4 2 3 3 +--R 8a c + (- 6a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (b - 22a b + 24a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 18a b + 8a )c - b + 3a b - 2a b +--R * +--R e +--R + +--R 4 3 2 3 +--R 4a b c + (- b + 4a b)c +--R + +--R 3 3 2 5 2 3 4 +--R (- 5a b - 4a b)c + (b + 5a b - 4a b)c +--R + +--R 5 3 3 +--R - a b + a b +--R * +--R d +--R * +--R cos(x) +--R + +--R 2 4 2 3 3 +--R 8a c + (- 6a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (b - 22a b + 24a )c + (8a b - 18a b + 8a )c +--R + +--R 6 2 4 4 2 +--R - b + 3a b - 2a b +--R * +--R e +--R + +--R 4 3 2 3 3 3 2 +--R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (b + 5a b - 4a b)c - a b + a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 4 3 +--R (4a b c - b )e +--R + +--R 2 3 2 3 2 +--R (- 12a b c + (3b - 12a b)c + 3a b )d e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (8a c + (- 2b + 16a )c + 8a c - b - 2a b )d e +--R + +--R 2 3 2 3 3 +--R (- 4a b c + (b - 4a b)c + a b )d +--R * +--R cos(x) +--R + +--R 2 4 3 +--R (4a b c - b )e +--R + +--R 2 3 2 3 2 +--R (- 12a b c + (3b - 12a b)c + 3a b )d e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (8a c + (- 2b + 16a )c + 8a c - b - 2a b )d e +--R + +--R 2 3 2 3 3 +--R (- 4a b c + (b - 4a b)c + a b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R 2b - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 3 2 +--R 2a b - 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4a b c - 2b )d e + 2b c d +--R * +--R cos(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c - 4a b c - 2b )d e + 2b c d +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 2 2 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e + (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 2 4 2 3 3 +--R - 8a c + (6a b - 24a )c +--R + +--R 4 2 2 4 2 +--R (- b + 22a b - 24a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (- 8a b + 18a b - 8a )c + b - 3a b + 2a b +--R * +--R e +--R + +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R d +--R * +--R cos(x) +--R + +--R 2 4 2 3 3 +--R - 8a c + (6a b - 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (- b + 22a b - 24a )c + (- 8a b + 18a b - 8a )c +--R + +--R 6 2 4 4 2 +--R b - 3a b + 2a b +--R * +--R e +--R + +--R 4 3 2 3 3 3 2 +--R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R + +--R 5 2 3 4 5 3 3 +--R (- b - 5a b + 4a b)c + a b - a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 4 3 +--R (- 4a b c + b )e +--R + +--R 2 3 2 3 2 +--R (12a b c + (- 3b + 12a b)c - 3a b )d e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (- 8a c + (2b - 16a )c - 8a c + b + 2a b )d e +--R + +--R 2 3 2 3 3 +--R (4a b c + (- b + 4a b)c - a b )d +--R * +--R cos(x) +--R + +--R 2 4 3 +--R (- 4a b c + b )e +--R + +--R 2 3 2 3 2 +--R (12a b c + (- 3b + 12a b)c - 3a b )d e +--R + +--R 3 2 2 2 3 4 2 2 2 +--R (- 8a c + (2b - 16a )c - 8a c + b + 2a b )d e +--R + +--R 2 3 2 3 3 +--R (4a b c + (- b + 4a b)c - a b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 2 3 2 3 2 2 2 4 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 3 2 +--R 2a b - 2a b +--R * +--R 2 +--R e +--R + +--R 3 3 2 2 3 3 5 +--R - 8a b c + (2b - 16a b)c + (12a b - 8a b)c - 2b +--R + +--R 2 3 +--R 2a b +--R * +--R d e +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R 2 +--R d +--R * +--R cos(x) +--R + +--R 2 3 2 3 2 2 2 4 4 +--R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c + 2a b +--R + +--R 3 2 +--R - 2a b +--R * +--R 2 +--R e +--R + +--R 3 3 2 2 3 3 5 +--R - 8a b c + (2b - 16a b)c + (12a b - 8a b)c - 2b +--R + +--R 2 3 +--R 2a b +--R * +--R d e +--R + +--R 4 2 2 3 2 3 2 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R (2b - 2a b )c +--R * +--R 2 +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 4 2 2 3 3 2 2 2 +--R 4a b e + (- 8a c - 4a b - 8a )d e + (12a b c + 12a b)d e +--R + +--R 2 2 2 3 4 +--R (- 8a c - 8a c - 4a b )d e + 4a b c d +--R * +--R sin(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c - 4a b c - 2b )d e + 2b c d +--R * +--R cos(x) +--R + +--R 2 4 3 2 3 2 2 2 2 +--R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e +--R + +--R 2 3 3 2 4 +--R (- 4b c - 4a b c - 2b )d e + 2b c d +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 349 + +--S 350 of 526 ok to fail due to known bug (see above) +m0864:= a0864-r0864 +--R +--R +--R (3) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (2e\|- 4a c + b + 2b e - 4c d)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + b tan(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (- e\|2 \|- 4a c + b + (b e - 2c d)\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +-+ +--R \|2 tan(-)\|- 4a c + b - b\|2 tan(-) - 2c\|2 +--R 2 2 +--R atanh(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R a0864\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 350 + +--S 351 of 526 +--d0864:= D(m0864,x) +--E 351 + +)clear all + + +--S 352 of 526 +t0865:= 1/(a+b*cos(x)+c*cos(x)^2) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 +--R c cos(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 526 +r0865:= -2*2^(1/2)*c*atanh(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*_ + tan(1/2*x)*2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ + (b^2-4*a*c)^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)+_ + 4*c*atanh((b+(b^2-4*a*c)^(1/2)-2*c)*tan(1/2*x)/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/(b^2-4*a*c)^(1/2)/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 4c\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-------------------------------------+ +--R | +-----------+ +--R +-+ | | 2 2 2 +--R 2c\|2 \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 353 + +--S 354 of 526 +a0865:= integrate(t0865,x) +--R +--R +--R (3) +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4b c sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )cos(x) - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4b c sin(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4b c sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )cos(x) - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R 2b - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4b c sin(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 354 + +--S 355 of 526 +m0865:= a0865-r0865 +--R +--R +--R (4) +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4b c sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )cos(x) - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4b c sin(x) +--R / +--R cos(x) + 1 +--R + +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4b c sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )cos(x) - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R 2b - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4b c sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 8c\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R - +--R +-------------------------------------+ +--R | +-----------+ +--R +-+ | | 2 2 2 +--R 4c\|2 \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 355 + +--S 356 of 526 +d0865:= D(m0865,x) +--R +--R +--R (5) +--R 4 +--R (c - b + a)sin(x) +--R + +--R 2 2 +--R ((6c - 4b + 2a)cos(x) + (10c - 6b + 2a)cos(x) + 4c - 2b)sin(x) +--R + +--R 4 3 2 +--R (c - 3b + a)cos(x) + (2c - 10b + 2a)cos(x) - 12b cos(x) +--R + +--R (- 2c - 6b - 2a)cos(x) - c - b - a +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 +--R (- 6c + 2b + 2a)sin(x) +--R + +--R 2 2 +--R ((- 4c + 4a)cos(x) + (- 4c + 4a)cos(x))sin(x) +--R + +--R 4 3 +--R (- 6c - 2b + 2a)cos(x) + (- 20c - 8b + 4a)cos(x) +--R + +--R 2 +--R (- 24c - 12b)cos(x) + (- 12c - 8b - 4a)cos(x) - 2c - 2b - 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 +--R (c + 3b + a)sin(x) +--R + +--R 2 2 +--R ((6c + 4b + 2a)cos(x) + (10c + 6b + 2a)cos(x) + 4c + 2b)sin(x) +--R + +--R 4 3 +--R (c + b + a)cos(x) + (2c + 2b + 2a)cos(x) + (- 2c - 2b - 2a)cos(x) - c +--R + +--R - b - a +--R / +--R 2 2 2 4 +--R (c + (- 2b + 2a)c + b - 2a b + a )sin(x) +--R + +--R 2 2 2 +--R (- 2c + 2b c - 2a b + 2a )cos(x) +--R + +--R 2 2 2 2 +--R (- 4c + 4b c - 4a b + 4a )cos(x) - 2c + 2b c - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 3 +--R (c + 2a c - b + a )cos(x) + (4c + 8a c - 4b + 4a )cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R (6c + 12a c - 6b + 6a )cos(x) + (4c + 8a c - 4b + 4a )cos(x) +--R + +--R 2 2 2 +--R c + 2a c - b + a +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 2 4 +--R (- 2c + 2b c - 2a b + 2a )sin(x) +--R + +--R 2 2 2 2 2 2 +--R (4c - 8a c + 4a )cos(x) + (8c - 16a c + 8a )cos(x) + 4c +--R + +--R 2 +--R - 8a c + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 +--R (- 2c - 2b c + 2a b + 2a )cos(x) +--R + +--R 2 2 3 +--R (- 8c - 8b c + 8a b + 8a )cos(x) +--R + +--R 2 2 2 +--R (- 12c - 12b c + 12a b + 12a )cos(x) +--R + +--R 2 2 2 2 +--R (- 8c - 8b c + 8a b + 8a )cos(x) - 2c - 2b c + 2a b + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 +--R (c + 2a c - b + a )sin(x) +--R + +--R 2 2 2 +--R (- 2c - 2b c + 2a b + 2a )cos(x) +--R + +--R 2 2 2 2 +--R (- 4c - 4b c + 4a b + 4a )cos(x) - 2c - 2b c + 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 +--R (c + (2b + 2a)c + b + 2a b + a )cos(x) +--R + +--R 2 2 2 3 +--R (4c + (8b + 8a)c + 4b + 8a b + 4a )cos(x) +--R + +--R 2 2 2 2 +--R (6c + (12b + 12a)c + 6b + 12a b + 6a )cos(x) +--R + +--R 2 2 2 2 2 +--R (4c + (8b + 8a)c + 4b + 8a b + 4a )cos(x) + c + (2b + 2a)c + b + 2a b +--R + +--R 2 +--R a +--R Type: Expression(Integer) +--E 356 + +)clear all + + +--S 357 of 526 +t0866:= cos(x)/(a+b*cos(x)+c*cos(x)^2) +--R +--R +--R cos(x) +--R (1) ------------------------ +--R 2 +--R c cos(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 357 + +--S 358 of 526 +r0866:= -2^(1/2)*(1-b/(b^2-4*a*c)^(1/2))*_ + atanh(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*tan(1/2*x)*_ + 2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)-_ + 2*(1+b/(b^2-4*a*c)^(1/2))*atanh((b+(b^2-4*a*c)^(1/2)-2*c)*_ + tan(1/2*x)/(4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (- 2\|- 4a c + b - 2b)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 2 2 +--R (\|2 \|- 4a c + b - b\|2 )\|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 358 + +--S 359 of 526 +a0866:= integrate(t0866,x) +--R +--R +--R (3) +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b +--R + +--R 2 3 3 2 +--R - a b - 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b +--R + +--R 3 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )cos(x) - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R 2b - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4a b sin(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b +--R + +--R 3 2 +--R - 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b +--R + +--R 3 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4a b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b +--R + +--R 2 3 3 2 +--R a b + 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b + a b +--R + +--R 3 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )cos(x) - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4a b sin(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b + a b +--R + +--R 3 2 +--R 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 3 2 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b + a b + 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4a b sin(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 359 + +--S 360 of 526 +m0866:= a0866-r0866 +--R +--R +--R (4) +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b +--R + +--R 2 3 3 2 +--R - a b - 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b +--R + +--R 3 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )cos(x) - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R 2b - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4a b sin(x) +--R / +--R cos(x) + 1 +--R + +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b +--R + +--R 3 2 +--R - 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b +--R + +--R 3 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4a b sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b +--R + +--R 2 3 3 2 +--R a b + 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b + a b +--R + +--R 3 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )cos(x) - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4a b sin(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b + a b +--R + +--R 3 2 +--R 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 3 2 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b + a b + 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4a b sin(x) +--R / +--R cos(x) + 1 +--R + +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (4\|- 4a c + b + 4b)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (- 2\|2 \|- 4a c + b + 2b\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 360 + +--S 361 of 526 +d0866:= D(m0866,x) +--R +--R +--R (5) +--R 4 +--R (- c + b - a)sin(x) +--R + +--R 2 2 +--R ((- 2c + 2a)cos(x) + (- 2c - 2b + 6a)cos(x) - 2b + 4a)sin(x) +--R + +--R 4 3 2 +--R (3c - b + 3a)cos(x) + (10c - 2b + 10a)cos(x) + (12c + 12a)cos(x) +--R + +--R (6c + 2b + 6a)cos(x) + c + b + a +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 2 +--R (4c - 4a)sin(x) + ((- 4c + 4a)cos(x) - 4c + 4a)sin(x) +--R + +--R 4 3 2 +--R (- 4c + 4a)cos(x) + (- 12c + 12a)cos(x) + (- 12c + 12a)cos(x) +--R + +--R (- 4c + 4a)cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 +--R (- 3c - b - 3a)sin(x) +--R + +--R 2 2 +--R ((2c - 2a)cos(x) + (6c + 2b - 2a)cos(x) + 4c + 2b)sin(x) +--R + +--R 4 3 +--R (c + b + a)cos(x) + (2c + 2b + 2a)cos(x) + (- 2c - 2b - 2a)cos(x) - c +--R + +--R - b - a +--R / +--R 2 2 2 4 +--R (c + (- 2b + 2a)c + b - 2a b + a )sin(x) +--R + +--R 2 2 2 +--R (- 2c + 2b c - 2a b + 2a )cos(x) +--R + +--R 2 2 2 2 +--R (- 4c + 4b c - 4a b + 4a )cos(x) - 2c + 2b c - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 3 +--R (c + 2a c - b + a )cos(x) + (4c + 8a c - 4b + 4a )cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R (6c + 12a c - 6b + 6a )cos(x) + (4c + 8a c - 4b + 4a )cos(x) +--R + +--R 2 2 2 +--R c + 2a c - b + a +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 2 4 +--R (- 2c + 2b c - 2a b + 2a )sin(x) +--R + +--R 2 2 2 2 2 2 +--R (4c - 8a c + 4a )cos(x) + (8c - 16a c + 8a )cos(x) + 4c +--R + +--R 2 +--R - 8a c + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 +--R (- 2c - 2b c + 2a b + 2a )cos(x) +--R + +--R 2 2 3 +--R (- 8c - 8b c + 8a b + 8a )cos(x) +--R + +--R 2 2 2 +--R (- 12c - 12b c + 12a b + 12a )cos(x) +--R + +--R 2 2 2 2 +--R (- 8c - 8b c + 8a b + 8a )cos(x) - 2c - 2b c + 2a b + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 +--R (c + 2a c - b + a )sin(x) +--R + +--R 2 2 2 +--R (- 2c - 2b c + 2a b + 2a )cos(x) +--R + +--R 2 2 2 2 +--R (- 4c - 4b c + 4a b + 4a )cos(x) - 2c - 2b c + 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 +--R (c + (2b + 2a)c + b + 2a b + a )cos(x) +--R + +--R 2 2 2 3 +--R (4c + (8b + 8a)c + 4b + 8a b + 4a )cos(x) +--R + +--R 2 2 2 2 +--R (6c + (12b + 12a)c + 6b + 12a b + 6a )cos(x) +--R + +--R 2 2 2 2 2 +--R (4c + (8b + 8a)c + 4b + 8a b + 4a )cos(x) + c + (2b + 2a)c + b + 2a b +--R + +--R 2 +--R a +--R Type: Expression(Integer) +--E 361 + +)clear all + + +--S 362 of 526 +t0867:= cos(x)^2/(a+b*cos(x)+c*cos(x)^2) +--R +--R +--R 2 +--R cos(x) +--R (1) ------------------------ +--R 2 +--R c cos(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 362 + +--S 363 of 526 +r0867:= x/c+2^(1/2)*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ + atanh(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*tan(1/2*x)*2^(1/2)/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/c/(-b^2+2*c*(a+c)+_ + (b^2-4*a*c)^(1/2)*b)^(1/2)+2*(b+(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ + atanh((b+(b^2-4*a*c)^(1/2)-2*c)*tan(1/2*x)/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/c/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 2 | | 2 2 2 +--R (2b\|- 4a c + b - 4a c + 2b )\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +--R (- b\|2 \|- 4a c + b + (- 2a c + b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R x\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 363 + +--S 364 of 526 +a0867:= integrate(t0867,x) +--R +--R +--R (3) +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 6 2 2 3 5 +--R 8a c + (- 6a b - 4a b + 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (b + a b - 20a b - 8a b + 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (8a b + 6a b - 6a b - 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )c +--R * +--R cos(x) +--R + +--R 2 6 2 2 3 5 +--R 8a c + (- 6a b - 4a b + 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (b + a b - 20a b - 8a b + 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (8a b + 6a b - 6a b - 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 2 4 2 3 3 2 4 +--R (- 8a b - 8a b)c + (6a b + 6a b - 4a b - 4a b)c +--R + +--R 6 5 2 4 3 3 +--R - b - a b + a b + a b +--R * +--R cos(x) +--R + +--R 2 2 3 2 4 2 3 3 2 4 6 +--R (- 8a b - 8a b)c + (6a b + 6a b - 4a b - 4a b)c - b +--R + +--R 5 2 4 3 3 +--R - a b + a b + a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 2 3 4 +--R (8a b c - 4a b + 4a b)sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 6 2 2 3 5 +--R 8a c + (- 6a b - 4a b + 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (b + a b - 20a b - 8a b + 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (8a b + 6a b - 6a b - 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )c +--R * +--R cos(x) +--R + +--R 2 6 2 2 3 5 +--R 8a c + (- 6a b - 4a b + 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (b + a b - 20a b - 8a b + 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (8a b + 6a b - 6a b - 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 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8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 6 2 2 3 5 +--R - 8a c + (6a b + 4a b - 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (- b - a b + 20a b + 8a b - 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 6a b + 6a b + 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )c +--R * +--R cos(x) +--R + +--R 2 6 2 2 3 5 +--R - 8a c + (6a b + 4a b - 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (- b - a b + 20a b + 8a b - 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 6a b + 6a b + 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 2 4 2 3 3 2 4 +--R (- 8a b - 8a b)c + (6a b + 6a b - 4a b - 4a b)c +--R + +--R 6 5 2 4 3 3 +--R - b - a b + a b + a b +--R * +--R cos(x) +--R + +--R 2 2 3 2 4 2 3 3 2 4 6 +--R (- 8a b - 8a b)c + (6a b + 6a b - 4a b - 4a b)c - b +--R + +--R 5 2 4 3 3 +--R - a b + a b + a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 2 3 4 +--R (8a b c - 4a b + 4a b)sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R c +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 6 2 2 3 5 +--R - 8a c + (6a b + 4a b - 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (- b - a b + 20a b + 8a b - 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 6a b + 6a b + 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )c +--R * +--R cos(x) +--R + +--R 2 6 2 2 3 5 +--R - 8a c + (6a b + 4a b - 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (- b - a b + 20a b + 8a b - 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 6a b + 6a b + 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 2 2 3 2 4 2 3 3 2 4 +--R (8a b + 8a b)c + (- 6a b - 6a b + 4a b + 4a b)c +--R + +--R 6 5 2 4 3 3 +--R b + a b - a b - a b +--R * +--R cos(x) +--R + +--R 2 2 3 2 4 2 3 3 2 4 6 +--R (8a b + 8a b)c + (- 6a b - 6a b + 4a b + 4a b)c + b +--R + +--R 5 2 4 3 3 +--R a b - a b - a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 7 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 2 3 4 +--R (8a b c - 4a b + 4a b)sin(x) +--R / +--R cos(x) + 1 +--R + +--R 2x +--R / +--R 2c +--R Type: Union(Expression(Integer),...) +--E 364 + +--S 365 of 526 +m0867:= a0867-r0867 +--R +--R +--R (4) +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - 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6a b - 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 2 4 2 3 3 2 4 +--R (- 8a b - 8a b)c + (6a b + 6a b - 4a b - 4a b)c +--R + +--R 6 5 2 4 3 3 +--R - b - a b + a b + a b +--R * +--R cos(x) +--R + +--R 2 2 3 2 4 2 3 3 2 4 6 +--R (- 8a b - 8a b)c + (6a b + 6a b - 4a b - 4a b)c - b +--R + +--R 5 2 4 3 3 +--R - a b + a b + a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 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2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 6 2 2 3 5 +--R 8a c + (- 6a b - 4a b + 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (b + a b - 20a b - 8a b + 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (8a b + 6a b - 6a b - 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )c +--R * +--R cos(x) +--R + +--R 2 6 2 2 3 5 +--R 8a c + (- 6a b - 4a b + 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (b + a b - 20a b - 8a b + 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (8a b + 6a b - 6a b - 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (- b - a b + a b + a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 2 2 3 2 4 2 3 3 2 4 +--R (8a b + 8a b)c + (- 6a b - 6a b + 4a b + 4a b)c +--R + +--R 6 5 2 4 3 3 +--R b + a b - a b - a b +--R * +--R cos(x) +--R + +--R 2 2 3 2 4 2 3 3 2 4 6 +--R (8a b + 8a b)c + (- 6a b - 6a b + 4a b + 4a b)c + b +--R + +--R 5 2 4 3 3 +--R a b - a b - a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 7 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 2 3 4 +--R (8a b c - 4a b + 4a b)sin(x) +--R / +--R cos(x) + 1 +--R + +--R +-----------+ +--R | 2 +--R c\|- 4a c + b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 6 2 2 3 5 +--R - 8a c + (6a b + 4a b - 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (- b - a b + 20a b + 8a b - 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 6a b + 6a b + 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )c +--R * +--R cos(x) +--R + +--R 2 6 2 2 3 5 +--R - 8a c + (6a b + 4a b - 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (- b - a b + 20a b + 8a b - 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 6a b + 6a b + 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 3 2 4 2 3 3 2 4 +--R (- 8a b - 8a b)c + (6a b + 6a b - 4a b - 4a b)c +--R + +--R 6 5 2 4 3 3 +--R - b - a b + a b + a b +--R * +--R cos(x) +--R + +--R 2 2 3 2 4 2 3 3 2 4 6 +--R (- 8a b - 8a b)c + (6a b + 6a b - 4a b - 4a b)c - b +--R + +--R 5 2 4 3 3 +--R - a b + a b + a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c +--R + +--R 4 2 2 2 +--R (- 2b + 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 2 3 4 +--R (8a b c - 4a b + 4a b)sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 4 3 2 5 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 4 2 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 6 2 2 3 5 +--R - 8a c + (6a b + 4a b - 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (- b - a b + 20a b + 8a b - 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 6a b + 6a b + 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )c +--R * +--R cos(x) +--R + +--R 2 6 2 2 3 5 +--R - 8a c + (6a b + 4a b - 16a )c +--R + +--R 4 3 2 2 3 4 4 +--R (- b - a b + 20a b + 8a b - 8a )c +--R + +--R 4 2 3 3 2 4 3 +--R (- 8a b - 6a b + 6a b + 4a b)c +--R + +--R 6 5 2 4 3 3 2 +--R (b + a b - a b - a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 4 2 +--R - 4a b c + (4a b - 4a b )c - b + 2a b - a b +--R / +--R 9 2 2 8 2 3 7 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 6 2 4 4 2 4 +--R (8a b - 12a b + 4a )c + (- b + 2a b - a b )c +--R + +--R 2 2 3 2 4 2 3 3 2 4 +--R (8a b + 8a b)c + (- 6a b - 6a b + 4a b + 4a b)c +--R + +--R 6 5 2 4 3 3 +--R b + a b - a b - a b +--R * +--R cos(x) +--R + +--R 2 2 3 2 4 2 3 3 2 4 6 +--R (8a b + 8a b)c + (- 6a b - 6a b + 4a b + 4a b)c + b +--R + +--R 5 2 4 3 3 +--R a b - a b - a b +--R * +--R ROOT +--R 5 2 2 4 2 3 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 2 +--R (2b - 2a b )c +--R * +--R ROOT +--R 2 2 2 4 3 2 6 2 4 +--R - 4a b c + (4a b - 4a b )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R / +--R 9 2 2 8 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 7 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 6 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 5 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 4 +--R (- b + 2a b - a b )c +--R + +--R 2 2 2 3 4 2 2 +--R - 4a c + (8a b - 4a )c - 2b + 2a b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 2 +--R (b - a b )c +--R + +--R 3 2 3 4 +--R (8a b c - 4a b + 4a b)sin(x) +--R / +--R cos(x) + 1 +--R + +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 2 | | 2 2 2 +--R (- 4b\|- 4a c + b + 8a c - 4b )\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 2 +-+ +--R (2b\|2 \|- 4a c + b + (4a c - 2b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2c\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 365 + +--S 366 of 526 +d0867:= D(m0867,x) +--R +--R +--R (5) +--R 2 2 4 +--R ((b - a)c - b + 2a b - a )sin(x) +--R + +--R 2 2 +--R ((2b - 6a)c + 2a b - 2a )cos(x) +--R + +--R 2 2 2 +--R ((2b - 10a)c + 2b - 2a )cos(x) - 4a c + 2b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 2 2 3 +--R ((- 3b - a)c + b - a )cos(x) + ((- 10b - 2a)c + 2b - 2a )cos(x) +--R + +--R 2 2 2 2 +--R - 12b c cos(x) + ((- 6b + 2a)c - 2b + 2a )cos(x) + (- b + a)c - b +--R + +--R 2 +--R a +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 4 +--R ((- 4b + 6a)c + 2a b - 2a )sin(x) +--R + +--R 2 2 2 +--R (4a c - 4a )cos(x) + ((4b + 4a)c - 4a b - 4a )cos(x) + 4b c +--R + +--R - 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 4 2 3 +--R ((4b + 6a)c - 2a b - 2a )cos(x) + ((12b + 20a)c - 4a b - 4a )cos(x) +--R + +--R 2 2 +--R (12b + 24a)c cos(x) + ((4b + 12a)c + 4a b + 4a )cos(x) + 2a c + 2a b +--R + +--R 2 +--R 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 4 +--R ((3b - a)c + b - a )sin(x) +--R + +--R 2 2 +--R ((- 2b - 6a)c - 2a b - 2a )cos(x) +--R + +--R 2 2 2 +--R ((- 6b - 10a)c - 2b - 4a b - 2a )cos(x) + (- 4b - 4a)c - 2b - 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 +--R ((- b - a)c - b - 2a b - a )cos(x) +--R + +--R 2 2 3 +--R ((- 2b - 2a)c - 2b - 4a b - 2a )cos(x) +--R + +--R 2 2 2 2 +--R ((2b + 2a)c + 2b + 4a b + 2a )cos(x) + (b + a)c + b + 2a b + a +--R / +--R 3 2 2 2 4 +--R (c + (- 2b + 2a)c + (b - 2a b + a )c)sin(x) +--R + +--R 3 2 2 2 +--R (- 2c + 2b c + (- 2a b + 2a )c)cos(x) +--R + +--R 3 2 2 3 2 +--R (- 4c + 4b c + (- 4a b + 4a )c)cos(x) - 2c + 2b c +--R + +--R 2 +--R (- 2a b + 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 2 4 +--R (c + 2a c + (- b + a )c)cos(x) +--R + +--R 3 2 2 2 3 +--R (4c + 8a c + (- 4b + 4a )c)cos(x) +--R + +--R 3 2 2 2 2 +--R (6c + 12a c + (- 6b + 6a )c)cos(x) +--R + +--R 3 2 2 2 3 2 2 2 +--R (4c + 8a c + (- 4b + 4a )c)cos(x) + c + 2a c + (- b + a )c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 3 2 2 4 +--R (- 2c + 2b c + (- 2a b + 2a )c)sin(x) +--R + +--R 3 2 2 2 3 2 2 3 +--R (4c - 8a c + 4a c)cos(x) + (8c - 16a c + 8a c)cos(x) + 4c +--R + +--R 2 2 +--R - 8a c + 4a c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 4 +--R (- 2c - 2b c + (2a b + 2a )c)cos(x) +--R + +--R 3 2 2 3 +--R (- 8c - 8b c + (8a b + 8a )c)cos(x) +--R + +--R 3 2 2 2 +--R (- 12c - 12b c + (12a b + 12a )c)cos(x) +--R + +--R 3 2 2 3 2 2 +--R (- 8c - 8b c + (8a b + 8a )c)cos(x) - 2c - 2b c + (2a b + 2a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 3 2 2 2 4 +--R (c + 2a c + (- b + a )c)sin(x) +--R + +--R 3 2 2 2 +--R (- 2c - 2b c + (2a b + 2a )c)cos(x) +--R + +--R 3 2 2 3 2 2 +--R (- 4c - 4b c + (4a b + 4a )c)cos(x) - 2c - 2b c + (2a b + 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 3 2 2 2 4 +--R (c + (2b + 2a)c + (b + 2a b + a )c)cos(x) +--R + +--R 3 2 2 2 3 +--R (4c + (8b + 8a)c + (4b + 8a b + 4a )c)cos(x) +--R + +--R 3 2 2 2 2 +--R (6c + (12b + 12a)c + (6b + 12a b + 6a )c)cos(x) +--R + +--R 3 2 2 2 3 2 +--R (4c + (8b + 8a)c + (4b + 8a b + 4a )c)cos(x) + c + (2b + 2a)c +--R + +--R 2 2 +--R (b + 2a b + a )c +--R Type: Expression(Integer) +--E 366 + +)clear all + + +--S 367 of 526 +t0868:= cos(x)^3/(a+b*cos(x)+c*cos(x)^2) +--R +--R +--R 3 +--R cos(x) +--R (1) ------------------------ +--R 2 +--R c cos(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 367 + +--S 368 of 526 +r0868:= -b*x/c^2-2^(1/2)*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ + atanh(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*tan(1/2*x)*2^(1/2)/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/c^2/(-b^2+2*c*(a+c)+_ + (b^2-4*a*c)^(1/2)*b)^(1/2)-2*(b^2-a*c+b*(b^2-3*a*c)/_ + (b^2-4*a*c)^(1/2))*atanh((b+(b^2-4*a*c)^(1/2)-2*c)*_ + tan(1/2*x)/(4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/c^2/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2)+sin(x)/c +--R +--R +--R (2) +--R +-----------+ +--R 2 | 2 3 +--R ((2a c - 2b )\|- 4a c + b + 6a b c - 2b ) +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R 2 +-+ | 2 3 +-+ +--R ((- a c + b )\|2 \|- 4a c + b + (3a b c - b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (c sin(x) - b x)\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 2 2 +--R c \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 368 + +--S 369 of 526 +a0868:= integrate(t0868,x) +--R +--R +--R (3) +--R 2 +--R c +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 2 4 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b + 2a b +--R / +--R 7 2 2 6 2 3 5 4 2 2 4 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + (b - a b )c +--R * +--R log +--R 2 3 8 3 2 2 3 4 7 +--R (12a b + 8a )c + (- 7a b - 6a b + 24a b + 16a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (b + a b - 26a b - 20a b + 12a b + 8a )c +--R + +--R 5 2 4 3 3 4 2 5 +--R (9a b + 8a b - 7a b - 6a b )c +--R + +--R 7 6 2 5 3 4 4 +--R (- b - a b + a b + a b )c +--R * +--R cos(x) +--R + +--R 2 3 8 3 2 2 3 4 7 +--R (12a b + 8a )c + (- 7a b - 6a b + 24a b + 16a )c +--R + +--R 5 4 2 3 3 2 4 5 6 +--R (b + a b - 26a b - 20a b + 12a b + 8a )c +--R + +--R 5 2 4 3 3 4 2 5 +--R (9a b + 8a b - 7a b - 6a b )c +--R + +--R 7 6 2 5 3 4 4 +--R (- b - a b + a b + a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 12a b + 4a b )c - b + 2a b - a b +--R / +--R 13 2 2 12 2 3 11 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 4 3 2 5 9 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 4 4 3 3 4 2 5 3 +--R - 12a b c + (31a b + 12a b - 8a b)c +--R + +--R 2 5 3 4 4 3 5 2 2 +--R (- 27a b - 19a b + 14a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 9 8 2 7 3 6 +--R (9a b + 8a b - 7a b - 6a b )c - b - a b + a b + a b +--R * +--R cos(x) +--R + +--R 4 4 3 3 4 2 5 3 +--R - 12a b c + (31a b + 12a b - 8a b)c +--R + +--R 2 5 3 4 4 3 5 2 2 +--R (- 27a b - 19a b + 14a b + 8a b )c +--R + +--R 7 2 6 3 5 4 4 9 8 2 7 3 6 +--R (9a b + 8a b - 7a b - 6a b )c - b - a b + a b + a b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 4 6 +--R (8a b - 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2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 +--R (8a b - 12a b + 4a b )c - b + 2a b +--R + +--R 4 6 +--R - a b +--R / +--R 13 2 2 12 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 11 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b +--R + +--R 2 4 +--R 2a b +--R / +--R 7 2 2 6 2 3 5 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 4 +--R (b - a b )c +--R + +--R 5 2 4 3 6 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + 4a b - 4a b )sin(x) +--R / +--R cos(x) + 1 +--R + +--R 2c sin(x) - 2b x +--R / +--R 2 +--R 2c +--R Type: Union(Expression(Integer),...) +--E 369 + +--S 370 of 526 +m0868:= a0868-r0868 +--R +--R +--R (4) +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 2 2 +--R c \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 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12a b + 8a b)c +--R + +--R 2 5 3 4 4 3 5 2 2 +--R (27a b + 19a b - 14a b - 8a b )c +--R + +--R 7 2 6 3 5 4 4 9 8 2 7 +--R (- 9a b - 8a b + 7a b + 6a b )c + b + a b - a b +--R + +--R 3 6 +--R - a b +--R * +--R ROOT +--R 7 2 2 6 2 3 5 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 4 +--R (2b - 2a b )c +--R * +--R ROOT +--R 4 2 4 3 4 5 2 3 +--R - 9a b c + (24a b - 12a b )c +--R + +--R 2 6 4 4 6 2 2 +--R (- 22a b + 22a b - 4a b )c +--R + +--R 8 3 6 5 4 10 2 8 +--R (8a b - 12a b + 4a b )c - b + 2a b +--R + +--R 4 6 +--R - a b +--R / +--R 13 2 2 12 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 11 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 10 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 9 +--R (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 8 +--R (- b + 2a b - a b )c +--R + +--R 3 3 2 2 4 2 4 3 2 6 +--R 4a c + (- 18a b + 4a )c + (12a b - 8a b )c - 2b +--R + +--R 2 4 +--R 2a b +--R / +--R 7 2 2 6 2 3 5 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c +--R + +--R 4 2 2 4 +--R (b - a b )c +--R + +--R 5 2 4 3 6 3 5 5 3 +--R (12a b c + (- 16a b + 8a b)c + 4a b - 4a b )sin(x) +--R / +--R cos(x) + 1 +--R + +--R +-----------+ +--R 2 | 2 3 +--R ((- 4a c + 4b )\|- 4a c + b - 12a b c + 4b ) +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R 2 +-+ | 2 3 +-+ +--R ((2a c - 2b )\|2 \|- 4a c + b + (- 6a b c + 2b )\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R 2 | 2 | | 2 2 2 +--R 2c \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 370 + +--S 371 of 526 +d0868:= D(m0868,x) +--R +--R +--R (5) +--R 2 2 2 3 2 2 4 +--R (a c + (- b + a )c + b - 2a b + a b)sin(x) +--R + +--R 2 2 2 2 2 2 +--R (2a c + (- 2b + 6a b - 2a )c - 2a b + 2a b)cos(x) +--R + +--R 2 2 2 3 2 +--R (2a c + (- 2b + 12a b - 6a )c - 2b + 2a b)cos(x) +--R + +--R 2 3 2 +--R (6a b - 4a )c - 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 3 2 4 +--R (- 3a c + (3b + 2a b - 3a )c - b + a b)cos(x) +--R + +--R 2 2 2 3 2 3 +--R (- 10a c + (10b + 4a b - 10a )c - 2b + 2a b)cos(x) +--R + +--R 2 2 2 2 +--R (- 12a c + (12b - 12a )c)cos(x) +--R + +--R 2 2 2 3 2 2 +--R (- 6a c + (6b - 4a b - 6a )c + 2b - 2a b)cos(x) - a c +--R + +--R 2 2 3 2 +--R (b - 2a b - a )c + b - a b +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 2 2 2 2 4 +--R (- 4a c + (4b - 6a b + 4a )c - 2a b + 2a b)sin(x) +--R + +--R 2 2 +--R (- 4a b c + 4a b)cos(x) +--R + +--R 2 2 2 2 2 2 +--R (4a c + (- 4b - 4a b - 4a )c + 4a b + 4a b)cos(x) + 4a c +--R + +--R 2 2 2 +--R (- 4b - 4a )c + 4a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 2 2 4 +--R (4a c + (- 4b - 6a b - 4a )c + 2a b + 2a b)cos(x) +--R + +--R 2 2 2 2 2 3 +--R (12a c + (- 12b - 20a b - 12a )c + 4a b + 4a b)cos(x) +--R + +--R 2 2 2 2 +--R (12a c + (- 12b - 24a b - 12a )c)cos(x) +--R + +--R 2 2 2 2 2 +--R (4a c + (- 4b - 12a b - 4a )c - 4a b - 4a b)cos(x) - 2a b c +--R + +--R 2 2 +--R - 2a b - 2a b +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 3 2 4 +--R (3a c + (- 3b + 2a b + 3a )c - b + a b)sin(x) +--R + +--R 2 2 2 2 2 2 +--R (- 2a c + (2b + 6a b + 2a )c + 2a b + 2a b)cos(x) +--R + +--R 2 2 2 3 2 2 2 +--R (- 6a c + (6b + 8a b + 2a )c + 2b + 4a b + 2a b)cos(x) - 4a c +--R + +--R 2 3 2 +--R (4b + 2a b)c + 2b + 2a b +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 3 2 2 4 +--R (- a c + (b - a )c + b + 2a b + a b)cos(x) +--R + +--R 2 2 2 3 2 2 3 +--R (- 2a c + (2b - 2a )c + 2b + 4a b + 2a b)cos(x) +--R + +--R 2 2 2 3 2 2 2 2 2 +--R (2a c + (- 2b + 2a )c - 2b - 4a b - 2a b)cos(x) + a c + (- b + a )c +--R + +--R 3 2 2 +--R - b - 2a b - a b +--R / +--R 4 3 2 2 2 4 +--R (c + (- 2b + 2a)c + (b - 2a b + a )c )sin(x) +--R + +--R 4 3 2 2 2 +--R (- 2c + 2b c + (- 2a b + 2a )c )cos(x) +--R + +--R 4 3 2 2 4 3 +--R (- 4c + 4b c + (- 4a b + 4a )c )cos(x) - 2c + 2b c +--R + +--R 2 2 +--R (- 2a b + 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 2 4 +--R (c + 2a c + (- b + a )c )cos(x) +--R + +--R 4 3 2 2 2 3 +--R (4c + 8a c + (- 4b + 4a )c )cos(x) +--R + +--R 4 3 2 2 2 2 +--R (6c + 12a c + (- 6b + 6a )c )cos(x) +--R + +--R 4 3 2 2 2 4 3 2 2 2 +--R (4c + 8a c + (- 4b + 4a )c )cos(x) + c + 2a c + (- b + a )c +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 4 +--R (- 2c + 2b c + (- 2a b + 2a )c )sin(x) +--R + +--R 4 3 2 2 2 4 3 2 2 4 +--R (4c - 8a c + 4a c )cos(x) + (8c - 16a c + 8a c )cos(x) + 4c +--R + +--R 3 2 2 +--R - 8a c + 4a c +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 4 +--R (- 2c - 2b c + (2a b + 2a )c )cos(x) +--R + +--R 4 3 2 2 3 +--R (- 8c - 8b c + (8a b + 8a )c )cos(x) +--R + +--R 4 3 2 2 2 +--R (- 12c - 12b c + (12a b + 12a )c )cos(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R (- 8c - 8b c + (8a b + 8a )c )cos(x) - 2c - 2b c + (2a b + 2a )c +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 3 2 2 2 4 +--R (c + 2a c + (- b + a )c )sin(x) +--R + +--R 4 3 2 2 2 +--R (- 2c - 2b c + (2a b + 2a )c )cos(x) +--R + +--R 4 3 2 2 4 3 2 2 +--R (- 4c - 4b c + (4a b + 4a )c )cos(x) - 2c - 2b c + (2a b + 2a )c +--R * +--R 2 +--R sin(x) +--R + +--R 4 3 2 2 2 4 +--R (c + (2b + 2a)c + (b + 2a b + a )c )cos(x) +--R + +--R 4 3 2 2 2 3 +--R (4c + (8b + 8a)c + (4b + 8a b + 4a )c )cos(x) +--R + +--R 4 3 2 2 2 2 +--R (6c + (12b + 12a)c + (6b + 12a b + 6a )c )cos(x) +--R + +--R 4 3 2 2 2 4 3 +--R (4c + (8b + 8a)c + (4b + 8a b + 4a )c )cos(x) + c + (2b + 2a)c +--R + +--R 2 2 2 +--R (b + 2a b + a )c +--R Type: Expression(Integer) +--E 371 + +)clear all + + +--S 372 of 526 +t0869:= (d+e*cos(x))/(a+b*cos(x)+c*cos(x)^2) +--R +--R +--R e cos(x) + d +--R (1) ------------------------ +--R 2 +--R c cos(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 372 + +--S 373 of 526 +r0869:= -2^(1/2)*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atanh(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*tan(1/2*x)*2^(1/2)/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)-_ + 2*(e-(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*atanh((b+(b^2-4*a*c)^(1/2)-2*c)*_ + tan(1/2*x)/(4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (- 2e\|- 4a c + b - 2b e + 4c d)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (e\|2 \|- 4a c + b + (- b e + 2c d)\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 373 + +--S 374 of 526 +a0869:= integrate(t0869,x) +--R +--R +--R (3) +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 2 3 +--R (4a b + 8a )c +--R + +--R 3 2 2 3 2 +--R (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b +--R + +--R 2 3 3 2 +--R - a b - 2a b +--R * +--R e +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R d +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b +--R + +--R 2 3 3 2 +--R - a b - 2a b +--R * +--R e +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )e +--R + +--R 2 2 2 3 2 2 +--R (8a c + (- 2b - 4a b + 8a )c + b - 2a b )d e +--R + +--R 2 2 2 3 2 2 +--R (8a c + (- 2b - 4a b + 8a )c + b - 2a b )d e +--R + +--R 3 3 +--R (- 4a b c + b )d +--R * +--R cos(x) +--R + +--R 3 3 +--R (- 4a b c + b )e +--R + +--R 2 2 2 3 2 2 +--R (8a c + (- 2b - 4a b + 8a )c + b - 2a b )d e +--R + +--R 2 2 2 3 2 2 +--R (8a c + (- 2b - 4a b + 8a )c + b - 2a b )d e +--R + +--R 3 3 +--R (- 4a b c + b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R 2b - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 2 +--R 4a b e + (- 8a c - 4b - 8a )d e + (12b c + 12a b)d e +--R + +--R 2 2 3 4 +--R (- 8c - 8a c - 4b )d e + 4b c d +--R * +--R sin(x) +--R / +--R cos(x) + 1 +--R + +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 2 2 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e + (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b +--R + +--R 2 3 3 2 +--R - a b - 2a b +--R * +--R e +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R d +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b +--R + +--R 3 2 +--R - 2a b +--R * +--R e +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 3 3 +--R (4a b c - b )d +--R * +--R cos(x) +--R + +--R 3 3 +--R (4a b c - b )e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 3 3 +--R (4a b c - b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - 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a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 2 +--R 4a b e + (- 8a c - 4b - 8a )d e + (12b c + 12a b)d e +--R + +--R 2 2 3 4 +--R (- 8c - 8a c - 4b )d e + 4b c d +--R * +--R sin(x) +--R / +--R cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 374 + +--S 375 of 526 +m0869:= a0869-r0869 +--R +--R +--R (4) +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 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b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 2 2 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e + (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b +--R + +--R 2 3 3 2 +--R - a b - 2a b +--R * +--R e +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R d +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b +--R + +--R 3 2 +--R - 2a b +--R * +--R e +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 3 3 +--R (4a b c - b )d +--R * +--R cos(x) +--R + +--R 3 3 +--R (4a b c - b )e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 3 3 +--R (4a b c - b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 2 +--R 4a b e + (- 8a c - 4b - 8a )d e + (12b c + 12a b)d e +--R + +--R 2 2 3 4 +--R (- 8c - 8a c - 4b )d e + 4b c d +--R * +--R sin(x) +--R / +--R cos(x) + 1 +--R + +--R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 3 +--R (- 4a b - 8a )c +--R + +--R 3 2 2 3 2 +--R (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b +--R + +--R 2 3 3 2 +--R a b + 2a b +--R * +--R e +--R + +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R d +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b +--R + +--R 2 3 3 2 +--R a b + 2a b +--R * +--R e +--R + +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )e +--R + +--R 2 2 2 3 2 2 +--R (8a c + (- 2b - 4a b + 8a )c + b - 2a b )d e +--R + +--R 2 2 2 3 2 2 +--R (8a c + (- 2b - 4a b + 8a )c + b - 2a b )d e +--R + +--R 3 3 +--R (- 4a b c + b )d +--R * +--R cos(x) +--R + +--R 3 3 +--R (- 4a b c + b )e +--R + +--R 2 2 2 3 2 2 +--R (8a c + (- 2b - 4a b + 8a )c + b - 2a b )d e +--R + +--R 2 2 2 3 2 2 +--R (8a c + (- 2b - 4a b + 8a )c + b - 2a b )d e +--R + +--R 3 3 +--R (- 4a b c + b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R + +--R 2 2 +--R 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 2 +--R 4a b e + (- 8a c - 4b - 8a )d e + (12b c + 12a b)d e +--R + +--R 2 2 3 4 +--R (- 8c - 8a c - 4b )d e + 4b c d +--R * +--R sin(x) +--R / +--R cos(x) + 1 +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 2 4 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 6 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b +--R + +--R 2 4 4 2 +--R 2a b - a b +--R + +--R 2 2 2 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e + (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * +--R log +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b +--R + +--R 2 3 3 2 +--R a b + 2a b +--R * +--R e +--R + +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R d +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b + a b +--R + +--R 3 2 +--R 2a b +--R * +--R e +--R + +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R d +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 3 +--R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e +--R + +--R 2 4 +--R - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 3 3 +--R (4a b c - b )d +--R * +--R cos(x) +--R + +--R 3 3 +--R (4a b c - b )e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 2 2 2 3 2 2 +--R (- 8a c + (2b + 4a b - 8a )c - b + 2a b )d e +--R + +--R 3 3 +--R (4a b c - b )d +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R 2 4 3 +--R - b e + (4b c + 4a b)d e +--R + +--R 2 2 2 2 2 +--R (- 4c - 8a c - 2b - 4a )d e +--R + +--R 3 2 4 +--R (4b c + 4a b)d e - b d +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 2 +--R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R + +--R 2 2 2 +--R (- 4c - 4a c + 2b )d +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4 2 2 3 2 2 +--R 4a b e + (- 8a c - 4b - 8a )d e + (12b c + 12a b)d e +--R + +--R 2 2 3 4 +--R (- 8c - 8a c - 4b )d e + 4b c d +--R * +--R sin(x) +--R / +--R cos(x) + 1 +--R + +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (4e\|- 4a c + b + 4b e - 8c d)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (- 2e\|2 \|- 4a c + b + (2b e - 4c d)\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 375 + +--S 376 of 526 +d0869:= D(m0869,x) +--R +--R +--R (5) +--R 4 +--R ((- c + b - a)e + (c - b + a)d)sin(x) +--R + +--R 2 +--R ((- 2c + 2a)e + (6c - 4b + 2a)d)cos(x) +--R + +--R ((- 2c - 2b + 6a)e + (10c - 6b + 2a)d)cos(x) + (- 2b + 4a)e +--R + +--R (4c - 2b)d +--R * +--R 2 +--R sin(x) +--R + +--R 4 +--R ((3c - b + 3a)e + (c - 3b + a)d)cos(x) +--R + +--R 3 +--R ((10c - 2b + 10a)e + (2c - 10b + 2a)d)cos(x) +--R + +--R 2 +--R ((12c + 12a)e - 12b d)cos(x) +--R + +--R ((6c + 2b + 6a)e + (- 2c - 6b - 2a)d)cos(x) + (c + b + a)e +--R + +--R (- c - b - a)d +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 +--R ((4c - 4a)e + (- 6c + 2b + 2a)d)sin(x) +--R + +--R 2 +--R (- 4c + 4a)d cos(x) + ((- 4c + 4a)e + (- 4c + 4a)d)cos(x) +--R + +--R (- 4c + 4a)e +--R * +--R 2 +--R sin(x) +--R + +--R 4 +--R ((- 4c + 4a)e + (- 6c - 2b + 2a)d)cos(x) +--R + +--R 3 +--R ((- 12c + 12a)e + (- 20c - 8b + 4a)d)cos(x) +--R + +--R 2 +--R ((- 12c + 12a)e + (- 24c - 12b)d)cos(x) +--R + +--R ((- 4c + 4a)e + (- 12c - 8b - 4a)d)cos(x) + (- 2c - 2b - 2a)d +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 +--R ((- 3c - b - 3a)e + (c + 3b + a)d)sin(x) +--R + +--R 2 +--R ((2c - 2a)e + (6c + 4b + 2a)d)cos(x) +--R + +--R ((6c + 2b - 2a)e + (10c + 6b + 2a)d)cos(x) + (4c + 2b)e + (4c + 2b)d +--R * +--R 2 +--R sin(x) +--R + +--R 4 +--R ((c + b + a)e + (c + b + a)d)cos(x) +--R + +--R 3 +--R ((2c + 2b + 2a)e + (2c + 2b + 2a)d)cos(x) +--R + +--R ((- 2c - 2b - 2a)e + (- 2c - 2b - 2a)d)cos(x) + (- c - b - a)e +--R + +--R (- c - b - a)d +--R / +--R 2 2 2 4 +--R (c + (- 2b + 2a)c + b - 2a b + a )sin(x) +--R + +--R 2 2 2 +--R (- 2c + 2b c - 2a b + 2a )cos(x) +--R + +--R 2 2 2 2 +--R (- 4c + 4b c - 4a b + 4a )cos(x) - 2c + 2b c - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 3 +--R (c + 2a c - b + a )cos(x) + (4c + 8a c - 4b + 4a )cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R (6c + 12a c - 6b + 6a )cos(x) + (4c + 8a c - 4b + 4a )cos(x) +--R + +--R 2 2 2 +--R c + 2a c - b + a +--R * +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 2 4 +--R (- 2c + 2b c - 2a b + 2a )sin(x) +--R + +--R 2 2 2 2 2 2 +--R (4c - 8a c + 4a )cos(x) + (8c - 16a c + 8a )cos(x) + 4c +--R + +--R 2 +--R - 8a c + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 +--R (- 2c - 2b c + 2a b + 2a )cos(x) +--R + +--R 2 2 3 +--R (- 8c - 8b c + 8a b + 8a )cos(x) +--R + +--R 2 2 2 +--R (- 12c - 12b c + 12a b + 12a )cos(x) +--R + +--R 2 2 2 2 +--R (- 8c - 8b c + 8a b + 8a )cos(x) - 2c - 2b c + 2a b + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 +--R (c + 2a c - b + a )sin(x) +--R + +--R 2 2 2 +--R (- 2c - 2b c + 2a b + 2a )cos(x) +--R + +--R 2 2 2 2 +--R (- 4c - 4b c + 4a b + 4a )cos(x) - 2c - 2b c + 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 +--R (c + (2b + 2a)c + b + 2a b + a )cos(x) +--R + +--R 2 2 2 3 +--R (4c + (8b + 8a)c + 4b + 8a b + 4a )cos(x) +--R + +--R 2 2 2 2 +--R (6c + (12b + 12a)c + 6b + 12a b + 6a )cos(x) +--R + +--R 2 2 2 2 2 +--R (4c + (8b + 8a)c + 4b + 8a b + 4a )cos(x) + c + (2b + 2a)c + b + 2a b +--R + +--R 2 +--R a +--R Type: Expression(Integer) +--E 376 + +)clear all + + +--S 377 of 526 +t0870:= cos(x)/(2-3*sin(x)+sin(x)^2) +--R +--R +--R cos(x) +--R (1) --------------------- +--R 2 +--R sin(x) - 3sin(x) + 2 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 526 +r0870:= -2*atanh(-3+2*sin(x)) +--R +--R +--R (2) - 2atanh(2sin(x) - 3) +--R Type: Expression(Integer) +--E 378 + +--S 379 of 526 +a0870:= integrate(t0870,x) +--R +--R +--R sin(x) - cos(x) - 1 - sin(x) + 2 +--R (3) - 2log(-------------------) + log(------------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 379 + +--S 380 of 526 +m0870:= a0870-r0870 +--R +--R +--R sin(x) - cos(x) - 1 - sin(x) + 2 +--R (4) - 2log(-------------------) + log(------------) + 2atanh(2sin(x) - 3) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 526 +d0870:= D(m0870,x) +--R +--R +--R (5) +--R 3 2 2 3 +--R - sin(x) - cos(x)sin(x) + (- cos(x) + 1)sin(x) - cos(x) + cos(x) +--R ----------------------------------------------------------------------------- +--R 2 2 2 +--R (cos(x) + 1)sin(x) + (- cos(x) - 3cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 381 + +)clear all + + +--S 382 of 526 +t0871:= csc(x)*(cos(x)+sin(x))^(1/2)/cos(x)^(3/2) +--R +--R +--R +---------------+ +--R csc(x)\|sin(x) + cos(x) +--R (1) ------------------------ +--R +------+ +--R cos(x)\|cos(x) +--R Type: Expression(Integer) +--E 382 + +--S 383 of 526 +r0871:= -log(sin(x))+2*log(-cos(x)^(1/2)+(cos(x)+sin(x))^(1/2))+_ + 2*(cos(x)+sin(x))^(1/2)/cos(x)^(1/2) +--R +--R +--R (2) +--R +------+ +---------------+ +------+ +---------------+ +--R 2\|cos(x) log(\|sin(x) + cos(x) - \|cos(x) ) + 2\|sin(x) + cos(x) +--R + +--R +------+ +--R - log(sin(x))\|cos(x) +--R / +--R +------+ +--R \|cos(x) +--R Type: Expression(Integer) +--E 383 + +--S 384 of 526 +a0871:= integrate(t0871,x) +--R +--R +--R >> Error detected within library code: +--R Imaginary part is nonzero. Cannot retract. +--R +--R Continuing to read the file... +--R +--E 384 + +--S 385 of 526 +m0871:= a0871-r0871 +--R +--R +--R (3) +--R +------+ +---------------+ +------+ +---------------+ +--R - 2\|cos(x) log(\|sin(x) + cos(x) - \|cos(x) ) - 2\|sin(x) + cos(x) +--R + +--R +------+ +--R (log(sin(x)) + a0871)\|cos(x) +--R / +--R +------+ +--R \|cos(x) +--R Type: Expression(Integer) +--E 385 + +--S 386 of 526 +d0871:= D(m0871,x) +--R +--R +--R (4) +--R 2 2 +------+ +---------------+ 3 2 +--R (sin(x) + cos(x) )\|cos(x) \|sin(x) + cos(x) - sin(x) - cos(x)sin(x) +--R + +--R 2 3 +--R - cos(x) sin(x) - cos(x) +--R / +--R +------+ +---------------+ 2 +--R cos(x)sin(x)\|cos(x) \|sin(x) + cos(x) - cos(x) sin(x) +--R Type: Expression(Integer) +--E 386 + +)clear all + + +--S 387 of 526 +t0872:= (cos(x)+sin(x))/(1+sin(2*x))^(1/2) +--R +--R +--R sin(x) + cos(x) +--R (1) --------------- +--R +-----------+ +--R \|sin(2x) + 1 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 526 +r0872:= x*(cos(x)+sin(x))/(1+sin(2*x))^(1/2) +--R +--R +--R x sin(x) + x cos(x) +--R (2) ------------------- +--R +-----------+ +--R \|sin(2x) + 1 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 526 +a0872:= integrate(t0872,x) +--R +--R +--R (3) - x +--R Type: Union(Expression(Integer),...) +--E 389 + +--S 390 of 526 +m0872:= a0872-r0872 +--R +--R +--R +-----------+ +--R - x\|sin(2x) + 1 - x sin(x) - x cos(x) +--R (4) --------------------------------------- +--R +-----------+ +--R \|sin(2x) + 1 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 526 +d0872:= D(m0872,x) +--R +--R +--R (5) +--R +-----------+ +--R (- sin(2x) - 1)\|sin(2x) + 1 + ((x - 1)sin(x) + (- x - 1)cos(x))sin(2x) +--R + +--R (x cos(2x) + x - 1)sin(x) + x cos(x)cos(2x) + (- x - 1)cos(x) +--R / +--R +-----------+ +--R (sin(2x) + 1)\|sin(2x) + 1 +--R Type: Expression(Integer) +--E 391 + +)clear all + + +--S 392 of 526 +t0873:= csc(x)^(1/2)*(x*cos(x)-4*sec(x)*tan(x)) +--R +--R +--R +------+ +--R (1) (- 4sec(x)tan(x) + x cos(x))\|csc(x) +--R Type: Expression(Integer) +--E 392 + +--S 393 of 526 +r0873:= 2*x/csc(x)^(1/2)-4*sec(x)/csc(x)^(3/2) +--R +--R +--R - 4sec(x) + 2x csc(x) +--R (2) --------------------- +--R +------+ +--R csc(x)\|csc(x) +--R Type: Expression(Integer) +--E 393 + +--S 394 of 526 +a0873:= integrate(t0873,x) +--R +--R +--R >> Error detected within library code: +--R integrate: implementation incomplete (constant residues) +--R +--R Continuing to read the file... +--R +--E 394 + +--S 395 of 526 +m0873:= a0873-r0873 +--R +--R +--R +------+ +--R a0873 csc(x)\|csc(x) + 4sec(x) - 2x csc(x) +--R (3) ------------------------------------------- +--R +------+ +--R csc(x)\|csc(x) +--R Type: Expression(Integer) +--E 395 + +--S 396 of 526 +d0873:= D(m0873,x) +--R +--R +--R 4sec(x)tan(x) + 6cot(x)sec(x) + (- x cot(x) - 2)csc(x) +--R (4) ------------------------------------------------------ +--R +------+ +--R csc(x)\|csc(x) +--R Type: Expression(Integer) +--E 396 + +)clear all + + +--S 397 of 526 +t0874:= cos(x)*(-1+csc(x)^2)^(1/2)*(1-sin(x)^2)^3 +--R +--R +--R (1) +--R +-----------+ +--R 6 4 2 | 2 +--R (- cos(x)sin(x) + 3cos(x)sin(x) - 3cos(x)sin(x) + cos(x))\|csc(x) - 1 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 526 +r0874:= -1/105*(105*atanh(cos(x))-105*cos(x)-35*cos(x)^3-_ + 21*cos(x)^5-15*cos(x)^7)*(cot(x)^2)^(1/2)*tan(x) +--R +--R +--R (2) +--R - 105tan(x)atanh(cos(x)) +--R + +--R 7 5 3 +--R (15cos(x) + 21cos(x) + 35cos(x) + 105cos(x))tan(x) +--R * +--R +-------+ +--R | 2 +--R \|cot(x) +--R / +--R 105 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 526 +a0874:= integrate(t0874,x) +--R +--R +--R sin(x) 7 5 3 +--R - 105log(----------) - 15cos(x) - 21cos(x) - 35cos(x) - 105cos(x) +--R cos(x) + 1 +--R (3) -------------------------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 526 +m0874:= a0874-r0874 +--R +--R +--R (4) +--R 105tan(x)atanh(cos(x)) +--R + +--R 7 5 3 +--R (- 15cos(x) - 21cos(x) - 35cos(x) - 105cos(x))tan(x) +--R * +--R +-------+ +--R | 2 +--R \|cot(x) +--R + +--R sin(x) 7 5 3 +--R - 105log(----------) - 15cos(x) - 21cos(x) - 35cos(x) - 105cos(x) +--R cos(x) + 1 +--R / +--R 105 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 526 +d0874:= D(m0874,x) +--R +--R +--R (5) +--R +-------+ +--R 8 2 3 | 2 +--R ((105cos(x) - 105cos(x))sin(x) - 105cos(x) + 105cos(x))\|cot(x) +--R + +--R 2 2 2 +--R (105cos(x) - 105)cot(x) sin(x)tan(x) +--R + +--R 2 3 2 +--R ((- 105cos(x) + 105)cot(x) + (- 105cos(x) + 105)cot(x))sin(x) +--R * +--R tan(x) +--R + +--R 2 2 +--R (105cos(x) - 105)cot(x) sin(x) +--R * +--R atanh(cos(x)) +--R + +--R 9 7 5 3 2 +--R (- 15cos(x) - 6cos(x) - 14cos(x) - 70cos(x) + 105cos(x))cot(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R 8 2 2 +--R 105cos(x) cot(x) sin(x) +--R + +--R 9 7 5 3 3 +--R (15cos(x) + 6cos(x) + 14cos(x) + 70cos(x) - 105cos(x))cot(x) +--R + +--R 9 7 5 3 +--R (15cos(x) + 6cos(x) + 14cos(x) + 70cos(x) - 105cos(x))cot(x) +--R * +--R sin(x) +--R * +--R tan(x) +--R + +--R 9 7 5 3 2 +--R (- 15cos(x) - 6cos(x) - 14cos(x) - 70cos(x) + 105cos(x))cot(x) sin(x) +--R / +--R +-------+ +--R 2 | 2 +--R (105cos(x) - 105)sin(x)\|cot(x) +--R Type: Expression(Integer) +--E 401 + +)clear all + + +--S 402 of 526 +t0875:= cos(x)*csc(x)^(7/3) +--R +--R +--R 2 3+------+ +--R (1) cos(x)csc(x) \|csc(x) +--R Type: Expression(Integer) +--E 402 + +--S 403 of 526 +r0875:= -3/4*csc(x)^(4/3) +--R +--R +--R 3+------+ +--R 3csc(x)\|csc(x) +--R (2) - ---------------- +--R 4 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 526 +a0875:= integrate(t0875,x) +--R +--R +--R +-------------+ +--R 2 | 1 +--R (6cos(x) - 3)sin(x) |- ----------- +--R 6| 2 +--R \| cos(x) - 1 +--R (3) ------------------------------------ +--R 4 2 +--R 16cos(x) - 32cos(x) + 16 +--R Type: Union(Expression(Integer),...) +--E 404 + +--S 405 of 526 +m0875:= a0875-r0875 +--R +--R +--R (4) +--R 4 2 3+------+ +--R (12cos(x) - 24cos(x) + 12)csc(x)\|csc(x) +--R + +--R +-------------+ +--R 2 | 1 +--R (6cos(x) - 3)sin(x) |- ----------- +--R 6| 2 +--R \| cos(x) - 1 +--R / +--R 4 2 +--R 16cos(x) - 32cos(x) + 16 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 526 +d0875:= D(m0875,x) +--R +--R +--R (5) +--R 3 2 5 3 3+------+2 +--R ((- 14cos(x) + cos(x))sin(x) - 6cos(x) + 9cos(x) - 3cos(x))\|csc(x) +--R + +--R 8 6 4 2 2 +--R (- 16cos(x) + 64cos(x) - 96cos(x) + 64cos(x) - 16)cot(x)csc(x) +--R * +--R +-------------+5 +--R | 1 +--R |- ----------- +--R 6| 2 +--R \| cos(x) - 1 +--R / +--R +-------------+5 +--R 8 6 4 2 | 1 +--R (16cos(x) - 64cos(x) + 96cos(x) - 64cos(x) + 16) |- ----------- +--R 6| 2 +--R \| cos(x) - 1 +--R * +--R 3+------+2 +--R \|csc(x) +--R Type: Expression(Integer) +--E 406 + +)clear all + + +--S 407 of 526 +t0876:= cos(x)*(1+csc(x))^(1/2) +--R +--R +--R +----------+ +--R (1) cos(x)\|csc(x) + 1 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 526 +r0876:= atanh((1+csc(x))^(1/2))+(1+csc(x))^(1/2)*sin(x) +--R +--R +--R +----------+ +----------+ +--R (2) atanh(\|csc(x) + 1 ) + sin(x)\|csc(x) + 1 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 526 +a0876:= integrate(t0876,x) +--R +--R +--R (3) +--R log +--R +-------------+2 +--R |- 4cos(x) + 4 +--R (cos(x) + 1) 4|------------- +--R \| cos(x) + 1 +--R + +--R +-------------+ +--R |- 4cos(x) + 4 +--R (2sin(x) + 2cos(x) + 2) 4|------------- + 2sin(x) + 2 +--R \| cos(x) + 1 +--R / +--R cos(x) + 1 +--R + +--R - +--R log +--R +-------------+2 +--R |- 4cos(x) + 4 +--R (cos(x) + 1) 4|------------- +--R \| cos(x) + 1 +--R + +--R +-------------+ +--R |- 4cos(x) + 4 +--R (- 2sin(x) - 2cos(x) - 2) 4|------------- + 2sin(x) + 2 +--R \| cos(x) + 1 +--R / +--R cos(x) + 1 +--R + +--R +-------------+ +--R |- 4cos(x) + 4 +--R (2sin(x) + 2cos(x) + 2) 4|------------- +--R \| cos(x) + 1 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 409 + +--S 410 of 526 +m0876:= a0876-r0876 +--R +--R +--R (4) +--R log +--R +-------------+2 +--R |- 4cos(x) + 4 +--R (cos(x) + 1) 4|------------- +--R \| cos(x) + 1 +--R + +--R +-------------+ +--R |- 4cos(x) + 4 +--R (2sin(x) + 2cos(x) + 2) 4|------------- + 2sin(x) + 2 +--R \| cos(x) + 1 +--R / +--R cos(x) + 1 +--R + +--R - +--R log +--R +-------------+2 +--R |- 4cos(x) + 4 +--R (cos(x) + 1) 4|------------- +--R \| cos(x) + 1 +--R + +--R +-------------+ +--R |- 4cos(x) + 4 +--R (- 2sin(x) - 2cos(x) - 2) 4|------------- + 2sin(x) + 2 +--R \| cos(x) + 1 +--R / +--R cos(x) + 1 +--R + +--R +----------+ +----------+ +--R - 4atanh(\|csc(x) + 1 ) - 4sin(x)\|csc(x) + 1 +--R + +--R +-------------+ +--R |- 4cos(x) + 4 +--R (2sin(x) + 2cos(x) + 2) 4|------------- +--R \| cos(x) + 1 +--R / +--R 4 +--R Type: Expression(Integer) +--E 410 + +--S 411 of 526 +d0876:= D(m0876,x) +--R +--R +--R (5) +--R 4 3 2 3 +--R (cos(x) + 1)sin(x) + (2cos(x) + 3cos(x) + 3cos(x) + 2)sin(x) +--R + +--R 4 3 2 2 +--R (- 2cos(x) + 3cos(x) + 10cos(x) + 5cos(x))sin(x) +--R + +--R 5 4 3 2 +--R (- 2cos(x) - 7cos(x) + 2cos(x) + 14cos(x) + 4cos(x) - 3) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 2cos(x) + 4cos(x) - 4cos(x) - 8cos(x) + 2cos(x) + 4cos(x) +--R * +--R +-------------+2 +--R |- 4cos(x) + 4 +--R 4|------------- +--R \| cos(x) + 1 +--R + +--R 4 3 3 +--R (4cos(x) - 4)sin(x) + (8cos(x) - 8cos(x))sin(x) +--R + +--R 3 2 2 +--R (20cos(x) - 6cos(x) - 20cos(x) + 6)sin(x) +--R + +--R 4 3 2 6 +--R (4cos(x) + 6cos(x) - 2cos(x) - 6cos(x) - 2)sin(x) - 8cos(x) +--R + +--R 5 4 3 2 +--R 4cos(x) + 16cos(x) - 8cos(x) - 8cos(x) + 4cos(x) +--R * +--R +----------+ +--R \|csc(x) + 1 +--R + +--R 3 2 3 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2)cot(x)csc(x)sin(x) +--R + +--R 4 3 4 +--R (2cos(x) + 4cos(x) - 4cos(x) - 2)cot(x) - 4cos(x) +--R + +--R 3 2 +--R - 4cos(x) + 4cos(x) + 4cos(x) +--R * +--R csc(x) +--R + +--R 3 2 4 3 +--R (- 2cos(x) - 2cos(x) + 2cos(x) + 2)cot(x) - 4cos(x) - 4cos(x) +--R + +--R 2 +--R 4cos(x) + 4cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 2 5 +--R (2cos(x) + 4cos(x) - 4cos(x) - 2cos(x))cot(x) - 4cos(x) +--R + +--R 4 2 +--R - 8cos(x) + 8cos(x) + 4cos(x) +--R * +--R csc(x) +--R + +--R 4 3 5 4 +--R (- 2cos(x) - 4cos(x) + 4cos(x) + 2)cot(x) - 4cos(x) - 8cos(x) +--R + +--R 2 +--R 8cos(x) + 4cos(x) +--R * +--R sin(x) +--R + +--R 6 5 3 2 +--R (- 4cos(x) - 8cos(x) + 8cos(x) + 4cos(x) )csc(x) +--R + +--R 5 4 2 6 +--R (- 2cos(x) - 4cos(x) + 4cos(x) + 2cos(x))cot(x) - 4cos(x) +--R + +--R 5 3 2 +--R - 8cos(x) + 8cos(x) + 4cos(x) +--R * +--R +-------------+3 +--R |- 4cos(x) + 4 +--R 4|------------- +--R \| cos(x) + 1 +--R + +--R 3 2 3 +--R (- 2cos(x) - 2cos(x) + 2cos(x) + 2)cot(x)csc(x)sin(x) +--R + +--R 3 2 4 +--R (- 4cos(x) - 4cos(x) + 4cos(x) + 4)cot(x) + 4cos(x) +--R + +--R 3 2 +--R 4cos(x) - 4cos(x) - 4cos(x) +--R * +--R csc(x) +--R + +--R 3 2 4 3 +--R (2cos(x) + 2cos(x) - 2cos(x) - 2)cot(x) + 4cos(x) + 4cos(x) +--R + +--R 2 +--R - 4cos(x) - 4cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 5 4 3 2 +--R (2cos(x) + 2cos(x) - 6cos(x) - 6cos(x) + 4cos(x) + 4) +--R * +--R cot(x) +--R + +--R 4 3 2 +--R 8cos(x) + 8cos(x) - 8cos(x) - 8cos(x) +--R * +--R csc(x) +--R + +--R 3 2 4 3 +--R (4cos(x) + 4cos(x) - 4cos(x) - 4)cot(x) + 8cos(x) + 8cos(x) +--R + +--R 2 +--R - 8cos(x) - 8cos(x) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 4cos(x) - 4cos(x) + 12cos(x) + 12cos(x) - 8cos(x) +--R + +--R - 8cos(x) +--R * +--R csc(x) +--R + +--R 5 4 3 2 +--R (- 2cos(x) - 2cos(x) + 6cos(x) + 6cos(x) - 4cos(x) - 4)cot(x) +--R + +--R 6 5 4 3 2 +--R - 4cos(x) - 4cos(x) + 12cos(x) + 12cos(x) - 8cos(x) - 8cos(x) +--R * +--R +-------------+ +--R |- 4cos(x) + 4 +--R 4|------------- +--R \| cos(x) + 1 +--R / +--R 3 2 2 +--R (4cos(x) + 4cos(x) - 4cos(x) - 4)sin(x) +--R + +--R 4 3 5 4 +--R (4cos(x) + 8cos(x) - 8cos(x) - 4)sin(x) + 4cos(x) + 8cos(x) +--R + +--R 2 +--R - 8cos(x) - 4cos(x) +--R * +--R +-------------+3 +--R |- 4cos(x) + 4 +--R 4|------------- +--R \| cos(x) + 1 +--R + +--R 3 2 2 +--R (- 4cos(x) - 4cos(x) + 4cos(x) + 4)sin(x) +--R + +--R 3 2 5 4 +--R (- 8cos(x) - 8cos(x) + 8cos(x) + 8)sin(x) + 4cos(x) + 4cos(x) +--R + +--R 3 2 +--R - 12cos(x) - 12cos(x) + 8cos(x) + 8 +--R * +--R +-------------+ +--R |- 4cos(x) + 4 +--R 4|------------- +--R \| cos(x) + 1 +--R * +--R +----------+ +--R \|csc(x) + 1 +--R Type: Expression(Integer) +--E 411 + +)clear all + + +--S 412 of 526 +t0877:= cos(x)^3/(sin(x)^3)^(1/2) +--R +--R +--R 3 +--R cos(x) +--R (1) ---------- +--R +-------+ +--R | 3 +--R \|sin(x) +--R Type: Expression(Integer) +--E 412 + +--S 413 of 526 +r0877:= 2/3*(-4+cos(x)^2)*sin(x)/(sin(x)^3)^(1/2) +--R +--R +--R 2 +--R (2cos(x) - 8)sin(x) +--R (2) -------------------- +--R +-------+ +--R | 3 +--R 3\|sin(x) +--R Type: Expression(Integer) +--E 413 + +--S 414 of 526 +a0877:= integrate(t0877,x) +--R +--R +--R 2 +------+ +--R (- 2cos(x) + 8)sin(x)\|sin(x) +--R (3) ------------------------------- +--R 2 +--R 3cos(x) - 3 +--R Type: Union(Expression(Integer),...) +--E 414 + +--S 415 of 526 +m0877:= a0877-r0877 +--R +--R +--R (4) +--R +-------+ +--R 2 +------+ | 3 +--R (- 2cos(x) + 8)sin(x)\|sin(x) \|sin(x) +--R + +--R 4 2 +--R (- 2cos(x) + 10cos(x) - 8)sin(x) +--R / +--R +-------+ +--R 2 | 3 +--R (3cos(x) - 3)\|sin(x) +--R Type: Expression(Integer) +--E 415 + +--S 416 of 526 +d0877:= D(m0877,x) +--R +--R +--R (5) +--R +-------+ +--R 3 5 3 | 3 +--R (12cos(x)sin(x) + (- 3cos(x) + 15cos(x) - 12cos(x))sin(x))\|sin(x) +--R + +--R 5 3 2 7 5 +--R (4cos(x) - 8cos(x) + 4cos(x))sin(x) + cos(x) - 6cos(x) +--R + +--R 3 +--R 9cos(x) - 4cos(x) +--R * +--R +------+ +--R \|sin(x) +--R / +--R +-------+ +--R 4 2 +------+ | 3 +--R (3cos(x) - 6cos(x) + 3)\|sin(x) \|sin(x) +--R Type: Expression(Integer) +--E 416 + +)clear all + + +--S 417 of 526 +t0878:= cos(x)^3*csc(x)^(1/2) +--R +--R +--R 3 +------+ +--R (1) cos(x) \|csc(x) +--R Type: Expression(Integer) +--E 417 + +--S 418 of 526 +r0878:= -2/5*(-5+sin(x)^2)/(1/sin(x))^(1/2) +--R +--R +--R 2 +--R - 2sin(x) + 10 +--R (2) --------------- +--R +------+ +--R | 1 +--R 5 |------ +--R \|sin(x) +--R Type: Expression(Integer) +--E 418 + +--S 419 of 526 +a0878:= integrate(t0878,x) +--R +--R +--R +-------------+ +--R 2 | 1 +--R (2cos(x) + 8)sin(x) |- ----------- +--R 4| 2 +--R \| cos(x) - 1 +--R (3) ------------------------------------ +--R 5 +--R Type: Union(Expression(Integer),...) +--E 419 + +--S 420 of 526 +m0878:= a0878-r0878 +--R +--R +--R +-------------+ +------+ +--R 2 | 1 | 1 2 +--R (2cos(x) + 8)sin(x) |- ----------- |------ + 2sin(x) - 10 +--R 4| 2 \|sin(x) +--R \| cos(x) - 1 +--R (4) ------------------------------------------------------------- +--R +------+ +--R | 1 +--R 5 |------ +--R \|sin(x) +--R Type: Expression(Integer) +--E 420 + +--S 421 of 526 +d0878:= D(m0878,x) +--R +--R +--R (5) +--R 3 3 5 3 +--R ((3cos(x) - 8cos(x))sin(x) + (- 2cos(x) - 6cos(x) + 8cos(x))sin(x)) +--R * +--R +------+ +--R | 1 +--R |------ +--R \|sin(x) +--R + +--R 5 3 2 5 3 +--R (5cos(x) - 10cos(x) + 5cos(x))sin(x) - 5cos(x) + 10cos(x) +--R + +--R - 5cos(x) +--R * +--R +-------------+3 +--R | 1 +--R |- ----------- +--R 4| 2 +--R \| cos(x) - 1 +--R / +--R +-------------+3 +------+ +--R 4 2 | 1 | 1 +--R (5cos(x) - 10cos(x) + 5)sin(x) |- ----------- |------ +--R 4| 2 \|sin(x) +--R \| cos(x) - 1 +--R Type: Expression(Integer) +--E 421 + +)clear all + + +--S 422 of 526 +t0879:= cos(x)^3*csc(x)^(9/2) +--R +--R +--R 3 4 +------+ +--R (1) cos(x) csc(x) \|csc(x) +--R Type: Expression(Integer) +--E 422 + +--S 423 of 526 +r0879:= 2/3*csc(x)^(3/2)-2/7*csc(x)^(7/2) +--R +--R +--R 3 +------+ +--R (- 6csc(x) + 14csc(x))\|csc(x) +--R (2) -------------------------------- +--R 21 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 526 +a0879:= integrate(t0879,x) +--R +--R +--R +-------------+ +--R 4 2 | 1 +--R (- 14cos(x) + 15cos(x) - 4)sin(x) |- ----------- +--R 4| 2 +--R \| cos(x) - 1 +--R (3) --------------------------------------------------- +--R 6 4 2 +--R 42cos(x) - 126cos(x) + 126cos(x) - 42 +--R Type: Union(Expression(Integer),...) +--E 424 + +--S 425 of 526 +m0879:= a0879-r0879 +--R +--R +--R (4) +--R 6 4 2 3 +--R (12cos(x) - 36cos(x) + 36cos(x) - 12)csc(x) +--R + +--R 6 4 2 +--R (- 28cos(x) + 84cos(x) - 84cos(x) + 28)csc(x) +--R * +--R +------+ +--R \|csc(x) +--R + +--R +-------------+ +--R 4 2 | 1 +--R (- 14cos(x) + 15cos(x) - 4)sin(x) |- ----------- +--R 4| 2 +--R \| cos(x) - 1 +--R / +--R 6 4 2 +--R 42cos(x) - 126cos(x) + 126cos(x) - 42 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 526 +d0879:= D(m0879,x) +--R +--R +--R (5) +--R 5 3 2 7 5 +--R (70cos(x) - 23cos(x) - 8cos(x))sin(x) + 28cos(x) - 58cos(x) +--R + +--R 3 +--R 38cos(x) - 8cos(x) +--R * +--R +------+ +--R \|csc(x) +--R + +--R 10 8 6 4 2 +--R - 84cos(x) + 420cos(x) - 840cos(x) + 840cos(x) - 420cos(x) +--R + +--R 84 +--R * +--R 4 +--R cot(x)csc(x) +--R + +--R 10 8 6 4 2 +--R 84cos(x) - 420cos(x) + 840cos(x) - 840cos(x) + 420cos(x) +--R + +--R - 84 +--R * +--R 2 +--R cot(x)csc(x) +--R * +--R +-------------+3 +--R | 1 +--R |- ----------- +--R 4| 2 +--R \| cos(x) - 1 +--R / +--R 10 8 6 4 2 +--R (84cos(x) - 420cos(x) + 840cos(x) - 840cos(x) + 420cos(x) - 84) +--R * +--R +-------------+3 +--R | 1 +------+ +--R |- ----------- \|csc(x) +--R 4| 2 +--R \| cos(x) - 1 +--R Type: Expression(Integer) +--E 426 + +)clear all + + +--S 427 of 526 +t0880:= sec(x)^2*(a+b*tan(x))^n +--R +--R +--R 2 n +--R (1) sec(x) (b tan(x) + a) +--R Type: Expression(Integer) +--E 427 + +--S 428 of 526 +r0880:= (a+b*tan(x))^(1+n)/b/(1+n) +--R +--R +--R n + 1 +--R (b tan(x) + a) +--R (2) ------------------- +--R b n + b +--R Type: Expression(Integer) +--E 428 + +--S 429 of 526 +a0880:= integrate(t0880,x) +--R +--R +--R b sin(x) + a cos(x) +--R n log(-------------------) +--R cos(x) +--R (b sin(x) + a cos(x))%e +--R (3) ------------------------------------------------- +--R (b n + b)cos(x) +--R Type: Union(Expression(Integer),...) +--E 429 + +--S 430 of 526 +m0880:= a0880-r0880 +--R +--R +--R (4) +--R b sin(x) + a cos(x) +--R n log(-------------------) +--R cos(x) n + 1 +--R (b sin(x) + a cos(x))%e - cos(x)(b tan(x) + a) +--R ----------------------------------------------------------------------------- +--R (b n + b)cos(x) +--R Type: Expression(Integer) +--E 430 + +--S 431 of 526 +d0880:= D(m0880,x) +--R +--R +--R (5) +--R b sin(x) + a cos(x) +--R n log(-------------------) +--R 2 2 cos(x) +--R (sin(x) + cos(x) )%e +--R + +--R 2 2 2 n +--R (- cos(x) tan(x) - cos(x) )(b tan(x) + a) +--R / +--R 2 +--R cos(x) +--R Type: Expression(Integer) +--E 431 + +)clear all + + +--S 432 of 526 +t0881:= sec(x)^2/(tan(x)^2+tan(x)^3) +--R +--R +--R 2 +--R sec(x) +--R (1) ----------------- +--R 3 2 +--R tan(x) + tan(x) +--R Type: Expression(Integer) +--E 432 + +--S 433 of 526 +r0881:= -cot(x)+log(1+cot(x)) +--R +--R +--R (2) log(cot(x) + 1) - cot(x) +--R Type: Expression(Integer) +--E 433 + +--S 434 of 526 +a0881:= integrate(t0881,x) +--R +--R +--R sin(x) - 2sin(x) - 2cos(x) +--R - sin(x)log(----------) + sin(x)log(-------------------) - cos(x) +--R cos(x) + 1 cos(x) + 1 +--R (3) ----------------------------------------------------------------- +--R sin(x) +--R Type: Union(Expression(Integer),...) +--E 434 + +--S 435 of 526 +m0881:= a0881-r0881 +--R +--R +--R (4) +--R sin(x) +--R - sin(x)log(----------) - sin(x)log(cot(x) + 1) +--R cos(x) + 1 +--R + +--R - 2sin(x) - 2cos(x) +--R sin(x)log(-------------------) + cot(x)sin(x) - cos(x) +--R cos(x) + 1 +--R / +--R sin(x) +--R Type: Expression(Integer) +--E 435 + +--S 436 of 526 +d0881:= D(m0881,x) +--R +--R +--R (5) +--R 3 3 3 2 +--R (- cot(x) - cot(x))sin(x) + (- cos(x)cot(x) + cos(x))sin(x) +--R + +--R 3 3 +--R cos(x) cot(x) + cos(x) +--R / +--R 3 2 +--R (cot(x) + 1)sin(x) + (cos(x)cot(x) + cos(x))sin(x) +--R Type: Expression(Integer) +--E 436 + +)clear all + + +--S 437 of 526 +t0882:= sec(x)^2/(-tan(x)^2+tan(x)^3) +--R +--R +--R 2 +--R sec(x) +--R (1) ----------------- +--R 3 2 +--R tan(x) - tan(x) +--R Type: Expression(Integer) +--E 437 + +--S 438 of 526 +r0882:= cot(x)+log(1-cot(x)) +--R +--R +--R (2) log(- cot(x) + 1) + cot(x) +--R Type: Expression(Integer) +--E 438 + +--S 439 of 526 +a0882:= integrate(t0882,x) +--R +--R +--R 2sin(x) - 2cos(x) sin(x) +--R sin(x)log(-----------------) - sin(x)log(----------) + cos(x) +--R cos(x) + 1 cos(x) + 1 +--R (3) ------------------------------------------------------------- +--R sin(x) +--R Type: Union(Expression(Integer),...) +--E 439 + +--S 440 of 526 +m0882:= a0882-r0882 +--R +--R +--R (4) +--R 2sin(x) - 2cos(x) sin(x) +--R sin(x)log(-----------------) - sin(x)log(----------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R - sin(x)log(- cot(x) + 1) - cot(x)sin(x) + cos(x) +--R / +--R sin(x) +--R Type: Expression(Integer) +--E 440 + +--S 441 of 526 +d0882:= D(m0882,x) +--R +--R +--R (5) +--R 3 3 3 2 +--R (cot(x) + cot(x))sin(x) + (- cos(x)cot(x) - cos(x))sin(x) +--R + +--R 3 3 +--R cos(x) cot(x) - cos(x) +--R / +--R 3 2 +--R (cot(x) - 1)sin(x) + (- cos(x)cot(x) + cos(x))sin(x) +--R Type: Expression(Integer) +--E 441 + +)clear all + + +--S 442 of 526 +t0883:= sec(x)^2/(3-4*tan(x)^3) +--R +--R +--R 2 +--R sec(x) +--R (1) - ------------ +--R 3 +--R 4tan(x) - 3 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 526 +r0883:= 1/18*atan(1/6*(6^(1/3)+4*tan(x))*2^(2/3)*3^(1/6))*2^(1/3)*3^(5/6)-_ + 1/18*log(6^(1/3)-2*tan(x))*6^(1/3)+1/36*log(6^(2/3)+_ + 2*6^(1/3)*tan(x)+4*tan(x)^2)*6^(1/3) +--R +--R +--R (2) +--R 3+-+ 2 3+-+ 3+-+2 3+-+ 3+-+ +--R \|6 log(4tan(x) + 2\|6 tan(x) + \|6 ) - 2\|6 log(- 2tan(x) + \|6 ) +--R + +--R 3+-+2 6+-+ 3+-+2 6+-+3+-+ +--R 3+-+6+-+5 4\|2 \|3 tan(x + \|2 \|3 \|6 +--R 2\|2 \|3 atan(--------------------------------) +--R 6 +--R / +--R 36 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 526 +a0883:= integrate(t0883,x) +--R +--R +--R (3) +--R - +--R 3+---+ +-+ +--R \|- 1 \|3 +--R * +--R log +--R 3+---+2 3+--+2 3+--+ 3+---+ 2 +--R 4\|- 1 \|36 cos(x)sin(x + (12\|36 + 48\|- 1 )cos(x) +--R + +--R 3+---+ +--R - 48\|- 1 +--R / +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R 3+---+2 3+--+2 +--R 3+---+ +-+ 24\|- 1 sin(x) - 2\|36 cos(x) +--R 2\|- 1 \|3 log(-------------------------------) +--R cos(x) + 1 +--R + +--R +-+3+--+2 3+---+2 +-+ 3+---+2 +-+ +--R 3+---+ \|3 \|36 sin(x) - 12\|- 1 \|3 cos(x) - 12\|- 1 \|3 +--R - 6\|- 1 atan(------------------------------------------------------) +--R 3+---+2 3+---+2 +--R 36\|- 1 cos(x) + 36\|- 1 +--R + +--R 3+---+ +--R 6\|- 1 +--R * +--R atan +--R 3+--+ 3+---+ 3+---+ +--R ((6\|36 + 48\|- 1 )cos(x) + 48\|- 1 )sin(x) +--R + +--R 3+---+2 3+--+2 2 3+---+2 3+--+2 3+---+2 3+--+2 +--R - 3\|- 1 \|36 cos(x) - 2\|- 1 \|36 cos(x + \|- 1 \|36 +--R / +--R 3+---+2 +-+3+--+2 2 3+---+2 +-+3+--+2 +--R \|- 1 \|3 \|36 cos(x) + 2\|- 1 \|3 \|36 cos(x) +--R + +--R 3+---+2 +-+3+--+2 +--R \|- 1 \|3 \|36 +--R / +--R +-+3+--+ +--R 6\|3 \|36 +--R Type: Union(Expression(Integer),...) +--E 444 + +--S 445 of 526 +m0883:= a0883-r0883 +--R +--R +--R (4) +--R +-+3+-+3+--+ 2 3+-+ 3+-+2 +--R - \|3 \|6 \|36 log(4tan(x) + 2\|6 tan(x) + \|6 ) +--R + +--R - +--R 3+---+ +-+ +--R 6\|- 1 \|3 +--R * +--R log +--R 3+---+2 3+--+2 3+--+ 3+---+ 2 +--R 4\|- 1 \|36 cos(x)sin(x + (12\|36 + 48\|- 1 )cos(x) +--R + +--R 3+---+ +--R - 48\|- 1 +--R / +--R 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R 3+---+2 3+--+2 +--R 3+---+ +-+ 24\|- 1 sin(x) - 2\|36 cos(x) +--R 12\|- 1 \|3 log(-------------------------------) +--R cos(x) + 1 +--R + +--R +-+3+-+3+--+ 3+-+ +--R 2\|3 \|6 \|36 log(- 2tan(x) + \|6 ) +--R + +--R 3+-+2 6+-+ 3+-+2 6+-+3+-+ +--R 3+-+ +-+6+-+5 3+--+ 4\|2 \|3 tan(x + \|2 \|3 \|6 +--R - 2\|2 \|3 \|3 \|36 atan(--------------------------------) +--R 6 +--R + +--R +-+3+--+2 3+---+2 +-+ 3+---+2 +-+ +--R 3+---+ \|3 \|36 sin(x) - 12\|- 1 \|3 cos(x) - 12\|- 1 \|3 +--R - 36\|- 1 atan(------------------------------------------------------) +--R 3+---+2 3+---+2 +--R 36\|- 1 cos(x) + 36\|- 1 +--R + +--R 3+---+ +--R 36\|- 1 +--R * +--R atan +--R 3+--+ 3+---+ 3+---+ +--R ((6\|36 + 48\|- 1 )cos(x) + 48\|- 1 )sin(x) +--R + +--R 3+---+2 3+--+2 2 3+---+2 3+--+2 3+---+2 3+--+2 +--R - 3\|- 1 \|36 cos(x) - 2\|- 1 \|36 cos(x + \|- 1 \|36 +--R / +--R 3+---+2 +-+3+--+2 2 3+---+2 +-+3+--+2 +--R \|- 1 \|3 \|36 cos(x) + 2\|- 1 \|3 \|36 cos(x) +--R + +--R 3+---+2 +-+3+--+2 +--R \|- 1 \|3 \|36 +--R / +--R +-+3+--+ +--R 36\|3 \|36 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 526 +--d0883:= D(m0883,x) +--E 446 + +)clear all + + +--S 447 of 526 +t0884:= sec(x)^2/(1+sec(x)^2-3*tan(x)) +--R +--R +--R 2 +--R sec(x) +--R (1) - --------------------- +--R 2 +--R 3tan(x) - sec(x) - 1 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 526 +r0884:= -2*atanh(-3+2*tan(x)) +--R +--R +--R (2) - 2atanh(2tan(x) - 3) +--R Type: Expression(Integer) +--E 448 + +--S 449 of 526 +a0884:= integrate(t0884,x) +--R +--R +--R 2sin(x) - 2cos(x) sin(x) - 2cos(x) +--R (3) - log(-----------------) + log(----------------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 449 + +--S 450 of 526 +m0884:= a0884-r0884 +--R +--R +--R 2sin(x) - 2cos(x) sin(x) - 2cos(x) +--R (4) - log(-----------------) + log(----------------) + 2atanh(2tan(x) - 3) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 450 + +--S 451 of 526 +d0884:= D(m0884,x) +--R +--R +--R (5) +--R 2 2 2 2 +--R (3cos(x)sin(x) - cos(x) )tan(x) + (- 3sin(x) - 3cos(x) )tan(x) +--R + +--R 2 +--R sin(x) + 3cos(x)sin(x) +--R / +--R 2 2 2 +--R (sin(x) - 3cos(x)sin(x) + 2cos(x) )tan(x) +--R + +--R 2 2 2 +--R (- 3sin(x) + 9cos(x)sin(x) - 6cos(x) )tan(x) + 2sin(x) - 6cos(x)sin(x) +--R + +--R 2 +--R 4cos(x) +--R Type: Expression(Integer) +--E 451 + +)clear all + + +--S 452 of 526 +t0885:= sec(x)^2*(a+b*tan(x))^2/(c+d*tan(x)) +--R +--R +--R 2 2 2 2 2 2 +--R b sec(x) tan(x) + 2a b sec(x) tan(x) + a sec(x) +--R (1) ------------------------------------------------- +--R d tan(x) + c +--R Type: Expression(Integer) +--E 452 + +--S 453 of 526 +r0885:= (b*c-a*d)^2*log(c+d*tan(x))/d^3-b*(b*c-a*d)*_ + tan(x)/d^2+1/2*(a+b*tan(x))^2/d +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (2a d - 4a b c d + 2b c )log(d tan(x) + c) + b d tan(x) +--R + +--R 2 2 2 2 +--R (4a b d - 2b c d)tan(x) + a d +--R / +--R 3 +--R 2d +--R Type: Expression(Integer) +--E 453 + +--S 454 of 526 +a0885:= integrate(t0885,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2cos(x) +--R (- 2a d + 4a b c d - 2b c )cos(x) log(- ----------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 - 2d sin(x) - 2c cos(x) +--R (2a d - 4a b c d + 2b c )cos(x) log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 2 2 +--R (4a b d - 2b c d)cos(x)sin(x) - b d cos(x) + b d +--R / +--R 3 2 +--R 2d cos(x) +--R Type: Union(Expression(Integer),...) +--E 454 + +--S 455 of 526 +m0885:= a0885-r0885 +--R +--R +--R (4) +--R 2 2 2 2 2 +--R (- 2a d + 4a b c d - 2b c )cos(x) log(d tan(x) + c) +--R + +--R 2 2 2 2 2 2cos(x) +--R (- 2a d + 4a b c d - 2b c )cos(x) log(- ----------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 - 2d sin(x) - 2c cos(x) +--R (2a d - 4a b c d + 2b c )cos(x) log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 2 2 +--R - b d cos(x) tan(x) + (- 4a b d + 2b c d)cos(x) tan(x) +--R + +--R 2 2 2 2 2 2 2 2 +--R (4a b d - 2b c d)cos(x)sin(x) + (- b - a )d cos(x) + b d +--R / +--R 3 2 +--R 2d cos(x) +--R Type: Expression(Integer) +--E 455 + +--S 456 of 526 +d0885:= D(m0885,x) +--R +--R +--R (5) +--R 2 2 3 2 4 4 +--R (- b d cos(x) sin(x) - b c d cos(x) )tan(x) +--R + +--R 2 3 4 3 +--R (- 2a b d cos(x) sin(x) - 2a b c d cos(x) )tan(x) +--R + +--R 2 2 2 3 2 2 4 2 +--R ((- b - a )d cos(x) sin(x) + (- b - a )c d cos(x) )tan(x) +--R + +--R 2 2 3 2 2 2 2 2 2 +--R (2a b d - b c d)cos(x)sin(x) + (a d cos(x) + b d )sin(x) +--R + +--R 2 3 2 2 2 4 +--R (- b c d cos(x) + b c d cos(x))sin(x) + (a d - 2a b c d)cos(x) +--R * +--R tan(x) +--R + +--R 2 2 3 2 2 2 2 +--R (2a b c d - b c )cos(x)sin(x) + (a c d cos(x) + b c d)sin(x) +--R + +--R 2 2 2 2 3 2 2 +--R ((- a d + 2a b c d - b c )cos(x) + b c cos(x))sin(x) +--R / +--R 3 3 2 4 2 3 2 4 +--R (d cos(x) sin(x) + c d cos(x) )tan(x) + c d cos(x) sin(x) + c d cos(x) +--R Type: Expression(Integer) +--E 456 + +)clear all + + +--S 457 of 526 +t0886:= sec(x)^2*(a+b*tan(x))^3/(c+d*tan(x)) +--R +--R +--R (1) +--R 3 2 3 2 2 2 2 2 3 2 +--R b sec(x) tan(x) + 3a b sec(x) tan(x) + 3a b sec(x) tan(x) + a sec(x) +--R ----------------------------------------------------------------------- +--R d tan(x) + c +--R Type: Expression(Integer) +--E 457 + +--S 458 of 526 +r0886:= -(b*c-a*d)^3*log(c+d*tan(x))/d^4+b*(b*c-a*d)^2*_ + tan(x)/d^3-1/2*(b*c-a*d)*(a+b*tan(x))^2/d^2+1/3*(a+b*tan(x))^3/d +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )log(d tan(x) + c) + 2b d tan(x) +--R + +--R 2 3 3 2 2 2 3 2 2 3 2 +--R (9a b d - 3b c d )tan(x) + (18a b d - 18a b c d + 6b c d)tan(x) +--R + +--R 3 3 2 2 +--R 5a d - 3a b c d +--R / +--R 4 +--R 6d +--R Type: Expression(Integer) +--E 458 + +--S 459 of 526 +a0886:= integrate(t0886,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 3 2cos(x) +--R (- 6a d + 18a b c d - 18a b c d + 6b c )cos(x) log(- ----------) +--R cos(x) + 1 +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )cos(x) +--R * +--R - 2d sin(x) - 2c cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 3 2 3 2 2 3 2 2 3 3 +--R (((- 2b + 18a b)d - 18a b c d + 6b c d)cos(x) + 2b d )sin(x) +--R + +--R 2 3 3 2 3 2 3 3 2 +--R (- 9a b d + 3b c d )cos(x) + (9a b d - 3b c d )cos(x) +--R / +--R 4 3 +--R 6d cos(x) +--R Type: Union(Expression(Integer),...) +--E 459 + +--S 460 of 526 +m0886:= a0886-r0886 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 3 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )cos(x) log(d tan(x) + c) +--R + +--R 3 3 2 2 2 2 3 3 3 2cos(x) +--R (- 6a d + 18a b c d - 18a b c d + 6b c )cos(x) log(- ----------) +--R cos(x) + 1 +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (6a d - 18a b c d + 18a b c d - 6b c )cos(x) +--R * +--R - 2d sin(x) - 2c cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 3 3 3 3 2 3 3 2 3 2 +--R - 2b d cos(x) tan(x) + (- 9a b d + 3b c d )cos(x) tan(x) +--R + +--R 2 3 2 2 3 2 3 +--R (- 18a b d + 18a b c d - 6b c d)cos(x) tan(x) +--R + +--R 3 2 3 2 2 3 2 2 3 3 +--R (((- 2b + 18a b)d - 18a b c d + 6b c d)cos(x) + 2b d )sin(x) +--R + +--R 2 3 3 3 2 2 3 2 3 3 2 +--R ((- 9a b - 5a )d + (3b + 3a b)c d )cos(x) + (9a b d - 3b c d )cos(x) +--R / +--R 4 3 +--R 6d cos(x) +--R Type: Expression(Integer) +--E 460 + +--S 461 of 526 +d0886:= D(m0886,x) +--R +--R +--R (5) +--R 3 3 4 3 2 5 5 +--R (- 3b d cos(x) sin(x) - 3b c d cos(x) )tan(x) +--R + +--R 2 3 4 2 2 5 4 +--R (- 9a b d cos(x) sin(x) - 9a b c d cos(x) )tan(x) +--R + +--R 3 2 3 4 3 2 2 5 3 +--R ((- 3b - 9a b)d cos(x) sin(x) + (- 3b - 9a b)c d cos(x) )tan(x) +--R + +--R 2 3 3 4 2 3 2 5 2 +--R ((- 9a b - 3a )d cos(x) sin(x) + (- 9a b - 3a )c d cos(x) )tan(x) +--R + +--R 3 2 3 2 2 3 2 2 3 3 3 +--R (((- b + 9a b)d - 9a b c d + 3b c d)cos(x) + 3b d )sin(x) +--R + +--R 3 3 3 2 3 2 3 2 +--R ((3a d - b c d )cos(x) + 9a b d cos(x))sin(x) +--R + +--R 3 3 2 2 3 2 4 +--R (- b d - 9a b c d + 3b c d)cos(x) +--R + +--R 3 3 2 2 3 2 2 +--R (b d + 9a b c d - 3b c d)cos(x) +--R * +--R sin(x) +--R + +--R 3 3 3 2 2 5 3 2 3 +--R (3a d + (- b - 9a b)c d )cos(x) + b c d cos(x) +--R * +--R tan(x) +--R + +--R 3 2 2 2 2 3 3 2 3 2 3 +--R (((- b + 9a b)c d - 9a b c d + 3b c )cos(x) + 3b c d )sin(x) +--R + +--R 3 2 3 2 3 2 2 2 +--R ((3a c d - b c d)cos(x) + 9a b c d cos(x))sin(x) +--R + +--R 3 3 3 2 2 2 2 3 3 4 +--R (- 3a d + (- b + 9a b)c d - 9a b c d + 3b c )cos(x) +--R + +--R 3 2 2 2 3 3 2 +--R (b c d + 9a b c d - 3b c )cos(x) +--R * +--R sin(x) +--R + +--R 3 2 5 3 2 3 +--R - b c d cos(x) + b c d cos(x) +--R / +--R 4 4 3 5 3 4 2 2 5 +--R (3d cos(x) sin(x) + 3c d cos(x) )tan(x) + 3c d cos(x) sin(x) + 3c d cos(x) +--R Type: Expression(Integer) +--E 461 + +)clear all + + +--S 462 of 526 +t0887:= sec(x)^4*(-1+sec(x)^2)^2*tan(x) +--R +--R +--R 8 6 4 +--R (1) (sec(x) - 2sec(x) + sec(x) )tan(x) +--R Type: Expression(Integer) +--E 462 + +--S 463 of 526 +r0887:= 1/24*tan(x)^6*(4+3*tan(x)^2) +--R +--R +--R 8 6 +--R 3tan(x) + 4tan(x) +--R (2) ------------------- +--R 24 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 526 +a0887:= integrate(t0887,x) +--R +--R +--R 8 4 2 +--R - cos(x) + 6cos(x) - 8cos(x) + 3 +--R (3) ----------------------------------- +--R 8 +--R 24cos(x) +--R Type: Union(Expression(Integer),...) +--E 464 + +--S 465 of 526 +m0887:= a0887-r0887 +--R +--R +--R (4) +--R 8 8 8 6 8 4 2 +--R - 3cos(x) tan(x) - 4cos(x) tan(x) - cos(x) + 6cos(x) - 8cos(x) + 3 +--R ----------------------------------------------------------------------- +--R 8 +--R 24cos(x) +--R Type: Expression(Integer) +--E 465 + +--S 466 of 526 +d0887:= D(m0887,x) +--R +--R +--R (5) +--R 9 9 9 7 9 5 +--R - cos(x) tan(x) - 2cos(x) tan(x) - cos(x) tan(x) +--R + +--R 4 2 +--R (cos(x) - 2cos(x) + 1)sin(x) +--R / +--R 9 +--R cos(x) +--R Type: Expression(Integer) +--E 466 + +)clear all + + +--S 467 of 526 +t0888:= tan(x)^n*sec(x)^4 +--R +--R +--R 4 n +--R (1) sec(x) tan(x) +--R Type: Expression(Integer) +--E 467 + +--S 468 of 526 +r0888:= tan(x)^(1+n)/(1+n)+tan(x)^(3+n)/(3+n) +--R +--R +--R n + 3 n + 1 +--R (n + 1)tan(x) + (n + 3)tan(x) +--R (2) --------------------------------------- +--R 2 +--R n + 4n + 3 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 526 +a0888:= integrate(t0888,x) +--R +--R +--R sin(x) +--R n log(------) +--R 2 cos(x) +--R (2cos(x) + n + 1)sin(x)%e +--R (3) --------------------------------------- +--R 2 3 +--R (n + 4n + 3)cos(x) +--R Type: Union(Expression(Integer),...) +--E 469 + +--S 470 of 526 +m0888:= a0888-r0888 +--R +--R +--R (4) +--R sin(x) +--R n log(------) +--R 2 cos(x) 3 n + 3 +--R (2cos(x) + n + 1)sin(x)%e + (- n - 1)cos(x) tan(x) +--R + +--R 3 n + 1 +--R (- n - 3)cos(x) tan(x) +--R / +--R 2 3 +--R (n + 4n + 3)cos(x) +--R Type: Expression(Integer) +--E 470 + +--S 471 of 526 +d0888:= D(m0888,x) +--R +--R +--R (5) +--R sin(x) +--R n log(------) +--R 2 2 4 2 cos(x) +--R ((2cos(x) + n + 3)sin(x) + 2cos(x) + (n + 1)cos(x) )%e +--R + +--R 4 2 4 n + 2 +--R ((- n - 3)cos(x) tan(x) + (- n - 3)cos(x) )tan(x) +--R + +--R 4 2 4 n +--R ((- n - 3)cos(x) tan(x) + (- n - 3)cos(x) )tan(x) +--R / +--R 4 +--R (n + 3)cos(x) +--R Type: Expression(Integer) +--E 471 + +)clear all + + +--S 472 of 526 +t0889:= sec(x)^2/(4-sec(x)^2)^(1/2) +--R +--R +--R 2 +--R sec(x) +--R (1) ---------------- +--R +-------------+ +--R | 2 +--R \|- sec(x) + 4 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 526 +r0889:= asin(1/3*tan(x)*3^(1/2)) +--R +--R +--R +-+ +--R \|3 tan(x) +--R (2) asin(----------) +--R 3 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 526 +a0889:= integrate(t0889,x) +--R +--R +--R +---------------------+ +--R | 2 +--R | 16cos(x) - 4 +--R (cos(x) + 1)sin(x) |--------------------- - 4cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R (3) atan(-----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | 16cos(x) - 4 2 +--R (2cos(x) + 2cos(x)) |--------------------- - 8cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 474 + +--S 475 of 526 +m0889:= a0889-r0889 +--R +--R +--R (4) +--R +---------------------+ +--R | 2 +--R | 16cos(x) - 4 +--R (cos(x) + 1)sin(x) |--------------------- - 4cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(-----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | 16cos(x) - 4 2 +--R (2cos(x) + 2cos(x)) |--------------------- - 8cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ +--R \|3 tan(x) +--R - asin(----------) +--R 3 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 526 +d0889:= D(m0889,x) +--R +--R +--R (5) +--R 2 3 2 2 +--R ((- cos(x) - 1)sin(x) - 4cos(x) - 4cos(x) + cos(x) + 1)tan(x) +--R + +--R 2 3 2 +--R (- cos(x) - 1)sin(x) - 4cos(x) - 4cos(x) + cos(x) + 1 +--R * +--R +---------------------+ +--R | 2 +--R | 16cos(x) - 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-------------+ +--R 2 3 | 2 +--R (- 8cos(x)sin(x) - 8cos(x) + 2cos(x))\|- tan(x) + 3 +--R / +--R +-------------+ +--R 2 3 2 | 2 +--R ((cos(x) + 1)sin(x) + 4cos(x) + 4cos(x) - cos(x) - 1)\|- tan(x) + 3 +--R * +--R +---------------------+ +--R | 2 +--R | 16cos(x) - 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 476 + +)clear all + + +--S 477 of 526 +t0890:= sec(x)^2/(1-4*tan(x)^2)^(1/2) +--R +--R +--R 2 +--R sec(x) +--R (1) ----------------- +--R +--------------+ +--R | 2 +--R \|- 4tan(x) + 1 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 526 +r0890:= 1/2*asin(2*tan(x)) +--R +--R +--R asin(2tan(x)) +--R (2) ------------- +--R 2 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 526 +a0890:= integrate(t0890,x) +--R +--R +--R (3) +--R +---------------------+ +--R | 2 +--R | 20cos(x) - 16 +-+ +--R (2cos(x) + 2)sin(x) |--------------------- - 4\|5 cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(------------------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R +-+ 2 +-+ | 20cos(x) - 16 2 +--R (\|5 cos(x) + \|5 cos(x)) |--------------------- - 10cos(x) + 8 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R ------------------------------------------------------------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 479 + +--S 480 of 526 +m0890:= a0890-r0890 +--R +--R +--R (4) +--R +---------------------+ +--R | 2 +--R | 20cos(x) - 16 +-+ +--R (2cos(x) + 2)sin(x) |--------------------- - 4\|5 cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(------------------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R +-+ 2 +-+ | 20cos(x) - 16 2 +--R (\|5 cos(x) + \|5 cos(x)) |--------------------- - 10cos(x) + 8 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - asin(2tan(x)) +--R / +--R 2 +--R Type: Expression(Integer) +--E 480 + +--S 481 of 526 +d0890:= D(m0890,x) +--R +--R +--R (5) +--R 2 3 2 2 +--R ((- 4cos(x) - 4)sin(x) - 5cos(x) - 5cos(x) + 4cos(x) + 4)tan(x) +--R + +--R 2 3 2 +--R (- 4cos(x) - 4)sin(x) - 5cos(x) - 5cos(x) + 4cos(x) + 4 +--R * +--R +---------------------+ +--R | 2 +--R | 20cos(x) - 16 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +--------------+ +--R 2 3 | 2 +--R (- 10cos(x)sin(x) - 10cos(x) + 8cos(x))\|- 4tan(x) + 1 +--R / +--R 2 3 2 +--R ((4cos(x) + 4)sin(x) + 5cos(x) + 5cos(x) - 4cos(x) - 4) +--R * +--R +---------------------+ +--R +--------------+ | 2 +--R | 2 | 20cos(x) - 16 +--R \|- 4tan(x) + 1 |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 481 + +)clear all + + +--S 482 of 526 +t0891:= sec(x)^2/(-4+tan(x)^2)^(1/2) +--R +--R +--R 2 +--R sec(x) +--R (1) -------------- +--R +-----------+ +--R | 2 +--R \|tan(x) - 4 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 526 +r0891:= atanh(cot(x)*(-4+tan(x)^2)^(1/2)) +--R +--R +--R +-----------+ +--R | 2 +--R (2) atanh(cot(x)\|tan(x) - 4 ) +--R Type: Expression(Integer) +--E 483 + +--S 484 of 526 +a0891:= integrate(t0891,x) +--R +--R +--R (3) +--R +---------------------+ +--R | 2 +--R | - 5cos(x) + 1 +-+ 2 +--R - log((cos(x) + 1)sin(x) |--------------------- + \|5 cos(x) + 1) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 2 +--R | - 5cos(x) + 1 +-+ 2 +--R log((- cos(x) - 1)sin(x) |--------------------- - \|5 cos(x) + 1) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 484 + +--S 485 of 526 +m0891:= a0891-r0891 +--R +--R +--R (4) +--R +---------------------+ +--R | 2 +--R | - 5cos(x) + 1 +-+ 2 +--R - log((cos(x) + 1)sin(x) |--------------------- + \|5 cos(x) + 1) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 2 +--R | - 5cos(x) + 1 +-+ 2 +--R log((- cos(x) - 1)sin(x) |--------------------- - \|5 cos(x) + 1) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-----------+ +--R | 2 +--R - 2atanh(cot(x)\|tan(x) - 4 ) +--R / +--R 2 +--R Type: Expression(Integer) +--E 485 + +--S 486 of 526 +d0891:= D(m0891,x) +--R +--R +--R (5) +--R 2 2 2 +--R (- 5cos(x) - 5cos(x))cot(x) sin(x) +--R + +--R 4 3 2 2 +--R (5cos(x) + 5cos(x) - cos(x) - cos(x))cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R 2 2 2 2 +--R ((20cos(x) + 20cos(x))cot(x) + 5cos(x) + 5cos(x))sin(x) +--R + +--R 4 3 2 2 4 +--R (- 20cos(x) - 20cos(x) + 4cos(x) + 4cos(x))cot(x) - 5cos(x) +--R + +--R 3 2 +--R - 5cos(x) + cos(x) + cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 5cos(x) + 1 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 3 +-+ 2 2 +--R (- 10\|5 cos(x) + 2\|5 cos(x))cot(x) sin(x)tan(x) +--R + +--R +-+ 3 +-+ 2 +-+ 3 +--R (40\|5 cos(x) - 8\|5 cos(x))cot(x) + 10\|5 cos(x) +--R + +--R +-+ +--R - 2\|5 cos(x) +--R * +--R sin(x) +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) - 4 +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (10\|5 cos(x) + 10\|5 cos(x) - 2\|5 cos(x) - 2\|5 cos(x) )cot(x) +--R * +--R 3 +--R sin(x)tan(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (- 10\|5 cos(x) - 10\|5 cos(x) + 2\|5 cos(x) + 2\|5 cos(x) ) +--R * +--R 2 +--R cot(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R - 10\|5 cos(x) - 10\|5 cos(x) + 2\|5 cos(x) + 2\|5 cos(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (10\|5 cos(x) + 10\|5 cos(x) - 2\|5 cos(x) - 2\|5 cos(x) )cot(x) +--R * +--R sin(x)tan(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (40\|5 cos(x) + 40\|5 cos(x) - 8\|5 cos(x) - 8\|5 cos(x) ) +--R * +--R 2 +--R cot(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R 40\|5 cos(x) + 40\|5 cos(x) - 8\|5 cos(x) - 8\|5 cos(x) +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 5cos(x) + 1 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 2 +--R (- 25cos(x) + 10cos(x) - 1)cot(x)sin(x) +--R + +--R 6 4 2 +--R (25cos(x) - 5cos(x) - 5cos(x) + 1)cot(x) +--R * +--R 3 +--R tan(x) +--R + +--R 4 2 2 4 2 +--R ((25cos(x) - 10cos(x) + 1)cot(x) + 25cos(x) - 10cos(x) + 1) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 2 2 6 4 +--R (- 25cos(x) + 5cos(x) + 5cos(x) - 1)cot(x) - 25cos(x) + 5cos(x) +--R + +--R 2 +--R 5cos(x) - 1 +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 2 +--R (- 25cos(x) + 10cos(x) - 1)cot(x)sin(x) +--R + +--R 6 4 2 +--R (25cos(x) - 5cos(x) - 5cos(x) + 1)cot(x) +--R * +--R tan(x) +--R + +--R 4 2 2 4 2 +--R ((- 100cos(x) + 40cos(x) - 4)cot(x) - 100cos(x) + 40cos(x) - 4) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 2 2 6 4 +--R (100cos(x) - 20cos(x) - 20cos(x) + 4)cot(x) + 100cos(x) - 20cos(x) +--R + +--R 2 +--R - 20cos(x) + 4 +--R / +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (10\|5 cos(x) + 10\|5 cos(x) - 2\|5 cos(x) - 2\|5 cos(x) ) +--R * +--R 2 2 +--R cot(x) sin(x)tan(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 40\|5 cos(x) - 40\|5 cos(x) + 8\|5 cos(x) +--R + +--R +-+ 2 +--R 8\|5 cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R - 10\|5 cos(x) - 10\|5 cos(x) + 2\|5 cos(x) + 2\|5 cos(x) +--R * +--R sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 5cos(x) + 1 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 2 2 +--R (- 25cos(x) + 10cos(x) - 1)cot(x) sin(x) +--R + +--R 6 4 2 2 +--R (25cos(x) - 5cos(x) - 5cos(x) + 1)cot(x) +--R * +--R 2 +--R tan(x) +--R + +--R 4 2 2 4 2 +--R ((100cos(x) - 40cos(x) + 4)cot(x) + 25cos(x) - 10cos(x) + 1) +--R * +--R 2 +--R sin(x) +--R + +--R 6 4 2 2 6 +--R (- 100cos(x) + 20cos(x) + 20cos(x) - 4)cot(x) - 25cos(x) +--R + +--R 4 2 +--R 5cos(x) + 5cos(x) - 1 +--R * +--R +-----------+ +--R | 2 +--R \|tan(x) - 4 +--R Type: Expression(Integer) +--E 486 + +)clear all + + +--S 487 of 526 +t0892:= sec(x)^2*(1-cot(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (1) sec(x) \|- cot(x) + 1 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 526 +r0892:= asin(cot(x))+(1-cot(x)^2)^(1/2)*tan(x) +--R +--R +--R +-------------+ +--R | 2 +--R (2) tan(x)\|- cot(x) + 1 + asin(cot(x)) +--R Type: Expression(Integer) +--E 488 + +--S 489 of 526 +a0892:= integrate(t0892,x) +--R +--R +--R (3) +--R +---------------------+ +--R | 2 +--R +-+ 2 +-+ | - 8cos(x) + 4 +--R (- 2\|2 cos(x) - 2\|2 cos(x))sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R - 8cos(x) + 6cos(x) +--R * +--R +---------------------+ +--R | 2 +--R 2 | - 8cos(x) + 4 +-+ +--R (cos(x) + cos(x)) |--------------------- - 2\|2 cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R +-+ +-+ | - 8cos(x) + 4 2 +--R (\|2 cos(x) + \|2 )sin(x) |--------------------- + 4cos(x) - 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +---------------------+ +--R | 2 +--R 3 2 | - 8cos(x) + 4 +--R (4cos(x) + 4cos(x) - 3cos(x) - 3) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 2 +-+ +--R (- 8\|2 cos(x) + 4\|2 )sin(x) +--R / +--R +---------------------+ +--R | 2 +--R +-+ 2 +-+ | - 8cos(x) + 4 3 +--R (2\|2 cos(x) + 2\|2 cos(x))sin(x) |--------------------- + 8cos(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - 6cos(x) +--R Type: Union(Expression(Integer),...) +--E 489 + +--S 490 of 526 +m0892:= a0892-r0892 +--R +--R +--R (4) +--R +---------------------+ +--R | 2 +--R +-+ 2 +-+ | - 8cos(x) + 4 +--R (- 2\|2 cos(x) - 2\|2 cos(x))sin(x) |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R - 8cos(x) + 6cos(x) +--R * +--R +---------------------+ +--R | 2 +--R 2 | - 8cos(x) + 4 +-+ +--R (cos(x) + cos(x)) |--------------------- - 2\|2 cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(----------------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R +-+ +-+ | - 8cos(x) + 4 2 +--R (\|2 cos(x) + \|2 )sin(x) |--------------------- + 4cos(x) - 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-------------+ +--R +-+ 2 +-+ | 2 +--R (- 2\|2 cos(x) - 2\|2 cos(x))sin(x)tan(x)\|- cot(x) + 1 +--R + +--R +-+ 2 +-+ 3 +--R (- 2\|2 cos(x) - 2\|2 cos(x))sin(x)asin(cot(x)) + 4cos(x) +--R + +--R 2 +--R 4cos(x) - 3cos(x) - 3 +--R * +--R +---------------------+ +--R | 2 +--R | - 8cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-------------+ +--R 3 | 2 +--R (- 8cos(x) + 6cos(x))tan(x)\|- cot(x) + 1 +--R + +--R 3 +-+ 2 +-+ +--R (- 8cos(x) + 6cos(x))asin(cot(x)) + (- 8\|2 cos(x) + 4\|2 )sin(x) +--R / +--R +---------------------+ +--R | 2 +--R +-+ 2 +-+ | - 8cos(x) + 4 3 +--R (2\|2 cos(x) + 2\|2 cos(x))sin(x) |--------------------- + 8cos(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R - 6cos(x) +--R Type: Expression(Integer) +--E 490 + +--S 491 of 526 +d0892:= D(m0892,x) +--R +--R +--R (5) +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R - 32\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) + 40\|2 cos(x) +--R + +--R +-+ +-+ +--R - 12\|2 cos(x) - 12\|2 +--R * +--R +-------------+ +--R 2 | 2 +--R sin(x) \|- cot(x) + 1 +--R + +--R 7 6 5 4 3 +--R 16cos(x) + 16cos(x) - 24cos(x) - 24cos(x) + 8cos(x) +--R + +--R 2 +--R 8cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 7 6 5 4 3 +--R - 16cos(x) - 16cos(x) + 24cos(x) + 24cos(x) - 8cos(x) +--R + +--R 2 +--R - 8cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R - 16cos(x) - 16cos(x) + 40cos(x) + 40cos(x) - 33cos(x) +--R + +--R 4 3 2 +--R - 33cos(x) + 9cos(x) + 9cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 9 8 7 6 5 +--R 16cos(x) + 16cos(x) - 40cos(x) - 40cos(x) + 33cos(x) +--R + +--R 4 3 2 +--R 33cos(x) - 9cos(x) - 9cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 7 6 5 4 +--R - 16cos(x) - 16cos(x) + 24cos(x) + 24cos(x) +--R + +--R 3 2 +--R - 8cos(x) - 8cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 7 6 5 4 +--R - 16cos(x) - 16cos(x) + 24cos(x) + 24cos(x) +--R + +--R 3 2 +--R - 8cos(x) - 8cos(x) +--R * +--R cot(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R 16cos(x) + 16cos(x) - 40cos(x) - 40cos(x) + 33cos(x) +--R + +--R 4 3 2 +--R 33cos(x) - 9cos(x) - 9cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 9 8 7 6 5 +--R 16cos(x) + 16cos(x) - 40cos(x) - 40cos(x) + 33cos(x) +--R + +--R 4 3 2 +--R 33cos(x) - 9cos(x) - 9cos(x) +--R * +--R cot(x) +--R * +--R tan(x) +--R + +--R 7 6 5 4 3 +--R 32cos(x) + 32cos(x) - 48cos(x) - 48cos(x) + 16cos(x) +--R + +--R 2 +--R 16cos(x) +--R * +--R 2 2 +--R cot(x) sin(x) +--R + +--R 9 8 7 6 5 +--R - 32cos(x) - 32cos(x) + 80cos(x) + 80cos(x) - 66cos(x) +--R + +--R 4 3 2 +--R - 66cos(x) + 18cos(x) + 18cos(x) +--R * +--R 2 +--R cot(x) +--R * +--R +---------------------+ +--R | 2 +--R | - 8cos(x) + 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 4 2 3 +--R (64cos(x) - 64cos(x) + 16)sin(x) +--R + +--R 6 4 2 +--R (- 64cos(x) + 128cos(x) - 84cos(x) + 18)sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) + 1 +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (64\|2 cos(x) - 144\|2 cos(x) + 104\|2 cos(x) - 24\|2 cos(x) ) +--R * +--R 2 +--R cot(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R - 64\|2 cos(x) + 144\|2 cos(x) - 104\|2 cos(x) + 24\|2 cos(x) +--R * +--R 2 +--R sin(x)tan(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (- 64\|2 cos(x) + 144\|2 cos(x) - 104\|2 cos(x) + 24\|2 cos(x) ) +--R * +--R 3 +--R cot(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (- 64\|2 cos(x) + 144\|2 cos(x) - 104\|2 cos(x) + 24\|2 cos(x) ) +--R * +--R cot(x) +--R * +--R sin(x)tan(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (128\|2 cos(x) - 288\|2 cos(x) + 208\|2 cos(x) - 48\|2 cos(x) ) +--R * +--R 2 +--R cot(x) sin(x) +--R / +--R 7 6 5 4 3 +--R 16cos(x) + 16cos(x) - 24cos(x) - 24cos(x) + 8cos(x) +--R + +--R 2 +--R 8cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 9 8 7 6 5 +--R - 16cos(x) - 16cos(x) + 40cos(x) + 40cos(x) - 33cos(x) +--R + +--R 4 3 2 +--R - 33cos(x) + 9cos(x) + 9cos(x) +--R * +--R +---------------------+ +--R +-------------+ | 2 +--R | 2 | - 8cos(x) + 4 +--R \|- cot(x) + 1 |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 8 +-+ 6 +-+ 4 +-+ 2 +--R (64\|2 cos(x) - 144\|2 cos(x) + 104\|2 cos(x) - 24\|2 cos(x) )sin(x) +--R * +--R +-------------+ +--R | 2 +--R \|- cot(x) + 1 +--R Type: Expression(Integer) +--E 491 + +)clear all + + +--S 492 of 526 +t0893:= sec(x)^2*(1-tan(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R 2 | 2 +--R (1) sec(x) \|- tan(x) + 1 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 526 +r0893:= 1/2*asin(tan(x))+1/2*tan(x)*(1-tan(x)^2)^(1/2) +--R +--R +--R +-------------+ +--R | 2 +--R tan(x)\|- tan(x) + 1 + asin(tan(x)) +--R (2) ------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 526 +a0893:= integrate(t0893,x) +--R +--R +--R (3) +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R (16\|2 cos(x) + 16\|2 cos(x) - 4\|2 cos(x) - 4\|2 cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 8cos(x) - 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 64cos(x) + 32cos(x) - 2cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 8cos(x) - 4 +-+ +--R (cos(x) + 1)sin(x) |--------------------- - 2\|2 cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(-----------------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R +-+ 2 +-+ | 8cos(x) - 4 2 +--R (\|2 cos(x) + \|2 cos(x)) |--------------------- - 4cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 5 4 3 2 +--R (32cos(x) + 32cos(x) - 16cos(x) - 16cos(x) + cos(x) + 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 8cos(x) - 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 64\|2 cos(x) + 48\|2 cos(x) - 8\|2 cos(x))sin(x) +--R / +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R (32\|2 cos(x) + 32\|2 cos(x) - 8\|2 cos(x) - 8\|2 cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 8cos(x) - 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 128cos(x) + 64cos(x) - 4cos(x) +--R Type: Union(Expression(Integer),...) +--E 494 + +--S 495 of 526 +m0893:= a0893-r0893 +--R +--R +--R (4) +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R (16\|2 cos(x) + 16\|2 cos(x) - 4\|2 cos(x) - 4\|2 cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 8cos(x) - 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 64cos(x) + 32cos(x) - 2cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 8cos(x) - 4 +-+ +--R (cos(x) + 1)sin(x) |--------------------- - 2\|2 cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R atan(-----------------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R +-+ 2 +-+ | 8cos(x) - 4 2 +--R (\|2 cos(x) + \|2 cos(x)) |--------------------- - 4cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R (- 16\|2 cos(x) - 16\|2 cos(x) + 4\|2 cos(x) + 4\|2 cos(x) ) +--R * +--R +-------------+ +--R | 2 +--R tan(x)\|- tan(x) + 1 +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R (- 16\|2 cos(x) - 16\|2 cos(x) + 4\|2 cos(x) + 4\|2 cos(x) ) +--R * +--R asin(tan(x)) +--R + +--R 5 4 3 2 +--R (32cos(x) + 32cos(x) - 16cos(x) - 16cos(x) + cos(x) + 1)sin(x) +--R * +--R +---------------------+ +--R | 2 +--R | 8cos(x) - 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-------------+ +--R 6 4 2 | 2 +--R (64cos(x) - 32cos(x) + 2cos(x) )tan(x)\|- tan(x) + 1 +--R + +--R 6 4 2 +--R (64cos(x) - 32cos(x) + 2cos(x) )asin(tan(x)) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 64\|2 cos(x) + 48\|2 cos(x) - 8\|2 cos(x))sin(x) +--R / +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R (32\|2 cos(x) + 32\|2 cos(x) - 8\|2 cos(x) - 8\|2 cos(x) ) +--R * +--R +---------------------+ +--R | 2 +--R | 8cos(x) - 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 6 4 2 +--R - 128cos(x) + 64cos(x) - 4cos(x) +--R Type: Expression(Integer) +--E 495 + +--S 496 of 526 +d0893:= D(m0893,x) +--R +--R +--R (5) +--R +-+ 10 +-+ 9 +-+ 8 +--R 1024\|2 cos(x) + 1024\|2 cos(x) - 1792\|2 cos(x) +--R + +--R +-+ 7 +-+ 6 +-+ 5 +--R - 1792\|2 cos(x) + 928\|2 cos(x) + 928\|2 cos(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +-+ +--R - 168\|2 cos(x) - 168\|2 cos(x) + 8\|2 cos(x) + 8\|2 cos(x) +--R * +--R 4 +--R sin(x) +--R + +--R +-+ 12 +-+ 11 +-+ 10 +--R 4096\|2 cos(x) + 4096\|2 cos(x) - 6656\|2 cos(x) +--R + +--R +-+ 9 +-+ 8 +-+ 7 +--R - 6656\|2 cos(x) + 4352\|2 cos(x) + 4352\|2 cos(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +--R - 1360\|2 cos(x) - 1360\|2 cos(x) + 188\|2 cos(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R 188\|2 cos(x) - 8\|2 cos(x) - 8\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 14 +-+ 13 +-+ 12 +--R 3072\|2 cos(x) + 3072\|2 cos(x) - 4864\|2 cos(x) +--R + +--R +-+ 11 +-+ 10 +-+ 9 +--R - 4864\|2 cos(x) + 2912\|2 cos(x) + 2912\|2 cos(x) +--R + +--R +-+ 8 +-+ 7 +-+ 6 +--R - 808\|2 cos(x) - 808\|2 cos(x) + 100\|2 cos(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R 100\|2 cos(x) - 4\|2 cos(x) - 4\|2 cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) + 1 +--R + +--R 12 11 10 9 +--R 2048cos(x) + 2048cos(x) - 2048cos(x) - 2048cos(x) +--R + +--R 8 7 6 5 4 +--R 640cos(x) + 640cos(x) - 64cos(x) - 64cos(x) + cos(x) +--R + +--R 3 +--R cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 14 13 12 11 +--R 4096cos(x) + 4096cos(x) - 6144cos(x) - 6144cos(x) +--R + +--R 10 9 8 7 6 +--R 3328cos(x) + 3328cos(x) - 768cos(x) - 768cos(x) + 66cos(x) +--R + +--R 5 4 3 +--R 66cos(x) - cos(x) - cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 12 11 10 9 +--R - 2048cos(x) - 2048cos(x) + 2048cos(x) + 2048cos(x) +--R + +--R 8 7 6 5 4 +--R - 640cos(x) - 640cos(x) + 64cos(x) + 64cos(x) - cos(x) +--R + +--R 3 +--R - cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 14 13 12 11 +--R - 4096cos(x) - 4096cos(x) + 6144cos(x) + 6144cos(x) +--R + +--R 10 9 8 7 6 +--R - 3328cos(x) - 3328cos(x) + 768cos(x) + 768cos(x) - 66cos(x) +--R + +--R 5 4 3 +--R - 66cos(x) + cos(x) + cos(x) +--R * +--R +---------------------+ +--R | 2 +--R | 8cos(x) - 4 +--R |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R 10 8 6 4 +--R - 4096cos(x) + 8192cos(x) - 5376cos(x) + 1408cos(x) +--R + +--R 2 +--R - 130cos(x) + 2 +--R * +--R 4 +--R sin(x) +--R + +--R 12 10 8 6 +--R - 16384cos(x) + 30720cos(x) - 23552cos(x) + 9088cos(x) +--R + +--R 4 2 +--R - 1736cos(x) + 135cos(x) - 2 +--R * +--R 2 +--R sin(x) +--R + +--R 14 12 10 8 +--R - 12288cos(x) + 22528cos(x) - 16128cos(x) + 5632cos(x) +--R + +--R 6 4 2 +--R - 966cos(x) + 69cos(x) - cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) + 1 +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 4096\|2 cos(x) + 5120\|2 cos(x) - 2176\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +--R 352\|2 cos(x) - 16\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 8192\|2 cos(x) + 14336\|2 cos(x) - 9472\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 2880\|2 cos(x) - 384\|2 cos(x) + 16\|2 cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R 4096\|2 cos(x) - 5120\|2 cos(x) + 2176\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +--R - 352\|2 cos(x) + 16\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +-+ 8 +--R 8192\|2 cos(x) - 14336\|2 cos(x) + 9472\|2 cos(x) - 2880\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +--R 384\|2 cos(x) - 16\|2 cos(x) +--R / +--R 12 11 10 9 +--R 2048cos(x) + 2048cos(x) - 2048cos(x) - 2048cos(x) +--R + +--R 8 7 6 5 4 3 +--R 640cos(x) + 640cos(x) - 64cos(x) - 64cos(x) + cos(x) + cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 14 13 12 11 +--R 4096cos(x) + 4096cos(x) - 6144cos(x) - 6144cos(x) +--R + +--R 10 9 8 7 6 +--R 3328cos(x) + 3328cos(x) - 768cos(x) - 768cos(x) + 66cos(x) +--R + +--R 5 4 3 +--R 66cos(x) - cos(x) - cos(x) +--R * +--R +---------------------+ +--R +-------------+ | 2 +--R | 2 | 8cos(x) - 4 +--R \|- tan(x) + 1 |--------------------- +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R + +--R +-+ 12 +-+ 10 +-+ 8 +--R - 4096\|2 cos(x) + 5120\|2 cos(x) - 2176\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +--R 352\|2 cos(x) - 16\|2 cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 14 +-+ 12 +-+ 10 +--R - 8192\|2 cos(x) + 14336\|2 cos(x) - 9472\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 2880\|2 cos(x) - 384\|2 cos(x) + 16\|2 cos(x) +--R * +--R +-------------+ +--R | 2 +--R \|- tan(x) + 1 +--R Type: Expression(Integer) +--E 496 + +)clear all + + +--S 497 of 526 +t0894:= csc(x)^2/(a+b*cot(x)) +--R +--R +--R 2 +--R csc(x) +--R (1) ------------ +--R b cot(x) + a +--R Type: Expression(Integer) +--E 497 + +--S 498 of 526 +r0894:= -log(a+b*cot(x))/b +--R +--R +--R log(b cot(x) + a) +--R (2) - ----------------- +--R b +--R Type: Expression(Integer) +--E 498 + +--S 499 of 526 +a0894:= integrate(t0894,x) +--R +--R +--R sin(x) - 2a sin(x) - 2b cos(x) +--R log(----------) - log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R (3) ---------------------------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 499 + +--S 500 of 526 +m0894:= a0894-r0894 +--R +--R +--R sin(x) - 2a sin(x) - 2b cos(x) +--R log(----------) + log(b cot(x) + a) - log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R (4) ------------------------------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 500 + +--S 501 of 526 +d0894:= D(m0894,x) +--R +--R +--R (5) +--R 2 2 2 +--R (- a cot(x) + b cot(x))sin(x) + (- b cos(x)cot(x) - b cos(x))sin(x) +--R + +--R 2 2 +--R b cos(x) cot(x) + a cos(x) +--R / +--R 2 2 2 +--R (a b cot(x) + a )sin(x) + (b cos(x)cot(x) + a b cos(x))sin(x) +--R Type: Expression(Integer) +--E 501 + +)clear all + + +--S 502 of 526 +t0895:= csc(x)^2*(a+b*cot(x))^n +--R +--R +--R 2 n +--R (1) csc(x) (b cot(x) + a) +--R Type: Expression(Integer) +--E 502 + +--S 503 of 526 +r0895:= -(a+b*cot(x))^(1+n)/b/(1+n) +--R +--R +--R n + 1 +--R (b cot(x) + a) +--R (2) - ------------------- +--R b n + b +--R Type: Expression(Integer) +--E 503 + +--S 504 of 526 +a0895:= integrate(t0895,x) +--R +--R +--R a sin(x) + b cos(x) +--R n log(-------------------) +--R sin(x) +--R (- a sin(x) - b cos(x))%e +--R (3) --------------------------------------------------- +--R (b n + b)sin(x) +--R Type: Union(Expression(Integer),...) +--E 504 + +--S 505 of 526 +m0895:= a0895-r0895 +--R +--R +--R (4) +--R a sin(x) + b cos(x) +--R n log(-------------------) +--R sin(x) +--R (- a sin(x) - b cos(x))%e +--R + +--R n + 1 +--R sin(x)(b cot(x) + a) +--R / +--R (b n + b)sin(x) +--R Type: Expression(Integer) +--E 505 + +--S 506 of 526 +d0895:= D(m0895,x) +--R +--R +--R (5) +--R a sin(x) + b cos(x) +--R n log(-------------------) +--R 2 2 sin(x) +--R (sin(x) + cos(x) )%e +--R + +--R 2 2 n +--R (- cot(x) - 1)sin(x) (b cot(x) + a) +--R / +--R 2 +--R sin(x) +--R Type: Expression(Integer) +--E 506 + +)clear all + + +--S 507 of 526 +t0896:= 2+cot(x)^2 +--R +--R +--R 2 +--R (1) cot(x) + 2 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 526 +r0896:= x-cot(x) +--R +--R +--R (2) - cot(x) + x +--R Type: Expression(Integer) +--E 508 + +--S 509 of 526 +a0896:= integrate(t0896,x) +--R +--R +--R x sin(2x) - cos(2x) - 1 +--R (3) ----------------------- +--R sin(2x) +--R Type: Union(Expression(Integer),...) +--E 509 + +--S 510 of 526 +m0896:= a0896-r0896 +--R +--R +--R cot(x)sin(2x) - cos(2x) - 1 +--R (4) --------------------------- +--R sin(2x) +--R Type: Expression(Integer) +--E 510 + +--S 511 of 526 +d0896:= D(m0896,x) +--R +--R +--R 2 2 2 +--R (- cot(x) + 1)sin(2x) + 2cos(2x) + 2cos(2x) +--R (5) ---------------------------------------------- +--R 2 +--R sin(2x) +--R Type: Expression(Integer) +--E 511 + +)clear all + + +--S 512 of 526 +t0897:= csc(x)^2*(a+b*cot(x))/(c+d*cot(x)) +--R +--R +--R 2 +--R (b cot(x) + a)csc(x) +--R (1) --------------------- +--R d cot(x) + c +--R Type: Expression(Integer) +--E 512 + +--S 513 of 526 +r0897:= -b*cot(x)/d+(b*c-a*d)*log(c+d*cot(x))/d^2 +--R +--R +--R (- a d + b c)log(d cot(x) + c) - b d cot(x) +--R (2) ------------------------------------------- +--R 2 +--R d +--R Type: Expression(Integer) +--E 513 + +--S 514 of 526 +a0897:= integrate(t0897,x) +--R +--R +--R (3) +--R sin(x) +--R (a d - b c)sin(x)log(----------) +--R cos(x) + 1 +--R + +--R - 2c sin(x) - 2d cos(x) +--R (- a d + b c)sin(x)log(-----------------------) - b d cos(x) +--R cos(x) + 1 +--R / +--R 2 +--R d sin(x) +--R Type: Union(Expression(Integer),...) +--E 514 + +--S 515 of 526 +m0897:= a0897-r0897 +--R +--R +--R (4) +--R sin(x) +--R (a d - b c)sin(x)log(----------) + (a d - b c)sin(x)log(d cot(x) + c) +--R cos(x) + 1 +--R + +--R - 2c sin(x) - 2d cos(x) +--R (- a d + b c)sin(x)log(-----------------------) + b d cot(x)sin(x) +--R cos(x) + 1 +--R + +--R - b d cos(x) +--R / +--R 2 +--R d sin(x) +--R Type: Expression(Integer) +--E 515 + +--S 516 of 526 +d0897:= D(m0897,x) +--R +--R +--R (5) +--R 3 2 3 +--R (- b c cot(x) - a c cot(x) + (a d - b c)cot(x))sin(x) +--R + +--R 3 2 2 +--R (- b d cos(x)cot(x) - a d cos(x)cot(x) + (- a d + b c)cos(x))sin(x) +--R + +--R 2 2 3 3 +--R (a d cos(x) cot(x) + a c cos(x) )sin(x) + b d cos(x) cot(x) + b c cos(x) +--R / +--R 2 3 2 2 +--R (c d cot(x) + c )sin(x) + (d cos(x)cot(x) + c d cos(x))sin(x) +--R Type: Expression(Integer) +--E 516 + +)clear all + + +--S 517 of 526 +t0898:= csc(x)^2*(a+b*cot(x))^2/(c+d*cot(x)) +--R +--R +--R 2 2 2 2 +--R (b cot(x) + 2a b cot(x) + a )csc(x) +--R (1) ------------------------------------- +--R d cot(x) + c +--R Type: Expression(Integer) +--E 517 + +--S 518 of 526 +r0898:= b*(b*c-a*d)*cot(x)/d^2-1/2*(a+b*cot(x))^2/d-_ + (b*c-a*d)^2*log(c+d*cot(x))/d^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 +--R (- 2a d + 4a b c d - 2b c )log(d cot(x) + c) - b d cot(x) +--R + +--R 2 2 2 2 +--R (- 4a b d + 2b c d)cot(x) - a d +--R / +--R 3 +--R 2d +--R Type: Expression(Integer) +--E 518 + +--S 519 of 526 +a0898:= integrate(t0898,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 2 2 2 +--R ((4a d - 8a b c d + 4b c )cos(x) - 4a d + 8a b c d - 4b c ) +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- 4a d + 8a b c d - 4b c )cos(x) + 4a d - 8a b c d + 4b c ) +--R * +--R - 2c sin(x) - 2d cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 2 2 +--R (8a b d - 4b c d)cos(x)sin(x) + b d cos(x) + b d +--R / +--R 3 2 3 +--R 4d cos(x) - 4d +--R Type: Union(Expression(Integer),...) +--E 519 + +--S 520 of 526 +m0898:= a0898-r0898 +--R +--R +--R (4) +--R 2 2 2 2 2 2 2 2 2 +--R ((4a d - 8a b c d + 4b c )cos(x) - 4a d + 8a b c d - 4b c ) +--R * +--R sin(x) +--R log(----------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((4a d - 8a b c d + 4b c )cos(x) - 4a d + 8a b c d - 4b c ) +--R * +--R log(d cot(x) + c) +--R + +--R 2 2 2 2 2 2 2 2 2 +--R ((- 4a d + 8a b c d - 4b c )cos(x) + 4a d - 8a b c d + 4b c ) +--R * +--R - 2c sin(x) - 2d cos(x) +--R log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 2 2 2 2 2 2 2 +--R (8a b d - 4b c d)cos(x)sin(x) + (2b d cos(x) - 2b d )cot(x) +--R + +--R 2 2 2 2 2 +--R ((8a b d - 4b c d)cos(x) - 8a b d + 4b c d)cot(x) +--R + +--R 2 2 2 2 2 2 2 +--R (b + 2a )d cos(x) + (b - 2a )d +--R / +--R 3 2 3 +--R 4d cos(x) - 4d +--R Type: Expression(Integer) +--E 520 + +--S 521 of 526 +d0898:= D(m0898,x) +--R +--R +--R (5) +--R 2 2 2 2 2 2 2 +--R ((2a b c d - b c d)cos(x) + 2a b c d - b c d)cot(x) +--R + +--R 2 2 3 2 2 2 3 +--R (2a b c d - b c )cos(x) + 2a b c d - b c +--R * +--R 4 +--R sin(x) +--R + +--R 3 2 2 3 3 +--R ((2a b d - b c d )cos(x) + 2a b d cos(x))cot(x) +--R + +--R 2 2 2 3 2 +--R (2a b c d - b c d)cos(x) + 2a b c d cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 2 2 4 2 2 2 2 2 4 +--R (- b c d cos(x) + 2b c d cos(x) - b c d )cot(x) +--R + +--R 2 4 2 2 2 3 +--R (- 2a b c d cos(x) + 4a b c d cos(x) - 2a b c d )cot(x) +--R + +--R 2 2 2 4 2 2 2 2 2 2 2 +--R ((- b - a )c d cos(x) + (2b + 2a )c d cos(x) + (- b - a )c d ) +--R * +--R 2 +--R cot(x) +--R + +--R 2 3 2 4 +--R (a d - 2a b c d )cos(x) +--R + +--R 2 2 3 2 2 2 2 2 3 2 +--R ((b - 2a )d + 6a b c d - b c d)cos(x) + a d - 4a b c d +--R + +--R 2 2 +--R b c d +--R * +--R cot(x) +--R + +--R 2 2 2 2 3 2 2 2 3 +--R (b c d + 2a b c d - b c )cos(x) - 2a b c d + b c +--R * +--R 2 +--R sin(x) +--R + +--R 2 3 5 2 3 3 2 3 4 +--R (- b d cos(x) + 2b d cos(x) - b d cos(x))cot(x) +--R + +--R 3 5 3 3 3 3 +--R (- 2a b d cos(x) + 4a b d cos(x) - 2a b d cos(x))cot(x) +--R + +--R 2 2 3 5 2 2 3 3 2 2 3 +--R ((- b - a )d cos(x) + (2b + 2a )d cos(x) + (- b - a )d cos(x)) +--R * +--R 2 +--R cot(x) +--R + +--R 2 2 5 3 2 2 3 3 +--R (- b c d cos(x) + (2a b d + b c d )cos(x) - 2a b d cos(x))cot(x) +--R + +--R 2 3 2 2 2 5 +--R (- a d + 2a b c d - b c d)cos(x) +--R + +--R 2 3 2 2 2 3 2 3 +--R (2a d - 2a b c d + b c d)cos(x) - a d cos(x) +--R * +--R sin(x) +--R + +--R 2 3 2 2 2 6 +--R (a d - 2a b c d + b c d)cos(x) +--R + +--R 2 3 2 2 2 4 +--R (- 2a d + 4a b c d - 2b c d)cos(x) +--R + +--R 2 3 2 2 2 2 +--R (a d - 2a b c d + b c d)cos(x) +--R * +--R cot(x) +--R + +--R 2 2 2 2 3 6 2 2 2 2 3 4 +--R (a c d - 2a b c d + b c )cos(x) + (- 2a c d + 4a b c d - 2b c )cos(x) +--R + +--R 2 2 2 2 3 2 +--R (a c d - 2a b c d + b c )cos(x) +--R / +--R 3 4 3 2 3 2 2 4 +--R (c d cos(x) - 2c d cos(x) + c d )cot(x) + c d cos(x) +--R + +--R 2 2 2 2 2 +--R - 2c d cos(x) + c d +--R * +--R 2 +--R sin(x) +--R + +--R 4 5 4 3 4 3 5 +--R (d cos(x) - 2d cos(x) + d cos(x))cot(x) + c d cos(x) +--R + +--R 3 3 3 +--R - 2c d cos(x) + c d cos(x) +--R * +--R sin(x) +--R Type: Expression(Integer) +--E 521 + +)clear all + + +--S 522 of 526 +t0899:= csc(x)^2*(a+b*cot(x))^3/(c+d*cot(x)) +--R +--R +--R 3 3 2 2 2 3 2 +--R (b cot(x) + 3a b cot(x) + 3a b cot(x) + a )csc(x) +--R (1) ---------------------------------------------------- +--R d cot(x) + c +--R Type: Expression(Integer) +--E 522 + +--S 523 of 526 +r0899:= -b*(b*c-a*d)^2*cot(x)/d^3+1/2*(b*c-a*d)*(a+b*cot(x))^2/d^2-_ + 1/3*(a+b*cot(x))^3/d+(b*c-a*d)^3*log(c+d*cot(x))/d^4 +--R +--R +--R (2) +--R 3 3 2 2 2 2 3 3 +--R (- 6a d + 18a b c d - 18a b c d + 6b c )log(d cot(x) + c) +--R + +--R 3 3 3 2 3 3 2 2 +--R - 2b d cot(x) + (- 9a b d + 3b c d )cot(x) +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 18a b d + 18a b c d - 6b c d)cot(x) - 5a d + 3a b c d +--R / +--R 4 +--R 6d +--R Type: Expression(Integer) +--E 523 + +--S 524 of 526 +a0899:= integrate(t0899,x) +--R +--R +--R (3) +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (12a d - 36a b c d + 36a b c d - 12b c )cos(x) - 12a d +--R + +--R 2 2 2 2 3 3 +--R 36a b c d - 36a b c d + 12b c +--R * +--R sin(x) +--R sin(x)log(----------) +--R cos(x) + 1 +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 12a d + 36a b c d - 36a b c d + 12b c )cos(x) + 12a d +--R + +--R 2 2 2 2 3 3 +--R - 36a b c d + 36a b c d - 12b c +--R * +--R - 2c sin(x) - 2d cos(x) +--R sin(x)log(-----------------------) +--R cos(x) + 1 +--R + +--R 2 3 3 2 2 2 3 3 2 +--R ((9a b d - 3b c d )cos(x) + 9a b d - 3b c d )sin(x) +--R + +--R 3 2 3 2 2 3 2 3 +--R ((4b - 36a b)d + 36a b c d - 12b c d)cos(x) +--R + +--R 2 3 2 2 3 2 +--R (36a b d - 36a b c d + 12b c d)cos(x) +--R / +--R 4 2 4 +--R (12d cos(x) - 12d )sin(x) +--R Type: Union(Expression(Integer),...) +--E 524 + +--S 525 of 526 +m0899:= a0899-r0899 +--R +--R +--R (4) +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (12a d - 36a b c d + 36a b c d - 12b c )cos(x) - 12a d +--R + +--R 2 2 2 2 3 3 +--R 36a b c d - 36a b c d + 12b c +--R * +--R sin(x) +--R sin(x)log(----------) +--R cos(x) + 1 +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (12a d - 36a b c d + 36a b c d - 12b c )cos(x) - 12a d +--R + +--R 2 2 2 2 3 3 +--R 36a b c d - 36a b c d + 12b c +--R * +--R sin(x)log(d cot(x) + c) +--R + +--R 3 3 2 2 2 2 3 3 2 3 3 +--R (- 12a d + 36a b c d - 36a b c d + 12b c )cos(x) + 12a d +--R + +--R 2 2 2 2 3 3 +--R - 36a b c d + 36a b c d - 12b c +--R * +--R - 2c sin(x) - 2d cos(x) +--R sin(x)log(-----------------------) +--R cos(x) + 1 +--R + +--R 3 3 2 3 3 3 +--R (4b d cos(x) - 4b d )cot(x) +--R + +--R 2 3 3 2 2 2 3 3 2 2 +--R ((18a b d - 6b c d )cos(x) - 18a b d + 6b c d )cot(x) +--R + +--R 2 3 2 2 3 2 2 2 3 2 2 +--R (36a b d - 36a b c d + 12b c d)cos(x) - 36a b d + 36a b c d +--R + +--R 3 2 +--R - 12b c d +--R * +--R cot(x) +--R + +--R 2 3 3 3 2 2 2 2 3 3 +--R ((9a b + 10a )d + (- 3b - 6a b)c d )cos(x) + (9a b - 10a )d +--R + +--R 3 2 2 +--R (- 3b + 6a b)c d +--R * +--R sin(x) +--R + +--R 3 2 3 2 2 3 2 3 +--R ((4b - 36a b)d + 36a b c d - 12b c d)cos(x) +--R + +--R 2 3 2 2 3 2 +--R (36a b d - 36a b c d + 12b c d)cos(x) +--R / +--R 4 2 4 +--R (12d cos(x) - 12d )sin(x) +--R Type: Expression(Integer) +--E 525 + +--S 526 of 526 +d0899:= D(m0899,x) +--R +--R +--R (5) +--R 2 2 3 2 2 2 3 3 4 +--R ((9a b c d - 3b c d)cos(x)cot(x) + (9a b c d - 3b c )cos(x))sin(x) +--R + +--R 3 2 4 3 2 2 3 2 5 +--R (- 3b c d cos(x) + 6b c d cos(x) - 3b c d )cot(x) +--R + +--R 2 2 4 2 2 2 2 2 4 +--R (- 9a b c d cos(x) + 18a b c d cos(x) - 9a b c d )cot(x) +--R + +--R 3 2 2 4 3 2 2 2 +--R (- 3b - 9a b)c d cos(x) + (6b + 18a b)c d cos(x) +--R + +--R 3 2 2 +--R (- 3b - 9a b)c d +--R * +--R 3 +--R cot(x) +--R + +--R 2 3 2 4 2 3 2 2 +--R (- 9a b - 3a )c d cos(x) + (18a b + 6a )c d cos(x) +--R + +--R 2 3 2 +--R (- 9a b - 3a )c d +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 3 2 2 4 +--R (3a d + (- b - 9a b)c d )cos(x) +--R + +--R 2 3 3 2 2 2 3 3 2 2 +--R ((9a b - 6a )d + 18a b c d )cos(x) + 3a d - 9a b c d +--R * +--R cot(x) +--R + +--R 3 2 4 2 2 2 +--R - b c d cos(x) + 9a b c d cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 3 3 5 3 3 3 3 3 5 +--R (- 3b d cos(x) + 6b d cos(x) - 3b d cos(x))cot(x) +--R + +--R 2 3 5 2 3 3 2 3 4 +--R (- 9a b d cos(x) + 18a b d cos(x) - 9a b d cos(x))cot(x) +--R + +--R 3 2 3 5 3 2 3 3 +--R (- 3b - 9a b)d cos(x) + (6b + 18a b)d cos(x) +--R + +--R 3 2 3 +--R (- 3b - 9a b)d cos(x) +--R * +--R 3 +--R cot(x) +--R + +--R 2 3 3 5 2 3 3 3 +--R (- 9a b - 3a )d cos(x) + (18a b + 6a )d cos(x) +--R + +--R 2 3 3 +--R (- 9a b - 3a )d cos(x) +--R * +--R 2 +--R cot(x) +--R + +--R 3 3 2 2 3 2 5 +--R (- b d - 9a b c d + 3b c d)cos(x) +--R + +--R 3 3 2 2 3 2 3 2 2 3 2 +--R (3b d + 18a b c d - 6b c d)cos(x) + (- 9a b c d + 3b c d)cos(x) +--R * +--R cot(x) +--R + +--R 3 3 3 2 2 2 2 3 3 5 +--R (- 3a d + (- b + 9a b)c d - 9a b c d + 3b c )cos(x) +--R + +--R 3 3 3 2 2 2 2 3 3 3 +--R (6a d + (3b - 18a b)c d + 18a b c d - 6b c )cos(x) +--R + +--R 3 3 2 2 2 2 3 3 +--R (- 3a d + 9a b c d - 9a b c d + 3b c )cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R 3 3 3 2 6 3 3 3 2 4 +--R (3a d - b c d )cos(x) + (- 6a d + b c d )cos(x) +--R + +--R 3 3 2 +--R 3a d cos(x) +--R * +--R cot(x) +--R + +--R 3 2 3 2 6 3 2 3 2 4 3 2 2 +--R (3a c d - b c d)cos(x) + (- 6a c d + b c d)cos(x) + 3a c d cos(x) +--R * +--R sin(x) +--R + +--R 3 2 3 2 2 3 2 7 +--R ((- b + 9a b)d - 9a b c d + 3b c d)cos(x) +--R + +--R 3 2 3 2 2 3 2 5 +--R ((b - 18a b)d + 18a b c d - 6b c d)cos(x) +--R + +--R 2 3 2 2 3 2 3 +--R (9a b d - 9a b c d + 3b c d)cos(x) +--R * +--R cot(x) +--R + +--R 3 2 2 2 2 3 3 7 +--R ((- b + 9a b)c d - 9a b c d + 3b c )cos(x) +--R + +--R 3 2 2 2 2 3 3 5 +--R ((b - 18a b)c d + 18a b c d - 6b c )cos(x) +--R + +--R 2 2 2 2 3 3 3 +--R (9a b c d - 9a b c d + 3b c )cos(x) +--R / +--R 3 4 3 2 3 2 2 4 +--R (3c d cos(x) - 6c d cos(x) + 3c d )cot(x) + 3c d cos(x) +--R + +--R 2 2 2 2 2 +--R - 6c d cos(x) + 3c d +--R * +--R 3 +--R sin(x) +--R + +--R 4 5 4 3 4 3 5 +--R (3d cos(x) - 6d cos(x) + 3d cos(x))cot(x) + 3c d cos(x) +--R + +--R 3 3 3 +--R - 6c d cos(x) + 3c d cos(x) +--R * +--R 2 +--R sin(x) +--R Type: Expression(Integer) +--E 526 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richtrig800-899.input.pdf b/src/axiom-website/CATS/richtrig800-899.input.pdf new file mode 100644 index 0000000..116c1aa Binary files /dev/null and b/src/axiom-website/CATS/richtrig800-899.input.pdf differ diff --git a/src/axiom-website/CATS/richtrig900-920.input.pamphlet b/src/axiom-website/CATS/richtrig900-920.input.pamphlet new file mode 100644 index 0000000..d55276b --- /dev/null +++ b/src/axiom-website/CATS/richtrig900-920.input.pamphlet @@ -0,0 +1,6036 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richtrig900-920.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richtrig900-920.output +)spool richtrig900-920.output +)set message auto off +)clear all + +--S 1 of 105 +t0900:= cot(x)^n*csc(x)^4 +--R +--R +--R 4 n +--R (1) csc(x) cot(x) +--R Type: Expression(Integer) +--E 1 + +--S 2 of 105 +r0900:= -cot(x)^(1+n)/(1+n)-cot(x)^(3+n)/(3+n) +--R +--R +--R n + 3 n + 1 +--R (- n - 1)cot(x) + (- n - 3)cot(x) +--R (2) ------------------------------------------- +--R 2 +--R n + 4n + 3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 105 +a0900:= integrate(t0900,x) +--R +--R +--R cos(x) +--R n log(------) +--R 3 sin(x) +--R (- 2cos(x) + (n + 3)cos(x))%e +--R (3) ------------------------------------------- +--R 2 2 2 +--R ((n + 4n + 3)cos(x) - n - 4n - 3)sin(x) +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 105 +m0900:= a0900-r0900 +--R +--R +--R (4) +--R cos(x) +--R n log(------) +--R 3 sin(x) +--R (- 2cos(x) + (n + 3)cos(x))%e +--R + +--R 2 n + 3 +--R ((n + 1)cos(x) - n - 1)sin(x)cot(x) +--R + +--R 2 n + 1 +--R ((n + 3)cos(x) - n - 3)sin(x)cot(x) +--R / +--R 2 2 2 +--R ((n + 4n + 3)cos(x) - n - 4n - 3)sin(x) +--R Type: Expression(Integer) +--E 4 + +--S 5 of 105 +d0900:= D(m0900,x) +--R +--R +--R (5) +--R 4 2 2 6 +--R (2cos(x) + (- n - 3)cos(x) + n + 3)sin(x) + 2cos(x) +--R + +--R 4 2 +--R (- n - 5)cos(x) + (n + 3)cos(x) +--R * +--R cos(x) +--R n log(------) +--R sin(x) +--R %e +--R + +--R 4 2 2 +--R ((- n - 3)cos(x) + (2n + 6)cos(x) - n - 3)cot(x) +--R + +--R 4 2 +--R (- n - 3)cos(x) + (2n + 6)cos(x) - n - 3 +--R * +--R 2 n + 2 +--R sin(x) cot(x) +--R + +--R 4 2 2 +--R ((- n - 3)cos(x) + (2n + 6)cos(x) - n - 3)cot(x) +--R + +--R 4 2 +--R (- n - 3)cos(x) + (2n + 6)cos(x) - n - 3 +--R * +--R 2 n +--R sin(x) cot(x) +--R / +--R 4 2 2 +--R ((n + 3)cos(x) + (- 2n - 6)cos(x) + n + 3)sin(x) +--R Type: Expression(Integer) +--E 5 + +--S 6 of 105 +t0901:= sec(x)*tan(x)/(sec(x)+sec(x)^2) +--R +--R +--R tan(x) +--R (6) ---------- +--R sec(x) + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 105 +r0901:= -log(cos(x)+1) +--R +--R +--R (7) - log(cos(x) + 1) +--R Type: Expression(Integer) +--E 7 + +--S 8 of 105 +a0901:= integrate(t0901,x) +--R +--R +--R 2 +--R (8) log(----------) +--R cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 105 +m0901:= a0901-r0901 +--R +--R +--R 2 +--R (9) log(cos(x) + 1) + log(----------) +--R cos(x) + 1 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 105 +d0901:= D(m0901,x) +--R +--R +--R (10) 0 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 105 +t0902:= cos(x)*sec(sin(x)) +--R +--R +--R (11) cos(x)sec(sin(x)) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 105 +r0902:= atanh(sin(sin(x))) +--R +--R +--R (12) atanh(sin(sin(x))) +--R Type: Expression(Integer) +--E 12 + +--S 13 of 105 +a0902:= integrate(t0902,x) +--R +--R +--R log(sin(sin(x)) + 1) - log(sin(sin(x)) - 1) +--R (13) ------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 105 +m0902:= a0902-r0902 +--R +--R +--R log(sin(sin(x)) + 1) - log(sin(sin(x)) - 1) - 2atanh(sin(sin(x))) +--R (14) ----------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 105 +d0902:= D(m0902,x) +--R +--R +--R (15) 0 +--R Type: Expression(Integer) +--E 15 + +--S 16 of 105 +t0903:= sec(x)*(1-sin(x)) +--R +--R +--R (16) - sec(x)sin(x) + sec(x) +--R Type: Expression(Integer) +--E 16 + +--S 17 of 105 +r0903:= log(1+sin(x)) +--R +--R +--R (17) log(sin(x) + 1) +--R Type: Expression(Integer) +--E 17 + +--S 18 of 105 +a0903:= integrate(t0903,x) +--R +--R +--R sin(x) + cos(x) + 1 2 +--R (18) 2log(-------------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 105 +m0903:= a0903-r0903 +--R +--R +--R sin(x) + cos(x) + 1 2 +--R (19) - log(sin(x) + 1) + 2log(-------------------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 105 +d0903:= D(m0903,x) +--R +--R +--R (20) +--R 3 2 2 3 +--R sin(x) - cos(x)sin(x) + (cos(x) - 1)sin(x) - cos(x) + cos(x) +--R --------------------------------------------------------------------------- +--R 2 2 2 +--R (cos(x) + 1)sin(x) + (cos(x) + 3cos(x) + 2)sin(x) + cos(x) + 2cos(x) + 1 +--R Type: Expression(Integer) +--E 20 + +--S 21 of 105 +t0904:= (cos(x)+1)*csc(x) +--R +--R +--R (21) (cos(x) + 1)csc(x) +--R Type: Expression(Integer) +--E 21 + +--S 22 of 105 +r0904:= log(1-cos(x)) +--R +--R +--R (22) log(- cos(x) + 1) +--R Type: Expression(Integer) +--E 22 + +--S 23 of 105 +a0904:= integrate(t0904,x) +--R +--R +--R sin(x) 2 +--R (23) 2log(----------) - log(----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 105 +m0904:= a0904-r0904 +--R +--R +--R sin(x) 2 +--R (24) 2log(----------) - log(----------) - log(- cos(x) + 1) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 105 +d0904:= D(m0904,x) +--R +--R +--R 2 3 +--R 2cos(x)sin(x) + 2cos(x) - 2cos(x) +--R (25) ----------------------------------- +--R 2 +--R (cos(x) - 1)sin(x) +--R Type: Expression(Integer) +--E 25 + +--S 26 of 105 +t0905:= csc(2*x)*(cos(x)+sin(x)) +--R +--R +--R (26) csc(2x)sin(x) + cos(x)csc(2x) +--R Type: Expression(Integer) +--E 26 + +--S 27 of 105 +r0905:= -1/2*atanh(cos(x))+1/2*atanh(sin(x)) +--R +--R +--R atanh(sin(x)) - atanh(cos(x)) +--R (27) ----------------------------- +--R 2 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 105 +a0905:= integrate(t0905,x) +--R +--R +--R sin(x) - cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R (28) --------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 105 +m0905:= a0905-r0905 +--R +--R +--R (29) +--R sin(x) - cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R + +--R atanh(cos(x)) +--R / +--R 2 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 105 +d0905:= D(m0905,x) +--R +--R +--R (30) +--R 5 4 2 3 3 2 +--R sin(x) - 2cos(x)sin(x) - cos(x) sin(x) + (- cos(x) + 3cos(x))sin(x) +--R + +--R 4 2 5 +--R (- 2cos(x) + 3cos(x) - 1)sin(x) + cos(x) - cos(x) +--R / +--R 2 4 3 3 +--R (2cos(x) - 2)sin(x) + (- 4cos(x) + 4cos(x))sin(x) +--R + +--R 4 2 2 3 4 +--R (2cos(x) - 6cos(x) + 4)sin(x) + (4cos(x) - 4cos(x))sin(x) - 2cos(x) +--R + +--R 2 +--R 4cos(x) - 2 +--R Type: Expression(Integer) +--E 30 + +--S 31 of 105 +t0906:= 2*cot(2*x)-3*sin(3*x) +--R +--R +--R (31) - 3sin(3x) + 2cot(2x) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 105 +r0906:= cos(3*x)+log(sin(2*x)) +--R +--R +--R (32) log(sin(2x)) + cos(3x) +--R Type: Expression(Integer) +--E 32 + +--S 33 of 105 +a0906:= integrate(t0906,x) +--R +--R +--R (33) +--R 2 2cos(x)sin(x) 3 +--R - 2log(----------) + log(- ---------------------) + 4cos(x) - 3cos(x) +--R cos(x) + 1 2 +--R cos(x) + 2cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 105 +m0906:= a0906-r0906 +--R +--R +--R (34) +--R 2 2cos(x)sin(x) +--R - log(sin(2x)) - 2log(----------) + log(- ---------------------) - cos(3x) +--R cos(x) + 1 2 +--R cos(x) + 2cos(x) + 1 +--R + +--R 3 +--R 4cos(x) - 3cos(x) +--R Type: Expression(Integer) +--E 34 + +--S 35 of 105 +d0906:= D(m0906,x) +--R +--R +--R (35) +--R 3cos(x)sin(x)sin(2x)sin(3x) +--R + +--R 3 2 2 +--R ((- 12cos(x) + 3cos(x) - 1)sin(x) + cos(x) )sin(2x) +--R + +--R - 2cos(x)cos(2x)sin(x) +--R / +--R cos(x)sin(x)sin(2x) +--R Type: Expression(Integer) +--E 35 + +--S 36 of 105 +t0907:= x*sec(-5+x^2) +--R +--R +--R 2 +--R (36) x sec(x - 5) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 105 +r0907:= 1/2*atanh(sin(-5+x^2)) +--R +--R +--R 2 +--R atanh(sin(x - 5)) +--R (37) ------------------ +--R 2 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 105 +a0907:= integrate(t0907,x) +--R +--R +--R (38) +--R 2 2 2 2 +--R sin(x - 5) + cos(x - 5) + 1 sin(x - 5) - cos(x - 5) - 1 +--R log(-----------------------------) - log(-----------------------------) +--R 2 2 +--R cos(x - 5) + 1 cos(x - 5) + 1 +--R ----------------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 105 +m0907:= a0907-r0907 +--R +--R +--R (39) +--R 2 2 2 2 +--R sin(x - 5) + cos(x - 5) + 1 sin(x - 5) - cos(x - 5) - 1 +--R log(-----------------------------) - log(-----------------------------) +--R 2 2 +--R cos(x - 5) + 1 cos(x - 5) + 1 +--R + +--R 2 +--R - atanh(sin(x - 5)) +--R / +--R 2 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 105 +d0907:= D(m0907,x) +--R +--R +--R (40) +--R 2 4 2 2 2 2 2 +--R - 2x sin(x - 5) + (- 2x cos(x - 5) - x cos(x - 5) + 2x)sin(x - 5) +--R + +--R 2 3 2 +--R - x cos(x - 5) + x cos(x - 5) +--R / +--R 2 4 2 2 2 2 2 +--R sin(x - 5) + (- cos(x - 5) - 2cos(x - 5) - 2)sin(x - 5) +--R + +--R 2 2 2 +--R cos(x - 5) + 2cos(x - 5) + 1 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 105 +t0908:= csc(1/x)/x^2 +--R +--R +--R 1 +--R csc(-) +--R x +--R (41) ------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 105 +r0908:= atanh(cos(1/x)) +--R +--R +--R 1 +--R (42) atanh(cos(-)) +--R x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 105 +a0908:= integrate(t0908,x) +--R +--R +--R 1 +--R sin(-) +--R x +--R (43) - log(----------) +--R 1 +--R cos(-) + 1 +--R x +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 105 +m0908:= a0908-r0908 +--R +--R +--R 1 +--R sin(-) +--R x 1 +--R (44) - log(----------) - atanh(cos(-)) +--R 1 x +--R cos(-) + 1 +--R x +--R Type: Expression(Integer) +--E 44 + +--S 45 of 105 +d0908:= D(m0908,x) +--R +--R +--R 1 1 2 1 3 1 +--R cos(-)sin(-) + cos(-) - cos(-) +--R x x x x +--R (45) -------------------------------- +--R 2 1 2 2 1 +--R (x cos(-) - x )sin(-) +--R x x +--R Type: Expression(Integer) +--E 45 + +--S 46 of 105 +t0909:= cos(x)/(-sin(x)+sin(x)^3) +--R +--R +--R cos(x) +--R (46) ---------------- +--R 3 +--R sin(x) - sin(x) +--R Type: Expression(Integer) +--E 46 + +--S 47 of 105 +r0909:= -log(tan(x)) +--R +--R +--R (47) - log(tan(x)) +--R Type: Expression(Integer) +--E 47 + +--S 48 of 105 +a0909:= integrate(t0909,x) +--R +--R +--R sin(x) 2cos(x) +--R (48) - log(----------) + log(- ----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 105 +m0909:= a0909-r0909 +--R +--R +--R sin(x) 2cos(x) +--R (49) log(tan(x)) - log(----------) + log(- ----------) +--R cos(x) + 1 cos(x) + 1 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 105 +d0909:= D(m0909,x) +--R +--R +--R 2 2 2 +--R cos(x)sin(x)tan(x) + (- sin(x) - cos(x) )tan(x) + cos(x)sin(x) +--R (50) ---------------------------------------------------------------- +--R cos(x)sin(x)tan(x) +--R Type: Expression(Integer) +--E 50 + +--S 51 of 105 +t0910:= 1/(4+3*cos(x)+4*sin(x)) +--R +--R +--R 1 +--R (51) --------------------- +--R 4sin(x) + 3cos(x) + 4 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 105 +r0910:= -2/3*atanh(4/3+1/3*tan(1/2*x)) +--R +--R +--R x +--R tan(-) + 4 +--R 2 +--R 2atanh(----------) +--R 3 +--R (52) - ------------------ +--R 3 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 105 +a0910:= integrate(t0910,x) +--R +--R +--R sin(x) + 7cos(x) + 7 sin(x) + cos(x) + 1 +--R - log(--------------------) + log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R (53) ------------------------------------------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 105 +m0910:= a0910-r0910 +--R +--R +--R (54) +--R x +--R tan(-) + 4 +--R sin(x) + 7cos(x) + 7 sin(x) + cos(x) + 1 2 +--R - log(--------------------) + log(-------------------) + 2atanh(----------) +--R cos(x) + 1 cos(x) + 1 3 +--R --------------------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 105 +d0910:= D(m0910,x) +--R +--R +--R (55) +--R 2 2 x 2 +--R (sin(x) + (- 8cos(x) - 8)sin(x) - 5cos(x) - 12cos(x) - 7)tan(-) +--R 2 +--R + +--R 2 2 x 2 +--R (16sin(x) + 16cos(x) + 16cos(x))tan(-) + 13sin(x) +--R 2 +--R + +--R 2 +--R (- 8cos(x) - 8)sin(x) + 7cos(x) - 7 +--R / +--R 2 2 x 2 +--R (sin(x) + (8cos(x) + 8)sin(x) + 7cos(x) + 14cos(x) + 7)tan(-) +--R 2 +--R + +--R 2 2 x +--R (8sin(x) + (64cos(x) + 64)sin(x) + 56cos(x) + 112cos(x) + 56)tan(-) +--R 2 +--R + +--R 2 2 +--R 7sin(x) + (56cos(x) + 56)sin(x) + 49cos(x) + 98cos(x) + 49 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 105 +t0911:= (sin(x)-cos(x))*(cos(x)+sin(x))^5 +--R +--R +--R (56) +--R 6 5 2 4 4 2 +--R sin(x) + 4cos(x)sin(x) + 5cos(x) sin(x) - 5cos(x) sin(x) +--R + +--R 5 6 +--R - 4cos(x) sin(x) - cos(x) +--R Type: Expression(Integer) +--E 56 + +--S 57 of 105 +r0911:= -1/6*(cos(x)+sin(x))^6 +--R +--R +--R (57) +--R 6 5 2 4 3 3 +--R - sin(x) - 6cos(x)sin(x) - 15cos(x) sin(x) - 20cos(x) sin(x) +--R + +--R 4 2 5 6 +--R - 15cos(x) sin(x) - 6cos(x) sin(x) - cos(x) +--R / +--R 6 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 105 +a0911:= integrate(t0911,x) +--R +--R +--R 5 3 4 2 +--R (4cos(x) - 4cos(x) - 3cos(x))sin(x) + 6cos(x) - 6cos(x) +--R (58) ----------------------------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 105 +m0911:= a0911-r0911 +--R +--R +--R (59) +--R 6 5 2 4 3 3 +--R sin(x) + 6cos(x)sin(x) + 15cos(x) sin(x) + 20cos(x) sin(x) +--R + +--R 4 2 5 3 6 +--R 15cos(x) sin(x) + (14cos(x) - 8cos(x) - 6cos(x))sin(x) + cos(x) +--R + +--R 4 2 +--R 12cos(x) - 12cos(x) +--R / +--R 6 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 105 +d0911:= D(m0911,x) +--R +--R +--R (60) +--R 6 5 2 4 +--R - 3sin(x) - 12cos(x)sin(x) - 15cos(x) sin(x) +--R + +--R 4 2 2 +--R (- 5cos(x) + 12cos(x) + 3)sin(x) +--R + +--R 5 3 6 4 2 +--R (12cos(x) - 24cos(x) + 12cos(x))sin(x) + 7cos(x) - 4cos(x) - 3cos(x) +--R / +--R 3 +--R Type: Expression(Integer) +--E 60 + +--S 61 of 105 +t0912:= sin(x)/(cos(x)^3-cos(x)^5) +--R +--R +--R sin(x) +--R (61) - ----------------- +--R 5 3 +--R cos(x) - cos(x) +--R Type: Expression(Integer) +--E 61 + +--S 62 of 105 +r0912:= log(tan(x))+1/2*tan(x)^2 +--R +--R +--R 2 +--R 2log(tan(x)) + tan(x) +--R (62) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 105 +a0912:= integrate(t0912,x) +--R +--R +--R 2 sin(x) 2 2cos(x) 2 +--R 2cos(x) log(----------) - 2cos(x) log(- ----------) - cos(x) + 1 +--R cos(x) + 1 cos(x) + 1 +--R (63) ----------------------------------------------------------------- +--R 2 +--R 2cos(x) +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 105 +m0912:= a0912-r0912 +--R +--R +--R (64) +--R 2 2 sin(x) +--R - 2cos(x) log(tan(x)) + 2cos(x) log(----------) +--R cos(x) + 1 +--R + +--R 2 2cos(x) 2 2 2 +--R - 2cos(x) log(- ----------) - cos(x) tan(x) - cos(x) + 1 +--R cos(x) + 1 +--R / +--R 2 +--R 2cos(x) +--R Type: Expression(Integer) +--E 64 + +--S 65 of 105 +d0912:= D(m0912,x) +--R +--R +--R (65) +--R 3 4 3 2 +--R - cos(x) sin(x)tan(x) - 2cos(x) sin(x)tan(x) +--R + +--R 2 2 4 3 +--R ((cos(x) + 1)sin(x) + cos(x) )tan(x) - cos(x) sin(x) +--R / +--R 3 +--R cos(x) sin(x)tan(x) +--R Type: Expression(Integer) +--E 65 + +--S 66 of 105 +t0913:= sin(x)*tan(x)^5 +--R +--R +--R 5 +--R (66) sin(x)tan(x) +--R Type: Expression(Integer) +--E 66 + +--S 67 of 105 +r0913:= 15/8*atanh(sin(x))-15/8*sin(x)-5/8*sin(x)*tan(x)^2+1/4*sin(x)*tan(x)^4 +--R +--R +--R 4 2 +--R 15atanh(sin(x)) + 2sin(x)tan(x) - 5sin(x)tan(x) - 15sin(x) +--R (67) ------------------------------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 105 +a0913:= integrate(t0913,x) +--R +--R +--R (68) +--R 4 sin(x) + cos(x) + 1 4 sin(x) - cos(x) - 1 +--R 15cos(x) log(-------------------) - 15cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 4 2 +--R (- 8cos(x) - 9cos(x) + 2)sin(x) +--R / +--R 4 +--R 8cos(x) +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 105 +m0913:= a0913-r0913 +--R +--R +--R (69) +--R 4 sin(x) + cos(x) + 1 4 sin(x) - cos(x) - 1 +--R 15cos(x) log(-------------------) - 15cos(x) log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R 4 4 4 4 2 +--R - 15cos(x) atanh(sin(x)) - 2cos(x) sin(x)tan(x) + 5cos(x) sin(x)tan(x) +--R + +--R 4 2 +--R (7cos(x) - 9cos(x) + 2)sin(x) +--R / +--R 4 +--R 8cos(x) +--R Type: Expression(Integer) +--E 69 + +--S 70 of 105 +d0913:= D(m0913,x) +--R +--R +--R (70) +--R 5 5 7 6 5 3 +--R - 8cos(x) sin(x) + (8cos(x) + 16cos(x) + 16cos(x) )sin(x) +--R + +--R 7 6 5 +--R (- 8cos(x) - 16cos(x) - 8cos(x) )sin(x) +--R * +--R 5 +--R tan(x) +--R + +--R 6 4 8 7 6 2 +--R - 2cos(x) sin(x) + (2cos(x) + 4cos(x) + 4cos(x) )sin(x) +--R + +--R 8 7 6 +--R - 2cos(x) - 4cos(x) - 2cos(x) +--R * +--R 4 +--R tan(x) +--R + +--R 5 5 7 6 5 3 +--R 2cos(x) sin(x) + (- 2cos(x) - 4cos(x) - 4cos(x) )sin(x) +--R + +--R 7 6 5 +--R (2cos(x) + 4cos(x) + 2cos(x) )sin(x) +--R * +--R 3 +--R tan(x) +--R + +--R 6 4 8 7 6 2 +--R 5cos(x) sin(x) + (- 5cos(x) - 10cos(x) - 10cos(x) )sin(x) +--R + +--R 8 7 6 +--R 5cos(x) + 10cos(x) + 5cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R 5 5 7 6 5 3 +--R 10cos(x) sin(x) + (- 10cos(x) - 20cos(x) - 20cos(x) )sin(x) +--R + +--R 7 6 5 +--R (10cos(x) + 20cos(x) + 10cos(x) )sin(x) +--R * +--R tan(x) +--R + +--R 2 6 +--R (- 18cos(x) + 8)sin(x) +--R + +--R 6 5 4 3 2 +--R 7cos(x) - 30cos(x) + 9cos(x) + 36cos(x) + 30cos(x) - 16cos(x) +--R + +--R - 16 +--R * +--R 4 +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 7cos(x) - 44cos(x) - 20cos(x) + 48cos(x) - 2cos(x) - 40cos(x) +--R + +--R 2 +--R - 14cos(x) + 16cos(x) + 8 +--R * +--R 2 +--R sin(x) +--R + +--R 8 7 6 5 4 3 +--R - 8cos(x) + 14cos(x) + 13cos(x) - 18cos(x) - 7cos(x) + 4cos(x) +--R + +--R 2 +--R 2cos(x) +--R / +--R 5 4 7 6 5 2 7 +--R 8cos(x) sin(x) + (- 8cos(x) - 16cos(x) - 16cos(x) )sin(x) + 8cos(x) +--R + +--R 6 5 +--R 16cos(x) + 8cos(x) +--R Type: Expression(Integer) +--E 70 + +--S 71 of 105 +t0914:= sec(x)*tan(x)^2/(4+3*sec(x)) +--R +--R +--R 2 +--R sec(x)tan(x) +--R (71) ------------- +--R 3sec(x) + 4 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 105 +r0914:= -4/9*atanh(sin(x))+2/9*7^(1/2)*atanh(1/7*tan(1/2*x)*7^(1/2))+1/3*tan(x) +--R +--R +--R +-+ x +--R \|7 tan(-) +--R +-+ 2 +--R 2\|7 atanh(----------) - 4atanh(sin(x)) + 3tan(x) +--R 7 +--R (72) ------------------------------------------------- +--R 9 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 105 +a0914:= integrate(t0914,x) +--R +--R +--R (73) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - 4cos(x)log(-------------------) + 4cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-+ +--R +-+ - \|7 sin(x) - 3cos(x) - 4 +--R \|7 cos(x)log(--------------------------) + 3sin(x) +--R 4cos(x) + 3 +--R / +--R 9cos(x) +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 105 +m0914:= a0914-r0914 +--R +--R +--R (74) +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R - 4cos(x)log(-------------------) + 4cos(x)log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R + +--R +-+ x +--R +-+ \|7 tan(-) +--R +-+ - \|7 sin(x) - 3cos(x) - 4 +-+ 2 +--R \|7 cos(x)log(--------------------------) - 2\|7 cos(x)atanh(----------) +--R 4cos(x) + 3 7 +--R + +--R 4cos(x)atanh(sin(x)) - 3cos(x)tan(x) + 3sin(x) +--R / +--R 9cos(x) +--R Type: Expression(Integer) +--E 74 + +--S 75 of 105 +d0914:= D(m0914,x) +--R +--R +--R (75) +--R +-+ 3 +-+ 2 5 +--R (- 12\|7 cos(x) - 9\|7 cos(x) )sin(x) +--R + +--R 4 3 2 4 +--R (- 36cos(x) - 75cos(x) - 36cos(x) )sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (12\|7 cos(x) + 33\|7 cos(x) + 42\|7 cos(x) + 18\|7 cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (36cos(x) + 147cos(x) + 258cos(x) + 222cos(x) + 72cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 12\|7 cos(x) - 33\|7 cos(x) - 30\|7 cos(x) +--R + +--R +-+ 2 +--R - 9\|7 cos(x) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 36cos(x) - 147cos(x) - 222cos(x) - 147cos(x) - 36cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R +-+ 3 +-+ 2 5 +--R (84\|7 cos(x) + 63\|7 cos(x) )sin(x) +--R + +--R 4 3 2 4 +--R (252cos(x) + 525cos(x) + 252cos(x) )sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +--R - 84\|7 cos(x) - 231\|7 cos(x) - 294\|7 cos(x) +--R + +--R +-+ 2 +--R - 126\|7 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 +--R - 252cos(x) - 1029cos(x) - 1806cos(x) - 1554cos(x) +--R + +--R 2 +--R - 504cos(x) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (84\|7 cos(x) + 231\|7 cos(x) + 210\|7 cos(x) + 63\|7 cos(x) ) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R 252cos(x) + 1029cos(x) + 1554cos(x) + 1029cos(x) + 252cos(x) +--R * +--R 2 +--R tan(x) +--R + +--R +-+ +-+ 7 2 6 +--R (12\|7 cos(x) + 9\|7 )sin(x) + (64cos(x) + 75cos(x) + 36)sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ 5 +--R (48\|7 cos(x) + 19\|7 cos(x) - 42\|7 cos(x) - 18\|7 )sin(x) +--R + +--R 4 3 2 4 +--R (144cos(x) + 193cos(x) - 134cos(x) - 222cos(x) - 72)sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R 4\|7 cos(x) - 44\|7 cos(x) - 120\|7 cos(x) - 47\|7 cos(x) +--R + +--R +-+ +-+ +--R 30\|7 cos(x) + 9\|7 +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 16cos(x) - 172cos(x) - 536cos(x) - 509cos(x) - 14cos(x) +--R + +--R 147cos(x) + 36 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R 16\|7 cos(x) + 40\|7 cos(x) + 68\|7 cos(x) + 72\|7 cos(x) +--R + +--R +-+ 2 +--R 28\|7 cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R 48cos(x) + 212cos(x) + 420cos(x) + 488cos(x) + 316cos(x) +--R + +--R 2 +--R 84cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R +-+ +-+ 7 +--R (- 84\|7 cos(x) - 63\|7 )sin(x) +--R + +--R 2 6 +--R (- 448cos(x) - 525cos(x) - 252)sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +-+ 5 +--R (- 112\|7 cos(x) + 35\|7 cos(x) + 294\|7 cos(x) + 126\|7 )sin(x) +--R + +--R 4 3 2 4 +--R (- 336cos(x) + 49cos(x) + 1610cos(x) + 1554cos(x) + 504)sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R - 252\|7 cos(x) - 308\|7 cos(x) + 56\|7 cos(x) - 7\|7 cos(x) +--R + +--R +-+ +-+ +--R - 210\|7 cos(x) - 63\|7 +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 560cos(x) - 1540cos(x) - 1064cos(x) - 581cos(x) - 1246cos(x) +--R + +--R - 1029cos(x) - 252 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 6 +-+ 5 +-+ 4 +-+ 3 +--R - 112\|7 cos(x) - 56\|7 cos(x) + 140\|7 cos(x) + 56\|7 cos(x) +--R + +--R +-+ 2 +--R - 28\|7 cos(x) +--R * +--R sin(x) +--R + +--R 7 6 5 4 3 +--R - 336cos(x) - 812cos(x) - 196cos(x) + 728cos(x) + 532cos(x) +--R + +--R 2 +--R 84cos(x) +--R / +--R +-+ 3 +-+ 2 5 +--R (36\|7 cos(x) + 27\|7 cos(x) )sin(x) +--R + +--R 4 3 2 4 +--R (108cos(x) + 225cos(x) + 108cos(x) )sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (- 36\|7 cos(x) - 99\|7 cos(x) - 126\|7 cos(x) - 54\|7 cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (- 108cos(x) - 441cos(x) - 774cos(x) - 666cos(x) - 216cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (36\|7 cos(x) + 99\|7 cos(x) + 90\|7 cos(x) + 27\|7 cos(x) )sin(x) +--R + +--R 6 5 4 3 2 +--R 108cos(x) + 441cos(x) + 666cos(x) + 441cos(x) + 108cos(x) +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R +-+ 3 +-+ 2 5 +--R (- 252\|7 cos(x) - 189\|7 cos(x) )sin(x) +--R + +--R 4 3 2 4 +--R (- 756cos(x) - 1575cos(x) - 756cos(x) )sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (252\|7 cos(x) + 693\|7 cos(x) + 882\|7 cos(x) + 378\|7 cos(x) ) +--R * +--R 3 +--R sin(x) +--R + +--R 6 5 4 3 2 +--R (756cos(x) + 3087cos(x) + 5418cos(x) + 4662cos(x) + 1512cos(x) ) +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 5 +-+ 4 +-+ 3 +-+ 2 +--R (- 252\|7 cos(x) - 693\|7 cos(x) - 630\|7 cos(x) - 189\|7 cos(x) ) +--R * +--R sin(x) +--R + +--R 6 5 4 3 2 +--R - 756cos(x) - 3087cos(x) - 4662cos(x) - 3087cos(x) - 756cos(x) +--R Type: Expression(Integer) +--E 75 + +--S 76 of 105 +t0915:= x*sec(1+x)*tan(1+x) +--R +--R +--R (76) x sec(x + 1)tan(x + 1) +--R Type: Expression(Integer) +--E 76 + +--S 77 of 105 +r0915:= -atanh(sin(1+x))+x*sec(1+x) +--R +--R +--R (77) - atanh(sin(x + 1)) + x sec(x + 1) +--R Type: Expression(Integer) +--E 77 + +--S 78 of 105 +a0915:= integrate(t0915,x) +--R +--R +--R (78) +--R sin(x + 1) + cos(x + 1) + 1 +--R - cos(x + 1)log(---------------------------) +--R cos(x + 1) + 1 +--R + +--R sin(x + 1) - cos(x + 1) - 1 +--R cos(x + 1)log(---------------------------) + x +--R cos(x + 1) + 1 +--R / +--R cos(x + 1) +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 105 +m0915:= a0915-r0915 +--R +--R +--R (79) +--R sin(x + 1) + cos(x + 1) + 1 +--R - cos(x + 1)log(---------------------------) +--R cos(x + 1) + 1 +--R + +--R sin(x + 1) - cos(x + 1) - 1 +--R cos(x + 1)log(---------------------------) + cos(x + 1)atanh(sin(x + 1)) +--R cos(x + 1) + 1 +--R + +--R - x cos(x + 1)sec(x + 1) + x +--R / +--R cos(x + 1) +--R Type: Expression(Integer) +--E 79 + +--S 80 of 105 +d0915:= D(m0915,x) +--R +--R +--R (80) +--R 2 4 +--R - x cos(x + 1) sec(x + 1)sin(x + 1) +--R + +--R 4 3 2 +--R (x cos(x + 1) + 2x cos(x + 1) + 2x cos(x + 1) )sec(x + 1) +--R * +--R 2 +--R sin(x + 1) +--R + +--R 4 3 2 +--R (- x cos(x + 1) - 2x cos(x + 1) - x cos(x + 1) )sec(x + 1) +--R * +--R tan(x + 1) +--R + +--R 5 +--R x sin(x + 1) +--R + +--R 2 2 4 +--R (- cos(x + 1) sec(x + 1) + 2cos(x + 1) + cos(x + 1))sin(x + 1) +--R + +--R 2 3 +--R (- x cos(x + 1) - 2x cos(x + 1) - 2x)sin(x + 1) +--R + +--R 4 3 2 4 +--R (cos(x + 1) + 2cos(x + 1) + 2cos(x + 1) )sec(x + 1) + 2cos(x + 1) +--R + +--R 2 +--R - 4cos(x + 1) - 2cos(x + 1) +--R * +--R 2 +--R sin(x + 1) +--R + +--R 2 +--R (x cos(x + 1) + 2x cos(x + 1) + x)sin(x + 1) +--R + +--R 4 3 2 5 +--R (- cos(x + 1) - 2cos(x + 1) - cos(x + 1) )sec(x + 1) + cos(x + 1) +--R + +--R 2 +--R 2cos(x + 1) + cos(x + 1) +--R / +--R 2 4 +--R cos(x + 1) sin(x + 1) +--R + +--R 4 3 2 2 4 +--R (- cos(x + 1) - 2cos(x + 1) - 2cos(x + 1) )sin(x + 1) + cos(x + 1) +--R + +--R 3 2 +--R 2cos(x + 1) + cos(x + 1) +--R Type: Expression(Integer) +--E 80 + +--S 81 of 105 +t0916:= cos(x)/(sin(x)+sin(x)^(2^(1/2))) +--R +--R +--R cos(x) +--R (81) ------------------- +--R +-+ +--R \|2 +--R sin(x) + sin(x) +--R Type: Expression(Integer) +--E 81 + +--S 82 of 105 +r0916:= -log(1+sin(x)^(-2^(1/2)+1))/(2^(1/2)-1) +--R +--R +--R +-+ +--R - \|2 + 1 +--R log(sin(x) + 1) +--R (82) - ------------------------- +--R +-+ +--R \|2 - 1 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 105 +a0916:= integrate(t0916,x) +--R +--R +--R +-+ +--R \|2 log(sin(x)) +-+ 2 +--R - 2log(%e + sin(x)) + \|2 log(cos(x) - 1) +--R (83) --------------------------------------------------------- +--R +-+ +--R 2\|2 - 2 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 105 +m0916:= a0916-r0916 +--R +--R +--R (84) +--R +-+ +-+ +--R \|2 log(sin(x)) - \|2 + 1 +--R - 2log(%e + sin(x)) + 2log(sin(x) + 1) +--R + +--R +-+ 2 +--R \|2 log(cos(x) - 1) +--R / +--R +-+ +--R 2\|2 - 2 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 105 +d0916:= D(m0916,x) +--R +--R +--R (85) +--R +-+ 2 +-+ 3 +--R (- \|2 + 2)cos(x)sin(x) + (- \|2 + 2)cos(x) +--R + +--R +-+ +--R (\|2 - 2)cos(x) +--R * +--R +-+ +--R - \|2 + 1 +--R sin(x) +--R + +--R +-+ +--R +-+ 3 +-+ - \|2 +--R ((- 2\|2 + 3)cos(x) + (2\|2 - 3)cos(x))sin(x)sin(x) +--R + +--R +-+ 2 +-+ 3 +-+ +--R (- \|2 + 2)cos(x)sin(x) + (- \|2 + 2)cos(x) + (\|2 - 2)cos(x) +--R * +--R +-+ +--R \|2 log(sin(x)) +--R %e +--R + +--R +-+ 3 +--R (- \|2 + 2)cos(x)sin(x) +--R + +--R +-+ 3 +-+ +--R ((\|2 - 1)cos(x) + (- \|2 + 1)cos(x))sin(x) +--R * +--R +-+ +--R - \|2 + 1 +--R sin(x) +--R + +--R +-+ +--R +-+ 3 +-+ 2 - \|2 +--R ((- 2\|2 + 3)cos(x) + (2\|2 - 3)cos(x))sin(x) sin(x) +--R + +--R +-+ 3 +-+ 3 +-+ +--R (- \|2 + 2)cos(x)sin(x) + ((\|2 - 1)cos(x) + (- \|2 + 1)cos(x))sin(x) +--R / +--R +-+ +--R +-+ 2 +-+ - \|2 + 1 +--R ((2\|2 - 3)cos(x) - 2\|2 + 3)sin(x)sin(x) +--R + +--R +-+ 2 +-+ +--R ((2\|2 - 3)cos(x) - 2\|2 + 3)sin(x) +--R * +--R +-+ +--R \|2 log(sin(x)) +--R %e +--R + +--R +-+ +--R +-+ 2 +-+ 2 - \|2 + 1 +--R ((2\|2 - 3)cos(x) - 2\|2 + 3)sin(x) sin(x) +--R + +--R +-+ 2 +-+ 2 +--R ((2\|2 - 3)cos(x) - 2\|2 + 3)sin(x) +--R Type: Expression(Integer) +--E 85 + +--S 86 of 105 +t0917:= (-1+sec(x))/(1-tan(x)) +--R +--R +--R - sec(x) + 1 +--R (86) ------------ +--R tan(x) - 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 105 +r0917:= -1/2*x+1/2*atanh(1/2*(cos(x)+sin(x))*2^(1/2))*2^(1/2)+1/2*log(cos(x)-sin(x)) +--R +--R +--R +-+ +-+ +--R +-+ \|2 sin(x) + \|2 cos(x) +--R log(- sin(x) + cos(x)) + \|2 atanh(-----------------------) - x +--R 2 +--R (87) --------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 105 +a0917:= integrate(t0917,x) +--R +--R +--R (88) +--R 2sin(x) - 2cos(x) +--R log(-----------------) +--R cos(x) + 1 +--R + +--R +-+ +-+ +-+ +--R +-+ (\|2 + 1)sin(x) + (\|2 + 1)cos(x) + \|2 + 2 2 +--R \|2 log(----------------------------------------------) - log(----------) +--R sin(x) - cos(x) cos(x) + 1 +--R + +--R - x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 105 +m0917:= a0917-r0917 +--R +--R +--R (89) +--R 2sin(x) - 2cos(x) +--R log(-----------------) +--R cos(x) + 1 +--R + +--R +-+ +-+ +-+ +--R +-+ (\|2 + 1)sin(x) + (\|2 + 1)cos(x) + \|2 + 2 2 +--R \|2 log(----------------------------------------------) - log(----------) +--R sin(x) - cos(x) cos(x) + 1 +--R + +--R +-+ +-+ +--R +-+ \|2 sin(x) + \|2 cos(x) +--R - log(- sin(x) + cos(x)) - \|2 atanh(-----------------------) +--R 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 105 +d0917:= D(m0917,x) +--R +--R +--R (90) +--R +-+ 4 +-+ +-+ 3 +--R (- \|2 - 2)sin(x) + ((- 2\|2 - 4)cos(x) - 2\|2 - 2)sin(x) +--R + +--R +-+ 2 +-+ +-+ 2 +--R ((- 2\|2 - 4)cos(x) + (- 2\|2 - 2)cos(x) + \|2 + 2)sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R (- 2\|2 - 4)cos(x) + (- 2\|2 - 2)cos(x) + (2\|2 + 4)cos(x) +--R + +--R +-+ +--R 2\|2 + 2 +--R * +--R sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R (- \|2 - 2)cos(x) + (- 2\|2 - 2)cos(x) + (\|2 + 2)cos(x) +--R + +--R +-+ +--R (2\|2 + 2)cos(x) +--R / +--R +-+ 4 +-+ +-+ 3 +--R (\|2 + 1)sin(x) + ((2\|2 + 2)cos(x) + \|2 + 2)sin(x) +--R + +--R +-+ +-+ 2 +--R ((\|2 + 2)cos(x) - 2\|2 - 2)sin(x) +--R + +--R +-+ 3 +-+ 2 +-+ +--R ((- 2\|2 - 2)cos(x) + (- \|2 - 2)cos(x) - 2\|2 - 4)sin(x) +--R + +--R +-+ 4 +-+ 3 +-+ 2 +--R (- \|2 - 1)cos(x) + (- \|2 - 2)cos(x) + (2\|2 + 2)cos(x) +--R + +--R +-+ +--R (2\|2 + 4)cos(x) +--R Type: Expression(Integer) +--E 90 + +--S 91 of 105 +t0918:= cos(x)^2*tan(x)^(1/2) +--R +--R +--R 2 +------+ +--R (91) cos(x) \|tan(x) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 105 +r0918:= 1/8*2^(1/2)*atan(-1+2^(1/2)*tan(x)^(1/2))+_ + 1/8*2^(1/2)*atan(1+2^(1/2)*tan(x)^(1/2))+_ + 1/16*log(1-2^(1/2)*tan(x)^(1/2)+tan(x))*2^(1/2)-_ + 1/16*log(1+2^(1/2)*tan(x)^(1/2)+tan(x))*2^(1/2)+_ + 1/2*cos(x)^2*tan(x)^(3/2) +--R +--R +--R (92) +--R +-+ +-+ +------+ +--R - \|2 log(\|2 \|tan(x) + tan(x) + 1) +--R + +--R +-+ +-+ +------+ +-+ +-+ +------+ +--R \|2 log(- \|2 \|tan(x) + tan(x) + 1) + 2\|2 atan(\|2 \|tan(x) + 1) +--R + +--R +-+ +-+ +------+ 2 +------+ +--R 2\|2 atan(\|2 \|tan(x) - 1) + 8cos(x) tan(x)\|tan(x) +--R / +--R 16 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 105 +a0918:= integrate(t0918,x) +--R +--R +--R (93) +--R +------+ +--R 3 4 2 |sin(x) +--R ((32cos(x) + 8cos(x))sin(x) - 32cos(x) + 40cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 16\|2 cos(x)sin(x) + 32\|2 cos(x) - 32\|2 cos(x) - \|2 +--R * +--R +------+ +--R +-+ +-+ 2 |sin(x) +--R log((- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------ + 4cos(x)sin(x) + 1) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((32cos(x) + 8cos(x))sin(x) - 32cos(x) + 40cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 16\|2 cos(x)sin(x) + 32\|2 cos(x) - 32\|2 cos(x) - \|2 +--R * +--R +------+ +--R +-+ +-+ 2 |sin(x) +--R log((- 4\|2 cos(x)sin(x) - 4\|2 cos(x) ) |------ + 8cos(x)sin(x) + 2) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((64cos(x) + 16cos(x))sin(x) - 64cos(x) + 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 32\|2 cos(x)sin(x) + 64\|2 cos(x) - 64\|2 cos(x) - 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +-+ +--R 2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x) - \|2 +--R \|cos(x) +--R atan(--------------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +--R 2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 64cos(x) - 16cos(x))sin(x) + 64cos(x) - 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 32\|2 cos(x)sin(x) - 64\|2 cos(x) + 64\|2 cos(x) + 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +-+ +--R 4cos(x)sin(x) |------ - 2\|2 cos(x)sin(x) + 2\|2 cos(x) - \|2 +--R \|cos(x) +--R atan(----------------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +-+ +--R 4cos(x) |------ - 2\|2 cos(x)sin(x) - 2\|2 cos(x) + \|2 +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 64cos(x) - 16cos(x))sin(x) + 64cos(x) - 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 32\|2 cos(x)sin(x) - 64\|2 cos(x) + 64\|2 cos(x) + 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +--R 2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x) +--R \|cos(x) +--R atan(---------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +-+ +--R 2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x) + \|2 +--R \|cos(x) +--R + +--R 5 3 +--R (512cos(x) + (- 32log(2) - 448)cos(x) - 8log(2)cos(x))sin(x) +--R + +--R 4 2 +--R (32log(2) + 192)cos(x) + (- 40log(2) - 176)cos(x) +--R * +--R +------+ +--R |sin(x) +--R |------ +--R \|cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 256\|2 cos(x) + 192\|2 cos(x) + (16log(2) + 32)\|2 cos(x))sin(x) +--R + +--R +-+ 6 +-+ 4 +--R 256\|2 cos(x) + (- 32log(2) - 512)\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R (32log(2) + 256)\|2 cos(x) + (log(2) - 2)\|2 +--R / +--R +-+ 3 +-+ +-+ 4 +--R (512\|2 cos(x) + 128\|2 cos(x))sin(x) - 512\|2 cos(x) +--R + +--R +-+ 2 +--R 640\|2 cos(x) +--R * +--R +------+ +--R |sin(x) +--R |------ +--R \|cos(x) +--R + +--R 4 2 +--R - 512cos(x)sin(x) + 1024cos(x) - 1024cos(x) - 32 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 105 +m0918:= a0918-r0918 +--R +--R +--R (94) +--R +------+ +--R 3 4 2 |sin(x) +--R ((64cos(x) + 16cos(x))sin(x) - 64cos(x) + 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 32\|2 cos(x)sin(x) + 64\|2 cos(x) - 64\|2 cos(x) - 2\|2 +--R * +--R +-+ +------+ +--R log(\|2 \|tan(x) + tan(x) + 1) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((32cos(x) + 8cos(x))sin(x) - 32cos(x) + 40cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 16\|2 cos(x)sin(x) + 32\|2 cos(x) - 32\|2 cos(x) - \|2 +--R * +--R +------+ +--R +-+ +-+ 2 |sin(x) +--R log((- 2\|2 cos(x)sin(x) - 2\|2 cos(x) ) |------ + 4cos(x)sin(x) + 1) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((32cos(x) + 8cos(x))sin(x) - 32cos(x) + 40cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 16\|2 cos(x)sin(x) + 32\|2 cos(x) - 32\|2 cos(x) - \|2 +--R * +--R +------+ +--R +-+ +-+ 2 |sin(x) +--R log((- 4\|2 cos(x)sin(x) - 4\|2 cos(x) ) |------ + 8cos(x)sin(x) + 2) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 64cos(x) - 16cos(x))sin(x) + 64cos(x) - 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 32\|2 cos(x)sin(x) - 64\|2 cos(x) + 64\|2 cos(x) + 2\|2 +--R * +--R +-+ +------+ +--R log(- \|2 \|tan(x) + tan(x) + 1) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 128cos(x) - 32cos(x))sin(x) + 128cos(x) - 160cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 64\|2 cos(x)sin(x) - 128\|2 cos(x) + 128\|2 cos(x) + 4\|2 +--R * +--R +-+ +------+ +--R atan(\|2 \|tan(x) + 1) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 128cos(x) - 32cos(x))sin(x) + 128cos(x) - 160cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 64\|2 cos(x)sin(x) - 128\|2 cos(x) + 128\|2 cos(x) + 4\|2 +--R * +--R +-+ +------+ +--R atan(\|2 \|tan(x) - 1) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((64cos(x) + 16cos(x))sin(x) - 64cos(x) + 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R - 32\|2 cos(x)sin(x) + 64\|2 cos(x) - 64\|2 cos(x) - 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +-+ +--R 2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x) - \|2 +--R \|cos(x) +--R atan(--------------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +--R 2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x) +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 64cos(x) - 16cos(x))sin(x) + 64cos(x) - 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 32\|2 cos(x)sin(x) - 64\|2 cos(x) + 64\|2 cos(x) + 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +-+ +--R 4cos(x)sin(x) |------ - 2\|2 cos(x)sin(x) + 2\|2 cos(x) - \|2 +--R \|cos(x) +--R atan(----------------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +-+ +--R 4cos(x) |------ - 2\|2 cos(x)sin(x) - 2\|2 cos(x) + \|2 +--R \|cos(x) +--R + +--R +------+ +--R 3 4 2 |sin(x) +--R ((- 64cos(x) - 16cos(x))sin(x) + 64cos(x) - 80cos(x) ) |------ +--R \|cos(x) +--R + +--R +-+ +-+ 4 +-+ 2 +-+ +--R 32\|2 cos(x)sin(x) - 64\|2 cos(x) + 64\|2 cos(x) + 2\|2 +--R * +--R +------+ +--R |sin(x) +-+ +-+ 2 +--R 2cos(x)sin(x) |------ - \|2 cos(x)sin(x) + \|2 cos(x) +--R \|cos(x) +--R atan(---------------------------------------------------------) +--R +------+ +--R 2 |sin(x) +-+ +-+ 2 +-+ +--R 2cos(x) |------ - \|2 cos(x)sin(x) - \|2 cos(x) + \|2 +--R \|cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ 6 +--R (- 256\|2 cos(x) - 64\|2 cos(x) )sin(x) + 256\|2 cos(x) +--R + +--R +-+ 4 +--R - 320\|2 cos(x) +--R * +--R +------+ +--R |sin(x) +--R tan(x) |------ +--R \|cos(x) +--R + +--R 3 6 4 2 +--R (256cos(x) sin(x) - 512cos(x) + 512cos(x) + 16cos(x) )tan(x) +--R * +--R +------+ +--R \|tan(x) +--R + +--R 5 3 +--R (512cos(x) + (- 32log(2) - 448)cos(x) - 8log(2)cos(x))sin(x) +--R + +--R 4 2 +--R (32log(2) + 192)cos(x) + (- 40log(2) - 176)cos(x) +--R * +--R +------+ +--R |sin(x) +--R |------ +--R \|cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R (- 256\|2 cos(x) + 192\|2 cos(x) + (16log(2) + 32)\|2 cos(x))sin(x) +--R + +--R +-+ 6 +-+ 4 +--R 256\|2 cos(x) + (- 32log(2) - 512)\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R (32log(2) + 256)\|2 cos(x) + (log(2) - 2)\|2 +--R / +--R +-+ 3 +-+ +-+ 4 +--R (512\|2 cos(x) + 128\|2 cos(x))sin(x) - 512\|2 cos(x) +--R + +--R +-+ 2 +--R 640\|2 cos(x) +--R * +--R +------+ +--R |sin(x) +--R |------ +--R \|cos(x) +--R + +--R 4 2 +--R - 512cos(x)sin(x) + 1024cos(x) - 1024cos(x) - 32 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 105 +d0918:= D(m0918,x) +--R +--R +--R (95) +--R +-+ 14 +-+ 12 +--R - 2097152\|2 cos(x) - 1114112\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +--R 425984\|2 cos(x) - 4096\|2 cos(x) +--R * +--R 22 +--R sin(x) +--R + +--R +-+ 15 +-+ 13 +--R - 281542656\|2 cos(x) - 185139200\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 71663616\|2 cos(x) - 2125824\|2 cos(x) + 12288\|2 cos(x) +--R * +--R 21 +--R sin(x) +--R + +--R +-+ 16 +-+ 14 +--R - 5922357248\|2 cos(x) - 4811784192\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R 2164424704\|2 cos(x) - 183029760\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +--R 3291136\|2 cos(x) - 13312\|2 cos(x) +--R * +--R 20 +--R sin(x) +--R + +--R +-+ 17 +-+ 15 +--R - 44349521920\|2 cos(x) - 49788485632\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R 24705859584\|2 cos(x) - 3421900800\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R 144923648\|2 cos(x) - 1888384\|2 cos(x) + 6144\|2 cos(x) +--R * +--R 19 +--R sin(x) +--R + +--R +-+ 18 +-+ 16 +--R - 153987579904\|2 cos(x) - 274652659712\|2 cos(x) +--R + +--R +-+ 14 +-+ 12 +--R 137678946304\|2 cos(x) - 23697547264\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +--R 1290334208\|2 cos(x) - 18452864\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +--R 167296\|2 cos(x) - 1024\|2 cos(x) +--R * +--R 18 +--R sin(x) +--R + +--R +-+ 19 +-+ 17 +--R - 302523088896\|2 cos(x) - 899057123328\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +--R 438689202176\|2 cos(x) - 79881003008\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +--R 2782665728\|2 cos(x) + 373268864\|2 cos(x) +--R + +--R +-+ 7 +-+ 5 +--R - 18033920\|2 cos(x) + 146016\|2 cos(x) +--R * +--R 17 +--R sin(x) +--R + +--R +-+ 20 +-+ 18 +--R - 453085495296\|2 cos(x) - 1862692110336\|2 cos(x) +--R + +--R +-+ 16 +-+ 14 +--R 934049742848\|2 cos(x) - 189419495424\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R 5531232256\|2 cos(x) + 2489199744\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 149855232\|2 cos(x) + 2158464\|2 cos(x) - 11584\|2 cos(x) +--R * +--R 16 +--R sin(x) +--R + +--R +-+ 21 +-+ 19 +--R - 639685885952\|2 cos(x) - 2739569426432\|2 cos(x) +--R + +--R +-+ 17 +-+ 15 +--R 1641249898496\|2 cos(x) - 462687387648\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R 50612662272\|2 cos(x) + 2606540288\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +--R 95881728\|2 cos(x) - 55188768\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +--R 1521728\|2 cos(x) - 6688\|2 cos(x) +--R * +--R 15 +--R sin(x) +--R + +--R +-+ 22 +-+ 20 +--R - 830157619200\|2 cos(x) - 3121456218112\|2 cos(x) +--R + +--R +-+ 18 +-+ 16 +--R 2469378850816\|2 cos(x) - 915660496896\|2 cos(x) +--R + +--R +-+ 14 +-+ 12 +--R 140313673728\|2 cos(x) + 11607306752\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +--R - 1719996928\|2 cos(x) - 102631264\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +--R 3649856\|2 cos(x) - 15608\|2 cos(x) +--R * +--R 14 +--R sin(x) +--R + +--R +-+ 23 +-+ 21 +--R - 1161596764160\|2 cos(x) - 2173674586112\|2 cos(x) +--R + +--R +-+ 19 +-+ 17 +--R 2297619087360\|2 cos(x) - 990562197504\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +--R 155274792960\|2 cos(x) + 39739061760\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +--R - 7197459968\|2 cos(x) - 122979168\|2 cos(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R - 36197056\|2 cos(x) + 4226808\|2 cos(x) - 49488\|2 cos(x) +--R * +--R 13 +--R sin(x) +--R + +--R +-+ 24 +-+ 22 +--R - 1711678685184\|2 cos(x) + 400772300800\|2 cos(x) +--R + +--R +-+ 20 +-+ 18 +--R 326740148224\|2 cos(x) - 446427619328\|2 cos(x) +--R + +--R +-+ 16 +-+ 14 +--R 269662072832\|2 cos(x) - 65689212416\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R 26325821440\|2 cos(x) - 7184733856\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +--R 547755296\|2 cos(x) - 15015520\|2 cos(x) +--R + +--R +-+ 4 +-+ 2 +--R 493912\|2 cos(x) - 5432\|2 cos(x) +--R * +--R 12 +--R sin(x) +--R + +--R +-+ 25 +-+ 23 +--R - 2220189810688\|2 cos(x) + 3521448509440\|2 cos(x) +--R + +--R +-+ 21 +-+ 19 +--R - 2808402345984\|2 cos(x) + 650672152576\|2 cos(x) +--R + +--R +-+ 17 +-+ 15 +--R 422012471296\|2 cos(x) - 281626797824\|2 cos(x) +--R + +--R +-+ 13 +-+ 11 +--R 83021586944\|2 cos(x) - 14575582112\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +--R 714057280\|2 cos(x) + 22550128\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +--R 1531752\|2 cos(x) - 100396\|2 cos(x) +--R * +--R 11 +--R sin(x) +--R + +--R +-+ 26 +-+ 24 +--R - 2549142781952\|2 cos(x) + 6421529362432\|2 cos(x) +--R + +--R +-+ 22 +-+ 20 +--R - 6996507361280\|2 cos(x) + 3405735657472\|2 cos(x) +--R + +--R +-+ 18 +-+ 16 +--R - 456379588608\|2 cos(x) - 186151154944\|2 cos(x) +--R + +--R +-+ 14 +-+ 12 +--R 85985568000\|2 cos(x) - 14278312160\|2 cos(x) +--R + +--R +-+ 10 +-+ 8 +--R - 213280128\|2 cos(x) + 286796632\|2 cos(x) +--R + +--R +-+ 6 +-+ 4 +-+ 2 +--R - 20174760\|2 cos(x) + 841080\|2 cos(x) - 17948\|2 cos(x) +--R * +--R 10 +--R sin(x) +--R + +--R +-+ 27 +-+ 25 +--R - 2479887482880\|2 cos(x) + 7870159126528\|2 cos(x) +--R + +--R +-+ 23 +-+ 21 +--R - 10353555144704\|2 cos(x) + 6732947423232\|2 cos(x) +--R + +--R +-+ 19 +-+ 17 +--R - 2071938545664\|2 cos(x) + 81108729088\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +--R 172601294848\|2 cos(x) - 71792372000\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +--R 14310564160\|2 cos(x) - 1632334776\|2 cos(x) +--R + +--R +-+ 7 +-+ 5 +-+ 3 +--R 128659544\|2 cos(x) - 5331932\|2 cos(x) + 44444\|2 cos(x) +--R + +--R +-+ +--R - 888\|2 cos(x) +--R * +--R 9 +--R sin(x) +--R + +--R +-+ 28 +-+ 26 +--R - 1951022448640\|2 cos(x) + 7130538835968\|2 cos(x) +--R + +--R +-+ 24 +-+ 22 +--R - 10748774973440\|2 cos(x) + 8371205210112\|2 cos(x) +--R + +--R +-+ 20 +-+ 18 +--R - 3408617058304\|2 cos(x) + 455859828480\|2 cos(x) +--R + +--R +-+ 16 +-+ 14 +--R 223327467520\|2 cos(x) - 129734010912\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R 28300149472\|2 cos(x) - 2608441488\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R 32491472\|2 cos(x) + 9292624\|2 cos(x) - 399288\|2 cos(x) +--R + +--R +-+ 2 +--R - 8251\|2 cos(x) +--R * +--R 8 +--R sin(x) +--R + +--R +-+ 29 +-+ 27 +--R - 1260543541248\|2 cos(x) + 5170466390016\|2 cos(x) +--R + +--R +-+ 25 +-+ 23 +--R - 8944498638848\|2 cos(x) + 8453465423872\|2 cos(x) +--R + +--R +-+ 21 +-+ 19 +--R - 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30808709632\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +--R 14189916416\|2 cos(x) - 4358633920\|2 cos(x) +--R + +--R +-+ 11 +-+ 9 +-+ 7 +--R 823319040\|2 cos(x) - 68399424\|2 cos(x) - 4878496\|2 cos(x) +--R + +--R +-+ 5 +-+ 3 +-+ +--R 1455840\|2 cos(x) - 73696\|2 cos(x) - 1328\|2 cos(x) +--R * +--R 3 +--R sin(x) +--R + +--R +-+ 32 +-+ 30 +--R - 50331648\|2 cos(x) + 132120576\|2 cos(x) +--R + +--R +-+ 28 +-+ 26 +--R 313655296\|2 cos(x) - 2038005760\|2 cos(x) +--R + +--R +-+ 24 +-+ 22 +--R 4439543808\|2 cos(x) - 5541152768\|2 cos(x) +--R + +--R +-+ 20 +-+ 18 +--R 4355552256\|2 cos(x) - 2070590208\|2 cos(x) +--R + +--R +-+ 16 +-+ 14 +--R 386927616\|2 cos(x) + 199519936\|2 cos(x) +--R + +--R +-+ 12 +-+ 10 +--R - 182637120\|2 cos(x) + 67859328\|2 cos(x) +--R + +--R +-+ 8 +-+ 6 +-+ 4 +--R - 13844416\|2 cos(x) + 1424384\|2 cos(x) - 39072\|2 cos(x) +--R + +--R +-+ 2 +-+ +--R - 2560\|2 cos(x) - 16\|2 +--R * +--R 2 +--R sin(x) +--R + +--R +-+ 31 +-+ 29 +-+ 27 +--R - 2097152\|2 cos(x) + 11534336\|2 cos(x) - 22020096\|2 cos(x) +--R + +--R +-+ 25 +-+ 23 +-+ 21 +--R 704512\|2 cos(x) + 78899200\|2 cos(x) - 182747648\|2 cos(x) +--R + +--R +-+ 19 +-+ 17 +--R 235505408\|2 cos(x) - 203157632\|2 cos(x) +--R + +--R +-+ 15 +-+ 13 +-+ 11 +--R 123476032\|2 cos(x) - 53190848\|2 cos(x) + 15809440\|2 cos(x) +--R + +--R +-+ 9 +-+ 7 +-+ 5 +--R - 3013984\|2 cos(x) + 304960\|2 cos(x) - 5440\|2 cos(x) +--R + +--R +-+ 3 +-+ +--R - 1072\|2 cos(x) - 16\|2 cos(x) +--R * +--R sin(x) +--R * +--R +------+ +--R \|tan(x) +--R Type: Expression(Integer) +--E 95 + +--S 96 of 105 +t0919:= cos(a+b*x)^n*sin(a+b*x)^(-2-n) +--R +--R +--R n - n - 2 +--R (96) cos(b x + a) sin(b x + a) +--R Type: Expression(Integer) +--E 96 + +--S 97 of 105 +r0919:= -cos(a+b*x)^(1+n)*sin(a+b*x)^(-1-n)/b/(1+n) +--R +--R +--R n + 1 - n - 1 +--R cos(b x + a) sin(b x + a) +--R (97) - ------------------------------------ +--R b n + b +--R Type: Expression(Integer) +--E 97 + +--S 98 of 105 +a0919:= integrate(t0919,x) +--R +--R +--R x +--R ++ n - n - 2 +--R (98) | cos(%I b + a) sin(%I b + a) d%I +--R ++ +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 105 +m0919:= a0919-r0919 +--R +--R +--R (99) +--R x +--R ++ n - n - 2 +--R (b n + b) | cos(%I b + a) sin(%I b + a) d%I +--R ++ +--R + +--R n + 1 - n - 1 +--R cos(b x + a) sin(b x + a) +--R / +--R b n + b +--R Type: Expression(Integer) +--E 99 + +--S 100 of 105 +d0919:= D(m0919,x) +--R +--R +--R (100) +--R n - n - 1 +--R - sin(b x + a)cos(b x + a) sin(b x + a) +--R + +--R n + 1 n - n - 2 +--R (- cos(b x + a)cos(b x + a) + cos(b x + a) )sin(b x + a) +--R Type: Expression(Integer) +--E 100 + +--S 101 of 105 +t0920:= x^5*sec(a+b*x^3)^7*tan(a+b*x^3) +--R +--R +--R 5 3 7 3 +--R (101) x sec(b x + a) tan(b x + a) +--R Type: Expression(Integer) +--E 101 + +--S 102 of 105 +r0920:= -1/1008*(15*atanh(sin(a+b*x^3))*cos(a+b*x^3)^7-48*b*x^3+_ + 15*cos(a+b*x^3)^5*sin(a+b*x^3)+10*cos(a+b*x^3)^3*sin(a+b*x^3)+_ + 8*cos(a+b*x^3)*sin(a+b*x^3))/cos(a+b*x^3)^7/b^2 +--R +--R +--R (102) +--R 3 7 3 +--R - 15cos(b x + a) atanh(sin(b x + a)) +--R + +--R 3 5 3 3 3 3 +--R (- 15cos(b x + a) - 10cos(b x + a) - 8cos(b x + a))sin(b x + a) +--R + +--R 3 +--R 48b x +--R / +--R 2 3 7 +--R 1008b cos(b x + a) +--R Type: Expression(Integer) +--E 102 + +--S 103 of 105 +a0920:= integrate(t0920,x) +--R +--R +--R (103) +--R 3 3 +--R 3 7 sin(b x + a) + cos(b x + a) + 1 +--R - 15cos(b x + a) log(---------------------------------) +--R 3 +--R cos(b x + a) + 1 +--R + +--R 3 3 +--R 3 7 sin(b x + a) - cos(b x + a) - 1 +--R 15cos(b x + a) log(---------------------------------) +--R 3 +--R cos(b x + a) + 1 +--R + +--R 3 5 3 3 3 3 +--R (- 15cos(b x + a) - 10cos(b x + a) - 8cos(b x + a))sin(b x + a) +--R + +--R 3 +--R 48b x +--R / +--R 2 3 7 +--R 1008b cos(b x + a) +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 105 +m0920:= a0920-r0920 +--R +--R +--R (104) +--R 3 3 +--R sin(b x + a) + cos(b x + a) + 1 +--R - 5log(---------------------------------) +--R 3 +--R cos(b x + a) + 1 +--R + +--R 3 3 +--R sin(b x + a) - cos(b x + a) - 1 3 +--R 5log(---------------------------------) + 5atanh(sin(b x + a)) +--R 3 +--R cos(b x + a) + 1 +--R / +--R 2 +--R 336b +--R Type: Expression(Integer) +--E 104 + +--S 105 of 105 +d0920:= D(m0920,x) +--R +--R +--R (105) +--R 2 3 4 +--R 10x sin(b x + a) +--R + +--R 2 3 2 2 3 2 3 2 +--R (10x cos(b x + a) + 5x cos(b x + a) - 10x )sin(b x + a) +--R + +--R 2 3 3 2 3 +--R 5x cos(b x + a) - 5x cos(b x + a) +--R / +--R 3 4 +--R 112b sin(b x + a) +--R + +--R 3 2 3 3 2 +--R (- 112b cos(b x + a) - 224b cos(b x + a) - 224b)sin(b x + a) +--R + +--R 3 2 3 +--R 112b cos(b x + a) + 224b cos(b x + a) + 112b +--R Type: Expression(Integer) +--E 105 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} Albert D. Rich ``Rule-based Mathematics'' +\verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richtrig900-920.input.pdf b/src/axiom-website/CATS/richtrig900-920.input.pdf new file mode 100644 index 0000000..67dfe44 Binary files /dev/null and b/src/axiom-website/CATS/richtrig900-920.input.pdf differ diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 22461ef..f15addf 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4228,6 +4228,8 @@ src/interp/Makefile make cleanup src/interp/Makefile make cleanup 20130702.01.tpd.patch books/bookvolbib add Griesmer ref, sort items +20130714.01.tpd.patch +add rich integral set to CATS test suite